LMFDB - Embedded newform 1859.4.a.g.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,4,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$109.684550701$
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			1.15
Root			$-4.15571$ 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)

$f(q)$	$=$	$q+4.15571 q^{2} +7.17608 q^{3} +9.26990 q^{4} -11.1721 q^{5} +29.8217 q^{6} -7.78423 q^{7} +5.27734 q^{8} +24.4962 q^{9} +O(q^{10})$	\(q+4.15571 q^{2} +7.17608 q^{3} +9.26990 q^{4} -11.1721 q^{5} +29.8217 q^{6} -7.78423 q^{7} +5.27734 q^{8} +24.4962 q^{9} -46.4282 q^{10} +11.0000 q^{11} +66.5216 q^{12} -32.3490 q^{14} -80.1722 q^{15} -52.2281 q^{16} -11.1357 q^{17} +101.799 q^{18} -129.117 q^{19} -103.565 q^{20} -55.8602 q^{21} +45.7128 q^{22} +194.310 q^{23} +37.8707 q^{24} -0.183205 q^{25} -17.9678 q^{27} -72.1590 q^{28} -130.515 q^{29} -333.172 q^{30} +160.453 q^{31} -259.264 q^{32} +78.9369 q^{33} -46.2766 q^{34} +86.9665 q^{35} +227.077 q^{36} -91.1462 q^{37} -536.571 q^{38} -58.9593 q^{40} -298.478 q^{41} -232.139 q^{42} +111.893 q^{43} +101.969 q^{44} -273.675 q^{45} +807.495 q^{46} -247.250 q^{47} -374.793 q^{48} -282.406 q^{49} -0.761344 q^{50} -79.9105 q^{51} -353.642 q^{53} -74.6689 q^{54} -122.894 q^{55} -41.0800 q^{56} -926.552 q^{57} -542.384 q^{58} +162.588 q^{59} -743.189 q^{60} +194.676 q^{61} +666.797 q^{62} -190.684 q^{63} -659.598 q^{64} +328.039 q^{66} -956.307 q^{67} -103.227 q^{68} +1394.38 q^{69} +361.407 q^{70} -420.544 q^{71} +129.275 q^{72} -306.549 q^{73} -378.777 q^{74} -1.31469 q^{75} -1196.90 q^{76} -85.6265 q^{77} -545.170 q^{79} +583.500 q^{80} -790.335 q^{81} -1240.39 q^{82} -452.825 q^{83} -517.819 q^{84} +124.409 q^{85} +464.994 q^{86} -936.590 q^{87} +58.0508 q^{88} +282.957 q^{89} -1137.31 q^{90} +1801.23 q^{92} +1151.43 q^{93} -1027.50 q^{94} +1442.51 q^{95} -1860.50 q^{96} +213.494 q^{97} -1173.60 q^{98} +269.458 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9}+O(q^{10}) $ 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9	\( 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9} + 2 q^{10} + 187 q^{11} - 127 q^{12} - 148 q^{15} + 126 q^{16} - 74 q^{17} + 90 q^{18} - 159 q^{19} - 222 q^{20} - 184 q^{21} - 215 q^{23} + 214 q^{24} + 95 q^{25} - 192 q^{27} - 358 q^{28} - 157 q^{29} + 829 q^{30} - 394 q^{31} - 553 q^{32} - 66 q^{33} - 702 q^{34} + 58 q^{35} - 700 q^{36} + 88 q^{37} - 1318 q^{38} + 733 q^{40} - 512 q^{41} + 337 q^{42} + 927 q^{43} + 550 q^{44} - 1482 q^{45} - 1361 q^{46} - 143 q^{47} - 178 q^{48} + 1835 q^{49} - 583 q^{50} - 568 q^{51} + 106 q^{53} - 67 q^{54} - 264 q^{55} + 2059 q^{56} + 1298 q^{57} - 1690 q^{58} - 266 q^{59} + 37 q^{60} - 624 q^{61} + 643 q^{62} - 2360 q^{63} - 1589 q^{64} + 176 q^{66} - 676 q^{67} - 413 q^{68} + 764 q^{69} - 1061 q^{70} - 763 q^{71} - 1366 q^{72} - 2374 q^{73} - 1649 q^{74} + 2420 q^{75} - 2101 q^{76} - 682 q^{77} + 2164 q^{79} - 1013 q^{80} + 537 q^{81} + 3152 q^{82} + 777 q^{83} - 3381 q^{84} - 1690 q^{85} + 2894 q^{86} - 4200 q^{87} - 231 q^{88} - 1687 q^{89} - 5399 q^{90} + 5542 q^{92} - 4310 q^{93} + 1777 q^{94} + 1124 q^{95} - 3465 q^{96} - 2047 q^{97} + 1553 q^{98} + 1485 q^{99}+O(q^{100}) \) 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

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	4.15571	1.46926	0.734632	−	0.678466i	$-0.237355\pi$
$2$	4.15571	1.46926	0.734632	+	0.678466i	$0.237355\pi$
$3$	7.17608	1.38104	0.690519	−	0.723314i	$-0.257382\pi$
$3$	7.17608	1.38104	0.690519	+	0.723314i	$0.257382\pi$
$4$	9.26990	1.15874
$5$	−11.1721	−0.999267	−0.499633	−	0.866237i	$-0.666532\pi$
$5$	−11.1721	−0.999267	−0.499633	+	0.866237i	$0.666532\pi$
$6$	29.8217	2.02911
$7$	−7.78423	−0.420309	−0.210154	−	0.977668i	$-0.567397\pi$
$7$	−7.78423	−0.420309	−0.210154	+	0.977668i	$0.567397\pi$
$8$	5.27734	0.233228
$9$	24.4962	0.907265
$10$	−46.4282	−1.46819
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	66.5216	1.60026
$13$	0	0
$13$	0	0
$14$	−32.3490	−0.617545
$15$	−80.1722	−1.38003
$16$	−52.2281	−0.816064
$17$	−11.1357	−0.158870	−0.0794352	−	0.996840i	$-0.525312\pi$
$17$	−11.1357	−0.158870	−0.0794352	+	0.996840i	$0.525312\pi$
$18$	101.799	1.33301
$19$	−129.117	−1.55902	−0.779510	−	0.626390i	$-0.784532\pi$
$19$	−129.117	−1.55902	−0.779510	+	0.626390i	$0.784532\pi$
$20$	−103.565	−1.15789
$21$	−55.8602	−0.580462
$22$	45.7128	0.443000
$23$	194.310	1.76158	0.880792	−	0.473504i	$-0.157011\pi$
$23$	194.310	1.76158	0.880792	+	0.473504i	$0.157011\pi$
$24$	37.8707	0.322097
$25$	−0.183205	−0.00146564
$26$	0	0
$27$	−17.9678	−0.128070
$28$	−72.1590	−0.487028
$29$	−130.515	−0.835728	−0.417864	−	0.908510i	$-0.637221\pi$
$29$	−130.515	−0.835728	−0.417864	+	0.908510i	$0.637221\pi$
$30$	−333.172	−2.02762
$31$	160.453	0.929621	0.464810	−	0.885410i	$-0.346122\pi$
$31$	160.453	0.929621	0.464810	+	0.885410i	$0.346122\pi$
$32$	−259.264	−1.43224
$33$	78.9369	0.416399
$34$	−46.2766	−0.233423
$35$	86.9665	0.420001
$36$	227.077	1.05128
$37$	−91.1462	−0.404982	−0.202491	−	0.979284i	$-0.564904\pi$
$37$	−91.1462	−0.404982	−0.202491	+	0.979284i	$0.564904\pi$
$38$	−536.571	−2.29061
$39$	0	0
$40$	−58.9593	−0.233057
$41$	−298.478	−1.13694	−0.568469	−	0.822704i	$-0.692464\pi$
$41$	−298.478	−1.13694	−0.568469	+	0.822704i	$0.692464\pi$
$42$	−232.139	−0.852852
$43$	111.893	0.396826	0.198413	−	0.980119i	$-0.436421\pi$
$43$	111.893	0.396826	0.198413	+	0.980119i	$0.436421\pi$
$44$	101.969	0.349373
$45$	−273.675	−0.906600
$46$	807.495	2.58823
$47$	−247.250	−0.767342	−0.383671	−	0.923470i	$-0.625340\pi$
$47$	−247.250	−0.767342	−0.383671	+	0.923470i	$0.625340\pi$
$48$	−374.793	−1.12702
$49$	−282.406	−0.823341
$50$	−0.761344	−0.00215341
$51$	−79.9105	−0.219406
$52$	0	0
$53$	−353.642	−0.916536	−0.458268	−	0.888814i	$-0.651530\pi$
$53$	−353.642	−0.916536	−0.458268	+	0.888814i	$0.651530\pi$
$54$	−74.6689	−0.188169
$55$	−122.894	−0.301290
$56$	−41.0800	−0.0980277
$57$	−926.552	−2.15307
$58$	−542.384	−1.22791
$59$	162.588	0.358764	0.179382	−	0.983779i	$-0.442590\pi$
$59$	162.588	0.358764	0.179382	+	0.983779i	$0.442590\pi$
$60$	−743.189	−1.59909
$61$	194.676	0.408618	0.204309	−	0.978906i	$-0.434505\pi$
$61$	194.676	0.408618	0.204309	+	0.978906i	$0.434505\pi$
$62$	666.797	1.36586
$63$	−190.684	−0.381331
$64$	−659.598	−1.28828
$65$	0	0
$66$	328.039	0.611800
$67$	−956.307	−1.74375	−0.871877	−	0.489725i	$-0.837097\pi$
$67$	−956.307	−1.74375	−0.871877	+	0.489725i	$0.837097\pi$
$68$	−103.227	−0.184089
$69$	1394.38	2.43281
$70$	361.407	0.617092
$71$	−420.544	−0.702949	−0.351474	−	0.936197i	$-0.614320\pi$
$71$	−420.544	−0.702949	−0.351474	+	0.936197i	$0.614320\pi$
$72$	129.275	0.211600
$73$	−306.549	−0.491491	−0.245746	−	0.969334i	$-0.579033\pi$
$73$	−306.549	−0.491491	−0.245746	+	0.969334i	$0.579033\pi$
$74$	−378.777	−0.595026
$75$	−1.31469	−0.00202410
$76$	−1196.90	−1.80650
$77$	−85.6265	−0.126728
$78$	0	0
$79$	−545.170	−0.776410	−0.388205	−	0.921573i	$-0.626905\pi$
$79$	−545.170	−0.776410	−0.388205	+	0.921573i	$0.626905\pi$
$80$	583.500	0.815466
$81$	−790.335	−1.08414
$82$	−1240.39	−1.67046
$83$	−452.825	−0.598844	−0.299422	−	0.954121i	$-0.596794\pi$
$83$	−452.825	−0.598844	−0.299422	+	0.954121i	$0.596794\pi$
$84$	−517.819	−0.672603
$85$	124.409	0.158754
$86$	464.994	0.583042
$87$	−936.590	−1.15417
$88$	58.0508	0.0703209
$89$	282.957	0.337005	0.168502	−	0.985701i	$-0.446107\pi$
$89$	282.957	0.337005	0.168502	+	0.985701i	$0.446107\pi$
$90$	−1137.31	−1.33204
$91$	0	0
$92$	1801.23	2.04121
$93$	1151.43	1.28384
$94$	−1027.50	−1.12743
$95$	1442.51	1.55788
$96$	−1860.50	−1.97798
$97$	213.494	0.223475	0.111737	−	0.993738i	$-0.464358\pi$
$97$	213.494	0.223475	0.111737	+	0.993738i	$0.464358\pi$
$98$	−1173.60	−1.20971
$99$	269.458	0.273551
$100$	−1.69829	−0.00169829
$101$	1725.15	1.69959	0.849795	−	0.527113i	$-0.176726\pi$
$101$	1725.15	1.69959	0.849795	+	0.527113i	$0.176726\pi$
$102$	−332.085	−0.322365
$103$	1416.79	1.35534	0.677672	−	0.735364i	$-0.262989\pi$
$103$	1416.79	1.35534	0.677672	+	0.735364i	$0.262989\pi$
$104$	0	0
$105$	624.079	0.580037
$106$	−1469.63	−1.34663
$107$	−292.995	−0.264719	−0.132359	−	0.991202i	$-0.542255\pi$
$107$	−292.995	−0.264719	−0.132359	+	0.991202i	$0.542255\pi$
$108$	−166.560	−0.148400
$109$	−180.669	−0.158761	−0.0793806	−	0.996844i	$-0.525294\pi$
$109$	−180.669	−0.158761	−0.0793806	+	0.996844i	$0.525294\pi$
$110$	−510.710	−0.442675
$111$	−654.072	−0.559296
$112$	406.555	0.342999
$113$	996.141	0.829284	0.414642	−	0.909985i	$-0.363907\pi$
$113$	996.141	0.829284	0.414642	+	0.909985i	$0.363907\pi$
$114$	−3850.48	−3.16342
$115$	−2170.86	−1.76029
$116$	−1209.87	−0.968390
$117$	0	0
$118$	675.666	0.527120
$119$	86.6826	0.0667746
$120$	−423.096	−0.321860
$121$	121.000	0.0909091
$122$	809.017	0.600368
$123$	−2141.91	−1.57016
$124$	1487.39	1.07719
$125$	1398.56	1.00073
$126$	−792.425	−0.560277
$127$	2271.17	1.58688	0.793440	−	0.608648i	$-0.208288\pi$
$127$	2271.17	1.58688	0.793440	+	0.608648i	$0.208288\pi$
$128$	−666.990	−0.460579
$129$	802.952	0.548031
$130$	0	0
$131$	−1917.39	−1.27880	−0.639402	−	0.768872i	$-0.720818\pi$
$131$	−1917.39	−1.27880	−0.639402	+	0.768872i	$0.720818\pi$
$132$	731.737	0.482497
$133$	1005.07	0.655270
$134$	−3974.13	−2.56204
$135$	200.739	0.127977
$136$	−58.7668	−0.0370530
$137$	−1295.44	−0.807858	−0.403929	−	0.914790i	$-0.632356\pi$
$137$	−1295.44	−0.807858	−0.403929	+	0.914790i	$0.632356\pi$
$138$	5794.65	3.57445
$139$	2855.42	1.74240	0.871200	−	0.490928i	$-0.163342\pi$
$139$	2855.42	1.74240	0.871200	+	0.490928i	$0.163342\pi$
$140$	806.171	0.486671
$141$	−1774.28	−1.05973
$142$	−1747.66	−1.03282
$143$	0	0
$144$	−1279.39	−0.740387
$145$	1458.14	0.835115
$146$	−1273.93	−0.722131
$147$	−2026.57	−1.13706
$148$	−844.916	−0.469268
$149$	−628.990	−0.345831	−0.172916	−	0.984937i	$-0.555319\pi$
$149$	−628.990	−0.345831	−0.172916	+	0.984937i	$0.555319\pi$
$150$	−5.46347	−0.00297394
$151$	−13.3455	−0.00719233	−0.00359617	−	0.999994i	$-0.501145\pi$
$151$	−13.3455	−0.00719233	−0.00359617	+	0.999994i	$0.501145\pi$
$152$	−681.393	−0.363607
$153$	−272.781	−0.144138
$154$	−355.839	−0.186197
$155$	−1792.61	−0.928939
$156$	0	0
$157$	−1586.13	−0.806288	−0.403144	−	0.915137i	$-0.632083\pi$
$157$	−1586.13	−0.806288	−0.403144	+	0.915137i	$0.632083\pi$
$158$	−2265.57	−1.14075
$159$	−2537.76	−1.26577
$160$	2896.53	1.43119
$161$	−1512.55	−0.740409
$162$	−3284.40	−1.59288
$163$	608.074	0.292197	0.146098	−	0.989270i	$-0.453328\pi$
$163$	608.074	0.292197	0.146098	+	0.989270i	$0.453328\pi$
$164$	−2766.87	−1.31741
$165$	−881.894	−0.416093
$166$	−1881.81	−0.879860
$167$	−1054.79	−0.488757	−0.244379	−	0.969680i	$-0.578584\pi$
$167$	−1054.79	−0.488757	−0.244379	+	0.969680i	$0.578584\pi$
$168$	−294.794	−0.135380
$169$	0	0
$170$	517.009	0.233251
$171$	−3162.86	−1.41444
$172$	1037.24	0.459817
$173$	3308.78	1.45411	0.727057	−	0.686577i	$-0.240887\pi$
$173$	3308.78	1.45411	0.727057	+	0.686577i	$0.240887\pi$
$174$	−3892.19	−1.69578
$175$	1.42611	0.000616020 0
$176$	−574.509	−0.246053
$177$	1166.74	0.495467
$178$	1175.89	0.495149
$179$	−2055.31	−0.858216	−0.429108	−	0.903253i	$-0.641172\pi$
$179$	−2055.31	−0.858216	−0.429108	+	0.903253i	$0.641172\pi$
$180$	−2536.94	−1.05051
$181$	−4694.21	−1.92772	−0.963862	−	0.266403i	$-0.914165\pi$
$181$	−4694.21	−1.92772	−0.963862	+	0.266403i	$0.914165\pi$
$182$	0	0
$183$	1397.01	0.564317
$184$	1025.44	0.410850
$185$	1018.30	0.404685
$186$	4784.99	1.88630
$187$	−122.492	−0.0479012
$188$	−2291.98	−0.889148
$189$	139.865	0.0538291
$190$	5994.65	2.28893
$191$	−1623.56	−0.615060	−0.307530	−	0.951538i	$-0.599502\pi$
$191$	−1623.56	−0.615060	−0.307530	+	0.951538i	$0.599502\pi$
$192$	−4733.33	−1.77916
$193$	5166.40	1.92687	0.963435	−	0.267943i	$-0.0863440\pi$
$193$	5166.40	1.92687	0.963435	+	0.267943i	$0.0863440\pi$
$194$	887.219	0.328343
$195$	0	0
$196$	−2617.87	−0.954036
$197$	897.994	0.324769	0.162384	−	0.986728i	$-0.448082\pi$
$197$	897.994	0.324769	0.162384	+	0.986728i	$0.448082\pi$
$198$	1119.79	0.401918
$199$	−33.6671	−0.0119930	−0.00599648	−	0.999982i	$-0.501909\pi$
$199$	−33.6671	−0.0119930	−0.00599648	+	0.999982i	$0.501909\pi$
$200$	−0.966833	−0.000341827 0
$201$	−6862.54	−2.40819
$202$	7169.21	2.49715
$203$	1015.96	0.351264
$204$	−740.762	−0.254234
$205$	3334.64	1.13611
$206$	5887.76	1.99136
$207$	4759.85	1.59822
$208$	0	0
$209$	−1420.28	−0.470062
$210$	2593.49	0.852227
$211$	4628.15	1.51002	0.755012	−	0.655711i	$-0.227631\pi$
$211$	4628.15	1.51002	0.755012	+	0.655711i	$0.227631\pi$
$212$	−3278.22	−1.06203
$213$	−3017.86	−0.970799
$214$	−1217.60	−0.388942
$215$	−1250.08	−0.396535
$216$	−94.8222	−0.0298696
$217$	−1249.00	−0.390728
$218$	−750.808	−0.233262
$219$	−2199.82	−0.678768
$220$	−1139.21	−0.349116
$221$	0	0
$222$	−2718.13	−0.821753
$223$	−1929.94	−0.579546	−0.289773	−	0.957095i	$-0.593580\pi$
$223$	−1929.94	−0.579546	−0.289773	+	0.957095i	$0.593580\pi$
$224$	2018.17	0.601984
$225$	−4.48781	−0.00132972
$226$	4139.67	1.21844
$227$	1651.71	0.482941	0.241470	−	0.970408i	$-0.422370\pi$
$227$	1651.71	0.482941	0.241470	+	0.970408i	$0.422370\pi$
$228$	−8589.04	−2.49484
$229$	5935.63	1.71283	0.856414	−	0.516290i	$-0.172687\pi$
$229$	5935.63	1.71283	0.856414	+	0.516290i	$0.172687\pi$
$230$	−9021.45	−2.58633
$231$	−614.463	−0.175016
$232$	−688.775	−0.194915
$233$	−1019.92	−0.286770	−0.143385	−	0.989667i	$-0.545799\pi$
$233$	−1019.92	−0.286770	−0.143385	+	0.989667i	$0.545799\pi$
$234$	0	0
$235$	2762.31	0.766779
$236$	1507.17	0.415714
$237$	−3912.18	−1.07225
$238$	360.227	0.0981095
$239$	3250.81	0.879821	0.439911	−	0.898042i	$-0.355010\pi$
$239$	3250.81	0.879821	0.439911	+	0.898042i	$0.355010\pi$
$240$	4187.24	1.12619
$241$	3012.71	0.805252	0.402626	−	0.915365i	$-0.368098\pi$
$241$	3012.71	0.805252	0.402626	+	0.915365i	$0.368098\pi$
$242$	502.841	0.133569
$243$	−5186.38	−1.36916
$244$	1804.63	0.473482
$245$	3155.08	0.822737
$246$	−8901.13	−2.30697
$247$	0	0
$248$	846.767	0.216814
$249$	−3249.51	−0.827026
$250$	5812.03	1.47034
$251$	5777.09	1.45277	0.726387	−	0.687286i	$-0.241198\pi$
$251$	5777.09	1.45277	0.726387	+	0.687286i	$0.241198\pi$
$252$	−1767.62	−0.441863
$253$	2137.41	0.531137
$254$	9438.32	2.33155
$255$	892.771	0.219245
$256$	2504.97	0.611566
$257$	−7933.34	−1.92556	−0.962779	−	0.270291i	$-0.912880\pi$
$257$	−7933.34	−1.92556	−0.962779	+	0.270291i	$0.912880\pi$
$258$	3336.84	0.805203
$259$	709.502	0.170218
$260$	0	0
$261$	−3197.13	−0.758227
$262$	−7968.12	−1.87890
$263$	3683.45	0.863617	0.431808	−	0.901965i	$-0.357876\pi$
$263$	3683.45	0.863617	0.431808	+	0.901965i	$0.357876\pi$
$264$	416.577	0.0971158
$265$	3950.94	0.915864
$266$	4176.79	0.962765
$267$	2030.53	0.465416
$268$	−8864.87	−2.02055
$269$	−2590.92	−0.587253	−0.293626	−	0.955920i	$-0.594862\pi$
$269$	−2590.92	−0.587253	−0.293626	+	0.955920i	$0.594862\pi$
$270$	834.211	0.188031
$271$	−6212.12	−1.39247	−0.696235	−	0.717814i	$-0.745143\pi$
$271$	−6212.12	−1.39247	−0.696235	+	0.717814i	$0.745143\pi$
$272$	581.595	0.129648
$273$	0	0
$274$	−5383.45	−1.18696
$275$	−2.01525	−0.000441906 0
$276$	12925.8	2.81899
$277$	−4428.12	−0.960506	−0.480253	−	0.877130i	$-0.659455\pi$
$277$	−4428.12	−0.960506	−0.480253	+	0.877130i	$0.659455\pi$
$278$	11866.3	2.56005
$279$	3930.49	0.843412
$280$	458.952	0.0979558
$281$	−3913.26	−0.830766	−0.415383	−	0.909647i	$-0.636352\pi$
$281$	−3913.26	−0.830766	−0.415383	+	0.909647i	$0.636352\pi$
$282$	−7373.40	−1.55702
$283$	3130.23	0.657501	0.328751	−	0.944417i	$-0.393372\pi$
$283$	3130.23	0.657501	0.328751	+	0.944417i	$0.393372\pi$
$284$	−3898.40	−0.814533
$285$	10351.6	2.15149
$286$	0	0
$287$	2323.42	0.477865
$288$	−6350.96	−1.29942
$289$	−4789.00	−0.974760
$290$	6059.59	1.22701
$291$	1532.05	0.308627
$292$	−2841.68	−0.569510
$293$	549.608	0.109585	0.0547926	−	0.998498i	$-0.482550\pi$
$293$	549.608	0.109585	0.0547926	+	0.998498i	$0.482550\pi$
$294$	−8421.82	−1.67065
$295$	−1816.45	−0.358501
$296$	−481.010	−0.0944531
$297$	−197.646	−0.0386147
$298$	−2613.90	−0.508118
$299$	0	0
$300$	−12.1871	−0.00234540
$301$	−870.999	−0.166789
$302$	−55.4600	−0.0105674
$303$	12379.8	2.34720
$304$	6743.52	1.27226
$305$	−2174.95	−0.408319
$306$	−1133.60	−0.211776
$307$	−9304.94	−1.72984	−0.864920	−	0.501909i	$-0.832631\pi$
$307$	−9304.94	−1.72984	−0.864920	+	0.501909i	$0.832631\pi$
$308$	−793.749	−0.146844
$309$	10167.0	1.87178
$310$	−7449.55	−1.36486
$311$	−10035.9	−1.82985	−0.914927	−	0.403620i	$-0.867752\pi$
$311$	−10035.9	−1.82985	−0.914927	+	0.403620i	$0.867752\pi$
$312$	0	0
$313$	3971.28	0.717156	0.358578	−	0.933500i	$-0.383262\pi$
$313$	3971.28	0.717156	0.358578	+	0.933500i	$0.383262\pi$
$314$	−6591.51	−1.18465
$315$	2130.34	0.381052
$316$	−5053.67	−0.899655
$317$	−1403.12	−0.248603	−0.124302	−	0.992244i	$-0.539669\pi$
$317$	−1403.12	−0.248603	−0.124302	+	0.992244i	$0.539669\pi$
$318$	−10546.2	−1.85975
$319$	−1435.67	−0.251982
$320$	7369.13	1.28733
$321$	−2102.56	−0.365586
$322$	−6285.72	−1.08786
$323$	1437.80	0.247682
$324$	−7326.32	−1.25623
$325$	0	0
$326$	2526.98	0.429314
$327$	−1296.50	−0.219255
$328$	−1575.17	−0.265166
$329$	1924.65	0.322520
$330$	−3664.90	−0.611351
$331$	2298.36	0.381660	0.190830	−	0.981623i	$-0.438882\pi$
$331$	2298.36	0.381660	0.190830	+	0.981623i	$0.438882\pi$
$332$	−4197.65	−0.693903
$333$	−2232.73	−0.367426
$334$	−4383.42	−0.718114
$335$	10684.0	1.74248
$336$	2917.48	0.473694
$337$	6515.63	1.05320	0.526601	−	0.850112i	$-0.323466\pi$
$337$	6515.63	1.05320	0.526601	+	0.850112i	$0.323466\pi$
$338$	0	0
$339$	7148.39	1.14527
$340$	1153.26	0.183954
$341$	1764.99	0.280291
$342$	−13143.9	−2.07819
$343$	4868.30	0.766366
$344$	590.497	0.0925508
$345$	−15578.3	−2.43103
$346$	13750.3	2.13648
$347$	10362.0	1.60306	0.801528	−	0.597958i	$-0.204021\pi$
$347$	10362.0	1.60306	0.801528	+	0.597958i	$0.204021\pi$
$348$	−8682.10	−1.33738
$349$	155.253	0.0238123	0.0119061	−	0.999929i	$-0.496210\pi$
$349$	155.253	0.0238123	0.0119061	+	0.999929i	$0.496210\pi$
$350$	5.92648	0.000905096 0
$351$	0	0
$352$	−2851.90	−0.431837
$353$	−5156.65	−0.777509	−0.388755	−	0.921341i	$-0.627095\pi$
$353$	−5156.65	−0.777509	−0.388755	+	0.921341i	$0.627095\pi$
$354$	4848.64	0.727972
$355$	4698.38	0.702434
$356$	2622.99	0.390500
$357$	622.041	0.0922182
$358$	−8541.25	−1.26095
$359$	−48.8381	−0.00717987	−0.00358994	−	0.999994i	$-0.501143\pi$
$359$	−48.8381	−0.00717987	−0.00358994	+	0.999994i	$0.501143\pi$
$360$	−1444.28	−0.211444
$361$	9812.11	1.43054
$362$	−19507.8	−2.83234
$363$	868.306	0.125549
$364$	0	0
$365$	3424.81	0.491131
$366$	5805.57	0.829131
$367$	9434.90	1.34196	0.670978	−	0.741477i	$-0.265874\pi$
$367$	9434.90	1.34196	0.670978	+	0.741477i	$0.265874\pi$
$368$	−10148.4	−1.43757
$369$	−7311.57	−1.03150
$370$	4231.75	0.594590
$371$	2752.83	0.385228
$372$	10673.6	1.48764
$373$	−4554.73	−0.632265	−0.316132	−	0.948715i	$-0.602384\pi$
$373$	−4554.73	−0.632265	−0.316132	+	0.948715i	$0.602384\pi$
$374$	−509.042	−0.0703796
$375$	10036.2	1.38205
$376$	−1304.82	−0.178965
$377$	0	0
$378$	581.239	0.0790892
$379$	8350.92	1.13182	0.565908	−	0.824469i	$-0.308526\pi$
$379$	8350.92	1.13182	0.565908	+	0.824469i	$0.308526\pi$
$380$	13371.9	1.80517
$381$	16298.1	2.19154
$382$	−6747.03	−0.903686
$383$	−10610.0	−1.41553	−0.707764	−	0.706449i	$-0.750296\pi$
$383$	−10610.0	−1.41553	−0.707764	+	0.706449i	$0.750296\pi$
$384$	−4786.37	−0.636077
$385$	956.631	0.126635
$386$	21470.1	2.83108
$387$	2740.95	0.360026
$388$	1979.07	0.258948
$389$	197.769	0.0257771	0.0128886	−	0.999917i	$-0.495897\pi$
$389$	197.769	0.0257771	0.0128886	+	0.999917i	$0.495897\pi$
$390$	0	0
$391$	−2163.77	−0.279863
$392$	−1490.35	−0.192026
$393$	−13759.4	−1.76608
$394$	3731.80	0.477171
$395$	6090.71	0.775841
$396$	2497.85	0.316974
$397$	−6788.75	−0.858230	−0.429115	−	0.903250i	$-0.641175\pi$
$397$	−6788.75	−0.858230	−0.429115	+	0.903250i	$0.641175\pi$
$398$	−139.911	−0.0176208
$399$	7212.49	0.904952
$400$	9.56843	0.00119605
$401$	10404.0	1.29564	0.647818	−	0.761795i	$-0.275682\pi$
$401$	10404.0	1.29564	0.647818	+	0.761795i	$0.275682\pi$
$402$	−28518.7	−3.53827
$403$	0	0
$404$	15991.9	1.96938
$405$	8829.73	1.08334
$406$	4222.04	0.516099
$407$	−1002.61	−0.122107
$408$	−421.715	−0.0511716
$409$	−7889.90	−0.953864	−0.476932	−	0.878940i	$-0.658251\pi$
$409$	−7889.90	−0.953864	−0.476932	+	0.878940i	$0.658251\pi$
$410$	13857.8	1.66924
$411$	−9296.15	−1.11568
$412$	13133.5	1.57049
$413$	−1265.62	−0.150792
$414$	19780.5	2.34821
$415$	5059.03	0.598405
$416$	0	0
$417$	20490.7	2.40632
$418$	−5902.28	−0.690646
$419$	−7322.27	−0.853738	−0.426869	−	0.904313i	$-0.640384\pi$
$419$	−7322.27	−0.853738	−0.426869	+	0.904313i	$0.640384\pi$
$420$	5785.15	0.672110
$421$	−12052.1	−1.39521	−0.697605	−	0.716482i	$-0.745751\pi$
$421$	−12052.1	−1.39521	−0.697605	+	0.716482i	$0.745751\pi$
$422$	19233.2	2.21862
$423$	−6056.66	−0.696182
$424$	−1866.29	−0.213762
$425$	2.04010	0.000232846 0
$426$	−12541.3	−1.42636
$427$	−1515.40	−0.171746
$428$	−2716.03	−0.306739
$429$	0	0
$430$	−5194.98	−0.582614
$431$	−3557.05	−0.397534	−0.198767	−	0.980047i	$-0.563694\pi$
$431$	−3557.05	−0.397534	−0.198767	+	0.980047i	$0.563694\pi$
$432$	938.424	0.104514
$433$	5437.16	0.603449	0.301724	−	0.953395i	$-0.402438\pi$
$433$	5437.16	0.603449	0.301724	+	0.953395i	$0.402438\pi$
$434$	−5190.49	−0.574082
$435$	10463.7	1.15333
$436$	−1674.79	−0.183963
$437$	−25088.6	−2.74634
$438$	−9141.82	−0.997290
$439$	−2203.18	−0.239526	−0.119763	−	0.992803i	$-0.538213\pi$
$439$	−2203.18	−0.239526	−0.119763	+	0.992803i	$0.538213\pi$
$440$	−648.552	−0.0702693
$441$	−6917.86	−0.746988
$442$	0	0
$443$	14546.1	1.56006	0.780028	−	0.625744i	$-0.215205\pi$
$443$	14546.1	1.56006	0.780028	+	0.625744i	$0.215205\pi$
$444$	−6063.19	−0.648077
$445$	−3161.24	−0.336758
$446$	−8020.29	−0.851506
$447$	−4513.68	−0.477606
$448$	5134.46	0.541474
$449$	−4374.02	−0.459739	−0.229870	−	0.973221i	$-0.573830\pi$
$449$	−4374.02	−0.459739	−0.229870	+	0.973221i	$0.573830\pi$
$450$	−18.6500	−0.00195371
$451$	−3283.26	−0.342800
$452$	9234.13	0.960923
$453$	−95.7684	−0.00993288
$454$	6864.01	0.709568
$455$	0	0
$456$	−4889.73	−0.502155
$457$	8968.91	0.918048	0.459024	−	0.888424i	$-0.348199\pi$
$457$	8968.91	0.918048	0.459024	+	0.888424i	$0.348199\pi$
$458$	24666.7	2.51660
$459$	200.083	0.0203466
$460$	−20123.6	−2.03972
$461$	9349.49	0.944575	0.472287	−	0.881445i	$-0.343428\pi$
$461$	9349.49	0.944575	0.472287	+	0.881445i	$0.343428\pi$
$462$	−2553.53	−0.257145
$463$	−12529.4	−1.25764	−0.628821	−	0.777550i	$-0.716462\pi$
$463$	−12529.4	−1.25764	−0.628821	+	0.777550i	$0.716462\pi$
$464$	6816.58	0.682008
$465$	−12863.9	−1.28290
$466$	−4238.50	−0.421341
$467$	−14842.5	−1.47073	−0.735363	−	0.677673i	$-0.762988\pi$
$467$	−14842.5	−1.47073	−0.735363	+	0.677673i	$0.762988\pi$
$468$	0	0
$469$	7444.11	0.732915
$470$	11479.3	1.12660
$471$	−11382.2	−1.11351
$472$	858.031	0.0836739
$473$	1230.82	0.119647
$474$	−16257.9	−1.57542
$475$	23.6548	0.00228496
$476$	803.539	0.0773743
$477$	−8662.86	−0.831541
$478$	13509.4	1.29269
$479$	10474.9	0.999189	0.499595	−	0.866259i	$-0.333482\pi$
$479$	10474.9	0.999189	0.499595	+	0.866259i	$0.333482\pi$
$480$	20785.7	1.97653
$481$	0	0
$482$	12519.9	1.18313
$483$	−10854.2	−1.02253
$484$	1121.66	0.105340
$485$	−2385.19	−0.223311
$486$	−21553.1	−2.01166
$487$	−14509.5	−1.35008	−0.675041	−	0.737780i	$-0.735874\pi$
$487$	−14509.5	−1.35008	−0.675041	+	0.737780i	$0.735874\pi$
$488$	1027.37	0.0953012
$489$	4363.59	0.403535
$490$	13111.6	1.20882
$491$	−6113.34	−0.561896	−0.280948	−	0.959723i	$-0.590649\pi$
$491$	−6113.34	−0.561896	−0.280948	+	0.959723i	$0.590649\pi$
$492$	−19855.3	−1.81940
$493$	1453.38	0.132772
$494$	0	0
$495$	−3010.42	−0.273350
$496$	−8380.17	−0.758630
$497$	3273.61	0.295455
$498$	−13504.0	−1.21512
$499$	6673.94	0.598731	0.299365	−	0.954139i	$-0.403225\pi$
$499$	6673.94	0.598731	0.299365	+	0.954139i	$0.403225\pi$
$500$	12964.6	1.15959
$501$	−7569.29	−0.674992
$502$	24007.9	2.13451
$503$	−21506.6	−1.90642	−0.953211	−	0.302304i	$-0.902244\pi$
$503$	−21506.6	−1.90642	−0.953211	+	0.302304i	$0.902244\pi$
$504$	−1006.30	−0.0889371
$505$	−19273.6	−1.69834
$506$	8882.45	0.780381
$507$	0	0
$508$	21053.5	1.83878
$509$	164.953	0.0143643	0.00718214	−	0.999974i	$-0.497714\pi$
$509$	164.953	0.0143643	0.00718214	+	0.999974i	$0.497714\pi$
$510$	3710.10	0.322129
$511$	2386.25	0.206578
$512$	15745.9	1.35913
$513$	2319.94	0.199664
$514$	−32968.6	−2.82915
$515$	−15828.6	−1.35435
$516$	7443.29	0.635024
$517$	−2719.75	−0.231362
$518$	2948.48	0.250095
$519$	23744.1	2.00819
$520$	0	0
$521$	6259.09	0.526325	0.263163	−	0.964751i	$-0.415234\pi$
$521$	6259.09	0.526325	0.263163	+	0.964751i	$0.415234\pi$
$522$	−13286.3	−1.11404
$523$	−11948.5	−0.998988	−0.499494	−	0.866317i	$-0.666481\pi$
$523$	−11948.5	−0.998988	−0.499494	+	0.866317i	$0.666481\pi$
$524$	−17774.0	−1.48180
$525$	10.2338	0.000850746 0
$526$	15307.3	1.26888
$527$	−1786.75	−0.147689
$528$	−4122.73	−0.339808
$529$	25589.3	2.10318
$530$	16418.9	1.34565
$531$	3982.77	0.325494
$532$	9316.93	0.759286
$533$	0	0
$534$	8438.27	0.683819
$535$	3273.38	0.264525
$536$	−5046.76	−0.406692
$537$	−14749.0	−1.18523
$538$	−10767.1	−0.862830
$539$	−3106.46	−0.248247
$540$	1860.83	0.148291
$541$	−6559.40	−0.521277	−0.260638	−	0.965436i	$-0.583933\pi$
$541$	−6559.40	−0.521277	−0.260638	+	0.965436i	$0.583933\pi$
$542$	−25815.7	−2.04591
$543$	−33686.0	−2.66226
$544$	2887.07	0.227541
$545$	2018.46	0.158645
$546$	0	0
$547$	−7968.14	−0.622839	−0.311420	−	0.950273i	$-0.600804\pi$
$547$	−7968.14	−0.622839	−0.311420	+	0.950273i	$0.600804\pi$
$548$	−12008.6	−0.936096
$549$	4768.82	0.370725
$550$	−8.37479	−0.000649277 0
$551$	16851.7	1.30292
$552$	7358.65	0.567400
$553$	4243.72	0.326332
$554$	−18402.0	−1.41124
$555$	7307.39	0.558886
$556$	26469.5	2.01899
$557$	12153.6	0.924530	0.462265	−	0.886742i	$-0.347037\pi$
$557$	12153.6	0.924530	0.462265	+	0.886742i	$0.347037\pi$
$558$	16334.0	1.23920
$559$	0	0
$560$	−4542.10	−0.342747
$561$	−879.015	−0.0661534
$562$	−16262.3	−1.22062
$563$	23955.4	1.79325	0.896623	−	0.442794i	$-0.146013\pi$
$563$	23955.4	1.79325	0.896623	+	0.442794i	$0.146013\pi$
$564$	−16447.4	−1.22795
$565$	−11129.0	−0.828676
$566$	13008.3	0.966043
$567$	6152.14	0.455671
$568$	−2219.35	−0.163947
$569$	−2272.47	−0.167429	−0.0837143	−	0.996490i	$-0.526678\pi$
$569$	−2272.47	−0.167429	−0.0837143	+	0.996490i	$0.526678\pi$
$570$	43018.1	3.16110
$571$	5926.97	0.434389	0.217195	−	0.976128i	$-0.430309\pi$
$571$	5926.97	0.434389	0.217195	+	0.976128i	$0.430309\pi$
$572$	0	0
$573$	−11650.8	−0.849421
$574$	9655.46	0.702110
$575$	−35.5985	−0.00258184
$576$	−16157.6	−1.16881
$577$	23464.6	1.69297	0.846487	−	0.532410i	$-0.178713\pi$
$577$	23464.6	1.69297	0.846487	+	0.532410i	$0.178713\pi$
$578$	−19901.7	−1.43218
$579$	37074.5	2.66108
$580$	13516.8	0.967680
$581$	3524.89	0.251699
$582$	6366.75	0.453454
$583$	−3890.06	−0.276346
$584$	−1617.77	−0.114629
$585$	0	0
$586$	2284.01	0.161010
$587$	−19561.0	−1.37541	−0.687707	−	0.725988i	$-0.741383\pi$
$587$	−19561.0	−1.37541	−0.687707	+	0.725988i	$0.741383\pi$
$588$	−18786.1	−1.31756
$589$	−20717.2	−1.44930
$590$	−7548.64	−0.526733
$591$	6444.08	0.448518
$592$	4760.39	0.330492
$593$	−26822.1	−1.85742	−0.928710	−	0.370807i	$-0.879081\pi$
$593$	−26822.1	−1.85742	−0.928710	+	0.370807i	$0.879081\pi$
$594$	−821.358	−0.0567352
$595$	−968.430	−0.0667256
$596$	−5830.68	−0.400728
$597$	−241.598	−0.0165627
$598$	0	0
$599$	−13911.1	−0.948902	−0.474451	−	0.880282i	$-0.657353\pi$
$599$	−13911.1	−0.948902	−0.474451	+	0.880282i	$0.657353\pi$
$600$	−6.93808	−0.000472076 0
$601$	11982.3	0.813261	0.406630	−	0.913593i	$-0.366704\pi$
$601$	11982.3	0.813261	0.406630	+	0.913593i	$0.366704\pi$
$602$	−3619.62	−0.245057
$603$	−23425.8	−1.58205
$604$	−123.712	−0.00833403
$605$	−1351.83	−0.0908424
$606$	51446.8	3.44865
$607$	−21834.1	−1.46000	−0.729999	−	0.683448i	$-0.760479\pi$
$607$	−21834.1	−1.46000	−0.729999	+	0.683448i	$0.760479\pi$
$608$	33475.2	2.23290
$609$	7290.63	0.485108
$610$	−9038.45	−0.599928
$611$	0	0
$612$	−2528.65	−0.167018
$613$	−28040.3	−1.84753	−0.923765	−	0.382961i	$-0.874904\pi$
$613$	−28040.3	−1.84753	−0.923765	+	0.382961i	$0.874904\pi$
$614$	−38668.6	−2.54159
$615$	23929.7	1.56900
$616$	−451.880	−0.0295565
$617$	26865.7	1.75295	0.876476	−	0.481445i	$-0.159888\pi$
$617$	26865.7	1.75295	0.876476	+	0.481445i	$0.159888\pi$
$618$	42251.1	2.75014
$619$	−3647.24	−0.236826	−0.118413	−	0.992964i	$-0.537781\pi$
$619$	−3647.24	−0.236826	−0.118413	+	0.992964i	$0.537781\pi$
$620$	−16617.3	−1.07640
$621$	−3491.32	−0.225607
$622$	−41706.3	−2.68854
$623$	−2202.60	−0.141646
$624$	0	0
$625$	−15602.1	−0.998532
$626$	16503.5	1.05369
$627$	−10192.1	−0.649174
$628$	−14703.3	−0.934276
$629$	1014.97	0.0643397
$630$	8853.09	0.559866
$631$	−29088.6	−1.83518	−0.917590	−	0.397528i	$-0.869868\pi$
$631$	−29088.6	−1.83518	−0.917590	+	0.397528i	$0.869868\pi$
$632$	−2877.05	−0.181080
$633$	33212.0	2.08540
$634$	−5830.97	−0.365264
$635$	−25373.8	−1.58572
$636$	−23524.8	−1.46670
$637$	0	0
$638$	−5966.23	−0.370227
$639$	−10301.7	−0.637761
$640$	7451.70	0.460241
$641$	−12306.8	−0.758330	−0.379165	−	0.925329i	$-0.623789\pi$
$641$	−12306.8	−0.758330	−0.379165	+	0.925329i	$0.623789\pi$
$642$	−8737.61	−0.537143
$643$	−15877.3	−0.973778	−0.486889	−	0.873464i	$-0.661868\pi$
$643$	−15877.3	−0.973778	−0.486889	+	0.873464i	$0.661868\pi$
$644$	−14021.2	−0.857940
$645$	−8970.70	−0.547629
$646$	5975.08	0.363911
$647$	−15202.0	−0.923731	−0.461866	−	0.886950i	$-0.652820\pi$
$647$	−15202.0	−0.923731	−0.461866	+	0.886950i	$0.652820\pi$
$648$	−4170.87	−0.252851
$649$	1788.46	0.108172
$650$	0	0
$651$	−8962.95	−0.539610
$652$	5636.79	0.338579
$653$	−11161.0	−0.668858	−0.334429	−	0.942421i	$-0.608543\pi$
$653$	−11161.0	−0.668858	−0.334429	+	0.942421i	$0.608543\pi$
$654$	−5387.86	−0.322144
$655$	21421.4	1.27787
$656$	15589.0	0.927815
$657$	−7509.28	−0.445913
$658$	7998.27	0.473868
$659$	−25379.2	−1.50020	−0.750101	−	0.661323i	$-0.769995\pi$
$659$	−25379.2	−1.50020	−0.750101	+	0.661323i	$0.769995\pi$
$660$	−8175.08	−0.482143
$661$	−15953.5	−0.938758	−0.469379	−	0.882997i	$-0.655522\pi$
$661$	−15953.5	−0.938758	−0.469379	+	0.882997i	$0.655522\pi$
$662$	9551.31	0.560759
$663$	0	0
$664$	−2389.72	−0.139667
$665$	−11228.8	−0.654789
$666$	−9278.58	−0.539846
$667$	−25360.5	−1.47220
$668$	−9777.84	−0.566342
$669$	−13849.4	−0.800374
$670$	44399.6	2.56016
$671$	2141.44	0.123203
$672$	14482.5	0.831362
$673$	12238.2	0.700965	0.350483	−	0.936569i	$-0.386018\pi$
$673$	12238.2	0.700965	0.350483	+	0.936569i	$0.386018\pi$
$674$	27077.1	1.54743
$675$	3.29178	0.000187705 0
$676$	0	0
$677$	−11536.2	−0.654905	−0.327453	−	0.944868i	$-0.606190\pi$
$677$	−11536.2	−0.654905	−0.327453	+	0.944868i	$0.606190\pi$
$678$	29706.6	1.68271
$679$	−1661.89	−0.0939283
$680$	656.551	0.0370258
$681$	11852.8	0.666959
$682$	7334.76	0.411822
$683$	−331.665	−0.0185810	−0.00929048	−	0.999957i	$-0.502957\pi$
$683$	−331.665	−0.0185810	−0.00929048	+	0.999957i	$0.502957\pi$
$684$	−29319.4	−1.63897
$685$	14472.8	0.807266
$686$	20231.2	1.12599
$687$	42594.6	2.36548
$688$	−5843.95	−0.323835
$689$	0	0
$690$	−64738.7	−3.57183
$691$	6796.51	0.374170	0.187085	−	0.982344i	$-0.440096\pi$
$691$	6796.51	0.374170	0.187085	+	0.982344i	$0.440096\pi$
$692$	30672.1	1.68494
$693$	−2097.52	−0.114976
$694$	43061.4	2.35531
$695$	−31901.2	−1.74112
$696$	−4942.71	−0.269185
$697$	3323.76	0.180626
$698$	645.185	0.0349866
$699$	−7319.05	−0.396040
$700$	13.2199	0.000713805 0
$701$	−8381.34	−0.451582	−0.225791	−	0.974176i	$-0.572497\pi$
$701$	−8381.34	−0.451582	−0.225791	+	0.974176i	$0.572497\pi$
$702$	0	0
$703$	11768.5	0.631375
$704$	−7255.58	−0.388430
$705$	19822.5	1.05895
$706$	−21429.5	−1.14237
$707$	−13428.9	−0.714352
$708$	10815.6	0.574116
$709$	−1621.90	−0.0859124	−0.0429562	−	0.999077i	$-0.513678\pi$
$709$	−1621.90	−0.0859124	−0.0429562	+	0.999077i	$0.513678\pi$
$710$	19525.1	1.03206
$711$	−13354.6	−0.704410
$712$	1493.26	0.0785989
$713$	31177.6	1.63760
$714$	2585.02	0.135493
$715$	0	0
$716$	−19052.5	−0.994448
$717$	23328.1	1.21507
$718$	−202.957	−0.0105491
$719$	16139.1	0.837118	0.418559	−	0.908190i	$-0.362535\pi$
$719$	16139.1	0.837118	0.418559	+	0.908190i	$0.362535\pi$
$720$	14293.5	0.739844
$721$	−11028.6	−0.569663
$722$	40776.2	2.10185
$723$	21619.5	1.11208
$724$	−43514.9	−2.23373
$725$	23.9110	0.00122487
$726$	3608.43	0.184464
$727$	−4250.84	−0.216857	−0.108428	−	0.994104i	$-0.534582\pi$
$727$	−4250.84	−0.216857	−0.108428	+	0.994104i	$0.534582\pi$
$728$	0	0
$729$	−15878.8	−0.806728
$730$	14232.5	0.721601
$731$	−1246.00	−0.0630438
$732$	12950.2	0.653896
$733$	−25348.0	−1.27729	−0.638643	−	0.769503i	$-0.720504\pi$
$733$	−25348.0	−1.27729	−0.638643	+	0.769503i	$0.720504\pi$
$734$	39208.7	1.97169
$735$	22641.1	1.13623
$736$	−50377.5	−2.52301
$737$	−10519.4	−0.525762
$738$	−30384.8	−1.51555
$739$	−1476.69	−0.0735059	−0.0367530	−	0.999324i	$-0.511701\pi$
$739$	−1476.69	−0.0735059	−0.0367530	+	0.999324i	$0.511701\pi$
$740$	9439.53	0.468924
$741$	0	0
$742$	11439.9	0.566002
$743$	−11223.5	−0.554174	−0.277087	−	0.960845i	$-0.589369\pi$
$743$	−11223.5	−0.554174	−0.277087	+	0.960845i	$0.589369\pi$
$744$	6076.47	0.299428
$745$	7027.17	0.345578
$746$	−18928.1	−0.928964
$747$	−11092.5	−0.543310
$748$	−1135.49	−0.0555050
$749$	2280.74	0.111264
$750$	41707.6	2.03059
$751$	−3823.76	−0.185793	−0.0928967	−	0.995676i	$-0.529613\pi$
$751$	−3823.76	−0.185793	−0.0928967	+	0.995676i	$0.529613\pi$
$752$	12913.4	0.626200
$753$	41456.8	2.00634
$754$	0	0
$755$	149.098	0.00718706
$756$	1296.54	0.0623738
$757$	1210.99	0.0581427	0.0290714	−	0.999577i	$-0.490745\pi$
$757$	1210.99	0.0581427	0.0290714	+	0.999577i	$0.490745\pi$
$758$	34704.0	1.66294
$759$	15338.2	0.733521
$760$	7612.62	0.363341
$761$	35356.7	1.68420	0.842101	−	0.539320i	$-0.181319\pi$
$761$	35356.7	1.68420	0.842101	+	0.539320i	$0.181319\pi$
$762$	67730.2	3.21995
$763$	1406.37	0.0667287
$764$	−15050.2	−0.712693
$765$	3047.55	0.144032
$766$	−44092.2	−2.07978
$767$	0	0
$768$	17975.9	0.844596
$769$	18680.1	0.875972	0.437986	−	0.898982i	$-0.355692\pi$
$769$	18680.1	0.875972	0.437986	+	0.898982i	$0.355692\pi$
$770$	3975.48	0.186060
$771$	−56930.3	−2.65927
$772$	47892.0	2.23274
$773$	26899.2	1.25161	0.625807	−	0.779978i	$-0.284770\pi$
$773$	26899.2	1.25161	0.625807	+	0.779978i	$0.284770\pi$
$774$	11390.6	0.528973
$775$	−29.3958	−0.00136249
$776$	1126.68	0.0521205
$777$	5091.45	0.235077
$778$	821.872	0.0378734
$779$	38538.5	1.77251
$780$	0	0
$781$	−4625.98	−0.211947
$782$	−8992.00	−0.411193
$783$	2345.07	0.107032
$784$	14749.5	0.671899
$785$	17720.5	0.805697
$786$	−57179.9	−2.59483
$787$	12613.5	0.571313	0.285657	−	0.958332i	$-0.407788\pi$
$787$	12613.5	0.571313	0.285657	+	0.958332i	$0.407788\pi$
$788$	8324.32	0.376322
$789$	26432.7	1.19269
$790$	25311.2	1.13992
$791$	−7754.19	−0.348555
$792$	1422.02	0.0637997
$793$	0	0
$794$	−28212.0	−1.26097
$795$	28352.2	1.26484
$796$	−312.091	−0.0138967
$797$	6998.03	0.311020	0.155510	−	0.987834i	$-0.450298\pi$
$797$	6998.03	0.311020	0.155510	+	0.987834i	$0.450298\pi$
$798$	29973.0	1.32961
$799$	2753.29	0.121908
$800$	47.4983	0.00209915
$801$	6931.37	0.305753
$802$	43235.9	1.90363
$803$	−3372.04	−0.148190
$804$	−63615.1	−2.79046
$805$	16898.5	0.739866
$806$	0	0
$807$	−18592.6	−0.811018
$808$	9104.20	0.396392
$809$	−11996.1	−0.521336	−0.260668	−	0.965428i	$-0.583943\pi$
$809$	−11996.1	−0.521336	−0.260668	+	0.965428i	$0.583943\pi$
$810$	36693.8	1.59171
$811$	−33568.2	−1.45344	−0.726719	−	0.686935i	$-0.758956\pi$
$811$	−33568.2	−1.45344	−0.726719	+	0.686935i	$0.758956\pi$
$812$	9417.87	0.407023
$813$	−44578.7	−1.92305
$814$	−4166.55	−0.179407
$815$	−6793.49	−0.291982
$816$	4173.57	0.179049
$817$	−14447.2	−0.618659
$818$	−32788.1	−1.40148
$819$	0	0
$820$	30911.8	1.31645
$821$	37248.2	1.58340	0.791701	−	0.610909i	$-0.209196\pi$
$821$	37248.2	1.58340	0.791701	+	0.610909i	$0.209196\pi$
$822$	−38632.1	−1.63923
$823$	44135.3	1.86933	0.934665	−	0.355529i	$-0.115699\pi$
$823$	44135.3	1.86933	0.934665	+	0.355529i	$0.115699\pi$
$824$	7476.89	0.316104
$825$	−14.4616	−0.000610289 0
$826$	−5259.54	−0.221553
$827$	6716.66	0.282420	0.141210	−	0.989980i	$-0.454901\pi$
$827$	6716.66	0.282420	0.141210	+	0.989980i	$0.454901\pi$
$828$	44123.3	1.85192
$829$	−34024.0	−1.42546	−0.712728	−	0.701441i	$-0.752540\pi$
$829$	−34024.0	−1.42546	−0.712728	+	0.701441i	$0.752540\pi$
$830$	21023.8	0.879215
$831$	−31776.6	−1.32649
$832$	0	0
$833$	3144.78	0.130804
$834$	85153.5	3.53552
$835$	11784.3	0.488399
$836$	−13165.9	−0.544679
$837$	−2882.99	−0.119057
$838$	−30429.2	−1.25437
$839$	9241.26	0.380267	0.190133	−	0.981758i	$-0.439108\pi$
$839$	9241.26	0.380267	0.190133	+	0.981758i	$0.439108\pi$
$840$	3293.48	0.135281
$841$	−7354.71	−0.301558
$842$	−50085.0	−2.04993
$843$	−28081.8	−1.14732
$844$	42902.5	1.74972
$845$	0	0
$846$	−25169.7	−1.02288
$847$	−941.891	−0.0382099
$848$	18470.0	0.747953
$849$	22462.8	0.908034
$850$	8.47808	0.000342113 0
$851$	−17710.6	−0.713410
$852$	−27975.2	−1.12490
$853$	−47127.6	−1.89170	−0.945849	−	0.324607i	$-0.894768\pi$
$853$	−47127.6	−1.89170	−0.945849	+	0.324607i	$0.894768\pi$
$854$	−6297.57	−0.252340
$855$	35335.9	1.41341
$856$	−1546.24	−0.0617398
$857$	24176.7	0.963665	0.481833	−	0.876263i	$-0.339971\pi$
$857$	24176.7	0.963665	0.481833	+	0.876263i	$0.339971\pi$
$858$	0	0
$859$	−797.373	−0.0316717	−0.0158359	−	0.999875i	$-0.505041\pi$
$859$	−797.373	−0.0316717	−0.0158359	+	0.999875i	$0.505041\pi$
$860$	−11588.1	−0.459480
$861$	16673.1	0.659950
$862$	−14782.1	−0.584083
$863$	27776.1	1.09561	0.547805	−	0.836606i	$-0.315464\pi$
$863$	27776.1	1.09561	0.547805	+	0.836606i	$0.315464\pi$
$864$	4658.39	0.183428
$865$	−36966.2	−1.45305
$866$	22595.3	0.886626
$867$	−34366.2	−1.34618
$868$	−11578.1	−0.452751
$869$	−5996.87	−0.234096
$870$	43484.1	1.69454
$871$	0	0
$872$	−953.453	−0.0370275
$873$	5229.78	0.202751
$874$	−104261.	−4.03511
$875$	−10886.7	−0.420616
$876$	−20392.1	−0.786514
$877$	−10727.4	−0.413043	−0.206522	−	0.978442i	$-0.566214\pi$
$877$	−10727.4	−0.413043	−0.206522	+	0.978442i	$0.566214\pi$
$878$	−9155.76	−0.351927
$879$	3944.03	0.151341
$880$	6418.50	0.245872
$881$	10155.1	0.388349	0.194174	−	0.980967i	$-0.437797\pi$
$881$	10155.1	0.388349	0.194174	+	0.980967i	$0.437797\pi$
$882$	−28748.6	−1.09752
$883$	−40449.8	−1.54161	−0.770806	−	0.637070i	$-0.780146\pi$
$883$	−40449.8	−1.54161	−0.770806	+	0.637070i	$0.780146\pi$
$884$	0	0
$885$	−13035.0	−0.495104
$886$	60449.3	2.29214
$887$	−15719.7	−0.595056	−0.297528	−	0.954713i	$-0.596162\pi$
$887$	−15719.7	−0.595056	−0.297528	+	0.954713i	$0.596162\pi$
$888$	−3451.77	−0.130443
$889$	−17679.3	−0.666980
$890$	−13137.2	−0.494786
$891$	−8693.68	−0.326879
$892$	−17890.4	−0.671541
$893$	31924.0	1.19630
$894$	−18757.6	−0.701730
$895$	22962.2	0.857587
$896$	5192.00	0.193585
$897$	0	0
$898$	−18177.2	−0.675478
$899$	−20941.6	−0.776910
$900$	−41.6015	−0.00154080
$901$	3938.04	0.145610
$902$	−13644.3	−0.503664
$903$	−6250.36	−0.230342
$904$	5256.98	0.193412
$905$	52444.4	1.92631
$906$	−397.986	−0.0145940
$907$	51799.5	1.89633	0.948166	−	0.317776i	$-0.102936\pi$
$907$	51799.5	1.89633	0.948166	+	0.317776i	$0.102936\pi$
$908$	15311.2	0.559602
$909$	42259.5	1.54198
$910$	0	0
$911$	−13518.0	−0.491628	−0.245814	−	0.969317i	$-0.579055\pi$
$911$	−13518.0	−0.491628	−0.245814	+	0.969317i	$0.579055\pi$
$912$	48392.1	1.75704
$913$	−4981.08	−0.180558
$914$	37272.2	1.34885
$915$	−15607.6	−0.563904
$916$	55022.7	1.98472
$917$	14925.4	0.537493
$918$	831.488	0.0298945
$919$	−3727.19	−0.133785	−0.0668926	−	0.997760i	$-0.521308\pi$
$919$	−3727.19	−0.133785	−0.0668926	+	0.997760i	$0.521308\pi$
$920$	−11456.4	−0.410549
$921$	−66773.0	−2.38898
$922$	38853.7	1.38783
$923$	0	0
$924$	−5696.01	−0.202798
$925$	16.6984	0.000593556 0
$926$	−52068.3	−1.84781
$927$	34705.9	1.22966
$928$	33837.9	1.19697
$929$	27859.8	0.983909	0.491955	−	0.870621i	$-0.336283\pi$
$929$	27859.8	0.983909	0.491955	+	0.870621i	$0.336283\pi$
$930$	−53458.6	−1.88492
$931$	36463.3	1.28360
$932$	−9454.58	−0.332291
$933$	−72018.5	−2.52710
$934$	−61681.1	−2.16089
$935$	1368.50	0.0478661
$936$	0	0
$937$	−6058.26	−0.211222	−0.105611	−	0.994408i	$-0.533680\pi$
$937$	−6058.26	−0.211222	−0.105611	+	0.994408i	$0.533680\pi$
$938$	30935.5	1.07685
$939$	28498.2	0.990419
$940$	25606.3	0.888496
$941$	50684.6	1.75587	0.877934	−	0.478781i	$-0.158921\pi$
$941$	50684.6	1.75587	0.877934	+	0.478781i	$0.158921\pi$
$942$	−47301.2	−1.63605
$943$	−57997.3	−2.00281
$944$	−8491.64	−0.292775
$945$	−1562.60	−0.0537897
$946$	5114.93	0.175794
$947$	−26010.4	−0.892529	−0.446265	−	0.894901i	$-0.647246\pi$
$947$	−26010.4	−0.892529	−0.446265	+	0.894901i	$0.647246\pi$
$948$	−36265.5	−1.24246
$949$	0	0
$950$	98.3022	0.00335721
$951$	−10068.9	−0.343331
$952$	457.454	0.0155737
$953$	16634.8	0.565428	0.282714	−	0.959204i	$-0.408765\pi$
$953$	16634.8	0.565428	0.282714	+	0.959204i	$0.408765\pi$
$954$	−36000.3	−1.22175
$955$	18138.6	0.614609
$956$	30134.7	1.01948
$957$	−10302.5	−0.347996
$958$	43530.7	1.46807
$959$	10084.0	0.339550
$960$	52881.5	1.77786
$961$	−4045.77	−0.135805
$962$	0	0
$963$	−7177.25	−0.240170
$964$	27927.5	0.933076
$965$	−57719.8	−1.92546
$966$	−45106.9	−1.50237
$967$	26428.0	0.878870	0.439435	−	0.898274i	$-0.355179\pi$
$967$	26428.0	0.878870	0.439435	+	0.898274i	$0.355179\pi$
$968$	638.559	0.0212025
$969$	10317.8	0.342058
$970$	−9912.13	−0.328103
$971$	−49893.0	−1.64896	−0.824481	−	0.565889i	$-0.808533\pi$
$971$	−49893.0	−1.64896	−0.824481	+	0.565889i	$0.808533\pi$
$972$	−48077.2	−1.58650
$973$	−22227.2	−0.732346
$974$	−60297.4	−1.98363
$975$	0	0
$976$	−10167.6	−0.333459
$977$	−1030.29	−0.0337379	−0.0168690	−	0.999858i	$-0.505370\pi$
$977$	−1030.29	−0.0337379	−0.0168690	+	0.999858i	$0.505370\pi$
$978$	18133.8	0.592899
$979$	3112.53	0.101611
$980$	29247.3	0.953337
$981$	−4425.70	−0.144038
$982$	−25405.2	−0.825574
$983$	−1300.89	−0.0422095	−0.0211047	−	0.999777i	$-0.506718\pi$
$983$	−1300.89	−0.0422095	−0.0211047	+	0.999777i	$0.506718\pi$
$984$	−11303.6	−0.366204
$985$	−10032.5	−0.324531
$986$	6039.81	0.195078
$987$	13811.4	0.445413
$988$	0	0
$989$	21741.9	0.699041
$990$	−12510.4	−0.401624
$991$	44003.6	1.41052	0.705258	−	0.708951i	$-0.250831\pi$
$991$	44003.6	1.41052	0.705258	+	0.708951i	$0.250831\pi$
$992$	−41599.7	−1.33144
$993$	16493.2	0.527086
$994$	13604.2	0.434102
$995$	376.134	0.0119842
$996$	−30122.7	−0.958306
$997$	−53373.6	−1.69545	−0.847723	−	0.530439i	$-0.822027\pi$
$997$	−53373.6	−1.69545	−0.847723	+	0.530439i	$0.822027\pi$
$998$	27734.9	0.879694
$999$	1637.70	0.0518663

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.g.1.15		17
13.3	even	3		143.4.e.b.100.3	✓	34
13.9	even	3		143.4.e.b.133.3	yes	34
13.12	even	2		1859.4.a.h.1.3		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.b.100.3	✓	34	13.3	even	3
143.4.e.b.133.3	yes	34	13.9	even	3
1859.4.a.g.1.15		17	1.1	even	1	trivial
1859.4.a.h.1.3		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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+4.15571 q^{2} +7.17608 q^{3} +9.26990 q^{4} -11.1721 q^{5} +29.8217 q^{6} -7.78423 q^{7} +5.27734 q^{8} +24.4962 q^{9} +O(q^{10})\)	\(q+4.15571 q^{2} +7.17608 q^{3} +9.26990 q^{4} -11.1721 q^{5} +29.8217 q^{6} -7.78423 q^{7} +5.27734 q^{8} +24.4962 q^{9} -46.4282 q^{10} +11.0000 q^{11} +66.5216 q^{12} -32.3490 q^{14} -80.1722 q^{15} -52.2281 q^{16} -11.1357 q^{17} +101.799 q^{18} -129.117 q^{19} -103.565 q^{20} -55.8602 q^{21} +45.7128 q^{22} +194.310 q^{23} +37.8707 q^{24} -0.183205 q^{25} -17.9678 q^{27} -72.1590 q^{28} -130.515 q^{29} -333.172 q^{30} +160.453 q^{31} -259.264 q^{32} +78.9369 q^{33} -46.2766 q^{34} +86.9665 q^{35} +227.077 q^{36} -91.1462 q^{37} -536.571 q^{38} -58.9593 q^{40} -298.478 q^{41} -232.139 q^{42} +111.893 q^{43} +101.969 q^{44} -273.675 q^{45} +807.495 q^{46} -247.250 q^{47} -374.793 q^{48} -282.406 q^{49} -0.761344 q^{50} -79.9105 q^{51} -353.642 q^{53} -74.6689 q^{54} -122.894 q^{55} -41.0800 q^{56} -926.552 q^{57} -542.384 q^{58} +162.588 q^{59} -743.189 q^{60} +194.676 q^{61} +666.797 q^{62} -190.684 q^{63} -659.598 q^{64} +328.039 q^{66} -956.307 q^{67} -103.227 q^{68} +1394.38 q^{69} +361.407 q^{70} -420.544 q^{71} +129.275 q^{72} -306.549 q^{73} -378.777 q^{74} -1.31469 q^{75} -1196.90 q^{76} -85.6265 q^{77} -545.170 q^{79} +583.500 q^{80} -790.335 q^{81} -1240.39 q^{82} -452.825 q^{83} -517.819 q^{84} +124.409 q^{85} +464.994 q^{86} -936.590 q^{87} +58.0508 q^{88} +282.957 q^{89} -1137.31 q^{90} +1801.23 q^{92} +1151.43 q^{93} -1027.50 q^{94} +1442.51 q^{95} -1860.50 q^{96} +213.494 q^{97} -1173.60 q^{98} +269.458 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9}+O(q^{10}) \) 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9	\( 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9} + 2 q^{10} + 187 q^{11} - 127 q^{12} - 148 q^{15} + 126 q^{16} - 74 q^{17} + 90 q^{18} - 159 q^{19} - 222 q^{20} - 184 q^{21} - 215 q^{23} + 214 q^{24} + 95 q^{25} - 192 q^{27} - 358 q^{28} - 157 q^{29} + 829 q^{30} - 394 q^{31} - 553 q^{32} - 66 q^{33} - 702 q^{34} + 58 q^{35} - 700 q^{36} + 88 q^{37} - 1318 q^{38} + 733 q^{40} - 512 q^{41} + 337 q^{42} + 927 q^{43} + 550 q^{44} - 1482 q^{45} - 1361 q^{46} - 143 q^{47} - 178 q^{48} + 1835 q^{49} - 583 q^{50} - 568 q^{51} + 106 q^{53} - 67 q^{54} - 264 q^{55} + 2059 q^{56} + 1298 q^{57} - 1690 q^{58} - 266 q^{59} + 37 q^{60} - 624 q^{61} + 643 q^{62} - 2360 q^{63} - 1589 q^{64} + 176 q^{66} - 676 q^{67} - 413 q^{68} + 764 q^{69} - 1061 q^{70} - 763 q^{71} - 1366 q^{72} - 2374 q^{73} - 1649 q^{74} + 2420 q^{75} - 2101 q^{76} - 682 q^{77} + 2164 q^{79} - 1013 q^{80} + 537 q^{81} + 3152 q^{82} + 777 q^{83} - 3381 q^{84} - 1690 q^{85} + 2894 q^{86} - 4200 q^{87} - 231 q^{88} - 1687 q^{89} - 5399 q^{90} + 5542 q^{92} - 4310 q^{93} + 1777 q^{94} + 1124 q^{95} - 3465 q^{96} - 2047 q^{97} + 1553 q^{98} + 1485 q^{99}+O(q^{100}) \) 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

Properties

Related objects

Downloads

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