LMFDB - Embedded newform 2550.2.d.v.2449.1

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			2449.1
Root			$-3.37228i$ of defining polynomial
Character	$\chi$	$=$	2550.2449
Dual form			2550.2.d.v.2449.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} -3.37228i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} -3.37228i q^{7} +1.00000i q^{8} -1.00000 q^{9} -1.37228 q^{11} -1.00000i q^{12} +2.00000i q^{13} -3.37228 q^{14} +1.00000 q^{16} +1.00000i q^{17} +1.00000i q^{18} -3.37228 q^{19} +3.37228 q^{21} +1.37228i q^{22} +4.37228i q^{23} -1.00000 q^{24} +2.00000 q^{26} -1.00000i q^{27} +3.37228i q^{28} +2.74456 q^{29} -8.11684 q^{31} -1.00000i q^{32} -1.37228i q^{33} +1.00000 q^{34} +1.00000 q^{36} +1.00000i q^{37} +3.37228i q^{38} -2.00000 q^{39} +4.37228 q^{41} -3.37228i q^{42} +9.37228i q^{43} +1.37228 q^{44} +4.37228 q^{46} +7.37228i q^{47} +1.00000i q^{48} -4.37228 q^{49} -1.00000 q^{51} -2.00000i q^{52} -5.74456i q^{53} -1.00000 q^{54} +3.37228 q^{56} -3.37228i q^{57} -2.74456i q^{58} +7.11684 q^{59} +9.11684 q^{61} +8.11684i q^{62} +3.37228i q^{63} -1.00000 q^{64} -1.37228 q^{66} +5.37228i q^{67} -1.00000i q^{68} -4.37228 q^{69} +4.37228 q^{71} -1.00000i q^{72} +8.00000i q^{73} +1.00000 q^{74} +3.37228 q^{76} +4.62772i q^{77} +2.00000i q^{78} -6.11684 q^{79} +1.00000 q^{81} -4.37228i q^{82} -4.37228i q^{83} -3.37228 q^{84} +9.37228 q^{86} +2.74456i q^{87} -1.37228i q^{88} -8.74456 q^{89} +6.74456 q^{91} -4.37228i q^{92} -8.11684i q^{93} +7.37228 q^{94} +1.00000 q^{96} +1.25544i q^{97} +4.37228i q^{98} +1.37228 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	− 3.37228i	− 1.27460i	−0.770615	−	0.637301i	$-0.780051\pi$
$7$	− 3.37228i	− 1.27460i	0.770615	−	0.637301i	$-0.219949\pi$
$8$	1.00000i	0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−1.37228	−0.413758	−0.206879	−	0.978366i	$-0.566331\pi$
$11$	−1.37228	−0.413758	−0.206879	+	0.978366i	$0.566331\pi$
$12$	− 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	$0.910544\pi$
$14$	−3.37228	−0.901280
$15$	0	0
$16$	1.00000	0.250000
$17$	1.00000i	0.242536i
$17$	1.00000i	0.242536i
$18$	1.00000i	0.235702i
$19$	−3.37228	−0.773654	−0.386827	−	0.922152i	$-0.626429\pi$
$19$	−3.37228	−0.773654	−0.386827	+	0.922152i	$0.626429\pi$
$20$	0	0
$21$	3.37228	0.735892
$22$	1.37228i	0.292571i
$23$	4.37228i	0.911684i	0.890061	+	0.455842i	$0.150662\pi$
$23$	4.37228i	0.911684i	−0.890061	+	0.455842i	$0.849338\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	2.00000	0.392232
$27$	− 1.00000i	− 0.192450i
$28$	3.37228i	0.637301i
$29$	2.74456	0.509652	0.254826	−	0.966987i	$-0.417982\pi$
$29$	2.74456	0.509652	0.254826	+	0.966987i	$0.417982\pi$
$30$	0	0
$31$	−8.11684	−1.45783	−0.728914	−	0.684605i	$-0.759975\pi$
$31$	−8.11684	−1.45783	−0.728914	+	0.684605i	$0.759975\pi$
$32$	− 1.00000i	− 0.176777i
$33$	− 1.37228i	− 0.238884i
$34$	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	$0.973806\pi$
$38$	3.37228i	0.547056i
$39$	−2.00000	−0.320256
$40$	0	0
$41$	4.37228	0.682836	0.341418	−	0.939912i	$-0.389093\pi$
$41$	4.37228	0.682836	0.341418	+	0.939912i	$0.389093\pi$
$42$	− 3.37228i	− 0.520354i
$43$	9.37228i	1.42926i	0.699503	+	0.714630i	$0.253405\pi$
$43$	9.37228i	1.42926i	−0.699503	+	0.714630i	$0.746595\pi$
$44$	1.37228	0.206879
$45$	0	0
$46$	4.37228	0.644658
$47$	7.37228i	1.07536i	0.843150	+	0.537679i	$0.180699\pi$
$47$	7.37228i	1.07536i	−0.843150	+	0.537679i	$0.819301\pi$
$48$	1.00000i	0.144338i
$49$	−4.37228	−0.624612
$50$	0	0
$51$	−1.00000	−0.140028
$52$	− 2.00000i	− 0.277350i
$53$	− 5.74456i	− 0.789076i	−0.918880	−	0.394538i	$-0.870905\pi$
$53$	− 5.74456i	− 0.789076i	0.918880	−	0.394538i	$-0.129095\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	3.37228	0.450640
$57$	− 3.37228i	− 0.446670i
$58$	− 2.74456i	− 0.360379i
$59$	7.11684	0.926534	0.463267	−	0.886219i	$-0.346677\pi$
$59$	7.11684	0.926534	0.463267	+	0.886219i	$0.346677\pi$
$60$	0	0
$61$	9.11684	1.16729	0.583646	−	0.812008i	$-0.301626\pi$
$61$	9.11684	1.16729	0.583646	+	0.812008i	$0.301626\pi$
$62$	8.11684i	1.03084i
$63$	3.37228i	0.424868i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−1.37228	−0.168916
$67$	5.37228i	0.656329i	0.944621	+	0.328164i	$0.106430\pi$
$67$	5.37228i	0.656329i	−0.944621	+	0.328164i	$0.893570\pi$
$68$	− 1.00000i	− 0.121268i
$69$	−4.37228	−0.526361
$70$	0	0
$71$	4.37228	0.518894	0.259447	−	0.965757i	$-0.416460\pi$
$71$	4.37228	0.518894	0.259447	+	0.965757i	$0.416460\pi$
$72$	− 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
$76$	3.37228	0.386827
$77$	4.62772i	0.527377i
$78$	2.00000i	0.226455i
$79$	−6.11684	−0.688199	−0.344099	−	0.938933i	$-0.611816\pi$
$79$	−6.11684	−0.688199	−0.344099	+	0.938933i	$0.611816\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	− 4.37228i	− 0.482838i
$83$	− 4.37228i	− 0.479920i	−0.970783	−	0.239960i	$-0.922866\pi$
$83$	− 4.37228i	− 0.479920i	0.970783	−	0.239960i	$-0.0771344\pi$
$84$	−3.37228	−0.367946
$85$	0	0
$86$	9.37228	1.01064
$87$	2.74456i	0.294248i
$88$	− 1.37228i	− 0.146286i
$89$	−8.74456	−0.926922	−0.463461	−	0.886117i	$-0.653393\pi$
$89$	−8.74456	−0.926922	−0.463461	+	0.886117i	$0.653393\pi$
$90$	0	0
$91$	6.74456	0.707022
$92$	− 4.37228i	− 0.455842i
$93$	− 8.11684i	− 0.841678i
$94$	7.37228	0.760393
$95$	0	0
$96$	1.00000	0.102062
$97$	1.25544i	0.127470i	0.997967	+	0.0637352i	$0.0203013\pi$
$97$	1.25544i	0.127470i	−0.997967	+	0.0637352i	$0.979699\pi$
$98$	4.37228i	0.441667i
$99$	1.37228	0.137919
$100$	0	0
$101$	−4.11684	−0.409641	−0.204821	−	0.978800i	$-0.565661\pi$
$101$	−4.11684	−0.409641	−0.204821	+	0.978800i	$0.565661\pi$
$102$	1.00000i	0.0990148i
$103$	9.62772i	0.948647i	0.880351	+	0.474324i	$0.157307\pi$
$103$	9.62772i	0.948647i	−0.880351	+	0.474324i	$0.842693\pi$
$104$	−2.00000	−0.196116
$105$	0	0
$106$	−5.74456	−0.557961
$107$	4.62772i	0.447378i	0.974661	+	0.223689i	$0.0718101\pi$
$107$	4.62772i	0.447378i	−0.974661	+	0.223689i	$0.928190\pi$
$108$	1.00000i	0.0962250i
$109$	8.11684	0.777453	0.388726	−	0.921353i	$-0.372915\pi$
$109$	8.11684	0.777453	0.388726	+	0.921353i	$0.372915\pi$
$110$	0	0
$111$	−1.00000	−0.0949158
$112$	− 3.37228i	− 0.318651i
$113$	− 0.255437i	− 0.0240295i	−0.999928	−	0.0120148i	$-0.996175\pi$
$113$	− 0.255437i	− 0.0240295i	0.999928	−	0.0120148i	$-0.00382451\pi$
$114$	−3.37228	−0.315843
$115$	0	0
$116$	−2.74456	−0.254826
$117$	− 2.00000i	− 0.184900i
$118$	− 7.11684i	− 0.655159i
$119$	3.37228	0.309137
$120$	0	0
$121$	−9.11684	−0.828804
$122$	− 9.11684i	− 0.825400i
$123$	4.37228i	0.394235i
$124$	8.11684	0.728914
$125$	0	0
$126$	3.37228	0.300427
$127$	21.4891i	1.90685i	0.301628	+	0.953426i	$0.402470\pi$
$127$	21.4891i	1.90685i	−0.301628	+	0.953426i	$0.597530\pi$
$128$	1.00000i	0.0883883i
$129$	−9.37228	−0.825183
$130$	0	0
$131$	−5.48913	−0.479587	−0.239794	−	0.970824i	$-0.577080\pi$
$131$	−5.48913	−0.479587	−0.239794	+	0.970824i	$0.577080\pi$
$132$	1.37228i	0.119442i
$133$	11.3723i	0.986102i
$134$	5.37228	0.464094
$135$	0	0
$136$	−1.00000	−0.0857493
$137$	17.4891i	1.49420i	0.664713	+	0.747098i	$0.268554\pi$
$137$	17.4891i	1.49420i	−0.664713	+	0.747098i	$0.731446\pi$
$138$	4.37228i	0.372193i
$139$	−0.883156	−0.0749083	−0.0374542	−	0.999298i	$-0.511925\pi$
$139$	−0.883156	−0.0749083	−0.0374542	+	0.999298i	$0.511925\pi$
$140$	0	0
$141$	−7.37228	−0.620858
$142$	− 4.37228i	− 0.366914i
$143$	− 2.74456i	− 0.229512i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	8.00000	0.662085
$147$	− 4.37228i	− 0.360620i
$148$	− 1.00000i	− 0.0821995i
$149$	−21.8614	−1.79096	−0.895478	−	0.445106i	$-0.853166\pi$
$149$	−21.8614	−1.79096	−0.895478	+	0.445106i	$0.853166\pi$
$150$	0	0
$151$	3.11684	0.253645	0.126823	−	0.991925i	$-0.459522\pi$
$151$	3.11684	0.253645	0.126823	+	0.991925i	$0.459522\pi$
$152$	− 3.37228i	− 0.273528i
$153$	− 1.00000i	− 0.0808452i
$154$	4.62772	0.372912
$155$	0	0
$156$	2.00000	0.160128
$157$	7.25544i	0.579047i	0.957171	+	0.289523i	$0.0934968\pi$
$157$	7.25544i	0.579047i	−0.957171	+	0.289523i	$0.906503\pi$
$158$	6.11684i	0.486630i
$159$	5.74456	0.455573
$160$	0	0
$161$	14.7446	1.16203
$162$	− 1.00000i	− 0.0785674i
$163$	15.1168i	1.18404i	0.805922	+	0.592021i	$0.201670\pi$
$163$	15.1168i	1.18404i	−0.805922	+	0.592021i	$0.798330\pi$
$164$	−4.37228	−0.341418
$165$	0	0
$166$	−4.37228	−0.339355
$167$	9.25544i	0.716207i	0.933682	+	0.358104i	$0.116577\pi$
$167$	9.25544i	0.716207i	−0.933682	+	0.358104i	$0.883423\pi$
$168$	3.37228i	0.260177i
$169$	9.00000	0.692308
$170$	0	0
$171$	3.37228	0.257885
$172$	− 9.37228i	− 0.714630i
$173$	− 12.0000i	− 0.912343i	−0.889892	−	0.456172i	$-0.849220\pi$
$173$	− 12.0000i	− 0.912343i	0.889892	−	0.456172i	$-0.150780\pi$
$174$	2.74456	0.208065
$175$	0	0
$176$	−1.37228	−0.103440
$177$	7.11684i	0.534935i
$178$	8.74456i	0.655433i
$179$	−7.11684	−0.531938	−0.265969	−	0.963982i	$-0.585692\pi$
$179$	−7.11684	−0.531938	−0.265969	+	0.963982i	$0.585692\pi$
$180$	0	0
$181$	22.4891	1.67160	0.835802	−	0.549031i	$-0.185003\pi$
$181$	22.4891	1.67160	0.835802	+	0.549031i	$0.185003\pi$
$182$	− 6.74456i	− 0.499940i
$183$	9.11684i	0.673936i
$184$	−4.37228	−0.322329
$185$	0	0
$186$	−8.11684	−0.595156
$187$	− 1.37228i	− 0.100351i
$188$	− 7.37228i	− 0.537679i
$189$	−3.37228	−0.245297
$190$	0	0
$191$	24.3505	1.76194	0.880971	−	0.473170i	$-0.156890\pi$
$191$	24.3505	1.76194	0.880971	+	0.473170i	$0.156890\pi$
$192$	− 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	$0.907034\pi$
$194$	1.25544	0.0901351
$195$	0	0
$196$	4.37228	0.312306
$197$	20.7446i	1.47799i	0.673712	+	0.738994i	$0.264699\pi$
$197$	20.7446i	1.47799i	−0.673712	+	0.738994i	$0.735301\pi$
$198$	− 1.37228i	− 0.0975238i
$199$	−3.88316	−0.275270	−0.137635	−	0.990483i	$-0.543950\pi$
$199$	−3.88316	−0.275270	−0.137635	+	0.990483i	$0.543950\pi$
$200$	0	0
$201$	−5.37228	−0.378932
$202$	4.11684i	0.289660i
$203$	− 9.25544i	− 0.649604i
$204$	1.00000	0.0700140
$205$	0	0
$206$	9.62772	0.670795
$207$	− 4.37228i	− 0.303895i
$208$	2.00000i	0.138675i
$209$	4.62772	0.320106
$210$	0	0
$211$	−24.2337	−1.66832	−0.834158	−	0.551526i	$-0.814046\pi$
$211$	−24.2337	−1.66832	−0.834158	+	0.551526i	$0.814046\pi$
$212$	5.74456i	0.394538i
$213$	4.37228i	0.299584i
$214$	4.62772	0.316344
$215$	0	0
$216$	1.00000	0.0680414
$217$	27.3723i	1.85815i
$218$	− 8.11684i	− 0.549742i
$219$	−8.00000	−0.540590
$220$	0	0
$221$	−2.00000	−0.134535
$222$	1.00000i	0.0671156i
$223$	9.11684i	0.610509i	0.952271	+	0.305255i	$0.0987415\pi$
$223$	9.11684i	0.610509i	−0.952271	+	0.305255i	$0.901258\pi$
$224$	−3.37228	−0.225320
$225$	0	0
$226$	−0.255437	−0.0169914
$227$	− 1.37228i	− 0.0910815i	−0.998962	−	0.0455408i	$-0.985499\pi$
$227$	− 1.37228i	− 0.0910815i	0.998962	−	0.0455408i	$-0.0145011\pi$
$228$	3.37228i	0.223335i
$229$	−22.2337	−1.46924	−0.734622	−	0.678477i	$-0.762640\pi$
$229$	−22.2337	−1.46924	−0.734622	+	0.678477i	$0.762640\pi$
$230$	0	0
$231$	−4.62772	−0.304482
$232$	2.74456i	0.180189i
$233$	− 16.3723i	− 1.07258i	−0.844033	−	0.536292i	$-0.819825\pi$
$233$	− 16.3723i	− 1.07258i	0.844033	−	0.536292i	$-0.180175\pi$
$234$	−2.00000	−0.130744
$235$	0	0
$236$	−7.11684	−0.463267
$237$	− 6.11684i	− 0.397332i
$238$	− 3.37228i	− 0.218593i
$239$	−4.11684	−0.266296	−0.133148	−	0.991096i	$-0.542509\pi$
$239$	−4.11684	−0.266296	−0.133148	+	0.991096i	$0.542509\pi$
$240$	0	0
$241$	−6.23369	−0.401547	−0.200774	−	0.979638i	$-0.564346\pi$
$241$	−6.23369	−0.401547	−0.200774	+	0.979638i	$0.564346\pi$
$242$	9.11684i	0.586053i
$243$	1.00000i	0.0641500i
$244$	−9.11684	−0.583646
$245$	0	0
$246$	4.37228	0.278766
$247$	− 6.74456i	− 0.429146i
$248$	− 8.11684i	− 0.515420i
$249$	4.37228	0.277082
$250$	0	0
$251$	−2.74456	−0.173235	−0.0866176	−	0.996242i	$-0.527606\pi$
$251$	−2.74456	−0.173235	−0.0866176	+	0.996242i	$0.527606\pi$
$252$	− 3.37228i	− 0.212434i
$253$	− 6.00000i	− 0.377217i
$254$	21.4891	1.34835
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 20.2337i	− 1.26214i	−0.775725	−	0.631071i	$-0.782615\pi$
$257$	− 20.2337i	− 1.26214i	0.775725	−	0.631071i	$-0.217385\pi$
$258$	9.37228i	0.583493i
$259$	3.37228	0.209543
$260$	0	0
$261$	−2.74456	−0.169884
$262$	5.48913i	0.339119i
$263$	− 31.3723i	− 1.93450i	−0.253830	−	0.967249i	$-0.581690\pi$
$263$	− 31.3723i	− 1.93450i	0.253830	−	0.967249i	$-0.418310\pi$
$264$	1.37228	0.0844581
$265$	0	0
$266$	11.3723	0.697279
$267$	− 8.74456i	− 0.535159i
$268$	− 5.37228i	− 0.328164i
$269$	11.4891	0.700504	0.350252	−	0.936655i	$-0.386096\pi$
$269$	11.4891	0.700504	0.350252	+	0.936655i	$0.386096\pi$
$270$	0	0
$271$	−8.37228	−0.508580	−0.254290	−	0.967128i	$-0.581842\pi$
$271$	−8.37228	−0.508580	−0.254290	+	0.967128i	$0.581842\pi$
$272$	1.00000i	0.0606339i
$273$	6.74456i	0.408200i
$274$	17.4891	1.05656
$275$	0	0
$276$	4.37228	0.263180
$277$	13.0000i	0.781094i	0.920583	+	0.390547i	$0.127714\pi$
$277$	13.0000i	0.781094i	−0.920583	+	0.390547i	$0.872286\pi$
$278$	0.883156i	0.0529682i
$279$	8.11684	0.485943
$280$	0	0
$281$	23.4891	1.40124	0.700622	−	0.713533i	$-0.252906\pi$
$281$	23.4891	1.40124	0.700622	+	0.713533i	$0.252906\pi$
$282$	7.37228i	0.439013i
$283$	− 5.11684i	− 0.304165i	−0.988368	−	0.152082i	$-0.951402\pi$
$283$	− 5.11684i	− 0.304165i	0.988368	−	0.152082i	$-0.0485979\pi$
$284$	−4.37228	−0.259447
$285$	0	0
$286$	−2.74456	−0.162289
$287$	− 14.7446i	− 0.870344i
$288$	1.00000i	0.0589256i
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	−1.25544	−0.0735950
$292$	− 8.00000i	− 0.468165i
$293$	− 10.8832i	− 0.635801i	−0.948124	−	0.317900i	$-0.897022\pi$
$293$	− 10.8832i	− 0.635801i	0.948124	−	0.317900i	$-0.102978\pi$
$294$	−4.37228	−0.254997
$295$	0	0
$296$	−1.00000	−0.0581238
$297$	1.37228i	0.0796278i
$298$	21.8614i	1.26640i
$299$	−8.74456	−0.505711
$300$	0	0
$301$	31.6060	1.82174
$302$	− 3.11684i	− 0.179354i
$303$	− 4.11684i	− 0.236507i
$304$	−3.37228	−0.193414
$305$	0	0
$306$	−1.00000	−0.0571662
$307$	18.2337i	1.04065i	0.853968	+	0.520326i	$0.174189\pi$
$307$	18.2337i	1.04065i	−0.853968	+	0.520326i	$0.825811\pi$
$308$	− 4.62772i	− 0.263689i
$309$	−9.62772	−0.547702
$310$	0	0
$311$	−10.8832	−0.617127	−0.308564	−	0.951204i	$-0.599848\pi$
$311$	−10.8832	−0.617127	−0.308564	+	0.951204i	$0.599848\pi$
$312$	− 2.00000i	− 0.113228i
$313$	− 6.74456i	− 0.381225i	−0.981665	−	0.190613i	$-0.938953\pi$
$313$	− 6.74456i	− 0.381225i	0.981665	−	0.190613i	$-0.0610474\pi$
$314$	7.25544	0.409448
$315$	0	0
$316$	6.11684	0.344099
$317$	− 3.25544i	− 0.182844i	−0.995812	−	0.0914218i	$-0.970859\pi$
$317$	− 3.25544i	− 0.182844i	0.995812	−	0.0914218i	$-0.0291411\pi$
$318$	− 5.74456i	− 0.322139i
$319$	−3.76631	−0.210873
$320$	0	0
$321$	−4.62772	−0.258294
$322$	− 14.7446i	− 0.821682i
$323$	− 3.37228i	− 0.187639i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	15.1168	0.837245
$327$	8.11684i	0.448862i
$328$	4.37228i	0.241419i
$329$	24.8614	1.37065
$330$	0	0
$331$	−25.6060	−1.40743	−0.703716	−	0.710482i	$-0.748477\pi$
$331$	−25.6060	−1.40743	−0.703716	+	0.710482i	$0.748477\pi$
$332$	4.37228i	0.239960i
$333$	− 1.00000i	− 0.0547997i
$334$	9.25544	0.506435
$335$	0	0
$336$	3.37228	0.183973
$337$	− 10.2337i	− 0.557465i	−0.960369	−	0.278732i	$-0.910086\pi$
$337$	− 10.2337i	− 0.557465i	0.960369	−	0.278732i	$-0.0899142\pi$
$338$	− 9.00000i	− 0.489535i
$339$	0.255437	0.0138735
$340$	0	0
$341$	11.1386	0.603189
$342$	− 3.37228i	− 0.182352i
$343$	− 8.86141i	− 0.478471i
$344$	−9.37228	−0.505320
$345$	0	0
$346$	−12.0000	−0.645124
$347$	− 16.6277i	− 0.892623i	−0.894878	−	0.446311i	$-0.852737\pi$
$347$	− 16.6277i	− 0.892623i	0.894878	−	0.446311i	$-0.147263\pi$
$348$	− 2.74456i	− 0.147124i
$349$	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
$352$	1.37228i	0.0731428i
$353$	− 26.7446i	− 1.42347i	−0.702448	−	0.711735i	$-0.747910\pi$
$353$	− 26.7446i	− 1.42347i	0.702448	−	0.711735i	$-0.252090\pi$
$354$	7.11684	0.378256
$355$	0	0
$356$	8.74456	0.463461
$357$	3.37228i	0.178480i
$358$	7.11684i	0.376137i
$359$	19.3723	1.02243	0.511215	−	0.859453i	$-0.329196\pi$
$359$	19.3723	1.02243	0.511215	+	0.859453i	$0.329196\pi$
$360$	0	0
$361$	−7.62772	−0.401459
$362$	− 22.4891i	− 1.18200i
$363$	− 9.11684i	− 0.478510i
$364$	−6.74456	−0.353511
$365$	0	0
$366$	9.11684	0.476545
$367$	25.6060i	1.33662i	0.743883	+	0.668310i	$0.232982\pi$
$367$	25.6060i	1.33662i	−0.743883	+	0.668310i	$0.767018\pi$
$368$	4.37228i	0.227921i
$369$	−4.37228	−0.227612
$370$	0	0
$371$	−19.3723	−1.00576
$372$	8.11684i	0.420839i
$373$	− 36.2337i	− 1.87611i	−0.346487	−	0.938055i	$-0.612626\pi$
$373$	− 36.2337i	− 1.87611i	0.346487	−	0.938055i	$-0.387374\pi$
$374$	−1.37228	−0.0709590
$375$	0	0
$376$	−7.37228	−0.380196
$377$	5.48913i	0.282704i
$378$	3.37228i	0.173451i
$379$	−20.6060	−1.05846	−0.529229	−	0.848479i	$-0.677519\pi$
$379$	−20.6060	−1.05846	−0.529229	+	0.848479i	$0.677519\pi$
$380$	0	0
$381$	−21.4891	−1.10092
$382$	− 24.3505i	− 1.24588i
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	8.00000	0.407189
$387$	− 9.37228i	− 0.476420i
$388$	− 1.25544i	− 0.0637352i
$389$	−6.25544	−0.317163	−0.158582	−	0.987346i	$-0.550692\pi$
$389$	−6.25544	−0.317163	−0.158582	+	0.987346i	$0.550692\pi$
$390$	0	0
$391$	−4.37228	−0.221116
$392$	− 4.37228i	− 0.220834i
$393$	− 5.48913i	− 0.276890i
$394$	20.7446	1.04510
$395$	0	0
$396$	−1.37228	−0.0689597
$397$	1.00000i	0.0501886i	0.999685	+	0.0250943i	$0.00798860\pi$
$397$	1.00000i	0.0501886i	−0.999685	+	0.0250943i	$0.992011\pi$
$398$	3.88316i	0.194645i
$399$	−11.3723	−0.569326
$400$	0	0
$401$	−13.1168	−0.655024	−0.327512	−	0.944847i	$-0.606210\pi$
$401$	−13.1168	−0.655024	−0.327512	+	0.944847i	$0.606210\pi$
$402$	5.37228i	0.267945i
$403$	− 16.2337i	− 0.808658i
$404$	4.11684	0.204821
$405$	0	0
$406$	−9.25544	−0.459340
$407$	− 1.37228i	− 0.0680215i
$408$	− 1.00000i	− 0.0495074i
$409$	13.8614	0.685402	0.342701	−	0.939444i	$-0.388658\pi$
$409$	13.8614	0.685402	0.342701	+	0.939444i	$0.388658\pi$
$410$	0	0
$411$	−17.4891	−0.862675
$412$	− 9.62772i	− 0.474324i
$413$	− 24.0000i	− 1.18096i
$414$	−4.37228	−0.214886
$415$	0	0
$416$	2.00000	0.0980581
$417$	− 0.883156i	− 0.0432483i
$418$	− 4.62772i	− 0.226349i
$419$	34.9783	1.70880	0.854400	−	0.519616i	$-0.173925\pi$
$419$	34.9783	1.70880	0.854400	+	0.519616i	$0.173925\pi$
$420$	0	0
$421$	16.2337	0.791182	0.395591	−	0.918427i	$-0.370540\pi$
$421$	16.2337	0.791182	0.395591	+	0.918427i	$0.370540\pi$
$422$	24.2337i	1.17968i
$423$	− 7.37228i	− 0.358453i
$424$	5.74456	0.278981
$425$	0	0
$426$	4.37228	0.211838
$427$	− 30.7446i	− 1.48783i
$428$	− 4.62772i	− 0.223689i
$429$	2.74456	0.132509
$430$	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
$433$	23.0951i	1.10988i	0.831891	+	0.554940i	$0.187259\pi$
$433$	23.0951i	1.10988i	−0.831891	+	0.554940i	$0.812741\pi$
$434$	27.3723	1.31391
$435$	0	0
$436$	−8.11684	−0.388726
$437$	− 14.7446i	− 0.705328i
$438$	8.00000i	0.382255i
$439$	−25.4891	−1.21653	−0.608265	−	0.793734i	$-0.708134\pi$
$439$	−25.4891	−1.21653	−0.608265	+	0.793734i	$0.708134\pi$
$440$	0	0
$441$	4.37228	0.208204
$442$	2.00000i	0.0951303i
$443$	− 1.62772i	− 0.0773352i	−0.999252	−	0.0386676i	$-0.987689\pi$
$443$	− 1.62772i	− 0.0773352i	0.999252	−	0.0386676i	$-0.0123114\pi$
$444$	1.00000	0.0474579
$445$	0	0
$446$	9.11684	0.431695
$447$	− 21.8614i	− 1.03401i
$448$	3.37228i	0.159325i
$449$	5.13859	0.242505	0.121253	−	0.992622i	$-0.461309\pi$
$449$	5.13859	0.242505	0.121253	+	0.992622i	$0.461309\pi$
$450$	0	0
$451$	−6.00000	−0.282529
$452$	0.255437i	0.0120148i
$453$	3.11684i	0.146442i
$454$	−1.37228	−0.0644044
$455$	0	0
$456$	3.37228	0.157922
$457$	− 23.0000i	− 1.07589i	−0.842978	−	0.537947i	$-0.819200\pi$
$457$	− 23.0000i	− 1.07589i	0.842978	−	0.537947i	$-0.180800\pi$
$458$	22.2337i	1.03891i
$459$	1.00000	0.0466760
$460$	0	0
$461$	−22.7228	−1.05831	−0.529153	−	0.848526i	$-0.677490\pi$
$461$	−22.7228	−1.05831	−0.529153	+	0.848526i	$0.677490\pi$
$462$	4.62772i	0.215301i
$463$	20.6060i	0.957641i	0.877913	+	0.478820i	$0.158935\pi$
$463$	20.6060i	0.957641i	−0.877913	+	0.478820i	$0.841065\pi$
$464$	2.74456	0.127413
$465$	0	0
$466$	−16.3723	−0.758431
$467$	1.11684i	0.0516814i	0.999666	+	0.0258407i	$0.00822626\pi$
$467$	1.11684i	0.0516814i	−0.999666	+	0.0258407i	$0.991774\pi$
$468$	2.00000i	0.0924500i
$469$	18.1168	0.836558
$470$	0	0
$471$	−7.25544	−0.334313
$472$	7.11684i	0.327579i
$473$	− 12.8614i	− 0.591368i
$474$	−6.11684	−0.280956
$475$	0	0
$476$	−3.37228	−0.154568
$477$	5.74456i	0.263025i
$478$	4.11684i	0.188300i
$479$	−25.7228	−1.17531	−0.587653	−	0.809113i	$-0.699948\pi$
$479$	−25.7228	−1.17531	−0.587653	+	0.809113i	$0.699948\pi$
$480$	0	0
$481$	−2.00000	−0.0911922
$482$	6.23369i	0.283937i
$483$	14.7446i	0.670901i
$484$	9.11684	0.414402
$485$	0	0
$486$	1.00000	0.0453609
$487$	− 22.2337i	− 1.00750i	−0.863848	−	0.503752i	$-0.831952\pi$
$487$	− 22.2337i	− 1.00750i	0.863848	−	0.503752i	$-0.168048\pi$
$488$	9.11684i	0.412700i
$489$	−15.1168	−0.683607
$490$	0	0
$491$	−25.6277	−1.15656	−0.578281	−	0.815837i	$-0.696276\pi$
$491$	−25.6277	−1.15656	−0.578281	+	0.815837i	$0.696276\pi$
$492$	− 4.37228i	− 0.197118i
$493$	2.74456i	0.123609i
$494$	−6.74456	−0.303452
$495$	0	0
$496$	−8.11684	−0.364457
$497$	− 14.7446i	− 0.661384i
$498$	− 4.37228i	− 0.195927i
$499$	−24.3723	−1.09105	−0.545527	−	0.838094i	$-0.683670\pi$
$499$	−24.3723	−1.09105	−0.545527	+	0.838094i	$0.683670\pi$
$500$	0	0
$501$	−9.25544	−0.413502
$502$	2.74456i	0.122496i
$503$	30.6060i	1.36465i	0.731048	+	0.682326i	$0.239032\pi$
$503$	30.6060i	1.36465i	−0.731048	+	0.682326i	$0.760968\pi$
$504$	−3.37228	−0.150213
$505$	0	0
$506$	−6.00000	−0.266733
$507$	9.00000i	0.399704i
$508$	− 21.4891i	− 0.953426i
$509$	25.3723	1.12461	0.562303	−	0.826931i	$-0.309915\pi$
$509$	25.3723	1.12461	0.562303	+	0.826931i	$0.309915\pi$
$510$	0	0
$511$	26.9783	1.19345
$512$	− 1.00000i	− 0.0441942i
$513$	3.37228i	0.148890i
$514$	−20.2337	−0.892470
$515$	0	0
$516$	9.37228	0.412592
$517$	− 10.1168i	− 0.444938i
$518$	− 3.37228i	− 0.148170i
$519$	12.0000	0.526742
$520$	0	0
$521$	24.3505	1.06682	0.533408	−	0.845858i	$-0.320911\pi$
$521$	24.3505	1.06682	0.533408	+	0.845858i	$0.320911\pi$
$522$	2.74456i	0.120126i
$523$	− 18.2337i	− 0.797304i	−0.917102	−	0.398652i	$-0.869478\pi$
$523$	− 18.2337i	− 0.797304i	0.917102	−	0.398652i	$-0.130522\pi$
$524$	5.48913	0.239794
$525$	0	0
$526$	−31.3723	−1.36790
$527$	− 8.11684i	− 0.353575i
$528$	− 1.37228i	− 0.0597209i
$529$	3.88316	0.168833
$530$	0	0
$531$	−7.11684	−0.308845
$532$	− 11.3723i	− 0.493051i
$533$	8.74456i	0.378769i
$534$	−8.74456	−0.378414
$535$	0	0
$536$	−5.37228	−0.232047
$537$	− 7.11684i	− 0.307114i
$538$	− 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	$0.465721\pi$
$542$	8.37228i	0.359620i
$543$	22.4891i	0.965101i
$544$	1.00000	0.0428746
$545$	0	0
$546$	6.74456	0.288641
$547$	− 36.3723i	− 1.55517i	−0.628780	−	0.777583i	$-0.716445\pi$
$547$	− 36.3723i	− 1.55517i	0.628780	−	0.777583i	$-0.283555\pi$
$548$	− 17.4891i	− 0.747098i
$549$	−9.11684	−0.389097
$550$	0	0
$551$	−9.25544	−0.394295
$552$	− 4.37228i	− 0.186097i
$553$	20.6277i	0.877180i
$554$	13.0000	0.552317
$555$	0	0
$556$	0.883156	0.0374542
$557$	35.7446i	1.51455i	0.653099	+	0.757273i	$0.273469\pi$
$557$	35.7446i	1.51455i	−0.653099	+	0.757273i	$0.726531\pi$
$558$	− 8.11684i	− 0.343613i
$559$	−18.7446	−0.792811
$560$	0	0
$561$	1.37228	0.0579378
$562$	− 23.4891i	− 0.990829i
$563$	− 33.3505i	− 1.40556i	−0.711409	−	0.702779i	$-0.751942\pi$
$563$	− 33.3505i	− 1.40556i	0.711409	−	0.702779i	$-0.248058\pi$
$564$	7.37228	0.310429
$565$	0	0
$566$	−5.11684	−0.215077
$567$	− 3.37228i	− 0.141623i
$568$	4.37228i	0.183457i
$569$	20.7446	0.869657	0.434829	−	0.900513i	$-0.356809\pi$
$569$	20.7446	0.869657	0.434829	+	0.900513i	$0.356809\pi$
$570$	0	0
$571$	−38.3723	−1.60583	−0.802915	−	0.596094i	$-0.796719\pi$
$571$	−38.3723	−1.60583	−0.802915	+	0.596094i	$0.796719\pi$
$572$	2.74456i	0.114756i
$573$	24.3505i	1.01726i
$574$	−14.7446	−0.615426
$575$	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
$581$	−14.7446	−0.611708
$582$	1.25544i	0.0520396i
$583$	7.88316i	0.326487i
$584$	−8.00000	−0.331042
$585$	0	0
$586$	−10.8832	−0.449579
$587$	− 2.13859i	− 0.0882692i	−0.999026	−	0.0441346i	$-0.985947\pi$
$587$	− 2.13859i	− 0.0882692i	0.999026	−	0.0441346i	$-0.0140530\pi$
$588$	4.37228i	0.180310i
$589$	27.3723	1.12786
$590$	0	0
$591$	−20.7446	−0.853317
$592$	1.00000i	0.0410997i
$593$	28.4674i	1.16902i	0.811388	+	0.584508i	$0.198712\pi$
$593$	28.4674i	1.16902i	−0.811388	+	0.584508i	$0.801288\pi$
$594$	1.37228	0.0563054
$595$	0	0
$596$	21.8614	0.895478
$597$	− 3.88316i	− 0.158927i
$598$	8.74456i	0.357592i
$599$	7.37228	0.301223	0.150612	−	0.988593i	$-0.451876\pi$
$599$	7.37228	0.301223	0.150612	+	0.988593i	$0.451876\pi$
$600$	0	0
$601$	−8.97825	−0.366230	−0.183115	−	0.983091i	$-0.558618\pi$
$601$	−8.97825	−0.366230	−0.183115	+	0.983091i	$0.558618\pi$
$602$	− 31.6060i	− 1.28816i
$603$	− 5.37228i	− 0.218776i
$604$	−3.11684	−0.126823
$605$	0	0
$606$	−4.11684	−0.167235
$607$	− 5.76631i	− 0.234047i	−0.993129	−	0.117024i	$-0.962665\pi$
$607$	− 5.76631i	− 0.234047i	0.993129	−	0.117024i	$-0.0373353\pi$
$608$	3.37228i	0.136764i
$609$	9.25544	0.375049
$610$	0	0
$611$	−14.7446	−0.596501
$612$	1.00000i	0.0404226i
$613$	19.4891i	0.787158i	0.919291	+	0.393579i	$0.128763\pi$
$613$	19.4891i	0.787158i	−0.919291	+	0.393579i	$0.871237\pi$
$614$	18.2337	0.735852
$615$	0	0
$616$	−4.62772	−0.186456
$617$	29.8397i	1.20130i	0.799512	+	0.600650i	$0.205091\pi$
$617$	29.8397i	1.20130i	−0.799512	+	0.600650i	$0.794909\pi$
$618$	9.62772i	0.387284i
$619$	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
$621$	4.37228	0.175454
$622$	10.8832i	0.436375i
$623$	29.4891i	1.18146i
$624$	−2.00000	−0.0800641
$625$	0	0
$626$	−6.74456	−0.269567
$627$	4.62772i	0.184813i
$628$	− 7.25544i	− 0.289523i
$629$	−1.00000	−0.0398726
$630$	0	0
$631$	−6.13859	−0.244374	−0.122187	−	0.992507i	$-0.538991\pi$
$631$	−6.13859	−0.244374	−0.122187	+	0.992507i	$0.538991\pi$
$632$	− 6.11684i	− 0.243315i
$633$	− 24.2337i	− 0.963203i
$634$	−3.25544	−0.129290
$635$	0	0
$636$	−5.74456	−0.227787
$637$	− 8.74456i	− 0.346472i
$638$	3.76631i	0.149110i
$639$	−4.37228	−0.172965
$640$	0	0
$641$	−4.97825	−0.196629	−0.0983145	−	0.995155i	$-0.531345\pi$
$641$	−4.97825	−0.196629	−0.0983145	+	0.995155i	$0.531345\pi$
$642$	4.62772i	0.182641i
$643$	6.88316i	0.271445i	0.990747	+	0.135723i	$0.0433356\pi$
$643$	6.88316i	0.271445i	−0.990747	+	0.135723i	$0.956664\pi$
$644$	−14.7446	−0.581017
$645$	0	0
$646$	−3.37228	−0.132681
$647$	− 31.7228i	− 1.24715i	−0.781763	−	0.623576i	$-0.785679\pi$
$647$	− 31.7228i	− 1.24715i	0.781763	−	0.623576i	$-0.214321\pi$
$648$	1.00000i	0.0392837i
$649$	−9.76631	−0.383361
$650$	0	0
$651$	−27.3723	−1.07280
$652$	− 15.1168i	− 0.592021i
$653$	22.9783i	0.899208i	0.893228	+	0.449604i	$0.148435\pi$
$653$	22.9783i	0.899208i	−0.893228	+	0.449604i	$0.851565\pi$
$654$	8.11684	0.317394
$655$	0	0
$656$	4.37228	0.170709
$657$	− 8.00000i	− 0.312110i
$658$	− 24.8614i	− 0.969199i
$659$	−29.4891	−1.14873	−0.574367	−	0.818598i	$-0.694752\pi$
$659$	−29.4891	−1.14873	−0.574367	+	0.818598i	$0.694752\pi$
$660$	0	0
$661$	−24.7446	−0.962452	−0.481226	−	0.876597i	$-0.659808\pi$
$661$	−24.7446	−0.962452	−0.481226	+	0.876597i	$0.659808\pi$
$662$	25.6060i	0.995204i
$663$	− 2.00000i	− 0.0776736i
$664$	4.37228	0.169677
$665$	0	0
$666$	−1.00000	−0.0387492
$667$	12.0000i	0.464642i
$668$	− 9.25544i	− 0.358104i
$669$	−9.11684	−0.352478
$670$	0	0
$671$	−12.5109	−0.482977
$672$	− 3.37228i	− 0.130089i
$673$	− 17.7228i	− 0.683164i	−0.939852	−	0.341582i	$-0.889037\pi$
$673$	− 17.7228i	− 0.683164i	0.939852	−	0.341582i	$-0.110963\pi$
$674$	−10.2337	−0.394187
$675$	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	$0.847420\pi$
$678$	− 0.255437i	− 0.00981001i
$679$	4.23369	0.162474
$680$	0	0
$681$	1.37228	0.0525859
$682$	− 11.1386i	− 0.426519i
$683$	20.7446i	0.793769i	0.917869	+	0.396884i	$0.129909\pi$
$683$	20.7446i	0.793769i	−0.917869	+	0.396884i	$0.870091\pi$
$684$	−3.37228	−0.128942
$685$	0	0
$686$	−8.86141	−0.338330
$687$	− 22.2337i	− 0.848268i
$688$	9.37228i	0.357315i
$689$	11.4891	0.437701
$690$	0	0
$691$	33.6277	1.27926	0.639629	−	0.768683i	$-0.279088\pi$
$691$	33.6277	1.27926	0.639629	+	0.768683i	$0.279088\pi$
$692$	12.0000i	0.456172i
$693$	− 4.62772i	− 0.175792i
$694$	−16.6277	−0.631180
$695$	0	0
$696$	−2.74456	−0.104032
$697$	4.37228i	0.165612i
$698$	− 10.0000i	− 0.378506i
$699$	16.3723	0.619257
$700$	0	0
$701$	−30.6060	−1.15597	−0.577986	−	0.816047i	$-0.696161\pi$
$701$	−30.6060	−1.15597	−0.577986	+	0.816047i	$0.696161\pi$
$702$	− 2.00000i	− 0.0754851i
$703$	− 3.37228i	− 0.127188i
$704$	1.37228	0.0517198
$705$	0	0
$706$	−26.7446	−1.00654
$707$	13.8832i	0.522130i
$708$	− 7.11684i	− 0.267467i
$709$	2.62772	0.0986860	0.0493430	−	0.998782i	$-0.484287\pi$
$709$	2.62772	0.0986860	0.0493430	+	0.998782i	$0.484287\pi$
$710$	0	0
$711$	6.11684	0.229400
$712$	− 8.74456i	− 0.327716i
$713$	− 35.4891i	− 1.32908i
$714$	3.37228	0.126204
$715$	0	0
$716$	7.11684	0.265969
$717$	− 4.11684i	− 0.153746i
$718$	− 19.3723i	− 0.722967i
$719$	38.7446	1.44493	0.722464	−	0.691408i	$-0.243009\pi$
$719$	38.7446	1.44493	0.722464	+	0.691408i	$0.243009\pi$
$720$	0	0
$721$	32.4674	1.20915
$722$	7.62772i	0.283874i
$723$	− 6.23369i	− 0.231833i
$724$	−22.4891	−0.835802
$725$	0	0
$726$	−9.11684	−0.338358
$727$	42.7446i	1.58531i	0.609672	+	0.792654i	$0.291301\pi$
$727$	42.7446i	1.58531i	−0.609672	+	0.792654i	$0.708699\pi$
$728$	6.74456i	0.249970i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−9.37228	−0.346646
$732$	− 9.11684i	− 0.336968i
$733$	− 12.7446i	− 0.470731i	−0.971907	−	0.235366i	$-0.924371\pi$
$733$	− 12.7446i	− 0.470731i	0.971907	−	0.235366i	$-0.0756287\pi$
$734$	25.6060	0.945134
$735$	0	0
$736$	4.37228	0.161164
$737$	− 7.37228i	− 0.271561i
$738$	4.37228i	0.160946i
$739$	−39.3723	−1.44833	−0.724166	−	0.689625i	$-0.757775\pi$
$739$	−39.3723	−1.44833	−0.724166	+	0.689625i	$0.757775\pi$
$740$	0	0
$741$	6.74456	0.247768
$742$	19.3723i	0.711179i
$743$	28.3723i	1.04088i	0.853899	+	0.520439i	$0.174232\pi$
$743$	28.3723i	1.04088i	−0.853899	+	0.520439i	$0.825768\pi$
$744$	8.11684	0.297578
$745$	0	0
$746$	−36.2337	−1.32661
$747$	4.37228i	0.159973i
$748$	1.37228i	0.0501756i
$749$	15.6060	0.570230
$750$	0	0
$751$	36.4674	1.33071	0.665357	−	0.746526i	$-0.268279\pi$
$751$	36.4674	1.33071	0.665357	+	0.746526i	$0.268279\pi$
$752$	7.37228i	0.268839i
$753$	− 2.74456i	− 0.100017i
$754$	5.48913	0.199902
$755$	0	0
$756$	3.37228	0.122649
$757$	0.233688i	0.00849353i	0.999991	+	0.00424677i	$0.00135179\pi$
$757$	0.233688i	0.00849353i	−0.999991	+	0.00424677i	$0.998648\pi$
$758$	20.6060i	0.748443i
$759$	6.00000	0.217786
$760$	0	0
$761$	5.48913	0.198981	0.0994903	−	0.995039i	$-0.468279\pi$
$761$	5.48913	0.198981	0.0994903	+	0.995039i	$0.468279\pi$
$762$	21.4891i	0.778469i
$763$	− 27.3723i	− 0.990943i
$764$	−24.3505	−0.880971
$765$	0	0
$766$	0	0
$767$	14.2337i	0.513949i
$768$	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
$771$	20.2337	0.728698
$772$	− 8.00000i	− 0.287926i
$773$	− 45.8614i	− 1.64952i	−0.565483	−	0.824760i	$-0.691310\pi$
$773$	− 45.8614i	− 1.64952i	0.565483	−	0.824760i	$-0.308690\pi$
$774$	−9.37228	−0.336880
$775$	0	0
$776$	−1.25544	−0.0450676
$777$	3.37228i	0.120980i
$778$	6.25544i	0.224268i
$779$	−14.7446	−0.528279
$780$	0	0
$781$	−6.00000	−0.214697
$782$	4.37228i	0.156352i
$783$	− 2.74456i	− 0.0980827i
$784$	−4.37228	−0.156153
$785$	0	0
$786$	−5.48913	−0.195791
$787$	7.35053i	0.262018i	0.991381	+	0.131009i	$0.0418217\pi$
$787$	7.35053i	0.262018i	−0.991381	+	0.131009i	$0.958178\pi$
$788$	− 20.7446i	− 0.738994i
$789$	31.3723	1.11688
$790$	0	0
$791$	−0.861407	−0.0306281
$792$	1.37228i	0.0487619i
$793$	18.2337i	0.647497i
$794$	1.00000	0.0354887
$795$	0	0
$796$	3.88316	0.137635
$797$	− 17.7446i	− 0.628545i	−0.949333	−	0.314272i	$-0.898239\pi$
$797$	− 17.7446i	− 0.628545i	0.949333	−	0.314272i	$-0.101761\pi$
$798$	11.3723i	0.402574i
$799$	−7.37228	−0.260813
$800$	0	0
$801$	8.74456	0.308974
$802$	13.1168i	0.463172i
$803$	− 10.9783i	− 0.387414i
$804$	5.37228	0.189466
$805$	0	0
$806$	−16.2337	−0.571807
$807$	11.4891i	0.404436i
$808$	− 4.11684i	− 0.144830i
$809$	21.6060	0.759625	0.379813	−	0.925063i	$-0.375988\pi$
$809$	21.6060	0.759625	0.379813	+	0.925063i	$0.375988\pi$
$810$	0	0
$811$	44.0000	1.54505	0.772524	−	0.634985i	$-0.218994\pi$
$811$	44.0000	1.54505	0.772524	+	0.634985i	$0.218994\pi$
$812$	9.25544i	0.324802i
$813$	− 8.37228i	− 0.293629i
$814$	−1.37228	−0.0480984
$815$	0	0
$816$	−1.00000	−0.0350070
$817$	− 31.6060i	− 1.10575i
$818$	− 13.8614i	− 0.484653i
$819$	−6.74456	−0.235674
$820$	0	0
$821$	−33.2554	−1.16062	−0.580311	−	0.814395i	$-0.697069\pi$
$821$	−33.2554	−1.16062	−0.580311	+	0.814395i	$0.697069\pi$
$822$	17.4891i	0.610003i
$823$	48.4674i	1.68947i	0.535188	+	0.844733i	$0.320241\pi$
$823$	48.4674i	1.68947i	−0.535188	+	0.844733i	$0.679759\pi$
$824$	−9.62772	−0.335397
$825$	0	0
$826$	−24.0000	−0.835067
$827$	− 51.0951i	− 1.77675i	−0.459118	−	0.888375i	$-0.651835\pi$
$827$	− 51.0951i	− 1.77675i	0.459118	−	0.888375i	$-0.348165\pi$
$828$	4.37228i	0.151947i
$829$	−29.2554	−1.01608	−0.508042	−	0.861332i	$-0.669630\pi$
$829$	−29.2554	−1.01608	−0.508042	+	0.861332i	$0.669630\pi$
$830$	0	0
$831$	−13.0000	−0.450965
$832$	− 2.00000i	− 0.0693375i
$833$	− 4.37228i	− 0.151491i
$834$	−0.883156	−0.0305812
$835$	0	0
$836$	−4.62772	−0.160053
$837$	8.11684i	0.280559i
$838$	− 34.9783i	− 1.20830i
$839$	−1.62772	−0.0561951	−0.0280975	−	0.999605i	$-0.508945\pi$
$839$	−1.62772	−0.0561951	−0.0280975	+	0.999605i	$0.508945\pi$
$840$	0	0
$841$	−21.4674	−0.740254
$842$	− 16.2337i	− 0.559450i
$843$	23.4891i	0.809008i
$844$	24.2337	0.834158
$845$	0	0
$846$	−7.37228	−0.253464
$847$	30.7446i	1.05640i
$848$	− 5.74456i	− 0.197269i
$849$	5.11684	0.175610
$850$	0	0
$851$	−4.37228	−0.149880
$852$	− 4.37228i	− 0.149792i
$853$	− 10.8614i	− 0.371887i	−0.982560	−	0.185944i	$-0.940466\pi$
$853$	− 10.8614i	− 0.371887i	0.982560	−	0.185944i	$-0.0595342\pi$
$854$	−30.7446	−1.05206
$855$	0	0
$856$	−4.62772	−0.158172
$857$	− 29.7446i	− 1.01605i	−0.861341	−	0.508027i	$-0.830375\pi$
$857$	− 29.7446i	− 1.01605i	0.861341	−	0.508027i	$-0.169625\pi$
$858$	− 2.74456i	− 0.0936978i
$859$	−38.3505	−1.30850	−0.654252	−	0.756277i	$-0.727016\pi$
$859$	−38.3505	−1.30850	−0.654252	+	0.756277i	$0.727016\pi$
$860$	0	0
$861$	14.7446	0.502493
$862$	− 12.0000i	− 0.408722i
$863$	− 19.3723i	− 0.659440i	−0.944079	−	0.329720i	$-0.893046\pi$
$863$	− 19.3723i	− 0.659440i	0.944079	−	0.329720i	$-0.106954\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	23.0951	0.784803
$867$	− 1.00000i	− 0.0339618i
$868$	− 27.3723i	− 0.929076i
$869$	8.39403	0.284748
$870$	0	0
$871$	−10.7446	−0.364066
$872$	8.11684i	0.274871i
$873$	− 1.25544i	− 0.0424901i
$874$	−14.7446	−0.498742
$875$	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	$0.716915\pi$
$878$	25.4891i	0.860216i
$879$	10.8832	0.367080
$880$	0	0
$881$	46.2119	1.55692	0.778460	−	0.627694i	$-0.216001\pi$
$881$	46.2119	1.55692	0.778460	+	0.627694i	$0.216001\pi$
$882$	− 4.37228i	− 0.147222i
$883$	− 42.2337i	− 1.42128i	−0.703557	−	0.710638i	$-0.748406\pi$
$883$	− 42.2337i	− 1.42128i	0.703557	−	0.710638i	$-0.251594\pi$
$884$	2.00000	0.0672673
$885$	0	0
$886$	−1.62772	−0.0546843
$887$	0.605969i	0.0203465i	0.999948	+	0.0101732i	$0.00323829\pi$
$887$	0.605969i	0.0203465i	−0.999948	+	0.0101732i	$0.996762\pi$
$888$	− 1.00000i	− 0.0335578i
$889$	72.4674	2.43048
$890$	0	0
$891$	−1.37228	−0.0459732
$892$	− 9.11684i	− 0.305255i
$893$	− 24.8614i	− 0.831955i
$894$	−21.8614	−0.731155
$895$	0	0
$896$	3.37228	0.112660
$897$	− 8.74456i	− 0.291972i
$898$	− 5.13859i	− 0.171477i
$899$	−22.2772	−0.742986
$900$	0	0
$901$	5.74456	0.191379
$902$	6.00000i	0.199778i
$903$	31.6060i	1.05178i
$904$	0.255437	0.00849572
$905$	0	0
$906$	3.11684	0.103550
$907$	− 50.6060i	− 1.68034i	−0.542320	−	0.840172i	$-0.682454\pi$
$907$	− 50.6060i	− 1.68034i	0.542320	−	0.840172i	$-0.317546\pi$
$908$	1.37228i	0.0455408i
$909$	4.11684	0.136547
$910$	0	0
$911$	−29.4891	−0.977018	−0.488509	−	0.872559i	$-0.662459\pi$
$911$	−29.4891	−0.977018	−0.488509	+	0.872559i	$0.662459\pi$
$912$	− 3.37228i	− 0.111667i
$913$	6.00000i	0.198571i
$914$	−23.0000	−0.760772
$915$	0	0
$916$	22.2337	0.734622
$917$	18.5109i	0.611283i
$918$	− 1.00000i	− 0.0330049i
$919$	−43.5842	−1.43771	−0.718855	−	0.695160i	$-0.755334\pi$
$919$	−43.5842	−1.43771	−0.718855	+	0.695160i	$0.755334\pi$
$920$	0	0
$921$	−18.2337	−0.600820
$922$	22.7228i	0.748336i
$923$	8.74456i	0.287831i
$924$	4.62772	0.152241
$925$	0	0
$926$	20.6060	0.677154
$927$	− 9.62772i	− 0.316216i
$928$	− 2.74456i	− 0.0900947i
$929$	−16.7228	−0.548658	−0.274329	−	0.961636i	$-0.588456\pi$
$929$	−16.7228	−0.548658	−0.274329	+	0.961636i	$0.588456\pi$
$930$	0	0
$931$	14.7446	0.483234
$932$	16.3723i	0.536292i
$933$	− 10.8832i	− 0.356299i
$934$	1.11684	0.0365443
$935$	0	0
$936$	2.00000	0.0653720
$937$	− 1.39403i	− 0.0455410i	−0.999741	−	0.0227705i	$-0.992751\pi$
$937$	− 1.39403i	− 0.0455410i	0.999741	−	0.0227705i	$-0.00724870\pi$
$938$	− 18.1168i	− 0.591536i
$939$	6.74456	0.220100
$940$	0	0
$941$	46.4674	1.51479	0.757397	−	0.652955i	$-0.226471\pi$
$941$	46.4674	1.51479	0.757397	+	0.652955i	$0.226471\pi$
$942$	7.25544i	0.236395i
$943$	19.1168i	0.622530i
$944$	7.11684	0.231634
$945$	0	0
$946$	−12.8614	−0.418160
$947$	− 28.6277i	− 0.930276i	−0.885238	−	0.465138i	$-0.846005\pi$
$947$	− 28.6277i	− 0.930276i	0.885238	−	0.465138i	$-0.153995\pi$
$948$	6.11684i	0.198666i
$949$	−16.0000	−0.519382
$950$	0	0
$951$	3.25544	0.105565
$952$	3.37228i	0.109296i
$953$	− 4.97825i	− 0.161261i	−0.996744	−	0.0806307i	$-0.974307\pi$
$953$	− 4.97825i	− 0.161261i	0.996744	−	0.0806307i	$-0.0256934\pi$
$954$	5.74456	0.185987
$955$	0	0
$956$	4.11684	0.133148
$957$	− 3.76631i	− 0.121748i
$958$	25.7228i	0.831066i
$959$	58.9783	1.90451
$960$	0	0
$961$	34.8832	1.12526
$962$	2.00000i	0.0644826i
$963$	− 4.62772i	− 0.149126i
$964$	6.23369	0.200774
$965$	0	0
$966$	14.7446	0.474399
$967$	− 29.3505i	− 0.943849i	−0.881639	−	0.471925i	$-0.843559\pi$
$967$	− 29.3505i	− 0.943849i	0.881639	−	0.471925i	$-0.156441\pi$
$968$	− 9.11684i	− 0.293026i
$969$	3.37228	0.108333
$970$	0	0
$971$	21.8614	0.701566	0.350783	−	0.936457i	$-0.385915\pi$
$971$	21.8614	0.701566	0.350783	+	0.936457i	$0.385915\pi$
$972$	− 1.00000i	− 0.0320750i
$973$	2.97825i	0.0954783i
$974$	−22.2337	−0.712413
$975$	0	0
$976$	9.11684	0.291823
$977$	− 6.00000i	− 0.191957i	−0.995383	−	0.0959785i	$-0.969402\pi$
$977$	− 6.00000i	− 0.191957i	0.995383	−	0.0959785i	$-0.0305980\pi$
$978$	15.1168i	0.483383i
$979$	12.0000	0.383522
$980$	0	0
$981$	−8.11684	−0.259151
$982$	25.6277i	0.817813i
$983$	44.2337i	1.41084i	0.708792	+	0.705418i	$0.249241\pi$
$983$	44.2337i	1.41084i	−0.708792	+	0.705418i	$0.750759\pi$
$984$	−4.37228	−0.139383
$985$	0	0
$986$	2.74456	0.0874047
$987$	24.8614i	0.791347i
$988$	6.74456i	0.214573i
$989$	−40.9783	−1.30303
$990$	0	0
$991$	−8.46738	−0.268975	−0.134488	−	0.990915i	$-0.542939\pi$
$991$	−8.46738	−0.268975	−0.134488	+	0.990915i	$0.542939\pi$
$992$	8.11684i	0.257710i
$993$	− 25.6060i	− 0.812581i
$994$	−14.7446	−0.467669
$995$	0	0
$996$	−4.37228	−0.138541
$997$	− 15.8832i	− 0.503025i	−0.967854	−	0.251512i	$-0.919072\pi$
$997$	− 15.8832i	− 0.503025i	0.967854	−	0.251512i	$-0.0809279\pi$
$998$	24.3723i	0.771491i
$999$	1.00000	0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2550.2.d.v.2449.1		4
5.2	odd	4		2550.2.a.bm.1.2	yes	2
5.3	odd	4		2550.2.a.bg.1.1	✓	2
5.4	even	2	inner	2550.2.d.v.2449.4		4
15.2	even	4		7650.2.a.cv.1.2		2
15.8	even	4		7650.2.a.df.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2550.2.a.bg.1.1	✓	2	5.3	odd	4
2550.2.a.bm.1.2	yes	2	5.2	odd	4
2550.2.d.v.2449.1		4	1.1	even	1	trivial
2550.2.d.v.2449.4		4	5.4	even	2	inner
7650.2.a.cv.1.2		2	15.2	even	4
7650.2.a.df.1.1		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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} -3.37228i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} -3.37228i q^{7} +1.00000i q^{8} -1.00000 q^{9} -1.37228 q^{11} -1.00000i q^{12} +2.00000i q^{13} -3.37228 q^{14} +1.00000 q^{16} +1.00000i q^{17} +1.00000i q^{18} -3.37228 q^{19} +3.37228 q^{21} +1.37228i q^{22} +4.37228i q^{23} -1.00000 q^{24} +2.00000 q^{26} -1.00000i q^{27} +3.37228i q^{28} +2.74456 q^{29} -8.11684 q^{31} -1.00000i q^{32} -1.37228i q^{33} +1.00000 q^{34} +1.00000 q^{36} +1.00000i q^{37} +3.37228i q^{38} -2.00000 q^{39} +4.37228 q^{41} -3.37228i q^{42} +9.37228i q^{43} +1.37228 q^{44} +4.37228 q^{46} +7.37228i q^{47} +1.00000i q^{48} -4.37228 q^{49} -1.00000 q^{51} -2.00000i q^{52} -5.74456i q^{53} -1.00000 q^{54} +3.37228 q^{56} -3.37228i q^{57} -2.74456i q^{58} +7.11684 q^{59} +9.11684 q^{61} +8.11684i q^{62} +3.37228i q^{63} -1.00000 q^{64} -1.37228 q^{66} +5.37228i q^{67} -1.00000i q^{68} -4.37228 q^{69} +4.37228 q^{71} -1.00000i q^{72} +8.00000i q^{73} +1.00000 q^{74} +3.37228 q^{76} +4.62772i q^{77} +2.00000i q^{78} -6.11684 q^{79} +1.00000 q^{81} -4.37228i q^{82} -4.37228i q^{83} -3.37228 q^{84} +9.37228 q^{86} +2.74456i q^{87} -1.37228i q^{88} -8.74456 q^{89} +6.74456 q^{91} -4.37228i q^{92} -8.11684i q^{93} +7.37228 q^{94} +1.00000 q^{96} +1.25544i q^{97} +4.37228i q^{98} +1.37228 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9}+O(q^{10}) \) 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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