LMFDB - Embedded newform 2366.2.d.j.337.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2366,2,Mod(337,2366)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2366, 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("2366.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2366 = 2 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2366.d (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:	$18.8926051182$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	2366.337
Dual form			2366.2.d.j.337.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +3.00000 q^{3} -1.00000 q^{4} +4.00000i q^{5} -3.00000i q^{6} -1.00000i q^{7} +1.00000i q^{8} +6.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +3.00000 q^{3} -1.00000 q^{4} +4.00000i q^{5} -3.00000i q^{6} -1.00000i q^{7} +1.00000i q^{8} +6.00000 q^{9} +4.00000 q^{10} +1.00000i q^{11} -3.00000 q^{12} -1.00000 q^{14} +12.0000i q^{15} +1.00000 q^{16} -6.00000i q^{18} +6.00000i q^{19} -4.00000i q^{20} -3.00000i q^{21} +1.00000 q^{22} +7.00000 q^{23} +3.00000i q^{24} -11.0000 q^{25} +9.00000 q^{27} +1.00000i q^{28} -4.00000 q^{29} +12.0000 q^{30} -7.00000i q^{31} -1.00000i q^{32} +3.00000i q^{33} +4.00000 q^{35} -6.00000 q^{36} +9.00000i q^{37} +6.00000 q^{38} -4.00000 q^{40} +3.00000i q^{41} -3.00000 q^{42} -4.00000 q^{43} -1.00000i q^{44} +24.0000i q^{45} -7.00000i q^{46} +7.00000i q^{47} +3.00000 q^{48} -1.00000 q^{49} +11.0000i q^{50} -9.00000i q^{54} -4.00000 q^{55} +1.00000 q^{56} +18.0000i q^{57} +4.00000i q^{58} -10.0000i q^{59} -12.0000i q^{60} +1.00000 q^{61} -7.00000 q^{62} -6.00000i q^{63} -1.00000 q^{64} +3.00000 q^{66} -1.00000i q^{67} +21.0000 q^{69} -4.00000i q^{70} -16.0000i q^{71} +6.00000i q^{72} +5.00000i q^{73} +9.00000 q^{74} -33.0000 q^{75} -6.00000i q^{76} +1.00000 q^{77} +11.0000 q^{79} +4.00000i q^{80} +9.00000 q^{81} +3.00000 q^{82} +3.00000i q^{84} +4.00000i q^{86} -12.0000 q^{87} -1.00000 q^{88} -6.00000i q^{89} +24.0000 q^{90} -7.00000 q^{92} -21.0000i q^{93} +7.00000 q^{94} -24.0000 q^{95} -3.00000i q^{96} +1.00000i q^{97} +1.00000i q^{98} +6.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 6 q^{3} - 2 q^{4} + 12 q^{9}+O(q^{10}) $ 2 * q + 6 * q^3 - 2 * q^4 + 12 * q^9	$ 2 q + 6 q^{3} - 2 q^{4} + 12 q^{9} + 8 q^{10} - 6 q^{12} - 2 q^{14} + 2 q^{16} + 2 q^{22} + 14 q^{23} - 22 q^{25} + 18 q^{27} - 8 q^{29} + 24 q^{30} + 8 q^{35} - 12 q^{36} + 12 q^{38} - 8 q^{40} - 6 q^{42} - 8 q^{43} + 6 q^{48} - 2 q^{49} - 8 q^{55} + 2 q^{56} + 2 q^{61} - 14 q^{62} - 2 q^{64} + 6 q^{66} + 42 q^{69} + 18 q^{74} - 66 q^{75} + 2 q^{77} + 22 q^{79} + 18 q^{81} + 6 q^{82} - 24 q^{87} - 2 q^{88} + 48 q^{90} - 14 q^{92} + 14 q^{94} - 48 q^{95}+O(q^{100}) $ 2 * q + 6 * q^3 - 2 * q^4 + 12 * q^9 + 8 * q^10 - 6 * q^12 - 2 * q^14 + 2 * q^16 + 2 * q^22 + 14 * q^23 - 22 * q^25 + 18 * q^27 - 8 * q^29 + 24 * q^30 + 8 * q^35 - 12 * q^36 + 12 * q^38 - 8 * q^40 - 6 * q^42 - 8 * q^43 + 6 * q^48 - 2 * q^49 - 8 * q^55 + 2 * q^56 + 2 * q^61 - 14 * q^62 - 2 * q^64 + 6 * q^66 + 42 * q^69 + 18 * q^74 - 66 * q^75 + 2 * q^77 + 22 * q^79 + 18 * q^81 + 6 * q^82 - 24 * q^87 - 2 * q^88 + 48 * q^90 - 14 * q^92 + 14 * q^94 - 48 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2366\mathbb{Z}\right)^\times$.

$n$	$339$	$2199$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 1.00000i	− 0.707107i
$2$	− 1.00000i	− 0.707107i
$3$	3.00000	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$3$	3.00000	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$4$	−1.00000	−0.500000
$5$	4.00000i	1.78885i	0.447214	+	0.894427i	$0.352416\pi$
$5$	4.00000i	1.78885i	−0.447214	+	0.894427i	$0.647584\pi$
$6$	− 3.00000i	− 1.22474i
$7$	− 1.00000i	− 0.377964i
$7$	− 1.00000i	− 0.377964i
$8$	1.00000i	0.353553i
$9$	6.00000	2.00000
$10$	4.00000	1.26491
$11$	1.00000i	0.301511i	0.988571	+	0.150756i	$0.0481707\pi$
$11$	1.00000i	0.301511i	−0.988571	+	0.150756i	$0.951829\pi$
$12$	−3.00000	−0.866025
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	12.0000i	3.09839i
$16$	1.00000	0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	− 6.00000i	− 1.41421i
$19$	6.00000i	1.37649i	0.725476	+	0.688247i	$0.241620\pi$
$19$	6.00000i	1.37649i	−0.725476	+	0.688247i	$0.758380\pi$
$20$	− 4.00000i	− 0.894427i
$21$	− 3.00000i	− 0.654654i
$22$	1.00000	0.213201
$23$	7.00000	1.45960	0.729800	−	0.683660i	$-0.239613\pi$
$23$	7.00000	1.45960	0.729800	+	0.683660i	$0.239613\pi$
$24$	3.00000i	0.612372i
$25$	−11.0000	−2.20000
$26$	0	0
$27$	9.00000	1.73205
$28$	1.00000i	0.188982i
$29$	−4.00000	−0.742781	−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000	−0.742781	−0.371391	+	0.928477i	$0.621119\pi$
$30$	12.0000	2.19089
$31$	− 7.00000i	− 1.25724i	−0.777714	−	0.628619i	$-0.783621\pi$
$31$	− 7.00000i	− 1.25724i	0.777714	−	0.628619i	$-0.216379\pi$
$32$	− 1.00000i	− 0.176777i
$33$	3.00000i	0.522233i
$34$	0	0
$35$	4.00000	0.676123
$36$	−6.00000	−1.00000
$37$	9.00000i	1.47959i	0.672832	+	0.739795i	$0.265078\pi$
$37$	9.00000i	1.47959i	−0.672832	+	0.739795i	$0.734922\pi$
$38$	6.00000	0.973329
$39$	0	0
$40$	−4.00000	−0.632456
$41$	3.00000i	0.468521i	0.972174	+	0.234261i	$0.0752669\pi$
$41$	3.00000i	0.468521i	−0.972174	+	0.234261i	$0.924733\pi$
$42$	−3.00000	−0.462910
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	− 1.00000i	− 0.150756i
$45$	24.0000i	3.57771i
$46$	− 7.00000i	− 1.03209i
$47$	7.00000i	1.02105i	0.859861	+	0.510527i	$0.170550\pi$
$47$	7.00000i	1.02105i	−0.859861	+	0.510527i	$0.829450\pi$
$48$	3.00000	0.433013
$49$	−1.00000	−0.142857
$50$	11.0000i	1.55563i
$51$	0	0
$52$	0	0
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	− 9.00000i	− 1.22474i
$55$	−4.00000	−0.539360
$56$	1.00000	0.133631
$57$	18.0000i	2.38416i
$58$	4.00000i	0.525226i
$59$	− 10.0000i	− 1.30189i	−0.759125	−	0.650945i	$-0.774373\pi$
$59$	− 10.0000i	− 1.30189i	0.759125	−	0.650945i	$-0.225627\pi$
$60$	− 12.0000i	− 1.54919i
$61$	1.00000	0.128037	0.0640184	−	0.997949i	$-0.479608\pi$
$61$	1.00000	0.128037	0.0640184	+	0.997949i	$0.479608\pi$
$62$	−7.00000	−0.889001
$63$	− 6.00000i	− 0.755929i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	3.00000	0.369274
$67$	− 1.00000i	− 0.122169i	−0.998133	−	0.0610847i	$-0.980544\pi$
$67$	− 1.00000i	− 0.122169i	0.998133	−	0.0610847i	$-0.0194560\pi$
$68$	0	0
$69$	21.0000	2.52810
$70$	− 4.00000i	− 0.478091i
$71$	− 16.0000i	− 1.89885i	−0.313993	−	0.949425i	$-0.601667\pi$
$71$	− 16.0000i	− 1.89885i	0.313993	−	0.949425i	$-0.398333\pi$
$72$	6.00000i	0.707107i
$73$	5.00000i	0.585206i	0.956234	+	0.292603i	$0.0945214\pi$
$73$	5.00000i	0.585206i	−0.956234	+	0.292603i	$0.905479\pi$
$74$	9.00000	1.04623
$75$	−33.0000	−3.81051
$76$	− 6.00000i	− 0.688247i
$77$	1.00000	0.113961
$78$	0	0
$79$	11.0000	1.23760	0.618798	−	0.785550i	$-0.287620\pi$
$79$	11.0000	1.23760	0.618798	+	0.785550i	$0.287620\pi$
$80$	4.00000i	0.447214i
$81$	9.00000	1.00000
$82$	3.00000	0.331295
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	3.00000i	0.327327i
$85$	0	0
$86$	4.00000i	0.431331i
$87$	−12.0000	−1.28654
$88$	−1.00000	−0.106600
$89$	− 6.00000i	− 0.635999i	−0.948091	−	0.317999i	$-0.896989\pi$
$89$	− 6.00000i	− 0.635999i	0.948091	−	0.317999i	$-0.103011\pi$
$90$	24.0000	2.52982
$91$	0	0
$92$	−7.00000	−0.729800
$93$	− 21.0000i	− 2.17760i
$94$	7.00000	0.721995
$95$	−24.0000	−2.46235
$96$	− 3.00000i	− 0.306186i
$97$	1.00000i	0.101535i	0.998711	+	0.0507673i	$0.0161667\pi$
$97$	1.00000i	0.101535i	−0.998711	+	0.0507673i	$0.983833\pi$
$98$	1.00000i	0.101015i
$99$	6.00000i	0.603023i
$100$	11.0000	1.10000
$101$	5.00000	0.497519	0.248759	−	0.968565i	$-0.419977\pi$
$101$	5.00000	0.497519	0.248759	+	0.968565i	$0.419977\pi$
$102$	0	0
$103$	14.0000	1.37946	0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000	1.37946	0.689730	+	0.724066i	$0.257729\pi$
$104$	0	0
$105$	12.0000	1.17108
$106$	0	0
$107$	−4.00000	−0.386695	−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000	−0.386695	−0.193347	+	0.981130i	$0.561934\pi$
$108$	−9.00000	−0.866025
$109$	14.0000i	1.34096i	0.741929	+	0.670478i	$0.233911\pi$
$109$	14.0000i	1.34096i	−0.741929	+	0.670478i	$0.766089\pi$
$110$	4.00000i	0.381385i
$111$	27.0000i	2.56273i
$112$	− 1.00000i	− 0.0944911i
$113$	−7.00000	−0.658505	−0.329252	−	0.944242i	$-0.606797\pi$
$113$	−7.00000	−0.658505	−0.329252	+	0.944242i	$0.606797\pi$
$114$	18.0000	1.68585
$115$	28.0000i	2.61101i
$116$	4.00000	0.371391
$117$	0	0
$118$	−10.0000	−0.920575
$119$	0	0
$120$	−12.0000	−1.09545
$121$	10.0000	0.909091
$122$	− 1.00000i	− 0.0905357i
$123$	9.00000i	0.811503i
$124$	7.00000i	0.628619i
$125$	− 24.0000i	− 2.14663i
$126$	−6.00000	−0.534522
$127$	11.0000	0.976092	0.488046	−	0.872818i	$-0.337710\pi$
$127$	11.0000	0.976092	0.488046	+	0.872818i	$0.337710\pi$
$128$	1.00000i	0.0883883i
$129$	−12.0000	−1.05654
$130$	0	0
$131$	8.00000	0.698963	0.349482	−	0.936943i	$-0.386358\pi$
$131$	8.00000	0.698963	0.349482	+	0.936943i	$0.386358\pi$
$132$	− 3.00000i	− 0.261116i
$133$	6.00000	0.520266
$134$	−1.00000	−0.0863868
$135$	36.0000i	3.09839i
$136$	0	0
$137$	− 6.00000i	− 0.512615i	−0.966595	−	0.256307i	$-0.917494\pi$
$137$	− 6.00000i	− 0.512615i	0.966595	−	0.256307i	$-0.0825059\pi$
$138$	− 21.0000i	− 1.78764i
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	−4.00000	−0.338062
$141$	21.0000i	1.76852i
$142$	−16.0000	−1.34269
$143$	0	0
$144$	6.00000	0.500000
$145$	− 16.0000i	− 1.32873i
$146$	5.00000	0.413803
$147$	−3.00000	−0.247436
$148$	− 9.00000i	− 0.739795i
$149$	− 9.00000i	− 0.737309i	−0.929567	−	0.368654i	$-0.879819\pi$
$149$	− 9.00000i	− 0.737309i	0.929567	−	0.368654i	$-0.120181\pi$
$150$	33.0000i	2.69444i
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	−6.00000	−0.486664
$153$	0	0
$154$	− 1.00000i	− 0.0805823i
$155$	28.0000	2.24901
$156$	0	0
$157$	5.00000	0.399043	0.199522	−	0.979893i	$-0.436061\pi$
$157$	5.00000	0.399043	0.199522	+	0.979893i	$0.436061\pi$
$158$	− 11.0000i	− 0.875113i
$159$	0	0
$160$	4.00000	0.316228
$161$	− 7.00000i	− 0.551677i
$162$	− 9.00000i	− 0.707107i
$163$	− 4.00000i	− 0.313304i	−0.987654	−	0.156652i	$-0.949930\pi$
$163$	− 4.00000i	− 0.313304i	0.987654	−	0.156652i	$-0.0500701\pi$
$164$	− 3.00000i	− 0.234261i
$165$	−12.0000	−0.934199
$166$	0	0
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	3.00000	0.231455
$169$	0	0
$170$	0	0
$171$	36.0000i	2.75299i
$172$	4.00000	0.304997
$173$	−2.00000	−0.152057	−0.0760286	−	0.997106i	$-0.524224\pi$
$173$	−2.00000	−0.152057	−0.0760286	+	0.997106i	$0.524224\pi$
$174$	12.0000i	0.909718i
$175$	11.0000i	0.831522i
$176$	1.00000i	0.0753778i
$177$	− 30.0000i	− 2.25494i
$178$	−6.00000	−0.449719
$179$	6.00000	0.448461	0.224231	−	0.974536i	$-0.428013\pi$
$179$	6.00000	0.448461	0.224231	+	0.974536i	$0.428013\pi$
$180$	− 24.0000i	− 1.78885i
$181$	−15.0000	−1.11494	−0.557471	−	0.830197i	$-0.688228\pi$
$181$	−15.0000	−1.11494	−0.557471	+	0.830197i	$0.688228\pi$
$182$	0	0
$183$	3.00000	0.221766
$184$	7.00000i	0.516047i
$185$	−36.0000	−2.64677
$186$	−21.0000	−1.53979
$187$	0	0
$188$	− 7.00000i	− 0.510527i
$189$	− 9.00000i	− 0.654654i
$190$	24.0000i	1.74114i
$191$	−8.00000	−0.578860	−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000	−0.578860	−0.289430	+	0.957199i	$0.593466\pi$
$192$	−3.00000	−0.216506
$193$	20.0000i	1.43963i	0.694165	+	0.719816i	$0.255774\pi$
$193$	20.0000i	1.43963i	−0.694165	+	0.719816i	$0.744226\pi$
$194$	1.00000	0.0717958
$195$	0	0
$196$	1.00000	0.0714286
$197$	27.0000i	1.92367i	0.273629	+	0.961835i	$0.411776\pi$
$197$	27.0000i	1.92367i	−0.273629	+	0.961835i	$0.588224\pi$
$198$	6.00000	0.426401
$199$	4.00000	0.283552	0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000	0.283552	0.141776	+	0.989899i	$0.454719\pi$
$200$	− 11.0000i	− 0.777817i
$201$	− 3.00000i	− 0.211604i
$202$	− 5.00000i	− 0.351799i
$203$	4.00000i	0.280745i
$204$	0	0
$205$	−12.0000	−0.838116
$206$	− 14.0000i	− 0.975426i
$207$	42.0000	2.91920
$208$	0	0
$209$	−6.00000	−0.415029
$210$	− 12.0000i	− 0.828079i
$211$	−10.0000	−0.688428	−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000	−0.688428	−0.344214	+	0.938891i	$0.611855\pi$
$212$	0	0
$213$	− 48.0000i	− 3.28891i
$214$	4.00000i	0.273434i
$215$	− 16.0000i	− 1.09119i
$216$	9.00000i	0.612372i
$217$	−7.00000	−0.475191
$218$	14.0000	0.948200
$219$	15.0000i	1.01361i
$220$	4.00000	0.269680
$221$	0	0
$222$	27.0000	1.81212
$223$	− 21.0000i	− 1.40626i	−0.711059	−	0.703132i	$-0.751784\pi$
$223$	− 21.0000i	− 1.40626i	0.711059	−	0.703132i	$-0.248216\pi$
$224$	−1.00000	−0.0668153
$225$	−66.0000	−4.40000
$226$	7.00000i	0.465633i
$227$	− 24.0000i	− 1.59294i	−0.604681	−	0.796468i	$-0.706699\pi$
$227$	− 24.0000i	− 1.59294i	0.604681	−	0.796468i	$-0.293301\pi$
$228$	− 18.0000i	− 1.19208i
$229$	− 24.0000i	− 1.58596i	−0.609245	−	0.792982i	$-0.708527\pi$
$229$	− 24.0000i	− 1.58596i	0.609245	−	0.792982i	$-0.291473\pi$
$230$	28.0000	1.84627
$231$	3.00000	0.197386
$232$	− 4.00000i	− 0.262613i
$233$	5.00000	0.327561	0.163780	−	0.986497i	$-0.447631\pi$
$233$	5.00000	0.327561	0.163780	+	0.986497i	$0.447631\pi$
$234$	0	0
$235$	−28.0000	−1.82652
$236$	10.0000i	0.650945i
$237$	33.0000	2.14358
$238$	0	0
$239$	− 6.00000i	− 0.388108i	−0.980991	−	0.194054i	$-0.937836\pi$
$239$	− 6.00000i	− 0.388108i	0.980991	−	0.194054i	$-0.0621637\pi$
$240$	12.0000i	0.774597i
$241$	− 18.0000i	− 1.15948i	−0.814801	−	0.579741i	$-0.803154\pi$
$241$	− 18.0000i	− 1.15948i	0.814801	−	0.579741i	$-0.196846\pi$
$242$	− 10.0000i	− 0.642824i
$243$	0	0
$244$	−1.00000	−0.0640184
$245$	− 4.00000i	− 0.255551i
$246$	9.00000	0.573819
$247$	0	0
$248$	7.00000	0.444500
$249$	0	0
$250$	−24.0000	−1.51789
$251$	−3.00000	−0.189358	−0.0946792	−	0.995508i	$-0.530183\pi$
$251$	−3.00000	−0.189358	−0.0946792	+	0.995508i	$0.530183\pi$
$252$	6.00000i	0.377964i
$253$	7.00000i	0.440086i
$254$	− 11.0000i	− 0.690201i
$255$	0	0
$256$	1.00000	0.0625000
$257$	−24.0000	−1.49708	−0.748539	−	0.663090i	$-0.769245\pi$
$257$	−24.0000	−1.49708	−0.748539	+	0.663090i	$0.769245\pi$
$258$	12.0000i	0.747087i
$259$	9.00000	0.559233
$260$	0	0
$261$	−24.0000	−1.48556
$262$	− 8.00000i	− 0.494242i
$263$	24.0000	1.47990	0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000	1.47990	0.739952	+	0.672660i	$0.234848\pi$
$264$	−3.00000	−0.184637
$265$	0	0
$266$	− 6.00000i	− 0.367884i
$267$	− 18.0000i	− 1.10158i
$268$	1.00000i	0.0610847i
$269$	9.00000	0.548740	0.274370	−	0.961624i	$-0.411531\pi$
$269$	9.00000	0.548740	0.274370	+	0.961624i	$0.411531\pi$
$270$	36.0000	2.19089
$271$	− 23.0000i	− 1.39715i	−0.715537	−	0.698575i	$-0.753818\pi$
$271$	− 23.0000i	− 1.39715i	0.715537	−	0.698575i	$-0.246182\pi$
$272$	0	0
$273$	0	0
$274$	−6.00000	−0.362473
$275$	− 11.0000i	− 0.663325i
$276$	−21.0000	−1.26405
$277$	18.0000	1.08152	0.540758	−	0.841178i	$-0.318138\pi$
$277$	18.0000	1.08152	0.540758	+	0.841178i	$0.318138\pi$
$278$	− 4.00000i	− 0.239904i
$279$	− 42.0000i	− 2.51447i
$280$	4.00000i	0.239046i
$281$	− 8.00000i	− 0.477240i	−0.971113	−	0.238620i	$-0.923305\pi$
$281$	− 8.00000i	− 0.477240i	0.971113	−	0.238620i	$-0.0766950\pi$
$282$	21.0000	1.25053
$283$	−19.0000	−1.12943	−0.564716	−	0.825285i	$-0.691014\pi$
$283$	−19.0000	−1.12943	−0.564716	+	0.825285i	$0.691014\pi$
$284$	16.0000i	0.949425i
$285$	−72.0000	−4.26491
$286$	0	0
$287$	3.00000	0.177084
$288$	− 6.00000i	− 0.353553i
$289$	−17.0000	−1.00000
$290$	−16.0000	−0.939552
$291$	3.00000i	0.175863i
$292$	− 5.00000i	− 0.292603i
$293$	− 26.0000i	− 1.51894i	−0.650545	−	0.759468i	$-0.725459\pi$
$293$	− 26.0000i	− 1.51894i	0.650545	−	0.759468i	$-0.274541\pi$
$294$	3.00000i	0.174964i
$295$	40.0000	2.32889
$296$	−9.00000	−0.523114
$297$	9.00000i	0.522233i
$298$	−9.00000	−0.521356
$299$	0	0
$300$	33.0000	1.90526
$301$	4.00000i	0.230556i
$302$	0	0
$303$	15.0000	0.861727
$304$	6.00000i	0.344124i
$305$	4.00000i	0.229039i
$306$	0	0
$307$	− 4.00000i	− 0.228292i	−0.993464	−	0.114146i	$-0.963587\pi$
$307$	− 4.00000i	− 0.228292i	0.993464	−	0.114146i	$-0.0364132\pi$
$308$	−1.00000	−0.0569803
$309$	42.0000	2.38930
$310$	− 28.0000i	− 1.59029i
$311$	−30.0000	−1.70114	−0.850572	−	0.525859i	$-0.823744\pi$
$311$	−30.0000	−1.70114	−0.850572	+	0.525859i	$0.823744\pi$
$312$	0	0
$313$	14.0000	0.791327	0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000	0.791327	0.395663	+	0.918396i	$0.370515\pi$
$314$	− 5.00000i	− 0.282166i
$315$	24.0000	1.35225
$316$	−11.0000	−0.618798
$317$	− 21.0000i	− 1.17948i	−0.807594	−	0.589739i	$-0.799231\pi$
$317$	− 21.0000i	− 1.17948i	0.807594	−	0.589739i	$-0.200769\pi$
$318$	0	0
$319$	− 4.00000i	− 0.223957i
$320$	− 4.00000i	− 0.223607i
$321$	−12.0000	−0.669775
$322$	−7.00000	−0.390095
$323$	0	0
$324$	−9.00000	−0.500000
$325$	0	0
$326$	−4.00000	−0.221540
$327$	42.0000i	2.32261i
$328$	−3.00000	−0.165647
$329$	7.00000	0.385922
$330$	12.0000i	0.660578i
$331$	7.00000i	0.384755i	0.981321	+	0.192377i	$0.0616198\pi$
$331$	7.00000i	0.384755i	−0.981321	+	0.192377i	$0.938380\pi$
$332$	0	0
$333$	54.0000i	2.95918i
$334$	0	0
$335$	4.00000	0.218543
$336$	− 3.00000i	− 0.163663i
$337$	−17.0000	−0.926049	−0.463025	−	0.886345i	$-0.653236\pi$
$337$	−17.0000	−0.926049	−0.463025	+	0.886345i	$0.653236\pi$
$338$	0	0
$339$	−21.0000	−1.14056
$340$	0	0
$341$	7.00000	0.379071
$342$	36.0000	1.94666
$343$	1.00000i	0.0539949i
$344$	− 4.00000i	− 0.215666i
$345$	84.0000i	4.52241i
$346$	2.00000i	0.107521i
$347$	−24.0000	−1.28839	−0.644194	−	0.764862i	$-0.722807\pi$
$347$	−24.0000	−1.28839	−0.644194	+	0.764862i	$0.722807\pi$
$348$	12.0000	0.643268
$349$	− 26.0000i	− 1.39175i	−0.718164	−	0.695874i	$-0.755017\pi$
$349$	− 26.0000i	− 1.39175i	0.718164	−	0.695874i	$-0.244983\pi$
$350$	11.0000	0.587975
$351$	0	0
$352$	1.00000	0.0533002
$353$	− 25.0000i	− 1.33062i	−0.746569	−	0.665308i	$-0.768300\pi$
$353$	− 25.0000i	− 1.33062i	0.746569	−	0.665308i	$-0.231700\pi$
$354$	−30.0000	−1.59448
$355$	64.0000	3.39677
$356$	6.00000i	0.317999i
$357$	0	0
$358$	− 6.00000i	− 0.317110i
$359$	12.0000i	0.633336i	0.948536	+	0.316668i	$0.102564\pi$
$359$	12.0000i	0.633336i	−0.948536	+	0.316668i	$0.897436\pi$
$360$	−24.0000	−1.26491
$361$	−17.0000	−0.894737
$362$	15.0000i	0.788382i
$363$	30.0000	1.57459
$364$	0	0
$365$	−20.0000	−1.04685
$366$	− 3.00000i	− 0.156813i
$367$	32.0000	1.67039	0.835193	−	0.549957i	$-0.185356\pi$
$367$	32.0000	1.67039	0.835193	+	0.549957i	$0.185356\pi$
$368$	7.00000	0.364900
$369$	18.0000i	0.937043i
$370$	36.0000i	1.87155i
$371$	0	0
$372$	21.0000i	1.08880i
$373$	−16.0000	−0.828449	−0.414224	−	0.910175i	$-0.635947\pi$
$373$	−16.0000	−0.828449	−0.414224	+	0.910175i	$0.635947\pi$
$374$	0	0
$375$	− 72.0000i	− 3.71806i
$376$	−7.00000	−0.360997
$377$	0	0
$378$	−9.00000	−0.462910
$379$	8.00000i	0.410932i	0.978664	+	0.205466i	$0.0658711\pi$
$379$	8.00000i	0.410932i	−0.978664	+	0.205466i	$0.934129\pi$
$380$	24.0000	1.23117
$381$	33.0000	1.69064
$382$	8.00000i	0.409316i
$383$	15.0000i	0.766464i	0.923652	+	0.383232i	$0.125189\pi$
$383$	15.0000i	0.766464i	−0.923652	+	0.383232i	$0.874811\pi$
$384$	3.00000i	0.153093i
$385$	4.00000i	0.203859i
$386$	20.0000	1.01797
$387$	−24.0000	−1.21999
$388$	− 1.00000i	− 0.0507673i
$389$	36.0000	1.82527	0.912636	−	0.408773i	$-0.134043\pi$
$389$	36.0000	1.82527	0.912636	+	0.408773i	$0.134043\pi$
$390$	0	0
$391$	0	0
$392$	− 1.00000i	− 0.0505076i
$393$	24.0000	1.21064
$394$	27.0000	1.36024
$395$	44.0000i	2.21388i
$396$	− 6.00000i	− 0.301511i
$397$	− 28.0000i	− 1.40528i	−0.711546	−	0.702640i	$-0.752005\pi$
$397$	− 28.0000i	− 1.40528i	0.711546	−	0.702640i	$-0.247995\pi$
$398$	− 4.00000i	− 0.200502i
$399$	18.0000	0.901127
$400$	−11.0000	−0.550000
$401$	12.0000i	0.599251i	0.954057	+	0.299626i	$0.0968618\pi$
$401$	12.0000i	0.599251i	−0.954057	+	0.299626i	$0.903138\pi$
$402$	−3.00000	−0.149626
$403$	0	0
$404$	−5.00000	−0.248759
$405$	36.0000i	1.78885i
$406$	4.00000	0.198517
$407$	−9.00000	−0.446113
$408$	0	0
$409$	26.0000i	1.28562i	0.766027	+	0.642809i	$0.222231\pi$
$409$	26.0000i	1.28562i	−0.766027	+	0.642809i	$0.777769\pi$
$410$	12.0000i	0.592638i
$411$	− 18.0000i	− 0.887875i
$412$	−14.0000	−0.689730
$413$	−10.0000	−0.492068
$414$	− 42.0000i	− 2.06419i
$415$	0	0
$416$	0	0
$417$	12.0000	0.587643
$418$	6.00000i	0.293470i
$419$	15.0000	0.732798	0.366399	−	0.930458i	$-0.380591\pi$
$419$	15.0000	0.732798	0.366399	+	0.930458i	$0.380591\pi$
$420$	−12.0000	−0.585540
$421$	− 19.0000i	− 0.926003i	−0.886357	−	0.463002i	$-0.846772\pi$
$421$	− 19.0000i	− 0.926003i	0.886357	−	0.463002i	$-0.153228\pi$
$422$	10.0000i	0.486792i
$423$	42.0000i	2.04211i
$424$	0	0
$425$	0	0
$426$	−48.0000	−2.32561
$427$	− 1.00000i	− 0.0483934i
$428$	4.00000	0.193347
$429$	0	0
$430$	−16.0000	−0.771589
$431$	− 18.0000i	− 0.867029i	−0.901146	−	0.433515i	$-0.857273\pi$
$431$	− 18.0000i	− 0.867029i	0.901146	−	0.433515i	$-0.142727\pi$
$432$	9.00000	0.433013
$433$	−34.0000	−1.63394	−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000	−1.63394	−0.816968	+	0.576683i	$0.804347\pi$
$434$	7.00000i	0.336011i
$435$	− 48.0000i	− 2.30142i
$436$	− 14.0000i	− 0.670478i
$437$	42.0000i	2.00913i
$438$	15.0000	0.716728
$439$	−2.00000	−0.0954548	−0.0477274	−	0.998860i	$-0.515198\pi$
$439$	−2.00000	−0.0954548	−0.0477274	+	0.998860i	$0.515198\pi$
$440$	− 4.00000i	− 0.190693i
$441$	−6.00000	−0.285714
$442$	0	0
$443$	12.0000	0.570137	0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000	0.570137	0.285069	+	0.958507i	$0.407984\pi$
$444$	− 27.0000i	− 1.28136i
$445$	24.0000	1.13771
$446$	−21.0000	−0.994379
$447$	− 27.0000i	− 1.27706i
$448$	1.00000i	0.0472456i
$449$	− 2.00000i	− 0.0943858i	−0.998886	−	0.0471929i	$-0.984972\pi$
$449$	− 2.00000i	− 0.0943858i	0.998886	−	0.0471929i	$-0.0150276\pi$
$450$	66.0000i	3.11127i
$451$	−3.00000	−0.141264
$452$	7.00000	0.329252
$453$	0	0
$454$	−24.0000	−1.12638
$455$	0	0
$456$	−18.0000	−0.842927
$457$	26.0000i	1.21623i	0.793849	+	0.608114i	$0.208074\pi$
$457$	26.0000i	1.21623i	−0.793849	+	0.608114i	$0.791926\pi$
$458$	−24.0000	−1.12145
$459$	0	0
$460$	− 28.0000i	− 1.30551i
$461$	− 12.0000i	− 0.558896i	−0.960161	−	0.279448i	$-0.909849\pi$
$461$	− 12.0000i	− 0.558896i	0.960161	−	0.279448i	$-0.0901514\pi$
$462$	− 3.00000i	− 0.139573i
$463$	16.0000i	0.743583i	0.928316	+	0.371792i	$0.121256\pi$
$463$	16.0000i	0.743583i	−0.928316	+	0.371792i	$0.878744\pi$
$464$	−4.00000	−0.185695
$465$	84.0000	3.89541
$466$	− 5.00000i	− 0.231621i
$467$	4.00000	0.185098	0.0925490	−	0.995708i	$-0.470499\pi$
$467$	4.00000	0.185098	0.0925490	+	0.995708i	$0.470499\pi$
$468$	0	0
$469$	−1.00000	−0.0461757
$470$	28.0000i	1.29154i
$471$	15.0000	0.691164
$472$	10.0000	0.460287
$473$	− 4.00000i	− 0.183920i
$474$	− 33.0000i	− 1.51574i
$475$	− 66.0000i	− 3.02829i
$476$	0	0
$477$	0	0
$478$	−6.00000	−0.274434
$479$	24.0000i	1.09659i	0.836286	+	0.548294i	$0.184723\pi$
$479$	24.0000i	1.09659i	−0.836286	+	0.548294i	$0.815277\pi$
$480$	12.0000	0.547723
$481$	0	0
$482$	−18.0000	−0.819878
$483$	− 21.0000i	− 0.955533i
$484$	−10.0000	−0.454545
$485$	−4.00000	−0.181631
$486$	0	0
$487$	− 38.0000i	− 1.72194i	−0.508652	−	0.860972i	$-0.669856\pi$
$487$	− 38.0000i	− 1.72194i	0.508652	−	0.860972i	$-0.330144\pi$
$488$	1.00000i	0.0452679i
$489$	− 12.0000i	− 0.542659i
$490$	−4.00000	−0.180702
$491$	−16.0000	−0.722070	−0.361035	−	0.932552i	$-0.617576\pi$
$491$	−16.0000	−0.722070	−0.361035	+	0.932552i	$0.617576\pi$
$492$	− 9.00000i	− 0.405751i
$493$	0	0
$494$	0	0
$495$	−24.0000	−1.07872
$496$	− 7.00000i	− 0.314309i
$497$	−16.0000	−0.717698
$498$	0	0
$499$	5.00000i	0.223831i	0.993718	+	0.111915i	$0.0356986\pi$
$499$	5.00000i	0.223831i	−0.993718	+	0.111915i	$0.964301\pi$
$500$	24.0000i	1.07331i
$501$	0	0
$502$	3.00000i	0.133897i
$503$	−20.0000	−0.891756	−0.445878	−	0.895094i	$-0.647108\pi$
$503$	−20.0000	−0.891756	−0.445878	+	0.895094i	$0.647108\pi$
$504$	6.00000	0.267261
$505$	20.0000i	0.889988i
$506$	7.00000	0.311188
$507$	0	0
$508$	−11.0000	−0.488046
$509$	− 10.0000i	− 0.443242i	−0.975133	−	0.221621i	$-0.928865\pi$
$509$	− 10.0000i	− 0.443242i	0.975133	−	0.221621i	$-0.0711348\pi$
$510$	0	0
$511$	5.00000	0.221187
$512$	− 1.00000i	− 0.0441942i
$513$	54.0000i	2.38416i
$514$	24.0000i	1.05859i
$515$	56.0000i	2.46765i
$516$	12.0000	0.528271
$517$	−7.00000	−0.307860
$518$	− 9.00000i	− 0.395437i
$519$	−6.00000	−0.263371
$520$	0	0
$521$	−18.0000	−0.788594	−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000	−0.788594	−0.394297	+	0.918983i	$0.629012\pi$
$522$	24.0000i	1.05045i
$523$	27.0000	1.18063	0.590314	−	0.807174i	$-0.299004\pi$
$523$	27.0000	1.18063	0.590314	+	0.807174i	$0.299004\pi$
$524$	−8.00000	−0.349482
$525$	33.0000i	1.44024i
$526$	− 24.0000i	− 1.04645i
$527$	0	0
$528$	3.00000i	0.130558i
$529$	26.0000	1.13043
$530$	0	0
$531$	− 60.0000i	− 2.60378i
$532$	−6.00000	−0.260133
$533$	0	0
$534$	−18.0000	−0.778936
$535$	− 16.0000i	− 0.691740i
$536$	1.00000	0.0431934
$537$	18.0000	0.776757
$538$	− 9.00000i	− 0.388018i
$539$	− 1.00000i	− 0.0430730i
$540$	− 36.0000i	− 1.54919i
$541$	− 10.0000i	− 0.429934i	−0.976621	−	0.214967i	$-0.931036\pi$
$541$	− 10.0000i	− 0.429934i	0.976621	−	0.214967i	$-0.0689643\pi$
$542$	−23.0000	−0.987935
$543$	−45.0000	−1.93113
$544$	0	0
$545$	−56.0000	−2.39878
$546$	0	0
$547$	28.0000	1.19719	0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000	1.19719	0.598597	+	0.801050i	$0.295725\pi$
$548$	6.00000i	0.256307i
$549$	6.00000	0.256074
$550$	−11.0000	−0.469042
$551$	− 24.0000i	− 1.02243i
$552$	21.0000i	0.893819i
$553$	− 11.0000i	− 0.467768i
$554$	− 18.0000i	− 0.764747i
$555$	−108.000	−4.58434
$556$	−4.00000	−0.169638
$557$	9.00000i	0.381342i	0.981654	+	0.190671i	$0.0610664\pi$
$557$	9.00000i	0.381342i	−0.981654	+	0.190671i	$0.938934\pi$
$558$	−42.0000	−1.77800
$559$	0	0
$560$	4.00000	0.169031
$561$	0	0
$562$	−8.00000	−0.337460
$563$	−11.0000	−0.463595	−0.231797	−	0.972764i	$-0.574461\pi$
$563$	−11.0000	−0.463595	−0.231797	+	0.972764i	$0.574461\pi$
$564$	− 21.0000i	− 0.884260i
$565$	− 28.0000i	− 1.17797i
$566$	19.0000i	0.798630i
$567$	− 9.00000i	− 0.377964i
$568$	16.0000	0.671345
$569$	35.0000	1.46728	0.733638	−	0.679540i	$-0.237821\pi$
$569$	35.0000	1.46728	0.733638	+	0.679540i	$0.237821\pi$
$570$	72.0000i	3.01575i
$571$	−6.00000	−0.251092	−0.125546	−	0.992088i	$-0.540068\pi$
$571$	−6.00000	−0.251092	−0.125546	+	0.992088i	$0.540068\pi$
$572$	0	0
$573$	−24.0000	−1.00261
$574$	− 3.00000i	− 0.125218i
$575$	−77.0000	−3.21112
$576$	−6.00000	−0.250000
$577$	− 30.0000i	− 1.24892i	−0.781058	−	0.624458i	$-0.785320\pi$
$577$	− 30.0000i	− 1.24892i	0.781058	−	0.624458i	$-0.214680\pi$
$578$	17.0000i	0.707107i
$579$	60.0000i	2.49351i
$580$	16.0000i	0.664364i
$581$	0	0
$582$	3.00000	0.124354
$583$	0	0
$584$	−5.00000	−0.206901
$585$	0	0
$586$	−26.0000	−1.07405
$587$	− 14.0000i	− 0.577842i	−0.957353	−	0.288921i	$-0.906704\pi$
$587$	− 14.0000i	− 0.577842i	0.957353	−	0.288921i	$-0.0932965\pi$
$588$	3.00000	0.123718
$589$	42.0000	1.73058
$590$	− 40.0000i	− 1.64677i
$591$	81.0000i	3.33189i
$592$	9.00000i	0.369898i
$593$	14.0000i	0.574911i	0.957794	+	0.287456i	$0.0928094\pi$
$593$	14.0000i	0.574911i	−0.957794	+	0.287456i	$0.907191\pi$
$594$	9.00000	0.369274
$595$	0	0
$596$	9.00000i	0.368654i
$597$	12.0000	0.491127
$598$	0	0
$599$	−29.0000	−1.18491	−0.592454	−	0.805604i	$-0.701841\pi$
$599$	−29.0000	−1.18491	−0.592454	+	0.805604i	$0.701841\pi$
$600$	− 33.0000i	− 1.34722i
$601$	−26.0000	−1.06056	−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000	−1.06056	−0.530281	+	0.847822i	$0.677914\pi$
$602$	4.00000	0.163028
$603$	− 6.00000i	− 0.244339i
$604$	0	0
$605$	40.0000i	1.62623i
$606$	− 15.0000i	− 0.609333i
$607$	6.00000	0.243532	0.121766	−	0.992559i	$-0.461144\pi$
$607$	6.00000	0.243532	0.121766	+	0.992559i	$0.461144\pi$
$608$	6.00000	0.243332
$609$	12.0000i	0.486265i
$610$	4.00000	0.161955
$611$	0	0
$612$	0	0
$613$	49.0000i	1.97909i	0.144220	+	0.989546i	$0.453933\pi$
$613$	49.0000i	1.97909i	−0.144220	+	0.989546i	$0.546067\pi$
$614$	−4.00000	−0.161427
$615$	−36.0000	−1.45166
$616$	1.00000i	0.0402911i
$617$	− 22.0000i	− 0.885687i	−0.896599	−	0.442843i	$-0.853970\pi$
$617$	− 22.0000i	− 0.885687i	0.896599	−	0.442843i	$-0.146030\pi$
$618$	− 42.0000i	− 1.68949i
$619$	22.0000i	0.884255i	0.896952	+	0.442127i	$0.145776\pi$
$619$	22.0000i	0.884255i	−0.896952	+	0.442127i	$0.854224\pi$
$620$	−28.0000	−1.12451
$621$	63.0000	2.52810
$622$	30.0000i	1.20289i
$623$	−6.00000	−0.240385
$624$	0	0
$625$	41.0000	1.64000
$626$	− 14.0000i	− 0.559553i
$627$	−18.0000	−0.718851
$628$	−5.00000	−0.199522
$629$	0	0
$630$	− 24.0000i	− 0.956183i
$631$	− 2.00000i	− 0.0796187i	−0.999207	−	0.0398094i	$-0.987325\pi$
$631$	− 2.00000i	− 0.0796187i	0.999207	−	0.0398094i	$-0.0126751\pi$
$632$	11.0000i	0.437557i
$633$	−30.0000	−1.19239
$634$	−21.0000	−0.834017
$635$	44.0000i	1.74609i
$636$	0	0
$637$	0	0
$638$	−4.00000	−0.158362
$639$	− 96.0000i	− 3.79770i
$640$	−4.00000	−0.158114
$641$	−7.00000	−0.276483	−0.138242	−	0.990399i	$-0.544145\pi$
$641$	−7.00000	−0.276483	−0.138242	+	0.990399i	$0.544145\pi$
$642$	12.0000i	0.473602i
$643$	16.0000i	0.630978i	0.948929	+	0.315489i	$0.102169\pi$
$643$	16.0000i	0.630978i	−0.948929	+	0.315489i	$0.897831\pi$
$644$	7.00000i	0.275839i
$645$	− 48.0000i	− 1.89000i
$646$	0	0
$647$	8.00000	0.314512	0.157256	−	0.987558i	$-0.449735\pi$
$647$	8.00000	0.314512	0.157256	+	0.987558i	$0.449735\pi$
$648$	9.00000i	0.353553i
$649$	10.0000	0.392534
$650$	0	0
$651$	−21.0000	−0.823055
$652$	4.00000i	0.156652i
$653$	−36.0000	−1.40879	−0.704394	−	0.709809i	$-0.748781\pi$
$653$	−36.0000	−1.40879	−0.704394	+	0.709809i	$0.748781\pi$
$654$	42.0000	1.64233
$655$	32.0000i	1.25034i
$656$	3.00000i	0.117130i
$657$	30.0000i	1.17041i
$658$	− 7.00000i	− 0.272888i
$659$	−18.0000	−0.701180	−0.350590	−	0.936529i	$-0.614019\pi$
$659$	−18.0000	−0.701180	−0.350590	+	0.936529i	$0.614019\pi$
$660$	12.0000	0.467099
$661$	− 4.00000i	− 0.155582i	−0.996970	−	0.0777910i	$-0.975213\pi$
$661$	− 4.00000i	− 0.155582i	0.996970	−	0.0777910i	$-0.0247867\pi$
$662$	7.00000	0.272063
$663$	0	0
$664$	0	0
$665$	24.0000i	0.930680i
$666$	54.0000	2.09246
$667$	−28.0000	−1.08416
$668$	0	0
$669$	− 63.0000i	− 2.43572i
$670$	− 4.00000i	− 0.154533i
$671$	1.00000i	0.0386046i
$672$	−3.00000	−0.115728
$673$	−7.00000	−0.269830	−0.134915	−	0.990857i	$-0.543076\pi$
$673$	−7.00000	−0.269830	−0.134915	+	0.990857i	$0.543076\pi$
$674$	17.0000i	0.654816i
$675$	−99.0000	−3.81051
$676$	0	0
$677$	39.0000	1.49889	0.749446	−	0.662066i	$-0.230320\pi$
$677$	39.0000	1.49889	0.749446	+	0.662066i	$0.230320\pi$
$678$	21.0000i	0.806500i
$679$	1.00000	0.0383765
$680$	0	0
$681$	− 72.0000i	− 2.75905i
$682$	− 7.00000i	− 0.268044i
$683$	1.00000i	0.0382639i	0.999817	+	0.0191320i	$0.00609027\pi$
$683$	1.00000i	0.0382639i	−0.999817	+	0.0191320i	$0.993910\pi$
$684$	− 36.0000i	− 1.37649i
$685$	24.0000	0.916993
$686$	1.00000	0.0381802
$687$	− 72.0000i	− 2.74697i
$688$	−4.00000	−0.152499
$689$	0	0
$690$	84.0000	3.19783
$691$	32.0000i	1.21734i	0.793424	+	0.608669i	$0.208296\pi$
$691$	32.0000i	1.21734i	−0.793424	+	0.608669i	$0.791704\pi$
$692$	2.00000	0.0760286
$693$	6.00000	0.227921
$694$	24.0000i	0.911028i
$695$	16.0000i	0.606915i
$696$	− 12.0000i	− 0.454859i
$697$	0	0
$698$	−26.0000	−0.984115
$699$	15.0000	0.567352
$700$	− 11.0000i	− 0.415761i
$701$	0	0		−	1.00000i	$-0.5\pi$
$701$	0	0			1.00000i	$0.5\pi$
$702$	0	0
$703$	−54.0000	−2.03665
$704$	− 1.00000i	− 0.0376889i
$705$	−84.0000	−3.16362
$706$	−25.0000	−0.940887
$707$	− 5.00000i	− 0.188044i
$708$	30.0000i	1.12747i
$709$	− 13.0000i	− 0.488225i	−0.969747	−	0.244113i	$-0.921503\pi$
$709$	− 13.0000i	− 0.488225i	0.969747	−	0.244113i	$-0.0784967\pi$
$710$	− 64.0000i	− 2.40188i
$711$	66.0000	2.47519
$712$	6.00000	0.224860
$713$	− 49.0000i	− 1.83506i
$714$	0	0
$715$	0	0
$716$	−6.00000	−0.224231
$717$	− 18.0000i	− 0.672222i
$718$	12.0000	0.447836
$719$	−2.00000	−0.0745874	−0.0372937	−	0.999304i	$-0.511874\pi$
$719$	−2.00000	−0.0745874	−0.0372937	+	0.999304i	$0.511874\pi$
$720$	24.0000i	0.894427i
$721$	− 14.0000i	− 0.521387i
$722$	17.0000i	0.632674i
$723$	− 54.0000i	− 2.00828i
$724$	15.0000	0.557471
$725$	44.0000	1.63412
$726$	− 30.0000i	− 1.11340i
$727$	26.0000	0.964287	0.482143	−	0.876092i	$-0.339858\pi$
$727$	26.0000	0.964287	0.482143	+	0.876092i	$0.339858\pi$
$728$	0	0
$729$	−27.0000	−1.00000
$730$	20.0000i	0.740233i
$731$	0	0
$732$	−3.00000	−0.110883
$733$	4.00000i	0.147743i	0.997268	+	0.0738717i	$0.0235355\pi$
$733$	4.00000i	0.147743i	−0.997268	+	0.0738717i	$0.976464\pi$
$734$	− 32.0000i	− 1.18114i
$735$	− 12.0000i	− 0.442627i
$736$	− 7.00000i	− 0.258023i
$737$	1.00000	0.0368355
$738$	18.0000	0.662589
$739$	24.0000i	0.882854i	0.897297	+	0.441427i	$0.145528\pi$
$739$	24.0000i	0.882854i	−0.897297	+	0.441427i	$0.854472\pi$
$740$	36.0000	1.32339
$741$	0	0
$742$	0	0
$743$	− 16.0000i	− 0.586983i	−0.955962	−	0.293492i	$-0.905183\pi$
$743$	− 16.0000i	− 0.586983i	0.955962	−	0.293492i	$-0.0948173\pi$
$744$	21.0000	0.769897
$745$	36.0000	1.31894
$746$	16.0000i	0.585802i
$747$	0	0
$748$	0	0
$749$	4.00000i	0.146157i
$750$	−72.0000	−2.62907
$751$	27.0000	0.985244	0.492622	−	0.870243i	$-0.336039\pi$
$751$	27.0000	0.985244	0.492622	+	0.870243i	$0.336039\pi$
$752$	7.00000i	0.255264i
$753$	−9.00000	−0.327978
$754$	0	0
$755$	0	0
$756$	9.00000i	0.327327i
$757$	54.0000	1.96266	0.981332	−	0.192323i	$-0.0616021\pi$
$757$	54.0000	1.96266	0.981332	+	0.192323i	$0.0616021\pi$
$758$	8.00000	0.290573
$759$	21.0000i	0.762252i
$760$	− 24.0000i	− 0.870572i
$761$	45.0000i	1.63125i	0.578582	+	0.815624i	$0.303606\pi$
$761$	45.0000i	1.63125i	−0.578582	+	0.815624i	$0.696394\pi$
$762$	− 33.0000i	− 1.19546i
$763$	14.0000	0.506834
$764$	8.00000	0.289430
$765$	0	0
$766$	15.0000	0.541972
$767$	0	0
$768$	3.00000	0.108253
$769$	− 21.0000i	− 0.757279i	−0.925544	−	0.378640i	$-0.876392\pi$
$769$	− 21.0000i	− 0.757279i	0.925544	−	0.378640i	$-0.123608\pi$
$770$	4.00000	0.144150
$771$	−72.0000	−2.59302
$772$	− 20.0000i	− 0.719816i
$773$	− 14.0000i	− 0.503545i	−0.967786	−	0.251773i	$-0.918987\pi$
$773$	− 14.0000i	− 0.503545i	0.967786	−	0.251773i	$-0.0810135\pi$
$774$	24.0000i	0.862662i
$775$	77.0000i	2.76592i
$776$	−1.00000	−0.0358979
$777$	27.0000	0.968620
$778$	− 36.0000i	− 1.29066i
$779$	−18.0000	−0.644917
$780$	0	0
$781$	16.0000	0.572525
$782$	0	0
$783$	−36.0000	−1.28654
$784$	−1.00000	−0.0357143
$785$	20.0000i	0.713831i
$786$	− 24.0000i	− 0.856052i
$787$	32.0000i	1.14068i	0.821410	+	0.570338i	$0.193188\pi$
$787$	32.0000i	1.14068i	−0.821410	+	0.570338i	$0.806812\pi$
$788$	− 27.0000i	− 0.961835i
$789$	72.0000	2.56327
$790$	44.0000	1.56545
$791$	7.00000i	0.248891i
$792$	−6.00000	−0.213201
$793$	0	0
$794$	−28.0000	−0.993683
$795$	0	0
$796$	−4.00000	−0.141776
$797$	−15.0000	−0.531327	−0.265664	−	0.964066i	$-0.585591\pi$
$797$	−15.0000	−0.531327	−0.265664	+	0.964066i	$0.585591\pi$
$798$	− 18.0000i	− 0.637193i
$799$	0	0
$800$	11.0000i	0.388909i
$801$	− 36.0000i	− 1.27200i
$802$	12.0000	0.423735
$803$	−5.00000	−0.176446
$804$	3.00000i	0.105802i
$805$	28.0000	0.986870
$806$	0	0
$807$	27.0000	0.950445
$808$	5.00000i	0.175899i
$809$	6.00000	0.210949	0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000	0.210949	0.105474	+	0.994422i	$0.466364\pi$
$810$	36.0000	1.26491
$811$	28.0000i	0.983213i	0.870817	+	0.491606i	$0.163590\pi$
$811$	28.0000i	0.983213i	−0.870817	+	0.491606i	$0.836410\pi$
$812$	− 4.00000i	− 0.140372i
$813$	− 69.0000i	− 2.41994i
$814$	9.00000i	0.315450i
$815$	16.0000	0.560456
$816$	0	0
$817$	− 24.0000i	− 0.839654i
$818$	26.0000	0.909069
$819$	0	0
$820$	12.0000	0.419058
$821$	46.0000i	1.60541i	0.596376	+	0.802706i	$0.296607\pi$
$821$	46.0000i	1.60541i	−0.596376	+	0.802706i	$0.703393\pi$
$822$	−18.0000	−0.627822
$823$	3.00000	0.104573	0.0522867	−	0.998632i	$-0.483349\pi$
$823$	3.00000	0.104573	0.0522867	+	0.998632i	$0.483349\pi$
$824$	14.0000i	0.487713i
$825$	− 33.0000i	− 1.14891i
$826$	10.0000i	0.347945i
$827$	− 12.0000i	− 0.417281i	−0.977992	−	0.208640i	$-0.933096\pi$
$827$	− 12.0000i	− 0.417281i	0.977992	−	0.208640i	$-0.0669038\pi$
$828$	−42.0000	−1.45960
$829$	14.0000	0.486240	0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000	0.486240	0.243120	+	0.969996i	$0.421829\pi$
$830$	0	0
$831$	54.0000	1.87324
$832$	0	0
$833$	0	0
$834$	− 12.0000i	− 0.415526i
$835$	0	0
$836$	6.00000	0.207514
$837$	− 63.0000i	− 2.17760i
$838$	− 15.0000i	− 0.518166i
$839$	17.0000i	0.586905i	0.955974	+	0.293453i	$0.0948043\pi$
$839$	17.0000i	0.586905i	−0.955974	+	0.293453i	$0.905196\pi$
$840$	12.0000i	0.414039i
$841$	−13.0000	−0.448276
$842$	−19.0000	−0.654783
$843$	− 24.0000i	− 0.826604i
$844$	10.0000	0.344214
$845$	0	0
$846$	42.0000	1.44399
$847$	− 10.0000i	− 0.343604i
$848$	0	0
$849$	−57.0000	−1.95623
$850$	0	0
$851$	63.0000i	2.15961i
$852$	48.0000i	1.64445i
$853$	16.0000i	0.547830i	0.961754	+	0.273915i	$0.0883186\pi$
$853$	16.0000i	0.547830i	−0.961754	+	0.273915i	$0.911681\pi$
$854$	−1.00000	−0.0342193
$855$	−144.000	−4.92470
$856$	− 4.00000i	− 0.136717i
$857$	−22.0000	−0.751506	−0.375753	−	0.926720i	$-0.622616\pi$
$857$	−22.0000	−0.751506	−0.375753	+	0.926720i	$0.622616\pi$
$858$	0	0
$859$	5.00000	0.170598	0.0852989	−	0.996355i	$-0.472815\pi$
$859$	5.00000	0.170598	0.0852989	+	0.996355i	$0.472815\pi$
$860$	16.0000i	0.545595i
$861$	9.00000	0.306719
$862$	−18.0000	−0.613082
$863$	− 28.0000i	− 0.953131i	−0.879139	−	0.476566i	$-0.841881\pi$
$863$	− 28.0000i	− 0.953131i	0.879139	−	0.476566i	$-0.158119\pi$
$864$	− 9.00000i	− 0.306186i
$865$	− 8.00000i	− 0.272008i
$866$	34.0000i	1.15537i
$867$	−51.0000	−1.73205
$868$	7.00000	0.237595
$869$	11.0000i	0.373149i
$870$	−48.0000	−1.62735
$871$	0	0
$872$	−14.0000	−0.474100
$873$	6.00000i	0.203069i
$874$	42.0000	1.42067
$875$	−24.0000	−0.811348
$876$	− 15.0000i	− 0.506803i
$877$	45.0000i	1.51954i	0.650191	+	0.759771i	$0.274689\pi$
$877$	45.0000i	1.51954i	−0.650191	+	0.759771i	$0.725311\pi$
$878$	2.00000i	0.0674967i
$879$	− 78.0000i	− 2.63087i
$880$	−4.00000	−0.134840
$881$	−18.0000	−0.606435	−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000	−0.606435	−0.303218	+	0.952921i	$0.598061\pi$
$882$	6.00000i	0.202031i
$883$	14.0000	0.471138	0.235569	−	0.971858i	$-0.424305\pi$
$883$	14.0000	0.471138	0.235569	+	0.971858i	$0.424305\pi$
$884$	0	0
$885$	120.000	4.03376
$886$	− 12.0000i	− 0.403148i
$887$	−38.0000	−1.27592	−0.637958	−	0.770072i	$-0.720220\pi$
$887$	−38.0000	−1.27592	−0.637958	+	0.770072i	$0.720220\pi$
$888$	−27.0000	−0.906061
$889$	− 11.0000i	− 0.368928i
$890$	− 24.0000i	− 0.804482i
$891$	9.00000i	0.301511i
$892$	21.0000i	0.703132i
$893$	−42.0000	−1.40548
$894$	−27.0000	−0.903015
$895$	24.0000i	0.802232i
$896$	1.00000	0.0334077
$897$	0	0
$898$	−2.00000	−0.0667409
$899$	28.0000i	0.933852i
$900$	66.0000	2.20000
$901$	0	0
$902$	3.00000i	0.0998891i
$903$	12.0000i	0.399335i
$904$	− 7.00000i	− 0.232817i
$905$	− 60.0000i	− 1.99447i
$906$	0	0
$907$	30.0000	0.996134	0.498067	−	0.867139i	$-0.334043\pi$
$907$	30.0000	0.996134	0.498067	+	0.867139i	$0.334043\pi$
$908$	24.0000i	0.796468i
$909$	30.0000	0.995037
$910$	0	0
$911$	36.0000	1.19273	0.596367	−	0.802712i	$-0.296610\pi$
$911$	36.0000	1.19273	0.596367	+	0.802712i	$0.296610\pi$
$912$	18.0000i	0.596040i
$913$	0	0
$914$	26.0000	0.860004
$915$	12.0000i	0.396708i
$916$	24.0000i	0.792982i
$917$	− 8.00000i	− 0.264183i
$918$	0	0
$919$	27.0000	0.890648	0.445324	−	0.895370i	$-0.353089\pi$
$919$	27.0000	0.890648	0.445324	+	0.895370i	$0.353089\pi$
$920$	−28.0000	−0.923133
$921$	− 12.0000i	− 0.395413i
$922$	−12.0000	−0.395199
$923$	0	0
$924$	−3.00000	−0.0986928
$925$	− 99.0000i	− 3.25510i
$926$	16.0000	0.525793
$927$	84.0000	2.75892
$928$	4.00000i	0.131306i
$929$	15.0000i	0.492134i	0.969253	+	0.246067i	$0.0791383\pi$
$929$	15.0000i	0.492134i	−0.969253	+	0.246067i	$0.920862\pi$
$930$	− 84.0000i	− 2.75447i
$931$	− 6.00000i	− 0.196642i
$932$	−5.00000	−0.163780
$933$	−90.0000	−2.94647
$934$	− 4.00000i	− 0.130884i
$935$	0	0
$936$	0	0
$937$	−36.0000	−1.17607	−0.588034	−	0.808836i	$-0.700098\pi$
$937$	−36.0000	−1.17607	−0.588034	+	0.808836i	$0.700098\pi$
$938$	1.00000i	0.0326512i
$939$	42.0000	1.37062
$940$	28.0000	0.913259
$941$	50.0000i	1.62995i	0.579494	+	0.814977i	$0.303250\pi$
$941$	50.0000i	1.62995i	−0.579494	+	0.814977i	$0.696750\pi$
$942$	− 15.0000i	− 0.488726i
$943$	21.0000i	0.683854i
$944$	− 10.0000i	− 0.325472i
$945$	36.0000	1.17108
$946$	−4.00000	−0.130051
$947$	24.0000i	0.779895i	0.920837	+	0.389948i	$0.127507\pi$
$947$	24.0000i	0.779895i	−0.920837	+	0.389948i	$0.872493\pi$
$948$	−33.0000	−1.07179
$949$	0	0
$950$	−66.0000	−2.14132
$951$	− 63.0000i	− 2.04291i
$952$	0	0
$953$	34.0000	1.10137	0.550684	−	0.834714i	$-0.314367\pi$
$953$	34.0000	1.10137	0.550684	+	0.834714i	$0.314367\pi$
$954$	0	0
$955$	− 32.0000i	− 1.03550i
$956$	6.00000i	0.194054i
$957$	− 12.0000i	− 0.387905i
$958$	24.0000	0.775405
$959$	−6.00000	−0.193750
$960$	− 12.0000i	− 0.387298i
$961$	−18.0000	−0.580645
$962$	0	0
$963$	−24.0000	−0.773389
$964$	18.0000i	0.579741i
$965$	−80.0000	−2.57529
$966$	−21.0000	−0.675664
$967$	22.0000i	0.707472i	0.935345	+	0.353736i	$0.115089\pi$
$967$	22.0000i	0.707472i	−0.935345	+	0.353736i	$0.884911\pi$
$968$	10.0000i	0.321412i
$969$	0	0
$970$	4.00000i	0.128432i
$971$	−15.0000	−0.481373	−0.240686	−	0.970603i	$-0.577373\pi$
$971$	−15.0000	−0.481373	−0.240686	+	0.970603i	$0.577373\pi$
$972$	0	0
$973$	− 4.00000i	− 0.128234i
$974$	−38.0000	−1.21760
$975$	0	0
$976$	1.00000	0.0320092
$977$	− 42.0000i	− 1.34370i	−0.740688	−	0.671850i	$-0.765500\pi$
$977$	− 42.0000i	− 1.34370i	0.740688	−	0.671850i	$-0.234500\pi$
$978$	−12.0000	−0.383718
$979$	6.00000	0.191761
$980$	4.00000i	0.127775i
$981$	84.0000i	2.68191i
$982$	16.0000i	0.510581i
$983$	− 40.0000i	− 1.27580i	−0.770118	−	0.637901i	$-0.779803\pi$
$983$	− 40.0000i	− 1.27580i	0.770118	−	0.637901i	$-0.220197\pi$
$984$	−9.00000	−0.286910
$985$	−108.000	−3.44117
$986$	0	0
$987$	21.0000	0.668437
$988$	0	0
$989$	−28.0000	−0.890348
$990$	24.0000i	0.762770i
$991$	−57.0000	−1.81066	−0.905332	−	0.424704i	$-0.860378\pi$
$991$	−57.0000	−1.81066	−0.905332	+	0.424704i	$0.860378\pi$
$992$	−7.00000	−0.222250
$993$	21.0000i	0.666415i
$994$	16.0000i	0.507489i
$995$	16.0000i	0.507234i
$996$	0	0
$997$	5.00000	0.158352	0.0791758	−	0.996861i	$-0.474771\pi$
$997$	5.00000	0.158352	0.0791758	+	0.996861i	$0.474771\pi$
$998$	5.00000	0.158272
$999$	81.0000i	2.56273i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.d.j.337.1		2
13.5	odd	4		2366.2.a.h.1.1		1
13.8	odd	4		182.2.a.e.1.1	✓	1
13.12	even	2	inner	2366.2.d.j.337.2		2
39.8	even	4		1638.2.a.j.1.1		1
52.47	even	4		1456.2.a.a.1.1		1
65.34	odd	4		4550.2.a.a.1.1		1
91.34	even	4		1274.2.a.h.1.1		1
91.47	even	12		1274.2.f.k.1145.1		2
91.60	odd	12		1274.2.f.b.79.1		2
91.73	even	12		1274.2.f.k.79.1		2
91.86	odd	12		1274.2.f.b.1145.1		2
104.21	odd	4		5824.2.a.b.1.1		1
104.99	even	4		5824.2.a.bf.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.a.e.1.1	✓	1	13.8	odd	4
1274.2.a.h.1.1		1	91.34	even	4
1274.2.f.b.79.1		2	91.60	odd	12
1274.2.f.b.1145.1		2	91.86	odd	12
1274.2.f.k.79.1		2	91.73	even	12
1274.2.f.k.1145.1		2	91.47	even	12
1456.2.a.a.1.1		1	52.47	even	4
1638.2.a.j.1.1		1	39.8	even	4
2366.2.a.h.1.1		1	13.5	odd	4
2366.2.d.j.337.1		2	1.1	even	1	trivial
2366.2.d.j.337.2		2	13.12	even	2	inner
4550.2.a.a.1.1		1	65.34	odd	4
5824.2.a.b.1.1		1	104.21	odd	4
5824.2.a.bf.1.1		1	104.99	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:	\( N \)	\(=\)	\( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2366.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +3.00000 q^{3} -1.00000 q^{4} +4.00000i q^{5} -3.00000i q^{6} -1.00000i q^{7} +1.00000i q^{8} +6.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +3.00000 q^{3} -1.00000 q^{4} +4.00000i q^{5} -3.00000i q^{6} -1.00000i q^{7} +1.00000i q^{8} +6.00000 q^{9} +4.00000 q^{10} +1.00000i q^{11} -3.00000 q^{12} -1.00000 q^{14} +12.0000i q^{15} +1.00000 q^{16} -6.00000i q^{18} +6.00000i q^{19} -4.00000i q^{20} -3.00000i q^{21} +1.00000 q^{22} +7.00000 q^{23} +3.00000i q^{24} -11.0000 q^{25} +9.00000 q^{27} +1.00000i q^{28} -4.00000 q^{29} +12.0000 q^{30} -7.00000i q^{31} -1.00000i q^{32} +3.00000i q^{33} +4.00000 q^{35} -6.00000 q^{36} +9.00000i q^{37} +6.00000 q^{38} -4.00000 q^{40} +3.00000i q^{41} -3.00000 q^{42} -4.00000 q^{43} -1.00000i q^{44} +24.0000i q^{45} -7.00000i q^{46} +7.00000i q^{47} +3.00000 q^{48} -1.00000 q^{49} +11.0000i q^{50} -9.00000i q^{54} -4.00000 q^{55} +1.00000 q^{56} +18.0000i q^{57} +4.00000i q^{58} -10.0000i q^{59} -12.0000i q^{60} +1.00000 q^{61} -7.00000 q^{62} -6.00000i q^{63} -1.00000 q^{64} +3.00000 q^{66} -1.00000i q^{67} +21.0000 q^{69} -4.00000i q^{70} -16.0000i q^{71} +6.00000i q^{72} +5.00000i q^{73} +9.00000 q^{74} -33.0000 q^{75} -6.00000i q^{76} +1.00000 q^{77} +11.0000 q^{79} +4.00000i q^{80} +9.00000 q^{81} +3.00000 q^{82} +3.00000i q^{84} +4.00000i q^{86} -12.0000 q^{87} -1.00000 q^{88} -6.00000i q^{89} +24.0000 q^{90} -7.00000 q^{92} -21.0000i q^{93} +7.00000 q^{94} -24.0000 q^{95} -3.00000i q^{96} +1.00000i q^{97} +1.00000i q^{98} +6.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 6 q^{3} - 2 q^{4} + 12 q^{9}+O(q^{10}) \) 2 * q + 6 * q^3 - 2 * q^4 + 12 * q^9	\( 2 q + 6 q^{3} - 2 q^{4} + 12 q^{9} + 8 q^{10} - 6 q^{12} - 2 q^{14} + 2 q^{16} + 2 q^{22} + 14 q^{23} - 22 q^{25} + 18 q^{27} - 8 q^{29} + 24 q^{30} + 8 q^{35} - 12 q^{36} + 12 q^{38} - 8 q^{40} - 6 q^{42} - 8 q^{43} + 6 q^{48} - 2 q^{49} - 8 q^{55} + 2 q^{56} + 2 q^{61} - 14 q^{62} - 2 q^{64} + 6 q^{66} + 42 q^{69} + 18 q^{74} - 66 q^{75} + 2 q^{77} + 22 q^{79} + 18 q^{81} + 6 q^{82} - 24 q^{87} - 2 q^{88} + 48 q^{90} - 14 q^{92} + 14 q^{94} - 48 q^{95}+O(q^{100}) \) 2 * q + 6 * q^3 - 2 * q^4 + 12 * q^9 + 8 * q^10 - 6 * q^12 - 2 * q^14 + 2 * q^16 + 2 * q^22 + 14 * q^23 - 22 * q^25 + 18 * q^27 - 8 * q^29 + 24 * q^30 + 8 * q^35 - 12 * q^36 + 12 * q^38 - 8 * q^40 - 6 * q^42 - 8 * q^43 + 6 * q^48 - 2 * q^49 - 8 * q^55 + 2 * q^56 + 2 * q^61 - 14 * q^62 - 2 * q^64 + 6 * q^66 + 42 * q^69 + 18 * q^74 - 66 * q^75 + 2 * q^77 + 22 * q^79 + 18 * q^81 + 6 * q^82 - 24 * q^87 - 2 * q^88 + 48 * q^90 - 14 * q^92 + 14 * q^94 - 48 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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