LMFDB - Embedded newform 5054.2.a.be.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.a (trivial)

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:	yes
Analytic conductor:	$40.3563931816$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.36538000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 13x^{4} - 4x^{3} + 41x^{2} + 16x - 16 $ x^6 - 13x^4 - 4x^3 + 41x^2 + 16x - 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-2.14489$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.14489 q^{3} +1.00000 q^{4} +2.45305 q^{5} +2.14489 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.60057 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.14489 q^{3} +1.00000 q^{4} +2.45305 q^{5} +2.14489 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.60057 q^{9} +2.45305 q^{10} +4.66096 q^{11} +2.14489 q^{12} -1.96912 q^{13} +1.00000 q^{14} +5.26154 q^{15} +1.00000 q^{16} -1.67933 q^{17} +1.60057 q^{18} +2.45305 q^{20} +2.14489 q^{21} +4.66096 q^{22} +0.371174 q^{23} +2.14489 q^{24} +1.01746 q^{25} -1.96912 q^{26} -3.00162 q^{27} +1.00000 q^{28} +6.25075 q^{29} +5.26154 q^{30} +7.32289 q^{31} +1.00000 q^{32} +9.99728 q^{33} -1.67933 q^{34} +2.45305 q^{35} +1.60057 q^{36} -0.646287 q^{37} -4.22356 q^{39} +2.45305 q^{40} -1.10585 q^{41} +2.14489 q^{42} -9.92250 q^{43} +4.66096 q^{44} +3.92629 q^{45} +0.371174 q^{46} -12.6448 q^{47} +2.14489 q^{48} +1.00000 q^{49} +1.01746 q^{50} -3.60199 q^{51} -1.96912 q^{52} +5.55239 q^{53} -3.00162 q^{54} +11.4336 q^{55} +1.00000 q^{56} +6.25075 q^{58} +2.02042 q^{59} +5.26154 q^{60} -11.6961 q^{61} +7.32289 q^{62} +1.60057 q^{63} +1.00000 q^{64} -4.83035 q^{65} +9.99728 q^{66} -6.75247 q^{67} -1.67933 q^{68} +0.796130 q^{69} +2.45305 q^{70} +8.28979 q^{71} +1.60057 q^{72} -2.51209 q^{73} -0.646287 q^{74} +2.18235 q^{75} +4.66096 q^{77} -4.22356 q^{78} +9.58177 q^{79} +2.45305 q^{80} -11.2399 q^{81} -1.10585 q^{82} +9.73988 q^{83} +2.14489 q^{84} -4.11949 q^{85} -9.92250 q^{86} +13.4072 q^{87} +4.66096 q^{88} -1.96542 q^{89} +3.92629 q^{90} -1.96912 q^{91} +0.371174 q^{92} +15.7068 q^{93} -12.6448 q^{94} +2.14489 q^{96} +10.8945 q^{97} +1.00000 q^{98} +7.46021 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{4} - q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^4 - q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9	$ 6 q + 6 q^{2} + 6 q^{4} - q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9} - q^{10} + 4 q^{11} + 15 q^{13} + 6 q^{14} + 6 q^{15} + 6 q^{16} - 9 q^{17} + 8 q^{18} - q^{20} + 4 q^{22} + 4 q^{23} + q^{25} + 15 q^{26} - 12 q^{27} + 6 q^{28} + 7 q^{29} + 6 q^{30} + 4 q^{31} + 6 q^{32} + 28 q^{33} - 9 q^{34} - q^{35} + 8 q^{36} + 3 q^{37} - 8 q^{39} - q^{40} + 11 q^{41} - 10 q^{43} + 4 q^{44} + 19 q^{45} + 4 q^{46} + 12 q^{47} + 6 q^{49} + q^{50} + 44 q^{51} + 15 q^{52} - 5 q^{53} - 12 q^{54} - 8 q^{55} + 6 q^{56} + 7 q^{58} + 4 q^{59} + 6 q^{60} - 21 q^{61} + 4 q^{62} + 8 q^{63} + 6 q^{64} - 20 q^{65} + 28 q^{66} + 14 q^{67} - 9 q^{68} - 24 q^{69} - q^{70} + 24 q^{71} + 8 q^{72} - 21 q^{73} + 3 q^{74} + 12 q^{75} + 4 q^{77} - 8 q^{78} + 58 q^{79} - q^{80} - 6 q^{81} + 11 q^{82} + 20 q^{83} - 4 q^{85} - 10 q^{86} - 8 q^{87} + 4 q^{88} + 7 q^{89} + 19 q^{90} + 15 q^{91} + 4 q^{92} - 22 q^{93} + 12 q^{94} + 7 q^{97} + 6 q^{98} - 26 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^4 - q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9 - q^10 + 4 * q^11 + 15 * q^13 + 6 * q^14 + 6 * q^15 + 6 * q^16 - 9 * q^17 + 8 * q^18 - q^20 + 4 * q^22 + 4 * q^23 + q^25 + 15 * q^26 - 12 * q^27 + 6 * q^28 + 7 * q^29 + 6 * q^30 + 4 * q^31 + 6 * q^32 + 28 * q^33 - 9 * q^34 - q^35 + 8 * q^36 + 3 * q^37 - 8 * q^39 - q^40 + 11 * q^41 - 10 * q^43 + 4 * q^44 + 19 * q^45 + 4 * q^46 + 12 * q^47 + 6 * q^49 + q^50 + 44 * q^51 + 15 * q^52 - 5 * q^53 - 12 * q^54 - 8 * q^55 + 6 * q^56 + 7 * q^58 + 4 * q^59 + 6 * q^60 - 21 * q^61 + 4 * q^62 + 8 * q^63 + 6 * q^64 - 20 * q^65 + 28 * q^66 + 14 * q^67 - 9 * q^68 - 24 * q^69 - q^70 + 24 * q^71 + 8 * q^72 - 21 * q^73 + 3 * q^74 + 12 * q^75 + 4 * q^77 - 8 * q^78 + 58 * q^79 - q^80 - 6 * q^81 + 11 * q^82 + 20 * q^83 - 4 * q^85 - 10 * q^86 - 8 * q^87 + 4 * q^88 + 7 * q^89 + 19 * q^90 + 15 * q^91 + 4 * q^92 - 22 * q^93 + 12 * q^94 + 7 * q^97 + 6 * q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.14489	1.23836	0.619178	−	0.785251i	$-0.287466\pi$
$3$	2.14489	1.23836	0.619178	+	0.785251i	$0.287466\pi$
$4$	1.00000	0.500000
$5$	2.45305	1.09704	0.548519	−	0.836138i	$-0.315192\pi$
$5$	2.45305	1.09704	0.548519	+	0.836138i	$0.315192\pi$
$6$	2.14489	0.875650
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.60057	0.533524
$10$	2.45305	0.775723
$11$	4.66096	1.40533	0.702667	−	0.711519i	$-0.251993\pi$
$11$	4.66096	1.40533	0.702667	+	0.711519i	$0.251993\pi$
$12$	2.14489	0.619178
$13$	−1.96912	−0.546136	−0.273068	−	0.961995i	$-0.588038\pi$
$13$	−1.96912	−0.546136	−0.273068	+	0.961995i	$0.588038\pi$
$14$	1.00000	0.267261
$15$	5.26154	1.35852
$16$	1.00000	0.250000
$17$	−1.67933	−0.407298	−0.203649	−	0.979044i	$-0.565280\pi$
$17$	−1.67933	−0.407298	−0.203649	+	0.979044i	$0.565280\pi$
$18$	1.60057	0.377259
$19$	0	0
$19$	0	0
$20$	2.45305	0.548519
$21$	2.14489	0.468054
$22$	4.66096	0.993721
$23$	0.371174	0.0773952	0.0386976	−	0.999251i	$-0.487679\pi$
$23$	0.371174	0.0773952	0.0386976	+	0.999251i	$0.487679\pi$
$24$	2.14489	0.437825
$25$	1.01746	0.203492
$26$	−1.96912	−0.386176
$27$	−3.00162	−0.577663
$28$	1.00000	0.188982
$29$	6.25075	1.16073	0.580367	−	0.814355i	$-0.302909\pi$
$29$	6.25075	1.16073	0.580367	+	0.814355i	$0.302909\pi$
$30$	5.26154	0.960621
$31$	7.32289	1.31523	0.657615	−	0.753354i	$-0.271565\pi$
$31$	7.32289	1.31523	0.657615	+	0.753354i	$0.271565\pi$
$32$	1.00000	0.176777
$33$	9.99728	1.74030
$34$	−1.67933	−0.288003
$35$	2.45305	0.414641
$36$	1.60057	0.266762
$37$	−0.646287	−0.106249	−0.0531244	−	0.998588i	$-0.516918\pi$
$37$	−0.646287	−0.106249	−0.0531244	+	0.998588i	$0.516918\pi$
$38$	0	0
$39$	−4.22356	−0.676310
$40$	2.45305	0.387861
$41$	−1.10585	−0.172705	−0.0863524	−	0.996265i	$-0.527521\pi$
$41$	−1.10585	−0.172705	−0.0863524	+	0.996265i	$0.527521\pi$
$42$	2.14489	0.330964
$43$	−9.92250	−1.51317	−0.756584	−	0.653897i	$-0.773133\pi$
$43$	−9.92250	−1.51317	−0.756584	+	0.653897i	$0.773133\pi$
$44$	4.66096	0.702667
$45$	3.92629	0.585296
$46$	0.371174	0.0547267
$47$	−12.6448	−1.84444	−0.922218	−	0.386669i	$-0.873625\pi$
$47$	−12.6448	−1.84444	−0.922218	+	0.386669i	$0.873625\pi$
$48$	2.14489	0.309589
$49$	1.00000	0.142857
$50$	1.01746	0.143891
$51$	−3.60199	−0.504379
$52$	−1.96912	−0.273068
$53$	5.55239	0.762679	0.381340	−	0.924435i	$-0.375463\pi$
$53$	5.55239	0.762679	0.381340	+	0.924435i	$0.375463\pi$
$54$	−3.00162	−0.408469
$55$	11.4336	1.54170
$56$	1.00000	0.133631
$57$	0	0
$58$	6.25075	0.820763
$59$	2.02042	0.263037	0.131518	−	0.991314i	$-0.458015\pi$
$59$	2.02042	0.263037	0.131518	+	0.991314i	$0.458015\pi$
$60$	5.26154	0.679261
$61$	−11.6961	−1.49753	−0.748764	−	0.662837i	$-0.769352\pi$
$61$	−11.6961	−1.49753	−0.748764	+	0.662837i	$0.769352\pi$
$62$	7.32289	0.930008
$63$	1.60057	0.201653
$64$	1.00000	0.125000
$65$	−4.83035	−0.599132
$66$	9.99728	1.23058
$67$	−6.75247	−0.824946	−0.412473	−	0.910970i	$-0.635335\pi$
$67$	−6.75247	−0.824946	−0.412473	+	0.910970i	$0.635335\pi$
$68$	−1.67933	−0.203649
$69$	0.796130	0.0958428
$70$	2.45305	0.293196
$71$	8.28979	0.983817	0.491908	−	0.870647i	$-0.336299\pi$
$71$	8.28979	0.983817	0.491908	+	0.870647i	$0.336299\pi$
$72$	1.60057	0.188629
$73$	−2.51209	−0.294017	−0.147009	−	0.989135i	$-0.546965\pi$
$73$	−2.51209	−0.294017	−0.147009	+	0.989135i	$0.546965\pi$
$74$	−0.646287	−0.0751293
$75$	2.18235	0.251996
$76$	0	0
$77$	4.66096	0.531166
$78$	−4.22356	−0.478224
$79$	9.58177	1.07803	0.539017	−	0.842295i	$-0.318796\pi$
$79$	9.58177	1.07803	0.539017	+	0.842295i	$0.318796\pi$
$80$	2.45305	0.274259
$81$	−11.2399	−1.24888
$82$	−1.10585	−0.122121
$83$	9.73988	1.06909	0.534545	−	0.845140i	$-0.320483\pi$
$83$	9.73988	1.06909	0.534545	+	0.845140i	$0.320483\pi$
$84$	2.14489	0.234027
$85$	−4.11949	−0.446821
$86$	−9.92250	−1.06997
$87$	13.4072	1.43740
$88$	4.66096	0.496860
$89$	−1.96542	−0.208334	−0.104167	−	0.994560i	$-0.533218\pi$
$89$	−1.96542	−0.208334	−0.104167	+	0.994560i	$0.533218\pi$
$90$	3.92629	0.413867
$91$	−1.96912	−0.206420
$92$	0.371174	0.0386976
$93$	15.7068	1.62872
$94$	−12.6448	−1.30421
$95$	0	0
$96$	2.14489	0.218912
$97$	10.8945	1.10617	0.553086	−	0.833124i	$-0.313450\pi$
$97$	10.8945	1.10617	0.553086	+	0.833124i	$0.313450\pi$
$98$	1.00000	0.101015
$99$	7.46021	0.749780
$100$	1.01746	0.101746
$101$	−18.0979	−1.80081	−0.900406	−	0.435051i	$-0.856730\pi$
$101$	−18.0979	−1.80081	−0.900406	+	0.435051i	$0.856730\pi$
$102$	−3.60199	−0.356650
$103$	−19.3790	−1.90947	−0.954733	−	0.297465i	$-0.903859\pi$
$103$	−19.3790	−1.90947	−0.954733	+	0.297465i	$0.903859\pi$
$104$	−1.96912	−0.193088
$105$	5.26154	0.513473
$106$	5.55239	0.539296
$107$	20.1089	1.94400	0.971998	−	0.234989i	$-0.0755053\pi$
$107$	20.1089	1.94400	0.971998	+	0.234989i	$0.0755053\pi$
$108$	−3.00162	−0.288831
$109$	12.3454	1.18247	0.591237	−	0.806498i	$-0.298640\pi$
$109$	12.3454	1.18247	0.591237	+	0.806498i	$0.298640\pi$
$110$	11.4336	1.09015
$111$	−1.38622	−0.131574
$112$	1.00000	0.0944911
$113$	5.92051	0.556954	0.278477	−	0.960443i	$-0.410170\pi$
$113$	5.92051	0.556954	0.278477	+	0.960443i	$0.410170\pi$
$114$	0	0
$115$	0.910510	0.0849055
$116$	6.25075	0.580367
$117$	−3.15172	−0.291377
$118$	2.02042	0.185995
$119$	−1.67933	−0.153944
$120$	5.26154	0.480310
$121$	10.7246	0.974962
$122$	−11.6961	−1.05891
$123$	−2.37193	−0.213870
$124$	7.32289	0.657615
$125$	−9.76937	−0.873799
$126$	1.60057	0.142590
$127$	−18.0378	−1.60060	−0.800299	−	0.599600i	$-0.795326\pi$
$127$	−18.0378	−1.60060	−0.800299	+	0.599600i	$0.795326\pi$
$128$	1.00000	0.0883883
$129$	−21.2827	−1.87384
$130$	−4.83035	−0.423650
$131$	2.03649	0.177929	0.0889643	−	0.996035i	$-0.471644\pi$
$131$	2.03649	0.177929	0.0889643	+	0.996035i	$0.471644\pi$
$132$	9.99728	0.870151
$133$	0	0
$134$	−6.75247	−0.583325
$135$	−7.36314	−0.633718
$136$	−1.67933	−0.144001
$137$	9.02736	0.771259	0.385630	−	0.922654i	$-0.373984\pi$
$137$	9.02736	0.771259	0.385630	+	0.922654i	$0.373984\pi$
$138$	0.796130	0.0677711
$139$	4.89160	0.414900	0.207450	−	0.978246i	$-0.433484\pi$
$139$	4.89160	0.414900	0.207450	+	0.978246i	$0.433484\pi$
$140$	2.45305	0.207321
$141$	−27.1218	−2.28407
$142$	8.28979	0.695664
$143$	−9.17800	−0.767503
$144$	1.60057	0.133381
$145$	15.3334	1.27337
$146$	−2.51209	−0.207902
$147$	2.14489	0.176908
$148$	−0.646287	−0.0531244
$149$	−1.97345	−0.161671	−0.0808356	−	0.996727i	$-0.525759\pi$
$149$	−1.97345	−0.161671	−0.0808356	+	0.996727i	$0.525759\pi$
$150$	2.18235	0.178188
$151$	−5.21877	−0.424697	−0.212349	−	0.977194i	$-0.568111\pi$
$151$	−5.21877	−0.424697	−0.212349	+	0.977194i	$0.568111\pi$
$152$	0	0
$153$	−2.68789	−0.217303
$154$	4.66096	0.375591
$155$	17.9634	1.44286
$156$	−4.22356	−0.338155
$157$	6.50205	0.518920	0.259460	−	0.965754i	$-0.416455\pi$
$157$	6.50205	0.518920	0.259460	+	0.965754i	$0.416455\pi$
$158$	9.58177	0.762285
$159$	11.9093	0.944468
$160$	2.45305	0.193931
$161$	0.371174	0.0292526
$162$	−11.2399	−0.883089
$163$	−20.9999	−1.64484	−0.822418	−	0.568884i	$-0.807375\pi$
$163$	−20.9999	−1.64484	−0.822418	+	0.568884i	$0.807375\pi$
$164$	−1.10585	−0.0863524
$165$	24.5238	1.90918
$166$	9.73988	0.755961
$167$	−20.1931	−1.56259	−0.781295	−	0.624162i	$-0.785440\pi$
$167$	−20.1931	−1.56259	−0.781295	+	0.624162i	$0.785440\pi$
$168$	2.14489	0.165482
$169$	−9.12256	−0.701736
$170$	−4.11949	−0.315950
$171$	0	0
$172$	−9.92250	−0.756584
$173$	−15.0110	−1.14127	−0.570634	−	0.821204i	$-0.693303\pi$
$173$	−15.0110	−1.14127	−0.570634	+	0.821204i	$0.693303\pi$
$174$	13.4072	1.01640
$175$	1.01746	0.0769128
$176$	4.66096	0.351333
$177$	4.33359	0.325733
$178$	−1.96542	−0.147315
$179$	−20.4827	−1.53095	−0.765476	−	0.643464i	$-0.777496\pi$
$179$	−20.4827	−1.53095	−0.765476	+	0.643464i	$0.777496\pi$
$180$	3.92629	0.292648
$181$	9.69046	0.720286	0.360143	−	0.932897i	$-0.382728\pi$
$181$	9.69046	0.720286	0.360143	+	0.932897i	$0.382728\pi$
$182$	−1.96912	−0.145961
$183$	−25.0868	−1.85447
$184$	0.371174	0.0273633
$185$	−1.58537	−0.116559
$186$	15.7068	1.15168
$187$	−7.82730	−0.572389
$188$	−12.6448	−0.922218
$189$	−3.00162	−0.218336
$190$	0	0
$191$	−7.42834	−0.537496	−0.268748	−	0.963211i	$-0.586610\pi$
$191$	−7.42834	−0.537496	−0.268748	+	0.963211i	$0.586610\pi$
$192$	2.14489	0.154794
$193$	−15.8766	−1.14282	−0.571411	−	0.820664i	$-0.693604\pi$
$193$	−15.8766	−1.14282	−0.571411	+	0.820664i	$0.693604\pi$
$194$	10.8945	0.782182
$195$	−10.3606	−0.741938
$196$	1.00000	0.0714286
$197$	19.4013	1.38229	0.691144	−	0.722717i	$-0.257107\pi$
$197$	19.4013	1.38229	0.691144	+	0.722717i	$0.257107\pi$
$198$	7.46021	0.530174
$199$	16.8874	1.19711	0.598557	−	0.801080i	$-0.295741\pi$
$199$	16.8874	1.19711	0.598557	+	0.801080i	$0.295741\pi$
$200$	1.01746	0.0719454
$201$	−14.4833	−1.02158
$202$	−18.0979	−1.27337
$203$	6.25075	0.438716
$204$	−3.60199	−0.252190
$205$	−2.71271	−0.189464
$206$	−19.3790	−1.35020
$207$	0.594092	0.0412922
$208$	−1.96912	−0.136534
$209$	0	0
$210$	5.26154	0.363081
$211$	13.9533	0.960588	0.480294	−	0.877108i	$-0.340530\pi$
$211$	13.9533	0.960588	0.480294	+	0.877108i	$0.340530\pi$
$212$	5.55239	0.381340
$213$	17.7807	1.21832
$214$	20.1089	1.37461
$215$	−24.3404	−1.66000
$216$	−3.00162	−0.204235
$217$	7.32289	0.497110
$218$	12.3454	0.836136
$219$	−5.38816	−0.364098
$220$	11.4336	0.770852
$221$	3.30681	0.222440
$222$	−1.38622	−0.0930368
$223$	−9.61825	−0.644086	−0.322043	−	0.946725i	$-0.604370\pi$
$223$	−9.61825	−0.644086	−0.322043	+	0.946725i	$0.604370\pi$
$224$	1.00000	0.0668153
$225$	1.62852	0.108568
$226$	5.92051	0.393826
$227$	17.5348	1.16382	0.581912	−	0.813251i	$-0.302305\pi$
$227$	17.5348	1.16382	0.581912	+	0.813251i	$0.302305\pi$
$228$	0	0
$229$	−3.06018	−0.202223	−0.101111	−	0.994875i	$-0.532240\pi$
$229$	−3.06018	−0.202223	−0.101111	+	0.994875i	$0.532240\pi$
$230$	0.910510	0.0600373
$231$	9.99728	0.657772
$232$	6.25075	0.410382
$233$	26.3535	1.72648	0.863238	−	0.504798i	$-0.168433\pi$
$233$	26.3535	1.72648	0.863238	+	0.504798i	$0.168433\pi$
$234$	−3.15172	−0.206034
$235$	−31.0184	−2.02342
$236$	2.02042	0.131518
$237$	20.5519	1.33499
$238$	−1.67933	−0.108855
$239$	27.4395	1.77491	0.887456	−	0.460893i	$-0.152471\pi$
$239$	27.4395	1.77491	0.887456	+	0.460893i	$0.152471\pi$
$240$	5.26154	0.339631
$241$	14.9775	0.964786	0.482393	−	0.875955i	$-0.339768\pi$
$241$	14.9775	0.964786	0.482393	+	0.875955i	$0.339768\pi$
$242$	10.7246	0.689402
$243$	−15.1035	−0.968890
$244$	−11.6961	−0.748764
$245$	2.45305	0.156720
$246$	−2.37193	−0.151229
$247$	0	0
$248$	7.32289	0.465004
$249$	20.8910	1.32391
$250$	−9.76937	−0.617869
$251$	14.1051	0.890307	0.445154	−	0.895454i	$-0.353149\pi$
$251$	14.1051	0.890307	0.445154	+	0.895454i	$0.353149\pi$
$252$	1.60057	0.100827
$253$	1.73003	0.108766
$254$	−18.0378	−1.13179
$255$	−8.83586	−0.553323
$256$	1.00000	0.0625000
$257$	10.0917	0.629505	0.314752	−	0.949174i	$-0.398079\pi$
$257$	10.0917	0.629505	0.314752	+	0.949174i	$0.398079\pi$
$258$	−21.2827	−1.32500
$259$	−0.646287	−0.0401583
$260$	−4.83035	−0.299566
$261$	10.0048	0.619280
$262$	2.03649	0.125815
$263$	−23.8534	−1.47086	−0.735432	−	0.677598i	$-0.763021\pi$
$263$	−23.8534	−1.47086	−0.735432	+	0.677598i	$0.763021\pi$
$264$	9.99728	0.615290
$265$	13.6203	0.836688
$266$	0	0
$267$	−4.21563	−0.257992
$268$	−6.75247	−0.412473
$269$	8.77050	0.534747	0.267374	−	0.963593i	$-0.413844\pi$
$269$	8.77050	0.534747	0.267374	+	0.963593i	$0.413844\pi$
$270$	−7.36314	−0.448106
$271$	6.08145	0.369422	0.184711	−	0.982793i	$-0.440865\pi$
$271$	6.08145	0.369422	0.184711	+	0.982793i	$0.440865\pi$
$272$	−1.67933	−0.101824
$273$	−4.22356	−0.255621
$274$	9.02736	0.545363
$275$	4.74235	0.285974
$276$	0.796130	0.0479214
$277$	−25.0478	−1.50498	−0.752488	−	0.658606i	$-0.771147\pi$
$277$	−25.0478	−1.50498	−0.752488	+	0.658606i	$0.771147\pi$
$278$	4.89160	0.293379
$279$	11.7208	0.701707
$280$	2.45305	0.146598
$281$	8.07617	0.481784	0.240892	−	0.970552i	$-0.422560\pi$
$281$	8.07617	0.481784	0.240892	+	0.970552i	$0.422560\pi$
$282$	−27.1218	−1.61508
$283$	−9.35289	−0.555971	−0.277986	−	0.960585i	$-0.589667\pi$
$283$	−9.35289	−0.555971	−0.277986	+	0.960585i	$0.589667\pi$
$284$	8.28979	0.491908
$285$	0	0
$286$	−9.17800	−0.542706
$287$	−1.10585	−0.0652763
$288$	1.60057	0.0943147
$289$	−14.1798	−0.834109
$290$	15.3334	0.900408
$291$	23.3676	1.36983
$292$	−2.51209	−0.147009
$293$	13.5630	0.792360	0.396180	−	0.918173i	$-0.370336\pi$
$293$	13.5630	0.792360	0.396180	+	0.918173i	$0.370336\pi$
$294$	2.14489	0.125093
$295$	4.95620	0.288561
$296$	−0.646287	−0.0375646
$297$	−13.9905	−0.811809
$298$	−1.97345	−0.114319
$299$	−0.730887	−0.0422683
$300$	2.18235	0.125998
$301$	−9.92250	−0.571923
$302$	−5.21877	−0.300306
$303$	−38.8182	−2.23004
$304$	0	0
$305$	−28.6910	−1.64284
$306$	−2.68789	−0.153657
$307$	0.739222	0.0421896	0.0210948	−	0.999777i	$-0.493285\pi$
$307$	0.739222	0.0421896	0.0210948	+	0.999777i	$0.493285\pi$
$308$	4.66096	0.265583
$309$	−41.5658	−2.36460
$310$	17.9634	1.02025
$311$	0.944861	0.0535782	0.0267891	−	0.999641i	$-0.491472\pi$
$311$	0.944861	0.0535782	0.0267891	+	0.999641i	$0.491472\pi$
$312$	−4.22356	−0.239112
$313$	−16.8338	−0.951504	−0.475752	−	0.879579i	$-0.657824\pi$
$313$	−16.8338	−0.951504	−0.475752	+	0.879579i	$0.657824\pi$
$314$	6.50205	0.366932
$315$	3.92629	0.221221
$316$	9.58177	0.539017
$317$	−4.26863	−0.239750	−0.119875	−	0.992789i	$-0.538249\pi$
$317$	−4.26863	−0.239750	−0.119875	+	0.992789i	$0.538249\pi$
$318$	11.9093	0.667840
$319$	29.1345	1.63122
$320$	2.45305	0.137130
$321$	43.1314	2.40736
$322$	0.371174	0.0206847
$323$	0	0
$324$	−11.2399	−0.624438
$325$	−2.00350	−0.111134
$326$	−20.9999	−1.16307
$327$	26.4796	1.46432
$328$	−1.10585	−0.0610604
$329$	−12.6448	−0.697132
$330$	24.5238	1.34999
$331$	−25.9974	−1.42895	−0.714473	−	0.699663i	$-0.753333\pi$
$331$	−25.9974	−1.42895	−0.714473	+	0.699663i	$0.753333\pi$
$332$	9.73988	0.534545
$333$	−1.03443	−0.0566863
$334$	−20.1931	−1.10492
$335$	−16.5642	−0.904997
$336$	2.14489	0.117014
$337$	−11.6954	−0.637087	−0.318544	−	0.947908i	$-0.603194\pi$
$337$	−11.6954	−0.637087	−0.318544	+	0.947908i	$0.603194\pi$
$338$	−9.12256	−0.496202
$339$	12.6989	0.689707
$340$	−4.11949	−0.223410
$341$	34.1317	1.84834
$342$	0	0
$343$	1.00000	0.0539949
$344$	−9.92250	−0.534985
$345$	1.95295	0.105143
$346$	−15.0110	−0.806999
$347$	−19.4270	−1.04290	−0.521449	−	0.853282i	$-0.674608\pi$
$347$	−19.4270	−1.04290	−0.521449	+	0.853282i	$0.674608\pi$
$348$	13.4072	0.718701
$349$	6.79008	0.363465	0.181732	−	0.983348i	$-0.441830\pi$
$349$	6.79008	0.363465	0.181732	+	0.983348i	$0.441830\pi$
$350$	1.01746	0.0543856
$351$	5.91056	0.315482
$352$	4.66096	0.248430
$353$	2.61595	0.139233	0.0696164	−	0.997574i	$-0.477822\pi$
$353$	2.61595	0.139233	0.0696164	+	0.997574i	$0.477822\pi$
$354$	4.33359	0.230328
$355$	20.3353	1.07928
$356$	−1.96542	−0.104167
$357$	−3.60199	−0.190637
$358$	−20.4827	−1.08255
$359$	−19.7876	−1.04435	−0.522174	−	0.852839i	$-0.674879\pi$
$359$	−19.7876	−1.04435	−0.522174	+	0.852839i	$0.674879\pi$
$360$	3.92629	0.206934
$361$	0	0
$362$	9.69046	0.509319
$363$	23.0031	1.20735
$364$	−1.96912	−0.103210
$365$	−6.16228	−0.322548
$366$	−25.0868	−1.31131
$367$	−29.0819	−1.51806	−0.759032	−	0.651054i	$-0.774327\pi$
$367$	−29.0819	−1.51806	−0.759032	+	0.651054i	$0.774327\pi$
$368$	0.371174	0.0193488
$369$	−1.76999	−0.0921422
$370$	−1.58537	−0.0824197
$371$	5.55239	0.288266
$372$	15.7068	0.814361
$373$	6.65147	0.344400	0.172200	−	0.985062i	$-0.444912\pi$
$373$	6.65147	0.344400	0.172200	+	0.985062i	$0.444912\pi$
$374$	−7.82730	−0.404740
$375$	−20.9543	−1.08207
$376$	−12.6448	−0.652107
$377$	−12.3085	−0.633918
$378$	−3.00162	−0.154387
$379$	−4.62364	−0.237500	−0.118750	−	0.992924i	$-0.537889\pi$
$379$	−4.62364	−0.237500	−0.118750	+	0.992924i	$0.537889\pi$
$380$	0	0
$381$	−38.6893	−1.98211
$382$	−7.42834	−0.380067
$383$	−22.5475	−1.15212	−0.576061	−	0.817407i	$-0.695411\pi$
$383$	−22.5475	−1.15212	−0.576061	+	0.817407i	$0.695411\pi$
$384$	2.14489	0.109456
$385$	11.4336	0.582709
$386$	−15.8766	−0.808098
$387$	−15.8817	−0.807311
$388$	10.8945	0.553086
$389$	−15.1594	−0.768614	−0.384307	−	0.923205i	$-0.625560\pi$
$389$	−15.1594	−0.768614	−0.384307	+	0.923205i	$0.625560\pi$
$390$	−10.3606	−0.524629
$391$	−0.623325	−0.0315229
$392$	1.00000	0.0505076
$393$	4.36805	0.220339
$394$	19.4013	0.977426
$395$	23.5046	1.18264
$396$	7.46021	0.374890
$397$	38.5487	1.93470	0.967351	−	0.253440i	$-0.0815622\pi$
$397$	38.5487	1.93470	0.967351	+	0.253440i	$0.0815622\pi$
$398$	16.8874	0.846487
$399$	0	0
$400$	1.01746	0.0508731
$401$	21.9495	1.09611	0.548054	−	0.836443i	$-0.315369\pi$
$401$	21.9495	1.09611	0.548054	+	0.836443i	$0.315369\pi$
$402$	−14.4833	−0.722363
$403$	−14.4197	−0.718294
$404$	−18.0979	−0.900406
$405$	−27.5720	−1.37006
$406$	6.25075	0.310219
$407$	−3.01232	−0.149315
$408$	−3.60199	−0.178325
$409$	26.2379	1.29738	0.648691	−	0.761052i	$-0.275317\pi$
$409$	26.2379	1.29738	0.648691	+	0.761052i	$0.275317\pi$
$410$	−2.71271	−0.133971
$411$	19.3627	0.955093
$412$	−19.3790	−0.954733
$413$	2.02042	0.0994185
$414$	0.594092	0.0291980
$415$	23.8924	1.17283
$416$	−1.96912	−0.0965441
$417$	10.4920	0.513794
$418$	0	0
$419$	−14.7648	−0.721306	−0.360653	−	0.932700i	$-0.617446\pi$
$419$	−14.7648	−0.721306	−0.360653	+	0.932700i	$0.617446\pi$
$420$	5.26154	0.256737
$421$	9.35190	0.455784	0.227892	−	0.973686i	$-0.426817\pi$
$421$	9.35190	0.455784	0.227892	+	0.973686i	$0.426817\pi$
$422$	13.9533	0.679238
$423$	−20.2390	−0.984052
$424$	5.55239	0.269648
$425$	−1.70865	−0.0828819
$426$	17.7807	0.861479
$427$	−11.6961	−0.566012
$428$	20.1089	0.971998
$429$	−19.6858	−0.950441
$430$	−24.3404	−1.17380
$431$	23.8387	1.14827	0.574134	−	0.818761i	$-0.305339\pi$
$431$	23.8387	1.14827	0.574134	+	0.818761i	$0.305339\pi$
$432$	−3.00162	−0.144416
$433$	−38.4316	−1.84690	−0.923452	−	0.383714i	$-0.874645\pi$
$433$	−38.4316	−1.84690	−0.923452	+	0.383714i	$0.874645\pi$
$434$	7.32289	0.351510
$435$	32.8885	1.57688
$436$	12.3454	0.591237
$437$	0	0
$438$	−5.38816	−0.257456
$439$	−8.78467	−0.419269	−0.209635	−	0.977780i	$-0.567227\pi$
$439$	−8.78467	−0.419269	−0.209635	+	0.977780i	$0.567227\pi$
$440$	11.4336	0.545075
$441$	1.60057	0.0762178
$442$	3.30681	0.157289
$443$	10.6376	0.505409	0.252704	−	0.967544i	$-0.418680\pi$
$443$	10.6376	0.505409	0.252704	+	0.967544i	$0.418680\pi$
$444$	−1.38622	−0.0657869
$445$	−4.82128	−0.228551
$446$	−9.61825	−0.455437
$447$	−4.23284	−0.200207
$448$	1.00000	0.0472456
$449$	−9.25065	−0.436565	−0.218282	−	0.975886i	$-0.570045\pi$
$449$	−9.25065	−0.436565	−0.218282	+	0.975886i	$0.570045\pi$
$450$	1.62852	0.0767692
$451$	−5.15433	−0.242708
$452$	5.92051	0.278477
$453$	−11.1937	−0.525926
$454$	17.5348	0.822948
$455$	−4.83035	−0.226450
$456$	0	0
$457$	−14.2859	−0.668265	−0.334132	−	0.942526i	$-0.608443\pi$
$457$	−14.2859	−0.668265	−0.334132	+	0.942526i	$0.608443\pi$
$458$	−3.06018	−0.142993
$459$	5.04072	0.235281
$460$	0.910510	0.0424528
$461$	−3.02462	−0.140871	−0.0704354	−	0.997516i	$-0.522439\pi$
$461$	−3.02462	−0.140871	−0.0704354	+	0.997516i	$0.522439\pi$
$462$	9.99728	0.465115
$463$	4.98327	0.231592	0.115796	−	0.993273i	$-0.463058\pi$
$463$	4.98327	0.231592	0.115796	+	0.993273i	$0.463058\pi$
$464$	6.25075	0.290184
$465$	38.5297	1.78677
$466$	26.3535	1.22080
$467$	18.1672	0.840679	0.420340	−	0.907367i	$-0.361911\pi$
$467$	18.1672	0.840679	0.420340	+	0.907367i	$0.361911\pi$
$468$	−3.15172	−0.145688
$469$	−6.75247	−0.311800
$470$	−31.0184	−1.43077
$471$	13.9462	0.642607
$472$	2.02042	0.0929975
$473$	−46.2484	−2.12650
$474$	20.5519	0.943980
$475$	0	0
$476$	−1.67933	−0.0769720
$477$	8.88700	0.406908
$478$	27.4395	1.25505
$479$	26.4885	1.21029	0.605144	−	0.796116i	$-0.293115\pi$
$479$	26.4885	1.21029	0.605144	+	0.796116i	$0.293115\pi$
$480$	5.26154	0.240155
$481$	1.27262	0.0580263
$482$	14.9775	0.682207
$483$	0.796130	0.0362252
$484$	10.7246	0.487481
$485$	26.7248	1.21351
$486$	−15.1035	−0.685109
$487$	34.4343	1.56037	0.780184	−	0.625550i	$-0.215126\pi$
$487$	34.4343	1.56037	0.780184	+	0.625550i	$0.215126\pi$
$488$	−11.6961	−0.529456
$489$	−45.0425	−2.03689
$490$	2.45305	0.110818
$491$	38.9864	1.75943	0.879715	−	0.475502i	$-0.157733\pi$
$491$	38.9864	1.75943	0.879715	+	0.475502i	$0.157733\pi$
$492$	−2.37193	−0.106935
$493$	−10.4971	−0.472764
$494$	0	0
$495$	18.3003	0.822537
$496$	7.32289	0.328808
$497$	8.28979	0.371848
$498$	20.8910	0.936149
$499$	20.0894	0.899325	0.449662	−	0.893199i	$-0.351544\pi$
$499$	20.0894	0.899325	0.449662	+	0.893199i	$0.351544\pi$
$500$	−9.76937	−0.436900
$501$	−43.3121	−1.93504
$502$	14.1051	0.629542
$503$	20.7208	0.923895	0.461948	−	0.886907i	$-0.347151\pi$
$503$	20.7208	0.923895	0.461948	+	0.886907i	$0.347151\pi$
$504$	1.60057	0.0712952
$505$	−44.3952	−1.97556
$506$	1.73003	0.0769093
$507$	−19.5669	−0.868998
$508$	−18.0378	−0.800299
$509$	−12.0371	−0.533535	−0.266767	−	0.963761i	$-0.585955\pi$
$509$	−12.0371	−0.533535	−0.266767	+	0.963761i	$0.585955\pi$
$510$	−8.83586	−0.391259
$511$	−2.51209	−0.111128
$512$	1.00000	0.0441942
$513$	0	0
$514$	10.0917	0.445127
$515$	−47.5376	−2.09476
$516$	−21.2827	−0.936919
$517$	−58.9371	−2.59205
$518$	−0.646287	−0.0283962
$519$	−32.1971	−1.41330
$520$	−4.83035	−0.211825
$521$	12.7325	0.557822	0.278911	−	0.960317i	$-0.410027\pi$
$521$	12.7325	0.557822	0.278911	+	0.960317i	$0.410027\pi$
$522$	10.0048	0.437897
$523$	−17.3287	−0.757731	−0.378865	−	0.925452i	$-0.623686\pi$
$523$	−17.3287	−0.757731	−0.378865	+	0.925452i	$0.623686\pi$
$524$	2.03649	0.0889643
$525$	2.18235	0.0952454
$526$	−23.8534	−1.04006
$527$	−12.2976	−0.535690
$528$	9.99728	0.435076
$529$	−22.8622	−0.994010
$530$	13.6203	0.591628
$531$	3.23383	0.140336
$532$	0	0
$533$	2.17755	0.0943203
$534$	−4.21563	−0.182428
$535$	49.3280	2.13264
$536$	−6.75247	−0.291662
$537$	−43.9333	−1.89586
$538$	8.77050	0.378123
$539$	4.66096	0.200762
$540$	−7.36314	−0.316859
$541$	−22.4788	−0.966438	−0.483219	−	0.875500i	$-0.660533\pi$
$541$	−22.4788	−0.966438	−0.483219	+	0.875500i	$0.660533\pi$
$542$	6.08145	0.261221
$543$	20.7850	0.891970
$544$	−1.67933	−0.0720007
$545$	30.2839	1.29722
$546$	−4.22356	−0.180752
$547$	28.7786	1.23048	0.615242	−	0.788338i	$-0.289058\pi$
$547$	28.7786	1.23048	0.615242	+	0.788338i	$0.289058\pi$
$548$	9.02736	0.385630
$549$	−18.7204	−0.798967
$550$	4.74235	0.202214
$551$	0	0
$552$	0.796130	0.0338856
$553$	9.58177	0.407458
$554$	−25.0478	−1.06418
$555$	−3.40046	−0.144342
$556$	4.89160	0.207450
$557$	19.4872	0.825698	0.412849	−	0.910800i	$-0.364534\pi$
$557$	19.4872	0.825698	0.412849	+	0.910800i	$0.364534\pi$
$558$	11.7208	0.496182
$559$	19.5386	0.826395
$560$	2.45305	0.103660
$561$	−16.7887	−0.708821
$562$	8.07617	0.340673
$563$	−30.7775	−1.29711	−0.648557	−	0.761166i	$-0.724627\pi$
$563$	−30.7775	−1.29711	−0.648557	+	0.761166i	$0.724627\pi$
$564$	−27.1218	−1.14203
$565$	14.5233	0.611000
$566$	−9.35289	−0.393131
$567$	−11.2399	−0.472031
$568$	8.28979	0.347832
$569$	−5.30686	−0.222475	−0.111237	−	0.993794i	$-0.535481\pi$
$569$	−5.30686	−0.222475	−0.111237	+	0.993794i	$0.535481\pi$
$570$	0	0
$571$	−33.0139	−1.38159	−0.690794	−	0.723052i	$-0.742739\pi$
$571$	−33.0139	−1.38159	−0.690794	+	0.723052i	$0.742739\pi$
$572$	−9.17800	−0.383751
$573$	−15.9330	−0.665611
$574$	−1.10585	−0.0461573
$575$	0.377656	0.0157493
$576$	1.60057	0.0666905
$577$	−32.6599	−1.35965	−0.679824	−	0.733375i	$-0.737944\pi$
$577$	−32.6599	−1.35965	−0.679824	+	0.733375i	$0.737944\pi$
$578$	−14.1798	−0.589804
$579$	−34.0536	−1.41522
$580$	15.3334	0.636685
$581$	9.73988	0.404078
$582$	23.3676	0.968619
$583$	25.8795	1.07182
$584$	−2.51209	−0.103951
$585$	−7.73133	−0.319651
$586$	13.5630	0.560283
$587$	0.00708371	0.000292376 0	0.000146188	−	1.00000i	$-0.499953\pi$
$587$	0.00708371	0.000292376 0	0.000146188		1.00000i	$0.499953\pi$
$588$	2.14489	0.0884540
$589$	0	0
$590$	4.95620	0.204044
$591$	41.6138	1.71176
$592$	−0.646287	−0.0265622
$593$	−19.6830	−0.808285	−0.404143	−	0.914696i	$-0.632430\pi$
$593$	−19.6830	−0.808285	−0.404143	+	0.914696i	$0.632430\pi$
$594$	−13.9905	−0.574035
$595$	−4.11949	−0.168882
$596$	−1.97345	−0.0808356
$597$	36.2216	1.48245
$598$	−0.730887	−0.0298882
$599$	44.7592	1.82881	0.914405	−	0.404801i	$-0.132659\pi$
$599$	44.7592	1.82881	0.914405	+	0.404801i	$0.132659\pi$
$600$	2.18235	0.0890939
$601$	22.6915	0.925604	0.462802	−	0.886462i	$-0.346844\pi$
$601$	22.6915	0.925604	0.462802	+	0.886462i	$0.346844\pi$
$602$	−9.92250	−0.404411
$603$	−10.8078	−0.440129
$604$	−5.21877	−0.212349
$605$	26.3080	1.06957
$606$	−38.8182	−1.57688
$607$	−1.23495	−0.0501250	−0.0250625	−	0.999686i	$-0.507978\pi$
$607$	−1.23495	−0.0501250	−0.0250625	+	0.999686i	$0.507978\pi$
$608$	0	0
$609$	13.4072	0.543287
$610$	−28.6910	−1.16167
$611$	24.8992	1.00731
$612$	−2.68789	−0.108652
$613$	32.0569	1.29477	0.647383	−	0.762165i	$-0.275864\pi$
$613$	32.0569	1.29477	0.647383	+	0.762165i	$0.275864\pi$
$614$	0.739222	0.0298326
$615$	−5.81847	−0.234623
$616$	4.66096	0.187796
$617$	−23.9413	−0.963839	−0.481919	−	0.876216i	$-0.660060\pi$
$617$	−23.9413	−0.963839	−0.481919	+	0.876216i	$0.660060\pi$
$618$	−41.5658	−1.67202
$619$	−23.3629	−0.939033	−0.469516	−	0.882924i	$-0.655572\pi$
$619$	−23.3629	−0.939033	−0.469516	+	0.882924i	$0.655572\pi$
$620$	17.9634	0.721429
$621$	−1.11413	−0.0447083
$622$	0.944861	0.0378855
$623$	−1.96542	−0.0787430
$624$	−4.22356	−0.169078
$625$	−29.0521	−1.16208
$626$	−16.8338	−0.672815
$627$	0	0
$628$	6.50205	0.259460
$629$	1.08533	0.0432749
$630$	3.92629	0.156427
$631$	32.4789	1.29296	0.646482	−	0.762929i	$-0.276240\pi$
$631$	32.4789	1.29296	0.646482	+	0.762929i	$0.276240\pi$
$632$	9.58177	0.381142
$633$	29.9285	1.18955
$634$	−4.26863	−0.169529
$635$	−44.2477	−1.75592
$636$	11.9093	0.472234
$637$	−1.96912	−0.0780194
$638$	29.1345	1.15345
$639$	13.2684	0.524890
$640$	2.45305	0.0969654
$641$	7.57108	0.299040	0.149520	−	0.988759i	$-0.452227\pi$
$641$	7.57108	0.299040	0.149520	+	0.988759i	$0.452227\pi$
$642$	43.1314	1.70226
$643$	10.3612	0.408605	0.204303	−	0.978908i	$-0.434507\pi$
$643$	10.3612	0.408605	0.204303	+	0.978908i	$0.434507\pi$
$644$	0.371174	0.0146263
$645$	−52.2076	−2.05567
$646$	0	0
$647$	34.0826	1.33993	0.669963	−	0.742395i	$-0.266310\pi$
$647$	34.0826	1.33993	0.669963	+	0.742395i	$0.266310\pi$
$648$	−11.2399	−0.441544
$649$	9.41712	0.369654
$650$	−2.00350	−0.0785839
$651$	15.7068	0.615599
$652$	−20.9999	−0.822418
$653$	−14.6817	−0.574537	−0.287269	−	0.957850i	$-0.592747\pi$
$653$	−14.6817	−0.574537	−0.287269	+	0.957850i	$0.592747\pi$
$654$	26.4796	1.03543
$655$	4.99560	0.195194
$656$	−1.10585	−0.0431762
$657$	−4.02078	−0.156865
$658$	−12.6448	−0.492946
$659$	−26.3608	−1.02687	−0.513435	−	0.858128i	$-0.671627\pi$
$659$	−26.3608	−1.02687	−0.513435	+	0.858128i	$0.671627\pi$
$660$	24.5238	0.954589
$661$	−36.6051	−1.42378	−0.711888	−	0.702294i	$-0.752159\pi$
$661$	−36.6051	−1.42378	−0.711888	+	0.702294i	$0.752159\pi$
$662$	−25.9974	−1.01042
$663$	7.09275	0.275460
$664$	9.73988	0.377981
$665$	0	0
$666$	−1.03443	−0.0400833
$667$	2.32012	0.0898353
$668$	−20.1931	−0.781295
$669$	−20.6301	−0.797607
$670$	−16.5642	−0.639929
$671$	−54.5149	−2.10453
$672$	2.14489	0.0827411
$673$	28.9120	1.11448	0.557238	−	0.830353i	$-0.311861\pi$
$673$	28.9120	1.11448	0.557238	+	0.830353i	$0.311861\pi$
$674$	−11.6954	−0.450489
$675$	−3.05404	−0.117550
$676$	−9.12256	−0.350868
$677$	26.1788	1.00613	0.503067	−	0.864248i	$-0.332205\pi$
$677$	26.1788	1.00613	0.503067	+	0.864248i	$0.332205\pi$
$678$	12.6989	0.487697
$679$	10.8945	0.418094
$680$	−4.11949	−0.157975
$681$	37.6103	1.44123
$682$	34.1317	1.30697
$683$	−31.7764	−1.21589	−0.607946	−	0.793979i	$-0.708006\pi$
$683$	−31.7764	−1.21589	−0.607946	+	0.793979i	$0.708006\pi$
$684$	0	0
$685$	22.1446	0.846101
$686$	1.00000	0.0381802
$687$	−6.56377	−0.250424
$688$	−9.92250	−0.378292
$689$	−10.9333	−0.416526
$690$	1.95295	0.0743475
$691$	−23.4349	−0.891504	−0.445752	−	0.895156i	$-0.647064\pi$
$691$	−23.4349	−0.891504	−0.445752	+	0.895156i	$0.647064\pi$
$692$	−15.0110	−0.570634
$693$	7.46021	0.283390
$694$	−19.4270	−0.737441
$695$	11.9994	0.455161
$696$	13.4072	0.508198
$697$	1.85709	0.0703423
$698$	6.79008	0.257008
$699$	56.5255	2.13799
$700$	1.01746	0.0384564
$701$	13.9672	0.527535	0.263767	−	0.964586i	$-0.415035\pi$
$701$	13.9672	0.527535	0.263767	+	0.964586i	$0.415035\pi$
$702$	5.91056	0.223080
$703$	0	0
$704$	4.66096	0.175667
$705$	−66.5312	−2.50571
$706$	2.61595	0.0984525
$707$	−18.0979	−0.680643
$708$	4.33359	0.162866
$709$	15.1140	0.567619	0.283810	−	0.958881i	$-0.408402\pi$
$709$	15.1140	0.567619	0.283810	+	0.958881i	$0.408402\pi$
$710$	20.3353	0.763169
$711$	15.3363	0.575157
$712$	−1.96542	−0.0736573
$713$	2.71807	0.101793
$714$	−3.60199	−0.134801
$715$	−22.5141	−0.841980
$716$	−20.4827	−0.765476
$717$	58.8548	2.19797
$718$	−19.7876	−0.738466
$719$	9.56757	0.356810	0.178405	−	0.983957i	$-0.442906\pi$
$719$	9.56757	0.356810	0.178405	+	0.983957i	$0.442906\pi$
$720$	3.92629	0.146324
$721$	−19.3790	−0.721710
$722$	0	0
$723$	32.1252	1.19475
$724$	9.69046	0.360143
$725$	6.35989	0.236200
$726$	23.0031	0.853725
$727$	45.2628	1.67870	0.839351	−	0.543589i	$-0.182935\pi$
$727$	45.2628	1.67870	0.839351	+	0.543589i	$0.182935\pi$
$728$	−1.96912	−0.0729805
$729$	1.32424	0.0490460
$730$	−6.16228	−0.228076
$731$	16.6632	0.616309
$732$	−25.0868	−0.927236
$733$	15.6509	0.578079	0.289039	−	0.957317i	$-0.406664\pi$
$733$	15.6509	0.578079	0.289039	+	0.957317i	$0.406664\pi$
$734$	−29.0819	−1.07343
$735$	5.26154	0.194075
$736$	0.371174	0.0136817
$737$	−31.4730	−1.15932
$738$	−1.76999	−0.0651544
$739$	−29.8506	−1.09807	−0.549035	−	0.835799i	$-0.685005\pi$
$739$	−29.8506	−1.09807	−0.549035	+	0.835799i	$0.685005\pi$
$740$	−1.58537	−0.0582795
$741$	0	0
$742$	5.55239	0.203835
$743$	19.4553	0.713746	0.356873	−	0.934153i	$-0.383843\pi$
$743$	19.4553	0.713746	0.356873	+	0.934153i	$0.383843\pi$
$744$	15.7068	0.575841
$745$	−4.84097	−0.177360
$746$	6.65147	0.243528
$747$	15.5894	0.570386
$748$	−7.82730	−0.286195
$749$	20.1089	0.734761
$750$	−20.9543	−0.765142
$751$	10.4124	0.379953	0.189977	−	0.981789i	$-0.439159\pi$
$751$	10.4124	0.379953	0.189977	+	0.981789i	$0.439159\pi$
$752$	−12.6448	−0.461109
$753$	30.2540	1.10252
$754$	−12.3085	−0.448248
$755$	−12.8019	−0.465909
$756$	−3.00162	−0.109168
$757$	−13.6379	−0.495678	−0.247839	−	0.968801i	$-0.579720\pi$
$757$	−13.6379	−0.495678	−0.247839	+	0.968801i	$0.579720\pi$
$758$	−4.62364	−0.167938
$759$	3.71073	0.134691
$760$	0	0
$761$	3.29787	0.119548	0.0597738	−	0.998212i	$-0.480962\pi$
$761$	3.29787	0.119548	0.0597738	+	0.998212i	$0.480962\pi$
$762$	−38.6893	−1.40156
$763$	12.3454	0.446934
$764$	−7.42834	−0.268748
$765$	−6.59354	−0.238390
$766$	−22.5475	−0.814673
$767$	−3.97846	−0.143654
$768$	2.14489	0.0773972
$769$	2.62924	0.0948129	0.0474064	−	0.998876i	$-0.484904\pi$
$769$	2.62924	0.0948129	0.0474064	+	0.998876i	$0.484904\pi$
$770$	11.4336	0.412038
$771$	21.6457	0.779550
$772$	−15.8766	−0.571411
$773$	8.76330	0.315194	0.157597	−	0.987504i	$-0.449625\pi$
$773$	8.76330	0.315194	0.157597	+	0.987504i	$0.449625\pi$
$774$	−15.8817	−0.570855
$775$	7.45076	0.267639
$776$	10.8945	0.391091
$777$	−1.38622	−0.0497302
$778$	−15.1594	−0.543492
$779$	0	0
$780$	−10.3606	−0.370969
$781$	38.6384	1.38259
$782$	−0.623325	−0.0222901
$783$	−18.7624	−0.670513
$784$	1.00000	0.0357143
$785$	15.9499	0.569275
$786$	4.36805	0.155803
$787$	29.4525	1.04987	0.524934	−	0.851143i	$-0.324090\pi$
$787$	29.4525	1.04987	0.524934	+	0.851143i	$0.324090\pi$
$788$	19.4013	0.691144
$789$	−51.1631	−1.82145
$790$	23.5046	0.836256
$791$	5.92051	0.210509
$792$	7.46021	0.265087
$793$	23.0310	0.817853
$794$	38.5487	1.36804
$795$	29.2141	1.03612
$796$	16.8874	0.598557
$797$	−31.9299	−1.13102	−0.565508	−	0.824743i	$-0.691320\pi$
$797$	−31.9299	−1.13102	−0.565508	+	0.824743i	$0.691320\pi$
$798$	0	0
$799$	21.2348	0.751235
$800$	1.01746	0.0359727
$801$	−3.14580	−0.111151
$802$	21.9495	0.775065
$803$	−11.7087	−0.413193
$804$	−14.4833	−0.510788
$805$	0.910510	0.0320913
$806$	−14.4197	−0.507911
$807$	18.8118	0.662207
$808$	−18.0979	−0.636683
$809$	−10.5294	−0.370193	−0.185097	−	0.982720i	$-0.559260\pi$
$809$	−10.5294	−0.370193	−0.185097	+	0.982720i	$0.559260\pi$
$810$	−27.5720	−0.968782
$811$	17.2804	0.606795	0.303398	−	0.952864i	$-0.401879\pi$
$811$	17.2804	0.606795	0.303398	+	0.952864i	$0.401879\pi$
$812$	6.25075	0.219358
$813$	13.0441	0.457476
$814$	−3.01232	−0.105582
$815$	−51.5137	−1.80445
$816$	−3.60199	−0.126095
$817$	0	0
$818$	26.2379	0.917388
$819$	−3.15172	−0.110130
$820$	−2.71271	−0.0947319
$821$	55.1719	1.92551	0.962757	−	0.270368i	$-0.0871454\pi$
$821$	55.1719	1.92551	0.962757	+	0.270368i	$0.0871454\pi$
$822$	19.3627	0.675353
$823$	22.7550	0.793190	0.396595	−	0.917994i	$-0.370192\pi$
$823$	22.7550	0.793190	0.396595	+	0.917994i	$0.370192\pi$
$824$	−19.3790	−0.675098
$825$	10.1718	0.354138
$826$	2.02042	0.0702995
$827$	11.7599	0.408931	0.204465	−	0.978874i	$-0.434454\pi$
$827$	11.7599	0.408931	0.204465	+	0.978874i	$0.434454\pi$
$828$	0.594092	0.0206461
$829$	−36.5744	−1.27028	−0.635141	−	0.772397i	$-0.719058\pi$
$829$	−36.5744	−1.27028	−0.635141	+	0.772397i	$0.719058\pi$
$830$	23.8924	0.829318
$831$	−53.7249	−1.86370
$832$	−1.96912	−0.0682670
$833$	−1.67933	−0.0581854
$834$	10.4920	0.363307
$835$	−49.5347	−1.71422
$836$	0	0
$837$	−21.9806	−0.759760
$838$	−14.7648	−0.510040
$839$	−21.4530	−0.740640	−0.370320	−	0.928904i	$-0.620752\pi$
$839$	−21.4530	−0.740640	−0.370320	+	0.928904i	$0.620752\pi$
$840$	5.26154	0.181540
$841$	10.0718	0.347304
$842$	9.35190	0.322288
$843$	17.3225	0.596620
$844$	13.9533	0.480294
$845$	−22.3781	−0.769831
$846$	−20.2390	−0.695830
$847$	10.7246	0.368501
$848$	5.55239	0.190670
$849$	−20.0610	−0.688490
$850$	−1.70865	−0.0586064
$851$	−0.239885	−0.00822315
$852$	17.7807	0.609158
$853$	−8.29792	−0.284115	−0.142058	−	0.989858i	$-0.545372\pi$
$853$	−8.29792	−0.284115	−0.142058	+	0.989858i	$0.545372\pi$
$854$	−11.6961	−0.400231
$855$	0	0
$856$	20.1089	0.687306
$857$	−17.1840	−0.586995	−0.293498	−	0.955960i	$-0.594819\pi$
$857$	−17.1840	−0.586995	−0.293498	+	0.955960i	$0.594819\pi$
$858$	−19.6858	−0.672064
$859$	27.7559	0.947019	0.473510	−	0.880789i	$-0.342987\pi$
$859$	27.7559	0.947019	0.473510	+	0.880789i	$0.342987\pi$
$860$	−24.3404	−0.830001
$861$	−2.37193	−0.0808353
$862$	23.8387	0.811948
$863$	−28.5248	−0.970995	−0.485497	−	0.874238i	$-0.661361\pi$
$863$	−28.5248	−0.970995	−0.485497	+	0.874238i	$0.661361\pi$
$864$	−3.00162	−0.102117
$865$	−36.8229	−1.25202
$866$	−38.4316	−1.30596
$867$	−30.4143	−1.03292
$868$	7.32289	0.248555
$869$	44.6603	1.51500
$870$	32.8885	1.11503
$871$	13.2964	0.450532
$872$	12.3454	0.418068
$873$	17.4375	0.590170
$874$	0	0
$875$	−9.76937	−0.330265
$876$	−5.38816	−0.182049
$877$	−26.2838	−0.887542	−0.443771	−	0.896140i	$-0.646360\pi$
$877$	−26.2838	−0.887542	−0.443771	+	0.896140i	$0.646360\pi$
$878$	−8.78467	−0.296468
$879$	29.0913	0.981224
$880$	11.4336	0.385426
$881$	31.7390	1.06931	0.534657	−	0.845069i	$-0.320441\pi$
$881$	31.7390	1.06931	0.534657	+	0.845069i	$0.320441\pi$
$882$	1.60057	0.0538941
$883$	−37.9601	−1.27746	−0.638729	−	0.769432i	$-0.720540\pi$
$883$	−37.9601	−1.27746	−0.638729	+	0.769432i	$0.720540\pi$
$884$	3.30681	0.111220
$885$	10.6305	0.357341
$886$	10.6376	0.357378
$887$	−53.7619	−1.80515	−0.902574	−	0.430535i	$-0.858325\pi$
$887$	−53.7619	−1.80515	−0.902574	+	0.430535i	$0.858325\pi$
$888$	−1.38622	−0.0465184
$889$	−18.0378	−0.604970
$890$	−4.82128	−0.161610
$891$	−52.3887	−1.75509
$892$	−9.61825	−0.322043
$893$	0	0
$894$	−4.23284	−0.141567
$895$	−50.2452	−1.67951
$896$	1.00000	0.0334077
$897$	−1.56768	−0.0523432
$898$	−9.25065	−0.308698
$899$	45.7735	1.52663
$900$	1.62852	0.0542840
$901$	−9.32430	−0.310637
$902$	−5.15433	−0.171620
$903$	−21.2827	−0.708245
$904$	5.92051	0.196913
$905$	23.7712	0.790181
$906$	−11.1937	−0.371886
$907$	26.3458	0.874798	0.437399	−	0.899268i	$-0.355900\pi$
$907$	26.3458	0.874798	0.437399	+	0.899268i	$0.355900\pi$
$908$	17.5348	0.581912
$909$	−28.9671	−0.960777
$910$	−4.83035	−0.160125
$911$	11.1591	0.369719	0.184859	−	0.982765i	$-0.440817\pi$
$911$	11.1591	0.369719	0.184859	+	0.982765i	$0.440817\pi$
$912$	0	0
$913$	45.3972	1.50243
$914$	−14.2859	−0.472535
$915$	−61.5393	−2.03443
$916$	−3.06018	−0.101111
$917$	2.03649	0.0672507
$918$	5.04072	0.166369
$919$	−4.71602	−0.155567	−0.0777835	−	0.996970i	$-0.524784\pi$
$919$	−4.71602	−0.155567	−0.0777835	+	0.996970i	$0.524784\pi$
$920$	0.910510	0.0300186
$921$	1.58555	0.0522457
$922$	−3.02462	−0.0996107
$923$	−16.3236	−0.537298
$924$	9.99728	0.328886
$925$	−0.657571	−0.0216208
$926$	4.98327	0.163761
$927$	−31.0174	−1.01875
$928$	6.25075	0.205191
$929$	−51.0261	−1.67411	−0.837056	−	0.547117i	$-0.815725\pi$
$929$	−51.0261	−1.67411	−0.837056	+	0.547117i	$0.815725\pi$
$930$	38.5297	1.26344
$931$	0	0
$932$	26.3535	0.863238
$933$	2.02663	0.0663488
$934$	18.1672	0.594450
$935$	−19.2008	−0.627932
$936$	−3.15172	−0.103017
$937$	−51.8709	−1.69455	−0.847274	−	0.531156i	$-0.821758\pi$
$937$	−51.8709	−1.69455	−0.847274	+	0.531156i	$0.821758\pi$
$938$	−6.75247	−0.220476
$939$	−36.1068	−1.17830
$940$	−31.0184	−1.01171
$941$	−1.79295	−0.0584486	−0.0292243	−	0.999573i	$-0.509304\pi$
$941$	−1.79295	−0.0584486	−0.0292243	+	0.999573i	$0.509304\pi$
$942$	13.9462	0.454392
$943$	−0.410464	−0.0133665
$944$	2.02042	0.0657592
$945$	−7.36314	−0.239523
$946$	−46.2484	−1.50367
$947$	6.46733	0.210160	0.105080	−	0.994464i	$-0.466490\pi$
$947$	6.46733	0.210160	0.105080	+	0.994464i	$0.466490\pi$
$948$	20.5519	0.667495
$949$	4.94660	0.160573
$950$	0	0
$951$	−9.15576	−0.296896
$952$	−1.67933	−0.0544274
$953$	−30.6939	−0.994274	−0.497137	−	0.867672i	$-0.665615\pi$
$953$	−30.6939	−0.994274	−0.497137	+	0.867672i	$0.665615\pi$
$954$	8.88700	0.287727
$955$	−18.2221	−0.589653
$956$	27.4395	0.887456
$957$	62.4904	2.02003
$958$	26.4885	0.855803
$959$	9.02736	0.291509
$960$	5.26154	0.169815
$961$	22.6248	0.729831
$962$	1.27262	0.0410308
$963$	32.1857	1.03717
$964$	14.9775	0.482393
$965$	−38.9461	−1.25372
$966$	0.796130	0.0256151
$967$	17.7358	0.570345	0.285172	−	0.958476i	$-0.407949\pi$
$967$	17.7358	0.570345	0.285172	+	0.958476i	$0.407949\pi$
$968$	10.7246	0.344701
$969$	0	0
$970$	26.7248	0.858083
$971$	−33.8991	−1.08788	−0.543938	−	0.839126i	$-0.683067\pi$
$971$	−33.8991	−1.08788	−0.543938	+	0.839126i	$0.683067\pi$
$972$	−15.1035	−0.484445
$973$	4.89160	0.156818
$974$	34.4343	1.10335
$975$	−4.29730	−0.137624
$976$	−11.6961	−0.374382
$977$	31.7370	1.01536	0.507678	−	0.861547i	$-0.330504\pi$
$977$	31.7370	1.01536	0.507678	+	0.861547i	$0.330504\pi$
$978$	−45.0425	−1.44030
$979$	−9.16077	−0.292779
$980$	2.45305	0.0783599
$981$	19.7597	0.630879
$982$	38.9864	1.24410
$983$	−38.9896	−1.24358	−0.621788	−	0.783186i	$-0.713593\pi$
$983$	−38.9896	−1.24358	−0.621788	+	0.783186i	$0.713593\pi$
$984$	−2.37193	−0.0756145
$985$	47.5925	1.51642
$986$	−10.4971	−0.334295
$987$	−27.1218	−0.863297
$988$	0	0
$989$	−3.68298	−0.117112
$990$	18.3003	0.581621
$991$	−3.37997	−0.107368	−0.0536841	−	0.998558i	$-0.517096\pi$
$991$	−3.37997	−0.107368	−0.0536841	+	0.998558i	$0.517096\pi$
$992$	7.32289	0.232502
$993$	−55.7616	−1.76954
$994$	8.28979	0.262936
$995$	41.4256	1.31328
$996$	20.8910	0.661957
$997$	−38.2557	−1.21157	−0.605785	−	0.795628i	$-0.707141\pi$
$997$	−38.2557	−1.21157	−0.605785	+	0.795628i	$0.707141\pi$
$998$	20.0894	0.635919
$999$	1.93991	0.0613760

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.be.1.5	yes	6
19.18	odd	2		5054.2.a.z.1.2	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5054.2.a.z.1.2	✓	6	19.18	odd	2
5054.2.a.be.1.5	yes	6	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.14489 q^{3} +1.00000 q^{4} +2.45305 q^{5} +2.14489 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.60057 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.14489 q^{3} +1.00000 q^{4} +2.45305 q^{5} +2.14489 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.60057 q^{9} +2.45305 q^{10} +4.66096 q^{11} +2.14489 q^{12} -1.96912 q^{13} +1.00000 q^{14} +5.26154 q^{15} +1.00000 q^{16} -1.67933 q^{17} +1.60057 q^{18} +2.45305 q^{20} +2.14489 q^{21} +4.66096 q^{22} +0.371174 q^{23} +2.14489 q^{24} +1.01746 q^{25} -1.96912 q^{26} -3.00162 q^{27} +1.00000 q^{28} +6.25075 q^{29} +5.26154 q^{30} +7.32289 q^{31} +1.00000 q^{32} +9.99728 q^{33} -1.67933 q^{34} +2.45305 q^{35} +1.60057 q^{36} -0.646287 q^{37} -4.22356 q^{39} +2.45305 q^{40} -1.10585 q^{41} +2.14489 q^{42} -9.92250 q^{43} +4.66096 q^{44} +3.92629 q^{45} +0.371174 q^{46} -12.6448 q^{47} +2.14489 q^{48} +1.00000 q^{49} +1.01746 q^{50} -3.60199 q^{51} -1.96912 q^{52} +5.55239 q^{53} -3.00162 q^{54} +11.4336 q^{55} +1.00000 q^{56} +6.25075 q^{58} +2.02042 q^{59} +5.26154 q^{60} -11.6961 q^{61} +7.32289 q^{62} +1.60057 q^{63} +1.00000 q^{64} -4.83035 q^{65} +9.99728 q^{66} -6.75247 q^{67} -1.67933 q^{68} +0.796130 q^{69} +2.45305 q^{70} +8.28979 q^{71} +1.60057 q^{72} -2.51209 q^{73} -0.646287 q^{74} +2.18235 q^{75} +4.66096 q^{77} -4.22356 q^{78} +9.58177 q^{79} +2.45305 q^{80} -11.2399 q^{81} -1.10585 q^{82} +9.73988 q^{83} +2.14489 q^{84} -4.11949 q^{85} -9.92250 q^{86} +13.4072 q^{87} +4.66096 q^{88} -1.96542 q^{89} +3.92629 q^{90} -1.96912 q^{91} +0.371174 q^{92} +15.7068 q^{93} -12.6448 q^{94} +2.14489 q^{96} +10.8945 q^{97} +1.00000 q^{98} +7.46021 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{4} - q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^4 - q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9	\( 6 q + 6 q^{2} + 6 q^{4} - q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9} - q^{10} + 4 q^{11} + 15 q^{13} + 6 q^{14} + 6 q^{15} + 6 q^{16} - 9 q^{17} + 8 q^{18} - q^{20} + 4 q^{22} + 4 q^{23} + q^{25} + 15 q^{26} - 12 q^{27} + 6 q^{28} + 7 q^{29} + 6 q^{30} + 4 q^{31} + 6 q^{32} + 28 q^{33} - 9 q^{34} - q^{35} + 8 q^{36} + 3 q^{37} - 8 q^{39} - q^{40} + 11 q^{41} - 10 q^{43} + 4 q^{44} + 19 q^{45} + 4 q^{46} + 12 q^{47} + 6 q^{49} + q^{50} + 44 q^{51} + 15 q^{52} - 5 q^{53} - 12 q^{54} - 8 q^{55} + 6 q^{56} + 7 q^{58} + 4 q^{59} + 6 q^{60} - 21 q^{61} + 4 q^{62} + 8 q^{63} + 6 q^{64} - 20 q^{65} + 28 q^{66} + 14 q^{67} - 9 q^{68} - 24 q^{69} - q^{70} + 24 q^{71} + 8 q^{72} - 21 q^{73} + 3 q^{74} + 12 q^{75} + 4 q^{77} - 8 q^{78} + 58 q^{79} - q^{80} - 6 q^{81} + 11 q^{82} + 20 q^{83} - 4 q^{85} - 10 q^{86} - 8 q^{87} + 4 q^{88} + 7 q^{89} + 19 q^{90} + 15 q^{91} + 4 q^{92} - 22 q^{93} + 12 q^{94} + 7 q^{97} + 6 q^{98} - 26 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^4 - q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9 - q^10 + 4 * q^11 + 15 * q^13 + 6 * q^14 + 6 * q^15 + 6 * q^16 - 9 * q^17 + 8 * q^18 - q^20 + 4 * q^22 + 4 * q^23 + q^25 + 15 * q^26 - 12 * q^27 + 6 * q^28 + 7 * q^29 + 6 * q^30 + 4 * q^31 + 6 * q^32 + 28 * q^33 - 9 * q^34 - q^35 + 8 * q^36 + 3 * q^37 - 8 * q^39 - q^40 + 11 * q^41 - 10 * q^43 + 4 * q^44 + 19 * q^45 + 4 * q^46 + 12 * q^47 + 6 * q^49 + q^50 + 44 * q^51 + 15 * q^52 - 5 * q^53 - 12 * q^54 - 8 * q^55 + 6 * q^56 + 7 * q^58 + 4 * q^59 + 6 * q^60 - 21 * q^61 + 4 * q^62 + 8 * q^63 + 6 * q^64 - 20 * q^65 + 28 * q^66 + 14 * q^67 - 9 * q^68 - 24 * q^69 - q^70 + 24 * q^71 + 8 * q^72 - 21 * q^73 + 3 * q^74 + 12 * q^75 + 4 * q^77 - 8 * q^78 + 58 * q^79 - q^80 - 6 * q^81 + 11 * q^82 + 20 * q^83 - 4 * q^85 - 10 * q^86 - 8 * q^87 + 4 * q^88 + 7 * q^89 + 19 * q^90 + 15 * q^91 + 4 * q^92 - 22 * q^93 + 12 * q^94 + 7 * q^97 + 6 * q^98 - 26 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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