LMFDB - Embedded newform 4018.2.a.be.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4018,2,Mod(1,4018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4018, 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("4018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4018 = 2 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4018.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:	$32.0838915322$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.404.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x - 1 $ x^3 - x^2 - 5*x - 1
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			1.2
Root			$2.86620$ of defining polynomial
Character	$\chi$	$=$	4018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.517304 q^{3} +1.00000 q^{4} -1.86620 q^{5} +0.517304 q^{6} -1.00000 q^{8} -2.73240 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.517304 q^{3} +1.00000 q^{4} -1.86620 q^{5} +0.517304 q^{6} -1.00000 q^{8} -2.73240 q^{9} +1.86620 q^{10} -1.34889 q^{11} -0.517304 q^{12} -5.21509 q^{13} +0.965392 q^{15} +1.00000 q^{16} +4.51730 q^{17} +2.73240 q^{18} -3.21509 q^{19} -1.86620 q^{20} +1.34889 q^{22} -6.18048 q^{23} +0.517304 q^{24} -1.51730 q^{25} +5.21509 q^{26} +2.96539 q^{27} -8.11590 q^{29} -0.965392 q^{30} -0.697788 q^{31} -1.00000 q^{32} +0.697788 q^{33} -4.51730 q^{34} -2.73240 q^{36} +7.03461 q^{37} +3.21509 q^{38} +2.69779 q^{39} +1.86620 q^{40} -1.00000 q^{41} -5.03461 q^{43} -1.34889 q^{44} +5.09919 q^{45} +6.18048 q^{46} +2.78491 q^{47} -0.517304 q^{48} +1.51730 q^{50} -2.33682 q^{51} -5.21509 q^{52} -6.38350 q^{53} -2.96539 q^{54} +2.51730 q^{55} +1.66318 q^{57} +8.11590 q^{58} +11.5986 q^{59} +0.965392 q^{60} -13.5294 q^{61} +0.697788 q^{62} +1.00000 q^{64} +9.73240 q^{65} -0.697788 q^{66} -9.77908 q^{67} +4.51730 q^{68} +3.19719 q^{69} +1.66318 q^{71} +2.73240 q^{72} +2.96539 q^{73} -7.03461 q^{74} +0.784908 q^{75} -3.21509 q^{76} -2.69779 q^{78} -7.46479 q^{79} -1.86620 q^{80} +6.66318 q^{81} +1.00000 q^{82} -14.5640 q^{83} -8.43018 q^{85} +5.03461 q^{86} +4.19839 q^{87} +1.34889 q^{88} +15.1280 q^{89} -5.09919 q^{90} -6.18048 q^{92} +0.360969 q^{93} -2.78491 q^{94} +6.00000 q^{95} +0.517304 q^{96} -3.93078 q^{97} +3.68571 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{4} + 2 q^{5} - 3 q^{8} + 7 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^4 + 2 * q^5 - 3 * q^8 + 7 * q^9	$ 3 q - 3 q^{2} + 3 q^{4} + 2 q^{5} - 3 q^{8} + 7 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{13} + 6 q^{15} + 3 q^{16} + 12 q^{17} - 7 q^{18} + 4 q^{19} + 2 q^{20} - 2 q^{22} - 8 q^{23} - 3 q^{25} + 2 q^{26} + 12 q^{27} - 6 q^{30} + 10 q^{31} - 3 q^{32} - 10 q^{33} - 12 q^{34} + 7 q^{36} + 18 q^{37} - 4 q^{38} - 4 q^{39} - 2 q^{40} - 3 q^{41} - 12 q^{43} + 2 q^{44} + 26 q^{45} + 8 q^{46} + 22 q^{47} + 3 q^{50} - 16 q^{51} - 2 q^{52} - 10 q^{53} - 12 q^{54} + 6 q^{55} - 4 q^{57} + 12 q^{59} + 6 q^{60} - 24 q^{61} - 10 q^{62} + 3 q^{64} + 14 q^{65} + 10 q^{66} + 4 q^{67} + 12 q^{68} - 36 q^{69} - 4 q^{71} - 7 q^{72} + 12 q^{73} - 18 q^{74} + 16 q^{75} + 4 q^{76} + 4 q^{78} + 8 q^{79} + 2 q^{80} + 11 q^{81} + 3 q^{82} - 24 q^{83} + 2 q^{85} + 12 q^{86} + 34 q^{87} - 2 q^{88} + 6 q^{89} - 26 q^{90} - 8 q^{92} - 20 q^{93} - 22 q^{94} + 18 q^{95} - 18 q^{97} + 14 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^4 + 2 * q^5 - 3 * q^8 + 7 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^13 + 6 * q^15 + 3 * q^16 + 12 * q^17 - 7 * q^18 + 4 * q^19 + 2 * q^20 - 2 * q^22 - 8 * q^23 - 3 * q^25 + 2 * q^26 + 12 * q^27 - 6 * q^30 + 10 * q^31 - 3 * q^32 - 10 * q^33 - 12 * q^34 + 7 * q^36 + 18 * q^37 - 4 * q^38 - 4 * q^39 - 2 * q^40 - 3 * q^41 - 12 * q^43 + 2 * q^44 + 26 * q^45 + 8 * q^46 + 22 * q^47 + 3 * q^50 - 16 * q^51 - 2 * q^52 - 10 * q^53 - 12 * q^54 + 6 * q^55 - 4 * q^57 + 12 * q^59 + 6 * q^60 - 24 * q^61 - 10 * q^62 + 3 * q^64 + 14 * q^65 + 10 * q^66 + 4 * q^67 + 12 * q^68 - 36 * q^69 - 4 * q^71 - 7 * q^72 + 12 * q^73 - 18 * q^74 + 16 * q^75 + 4 * q^76 + 4 * q^78 + 8 * q^79 + 2 * q^80 + 11 * q^81 + 3 * q^82 - 24 * q^83 + 2 * q^85 + 12 * q^86 + 34 * q^87 - 2 * q^88 + 6 * q^89 - 26 * q^90 - 8 * q^92 - 20 * q^93 - 22 * q^94 + 18 * q^95 - 18 * q^97 + 14 * 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
$3$	−0.517304	−0.298666	−0.149333	−	0.988787i	$-0.547713\pi$
$3$	−0.517304	−0.298666	−0.149333	+	0.988787i	$0.547713\pi$
$4$	1.00000	0.500000
$5$	−1.86620	−0.834589	−0.417295	−	0.908771i	$-0.637022\pi$
$5$	−1.86620	−0.834589	−0.417295	+	0.908771i	$0.637022\pi$
$6$	0.517304	0.211188
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	−2.73240	−0.910799
$10$	1.86620	0.590144
$11$	−1.34889	−0.406707	−0.203353	−	0.979105i	$-0.565184\pi$
$11$	−1.34889	−0.406707	−0.203353	+	0.979105i	$0.565184\pi$
$12$	−0.517304	−0.149333
$13$	−5.21509	−1.44641	−0.723203	−	0.690635i	$-0.757331\pi$
$13$	−5.21509	−1.44641	−0.723203	+	0.690635i	$0.757331\pi$
$14$	0	0
$15$	0.965392	0.249263
$16$	1.00000	0.250000
$17$	4.51730	1.09561	0.547804	−	0.836607i	$-0.315464\pi$
$17$	4.51730	1.09561	0.547804	+	0.836607i	$0.315464\pi$
$18$	2.73240	0.644032
$19$	−3.21509	−0.737593	−0.368796	−	0.929510i	$-0.620230\pi$
$19$	−3.21509	−0.737593	−0.368796	+	0.929510i	$0.620230\pi$
$20$	−1.86620	−0.417295
$21$	0	0
$22$	1.34889	0.287585
$23$	−6.18048	−1.28872	−0.644360	−	0.764722i	$-0.722876\pi$
$23$	−6.18048	−1.28872	−0.644360	+	0.764722i	$0.722876\pi$
$24$	0.517304	0.105594
$25$	−1.51730	−0.303461
$26$	5.21509	1.02276
$27$	2.96539	0.570690
$28$	0	0
$29$	−8.11590	−1.50708	−0.753542	−	0.657399i	$-0.771656\pi$
$29$	−8.11590	−1.50708	−0.753542	+	0.657399i	$0.771656\pi$
$30$	−0.965392	−0.176256
$31$	−0.697788	−0.125327	−0.0626633	−	0.998035i	$-0.519959\pi$
$31$	−0.697788	−0.125327	−0.0626633	+	0.998035i	$0.519959\pi$
$32$	−1.00000	−0.176777
$33$	0.697788	0.121469
$34$	−4.51730	−0.774711
$35$	0	0
$36$	−2.73240	−0.455399
$37$	7.03461	1.15648	0.578241	−	0.815866i	$-0.303739\pi$
$37$	7.03461	1.15648	0.578241	+	0.815866i	$0.303739\pi$
$38$	3.21509	0.521557
$39$	2.69779	0.431992
$40$	1.86620	0.295072
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−5.03461	−0.767771	−0.383885	−	0.923381i	$-0.625414\pi$
$43$	−5.03461	−0.767771	−0.383885	+	0.923381i	$0.625414\pi$
$44$	−1.34889	−0.203353
$45$	5.09919	0.760143
$46$	6.18048	0.911263
$47$	2.78491	0.406221	0.203110	−	0.979156i	$-0.434895\pi$
$47$	2.78491	0.406221	0.203110	+	0.979156i	$0.434895\pi$
$48$	−0.517304	−0.0746664
$49$	0	0
$50$	1.51730	0.214579
$51$	−2.33682	−0.327220
$52$	−5.21509	−0.723203
$53$	−6.38350	−0.876841	−0.438421	−	0.898770i	$-0.644462\pi$
$53$	−6.38350	−0.876841	−0.438421	+	0.898770i	$0.644462\pi$
$54$	−2.96539	−0.403539
$55$	2.51730	0.339433
$56$	0	0
$57$	1.66318	0.220294
$58$	8.11590	1.06567
$59$	11.5986	1.51001	0.755004	−	0.655720i	$-0.227635\pi$
$59$	11.5986	1.51001	0.755004	+	0.655720i	$0.227635\pi$
$60$	0.965392	0.124632
$61$	−13.5294	−1.73226	−0.866130	−	0.499819i	$-0.833400\pi$
$61$	−13.5294	−1.73226	−0.866130	+	0.499819i	$0.833400\pi$
$62$	0.697788	0.0886192
$63$	0	0
$64$	1.00000	0.125000
$65$	9.73240	1.20716
$66$	−0.697788	−0.0858918
$67$	−9.77908	−1.19470	−0.597352	−	0.801979i	$-0.703781\pi$
$67$	−9.77908	−1.19470	−0.597352	+	0.801979i	$0.703781\pi$
$68$	4.51730	0.547804
$69$	3.19719	0.384896
$70$	0	0
$71$	1.66318	0.197383	0.0986916	−	0.995118i	$-0.468534\pi$
$71$	1.66318	0.197383	0.0986916	+	0.995118i	$0.468534\pi$
$72$	2.73240	0.322016
$73$	2.96539	0.347073	0.173536	−	0.984827i	$-0.444481\pi$
$73$	2.96539	0.347073	0.173536	+	0.984827i	$0.444481\pi$
$74$	−7.03461	−0.817757
$75$	0.784908	0.0906333
$76$	−3.21509	−0.368796
$77$	0	0
$78$	−2.69779	−0.305464
$79$	−7.46479	−0.839855	−0.419927	−	0.907558i	$-0.637944\pi$
$79$	−7.46479	−0.839855	−0.419927	+	0.907558i	$0.637944\pi$
$80$	−1.86620	−0.208647
$81$	6.66318	0.740353
$82$	1.00000	0.110432
$83$	−14.5640	−1.59861	−0.799303	−	0.600929i	$-0.794798\pi$
$83$	−14.5640	−1.59861	−0.799303	+	0.600929i	$0.794798\pi$
$84$	0	0
$85$	−8.43018	−0.914382
$86$	5.03461	0.542896
$87$	4.19839	0.450114
$88$	1.34889	0.143793
$89$	15.1280	1.60356	0.801781	−	0.597618i	$-0.203886\pi$
$89$	15.1280	1.60356	0.801781	+	0.597618i	$0.203886\pi$
$90$	−5.09919	−0.537502
$91$	0	0
$92$	−6.18048	−0.644360
$93$	0.360969	0.0374307
$94$	−2.78491	−0.287241
$95$	6.00000	0.615587
$96$	0.517304	0.0527971
$97$	−3.93078	−0.399111	−0.199555	−	0.979887i	$-0.563950\pi$
$97$	−3.93078	−0.399111	−0.199555	+	0.979887i	$0.563950\pi$
$98$	0	0
$99$	3.68571	0.370428
$100$	−1.51730	−0.151730
$101$	14.2497	1.41790	0.708949	−	0.705260i	$-0.249170\pi$
$101$	14.2497	1.41790	0.708949	+	0.705260i	$0.249170\pi$
$102$	2.33682	0.231380
$103$	10.1626	1.00135	0.500674	−	0.865636i	$-0.333085\pi$
$103$	10.1626	1.00135	0.500674	+	0.865636i	$0.333085\pi$
$104$	5.21509	0.511382
$105$	0	0
$106$	6.38350	0.620021
$107$	1.30221	0.125890	0.0629448	−	0.998017i	$-0.479951\pi$
$107$	1.30221	0.125890	0.0629448	+	0.998017i	$0.479951\pi$
$108$	2.96539	0.285345
$109$	9.70986	0.930036	0.465018	−	0.885301i	$-0.346048\pi$
$109$	9.70986	0.930036	0.465018	+	0.885301i	$0.346048\pi$
$110$	−2.51730	−0.240016
$111$	−3.63903	−0.345402
$112$	0	0
$113$	−9.48270	−0.892057	−0.446028	−	0.895019i	$-0.647162\pi$
$113$	−9.48270	−0.892057	−0.446028	+	0.895019i	$0.647162\pi$
$114$	−1.66318	−0.155771
$115$	11.5340	1.07555
$116$	−8.11590	−0.753542
$117$	14.2497	1.31739
$118$	−11.5986	−1.06774
$119$	0	0
$120$	−0.965392	−0.0881278
$121$	−9.18048	−0.834589
$122$	13.5294	1.22489
$123$	0.517304	0.0466437
$124$	−0.697788	−0.0626633
$125$	12.1626	1.08785
$126$	0	0
$127$	18.1805	1.61326	0.806629	−	0.591059i	$-0.201290\pi$
$127$	18.1805	1.61326	0.806629	+	0.591059i	$0.201290\pi$
$128$	−1.00000	−0.0883883
$129$	2.60442	0.229307
$130$	−9.73240	−0.853588
$131$	−7.93541	−0.693320	−0.346660	−	0.937991i	$-0.612684\pi$
$131$	−7.93541	−0.693320	−0.346660	+	0.937991i	$0.612684\pi$
$132$	0.697788	0.0607347
$133$	0	0
$134$	9.77908	0.844784
$135$	−5.53401	−0.476292
$136$	−4.51730	−0.387356
$137$	−9.19719	−0.785769	−0.392884	−	0.919588i	$-0.628523\pi$
$137$	−9.19719	−0.785769	−0.392884	+	0.919588i	$0.628523\pi$
$138$	−3.19719	−0.272163
$139$	0.831590	0.0705346	0.0352673	−	0.999378i	$-0.488772\pi$
$139$	0.831590	0.0705346	0.0352673	+	0.999378i	$0.488772\pi$
$140$	0	0
$141$	−1.44064	−0.121324
$142$	−1.66318	−0.139571
$143$	7.03461	0.588263
$144$	−2.73240	−0.227700
$145$	15.1459	1.25780
$146$	−2.96539	−0.245418
$147$	0	0
$148$	7.03461	0.578241
$149$	1.77908	0.145748	0.0728739	−	0.997341i	$-0.476783\pi$
$149$	1.77908	0.145748	0.0728739	+	0.997341i	$0.476783\pi$
$150$	−0.784908	−0.0640874
$151$	−3.93078	−0.319883	−0.159941	−	0.987127i	$-0.551131\pi$
$151$	−3.93078	−0.319883	−0.159941	+	0.987127i	$0.551131\pi$
$152$	3.21509	0.260778
$153$	−12.3431	−0.997878
$154$	0	0
$155$	1.30221	0.104596
$156$	2.69779	0.215996
$157$	−4.58652	−0.366044	−0.183022	−	0.983109i	$-0.558588\pi$
$157$	−4.58652	−0.366044	−0.183022	+	0.983109i	$0.558588\pi$
$158$	7.46479	0.593867
$159$	3.30221	0.261882
$160$	1.86620	0.147536
$161$	0	0
$162$	−6.66318	−0.523509
$163$	−24.2318	−1.89798	−0.948990	−	0.315305i	$-0.897893\pi$
$163$	−24.2318	−1.89798	−0.948990	+	0.315305i	$0.897893\pi$
$164$	−1.00000	−0.0780869
$165$	−1.30221	−0.101377
$166$	14.5640	1.13038
$167$	3.23300	0.250177	0.125088	−	0.992146i	$-0.460079\pi$
$167$	3.23300	0.250177	0.125088	+	0.992146i	$0.460079\pi$
$168$	0	0
$169$	14.1972	1.09209
$170$	8.43018	0.646566
$171$	8.78491	0.671799
$172$	−5.03461	−0.383885
$173$	3.23763	0.246152	0.123076	−	0.992397i	$-0.460724\pi$
$173$	3.23763	0.246152	0.123076	+	0.992397i	$0.460724\pi$
$174$	−4.19839	−0.318279
$175$	0	0
$176$	−1.34889	−0.101677
$177$	−6.00000	−0.450988
$178$	−15.1280	−1.13389
$179$	4.38350	0.327638	0.163819	−	0.986490i	$-0.447619\pi$
$179$	4.38350	0.327638	0.163819	+	0.986490i	$0.447619\pi$
$180$	5.09919	0.380071
$181$	−4.18048	−0.310733	−0.155366	−	0.987857i	$-0.549656\pi$
$181$	−4.18048	−0.310733	−0.155366	+	0.987857i	$0.549656\pi$
$182$	0	0
$183$	6.99880	0.517366
$184$	6.18048	0.455631
$185$	−13.1280	−0.965188
$186$	−0.360969	−0.0264675
$187$	−6.09337	−0.445591
$188$	2.78491	0.203110
$189$	0	0
$190$	−6.00000	−0.435286
$191$	20.5928	1.49004	0.745020	−	0.667042i	$-0.232440\pi$
$191$	20.5928	1.49004	0.745020	+	0.667042i	$0.232440\pi$
$192$	−0.517304	−0.0373332
$193$	−4.76700	−0.343137	−0.171568	−	0.985172i	$-0.554883\pi$
$193$	−4.76700	−0.343137	−0.171568	+	0.985172i	$0.554883\pi$
$194$	3.93078	0.282214
$195$	−5.03461	−0.360536
$196$	0	0
$197$	26.0576	1.85652	0.928262	−	0.371927i	$-0.121303\pi$
$197$	26.0576	1.85652	0.928262	+	0.371927i	$0.121303\pi$
$198$	−3.68571	−0.261932
$199$	9.71449	0.688642	0.344321	−	0.938852i	$-0.388109\pi$
$199$	9.71449	0.688642	0.344321	+	0.938852i	$0.388109\pi$
$200$	1.51730	0.107290
$201$	5.05876	0.356817
$202$	−14.2497	−1.00261
$203$	0	0
$204$	−2.33682	−0.163610
$205$	1.86620	0.130341
$206$	−10.1626	−0.708061
$207$	16.8875	1.17376
$208$	−5.21509	−0.361602
$209$	4.33682	0.299984
$210$	0	0
$211$	−22.4769	−1.54737	−0.773686	−	0.633570i	$-0.781589\pi$
$211$	−22.4769	−1.54737	−0.773686	+	0.633570i	$0.781589\pi$
$212$	−6.38350	−0.438421
$213$	−0.860370	−0.0589516
$214$	−1.30221	−0.0890173
$215$	9.39558	0.640773
$216$	−2.96539	−0.201769
$217$	0	0
$218$	−9.70986	−0.657635
$219$	−1.53401	−0.103659
$220$	2.51730	0.169717
$221$	−23.5582	−1.58469
$222$	3.63903	0.244236
$223$	−17.5340	−1.17416	−0.587082	−	0.809527i	$-0.699723\pi$
$223$	−17.5340	−1.17416	−0.587082	+	0.809527i	$0.699723\pi$
$224$	0	0
$225$	4.14588	0.276392
$226$	9.48270	0.630780
$227$	18.9475	1.25759	0.628795	−	0.777572i	$-0.283549\pi$
$227$	18.9475	1.25759	0.628795	+	0.777572i	$0.283549\pi$
$228$	1.66318	0.110147
$229$	−9.75030	−0.644318	−0.322159	−	0.946686i	$-0.604409\pi$
$229$	−9.75030	−0.644318	−0.322159	+	0.946686i	$0.604409\pi$
$230$	−11.5340	−0.760530
$231$	0	0
$232$	8.11590	0.532835
$233$	16.5686	1.08545	0.542723	−	0.839912i	$-0.317393\pi$
$233$	16.5686	1.08545	0.542723	+	0.839912i	$0.317393\pi$
$234$	−14.2497	−0.931532
$235$	−5.19719	−0.339027
$236$	11.5986	0.755004
$237$	3.86157	0.250836
$238$	0	0
$239$	4.06922	0.263216	0.131608	−	0.991302i	$-0.457986\pi$
$239$	4.06922	0.263216	0.131608	+	0.991302i	$0.457986\pi$
$240$	0.965392	0.0623158
$241$	3.89498	0.250898	0.125449	−	0.992100i	$-0.459963\pi$
$241$	3.89498	0.250898	0.125449	+	0.992100i	$0.459963\pi$
$242$	9.18048	0.590144
$243$	−12.3431	−0.791808
$244$	−13.5294	−0.866130
$245$	0	0
$246$	−0.517304	−0.0329821
$247$	16.7670	1.06686
$248$	0.697788	0.0443096
$249$	7.53401	0.477448
$250$	−12.1626	−0.769229
$251$	−27.4244	−1.73101	−0.865505	−	0.500900i	$-0.833002\pi$
$251$	−27.4244	−1.73101	−0.865505	+	0.500900i	$0.833002\pi$
$252$	0	0
$253$	8.33682	0.524131
$254$	−18.1805	−1.14075
$255$	4.36097	0.273094
$256$	1.00000	0.0625000
$257$	−28.5236	−1.77925	−0.889625	−	0.456692i	$-0.849034\pi$
$257$	−28.5236	−1.77925	−0.889625	+	0.456692i	$0.849034\pi$
$258$	−2.60442	−0.162144
$259$	0	0
$260$	9.73240	0.603578
$261$	22.1759	1.37265
$262$	7.93541	0.490252
$263$	−10.4302	−0.643153	−0.321576	−	0.946884i	$-0.604213\pi$
$263$	−10.4302	−0.643153	−0.321576	+	0.946884i	$0.604213\pi$
$264$	−0.697788	−0.0429459
$265$	11.9129	0.731802
$266$	0	0
$267$	−7.82576	−0.478929
$268$	−9.77908	−0.597352
$269$	−0.133802	−0.00815804	−0.00407902	−	0.999992i	$-0.501298\pi$
$269$	−0.133802	−0.00815804	−0.00407902	+	0.999992i	$0.501298\pi$
$270$	5.53401	0.336789
$271$	28.9296	1.75735	0.878674	−	0.477423i	$-0.158429\pi$
$271$	28.9296	1.75735	0.878674	+	0.477423i	$0.158429\pi$
$272$	4.51730	0.273902
$273$	0	0
$274$	9.19719	0.555623
$275$	2.04668	0.123420
$276$	3.19719	0.192448
$277$	19.1280	1.14929	0.574644	−	0.818403i	$-0.305140\pi$
$277$	19.1280	1.14929	0.574644	+	0.818403i	$0.305140\pi$
$278$	−0.831590	−0.0498755
$279$	1.90663	0.114147
$280$	0	0
$281$	−6.49940	−0.387722	−0.193861	−	0.981029i	$-0.562101\pi$
$281$	−6.49940	−0.387722	−0.193861	+	0.981029i	$0.562101\pi$
$282$	1.44064	0.0857891
$283$	30.9942	1.84241	0.921206	−	0.389075i	$-0.127205\pi$
$283$	30.9942	1.84241	0.921206	+	0.389075i	$0.127205\pi$
$284$	1.66318	0.0986916
$285$	−3.10382	−0.183855
$286$	−7.03461	−0.415965
$287$	0	0
$288$	2.73240	0.161008
$289$	3.40604	0.200355
$290$	−15.1459	−0.889396
$291$	2.03341	0.119201
$292$	2.96539	0.173536
$293$	9.48270	0.553985	0.276993	−	0.960872i	$-0.410662\pi$
$293$	9.48270	0.553985	0.276993	+	0.960872i	$0.410662\pi$
$294$	0	0
$295$	−21.6453	−1.26024
$296$	−7.03461	−0.408878
$297$	−4.00000	−0.232104
$298$	−1.77908	−0.103059
$299$	32.2318	1.86401
$300$	0.784908	0.0453167
$301$	0	0
$302$	3.93078	0.226191
$303$	−7.37143	−0.423477
$304$	−3.21509	−0.184398
$305$	25.2485	1.44573
$306$	12.3431	0.705606
$307$	31.1326	1.77683	0.888416	−	0.459040i	$-0.151806\pi$
$307$	31.1326	1.77683	0.888416	+	0.459040i	$0.151806\pi$
$308$	0	0
$309$	−5.25714	−0.299069
$310$	−1.30221	−0.0739606
$311$	7.68108	0.435554	0.217777	−	0.975999i	$-0.430119\pi$
$311$	7.68108	0.435554	0.217777	+	0.975999i	$0.430119\pi$
$312$	−2.69779	−0.152732
$313$	24.3431	1.37595	0.687976	−	0.725734i	$-0.258500\pi$
$313$	24.3431	1.37595	0.687976	+	0.725734i	$0.258500\pi$
$314$	4.58652	0.258832
$315$	0	0
$316$	−7.46479	−0.419927
$317$	8.88290	0.498914	0.249457	−	0.968386i	$-0.419748\pi$
$317$	8.88290	0.498914	0.249457	+	0.968386i	$0.419748\pi$
$318$	−3.30221	−0.185179
$319$	10.9475	0.612942
$320$	−1.86620	−0.104324
$321$	−0.673639	−0.0375989
$322$	0	0
$323$	−14.5236	−0.808112
$324$	6.66318	0.370177
$325$	7.91288	0.438928
$326$	24.2318	1.34208
$327$	−5.02295	−0.277770
$328$	1.00000	0.0552158
$329$	0	0
$330$	1.30221	0.0716844
$331$	−35.5356	−1.95321	−0.976607	−	0.215031i	$-0.931015\pi$
$331$	−35.5356	−1.95321	−0.976607	+	0.215031i	$0.931015\pi$
$332$	−14.5640	−0.799303
$333$	−19.2213	−1.05332
$334$	−3.23300	−0.176902
$335$	18.2497	0.997088
$336$	0	0
$337$	14.3252	0.780341	0.390171	−	0.920743i	$-0.372416\pi$
$337$	14.3252	0.780341	0.390171	+	0.920743i	$0.372416\pi$
$338$	−14.1972	−0.772225
$339$	4.90544	0.266427
$340$	−8.43018	−0.457191
$341$	0.941243	0.0509712
$342$	−8.78491	−0.475033
$343$	0	0
$344$	5.03461	0.271448
$345$	−5.96659	−0.321230
$346$	−3.23763	−0.174056
$347$	17.4423	0.936350	0.468175	−	0.883636i	$-0.344912\pi$
$347$	17.4423	0.936350	0.468175	+	0.883636i	$0.344912\pi$
$348$	4.19839	0.225057
$349$	12.7266	0.681238	0.340619	−	0.940201i	$-0.389363\pi$
$349$	12.7266	0.681238	0.340619	+	0.940201i	$0.389363\pi$
$350$	0	0
$351$	−15.4648	−0.825450
$352$	1.34889	0.0718963
$353$	14.4060	0.766756	0.383378	−	0.923592i	$-0.374761\pi$
$353$	14.4060	0.766756	0.383378	+	0.923592i	$0.374761\pi$
$354$	6.00000	0.318896
$355$	−3.10382	−0.164734
$356$	15.1280	0.801781
$357$	0	0
$358$	−4.38350	−0.231675
$359$	5.30221	0.279840	0.139920	−	0.990163i	$-0.455315\pi$
$359$	5.30221	0.279840	0.139920	+	0.990163i	$0.455315\pi$
$360$	−5.09919	−0.268751
$361$	−8.66318	−0.455957
$362$	4.18048	0.219721
$363$	4.74910	0.249263
$364$	0	0
$365$	−5.53401	−0.289663
$366$	−6.99880	−0.365833
$367$	−13.6032	−0.710083	−0.355041	−	0.934851i	$-0.615533\pi$
$367$	−13.6032	−0.710083	−0.355041	+	0.934851i	$0.615533\pi$
$368$	−6.18048	−0.322180
$369$	2.73240	0.142243
$370$	13.1280	0.682491
$371$	0	0
$372$	0.360969	0.0187154
$373$	−20.3010	−1.05115	−0.525573	−	0.850748i	$-0.676149\pi$
$373$	−20.3010	−1.05115	−0.525573	+	0.850748i	$0.676149\pi$
$374$	6.09337	0.315080
$375$	−6.29175	−0.324905
$376$	−2.78491	−0.143621
$377$	42.3252	2.17986
$378$	0	0
$379$	−6.29175	−0.323186	−0.161593	−	0.986858i	$-0.551663\pi$
$379$	−6.29175	−0.323186	−0.161593	+	0.986858i	$0.551663\pi$
$380$	6.00000	0.307794
$381$	−9.40484	−0.481824
$382$	−20.5928	−1.05362
$383$	18.3010	0.935138	0.467569	−	0.883957i	$-0.345130\pi$
$383$	18.3010	0.935138	0.467569	+	0.883957i	$0.345130\pi$
$384$	0.517304	0.0263986
$385$	0	0
$386$	4.76700	0.242634
$387$	13.7565	0.699285
$388$	−3.93078	−0.199555
$389$	1.32636	0.0672492	0.0336246	−	0.999435i	$-0.489295\pi$
$389$	1.32636	0.0672492	0.0336246	+	0.999435i	$0.489295\pi$
$390$	5.03461	0.254937
$391$	−27.9191	−1.41193
$392$	0	0
$393$	4.10502	0.207071
$394$	−26.0576	−1.31276
$395$	13.9308	0.700934
$396$	3.68571	0.185214
$397$	−8.31892	−0.417514	−0.208757	−	0.977967i	$-0.566942\pi$
$397$	−8.31892	−0.417514	−0.208757	+	0.977967i	$0.566942\pi$
$398$	−9.71449	−0.486944
$399$	0	0
$400$	−1.51730	−0.0758652
$401$	13.0859	0.653480	0.326740	−	0.945114i	$-0.394050\pi$
$401$	13.0859	0.653480	0.326740	+	0.945114i	$0.394050\pi$
$402$	−5.05876	−0.252308
$403$	3.63903	0.181273
$404$	14.2497	0.708949
$405$	−12.4348	−0.617891
$406$	0	0
$407$	−9.48894	−0.470349
$408$	2.33682	0.115690
$409$	−15.9308	−0.787727	−0.393863	−	0.919169i	$-0.628862\pi$
$409$	−15.9308	−0.787727	−0.393863	+	0.919169i	$0.628862\pi$
$410$	−1.86620	−0.0921650
$411$	4.75774	0.234682
$412$	10.1626	0.500674
$413$	0	0
$414$	−16.8875	−0.829977
$415$	27.1793	1.33418
$416$	5.21509	0.255691
$417$	−0.430185	−0.0210662
$418$	−4.33682	−0.212121
$419$	8.92496	0.436013	0.218006	−	0.975947i	$-0.430045\pi$
$419$	8.92496	0.436013	0.218006	+	0.975947i	$0.430045\pi$
$420$	0	0
$421$	7.08129	0.345121	0.172560	−	0.984999i	$-0.444796\pi$
$421$	7.08129	0.345121	0.172560	+	0.984999i	$0.444796\pi$
$422$	22.4769	1.09416
$423$	−7.60947	−0.369985
$424$	6.38350	0.310010
$425$	−6.85412	−0.332474
$426$	0.860370	0.0416851
$427$	0	0
$428$	1.30221	0.0629448
$429$	−3.63903	−0.175694
$430$	−9.39558	−0.453095
$431$	14.1805	0.683050	0.341525	−	0.939873i	$-0.389057\pi$
$431$	14.1805	0.683050	0.341525	+	0.939873i	$0.389057\pi$
$432$	2.96539	0.142672
$433$	15.0346	0.722517	0.361259	−	0.932466i	$-0.382347\pi$
$433$	15.0346	0.722517	0.361259	+	0.932466i	$0.382347\pi$
$434$	0	0
$435$	−7.83502	−0.375661
$436$	9.70986	0.465018
$437$	19.8708	0.950551
$438$	1.53401	0.0732978
$439$	−22.7491	−1.08576	−0.542878	−	0.839812i	$-0.682665\pi$
$439$	−22.7491	−1.08576	−0.542878	+	0.839812i	$0.682665\pi$
$440$	−2.51730	−0.120008
$441$	0	0
$442$	23.5582	1.12055
$443$	−13.3956	−0.636443	−0.318222	−	0.948016i	$-0.603086\pi$
$443$	−13.3956	−0.636443	−0.318222	+	0.948016i	$0.603086\pi$
$444$	−3.63903	−0.172701
$445$	−28.2318	−1.33832
$446$	17.5340	0.830259
$447$	−0.920325	−0.0435299
$448$	0	0
$449$	−23.6632	−1.11673	−0.558367	−	0.829594i	$-0.688572\pi$
$449$	−23.6632	−1.11673	−0.558367	+	0.829594i	$0.688572\pi$
$450$	−4.14588	−0.195438
$451$	1.34889	0.0635169
$452$	−9.48270	−0.446028
$453$	2.03341	0.0955380
$454$	−18.9475	−0.889250
$455$	0	0
$456$	−1.66318	−0.0778856
$457$	−12.5928	−0.589065	−0.294532	−	0.955641i	$-0.595164\pi$
$457$	−12.5928	−0.589065	−0.294532	+	0.955641i	$0.595164\pi$
$458$	9.75030	0.455602
$459$	13.3956	0.625252
$460$	11.5340	0.537776
$461$	35.1326	1.63629	0.818144	−	0.575013i	$-0.195003\pi$
$461$	35.1326	1.63629	0.818144	+	0.575013i	$0.195003\pi$
$462$	0	0
$463$	32.6861	1.51905	0.759527	−	0.650476i	$-0.225431\pi$
$463$	32.6861	1.51905	0.759527	+	0.650476i	$0.225431\pi$
$464$	−8.11590	−0.376771
$465$	−0.673639	−0.0312393
$466$	−16.5686	−0.767526
$467$	15.4244	0.713754	0.356877	−	0.934151i	$-0.383842\pi$
$467$	15.4244	0.713754	0.356877	+	0.934151i	$0.383842\pi$
$468$	14.2497	0.658693
$469$	0	0
$470$	5.19719	0.239728
$471$	2.37263	0.109325
$472$	−11.5986	−0.533869
$473$	6.79115	0.312258
$474$	−3.86157	−0.177368
$475$	4.87827	0.223831
$476$	0	0
$477$	17.4423	0.798626
$478$	−4.06922	−0.186122
$479$	−30.0397	−1.37255	−0.686273	−	0.727344i	$-0.740755\pi$
$479$	−30.0397	−1.37255	−0.686273	+	0.727344i	$0.740755\pi$
$480$	−0.965392	−0.0440639
$481$	−36.6861	−1.67274
$482$	−3.89498	−0.177411
$483$	0	0
$484$	−9.18048	−0.417295
$485$	7.33562	0.333093
$486$	12.3431	0.559893
$487$	6.83622	0.309779	0.154889	−	0.987932i	$-0.450498\pi$
$487$	6.83622	0.309779	0.154889	+	0.987932i	$0.450498\pi$
$488$	13.5294	0.612446
$489$	12.5352	0.566862
$490$	0	0
$491$	10.4302	0.470708	0.235354	−	0.971910i	$-0.424375\pi$
$491$	10.4302	0.470708	0.235354	+	0.971910i	$0.424375\pi$
$492$	0.517304	0.0233219
$493$	−36.6620	−1.65117
$494$	−16.7670	−0.754383
$495$	−6.87827	−0.309155
$496$	−0.697788	−0.0313316
$497$	0	0
$498$	−7.53401	−0.337607
$499$	−12.7895	−0.572538	−0.286269	−	0.958149i	$-0.592415\pi$
$499$	−12.7895	−0.572538	−0.286269	+	0.958149i	$0.592415\pi$
$500$	12.1626	0.543927
$501$	−1.67244	−0.0747192
$502$	27.4244	1.22401
$503$	33.3956	1.48904	0.744518	−	0.667603i	$-0.232680\pi$
$503$	33.3956	1.48904	0.744518	+	0.667603i	$0.232680\pi$
$504$	0	0
$505$	−26.5928	−1.18336
$506$	−8.33682	−0.370617
$507$	−7.34426	−0.326170
$508$	18.1805	0.806629
$509$	−20.6799	−0.916620	−0.458310	−	0.888792i	$-0.651545\pi$
$509$	−20.6799	−0.916620	−0.458310	+	0.888792i	$0.651545\pi$
$510$	−4.36097	−0.193107
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−9.53401	−0.420937
$514$	28.5236	1.25812
$515$	−18.9654	−0.835715
$516$	2.60442	0.114653
$517$	−3.75655	−0.165213
$518$	0	0
$519$	−1.67484	−0.0735172
$520$	−9.73240	−0.426794
$521$	9.23924	0.404779	0.202389	−	0.979305i	$-0.435129\pi$
$521$	9.23924	0.404779	0.202389	+	0.979305i	$0.435129\pi$
$522$	−22.1759	−0.970611
$523$	−3.46016	−0.151302	−0.0756512	−	0.997134i	$-0.524104\pi$
$523$	−3.46016	−0.151302	−0.0756512	+	0.997134i	$0.524104\pi$
$524$	−7.93541	−0.346660
$525$	0	0
$526$	10.4302	0.454778
$527$	−3.15212	−0.137309
$528$	0.697788	0.0303673
$529$	15.1984	0.660799
$530$	−11.9129	−0.517462
$531$	−31.6920	−1.37531
$532$	0	0
$533$	5.21509	0.225891
$534$	7.82576	0.338654
$535$	−2.43018	−0.105066
$536$	9.77908	0.422392
$537$	−2.26760	−0.0978543
$538$	0.133802	0.00576860
$539$	0	0
$540$	−5.53401	−0.238146
$541$	−23.7207	−1.01983	−0.509917	−	0.860224i	$-0.670324\pi$
$541$	−23.7207	−1.01983	−0.509917	+	0.860224i	$0.670324\pi$
$542$	−28.9296	−1.24263
$543$	2.16258	0.0928053
$544$	−4.51730	−0.193678
$545$	−18.1205	−0.776198
$546$	0	0
$547$	−29.6165	−1.26631	−0.633155	−	0.774025i	$-0.718240\pi$
$547$	−29.6165	−1.26631	−0.633155	+	0.774025i	$0.718240\pi$
$548$	−9.19719	−0.392884
$549$	36.9676	1.57774
$550$	−2.04668	−0.0872708
$551$	26.0934	1.11161
$552$	−3.19719	−0.136081
$553$	0	0
$554$	−19.1280	−0.812670
$555$	6.79115	0.288268
$556$	0.831590	0.0352673
$557$	11.6406	0.493230	0.246615	−	0.969114i	$-0.420682\pi$
$557$	11.6406	0.493230	0.246615	+	0.969114i	$0.420682\pi$
$558$	−1.90663	−0.0807143
$559$	26.2559	1.11051
$560$	0	0
$561$	3.15212	0.133083
$562$	6.49940	0.274161
$563$	37.9129	1.59784	0.798919	−	0.601439i	$-0.205406\pi$
$563$	37.9129	1.59784	0.798919	+	0.601439i	$0.205406\pi$
$564$	−1.44064	−0.0606621
$565$	17.6966	0.744501
$566$	−30.9942	−1.30278
$567$	0	0
$568$	−1.66318	−0.0697855
$569$	13.4827	0.565224	0.282612	−	0.959234i	$-0.408799\pi$
$569$	13.4827	0.565224	0.282612	+	0.959234i	$0.408799\pi$
$570$	3.10382	0.130005
$571$	−7.52313	−0.314833	−0.157417	−	0.987532i	$-0.550317\pi$
$571$	−7.52313	−0.314833	−0.157417	+	0.987532i	$0.550317\pi$
$572$	7.03461	0.294132
$573$	−10.6527	−0.445024
$574$	0	0
$575$	9.37767	0.391076
$576$	−2.73240	−0.113850
$577$	−44.1688	−1.83877	−0.919386	−	0.393356i	$-0.871314\pi$
$577$	−44.1688	−1.83877	−0.919386	+	0.393356i	$0.871314\pi$
$578$	−3.40604	−0.141672
$579$	2.46599	0.102483
$580$	15.1459	0.628898
$581$	0	0
$582$	−2.03341	−0.0842876
$583$	8.61067	0.356617
$584$	−2.96539	−0.122709
$585$	−26.5928	−1.09948
$586$	−9.48270	−0.391727
$587$	31.4018	1.29609	0.648046	−	0.761601i	$-0.275586\pi$
$587$	31.4018	1.29609	0.648046	+	0.761601i	$0.275586\pi$
$588$	0	0
$589$	2.24345	0.0924399
$590$	21.6453	0.891122
$591$	−13.4797	−0.554480
$592$	7.03461	0.289121
$593$	−20.4302	−0.838967	−0.419484	−	0.907763i	$-0.637789\pi$
$593$	−20.4302	−0.838967	−0.419484	+	0.907763i	$0.637789\pi$
$594$	4.00000	0.164122
$595$	0	0
$596$	1.77908	0.0728739
$597$	−5.02535	−0.205674
$598$	−32.2318	−1.31806
$599$	6.30101	0.257452	0.128726	−	0.991680i	$-0.458911\pi$
$599$	6.30101	0.257452	0.128726	+	0.991680i	$0.458911\pi$
$600$	−0.784908	−0.0320437
$601$	−43.0501	−1.75605	−0.878025	−	0.478614i	$-0.841139\pi$
$601$	−43.0501	−1.75605	−0.878025	+	0.478614i	$0.841139\pi$
$602$	0	0
$603$	26.7203	1.08814
$604$	−3.93078	−0.159941
$605$	17.1326	0.696539
$606$	7.37143	0.299444
$607$	−10.0000	−0.405887	−0.202944	−	0.979190i	$-0.565051\pi$
$607$	−10.0000	−0.405887	−0.202944	+	0.979190i	$0.565051\pi$
$608$	3.21509	0.130389
$609$	0	0
$610$	−25.2485	−1.02228
$611$	−14.5236	−0.587560
$612$	−12.3431	−0.498939
$613$	−33.0680	−1.33560	−0.667802	−	0.744339i	$-0.732765\pi$
$613$	−33.0680	−1.33560	−0.667802	+	0.744339i	$0.732765\pi$
$614$	−31.1326	−1.25641
$615$	−0.965392	−0.0389284
$616$	0	0
$617$	31.5519	1.27023	0.635116	−	0.772417i	$-0.280952\pi$
$617$	31.5519	1.27023	0.635116	+	0.772417i	$0.280952\pi$
$618$	5.25714	0.211473
$619$	2.92496	0.117564	0.0587819	−	0.998271i	$-0.481278\pi$
$619$	2.92496	0.117564	0.0587819	+	0.998271i	$0.481278\pi$
$620$	1.30221	0.0522981
$621$	−18.3276	−0.735460
$622$	−7.68108	−0.307983
$623$	0	0
$624$	2.69779	0.107998
$625$	−15.1113	−0.604451
$626$	−24.3431	−0.972945
$627$	−2.24345	−0.0895949
$628$	−4.58652	−0.183022
$629$	31.7775	1.26705
$630$	0	0
$631$	−8.87827	−0.353438	−0.176719	−	0.984261i	$-0.556548\pi$
$631$	−8.87827	−0.353438	−0.176719	+	0.984261i	$0.556548\pi$
$632$	7.46479	0.296934
$633$	11.6274	0.462147
$634$	−8.88290	−0.352785
$635$	−33.9284	−1.34641
$636$	3.30221	0.130941
$637$	0	0
$638$	−10.9475	−0.433415
$639$	−4.54447	−0.179776
$640$	1.86620	0.0737680
$641$	8.49014	0.335340	0.167670	−	0.985843i	$-0.446376\pi$
$641$	8.49014	0.335340	0.167670	+	0.985843i	$0.446376\pi$
$642$	0.673639	0.0265864
$643$	45.3777	1.78952	0.894760	−	0.446547i	$-0.147346\pi$
$643$	45.3777	1.78952	0.894760	+	0.446547i	$0.147346\pi$
$644$	0	0
$645$	−4.86037	−0.191377
$646$	14.5236	0.571421
$647$	11.5940	0.455806	0.227903	−	0.973684i	$-0.426813\pi$
$647$	11.5940	0.455806	0.227903	+	0.973684i	$0.426813\pi$
$648$	−6.66318	−0.261754
$649$	−15.6453	−0.614131
$650$	−7.91288	−0.310369
$651$	0	0
$652$	−24.2318	−0.948990
$653$	−5.82415	−0.227916	−0.113958	−	0.993486i	$-0.536353\pi$
$653$	−5.82415	−0.227916	−0.113958	+	0.993486i	$0.536353\pi$
$654$	5.02295	0.196413
$655$	14.8091	0.578638
$656$	−1.00000	−0.0390434
$657$	−8.10263	−0.316114
$658$	0	0
$659$	13.1863	0.513666	0.256833	−	0.966456i	$-0.417321\pi$
$659$	13.1863	0.513666	0.256833	+	0.966456i	$0.417321\pi$
$660$	−1.30221	−0.0506885
$661$	−23.5052	−0.914247	−0.457124	−	0.889403i	$-0.651120\pi$
$661$	−23.5052	−0.914247	−0.457124	+	0.889403i	$0.651120\pi$
$662$	35.5356	1.38113
$663$	12.1867	0.473293
$664$	14.5640	0.565192
$665$	0	0
$666$	19.2213	0.744812
$667$	50.1602	1.94221
$668$	3.23300	0.125088
$669$	9.07041	0.350682
$670$	−18.2497	−0.705047
$671$	18.2497	0.704522
$672$	0	0
$673$	31.4531	1.21243	0.606215	−	0.795301i	$-0.292687\pi$
$673$	31.4531	1.21243	0.606215	+	0.795301i	$0.292687\pi$
$674$	−14.3252	−0.551785
$675$	−4.49940	−0.173182
$676$	14.1972	0.546046
$677$	−45.7495	−1.75830	−0.879148	−	0.476548i	$-0.841888\pi$
$677$	−45.7495	−1.75830	−0.879148	+	0.476548i	$0.841888\pi$
$678$	−4.90544	−0.188392
$679$	0	0
$680$	8.43018	0.323283
$681$	−9.80161	−0.375599
$682$	−0.941243	−0.0360420
$683$	15.2105	0.582012	0.291006	−	0.956721i	$-0.406010\pi$
$683$	15.2105	0.582012	0.291006	+	0.956721i	$0.406010\pi$
$684$	8.78491	0.335899
$685$	17.1638	0.655794
$686$	0	0
$687$	5.04387	0.192436
$688$	−5.03461	−0.191943
$689$	33.2906	1.26827
$690$	5.96659	0.227144
$691$	7.17929	0.273113	0.136556	−	0.990632i	$-0.456396\pi$
$691$	7.17929	0.273113	0.136556	+	0.990632i	$0.456396\pi$
$692$	3.23763	0.123076
$693$	0	0
$694$	−17.4423	−0.662099
$695$	−1.55191	−0.0588674
$696$	−4.19839	−0.159139
$697$	−4.51730	−0.171105
$698$	−12.7266	−0.481708
$699$	−8.57101	−0.324185
$700$	0	0
$701$	−26.5928	−1.00439	−0.502197	−	0.864753i	$-0.667475\pi$
$701$	−26.5928	−1.00439	−0.502197	+	0.864753i	$0.667475\pi$
$702$	15.4648	0.583681
$703$	−22.6169	−0.853013
$704$	−1.34889	−0.0508384
$705$	2.68853	0.101256
$706$	−14.4060	−0.542178
$707$	0	0
$708$	−6.00000	−0.225494
$709$	−6.20926	−0.233194	−0.116597	−	0.993179i	$-0.537199\pi$
$709$	−6.20926	−0.233194	−0.116597	+	0.993179i	$0.537199\pi$
$710$	3.10382	0.116484
$711$	20.3968	0.764939
$712$	−15.1280	−0.566945
$713$	4.31267	0.161511
$714$	0	0
$715$	−13.1280	−0.490958
$716$	4.38350	0.163819
$717$	−2.10502	−0.0786135
$718$	−5.30221	−0.197877
$719$	−17.3022	−0.645264	−0.322632	−	0.946525i	$-0.604568\pi$
$719$	−17.3022	−0.645264	−0.322632	+	0.946525i	$0.604568\pi$
$720$	5.09919	0.190036
$721$	0	0
$722$	8.66318	0.322410
$723$	−2.01489	−0.0749345
$724$	−4.18048	−0.155366
$725$	12.3143	0.457341
$726$	−4.74910	−0.176256
$727$	2.55936	0.0949213	0.0474606	−	0.998873i	$-0.484887\pi$
$727$	2.55936	0.0949213	0.0474606	+	0.998873i	$0.484887\pi$
$728$	0	0
$729$	−13.6044	−0.503868
$730$	5.53401	0.204823
$731$	−22.7429	−0.841175
$732$	6.99880	0.258683
$733$	−23.6678	−0.874191	−0.437095	−	0.899415i	$-0.643993\pi$
$733$	−23.6678	−0.874191	−0.437095	+	0.899415i	$0.643993\pi$
$734$	13.6032	0.502104
$735$	0	0
$736$	6.18048	0.227816
$737$	13.1909	0.485895
$738$	−2.73240	−0.100581
$739$	−13.8950	−0.511135	−0.255568	−	0.966791i	$-0.582262\pi$
$739$	−13.8950	−0.511135	−0.255568	+	0.966791i	$0.582262\pi$
$740$	−13.1280	−0.482594
$741$	−8.67364	−0.318634
$742$	0	0
$743$	41.8592	1.53566	0.767832	−	0.640651i	$-0.221336\pi$
$743$	41.8592	1.53566	0.767832	+	0.640651i	$0.221336\pi$
$744$	−0.360969	−0.0132338
$745$	−3.32011	−0.121640
$746$	20.3010	0.743273
$747$	39.7946	1.45601
$748$	−6.09337	−0.222796
$749$	0	0
$750$	6.29175	0.229742
$751$	37.1163	1.35439	0.677197	−	0.735802i	$-0.263195\pi$
$751$	37.1163	1.35439	0.677197	+	0.735802i	$0.263195\pi$
$752$	2.78491	0.101555
$753$	14.1867	0.516993
$754$	−42.3252	−1.54139
$755$	7.33562	0.266971
$756$	0	0
$757$	22.7779	0.827876	0.413938	−	0.910305i	$-0.364153\pi$
$757$	22.7779	0.827876	0.413938	+	0.910305i	$0.364153\pi$
$758$	6.29175	0.228527
$759$	−4.31267	−0.156540
$760$	−6.00000	−0.217643
$761$	−31.7324	−1.15030	−0.575149	−	0.818049i	$-0.695056\pi$
$761$	−31.7324	−1.15030	−0.575149	+	0.818049i	$0.695056\pi$
$762$	9.40484	0.340701
$763$	0	0
$764$	20.5928	0.745020
$765$	23.0346	0.832818
$766$	−18.3010	−0.661243
$767$	−60.4877	−2.18409
$768$	−0.517304	−0.0186666
$769$	15.9191	0.574058	0.287029	−	0.957922i	$-0.407332\pi$
$769$	15.9191	0.574058	0.287029	+	0.957922i	$0.407332\pi$
$770$	0	0
$771$	14.7553	0.531401
$772$	−4.76700	−0.171568
$773$	3.18168	0.114437	0.0572186	−	0.998362i	$-0.481777\pi$
$773$	3.18168	0.114437	0.0572186	+	0.998362i	$0.481777\pi$
$774$	−13.7565	−0.494469
$775$	1.05876	0.0380317
$776$	3.93078	0.141107
$777$	0	0
$778$	−1.32636	−0.0475523
$779$	3.21509	0.115193
$780$	−5.03461	−0.180268
$781$	−2.24345	−0.0802771
$782$	27.9191	0.998386
$783$	−24.0668	−0.860078
$784$	0	0
$785$	8.55936	0.305497
$786$	−4.10502	−0.146421
$787$	−32.4014	−1.15499	−0.577493	−	0.816396i	$-0.695969\pi$
$787$	−32.4014	−1.15499	−0.577493	+	0.816396i	$0.695969\pi$
$788$	26.0576	0.928262
$789$	5.39558	0.192088
$790$	−13.9308	−0.495635
$791$	0	0
$792$	−3.68571	−0.130966
$793$	70.5570	2.50555
$794$	8.31892	0.295227
$795$	−6.16258	−0.218564
$796$	9.71449	0.344321
$797$	−36.5974	−1.29635	−0.648173	−	0.761493i	$-0.724467\pi$
$797$	−36.5974	−1.29635	−0.648173	+	0.761493i	$0.724467\pi$
$798$	0	0
$799$	12.5803	0.445058
$800$	1.51730	0.0536448
$801$	−41.3356	−1.46052
$802$	−13.0859	−0.462080
$803$	−4.00000	−0.141157
$804$	5.05876	0.178409
$805$	0	0
$806$	−3.63903	−0.128179
$807$	0.0692162	0.00243652
$808$	−14.2497	−0.501303
$809$	−45.7658	−1.60904	−0.804520	−	0.593926i	$-0.797577\pi$
$809$	−45.7658	−1.60904	−0.804520	+	0.593926i	$0.797577\pi$
$810$	12.4348	0.436915
$811$	−23.7612	−0.834368	−0.417184	−	0.908822i	$-0.636983\pi$
$811$	−23.7612	−0.834368	−0.417184	+	0.908822i	$0.636983\pi$
$812$	0	0
$813$	−14.9654	−0.524859
$814$	9.48894	0.332587
$815$	45.2213	1.58403
$816$	−2.33682	−0.0818051
$817$	16.1867	0.566302
$818$	15.9308	0.557007
$819$	0	0
$820$	1.86620	0.0651705
$821$	−35.5698	−1.24140	−0.620698	−	0.784050i	$-0.713151\pi$
$821$	−35.5698	−1.24140	−0.620698	+	0.784050i	$0.713151\pi$
$822$	−4.75774	−0.165945
$823$	20.0576	0.699163	0.349581	−	0.936906i	$-0.386324\pi$
$823$	20.0576	0.699163	0.349581	+	0.936906i	$0.386324\pi$
$824$	−10.1626	−0.354030
$825$	−1.05876	−0.0368612
$826$	0	0
$827$	−47.1839	−1.64075	−0.820373	−	0.571829i	$-0.806234\pi$
$827$	−47.1839	−1.64075	−0.820373	+	0.571829i	$0.806234\pi$
$828$	16.8875	0.586882
$829$	−55.7612	−1.93667	−0.968333	−	0.249663i	$-0.919680\pi$
$829$	−55.7612	−1.93667	−0.968333	+	0.249663i	$0.919680\pi$
$830$	−27.1793	−0.943407
$831$	−9.89498	−0.343253
$832$	−5.21509	−0.180801
$833$	0	0
$834$	0.430185	0.0148961
$835$	−6.03341	−0.208795
$836$	4.33682	0.149992
$837$	−2.06922	−0.0715226
$838$	−8.92496	−0.308307
$839$	−29.0050	−1.00137	−0.500683	−	0.865631i	$-0.666918\pi$
$839$	−29.0050	−1.00137	−0.500683	+	0.865631i	$0.666918\pi$
$840$	0	0
$841$	36.8678	1.27130
$842$	−7.08129	−0.244037
$843$	3.36217	0.115799
$844$	−22.4769	−0.773686
$845$	−26.4948	−0.911448
$846$	7.60947	0.261619
$847$	0	0
$848$	−6.38350	−0.219210
$849$	−16.0334	−0.550265
$850$	6.85412	0.235095
$851$	−43.4773	−1.49038
$852$	−0.860370	−0.0294758
$853$	47.1660	1.61493	0.807467	−	0.589913i	$-0.200838\pi$
$853$	47.1660	1.61493	0.807467	+	0.589913i	$0.200838\pi$
$854$	0	0
$855$	−16.3944	−0.560676
$856$	−1.30221	−0.0445087
$857$	−11.7565	−0.401596	−0.200798	−	0.979633i	$-0.564353\pi$
$857$	−11.7565	−0.401596	−0.200798	+	0.979633i	$0.564353\pi$
$858$	3.63903	0.124234
$859$	−15.3551	−0.523911	−0.261955	−	0.965080i	$-0.584367\pi$
$859$	−15.3551	−0.523911	−0.261955	+	0.965080i	$0.584367\pi$
$860$	9.39558	0.320387
$861$	0	0
$862$	−14.1805	−0.482989
$863$	−6.55936	−0.223283	−0.111642	−	0.993749i	$-0.535611\pi$
$863$	−6.55936	−0.223283	−0.111642	+	0.993749i	$0.535611\pi$
$864$	−2.96539	−0.100885
$865$	−6.04205	−0.205436
$866$	−15.0346	−0.510897
$867$	−1.76196	−0.0598392
$868$	0	0
$869$	10.0692	0.341575
$870$	7.83502	0.265632
$871$	50.9988	1.72803
$872$	−9.70986	−0.328817
$873$	10.7405	0.363509
$874$	−19.8708	−0.672141
$875$	0	0
$876$	−1.53401	−0.0518294
$877$	−7.52475	−0.254093	−0.127046	−	0.991897i	$-0.540550\pi$
$877$	−7.52475	−0.254093	−0.127046	+	0.991897i	$0.540550\pi$
$878$	22.7491	0.767745
$879$	−4.90544	−0.165456
$880$	2.51730	0.0848583
$881$	−1.59396	−0.0537020	−0.0268510	−	0.999639i	$-0.508548\pi$
$881$	−1.59396	−0.0537020	−0.0268510	+	0.999639i	$0.508548\pi$
$882$	0	0
$883$	−8.98793	−0.302468	−0.151234	−	0.988498i	$-0.548325\pi$
$883$	−8.98793	−0.302468	−0.151234	+	0.988498i	$0.548325\pi$
$884$	−23.5582	−0.792347
$885$	11.1972	0.376389
$886$	13.3956	0.450033
$887$	37.0050	1.24251	0.621254	−	0.783609i	$-0.286624\pi$
$887$	37.0050	1.24251	0.621254	+	0.783609i	$0.286624\pi$
$888$	3.63903	0.122118
$889$	0	0
$890$	28.2318	0.946332
$891$	−8.98793	−0.301107
$892$	−17.5340	−0.587082
$893$	−8.95374	−0.299625
$894$	0.920325	0.0307803
$895$	−8.18048	−0.273443
$896$	0	0
$897$	−16.6736	−0.556717
$898$	23.6632	0.789651
$899$	5.66318	0.188878
$900$	4.14588	0.138196
$901$	−28.8362	−0.960674
$902$	−1.34889	−0.0449133
$903$	0	0
$904$	9.48270	0.315390
$905$	7.80161	0.259334
$906$	−2.03341	−0.0675555
$907$	−2.79115	−0.0926787	−0.0463394	−	0.998926i	$-0.514756\pi$
$907$	−2.79115	−0.0926787	−0.0463394	+	0.998926i	$0.514756\pi$
$908$	18.9475	0.628795
$909$	−38.9358	−1.29142
$910$	0	0
$911$	41.2485	1.36662	0.683312	−	0.730127i	$-0.260539\pi$
$911$	41.2485	1.36662	0.683312	+	0.730127i	$0.260539\pi$
$912$	1.66318	0.0550734
$913$	19.6453	0.650164
$914$	12.5928	0.416532
$915$	−13.0612	−0.431788
$916$	−9.75030	−0.322159
$917$	0	0
$918$	−13.3956	−0.442120
$919$	−31.7324	−1.04676	−0.523378	−	0.852101i	$-0.675328\pi$
$919$	−31.7324	−1.04676	−0.523378	+	0.852101i	$0.675328\pi$
$920$	−11.5340	−0.380265
$921$	−16.1050	−0.530679
$922$	−35.1326	−1.15703
$923$	−8.67364	−0.285496
$924$	0	0
$925$	−10.6736	−0.350947
$926$	−32.6861	−1.07413
$927$	−27.7682	−0.912027
$928$	8.11590	0.266417
$929$	−35.3022	−1.15823	−0.579114	−	0.815247i	$-0.696601\pi$
$929$	−35.3022	−1.15823	−0.579114	+	0.815247i	$0.696601\pi$
$930$	0.673639	0.0220895
$931$	0	0
$932$	16.5686	0.542723
$933$	−3.97346	−0.130085
$934$	−15.4244	−0.504700
$935$	11.3714	0.371885
$936$	−14.2497	−0.465766
$937$	−21.4290	−0.700054	−0.350027	−	0.936740i	$-0.613828\pi$
$937$	−21.4290	−0.700054	−0.350027	+	0.936740i	$0.613828\pi$
$938$	0	0
$939$	−12.5928	−0.410949
$940$	−5.19719	−0.169514
$941$	−37.9930	−1.23854	−0.619268	−	0.785180i	$-0.712570\pi$
$941$	−37.9930	−1.23854	−0.619268	+	0.785180i	$0.712570\pi$
$942$	−2.37263	−0.0773043
$943$	6.18048	0.201264
$944$	11.5986	0.377502
$945$	0	0
$946$	−6.79115	−0.220799
$947$	−57.5465	−1.87001	−0.935005	−	0.354634i	$-0.884605\pi$
$947$	−57.5465	−1.87001	−0.935005	+	0.354634i	$0.884605\pi$
$948$	3.86157	0.125418
$949$	−15.4648	−0.502008
$950$	−4.87827	−0.158272
$951$	−4.59516	−0.149008
$952$	0	0
$953$	−53.5044	−1.73318	−0.866590	−	0.499022i	$-0.833693\pi$
$953$	−53.5044	−1.73318	−0.866590	+	0.499022i	$0.833693\pi$
$954$	−17.4423	−0.564714
$955$	−38.4302	−1.24357
$956$	4.06922	0.131608
$957$	−5.66318	−0.183065
$958$	30.0397	0.970537
$959$	0	0
$960$	0.965392	0.0311579
$961$	−30.5131	−0.984293
$962$	36.6861	1.18281
$963$	−3.55816	−0.114660
$964$	3.89498	0.125449
$965$	8.89618	0.286378
$966$	0	0
$967$	22.9895	0.739294	0.369647	−	0.929172i	$-0.379479\pi$
$967$	22.9895	0.739294	0.369647	+	0.929172i	$0.379479\pi$
$968$	9.18048	0.295072
$969$	7.51309	0.241355
$970$	−7.33562	−0.235533
$971$	−17.4585	−0.560271	−0.280136	−	0.959960i	$-0.590379\pi$
$971$	−17.4585	−0.560271	−0.280136	+	0.959960i	$0.590379\pi$
$972$	−12.3431	−0.395904
$973$	0	0
$974$	−6.83622	−0.219047
$975$	−4.09337	−0.131093
$976$	−13.5294	−0.433065
$977$	−5.45553	−0.174538	−0.0872690	−	0.996185i	$-0.527814\pi$
$977$	−5.45553	−0.174538	−0.0872690	+	0.996185i	$0.527814\pi$
$978$	−12.5352	−0.400832
$979$	−20.4060	−0.652180
$980$	0	0
$981$	−26.5312	−0.847076
$982$	−10.4302	−0.332841
$983$	−5.95493	−0.189933	−0.0949664	−	0.995480i	$-0.530274\pi$
$983$	−5.95493	−0.189933	−0.0949664	+	0.995480i	$0.530274\pi$
$984$	−0.517304	−0.0164911
$985$	−48.6286	−1.54944
$986$	36.6620	1.16756
$987$	0	0
$988$	16.7670	0.533429
$989$	31.1163	0.989441
$990$	6.87827	0.218606
$991$	22.3010	0.708415	0.354208	−	0.935167i	$-0.384751\pi$
$991$	22.3010	0.708415	0.354208	+	0.935167i	$0.384751\pi$
$992$	0.697788	0.0221548
$993$	18.3827	0.583358
$994$	0	0
$995$	−18.1292	−0.574733
$996$	7.53401	0.238724
$997$	−44.4123	−1.40655	−0.703276	−	0.710917i	$-0.748280\pi$
$997$	−44.4123	−1.40655	−0.703276	+	0.710917i	$0.748280\pi$
$998$	12.7895	0.404846
$999$	20.8604	0.659993

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.be.1.2	yes	3
7.6	odd	2		4018.2.a.bd.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4018.2.a.bd.1.2	✓	3	7.6	odd	2
4018.2.a.be.1.2	yes	3	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:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.517304 q^{3} +1.00000 q^{4} -1.86620 q^{5} +0.517304 q^{6} -1.00000 q^{8} -2.73240 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.517304 q^{3} +1.00000 q^{4} -1.86620 q^{5} +0.517304 q^{6} -1.00000 q^{8} -2.73240 q^{9} +1.86620 q^{10} -1.34889 q^{11} -0.517304 q^{12} -5.21509 q^{13} +0.965392 q^{15} +1.00000 q^{16} +4.51730 q^{17} +2.73240 q^{18} -3.21509 q^{19} -1.86620 q^{20} +1.34889 q^{22} -6.18048 q^{23} +0.517304 q^{24} -1.51730 q^{25} +5.21509 q^{26} +2.96539 q^{27} -8.11590 q^{29} -0.965392 q^{30} -0.697788 q^{31} -1.00000 q^{32} +0.697788 q^{33} -4.51730 q^{34} -2.73240 q^{36} +7.03461 q^{37} +3.21509 q^{38} +2.69779 q^{39} +1.86620 q^{40} -1.00000 q^{41} -5.03461 q^{43} -1.34889 q^{44} +5.09919 q^{45} +6.18048 q^{46} +2.78491 q^{47} -0.517304 q^{48} +1.51730 q^{50} -2.33682 q^{51} -5.21509 q^{52} -6.38350 q^{53} -2.96539 q^{54} +2.51730 q^{55} +1.66318 q^{57} +8.11590 q^{58} +11.5986 q^{59} +0.965392 q^{60} -13.5294 q^{61} +0.697788 q^{62} +1.00000 q^{64} +9.73240 q^{65} -0.697788 q^{66} -9.77908 q^{67} +4.51730 q^{68} +3.19719 q^{69} +1.66318 q^{71} +2.73240 q^{72} +2.96539 q^{73} -7.03461 q^{74} +0.784908 q^{75} -3.21509 q^{76} -2.69779 q^{78} -7.46479 q^{79} -1.86620 q^{80} +6.66318 q^{81} +1.00000 q^{82} -14.5640 q^{83} -8.43018 q^{85} +5.03461 q^{86} +4.19839 q^{87} +1.34889 q^{88} +15.1280 q^{89} -5.09919 q^{90} -6.18048 q^{92} +0.360969 q^{93} -2.78491 q^{94} +6.00000 q^{95} +0.517304 q^{96} -3.93078 q^{97} +3.68571 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{4} + 2 q^{5} - 3 q^{8} + 7 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^4 + 2 * q^5 - 3 * q^8 + 7 * q^9	\( 3 q - 3 q^{2} + 3 q^{4} + 2 q^{5} - 3 q^{8} + 7 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{13} + 6 q^{15} + 3 q^{16} + 12 q^{17} - 7 q^{18} + 4 q^{19} + 2 q^{20} - 2 q^{22} - 8 q^{23} - 3 q^{25} + 2 q^{26} + 12 q^{27} - 6 q^{30} + 10 q^{31} - 3 q^{32} - 10 q^{33} - 12 q^{34} + 7 q^{36} + 18 q^{37} - 4 q^{38} - 4 q^{39} - 2 q^{40} - 3 q^{41} - 12 q^{43} + 2 q^{44} + 26 q^{45} + 8 q^{46} + 22 q^{47} + 3 q^{50} - 16 q^{51} - 2 q^{52} - 10 q^{53} - 12 q^{54} + 6 q^{55} - 4 q^{57} + 12 q^{59} + 6 q^{60} - 24 q^{61} - 10 q^{62} + 3 q^{64} + 14 q^{65} + 10 q^{66} + 4 q^{67} + 12 q^{68} - 36 q^{69} - 4 q^{71} - 7 q^{72} + 12 q^{73} - 18 q^{74} + 16 q^{75} + 4 q^{76} + 4 q^{78} + 8 q^{79} + 2 q^{80} + 11 q^{81} + 3 q^{82} - 24 q^{83} + 2 q^{85} + 12 q^{86} + 34 q^{87} - 2 q^{88} + 6 q^{89} - 26 q^{90} - 8 q^{92} - 20 q^{93} - 22 q^{94} + 18 q^{95} - 18 q^{97} + 14 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^4 + 2 * q^5 - 3 * q^8 + 7 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^13 + 6 * q^15 + 3 * q^16 + 12 * q^17 - 7 * q^18 + 4 * q^19 + 2 * q^20 - 2 * q^22 - 8 * q^23 - 3 * q^25 + 2 * q^26 + 12 * q^27 - 6 * q^30 + 10 * q^31 - 3 * q^32 - 10 * q^33 - 12 * q^34 + 7 * q^36 + 18 * q^37 - 4 * q^38 - 4 * q^39 - 2 * q^40 - 3 * q^41 - 12 * q^43 + 2 * q^44 + 26 * q^45 + 8 * q^46 + 22 * q^47 + 3 * q^50 - 16 * q^51 - 2 * q^52 - 10 * q^53 - 12 * q^54 + 6 * q^55 - 4 * q^57 + 12 * q^59 + 6 * q^60 - 24 * q^61 - 10 * q^62 + 3 * q^64 + 14 * q^65 + 10 * q^66 + 4 * q^67 + 12 * q^68 - 36 * q^69 - 4 * q^71 - 7 * q^72 + 12 * q^73 - 18 * q^74 + 16 * q^75 + 4 * q^76 + 4 * q^78 + 8 * q^79 + 2 * q^80 + 11 * q^81 + 3 * q^82 - 24 * q^83 + 2 * q^85 + 12 * q^86 + 34 * q^87 - 2 * q^88 + 6 * q^89 - 26 * q^90 - 8 * q^92 - 20 * q^93 - 22 * q^94 + 18 * q^95 - 18 * q^97 + 14 * q^99

Introduction

L-functions

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