LMFDB - Embedded newform 2842.2.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2842,2,Mod(1,2842)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2842, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2842.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2842 = 2 \cdot 7^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2842.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:	$22.6934842544$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.568.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 6x - 2 $ x^3 - x^2 - 6*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 406)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.363328$ of defining polynomial
Character	$\chi$	$=$	2842.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.14134 q^{3} +1.00000 q^{4} -2.36333 q^{5} +3.14134 q^{6} -1.00000 q^{8} +6.86799 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.14134 q^{3} +1.00000 q^{4} -2.36333 q^{5} +3.14134 q^{6} -1.00000 q^{8} +6.86799 q^{9} +2.36333 q^{10} -3.86799 q^{11} -3.14134 q^{12} -1.63667 q^{13} +7.42401 q^{15} +1.00000 q^{16} -4.77801 q^{17} -6.86799 q^{18} +8.28267 q^{19} -2.36333 q^{20} +3.86799 q^{22} -5.00933 q^{23} +3.14134 q^{24} +0.585320 q^{25} +1.63667 q^{26} -12.1507 q^{27} +1.00000 q^{29} -7.42401 q^{30} +4.64600 q^{31} -1.00000 q^{32} +12.1507 q^{33} +4.77801 q^{34} +6.86799 q^{36} +4.72666 q^{37} -8.28267 q^{38} +5.14134 q^{39} +2.36333 q^{40} +3.78734 q^{41} -3.58532 q^{43} -3.86799 q^{44} -16.2313 q^{45} +5.00933 q^{46} -2.36333 q^{47} -3.14134 q^{48} -0.585320 q^{50} +15.0093 q^{51} -1.63667 q^{52} +7.86799 q^{53} +12.1507 q^{54} +9.14134 q^{55} -26.0187 q^{57} -1.00000 q^{58} -7.22199 q^{59} +7.42401 q^{60} +4.72666 q^{61} -4.64600 q^{62} +1.00000 q^{64} +3.86799 q^{65} -12.1507 q^{66} +3.73599 q^{67} -4.77801 q^{68} +15.7360 q^{69} +15.2920 q^{71} -6.86799 q^{72} +3.22199 q^{73} -4.72666 q^{74} -1.83869 q^{75} +8.28267 q^{76} -5.14134 q^{78} +7.42401 q^{79} -2.36333 q^{80} +17.5653 q^{81} -3.78734 q^{82} +3.32469 q^{83} +11.2920 q^{85} +3.58532 q^{86} -3.14134 q^{87} +3.86799 q^{88} +18.0700 q^{89} +16.2313 q^{90} -5.00933 q^{92} -14.5946 q^{93} +2.36333 q^{94} -19.5747 q^{95} +3.14134 q^{96} +17.2406 q^{97} -26.5653 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - q^{3} + 3 q^{4} - 5 q^{5} + q^{6} - 3 q^{8} + 8 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - q^3 + 3 * q^4 - 5 * q^5 + q^6 - 3 * q^8 + 8 * q^9	$ 3 q - 3 q^{2} - q^{3} + 3 q^{4} - 5 q^{5} + q^{6} - 3 q^{8} + 8 q^{9} + 5 q^{10} + q^{11} - q^{12} - 7 q^{13} - 3 q^{15} + 3 q^{16} - 8 q^{17} - 8 q^{18} + 8 q^{19} - 5 q^{20} - q^{22} + 6 q^{23} + q^{24} + 6 q^{25} + 7 q^{26} - 7 q^{27} + 3 q^{29} + 3 q^{30} - 5 q^{31} - 3 q^{32} + 7 q^{33} + 8 q^{34} + 8 q^{36} + 10 q^{37} - 8 q^{38} + 7 q^{39} + 5 q^{40} - 16 q^{41} - 15 q^{43} + q^{44} - 34 q^{45} - 6 q^{46} - 5 q^{47} - q^{48} - 6 q^{50} + 24 q^{51} - 7 q^{52} + 11 q^{53} + 7 q^{54} + 19 q^{55} - 36 q^{57} - 3 q^{58} - 28 q^{59} - 3 q^{60} + 10 q^{61} + 5 q^{62} + 3 q^{64} - q^{65} - 7 q^{66} - 14 q^{67} - 8 q^{68} + 22 q^{69} + 8 q^{71} - 8 q^{72} + 16 q^{73} - 10 q^{74} + 24 q^{75} + 8 q^{76} - 7 q^{78} - 3 q^{79} - 5 q^{80} + 19 q^{81} + 16 q^{82} + 12 q^{83} - 4 q^{85} + 15 q^{86} - q^{87} - q^{88} + 10 q^{89} + 34 q^{90} + 6 q^{92} - 27 q^{93} + 5 q^{94} - 4 q^{95} + q^{96} + 16 q^{97} - 46 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - q^3 + 3 * q^4 - 5 * q^5 + q^6 - 3 * q^8 + 8 * q^9 + 5 * q^10 + q^11 - q^12 - 7 * q^13 - 3 * q^15 + 3 * q^16 - 8 * q^17 - 8 * q^18 + 8 * q^19 - 5 * q^20 - q^22 + 6 * q^23 + q^24 + 6 * q^25 + 7 * q^26 - 7 * q^27 + 3 * q^29 + 3 * q^30 - 5 * q^31 - 3 * q^32 + 7 * q^33 + 8 * q^34 + 8 * q^36 + 10 * q^37 - 8 * q^38 + 7 * q^39 + 5 * q^40 - 16 * q^41 - 15 * q^43 + q^44 - 34 * q^45 - 6 * q^46 - 5 * q^47 - q^48 - 6 * q^50 + 24 * q^51 - 7 * q^52 + 11 * q^53 + 7 * q^54 + 19 * q^55 - 36 * q^57 - 3 * q^58 - 28 * q^59 - 3 * q^60 + 10 * q^61 + 5 * q^62 + 3 * q^64 - q^65 - 7 * q^66 - 14 * q^67 - 8 * q^68 + 22 * q^69 + 8 * q^71 - 8 * q^72 + 16 * q^73 - 10 * q^74 + 24 * q^75 + 8 * q^76 - 7 * q^78 - 3 * q^79 - 5 * q^80 + 19 * q^81 + 16 * q^82 + 12 * q^83 - 4 * q^85 + 15 * q^86 - q^87 - q^88 + 10 * q^89 + 34 * q^90 + 6 * q^92 - 27 * q^93 + 5 * q^94 - 4 * q^95 + q^96 + 16 * q^97 - 46 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.14134	−1.81365	−0.906826	−	0.421506i	$-0.861502\pi$
$3$	−3.14134	−1.81365	−0.906826	+	0.421506i	$0.861502\pi$
$4$	1.00000	0.500000
$5$	−2.36333	−1.05691	−0.528456	−	0.848961i	$-0.677229\pi$
$5$	−2.36333	−1.05691	−0.528456	+	0.848961i	$0.677229\pi$
$6$	3.14134	1.28245
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	6.86799	2.28933
$10$	2.36333	0.747350
$11$	−3.86799	−1.16624	−0.583122	−	0.812385i	$-0.698169\pi$
$11$	−3.86799	−1.16624	−0.583122	+	0.812385i	$0.698169\pi$
$12$	−3.14134	−0.906826
$13$	−1.63667	−0.453931	−0.226966	−	0.973903i	$-0.572880\pi$
$13$	−1.63667	−0.453931	−0.226966	+	0.973903i	$0.572880\pi$
$14$	0	0
$15$	7.42401	1.91687
$16$	1.00000	0.250000
$17$	−4.77801	−1.15884	−0.579419	−	0.815030i	$-0.696720\pi$
$17$	−4.77801	−1.15884	−0.579419	+	0.815030i	$0.696720\pi$
$18$	−6.86799	−1.61880
$19$	8.28267	1.90018	0.950088	−	0.311983i	$-0.100993\pi$
$19$	8.28267	1.90018	0.950088	+	0.311983i	$0.100993\pi$
$20$	−2.36333	−0.528456
$21$	0	0
$22$	3.86799	0.824659
$23$	−5.00933	−1.04452	−0.522259	−	0.852787i	$-0.674910\pi$
$23$	−5.00933	−1.04452	−0.522259	+	0.852787i	$0.674910\pi$
$24$	3.14134	0.641223
$25$	0.585320	0.117064
$26$	1.63667	0.320978
$27$	−12.1507	−2.33840
$28$	0	0
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−7.42401	−1.35543
$31$	4.64600	0.834446	0.417223	−	0.908804i	$-0.363003\pi$
$31$	4.64600	0.834446	0.417223	+	0.908804i	$0.363003\pi$
$32$	−1.00000	−0.176777
$33$	12.1507	2.11516
$34$	4.77801	0.819422
$35$	0	0
$36$	6.86799	1.14467
$37$	4.72666	0.777058	0.388529	−	0.921437i	$-0.372983\pi$
$37$	4.72666	0.777058	0.388529	+	0.921437i	$0.372983\pi$
$38$	−8.28267	−1.34363
$39$	5.14134	0.823273
$40$	2.36333	0.373675
$41$	3.78734	0.591483	0.295741	−	0.955268i	$-0.404433\pi$
$41$	3.78734	0.591483	0.295741	+	0.955268i	$0.404433\pi$
$42$	0	0
$43$	−3.58532	−0.546756	−0.273378	−	0.961907i	$-0.588141\pi$
$43$	−3.58532	−0.546756	−0.273378	+	0.961907i	$0.588141\pi$
$44$	−3.86799	−0.583122
$45$	−16.2313	−2.41962
$46$	5.00933	0.738585
$47$	−2.36333	−0.344727	−0.172363	−	0.985033i	$-0.555140\pi$
$47$	−2.36333	−0.344727	−0.172363	+	0.985033i	$0.555140\pi$
$48$	−3.14134	−0.453413
$49$	0	0
$50$	−0.585320	−0.0827768
$51$	15.0093	2.10173
$52$	−1.63667	−0.226966
$53$	7.86799	1.08075	0.540376	−	0.841424i	$-0.318282\pi$
$53$	7.86799	1.08075	0.540376	+	0.841424i	$0.318282\pi$
$54$	12.1507	1.65350
$55$	9.14134	1.23262
$56$	0	0
$57$	−26.0187	−3.44626
$58$	−1.00000	−0.131306
$59$	−7.22199	−0.940223	−0.470112	−	0.882607i	$-0.655786\pi$
$59$	−7.22199	−0.940223	−0.470112	+	0.882607i	$0.655786\pi$
$60$	7.42401	0.958435
$61$	4.72666	0.605186	0.302593	−	0.953120i	$-0.402148\pi$
$61$	4.72666	0.605186	0.302593	+	0.953120i	$0.402148\pi$
$62$	−4.64600	−0.590043
$63$	0	0
$64$	1.00000	0.125000
$65$	3.86799	0.479765
$66$	−12.1507	−1.49564
$67$	3.73599	0.456423	0.228212	−	0.973612i	$-0.426712\pi$
$67$	3.73599	0.456423	0.228212	+	0.973612i	$0.426712\pi$
$68$	−4.77801	−0.579419
$69$	15.7360	1.89439
$70$	0	0
$71$	15.2920	1.81483	0.907413	−	0.420239i	$-0.138054\pi$
$71$	15.2920	1.81483	0.907413	+	0.420239i	$0.138054\pi$
$72$	−6.86799	−0.809401
$73$	3.22199	0.377106	0.188553	−	0.982063i	$-0.439620\pi$
$73$	3.22199	0.377106	0.188553	+	0.982063i	$0.439620\pi$
$74$	−4.72666	−0.549463
$75$	−1.83869	−0.212313
$76$	8.28267	0.950088
$77$	0	0
$78$	−5.14134	−0.582142
$79$	7.42401	0.835266	0.417633	−	0.908616i	$-0.362860\pi$
$79$	7.42401	0.835266	0.417633	+	0.908616i	$0.362860\pi$
$80$	−2.36333	−0.264228
$81$	17.5653	1.95170
$82$	−3.78734	−0.418241
$83$	3.32469	0.364933	0.182466	−	0.983212i	$-0.441592\pi$
$83$	3.32469	0.364933	0.182466	+	0.983212i	$0.441592\pi$
$84$	0	0
$85$	11.2920	1.22479
$86$	3.58532	0.386615
$87$	−3.14134	−0.336787
$88$	3.86799	0.412329
$89$	18.0700	1.91542	0.957709	−	0.287740i	$-0.0929039\pi$
$89$	18.0700	1.91542	0.957709	+	0.287740i	$0.0929039\pi$
$90$	16.2313	1.71093
$91$	0	0
$92$	−5.00933	−0.522259
$93$	−14.5946	−1.51339
$94$	2.36333	0.243759
$95$	−19.5747	−2.00832
$96$	3.14134	0.320611
$97$	17.2406	1.75052	0.875261	−	0.483650i	$-0.160689\pi$
$97$	17.2406	1.75052	0.875261	+	0.483650i	$0.160689\pi$
$98$	0	0
$99$	−26.5653	−2.66992
$100$	0.585320	0.0585320
$101$	−13.5560	−1.34887	−0.674437	−	0.738332i	$-0.735614\pi$
$101$	−13.5560	−1.34887	−0.674437	+	0.738332i	$0.735614\pi$
$102$	−15.0093	−1.48614
$103$	1.55602	0.153319	0.0766594	−	0.997057i	$-0.475575\pi$
$103$	1.55602	0.153319	0.0766594	+	0.997057i	$0.475575\pi$
$104$	1.63667	0.160489
$105$	0	0
$106$	−7.86799	−0.764207
$107$	−15.7360	−1.52126	−0.760628	−	0.649189i	$-0.775109\pi$
$107$	−15.7360	−1.52126	−0.760628	+	0.649189i	$0.775109\pi$
$108$	−12.1507	−1.16920
$109$	−18.7160	−1.79267	−0.896334	−	0.443379i	$-0.853780\pi$
$109$	−18.7160	−1.79267	−0.896334	+	0.443379i	$0.853780\pi$
$110$	−9.14134	−0.871592
$111$	−14.8480	−1.40931
$112$	0	0
$113$	12.7453	1.19898	0.599489	−	0.800383i	$-0.295370\pi$
$113$	12.7453	1.19898	0.599489	+	0.800383i	$0.295370\pi$
$114$	26.0187	2.43687
$115$	11.8387	1.10396
$116$	1.00000	0.0928477
$117$	−11.2406	−1.03920
$118$	7.22199	0.664838
$119$	0	0
$120$	−7.42401	−0.677716
$121$	3.96137	0.360124
$122$	−4.72666	−0.427931
$123$	−11.8973	−1.07274
$124$	4.64600	0.417223
$125$	10.4333	0.933186
$126$	0	0
$127$	−17.5560	−1.55784	−0.778922	−	0.627121i	$-0.784233\pi$
$127$	−17.5560	−1.55784	−0.778922	+	0.627121i	$0.784233\pi$
$128$	−1.00000	−0.0883883
$129$	11.2627	0.991625
$130$	−3.86799	−0.339245
$131$	−15.1893	−1.32710	−0.663548	−	0.748134i	$-0.730950\pi$
$131$	−15.1893	−1.32710	−0.663548	+	0.748134i	$0.730950\pi$
$132$	12.1507	1.05758
$133$	0	0
$134$	−3.73599	−0.322740
$135$	28.7160	2.47148
$136$	4.77801	0.409711
$137$	23.0280	1.96741	0.983707	−	0.179780i	$-0.0575386\pi$
$137$	23.0280	1.96741	0.983707	+	0.179780i	$0.0575386\pi$
$138$	−15.7360	−1.33954
$139$	−10.9580	−0.929444	−0.464722	−	0.885457i	$-0.653846\pi$
$139$	−10.9580	−0.929444	−0.464722	+	0.885457i	$0.653846\pi$
$140$	0	0
$141$	7.42401	0.625214
$142$	−15.2920	−1.28328
$143$	6.33063	0.529394
$144$	6.86799	0.572333
$145$	−2.36333	−0.196264
$146$	−3.22199	−0.266654
$147$	0	0
$148$	4.72666	0.388529
$149$	−6.31198	−0.517097	−0.258549	−	0.965998i	$-0.583244\pi$
$149$	−6.31198	−0.517097	−0.258549	+	0.965998i	$0.583244\pi$
$150$	1.83869	0.150128
$151$	13.5747	1.10469	0.552346	−	0.833615i	$-0.313733\pi$
$151$	13.5747	1.10469	0.552346	+	0.833615i	$0.313733\pi$
$152$	−8.28267	−0.671813
$153$	−32.8153	−2.65296
$154$	0	0
$155$	−10.9800	−0.881937
$156$	5.14134	0.411636
$157$	−4.56534	−0.364354	−0.182177	−	0.983266i	$-0.558314\pi$
$157$	−4.56534	−0.364354	−0.182177	+	0.983266i	$0.558314\pi$
$158$	−7.42401	−0.590622
$159$	−24.7160	−1.96011
$160$	2.36333	0.186838
$161$	0	0
$162$	−17.5653	−1.38006
$163$	−10.9800	−0.860022	−0.430011	−	0.902824i	$-0.641490\pi$
$163$	−10.9800	−0.860022	−0.430011	+	0.902824i	$0.641490\pi$
$164$	3.78734	0.295741
$165$	−28.7160	−2.23554
$166$	−3.32469	−0.258046
$167$	−19.1120	−1.47893	−0.739467	−	0.673193i	$-0.764922\pi$
$167$	−19.1120	−1.47893	−0.739467	+	0.673193i	$0.764922\pi$
$168$	0	0
$169$	−10.3213	−0.793947
$170$	−11.2920	−0.866057
$171$	56.8853	4.35013
$172$	−3.58532	−0.273378
$173$	−3.76868	−0.286527	−0.143264	−	0.989685i	$-0.545760\pi$
$173$	−3.76868	−0.286527	−0.143264	+	0.989685i	$0.545760\pi$
$174$	3.14134	0.238144
$175$	0	0
$176$	−3.86799	−0.291561
$177$	22.6867	1.70524
$178$	−18.0700	−1.35440
$179$	−1.45331	−0.108626	−0.0543129	−	0.998524i	$-0.517297\pi$
$179$	−1.45331	−0.108626	−0.0543129	+	0.998524i	$0.517297\pi$
$180$	−16.2313	−1.20981
$181$	9.26995	0.689030	0.344515	−	0.938781i	$-0.388043\pi$
$181$	9.26995	0.689030	0.344515	+	0.938781i	$0.388043\pi$
$182$	0	0
$183$	−14.8480	−1.09760
$184$	5.00933	0.369293
$185$	−11.1706	−0.821282
$186$	14.5946	1.07013
$187$	18.4813	1.35149
$188$	−2.36333	−0.172363
$189$	0	0
$190$	19.5747	1.42010
$191$	1.55602	0.112589	0.0562947	−	0.998414i	$-0.482071\pi$
$191$	1.55602	0.112589	0.0562947	+	0.998414i	$0.482071\pi$
$192$	−3.14134	−0.226706
$193$	−1.27334	−0.0916573	−0.0458286	−	0.998949i	$-0.514593\pi$
$193$	−1.27334	−0.0916573	−0.0458286	+	0.998949i	$0.514593\pi$
$194$	−17.2406	−1.23781
$195$	−12.1507	−0.870127
$196$	0	0
$197$	16.1214	1.14860	0.574300	−	0.818645i	$-0.305274\pi$
$197$	16.1214	1.14860	0.574300	+	0.818645i	$0.305274\pi$
$198$	26.5653	1.88792
$199$	−11.5747	−0.820507	−0.410253	−	0.911972i	$-0.634560\pi$
$199$	−11.5747	−0.820507	−0.410253	+	0.911972i	$0.634560\pi$
$200$	−0.585320	−0.0413884
$201$	−11.7360	−0.827793
$202$	13.5560	0.953798
$203$	0	0
$204$	15.0093	1.05086
$205$	−8.95072	−0.625145
$206$	−1.55602	−0.108413
$207$	−34.4040	−2.39125
$208$	−1.63667	−0.113483
$209$	−32.0373	−2.21607
$210$	0	0
$211$	−16.7160	−1.15078	−0.575389	−	0.817880i	$-0.695149\pi$
$211$	−16.7160	−1.15078	−0.575389	+	0.817880i	$0.695149\pi$
$212$	7.86799	0.540376
$213$	−48.0373	−3.29146
$214$	15.7360	1.07569
$215$	8.47329	0.577874
$216$	12.1507	0.826748
$217$	0	0
$218$	18.7160	1.26761
$219$	−10.1214	−0.683938
$220$	9.14134	0.616309
$221$	7.82003	0.526032
$222$	14.8480	0.996534
$223$	−1.55602	−0.104199	−0.0520993	−	0.998642i	$-0.516591\pi$
$223$	−1.55602	−0.104199	−0.0520993	+	0.998642i	$0.516591\pi$
$224$	0	0
$225$	4.01998	0.267998
$226$	−12.7453	−0.847806
$227$	−7.94865	−0.527570	−0.263785	−	0.964581i	$-0.584971\pi$
$227$	−7.94865	−0.527570	−0.263785	+	0.964581i	$0.584971\pi$
$228$	−26.0187	−1.72313
$229$	−17.1893	−1.13590	−0.567950	−	0.823063i	$-0.692263\pi$
$229$	−17.1893	−1.13590	−0.567950	+	0.823063i	$0.692263\pi$
$230$	−11.8387	−0.780620
$231$	0	0
$232$	−1.00000	−0.0656532
$233$	−29.2627	−1.91706	−0.958531	−	0.284987i	$-0.908011\pi$
$233$	−29.2627	−1.91706	−0.958531	+	0.284987i	$0.908011\pi$
$234$	11.2406	0.734824
$235$	5.58532	0.364346
$236$	−7.22199	−0.470112
$237$	−23.3213	−1.51488
$238$	0	0
$239$	−11.1120	−0.718778	−0.359389	−	0.933188i	$-0.617015\pi$
$239$	−11.1120	−0.718778	−0.359389	+	0.933188i	$0.617015\pi$
$240$	7.42401	0.479218
$241$	−9.52671	−0.613669	−0.306835	−	0.951763i	$-0.599270\pi$
$241$	−9.52671	−0.613669	−0.306835	+	0.951763i	$0.599270\pi$
$242$	−3.96137	−0.254646
$243$	−18.7267	−1.20132
$244$	4.72666	0.302593
$245$	0	0
$246$	11.8973	0.758544
$247$	−13.5560	−0.862549
$248$	−4.64600	−0.295021
$249$	−10.4440	−0.661861
$250$	−10.4333	−0.659862
$251$	17.8867	1.12900	0.564498	−	0.825435i	$-0.309070\pi$
$251$	17.8867	1.12900	0.564498	+	0.825435i	$0.309070\pi$
$252$	0	0
$253$	19.3760	1.21816
$254$	17.5560	1.10156
$255$	−35.4720	−2.22134
$256$	1.00000	0.0625000
$257$	18.0480	1.12580	0.562900	−	0.826525i	$-0.309685\pi$
$257$	18.0480	1.12580	0.562900	+	0.826525i	$0.309685\pi$
$258$	−11.2627	−0.701185
$259$	0	0
$260$	3.86799	0.239883
$261$	6.86799	0.425118
$262$	15.1893	0.938398
$263$	12.6133	0.777770	0.388885	−	0.921286i	$-0.372860\pi$
$263$	12.6133	0.777770	0.388885	+	0.921286i	$0.372860\pi$
$264$	−12.1507	−0.747822
$265$	−18.5946	−1.14226
$266$	0	0
$267$	−56.7640	−3.47390
$268$	3.73599	0.228212
$269$	0.990671	0.0604023	0.0302011	−	0.999544i	$-0.490385\pi$
$269$	0.990671	0.0604023	0.0302011	+	0.999544i	$0.490385\pi$
$270$	−28.7160	−1.74760
$271$	−17.1086	−1.03928	−0.519638	−	0.854387i	$-0.673933\pi$
$271$	−17.1086	−1.03928	−0.519638	+	0.854387i	$0.673933\pi$
$272$	−4.77801	−0.289709
$273$	0	0
$274$	−23.0280	−1.39117
$275$	−2.26401	−0.136525
$276$	15.7360	0.947195
$277$	19.5560	1.17501	0.587504	−	0.809222i	$-0.300111\pi$
$277$	19.5560	1.17501	0.587504	+	0.809222i	$0.300111\pi$
$278$	10.9580	0.657216
$279$	31.9087	1.91032
$280$	0	0
$281$	11.0573	0.659623	0.329811	−	0.944047i	$-0.393015\pi$
$281$	11.0573	0.659623	0.329811	+	0.944047i	$0.393015\pi$
$282$	−7.42401	−0.442093
$283$	−12.6167	−0.749985	−0.374992	−	0.927028i	$-0.622355\pi$
$283$	−12.6167	−0.749985	−0.374992	+	0.927028i	$0.622355\pi$
$284$	15.2920	0.907413
$285$	61.4906	3.64239
$286$	−6.33063	−0.374338
$287$	0	0
$288$	−6.86799	−0.404700
$289$	5.82936	0.342903
$290$	2.36333	0.138779
$291$	−54.1587	−3.17484
$292$	3.22199	0.188553
$293$	10.8480	0.633748	0.316874	−	0.948468i	$-0.397367\pi$
$293$	10.8480	0.633748	0.316874	+	0.948468i	$0.397367\pi$
$294$	0	0
$295$	17.0679	0.993734
$296$	−4.72666	−0.274731
$297$	46.9987	2.72714
$298$	6.31198	0.365643
$299$	8.19863	0.474139
$300$	−1.83869	−0.106157
$301$	0	0
$302$	−13.5747	−0.781135
$303$	42.5840	2.44639
$304$	8.28267	0.475044
$305$	−11.1706	−0.639629
$306$	32.8153	1.87593
$307$	−8.33063	−0.475454	−0.237727	−	0.971332i	$-0.576402\pi$
$307$	−8.33063	−0.475454	−0.237727	+	0.971332i	$0.576402\pi$
$308$	0	0
$309$	−4.88797	−0.278067
$310$	10.9800	0.623623
$311$	−12.0700	−0.684427	−0.342214	−	0.939622i	$-0.611177\pi$
$311$	−12.0700	−0.684427	−0.342214	+	0.939622i	$0.611177\pi$
$312$	−5.14134	−0.291071
$313$	−22.4147	−1.26695	−0.633476	−	0.773762i	$-0.718373\pi$
$313$	−22.4147	−1.26695	−0.633476	+	0.773762i	$0.718373\pi$
$314$	4.56534	0.257637
$315$	0	0
$316$	7.42401	0.417633
$317$	−10.5653	−0.593409	−0.296704	−	0.954969i	$-0.595888\pi$
$317$	−10.5653	−0.593409	−0.296704	+	0.954969i	$0.595888\pi$
$318$	24.7160	1.38600
$319$	−3.86799	−0.216566
$320$	−2.36333	−0.132114
$321$	49.4320	2.75903
$322$	0	0
$323$	−39.5747	−2.20199
$324$	17.5653	0.975852
$325$	−0.957977	−0.0531390
$326$	10.9800	0.608127
$327$	58.7933	3.25128
$328$	−3.78734	−0.209121
$329$	0	0
$330$	28.7160	1.58076
$331$	13.3400	0.733231	0.366615	−	0.930373i	$-0.380517\pi$
$331$	13.3400	0.733231	0.366615	+	0.930373i	$0.380517\pi$
$332$	3.32469	0.182466
$333$	32.4626	1.77894
$334$	19.1120	1.04576
$335$	−8.82936	−0.482399
$336$	0	0
$337$	−14.5653	−0.793425	−0.396712	−	0.917943i	$-0.629849\pi$
$337$	−14.5653	−0.793425	−0.396712	+	0.917943i	$0.629849\pi$
$338$	10.3213	0.561405
$339$	−40.0373	−2.17453
$340$	11.2920	0.612395
$341$	−17.9707	−0.973168
$342$	−56.8853	−3.07601
$343$	0	0
$344$	3.58532	0.193308
$345$	−37.1893	−2.00220
$346$	3.76868	0.202605
$347$	17.2920	0.928283	0.464142	−	0.885761i	$-0.346363\pi$
$347$	17.2920	0.928283	0.464142	+	0.885761i	$0.346363\pi$
$348$	−3.14134	−0.168393
$349$	−27.9193	−1.49449	−0.747244	−	0.664550i	$-0.768623\pi$
$349$	−27.9193	−1.49449	−0.747244	+	0.664550i	$0.768623\pi$
$350$	0	0
$351$	19.8867	1.06147
$352$	3.86799	0.206165
$353$	30.0373	1.59872	0.799362	−	0.600849i	$-0.205171\pi$
$353$	30.0373	1.59872	0.799362	+	0.600849i	$0.205171\pi$
$354$	−22.6867	−1.20578
$355$	−36.1400	−1.91811
$356$	18.0700	0.957709
$357$	0	0
$358$	1.45331	0.0768100
$359$	4.31198	0.227577	0.113789	−	0.993505i	$-0.463701\pi$
$359$	4.31198	0.227577	0.113789	+	0.993505i	$0.463701\pi$
$360$	16.2313	0.855466
$361$	49.6027	2.61067
$362$	−9.26995	−0.487218
$363$	−12.4440	−0.653140
$364$	0	0
$365$	−7.61462	−0.398568
$366$	14.8480	0.776118
$367$	6.51399	0.340028	0.170014	−	0.985442i	$-0.445619\pi$
$367$	6.51399	0.340028	0.170014	+	0.985442i	$0.445619\pi$
$368$	−5.00933	−0.261129
$369$	26.0114	1.35410
$370$	11.1706	0.580734
$371$	0	0
$372$	−14.5946	−0.756697
$373$	−7.40535	−0.383435	−0.191717	−	0.981450i	$-0.561406\pi$
$373$	−7.40535	−0.383435	−0.191717	+	0.981450i	$0.561406\pi$
$374$	−18.4813	−0.955645
$375$	−32.7746	−1.69247
$376$	2.36333	0.121879
$377$	−1.63667	−0.0842929
$378$	0	0
$379$	15.6774	0.805293	0.402646	−	0.915356i	$-0.368090\pi$
$379$	15.6774	0.805293	0.402646	+	0.915356i	$0.368090\pi$
$380$	−19.5747	−1.00416
$381$	55.1493	2.82539
$382$	−1.55602	−0.0796127
$383$	−10.2827	−0.525420	−0.262710	−	0.964875i	$-0.584616\pi$
$383$	−10.2827	−0.525420	−0.262710	+	0.964875i	$0.584616\pi$
$384$	3.14134	0.160306
$385$	0	0
$386$	1.27334	0.0648115
$387$	−24.6240	−1.25171
$388$	17.2406	0.875261
$389$	−5.91595	−0.299951	−0.149975	−	0.988690i	$-0.547919\pi$
$389$	−5.91595	−0.299951	−0.149975	+	0.988690i	$0.547919\pi$
$390$	12.1507	0.615273
$391$	23.9346	1.21043
$392$	0	0
$393$	47.7147	2.40689
$394$	−16.1214	−0.812182
$395$	−17.5454	−0.882803
$396$	−26.5653	−1.33496
$397$	9.01272	0.452335	0.226168	−	0.974088i	$-0.427380\pi$
$397$	9.01272	0.452335	0.226168	+	0.974088i	$0.427380\pi$
$398$	11.5747	0.580186
$399$	0	0
$400$	0.585320	0.0292660
$401$	10.7746	0.538059	0.269029	−	0.963132i	$-0.413297\pi$
$401$	10.7746	0.538059	0.269029	+	0.963132i	$0.413297\pi$
$402$	11.7360	0.585338
$403$	−7.60398	−0.378781
$404$	−13.5560	−0.674437
$405$	−41.5127	−2.06278
$406$	0	0
$407$	−18.2827	−0.906238
$408$	−15.0093	−0.743072
$409$	−2.79667	−0.138286	−0.0691431	−	0.997607i	$-0.522027\pi$
$409$	−2.79667	−0.138286	−0.0691431	+	0.997607i	$0.522027\pi$
$410$	8.95072	0.442045
$411$	−72.3386	−3.56820
$412$	1.55602	0.0766594
$413$	0	0
$414$	34.4040	1.69087
$415$	−7.85735	−0.385702
$416$	1.63667	0.0802444
$417$	34.4227	1.68569
$418$	32.0373	1.56700
$419$	−27.8900	−1.36252	−0.681259	−	0.732043i	$-0.738567\pi$
$419$	−27.8900	−1.36252	−0.681259	+	0.732043i	$0.738567\pi$
$420$	0	0
$421$	31.8387	1.55172	0.775861	−	0.630903i	$-0.217316\pi$
$421$	31.8387	1.55172	0.775861	+	0.630903i	$0.217316\pi$
$422$	16.7160	0.813723
$423$	−16.2313	−0.789194
$424$	−7.86799	−0.382103
$425$	−2.79667	−0.135658
$426$	48.0373	2.32742
$427$	0	0
$428$	−15.7360	−0.760628
$429$	−19.8867	−0.960137
$430$	−8.47329	−0.408618
$431$	−3.43466	−0.165442	−0.0827208	−	0.996573i	$-0.526361\pi$
$431$	−3.43466	−0.165442	−0.0827208	+	0.996573i	$0.526361\pi$
$432$	−12.1507	−0.584599
$433$	31.7287	1.52479	0.762393	−	0.647115i	$-0.224025\pi$
$433$	31.7287	1.52479	0.762393	+	0.647115i	$0.224025\pi$
$434$	0	0
$435$	7.42401	0.355954
$436$	−18.7160	−0.896334
$437$	−41.4906	−1.98477
$438$	10.1214	0.483617
$439$	−29.7546	−1.42011	−0.710056	−	0.704145i	$-0.751330\pi$
$439$	−29.7546	−1.42011	−0.710056	+	0.704145i	$0.751330\pi$
$440$	−9.14134	−0.435796
$441$	0	0
$442$	−7.82003	−0.371961
$443$	−14.3013	−0.679477	−0.339738	−	0.940520i	$-0.610339\pi$
$443$	−14.3013	−0.679477	−0.339738	+	0.940520i	$0.610339\pi$
$444$	−14.8480	−0.704656
$445$	−42.7054	−2.02443
$446$	1.55602	0.0736795
$447$	19.8280	0.937834
$448$	0	0
$449$	7.15198	0.337523	0.168761	−	0.985657i	$-0.446023\pi$
$449$	7.15198	0.337523	0.168761	+	0.985657i	$0.446023\pi$
$450$	−4.01998	−0.189503
$451$	−14.6494	−0.689813
$452$	12.7453	0.599489
$453$	−42.6426	−2.00352
$454$	7.94865	0.373049
$455$	0	0
$456$	26.0187	1.21844
$457$	−0.264015	−0.0123501	−0.00617505	−	0.999981i	$-0.501966\pi$
$457$	−0.264015	−0.0123501	−0.00617505	+	0.999981i	$0.501966\pi$
$458$	17.1893	0.803203
$459$	58.0560	2.70982
$460$	11.8387	0.551982
$461$	−7.00933	−0.326457	−0.163228	−	0.986588i	$-0.552191\pi$
$461$	−7.00933	−0.326457	−0.163228	+	0.986588i	$0.552191\pi$
$462$	0	0
$463$	−3.29200	−0.152992	−0.0764961	−	0.997070i	$-0.524373\pi$
$463$	−3.29200	−0.152992	−0.0764961	+	0.997070i	$0.524373\pi$
$464$	1.00000	0.0464238
$465$	34.4919	1.59953
$466$	29.2627	1.35557
$467$	−2.77462	−0.128394	−0.0641970	−	0.997937i	$-0.520449\pi$
$467$	−2.77462	−0.128394	−0.0641970	+	0.997937i	$0.520449\pi$
$468$	−11.2406	−0.519599
$469$	0	0
$470$	−5.58532	−0.257632
$471$	14.3413	0.660811
$472$	7.22199	0.332419
$473$	13.8680	0.637651
$474$	23.3213	1.07118
$475$	4.84802	0.222442
$476$	0	0
$477$	54.0373	2.47420
$478$	11.1120	0.508252
$479$	36.9473	1.68817	0.844083	−	0.536212i	$-0.180145\pi$
$479$	36.9473	1.68817	0.844083	+	0.536212i	$0.180145\pi$
$480$	−7.42401	−0.338858
$481$	−7.73599	−0.352731
$482$	9.52671	0.433930
$483$	0	0
$484$	3.96137	0.180062
$485$	−40.7453	−1.85015
$486$	18.7267	0.849458
$487$	14.5467	0.659173	0.329587	−	0.944125i	$-0.393091\pi$
$487$	14.5467	0.659173	0.329587	+	0.944125i	$0.393091\pi$
$488$	−4.72666	−0.213966
$489$	34.4919	1.55978
$490$	0	0
$491$	21.6040	0.974974	0.487487	−	0.873130i	$-0.337914\pi$
$491$	21.6040	0.974974	0.487487	+	0.873130i	$0.337914\pi$
$492$	−11.8973	−0.536372
$493$	−4.77801	−0.215191
$494$	13.5560	0.609914
$495$	62.7826	2.82187
$496$	4.64600	0.208612
$497$	0	0
$498$	10.4440	0.468006
$499$	−11.7360	−0.525375	−0.262687	−	0.964881i	$-0.584609\pi$
$499$	−11.7360	−0.525375	−0.262687	+	0.964881i	$0.584609\pi$
$500$	10.4333	0.466593
$501$	60.0373	2.68227
$502$	−17.8867	−0.798320
$503$	−1.84208	−0.0821342	−0.0410671	−	0.999156i	$-0.513076\pi$
$503$	−1.84208	−0.0821342	−0.0410671	+	0.999156i	$0.513076\pi$
$504$	0	0
$505$	32.0373	1.42564
$506$	−19.3760	−0.861370
$507$	32.4227	1.43994
$508$	−17.5560	−0.778922
$509$	1.63667	0.0725442	0.0362721	−	0.999342i	$-0.488452\pi$
$509$	1.63667	0.0725442	0.0362721	+	0.999342i	$0.488452\pi$
$510$	35.4720	1.57073
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−100.640	−4.44336
$514$	−18.0480	−0.796061
$515$	−3.67738	−0.162045
$516$	11.2627	0.495813
$517$	9.14134	0.402036
$518$	0	0
$519$	11.8387	0.519661
$520$	−3.86799	−0.169623
$521$	−43.7440	−1.91646	−0.958230	−	0.286000i	$-0.907674\pi$
$521$	−43.7440	−1.91646	−0.958230	+	0.286000i	$0.907674\pi$
$522$	−6.86799	−0.300604
$523$	11.6260	0.508371	0.254185	−	0.967156i	$-0.418193\pi$
$523$	11.6260	0.508371	0.254185	+	0.967156i	$0.418193\pi$
$524$	−15.1893	−0.663548
$525$	0	0
$526$	−12.6133	−0.549966
$527$	−22.1986	−0.966987
$528$	12.1507	0.528790
$529$	2.09337	0.0910163
$530$	18.5946	0.807700
$531$	−49.6006	−2.15248
$532$	0	0
$533$	−6.19863	−0.268492
$534$	56.7640	2.45642
$535$	37.1893	1.60783
$536$	−3.73599	−0.161370
$537$	4.56534	0.197009
$538$	−0.990671	−0.0427109
$539$	0	0
$540$	28.7160	1.23574
$541$	−30.8667	−1.32706	−0.663531	−	0.748149i	$-0.730943\pi$
$541$	−30.8667	−1.32706	−0.663531	+	0.748149i	$0.730943\pi$
$542$	17.1086	0.734879
$543$	−29.1200	−1.24966
$544$	4.77801	0.204855
$545$	44.2321	1.89469
$546$	0	0
$547$	−19.6333	−0.839459	−0.419729	−	0.907649i	$-0.637875\pi$
$547$	−19.6333	−0.839459	−0.419729	+	0.907649i	$0.637875\pi$
$548$	23.0280	0.983707
$549$	32.4626	1.38547
$550$	2.26401	0.0965379
$551$	8.28267	0.352854
$552$	−15.7360	−0.669768
$553$	0	0
$554$	−19.5560	−0.830855
$555$	35.0907	1.48952
$556$	−10.9580	−0.464722
$557$	−41.1120	−1.74197	−0.870986	−	0.491307i	$-0.836519\pi$
$557$	−41.1120	−1.74197	−0.870986	+	0.491307i	$0.836519\pi$
$558$	−31.9087	−1.35080
$559$	5.86799	0.248190
$560$	0	0
$561$	−58.0560	−2.45113
$562$	−11.0573	−0.466424
$563$	−27.0173	−1.13865	−0.569323	−	0.822114i	$-0.692794\pi$
$563$	−27.0173	−1.13865	−0.569323	+	0.822114i	$0.692794\pi$
$564$	7.42401	0.312607
$565$	−30.1214	−1.26722
$566$	12.6167	0.530319
$567$	0	0
$568$	−15.2920	−0.641638
$569$	−6.35994	−0.266623	−0.133311	−	0.991074i	$-0.542561\pi$
$569$	−6.35994	−0.266623	−0.133311	+	0.991074i	$0.542561\pi$
$570$	−61.4906	−2.57556
$571$	5.85735	0.245122	0.122561	−	0.992461i	$-0.460889\pi$
$571$	5.85735	0.245122	0.122561	+	0.992461i	$0.460889\pi$
$572$	6.33063	0.264697
$573$	−4.88797	−0.204198
$574$	0	0
$575$	−2.93206	−0.122275
$576$	6.86799	0.286166
$577$	−19.0980	−0.795060	−0.397530	−	0.917589i	$-0.630133\pi$
$577$	−19.0980	−0.795060	−0.397530	+	0.917589i	$0.630133\pi$
$578$	−5.82936	−0.242469
$579$	4.00000	0.166234
$580$	−2.36333	−0.0981319
$581$	0	0
$582$	54.1587	2.24495
$583$	−30.4333	−1.26042
$584$	−3.22199	−0.133327
$585$	26.5653	1.09834
$586$	−10.8480	−0.448127
$587$	−31.8833	−1.31596	−0.657981	−	0.753034i	$-0.728590\pi$
$587$	−31.8833	−1.31596	−0.657981	+	0.753034i	$0.728590\pi$
$588$	0	0
$589$	38.4813	1.58559
$590$	−17.0679	−0.702676
$591$	−50.6426	−2.08316
$592$	4.72666	0.194264
$593$	30.9800	1.27220	0.636099	−	0.771608i	$-0.280547\pi$
$593$	30.9800	1.27220	0.636099	+	0.771608i	$0.280547\pi$
$594$	−46.9987	−1.92838
$595$	0	0
$596$	−6.31198	−0.258549
$597$	36.3599	1.48811
$598$	−8.19863	−0.335267
$599$	24.3120	0.993360	0.496680	−	0.867934i	$-0.334552\pi$
$599$	24.3120	0.993360	0.496680	+	0.867934i	$0.334552\pi$
$600$	1.83869	0.0750641
$601$	6.23132	0.254181	0.127090	−	0.991891i	$-0.459436\pi$
$601$	6.23132	0.254181	0.127090	+	0.991891i	$0.459436\pi$
$602$	0	0
$603$	25.6587	1.04490
$604$	13.5747	0.552346
$605$	−9.36201	−0.380620
$606$	−42.5840	−1.72986
$607$	−8.11797	−0.329498	−0.164749	−	0.986336i	$-0.552681\pi$
$607$	−8.11797	−0.329498	−0.164749	+	0.986336i	$0.552681\pi$
$608$	−8.28267	−0.335907
$609$	0	0
$610$	11.1706	0.452286
$611$	3.86799	0.156482
$612$	−32.8153	−1.32648
$613$	11.7653	0.475196	0.237598	−	0.971364i	$-0.423640\pi$
$613$	11.7653	0.475196	0.237598	+	0.971364i	$0.423640\pi$
$614$	8.33063	0.336197
$615$	28.1172	1.13380
$616$	0	0
$617$	−29.7360	−1.19713	−0.598563	−	0.801076i	$-0.704261\pi$
$617$	−29.7360	−1.19713	−0.598563	+	0.801076i	$0.704261\pi$
$618$	4.88797	0.196623
$619$	17.2627	0.693846	0.346923	−	0.937894i	$-0.387226\pi$
$619$	17.2627	0.693846	0.346923	+	0.937894i	$0.387226\pi$
$620$	−10.9800	−0.440968
$621$	60.8667	2.44250
$622$	12.0700	0.483963
$623$	0	0
$624$	5.14134	0.205818
$625$	−27.5840	−1.10336
$626$	22.4147	0.895871
$627$	100.640	4.01917
$628$	−4.56534	−0.182177
$629$	−22.5840	−0.900483
$630$	0	0
$631$	35.1120	1.39779	0.698894	−	0.715225i	$-0.253676\pi$
$631$	35.1120	1.39779	0.698894	+	0.715225i	$0.253676\pi$
$632$	−7.42401	−0.295311
$633$	52.5106	2.08711
$634$	10.5653	0.419603
$635$	41.4906	1.64651
$636$	−24.7160	−0.980054
$637$	0	0
$638$	3.86799	0.153135
$639$	105.025	4.15474
$640$	2.36333	0.0934188
$641$	6.82936	0.269743	0.134872	−	0.990863i	$-0.456938\pi$
$641$	6.82936	0.269743	0.134872	+	0.990863i	$0.456938\pi$
$642$	−49.4320	−1.95093
$643$	−30.3713	−1.19773	−0.598864	−	0.800850i	$-0.704381\pi$
$643$	−30.3713	−1.19773	−0.598864	+	0.800850i	$0.704381\pi$
$644$	0	0
$645$	−26.6174	−1.04806
$646$	39.5747	1.55704
$647$	2.12136	0.0833993	0.0416996	−	0.999130i	$-0.486723\pi$
$647$	2.12136	0.0833993	0.0416996	+	0.999130i	$0.486723\pi$
$648$	−17.5653	−0.690032
$649$	27.9346	1.09653
$650$	0.957977	0.0375750
$651$	0	0
$652$	−10.9800	−0.430011
$653$	−35.3947	−1.38510	−0.692551	−	0.721369i	$-0.743513\pi$
$653$	−35.3947	−1.38510	−0.692551	+	0.721369i	$0.743513\pi$
$654$	−58.7933	−2.29900
$655$	35.8973	1.40262
$656$	3.78734	0.147871
$657$	22.1286	0.863320
$658$	0	0
$659$	5.52671	0.215290	0.107645	−	0.994189i	$-0.465669\pi$
$659$	5.52671	0.215290	0.107645	+	0.994189i	$0.465669\pi$
$660$	−28.7160	−1.11777
$661$	32.8994	1.27964	0.639819	−	0.768526i	$-0.279009\pi$
$661$	32.8994	1.27964	0.639819	+	0.768526i	$0.279009\pi$
$662$	−13.3400	−0.518472
$663$	−24.5653	−0.954039
$664$	−3.32469	−0.129023
$665$	0	0
$666$	−32.4626	−1.25790
$667$	−5.00933	−0.193962
$668$	−19.1120	−0.739467
$669$	4.88797	0.188980
$670$	8.82936	0.341108
$671$	−18.2827	−0.705795
$672$	0	0
$673$	−3.26270	−0.125768	−0.0628839	−	0.998021i	$-0.520030\pi$
$673$	−3.26270	−0.125768	−0.0628839	+	0.998021i	$0.520030\pi$
$674$	14.5653	0.561036
$675$	−7.11203	−0.273742
$676$	−10.3213	−0.396973
$677$	40.0373	1.53876	0.769380	−	0.638792i	$-0.220566\pi$
$677$	40.0373	1.53876	0.769380	+	0.638792i	$0.220566\pi$
$678$	40.0373	1.53762
$679$	0	0
$680$	−11.2920	−0.433028
$681$	24.9694	0.956829
$682$	17.9707	0.688133
$683$	−36.2427	−1.38679	−0.693395	−	0.720558i	$-0.743886\pi$
$683$	−36.2427	−1.38679	−0.693395	+	0.720558i	$0.743886\pi$
$684$	56.8853	2.17507
$685$	−54.4227	−2.07938
$686$	0	0
$687$	53.9974	2.06013
$688$	−3.58532	−0.136689
$689$	−12.8773	−0.490587
$690$	37.1893	1.41577
$691$	50.1659	1.90840	0.954201	−	0.299166i	$-0.0967085\pi$
$691$	50.1659	1.90840	0.954201	+	0.299166i	$0.0967085\pi$
$692$	−3.76868	−0.143264
$693$	0	0
$694$	−17.2920	−0.656395
$695$	25.8973	0.982340
$696$	3.14134	0.119072
$697$	−18.0959	−0.685432
$698$	27.9193	1.05676
$699$	91.9240	3.47688
$700$	0	0
$701$	2.04796	0.0773505	0.0386752	−	0.999252i	$-0.487686\pi$
$701$	2.04796	0.0773505	0.0386752	+	0.999252i	$0.487686\pi$
$702$	−19.8867	−0.750573
$703$	39.1493	1.47655
$704$	−3.86799	−0.145780
$705$	−17.5454	−0.660797
$706$	−30.0373	−1.13047
$707$	0	0
$708$	22.6867	0.852619
$709$	−17.8867	−0.671747	−0.335874	−	0.941907i	$-0.609032\pi$
$709$	−17.8867	−0.671747	−0.335874	+	0.941907i	$0.609032\pi$
$710$	36.1400	1.35631
$711$	50.9880	1.91220
$712$	−18.0700	−0.677202
$713$	−23.2733	−0.871594
$714$	0	0
$715$	−14.9614	−0.559523
$716$	−1.45331	−0.0543129
$717$	34.9066	1.30361
$718$	−4.31198	−0.160922
$719$	7.80137	0.290942	0.145471	−	0.989363i	$-0.453530\pi$
$719$	7.80137	0.290942	0.145471	+	0.989363i	$0.453530\pi$
$720$	−16.2313	−0.604906
$721$	0	0
$722$	−49.6027	−1.84602
$723$	29.9266	1.11298
$724$	9.26995	0.344515
$725$	0.585320	0.0217383
$726$	12.4440	0.461840
$727$	49.5233	1.83672	0.918359	−	0.395748i	$-0.129515\pi$
$727$	49.5233	1.83672	0.918359	+	0.395748i	$0.129515\pi$
$728$	0	0
$729$	6.13069	0.227063
$730$	7.61462	0.281830
$731$	17.1307	0.633601
$732$	−14.8480	−0.548798
$733$	−14.1800	−0.523749	−0.261875	−	0.965102i	$-0.584341\pi$
$733$	−14.1800	−0.523749	−0.261875	+	0.965102i	$0.584341\pi$
$734$	−6.51399	−0.240436
$735$	0	0
$736$	5.00933	0.184646
$737$	−14.4508	−0.532301
$738$	−26.0114	−0.957493
$739$	−7.84934	−0.288742	−0.144371	−	0.989524i	$-0.546116\pi$
$739$	−7.84934	−0.288742	−0.144371	+	0.989524i	$0.546116\pi$
$740$	−11.1706	−0.410641
$741$	42.5840	1.56436
$742$	0	0
$743$	−10.0187	−0.367549	−0.183774	−	0.982968i	$-0.558832\pi$
$743$	−10.0187	−0.367549	−0.183774	+	0.982968i	$0.558832\pi$
$744$	14.5946	0.535066
$745$	14.9173	0.546527
$746$	7.40535	0.271129
$747$	22.8340	0.835452
$748$	18.4813	0.675743
$749$	0	0
$750$	32.7746	1.19676
$751$	−10.3413	−0.377359	−0.188679	−	0.982039i	$-0.560421\pi$
$751$	−10.3413	−0.377359	−0.188679	+	0.982039i	$0.560421\pi$
$752$	−2.36333	−0.0861817
$753$	−56.1880	−2.04760
$754$	1.63667	0.0596041
$755$	−32.0814	−1.16756
$756$	0	0
$757$	21.2334	0.771741	0.385870	−	0.922553i	$-0.373901\pi$
$757$	21.2334	0.771741	0.385870	+	0.922553i	$0.373901\pi$
$758$	−15.6774	−0.569428
$759$	−60.8667	−2.20932
$760$	19.5747	0.710048
$761$	−43.1680	−1.56484	−0.782419	−	0.622752i	$-0.786015\pi$
$761$	−43.1680	−1.56484	−0.782419	+	0.622752i	$0.786015\pi$
$762$	−55.1493	−1.99785
$763$	0	0
$764$	1.55602	0.0562947
$765$	77.5534	2.80395
$766$	10.2827	0.371528
$767$	11.8200	0.426797
$768$	−3.14134	−0.113353
$769$	17.4461	0.629121	0.314560	−	0.949237i	$-0.398143\pi$
$769$	17.4461	0.629121	0.314560	+	0.949237i	$0.398143\pi$
$770$	0	0
$771$	−56.6947	−2.04181
$772$	−1.27334	−0.0458286
$773$	15.4720	0.556488	0.278244	−	0.960510i	$-0.410248\pi$
$773$	15.4720	0.556488	0.278244	+	0.960510i	$0.410248\pi$
$774$	24.6240	0.885090
$775$	2.71940	0.0976837
$776$	−17.2406	−0.618903
$777$	0	0
$778$	5.91595	0.212097
$779$	31.3693	1.12392
$780$	−12.1507	−0.435064
$781$	−59.1493	−2.11653
$782$	−23.9346	−0.855900
$783$	−12.1507	−0.434229
$784$	0	0
$785$	10.7894	0.385090
$786$	−47.7147	−1.70193
$787$	11.3620	0.405012	0.202506	−	0.979281i	$-0.435091\pi$
$787$	11.3620	0.405012	0.202506	+	0.979281i	$0.435091\pi$
$788$	16.1214	0.574300
$789$	−39.6226	−1.41060
$790$	17.5454	0.624236
$791$	0	0
$792$	26.5653	0.943958
$793$	−7.73599	−0.274713
$794$	−9.01272	−0.319849
$795$	58.4120	2.07166
$796$	−11.5747	−0.410253
$797$	−1.98134	−0.0701828	−0.0350914	−	0.999384i	$-0.511172\pi$
$797$	−1.98134	−0.0701828	−0.0350914	+	0.999384i	$0.511172\pi$
$798$	0	0
$799$	11.2920	0.399482
$800$	−0.585320	−0.0206942
$801$	124.105	4.38502
$802$	−10.7746	−0.380465
$803$	−12.4626	−0.439797
$804$	−11.7360	−0.413896
$805$	0	0
$806$	7.60398	0.267839
$807$	−3.11203	−0.109549
$808$	13.5560	0.476899
$809$	−21.7801	−0.765747	−0.382873	−	0.923801i	$-0.625065\pi$
$809$	−21.7801	−0.765747	−0.382873	+	0.923801i	$0.625065\pi$
$810$	41.5127	1.45861
$811$	1.60737	0.0564423	0.0282211	−	0.999602i	$-0.491016\pi$
$811$	1.60737	0.0564423	0.0282211	+	0.999602i	$0.491016\pi$
$812$	0	0
$813$	53.7440	1.88488
$814$	18.2827	0.640807
$815$	25.9494	0.908968
$816$	15.0093	0.525432
$817$	−29.6960	−1.03893
$818$	2.79667	0.0977831
$819$	0	0
$820$	−8.95072	−0.312573
$821$	31.0759	1.08456	0.542279	−	0.840198i	$-0.317562\pi$
$821$	31.0759	1.08456	0.542279	+	0.840198i	$0.317562\pi$
$822$	72.3386	2.52310
$823$	−52.6027	−1.83361	−0.916807	−	0.399331i	$-0.869242\pi$
$823$	−52.6027	−1.83361	−0.916807	+	0.399331i	$0.869242\pi$
$824$	−1.55602	−0.0542064
$825$	7.11203	0.247609
$826$	0	0
$827$	−5.84934	−0.203401	−0.101701	−	0.994815i	$-0.532428\pi$
$827$	−5.84934	−0.203401	−0.101701	+	0.994815i	$0.532428\pi$
$828$	−34.4040	−1.19562
$829$	−13.8786	−0.482025	−0.241013	−	0.970522i	$-0.577479\pi$
$829$	−13.8786	−0.482025	−0.241013	+	0.970522i	$0.577479\pi$
$830$	7.85735	0.272732
$831$	−61.4320	−2.13105
$832$	−1.63667	−0.0567414
$833$	0	0
$834$	−34.4227	−1.19196
$835$	45.1680	1.56310
$836$	−32.0373	−1.10803
$837$	−56.4520	−1.95127
$838$	27.8900	0.963445
$839$	15.2954	0.528056	0.264028	−	0.964515i	$-0.414949\pi$
$839$	15.2954	0.528056	0.264028	+	0.964515i	$0.414949\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−31.8387	−1.09723
$843$	−34.7347	−1.19633
$844$	−16.7160	−0.575389
$845$	24.3926	0.839132
$846$	16.2313	0.558044
$847$	0	0
$848$	7.86799	0.270188
$849$	39.6333	1.36021
$850$	2.79667	0.0959248
$851$	−23.6774	−0.811650
$852$	−48.0373	−1.64573
$853$	−27.8387	−0.953179	−0.476589	−	0.879126i	$-0.658127\pi$
$853$	−27.8387	−0.953179	−0.476589	+	0.879126i	$0.658127\pi$
$854$	0	0
$855$	−134.439	−4.59771
$856$	15.7360	0.537845
$857$	−8.07340	−0.275782	−0.137891	−	0.990447i	$-0.544032\pi$
$857$	−8.07340	−0.275782	−0.137891	+	0.990447i	$0.544032\pi$
$858$	19.8867	0.678919
$859$	13.2186	0.451013	0.225506	−	0.974242i	$-0.427596\pi$
$859$	13.2186	0.451013	0.225506	+	0.974242i	$0.427596\pi$
$860$	8.47329	0.288937
$861$	0	0
$862$	3.43466	0.116985
$863$	−31.0280	−1.05620	−0.528102	−	0.849181i	$-0.677096\pi$
$863$	−31.0280	−1.05620	−0.528102	+	0.849181i	$0.677096\pi$
$864$	12.1507	0.413374
$865$	8.90663	0.302834
$866$	−31.7287	−1.07819
$867$	−18.3120	−0.621907
$868$	0	0
$869$	−28.7160	−0.974124
$870$	−7.42401	−0.251697
$871$	−6.11458	−0.207185
$872$	18.7160	0.633804
$873$	118.409	4.00753
$874$	41.4906	1.40344
$875$	0	0
$876$	−10.1214	−0.341969
$877$	52.5734	1.77528	0.887638	−	0.460542i	$-0.152345\pi$
$877$	52.5734	1.77528	0.887638	+	0.460542i	$0.152345\pi$
$878$	29.7546	1.00417
$879$	−34.0773	−1.14940
$880$	9.14134	0.308154
$881$	−1.60737	−0.0541536	−0.0270768	−	0.999633i	$-0.508620\pi$
$881$	−1.60737	−0.0541536	−0.0270768	+	0.999633i	$0.508620\pi$
$882$	0	0
$883$	29.7173	1.00007	0.500034	−	0.866006i	$-0.333321\pi$
$883$	29.7173	1.00007	0.500034	+	0.866006i	$0.333321\pi$
$884$	7.82003	0.263016
$885$	−53.6161	−1.80229
$886$	14.3013	0.480463
$887$	31.0900	1.04390	0.521950	−	0.852976i	$-0.325205\pi$
$887$	31.0900	1.04390	0.521950	+	0.852976i	$0.325205\pi$
$888$	14.8480	0.498267
$889$	0	0
$890$	42.7054	1.43149
$891$	−67.9426	−2.27616
$892$	−1.55602	−0.0520993
$893$	−19.5747	−0.655041
$894$	−19.8280	−0.663149
$895$	3.43466	0.114808
$896$	0	0
$897$	−25.7546	−0.859922
$898$	−7.15198	−0.238665
$899$	4.64600	0.154953
$900$	4.01998	0.133999
$901$	−37.5933	−1.25242
$902$	14.6494	0.487771
$903$	0	0
$904$	−12.7453	−0.423903
$905$	−21.9079	−0.728245
$906$	42.6426	1.41671
$907$	−46.8667	−1.55618	−0.778091	−	0.628151i	$-0.783812\pi$
$907$	−46.8667	−1.55618	−0.778091	+	0.628151i	$0.783812\pi$
$908$	−7.94865	−0.263785
$909$	−93.1026	−3.08802
$910$	0	0
$911$	−46.6320	−1.54499	−0.772493	−	0.635023i	$-0.780990\pi$
$911$	−46.6320	−1.54499	−0.772493	+	0.635023i	$0.780990\pi$
$912$	−26.0187	−0.861564
$913$	−12.8599	−0.425600
$914$	0.264015	0.00873283
$915$	35.0907	1.16006
$916$	−17.1893	−0.567950
$917$	0	0
$918$	−58.0560	−1.91613
$919$	−5.89730	−0.194534	−0.0972669	−	0.995258i	$-0.531010\pi$
$919$	−5.89730	−0.194534	−0.0972669	+	0.995258i	$0.531010\pi$
$920$	−11.8387	−0.390310
$921$	26.1693	0.862308
$922$	7.00933	0.230840
$923$	−25.0280	−0.823806
$924$	0	0
$925$	2.76661	0.0909655
$926$	3.29200	0.108182
$927$	10.6867	0.350997
$928$	−1.00000	−0.0328266
$929$	−10.6027	−0.347862	−0.173931	−	0.984758i	$-0.555647\pi$
$929$	−10.6027	−0.347862	−0.173931	+	0.984758i	$0.555647\pi$
$930$	−34.4919	−1.13104
$931$	0	0
$932$	−29.2627	−0.958531
$933$	37.9160	1.24131
$934$	2.77462	0.0907883
$935$	−43.6774	−1.42840
$936$	11.2406	0.367412
$937$	−12.5467	−0.409882	−0.204941	−	0.978774i	$-0.565700\pi$
$937$	−12.5467	−0.409882	−0.204941	+	0.978774i	$0.565700\pi$
$938$	0	0
$939$	70.4120	2.29781
$940$	5.58532	0.182173
$941$	−13.4100	−0.437153	−0.218576	−	0.975820i	$-0.570141\pi$
$941$	−13.4100	−0.437153	−0.218576	+	0.975820i	$0.570141\pi$
$942$	−14.3413	−0.467264
$943$	−18.9720	−0.617814
$944$	−7.22199	−0.235056
$945$	0	0
$946$	−13.8680	−0.450887
$947$	17.5081	0.568935	0.284468	−	0.958686i	$-0.408183\pi$
$947$	17.5081	0.568935	0.284468	+	0.958686i	$0.408183\pi$
$948$	−23.3213	−0.757441
$949$	−5.27334	−0.171180
$950$	−4.84802	−0.157290
$951$	33.1893	1.07624
$952$	0	0
$953$	3.37991	0.109486	0.0547431	−	0.998500i	$-0.482566\pi$
$953$	3.37991	0.109486	0.0547431	+	0.998500i	$0.482566\pi$
$954$	−54.0373	−1.74952
$955$	−3.67738	−0.118997
$956$	−11.1120	−0.359389
$957$	12.1507	0.392775
$958$	−36.9473	−1.19371
$959$	0	0
$960$	7.42401	0.239609
$961$	−9.41468	−0.303699
$962$	7.73599	0.249418
$963$	−108.075	−3.48266
$964$	−9.52671	−0.306835
$965$	3.00933	0.0968737
$966$	0	0
$967$	−25.5081	−0.820284	−0.410142	−	0.912022i	$-0.634521\pi$
$967$	−25.5081	−0.820284	−0.410142	+	0.912022i	$0.634521\pi$
$968$	−3.96137	−0.127323
$969$	124.317	3.99365
$970$	40.7453	1.30825
$971$	−52.3200	−1.67903	−0.839514	−	0.543338i	$-0.817160\pi$
$971$	−52.3200	−1.67903	−0.839514	+	0.543338i	$0.817160\pi$
$972$	−18.7267	−0.600658
$973$	0	0
$974$	−14.5467	−0.466106
$975$	3.00933	0.0963757
$976$	4.72666	0.151297
$977$	33.1854	1.06170	0.530848	−	0.847467i	$-0.321874\pi$
$977$	33.1854	1.06170	0.530848	+	0.847467i	$0.321874\pi$
$978$	−34.4919	−1.10293
$979$	−69.8947	−2.23384
$980$	0	0
$981$	−128.541	−4.10401
$982$	−21.6040	−0.689411
$983$	−11.4940	−0.366602	−0.183301	−	0.983057i	$-0.558678\pi$
$983$	−11.4940	−0.366602	−0.183301	+	0.983057i	$0.558678\pi$
$984$	11.8973	0.379272
$985$	−38.1001	−1.21397
$986$	4.77801	0.152163
$987$	0	0
$988$	−13.5560	−0.431274
$989$	17.9600	0.571096
$990$	−62.7826	−1.99536
$991$	−35.2080	−1.11842	−0.559209	−	0.829027i	$-0.688895\pi$
$991$	−35.2080	−1.11842	−0.559209	+	0.829027i	$0.688895\pi$
$992$	−4.64600	−0.147511
$993$	−41.9053	−1.32982
$994$	0	0
$995$	27.3548	0.867204
$996$	−10.4440	−0.330930
$997$	−41.6519	−1.31913	−0.659565	−	0.751647i	$-0.729260\pi$
$997$	−41.6519	−1.31913	−0.659565	+	0.751647i	$0.729260\pi$
$998$	11.7360	0.371496
$999$	−57.4320	−1.81707

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2842.2.a.n.1.1		3
7.6	odd	2		406.2.a.f.1.3	✓	3
21.20	even	2		3654.2.a.bc.1.2		3
28.27	even	2		3248.2.a.u.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.a.f.1.3	✓	3	7.6	odd	2
2842.2.a.n.1.1		3	1.1	even	1	trivial
3248.2.a.u.1.1		3	28.27	even	2
3654.2.a.bc.1.2		3	21.20	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:	\( N \)	\(=\)	\( 2842 = 2 \cdot 7^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2842.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.14134 q^{3} +1.00000 q^{4} -2.36333 q^{5} +3.14134 q^{6} -1.00000 q^{8} +6.86799 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.14134 q^{3} +1.00000 q^{4} -2.36333 q^{5} +3.14134 q^{6} -1.00000 q^{8} +6.86799 q^{9} +2.36333 q^{10} -3.86799 q^{11} -3.14134 q^{12} -1.63667 q^{13} +7.42401 q^{15} +1.00000 q^{16} -4.77801 q^{17} -6.86799 q^{18} +8.28267 q^{19} -2.36333 q^{20} +3.86799 q^{22} -5.00933 q^{23} +3.14134 q^{24} +0.585320 q^{25} +1.63667 q^{26} -12.1507 q^{27} +1.00000 q^{29} -7.42401 q^{30} +4.64600 q^{31} -1.00000 q^{32} +12.1507 q^{33} +4.77801 q^{34} +6.86799 q^{36} +4.72666 q^{37} -8.28267 q^{38} +5.14134 q^{39} +2.36333 q^{40} +3.78734 q^{41} -3.58532 q^{43} -3.86799 q^{44} -16.2313 q^{45} +5.00933 q^{46} -2.36333 q^{47} -3.14134 q^{48} -0.585320 q^{50} +15.0093 q^{51} -1.63667 q^{52} +7.86799 q^{53} +12.1507 q^{54} +9.14134 q^{55} -26.0187 q^{57} -1.00000 q^{58} -7.22199 q^{59} +7.42401 q^{60} +4.72666 q^{61} -4.64600 q^{62} +1.00000 q^{64} +3.86799 q^{65} -12.1507 q^{66} +3.73599 q^{67} -4.77801 q^{68} +15.7360 q^{69} +15.2920 q^{71} -6.86799 q^{72} +3.22199 q^{73} -4.72666 q^{74} -1.83869 q^{75} +8.28267 q^{76} -5.14134 q^{78} +7.42401 q^{79} -2.36333 q^{80} +17.5653 q^{81} -3.78734 q^{82} +3.32469 q^{83} +11.2920 q^{85} +3.58532 q^{86} -3.14134 q^{87} +3.86799 q^{88} +18.0700 q^{89} +16.2313 q^{90} -5.00933 q^{92} -14.5946 q^{93} +2.36333 q^{94} -19.5747 q^{95} +3.14134 q^{96} +17.2406 q^{97} -26.5653 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - q^{3} + 3 q^{4} - 5 q^{5} + q^{6} - 3 q^{8} + 8 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - q^3 + 3 * q^4 - 5 * q^5 + q^6 - 3 * q^8 + 8 * q^9	\( 3 q - 3 q^{2} - q^{3} + 3 q^{4} - 5 q^{5} + q^{6} - 3 q^{8} + 8 q^{9} + 5 q^{10} + q^{11} - q^{12} - 7 q^{13} - 3 q^{15} + 3 q^{16} - 8 q^{17} - 8 q^{18} + 8 q^{19} - 5 q^{20} - q^{22} + 6 q^{23} + q^{24} + 6 q^{25} + 7 q^{26} - 7 q^{27} + 3 q^{29} + 3 q^{30} - 5 q^{31} - 3 q^{32} + 7 q^{33} + 8 q^{34} + 8 q^{36} + 10 q^{37} - 8 q^{38} + 7 q^{39} + 5 q^{40} - 16 q^{41} - 15 q^{43} + q^{44} - 34 q^{45} - 6 q^{46} - 5 q^{47} - q^{48} - 6 q^{50} + 24 q^{51} - 7 q^{52} + 11 q^{53} + 7 q^{54} + 19 q^{55} - 36 q^{57} - 3 q^{58} - 28 q^{59} - 3 q^{60} + 10 q^{61} + 5 q^{62} + 3 q^{64} - q^{65} - 7 q^{66} - 14 q^{67} - 8 q^{68} + 22 q^{69} + 8 q^{71} - 8 q^{72} + 16 q^{73} - 10 q^{74} + 24 q^{75} + 8 q^{76} - 7 q^{78} - 3 q^{79} - 5 q^{80} + 19 q^{81} + 16 q^{82} + 12 q^{83} - 4 q^{85} + 15 q^{86} - q^{87} - q^{88} + 10 q^{89} + 34 q^{90} + 6 q^{92} - 27 q^{93} + 5 q^{94} - 4 q^{95} + q^{96} + 16 q^{97} - 46 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - q^3 + 3 * q^4 - 5 * q^5 + q^6 - 3 * q^8 + 8 * q^9 + 5 * q^10 + q^11 - q^12 - 7 * q^13 - 3 * q^15 + 3 * q^16 - 8 * q^17 - 8 * q^18 + 8 * q^19 - 5 * q^20 - q^22 + 6 * q^23 + q^24 + 6 * q^25 + 7 * q^26 - 7 * q^27 + 3 * q^29 + 3 * q^30 - 5 * q^31 - 3 * q^32 + 7 * q^33 + 8 * q^34 + 8 * q^36 + 10 * q^37 - 8 * q^38 + 7 * q^39 + 5 * q^40 - 16 * q^41 - 15 * q^43 + q^44 - 34 * q^45 - 6 * q^46 - 5 * q^47 - q^48 - 6 * q^50 + 24 * q^51 - 7 * q^52 + 11 * q^53 + 7 * q^54 + 19 * q^55 - 36 * q^57 - 3 * q^58 - 28 * q^59 - 3 * q^60 + 10 * q^61 + 5 * q^62 + 3 * q^64 - q^65 - 7 * q^66 - 14 * q^67 - 8 * q^68 + 22 * q^69 + 8 * q^71 - 8 * q^72 + 16 * q^73 - 10 * q^74 + 24 * q^75 + 8 * q^76 - 7 * q^78 - 3 * q^79 - 5 * q^80 + 19 * q^81 + 16 * q^82 + 12 * q^83 - 4 * q^85 + 15 * q^86 - q^87 - q^88 + 10 * q^89 + 34 * q^90 + 6 * q^92 - 27 * q^93 + 5 * q^94 - 4 * q^95 + q^96 + 16 * q^97 - 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more