LMFDB - Embedded newform 189.2.h.b.46.3

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			46.3
Root			$0.247934 + 0.429435i$ of defining polynomial
Character	$\chi$	$=$	189.46
Dual form			189.2.h.b.37.3

$q$-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 $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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	0.0757082	+	0.997130i	$0.475878\pi$
$5$	−1.84629	+	3.19787i	−0.825686	+	1.43013i	−0.901394	+	0.433000i	$0.857455\pi$
$6$		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	0.790869	−	0.611985i	$-0.209629\pi$
$11$	−0.446284	−	0.772987i	−0.134560	−	0.233064i	−0.925429	+	0.378921i	$0.876295\pi$
$12$		0			0
$13$	0.598355	+	1.03638i	0.165954	+	0.287441i	0.936994	−	0.349346i	$-0.113596\pi$
$13$	0.598355	+	1.03638i	0.165954	+	0.287441i	−0.771040	+	0.636787i	$0.780263\pi$
$14$	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	−0.850470	−	0.526024i	$-0.823682\pi$
$17$	0.124991	−	0.216492i	0.0303149	−	0.0525069i	0.880785	+	0.473517i	$0.157016\pi$
$18$		0			0
$19$	1.40414	+	2.43204i	0.322131	+	0.557948i	0.980928	−	0.194374i	$-0.0622675\pi$
$19$	1.40414	+	2.43204i	0.322131	+	0.557948i	−0.658796	+	0.752321i	$0.728934\pi$
$20$	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	−0.707472	−	0.706741i	$-0.750165\pi$
$23$	1.23886	−	2.14576i	0.258320	−	0.447423i	0.965792	+	0.259318i	$0.0834979\pi$
$24$		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	−0.991717	−	0.128440i	$-0.959003\pi$
$29$	−2.07128	+	3.58755i	−0.384626	+	0.666192i	0.607091	+	0.794632i	$0.292336\pi$
$30$		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	0.603389	−	0.797447i	$-0.293817\pi$
$37$	−2.36568	−	4.09747i	−0.388915	−	0.673621i	−0.992304	+	0.123826i	$0.960483\pi$
$38$	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	0.990086	−	0.140461i	$-0.0448584\pi$
$41$	2.39093	+	4.14121i	0.373400	+	0.646748i	−0.616686	+	0.787209i	$0.711525\pi$
$42$		0			0
$43$	−4.98928	+	8.64169i	−0.760859	+	1.31785i	0.181550	+	0.983382i	$0.441889\pi$
$43$	−4.98928	+	8.64169i	−0.760859	+	1.31785i	−0.942408	+	0.334464i	$0.891445\pi$
$44$	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	−0.296023	−	0.955181i	$-0.595661\pi$
$53$	4.94465	−	8.56438i	0.679199	−	1.17641i	0.975222	−	0.221227i	$-0.0710061\pi$
$54$		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	−0.914604	−	0.404351i	$-0.867497\pi$
$73$	−0.915262	+	1.58528i	−0.107123	+	0.185543i	0.807480	+	0.589894i	$0.200831\pi$
$74$	−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	0.299763	+	0.954014i	$0.403092\pi$
$83$	−6.16156	+	10.6721i	−0.676319	+	1.17142i	−0.976082	+	0.217405i	$0.930241\pi$
$84$		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	0.922743	−	0.385415i	$-0.125942\pi$
$89$	1.20370	+	2.08488i	0.127592	+	0.220997i	−0.795151	+	0.606412i	$0.792608\pi$
$90$		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	−0.436752	−	0.899582i	$-0.643871\pi$
$97$	5.52210	−	9.56456i	0.560684	−	0.971134i	0.997437	−	0.0715522i	$-0.0227952\pi$
$98$	−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	0.794083	−	0.607810i	$-0.207952\pi$
$101$	−1.29982	−	2.25136i	−0.129337	−	0.224018i	−0.923420	+	0.383791i	$0.874618\pi$
$102$		0			0
$103$	−4.85578	+	8.41045i	−0.478454	+	0.828706i	−0.999695	−	0.0247032i	$-0.992136\pi$
$103$	−4.85578	+	8.41045i	−0.478454	+	0.828706i	0.521241	+	0.853409i	$0.325469\pi$
$104$	−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	0.999509	+	0.0313403i	$0.00997757\pi$
$107$	5.45025	+	9.44012i	0.526896	+	0.912610i	−0.472613	+	0.881270i	$0.656689\pi$
$108$		0			0
$109$	−1.06096	+	1.83764i	−0.101622	+	0.176014i	−0.912353	−	0.409404i	$-0.865737\pi$
$109$	−1.06096	+	1.83764i	−0.101622	+	0.176014i	0.810731	+	0.585419i	$0.199070\pi$
$110$	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	−0.950470	−	0.310816i	$-0.899398\pi$
$113$	−7.91318	−	13.7060i	−0.744409	−	1.28935i	0.206061	−	0.978539i	$-0.433935\pi$
$114$		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	0.324965	+	0.945726i	$0.394647\pi$
$131$	−7.51444	+	13.0154i	−0.656540	+	1.13716i	−0.981505	+	0.191435i	$0.938686\pi$
$132$		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	0.855403	−	0.517963i	$-0.173309\pi$
$137$	−0.244246	−	0.423047i	−0.0208674	−	0.0361433i	−0.876271	+	0.481819i	$0.839976\pi$
$138$		0			0
$139$	−4.93487	−	8.54745i	−0.418570	−	0.724985i	0.577226	−	0.816585i	$-0.304135\pi$
$139$	−4.93487	−	8.54745i	−0.418570	−	0.724985i	−0.995796	+	0.0915997i	$0.970802\pi$
$140$	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	−0.00962096	−	0.999954i	$-0.503062\pi$
$149$	10.5120	−	18.2073i	0.861175	−	1.49160i	0.870796	−	0.491645i	$-0.163604\pi$
$150$		0			0
$151$	−0.749191	−	1.29764i	−0.0609683	−	0.105600i	0.833930	−	0.551870i	$-0.186086\pi$
$151$	−0.749191	−	1.29764i	−0.0609683	−	0.105600i	−0.894898	+	0.446270i	$0.852752\pi$
$152$	−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	0.704983	−	0.709224i	$-0.250954\pi$
$163$	−3.34135	−	5.78738i	−0.261714	−	0.453303i	−0.966698	+	0.255921i	$0.917621\pi$
$164$	−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	−0.974319	−	0.225170i	$-0.927706\pi$
$167$	−8.81549	−	15.2689i	−0.682163	−	1.18154i	0.292156	−	0.956371i	$-0.405627\pi$
$168$		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	−0.969915	−	0.243445i	$-0.921723\pi$
$179$	−3.66758	+	6.35244i	−0.274128	+	0.474804i	0.695787	+	0.718248i	$0.255056\pi$
$180$		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	−0.449072	−	0.893496i	$-0.648245\pi$
$199$	7.74818	−	13.4202i	0.549254	−	0.951336i	0.998326	−	0.0578402i	$-0.0184214\pi$
$200$	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	0.891372	−	0.453273i	$-0.149744\pi$
$211$	0.771898	+	1.33697i	0.0531397	+	0.0920406i	−0.838232	+	0.545314i	$0.816410\pi$
$212$	−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	−0.942649	−	0.333784i	$-0.891674\pi$
$223$	−2.72171	+	4.71414i	−0.182259	+	0.315682i	0.760390	+	0.649466i	$0.225008\pi$
$224$	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	−0.999234	−	0.0391399i	$-0.987538\pi$
$227$	−8.03818	−	13.9225i	−0.533513	−	0.924072i	0.465721	−	0.884932i	$-0.345795\pi$
$228$		0			0
$229$	4.98420	−	8.63289i	0.329365	−	0.570477i	−0.653021	−	0.757340i	$-0.726499\pi$
$229$	4.98420	−	8.63289i	0.329365	−	0.570477i	0.982386	+	0.186863i	$0.0598319\pi$
$230$	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	−0.998800	−	0.0489765i	$-0.984404\pi$
$233$	−8.27045	−	14.3248i	−0.541815	−	0.938451i	0.456985	−	0.889474i	$-0.348929\pi$
$234$		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	0.963990	+	0.265937i	$0.0856813\pi$
$239$	11.0119	+	19.0732i	0.712303	+	1.23375i	−0.251687	+	0.967809i	$0.580985\pi$
$240$		0			0
$241$	−8.36004	−	14.4800i	−0.538517	−	0.932739i	−0.998984	−	0.0450623i	$-0.985651\pi$
$241$	−8.36004	−	14.4800i	−0.538517	−	0.932739i	0.460467	−	0.887677i	$-0.347682\pi$
$242$	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	0.465264	+	0.885172i	$0.345959\pi$
$257$	−8.55986	+	14.8261i	−0.533950	+	0.924828i	−0.999213	+	0.0396557i	$0.987374\pi$
$258$		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	0.986796	+	0.161967i	$0.0517838\pi$
$263$	10.2763	+	17.7991i	0.633666	+	1.09754i	−0.353130	+	0.935574i	$0.614883\pi$
$264$		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	0.387057	+	0.922056i	$0.373492\pi$
$269$	−9.92267	+	17.1866i	−0.604996	+	1.04788i	−0.992052	+	0.125827i	$0.959842\pi$
$270$		0			0
$271$	5.32056	+	9.21548i	0.323201	+	0.559801i	0.981147	−	0.193265i	$-0.0619077\pi$
$271$	5.32056	+	9.21548i	0.323201	+	0.559801i	−0.657946	+	0.753065i	$0.728574\pi$
$272$	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	0.949024	+	0.315205i	$0.102073\pi$
$277$	12.4407	+	21.5479i	0.747487	+	1.29469i	−0.201536	+	0.979481i	$0.564593\pi$
$278$	−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	−0.586771	−	0.809753i	$-0.699601\pi$
$281$	6.83733	−	11.8426i	0.407881	−	0.706470i	0.994652	+	0.103282i	$0.0329346\pi$
$282$		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	0.901880	−	0.431987i	$-0.142188\pi$
$293$	1.31508	+	2.27778i	0.0768277	+	0.133069i	−0.825052	+	0.565057i	$0.808854\pi$
$294$		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	−0.974557	−	0.224139i	$-0.928043\pi$
$337$	−12.5086	−	21.6656i	−0.681389	−	1.18020i	0.293168	−	0.956061i	$-0.405290\pi$
$338$	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	−0.906644	−	0.421897i	$-0.861364\pi$
$349$	−1.64301	+	2.84577i	−0.0879482	+	0.152331i	0.818695	+	0.574228i	$0.194698\pi$
$350$	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	0.998229	−	0.0594866i	$-0.0189463\pi$
$353$	8.40960	+	14.5658i	0.447598	+	0.775262i	−0.550631	+	0.834748i	$0.685613\pi$
$354$		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	−0.988024	−	0.154303i	$-0.950687\pi$
$359$	−11.8921	−	20.5978i	−0.627642	−	1.08711i	0.360382	−	0.932805i	$-0.382646\pi$
$360$		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	0.874889	−	0.484323i	$-0.160934\pi$
$367$	0.344992	+	0.597544i	0.0180084	+	0.0311915i	−0.856881	+	0.515515i	$0.827601\pi$
$368$	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	−0.813239	−	0.581929i	$-0.802298\pi$
$373$	1.88006	−	3.25636i	0.0973457	−	0.168608i	0.910585	+	0.413321i	$0.135631\pi$
$374$	−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	−0.879403	−	0.476078i	$-0.842058\pi$
$383$	−0.536335	+	0.928960i	−0.0274055	+	0.0474676i	0.851997	+	0.523546i	$0.175391\pi$
$384$		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	−0.992529	−	0.122006i	$-0.961067\pi$
$389$	−11.8718	−	20.5626i	−0.601925	−	1.04256i	0.390605	−	0.920559i	$-0.372266\pi$
$390$		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	0.865622	−	0.500697i	$-0.166923\pi$
$397$	−0.0160489	−	0.0277975i	−0.000805471	−	0.00139512i	−0.866428	+	0.499302i	$0.833590\pi$
$398$	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	−0.378465	−	0.925616i	$-0.623548\pi$
$401$	12.2628	−	21.2398i	0.612374	−	1.06066i	0.990839	−	0.135048i	$-0.0431188\pi$
$402$		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	0.999864	+	0.0165215i	$0.00525920\pi$
$419$	10.5262	+	18.2320i	0.514240	+	0.890689i	−0.485624	+	0.874168i	$0.661407\pi$
$420$		0			0
$421$	−7.44533	+	12.8957i	−0.362863	+	0.628498i	−0.988431	−	0.151672i	$-0.951534\pi$
$421$	−7.44533	+	12.8957i	−0.362863	+	0.628498i	0.625568	+	0.780170i	$0.284867\pi$
$422$	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	−0.608463	−	0.793582i	$-0.708214\pi$
$431$	7.95192	−	13.7731i	0.383031	−	0.663428i	0.991494	+	0.130154i	$0.0415471\pi$
$432$		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	0.0449122	+	0.998991i	$0.485699\pi$
$461$	−18.0934	+	31.3388i	−0.842695	+	1.45959i	−0.887608	+	0.460600i	$0.847634\pi$
$462$		0			0
$463$	8.19224	+	14.1894i	0.380726	+	0.659436i	0.991166	−	0.132626i	$-0.0423409\pi$
$463$	8.19224	+	14.1894i	0.380726	+	0.659436i	−0.610440	+	0.792062i	$0.709008\pi$
$464$	−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	0.948949	−	0.315430i	$-0.102149\pi$
$467$	4.35022	+	7.53480i	0.201304	+	0.348669i	−0.747645	+	0.664099i	$0.768815\pi$
$468$		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	0.588520	−	0.808483i	$-0.299711\pi$
$479$	−8.88370	−	15.3870i	−0.405907	−	0.703051i	−0.994427	+	0.105432i	$0.966378\pi$
$480$		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	−0.613316	−	0.789837i	$-0.710165\pi$
$487$	8.32763	−	14.4239i	0.377361	−	0.653608i	0.990677	+	0.136229i	$0.0434983\pi$
$488$	−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	0.929326	−	0.369260i	$-0.120389\pi$
$491$	3.21021	+	5.56025i	0.144875	+	0.250930i	−0.784451	+	0.620190i	$0.787055\pi$
$492$		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	−0.963382	−	0.268134i	$-0.913593\pi$
$499$	−5.57296	+	9.65264i	−0.249480	+	0.432112i	0.713902	+	0.700246i	$0.246926\pi$
$500$	−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	−0.283362	−	0.959013i	$-0.591450\pi$
$509$	15.5411	−	26.9180i	0.688848	−	1.19312i	0.972211	−	0.234107i	$-0.0752167\pi$
$510$		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	−0.809174	−	0.587570i	$-0.800085\pi$
$521$	2.37986	−	4.12203i	0.104263	−	0.180590i	0.913437	+	0.406980i	$0.133418\pi$
$522$		0			0
$523$	20.1258	+	34.8588i	0.880038	+	1.52427i	0.851298	+	0.524683i	$0.175816\pi$
$523$	20.1258	+	34.8588i	0.880038	+	1.52427i	0.0287402	+	0.999587i	$0.490850\pi$
$524$	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	0.999775	+	0.0212301i	$0.00675826\pi$
$541$	12.0547	+	20.8794i	0.518273	+	0.897675i	−0.481502	+	0.876445i	$0.659908\pi$
$542$	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	−0.967336	−	0.253499i	$-0.918419\pi$
$547$	−6.17751	+	10.6998i	−0.264131	+	0.457489i	0.703204	+	0.710988i	$0.251752\pi$
$548$	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	−0.938810	−	0.344436i	$-0.888070\pi$
$557$	−4.03845	+	6.99479i	−0.171114	+	0.296379i	0.767695	+	0.640815i	$0.221403\pi$
$558$		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	0.307465	+	0.951559i	$0.400519\pi$
$577$	−16.1022	+	27.8898i	−0.670342	+	1.16107i	−0.977807	+	0.209508i	$0.932814\pi$
$578$	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	−0.592572	−	0.805518i	$-0.701887\pi$
$587$	9.72304	−	16.8408i	0.401313	−	0.695094i	0.993885	+	0.110424i	$0.0352208\pi$
$588$		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	0.993940	+	0.109925i	$0.0350611\pi$
$593$	14.4202	+	24.9766i	0.592168	+	1.02566i	−0.401772	+	0.915740i	$0.631606\pi$
$594$		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	−0.980178	−	0.198119i	$-0.936517\pi$
$601$	−7.80843	+	13.5246i	−0.318512	+	0.551680i	0.661665	+	0.749799i	$0.269850\pi$
$602$	−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	−0.413802	−	0.910367i	$-0.635800\pi$
$607$	14.3266	−	24.8144i	0.581500	−	1.00719i	0.995302	−	0.0968200i	$-0.0308671\pi$
$608$	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	−0.401220	−	0.915982i	$-0.631414\pi$
$613$	14.6734	−	25.4151i	0.592653	−	1.02651i	0.993873	−	0.110524i	$-0.0352529\pi$
$614$	−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	0.821484	−	0.570232i	$-0.193147\pi$
$617$	−2.06401	−	3.57497i	−0.0830938	−	0.143923i	−0.904577	+	0.426310i	$0.859813\pi$
$618$		0			0
$619$	−11.3565	−	19.6700i	−0.456456	−	0.790605i	0.542315	−	0.840175i	$-0.317548\pi$
$619$	−11.3565	−	19.6700i	−0.456456	−	0.790605i	−0.998771	+	0.0495708i	$0.984215\pi$
$620$	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	−0.997295	−	0.0735002i	$-0.976583\pi$
$641$	−14.2363	−	24.6580i	−0.562301	−	0.973933i	0.434995	−	0.900433i	$-0.356750\pi$
$642$		0			0
$643$	−8.52125	−	14.7592i	−0.336045	−	0.582048i	0.647640	−	0.761947i	$-0.275756\pi$
$643$	−8.52125	−	14.7592i	−0.336045	−	0.582048i	−0.983685	+	0.179899i	$0.942423\pi$
$644$	−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	−0.897299	−	0.441423i	$-0.854474\pi$
$647$	−1.68809	+	2.92386i	−0.0663657	+	0.114949i	0.830933	+	0.556372i	$0.187807\pi$
$648$		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	−0.987786	−	0.155819i	$-0.950198\pi$
$653$	−9.17255	+	15.8873i	−0.358950	+	0.621719i	0.628836	+	0.777538i	$0.283532\pi$
$654$		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	−0.456332	−	0.889810i	$-0.650837\pi$
$659$	13.9248	−	24.1184i	0.542432	−	0.939519i	0.998764	−	0.0497098i	$-0.0158297\pi$
$660$		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	0.201014	−	0.979588i	$-0.435576\pi$
$673$	24.6154	−	42.6352i	0.948856	−	1.64347i	0.747841	−	0.663878i	$-0.231090\pi$
$674$	−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	−0.415251	−	0.909707i	$-0.636306\pi$
$683$	15.1632	−	26.2634i	0.580204	−	1.00494i	0.995455	−	0.0952356i	$-0.0303604\pi$
$684$		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	0.951013	−	0.309152i	$-0.100045\pi$
$719$	5.57126	+	9.64970i	0.207773	+	0.359873i	−0.743240	+	0.669025i	$0.766712\pi$
$720$		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	0.467430	+	0.884030i	$0.345180\pi$
$727$	−14.3410	+	24.8393i	−0.531878	+	0.921239i	−0.999308	+	0.0372089i	$0.988153\pi$
$728$	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	−0.536419	−	0.843952i	$-0.680223\pi$
$733$	12.5264	−	21.6964i	0.462674	−	0.801375i	0.999093	+	0.0425768i	$0.0135567\pi$
$734$	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	−0.493776	−	0.869589i	$-0.664384\pi$
$739$	13.7608	−	23.8344i	0.506198	−	0.876761i	0.999974	−	0.00717223i	$-0.00228301\pi$
$740$	−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	0.965444	−	0.260609i	$-0.0839233\pi$
$743$	7.00608	+	12.1349i	0.257028	+	0.445186i	−0.708416	+	0.705795i	$0.750590\pi$
$744$		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	0.215692	−	0.976461i	$-0.430799\pi$
$751$	26.1297	−	45.2580i	0.953486	−	1.65149i	0.737795	−	0.675025i	$-0.235867\pi$
$752$	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	−0.978940	−	0.204146i	$-0.934558\pi$
$761$	−8.62550	+	14.9398i	−0.312674	+	0.541568i	0.666266	+	0.745714i	$0.267891\pi$
$762$		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	0.606884	−	0.794790i	$-0.292419\pi$
$769$	−10.6727	−	18.4856i	−0.384867	−	0.666609i	−0.991751	+	0.128182i	$0.959086\pi$
$770$	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	−0.723254	−	0.690582i	$-0.757354\pi$
$773$	6.57357	−	11.3858i	0.236435	−	0.409517i	0.959689	+	0.281065i	$0.0906877\pi$
$774$		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	0.542917	−	0.839786i	$-0.317320\pi$
$797$	−12.8683	−	22.2885i	−0.455817	−	0.789499i	−0.998735	+	0.0502873i	$0.983986\pi$
$798$		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	0.437220	+	0.899355i	$0.355963\pi$
$809$	−15.9353	+	27.6007i	−0.560254	+	0.970388i	−0.997474	+	0.0710338i	$0.977370\pi$
$810$		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	−0.573899	−	0.818926i	$-0.694570\pi$
$829$	12.1579	−	21.0581i	0.422261	−	0.731377i	0.996160	+	0.0875485i	$0.0279033\pi$
$830$	−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	−0.554629	−	0.832098i	$-0.687140\pi$
$839$	12.8405	−	22.2404i	0.443303	−	0.767824i	0.997932	+	0.0642741i	$0.0204732\pi$
$840$		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	−0.503959	−	0.863728i	$-0.668124\pi$
$853$	14.4872	−	25.0925i	0.496031	−	0.859150i	0.999990	+	0.00457743i	$0.00145705\pi$
$854$	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	0.563582	−	0.826060i	$-0.309423\pi$
$857$	−12.6934	−	21.9856i	−0.433598	−	0.751015i	−0.997180	+	0.0750458i	$0.976090\pi$
$858$		0			0
$859$	2.97891	−	5.15963i	0.101639	−	0.176044i	−0.810721	−	0.585433i	$-0.800925\pi$
$859$	2.97891	−	5.15963i	0.101639	−	0.176044i	0.912360	+	0.409388i	$0.134258\pi$
$860$	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	0.692154	−	0.721750i	$-0.256662\pi$
$863$	−8.19545	−	14.1949i	−0.278977	−	0.483201i	−0.971131	+	0.238548i	$0.923328\pi$
$864$		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	0.398295	+	0.917257i	$0.369602\pi$
$877$	−17.6270	+	30.5308i	−0.595220	+	1.03095i	−0.993516	+	0.113695i	$0.963731\pi$
$878$	−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	−0.968093	−	0.250590i	$-0.919376\pi$
$887$	−7.95282	+	13.7747i	−0.267030	+	0.462509i	0.701064	+	0.713099i	$0.252709\pi$
$888$		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	0.972311	−	0.233691i	$-0.0750804\pi$
$907$	8.54624	+	14.8025i	0.283773	+	0.491510i	−0.688538	+	0.725201i	$0.741747\pi$
$908$	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	−0.999984	−	0.00564955i	$-0.998202\pi$
$911$	−14.9435	+	25.8829i	−0.495099	+	0.857537i	0.504885	+	0.863187i	$0.331535\pi$
$912$		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	0.992473	−	0.122462i	$-0.0390791\pi$
$919$	11.8283	+	20.4873i	0.390181	+	0.675813i	−0.602292	+	0.798276i	$0.705746\pi$
$920$	−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	0.974362	−	0.224986i	$-0.0722338\pi$
$967$	9.09069	+	15.7455i	0.292337	+	0.506342i	−0.682025	+	0.731329i	$0.738900\pi$
$968$	−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	−0.986823	−	0.161804i	$-0.948269\pi$
$971$	−19.7416	−	34.1935i	−0.633538	−	1.09732i	0.353285	−	0.935516i	$-0.385065\pi$
$972$		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	0.680233	−	0.732996i	$-0.261879\pi$
$983$	−9.23896	−	16.0024i	−0.294677	−	0.510396i	−0.974910	+	0.222601i	$0.928545\pi$
$984$		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	−0.949066	−	0.315079i	$-0.897969\pi$
$991$	−6.34850	+	10.9959i	−0.201667	+	0.349297i	0.747399	+	0.664376i	$0.231302\pi$
$992$	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	−0.979464	−	0.201617i	$-0.935380\pi$
$997$	−20.9767	−	36.3327i	−0.664338	−	1.15067i	0.315127	−	0.949050i	$-0.397953\pi$
$998$	−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.46.3		10
3.2	odd	2		63.2.h.b.25.3	yes	10
4.3	odd	2		3024.2.q.i.2881.1		10
7.2	even	3		189.2.g.b.100.3		10
7.3	odd	6		1323.2.f.f.883.3		10
7.4	even	3		1323.2.f.e.883.3		10
7.5	odd	6		1323.2.g.f.667.3		10
7.6	odd	2		1323.2.h.f.802.3		10
9.2	odd	6		567.2.e.f.487.3		10
9.4	even	3		189.2.g.b.172.3		10
9.5	odd	6		63.2.g.b.4.3	✓	10
9.7	even	3		567.2.e.e.487.3		10
12.11	even	2		1008.2.q.i.529.3		10
21.2	odd	6		63.2.g.b.16.3	yes	10
21.5	even	6		441.2.g.f.79.3		10
21.11	odd	6		441.2.f.e.295.3		10
21.17	even	6		441.2.f.f.295.3		10
21.20	even	2		441.2.h.f.214.3		10
28.23	odd	6		3024.2.t.i.289.5		10
36.23	even	6		1008.2.t.i.193.1		10
36.31	odd	6		3024.2.t.i.1873.5		10
63.2	odd	6		567.2.e.f.163.3		10
63.4	even	3		1323.2.f.e.442.3		10
63.5	even	6		441.2.h.f.373.3		10
63.11	odd	6		3969.2.a.z.1.3		5
63.13	odd	6		1323.2.g.f.361.3		10
63.16	even	3		567.2.e.e.163.3		10
63.23	odd	6		63.2.h.b.58.3	yes	10
63.25	even	3		3969.2.a.bc.1.3		5
63.31	odd	6		1323.2.f.f.442.3		10
63.32	odd	6		441.2.f.e.148.3		10
63.38	even	6		3969.2.a.ba.1.3		5
63.40	odd	6		1323.2.h.f.226.3		10
63.41	even	6		441.2.g.f.67.3		10
63.52	odd	6		3969.2.a.bb.1.3		5
63.58	even	3	inner	189.2.h.b.37.3		10
63.59	even	6		441.2.f.f.148.3		10
84.23	even	6		1008.2.t.i.961.1		10
252.23	even	6		1008.2.q.i.625.3		10
252.247	odd	6		3024.2.q.i.2305.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.3	✓	10	9.5	odd	6
63.2.g.b.16.3	yes	10	21.2	odd	6
63.2.h.b.25.3	yes	10	3.2	odd	2
63.2.h.b.58.3	yes	10	63.23	odd	6
189.2.g.b.100.3		10	7.2	even	3
189.2.g.b.172.3		10	9.4	even	3
189.2.h.b.37.3		10	63.58	even	3	inner
189.2.h.b.46.3		10	1.1	even	1	trivial
441.2.f.e.148.3		10	63.32	odd	6
441.2.f.e.295.3		10	21.11	odd	6
441.2.f.f.148.3		10	63.59	even	6
441.2.f.f.295.3		10	21.17	even	6
441.2.g.f.67.3		10	63.41	even	6
441.2.g.f.79.3		10	21.5	even	6
441.2.h.f.214.3		10	21.20	even	2
441.2.h.f.373.3		10	63.5	even	6
567.2.e.e.163.3		10	63.16	even	3
567.2.e.e.487.3		10	9.7	even	3
567.2.e.f.163.3		10	63.2	odd	6
567.2.e.f.487.3		10	9.2	odd	6
1008.2.q.i.529.3		10	12.11	even	2
1008.2.q.i.625.3		10	252.23	even	6
1008.2.t.i.193.1		10	36.23	even	6
1008.2.t.i.961.1		10	84.23	even	6
1323.2.f.e.442.3		10	63.4	even	3
1323.2.f.e.883.3		10	7.4	even	3
1323.2.f.f.442.3		10	63.31	odd	6
1323.2.f.f.883.3		10	7.3	odd	6
1323.2.g.f.361.3		10	63.13	odd	6
1323.2.g.f.667.3		10	7.5	odd	6
1323.2.h.f.226.3		10	63.40	odd	6
1323.2.h.f.802.3		10	7.6	odd	2
3024.2.q.i.2305.1		10	252.247	odd	6
3024.2.q.i.2881.1		10	4.3	odd	2
3024.2.t.i.289.5		10	28.23	odd	6
3024.2.t.i.1873.5		10	36.31	odd	6
3969.2.a.z.1.3		5	63.11	odd	6
3969.2.a.ba.1.3		5	63.38	even	6
3969.2.a.bb.1.3		5	63.52	odd	6
3969.2.a.bc.1.3		5	63.25	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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more