LMFDB - Embedded newform 1183.2.c.d.337.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(337,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1183.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.2
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1183.337
Dual form			1183.2.c.d.337.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +1.41421 q^{3} +1.58579i q^{5} -2.00000i q^{6} -1.00000i q^{7} -2.82843i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +1.41421 q^{3} +1.58579i q^{5} -2.00000i q^{6} -1.00000i q^{7} -2.82843i q^{8} -1.00000 q^{9} +2.24264 q^{10} -4.24264i q^{11} -1.41421 q^{14} +2.24264i q^{15} -4.00000 q^{16} -1.41421 q^{17} +1.41421i q^{18} -7.24264i q^{19} -1.41421i q^{21} -6.00000 q^{22} +5.82843 q^{23} -4.00000i q^{24} +2.48528 q^{25} -5.65685 q^{27} +0.171573 q^{29} +3.17157 q^{30} +3.24264i q^{31} -6.00000i q^{33} +2.00000i q^{34} +1.58579 q^{35} -2.24264i q^{37} -10.2426 q^{38} +4.48528 q^{40} +8.82843i q^{41} -2.00000 q^{42} +5.00000 q^{43} -1.58579i q^{45} -8.24264i q^{46} -1.58579i q^{47} -5.65685 q^{48} -1.00000 q^{49} -3.51472i q^{50} -2.00000 q^{51} -0.171573 q^{53} +8.00000i q^{54} +6.72792 q^{55} -2.82843 q^{56} -10.2426i q^{57} -0.242641i q^{58} -0.343146i q^{59} +6.00000 q^{61} +4.58579 q^{62} +1.00000i q^{63} -8.00000 q^{64} -8.48528 q^{66} -14.4853i q^{67} +8.24264 q^{69} -2.24264i q^{70} -13.0711i q^{71} +2.82843i q^{72} +9.24264i q^{73} -3.17157 q^{74} +3.51472 q^{75} -4.24264 q^{77} +15.4853 q^{79} -6.34315i q^{80} -5.00000 q^{81} +12.4853 q^{82} +13.2426i q^{83} -2.24264i q^{85} -7.07107i q^{86} +0.242641 q^{87} -12.0000 q^{88} -1.58579i q^{89} -2.24264 q^{90} +4.58579i q^{93} -2.24264 q^{94} +11.4853 q^{95} +11.7279i q^{97} +1.41421i q^{98} +4.24264i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^9	$ 4 q - 4 q^{9} - 8 q^{10} - 16 q^{16} - 24 q^{22} + 12 q^{23} - 24 q^{25} + 12 q^{29} + 24 q^{30} + 12 q^{35} - 24 q^{38} - 16 q^{40} - 8 q^{42} + 20 q^{43} - 4 q^{49} - 8 q^{51} - 12 q^{53} - 24 q^{55} + 24 q^{61} + 24 q^{62} - 32 q^{64} + 16 q^{69} - 24 q^{74} + 48 q^{75} + 28 q^{79} - 20 q^{81} + 16 q^{82} - 16 q^{87} - 48 q^{88} + 8 q^{90} + 8 q^{94} + 12 q^{95}+O(q^{100}) $ 4 * q - 4 * q^9 - 8 * q^10 - 16 * q^16 - 24 * q^22 + 12 * q^23 - 24 * q^25 + 12 * q^29 + 24 * q^30 + 12 * q^35 - 24 * q^38 - 16 * q^40 - 8 * q^42 + 20 * q^43 - 4 * q^49 - 8 * q^51 - 12 * q^53 - 24 * q^55 + 24 * q^61 + 24 * q^62 - 32 * q^64 + 16 * q^69 - 24 * q^74 + 48 * q^75 + 28 * q^79 - 20 * q^81 + 16 * q^82 - 16 * q^87 - 48 * q^88 + 8 * q^90 + 8 * q^94 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 1.41421i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$2$	− 1.41421i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$3$	1.41421	0.816497	0.408248	−	0.912871i	$-0.366140\pi$
$3$	1.41421	0.816497	0.408248	+	0.912871i	$0.366140\pi$
$4$	0	0
$5$	1.58579i	0.709185i	0.935021	+	0.354593i	$0.115380\pi$
$5$	1.58579i	0.709185i	−0.935021	+	0.354593i	$0.884620\pi$
$6$	− 2.00000i	− 0.816497i
$7$	− 1.00000i	− 0.377964i
$7$	− 1.00000i	− 0.377964i
$8$	− 2.82843i	− 1.00000i
$9$	−1.00000	−0.333333
$10$	2.24264	0.709185
$11$	− 4.24264i	− 1.27920i	−0.768706	−	0.639602i	$-0.779099\pi$
$11$	− 4.24264i	− 1.27920i	0.768706	−	0.639602i	$-0.220901\pi$
$12$	0	0
$13$	0	0
$13$	0	0
$14$	−1.41421	−0.377964
$15$	2.24264i	0.579047i
$16$	−4.00000	−1.00000
$17$	−1.41421	−0.342997	−0.171499	−	0.985184i	$-0.554861\pi$
$17$	−1.41421	−0.342997	−0.171499	+	0.985184i	$0.554861\pi$
$18$	1.41421i	0.333333i
$19$	− 7.24264i	− 1.66158i	−0.556589	−	0.830788i	$-0.687890\pi$
$19$	− 7.24264i	− 1.66158i	0.556589	−	0.830788i	$-0.312110\pi$
$20$	0	0
$21$	− 1.41421i	− 0.308607i
$22$	−6.00000	−1.27920
$23$	5.82843	1.21531	0.607656	−	0.794201i	$-0.292110\pi$
$23$	5.82843	1.21531	0.607656	+	0.794201i	$0.292110\pi$
$24$	− 4.00000i	− 0.816497i
$25$	2.48528	0.497056
$26$	0	0
$27$	−5.65685	−1.08866
$28$	0	0
$29$	0.171573	0.0318603	0.0159301	−	0.999873i	$-0.494929\pi$
$29$	0.171573	0.0318603	0.0159301	+	0.999873i	$0.494929\pi$
$30$	3.17157	0.579047
$31$	3.24264i	0.582395i	0.956663	+	0.291198i	$0.0940538\pi$
$31$	3.24264i	0.582395i	−0.956663	+	0.291198i	$0.905946\pi$
$32$	0	0
$33$	− 6.00000i	− 1.04447i
$34$	2.00000i	0.342997i
$35$	1.58579	0.268047
$36$	0	0
$37$	− 2.24264i	− 0.368688i	−0.982862	−	0.184344i	$-0.940984\pi$
$37$	− 2.24264i	− 0.368688i	0.982862	−	0.184344i	$-0.0590160\pi$
$38$	−10.2426	−1.66158
$39$	0	0
$40$	4.48528	0.709185
$41$	8.82843i	1.37877i	0.724396	+	0.689384i	$0.242119\pi$
$41$	8.82843i	1.37877i	−0.724396	+	0.689384i	$0.757881\pi$
$42$	−2.00000	−0.308607
$43$	5.00000	0.762493	0.381246	−	0.924473i	$-0.375495\pi$
$43$	5.00000	0.762493	0.381246	+	0.924473i	$0.375495\pi$
$44$	0	0
$45$	− 1.58579i	− 0.236395i
$46$	− 8.24264i	− 1.21531i
$47$	− 1.58579i	− 0.231311i	−0.993289	−	0.115655i	$-0.963103\pi$
$47$	− 1.58579i	− 0.231311i	0.993289	−	0.115655i	$-0.0368968\pi$
$48$	−5.65685	−0.816497
$49$	−1.00000	−0.142857
$50$	− 3.51472i	− 0.497056i
$51$	−2.00000	−0.280056
$52$	0	0
$53$	−0.171573	−0.0235673	−0.0117837	−	0.999931i	$-0.503751\pi$
$53$	−0.171573	−0.0235673	−0.0117837	+	0.999931i	$0.503751\pi$
$54$	8.00000i	1.08866i
$55$	6.72792	0.907193
$56$	−2.82843	−0.377964
$57$	− 10.2426i	− 1.35667i
$58$	− 0.242641i	− 0.0318603i
$59$	− 0.343146i	− 0.0446738i	−0.999751	−	0.0223369i	$-0.992889\pi$
$59$	− 0.343146i	− 0.0446738i	0.999751	−	0.0223369i	$-0.00711064\pi$
$60$	0	0
$61$	6.00000	0.768221	0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000	0.768221	0.384111	+	0.923287i	$0.374508\pi$
$62$	4.58579	0.582395
$63$	1.00000i	0.125988i
$64$	−8.00000	−1.00000
$65$	0	0
$66$	−8.48528	−1.04447
$67$	− 14.4853i	− 1.76966i	−0.465915	−	0.884829i	$-0.654275\pi$
$67$	− 14.4853i	− 1.76966i	0.465915	−	0.884829i	$-0.345725\pi$
$68$	0	0
$69$	8.24264	0.992297
$70$	− 2.24264i	− 0.268047i
$71$	− 13.0711i	− 1.55125i	−0.631194	−	0.775625i	$-0.717435\pi$
$71$	− 13.0711i	− 1.55125i	0.631194	−	0.775625i	$-0.282565\pi$
$72$	2.82843i	0.333333i
$73$	9.24264i	1.08177i	0.841097	+	0.540885i	$0.181910\pi$
$73$	9.24264i	1.08177i	−0.841097	+	0.540885i	$0.818090\pi$
$74$	−3.17157	−0.368688
$75$	3.51472	0.405845
$76$	0	0
$77$	−4.24264	−0.483494
$78$	0	0
$79$	15.4853	1.74223	0.871115	−	0.491079i	$-0.163397\pi$
$79$	15.4853	1.74223	0.871115	+	0.491079i	$0.163397\pi$
$80$	− 6.34315i	− 0.709185i
$81$	−5.00000	−0.555556
$82$	12.4853	1.37877
$83$	13.2426i	1.45357i	0.686866	+	0.726784i	$0.258986\pi$
$83$	13.2426i	1.45357i	−0.686866	+	0.726784i	$0.741014\pi$
$84$	0	0
$85$	− 2.24264i	− 0.243249i
$86$	− 7.07107i	− 0.762493i
$87$	0.242641	0.0260138
$88$	−12.0000	−1.27920
$89$	− 1.58579i	− 0.168093i	−0.996462	−	0.0840465i	$-0.973216\pi$
$89$	− 1.58579i	− 0.168093i	0.996462	−	0.0840465i	$-0.0267844\pi$
$90$	−2.24264	−0.236395
$91$	0	0
$92$	0	0
$93$	4.58579i	0.475524i
$94$	−2.24264	−0.231311
$95$	11.4853	1.17837
$96$	0	0
$97$	11.7279i	1.19079i	0.803433	+	0.595395i	$0.203004\pi$
$97$	11.7279i	1.19079i	−0.803433	+	0.595395i	$0.796996\pi$
$98$	1.41421i	0.142857i
$99$	4.24264i	0.426401i
$100$	0	0
$101$	−10.2426	−1.01918	−0.509590	−	0.860417i	$-0.670203\pi$
$101$	−10.2426	−1.01918	−0.509590	+	0.860417i	$0.670203\pi$
$102$	2.82843i	0.280056i
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	0	0
$105$	2.24264	0.218859
$106$	0.242641i	0.0235673i
$107$	−20.1421	−1.94721	−0.973607	−	0.228232i	$-0.926706\pi$
$107$	−20.1421	−1.94721	−0.973607	+	0.228232i	$0.926706\pi$
$108$	0	0
$109$	16.7279i	1.60224i	0.598501	+	0.801122i	$0.295763\pi$
$109$	16.7279i	1.60224i	−0.598501	+	0.801122i	$0.704237\pi$
$110$	− 9.51472i	− 0.907193i
$111$	− 3.17157i	− 0.301032i
$112$	4.00000i	0.377964i
$113$	2.31371	0.217655	0.108828	−	0.994061i	$-0.465290\pi$
$113$	2.31371	0.217655	0.108828	+	0.994061i	$0.465290\pi$
$114$	−14.4853	−1.35667
$115$	9.24264i	0.861881i
$116$	0	0
$117$	0	0
$118$	−0.485281	−0.0446738
$119$	1.41421i	0.129641i
$120$	6.34315	0.579047
$121$	−7.00000	−0.636364
$122$	− 8.48528i	− 0.768221i
$123$	12.4853i	1.12576i
$124$	0	0
$125$	11.8701i	1.06169i
$126$	1.41421	0.125988
$127$	−2.00000	−0.177471	−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000	−0.177471	−0.0887357	+	0.996055i	$0.528283\pi$
$128$	11.3137i	1.00000i
$129$	7.07107	0.622573
$130$	0	0
$131$	−2.82843	−0.247121	−0.123560	−	0.992337i	$-0.539431\pi$
$131$	−2.82843	−0.247121	−0.123560	+	0.992337i	$0.539431\pi$
$132$	0	0
$133$	−7.24264	−0.628017
$134$	−20.4853	−1.76966
$135$	− 8.97056i	− 0.772063i
$136$	4.00000i	0.342997i
$137$	4.58579i	0.391790i	0.980625	+	0.195895i	$0.0627612\pi$
$137$	4.58579i	0.391790i	−0.980625	+	0.195895i	$0.937239\pi$
$138$	− 11.6569i	− 0.992297i
$139$	6.24264	0.529494	0.264747	−	0.964318i	$-0.414712\pi$
$139$	6.24264	0.529494	0.264747	+	0.964318i	$0.414712\pi$
$140$	0	0
$141$	− 2.24264i	− 0.188864i
$142$	−18.4853	−1.55125
$143$	0	0
$144$	4.00000	0.333333
$145$	0.272078i	0.0225948i
$146$	13.0711	1.08177
$147$	−1.41421	−0.116642
$148$	0	0
$149$	16.2426i	1.33065i	0.746554	+	0.665324i	$0.231707\pi$
$149$	16.2426i	1.33065i	−0.746554	+	0.665324i	$0.768293\pi$
$150$	− 4.97056i	− 0.405845i
$151$	9.75736i	0.794043i	0.917809	+	0.397021i	$0.129956\pi$
$151$	9.75736i	0.794043i	−0.917809	+	0.397021i	$0.870044\pi$
$152$	−20.4853	−1.66158
$153$	1.41421	0.114332
$154$	6.00000i	0.483494i
$155$	−5.14214	−0.413026
$156$	0	0
$157$	−3.75736	−0.299870	−0.149935	−	0.988696i	$-0.547906\pi$
$157$	−3.75736	−0.299870	−0.149935	+	0.988696i	$0.547906\pi$
$158$	− 21.8995i	− 1.74223i
$159$	−0.242641	−0.0192427
$160$	0	0
$161$	− 5.82843i	− 0.459344i
$162$	7.07107i	0.555556i
$163$	− 8.48528i	− 0.664619i	−0.943170	−	0.332309i	$-0.892172\pi$
$163$	− 8.48528i	− 0.664619i	0.943170	−	0.332309i	$-0.107828\pi$
$164$	0	0
$165$	9.51472	0.740720
$166$	18.7279	1.45357
$167$	− 15.3848i	− 1.19051i	−0.803537	−	0.595255i	$-0.797051\pi$
$167$	− 15.3848i	− 1.19051i	0.803537	−	0.595255i	$-0.202949\pi$
$168$	−4.00000	−0.308607
$169$	0	0
$170$	−3.17157	−0.243249
$171$	7.24264i	0.553859i
$172$	0	0
$173$	−24.7279	−1.88003	−0.940015	−	0.341134i	$-0.889189\pi$
$173$	−24.7279	−1.88003	−0.940015	+	0.341134i	$0.889189\pi$
$174$	− 0.343146i	− 0.0260138i
$175$	− 2.48528i	− 0.187870i
$176$	16.9706i	1.27920i
$177$	− 0.485281i	− 0.0364760i
$178$	−2.24264	−0.168093
$179$	9.00000	0.672692	0.336346	−	0.941739i	$-0.390809\pi$
$179$	9.00000	0.672692	0.336346	+	0.941739i	$0.390809\pi$
$180$	0	0
$181$	18.7279	1.39204	0.696018	−	0.718025i	$-0.254953\pi$
$181$	18.7279	1.39204	0.696018	+	0.718025i	$0.254953\pi$
$182$	0	0
$183$	8.48528	0.627250
$184$	− 16.4853i	− 1.21531i
$185$	3.55635	0.261468
$186$	6.48528	0.475524
$187$	6.00000i	0.438763i
$188$	0	0
$189$	5.65685i	0.411476i
$190$	− 16.2426i	− 1.17837i
$191$	15.1716	1.09778	0.548888	−	0.835896i	$-0.315051\pi$
$191$	15.1716	1.09778	0.548888	+	0.835896i	$0.315051\pi$
$192$	−11.3137	−0.816497
$193$	14.4853i	1.04267i	0.853351	+	0.521337i	$0.174566\pi$
$193$	14.4853i	1.04267i	−0.853351	+	0.521337i	$0.825434\pi$
$194$	16.5858	1.19079
$195$	0	0
$196$	0	0
$197$	12.3431i	0.879413i	0.898142	+	0.439706i	$0.144917\pi$
$197$	12.3431i	0.879413i	−0.898142	+	0.439706i	$0.855083\pi$
$198$	6.00000	0.426401
$199$	3.75736	0.266352	0.133176	−	0.991092i	$-0.457482\pi$
$199$	3.75736	0.266352	0.133176	+	0.991092i	$0.457482\pi$
$200$	− 7.02944i	− 0.497056i
$201$	− 20.4853i	− 1.44492i
$202$	14.4853i	1.01918i
$203$	− 0.171573i	− 0.0120421i
$204$	0	0
$205$	−14.0000	−0.977802
$206$	− 11.3137i	− 0.788263i
$207$	−5.82843	−0.405104
$208$	0	0
$209$	−30.7279	−2.12549
$210$	− 3.17157i	− 0.218859i
$211$	−15.9706	−1.09946	−0.549729	−	0.835343i	$-0.685269\pi$
$211$	−15.9706	−1.09946	−0.549729	+	0.835343i	$0.685269\pi$
$212$	0	0
$213$	− 18.4853i	− 1.26659i
$214$	28.4853i	1.94721i
$215$	7.92893i	0.540749i
$216$	16.0000i	1.08866i
$217$	3.24264	0.220125
$218$	23.6569	1.60224
$219$	13.0711i	0.883261i
$220$	0	0
$221$	0	0
$222$	−4.48528	−0.301032
$223$	0.757359i	0.0507165i	0.999678	+	0.0253583i	$0.00807265\pi$
$223$	0.757359i	0.0507165i	−0.999678	+	0.0253583i	$0.991927\pi$
$224$	0	0
$225$	−2.48528	−0.165685
$226$	− 3.27208i	− 0.217655i
$227$	26.8284i	1.78067i	0.455311	+	0.890333i	$0.349528\pi$
$227$	26.8284i	1.78067i	−0.455311	+	0.890333i	$0.650472\pi$
$228$	0	0
$229$	− 29.4558i	− 1.94650i	−0.229755	−	0.973248i	$-0.573793\pi$
$229$	− 29.4558i	− 1.94650i	0.229755	−	0.973248i	$-0.426207\pi$
$230$	13.0711	0.861881
$231$	−6.00000	−0.394771
$232$	− 0.485281i	− 0.0318603i
$233$	14.6569	0.960202	0.480101	−	0.877213i	$-0.340600\pi$
$233$	14.6569	0.960202	0.480101	+	0.877213i	$0.340600\pi$
$234$	0	0
$235$	2.51472	0.164042
$236$	0	0
$237$	21.8995	1.42253
$238$	2.00000	0.129641
$239$	3.51472i	0.227348i	0.993518	+	0.113674i	$0.0362620\pi$
$239$	3.51472i	0.227348i	−0.993518	+	0.113674i	$0.963738\pi$
$240$	− 8.97056i	− 0.579047i
$241$	20.2132i	1.30205i	0.759058	+	0.651023i	$0.225660\pi$
$241$	20.2132i	1.30205i	−0.759058	+	0.651023i	$0.774340\pi$
$242$	9.89949i	0.636364i
$243$	9.89949	0.635053
$244$	0	0
$245$	− 1.58579i	− 0.101312i
$246$	17.6569	1.12576
$247$	0	0
$248$	9.17157	0.582395
$249$	18.7279i	1.18683i
$250$	16.7868	1.06169
$251$	−16.5858	−1.04689	−0.523443	−	0.852061i	$-0.675353\pi$
$251$	−16.5858	−1.04689	−0.523443	+	0.852061i	$0.675353\pi$
$252$	0	0
$253$	− 24.7279i	− 1.55463i
$254$	2.82843i	0.177471i
$255$	− 3.17157i	− 0.198612i
$256$	0	0
$257$	19.4142	1.21103	0.605513	−	0.795836i	$-0.292968\pi$
$257$	19.4142	1.21103	0.605513	+	0.795836i	$0.292968\pi$
$258$	− 10.0000i	− 0.622573i
$259$	−2.24264	−0.139351
$260$	0	0
$261$	−0.171573	−0.0106201
$262$	4.00000i	0.247121i
$263$	1.97056	0.121510	0.0607551	−	0.998153i	$-0.480649\pi$
$263$	1.97056	0.121510	0.0607551	+	0.998153i	$0.480649\pi$
$264$	−16.9706	−1.04447
$265$	− 0.272078i	− 0.0167136i
$266$	10.2426i	0.628017i
$267$	− 2.24264i	− 0.137247i
$268$	0	0
$269$	9.17157	0.559201	0.279600	−	0.960116i	$-0.409798\pi$
$269$	9.17157	0.559201	0.279600	+	0.960116i	$0.409798\pi$
$270$	−12.6863	−0.772063
$271$	− 20.0000i	− 1.21491i	−0.794353	−	0.607457i	$-0.792190\pi$
$271$	− 20.0000i	− 1.21491i	0.794353	−	0.607457i	$-0.207810\pi$
$272$	5.65685	0.342997
$273$	0	0
$274$	6.48528	0.391790
$275$	− 10.5442i	− 0.635837i
$276$	0	0
$277$	7.48528	0.449747	0.224873	−	0.974388i	$-0.427803\pi$
$277$	7.48528	0.449747	0.224873	+	0.974388i	$0.427803\pi$
$278$	− 8.82843i	− 0.529494i
$279$	− 3.24264i	− 0.194132i
$280$	− 4.48528i	− 0.268047i
$281$	− 15.5563i	− 0.928014i	−0.885832	−	0.464007i	$-0.846411\pi$
$281$	− 15.5563i	− 0.928014i	0.885832	−	0.464007i	$-0.153589\pi$
$282$	−3.17157	−0.188864
$283$	8.48528	0.504398	0.252199	−	0.967675i	$-0.418846\pi$
$283$	8.48528	0.504398	0.252199	+	0.967675i	$0.418846\pi$
$284$	0	0
$285$	16.2426	0.962131
$286$	0	0
$287$	8.82843	0.521126
$288$	0	0
$289$	−15.0000	−0.882353
$290$	0.384776	0.0225948
$291$	16.5858i	0.972276i
$292$	0	0
$293$	− 15.3848i	− 0.898788i	−0.893334	−	0.449394i	$-0.851640\pi$
$293$	− 15.3848i	− 0.898788i	0.893334	−	0.449394i	$-0.148360\pi$
$294$	2.00000i	0.116642i
$295$	0.544156	0.0316820
$296$	−6.34315	−0.368688
$297$	24.0000i	1.39262i
$298$	22.9706	1.33065
$299$	0	0
$300$	0	0
$301$	− 5.00000i	− 0.288195i
$302$	13.7990	0.794043
$303$	−14.4853	−0.832158
$304$	28.9706i	1.66158i
$305$	9.51472i	0.544811i
$306$	− 2.00000i	− 0.114332i
$307$	− 13.2426i	− 0.755797i	−0.925847	−	0.377899i	$-0.876647\pi$
$307$	− 13.2426i	− 0.755797i	0.925847	−	0.377899i	$-0.123353\pi$
$308$	0	0
$309$	11.3137	0.643614
$310$	7.27208i	0.413026i
$311$	7.41421	0.420421	0.210211	−	0.977656i	$-0.432585\pi$
$311$	7.41421	0.420421	0.210211	+	0.977656i	$0.432585\pi$
$312$	0	0
$313$	23.2132	1.31209	0.656044	−	0.754723i	$-0.272229\pi$
$313$	23.2132	1.31209	0.656044	+	0.754723i	$0.272229\pi$
$314$	5.31371i	0.299870i
$315$	−1.58579	−0.0893489
$316$	0	0
$317$	− 11.3137i	− 0.635441i	−0.948184	−	0.317721i	$-0.897083\pi$
$317$	− 11.3137i	− 0.635441i	0.948184	−	0.317721i	$-0.102917\pi$
$318$	0.343146i	0.0192427i
$319$	− 0.727922i	− 0.0407558i
$320$	− 12.6863i	− 0.709185i
$321$	−28.4853	−1.58989
$322$	−8.24264	−0.459344
$323$	10.2426i	0.569916i
$324$	0	0
$325$	0	0
$326$	−12.0000	−0.664619
$327$	23.6569i	1.30823i
$328$	24.9706	1.37877
$329$	−1.58579	−0.0874272
$330$	− 13.4558i	− 0.740720i
$331$	− 18.0000i	− 0.989369i	−0.869072	−	0.494685i	$-0.835284\pi$
$331$	− 18.0000i	− 0.989369i	0.869072	−	0.494685i	$-0.164716\pi$
$332$	0	0
$333$	2.24264i	0.122896i
$334$	−21.7574	−1.19051
$335$	22.9706	1.25502
$336$	5.65685i	0.308607i
$337$	33.0000	1.79762	0.898812	−	0.438334i	$-0.144431\pi$
$337$	33.0000	1.79762	0.898812	+	0.438334i	$0.144431\pi$
$338$	0	0
$339$	3.27208	0.177715
$340$	0	0
$341$	13.7574	0.745003
$342$	10.2426	0.553859
$343$	1.00000i	0.0539949i
$344$	− 14.1421i	− 0.762493i
$345$	13.0711i	0.703723i
$346$	34.9706i	1.88003i
$347$	−5.65685	−0.303676	−0.151838	−	0.988405i	$-0.548519\pi$
$347$	−5.65685	−0.303676	−0.151838	+	0.988405i	$0.548519\pi$
$348$	0	0
$349$	25.7279i	1.37718i	0.725149	+	0.688592i	$0.241771\pi$
$349$	25.7279i	1.37718i	−0.725149	+	0.688592i	$0.758229\pi$
$350$	−3.51472	−0.187870
$351$	0	0
$352$	0	0
$353$	− 8.48528i	− 0.451626i	−0.974171	−	0.225813i	$-0.927496\pi$
$353$	− 8.48528i	− 0.451626i	0.974171	−	0.225813i	$-0.0725038\pi$
$354$	−0.686292	−0.0364760
$355$	20.7279	1.10012
$356$	0	0
$357$	2.00000i	0.105851i
$358$	− 12.7279i	− 0.672692i
$359$	27.8995i	1.47248i	0.676721	+	0.736240i	$0.263400\pi$
$359$	27.8995i	1.47248i	−0.676721	+	0.736240i	$0.736600\pi$
$360$	−4.48528	−0.236395
$361$	−33.4558	−1.76083
$362$	− 26.4853i	− 1.39204i
$363$	−9.89949	−0.519589
$364$	0	0
$365$	−14.6569	−0.767175
$366$	− 12.0000i	− 0.627250i
$367$	10.2426	0.534661	0.267331	−	0.963605i	$-0.413858\pi$
$367$	10.2426	0.534661	0.267331	+	0.963605i	$0.413858\pi$
$368$	−23.3137	−1.21531
$369$	− 8.82843i	− 0.459590i
$370$	− 5.02944i	− 0.261468i
$371$	0.171573i	0.00890762i
$372$	0	0
$373$	8.48528	0.439351	0.219676	−	0.975573i	$-0.429500\pi$
$373$	8.48528	0.439351	0.219676	+	0.975573i	$0.429500\pi$
$374$	8.48528	0.438763
$375$	16.7868i	0.866866i
$376$	−4.48528	−0.231311
$377$	0	0
$378$	8.00000	0.411476
$379$	23.7574i	1.22033i	0.792273	+	0.610167i	$0.208898\pi$
$379$	23.7574i	1.22033i	−0.792273	+	0.610167i	$0.791102\pi$
$380$	0	0
$381$	−2.82843	−0.144905
$382$	− 21.4558i	− 1.09778i
$383$	− 20.4853i	− 1.04675i	−0.852103	−	0.523374i	$-0.824673\pi$
$383$	− 20.4853i	− 1.04675i	0.852103	−	0.523374i	$-0.175327\pi$
$384$	16.0000i	0.816497i
$385$	− 6.72792i	− 0.342887i
$386$	20.4853	1.04267
$387$	−5.00000	−0.254164
$388$	0	0
$389$	−29.6569	−1.50366	−0.751831	−	0.659356i	$-0.770829\pi$
$389$	−29.6569	−1.50366	−0.751831	+	0.659356i	$0.770829\pi$
$390$	0	0
$391$	−8.24264	−0.416848
$392$	2.82843i	0.142857i
$393$	−4.00000	−0.201773
$394$	17.4558	0.879413
$395$	24.5563i	1.23556i
$396$	0	0
$397$	18.2132i	0.914094i	0.889442	+	0.457047i	$0.151093\pi$
$397$	18.2132i	0.914094i	−0.889442	+	0.457047i	$0.848907\pi$
$398$	− 5.31371i	− 0.266352i
$399$	−10.2426	−0.512773
$400$	−9.94113	−0.497056
$401$	− 6.34315i	− 0.316762i	−0.987378	−	0.158381i	$-0.949373\pi$
$401$	− 6.34315i	− 0.316762i	0.987378	−	0.158381i	$-0.0506274\pi$
$402$	−28.9706	−1.44492
$403$	0	0
$404$	0	0
$405$	− 7.92893i	− 0.393992i
$406$	−0.242641	−0.0120421
$407$	−9.51472	−0.471627
$408$	5.65685i	0.280056i
$409$	3.24264i	0.160338i	0.996781	+	0.0801691i	$0.0255460\pi$
$409$	3.24264i	0.160338i	−0.996781	+	0.0801691i	$0.974454\pi$
$410$	19.7990i	0.977802i
$411$	6.48528i	0.319895i
$412$	0	0
$413$	−0.343146	−0.0168851
$414$	8.24264i	0.405104i
$415$	−21.0000	−1.03085
$416$	0	0
$417$	8.82843	0.432330
$418$	43.4558i	2.12549i
$419$	−20.8701	−1.01957	−0.509785	−	0.860302i	$-0.670275\pi$
$419$	−20.8701	−1.01957	−0.509785	+	0.860302i	$0.670275\pi$
$420$	0	0
$421$	6.72792i	0.327899i	0.986469	+	0.163949i	$0.0524234\pi$
$421$	6.72792i	0.327899i	−0.986469	+	0.163949i	$0.947577\pi$
$422$	22.5858i	1.09946i
$423$	1.58579i	0.0771036i
$424$	0.485281i	0.0235673i
$425$	−3.51472	−0.170489
$426$	−26.1421	−1.26659
$427$	− 6.00000i	− 0.290360i
$428$	0	0
$429$	0	0
$430$	11.2132	0.540749
$431$	− 12.3431i	− 0.594548i	−0.954792	−	0.297274i	$-0.903922\pi$
$431$	− 12.3431i	− 0.594548i	0.954792	−	0.297274i	$-0.0960775\pi$
$432$	22.6274	1.08866
$433$	24.9706	1.20001	0.600004	−	0.799997i	$-0.295166\pi$
$433$	24.9706	1.20001	0.600004	+	0.799997i	$0.295166\pi$
$434$	− 4.58579i	− 0.220125i
$435$	0.384776i	0.0184486i
$436$	0	0
$437$	− 42.2132i	− 2.01933i
$438$	18.4853	0.883261
$439$	34.4853	1.64589	0.822946	−	0.568119i	$-0.192329\pi$
$439$	34.4853	1.64589	0.822946	+	0.568119i	$0.192329\pi$
$440$	− 19.0294i	− 0.907193i
$441$	1.00000	0.0476190
$442$	0	0
$443$	−3.68629	−0.175141	−0.0875705	−	0.996158i	$-0.527910\pi$
$443$	−3.68629	−0.175141	−0.0875705	+	0.996158i	$0.527910\pi$
$444$	0	0
$445$	2.51472	0.119209
$446$	1.07107	0.0507165
$447$	22.9706i	1.08647i
$448$	8.00000i	0.377964i
$449$	− 21.1716i	− 0.999148i	−0.866271	−	0.499574i	$-0.833490\pi$
$449$	− 21.1716i	− 0.999148i	0.866271	−	0.499574i	$-0.166510\pi$
$450$	3.51472i	0.165685i
$451$	37.4558	1.76373
$452$	0	0
$453$	13.7990i	0.648333i
$454$	37.9411	1.78067
$455$	0	0
$456$	−28.9706	−1.35667
$457$	− 7.21320i	− 0.337419i	−0.985666	−	0.168710i	$-0.946040\pi$
$457$	− 7.21320i	− 0.337419i	0.985666	−	0.168710i	$-0.0539600\pi$
$458$	−41.6569	−1.94650
$459$	8.00000	0.373408
$460$	0	0
$461$	8.82843i	0.411181i	0.978638	+	0.205590i	$0.0659115\pi$
$461$	8.82843i	0.411181i	−0.978638	+	0.205590i	$0.934089\pi$
$462$	8.48528i	0.394771i
$463$	4.24264i	0.197172i	0.995129	+	0.0985861i	$0.0314320\pi$
$463$	4.24264i	0.197172i	−0.995129	+	0.0985861i	$0.968568\pi$
$464$	−0.686292	−0.0318603
$465$	−7.27208	−0.337235
$466$	− 20.7279i	− 0.960202i
$467$	3.89949	0.180447	0.0902236	−	0.995922i	$-0.471242\pi$
$467$	3.89949	0.180447	0.0902236	+	0.995922i	$0.471242\pi$
$468$	0	0
$469$	−14.4853	−0.668868
$470$	− 3.55635i	− 0.164042i
$471$	−5.31371	−0.244843
$472$	−0.970563	−0.0446738
$473$	− 21.2132i	− 0.975384i
$474$	− 30.9706i	− 1.42253i
$475$	− 18.0000i	− 0.825897i
$476$	0	0
$477$	0.171573	0.00785578
$478$	4.97056	0.227348
$479$	6.21320i	0.283889i	0.989875	+	0.141944i	$0.0453354\pi$
$479$	6.21320i	0.283889i	−0.989875	+	0.141944i	$0.954665\pi$
$480$	0	0
$481$	0	0
$482$	28.5858	1.30205
$483$	− 8.24264i	− 0.375053i
$484$	0	0
$485$	−18.5980	−0.844491
$486$	− 14.0000i	− 0.635053i
$487$	− 11.4558i	− 0.519114i	−0.965728	−	0.259557i	$-0.916423\pi$
$487$	− 11.4558i	− 0.519114i	0.965728	−	0.259557i	$-0.0835765\pi$
$488$	− 16.9706i	− 0.768221i
$489$	− 12.0000i	− 0.542659i
$490$	−2.24264	−0.101312
$491$	−16.6274	−0.750385	−0.375192	−	0.926947i	$-0.622423\pi$
$491$	−16.6274	−0.750385	−0.375192	+	0.926947i	$0.622423\pi$
$492$	0	0
$493$	−0.242641	−0.0109280
$494$	0	0
$495$	−6.72792	−0.302398
$496$	− 12.9706i	− 0.582395i
$497$	−13.0711	−0.586318
$498$	26.4853	1.18683
$499$	− 13.2721i	− 0.594140i	−0.954856	−	0.297070i	$-0.903991\pi$
$499$	− 13.2721i	− 0.594140i	0.954856	−	0.297070i	$-0.0960094\pi$
$500$	0	0
$501$	− 21.7574i	− 0.972047i
$502$	23.4558i	1.04689i
$503$	−28.6274	−1.27643	−0.638217	−	0.769857i	$-0.720328\pi$
$503$	−28.6274	−1.27643	−0.638217	+	0.769857i	$0.720328\pi$
$504$	2.82843	0.125988
$505$	− 16.2426i	− 0.722788i
$506$	−34.9706	−1.55463
$507$	0	0
$508$	0	0
$509$	− 5.10051i	− 0.226076i	−0.993591	−	0.113038i	$-0.963942\pi$
$509$	− 5.10051i	− 0.226076i	0.993591	−	0.113038i	$-0.0360582\pi$
$510$	−4.48528	−0.198612
$511$	9.24264	0.408870
$512$	22.6274i	1.00000i
$513$	40.9706i	1.80889i
$514$	− 27.4558i	− 1.21103i
$515$	12.6863i	0.559025i
$516$	0	0
$517$	−6.72792	−0.295894
$518$	3.17157i	0.139351i
$519$	−34.9706	−1.53504
$520$	0	0
$521$	−6.34315	−0.277898	−0.138949	−	0.990300i	$-0.544372\pi$
$521$	−6.34315	−0.277898	−0.138949	+	0.990300i	$0.544372\pi$
$522$	0.242641i	0.0106201i
$523$	30.9706	1.35425	0.677124	−	0.735869i	$-0.263226\pi$
$523$	30.9706	1.35425	0.677124	+	0.735869i	$0.263226\pi$
$524$	0	0
$525$	− 3.51472i	− 0.153395i
$526$	− 2.78680i	− 0.121510i
$527$	− 4.58579i	− 0.199760i
$528$	24.0000i	1.04447i
$529$	10.9706	0.476981
$530$	−0.384776	−0.0167136
$531$	0.343146i	0.0148913i
$532$	0	0
$533$	0	0
$534$	−3.17157	−0.137247
$535$	− 31.9411i	− 1.38094i
$536$	−40.9706	−1.76966
$537$	12.7279	0.549250
$538$	− 12.9706i	− 0.559201i
$539$	4.24264i	0.182743i
$540$	0	0
$541$	7.21320i	0.310120i	0.987905	+	0.155060i	$0.0495571\pi$
$541$	7.21320i	0.310120i	−0.987905	+	0.155060i	$0.950443\pi$
$542$	−28.2843	−1.21491
$543$	26.4853	1.13659
$544$	0	0
$545$	−26.5269	−1.13629
$546$	0	0
$547$	35.4853	1.51724	0.758621	−	0.651533i	$-0.225874\pi$
$547$	35.4853	1.51724	0.758621	+	0.651533i	$0.225874\pi$
$548$	0	0
$549$	−6.00000	−0.256074
$550$	−14.9117	−0.635837
$551$	− 1.24264i	− 0.0529383i
$552$	− 23.3137i	− 0.992297i
$553$	− 15.4853i	− 0.658501i
$554$	− 10.5858i	− 0.449747i
$555$	5.02944	0.213488
$556$	0	0
$557$	− 12.0000i	− 0.508456i	−0.967144	−	0.254228i	$-0.918179\pi$
$557$	− 12.0000i	− 0.508456i	0.967144	−	0.254228i	$-0.0818214\pi$
$558$	−4.58579	−0.194132
$559$	0	0
$560$	−6.34315	−0.268047
$561$	8.48528i	0.358249i
$562$	−22.0000	−0.928014
$563$	6.34315	0.267332	0.133666	−	0.991026i	$-0.457325\pi$
$563$	6.34315	0.267332	0.133666	+	0.991026i	$0.457325\pi$
$564$	0	0
$565$	3.66905i	0.154358i
$566$	− 12.0000i	− 0.504398i
$567$	5.00000i	0.209980i
$568$	−36.9706	−1.55125
$569$	−5.14214	−0.215570	−0.107785	−	0.994174i	$-0.534376\pi$
$569$	−5.14214	−0.215570	−0.107785	+	0.994174i	$0.534376\pi$
$570$	− 22.9706i	− 0.962131i
$571$	−42.4558	−1.77672	−0.888361	−	0.459146i	$-0.848156\pi$
$571$	−42.4558	−1.77672	−0.888361	+	0.459146i	$0.848156\pi$
$572$	0	0
$573$	21.4558	0.896331
$574$	− 12.4853i	− 0.521126i
$575$	14.4853	0.604078
$576$	8.00000	0.333333
$577$	− 6.97056i	− 0.290188i	−0.989418	−	0.145094i	$-0.953651\pi$
$577$	− 6.97056i	− 0.290188i	0.989418	−	0.145094i	$-0.0463485\pi$
$578$	21.2132i	0.882353i
$579$	20.4853i	0.851339i
$580$	0	0
$581$	13.2426	0.549397
$582$	23.4558	0.972276
$583$	0.727922i	0.0301475i
$584$	26.1421	1.08177
$585$	0	0
$586$	−21.7574	−0.898788
$587$	− 6.55635i	− 0.270609i	−0.990804	−	0.135305i	$-0.956799\pi$
$587$	− 6.55635i	− 0.270609i	0.990804	−	0.135305i	$-0.0432013\pi$
$588$	0	0
$589$	23.4853	0.967694
$590$	− 0.769553i	− 0.0316820i
$591$	17.4558i	0.718037i
$592$	8.97056i	0.368688i
$593$	0.556349i	0.0228465i	0.999935	+	0.0114233i	$0.00363622\pi$
$593$	0.556349i	0.0228465i	−0.999935	+	0.0114233i	$0.996364\pi$
$594$	33.9411	1.39262
$595$	−2.24264	−0.0919393
$596$	0	0
$597$	5.31371	0.217476
$598$	0	0
$599$	−28.7990	−1.17669	−0.588347	−	0.808608i	$-0.700221\pi$
$599$	−28.7990	−1.17669	−0.588347	+	0.808608i	$0.700221\pi$
$600$	− 9.94113i	− 0.405845i
$601$	−38.9706	−1.58964	−0.794821	−	0.606844i	$-0.792435\pi$
$601$	−38.9706	−1.58964	−0.794821	+	0.606844i	$0.792435\pi$
$602$	−7.07107	−0.288195
$603$	14.4853i	0.589886i
$604$	0	0
$605$	− 11.1005i	− 0.451300i
$606$	20.4853i	0.832158i
$607$	−26.7279	−1.08485	−0.542426	−	0.840103i	$-0.682494\pi$
$607$	−26.7279	−1.08485	−0.542426	+	0.840103i	$0.682494\pi$
$608$	0	0
$609$	− 0.242641i	− 0.00983230i
$610$	13.4558	0.544811
$611$	0	0
$612$	0	0
$613$	− 16.0000i	− 0.646234i	−0.946359	−	0.323117i	$-0.895269\pi$
$613$	− 16.0000i	− 0.646234i	0.946359	−	0.323117i	$-0.104731\pi$
$614$	−18.7279	−0.755797
$615$	−19.7990	−0.798372
$616$	12.0000i	0.483494i
$617$	12.3431i	0.496916i	0.968643	+	0.248458i	$0.0799239\pi$
$617$	12.3431i	0.496916i	−0.968643	+	0.248458i	$0.920076\pi$
$618$	− 16.0000i	− 0.643614i
$619$	− 0.970563i	− 0.0390102i	−0.999810	−	0.0195051i	$-0.993791\pi$
$619$	− 0.970563i	− 0.0390102i	0.999810	−	0.0195051i	$-0.00620906\pi$
$620$	0	0
$621$	−32.9706	−1.32306
$622$	− 10.4853i	− 0.420421i
$623$	−1.58579	−0.0635332
$624$	0	0
$625$	−6.39697	−0.255879
$626$	− 32.8284i	− 1.31209i
$627$	−43.4558	−1.73546
$628$	0	0
$629$	3.17157i	0.126459i
$630$	2.24264i	0.0893489i
$631$	− 2.00000i	− 0.0796187i	−0.999207	−	0.0398094i	$-0.987325\pi$
$631$	− 2.00000i	− 0.0796187i	0.999207	−	0.0398094i	$-0.0126751\pi$
$632$	− 43.7990i	− 1.74223i
$633$	−22.5858	−0.897704
$634$	−16.0000	−0.635441
$635$	− 3.17157i	− 0.125860i
$636$	0	0
$637$	0	0
$638$	−1.02944	−0.0407558
$639$	13.0711i	0.517083i
$640$	−17.9411	−0.709185
$641$	−15.3431	−0.606018	−0.303009	−	0.952988i	$-0.597991\pi$
$641$	−15.3431	−0.606018	−0.303009	+	0.952988i	$0.597991\pi$
$642$	40.2843i	1.58989i
$643$	− 12.4853i	− 0.492371i	−0.969223	−	0.246186i	$-0.920823\pi$
$643$	− 12.4853i	− 0.492371i	0.969223	−	0.246186i	$-0.0791773\pi$
$644$	0	0
$645$	11.2132i	0.441519i
$646$	14.4853	0.569916
$647$	−14.5269	−0.571112	−0.285556	−	0.958362i	$-0.592178\pi$
$647$	−14.5269	−0.571112	−0.285556	+	0.958362i	$0.592178\pi$
$648$	14.1421i	0.555556i
$649$	−1.45584	−0.0571469
$650$	0	0
$651$	4.58579	0.179731
$652$	0	0
$653$	17.3137	0.677538	0.338769	−	0.940870i	$-0.389990\pi$
$653$	17.3137	0.677538	0.338769	+	0.940870i	$0.389990\pi$
$654$	33.4558	1.30823
$655$	− 4.48528i	− 0.175254i
$656$	− 35.3137i	− 1.37877i
$657$	− 9.24264i	− 0.360590i
$658$	2.24264i	0.0874272i
$659$	−15.3431	−0.597684	−0.298842	−	0.954303i	$-0.596600\pi$
$659$	−15.3431	−0.597684	−0.298842	+	0.954303i	$0.596600\pi$
$660$	0	0
$661$	10.7574i	0.418413i	0.977872	+	0.209206i	$0.0670880\pi$
$661$	10.7574i	0.418413i	−0.977872	+	0.209206i	$0.932912\pi$
$662$	−25.4558	−0.989369
$663$	0	0
$664$	37.4558	1.45357
$665$	− 11.4853i	− 0.445380i
$666$	3.17157	0.122896
$667$	1.00000	0.0387202
$668$	0	0
$669$	1.07107i	0.0414099i
$670$	− 32.4853i	− 1.25502i
$671$	− 25.4558i	− 0.982712i
$672$	0	0
$673$	26.9411	1.03850	0.519252	−	0.854621i	$-0.326211\pi$
$673$	26.9411	1.03850	0.519252	+	0.854621i	$0.326211\pi$
$674$	− 46.6690i	− 1.79762i
$675$	−14.0589	−0.541126
$676$	0	0
$677$	−41.3553	−1.58941	−0.794707	−	0.606993i	$-0.792376\pi$
$677$	−41.3553	−1.58941	−0.794707	+	0.606993i	$0.792376\pi$
$678$	− 4.62742i	− 0.177715i
$679$	11.7279	0.450076
$680$	−6.34315	−0.243249
$681$	37.9411i	1.45391i
$682$	− 19.4558i	− 0.745003i
$683$	21.1716i	0.810108i	0.914293	+	0.405054i	$0.132747\pi$
$683$	21.1716i	0.810108i	−0.914293	+	0.405054i	$0.867253\pi$
$684$	0	0
$685$	−7.27208	−0.277852
$686$	1.41421	0.0539949
$687$	− 41.6569i	− 1.58931i
$688$	−20.0000	−0.762493
$689$	0	0
$690$	18.4853	0.703723
$691$	28.6985i	1.09174i	0.837869	+	0.545871i	$0.183801\pi$
$691$	28.6985i	1.09174i	−0.837869	+	0.545871i	$0.816199\pi$
$692$	0	0
$693$	4.24264	0.161165
$694$	8.00000i	0.303676i
$695$	9.89949i	0.375509i
$696$	− 0.686292i	− 0.0260138i
$697$	− 12.4853i	− 0.472914i
$698$	36.3848	1.37718
$699$	20.7279	0.784002
$700$	0	0
$701$	10.7990	0.407872	0.203936	−	0.978984i	$-0.434627\pi$
$701$	10.7990	0.407872	0.203936	+	0.978984i	$0.434627\pi$
$702$	0	0
$703$	−16.2426	−0.612603
$704$	33.9411i	1.27920i
$705$	3.55635	0.133940
$706$	−12.0000	−0.451626
$707$	10.2426i	0.385214i
$708$	0	0
$709$	− 0.727922i	− 0.0273377i	−0.999907	−	0.0136688i	$-0.995649\pi$
$709$	− 0.727922i	− 0.0273377i	0.999907	−	0.0136688i	$-0.00435106\pi$
$710$	− 29.3137i	− 1.10012i
$711$	−15.4853	−0.580743
$712$	−4.48528	−0.168093
$713$	18.8995i	0.707792i
$714$	2.82843	0.105851
$715$	0	0
$716$	0	0
$717$	4.97056i	0.185629i
$718$	39.4558	1.47248
$719$	1.75736	0.0655384	0.0327692	−	0.999463i	$-0.489567\pi$
$719$	1.75736	0.0655384	0.0327692	+	0.999463i	$0.489567\pi$
$720$	6.34315i	0.236395i
$721$	− 8.00000i	− 0.297936i
$722$	47.3137i	1.76083i
$723$	28.5858i	1.06312i
$724$	0	0
$725$	0.426407	0.0158364
$726$	14.0000i	0.519589i
$727$	−42.0000	−1.55769	−0.778847	−	0.627214i	$-0.784195\pi$
$727$	−42.0000	−1.55769	−0.778847	+	0.627214i	$0.784195\pi$
$728$	0	0
$729$	29.0000	1.07407
$730$	20.7279i	0.767175i
$731$	−7.07107	−0.261533
$732$	0	0
$733$	− 16.6985i	− 0.616773i	−0.951261	−	0.308386i	$-0.900211\pi$
$733$	− 16.6985i	− 0.616773i	0.951261	−	0.308386i	$-0.0997889\pi$
$734$	− 14.4853i	− 0.534661i
$735$	− 2.24264i	− 0.0827210i
$736$	0	0
$737$	−61.4558	−2.26376
$738$	−12.4853	−0.459590
$739$	17.6985i	0.651049i	0.945534	+	0.325525i	$0.105541\pi$
$739$	17.6985i	0.651049i	−0.945534	+	0.325525i	$0.894459\pi$
$740$	0	0
$741$	0	0
$742$	0.242641	0.00890762
$743$	− 29.6569i	− 1.08800i	−0.839084	−	0.544002i	$-0.816908\pi$
$743$	− 29.6569i	− 1.08800i	0.839084	−	0.544002i	$-0.183092\pi$
$744$	12.9706	0.475524
$745$	−25.7574	−0.943677
$746$	− 12.0000i	− 0.439351i
$747$	− 13.2426i	− 0.484523i
$748$	0	0
$749$	20.1421i	0.735978i
$750$	23.7401	0.866866
$751$	−15.4853	−0.565066	−0.282533	−	0.959258i	$-0.591175\pi$
$751$	−15.4853	−0.565066	−0.282533	+	0.959258i	$0.591175\pi$
$752$	6.34315i	0.231311i
$753$	−23.4558	−0.854778
$754$	0	0
$755$	−15.4731	−0.563123
$756$	0	0
$757$	21.4853	0.780896	0.390448	−	0.920625i	$-0.372320\pi$
$757$	21.4853	0.780896	0.390448	+	0.920625i	$0.372320\pi$
$758$	33.5980	1.22033
$759$	− 34.9706i	− 1.26935i
$760$	− 32.4853i	− 1.17837i
$761$	− 34.7574i	− 1.25995i	−0.776614	−	0.629977i	$-0.783064\pi$
$761$	− 34.7574i	− 1.25995i	0.776614	−	0.629977i	$-0.216936\pi$
$762$	4.00000i	0.144905i
$763$	16.7279	0.605591
$764$	0	0
$765$	2.24264i	0.0810828i
$766$	−28.9706	−1.04675
$767$	0	0
$768$	0	0
$769$	52.2132i	1.88286i	0.337214	+	0.941428i	$0.390516\pi$
$769$	52.2132i	1.88286i	−0.337214	+	0.941428i	$0.609484\pi$
$770$	−9.51472	−0.342887
$771$	27.4558	0.988798
$772$	0	0
$773$	− 32.8284i	− 1.18076i	−0.807127	−	0.590378i	$-0.798979\pi$
$773$	− 32.8284i	− 1.18076i	0.807127	−	0.590378i	$-0.201021\pi$
$774$	7.07107i	0.254164i
$775$	8.05887i	0.289483i
$776$	33.1716	1.19079
$777$	−3.17157	−0.113780
$778$	41.9411i	1.50366i
$779$	63.9411	2.29093
$780$	0	0
$781$	−55.4558	−1.98437
$782$	11.6569i	0.416848i
$783$	−0.970563	−0.0346851
$784$	4.00000	0.142857
$785$	− 5.95837i	− 0.212663i
$786$	5.65685i	0.201773i
$787$	24.7574i	0.882505i	0.897383	+	0.441252i	$0.145466\pi$
$787$	24.7574i	0.882505i	−0.897383	+	0.441252i	$0.854534\pi$
$788$	0	0
$789$	2.78680	0.0992126
$790$	34.7279	1.23556
$791$	− 2.31371i	− 0.0822660i
$792$	12.0000	0.426401
$793$	0	0
$794$	25.7574	0.914094
$795$	− 0.384776i	− 0.0136466i
$796$	0	0
$797$	24.3431	0.862278	0.431139	−	0.902285i	$-0.358112\pi$
$797$	24.3431	0.862278	0.431139	+	0.902285i	$0.358112\pi$
$798$	14.4853i	0.512773i
$799$	2.24264i	0.0793389i
$800$	0	0
$801$	1.58579i	0.0560310i
$802$	−8.97056	−0.316762
$803$	39.2132	1.38380
$804$	0	0
$805$	9.24264	0.325760
$806$	0	0
$807$	12.9706	0.456585
$808$	28.9706i	1.01918i
$809$	17.4853	0.614750	0.307375	−	0.951589i	$-0.400549\pi$
$809$	17.4853	0.614750	0.307375	+	0.951589i	$0.400549\pi$
$810$	−11.2132	−0.393992
$811$	− 21.9411i	− 0.770457i	−0.922821	−	0.385229i	$-0.874123\pi$
$811$	− 21.9411i	− 0.770457i	0.922821	−	0.385229i	$-0.125877\pi$
$812$	0	0
$813$	− 28.2843i	− 0.991973i
$814$	13.4558i	0.471627i
$815$	13.4558	0.471338
$816$	8.00000	0.280056
$817$	− 36.2132i	− 1.26694i
$818$	4.58579	0.160338
$819$	0	0
$820$	0	0
$821$	− 20.1421i	− 0.702965i	−0.936194	−	0.351483i	$-0.885678\pi$
$821$	− 20.1421i	− 0.702965i	0.936194	−	0.351483i	$-0.114322\pi$
$822$	9.17157	0.319895
$823$	−10.4853	−0.365494	−0.182747	−	0.983160i	$-0.558499\pi$
$823$	−10.4853	−0.365494	−0.182747	+	0.983160i	$0.558499\pi$
$824$	− 22.6274i	− 0.788263i
$825$	− 14.9117i	− 0.519158i
$826$	0.485281i	0.0168851i
$827$	49.4558i	1.71975i	0.510506	+	0.859874i	$0.329458\pi$
$827$	49.4558i	1.71975i	−0.510506	+	0.859874i	$0.670542\pi$
$828$	0	0
$829$	−50.7279	−1.76185	−0.880927	−	0.473253i	$-0.843080\pi$
$829$	−50.7279	−1.76185	−0.880927	+	0.473253i	$0.843080\pi$
$830$	29.6985i	1.03085i
$831$	10.5858	0.367217
$832$	0	0
$833$	1.41421	0.0489996
$834$	− 12.4853i	− 0.432330i
$835$	24.3970	0.844292
$836$	0	0
$837$	− 18.3431i	− 0.634032i
$838$	29.5147i	1.01957i
$839$	33.1716i	1.14521i	0.819831	+	0.572605i	$0.194067\pi$
$839$	33.1716i	1.14521i	−0.819831	+	0.572605i	$0.805933\pi$
$840$	− 6.34315i	− 0.218859i
$841$	−28.9706	−0.998985
$842$	9.51472	0.327899
$843$	− 22.0000i	− 0.757720i
$844$	0	0
$845$	0	0
$846$	2.24264	0.0771036
$847$	7.00000i	0.240523i
$848$	0.686292	0.0235673
$849$	12.0000	0.411839
$850$	4.97056i	0.170489i
$851$	− 13.0711i	− 0.448070i
$852$	0	0
$853$	− 39.7279i	− 1.36026i	−0.733092	−	0.680129i	$-0.761924\pi$
$853$	− 39.7279i	− 1.36026i	0.733092	−	0.680129i	$-0.238076\pi$
$854$	−8.48528	−0.290360
$855$	−11.4853	−0.392788
$856$	56.9706i	1.94721i
$857$	54.7696	1.87089	0.935446	−	0.353469i	$-0.114998\pi$
$857$	54.7696	1.87089	0.935446	+	0.353469i	$0.114998\pi$
$858$	0	0
$859$	30.9706	1.05670	0.528351	−	0.849026i	$-0.322811\pi$
$859$	30.9706	1.05670	0.528351	+	0.849026i	$0.322811\pi$
$860$	0	0
$861$	12.4853	0.425497
$862$	−17.4558	−0.594548
$863$	28.2843i	0.962808i	0.876499	+	0.481404i	$0.159873\pi$
$863$	28.2843i	0.962808i	−0.876499	+	0.481404i	$0.840127\pi$
$864$	0	0
$865$	− 39.2132i	− 1.33329i
$866$	− 35.3137i	− 1.20001i
$867$	−21.2132	−0.720438
$868$	0	0
$869$	− 65.6985i	− 2.22867i
$870$	0.544156	0.0184486
$871$	0	0
$872$	47.3137	1.60224
$873$	− 11.7279i	− 0.396930i
$874$	−59.6985	−2.01933
$875$	11.8701	0.401281
$876$	0	0
$877$	− 10.2426i	− 0.345869i	−0.984933	−	0.172935i	$-0.944675\pi$
$877$	− 10.2426i	− 0.345869i	0.984933	−	0.172935i	$-0.0553250\pi$
$878$	− 48.7696i	− 1.64589i
$879$	− 21.7574i	− 0.733858i
$880$	−26.9117	−0.907193
$881$	−13.1127	−0.441778	−0.220889	−	0.975299i	$-0.570896\pi$
$881$	−13.1127	−0.441778	−0.220889	+	0.975299i	$0.570896\pi$
$882$	− 1.41421i	− 0.0476190i
$883$	−2.00000	−0.0673054	−0.0336527	−	0.999434i	$-0.510714\pi$
$883$	−2.00000	−0.0673054	−0.0336527	+	0.999434i	$0.510714\pi$
$884$	0	0
$885$	0.769553	0.0258682
$886$	5.21320i	0.175141i
$887$	19.1127	0.641742	0.320871	−	0.947123i	$-0.396024\pi$
$887$	19.1127	0.641742	0.320871	+	0.947123i	$0.396024\pi$
$888$	−8.97056	−0.301032
$889$	2.00000i	0.0670778i
$890$	− 3.55635i	− 0.119209i
$891$	21.2132i	0.710669i
$892$	0	0
$893$	−11.4853	−0.384340
$894$	32.4853	1.08647
$895$	14.2721i	0.477063i
$896$	11.3137	0.377964
$897$	0	0
$898$	−29.9411	−0.999148
$899$	0.556349i	0.0185553i
$900$	0	0
$901$	0.242641	0.00808353
$902$	− 52.9706i	− 1.76373i
$903$	− 7.07107i	− 0.235310i
$904$	− 6.54416i	− 0.217655i
$905$	29.6985i	0.987211i
$906$	19.5147	0.648333
$907$	−1.97056	−0.0654315	−0.0327157	−	0.999465i	$-0.510416\pi$
$907$	−1.97056	−0.0654315	−0.0327157	+	0.999465i	$0.510416\pi$
$908$	0	0
$909$	10.2426	0.339727
$910$	0	0
$911$	−43.9706	−1.45681	−0.728405	−	0.685147i	$-0.759738\pi$
$911$	−43.9706	−1.45681	−0.728405	+	0.685147i	$0.759738\pi$
$912$	40.9706i	1.35667i
$913$	56.1838	1.85941
$914$	−10.2010	−0.337419
$915$	13.4558i	0.444836i
$916$	0	0
$917$	2.82843i	0.0934029i
$918$	− 11.3137i	− 0.373408i
$919$	24.0000	0.791687	0.395843	−	0.918318i	$-0.370452\pi$
$919$	24.0000	0.791687	0.395843	+	0.918318i	$0.370452\pi$
$920$	26.1421	0.861881
$921$	− 18.7279i	− 0.617106i
$922$	12.4853	0.411181
$923$	0	0
$924$	0	0
$925$	− 5.57359i	− 0.183259i
$926$	6.00000	0.197172
$927$	−8.00000	−0.262754
$928$	0	0
$929$	36.8995i	1.21063i	0.795985	+	0.605317i	$0.206953\pi$
$929$	36.8995i	1.21063i	−0.795985	+	0.605317i	$0.793047\pi$
$930$	10.2843i	0.337235i
$931$	7.24264i	0.237368i
$932$	0	0
$933$	10.4853	0.343273
$934$	− 5.51472i	− 0.180447i
$935$	−9.51472	−0.311165
$936$	0	0
$937$	45.2132	1.47705	0.738525	−	0.674226i	$-0.235522\pi$
$937$	45.2132	1.47705	0.738525	+	0.674226i	$0.235522\pi$
$938$	20.4853i	0.668868i
$939$	32.8284	1.07132
$940$	0	0
$941$	40.0711i	1.30628i	0.757237	+	0.653140i	$0.226549\pi$
$941$	40.0711i	1.30628i	−0.757237	+	0.653140i	$0.773451\pi$
$942$	7.51472i	0.244843i
$943$	51.4558i	1.67563i
$944$	1.37258i	0.0446738i
$945$	−8.97056	−0.291812
$946$	−30.0000	−0.975384
$947$	− 15.1716i	− 0.493010i	−0.969142	−	0.246505i	$-0.920718\pi$
$947$	− 15.1716i	− 0.493010i	0.969142	−	0.246505i	$-0.0792822\pi$
$948$	0	0
$949$	0	0
$950$	−25.4558	−0.825897
$951$	− 16.0000i	− 0.518836i
$952$	4.00000	0.129641
$953$	−11.1421	−0.360929	−0.180465	−	0.983581i	$-0.557760\pi$
$953$	−11.1421	−0.360929	−0.180465	+	0.983581i	$0.557760\pi$
$954$	− 0.242641i	− 0.00785578i
$955$	24.0589i	0.778527i
$956$	0	0
$957$	− 1.02944i	− 0.0332770i
$958$	8.78680	0.283889
$959$	4.58579	0.148083
$960$	− 17.9411i	− 0.579047i
$961$	20.4853	0.660816
$962$	0	0
$963$	20.1421	0.649071
$964$	0	0
$965$	−22.9706	−0.739449
$966$	−11.6569	−0.375053
$967$	17.6985i	0.569145i	0.958655	+	0.284572i	$0.0918516\pi$
$967$	17.6985i	0.569145i	−0.958655	+	0.284572i	$0.908148\pi$
$968$	19.7990i	0.636364i
$969$	14.4853i	0.465334i
$970$	26.3015i	0.844491i
$971$	43.4558	1.39456	0.697282	−	0.716797i	$-0.254392\pi$
$971$	43.4558	1.39456	0.697282	+	0.716797i	$0.254392\pi$
$972$	0	0
$973$	− 6.24264i	− 0.200130i
$974$	−16.2010	−0.519114
$975$	0	0
$976$	−24.0000	−0.768221
$977$	24.0416i	0.769160i	0.923092	+	0.384580i	$0.125654\pi$
$977$	24.0416i	0.769160i	−0.923092	+	0.384580i	$0.874346\pi$
$978$	−16.9706	−0.542659
$979$	−6.72792	−0.215025
$980$	0	0
$981$	− 16.7279i	− 0.534081i
$982$	23.5147i	0.750385i
$983$	15.0416i	0.479754i	0.970803	+	0.239877i	$0.0771070\pi$
$983$	15.0416i	0.479754i	−0.970803	+	0.239877i	$0.922893\pi$
$984$	35.3137	1.12576
$985$	−19.5736	−0.623667
$986$	0.343146i	0.0109280i
$987$	−2.24264	−0.0713840
$988$	0	0
$989$	29.1421	0.926666
$990$	9.51472i	0.302398i
$991$	1.02944	0.0327012	0.0163506	−	0.999866i	$-0.494795\pi$
$991$	1.02944	0.0327012	0.0163506	+	0.999866i	$0.494795\pi$
$992$	0	0
$993$	− 25.4558i	− 0.807817i
$994$	18.4853i	0.586318i
$995$	5.95837i	0.188893i
$996$	0	0
$997$	−11.5147	−0.364675	−0.182337	−	0.983236i	$-0.558366\pi$
$997$	−11.5147	−0.364675	−0.182337	+	0.983236i	$0.558366\pi$
$998$	−18.7696	−0.594140
$999$	12.6863i	0.401377i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.c.d.337.2		4
13.5	odd	4		91.2.a.c.1.1	✓	2
13.8	odd	4		1183.2.a.d.1.2		2
13.12	even	2	inner	1183.2.c.d.337.4		4
39.5	even	4		819.2.a.h.1.2		2
52.31	even	4		1456.2.a.q.1.1		2
65.44	odd	4		2275.2.a.j.1.2		2
91.5	even	12		637.2.e.g.508.2		4
91.18	odd	12		637.2.e.f.79.2		4
91.31	even	12		637.2.e.g.79.2		4
91.34	even	4		8281.2.a.v.1.2		2
91.44	odd	12		637.2.e.f.508.2		4
91.83	even	4		637.2.a.g.1.1		2
104.5	odd	4		5824.2.a.bl.1.1		2
104.83	even	4		5824.2.a.bk.1.2		2
273.83	odd	4		5733.2.a.s.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.a.c.1.1	✓	2	13.5	odd	4
637.2.a.g.1.1		2	91.83	even	4
637.2.e.f.79.2		4	91.18	odd	12
637.2.e.f.508.2		4	91.44	odd	12
637.2.e.g.79.2		4	91.31	even	12
637.2.e.g.508.2		4	91.5	even	12
819.2.a.h.1.2		2	39.5	even	4
1183.2.a.d.1.2		2	13.8	odd	4
1183.2.c.d.337.2		4	1.1	even	1	trivial
1183.2.c.d.337.4		4	13.12	even	2	inner
1456.2.a.q.1.1		2	52.31	even	4
2275.2.a.j.1.2		2	65.44	odd	4
5733.2.a.s.1.2		2	273.83	odd	4
5824.2.a.bk.1.2		2	104.83	even	4
5824.2.a.bl.1.1		2	104.5	odd	4
8281.2.a.v.1.2		2	91.34	even	4

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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +1.41421 q^{3} +1.58579i q^{5} -2.00000i q^{6} -1.00000i q^{7} -2.82843i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +1.41421 q^{3} +1.58579i q^{5} -2.00000i q^{6} -1.00000i q^{7} -2.82843i q^{8} -1.00000 q^{9} +2.24264 q^{10} -4.24264i q^{11} -1.41421 q^{14} +2.24264i q^{15} -4.00000 q^{16} -1.41421 q^{17} +1.41421i q^{18} -7.24264i q^{19} -1.41421i q^{21} -6.00000 q^{22} +5.82843 q^{23} -4.00000i q^{24} +2.48528 q^{25} -5.65685 q^{27} +0.171573 q^{29} +3.17157 q^{30} +3.24264i q^{31} -6.00000i q^{33} +2.00000i q^{34} +1.58579 q^{35} -2.24264i q^{37} -10.2426 q^{38} +4.48528 q^{40} +8.82843i q^{41} -2.00000 q^{42} +5.00000 q^{43} -1.58579i q^{45} -8.24264i q^{46} -1.58579i q^{47} -5.65685 q^{48} -1.00000 q^{49} -3.51472i q^{50} -2.00000 q^{51} -0.171573 q^{53} +8.00000i q^{54} +6.72792 q^{55} -2.82843 q^{56} -10.2426i q^{57} -0.242641i q^{58} -0.343146i q^{59} +6.00000 q^{61} +4.58579 q^{62} +1.00000i q^{63} -8.00000 q^{64} -8.48528 q^{66} -14.4853i q^{67} +8.24264 q^{69} -2.24264i q^{70} -13.0711i q^{71} +2.82843i q^{72} +9.24264i q^{73} -3.17157 q^{74} +3.51472 q^{75} -4.24264 q^{77} +15.4853 q^{79} -6.34315i q^{80} -5.00000 q^{81} +12.4853 q^{82} +13.2426i q^{83} -2.24264i q^{85} -7.07107i q^{86} +0.242641 q^{87} -12.0000 q^{88} -1.58579i q^{89} -2.24264 q^{90} +4.58579i q^{93} -2.24264 q^{94} +11.4853 q^{95} +11.7279i q^{97} +1.41421i q^{98} +4.24264i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^9	\( 4 q - 4 q^{9} - 8 q^{10} - 16 q^{16} - 24 q^{22} + 12 q^{23} - 24 q^{25} + 12 q^{29} + 24 q^{30} + 12 q^{35} - 24 q^{38} - 16 q^{40} - 8 q^{42} + 20 q^{43} - 4 q^{49} - 8 q^{51} - 12 q^{53} - 24 q^{55} + 24 q^{61} + 24 q^{62} - 32 q^{64} + 16 q^{69} - 24 q^{74} + 48 q^{75} + 28 q^{79} - 20 q^{81} + 16 q^{82} - 16 q^{87} - 48 q^{88} + 8 q^{90} + 8 q^{94} + 12 q^{95}+O(q^{100}) \) 4 * q - 4 * q^9 - 8 * q^10 - 16 * q^16 - 24 * q^22 + 12 * q^23 - 24 * q^25 + 12 * q^29 + 24 * q^30 + 12 * q^35 - 24 * q^38 - 16 * q^40 - 8 * q^42 + 20 * q^43 - 4 * q^49 - 8 * q^51 - 12 * q^53 - 24 * q^55 + 24 * q^61 + 24 * q^62 - 32 * q^64 + 16 * q^69 - 24 * q^74 + 48 * q^75 + 28 * q^79 - 20 * q^81 + 16 * q^82 - 16 * q^87 - 48 * q^88 + 8 * q^90 + 8 * q^94 + 12 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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