LMFDB - Embedded newform 700.2.c.b.699.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(699,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("700.699");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.c (of order $2$, degree $1$, 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:	$5.58952814149$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			699.3
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	700.699
Dual form			700.2.c.b.699.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 - 1.36603i) q^{2} -1.73205i q^{3} +(-1.73205 - 1.00000i) q^{4} +(-2.36603 - 0.633975i) q^{6} +(-2.00000 + 1.73205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})$	\(q+(0.366025 - 1.36603i) q^{2} -1.73205i q^{3} +(-1.73205 - 1.00000i) q^{4} +(-2.36603 - 0.633975i) q^{6} +(-2.00000 + 1.73205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +3.73205i q^{11} +(-1.73205 + 3.00000i) q^{12} -6.46410 q^{13} +(1.63397 + 3.36603i) q^{14} +(2.00000 + 3.46410i) q^{16} +0.464102 q^{17} -6.00000 q^{19} +(3.00000 + 3.46410i) q^{21} +(5.09808 + 1.36603i) q^{22} -5.46410 q^{23} +(3.46410 + 3.46410i) q^{24} +(-2.36603 + 8.83013i) q^{26} -5.19615i q^{27} +(5.19615 - 1.00000i) q^{28} +5.92820 q^{29} -6.00000 q^{31} +(5.46410 - 1.46410i) q^{32} +6.46410 q^{33} +(0.169873 - 0.633975i) q^{34} -2.53590i q^{37} +(-2.19615 + 8.19615i) q^{38} +11.1962i q^{39} -3.46410i q^{41} +(5.83013 - 2.83013i) q^{42} +2.00000 q^{43} +(3.73205 - 6.46410i) q^{44} +(-2.00000 + 7.46410i) q^{46} -1.73205i q^{47} +(6.00000 - 3.46410i) q^{48} +(1.00000 - 6.92820i) q^{49} -0.803848i q^{51} +(11.1962 + 6.46410i) q^{52} -2.00000i q^{53} +(-7.09808 - 1.90192i) q^{54} +(0.535898 - 7.46410i) q^{56} +10.3923i q^{57} +(2.16987 - 8.09808i) q^{58} -3.46410 q^{59} -2.53590i q^{61} +(-2.19615 + 8.19615i) q^{62} -8.00000i q^{64} +(2.36603 - 8.83013i) q^{66} -3.46410 q^{67} +(-0.803848 - 0.464102i) q^{68} +9.46410i q^{69} +0.535898i q^{71} +0.928203 q^{73} +(-3.46410 - 0.928203i) q^{74} +(10.3923 + 6.00000i) q^{76} +(-6.46410 - 7.46410i) q^{77} +(15.2942 + 4.09808i) q^{78} +2.66025i q^{79} -9.00000 q^{81} +(-4.73205 - 1.26795i) q^{82} -8.53590i q^{83} +(-1.73205 - 9.00000i) q^{84} +(0.732051 - 2.73205i) q^{86} -10.2679i q^{87} +(-7.46410 - 7.46410i) q^{88} +9.46410i q^{89} +(12.9282 - 11.1962i) q^{91} +(9.46410 + 5.46410i) q^{92} +10.3923i q^{93} +(-2.36603 - 0.633975i) q^{94} +(-2.53590 - 9.46410i) q^{96} +7.39230 q^{97} +(-9.09808 - 3.90192i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 6 q^{6} - 8 q^{7} - 8 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 6 * q^6 - 8 * q^7 - 8 * q^8	$ 4 q - 2 q^{2} - 6 q^{6} - 8 q^{7} - 8 q^{8} - 12 q^{13} + 10 q^{14} + 8 q^{16} - 12 q^{17} - 24 q^{19} + 12 q^{21} + 10 q^{22} - 8 q^{23} - 6 q^{26} - 4 q^{29} - 24 q^{31} + 8 q^{32} + 12 q^{33} + 18 q^{34} + 12 q^{38} + 6 q^{42} + 8 q^{43} + 8 q^{44} - 8 q^{46} + 24 q^{48} + 4 q^{49} + 24 q^{52} - 18 q^{54} + 16 q^{56} + 26 q^{58} + 12 q^{62} + 6 q^{66} - 24 q^{68} - 24 q^{73} - 12 q^{77} + 30 q^{78} - 36 q^{81} - 12 q^{82} - 4 q^{86} - 16 q^{88} + 24 q^{91} + 24 q^{92} - 6 q^{94} - 24 q^{96} - 12 q^{97} - 26 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 6 * q^6 - 8 * q^7 - 8 * q^8 - 12 * q^13 + 10 * q^14 + 8 * q^16 - 12 * q^17 - 24 * q^19 + 12 * q^21 + 10 * q^22 - 8 * q^23 - 6 * q^26 - 4 * q^29 - 24 * q^31 + 8 * q^32 + 12 * q^33 + 18 * q^34 + 12 * q^38 + 6 * q^42 + 8 * q^43 + 8 * q^44 - 8 * q^46 + 24 * q^48 + 4 * q^49 + 24 * q^52 - 18 * q^54 + 16 * q^56 + 26 * q^58 + 12 * q^62 + 6 * q^66 - 24 * q^68 - 24 * q^73 - 12 * q^77 + 30 * q^78 - 36 * q^81 - 12 * q^82 - 4 * q^86 - 16 * q^88 + 24 * q^91 + 24 * q^92 - 6 * q^94 - 24 * q^96 - 12 * q^97 - 26 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.366025	−	1.36603i	0.258819	−	0.965926i
$2$	0.366025	−	1.36603i	0.258819	−	0.965926i
$3$		−	1.73205i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$3$		−	1.73205i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$4$	−1.73205	−	1.00000i	−0.866025	−	0.500000i
$5$		0			0
$5$		0			0
$6$	−2.36603	−	0.633975i	−0.965926	−	0.258819i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$		0			0
$10$		0			0
$11$			3.73205i			1.12526i	0.826710	+	0.562628i	$0.190210\pi$
$11$			3.73205i			1.12526i	−0.826710	+	0.562628i	$0.809790\pi$
$12$	−1.73205	+	3.00000i	−0.500000	+	0.866025i
$13$	−6.46410			−1.79282			−0.896410	−	0.443227i	$-0.853834\pi$
$13$	−6.46410			−1.79282			−0.896410	+	0.443227i	$0.853834\pi$
$14$	1.63397	+	3.36603i	0.436698	+	0.899608i
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	0.464102			0.112561			0.0562806	−	0.998415i	$-0.482076\pi$
$17$	0.464102			0.112561			0.0562806	+	0.998415i	$0.482076\pi$
$18$		0			0
$19$	−6.00000			−1.37649			−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000			−1.37649			−0.688247	+	0.725476i	$0.741620\pi$
$20$		0			0
$21$	3.00000	+	3.46410i	0.654654	+	0.755929i
$22$	5.09808	+	1.36603i	1.08691	+	0.291238i
$23$	−5.46410			−1.13934			−0.569672	−	0.821872i	$-0.692930\pi$
$23$	−5.46410			−1.13934			−0.569672	+	0.821872i	$0.692930\pi$
$24$	3.46410	+	3.46410i	0.707107	+	0.707107i
$25$		0			0
$26$	−2.36603	+	8.83013i	−0.464016	+	1.73173i
$27$		−	5.19615i		−	1.00000i
$28$	5.19615	−	1.00000i	0.981981	−	0.188982i
$29$	5.92820			1.10084			0.550420	−	0.834888i	$-0.314468\pi$
$29$	5.92820			1.10084			0.550420	+	0.834888i	$0.314468\pi$
$30$		0			0
$31$	−6.00000			−1.07763			−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000			−1.07763			−0.538816	+	0.842424i	$0.681128\pi$
$32$	5.46410	−	1.46410i	0.965926	−	0.258819i
$33$	6.46410			1.12526
$34$	0.169873	−	0.633975i	0.0291330	−	0.108726i
$35$		0			0
$36$		0			0
$37$		−	2.53590i		−	0.416899i	−0.978033	−	0.208450i	$-0.933158\pi$
$37$		−	2.53590i		−	0.416899i	0.978033	−	0.208450i	$-0.0668417\pi$
$38$	−2.19615	+	8.19615i	−0.356263	+	1.32959i
$39$			11.1962i			1.79282i
$40$		0			0
$41$		−	3.46410i		−	0.541002i	−0.962720	−	0.270501i	$-0.912811\pi$
$41$		−	3.46410i		−	0.541002i	0.962720	−	0.270501i	$-0.0871893\pi$
$42$	5.83013	−	2.83013i	0.899608	−	0.436698i
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	3.73205	−	6.46410i	0.562628	−	0.974500i
$45$		0			0
$46$	−2.00000	+	7.46410i	−0.294884	+	1.10052i
$47$		−	1.73205i		−	0.252646i	−0.991989	−	0.126323i	$-0.959682\pi$
$47$		−	1.73205i		−	0.252646i	0.991989	−	0.126323i	$-0.0403175\pi$
$48$	6.00000	−	3.46410i	0.866025	−	0.500000i
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$		0			0
$51$		−	0.803848i		−	0.112561i
$52$	11.1962	+	6.46410i	1.55263	+	0.896410i
$53$		−	2.00000i		−	0.274721i	−0.990521	−	0.137361i	$-0.956138\pi$
$53$		−	2.00000i		−	0.274721i	0.990521	−	0.137361i	$-0.0438619\pi$
$54$	−7.09808	−	1.90192i	−0.965926	−	0.258819i
$55$		0			0
$56$	0.535898	−	7.46410i	0.0716124	−	0.997433i
$57$			10.3923i			1.37649i
$58$	2.16987	−	8.09808i	0.284918	−	1.06333i
$59$	−3.46410			−0.450988			−0.225494	−	0.974245i	$-0.572400\pi$
$59$	−3.46410			−0.450988			−0.225494	+	0.974245i	$0.572400\pi$
$60$		0			0
$61$		−	2.53590i		−	0.324689i	−0.986734	−	0.162344i	$-0.948094\pi$
$61$		−	2.53590i		−	0.324689i	0.986734	−	0.162344i	$-0.0519055\pi$
$62$	−2.19615	+	8.19615i	−0.278912	+	1.04091i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$		0			0
$66$	2.36603	−	8.83013i	0.291238	−	1.08691i
$67$	−3.46410			−0.423207			−0.211604	−	0.977356i	$-0.567869\pi$
$67$	−3.46410			−0.423207			−0.211604	+	0.977356i	$0.567869\pi$
$68$	−0.803848	−	0.464102i	−0.0974808	−	0.0562806i
$69$			9.46410i			1.13934i
$70$		0			0
$71$			0.535898i			0.0635994i	0.999494	+	0.0317997i	$0.0101239\pi$
$71$			0.535898i			0.0635994i	−0.999494	+	0.0317997i	$0.989876\pi$
$72$		0			0
$73$	0.928203			0.108638			0.0543190	−	0.998524i	$-0.482701\pi$
$73$	0.928203			0.108638			0.0543190	+	0.998524i	$0.482701\pi$
$74$	−3.46410	−	0.928203i	−0.402694	−	0.107901i
$75$		0			0
$76$	10.3923	+	6.00000i	1.19208	+	0.688247i
$77$	−6.46410	−	7.46410i	−0.736653	−	0.850613i
$78$	15.2942	+	4.09808i	1.73173	+	0.464016i
$79$			2.66025i			0.299302i	0.988739	+	0.149651i	$0.0478150\pi$
$79$			2.66025i			0.299302i	−0.988739	+	0.149651i	$0.952185\pi$
$80$		0			0
$81$	−9.00000			−1.00000
$82$	−4.73205	−	1.26795i	−0.522568	−	0.140022i
$83$		−	8.53590i		−	0.936937i	−0.883480	−	0.468468i	$-0.844806\pi$
$83$		−	8.53590i		−	0.936937i	0.883480	−	0.468468i	$-0.155194\pi$
$84$	−1.73205	−	9.00000i	−0.188982	−	0.981981i
$85$		0			0
$86$	0.732051	−	2.73205i	0.0789391	−	0.294605i
$87$		−	10.2679i		−	1.10084i
$88$	−7.46410	−	7.46410i	−0.795676	−	0.795676i
$89$			9.46410i			1.00319i	0.865102	+	0.501596i	$0.167254\pi$
$89$			9.46410i			1.00319i	−0.865102	+	0.501596i	$0.832746\pi$
$90$		0			0
$91$	12.9282	−	11.1962i	1.35524	−	1.17368i
$92$	9.46410	+	5.46410i	0.986701	+	0.569672i
$93$			10.3923i			1.07763i
$94$	−2.36603	−	0.633975i	−0.244037	−	0.0653895i
$95$		0			0
$96$	−2.53590	−	9.46410i	−0.258819	−	0.965926i
$97$	7.39230			0.750575			0.375287	−	0.926908i	$-0.377544\pi$
$97$	7.39230			0.750575			0.375287	+	0.926908i	$0.377544\pi$
$98$	−9.09808	−	3.90192i	−0.919044	−	0.394154i
$99$		0			0
$100$		0			0
$101$			8.53590i			0.849354i	0.905345	+	0.424677i	$0.139612\pi$
$101$			8.53590i			0.849354i	−0.905345	+	0.424677i	$0.860388\pi$
$102$	−1.09808	−	0.294229i	−0.108726	−	0.0291330i
$103$			17.1962i			1.69439i	0.531284	+	0.847194i	$0.321710\pi$
$103$			17.1962i			1.69439i	−0.531284	+	0.847194i	$0.678290\pi$
$104$	12.9282	−	12.9282i	1.26771	−	1.26771i
$105$		0			0
$106$	−2.73205	−	0.732051i	−0.265360	−	0.0711031i
$107$	−18.3923			−1.77805			−0.889026	−	0.457857i	$-0.848617\pi$
$107$	−18.3923			−1.77805			−0.889026	+	0.457857i	$0.848617\pi$
$108$	−5.19615	+	9.00000i	−0.500000	+	0.866025i
$109$	−15.9282			−1.52565			−0.762823	−	0.646608i	$-0.776187\pi$
$109$	−15.9282			−1.52565			−0.762823	+	0.646608i	$0.776187\pi$
$110$		0			0
$111$	−4.39230			−0.416899
$112$	−10.0000	−	3.46410i	−0.944911	−	0.327327i
$113$			1.46410i			0.137731i	0.997626	+	0.0688655i	$0.0219379\pi$
$113$			1.46410i			0.137731i	−0.997626	+	0.0688655i	$0.978062\pi$
$114$	14.1962	+	3.80385i	1.32959	+	0.356263i
$115$		0			0
$116$	−10.2679	−	5.92820i	−0.953355	−	0.550420i
$117$		0			0
$118$	−1.26795	+	4.73205i	−0.116724	+	0.435621i
$119$	−0.928203	+	0.803848i	−0.0850883	+	0.0736886i
$120$		0			0
$121$	−2.92820			−0.266200
$122$	−3.46410	−	0.928203i	−0.313625	−	0.0840356i
$123$	−6.00000			−0.541002
$124$	10.3923	+	6.00000i	0.933257	+	0.538816i
$125$		0			0
$126$		0			0
$127$	8.53590			0.757438			0.378719	−	0.925512i	$-0.376365\pi$
$127$	8.53590			0.757438			0.378719	+	0.925512i	$0.376365\pi$
$128$	−10.9282	−	2.92820i	−0.965926	−	0.258819i
$129$		−	3.46410i		−	0.304997i
$130$		0			0
$131$	9.46410			0.826882			0.413441	−	0.910531i	$-0.364327\pi$
$131$	9.46410			0.826882			0.413441	+	0.910531i	$0.364327\pi$
$132$	−11.1962	−	6.46410i	−0.974500	−	0.562628i
$133$	12.0000	−	10.3923i	1.04053	−	0.901127i
$134$	−1.26795	+	4.73205i	−0.109534	+	0.408787i
$135$		0			0
$136$	−0.928203	+	0.928203i	−0.0795928	+	0.0795928i
$137$		−	0.392305i		−	0.0335169i	−0.999860	−	0.0167584i	$-0.994665\pi$
$137$		−	0.392305i		−	0.0335169i	0.999860	−	0.0167584i	$-0.00533462\pi$
$138$	12.9282	+	3.46410i	1.10052	+	0.294884i
$139$	6.92820			0.587643			0.293821	−	0.955860i	$-0.405073\pi$
$139$	6.92820			0.587643			0.293821	+	0.955860i	$0.405073\pi$
$140$		0			0
$141$	−3.00000			−0.252646
$142$	0.732051	+	0.196152i	0.0614323	+	0.0164607i
$143$		−	24.1244i		−	2.01738i
$144$		0			0
$145$		0			0
$146$	0.339746	−	1.26795i	0.0281176	−	0.104936i
$147$	−12.0000	−	1.73205i	−0.989743	−	0.142857i
$148$	−2.53590	+	4.39230i	−0.208450	+	0.361045i
$149$	−16.9282			−1.38681			−0.693406	−	0.720547i	$-0.743891\pi$
$149$	−16.9282			−1.38681			−0.693406	+	0.720547i	$0.743891\pi$
$150$		0			0
$151$			4.80385i			0.390932i	0.980711	+	0.195466i	$0.0626219\pi$
$151$			4.80385i			0.390932i	−0.980711	+	0.195466i	$0.937378\pi$
$152$	12.0000	−	12.0000i	0.973329	−	0.973329i
$153$		0			0
$154$	−12.5622	+	6.09808i	−1.01229	+	0.491397i
$155$		0			0
$156$	11.1962	−	19.3923i	0.896410	−	1.55263i
$157$	−19.8564			−1.58471			−0.792357	−	0.610058i	$-0.791146\pi$
$157$	−19.8564			−1.58471			−0.792357	+	0.610058i	$0.791146\pi$
$158$	3.63397	+	0.973721i	0.289103	+	0.0774650i
$159$	−3.46410			−0.274721
$160$		0			0
$161$	10.9282	−	9.46410i	0.861263	−	0.745876i
$162$	−3.29423	+	12.2942i	−0.258819	+	0.965926i
$163$	20.7846			1.62798			0.813988	−	0.580881i	$-0.197292\pi$
$163$	20.7846			1.62798			0.813988	+	0.580881i	$0.197292\pi$
$164$	−3.46410	+	6.00000i	−0.270501	+	0.468521i
$165$		0			0
$166$	−11.6603	−	3.12436i	−0.905011	−	0.242497i
$167$			5.19615i			0.402090i	0.979582	+	0.201045i	$0.0644338\pi$
$167$			5.19615i			0.402090i	−0.979582	+	0.201045i	$0.935566\pi$
$168$	−12.9282	−	0.928203i	−0.997433	−	0.0716124i
$169$	28.7846			2.21420
$170$		0			0
$171$		0			0
$172$	−3.46410	−	2.00000i	−0.264135	−	0.152499i
$173$	−20.3205			−1.54494			−0.772470	−	0.635051i	$-0.780979\pi$
$173$	−20.3205			−1.54494			−0.772470	+	0.635051i	$0.780979\pi$
$174$	−14.0263	−	3.75833i	−1.06333	−	0.284918i
$175$		0			0
$176$	−12.9282	+	7.46410i	−0.974500	+	0.562628i
$177$			6.00000i			0.450988i
$178$	12.9282	+	3.46410i	0.969010	+	0.259645i
$179$		−	14.3923i		−	1.07573i	−0.843031	−	0.537866i	$-0.819231\pi$
$179$		−	14.3923i		−	1.07573i	0.843031	−	0.537866i	$-0.180769\pi$
$180$		0			0
$181$		−	12.9282i		−	0.960946i	−0.877010	−	0.480473i	$-0.840465\pi$
$181$		−	12.9282i		−	0.960946i	0.877010	−	0.480473i	$-0.159535\pi$
$182$	−10.5622	−	21.7583i	−0.782921	−	1.61283i
$183$	−4.39230			−0.324689
$184$	10.9282	−	10.9282i	0.805638	−	0.805638i
$185$		0			0
$186$	14.1962	+	3.80385i	1.04091	+	0.278912i
$187$			1.73205i			0.126660i
$188$	−1.73205	+	3.00000i	−0.126323	+	0.218797i
$189$	9.00000	+	10.3923i	0.654654	+	0.755929i
$190$		0			0
$191$		−	3.19615i		−	0.231265i	−0.993292	−	0.115633i	$-0.963110\pi$
$191$		−	3.19615i		−	0.231265i	0.993292	−	0.115633i	$-0.0368896\pi$
$192$	−13.8564			−1.00000
$193$			2.53590i			0.182538i	0.995826	+	0.0912690i	$0.0290923\pi$
$193$			2.53590i			0.182538i	−0.995826	+	0.0912690i	$0.970908\pi$
$194$	2.70577	−	10.0981i	0.194263	−	0.725000i
$195$		0			0
$196$	−8.66025	+	11.0000i	−0.618590	+	0.785714i
$197$			21.3205i			1.51902i	0.650494	+	0.759512i	$0.274562\pi$
$197$			21.3205i			1.51902i	−0.650494	+	0.759512i	$0.725438\pi$
$198$		0			0
$199$	3.46410			0.245564			0.122782	−	0.992434i	$-0.460818\pi$
$199$	3.46410			0.245564			0.122782	+	0.992434i	$0.460818\pi$
$200$		0			0
$201$			6.00000i			0.423207i
$202$	11.6603	+	3.12436i	0.820413	+	0.219829i
$203$	−11.8564	+	10.2679i	−0.832157	+	0.720669i
$204$	−0.803848	+	1.39230i	−0.0562806	+	0.0974808i
$205$		0			0
$206$	23.4904	+	6.29423i	1.63665	+	0.438540i
$207$		0			0
$208$	−12.9282	−	22.3923i	−0.896410	−	1.55263i
$209$		−	22.3923i		−	1.54891i
$210$		0			0
$211$		−	7.19615i		−	0.495404i	−0.968836	−	0.247702i	$-0.920325\pi$
$211$		−	7.19615i		−	0.495404i	0.968836	−	0.247702i	$-0.0796753\pi$
$212$	−2.00000	+	3.46410i	−0.137361	+	0.237915i
$213$	0.928203			0.0635994
$214$	−6.73205	+	25.1244i	−0.460194	+	1.71747i
$215$		0			0
$216$	10.3923	+	10.3923i	0.707107	+	0.707107i
$217$	12.0000	−	10.3923i	0.814613	−	0.705476i
$218$	−5.83013	+	21.7583i	−0.394866	+	1.47366i
$219$		−	1.60770i		−	0.108638i
$220$		0			0
$221$	−3.00000			−0.201802
$222$	−1.60770	+	6.00000i	−0.107901	+	0.402694i
$223$			10.2679i			0.687593i	0.939044	+	0.343796i	$0.111713\pi$
$223$			10.2679i			0.687593i	−0.939044	+	0.343796i	$0.888287\pi$
$224$	−8.39230	+	12.3923i	−0.560734	+	0.827996i
$225$		0			0
$226$	2.00000	+	0.535898i	0.133038	+	0.0356474i
$227$			3.33975i			0.221667i	0.993839	+	0.110833i	$0.0353520\pi$
$227$			3.33975i			0.221667i	−0.993839	+	0.110833i	$0.964648\pi$
$228$	10.3923	−	18.0000i	0.688247	−	1.19208i
$229$		−	15.4641i		−	1.02190i	−0.859611	−	0.510948i	$-0.829294\pi$
$229$		−	15.4641i		−	1.02190i	0.859611	−	0.510948i	$-0.170706\pi$
$230$		0			0
$231$	−12.9282	+	11.1962i	−0.850613	+	0.736653i
$232$	−11.8564	+	11.8564i	−0.778411	+	0.778411i
$233$			22.9282i			1.50208i	0.660259	+	0.751038i	$0.270447\pi$
$233$			22.9282i			1.50208i	−0.660259	+	0.751038i	$0.729553\pi$
$234$		0			0
$235$		0			0
$236$	6.00000	+	3.46410i	0.390567	+	0.225494i
$237$	4.60770			0.299302
$238$	0.758330	+	1.56218i	0.0491552	+	0.101261i
$239$		−	27.9808i		−	1.80993i	−0.425491	−	0.904963i	$-0.639899\pi$
$239$		−	27.9808i		−	1.80993i	0.425491	−	0.904963i	$-0.360101\pi$
$240$		0			0
$241$			4.39230i			0.282933i	0.989943	+	0.141467i	$0.0451818\pi$
$241$			4.39230i			0.282933i	−0.989943	+	0.141467i	$0.954818\pi$
$242$	−1.07180	+	4.00000i	−0.0688977	+	0.257130i
$243$		0			0
$244$	−2.53590	+	4.39230i	−0.162344	+	0.281189i
$245$		0			0
$246$	−2.19615	+	8.19615i	−0.140022	+	0.522568i
$247$	38.7846			2.46781
$248$	12.0000	−	12.0000i	0.762001	−	0.762001i
$249$	−14.7846			−0.936937
$250$		0			0
$251$	1.85641			0.117175			0.0585877	−	0.998282i	$-0.481340\pi$
$251$	1.85641			0.117175			0.0585877	+	0.998282i	$0.481340\pi$
$252$		0			0
$253$		−	20.3923i		−	1.28205i
$254$	3.12436	−	11.6603i	0.196040	−	0.731629i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	6.00000			0.374270			0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000			0.374270			0.187135	+	0.982334i	$0.440080\pi$
$258$	−4.73205	−	1.26795i	−0.294605	−	0.0789391i
$259$	4.39230	+	5.07180i	0.272925	+	0.315146i
$260$		0			0
$261$		0			0
$262$	3.46410	−	12.9282i	0.214013	−	0.798707i
$263$	−4.53590			−0.279695			−0.139848	−	0.990173i	$-0.544661\pi$
$263$	−4.53590			−0.279695			−0.139848	+	0.990173i	$0.544661\pi$
$264$	−12.9282	+	12.9282i	−0.795676	+	0.795676i
$265$		0			0
$266$	−9.80385	−	20.1962i	−0.601112	−	1.23831i
$267$	16.3923			1.00319
$268$	6.00000	+	3.46410i	0.366508	+	0.211604i
$269$		−	12.0000i		−	0.731653i	−0.930683	−	0.365826i	$-0.880786\pi$
$269$		−	12.0000i		−	0.731653i	0.930683	−	0.365826i	$-0.119214\pi$
$270$		0			0
$271$	2.53590			0.154045			0.0770224	−	0.997029i	$-0.475459\pi$
$271$	2.53590			0.154045			0.0770224	+	0.997029i	$0.475459\pi$
$272$	0.928203	+	1.60770i	0.0562806	+	0.0974808i
$273$	−19.3923	−	22.3923i	−1.17368	−	1.35524i
$274$	−0.535898	−	0.143594i	−0.0323748	−	0.00867480i
$275$		0			0
$276$	9.46410	−	16.3923i	0.569672	−	0.986701i
$277$		−	24.7846i		−	1.48916i	−0.667532	−	0.744581i	$-0.732649\pi$
$277$		−	24.7846i		−	1.48916i	0.667532	−	0.744581i	$-0.267351\pi$
$278$	2.53590	−	9.46410i	0.152093	−	0.567619i
$279$		0			0
$280$		0			0
$281$	5.92820			0.353647			0.176823	−	0.984243i	$-0.443418\pi$
$281$	5.92820			0.353647			0.176823	+	0.984243i	$0.443418\pi$
$282$	−1.09808	+	4.09808i	−0.0653895	+	0.244037i
$283$			12.1244i			0.720718i	0.932814	+	0.360359i	$0.117346\pi$
$283$			12.1244i			0.720718i	−0.932814	+	0.360359i	$0.882654\pi$
$284$	0.535898	−	0.928203i	0.0317997	−	0.0550787i
$285$		0			0
$286$	−32.9545	−	8.83013i	−1.94864	−	0.522136i
$287$	6.00000	+	6.92820i	0.354169	+	0.408959i
$288$		0			0
$289$	−16.7846			−0.987330
$290$		0			0
$291$		−	12.8038i		−	0.750575i
$292$	−1.60770	−	0.928203i	−0.0940832	−	0.0543190i
$293$	14.3205			0.836613			0.418307	−	0.908306i	$-0.362624\pi$
$293$	14.3205			0.836613			0.418307	+	0.908306i	$0.362624\pi$
$294$	−6.75833	+	15.7583i	−0.394154	+	0.919044i
$295$		0			0
$296$	5.07180	+	5.07180i	0.294792	+	0.294792i
$297$	19.3923			1.12526
$298$	−6.19615	+	23.1244i	−0.358933	+	1.33956i
$299$	35.3205			2.04264
$300$		0			0
$301$	−4.00000	+	3.46410i	−0.230556	+	0.199667i
$302$	6.56218	+	1.75833i	0.377611	+	0.101181i
$303$	14.7846			0.849354
$304$	−12.0000	−	20.7846i	−0.688247	−	1.19208i
$305$		0			0
$306$		0			0
$307$		−	1.73205i		−	0.0988534i	−0.998778	−	0.0494267i	$-0.984261\pi$
$307$		−	1.73205i		−	0.0988534i	0.998778	−	0.0494267i	$-0.0157394\pi$
$308$	3.73205	+	19.3923i	0.212653	+	1.10498i
$309$	29.7846			1.69439
$310$		0			0
$311$	−19.8564			−1.12595			−0.562977	−	0.826473i	$-0.690344\pi$
$311$	−19.8564			−1.12595			−0.562977	+	0.826473i	$0.690344\pi$
$312$	−22.3923	−	22.3923i	−1.26771	−	1.26771i
$313$	24.4641			1.38279			0.691396	−	0.722476i	$-0.256996\pi$
$313$	24.4641			1.38279			0.691396	+	0.722476i	$0.256996\pi$
$314$	−7.26795	+	27.1244i	−0.410154	+	1.53072i
$315$		0			0
$316$	2.66025	−	4.60770i	0.149651	−	0.259203i
$317$		−	16.9282i		−	0.950783i	−0.879774	−	0.475391i	$-0.842306\pi$
$317$		−	16.9282i		−	0.950783i	0.879774	−	0.475391i	$-0.157694\pi$
$318$	−1.26795	+	4.73205i	−0.0711031	+	0.265360i
$319$			22.1244i			1.23873i
$320$		0			0
$321$			31.8564i			1.77805i
$322$	−8.92820	−	18.3923i	−0.497549	−	1.02496i
$323$	−2.78461			−0.154940
$324$	15.5885	+	9.00000i	0.866025	+	0.500000i
$325$		0			0
$326$	7.60770	−	28.3923i	0.421351	−	1.57250i
$327$			27.5885i			1.52565i
$328$	6.92820	+	6.92820i	0.382546	+	0.382546i
$329$	3.00000	+	3.46410i	0.165395	+	0.190982i
$330$		0			0
$331$		−	5.60770i		−	0.308227i	−0.988053	−	0.154113i	$-0.950748\pi$
$331$		−	5.60770i		−	0.308227i	0.988053	−	0.154113i	$-0.0492521\pi$
$332$	−8.53590	+	14.7846i	−0.468468	+	0.811411i
$333$		0			0
$334$	7.09808	+	1.90192i	0.388389	+	0.104069i
$335$		0			0
$336$	−6.00000	+	17.3205i	−0.327327	+	0.944911i
$337$		0			0		1.00000			$0$
$337$		0			0		−1.00000			$\pi$
$338$	10.5359	−	39.3205i	0.573077	−	2.13875i
$339$	2.53590			0.137731
$340$		0			0
$341$		−	22.3923i		−	1.21261i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	−4.00000	+	4.00000i	−0.215666	+	0.215666i
$345$		0			0
$346$	−7.43782	+	27.7583i	−0.399860	+	1.49230i
$347$	14.2487			0.764911			0.382455	−	0.923974i	$-0.375079\pi$
$347$	14.2487			0.764911			0.382455	+	0.923974i	$0.375079\pi$
$348$	−10.2679	+	17.7846i	−0.550420	+	0.953355i
$349$			29.3205i			1.56949i	0.619818	+	0.784745i	$0.287206\pi$
$349$			29.3205i			1.56949i	−0.619818	+	0.784745i	$0.712794\pi$
$350$		0			0
$351$			33.5885i			1.79282i
$352$	5.46410	+	20.3923i	0.291238	+	1.08691i
$353$	−13.3923			−0.712800			−0.356400	−	0.934333i	$-0.615996\pi$
$353$	−13.3923			−0.712800			−0.356400	+	0.934333i	$0.615996\pi$
$354$	8.19615	+	2.19615i	0.435621	+	0.116724i
$355$		0			0
$356$	9.46410	−	16.3923i	0.501596	−	0.868790i
$357$	1.39230	+	1.60770i	0.0736886	+	0.0850883i
$358$	−19.6603	−	5.26795i	−1.03908	−	0.278420i
$359$			9.32051i			0.491918i	0.969280	+	0.245959i	$0.0791028\pi$
$359$			9.32051i			0.491918i	−0.969280	+	0.245959i	$0.920897\pi$
$360$		0			0
$361$	17.0000			0.894737
$362$	−17.6603	−	4.73205i	−0.928202	−	0.248711i
$363$			5.07180i			0.266200i
$364$	−33.5885	+	6.46410i	−1.76051	+	0.338811i
$365$		0			0
$366$	−1.60770	+	6.00000i	−0.0840356	+	0.313625i
$367$			36.1244i			1.88568i	0.333251	+	0.942838i	$0.391854\pi$
$367$			36.1244i			1.88568i	−0.333251	+	0.942838i	$0.608146\pi$
$368$	−10.9282	−	18.9282i	−0.569672	−	0.986701i
$369$		0			0
$370$		0			0
$371$	3.46410	+	4.00000i	0.179847	+	0.207670i
$372$	10.3923	−	18.0000i	0.538816	−	0.933257i
$373$			24.3923i			1.26299i	0.775382	+	0.631493i	$0.217557\pi$
$373$			24.3923i			1.26299i	−0.775382	+	0.631493i	$0.782443\pi$
$374$	2.36603	+	0.633975i	0.122344	+	0.0327820i
$375$		0			0
$376$	3.46410	+	3.46410i	0.178647	+	0.178647i
$377$	−38.3205			−1.97361
$378$	17.4904	−	8.49038i	0.899608	−	0.436698i
$379$		−	26.3923i		−	1.35568i	−0.735209	−	0.677841i	$-0.762916\pi$
$379$		−	26.3923i		−	1.35568i	0.735209	−	0.677841i	$-0.237084\pi$
$380$		0			0
$381$		−	14.7846i		−	0.757438i
$382$	−4.36603	−	1.16987i	−0.223385	−	0.0598559i
$383$		−	20.5359i		−	1.04934i	−0.851307	−	0.524668i	$-0.824190\pi$
$383$		−	20.5359i		−	1.04934i	0.851307	−	0.524668i	$-0.175810\pi$
$384$	−5.07180	+	18.9282i	−0.258819	+	0.965926i
$385$		0			0
$386$	3.46410	+	0.928203i	0.176318	+	0.0472443i
$387$		0			0
$388$	−12.8038	−	7.39230i	−0.650017	−	0.375287i
$389$	−6.85641			−0.347634			−0.173817	−	0.984778i	$-0.555610\pi$
$389$	−6.85641			−0.347634			−0.173817	+	0.984778i	$0.555610\pi$
$390$		0			0
$391$	−2.53590			−0.128246
$392$	11.8564	+	15.8564i	0.598839	+	0.800869i
$393$		−	16.3923i		−	0.826882i
$394$	29.1244	+	7.80385i	1.46726	+	0.393152i
$395$		0			0
$396$		0			0
$397$	5.53590			0.277839			0.138919	−	0.990304i	$-0.455637\pi$
$397$	5.53590			0.277839			0.138919	+	0.990304i	$0.455637\pi$
$398$	1.26795	−	4.73205i	0.0635566	−	0.237196i
$399$	−18.0000	−	20.7846i	−0.901127	−	1.04053i
$400$		0			0
$401$	−23.9282			−1.19492			−0.597459	−	0.801900i	$-0.703823\pi$
$401$	−23.9282			−1.19492			−0.597459	+	0.801900i	$0.703823\pi$
$402$	8.19615	+	2.19615i	0.408787	+	0.109534i
$403$	38.7846			1.93200
$404$	8.53590	−	14.7846i	0.424677	−	0.735562i
$405$		0			0
$406$	9.68653	+	19.9545i	0.480735	+	0.990324i
$407$	9.46410			0.469118
$408$	1.60770	+	1.60770i	0.0795928	+	0.0795928i
$409$			31.8564i			1.57520i	0.616188	+	0.787599i	$0.288676\pi$
$409$			31.8564i			1.57520i	−0.616188	+	0.787599i	$0.711324\pi$
$410$		0			0
$411$	−0.679492			−0.0335169
$412$	17.1962	−	29.7846i	0.847194	−	1.46738i
$413$	6.92820	−	6.00000i	0.340915	−	0.295241i
$414$		0			0
$415$		0			0
$416$	−35.3205	+	9.46410i	−1.73173	+	0.464016i
$417$		−	12.0000i		−	0.587643i
$418$	−30.5885	−	8.19615i	−1.49613	−	0.400887i
$419$	−24.2487			−1.18463			−0.592314	−	0.805708i	$-0.701785\pi$
$419$	−24.2487			−1.18463			−0.592314	+	0.805708i	$0.701785\pi$
$420$		0			0
$421$	19.0000			0.926003			0.463002	−	0.886357i	$-0.346772\pi$
$421$	19.0000			0.926003			0.463002	+	0.886357i	$0.346772\pi$
$422$	−9.83013	−	2.63397i	−0.478523	−	0.128220i
$423$		0			0
$424$	4.00000	+	4.00000i	0.194257	+	0.194257i
$425$		0			0
$426$	0.339746	−	1.26795i	0.0164607	−	0.0614323i
$427$	4.39230	+	5.07180i	0.212559	+	0.245441i
$428$	31.8564	+	18.3923i	1.53984	+	0.889026i
$429$	−41.7846			−2.01738
$430$		0			0
$431$			17.5885i			0.847206i	0.905848	+	0.423603i	$0.139235\pi$
$431$			17.5885i			0.847206i	−0.905848	+	0.423603i	$0.860765\pi$
$432$	18.0000	−	10.3923i	0.866025	−	0.500000i
$433$	4.14359			0.199128			0.0995642	−	0.995031i	$-0.468255\pi$
$433$	4.14359			0.199128			0.0995642	+	0.995031i	$0.468255\pi$
$434$	−9.80385	−	20.1962i	−0.470600	−	0.969446i
$435$		0			0
$436$	27.5885	+	15.9282i	1.32125	+	0.762823i
$437$	32.7846			1.56830
$438$	−2.19615	−	0.588457i	−0.104936	−	0.0281176i
$439$	−15.7128			−0.749932			−0.374966	−	0.927039i	$-0.622346\pi$
$439$	−15.7128			−0.749932			−0.374966	+	0.927039i	$0.622346\pi$
$440$		0			0
$441$		0			0
$442$	−1.09808	+	4.09808i	−0.0522302	+	0.194926i
$443$	−26.0000			−1.23530			−0.617649	−	0.786454i	$-0.711915\pi$
$443$	−26.0000			−1.23530			−0.617649	+	0.786454i	$0.711915\pi$
$444$	7.60770	+	4.39230i	0.361045	+	0.208450i
$445$		0			0
$446$	14.0263	+	3.75833i	0.664164	+	0.177962i
$447$			29.3205i			1.38681i
$448$	13.8564	+	16.0000i	0.654654	+	0.755929i
$449$	1.92820			0.0909975			0.0454988	−	0.998964i	$-0.485512\pi$
$449$	1.92820			0.0909975			0.0454988	+	0.998964i	$0.485512\pi$
$450$		0			0
$451$	12.9282			0.608765
$452$	1.46410	−	2.53590i	0.0688655	−	0.119279i
$453$	8.32051			0.390932
$454$	4.56218	+	1.22243i	0.214114	+	0.0573716i
$455$		0			0
$456$	−20.7846	−	20.7846i	−0.973329	−	0.973329i
$457$			27.4641i			1.28472i	0.766405	+	0.642358i	$0.222044\pi$
$457$			27.4641i			1.28472i	−0.766405	+	0.642358i	$0.777956\pi$
$458$	−21.1244	−	5.66025i	−0.987076	−	0.264486i
$459$		−	2.41154i		−	0.112561i
$460$		0			0
$461$			27.7128i			1.29071i	0.763881	+	0.645357i	$0.223291\pi$
$461$			27.7128i			1.29071i	−0.763881	+	0.645357i	$0.776709\pi$
$462$	10.5622	+	21.7583i	0.491397	+	1.01229i
$463$	4.39230			0.204128			0.102064	−	0.994778i	$-0.467455\pi$
$463$	4.39230			0.204128			0.102064	+	0.994778i	$0.467455\pi$
$464$	11.8564	+	20.5359i	0.550420	+	0.953355i
$465$		0			0
$466$	31.3205	+	8.39230i	1.45089	+	0.388766i
$467$		−	22.5167i		−	1.04195i	−0.853573	−	0.520973i	$-0.825569\pi$
$467$		−	22.5167i		−	1.04195i	0.853573	−	0.520973i	$-0.174431\pi$
$468$		0			0
$469$	6.92820	−	6.00000i	0.319915	−	0.277054i
$470$		0			0
$471$			34.3923i			1.58471i
$472$	6.92820	−	6.92820i	0.318896	−	0.318896i
$473$			7.46410i			0.343200i
$474$	1.68653	−	6.29423i	0.0774650	−	0.289103i
$475$		0			0
$476$	2.41154	−	0.464102i	0.110533	−	0.0212721i
$477$		0			0
$478$	−38.2224	−	10.2417i	−1.74825	−	0.468443i
$479$	37.1769			1.69866			0.849328	−	0.527865i	$-0.177007\pi$
$479$	37.1769			1.69866			0.849328	+	0.527865i	$0.177007\pi$
$480$		0			0
$481$			16.3923i			0.747425i
$482$	6.00000	+	1.60770i	0.273293	+	0.0732285i
$483$	−16.3923	−	18.9282i	−0.745876	−	0.861263i
$484$	5.07180	+	2.92820i	0.230536	+	0.133100i
$485$		0			0
$486$		0			0
$487$	−28.7846			−1.30436			−0.652178	−	0.758066i	$-0.726144\pi$
$487$	−28.7846			−1.30436			−0.652178	+	0.758066i	$0.726144\pi$
$488$	5.07180	+	5.07180i	0.229589	+	0.229589i
$489$		−	36.0000i		−	1.62798i
$490$		0			0
$491$		−	34.1244i		−	1.54001i	−0.638037	−	0.770005i	$-0.720254\pi$
$491$		−	34.1244i		−	1.54001i	0.638037	−	0.770005i	$-0.279746\pi$
$492$	10.3923	+	6.00000i	0.468521	+	0.270501i
$493$	2.75129			0.123912
$494$	14.1962	−	52.9808i	0.638715	−	2.38372i
$495$		0			0
$496$	−12.0000	−	20.7846i	−0.538816	−	0.933257i
$497$	−0.928203	−	1.07180i	−0.0416356	−	0.0480767i
$498$	−5.41154	+	20.1962i	−0.242497	+	0.905011i
$499$			5.58846i			0.250174i	0.992146	+	0.125087i	$0.0399210\pi$
$499$			5.58846i			0.250174i	−0.992146	+	0.125087i	$0.960079\pi$
$500$		0			0
$501$	9.00000			0.402090
$502$	0.679492	−	2.53590i	0.0303272	−	0.113183i
$503$		−	15.5885i		−	0.695055i	−0.937670	−	0.347527i	$-0.887021\pi$
$503$		−	15.5885i		−	0.695055i	0.937670	−	0.347527i	$-0.112979\pi$
$504$		0			0
$505$		0			0
$506$	−27.8564	−	7.46410i	−1.23837	−	0.331820i
$507$		−	49.8564i		−	2.21420i
$508$	−14.7846	−	8.53590i	−0.655961	−	0.378719i
$509$		−	1.85641i		−	0.0822838i	−0.999153	−	0.0411419i	$-0.986900\pi$
$509$		−	1.85641i		−	0.0822838i	0.999153	−	0.0411419i	$-0.0130996\pi$
$510$		0			0
$511$	−1.85641	+	1.60770i	−0.0821226	+	0.0711202i
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$			31.1769i			1.37649i
$514$	2.19615	−	8.19615i	0.0968681	−	0.361517i
$515$		0			0
$516$	−3.46410	+	6.00000i	−0.152499	+	0.264135i
$517$	6.46410			0.284291
$518$	8.53590	−	4.14359i	0.375046	−	0.182059i
$519$			35.1962i			1.54494i
$520$		0			0
$521$		−	34.3923i		−	1.50675i	−0.657589	−	0.753377i	$-0.728424\pi$
$521$		−	34.3923i		−	1.50675i	0.657589	−	0.753377i	$-0.271576\pi$
$522$		0			0
$523$		−	24.2487i		−	1.06032i	−0.847897	−	0.530161i	$-0.822131\pi$
$523$		−	24.2487i		−	1.06032i	0.847897	−	0.530161i	$-0.177869\pi$
$524$	−16.3923	−	9.46410i	−0.716101	−	0.413441i
$525$		0			0
$526$	−1.66025	+	6.19615i	−0.0723905	+	0.270165i
$527$	−2.78461			−0.121300
$528$	12.9282	+	22.3923i	0.562628	+	0.974500i
$529$	6.85641			0.298105
$530$		0			0
$531$		0			0
$532$	−31.1769	+	6.00000i	−1.35169	+	0.260133i
$533$			22.3923i			0.969918i
$534$	6.00000	−	22.3923i	0.259645	−	0.969010i
$535$		0			0
$536$	6.92820	−	6.92820i	0.299253	−	0.299253i
$537$	−24.9282			−1.07573
$538$	−16.3923	−	4.39230i	−0.706722	−	0.189366i
$539$	25.8564	+	3.73205i	1.11371	+	0.160751i
$540$		0			0
$541$	−33.7846			−1.45251			−0.726257	−	0.687423i	$-0.758742\pi$
$541$	−33.7846			−1.45251			−0.726257	+	0.687423i	$0.758742\pi$
$542$	0.928203	−	3.46410i	0.0398697	−	0.148796i
$543$	−22.3923			−0.960946
$544$	2.53590	−	0.679492i	0.108726	−	0.0291330i
$545$		0			0
$546$	−37.6865	+	18.2942i	−1.61283	+	0.782921i
$547$	−14.5359			−0.621510			−0.310755	−	0.950490i	$-0.600582\pi$
$547$	−14.5359			−0.621510			−0.310755	+	0.950490i	$0.600582\pi$
$548$	−0.392305	+	0.679492i	−0.0167584	+	0.0290265i
$549$		0			0
$550$		0			0
$551$	−35.5692			−1.51530
$552$	−18.9282	−	18.9282i	−0.805638	−	0.805638i
$553$	−4.60770	−	5.32051i	−0.195939	−	0.226251i
$554$	−33.8564	−	9.07180i	−1.43842	−	0.385424i
$555$		0			0
$556$	−12.0000	−	6.92820i	−0.508913	−	0.293821i
$557$			5.85641i			0.248144i	0.992273	+	0.124072i	$0.0395954\pi$
$557$			5.85641i			0.248144i	−0.992273	+	0.124072i	$0.960405\pi$
$558$		0			0
$559$	−12.9282			−0.546805
$560$		0			0
$561$	3.00000			0.126660
$562$	2.16987	−	8.09808i	0.0915306	−	0.341597i
$563$			43.1769i			1.81969i	0.414948	+	0.909845i	$0.363800\pi$
$563$			43.1769i			1.81969i	−0.414948	+	0.909845i	$0.636200\pi$
$564$	5.19615	+	3.00000i	0.218797	+	0.126323i
$565$		0			0
$566$	16.5622	+	4.43782i	0.696160	+	0.186536i
$567$	18.0000	−	15.5885i	0.755929	−	0.654654i
$568$	−1.07180	−	1.07180i	−0.0449716	−	0.0449716i
$569$	−20.9282			−0.877356			−0.438678	−	0.898644i	$-0.644553\pi$
$569$	−20.9282			−0.877356			−0.438678	+	0.898644i	$0.644553\pi$
$570$		0			0
$571$		−	41.3205i		−	1.72921i	−0.502453	−	0.864605i	$-0.667569\pi$
$571$		−	41.3205i		−	1.72921i	0.502453	−	0.864605i	$-0.332431\pi$
$572$	−24.1244	+	41.7846i	−1.00869	+	1.74710i
$573$	−5.53590			−0.231265
$574$	11.6603	−	5.66025i	0.486690	−	0.236254i
$575$		0			0
$576$		0			0
$577$	−1.39230			−0.0579624			−0.0289812	−	0.999580i	$-0.509226\pi$
$577$	−1.39230			−0.0579624			−0.0289812	+	0.999580i	$0.509226\pi$
$578$	−6.14359	+	22.9282i	−0.255540	+	0.953688i
$579$	4.39230			0.182538
$580$		0			0
$581$	14.7846	+	17.0718i	0.613369	+	0.708257i
$582$	−17.4904	−	4.68653i	−0.725000	−	0.194263i
$583$	7.46410			0.309132
$584$	−1.85641	+	1.85641i	−0.0768186	+	0.0768186i
$585$		0			0
$586$	5.24167	−	19.5622i	0.216531	−	0.808106i
$587$		−	27.4641i		−	1.13356i	−0.823868	−	0.566782i	$-0.808188\pi$
$587$		−	27.4641i		−	1.13356i	0.823868	−	0.566782i	$-0.191812\pi$
$588$	19.0526	+	15.0000i	0.785714	+	0.618590i
$589$	36.0000			1.48335
$590$		0			0
$591$	36.9282			1.51902
$592$	8.78461	−	5.07180i	0.361045	−	0.208450i
$593$	−23.5359			−0.966504			−0.483252	−	0.875481i	$-0.660544\pi$
$593$	−23.5359			−0.966504			−0.483252	+	0.875481i	$0.660544\pi$
$594$	7.09808	−	26.4904i	0.291238	−	1.08691i
$595$		0			0
$596$	29.3205	+	16.9282i	1.20101	+	0.693406i
$597$		−	6.00000i		−	0.245564i
$598$	12.9282	−	48.2487i	0.528674	−	1.97304i
$599$		−	14.1244i		−	0.577106i	−0.957464	−	0.288553i	$-0.906826\pi$
$599$		−	14.1244i		−	0.577106i	0.957464	−	0.288553i	$-0.0931741\pi$
$600$		0			0
$601$		−	26.7846i		−	1.09257i	−0.837600	−	0.546284i	$-0.816042\pi$
$601$		−	26.7846i		−	1.09257i	0.837600	−	0.546284i	$-0.183958\pi$
$602$	3.26795	+	6.73205i	0.133192	+	0.274378i
$603$		0			0
$604$	4.80385	−	8.32051i	0.195466	−	0.338557i
$605$		0			0
$606$	5.41154	−	20.1962i	0.219829	−	0.820413i
$607$		−	18.8038i		−	0.763225i	−0.924322	−	0.381612i	$-0.875369\pi$
$607$		−	18.8038i		−	0.763225i	0.924322	−	0.381612i	$-0.124631\pi$
$608$	−32.7846	+	8.78461i	−1.32959	+	0.356263i
$609$	17.7846	+	20.5359i	0.720669	+	0.832157i
$610$		0			0
$611$			11.1962i			0.452948i
$612$		0			0
$613$			10.0000i			0.403896i	0.979396	+	0.201948i	$0.0647272\pi$
$613$			10.0000i			0.403896i	−0.979396	+	0.201948i	$0.935273\pi$
$614$	−2.36603	−	0.633975i	−0.0954850	−	0.0255851i
$615$		0			0
$616$	27.8564	+	2.00000i	1.12237	+	0.0805823i
$617$		−	9.07180i		−	0.365217i	−0.983186	−	0.182608i	$-0.941546\pi$
$617$		−	9.07180i		−	0.365217i	0.983186	−	0.182608i	$-0.0584540\pi$
$618$	10.9019	−	40.6865i	0.438540	−	1.63665i
$619$	−35.3205			−1.41965			−0.709826	−	0.704378i	$-0.751226\pi$
$619$	−35.3205			−1.41965			−0.709826	+	0.704378i	$0.751226\pi$
$620$		0			0
$621$			28.3923i			1.13934i
$622$	−7.26795	+	27.1244i	−0.291418	+	1.08759i
$623$	−16.3923	−	18.9282i	−0.656744	−	0.758342i
$624$	−38.7846	+	22.3923i	−1.55263	+	0.896410i
$625$		0			0
$626$	8.95448	−	33.4186i	0.357893	−	1.33568i
$627$	−38.7846			−1.54891
$628$	34.3923	+	19.8564i	1.37240	+	0.792357i
$629$		−	1.17691i		−	0.0469267i
$630$		0			0
$631$		−	26.9090i		−	1.07123i	−0.844463	−	0.535614i	$-0.820080\pi$
$631$		−	26.9090i		−	1.07123i	0.844463	−	0.535614i	$-0.179920\pi$
$632$	−5.32051	−	5.32051i	−0.211638	−	0.211638i
$633$	−12.4641			−0.495404
$634$	−23.1244	−	6.19615i	−0.918385	−	0.246081i
$635$		0			0
$636$	6.00000	+	3.46410i	0.237915	+	0.137361i
$637$	−6.46410	+	44.7846i	−0.256117	+	1.77443i
$638$	30.2224	+	8.09808i	1.19652	+	0.320606i
$639$		0			0
$640$		0			0
$641$	−4.92820			−0.194652			−0.0973262	−	0.995253i	$-0.531029\pi$
$641$	−4.92820			−0.194652			−0.0973262	+	0.995253i	$0.531029\pi$
$642$	43.5167	+	11.6603i	1.71747	+	0.460194i
$643$			31.0526i			1.22459i	0.790628	+	0.612297i	$0.209754\pi$
$643$			31.0526i			1.22459i	−0.790628	+	0.612297i	$0.790246\pi$
$644$	−28.3923	+	5.46410i	−1.11881	+	0.215316i
$645$		0			0
$646$	−1.01924	+	3.80385i	−0.0401014	+	0.149660i
$647$			10.3923i			0.408564i	0.978912	+	0.204282i	$0.0654859\pi$
$647$			10.3923i			0.408564i	−0.978912	+	0.204282i	$0.934514\pi$
$648$	18.0000	−	18.0000i	0.707107	−	0.707107i
$649$		−	12.9282i		−	0.507476i
$650$		0			0
$651$	−18.0000	−	20.7846i	−0.705476	−	0.814613i
$652$	−36.0000	−	20.7846i	−1.40987	−	0.813988i
$653$		−	38.3923i		−	1.50241i	−0.660071	−	0.751203i	$-0.729474\pi$
$653$		−	38.3923i		−	1.50241i	0.660071	−	0.751203i	$-0.270526\pi$
$654$	37.6865	+	10.0981i	1.47366	+	0.394866i
$655$		0			0
$656$	12.0000	−	6.92820i	0.468521	−	0.270501i
$657$		0			0
$658$	5.83013	−	2.83013i	0.227282	−	0.110330i
$659$			20.8038i			0.810403i	0.914227	+	0.405201i	$0.132799\pi$
$659$			20.8038i			0.810403i	−0.914227	+	0.405201i	$0.867201\pi$
$660$		0			0
$661$			15.7128i			0.611158i	0.952167	+	0.305579i	$0.0988499\pi$
$661$			15.7128i			0.611158i	−0.952167	+	0.305579i	$0.901150\pi$
$662$	−7.66025	−	2.05256i	−0.297724	−	0.0797750i
$663$			5.19615i			0.201802i
$664$	17.0718	+	17.0718i	0.662514	+	0.662514i
$665$		0			0
$666$		0			0
$667$	−32.3923			−1.25424
$668$	5.19615	−	9.00000i	0.201045	−	0.348220i
$669$	17.7846			0.687593
$670$		0			0
$671$	9.46410			0.365358
$672$	21.4641	+	14.5359i	0.827996	+	0.560734i
$673$		−	49.1769i		−	1.89563i	−0.318820	−	0.947815i	$-0.603286\pi$
$673$		−	49.1769i		−	1.89563i	0.318820	−	0.947815i	$-0.396714\pi$
$674$		0			0
$675$		0			0
$676$	−49.8564	−	28.7846i	−1.91755	−	1.10710i
$677$	−4.60770			−0.177088			−0.0885441	−	0.996072i	$-0.528221\pi$
$677$	−4.60770			−0.177088			−0.0885441	+	0.996072i	$0.528221\pi$
$678$	0.928203	−	3.46410i	0.0356474	−	0.133038i
$679$	−14.7846	+	12.8038i	−0.567381	+	0.491367i
$680$		0			0
$681$	5.78461			0.221667
$682$	−30.5885	−	8.19615i	−1.17129	−	0.313847i
$683$	−27.3205			−1.04539			−0.522695	−	0.852520i	$-0.675073\pi$
$683$	−27.3205			−1.04539			−0.522695	+	0.852520i	$0.675073\pi$
$684$		0			0
$685$		0			0
$686$	24.9545	−	7.95448i	0.952767	−	0.303704i
$687$	−26.7846			−1.02190
$688$	4.00000	+	6.92820i	0.152499	+	0.264135i
$689$			12.9282i			0.492525i
$690$		0			0
$691$	46.6410			1.77431			0.887154	−	0.461474i	$-0.152679\pi$
$691$	46.6410			1.77431			0.887154	+	0.461474i	$0.152679\pi$
$692$	35.1962	+	20.3205i	1.33796	+	0.772470i
$693$		0			0
$694$	5.21539	−	19.4641i	0.197974	−	0.738847i
$695$		0			0
$696$	20.5359	+	20.5359i	0.778411	+	0.778411i
$697$		−	1.60770i		−	0.0608958i
$698$	40.0526	+	10.7321i	1.51601	+	0.406214i
$699$	39.7128			1.50208
$700$		0			0
$701$	3.78461			0.142943			0.0714714	−	0.997443i	$-0.477231\pi$
$701$	3.78461			0.142943			0.0714714	+	0.997443i	$0.477231\pi$
$702$	45.8827	+	12.2942i	1.73173	+	0.464016i
$703$			15.2154i			0.573859i
$704$	29.8564			1.12526
$705$		0			0
$706$	−4.90192	+	18.2942i	−0.184486	+	0.688512i
$707$	−14.7846	−	17.0718i	−0.556032	−	0.642051i
$708$	6.00000	−	10.3923i	0.225494	−	0.390567i
$709$	−21.0000			−0.788672			−0.394336	−	0.918966i	$-0.629025\pi$
$709$	−21.0000			−0.788672			−0.394336	+	0.918966i	$0.629025\pi$
$710$		0			0
$711$		0			0
$712$	−18.9282	−	18.9282i	−0.709364	−	0.709364i
$713$	32.7846			1.22779
$714$	2.70577	−	1.31347i	0.101261	−	0.0491552i
$715$		0			0
$716$	−14.3923	+	24.9282i	−0.537866	+	0.931611i
$717$	−48.4641			−1.80993
$718$	12.7321	+	3.41154i	0.475156	+	0.127318i
$719$	−45.4641			−1.69552			−0.847762	−	0.530376i	$-0.822051\pi$
$719$	−45.4641			−1.69552			−0.847762	+	0.530376i	$0.822051\pi$
$720$		0			0
$721$	−29.7846	−	34.3923i	−1.10924	−	1.28084i
$722$	6.22243	−	23.2224i	0.231575	−	0.864249i
$723$	7.60770			0.282933
$724$	−12.9282	+	22.3923i	−0.480473	+	0.832203i
$725$		0			0
$726$	6.92820	+	1.85641i	0.257130	+	0.0688977i
$727$		−	34.3923i		−	1.27554i	−0.770227	−	0.637770i	$-0.779857\pi$
$727$		−	34.3923i		−	1.27554i	0.770227	−	0.637770i	$-0.220143\pi$
$728$	−3.46410	+	48.2487i	−0.128388	+	1.78822i
$729$	−27.0000			−1.00000
$730$		0			0
$731$	0.928203			0.0343308
$732$	7.60770	+	4.39230i	0.281189	+	0.162344i
$733$	−18.4641			−0.681987			−0.340994	−	0.940066i	$-0.610763\pi$
$733$	−18.4641			−0.681987			−0.340994	+	0.940066i	$0.610763\pi$
$734$	49.3468	+	13.2224i	1.82142	+	0.488049i
$735$		0			0
$736$	−29.8564	+	8.00000i	−1.10052	+	0.294884i
$737$		−	12.9282i		−	0.476216i
$738$		0			0
$739$			7.73205i			0.284428i	0.989836	+	0.142214i	$0.0454221\pi$
$739$			7.73205i			0.284428i	−0.989836	+	0.142214i	$0.954578\pi$
$740$		0			0
$741$		−	67.1769i		−	2.46781i
$742$	6.73205	−	3.26795i	0.247141	−	0.119970i
$743$	9.60770			0.352472			0.176236	−	0.984348i	$-0.443608\pi$
$743$	9.60770			0.352472			0.176236	+	0.984348i	$0.443608\pi$
$744$	−20.7846	−	20.7846i	−0.762001	−	0.762001i
$745$		0			0
$746$	33.3205	+	8.92820i	1.21995	+	0.326885i
$747$		0			0
$748$	1.73205	−	3.00000i	0.0633300	−	0.109691i
$749$	36.7846	−	31.8564i	1.34408	−	1.16401i
$750$		0			0
$751$			5.58846i			0.203926i	0.994788	+	0.101963i	$0.0325123\pi$
$751$			5.58846i			0.203926i	−0.994788	+	0.101963i	$0.967488\pi$
$752$	6.00000	−	3.46410i	0.218797	−	0.126323i
$753$		−	3.21539i		−	0.117175i
$754$	−14.0263	+	52.3468i	−0.510807	+	1.90636i
$755$		0			0
$756$	−5.19615	−	27.0000i	−0.188982	−	0.981981i
$757$			10.1436i			0.368675i	0.982863	+	0.184338i	$0.0590140\pi$
$757$			10.1436i			0.368675i	−0.982863	+	0.184338i	$0.940986\pi$
$758$	−36.0526	−	9.66025i	−1.30949	−	0.350876i
$759$	−35.3205			−1.28205
$760$		0			0
$761$		−	6.24871i		−	0.226516i	−0.993566	−	0.113258i	$-0.963871\pi$
$761$		−	6.24871i		−	0.226516i	0.993566	−	0.113258i	$-0.0361286\pi$
$762$	−20.1962	−	5.41154i	−0.731629	−	0.196040i
$763$	31.8564	−	27.5885i	1.15328	−	0.998769i
$764$	−3.19615	+	5.53590i	−0.115633	+	0.200282i
$765$		0			0
$766$	−28.0526	−	7.51666i	−1.01358	−	0.271588i
$767$	22.3923			0.808539
$768$	24.0000	+	13.8564i	0.866025	+	0.500000i
$769$			18.0000i			0.649097i	0.945869	+	0.324548i	$0.105212\pi$
$769$			18.0000i			0.649097i	−0.945869	+	0.324548i	$0.894788\pi$
$770$		0			0
$771$		−	10.3923i		−	0.374270i
$772$	2.53590	−	4.39230i	0.0912690	−	0.158083i
$773$	12.4641			0.448303			0.224151	−	0.974554i	$-0.428039\pi$
$773$	12.4641			0.448303			0.224151	+	0.974554i	$0.428039\pi$
$774$		0			0
$775$		0			0
$776$	−14.7846	+	14.7846i	−0.530737	+	0.530737i
$777$	8.78461	−	7.60770i	0.315146	−	0.272925i
$778$	−2.50962	+	9.36603i	−0.0899742	+	0.335788i
$779$			20.7846i			0.744686i
$780$		0			0
$781$	−2.00000			−0.0715656

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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 - 1.36603i) q^{2} -1.73205i q^{3} +(-1.73205 - 1.00000i) q^{4} +(-2.36603 - 0.633975i) q^{6} +(-2.00000 + 1.73205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})\)	\(q+(0.366025 - 1.36603i) q^{2} -1.73205i q^{3} +(-1.73205 - 1.00000i) q^{4} +(-2.36603 - 0.633975i) q^{6} +(-2.00000 + 1.73205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +3.73205i q^{11} +(-1.73205 + 3.00000i) q^{12} -6.46410 q^{13} +(1.63397 + 3.36603i) q^{14} +(2.00000 + 3.46410i) q^{16} +0.464102 q^{17} -6.00000 q^{19} +(3.00000 + 3.46410i) q^{21} +(5.09808 + 1.36603i) q^{22} -5.46410 q^{23} +(3.46410 + 3.46410i) q^{24} +(-2.36603 + 8.83013i) q^{26} -5.19615i q^{27} +(5.19615 - 1.00000i) q^{28} +5.92820 q^{29} -6.00000 q^{31} +(5.46410 - 1.46410i) q^{32} +6.46410 q^{33} +(0.169873 - 0.633975i) q^{34} -2.53590i q^{37} +(-2.19615 + 8.19615i) q^{38} +11.1962i q^{39} -3.46410i q^{41} +(5.83013 - 2.83013i) q^{42} +2.00000 q^{43} +(3.73205 - 6.46410i) q^{44} +(-2.00000 + 7.46410i) q^{46} -1.73205i q^{47} +(6.00000 - 3.46410i) q^{48} +(1.00000 - 6.92820i) q^{49} -0.803848i q^{51} +(11.1962 + 6.46410i) q^{52} -2.00000i q^{53} +(-7.09808 - 1.90192i) q^{54} +(0.535898 - 7.46410i) q^{56} +10.3923i q^{57} +(2.16987 - 8.09808i) q^{58} -3.46410 q^{59} -2.53590i q^{61} +(-2.19615 + 8.19615i) q^{62} -8.00000i q^{64} +(2.36603 - 8.83013i) q^{66} -3.46410 q^{67} +(-0.803848 - 0.464102i) q^{68} +9.46410i q^{69} +0.535898i q^{71} +0.928203 q^{73} +(-3.46410 - 0.928203i) q^{74} +(10.3923 + 6.00000i) q^{76} +(-6.46410 - 7.46410i) q^{77} +(15.2942 + 4.09808i) q^{78} +2.66025i q^{79} -9.00000 q^{81} +(-4.73205 - 1.26795i) q^{82} -8.53590i q^{83} +(-1.73205 - 9.00000i) q^{84} +(0.732051 - 2.73205i) q^{86} -10.2679i q^{87} +(-7.46410 - 7.46410i) q^{88} +9.46410i q^{89} +(12.9282 - 11.1962i) q^{91} +(9.46410 + 5.46410i) q^{92} +10.3923i q^{93} +(-2.36603 - 0.633975i) q^{94} +(-2.53590 - 9.46410i) q^{96} +7.39230 q^{97} +(-9.09808 - 3.90192i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 6 q^{6} - 8 q^{7} - 8 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 6 * q^6 - 8 * q^7 - 8 * q^8	\( 4 q - 2 q^{2} - 6 q^{6} - 8 q^{7} - 8 q^{8} - 12 q^{13} + 10 q^{14} + 8 q^{16} - 12 q^{17} - 24 q^{19} + 12 q^{21} + 10 q^{22} - 8 q^{23} - 6 q^{26} - 4 q^{29} - 24 q^{31} + 8 q^{32} + 12 q^{33} + 18 q^{34} + 12 q^{38} + 6 q^{42} + 8 q^{43} + 8 q^{44} - 8 q^{46} + 24 q^{48} + 4 q^{49} + 24 q^{52} - 18 q^{54} + 16 q^{56} + 26 q^{58} + 12 q^{62} + 6 q^{66} - 24 q^{68} - 24 q^{73} - 12 q^{77} + 30 q^{78} - 36 q^{81} - 12 q^{82} - 4 q^{86} - 16 q^{88} + 24 q^{91} + 24 q^{92} - 6 q^{94} - 24 q^{96} - 12 q^{97} - 26 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 6 * q^6 - 8 * q^7 - 8 * q^8 - 12 * q^13 + 10 * q^14 + 8 * q^16 - 12 * q^17 - 24 * q^19 + 12 * q^21 + 10 * q^22 - 8 * q^23 - 6 * q^26 - 4 * q^29 - 24 * q^31 + 8 * q^32 + 12 * q^33 + 18 * q^34 + 12 * q^38 + 6 * q^42 + 8 * q^43 + 8 * q^44 - 8 * q^46 + 24 * q^48 + 4 * q^49 + 24 * q^52 - 18 * q^54 + 16 * q^56 + 26 * q^58 + 12 * q^62 + 6 * q^66 - 24 * q^68 - 24 * q^73 - 12 * q^77 + 30 * q^78 - 36 * q^81 - 12 * q^82 - 4 * q^86 - 16 * q^88 + 24 * q^91 + 24 * q^92 - 6 * q^94 - 24 * q^96 - 12 * q^97 - 26 * q^98

Introduction

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