LMFDB - Embedded newform 6897.2.a.bn.1.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [6897,2,Mod(1,6897)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("6897.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6897, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 6897 = 3 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6897.a (trivial)

Newform invariants

comment:select newform

sage:traces = [20,-3,-20,21,-9,3,3,-6,20,-5,0,-21,-9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$55.0728222741$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} - 26 x^{18} + 81 x^{17} + 273 x^{16} - 901 x^{15} - 1480 x^{14} + 5366 x^{13} + \cdots - 304 $ x^20 - 3x^19 - 26x^18 + 81x^17 + 273x^16 - 901x^15 - 1480x^14 + 5366x^13 + 4326x^12 - 18600x^11 - 6056x^10 + 38147x^9 + 883x^8 - 44920x^7 + 7842x^6 + 28010x^5 - 8379x^4 - 7968x^3 + 2928x^2 + 760*x - 304
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 627)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.64839$ of defining polynomial
Character	$\chi$	$=$	6897.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.64839 q^{2} -1.00000 q^{3} +0.717181 q^{4} +0.941331 q^{5} +1.64839 q^{6} -2.54422 q^{7} +2.11458 q^{8} +1.00000 q^{9} -1.55168 q^{10} -0.717181 q^{12} +0.125773 q^{13} +4.19387 q^{14} -0.941331 q^{15} -4.92001 q^{16} -3.18574 q^{17} -1.64839 q^{18} +1.00000 q^{19} +0.675104 q^{20} +2.54422 q^{21} -6.09645 q^{23} -2.11458 q^{24} -4.11390 q^{25} -0.207323 q^{26} -1.00000 q^{27} -1.82467 q^{28} +10.2638 q^{29} +1.55168 q^{30} +2.96622 q^{31} +3.88092 q^{32} +5.25134 q^{34} -2.39496 q^{35} +0.717181 q^{36} +4.43442 q^{37} -1.64839 q^{38} -0.125773 q^{39} +1.99052 q^{40} +10.9416 q^{41} -4.19387 q^{42} +2.13525 q^{43} +0.941331 q^{45} +10.0493 q^{46} -8.28522 q^{47} +4.92001 q^{48} -0.526924 q^{49} +6.78129 q^{50} +3.18574 q^{51} +0.0902021 q^{52} +11.8706 q^{53} +1.64839 q^{54} -5.37997 q^{56} -1.00000 q^{57} -16.9187 q^{58} -1.12531 q^{59} -0.675104 q^{60} -2.09759 q^{61} -4.88947 q^{62} -2.54422 q^{63} +3.44276 q^{64} +0.118394 q^{65} -13.4724 q^{67} -2.28475 q^{68} +6.09645 q^{69} +3.94782 q^{70} -1.09125 q^{71} +2.11458 q^{72} -13.9196 q^{73} -7.30965 q^{74} +4.11390 q^{75} +0.717181 q^{76} +0.207323 q^{78} +2.21350 q^{79} -4.63136 q^{80} +1.00000 q^{81} -18.0361 q^{82} -10.3345 q^{83} +1.82467 q^{84} -2.99884 q^{85} -3.51971 q^{86} -10.2638 q^{87} -10.9034 q^{89} -1.55168 q^{90} -0.319995 q^{91} -4.37225 q^{92} -2.96622 q^{93} +13.6573 q^{94} +0.941331 q^{95} -3.88092 q^{96} +11.8881 q^{97} +0.868574 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 3 q^{2} - 20 q^{3} + 21 q^{4} - 9 q^{5} + 3 q^{6} + 3 q^{7} - 6 q^{8} + 20 q^{9} - 5 q^{10} - 21 q^{12} - 9 q^{13} - 26 q^{14} + 9 q^{15} + 19 q^{16} + 7 q^{17} - 3 q^{18} + 20 q^{19} - 28 q^{20}+ \cdots - 39 q^{98}+O(q^{100}) $ 20 * q - 3 * q^2 - 20 * q^3 + 21 * q^4 - 9 * q^5 + 3 * q^6 + 3 * q^7 - 6 * q^8 + 20 * q^9 - 5 * q^10 - 21 * q^12 - 9 * q^13 - 26 * q^14 + 9 * q^15 + 19 * q^16 + 7 * q^17 - 3 * q^18 + 20 * q^19 - 28 * q^20 - 3 * q^21 - 30 * q^23 + 6 * q^24 + 31 * q^25 - 10 * q^26 - 20 * q^27 + 35 * q^28 - 15 * q^29 + 5 * q^30 - 11 * q^31 - 20 * q^32 - 5 * q^34 - 2 * q^35 + 21 * q^36 + 16 * q^37 - 3 * q^38 + 9 * q^39 - 10 * q^40 - 9 * q^41 + 26 * q^42 + 3 * q^43 - 9 * q^45 - 25 * q^46 - 57 * q^47 - 19 * q^48 + 23 * q^49 + 60 * q^50 - 7 * q^51 + 5 * q^52 - 28 * q^53 + 3 * q^54 - 62 * q^56 - 20 * q^57 - 25 * q^58 - 49 * q^59 + 28 * q^60 + 46 * q^61 + 15 * q^62 + 3 * q^63 + 40 * q^64 - 18 * q^65 - 44 * q^67 - 20 * q^68 + 30 * q^69 + 31 * q^70 - 55 * q^71 - 6 * q^72 - 19 * q^73 + 7 * q^74 - 31 * q^75 + 21 * q^76 + 10 * q^78 + 23 * q^79 - 102 * q^80 + 20 * q^81 - 60 * q^82 + 32 * q^83 - 35 * q^84 + 12 * q^85 + 31 * q^86 + 15 * q^87 - 37 * q^89 - 5 * q^90 - 12 * q^91 - 25 * q^92 + 11 * q^93 + 35 * q^94 - 9 * q^95 + 20 * q^96 - 6 * q^97 - 39 * q^98

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 $

$2$	−1.64839	−1.16559	−0.582793	−	0.812621i	$-0.698040\pi$
$2$	−1.64839	−1.16559	−0.582793	+	0.812621i	$0.698040\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.717181	0.358590
$5$	0.941331	0.420976	0.210488	−	0.977596i	$-0.432495\pi$
$5$	0.941331	0.420976	0.210488	+	0.977596i	$0.432495\pi$
$6$	1.64839	0.672951
$7$	−2.54422	−0.961626	−0.480813	−	0.876823i	$-0.659658\pi$
$7$	−2.54422	−0.961626	−0.480813	+	0.876823i	$0.659658\pi$
$8$	2.11458	0.747618
$9$	1.00000	0.333333
$10$	−1.55168	−0.490684
$11$	0	0
$11$	0	0
$12$	−0.717181	−0.207032
$13$	0.125773	0.0348832	0.0174416	−	0.999848i	$-0.494448\pi$
$13$	0.125773	0.0348832	0.0174416	+	0.999848i	$0.494448\pi$
$14$	4.19387	1.12086
$15$	−0.941331	−0.243051
$16$	−4.92001	−1.23000
$17$	−3.18574	−0.772656	−0.386328	−	0.922361i	$-0.626257\pi$
$17$	−3.18574	−0.772656	−0.386328	+	0.922361i	$0.626257\pi$
$18$	−1.64839	−0.388529
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0.675104	0.150958
$21$	2.54422	0.555195
$22$	0	0
$23$	−6.09645	−1.27120	−0.635598	−	0.772020i	$-0.719247\pi$
$23$	−6.09645	−1.27120	−0.635598	+	0.772020i	$0.719247\pi$
$24$	−2.11458	−0.431637
$25$	−4.11390	−0.822779
$26$	−0.207323	−0.0406594
$27$	−1.00000	−0.192450
$28$	−1.82467	−0.344830
$29$	10.2638	1.90594	0.952970	−	0.303064i	$-0.0980095\pi$
$29$	10.2638	1.90594	0.952970	+	0.303064i	$0.0980095\pi$
$30$	1.55168	0.283296
$31$	2.96622	0.532748	0.266374	−	0.963870i	$-0.414174\pi$
$31$	2.96622	0.532748	0.266374	+	0.963870i	$0.414174\pi$
$32$	3.88092	0.686056
$33$	0	0
$34$	5.25134	0.900597
$35$	−2.39496	−0.404822
$36$	0.717181	0.119530
$37$	4.43442	0.729015	0.364507	−	0.931201i	$-0.381237\pi$
$37$	4.43442	0.729015	0.364507	+	0.931201i	$0.381237\pi$
$38$	−1.64839	−0.267404
$39$	−0.125773	−0.0201398
$40$	1.99052	0.314729
$41$	10.9416	1.70880	0.854398	−	0.519618i	$-0.173926\pi$
$41$	10.9416	1.70880	0.854398	+	0.519618i	$0.173926\pi$
$42$	−4.19387	−0.647128
$43$	2.13525	0.325622	0.162811	−	0.986657i	$-0.447944\pi$
$43$	2.13525	0.325622	0.162811	+	0.986657i	$0.447944\pi$
$44$	0	0
$45$	0.941331	0.140325
$46$	10.0493	1.48169
$47$	−8.28522	−1.20852	−0.604262	−	0.796786i	$-0.706532\pi$
$47$	−8.28522	−1.20852	−0.604262	+	0.796786i	$0.706532\pi$
$48$	4.92001	0.710143
$49$	−0.526924	−0.0752748
$50$	6.78129	0.959020
$51$	3.18574	0.446093
$52$	0.0902021	0.0125088
$53$	11.8706	1.63055	0.815273	−	0.579076i	$-0.196587\pi$
$53$	11.8706	1.63055	0.815273	+	0.579076i	$0.196587\pi$
$54$	1.64839	0.224317
$55$	0	0
$56$	−5.37997	−0.718929
$57$	−1.00000	−0.132453
$58$	−16.9187	−2.22154
$59$	−1.12531	−0.146502	−0.0732511	−	0.997314i	$-0.523337\pi$
$59$	−1.12531	−0.146502	−0.0732511	+	0.997314i	$0.523337\pi$
$60$	−0.675104	−0.0871556
$61$	−2.09759	−0.268568	−0.134284	−	0.990943i	$-0.542874\pi$
$61$	−2.09759	−0.268568	−0.134284	+	0.990943i	$0.542874\pi$
$62$	−4.88947	−0.620964
$63$	−2.54422	−0.320542
$64$	3.44276	0.430346
$65$	0.118394	0.0146850
$66$	0	0
$67$	−13.4724	−1.64592	−0.822958	−	0.568102i	$-0.807678\pi$
$67$	−13.4724	−1.64592	−0.822958	+	0.568102i	$0.807678\pi$
$68$	−2.28475	−0.277067
$69$	6.09645	0.733926
$70$	3.94782	0.471854
$71$	−1.09125	−0.129508	−0.0647538	−	0.997901i	$-0.520626\pi$
$71$	−1.09125	−0.129508	−0.0647538	+	0.997901i	$0.520626\pi$
$72$	2.11458	0.249206
$73$	−13.9196	−1.62916	−0.814581	−	0.580049i	$-0.803033\pi$
$73$	−13.9196	−1.62916	−0.814581	+	0.580049i	$0.803033\pi$
$74$	−7.30965	−0.849729
$75$	4.11390	0.475032
$76$	0.717181	0.0822663
$77$	0	0
$78$	0.207323	0.0234747
$79$	2.21350	0.249038	0.124519	−	0.992217i	$-0.460261\pi$
$79$	2.21350	0.249038	0.124519	+	0.992217i	$0.460261\pi$
$80$	−4.63136	−0.517802
$81$	1.00000	0.111111
$82$	−18.0361	−1.99175
$83$	−10.3345	−1.13436	−0.567182	−	0.823593i	$-0.691966\pi$
$83$	−10.3345	−1.13436	−0.567182	+	0.823593i	$0.691966\pi$
$84$	1.82467	0.199088
$85$	−2.99884	−0.325270
$86$	−3.51971	−0.379540
$87$	−10.2638	−1.10040
$88$	0	0
$89$	−10.9034	−1.15576	−0.577878	−	0.816123i	$-0.696119\pi$
$89$	−10.9034	−1.15576	−0.577878	+	0.816123i	$0.696119\pi$
$90$	−1.55168	−0.163561
$91$	−0.319995	−0.0335446
$92$	−4.37225	−0.455839
$93$	−2.96622	−0.307582
$94$	13.6573	1.40864
$95$	0.941331	0.0965785
$96$	−3.88092	−0.396095
$97$	11.8881	1.20706	0.603528	−	0.797342i	$-0.293761\pi$
$97$	11.8881	1.20706	0.603528	+	0.797342i	$0.293761\pi$
$98$	0.868574	0.0877392
$99$	0	0
$100$	−2.95041	−0.295041
$101$	16.1065	1.60265	0.801326	−	0.598227i	$-0.204128\pi$
$101$	16.1065	1.60265	0.801326	+	0.598227i	$0.204128\pi$
$102$	−5.25134	−0.519960
$103$	0.801115	0.0789363	0.0394681	−	0.999221i	$-0.487434\pi$
$103$	0.801115	0.0789363	0.0394681	+	0.999221i	$0.487434\pi$
$104$	0.265958	0.0260793
$105$	2.39496	0.233724
$106$	−19.5673	−1.90054
$107$	1.09532	0.105889	0.0529445	−	0.998597i	$-0.483139\pi$
$107$	1.09532	0.105889	0.0529445	+	0.998597i	$0.483139\pi$
$108$	−0.717181	−0.0690108
$109$	−4.72183	−0.452269	−0.226135	−	0.974096i	$-0.572609\pi$
$109$	−4.72183	−0.452269	−0.226135	+	0.974096i	$0.572609\pi$
$110$	0	0
$111$	−4.43442	−0.420897
$112$	12.5176	1.18280
$113$	13.2746	1.24877	0.624386	−	0.781116i	$-0.285349\pi$
$113$	13.2746	1.24877	0.624386	+	0.781116i	$0.285349\pi$
$114$	1.64839	0.154386
$115$	−5.73877	−0.535143
$116$	7.36100	0.683452
$117$	0.125773	0.0116277
$118$	1.85494	0.170761
$119$	8.10524	0.743006
$120$	−1.99052	−0.181709
$121$	0	0
$122$	3.45763	0.313040
$123$	−10.9416	−0.986574
$124$	2.12731	0.191038
$125$	−8.57919	−0.767346
$126$	4.19387	0.373619
$127$	14.3743	1.27552	0.637759	−	0.770236i	$-0.279862\pi$
$127$	14.3743	1.27552	0.637759	+	0.770236i	$0.279862\pi$
$128$	−13.4369	−1.18766
$129$	−2.13525	−0.187998
$130$	−0.195159	−0.0171166
$131$	−2.76308	−0.241411	−0.120706	−	0.992688i	$-0.538516\pi$
$131$	−2.76308	−0.241411	−0.120706	+	0.992688i	$0.538516\pi$
$132$	0	0
$133$	−2.54422	−0.220612
$134$	22.2077	1.91846
$135$	−0.941331	−0.0810168
$136$	−6.73652	−0.577652
$137$	−14.6901	−1.25506	−0.627532	−	0.778591i	$-0.715935\pi$
$137$	−14.6901	−1.25506	−0.627532	+	0.778591i	$0.715935\pi$
$138$	−10.0493	−0.855454
$139$	14.0710	1.19349	0.596744	−	0.802432i	$-0.296461\pi$
$139$	14.0710	1.19349	0.596744	+	0.802432i	$0.296461\pi$
$140$	−1.71762	−0.145165
$141$	8.28522	0.697742
$142$	1.79880	0.150952
$143$	0	0
$144$	−4.92001	−0.410001
$145$	9.66163	0.802355
$146$	22.9448	1.89893
$147$	0.526924	0.0434599
$148$	3.18028	0.261418
$149$	20.7385	1.69897	0.849483	−	0.527617i	$-0.176914\pi$
$149$	20.7385	1.69897	0.849483	+	0.527617i	$0.176914\pi$
$150$	−6.78129	−0.553690
$151$	13.1571	1.07071	0.535353	−	0.844628i	$-0.320178\pi$
$151$	13.1571	1.07071	0.535353	+	0.844628i	$0.320178\pi$
$152$	2.11458	0.171515
$153$	−3.18574	−0.257552
$154$	0	0
$155$	2.79219	0.224274
$156$	−0.0902021	−0.00722195
$157$	−4.71598	−0.376376	−0.188188	−	0.982133i	$-0.560261\pi$
$157$	−4.71598	−0.376376	−0.188188	+	0.982133i	$0.560261\pi$
$158$	−3.64871	−0.290276
$159$	−11.8706	−0.941397
$160$	3.65323	0.288813
$161$	15.5107	1.22242
$162$	−1.64839	−0.129510
$163$	4.17382	0.326919	0.163459	−	0.986550i	$-0.447735\pi$
$163$	4.17382	0.326919	0.163459	+	0.986550i	$0.447735\pi$
$164$	7.84713	0.612758
$165$	0	0
$166$	17.0353	1.32220
$167$	−11.3775	−0.880417	−0.440208	−	0.897896i	$-0.645095\pi$
$167$	−11.3775	−0.880417	−0.440208	+	0.897896i	$0.645095\pi$
$168$	5.37997	0.415074
$169$	−12.9842	−0.998783
$170$	4.94325	0.379130
$171$	1.00000	0.0764719
$172$	1.53136	0.116765
$173$	−0.649550	−0.0493844	−0.0246922	−	0.999695i	$-0.507861\pi$
$173$	−0.649550	−0.0493844	−0.0246922	+	0.999695i	$0.507861\pi$
$174$	16.9187	1.28261
$175$	10.4667	0.791206
$176$	0	0
$177$	1.12531	0.0845831
$178$	17.9730	1.34713
$179$	−21.3575	−1.59634	−0.798168	−	0.602435i	$-0.794197\pi$
$179$	−21.3575	−1.59634	−0.798168	+	0.602435i	$0.794197\pi$
$180$	0.675104	0.0503193
$181$	17.7744	1.32116	0.660582	−	0.750754i	$-0.270310\pi$
$181$	17.7744	1.32116	0.660582	+	0.750754i	$0.270310\pi$
$182$	0.527476	0.0390991
$183$	2.09759	0.155058
$184$	−12.8914	−0.950370
$185$	4.17426	0.306898
$186$	4.88947	0.358514
$187$	0	0
$188$	−5.94200	−0.433365
$189$	2.54422	0.185065
$190$	−1.55168	−0.112571
$191$	20.4676	1.48098	0.740492	−	0.672065i	$-0.234592\pi$
$191$	20.4676	1.48098	0.740492	+	0.672065i	$0.234592\pi$
$192$	−3.44276	−0.248460
$193$	11.0979	0.798841	0.399421	−	0.916768i	$-0.369211\pi$
$193$	11.0979	0.798841	0.399421	+	0.916768i	$0.369211\pi$
$194$	−19.5962	−1.40693
$195$	−0.118394	−0.00847838
$196$	−0.377899	−0.0269928
$197$	−9.53633	−0.679435	−0.339718	−	0.940527i	$-0.610332\pi$
$197$	−9.53633	−0.679435	−0.339718	+	0.940527i	$0.610332\pi$
$198$	0	0
$199$	−9.10785	−0.645639	−0.322819	−	0.946461i	$-0.604631\pi$
$199$	−9.10785	−0.645639	−0.322819	+	0.946461i	$0.604631\pi$
$200$	−8.69918	−0.615125
$201$	13.4724	0.950270
$202$	−26.5497	−1.86803
$203$	−26.1134	−1.83280
$204$	2.28475	0.159965
$205$	10.2997	0.719362
$206$	−1.32055	−0.0920070
$207$	−6.09645	−0.423732
$208$	−0.618806	−0.0429065
$209$	0	0
$210$	−3.94782	−0.272425
$211$	−10.2129	−0.703086	−0.351543	−	0.936172i	$-0.614343\pi$
$211$	−10.2129	−0.703086	−0.351543	+	0.936172i	$0.614343\pi$
$212$	8.51334	0.584698
$213$	1.09125	0.0747712
$214$	−1.80552	−0.123423
$215$	2.00997	0.137079
$216$	−2.11458	−0.143879
$217$	−7.54672	−0.512305
$218$	7.78341	0.527159
$219$	13.9196	0.940598
$220$	0	0
$221$	−0.400681	−0.0269527
$222$	7.30965	0.490591
$223$	15.3678	1.02910	0.514550	−	0.857460i	$-0.327959\pi$
$223$	15.3678	1.02910	0.514550	+	0.857460i	$0.327959\pi$
$224$	−9.87393	−0.659730
$225$	−4.11390	−0.274260
$226$	−21.8817	−1.45555
$227$	−28.2307	−1.87374	−0.936869	−	0.349680i	$-0.886290\pi$
$227$	−28.2307	−1.87374	−0.936869	+	0.349680i	$0.886290\pi$
$228$	−0.717181	−0.0474965
$229$	−5.18156	−0.342407	−0.171204	−	0.985236i	$-0.554766\pi$
$229$	−5.18156	−0.342407	−0.171204	+	0.985236i	$0.554766\pi$
$230$	9.45972	0.623755
$231$	0	0
$232$	21.7037	1.42492
$233$	13.5062	0.884821	0.442411	−	0.896813i	$-0.354123\pi$
$233$	13.5062	0.884821	0.442411	+	0.896813i	$0.354123\pi$
$234$	−0.207323	−0.0135531
$235$	−7.79914	−0.508760
$236$	−0.807047	−0.0525343
$237$	−2.21350	−0.143782
$238$	−13.3606	−0.866038
$239$	30.8408	1.99492	0.997462	−	0.0712028i	$-0.0226837\pi$
$239$	30.8408	1.99492	0.997462	+	0.0712028i	$0.0226837\pi$
$240$	4.63136	0.298953
$241$	−3.01568	−0.194257	−0.0971285	−	0.995272i	$-0.530966\pi$
$241$	−3.01568	−0.194257	−0.0971285	+	0.995272i	$0.530966\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	−1.50435	−0.0963060
$245$	−0.496009	−0.0316889
$246$	18.0361	1.14994
$247$	0.125773	0.00800276
$248$	6.27231	0.398292
$249$	10.3345	0.654925
$250$	14.1418	0.894408
$251$	−30.2264	−1.90787	−0.953937	−	0.300006i	$-0.903011\pi$
$251$	−30.2264	−1.90787	−0.953937	+	0.300006i	$0.903011\pi$
$252$	−1.82467	−0.114943
$253$	0	0
$254$	−23.6945	−1.48672
$255$	2.99884	0.187794
$256$	15.2636	0.953976
$257$	−2.94672	−0.183811	−0.0919057	−	0.995768i	$-0.529296\pi$
$257$	−2.94672	−0.183811	−0.0919057	+	0.995768i	$0.529296\pi$
$258$	3.51971	0.219128
$259$	−11.2822	−0.701040
$260$	0.0849100	0.00526590
$261$	10.2638	0.635314
$262$	4.55463	0.281386
$263$	−0.378241	−0.0233234	−0.0116617	−	0.999932i	$-0.503712\pi$
$263$	−0.378241	−0.0233234	−0.0116617	+	0.999932i	$0.503712\pi$
$264$	0	0
$265$	11.1741	0.686421
$266$	4.19387	0.257142
$267$	10.9034	0.667276
$268$	−9.66215	−0.590210
$269$	−11.6733	−0.711733	−0.355866	−	0.934537i	$-0.615814\pi$
$269$	−11.6733	−0.711733	−0.355866	+	0.934537i	$0.615814\pi$
$270$	1.55168	0.0944321
$271$	−0.617222	−0.0374936	−0.0187468	−	0.999824i	$-0.505968\pi$
$271$	−0.617222	−0.0374936	−0.0187468	+	0.999824i	$0.505968\pi$
$272$	15.6739	0.950369
$273$	0.319995	0.0193670
$274$	24.2150	1.46288
$275$	0	0
$276$	4.37225	0.263179
$277$	19.8397	1.19205	0.596026	−	0.802965i	$-0.296746\pi$
$277$	19.8397	1.19205	0.596026	+	0.802965i	$0.296746\pi$
$278$	−23.1945	−1.39111
$279$	2.96622	0.177583
$280$	−5.06433	−0.302652
$281$	−18.3244	−1.09314	−0.546572	−	0.837412i	$-0.684068\pi$
$281$	−18.3244	−1.09314	−0.546572	+	0.837412i	$0.684068\pi$
$282$	−13.6573	−0.813278
$283$	5.98177	0.355580	0.177790	−	0.984068i	$-0.443105\pi$
$283$	5.98177	0.355580	0.177790	+	0.984068i	$0.443105\pi$
$284$	−0.782624	−0.0464402
$285$	−0.941331	−0.0557596
$286$	0	0
$287$	−27.8380	−1.64322
$288$	3.88092	0.228685
$289$	−6.85104	−0.403003
$290$	−15.9261	−0.935214
$291$	−11.8881	−0.696894
$292$	−9.98285	−0.584202
$293$	−4.46485	−0.260839	−0.130420	−	0.991459i	$-0.541632\pi$
$293$	−4.46485	−0.260839	−0.130420	+	0.991459i	$0.541632\pi$
$294$	−0.868574	−0.0506563
$295$	−1.05928	−0.0616739
$296$	9.37695	0.545024
$297$	0	0
$298$	−34.1851	−1.98029
$299$	−0.766770	−0.0443434
$300$	2.95041	0.170342
$301$	−5.43254	−0.313127
$302$	−21.6879	−1.24800
$303$	−16.1065	−0.925292
$304$	−4.92001	−0.282182
$305$	−1.97452	−0.113061
$306$	5.25134	0.300199
$307$	−2.31765	−0.132275	−0.0661377	−	0.997811i	$-0.521068\pi$
$307$	−2.31765	−0.132275	−0.0661377	+	0.997811i	$0.521068\pi$
$308$	0	0
$309$	−0.801115	−0.0455739
$310$	−4.60261	−0.261411
$311$	3.40353	0.192997	0.0964983	−	0.995333i	$-0.469236\pi$
$311$	3.40353	0.192997	0.0964983	+	0.995333i	$0.469236\pi$
$312$	−0.265958	−0.0150569
$313$	17.3690	0.981754	0.490877	−	0.871229i	$-0.336676\pi$
$313$	17.3690	0.981754	0.490877	+	0.871229i	$0.336676\pi$
$314$	7.77376	0.438699
$315$	−2.39496	−0.134941
$316$	1.58748	0.0893027
$317$	−13.7335	−0.771351	−0.385675	−	0.922635i	$-0.626032\pi$
$317$	−13.7335	−0.771351	−0.385675	+	0.922635i	$0.626032\pi$
$318$	19.5673	1.09728
$319$	0	0
$320$	3.24078	0.181165
$321$	−1.09532	−0.0611351
$322$	−25.5677	−1.42483
$323$	−3.18574	−0.177259
$324$	0.717181	0.0398434
$325$	−0.517418	−0.0287012
$326$	−6.88007	−0.381052
$327$	4.72183	0.261118
$328$	23.1370	1.27753
$329$	21.0795	1.16215
$330$	0	0
$331$	10.8390	0.595766	0.297883	−	0.954602i	$-0.403720\pi$
$331$	10.8390	0.595766	0.297883	+	0.954602i	$0.403720\pi$
$332$	−7.41174	−0.406772
$333$	4.43442	0.243005
$334$	18.7545	1.02620
$335$	−12.6820	−0.692891
$336$	−12.5176	−0.682892
$337$	24.7901	1.35040	0.675200	−	0.737635i	$-0.264057\pi$
$337$	24.7901	1.35040	0.675200	+	0.737635i	$0.264057\pi$
$338$	21.4030	1.16417
$339$	−13.2746	−0.720979
$340$	−2.15071	−0.116639
$341$	0	0
$342$	−1.64839	−0.0891346
$343$	19.1502	1.03401
$344$	4.51515	0.243441
$345$	5.73877	0.308965
$346$	1.07071	0.0575617
$347$	−0.165962	−0.00890929	−0.00445464	−	0.999990i	$-0.501418\pi$
$347$	−0.165962	−0.00890929	−0.00445464	+	0.999990i	$0.501418\pi$
$348$	−7.36100	−0.394591
$349$	−29.7310	−1.59146	−0.795731	−	0.605650i	$-0.792913\pi$
$349$	−29.7310	−1.59146	−0.795731	+	0.605650i	$0.792913\pi$
$350$	−17.2531	−0.922219
$351$	−0.125773	−0.00671328
$352$	0	0
$353$	−15.8172	−0.841862	−0.420931	−	0.907093i	$-0.638297\pi$
$353$	−15.8172	−0.841862	−0.420931	+	0.907093i	$0.638297\pi$
$354$	−1.85494	−0.0985889
$355$	−1.02723	−0.0545196
$356$	−7.81969	−0.414443
$357$	−8.10524	−0.428975
$358$	35.2055	1.86067
$359$	−29.2655	−1.54457	−0.772286	−	0.635275i	$-0.780887\pi$
$359$	−29.2655	−1.54457	−0.772286	+	0.635275i	$0.780887\pi$
$360$	1.99052	0.104910
$361$	1.00000	0.0526316
$362$	−29.2992	−1.53993
$363$	0	0
$364$	−0.229494	−0.0120288
$365$	−13.1029	−0.685838
$366$	−3.45763	−0.180733
$367$	33.4588	1.74654	0.873268	−	0.487240i	$-0.161996\pi$
$367$	33.4588	1.74654	0.873268	+	0.487240i	$0.161996\pi$
$368$	29.9946	1.56358
$369$	10.9416	0.569599
$370$	−6.88079	−0.357715
$371$	−30.2014	−1.56798
$372$	−2.12731	−0.110296
$373$	−17.7830	−0.920769	−0.460385	−	0.887720i	$-0.652289\pi$
$373$	−17.7830	−0.920769	−0.460385	+	0.887720i	$0.652289\pi$
$374$	0	0
$375$	8.57919	0.443028
$376$	−17.5198	−0.903514
$377$	1.29091	0.0664853
$378$	−4.19387	−0.215709
$379$	−3.58762	−0.184283	−0.0921417	−	0.995746i	$-0.529371\pi$
$379$	−3.58762	−0.184283	−0.0921417	+	0.995746i	$0.529371\pi$
$380$	0.675104	0.0346321
$381$	−14.3743	−0.736420
$382$	−33.7385	−1.72621
$383$	1.80333	0.0921459	0.0460729	−	0.998938i	$-0.485329\pi$
$383$	1.80333	0.0921459	0.0460729	+	0.998938i	$0.485329\pi$
$384$	13.4369	0.685697
$385$	0	0
$386$	−18.2936	−0.931118
$387$	2.13525	0.108541
$388$	8.52593	0.432839
$389$	−30.7081	−1.55696	−0.778481	−	0.627668i	$-0.784010\pi$
$389$	−30.7081	−1.55696	−0.778481	+	0.627668i	$0.784010\pi$
$390$	0.195159	0.00988228
$391$	19.4217	0.982198
$392$	−1.11422	−0.0562768
$393$	2.76308	0.139379
$394$	15.7196	0.791940
$395$	2.08364	0.104839
$396$	0	0
$397$	10.9434	0.549232	0.274616	−	0.961554i	$-0.411449\pi$
$397$	10.9434	0.549232	0.274616	+	0.961554i	$0.411449\pi$
$398$	15.0133	0.752547
$399$	2.54422	0.127371
$400$	20.2404	1.01202
$401$	−15.6667	−0.782358	−0.391179	−	0.920315i	$-0.627933\pi$
$401$	−15.6667	−0.782358	−0.391179	+	0.920315i	$0.627933\pi$
$402$	−22.2077	−1.10762
$403$	0.373071	0.0185840
$404$	11.5512	0.574696
$405$	0.941331	0.0467751
$406$	43.0450	2.13629
$407$	0	0
$408$	6.73652	0.333507
$409$	0.0765291	0.00378412	0.00189206	−	0.999998i	$-0.499398\pi$
$409$	0.0765291	0.00378412	0.00189206	+	0.999998i	$0.499398\pi$
$410$	−16.9779	−0.838479
$411$	14.6901	0.724611
$412$	0.574545	0.0283058
$413$	2.86303	0.140880
$414$	10.0493	0.493896
$415$	−9.72822	−0.477540
$416$	0.488116	0.0239319
$417$	−14.0710	−0.689061
$418$	0	0
$419$	−5.41913	−0.264742	−0.132371	−	0.991200i	$-0.542259\pi$
$419$	−5.41913	−0.264742	−0.132371	+	0.991200i	$0.542259\pi$
$420$	1.71762	0.0838111
$421$	−16.7633	−0.816992	−0.408496	−	0.912760i	$-0.633947\pi$
$421$	−16.7633	−0.816992	−0.408496	+	0.912760i	$0.633947\pi$
$422$	16.8348	0.819507
$423$	−8.28522	−0.402841
$424$	25.1013	1.21903
$425$	13.1058	0.635725
$426$	−1.79880	−0.0871523
$427$	5.33673	0.258262
$428$	0.785546	0.0379708
$429$	0	0
$430$	−3.31321	−0.159777
$431$	4.82831	0.232571	0.116286	−	0.993216i	$-0.462901\pi$
$431$	4.82831	0.232571	0.116286	+	0.993216i	$0.462901\pi$
$432$	4.92001	0.236714
$433$	−26.5914	−1.27790	−0.638950	−	0.769248i	$-0.720631\pi$
$433$	−26.5914	−1.27790	−0.638950	+	0.769248i	$0.720631\pi$
$434$	12.4399	0.597135
$435$	−9.66163	−0.463240
$436$	−3.38641	−0.162179
$437$	−6.09645	−0.291633
$438$	−22.9448	−1.09635
$439$	15.7871	0.753479	0.376740	−	0.926319i	$-0.377045\pi$
$439$	15.7871	0.753479	0.376740	+	0.926319i	$0.377045\pi$
$440$	0	0
$441$	−0.526924	−0.0250916
$442$	0.660478	0.0314157
$443$	−23.9635	−1.13854	−0.569271	−	0.822150i	$-0.692774\pi$
$443$	−23.9635	−1.13854	−0.569271	+	0.822150i	$0.692774\pi$
$444$	−3.18028	−0.150930
$445$	−10.2637	−0.486545
$446$	−25.3320	−1.19951
$447$	−20.7385	−0.980898
$448$	−8.75916	−0.413832
$449$	40.6178	1.91687	0.958437	−	0.285305i	$-0.0920949\pi$
$449$	40.6178	1.91687	0.958437	+	0.285305i	$0.0920949\pi$
$450$	6.78129	0.319673
$451$	0	0
$452$	9.52031	0.447798
$453$	−13.1571	−0.618173
$454$	46.5352	2.18400
$455$	−0.301221	−0.0141215
$456$	−2.11458	−0.0990244
$457$	−35.9511	−1.68172	−0.840861	−	0.541252i	$-0.817951\pi$
$457$	−35.9511	−1.68172	−0.840861	+	0.541252i	$0.817951\pi$
$458$	8.54122	0.399105
$459$	3.18574	0.148698
$460$	−4.11574	−0.191897
$461$	−23.8422	−1.11044	−0.555222	−	0.831702i	$-0.687367\pi$
$461$	−23.8422	−1.11044	−0.555222	+	0.831702i	$0.687367\pi$
$462$	0	0
$463$	−4.50998	−0.209597	−0.104798	−	0.994493i	$-0.533420\pi$
$463$	−4.50998	−0.209597	−0.104798	+	0.994493i	$0.533420\pi$
$464$	−50.4981	−2.34431
$465$	−2.79219	−0.129485
$466$	−22.2635	−1.03134
$467$	4.90185	0.226831	0.113415	−	0.993548i	$-0.463821\pi$
$467$	4.90185	0.226831	0.113415	+	0.993548i	$0.463821\pi$
$468$	0.0902021	0.00416959
$469$	34.2768	1.58276
$470$	12.8560	0.593003
$471$	4.71598	0.217301
$472$	−2.37955	−0.109528
$473$	0	0
$474$	3.64871	0.167591
$475$	−4.11390	−0.188759
$476$	5.81292	0.266435
$477$	11.8706	0.543516
$478$	−50.8375	−2.32525
$479$	−19.2082	−0.877645	−0.438823	−	0.898574i	$-0.644604\pi$
$479$	−19.2082	−0.877645	−0.438823	+	0.898574i	$0.644604\pi$
$480$	−3.65323	−0.166746
$481$	0.557732	0.0254304
$482$	4.97101	0.226423
$483$	−15.5107	−0.705762
$484$	0	0
$485$	11.1907	0.508141
$486$	1.64839	0.0747724
$487$	−5.31822	−0.240992	−0.120496	−	0.992714i	$-0.538448\pi$
$487$	−5.31822	−0.240992	−0.120496	+	0.992714i	$0.538448\pi$
$488$	−4.43552	−0.200787
$489$	−4.17382	−0.188747
$490$	0.817616	0.0369361
$491$	31.5619	1.42437	0.712185	−	0.701992i	$-0.247706\pi$
$491$	31.5619	1.42437	0.712185	+	0.701992i	$0.247706\pi$
$492$	−7.84713	−0.353776
$493$	−32.6978	−1.47264
$494$	−0.207323	−0.00932790
$495$	0	0
$496$	−14.5938	−0.655282
$497$	2.77638	0.124538
$498$	−17.0353	−0.763371
$499$	−7.25278	−0.324679	−0.162340	−	0.986735i	$-0.551904\pi$
$499$	−7.25278	−0.324679	−0.162340	+	0.986735i	$0.551904\pi$
$500$	−6.15283	−0.275163
$501$	11.3775	0.508309
$502$	49.8248	2.22379
$503$	−7.33499	−0.327051	−0.163526	−	0.986539i	$-0.552287\pi$
$503$	−7.33499	−0.327051	−0.163526	+	0.986539i	$0.552287\pi$
$504$	−5.37997	−0.239643
$505$	15.1615	0.674678
$506$	0	0
$507$	12.9842	0.576648
$508$	10.3090	0.457388
$509$	−10.1810	−0.451263	−0.225632	−	0.974213i	$-0.572445\pi$
$509$	−10.1810	−0.451263	−0.225632	+	0.974213i	$0.572445\pi$
$510$	−4.94325	−0.218891
$511$	35.4145	1.56665
$512$	1.71337	0.0757208
$513$	−1.00000	−0.0441511
$514$	4.85734	0.214248
$515$	0.754115	0.0332303
$516$	−1.53136	−0.0674142
$517$	0	0
$518$	18.5974	0.817122
$519$	0.649550	0.0285121
$520$	0.250354	0.0109788
$521$	20.8153	0.911935	0.455967	−	0.889997i	$-0.349293\pi$
$521$	20.8153	0.911935	0.455967	+	0.889997i	$0.349293\pi$
$522$	−16.9187	−0.740512
$523$	−18.5921	−0.812975	−0.406487	−	0.913656i	$-0.633246\pi$
$523$	−18.5921	−0.812975	−0.406487	+	0.913656i	$0.633246\pi$
$524$	−1.98163	−0.0865678
$525$	−10.4667	−0.456803
$526$	0.623488	0.0271854
$527$	−9.44960	−0.411631
$528$	0	0
$529$	14.1667	0.615942
$530$	−18.4193	−0.800083
$531$	−1.12531	−0.0488341
$532$	−1.82467	−0.0791094
$533$	1.37617	0.0596083
$534$	−17.9730	−0.777767
$535$	1.03106	0.0445767
$536$	−28.4885	−1.23052
$537$	21.3575	0.921645
$538$	19.2421	0.829586
$539$	0	0
$540$	−0.675104	−0.0290519
$541$	4.86690	0.209244	0.104622	−	0.994512i	$-0.466637\pi$
$541$	4.86690	0.209244	0.104622	+	0.994512i	$0.466637\pi$
$542$	1.01742	0.0437020
$543$	−17.7744	−0.762774
$544$	−12.3636	−0.530086
$545$	−4.44480	−0.190395
$546$	−0.527476	−0.0225739
$547$	−7.17177	−0.306643	−0.153321	−	0.988176i	$-0.548997\pi$
$547$	−7.17177	−0.306643	−0.153321	+	0.988176i	$0.548997\pi$
$548$	−10.5355	−0.450054
$549$	−2.09759	−0.0895228
$550$	0	0
$551$	10.2638	0.437253
$552$	12.8914	0.548696
$553$	−5.63164	−0.239482
$554$	−32.7035	−1.38944
$555$	−4.17426	−0.177187
$556$	10.0915	0.427973
$557$	−28.2490	−1.19695	−0.598475	−	0.801141i	$-0.704227\pi$
$557$	−28.2490	−1.19695	−0.598475	+	0.801141i	$0.704227\pi$
$558$	−4.88947	−0.206988
$559$	0.268557	0.0113587
$560$	11.7832	0.497932
$561$	0	0
$562$	30.2058	1.27415
$563$	−29.5922	−1.24716	−0.623581	−	0.781758i	$-0.714323\pi$
$563$	−29.5922	−1.24716	−0.623581	+	0.781758i	$0.714323\pi$
$564$	5.94200	0.250203
$565$	12.4958	0.525703
$566$	−9.86028	−0.414458
$567$	−2.54422	−0.106847
$568$	−2.30754	−0.0968222
$569$	3.62193	0.151839	0.0759197	−	0.997114i	$-0.475811\pi$
$569$	3.62193	0.151839	0.0759197	+	0.997114i	$0.475811\pi$
$570$	1.55168	0.0649926
$571$	14.2793	0.597571	0.298785	−	0.954320i	$-0.403418\pi$
$571$	14.2793	0.597571	0.298785	+	0.954320i	$0.403418\pi$
$572$	0	0
$573$	−20.4676	−0.855047
$574$	45.8878	1.91532
$575$	25.0801	1.04591
$576$	3.44276	0.143449
$577$	−41.6547	−1.73411	−0.867054	−	0.498214i	$-0.833989\pi$
$577$	−41.6547	−1.73411	−0.867054	+	0.498214i	$0.833989\pi$
$578$	11.2932	0.469734
$579$	−11.0979	−0.461211
$580$	6.92914	0.287717
$581$	26.2934	1.09083
$582$	19.5962	0.812290
$583$	0	0
$584$	−29.4341	−1.21799
$585$	0.118394	0.00489500
$586$	7.35980	0.304030
$587$	−22.9222	−0.946099	−0.473050	−	0.881036i	$-0.656847\pi$
$587$	−22.9222	−0.946099	−0.473050	+	0.881036i	$0.656847\pi$
$588$	0.377899	0.0155843
$589$	2.96622	0.122221
$590$	1.74611	0.0718863
$591$	9.53633	0.392272
$592$	−21.8174	−0.896690
$593$	−37.3157	−1.53237	−0.766186	−	0.642618i	$-0.777848\pi$
$593$	−37.3157	−1.53237	−0.766186	+	0.642618i	$0.777848\pi$
$594$	0	0
$595$	7.62971	0.312788
$596$	14.8733	0.609233
$597$	9.10785	0.372760
$598$	1.26393	0.0516861
$599$	−35.9083	−1.46717	−0.733587	−	0.679596i	$-0.762155\pi$
$599$	−35.9083	−1.46717	−0.733587	+	0.679596i	$0.762155\pi$
$600$	8.69918	0.355142
$601$	−18.2093	−0.742774	−0.371387	−	0.928478i	$-0.621118\pi$
$601$	−18.2093	−0.742774	−0.371387	+	0.928478i	$0.621118\pi$
$602$	8.95494	0.364976
$603$	−13.4724	−0.548639
$604$	9.43599	0.383945
$605$	0	0
$606$	26.5497	1.07851
$607$	−3.72610	−0.151238	−0.0756188	−	0.997137i	$-0.524093\pi$
$607$	−3.72610	−0.151238	−0.0756188	+	0.997137i	$0.524093\pi$
$608$	3.88092	0.157392
$609$	26.1134	1.05817
$610$	3.25478	0.131782
$611$	−1.04206	−0.0421572
$612$	−2.28475	−0.0923557
$613$	−12.7679	−0.515690	−0.257845	−	0.966186i	$-0.583012\pi$
$613$	−12.7679	−0.515690	−0.257845	+	0.966186i	$0.583012\pi$
$614$	3.82039	0.154178
$615$	−10.2997	−0.415324
$616$	0	0
$617$	−0.724060	−0.0291496	−0.0145748	−	0.999894i	$-0.504639\pi$
$617$	−0.724060	−0.0291496	−0.0145748	+	0.999894i	$0.504639\pi$
$618$	1.32055	0.0531203
$619$	−21.6761	−0.871237	−0.435619	−	0.900131i	$-0.643470\pi$
$619$	−21.6761	−0.871237	−0.435619	+	0.900131i	$0.643470\pi$
$620$	2.00251	0.0804226
$621$	6.09645	0.244642
$622$	−5.61034	−0.224954
$623$	27.7406	1.11141
$624$	0.618806	0.0247721
$625$	12.4936	0.499745
$626$	−28.6309	−1.14432
$627$	0	0
$628$	−3.38221	−0.134965
$629$	−14.1269	−0.563278
$630$	3.94782	0.157285
$631$	−20.0616	−0.798640	−0.399320	−	0.916812i	$-0.630754\pi$
$631$	−20.0616	−0.798640	−0.399320	+	0.916812i	$0.630754\pi$
$632$	4.68063	0.186185
$633$	10.2129	0.405927
$634$	22.6381	0.899076
$635$	13.5310	0.536962
$636$	−8.51334	−0.337576
$637$	−0.0662729	−0.00262583
$638$	0	0
$639$	−1.09125	−0.0431692
$640$	−12.6485	−0.499977
$641$	3.84506	0.151871	0.0759354	−	0.997113i	$-0.475806\pi$
$641$	3.84506	0.151871	0.0759354	+	0.997113i	$0.475806\pi$
$642$	1.80552	0.0712582
$643$	32.3902	1.27735	0.638673	−	0.769478i	$-0.279484\pi$
$643$	32.3902	1.27735	0.638673	+	0.769478i	$0.279484\pi$
$644$	11.1240	0.438347
$645$	−2.00997	−0.0791426
$646$	5.25134	0.206611
$647$	−34.3978	−1.35232	−0.676159	−	0.736756i	$-0.736357\pi$
$647$	−34.3978	−1.35232	−0.676159	+	0.736756i	$0.736357\pi$
$648$	2.11458	0.0830687
$649$	0	0
$650$	0.852905	0.0334537
$651$	7.54672	0.295779
$652$	2.99338	0.117230
$653$	−22.0629	−0.863387	−0.431694	−	0.902020i	$-0.642084\pi$
$653$	−22.0629	−0.863387	−0.431694	+	0.902020i	$0.642084\pi$
$654$	−7.78341	−0.304355
$655$	−2.60097	−0.101628
$656$	−53.8330	−2.10183
$657$	−13.9196	−0.543054
$658$	−34.7471	−1.35458
$659$	−4.38630	−0.170866	−0.0854330	−	0.996344i	$-0.527227\pi$
$659$	−4.38630	−0.170866	−0.0854330	+	0.996344i	$0.527227\pi$
$660$	0	0
$661$	41.4634	1.61274	0.806369	−	0.591412i	$-0.201429\pi$
$661$	41.4634	1.61274	0.806369	+	0.591412i	$0.201429\pi$
$662$	−17.8669	−0.694416
$663$	0.400681	0.0155612
$664$	−21.8532	−0.848071
$665$	−2.39496	−0.0928724
$666$	−7.30965	−0.283243
$667$	−62.5727	−2.42283
$668$	−8.15972	−0.315709
$669$	−15.3678	−0.594152
$670$	20.9048	0.807624
$671$	0	0
$672$	9.87393	0.380895
$673$	12.0297	0.463712	0.231856	−	0.972750i	$-0.425520\pi$
$673$	12.0297	0.463712	0.231856	+	0.972750i	$0.425520\pi$
$674$	−40.8636	−1.57401
$675$	4.11390	0.158344
$676$	−9.31200	−0.358154
$677$	−38.5943	−1.48330	−0.741649	−	0.670788i	$-0.765956\pi$
$677$	−38.5943	−1.48330	−0.741649	+	0.670788i	$0.765956\pi$
$678$	21.8817	0.840363
$679$	−30.2460	−1.16074
$680$	−6.34129	−0.243177
$681$	28.2307	1.08180
$682$	0	0
$683$	14.2530	0.545377	0.272688	−	0.962102i	$-0.412087\pi$
$683$	14.2530	0.545377	0.272688	+	0.962102i	$0.412087\pi$
$684$	0.717181	0.0274221
$685$	−13.8283	−0.528351
$686$	−31.5669	−1.20523
$687$	5.18156	0.197689
$688$	−10.5054	−0.400516
$689$	1.49300	0.0568787
$690$	−9.45972	−0.360125
$691$	−30.4757	−1.15935	−0.579674	−	0.814848i	$-0.696820\pi$
$691$	−30.4757	−1.15935	−0.579674	+	0.814848i	$0.696820\pi$
$692$	−0.465845	−0.0177088
$693$	0	0
$694$	0.273569	0.0103845
$695$	13.2455	0.502430
$696$	−21.7037	−0.822675
$697$	−34.8572	−1.32031
$698$	49.0082	1.85499
$699$	−13.5062	−0.510852
$700$	7.50650	0.283719
$701$	−14.6836	−0.554592	−0.277296	−	0.960784i	$-0.589438\pi$
$701$	−14.6836	−0.554592	−0.277296	+	0.960784i	$0.589438\pi$
$702$	0.207323	0.00782490
$703$	4.43442	0.167247
$704$	0	0
$705$	7.79914	0.293732
$706$	26.0728	0.981263
$707$	−40.9784	−1.54115
$708$	0.807047	0.0303307
$709$	−3.30950	−0.124291	−0.0621454	−	0.998067i	$-0.519794\pi$
$709$	−3.30950	−0.124291	−0.0621454	+	0.998067i	$0.519794\pi$
$710$	1.69327	0.0635472
$711$	2.21350	0.0830128
$712$	−23.0561	−0.864064
$713$	−18.0834	−0.677228
$714$	13.3606	0.500007
$715$	0	0
$716$	−15.3172	−0.572431
$717$	−30.8408	−1.15177
$718$	48.2408	1.80033
$719$	−3.35577	−0.125149	−0.0625745	−	0.998040i	$-0.519931\pi$
$719$	−3.35577	−0.125149	−0.0625745	+	0.998040i	$0.519931\pi$
$720$	−4.63136	−0.172601
$721$	−2.03822	−0.0759072
$722$	−1.64839	−0.0613466
$723$	3.01568	0.112154
$724$	12.7475	0.473757
$725$	−42.2242	−1.56817
$726$	0	0
$727$	−23.1461	−0.858440	−0.429220	−	0.903200i	$-0.641212\pi$
$727$	−23.1461	−0.858440	−0.429220	+	0.903200i	$0.641212\pi$
$728$	−0.676656	−0.0250786
$729$	1.00000	0.0370370
$730$	21.5987	0.799403
$731$	−6.80234	−0.251594
$732$	1.50435	0.0556023
$733$	31.6217	1.16797	0.583987	−	0.811763i	$-0.301492\pi$
$733$	31.6217	1.16797	0.583987	+	0.811763i	$0.301492\pi$
$734$	−55.1531	−2.03574
$735$	0.496009	0.0182956
$736$	−23.6598	−0.872113
$737$	0	0
$738$	−18.0361	−0.663917
$739$	5.09809	0.187536	0.0937681	−	0.995594i	$-0.470109\pi$
$739$	5.09809	0.187536	0.0937681	+	0.995594i	$0.470109\pi$
$740$	2.99370	0.110051
$741$	−0.125773	−0.00462039
$742$	49.7835	1.82761
$743$	−17.4215	−0.639132	−0.319566	−	0.947564i	$-0.603537\pi$
$743$	−17.4215	−0.639132	−0.319566	+	0.947564i	$0.603537\pi$
$744$	−6.27231	−0.229954
$745$	19.5218	0.715223
$746$	29.3133	1.07324
$747$	−10.3345	−0.378121
$748$	0	0
$749$	−2.78675	−0.101826
$750$	−14.1418	−0.516387
$751$	−13.3648	−0.487689	−0.243845	−	0.969814i	$-0.578409\pi$
$751$	−13.3648	−0.487689	−0.243845	+	0.969814i	$0.578409\pi$
$752$	40.7634	1.48649
$753$	30.2264	1.10151
$754$	−2.12792	−0.0774944
$755$	12.3851	0.450742
$756$	1.82467	0.0663626
$757$	−7.86710	−0.285935	−0.142967	−	0.989727i	$-0.545664\pi$
$757$	−7.86710	−0.285935	−0.142967	+	0.989727i	$0.545664\pi$
$758$	5.91378	0.214798
$759$	0	0
$760$	1.99052	0.0722038
$761$	−23.0854	−0.836846	−0.418423	−	0.908252i	$-0.637417\pi$
$761$	−23.0854	−0.836846	−0.418423	+	0.908252i	$0.637417\pi$
$762$	23.6945	0.858361
$763$	12.0134	0.434914
$764$	14.6790	0.531067
$765$	−2.99884	−0.108423
$766$	−2.97259	−0.107404
$767$	−0.141533	−0.00511047
$768$	−15.2636	−0.550778
$769$	−19.8978	−0.717535	−0.358767	−	0.933427i	$-0.616803\pi$
$769$	−19.8978	−0.717535	−0.358767	+	0.933427i	$0.616803\pi$
$770$	0	0
$771$	2.94672	0.106124
$772$	7.95917	0.286457
$773$	49.8795	1.79404	0.897021	−	0.441988i	$-0.145727\pi$
$773$	49.8795	1.79404	0.897021	+	0.441988i	$0.145727\pi$
$774$	−3.51971	−0.126513
$775$	−12.2027	−0.438334
$776$	25.1384	0.902417
$777$	11.2822	0.404745
$778$	50.6188	1.81477
$779$	10.9416	0.392025
$780$	−0.0849100	−0.00304027
$781$	0	0
$782$	−32.0145	−1.14484
$783$	−10.2638	−0.366798
$784$	2.59247	0.0925883
$785$	−4.43930	−0.158445
$786$	−4.55463	−0.162458
$787$	2.90418	0.103523	0.0517614	−	0.998659i	$-0.483516\pi$
$787$	2.90418	0.103523	0.0517614	+	0.998659i	$0.483516\pi$
$788$	−6.83927	−0.243639
$789$	0.378241	0.0134657
$790$	−3.43464	−0.122199
$791$	−33.7736	−1.20085
$792$	0	0
$793$	−0.263820	−0.00936853
$794$	−18.0389	−0.640177
$795$	−11.1741	−0.396305
$796$	−6.53198	−0.231520
$797$	−3.85381	−0.136509	−0.0682545	−	0.997668i	$-0.521743\pi$
$797$	−3.85381	−0.136509	−0.0682545	+	0.997668i	$0.521743\pi$
$798$	−4.19387	−0.148461
$799$	26.3946	0.933773
$800$	−15.9657	−0.564473
$801$	−10.9034	−0.385252
$802$	25.8248	0.911906
$803$	0	0
$804$	9.66215	0.340758
$805$	14.6007	0.514608
$806$	−0.614965	−0.0216612
$807$	11.6733	0.410919
$808$	34.0584	1.19817
$809$	−50.9800	−1.79236	−0.896181	−	0.443689i	$-0.853670\pi$
$809$	−50.9800	−1.79236	−0.896181	+	0.443689i	$0.853670\pi$
$810$	−1.55168	−0.0545204
$811$	−8.46595	−0.297280	−0.148640	−	0.988891i	$-0.547490\pi$
$811$	−8.46595	−0.297280	−0.148640	+	0.988891i	$0.547490\pi$
$812$	−18.7280	−0.657225
$813$	0.617222	0.0216469
$814$	0	0
$815$	3.92894	0.137625
$816$	−15.6739	−0.548696
$817$	2.13525	0.0747028
$818$	−0.126150	−0.00441071
$819$	−0.319995	−0.0111815
$820$	7.38675	0.257956
$821$	−1.44966	−0.0505935	−0.0252967	−	0.999680i	$-0.508053\pi$
$821$	−1.44966	−0.0505935	−0.0252967	+	0.999680i	$0.508053\pi$
$822$	−24.2150	−0.844597
$823$	21.2941	0.742266	0.371133	−	0.928580i	$-0.378969\pi$
$823$	21.2941	0.742266	0.371133	+	0.928580i	$0.378969\pi$
$824$	1.69403	0.0590142
$825$	0	0
$826$	−4.71938	−0.164208
$827$	−5.89346	−0.204936	−0.102468	−	0.994736i	$-0.532674\pi$
$827$	−5.89346	−0.204936	−0.102468	+	0.994736i	$0.532674\pi$
$828$	−4.37225	−0.151946
$829$	19.2285	0.667832	0.333916	−	0.942603i	$-0.391630\pi$
$829$	19.2285	0.667832	0.333916	+	0.942603i	$0.391630\pi$
$830$	16.0359	0.556613
$831$	−19.8397	−0.688232
$832$	0.433008	0.0150118
$833$	1.67864	0.0581615
$834$	23.1945	0.803160
$835$	−10.7100	−0.370634
$836$	0	0
$837$	−2.96622	−0.102527
$838$	8.93282	0.308579
$839$	3.58138	0.123643	0.0618215	−	0.998087i	$-0.480309\pi$
$839$	3.58138	0.123643	0.0618215	+	0.998087i	$0.480309\pi$
$840$	5.06433	0.174736
$841$	76.3457	2.63261
$842$	27.6324	0.952274
$843$	18.3244	0.631127
$844$	−7.32451	−0.252120
$845$	−12.2224	−0.420464
$846$	13.6573	0.469546
$847$	0	0
$848$	−58.4033	−2.00558
$849$	−5.98177	−0.205294
$850$	−21.6035	−0.740993
$851$	−27.0342	−0.926721
$852$	0.782624	0.0268122
$853$	−12.7418	−0.436272	−0.218136	−	0.975918i	$-0.569998\pi$
$853$	−12.7418	−0.436272	−0.218136	+	0.975918i	$0.569998\pi$
$854$	−8.79700	−0.301027
$855$	0.941331	0.0321928
$856$	2.31616	0.0791646
$857$	11.0419	0.377186	0.188593	−	0.982055i	$-0.439607\pi$
$857$	11.0419	0.377186	0.188593	+	0.982055i	$0.439607\pi$
$858$	0	0
$859$	−15.6763	−0.534868	−0.267434	−	0.963576i	$-0.586176\pi$
$859$	−15.6763	−0.534868	−0.267434	+	0.963576i	$0.586176\pi$
$860$	1.44151	0.0491552
$861$	27.8380	0.948716
$862$	−7.95892	−0.271082
$863$	11.1263	0.378743	0.189372	−	0.981905i	$-0.439355\pi$
$863$	11.1263	0.378743	0.189372	+	0.981905i	$0.439355\pi$
$864$	−3.88092	−0.132032
$865$	−0.611441	−0.0207896
$866$	43.8329	1.48950
$867$	6.85104	0.232674
$868$	−5.41236	−0.183708
$869$	0	0
$870$	15.9261	0.539946
$871$	−1.69447	−0.0574149
$872$	−9.98470	−0.338125
$873$	11.8881	0.402352
$874$	10.0493	0.339923
$875$	21.8274	0.737900
$876$	9.98285	0.337289
$877$	−26.7468	−0.903174	−0.451587	−	0.892227i	$-0.649142\pi$
$877$	−26.7468	−0.903174	−0.451587	+	0.892227i	$0.649142\pi$
$878$	−26.0233	−0.878245
$879$	4.46485	0.150596
$880$	0	0
$881$	31.8226	1.07213	0.536065	−	0.844176i	$-0.319910\pi$
$881$	31.8226	1.07213	0.536065	+	0.844176i	$0.319910\pi$
$882$	0.868574	0.0292464
$883$	0.547415	0.0184220	0.00921099	−	0.999958i	$-0.497068\pi$
$883$	0.547415	0.0184220	0.00921099	+	0.999958i	$0.497068\pi$
$884$	−0.287361	−0.00966499
$885$	1.05928	0.0356075
$886$	39.5012	1.32707
$887$	37.3178	1.25301	0.626504	−	0.779418i	$-0.284485\pi$
$887$	37.3178	1.25301	0.626504	+	0.779418i	$0.284485\pi$
$888$	−9.37695	−0.314670
$889$	−36.5716	−1.22657
$890$	16.9185	0.567110
$891$	0	0
$892$	11.0215	0.369026
$893$	−8.28522	−0.277254
$894$	34.1851	1.14332
$895$	−20.1045	−0.672019
$896$	34.1864	1.14209
$897$	0.766770	0.0256017
$898$	−66.9539	−2.23428
$899$	30.4447	1.01539
$900$	−2.95041	−0.0983469
$901$	−37.8165	−1.25985
$902$	0	0
$903$	5.43254	0.180784
$904$	28.0703	0.933604
$905$	16.7316	0.556178
$906$	21.6879	0.720533
$907$	7.59425	0.252163	0.126082	−	0.992020i	$-0.459760\pi$
$907$	7.59425	0.252163	0.126082	+	0.992020i	$0.459760\pi$
$908$	−20.2465	−0.671905
$909$	16.1065	0.534218
$910$	0.496529	0.0164598
$911$	−18.2790	−0.605610	−0.302805	−	0.953053i	$-0.597923\pi$
$911$	−18.2790	−0.605610	−0.302805	+	0.953053i	$0.597923\pi$
$912$	4.92001	0.162918
$913$	0	0
$914$	59.2613	1.96019
$915$	1.97452	0.0652757
$916$	−3.71612	−0.122784
$917$	7.02990	0.232148
$918$	−5.25134	−0.173320
$919$	−20.6326	−0.680606	−0.340303	−	0.940316i	$-0.610530\pi$
$919$	−20.6326	−0.680606	−0.340303	+	0.940316i	$0.610530\pi$
$920$	−12.1351	−0.400083
$921$	2.31765	0.0763693
$922$	39.3012	1.29432
$923$	−0.137250	−0.00451764
$924$	0	0
$925$	−18.2428	−0.599818
$926$	7.43420	0.244303
$927$	0.801115	0.0263121
$928$	39.8330	1.30758
$929$	1.53779	0.0504534	0.0252267	−	0.999682i	$-0.491969\pi$
$929$	1.53779	0.0504534	0.0252267	+	0.999682i	$0.491969\pi$
$930$	4.60261	0.150926
$931$	−0.526924	−0.0172692
$932$	9.68639	0.317288
$933$	−3.40353	−0.111427
$934$	−8.08015	−0.264391
$935$	0	0
$936$	0.265958	0.00869311
$937$	−44.0234	−1.43818	−0.719091	−	0.694916i	$-0.755441\pi$
$937$	−44.0234	−1.43818	−0.719091	+	0.694916i	$0.755441\pi$
$938$	−56.5015	−1.84484
$939$	−17.3690	−0.566816
$940$	−5.59339	−0.182436
$941$	50.7897	1.65570	0.827848	−	0.560952i	$-0.189565\pi$
$941$	50.7897	1.65570	0.827848	+	0.560952i	$0.189565\pi$
$942$	−7.77376	−0.253283
$943$	−66.7051	−2.17222
$944$	5.53652	0.180198
$945$	2.39496	0.0779079
$946$	0	0
$947$	−43.7790	−1.42263	−0.711313	−	0.702875i	$-0.751899\pi$
$947$	−43.7790	−1.42263	−0.711313	+	0.702875i	$0.751899\pi$
$948$	−1.58748	−0.0515590
$949$	−1.75071	−0.0568304
$950$	6.78129	0.220014
$951$	13.7335	0.445340
$952$	17.1392	0.555485
$953$	0.586780	0.0190077	0.00950384	−	0.999955i	$-0.496975\pi$
$953$	0.586780	0.0190077	0.00950384	+	0.999955i	$0.496975\pi$
$954$	−19.5673	−0.633514
$955$	19.2668	0.623459
$956$	22.1184	0.715360
$957$	0	0
$958$	31.6626	1.02297
$959$	37.3750	1.20690
$960$	−3.24078	−0.104596
$961$	−22.2016	−0.716179
$962$	−0.919358	−0.0296413
$963$	1.09532	0.0352964
$964$	−2.16279	−0.0696587
$965$	10.4468	0.336293
$966$	25.5677	0.822627
$967$	24.4395	0.785923	0.392961	−	0.919555i	$-0.371451\pi$
$967$	24.4395	0.785923	0.392961	+	0.919555i	$0.371451\pi$
$968$	0	0
$969$	3.18574	0.102341
$970$	−18.4465	−0.592283
$971$	−39.3558	−1.26299	−0.631495	−	0.775380i	$-0.717558\pi$
$971$	−39.3558	−1.26299	−0.631495	+	0.775380i	$0.717558\pi$
$972$	−0.717181	−0.0230036
$973$	−35.7998	−1.14769
$974$	8.76649	0.280896
$975$	0.517418	0.0165706
$976$	10.3202	0.330340
$977$	38.0520	1.21739	0.608696	−	0.793403i	$-0.291693\pi$
$977$	38.0520	1.21739	0.608696	+	0.793403i	$0.291693\pi$
$978$	6.88007	0.220000
$979$	0	0
$980$	−0.355728	−0.0113633
$981$	−4.72183	−0.150756
$982$	−52.0263	−1.66023
$983$	−34.7561	−1.10855	−0.554274	−	0.832334i	$-0.687004\pi$
$983$	−34.7561	−1.10855	−0.554274	+	0.832334i	$0.687004\pi$
$984$	−23.1370	−0.737581
$985$	−8.97684	−0.286026
$986$	53.8987	1.71648
$987$	−21.0795	−0.670967
$988$	0.0902021	0.00286971
$989$	−13.0174	−0.413930
$990$	0	0
$991$	−23.4653	−0.745399	−0.372700	−	0.927952i	$-0.621568\pi$
$991$	−23.4653	−0.745399	−0.372700	+	0.927952i	$0.621568\pi$
$992$	11.5117	0.365495
$993$	−10.8390	−0.343965
$994$	−4.57656	−0.145160
$995$	−8.57350	−0.271798
$996$	7.41174	0.234850
$997$	7.10627	0.225058	0.112529	−	0.993648i	$-0.464105\pi$
$997$	7.10627	0.225058	0.112529	+	0.993648i	$0.464105\pi$
$998$	11.9554	0.378441
$999$	−4.43442	−0.140299

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6897.2.a.bn.1.6		20
11.2	odd	10		627.2.j.c.400.3	yes	40
11.6	odd	10		627.2.j.c.58.3	✓	40
11.10	odd	2		6897.2.a.bo.1.15		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
627.2.j.c.58.3	✓	40	11.6	odd	10
627.2.j.c.400.3	yes	40	11.2	odd	10
6897.2.a.bn.1.6		20	1.1	even	1	trivial
6897.2.a.bo.1.15		20	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 6897 = 3 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6897.a (trivial)

\(f(q)\)	\(=\)	\(q-1.64839 q^{2} -1.00000 q^{3} +0.717181 q^{4} +0.941331 q^{5} +1.64839 q^{6} -2.54422 q^{7} +2.11458 q^{8} +1.00000 q^{9} -1.55168 q^{10} -0.717181 q^{12} +0.125773 q^{13} +4.19387 q^{14} -0.941331 q^{15} -4.92001 q^{16} -3.18574 q^{17} -1.64839 q^{18} +1.00000 q^{19} +0.675104 q^{20} +2.54422 q^{21} -6.09645 q^{23} -2.11458 q^{24} -4.11390 q^{25} -0.207323 q^{26} -1.00000 q^{27} -1.82467 q^{28} +10.2638 q^{29} +1.55168 q^{30} +2.96622 q^{31} +3.88092 q^{32} +5.25134 q^{34} -2.39496 q^{35} +0.717181 q^{36} +4.43442 q^{37} -1.64839 q^{38} -0.125773 q^{39} +1.99052 q^{40} +10.9416 q^{41} -4.19387 q^{42} +2.13525 q^{43} +0.941331 q^{45} +10.0493 q^{46} -8.28522 q^{47} +4.92001 q^{48} -0.526924 q^{49} +6.78129 q^{50} +3.18574 q^{51} +0.0902021 q^{52} +11.8706 q^{53} +1.64839 q^{54} -5.37997 q^{56} -1.00000 q^{57} -16.9187 q^{58} -1.12531 q^{59} -0.675104 q^{60} -2.09759 q^{61} -4.88947 q^{62} -2.54422 q^{63} +3.44276 q^{64} +0.118394 q^{65} -13.4724 q^{67} -2.28475 q^{68} +6.09645 q^{69} +3.94782 q^{70} -1.09125 q^{71} +2.11458 q^{72} -13.9196 q^{73} -7.30965 q^{74} +4.11390 q^{75} +0.717181 q^{76} +0.207323 q^{78} +2.21350 q^{79} -4.63136 q^{80} +1.00000 q^{81} -18.0361 q^{82} -10.3345 q^{83} +1.82467 q^{84} -2.99884 q^{85} -3.51971 q^{86} -10.2638 q^{87} -10.9034 q^{89} -1.55168 q^{90} -0.319995 q^{91} -4.37225 q^{92} -2.96622 q^{93} +13.6573 q^{94} +0.941331 q^{95} -3.88092 q^{96} +11.8881 q^{97} +0.868574 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 3 q^{2} - 20 q^{3} + 21 q^{4} - 9 q^{5} + 3 q^{6} + 3 q^{7} - 6 q^{8} + 20 q^{9} - 5 q^{10} - 21 q^{12} - 9 q^{13} - 26 q^{14} + 9 q^{15} + 19 q^{16} + 7 q^{17} - 3 q^{18} + 20 q^{19} - 28 q^{20}+ \cdots - 39 q^{98}+O(q^{100}) \) 20 * q - 3 * q^2 - 20 * q^3 + 21 * q^4 - 9 * q^5 + 3 * q^6 + 3 * q^7 - 6 * q^8 + 20 * q^9 - 5 * q^10 - 21 * q^12 - 9 * q^13 - 26 * q^14 + 9 * q^15 + 19 * q^16 + 7 * q^17 - 3 * q^18 + 20 * q^19 - 28 * q^20 - 3 * q^21 - 30 * q^23 + 6 * q^24 + 31 * q^25 - 10 * q^26 - 20 * q^27 + 35 * q^28 - 15 * q^29 + 5 * q^30 - 11 * q^31 - 20 * q^32 - 5 * q^34 - 2 * q^35 + 21 * q^36 + 16 * q^37 - 3 * q^38 + 9 * q^39 - 10 * q^40 - 9 * q^41 + 26 * q^42 + 3 * q^43 - 9 * q^45 - 25 * q^46 - 57 * q^47 - 19 * q^48 + 23 * q^49 + 60 * q^50 - 7 * q^51 + 5 * q^52 - 28 * q^53 + 3 * q^54 - 62 * q^56 - 20 * q^57 - 25 * q^58 - 49 * q^59 + 28 * q^60 + 46 * q^61 + 15 * q^62 + 3 * q^63 + 40 * q^64 - 18 * q^65 - 44 * q^67 - 20 * q^68 + 30 * q^69 + 31 * q^70 - 55 * q^71 - 6 * q^72 - 19 * q^73 + 7 * q^74 - 31 * q^75 + 21 * q^76 + 10 * q^78 + 23 * q^79 - 102 * q^80 + 20 * q^81 - 60 * q^82 + 32 * q^83 - 35 * q^84 + 12 * q^85 + 31 * q^86 + 15 * q^87 - 37 * q^89 - 5 * q^90 - 12 * q^91 - 25 * q^92 + 11 * q^93 + 35 * q^94 - 9 * q^95 + 20 * q^96 - 6 * q^97 - 39 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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