LMFDB - Embedded newform 2695.2.a.h.1.2

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:	$0$
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			1.2
Root			$2.17009$ 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)

$f(q)$	$=$	$q-1.53919 q^{2} +3.17009 q^{3} +0.369102 q^{4} +1.00000 q^{5} -4.87936 q^{6} +2.51026 q^{8} +7.04945 q^{9} +O(q^{10})$	\(q-1.53919 q^{2} +3.17009 q^{3} +0.369102 q^{4} +1.00000 q^{5} -4.87936 q^{6} +2.51026 q^{8} +7.04945 q^{9} -1.53919 q^{10} +1.00000 q^{11} +1.17009 q^{12} +0.829914 q^{13} +3.17009 q^{15} -4.60197 q^{16} +2.82991 q^{17} -10.8504 q^{18} -6.49693 q^{19} +0.369102 q^{20} -1.53919 q^{22} -6.97107 q^{23} +7.95774 q^{24} +1.00000 q^{25} -1.27739 q^{26} +12.8371 q^{27} +3.26180 q^{29} -4.87936 q^{30} +10.2979 q^{31} +2.06278 q^{32} +3.17009 q^{33} -4.35577 q^{34} +2.60197 q^{36} +11.3112 q^{37} +10.0000 q^{38} +2.63090 q^{39} +2.51026 q^{40} +0.199016 q^{41} -0.447480 q^{43} +0.369102 q^{44} +7.04945 q^{45} +10.7298 q^{46} +6.82991 q^{47} -14.5886 q^{48} -1.53919 q^{50} +8.97107 q^{51} +0.306323 q^{52} -7.31124 q^{53} -19.7587 q^{54} +1.00000 q^{55} -20.5958 q^{57} -5.02052 q^{58} +7.95774 q^{59} +1.17009 q^{60} +6.87936 q^{61} -15.8504 q^{62} +6.02893 q^{64} +0.829914 q^{65} -4.87936 q^{66} +6.20620 q^{67} +1.04453 q^{68} -22.0989 q^{69} -11.4186 q^{71} +17.6959 q^{72} -5.66701 q^{73} -17.4101 q^{74} +3.17009 q^{75} -2.39803 q^{76} -4.04945 q^{78} -14.5464 q^{79} -4.60197 q^{80} +19.5464 q^{81} -0.306323 q^{82} -2.89496 q^{83} +2.82991 q^{85} +0.688756 q^{86} +10.3402 q^{87} +2.51026 q^{88} +0.581449 q^{89} -10.8504 q^{90} -2.57304 q^{92} +32.6453 q^{93} -10.5125 q^{94} -6.49693 q^{95} +6.53919 q^{96} +2.15676 q^{97} +7.04945 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 4 q^{3} + 5 q^{4} + 3 q^{5} - 2 q^{6} - 9 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 4 * q^3 + 5 * q^4 + 3 * q^5 - 2 * q^6 - 9 * q^8 + 3 * q^9	$ 3 q - 3 q^{2} + 4 q^{3} + 5 q^{4} + 3 q^{5} - 2 q^{6} - 9 q^{8} + 3 q^{9} - 3 q^{10} + 3 q^{11} - 2 q^{12} + 8 q^{13} + 4 q^{15} + 5 q^{16} + 14 q^{17} - 5 q^{18} - 2 q^{19} + 5 q^{20} - 3 q^{22} - 6 q^{23} + 8 q^{24} + 3 q^{25} - 10 q^{26} + 10 q^{27} + 2 q^{29} - 2 q^{30} + 4 q^{31} - 11 q^{32} + 4 q^{33} - 16 q^{34} - 11 q^{36} + 8 q^{37} + 30 q^{38} + 4 q^{39} - 9 q^{40} + 10 q^{41} - 2 q^{43} + 5 q^{44} + 3 q^{45} - 8 q^{46} + 26 q^{47} - 24 q^{48} - 3 q^{50} + 12 q^{51} + 22 q^{52} + 4 q^{53} - 34 q^{54} + 3 q^{55} - 8 q^{57} + 18 q^{58} + 8 q^{59} - 2 q^{60} + 8 q^{61} - 20 q^{62} + 33 q^{64} + 8 q^{65} - 2 q^{66} - 6 q^{67} + 32 q^{68} - 30 q^{69} - 20 q^{71} + 45 q^{72} + 6 q^{73} + 10 q^{74} + 4 q^{75} - 26 q^{76} + 6 q^{78} - 8 q^{79} + 5 q^{80} + 23 q^{81} - 22 q^{82} - 10 q^{83} + 14 q^{85} + 28 q^{86} + 20 q^{87} - 9 q^{88} + 16 q^{89} - 5 q^{90} + 26 q^{92} + 26 q^{93} - 28 q^{94} - 2 q^{95} + 18 q^{96} + 3 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 4 * q^3 + 5 * q^4 + 3 * q^5 - 2 * q^6 - 9 * q^8 + 3 * q^9 - 3 * q^10 + 3 * q^11 - 2 * q^12 + 8 * q^13 + 4 * q^15 + 5 * q^16 + 14 * q^17 - 5 * q^18 - 2 * q^19 + 5 * q^20 - 3 * q^22 - 6 * q^23 + 8 * q^24 + 3 * q^25 - 10 * q^26 + 10 * q^27 + 2 * q^29 - 2 * q^30 + 4 * q^31 - 11 * q^32 + 4 * q^33 - 16 * q^34 - 11 * q^36 + 8 * q^37 + 30 * q^38 + 4 * q^39 - 9 * q^40 + 10 * q^41 - 2 * q^43 + 5 * q^44 + 3 * q^45 - 8 * q^46 + 26 * q^47 - 24 * q^48 - 3 * q^50 + 12 * q^51 + 22 * q^52 + 4 * q^53 - 34 * q^54 + 3 * q^55 - 8 * q^57 + 18 * q^58 + 8 * q^59 - 2 * q^60 + 8 * q^61 - 20 * q^62 + 33 * q^64 + 8 * q^65 - 2 * q^66 - 6 * q^67 + 32 * q^68 - 30 * q^69 - 20 * q^71 + 45 * q^72 + 6 * q^73 + 10 * q^74 + 4 * q^75 - 26 * q^76 + 6 * q^78 - 8 * q^79 + 5 * q^80 + 23 * q^81 - 22 * q^82 - 10 * q^83 + 14 * q^85 + 28 * q^86 + 20 * q^87 - 9 * q^88 + 16 * q^89 - 5 * q^90 + 26 * q^92 + 26 * q^93 - 28 * q^94 - 2 * q^95 + 18 * q^96 + 3 * 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 $

$2$	−1.53919	−1.08837	−0.544185	−	0.838965i	$-0.683161\pi$
$2$	−1.53919	−1.08837	−0.544185	+	0.838965i	$0.683161\pi$
$3$	3.17009	1.83025	0.915125	−	0.403170i	$-0.132092\pi$
$3$	3.17009	1.83025	0.915125	+	0.403170i	$0.132092\pi$
$4$	0.369102	0.184551
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−4.87936	−1.99199
$7$	0	0
$7$	0	0
$8$	2.51026	0.887511
$9$	7.04945	2.34982
$10$	−1.53919	−0.486734
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.17009	0.337775
$13$	0.829914	0.230177	0.115088	−	0.993355i	$-0.463285\pi$
$13$	0.829914	0.230177	0.115088	+	0.993355i	$0.463285\pi$
$14$	0	0
$15$	3.17009	0.818513
$16$	−4.60197	−1.15049
$17$	2.82991	0.686355	0.343177	−	0.939271i	$-0.388497\pi$
$17$	2.82991	0.686355	0.343177	+	0.939271i	$0.388497\pi$
$18$	−10.8504	−2.55747
$19$	−6.49693	−1.49050	−0.745249	−	0.666786i	$-0.767669\pi$
$19$	−6.49693	−1.49050	−0.745249	+	0.666786i	$0.767669\pi$
$20$	0.369102	0.0825338
$21$	0	0
$22$	−1.53919	−0.328156
$23$	−6.97107	−1.45357	−0.726784	−	0.686866i	$-0.758986\pi$
$23$	−6.97107	−1.45357	−0.726784	+	0.686866i	$0.758986\pi$
$24$	7.95774	1.62437
$25$	1.00000	0.200000
$26$	−1.27739	−0.250518
$27$	12.8371	2.47050
$28$	0	0
$29$	3.26180	0.605700	0.302850	−	0.953038i	$-0.402062\pi$
$29$	3.26180	0.605700	0.302850	+	0.953038i	$0.402062\pi$
$30$	−4.87936	−0.890846
$31$	10.2979	1.84956	0.924780	−	0.380503i	$-0.124249\pi$
$31$	10.2979	1.84956	0.924780	+	0.380503i	$0.124249\pi$
$32$	2.06278	0.364651
$33$	3.17009	0.551841
$34$	−4.35577	−0.747009
$35$	0	0
$36$	2.60197	0.433661
$37$	11.3112	1.85956	0.929778	−	0.368119i	$-0.119998\pi$
$37$	11.3112	1.85956	0.929778	+	0.368119i	$0.119998\pi$
$38$	10.0000	1.62221
$39$	2.63090	0.421281
$40$	2.51026	0.396907
$41$	0.199016	0.0310811	0.0155405	−	0.999879i	$-0.495053\pi$
$41$	0.199016	0.0310811	0.0155405	+	0.999879i	$0.495053\pi$
$42$	0	0
$43$	−0.447480	−0.0682401	−0.0341200	−	0.999418i	$-0.510863\pi$
$43$	−0.447480	−0.0682401	−0.0341200	+	0.999418i	$0.510863\pi$
$44$	0.369102	0.0556443
$45$	7.04945	1.05087
$46$	10.7298	1.58202
$47$	6.82991	0.996245	0.498123	−	0.867107i	$-0.334023\pi$
$47$	6.82991	0.996245	0.498123	+	0.867107i	$0.334023\pi$
$48$	−14.5886	−2.10569
$49$	0	0
$50$	−1.53919	−0.217674
$51$	8.97107	1.25620
$52$	0.306323	0.0424794
$53$	−7.31124	−1.00428	−0.502138	−	0.864787i	$-0.667453\pi$
$53$	−7.31124	−1.00428	−0.502138	+	0.864787i	$0.667453\pi$
$54$	−19.7587	−2.68882
$55$	1.00000	0.134840
$56$	0	0
$57$	−20.5958	−2.72798
$58$	−5.02052	−0.659226
$59$	7.95774	1.03601	0.518005	−	0.855378i	$-0.326675\pi$
$59$	7.95774	1.03601	0.518005	+	0.855378i	$0.326675\pi$
$60$	1.17009	0.151058
$61$	6.87936	0.880812	0.440406	−	0.897799i	$-0.354835\pi$
$61$	6.87936	0.880812	0.440406	+	0.897799i	$0.354835\pi$
$62$	−15.8504	−2.01301
$63$	0	0
$64$	6.02893	0.753616
$65$	0.829914	0.102938
$66$	−4.87936	−0.600608
$67$	6.20620	0.758208	0.379104	−	0.925354i	$-0.376232\pi$
$67$	6.20620	0.758208	0.379104	+	0.925354i	$0.376232\pi$
$68$	1.04453	0.126668
$69$	−22.0989	−2.66039
$70$	0	0
$71$	−11.4186	−1.35513	−0.677566	−	0.735462i	$-0.736965\pi$
$71$	−11.4186	−1.35513	−0.677566	+	0.735462i	$0.736965\pi$
$72$	17.6959	2.08549
$73$	−5.66701	−0.663274	−0.331637	−	0.943407i	$-0.607601\pi$
$73$	−5.66701	−0.663274	−0.331637	+	0.943407i	$0.607601\pi$
$74$	−17.4101	−2.02389
$75$	3.17009	0.366050
$76$	−2.39803	−0.275073
$77$	0	0
$78$	−4.04945	−0.458510
$79$	−14.5464	−1.63660	−0.818298	−	0.574795i	$-0.805082\pi$
$79$	−14.5464	−1.63660	−0.818298	+	0.574795i	$0.805082\pi$
$80$	−4.60197	−0.514516
$81$	19.5464	2.17182
$82$	−0.306323	−0.0338277
$83$	−2.89496	−0.317763	−0.158882	−	0.987298i	$-0.550789\pi$
$83$	−2.89496	−0.317763	−0.158882	+	0.987298i	$0.550789\pi$
$84$	0	0
$85$	2.82991	0.306947
$86$	0.688756	0.0742705
$87$	10.3402	1.10858
$88$	2.51026	0.267595
$89$	0.581449	0.0616335	0.0308168	−	0.999525i	$-0.490189\pi$
$89$	0.581449	0.0616335	0.0308168	+	0.999525i	$0.490189\pi$
$90$	−10.8504	−1.14374
$91$	0	0
$92$	−2.57304	−0.268258
$93$	32.6453	3.38516
$94$	−10.5125	−1.08428
$95$	−6.49693	−0.666571
$96$	6.53919	0.667403
$97$	2.15676	0.218985	0.109493	−	0.993988i	$-0.465077\pi$
$97$	2.15676	0.218985	0.109493	+	0.993988i	$0.465077\pi$
$98$	0	0
$99$	7.04945	0.708496
$100$	0.369102	0.0369102
$101$	7.21953	0.718371	0.359185	−	0.933266i	$-0.383055\pi$
$101$	7.21953	0.718371	0.359185	+	0.933266i	$0.383055\pi$
$102$	−13.8082	−1.36721
$103$	−3.66701	−0.361322	−0.180661	−	0.983545i	$-0.557824\pi$
$103$	−3.66701	−0.361322	−0.180661	+	0.983545i	$0.557824\pi$
$104$	2.08330	0.204284
$105$	0	0
$106$	11.2534	1.09303
$107$	−9.26180	−0.895372	−0.447686	−	0.894191i	$-0.647752\pi$
$107$	−9.26180	−0.895372	−0.447686	+	0.894191i	$0.647752\pi$
$108$	4.73820	0.455934
$109$	6.86376	0.657429	0.328715	−	0.944429i	$-0.393385\pi$
$109$	6.86376	0.657429	0.328715	+	0.944429i	$0.393385\pi$
$110$	−1.53919	−0.146756
$111$	35.8576	3.40345
$112$	0	0
$113$	−3.75872	−0.353591	−0.176795	−	0.984248i	$-0.556573\pi$
$113$	−3.75872	−0.353591	−0.176795	+	0.984248i	$0.556573\pi$
$114$	31.7009	2.96906
$115$	−6.97107	−0.650056
$116$	1.20394	0.111783
$117$	5.85043	0.540873
$118$	−12.2485	−1.12756
$119$	0	0
$120$	7.95774	0.726439
$121$	1.00000	0.0909091
$122$	−10.5886	−0.958650
$123$	0.630898	0.0568861
$124$	3.80098	0.341338
$125$	1.00000	0.0894427
$126$	0	0
$127$	−21.5441	−1.91173	−0.955865	−	0.293805i	$-0.905078\pi$
$127$	−21.5441	−1.91173	−0.955865	+	0.293805i	$0.905078\pi$
$128$	−13.4052	−1.18487
$129$	−1.41855	−0.124896
$130$	−1.27739	−0.112035
$131$	12.6803	1.10789	0.553943	−	0.832554i	$-0.313122\pi$
$131$	12.6803	1.10789	0.553943	+	0.832554i	$0.313122\pi$
$132$	1.17009	0.101843
$133$	0	0
$134$	−9.55252	−0.825212
$135$	12.8371	1.10484
$136$	7.10382	0.609147
$137$	19.6248	1.67666	0.838328	−	0.545166i	$-0.183533\pi$
$137$	19.6248	1.67666	0.838328	+	0.545166i	$0.183533\pi$
$138$	34.0144	2.89550
$139$	0.496928	0.0421489	0.0210745	−	0.999778i	$-0.493291\pi$
$139$	0.496928	0.0421489	0.0210745	+	0.999778i	$0.493291\pi$
$140$	0	0
$141$	21.6514	1.82338
$142$	17.5753	1.47489
$143$	0.829914	0.0694009
$144$	−32.4413	−2.70344
$145$	3.26180	0.270877
$146$	8.72261	0.721888
$147$	0	0
$148$	4.17501	0.343183
$149$	−13.3340	−1.09237	−0.546183	−	0.837666i	$-0.683920\pi$
$149$	−13.3340	−1.09237	−0.546183	+	0.837666i	$0.683920\pi$
$150$	−4.87936	−0.398398
$151$	−1.05559	−0.0859028	−0.0429514	−	0.999077i	$-0.513676\pi$
$151$	−1.05559	−0.0859028	−0.0429514	+	0.999077i	$0.513676\pi$
$152$	−16.3090	−1.32283
$153$	19.9493	1.61281
$154$	0	0
$155$	10.2979	0.827148
$156$	0.971071	0.0777479
$157$	0.496928	0.0396592	0.0198296	−	0.999803i	$-0.493688\pi$
$157$	0.496928	0.0396592	0.0198296	+	0.999803i	$0.493688\pi$
$158$	22.3896	1.78122
$159$	−23.1773	−1.83808
$160$	2.06278	0.163077
$161$	0	0
$162$	−30.0856	−2.36375
$163$	1.31124	0.102705	0.0513523	−	0.998681i	$-0.483647\pi$
$163$	1.31124	0.102705	0.0513523	+	0.998681i	$0.483647\pi$
$164$	0.0734572	0.00573605
$165$	3.17009	0.246791
$166$	4.45589	0.345844
$167$	−3.17727	−0.245865	−0.122932	−	0.992415i	$-0.539230\pi$
$167$	−3.17727	−0.245865	−0.122932	+	0.992415i	$0.539230\pi$
$168$	0	0
$169$	−12.3112	−0.947019
$170$	−4.35577	−0.334072
$171$	−45.7998	−3.50240
$172$	−0.165166	−0.0125938
$173$	17.9493	1.36466	0.682331	−	0.731043i	$-0.260966\pi$
$173$	17.9493	1.36466	0.682331	+	0.731043i	$0.260966\pi$
$174$	−15.9155	−1.20655
$175$	0	0
$176$	−4.60197	−0.346886
$177$	25.2267	1.89616
$178$	−0.894960	−0.0670801
$179$	15.7321	1.17587	0.587935	−	0.808908i	$-0.299941\pi$
$179$	15.7321	1.17587	0.587935	+	0.808908i	$0.299941\pi$
$180$	2.60197	0.193939
$181$	16.8104	1.24951	0.624755	−	0.780821i	$-0.285199\pi$
$181$	16.8104	1.24951	0.624755	+	0.780821i	$0.285199\pi$
$182$	0	0
$183$	21.8082	1.61211
$184$	−17.4992	−1.29006
$185$	11.3112	0.831619
$186$	−50.2472	−3.68431
$187$	2.82991	0.206944
$188$	2.52094	0.183858
$189$	0	0
$190$	10.0000	0.725476
$191$	−2.92162	−0.211401	−0.105701	−	0.994398i	$-0.533709\pi$
$191$	−2.92162	−0.211401	−0.105701	+	0.994398i	$0.533709\pi$
$192$	19.1122	1.37931
$193$	−22.8287	−1.64325	−0.821623	−	0.570032i	$-0.806931\pi$
$193$	−22.8287	−1.64325	−0.821623	+	0.570032i	$0.806931\pi$
$194$	−3.31965	−0.238337
$195$	2.63090	0.188402
$196$	0	0
$197$	19.7237	1.40525	0.702626	−	0.711559i	$-0.252011\pi$
$197$	19.7237	1.40525	0.702626	+	0.711559i	$0.252011\pi$
$198$	−10.8504	−0.771107
$199$	10.6381	0.754114	0.377057	−	0.926190i	$-0.376936\pi$
$199$	10.6381	0.754114	0.377057	+	0.926190i	$0.376936\pi$
$200$	2.51026	0.177502
$201$	19.6742	1.38771
$202$	−11.1122	−0.781854
$203$	0	0
$204$	3.31124	0.231833
$205$	0.199016	0.0138999
$206$	5.64423	0.393252
$207$	−49.1422	−3.41562
$208$	−3.81924	−0.264816
$209$	−6.49693	−0.449402
$210$	0	0
$211$	7.50307	0.516533	0.258266	−	0.966074i	$-0.416849\pi$
$211$	7.50307	0.516533	0.258266	+	0.966074i	$0.416849\pi$
$212$	−2.69860	−0.185340
$213$	−36.1978	−2.48023
$214$	14.2557	0.974496
$215$	−0.447480	−0.0305179
$216$	32.2245	2.19260
$217$	0	0
$218$	−10.5646	−0.715527
$219$	−17.9649	−1.21396
$220$	0.369102	0.0248849
$221$	2.34858	0.157983
$222$	−55.1917	−3.70422
$223$	−24.0338	−1.60943	−0.804713	−	0.593664i	$-0.797681\pi$
$223$	−24.0338	−1.60943	−0.804713	+	0.593664i	$0.797681\pi$
$224$	0	0
$225$	7.04945	0.469963
$226$	5.78539	0.384838
$227$	−1.47641	−0.0979927	−0.0489964	−	0.998799i	$-0.515602\pi$
$227$	−1.47641	−0.0979927	−0.0489964	+	0.998799i	$0.515602\pi$
$228$	−7.60197	−0.503453
$229$	−8.07223	−0.533428	−0.266714	−	0.963776i	$-0.585938\pi$
$229$	−8.07223	−0.533428	−0.266714	+	0.963776i	$0.585938\pi$
$230$	10.7298	0.707502
$231$	0	0
$232$	8.18795	0.537565
$233$	−6.44748	−0.422388	−0.211194	−	0.977444i	$-0.567735\pi$
$233$	−6.44748	−0.422388	−0.211194	+	0.977444i	$0.567735\pi$
$234$	−9.00492	−0.588670
$235$	6.82991	0.445534
$236$	2.93722	0.191197
$237$	−46.1133	−2.99538
$238$	0	0
$239$	−8.18342	−0.529341	−0.264671	−	0.964339i	$-0.585263\pi$
$239$	−8.18342	−0.529341	−0.264671	+	0.964339i	$0.585263\pi$
$240$	−14.5886	−0.941692
$241$	−10.9060	−0.702519	−0.351259	−	0.936278i	$-0.614246\pi$
$241$	−10.9060	−0.702519	−0.351259	+	0.936278i	$0.614246\pi$
$242$	−1.53919	−0.0989428
$243$	23.4524	1.50447
$244$	2.53919	0.162555
$245$	0	0
$246$	−0.971071	−0.0619132
$247$	−5.39189	−0.343078
$248$	25.8504	1.64150
$249$	−9.17727	−0.581586
$250$	−1.53919	−0.0973469
$251$	−18.7948	−1.18632	−0.593160	−	0.805085i	$-0.702120\pi$
$251$	−18.7948	−1.18632	−0.593160	+	0.805085i	$0.702120\pi$
$252$	0	0
$253$	−6.97107	−0.438267
$254$	33.1605	2.08067
$255$	8.97107	0.561790
$256$	8.57531	0.535957
$257$	13.0784	0.815807	0.407903	−	0.913025i	$-0.366260\pi$
$257$	13.0784	0.815807	0.407903	+	0.913025i	$0.366260\pi$
$258$	2.18342	0.135934
$259$	0	0
$260$	0.306323	0.0189973
$261$	22.9939	1.42328
$262$	−19.5174	−1.20579
$263$	−10.0267	−0.618270	−0.309135	−	0.951018i	$-0.600040\pi$
$263$	−10.0267	−0.618270	−0.309135	+	0.951018i	$0.600040\pi$
$264$	7.95774	0.489765
$265$	−7.31124	−0.449126
$266$	0	0
$267$	1.84324	0.112805
$268$	2.29072	0.139928
$269$	11.9155	0.726500	0.363250	−	0.931692i	$-0.381667\pi$
$269$	11.9155	0.726500	0.363250	+	0.931692i	$0.381667\pi$
$270$	−19.7587	−1.20248
$271$	−25.1773	−1.52941	−0.764705	−	0.644380i	$-0.777115\pi$
$271$	−25.1773	−1.52941	−0.764705	+	0.644380i	$0.777115\pi$
$272$	−13.0232	−0.789646
$273$	0	0
$274$	−30.2062	−1.82482
$275$	1.00000	0.0603023
$276$	−8.15676	−0.490979
$277$	−5.33791	−0.320724	−0.160362	−	0.987058i	$-0.551266\pi$
$277$	−5.33791	−0.320724	−0.160362	+	0.987058i	$0.551266\pi$
$278$	−0.764867	−0.0458737
$279$	72.5946	4.34613
$280$	0	0
$281$	16.4703	0.982534	0.491267	−	0.871009i	$-0.336534\pi$
$281$	16.4703	0.982534	0.491267	+	0.871009i	$0.336534\pi$
$282$	−33.3256	−1.98451
$283$	0.948284	0.0563696	0.0281848	−	0.999603i	$-0.491027\pi$
$283$	0.948284	0.0563696	0.0281848	+	0.999603i	$0.491027\pi$
$284$	−4.21461	−0.250091
$285$	−20.5958	−1.21999
$286$	−1.27739	−0.0755339
$287$	0	0
$288$	14.5415	0.856864
$289$	−8.99159	−0.528917
$290$	−5.02052	−0.294815
$291$	6.83710	0.400798
$292$	−2.09171	−0.122408
$293$	7.72487	0.451292	0.225646	−	0.974209i	$-0.427551\pi$
$293$	7.72487	0.451292	0.225646	+	0.974209i	$0.427551\pi$
$294$	0	0
$295$	7.95774	0.463318
$296$	28.3942	1.65038
$297$	12.8371	0.744884
$298$	20.5236	1.18890
$299$	−5.78539	−0.334577
$300$	1.17009	0.0675550
$301$	0	0
$302$	1.62475	0.0934941
$303$	22.8865	1.31480
$304$	29.8987	1.71481
$305$	6.87936	0.393911
$306$	−30.7058	−1.75533
$307$	32.7526	1.86929	0.934644	−	0.355584i	$-0.115718\pi$
$307$	32.7526	1.86929	0.934644	+	0.355584i	$0.115718\pi$
$308$	0	0
$309$	−11.6248	−0.661309
$310$	−15.8504	−0.900244
$311$	−22.9204	−1.29970	−0.649848	−	0.760064i	$-0.725168\pi$
$311$	−22.9204	−1.29970	−0.649848	+	0.760064i	$0.725168\pi$
$312$	6.60424	0.373891
$313$	11.5753	0.654275	0.327137	−	0.944977i	$-0.393916\pi$
$313$	11.5753	0.654275	0.327137	+	0.944977i	$0.393916\pi$
$314$	−0.764867	−0.0431639
$315$	0	0
$316$	−5.36910	−0.302036
$317$	12.5236	0.703395	0.351697	−	0.936114i	$-0.385605\pi$
$317$	12.5236	0.703395	0.351697	+	0.936114i	$0.385605\pi$
$318$	35.6742	2.00051
$319$	3.26180	0.182625
$320$	6.02893	0.337027
$321$	−29.3607	−1.63875
$322$	0	0
$323$	−18.3857	−1.02301
$324$	7.21461	0.400812
$325$	0.829914	0.0460353
$326$	−2.01825	−0.111781
$327$	21.7587	1.20326
$328$	0.499582	0.0275848
$329$	0	0
$330$	−4.87936	−0.268600
$331$	−18.1711	−0.998776	−0.499388	−	0.866379i	$-0.666442\pi$
$331$	−18.1711	−0.998776	−0.499388	+	0.866379i	$0.666442\pi$
$332$	−1.06854	−0.0586436
$333$	79.7380	4.36962
$334$	4.89043	0.267592
$335$	6.20620	0.339081
$336$	0	0
$337$	28.0905	1.53019	0.765093	−	0.643920i	$-0.222693\pi$
$337$	28.0905	1.53019	0.765093	+	0.643920i	$0.222693\pi$
$338$	18.9493	1.03071
$339$	−11.9155	−0.647160
$340$	1.04453	0.0566475
$341$	10.2979	0.557663
$342$	70.4945	3.81191
$343$	0	0
$344$	−1.12329	−0.0605638
$345$	−22.0989	−1.18976
$346$	−27.6274	−1.48526
$347$	22.0761	1.18511	0.592554	−	0.805531i	$-0.298120\pi$
$347$	22.0761	1.18511	0.592554	+	0.805531i	$0.298120\pi$
$348$	3.81658	0.204590
$349$	−18.2134	−0.974941	−0.487470	−	0.873140i	$-0.662080\pi$
$349$	−18.2134	−0.974941	−0.487470	+	0.873140i	$0.662080\pi$
$350$	0	0
$351$	10.6537	0.568652
$352$	2.06278	0.109947
$353$	1.41855	0.0755018	0.0377509	−	0.999287i	$-0.487981\pi$
$353$	1.41855	0.0755018	0.0377509	+	0.999287i	$0.487981\pi$
$354$	−38.8287	−2.06372
$355$	−11.4186	−0.606034
$356$	0.214614	0.0113745
$357$	0	0
$358$	−24.2146	−1.27978
$359$	13.0700	0.689806	0.344903	−	0.938638i	$-0.387912\pi$
$359$	13.0700	0.689806	0.344903	+	0.938638i	$0.387912\pi$
$360$	17.6959	0.932658
$361$	23.2101	1.22158
$362$	−25.8744	−1.35993
$363$	3.17009	0.166386
$364$	0	0
$365$	−5.66701	−0.296625
$366$	−33.5669	−1.75457
$367$	−19.7926	−1.03316	−0.516582	−	0.856238i	$-0.672796\pi$
$367$	−19.7926	−1.03316	−0.516582	+	0.856238i	$0.672796\pi$
$368$	32.0806	1.67232
$369$	1.40295	0.0730348
$370$	−17.4101	−0.905110
$371$	0	0
$372$	12.0494	0.624735
$373$	−31.4101	−1.62636	−0.813178	−	0.582015i	$-0.802264\pi$
$373$	−31.4101	−1.62636	−0.813178	+	0.582015i	$0.802264\pi$
$374$	−4.35577	−0.225232
$375$	3.17009	0.163703
$376$	17.1449	0.884178
$377$	2.70701	0.139418
$378$	0	0
$379$	21.9421	1.12709	0.563546	−	0.826085i	$-0.309437\pi$
$379$	21.9421	1.12709	0.563546	+	0.826085i	$0.309437\pi$
$380$	−2.39803	−0.123016
$381$	−68.2967	−3.49895
$382$	4.49693	0.230083
$383$	−6.95547	−0.355408	−0.177704	−	0.984084i	$-0.556867\pi$
$383$	−6.95547	−0.355408	−0.177704	+	0.984084i	$0.556867\pi$
$384$	−42.4957	−2.16860
$385$	0	0
$386$	35.1377	1.78846
$387$	−3.15449	−0.160352
$388$	0.796064	0.0404140
$389$	2.76487	0.140184	0.0700922	−	0.997541i	$-0.477671\pi$
$389$	2.76487	0.140184	0.0700922	+	0.997541i	$0.477671\pi$
$390$	−4.04945	−0.205052
$391$	−19.7275	−0.997664
$392$	0	0
$393$	40.1978	2.02771
$394$	−30.3584	−1.52944
$395$	−14.5464	−0.731908
$396$	2.60197	0.130754
$397$	−6.92162	−0.347386	−0.173693	−	0.984800i	$-0.555570\pi$
$397$	−6.92162	−0.347386	−0.173693	+	0.984800i	$0.555570\pi$
$398$	−16.3740	−0.820756
$399$	0	0
$400$	−4.60197	−0.230098
$401$	−6.68035	−0.333601	−0.166800	−	0.985991i	$-0.553344\pi$
$401$	−6.68035	−0.333601	−0.166800	+	0.985991i	$0.553344\pi$
$402$	−30.2823	−1.51034
$403$	8.54638	0.425725
$404$	2.66475	0.132576
$405$	19.5464	0.971267
$406$	0	0
$407$	11.3112	0.560678
$408$	22.5197	1.11489
$409$	−15.0772	−0.745517	−0.372759	−	0.927928i	$-0.621588\pi$
$409$	−15.0772	−0.745517	−0.372759	+	0.927928i	$0.621588\pi$
$410$	−0.306323	−0.0151282
$411$	62.2122	3.06870
$412$	−1.35350	−0.0666824
$413$	0	0
$414$	75.6391	3.71746
$415$	−2.89496	−0.142108
$416$	1.71193	0.0839342
$417$	1.57531	0.0771431
$418$	10.0000	0.489116
$419$	9.54533	0.466320	0.233160	−	0.972438i	$-0.425093\pi$
$419$	9.54533	0.466320	0.233160	+	0.972438i	$0.425093\pi$
$420$	0	0
$421$	−32.7442	−1.59585	−0.797927	−	0.602755i	$-0.794070\pi$
$421$	−32.7442	−1.59585	−0.797927	+	0.602755i	$0.794070\pi$
$422$	−11.5486	−0.562179
$423$	48.1471	2.34099
$424$	−18.3531	−0.891306
$425$	2.82991	0.137271
$426$	55.7152	2.69941
$427$	0	0
$428$	−3.41855	−0.165242
$429$	2.63090	0.127021
$430$	0.688756	0.0332148
$431$	−23.0289	−1.10926	−0.554632	−	0.832096i	$-0.687141\pi$
$431$	−23.0289	−1.10926	−0.554632	+	0.832096i	$0.687141\pi$
$432$	−59.0759	−2.84229
$433$	34.3279	1.64969	0.824846	−	0.565357i	$-0.191262\pi$
$433$	34.3279	1.64969	0.824846	+	0.565357i	$0.191262\pi$
$434$	0	0
$435$	10.3402	0.495773
$436$	2.53343	0.121329
$437$	45.2905	2.16654
$438$	27.6514	1.32124
$439$	16.5958	0.792076	0.396038	−	0.918234i	$-0.370385\pi$
$439$	16.5958	0.792076	0.396038	+	0.918234i	$0.370385\pi$
$440$	2.51026	0.119672
$441$	0	0
$442$	−3.61491	−0.171944
$443$	10.9177	0.518718	0.259359	−	0.965781i	$-0.416489\pi$
$443$	10.9177	0.518718	0.259359	+	0.965781i	$0.416489\pi$
$444$	13.2351	0.628112
$445$	0.581449	0.0275633
$446$	36.9926	1.75165
$447$	−42.2700	−1.99930
$448$	0	0
$449$	−24.5997	−1.16093	−0.580466	−	0.814285i	$-0.697130\pi$
$449$	−24.5997	−1.16093	−0.580466	+	0.814285i	$0.697130\pi$
$450$	−10.8504	−0.511494
$451$	0.199016	0.00937129
$452$	−1.38735	−0.0652556
$453$	−3.34632	−0.157224
$454$	2.27247	0.106652
$455$	0	0
$456$	−51.7009	−2.42111
$457$	−36.9854	−1.73011	−0.865053	−	0.501680i	$-0.832715\pi$
$457$	−36.9854	−1.73011	−0.865053	+	0.501680i	$0.832715\pi$
$458$	12.4247	0.580568
$459$	36.3279	1.69564
$460$	−2.57304	−0.119969
$461$	−37.3595	−1.74000	−0.870002	−	0.493048i	$-0.835883\pi$
$461$	−37.3595	−1.74000	−0.870002	+	0.493048i	$0.835883\pi$
$462$	0	0
$463$	7.05559	0.327901	0.163951	−	0.986469i	$-0.447576\pi$
$463$	7.05559	0.327901	0.163951	+	0.986469i	$0.447576\pi$
$464$	−15.0107	−0.696853
$465$	32.6453	1.51389
$466$	9.92389	0.459715
$467$	19.8648	0.919234	0.459617	−	0.888117i	$-0.347987\pi$
$467$	19.8648	0.919234	0.459617	+	0.888117i	$0.347987\pi$
$468$	2.15941	0.0998187
$469$	0	0
$470$	−10.5125	−0.484907
$471$	1.57531	0.0725863
$472$	19.9760	0.919470
$473$	−0.447480	−0.0205752
$474$	70.9770	3.26008
$475$	−6.49693	−0.298100
$476$	0	0
$477$	−51.5402	−2.35987
$478$	12.5958	0.576120
$479$	−6.39803	−0.292334	−0.146167	−	0.989260i	$-0.546694\pi$
$479$	−6.39803	−0.292334	−0.146167	+	0.989260i	$0.546694\pi$
$480$	6.53919	0.298472
$481$	9.38735	0.428026
$482$	16.7864	0.764601
$483$	0	0
$484$	0.369102	0.0167774
$485$	2.15676	0.0979332
$486$	−36.0977	−1.63742
$487$	−25.8082	−1.16948	−0.584740	−	0.811221i	$-0.698803\pi$
$487$	−25.8082	−1.16948	−0.584740	+	0.811221i	$0.698803\pi$
$488$	17.2690	0.781730
$489$	4.15676	0.187975
$490$	0	0
$491$	−17.1689	−0.774820	−0.387410	−	0.921908i	$-0.626630\pi$
$491$	−17.1689	−0.774820	−0.387410	+	0.921908i	$0.626630\pi$
$492$	0.232866	0.0104984
$493$	9.23060	0.415725
$494$	8.29914	0.373396
$495$	7.04945	0.316849
$496$	−47.3907	−2.12790
$497$	0	0
$498$	14.1256	0.632981
$499$	−13.1629	−0.589252	−0.294626	−	0.955613i	$-0.595195\pi$
$499$	−13.1629	−0.589252	−0.294626	+	0.955613i	$0.595195\pi$
$500$	0.369102	0.0165068
$501$	−10.0722	−0.449994
$502$	28.9288	1.29116
$503$	30.7259	1.37000	0.685000	−	0.728543i	$-0.259802\pi$
$503$	30.7259	1.37000	0.685000	+	0.728543i	$0.259802\pi$
$504$	0	0
$505$	7.21953	0.321265
$506$	10.7298	0.476998
$507$	−39.0277	−1.73328
$508$	−7.95198	−0.352812
$509$	−25.2183	−1.11778	−0.558891	−	0.829241i	$-0.688773\pi$
$509$	−25.2183	−1.11778	−0.558891	+	0.829241i	$0.688773\pi$
$510$	−13.8082	−0.611436
$511$	0	0
$512$	13.6114	0.601546
$513$	−83.4017	−3.68228
$514$	−20.1301	−0.887900
$515$	−3.66701	−0.161588
$516$	−0.523590	−0.0230498
$517$	6.82991	0.300379
$518$	0	0
$519$	56.9009	2.49767
$520$	2.08330	0.0913587
$521$	−0.183417	−0.00803567	−0.00401783	−	0.999992i	$-0.501279\pi$
$521$	−0.183417	−0.00803567	−0.00401783	+	0.999992i	$0.501279\pi$
$522$	−35.3919	−1.54906
$523$	4.86830	0.212876	0.106438	−	0.994319i	$-0.466055\pi$
$523$	4.86830	0.212876	0.106438	+	0.994319i	$0.466055\pi$
$524$	4.68035	0.204462
$525$	0	0
$526$	15.4329	0.672908
$527$	29.1422	1.26945
$528$	−14.5886	−0.634889
$529$	25.5958	1.11286
$530$	11.2534	0.488816
$531$	56.0977	2.43443
$532$	0	0
$533$	0.165166	0.00715413
$534$	−2.83710	−0.122773
$535$	−9.26180	−0.400422
$536$	15.5792	0.672918
$537$	49.8720	2.15214
$538$	−18.3402	−0.790701
$539$	0	0
$540$	4.73820	0.203900
$541$	−45.7009	−1.96483	−0.982417	−	0.186701i	$-0.940221\pi$
$541$	−45.7009	−1.96483	−0.982417	+	0.186701i	$0.940221\pi$
$542$	38.7526	1.66457
$543$	53.2905	2.28692
$544$	5.83749	0.250280
$545$	6.86376	0.294011
$546$	0	0
$547$	−24.5958	−1.05164	−0.525821	−	0.850595i	$-0.676242\pi$
$547$	−24.5958	−1.05164	−0.525821	+	0.850595i	$0.676242\pi$
$548$	7.24354	0.309429
$549$	48.4957	2.06975
$550$	−1.53919	−0.0656312
$551$	−21.1917	−0.902795
$552$	−55.4740	−2.36113
$553$	0	0
$554$	8.21604	0.349066
$555$	35.8576	1.52207
$556$	0.183417	0.00777863
$557$	33.6514	1.42586	0.712928	−	0.701237i	$-0.247369\pi$
$557$	33.6514	1.42586	0.712928	+	0.701237i	$0.247369\pi$
$558$	−111.737	−4.73020
$559$	−0.371370	−0.0157073
$560$	0	0
$561$	8.97107	0.378759
$562$	−25.3509	−1.06936
$563$	32.2290	1.35829	0.679145	−	0.734004i	$-0.262351\pi$
$563$	32.2290	1.35829	0.679145	+	0.734004i	$0.262351\pi$
$564$	7.99159	0.336507
$565$	−3.75872	−0.158131
$566$	−1.45959	−0.0613511
$567$	0	0
$568$	−28.6635	−1.20269
$569$	5.33403	0.223614	0.111807	−	0.993730i	$-0.464336\pi$
$569$	5.33403	0.223614	0.111807	+	0.993730i	$0.464336\pi$
$570$	31.7009	1.32780
$571$	−29.5441	−1.23638	−0.618191	−	0.786028i	$-0.712134\pi$
$571$	−29.5441	−1.23638	−0.618191	+	0.786028i	$0.712134\pi$
$572$	0.306323	0.0128080
$573$	−9.26180	−0.386917
$574$	0	0
$575$	−6.97107	−0.290714
$576$	42.5006	1.77086
$577$	−3.78539	−0.157588	−0.0787938	−	0.996891i	$-0.525107\pi$
$577$	−3.78539	−0.157588	−0.0787938	+	0.996891i	$0.525107\pi$
$578$	13.8398	0.575658
$579$	−72.3689	−3.00755
$580$	1.20394	0.0499907
$581$	0	0
$582$	−10.5236	−0.436217
$583$	−7.31124	−0.302801
$584$	−14.2257	−0.588663
$585$	5.85043	0.241886
$586$	−11.8900	−0.491173
$587$	−14.5353	−0.599937	−0.299968	−	0.953949i	$-0.596976\pi$
$587$	−14.5353	−0.599937	−0.299968	+	0.953949i	$0.596976\pi$
$588$	0	0
$589$	−66.9048	−2.75676
$590$	−12.2485	−0.504261
$591$	62.5257	2.57196
$592$	−52.0540	−2.13941
$593$	−43.6814	−1.79378	−0.896890	−	0.442254i	$-0.854179\pi$
$593$	−43.6814	−1.79378	−0.896890	+	0.442254i	$0.854179\pi$
$594$	−19.7587	−0.810710
$595$	0	0
$596$	−4.92162	−0.201598
$597$	33.7237	1.38022
$598$	8.90480	0.364144
$599$	−22.8371	−0.933099	−0.466549	−	0.884495i	$-0.654503\pi$
$599$	−22.8371	−0.933099	−0.466549	+	0.884495i	$0.654503\pi$
$600$	7.95774	0.324873
$601$	27.8687	1.13679	0.568394	−	0.822757i	$-0.307565\pi$
$601$	27.8687	1.13679	0.568394	+	0.822757i	$0.307565\pi$
$602$	0	0
$603$	43.7503	1.78165
$604$	−0.389621	−0.0158535
$605$	1.00000	0.0406558
$606$	−35.2267	−1.43099
$607$	−29.8987	−1.21355	−0.606775	−	0.794874i	$-0.707537\pi$
$607$	−29.8987	−1.21355	−0.606775	+	0.794874i	$0.707537\pi$
$608$	−13.4017	−0.543512
$609$	0	0
$610$	−10.5886	−0.428721
$611$	5.66824	0.229312
$612$	7.36334	0.297646
$613$	21.0700	0.851008	0.425504	−	0.904957i	$-0.360097\pi$
$613$	21.0700	0.851008	0.425504	+	0.904957i	$0.360097\pi$
$614$	−50.4124	−2.03448
$615$	0.630898	0.0254402
$616$	0	0
$617$	4.10731	0.165354	0.0826770	−	0.996576i	$-0.473653\pi$
$617$	4.10731	0.165354	0.0826770	+	0.996576i	$0.473653\pi$
$618$	17.8927	0.719750
$619$	14.5536	0.584957	0.292479	−	0.956272i	$-0.405520\pi$
$619$	14.5536	0.584957	0.292479	+	0.956272i	$0.405520\pi$
$620$	3.80098	0.152651
$621$	−89.4883	−3.59104
$622$	35.2788	1.41455
$623$	0	0
$624$	−12.1073	−0.484680
$625$	1.00000	0.0400000
$626$	−17.8166	−0.712094
$627$	−20.5958	−0.822518
$628$	0.183417	0.00731915
$629$	32.0098	1.27632
$630$	0	0
$631$	12.9939	0.517277	0.258639	−	0.965974i	$-0.416726\pi$
$631$	12.9939	0.517277	0.258639	+	0.965974i	$0.416726\pi$
$632$	−36.5152	−1.45250
$633$	23.7854	0.945384
$634$	−19.2762	−0.765555
$635$	−21.5441	−0.854952
$636$	−8.55479	−0.339219
$637$	0	0
$638$	−5.02052	−0.198764
$639$	−80.4945	−3.18431
$640$	−13.4052	−0.529888
$641$	8.54638	0.337562	0.168781	−	0.985654i	$-0.446017\pi$
$641$	8.54638	0.337562	0.168781	+	0.985654i	$0.446017\pi$
$642$	45.1917	1.78357
$643$	−17.7659	−0.700619	−0.350310	−	0.936634i	$-0.613924\pi$
$643$	−17.7659	−0.700619	−0.350310	+	0.936634i	$0.613924\pi$
$644$	0	0
$645$	−1.41855	−0.0558554
$646$	28.2991	1.11341
$647$	−44.9698	−1.76795	−0.883974	−	0.467537i	$-0.845142\pi$
$647$	−44.9698	−1.76795	−0.883974	+	0.467537i	$0.845142\pi$
$648$	49.0665	1.92751
$649$	7.95774	0.312369
$650$	−1.27739	−0.0501035
$651$	0	0
$652$	0.483983	0.0189542
$653$	−4.75258	−0.185983	−0.0929914	−	0.995667i	$-0.529643\pi$
$653$	−4.75258	−0.185983	−0.0929914	+	0.995667i	$0.529643\pi$
$654$	−33.4908	−1.30959
$655$	12.6803	0.495462
$656$	−0.915865	−0.0357585
$657$	−39.9493	−1.55857
$658$	0	0
$659$	−17.2990	−0.673872	−0.336936	−	0.941528i	$-0.609391\pi$
$659$	−17.2990	−0.673872	−0.336936	+	0.941528i	$0.609391\pi$
$660$	1.17009	0.0455456
$661$	−29.1629	−1.13431	−0.567153	−	0.823613i	$-0.691955\pi$
$661$	−29.1629	−1.13431	−0.567153	+	0.823613i	$0.691955\pi$
$662$	27.9688	1.08704
$663$	7.44521	0.289148
$664$	−7.26710	−0.282018
$665$	0	0
$666$	−122.732	−4.75576
$667$	−22.7382	−0.880427
$668$	−1.17274	−0.0453747
$669$	−76.1894	−2.94565
$670$	−9.55252	−0.369046
$671$	6.87936	0.265575
$672$	0	0
$673$	36.0905	1.39119	0.695593	−	0.718436i	$-0.255142\pi$
$673$	36.0905	1.39119	0.695593	+	0.718436i	$0.255142\pi$
$674$	−43.2366	−1.66541
$675$	12.8371	0.494100
$676$	−4.54411	−0.174773
$677$	12.7310	0.489293	0.244646	−	0.969612i	$-0.421328\pi$
$677$	12.7310	0.489293	0.244646	+	0.969612i	$0.421328\pi$
$678$	18.3402	0.704350
$679$	0	0
$680$	7.10382	0.272419
$681$	−4.68035	−0.179351
$682$	−15.8504	−0.606944
$683$	−5.47253	−0.209401	−0.104700	−	0.994504i	$-0.533388\pi$
$683$	−5.47253	−0.209401	−0.104700	+	0.994504i	$0.533388\pi$
$684$	−16.9048	−0.646371
$685$	19.6248	0.749823
$686$	0	0
$687$	−25.5897	−0.976307
$688$	2.05929	0.0785097
$689$	−6.06770	−0.231161
$690$	34.0144	1.29491
$691$	−30.7226	−1.16874	−0.584372	−	0.811486i	$-0.698659\pi$
$691$	−30.7226	−1.16874	−0.584372	+	0.811486i	$0.698659\pi$
$692$	6.62514	0.251850
$693$	0	0
$694$	−33.9793	−1.28984
$695$	0.496928	0.0188496
$696$	25.9565	0.983879
$697$	0.563198	0.0213326
$698$	28.0338	1.06110
$699$	−20.4391	−0.773077
$700$	0	0
$701$	−14.7649	−0.557661	−0.278831	−	0.960340i	$-0.589947\pi$
$701$	−14.7649	−0.557661	−0.278831	+	0.960340i	$0.589947\pi$
$702$	−16.3980	−0.618904
$703$	−73.4883	−2.77167
$704$	6.02893	0.227224
$705$	21.6514	0.815440
$706$	−2.18342	−0.0821740
$707$	0	0
$708$	9.31124	0.349938
$709$	−5.63317	−0.211558	−0.105779	−	0.994390i	$-0.533734\pi$
$709$	−5.63317	−0.211558	−0.105779	+	0.994390i	$0.533734\pi$
$710$	17.5753	0.659589
$711$	−102.544	−3.84570
$712$	1.45959	0.0547004
$713$	−71.7875	−2.68846
$714$	0	0
$715$	0.829914	0.0310370
$716$	5.80674	0.217008
$717$	−25.9421	−0.968827
$718$	−20.1171	−0.750765
$719$	−35.0505	−1.30716	−0.653581	−	0.756856i	$-0.726734\pi$
$719$	−35.0505	−1.30716	−0.653581	+	0.756856i	$0.726734\pi$
$720$	−32.4413	−1.20902
$721$	0	0
$722$	−35.7247	−1.32954
$723$	−34.5730	−1.28579
$724$	6.20477	0.230599
$725$	3.26180	0.121140
$726$	−4.87936	−0.181090
$727$	1.80486	0.0669385	0.0334693	−	0.999440i	$-0.489344\pi$
$727$	1.80486	0.0669385	0.0334693	+	0.999440i	$0.489344\pi$
$728$	0	0
$729$	15.7070	0.581741
$730$	8.72261	0.322838
$731$	−1.26633	−0.0468369
$732$	8.04945	0.297516
$733$	34.0338	1.25707	0.628534	−	0.777782i	$-0.283655\pi$
$733$	34.0338	1.25707	0.628534	+	0.777782i	$0.283655\pi$
$734$	30.4645	1.12447
$735$	0	0
$736$	−14.3798	−0.530046
$737$	6.20620	0.228608
$738$	−2.15941	−0.0794889
$739$	−14.1568	−0.520765	−0.260382	−	0.965506i	$-0.583849\pi$
$739$	−14.1568	−0.520765	−0.260382	+	0.965506i	$0.583849\pi$
$740$	4.17501	0.153476
$741$	−17.0928	−0.627918
$742$	0	0
$743$	6.62249	0.242955	0.121478	−	0.992594i	$-0.461237\pi$
$743$	6.62249	0.242955	0.121478	+	0.992594i	$0.461237\pi$
$744$	81.9481	3.00436
$745$	−13.3340	−0.488521
$746$	48.3461	1.77008
$747$	−20.4079	−0.746685
$748$	1.04453	0.0381917
$749$	0	0
$750$	−4.87936	−0.178169
$751$	28.6947	1.04709	0.523543	−	0.851999i	$-0.324610\pi$
$751$	28.6947	1.04709	0.523543	+	0.851999i	$0.324610\pi$
$752$	−31.4310	−1.14617
$753$	−59.5813	−2.17126
$754$	−4.16660	−0.151738
$755$	−1.05559	−0.0384169
$756$	0	0
$757$	13.3874	0.486572	0.243286	−	0.969955i	$-0.421775\pi$
$757$	13.3874	0.486572	0.243286	+	0.969955i	$0.421775\pi$
$758$	−33.7731	−1.22669
$759$	−22.0989	−0.802139
$760$	−16.3090	−0.591589
$761$	−37.3041	−1.35227	−0.676135	−	0.736777i	$-0.736347\pi$
$761$	−37.3041	−1.35227	−0.676135	+	0.736777i	$0.736347\pi$
$762$	105.122	3.80815
$763$	0	0
$764$	−1.07838	−0.0390143
$765$	19.9493	0.721270
$766$	10.7058	0.386816
$767$	6.60424	0.238465
$768$	27.1845	0.980935
$769$	12.0156	0.433294	0.216647	−	0.976250i	$-0.430488\pi$
$769$	12.0156	0.433294	0.216647	+	0.976250i	$0.430488\pi$
$770$	0	0
$771$	41.4596	1.49313
$772$	−8.42612	−0.303263
$773$	−3.20394	−0.115238	−0.0576188	−	0.998339i	$-0.518351\pi$
$773$	−3.20394	−0.115238	−0.0576188	+	0.998339i	$0.518351\pi$
$774$	4.85535	0.174522
$775$	10.2979	0.369912
$776$	5.41402	0.194352
$777$	0	0
$778$	−4.25565	−0.152573
$779$	−1.29299	−0.0463262
$780$	0.971071	0.0347699
$781$	−11.4186	−0.408588
$782$	30.3644	1.08583
$783$	41.8720	1.49638
$784$	0	0
$785$	0.496928	0.0177361
$786$	−61.8720	−2.20690
$787$	5.13170	0.182925	0.0914627	−	0.995809i	$-0.470846\pi$
$787$	5.13170	0.182925	0.0914627	+	0.995809i	$0.470846\pi$
$788$	7.28005	0.259341
$789$	−31.7854	−1.13159
$790$	22.3896	0.796587
$791$	0	0
$792$	17.6959	0.628798
$793$	5.70928	0.202742
$794$	10.6537	0.378085
$795$	−23.1773	−0.822013
$796$	3.92654	0.139173
$797$	−8.86376	−0.313971	−0.156985	−	0.987601i	$-0.550178\pi$
$797$	−8.86376	−0.313971	−0.156985	+	0.987601i	$0.550178\pi$
$798$	0	0
$799$	19.3281	0.683778
$800$	2.06278	0.0729303
$801$	4.09890	0.144827
$802$	10.2823	0.363081
$803$	−5.66701	−0.199985
$804$	7.26180	0.256104
$805$	0	0
$806$	−13.1545	−0.463347
$807$	37.7731	1.32968
$808$	18.1229	0.637562
$809$	16.7915	0.590359	0.295179	−	0.955442i	$-0.404621\pi$
$809$	16.7915	0.590359	0.295179	+	0.955442i	$0.404621\pi$
$810$	−30.0856	−1.05710
$811$	−23.9421	−0.840722	−0.420361	−	0.907357i	$-0.638097\pi$
$811$	−23.9421	−0.840722	−0.420361	+	0.907357i	$0.638097\pi$
$812$	0	0
$813$	−79.8141	−2.79920
$814$	−17.4101	−0.610225
$815$	1.31124	0.0459309
$816$	−41.2846	−1.44525
$817$	2.90725	0.101712
$818$	23.2066	0.811399
$819$	0	0
$820$	0.0734572	0.00256524
$821$	15.7054	0.548122	0.274061	−	0.961712i	$-0.411633\pi$
$821$	15.7054	0.548122	0.274061	+	0.961712i	$0.411633\pi$
$822$	−95.7563	−3.33988
$823$	−40.5152	−1.41227	−0.706135	−	0.708077i	$-0.749563\pi$
$823$	−40.5152	−1.41227	−0.706135	+	0.708077i	$0.749563\pi$
$824$	−9.20516	−0.320677
$825$	3.17009	0.110368
$826$	0	0
$827$	29.6391	1.03065	0.515327	−	0.856994i	$-0.327671\pi$
$827$	29.6391	1.03065	0.515327	+	0.856994i	$0.327671\pi$
$828$	−18.1385	−0.630357
$829$	−28.7838	−0.999702	−0.499851	−	0.866111i	$-0.666612\pi$
$829$	−28.7838	−0.999702	−0.499851	+	0.866111i	$0.666612\pi$
$830$	4.45589	0.154666
$831$	−16.9216	−0.587005
$832$	5.00349	0.173465
$833$	0	0
$834$	−2.42469	−0.0839603
$835$	−3.17727	−0.109954
$836$	−2.39803	−0.0829377
$837$	132.195	4.56934
$838$	−14.6921	−0.507529
$839$	11.1350	0.384423	0.192212	−	0.981353i	$-0.438434\pi$
$839$	11.1350	0.384423	0.192212	+	0.981353i	$0.438434\pi$
$840$	0	0
$841$	−18.3607	−0.633127
$842$	50.3995	1.73688
$843$	52.2122	1.79828
$844$	2.76940	0.0953267
$845$	−12.3112	−0.423520
$846$	−74.1075	−2.54787
$847$	0	0
$848$	33.6461	1.15541
$849$	3.00614	0.103171
$850$	−4.35577	−0.149402
$851$	−78.8515	−2.70299
$852$	−13.3607	−0.457730
$853$	−2.00719	−0.0687248	−0.0343624	−	0.999409i	$-0.510940\pi$
$853$	−2.00719	−0.0687248	−0.0343624	+	0.999409i	$0.510940\pi$
$854$	0	0
$855$	−45.7998	−1.56632
$856$	−23.2495	−0.794652
$857$	−21.2013	−0.724222	−0.362111	−	0.932135i	$-0.617944\pi$
$857$	−21.2013	−0.724222	−0.362111	+	0.932135i	$0.617944\pi$
$858$	−4.04945	−0.138246
$859$	−38.6959	−1.32029	−0.660144	−	0.751139i	$-0.729505\pi$
$859$	−38.6959	−1.32029	−0.660144	+	0.751139i	$0.729505\pi$
$860$	−0.165166	−0.00563211
$861$	0	0
$862$	35.4459	1.20729
$863$	38.3728	1.30623	0.653113	−	0.757261i	$-0.273463\pi$
$863$	38.3728	1.30623	0.653113	+	0.757261i	$0.273463\pi$
$864$	26.4801	0.900872
$865$	17.9493	0.610295
$866$	−52.8371	−1.79548
$867$	−28.5041	−0.968051
$868$	0	0
$869$	−14.5464	−0.493452
$870$	−15.9155	−0.539585
$871$	5.15061	0.174522
$872$	17.2298	0.583476
$873$	15.2039	0.514575
$874$	−69.7107	−2.35800
$875$	0	0
$876$	−6.63090	−0.224037
$877$	−32.3195	−1.09135	−0.545676	−	0.837997i	$-0.683727\pi$
$877$	−32.3195	−1.09135	−0.545676	+	0.837997i	$0.683727\pi$
$878$	−25.5441	−0.862072
$879$	24.4885	0.825977
$880$	−4.60197	−0.155132
$881$	45.3217	1.52693	0.763464	−	0.645850i	$-0.223497\pi$
$881$	45.3217	1.52693	0.763464	+	0.645850i	$0.223497\pi$
$882$	0	0
$883$	42.5197	1.43090	0.715451	−	0.698663i	$-0.246221\pi$
$883$	42.5197	1.43090	0.715451	+	0.698663i	$0.246221\pi$
$884$	0.866868	0.0291559
$885$	25.2267	0.847987
$886$	−16.8045	−0.564557
$887$	44.6947	1.50070	0.750351	−	0.661040i	$-0.229885\pi$
$887$	44.6947	1.50070	0.750351	+	0.661040i	$0.229885\pi$
$888$	90.0119	3.02060
$889$	0	0
$890$	−0.894960	−0.0299991
$891$	19.5464	0.654828
$892$	−8.87095	−0.297021
$893$	−44.3735	−1.48490
$894$	65.0616	2.17598
$895$	15.7321	0.525865
$896$	0	0
$897$	−18.3402	−0.612361
$898$	37.8636	1.26352
$899$	33.5897	1.12028
$900$	2.60197	0.0867323
$901$	−20.6902	−0.689290
$902$	−0.306323	−0.0101994
$903$	0	0
$904$	−9.43537	−0.313816
$905$	16.8104	0.558798
$906$	5.15061	0.171118
$907$	5.28912	0.175622	0.0878111	−	0.996137i	$-0.472013\pi$
$907$	5.28912	0.175622	0.0878111	+	0.996137i	$0.472013\pi$
$908$	−0.544946	−0.0180847
$909$	50.8937	1.68804
$910$	0	0
$911$	−47.7321	−1.58143	−0.790717	−	0.612182i	$-0.790292\pi$
$911$	−47.7321	−1.58143	−0.790717	+	0.612182i	$0.790292\pi$
$912$	94.7813	3.13852
$913$	−2.89496	−0.0958092
$914$	56.9276	1.88300
$915$	21.8082	0.720956
$916$	−2.97948	−0.0984448
$917$	0	0
$918$	−55.9155	−1.84549
$919$	45.6886	1.50713	0.753564	−	0.657375i	$-0.228333\pi$
$919$	45.6886	1.50713	0.753564	+	0.657375i	$0.228333\pi$
$920$	−17.4992	−0.576931
$921$	103.829	3.42127
$922$	57.5033	1.89377
$923$	−9.47641	−0.311920
$924$	0	0
$925$	11.3112	0.371911
$926$	−10.8599	−0.356878
$927$	−25.8504	−0.849040
$928$	6.72836	0.220869
$929$	−35.3874	−1.16102	−0.580511	−	0.814253i	$-0.697147\pi$
$929$	−35.3874	−1.16102	−0.580511	+	0.814253i	$0.697147\pi$
$930$	−50.2472	−1.64767
$931$	0	0
$932$	−2.37978	−0.0779523
$933$	−72.6596	−2.37877
$934$	−30.5757	−1.00047
$935$	2.82991	0.0925481
$936$	14.6861	0.480030
$937$	23.2378	0.759145	0.379573	−	0.925162i	$-0.376071\pi$
$937$	23.2378	0.759145	0.379573	+	0.925162i	$0.376071\pi$
$938$	0	0
$939$	36.6947	1.19749
$940$	2.52094	0.0822239
$941$	−29.2651	−0.954015	−0.477008	−	0.878899i	$-0.658279\pi$
$941$	−29.2651	−0.954015	−0.477008	+	0.878899i	$0.658279\pi$
$942$	−2.42469	−0.0790008
$943$	−1.38735	−0.0451785
$944$	−36.6213	−1.19192
$945$	0	0
$946$	0.688756	0.0223934
$947$	−5.55705	−0.180580	−0.0902900	−	0.995916i	$-0.528779\pi$
$947$	−5.55705	−0.180580	−0.0902900	+	0.995916i	$0.528779\pi$
$948$	−17.0205	−0.552801
$949$	−4.70313	−0.152670
$950$	10.0000	0.324443
$951$	39.7009	1.28739
$952$	0	0
$953$	−11.7548	−0.380777	−0.190388	−	0.981709i	$-0.560975\pi$
$953$	−11.7548	−0.380777	−0.190388	+	0.981709i	$0.560975\pi$
$954$	79.3302	2.56841
$955$	−2.92162	−0.0945415
$956$	−3.02052	−0.0976906
$957$	10.3402	0.334250
$958$	9.84778	0.318167
$959$	0	0
$960$	19.1122	0.616844
$961$	75.0470	2.42087
$962$	−14.4489	−0.465852
$963$	−65.2905	−2.10396
$964$	−4.02544	−0.129651
$965$	−22.8287	−0.734882
$966$	0	0
$967$	33.2267	1.06850	0.534250	−	0.845327i	$-0.320594\pi$
$967$	33.2267	1.06850	0.534250	+	0.845327i	$0.320594\pi$
$968$	2.51026	0.0806828
$969$	−58.2844	−1.87236
$970$	−3.31965	−0.106588
$971$	−3.16621	−0.101609	−0.0508043	−	0.998709i	$-0.516178\pi$
$971$	−3.16621	−0.101609	−0.0508043	+	0.998709i	$0.516178\pi$
$972$	8.65634	0.277652
$973$	0	0
$974$	39.7237	1.27283
$975$	2.63090	0.0842562
$976$	−31.6586	−1.01337
$977$	−32.4391	−1.03782	−0.518909	−	0.854830i	$-0.673662\pi$
$977$	−32.4391	−1.03782	−0.518909	+	0.854830i	$0.673662\pi$
$978$	−6.39803	−0.204586
$979$	0.581449	0.0185832
$980$	0	0
$981$	48.3857	1.54484
$982$	26.4261	0.843292
$983$	30.1496	0.961622	0.480811	−	0.876824i	$-0.340342\pi$
$983$	30.1496	0.961622	0.480811	+	0.876824i	$0.340342\pi$
$984$	1.58372	0.0504870
$985$	19.7237	0.628448
$986$	−14.2076	−0.452463
$987$	0	0
$988$	−1.99016	−0.0633154
$989$	3.11942	0.0991916
$990$	−10.8504	−0.344849
$991$	−21.4452	−0.681230	−0.340615	−	0.940203i	$-0.610635\pi$
$991$	−21.4452	−0.681230	−0.340615	+	0.940203i	$0.610635\pi$
$992$	21.2423	0.674444
$993$	−57.6041	−1.82801
$994$	0	0
$995$	10.6381	0.337250
$996$	−3.38735	−0.107332
$997$	−39.6547	−1.25588	−0.627939	−	0.778263i	$-0.716101\pi$
$997$	−39.6547	−1.25588	−0.627939	+	0.778263i	$0.716101\pi$
$998$	20.2602	0.641325
$999$	145.204	4.59404

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.2.a.h.1.2		3
7.6	odd	2		385.2.a.e.1.2	✓	3
21.20	even	2		3465.2.a.bi.1.2		3
28.27	even	2		6160.2.a.bo.1.3		3
35.13	even	4		1925.2.b.m.1849.5		6
35.27	even	4		1925.2.b.m.1849.2		6
35.34	odd	2		1925.2.a.w.1.2		3
77.76	even	2		4235.2.a.p.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.a.e.1.2	✓	3	7.6	odd	2
1925.2.a.w.1.2		3	35.34	odd	2
1925.2.b.m.1849.2		6	35.27	even	4
1925.2.b.m.1849.5		6	35.13	even	4
2695.2.a.h.1.2		3	1.1	even	1	trivial
3465.2.a.bi.1.2		3	21.20	even	2
4235.2.a.p.1.2		3	77.76	even	2
6160.2.a.bo.1.3		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)

\(f(q)\)	\(=\)	\(q-1.53919 q^{2} +3.17009 q^{3} +0.369102 q^{4} +1.00000 q^{5} -4.87936 q^{6} +2.51026 q^{8} +7.04945 q^{9} +O(q^{10})\)	\(q-1.53919 q^{2} +3.17009 q^{3} +0.369102 q^{4} +1.00000 q^{5} -4.87936 q^{6} +2.51026 q^{8} +7.04945 q^{9} -1.53919 q^{10} +1.00000 q^{11} +1.17009 q^{12} +0.829914 q^{13} +3.17009 q^{15} -4.60197 q^{16} +2.82991 q^{17} -10.8504 q^{18} -6.49693 q^{19} +0.369102 q^{20} -1.53919 q^{22} -6.97107 q^{23} +7.95774 q^{24} +1.00000 q^{25} -1.27739 q^{26} +12.8371 q^{27} +3.26180 q^{29} -4.87936 q^{30} +10.2979 q^{31} +2.06278 q^{32} +3.17009 q^{33} -4.35577 q^{34} +2.60197 q^{36} +11.3112 q^{37} +10.0000 q^{38} +2.63090 q^{39} +2.51026 q^{40} +0.199016 q^{41} -0.447480 q^{43} +0.369102 q^{44} +7.04945 q^{45} +10.7298 q^{46} +6.82991 q^{47} -14.5886 q^{48} -1.53919 q^{50} +8.97107 q^{51} +0.306323 q^{52} -7.31124 q^{53} -19.7587 q^{54} +1.00000 q^{55} -20.5958 q^{57} -5.02052 q^{58} +7.95774 q^{59} +1.17009 q^{60} +6.87936 q^{61} -15.8504 q^{62} +6.02893 q^{64} +0.829914 q^{65} -4.87936 q^{66} +6.20620 q^{67} +1.04453 q^{68} -22.0989 q^{69} -11.4186 q^{71} +17.6959 q^{72} -5.66701 q^{73} -17.4101 q^{74} +3.17009 q^{75} -2.39803 q^{76} -4.04945 q^{78} -14.5464 q^{79} -4.60197 q^{80} +19.5464 q^{81} -0.306323 q^{82} -2.89496 q^{83} +2.82991 q^{85} +0.688756 q^{86} +10.3402 q^{87} +2.51026 q^{88} +0.581449 q^{89} -10.8504 q^{90} -2.57304 q^{92} +32.6453 q^{93} -10.5125 q^{94} -6.49693 q^{95} +6.53919 q^{96} +2.15676 q^{97} +7.04945 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 4 q^{3} + 5 q^{4} + 3 q^{5} - 2 q^{6} - 9 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 4 * q^3 + 5 * q^4 + 3 * q^5 - 2 * q^6 - 9 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 4 q^{3} + 5 q^{4} + 3 q^{5} - 2 q^{6} - 9 q^{8} + 3 q^{9} - 3 q^{10} + 3 q^{11} - 2 q^{12} + 8 q^{13} + 4 q^{15} + 5 q^{16} + 14 q^{17} - 5 q^{18} - 2 q^{19} + 5 q^{20} - 3 q^{22} - 6 q^{23} + 8 q^{24} + 3 q^{25} - 10 q^{26} + 10 q^{27} + 2 q^{29} - 2 q^{30} + 4 q^{31} - 11 q^{32} + 4 q^{33} - 16 q^{34} - 11 q^{36} + 8 q^{37} + 30 q^{38} + 4 q^{39} - 9 q^{40} + 10 q^{41} - 2 q^{43} + 5 q^{44} + 3 q^{45} - 8 q^{46} + 26 q^{47} - 24 q^{48} - 3 q^{50} + 12 q^{51} + 22 q^{52} + 4 q^{53} - 34 q^{54} + 3 q^{55} - 8 q^{57} + 18 q^{58} + 8 q^{59} - 2 q^{60} + 8 q^{61} - 20 q^{62} + 33 q^{64} + 8 q^{65} - 2 q^{66} - 6 q^{67} + 32 q^{68} - 30 q^{69} - 20 q^{71} + 45 q^{72} + 6 q^{73} + 10 q^{74} + 4 q^{75} - 26 q^{76} + 6 q^{78} - 8 q^{79} + 5 q^{80} + 23 q^{81} - 22 q^{82} - 10 q^{83} + 14 q^{85} + 28 q^{86} + 20 q^{87} - 9 q^{88} + 16 q^{89} - 5 q^{90} + 26 q^{92} + 26 q^{93} - 28 q^{94} - 2 q^{95} + 18 q^{96} + 3 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 4 * q^3 + 5 * q^4 + 3 * q^5 - 2 * q^6 - 9 * q^8 + 3 * q^9 - 3 * q^10 + 3 * q^11 - 2 * q^12 + 8 * q^13 + 4 * q^15 + 5 * q^16 + 14 * q^17 - 5 * q^18 - 2 * q^19 + 5 * q^20 - 3 * q^22 - 6 * q^23 + 8 * q^24 + 3 * q^25 - 10 * q^26 + 10 * q^27 + 2 * q^29 - 2 * q^30 + 4 * q^31 - 11 * q^32 + 4 * q^33 - 16 * q^34 - 11 * q^36 + 8 * q^37 + 30 * q^38 + 4 * q^39 - 9 * q^40 + 10 * q^41 - 2 * q^43 + 5 * q^44 + 3 * q^45 - 8 * q^46 + 26 * q^47 - 24 * q^48 - 3 * q^50 + 12 * q^51 + 22 * q^52 + 4 * q^53 - 34 * q^54 + 3 * q^55 - 8 * q^57 + 18 * q^58 + 8 * q^59 - 2 * q^60 + 8 * q^61 - 20 * q^62 + 33 * q^64 + 8 * q^65 - 2 * q^66 - 6 * q^67 + 32 * q^68 - 30 * q^69 - 20 * q^71 + 45 * q^72 + 6 * q^73 + 10 * q^74 + 4 * q^75 - 26 * q^76 + 6 * q^78 - 8 * q^79 + 5 * q^80 + 23 * q^81 - 22 * q^82 - 10 * q^83 + 14 * q^85 + 28 * q^86 + 20 * q^87 - 9 * q^88 + 16 * q^89 - 5 * q^90 + 26 * q^92 + 26 * q^93 - 28 * q^94 - 2 * q^95 + 18 * q^96 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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