LMFDB - Embedded newform 2695.2.a.g.1.3

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:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 385)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.311108$ 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)

$f(q)$	$=$	$q+1.21432 q^{2} +0.688892 q^{3} -0.525428 q^{4} +1.00000 q^{5} +0.836535 q^{6} -3.06668 q^{8} -2.52543 q^{9} +O(q^{10})$	\(q+1.21432 q^{2} +0.688892 q^{3} -0.525428 q^{4} +1.00000 q^{5} +0.836535 q^{6} -3.06668 q^{8} -2.52543 q^{9} +1.21432 q^{10} -1.00000 q^{11} -0.361963 q^{12} +3.73975 q^{13} +0.688892 q^{15} -2.67307 q^{16} -0.0666765 q^{17} -3.06668 q^{18} -6.42864 q^{19} -0.525428 q^{20} -1.21432 q^{22} -1.09679 q^{23} -2.11261 q^{24} +1.00000 q^{25} +4.54125 q^{26} -3.80642 q^{27} -7.80642 q^{29} +0.836535 q^{30} +5.59210 q^{31} +2.88739 q^{32} -0.688892 q^{33} -0.0809666 q^{34} +1.32693 q^{36} +1.33185 q^{37} -7.80642 q^{38} +2.57628 q^{39} -3.06668 q^{40} -6.64296 q^{41} -11.7605 q^{43} +0.525428 q^{44} -2.52543 q^{45} -1.33185 q^{46} +2.26025 q^{47} -1.84146 q^{48} +1.21432 q^{50} -0.0459330 q^{51} -1.96497 q^{52} -1.71900 q^{53} -4.62222 q^{54} -1.00000 q^{55} -4.42864 q^{57} -9.47949 q^{58} -2.54125 q^{59} -0.361963 q^{60} -14.4494 q^{61} +6.79060 q^{62} +8.85236 q^{64} +3.73975 q^{65} -0.836535 q^{66} +10.3827 q^{67} +0.0350337 q^{68} -0.755569 q^{69} -12.5620 q^{71} +7.74467 q^{72} -1.17775 q^{73} +1.61729 q^{74} +0.688892 q^{75} +3.37778 q^{76} +3.12843 q^{78} -8.51606 q^{79} -2.67307 q^{80} +4.95407 q^{81} -8.06668 q^{82} +12.1017 q^{83} -0.0666765 q^{85} -14.2810 q^{86} -5.37778 q^{87} +3.06668 q^{88} -15.6128 q^{89} -3.06668 q^{90} +0.576283 q^{92} +3.85236 q^{93} +2.74467 q^{94} -6.42864 q^{95} +1.98910 q^{96} +13.4193 q^{97} +2.52543 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 2 q^{3} + 5 q^{4} + 3 q^{5} - 4 q^{6} - 9 q^{8} - q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 2 * q^3 + 5 * q^4 + 3 * q^5 - 4 * q^6 - 9 * q^8 - q^9	$ 3 q - 3 q^{2} + 2 q^{3} + 5 q^{4} + 3 q^{5} - 4 q^{6} - 9 q^{8} - q^{9} - 3 q^{10} - 3 q^{11} + 12 q^{12} - 2 q^{13} + 2 q^{15} + 5 q^{16} - 9 q^{18} - 6 q^{19} + 5 q^{20} + 3 q^{22} - 10 q^{23} - 26 q^{24} + 3 q^{25} + 20 q^{26} + 2 q^{27} - 10 q^{29} - 4 q^{30} + 10 q^{31} - 11 q^{32} - 2 q^{33} + 6 q^{34} + 17 q^{36} - 16 q^{37} - 10 q^{38} - 12 q^{39} - 9 q^{40} - 2 q^{43} - 5 q^{44} - q^{45} + 16 q^{46} + 20 q^{47} + 34 q^{48} - 3 q^{50} - 20 q^{51} - 32 q^{52} - 12 q^{53} - 14 q^{54} - 3 q^{55} - 2 q^{58} - 14 q^{59} + 12 q^{60} - 10 q^{61} - 6 q^{62} + 33 q^{64} - 2 q^{65} + 4 q^{66} - 2 q^{67} - 26 q^{68} - 2 q^{69} - 24 q^{71} - 23 q^{72} - 4 q^{73} + 38 q^{74} + 2 q^{75} + 10 q^{76} + 42 q^{78} + 8 q^{79} + 5 q^{80} - 5 q^{81} - 24 q^{82} + 10 q^{83} - 36 q^{86} - 16 q^{87} + 9 q^{88} - 20 q^{89} - 9 q^{90} - 18 q^{92} + 18 q^{93} - 38 q^{94} - 6 q^{95} - 40 q^{96} + q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 2 * q^3 + 5 * q^4 + 3 * q^5 - 4 * q^6 - 9 * q^8 - q^9 - 3 * q^10 - 3 * q^11 + 12 * q^12 - 2 * q^13 + 2 * q^15 + 5 * q^16 - 9 * q^18 - 6 * q^19 + 5 * q^20 + 3 * q^22 - 10 * q^23 - 26 * q^24 + 3 * q^25 + 20 * q^26 + 2 * q^27 - 10 * q^29 - 4 * q^30 + 10 * q^31 - 11 * q^32 - 2 * q^33 + 6 * q^34 + 17 * q^36 - 16 * q^37 - 10 * q^38 - 12 * q^39 - 9 * q^40 - 2 * q^43 - 5 * q^44 - q^45 + 16 * q^46 + 20 * q^47 + 34 * q^48 - 3 * q^50 - 20 * q^51 - 32 * q^52 - 12 * q^53 - 14 * q^54 - 3 * q^55 - 2 * q^58 - 14 * q^59 + 12 * q^60 - 10 * q^61 - 6 * q^62 + 33 * q^64 - 2 * q^65 + 4 * q^66 - 2 * q^67 - 26 * q^68 - 2 * q^69 - 24 * q^71 - 23 * q^72 - 4 * q^73 + 38 * q^74 + 2 * q^75 + 10 * q^76 + 42 * q^78 + 8 * q^79 + 5 * q^80 - 5 * q^81 - 24 * q^82 + 10 * q^83 - 36 * q^86 - 16 * q^87 + 9 * q^88 - 20 * q^89 - 9 * q^90 - 18 * q^92 + 18 * q^93 - 38 * q^94 - 6 * q^95 - 40 * q^96 + 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 $

$2$	1.21432	0.858654	0.429327	−	0.903149i	$-0.358751\pi$
$2$	1.21432	0.858654	0.429327	+	0.903149i	$0.358751\pi$
$3$	0.688892	0.397732	0.198866	−	0.980027i	$-0.436274\pi$
$3$	0.688892	0.397732	0.198866	+	0.980027i	$0.436274\pi$
$4$	−0.525428	−0.262714
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.836535	0.341514
$7$	0	0
$7$	0	0
$8$	−3.06668	−1.08423
$9$	−2.52543	−0.841809
$10$	1.21432	0.384002
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.361963	−0.104490
$13$	3.73975	1.03722	0.518610	−	0.855011i	$-0.326450\pi$
$13$	3.73975	1.03722	0.518610	+	0.855011i	$0.326450\pi$
$14$	0	0
$15$	0.688892	0.177871
$16$	−2.67307	−0.668268
$17$	−0.0666765	−0.0161714	−0.00808572	−	0.999967i	$-0.502574\pi$
$17$	−0.0666765	−0.0161714	−0.00808572	+	0.999967i	$0.502574\pi$
$18$	−3.06668	−0.722823
$19$	−6.42864	−1.47483	−0.737416	−	0.675439i	$-0.763954\pi$
$19$	−6.42864	−1.47483	−0.737416	+	0.675439i	$0.763954\pi$
$20$	−0.525428	−0.117489
$21$	0	0
$22$	−1.21432	−0.258894
$23$	−1.09679	−0.228696	−0.114348	−	0.993441i	$-0.536478\pi$
$23$	−1.09679	−0.228696	−0.114348	+	0.993441i	$0.536478\pi$
$24$	−2.11261	−0.431235
$25$	1.00000	0.200000
$26$	4.54125	0.890612
$27$	−3.80642	−0.732547
$28$	0	0
$29$	−7.80642	−1.44962	−0.724808	−	0.688951i	$-0.758072\pi$
$29$	−7.80642	−1.44962	−0.724808	+	0.688951i	$0.758072\pi$
$30$	0.836535	0.152730
$31$	5.59210	1.00437	0.502186	−	0.864760i	$-0.332529\pi$
$31$	5.59210	1.00437	0.502186	+	0.864760i	$0.332529\pi$
$32$	2.88739	0.510423
$33$	−0.688892	−0.119921
$34$	−0.0809666	−0.0138857
$35$	0	0
$36$	1.32693	0.221155
$37$	1.33185	0.218955	0.109478	−	0.993989i	$-0.465082\pi$
$37$	1.33185	0.218955	0.109478	+	0.993989i	$0.465082\pi$
$38$	−7.80642	−1.26637
$39$	2.57628	0.412535
$40$	−3.06668	−0.484884
$41$	−6.64296	−1.03746	−0.518728	−	0.854939i	$-0.673594\pi$
$41$	−6.64296	−1.03746	−0.518728	+	0.854939i	$0.673594\pi$
$42$	0	0
$43$	−11.7605	−1.79346	−0.896729	−	0.442580i	$-0.854063\pi$
$43$	−11.7605	−1.79346	−0.896729	+	0.442580i	$0.854063\pi$
$44$	0.525428	0.0792112
$45$	−2.52543	−0.376469
$46$	−1.33185	−0.196371
$47$	2.26025	0.329692	0.164846	−	0.986319i	$-0.447287\pi$
$47$	2.26025	0.329692	0.164846	+	0.986319i	$0.447287\pi$
$48$	−1.84146	−0.265792
$49$	0	0
$50$	1.21432	0.171731
$51$	−0.0459330	−0.00643190
$52$	−1.96497	−0.272492
$53$	−1.71900	−0.236123	−0.118062	−	0.993006i	$-0.537668\pi$
$53$	−1.71900	−0.236123	−0.118062	+	0.993006i	$0.537668\pi$
$54$	−4.62222	−0.629004
$55$	−1.00000	−0.134840
$56$	0	0
$57$	−4.42864	−0.586588
$58$	−9.47949	−1.24472
$59$	−2.54125	−0.330842	−0.165421	−	0.986223i	$-0.552898\pi$
$59$	−2.54125	−0.330842	−0.165421	+	0.986223i	$0.552898\pi$
$60$	−0.361963	−0.0467292
$61$	−14.4494	−1.85005	−0.925027	−	0.379901i	$-0.875958\pi$
$61$	−14.4494	−1.85005	−0.925027	+	0.379901i	$0.875958\pi$
$62$	6.79060	0.862407
$63$	0	0
$64$	8.85236	1.10654
$65$	3.73975	0.463859
$66$	−0.836535	−0.102970
$67$	10.3827	1.26845	0.634225	−	0.773149i	$-0.281319\pi$
$67$	10.3827	1.26845	0.634225	+	0.773149i	$0.281319\pi$
$68$	0.0350337	0.00424846
$69$	−0.755569	−0.0909598
$70$	0	0
$71$	−12.5620	−1.49083	−0.745417	−	0.666598i	$-0.767750\pi$
$71$	−12.5620	−1.49083	−0.745417	+	0.666598i	$0.767750\pi$
$72$	7.74467	0.912718
$73$	−1.17775	−0.137846	−0.0689229	−	0.997622i	$-0.521956\pi$
$73$	−1.17775	−0.137846	−0.0689229	+	0.997622i	$0.521956\pi$
$74$	1.61729	0.188007
$75$	0.688892	0.0795464
$76$	3.37778	0.387458
$77$	0	0
$78$	3.12843	0.354225
$79$	−8.51606	−0.958132	−0.479066	−	0.877779i	$-0.659024\pi$
$79$	−8.51606	−0.958132	−0.479066	+	0.877779i	$0.659024\pi$
$80$	−2.67307	−0.298858
$81$	4.95407	0.550452
$82$	−8.06668	−0.890815
$83$	12.1017	1.32834	0.664168	−	0.747584i	$-0.268786\pi$
$83$	12.1017	1.32834	0.664168	+	0.747584i	$0.268786\pi$
$84$	0	0
$85$	−0.0666765	−0.00723209
$86$	−14.2810	−1.53996
$87$	−5.37778	−0.576559
$88$	3.06668	0.326909
$89$	−15.6128	−1.65496	−0.827479	−	0.561496i	$-0.810226\pi$
$89$	−15.6128	−1.65496	−0.827479	+	0.561496i	$0.810226\pi$
$90$	−3.06668	−0.323256
$91$	0	0
$92$	0.576283	0.0600816
$93$	3.85236	0.399471
$94$	2.74467	0.283091
$95$	−6.42864	−0.659564
$96$	1.98910	0.203012
$97$	13.4193	1.36252	0.681260	−	0.732041i	$-0.261432\pi$
$97$	13.4193	1.36252	0.681260	+	0.732041i	$0.261432\pi$
$98$	0	0
$99$	2.52543	0.253815
$100$	−0.525428	−0.0525428
$101$	8.44938	0.840745	0.420373	−	0.907352i	$-0.361899\pi$
$101$	8.44938	0.840745	0.420373	+	0.907352i	$0.361899\pi$
$102$	−0.0557773	−0.00552277
$103$	9.54617	0.940612	0.470306	−	0.882503i	$-0.344144\pi$
$103$	9.54617	0.940612	0.470306	+	0.882503i	$0.344144\pi$
$104$	−11.4686	−1.12459
$105$	0	0
$106$	−2.08742	−0.202748
$107$	−8.56199	−0.827719	−0.413860	−	0.910341i	$-0.635820\pi$
$107$	−8.56199	−0.827719	−0.413860	+	0.910341i	$0.635820\pi$
$108$	2.00000	0.192450
$109$	−6.99063	−0.669581	−0.334791	−	0.942293i	$-0.608666\pi$
$109$	−6.99063	−0.669581	−0.334791	+	0.942293i	$0.608666\pi$
$110$	−1.21432	−0.115781
$111$	0.917502	0.0870854
$112$	0	0
$113$	−1.57136	−0.147821	−0.0739106	−	0.997265i	$-0.523548\pi$
$113$	−1.57136	−0.147821	−0.0739106	+	0.997265i	$0.523548\pi$
$114$	−5.37778	−0.503676
$115$	−1.09679	−0.102276
$116$	4.10171	0.380834
$117$	−9.44446	−0.873141
$118$	−3.08589	−0.284079
$119$	0	0
$120$	−2.11261	−0.192854
$121$	1.00000	0.0909091
$122$	−17.5462	−1.58856
$123$	−4.57628	−0.412630
$124$	−2.93825	−0.263862
$125$	1.00000	0.0894427
$126$	0	0
$127$	−13.3778	−1.18709	−0.593543	−	0.804802i	$-0.702271\pi$
$127$	−13.3778	−1.18709	−0.593543	+	0.804802i	$0.702271\pi$
$128$	4.97481	0.439715
$129$	−8.10171	−0.713316
$130$	4.54125	0.398294
$131$	2.75557	0.240755	0.120378	−	0.992728i	$-0.461589\pi$
$131$	2.75557	0.240755	0.120378	+	0.992728i	$0.461589\pi$
$132$	0.361963	0.0315048
$133$	0	0
$134$	12.6079	1.08916
$135$	−3.80642	−0.327605
$136$	0.204475	0.0175336
$137$	−17.8938	−1.52877	−0.764387	−	0.644758i	$-0.776958\pi$
$137$	−17.8938	−1.52877	−0.764387	+	0.644758i	$0.776958\pi$
$138$	−0.917502	−0.0781030
$139$	3.86665	0.327965	0.163982	−	0.986463i	$-0.447566\pi$
$139$	3.86665	0.327965	0.163982	+	0.986463i	$0.447566\pi$
$140$	0	0
$141$	1.55707	0.131129
$142$	−15.2543	−1.28011
$143$	−3.73975	−0.312733
$144$	6.75065	0.562554
$145$	−7.80642	−0.648288
$146$	−1.43017	−0.118362
$147$	0	0
$148$	−0.699791	−0.0575225
$149$	4.88892	0.400516	0.200258	−	0.979743i	$-0.435822\pi$
$149$	4.88892	0.400516	0.200258	+	0.979743i	$0.435822\pi$
$150$	0.836535	0.0683028
$151$	22.1891	1.80573	0.902863	−	0.429929i	$-0.141461\pi$
$151$	22.1891	1.80573	0.902863	+	0.429929i	$0.141461\pi$
$152$	19.7146	1.59906
$153$	0.168387	0.0136133
$154$	0	0
$155$	5.59210	0.449169
$156$	−1.35365	−0.108379
$157$	4.81579	0.384342	0.192171	−	0.981361i	$-0.438447\pi$
$157$	4.81579	0.384342	0.192171	+	0.981361i	$0.438447\pi$
$158$	−10.3412	−0.822703
$159$	−1.18421	−0.0939138
$160$	2.88739	0.228268
$161$	0	0
$162$	6.01582	0.472648
$163$	6.08742	0.476804	0.238402	−	0.971167i	$-0.423376\pi$
$163$	6.08742	0.476804	0.238402	+	0.971167i	$0.423376\pi$
$164$	3.49039	0.272554
$165$	−0.688892	−0.0536302
$166$	14.6953	1.14058
$167$	3.67307	0.284231	0.142115	−	0.989850i	$-0.454610\pi$
$167$	3.67307	0.284231	0.142115	+	0.989850i	$0.454610\pi$
$168$	0	0
$169$	0.985710	0.0758238
$170$	−0.0809666	−0.00620986
$171$	16.2351	1.24153
$172$	6.17929	0.471166
$173$	0.628669	0.0477968	0.0238984	−	0.999714i	$-0.492392\pi$
$173$	0.628669	0.0477968	0.0238984	+	0.999714i	$0.492392\pi$
$174$	−6.53035	−0.495065
$175$	0	0
$176$	2.67307	0.201490
$177$	−1.75065	−0.131587
$178$	−18.9590	−1.42104
$179$	−7.70471	−0.575877	−0.287939	−	0.957649i	$-0.592970\pi$
$179$	−7.70471	−0.575877	−0.287939	+	0.957649i	$0.592970\pi$
$180$	1.32693	0.0989035
$181$	−10.9175	−0.811492	−0.405746	−	0.913986i	$-0.632988\pi$
$181$	−10.9175	−0.811492	−0.405746	+	0.913986i	$0.632988\pi$
$182$	0	0
$183$	−9.95407	−0.735826
$184$	3.36349	0.247960
$185$	1.33185	0.0979197
$186$	4.67799	0.343007
$187$	0.0666765	0.00487587
$188$	−1.18760	−0.0866146
$189$	0	0
$190$	−7.80642	−0.566338
$191$	−10.9175	−0.789963	−0.394981	−	0.918689i	$-0.629249\pi$
$191$	−10.9175	−0.789963	−0.394981	+	0.918689i	$0.629249\pi$
$192$	6.09832	0.440108
$193$	11.7003	0.842204	0.421102	−	0.907013i	$-0.361643\pi$
$193$	11.7003	0.842204	0.421102	+	0.907013i	$0.361643\pi$
$194$	16.2953	1.16993
$195$	2.57628	0.184491
$196$	0	0
$197$	10.8430	0.772531	0.386265	−	0.922388i	$-0.373765\pi$
$197$	10.8430	0.772531	0.386265	+	0.922388i	$0.373765\pi$
$198$	3.06668	0.217939
$199$	−2.08097	−0.147516	−0.0737579	−	0.997276i	$-0.523499\pi$
$199$	−2.08097	−0.147516	−0.0737579	+	0.997276i	$0.523499\pi$
$200$	−3.06668	−0.216847
$201$	7.15257	0.504503
$202$	10.2603	0.721909
$203$	0	0
$204$	0.0241344	0.00168975
$205$	−6.64296	−0.463964
$206$	11.5921	0.807660
$207$	2.76986	0.192518
$208$	−9.99661	−0.693140
$209$	6.42864	0.444678
$210$	0	0
$211$	23.0923	1.58974	0.794871	−	0.606778i	$-0.207538\pi$
$211$	23.0923	1.58974	0.794871	+	0.606778i	$0.207538\pi$
$212$	0.903212	0.0620328
$213$	−8.65386	−0.592953
$214$	−10.3970	−0.710724
$215$	−11.7605	−0.802059
$216$	11.6731	0.794252
$217$	0	0
$218$	−8.48886	−0.574938
$219$	−0.811346	−0.0548257
$220$	0.525428	0.0354243
$221$	−0.249353	−0.0167733
$222$	1.11414	0.0747762
$223$	21.5462	1.44284	0.721419	−	0.692499i	$-0.243490\pi$
$223$	21.5462	1.44284	0.721419	+	0.692499i	$0.243490\pi$
$224$	0	0
$225$	−2.52543	−0.168362
$226$	−1.90813	−0.126927
$227$	27.2257	1.80703	0.903516	−	0.428553i	$-0.140977\pi$
$227$	27.2257	1.80703	0.903516	+	0.428553i	$0.140977\pi$
$228$	2.32693	0.154105
$229$	−25.0005	−1.65208	−0.826039	−	0.563613i	$-0.809411\pi$
$229$	−25.0005	−1.65208	−0.826039	+	0.563613i	$0.809411\pi$
$230$	−1.33185	−0.0878197
$231$	0	0
$232$	23.9398	1.57172
$233$	−3.65878	−0.239695	−0.119847	−	0.992792i	$-0.538241\pi$
$233$	−3.65878	−0.239695	−0.119847	+	0.992792i	$0.538241\pi$
$234$	−11.4686	−0.749726
$235$	2.26025	0.147443
$236$	1.33524	0.0869169
$237$	−5.86665	−0.381080
$238$	0	0
$239$	14.7052	0.951200	0.475600	−	0.879662i	$-0.342231\pi$
$239$	14.7052	0.951200	0.475600	+	0.879662i	$0.342231\pi$
$240$	−1.84146	−0.118866
$241$	−13.6938	−0.882096	−0.441048	−	0.897483i	$-0.645393\pi$
$241$	−13.6938	−0.882096	−0.441048	+	0.897483i	$0.645393\pi$
$242$	1.21432	0.0780594
$243$	14.8321	0.951479
$244$	7.59210	0.486035
$245$	0	0
$246$	−5.55707	−0.354306
$247$	−24.0415	−1.52972
$248$	−17.1492	−1.08897
$249$	8.33677	0.528322
$250$	1.21432	0.0768003
$251$	11.0114	0.695032	0.347516	−	0.937674i	$-0.387025\pi$
$251$	11.0114	0.695032	0.347516	+	0.937674i	$0.387025\pi$
$252$	0	0
$253$	1.09679	0.0689545
$254$	−16.2449	−1.01930
$255$	−0.0459330	−0.00287643
$256$	−11.6637	−0.728981
$257$	15.9496	0.994910	0.497455	−	0.867490i	$-0.334268\pi$
$257$	15.9496	0.994910	0.497455	+	0.867490i	$0.334268\pi$
$258$	−9.83807	−0.612491
$259$	0	0
$260$	−1.96497	−0.121862
$261$	19.7146	1.22030
$262$	3.34614	0.206725
$263$	−5.11108	−0.315163	−0.157581	−	0.987506i	$-0.550370\pi$
$263$	−5.11108	−0.315163	−0.157581	+	0.987506i	$0.550370\pi$
$264$	2.11261	0.130022
$265$	−1.71900	−0.105598
$266$	0	0
$267$	−10.7556	−0.658230
$268$	−5.45536	−0.333239
$269$	18.2351	1.11181	0.555906	−	0.831245i	$-0.312372\pi$
$269$	18.2351	1.11181	0.555906	+	0.831245i	$0.312372\pi$
$270$	−4.62222	−0.281299
$271$	−6.23506	−0.378753	−0.189377	−	0.981905i	$-0.560647\pi$
$271$	−6.23506	−0.378753	−0.189377	+	0.981905i	$0.560647\pi$
$272$	0.178231	0.0108068
$273$	0	0
$274$	−21.7288	−1.31269
$275$	−1.00000	−0.0603023
$276$	0.396997	0.0238964
$277$	6.32248	0.379881	0.189941	−	0.981796i	$-0.439170\pi$
$277$	6.32248	0.379881	0.189941	+	0.981796i	$0.439170\pi$
$278$	4.69535	0.281608
$279$	−14.1225	−0.845489
$280$	0	0
$281$	−25.2257	−1.50484	−0.752419	−	0.658684i	$-0.771113\pi$
$281$	−25.2257	−1.50484	−0.752419	+	0.658684i	$0.771113\pi$
$282$	1.89078	0.112594
$283$	−13.4193	−0.797693	−0.398846	−	0.917018i	$-0.630589\pi$
$283$	−13.4193	−0.797693	−0.398846	+	0.917018i	$0.630589\pi$
$284$	6.60042	0.391663
$285$	−4.42864	−0.262330
$286$	−4.54125	−0.268530
$287$	0	0
$288$	−7.29190	−0.429679
$289$	−16.9956	−0.999738
$290$	−9.47949	−0.556655
$291$	9.24443	0.541918
$292$	0.618825	0.0362140
$293$	−17.6064	−1.02858	−0.514288	−	0.857617i	$-0.671944\pi$
$293$	−17.6064	−1.02858	−0.514288	+	0.857617i	$0.671944\pi$
$294$	0	0
$295$	−2.54125	−0.147957
$296$	−4.08436	−0.237398
$297$	3.80642	0.220871
$298$	5.93671	0.343905
$299$	−4.10171	−0.237208
$300$	−0.361963	−0.0208979
$301$	0	0
$302$	26.9447	1.55049
$303$	5.82071	0.334391
$304$	17.1842	0.985582
$305$	−14.4494	−0.827369
$306$	0.204475	0.0116891
$307$	−26.3368	−1.50312	−0.751560	−	0.659665i	$-0.770698\pi$
$307$	−26.3368	−1.50312	−0.751560	+	0.659665i	$0.770698\pi$
$308$	0	0
$309$	6.57628	0.374112
$310$	6.79060	0.385680
$311$	−5.96052	−0.337990	−0.168995	−	0.985617i	$-0.554052\pi$
$311$	−5.96052	−0.337990	−0.168995	+	0.985617i	$0.554052\pi$
$312$	−7.90063	−0.447285
$313$	5.52098	0.312064	0.156032	−	0.987752i	$-0.450130\pi$
$313$	5.52098	0.312064	0.156032	+	0.987752i	$0.450130\pi$
$314$	5.84791	0.330017
$315$	0	0
$316$	4.47457	0.251714
$317$	−15.7146	−0.882618	−0.441309	−	0.897355i	$-0.645486\pi$
$317$	−15.7146	−0.882618	−0.441309	+	0.897355i	$0.645486\pi$
$318$	−1.43801	−0.0806395
$319$	7.80642	0.437076
$320$	8.85236	0.494862
$321$	−5.89829	−0.329210
$322$	0	0
$323$	0.428639	0.0238501
$324$	−2.60300	−0.144611
$325$	3.73975	0.207444
$326$	7.39207	0.409409
$327$	−4.81579	−0.266314
$328$	20.3718	1.12484
$329$	0	0
$330$	−0.836535	−0.0460498
$331$	18.2351	1.00229	0.501145	−	0.865363i	$-0.332912\pi$
$331$	18.2351	1.00229	0.501145	+	0.865363i	$0.332912\pi$
$332$	−6.35857	−0.348972
$333$	−3.36349	−0.184318
$334$	4.46028	0.244056
$335$	10.3827	0.567268
$336$	0	0
$337$	32.2908	1.75899	0.879497	−	0.475904i	$-0.157879\pi$
$337$	32.2908	1.75899	0.879497	+	0.475904i	$0.157879\pi$
$338$	1.19697	0.0651064
$339$	−1.08250	−0.0587932
$340$	0.0350337	0.00189997
$341$	−5.59210	−0.302829
$342$	19.7146	1.06604
$343$	0	0
$344$	36.0656	1.94453
$345$	−0.755569	−0.0406785
$346$	0.763405	0.0410409
$347$	22.6909	1.21811	0.609056	−	0.793127i	$-0.291549\pi$
$347$	22.6909	1.21811	0.609056	+	0.793127i	$0.291549\pi$
$348$	2.82564	0.151470
$349$	−16.9097	−0.905154	−0.452577	−	0.891725i	$-0.649495\pi$
$349$	−16.9097	−0.905154	−0.452577	+	0.891725i	$0.649495\pi$
$350$	0	0
$351$	−14.2351	−0.759811
$352$	−2.88739	−0.153898
$353$	−24.3970	−1.29852	−0.649261	−	0.760566i	$-0.724922\pi$
$353$	−24.3970	−1.29852	−0.649261	+	0.760566i	$0.724922\pi$
$354$	−2.12584	−0.112987
$355$	−12.5620	−0.666721
$356$	8.20342	0.434780
$357$	0	0
$358$	−9.35599	−0.494479
$359$	−32.8113	−1.73172	−0.865858	−	0.500289i	$-0.833227\pi$
$359$	−32.8113	−1.73172	−0.865858	+	0.500289i	$0.833227\pi$
$360$	7.74467	0.408180
$361$	22.3274	1.17513
$362$	−13.2573	−0.696790
$363$	0.688892	0.0361575
$364$	0	0
$365$	−1.17775	−0.0616465
$366$	−12.0874	−0.631820
$367$	6.94269	0.362406	0.181203	−	0.983446i	$-0.442001\pi$
$367$	6.94269	0.362406	0.181203	+	0.983446i	$0.442001\pi$
$368$	2.93179	0.152830
$369$	16.7763	0.873340
$370$	1.61729	0.0840791
$371$	0	0
$372$	−2.02413	−0.104946
$373$	36.9733	1.91440	0.957202	−	0.289421i	$-0.0934627\pi$
$373$	36.9733	1.91440	0.957202	+	0.289421i	$0.0934627\pi$
$374$	0.0809666	0.00418669
$375$	0.688892	0.0355742
$376$	−6.93146	−0.357463
$377$	−29.1941	−1.50357
$378$	0	0
$379$	−23.6414	−1.21438	−0.607189	−	0.794557i	$-0.707703\pi$
$379$	−23.6414	−1.21438	−0.607189	+	0.794557i	$0.707703\pi$
$380$	3.37778	0.173277
$381$	−9.21585	−0.472142
$382$	−13.2573	−0.678304
$383$	−13.7210	−0.701111	−0.350555	−	0.936542i	$-0.614007\pi$
$383$	−13.7210	−0.701111	−0.350555	+	0.936542i	$0.614007\pi$
$384$	3.42711	0.174889
$385$	0	0
$386$	14.2079	0.723161
$387$	29.7003	1.50975
$388$	−7.05086	−0.357953
$389$	−15.5526	−0.788549	−0.394275	−	0.918993i	$-0.629004\pi$
$389$	−15.5526	−0.788549	−0.394275	+	0.918993i	$0.629004\pi$
$390$	3.12843	0.158414
$391$	0.0731300	0.00369835
$392$	0	0
$393$	1.89829	0.0957561
$394$	13.1669	0.663337
$395$	−8.51606	−0.428489
$396$	−1.32693	−0.0666807
$397$	0.253799	0.0127378	0.00636891	−	0.999980i	$-0.497973\pi$
$397$	0.253799	0.0127378	0.00636891	+	0.999980i	$0.497973\pi$
$398$	−2.52696	−0.126665
$399$	0	0
$400$	−2.67307	−0.133654
$401$	20.3684	1.01715	0.508575	−	0.861018i	$-0.330172\pi$
$401$	20.3684	1.01715	0.508575	+	0.861018i	$0.330172\pi$
$402$	8.68550	0.433193
$403$	20.9131	1.04175
$404$	−4.43954	−0.220875
$405$	4.95407	0.246170
$406$	0	0
$407$	−1.33185	−0.0660174
$408$	0.140862	0.00697368
$409$	−12.1225	−0.599417	−0.299708	−	0.954031i	$-0.596889\pi$
$409$	−12.1225	−0.599417	−0.299708	+	0.954031i	$0.596889\pi$
$410$	−8.06668	−0.398385
$411$	−12.3269	−0.608043
$412$	−5.01582	−0.247112
$413$	0	0
$414$	3.36349	0.165307
$415$	12.1017	0.594050
$416$	10.7981	0.529421
$417$	2.66370	0.130442
$418$	7.80642	0.381825
$419$	21.4400	1.04741	0.523707	−	0.851899i	$-0.324549\pi$
$419$	21.4400	1.04741	0.523707	+	0.851899i	$0.324549\pi$
$420$	0	0
$421$	29.8622	1.45539	0.727697	−	0.685898i	$-0.240591\pi$
$421$	29.8622	1.45539	0.727697	+	0.685898i	$0.240591\pi$
$422$	28.0415	1.36504
$423$	−5.70810	−0.277538
$424$	5.27163	0.256013
$425$	−0.0666765	−0.00323429
$426$	−10.5086	−0.509141
$427$	0	0
$428$	4.49871	0.217453
$429$	−2.57628	−0.124384
$430$	−14.2810	−0.688691
$431$	−19.6588	−0.946930	−0.473465	−	0.880813i	$-0.656997\pi$
$431$	−19.6588	−0.946930	−0.473465	+	0.880813i	$0.656997\pi$
$432$	10.1748	0.489537
$433$	32.9719	1.58453	0.792264	−	0.610178i	$-0.208902\pi$
$433$	32.9719	1.58453	0.792264	+	0.610178i	$0.208902\pi$
$434$	0	0
$435$	−5.37778	−0.257845
$436$	3.67307	0.175908
$437$	7.05086	0.337288
$438$	−0.985233	−0.0470763
$439$	0.815792	0.0389356	0.0194678	−	0.999810i	$-0.493803\pi$
$439$	0.815792	0.0389356	0.0194678	+	0.999810i	$0.493803\pi$
$440$	3.06668	0.146198
$441$	0	0
$442$	−0.302795	−0.0144025
$443$	24.9763	1.18666	0.593331	−	0.804959i	$-0.297813\pi$
$443$	24.9763	1.18666	0.593331	+	0.804959i	$0.297813\pi$
$444$	−0.482081	−0.0228785
$445$	−15.6128	−0.740120
$446$	26.1639	1.23890
$447$	3.36794	0.159298
$448$	0	0
$449$	0.414349	0.0195544	0.00977718	−	0.999952i	$-0.496888\pi$
$449$	0.414349	0.0195544	0.00977718	+	0.999952i	$0.496888\pi$
$450$	−3.06668	−0.144565
$451$	6.64296	0.312805
$452$	0.825636	0.0388347
$453$	15.2859	0.718195
$454$	33.0607	1.55162
$455$	0	0
$456$	13.5812	0.635998
$457$	9.33185	0.436526	0.218263	−	0.975890i	$-0.429961\pi$
$457$	9.33185	0.436526	0.218263	+	0.975890i	$0.429961\pi$
$458$	−30.3586	−1.41856
$459$	0.253799	0.0118463
$460$	0.576283	0.0268693
$461$	−29.9891	−1.39673	−0.698366	−	0.715741i	$-0.746089\pi$
$461$	−29.9891	−1.39673	−0.698366	+	0.715741i	$0.746089\pi$
$462$	0	0
$463$	−31.5353	−1.46557	−0.732784	−	0.680461i	$-0.761780\pi$
$463$	−31.5353	−1.46557	−0.732784	+	0.680461i	$0.761780\pi$
$464$	20.8671	0.968732
$465$	3.85236	0.178649
$466$	−4.44293	−0.205815
$467$	5.67952	0.262817	0.131409	−	0.991328i	$-0.458050\pi$
$467$	5.67952	0.262817	0.131409	+	0.991328i	$0.458050\pi$
$468$	4.96238	0.229386
$469$	0	0
$470$	2.74467	0.126602
$471$	3.31756	0.152865
$472$	7.79319	0.358711
$473$	11.7605	0.540748
$474$	−7.12399	−0.327215
$475$	−6.42864	−0.294966
$476$	0	0
$477$	4.34122	0.198771
$478$	17.8568	0.816751
$479$	39.4608	1.80301	0.901504	−	0.432771i	$-0.142464\pi$
$479$	39.4608	1.80301	0.901504	+	0.432771i	$0.142464\pi$
$480$	1.98910	0.0907896
$481$	4.98079	0.227104
$482$	−16.6287	−0.757415
$483$	0	0
$484$	−0.525428	−0.0238831
$485$	13.4193	0.609338
$486$	18.0109	0.816991
$487$	−3.19850	−0.144938	−0.0724689	−	0.997371i	$-0.523088\pi$
$487$	−3.19850	−0.144938	−0.0724689	+	0.997371i	$0.523088\pi$
$488$	44.3116	2.00589
$489$	4.19358	0.189640
$490$	0	0
$491$	26.3511	1.18921	0.594603	−	0.804019i	$-0.297309\pi$
$491$	26.3511	1.18921	0.594603	+	0.804019i	$0.297309\pi$
$492$	2.40451	0.108403
$493$	0.520505	0.0234424
$494$	−29.1941	−1.31350
$495$	2.52543	0.113510
$496$	−14.9481	−0.671189
$497$	0	0
$498$	10.1235	0.453645
$499$	3.52987	0.158019	0.0790094	−	0.996874i	$-0.474824\pi$
$499$	3.52987	0.158019	0.0790094	+	0.996874i	$0.474824\pi$
$500$	−0.525428	−0.0234978
$501$	2.53035	0.113048
$502$	13.3713	0.596792
$503$	−22.7368	−1.01379	−0.506893	−	0.862009i	$-0.669206\pi$
$503$	−22.7368	−1.01379	−0.506893	+	0.862009i	$0.669206\pi$
$504$	0	0
$505$	8.44938	0.375993
$506$	1.33185	0.0592080
$507$	0.679048	0.0301576
$508$	7.02906	0.311864
$509$	36.2351	1.60609	0.803045	−	0.595918i	$-0.203212\pi$
$509$	36.2351	1.60609	0.803045	+	0.595918i	$0.203212\pi$
$510$	−0.0557773	−0.00246986
$511$	0	0
$512$	−24.1131	−1.06566
$513$	24.4701	1.08038
$514$	19.3679	0.854283
$515$	9.54617	0.420655
$516$	4.25686	0.187398
$517$	−2.26025	−0.0994058
$518$	0	0
$519$	0.433085	0.0190103
$520$	−11.4686	−0.502931
$521$	6.79706	0.297784	0.148892	−	0.988853i	$-0.452429\pi$
$521$	6.79706	0.297784	0.148892	+	0.988853i	$0.452429\pi$
$522$	23.9398	1.04782
$523$	−34.0701	−1.48978	−0.744890	−	0.667187i	$-0.767498\pi$
$523$	−34.0701	−1.48978	−0.744890	+	0.667187i	$0.767498\pi$
$524$	−1.44785	−0.0632497
$525$	0	0
$526$	−6.20648	−0.270616
$527$	−0.372862	−0.0162421
$528$	1.84146	0.0801392
$529$	−21.7971	−0.947698
$530$	−2.08742	−0.0906717
$531$	6.41774	0.278506
$532$	0	0
$533$	−24.8430	−1.07607
$534$	−13.0607	−0.565192
$535$	−8.56199	−0.370167
$536$	−31.8404	−1.37530
$537$	−5.30772	−0.229045
$538$	22.1432	0.954661
$539$	0	0
$540$	2.00000	0.0860663
$541$	−27.1941	−1.16916	−0.584582	−	0.811335i	$-0.698741\pi$
$541$	−27.1941	−1.16916	−0.584582	+	0.811335i	$0.698741\pi$
$542$	−7.57136	−0.325218
$543$	−7.52098	−0.322756
$544$	−0.192521	−0.00825428
$545$	−6.99063	−0.299446
$546$	0	0
$547$	−40.2449	−1.72075	−0.860374	−	0.509663i	$-0.829770\pi$
$547$	−40.2449	−1.72075	−0.860374	+	0.509663i	$0.829770\pi$
$548$	9.40192	0.401630
$549$	36.4909	1.55739
$550$	−1.21432	−0.0517788
$551$	50.1847	2.13794
$552$	2.31708	0.0986217
$553$	0	0
$554$	7.67752	0.326186
$555$	0.917502	0.0389458
$556$	−2.03164	−0.0861608
$557$	−7.09679	−0.300701	−0.150350	−	0.988633i	$-0.548040\pi$
$557$	−7.09679	−0.300701	−0.150350	+	0.988633i	$0.548040\pi$
$558$	−17.1492	−0.725982
$559$	−43.9813	−1.86021
$560$	0	0
$561$	0.0459330	0.00193929
$562$	−30.6321	−1.29214
$563$	18.7971	0.792201	0.396101	−	0.918207i	$-0.370363\pi$
$563$	18.7971	0.792201	0.396101	+	0.918207i	$0.370363\pi$
$564$	−0.818128	−0.0344494
$565$	−1.57136	−0.0661076
$566$	−16.2953	−0.684942
$567$	0	0
$568$	38.5236	1.61641
$569$	−0.0316429	−0.00132654	−0.000663269	−	1.00000i	$-0.500211\pi$
$569$	−0.0316429	−0.00132654	−0.000663269		1.00000i	$0.500211\pi$
$570$	−5.37778	−0.225251
$571$	0.0503787	0.00210828	0.00105414	−	0.999999i	$-0.499664\pi$
$571$	0.0503787	0.00210828	0.00105414	+	0.999999i	$0.499664\pi$
$572$	1.96497	0.0821594
$573$	−7.52098	−0.314194
$574$	0	0
$575$	−1.09679	−0.0457392
$576$	−22.3560	−0.931499
$577$	13.6316	0.567490	0.283745	−	0.958900i	$-0.408423\pi$
$577$	13.6316	0.567490	0.283745	+	0.958900i	$0.408423\pi$
$578$	−20.6380	−0.858429
$579$	8.06022	0.334971
$580$	4.10171	0.170314
$581$	0	0
$582$	11.2257	0.465320
$583$	1.71900	0.0711939
$584$	3.61179	0.149457
$585$	−9.44446	−0.390480
$586$	−21.3798	−0.883191
$587$	−1.63804	−0.0676090	−0.0338045	−	0.999428i	$-0.510762\pi$
$587$	−1.63804	−0.0676090	−0.0338045	+	0.999428i	$0.510762\pi$
$588$	0	0
$589$	−35.9496	−1.48128
$590$	−3.08589	−0.127044
$591$	7.46965	0.307260
$592$	−3.56013	−0.146321
$593$	−8.46367	−0.347561	−0.173781	−	0.984784i	$-0.555598\pi$
$593$	−8.46367	−0.347561	−0.173781	+	0.984784i	$0.555598\pi$
$594$	4.62222	0.189652
$595$	0	0
$596$	−2.56877	−0.105221
$597$	−1.43356	−0.0586718
$598$	−4.98079	−0.203680
$599$	−26.9590	−1.10151	−0.550757	−	0.834665i	$-0.685661\pi$
$599$	−26.9590	−1.10151	−0.550757	+	0.834665i	$0.685661\pi$
$600$	−2.11261	−0.0862469
$601$	16.4909	0.672677	0.336338	−	0.941741i	$-0.390811\pi$
$601$	16.4909	0.672677	0.336338	+	0.941741i	$0.390811\pi$
$602$	0	0
$603$	−26.2208	−1.06779
$604$	−11.6588	−0.474389
$605$	1.00000	0.0406558
$606$	7.06821	0.287126
$607$	−19.5526	−0.793617	−0.396808	−	0.917902i	$-0.629882\pi$
$607$	−19.5526	−0.793617	−0.396808	+	0.917902i	$0.629882\pi$
$608$	−18.5620	−0.752788
$609$	0	0
$610$	−17.5462	−0.710424
$611$	8.45277	0.341963
$612$	−0.0884751	−0.00357639
$613$	−39.5955	−1.59925	−0.799623	−	0.600502i	$-0.794968\pi$
$613$	−39.5955	−1.59925	−0.799623	+	0.600502i	$0.794968\pi$
$614$	−31.9813	−1.29066
$615$	−4.57628	−0.184534
$616$	0	0
$617$	23.1669	0.932662	0.466331	−	0.884610i	$-0.345575\pi$
$617$	23.1669	0.932662	0.466331	+	0.884610i	$0.345575\pi$
$618$	7.98571	0.321232
$619$	−3.43017	−0.137870	−0.0689351	−	0.997621i	$-0.521960\pi$
$619$	−3.43017	−0.137870	−0.0689351	+	0.997621i	$0.521960\pi$
$620$	−2.93825	−0.118003
$621$	4.17484	0.167531
$622$	−7.23798	−0.290216
$623$	0	0
$624$	−6.88659	−0.275684
$625$	1.00000	0.0400000
$626$	6.70424	0.267955
$627$	4.42864	0.176863
$628$	−2.53035	−0.100972
$629$	−0.0888033	−0.00354082
$630$	0	0
$631$	10.9590	0.436270	0.218135	−	0.975919i	$-0.430003\pi$
$631$	10.9590	0.436270	0.218135	+	0.975919i	$0.430003\pi$
$632$	26.1160	1.03884
$633$	15.9081	0.632292
$634$	−19.0825	−0.757863
$635$	−13.3778	−0.530881
$636$	0.622216	0.0246725
$637$	0	0
$638$	9.47949	0.375297
$639$	31.7244	1.25500
$640$	4.97481	0.196647
$641$	−14.9862	−0.591919	−0.295959	−	0.955201i	$-0.595639\pi$
$641$	−14.9862	−0.591919	−0.295959	+	0.955201i	$0.595639\pi$
$642$	−7.16241	−0.282678
$643$	14.4222	0.568755	0.284378	−	0.958712i	$-0.408213\pi$
$643$	14.4222	0.568755	0.284378	+	0.958712i	$0.408213\pi$
$644$	0	0
$645$	−8.10171	−0.319005
$646$	0.520505	0.0204790
$647$	33.7309	1.32610	0.663048	−	0.748577i	$-0.269262\pi$
$647$	33.7309	1.32610	0.663048	+	0.748577i	$0.269262\pi$
$648$	−15.1925	−0.596819
$649$	2.54125	0.0997527
$650$	4.54125	0.178122
$651$	0	0
$652$	−3.19850	−0.125263
$653$	36.7971	1.43998	0.719990	−	0.693984i	$-0.244146\pi$
$653$	36.7971	1.43998	0.719990	+	0.693984i	$0.244146\pi$
$654$	−5.84791	−0.228671
$655$	2.75557	0.107669
$656$	17.7571	0.693298
$657$	2.97433	0.116040
$658$	0	0
$659$	3.79213	0.147721	0.0738603	−	0.997269i	$-0.476468\pi$
$659$	3.79213	0.147721	0.0738603	+	0.997269i	$0.476468\pi$
$660$	0.361963	0.0140894
$661$	35.2543	1.37123	0.685616	−	0.727963i	$-0.259533\pi$
$661$	35.2543	1.37123	0.685616	+	0.727963i	$0.259533\pi$
$662$	22.1432	0.860620
$663$	−0.171778	−0.00667129
$664$	−37.1120	−1.44023
$665$	0	0
$666$	−4.08436	−0.158266
$667$	8.56199	0.331522
$668$	−1.92993	−0.0746713
$669$	14.8430	0.573863
$670$	12.6079	0.487087
$671$	14.4494	0.557812
$672$	0	0
$673$	−35.1383	−1.35448	−0.677240	−	0.735762i	$-0.736824\pi$
$673$	−35.1383	−1.35448	−0.677240	+	0.735762i	$0.736824\pi$
$674$	39.2114	1.51037
$675$	−3.80642	−0.146509
$676$	−0.517919	−0.0199200
$677$	−23.1907	−0.891290	−0.445645	−	0.895210i	$-0.647026\pi$
$677$	−23.1907	−0.891290	−0.445645	+	0.895210i	$0.647026\pi$
$678$	−1.31450	−0.0504830
$679$	0	0
$680$	0.204475	0.00784127
$681$	18.7556	0.718715
$682$	−6.79060	−0.260026
$683$	−7.74758	−0.296453	−0.148227	−	0.988953i	$-0.547356\pi$
$683$	−7.74758	−0.296453	−0.148227	+	0.988953i	$0.547356\pi$
$684$	−8.53035	−0.326166
$685$	−17.8938	−0.683689
$686$	0	0
$687$	−17.2226	−0.657084
$688$	31.4366	1.19851
$689$	−6.42864	−0.244912
$690$	−0.917502	−0.0349287
$691$	14.7763	0.562117	0.281059	−	0.959691i	$-0.409314\pi$
$691$	14.7763	0.562117	0.281059	+	0.959691i	$0.409314\pi$
$692$	−0.330320	−0.0125569
$693$	0	0
$694$	27.5540	1.04594
$695$	3.86665	0.146670
$696$	16.4919	0.625125
$697$	0.442930	0.0167772
$698$	−20.5337	−0.777214
$699$	−2.52051	−0.0953343
$700$	0	0
$701$	−19.8765	−0.750725	−0.375362	−	0.926878i	$-0.622482\pi$
$701$	−19.8765	−0.750725	−0.375362	+	0.926878i	$0.622482\pi$
$702$	−17.2859	−0.652415
$703$	−8.56199	−0.322922
$704$	−8.85236	−0.333636
$705$	1.55707	0.0586427
$706$	−29.6258	−1.11498
$707$	0	0
$708$	0.919838	0.0345696
$709$	0.368416	0.0138362	0.00691808	−	0.999976i	$-0.497798\pi$
$709$	0.368416	0.0138362	0.00691808	+	0.999976i	$0.497798\pi$
$710$	−15.2543	−0.572483
$711$	21.5067	0.806564
$712$	47.8796	1.79436
$713$	−6.13335	−0.229696
$714$	0	0
$715$	−3.73975	−0.139859
$716$	4.04827	0.151291
$717$	10.1303	0.378323
$718$	−39.8435	−1.48694
$719$	5.86865	0.218864	0.109432	−	0.993994i	$-0.465097\pi$
$719$	5.86865	0.218864	0.109432	+	0.993994i	$0.465097\pi$
$720$	6.75065	0.251582
$721$	0	0
$722$	27.1126	1.00903
$723$	−9.43356	−0.350838
$724$	5.73636	0.213190
$725$	−7.80642	−0.289923
$726$	0.836535	0.0310467
$727$	−1.19066	−0.0441592	−0.0220796	−	0.999756i	$-0.507029\pi$
$727$	−1.19066	−0.0441592	−0.0220796	+	0.999756i	$0.507029\pi$
$728$	0	0
$729$	−4.64449	−0.172018
$730$	−1.43017	−0.0529330
$731$	0.784149	0.0290028
$732$	5.23014	0.193312
$733$	−19.6795	−0.726880	−0.363440	−	0.931618i	$-0.618398\pi$
$733$	−19.6795	−0.726880	−0.363440	+	0.931618i	$0.618398\pi$
$734$	8.43065	0.311181
$735$	0	0
$736$	−3.16686	−0.116732
$737$	−10.3827	−0.382452
$738$	20.3718	0.749897
$739$	27.1427	0.998461	0.499231	−	0.866469i	$-0.333616\pi$
$739$	27.1427	0.998461	0.499231	+	0.866469i	$0.333616\pi$
$740$	−0.699791	−0.0257248
$741$	−16.5620	−0.608420
$742$	0	0
$743$	−31.0509	−1.13915	−0.569573	−	0.821941i	$-0.692891\pi$
$743$	−31.0509	−1.13915	−0.569573	+	0.821941i	$0.692891\pi$
$744$	−11.8139	−0.433120
$745$	4.88892	0.179116
$746$	44.8974	1.64381
$747$	−30.5620	−1.11820
$748$	−0.0350337	−0.00128096
$749$	0	0
$750$	0.836535	0.0305460
$751$	−35.8292	−1.30743	−0.653713	−	0.756743i	$-0.726789\pi$
$751$	−35.8292	−1.30743	−0.653713	+	0.756743i	$0.726789\pi$
$752$	−6.04182	−0.220322
$753$	7.58565	0.276436
$754$	−35.4509	−1.29105
$755$	22.1891	0.807545
$756$	0	0
$757$	−1.15563	−0.0420020	−0.0210010	−	0.999779i	$-0.506685\pi$
$757$	−1.15563	−0.0420020	−0.0210010	+	0.999779i	$0.506685\pi$
$758$	−28.7083	−1.04273
$759$	0.755569	0.0274254
$760$	19.7146	0.715122
$761$	−36.5640	−1.32544	−0.662722	−	0.748866i	$-0.730599\pi$
$761$	−36.5640	−1.32544	−0.662722	+	0.748866i	$0.730599\pi$
$762$	−11.1910	−0.405407
$763$	0	0
$764$	5.73636	0.207534
$765$	0.168387	0.00608804
$766$	−16.6617	−0.602012
$767$	−9.50363	−0.343156
$768$	−8.03503	−0.289939
$769$	38.7545	1.39752	0.698762	−	0.715354i	$-0.253735\pi$
$769$	38.7545	1.39752	0.698762	+	0.715354i	$0.253735\pi$
$770$	0	0
$771$	10.9876	0.395708
$772$	−6.14764	−0.221259
$773$	−55.3372	−1.99034	−0.995171	−	0.0981537i	$-0.968706\pi$
$773$	−55.3372	−1.99034	−0.995171	+	0.0981537i	$0.968706\pi$
$774$	36.0656	1.29635
$775$	5.59210	0.200874
$776$	−41.1526	−1.47729
$777$	0	0
$778$	−18.8859	−0.677091
$779$	42.7052	1.53007
$780$	−1.35365	−0.0484684
$781$	12.5620	0.449503
$782$	0.0888033	0.00317560
$783$	29.7146	1.06191
$784$	0	0
$785$	4.81579	0.171883
$786$	2.30513	0.0822213
$787$	13.6731	0.487392	0.243696	−	0.969852i	$-0.421640\pi$
$787$	13.6731	0.487392	0.243696	+	0.969852i	$0.421640\pi$
$788$	−5.69721	−0.202955
$789$	−3.52098	−0.125350
$790$	−10.3412	−0.367924
$791$	0	0
$792$	−7.74467	−0.275195
$793$	−54.0370	−1.91891
$794$	0.308193	0.0109374
$795$	−1.18421	−0.0419995
$796$	1.09340	0.0387544
$797$	−17.8765	−0.633218	−0.316609	−	0.948556i	$-0.602544\pi$
$797$	−17.8765	−0.633218	−0.316609	+	0.948556i	$0.602544\pi$
$798$	0	0
$799$	−0.150706	−0.00533159
$800$	2.88739	0.102085
$801$	39.4291	1.39316
$802$	24.7338	0.873380
$803$	1.17775	0.0415621
$804$	−3.75815	−0.132540
$805$	0	0
$806$	25.3951	0.894506
$807$	12.5620	0.442203
$808$	−25.9115	−0.911564
$809$	14.6450	0.514890	0.257445	−	0.966293i	$-0.417119\pi$
$809$	14.6450	0.514890	0.257445	+	0.966293i	$0.417119\pi$
$810$	6.01582	0.211374
$811$	−30.2667	−1.06281	−0.531404	−	0.847119i	$-0.678335\pi$
$811$	−30.2667	−1.06281	−0.531404	+	0.847119i	$0.678335\pi$
$812$	0	0
$813$	−4.29529	−0.150642
$814$	−1.61729	−0.0566861
$815$	6.08742	0.213233
$816$	0.122782	0.00429823
$817$	75.6040	2.64505
$818$	−14.7205	−0.514691
$819$	0	0
$820$	3.49039	0.121890
$821$	10.4286	0.363962	0.181981	−	0.983302i	$-0.441749\pi$
$821$	10.4286	0.363962	0.181981	+	0.983302i	$0.441749\pi$
$822$	−14.9688	−0.522098
$823$	4.28100	0.149226	0.0746131	−	0.997213i	$-0.476228\pi$
$823$	4.28100	0.149226	0.0746131	+	0.997213i	$0.476228\pi$
$824$	−29.2750	−1.01984
$825$	−0.688892	−0.0239841
$826$	0	0
$827$	−13.8336	−0.481042	−0.240521	−	0.970644i	$-0.577318\pi$
$827$	−13.8336	−0.481042	−0.240521	+	0.970644i	$0.577318\pi$
$828$	−1.45536	−0.0505773
$829$	−10.8573	−0.377089	−0.188544	−	0.982065i	$-0.560377\pi$
$829$	−10.8573	−0.377089	−0.188544	+	0.982065i	$0.560377\pi$
$830$	14.6953	0.510083
$831$	4.35551	0.151091
$832$	33.1056	1.14773
$833$	0	0
$834$	3.23459	0.112005
$835$	3.67307	0.127112
$836$	−3.37778	−0.116823
$837$	−21.2859	−0.735749
$838$	26.0350	0.899365
$839$	−52.4820	−1.81188	−0.905940	−	0.423407i	$-0.860834\pi$
$839$	−52.4820	−1.81188	−0.905940	+	0.423407i	$0.860834\pi$
$840$	0	0
$841$	31.9403	1.10139
$842$	36.2623	1.24968
$843$	−17.3778	−0.598523
$844$	−12.1334	−0.417647
$845$	0.985710	0.0339095
$846$	−6.93146	−0.238309
$847$	0	0
$848$	4.59502	0.157794
$849$	−9.24443	−0.317268
$850$	−0.0809666	−0.00277713
$851$	−1.46076	−0.0500742
$852$	4.54698	0.155777
$853$	−9.89184	−0.338690	−0.169345	−	0.985557i	$-0.554165\pi$
$853$	−9.89184	−0.338690	−0.169345	+	0.985557i	$0.554165\pi$
$854$	0	0
$855$	16.2351	0.555227
$856$	26.2569	0.897441
$857$	3.58766	0.122552	0.0612760	−	0.998121i	$-0.480483\pi$
$857$	3.58766	0.122552	0.0612760	+	0.998121i	$0.480483\pi$
$858$	−3.12843	−0.106803
$859$	17.2050	0.587025	0.293513	−	0.955955i	$-0.405176\pi$
$859$	17.2050	0.587025	0.293513	+	0.955955i	$0.405176\pi$
$860$	6.17929	0.210712
$861$	0	0
$862$	−23.8720	−0.813085
$863$	15.0781	0.513263	0.256631	−	0.966509i	$-0.417387\pi$
$863$	15.0781	0.513263	0.256631	+	0.966509i	$0.417387\pi$
$864$	−10.9906	−0.373909
$865$	0.628669	0.0213754
$866$	40.0384	1.36056
$867$	−11.7081	−0.397628
$868$	0	0
$869$	8.51606	0.288888
$870$	−6.53035	−0.221400
$871$	38.8287	1.31566
$872$	21.4380	0.725983
$873$	−33.8894	−1.14698
$874$	8.56199	0.289614
$875$	0	0
$876$	0.426304	0.0144035
$877$	−31.4750	−1.06284	−0.531418	−	0.847109i	$-0.678341\pi$
$877$	−31.4750	−1.06284	−0.531418	+	0.847109i	$0.678341\pi$
$878$	0.990632	0.0334322
$879$	−12.1289	−0.409098
$880$	2.67307	0.0901092
$881$	47.1209	1.58754	0.793772	−	0.608215i	$-0.208114\pi$
$881$	47.1209	1.58754	0.793772	+	0.608215i	$0.208114\pi$
$882$	0	0
$883$	33.8118	1.13786	0.568929	−	0.822386i	$-0.307358\pi$
$883$	33.8118	1.13786	0.568929	+	0.822386i	$0.307358\pi$
$884$	0.131017	0.00440658
$885$	−1.75065	−0.0588473
$886$	30.3293	1.01893
$887$	31.6258	1.06189	0.530944	−	0.847407i	$-0.321837\pi$
$887$	31.6258	1.06189	0.530944	+	0.847407i	$0.321837\pi$
$888$	−2.81368	−0.0944210
$889$	0	0
$890$	−18.9590	−0.635507
$891$	−4.95407	−0.165967
$892$	−11.3210	−0.379054
$893$	−14.5303	−0.486240
$894$	4.08976	0.136782
$895$	−7.70471	−0.257540
$896$	0	0
$897$	−2.82564	−0.0943452
$898$	0.503153	0.0167904
$899$	−43.6543	−1.45595
$900$	1.32693	0.0442310
$901$	0.114617	0.00381845
$902$	8.06668	0.268591
$903$	0	0
$904$	4.81885	0.160273
$905$	−10.9175	−0.362910
$906$	18.5620	0.616681
$907$	−46.8943	−1.55710	−0.778550	−	0.627582i	$-0.784045\pi$
$907$	−46.8943	−1.55710	−0.778550	+	0.627582i	$0.784045\pi$
$908$	−14.3051	−0.474732
$909$	−21.3383	−0.707747
$910$	0	0
$911$	−28.5620	−0.946301	−0.473151	−	0.880982i	$-0.656883\pi$
$911$	−28.5620	−0.946301	−0.473151	+	0.880982i	$0.656883\pi$
$912$	11.8381	0.391998
$913$	−12.1017	−0.400508
$914$	11.3319	0.374824
$915$	−9.95407	−0.329071
$916$	13.1359	0.434024
$917$	0	0
$918$	0.308193	0.0101719
$919$	30.3555	1.00134	0.500668	−	0.865639i	$-0.333088\pi$
$919$	30.3555	1.00134	0.500668	+	0.865639i	$0.333088\pi$
$920$	3.36349	0.110891
$921$	−18.1432	−0.597839
$922$	−36.4164	−1.19931
$923$	−46.9787	−1.54632
$924$	0	0
$925$	1.33185	0.0437910
$926$	−38.2939	−1.25842
$927$	−24.1082	−0.791816
$928$	−22.5402	−0.739918
$929$	−2.71408	−0.0890461	−0.0445231	−	0.999008i	$-0.514177\pi$
$929$	−2.71408	−0.0890461	−0.0445231	+	0.999008i	$0.514177\pi$
$930$	4.67799	0.153397
$931$	0	0
$932$	1.92242	0.0629711
$933$	−4.10616	−0.134430
$934$	6.89676	0.225669
$935$	0.0666765	0.00218056
$936$	28.9631	0.946689
$937$	−13.7081	−0.447824	−0.223912	−	0.974609i	$-0.571883\pi$
$937$	−13.7081	−0.447824	−0.223912	+	0.974609i	$0.571883\pi$
$938$	0	0
$939$	3.80336	0.124118
$940$	−1.18760	−0.0387352
$941$	21.1635	0.689909	0.344955	−	0.938619i	$-0.387894\pi$
$941$	21.1635	0.689909	0.344955	+	0.938619i	$0.387894\pi$
$942$	4.02858	0.131258
$943$	7.28592	0.237262
$944$	6.79294	0.221091
$945$	0	0
$946$	14.2810	0.464315
$947$	−14.8746	−0.483361	−0.241680	−	0.970356i	$-0.577699\pi$
$947$	−14.8746	−0.483361	−0.241680	+	0.970356i	$0.577699\pi$
$948$	3.08250	0.100115
$949$	−4.40451	−0.142976
$950$	−7.80642	−0.253274
$951$	−10.8256	−0.351045
$952$	0	0
$953$	35.0968	1.13690	0.568448	−	0.822719i	$-0.307544\pi$
$953$	35.0968	1.13690	0.568448	+	0.822719i	$0.307544\pi$
$954$	5.27163	0.170675
$955$	−10.9175	−0.353282
$956$	−7.72651	−0.249893
$957$	5.37778	0.173839
$958$	47.9180	1.54816
$959$	0	0
$960$	6.09832	0.196822
$961$	0.271628	0.00876221
$962$	6.04827	0.195004
$963$	21.6227	0.696782
$964$	7.19511	0.231739
$965$	11.7003	0.376645
$966$	0	0
$967$	−53.0879	−1.70719	−0.853596	−	0.520936i	$-0.825583\pi$
$967$	−53.0879	−1.70719	−0.853596	+	0.520936i	$0.825583\pi$
$968$	−3.06668	−0.0985667
$969$	0.295286	0.00948597
$970$	16.2953	0.523210
$971$	−21.4400	−0.688043	−0.344021	−	0.938962i	$-0.611789\pi$
$971$	−21.4400	−0.688043	−0.344021	+	0.938962i	$0.611789\pi$
$972$	−7.79319	−0.249967
$973$	0	0
$974$	−3.88400	−0.124451
$975$	2.57628	0.0825071
$976$	38.6242	1.23633
$977$	−54.0415	−1.72894	−0.864470	−	0.502684i	$-0.832346\pi$
$977$	−54.0415	−1.72894	−0.864470	+	0.502684i	$0.832346\pi$
$978$	5.09234	0.162835
$979$	15.6128	0.498989
$980$	0	0
$981$	17.6543	0.563660
$982$	31.9986	1.02112
$983$	38.3432	1.22296	0.611480	−	0.791260i	$-0.290575\pi$
$983$	38.3432	1.22296	0.611480	+	0.791260i	$0.290575\pi$
$984$	14.0340	0.447387
$985$	10.8430	0.345486
$986$	0.632060	0.0201289
$987$	0	0
$988$	12.6321	0.401879
$989$	12.8988	0.410157
$990$	3.06668	0.0974654
$991$	51.6543	1.64085	0.820427	−	0.571751i	$-0.193736\pi$
$991$	51.6543	1.64085	0.820427	+	0.571751i	$0.193736\pi$
$992$	16.1466	0.512655
$993$	12.5620	0.398643
$994$	0	0
$995$	−2.08097	−0.0659711
$996$	−4.38037	−0.138797
$997$	−41.4445	−1.31256	−0.656280	−	0.754518i	$-0.727871\pi$
$997$	−41.4445	−1.31256	−0.656280	+	0.754518i	$0.727871\pi$
$998$	4.28639	0.135683
$999$	−5.06959	−0.160395

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.2.a.g.1.3		3
7.6	odd	2		385.2.a.f.1.3	✓	3
21.20	even	2		3465.2.a.bh.1.1		3
28.27	even	2		6160.2.a.bn.1.2		3
35.13	even	4		1925.2.b.n.1849.3		6
35.27	even	4		1925.2.b.n.1849.4		6
35.34	odd	2		1925.2.a.v.1.1		3
77.76	even	2		4235.2.a.q.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.a.f.1.3	✓	3	7.6	odd	2
1925.2.a.v.1.1		3	35.34	odd	2
1925.2.b.n.1849.3		6	35.13	even	4
1925.2.b.n.1849.4		6	35.27	even	4
2695.2.a.g.1.3		3	1.1	even	1	trivial
3465.2.a.bh.1.1		3	21.20	even	2
4235.2.a.q.1.1		3	77.76	even	2
6160.2.a.bn.1.2		3	28.27	even	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)

\(f(q)\)	\(=\)	\(q+1.21432 q^{2} +0.688892 q^{3} -0.525428 q^{4} +1.00000 q^{5} +0.836535 q^{6} -3.06668 q^{8} -2.52543 q^{9} +O(q^{10})\)	\(q+1.21432 q^{2} +0.688892 q^{3} -0.525428 q^{4} +1.00000 q^{5} +0.836535 q^{6} -3.06668 q^{8} -2.52543 q^{9} +1.21432 q^{10} -1.00000 q^{11} -0.361963 q^{12} +3.73975 q^{13} +0.688892 q^{15} -2.67307 q^{16} -0.0666765 q^{17} -3.06668 q^{18} -6.42864 q^{19} -0.525428 q^{20} -1.21432 q^{22} -1.09679 q^{23} -2.11261 q^{24} +1.00000 q^{25} +4.54125 q^{26} -3.80642 q^{27} -7.80642 q^{29} +0.836535 q^{30} +5.59210 q^{31} +2.88739 q^{32} -0.688892 q^{33} -0.0809666 q^{34} +1.32693 q^{36} +1.33185 q^{37} -7.80642 q^{38} +2.57628 q^{39} -3.06668 q^{40} -6.64296 q^{41} -11.7605 q^{43} +0.525428 q^{44} -2.52543 q^{45} -1.33185 q^{46} +2.26025 q^{47} -1.84146 q^{48} +1.21432 q^{50} -0.0459330 q^{51} -1.96497 q^{52} -1.71900 q^{53} -4.62222 q^{54} -1.00000 q^{55} -4.42864 q^{57} -9.47949 q^{58} -2.54125 q^{59} -0.361963 q^{60} -14.4494 q^{61} +6.79060 q^{62} +8.85236 q^{64} +3.73975 q^{65} -0.836535 q^{66} +10.3827 q^{67} +0.0350337 q^{68} -0.755569 q^{69} -12.5620 q^{71} +7.74467 q^{72} -1.17775 q^{73} +1.61729 q^{74} +0.688892 q^{75} +3.37778 q^{76} +3.12843 q^{78} -8.51606 q^{79} -2.67307 q^{80} +4.95407 q^{81} -8.06668 q^{82} +12.1017 q^{83} -0.0666765 q^{85} -14.2810 q^{86} -5.37778 q^{87} +3.06668 q^{88} -15.6128 q^{89} -3.06668 q^{90} +0.576283 q^{92} +3.85236 q^{93} +2.74467 q^{94} -6.42864 q^{95} +1.98910 q^{96} +13.4193 q^{97} +2.52543 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 2 q^{3} + 5 q^{4} + 3 q^{5} - 4 q^{6} - 9 q^{8} - q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 2 * q^3 + 5 * q^4 + 3 * q^5 - 4 * q^6 - 9 * q^8 - q^9	\( 3 q - 3 q^{2} + 2 q^{3} + 5 q^{4} + 3 q^{5} - 4 q^{6} - 9 q^{8} - q^{9} - 3 q^{10} - 3 q^{11} + 12 q^{12} - 2 q^{13} + 2 q^{15} + 5 q^{16} - 9 q^{18} - 6 q^{19} + 5 q^{20} + 3 q^{22} - 10 q^{23} - 26 q^{24} + 3 q^{25} + 20 q^{26} + 2 q^{27} - 10 q^{29} - 4 q^{30} + 10 q^{31} - 11 q^{32} - 2 q^{33} + 6 q^{34} + 17 q^{36} - 16 q^{37} - 10 q^{38} - 12 q^{39} - 9 q^{40} - 2 q^{43} - 5 q^{44} - q^{45} + 16 q^{46} + 20 q^{47} + 34 q^{48} - 3 q^{50} - 20 q^{51} - 32 q^{52} - 12 q^{53} - 14 q^{54} - 3 q^{55} - 2 q^{58} - 14 q^{59} + 12 q^{60} - 10 q^{61} - 6 q^{62} + 33 q^{64} - 2 q^{65} + 4 q^{66} - 2 q^{67} - 26 q^{68} - 2 q^{69} - 24 q^{71} - 23 q^{72} - 4 q^{73} + 38 q^{74} + 2 q^{75} + 10 q^{76} + 42 q^{78} + 8 q^{79} + 5 q^{80} - 5 q^{81} - 24 q^{82} + 10 q^{83} - 36 q^{86} - 16 q^{87} + 9 q^{88} - 20 q^{89} - 9 q^{90} - 18 q^{92} + 18 q^{93} - 38 q^{94} - 6 q^{95} - 40 q^{96} + q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 2 * q^3 + 5 * q^4 + 3 * q^5 - 4 * q^6 - 9 * q^8 - q^9 - 3 * q^10 - 3 * q^11 + 12 * q^12 - 2 * q^13 + 2 * q^15 + 5 * q^16 - 9 * q^18 - 6 * q^19 + 5 * q^20 + 3 * q^22 - 10 * q^23 - 26 * q^24 + 3 * q^25 + 20 * q^26 + 2 * q^27 - 10 * q^29 - 4 * q^30 + 10 * q^31 - 11 * q^32 - 2 * q^33 + 6 * q^34 + 17 * q^36 - 16 * q^37 - 10 * q^38 - 12 * q^39 - 9 * q^40 - 2 * q^43 - 5 * q^44 - q^45 + 16 * q^46 + 20 * q^47 + 34 * q^48 - 3 * q^50 - 20 * q^51 - 32 * q^52 - 12 * q^53 - 14 * q^54 - 3 * q^55 - 2 * q^58 - 14 * q^59 + 12 * q^60 - 10 * q^61 - 6 * q^62 + 33 * q^64 - 2 * q^65 + 4 * q^66 - 2 * q^67 - 26 * q^68 - 2 * q^69 - 24 * q^71 - 23 * q^72 - 4 * q^73 + 38 * q^74 + 2 * q^75 + 10 * q^76 + 42 * q^78 + 8 * q^79 + 5 * q^80 - 5 * q^81 - 24 * q^82 + 10 * q^83 - 36 * q^86 - 16 * q^87 + 9 * q^88 - 20 * q^89 - 9 * q^90 - 18 * q^92 + 18 * q^93 - 38 * q^94 - 6 * q^95 - 40 * q^96 + q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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