LMFDB - Embedded newform 4018.2.a.v.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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{33}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 8 $ x^2 - x - 8
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 574)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.37228$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +3.37228 q^{3} +1.00000 q^{4} -3.37228 q^{5} -3.37228 q^{6} -1.00000 q^{8} +8.37228 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.37228 q^{3} +1.00000 q^{4} -3.37228 q^{5} -3.37228 q^{6} -1.00000 q^{8} +8.37228 q^{9} +3.37228 q^{10} +1.37228 q^{11} +3.37228 q^{12} +0.372281 q^{13} -11.3723 q^{15} +1.00000 q^{16} -4.74456 q^{17} -8.37228 q^{18} -5.37228 q^{19} -3.37228 q^{20} -1.37228 q^{22} -8.74456 q^{23} -3.37228 q^{24} +6.37228 q^{25} -0.372281 q^{26} +18.1168 q^{27} -7.11684 q^{29} +11.3723 q^{30} +2.74456 q^{31} -1.00000 q^{32} +4.62772 q^{33} +4.74456 q^{34} +8.37228 q^{36} -2.00000 q^{37} +5.37228 q^{38} +1.25544 q^{39} +3.37228 q^{40} -1.00000 q^{41} -6.37228 q^{43} +1.37228 q^{44} -28.2337 q^{45} +8.74456 q^{46} +8.00000 q^{47} +3.37228 q^{48} -6.37228 q^{50} -16.0000 q^{51} +0.372281 q^{52} -10.0000 q^{53} -18.1168 q^{54} -4.62772 q^{55} -18.1168 q^{57} +7.11684 q^{58} -0.372281 q^{59} -11.3723 q^{60} +2.62772 q^{61} -2.74456 q^{62} +1.00000 q^{64} -1.25544 q^{65} -4.62772 q^{66} -8.00000 q^{67} -4.74456 q^{68} -29.4891 q^{69} -11.7446 q^{71} -8.37228 q^{72} +13.1168 q^{73} +2.00000 q^{74} +21.4891 q^{75} -5.37228 q^{76} -1.25544 q^{78} -4.62772 q^{79} -3.37228 q^{80} +35.9783 q^{81} +1.00000 q^{82} -0.372281 q^{83} +16.0000 q^{85} +6.37228 q^{86} -24.0000 q^{87} -1.37228 q^{88} -2.00000 q^{89} +28.2337 q^{90} -8.74456 q^{92} +9.25544 q^{93} -8.00000 q^{94} +18.1168 q^{95} -3.37228 q^{96} +8.00000 q^{97} +11.4891 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{5} - q^{6} - 2 q^{8} + 11 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^5 - q^6 - 2 * q^8 + 11 * q^9	$ 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{5} - q^{6} - 2 q^{8} + 11 q^{9} + q^{10} - 3 q^{11} + q^{12} - 5 q^{13} - 17 q^{15} + 2 q^{16} + 2 q^{17} - 11 q^{18} - 5 q^{19} - q^{20} + 3 q^{22} - 6 q^{23} - q^{24} + 7 q^{25} + 5 q^{26} + 19 q^{27} + 3 q^{29} + 17 q^{30} - 6 q^{31} - 2 q^{32} + 15 q^{33} - 2 q^{34} + 11 q^{36} - 4 q^{37} + 5 q^{38} + 14 q^{39} + q^{40} - 2 q^{41} - 7 q^{43} - 3 q^{44} - 22 q^{45} + 6 q^{46} + 16 q^{47} + q^{48} - 7 q^{50} - 32 q^{51} - 5 q^{52} - 20 q^{53} - 19 q^{54} - 15 q^{55} - 19 q^{57} - 3 q^{58} + 5 q^{59} - 17 q^{60} + 11 q^{61} + 6 q^{62} + 2 q^{64} - 14 q^{65} - 15 q^{66} - 16 q^{67} + 2 q^{68} - 36 q^{69} - 12 q^{71} - 11 q^{72} + 9 q^{73} + 4 q^{74} + 20 q^{75} - 5 q^{76} - 14 q^{78} - 15 q^{79} - q^{80} + 26 q^{81} + 2 q^{82} + 5 q^{83} + 32 q^{85} + 7 q^{86} - 48 q^{87} + 3 q^{88} - 4 q^{89} + 22 q^{90} - 6 q^{92} + 30 q^{93} - 16 q^{94} + 19 q^{95} - q^{96} + 16 q^{97}+O(q^{100}) $ 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^5 - q^6 - 2 * q^8 + 11 * q^9 + q^10 - 3 * q^11 + q^12 - 5 * q^13 - 17 * q^15 + 2 * q^16 + 2 * q^17 - 11 * q^18 - 5 * q^19 - q^20 + 3 * q^22 - 6 * q^23 - q^24 + 7 * q^25 + 5 * q^26 + 19 * q^27 + 3 * q^29 + 17 * q^30 - 6 * q^31 - 2 * q^32 + 15 * q^33 - 2 * q^34 + 11 * q^36 - 4 * q^37 + 5 * q^38 + 14 * q^39 + q^40 - 2 * q^41 - 7 * q^43 - 3 * q^44 - 22 * q^45 + 6 * q^46 + 16 * q^47 + q^48 - 7 * q^50 - 32 * q^51 - 5 * q^52 - 20 * q^53 - 19 * q^54 - 15 * q^55 - 19 * q^57 - 3 * q^58 + 5 * q^59 - 17 * q^60 + 11 * q^61 + 6 * q^62 + 2 * q^64 - 14 * q^65 - 15 * q^66 - 16 * q^67 + 2 * q^68 - 36 * q^69 - 12 * q^71 - 11 * q^72 + 9 * q^73 + 4 * q^74 + 20 * q^75 - 5 * q^76 - 14 * q^78 - 15 * q^79 - q^80 + 26 * q^81 + 2 * q^82 + 5 * q^83 + 32 * q^85 + 7 * q^86 - 48 * q^87 + 3 * q^88 - 4 * q^89 + 22 * q^90 - 6 * q^92 + 30 * q^93 - 16 * q^94 + 19 * q^95 - q^96 + 16 * q^97

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
$3$	3.37228	1.94699	0.973494	−	0.228714i	$-0.0734519\pi$
$3$	3.37228	1.94699	0.973494	+	0.228714i	$0.0734519\pi$
$4$	1.00000	0.500000
$5$	−3.37228	−1.50813	−0.754065	−	0.656800i	$-0.771910\pi$
$5$	−3.37228	−1.50813	−0.754065	+	0.656800i	$0.771910\pi$
$6$	−3.37228	−1.37673
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	8.37228	2.79076
$10$	3.37228	1.06641
$11$	1.37228	0.413758	0.206879	−	0.978366i	$-0.433669\pi$
$11$	1.37228	0.413758	0.206879	+	0.978366i	$0.433669\pi$
$12$	3.37228	0.973494
$13$	0.372281	0.103252	0.0516261	−	0.998666i	$-0.483560\pi$
$13$	0.372281	0.103252	0.0516261	+	0.998666i	$0.483560\pi$
$14$	0	0
$15$	−11.3723	−2.93631
$16$	1.00000	0.250000
$17$	−4.74456	−1.15073	−0.575363	−	0.817898i	$-0.695139\pi$
$17$	−4.74456	−1.15073	−0.575363	+	0.817898i	$0.695139\pi$
$18$	−8.37228	−1.97337
$19$	−5.37228	−1.23249	−0.616243	−	0.787556i	$-0.711346\pi$
$19$	−5.37228	−1.23249	−0.616243	+	0.787556i	$0.711346\pi$
$20$	−3.37228	−0.754065
$21$	0	0
$22$	−1.37228	−0.292571
$23$	−8.74456	−1.82337	−0.911684	−	0.410893i	$-0.865217\pi$
$23$	−8.74456	−1.82337	−0.911684	+	0.410893i	$0.865217\pi$
$24$	−3.37228	−0.688364
$25$	6.37228	1.27446
$26$	−0.372281	−0.0730104
$27$	18.1168	3.48659
$28$	0	0
$29$	−7.11684	−1.32156	−0.660782	−	0.750578i	$-0.729775\pi$
$29$	−7.11684	−1.32156	−0.660782	+	0.750578i	$0.729775\pi$
$30$	11.3723	2.07629
$31$	2.74456	0.492938	0.246469	−	0.969151i	$-0.420730\pi$
$31$	2.74456	0.492938	0.246469	+	0.969151i	$0.420730\pi$
$32$	−1.00000	−0.176777
$33$	4.62772	0.805582
$34$	4.74456	0.813686
$35$	0	0
$36$	8.37228	1.39538
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	5.37228	0.871499
$39$	1.25544	0.201031
$40$	3.37228	0.533204
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−6.37228	−0.971764	−0.485882	−	0.874024i	$-0.661501\pi$
$43$	−6.37228	−0.971764	−0.485882	+	0.874024i	$0.661501\pi$
$44$	1.37228	0.206879
$45$	−28.2337	−4.20883
$46$	8.74456	1.28932
$47$	8.00000	1.16692	0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000	1.16692	0.583460	+	0.812142i	$0.301699\pi$
$48$	3.37228	0.486747
$49$	0	0
$50$	−6.37228	−0.901177
$51$	−16.0000	−2.24045
$52$	0.372281	0.0516261
$53$	−10.0000	−1.37361	−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000	−1.37361	−0.686803	+	0.726844i	$0.740986\pi$
$54$	−18.1168	−2.46539
$55$	−4.62772	−0.624001
$56$	0	0
$57$	−18.1168	−2.39963
$58$	7.11684	0.934487
$59$	−0.372281	−0.0484669	−0.0242335	−	0.999706i	$-0.507715\pi$
$59$	−0.372281	−0.0484669	−0.0242335	+	0.999706i	$0.507715\pi$
$60$	−11.3723	−1.46816
$61$	2.62772	0.336445	0.168222	−	0.985749i	$-0.446197\pi$
$61$	2.62772	0.336445	0.168222	+	0.985749i	$0.446197\pi$
$62$	−2.74456	−0.348560
$63$	0	0
$64$	1.00000	0.125000
$65$	−1.25544	−0.155718
$66$	−4.62772	−0.569633
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	−4.74456	−0.575363
$69$	−29.4891	−3.55007
$70$	0	0
$71$	−11.7446	−1.39382	−0.696912	−	0.717157i	$-0.745443\pi$
$71$	−11.7446	−1.39382	−0.696912	+	0.717157i	$0.745443\pi$
$72$	−8.37228	−0.986683
$73$	13.1168	1.53521	0.767605	−	0.640923i	$-0.221448\pi$
$73$	13.1168	1.53521	0.767605	+	0.640923i	$0.221448\pi$
$74$	2.00000	0.232495
$75$	21.4891	2.48135
$76$	−5.37228	−0.616243
$77$	0	0
$78$	−1.25544	−0.142150
$79$	−4.62772	−0.520659	−0.260330	−	0.965520i	$-0.583831\pi$
$79$	−4.62772	−0.520659	−0.260330	+	0.965520i	$0.583831\pi$
$80$	−3.37228	−0.377033
$81$	35.9783	3.99758
$82$	1.00000	0.110432
$83$	−0.372281	−0.0408632	−0.0204316	−	0.999791i	$-0.506504\pi$
$83$	−0.372281	−0.0408632	−0.0204316	+	0.999791i	$0.506504\pi$
$84$	0	0
$85$	16.0000	1.73544
$86$	6.37228	0.687141
$87$	−24.0000	−2.57307
$88$	−1.37228	−0.146286
$89$	−2.00000	−0.212000	−0.106000	−	0.994366i	$-0.533804\pi$
$89$	−2.00000	−0.212000	−0.106000	+	0.994366i	$0.533804\pi$
$90$	28.2337	2.97609
$91$	0	0
$92$	−8.74456	−0.911684
$93$	9.25544	0.959744
$94$	−8.00000	−0.825137
$95$	18.1168	1.85875
$96$	−3.37228	−0.344182
$97$	8.00000	0.812277	0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000	0.812277	0.406138	+	0.913812i	$0.366875\pi$
$98$	0	0
$99$	11.4891	1.15470
$100$	6.37228	0.637228
$101$	3.25544	0.323928	0.161964	−	0.986797i	$-0.448217\pi$
$101$	3.25544	0.323928	0.161964	+	0.986797i	$0.448217\pi$
$102$	16.0000	1.58424
$103$	−10.7446	−1.05869	−0.529347	−	0.848406i	$-0.677563\pi$
$103$	−10.7446	−1.05869	−0.529347	+	0.848406i	$0.677563\pi$
$104$	−0.372281	−0.0365052
$105$	0	0
$106$	10.0000	0.971286
$107$	1.11684	0.107969	0.0539847	−	0.998542i	$-0.482808\pi$
$107$	1.11684	0.107969	0.0539847	+	0.998542i	$0.482808\pi$
$108$	18.1168	1.74329
$109$	5.62772	0.539038	0.269519	−	0.962995i	$-0.413135\pi$
$109$	5.62772	0.539038	0.269519	+	0.962995i	$0.413135\pi$
$110$	4.62772	0.441236
$111$	−6.74456	−0.640166
$112$	0	0
$113$	6.48913	0.610446	0.305223	−	0.952281i	$-0.401269\pi$
$113$	6.48913	0.610446	0.305223	+	0.952281i	$0.401269\pi$
$114$	18.1168	1.69680
$115$	29.4891	2.74988
$116$	−7.11684	−0.660782
$117$	3.11684	0.288152
$118$	0.372281	0.0342713
$119$	0	0
$120$	11.3723	1.03814
$121$	−9.11684	−0.828804
$122$	−2.62772	−0.237902
$123$	−3.37228	−0.304068
$124$	2.74456	0.246469
$125$	−4.62772	−0.413916
$126$	0	0
$127$	−6.00000	−0.532414	−0.266207	−	0.963916i	$-0.585770\pi$
$127$	−6.00000	−0.532414	−0.266207	+	0.963916i	$0.585770\pi$
$128$	−1.00000	−0.0883883
$129$	−21.4891	−1.89201
$130$	1.25544	0.110109
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	4.62772	0.402791
$133$	0	0
$134$	8.00000	0.691095
$135$	−61.0951	−5.25823
$136$	4.74456	0.406843
$137$	2.74456	0.234484	0.117242	−	0.993103i	$-0.462595\pi$
$137$	2.74456	0.234484	0.117242	+	0.993103i	$0.462595\pi$
$138$	29.4891	2.51028
$139$	5.25544	0.445760	0.222880	−	0.974846i	$-0.428454\pi$
$139$	5.25544	0.445760	0.222880	+	0.974846i	$0.428454\pi$
$140$	0	0
$141$	26.9783	2.27198
$142$	11.7446	0.985582
$143$	0.510875	0.0427215
$144$	8.37228	0.697690
$145$	24.0000	1.99309
$146$	−13.1168	−1.08556
$147$	0	0
$148$	−2.00000	−0.164399
$149$	2.88316	0.236197	0.118099	−	0.993002i	$-0.462320\pi$
$149$	2.88316	0.236197	0.118099	+	0.993002i	$0.462320\pi$
$150$	−21.4891	−1.75458
$151$	−0.883156	−0.0718702	−0.0359351	−	0.999354i	$-0.511441\pi$
$151$	−0.883156	−0.0718702	−0.0359351	+	0.999354i	$0.511441\pi$
$152$	5.37228	0.435750
$153$	−39.7228	−3.21140
$154$	0	0
$155$	−9.25544	−0.743415
$156$	1.25544	0.100515
$157$	−15.8614	−1.26588	−0.632939	−	0.774202i	$-0.718152\pi$
$157$	−15.8614	−1.26588	−0.632939	+	0.774202i	$0.718152\pi$
$158$	4.62772	0.368162
$159$	−33.7228	−2.67439
$160$	3.37228	0.266602
$161$	0	0
$162$	−35.9783	−2.82672
$163$	13.1168	1.02739	0.513695	−	0.857973i	$-0.328276\pi$
$163$	13.1168	1.02739	0.513695	+	0.857973i	$0.328276\pi$
$164$	−1.00000	−0.0780869
$165$	−15.6060	−1.21492
$166$	0.372281	0.0288946
$167$	−13.6277	−1.05454	−0.527272	−	0.849696i	$-0.676785\pi$
$167$	−13.6277	−1.05454	−0.527272	+	0.849696i	$0.676785\pi$
$168$	0	0
$169$	−12.8614	−0.989339
$170$	−16.0000	−1.22714
$171$	−44.9783	−3.43957
$172$	−6.37228	−0.485882
$173$	−10.1168	−0.769169	−0.384585	−	0.923090i	$-0.625655\pi$
$173$	−10.1168	−0.769169	−0.384585	+	0.923090i	$0.625655\pi$
$174$	24.0000	1.81944
$175$	0	0
$176$	1.37228	0.103440
$177$	−1.25544	−0.0943645
$178$	2.00000	0.149906
$179$	13.3723	0.999491	0.499746	−	0.866172i	$-0.333427\pi$
$179$	13.3723	0.999491	0.499746	+	0.866172i	$0.333427\pi$
$180$	−28.2337	−2.10441
$181$	23.4891	1.74593	0.872966	−	0.487780i	$-0.162193\pi$
$181$	23.4891	1.74593	0.872966	+	0.487780i	$0.162193\pi$
$182$	0	0
$183$	8.86141	0.655054
$184$	8.74456	0.644658
$185$	6.74456	0.495870
$186$	−9.25544	−0.678642
$187$	−6.51087	−0.476122
$188$	8.00000	0.583460
$189$	0	0
$190$	−18.1168	−1.31433
$191$	−13.6277	−0.986067	−0.493034	−	0.870010i	$-0.664112\pi$
$191$	−13.6277	−0.986067	−0.493034	+	0.870010i	$0.664112\pi$
$192$	3.37228	0.243373
$193$	1.25544	0.0903684	0.0451842	−	0.998979i	$-0.485613\pi$
$193$	1.25544	0.0903684	0.0451842	+	0.998979i	$0.485613\pi$
$194$	−8.00000	−0.574367
$195$	−4.23369	−0.303181
$196$	0	0
$197$	7.37228	0.525253	0.262627	−	0.964898i	$-0.415411\pi$
$197$	7.37228	0.525253	0.262627	+	0.964898i	$0.415411\pi$
$198$	−11.4891	−0.816497
$199$	2.37228	0.168167	0.0840833	−	0.996459i	$-0.473204\pi$
$199$	2.37228	0.168167	0.0840833	+	0.996459i	$0.473204\pi$
$200$	−6.37228	−0.450588
$201$	−26.9783	−1.90290
$202$	−3.25544	−0.229052
$203$	0	0
$204$	−16.0000	−1.12022
$205$	3.37228	0.235530
$206$	10.7446	0.748609
$207$	−73.2119	−5.08858
$208$	0.372281	0.0258131
$209$	−7.37228	−0.509951
$210$	0	0
$211$	−8.11684	−0.558787	−0.279393	−	0.960177i	$-0.590133\pi$
$211$	−8.11684	−0.558787	−0.279393	+	0.960177i	$0.590133\pi$
$212$	−10.0000	−0.686803
$213$	−39.6060	−2.71376
$214$	−1.11684	−0.0763459
$215$	21.4891	1.46555
$216$	−18.1168	−1.23270
$217$	0	0
$218$	−5.62772	−0.381157
$219$	44.2337	2.98904
$220$	−4.62772	−0.312001
$221$	−1.76631	−0.118815
$222$	6.74456	0.452665
$223$	3.25544	0.218000	0.109000	−	0.994042i	$-0.465235\pi$
$223$	3.25544	0.218000	0.109000	+	0.994042i	$0.465235\pi$
$224$	0	0
$225$	53.3505	3.55670
$226$	−6.48913	−0.431650
$227$	11.3723	0.754805	0.377402	−	0.926049i	$-0.376817\pi$
$227$	11.3723	0.754805	0.377402	+	0.926049i	$0.376817\pi$
$228$	−18.1168	−1.19982
$229$	−5.62772	−0.371890	−0.185945	−	0.982560i	$-0.559535\pi$
$229$	−5.62772	−0.371890	−0.185945	+	0.982560i	$0.559535\pi$
$230$	−29.4891	−1.94446
$231$	0	0
$232$	7.11684	0.467244
$233$	−23.4891	−1.53882	−0.769412	−	0.638753i	$-0.779451\pi$
$233$	−23.4891	−1.53882	−0.769412	+	0.638753i	$0.779451\pi$
$234$	−3.11684	−0.203754
$235$	−26.9783	−1.75987
$236$	−0.372281	−0.0242335
$237$	−15.6060	−1.01372
$238$	0	0
$239$	−19.3723	−1.25309	−0.626544	−	0.779386i	$-0.715531\pi$
$239$	−19.3723	−1.25309	−0.626544	+	0.779386i	$0.715531\pi$
$240$	−11.3723	−0.734078
$241$	−6.88316	−0.443383	−0.221692	−	0.975117i	$-0.571158\pi$
$241$	−6.88316	−0.443383	−0.221692	+	0.975117i	$0.571158\pi$
$242$	9.11684	0.586053
$243$	66.9783	4.29666
$244$	2.62772	0.168222
$245$	0	0
$246$	3.37228	0.215009
$247$	−2.00000	−0.127257
$248$	−2.74456	−0.174280
$249$	−1.25544	−0.0795601
$250$	4.62772	0.292683
$251$	13.8614	0.874924	0.437462	−	0.899237i	$-0.355877\pi$
$251$	13.8614	0.874924	0.437462	+	0.899237i	$0.355877\pi$
$252$	0	0
$253$	−12.0000	−0.754434
$254$	6.00000	0.376473
$255$	53.9565	3.37889
$256$	1.00000	0.0625000
$257$	0	0		−	1.00000i	$-0.5\pi$
$257$	0	0			1.00000i	$0.5\pi$
$258$	21.4891	1.33785
$259$	0	0
$260$	−1.25544	−0.0778589
$261$	−59.5842	−3.68817
$262$	12.0000	0.741362
$263$	−13.6277	−0.840321	−0.420161	−	0.907450i	$-0.638026\pi$
$263$	−13.6277	−0.840321	−0.420161	+	0.907450i	$0.638026\pi$
$264$	−4.62772	−0.284816
$265$	33.7228	2.07158
$266$	0	0
$267$	−6.74456	−0.412761
$268$	−8.00000	−0.488678
$269$	28.3505	1.72856	0.864281	−	0.503009i	$-0.167774\pi$
$269$	28.3505	1.72856	0.864281	+	0.503009i	$0.167774\pi$
$270$	61.0951	3.71813
$271$	−28.7446	−1.74611	−0.873054	−	0.487624i	$-0.837864\pi$
$271$	−28.7446	−1.74611	−0.873054	+	0.487624i	$0.837864\pi$
$272$	−4.74456	−0.287681
$273$	0	0
$274$	−2.74456	−0.165805
$275$	8.74456	0.527317
$276$	−29.4891	−1.77504
$277$	17.6060	1.05784	0.528920	−	0.848672i	$-0.322597\pi$
$277$	17.6060	1.05784	0.528920	+	0.848672i	$0.322597\pi$
$278$	−5.25544	−0.315200
$279$	22.9783	1.37567
$280$	0	0
$281$	−7.25544	−0.432823	−0.216412	−	0.976302i	$-0.569435\pi$
$281$	−7.25544	−0.432823	−0.216412	+	0.976302i	$0.569435\pi$
$282$	−26.9783	−1.60653
$283$	−19.6277	−1.16675	−0.583373	−	0.812204i	$-0.698268\pi$
$283$	−19.6277	−1.16675	−0.583373	+	0.812204i	$0.698268\pi$
$284$	−11.7446	−0.696912
$285$	61.0951	3.61896
$286$	−0.510875	−0.0302087
$287$	0	0
$288$	−8.37228	−0.493341
$289$	5.51087	0.324169
$290$	−24.0000	−1.40933
$291$	26.9783	1.58149
$292$	13.1168	0.767605
$293$	−1.62772	−0.0950923	−0.0475462	−	0.998869i	$-0.515140\pi$
$293$	−1.62772	−0.0950923	−0.0475462	+	0.998869i	$0.515140\pi$
$294$	0	0
$295$	1.25544	0.0730944
$296$	2.00000	0.116248
$297$	24.8614	1.44261
$298$	−2.88316	−0.167017
$299$	−3.25544	−0.188267
$300$	21.4891	1.24068
$301$	0	0
$302$	0.883156	0.0508199
$303$	10.9783	0.630684
$304$	−5.37228	−0.308121
$305$	−8.86141	−0.507403
$306$	39.7228	2.27080
$307$	23.8614	1.36184	0.680921	−	0.732357i	$-0.261580\pi$
$307$	23.8614	1.36184	0.680921	+	0.732357i	$0.261580\pi$
$308$	0	0
$309$	−36.2337	−2.06126
$310$	9.25544	0.525674
$311$	10.3723	0.588158	0.294079	−	0.955781i	$-0.404987\pi$
$311$	10.3723	0.588158	0.294079	+	0.955781i	$0.404987\pi$
$312$	−1.25544	−0.0710751
$313$	0	0		−	1.00000i	$-0.5\pi$
$313$	0	0			1.00000i	$0.5\pi$
$314$	15.8614	0.895111
$315$	0	0
$316$	−4.62772	−0.260330
$317$	−24.7446	−1.38979	−0.694897	−	0.719110i	$-0.744550\pi$
$317$	−24.7446	−1.38979	−0.694897	+	0.719110i	$0.744550\pi$
$318$	33.7228	1.89108
$319$	−9.76631	−0.546808
$320$	−3.37228	−0.188516
$321$	3.76631	0.210215
$322$	0	0
$323$	25.4891	1.41825
$324$	35.9783	1.99879
$325$	2.37228	0.131590
$326$	−13.1168	−0.726475
$327$	18.9783	1.04950
$328$	1.00000	0.0552158
$329$	0	0
$330$	15.6060	0.859080
$331$	−0.744563	−0.0409249	−0.0204624	−	0.999791i	$-0.506514\pi$
$331$	−0.744563	−0.0409249	−0.0204624	+	0.999791i	$0.506514\pi$
$332$	−0.372281	−0.0204316
$333$	−16.7446	−0.917596
$334$	13.6277	0.745676
$335$	26.9783	1.47398
$336$	0	0
$337$	−5.00000	−0.272367	−0.136184	−	0.990684i	$-0.543484\pi$
$337$	−5.00000	−0.272367	−0.136184	+	0.990684i	$0.543484\pi$
$338$	12.8614	0.699568
$339$	21.8832	1.18853
$340$	16.0000	0.867722
$341$	3.76631	0.203957
$342$	44.9783	2.43215
$343$	0	0
$344$	6.37228	0.343570
$345$	99.4456	5.35397
$346$	10.1168	0.543885
$347$	−15.6060	−0.837772	−0.418886	−	0.908039i	$-0.637579\pi$
$347$	−15.6060	−0.837772	−0.418886	+	0.908039i	$0.637579\pi$
$348$	−24.0000	−1.28654
$349$	22.7446	1.21749	0.608744	−	0.793367i	$-0.291674\pi$
$349$	22.7446	1.21749	0.608744	+	0.793367i	$0.291674\pi$
$350$	0	0
$351$	6.74456	0.359998
$352$	−1.37228	−0.0731428
$353$	−35.0000	−1.86286	−0.931431	−	0.363918i	$-0.881439\pi$
$353$	−35.0000	−1.86286	−0.931431	+	0.363918i	$0.881439\pi$
$354$	1.25544	0.0667257
$355$	39.6060	2.10207
$356$	−2.00000	−0.106000
$357$	0	0
$358$	−13.3723	−0.706747
$359$	35.4891	1.87304	0.936522	−	0.350608i	$-0.114025\pi$
$359$	35.4891	1.87304	0.936522	+	0.350608i	$0.114025\pi$
$360$	28.2337	1.48805
$361$	9.86141	0.519021
$362$	−23.4891	−1.23456
$363$	−30.7446	−1.61367
$364$	0	0
$365$	−44.2337	−2.31530
$366$	−8.86141	−0.463193
$367$	−10.0000	−0.521996	−0.260998	−	0.965339i	$-0.584052\pi$
$367$	−10.0000	−0.521996	−0.260998	+	0.965339i	$0.584052\pi$
$368$	−8.74456	−0.455842
$369$	−8.37228	−0.435844
$370$	−6.74456	−0.350633
$371$	0	0
$372$	9.25544	0.479872
$373$	−14.6277	−0.757395	−0.378697	−	0.925521i	$-0.623628\pi$
$373$	−14.6277	−0.757395	−0.378697	+	0.925521i	$0.623628\pi$
$374$	6.51087	0.336669
$375$	−15.6060	−0.805889
$376$	−8.00000	−0.412568
$377$	−2.64947	−0.136455
$378$	0	0
$379$	33.8614	1.73934	0.869672	−	0.493630i	$-0.164330\pi$
$379$	33.8614	1.73934	0.869672	+	0.493630i	$0.164330\pi$
$380$	18.1168	0.929374
$381$	−20.2337	−1.03660
$382$	13.6277	0.697255
$383$	35.4674	1.81230	0.906149	−	0.422958i	$-0.139008\pi$
$383$	35.4674	1.81230	0.906149	+	0.422958i	$0.139008\pi$
$384$	−3.37228	−0.172091
$385$	0	0
$386$	−1.25544	−0.0639001
$387$	−53.3505	−2.71196
$388$	8.00000	0.406138
$389$	−2.11684	−0.107328	−0.0536641	−	0.998559i	$-0.517090\pi$
$389$	−2.11684	−0.107328	−0.0536641	+	0.998559i	$0.517090\pi$
$390$	4.23369	0.214381
$391$	41.4891	2.09820
$392$	0	0
$393$	−40.4674	−2.04131
$394$	−7.37228	−0.371410
$395$	15.6060	0.785222
$396$	11.4891	0.577350
$397$	−14.0000	−0.702640	−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000	−0.702640	−0.351320	+	0.936255i	$0.614267\pi$
$398$	−2.37228	−0.118912
$399$	0	0
$400$	6.37228	0.318614
$401$	−13.7446	−0.686371	−0.343185	−	0.939268i	$-0.611506\pi$
$401$	−13.7446	−0.686371	−0.343185	+	0.939268i	$0.611506\pi$
$402$	26.9783	1.34555
$403$	1.02175	0.0508970
$404$	3.25544	0.161964
$405$	−121.329	−6.02888
$406$	0	0
$407$	−2.74456	−0.136043
$408$	16.0000	0.792118
$409$	−15.7446	−0.778519	−0.389259	−	0.921128i	$-0.627269\pi$
$409$	−15.7446	−0.778519	−0.389259	+	0.921128i	$0.627269\pi$
$410$	−3.37228	−0.166545
$411$	9.25544	0.456537
$412$	−10.7446	−0.529347
$413$	0	0
$414$	73.2119	3.59817
$415$	1.25544	0.0616270
$416$	−0.372281	−0.0182526
$417$	17.7228	0.867890
$418$	7.37228	0.360590
$419$	0.138593	0.00677073	0.00338536	−	0.999994i	$-0.498922\pi$
$419$	0.138593	0.00677073	0.00338536	+	0.999994i	$0.498922\pi$
$420$	0	0
$421$	2.00000	0.0974740	0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000	0.0974740	0.0487370	+	0.998812i	$0.484480\pi$
$422$	8.11684	0.395122
$423$	66.9783	3.25659
$424$	10.0000	0.485643
$425$	−30.2337	−1.46655
$426$	39.6060	1.91892
$427$	0	0
$428$	1.11684	0.0539847
$429$	1.72281	0.0831782
$430$	−21.4891	−1.03630
$431$	−9.48913	−0.457075	−0.228538	−	0.973535i	$-0.573394\pi$
$431$	−9.48913	−0.457075	−0.228538	+	0.973535i	$0.573394\pi$
$432$	18.1168	0.871647
$433$	−10.6277	−0.510736	−0.255368	−	0.966844i	$-0.582197\pi$
$433$	−10.6277	−0.510736	−0.255368	+	0.966844i	$0.582197\pi$
$434$	0	0
$435$	80.9348	3.88052
$436$	5.62772	0.269519
$437$	46.9783	2.24727
$438$	−44.2337	−2.11357
$439$	−3.74456	−0.178718	−0.0893591	−	0.995999i	$-0.528482\pi$
$439$	−3.74456	−0.178718	−0.0893591	+	0.995999i	$0.528482\pi$
$440$	4.62772	0.220618
$441$	0	0
$442$	1.76631	0.0840149
$443$	33.3505	1.58453	0.792266	−	0.610176i	$-0.208901\pi$
$443$	33.3505	1.58453	0.792266	+	0.610176i	$0.208901\pi$
$444$	−6.74456	−0.320083
$445$	6.74456	0.319723
$446$	−3.25544	−0.154149
$447$	9.72281	0.459873
$448$	0	0
$449$	23.2337	1.09647	0.548233	−	0.836326i	$-0.315301\pi$
$449$	23.2337	1.09647	0.548233	+	0.836326i	$0.315301\pi$
$450$	−53.3505	−2.51497
$451$	−1.37228	−0.0646182
$452$	6.48913	0.305223
$453$	−2.97825	−0.139930
$454$	−11.3723	−0.533728
$455$	0	0
$456$	18.1168	0.848399
$457$	26.2337	1.22716	0.613580	−	0.789632i	$-0.289729\pi$
$457$	26.2337	1.22716	0.613580	+	0.789632i	$0.289729\pi$
$458$	5.62772	0.262966
$459$	−85.9565	−4.01211
$460$	29.4891	1.37494
$461$	−3.60597	−0.167947	−0.0839734	−	0.996468i	$-0.526761\pi$
$461$	−3.60597	−0.167947	−0.0839734	+	0.996468i	$0.526761\pi$
$462$	0	0
$463$	17.7446	0.824660	0.412330	−	0.911035i	$-0.364715\pi$
$463$	17.7446	0.824660	0.412330	+	0.911035i	$0.364715\pi$
$464$	−7.11684	−0.330391
$465$	−31.2119	−1.44742
$466$	23.4891	1.08811
$467$	−10.5109	−0.486385	−0.243193	−	0.969978i	$-0.578195\pi$
$467$	−10.5109	−0.486385	−0.243193	+	0.969978i	$0.578195\pi$
$468$	3.11684	0.144076
$469$	0	0
$470$	26.9783	1.24441
$471$	−53.4891	−2.46465
$472$	0.372281	0.0171356
$473$	−8.74456	−0.402075
$474$	15.6060	0.716806
$475$	−34.2337	−1.57075
$476$	0	0
$477$	−83.7228	−3.83340
$478$	19.3723	0.886068
$479$	24.4891	1.11894	0.559468	−	0.828852i	$-0.311005\pi$
$479$	24.4891	1.11894	0.559468	+	0.828852i	$0.311005\pi$
$480$	11.3723	0.519071
$481$	−0.744563	−0.0339491
$482$	6.88316	0.313519
$483$	0	0
$484$	−9.11684	−0.414402
$485$	−26.9783	−1.22502
$486$	−66.9783	−3.03820
$487$	−13.2554	−0.600661	−0.300331	−	0.953835i	$-0.597097\pi$
$487$	−13.2554	−0.600661	−0.300331	+	0.953835i	$0.597097\pi$
$488$	−2.62772	−0.118951
$489$	44.2337	2.00032
$490$	0	0
$491$	−17.1168	−0.772472	−0.386236	−	0.922400i	$-0.626225\pi$
$491$	−17.1168	−0.772472	−0.386236	+	0.922400i	$0.626225\pi$
$492$	−3.37228	−0.152034
$493$	33.7663	1.52076
$494$	2.00000	0.0899843
$495$	−38.7446	−1.74144
$496$	2.74456	0.123235
$497$	0	0
$498$	1.25544	0.0562575
$499$	−4.74456	−0.212396	−0.106198	−	0.994345i	$-0.533868\pi$
$499$	−4.74456	−0.212396	−0.106198	+	0.994345i	$0.533868\pi$
$500$	−4.62772	−0.206958
$501$	−45.9565	−2.05319
$502$	−13.8614	−0.618665
$503$	−35.3723	−1.57717	−0.788586	−	0.614924i	$-0.789186\pi$
$503$	−35.3723	−1.57717	−0.788586	+	0.614924i	$0.789186\pi$
$504$	0	0
$505$	−10.9783	−0.488526
$506$	12.0000	0.533465
$507$	−43.3723	−1.92623
$508$	−6.00000	−0.266207
$509$	−30.0951	−1.33394	−0.666971	−	0.745084i	$-0.732409\pi$
$509$	−30.0951	−1.33394	−0.666971	+	0.745084i	$0.732409\pi$
$510$	−53.9565	−2.38923
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−97.3288	−4.29717
$514$	0	0
$515$	36.2337	1.59665
$516$	−21.4891	−0.946006
$517$	10.9783	0.482823
$518$	0	0
$519$	−34.1168	−1.49756
$520$	1.25544	0.0550546
$521$	−1.25544	−0.0550017	−0.0275009	−	0.999622i	$-0.508755\pi$
$521$	−1.25544	−0.0550017	−0.0275009	+	0.999622i	$0.508755\pi$
$522$	59.5842	2.60793
$523$	−28.4674	−1.24479	−0.622396	−	0.782703i	$-0.713841\pi$
$523$	−28.4674	−1.24479	−0.622396	+	0.782703i	$0.713841\pi$
$524$	−12.0000	−0.524222
$525$	0	0
$526$	13.6277	0.594197
$527$	−13.0217	−0.567236
$528$	4.62772	0.201396
$529$	53.4674	2.32467
$530$	−33.7228	−1.46483
$531$	−3.11684	−0.135260
$532$	0	0
$533$	−0.372281	−0.0161253
$534$	6.74456	0.291866
$535$	−3.76631	−0.162832
$536$	8.00000	0.345547
$537$	45.0951	1.94600
$538$	−28.3505	−1.22228
$539$	0	0
$540$	−61.0951	−2.62911
$541$	28.9783	1.24587	0.622936	−	0.782273i	$-0.285940\pi$
$541$	28.9783	1.24587	0.622936	+	0.782273i	$0.285940\pi$
$542$	28.7446	1.23468
$543$	79.2119	3.39931
$544$	4.74456	0.203421
$545$	−18.9783	−0.812939
$546$	0	0
$547$	5.48913	0.234698	0.117349	−	0.993091i	$-0.462560\pi$
$547$	5.48913	0.234698	0.117349	+	0.993091i	$0.462560\pi$
$548$	2.74456	0.117242
$549$	22.0000	0.938937
$550$	−8.74456	−0.372869
$551$	38.2337	1.62881
$552$	29.4891	1.25514
$553$	0	0
$554$	−17.6060	−0.748006
$555$	22.7446	0.965453
$556$	5.25544	0.222880
$557$	−35.3505	−1.49785	−0.748925	−	0.662655i	$-0.769430\pi$
$557$	−35.3505	−1.49785	−0.748925	+	0.662655i	$0.769430\pi$
$558$	−22.9783	−0.972747
$559$	−2.37228	−0.100337
$560$	0	0
$561$	−21.9565	−0.927004
$562$	7.25544	0.306052
$563$	−17.3723	−0.732154	−0.366077	−	0.930584i	$-0.619299\pi$
$563$	−17.3723	−0.732154	−0.366077	+	0.930584i	$0.619299\pi$
$564$	26.9783	1.13599
$565$	−21.8832	−0.920631
$566$	19.6277	0.825015
$567$	0	0
$568$	11.7446	0.492791
$569$	44.8397	1.87978	0.939888	−	0.341483i	$-0.110929\pi$
$569$	44.8397	1.87978	0.939888	+	0.341483i	$0.110929\pi$
$570$	−61.0951	−2.55899
$571$	25.6060	1.07158	0.535788	−	0.844352i	$-0.320015\pi$
$571$	25.6060	1.07158	0.535788	+	0.844352i	$0.320015\pi$
$572$	0.510875	0.0213607
$573$	−45.9565	−1.91986
$574$	0	0
$575$	−55.7228	−2.32380
$576$	8.37228	0.348845
$577$	21.2554	0.884875	0.442438	−	0.896799i	$-0.354114\pi$
$577$	21.2554	0.884875	0.442438	+	0.896799i	$0.354114\pi$
$578$	−5.51087	−0.229222
$579$	4.23369	0.175946
$580$	24.0000	0.996546
$581$	0	0
$582$	−26.9783	−1.11828
$583$	−13.7228	−0.568341
$584$	−13.1168	−0.542779
$585$	−10.5109	−0.434571
$586$	1.62772	0.0672404
$587$	37.3723	1.54252	0.771260	−	0.636521i	$-0.219627\pi$
$587$	37.3723	1.54252	0.771260	+	0.636521i	$0.219627\pi$
$588$	0	0
$589$	−14.7446	−0.607539
$590$	−1.25544	−0.0516855
$591$	24.8614	1.02266
$592$	−2.00000	−0.0821995
$593$	26.2337	1.07729	0.538644	−	0.842533i	$-0.318937\pi$
$593$	26.2337	1.07729	0.538644	+	0.842533i	$0.318937\pi$
$594$	−24.8614	−1.02008
$595$	0	0
$596$	2.88316	0.118099
$597$	8.00000	0.327418
$598$	3.25544	0.133125
$599$	6.51087	0.266027	0.133014	−	0.991114i	$-0.457535\pi$
$599$	6.51087	0.266027	0.133014	+	0.991114i	$0.457535\pi$
$600$	−21.4891	−0.877290
$601$	26.0000	1.06056	0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000	1.06056	0.530281	+	0.847822i	$0.322086\pi$
$602$	0	0
$603$	−66.9783	−2.72757
$604$	−0.883156	−0.0359351
$605$	30.7446	1.24994
$606$	−10.9783	−0.445961
$607$	−11.4891	−0.466329	−0.233165	−	0.972437i	$-0.574908\pi$
$607$	−11.4891	−0.466329	−0.233165	+	0.972437i	$0.574908\pi$
$608$	5.37228	0.217875
$609$	0	0
$610$	8.86141	0.358788
$611$	2.97825	0.120487
$612$	−39.7228	−1.60570
$613$	−27.3723	−1.10556	−0.552778	−	0.833329i	$-0.686432\pi$
$613$	−27.3723	−1.10556	−0.552778	+	0.833329i	$0.686432\pi$
$614$	−23.8614	−0.962968
$615$	11.3723	0.458575
$616$	0	0
$617$	19.5109	0.785478	0.392739	−	0.919650i	$-0.371528\pi$
$617$	19.5109	0.785478	0.392739	+	0.919650i	$0.371528\pi$
$618$	36.2337	1.45753
$619$	−46.6060	−1.87325	−0.936626	−	0.350331i	$-0.886069\pi$
$619$	−46.6060	−1.87325	−0.936626	+	0.350331i	$0.886069\pi$
$620$	−9.25544	−0.371707
$621$	−158.424	−6.35733
$622$	−10.3723	−0.415891
$623$	0	0
$624$	1.25544	0.0502577
$625$	−16.2554	−0.650217
$626$	0	0
$627$	−24.8614	−0.992869
$628$	−15.8614	−0.632939
$629$	9.48913	0.378356
$630$	0	0
$631$	14.0000	0.557331	0.278666	−	0.960388i	$-0.410108\pi$
$631$	14.0000	0.557331	0.278666	+	0.960388i	$0.410108\pi$
$632$	4.62772	0.184081
$633$	−27.3723	−1.08795
$634$	24.7446	0.982732
$635$	20.2337	0.802949
$636$	−33.7228	−1.33720
$637$	0	0
$638$	9.76631	0.386652
$639$	−98.3288	−3.88983
$640$	3.37228	0.133301
$641$	−38.4674	−1.51937	−0.759685	−	0.650291i	$-0.774647\pi$
$641$	−38.4674	−1.51937	−0.759685	+	0.650291i	$0.774647\pi$
$642$	−3.76631	−0.148644
$643$	31.0951	1.22627	0.613135	−	0.789978i	$-0.289908\pi$
$643$	31.0951	1.22627	0.613135	+	0.789978i	$0.289908\pi$
$644$	0	0
$645$	72.4674	2.85340
$646$	−25.4891	−1.00286
$647$	8.23369	0.323700	0.161850	−	0.986815i	$-0.448254\pi$
$647$	8.23369	0.323700	0.161850	+	0.986815i	$0.448254\pi$
$648$	−35.9783	−1.41336
$649$	−0.510875	−0.0200536
$650$	−2.37228	−0.0930485
$651$	0	0
$652$	13.1168	0.513695
$653$	3.86141	0.151109	0.0755543	−	0.997142i	$-0.475927\pi$
$653$	3.86141	0.151109	0.0755543	+	0.997142i	$0.475927\pi$
$654$	−18.9783	−0.742108
$655$	40.4674	1.58119
$656$	−1.00000	−0.0390434
$657$	109.818	4.28440
$658$	0	0
$659$	5.48913	0.213826	0.106913	−	0.994268i	$-0.465903\pi$
$659$	5.48913	0.213826	0.106913	+	0.994268i	$0.465903\pi$
$660$	−15.6060	−0.607462
$661$	29.3723	1.14245	0.571225	−	0.820794i	$-0.306469\pi$
$661$	29.3723	1.14245	0.571225	+	0.820794i	$0.306469\pi$
$662$	0.744563	0.0289382
$663$	−5.95650	−0.231331
$664$	0.372281	0.0144473
$665$	0	0
$666$	16.7446	0.648839
$667$	62.2337	2.40970
$668$	−13.6277	−0.527272
$669$	10.9783	0.424444
$670$	−26.9783	−1.04226
$671$	3.60597	0.139207
$672$	0	0
$673$	−8.51087	−0.328070	−0.164035	−	0.986455i	$-0.552451\pi$
$673$	−8.51087	−0.328070	−0.164035	+	0.986455i	$0.552451\pi$
$674$	5.00000	0.192593
$675$	115.446	4.44350
$676$	−12.8614	−0.494669
$677$	−13.8832	−0.533573	−0.266787	−	0.963756i	$-0.585962\pi$
$677$	−13.8832	−0.533573	−0.266787	+	0.963756i	$0.585962\pi$
$678$	−21.8832	−0.840418
$679$	0	0
$680$	−16.0000	−0.613572
$681$	38.3505	1.46960
$682$	−3.76631	−0.144220
$683$	−20.7446	−0.793769	−0.396884	−	0.917869i	$-0.629909\pi$
$683$	−20.7446	−0.793769	−0.396884	+	0.917869i	$0.629909\pi$
$684$	−44.9783	−1.71979
$685$	−9.25544	−0.353632
$686$	0	0
$687$	−18.9783	−0.724065
$688$	−6.37228	−0.242941
$689$	−3.72281	−0.141828
$690$	−99.4456	−3.78583
$691$	0.627719	0.0238795	0.0119398	−	0.999929i	$-0.496199\pi$
$691$	0.627719	0.0238795	0.0119398	+	0.999929i	$0.496199\pi$
$692$	−10.1168	−0.384585
$693$	0	0
$694$	15.6060	0.592394
$695$	−17.7228	−0.672265
$696$	24.0000	0.909718
$697$	4.74456	0.179713
$698$	−22.7446	−0.860894
$699$	−79.2119	−2.99607
$700$	0	0
$701$	4.11684	0.155491	0.0777455	−	0.996973i	$-0.475228\pi$
$701$	4.11684	0.155491	0.0777455	+	0.996973i	$0.475228\pi$
$702$	−6.74456	−0.254557
$703$	10.7446	0.405239
$704$	1.37228	0.0517198
$705$	−90.9783	−3.42644
$706$	35.0000	1.31724
$707$	0	0
$708$	−1.25544	−0.0471822
$709$	42.3723	1.59132	0.795662	−	0.605741i	$-0.207123\pi$
$709$	42.3723	1.59132	0.795662	+	0.605741i	$0.207123\pi$
$710$	−39.6060	−1.48639
$711$	−38.7446	−1.45303
$712$	2.00000	0.0749532
$713$	−24.0000	−0.898807
$714$	0	0
$715$	−1.72281	−0.0644296
$716$	13.3723	0.499746
$717$	−65.3288	−2.43975
$718$	−35.4891	−1.32444
$719$	11.2337	0.418946	0.209473	−	0.977814i	$-0.432825\pi$
$719$	11.2337	0.418946	0.209473	+	0.977814i	$0.432825\pi$
$720$	−28.2337	−1.05221
$721$	0	0
$722$	−9.86141	−0.367004
$723$	−23.2119	−0.863261
$724$	23.4891	0.872966
$725$	−45.3505	−1.68428
$726$	30.7446	1.14104
$727$	37.3505	1.38525	0.692627	−	0.721296i	$-0.256453\pi$
$727$	37.3505	1.38525	0.692627	+	0.721296i	$0.256453\pi$
$728$	0	0
$729$	117.935	4.36795
$730$	44.2337	1.63716
$731$	30.2337	1.11823
$732$	8.86141	0.327527
$733$	−29.2554	−1.08057	−0.540287	−	0.841481i	$-0.681684\pi$
$733$	−29.2554	−1.08057	−0.540287	+	0.841481i	$0.681684\pi$
$734$	10.0000	0.369107
$735$	0	0
$736$	8.74456	0.322329
$737$	−10.9783	−0.404389
$738$	8.37228	0.308188
$739$	11.6277	0.427733	0.213866	−	0.976863i	$-0.431394\pi$
$739$	11.6277	0.427733	0.213866	+	0.976863i	$0.431394\pi$
$740$	6.74456	0.247935
$741$	−6.74456	−0.247768
$742$	0	0
$743$	−23.7228	−0.870306	−0.435153	−	0.900357i	$-0.643306\pi$
$743$	−23.7228	−0.870306	−0.435153	+	0.900357i	$0.643306\pi$
$744$	−9.25544	−0.339321
$745$	−9.72281	−0.356216
$746$	14.6277	0.535559
$747$	−3.11684	−0.114039
$748$	−6.51087	−0.238061
$749$	0	0
$750$	15.6060	0.569849
$751$	40.9565	1.49452	0.747262	−	0.664530i	$-0.231368\pi$
$751$	40.9565	1.49452	0.747262	+	0.664530i	$0.231368\pi$
$752$	8.00000	0.291730
$753$	46.7446	1.70347
$754$	2.64947	0.0964879
$755$	2.97825	0.108390
$756$	0	0
$757$	9.35053	0.339851	0.169925	−	0.985457i	$-0.445647\pi$
$757$	9.35053	0.339851	0.169925	+	0.985457i	$0.445647\pi$
$758$	−33.8614	−1.22990
$759$	−40.4674	−1.46887
$760$	−18.1168	−0.657167
$761$	−48.9783	−1.77546	−0.887730	−	0.460364i	$-0.847719\pi$
$761$	−48.9783	−1.77546	−0.887730	+	0.460364i	$0.847719\pi$
$762$	20.2337	0.732989
$763$	0	0
$764$	−13.6277	−0.493034
$765$	133.957	4.84321
$766$	−35.4674	−1.28149
$767$	−0.138593	−0.00500432
$768$	3.37228	0.121687
$769$	−10.6277	−0.383245	−0.191623	−	0.981469i	$-0.561375\pi$
$769$	−10.6277	−0.383245	−0.191623	+	0.981469i	$0.561375\pi$
$770$	0	0
$771$	0	0
$772$	1.25544	0.0451842
$773$	4.51087	0.162245	0.0811224	−	0.996704i	$-0.474150\pi$
$773$	4.51087	0.162245	0.0811224	+	0.996704i	$0.474150\pi$
$774$	53.3505	1.91765
$775$	17.4891	0.628228
$776$	−8.00000	−0.287183
$777$	0	0
$778$	2.11684	0.0758925
$779$	5.37228	0.192482
$780$	−4.23369	−0.151590
$781$	−16.1168	−0.576706
$782$	−41.4891	−1.48365
$783$	−128.935	−4.60775
$784$	0	0
$785$	53.4891	1.90911
$786$	40.4674	1.44342
$787$	20.0000	0.712923	0.356462	−	0.934310i	$-0.383983\pi$
$787$	20.0000	0.712923	0.356462	+	0.934310i	$0.383983\pi$
$788$	7.37228	0.262627
$789$	−45.9565	−1.63609
$790$	−15.6060	−0.555235
$791$	0	0
$792$	−11.4891	−0.408248
$793$	0.978251	0.0347387
$794$	14.0000	0.496841
$795$	113.723	4.03333
$796$	2.37228	0.0840833
$797$	−41.2554	−1.46134	−0.730671	−	0.682729i	$-0.760793\pi$
$797$	−41.2554	−1.46134	−0.730671	+	0.682729i	$0.760793\pi$
$798$	0	0
$799$	−37.9565	−1.34280
$800$	−6.37228	−0.225294
$801$	−16.7446	−0.591640
$802$	13.7446	0.485337
$803$	18.0000	0.635206
$804$	−26.9783	−0.951450
$805$	0	0
$806$	−1.02175	−0.0359896
$807$	95.6060	3.36549
$808$	−3.25544	−0.114526
$809$	1.48913	0.0523549	0.0261774	−	0.999657i	$-0.491667\pi$
$809$	1.48913	0.0523549	0.0261774	+	0.999657i	$0.491667\pi$
$810$	121.329	4.26306
$811$	−32.8397	−1.15316	−0.576578	−	0.817042i	$-0.695612\pi$
$811$	−32.8397	−1.15316	−0.576578	+	0.817042i	$0.695612\pi$
$812$	0	0
$813$	−96.9348	−3.39965
$814$	2.74456	0.0961969
$815$	−44.2337	−1.54944
$816$	−16.0000	−0.560112
$817$	34.2337	1.19769
$818$	15.7446	0.550496
$819$	0	0
$820$	3.37228	0.117765
$821$	37.6060	1.31246	0.656229	−	0.754562i	$-0.272151\pi$
$821$	37.6060	1.31246	0.656229	+	0.754562i	$0.272151\pi$
$822$	−9.25544	−0.322820
$823$	18.1168	0.631513	0.315757	−	0.948840i	$-0.397742\pi$
$823$	18.1168	0.631513	0.315757	+	0.948840i	$0.397742\pi$
$824$	10.7446	0.374305
$825$	29.4891	1.02668
$826$	0	0
$827$	34.9783	1.21631	0.608156	−	0.793817i	$-0.291909\pi$
$827$	34.9783	1.21631	0.608156	+	0.793817i	$0.291909\pi$
$828$	−73.2119	−2.54429
$829$	17.7228	0.615539	0.307769	−	0.951461i	$-0.400417\pi$
$829$	17.7228	0.615539	0.307769	+	0.951461i	$0.400417\pi$
$830$	−1.25544	−0.0435769
$831$	59.3723	2.05960
$832$	0.372281	0.0129065
$833$	0	0
$834$	−17.7228	−0.613691
$835$	45.9565	1.59039
$836$	−7.37228	−0.254976
$837$	49.7228	1.71867
$838$	−0.138593	−0.00478763
$839$	20.7663	0.716933	0.358466	−	0.933543i	$-0.383300\pi$
$839$	20.7663	0.716933	0.358466	+	0.933543i	$0.383300\pi$
$840$	0	0
$841$	21.6495	0.746533
$842$	−2.00000	−0.0689246
$843$	−24.4674	−0.842701
$844$	−8.11684	−0.279393
$845$	43.3723	1.49205
$846$	−66.9783	−2.30276
$847$	0	0
$848$	−10.0000	−0.343401
$849$	−66.1902	−2.27164
$850$	30.2337	1.03701
$851$	17.4891	0.599519
$852$	−39.6060	−1.35688
$853$	17.6060	0.602817	0.301408	−	0.953495i	$-0.402543\pi$
$853$	17.6060	0.602817	0.301408	+	0.953495i	$0.402543\pi$
$854$	0	0
$855$	151.679	5.18732
$856$	−1.11684	−0.0381729
$857$	35.2337	1.20356	0.601780	−	0.798662i	$-0.294458\pi$
$857$	35.2337	1.20356	0.601780	+	0.798662i	$0.294458\pi$
$858$	−1.72281	−0.0588159
$859$	19.3505	0.660232	0.330116	−	0.943940i	$-0.392912\pi$
$859$	19.3505	0.660232	0.330116	+	0.943940i	$0.392912\pi$
$860$	21.4891	0.732773
$861$	0	0
$862$	9.48913	0.323201
$863$	−51.4891	−1.75271	−0.876355	−	0.481666i	$-0.840032\pi$
$863$	−51.4891	−1.75271	−0.876355	+	0.481666i	$0.840032\pi$
$864$	−18.1168	−0.616348
$865$	34.1168	1.16001
$866$	10.6277	0.361145
$867$	18.5842	0.631153
$868$	0	0
$869$	−6.35053	−0.215427
$870$	−80.9348	−2.74395
$871$	−2.97825	−0.100914
$872$	−5.62772	−0.190579
$873$	66.9783	2.26687
$874$	−46.9783	−1.58906
$875$	0	0
$876$	44.2337	1.49452
$877$	10.1168	0.341622	0.170811	−	0.985304i	$-0.445361\pi$
$877$	10.1168	0.341622	0.170811	+	0.985304i	$0.445361\pi$
$878$	3.74456	0.126373
$879$	−5.48913	−0.185144
$880$	−4.62772	−0.156000
$881$	35.9783	1.21214	0.606069	−	0.795412i	$-0.292746\pi$
$881$	35.9783	1.21214	0.606069	+	0.795412i	$0.292746\pi$
$882$	0	0
$883$	26.2337	0.882834	0.441417	−	0.897302i	$-0.354476\pi$
$883$	26.2337	0.882834	0.441417	+	0.897302i	$0.354476\pi$
$884$	−1.76631	−0.0594075
$885$	4.23369	0.142314
$886$	−33.3505	−1.12043
$887$	31.2337	1.04872	0.524362	−	0.851495i	$-0.324304\pi$
$887$	31.2337	1.04872	0.524362	+	0.851495i	$0.324304\pi$
$888$	6.74456	0.226333
$889$	0	0
$890$	−6.74456	−0.226078
$891$	49.3723	1.65403
$892$	3.25544	0.109000
$893$	−42.9783	−1.43821
$894$	−9.72281	−0.325180
$895$	−45.0951	−1.50736
$896$	0	0
$897$	−10.9783	−0.366553
$898$	−23.2337	−0.775318
$899$	−19.5326	−0.651449
$900$	53.3505	1.77835
$901$	47.4456	1.58064
$902$	1.37228	0.0456920
$903$	0	0
$904$	−6.48913	−0.215825
$905$	−79.2119	−2.63309
$906$	2.97825	0.0989457
$907$	5.86141	0.194625	0.0973124	−	0.995254i	$-0.468975\pi$
$907$	5.86141	0.194625	0.0973124	+	0.995254i	$0.468975\pi$
$908$	11.3723	0.377402
$909$	27.2554	0.904006
$910$	0	0
$911$	−56.7446	−1.88003	−0.940016	−	0.341131i	$-0.889190\pi$
$911$	−56.7446	−1.88003	−0.940016	+	0.341131i	$0.889190\pi$
$912$	−18.1168	−0.599909
$913$	−0.510875	−0.0169075
$914$	−26.2337	−0.867733
$915$	−29.8832	−0.987907
$916$	−5.62772	−0.185945
$917$	0	0
$918$	85.9565	2.83699
$919$	33.0000	1.08857	0.544285	−	0.838901i	$-0.316801\pi$
$919$	33.0000	1.08857	0.544285	+	0.838901i	$0.316801\pi$
$920$	−29.4891	−0.972228
$921$	80.4674	2.65149
$922$	3.60597	0.118756
$923$	−4.37228	−0.143915
$924$	0	0
$925$	−12.7446	−0.419039
$926$	−17.7446	−0.583123
$927$	−89.9565	−2.95456
$928$	7.11684	0.233622
$929$	34.0000	1.11550	0.557752	−	0.830008i	$-0.311664\pi$
$929$	34.0000	1.11550	0.557752	+	0.830008i	$0.311664\pi$
$930$	31.2119	1.02348
$931$	0	0
$932$	−23.4891	−0.769412
$933$	34.9783	1.14514
$934$	10.5109	0.343926
$935$	21.9565	0.718054
$936$	−3.11684	−0.101877
$937$	−40.4674	−1.32201	−0.661006	−	0.750381i	$-0.729870\pi$
$937$	−40.4674	−1.32201	−0.661006	+	0.750381i	$0.729870\pi$
$938$	0	0
$939$	0	0
$940$	−26.9783	−0.879934
$941$	0.394031	0.0128450	0.00642252	−	0.999979i	$-0.497956\pi$
$941$	0.394031	0.0128450	0.00642252	+	0.999979i	$0.497956\pi$
$942$	53.4891	1.74277
$943$	8.74456	0.284762
$944$	−0.372281	−0.0121167
$945$	0	0
$946$	8.74456	0.284310
$947$	−18.0951	−0.588012	−0.294006	−	0.955804i	$-0.594988\pi$
$947$	−18.0951	−0.588012	−0.294006	+	0.955804i	$0.594988\pi$
$948$	−15.6060	−0.506858
$949$	4.88316	0.158514
$950$	34.2337	1.11069
$951$	−83.4456	−2.70591
$952$	0	0
$953$	−41.8614	−1.35602	−0.678012	−	0.735051i	$-0.737158\pi$
$953$	−41.8614	−1.35602	−0.678012	+	0.735051i	$0.737158\pi$
$954$	83.7228	2.71063
$955$	45.9565	1.48712
$956$	−19.3723	−0.626544
$957$	−32.9348	−1.06463
$958$	−24.4891	−0.791208
$959$	0	0
$960$	−11.3723	−0.367039
$961$	−23.4674	−0.757012
$962$	0.744563	0.0240057
$963$	9.35053	0.301317
$964$	−6.88316	−0.221692
$965$	−4.23369	−0.136287
$966$	0	0
$967$	15.5109	0.498796	0.249398	−	0.968401i	$-0.419767\pi$
$967$	15.5109	0.498796	0.249398	+	0.968401i	$0.419767\pi$
$968$	9.11684	0.293026
$969$	85.9565	2.76132
$970$	26.9783	0.866219
$971$	12.0000	0.385098	0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000	0.385098	0.192549	+	0.981287i	$0.438325\pi$
$972$	66.9783	2.14833
$973$	0	0
$974$	13.2554	0.424732
$975$	8.00000	0.256205
$976$	2.62772	0.0841112
$977$	14.7446	0.471720	0.235860	−	0.971787i	$-0.424209\pi$
$977$	14.7446	0.471720	0.235860	+	0.971787i	$0.424209\pi$
$978$	−44.2337	−1.41444
$979$	−2.74456	−0.0877166
$980$	0	0
$981$	47.1168	1.50433
$982$	17.1168	0.546220
$983$	12.0000	0.382741	0.191370	−	0.981518i	$-0.438707\pi$
$983$	12.0000	0.382741	0.191370	+	0.981518i	$0.438707\pi$
$984$	3.37228	0.107504
$985$	−24.8614	−0.792150
$986$	−33.7663	−1.07534
$987$	0	0
$988$	−2.00000	−0.0636285
$989$	55.7228	1.77188
$990$	38.7446	1.23138
$991$	−23.9783	−0.761694	−0.380847	−	0.924638i	$-0.624368\pi$
$991$	−23.9783	−0.761694	−0.380847	+	0.924638i	$0.624368\pi$
$992$	−2.74456	−0.0871400
$993$	−2.51087	−0.0796802
$994$	0	0
$995$	−8.00000	−0.253617
$996$	−1.25544	−0.0397801
$997$	31.3505	0.992881	0.496441	−	0.868071i	$-0.334640\pi$
$997$	31.3505	0.992881	0.496441	+	0.868071i	$0.334640\pi$
$998$	4.74456	0.150187
$999$	−36.2337	−1.14638

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.v.1.2		2
7.2	even	3		574.2.e.d.165.1	✓	4
7.4	even	3		574.2.e.d.247.1	yes	4
7.6	odd	2		4018.2.a.u.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.e.d.165.1	✓	4	7.2	even	3
574.2.e.d.247.1	yes	4	7.4	even	3
4018.2.a.u.1.1		2	7.6	odd	2
4018.2.a.v.1.2		2	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.37228 q^{3} +1.00000 q^{4} -3.37228 q^{5} -3.37228 q^{6} -1.00000 q^{8} +8.37228 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.37228 q^{3} +1.00000 q^{4} -3.37228 q^{5} -3.37228 q^{6} -1.00000 q^{8} +8.37228 q^{9} +3.37228 q^{10} +1.37228 q^{11} +3.37228 q^{12} +0.372281 q^{13} -11.3723 q^{15} +1.00000 q^{16} -4.74456 q^{17} -8.37228 q^{18} -5.37228 q^{19} -3.37228 q^{20} -1.37228 q^{22} -8.74456 q^{23} -3.37228 q^{24} +6.37228 q^{25} -0.372281 q^{26} +18.1168 q^{27} -7.11684 q^{29} +11.3723 q^{30} +2.74456 q^{31} -1.00000 q^{32} +4.62772 q^{33} +4.74456 q^{34} +8.37228 q^{36} -2.00000 q^{37} +5.37228 q^{38} +1.25544 q^{39} +3.37228 q^{40} -1.00000 q^{41} -6.37228 q^{43} +1.37228 q^{44} -28.2337 q^{45} +8.74456 q^{46} +8.00000 q^{47} +3.37228 q^{48} -6.37228 q^{50} -16.0000 q^{51} +0.372281 q^{52} -10.0000 q^{53} -18.1168 q^{54} -4.62772 q^{55} -18.1168 q^{57} +7.11684 q^{58} -0.372281 q^{59} -11.3723 q^{60} +2.62772 q^{61} -2.74456 q^{62} +1.00000 q^{64} -1.25544 q^{65} -4.62772 q^{66} -8.00000 q^{67} -4.74456 q^{68} -29.4891 q^{69} -11.7446 q^{71} -8.37228 q^{72} +13.1168 q^{73} +2.00000 q^{74} +21.4891 q^{75} -5.37228 q^{76} -1.25544 q^{78} -4.62772 q^{79} -3.37228 q^{80} +35.9783 q^{81} +1.00000 q^{82} -0.372281 q^{83} +16.0000 q^{85} +6.37228 q^{86} -24.0000 q^{87} -1.37228 q^{88} -2.00000 q^{89} +28.2337 q^{90} -8.74456 q^{92} +9.25544 q^{93} -8.00000 q^{94} +18.1168 q^{95} -3.37228 q^{96} +8.00000 q^{97} +11.4891 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{5} - q^{6} - 2 q^{8} + 11 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^5 - q^6 - 2 * q^8 + 11 * q^9	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{5} - q^{6} - 2 q^{8} + 11 q^{9} + q^{10} - 3 q^{11} + q^{12} - 5 q^{13} - 17 q^{15} + 2 q^{16} + 2 q^{17} - 11 q^{18} - 5 q^{19} - q^{20} + 3 q^{22} - 6 q^{23} - q^{24} + 7 q^{25} + 5 q^{26} + 19 q^{27} + 3 q^{29} + 17 q^{30} - 6 q^{31} - 2 q^{32} + 15 q^{33} - 2 q^{34} + 11 q^{36} - 4 q^{37} + 5 q^{38} + 14 q^{39} + q^{40} - 2 q^{41} - 7 q^{43} - 3 q^{44} - 22 q^{45} + 6 q^{46} + 16 q^{47} + q^{48} - 7 q^{50} - 32 q^{51} - 5 q^{52} - 20 q^{53} - 19 q^{54} - 15 q^{55} - 19 q^{57} - 3 q^{58} + 5 q^{59} - 17 q^{60} + 11 q^{61} + 6 q^{62} + 2 q^{64} - 14 q^{65} - 15 q^{66} - 16 q^{67} + 2 q^{68} - 36 q^{69} - 12 q^{71} - 11 q^{72} + 9 q^{73} + 4 q^{74} + 20 q^{75} - 5 q^{76} - 14 q^{78} - 15 q^{79} - q^{80} + 26 q^{81} + 2 q^{82} + 5 q^{83} + 32 q^{85} + 7 q^{86} - 48 q^{87} + 3 q^{88} - 4 q^{89} + 22 q^{90} - 6 q^{92} + 30 q^{93} - 16 q^{94} + 19 q^{95} - q^{96} + 16 q^{97}+O(q^{100}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^5 - q^6 - 2 * q^8 + 11 * q^9 + q^10 - 3 * q^11 + q^12 - 5 * q^13 - 17 * q^15 + 2 * q^16 + 2 * q^17 - 11 * q^18 - 5 * q^19 - q^20 + 3 * q^22 - 6 * q^23 - q^24 + 7 * q^25 + 5 * q^26 + 19 * q^27 + 3 * q^29 + 17 * q^30 - 6 * q^31 - 2 * q^32 + 15 * q^33 - 2 * q^34 + 11 * q^36 - 4 * q^37 + 5 * q^38 + 14 * q^39 + q^40 - 2 * q^41 - 7 * q^43 - 3 * q^44 - 22 * q^45 + 6 * q^46 + 16 * q^47 + q^48 - 7 * q^50 - 32 * q^51 - 5 * q^52 - 20 * q^53 - 19 * q^54 - 15 * q^55 - 19 * q^57 - 3 * q^58 + 5 * q^59 - 17 * q^60 + 11 * q^61 + 6 * q^62 + 2 * q^64 - 14 * q^65 - 15 * q^66 - 16 * q^67 + 2 * q^68 - 36 * q^69 - 12 * q^71 - 11 * q^72 + 9 * q^73 + 4 * q^74 + 20 * q^75 - 5 * q^76 - 14 * q^78 - 15 * q^79 - q^80 + 26 * q^81 + 2 * q^82 + 5 * q^83 + 32 * q^85 + 7 * q^86 - 48 * q^87 + 3 * q^88 - 4 * q^89 + 22 * q^90 - 6 * q^92 + 30 * q^93 - 16 * q^94 + 19 * q^95 - q^96 + 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more