LMFDB - Embedded newform 1859.4.a.g.1.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1859,4,Mod(1,1859)] 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("1859.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1859, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1859.a (trivial)

Newform invariants

comment:select newform

sage:traces = [17,0,-6,50,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$109.684550701$
Analytic rank:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 93 x^{15} - 7 x^{14} + 3449 x^{13} + 406 x^{12} - 65242 x^{11} - 7942 x^{10} + 669163 x^{9} + \cdots - 2210688 $ x^17 - 93x^15 - 7x^14 + 3449x^13 + 406x^12 - 65242x^11 - 7942x^10 + 669163x^9 + 59532x^8 - 3663297x^7 - 79027x^6 + 9967603x^5 - 984554x^4 - 12177120x^3 + 3207432x^2 + 5215872*x - 2210688
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$-4.13824$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.13824 q^{2} -5.47866 q^{3} +9.12507 q^{4} -3.23279 q^{5} -22.6720 q^{6} +3.07367 q^{7} +4.65582 q^{8} +3.01573 q^{9} -13.3781 q^{10} +11.0000 q^{11} -49.9932 q^{12} +12.7196 q^{14} +17.7114 q^{15} -53.7336 q^{16} +108.135 q^{17} +12.4798 q^{18} +92.3270 q^{19} -29.4995 q^{20} -16.8396 q^{21} +45.5207 q^{22} -110.402 q^{23} -25.5077 q^{24} -114.549 q^{25} +131.402 q^{27} +28.0475 q^{28} +7.82111 q^{29} +73.2940 q^{30} +96.9102 q^{31} -259.610 q^{32} -60.2653 q^{33} +447.489 q^{34} -9.93654 q^{35} +27.5187 q^{36} -234.183 q^{37} +382.072 q^{38} -15.0513 q^{40} +433.525 q^{41} -69.6864 q^{42} +132.932 q^{43} +100.376 q^{44} -9.74923 q^{45} -456.869 q^{46} -415.715 q^{47} +294.388 q^{48} -333.553 q^{49} -474.032 q^{50} -592.435 q^{51} +69.7025 q^{53} +543.772 q^{54} -35.5607 q^{55} +14.3105 q^{56} -505.828 q^{57} +32.3657 q^{58} +1.32853 q^{59} +161.618 q^{60} +243.415 q^{61} +401.038 q^{62} +9.26936 q^{63} -644.459 q^{64} -249.392 q^{66} +273.666 q^{67} +986.740 q^{68} +604.853 q^{69} -41.1198 q^{70} -1081.72 q^{71} +14.0407 q^{72} +99.5536 q^{73} -969.106 q^{74} +627.575 q^{75} +842.490 q^{76} +33.8104 q^{77} -1173.86 q^{79} +173.710 q^{80} -801.330 q^{81} +1794.03 q^{82} +468.226 q^{83} -153.663 q^{84} -349.578 q^{85} +550.106 q^{86} -42.8492 q^{87} +51.2140 q^{88} -1031.51 q^{89} -40.3447 q^{90} -1007.42 q^{92} -530.938 q^{93} -1720.33 q^{94} -298.474 q^{95} +1422.31 q^{96} -980.595 q^{97} -1380.32 q^{98} +33.1730 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9} + 2 q^{10} + 187 q^{11} - 127 q^{12} - 148 q^{15} + 126 q^{16} - 74 q^{17} + 90 q^{18} - 159 q^{19} - 222 q^{20} - 184 q^{21}+ \cdots + 1485 q^{99}+O(q^{100}) $ 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9 + 2 * q^10 + 187 * q^11 - 127 * q^12 - 148 * q^15 + 126 * q^16 - 74 * q^17 + 90 * q^18 - 159 * q^19 - 222 * q^20 - 184 * q^21 - 215 * q^23 + 214 * q^24 + 95 * q^25 - 192 * q^27 - 358 * q^28 - 157 * q^29 + 829 * q^30 - 394 * q^31 - 553 * q^32 - 66 * q^33 - 702 * q^34 + 58 * q^35 - 700 * q^36 + 88 * q^37 - 1318 * q^38 + 733 * q^40 - 512 * q^41 + 337 * q^42 + 927 * q^43 + 550 * q^44 - 1482 * q^45 - 1361 * q^46 - 143 * q^47 - 178 * q^48 + 1835 * q^49 - 583 * q^50 - 568 * q^51 + 106 * q^53 - 67 * q^54 - 264 * q^55 + 2059 * q^56 + 1298 * q^57 - 1690 * q^58 - 266 * q^59 + 37 * q^60 - 624 * q^61 + 643 * q^62 - 2360 * q^63 - 1589 * q^64 + 176 * q^66 - 676 * q^67 - 413 * q^68 + 764 * q^69 - 1061 * q^70 - 763 * q^71 - 1366 * q^72 - 2374 * q^73 - 1649 * q^74 + 2420 * q^75 - 2101 * q^76 - 682 * q^77 + 2164 * q^79 - 1013 * q^80 + 537 * q^81 + 3152 * q^82 + 777 * q^83 - 3381 * q^84 - 1690 * q^85 + 2894 * q^86 - 4200 * q^87 - 231 * q^88 - 1687 * q^89 - 5399 * q^90 + 5542 * q^92 - 4310 * q^93 + 1777 * q^94 + 1124 * q^95 - 3465 * q^96 - 2047 * q^97 + 1553 * q^98 + 1485 * q^99

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 $

$2$	4.13824	1.46309	0.731545	−	0.681793i	$-0.238799\pi$
$2$	4.13824	1.46309	0.731545	+	0.681793i	$0.238799\pi$
$3$	−5.47866	−1.05437	−0.527184	−	0.849751i	$-0.676752\pi$
$3$	−5.47866	−1.05437	−0.527184	+	0.849751i	$0.676752\pi$
$4$	9.12507	1.14063
$5$	−3.23279	−0.289150	−0.144575	−	0.989494i	$-0.546181\pi$
$5$	−3.23279	−0.289150	−0.144575	+	0.989494i	$0.546181\pi$
$6$	−22.6720	−1.54264
$7$	3.07367	0.165963	0.0829813	−	0.996551i	$-0.473556\pi$
$7$	3.07367	0.165963	0.0829813	+	0.996551i	$0.473556\pi$
$8$	4.65582	0.205760
$9$	3.01573	0.111694
$10$	−13.3781	−0.423052
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−49.9932	−1.20265
$13$	0	0
$13$	0	0
$14$	12.7196	0.242818
$15$	17.7114	0.304870
$16$	−53.7336	−0.839588
$17$	108.135	1.54274	0.771370	−	0.636386i	$-0.219572\pi$
$17$	108.135	1.54274	0.771370	+	0.636386i	$0.219572\pi$
$18$	12.4798	0.163418
$19$	92.3270	1.11480	0.557401	−	0.830243i	$-0.311798\pi$
$19$	92.3270	1.11480	0.557401	+	0.830243i	$0.311798\pi$
$20$	−29.4995	−0.329814
$21$	−16.8396	−0.174986
$22$	45.5207	0.441138
$23$	−110.402	−1.00088	−0.500442	−	0.865770i	$-0.666829\pi$
$23$	−110.402	−1.00088	−0.500442	+	0.865770i	$0.666829\pi$
$24$	−25.5077	−0.216947
$25$	−114.549	−0.916392
$26$	0	0
$27$	131.402	0.936603
$28$	28.0475	0.189303
$29$	7.82111	0.0500808	0.0250404	−	0.999686i	$-0.492029\pi$
$29$	7.82111	0.0500808	0.0250404	+	0.999686i	$0.492029\pi$
$30$	73.2940	0.446053
$31$	96.9102	0.561471	0.280735	−	0.959785i	$-0.409422\pi$
$31$	96.9102	0.561471	0.280735	+	0.959785i	$0.409422\pi$
$32$	−259.610	−1.43415
$33$	−60.2653	−0.317904
$34$	447.489	2.25717
$35$	−9.93654	−0.0479880
$36$	27.5187	0.127402
$37$	−234.183	−1.04053	−0.520263	−	0.854006i	$-0.674166\pi$
$37$	−234.183	−1.04053	−0.520263	+	0.854006i	$0.674166\pi$
$38$	382.072	1.63106
$39$	0	0
$40$	−15.0513	−0.0594955
$41$	433.525	1.65135	0.825673	−	0.564149i	$-0.190795\pi$
$41$	433.525	1.65135	0.825673	+	0.564149i	$0.190795\pi$
$42$	−69.6864	−0.256020
$43$	132.932	0.471441	0.235720	−	0.971821i	$-0.424255\pi$
$43$	132.932	0.471441	0.235720	+	0.971821i	$0.424255\pi$
$44$	100.376	0.343914
$45$	−9.74923	−0.0322962
$46$	−456.869	−1.46438
$47$	−415.715	−1.29018	−0.645088	−	0.764108i	$-0.723179\pi$
$47$	−415.715	−1.29018	−0.645088	+	0.764108i	$0.723179\pi$
$48$	294.388	0.885236
$49$	−333.553	−0.972456
$50$	−474.032	−1.34077
$51$	−592.435	−1.62662
$52$	0	0
$53$	69.7025	0.180648	0.0903242	−	0.995912i	$-0.471210\pi$
$53$	69.7025	0.180648	0.0903242	+	0.995912i	$0.471210\pi$
$54$	543.772	1.37033
$55$	−35.5607	−0.0871819
$56$	14.3105	0.0341485
$57$	−505.828	−1.17541
$58$	32.3657	0.0732728
$59$	1.32853	0.00293152	0.00146576	−	0.999999i	$-0.499533\pi$
$59$	1.32853	0.00293152	0.00146576	+	0.999999i	$0.499533\pi$
$60$	161.618	0.347746
$61$	243.415	0.510920	0.255460	−	0.966820i	$-0.417773\pi$
$61$	243.415	0.510920	0.255460	+	0.966820i	$0.417773\pi$
$62$	401.038	0.821482
$63$	9.26936	0.0185370
$64$	−644.459	−1.25871
$65$	0	0
$66$	−249.392	−0.465123
$67$	273.666	0.499009	0.249504	−	0.968374i	$-0.419732\pi$
$67$	273.666	0.499009	0.249504	+	0.968374i	$0.419732\pi$
$68$	986.740	1.75970
$69$	604.853	1.05530
$70$	−41.1198	−0.0702108
$71$	−1081.72	−1.80811	−0.904057	−	0.427412i	$-0.859425\pi$
$71$	−1081.72	−1.80811	−0.904057	+	0.427412i	$0.859425\pi$
$72$	14.0407	0.0229821
$73$	99.5536	0.159615	0.0798073	−	0.996810i	$-0.474569\pi$
$73$	99.5536	0.159615	0.0798073	+	0.996810i	$0.474569\pi$
$74$	−969.106	−1.52238
$75$	627.575	0.966216
$76$	842.490	1.27158
$77$	33.8104	0.0500396
$78$	0	0
$79$	−1173.86	−1.67177	−0.835887	−	0.548902i	$-0.815046\pi$
$79$	−1173.86	−1.67177	−0.835887	+	0.548902i	$0.815046\pi$
$80$	173.710	0.242767
$81$	−801.330	−1.09922
$82$	1794.03	2.41607
$83$	468.226	0.619211	0.309605	−	0.950865i	$-0.399803\pi$
$83$	468.226	0.619211	0.309605	+	0.950865i	$0.399803\pi$
$84$	−153.663	−0.199595
$85$	−349.578	−0.446083
$86$	550.106	0.689761
$87$	−42.8492	−0.0528036
$88$	51.2140	0.0620390
$89$	−1031.51	−1.22853	−0.614266	−	0.789099i	$-0.710548\pi$
$89$	−1031.51	−1.22853	−0.614266	+	0.789099i	$0.710548\pi$
$90$	−40.3447	−0.0472523
$91$	0	0
$92$	−1007.42	−1.14164
$93$	−530.938	−0.591997
$94$	−1720.33	−1.88765
$95$	−298.474	−0.322345
$96$	1422.31	1.51213
$97$	−980.595	−1.02644	−0.513218	−	0.858258i	$-0.671547\pi$
$97$	−980.595	−1.02644	−0.513218	+	0.858258i	$0.671547\pi$
$98$	−1380.32	−1.42279
$99$	33.1730	0.0336769
$100$	−1045.27	−1.04527
$101$	187.734	0.184953	0.0924764	−	0.995715i	$-0.470522\pi$
$101$	187.734	0.184953	0.0924764	+	0.995715i	$0.470522\pi$
$102$	−2451.64	−2.37989
$103$	−400.158	−0.382803	−0.191402	−	0.981512i	$-0.561303\pi$
$103$	−400.158	−0.382803	−0.191402	+	0.981512i	$0.561303\pi$
$104$	0	0
$105$	54.4389	0.0505971
$106$	288.446	0.264305
$107$	−335.665	−0.303271	−0.151635	−	0.988437i	$-0.548454\pi$
$107$	−335.665	−0.303271	−0.151635	+	0.988437i	$0.548454\pi$
$108$	1199.05	1.06832
$109$	7.36478	0.00647173	0.00323586	−	0.999995i	$-0.498970\pi$
$109$	7.36478	0.00647173	0.00323586	+	0.999995i	$0.498970\pi$
$110$	−147.159	−0.127555
$111$	1283.01	1.09710
$112$	−165.159	−0.139340
$113$	−2227.71	−1.85456	−0.927279	−	0.374372i	$-0.877858\pi$
$113$	−2227.71	−1.85456	−0.927279	+	0.374372i	$0.877858\pi$
$114$	−2093.24	−1.71974
$115$	356.905	0.289405
$116$	71.3682	0.0571239
$117$	0	0
$118$	5.49777	0.00428907
$119$	332.371	0.256037
$120$	82.4610	0.0627302
$121$	121.000	0.0909091
$122$	1007.31	0.747522
$123$	−2375.14	−1.74113
$124$	884.313	0.640432
$125$	774.412	0.554124
$126$	38.3589	0.0271213
$127$	−1126.12	−0.786825	−0.393412	−	0.919362i	$-0.628706\pi$
$127$	−1126.12	−0.786825	−0.393412	+	0.919362i	$0.628706\pi$
$128$	−590.052	−0.407451
$129$	−728.290	−0.497073
$130$	0	0
$131$	−1230.07	−0.820397	−0.410198	−	0.911996i	$-0.634541\pi$
$131$	−1230.07	−0.820397	−0.410198	+	0.911996i	$0.634541\pi$
$132$	−549.925	−0.362612
$133$	283.783	0.185016
$134$	1132.50	0.730095
$135$	−424.794	−0.270818
$136$	503.457	0.317435
$137$	727.408	0.453625	0.226813	−	0.973938i	$-0.427169\pi$
$137$	727.408	0.453625	0.226813	+	0.973938i	$0.427169\pi$
$138$	2503.03	1.54400
$139$	−1204.06	−0.734726	−0.367363	−	0.930078i	$-0.619739\pi$
$139$	−1204.06	−0.734726	−0.367363	+	0.930078i	$0.619739\pi$
$140$	−90.6716	−0.0547368
$141$	2277.56	1.36032
$142$	−4476.41	−2.64543
$143$	0	0
$144$	−162.046	−0.0937767
$145$	−25.2840	−0.0144809
$146$	411.977	0.233531
$147$	1827.42	1.02533
$148$	−2136.94	−1.18686
$149$	1031.23	0.566990	0.283495	−	0.958974i	$-0.408506\pi$
$149$	1031.23	0.566990	0.283495	+	0.958974i	$0.408506\pi$
$150$	2597.06	1.41366
$151$	255.236	0.137555	0.0687774	−	0.997632i	$-0.478090\pi$
$151$	255.236	0.137555	0.0687774	+	0.997632i	$0.478090\pi$
$152$	429.858	0.229382
$153$	326.106	0.172314
$154$	139.916	0.0732125
$155$	−313.291	−0.162349
$156$	0	0
$157$	−1516.26	−0.770770	−0.385385	−	0.922756i	$-0.625931\pi$
$157$	−1516.26	−0.770770	−0.385385	+	0.922756i	$0.625931\pi$
$158$	−4857.74	−2.44596
$159$	−381.876	−0.190470
$160$	839.264	0.414685
$161$	−339.338	−0.166109
$162$	−3316.10	−1.60826
$163$	2615.63	1.25689	0.628443	−	0.777856i	$-0.283693\pi$
$163$	2615.63	1.25689	0.628443	+	0.777856i	$0.283693\pi$
$164$	3955.95	1.88358
$165$	194.825	0.0919219
$166$	1937.63	0.905961
$167$	1119.67	0.518820	0.259410	−	0.965767i	$-0.416472\pi$
$167$	1119.67	0.518820	0.259410	+	0.965767i	$0.416472\pi$
$168$	−78.4022	−0.0360051
$169$	0	0
$170$	−1446.64	−0.652660
$171$	278.433	0.124516
$172$	1213.02	0.537742
$173$	−3927.62	−1.72608	−0.863039	−	0.505138i	$-0.831442\pi$
$173$	−3927.62	−1.72608	−0.863039	+	0.505138i	$0.831442\pi$
$174$	−177.321	−0.0772565
$175$	−352.086	−0.152087
$176$	−591.070	−0.253145
$177$	−7.27855	−0.00309090
$178$	−4268.62	−1.79745
$179$	−3795.33	−1.58478	−0.792392	−	0.610012i	$-0.791164\pi$
$179$	−3795.33	−1.58478	−0.792392	+	0.610012i	$0.791164\pi$
$180$	−88.9624	−0.0368381
$181$	3397.19	1.39509	0.697545	−	0.716541i	$-0.254276\pi$
$181$	3397.19	1.39509	0.697545	+	0.716541i	$0.254276\pi$
$182$	0	0
$183$	−1333.59	−0.538698
$184$	−514.010	−0.205942
$185$	757.065	0.300868
$186$	−2197.15	−0.866145
$187$	1189.49	0.465154
$188$	−3793.43	−1.47162
$189$	403.885	0.155441
$190$	−1235.16	−0.471620
$191$	3666.36	1.38895	0.694473	−	0.719519i	$-0.255638\pi$
$191$	3666.36	1.38895	0.694473	+	0.719519i	$0.255638\pi$
$192$	3530.77	1.32714
$193$	−3787.38	−1.41255	−0.706274	−	0.707939i	$-0.749625\pi$
$193$	−3787.38	−1.41255	−0.706274	+	0.707939i	$0.749625\pi$
$194$	−4057.94	−1.50177
$195$	0	0
$196$	−3043.69	−1.10922
$197$	−1094.19	−0.395724	−0.197862	−	0.980230i	$-0.563400\pi$
$197$	−1094.19	−0.395724	−0.197862	+	0.980230i	$0.563400\pi$
$198$	137.278	0.0492724
$199$	−2686.39	−0.956950	−0.478475	−	0.878101i	$-0.658810\pi$
$199$	−2686.39	−0.956950	−0.478475	+	0.878101i	$0.658810\pi$
$200$	−533.320	−0.188557
$201$	−1499.32	−0.526139
$202$	776.889	0.270603
$203$	24.0395	0.00831154
$204$	−5406.01	−1.85538
$205$	−1401.50	−0.477486
$206$	−1655.95	−0.560076
$207$	−332.941	−0.111792
$208$	0	0
$209$	1015.60	0.336126
$210$	225.282	0.0740281
$211$	−652.196	−0.212792	−0.106396	−	0.994324i	$-0.533931\pi$
$211$	−652.196	−0.212792	−0.106396	+	0.994324i	$0.533931\pi$
$212$	636.040	0.206054
$213$	5926.36	1.90642
$214$	−1389.06	−0.443712
$215$	−429.742	−0.136317
$216$	611.783	0.192716
$217$	297.870	0.0931831
$218$	30.4773	0.00946872
$219$	−545.421	−0.168293
$220$	−324.494	−0.0994427
$221$	0	0
$222$	5309.40	1.60515
$223$	1279.96	0.384359	0.192180	−	0.981360i	$-0.438444\pi$
$223$	1279.96	0.384359	0.192180	+	0.981360i	$0.438444\pi$
$224$	−797.954	−0.238016
$225$	−345.449	−0.102355
$226$	−9218.79	−2.71339
$227$	−767.048	−0.224276	−0.112138	−	0.993693i	$-0.535770\pi$
$227$	−767.048	−0.224276	−0.112138	+	0.993693i	$0.535770\pi$
$228$	−4615.72	−1.34072
$229$	1294.52	0.373555	0.186778	−	0.982402i	$-0.440196\pi$
$229$	1294.52	0.373555	0.186778	+	0.982402i	$0.440196\pi$
$230$	1476.96	0.423426
$231$	−185.236	−0.0527602
$232$	36.4137	0.0103046
$233$	6247.63	1.75663	0.878317	−	0.478079i	$-0.158667\pi$
$233$	6247.63	1.75663	0.878317	+	0.478079i	$0.158667\pi$
$234$	0	0
$235$	1343.92	0.373054
$236$	12.1229	0.00334379
$237$	6431.21	1.76267
$238$	1375.43	0.374606
$239$	−5367.13	−1.45260	−0.726299	−	0.687379i	$-0.758761\pi$
$239$	−5367.13	−1.45260	−0.726299	+	0.687379i	$0.758761\pi$
$240$	−951.697	−0.255966
$241$	327.766	0.0876070	0.0438035	−	0.999040i	$-0.486052\pi$
$241$	327.766	0.0876070	0.0438035	+	0.999040i	$0.486052\pi$
$242$	500.728	0.133008
$243$	842.370	0.222379
$244$	2221.18	0.582772
$245$	1078.31	0.281186
$246$	−9828.89	−2.54743
$247$	0	0
$248$	451.197	0.115528
$249$	−2565.25	−0.652876
$250$	3204.71	0.810734
$251$	4172.03	1.04915	0.524575	−	0.851364i	$-0.324224\pi$
$251$	4172.03	1.04915	0.524575	+	0.851364i	$0.324224\pi$
$252$	84.5835	0.0211439
$253$	−1214.42	−0.301778
$254$	−4660.15	−1.15120
$255$	1915.22	0.470336
$256$	2713.89	0.662571
$257$	−484.450	−0.117584	−0.0587921	−	0.998270i	$-0.518725\pi$
$257$	−484.450	−0.117584	−0.0587921	+	0.998270i	$0.518725\pi$
$258$	−3013.84	−0.727262
$259$	−719.801	−0.172688
$260$	0	0
$261$	23.5863	0.00559371
$262$	−5090.34	−1.20031
$263$	−7426.95	−1.74131	−0.870656	−	0.491892i	$-0.836305\pi$
$263$	−7426.95	−1.74131	−0.870656	+	0.491892i	$0.836305\pi$
$264$	−280.584	−0.0654120
$265$	−225.334	−0.0522345
$266$	1174.36	0.270695
$267$	5651.27	1.29533
$268$	2497.22	0.569186
$269$	−7383.59	−1.67355	−0.836776	−	0.547545i	$-0.815562\pi$
$269$	−7383.59	−1.67355	−0.836776	+	0.547545i	$0.815562\pi$
$270$	−1757.90	−0.396232
$271$	−3292.47	−0.738019	−0.369010	−	0.929426i	$-0.620303\pi$
$271$	−3292.47	−0.738019	−0.369010	+	0.929426i	$0.620303\pi$
$272$	−5810.49	−1.29527
$273$	0	0
$274$	3010.19	0.663695
$275$	−1260.04	−0.276303
$276$	5519.33	1.20371
$277$	3111.37	0.674889	0.337445	−	0.941345i	$-0.390437\pi$
$277$	3111.37	0.674889	0.337445	+	0.941345i	$0.390437\pi$
$278$	−4982.69	−1.07497
$279$	292.255	0.0627127
$280$	−46.2627	−0.00987403
$281$	−7334.55	−1.55709	−0.778545	−	0.627589i	$-0.784042\pi$
$281$	−7334.55	−1.55709	−0.778545	+	0.627589i	$0.784042\pi$
$282$	9425.12	1.99027
$283$	−2665.32	−0.559848	−0.279924	−	0.960022i	$-0.590309\pi$
$283$	−2665.32	−0.559848	−0.279924	+	0.960022i	$0.590309\pi$
$284$	−9870.74	−2.06240
$285$	1635.24	0.339871
$286$	0	0
$287$	1332.51	0.274062
$288$	−782.912	−0.160186
$289$	6780.18	1.38005
$290$	−104.631	−0.0211868
$291$	5372.35	1.08224
$292$	908.434	0.182062
$293$	1182.67	0.235810	0.117905	−	0.993025i	$-0.462382\pi$
$293$	1182.67	0.235810	0.117905	+	0.993025i	$0.462382\pi$
$294$	7562.32	1.50015
$295$	−4.29485	−0.000847647 0
$296$	−1090.31	−0.214099
$297$	1445.42	0.282396
$298$	4267.48	0.829558
$299$	0	0
$300$	5726.67	1.10210
$301$	408.590	0.0782416
$302$	1056.23	0.201255
$303$	−1028.53	−0.195008
$304$	−4961.06	−0.935975
$305$	−786.910	−0.147732
$306$	1349.51	0.252112
$307$	5375.34	0.999306	0.499653	−	0.866226i	$-0.333461\pi$
$307$	5375.34	0.999306	0.499653	+	0.866226i	$0.333461\pi$
$308$	308.522	0.0570769
$309$	2192.33	0.403616
$310$	−1296.47	−0.237531
$311$	−1510.90	−0.275483	−0.137741	−	0.990468i	$-0.543984\pi$
$311$	−1510.90	−0.275483	−0.137741	+	0.990468i	$0.543984\pi$
$312$	0	0
$313$	9251.65	1.67072	0.835358	−	0.549706i	$-0.185260\pi$
$313$	9251.65	1.67072	0.835358	+	0.549706i	$0.185260\pi$
$314$	−6274.67	−1.12771
$315$	−29.9659	−0.00535996
$316$	−10711.6	−1.90688
$317$	−333.065	−0.0590120	−0.0295060	−	0.999565i	$-0.509393\pi$
$317$	−333.065	−0.0590120	−0.0295060	+	0.999565i	$0.509393\pi$
$318$	−1580.30	−0.278675
$319$	86.0322	0.0150999
$320$	2083.40	0.363955
$321$	1838.99	0.319759
$322$	−1404.26	−0.243033
$323$	9983.78	1.71985
$324$	−7312.19	−1.25381
$325$	0	0
$326$	10824.1	1.83894
$327$	−40.3492	−0.00682359
$328$	2018.41	0.339781
$329$	−1277.77	−0.214121
$330$	806.234	0.134490
$331$	−1866.39	−0.309927	−0.154964	−	0.987920i	$-0.549526\pi$
$331$	−1866.39	−0.309927	−0.154964	+	0.987920i	$0.549526\pi$
$332$	4272.60	0.706293
$333$	−706.232	−0.116220
$334$	4633.48	0.759080
$335$	−884.704	−0.144288
$336$	904.853	0.146916
$337$	8318.96	1.34470	0.672348	−	0.740235i	$-0.265286\pi$
$337$	8318.96	1.34470	0.672348	+	0.740235i	$0.265286\pi$
$338$	0	0
$339$	12204.8	1.95539
$340$	−3189.92	−0.508818
$341$	1066.01	0.169290
$342$	1152.22	0.182179
$343$	−2079.50	−0.327354
$344$	618.908	0.0970038
$345$	−1955.36	−0.305140
$346$	−16253.4	−2.52541
$347$	−2059.59	−0.318630	−0.159315	−	0.987228i	$-0.550929\pi$
$347$	−2059.59	−0.318630	−0.159315	+	0.987228i	$0.550929\pi$
$348$	−391.002	−0.0602296
$349$	1417.89	0.217472	0.108736	−	0.994071i	$-0.465320\pi$
$349$	1417.89	0.217472	0.108736	+	0.994071i	$0.465320\pi$
$350$	−1457.02	−0.222517
$351$	0	0
$352$	−2855.71	−0.432414
$353$	−4950.04	−0.746357	−0.373178	−	0.927760i	$-0.621732\pi$
$353$	−4950.04	−0.746357	−0.373178	+	0.927760i	$0.621732\pi$
$354$	−30.1204	−0.00452226
$355$	3496.96	0.522816
$356$	−9412.56	−1.40131
$357$	−1820.95	−0.269958
$358$	−15706.0	−2.31868
$359$	−344.471	−0.0506420	−0.0253210	−	0.999679i	$-0.508061\pi$
$359$	−344.471	−0.0506420	−0.0253210	+	0.999679i	$0.508061\pi$
$360$	−45.3907	−0.00664527
$361$	1665.27	0.242786
$362$	14058.4	2.04114
$363$	−662.918	−0.0958517
$364$	0	0
$365$	−321.836	−0.0461525
$366$	−5518.72	−0.788164
$367$	−3595.14	−0.511348	−0.255674	−	0.966763i	$-0.582297\pi$
$367$	−3595.14	−0.511348	−0.255674	+	0.966763i	$0.582297\pi$
$368$	5932.28	0.840330
$369$	1307.39	0.184445
$370$	3132.92	0.440196
$371$	214.242	0.0299809
$372$	−4844.85	−0.675252
$373$	6206.27	0.861525	0.430762	−	0.902465i	$-0.358245\pi$
$373$	6206.27	0.861525	0.430762	+	0.902465i	$0.358245\pi$
$374$	4922.38	0.680562
$375$	−4242.74	−0.584251
$376$	−1935.50	−0.265467
$377$	0	0
$378$	1671.38	0.227424
$379$	−10764.9	−1.45899	−0.729493	−	0.683988i	$-0.760244\pi$
$379$	−10764.9	−1.45899	−0.729493	+	0.683988i	$0.760244\pi$
$380$	−2723.60	−0.367678
$381$	6169.62	0.829604
$382$	15172.3	2.03215
$383$	13739.1	1.83298	0.916492	−	0.400053i	$-0.131008\pi$
$383$	13739.1	1.83298	0.916492	+	0.400053i	$0.131008\pi$
$384$	3232.69	0.429603
$385$	−109.302	−0.0144689
$386$	−15673.1	−2.06669
$387$	400.887	0.0526570
$388$	−8948.00	−1.17079
$389$	−10629.5	−1.38544	−0.692721	−	0.721206i	$-0.743588\pi$
$389$	−10629.5	−1.38544	−0.692721	+	0.721206i	$0.743588\pi$
$390$	0	0
$391$	−11938.3	−1.54410
$392$	−1552.96	−0.200093
$393$	6739.15	0.865001
$394$	−4528.02	−0.578981
$395$	3794.86	0.483393
$396$	302.706	0.0384130
$397$	−14762.8	−1.86631	−0.933155	−	0.359475i	$-0.882956\pi$
$397$	−14762.8	−1.86631	−0.933155	+	0.359475i	$0.882956\pi$
$398$	−11116.9	−1.40010
$399$	−1554.75	−0.195075
$400$	6155.14	0.769392
$401$	5159.90	0.642576	0.321288	−	0.946981i	$-0.395884\pi$
$401$	5159.90	0.642576	0.321288	+	0.946981i	$0.395884\pi$
$402$	−6204.56	−0.769789
$403$	0	0
$404$	1713.09	0.210963
$405$	2590.53	0.317839
$406$	99.4814	0.0121605
$407$	−2576.01	−0.313730
$408$	−2758.27	−0.334693
$409$	−11113.5	−1.34359	−0.671795	−	0.740737i	$-0.734476\pi$
$409$	−11113.5	−1.34359	−0.671795	+	0.740737i	$0.734476\pi$
$410$	−5799.73	−0.698606
$411$	−3985.22	−0.478288
$412$	−3651.47	−0.436638
$413$	4.08345	0.000486522 0
$414$	−1377.79	−0.163562
$415$	−1513.68	−0.179045
$416$	0	0
$417$	6596.63	0.774673
$418$	4202.79	0.491782
$419$	9745.59	1.13628	0.568142	−	0.822930i	$-0.307662\pi$
$419$	9745.59	1.13628	0.568142	+	0.822930i	$0.307662\pi$
$420$	496.759	0.0577128
$421$	−7072.29	−0.818722	−0.409361	−	0.912372i	$-0.634248\pi$
$421$	−7072.29	−0.818722	−0.409361	+	0.912372i	$0.634248\pi$
$422$	−2698.95	−0.311334
$423$	−1253.68	−0.144105
$424$	324.522	0.0371703
$425$	−12386.8	−1.41376
$426$	24524.7	2.78926
$427$	748.177	0.0847935
$428$	−3062.97	−0.345921
$429$	0	0
$430$	−1778.38	−0.199444
$431$	−8471.03	−0.946717	−0.473358	−	0.880870i	$-0.656958\pi$
$431$	−8471.03	−0.946717	−0.473358	+	0.880870i	$0.656958\pi$
$432$	−7060.69	−0.786360
$433$	−8332.03	−0.924739	−0.462370	−	0.886687i	$-0.653001\pi$
$433$	−8332.03	−0.924739	−0.462370	+	0.886687i	$0.653001\pi$
$434$	1232.66	0.136335
$435$	138.523	0.0152682
$436$	67.2042	0.00738187
$437$	−10193.0	−1.11579
$438$	−2257.08	−0.246228
$439$	16042.2	1.74408	0.872041	−	0.489433i	$-0.162796\pi$
$439$	16042.2	1.74408	0.872041	+	0.489433i	$0.162796\pi$
$440$	−165.564	−0.0179386
$441$	−1005.90	−0.108617
$442$	0	0
$443$	498.063	0.0534169	0.0267085	−	0.999643i	$-0.491497\pi$
$443$	498.063	0.0534169	0.0267085	+	0.999643i	$0.491497\pi$
$444$	11707.5	1.25139
$445$	3334.64	0.355230
$446$	5296.77	0.562352
$447$	−5649.75	−0.597817
$448$	−1980.85	−0.208899
$449$	9530.13	1.00168	0.500840	−	0.865540i	$-0.333024\pi$
$449$	9530.13	1.00168	0.500840	+	0.865540i	$0.333024\pi$
$450$	−1429.55	−0.149755
$451$	4768.77	0.497900
$452$	−20328.0	−2.11537
$453$	−1398.35	−0.145034
$454$	−3174.23	−0.328137
$455$	0	0
$456$	−2355.05	−0.241853
$457$	−6589.12	−0.674455	−0.337227	−	0.941423i	$-0.609489\pi$
$457$	−6589.12	−0.674455	−0.337227	+	0.941423i	$0.609489\pi$
$458$	5357.03	0.546545
$459$	14209.1	1.44493
$460$	3256.79	0.330105
$461$	−10954.4	−1.10671	−0.553357	−	0.832944i	$-0.686654\pi$
$461$	−10954.4	−1.10671	−0.553357	+	0.832944i	$0.686654\pi$
$462$	−766.550	−0.0771929
$463$	−12996.6	−1.30454	−0.652270	−	0.757987i	$-0.726183\pi$
$463$	−12996.6	−1.30454	−0.652270	+	0.757987i	$0.726183\pi$
$464$	−420.257	−0.0420473
$465$	1716.41	0.171176
$466$	25854.2	2.57011
$467$	15442.2	1.53015	0.765073	−	0.643943i	$-0.222703\pi$
$467$	15442.2	1.53015	0.765073	+	0.643943i	$0.222703\pi$
$468$	0	0
$469$	841.158	0.0828168
$470$	5561.48	0.545812
$471$	8307.09	0.812676
$472$	6.18538	0.000603189 0
$473$	1462.25	0.142145
$474$	26613.9	2.57894
$475$	−10576.0	−1.02160
$476$	3032.91	0.292045
$477$	210.204	0.0201773
$478$	−22210.5	−2.12528
$479$	14879.9	1.41937	0.709687	−	0.704517i	$-0.248836\pi$
$479$	14879.9	1.41937	0.709687	+	0.704517i	$0.248836\pi$
$480$	−4598.04	−0.437231
$481$	0	0
$482$	1356.38	0.128177
$483$	1859.12	0.175140
$484$	1104.13	0.103694
$485$	3170.06	0.296794
$486$	3485.93	0.325360
$487$	11602.3	1.07957	0.539784	−	0.841803i	$-0.318506\pi$
$487$	11602.3	1.07957	0.539784	+	0.841803i	$0.318506\pi$
$488$	1133.30	0.105127
$489$	−14330.2	−1.32522
$490$	4462.29	0.411400
$491$	7050.00	0.647988	0.323994	−	0.946059i	$-0.394974\pi$
$491$	7050.00	0.647988	0.323994	+	0.946059i	$0.394974\pi$
$492$	−21673.3	−1.98599
$493$	845.736	0.0772617
$494$	0	0
$495$	−107.241	−0.00973767
$496$	−5207.34	−0.471404
$497$	−3324.84	−0.300079
$498$	−10615.6	−0.955217
$499$	18183.7	1.63129	0.815646	−	0.578552i	$-0.196382\pi$
$499$	18183.7	1.63129	0.815646	+	0.578552i	$0.196382\pi$
$500$	7066.57	0.632053
$501$	−6134.31	−0.547027
$502$	17264.9	1.53500
$503$	14372.9	1.27407	0.637034	−	0.770836i	$-0.280161\pi$
$503$	14372.9	1.27407	0.637034	+	0.770836i	$0.280161\pi$
$504$	43.1565	0.00381417
$505$	−606.905	−0.0534790
$506$	−5025.56	−0.441528
$507$	0	0
$508$	−10275.9	−0.897479
$509$	−1165.95	−0.101532	−0.0507661	−	0.998711i	$-0.516166\pi$
$509$	−1165.95	−0.101532	−0.0507661	+	0.998711i	$0.516166\pi$
$510$	7925.65	0.688144
$511$	305.995	0.0264901
$512$	15951.2	1.37685
$513$	12131.9	1.04413
$514$	−2004.77	−0.172036
$515$	1293.63	0.110687
$516$	−6645.70	−0.566978
$517$	−4572.87	−0.389003
$518$	−2978.71	−0.252659
$519$	21518.1	1.81992
$520$	0	0
$521$	2969.89	0.249737	0.124869	−	0.992173i	$-0.460149\pi$
$521$	2969.89	0.249737	0.124869	+	0.992173i	$0.460149\pi$
$522$	97.6061	0.00818410
$523$	−4360.27	−0.364553	−0.182277	−	0.983247i	$-0.558347\pi$
$523$	−4360.27	−0.364553	−0.182277	+	0.983247i	$0.558347\pi$
$524$	−11224.5	−0.935772
$525$	1928.96	0.160356
$526$	−30734.5	−2.54770
$527$	10479.4	0.866204
$528$	3238.27	0.266909
$529$	21.5082	0.00176775
$530$	−932.485	−0.0764237
$531$	4.00647	0.000327432 0
$532$	2589.54	0.211035
$533$	0	0
$534$	23386.3	1.89518
$535$	1085.14	0.0876906
$536$	1274.14	0.102676
$537$	20793.3	1.67095
$538$	−30555.1	−2.44856
$539$	−3669.08	−0.293207
$540$	−3876.28	−0.308905
$541$	17242.0	1.37023	0.685113	−	0.728437i	$-0.259753\pi$
$541$	17242.0	1.37023	0.685113	+	0.728437i	$0.259753\pi$
$542$	−13625.0	−1.07979
$543$	−18612.1	−1.47094
$544$	−28072.9	−2.21253
$545$	−23.8088	−0.00187130
$546$	0	0
$547$	−2415.39	−0.188802	−0.0944008	−	0.995534i	$-0.530094\pi$
$547$	−2415.39	−0.188802	−0.0944008	+	0.995534i	$0.530094\pi$
$548$	6637.65	0.517420
$549$	734.074	0.0570665
$550$	−5214.35	−0.404256
$551$	722.099	0.0558302
$552$	2816.09	0.217139
$553$	−3608.07	−0.277452
$554$	12875.6	0.987424
$555$	−4147.70	−0.317225
$556$	−10987.1	−0.838054
$557$	20942.6	1.59312	0.796559	−	0.604560i	$-0.206651\pi$
$557$	20942.6	1.59312	0.796559	+	0.604560i	$0.206651\pi$
$558$	1209.42	0.0917544
$559$	0	0
$560$	533.926	0.0402902
$561$	−6516.79	−0.490444
$562$	−30352.1	−2.27816
$563$	−6176.56	−0.462364	−0.231182	−	0.972910i	$-0.574259\pi$
$563$	−6176.56	−0.462364	−0.231182	+	0.972910i	$0.574259\pi$
$564$	20782.9	1.55163
$565$	7201.71	0.536245
$566$	−11029.8	−0.819109
$567$	−2463.02	−0.182429
$568$	−5036.28	−0.372038
$569$	4914.15	0.362059	0.181030	−	0.983478i	$-0.442057\pi$
$569$	4914.15	0.362059	0.181030	+	0.983478i	$0.442057\pi$
$570$	6767.01	0.497261
$571$	13116.8	0.961332	0.480666	−	0.876904i	$-0.340395\pi$
$571$	13116.8	0.961332	0.480666	+	0.876904i	$0.340395\pi$
$572$	0	0
$573$	−20086.8	−1.46446
$574$	5514.26	0.400977
$575$	12646.4	0.917202
$576$	−1943.51	−0.140590
$577$	1409.16	0.101671	0.0508353	−	0.998707i	$-0.483812\pi$
$577$	1409.16	0.101671	0.0508353	+	0.998707i	$0.483812\pi$
$578$	28058.1	2.01914
$579$	20749.8	1.48935
$580$	−230.719	−0.0165174
$581$	1439.17	0.102766
$582$	22232.1	1.58342
$583$	766.727	0.0544676
$584$	463.504	0.0328423
$585$	0	0
$586$	4894.18	0.345011
$587$	−12830.0	−0.902133	−0.451066	−	0.892490i	$-0.648956\pi$
$587$	−12830.0	−0.902133	−0.451066	+	0.892490i	$0.648956\pi$
$588$	16675.4	1.16952
$589$	8947.42	0.625929
$590$	−17.7731	−0.00124018
$591$	5994.69	0.417239
$592$	12583.5	0.873612
$593$	14238.3	0.986000	0.493000	−	0.870029i	$-0.335900\pi$
$593$	14238.3	0.986000	0.493000	+	0.870029i	$0.335900\pi$
$594$	5981.50	0.413171
$595$	−1074.49	−0.0740331
$596$	9410.04	0.646728
$597$	14717.8	1.00898
$598$	0	0
$599$	−20160.7	−1.37520	−0.687599	−	0.726090i	$-0.741335\pi$
$599$	−20160.7	−1.37520	−0.687599	+	0.726090i	$0.741335\pi$
$600$	2921.88	0.198809
$601$	6735.55	0.457153	0.228576	−	0.973526i	$-0.426593\pi$
$601$	6735.55	0.457153	0.228576	+	0.973526i	$0.426593\pi$
$602$	1690.84	0.114474
$603$	825.302	0.0557361
$604$	2329.04	0.156900
$605$	−391.168	−0.0262863
$606$	−4256.31	−0.285315
$607$	−5795.95	−0.387562	−0.193781	−	0.981045i	$-0.562075\pi$
$607$	−5795.95	−0.387562	−0.193781	+	0.981045i	$0.562075\pi$
$608$	−23969.0	−1.59880
$609$	−131.704	−0.00876343
$610$	−3256.43	−0.216146
$611$	0	0
$612$	2975.74	0.196548
$613$	−9402.80	−0.619536	−0.309768	−	0.950812i	$-0.600251\pi$
$613$	−9402.80	−0.619536	−0.309768	+	0.950812i	$0.600251\pi$
$614$	22244.5	1.46208
$615$	7678.32	0.503447
$616$	157.415	0.0102962
$617$	10512.7	0.685943	0.342972	−	0.939346i	$-0.388567\pi$
$617$	10512.7	0.685943	0.342972	+	0.939346i	$0.388567\pi$
$618$	9072.40	0.590527
$619$	−18242.8	−1.18455	−0.592277	−	0.805735i	$-0.701771\pi$
$619$	−18242.8	−1.18455	−0.592277	+	0.805735i	$0.701771\pi$
$620$	−2858.80	−0.185181
$621$	−14507.0	−0.937430
$622$	−6252.46	−0.403056
$623$	−3170.51	−0.203890
$624$	0	0
$625$	11815.1	0.756168
$626$	38285.6	2.44441
$627$	−5564.11	−0.354401
$628$	−13836.0	−0.879167
$629$	−25323.4	−1.60526
$630$	−124.006	−0.00784211
$631$	−110.633	−0.00697979	−0.00348989	−	0.999994i	$-0.501111\pi$
$631$	−110.633	−0.00697979	−0.00348989	+	0.999994i	$0.501111\pi$
$632$	−5465.30	−0.343984
$633$	3573.16	0.224361
$634$	−1378.31	−0.0863400
$635$	3640.50	0.227510
$636$	−3484.65	−0.217257
$637$	0	0
$638$	356.022	0.0220926
$639$	−3262.16	−0.201955
$640$	1907.52	0.117814
$641$	21133.5	1.30222	0.651110	−	0.758984i	$-0.274304\pi$
$641$	21133.5	1.30222	0.651110	+	0.758984i	$0.274304\pi$
$642$	7610.21	0.467837
$643$	6375.60	0.391025	0.195513	−	0.980701i	$-0.437363\pi$
$643$	6375.60	0.391025	0.195513	+	0.980701i	$0.437363\pi$
$644$	−3096.48	−0.189470
$645$	2354.41	0.143728
$646$	41315.3	2.51630
$647$	16370.2	0.994715	0.497357	−	0.867546i	$-0.334304\pi$
$647$	16370.2	0.994715	0.497357	+	0.867546i	$0.334304\pi$
$648$	−3730.85	−0.226175
$649$	14.6138	0.000883885 0
$650$	0	0
$651$	−1631.93	−0.0982494
$652$	23867.9	1.43365
$653$	−8137.20	−0.487647	−0.243823	−	0.969820i	$-0.578402\pi$
$653$	−8137.20	−0.487647	−0.243823	+	0.969820i	$0.578402\pi$
$654$	−166.975	−0.00998353
$655$	3976.57	0.237218
$656$	−23294.9	−1.38645
$657$	300.227	0.0178279
$658$	−5287.73	−0.313279
$659$	−1457.24	−0.0861398	−0.0430699	−	0.999072i	$-0.513714\pi$
$659$	−1457.24	−0.0861398	−0.0430699	+	0.999072i	$0.513714\pi$
$660$	1777.79	0.104849
$661$	−2974.15	−0.175009	−0.0875046	−	0.996164i	$-0.527889\pi$
$661$	−2974.15	−0.175009	−0.0875046	+	0.996164i	$0.527889\pi$
$662$	−7723.56	−0.453451
$663$	0	0
$664$	2179.98	0.127409
$665$	−917.410	−0.0534972
$666$	−2922.56	−0.170040
$667$	−863.463	−0.0501251
$668$	10217.1	0.591783
$669$	−7012.44	−0.405256
$670$	−3661.12	−0.211107
$671$	2677.57	0.154048
$672$	4371.72	0.250957
$673$	18003.1	1.03115	0.515577	−	0.856843i	$-0.327578\pi$
$673$	18003.1	1.03115	0.515577	+	0.856843i	$0.327578\pi$
$674$	34425.9	1.96741
$675$	−15051.9	−0.858295
$676$	0	0
$677$	−7063.81	−0.401011	−0.200505	−	0.979693i	$-0.564258\pi$
$677$	−7063.81	−0.401011	−0.200505	+	0.979693i	$0.564258\pi$
$678$	50506.7	2.86091
$679$	−3014.03	−0.170350
$680$	−1627.57	−0.0917861
$681$	4202.39	0.236470
$682$	4411.42	0.247686
$683$	−6111.70	−0.342398	−0.171199	−	0.985236i	$-0.554764\pi$
$683$	−6111.70	−0.342398	−0.171199	+	0.985236i	$0.554764\pi$
$684$	2540.72	0.142028
$685$	−2351.56	−0.131166
$686$	−8605.48	−0.478949
$687$	−7092.23	−0.393865
$688$	−7142.93	−0.395816
$689$	0	0
$690$	−8091.77	−0.446447
$691$	28998.0	1.59644	0.798218	−	0.602369i	$-0.205777\pi$
$691$	28998.0	1.59644	0.798218	+	0.602369i	$0.205777\pi$
$692$	−35839.8	−1.96882
$693$	101.963	0.00558911
$694$	−8523.09	−0.466184
$695$	3892.47	0.212446
$696$	−199.498	−0.0108649
$697$	46879.2	2.54760
$698$	5867.57	0.318182
$699$	−34228.6	−1.85214
$700$	−3212.81	−0.173475
$701$	22908.1	1.23428	0.617139	−	0.786854i	$-0.288292\pi$
$701$	22908.1	1.23428	0.617139	+	0.786854i	$0.288292\pi$
$702$	0	0
$703$	−21621.4	−1.15998
$704$	−7089.05	−0.379515
$705$	−7362.89	−0.393337
$706$	−20484.5	−1.09199
$707$	577.032	0.0306952
$708$	−66.4172	−0.00352558
$709$	−14733.6	−0.780440	−0.390220	−	0.920722i	$-0.627601\pi$
$709$	−14733.6	−0.780440	−0.390220	+	0.920722i	$0.627601\pi$
$710$	14471.3	0.764927
$711$	−3540.06	−0.186726
$712$	−4802.50	−0.252783
$713$	−10699.0	−0.561967
$714$	−7535.54	−0.394973
$715$	0	0
$716$	−34632.7	−1.80766
$717$	29404.7	1.53157
$718$	−1425.50	−0.0740938
$719$	13173.8	0.683308	0.341654	−	0.939826i	$-0.389013\pi$
$719$	13173.8	0.683308	0.341654	+	0.939826i	$0.389013\pi$
$720$	523.861	0.0271155
$721$	−1229.95	−0.0635310
$722$	6891.28	0.355217
$723$	−1795.72	−0.0923701
$724$	30999.6	1.59129
$725$	−895.901	−0.0458937
$726$	−2743.32	−0.140240
$727$	36109.7	1.84214	0.921068	−	0.389401i	$-0.127318\pi$
$727$	36109.7	1.84214	0.921068	+	0.389401i	$0.127318\pi$
$728$	0	0
$729$	17020.9	0.864749
$730$	−1331.84	−0.0675253
$731$	14374.6	0.727311
$732$	−12169.1	−0.614457
$733$	−828.387	−0.0417424	−0.0208712	−	0.999782i	$-0.506644\pi$
$733$	−828.387	−0.0417424	−0.0208712	+	0.999782i	$0.506644\pi$
$734$	−14877.6	−0.748149
$735$	−5907.67	−0.296473
$736$	28661.3	1.43542
$737$	3010.32	0.150457
$738$	5410.31	0.269860
$739$	−29665.0	−1.47665	−0.738324	−	0.674446i	$-0.764383\pi$
$739$	−29665.0	−1.47665	−0.738324	+	0.674446i	$0.764383\pi$
$740$	6908.27	0.343180
$741$	0	0
$742$	886.587	0.0438647
$743$	5579.15	0.275477	0.137738	−	0.990469i	$-0.456017\pi$
$743$	5579.15	0.275477	0.137738	+	0.990469i	$0.456017\pi$
$744$	−2471.95	−0.121809
$745$	−3333.75	−0.163945
$746$	25683.1	1.26049
$747$	1412.04	0.0691619
$748$	10854.1	0.530570
$749$	−1031.72	−0.0503316
$750$	−17557.5	−0.854813
$751$	12726.3	0.618363	0.309182	−	0.951003i	$-0.399945\pi$
$751$	12726.3	0.618363	0.309182	+	0.951003i	$0.399945\pi$
$752$	22337.9	1.08322
$753$	−22857.2	−1.10619
$754$	0	0
$755$	−825.124	−0.0397740
$756$	3685.48	0.177301
$757$	4558.65	0.218873	0.109437	−	0.993994i	$-0.465095\pi$
$757$	4558.65	0.218873	0.109437	+	0.993994i	$0.465095\pi$
$758$	−44547.8	−2.13463
$759$	6653.38	0.318185
$760$	−1389.64	−0.0663258
$761$	33224.3	1.58263	0.791315	−	0.611409i	$-0.209397\pi$
$761$	33224.3	1.58263	0.791315	+	0.611409i	$0.209397\pi$
$762$	25531.4	1.21379
$763$	22.6369	0.00107406
$764$	33455.8	1.58428
$765$	−1054.23	−0.0498247
$766$	56855.6	2.68182
$767$	0	0
$768$	−14868.5	−0.698594
$769$	−27508.8	−1.28998	−0.644990	−	0.764191i	$-0.723138\pi$
$769$	−27508.8	−1.28998	−0.644990	+	0.764191i	$0.723138\pi$
$770$	−452.318	−0.0211694
$771$	2654.13	0.123977
$772$	−34560.1	−1.61120
$773$	−39561.8	−1.84080	−0.920400	−	0.390979i	$-0.872137\pi$
$773$	−39561.8	−1.84080	−0.920400	+	0.390979i	$0.872137\pi$
$774$	1658.97	0.0770419
$775$	−11101.0	−0.514527
$776$	−4565.48	−0.211200
$777$	3943.55	0.182077
$778$	−43987.5	−2.02703
$779$	40026.0	1.84093
$780$	0	0
$781$	−11898.9	−0.545167
$782$	−49403.5	−2.25916
$783$	1027.71	0.0469058
$784$	17923.0	0.816463
$785$	4901.76	0.222868
$786$	27888.3	1.26557
$787$	−36638.5	−1.65949	−0.829747	−	0.558140i	$-0.811515\pi$
$787$	−36638.5	−1.65949	−0.829747	+	0.558140i	$0.811515\pi$
$788$	−9984.55	−0.451377
$789$	40689.7	1.83599
$790$	15704.1	0.707247
$791$	−6847.23	−0.307787
$792$	154.448	0.00692937
$793$	0	0
$794$	−61092.2	−2.73058
$795$	1234.53	0.0550744
$796$	−24513.5	−1.09153
$797$	−18061.1	−0.802707	−0.401354	−	0.915923i	$-0.631460\pi$
$797$	−18061.1	−0.802707	−0.401354	+	0.915923i	$0.631460\pi$
$798$	−6433.93	−0.285412
$799$	−44953.4	−1.99041
$800$	29738.0	1.31425
$801$	−3110.74	−0.137219
$802$	21352.9	0.940147
$803$	1095.09	0.0481256
$804$	−13681.4	−0.600132
$805$	1097.01	0.0480304
$806$	0	0
$807$	40452.2	1.76454
$808$	874.056	0.0380559
$809$	−39470.6	−1.71534	−0.857672	−	0.514198i	$-0.828090\pi$
$809$	−39470.6	−1.71534	−0.857672	+	0.514198i	$0.828090\pi$
$810$	10720.3	0.465027
$811$	34401.6	1.48952	0.744762	−	0.667330i	$-0.232563\pi$
$811$	34401.6	1.48952	0.744762	+	0.667330i	$0.232563\pi$
$812$	219.362	0.00948043
$813$	18038.3	0.778145
$814$	−10660.2	−0.459016
$815$	−8455.80	−0.363428
$816$	31833.7	1.36569
$817$	12273.2	0.525564
$818$	−45990.5	−1.96579
$819$	0	0
$820$	−12788.8	−0.544637
$821$	−21908.0	−0.931298	−0.465649	−	0.884970i	$-0.654179\pi$
$821$	−21908.0	−0.931298	−0.465649	+	0.884970i	$0.654179\pi$
$822$	−16491.8	−0.699779
$823$	−18545.6	−0.785493	−0.392746	−	0.919647i	$-0.628475\pi$
$823$	−18545.6	−0.785493	−0.392746	+	0.919647i	$0.628475\pi$
$824$	−1863.06	−0.0787657
$825$	6903.33	0.291325
$826$	16.8983	0.000711825 0
$827$	−35014.8	−1.47229	−0.736144	−	0.676825i	$-0.763356\pi$
$827$	−35014.8	−1.47229	−0.736144	+	0.676825i	$0.763356\pi$
$828$	−3038.11	−0.127514
$829$	−39014.7	−1.63454	−0.817271	−	0.576253i	$-0.804514\pi$
$829$	−39014.7	−1.63454	−0.817271	+	0.576253i	$0.804514\pi$
$830$	−6263.97	−0.261958
$831$	−17046.2	−0.711582
$832$	0	0
$833$	−36068.7	−1.50025
$834$	27298.5	1.13342
$835$	−3619.67	−0.150017
$836$	9267.39	0.383396
$837$	12734.2	0.525875
$838$	40329.7	1.66249
$839$	22077.8	0.908473	0.454237	−	0.890881i	$-0.349912\pi$
$839$	22077.8	0.908473	0.454237	+	0.890881i	$0.349912\pi$
$840$	253.458	0.0104109
$841$	−24327.8	−0.997492
$842$	−29266.8	−1.19786
$843$	40183.5	1.64175
$844$	−5951.34	−0.242717
$845$	0	0
$846$	−5188.05	−0.210838
$847$	371.914	0.0150875
$848$	−3745.37	−0.151670
$849$	14602.4	0.590287
$850$	−51259.5	−2.06845
$851$	25854.2	1.04144
$852$	54078.4	2.17453
$853$	−32422.4	−1.30143	−0.650716	−	0.759321i	$-0.725531\pi$
$853$	−32422.4	−1.30143	−0.650716	+	0.759321i	$0.725531\pi$
$854$	3096.14	0.124061
$855$	−900.116	−0.0360039
$856$	−1562.80	−0.0624010
$857$	21775.5	0.867955	0.433977	−	0.900924i	$-0.357110\pi$
$857$	21775.5	0.867955	0.433977	+	0.900924i	$0.357110\pi$
$858$	0	0
$859$	−19742.5	−0.784172	−0.392086	−	0.919929i	$-0.628246\pi$
$859$	−19742.5	−0.784172	−0.392086	+	0.919929i	$0.628246\pi$
$860$	−3921.43	−0.155488
$861$	−7300.38	−0.288962
$862$	−35055.2	−1.38513
$863$	−4855.49	−0.191521	−0.0957607	−	0.995404i	$-0.530528\pi$
$863$	−4855.49	−0.191521	−0.0957607	+	0.995404i	$0.530528\pi$
$864$	−34113.1	−1.34323
$865$	12697.2	0.499095
$866$	−34480.0	−1.35298
$867$	−37146.3	−1.45508
$868$	2718.09	0.106288
$869$	−12912.5	−0.504059
$870$	573.240	0.0223387
$871$	0	0
$872$	34.2891	0.00133162
$873$	−2957.21	−0.114646
$874$	−42181.3	−1.63250
$875$	2380.29	0.0919639
$876$	−4977.00	−0.191960
$877$	−41748.5	−1.60746	−0.803732	−	0.594991i	$-0.797156\pi$
$877$	−41748.5	−1.60746	−0.803732	+	0.594991i	$0.797156\pi$
$878$	66386.5	2.55175
$879$	−6479.45	−0.248631
$880$	1910.81	0.0731969
$881$	−25509.0	−0.975504	−0.487752	−	0.872982i	$-0.662183\pi$
$881$	−25509.0	−0.975504	−0.487752	+	0.872982i	$0.662183\pi$
$882$	−4162.68	−0.158917
$883$	−11347.1	−0.432456	−0.216228	−	0.976343i	$-0.569375\pi$
$883$	−11347.1	−0.432456	−0.216228	+	0.976343i	$0.569375\pi$
$884$	0	0
$885$	23.5300	0.000893732 0
$886$	2061.11	0.0781538
$887$	−33485.6	−1.26757	−0.633786	−	0.773509i	$-0.718500\pi$
$887$	−33485.6	−1.26757	−0.633786	+	0.773509i	$0.718500\pi$
$888$	5973.46	0.225739
$889$	−3461.31	−0.130583
$890$	13799.6	0.519733
$891$	−8814.63	−0.331427
$892$	11679.7	0.438413
$893$	−38381.7	−1.43829
$894$	−23380.1	−0.874660
$895$	12269.5	0.458240
$896$	−1813.62	−0.0676216
$897$	0	0
$898$	39438.0	1.46555
$899$	757.945	0.0281189
$900$	−3152.25	−0.116750
$901$	7537.28	0.278694
$902$	19734.4	0.728472
$903$	−2238.52	−0.0824955
$904$	−10371.8	−0.381594
$905$	−10982.4	−0.403390
$906$	−5786.72	−0.212197
$907$	39391.1	1.44207	0.721036	−	0.692898i	$-0.243666\pi$
$907$	39391.1	1.44207	0.721036	+	0.692898i	$0.243666\pi$
$908$	−6999.37	−0.255817
$909$	566.155	0.0206581
$910$	0	0
$911$	46463.7	1.68981	0.844903	−	0.534920i	$-0.179658\pi$
$911$	46463.7	1.68981	0.844903	+	0.534920i	$0.179658\pi$
$912$	27180.0	0.986863
$913$	5150.49	0.186699
$914$	−27267.4	−0.986788
$915$	4311.21	0.155764
$916$	11812.6	0.426090
$917$	−3780.84	−0.136155
$918$	58800.8	2.11407
$919$	−23792.0	−0.853999	−0.426999	−	0.904252i	$-0.640429\pi$
$919$	−23792.0	−0.853999	−0.426999	+	0.904252i	$0.640429\pi$
$920$	1661.69	0.0595481
$921$	−29449.7	−1.05364
$922$	−45331.8	−1.61922
$923$	0	0
$924$	−1690.29	−0.0601801
$925$	26825.4	0.953529
$926$	−53783.0	−1.90866
$927$	−1206.77	−0.0427567
$928$	−2030.43	−0.0718236
$929$	−26570.3	−0.938367	−0.469184	−	0.883101i	$-0.655452\pi$
$929$	−26570.3	−0.938367	−0.469184	+	0.883101i	$0.655452\pi$
$930$	7102.94	0.250446
$931$	−30795.9	−1.08410
$932$	57010.0	2.00368
$933$	8277.69	0.290460
$934$	63903.5	2.23874
$935$	−3845.36	−0.134499
$936$	0	0
$937$	24444.0	0.852241	0.426121	−	0.904666i	$-0.359880\pi$
$937$	24444.0	0.852241	0.426121	+	0.904666i	$0.359880\pi$
$938$	3480.92	0.121168
$939$	−50686.6	−1.76155
$940$	12263.4	0.425518
$941$	−25795.7	−0.893642	−0.446821	−	0.894623i	$-0.647444\pi$
$941$	−25795.7	−0.893642	−0.446821	+	0.894623i	$0.647444\pi$
$942$	34376.8	1.18902
$943$	−47861.8	−1.65281
$944$	−71.3866	−0.00246127
$945$	−1305.68	−0.0449457
$946$	6051.16	0.207971
$947$	−12957.3	−0.444621	−0.222310	−	0.974976i	$-0.571360\pi$
$947$	−12957.3	−0.444621	−0.222310	+	0.974976i	$0.571360\pi$
$948$	58685.2	2.01056
$949$	0	0
$950$	−43765.9	−1.49469
$951$	1824.75	0.0622205
$952$	1547.46	0.0526823
$953$	30774.4	1.04604	0.523022	−	0.852319i	$-0.324805\pi$
$953$	30774.4	1.04604	0.523022	+	0.852319i	$0.324805\pi$
$954$	869.874	0.0295212
$955$	−11852.6	−0.401613
$956$	−48975.4	−1.65688
$957$	−471.341	−0.0159209
$958$	61576.7	2.07667
$959$	2235.81	0.0752848
$960$	−11414.3	−0.383743
$961$	−20399.4	−0.684751
$962$	0	0
$963$	−1012.27	−0.0338734
$964$	2990.89	0.0999275
$965$	12243.8	0.408438
$966$	7693.49	0.256246
$967$	−29279.8	−0.973708	−0.486854	−	0.873483i	$-0.661856\pi$
$967$	−29279.8	−0.973708	−0.486854	+	0.873483i	$0.661856\pi$
$968$	563.354	0.0187055
$969$	−54697.7	−1.81336
$970$	13118.5	0.434236
$971$	−6849.41	−0.226373	−0.113186	−	0.993574i	$-0.536106\pi$
$971$	−6849.41	−0.226373	−0.113186	+	0.993574i	$0.536106\pi$
$972$	7686.69	0.253653
$973$	−3700.88	−0.121937
$974$	48013.1	1.57951
$975$	0	0
$976$	−13079.6	−0.428962
$977$	−24532.8	−0.803350	−0.401675	−	0.915782i	$-0.631572\pi$
$977$	−24532.8	−0.803350	−0.401675	+	0.915782i	$0.631572\pi$
$978$	−59301.8	−1.93892
$979$	−11346.6	−0.370416
$980$	9839.62	0.320730
$981$	22.2102	0.000722851 0
$982$	29174.6	0.948065
$983$	−13378.6	−0.434089	−0.217045	−	0.976162i	$-0.569642\pi$
$983$	−13378.6	−0.434089	−0.217045	+	0.976162i	$0.569642\pi$
$984$	−11058.2	−0.358255
$985$	3537.28	0.114424
$986$	3499.86	0.113041
$987$	7000.48	0.225763
$988$	0	0
$989$	−14675.9	−0.471857
$990$	−443.791	−0.0142471
$991$	−23347.0	−0.748377	−0.374189	−	0.927353i	$-0.622079\pi$
$991$	−23347.0	−0.748377	−0.374189	+	0.927353i	$0.622079\pi$
$992$	−25158.8	−0.805235
$993$	10225.3	0.326777
$994$	−13759.0	−0.439043
$995$	8684.54	0.276702
$996$	−23408.1	−0.744693
$997$	15451.7	0.490833	0.245417	−	0.969418i	$-0.421075\pi$
$997$	15451.7	0.490833	0.245417	+	0.969418i	$0.421075\pi$
$998$	75248.6	2.38673
$999$	−30772.0	−0.974558

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.g.1.14		17
13.3	even	3		143.4.e.b.100.4	✓	34
13.9	even	3		143.4.e.b.133.4	yes	34
13.12	even	2		1859.4.a.h.1.4		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.b.100.4	✓	34	13.3	even	3
143.4.e.b.133.4	yes	34	13.9	even	3
1859.4.a.g.1.14		17	1.1	even	1	trivial
1859.4.a.h.1.4		17	13.12	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q+4.13824 q^{2} -5.47866 q^{3} +9.12507 q^{4} -3.23279 q^{5} -22.6720 q^{6} +3.07367 q^{7} +4.65582 q^{8} +3.01573 q^{9} -13.3781 q^{10} +11.0000 q^{11} -49.9932 q^{12} +12.7196 q^{14} +17.7114 q^{15} -53.7336 q^{16} +108.135 q^{17} +12.4798 q^{18} +92.3270 q^{19} -29.4995 q^{20} -16.8396 q^{21} +45.5207 q^{22} -110.402 q^{23} -25.5077 q^{24} -114.549 q^{25} +131.402 q^{27} +28.0475 q^{28} +7.82111 q^{29} +73.2940 q^{30} +96.9102 q^{31} -259.610 q^{32} -60.2653 q^{33} +447.489 q^{34} -9.93654 q^{35} +27.5187 q^{36} -234.183 q^{37} +382.072 q^{38} -15.0513 q^{40} +433.525 q^{41} -69.6864 q^{42} +132.932 q^{43} +100.376 q^{44} -9.74923 q^{45} -456.869 q^{46} -415.715 q^{47} +294.388 q^{48} -333.553 q^{49} -474.032 q^{50} -592.435 q^{51} +69.7025 q^{53} +543.772 q^{54} -35.5607 q^{55} +14.3105 q^{56} -505.828 q^{57} +32.3657 q^{58} +1.32853 q^{59} +161.618 q^{60} +243.415 q^{61} +401.038 q^{62} +9.26936 q^{63} -644.459 q^{64} -249.392 q^{66} +273.666 q^{67} +986.740 q^{68} +604.853 q^{69} -41.1198 q^{70} -1081.72 q^{71} +14.0407 q^{72} +99.5536 q^{73} -969.106 q^{74} +627.575 q^{75} +842.490 q^{76} +33.8104 q^{77} -1173.86 q^{79} +173.710 q^{80} -801.330 q^{81} +1794.03 q^{82} +468.226 q^{83} -153.663 q^{84} -349.578 q^{85} +550.106 q^{86} -42.8492 q^{87} +51.2140 q^{88} -1031.51 q^{89} -40.3447 q^{90} -1007.42 q^{92} -530.938 q^{93} -1720.33 q^{94} -298.474 q^{95} +1422.31 q^{96} -980.595 q^{97} -1380.32 q^{98} +33.1730 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9} + 2 q^{10} + 187 q^{11} - 127 q^{12} - 148 q^{15} + 126 q^{16} - 74 q^{17} + 90 q^{18} - 159 q^{19} - 222 q^{20} - 184 q^{21}+ \cdots + 1485 q^{99}+O(q^{100}) \) 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9 + 2 * q^10 + 187 * q^11 - 127 * q^12 - 148 * q^15 + 126 * q^16 - 74 * q^17 + 90 * q^18 - 159 * q^19 - 222 * q^20 - 184 * q^21 - 215 * q^23 + 214 * q^24 + 95 * q^25 - 192 * q^27 - 358 * q^28 - 157 * q^29 + 829 * q^30 - 394 * q^31 - 553 * q^32 - 66 * q^33 - 702 * q^34 + 58 * q^35 - 700 * q^36 + 88 * q^37 - 1318 * q^38 + 733 * q^40 - 512 * q^41 + 337 * q^42 + 927 * q^43 + 550 * q^44 - 1482 * q^45 - 1361 * q^46 - 143 * q^47 - 178 * q^48 + 1835 * q^49 - 583 * q^50 - 568 * q^51 + 106 * q^53 - 67 * q^54 - 264 * q^55 + 2059 * q^56 + 1298 * q^57 - 1690 * q^58 - 266 * q^59 + 37 * q^60 - 624 * q^61 + 643 * q^62 - 2360 * q^63 - 1589 * q^64 + 176 * q^66 - 676 * q^67 - 413 * q^68 + 764 * q^69 - 1061 * q^70 - 763 * q^71 - 1366 * q^72 - 2374 * q^73 - 1649 * q^74 + 2420 * q^75 - 2101 * q^76 - 682 * q^77 + 2164 * q^79 - 1013 * q^80 + 537 * q^81 + 3152 * q^82 + 777 * q^83 - 3381 * q^84 - 1690 * q^85 + 2894 * q^86 - 4200 * q^87 - 231 * q^88 - 1687 * q^89 - 5399 * q^90 + 5542 * q^92 - 4310 * q^93 + 1777 * q^94 + 1124 * q^95 - 3465 * q^96 - 2047 * q^97 + 1553 * q^98 + 1485 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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