LMFDB - Embedded newform 2695.2.a.w.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2695,2,Mod(1,2695)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2695, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2695.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2695 = 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2695.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:	$21.5196833447$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 13x^{8} + 24x^{7} + 56x^{6} - 92x^{5} - 86x^{4} + 116x^{3} + 31x^{2} - 22x + 1 $ x^10 - 2x^9 - 13x^8 + 24x^7 + 56x^6 - 92x^5 - 86x^4 + 116x^3 + 31x^2 - 22*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$1.81378$ of defining polynomial
Character	$\chi$	$=$	2695.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.81378 q^{2} +1.20588 q^{3} +1.28980 q^{4} -1.00000 q^{5} +2.18721 q^{6} -1.28815 q^{8} -1.54584 q^{9} +O(q^{10})$	\(q+1.81378 q^{2} +1.20588 q^{3} +1.28980 q^{4} -1.00000 q^{5} +2.18721 q^{6} -1.28815 q^{8} -1.54584 q^{9} -1.81378 q^{10} -1.00000 q^{11} +1.55535 q^{12} -4.21925 q^{13} -1.20588 q^{15} -4.91602 q^{16} +1.71135 q^{17} -2.80382 q^{18} -2.74495 q^{19} -1.28980 q^{20} -1.81378 q^{22} +4.93420 q^{23} -1.55336 q^{24} +1.00000 q^{25} -7.65278 q^{26} -5.48176 q^{27} +2.93746 q^{29} -2.18721 q^{30} -2.51530 q^{31} -6.34027 q^{32} -1.20588 q^{33} +3.10401 q^{34} -1.99382 q^{36} +5.81846 q^{37} -4.97873 q^{38} -5.08792 q^{39} +1.28815 q^{40} -8.57606 q^{41} -7.38835 q^{43} -1.28980 q^{44} +1.54584 q^{45} +8.94956 q^{46} -11.3024 q^{47} -5.92815 q^{48} +1.81378 q^{50} +2.06369 q^{51} -5.44198 q^{52} -12.1022 q^{53} -9.94271 q^{54} +1.00000 q^{55} -3.31009 q^{57} +5.32790 q^{58} -3.07397 q^{59} -1.55535 q^{60} -8.10455 q^{61} -4.56221 q^{62} -1.66783 q^{64} +4.21925 q^{65} -2.18721 q^{66} +1.81137 q^{67} +2.20729 q^{68} +5.95008 q^{69} +1.33972 q^{71} +1.99128 q^{72} -9.74210 q^{73} +10.5534 q^{74} +1.20588 q^{75} -3.54043 q^{76} -9.22838 q^{78} +12.2992 q^{79} +4.91602 q^{80} -1.97285 q^{81} -15.5551 q^{82} +8.75414 q^{83} -1.71135 q^{85} -13.4008 q^{86} +3.54223 q^{87} +1.28815 q^{88} +6.24999 q^{89} +2.80382 q^{90} +6.36412 q^{92} -3.03317 q^{93} -20.5000 q^{94} +2.74495 q^{95} -7.64564 q^{96} +1.61351 q^{97} +1.54584 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 10 q^{4} - 10 q^{5} - 4 q^{6} + 6 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 + 10 * q^4 - 10 * q^5 - 4 * q^6 + 6 * q^8 + 10 * q^9	$ 10 q + 2 q^{2} + 10 q^{4} - 10 q^{5} - 4 q^{6} + 6 q^{8} + 10 q^{9} - 2 q^{10} - 10 q^{11} - 4 q^{12} - 8 q^{13} + 6 q^{16} - 28 q^{17} - 10 q^{18} - 8 q^{19} - 10 q^{20} - 2 q^{22} - 8 q^{23} - 32 q^{24} + 10 q^{25} - 12 q^{26} - 8 q^{29} + 4 q^{30} + 4 q^{31} + 14 q^{32} - 20 q^{34} - 22 q^{36} + 28 q^{37} - 24 q^{38} - 24 q^{39} - 6 q^{40} - 44 q^{41} + 20 q^{43} - 10 q^{44} - 10 q^{45} - 12 q^{46} - 12 q^{47} - 16 q^{48} + 2 q^{50} - 4 q^{51} - 36 q^{52} + 8 q^{54} + 10 q^{55} + 12 q^{57} - 8 q^{58} - 16 q^{59} + 4 q^{60} - 16 q^{61} - 36 q^{62} - 34 q^{64} + 8 q^{65} + 4 q^{66} + 20 q^{67} - 8 q^{68} - 4 q^{69} - 4 q^{71} + 10 q^{72} - 20 q^{73} - 16 q^{74} - 4 q^{76} + 52 q^{78} - 20 q^{79} - 6 q^{80} + 10 q^{81} + 32 q^{82} - 16 q^{83} + 28 q^{85} - 20 q^{86} - 20 q^{87} - 6 q^{88} - 44 q^{89} + 10 q^{90} - 24 q^{92} + 16 q^{93} - 24 q^{94} + 8 q^{95} + 4 q^{97} - 10 q^{99}+O(q^{100}) $ 10 * q + 2 * q^2 + 10 * q^4 - 10 * q^5 - 4 * q^6 + 6 * q^8 + 10 * q^9 - 2 * q^10 - 10 * q^11 - 4 * q^12 - 8 * q^13 + 6 * q^16 - 28 * q^17 - 10 * q^18 - 8 * q^19 - 10 * q^20 - 2 * q^22 - 8 * q^23 - 32 * q^24 + 10 * q^25 - 12 * q^26 - 8 * q^29 + 4 * q^30 + 4 * q^31 + 14 * q^32 - 20 * q^34 - 22 * q^36 + 28 * q^37 - 24 * q^38 - 24 * q^39 - 6 * q^40 - 44 * q^41 + 20 * q^43 - 10 * q^44 - 10 * q^45 - 12 * q^46 - 12 * q^47 - 16 * q^48 + 2 * q^50 - 4 * q^51 - 36 * q^52 + 8 * q^54 + 10 * q^55 + 12 * q^57 - 8 * q^58 - 16 * q^59 + 4 * q^60 - 16 * q^61 - 36 * q^62 - 34 * q^64 + 8 * q^65 + 4 * q^66 + 20 * q^67 - 8 * q^68 - 4 * q^69 - 4 * q^71 + 10 * q^72 - 20 * q^73 - 16 * q^74 - 4 * q^76 + 52 * q^78 - 20 * q^79 - 6 * q^80 + 10 * q^81 + 32 * q^82 - 16 * q^83 + 28 * q^85 - 20 * q^86 - 20 * q^87 - 6 * q^88 - 44 * q^89 + 10 * q^90 - 24 * q^92 + 16 * q^93 - 24 * q^94 + 8 * q^95 + 4 * q^97 - 10 * 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 $

$2$	1.81378	1.28254	0.641268	−	0.767317i	$-0.278409\pi$
$2$	1.81378	1.28254	0.641268	+	0.767317i	$0.278409\pi$
$3$	1.20588	0.696218	0.348109	−	0.937454i	$-0.386824\pi$
$3$	1.20588	0.696218	0.348109	+	0.937454i	$0.386824\pi$
$4$	1.28980	0.644899
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.18721	0.892925
$7$	0	0
$7$	0	0
$8$	−1.28815	−0.455430
$9$	−1.54584	−0.515281
$10$	−1.81378	−0.573568
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.55535	0.448990
$13$	−4.21925	−1.17021	−0.585104	−	0.810958i	$-0.698946\pi$
$13$	−4.21925	−1.17021	−0.585104	+	0.810958i	$0.698946\pi$
$14$	0	0
$15$	−1.20588	−0.311358
$16$	−4.91602	−1.22900
$17$	1.71135	0.415063	0.207531	−	0.978228i	$-0.433457\pi$
$17$	1.71135	0.415063	0.207531	+	0.978228i	$0.433457\pi$
$18$	−2.80382	−0.660866
$19$	−2.74495	−0.629734	−0.314867	−	0.949136i	$-0.601960\pi$
$19$	−2.74495	−0.629734	−0.314867	+	0.949136i	$0.601960\pi$
$20$	−1.28980	−0.288408
$21$	0	0
$22$	−1.81378	−0.386699
$23$	4.93420	1.02885	0.514426	−	0.857535i	$-0.328005\pi$
$23$	4.93420	1.02885	0.514426	+	0.857535i	$0.328005\pi$
$24$	−1.55336	−0.317078
$25$	1.00000	0.200000
$26$	−7.65278	−1.50083
$27$	−5.48176	−1.05497
$28$	0	0
$29$	2.93746	0.545472	0.272736	−	0.962089i	$-0.412071\pi$
$29$	2.93746	0.545472	0.272736	+	0.962089i	$0.412071\pi$
$30$	−2.18721	−0.399328
$31$	−2.51530	−0.451762	−0.225881	−	0.974155i	$-0.572526\pi$
$31$	−2.51530	−0.451762	−0.225881	+	0.974155i	$0.572526\pi$
$32$	−6.34027	−1.12081
$33$	−1.20588	−0.209918
$34$	3.10401	0.532333
$35$	0	0
$36$	−1.99382	−0.332304
$37$	5.81846	0.956550	0.478275	−	0.878210i	$-0.341262\pi$
$37$	5.81846	0.956550	0.478275	+	0.878210i	$0.341262\pi$
$38$	−4.97873	−0.807657
$39$	−5.08792	−0.814720
$40$	1.28815	0.203674
$41$	−8.57606	−1.33936	−0.669678	−	0.742652i	$-0.733568\pi$
$41$	−8.57606	−1.33936	−0.669678	+	0.742652i	$0.733568\pi$
$42$	0	0
$43$	−7.38835	−1.12671	−0.563356	−	0.826214i	$-0.690490\pi$
$43$	−7.38835	−1.12671	−0.563356	+	0.826214i	$0.690490\pi$
$44$	−1.28980	−0.194444
$45$	1.54584	0.230440
$46$	8.94956	1.31954
$47$	−11.3024	−1.64862	−0.824311	−	0.566137i	$-0.808437\pi$
$47$	−11.3024	−1.64862	−0.824311	+	0.566137i	$0.808437\pi$
$48$	−5.92815	−0.855655
$49$	0	0
$50$	1.81378	0.256507
$51$	2.06369	0.288974
$52$	−5.44198	−0.754666
$53$	−12.1022	−1.66237	−0.831185	−	0.555996i	$-0.812337\pi$
$53$	−12.1022	−1.66237	−0.831185	+	0.555996i	$0.812337\pi$
$54$	−9.94271	−1.35303
$55$	1.00000	0.134840
$56$	0	0
$57$	−3.31009	−0.438432
$58$	5.32790	0.699587
$59$	−3.07397	−0.400197	−0.200099	−	0.979776i	$-0.564126\pi$
$59$	−3.07397	−0.400197	−0.200099	+	0.979776i	$0.564126\pi$
$60$	−1.55535	−0.200795
$61$	−8.10455	−1.03768	−0.518841	−	0.854871i	$-0.673636\pi$
$61$	−8.10455	−1.03768	−0.518841	+	0.854871i	$0.673636\pi$
$62$	−4.56221	−0.579401
$63$	0	0
$64$	−1.66783	−0.208479
$65$	4.21925	0.523333
$66$	−2.18721	−0.269227
$67$	1.81137	0.221294	0.110647	−	0.993860i	$-0.464708\pi$
$67$	1.81137	0.221294	0.110647	+	0.993860i	$0.464708\pi$
$68$	2.20729	0.267674
$69$	5.95008	0.716305
$70$	0	0
$71$	1.33972	0.158995	0.0794976	−	0.996835i	$-0.474668\pi$
$71$	1.33972	0.158995	0.0794976	+	0.996835i	$0.474668\pi$
$72$	1.99128	0.234674
$73$	−9.74210	−1.14023	−0.570113	−	0.821566i	$-0.693101\pi$
$73$	−9.74210	−1.14023	−0.570113	+	0.821566i	$0.693101\pi$
$74$	10.5534	1.22681
$75$	1.20588	0.139244
$76$	−3.54043	−0.406115
$77$	0	0
$78$	−9.22838	−1.04491
$79$	12.2992	1.38377	0.691886	−	0.722007i	$-0.256780\pi$
$79$	12.2992	1.38377	0.691886	+	0.722007i	$0.256780\pi$
$80$	4.91602	0.549627
$81$	−1.97285	−0.219205
$82$	−15.5551	−1.71777
$83$	8.75414	0.960892	0.480446	−	0.877024i	$-0.340475\pi$
$83$	8.75414	0.960892	0.480446	+	0.877024i	$0.340475\pi$
$84$	0	0
$85$	−1.71135	−0.185622
$86$	−13.4008	−1.44505
$87$	3.54223	0.379767
$88$	1.28815	0.137317
$89$	6.24999	0.662498	0.331249	−	0.943543i	$-0.392530\pi$
$89$	6.24999	0.662498	0.331249	+	0.943543i	$0.392530\pi$
$90$	2.80382	0.295548
$91$	0	0
$92$	6.36412	0.663506
$93$	−3.03317	−0.314525
$94$	−20.5000	−2.11442
$95$	2.74495	0.281626
$96$	−7.64564	−0.780330
$97$	1.61351	0.163827	0.0819136	−	0.996639i	$-0.473897\pi$
$97$	1.61351	0.163827	0.0819136	+	0.996639i	$0.473897\pi$
$98$	0	0
$99$	1.54584	0.155363
$100$	1.28980	0.128980
$101$	−1.24902	−0.124282	−0.0621408	−	0.998067i	$-0.519793\pi$
$101$	−1.24902	−0.124282	−0.0621408	+	0.998067i	$0.519793\pi$
$102$	3.74308	0.370620
$103$	16.1171	1.58806	0.794032	−	0.607876i	$-0.207978\pi$
$103$	16.1171	1.58806	0.794032	+	0.607876i	$0.207978\pi$
$104$	5.43502	0.532948
$105$	0	0
$106$	−21.9508	−2.13205
$107$	8.62384	0.833698	0.416849	−	0.908976i	$-0.363134\pi$
$107$	8.62384	0.833698	0.416849	+	0.908976i	$0.363134\pi$
$108$	−7.07037	−0.680346
$109$	−5.19122	−0.497229	−0.248614	−	0.968603i	$-0.579975\pi$
$109$	−5.19122	−0.497229	−0.248614	+	0.968603i	$0.579975\pi$
$110$	1.81378	0.172937
$111$	7.01640	0.665967
$112$	0	0
$113$	15.2427	1.43391	0.716956	−	0.697118i	$-0.245535\pi$
$113$	15.2427	1.43391	0.716956	+	0.697118i	$0.245535\pi$
$114$	−6.00378	−0.562305
$115$	−4.93420	−0.460117
$116$	3.78873	0.351774
$117$	6.52229	0.602986
$118$	−5.57551	−0.513268
$119$	0	0
$120$	1.55336	0.141802
$121$	1.00000	0.0909091
$122$	−14.6999	−1.33086
$123$	−10.3417	−0.932483
$124$	−3.24423	−0.291341
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−13.2515	−1.17588	−0.587940	−	0.808904i	$-0.700061\pi$
$127$	−13.2515	−1.17588	−0.587940	+	0.808904i	$0.700061\pi$
$128$	9.65547	0.853431
$129$	−8.90950	−0.784437
$130$	7.65278	0.671194
$131$	9.74562	0.851478	0.425739	−	0.904846i	$-0.360014\pi$
$131$	9.74562	0.851478	0.425739	+	0.904846i	$0.360014\pi$
$132$	−1.55535	−0.135376
$133$	0	0
$134$	3.28542	0.283817
$135$	5.48176	0.471795
$136$	−2.20447	−0.189032
$137$	1.12680	0.0962693	0.0481347	−	0.998841i	$-0.484672\pi$
$137$	1.12680	0.0962693	0.0481347	+	0.998841i	$0.484672\pi$
$138$	10.7921	0.918687
$139$	7.27497	0.617055	0.308527	−	0.951215i	$-0.400164\pi$
$139$	7.27497	0.617055	0.308527	+	0.951215i	$0.400164\pi$
$140$	0	0
$141$	−13.6294	−1.14780
$142$	2.42995	0.203917
$143$	4.21925	0.352831
$144$	7.59938	0.633282
$145$	−2.93746	−0.243942
$146$	−17.6700	−1.46238
$147$	0	0
$148$	7.50465	0.616878
$149$	24.0416	1.96956	0.984780	−	0.173803i	$-0.0556057\pi$
$149$	24.0416	1.96956	0.984780	+	0.173803i	$0.0556057\pi$
$150$	2.18721	0.178585
$151$	−5.75963	−0.468712	−0.234356	−	0.972151i	$-0.575298\pi$
$151$	−5.75963	−0.468712	−0.234356	+	0.972151i	$0.575298\pi$
$152$	3.53590	0.286800
$153$	−2.64547	−0.213874
$154$	0	0
$155$	2.51530	0.202034
$156$	−6.56240	−0.525412
$157$	9.83002	0.784521	0.392261	−	0.919854i	$-0.371693\pi$
$157$	9.83002	0.784521	0.392261	+	0.919854i	$0.371693\pi$
$158$	22.3081	1.77474
$159$	−14.5939	−1.15737
$160$	6.34027	0.501243
$161$	0	0
$162$	−3.57831	−0.281139
$163$	5.33020	0.417494	0.208747	−	0.977970i	$-0.433062\pi$
$163$	5.33020	0.417494	0.208747	+	0.977970i	$0.433062\pi$
$164$	−11.0614	−0.863749
$165$	1.20588	0.0938780
$166$	15.8781	1.23238
$167$	−15.7355	−1.21765	−0.608823	−	0.793306i	$-0.708358\pi$
$167$	−15.7355	−1.21765	−0.608823	+	0.793306i	$0.708358\pi$
$168$	0	0
$169$	4.80204	0.369387
$170$	−3.10401	−0.238067
$171$	4.24325	0.324490
$172$	−9.52948	−0.726616
$173$	−9.92979	−0.754948	−0.377474	−	0.926020i	$-0.623207\pi$
$173$	−9.92979	−0.754948	−0.377474	+	0.926020i	$0.623207\pi$
$174$	6.42483	0.487065
$175$	0	0
$176$	4.91602	0.370559
$177$	−3.70686	−0.278625
$178$	11.3361	0.849677
$179$	8.82663	0.659733	0.329867	−	0.944028i	$-0.392996\pi$
$179$	8.82663	0.659733	0.329867	+	0.944028i	$0.392996\pi$
$180$	1.99382	0.148611
$181$	−8.21285	−0.610456	−0.305228	−	0.952279i	$-0.598733\pi$
$181$	−8.21285	−0.610456	−0.305228	+	0.952279i	$0.598733\pi$
$182$	0	0
$183$	−9.77316	−0.722453
$184$	−6.35599	−0.468570
$185$	−5.81846	−0.427782
$186$	−5.50150	−0.403389
$187$	−1.71135	−0.125146
$188$	−14.5778	−1.06320
$189$	0	0
$190$	4.97873	0.361195
$191$	−8.67950	−0.628026	−0.314013	−	0.949419i	$-0.601674\pi$
$191$	−8.67950	−0.628026	−0.314013	+	0.949419i	$0.601674\pi$
$192$	−2.01121	−0.145147
$193$	−10.6084	−0.763609	−0.381805	−	0.924243i	$-0.624697\pi$
$193$	−10.6084	−0.763609	−0.381805	+	0.924243i	$0.624697\pi$
$194$	2.92655	0.210114
$195$	5.08792	0.364354
$196$	0	0
$197$	14.3404	1.02171	0.510856	−	0.859666i	$-0.329329\pi$
$197$	14.3404	1.02171	0.510856	+	0.859666i	$0.329329\pi$
$198$	2.80382	0.199259
$199$	−20.2707	−1.43695	−0.718477	−	0.695550i	$-0.755161\pi$
$199$	−20.2707	−1.43695	−0.718477	+	0.695550i	$0.755161\pi$
$200$	−1.28815	−0.0910859
$201$	2.18430	0.154069
$202$	−2.26544	−0.159396
$203$	0	0
$204$	2.66174	0.186359
$205$	8.57606	0.598978
$206$	29.2329	2.03675
$207$	−7.62749	−0.530147
$208$	20.7419	1.43819
$209$	2.74495	0.189872
$210$	0	0
$211$	−25.4796	−1.75409	−0.877043	−	0.480413i	$-0.840487\pi$
$211$	−25.4796	−1.75409	−0.877043	+	0.480413i	$0.840487\pi$
$212$	−15.6094	−1.07206
$213$	1.61555	0.110695
$214$	15.6417	1.06925
$215$	7.38835	0.503881
$216$	7.06133	0.480463
$217$	0	0
$218$	−9.41573	−0.637714
$219$	−11.7479	−0.793846
$220$	1.28980	0.0869582
$221$	−7.22060	−0.485710
$222$	12.7262	0.854127
$223$	−16.3389	−1.09413	−0.547065	−	0.837090i	$-0.684255\pi$
$223$	−16.3389	−1.09413	−0.547065	+	0.837090i	$0.684255\pi$
$224$	0	0
$225$	−1.54584	−0.103056
$226$	27.6469	1.83904
$227$	0.932541	0.0618949	0.0309474	−	0.999521i	$-0.490148\pi$
$227$	0.932541	0.0618949	0.0309474	+	0.999521i	$0.490148\pi$
$228$	−4.26935	−0.282745
$229$	14.6741	0.969695	0.484848	−	0.874599i	$-0.338875\pi$
$229$	14.6741	0.969695	0.484848	+	0.874599i	$0.338875\pi$
$230$	−8.94956	−0.590116
$231$	0	0
$232$	−3.78388	−0.248424
$233$	0.735400	0.0481777	0.0240888	−	0.999710i	$-0.492332\pi$
$233$	0.735400	0.0481777	0.0240888	+	0.999710i	$0.492332\pi$
$234$	11.8300	0.773351
$235$	11.3024	0.737287
$236$	−3.96481	−0.258087
$237$	14.8315	0.963407
$238$	0	0
$239$	−21.2270	−1.37306	−0.686532	−	0.727100i	$-0.740868\pi$
$239$	−21.2270	−1.37306	−0.686532	+	0.727100i	$0.740868\pi$
$240$	5.92815	0.382660
$241$	21.4146	1.37944	0.689718	−	0.724078i	$-0.257734\pi$
$241$	21.4146	1.37944	0.689718	+	0.724078i	$0.257734\pi$
$242$	1.81378	0.116594
$243$	14.0663	0.902351
$244$	−10.4532	−0.669200
$245$	0	0
$246$	−18.7576	−1.19594
$247$	11.5816	0.736920
$248$	3.24009	0.205746
$249$	10.5565	0.668990
$250$	−1.81378	−0.114714
$251$	10.8799	0.686734	0.343367	−	0.939201i	$-0.388433\pi$
$251$	10.8799	0.686734	0.343367	+	0.939201i	$0.388433\pi$
$252$	0	0
$253$	−4.93420	−0.310211
$254$	−24.0353	−1.50811
$255$	−2.06369	−0.129233
$256$	20.8486	1.30304
$257$	−21.5972	−1.34719	−0.673597	−	0.739098i	$-0.735252\pi$
$257$	−21.5972	−1.34719	−0.673597	+	0.739098i	$0.735252\pi$
$258$	−16.1599	−1.00607
$259$	0	0
$260$	5.44198	0.337497
$261$	−4.54084	−0.281071
$262$	17.6764	1.09205
$263$	−25.5301	−1.57425	−0.787127	−	0.616791i	$-0.788432\pi$
$263$	−25.5301	−1.57425	−0.787127	+	0.616791i	$0.788432\pi$
$264$	1.55336	0.0956027
$265$	12.1022	0.743434
$266$	0	0
$267$	7.53677	0.461243
$268$	2.33630	0.142712
$269$	−14.3208	−0.873153	−0.436577	−	0.899667i	$-0.643809\pi$
$269$	−14.3208	−0.873153	−0.436577	+	0.899667i	$0.643809\pi$
$270$	9.94271	0.605094
$271$	15.3380	0.931719	0.465859	−	0.884859i	$-0.345745\pi$
$271$	15.3380	0.931719	0.465859	+	0.884859i	$0.345745\pi$
$272$	−8.41301	−0.510114
$273$	0	0
$274$	2.04377	0.123469
$275$	−1.00000	−0.0603023
$276$	7.67440	0.461945
$277$	29.6847	1.78358	0.891792	−	0.452446i	$-0.149449\pi$
$277$	29.6847	1.78358	0.891792	+	0.452446i	$0.149449\pi$
$278$	13.1952	0.791395
$279$	3.88826	0.232784
$280$	0	0
$281$	−2.52250	−0.150480	−0.0752400	−	0.997165i	$-0.523972\pi$
$281$	−2.52250	−0.150480	−0.0752400	+	0.997165i	$0.523972\pi$
$282$	−24.7207	−1.47210
$283$	−11.3711	−0.675942	−0.337971	−	0.941156i	$-0.609741\pi$
$283$	−11.3711	−0.675942	−0.337971	+	0.941156i	$0.609741\pi$
$284$	1.72797	0.102536
$285$	3.31009	0.196073
$286$	7.65278	0.452519
$287$	0	0
$288$	9.80106	0.577533
$289$	−14.0713	−0.827723
$290$	−5.32790	−0.312865
$291$	1.94571	0.114059
$292$	−12.5653	−0.735331
$293$	−23.6695	−1.38279	−0.691395	−	0.722477i	$-0.743003\pi$
$293$	−23.6695	−1.38279	−0.691395	+	0.722477i	$0.743003\pi$
$294$	0	0
$295$	3.07397	0.178974
$296$	−7.49505	−0.435641
$297$	5.48176	0.318084
$298$	43.6061	2.52603
$299$	−20.8186	−1.20397
$300$	1.55535	0.0897981
$301$	0	0
$302$	−10.4467	−0.601140
$303$	−1.50617	−0.0865271
$304$	13.4942	0.773946
$305$	8.10455	0.464065
$306$	−4.79831	−0.274301
$307$	−10.4165	−0.594503	−0.297251	−	0.954799i	$-0.596070\pi$
$307$	−10.4165	−0.594503	−0.297251	+	0.954799i	$0.596070\pi$
$308$	0	0
$309$	19.4354	1.10564
$310$	4.56221	0.259116
$311$	−4.79637	−0.271977	−0.135989	−	0.990710i	$-0.543421\pi$
$311$	−4.79637	−0.271977	−0.135989	+	0.990710i	$0.543421\pi$
$312$	6.55401	0.371048
$313$	17.6720	0.998879	0.499439	−	0.866349i	$-0.333539\pi$
$313$	17.6720	0.998879	0.499439	+	0.866349i	$0.333539\pi$
$314$	17.8295	1.00618
$315$	0	0
$316$	15.8635	0.892394
$317$	13.0231	0.731452	0.365726	−	0.930723i	$-0.380821\pi$
$317$	13.0231	0.731452	0.365726	+	0.930723i	$0.380821\pi$
$318$	−26.4701	−1.48437
$319$	−2.93746	−0.164466
$320$	1.66783	0.0932346
$321$	10.3994	0.580435
$322$	0	0
$323$	−4.69756	−0.261379
$324$	−2.54458	−0.141365
$325$	−4.21925	−0.234042
$326$	9.66781	0.535451
$327$	−6.26001	−0.346180
$328$	11.0472	0.609982
$329$	0	0
$330$	2.18721	0.120402
$331$	−25.7152	−1.41343	−0.706717	−	0.707496i	$-0.749825\pi$
$331$	−25.7152	−1.41343	−0.706717	+	0.707496i	$0.749825\pi$
$332$	11.2911	0.619678
$333$	−8.99442	−0.492891
$334$	−28.5407	−1.56168
$335$	−1.81137	−0.0989656
$336$	0	0
$337$	−17.2149	−0.937755	−0.468878	−	0.883263i	$-0.655341\pi$
$337$	−17.2149	−0.937755	−0.468878	+	0.883263i	$0.655341\pi$
$338$	8.70984	0.473753
$339$	18.3809	0.998316
$340$	−2.20729	−0.119707
$341$	2.51530	0.136211
$342$	7.69633	0.416170
$343$	0	0
$344$	9.51730	0.513138
$345$	−5.95008	−0.320341
$346$	−18.0105	−0.968248
$347$	−25.2605	−1.35606	−0.678028	−	0.735036i	$-0.737165\pi$
$347$	−25.2605	−1.35606	−0.678028	+	0.735036i	$0.737165\pi$
$348$	4.56877	0.244912
$349$	6.63690	0.355265	0.177632	−	0.984097i	$-0.443156\pi$
$349$	6.63690	0.355265	0.177632	+	0.984097i	$0.443156\pi$
$350$	0	0
$351$	23.1289	1.23453
$352$	6.34027	0.337938
$353$	30.1396	1.60417	0.802084	−	0.597211i	$-0.203725\pi$
$353$	30.1396	1.60417	0.802084	+	0.597211i	$0.203725\pi$
$354$	−6.72343	−0.357346
$355$	−1.33972	−0.0711048
$356$	8.06123	0.427244
$357$	0	0
$358$	16.0096	0.846132
$359$	9.51166	0.502006	0.251003	−	0.967986i	$-0.419240\pi$
$359$	9.51166	0.502006	0.251003	+	0.967986i	$0.419240\pi$
$360$	−1.99128	−0.104949
$361$	−11.4653	−0.603435
$362$	−14.8963	−0.782932
$363$	1.20588	0.0632925
$364$	0	0
$365$	9.74210	0.509925
$366$	−17.7264	−0.926572
$367$	−14.0290	−0.732310	−0.366155	−	0.930554i	$-0.619326\pi$
$367$	−14.0290	−0.732310	−0.366155	+	0.930554i	$0.619326\pi$
$368$	−24.2566	−1.26446
$369$	13.2572	0.690144
$370$	−10.5534	−0.548646
$371$	0	0
$372$	−3.91217	−0.202837
$373$	0.155293	0.00804075	0.00402038	−	0.999992i	$-0.498720\pi$
$373$	0.155293	0.00804075	0.00402038	+	0.999992i	$0.498720\pi$
$374$	−3.10401	−0.160504
$375$	−1.20588	−0.0622716
$376$	14.5592	0.750832
$377$	−12.3938	−0.638316
$378$	0	0
$379$	11.6932	0.600639	0.300320	−	0.953839i	$-0.402907\pi$
$379$	11.6932	0.600639	0.300320	+	0.953839i	$0.402907\pi$
$380$	3.54043	0.181620
$381$	−15.9798	−0.818669
$382$	−15.7427	−0.805467
$383$	20.7755	1.06158	0.530789	−	0.847504i	$-0.321896\pi$
$383$	20.7755	1.06158	0.530789	+	0.847504i	$0.321896\pi$
$384$	11.6434	0.594174
$385$	0	0
$386$	−19.2413	−0.979356
$387$	11.4212	0.580573
$388$	2.08110	0.105652
$389$	23.1404	1.17326	0.586632	−	0.809854i	$-0.300453\pi$
$389$	23.1404	1.17326	0.586632	+	0.809854i	$0.300453\pi$
$390$	9.22838	0.467297
$391$	8.44413	0.427038
$392$	0	0
$393$	11.7521	0.592815
$394$	26.0104	1.31038
$395$	−12.2992	−0.618842
$396$	1.99382	0.100193
$397$	−17.5632	−0.881472	−0.440736	−	0.897637i	$-0.645282\pi$
$397$	−17.5632	−0.881472	−0.440736	+	0.897637i	$0.645282\pi$
$398$	−36.7667	−1.84295
$399$	0	0
$400$	−4.91602	−0.245801
$401$	−14.3186	−0.715039	−0.357519	−	0.933906i	$-0.616377\pi$
$401$	−14.3186	−0.715039	−0.357519	+	0.933906i	$0.616377\pi$
$402$	3.96184	0.197599
$403$	10.6127	0.528655
$404$	−1.61098	−0.0801491
$405$	1.97285	0.0980316
$406$	0	0
$407$	−5.81846	−0.288411
$408$	−2.65834	−0.131607
$409$	10.7229	0.530216	0.265108	−	0.964219i	$-0.414592\pi$
$409$	10.7229	0.530216	0.265108	+	0.964219i	$0.414592\pi$
$410$	15.5551	0.768211
$411$	1.35880	0.0670244
$412$	20.7878	1.02414
$413$	0	0
$414$	−13.8346	−0.679933
$415$	−8.75414	−0.429724
$416$	26.7512	1.31158
$417$	8.77277	0.429605
$418$	4.97873	0.243518
$419$	25.5109	1.24629	0.623144	−	0.782107i	$-0.285855\pi$
$419$	25.5109	1.24629	0.623144	+	0.782107i	$0.285855\pi$
$420$	0	0
$421$	−22.3846	−1.09096	−0.545478	−	0.838125i	$-0.683652\pi$
$421$	−22.3846	−1.09096	−0.545478	+	0.838125i	$0.683652\pi$
$422$	−46.2143	−2.24968
$423$	17.4717	0.849503
$424$	15.5895	0.757092
$425$	1.71135	0.0830126
$426$	2.93024	0.141971
$427$	0	0
$428$	11.1230	0.537651
$429$	5.08792	0.245647
$430$	13.4008	0.646246
$431$	−8.94635	−0.430930	−0.215465	−	0.976512i	$-0.569127\pi$
$431$	−8.94635	−0.430930	−0.215465	+	0.976512i	$0.569127\pi$
$432$	26.9484	1.29656
$433$	−23.4227	−1.12562	−0.562812	−	0.826585i	$-0.690281\pi$
$433$	−23.4227	−1.12562	−0.562812	+	0.826585i	$0.690281\pi$
$434$	0	0
$435$	−3.54223	−0.169837
$436$	−6.69563	−0.320662
$437$	−13.5441	−0.647903
$438$	−21.3080	−1.01814
$439$	6.16229	0.294110	0.147055	−	0.989128i	$-0.453021\pi$
$439$	6.16229	0.294110	0.147055	+	0.989128i	$0.453021\pi$
$440$	−1.28815	−0.0614101
$441$	0	0
$442$	−13.0966	−0.622941
$443$	−35.6183	−1.69228	−0.846138	−	0.532964i	$-0.821078\pi$
$443$	−35.6183	−1.69228	−0.846138	+	0.532964i	$0.821078\pi$
$444$	9.04974	0.429482
$445$	−6.24999	−0.296278
$446$	−29.6351	−1.40326
$447$	28.9913	1.37124
$448$	0	0
$449$	−7.43614	−0.350933	−0.175467	−	0.984485i	$-0.556143\pi$
$449$	−7.43614	−0.350933	−0.175467	+	0.984485i	$0.556143\pi$
$450$	−2.80382	−0.132173
$451$	8.57606	0.403831
$452$	19.6600	0.924729
$453$	−6.94545	−0.326326
$454$	1.69142	0.0793825
$455$	0	0
$456$	4.26389	0.199675
$457$	37.1571	1.73813	0.869067	−	0.494694i	$-0.164720\pi$
$457$	37.1571	1.73813	0.869067	+	0.494694i	$0.164720\pi$
$458$	26.6157	1.24367
$459$	−9.38120	−0.437877
$460$	−6.36412	−0.296729
$461$	15.0941	0.703003	0.351502	−	0.936187i	$-0.385671\pi$
$461$	15.0941	0.703003	0.351502	+	0.936187i	$0.385671\pi$
$462$	0	0
$463$	24.5703	1.14188	0.570940	−	0.820992i	$-0.306579\pi$
$463$	24.5703	1.14188	0.570940	+	0.820992i	$0.306579\pi$
$464$	−14.4406	−0.670387
$465$	3.03317	0.140660
$466$	1.33385	0.0617896
$467$	−22.3213	−1.03291	−0.516453	−	0.856316i	$-0.672748\pi$
$467$	−22.3213	−1.03291	−0.516453	+	0.856316i	$0.672748\pi$
$468$	8.41243	0.388865
$469$	0	0
$470$	20.5000	0.945597
$471$	11.8539	0.546198
$472$	3.95974	0.182262
$473$	7.38835	0.339717
$474$	26.9010	1.23560
$475$	−2.74495	−0.125947
$476$	0	0
$477$	18.7081	0.856587
$478$	−38.5012	−1.76100
$479$	13.2003	0.603139	0.301569	−	0.953444i	$-0.402489\pi$
$479$	13.2003	0.603139	0.301569	+	0.953444i	$0.402489\pi$
$480$	7.64564	0.348974
$481$	−24.5495	−1.11936
$482$	38.8414	1.76918
$483$	0	0
$484$	1.28980	0.0586272
$485$	−1.61351	−0.0732657
$486$	25.5131	1.15730
$487$	−2.14542	−0.0972183	−0.0486092	−	0.998818i	$-0.515479\pi$
$487$	−2.14542	−0.0972183	−0.0486092	+	0.998818i	$0.515479\pi$
$488$	10.4399	0.472591
$489$	6.42761	0.290667
$490$	0	0
$491$	−7.78916	−0.351520	−0.175760	−	0.984433i	$-0.556238\pi$
$491$	−7.78916	−0.351520	−0.175760	+	0.984433i	$0.556238\pi$
$492$	−13.3388	−0.601358
$493$	5.02701	0.226405
$494$	21.0065	0.945127
$495$	−1.54584	−0.0694804
$496$	12.3653	0.555217
$497$	0	0
$498$	19.1471	0.858004
$499$	35.0083	1.56719	0.783594	−	0.621273i	$-0.213384\pi$
$499$	35.0083	1.56719	0.783594	+	0.621273i	$0.213384\pi$
$500$	−1.28980	−0.0576815
$501$	−18.9752	−0.847747
$502$	19.7338	0.880761
$503$	−23.1402	−1.03177	−0.515885	−	0.856658i	$-0.672537\pi$
$503$	−23.1402	−1.03177	−0.515885	+	0.856658i	$0.672537\pi$
$504$	0	0
$505$	1.24902	0.0555805
$506$	−8.94956	−0.397856
$507$	5.79070	0.257174
$508$	−17.0918	−0.758325
$509$	−24.6549	−1.09281	−0.546405	−	0.837521i	$-0.684004\pi$
$509$	−24.6549	−1.09281	−0.546405	+	0.837521i	$0.684004\pi$
$510$	−3.74308	−0.165746
$511$	0	0
$512$	18.5038	0.817759
$513$	15.0471	0.664348
$514$	−39.1725	−1.72783
$515$	−16.1171	−0.710204
$516$	−11.4915	−0.505883
$517$	11.3024	0.497078
$518$	0	0
$519$	−11.9742	−0.525608
$520$	−5.43502	−0.238341
$521$	−33.3736	−1.46212	−0.731062	−	0.682311i	$-0.760975\pi$
$521$	−33.3736	−1.46212	−0.731062	+	0.682311i	$0.760975\pi$
$522$	−8.23609	−0.360484
$523$	12.9762	0.567409	0.283704	−	0.958912i	$-0.408437\pi$
$523$	12.9762	0.567409	0.283704	+	0.958912i	$0.408437\pi$
$524$	12.5699	0.549118
$525$	0	0
$526$	−46.3060	−2.01904
$527$	−4.30456	−0.187510
$528$	5.92815	0.257990
$529$	1.34634	0.0585365
$530$	21.9508	0.953481
$531$	4.75188	0.206214
$532$	0	0
$533$	36.1845	1.56733
$534$	13.6700	0.591561
$535$	−8.62384	−0.372841
$536$	−2.33331	−0.100784
$537$	10.6439	0.459318
$538$	−25.9747	−1.11985
$539$	0	0
$540$	7.07037	0.304260
$541$	−3.03131	−0.130326	−0.0651632	−	0.997875i	$-0.520757\pi$
$541$	−3.03131	−0.130326	−0.0651632	+	0.997875i	$0.520757\pi$
$542$	27.8198	1.19496
$543$	−9.90375	−0.425011
$544$	−10.8504	−0.465208
$545$	5.19122	0.222367
$546$	0	0
$547$	−30.0537	−1.28500	−0.642502	−	0.766284i	$-0.722104\pi$
$547$	−30.0537	−1.28500	−0.642502	+	0.766284i	$0.722104\pi$
$548$	1.45335	0.0620840
$549$	12.5284	0.534697
$550$	−1.81378	−0.0773398
$551$	−8.06316	−0.343502
$552$	−7.66459	−0.326227
$553$	0	0
$554$	53.8416	2.28751
$555$	−7.01640	−0.297829
$556$	9.38324	0.397938
$557$	−14.6229	−0.619594	−0.309797	−	0.950803i	$-0.600261\pi$
$557$	−14.6229	−0.619594	−0.309797	+	0.950803i	$0.600261\pi$
$558$	7.05245	0.298554
$559$	31.1733	1.31849
$560$	0	0
$561$	−2.06369	−0.0871290
$562$	−4.57527	−0.192996
$563$	3.72890	0.157154	0.0785772	−	0.996908i	$-0.474962\pi$
$563$	3.72890	0.157154	0.0785772	+	0.996908i	$0.474962\pi$
$564$	−17.5792	−0.740216
$565$	−15.2427	−0.641265
$566$	−20.6247	−0.866920
$567$	0	0
$568$	−1.72576	−0.0724111
$569$	−35.1421	−1.47323	−0.736617	−	0.676310i	$-0.763578\pi$
$569$	−35.1421	−1.47323	−0.736617	+	0.676310i	$0.763578\pi$
$570$	6.00378	0.251470
$571$	−34.9532	−1.46275	−0.731373	−	0.681977i	$-0.761120\pi$
$571$	−34.9532	−1.46275	−0.731373	+	0.681977i	$0.761120\pi$
$572$	5.44198	0.227540
$573$	−10.4665	−0.437243
$574$	0	0
$575$	4.93420	0.205770
$576$	2.57820	0.107425
$577$	6.51174	0.271087	0.135544	−	0.990771i	$-0.456722\pi$
$577$	6.51174	0.271087	0.135544	+	0.990771i	$0.456722\pi$
$578$	−25.5222	−1.06158
$579$	−12.7925	−0.531638
$580$	−3.78873	−0.157318
$581$	0	0
$582$	3.52909	0.146285
$583$	12.1022	0.501223
$584$	12.5493	0.519293
$585$	−6.52229	−0.269663
$586$	−42.9313	−1.77348
$587$	41.3956	1.70858	0.854290	−	0.519796i	$-0.173992\pi$
$587$	41.3956	1.70858	0.854290	+	0.519796i	$0.173992\pi$
$588$	0	0
$589$	6.90437	0.284490
$590$	5.57551	0.229540
$591$	17.2929	0.711334
$592$	−28.6037	−1.17560
$593$	−34.1435	−1.40211	−0.701054	−	0.713109i	$-0.747287\pi$
$593$	−34.1435	−1.40211	−0.701054	+	0.713109i	$0.747287\pi$
$594$	9.94271	0.407954
$595$	0	0
$596$	31.0088	1.27017
$597$	−24.4442	−1.00043
$598$	−37.7604	−1.54414
$599$	−41.5425	−1.69738	−0.848690	−	0.528890i	$-0.822608\pi$
$599$	−41.5425	−1.69738	−0.848690	+	0.528890i	$0.822608\pi$
$600$	−1.55336	−0.0634157
$601$	−30.9886	−1.26405	−0.632026	−	0.774947i	$-0.717776\pi$
$601$	−30.9886	−1.26405	−0.632026	+	0.774947i	$0.717776\pi$
$602$	0	0
$603$	−2.80009	−0.114028
$604$	−7.42876	−0.302272
$605$	−1.00000	−0.0406558
$606$	−2.73186	−0.110974
$607$	6.72990	0.273158	0.136579	−	0.990629i	$-0.456389\pi$
$607$	6.72990	0.273158	0.136579	+	0.990629i	$0.456389\pi$
$608$	17.4037	0.705814
$609$	0	0
$610$	14.6999	0.595181
$611$	47.6876	1.92923
$612$	−3.41213	−0.137927
$613$	12.8990	0.520985	0.260493	−	0.965476i	$-0.416115\pi$
$613$	12.8990	0.520985	0.260493	+	0.965476i	$0.416115\pi$
$614$	−18.8933	−0.762471
$615$	10.3417	0.417019
$616$	0	0
$617$	−23.2732	−0.936945	−0.468472	−	0.883478i	$-0.655195\pi$
$617$	−23.2732	−0.936945	−0.468472	+	0.883478i	$0.655195\pi$
$618$	35.2515	1.41802
$619$	−2.56813	−0.103222	−0.0516109	−	0.998667i	$-0.516436\pi$
$619$	−2.56813	−0.103222	−0.0516109	+	0.998667i	$0.516436\pi$
$620$	3.24423	0.130292
$621$	−27.0481	−1.08540
$622$	−8.69956	−0.348821
$623$	0	0
$624$	25.0123	1.00129
$625$	1.00000	0.0400000
$626$	32.0531	1.28110
$627$	3.31009	0.132192
$628$	12.6787	0.505937
$629$	9.95741	0.397028
$630$	0	0
$631$	22.0897	0.879377	0.439689	−	0.898150i	$-0.355089\pi$
$631$	22.0897	0.879377	0.439689	+	0.898150i	$0.355089\pi$
$632$	−15.8433	−0.630211
$633$	−30.7254	−1.22123
$634$	23.6211	0.938113
$635$	13.2515	0.525870
$636$	−18.8232	−0.746388
$637$	0	0
$638$	−5.32790	−0.210934
$639$	−2.07099	−0.0819272
$640$	−9.65547	−0.381666
$641$	−21.8125	−0.861542	−0.430771	−	0.902461i	$-0.641758\pi$
$641$	−21.8125	−0.861542	−0.430771	+	0.902461i	$0.641758\pi$
$642$	18.8621	0.744429
$643$	−3.77920	−0.149037	−0.0745186	−	0.997220i	$-0.523742\pi$
$643$	−3.77920	−0.149037	−0.0745186	+	0.997220i	$0.523742\pi$
$644$	0	0
$645$	8.90950	0.350811
$646$	−8.52034	−0.335228
$647$	−22.8470	−0.898207	−0.449104	−	0.893480i	$-0.648257\pi$
$647$	−22.8470	−0.898207	−0.449104	+	0.893480i	$0.648257\pi$
$648$	2.54132	0.0998326
$649$	3.07397	0.120664
$650$	−7.65278	−0.300167
$651$	0	0
$652$	6.87488	0.269241
$653$	−15.6332	−0.611774	−0.305887	−	0.952068i	$-0.598953\pi$
$653$	−15.6332	−0.611774	−0.305887	+	0.952068i	$0.598953\pi$
$654$	−11.3543	−0.443988
$655$	−9.74562	−0.380793
$656$	42.1601	1.64607
$657$	15.0597	0.587537
$658$	0	0
$659$	22.5113	0.876914	0.438457	−	0.898752i	$-0.355525\pi$
$659$	22.5113	0.876914	0.438457	+	0.898752i	$0.355525\pi$
$660$	1.55535	0.0605419
$661$	13.1109	0.509956	0.254978	−	0.966947i	$-0.417932\pi$
$661$	13.1109	0.509956	0.254978	+	0.966947i	$0.417932\pi$
$662$	−46.6417	−1.81278
$663$	−8.70721	−0.338160
$664$	−11.2766	−0.437619
$665$	0	0
$666$	−16.3139	−0.632151
$667$	14.4940	0.561210
$668$	−20.2956	−0.785259
$669$	−19.7028	−0.761753
$670$	−3.28542	−0.126927
$671$	8.10455	0.312873
$672$	0	0
$673$	−31.3683	−1.20916	−0.604580	−	0.796544i	$-0.706659\pi$
$673$	−31.3683	−1.20916	−0.604580	+	0.796544i	$0.706659\pi$
$674$	−31.2240	−1.20270
$675$	−5.48176	−0.210993
$676$	6.19366	0.238218
$677$	−30.2193	−1.16142	−0.580711	−	0.814110i	$-0.697225\pi$
$677$	−30.2193	−1.16142	−0.580711	+	0.814110i	$0.697225\pi$
$678$	33.3390	1.28038
$679$	0	0
$680$	2.20447	0.0845376
$681$	1.12454	0.0430923
$682$	4.56221	0.174696
$683$	−8.30631	−0.317832	−0.158916	−	0.987292i	$-0.550800\pi$
$683$	−8.30631	−0.317832	−0.158916	+	0.987292i	$0.550800\pi$
$684$	5.47294	0.209263
$685$	−1.12680	−0.0430529
$686$	0	0
$687$	17.6953	0.675119
$688$	36.3212	1.38473
$689$	51.0623	1.94532
$690$	−10.7921	−0.410850
$691$	−6.64975	−0.252968	−0.126484	−	0.991969i	$-0.540369\pi$
$691$	−6.64975	−0.252968	−0.126484	+	0.991969i	$0.540369\pi$
$692$	−12.8074	−0.486865
$693$	0	0
$694$	−45.8170	−1.73919
$695$	−7.27497	−0.275955
$696$	−4.56293	−0.172957
$697$	−14.6766	−0.555917
$698$	12.0379	0.455640
$699$	0.886808	0.0335422
$700$	0	0
$701$	43.0872	1.62738	0.813691	−	0.581297i	$-0.197455\pi$
$701$	43.0872	1.62738	0.813691	+	0.581297i	$0.197455\pi$
$702$	41.9507	1.58333
$703$	−15.9714	−0.602372
$704$	1.66783	0.0628587
$705$	13.6294	0.513312
$706$	54.6666	2.05740
$707$	0	0
$708$	−4.78110	−0.179685
$709$	49.5166	1.85963	0.929817	−	0.368021i	$-0.119965\pi$
$709$	49.5166	1.85963	0.929817	+	0.368021i	$0.119965\pi$
$710$	−2.42995	−0.0911945
$711$	−19.0127	−0.713031
$712$	−8.05092	−0.301721
$713$	−12.4110	−0.464796
$714$	0	0
$715$	−4.21925	−0.157791
$716$	11.3846	0.425461
$717$	−25.5974	−0.955952
$718$	17.2521	0.643841
$719$	24.7219	0.921971	0.460985	−	0.887408i	$-0.347496\pi$
$719$	24.7219	0.921971	0.460985	+	0.887408i	$0.347496\pi$
$720$	−7.59938	−0.283212
$721$	0	0
$722$	−20.7955	−0.773927
$723$	25.8236	0.960388
$724$	−10.5929	−0.393683
$725$	2.93746	0.109094
$726$	2.18721	0.0811750
$727$	−7.26381	−0.269400	−0.134700	−	0.990886i	$-0.543007\pi$
$727$	−7.26381	−0.269400	−0.134700	+	0.990886i	$0.543007\pi$
$728$	0	0
$729$	22.8808	0.847438
$730$	17.6700	0.653997
$731$	−12.6440	−0.467656
$732$	−12.6054	−0.465909
$733$	11.1724	0.412661	0.206330	−	0.978482i	$-0.433848\pi$
$733$	11.1724	0.412661	0.206330	+	0.978482i	$0.433848\pi$
$734$	−25.4456	−0.939214
$735$	0	0
$736$	−31.2842	−1.15315
$737$	−1.81137	−0.0667226
$738$	24.0457	0.885135
$739$	−16.4763	−0.606090	−0.303045	−	0.952976i	$-0.598003\pi$
$739$	−16.4763	−0.606090	−0.303045	+	0.952976i	$0.598003\pi$
$740$	−7.50465	−0.275876
$741$	13.9661	0.513057
$742$	0	0
$743$	32.5460	1.19400	0.596999	−	0.802242i	$-0.296359\pi$
$743$	32.5460	1.19400	0.596999	+	0.802242i	$0.296359\pi$
$744$	3.90717	0.143244
$745$	−24.0416	−0.880814
$746$	0.281667	0.0103126
$747$	−13.5325	−0.495129
$748$	−2.20729	−0.0807066
$749$	0	0
$750$	−2.18721	−0.0798656
$751$	−44.7310	−1.63226	−0.816128	−	0.577871i	$-0.803884\pi$
$751$	−44.7310	−1.63226	−0.816128	+	0.577871i	$0.803884\pi$
$752$	55.5627	2.02616
$753$	13.1199	0.478117
$754$	−22.4797	−0.818663
$755$	5.75963	0.209614
$756$	0	0
$757$	45.0981	1.63912	0.819560	−	0.572994i	$-0.194218\pi$
$757$	45.0981	1.63912	0.819560	+	0.572994i	$0.194218\pi$
$758$	21.2089	0.770342
$759$	−5.95008	−0.215974
$760$	−3.53590	−0.128261
$761$	−41.5662	−1.50677	−0.753387	−	0.657578i	$-0.771581\pi$
$761$	−41.5662	−1.50677	−0.753387	+	0.657578i	$0.771581\pi$
$762$	−28.9838	−1.04997
$763$	0	0
$764$	−11.1948	−0.405014
$765$	2.64547	0.0956473
$766$	37.6821	1.36151
$767$	12.9699	0.468314
$768$	25.1410	0.907197
$769$	−25.0246	−0.902409	−0.451205	−	0.892421i	$-0.649006\pi$
$769$	−25.0246	−0.902409	−0.451205	+	0.892421i	$0.649006\pi$
$770$	0	0
$771$	−26.0437	−0.937941
$772$	−13.6827	−0.492451
$773$	−7.08947	−0.254990	−0.127495	−	0.991839i	$-0.540694\pi$
$773$	−7.08947	−0.254990	−0.127495	+	0.991839i	$0.540694\pi$
$774$	20.7156	0.744606
$775$	−2.51530	−0.0903524
$776$	−2.07844	−0.0746118
$777$	0	0
$778$	41.9716	1.50475
$779$	23.5408	0.843438
$780$	6.56240	0.234972
$781$	−1.33972	−0.0479389
$782$	15.3158	0.547692
$783$	−16.1024	−0.575454
$784$	0	0
$785$	−9.83002	−0.350849
$786$	21.3157	0.760306
$787$	−1.08098	−0.0385327	−0.0192663	−	0.999814i	$-0.506133\pi$
$787$	−1.08098	−0.0385327	−0.0192663	+	0.999814i	$0.506133\pi$
$788$	18.4962	0.658901
$789$	−30.7864	−1.09602
$790$	−22.3081	−0.793687
$791$	0	0
$792$	−1.99128	−0.0707569
$793$	34.1951	1.21430
$794$	−31.8558	−1.13052
$795$	14.5939	0.517592
$796$	−26.1452	−0.926691
$797$	−38.2991	−1.35662	−0.678311	−	0.734775i	$-0.737288\pi$
$797$	−38.2991	−1.35662	−0.678311	+	0.734775i	$0.737288\pi$
$798$	0	0
$799$	−19.3423	−0.684282
$800$	−6.34027	−0.224163
$801$	−9.66150	−0.341372
$802$	−25.9709	−0.917063
$803$	9.74210	0.343791
$804$	2.81731	0.0993588
$805$	0	0
$806$	19.2491	0.678020
$807$	−17.2692	−0.607905
$808$	1.60892	0.0566016
$809$	−24.0489	−0.845514	−0.422757	−	0.906243i	$-0.638938\pi$
$809$	−24.0489	−0.845514	−0.422757	+	0.906243i	$0.638938\pi$
$810$	3.57831	0.125729
$811$	−29.5223	−1.03667	−0.518334	−	0.855178i	$-0.673448\pi$
$811$	−29.5223	−1.03667	−0.518334	+	0.855178i	$0.673448\pi$
$812$	0	0
$813$	18.4959	0.648679
$814$	−10.5534	−0.369897
$815$	−5.33020	−0.186709
$816$	−10.1451	−0.355150
$817$	20.2806	0.709529
$818$	19.4491	0.680021
$819$	0	0
$820$	11.0614	0.386280
$821$	−18.2593	−0.637255	−0.318628	−	0.947880i	$-0.603222\pi$
$821$	−18.2593	−0.637255	−0.318628	+	0.947880i	$0.603222\pi$
$822$	2.46456	0.0859612
$823$	5.58542	0.194695	0.0973477	−	0.995250i	$-0.468964\pi$
$823$	5.58542	0.194695	0.0973477	+	0.995250i	$0.468964\pi$
$824$	−20.7612	−0.723252
$825$	−1.20588	−0.0419835
$826$	0	0
$827$	16.0067	0.556609	0.278304	−	0.960493i	$-0.410228\pi$
$827$	16.0067	0.556609	0.278304	+	0.960493i	$0.410228\pi$
$828$	−9.83793	−0.341892
$829$	42.2753	1.46828	0.734141	−	0.678997i	$-0.237585\pi$
$829$	42.2753	1.46828	0.734141	+	0.678997i	$0.237585\pi$
$830$	−15.8781	−0.551136
$831$	35.7964	1.24176
$832$	7.03699	0.243964
$833$	0	0
$834$	15.9119	0.550983
$835$	15.7355	0.544548
$836$	3.54043	0.122448
$837$	13.7883	0.476593
$838$	46.2711	1.59841
$839$	−46.1099	−1.59189	−0.795945	−	0.605369i	$-0.793025\pi$
$839$	−46.1099	−1.59189	−0.795945	+	0.605369i	$0.793025\pi$
$840$	0	0
$841$	−20.3714	−0.702460
$842$	−40.6007	−1.39919
$843$	−3.04185	−0.104767
$844$	−32.8635	−1.13121
$845$	−4.80204	−0.165195
$846$	31.6898	1.08952
$847$	0	0
$848$	59.4948	2.04306
$849$	−13.7122	−0.470603
$850$	3.10401	0.106467
$851$	28.7095	0.984148
$852$	2.08373	0.0713873
$853$	44.7096	1.53083	0.765413	−	0.643539i	$-0.222535\pi$
$853$	44.7096	1.53083	0.765413	+	0.643539i	$0.222535\pi$
$854$	0	0
$855$	−4.24325	−0.145116
$856$	−11.1088	−0.379691
$857$	22.5792	0.771291	0.385646	−	0.922647i	$-0.373979\pi$
$857$	22.5792	0.771291	0.385646	+	0.922647i	$0.373979\pi$
$858$	9.22838	0.315052
$859$	35.6627	1.21679	0.608397	−	0.793633i	$-0.291813\pi$
$859$	35.6627	1.21679	0.608397	+	0.793633i	$0.291813\pi$
$860$	9.52948	0.324953
$861$	0	0
$862$	−16.2267	−0.552684
$863$	5.34099	0.181809	0.0909047	−	0.995860i	$-0.471024\pi$
$863$	5.34099	0.181809	0.0909047	+	0.995860i	$0.471024\pi$
$864$	34.7559	1.18242
$865$	9.92979	0.337623
$866$	−42.4837	−1.44365
$867$	−16.9684	−0.576276
$868$	0	0
$869$	−12.2992	−0.417223
$870$	−6.42483	−0.217822
$871$	−7.64260	−0.258960
$872$	6.68707	0.226453
$873$	−2.49423	−0.0844170
$874$	−24.5661	−0.830959
$875$	0	0
$876$	−15.1524	−0.511951
$877$	−16.2061	−0.547240	−0.273620	−	0.961838i	$-0.588221\pi$
$877$	−16.2061	−0.547240	−0.273620	+	0.961838i	$0.588221\pi$
$878$	11.1770	0.377207
$879$	−28.5427	−0.962723
$880$	−4.91602	−0.165719
$881$	−0.397150	−0.0133803	−0.00669016	−	0.999978i	$-0.502130\pi$
$881$	−0.397150	−0.0133803	−0.00669016	+	0.999978i	$0.502130\pi$
$882$	0	0
$883$	3.27601	0.110247	0.0551233	−	0.998480i	$-0.482445\pi$
$883$	3.27601	0.110247	0.0551233	+	0.998480i	$0.482445\pi$
$884$	−9.31311	−0.313234
$885$	3.70686	0.124605
$886$	−64.6037	−2.17041
$887$	24.6061	0.826193	0.413097	−	0.910687i	$-0.364447\pi$
$887$	24.6061	0.826193	0.413097	+	0.910687i	$0.364447\pi$
$888$	−9.03817	−0.303301
$889$	0	0
$890$	−11.3361	−0.379987
$891$	1.97285	0.0660929
$892$	−21.0738	−0.705604
$893$	31.0245	1.03819
$894$	52.5839	1.75867
$895$	−8.82663	−0.295042
$896$	0	0
$897$	−25.1048	−0.838226
$898$	−13.4875	−0.450085
$899$	−7.38859	−0.246423
$900$	−1.99382	−0.0664608
$901$	−20.7111	−0.689988
$902$	15.5551	0.517928
$903$	0	0
$904$	−19.6349	−0.653046
$905$	8.21285	0.273004
$906$	−12.5975	−0.418525
$907$	27.3827	0.909226	0.454613	−	0.890689i	$-0.349777\pi$
$907$	27.3827	0.909226	0.454613	+	0.890689i	$0.349777\pi$
$908$	1.20279	0.0399160
$909$	1.93078	0.0640399
$910$	0	0
$911$	47.8954	1.58684	0.793422	−	0.608671i	$-0.208297\pi$
$911$	47.8954	1.58684	0.793422	+	0.608671i	$0.208297\pi$
$912$	16.2725	0.538835
$913$	−8.75414	−0.289720
$914$	67.3947	2.22922
$915$	9.77316	0.323091
$916$	18.9267	0.625356
$917$	0	0
$918$	−17.0154	−0.561593
$919$	21.4494	0.707551	0.353776	−	0.935330i	$-0.384898\pi$
$919$	21.4494	0.707551	0.353776	+	0.935330i	$0.384898\pi$
$920$	6.35599	0.209551
$921$	−12.5611	−0.413903
$922$	27.3774	0.901627
$923$	−5.65260	−0.186058
$924$	0	0
$925$	5.81846	0.191310
$926$	44.5652	1.46450
$927$	−24.9145	−0.818299
$928$	−18.6243	−0.611372
$929$	−33.5511	−1.10078	−0.550388	−	0.834909i	$-0.685520\pi$
$929$	−33.5511	−1.10078	−0.550388	+	0.834909i	$0.685520\pi$
$930$	5.50150	0.180401
$931$	0	0
$932$	0.948518	0.0310697
$933$	−5.78387	−0.189355
$934$	−40.4859	−1.32474
$935$	1.71135	0.0559671
$936$	−8.40168	−0.274618
$937$	−9.83847	−0.321409	−0.160704	−	0.987003i	$-0.551377\pi$
$937$	−9.83847	−0.321409	−0.160704	+	0.987003i	$0.551377\pi$
$938$	0	0
$939$	21.3104	0.695437
$940$	14.5778	0.475476
$941$	−42.6044	−1.38886	−0.694431	−	0.719559i	$-0.744344\pi$
$941$	−42.6044	−1.38886	−0.694431	+	0.719559i	$0.744344\pi$
$942$	21.5003	0.700518
$943$	−42.3160	−1.37800
$944$	15.1117	0.491844
$945$	0	0
$946$	13.4008	0.435699
$947$	−18.1764	−0.590653	−0.295326	−	0.955396i	$-0.595428\pi$
$947$	−18.1764	−0.590653	−0.295326	+	0.955396i	$0.595428\pi$
$948$	19.1296	0.621300
$949$	41.1043	1.33430
$950$	−4.97873	−0.161531
$951$	15.7044	0.509250
$952$	0	0
$953$	16.7503	0.542594	0.271297	−	0.962496i	$-0.412547\pi$
$953$	16.7503	0.542594	0.271297	+	0.962496i	$0.412547\pi$
$954$	33.9324	1.09860
$955$	8.67950	0.280862
$956$	−27.3786	−0.885488
$957$	−3.54223	−0.114504
$958$	23.9425	0.773548
$959$	0	0
$960$	2.01121	0.0649116
$961$	−24.6732	−0.795911
$962$	−44.5275	−1.43562
$963$	−13.3311	−0.429588
$964$	27.6205	0.889597
$965$	10.6084	0.341496
$966$	0	0
$967$	41.9573	1.34926	0.674628	−	0.738158i	$-0.264304\pi$
$967$	41.9573	1.34926	0.674628	+	0.738158i	$0.264304\pi$
$968$	−1.28815	−0.0414027
$969$	−5.66471	−0.181977
$970$	−2.92655	−0.0939660
$971$	23.7863	0.763340	0.381670	−	0.924299i	$-0.375349\pi$
$971$	23.7863	0.763340	0.381670	+	0.924299i	$0.375349\pi$
$972$	18.1426	0.581925
$973$	0	0
$974$	−3.89132	−0.124686
$975$	−5.08792	−0.162944
$976$	39.8421	1.27532
$977$	22.2591	0.712132	0.356066	−	0.934461i	$-0.384118\pi$
$977$	22.2591	0.712132	0.356066	+	0.934461i	$0.384118\pi$
$978$	11.6583	0.372790
$979$	−6.24999	−0.199751
$980$	0	0
$981$	8.02481	0.256212
$982$	−14.1278	−0.450837
$983$	−55.8969	−1.78283	−0.891417	−	0.453184i	$-0.850288\pi$
$983$	−55.8969	−1.78283	−0.891417	+	0.453184i	$0.850288\pi$
$984$	13.3217	0.424681
$985$	−14.3404	−0.456924
$986$	9.11789	0.290373
$987$	0	0
$988$	14.9379	0.475239
$989$	−36.4556	−1.15922
$990$	−2.80382	−0.0891112
$991$	21.5890	0.685798	0.342899	−	0.939372i	$-0.388591\pi$
$991$	21.5890	0.685798	0.342899	+	0.939372i	$0.388591\pi$
$992$	15.9477	0.506340
$993$	−31.0096	−0.984058
$994$	0	0
$995$	20.2707	0.642626
$996$	13.6157	0.431431
$997$	18.4228	0.583455	0.291728	−	0.956501i	$-0.405770\pi$
$997$	18.4228	0.583455	0.291728	+	0.956501i	$0.405770\pi$
$998$	63.4974	2.00998
$999$	−31.8954	−1.00913

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.2.a.w.1.8	✓	10
7.6	odd	2		2695.2.a.x.1.8	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2695.2.a.w.1.8	✓	10	1.1	even	1	trivial
2695.2.a.x.1.8	yes	10	7.6	odd	2

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:	\( N \)	\(=\)	\( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2695.a (trivial)

\(f(q)\)	\(=\)	\(q+1.81378 q^{2} +1.20588 q^{3} +1.28980 q^{4} -1.00000 q^{5} +2.18721 q^{6} -1.28815 q^{8} -1.54584 q^{9} +O(q^{10})\)	\(q+1.81378 q^{2} +1.20588 q^{3} +1.28980 q^{4} -1.00000 q^{5} +2.18721 q^{6} -1.28815 q^{8} -1.54584 q^{9} -1.81378 q^{10} -1.00000 q^{11} +1.55535 q^{12} -4.21925 q^{13} -1.20588 q^{15} -4.91602 q^{16} +1.71135 q^{17} -2.80382 q^{18} -2.74495 q^{19} -1.28980 q^{20} -1.81378 q^{22} +4.93420 q^{23} -1.55336 q^{24} +1.00000 q^{25} -7.65278 q^{26} -5.48176 q^{27} +2.93746 q^{29} -2.18721 q^{30} -2.51530 q^{31} -6.34027 q^{32} -1.20588 q^{33} +3.10401 q^{34} -1.99382 q^{36} +5.81846 q^{37} -4.97873 q^{38} -5.08792 q^{39} +1.28815 q^{40} -8.57606 q^{41} -7.38835 q^{43} -1.28980 q^{44} +1.54584 q^{45} +8.94956 q^{46} -11.3024 q^{47} -5.92815 q^{48} +1.81378 q^{50} +2.06369 q^{51} -5.44198 q^{52} -12.1022 q^{53} -9.94271 q^{54} +1.00000 q^{55} -3.31009 q^{57} +5.32790 q^{58} -3.07397 q^{59} -1.55535 q^{60} -8.10455 q^{61} -4.56221 q^{62} -1.66783 q^{64} +4.21925 q^{65} -2.18721 q^{66} +1.81137 q^{67} +2.20729 q^{68} +5.95008 q^{69} +1.33972 q^{71} +1.99128 q^{72} -9.74210 q^{73} +10.5534 q^{74} +1.20588 q^{75} -3.54043 q^{76} -9.22838 q^{78} +12.2992 q^{79} +4.91602 q^{80} -1.97285 q^{81} -15.5551 q^{82} +8.75414 q^{83} -1.71135 q^{85} -13.4008 q^{86} +3.54223 q^{87} +1.28815 q^{88} +6.24999 q^{89} +2.80382 q^{90} +6.36412 q^{92} -3.03317 q^{93} -20.5000 q^{94} +2.74495 q^{95} -7.64564 q^{96} +1.61351 q^{97} +1.54584 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 10 q^{4} - 10 q^{5} - 4 q^{6} + 6 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 + 10 * q^4 - 10 * q^5 - 4 * q^6 + 6 * q^8 + 10 * q^9	\( 10 q + 2 q^{2} + 10 q^{4} - 10 q^{5} - 4 q^{6} + 6 q^{8} + 10 q^{9} - 2 q^{10} - 10 q^{11} - 4 q^{12} - 8 q^{13} + 6 q^{16} - 28 q^{17} - 10 q^{18} - 8 q^{19} - 10 q^{20} - 2 q^{22} - 8 q^{23} - 32 q^{24} + 10 q^{25} - 12 q^{26} - 8 q^{29} + 4 q^{30} + 4 q^{31} + 14 q^{32} - 20 q^{34} - 22 q^{36} + 28 q^{37} - 24 q^{38} - 24 q^{39} - 6 q^{40} - 44 q^{41} + 20 q^{43} - 10 q^{44} - 10 q^{45} - 12 q^{46} - 12 q^{47} - 16 q^{48} + 2 q^{50} - 4 q^{51} - 36 q^{52} + 8 q^{54} + 10 q^{55} + 12 q^{57} - 8 q^{58} - 16 q^{59} + 4 q^{60} - 16 q^{61} - 36 q^{62} - 34 q^{64} + 8 q^{65} + 4 q^{66} + 20 q^{67} - 8 q^{68} - 4 q^{69} - 4 q^{71} + 10 q^{72} - 20 q^{73} - 16 q^{74} - 4 q^{76} + 52 q^{78} - 20 q^{79} - 6 q^{80} + 10 q^{81} + 32 q^{82} - 16 q^{83} + 28 q^{85} - 20 q^{86} - 20 q^{87} - 6 q^{88} - 44 q^{89} + 10 q^{90} - 24 q^{92} + 16 q^{93} - 24 q^{94} + 8 q^{95} + 4 q^{97} - 10 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 10 * q^4 - 10 * q^5 - 4 * q^6 + 6 * q^8 + 10 * q^9 - 2 * q^10 - 10 * q^11 - 4 * q^12 - 8 * q^13 + 6 * q^16 - 28 * q^17 - 10 * q^18 - 8 * q^19 - 10 * q^20 - 2 * q^22 - 8 * q^23 - 32 * q^24 + 10 * q^25 - 12 * q^26 - 8 * q^29 + 4 * q^30 + 4 * q^31 + 14 * q^32 - 20 * q^34 - 22 * q^36 + 28 * q^37 - 24 * q^38 - 24 * q^39 - 6 * q^40 - 44 * q^41 + 20 * q^43 - 10 * q^44 - 10 * q^45 - 12 * q^46 - 12 * q^47 - 16 * q^48 + 2 * q^50 - 4 * q^51 - 36 * q^52 + 8 * q^54 + 10 * q^55 + 12 * q^57 - 8 * q^58 - 16 * q^59 + 4 * q^60 - 16 * q^61 - 36 * q^62 - 34 * q^64 + 8 * q^65 + 4 * q^66 + 20 * q^67 - 8 * q^68 - 4 * q^69 - 4 * q^71 + 10 * q^72 - 20 * q^73 - 16 * q^74 - 4 * q^76 + 52 * q^78 - 20 * q^79 - 6 * q^80 + 10 * q^81 + 32 * q^82 - 16 * q^83 + 28 * q^85 - 20 * q^86 - 20 * q^87 - 6 * q^88 - 44 * q^89 + 10 * q^90 - 24 * q^92 + 16 * q^93 - 24 * q^94 + 8 * q^95 + 4 * q^97 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more