LMFDB - Embedded newform 2550.2.d.v.2449.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2550,2,Mod(2449,2550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2550, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2550.2449");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2550.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:	$20.3618525154$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{33})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 17x^{2} + 64 $ x^4 + 17*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2449.2
Root			$2.37228i$ of defining polynomial
Character	$\chi$	$=$	2550.2449
Dual form			2550.2.d.v.2449.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} +2.37228i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} +2.37228i q^{7} +1.00000i q^{8} -1.00000 q^{9} +4.37228 q^{11} -1.00000i q^{12} +2.00000i q^{13} +2.37228 q^{14} +1.00000 q^{16} +1.00000i q^{17} +1.00000i q^{18} +2.37228 q^{19} -2.37228 q^{21} -4.37228i q^{22} -1.37228i q^{23} -1.00000 q^{24} +2.00000 q^{26} -1.00000i q^{27} -2.37228i q^{28} -8.74456 q^{29} +9.11684 q^{31} -1.00000i q^{32} +4.37228i q^{33} +1.00000 q^{34} +1.00000 q^{36} +1.00000i q^{37} -2.37228i q^{38} -2.00000 q^{39} -1.37228 q^{41} +2.37228i q^{42} +3.62772i q^{43} -4.37228 q^{44} -1.37228 q^{46} +1.62772i q^{47} +1.00000i q^{48} +1.37228 q^{49} -1.00000 q^{51} -2.00000i q^{52} +5.74456i q^{53} -1.00000 q^{54} -2.37228 q^{56} +2.37228i q^{57} +8.74456i q^{58} -10.1168 q^{59} -8.11684 q^{61} -9.11684i q^{62} -2.37228i q^{63} -1.00000 q^{64} +4.37228 q^{66} -0.372281i q^{67} -1.00000i q^{68} +1.37228 q^{69} -1.37228 q^{71} -1.00000i q^{72} +8.00000i q^{73} +1.00000 q^{74} -2.37228 q^{76} +10.3723i q^{77} +2.00000i q^{78} +11.1168 q^{79} +1.00000 q^{81} +1.37228i q^{82} +1.37228i q^{83} +2.37228 q^{84} +3.62772 q^{86} -8.74456i q^{87} +4.37228i q^{88} +2.74456 q^{89} -4.74456 q^{91} +1.37228i q^{92} +9.11684i q^{93} +1.62772 q^{94} +1.00000 q^{96} +12.7446i q^{97} -1.37228i q^{98} -4.37228 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9	$ 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9} + 6 q^{11} - 2 q^{14} + 4 q^{16} - 2 q^{19} + 2 q^{21} - 4 q^{24} + 8 q^{26} - 12 q^{29} + 2 q^{31} + 4 q^{34} + 4 q^{36} - 8 q^{39} + 6 q^{41} - 6 q^{44} + 6 q^{46} - 6 q^{49} - 4 q^{51} - 4 q^{54} + 2 q^{56} - 6 q^{59} + 2 q^{61} - 4 q^{64} + 6 q^{66} - 6 q^{69} + 6 q^{71} + 4 q^{74} + 2 q^{76} + 10 q^{79} + 4 q^{81} - 2 q^{84} + 26 q^{86} - 12 q^{89} + 4 q^{91} + 18 q^{94} + 4 q^{96} - 6 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9 + 6 * q^11 - 2 * q^14 + 4 * q^16 - 2 * q^19 + 2 * q^21 - 4 * q^24 + 8 * q^26 - 12 * q^29 + 2 * q^31 + 4 * q^34 + 4 * q^36 - 8 * q^39 + 6 * q^41 - 6 * q^44 + 6 * q^46 - 6 * q^49 - 4 * q^51 - 4 * q^54 + 2 * q^56 - 6 * q^59 + 2 * q^61 - 4 * q^64 + 6 * q^66 - 6 * q^69 + 6 * q^71 + 4 * q^74 + 2 * q^76 + 10 * q^79 + 4 * q^81 - 2 * q^84 + 26 * q^86 - 12 * q^89 + 4 * q^91 + 18 * q^94 + 4 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2550\mathbb{Z}\right)^\times$.

$n$	$751$	$851$	$1327$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$	− 1.00000i	− 0.707107i
$2$	− 1.00000i	− 0.707107i
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	2.37228i	0.896638i	0.893874	+	0.448319i	$0.147977\pi$
$7$	2.37228i	0.896638i	−0.893874	+	0.448319i	$0.852023\pi$
$8$	1.00000i	0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	4.37228	1.31829	0.659146	−	0.752015i	$-0.270918\pi$
$11$	4.37228	1.31829	0.659146	+	0.752015i	$0.270918\pi$
$12$	− 1.00000i	− 0.288675i
$13$	2.00000i	0.554700i	0.960769	+	0.277350i	$0.0894562\pi$
$13$	2.00000i	0.554700i	−0.960769	+	0.277350i	$0.910544\pi$
$14$	2.37228	0.634019
$15$	0	0
$16$	1.00000	0.250000
$17$	1.00000i	0.242536i
$17$	1.00000i	0.242536i
$18$	1.00000i	0.235702i
$19$	2.37228	0.544239	0.272119	−	0.962264i	$-0.412275\pi$
$19$	2.37228	0.544239	0.272119	+	0.962264i	$0.412275\pi$
$20$	0	0
$21$	−2.37228	−0.517674
$22$	− 4.37228i	− 0.932174i
$23$	− 1.37228i	− 0.286140i	−0.989713	−	0.143070i	$-0.954303\pi$
$23$	− 1.37228i	− 0.286140i	0.989713	−	0.143070i	$-0.0456975\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	2.00000	0.392232
$27$	− 1.00000i	− 0.192450i
$28$	− 2.37228i	− 0.448319i
$29$	−8.74456	−1.62382	−0.811912	−	0.583779i	$-0.801573\pi$
$29$	−8.74456	−1.62382	−0.811912	+	0.583779i	$0.801573\pi$
$30$	0	0
$31$	9.11684	1.63743	0.818717	−	0.574198i	$-0.194686\pi$
$31$	9.11684	1.63743	0.818717	+	0.574198i	$0.194686\pi$
$32$	− 1.00000i	− 0.176777i
$33$	4.37228i	0.761116i
$34$	1.00000	0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	1.00000i	0.164399i	0.996616	+	0.0821995i	$0.0261945\pi$
$37$	1.00000i	0.164399i	−0.996616	+	0.0821995i	$0.973806\pi$
$38$	− 2.37228i	− 0.384835i
$39$	−2.00000	−0.320256
$40$	0	0
$41$	−1.37228	−0.214314	−0.107157	−	0.994242i	$-0.534175\pi$
$41$	−1.37228	−0.214314	−0.107157	+	0.994242i	$0.534175\pi$
$42$	2.37228i	0.366051i
$43$	3.62772i	0.553222i	0.960982	+	0.276611i	$0.0892113\pi$
$43$	3.62772i	0.553222i	−0.960982	+	0.276611i	$0.910789\pi$
$44$	−4.37228	−0.659146
$45$	0	0
$46$	−1.37228	−0.202332
$47$	1.62772i	0.237427i	0.992929	+	0.118714i	$0.0378770\pi$
$47$	1.62772i	0.237427i	−0.992929	+	0.118714i	$0.962123\pi$
$48$	1.00000i	0.144338i
$49$	1.37228	0.196040
$50$	0	0
$51$	−1.00000	−0.140028
$52$	− 2.00000i	− 0.277350i
$53$	5.74456i	0.789076i	0.918880	+	0.394538i	$0.129095\pi$
$53$	5.74456i	0.789076i	−0.918880	+	0.394538i	$0.870905\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−2.37228	−0.317009
$57$	2.37228i	0.314216i
$58$	8.74456i	1.14822i
$59$	−10.1168	−1.31710	−0.658550	−	0.752537i	$-0.728830\pi$
$59$	−10.1168	−1.31710	−0.658550	+	0.752537i	$0.728830\pi$
$60$	0	0
$61$	−8.11684	−1.03926	−0.519628	−	0.854393i	$-0.673929\pi$
$61$	−8.11684	−1.03926	−0.519628	+	0.854393i	$0.673929\pi$
$62$	− 9.11684i	− 1.15784i
$63$	− 2.37228i	− 0.298879i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	4.37228	0.538191
$67$	− 0.372281i	− 0.0454814i	−0.999741	−	0.0227407i	$-0.992761\pi$
$67$	− 0.372281i	− 0.0454814i	0.999741	−	0.0227407i	$-0.00723921\pi$
$68$	− 1.00000i	− 0.121268i
$69$	1.37228	0.165203
$70$	0	0
$71$	−1.37228	−0.162860	−0.0814299	−	0.996679i	$-0.525949\pi$
$71$	−1.37228	−0.162860	−0.0814299	+	0.996679i	$0.525949\pi$
$72$	− 1.00000i	− 0.117851i
$73$	8.00000i	0.936329i	0.883641	+	0.468165i	$0.155085\pi$
$73$	8.00000i	0.936329i	−0.883641	+	0.468165i	$0.844915\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	−2.37228	−0.272119
$77$	10.3723i	1.18203i
$78$	2.00000i	0.226455i
$79$	11.1168	1.25074	0.625371	−	0.780327i	$-0.284948\pi$
$79$	11.1168	1.25074	0.625371	+	0.780327i	$0.284948\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	1.37228i	0.151543i
$83$	1.37228i	0.150627i	0.997160	+	0.0753137i	$0.0239958\pi$
$83$	1.37228i	0.150627i	−0.997160	+	0.0753137i	$0.976004\pi$
$84$	2.37228	0.258837
$85$	0	0
$86$	3.62772	0.391187
$87$	− 8.74456i	− 0.937516i
$88$	4.37228i	0.466087i
$89$	2.74456	0.290923	0.145462	−	0.989364i	$-0.453533\pi$
$89$	2.74456	0.290923	0.145462	+	0.989364i	$0.453533\pi$
$90$	0	0
$91$	−4.74456	−0.497365
$92$	1.37228i	0.143070i
$93$	9.11684i	0.945373i
$94$	1.62772	0.167886
$95$	0	0
$96$	1.00000	0.102062
$97$	12.7446i	1.29401i	0.762484	+	0.647007i	$0.223980\pi$
$97$	12.7446i	1.29401i	−0.762484	+	0.647007i	$0.776020\pi$
$98$	− 1.37228i	− 0.138621i
$99$	−4.37228	−0.439431
$100$	0	0
$101$	13.1168	1.30517	0.652587	−	0.757713i	$-0.273684\pi$
$101$	13.1168	1.30517	0.652587	+	0.757713i	$0.273684\pi$
$102$	1.00000i	0.0990148i
$103$	15.3723i	1.51468i	0.653023	+	0.757338i	$0.273500\pi$
$103$	15.3723i	1.51468i	−0.653023	+	0.757338i	$0.726500\pi$
$104$	−2.00000	−0.196116
$105$	0	0
$106$	5.74456	0.557961
$107$	10.3723i	1.00273i	0.865237	+	0.501363i	$0.167168\pi$
$107$	10.3723i	1.00273i	−0.865237	+	0.501363i	$0.832832\pi$
$108$	1.00000i	0.0962250i
$109$	−9.11684	−0.873235	−0.436618	−	0.899647i	$-0.643824\pi$
$109$	−9.11684	−0.873235	−0.436618	+	0.899647i	$0.643824\pi$
$110$	0	0
$111$	−1.00000	−0.0949158
$112$	2.37228i	0.224160i
$113$	− 11.7446i	− 1.10484i	−0.833567	−	0.552418i	$-0.813705\pi$
$113$	− 11.7446i	− 1.10484i	0.833567	−	0.552418i	$-0.186295\pi$
$114$	2.37228	0.222185
$115$	0	0
$116$	8.74456	0.811912
$117$	− 2.00000i	− 0.184900i
$118$	10.1168i	0.931331i
$119$	−2.37228	−0.217467
$120$	0	0
$121$	8.11684	0.737895
$122$	8.11684i	0.734865i
$123$	− 1.37228i	− 0.123734i
$124$	−9.11684	−0.818717
$125$	0	0
$126$	−2.37228	−0.211340
$127$	− 1.48913i	− 0.132139i	−0.997815	−	0.0660693i	$-0.978954\pi$
$127$	− 1.48913i	− 0.132139i	0.997815	−	0.0660693i	$-0.0210458\pi$
$128$	1.00000i	0.0883883i
$129$	−3.62772	−0.319403
$130$	0	0
$131$	17.4891	1.52803	0.764016	−	0.645197i	$-0.223225\pi$
$131$	17.4891	1.52803	0.764016	+	0.645197i	$0.223225\pi$
$132$	− 4.37228i	− 0.380558i
$133$	5.62772i	0.487985i
$134$	−0.372281	−0.0321602
$135$	0	0
$136$	−1.00000	−0.0857493
$137$	− 5.48913i	− 0.468968i	−0.972120	−	0.234484i	$-0.924660\pi$
$137$	− 5.48913i	− 0.468968i	0.972120	−	0.234484i	$-0.0753400\pi$
$138$	− 1.37228i	− 0.116816i
$139$	−18.1168	−1.53665	−0.768325	−	0.640060i	$-0.778910\pi$
$139$	−18.1168	−1.53665	−0.768325	+	0.640060i	$0.778910\pi$
$140$	0	0
$141$	−1.62772	−0.137079
$142$	1.37228i	0.115159i
$143$	8.74456i	0.731257i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	8.00000	0.662085
$147$	1.37228i	0.113184i
$148$	− 1.00000i	− 0.0821995i
$149$	6.86141	0.562108	0.281054	−	0.959692i	$-0.409316\pi$
$149$	6.86141	0.562108	0.281054	+	0.959692i	$0.409316\pi$
$150$	0	0
$151$	−14.1168	−1.14881	−0.574406	−	0.818570i	$-0.694767\pi$
$151$	−14.1168	−1.14881	−0.574406	+	0.818570i	$0.694767\pi$
$152$	2.37228i	0.192417i
$153$	− 1.00000i	− 0.0808452i
$154$	10.3723	0.835822
$155$	0	0
$156$	2.00000	0.160128
$157$	18.7446i	1.49598i	0.663711	+	0.747989i	$0.268981\pi$
$157$	18.7446i	1.49598i	−0.663711	+	0.747989i	$0.731019\pi$
$158$	− 11.1168i	− 0.884409i
$159$	−5.74456	−0.455573
$160$	0	0
$161$	3.25544	0.256564
$162$	− 1.00000i	− 0.0785674i
$163$	− 2.11684i	− 0.165804i	−0.996558	−	0.0829020i	$-0.973581\pi$
$163$	− 2.11684i	− 0.165804i	0.996558	−	0.0829020i	$-0.0264188\pi$
$164$	1.37228	0.107157
$165$	0	0
$166$	1.37228	0.106510
$167$	20.7446i	1.60526i	0.596476	+	0.802631i	$0.296567\pi$
$167$	20.7446i	1.60526i	−0.596476	+	0.802631i	$0.703433\pi$
$168$	− 2.37228i	− 0.183025i
$169$	9.00000	0.692308
$170$	0	0
$171$	−2.37228	−0.181413
$172$	− 3.62772i	− 0.276611i
$173$	− 12.0000i	− 0.912343i	−0.889892	−	0.456172i	$-0.849220\pi$
$173$	− 12.0000i	− 0.912343i	0.889892	−	0.456172i	$-0.150780\pi$
$174$	−8.74456	−0.662924
$175$	0	0
$176$	4.37228	0.329573
$177$	− 10.1168i	− 0.760429i
$178$	− 2.74456i	− 0.205714i
$179$	10.1168	0.756168	0.378084	−	0.925771i	$-0.376583\pi$
$179$	10.1168	0.756168	0.378084	+	0.925771i	$0.376583\pi$
$180$	0	0
$181$	−0.489125	−0.0363564	−0.0181782	−	0.999835i	$-0.505787\pi$
$181$	−0.489125	−0.0363564	−0.0181782	+	0.999835i	$0.505787\pi$
$182$	4.74456i	0.351690i
$183$	− 8.11684i	− 0.600014i
$184$	1.37228	0.101166
$185$	0	0
$186$	9.11684	0.668479
$187$	4.37228i	0.319733i
$188$	− 1.62772i	− 0.118714i
$189$	2.37228	0.172558
$190$	0	0
$191$	−27.3505	−1.97902	−0.989508	−	0.144481i	$-0.953849\pi$
$191$	−27.3505	−1.97902	−0.989508	+	0.144481i	$0.953849\pi$
$192$	− 1.00000i	− 0.0721688i
$193$	8.00000i	0.575853i	0.957653	+	0.287926i	$0.0929658\pi$
$193$	8.00000i	0.575853i	−0.957653	+	0.287926i	$0.907034\pi$
$194$	12.7446	0.915006
$195$	0	0
$196$	−1.37228	−0.0980201
$197$	9.25544i	0.659423i	0.944082	+	0.329711i	$0.106951\pi$
$197$	9.25544i	0.659423i	−0.944082	+	0.329711i	$0.893049\pi$
$198$	4.37228i	0.310725i
$199$	−21.1168	−1.49693	−0.748467	−	0.663172i	$-0.769210\pi$
$199$	−21.1168	−1.49693	−0.748467	+	0.663172i	$0.769210\pi$
$200$	0	0
$201$	0.372281	0.0262587
$202$	− 13.1168i	− 0.922898i
$203$	− 20.7446i	− 1.45598i
$204$	1.00000	0.0700140
$205$	0	0
$206$	15.3723	1.07104
$207$	1.37228i	0.0953801i
$208$	2.00000i	0.138675i
$209$	10.3723	0.717466
$210$	0	0
$211$	10.2337	0.704516	0.352258	−	0.935903i	$-0.385414\pi$
$211$	10.2337	0.704516	0.352258	+	0.935903i	$0.385414\pi$
$212$	− 5.74456i	− 0.394538i
$213$	− 1.37228i	− 0.0940272i
$214$	10.3723	0.709035
$215$	0	0
$216$	1.00000	0.0680414
$217$	21.6277i	1.46819i
$218$	9.11684i	0.617471i
$219$	−8.00000	−0.540590
$220$	0	0
$221$	−2.00000	−0.134535
$222$	1.00000i	0.0671156i
$223$	− 8.11684i	− 0.543544i	−0.962362	−	0.271772i	$-0.912390\pi$
$223$	− 8.11684i	− 0.543544i	0.962362	−	0.271772i	$-0.0876097\pi$
$224$	2.37228	0.158505
$225$	0	0
$226$	−11.7446	−0.781237
$227$	4.37228i	0.290199i	0.989417	+	0.145099i	$0.0463501\pi$
$227$	4.37228i	0.290199i	−0.989417	+	0.145099i	$0.953650\pi$
$228$	− 2.37228i	− 0.157108i
$229$	12.2337	0.808425	0.404212	−	0.914665i	$-0.367546\pi$
$229$	12.2337	0.808425	0.404212	+	0.914665i	$0.367546\pi$
$230$	0	0
$231$	−10.3723	−0.682446
$232$	− 8.74456i	− 0.574109i
$233$	− 10.6277i	− 0.696245i	−0.937449	−	0.348122i	$-0.886819\pi$
$233$	− 10.6277i	− 0.696245i	0.937449	−	0.348122i	$-0.113181\pi$
$234$	−2.00000	−0.130744
$235$	0	0
$236$	10.1168	0.658550
$237$	11.1168i	0.722117i
$238$	2.37228i	0.153772i
$239$	13.1168	0.848458	0.424229	−	0.905555i	$-0.360545\pi$
$239$	13.1168	0.848458	0.424229	+	0.905555i	$0.360545\pi$
$240$	0	0
$241$	28.2337	1.81869	0.909346	−	0.416041i	$-0.136583\pi$
$241$	28.2337	1.81869	0.909346	+	0.416041i	$0.136583\pi$
$242$	− 8.11684i	− 0.521770i
$243$	1.00000i	0.0641500i
$244$	8.11684	0.519628
$245$	0	0
$246$	−1.37228	−0.0874935
$247$	4.74456i	0.301889i
$248$	9.11684i	0.578920i
$249$	−1.37228	−0.0869648
$250$	0	0
$251$	8.74456	0.551952	0.275976	−	0.961165i	$-0.410999\pi$
$251$	8.74456	0.551952	0.275976	+	0.961165i	$0.410999\pi$
$252$	2.37228i	0.149440i
$253$	− 6.00000i	− 0.377217i
$254$	−1.48913	−0.0934360
$255$	0	0
$256$	1.00000	0.0625000
$257$	14.2337i	0.887873i	0.896058	+	0.443937i	$0.146418\pi$
$257$	14.2337i	0.887873i	−0.896058	+	0.443937i	$0.853582\pi$
$258$	3.62772i	0.225852i
$259$	−2.37228	−0.147406
$260$	0	0
$261$	8.74456	0.541275
$262$	− 17.4891i	− 1.08048i
$263$	− 25.6277i	− 1.58027i	−0.612931	−	0.790136i	$-0.710010\pi$
$263$	− 25.6277i	− 1.58027i	0.612931	−	0.790136i	$-0.289990\pi$
$264$	−4.37228	−0.269095
$265$	0	0
$266$	5.62772	0.345058
$267$	2.74456i	0.167965i
$268$	0.372281i	0.0227407i
$269$	−11.4891	−0.700504	−0.350252	−	0.936655i	$-0.613904\pi$
$269$	−11.4891	−0.700504	−0.350252	+	0.936655i	$0.613904\pi$
$270$	0	0
$271$	−2.62772	−0.159623	−0.0798113	−	0.996810i	$-0.525432\pi$
$271$	−2.62772	−0.159623	−0.0798113	+	0.996810i	$0.525432\pi$
$272$	1.00000i	0.0606339i
$273$	− 4.74456i	− 0.287154i
$274$	−5.48913	−0.331610
$275$	0	0
$276$	−1.37228	−0.0826016
$277$	13.0000i	0.781094i	0.920583	+	0.390547i	$0.127714\pi$
$277$	13.0000i	0.781094i	−0.920583	+	0.390547i	$0.872286\pi$
$278$	18.1168i	1.08658i
$279$	−9.11684	−0.545811
$280$	0	0
$281$	0.510875	0.0304762	0.0152381	−	0.999884i	$-0.495149\pi$
$281$	0.510875	0.0304762	0.0152381	+	0.999884i	$0.495149\pi$
$282$	1.62772i	0.0969292i
$283$	12.1168i	0.720272i	0.932900	+	0.360136i	$0.117270\pi$
$283$	12.1168i	0.720272i	−0.932900	+	0.360136i	$0.882730\pi$
$284$	1.37228	0.0814299
$285$	0	0
$286$	8.74456	0.517077
$287$	− 3.25544i	− 0.192162i
$288$	1.00000i	0.0589256i
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	−12.7446	−0.747099
$292$	− 8.00000i	− 0.468165i
$293$	− 28.1168i	− 1.64260i	−0.570494	−	0.821302i	$-0.693248\pi$
$293$	− 28.1168i	− 1.64260i	0.570494	−	0.821302i	$-0.306752\pi$
$294$	1.37228	0.0800331
$295$	0	0
$296$	−1.00000	−0.0581238
$297$	− 4.37228i	− 0.253705i
$298$	− 6.86141i	− 0.397471i
$299$	2.74456	0.158722
$300$	0	0
$301$	−8.60597	−0.496040
$302$	14.1168i	0.812333i
$303$	13.1168i	0.753543i
$304$	2.37228	0.136060
$305$	0	0
$306$	−1.00000	−0.0571662
$307$	− 16.2337i	− 0.926506i	−0.886226	−	0.463253i	$-0.846682\pi$
$307$	− 16.2337i	− 0.926506i	0.886226	−	0.463253i	$-0.153318\pi$
$308$	− 10.3723i	− 0.591016i
$309$	−15.3723	−0.874499
$310$	0	0
$311$	−28.1168	−1.59436	−0.797180	−	0.603742i	$-0.793676\pi$
$311$	−28.1168	−1.59436	−0.797180	+	0.603742i	$0.793676\pi$
$312$	− 2.00000i	− 0.113228i
$313$	4.74456i	0.268179i	0.990969	+	0.134089i	$0.0428109\pi$
$313$	4.74456i	0.268179i	−0.990969	+	0.134089i	$0.957189\pi$
$314$	18.7446	1.05782
$315$	0	0
$316$	−11.1168	−0.625371
$317$	− 14.7446i	− 0.828137i	−0.910246	−	0.414069i	$-0.864107\pi$
$317$	− 14.7446i	− 0.828137i	0.910246	−	0.414069i	$-0.135893\pi$
$318$	5.74456i	0.322139i
$319$	−38.2337	−2.14068
$320$	0	0
$321$	−10.3723	−0.578924
$322$	− 3.25544i	− 0.181418i
$323$	2.37228i	0.131997i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	−2.11684	−0.117241
$327$	− 9.11684i	− 0.504163i
$328$	− 1.37228i	− 0.0757716i
$329$	−3.86141	−0.212886
$330$	0	0
$331$	14.6060	0.802817	0.401408	−	0.915899i	$-0.368521\pi$
$331$	14.6060	0.802817	0.401408	+	0.915899i	$0.368521\pi$
$332$	− 1.37228i	− 0.0753137i
$333$	− 1.00000i	− 0.0547997i
$334$	20.7446	1.13509
$335$	0	0
$336$	−2.37228	−0.129419
$337$	24.2337i	1.32009i	0.751225	+	0.660047i	$0.229463\pi$
$337$	24.2337i	1.32009i	−0.751225	+	0.660047i	$0.770537\pi$
$338$	− 9.00000i	− 0.489535i
$339$	11.7446	0.637877
$340$	0	0
$341$	39.8614	2.15862
$342$	2.37228i	0.128278i
$343$	19.8614i	1.07242i
$344$	−3.62772	−0.195593
$345$	0	0
$346$	−12.0000	−0.645124
$347$	− 22.3723i	− 1.20101i	−0.799622	−	0.600503i	$-0.794967\pi$
$347$	− 22.3723i	− 1.20101i	0.799622	−	0.600503i	$-0.205033\pi$
$348$	8.74456i	0.468758i
$349$	10.0000	0.535288	0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000	0.535288	0.267644	+	0.963518i	$0.413755\pi$
$350$	0	0
$351$	2.00000	0.106752
$352$	− 4.37228i	− 0.233043i
$353$	− 15.2554i	− 0.811965i	−0.913881	−	0.405983i	$-0.866929\pi$
$353$	− 15.2554i	− 0.811965i	0.913881	−	0.405983i	$-0.133071\pi$
$354$	−10.1168	−0.537704
$355$	0	0
$356$	−2.74456	−0.145462
$357$	− 2.37228i	− 0.125554i
$358$	− 10.1168i	− 0.534692i
$359$	13.6277	0.719243	0.359622	−	0.933098i	$-0.382906\pi$
$359$	13.6277	0.719243	0.359622	+	0.933098i	$0.382906\pi$
$360$	0	0
$361$	−13.3723	−0.703804
$362$	0.489125i	0.0257079i
$363$	8.11684i	0.426024i
$364$	4.74456	0.248683
$365$	0	0
$366$	−8.11684	−0.424274
$367$	− 14.6060i	− 0.762425i	−0.924487	−	0.381213i	$-0.875507\pi$
$367$	− 14.6060i	− 0.762425i	0.924487	−	0.381213i	$-0.124493\pi$
$368$	− 1.37228i	− 0.0715351i
$369$	1.37228	0.0714381
$370$	0	0
$371$	−13.6277	−0.707516
$372$	− 9.11684i	− 0.472686i
$373$	− 1.76631i	− 0.0914562i	−0.998954	−	0.0457281i	$-0.985439\pi$
$373$	− 1.76631i	− 0.0914562i	0.998954	−	0.0457281i	$-0.0145608\pi$
$374$	4.37228	0.226085
$375$	0	0
$376$	−1.62772	−0.0839432
$377$	− 17.4891i	− 0.900736i
$378$	− 2.37228i	− 0.122017i
$379$	19.6060	1.00709	0.503545	−	0.863969i	$-0.332029\pi$
$379$	19.6060	1.00709	0.503545	+	0.863969i	$0.332029\pi$
$380$	0	0
$381$	1.48913	0.0762902
$382$	27.3505i	1.39937i
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	8.00000	0.407189
$387$	− 3.62772i	− 0.184407i
$388$	− 12.7446i	− 0.647007i
$389$	−17.7446	−0.899685	−0.449843	−	0.893108i	$-0.648520\pi$
$389$	−17.7446	−0.899685	−0.449843	+	0.893108i	$0.648520\pi$
$390$	0	0
$391$	1.37228	0.0693992
$392$	1.37228i	0.0693107i
$393$	17.4891i	0.882210i
$394$	9.25544	0.466282
$395$	0	0
$396$	4.37228	0.219715
$397$	1.00000i	0.0501886i	0.999685	+	0.0250943i	$0.00798860\pi$
$397$	1.00000i	0.0501886i	−0.999685	+	0.0250943i	$0.992011\pi$
$398$	21.1168i	1.05849i
$399$	−5.62772	−0.281738
$400$	0	0
$401$	4.11684	0.205585	0.102793	−	0.994703i	$-0.467222\pi$
$401$	4.11684	0.205585	0.102793	+	0.994703i	$0.467222\pi$
$402$	− 0.372281i	− 0.0185677i
$403$	18.2337i	0.908285i
$404$	−13.1168	−0.652587
$405$	0	0
$406$	−20.7446	−1.02954
$407$	4.37228i	0.216726i
$408$	− 1.00000i	− 0.0495074i
$409$	−14.8614	−0.734849	−0.367425	−	0.930053i	$-0.619760\pi$
$409$	−14.8614	−0.734849	−0.367425	+	0.930053i	$0.619760\pi$
$410$	0	0
$411$	5.48913	0.270759
$412$	− 15.3723i	− 0.757338i
$413$	− 24.0000i	− 1.18096i
$414$	1.37228	0.0674439
$415$	0	0
$416$	2.00000	0.0980581
$417$	− 18.1168i	− 0.887186i
$418$	− 10.3723i	− 0.507325i
$419$	−10.9783	−0.536323	−0.268161	−	0.963374i	$-0.586416\pi$
$419$	−10.9783	−0.536323	−0.268161	+	0.963374i	$0.586416\pi$
$420$	0	0
$421$	−18.2337	−0.888656	−0.444328	−	0.895864i	$-0.646557\pi$
$421$	−18.2337	−0.888656	−0.444328	+	0.895864i	$0.646557\pi$
$422$	− 10.2337i	− 0.498168i
$423$	− 1.62772i	− 0.0791424i
$424$	−5.74456	−0.278981
$425$	0	0
$426$	−1.37228	−0.0664872
$427$	− 19.2554i	− 0.931836i
$428$	− 10.3723i	− 0.501363i
$429$	−8.74456	−0.422191
$430$	0	0
$431$	12.0000	0.578020	0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000	0.578020	0.289010	+	0.957326i	$0.406674\pi$
$432$	− 1.00000i	− 0.0481125i
$433$	− 40.0951i	− 1.92685i	−0.267983	−	0.963424i	$-0.586357\pi$
$433$	− 40.0951i	− 1.92685i	0.267983	−	0.963424i	$-0.413643\pi$
$434$	21.6277	1.03816
$435$	0	0
$436$	9.11684	0.436618
$437$	− 3.25544i	− 0.155729i
$438$	8.00000i	0.382255i
$439$	−2.51087	−0.119838	−0.0599188	−	0.998203i	$-0.519084\pi$
$439$	−2.51087	−0.119838	−0.0599188	+	0.998203i	$0.519084\pi$
$440$	0	0
$441$	−1.37228	−0.0653467
$442$	2.00000i	0.0951303i
$443$	− 7.37228i	− 0.350268i	−0.984545	−	0.175134i	$-0.943964\pi$
$443$	− 7.37228i	− 0.350268i	0.984545	−	0.175134i	$-0.0560358\pi$
$444$	1.00000	0.0474579
$445$	0	0
$446$	−8.11684	−0.384344
$447$	6.86141i	0.324533i
$448$	− 2.37228i	− 0.112080i
$449$	33.8614	1.59802	0.799009	−	0.601319i	$-0.205358\pi$
$449$	33.8614	1.59802	0.799009	+	0.601319i	$0.205358\pi$
$450$	0	0
$451$	−6.00000	−0.282529
$452$	11.7446i	0.552418i
$453$	− 14.1168i	− 0.663267i
$454$	4.37228	0.205201
$455$	0	0
$456$	−2.37228	−0.111092
$457$	− 23.0000i	− 1.07589i	−0.842978	−	0.537947i	$-0.819200\pi$
$457$	− 23.0000i	− 1.07589i	0.842978	−	0.537947i	$-0.180800\pi$
$458$	− 12.2337i	− 0.571643i
$459$	1.00000	0.0466760
$460$	0	0
$461$	34.7228	1.61720	0.808601	−	0.588357i	$-0.200225\pi$
$461$	34.7228	1.61720	0.808601	+	0.588357i	$0.200225\pi$
$462$	10.3723i	0.482562i
$463$	− 19.6060i	− 0.911167i	−0.890193	−	0.455583i	$-0.849431\pi$
$463$	− 19.6060i	− 0.911167i	0.890193	−	0.455583i	$-0.150569\pi$
$464$	−8.74456	−0.405956
$465$	0	0
$466$	−10.6277	−0.492320
$467$	− 16.1168i	− 0.745799i	−0.927872	−	0.372899i	$-0.878364\pi$
$467$	− 16.1168i	− 0.745799i	0.927872	−	0.372899i	$-0.121636\pi$
$468$	2.00000i	0.0924500i
$469$	0.883156	0.0407804
$470$	0	0
$471$	−18.7446	−0.863704
$472$	− 10.1168i	− 0.465665i
$473$	15.8614i	0.729308i
$474$	11.1168	0.510614
$475$	0	0
$476$	2.37228	0.108733
$477$	− 5.74456i	− 0.263025i
$478$	− 13.1168i	− 0.599950i
$479$	31.7228	1.44945	0.724726	−	0.689037i	$-0.241966\pi$
$479$	31.7228	1.44945	0.724726	+	0.689037i	$0.241966\pi$
$480$	0	0
$481$	−2.00000	−0.0911922
$482$	− 28.2337i	− 1.28601i
$483$	3.25544i	0.148128i
$484$	−8.11684	−0.368947
$485$	0	0
$486$	1.00000	0.0453609
$487$	12.2337i	0.554361i	0.960818	+	0.277181i	$0.0894001\pi$
$487$	12.2337i	0.554361i	−0.960818	+	0.277181i	$0.910600\pi$
$488$	− 8.11684i	− 0.367432i
$489$	2.11684	0.0957270
$490$	0	0
$491$	−31.3723	−1.41581	−0.707906	−	0.706307i	$-0.750360\pi$
$491$	−31.3723	−1.41581	−0.707906	+	0.706307i	$0.750360\pi$
$492$	1.37228i	0.0618672i
$493$	− 8.74456i	− 0.393835i
$494$	4.74456	0.213468
$495$	0	0
$496$	9.11684	0.409358
$497$	− 3.25544i	− 0.146026i
$498$	1.37228i	0.0614934i
$499$	−18.6277	−0.833891	−0.416946	−	0.908931i	$-0.636899\pi$
$499$	−18.6277	−0.833891	−0.416946	+	0.908931i	$0.636899\pi$
$500$	0	0
$501$	−20.7446	−0.926799
$502$	− 8.74456i	− 0.390289i
$503$	− 9.60597i	− 0.428309i	−0.976800	−	0.214154i	$-0.931300\pi$
$503$	− 9.60597i	− 0.428309i	0.976800	−	0.214154i	$-0.0686996\pi$
$504$	2.37228	0.105670
$505$	0	0
$506$	−6.00000	−0.266733
$507$	9.00000i	0.399704i
$508$	1.48913i	0.0660693i
$509$	19.6277	0.869983	0.434992	−	0.900434i	$-0.356751\pi$
$509$	19.6277	0.869983	0.434992	+	0.900434i	$0.356751\pi$
$510$	0	0
$511$	−18.9783	−0.839548
$512$	− 1.00000i	− 0.0441942i
$513$	− 2.37228i	− 0.104739i
$514$	14.2337	0.627821
$515$	0	0
$516$	3.62772	0.159701
$517$	7.11684i	0.312998i
$518$	2.37228i	0.104232i
$519$	12.0000	0.526742
$520$	0	0
$521$	−27.3505	−1.19825	−0.599124	−	0.800656i	$-0.704484\pi$
$521$	−27.3505	−1.19825	−0.599124	+	0.800656i	$0.704484\pi$
$522$	− 8.74456i	− 0.382739i
$523$	16.2337i	0.709850i	0.934895	+	0.354925i	$0.115494\pi$
$523$	16.2337i	0.709850i	−0.934895	+	0.354925i	$0.884506\pi$
$524$	−17.4891	−0.764016
$525$	0	0
$526$	−25.6277	−1.11742
$527$	9.11684i	0.397136i
$528$	4.37228i	0.190279i
$529$	21.1168	0.918124
$530$	0	0
$531$	10.1168	0.439034
$532$	− 5.62772i	− 0.243993i
$533$	− 2.74456i	− 0.118880i
$534$	2.74456	0.118769
$535$	0	0
$536$	0.372281	0.0160801
$537$	10.1168i	0.436574i
$538$	11.4891i	0.495331i
$539$	6.00000	0.258438
$540$	0	0
$541$	5.00000	0.214967	0.107483	−	0.994207i	$-0.465721\pi$
$541$	5.00000	0.214967	0.107483	+	0.994207i	$0.465721\pi$
$542$	2.62772i	0.112870i
$543$	− 0.489125i	− 0.0209904i
$544$	1.00000	0.0428746
$545$	0	0
$546$	−4.74456	−0.203049
$547$	− 30.6277i	− 1.30955i	−0.755825	−	0.654773i	$-0.772764\pi$
$547$	− 30.6277i	− 1.30955i	0.755825	−	0.654773i	$-0.227236\pi$
$548$	5.48913i	0.234484i
$549$	8.11684	0.346418
$550$	0	0
$551$	−20.7446	−0.883748
$552$	1.37228i	0.0584082i
$553$	26.3723i	1.12146i
$554$	13.0000	0.552317
$555$	0	0
$556$	18.1168	0.768325
$557$	24.2554i	1.02774i	0.857869	+	0.513868i	$0.171788\pi$
$557$	24.2554i	1.02774i	−0.857869	+	0.513868i	$0.828212\pi$
$558$	9.11684i	0.385947i
$559$	−7.25544	−0.306872
$560$	0	0
$561$	−4.37228	−0.184598
$562$	− 0.510875i	− 0.0215499i
$563$	18.3505i	0.773383i	0.922209	+	0.386691i	$0.126382\pi$
$563$	18.3505i	0.773383i	−0.922209	+	0.386691i	$0.873618\pi$
$564$	1.62772	0.0685393
$565$	0	0
$566$	12.1168	0.509309
$567$	2.37228i	0.0996265i
$568$	− 1.37228i	− 0.0575796i
$569$	9.25544	0.388008	0.194004	−	0.981001i	$-0.437853\pi$
$569$	9.25544	0.388008	0.194004	+	0.981001i	$0.437853\pi$
$570$	0	0
$571$	−32.6277	−1.36543	−0.682714	−	0.730686i	$-0.739200\pi$
$571$	−32.6277	−1.36543	−0.682714	+	0.730686i	$0.739200\pi$
$572$	− 8.74456i	− 0.365629i
$573$	− 27.3505i	− 1.14258i
$574$	−3.25544	−0.135879
$575$	0	0
$576$	1.00000	0.0416667
$577$	7.00000i	0.291414i	0.989328	+	0.145707i	$0.0465456\pi$
$577$	7.00000i	0.291414i	−0.989328	+	0.145707i	$0.953454\pi$
$578$	1.00000i	0.0415945i
$579$	−8.00000	−0.332469
$580$	0	0
$581$	−3.25544	−0.135058
$582$	12.7446i	0.528279i
$583$	25.1168i	1.04023i
$584$	−8.00000	−0.331042
$585$	0	0
$586$	−28.1168	−1.16150
$587$	− 30.8614i	− 1.27379i	−0.770952	−	0.636893i	$-0.780219\pi$
$587$	− 30.8614i	− 1.27379i	0.770952	−	0.636893i	$-0.219781\pi$
$588$	− 1.37228i	− 0.0565919i
$589$	21.6277	0.891155
$590$	0	0
$591$	−9.25544	−0.380718
$592$	1.00000i	0.0410997i
$593$	− 40.4674i	− 1.66180i	−0.556425	−	0.830898i	$-0.687827\pi$
$593$	− 40.4674i	− 1.66180i	0.556425	−	0.830898i	$-0.312173\pi$
$594$	−4.37228	−0.179397
$595$	0	0
$596$	−6.86141	−0.281054
$597$	− 21.1168i	− 0.864255i
$598$	− 2.74456i	− 0.112234i
$599$	1.62772	0.0665068	0.0332534	−	0.999447i	$-0.489413\pi$
$599$	1.62772	0.0665068	0.0332534	+	0.999447i	$0.489413\pi$
$600$	0	0
$601$	36.9783	1.50837	0.754187	−	0.656660i	$-0.228031\pi$
$601$	36.9783	1.50837	0.754187	+	0.656660i	$0.228031\pi$
$602$	8.60597i	0.350753i
$603$	0.372281i	0.0151605i
$604$	14.1168	0.574406
$605$	0	0
$606$	13.1168	0.532835
$607$	− 40.2337i	− 1.63304i	−0.577321	−	0.816518i	$-0.695902\pi$
$607$	− 40.2337i	− 1.63304i	0.577321	−	0.816518i	$-0.304098\pi$
$608$	− 2.37228i	− 0.0962087i
$609$	20.7446	0.840612
$610$	0	0
$611$	−3.25544	−0.131701
$612$	1.00000i	0.0404226i
$613$	− 3.48913i	− 0.140924i	−0.997514	−	0.0704622i	$-0.977553\pi$
$613$	− 3.48913i	− 0.140924i	0.997514	−	0.0704622i	$-0.0224474\pi$
$614$	−16.2337	−0.655138
$615$	0	0
$616$	−10.3723	−0.417911
$617$	− 44.8397i	− 1.80518i	−0.430505	−	0.902588i	$-0.641664\pi$
$617$	− 44.8397i	− 1.80518i	0.430505	−	0.902588i	$-0.358336\pi$
$618$	15.3723i	0.618364i
$619$	4.00000	0.160774	0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000	0.160774	0.0803868	+	0.996764i	$0.474384\pi$
$620$	0	0
$621$	−1.37228	−0.0550678
$622$	28.1168i	1.12738i
$623$	6.51087i	0.260853i
$624$	−2.00000	−0.0800641
$625$	0	0
$626$	4.74456	0.189631
$627$	10.3723i	0.414229i
$628$	− 18.7446i	− 0.747989i
$629$	−1.00000	−0.0398726
$630$	0	0
$631$	−34.8614	−1.38781	−0.693905	−	0.720066i	$-0.744111\pi$
$631$	−34.8614	−1.38781	−0.693905	+	0.720066i	$0.744111\pi$
$632$	11.1168i	0.442204i
$633$	10.2337i	0.406753i
$634$	−14.7446	−0.585581
$635$	0	0
$636$	5.74456	0.227787
$637$	2.74456i	0.108744i
$638$	38.2337i	1.51369i
$639$	1.37228	0.0542866
$640$	0	0
$641$	40.9783	1.61854	0.809272	−	0.587434i	$-0.199862\pi$
$641$	40.9783	1.61854	0.809272	+	0.587434i	$0.199862\pi$
$642$	10.3723i	0.409361i
$643$	24.1168i	0.951075i	0.879695	+	0.475538i	$0.157746\pi$
$643$	24.1168i	0.951075i	−0.879695	+	0.475538i	$0.842254\pi$
$644$	−3.25544	−0.128282
$645$	0	0
$646$	2.37228	0.0933362
$647$	25.7228i	1.01127i	0.862748	+	0.505634i	$0.168741\pi$
$647$	25.7228i	1.01127i	−0.862748	+	0.505634i	$0.831259\pi$
$648$	1.00000i	0.0392837i
$649$	−44.2337	−1.73632
$650$	0	0
$651$	−21.6277	−0.847657
$652$	2.11684i	0.0829020i
$653$	− 22.9783i	− 0.899208i	−0.893228	−	0.449604i	$-0.851565\pi$
$653$	− 22.9783i	− 0.899208i	0.893228	−	0.449604i	$-0.148435\pi$
$654$	−9.11684	−0.356497
$655$	0	0
$656$	−1.37228	−0.0535786
$657$	− 8.00000i	− 0.312110i
$658$	3.86141i	0.150533i
$659$	−6.51087	−0.253628	−0.126814	−	0.991927i	$-0.540475\pi$
$659$	−6.51087	−0.253628	−0.126814	+	0.991927i	$0.540475\pi$
$660$	0	0
$661$	−13.2554	−0.515577	−0.257788	−	0.966201i	$-0.582994\pi$
$661$	−13.2554	−0.515577	−0.257788	+	0.966201i	$0.582994\pi$
$662$	− 14.6060i	− 0.567677i
$663$	− 2.00000i	− 0.0776736i
$664$	−1.37228	−0.0532548
$665$	0	0
$666$	−1.00000	−0.0387492
$667$	12.0000i	0.464642i
$668$	− 20.7446i	− 0.802631i
$669$	8.11684	0.313815
$670$	0	0
$671$	−35.4891	−1.37004
$672$	2.37228i	0.0915127i
$673$	39.7228i	1.53120i	0.643316	+	0.765601i	$0.277558\pi$
$673$	39.7228i	1.53120i	−0.643316	+	0.765601i	$0.722442\pi$
$674$	24.2337	0.933447
$675$	0	0
$676$	−9.00000	−0.346154
$677$	24.0000i	0.922395i	0.887298	+	0.461197i	$0.152580\pi$
$677$	24.0000i	0.922395i	−0.887298	+	0.461197i	$0.847420\pi$
$678$	− 11.7446i	− 0.451047i
$679$	−30.2337	−1.16026
$680$	0	0
$681$	−4.37228	−0.167546
$682$	− 39.8614i	− 1.52637i
$683$	9.25544i	0.354149i	0.984197	+	0.177075i	$0.0566634\pi$
$683$	9.25544i	0.354149i	−0.984197	+	0.177075i	$0.943337\pi$
$684$	2.37228	0.0907064
$685$	0	0
$686$	19.8614	0.758312
$687$	12.2337i	0.466744i
$688$	3.62772i	0.138305i
$689$	−11.4891	−0.437701
$690$	0	0
$691$	39.3723	1.49779	0.748896	−	0.662687i	$-0.230584\pi$
$691$	39.3723	1.49779	0.748896	+	0.662687i	$0.230584\pi$
$692$	12.0000i	0.456172i
$693$	− 10.3723i	− 0.394010i
$694$	−22.3723	−0.849240
$695$	0	0
$696$	8.74456	0.331462
$697$	− 1.37228i	− 0.0519789i
$698$	− 10.0000i	− 0.378506i
$699$	10.6277	0.401977
$700$	0	0
$701$	9.60597	0.362812	0.181406	−	0.983408i	$-0.441935\pi$
$701$	9.60597	0.362812	0.181406	+	0.983408i	$0.441935\pi$
$702$	− 2.00000i	− 0.0754851i
$703$	2.37228i	0.0894723i
$704$	−4.37228	−0.164787
$705$	0	0
$706$	−15.2554	−0.574146
$707$	31.1168i	1.17027i
$708$	10.1168i	0.380214i
$709$	8.37228	0.314428	0.157214	−	0.987565i	$-0.449749\pi$
$709$	8.37228	0.314428	0.157214	+	0.987565i	$0.449749\pi$
$710$	0	0
$711$	−11.1168	−0.416914
$712$	2.74456i	0.102857i
$713$	− 12.5109i	− 0.468536i
$714$	−2.37228	−0.0887804
$715$	0	0
$716$	−10.1168	−0.378084
$717$	13.1168i	0.489858i
$718$	− 13.6277i	− 0.508582i
$719$	27.2554	1.01646	0.508228	−	0.861222i	$-0.330301\pi$
$719$	27.2554	1.01646	0.508228	+	0.861222i	$0.330301\pi$
$720$	0	0
$721$	−36.4674	−1.35812
$722$	13.3723i	0.497665i
$723$	28.2337i	1.05002i
$724$	0.489125	0.0181782
$725$	0	0
$726$	8.11684	0.301244
$727$	31.2554i	1.15920i	0.814901	+	0.579600i	$0.196791\pi$
$727$	31.2554i	1.15920i	−0.814901	+	0.579600i	$0.803209\pi$
$728$	− 4.74456i	− 0.175845i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−3.62772	−0.134176
$732$	8.11684i	0.300007i
$733$	− 1.25544i	− 0.0463706i	−0.999731	−	0.0231853i	$-0.992619\pi$
$733$	− 1.25544i	− 0.0463706i	0.999731	−	0.0231853i	$-0.00738078\pi$
$734$	−14.6060	−0.539116
$735$	0	0
$736$	−1.37228	−0.0505830
$737$	− 1.62772i	− 0.0599578i
$738$	− 1.37228i	− 0.0505144i
$739$	−33.6277	−1.23702	−0.618508	−	0.785779i	$-0.712262\pi$
$739$	−33.6277	−1.23702	−0.618508	+	0.785779i	$0.712262\pi$
$740$	0	0
$741$	−4.74456	−0.174296
$742$	13.6277i	0.500289i
$743$	22.6277i	0.830130i	0.909792	+	0.415065i	$0.136241\pi$
$743$	22.6277i	0.830130i	−0.909792	+	0.415065i	$0.863759\pi$
$744$	−9.11684	−0.334240
$745$	0	0
$746$	−1.76631	−0.0646693
$747$	− 1.37228i	− 0.0502091i
$748$	− 4.37228i	− 0.159866i
$749$	−24.6060	−0.899083
$750$	0	0
$751$	−32.4674	−1.18475	−0.592376	−	0.805662i	$-0.701810\pi$
$751$	−32.4674	−1.18475	−0.592376	+	0.805662i	$0.701810\pi$
$752$	1.62772i	0.0593568i
$753$	8.74456i	0.318670i
$754$	−17.4891	−0.636916
$755$	0	0
$756$	−2.37228	−0.0862790
$757$	− 34.2337i	− 1.24424i	−0.782920	−	0.622122i	$-0.786271\pi$
$757$	− 34.2337i	− 1.24424i	0.782920	−	0.622122i	$-0.213729\pi$
$758$	− 19.6060i	− 0.712121i
$759$	6.00000	0.217786
$760$	0	0
$761$	−17.4891	−0.633980	−0.316990	−	0.948429i	$-0.602672\pi$
$761$	−17.4891	−0.633980	−0.316990	+	0.948429i	$0.602672\pi$
$762$	− 1.48913i	− 0.0539453i
$763$	− 21.6277i	− 0.782976i
$764$	27.3505	0.989508
$765$	0	0
$766$	0	0
$767$	− 20.2337i	− 0.730596i
$768$	1.00000i	0.0360844i
$769$	13.0000	0.468792	0.234396	−	0.972141i	$-0.424689\pi$
$769$	13.0000	0.468792	0.234396	+	0.972141i	$0.424689\pi$
$770$	0	0
$771$	−14.2337	−0.512614
$772$	− 8.00000i	− 0.287926i
$773$	− 17.1386i	− 0.616432i	−0.951316	−	0.308216i	$-0.900268\pi$
$773$	− 17.1386i	− 0.616432i	0.951316	−	0.308216i	$-0.0997320\pi$
$774$	−3.62772	−0.130396
$775$	0	0
$776$	−12.7446	−0.457503
$777$	− 2.37228i	− 0.0851051i
$778$	17.7446i	0.636173i
$779$	−3.25544	−0.116638
$780$	0	0
$781$	−6.00000	−0.214697
$782$	− 1.37228i	− 0.0490727i
$783$	8.74456i	0.312505i
$784$	1.37228	0.0490100
$785$	0	0
$786$	17.4891	0.623816
$787$	− 44.3505i	− 1.58093i	−0.612510	−	0.790463i	$-0.709840\pi$
$787$	− 44.3505i	− 1.58093i	0.612510	−	0.790463i	$-0.290160\pi$
$788$	− 9.25544i	− 0.329711i
$789$	25.6277	0.912371
$790$	0	0
$791$	27.8614	0.990638
$792$	− 4.37228i	− 0.155362i
$793$	− 16.2337i	− 0.576475i
$794$	1.00000	0.0354887
$795$	0	0
$796$	21.1168	0.748467
$797$	− 6.25544i	− 0.221579i	−0.993844	−	0.110789i	$-0.964662\pi$
$797$	− 6.25544i	− 0.221579i	0.993844	−	0.110789i	$-0.0353379\pi$
$798$	5.62772i	0.199219i
$799$	−1.62772	−0.0575845
$800$	0	0
$801$	−2.74456	−0.0969744
$802$	− 4.11684i	− 0.145371i
$803$	34.9783i	1.23436i
$804$	−0.372281	−0.0131293
$805$	0	0
$806$	18.2337	0.642254
$807$	− 11.4891i	− 0.404436i
$808$	13.1168i	0.461449i
$809$	−18.6060	−0.654151	−0.327076	−	0.944998i	$-0.606063\pi$
$809$	−18.6060	−0.654151	−0.327076	+	0.944998i	$0.606063\pi$
$810$	0	0
$811$	44.0000	1.54505	0.772524	−	0.634985i	$-0.218994\pi$
$811$	44.0000	1.54505	0.772524	+	0.634985i	$0.218994\pi$
$812$	20.7446i	0.727991i
$813$	− 2.62772i	− 0.0921581i
$814$	4.37228	0.153248
$815$	0	0
$816$	−1.00000	−0.0350070
$817$	8.60597i	0.301085i
$818$	14.8614i	0.519617i
$819$	4.74456	0.165788
$820$	0	0
$821$	−44.7446	−1.56160	−0.780798	−	0.624784i	$-0.785187\pi$
$821$	−44.7446	−1.56160	−0.780798	+	0.624784i	$0.785187\pi$
$822$	− 5.48913i	− 0.191455i
$823$	− 20.4674i	− 0.713448i	−0.934210	−	0.356724i	$-0.883894\pi$
$823$	− 20.4674i	− 0.713448i	0.934210	−	0.356724i	$-0.116106\pi$
$824$	−15.3723	−0.535519
$825$	0	0
$826$	−24.0000	−0.835067
$827$	12.0951i	0.420588i	0.977638	+	0.210294i	$0.0674421\pi$
$827$	12.0951i	0.420588i	−0.977638	+	0.210294i	$0.932558\pi$
$828$	− 1.37228i	− 0.0476901i
$829$	−40.7446	−1.41512	−0.707559	−	0.706655i	$-0.750203\pi$
$829$	−40.7446	−1.41512	−0.707559	+	0.706655i	$0.750203\pi$
$830$	0	0
$831$	−13.0000	−0.450965
$832$	− 2.00000i	− 0.0693375i
$833$	1.37228i	0.0475467i
$834$	−18.1168	−0.627335
$835$	0	0
$836$	−10.3723	−0.358733
$837$	− 9.11684i	− 0.315124i
$838$	10.9783i	0.379237i
$839$	−7.37228	−0.254519	−0.127260	−	0.991869i	$-0.540618\pi$
$839$	−7.37228	−0.254519	−0.127260	+	0.991869i	$0.540618\pi$
$840$	0	0
$841$	47.4674	1.63681
$842$	18.2337i	0.628374i
$843$	0.510875i	0.0175955i
$844$	−10.2337	−0.352258
$845$	0	0
$846$	−1.62772	−0.0559621
$847$	19.2554i	0.661625i
$848$	5.74456i	0.197269i
$849$	−12.1168	−0.415849
$850$	0	0
$851$	1.37228	0.0470412
$852$	1.37228i	0.0470136i
$853$	17.8614i	0.611563i	0.952102	+	0.305781i	$0.0989177\pi$
$853$	17.8614i	0.611563i	−0.952102	+	0.305781i	$0.901082\pi$
$854$	−19.2554	−0.658908
$855$	0	0
$856$	−10.3723	−0.354517
$857$	− 18.2554i	− 0.623594i	−0.950149	−	0.311797i	$-0.899069\pi$
$857$	− 18.2554i	− 0.623594i	0.950149	−	0.311797i	$-0.100931\pi$
$858$	8.74456i	0.298534i
$859$	13.3505	0.455514	0.227757	−	0.973718i	$-0.426861\pi$
$859$	13.3505	0.455514	0.227757	+	0.973718i	$0.426861\pi$
$860$	0	0
$861$	3.25544	0.110945
$862$	− 12.0000i	− 0.408722i
$863$	− 13.6277i	− 0.463893i	−0.972729	−	0.231946i	$-0.925491\pi$
$863$	− 13.6277i	− 0.463893i	0.972729	−	0.231946i	$-0.0745094\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	−40.0951	−1.36249
$867$	− 1.00000i	− 0.0339618i
$868$	− 21.6277i	− 0.734093i
$869$	48.6060	1.64884
$870$	0	0
$871$	0.744563	0.0252285
$872$	− 9.11684i	− 0.308735i
$873$	− 12.7446i	− 0.431338i
$874$	−3.25544	−0.110117
$875$	0	0
$876$	8.00000	0.270295
$877$	46.0000i	1.55331i	0.629926	+	0.776655i	$0.283085\pi$
$877$	46.0000i	1.55331i	−0.629926	+	0.776655i	$0.716915\pi$
$878$	2.51087i	0.0847379i
$879$	28.1168	0.948358
$880$	0	0
$881$	−34.2119	−1.15263	−0.576315	−	0.817228i	$-0.695510\pi$
$881$	−34.2119	−1.15263	−0.576315	+	0.817228i	$0.695510\pi$
$882$	1.37228i	0.0462071i
$883$	− 7.76631i	− 0.261357i	−0.991425	−	0.130679i	$-0.958284\pi$
$883$	− 7.76631i	− 0.261357i	0.991425	−	0.130679i	$-0.0417156\pi$
$884$	2.00000	0.0672673
$885$	0	0
$886$	−7.37228	−0.247677
$887$	− 39.6060i	− 1.32984i	−0.746915	−	0.664919i	$-0.768466\pi$
$887$	− 39.6060i	− 1.32984i	0.746915	−	0.664919i	$-0.231534\pi$
$888$	− 1.00000i	− 0.0335578i
$889$	3.53262	0.118480
$890$	0	0
$891$	4.37228	0.146477
$892$	8.11684i	0.271772i
$893$	3.86141i	0.129217i
$894$	6.86141	0.229480
$895$	0	0
$896$	−2.37228	−0.0792524
$897$	2.74456i	0.0916383i
$898$	− 33.8614i	− 1.12997i
$899$	−79.7228	−2.65890
$900$	0	0
$901$	−5.74456	−0.191379
$902$	6.00000i	0.199778i
$903$	− 8.60597i	− 0.286389i
$904$	11.7446	0.390618
$905$	0	0
$906$	−14.1168	−0.469001
$907$	− 10.3940i	− 0.345128i	−0.984998	−	0.172564i	$-0.944795\pi$
$907$	− 10.3940i	− 0.345128i	0.984998	−	0.172564i	$-0.0552052\pi$
$908$	− 4.37228i	− 0.145099i
$909$	−13.1168	−0.435058
$910$	0	0
$911$	−6.51087	−0.215715	−0.107857	−	0.994166i	$-0.534399\pi$
$911$	−6.51087	−0.215715	−0.107857	+	0.994166i	$0.534399\pi$
$912$	2.37228i	0.0785541i
$913$	6.00000i	0.198571i
$914$	−23.0000	−0.760772
$915$	0	0
$916$	−12.2337	−0.404212
$917$	41.4891i	1.37009i
$918$	− 1.00000i	− 0.0330049i
$919$	42.5842	1.40472	0.702362	−	0.711820i	$-0.252129\pi$
$919$	42.5842	1.40472	0.702362	+	0.711820i	$0.252129\pi$
$920$	0	0
$921$	16.2337	0.534918
$922$	− 34.7228i	− 1.14353i
$923$	− 2.74456i	− 0.0903384i
$924$	10.3723	0.341223
$925$	0	0
$926$	−19.6060	−0.644292
$927$	− 15.3723i	− 0.504892i
$928$	8.74456i	0.287054i
$929$	40.7228	1.33607	0.668036	−	0.744129i	$-0.267135\pi$
$929$	40.7228	1.33607	0.668036	+	0.744129i	$0.267135\pi$
$930$	0	0
$931$	3.25544	0.106693
$932$	10.6277i	0.348122i
$933$	− 28.1168i	− 0.920504i
$934$	−16.1168	−0.527359
$935$	0	0
$936$	2.00000	0.0653720
$937$	− 41.6060i	− 1.35921i	−0.733579	−	0.679604i	$-0.762152\pi$
$937$	− 41.6060i	− 1.35921i	0.733579	−	0.679604i	$-0.237848\pi$
$938$	− 0.883156i	− 0.0288361i
$939$	−4.74456	−0.154833
$940$	0	0
$941$	−22.4674	−0.732416	−0.366208	−	0.930533i	$-0.619344\pi$
$941$	−22.4674	−0.732416	−0.366208	+	0.930533i	$0.619344\pi$
$942$	18.7446i	0.610731i
$943$	1.88316i	0.0613240i
$944$	−10.1168	−0.329275
$945$	0	0
$946$	15.8614	0.515699
$947$	− 34.3723i	− 1.11695i	−0.829522	−	0.558475i	$-0.811387\pi$
$947$	− 34.3723i	− 1.11695i	0.829522	−	0.558475i	$-0.188613\pi$
$948$	− 11.1168i	− 0.361058i
$949$	−16.0000	−0.519382
$950$	0	0
$951$	14.7446	0.478125
$952$	− 2.37228i	− 0.0768861i
$953$	40.9783i	1.32742i	0.747992	+	0.663708i	$0.231018\pi$
$953$	40.9783i	1.32742i	−0.747992	+	0.663708i	$0.768982\pi$
$954$	−5.74456	−0.185987
$955$	0	0
$956$	−13.1168	−0.424229
$957$	− 38.2337i	− 1.23592i
$958$	− 31.7228i	− 1.02492i
$959$	13.0217	0.420494
$960$	0	0
$961$	52.1168	1.68119
$962$	2.00000i	0.0644826i
$963$	− 10.3723i	− 0.334242i
$964$	−28.2337	−0.909346
$965$	0	0
$966$	3.25544	0.104742
$967$	22.3505i	0.718745i	0.933194	+	0.359372i	$0.117009\pi$
$967$	22.3505i	0.718745i	−0.933194	+	0.359372i	$0.882991\pi$
$968$	8.11684i	0.260885i
$969$	−2.37228	−0.0762087
$970$	0	0
$971$	−6.86141	−0.220193	−0.110097	−	0.993921i	$-0.535116\pi$
$971$	−6.86141	−0.220193	−0.110097	+	0.993921i	$0.535116\pi$
$972$	− 1.00000i	− 0.0320750i
$973$	− 42.9783i	− 1.37782i
$974$	12.2337	0.391993
$975$	0	0
$976$	−8.11684	−0.259814
$977$	− 6.00000i	− 0.191957i	−0.995383	−	0.0959785i	$-0.969402\pi$
$977$	− 6.00000i	− 0.191957i	0.995383	−	0.0959785i	$-0.0305980\pi$
$978$	− 2.11684i	− 0.0676892i
$979$	12.0000	0.383522
$980$	0	0
$981$	9.11684	0.291078
$982$	31.3723i	1.00113i
$983$	9.76631i	0.311497i	0.987797	+	0.155748i	$0.0497789\pi$
$983$	9.76631i	0.311497i	−0.987797	+	0.155748i	$0.950221\pi$
$984$	1.37228	0.0437467
$985$	0	0
$986$	−8.74456	−0.278484
$987$	− 3.86141i	− 0.122910i
$988$	− 4.74456i	− 0.150945i
$989$	4.97825	0.158299
$990$	0	0
$991$	60.4674	1.92081	0.960405	−	0.278609i	$-0.0898732\pi$
$991$	60.4674	1.92081	0.960405	+	0.278609i	$0.0898732\pi$
$992$	− 9.11684i	− 0.289460i
$993$	14.6060i	0.463506i
$994$	−3.25544	−0.103256
$995$	0	0
$996$	1.37228	0.0434824
$997$	− 33.1168i	− 1.04882i	−0.851466	−	0.524410i	$-0.824286\pi$
$997$	− 33.1168i	− 1.04882i	0.851466	−	0.524410i	$-0.175714\pi$
$998$	18.6277i	0.589650i
$999$	1.00000	0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2550.2.d.v.2449.2		4
5.2	odd	4		2550.2.a.bm.1.1	yes	2
5.3	odd	4		2550.2.a.bg.1.2	✓	2
5.4	even	2	inner	2550.2.d.v.2449.3		4
15.2	even	4		7650.2.a.cv.1.1		2
15.8	even	4		7650.2.a.df.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2550.2.a.bg.1.2	✓	2	5.3	odd	4
2550.2.a.bm.1.1	yes	2	5.2	odd	4
2550.2.d.v.2449.2		4	1.1	even	1	trivial
2550.2.d.v.2449.3		4	5.4	even	2	inner
7650.2.a.cv.1.1		2	15.2	even	4
7650.2.a.df.1.2		2	15.8	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:	\( N \)	\(=\)	\( 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2550.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} +2.37228i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} +2.37228i q^{7} +1.00000i q^{8} -1.00000 q^{9} +4.37228 q^{11} -1.00000i q^{12} +2.00000i q^{13} +2.37228 q^{14} +1.00000 q^{16} +1.00000i q^{17} +1.00000i q^{18} +2.37228 q^{19} -2.37228 q^{21} -4.37228i q^{22} -1.37228i q^{23} -1.00000 q^{24} +2.00000 q^{26} -1.00000i q^{27} -2.37228i q^{28} -8.74456 q^{29} +9.11684 q^{31} -1.00000i q^{32} +4.37228i q^{33} +1.00000 q^{34} +1.00000 q^{36} +1.00000i q^{37} -2.37228i q^{38} -2.00000 q^{39} -1.37228 q^{41} +2.37228i q^{42} +3.62772i q^{43} -4.37228 q^{44} -1.37228 q^{46} +1.62772i q^{47} +1.00000i q^{48} +1.37228 q^{49} -1.00000 q^{51} -2.00000i q^{52} +5.74456i q^{53} -1.00000 q^{54} -2.37228 q^{56} +2.37228i q^{57} +8.74456i q^{58} -10.1168 q^{59} -8.11684 q^{61} -9.11684i q^{62} -2.37228i q^{63} -1.00000 q^{64} +4.37228 q^{66} -0.372281i q^{67} -1.00000i q^{68} +1.37228 q^{69} -1.37228 q^{71} -1.00000i q^{72} +8.00000i q^{73} +1.00000 q^{74} -2.37228 q^{76} +10.3723i q^{77} +2.00000i q^{78} +11.1168 q^{79} +1.00000 q^{81} +1.37228i q^{82} +1.37228i q^{83} +2.37228 q^{84} +3.62772 q^{86} -8.74456i q^{87} +4.37228i q^{88} +2.74456 q^{89} -4.74456 q^{91} +1.37228i q^{92} +9.11684i q^{93} +1.62772 q^{94} +1.00000 q^{96} +12.7446i q^{97} -1.37228i q^{98} -4.37228 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9	\( 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9} + 6 q^{11} - 2 q^{14} + 4 q^{16} - 2 q^{19} + 2 q^{21} - 4 q^{24} + 8 q^{26} - 12 q^{29} + 2 q^{31} + 4 q^{34} + 4 q^{36} - 8 q^{39} + 6 q^{41} - 6 q^{44} + 6 q^{46} - 6 q^{49} - 4 q^{51} - 4 q^{54} + 2 q^{56} - 6 q^{59} + 2 q^{61} - 4 q^{64} + 6 q^{66} - 6 q^{69} + 6 q^{71} + 4 q^{74} + 2 q^{76} + 10 q^{79} + 4 q^{81} - 2 q^{84} + 26 q^{86} - 12 q^{89} + 4 q^{91} + 18 q^{94} + 4 q^{96} - 6 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9 + 6 * q^11 - 2 * q^14 + 4 * q^16 - 2 * q^19 + 2 * q^21 - 4 * q^24 + 8 * q^26 - 12 * q^29 + 2 * q^31 + 4 * q^34 + 4 * q^36 - 8 * q^39 + 6 * q^41 - 6 * q^44 + 6 * q^46 - 6 * q^49 - 4 * q^51 - 4 * q^54 + 2 * q^56 - 6 * q^59 + 2 * q^61 - 4 * q^64 + 6 * q^66 - 6 * q^69 + 6 * q^71 + 4 * q^74 + 2 * q^76 + 10 * q^79 + 4 * q^81 - 2 * q^84 + 26 * q^86 - 12 * q^89 + 4 * q^91 + 18 * q^94 + 4 * q^96 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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