LMFDB - Embedded newform 104.2.b.c.53.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [104,2,Mod(53,104)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("104.53"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(104, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 104 = 2^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	104.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.830444181021$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.399424.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			53.4
Root			$0.264658 - 1.38923i$ of defining polynomial
Character	$\chi$	$=$	104.53
Dual form			104.2.b.c.53.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.264658 + 1.38923i) q^{2} +3.24914i q^{3} +(-1.85991 - 0.735342i) q^{4} -1.00000i q^{5} +(-4.51380 - 0.859912i) q^{6} +3.24914 q^{7} +(1.51380 - 2.38923i) q^{8} -7.55691 q^{9} +(1.38923 + 0.264658i) q^{10} -1.05863i q^{11} +(2.38923 - 6.04312i) q^{12} +1.00000i q^{13} +(-0.859912 + 4.51380i) q^{14} +3.24914 q^{15} +(2.91855 + 2.73534i) q^{16} +1.00000 q^{17} +(2.00000 - 10.4983i) q^{18} +4.00000i q^{19} +(-0.735342 + 1.85991i) q^{20} +10.5569i q^{21} +(1.47068 + 0.280176i) q^{22} -2.94137 q^{23} +(7.76294 + 4.91855i) q^{24} +4.00000 q^{25} +(-1.38923 - 0.264658i) q^{26} -14.8061i q^{27} +(-6.04312 - 2.38923i) q^{28} -7.43965i q^{29} +(-0.859912 + 4.51380i) q^{30} +5.05863 q^{31} +(-4.57243 + 3.33060i) q^{32} +3.43965 q^{33} +(-0.264658 + 1.38923i) q^{34} -3.24914i q^{35} +(14.0552 + 5.55691i) q^{36} -6.55691i q^{37} +(-5.55691 - 1.05863i) q^{38} -3.24914 q^{39} +(-2.38923 - 1.51380i) q^{40} -9.43965 q^{41} +(-14.6660 - 2.79397i) q^{42} +0.307774i q^{43} +(-0.778457 + 1.96896i) q^{44} +7.55691i q^{45} +(0.778457 - 4.08623i) q^{46} +6.80605 q^{47} +(-8.88751 + 9.48276i) q^{48} +3.55691 q^{49} +(-1.05863 + 5.55691i) q^{50} +3.24914i q^{51} +(0.735342 - 1.85991i) q^{52} +1.55691i q^{53} +(20.5690 + 3.91855i) q^{54} -1.05863 q^{55} +(4.91855 - 7.76294i) q^{56} -12.9966 q^{57} +(10.3354 + 1.96896i) q^{58} +5.67418i q^{59} +(-6.04312 - 2.38923i) q^{60} -9.67418i q^{61} +(-1.33881 + 7.02760i) q^{62} -24.5535 q^{63} +(-3.41683 - 7.23362i) q^{64} +1.00000 q^{65} +(-0.910331 + 4.77846i) q^{66} +1.50172i q^{67} +(-1.85991 - 0.735342i) q^{68} -9.55691i q^{69} +(4.51380 + 0.859912i) q^{70} -5.36641 q^{71} +(-11.4396 + 18.0552i) q^{72} +3.55691 q^{73} +(9.10905 + 1.73534i) q^{74} +12.9966i q^{75} +(2.94137 - 7.43965i) q^{76} -3.43965i q^{77} +(0.859912 - 4.51380i) q^{78} -6.73281 q^{79} +(2.73534 - 2.91855i) q^{80} +25.4362 q^{81} +(2.49828 - 13.1138i) q^{82} -2.49828i q^{83} +(7.76294 - 19.6349i) q^{84} -1.00000i q^{85} +(-0.427568 - 0.0814549i) q^{86} +24.1725 q^{87} +(-2.52932 - 1.60256i) q^{88} +2.11727 q^{89} +(-10.4983 - 2.00000i) q^{90} +3.24914i q^{91} +(5.47068 + 2.16291i) q^{92} +16.4362i q^{93} +(-1.80128 + 9.45517i) q^{94} +4.00000 q^{95} +(-10.8216 - 14.8565i) q^{96} +7.67418 q^{97} +(-0.941367 + 4.94137i) q^{98} +8.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 2 q^{4} - 10 q^{6} + 2 q^{7} - 8 q^{8} - 12 q^{9} + 6 q^{12} + 4 q^{14} + 2 q^{15} + 10 q^{16} + 6 q^{17} + 12 q^{18} - 4 q^{20} + 8 q^{22} - 16 q^{23} + 12 q^{24} + 24 q^{25} - 20 q^{28}+ \cdots - 4 q^{98}+O(q^{100}) $ 6 * q - 2 * q^2 - 2 * q^4 - 10 * q^6 + 2 * q^7 - 8 * q^8 - 12 * q^9 + 6 * q^12 + 4 * q^14 + 2 * q^15 + 10 * q^16 + 6 * q^17 + 12 * q^18 - 4 * q^20 + 8 * q^22 - 16 * q^23 + 12 * q^24 + 24 * q^25 - 20 * q^28 + 4 * q^30 + 32 * q^31 - 12 * q^32 - 16 * q^33 - 2 * q^34 + 16 * q^36 - 2 * q^39 - 6 * q^40 - 20 * q^41 - 28 * q^42 + 12 * q^44 - 12 * q^46 - 10 * q^47 - 10 * q^48 - 12 * q^49 - 8 * q^50 + 4 * q^52 + 38 * q^54 - 8 * q^55 + 22 * q^56 - 8 * q^57 + 12 * q^58 - 20 * q^60 - 28 * q^62 - 44 * q^63 + 22 * q^64 + 6 * q^65 + 32 * q^66 - 2 * q^68 + 10 * q^70 - 18 * q^71 - 32 * q^72 - 12 * q^73 + 28 * q^74 + 16 * q^76 - 4 * q^78 - 12 * q^79 + 16 * q^80 + 46 * q^81 - 20 * q^82 + 12 * q^84 - 18 * q^86 + 80 * q^87 - 16 * q^88 + 16 * q^89 - 28 * q^90 + 32 * q^92 + 24 * q^95 - 32 * q^96 + 16 * q^97 - 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/104\mathbb{Z}\right)^\times$.

$n$	$41$	$53$	$79$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−0.264658	+	1.38923i	−0.187142	+	0.982333i
$2$	−0.264658	+	1.38923i	−0.187142	+	0.982333i
$3$			3.24914i			1.87589i	0.346781	+	0.937946i	$0.387275\pi$
$3$			3.24914i			1.87589i	−0.346781	+	0.937946i	$0.612725\pi$
$4$	−1.85991	−	0.735342i	−0.929956	−	0.367671i
$5$		−	1.00000i		−	0.447214i	−0.974679	−	0.223607i	$-0.928217\pi$
$5$		−	1.00000i		−	0.447214i	0.974679	−	0.223607i	$-0.0717831\pi$
$6$	−4.51380	−	0.859912i	−1.84275	−	0.351058i
$7$	3.24914			1.22806			0.614030	−	0.789283i	$-0.289547\pi$
$7$	3.24914			1.22806			0.614030	+	0.789283i	$0.289547\pi$
$8$	1.51380	−	2.38923i	0.535209	−	0.844720i
$9$	−7.55691			−2.51897
$10$	1.38923	+	0.264658i	0.439313	+	0.0836923i
$11$		−	1.05863i		−	0.319190i	−0.987183	−	0.159595i	$-0.948981\pi$
$11$		−	1.05863i		−	0.319190i	0.987183	−	0.159595i	$-0.0510188\pi$
$12$	2.38923	−	6.04312i	0.689711	−	1.74450i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	−0.859912	+	4.51380i	−0.229821	+	1.20636i
$15$	3.24914			0.838924
$16$	2.91855	+	2.73534i	0.729636	+	0.683835i
$17$	1.00000			0.242536			0.121268	−	0.992620i	$-0.461304\pi$
$17$	1.00000			0.242536			0.121268	+	0.992620i	$0.461304\pi$
$18$	2.00000	−	10.4983i	0.471405	−	2.47447i
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$	−0.735342	+	1.85991i	−0.164427	+	0.415889i
$21$			10.5569i			2.30371i
$22$	1.47068	+	0.280176i	0.313551	+	0.0597337i
$23$	−2.94137			−0.613317			−0.306659	−	0.951820i	$-0.599211\pi$
$23$	−2.94137			−0.613317			−0.306659	+	0.951820i	$0.599211\pi$
$24$	7.76294	+	4.91855i	1.58460	+	1.00399i
$25$	4.00000			0.800000
$26$	−1.38923	−	0.264658i	−0.272450	−	0.0519038i
$27$		−	14.8061i		−	2.84943i
$28$	−6.04312	−	2.38923i	−1.14204	−	0.451522i
$29$		−	7.43965i		−	1.38151i	−0.723090	−	0.690754i	$-0.757279\pi$
$29$		−	7.43965i		−	1.38151i	0.723090	−	0.690754i	$-0.242721\pi$
$30$	−0.859912	+	4.51380i	−0.156998	+	0.824103i
$31$	5.05863			0.908557			0.454279	−	0.890860i	$-0.349897\pi$
$31$	5.05863			0.908557			0.454279	+	0.890860i	$0.349897\pi$
$32$	−4.57243	+	3.33060i	−0.808299	+	0.588772i
$33$	3.43965			0.598766
$34$	−0.264658	+	1.38923i	−0.0453885	+	0.238251i
$35$		−	3.24914i		−	0.549205i
$36$	14.0552	+	5.55691i	2.34253	+	0.926152i
$37$		−	6.55691i		−	1.07795i	−0.842322	−	0.538975i	$-0.818812\pi$
$37$		−	6.55691i		−	1.07795i	0.842322	−	0.538975i	$-0.181188\pi$
$38$	−5.55691	−	1.05863i	−0.901451	−	0.171733i
$39$	−3.24914			−0.520279
$40$	−2.38923	−	1.51380i	−0.377770	−	0.239353i
$41$	−9.43965			−1.47423			−0.737113	−	0.675770i	$-0.763811\pi$
$41$	−9.43965			−1.47423			−0.737113	+	0.675770i	$0.763811\pi$
$42$	−14.6660	−	2.79397i	−2.26301	−	0.431120i
$43$			0.307774i			0.0469350i	0.999725	+	0.0234675i	$0.00747063\pi$
$43$			0.307774i			0.0469350i	−0.999725	+	0.0234675i	$0.992529\pi$
$44$	−0.778457	+	1.96896i	−0.117357	+	0.296833i
$45$			7.55691i			1.12652i
$46$	0.778457	−	4.08623i	0.114777	−	0.602482i
$47$	6.80605			0.992765			0.496383	−	0.868104i	$-0.334661\pi$
$47$	6.80605			0.992765			0.496383	+	0.868104i	$0.334661\pi$
$48$	−8.88751	+	9.48276i	−1.28280	+	1.36872i
$49$	3.55691			0.508131
$50$	−1.05863	+	5.55691i	−0.149713	+	0.785866i
$51$			3.24914i			0.454971i
$52$	0.735342	−	1.85991i	0.101974	−	0.257923i
$53$			1.55691i			0.213859i	0.994267	+	0.106929i	$0.0341019\pi$
$53$			1.55691i			0.213859i	−0.994267	+	0.106929i	$0.965898\pi$
$54$	20.5690	+	3.91855i	2.79909	+	0.533246i
$55$	−1.05863			−0.142746
$56$	4.91855	−	7.76294i	0.657268	−	1.03737i
$57$	−12.9966			−1.72144
$58$	10.3354	+	1.96896i	1.35710	+	0.258538i
$59$			5.67418i			0.738715i	0.929287	+	0.369358i	$0.120422\pi$
$59$			5.67418i			0.738715i	−0.929287	+	0.369358i	$0.879578\pi$
$60$	−6.04312	−	2.38923i	−0.780163	−	0.308448i
$61$		−	9.67418i		−	1.23865i	−0.785134	−	0.619326i	$-0.787406\pi$
$61$		−	9.67418i		−	1.23865i	0.785134	−	0.619326i	$-0.212594\pi$
$62$	−1.33881	+	7.02760i	−0.170029	+	0.892506i
$63$	−24.5535			−3.09345
$64$	−3.41683	−	7.23362i	−0.427103	−	0.904203i
$65$	1.00000			0.124035
$66$	−0.910331	+	4.77846i	−0.112054	+	0.588187i
$67$			1.50172i			0.183464i	0.995784	+	0.0917321i	$0.0292403\pi$
$67$			1.50172i			0.183464i	−0.995784	+	0.0917321i	$0.970760\pi$
$68$	−1.85991	−	0.735342i	−0.225547	−	0.0891733i
$69$		−	9.55691i		−	1.15052i
$70$	4.51380	+	0.859912i	0.539502	+	0.102779i
$71$	−5.36641			−0.636875			−0.318438	−	0.947944i	$-0.603158\pi$
$71$	−5.36641			−0.636875			−0.318438	+	0.947944i	$0.603158\pi$
$72$	−11.4396	+	18.0552i	−1.34818	+	2.12783i
$73$	3.55691			0.416305			0.208153	−	0.978096i	$-0.433255\pi$
$73$	3.55691			0.416305			0.208153	+	0.978096i	$0.433255\pi$
$74$	9.10905	+	1.73534i	1.05891	+	0.201729i
$75$			12.9966i			1.50071i
$76$	2.94137	−	7.43965i	0.337398	−	0.853386i
$77$		−	3.43965i		−	0.391984i
$78$	0.859912	−	4.51380i	0.0973659	−	0.511087i
$79$	−6.73281			−0.757501			−0.378750	−	0.925499i	$-0.623646\pi$
$79$	−6.73281			−0.757501			−0.378750	+	0.925499i	$0.623646\pi$
$80$	2.73534	−	2.91855i	0.305821	−	0.326303i
$81$	25.4362			2.82625
$82$	2.49828	−	13.1138i	0.275889	−	1.44818i
$83$		−	2.49828i		−	0.274222i	−0.990556	−	0.137111i	$-0.956218\pi$
$83$		−	2.49828i		−	0.274222i	0.990556	−	0.137111i	$-0.0437817\pi$
$84$	7.76294	−	19.6349i	0.847006	−	2.14235i
$85$		−	1.00000i		−	0.108465i
$86$	−0.427568	−	0.0814549i	−0.0461058	−	0.00878350i
$87$	24.1725			2.59156
$88$	−2.52932	−	1.60256i	−0.269626	−	0.170833i
$89$	2.11727			0.224430			0.112215	−	0.993684i	$-0.464205\pi$
$89$	2.11727			0.224430			0.112215	+	0.993684i	$0.464205\pi$
$90$	−10.4983	−	2.00000i	−1.10662	−	0.210819i
$91$			3.24914i			0.340602i
$92$	5.47068	+	2.16291i	0.570358	+	0.225499i
$93$			16.4362i			1.70436i
$94$	−1.80128	+	9.45517i	−0.185788	+	0.975226i
$95$	4.00000			0.410391
$96$	−10.8216	−	14.8565i	−1.10447	−	1.51628i
$97$	7.67418			0.779195			0.389597	−	0.920985i	$-0.372614\pi$
$97$	7.67418			0.779195			0.389597	+	0.920985i	$0.372614\pi$
$98$	−0.941367	+	4.94137i	−0.0950924	+	0.499153i
$99$			8.00000i			0.804030i
$100$	−7.43965	−	2.94137i	−0.743965	−	0.294137i
$101$		−	3.11383i		−	0.309838i	−0.987927	−	0.154919i	$-0.950488\pi$
$101$		−	3.11383i		−	0.309838i	0.987927	−	0.154919i	$-0.0495116\pi$
$102$	−4.51380	−	0.859912i	−0.446933	−	0.0851440i
$103$	−17.6121			−1.73537			−0.867686	−	0.497112i	$-0.834394\pi$
$103$	−17.6121			−1.73537			−0.867686	+	0.497112i	$0.834394\pi$
$104$	2.38923	+	1.51380i	0.234283	+	0.148440i
$105$	10.5569			1.03025
$106$	−2.16291	−	0.412050i	−0.210080	−	0.0400219i
$107$		−	10.9414i		−	1.05774i	−0.848702	−	0.528871i	$-0.822616\pi$
$107$		−	10.9414i		−	1.05774i	0.848702	−	0.528871i	$-0.177384\pi$
$108$	−10.8875	+	27.5380i	−1.04765	+	2.64984i
$109$			10.3224i			0.988705i	0.869262	+	0.494352i	$0.164595\pi$
$109$			10.3224i			0.988705i	−0.869262	+	0.494352i	$0.835405\pi$
$110$	0.280176	−	1.47068i	0.0267137	−	0.140224i
$111$	21.3043			2.02212
$112$	9.48276	+	8.88751i	0.896037	+	0.839791i
$113$	−17.1138			−1.60993			−0.804967	−	0.593320i	$-0.797817\pi$
$113$	−17.1138			−1.60993			−0.804967	+	0.593320i	$0.797817\pi$
$114$	3.43965	−	18.0552i	0.322153	−	1.69102i
$115$			2.94137i			0.274284i
$116$	−5.47068	+	13.8371i	−0.507940	+	1.28474i
$117$		−	7.55691i		−	0.698637i
$118$	−7.88273	−	1.50172i	−0.725664	−	0.138244i
$119$	3.24914			0.297848
$120$	4.91855	−	7.76294i	0.449000	−	0.708656i
$121$	9.87930			0.898118
$122$	13.4396	+	2.56035i	1.21677	+	0.231803i
$123$		−	30.6707i		−	2.76549i
$124$	−9.40861	−	3.71982i	−0.844918	−	0.334050i
$125$		−	9.00000i		−	0.804984i
$126$	6.49828	−	34.1104i	0.578913	−	3.03880i
$127$	−15.9379			−1.41426			−0.707131	−	0.707082i	$-0.750011\pi$
$127$	−15.9379			−1.41426			−0.707131	+	0.707082i	$0.750011\pi$
$128$	10.9534	−	2.83231i	0.968157	−	0.250344i
$129$	−1.00000			−0.0880451
$130$	−0.264658	+	1.38923i	−0.0232121	+	0.121843i
$131$			7.69223i			0.672073i	0.941849	+	0.336036i	$0.109087\pi$
$131$			7.69223i			0.672073i	−0.941849	+	0.336036i	$0.890913\pi$
$132$	−6.39744	−	2.52932i	−0.556826	−	0.220149i
$133$			12.9966i			1.12694i
$134$	−2.08623	−	0.397442i	−0.180223	−	0.0343338i
$135$	−14.8061			−1.27430
$136$	1.51380	−	2.38923i	0.129807	−	0.204875i
$137$	5.32238			0.454722			0.227361	−	0.973811i	$-0.426990\pi$
$137$	5.32238			0.454722			0.227361	+	0.973811i	$0.426990\pi$
$138$	13.2767	+	2.52932i	1.13019	+	0.215310i
$139$			12.4802i			1.05856i	0.848447	+	0.529280i	$0.177538\pi$
$139$			12.4802i			1.05856i	−0.848447	+	0.529280i	$0.822462\pi$
$140$	−2.38923	+	6.04312i	−0.201927	+	0.510736i
$141$			22.1138i			1.86232i
$142$	1.42026	−	7.45517i	0.119186	−	0.625624i
$143$	1.05863			0.0885274
$144$	−22.0552	−	20.6707i	−1.83793	−	1.72256i
$145$	−7.43965			−0.617829
$146$	−0.941367	+	4.94137i	−0.0779081	+	0.408950i
$147$			11.5569i			0.953198i
$148$	−4.82157	+	12.1953i	−0.396331	+	1.00245i
$149$			9.11383i			0.746634i	0.927704	+	0.373317i	$0.121780\pi$
$149$			9.11383i			0.746634i	−0.927704	+	0.373317i	$0.878220\pi$
$150$	−18.0552	−	3.43965i	−1.47420	−	0.280846i
$151$	−15.4216			−1.25499			−0.627496	−	0.778620i	$-0.715920\pi$
$151$	−15.4216			−1.25499			−0.627496	+	0.778620i	$0.715920\pi$
$152$	9.55691	+	6.05520i	0.775168	+	0.491141i
$153$	−7.55691			−0.610940
$154$	4.77846	+	0.910331i	0.385059	+	0.0733566i
$155$		−	5.05863i		−	0.406319i
$156$	6.04312	+	2.38923i	0.483836	+	0.191291i
$157$			3.79145i			0.302590i	0.988489	+	0.151295i	$0.0483444\pi$
$157$			3.79145i			0.302590i	−0.988489	+	0.151295i	$0.951656\pi$
$158$	1.78189	−	9.35342i	0.141760	−	0.744118i
$159$	−5.05863			−0.401176
$160$	3.33060	+	4.57243i	0.263307	+	0.361482i
$161$	−9.55691			−0.753190
$162$	−6.73190	+	35.3367i	−0.528908	+	2.77631i
$163$			4.17246i			0.326812i	0.986559	+	0.163406i	$0.0522481\pi$
$163$			4.17246i			0.326812i	−0.986559	+	0.163406i	$0.947752\pi$
$164$	17.5569	+	6.94137i	1.37096	+	0.542030i
$165$		−	3.43965i		−	0.267776i
$166$	3.47068	+	0.661191i	0.269377	+	0.0513184i
$167$	14.2897			1.10577			0.552886	−	0.833257i	$-0.313526\pi$
$167$	14.2897			1.10577			0.552886	+	0.833257i	$0.313526\pi$
$168$	25.2229	+	15.9810i	1.94599	+	1.23296i
$169$	−1.00000			−0.0769231
$170$	1.38923	+	0.264658i	0.106549	+	0.0202984i
$171$		−	30.2277i		−	2.31157i
$172$	0.226319	−	0.572432i	0.0172566	−	0.0436475i
$173$		−	6.99656i		−	0.531939i	−0.963981	−	0.265969i	$-0.914308\pi$
$173$		−	6.99656i		−	0.531939i	0.963981	−	0.265969i	$-0.0856920\pi$
$174$	−6.39744	+	33.5811i	−0.484989	+	2.54577i
$175$	12.9966			0.982448
$176$	2.89572	−	3.08967i	0.218273	−	0.232893i
$177$	−18.4362			−1.38575
$178$	−0.560352	+	2.94137i	−0.0420002	+	0.220465i
$179$			17.7474i			1.32650i	0.748396	+	0.663252i	$0.230824\pi$
$179$			17.7474i			1.32650i	−0.748396	+	0.663252i	$0.769176\pi$
$180$	5.55691	−	14.0552i	0.414188	−	1.04761i
$181$		−	8.11727i		−	0.603352i	−0.953411	−	0.301676i	$-0.902454\pi$
$181$		−	8.11727i		−	0.603352i	0.953411	−	0.301676i	$-0.0975460\pi$
$182$	−4.51380	−	0.859912i	−0.334585	−	0.0637409i
$183$	31.4328			2.32358
$184$	−4.45264	+	7.02760i	−0.328253	+	0.518081i
$185$	−6.55691			−0.482074
$186$	−22.8337	−	4.34998i	−1.67424	−	0.318956i
$187$		−	1.05863i		−	0.0774149i
$188$	−12.6587	−	5.00478i	−0.923228	−	0.365011i
$189$		−	48.1070i		−	3.49927i
$190$	−1.05863	+	5.55691i	−0.0768013	+	0.403141i
$191$	−19.9379			−1.44266			−0.721329	−	0.692593i	$-0.756468\pi$
$191$	−19.9379			−1.44266			−0.721329	+	0.692593i	$0.756468\pi$
$192$	23.5031	−	11.1017i	1.69619	−	0.801200i
$193$	4.11727			0.296367			0.148184	−	0.988960i	$-0.452657\pi$
$193$	4.11727			0.296367			0.148184	+	0.988960i	$0.452657\pi$
$194$	−2.03104	+	10.6612i	−0.145820	+	0.765429i
$195$			3.24914i			0.232676i
$196$	−6.61555	−	2.61555i	−0.472539	−	0.186825i
$197$			10.7914i			0.768859i	0.923154	+	0.384429i	$0.125602\pi$
$197$			10.7914i			0.768859i	−0.923154	+	0.384429i	$0.874398\pi$
$198$	−11.1138	−	2.11727i	−0.789825	−	0.150468i
$199$	0.615547			0.0436350			0.0218175	−	0.999762i	$-0.493055\pi$
$199$	0.615547			0.0436350			0.0218175	+	0.999762i	$0.493055\pi$
$200$	6.05520	−	9.55691i	0.428167	−	0.675776i
$201$	−4.87930			−0.344159
$202$	4.32582	+	0.824101i	0.304364	+	0.0579835i
$203$		−	24.1725i		−	1.69657i
$204$	2.38923	−	6.04312i	0.167279	−	0.423103i
$205$			9.43965i			0.659294i
$206$	4.66119	−	24.4672i	0.324761	−	1.70471i
$207$	22.2277			1.54493
$208$	−2.73534	+	2.91855i	−0.189662	+	0.202365i
$209$	4.23453			0.292909
$210$	−2.79397	+	14.6660i	−0.192803	+	1.01205i
$211$			1.80949i			0.124571i	0.998058	+	0.0622853i	$0.0198389\pi$
$211$			1.80949i			0.124571i	−0.998058	+	0.0622853i	$0.980161\pi$
$212$	1.14486	−	2.89572i	0.0786296	−	0.198879i
$213$		−	17.4362i		−	1.19471i
$214$	15.2001	+	2.89572i	1.03905	+	0.197948i
$215$	0.307774			0.0209900
$216$	−35.3750	−	22.4134i	−2.40697	−	1.52504i
$217$	16.4362			1.11576
$218$	−14.3401	−	2.73190i	−0.971237	−	0.185028i
$219$			11.5569i			0.780944i
$220$	1.96896	+	0.778457i	0.132748	+	0.0524836i
$221$			1.00000i			0.0672673i
$222$	−5.63837	+	29.5966i	−0.378423	+	1.98639i
$223$	−6.80605			−0.455767			−0.227884	−	0.973688i	$-0.573181\pi$
$223$	−6.80605			−0.455767			−0.227884	+	0.973688i	$0.573181\pi$
$224$	−14.8565	+	10.8216i	−0.992640	+	0.723047i
$225$	−30.2277			−2.01518
$226$	4.52932	−	23.7750i	0.301286	−	1.58149i
$227$		−	6.67074i		−	0.442753i	−0.975188	−	0.221376i	$-0.928945\pi$
$227$		−	6.67074i		−	0.442753i	0.975188	−	0.221376i	$-0.0710549\pi$
$228$	24.1725	+	9.55691i	1.60086	+	0.632922i
$229$		−	18.1138i		−	1.19700i	−0.801124	−	0.598498i	$-0.795765\pi$
$229$		−	18.1138i		−	1.19700i	0.801124	−	0.598498i	$-0.204235\pi$
$230$	−4.08623	−	0.778457i	−0.269438	−	0.0513299i
$231$	11.1759			0.735320
$232$	−17.7750	−	11.2621i	−1.16699	−	0.739395i
$233$	11.4362			0.749211			0.374606	−	0.927184i	$-0.377778\pi$
$233$	11.4362			0.749211			0.374606	+	0.927184i	$0.377778\pi$
$234$	10.4983	+	2.00000i	0.686294	+	0.130744i
$235$		−	6.80605i		−	0.443978i
$236$	4.17246	−	10.5535i	0.271604	−	0.686973i
$237$		−	21.8759i		−	1.42099i
$238$	−0.859912	+	4.51380i	−0.0557398	+	0.292586i
$239$	16.8613			1.09066			0.545332	−	0.838220i	$-0.316404\pi$
$239$	16.8613			1.09066			0.545332	+	0.838220i	$0.316404\pi$
$240$	9.48276	+	8.88751i	0.612110	+	0.573686i
$241$	−5.23109			−0.336964			−0.168482	−	0.985705i	$-0.553887\pi$
$241$	−5.23109			−0.336964			−0.168482	+	0.985705i	$0.553887\pi$
$242$	−2.61464	+	13.7246i	−0.168075	+	0.882251i
$243$			38.2277i			2.45231i
$244$	−7.11383	+	17.9931i	−0.455416	+	1.15189i
$245$		−	3.55691i		−	0.227243i
$246$	42.6087	+	8.11727i	2.71663	+	0.517538i
$247$	−4.00000			−0.254514
$248$	7.65775	−	12.0862i	0.486268	−	0.767476i
$249$	8.11727			0.514411
$250$	12.5031	+	2.38192i	0.790763	+	0.150646i
$251$			2.05520i			0.129723i	0.997894	+	0.0648614i	$0.0206605\pi$
$251$			2.05520i			0.129723i	−0.997894	+	0.0648614i	$0.979339\pi$
$252$	45.6673	+	18.0552i	2.87677	+	1.13737i
$253$			3.11383i			0.195765i
$254$	4.21811	−	22.1414i	0.264667	−	1.38928i
$255$	3.24914			0.203469
$256$	1.03581	+	15.9664i	0.0647382	+	0.997902i
$257$	−21.2277			−1.32414			−0.662072	−	0.749440i	$-0.730323\pi$
$257$	−21.2277			−1.32414			−0.662072	+	0.749440i	$0.730323\pi$
$258$	0.264658	−	1.38923i	0.0164769	−	0.0864896i
$259$		−	21.3043i		−	1.32379i
$260$	−1.85991	−	0.735342i	−0.115347	−	0.0456040i
$261$			56.2208i			3.47998i
$262$	−10.6863	−	2.03581i	−0.660199	−	0.125773i
$263$	23.5569			1.45258			0.726291	−	0.687388i	$-0.241243\pi$
$263$	23.5569			1.45258			0.726291	+	0.687388i	$0.241243\pi$
$264$	5.20693	−	8.21811i	0.320465	−	0.505789i
$265$	1.55691			0.0956405
$266$	−18.0552	−	3.43965i	−1.10704	−	0.210898i
$267$			6.87930i			0.421006i
$268$	1.10428	−	2.79307i	0.0674544	−	0.170614i
$269$			6.32582i			0.385692i	0.981229	+	0.192846i	$0.0617718\pi$
$269$			6.32582i			0.385692i	−0.981229	+	0.192846i	$0.938228\pi$
$270$	3.91855	−	20.5690i	0.238475	−	1.25179i
$271$	3.45769			0.210040			0.105020	−	0.994470i	$-0.466509\pi$
$271$	3.45769			0.210040			0.105020	+	0.994470i	$0.466509\pi$
$272$	2.91855	+	2.73534i	0.176963	+	0.165854i
$273$	−10.5569			−0.638934
$274$	−1.40861	+	7.39400i	−0.0850974	+	0.446688i
$275$		−	4.23453i		−	0.255352i
$276$	−7.02760	+	17.7750i	−0.423012	+	1.06993i
$277$			28.5535i			1.71561i	0.513974	+	0.857806i	$0.328173\pi$
$277$			28.5535i			1.71561i	−0.513974	+	0.857806i	$0.671827\pi$
$278$	−17.3379	−	3.30300i	−1.03986	−	0.198101i
$279$	−38.2277			−2.28863
$280$	−7.76294	−	4.91855i	−0.463924	−	0.293939i
$281$	24.9966			1.49117			0.745585	−	0.666411i	$-0.232170\pi$
$281$	24.9966			1.49117			0.745585	+	0.666411i	$0.232170\pi$
$282$	−30.7212	−	5.85261i	−1.82942	−	0.348518i
$283$		−	21.8207i		−	1.29710i	−0.761170	−	0.648552i	$-0.775375\pi$
$283$		−	21.8207i		−	1.29710i	0.761170	−	0.648552i	$-0.224625\pi$
$284$	9.98104	+	3.94614i	0.592266	+	0.234160i
$285$			12.9966i			0.769850i
$286$	−0.280176	+	1.47068i	−0.0165672	+	0.0869633i
$287$	−30.6707			−1.81044
$288$	34.5535	−	25.1690i	2.03608	−	1.48310i
$289$	−16.0000			−0.941176
$290$	1.96896	−	10.3354i	0.115622	−	0.606914i
$291$			24.9345i			1.46169i
$292$	−6.61555	−	2.61555i	−0.387146	−	0.153063i
$293$			27.4362i			1.60284i	0.598102	+	0.801420i	$0.295922\pi$
$293$			27.4362i			1.60284i	−0.598102	+	0.801420i	$0.704078\pi$
$294$	−16.0552	−	3.05863i	−0.936358	−	0.178383i
$295$	5.67418			0.330364
$296$	−15.6660	−	9.92585i	−0.910566	−	0.576928i
$297$	−15.6742			−0.909508
$298$	−12.6612	−	2.41205i	−0.733443	−	0.139726i
$299$		−	2.94137i		−	0.170104i
$300$	9.55691	−	24.1725i	0.551769	−	1.39560i
$301$			1.00000i			0.0576390i
$302$	4.08145	−	21.4241i	0.234861	−	1.23282i
$303$	10.1173			0.581222
$304$	−10.9414	+	11.6742i	−0.627530	+	0.669560i
$305$	−9.67418			−0.553942
$306$	2.00000	−	10.4983i	0.114332	−	0.600147i
$307$		−	26.6707i		−	1.52218i	−0.648646	−	0.761090i	$-0.724665\pi$
$307$		−	26.6707i		−	1.52218i	0.648646	−	0.761090i	$-0.275335\pi$
$308$	−2.52932	+	6.39744i	−0.144121	+	0.364528i
$309$		−	57.2242i		−	3.25537i
$310$	7.02760	+	1.33881i	0.399141	+	0.0760393i
$311$	6.87930			0.390089			0.195045	−	0.980794i	$-0.437515\pi$
$311$	6.87930			0.390089			0.195045	+	0.980794i	$0.437515\pi$
$312$	−4.91855	+	7.76294i	−0.278458	+	0.439490i
$313$	17.6707			0.998809			0.499405	−	0.866369i	$-0.333552\pi$
$313$	17.6707			0.998809			0.499405	+	0.866369i	$0.333552\pi$
$314$	−5.26719	−	1.00344i	−0.297245	−	0.0566273i
$315$			24.5535i			1.38343i
$316$	12.5224	+	4.95092i	0.704442	+	0.278511i
$317$			1.11383i			0.0625588i	0.999511	+	0.0312794i	$0.00995817\pi$
$317$			1.11383i			0.0625588i	−0.999511	+	0.0312794i	$0.990042\pi$
$318$	1.33881	−	7.02760i	0.0750767	−	0.394088i
$319$	−7.87586			−0.440963
$320$	−7.23362	+	3.41683i	−0.404372	+	0.191006i
$321$	35.5500			1.98421
$322$	2.52932	−	13.2767i	0.140953	−	0.739884i
$323$			4.00000i			0.222566i
$324$	−47.3091	−	18.7043i	−2.62828	−	1.03913i
$325$			4.00000i			0.221880i
$326$	−5.79650	−	1.10428i	−0.321039	−	0.0611602i
$327$	−33.5389			−1.85470
$328$	−14.2897	+	22.5535i	−0.789018	+	1.24531i
$329$	22.1138			1.21917
$330$	4.77846	+	0.910331i	0.263045	+	0.0501121i
$331$			18.4983i			1.01676i	0.861134	+	0.508379i	$0.169755\pi$
$331$			18.4983i			1.01676i	−0.861134	+	0.508379i	$0.830245\pi$
$332$	−1.83709	+	4.64658i	−0.100823	+	0.255014i
$333$			49.5500i			2.71533i
$334$	−3.78189	+	19.8517i	−0.206936	+	1.08624i
$335$	1.50172			0.0820477
$336$	−28.8768	+	30.8108i	−1.57536	+	1.68087i
$337$	−17.4362			−0.949811			−0.474905	−	0.880037i	$-0.657518\pi$
$337$	−17.4362			−0.949811			−0.474905	+	0.880037i	$0.657518\pi$
$338$	0.264658	−	1.38923i	0.0143955	−	0.0755641i
$339$		−	55.6052i		−	3.02006i
$340$	−0.735342	+	1.85991i	−0.0398795	+	0.100868i
$341$		−	5.35524i		−	0.290002i
$342$	41.9931	+	8.00000i	2.27073	+	0.432590i
$343$	−11.1871			−0.604045
$344$	0.735342	+	0.465907i	0.0396470	+	0.0251200i
$345$	−9.55691			−0.514527
$346$	9.71982	+	1.85170i	0.522541	+	0.0995479i
$347$		−	8.98539i		−	0.482361i	−0.970480	−	0.241181i	$-0.922465\pi$
$347$		−	8.98539i		−	0.482361i	0.970480	−	0.241181i	$-0.0775346\pi$
$348$	−44.9587	−	17.7750i	−2.41004	−	0.952841i
$349$			10.9931i			0.588448i	0.955736	+	0.294224i	$0.0950612\pi$
$349$			10.9931i			0.588448i	−0.955736	+	0.294224i	$0.904939\pi$
$350$	−3.43965	+	18.0552i	−0.183857	+	0.965091i
$351$	14.8061			0.790289
$352$	3.52588	+	4.84053i	0.187930	+	0.258001i
$353$	23.2311			1.23647			0.618233	−	0.785995i	$-0.287849\pi$
$353$	23.2311			1.23647			0.618233	+	0.785995i	$0.287849\pi$
$354$	4.87930	−	25.6121i	0.259332	−	1.36127i
$355$			5.36641i			0.284819i
$356$	−3.93793	−	1.55691i	−0.208710	−	0.0825163i
$357$			10.5569i			0.558731i
$358$	−24.6552	−	4.69700i	−1.30307	−	0.248244i
$359$	−11.2863			−0.595668			−0.297834	−	0.954618i	$-0.596264\pi$
$359$	−11.2863			−0.595668			−0.297834	+	0.954618i	$0.596264\pi$
$360$	18.0552	+	11.4396i	0.951592	+	0.602922i
$361$	3.00000			0.157895
$362$	11.2767	+	2.14830i	0.592692	+	0.112912i
$363$			32.0992i			1.68477i
$364$	2.38923	−	6.04312i	0.125230	−	0.316745i
$365$		−	3.55691i		−	0.186177i
$366$	−8.31894	+	43.6673i	−0.434838	+	2.28253i
$367$	13.6121			0.710546			0.355273	−	0.934763i	$-0.384388\pi$
$367$	13.6121			0.710546			0.355273	+	0.934763i	$0.384388\pi$
$368$	−8.58451	−	8.04564i	−0.447499	−	0.419408i
$369$	71.3346			3.71353
$370$	1.73534	−	9.10905i	0.0902161	−	0.473557i
$371$			5.05863i			0.262631i
$372$	12.0862	−	30.5699i	0.626642	−	1.58498i
$373$		−	33.1070i		−	1.71421i	−0.515139	−	0.857107i	$-0.672260\pi$
$373$		−	33.1070i		−	1.71421i	0.515139	−	0.857107i	$-0.327740\pi$
$374$	1.47068	+	0.280176i	0.0760472	+	0.0144876i
$375$	29.2423			1.51006
$376$	10.3030	−	16.2612i	0.531337	−	0.838608i
$377$	7.43965			0.383161
$378$	66.8316	+	12.7319i	3.43744	+	0.654858i
$379$			33.1690i			1.70378i	0.523722	+	0.851889i	$0.324543\pi$
$379$			33.1690i			1.70378i	−0.523722	+	0.851889i	$0.675457\pi$
$380$	−7.43965	−	2.94137i	−0.381646	−	0.150889i
$381$		−	51.7846i		−	2.65300i
$382$	5.27674	−	27.6983i	0.269981	−	1.41717i
$383$	33.0698			1.68979			0.844894	−	0.534934i	$-0.179663\pi$
$383$	33.0698			1.68979			0.844894	+	0.534934i	$0.179663\pi$
$384$	9.20259	+	35.5893i	0.469618	+	1.81616i
$385$	−3.43965			−0.175301
$386$	−1.08967	+	5.71982i	−0.0554627	+	0.291131i
$387$		−	2.32582i		−	0.118228i
$388$	−14.2733	−	5.64315i	−0.724617	−	0.286487i
$389$			19.5569i			0.991575i	0.868444	+	0.495787i	$0.165120\pi$
$389$			19.5569i			0.991575i	−0.868444	+	0.495787i	$0.834880\pi$
$390$	−4.51380	−	0.859912i	−0.228565	−	0.0435433i
$391$	−2.94137			−0.148751
$392$	5.38445	−	8.49828i	0.271956	−	0.429228i
$393$	−24.9931			−1.26074
$394$	−14.9918	−	2.85605i	−0.755275	−	0.143886i
$395$			6.73281i			0.338765i
$396$	5.88273	−	14.8793i	0.295618	−	0.747713i
$397$		−	34.2208i		−	1.71749i	−0.512402	−	0.858746i	$-0.671244\pi$
$397$		−	34.2208i		−	1.71749i	0.512402	−	0.858746i	$-0.328756\pi$
$398$	−0.162910	+	0.855136i	−0.00816593	+	0.0428641i
$399$	−42.2277			−2.11403
$400$	11.6742	+	10.9414i	0.583709	+	0.547068i
$401$	−32.6707			−1.63150			−0.815750	−	0.578405i	$-0.803675\pi$
$401$	−32.6707			−1.63150			−0.815750	+	0.578405i	$0.803675\pi$
$402$	1.29135	−	6.77846i	0.0644065	−	0.338079i
$403$			5.05863i			0.251988i
$404$	−2.28973	+	5.79145i	−0.113918	+	0.288135i
$405$		−	25.4362i		−	1.26394i
$406$	33.5811	+	6.39744i	1.66660	+	0.317500i
$407$	−6.94137			−0.344071
$408$	7.76294	+	4.91855i	0.384323	+	0.243504i
$409$	−6.20855			−0.306993			−0.153497	−	0.988149i	$-0.549053\pi$
$409$	−6.20855			−0.306993			−0.153497	+	0.988149i	$0.549053\pi$
$410$	−13.1138	−	2.49828i	−0.647646	−	0.123381i
$411$			17.2932i			0.853009i
$412$	32.7570	+	12.9509i	1.61382	+	0.638046i
$413$			18.4362i			0.907187i
$414$	−5.88273	+	30.8793i	−0.289121	+	1.51763i
$415$	−2.49828			−0.122636
$416$	−3.33060	−	4.57243i	−0.163296	−	0.224182i
$417$	−40.5500			−1.98574
$418$	−1.12070	+	5.88273i	−0.0548154	+	0.287734i
$419$			0.369845i			0.0180681i	0.999959	+	0.00903405i	$0.00287567\pi$
$419$			0.369845i			0.0180681i	−0.999959	+	0.00903405i	$0.997124\pi$
$420$	−19.6349	−	7.76294i	−0.958087	−	0.378793i
$421$		−	3.87930i		−	0.189065i	−0.995522	−	0.0945327i	$-0.969864\pi$
$421$		−	3.87930i		−	0.189065i	0.995522	−	0.0945327i	$-0.0301357\pi$
$422$	−2.51380	−	0.478897i	−0.122370	−	0.0233124i
$423$	−51.4328			−2.50075
$424$	3.71982	+	2.35685i	0.180651	+	0.114459i
$425$	4.00000			0.194029
$426$	24.2229	+	4.61464i	1.17360	+	0.223580i
$427$		−	31.4328i		−	1.52114i
$428$	−8.04564	+	20.3500i	−0.388901	+	0.983653i
$429$			3.43965i			0.166068i
$430$	−0.0814549	+	0.427568i	−0.00392810	+	0.0206192i
$431$	0.516327			0.0248706			0.0124353	−	0.999923i	$-0.496042\pi$
$431$	0.516327			0.0248706			0.0124353	+	0.999923i	$0.496042\pi$
$432$	40.4996	−	43.2121i	1.94854	−	2.07905i
$433$	30.7846			1.47941			0.739706	−	0.672930i	$-0.234965\pi$
$433$	30.7846			1.47941			0.739706	+	0.672930i	$0.234965\pi$
$434$	−4.34998	+	22.8337i	−0.208806	+	1.09605i
$435$		−	24.1725i		−	1.15898i
$436$	7.59048	−	19.1987i	0.363518	−	0.919452i
$437$		−	11.7655i		−	0.562819i
$438$	−16.0552	−	3.05863i	−0.767147	−	0.146147i
$439$	30.4362			1.45264			0.726321	−	0.687356i	$-0.241229\pi$
$439$	30.4362			1.45264			0.726321	+	0.687356i	$0.241229\pi$
$440$	−1.60256	+	2.52932i	−0.0763989	+	0.120580i
$441$	−26.8793			−1.27997
$442$	−1.38923	−	0.264658i	−0.0660789	−	0.0125885i
$443$			3.45769i			0.164280i	0.996621	+	0.0821400i	$0.0261755\pi$
$443$			3.45769i			0.164280i	−0.996621	+	0.0821400i	$0.973825\pi$
$444$	−39.6242	−	15.6660i	−1.88048	−	0.743474i
$445$		−	2.11727i		−	0.100368i
$446$	1.80128	−	9.45517i	0.0852930	−	0.447715i
$447$	−29.6121			−1.40060
$448$	−11.1017	−	23.5031i	−0.524508	−	1.11042i
$449$	14.7880			0.697889			0.348945	−	0.937143i	$-0.386540\pi$
$449$	14.7880			0.697889			0.348945	+	0.937143i	$0.386540\pi$
$450$	8.00000	−	41.9931i	0.377124	−	1.97957i
$451$			9.99312i			0.470558i
$452$	31.8302	+	12.5845i	1.49717	+	0.591926i
$453$		−	50.1070i		−	2.35423i
$454$	9.26719	+	1.76547i	0.434931	+	0.0828575i
$455$	3.24914			0.152322
$456$	−19.6742	+	31.0518i	−0.921328	+	1.45413i
$457$	31.8759			1.49109			0.745545	−	0.666455i	$-0.232189\pi$
$457$	31.8759			1.49109			0.745545	+	0.666455i	$0.232189\pi$
$458$	25.1642	+	4.79397i	1.17585	+	0.224008i
$459$		−	14.8061i		−	0.691087i
$460$	2.16291	−	5.47068i	0.100846	−	0.255072i
$461$			18.5569i			0.864282i	0.901806	+	0.432141i	$0.142242\pi$
$461$			18.5569i			0.864282i	−0.901806	+	0.432141i	$0.857758\pi$
$462$	−2.95779	+	15.5259i	−0.137609	+	0.722329i
$463$	−24.8241			−1.15367			−0.576837	−	0.816859i	$-0.695713\pi$
$463$	−24.8241			−1.15367			−0.576837	+	0.816859i	$0.695713\pi$
$464$	20.3500	−	21.7129i	0.944724	−	1.00800i
$465$	16.4362			0.762211
$466$	−3.02669	+	15.8875i	−0.140209	+	0.735975i
$467$			40.2829i			1.86407i	0.362371	+	0.932034i	$0.381967\pi$
$467$			40.2829i			1.86407i	−0.362371	+	0.932034i	$0.618033\pi$
$468$	−5.55691	+	14.0552i	−0.256868	+	0.649702i
$469$			4.87930i			0.225305i
$470$	9.45517	+	1.80128i	0.436134	+	0.0830868i
$471$	−12.3189			−0.567627
$472$	13.5569	+	8.58957i	0.624008	+	0.395367i
$473$	0.325819			0.0149812
$474$	30.3906	+	5.78963i	1.39588	+	0.265926i
$475$			16.0000i			0.734130i
$476$	−6.04312	−	2.38923i	−0.276986	−	0.109510i
$477$		−	11.7655i		−	0.538704i
$478$	−4.46247	+	23.4241i	−0.204109	+	1.07139i
$479$	−4.07324			−0.186111			−0.0930556	−	0.995661i	$-0.529663\pi$
$479$	−4.07324			−0.186111			−0.0930556	+	0.995661i	$0.529663\pi$
$480$	−14.8565	+	10.8216i	−0.678102	+	0.493935i
$481$	6.55691			0.298970
$482$	1.38445	−	7.26719i	0.0630601	−	0.331011i
$483$		−	31.0518i		−	1.41290i
$484$	−18.3746	−	7.26466i	−0.835210	−	0.330212i
$485$		−	7.67418i		−	0.348467i
$486$	−53.1070	−	10.1173i	−2.40898	−	0.458929i
$487$	15.0518			0.682060			0.341030	−	0.940052i	$-0.389224\pi$
$487$	15.0518			0.682060			0.341030	+	0.940052i	$0.389224\pi$
$488$	−23.1138	−	14.6448i	−1.04631	−	0.662937i
$489$	−13.5569			−0.613065
$490$	4.94137	+	0.941367i	0.223228	+	0.0425266i
$491$		−	3.92676i		−	0.177212i	−0.996067	−	0.0886061i	$-0.971759\pi$
$491$		−	3.92676i		−	0.177212i	0.996067	−	0.0886061i	$-0.0282412\pi$
$492$	−22.5535	+	57.0449i	−1.01679	+	2.57178i
$493$		−	7.43965i		−	0.335065i
$494$	1.05863	−	5.55691i	0.0476302	−	0.250017i
$495$	8.00000			0.359573
$496$	14.7638	+	13.8371i	0.662916	+	0.621304i
$497$	−17.4362			−0.782121
$498$	−2.14830	+	11.2767i	−0.0962677	+	0.505323i
$499$		−	32.3189i		−	1.44679i	−0.690432	−	0.723397i	$-0.742580\pi$
$499$		−	32.3189i		−	1.44679i	0.690432	−	0.723397i	$-0.257420\pi$
$500$	−6.61808	+	16.7392i	−0.295969	+	0.748600i
$501$			46.4293i			2.07431i
$502$	−2.85514	−	0.543924i	−0.127431	−	0.0242765i
$503$	−16.1104			−0.718327			−0.359163	−	0.933275i	$-0.616938\pi$
$503$	−16.1104			−0.718327			−0.359163	+	0.933275i	$0.616938\pi$
$504$	−37.1690	+	58.6639i	−1.65564	+	2.61310i
$505$	−3.11383			−0.138564
$506$	−4.32582	−	0.824101i	−0.192306	−	0.0366357i
$507$		−	3.24914i		−	0.144299i
$508$	29.6431	+	11.7198i	1.31520	+	0.519983i
$509$			16.2277i			0.719278i	0.933091	+	0.359639i	$0.117100\pi$
$509$			16.2277i			0.719278i	−0.933091	+	0.359639i	$0.882900\pi$
$510$	−0.859912	+	4.51380i	−0.0380775	+	0.199874i
$511$	11.5569			0.511248
$512$	−22.4552	−	2.78667i	−0.992387	−	0.123155i
$513$	59.2242			2.61481
$514$	5.61808	−	29.4901i	0.247803	−	1.30075i
$515$			17.6121i			0.776082i
$516$	1.85991	+	0.735342i	0.0818781	+	0.0323716i
$517$		−	7.20512i		−	0.316881i
$518$	29.5966	+	5.63837i	1.30040	+	0.247736i
$519$	22.7328			0.997860
$520$	1.51380	−	2.38923i	0.0663845	−	0.104775i
$521$	−8.32238			−0.364610			−0.182305	−	0.983242i	$-0.558356\pi$
$521$	−8.32238			−0.364610			−0.182305	+	0.983242i	$0.558356\pi$
$522$	−78.1035	−	14.8793i	−3.41850	−	0.651249i
$523$		−	32.2829i		−	1.41163i	−0.708396	−	0.705815i	$-0.750581\pi$
$523$		−	32.2829i		−	1.41163i	0.708396	−	0.705815i	$-0.249419\pi$
$524$	5.65641	−	14.3069i	0.247102	−	0.624998i
$525$			42.2277i			1.84297i
$526$	−6.23453	+	32.7259i	−0.271839	+	1.42692i
$527$	5.05863			0.220358
$528$	10.0388	+	9.40861i	0.436881	+	0.409457i
$529$	−14.3484			−0.623842
$530$	−0.412050	+	2.16291i	−0.0178983	+	0.0939508i
$531$		−	42.8793i		−	1.86080i
$532$	9.55691	−	24.1725i	0.414345	−	1.04801i
$533$		−	9.43965i		−	0.408877i
$534$	−9.55691	−	1.82066i	−0.413568	−	0.0787878i
$535$	−10.9414			−0.473037
$536$	3.58795	+	2.27330i	0.154976	+	0.0981916i
$537$	−57.6639			−2.48838
$538$	−8.78801	−	1.67418i	−0.378878	−	0.0721790i
$539$		−	3.76547i		−	0.162190i
$540$	27.5380	+	10.8875i	1.18505	+	0.468524i
$541$		−	2.32238i		−	0.0998470i	−0.998753	−	0.0499235i	$-0.984102\pi$
$541$		−	2.32238i		−	0.0998470i	0.998753	−	0.0499235i	$-0.0158977\pi$
$542$	−0.915107	+	4.80353i	−0.0393072	+	0.206329i
$543$	26.3741			1.13182
$544$	−4.57243	+	3.33060i	−0.196041	+	0.142798i
$545$	10.3224			0.442162
$546$	2.79397	−	14.6660i	0.119571	−	0.627645i
$547$			9.89390i			0.423033i	0.977374	+	0.211516i	$0.0678402\pi$
$547$			9.89390i			0.423033i	−0.977374	+	0.211516i	$0.932160\pi$
$548$	−9.89916	−	3.91377i	−0.422871	−	0.167188i
$549$			73.1070i			3.12013i
$550$	5.88273	+	1.12070i	0.250841	+	0.0477870i
$551$	29.7586			1.26776
$552$	−22.8337	−	14.4672i	−0.971865	−	0.615767i
$553$	−21.8759			−0.930256
$554$	−39.6673	−	7.55691i	−1.68530	−	0.321063i
$555$		−	21.3043i		−	0.904319i
$556$	9.17724	−	23.2121i	0.389202	−	0.984414i
$557$			30.3155i			1.28451i	0.766491	+	0.642255i	$0.222001\pi$
$557$			30.3155i			1.28451i	−0.766491	+	0.642255i	$0.777999\pi$
$558$	10.1173	−	53.1070i	0.428298	−	2.24820i
$559$	−0.307774			−0.0130174
$560$	8.88751	−	9.48276i	0.375566	−	0.400720i
$561$	3.43965			0.145222
$562$	−6.61555	+	34.7259i	−0.279060	+	1.46483i
$563$			38.7440i			1.63286i	0.577441	+	0.816432i	$0.304051\pi$
$563$			38.7440i			1.63286i	−0.577441	+	0.816432i	$0.695949\pi$
$564$	16.2612	−	41.1298i	0.684721	−	1.73188i
$565$			17.1138i			0.719984i
$566$	30.3139	+	5.77502i	1.27419	+	0.242742i
$567$	82.6458			3.47080
$568$	−8.12366	+	12.8216i	−0.340861	+	0.537981i
$569$	−19.2345			−0.806354			−0.403177	−	0.915122i	$-0.632094\pi$
$569$	−19.2345			−0.806354			−0.403177	+	0.915122i	$0.632094\pi$
$570$	−18.0552	−	3.43965i	−0.756249	−	0.144071i
$571$		−	10.8320i		−	0.453307i	−0.973976	−	0.226653i	$-0.927222\pi$
$571$		−	10.8320i		−	0.453307i	0.973976	−	0.226653i	$-0.0727784\pi$
$572$	−1.96896	−	0.778457i	−0.0823265	−	0.0325489i
$573$		−	64.7811i		−	2.70627i
$574$	8.11727	−	42.6087i	0.338808	−	1.77845i
$575$	−11.7655			−0.490654
$576$	25.8207	+	54.6639i	1.07586	+	2.27766i
$577$	−45.1329			−1.87891			−0.939454	−	0.342674i	$-0.888667\pi$
$577$	−45.1329			−1.87891			−0.939454	+	0.342674i	$0.888667\pi$
$578$	4.23453	−	22.2277i	0.176133	−	0.924549i
$579$			13.3776i			0.555953i
$580$	13.8371	+	5.47068i	0.574554	+	0.227158i
$581$		−	8.11727i		−	0.336761i
$582$	−34.6397	−	6.59912i	−1.43586	−	0.273542i
$583$	1.64820			0.0682615
$584$	5.38445	−	8.49828i	0.222810	−	0.351661i
$585$	−7.55691			−0.312440
$586$	−38.1152	−	7.26122i	−1.57452	−	0.299958i
$587$			5.05863i			0.208792i	0.994536	+	0.104396i	$0.0332910\pi$
$587$			5.05863i			0.208792i	−0.994536	+	0.104396i	$0.966709\pi$
$588$	8.49828	−	21.4948i	0.350463	−	0.886432i
$589$			20.2345i			0.833749i
$590$	−1.50172	+	7.88273i	−0.0618248	+	0.324527i
$591$	−35.0629			−1.44230
$592$	17.9354	−	19.1367i	0.737140	−	0.786511i
$593$	29.4328			1.20866			0.604330	−	0.796734i	$-0.293441\pi$
$593$	29.4328			1.20866			0.604330	+	0.796734i	$0.293441\pi$
$594$	4.14830	−	21.7750i	0.170207	−	0.893440i
$595$		−	3.24914i		−	0.133202i
$596$	6.70178	−	16.9509i	0.274516	−	0.694337i
$597$			2.00000i			0.0818546i
$598$	4.08623	+	0.778457i	0.167098	+	0.0318335i
$599$	−40.4293			−1.65190			−0.825949	−	0.563745i	$-0.809360\pi$
$599$	−40.4293			−1.65190			−0.825949	+	0.563745i	$0.809360\pi$
$600$	31.0518	+	19.6742i	1.26768	+	0.803195i
$601$	−22.9931			−0.937909			−0.468955	−	0.883222i	$-0.655369\pi$
$601$	−22.9931			−0.937909			−0.468955	+	0.883222i	$0.655369\pi$
$602$	−1.38923	−	0.264658i	−0.0566207	−	0.0107867i
$603$		−	11.3484i		−	0.462141i
$604$	28.6828	+	11.3401i	1.16709	+	0.461424i
$605$		−	9.87930i		−	0.401650i
$606$	−2.67762	+	14.0552i	−0.108771	+	0.570953i
$607$	17.7846			0.721853			0.360927	−	0.932594i	$-0.382460\pi$
$607$	17.7846			0.721853			0.360927	+	0.932594i	$0.382460\pi$
$608$	−13.3224	−	18.2897i	−0.540294	−	0.741746i
$609$	78.5397			3.18259
$610$	2.56035	−	13.4396i	0.103666	−	0.544155i
$611$			6.80605i			0.275344i
$612$	14.0552	+	5.55691i	0.568148	+	0.224625i
$613$		−	24.2277i		−	0.978546i	−0.872131	−	0.489273i	$-0.837262\pi$
$613$		−	24.2277i		−	0.978546i	0.872131	−	0.489273i	$-0.162738\pi$
$614$	37.0518	+	7.05863i	1.49529	+	0.284863i
$615$	−30.6707			−1.23676
$616$	−8.21811	−	5.20693i	−0.331117	−	0.209793i
$617$	−18.2277			−0.733818			−0.366909	−	0.930257i	$-0.619584\pi$
$617$	−18.2277			−0.733818			−0.366909	+	0.930257i	$0.619584\pi$
$618$	79.4975	+	15.1449i	3.19786	+	0.609216i
$619$			43.1982i			1.73628i	0.496316	+	0.868142i	$0.334686\pi$
$619$			43.1982i			1.73628i	−0.496316	+	0.868142i	$0.665314\pi$
$620$	−3.71982	+	9.40861i	−0.149392	+	0.377859i
$621$			43.5500i			1.74760i
$622$	−1.82066	+	9.55691i	−0.0730019	+	0.383197i
$623$	6.87930			0.275613
$624$	−9.48276	−	8.88751i	−0.379614	−	0.355785i
$625$	11.0000			0.440000
$626$	−4.67671	+	24.5487i	−0.186919	+	0.981163i
$627$			13.7586i			0.549465i
$628$	2.78801	−	7.05176i	0.111254	−	0.281396i
$629$		−	6.55691i		−	0.261441i
$630$	−34.1104	−	6.49828i	−1.35899	−	0.258898i
$631$	−7.07668			−0.281718			−0.140859	−	0.990030i	$-0.544986\pi$
$631$	−7.07668			−0.281718			−0.140859	+	0.990030i	$0.544986\pi$
$632$	−10.1921	+	16.0862i	−0.405421	+	0.639876i
$633$	−5.87930			−0.233681
$634$	−1.54736	−	0.294784i	−0.0614536	−	0.0117074i
$635$			15.9379i			0.632477i
$636$	9.40861	+	3.71982i	0.373076	+	0.147501i
$637$			3.55691i			0.140930i
$638$	2.08441	−	10.9414i	0.0825226	−	0.433173i
$639$	40.5535			1.60427
$640$	−2.83231	−	10.9534i	−0.111957	−	0.432973i
$641$	−28.2277			−1.11493			−0.557463	−	0.830202i	$-0.688225\pi$
$641$	−28.2277			−1.11493			−0.557463	+	0.830202i	$0.688225\pi$
$642$	−9.40861	+	49.3871i	−0.371328	+	1.94915i
$643$			2.73281i			0.107772i	0.998547	+	0.0538858i	$0.0171607\pi$
$643$			2.73281i			0.107772i	−0.998547	+	0.0538858i	$0.982839\pi$
$644$	17.7750	+	7.02760i	0.700434	+	0.276926i
$645$			1.00000i			0.0393750i
$646$	−5.55691	−	1.05863i	−0.218634	−	0.0416514i
$647$	−14.5604			−0.572427			−0.286213	−	0.958166i	$-0.592397\pi$
$647$	−14.5604			−0.572427			−0.286213	+	0.958166i	$0.592397\pi$
$648$	38.5053	−	60.7729i	1.51263	−	2.38739i
$649$	6.00688			0.235790
$650$	−5.55691	−	1.05863i	−0.217960	−	0.0415230i
$651$			53.4036i			2.09305i
$652$	3.06819	−	7.76041i	0.120159	−	0.303921i
$653$		−	29.3415i		−	1.14822i	−0.818778	−	0.574111i	$-0.805348\pi$
$653$		−	29.3415i		−	1.14822i	0.818778	−	0.574111i	$-0.194652\pi$
$654$	8.87634	−	46.5932i	0.347092	−	1.82194i
$655$	7.69223			0.300560
$656$	−27.5500	−	25.8207i	−1.07565	−	1.00813i
$657$	−26.8793			−1.04866
$658$	−5.85261	+	30.7212i	−0.228158	+	1.19764i
$659$		−	32.2829i		−	1.25756i	−0.777583	−	0.628781i	$-0.783554\pi$
$659$		−	32.2829i		−	1.25756i	0.777583	−	0.628781i	$-0.216446\pi$
$660$	−2.52932	+	6.39744i	−0.0984535	+	0.249020i
$661$		−	24.4102i		−	0.949448i	−0.880135	−	0.474724i	$-0.842548\pi$
$661$		−	24.4102i		−	0.949448i	0.880135	−	0.474724i	$-0.157452\pi$
$662$	−25.6983	−	4.89572i	−0.998794	−	0.190278i
$663$	−3.24914			−0.126186
$664$	−5.96896	−	3.78189i	−0.231641	−	0.146766i
$665$	12.9966			0.503985
$666$	−68.8363	−	13.1138i	−2.66735	−	0.508151i
$667$			21.8827i			0.847303i
$668$	−26.5776	−	10.5078i	−1.02832	−	0.406560i
$669$		−	22.1138i		−	0.854970i
$670$	−0.397442	+	2.08623i	−0.0153545	+	0.0805981i
$671$	−10.2414			−0.395365
$672$	−35.1608	−	48.2708i	−1.35636	−	1.86209i
$673$	11.8793			0.457913			0.228957	−	0.973437i	$-0.426469\pi$
$673$	11.8793			0.457913			0.228957	+	0.973437i	$0.426469\pi$
$674$	4.61464	−	24.2229i	0.177749	−	0.933031i
$675$		−	59.2242i		−	2.27954i
$676$	1.85991	+	0.735342i	0.0715351	+	0.0282824i
$677$			8.76891i			0.337016i	0.985700	+	0.168508i	$0.0538950\pi$
$677$			8.76891i			0.337016i	−0.985700	+	0.168508i	$0.946105\pi$
$678$	77.2484	+	14.7164i	2.96671	+	0.565179i
$679$	24.9345			0.956898
$680$	−2.38923	−	1.51380i	−0.0916227	−	0.0580515i
$681$	21.6742			0.830556
$682$	7.43965	+	1.41731i	0.284879	+	0.0542715i
$683$			3.38445i			0.129502i	0.997901	+	0.0647512i	$0.0206254\pi$
$683$			3.38445i			0.129502i	−0.997901	+	0.0647512i	$0.979375\pi$
$684$	−22.2277	+	56.2208i	−0.849896	+	2.14966i
$685$		−	5.32238i		−	0.203358i
$686$	2.96075	−	15.5414i	0.113042	−	0.593373i
$687$	58.8544			2.24543
$688$	−0.841866	+	0.898251i	−0.0320958	+	0.0342455i
$689$	−1.55691			−0.0593137
$690$	2.52932	−	13.2767i	0.0962894	−	0.505437i
$691$			11.2242i			0.426989i	0.976944	+	0.213495i	$0.0684846\pi$
$691$			11.2242i			0.426989i	−0.976944	+	0.213495i	$0.931515\pi$
$692$	−5.14486	+	13.0130i	−0.195578	+	0.494680i
$693$			25.9931i			0.987397i
$694$	12.4828	+	2.37806i	0.473839	+	0.0902699i
$695$	12.4802			0.473402
$696$	36.5922	−	57.7535i	1.38703	−	2.18914i
$697$	−9.43965			−0.357552
$698$	−15.2720	−	2.90942i	−0.578052	−	0.110123i
$699$			37.1579i			1.40544i
$700$	−24.1725	−	9.55691i	−0.913633	−	0.361217i
$701$		−	48.6707i		−	1.83827i	−0.393944	−	0.919134i	$-0.628890\pi$
$701$		−	48.6707i		−	1.83827i	0.393944	−	0.919134i	$-0.371110\pi$
$702$	−3.91855	+	20.5690i	−0.147896	+	0.776327i
$703$	26.2277			0.989195
$704$	−7.65775	+	3.61717i	−0.288612	+	0.136327i
$705$	22.1138			0.832855
$706$	−6.14830	+	32.2733i	−0.231394	+	1.21462i
$707$		−	10.1173i		−	0.380499i
$708$	34.2897	+	13.5569i	1.28869	+	0.509500i
$709$			11.7586i			0.441603i	0.975319	+	0.220802i	$0.0708673\pi$
$709$			11.7586i			0.441603i	−0.975319	+	0.220802i	$0.929133\pi$
$710$	−7.45517	−	1.42026i	−0.279787	−	0.0533016i
$711$	50.8793			1.90812
$712$	3.20512	−	5.05863i	0.120117	−	0.189580i
$713$	−14.8793			−0.557234
$714$	−14.6660	−	2.79397i	−0.548860	−	0.104562i
$715$		−	1.05863i		−	0.0395906i
$716$	13.0504	−	33.0086i	0.487717	−	1.23359i
$717$			54.7846i			2.04597i
$718$	2.98701	−	15.6792i	0.111474	−	0.585144i
$719$	−38.7191			−1.44398			−0.721989	−	0.691905i	$-0.756772\pi$
$719$	−38.7191			−1.44398			−0.721989	+	0.691905i	$0.756772\pi$
$720$	−20.6707	+	22.0552i	−0.770353	+	0.821949i
$721$	−57.2242			−2.13114
$722$	−0.793975	+	4.16769i	−0.0295487	+	0.155105i
$723$		−	16.9966i		−	0.632109i
$724$	−5.96896	+	15.0974i	−0.221835	+	0.561090i
$725$		−	29.7586i		−	1.10521i
$726$	−44.5932	−	8.49532i	−1.65501	−	0.315291i
$727$	−8.93449			−0.331362			−0.165681	−	0.986179i	$-0.552982\pi$
$727$	−8.93449			−0.331362			−0.165681	+	0.986179i	$0.552982\pi$
$728$	7.76294	+	4.91855i	0.287714	+	0.182293i
$729$	−47.8984			−1.77401
$730$	4.94137	+	0.941367i	0.182888	+	0.0348415i
$731$			0.307774i			0.0113834i
$732$	−58.4622	−	23.1138i	−2.16082	−	0.854312i
$733$		−	36.3484i		−	1.34256i	−0.741205	−	0.671279i	$-0.765745\pi$
$733$		−	36.3484i		−	1.34256i	0.741205	−	0.671279i	$-0.234255\pi$
$734$	−3.60256	+	18.9103i	−0.132973	+	0.697993i
$735$	11.5569			0.426283
$736$	13.4492	−	9.79650i	0.495744	−	0.361104i
$737$	1.58977			0.0585599
$738$	−18.8793	+	99.1001i	−0.694956	+	3.64792i
$739$		−	8.44309i		−	0.310584i	−0.987869	−	0.155292i	$-0.950368\pi$
$739$		−	8.44309i		−	0.310584i	0.987869	−	0.155292i	$-0.0496318\pi$
$740$	12.1953	+	4.82157i	0.448308	+	0.177245i
$741$		−	12.9966i		−	0.477441i
$742$	−7.02760	−	1.33881i	−0.257991	−	0.0491492i
$743$	22.5354			0.826745			0.413372	−	0.910562i	$-0.364351\pi$
$743$	22.5354			0.826745			0.413372	+	0.910562i	$0.364351\pi$
$744$	39.2699	+	24.8811i	1.43970	+	0.912186i
$745$	9.11383			0.333905
$746$	45.9931	+	8.76203i	1.68393	+	0.320801i
$747$			18.8793i			0.690757i
$748$	−0.778457	+	1.96896i	−0.0284632	+	0.0719925i
$749$		−	35.5500i		−	1.29897i
$750$	−7.73921	+	40.6242i	−0.282596	+	1.48339i
$751$	2.43621			0.0888986			0.0444493	−	0.999012i	$-0.485847\pi$
$751$	2.43621			0.0888986			0.0444493	+	0.999012i	$0.485847\pi$
$752$	19.8638	+	18.6169i	0.724357	+	0.678888i
$753$	−6.67762			−0.243346
$754$	−1.96896	+	10.3354i	−0.0717055	+	0.376392i
$755$			15.4216i			0.561250i
$756$	−35.3750	+	89.4747i	−1.28658	+	3.25416i
$757$			43.1329i			1.56769i	0.620955	+	0.783847i	$0.286745\pi$
$757$			43.1329i			1.56769i	−0.620955	+	0.783847i	$0.713255\pi$
$758$	−46.0794	−	8.77846i	−1.67368	−	0.318848i
$759$	−10.1173			−0.367234
$760$	6.05520	−	9.55691i	0.219645	−	0.346666i
$761$	30.0191			1.08819			0.544096	−	0.839023i	$-0.316873\pi$
$761$	30.0191			1.08819			0.544096	+	0.839023i	$0.316873\pi$
$762$	71.9406	+	13.7052i	2.60613	+	0.496488i
$763$			33.5389i			1.21419i
$764$	37.0828	+	14.6612i	1.34161	+	0.530423i
$765$			7.55691i			0.273221i
$766$	−8.75220	+	45.9415i	−0.316230	+	1.65993i
$767$	−5.67418			−0.204883
$768$	−51.8772	+	3.36550i	−1.87196	+	0.121442i
$769$	−35.3484			−1.27469			−0.637347	−	0.770577i	$-0.719968\pi$
$769$	−35.3484			−1.27469			−0.637347	+	0.770577i	$0.719968\pi$
$770$	0.910331	−	4.77846i	0.0328061	−	0.172204i
$771$		−	68.9716i		−	2.48395i
$772$	−7.65775	−	3.02760i	−0.275609	−	0.108966i
$773$		−	47.2277i		−	1.69866i	−0.527862	−	0.849330i	$-0.677006\pi$
$773$		−	47.2277i		−	1.69866i	0.527862	−	0.849330i	$-0.322994\pi$
$774$	3.23109	+	0.615547i	0.116139	+	0.0221254i
$775$	20.2345			0.726846
$776$	11.6172	−	18.3354i	0.417032	−	0.658201i
$777$	69.2208			2.48328
$778$	−27.1690	−	5.17590i	−0.974057	−	0.185565i
$779$		−	37.7586i		−	1.35284i
$780$	2.38923	−	6.04312i	0.0855481	−	0.216378i
$781$			5.68106i			0.203284i
$782$	0.778457	−	4.08623i	0.0278376	−	0.146123i
$783$	−110.152			−3.93651
$784$	10.3810	+	9.72938i	0.370751	+	0.347478i
$785$	3.79145			0.135323
$786$	6.61464	−	34.7212i	0.235936	−	1.23846i
$787$		−	24.7880i		−	0.883597i	−0.897114	−	0.441799i	$-0.854341\pi$
$787$		−	24.7880i		−	0.883597i	0.897114	−	0.441799i	$-0.145659\pi$
$788$	7.93540	−	20.0711i	0.282687	−	0.715005i
$789$			76.5397i			2.72489i
$790$	−9.35342	−	1.78189i	−0.332780	−	0.0633970i
$791$	−55.6052			−1.97709
$792$	19.1138	+	12.1104i	0.679180	+	0.430324i
$793$	9.67418			0.343540
$794$	47.5405	+	9.05681i	1.68715	+	0.321414i
$795$			5.05863i			0.179411i
$796$	−1.14486	−	0.452638i	−0.0405786	−	0.0160433i
$797$			32.1104i			1.13741i	0.822542	+	0.568704i	$0.192555\pi$
$797$			32.1104i			1.13741i	−0.822542	+	0.568704i	$0.807445\pi$
$798$	11.1759	−	58.6639i	0.395623	−	2.07668i
$799$	6.80605			0.240781
$800$	−18.2897	+	13.3224i	−0.646640	+	0.471017i
$801$	−16.0000			−0.565332
$802$	8.64658	−	45.3871i	0.305321	−	1.60268i
$803$		−	3.76547i		−	0.132880i
$804$	9.07506	+	3.58795i	0.320053	+	0.126537i
$805$			9.55691i			0.336837i
$806$	−7.02760	−	1.33881i	−0.247537	−	0.0471575i
$807$	−20.5535			−0.723517
$808$	−7.43965	−	4.71371i	−0.261726	−	0.165828i
$809$	4.55004			0.159971			0.0799854	−	0.996796i	$-0.474513\pi$
$809$	4.55004			0.159971			0.0799854	+	0.996796i	$0.474513\pi$
$810$	35.3367	+	6.73190i	1.24161	+	0.236535i
$811$			48.3449i			1.69762i	0.528698	+	0.848810i	$0.322680\pi$
$811$			48.3449i			1.69762i	−0.528698	+	0.848810i	$0.677320\pi$
$812$	−17.7750	+	44.9587i	−0.623781	+	1.57774i
$813$			11.2345i			0.394012i
$814$	1.83709	−	9.64315i	0.0643900	−	0.337992i
$815$	4.17246			0.146155
$816$	−8.88751	+	9.48276i	−0.311125	+	0.331963i
$817$	−1.23109			−0.0430706
$818$	1.64315	−	8.62510i	0.0574512	−	0.301570i
$819$		−	24.5535i		−	0.857968i
$820$	6.94137	−	17.5569i	0.242403	−	0.613114i
$821$		−	24.3484i		−	0.849764i	−0.905249	−	0.424882i	$-0.860316\pi$
$821$		−	24.3484i		−	0.849764i	0.905249	−	0.424882i	$-0.139684\pi$
$822$	−24.0242	−	4.57678i	−0.837939	−	0.159634i
$823$	−28.4431			−0.991464			−0.495732	−	0.868476i	$-0.665100\pi$
$823$	−28.4431			−0.991464			−0.495732	+	0.868476i	$0.665100\pi$
$824$	−26.6612	+	42.0794i	−0.928787	+	1.46590i
$825$	13.7586			0.479013
$826$	−25.6121	−	4.87930i	−0.891159	−	0.169772i
$827$		−	34.6448i		−	1.20472i	−0.798226	−	0.602358i	$-0.794228\pi$
$827$		−	34.6448i		−	1.20472i	0.798226	−	0.602358i	$-0.205772\pi$
$828$	−41.3415	−	16.3449i	−1.43672	−	0.568025i
$829$			34.2208i			1.18854i	0.804267	+	0.594268i	$0.202558\pi$
$829$			34.2208i			1.18854i	−0.804267	+	0.594268i	$0.797442\pi$
$830$	0.661191	−	3.47068i	0.0229503	−	0.120469i
$831$	−92.7743			−3.21830
$832$	7.23362	−	3.41683i	0.250781	−	0.118457i
$833$	3.55691			0.123240
$834$	10.7319	−	56.3333i	0.371615	−	1.95066i
$835$		−	14.2897i		−	0.494516i
$836$	−7.87586	−	3.11383i	−0.272392	−	0.107694i
$837$		−	74.8984i		−	2.58887i
$838$	−0.513799	−	0.0978825i	−0.0177489	−	0.00338129i
$839$	12.9345			0.446548			0.223274	−	0.974756i	$-0.428325\pi$
$839$	12.9345			0.446548			0.223274	+	0.974756i	$0.428325\pi$
$840$	15.9810	−	25.2229i	0.551398	−	0.870272i
$841$	−26.3484			−0.908564
$842$	5.38923	+	1.02669i	0.185725	+	0.0353820i
$843$			81.2173i			2.79727i
$844$	1.33060	−	3.36550i	0.0458010	−	0.115845i
$845$			1.00000i			0.0344010i
$846$	13.6121	−	71.4519i	0.467994	−	2.45657i
$847$	32.0992			1.10294
$848$	−4.25869	+	4.54392i	−0.146244	+	0.156039i
$849$	70.8984			2.43323
$850$	−1.05863	+	5.55691i	−0.0363108	+	0.190601i
$851$			19.2863i			0.661126i
$852$	−12.8216	+	32.4298i	−0.439260	+	1.11103i
$853$			31.6448i			1.08350i	0.840541	+	0.541748i	$0.182237\pi$
$853$			31.6448i			1.08350i	−0.840541	+	0.541748i	$0.817763\pi$
$854$	43.6673	+	8.31894i	1.49426	+	0.284668i
$855$	−30.2277			−1.03376
$856$	−26.1414	−	16.5630i	−0.893496	−	0.566113i
$857$	38.8724			1.32786			0.663928	−	0.747796i	$-0.268888\pi$
$857$	38.8724			1.32786			0.663928	+	0.747796i	$0.268888\pi$
$858$	−4.77846	−	0.910331i	−0.163134	−	0.0310782i
$859$		−	29.8207i		−	1.01747i	−0.860924	−	0.508734i	$-0.830114\pi$
$859$		−	29.8207i		−	1.01747i	0.860924	−	0.508734i	$-0.169886\pi$
$860$	−0.572432	−	0.226319i	−0.0195198	−	0.00771741i
$861$		−	99.6536i		−	3.39618i
$862$	−0.136650	+	0.717296i	−0.00465432	+	0.0244312i
$863$	24.5163			0.834545			0.417273	−	0.908781i	$-0.362986\pi$
$863$	24.5163			0.834545			0.417273	+	0.908781i	$0.362986\pi$
$864$	49.3130	+	67.6997i	1.67766	+	2.30319i
$865$	−6.99656			−0.237890
$866$	−8.14739	+	42.7668i	−0.276860	+	1.45328i
$867$		−	51.9862i		−	1.76555i
$868$	−30.5699	−	12.0862i	−1.03761	−	0.410233i
$869$			7.12758i			0.241787i
$870$	33.5811	+	6.39744i	1.13851	+	0.216894i
$871$	−1.50172			−0.0508838
$872$	24.6625	+	15.6260i	0.835179	+	0.529163i
$873$	−57.9931			−1.96277
$874$	16.3449	+	3.11383i	0.552875	+	0.105327i
$875$		−	29.2423i		−	0.988569i
$876$	8.49828	−	21.4948i	0.287130	−	0.726243i
$877$		−	4.34836i		−	0.146834i	−0.997301	−	0.0734169i	$-0.976610\pi$
$877$		−	4.34836i		−	0.146834i	0.997301	−	0.0734169i	$-0.0233904\pi$
$878$	−8.05520	+	42.2829i	−0.271850	+	1.42698i
$879$	−89.1441			−3.00676
$880$	−3.08967	−	2.89572i	−0.104153	−	0.0976148i
$881$	27.6967			0.933126			0.466563	−	0.884488i	$-0.345492\pi$
$881$	27.6967			0.933126			0.466563	+	0.884488i	$0.345492\pi$
$882$	7.11383	−	37.3415i	0.239535	−	1.25735i
$883$		−	14.0440i		−	0.472619i	−0.971678	−	0.236310i	$-0.924062\pi$
$883$		−	14.0440i		−	0.472619i	0.971678	−	0.236310i	$-0.0759379\pi$
$884$	0.735342	−	1.85991i	0.0247322	−	0.0625556i
$885$			18.4362i			0.619726i
$886$	−4.80353	−	0.915107i	−0.161378	−	0.0307436i
$887$	−3.66730			−0.123136			−0.0615680	−	0.998103i	$-0.519610\pi$
$887$	−3.66730			−0.123136			−0.0615680	+	0.998103i	$0.519610\pi$
$888$	32.2505	−	50.9009i	1.08226	−	1.70812i
$889$	−51.7846			−1.73680
$890$	2.94137	+	0.560352i	0.0985948	+	0.0187830i
$891$		−	26.9276i		−	0.902109i
$892$	12.6587	+	5.00478i	0.423843	+	0.167572i
$893$			27.2242i			0.911024i
$894$	7.83709	−	41.1380i	0.262112	−	1.37586i
$895$	17.7474			0.593231
$896$	35.5893	−	9.20259i	1.18895	−	0.307437i
$897$	9.55691			0.319096
$898$	−3.91377	+	20.5439i	−0.130604	+	0.685560i
$899$		−	37.6344i		−	1.25518i
$900$	56.2208	+	22.2277i	1.87403	+	0.740922i
$901$			1.55691i			0.0518683i
$902$	−13.8827	−	2.64476i	−0.462244	−	0.0880610i
$903$	−3.24914			−0.108125
$904$	−25.9069	+	40.8888i	−0.861650	+	1.35994i
$905$	−8.11727			−0.269827
$906$	69.6100	+	13.2612i	2.31264	+	0.440575i
$907$		−	9.39239i		−	0.311869i	−0.987767	−	0.155935i	$-0.950161\pi$
$907$		−	9.39239i		−	0.311869i	0.987767	−	0.155935i	$-0.0498389\pi$
$908$	−4.90528	+	12.4070i	−0.162787	+	0.411741i
$909$			23.5309i			0.780472i
$910$	−0.859912	+	4.51380i	−0.0285058	+	0.149631i
$911$	3.64496			0.120763			0.0603815	−	0.998175i	$-0.480768\pi$
$911$	3.64496			0.120763			0.0603815	+	0.998175i	$0.480768\pi$
$912$	−37.9311	−	35.5500i	−1.25602	−	1.17718i
$913$	−2.64476			−0.0875289
$914$	−8.43621	+	44.2829i	−0.279045	+	1.46475i
$915$		−	31.4328i		−	1.03914i
$916$	−13.3199	+	33.6901i	−0.440100	+	1.11315i
$917$			24.9931i			0.825346i
$918$	20.5690	+	3.91855i	0.678878	+	0.129331i
$919$	12.6516			0.417339			0.208670	−	0.977986i	$-0.433087\pi$
$919$	12.6516			0.417339			0.208670	+	0.977986i	$0.433087\pi$
$920$	7.02760	+	4.45264i	0.231693	+	0.146799i
$921$	86.6570			2.85544
$922$	−25.7798	−	4.91124i	−0.849012	−	0.161743i
$923$		−	5.36641i		−	0.176637i
$924$	−20.7862	−	8.21811i	−0.683815	−	0.270356i
$925$		−	26.2277i		−	0.862360i
$926$	6.56990	−	34.4863i	0.215900	−	1.13329i
$927$	133.093			4.37135
$928$	24.7785	+	34.0173i	0.813393	+	1.11667i
$929$	37.1070			1.21744			0.608720	−	0.793385i	$-0.291683\pi$
$929$	37.1070			1.21744			0.608720	+	0.793385i	$0.291683\pi$
$930$	−4.34998	+	22.8337i	−0.142641	+	0.748745i
$931$			14.2277i			0.466293i
$932$	−21.2703	−	8.40952i	−0.696733	−	0.275463i
$933$			22.3518i			0.731765i
$934$	−55.9621	−	10.6612i	−1.83114	−	0.348845i
$935$	−1.05863			−0.0346210
$936$	−18.0552	−	11.4396i	−0.590153	−	0.373917i
$937$	50.8724			1.66193			0.830965	−	0.556325i	$-0.187789\pi$
$937$	50.8724			1.66193			0.830965	+	0.556325i	$0.187789\pi$
$938$	−6.77846	−	1.29135i	−0.221324	−	0.0421639i
$939$			57.4147i			1.87366i
$940$	−5.00478	+	12.6587i	−0.163238	+	0.412880i
$941$			21.4622i			0.699647i	0.936816	+	0.349824i	$0.113759\pi$
$941$			21.4622i			0.699647i	−0.936816	+	0.349824i	$0.886241\pi$
$942$	3.26031	−	17.1138i	0.106227	−	0.557599i
$943$	27.7655			0.904168
$944$	−15.5208	+	16.5604i	−0.505160	+	0.538994i
$945$	−48.1070			−1.56492
$946$	−0.0862308	+	0.452638i	−0.00280361	+	0.0147165i
$947$			61.1690i			1.98773i	0.110617	+	0.993863i	$0.464717\pi$
$947$			61.1690i			1.98773i	−0.110617	+	0.993863i	$0.535283\pi$
$948$	−16.0862	+	40.6872i	−0.522456	+	1.32146i
$949$			3.55691i			0.115462i
$950$	−22.2277	−	4.23453i	−0.721160	−	0.137386i
$951$	−3.61899			−0.117354
$952$	4.91855	−	7.76294i	0.159411	−	0.251598i
$953$	13.2345			0.428709			0.214354	−	0.976756i	$-0.431235\pi$
$953$	13.2345			0.428709			0.214354	+	0.976756i	$0.431235\pi$
$954$	16.3449	+	3.11383i	0.529186	+	0.100814i
$955$			19.9379i			0.645176i
$956$	−31.3604	−	12.3988i	−1.01427	−	0.401005i
$957$		−	25.5898i		−	0.827200i
$958$	1.07802	−	5.65866i	0.0348291	−	0.182823i
$959$	17.2932			0.558425
$960$	−11.1017	−	23.5031i	−0.358307	−	0.758558i
$961$	−5.41023			−0.174524
$962$	−1.73534	+	9.10905i	−0.0559497	+	0.293688i
$963$			82.6830i			2.66442i
$964$	9.72938	+	3.84664i	0.313362	+	0.123892i
$965$		−	4.11727i		−	0.132539i
$966$	43.1380	+	8.21811i	1.38794	+	0.264413i
$967$	48.4441			1.55786			0.778929	−	0.627112i	$-0.215763\pi$
$967$	48.4441			1.55786			0.778929	+	0.627112i	$0.215763\pi$
$968$	14.9553	−	23.6039i	0.480680	−	0.758658i
$969$	−12.9966			−0.417510
$970$	10.6612	+	2.03104i	0.342310	+	0.0652126i
$971$			5.69910i			0.182893i	0.995810	+	0.0914464i	$0.0291490\pi$
$971$			5.69910i			0.182893i	−0.995810	+	0.0914464i	$0.970851\pi$
$972$	28.1104	−	71.1001i	0.901641	−	2.28054i
$973$			40.5500i			1.29997i
$974$	−3.98357	+	20.9103i	−0.127642	+	0.670010i
$975$	−12.9966			−0.416223
$976$	26.4622	−	28.2345i	0.847034	−	0.903765i
$977$	2.65164			0.0848334			0.0424167	−	0.999100i	$-0.486494\pi$
$977$	2.65164			0.0848334			0.0424167	+	0.999100i	$0.486494\pi$
$978$	3.58795	−	18.8337i	0.114730	−	0.602234i
$979$		−	2.24141i		−	0.0716357i
$980$	−2.61555	+	6.61555i	−0.0835506	+	0.211326i
$981$		−	78.0054i		−	2.49052i
$982$	5.45517	+	1.03925i	0.174081	+	0.0331638i
$983$	27.2491			0.869113			0.434556	−	0.900645i	$-0.356905\pi$
$983$	27.2491			0.869113			0.434556	+	0.900645i	$0.356905\pi$
$984$	−73.2794	−	46.4293i	−2.33606	−	1.48011i
$985$	10.7914			0.343844
$986$	10.3354	+	1.96896i	0.329145	+	0.0627046i
$987$			71.8509i			2.28704i
$988$	7.43965	+	2.94137i	0.236687	+	0.0935773i
$989$		−	0.905275i		−	0.0287861i
$990$	−2.11727	+	11.1138i	−0.0672911	+	0.353221i
$991$	22.7552			0.722841			0.361421	−	0.932403i	$-0.382292\pi$
$991$	22.7552			0.722841			0.361421	+	0.932403i	$0.382292\pi$
$992$	−23.1303	+	16.8483i	−0.734386	+	0.534933i
$993$	−60.1035			−1.90733
$994$	4.61464	−	24.2229i	0.146367	−	0.768303i
$995$		−	0.615547i		−	0.0195142i
$996$	−15.0974	−	5.96896i	−0.478379	−	0.189134i
$997$		−	4.79488i		−	0.151856i	−0.997113	−	0.0759278i	$-0.975808\pi$
$997$		−	4.79488i		−	0.151856i	0.997113	−	0.0759278i	$-0.0241918\pi$
$998$	44.8984	+	8.55348i	1.42123	+	0.270756i
$999$	−97.0820			−3.07154

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	104.2.b.c.53.4	yes	6
3.2	odd	2		936.2.g.c.469.3		6
4.3	odd	2		416.2.b.c.209.1		6
8.3	odd	2		416.2.b.c.209.6		6
8.5	even	2	inner	104.2.b.c.53.3	✓	6
12.11	even	2		3744.2.g.c.1873.4		6
16.3	odd	4		3328.2.a.bg.1.3		3
16.5	even	4		3328.2.a.bh.1.3		3
16.11	odd	4		3328.2.a.bf.1.1		3
16.13	even	4		3328.2.a.be.1.1		3
24.5	odd	2		936.2.g.c.469.4		6
24.11	even	2		3744.2.g.c.1873.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.b.c.53.3	✓	6	8.5	even	2	inner
104.2.b.c.53.4	yes	6	1.1	even	1	trivial
416.2.b.c.209.1		6	4.3	odd	2
416.2.b.c.209.6		6	8.3	odd	2
936.2.g.c.469.3		6	3.2	odd	2
936.2.g.c.469.4		6	24.5	odd	2
3328.2.a.be.1.1		3	16.13	even	4
3328.2.a.bf.1.1		3	16.11	odd	4
3328.2.a.bg.1.3		3	16.3	odd	4
3328.2.a.bh.1.3		3	16.5	even	4
3744.2.g.c.1873.1		6	24.11	even	2
3744.2.g.c.1873.4		6	12.11	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	104.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.264658 + 1.38923i) q^{2} +3.24914i q^{3} +(-1.85991 - 0.735342i) q^{4} -1.00000i q^{5} +(-4.51380 - 0.859912i) q^{6} +3.24914 q^{7} +(1.51380 - 2.38923i) q^{8} -7.55691 q^{9} +(1.38923 + 0.264658i) q^{10} -1.05863i q^{11} +(2.38923 - 6.04312i) q^{12} +1.00000i q^{13} +(-0.859912 + 4.51380i) q^{14} +3.24914 q^{15} +(2.91855 + 2.73534i) q^{16} +1.00000 q^{17} +(2.00000 - 10.4983i) q^{18} +4.00000i q^{19} +(-0.735342 + 1.85991i) q^{20} +10.5569i q^{21} +(1.47068 + 0.280176i) q^{22} -2.94137 q^{23} +(7.76294 + 4.91855i) q^{24} +4.00000 q^{25} +(-1.38923 - 0.264658i) q^{26} -14.8061i q^{27} +(-6.04312 - 2.38923i) q^{28} -7.43965i q^{29} +(-0.859912 + 4.51380i) q^{30} +5.05863 q^{31} +(-4.57243 + 3.33060i) q^{32} +3.43965 q^{33} +(-0.264658 + 1.38923i) q^{34} -3.24914i q^{35} +(14.0552 + 5.55691i) q^{36} -6.55691i q^{37} +(-5.55691 - 1.05863i) q^{38} -3.24914 q^{39} +(-2.38923 - 1.51380i) q^{40} -9.43965 q^{41} +(-14.6660 - 2.79397i) q^{42} +0.307774i q^{43} +(-0.778457 + 1.96896i) q^{44} +7.55691i q^{45} +(0.778457 - 4.08623i) q^{46} +6.80605 q^{47} +(-8.88751 + 9.48276i) q^{48} +3.55691 q^{49} +(-1.05863 + 5.55691i) q^{50} +3.24914i q^{51} +(0.735342 - 1.85991i) q^{52} +1.55691i q^{53} +(20.5690 + 3.91855i) q^{54} -1.05863 q^{55} +(4.91855 - 7.76294i) q^{56} -12.9966 q^{57} +(10.3354 + 1.96896i) q^{58} +5.67418i q^{59} +(-6.04312 - 2.38923i) q^{60} -9.67418i q^{61} +(-1.33881 + 7.02760i) q^{62} -24.5535 q^{63} +(-3.41683 - 7.23362i) q^{64} +1.00000 q^{65} +(-0.910331 + 4.77846i) q^{66} +1.50172i q^{67} +(-1.85991 - 0.735342i) q^{68} -9.55691i q^{69} +(4.51380 + 0.859912i) q^{70} -5.36641 q^{71} +(-11.4396 + 18.0552i) q^{72} +3.55691 q^{73} +(9.10905 + 1.73534i) q^{74} +12.9966i q^{75} +(2.94137 - 7.43965i) q^{76} -3.43965i q^{77} +(0.859912 - 4.51380i) q^{78} -6.73281 q^{79} +(2.73534 - 2.91855i) q^{80} +25.4362 q^{81} +(2.49828 - 13.1138i) q^{82} -2.49828i q^{83} +(7.76294 - 19.6349i) q^{84} -1.00000i q^{85} +(-0.427568 - 0.0814549i) q^{86} +24.1725 q^{87} +(-2.52932 - 1.60256i) q^{88} +2.11727 q^{89} +(-10.4983 - 2.00000i) q^{90} +3.24914i q^{91} +(5.47068 + 2.16291i) q^{92} +16.4362i q^{93} +(-1.80128 + 9.45517i) q^{94} +4.00000 q^{95} +(-10.8216 - 14.8565i) q^{96} +7.67418 q^{97} +(-0.941367 + 4.94137i) q^{98} +8.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 2 q^{4} - 10 q^{6} + 2 q^{7} - 8 q^{8} - 12 q^{9} + 6 q^{12} + 4 q^{14} + 2 q^{15} + 10 q^{16} + 6 q^{17} + 12 q^{18} - 4 q^{20} + 8 q^{22} - 16 q^{23} + 12 q^{24} + 24 q^{25} - 20 q^{28}+ \cdots - 4 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 - 2 * q^4 - 10 * q^6 + 2 * q^7 - 8 * q^8 - 12 * q^9 + 6 * q^12 + 4 * q^14 + 2 * q^15 + 10 * q^16 + 6 * q^17 + 12 * q^18 - 4 * q^20 + 8 * q^22 - 16 * q^23 + 12 * q^24 + 24 * q^25 - 20 * q^28 + 4 * q^30 + 32 * q^31 - 12 * q^32 - 16 * q^33 - 2 * q^34 + 16 * q^36 - 2 * q^39 - 6 * q^40 - 20 * q^41 - 28 * q^42 + 12 * q^44 - 12 * q^46 - 10 * q^47 - 10 * q^48 - 12 * q^49 - 8 * q^50 + 4 * q^52 + 38 * q^54 - 8 * q^55 + 22 * q^56 - 8 * q^57 + 12 * q^58 - 20 * q^60 - 28 * q^62 - 44 * q^63 + 22 * q^64 + 6 * q^65 + 32 * q^66 - 2 * q^68 + 10 * q^70 - 18 * q^71 - 32 * q^72 - 12 * q^73 + 28 * q^74 + 16 * q^76 - 4 * q^78 - 12 * q^79 + 16 * q^80 + 46 * q^81 - 20 * q^82 + 12 * q^84 - 18 * q^86 + 80 * q^87 - 16 * q^88 + 16 * q^89 - 28 * q^90 + 32 * q^92 + 24 * q^95 - 32 * q^96 + 16 * q^97 - 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more