LMFDB - Embedded newform 189.2.h.b.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(37,189)]

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([2, 2]))

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

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

chi := DirichletCharacter("189.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.h (of order $3$, 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 $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.3
Root			$0.247934 - 0.429435i$ of defining polynomial
Character	$\chi$	$=$	189.37
Dual form			189.2.h.b.46.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.495868 q^{2} -1.75411 q^{4} +(-1.84629 - 3.19787i) q^{5} +(0.926641 - 2.47817i) q^{7} -1.86155 q^{8} +O(q^{10})$	\(q+0.495868 q^{2} -1.75411 q^{4} +(-1.84629 - 3.19787i) q^{5} +(0.926641 - 2.47817i) q^{7} -1.86155 q^{8} +(-0.915516 - 1.58572i) q^{10} +(-0.446284 + 0.772987i) q^{11} +(0.598355 - 1.03638i) q^{13} +(0.459492 - 1.22885i) q^{14} +2.58515 q^{16} +(0.124991 + 0.216492i) q^{17} +(1.40414 - 2.43204i) q^{19} +(3.23860 + 5.60943i) q^{20} +(-0.221298 + 0.383300i) q^{22} +(1.23886 + 2.14576i) q^{23} +(-4.31757 + 7.47825i) q^{25} +(0.296705 - 0.513909i) q^{26} +(-1.62544 + 4.34700i) q^{28} +(-2.07128 - 3.58755i) q^{29} +3.58515 q^{31} +5.00499 q^{32} +(0.0619793 + 0.107351i) q^{34} +(-9.63571 + 1.61215i) q^{35} +(-2.36568 + 4.09747i) q^{37} +(0.696267 - 1.20597i) q^{38} +(3.43695 + 5.95298i) q^{40} +(2.39093 - 4.14121i) q^{41} +(-4.98928 - 8.64169i) q^{43} +(0.782834 - 1.35591i) q^{44} +(0.614310 + 1.06402i) q^{46} +10.1731 q^{47} +(-5.28267 - 4.59275i) q^{49} +(-2.14095 + 3.70823i) q^{50} +(-1.04958 + 1.81793i) q^{52} +(4.94465 + 8.56438i) q^{53} +3.29588 q^{55} +(-1.72499 + 4.61323i) q^{56} +(-1.02708 - 1.77895i) q^{58} -1.81237 q^{59} +10.8041 q^{61} +1.77776 q^{62} -2.68848 q^{64} -4.41895 q^{65} +1.02937 q^{67} +(-0.219249 - 0.379751i) q^{68} +(-4.77804 + 0.799412i) q^{70} +4.94533 q^{71} +(-0.915262 - 1.58528i) q^{73} +(-1.17306 + 2.03181i) q^{74} +(-2.46302 + 4.26607i) q^{76} +(1.50205 + 1.82225i) q^{77} -1.79912 q^{79} +(-4.77293 - 8.26696i) q^{80} +(1.18559 - 2.05350i) q^{82} +(-6.16156 - 10.6721i) q^{83} +(0.461541 - 0.799412i) q^{85} +(-2.47403 - 4.28514i) q^{86} +(0.830779 - 1.43895i) q^{88} +(1.20370 - 2.08488i) q^{89} +(-2.01387 - 2.44318i) q^{91} +(-2.17310 - 3.76392i) q^{92} +5.04450 q^{94} -10.3698 q^{95} +(5.52210 + 9.56456i) q^{97} +(-2.61951 - 2.27740i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 8 q^{4} - 4 q^{5} - 4 q^{7} + 6 q^{8}+O(q^{10}) $ 10 * q + 4 * q^2 + 8 * q^4 - 4 * q^5 - 4 * q^7 + 6 * q^8	$ 10 q + 4 q^{2} + 8 q^{4} - 4 q^{5} - 4 q^{7} + 6 q^{8} - 7 q^{10} - 4 q^{11} - 8 q^{13} + 20 q^{14} - 4 q^{16} - 12 q^{17} + q^{19} - 5 q^{20} - q^{22} - 3 q^{23} - q^{25} - 11 q^{26} - 2 q^{28} - 7 q^{29} + 6 q^{31} - 4 q^{32} + 3 q^{34} - 5 q^{35} - 20 q^{38} - 3 q^{40} - 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} + 54 q^{47} - 8 q^{49} - 19 q^{50} - 10 q^{52} + 21 q^{53} + 4 q^{55} - 18 q^{56} - 10 q^{58} + 60 q^{59} + 28 q^{61} + 12 q^{62} - 50 q^{64} - 22 q^{65} + 4 q^{67} - 27 q^{68} + 40 q^{70} + 6 q^{71} + 15 q^{73} + 36 q^{74} + 5 q^{76} - 11 q^{77} + 8 q^{79} - 20 q^{80} - 5 q^{82} - 9 q^{83} - 6 q^{85} + 8 q^{86} - 18 q^{88} - 28 q^{89} - 4 q^{91} - 27 q^{92} + 6 q^{94} - 28 q^{95} - 12 q^{97} - 59 q^{98}+O(q^{100}) $ 10 * q + 4 * q^2 + 8 * q^4 - 4 * q^5 - 4 * q^7 + 6 * q^8 - 7 * q^10 - 4 * q^11 - 8 * q^13 + 20 * q^14 - 4 * q^16 - 12 * q^17 + q^19 - 5 * q^20 - q^22 - 3 * q^23 - q^25 - 11 * q^26 - 2 * q^28 - 7 * q^29 + 6 * q^31 - 4 * q^32 + 3 * q^34 - 5 * q^35 - 20 * q^38 - 3 * q^40 - 5 * q^41 - 7 * q^43 + 10 * q^44 + 3 * q^46 + 54 * q^47 - 8 * q^49 - 19 * q^50 - 10 * q^52 + 21 * q^53 + 4 * q^55 - 18 * q^56 - 10 * q^58 + 60 * q^59 + 28 * q^61 + 12 * q^62 - 50 * q^64 - 22 * q^65 + 4 * q^67 - 27 * q^68 + 40 * q^70 + 6 * q^71 + 15 * q^73 + 36 * q^74 + 5 * q^76 - 11 * q^77 + 8 * q^79 - 20 * q^80 - 5 * q^82 - 9 * q^83 - 6 * q^85 + 8 * q^86 - 18 * q^88 - 28 * q^89 - 4 * q^91 - 27 * q^92 + 6 * q^94 - 28 * q^95 - 12 * q^97 - 59 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.495868			0.350632			0.175316	−	0.984512i	$-0.443905\pi$
$2$	0.495868			0.350632			0.175316	+	0.984512i	$0.443905\pi$
$3$		0			0
$3$		0			0
$4$	−1.75411			−0.877057
$5$	−1.84629	−	3.19787i	−0.825686	−	1.43013i	−0.901394	−	0.433000i	$-0.857455\pi$
$5$	−1.84629	−	3.19787i	−0.825686	−	1.43013i	0.0757082	−	0.997130i	$-0.475878\pi$
$6$		0			0
$7$	0.926641	−	2.47817i	0.350238	−	0.936661i
$7$	0.926641	−	2.47817i	0.350238	−	0.936661i
$8$	−1.86155			−0.658156
$9$		0			0
$10$	−0.915516	−	1.58572i	−0.289512	−	0.501449i
$11$	−0.446284	+	0.772987i	−0.134560	+	0.233064i	−0.925429	−	0.378921i	$-0.876295\pi$
$11$	−0.446284	+	0.772987i	−0.134560	+	0.233064i	0.790869	+	0.611985i	$0.209629\pi$
$12$		0			0
$13$	0.598355	−	1.03638i	0.165954	−	0.287441i	−0.771040	−	0.636787i	$-0.780263\pi$
$13$	0.598355	−	1.03638i	0.165954	−	0.287441i	0.936994	+	0.349346i	$0.113596\pi$
$14$	0.459492	−	1.22885i	0.122804	−	0.328423i
$15$		0			0
$16$	2.58515			0.646287
$17$	0.124991	+	0.216492i	0.0303149	+	0.0525069i	0.880785	−	0.473517i	$-0.157016\pi$
$17$	0.124991	+	0.216492i	0.0303149	+	0.0525069i	−0.850470	+	0.526024i	$0.823682\pi$
$18$		0			0
$19$	1.40414	−	2.43204i	0.322131	−	0.557948i	−0.658796	−	0.752321i	$-0.728934\pi$
$19$	1.40414	−	2.43204i	0.322131	−	0.557948i	0.980928	+	0.194374i	$0.0622675\pi$
$20$	3.23860	+	5.60943i	0.724174	+	1.25431i
$21$		0			0
$22$	−0.221298	+	0.383300i	−0.0471809	+	0.0817198i
$23$	1.23886	+	2.14576i	0.258320	+	0.447423i	0.965792	−	0.259318i	$-0.0834979\pi$
$23$	1.23886	+	2.14576i	0.258320	+	0.447423i	−0.707472	+	0.706741i	$0.750165\pi$
$24$		0			0
$25$	−4.31757	+	7.47825i	−0.863514	+	1.49565i
$26$	0.296705	−	0.513909i	0.0581887	−	0.100786i
$27$		0			0
$28$	−1.62544	+	4.34700i	−0.307178	+	0.821505i
$29$	−2.07128	−	3.58755i	−0.384626	−	0.666192i	0.607091	−	0.794632i	$-0.292336\pi$
$29$	−2.07128	−	3.58755i	−0.384626	−	0.666192i	−0.991717	+	0.128440i	$0.959003\pi$
$30$		0			0
$31$	3.58515			0.643912			0.321956	−	0.946755i	$-0.395660\pi$
$31$	3.58515			0.643912			0.321956	+	0.946755i	$0.395660\pi$
$32$	5.00499			0.884765
$33$		0			0
$34$	0.0619793	+	0.107351i	0.0106294	+	0.0184106i
$35$	−9.63571	+	1.61215i	−1.62873	+	0.272502i
$36$		0			0
$37$	−2.36568	+	4.09747i	−0.388915	+	0.673621i	−0.992304	−	0.123826i	$-0.960483\pi$
$37$	−2.36568	+	4.09747i	−0.388915	+	0.673621i	0.603389	+	0.797447i	$0.293817\pi$
$38$	0.696267	−	1.20597i	0.112949	−	0.195634i
$39$		0			0
$40$	3.43695	+	5.95298i	0.543430	+	0.941249i
$41$	2.39093	−	4.14121i	0.373400	−	0.646748i	−0.616686	−	0.787209i	$-0.711525\pi$
$41$	2.39093	−	4.14121i	0.373400	−	0.646748i	0.990086	+	0.140461i	$0.0448584\pi$
$42$		0			0
$43$	−4.98928	−	8.64169i	−0.760859	−	1.31785i	−0.942408	−	0.334464i	$-0.891445\pi$
$43$	−4.98928	−	8.64169i	−0.760859	−	1.31785i	0.181550	−	0.983382i	$-0.441889\pi$
$44$	0.782834	−	1.35591i	0.118017	−	0.204411i
$45$		0			0
$46$	0.614310	+	1.06402i	0.0905751	+	0.156881i
$47$	10.1731			1.48389			0.741947	−	0.670459i	$-0.233903\pi$
$47$	10.1731			1.48389			0.741947	+	0.670459i	$0.233903\pi$
$48$		0			0
$49$	−5.28267	−	4.59275i	−0.754667	−	0.656108i
$50$	−2.14095	+	3.70823i	−0.302776	+	0.524423i
$51$		0			0
$52$	−1.04958	+	1.81793i	−0.145551	+	0.252102i
$53$	4.94465	+	8.56438i	0.679199	+	1.17641i	0.975222	+	0.221227i	$0.0710061\pi$
$53$	4.94465	+	8.56438i	0.679199	+	1.17641i	−0.296023	+	0.955181i	$0.595661\pi$
$54$		0			0
$55$	3.29588			0.444416
$56$	−1.72499	+	4.61323i	−0.230511	+	0.616469i
$57$		0			0
$58$	−1.02708	−	1.77895i	−0.134862	−	0.233588i
$59$	−1.81237			−0.235951			−0.117975	−	0.993017i	$-0.537640\pi$
$59$	−1.81237			−0.235951			−0.117975	+	0.993017i	$0.537640\pi$
$60$		0			0
$61$	10.8041			1.38332			0.691662	−	0.722221i	$-0.256879\pi$
$61$	10.8041			1.38332			0.691662	+	0.722221i	$0.256879\pi$
$62$	1.77776			0.225776
$63$		0			0
$64$	−2.68848			−0.336060
$65$	−4.41895			−0.548103
$66$		0			0
$67$	1.02937			0.125757			0.0628787	−	0.998021i	$-0.479972\pi$
$67$	1.02937			0.125757			0.0628787	+	0.998021i	$0.479972\pi$
$68$	−0.219249	−	0.379751i	−0.0265879	−	0.0460516i
$69$		0			0
$70$	−4.77804	+	0.799412i	−0.571086	+	0.0955480i
$71$	4.94533			0.586903			0.293451	−	0.955974i	$-0.405196\pi$
$71$	4.94533			0.586903			0.293451	+	0.955974i	$0.405196\pi$
$72$		0			0
$73$	−0.915262	−	1.58528i	−0.107123	−	0.185543i	0.807480	−	0.589894i	$-0.200831\pi$
$73$	−0.915262	−	1.58528i	−0.107123	−	0.185543i	−0.914604	+	0.404351i	$0.867497\pi$
$74$	−1.17306	+	2.03181i	−0.136366	+	0.236193i
$75$		0			0
$76$	−2.46302	+	4.26607i	−0.282527	+	0.489352i
$77$	1.50205	+	1.82225i	0.171174	+	0.207665i
$78$		0			0
$79$	−1.79912			−0.202417			−0.101209	−	0.994865i	$-0.532271\pi$
$79$	−1.79912			−0.202417			−0.101209	+	0.994865i	$0.532271\pi$
$80$	−4.77293	−	8.26696i	−0.533630	−	0.924274i
$81$		0			0
$82$	1.18559	−	2.05350i	0.130926	−	0.226771i
$83$	−6.16156	−	10.6721i	−0.676319	−	1.17142i	−0.976082	−	0.217405i	$-0.930241\pi$
$83$	−6.16156	−	10.6721i	−0.676319	−	1.17142i	0.299763	−	0.954014i	$-0.403092\pi$
$84$		0			0
$85$	0.461541	−	0.799412i	0.0500611	−	0.0867084i
$86$	−2.47403	−	4.28514i	−0.266781	−	0.462079i
$87$		0			0
$88$	0.830779	−	1.43895i	0.0885613	−	0.153393i
$89$	1.20370	−	2.08488i	0.127592	−	0.220997i	−0.795151	−	0.606412i	$-0.792608\pi$
$89$	1.20370	−	2.08488i	0.127592	−	0.220997i	0.922743	+	0.385415i	$0.125942\pi$
$90$		0			0
$91$	−2.01387	−	2.44318i	−0.211111	−	0.256115i
$92$	−2.17310	−	3.76392i	−0.226561	−	0.392416i
$93$		0			0
$94$	5.04450			0.520300
$95$	−10.3698			−1.06392
$96$		0			0
$97$	5.52210	+	9.56456i	0.560684	+	0.971134i	0.997437	+	0.0715522i	$0.0227952\pi$
$97$	5.52210	+	9.56456i	0.560684	+	0.971134i	−0.436752	+	0.899582i	$0.643871\pi$
$98$	−2.61951	−	2.27740i	−0.264610	−	0.230052i
$99$		0			0
$100$	7.57351	−	13.1177i	0.757351	−	1.31177i
$101$	−1.29982	+	2.25136i	−0.129337	+	0.224018i	−0.923420	−	0.383791i	$-0.874618\pi$
$101$	−1.29982	+	2.25136i	−0.129337	+	0.224018i	0.794083	+	0.607810i	$0.207952\pi$
$102$		0			0
$103$	−4.85578	−	8.41045i	−0.478454	−	0.828706i	0.521241	−	0.853409i	$-0.325469\pi$
$103$	−4.85578	−	8.41045i	−0.478454	−	0.828706i	−0.999695	+	0.0247032i	$0.992136\pi$
$104$	−1.11387	+	1.92927i	−0.109224	+	0.189181i
$105$		0			0
$106$	2.45189	+	4.24680i	0.238149	+	0.412486i
$107$	5.45025	−	9.44012i	0.526896	−	0.912610i	−0.472613	−	0.881270i	$-0.656689\pi$
$107$	5.45025	−	9.44012i	0.526896	−	0.912610i	0.999509	−	0.0313403i	$-0.00997757\pi$
$108$		0			0
$109$	−1.06096	−	1.83764i	−0.101622	−	0.176014i	0.810731	−	0.585419i	$-0.199070\pi$
$109$	−1.06096	−	1.83764i	−0.101622	−	0.176014i	−0.912353	+	0.409404i	$0.865737\pi$
$110$	1.63432			0.155826
$111$		0			0
$112$	2.39550	−	6.40644i	0.226354	−	0.605352i
$113$	−7.91318	+	13.7060i	−0.744409	+	1.28935i	0.206061	+	0.978539i	$0.433935\pi$
$113$	−7.91318	+	13.7060i	−0.744409	+	1.28935i	−0.950470	+	0.310816i	$0.899398\pi$
$114$		0			0
$115$	4.57458	−	7.92341i	0.426582	−	0.738861i
$116$	3.63325	+	6.29298i	0.337339	+	0.584289i
$117$		0			0
$118$	−0.898698			−0.0827318
$119$	0.652326	−	0.109140i	0.0597986	−	0.0100049i
$120$		0			0
$121$	5.10166	+	8.83634i	0.463787	+	0.803303i
$122$	5.35741			0.485038
$123$		0			0
$124$	−6.28876			−0.564747
$125$	13.4230			1.20059
$126$		0			0
$127$	−1.26946			−0.112647			−0.0563233	−	0.998413i	$-0.517938\pi$
$127$	−1.26946			−0.112647			−0.0563233	+	0.998413i	$0.517938\pi$
$128$	−11.3431			−1.00260
$129$		0			0
$130$	−2.19122			−0.192182
$131$	−7.51444	−	13.0154i	−0.656540	−	1.13716i	−0.981505	−	0.191435i	$-0.938686\pi$
$131$	−7.51444	−	13.0154i	−0.656540	−	1.13716i	0.324965	−	0.945726i	$-0.394647\pi$
$132$		0			0
$133$	−4.72587	−	5.73332i	−0.409785	−	0.497142i
$134$	0.510432			0.0440946
$135$		0			0
$136$	−0.232677	−	0.403009i	−0.0199519	−	0.0345577i
$137$	−0.244246	+	0.423047i	−0.0208674	+	0.0361433i	−0.876271	−	0.481819i	$-0.839976\pi$
$137$	−0.244246	+	0.423047i	−0.0208674	+	0.0361433i	0.855403	+	0.517963i	$0.173309\pi$
$138$		0			0
$139$	−4.93487	+	8.54745i	−0.418570	+	0.724985i	−0.995796	−	0.0915997i	$-0.970802\pi$
$139$	−4.93487	+	8.54745i	−0.418570	+	0.724985i	0.577226	+	0.816585i	$0.304135\pi$
$140$	16.9021	−	2.82789i	1.42849	−	0.239000i
$141$		0			0
$142$	2.45223			0.205787
$143$	0.534073	+	0.925042i	0.0446614	+	0.0773559i
$144$		0			0
$145$	−7.64835	+	13.2473i	−0.635161	+	1.10013i
$146$	−0.453849	−	0.786090i	−0.0375609	−	0.0650573i
$147$		0			0
$148$	4.14967	−	7.18744i	0.341101	−	0.590804i
$149$	10.5120	+	18.2073i	0.861175	+	1.49160i	0.870796	+	0.491645i	$0.163604\pi$
$149$	10.5120	+	18.2073i	0.861175	+	1.49160i	−0.00962096	+	0.999954i	$0.503062\pi$
$150$		0			0
$151$	−0.749191	+	1.29764i	−0.0609683	+	0.105600i	−0.894898	−	0.446270i	$-0.852752\pi$
$151$	−0.749191	+	1.29764i	−0.0609683	+	0.105600i	0.833930	+	0.551870i	$0.186086\pi$
$152$	−2.61387	+	4.52735i	−0.212013	+	0.367217i
$153$		0			0
$154$	0.744818	+	0.903596i	0.0600192	+	0.0728139i
$155$	−6.61922	−	11.4648i	−0.531669	−	0.920877i
$156$		0			0
$157$	−16.6796			−1.33118			−0.665590	−	0.746317i	$-0.731820\pi$
$157$	−16.6796			−1.33118			−0.665590	+	0.746317i	$0.731820\pi$
$158$	−0.892128			−0.0709739
$159$		0			0
$160$	−9.24065	−	16.0053i	−0.730538	−	1.26533i
$161$	6.46555	−	1.08175i	0.509557	−	0.0852537i
$162$		0			0
$163$	−3.34135	+	5.78738i	−0.261714	+	0.453303i	−0.966698	−	0.255921i	$-0.917621\pi$
$163$	−3.34135	+	5.78738i	−0.261714	+	0.453303i	0.704983	+	0.709224i	$0.250954\pi$
$164$	−4.19396	+	7.26416i	−0.327494	+	0.567236i
$165$		0			0
$166$	−3.05532	−	5.29197i	−0.237139	−	0.410737i
$167$	−8.81549	+	15.2689i	−0.682163	+	1.18154i	0.292156	+	0.956371i	$0.405627\pi$
$167$	−8.81549	+	15.2689i	−0.682163	+	1.18154i	−0.974319	+	0.225170i	$0.927706\pi$
$168$		0			0
$169$	5.78394	+	10.0181i	0.444919	+	0.770622i
$170$	0.228863	−	0.396403i	0.0175530	−	0.0304027i
$171$		0			0
$172$	8.75178	+	15.1585i	0.667317	+	1.15583i
$173$	3.88685			0.295511			0.147756	−	0.989024i	$-0.452795\pi$
$173$	3.88685			0.295511			0.147756	+	0.989024i	$0.452795\pi$
$174$		0			0
$175$	14.5316	+	17.6293i	1.09848	+	1.33265i
$176$	−1.15371	+	1.99829i	−0.0869642	+	0.150626i
$177$		0			0
$178$	0.596879	−	1.03382i	0.0447380	−	0.0774884i
$179$	−3.66758	−	6.35244i	−0.274128	−	0.474804i	0.695787	−	0.718248i	$-0.255056\pi$
$179$	−3.66758	−	6.35244i	−0.274128	−	0.474804i	−0.969915	+	0.243445i	$0.921723\pi$
$180$		0			0
$181$	11.2566			0.836693			0.418346	−	0.908288i	$-0.362610\pi$
$181$	11.2566			0.836693			0.418346	+	0.908288i	$0.362610\pi$
$182$	−0.998615	−	1.21150i	−0.0740223	−	0.0898021i
$183$		0			0
$184$	−2.30619	−	3.99444i	−0.170015	−	0.294474i
$185$	17.4709			1.28449
$186$		0			0
$187$	−0.223127			−0.0163167
$188$	−17.8447			−1.30146
$189$		0			0
$190$	−5.14204			−0.373043
$191$	23.8459			1.72543			0.862715	−	0.505690i	$-0.168762\pi$
$191$	23.8459			1.72543			0.862715	+	0.505690i	$0.168762\pi$
$192$		0			0
$193$	5.93456			0.427179			0.213589	−	0.976924i	$-0.431485\pi$
$193$	5.93456			0.427179			0.213589	+	0.976924i	$0.431485\pi$
$194$	2.73823	+	4.74276i	0.196594	+	0.340510i
$195$		0			0
$196$	9.26641	+	8.05622i	0.661887	+	0.575444i
$197$	15.4682			1.10206			0.551032	−	0.834484i	$-0.314234\pi$
$197$	15.4682			1.10206			0.551032	+	0.834484i	$0.314234\pi$
$198$		0			0
$199$	7.74818	+	13.4202i	0.549254	+	0.951336i	0.998326	+	0.0578402i	$0.0184214\pi$
$199$	7.74818	+	13.4202i	0.549254	+	0.951336i	−0.449072	+	0.893496i	$0.648245\pi$
$200$	8.03736	−	13.9211i	0.568327	−	0.984371i
$201$		0			0
$202$	−0.644540	+	1.11638i	−0.0453497	+	0.0785480i
$203$	−10.8099	+	1.80860i	−0.758707	+	0.126939i
$204$		0			0
$205$	−17.6574			−1.23325
$206$	−2.40783	−	4.17048i	−0.167761	−	0.290571i
$207$		0			0
$208$	1.54684	−	2.67920i	0.107254	−	0.185769i
$209$	1.25329	+	2.17076i	0.0866918	+	0.150155i
$210$		0			0
$211$	0.771898	−	1.33697i	0.0531397	−	0.0920406i	−0.838232	−	0.545314i	$-0.816410\pi$
$211$	0.771898	−	1.33697i	0.0531397	−	0.0920406i	0.891372	+	0.453273i	$0.149744\pi$
$212$	−8.67347	−	15.0229i	−0.595697	−	1.03178i
$213$		0			0
$214$	2.70261	−	4.68105i	0.184746	−	0.319990i
$215$	−18.4233	+	31.9101i	−1.25646	+	2.17625i
$216$		0			0
$217$	3.32215	−	8.88461i	0.225522	−	0.603127i
$218$	−0.526098	−	0.911229i	−0.0356319	−	0.0617162i
$219$		0			0
$220$	−5.78135			−0.389779
$221$	0.299157			0.0201235
$222$		0			0
$223$	−2.72171	−	4.71414i	−0.182259	−	0.315682i	0.760390	−	0.649466i	$-0.225008\pi$
$223$	−2.72171	−	4.71414i	−0.182259	−	0.315682i	−0.942649	+	0.333784i	$0.891674\pi$
$224$	4.63783	−	12.4032i	0.309878	−	0.828725i
$225$		0			0
$226$	−3.92389	+	6.79638i	−0.261014	+	0.452089i
$227$	−8.03818	+	13.9225i	−0.533513	+	0.924072i	0.465721	+	0.884932i	$0.345795\pi$
$227$	−8.03818	+	13.9225i	−0.533513	+	0.924072i	−0.999234	+	0.0391399i	$0.987538\pi$
$228$		0			0
$229$	4.98420	+	8.63289i	0.329365	+	0.570477i	0.982386	−	0.186863i	$-0.0598319\pi$
$229$	4.98420	+	8.63289i	0.329365	+	0.570477i	−0.653021	+	0.757340i	$0.726499\pi$
$230$	2.26839	−	3.92897i	0.149573	−	0.259068i
$231$		0			0
$232$	3.85578	+	6.67840i	0.253144	+	0.438458i
$233$	−8.27045	+	14.3248i	−0.541815	+	0.938451i	0.456985	+	0.889474i	$0.348929\pi$
$233$	−8.27045	+	14.3248i	−0.541815	+	0.938451i	−0.998800	+	0.0489765i	$0.984404\pi$
$234$		0			0
$235$	−18.7824	−	32.5321i	−1.22523	−	2.12216i
$236$	3.17911			0.206942
$237$		0			0
$238$	0.323468	−	0.0541192i	0.0209673	−	0.00350803i
$239$	11.0119	−	19.0732i	0.712303	−	1.23375i	−0.251687	−	0.967809i	$-0.580985\pi$
$239$	11.0119	−	19.0732i	0.712303	−	1.23375i	0.963990	−	0.265937i	$-0.0856813\pi$
$240$		0			0
$241$	−8.36004	+	14.4800i	−0.538517	+	0.932739i	0.460467	+	0.887677i	$0.347682\pi$
$241$	−8.36004	+	14.4800i	−0.538517	+	0.932739i	−0.998984	+	0.0450623i	$0.985651\pi$
$242$	2.52975	+	4.38166i	0.162619	+	0.281664i
$243$		0			0
$244$	−18.9516			−1.21325
$245$	−4.93368	+	25.3728i	−0.315201	+	1.62101i
$246$		0			0
$247$	−1.68035	−	2.91045i	−0.106918	−	0.185187i
$248$	−6.67392			−0.423794
$249$		0			0
$250$	6.65606			0.420966
$251$	8.53099			0.538471			0.269236	−	0.963074i	$-0.413229\pi$
$251$	8.53099			0.538471			0.269236	+	0.963074i	$0.413229\pi$
$252$		0			0
$253$	−2.21153			−0.139038
$254$	−0.629487			−0.0394975
$255$		0			0
$256$	−0.247722			−0.0154826
$257$	−8.55986	−	14.8261i	−0.533950	−	0.924828i	−0.999213	−	0.0396557i	$-0.987374\pi$
$257$	−8.55986	−	14.8261i	−0.533950	−	0.924828i	0.465264	−	0.885172i	$-0.345959\pi$
$258$		0			0
$259$	7.96211	+	9.65945i	0.494741	+	0.600209i
$260$	7.75135			0.480718
$261$		0			0
$262$	−3.72617	−	6.45392i	−0.230204	−	0.398725i
$263$	10.2763	−	17.7991i	0.633666	−	1.09754i	−0.353130	−	0.935574i	$-0.614883\pi$
$263$	10.2763	−	17.7991i	0.633666	−	1.09754i	0.986796	−	0.161967i	$-0.0517838\pi$
$264$		0			0
$265$	18.2585	−	31.6246i	1.12161	−	1.94269i
$266$	−2.34341	−	2.84297i	−0.143684	−	0.174314i
$267$		0			0
$268$	−1.80563			−0.110297
$269$	−9.92267	−	17.1866i	−0.604996	−	1.04788i	−0.992052	−	0.125827i	$-0.959842\pi$
$269$	−9.92267	−	17.1866i	−0.604996	−	1.04788i	0.387057	−	0.922056i	$-0.373492\pi$
$270$		0			0
$271$	5.32056	−	9.21548i	0.323201	−	0.559801i	−0.657946	−	0.753065i	$-0.728574\pi$
$271$	5.32056	−	9.21548i	0.323201	−	0.559801i	0.981147	+	0.193265i	$0.0619077\pi$
$272$	0.323121	+	0.559663i	0.0195921	+	0.0339345i
$273$		0			0
$274$	−0.121114	+	0.209776i	−0.00731676	+	0.0126730i
$275$	−3.85373	−	6.67485i	−0.232388	−	0.402509i
$276$		0			0
$277$	12.4407	−	21.5479i	0.747487	−	1.29469i	−0.201536	−	0.979481i	$-0.564593\pi$
$277$	12.4407	−	21.5479i	0.747487	−	1.29469i	0.949024	−	0.315205i	$-0.102073\pi$
$278$	−2.44705	+	4.23841i	−0.146764	+	0.254203i
$279$		0			0
$280$	17.9373	−	3.00109i	1.07196	−	0.179349i
$281$	6.83733	+	11.8426i	0.407881	+	0.706470i	0.994652	−	0.103282i	$-0.0329346\pi$
$281$	6.83733	+	11.8426i	0.407881	+	0.706470i	−0.586771	+	0.809753i	$0.699601\pi$
$282$		0			0
$283$	6.32179			0.375791			0.187896	−	0.982189i	$-0.439833\pi$
$283$	6.32179			0.375791			0.187896	+	0.982189i	$0.439833\pi$
$284$	−8.67468			−0.514747
$285$		0			0
$286$	0.264830	+	0.458699i	0.0156597	+	0.0271234i
$287$	−8.04710	−	9.76255i	−0.475005	−	0.576265i
$288$		0			0
$289$	8.46875	−	14.6683i	0.498162	−	0.862842i
$290$	−3.79257	+	6.56893i	−0.222708	+	0.385741i
$291$		0			0
$292$	1.60547	+	2.78076i	0.0939533	+	0.162732i
$293$	1.31508	−	2.27778i	0.0768277	−	0.133069i	−0.825052	−	0.565057i	$-0.808854\pi$
$293$	1.31508	−	2.27778i	0.0768277	−	0.133069i	0.901880	+	0.431987i	$0.142188\pi$
$294$		0			0
$295$	3.34616	+	5.79573i	0.194821	+	0.337440i
$296$	4.40382	−	7.62764i	0.255967	−	0.443348i
$297$		0			0
$298$	5.21256	+	9.02841i	0.301955	+	0.523002i
$299$	2.96511			0.171477
$300$		0			0
$301$	−26.0389	+	4.35655i	−1.50086	+	0.251108i
$302$	−0.371500	+	0.643457i	−0.0213774	+	0.0370268i
$303$		0			0
$304$	3.62990	−	6.28717i	0.208189	−	0.360594i
$305$	−19.9475	−	34.5501i	−1.14219	−	1.97833i
$306$		0			0
$307$	−2.79496			−0.159517			−0.0797583	−	0.996814i	$-0.525415\pi$
$307$	−2.79496			−0.159517			−0.0797583	+	0.996814i	$0.525415\pi$
$308$	−2.63477	−	3.19644i	−0.150130	−	0.182134i
$309$		0			0
$310$	−3.28226	−	5.68504i	−0.186420	−	0.322889i
$311$	15.1003			0.856258			0.428129	−	0.903718i	$-0.359173\pi$
$311$	15.1003			0.856258			0.428129	+	0.903718i	$0.359173\pi$
$312$		0			0
$313$	−25.4785			−1.44013			−0.720064	−	0.693908i	$-0.755888\pi$
$313$	−25.4785			−1.44013			−0.720064	+	0.693908i	$0.755888\pi$
$314$	−8.27090			−0.466754
$315$		0			0
$316$	3.15587			0.177531
$317$	−32.5209			−1.82656			−0.913278	−	0.407337i	$-0.866457\pi$
$317$	−32.5209			−1.82656			−0.913278	+	0.407337i	$0.866457\pi$
$318$		0			0
$319$	3.69751			0.207021
$320$	4.96372	+	8.59741i	0.277480	+	0.480610i
$321$		0			0
$322$	3.20606	−	0.536405i	0.178667	−	0.0298927i
$323$	0.702021			0.0390615
$324$		0			0
$325$	5.16688	+	8.94931i	0.286607	+	0.496418i
$326$	−1.65687	+	2.86978i	−0.0917654	+	0.158942i
$327$		0			0
$328$	−4.45083	+	7.70906i	−0.245756	+	0.425661i
$329$	9.42678	−	25.2106i	0.519715	−	1.38991i
$330$		0			0
$331$	18.0948			0.994582			0.497291	−	0.867584i	$-0.334328\pi$
$331$	18.0948			0.994582			0.497291	+	0.867584i	$0.334328\pi$
$332$	10.8081	+	18.7201i	0.593170	+	1.02740i
$333$		0			0
$334$	−4.37132	+	7.57135i	−0.239188	+	0.414286i
$335$	−1.90051	−	3.29179i	−0.103836	−	0.179850i
$336$		0			0
$337$	−12.5086	+	21.6656i	−0.681389	+	1.18020i	0.293168	+	0.956061i	$0.405290\pi$
$337$	−12.5086	+	21.6656i	−0.681389	+	1.18020i	−0.974557	+	0.224139i	$0.928043\pi$
$338$	2.86807	+	4.96765i	0.156003	+	0.270204i
$339$		0			0
$340$	−0.809596	+	1.40226i	−0.0439065	+	0.0760483i
$341$	−1.59999	+	2.77127i	−0.0866446	+	0.150073i
$342$		0			0
$343$	−16.2768	+	8.83553i	−0.878863	+	0.477074i
$344$	9.28778	+	16.0869i	0.500764	+	0.867348i
$345$		0			0
$346$	1.92736			0.103616
$347$	−10.7489			−0.577030			−0.288515	−	0.957475i	$-0.593162\pi$
$347$	−10.7489			−0.577030			−0.288515	+	0.957475i	$0.593162\pi$
$348$		0			0
$349$	−1.64301	−	2.84577i	−0.0879482	−	0.152331i	0.818695	−	0.574228i	$-0.194698\pi$
$349$	−1.64301	−	2.84577i	−0.0879482	−	0.152331i	−0.906644	+	0.421897i	$0.861364\pi$
$350$	7.20574	+	8.74183i	0.385163	+	0.467270i
$351$		0			0
$352$	−2.23365	+	3.86879i	−0.119054	+	0.206207i
$353$	8.40960	−	14.5658i	0.447598	−	0.775262i	−0.550631	−	0.834748i	$-0.685613\pi$
$353$	8.40960	−	14.5658i	0.447598	−	0.775262i	0.998229	+	0.0594866i	$0.0189463\pi$
$354$		0			0
$355$	−9.13051	−	15.8145i	−0.484597	−	0.839347i
$356$	−2.11144	+	3.65711i	−0.111906	+	0.193827i
$357$		0			0
$358$	−1.81864	−	3.14997i	−0.0961180	−	0.166481i
$359$	−11.8921	+	20.5978i	−0.627642	+	1.08711i	0.360382	+	0.932805i	$0.382646\pi$
$359$	−11.8921	+	20.5978i	−0.627642	+	1.08711i	−0.988024	+	0.154303i	$0.950687\pi$
$360$		0			0
$361$	5.55680	+	9.62466i	0.292463	+	0.506561i
$362$	5.58177			0.293371
$363$		0			0
$364$	3.53256	+	4.28562i	0.185157	+	0.224628i
$365$	−3.37968	+	5.85377i	−0.176900	+	0.306401i
$366$		0			0
$367$	0.344992	−	0.597544i	0.0180084	−	0.0311915i	−0.856881	−	0.515515i	$-0.827601\pi$
$367$	0.344992	−	0.597544i	0.0180084	−	0.0311915i	0.874889	+	0.484323i	$0.160934\pi$
$368$	3.20263	+	5.54712i	0.166949	+	0.289164i
$369$		0			0
$370$	8.66327			0.450382
$371$	25.8059	−	4.31757i	1.33978	−	0.224157i
$372$		0			0
$373$	1.88006	+	3.25636i	0.0973457	+	0.168608i	0.910585	−	0.413321i	$-0.135631\pi$
$373$	1.88006	+	3.25636i	0.0973457	+	0.168608i	−0.813239	+	0.581929i	$0.802298\pi$
$374$	−0.110642			−0.00572114
$375$		0			0
$376$	−18.9376			−0.976634
$377$	−4.95744			−0.255321
$378$		0			0
$379$	32.8735			1.68860			0.844300	−	0.535872i	$-0.180017\pi$
$379$	32.8735			1.68860			0.844300	+	0.535872i	$0.180017\pi$
$380$	18.1898			0.933116
$381$		0			0
$382$	11.8244			0.604991
$383$	−0.536335	−	0.928960i	−0.0274055	−	0.0474676i	0.851997	−	0.523546i	$-0.175391\pi$
$383$	−0.536335	−	0.928960i	−0.0274055	−	0.0474676i	−0.879403	+	0.476078i	$0.842058\pi$
$384$		0			0
$385$	3.05410	−	8.16775i	0.155651	−	0.416267i
$386$	2.94276			0.149782
$387$		0			0
$388$	−9.68640	−	16.7773i	−0.491752	−	0.851740i
$389$	−11.8718	+	20.5626i	−0.601925	+	1.04256i	0.390605	+	0.920559i	$0.372266\pi$
$389$	−11.8718	+	20.5626i	−0.601925	+	1.04256i	−0.992529	+	0.122006i	$0.961067\pi$
$390$		0			0
$391$	−0.309693	+	0.536405i	−0.0156619	+	0.0271271i
$392$	9.83394	+	8.54962i	0.496689	+	0.431821i
$393$		0			0
$394$	7.67019			0.386419
$395$	3.32170	+	5.75336i	0.167133	+	0.289483i
$396$		0			0
$397$	−0.0160489	+	0.0277975i	−0.000805471	+	0.00139512i	−0.866428	−	0.499302i	$-0.833590\pi$
$397$	−0.0160489	+	0.0277975i	−0.000805471	+	0.00139512i	0.865622	+	0.500697i	$0.166923\pi$
$398$	3.84208	+	6.65467i	0.192586	+	0.333569i
$399$		0			0
$400$	−11.1616	+	19.3324i	−0.558078	+	0.966619i
$401$	12.2628	+	21.2398i	0.612374	+	1.06066i	0.990839	+	0.135048i	$0.0431188\pi$
$401$	12.2628	+	21.2398i	0.612374	+	1.06066i	−0.378465	+	0.925616i	$0.623548\pi$
$402$		0			0
$403$	2.14519	−	3.71558i	0.106860	−	0.185086i
$404$	2.28004	−	3.94914i	0.113436	−	0.196477i
$405$		0			0
$406$	−5.36029	+	0.896827i	−0.266027	+	0.0445088i
$407$	−2.11153	−	3.65728i	−0.104665	−	0.181284i
$408$		0			0
$409$	26.7897			1.32467			0.662333	−	0.749210i	$-0.269567\pi$
$409$	26.7897			1.32467			0.662333	+	0.749210i	$0.269567\pi$
$410$	−8.75574			−0.432415
$411$		0			0
$412$	8.51759	+	14.7529i	0.419631	+	0.726823i
$413$	−1.67942	+	4.49137i	−0.0826388	+	0.221006i
$414$		0			0
$415$	−22.7520	+	39.4077i	−1.11685	+	1.93445i
$416$	2.99476	−	5.18708i	0.146830	−	0.254317i
$417$		0			0
$418$	0.621466	+	1.07641i	0.0303969	+	0.0526490i
$419$	10.5262	−	18.2320i	0.514240	−	0.890689i	−0.485624	−	0.874168i	$-0.661407\pi$
$419$	10.5262	−	18.2320i	0.514240	−	0.890689i	0.999864	−	0.0165215i	$-0.00525920\pi$
$420$		0			0
$421$	−7.44533	−	12.8957i	−0.362863	−	0.628498i	0.625568	−	0.780170i	$-0.284867\pi$
$421$	−7.44533	−	12.8957i	−0.362863	−	0.628498i	−0.988431	+	0.151672i	$0.951534\pi$
$422$	0.382760	−	0.662959i	0.0186325	−	0.0322724i
$423$		0			0
$424$	−9.20469	−	15.9430i	−0.447019	−	0.774260i
$425$	−2.15864			−0.104709
$426$		0			0
$427$	10.0115	−	26.7744i	0.484492	−	1.29571i
$428$	−9.56037	+	16.5590i	−0.462118	+	0.800412i
$429$		0			0
$430$	−9.13554	+	15.8232i	−0.440555	+	0.763064i
$431$	7.95192	+	13.7731i	0.383031	+	0.663428i	0.991494	−	0.130154i	$-0.0415471\pi$
$431$	7.95192	+	13.7731i	0.383031	+	0.663428i	−0.608463	+	0.793582i	$0.708214\pi$
$432$		0			0
$433$	−16.3658			−0.786490			−0.393245	−	0.919434i	$-0.628648\pi$
$433$	−16.3658			−0.786490			−0.393245	+	0.919434i	$0.628648\pi$
$434$	1.64735	−	4.40560i	0.0790752	−	0.211475i
$435$		0			0
$436$	1.86105	+	3.22344i	0.0891282	+	0.154375i
$437$	6.95811			0.332851
$438$		0			0
$439$	−15.5447			−0.741909			−0.370954	−	0.928651i	$-0.620969\pi$
$439$	−15.5447			−0.741909			−0.370954	+	0.928651i	$0.620969\pi$
$440$	−6.13543			−0.292495
$441$		0			0
$442$	0.148343			0.00705594
$443$	−1.79005			−0.0850480			−0.0425240	−	0.999095i	$-0.513540\pi$
$443$	−1.79005			−0.0850480			−0.0425240	+	0.999095i	$0.513540\pi$
$444$		0			0
$445$	−8.88955			−0.421405
$446$	−1.34961	−	2.33759i	−0.0639058	−	0.110688i
$447$		0			0
$448$	−2.49126	+	6.66252i	−0.117701	+	0.314774i
$449$	−13.5666			−0.640250			−0.320125	−	0.947375i	$-0.603725\pi$
$449$	−13.5666			−0.640250			−0.320125	+	0.947375i	$0.603725\pi$
$450$		0			0
$451$	2.13407	+	3.69631i	0.100489	+	0.174053i
$452$	13.8806	−	24.0419i	0.652890	−	1.13084i
$453$		0			0
$454$	−3.98588	+	6.90375i	−0.187067	+	0.324009i
$455$	−4.09478	+	10.9509i	−0.191966	+	0.513387i
$456$		0			0
$457$	2.56917			0.120181			0.0600905	−	0.998193i	$-0.480861\pi$
$457$	2.56917			0.120181			0.0600905	+	0.998193i	$0.480861\pi$
$458$	2.47151	+	4.28078i	0.115486	+	0.200028i
$459$		0			0
$460$	−8.02434	+	13.8986i	−0.374137	+	0.648024i
$461$	−18.0934	−	31.3388i	−0.842695	−	1.45959i	−0.887608	−	0.460600i	$-0.847634\pi$
$461$	−18.0934	−	31.3388i	−0.842695	−	1.45959i	0.0449122	−	0.998991i	$-0.485699\pi$
$462$		0			0
$463$	8.19224	−	14.1894i	0.380726	−	0.659436i	−0.610440	−	0.792062i	$-0.709008\pi$
$463$	8.19224	−	14.1894i	0.380726	−	0.659436i	0.991166	+	0.132626i	$0.0423409\pi$
$464$	−5.35455	−	9.27436i	−0.248579	−	0.430551i
$465$		0			0
$466$	−4.10105	+	7.10323i	−0.189978	+	0.329051i
$467$	4.35022	−	7.53480i	0.201304	−	0.348669i	−0.747645	−	0.664099i	$-0.768815\pi$
$467$	4.35022	−	7.53480i	0.201304	−	0.348669i	0.948949	+	0.315430i	$0.102149\pi$
$468$		0			0
$469$	0.953856	−	2.55095i	0.0440450	−	0.117792i
$470$	−9.31361	−	16.1316i	−0.429605	−	0.744097i
$471$		0			0
$472$	3.37381			0.155292
$473$	8.90655			0.409524
$474$		0			0
$475$	12.1249	+	21.0010i	0.556330	+	0.963591i
$476$	−1.14425	+	0.191445i	−0.0524468	+	0.00877485i
$477$		0			0
$478$	5.46047	−	9.45782i	0.249756	−	0.432591i
$479$	−8.88370	+	15.3870i	−0.405907	+	0.703051i	−0.994427	−	0.105432i	$-0.966378\pi$
$479$	−8.88370	+	15.3870i	−0.405907	+	0.703051i	0.588520	+	0.808483i	$0.299711\pi$
$480$		0			0
$481$	2.83103	+	4.90349i	0.129084	+	0.223580i
$482$	−4.14548	+	7.18018i	−0.188821	+	0.327048i
$483$		0			0
$484$	−8.94890	−	15.4999i	−0.406768	−	0.704543i
$485$	20.3908	−	35.3179i	0.925898	−	1.60370i
$486$		0			0
$487$	8.32763	+	14.4239i	0.377361	+	0.653608i	0.990677	−	0.136229i	$-0.0434983\pi$
$487$	8.32763	+	14.4239i	0.377361	+	0.653608i	−0.613316	+	0.789837i	$0.710165\pi$
$488$	−20.1123			−0.910443
$489$		0			0
$490$	−2.44645	+	12.5816i	−0.110519	+	0.568378i
$491$	3.21021	−	5.56025i	0.144875	−	0.250930i	−0.784451	−	0.620190i	$-0.787055\pi$
$491$	3.21021	−	5.56025i	0.144875	−	0.250930i	0.929326	+	0.369260i	$0.120389\pi$
$492$		0			0
$493$	0.517784	−	0.896827i	0.0233198	−	0.0403911i
$494$	−0.833230	−	1.44320i	−0.0374888	−	0.0649325i
$495$		0			0
$496$	9.26814			0.416152
$497$	4.58255	−	12.2554i	0.205555	−	0.549729i
$498$		0			0
$499$	−5.57296	−	9.65264i	−0.249480	−	0.432112i	0.713902	−	0.700246i	$-0.246926\pi$
$499$	−5.57296	−	9.65264i	−0.249480	−	0.432112i	−0.963382	+	0.268134i	$0.913593\pi$
$500$	−23.5456			−1.05299
$501$		0			0
$502$	4.23025			0.188805
$503$	17.7223			0.790200			0.395100	−	0.918638i	$-0.370710\pi$
$503$	17.7223			0.790200			0.395100	+	0.918638i	$0.370710\pi$
$504$		0			0
$505$	9.59939			0.427167
$506$	−1.09663			−0.0487511
$507$		0			0
$508$	2.22678			0.0987976
$509$	15.5411	+	26.9180i	0.688848	+	1.19312i	0.972211	+	0.234107i	$0.0752167\pi$
$509$	15.5411	+	26.9180i	0.688848	+	1.19312i	−0.283362	+	0.959013i	$0.591450\pi$
$510$		0			0
$511$	−4.77672	+	0.799190i	−0.211310	+	0.0353541i
$512$	22.5634			0.997169
$513$		0			0
$514$	−4.24456	−	7.35180i	−0.187220	−	0.324274i
$515$	−17.9303	+	31.0563i	−0.790105	+	1.36850i
$516$		0			0
$517$	−4.54008	+	7.86365i	−0.199672	+	0.345843i
$518$	3.94816	+	4.78981i	0.173472	+	0.210452i
$519$		0			0
$520$	8.22608			0.360737
$521$	2.37986	+	4.12203i	0.104263	+	0.180590i	0.913437	−	0.406980i	$-0.133418\pi$
$521$	2.37986	+	4.12203i	0.104263	+	0.180590i	−0.809174	+	0.587570i	$0.800085\pi$
$522$		0			0
$523$	20.1258	−	34.8588i	0.880038	−	1.52427i	0.0287402	−	0.999587i	$-0.490850\pi$
$523$	20.1258	−	34.8588i	0.880038	−	1.52427i	0.851298	−	0.524683i	$-0.175816\pi$
$524$	13.1812	+	22.8305i	0.575823	+	0.997355i
$525$		0			0
$526$	5.09571	−	8.82602i	0.222183	−	0.384833i
$527$	0.448113	+	0.776154i	0.0195201	+	0.0338098i
$528$		0			0
$529$	8.43046	−	14.6020i	0.366542	−	0.634869i
$530$	9.05381	−	15.6817i	0.393272	−	0.681168i
$531$		0			0
$532$	8.28972	+	10.0569i	0.359405	+	0.436022i
$533$	−2.86125	−	4.95583i	−0.123935	−	0.214661i
$534$		0			0
$535$	−40.2510			−1.74020
$536$	−1.91622			−0.0827680
$537$		0			0
$538$	−4.92033	−	8.52227i	−0.212131	−	0.367421i
$539$	5.90771	−	2.03376i	0.254463	−	0.0876003i
$540$		0			0
$541$	12.0547	−	20.8794i	0.518273	−	0.897675i	−0.481502	−	0.876445i	$-0.659908\pi$
$541$	12.0547	−	20.8794i	0.518273	−	0.897675i	0.999775	−	0.0212301i	$-0.00675826\pi$
$542$	2.63830	−	4.56966i	0.113325	−	0.196284i
$543$		0			0
$544$	0.625580	+	1.08354i	0.0268215	+	0.0464563i
$545$	−3.91769	+	6.78564i	−0.167815	+	0.290665i
$546$		0			0
$547$	−6.17751	−	10.6998i	−0.264131	−	0.457489i	0.703204	−	0.710988i	$-0.251752\pi$
$547$	−6.17751	−	10.6998i	−0.264131	−	0.457489i	−0.967336	+	0.253499i	$0.918419\pi$
$548$	0.428436	−	0.742073i	0.0183019	−	0.0316998i
$549$		0			0
$550$	−1.91094	−	3.30985i	−0.0814828	−	0.141132i
$551$	−11.6334			−0.495600
$552$		0			0
$553$	−1.66714	+	4.45854i	−0.0708941	+	0.189596i
$554$	6.16893	−	10.6849i	0.262093	−	0.453958i
$555$		0			0
$556$	8.65633	−	14.9932i	0.367110	−	0.635853i
$557$	−4.03845	−	6.99479i	−0.171114	−	0.296379i	0.767695	−	0.640815i	$-0.221403\pi$
$557$	−4.03845	−	6.99479i	−0.171114	−	0.296379i	−0.938810	+	0.344436i	$0.888070\pi$
$558$		0			0
$559$	−11.9415			−0.505070
$560$	−24.9097	+	4.16764i	−1.05263	+	0.176115i
$561$		0			0
$562$	3.39041	+	5.87237i	0.143016	+	0.247711i
$563$	−45.2127			−1.90549			−0.952744	−	0.303774i	$-0.901753\pi$
$563$	−45.2127			−1.90549			−0.952744	+	0.303774i	$0.901753\pi$
$564$		0			0
$565$	58.4401			2.45859
$566$	3.13477			0.131764
$567$		0			0
$568$	−9.20596			−0.386274
$569$	−22.4299			−0.940309			−0.470155	−	0.882584i	$-0.655802\pi$
$569$	−22.4299			−0.940309			−0.470155	+	0.882584i	$0.655802\pi$
$570$		0			0
$571$	−21.8269			−0.913426			−0.456713	−	0.889614i	$-0.650973\pi$
$571$	−21.8269			−0.913426			−0.456713	+	0.889614i	$0.650973\pi$
$572$	−0.936826	−	1.62263i	−0.0391706	−	0.0678455i
$573$		0			0
$574$	−3.99030	−	4.84094i	−0.166552	−	0.202057i
$575$	−21.3954			−0.892251
$576$		0			0
$577$	−16.1022	−	27.8898i	−0.670342	−	1.16107i	−0.977807	−	0.209508i	$-0.932814\pi$
$577$	−16.1022	−	27.8898i	−0.670342	−	1.16107i	0.307465	−	0.951559i	$-0.400519\pi$
$578$	4.19939	−	7.27355i	0.174671	−	0.302540i
$579$		0			0
$580$	13.4161	−	23.2373i	0.557072	−	0.964878i
$581$	−32.1569	+	5.38016i	−1.33409	+	0.223207i
$582$		0			0
$583$	−8.82687			−0.365571
$584$	1.70380	+	2.95107i	0.0705039	+	0.122116i
$585$		0			0
$586$	0.652105	−	1.12948i	0.0269382	−	0.0466584i
$587$	9.72304	+	16.8408i	0.401313	+	0.695094i	0.993885	−	0.110424i	$-0.0352208\pi$
$587$	9.72304	+	16.8408i	0.401313	+	0.695094i	−0.592572	+	0.805518i	$0.701887\pi$
$588$		0			0
$589$	5.03404	−	8.71921i	0.207424	−	0.359269i
$590$	1.65926	+	2.87392i	0.0683105	+	0.118317i
$591$		0			0
$592$	−6.11563	+	10.5926i	−0.251351	+	0.435352i
$593$	14.4202	−	24.9766i	0.592168	−	1.02566i	−0.401772	−	0.915740i	$-0.631606\pi$
$593$	14.4202	−	24.9766i	0.592168	−	1.02566i	0.993940	−	0.109925i	$-0.0350611\pi$
$594$		0			0
$595$	−1.55340	−	1.88455i	−0.0636831	−	0.0772589i
$596$	−18.4392	−	31.9377i	−0.755300	−	1.30822i
$597$		0			0
$598$	1.47030			0.0601252
$599$	46.9989			1.92032			0.960161	−	0.279447i	$-0.0901511\pi$
$599$	46.9989			1.92032			0.960161	+	0.279447i	$0.0901511\pi$
$600$		0			0
$601$	−7.80843	−	13.5246i	−0.318512	−	0.551680i	0.661665	−	0.749799i	$-0.269850\pi$
$601$	−7.80843	−	13.5246i	−0.318512	−	0.551680i	−0.980178	+	0.198119i	$0.936517\pi$
$602$	−12.9119	+	2.16028i	−0.526248	+	0.0880463i
$603$		0			0
$604$	1.31417	−	2.27620i	0.0534727	−	0.0926174i
$605$	18.8383	−	32.6289i	0.765885	−	1.32655i
$606$		0			0
$607$	14.3266	+	24.8144i	0.581500	+	1.00719i	0.995302	+	0.0968200i	$0.0308671\pi$
$607$	14.3266	+	24.8144i	0.581500	+	1.00719i	−0.413802	+	0.910367i	$0.635800\pi$
$608$	7.02769	−	12.1723i	0.285010	−	0.493652i
$609$		0			0
$610$	−9.89134	−	17.1323i	−0.400489	−	0.693667i
$611$	6.08711	−	10.5432i	0.246258	−	0.426531i
$612$		0			0
$613$	14.6734	+	25.4151i	0.592653	+	1.02651i	0.993873	+	0.110524i	$0.0352529\pi$
$613$	14.6734	+	25.4151i	0.592653	+	1.02651i	−0.401220	+	0.915982i	$0.631414\pi$
$614$	−1.38593			−0.0559316
$615$		0			0
$616$	−2.79613	−	3.39220i	−0.112659	−	0.136676i
$617$	−2.06401	+	3.57497i	−0.0830938	+	0.143923i	−0.904577	−	0.426310i	$-0.859813\pi$
$617$	−2.06401	+	3.57497i	−0.0830938	+	0.143923i	0.821484	+	0.570232i	$0.193147\pi$
$618$		0			0
$619$	−11.3565	+	19.6700i	−0.456456	+	0.790605i	−0.998771	−	0.0495708i	$-0.984215\pi$
$619$	−11.3565	+	19.6700i	−0.456456	+	0.790605i	0.542315	+	0.840175i	$0.317548\pi$
$620$	11.6109	+	20.1106i	0.466304	+	0.807662i
$621$		0			0
$622$	7.48774			0.300231
$623$	−4.05128	−	4.91492i	−0.162311	−	0.196912i
$624$		0			0
$625$	−3.19498	−	5.53387i	−0.127799	−	0.221355i
$626$	−12.6340			−0.504955
$627$		0			0
$628$	29.2580			1.16752
$629$	−1.18276			−0.0471597
$630$		0			0
$631$	−38.6411			−1.53828			−0.769138	−	0.639082i	$-0.779314\pi$
$631$	−38.6411			−1.53828			−0.769138	+	0.639082i	$0.779314\pi$
$632$	3.34915			0.133222
$633$		0			0
$634$	−16.1261			−0.640449
$635$	2.34380	+	4.05958i	0.0930107	+	0.161099i
$636$		0			0
$637$	−7.92076	+	2.72677i	−0.313832	+	0.108038i
$638$	1.83348			0.0725881
$639$		0			0
$640$	20.9427	+	36.2737i	0.827831	+	1.43385i
$641$	−14.2363	+	24.6580i	−0.562301	+	0.973933i	0.434995	+	0.900433i	$0.356750\pi$
$641$	−14.2363	+	24.6580i	−0.562301	+	0.973933i	−0.997295	+	0.0735002i	$0.976583\pi$
$642$		0			0
$643$	−8.52125	+	14.7592i	−0.336045	+	0.582048i	−0.983685	−	0.179899i	$-0.942423\pi$
$643$	−8.52125	+	14.7592i	−0.336045	+	0.582048i	0.647640	+	0.761947i	$0.275756\pi$
$644$	−11.3413	+	1.89751i	−0.446911	+	0.0747724i
$645$		0			0
$646$	0.348110			0.0136962
$647$	−1.68809	−	2.92386i	−0.0663657	−	0.114949i	0.830933	−	0.556372i	$-0.187807\pi$
$647$	−1.68809	−	2.92386i	−0.0663657	−	0.114949i	−0.897299	+	0.441423i	$0.854474\pi$
$648$		0			0
$649$	0.808833	−	1.40094i	0.0317495	−	0.0549917i
$650$	2.56209	+	4.43768i	0.100494	+	0.174060i
$651$		0			0
$652$	5.86110	−	10.1517i	0.229538	−	0.397572i
$653$	−9.17255	−	15.8873i	−0.358950	−	0.621719i	0.628836	−	0.777538i	$-0.283532\pi$
$653$	−9.17255	−	15.8873i	−0.358950	−	0.621719i	−0.987786	+	0.155819i	$0.950198\pi$
$654$		0			0
$655$	−27.7477	+	48.0604i	−1.08419	+	1.87787i
$656$	6.18090	−	10.7056i	0.241324	−	0.417985i
$657$		0			0
$658$	4.67444	−	12.5011i	0.182229	−	0.487345i
$659$	13.9248	+	24.1184i	0.542432	+	0.939519i	0.998764	+	0.0497098i	$0.0158297\pi$
$659$	13.9248	+	24.1184i	0.542432	+	0.939519i	−0.456332	+	0.889810i	$0.650837\pi$
$660$		0			0
$661$	39.0141			1.51747			0.758737	−	0.651397i	$-0.225817\pi$
$661$	39.0141			1.51747			0.758737	+	0.651397i	$0.225817\pi$
$662$	8.97265			0.348732
$663$		0			0
$664$	11.4700	+	19.8667i	0.445123	+	0.770976i
$665$	−9.60906	+	25.6981i	−0.372624	+	0.996529i
$666$		0			0
$667$	5.13203	−	8.88894i	0.198713	−	0.344181i
$668$	15.4634	−	26.7834i	0.598296	−	1.03628i
$669$		0			0
$670$	−0.942405	−	1.63229i	−0.0364083	−	0.0630610i
$671$	−4.82170	+	8.35143i	−0.186140	+	0.322404i
$672$		0			0
$673$	24.6154	+	42.6352i	0.948856	+	1.64347i	0.747841	+	0.663878i	$0.231090\pi$
$673$	24.6154	+	42.6352i	0.948856	+	1.64347i	0.201014	+	0.979588i	$0.435576\pi$
$674$	−6.20264	+	10.7433i	−0.238917	+	0.413816i
$675$		0			0
$676$	−10.1457	−	17.5729i	−0.390219	−	0.675879i
$677$	23.3915			0.899010			0.449505	−	0.893278i	$-0.351600\pi$
$677$	23.3915			0.899010			0.449505	+	0.893278i	$0.351600\pi$
$678$		0			0
$679$	28.8196	−	4.82180i	1.10600	−	0.185044i
$680$	−0.859180	+	1.48814i	−0.0329480	+	0.0570677i
$681$		0			0
$682$	−0.793387	+	1.37419i	−0.0303803	+	0.0526203i
$683$	15.1632	+	26.2634i	0.580204	+	1.00494i	0.995455	+	0.0952356i	$0.0303604\pi$
$683$	15.1632	+	26.2634i	0.580204	+	1.00494i	−0.415251	+	0.909707i	$0.636306\pi$
$684$		0			0
$685$	1.80380			0.0689196
$686$	−8.07114	+	4.38126i	−0.308157	+	0.167277i
$687$		0			0
$688$	−12.8980	−	22.3401i	−0.491733	−	0.851707i
$689$	11.8346			0.450863
$690$		0			0
$691$	−4.11330			−0.156477			−0.0782387	−	0.996935i	$-0.524930\pi$
$691$	−4.11330			−0.156477			−0.0782387	+	0.996935i	$0.524930\pi$
$692$	−6.81797			−0.259180
$693$		0			0
$694$	−5.33003			−0.202325
$695$	36.4448			1.38243
$696$		0			0
$697$	1.19538			0.0452784
$698$	−0.814716	−	1.41113i	−0.0308375	−	0.0534120i
$699$		0			0
$700$	−25.4900	−	30.9239i	−0.963432	−	1.16881i
$701$	−29.1835			−1.10225			−0.551123	−	0.834424i	$-0.685800\pi$
$701$	−29.1835			−1.10225			−0.551123	+	0.834424i	$0.685800\pi$
$702$		0			0
$703$	6.64347	+	11.5068i	0.250563	+	0.433988i
$704$	1.19983	−	2.07816i	0.0452202	−	0.0783236i
$705$		0			0
$706$	4.17005	−	7.22274i	0.156942	−	0.271831i
$707$	4.37478	+	5.30738i	0.164531	+	0.199605i
$708$		0			0
$709$	−42.4617			−1.59468			−0.797342	−	0.603528i	$-0.793761\pi$
$709$	−42.4617			−1.59468			−0.797342	+	0.603528i	$0.793761\pi$
$710$	−4.52753	−	7.84192i	−0.169915	−	0.294302i
$711$		0			0
$712$	−2.24075	+	3.88109i	−0.0839757	+	0.145450i
$713$	4.44149	+	7.69288i	0.166335	+	0.288101i
$714$		0			0
$715$	1.97211	−	3.41579i	0.0737526	−	0.127743i
$716$	6.43336	+	11.1429i	0.240426	+	0.416430i
$717$		0			0
$718$	−5.89692	+	10.2138i	−0.220071	+	0.381175i
$719$	5.57126	−	9.64970i	0.207773	−	0.359873i	−0.743240	−	0.669025i	$-0.766712\pi$
$719$	5.57126	−	9.64970i	0.207773	−	0.359873i	0.951013	+	0.309152i	$0.100045\pi$
$720$		0			0
$721$	−25.3421	+	4.23997i	−0.943789	+	0.157905i
$722$	2.75544	+	4.77256i	0.102547	+	0.177616i
$723$		0			0
$724$	−19.7453			−0.733828
$725$	35.7715			1.32852
$726$		0			0
$727$	−14.3410	−	24.8393i	−0.531878	−	0.921239i	−0.999308	−	0.0372089i	$-0.988153\pi$
$727$	−14.3410	−	24.8393i	−0.531878	−	0.921239i	0.467430	−	0.884030i	$-0.345180\pi$
$728$	3.74892	+	4.54810i	0.138944	+	0.168564i
$729$		0			0
$730$	−1.67588	+	2.90270i	−0.0620269	+	0.107434i
$731$	1.24724	−	2.16028i	0.0461307	−	0.0799007i
$732$		0			0
$733$	12.5264	+	21.6964i	0.462674	+	0.801375i	0.999093	−	0.0425768i	$-0.0135567\pi$
$733$	12.5264	+	21.6964i	0.462674	+	0.801375i	−0.536419	+	0.843952i	$0.680223\pi$
$734$	0.171071	−	0.296303i	0.00631433	−	0.0109367i
$735$		0			0
$736$	6.20047	+	10.7395i	0.228552	+	0.395864i
$737$	−0.459391	+	0.795689i	−0.0169219	+	0.0293096i
$738$		0			0
$739$	13.7608	+	23.8344i	0.506198	+	0.876761i	0.999974	+	0.00717223i	$0.00228301\pi$
$739$	13.7608	+	23.8344i	0.506198	+	0.876761i	−0.493776	+	0.869589i	$0.664384\pi$
$740$	−30.6460			−1.12657
$741$		0			0
$742$	12.7963	−	2.14095i	0.469768	−	0.0785967i
$743$	7.00608	−	12.1349i	0.257028	−	0.445186i	−0.708416	−	0.705795i	$-0.750590\pi$
$743$	7.00608	−	12.1349i	0.257028	−	0.445186i	0.965444	+	0.260609i	$0.0839233\pi$
$744$		0			0
$745$	38.8163	−	67.2318i	1.42212	−	2.46318i
$746$	0.932261	+	1.61472i	0.0341325	+	0.0591192i
$747$		0			0
$748$	0.391390			0.0143106
$749$	−18.3438	−	22.2543i	−0.670268	−	0.813153i
$750$		0			0
$751$	26.1297	+	45.2580i	0.953486	+	1.65149i	0.737795	+	0.675025i	$0.235867\pi$
$751$	26.1297	+	45.2580i	0.953486	+	1.65149i	0.215692	+	0.976461i	$0.430799\pi$
$752$	26.2989			0.959021
$753$		0			0
$754$	−2.45824			−0.0895237
$755$	5.53289			0.201363
$756$		0			0
$757$	−43.3447			−1.57539			−0.787694	−	0.616066i	$-0.788725\pi$
$757$	−43.3447			−1.57539			−0.787694	+	0.616066i	$0.788725\pi$
$758$	16.3009			0.592077
$759$		0			0
$760$	19.3038			0.700223
$761$	−8.62550	−	14.9398i	−0.312674	−	0.541568i	0.666266	−	0.745714i	$-0.267891\pi$
$761$	−8.62550	−	14.9398i	−0.312674	−	0.541568i	−0.978940	+	0.204146i	$0.934558\pi$
$762$		0			0
$763$	−5.53713	+	0.926414i	−0.200457	+	0.0335384i
$764$	−41.8285			−1.51330
$765$		0			0
$766$	−0.265952	−	0.460642i	−0.00960922	−	0.0166437i
$767$	−1.08444	+	1.87831i	−0.0391570	+	0.0678218i
$768$		0			0
$769$	−10.6727	+	18.4856i	−0.384867	+	0.666609i	−0.991751	−	0.128182i	$-0.959086\pi$
$769$	−10.6727	+	18.4856i	−0.384867	+	0.666609i	0.606884	+	0.794790i	$0.292419\pi$
$770$	1.51443	−	4.05013i	0.0545763	−	0.145957i
$771$		0			0
$772$	−10.4099			−0.374660
$773$	6.57357	+	11.3858i	0.236435	+	0.409517i	0.959689	−	0.281065i	$-0.0906877\pi$
$773$	6.57357	+	11.3858i	0.236435	+	0.409517i	−0.723254	+	0.690582i	$0.757354\pi$
$774$		0			0
$775$	−15.4791	+	26.8106i	−0.556027	+	0.963066i
$776$	−10.2796	−	17.8049i	−0.369018	−	0.639158i
$777$		0			0
$778$	−5.88685	+	10.1963i	−0.211054	+	0.365556i
$779$	−6.71439	−	11.6297i	−0.240568	−	0.416676i
$780$		0			0
$781$	−2.20702	+	3.82268i	−0.0789735	+	0.136786i
$782$	−0.153567	+	0.265986i	−0.00549155	+	0.00951164i
$783$		0			0
$784$	−13.6565	−	11.8729i	−0.487732	−	0.424034i
$785$	30.7954	+	53.3393i	1.09914	+	1.90376i
$786$		0			0
$787$	−28.1301			−1.00273			−0.501364	−	0.865236i	$-0.667168\pi$
$787$	−28.1301			−1.00273			−0.501364	+	0.865236i	$0.667168\pi$
$788$	−27.1330			−0.966573
$789$		0			0
$790$	1.64713	+	2.85291i	0.0586021	+	0.101502i
$791$	26.6332	+	32.3108i	0.946968	+	1.14884i
$792$		0			0
$793$	6.46470	−	11.1972i	0.229568	−	0.397624i
$794$	−0.00795814	+	0.0137839i	−0.000282424	+	0.000489172i
$795$		0			0
$796$	−13.5912	−	23.5406i	−0.481727	−	0.834376i
$797$	−12.8683	+	22.2885i	−0.455817	+	0.789499i	−0.998735	−	0.0502873i	$-0.983986\pi$
$797$	−12.8683	+	22.2885i	−0.455817	+	0.789499i	0.542917	+	0.839786i	$0.317320\pi$
$798$		0			0
$799$	1.27155	+	2.20238i	0.0449841	+	0.0779147i
$800$	−21.6094	+	37.4285i	−0.764007	+	1.32330i
$801$		0			0
$802$	6.08073	+	10.5321i	0.214718	+	0.371902i
$803$	1.63387			0.0576580
$804$		0			0
$805$	−15.3966	−	18.6788i	−0.542658	−	0.658340i
$806$	1.06373	−	1.84244i	0.0374684	−	0.0648972i
$807$		0			0
$808$	2.41968	−	4.19100i	0.0851240	−	0.147439i
$809$	−15.9353	−	27.6007i	−0.560254	−	0.970388i	−0.997474	−	0.0710338i	$-0.977370\pi$
$809$	−15.9353	−	27.6007i	−0.560254	−	0.970388i	0.437220	−	0.899355i	$-0.355963\pi$
$810$		0			0
$811$	43.3860			1.52349			0.761744	−	0.647878i	$-0.224343\pi$
$811$	43.3860			1.52349			0.761744	+	0.647878i	$0.224343\pi$
$812$	18.9618	−	3.17249i	0.665429	−	0.111333i
$813$		0			0
$814$	−1.04704	−	1.81353i	−0.0366987	−	0.0635641i
$815$	24.6764			0.864375
$816$		0			0
$817$	−28.0226			−0.980385
$818$	13.2842			0.464470
$819$		0			0
$820$	30.9731			1.08163
$821$	16.3935			0.572139			0.286069	−	0.958209i	$-0.407651\pi$
$821$	16.3935			0.572139			0.286069	+	0.958209i	$0.407651\pi$
$822$		0			0
$823$	−26.3780			−0.919478			−0.459739	−	0.888054i	$-0.652057\pi$
$823$	−26.3780			−0.919478			−0.459739	+	0.888054i	$0.652057\pi$
$824$	9.03925	+	15.6564i	0.314897	+	0.545418i
$825$		0			0
$826$	−0.832771	+	2.22713i	−0.0289758	+	0.0774917i
$827$	−36.7225			−1.27697			−0.638484	−	0.769635i	$-0.720438\pi$
$827$	−36.7225			−1.27697			−0.638484	+	0.769635i	$0.720438\pi$
$828$		0			0
$829$	12.1579	+	21.0581i	0.422261	+	0.731377i	0.996160	−	0.0875485i	$-0.0279033\pi$
$829$	12.1579	+	21.0581i	0.422261	+	0.731377i	−0.573899	+	0.818926i	$0.694570\pi$
$830$	−11.2820	+	19.5410i	−0.391604	+	0.678279i
$831$		0			0
$832$	−1.60867	+	2.78629i	−0.0557705	+	0.0965974i
$833$	0.334004	−	1.71771i	0.0115725	−	0.0595151i
$834$		0			0
$835$	65.1038			2.25301
$836$	−2.19841	−	3.80776i	−0.0760337	−	0.131694i
$837$		0			0
$838$	5.21962	−	9.04065i	0.180309	−	0.312304i
$839$	12.8405	+	22.2404i	0.443303	+	0.767824i	0.997932	−	0.0642741i	$-0.0204732\pi$
$839$	12.8405	+	22.2404i	0.443303	+	0.767824i	−0.554629	+	0.832098i	$0.687140\pi$
$840$		0			0
$841$	5.91963	−	10.2531i	0.204125	−	0.353555i
$842$	−3.69190	−	6.39456i	−0.127231	−	0.220371i
$843$		0			0
$844$	−1.35400	+	2.34519i	−0.0466065	+	0.0807249i
$845$	21.3577	−	36.9926i	0.734726	−	1.27258i
$846$		0			0
$847$	26.6254	−	4.45468i	0.914859	−	0.153065i
$848$	12.7826	+	22.1402i	0.438958	+	0.760297i
$849$		0			0
$850$	−1.07040			−0.0367144
$851$	−11.7230			−0.401858
$852$		0			0
$853$	14.4872	+	25.0925i	0.496031	+	0.859150i	0.999990	−	0.00457743i	$-0.00145705\pi$
$853$	14.4872	+	25.0925i	0.496031	+	0.859150i	−0.503959	+	0.863728i	$0.668124\pi$
$854$	4.96440	−	13.2766i	0.169878	−	0.454316i
$855$		0			0
$856$	−10.1459	+	17.5732i	−0.346780	+	0.600640i
$857$	−12.6934	+	21.9856i	−0.433598	+	0.751015i	−0.997180	−	0.0750458i	$-0.976090\pi$
$857$	−12.6934	+	21.9856i	−0.433598	+	0.751015i	0.563582	+	0.826060i	$0.309423\pi$
$858$		0			0
$859$	2.97891	+	5.15963i	0.101639	+	0.176044i	0.912360	−	0.409388i	$-0.134258\pi$
$859$	2.97891	+	5.15963i	0.101639	+	0.176044i	−0.810721	+	0.585433i	$0.800925\pi$
$860$	32.3166	−	55.9740i	1.10199	−	1.90870i
$861$		0			0
$862$	3.94310	+	6.82966i	0.134303	+	0.232619i
$863$	−8.19545	+	14.1949i	−0.278977	+	0.483201i	−0.971131	−	0.238548i	$-0.923328\pi$
$863$	−8.19545	+	14.1949i	−0.278977	+	0.483201i	0.692154	+	0.721750i	$0.256662\pi$
$864$		0			0
$865$	−7.17624	−	12.4296i	−0.244000	−	0.422620i
$866$	−8.11528			−0.275768
$867$		0			0
$868$	−5.82743	+	15.5846i	−0.197796	+	0.528977i
$869$	0.802920	−	1.39070i	0.0272372	−	0.0471762i
$870$		0			0
$871$	0.615929	−	1.06682i	0.0208700	−	0.0361478i
$872$	1.97503	+	3.42086i	0.0668830	+	0.115845i
$873$		0			0
$874$	3.45030			0.116708
$875$	12.4384	−	33.2646i	0.420493	−	1.12455i
$876$		0			0
$877$	−17.6270	−	30.5308i	−0.595220	−	1.03095i	−0.993516	−	0.113695i	$-0.963731\pi$
$877$	−17.6270	−	30.5308i	−0.595220	−	1.03095i	0.398295	−	0.917257i	$-0.369602\pi$
$878$	−7.70813			−0.260137
$879$		0			0
$880$	8.52033			0.287220
$881$	−26.2582			−0.884661			−0.442331	−	0.896852i	$-0.645848\pi$
$881$	−26.2582			−0.884661			−0.442331	+	0.896852i	$0.645848\pi$
$882$		0			0
$883$	10.0087			0.336821			0.168410	−	0.985717i	$-0.446137\pi$
$883$	10.0087			0.336821			0.168410	+	0.985717i	$0.446137\pi$
$884$	−0.524756			−0.0176495
$885$		0			0
$886$	−0.887631			−0.0298205
$887$	−7.95282	−	13.7747i	−0.267030	−	0.462509i	0.701064	−	0.713099i	$-0.252709\pi$
$887$	−7.95282	−	13.7747i	−0.267030	−	0.462509i	−0.968093	+	0.250590i	$0.919376\pi$
$888$		0			0
$889$	−1.17634	+	3.14595i	−0.0394531	+	0.105512i
$890$	−4.40804			−0.147758
$891$		0			0
$892$	4.77419	+	8.26914i	0.159852	+	0.276871i
$893$	14.2844	−	24.7413i	0.478009	−	0.827935i
$894$		0			0
$895$	−13.5428	+	23.4569i	−0.452687	+	0.784077i
$896$	−10.5110	+	28.1102i	−0.351148	+	0.939095i
$897$		0			0
$898$	−6.72727			−0.224492
$899$	−7.42583	−	12.8619i	−0.247665	−	0.428969i
$900$		0			0
$901$	−1.23608	+	2.14095i	−0.0411797	+	0.0713253i
$902$	1.05822	+	1.83288i	0.0352348	+	0.0610284i
$903$		0			0
$904$	14.7307	−	25.5144i	0.489937	−	0.848597i
$905$	−20.7829	−	35.9970i	−0.690846	−	1.19658i
$906$		0			0
$907$	8.54624	−	14.8025i	0.283773	−	0.491510i	−0.688538	−	0.725201i	$-0.741747\pi$
$907$	8.54624	−	14.8025i	0.283773	−	0.491510i	0.972311	+	0.233691i	$0.0750804\pi$
$908$	14.0999	−	24.4217i	0.467922	−	0.810464i
$909$		0			0
$910$	−2.03047	+	5.43021i	−0.0673095	+	0.180010i
$911$	−14.9435	−	25.8829i	−0.495099	−	0.857537i	0.504885	−	0.863187i	$-0.331535\pi$
$911$	−14.9435	−	25.8829i	−0.495099	−	0.857537i	−0.999984	+	0.00564955i	$0.998202\pi$
$912$		0			0
$913$	10.9992			0.364021
$914$	1.27397			0.0421393
$915$		0			0
$916$	−8.74286	−	15.1431i	−0.288872	−	0.500341i
$917$	−39.2176	+	6.56148i	−1.29508	+	0.216679i
$918$		0			0
$919$	11.8283	−	20.4873i	0.390181	−	0.675813i	−0.602292	−	0.798276i	$-0.705746\pi$
$919$	11.8283	−	20.4873i	0.390181	−	0.675813i	0.992473	+	0.122462i	$0.0390791\pi$
$920$	−8.51579	+	14.7498i	−0.280757	+	0.486286i
$921$		0			0
$922$	−8.97196	−	15.5399i	−0.295476	−	0.511779i
$923$	2.95907	−	5.12525i	0.0973989	−	0.168700i
$924$		0			0
$925$	−20.4280	−	35.3823i	−0.671667	−	1.16336i
$926$	4.06227	−	7.03606i	0.133495	−	0.231219i
$927$		0			0
$928$	−10.3667	−	17.9557i	−0.340304	−	0.589423i
$929$	−12.6176			−0.413970			−0.206985	−	0.978344i	$-0.566365\pi$
$929$	−12.6176			−0.413970			−0.206985	+	0.978344i	$0.566365\pi$
$930$		0			0
$931$	−18.5873	+	6.39880i	−0.609176	+	0.209712i
$932$	14.5073	−	25.1274i	0.475203	−	0.823075i
$933$		0			0
$934$	2.15714	−	3.73627i	0.0705836	−	0.122254i
$935$	0.411957	+	0.713530i	0.0134724	+	0.0233349i
$936$		0			0
$937$	−26.3440			−0.860622			−0.430311	−	0.902681i	$-0.641596\pi$
$937$	−26.3440			−0.860622			−0.430311	+	0.902681i	$0.641596\pi$
$938$	0.472987	−	1.26494i	0.0154436	−	0.0413017i
$939$		0			0
$940$	32.9465	+	57.0651i	1.07460	+	1.86126i
$941$	−50.9397			−1.66059			−0.830294	−	0.557326i	$-0.811827\pi$
$941$	−50.9397			−1.66059			−0.830294	+	0.557326i	$0.811827\pi$
$942$		0			0
$943$	11.8481			0.385827
$944$	−4.68525			−0.152492
$945$		0			0
$946$	4.41648			0.143592
$947$	−27.6798			−0.899474			−0.449737	−	0.893161i	$-0.648482\pi$
$947$	−27.6798			−0.899474			−0.449737	+	0.893161i	$0.648482\pi$
$948$		0			0
$949$	−2.19061			−0.0711102
$950$	6.01236	+	10.4137i	0.195067	+	0.337866i
$951$		0			0
$952$	−1.21433	+	0.203170i	−0.0393568	+	0.00658477i
$953$	27.4017			0.887628			0.443814	−	0.896119i	$-0.353625\pi$
$953$	27.4017			0.887628			0.443814	+	0.896119i	$0.353625\pi$
$954$		0			0
$955$	−44.0265	−	76.2561i	−1.42466	−	2.46759i
$956$	−19.3162	+	33.4567i	−0.624731	+	1.08207i
$957$		0			0
$958$	−4.40515	+	7.62994i	−0.142324	+	0.246512i
$959$	0.822054	+	0.997297i	0.0265455	+	0.0322044i
$960$		0			0
$961$	−18.1467			−0.585378
$962$	1.40382	+	2.43149i	0.0452610	+	0.0783943i
$963$		0			0
$964$	14.6645	−	25.3996i	0.472310	−	0.818066i
$965$	−10.9569	−	18.9779i	−0.352715	−	0.610921i
$966$		0			0
$967$	9.09069	−	15.7455i	0.292337	−	0.506342i	−0.682025	−	0.731329i	$-0.738900\pi$
$967$	9.09069	−	15.7455i	0.292337	−	0.506342i	0.974362	+	0.224986i	$0.0722338\pi$
$968$	−9.49698	−	16.4492i	−0.305244	−	0.528699i
$969$		0			0
$970$	10.1111	−	17.5130i	0.324649	−	0.562309i
$971$	−19.7416	+	34.1935i	−0.633538	+	1.09732i	0.353285	+	0.935516i	$0.385065\pi$
$971$	−19.7416	+	34.1935i	−0.633538	+	1.09732i	−0.986823	+	0.161804i	$0.948269\pi$
$972$		0			0
$973$	16.6092	+	20.1499i	0.532466	+	0.645975i
$974$	4.12941	+	7.15234i	0.132315	+	0.229176i
$975$		0			0
$976$	27.9302			0.894024
$977$	−11.9156			−0.381215			−0.190608	−	0.981666i	$-0.561046\pi$
$977$	−11.9156			−0.381215			−0.190608	+	0.981666i	$0.561046\pi$
$978$		0			0
$979$	1.07439	+	1.86090i	0.0343376	+	0.0594745i
$980$	8.65423	−	44.5069i	0.276449	−	1.42172i
$981$		0			0
$982$	1.59184	−	2.75715i	0.0507977	−	0.0879842i
$983$	−9.23896	+	16.0024i	−0.294677	+	0.510396i	−0.974910	−	0.222601i	$-0.928545\pi$
$983$	−9.23896	+	16.0024i	−0.294677	+	0.510396i	0.680233	+	0.732996i	$0.261879\pi$
$984$		0			0
$985$	−28.5588	−	49.4653i	−0.909959	−	1.57609i
$986$	0.256752	−	0.444708i	0.00817666	−	0.0141624i
$987$		0			0
$988$	2.94752	+	5.10525i	0.0937731	+	0.162420i
$989$	12.3620	−	21.4117i	0.393090	−	0.680851i
$990$		0			0
$991$	−6.34850	−	10.9959i	−0.201667	−	0.349297i	0.747399	−	0.664376i	$-0.231302\pi$
$991$	−6.34850	−	10.9959i	−0.201667	−	0.349297i	−0.949066	+	0.315079i	$0.897969\pi$
$992$	17.9436			0.569710
$993$		0			0
$994$	2.27234	−	6.07706i	0.0720743	−	0.192752i
$995$	28.6108	−	49.5553i	0.907023	−	1.57101i
$996$		0			0
$997$	−20.9767	+	36.3327i	−0.664338	+	1.15067i	0.315127	+	0.949050i	$0.397953\pi$
$997$	−20.9767	+	36.3327i	−0.664338	+	1.15067i	−0.979464	+	0.201617i	$0.935380\pi$
$998$	−2.76345	−	4.78644i	−0.0874755	−	0.151512i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.h.b.37.3		10
3.2	odd	2		63.2.h.b.58.3	yes	10
4.3	odd	2		3024.2.q.i.2305.1		10
7.2	even	3		1323.2.f.e.442.3		10
7.3	odd	6		1323.2.g.f.361.3		10
7.4	even	3		189.2.g.b.172.3		10
7.5	odd	6		1323.2.f.f.442.3		10
7.6	odd	2		1323.2.h.f.226.3		10
9.2	odd	6		63.2.g.b.16.3	yes	10
9.4	even	3		567.2.e.e.163.3		10
9.5	odd	6		567.2.e.f.163.3		10
9.7	even	3		189.2.g.b.100.3		10
12.11	even	2		1008.2.q.i.625.3		10
21.2	odd	6		441.2.f.e.148.3		10
21.5	even	6		441.2.f.f.148.3		10
21.11	odd	6		63.2.g.b.4.3	✓	10
21.17	even	6		441.2.g.f.67.3		10
21.20	even	2		441.2.h.f.373.3		10
28.11	odd	6		3024.2.t.i.1873.5		10
36.7	odd	6		3024.2.t.i.289.5		10
36.11	even	6		1008.2.t.i.961.1		10
63.2	odd	6		441.2.f.e.295.3		10
63.4	even	3		567.2.e.e.487.3		10
63.5	even	6		3969.2.a.ba.1.3		5
63.11	odd	6		63.2.h.b.25.3	yes	10
63.16	even	3		1323.2.f.e.883.3		10
63.20	even	6		441.2.g.f.79.3		10
63.23	odd	6		3969.2.a.z.1.3		5
63.25	even	3	inner	189.2.h.b.46.3		10
63.32	odd	6		567.2.e.f.487.3		10
63.34	odd	6		1323.2.g.f.667.3		10
63.38	even	6		441.2.h.f.214.3		10
63.40	odd	6		3969.2.a.bb.1.3		5
63.47	even	6		441.2.f.f.295.3		10
63.52	odd	6		1323.2.h.f.802.3		10
63.58	even	3		3969.2.a.bc.1.3		5
63.61	odd	6		1323.2.f.f.883.3		10
84.11	even	6		1008.2.t.i.193.1		10
252.11	even	6		1008.2.q.i.529.3		10
252.151	odd	6		3024.2.q.i.2881.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.3	✓	10	21.11	odd	6
63.2.g.b.16.3	yes	10	9.2	odd	6
63.2.h.b.25.3	yes	10	63.11	odd	6
63.2.h.b.58.3	yes	10	3.2	odd	2
189.2.g.b.100.3		10	9.7	even	3
189.2.g.b.172.3		10	7.4	even	3
189.2.h.b.37.3		10	1.1	even	1	trivial
189.2.h.b.46.3		10	63.25	even	3	inner
441.2.f.e.148.3		10	21.2	odd	6
441.2.f.e.295.3		10	63.2	odd	6
441.2.f.f.148.3		10	21.5	even	6
441.2.f.f.295.3		10	63.47	even	6
441.2.g.f.67.3		10	21.17	even	6
441.2.g.f.79.3		10	63.20	even	6
441.2.h.f.214.3		10	63.38	even	6
441.2.h.f.373.3		10	21.20	even	2
567.2.e.e.163.3		10	9.4	even	3
567.2.e.e.487.3		10	63.4	even	3
567.2.e.f.163.3		10	9.5	odd	6
567.2.e.f.487.3		10	63.32	odd	6
1008.2.q.i.529.3		10	252.11	even	6
1008.2.q.i.625.3		10	12.11	even	2
1008.2.t.i.193.1		10	84.11	even	6
1008.2.t.i.961.1		10	36.11	even	6
1323.2.f.e.442.3		10	7.2	even	3
1323.2.f.e.883.3		10	63.16	even	3
1323.2.f.f.442.3		10	7.5	odd	6
1323.2.f.f.883.3		10	63.61	odd	6
1323.2.g.f.361.3		10	7.3	odd	6
1323.2.g.f.667.3		10	63.34	odd	6
1323.2.h.f.226.3		10	7.6	odd	2
1323.2.h.f.802.3		10	63.52	odd	6
3024.2.q.i.2305.1		10	4.3	odd	2
3024.2.q.i.2881.1		10	252.151	odd	6
3024.2.t.i.289.5		10	36.7	odd	6
3024.2.t.i.1873.5		10	28.11	odd	6
3969.2.a.z.1.3		5	63.23	odd	6
3969.2.a.ba.1.3		5	63.5	even	6
3969.2.a.bb.1.3		5	63.40	odd	6
3969.2.a.bc.1.3		5	63.58	even	3

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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.495868 q^{2} -1.75411 q^{4} +(-1.84629 - 3.19787i) q^{5} +(0.926641 - 2.47817i) q^{7} -1.86155 q^{8} +O(q^{10})\)	\(q+0.495868 q^{2} -1.75411 q^{4} +(-1.84629 - 3.19787i) q^{5} +(0.926641 - 2.47817i) q^{7} -1.86155 q^{8} +(-0.915516 - 1.58572i) q^{10} +(-0.446284 + 0.772987i) q^{11} +(0.598355 - 1.03638i) q^{13} +(0.459492 - 1.22885i) q^{14} +2.58515 q^{16} +(0.124991 + 0.216492i) q^{17} +(1.40414 - 2.43204i) q^{19} +(3.23860 + 5.60943i) q^{20} +(-0.221298 + 0.383300i) q^{22} +(1.23886 + 2.14576i) q^{23} +(-4.31757 + 7.47825i) q^{25} +(0.296705 - 0.513909i) q^{26} +(-1.62544 + 4.34700i) q^{28} +(-2.07128 - 3.58755i) q^{29} +3.58515 q^{31} +5.00499 q^{32} +(0.0619793 + 0.107351i) q^{34} +(-9.63571 + 1.61215i) q^{35} +(-2.36568 + 4.09747i) q^{37} +(0.696267 - 1.20597i) q^{38} +(3.43695 + 5.95298i) q^{40} +(2.39093 - 4.14121i) q^{41} +(-4.98928 - 8.64169i) q^{43} +(0.782834 - 1.35591i) q^{44} +(0.614310 + 1.06402i) q^{46} +10.1731 q^{47} +(-5.28267 - 4.59275i) q^{49} +(-2.14095 + 3.70823i) q^{50} +(-1.04958 + 1.81793i) q^{52} +(4.94465 + 8.56438i) q^{53} +3.29588 q^{55} +(-1.72499 + 4.61323i) q^{56} +(-1.02708 - 1.77895i) q^{58} -1.81237 q^{59} +10.8041 q^{61} +1.77776 q^{62} -2.68848 q^{64} -4.41895 q^{65} +1.02937 q^{67} +(-0.219249 - 0.379751i) q^{68} +(-4.77804 + 0.799412i) q^{70} +4.94533 q^{71} +(-0.915262 - 1.58528i) q^{73} +(-1.17306 + 2.03181i) q^{74} +(-2.46302 + 4.26607i) q^{76} +(1.50205 + 1.82225i) q^{77} -1.79912 q^{79} +(-4.77293 - 8.26696i) q^{80} +(1.18559 - 2.05350i) q^{82} +(-6.16156 - 10.6721i) q^{83} +(0.461541 - 0.799412i) q^{85} +(-2.47403 - 4.28514i) q^{86} +(0.830779 - 1.43895i) q^{88} +(1.20370 - 2.08488i) q^{89} +(-2.01387 - 2.44318i) q^{91} +(-2.17310 - 3.76392i) q^{92} +5.04450 q^{94} -10.3698 q^{95} +(5.52210 + 9.56456i) q^{97} +(-2.61951 - 2.27740i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 8 q^{4} - 4 q^{5} - 4 q^{7} + 6 q^{8}+O(q^{10}) \) 10 * q + 4 * q^2 + 8 * q^4 - 4 * q^5 - 4 * q^7 + 6 * q^8	\( 10 q + 4 q^{2} + 8 q^{4} - 4 q^{5} - 4 q^{7} + 6 q^{8} - 7 q^{10} - 4 q^{11} - 8 q^{13} + 20 q^{14} - 4 q^{16} - 12 q^{17} + q^{19} - 5 q^{20} - q^{22} - 3 q^{23} - q^{25} - 11 q^{26} - 2 q^{28} - 7 q^{29} + 6 q^{31} - 4 q^{32} + 3 q^{34} - 5 q^{35} - 20 q^{38} - 3 q^{40} - 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} + 54 q^{47} - 8 q^{49} - 19 q^{50} - 10 q^{52} + 21 q^{53} + 4 q^{55} - 18 q^{56} - 10 q^{58} + 60 q^{59} + 28 q^{61} + 12 q^{62} - 50 q^{64} - 22 q^{65} + 4 q^{67} - 27 q^{68} + 40 q^{70} + 6 q^{71} + 15 q^{73} + 36 q^{74} + 5 q^{76} - 11 q^{77} + 8 q^{79} - 20 q^{80} - 5 q^{82} - 9 q^{83} - 6 q^{85} + 8 q^{86} - 18 q^{88} - 28 q^{89} - 4 q^{91} - 27 q^{92} + 6 q^{94} - 28 q^{95} - 12 q^{97} - 59 q^{98}+O(q^{100}) \) 10 * q + 4 * q^2 + 8 * q^4 - 4 * q^5 - 4 * q^7 + 6 * q^8 - 7 * q^10 - 4 * q^11 - 8 * q^13 + 20 * q^14 - 4 * q^16 - 12 * q^17 + q^19 - 5 * q^20 - q^22 - 3 * q^23 - q^25 - 11 * q^26 - 2 * q^28 - 7 * q^29 + 6 * q^31 - 4 * q^32 + 3 * q^34 - 5 * q^35 - 20 * q^38 - 3 * q^40 - 5 * q^41 - 7 * q^43 + 10 * q^44 + 3 * q^46 + 54 * q^47 - 8 * q^49 - 19 * q^50 - 10 * q^52 + 21 * q^53 + 4 * q^55 - 18 * q^56 - 10 * q^58 + 60 * q^59 + 28 * q^61 + 12 * q^62 - 50 * q^64 - 22 * q^65 + 4 * q^67 - 27 * q^68 + 40 * q^70 + 6 * q^71 + 15 * q^73 + 36 * q^74 + 5 * q^76 - 11 * q^77 + 8 * q^79 - 20 * q^80 - 5 * q^82 - 9 * q^83 - 6 * q^85 + 8 * q^86 - 18 * q^88 - 28 * q^89 - 4 * q^91 - 27 * q^92 + 6 * q^94 - 28 * q^95 - 12 * q^97 - 59 * q^98

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