LMFDB - Embedded newform 2695.2.a.g.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:	$1$
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			1.2
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)

$f(q)$	$=$	$q-1.53919 q^{2} -1.17009 q^{3} +0.369102 q^{4} +1.00000 q^{5} +1.80098 q^{6} +2.51026 q^{8} -1.63090 q^{9} +O(q^{10})$	\(q-1.53919 q^{2} -1.17009 q^{3} +0.369102 q^{4} +1.00000 q^{5} +1.80098 q^{6} +2.51026 q^{8} -1.63090 q^{9} -1.53919 q^{10} -1.00000 q^{11} -0.431882 q^{12} +0.0917087 q^{13} -1.17009 q^{15} -4.60197 q^{16} +5.51026 q^{17} +2.51026 q^{18} -0.921622 q^{19} +0.369102 q^{20} +1.53919 q^{22} -5.70928 q^{23} -2.93722 q^{24} +1.00000 q^{25} -0.141157 q^{26} +5.41855 q^{27} +1.41855 q^{29} +1.80098 q^{30} -0.879362 q^{31} +2.06278 q^{32} +1.17009 q^{33} -8.48133 q^{34} -0.601968 q^{36} -8.78765 q^{37} +1.41855 q^{38} -0.107307 q^{39} +2.51026 q^{40} +1.61757 q^{41} +3.86603 q^{43} -0.369102 q^{44} -1.63090 q^{45} +8.78765 q^{46} +5.90829 q^{47} +5.38470 q^{48} -1.53919 q^{50} -6.44748 q^{51} +0.0338499 q^{52} -10.0494 q^{53} -8.34017 q^{54} -1.00000 q^{55} +1.07838 q^{57} -2.18342 q^{58} +2.14116 q^{59} -0.431882 q^{60} +3.03612 q^{61} +1.35350 q^{62} +6.02893 q^{64} +0.0917087 q^{65} -1.80098 q^{66} -1.52586 q^{67} +2.03385 q^{68} +6.68035 q^{69} +4.09890 q^{71} -4.09398 q^{72} -14.1906 q^{73} +13.5259 q^{74} -1.17009 q^{75} -0.340173 q^{76} +0.165166 q^{78} +14.5464 q^{79} -4.60197 q^{80} -1.44748 q^{81} -2.48974 q^{82} +8.52359 q^{83} +5.51026 q^{85} -5.95055 q^{86} -1.65983 q^{87} -2.51026 q^{88} +2.83710 q^{89} +2.51026 q^{90} -2.10731 q^{92} +1.02893 q^{93} -9.09398 q^{94} -0.921622 q^{95} -2.41363 q^{96} -14.2557 q^{97} +1.63090 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.53919	−1.08837	−0.544185	−	0.838965i	$-0.683161\pi$
$2$	−1.53919	−1.08837	−0.544185	+	0.838965i	$0.683161\pi$
$3$	−1.17009	−0.675550	−0.337775	−	0.941227i	$-0.609674\pi$
$3$	−1.17009	−0.675550	−0.337775	+	0.941227i	$0.609674\pi$
$4$	0.369102	0.184551
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.80098	0.735249
$7$	0	0
$7$	0	0
$8$	2.51026	0.887511
$9$	−1.63090	−0.543633
$10$	−1.53919	−0.486734
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.431882	−0.124674
$13$	0.0917087	0.0254354	0.0127177	−	0.999919i	$-0.495952\pi$
$13$	0.0917087	0.0254354	0.0127177	+	0.999919i	$0.495952\pi$
$14$	0	0
$15$	−1.17009	−0.302115
$16$	−4.60197	−1.15049
$17$	5.51026	1.33643	0.668217	−	0.743966i	$-0.267058\pi$
$17$	5.51026	1.33643	0.668217	+	0.743966i	$0.267058\pi$
$18$	2.51026	0.591674
$19$	−0.921622	−0.211435	−0.105717	−	0.994396i	$-0.533714\pi$
$19$	−0.921622	−0.211435	−0.105717	+	0.994396i	$0.533714\pi$
$20$	0.369102	0.0825338
$21$	0	0
$22$	1.53919	0.328156
$23$	−5.70928	−1.19047	−0.595233	−	0.803553i	$-0.702940\pi$
$23$	−5.70928	−1.19047	−0.595233	+	0.803553i	$0.702940\pi$
$24$	−2.93722	−0.599558
$25$	1.00000	0.200000
$26$	−0.141157	−0.0276832
$27$	5.41855	1.04280
$28$	0	0
$29$	1.41855	0.263418	0.131709	−	0.991288i	$-0.457954\pi$
$29$	1.41855	0.263418	0.131709	+	0.991288i	$0.457954\pi$
$30$	1.80098	0.328813
$31$	−0.879362	−0.157938	−0.0789690	−	0.996877i	$-0.525163\pi$
$31$	−0.879362	−0.157938	−0.0789690	+	0.996877i	$0.525163\pi$
$32$	2.06278	0.364651
$33$	1.17009	0.203686
$34$	−8.48133	−1.45454
$35$	0	0
$36$	−0.601968	−0.100328
$37$	−8.78765	−1.44468	−0.722341	−	0.691537i	$-0.756934\pi$
$37$	−8.78765	−1.44468	−0.722341	+	0.691537i	$0.756934\pi$
$38$	1.41855	0.230119
$39$	−0.107307	−0.0171829
$40$	2.51026	0.396907
$41$	1.61757	0.252621	0.126311	−	0.991991i	$-0.459686\pi$
$41$	1.61757	0.252621	0.126311	+	0.991991i	$0.459686\pi$
$42$	0	0
$43$	3.86603	0.589564	0.294782	−	0.955565i	$-0.404753\pi$
$43$	3.86603	0.589564	0.294782	+	0.955565i	$0.404753\pi$
$44$	−0.369102	−0.0556443
$45$	−1.63090	−0.243120
$46$	8.78765	1.29567
$47$	5.90829	0.861813	0.430906	−	0.902397i	$-0.358194\pi$
$47$	5.90829	0.861813	0.430906	+	0.902397i	$0.358194\pi$
$48$	5.38470	0.777215
$49$	0	0
$50$	−1.53919	−0.217674
$51$	−6.44748	−0.902828
$52$	0.0338499	0.00469414
$53$	−10.0494	−1.38040	−0.690199	−	0.723620i	$-0.742477\pi$
$53$	−10.0494	−1.38040	−0.690199	+	0.723620i	$0.742477\pi$
$54$	−8.34017	−1.13495
$55$	−1.00000	−0.134840
$56$	0	0
$57$	1.07838	0.142835
$58$	−2.18342	−0.286697
$59$	2.14116	0.278755	0.139377	−	0.990239i	$-0.455490\pi$
$59$	2.14116	0.278755	0.139377	+	0.990239i	$0.455490\pi$
$60$	−0.431882	−0.0557557
$61$	3.03612	0.388735	0.194367	−	0.980929i	$-0.437735\pi$
$61$	3.03612	0.388735	0.194367	+	0.980929i	$0.437735\pi$
$62$	1.35350	0.171895
$63$	0	0
$64$	6.02893	0.753616
$65$	0.0917087	0.0113751
$66$	−1.80098	−0.221686
$67$	−1.52586	−0.186413	−0.0932066	−	0.995647i	$-0.529712\pi$
$67$	−1.52586	−0.186413	−0.0932066	+	0.995647i	$0.529712\pi$
$68$	2.03385	0.246641
$69$	6.68035	0.804219
$70$	0	0
$71$	4.09890	0.486450	0.243225	−	0.969970i	$-0.421795\pi$
$71$	4.09890	0.486450	0.243225	+	0.969970i	$0.421795\pi$
$72$	−4.09398	−0.482480
$73$	−14.1906	−1.66088	−0.830442	−	0.557105i	$-0.811912\pi$
$73$	−14.1906	−1.66088	−0.830442	+	0.557105i	$0.811912\pi$
$74$	13.5259	1.57235
$75$	−1.17009	−0.135110
$76$	−0.340173	−0.0390205
$77$	0	0
$78$	0.165166	0.0187014
$79$	14.5464	1.63660	0.818298	−	0.574795i	$-0.194918\pi$
$79$	14.5464	1.63660	0.818298	+	0.574795i	$0.194918\pi$
$80$	−4.60197	−0.514516
$81$	−1.44748	−0.160831
$82$	−2.48974	−0.274946
$83$	8.52359	0.935586	0.467793	−	0.883838i	$-0.345049\pi$
$83$	8.52359	0.935586	0.467793	+	0.883838i	$0.345049\pi$
$84$	0	0
$85$	5.51026	0.597672
$86$	−5.95055	−0.641664
$87$	−1.65983	−0.177952
$88$	−2.51026	−0.267595
$89$	2.83710	0.300732	0.150366	−	0.988630i	$-0.451955\pi$
$89$	2.83710	0.300732	0.150366	+	0.988630i	$0.451955\pi$
$90$	2.51026	0.264605
$91$	0	0
$92$	−2.10731	−0.219702
$93$	1.02893	0.106695
$94$	−9.09398	−0.937972
$95$	−0.921622	−0.0945564
$96$	−2.41363	−0.246340
$97$	−14.2557	−1.44744	−0.723721	−	0.690093i	$-0.757570\pi$
$97$	−14.2557	−1.44744	−0.723721	+	0.690093i	$0.757570\pi$
$98$	0	0
$99$	1.63090	0.163911
$100$	0.369102	0.0369102
$101$	−9.03612	−0.899127	−0.449564	−	0.893248i	$-0.648421\pi$
$101$	−9.03612	−0.899127	−0.449564	+	0.893248i	$0.648421\pi$
$102$	9.92389	0.982611
$103$	−3.32684	−0.327803	−0.163902	−	0.986477i	$-0.552408\pi$
$103$	−3.32684	−0.327803	−0.163902	+	0.986477i	$0.552408\pi$
$104$	0.230213	0.0225742
$105$	0	0
$106$	15.4680	1.50238
$107$	8.09890	0.782950	0.391475	−	0.920189i	$-0.371965\pi$
$107$	8.09890	0.782950	0.391475	+	0.920189i	$0.371965\pi$
$108$	2.00000	0.192450
$109$	15.1773	1.45372	0.726860	−	0.686786i	$-0.240979\pi$
$109$	15.1773	1.45372	0.726860	+	0.686786i	$0.240979\pi$
$110$	1.53919	0.146756
$111$	10.2823	0.975954
$112$	0	0
$113$	−7.07838	−0.665878	−0.332939	−	0.942948i	$-0.608040\pi$
$113$	−7.07838	−0.665878	−0.332939	+	0.942948i	$0.608040\pi$
$114$	−1.65983	−0.155457
$115$	−5.70928	−0.532393
$116$	0.523590	0.0486142
$117$	−0.149568	−0.0138275
$118$	−3.29565	−0.303389
$119$	0	0
$120$	−2.93722	−0.268130
$121$	1.00000	0.0909091
$122$	−4.67316	−0.423088
$123$	−1.89269	−0.170658
$124$	−0.324575	−0.0291477
$125$	1.00000	0.0894427
$126$	0	0
$127$	−9.65983	−0.857171	−0.428586	−	0.903501i	$-0.640988\pi$
$127$	−9.65983	−0.857171	−0.428586	+	0.903501i	$0.640988\pi$
$128$	−13.4052	−1.18487
$129$	−4.52359	−0.398280
$130$	−0.141157	−0.0123803
$131$	−4.68035	−0.408924	−0.204462	−	0.978875i	$-0.565544\pi$
$131$	−4.68035	−0.408924	−0.204462	+	0.978875i	$0.565544\pi$
$132$	0.431882	0.0375905
$133$	0	0
$134$	2.34858	0.202887
$135$	5.41855	0.466355
$136$	13.8322	1.18610
$137$	8.88655	0.759229	0.379615	−	0.925145i	$-0.376057\pi$
$137$	8.88655	0.759229	0.379615	+	0.925145i	$0.376057\pi$
$138$	−10.2823	−0.875289
$139$	15.0205	1.27402	0.637012	−	0.770854i	$-0.280170\pi$
$139$	15.0205	1.27402	0.637012	+	0.770854i	$0.280170\pi$
$140$	0	0
$141$	−6.91321	−0.582197
$142$	−6.30898	−0.529438
$143$	−0.0917087	−0.00766907
$144$	7.50534	0.625445
$145$	1.41855	0.117804
$146$	21.8420	1.80766
$147$	0	0
$148$	−3.24354	−0.266618
$149$	−13.7009	−1.12242	−0.561209	−	0.827674i	$-0.689664\pi$
$149$	−13.7009	−1.12242	−0.561209	+	0.827674i	$0.689664\pi$
$150$	1.80098	0.147050
$151$	1.05559	0.0859028	0.0429514	−	0.999077i	$-0.486324\pi$
$151$	1.05559	0.0859028	0.0429514	+	0.999077i	$0.486324\pi$
$152$	−2.31351	−0.187651
$153$	−8.98667	−0.726529
$154$	0	0
$155$	−0.879362	−0.0706320
$156$	−0.0396073	−0.00317112
$157$	17.7587	1.41730	0.708650	−	0.705560i	$-0.249304\pi$
$157$	17.7587	1.41730	0.708650	+	0.705560i	$0.249304\pi$
$158$	−22.3896	−1.78122
$159$	11.7587	0.932527
$160$	2.06278	0.163077
$161$	0	0
$162$	2.22795	0.175044
$163$	−11.4680	−0.898243	−0.449122	−	0.893471i	$-0.648263\pi$
$163$	−11.4680	−0.898243	−0.449122	+	0.893471i	$0.648263\pi$
$164$	0.597048	0.0466216
$165$	1.17009	0.0910911
$166$	−13.1194	−1.01826
$167$	5.60197	0.433493	0.216747	−	0.976228i	$-0.430455\pi$
$167$	5.60197	0.433493	0.216747	+	0.976228i	$0.430455\pi$
$168$	0	0
$169$	−12.9916	−0.999353
$170$	−8.48133	−0.650488
$171$	1.50307	0.114943
$172$	1.42696	0.108805
$173$	−21.6092	−1.64291	−0.821457	−	0.570271i	$-0.806838\pi$
$173$	−21.6092	−1.64291	−0.821457	+	0.570271i	$0.806838\pi$
$174$	2.55479	0.193678
$175$	0	0
$176$	4.60197	0.346886
$177$	−2.50534	−0.188313
$178$	−4.36683	−0.327308
$179$	−2.05786	−0.153812	−0.0769058	−	0.997038i	$-0.524504\pi$
$179$	−2.05786	−0.153812	−0.0769058	+	0.997038i	$0.524504\pi$
$180$	−0.601968	−0.0448681
$181$	−20.2823	−1.50757	−0.753786	−	0.657120i	$-0.771775\pi$
$181$	−20.2823	−1.50757	−0.753786	+	0.657120i	$0.771775\pi$
$182$	0	0
$183$	−3.55252	−0.262610
$184$	−14.3318	−1.05655
$185$	−8.78765	−0.646081
$186$	−1.58372	−0.116124
$187$	−5.51026	−0.402950
$188$	2.18076	0.159049
$189$	0	0
$190$	1.41855	0.102912
$191$	−20.2823	−1.46758	−0.733788	−	0.679378i	$-0.762250\pi$
$191$	−20.2823	−1.46758	−0.733788	+	0.679378i	$0.762250\pi$
$192$	−7.05437	−0.509105
$193$	−24.3051	−1.74952	−0.874760	−	0.484557i	$-0.838981\pi$
$193$	−24.3051	−1.74952	−0.874760	+	0.484557i	$0.838981\pi$
$194$	21.9421	1.57535
$195$	−0.107307	−0.00768443
$196$	0	0
$197$	−14.1483	−1.00803	−0.504014	−	0.863696i	$-0.668144\pi$
$197$	−14.1483	−1.00803	−0.504014	+	0.863696i	$0.668144\pi$
$198$	−2.51026	−0.178396
$199$	−10.4813	−0.743002	−0.371501	−	0.928433i	$-0.621157\pi$
$199$	−10.4813	−0.743002	−0.371501	+	0.928433i	$0.621157\pi$
$200$	2.51026	0.177502
$201$	1.78539	0.125931
$202$	13.9083	0.978584
$203$	0	0
$204$	−2.37978	−0.166618
$205$	1.61757	0.112976
$206$	5.12064	0.356772
$207$	9.31124	0.647176
$208$	−0.422041	−0.0292633
$209$	0.921622	0.0637499
$210$	0	0
$211$	−2.65368	−0.182687	−0.0913436	−	0.995819i	$-0.529116\pi$
$211$	−2.65368	−0.182687	−0.0913436	+	0.995819i	$0.529116\pi$
$212$	−3.70928	−0.254754
$213$	−4.79606	−0.328621
$214$	−12.4657	−0.852140
$215$	3.86603	0.263661
$216$	13.6020	0.925497
$217$	0	0
$218$	−23.3607	−1.58219
$219$	16.6042	1.12201
$220$	−0.369102	−0.0248849
$221$	0.505339	0.0339928
$222$	−15.8264	−1.06220
$223$	8.67316	0.580798	0.290399	−	0.956906i	$-0.406212\pi$
$223$	8.67316	0.580798	0.290399	+	0.956906i	$0.406212\pi$
$224$	0	0
$225$	−1.63090	−0.108727
$226$	10.8950	0.724722
$227$	−9.67420	−0.642099	−0.321050	−	0.947062i	$-0.604036\pi$
$227$	−9.67420	−0.642099	−0.321050	+	0.947062i	$0.604036\pi$
$228$	0.398032	0.0263603
$229$	13.5486	0.895320	0.447660	−	0.894204i	$-0.352258\pi$
$229$	13.5486	0.895320	0.447660	+	0.894204i	$0.352258\pi$
$230$	8.78765	0.579441
$231$	0	0
$232$	3.56093	0.233787
$233$	8.38962	0.549622	0.274811	−	0.961498i	$-0.411385\pi$
$233$	8.38962	0.549622	0.274811	+	0.961498i	$0.411385\pi$
$234$	0.230213	0.0150495
$235$	5.90829	0.385414
$236$	0.790306	0.0514446
$237$	−17.0205	−1.10560
$238$	0	0
$239$	−29.4908	−1.90760	−0.953800	−	0.300442i	$-0.902866\pi$
$239$	−29.4908	−1.90760	−0.953800	+	0.300442i	$0.902866\pi$
$240$	5.38470	0.347581
$241$	−3.64423	−0.234745	−0.117373	−	0.993088i	$-0.537447\pi$
$241$	−3.64423	−0.234745	−0.117373	+	0.993088i	$0.537447\pi$
$242$	−1.53919	−0.0989428
$243$	−14.5620	−0.934151
$244$	1.12064	0.0717415
$245$	0	0
$246$	2.91321	0.185740
$247$	−0.0845208	−0.00537793
$248$	−2.20743	−0.140172
$249$	−9.97334	−0.632035
$250$	−1.53919	−0.0973469
$251$	−23.1350	−1.46027	−0.730135	−	0.683303i	$-0.760543\pi$
$251$	−23.1350	−1.46027	−0.730135	+	0.683303i	$0.760543\pi$
$252$	0	0
$253$	5.70928	0.358939
$254$	14.8683	0.932920
$255$	−6.44748	−0.403757
$256$	8.57531	0.535957
$257$	−20.8104	−1.29812	−0.649060	−	0.760737i	$-0.724838\pi$
$257$	−20.8104	−1.29812	−0.649060	+	0.760737i	$0.724838\pi$
$258$	6.96266	0.433476
$259$	0	0
$260$	0.0338499	0.00209928
$261$	−2.31351	−0.143203
$262$	7.20394	0.445061
$263$	−23.7009	−1.46146	−0.730729	−	0.682668i	$-0.760820\pi$
$263$	−23.7009	−1.46146	−0.730729	+	0.682668i	$0.760820\pi$
$264$	2.93722	0.180773
$265$	−10.0494	−0.617333
$266$	0	0
$267$	−3.31965	−0.203160
$268$	−0.563198	−0.0344028
$269$	3.50307	0.213586	0.106793	−	0.994281i	$-0.465942\pi$
$269$	3.50307	0.213586	0.106793	+	0.994281i	$0.465942\pi$
$270$	−8.34017	−0.507567
$271$	8.49693	0.516152	0.258076	−	0.966125i	$-0.416912\pi$
$271$	8.49693	0.516152	0.258076	+	0.966125i	$0.416912\pi$
$272$	−25.3580	−1.53756
$273$	0	0
$274$	−13.6781	−0.826323
$275$	−1.00000	−0.0603023
$276$	2.46573	0.148420
$277$	−25.9649	−1.56008	−0.780041	−	0.625729i	$-0.784802\pi$
$277$	−25.9649	−1.56008	−0.780041	+	0.625729i	$0.784802\pi$
$278$	−23.1194	−1.38661
$279$	1.43415	0.0858603
$280$	0	0
$281$	11.6742	0.696425	0.348212	−	0.937416i	$-0.386789\pi$
$281$	11.6742	0.696425	0.348212	+	0.937416i	$0.386789\pi$
$282$	10.6407	0.633647
$283$	14.2557	0.847411	0.423705	−	0.905800i	$-0.360729\pi$
$283$	14.2557	0.847411	0.423705	+	0.905800i	$0.360729\pi$
$284$	1.51291	0.0897748
$285$	1.07838	0.0638776
$286$	0.141157	0.00834679
$287$	0	0
$288$	−3.36418	−0.198236
$289$	13.3630	0.786056
$290$	−2.18342	−0.128215
$291$	16.6803	0.977819
$292$	−5.23779	−0.306518
$293$	−25.1122	−1.46707	−0.733536	−	0.679651i	$-0.762131\pi$
$293$	−25.1122	−1.46707	−0.733536	+	0.679651i	$0.762131\pi$
$294$	0	0
$295$	2.14116	0.124663
$296$	−22.0593	−1.28217
$297$	−5.41855	−0.314416
$298$	21.0882	1.22161
$299$	−0.523590	−0.0302800
$300$	−0.431882	−0.0249347
$301$	0	0
$302$	−1.62475	−0.0934941
$303$	10.5730	0.607405
$304$	4.24128	0.243254
$305$	3.03612	0.173848
$306$	13.8322	0.790733
$307$	−8.02666	−0.458106	−0.229053	−	0.973414i	$-0.573563\pi$
$307$	−8.02666	−0.458106	−0.229053	+	0.973414i	$0.573563\pi$
$308$	0	0
$309$	3.89269	0.221448
$310$	1.35350	0.0768739
$311$	26.3968	1.49683	0.748413	−	0.663233i	$-0.230816\pi$
$311$	26.3968	1.49683	0.748413	+	0.663233i	$0.230816\pi$
$312$	−0.269369	−0.0152500
$313$	−25.7321	−1.45446	−0.727231	−	0.686393i	$-0.759193\pi$
$313$	−25.7321	−1.45446	−0.727231	+	0.686393i	$0.759193\pi$
$314$	−27.3340	−1.54255
$315$	0	0
$316$	5.36910	0.302036
$317$	6.31351	0.354602	0.177301	−	0.984157i	$-0.443263\pi$
$317$	6.31351	0.354602	0.177301	+	0.984157i	$0.443263\pi$
$318$	−18.0989	−1.01494
$319$	−1.41855	−0.0794236
$320$	6.02893	0.337027
$321$	−9.47641	−0.528922
$322$	0	0
$323$	−5.07838	−0.282568
$324$	−0.534268	−0.0296816
$325$	0.0917087	0.00508709
$326$	17.6514	0.977622
$327$	−17.7587	−0.982060
$328$	4.06051	0.224204
$329$	0	0
$330$	−1.80098	−0.0991409
$331$	3.50307	0.192546	0.0962731	−	0.995355i	$-0.469308\pi$
$331$	3.50307	0.192546	0.0962731	+	0.995355i	$0.469308\pi$
$332$	3.14608	0.172663
$333$	14.3318	0.785376
$334$	−8.62249	−0.471802
$335$	−1.52586	−0.0833665
$336$	0	0
$337$	7.57918	0.412864	0.206432	−	0.978461i	$-0.433815\pi$
$337$	7.57918	0.412864	0.206432	+	0.978461i	$0.433815\pi$
$338$	19.9965	1.08767
$339$	8.28231	0.449834
$340$	2.03385	0.110301
$341$	0.879362	0.0476201
$342$	−2.31351	−0.125100
$343$	0	0
$344$	9.70474	0.523245
$345$	6.68035	0.359658
$346$	33.2606	1.78810
$347$	−35.4824	−1.90479	−0.952397	−	0.304861i	$-0.901390\pi$
$347$	−35.4824	−1.90479	−0.952397	+	0.304861i	$0.901390\pi$
$348$	−0.612646	−0.0328413
$349$	13.6586	0.731128	0.365564	−	0.930786i	$-0.380876\pi$
$349$	13.6586	0.731128	0.365564	+	0.930786i	$0.380876\pi$
$350$	0	0
$351$	0.496928	0.0265241
$352$	−2.06278	−0.109947
$353$	−26.4657	−1.40863	−0.704314	−	0.709888i	$-0.748745\pi$
$353$	−26.4657	−1.40863	−0.704314	+	0.709888i	$0.748745\pi$
$354$	3.85619	0.204954
$355$	4.09890	0.217547
$356$	1.04718	0.0555005
$357$	0	0
$358$	3.16743	0.167404
$359$	−15.3958	−0.812557	−0.406279	−	0.913749i	$-0.633174\pi$
$359$	−15.3958	−0.812557	−0.406279	+	0.913749i	$0.633174\pi$
$360$	−4.09398	−0.215771
$361$	−18.1506	−0.955295
$362$	31.2183	1.64080
$363$	−1.17009	−0.0614136
$364$	0	0
$365$	−14.1906	−0.742770
$366$	5.46800	0.285817
$367$	34.6875	1.81067	0.905337	−	0.424693i	$-0.139618\pi$
$367$	34.6875	1.81067	0.905337	+	0.424693i	$0.139618\pi$
$368$	26.2739	1.36962
$369$	−2.63809	−0.137333
$370$	13.5259	0.703176
$371$	0	0
$372$	0.379780	0.0196907
$373$	36.3584	1.88257	0.941284	−	0.337616i	$-0.109621\pi$
$373$	36.3584	1.88257	0.941284	+	0.337616i	$0.109621\pi$
$374$	8.48133	0.438559
$375$	−1.17009	−0.0604230
$376$	14.8313	0.764868
$377$	0.130094	0.00670016
$378$	0	0
$379$	−33.1461	−1.70260	−0.851300	−	0.524680i	$-0.824185\pi$
$379$	−33.1461	−1.70260	−0.851300	+	0.524680i	$0.824185\pi$
$380$	−0.340173	−0.0174505
$381$	11.3028	0.579062
$382$	31.2183	1.59727
$383$	34.2628	1.75075	0.875375	−	0.483445i	$-0.160615\pi$
$383$	34.2628	1.75075	0.875375	+	0.483445i	$0.160615\pi$
$384$	15.6853	0.800435
$385$	0	0
$386$	37.4101	1.90413
$387$	−6.30510	−0.320506
$388$	−5.26180	−0.267127
$389$	23.2762	1.18015	0.590074	−	0.807349i	$-0.299098\pi$
$389$	23.2762	1.18015	0.590074	+	0.807349i	$0.299098\pi$
$390$	0.165166	0.00836350
$391$	−31.4596	−1.59098
$392$	0	0
$393$	5.47641	0.276248
$394$	21.7770	1.09711
$395$	14.5464	0.731908
$396$	0.601968	0.0302500
$397$	29.8576	1.49851	0.749256	−	0.662281i	$-0.230412\pi$
$397$	29.8576	1.49851	0.749256	+	0.662281i	$0.230412\pi$
$398$	16.1327	0.808662
$399$	0	0
$400$	−4.60197	−0.230098
$401$	−5.51745	−0.275528	−0.137764	−	0.990465i	$-0.543992\pi$
$401$	−5.51745	−0.275528	−0.137764	+	0.990465i	$0.543992\pi$
$402$	−2.74805	−0.137060
$403$	−0.0806452	−0.00401722
$404$	−3.33525	−0.165935
$405$	−1.44748	−0.0719259
$406$	0	0
$407$	8.78765	0.435588
$408$	−16.1848	−0.801269
$409$	3.43415	0.169808	0.0849039	−	0.996389i	$-0.472942\pi$
$409$	3.43415	0.169808	0.0849039	+	0.996389i	$0.472942\pi$
$410$	−2.48974	−0.122960
$411$	−10.3980	−0.512897
$412$	−1.22795	−0.0604965
$413$	0	0
$414$	−14.3318	−0.704368
$415$	8.52359	0.418407
$416$	0.189175	0.00927506
$417$	−17.5753	−0.860666
$418$	−1.41855	−0.0693836
$419$	−18.2134	−0.889782	−0.444891	−	0.895585i	$-0.646758\pi$
$419$	−18.2134	−0.889782	−0.444891	+	0.895585i	$0.646758\pi$
$420$	0	0
$421$	10.6576	0.519418	0.259709	−	0.965687i	$-0.416373\pi$
$421$	10.6576	0.519418	0.259709	+	0.965687i	$0.416373\pi$
$422$	4.08452	0.198831
$423$	−9.63582	−0.468510
$424$	−25.2267	−1.22512
$425$	5.51026	0.267287
$426$	7.38205	0.357661
$427$	0	0
$428$	2.98932	0.144494
$429$	0.107307	0.00518084
$430$	−5.95055	−0.286961
$431$	−7.61038	−0.366579	−0.183290	−	0.983059i	$-0.558675\pi$
$431$	−7.61038	−0.366579	−0.183290	+	0.983059i	$0.558675\pi$
$432$	−24.9360	−1.19973
$433$	−33.5318	−1.61144	−0.805718	−	0.592299i	$-0.798220\pi$
$433$	−33.5318	−1.61144	−0.805718	+	0.592299i	$0.798220\pi$
$434$	0	0
$435$	−1.65983	−0.0795826
$436$	5.60197	0.268286
$437$	5.26180	0.251706
$438$	−25.5571	−1.22116
$439$	13.7587	0.656668	0.328334	−	0.944562i	$-0.393513\pi$
$439$	13.7587	0.656668	0.328334	+	0.944562i	$0.393513\pi$
$440$	−2.51026	−0.119672
$441$	0	0
$442$	−0.777812	−0.0369967
$443$	−11.1689	−0.530649	−0.265324	−	0.964159i	$-0.585479\pi$
$443$	−11.1689	−0.530649	−0.265324	+	0.964159i	$0.585479\pi$
$444$	3.79523	0.180113
$445$	2.83710	0.134492
$446$	−13.3496	−0.632123
$447$	16.0312	0.758250
$448$	0	0
$449$	−19.0700	−0.899967	−0.449984	−	0.893037i	$-0.648570\pi$
$449$	−19.0700	−0.899967	−0.449984	+	0.893037i	$0.648570\pi$
$450$	2.51026	0.118335
$451$	−1.61757	−0.0761682
$452$	−2.61265	−0.122889
$453$	−1.23513	−0.0580316
$454$	14.8904	0.698842
$455$	0	0
$456$	2.70701	0.126767
$457$	−0.787653	−0.0368449	−0.0184224	−	0.999830i	$-0.505864\pi$
$457$	−0.787653	−0.0368449	−0.0184224	+	0.999830i	$0.505864\pi$
$458$	−20.8539	−0.974440
$459$	29.8576	1.39363
$460$	−2.10731	−0.0982537
$461$	−25.5864	−1.19168	−0.595838	−	0.803105i	$-0.703180\pi$
$461$	−25.5864	−1.19168	−0.595838	+	0.803105i	$0.703180\pi$
$462$	0	0
$463$	−14.2595	−0.662696	−0.331348	−	0.943509i	$-0.607503\pi$
$463$	−14.2595	−0.662696	−0.331348	+	0.943509i	$0.607503\pi$
$464$	−6.52813	−0.303061
$465$	1.02893	0.0477155
$466$	−12.9132	−0.598193
$467$	−18.3474	−0.849015	−0.424507	−	0.905425i	$-0.639553\pi$
$467$	−18.3474	−0.849015	−0.424507	+	0.905425i	$0.639553\pi$
$468$	−0.0552057	−0.00255189
$469$	0	0
$470$	−9.09398	−0.419474
$471$	−20.7792	−0.957457
$472$	5.37486	0.247398
$473$	−3.86603	−0.177760
$474$	26.1978	1.20330
$475$	−0.921622	−0.0422869
$476$	0	0
$477$	16.3896	0.750429
$478$	45.3919	2.07618
$479$	−12.1711	−0.556113	−0.278057	−	0.960565i	$-0.589690\pi$
$479$	−12.1711	−0.556113	−0.278057	+	0.960565i	$0.589690\pi$
$480$	−2.41363	−0.110167
$481$	−0.805905	−0.0367461
$482$	5.60916	0.255490
$483$	0	0
$484$	0.369102	0.0167774
$485$	−14.2557	−0.647316
$486$	22.4136	1.01670
$487$	−4.23287	−0.191809	−0.0959047	−	0.995391i	$-0.530574\pi$
$487$	−4.23287	−0.191809	−0.0959047	+	0.995391i	$0.530574\pi$
$488$	7.62144	0.345006
$489$	13.4186	0.606808
$490$	0	0
$491$	22.0183	0.993670	0.496835	−	0.867845i	$-0.334495\pi$
$491$	22.0183	0.993670	0.496835	+	0.867845i	$0.334495\pi$
$492$	−0.698597	−0.0314952
$493$	7.81658	0.352041
$494$	0.130094	0.00585318
$495$	1.63090	0.0733034
$496$	4.04680	0.181706
$497$	0	0
$498$	15.3509	0.687888
$499$	32.9939	1.47701	0.738504	−	0.674249i	$-0.235533\pi$
$499$	32.9939	1.47701	0.738504	+	0.674249i	$0.235533\pi$
$500$	0.369102	0.0165068
$501$	−6.55479	−0.292846
$502$	35.6092	1.58931
$503$	29.0349	1.29460	0.647301	−	0.762235i	$-0.275898\pi$
$503$	29.0349	1.29460	0.647301	+	0.762235i	$0.275898\pi$
$504$	0	0
$505$	−9.03612	−0.402102
$506$	−8.78765	−0.390659
$507$	15.2013	0.675113
$508$	−3.56547	−0.158192
$509$	21.5031	0.953107	0.476553	−	0.879146i	$-0.341886\pi$
$509$	21.5031	0.953107	0.476553	+	0.879146i	$0.341886\pi$
$510$	9.92389	0.439437
$511$	0	0
$512$	13.6114	0.601546
$513$	−4.99386	−0.220484
$514$	32.0312	1.41284
$515$	−3.32684	−0.146598
$516$	−1.66967	−0.0735030
$517$	−5.90829	−0.259846
$518$	0	0
$519$	25.2846	1.10987
$520$	0.230213	0.0100955
$521$	−24.5958	−1.07756	−0.538781	−	0.842446i	$-0.681115\pi$
$521$	−24.5958	−1.07756	−0.538781	+	0.842446i	$0.681115\pi$
$522$	3.56093	0.155858
$523$	−38.0677	−1.66458	−0.832292	−	0.554337i	$-0.812972\pi$
$523$	−38.0677	−1.66458	−0.832292	+	0.554337i	$0.812972\pi$
$524$	−1.72753	−0.0754674
$525$	0	0
$526$	36.4801	1.59061
$527$	−4.84551	−0.211074
$528$	−5.38470	−0.234339
$529$	9.59583	0.417210
$530$	15.4680	0.671887
$531$	−3.49201	−0.151540
$532$	0	0
$533$	0.148345	0.00642554
$534$	5.10957	0.221113
$535$	8.09890	0.350146
$536$	−3.83030	−0.165444
$537$	2.40787	0.103907
$538$	−5.39189	−0.232461
$539$	0	0
$540$	2.00000	0.0860663
$541$	2.13009	0.0915799	0.0457899	−	0.998951i	$-0.485420\pi$
$541$	2.13009	0.0915799	0.0457899	+	0.998951i	$0.485420\pi$
$542$	−13.0784	−0.561764
$543$	23.7321	1.01844
$544$	11.3664	0.487332
$545$	15.1773	0.650123
$546$	0	0
$547$	−9.13170	−0.390443	−0.195222	−	0.980759i	$-0.562543\pi$
$547$	−9.13170	−0.390443	−0.195222	+	0.980759i	$0.562543\pi$
$548$	3.28005	0.140117
$549$	−4.95160	−0.211329
$550$	1.53919	0.0656312
$551$	−1.30737	−0.0556957
$552$	16.7694	0.713753
$553$	0	0
$554$	39.9649	1.69795
$555$	10.2823	0.436460
$556$	5.54411	0.235123
$557$	−11.7093	−0.496138	−0.248069	−	0.968742i	$-0.579796\pi$
$557$	−11.7093	−0.496138	−0.248069	+	0.968742i	$0.579796\pi$
$558$	−2.20743	−0.0934478
$559$	0.354549	0.0149958
$560$	0	0
$561$	6.44748	0.272213
$562$	−17.9688	−0.757968
$563$	−12.5958	−0.530851	−0.265425	−	0.964131i	$-0.585512\pi$
$563$	−12.5958	−0.530851	−0.265425	+	0.964131i	$0.585512\pi$
$564$	−2.55168	−0.107445
$565$	−7.07838	−0.297790
$566$	−21.9421	−0.922297
$567$	0	0
$568$	10.2893	0.431729
$569$	7.54411	0.316266	0.158133	−	0.987418i	$-0.449453\pi$
$569$	7.54411	0.316266	0.158133	+	0.987418i	$0.449453\pi$
$570$	−1.65983	−0.0695225
$571$	36.8104	1.54047	0.770234	−	0.637761i	$-0.220139\pi$
$571$	36.8104	1.54047	0.770234	+	0.637761i	$0.220139\pi$
$572$	−0.0338499	−0.00141534
$573$	23.7321	0.991421
$574$	0	0
$575$	−5.70928	−0.238093
$576$	−9.83257	−0.409690
$577$	39.5174	1.64513	0.822566	−	0.568669i	$-0.192541\pi$
$577$	39.5174	1.64513	0.822566	+	0.568669i	$0.192541\pi$
$578$	−20.5681	−0.855521
$579$	28.4391	1.18189
$580$	0.523590	0.0217409
$581$	0	0
$582$	−25.6742	−1.06423
$583$	10.0494	0.416206
$584$	−35.6221	−1.47405
$585$	−0.149568	−0.00618386
$586$	38.6525	1.59672
$587$	−1.56812	−0.0647232	−0.0323616	−	0.999476i	$-0.510303\pi$
$587$	−1.56812	−0.0647232	−0.0323616	+	0.999476i	$0.510303\pi$
$588$	0	0
$589$	0.810439	0.0333936
$590$	−3.29565	−0.135680
$591$	16.5548	0.680973
$592$	40.4405	1.66209
$593$	−4.95547	−0.203497	−0.101748	−	0.994810i	$-0.532444\pi$
$593$	−4.95547	−0.203497	−0.101748	+	0.994810i	$0.532444\pi$
$594$	8.34017	0.342201
$595$	0	0
$596$	−5.05702	−0.207144
$597$	12.2641	0.501935
$598$	0.805905	0.0329559
$599$	−12.3668	−0.505295	−0.252648	−	0.967558i	$-0.581301\pi$
$599$	−12.3668	−0.505295	−0.252648	+	0.967558i	$0.581301\pi$
$600$	−2.93722	−0.119912
$601$	−24.9516	−1.01780	−0.508898	−	0.860827i	$-0.669947\pi$
$601$	−24.9516	−1.01780	−0.508898	+	0.860827i	$0.669947\pi$
$602$	0	0
$603$	2.48852	0.101340
$604$	0.389621	0.0158535
$605$	1.00000	0.0406558
$606$	−16.2739	−0.661082
$607$	19.2762	0.782396	0.391198	−	0.920307i	$-0.372061\pi$
$607$	19.2762	0.782396	0.391198	+	0.920307i	$0.372061\pi$
$608$	−1.90110	−0.0770999
$609$	0	0
$610$	−4.67316	−0.189211
$611$	0.541842	0.0219206
$612$	−3.31700	−0.134082
$613$	−42.6986	−1.72458	−0.862290	−	0.506415i	$-0.830971\pi$
$613$	−42.6986	−1.72458	−0.862290	+	0.506415i	$0.830971\pi$
$614$	12.3545	0.498589
$615$	−1.89269	−0.0763207
$616$	0	0
$617$	31.7770	1.27929	0.639646	−	0.768669i	$-0.279081\pi$
$617$	31.7770	1.27929	0.639646	+	0.768669i	$0.279081\pi$
$618$	−5.99159	−0.241017
$619$	19.8420	0.797518	0.398759	−	0.917056i	$-0.369441\pi$
$619$	19.8420	0.797518	0.398759	+	0.917056i	$0.369441\pi$
$620$	−0.324575	−0.0130352
$621$	−30.9360	−1.24142
$622$	−40.6297	−1.62910
$623$	0	0
$624$	0.493824	0.0197688
$625$	1.00000	0.0400000
$626$	39.6065	1.58299
$627$	−1.07838	−0.0430663
$628$	6.55479	0.261564
$629$	−48.4222	−1.93072
$630$	0	0
$631$	−3.63317	−0.144634	−0.0723170	−	0.997382i	$-0.523039\pi$
$631$	−3.63317	−0.144634	−0.0723170	+	0.997382i	$0.523039\pi$
$632$	36.5152	1.45250
$633$	3.10504	0.123414
$634$	−9.71769	−0.385939
$635$	−9.65983	−0.383339
$636$	4.34017	0.172099
$637$	0	0
$638$	2.18342	0.0864423
$639$	−6.68488	−0.264450
$640$	−13.4052	−0.529888
$641$	37.5402	1.48275	0.741375	−	0.671091i	$-0.234174\pi$
$641$	37.5402	1.48275	0.741375	+	0.671091i	$0.234174\pi$
$642$	14.5860	0.575663
$643$	34.8710	1.37518	0.687588	−	0.726101i	$-0.258670\pi$
$643$	34.8710	1.37518	0.687588	+	0.726101i	$0.258670\pi$
$644$	0	0
$645$	−4.52359	−0.178116
$646$	7.81658	0.307539
$647$	−30.6342	−1.20436	−0.602178	−	0.798362i	$-0.705700\pi$
$647$	−30.6342	−1.20436	−0.602178	+	0.798362i	$0.705700\pi$
$648$	−3.63355	−0.142739
$649$	−2.14116	−0.0840478
$650$	−0.141157	−0.00553664
$651$	0	0
$652$	−4.23287	−0.165772
$653$	5.40417	0.211482	0.105741	−	0.994394i	$-0.466279\pi$
$653$	5.40417	0.211482	0.105741	+	0.994394i	$0.466279\pi$
$654$	27.3340	1.06885
$655$	−4.68035	−0.182876
$656$	−7.44399	−0.290639
$657$	23.1434	0.902911
$658$	0	0
$659$	−19.4101	−0.756112	−0.378056	−	0.925783i	$-0.623407\pi$
$659$	−19.4101	−0.756112	−0.378056	+	0.925783i	$0.623407\pi$
$660$	0.431882	0.0168110
$661$	26.3090	1.02330	0.511650	−	0.859194i	$-0.329034\pi$
$661$	26.3090	1.02330	0.511650	+	0.859194i	$0.329034\pi$
$662$	−5.39189	−0.209562
$663$	−0.591290	−0.0229638
$664$	21.3964	0.830342
$665$	0	0
$666$	−22.0593	−0.854780
$667$	−8.09890	−0.313591
$668$	2.06770	0.0800017
$669$	−10.1483	−0.392358
$670$	2.34858	0.0907337
$671$	−3.03612	−0.117208
$672$	0	0
$673$	−15.7938	−0.608806	−0.304403	−	0.952543i	$-0.598457\pi$
$673$	−15.7938	−0.608806	−0.304403	+	0.952543i	$0.598457\pi$
$674$	−11.6658	−0.449350
$675$	5.41855	0.208560
$676$	−4.79523	−0.184432
$677$	15.7081	0.603710	0.301855	−	0.953354i	$-0.402394\pi$
$677$	15.7081	0.603710	0.301855	+	0.953354i	$0.402394\pi$
$678$	−12.7480	−0.489586
$679$	0	0
$680$	13.8322	0.530440
$681$	11.3197	0.433770
$682$	−1.35350	−0.0518283
$683$	−44.0326	−1.68486	−0.842431	−	0.538805i	$-0.818876\pi$
$683$	−44.0326	−1.68486	−0.842431	+	0.538805i	$0.818876\pi$
$684$	0.554787	0.0212128
$685$	8.88655	0.339538
$686$	0	0
$687$	−15.8531	−0.604833
$688$	−17.7914	−0.678289
$689$	−0.921622	−0.0351110
$690$	−10.2823	−0.391441
$691$	−4.63809	−0.176441	−0.0882205	−	0.996101i	$-0.528118\pi$
$691$	−4.63809	−0.176441	−0.0882205	+	0.996101i	$0.528118\pi$
$692$	−7.97599	−0.303202
$693$	0	0
$694$	54.6141	2.07312
$695$	15.0205	0.569761
$696$	−4.16660	−0.157934
$697$	8.91321	0.337612
$698$	−21.0232	−0.795739
$699$	−9.81658	−0.371297
$700$	0	0
$701$	−14.6491	−0.553291	−0.276645	−	0.960972i	$-0.589223\pi$
$701$	−14.6491	−0.553291	−0.276645	+	0.960972i	$0.589223\pi$
$702$	−0.764867	−0.0288680
$703$	8.09890	0.305456
$704$	−6.02893	−0.227224
$705$	−6.91321	−0.260367
$706$	40.7358	1.53311
$707$	0	0
$708$	−0.924727	−0.0347534
$709$	−25.5174	−0.958328	−0.479164	−	0.877725i	$-0.659060\pi$
$709$	−25.5174	−0.958328	−0.479164	+	0.877725i	$0.659060\pi$
$710$	−6.30898	−0.236772
$711$	−23.7237	−0.889706
$712$	7.12186	0.266903
$713$	5.02052	0.188020
$714$	0	0
$715$	−0.0917087	−0.00342971
$716$	−0.759561	−0.0283861
$717$	34.5068	1.28868
$718$	23.6970	0.884364
$719$	−39.2918	−1.46534	−0.732668	−	0.680586i	$-0.761725\pi$
$719$	−39.2918	−1.46534	−0.732668	+	0.680586i	$0.761725\pi$
$720$	7.50534	0.279707
$721$	0	0
$722$	27.9372	1.03972
$723$	4.26406	0.158582
$724$	−7.48625	−0.278224
$725$	1.41855	0.0526837
$726$	1.80098	0.0668408
$727$	37.7081	1.39851	0.699257	−	0.714870i	$-0.253514\pi$
$727$	37.7081	1.39851	0.699257	+	0.714870i	$0.253514\pi$
$728$	0	0
$729$	21.3812	0.791897
$730$	21.8420	0.808410
$731$	21.3028	0.787914
$732$	−1.31124	−0.0484650
$733$	4.34736	0.160573	0.0802867	−	0.996772i	$-0.474416\pi$
$733$	4.34736	0.160573	0.0802867	+	0.996772i	$0.474416\pi$
$734$	−53.3907	−1.97069
$735$	0	0
$736$	−11.7770	−0.434105
$737$	1.52586	0.0562057
$738$	4.06051	0.149470
$739$	38.1568	1.40362	0.701809	−	0.712365i	$-0.252376\pi$
$739$	38.1568	1.40362	0.701809	+	0.712365i	$0.252376\pi$
$740$	−3.24354	−0.119235
$741$	0.0988967	0.00363306
$742$	0	0
$743$	−29.2618	−1.07351	−0.536756	−	0.843738i	$-0.680350\pi$
$743$	−29.2618	−1.07351	−0.536756	+	0.843738i	$0.680350\pi$
$744$	2.58288	0.0946930
$745$	−13.7009	−0.501961
$746$	−55.9625	−2.04893
$747$	−13.9011	−0.508615
$748$	−2.03385	−0.0743649
$749$	0	0
$750$	1.80098	0.0657626
$751$	41.6886	1.52124	0.760619	−	0.649199i	$-0.224896\pi$
$751$	41.6886	1.52124	0.760619	+	0.649199i	$0.224896\pi$
$752$	−27.1898	−0.991509
$753$	27.0700	0.986484
$754$	−0.200238	−0.00729225
$755$	1.05559	0.0384169
$756$	0	0
$757$	39.7419	1.44444	0.722222	−	0.691661i	$-0.243121\pi$
$757$	39.7419	1.44444	0.722222	+	0.691661i	$0.243121\pi$
$758$	51.0181	1.85306
$759$	−6.68035	−0.242481
$760$	−2.31351	−0.0839199
$761$	36.4112	1.31990	0.659952	−	0.751308i	$-0.270577\pi$
$761$	36.4112	1.31990	0.659952	+	0.751308i	$0.270577\pi$
$762$	−17.3972	−0.630234
$763$	0	0
$764$	−7.48625	−0.270843
$765$	−8.98667	−0.324914
$766$	−52.7370	−1.90546
$767$	0.196363	0.00709025
$768$	−10.0338	−0.362065
$769$	10.5347	0.379889	0.189945	−	0.981795i	$-0.439169\pi$
$769$	10.5347	0.379889	0.189945	+	0.981795i	$0.439169\pi$
$770$	0	0
$771$	24.3500	0.876944
$772$	−8.97107	−0.322876
$773$	1.52198	0.0547419	0.0273709	−	0.999625i	$-0.491286\pi$
$773$	1.52198	0.0547419	0.0273709	+	0.999625i	$0.491286\pi$
$774$	9.70474	0.348830
$775$	−0.879362	−0.0315876
$776$	−35.7854	−1.28462
$777$	0	0
$778$	−35.8264	−1.28444
$779$	−1.49079	−0.0534129
$780$	−0.0396073	−0.00141817
$781$	−4.09890	−0.146670
$782$	48.4222	1.73158
$783$	7.68649	0.274693
$784$	0	0
$785$	17.7587	0.633836
$786$	−8.42923	−0.300661
$787$	15.6020	0.556150	0.278075	−	0.960559i	$-0.410304\pi$
$787$	15.6020	0.556150	0.278075	+	0.960559i	$0.410304\pi$
$788$	−5.22219	−0.186033
$789$	27.7321	0.987288
$790$	−22.3896	−0.796587
$791$	0	0
$792$	4.09398	0.145473
$793$	0.278438	0.00988764
$794$	−45.9565	−1.63094
$795$	11.7587	0.417039
$796$	−3.86868	−0.137122
$797$	−12.6491	−0.448056	−0.224028	−	0.974583i	$-0.571921\pi$
$797$	−12.6491	−0.448056	−0.224028	+	0.974583i	$0.571921\pi$
$798$	0	0
$799$	32.5562	1.15176
$800$	2.06278	0.0729303
$801$	−4.62702	−0.163488
$802$	8.49239	0.299877
$803$	14.1906	0.500776
$804$	0.658990	0.0232408
$805$	0	0
$806$	0.124128	0.00437223
$807$	−4.09890	−0.144288
$808$	−22.6830	−0.797985
$809$	−49.9299	−1.75544	−0.877720	−	0.479174i	$-0.840936\pi$
$809$	−49.9299	−1.75544	−0.877720	+	0.479174i	$0.840936\pi$
$810$	2.22795	0.0782820
$811$	−7.95896	−0.279477	−0.139738	−	0.990188i	$-0.544626\pi$
$811$	−7.95896	−0.279477	−0.139738	+	0.990188i	$0.544626\pi$
$812$	0	0
$813$	−9.94214	−0.348686
$814$	−13.5259	−0.474081
$815$	−11.4680	−0.401706
$816$	29.6711	1.03870
$817$	−3.56302	−0.124654
$818$	−5.28580	−0.184814
$819$	0	0
$820$	0.597048	0.0208498
$821$	4.92162	0.171766	0.0858829	−	0.996305i	$-0.472629\pi$
$821$	4.92162	0.171766	0.0858829	+	0.996305i	$0.472629\pi$
$822$	16.0045	0.558222
$823$	−4.04945	−0.141155	−0.0705774	−	0.997506i	$-0.522484\pi$
$823$	−4.04945	−0.141155	−0.0705774	+	0.997506i	$0.522484\pi$
$824$	−8.35124	−0.290929
$825$	1.17009	0.0407372
$826$	0	0
$827$	33.3256	1.15885	0.579423	−	0.815027i	$-0.303278\pi$
$827$	33.3256	1.15885	0.579423	+	0.815027i	$0.303278\pi$
$828$	3.43680	0.119437
$829$	0.156755	0.00544434	0.00272217	−	0.999996i	$-0.499134\pi$
$829$	0.156755	0.00544434	0.00272217	+	0.999996i	$0.499134\pi$
$830$	−13.1194	−0.455382
$831$	30.3812	1.05391
$832$	0.552906	0.0191686
$833$	0	0
$834$	27.0517	0.936724
$835$	5.60197	0.193864
$836$	0.340173	0.0117651
$837$	−4.76487	−0.164698
$838$	28.0338	0.968413
$839$	49.6775	1.71506	0.857529	−	0.514435i	$-0.171998\pi$
$839$	49.6775	1.71506	0.857529	+	0.514435i	$0.171998\pi$
$840$	0	0
$841$	−26.9877	−0.930611
$842$	−16.4040	−0.565319
$843$	−13.6598	−0.470469
$844$	−0.979481	−0.0337151
$845$	−12.9916	−0.446924
$846$	14.8313	0.509912
$847$	0	0
$848$	46.2472	1.58814
$849$	−16.6803	−0.572468
$850$	−8.48133	−0.290907
$851$	50.1711	1.71984
$852$	−1.77024	−0.0606474
$853$	−39.4257	−1.34991	−0.674956	−	0.737858i	$-0.735837\pi$
$853$	−39.4257	−1.34991	−0.674956	+	0.737858i	$0.735837\pi$
$854$	0	0
$855$	1.50307	0.0514040
$856$	20.3303	0.694876
$857$	−33.2423	−1.13554	−0.567768	−	0.823189i	$-0.692193\pi$
$857$	−33.2423	−1.13554	−0.567768	+	0.823189i	$0.692193\pi$
$858$	−0.165166	−0.00563867
$859$	−7.71646	−0.263282	−0.131641	−	0.991297i	$-0.542025\pi$
$859$	−7.71646	−0.263282	−0.131641	+	0.991297i	$0.542025\pi$
$860$	1.42696	0.0486590
$861$	0	0
$862$	11.7138	0.398974
$863$	−24.6453	−0.838935	−0.419467	−	0.907770i	$-0.637783\pi$
$863$	−24.6453	−0.838935	−0.419467	+	0.907770i	$0.637783\pi$
$864$	11.1773	0.380259
$865$	−21.6092	−0.734733
$866$	51.6118	1.75384
$867$	−15.6358	−0.531020
$868$	0	0
$869$	−14.5464	−0.493452
$870$	2.55479	0.0866154
$871$	−0.139935	−0.00474150
$872$	38.0989	1.29019
$873$	23.2495	0.786877
$874$	−8.09890	−0.273949
$875$	0	0
$876$	6.12866	0.207068
$877$	6.17954	0.208668	0.104334	−	0.994542i	$-0.466729\pi$
$877$	6.17954	0.208668	0.104334	+	0.994542i	$0.466729\pi$
$878$	−21.1773	−0.714698
$879$	29.3835	0.991080
$880$	4.60197	0.155132
$881$	49.3295	1.66195	0.830976	−	0.556308i	$-0.187782\pi$
$881$	49.3295	1.66195	0.830976	+	0.556308i	$0.187782\pi$
$882$	0	0
$883$	−22.1529	−0.745504	−0.372752	−	0.927931i	$-0.621586\pi$
$883$	−22.1529	−0.745504	−0.372752	+	0.927931i	$0.621586\pi$
$884$	0.186522	0.00627341
$885$	−2.50534	−0.0842160
$886$	17.1910	0.577543
$887$	−38.7358	−1.30062	−0.650310	−	0.759669i	$-0.725361\pi$
$887$	−38.7358	−1.30062	−0.650310	+	0.759669i	$0.725361\pi$
$888$	25.8113	0.866170
$889$	0	0
$890$	−4.36683	−0.146377
$891$	1.44748	0.0484924
$892$	3.20128	0.107187
$893$	−5.44521	−0.182217
$894$	−24.6750	−0.825257
$895$	−2.05786	−0.0687866
$896$	0	0
$897$	0.612646	0.0204557
$898$	29.3523	0.979498
$899$	−1.24742	−0.0416038
$900$	−0.601968	−0.0200656
$901$	−55.3751	−1.84481
$902$	2.48974	0.0828993
$903$	0	0
$904$	−17.7686	−0.590974
$905$	−20.2823	−0.674207
$906$	1.90110	0.0631599
$907$	18.4352	0.612131	0.306065	−	0.952011i	$-0.400987\pi$
$907$	18.4352	0.612131	0.306065	+	0.952011i	$0.400987\pi$
$908$	−3.57077	−0.118500
$909$	14.7370	0.488795
$910$	0	0
$911$	−11.9011	−0.394301	−0.197151	−	0.980373i	$-0.563169\pi$
$911$	−11.9011	−0.394301	−0.197151	+	0.980373i	$0.563169\pi$
$912$	−4.96266	−0.164330
$913$	−8.52359	−0.282090
$914$	1.21235	0.0401009
$915$	−3.55252	−0.117443
$916$	5.00084	0.165232
$917$	0	0
$918$	−45.9565	−1.51679
$919$	56.3812	1.85984	0.929922	−	0.367756i	$-0.119874\pi$
$919$	56.3812	1.85984	0.929922	+	0.367756i	$0.119874\pi$
$920$	−14.3318	−0.472504
$921$	9.39189	0.309473
$922$	39.3823	1.29699
$923$	0.375905	0.0123731
$924$	0	0
$925$	−8.78765	−0.288936
$926$	21.9481	0.721260
$927$	5.42574	0.178205
$928$	2.92616	0.0960558
$929$	−19.2351	−0.631084	−0.315542	−	0.948912i	$-0.602186\pi$
$929$	−19.2351	−0.631084	−0.315542	+	0.948912i	$0.602186\pi$
$930$	−1.58372	−0.0519321
$931$	0	0
$932$	3.09663	0.101433
$933$	−30.8865	−1.01118
$934$	28.2401	0.924043
$935$	−5.51026	−0.180205
$936$	−0.375453	−0.0122721
$937$	−17.6358	−0.576137	−0.288069	−	0.957610i	$-0.593013\pi$
$937$	−17.6358	−0.576137	−0.288069	+	0.957610i	$0.593013\pi$
$938$	0	0
$939$	30.1087	0.982562
$940$	2.18076	0.0711287
$941$	20.1990	0.658469	0.329235	−	0.944248i	$-0.393209\pi$
$941$	20.1990	0.658469	0.329235	+	0.944248i	$0.393209\pi$
$942$	31.9832	1.04207
$943$	−9.23513	−0.300737
$944$	−9.85354	−0.320705
$945$	0	0
$946$	5.95055	0.193469
$947$	17.6925	0.574928	0.287464	−	0.957792i	$-0.407188\pi$
$947$	17.6925	0.574928	0.287464	+	0.957792i	$0.407188\pi$
$948$	−6.28231	−0.204040
$949$	−1.30140	−0.0422453
$950$	1.41855	0.0460239
$951$	−7.38735	−0.239551
$952$	0	0
$953$	39.7093	1.28631	0.643155	−	0.765736i	$-0.277625\pi$
$953$	39.7093	1.28631	0.643155	+	0.765736i	$0.277625\pi$
$954$	−25.2267	−0.816745
$955$	−20.2823	−0.656320
$956$	−10.8851	−0.352050
$957$	1.65983	0.0536546
$958$	18.7337	0.605257
$959$	0	0
$960$	−7.05437	−0.227679
$961$	−30.2267	−0.975056
$962$	1.24044	0.0399934
$963$	−13.2085	−0.425637
$964$	−1.34509	−0.0433225
$965$	−24.3051	−0.782409
$966$	0	0
$967$	3.01664	0.0970087	0.0485044	−	0.998823i	$-0.484555\pi$
$967$	3.01664	0.0970087	0.0485044	+	0.998823i	$0.484555\pi$
$968$	2.51026	0.0806828
$969$	5.94214	0.190889
$970$	21.9421	0.704520
$971$	18.2134	0.584496	0.292248	−	0.956343i	$-0.405597\pi$
$971$	18.2134	0.584496	0.292248	+	0.956343i	$0.405597\pi$
$972$	−5.37486	−0.172399
$973$	0	0
$974$	6.51518	0.208760
$975$	−0.107307	−0.00343658
$976$	−13.9721	−0.447237
$977$	−30.0845	−0.962489	−0.481245	−	0.876586i	$-0.659815\pi$
$977$	−30.0845	−0.962489	−0.481245	+	0.876586i	$0.659815\pi$
$978$	−20.6537	−0.660432
$979$	−2.83710	−0.0906742
$980$	0	0
$981$	−24.7526	−0.790289
$982$	−33.8902	−1.08148
$983$	−5.92267	−0.188904	−0.0944519	−	0.995529i	$-0.530110\pi$
$983$	−5.92267	−0.188904	−0.0944519	+	0.995529i	$0.530110\pi$
$984$	−4.75115	−0.151461
$985$	−14.1483	−0.450804
$986$	−12.0312	−0.383151
$987$	0	0
$988$	−0.0311968	−0.000992504 0
$989$	−22.0722	−0.701856
$990$	−2.51026	−0.0797813
$991$	9.24742	0.293754	0.146877	−	0.989155i	$-0.453078\pi$
$991$	9.24742	0.293754	0.146877	+	0.989155i	$0.453078\pi$
$992$	−1.81393	−0.0575923
$993$	−4.09890	−0.130075
$994$	0	0
$995$	−10.4813	−0.332281
$996$	−3.68118	−0.116643
$997$	−32.1496	−1.01819	−0.509094	−	0.860711i	$-0.670019\pi$
$997$	−32.1496	−1.01819	−0.509094	+	0.860711i	$0.670019\pi$
$998$	−50.7838	−1.60753
$999$	−47.6163	−1.50651

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.2.a.g.1.2		3
7.6	odd	2		385.2.a.f.1.2	✓	3
21.20	even	2		3465.2.a.bh.1.2		3
28.27	even	2		6160.2.a.bn.1.1		3
35.13	even	4		1925.2.b.n.1849.5		6
35.27	even	4		1925.2.b.n.1849.2		6
35.34	odd	2		1925.2.a.v.1.2		3
77.76	even	2		4235.2.a.q.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.a.f.1.2	✓	3	7.6	odd	2
1925.2.a.v.1.2		3	35.34	odd	2
1925.2.b.n.1849.2		6	35.27	even	4
1925.2.b.n.1849.5		6	35.13	even	4
2695.2.a.g.1.2		3	1.1	even	1	trivial
3465.2.a.bh.1.2		3	21.20	even	2
4235.2.a.q.1.2		3	77.76	even	2
6160.2.a.bn.1.1		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)

\(f(q)\)	\(=\)	\(q-1.53919 q^{2} -1.17009 q^{3} +0.369102 q^{4} +1.00000 q^{5} +1.80098 q^{6} +2.51026 q^{8} -1.63090 q^{9} +O(q^{10})\)	\(q-1.53919 q^{2} -1.17009 q^{3} +0.369102 q^{4} +1.00000 q^{5} +1.80098 q^{6} +2.51026 q^{8} -1.63090 q^{9} -1.53919 q^{10} -1.00000 q^{11} -0.431882 q^{12} +0.0917087 q^{13} -1.17009 q^{15} -4.60197 q^{16} +5.51026 q^{17} +2.51026 q^{18} -0.921622 q^{19} +0.369102 q^{20} +1.53919 q^{22} -5.70928 q^{23} -2.93722 q^{24} +1.00000 q^{25} -0.141157 q^{26} +5.41855 q^{27} +1.41855 q^{29} +1.80098 q^{30} -0.879362 q^{31} +2.06278 q^{32} +1.17009 q^{33} -8.48133 q^{34} -0.601968 q^{36} -8.78765 q^{37} +1.41855 q^{38} -0.107307 q^{39} +2.51026 q^{40} +1.61757 q^{41} +3.86603 q^{43} -0.369102 q^{44} -1.63090 q^{45} +8.78765 q^{46} +5.90829 q^{47} +5.38470 q^{48} -1.53919 q^{50} -6.44748 q^{51} +0.0338499 q^{52} -10.0494 q^{53} -8.34017 q^{54} -1.00000 q^{55} +1.07838 q^{57} -2.18342 q^{58} +2.14116 q^{59} -0.431882 q^{60} +3.03612 q^{61} +1.35350 q^{62} +6.02893 q^{64} +0.0917087 q^{65} -1.80098 q^{66} -1.52586 q^{67} +2.03385 q^{68} +6.68035 q^{69} +4.09890 q^{71} -4.09398 q^{72} -14.1906 q^{73} +13.5259 q^{74} -1.17009 q^{75} -0.340173 q^{76} +0.165166 q^{78} +14.5464 q^{79} -4.60197 q^{80} -1.44748 q^{81} -2.48974 q^{82} +8.52359 q^{83} +5.51026 q^{85} -5.95055 q^{86} -1.65983 q^{87} -2.51026 q^{88} +2.83710 q^{89} +2.51026 q^{90} -2.10731 q^{92} +1.02893 q^{93} -9.09398 q^{94} -0.921622 q^{95} -2.41363 q^{96} -14.2557 q^{97} +1.63090 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 2 q^{3} + 5 q^{4} + 3 q^{5} - 4 q^{6} - 9 q^{8} - q^{9}+O(q^{10}) \) 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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