LMFDB - Embedded newform 1450.2.b.j.349.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1450,2,Mod(349,1450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1450, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1450.349");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1450 = 2 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1450.b (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:	$11.5783082931$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.14077504.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 11x^{4} + 33x^{2} + 16 $ x^6 + 11x^4 + 33x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 290)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			349.3
Root			$2.39138i$ of defining polynomial
Character	$\chi$	$=$	1450.349
Dual form			1450.2.b.j.349.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.71871i q^{3} -1.00000 q^{4} +1.71871 q^{6} +2.39138i q^{7} +1.00000i q^{8} +0.0460370 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.71871i q^{3} -1.00000 q^{4} +1.71871 q^{6} +2.39138i q^{7} +1.00000i q^{8} +0.0460370 q^{9} +4.78276 q^{11} -1.71871i q^{12} -4.50147i q^{13} +2.39138 q^{14} +1.00000 q^{16} -0.391382i q^{17} -0.0460370i q^{18} +3.43742 q^{19} -4.11009 q^{21} -4.78276i q^{22} -1.71871i q^{23} -1.71871 q^{24} -4.50147 q^{26} +5.23525i q^{27} -2.39138i q^{28} -1.00000 q^{29} -3.73673 q^{31} -1.00000i q^{32} +8.22018i q^{33} -0.391382 q^{34} -0.0460370 q^{36} -2.78276i q^{37} -3.43742i q^{38} +7.73673 q^{39} +6.78276 q^{41} +4.11009i q^{42} +11.9569i q^{43} -4.78276 q^{44} -1.71871 q^{46} +8.00000i q^{47} +1.71871i q^{48} +1.28129 q^{49} +0.672673 q^{51} +4.50147i q^{52} -5.17415i q^{53} +5.23525 q^{54} -2.39138 q^{56} +5.90793i q^{57} +1.00000i q^{58} +9.93889 q^{59} +3.71871 q^{61} +3.73673i q^{62} +0.110092i q^{63} -1.00000 q^{64} +8.22018 q^{66} +6.87484i q^{67} +0.391382i q^{68} +2.95396 q^{69} +6.87484 q^{71} +0.0460370i q^{72} +5.70069i q^{73} -2.78276 q^{74} -3.43742 q^{76} +11.4374i q^{77} -7.73673i q^{78} -9.19217 q^{79} -8.85977 q^{81} -6.78276i q^{82} -4.56258i q^{83} +4.11009 q^{84} +11.9569 q^{86} -1.71871i q^{87} +4.78276i q^{88} -15.0029 q^{89} +10.7647 q^{91} +1.71871i q^{92} -6.42235i q^{93} +8.00000 q^{94} +1.71871 q^{96} -9.06406i q^{97} -1.28129i q^{98} +0.220184 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 2 q^{6} - 12 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 - 2 * q^6 - 12 * q^9	$ 6 q - 6 q^{4} - 2 q^{6} - 12 q^{9} + 4 q^{11} + 2 q^{14} + 6 q^{16} - 4 q^{19} + 2 q^{24} + 10 q^{26} - 6 q^{29} - 10 q^{31} + 10 q^{34} + 12 q^{36} + 34 q^{39} + 16 q^{41} - 4 q^{44} + 2 q^{46} + 20 q^{49} + 4 q^{51} + 56 q^{54} - 2 q^{56} - 2 q^{59} + 10 q^{61} - 6 q^{64} + 30 q^{69} - 8 q^{71} + 8 q^{74} + 4 q^{76} - 18 q^{79} + 70 q^{81} + 10 q^{86} - 16 q^{89} + 40 q^{91} + 48 q^{94} - 2 q^{96} - 48 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 - 2 * q^6 - 12 * q^9 + 4 * q^11 + 2 * q^14 + 6 * q^16 - 4 * q^19 + 2 * q^24 + 10 * q^26 - 6 * q^29 - 10 * q^31 + 10 * q^34 + 12 * q^36 + 34 * q^39 + 16 * q^41 - 4 * q^44 + 2 * q^46 + 20 * q^49 + 4 * q^51 + 56 * q^54 - 2 * q^56 - 2 * q^59 + 10 * q^61 - 6 * q^64 + 30 * q^69 - 8 * q^71 + 8 * q^74 + 4 * q^76 - 18 * q^79 + 70 * q^81 + 10 * q^86 - 16 * q^89 + 40 * q^91 + 48 * q^94 - 2 * q^96 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1450\mathbb{Z}\right)^\times$.

$n$	$901$	$1277$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$	− 1.00000i	− 0.707107i
$2$	− 1.00000i	− 0.707107i
$3$	1.71871i	0.992298i	0.868238	+	0.496149i	$0.165253\pi$
$3$	1.71871i	0.992298i	−0.868238	+	0.496149i	$0.834747\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	1.71871	0.701660
$7$	2.39138i	0.903858i	0.892054	+	0.451929i	$0.149264\pi$
$7$	2.39138i	0.903858i	−0.892054	+	0.451929i	$0.850736\pi$
$8$	1.00000i	0.353553i
$9$	0.0460370	0.0153457
$10$	0	0
$11$	4.78276	1.44206	0.721029	−	0.692905i	$-0.243669\pi$
$11$	4.78276	1.44206	0.721029	+	0.692905i	$0.243669\pi$
$12$	− 1.71871i	− 0.496149i
$13$	− 4.50147i	− 1.24848i	−0.781231	−	0.624242i	$-0.785408\pi$
$13$	− 4.50147i	− 1.24848i	0.781231	−	0.624242i	$-0.214592\pi$
$14$	2.39138	0.639124
$15$	0	0
$16$	1.00000	0.250000
$17$	− 0.391382i	− 0.0949242i	−0.998873	−	0.0474621i	$-0.984887\pi$
$17$	− 0.391382i	− 0.0949242i	0.998873	−	0.0474621i	$-0.0151133\pi$
$18$	− 0.0460370i	− 0.0108510i
$19$	3.43742	0.788598	0.394299	−	0.918982i	$-0.370987\pi$
$19$	3.43742	0.788598	0.394299	+	0.918982i	$0.370987\pi$
$20$	0	0
$21$	−4.11009	−0.896896
$22$	− 4.78276i	− 1.01969i
$23$	− 1.71871i	− 0.358376i	−0.983815	−	0.179188i	$-0.942653\pi$
$23$	− 1.71871i	− 0.358376i	0.983815	−	0.179188i	$-0.0573470\pi$
$24$	−1.71871	−0.350830
$25$	0	0
$26$	−4.50147	−0.882812
$27$	5.23525i	1.00752i
$28$	− 2.39138i	− 0.451929i
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0	0
$31$	−3.73673	−0.671136	−0.335568	−	0.942016i	$-0.608928\pi$
$31$	−3.73673	−0.671136	−0.335568	+	0.942016i	$0.608928\pi$
$32$	− 1.00000i	− 0.176777i
$33$	8.22018i	1.43095i
$34$	−0.391382	−0.0671215
$35$	0	0
$36$	−0.0460370	−0.00767283
$37$	− 2.78276i	− 0.457484i	−0.973487	−	0.228742i	$-0.926539\pi$
$37$	− 2.78276i	− 0.457484i	0.973487	−	0.228742i	$-0.0734612\pi$
$38$	− 3.43742i	− 0.557623i
$39$	7.73673	1.23887
$40$	0	0
$41$	6.78276	1.05929	0.529645	−	0.848219i	$-0.322325\pi$
$41$	6.78276	1.05929	0.529645	+	0.848219i	$0.322325\pi$
$42$	4.11009i	0.634201i
$43$	11.9569i	1.82341i	0.410843	+	0.911706i	$0.365234\pi$
$43$	11.9569i	1.82341i	−0.410843	+	0.911706i	$0.634766\pi$
$44$	−4.78276	−0.721029
$45$	0	0
$46$	−1.71871	−0.253410
$47$	8.00000i	1.16692i	0.812142	+	0.583460i	$0.198301\pi$
$47$	8.00000i	1.16692i	−0.812142	+	0.583460i	$0.801699\pi$
$48$	1.71871i	0.248074i
$49$	1.28129	0.183041
$50$	0	0
$51$	0.672673	0.0941930
$52$	4.50147i	0.624242i
$53$	− 5.17415i	− 0.710724i	−0.934729	−	0.355362i	$-0.884358\pi$
$53$	− 5.17415i	− 0.710724i	0.934729	−	0.355362i	$-0.115642\pi$
$54$	5.23525	0.712428
$55$	0	0
$56$	−2.39138	−0.319562
$57$	5.90793i	0.782524i
$58$	1.00000i	0.131306i
$59$	9.93889	1.29393	0.646967	−	0.762518i	$-0.276037\pi$
$59$	9.93889	1.29393	0.646967	+	0.762518i	$0.276037\pi$
$60$	0	0
$61$	3.71871	0.476132	0.238066	−	0.971249i	$-0.423487\pi$
$61$	3.71871	0.476132	0.238066	+	0.971249i	$0.423487\pi$
$62$	3.73673i	0.474565i
$63$	0.110092i	0.0138703i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	8.22018	1.01183
$67$	6.87484i	0.839895i	0.907548	+	0.419948i	$0.137952\pi$
$67$	6.87484i	0.839895i	−0.907548	+	0.419948i	$0.862048\pi$
$68$	0.391382i	0.0474621i
$69$	2.95396	0.355615
$70$	0	0
$71$	6.87484	0.815893	0.407947	−	0.913006i	$-0.366245\pi$
$71$	6.87484	0.815893	0.407947	+	0.913006i	$0.366245\pi$
$72$	0.0460370i	0.00542551i
$73$	5.70069i	0.667215i	0.942712	+	0.333608i	$0.108266\pi$
$73$	5.70069i	0.667215i	−0.942712	+	0.333608i	$0.891734\pi$
$74$	−2.78276	−0.323490
$75$	0	0
$76$	−3.43742	−0.394299
$77$	11.4374i	1.30341i
$78$	− 7.73673i	− 0.876012i
$79$	−9.19217	−1.03420	−0.517100	−	0.855925i	$-0.672988\pi$
$79$	−9.19217	−1.03420	−0.517100	+	0.855925i	$0.672988\pi$
$80$	0	0
$81$	−8.85977	−0.984419
$82$	− 6.78276i	− 0.749031i
$83$	− 4.56258i	− 0.500808i	−0.968141	−	0.250404i	$-0.919437\pi$
$83$	− 4.56258i	− 0.500808i	0.968141	−	0.250404i	$-0.0805635\pi$
$84$	4.11009	0.448448
$85$	0	0
$86$	11.9569	1.28935
$87$	− 1.71871i	− 0.184265i
$88$	4.78276i	0.509844i
$89$	−15.0029	−1.59031	−0.795155	−	0.606407i	$-0.792610\pi$
$89$	−15.0029	−1.59031	−0.795155	+	0.606407i	$0.792610\pi$
$90$	0	0
$91$	10.7647	1.12845
$92$	1.71871i	0.179188i
$93$	− 6.42235i	− 0.665967i
$94$	8.00000	0.825137
$95$	0	0
$96$	1.71871	0.175415
$97$	− 9.06406i	− 0.920315i	−0.887837	−	0.460158i	$-0.847793\pi$
$97$	− 9.06406i	− 0.920315i	0.887837	−	0.460158i	$-0.152207\pi$
$98$	− 1.28129i	− 0.129430i
$99$	0.220184	0.0221293
$100$	0	0
$101$	−2.40940	−0.239744	−0.119872	−	0.992789i	$-0.538248\pi$
$101$	−2.40940	−0.239744	−0.119872	+	0.992789i	$0.538248\pi$
$102$	− 0.672673i	− 0.0666045i
$103$	− 12.4404i	− 1.22579i	−0.790166	−	0.612893i	$-0.790006\pi$
$103$	− 12.4404i	− 1.22579i	0.790166	−	0.612893i	$-0.209994\pi$
$104$	4.50147	0.441406
$105$	0	0
$106$	−5.17415	−0.502558
$107$	18.3123i	1.77031i	0.465294	+	0.885156i	$0.345949\pi$
$107$	18.3123i	1.77031i	−0.465294	+	0.885156i	$0.654051\pi$
$108$	− 5.23525i	− 0.503762i
$109$	8.34829	0.799622	0.399811	−	0.916598i	$-0.369076\pi$
$109$	8.34829	0.799622	0.399811	+	0.916598i	$0.369076\pi$
$110$	0	0
$111$	4.78276	0.453960
$112$	2.39138i	0.225964i
$113$	15.9389i	1.49941i	0.661775	+	0.749703i	$0.269803\pi$
$113$	15.9389i	1.49941i	−0.661775	+	0.749703i	$0.730197\pi$
$114$	5.90793	0.553328
$115$	0	0
$116$	1.00000	0.0928477
$117$	− 0.207234i	− 0.0191588i
$118$	− 9.93889i	− 0.914949i
$119$	0.935945	0.0857979
$120$	0	0
$121$	11.8748	1.07953
$122$	− 3.71871i	− 0.336676i
$123$	11.6576i	1.05113i
$124$	3.73673	0.335568
$125$	0	0
$126$	0.110092	0.00980778
$127$	− 6.87484i	− 0.610043i	−0.952345	−	0.305022i	$-0.901336\pi$
$127$	− 6.87484i	− 0.610043i	0.952345	−	0.305022i	$-0.0986637\pi$
$128$	1.00000i	0.0883883i
$129$	−20.5505	−1.80937
$130$	0	0
$131$	13.5295	1.18208	0.591039	−	0.806643i	$-0.298718\pi$
$131$	13.5295	1.18208	0.591039	+	0.806643i	$0.298718\pi$
$132$	− 8.22018i	− 0.715475i
$133$	8.22018i	0.712780i
$134$	6.87484	0.593896
$135$	0	0
$136$	0.391382	0.0335608
$137$	1.62664i	0.138973i	0.997583	+	0.0694864i	$0.0221361\pi$
$137$	1.62664i	0.138973i	−0.997583	+	0.0694864i	$0.977864\pi$
$138$	− 2.95396i	− 0.251458i
$139$	−17.4864	−1.48318	−0.741589	−	0.670855i	$-0.765927\pi$
$139$	−17.4864	−1.48318	−0.741589	+	0.670855i	$0.765927\pi$
$140$	0	0
$141$	−13.7497	−1.15793
$142$	− 6.87484i	− 0.576924i
$143$	− 21.5295i	− 1.80039i
$144$	0.0460370	0.00383642
$145$	0	0
$146$	5.70069	0.471793
$147$	2.20217i	0.181632i
$148$	2.78276i	0.228742i
$149$	−24.3123	−1.99174	−0.995869	−	0.0908028i	$-0.971057\pi$
$149$	−24.3123	−1.99174	−0.995869	+	0.0908028i	$0.971057\pi$
$150$	0	0
$151$	21.0029	1.70920	0.854598	−	0.519290i	$-0.173804\pi$
$151$	21.0029	1.70920	0.854598	+	0.519290i	$0.173804\pi$
$152$	3.43742i	0.278812i
$153$	− 0.0180181i	− 0.00145667i
$154$	11.4374	0.921654
$155$	0	0
$156$	−7.73673	−0.619434
$157$	− 4.43447i	− 0.353909i	−0.984219	−	0.176955i	$-0.943375\pi$
$157$	− 4.43447i	− 0.353909i	0.984219	−	0.176955i	$-0.0566246\pi$
$158$	9.19217i	0.731289i
$159$	8.89286	0.705249
$160$	0	0
$161$	4.11009	0.323921
$162$	8.85977i	0.696089i
$163$	− 22.0059i	− 1.72363i	−0.507219	−	0.861817i	$-0.669326\pi$
$163$	− 22.0059i	− 1.72363i	0.507219	−	0.861817i	$-0.330674\pi$
$164$	−6.78276	−0.529645
$165$	0	0
$166$	−4.56258	−0.354125
$167$	10.3914i	0.804109i	0.915616	+	0.402055i	$0.131704\pi$
$167$	10.3914i	0.804109i	−0.915616	+	0.402055i	$0.868296\pi$
$168$	− 4.11009i	− 0.317100i
$169$	−7.26327	−0.558713
$170$	0	0
$171$	0.158248	0.0121016
$172$	− 11.9569i	− 0.911706i
$173$	10.0670i	0.765380i	0.923877	+	0.382690i	$0.125002\pi$
$173$	10.0670i	0.765380i	−0.923877	+	0.382690i	$0.874998\pi$
$174$	−1.71871	−0.130295
$175$	0	0
$176$	4.78276	0.360514
$177$	17.0821i	1.28397i
$178$	15.0029i	1.12452i
$179$	1.19217	0.0891066	0.0445533	−	0.999007i	$-0.485814\pi$
$179$	1.19217	0.0891066	0.0445533	+	0.999007i	$0.485814\pi$
$180$	0	0
$181$	15.0390	1.11784	0.558919	−	0.829222i	$-0.311216\pi$
$181$	15.0390	1.11784	0.558919	+	0.829222i	$0.311216\pi$
$182$	− 10.7647i	− 0.797936i
$183$	6.39138i	0.472465i
$184$	1.71871	0.126705
$185$	0	0
$186$	−6.42235	−0.470910
$187$	− 1.87189i	− 0.136886i
$188$	− 8.00000i	− 0.583460i
$189$	−12.5195	−0.910659
$190$	0	0
$191$	−23.3943	−1.69275	−0.846377	−	0.532584i	$-0.821221\pi$
$191$	−23.3943	−1.69275	−0.846377	+	0.532584i	$0.821221\pi$
$192$	− 1.71871i	− 0.124037i
$193$	20.9418i	1.50743i	0.657203	+	0.753713i	$0.271739\pi$
$193$	20.9418i	1.50743i	−0.657203	+	0.753713i	$0.728261\pi$
$194$	−9.06406	−0.650761
$195$	0	0
$196$	−1.28129	−0.0915207
$197$	− 8.57553i	− 0.610981i	−0.952195	−	0.305491i	$-0.901180\pi$
$197$	− 8.57553i	− 0.610981i	0.952195	−	0.305491i	$-0.0988205\pi$
$198$	− 0.220184i	− 0.0156478i
$199$	3.21724	0.228064	0.114032	−	0.993477i	$-0.463623\pi$
$199$	3.21724	0.228064	0.114032	+	0.993477i	$0.463623\pi$
$200$	0	0
$201$	−11.8159	−0.833426
$202$	2.40940i	0.169525i
$203$	− 2.39138i	− 0.167842i
$204$	−0.672673	−0.0470965
$205$	0	0
$206$	−12.4404	−0.866762
$207$	− 0.0791242i	− 0.00549951i
$208$	− 4.50147i	− 0.312121i
$209$	16.4404	1.13720
$210$	0	0
$211$	−4.78276	−0.329259	−0.164630	−	0.986355i	$-0.552643\pi$
$211$	−4.78276	−0.329259	−0.164630	+	0.986355i	$0.552643\pi$
$212$	5.17415i	0.355362i
$213$	11.8159i	0.809609i
$214$	18.3123	1.25180
$215$	0	0
$216$	−5.23525	−0.356214
$217$	− 8.93594i	− 0.606611i
$218$	− 8.34829i	− 0.565418i
$219$	−9.79783	−0.662076
$220$	0	0
$221$	−1.76180	−0.118511
$222$	− 4.78276i	− 0.320998i
$223$	− 16.5935i	− 1.11119i	−0.831454	−	0.555593i	$-0.812491\pi$
$223$	− 16.5935i	− 1.11119i	0.831454	−	0.555593i	$-0.187509\pi$
$224$	2.39138	0.159781
$225$	0	0
$226$	15.9389	1.06024
$227$	− 19.3512i	− 1.28439i	−0.766543	−	0.642194i	$-0.778025\pi$
$227$	− 19.3512i	− 1.28439i	0.766543	−	0.642194i	$-0.221975\pi$
$228$	− 5.90793i	− 0.391262i
$229$	13.3943	0.885122	0.442561	−	0.896738i	$-0.354070\pi$
$229$	13.3943	0.885122	0.442561	+	0.896738i	$0.354070\pi$
$230$	0	0
$231$	−19.6576	−1.29338
$232$	− 1.00000i	− 0.0656532i
$233$	− 22.4404i	− 1.47012i	−0.678003	−	0.735059i	$-0.737155\pi$
$233$	− 22.4404i	− 1.47012i	0.678003	−	0.735059i	$-0.262845\pi$
$234$	−0.207234	−0.0135473
$235$	0	0
$236$	−9.93889	−0.646967
$237$	− 15.7987i	− 1.02623i
$238$	− 0.935945i	− 0.0606683i
$239$	0.220184	0.0142425	0.00712126	−	0.999975i	$-0.497733\pi$
$239$	0.220184	0.0142425	0.00712126	+	0.999975i	$0.497733\pi$
$240$	0	0
$241$	−15.9749	−1.02904	−0.514518	−	0.857480i	$-0.672029\pi$
$241$	−15.9749	−1.02904	−0.514518	+	0.857480i	$0.672029\pi$
$242$	− 11.8748i	− 0.763344i
$243$	0.478388i	0.0306886i
$244$	−3.71871	−0.238066
$245$	0	0
$246$	11.6576	0.743262
$247$	− 15.4735i	− 0.984552i
$248$	− 3.73673i	− 0.237282i
$249$	7.84175	0.496951
$250$	0	0
$251$	−9.87189	−0.623108	−0.311554	−	0.950228i	$-0.600850\pi$
$251$	−9.87189	−0.623108	−0.311554	+	0.950228i	$0.600850\pi$
$252$	− 0.110092i	− 0.00693515i
$253$	− 8.22018i	− 0.516799i
$254$	−6.87484	−0.431366
$255$	0	0
$256$	1.00000	0.0625000
$257$	1.21724i	0.0759290i	0.999279	+	0.0379645i	$0.0120874\pi$
$257$	1.21724i	0.0759290i	−0.999279	+	0.0379645i	$0.987913\pi$
$258$	20.5505i	1.27942i
$259$	6.65465	0.413500
$260$	0	0
$261$	−0.0460370	−0.00284962
$262$	− 13.5295i	− 0.835855i
$263$	− 16.0000i	− 0.986602i	−0.869859	−	0.493301i	$-0.835790\pi$
$263$	− 16.0000i	− 0.986602i	0.869859	−	0.493301i	$-0.164210\pi$
$264$	−8.22018	−0.505917
$265$	0	0
$266$	8.22018	0.504012
$267$	− 25.7857i	− 1.57806i
$268$	− 6.87484i	− 0.419948i
$269$	2.26327	0.137994	0.0689971	−	0.997617i	$-0.478020\pi$
$269$	2.26327	0.137994	0.0689971	+	0.997617i	$0.478020\pi$
$270$	0	0
$271$	10.8748	0.660599	0.330300	−	0.943876i	$-0.392850\pi$
$271$	10.8748	0.660599	0.330300	+	0.943876i	$0.392850\pi$
$272$	− 0.391382i	− 0.0237310i
$273$	18.5015i	1.11976i
$274$	1.62664	0.0982687
$275$	0	0
$276$	−2.95396	−0.177808
$277$	− 3.30931i	− 0.198837i	−0.995046	−	0.0994186i	$-0.968302\pi$
$277$	− 3.30931i	− 0.198837i	0.995046	−	0.0994186i	$-0.0316983\pi$
$278$	17.4864i	1.04876i
$279$	−0.172028	−0.0102990
$280$	0	0
$281$	−22.7036	−1.35439	−0.677193	−	0.735806i	$-0.736804\pi$
$281$	−22.7036	−1.35439	−0.677193	+	0.735806i	$0.736804\pi$
$282$	13.7497i	0.818781i
$283$	− 15.6216i	− 0.928606i	−0.885676	−	0.464303i	$-0.846305\pi$
$283$	− 15.6216i	− 0.928606i	0.885676	−	0.464303i	$-0.153695\pi$
$284$	−6.87484	−0.407947
$285$	0	0
$286$	−21.5295	−1.27307
$287$	16.2202i	0.957447i
$288$	− 0.0460370i	− 0.00271276i
$289$	16.8468	0.990989
$290$	0	0
$291$	15.5785	0.913227
$292$	− 5.70069i	− 0.333608i
$293$	− 30.0980i	− 1.75834i	−0.476506	−	0.879171i	$-0.658097\pi$
$293$	− 30.0980i	− 1.75834i	0.476506	−	0.879171i	$-0.341903\pi$
$294$	2.20217	0.128433
$295$	0	0
$296$	2.78276	0.161745
$297$	25.0390i	1.45291i
$298$	24.3123i	1.40837i
$299$	−7.73673	−0.447427
$300$	0	0
$301$	−28.5935	−1.64810
$302$	− 21.0029i	− 1.20858i
$303$	− 4.14106i	− 0.237898i
$304$	3.43742	0.197150
$305$	0	0
$306$	−0.0180181	−0.00103002
$307$	− 13.5655i	− 0.774226i	−0.922032	−	0.387113i	$-0.873472\pi$
$307$	− 13.5655i	− 0.774226i	0.922032	−	0.387113i	$-0.126528\pi$
$308$	− 11.4374i	− 0.651707i
$309$	21.3814	1.21634
$310$	0	0
$311$	−14.5015	−0.822303	−0.411152	−	0.911567i	$-0.634873\pi$
$311$	−14.5015	−0.822303	−0.411152	+	0.911567i	$0.634873\pi$
$312$	7.73673i	0.438006i
$313$	19.5655i	1.10591i	0.833211	+	0.552955i	$0.186500\pi$
$313$	19.5655i	1.10591i	−0.833211	+	0.552955i	$0.813500\pi$
$314$	−4.43447	−0.250252
$315$	0	0
$316$	9.19217	0.517100
$317$	13.4374i	0.754721i	0.926067	+	0.377360i	$0.123168\pi$
$317$	13.4374i	0.754721i	−0.926067	+	0.377360i	$0.876832\pi$
$318$	− 8.89286i	− 0.498687i
$319$	−4.78276	−0.267783
$320$	0	0
$321$	−31.4735	−1.75668
$322$	− 4.11009i	− 0.229046i
$323$	− 1.34535i	− 0.0748570i
$324$	8.85977	0.492209
$325$	0	0
$326$	−22.0059	−1.21879
$327$	14.3483i	0.793462i
$328$	6.78276i	0.374516i
$329$	−19.1311	−1.05473
$330$	0	0
$331$	3.21724	0.176835	0.0884176	−	0.996083i	$-0.471819\pi$
$331$	3.21724	0.176835	0.0884176	+	0.996083i	$0.471819\pi$
$332$	4.56258i	0.250404i
$333$	− 0.128110i	− 0.00702039i
$334$	10.3914	0.568591
$335$	0	0
$336$	−4.11009	−0.224224
$337$	− 32.3052i	− 1.75978i	−0.475180	−	0.879888i	$-0.657617\pi$
$337$	− 32.3052i	− 1.75978i	0.475180	−	0.879888i	$-0.342383\pi$
$338$	7.26327i	0.395070i
$339$	−27.3943	−1.48786
$340$	0	0
$341$	−17.8719	−0.967817
$342$	− 0.158248i	− 0.00855710i
$343$	19.8037i	1.06930i
$344$	−11.9569	−0.644673
$345$	0	0
$346$	10.0670	0.541205
$347$	− 2.99705i	− 0.160890i	−0.996759	−	0.0804451i	$-0.974366\pi$
$347$	− 2.99705i	− 0.160890i	0.996759	−	0.0804451i	$-0.0256342\pi$
$348$	1.71871i	0.0921325i
$349$	16.6547	0.891503	0.445752	−	0.895157i	$-0.352936\pi$
$349$	16.6547	0.891503	0.445752	+	0.895157i	$0.352936\pi$
$350$	0	0
$351$	23.5664	1.25788
$352$	− 4.78276i	− 0.254922i
$353$	− 3.52949i	− 0.187856i	−0.995579	−	0.0939280i	$-0.970058\pi$
$353$	− 3.52949i	− 0.187856i	0.995579	−	0.0939280i	$-0.0299423\pi$
$354$	17.0821	0.907902
$355$	0	0
$356$	15.0029	0.795155
$357$	1.60862i	0.0851371i
$358$	− 1.19217i	− 0.0630079i
$359$	22.5015	1.18758	0.593791	−	0.804619i	$-0.297631\pi$
$359$	22.5015	1.18758	0.593791	+	0.804619i	$0.297631\pi$
$360$	0	0
$361$	−7.18415	−0.378113
$362$	− 15.0390i	− 0.790432i
$363$	20.4094i	1.07122i
$364$	−10.7647	−0.564226
$365$	0	0
$366$	6.39138	0.334083
$367$	28.3182i	1.47820i	0.673598	+	0.739098i	$0.264748\pi$
$367$	28.3182i	1.47820i	−0.673598	+	0.739098i	$0.735252\pi$
$368$	− 1.71871i	− 0.0895939i
$369$	0.312258	0.0162555
$370$	0	0
$371$	12.3734	0.642393
$372$	6.42235i	0.332983i
$373$	11.2662i	0.583343i	0.956519	+	0.291671i	$0.0942114\pi$
$373$	11.2662i	0.583343i	−0.956519	+	0.291671i	$0.905789\pi$
$374$	−1.87189	−0.0967931
$375$	0	0
$376$	−8.00000	−0.412568
$377$	4.50147i	0.231838i
$378$	12.5195i	0.643933i
$379$	−0.526544	−0.0270468	−0.0135234	−	0.999909i	$-0.504305\pi$
$379$	−0.526544	−0.0270468	−0.0135234	+	0.999909i	$0.504305\pi$
$380$	0	0
$381$	11.8159	0.605344
$382$	23.3943i	1.19696i
$383$	− 13.0821i	− 0.668463i	−0.942491	−	0.334231i	$-0.891523\pi$
$383$	− 13.0821i	− 0.668463i	0.942491	−	0.334231i	$-0.108477\pi$
$384$	−1.71871	−0.0877075
$385$	0	0
$386$	20.9418	1.06591
$387$	0.550460i	0.0279815i
$388$	9.06406i	0.460158i
$389$	−35.7497	−1.81258	−0.906290	−	0.422656i	$-0.861098\pi$
$389$	−35.7497	−1.81258	−0.906290	+	0.422656i	$0.861098\pi$
$390$	0	0
$391$	−0.672673	−0.0340185
$392$	1.28129i	0.0647149i
$393$	23.2533i	1.17297i
$394$	−8.57553	−0.432029
$395$	0	0
$396$	−0.220184	−0.0110647
$397$	23.2662i	1.16770i	0.811862	+	0.583849i	$0.198454\pi$
$397$	23.2662i	1.16770i	−0.811862	+	0.583849i	$0.801546\pi$
$398$	− 3.21724i	− 0.161265i
$399$	−14.1281	−0.707290
$400$	0	0
$401$	−29.2842	−1.46239	−0.731193	−	0.682171i	$-0.761036\pi$
$401$	−29.2842	−1.46239	−0.731193	+	0.682171i	$0.761036\pi$
$402$	11.8159i	0.589321i
$403$	16.8208i	0.837903i
$404$	2.40940	0.119872
$405$	0	0
$406$	−2.39138	−0.118682
$407$	− 13.3093i	− 0.659718i
$408$	0.672673i	0.0333023i
$409$	17.9640	0.888261	0.444130	−	0.895962i	$-0.353513\pi$
$409$	17.9640	0.888261	0.444130	+	0.895962i	$0.353513\pi$
$410$	0	0
$411$	−2.79571	−0.137902
$412$	12.4404i	0.612893i
$413$	23.7677i	1.16953i
$414$	−0.0791242	−0.00388874
$415$	0	0
$416$	−4.50147	−0.220703
$417$	− 30.0541i	− 1.47175i
$418$	− 16.4404i	− 0.804125i
$419$	−20.2633	−0.989926	−0.494963	−	0.868914i	$-0.664818\pi$
$419$	−20.2633	−0.989926	−0.494963	+	0.868914i	$0.664818\pi$
$420$	0	0
$421$	26.1841	1.27614	0.638069	−	0.769979i	$-0.279734\pi$
$421$	26.1841	1.27614	0.638069	+	0.769979i	$0.279734\pi$
$422$	4.78276i	0.232821i
$423$	0.368296i	0.0179072i
$424$	5.17415	0.251279
$425$	0	0
$426$	11.8159	0.572480
$427$	8.89286i	0.430356i
$428$	− 18.3123i	− 0.885156i
$429$	37.0029	1.78652
$430$	0	0
$431$	−11.4374	−0.550921	−0.275461	−	0.961312i	$-0.588830\pi$
$431$	−11.4374	−0.550921	−0.275461	+	0.961312i	$0.588830\pi$
$432$	5.23525i	0.251881i
$433$	− 37.3152i	− 1.79325i	−0.442786	−	0.896627i	$-0.646010\pi$
$433$	− 37.3152i	− 1.79325i	0.442786	−	0.896627i	$-0.353990\pi$
$434$	−8.93594	−0.428939
$435$	0	0
$436$	−8.34829	−0.399811
$437$	− 5.90793i	− 0.282614i
$438$	9.79783i	0.468159i
$439$	−22.6547	−1.08125	−0.540624	−	0.841264i	$-0.681812\pi$
$439$	−22.6547	−1.08125	−0.540624	+	0.841264i	$0.681812\pi$
$440$	0	0
$441$	0.0589868	0.00280889
$442$	1.76180i	0.0838002i
$443$	16.2872i	0.773828i	0.922116	+	0.386914i	$0.126459\pi$
$443$	16.2872i	0.773828i	−0.922116	+	0.386914i	$0.873541\pi$
$444$	−4.78276	−0.226980
$445$	0	0
$446$	−16.5935	−0.785727
$447$	− 41.7857i	− 1.97640i
$448$	− 2.39138i	− 0.112982i
$449$	−17.4735	−0.824623	−0.412312	−	0.911043i	$-0.635279\pi$
$449$	−17.4735	−0.824623	−0.412312	+	0.911043i	$0.635279\pi$
$450$	0	0
$451$	32.4404	1.52756
$452$	− 15.9389i	− 0.749703i
$453$	36.0980i	1.69603i
$454$	−19.3512	−0.908199
$455$	0	0
$456$	−5.90793	−0.276664
$457$	− 22.6966i	− 1.06170i	−0.847465	−	0.530851i	$-0.821872\pi$
$457$	− 22.6966i	− 1.06170i	0.847465	−	0.530851i	$-0.178128\pi$
$458$	− 13.3943i	− 0.625876i
$459$	2.04899	0.0956385
$460$	0	0
$461$	−14.5195	−0.676240	−0.338120	−	0.941103i	$-0.609791\pi$
$461$	−14.5195	−0.676240	−0.338120	+	0.941103i	$0.609791\pi$
$462$	19.6576i	0.914554i
$463$	− 12.0000i	− 0.557687i	−0.960337	−	0.278844i	$-0.910049\pi$
$463$	− 12.0000i	− 0.557687i	0.960337	−	0.278844i	$-0.0899511\pi$
$464$	−1.00000	−0.0464238
$465$	0	0
$466$	−22.4404	−1.03953
$467$	6.73378i	0.311602i	0.987788	+	0.155801i	$0.0497959\pi$
$467$	6.73378i	0.311602i	−0.987788	+	0.155801i	$0.950204\pi$
$468$	0.207234i	0.00957941i
$469$	−16.4404	−0.759146
$470$	0	0
$471$	7.62157	0.351183
$472$	9.93889i	0.457475i
$473$	57.1871i	2.62947i
$474$	−15.7987	−0.725657
$475$	0	0
$476$	−0.935945	−0.0428990
$477$	− 0.238202i	− 0.0109065i
$478$	− 0.220184i	− 0.0100710i
$479$	33.4002	1.52610	0.763048	−	0.646342i	$-0.223702\pi$
$479$	33.4002	1.52610	0.763048	+	0.646342i	$0.223702\pi$
$480$	0	0
$481$	−12.5265	−0.571161
$482$	15.9749i	0.727638i
$483$	7.06406i	0.321426i
$484$	−11.8748	−0.539765
$485$	0	0
$486$	0.478388	0.0217001
$487$	− 38.3432i	− 1.73750i	−0.495253	−	0.868749i	$-0.664925\pi$
$487$	− 38.3432i	− 1.73750i	0.495253	−	0.868749i	$-0.335075\pi$
$488$	3.71871i	0.168338i
$489$	37.8217	1.71036
$490$	0	0
$491$	16.0000	0.722070	0.361035	−	0.932552i	$-0.382424\pi$
$491$	16.0000	0.722070	0.361035	+	0.932552i	$0.382424\pi$
$492$	− 11.6576i	− 0.525565i
$493$	0.391382i	0.0176270i
$494$	−15.4735	−0.696184
$495$	0	0
$496$	−3.73673	−0.167784
$497$	16.4404i	0.737451i
$498$	− 7.84175i	− 0.351397i
$499$	−27.9448	−1.25098	−0.625490	−	0.780232i	$-0.715101\pi$
$499$	−27.9448	−1.25098	−0.625490	+	0.780232i	$0.715101\pi$
$500$	0	0
$501$	−17.8598	−0.797916
$502$	9.87189i	0.440604i
$503$	− 5.30931i	− 0.236730i	−0.992970	−	0.118365i	$-0.962235\pi$
$503$	− 5.30931i	− 0.236730i	0.992970	−	0.118365i	$-0.0377653\pi$
$504$	−0.110092	−0.00490389
$505$	0	0
$506$	−8.22018	−0.365432
$507$	− 12.4835i	− 0.554410i
$508$	6.87484i	0.305022i
$509$	−26.7828	−1.18713	−0.593563	−	0.804788i	$-0.702279\pi$
$509$	−26.7828	−1.18713	−0.593563	+	0.804788i	$0.702279\pi$
$510$	0	0
$511$	−13.6325	−0.603068
$512$	− 1.00000i	− 0.0441942i
$513$	17.9958i	0.794532i
$514$	1.21724	0.0536899
$515$	0	0
$516$	20.5505	0.904684
$517$	38.2621i	1.68277i
$518$	− 6.65465i	− 0.292389i
$519$	−17.3023	−0.759485
$520$	0	0
$521$	39.9268	1.74922	0.874612	−	0.484824i	$-0.161116\pi$
$521$	39.9268	1.74922	0.874612	+	0.484824i	$0.161116\pi$
$522$	0.0460370i	0.00201498i
$523$	− 3.43742i	− 0.150308i	−0.997172	−	0.0751539i	$-0.976055\pi$
$523$	− 3.43742i	− 0.150308i	0.997172	−	0.0751539i	$-0.0239448\pi$
$524$	−13.5295	−0.591039
$525$	0	0
$526$	−16.0000	−0.697633
$527$	1.46249i	0.0637070i
$528$	8.22018i	0.357738i
$529$	20.0460	0.871567
$530$	0	0
$531$	0.457557	0.0198563
$532$	− 8.22018i	− 0.356390i
$533$	− 30.5324i	− 1.32251i
$534$	−25.7857	−1.11586
$535$	0	0
$536$	−6.87484	−0.296948
$537$	2.04899i	0.0884203i
$538$	− 2.26327i	− 0.0975766i
$539$	6.12811	0.263956
$540$	0	0
$541$	−28.2692	−1.21539	−0.607693	−	0.794172i	$-0.707905\pi$
$541$	−28.2692	−1.21539	−0.607693	+	0.794172i	$0.707905\pi$
$542$	− 10.8748i	− 0.467114i
$543$	25.8476i	1.10923i
$544$	−0.391382	−0.0167804
$545$	0	0
$546$	18.5015	0.791790
$547$	6.56848i	0.280848i	0.990091	+	0.140424i	$0.0448465\pi$
$547$	6.56848i	0.280848i	−0.990091	+	0.140424i	$0.955153\pi$
$548$	− 1.62664i	− 0.0694864i
$549$	0.171198	0.00730656
$550$	0	0
$551$	−3.43742	−0.146439
$552$	2.95396i	0.125729i
$553$	− 21.9820i	− 0.934769i
$554$	−3.30931	−0.140599
$555$	0	0
$556$	17.4864	0.741589
$557$	15.9389i	0.675353i	0.941262	+	0.337676i	$0.109641\pi$
$557$	15.9389i	0.675353i	−0.941262	+	0.337676i	$0.890359\pi$
$558$	0.172028i	0.00728251i
$559$	53.8237	2.27650
$560$	0	0
$561$	3.21724	0.135832
$562$	22.7036i	0.957695i
$563$	− 16.2872i	− 0.686423i	−0.939258	−	0.343212i	$-0.888485\pi$
$563$	− 16.2872i	− 0.686423i	0.939258	−	0.343212i	$-0.111515\pi$
$564$	13.7497	0.578966
$565$	0	0
$566$	−15.6216	−0.656623
$567$	− 21.1871i	− 0.889774i
$568$	6.87484i	0.288462i
$569$	33.3512	1.39816	0.699078	−	0.715045i	$-0.253594\pi$
$569$	33.3512	1.39816	0.699078	+	0.715045i	$0.253594\pi$
$570$	0	0
$571$	−29.8167	−1.24779	−0.623895	−	0.781508i	$-0.714451\pi$
$571$	−29.8167	−1.24779	−0.623895	+	0.781508i	$0.714451\pi$
$572$	21.5295i	0.900193i
$573$	− 40.2081i	− 1.67972i
$574$	16.2202	0.677017
$575$	0	0
$576$	−0.0460370	−0.00191821
$577$	10.2272i	0.425765i	0.977078	+	0.212883i	$0.0682852\pi$
$577$	10.2272i	0.425765i	−0.977078	+	0.212883i	$0.931715\pi$
$578$	− 16.8468i	− 0.700735i
$579$	−35.9929	−1.49582
$580$	0	0
$581$	10.9109	0.452659
$582$	− 15.5785i	− 0.645749i
$583$	− 24.7467i	− 1.02490i
$584$	−5.70069	−0.235896
$585$	0	0
$586$	−30.0980	−1.24334
$587$	− 20.0360i	− 0.826976i	−0.910510	−	0.413488i	$-0.864310\pi$
$587$	− 20.0360i	− 0.826976i	0.910510	−	0.413488i	$-0.135690\pi$
$588$	− 2.20217i	− 0.0908158i
$589$	−12.8447	−0.529257
$590$	0	0
$591$	14.7388	0.606275
$592$	− 2.78276i	− 0.114371i
$593$	− 35.4433i	− 1.45548i	−0.685852	−	0.727741i	$-0.740570\pi$
$593$	− 35.4433i	− 1.45548i	0.685852	−	0.727741i	$-0.259430\pi$
$594$	25.0390	1.02736
$595$	0	0
$596$	24.3123	0.995869
$597$	5.52949i	0.226307i
$598$	7.73673i	0.316378i
$599$	11.6647	0.476605	0.238302	−	0.971191i	$-0.423409\pi$
$599$	11.6647	0.476605	0.238302	+	0.971191i	$0.423409\pi$
$600$	0	0
$601$	17.6936	0.721739	0.360869	−	0.932616i	$-0.382480\pi$
$601$	17.6936	0.721739	0.360869	+	0.932616i	$0.382480\pi$
$602$	28.5935i	1.16539i
$603$	0.316497i	0.0128888i
$604$	−21.0029	−0.854598
$605$	0	0
$606$	−4.14106	−0.168219
$607$	8.00000i	0.324710i	0.986732	+	0.162355i	$0.0519090\pi$
$607$	8.00000i	0.324710i	−0.986732	+	0.162355i	$0.948091\pi$
$608$	− 3.43742i	− 0.139406i
$609$	4.11009	0.166549
$610$	0	0
$611$	36.0118	1.45688
$612$	0.0180181i	0 0.000728337i
$613$	− 26.9959i	− 1.09035i	−0.838321	−	0.545177i	$-0.816462\pi$
$613$	− 26.9959i	− 1.09035i	0.838321	−	0.545177i	$-0.183538\pi$
$614$	−13.5655	−0.547460
$615$	0	0
$616$	−11.4374	−0.460827
$617$	− 14.2993i	− 0.575668i	−0.957680	−	0.287834i	$-0.907065\pi$
$617$	− 14.2993i	− 0.575668i	0.957680	−	0.287834i	$-0.0929352\pi$
$618$	− 21.3814i	− 0.860085i
$619$	49.1009	1.97353	0.986766	−	0.162149i	$-0.0518425\pi$
$619$	49.1009	1.97353	0.986766	+	0.162149i	$0.0518425\pi$
$620$	0	0
$621$	8.99788	0.361073
$622$	14.5015i	0.581456i
$623$	− 35.8778i	− 1.43741i
$624$	7.73673	0.309717
$625$	0	0
$626$	19.5655	0.781996
$627$	28.2562i	1.12844i
$628$	4.43447i	0.176955i
$629$	−1.08913	−0.0434263
$630$	0	0
$631$	−4.03604	−0.160672	−0.0803360	−	0.996768i	$-0.525599\pi$
$631$	−4.03604	−0.160672	−0.0803360	+	0.996768i	$0.525599\pi$
$632$	− 9.19217i	− 0.365645i
$633$	− 8.22018i	− 0.326723i
$634$	13.4374	0.533668
$635$	0	0
$636$	−8.89286	−0.352625
$637$	− 5.76770i	− 0.228524i
$638$	4.78276i	0.189351i
$639$	0.316497	0.0125204
$640$	0	0
$641$	28.5324	1.12696	0.563482	−	0.826128i	$-0.309461\pi$
$641$	28.5324	1.12696	0.563482	+	0.826128i	$0.309461\pi$
$642$	31.4735i	1.24216i
$643$	− 29.9079i	− 1.17945i	−0.807603	−	0.589727i	$-0.799235\pi$
$643$	− 29.9079i	− 1.17945i	0.807603	−	0.589727i	$-0.200765\pi$
$644$	−4.11009	−0.161960
$645$	0	0
$646$	−1.34535	−0.0529319
$647$	− 27.3152i	− 1.07387i	−0.843623	−	0.536936i	$-0.819582\pi$
$647$	− 27.3152i	− 1.07387i	0.843623	−	0.536936i	$-0.180418\pi$
$648$	− 8.85977i	− 0.348045i
$649$	47.5354	1.86593
$650$	0	0
$651$	15.3583	0.601939
$652$	22.0059i	0.861817i
$653$	40.8247i	1.59759i	0.601601	+	0.798797i	$0.294530\pi$
$653$	40.8247i	1.59759i	−0.601601	+	0.798797i	$0.705470\pi$
$654$	14.3483	0.561063
$655$	0	0
$656$	6.78276	0.264822
$657$	0.262443i	0.0102389i
$658$	19.1311i	0.745806i
$659$	−36.7828	−1.43285	−0.716427	−	0.697663i	$-0.754224\pi$
$659$	−36.7828	−1.43285	−0.716427	+	0.697663i	$0.754224\pi$
$660$	0	0
$661$	17.8778	0.695365	0.347683	−	0.937612i	$-0.386969\pi$
$661$	17.8778	0.695365	0.347683	+	0.937612i	$0.386969\pi$
$662$	− 3.21724i	− 0.125041i
$663$	− 3.02802i	− 0.117599i
$664$	4.56258	0.177062
$665$	0	0
$666$	−0.128110	−0.00496417
$667$	1.71871i	0.0665487i
$668$	− 10.3914i	− 0.402055i
$669$	28.5195	1.10263
$670$	0	0
$671$	17.7857	0.686610
$672$	4.11009i	0.158550i
$673$	8.34829i	0.321803i	0.986970	+	0.160902i	$0.0514402\pi$
$673$	8.34829i	0.321803i	−0.986970	+	0.160902i	$0.948560\pi$
$674$	−32.3052	−1.24435
$675$	0	0
$676$	7.26327	0.279357
$677$	− 4.21429i	− 0.161968i	−0.996715	−	0.0809841i	$-0.974194\pi$
$677$	− 4.21429i	− 0.161968i	0.996715	−	0.0809841i	$-0.0258063\pi$
$678$	27.3943i	1.05207i
$679$	21.6756	0.831834
$680$	0	0
$681$	33.2592	1.27449
$682$	17.8719i	0.684350i
$683$	15.6936i	0.600500i	0.953860	+	0.300250i	$0.0970702\pi$
$683$	15.6936i	0.600500i	−0.953860	+	0.300250i	$0.902930\pi$
$684$	−0.158248	−0.00605078
$685$	0	0
$686$	19.8037	0.756110
$687$	23.0210i	0.878305i
$688$	11.9569i	0.455853i
$689$	−23.2913	−0.887328
$690$	0	0
$691$	9.73083	0.370178	0.185089	−	0.982722i	$-0.440743\pi$
$691$	9.73083	0.370178	0.185089	+	0.982722i	$0.440743\pi$
$692$	− 10.0670i	− 0.382690i
$693$	0.526544i	0.0200018i
$694$	−2.99705	−0.113767
$695$	0	0
$696$	1.71871	0.0651475
$697$	− 2.65465i	− 0.100552i
$698$	− 16.6547i	− 0.630388i
$699$	38.5685	1.45879
$700$	0	0
$701$	−37.9499	−1.43335	−0.716673	−	0.697409i	$-0.754336\pi$
$701$	−37.9499	−1.43335	−0.716673	+	0.697409i	$0.754336\pi$
$702$	− 23.5664i	− 0.889455i
$703$	− 9.56553i	− 0.360771i
$704$	−4.78276	−0.180257
$705$	0	0
$706$	−3.52949	−0.132834
$707$	− 5.76180i	− 0.216695i
$708$	− 17.0821i	− 0.641984i
$709$	4.55668	0.171130	0.0855649	−	0.996333i	$-0.472730\pi$
$709$	4.55668	0.171130	0.0855649	+	0.996333i	$0.472730\pi$
$710$	0	0
$711$	−0.423180	−0.0158705
$712$	− 15.0029i	− 0.562259i
$713$	6.42235i	0.240519i
$714$	1.60862	0.0602010
$715$	0	0
$716$	−1.19217	−0.0445533
$717$	0.378433i	0.0141328i
$718$	− 22.5015i	− 0.839748i
$719$	12.5626	0.468505	0.234253	−	0.972176i	$-0.424736\pi$
$719$	12.5626	0.468505	0.234253	+	0.972176i	$0.424736\pi$
$720$	0	0
$721$	29.7497	1.10794
$722$	7.18415i	0.267366i
$723$	− 27.4563i	− 1.02111i
$724$	−15.0390	−0.558919
$725$	0	0
$726$	20.4094	0.757464
$727$	− 11.6576i	− 0.432357i	−0.976354	−	0.216178i	$-0.930641\pi$
$727$	− 11.6576i	− 0.432357i	0.976354	−	0.216178i	$-0.0693592\pi$
$728$	10.7647i	0.398968i
$729$	−27.4015	−1.01487
$730$	0	0
$731$	4.67972	0.173086
$732$	− 6.39138i	− 0.236232i
$733$	− 19.3453i	− 0.714537i	−0.934002	−	0.357268i	$-0.883708\pi$
$733$	− 19.3453i	− 0.714537i	0.934002	−	0.357268i	$-0.116292\pi$
$734$	28.3182	1.04524
$735$	0	0
$736$	−1.71871	−0.0633525
$737$	32.8807i	1.21118i
$738$	− 0.312258i	− 0.0114944i
$739$	−11.1311	−0.409463	−0.204731	−	0.978818i	$-0.565632\pi$
$739$	−11.1311	−0.409463	−0.204731	+	0.978818i	$0.565632\pi$
$740$	0	0
$741$	26.5944	0.976969
$742$	− 12.3734i	− 0.454240i
$743$	1.56553i	0.0574337i	0.999588	+	0.0287169i	$0.00914212\pi$
$743$	1.56553i	0.0574337i	−0.999588	+	0.0287169i	$0.990858\pi$
$744$	6.42235	0.235455
$745$	0	0
$746$	11.2662	0.412486
$747$	− 0.210048i	− 0.00768524i
$748$	1.87189i	0.0684431i
$749$	−43.7916	−1.60011
$750$	0	0
$751$	23.1311	0.844064	0.422032	−	0.906581i	$-0.361317\pi$
$751$	23.1311	0.844064	0.422032	+	0.906581i	$0.361317\pi$
$752$	8.00000i	0.291730i
$753$	− 16.9669i	− 0.618309i
$754$	4.50147	0.163934
$755$	0	0
$756$	12.5195	0.455330
$757$	1.40138i	0.0509341i	0.999676	+	0.0254671i	$0.00810730\pi$
$757$	1.40138i	0.0509341i	−0.999676	+	0.0254671i	$0.991893\pi$
$758$	0.526544i	0.0191250i
$759$	14.1281	0.512818
$760$	0	0
$761$	−29.4923	−1.06910	−0.534548	−	0.845138i	$-0.679518\pi$
$761$	−29.4923	−1.06910	−0.534548	+	0.845138i	$0.679518\pi$
$762$	− 11.8159i	− 0.428043i
$763$	19.9640i	0.722744i
$764$	23.3943	0.846377
$765$	0	0
$766$	−13.0821	−0.472675
$767$	− 44.7397i	− 1.61546i
$768$	1.71871i	0.0620186i
$769$	32.7526	1.18109	0.590545	−	0.807005i	$-0.298913\pi$
$769$	32.7526	1.18109	0.590545	+	0.807005i	$0.298913\pi$
$770$	0	0
$771$	−2.09207	−0.0753442
$772$	− 20.9418i	− 0.753713i
$773$	9.74378i	0.350459i	0.984528	+	0.175230i	$0.0560668\pi$
$773$	9.74378i	0.350459i	−0.984528	+	0.175230i	$0.943933\pi$
$774$	0.550460	0.0197859
$775$	0	0
$776$	9.06406	0.325381
$777$	11.4374i	0.410315i
$778$	35.7497i	1.28169i
$779$	23.3152	0.835354
$780$	0	0
$781$	32.8807	1.17657
$782$	0.672673i	0.0240547i
$783$	− 5.23525i	− 0.187093i
$784$	1.28129	0.0457604
$785$	0	0
$786$	23.2533	0.829417
$787$	− 54.3241i	− 1.93644i	−0.250093	−	0.968222i	$-0.580461\pi$
$787$	− 54.3241i	− 1.93644i	0.250093	−	0.968222i	$-0.419539\pi$
$788$	8.57553i	0.305491i
$789$	27.4994	0.979003
$790$	0	0
$791$	−38.1160	−1.35525
$792$	0.220184i	0.00782390i
$793$	− 16.7397i	− 0.594443i
$794$	23.2662	0.825687
$795$	0	0
$796$	−3.21724	−0.114032
$797$	− 17.2792i	− 0.612060i	−0.952022	−	0.306030i	$-0.900999\pi$
$797$	− 17.2792i	− 0.612060i	0.952022	−	0.306030i	$-0.0990007\pi$
$798$	14.1281i	0.500130i
$799$	3.13106	0.110769
$800$	0	0
$801$	−0.690691	−0.0244044
$802$	29.2842i	1.03406i
$803$	27.2651i	0.962163i
$804$	11.8159	0.416713
$805$	0	0
$806$	16.8208	0.592487
$807$	3.88991i	0.136931i
$808$	− 2.40940i	− 0.0847624i
$809$	−8.04193	−0.282739	−0.141370	−	0.989957i	$-0.545151\pi$
$809$	−8.04193	−0.282739	−0.141370	+	0.989957i	$0.545151\pi$
$810$	0	0
$811$	−10.6836	−0.375153	−0.187577	−	0.982250i	$-0.560063\pi$
$811$	−10.6836	−0.375153	−0.187577	+	0.982250i	$0.560063\pi$
$812$	2.39138i	0.0839211i
$813$	18.6907i	0.655511i
$814$	−13.3093	−0.466491
$815$	0	0
$816$	0.672673	0.0235483
$817$	41.1009i	1.43794i
$818$	− 17.9640i	− 0.628095i
$819$	0.495577	0.0173168
$820$	0	0
$821$	33.4374	1.16697	0.583487	−	0.812122i	$-0.301688\pi$
$821$	33.4374	1.16697	0.583487	+	0.812122i	$0.301688\pi$
$822$	2.79571i	0.0975117i
$823$	50.6665i	1.76612i	0.469259	+	0.883061i	$0.344521\pi$
$823$	50.6665i	1.76612i	−0.469259	+	0.883061i	$0.655479\pi$
$824$	12.4404	0.433381
$825$	0	0
$826$	23.7677	0.826984
$827$	35.9569i	1.25034i	0.780487	+	0.625172i	$0.214971\pi$
$827$	35.9569i	1.25034i	−0.780487	+	0.625172i	$0.785029\pi$
$828$	0.0791242i	0.00274976i
$829$	−44.3671	−1.54093	−0.770467	−	0.637480i	$-0.779977\pi$
$829$	−44.3671	−1.54093	−0.770467	+	0.637480i	$0.779977\pi$
$830$	0	0
$831$	5.68774	0.197306
$832$	4.50147i	0.156061i
$833$	− 0.501474i	− 0.0173751i
$834$	−30.0541	−1.04069
$835$	0	0
$836$	−16.4404	−0.568602
$837$	− 19.5627i	− 0.676186i
$838$	20.2633i	0.699983i
$839$	−35.3873	−1.22170	−0.610852	−	0.791745i	$-0.709173\pi$
$839$	−35.3873	−1.22170	−0.610852	+	0.791745i	$0.709173\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	− 26.1841i	− 0.902365i
$843$	− 39.0210i	− 1.34395i
$844$	4.78276	0.164630
$845$	0	0
$846$	0.368296	0.0126623
$847$	28.3973i	0.975742i
$848$	− 5.17415i	− 0.177681i
$849$	26.8489	0.921453
$850$	0	0
$851$	−4.78276	−0.163951
$852$	− 11.8159i	− 0.404804i
$853$	36.8607i	1.26209i	0.775747	+	0.631044i	$0.217373\pi$
$853$	36.8607i	1.26209i	−0.775747	+	0.631044i	$0.782627\pi$
$854$	8.89286	0.304307
$855$	0	0
$856$	−18.3123	−0.625900
$857$	− 8.12811i	− 0.277651i	−0.990317	−	0.138825i	$-0.955667\pi$
$857$	− 8.12811i	− 0.277651i	0.990317	−	0.138825i	$-0.0443327\pi$
$858$	− 37.0029i	− 1.26326i
$859$	−18.3843	−0.627265	−0.313633	−	0.949544i	$-0.601546\pi$
$859$	−18.3843	−0.627265	−0.313633	+	0.949544i	$0.601546\pi$
$860$	0	0
$861$	−27.8778	−0.950072
$862$	11.4374i	0.389560i
$863$	− 15.4065i	− 0.524442i	−0.965008	−	0.262221i	$-0.915545\pi$
$863$	− 15.4065i	− 0.524442i	0.965008	−	0.262221i	$-0.0844549\pi$
$864$	5.23525	0.178107
$865$	0	0
$866$	−37.3152	−1.26802
$867$	28.9548i	0.983356i
$868$	8.93594i	0.303306i
$869$	−43.9640	−1.49138
$870$	0	0
$871$	30.9469	1.04860
$872$	8.34829i	0.282709i
$873$	− 0.417282i	− 0.0141229i
$874$	−5.90793	−0.199839
$875$	0	0
$876$	9.79783	0.331038
$877$	31.9389i	1.07850i	0.842146	+	0.539250i	$0.181292\pi$
$877$	31.9389i	1.07850i	−0.842146	+	0.539250i	$0.818708\pi$
$878$	22.6547i	0.764558i
$879$	51.7297	1.74480
$880$	0	0
$881$	−43.6635	−1.47106	−0.735530	−	0.677492i	$-0.763067\pi$
$881$	−43.6635	−1.47106	−0.735530	+	0.677492i	$0.763067\pi$
$882$	− 0.0589868i	− 0.00198619i
$883$	29.4433i	0.990847i	0.868652	+	0.495423i	$0.164987\pi$
$883$	29.4433i	0.990847i	−0.868652	+	0.495423i	$0.835013\pi$
$884$	1.76180	0.0592557
$885$	0	0
$886$	16.2872	0.547179
$887$	6.50654i	0.218468i	0.994016	+	0.109234i	$0.0348398\pi$
$887$	6.50654i	0.218468i	−0.994016	+	0.109234i	$0.965160\pi$
$888$	4.78276i	0.160499i
$889$	16.4404	0.551392
$890$	0	0
$891$	−42.3742	−1.41959
$892$	16.5935i	0.555593i
$893$	27.4994i	0.920231i
$894$	−41.7857	−1.39752
$895$	0	0
$896$	−2.39138	−0.0798905
$897$	− 13.2972i	− 0.443980i
$898$	17.4735i	0.583097i
$899$	3.73673	0.124627
$900$	0	0
$901$	−2.02507	−0.0674649
$902$	− 32.4404i	− 1.08015i
$903$	− 49.1440i	− 1.63541i
$904$	−15.9389	−0.530120
$905$	0	0
$906$	36.0980	1.19927
$907$	3.07618i	0.102143i	0.998695	+	0.0510714i	$0.0162636\pi$
$907$	3.07618i	0.102143i	−0.998695	+	0.0510714i	$0.983736\pi$
$908$	19.3512i	0.642194i
$909$	−0.110922	−0.00367904
$910$	0	0
$911$	−8.67972	−0.287572	−0.143786	−	0.989609i	$-0.545928\pi$
$911$	−8.67972	−0.287572	−0.143786	+	0.989609i	$0.545928\pi$
$912$	5.90793i	0.195631i
$913$	− 21.8217i	− 0.722195i
$914$	−22.6966	−0.750736
$915$	0	0
$916$	−13.3943	−0.442561
$917$	32.3542i	1.06843i
$918$	− 2.04899i	− 0.0676266i
$919$	3.13106	0.103284	0.0516421	−	0.998666i	$-0.483555\pi$
$919$	3.13106	0.103284	0.0516421	+	0.998666i	$0.483555\pi$
$920$	0	0
$921$	23.3152	0.768262
$922$	14.5195i	0.478174i
$923$	− 30.9469i	− 1.01863i
$924$	19.6576	0.646688
$925$	0	0
$926$	−12.0000	−0.394344
$927$	− 0.572717i	− 0.0188105i
$928$	1.00000i	0.0328266i
$929$	43.9268	1.44119	0.720595	−	0.693356i	$-0.243869\pi$
$929$	43.9268	1.44119	0.720595	+	0.693356i	$0.243869\pi$
$930$	0	0
$931$	4.40433	0.144346
$932$	22.4404i	0.735059i
$933$	− 24.9238i	− 0.815969i
$934$	6.73378	0.220336
$935$	0	0
$936$	0.207234	0.00677367
$937$	− 8.27622i	− 0.270372i	−0.990820	−	0.135186i	$-0.956837\pi$
$937$	− 8.27622i	− 0.270372i	0.990820	−	0.135186i	$-0.0431633\pi$
$938$	16.4404i	0.536797i
$939$	−33.6275	−1.09739
$940$	0	0
$941$	−20.6665	−0.673707	−0.336854	−	0.941557i	$-0.609363\pi$
$941$	−20.6665	−0.673707	−0.336854	+	0.941557i	$0.609363\pi$
$942$	− 7.62157i	− 0.248324i
$943$	− 11.6576i	− 0.379624i
$944$	9.93889	0.323483
$945$	0	0
$946$	57.1871	1.85931
$947$	38.7217i	1.25828i	0.777290	+	0.629142i	$0.216594\pi$
$947$	38.7217i	1.25828i	−0.777290	+	0.629142i	$0.783406\pi$
$948$	15.7987i	0.513117i
$949$	25.6615	0.833008
$950$	0	0
$951$	−23.0950	−0.748907
$952$	0.935945i	0.0303341i
$953$	17.9279i	0.580743i	0.956914	+	0.290371i	$0.0937788\pi$
$953$	17.9279i	0.580743i	−0.956914	+	0.290371i	$0.906221\pi$
$954$	−0.238202	−0.00771208
$955$	0	0
$956$	−0.220184	−0.00712126
$957$	− 8.22018i	− 0.265721i
$958$	− 33.4002i	− 1.07911i
$959$	−3.88991	−0.125612
$960$	0	0
$961$	−17.0369	−0.549576
$962$	12.5265i	0.403872i
$963$	0.843041i	0.0271666i
$964$	15.9749	0.514518
$965$	0	0
$966$	7.06406	0.227282
$967$	− 54.7887i	− 1.76188i	−0.473224	−	0.880942i	$-0.656910\pi$
$967$	− 54.7887i	− 1.76188i	0.473224	−	0.880942i	$-0.343090\pi$
$968$	11.8748i	0.381672i
$969$	2.31226	0.0742804
$970$	0	0
$971$	−35.8778	−1.15137	−0.575686	−	0.817671i	$-0.695265\pi$
$971$	−35.8778	−1.15137	−0.575686	+	0.817671i	$0.695265\pi$
$972$	− 0.478388i	− 0.0153443i
$973$	− 41.8167i	− 1.34058i
$974$	−38.3432	−1.22860
$975$	0	0
$976$	3.71871	0.119033
$977$	− 28.8247i	− 0.922184i	−0.887352	−	0.461092i	$-0.847458\pi$
$977$	− 28.8247i	− 0.922184i	0.887352	−	0.461092i	$-0.152542\pi$
$978$	− 37.8217i	− 1.20941i
$979$	−71.7556	−2.29332
$980$	0	0
$981$	0.384330	0.0122707
$982$	− 16.0000i	− 0.510581i
$983$	20.8447i	0.664843i	0.943131	+	0.332421i	$0.107866\pi$
$983$	20.8447i	0.664843i	−0.943131	+	0.332421i	$0.892134\pi$
$984$	−11.6576	−0.371631
$985$	0	0
$986$	0.391382	0.0124642
$987$	− 32.8807i	− 1.04661i
$988$	15.4735i	0.492276i
$989$	20.5505	0.653467
$990$	0	0
$991$	48.4263	1.53831	0.769155	−	0.639062i	$-0.220677\pi$
$991$	48.4263	1.53831	0.769155	+	0.639062i	$0.220677\pi$
$992$	3.73673i	0.118641i
$993$	5.52949i	0.175473i
$994$	16.4404	0.521457
$995$	0	0
$996$	−7.84175	−0.248475
$997$	− 37.6216i	− 1.19149i	−0.803175	−	0.595743i	$-0.796857\pi$
$997$	− 37.6216i	− 1.19149i	0.803175	−	0.595743i	$-0.203143\pi$
$998$	27.9448i	0.884577i
$999$	14.5685	0.460926

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.b.j.349.3		6
5.2	odd	4		290.2.a.d.1.3	✓	3
5.3	odd	4		1450.2.a.r.1.1		3
5.4	even	2	inner	1450.2.b.j.349.4		6
15.2	even	4		2610.2.a.w.1.1		3
20.7	even	4		2320.2.a.q.1.1		3
40.27	even	4		9280.2.a.bn.1.3		3
40.37	odd	4		9280.2.a.bp.1.1		3
145.57	odd	4		8410.2.a.w.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.a.d.1.3	✓	3	5.2	odd	4
1450.2.a.r.1.1		3	5.3	odd	4
1450.2.b.j.349.3		6	1.1	even	1	trivial
1450.2.b.j.349.4		6	5.4	even	2	inner
2320.2.a.q.1.1		3	20.7	even	4
2610.2.a.w.1.1		3	15.2	even	4
8410.2.a.w.1.1		3	145.57	odd	4
9280.2.a.bn.1.3		3	40.27	even	4
9280.2.a.bp.1.1		3	40.37	odd	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:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.71871i q^{3} -1.00000 q^{4} +1.71871 q^{6} +2.39138i q^{7} +1.00000i q^{8} +0.0460370 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.71871i q^{3} -1.00000 q^{4} +1.71871 q^{6} +2.39138i q^{7} +1.00000i q^{8} +0.0460370 q^{9} +4.78276 q^{11} -1.71871i q^{12} -4.50147i q^{13} +2.39138 q^{14} +1.00000 q^{16} -0.391382i q^{17} -0.0460370i q^{18} +3.43742 q^{19} -4.11009 q^{21} -4.78276i q^{22} -1.71871i q^{23} -1.71871 q^{24} -4.50147 q^{26} +5.23525i q^{27} -2.39138i q^{28} -1.00000 q^{29} -3.73673 q^{31} -1.00000i q^{32} +8.22018i q^{33} -0.391382 q^{34} -0.0460370 q^{36} -2.78276i q^{37} -3.43742i q^{38} +7.73673 q^{39} +6.78276 q^{41} +4.11009i q^{42} +11.9569i q^{43} -4.78276 q^{44} -1.71871 q^{46} +8.00000i q^{47} +1.71871i q^{48} +1.28129 q^{49} +0.672673 q^{51} +4.50147i q^{52} -5.17415i q^{53} +5.23525 q^{54} -2.39138 q^{56} +5.90793i q^{57} +1.00000i q^{58} +9.93889 q^{59} +3.71871 q^{61} +3.73673i q^{62} +0.110092i q^{63} -1.00000 q^{64} +8.22018 q^{66} +6.87484i q^{67} +0.391382i q^{68} +2.95396 q^{69} +6.87484 q^{71} +0.0460370i q^{72} +5.70069i q^{73} -2.78276 q^{74} -3.43742 q^{76} +11.4374i q^{77} -7.73673i q^{78} -9.19217 q^{79} -8.85977 q^{81} -6.78276i q^{82} -4.56258i q^{83} +4.11009 q^{84} +11.9569 q^{86} -1.71871i q^{87} +4.78276i q^{88} -15.0029 q^{89} +10.7647 q^{91} +1.71871i q^{92} -6.42235i q^{93} +8.00000 q^{94} +1.71871 q^{96} -9.06406i q^{97} -1.28129i q^{98} +0.220184 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 2 q^{6} - 12 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 - 2 * q^6 - 12 * q^9	\( 6 q - 6 q^{4} - 2 q^{6} - 12 q^{9} + 4 q^{11} + 2 q^{14} + 6 q^{16} - 4 q^{19} + 2 q^{24} + 10 q^{26} - 6 q^{29} - 10 q^{31} + 10 q^{34} + 12 q^{36} + 34 q^{39} + 16 q^{41} - 4 q^{44} + 2 q^{46} + 20 q^{49} + 4 q^{51} + 56 q^{54} - 2 q^{56} - 2 q^{59} + 10 q^{61} - 6 q^{64} + 30 q^{69} - 8 q^{71} + 8 q^{74} + 4 q^{76} - 18 q^{79} + 70 q^{81} + 10 q^{86} - 16 q^{89} + 40 q^{91} + 48 q^{94} - 2 q^{96} - 48 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 - 2 * q^6 - 12 * q^9 + 4 * q^11 + 2 * q^14 + 6 * q^16 - 4 * q^19 + 2 * q^24 + 10 * q^26 - 6 * q^29 - 10 * q^31 + 10 * q^34 + 12 * q^36 + 34 * q^39 + 16 * q^41 - 4 * q^44 + 2 * q^46 + 20 * q^49 + 4 * q^51 + 56 * q^54 - 2 * q^56 - 2 * q^59 + 10 * q^61 - 6 * q^64 + 30 * q^69 - 8 * q^71 + 8 * q^74 + 4 * q^76 - 18 * q^79 + 70 * q^81 + 10 * q^86 - 16 * q^89 + 40 * q^91 + 48 * q^94 - 2 * q^96 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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