LMFDB - Embedded newform 1859.4.a.q.1.10

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:	$0$
Dimension:	$51$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-4.08285 q^{2} -3.72122 q^{3} +8.66965 q^{4} +2.40264 q^{5} +15.1932 q^{6} +5.44341 q^{7} -2.73408 q^{8} -13.1525 q^{9} +O(q^{10})$	\(q-4.08285 q^{2} -3.72122 q^{3} +8.66965 q^{4} +2.40264 q^{5} +15.1932 q^{6} +5.44341 q^{7} -2.73408 q^{8} -13.1525 q^{9} -9.80961 q^{10} +11.0000 q^{11} -32.2617 q^{12} -22.2246 q^{14} -8.94076 q^{15} -58.1944 q^{16} -100.248 q^{17} +53.6996 q^{18} -70.6645 q^{19} +20.8300 q^{20} -20.2562 q^{21} -44.9113 q^{22} +59.2830 q^{23} +10.1741 q^{24} -119.227 q^{25} +149.416 q^{27} +47.1925 q^{28} -122.463 q^{29} +36.5038 q^{30} -173.561 q^{31} +259.471 q^{32} -40.9335 q^{33} +409.297 q^{34} +13.0786 q^{35} -114.028 q^{36} -182.752 q^{37} +288.512 q^{38} -6.56902 q^{40} -382.742 q^{41} +82.7028 q^{42} +227.455 q^{43} +95.3662 q^{44} -31.6007 q^{45} -242.043 q^{46} +327.087 q^{47} +216.554 q^{48} -313.369 q^{49} +486.787 q^{50} +373.045 q^{51} +660.795 q^{53} -610.045 q^{54} +26.4290 q^{55} -14.8827 q^{56} +262.958 q^{57} +499.996 q^{58} +69.7551 q^{59} -77.5133 q^{60} -305.440 q^{61} +708.622 q^{62} -71.5944 q^{63} -593.828 q^{64} +167.125 q^{66} -452.399 q^{67} -869.115 q^{68} -220.605 q^{69} -53.3978 q^{70} -299.219 q^{71} +35.9600 q^{72} +688.583 q^{73} +746.151 q^{74} +443.672 q^{75} -612.636 q^{76} +59.8775 q^{77} +521.515 q^{79} -139.820 q^{80} -200.895 q^{81} +1562.68 q^{82} -764.260 q^{83} -175.614 q^{84} -240.860 q^{85} -928.663 q^{86} +455.711 q^{87} -30.0749 q^{88} -180.923 q^{89} +129.021 q^{90} +513.963 q^{92} +645.858 q^{93} -1335.45 q^{94} -169.781 q^{95} -965.551 q^{96} -203.903 q^{97} +1279.44 q^{98} -144.677 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9}+O(q^{10}) $ 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9} + 212 q^{10} + 561 q^{11} + 209 q^{12} + 280 q^{14} + 284 q^{15} + 1246 q^{16} + 164 q^{17} - 189 q^{18} + 26 q^{19} + 438 q^{20} + 134 q^{21} + 373 q^{23} - 354 q^{24} + 2048 q^{25} + 1470 q^{27} - 1245 q^{28} + 898 q^{29} + 427 q^{30} + 767 q^{31} + 1127 q^{32} + 231 q^{33} + 206 q^{34} + 54 q^{35} + 3415 q^{36} + 395 q^{37} + 1577 q^{38} + 3253 q^{40} - 354 q^{41} + 942 q^{42} + 484 q^{43} + 2574 q^{44} + 1452 q^{45} - 2117 q^{46} + 1925 q^{47} + 1780 q^{48} + 4535 q^{49} - 1093 q^{50} + 230 q^{51} + 1387 q^{53} - 5271 q^{54} + 451 q^{55} + 2568 q^{56} - 5738 q^{57} + 3695 q^{58} + 1145 q^{59} - 1590 q^{60} + 5382 q^{61} - 395 q^{62} + 710 q^{63} + 9839 q^{64} - 803 q^{66} - 210 q^{67} + 1742 q^{68} + 7028 q^{69} - 6747 q^{70} + 3693 q^{71} - 12481 q^{72} + 968 q^{73} + 1735 q^{74} - 727 q^{75} - 2801 q^{76} + 44 q^{77} + 4234 q^{79} + 2390 q^{80} + 7743 q^{81} + 4770 q^{82} - 2798 q^{83} + 14821 q^{84} - 1802 q^{85} + 6558 q^{86} + 1896 q^{87} - 231 q^{88} + 3927 q^{89} + 1927 q^{90} + 1984 q^{92} - 1332 q^{93} + 7590 q^{94} + 4944 q^{95} - 7280 q^{96} + 3913 q^{97} - 15201 q^{98} + 6534 q^{99}+O(q^{100}) \) 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9 + 212 * q^10 + 561 * q^11 + 209 * q^12 + 280 * q^14 + 284 * q^15 + 1246 * q^16 + 164 * q^17 - 189 * q^18 + 26 * q^19 + 438 * q^20 + 134 * q^21 + 373 * q^23 - 354 * q^24 + 2048 * q^25 + 1470 * q^27 - 1245 * q^28 + 898 * q^29 + 427 * q^30 + 767 * q^31 + 1127 * q^32 + 231 * q^33 + 206 * q^34 + 54 * q^35 + 3415 * q^36 + 395 * q^37 + 1577 * q^38 + 3253 * q^40 - 354 * q^41 + 942 * q^42 + 484 * q^43 + 2574 * q^44 + 1452 * q^45 - 2117 * q^46 + 1925 * q^47 + 1780 * q^48 + 4535 * q^49 - 1093 * q^50 + 230 * q^51 + 1387 * q^53 - 5271 * q^54 + 451 * q^55 + 2568 * q^56 - 5738 * q^57 + 3695 * q^58 + 1145 * q^59 - 1590 * q^60 + 5382 * q^61 - 395 * q^62 + 710 * q^63 + 9839 * q^64 - 803 * q^66 - 210 * q^67 + 1742 * q^68 + 7028 * q^69 - 6747 * q^70 + 3693 * q^71 - 12481 * q^72 + 968 * q^73 + 1735 * q^74 - 727 * q^75 - 2801 * q^76 + 44 * q^77 + 4234 * q^79 + 2390 * q^80 + 7743 * q^81 + 4770 * q^82 - 2798 * q^83 + 14821 * q^84 - 1802 * q^85 + 6558 * q^86 + 1896 * q^87 - 231 * q^88 + 3927 * q^89 + 1927 * q^90 + 1984 * q^92 - 1332 * q^93 + 7590 * q^94 + 4944 * q^95 - 7280 * q^96 + 3913 * q^97 - 15201 * q^98 + 6534 * 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 $

$2$	−4.08285	−1.44350	−0.721752	−	0.692151i	$-0.756663\pi$
$2$	−4.08285	−1.44350	−0.721752	+	0.692151i	$0.756663\pi$
$3$	−3.72122	−0.716150	−0.358075	−	0.933693i	$-0.616567\pi$
$3$	−3.72122	−0.716150	−0.358075	+	0.933693i	$0.616567\pi$
$4$	8.66965	1.08371
$5$	2.40264	0.214899	0.107449	−	0.994211i	$-0.465732\pi$
$5$	2.40264	0.214899	0.107449	+	0.994211i	$0.465732\pi$
$6$	15.1932	1.03377
$7$	5.44341	0.293917	0.146958	−	0.989143i	$-0.453052\pi$
$7$	5.44341	0.293917	0.146958	+	0.989143i	$0.453052\pi$
$8$	−2.73408	−0.120831
$9$	−13.1525	−0.487129
$10$	−9.80961	−0.310207
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−32.2617	−0.776096
$13$	0	0
$13$	0	0
$14$	−22.2246	−0.424270
$15$	−8.94076	−0.153900
$16$	−58.1944	−0.909287
$17$	−100.248	−1.43022	−0.715109	−	0.699013i	$-0.753623\pi$
$17$	−100.248	−1.43022	−0.715109	+	0.699013i	$0.753623\pi$
$18$	53.6996	0.703174
$19$	−70.6645	−0.853239	−0.426620	−	0.904431i	$-0.640296\pi$
$19$	−70.6645	−0.853239	−0.426620	+	0.904431i	$0.640296\pi$
$20$	20.8300	0.232887
$21$	−20.2562	−0.210488
$22$	−44.9113	−0.435233
$23$	59.2830	0.537450	0.268725	−	0.963217i	$-0.413398\pi$
$23$	59.2830	0.537450	0.268725	+	0.963217i	$0.413398\pi$
$24$	10.1741	0.0865328
$25$	−119.227	−0.953819
$26$	0	0
$27$	149.416	1.06501
$28$	47.1925	0.318519
$29$	−122.463	−0.784163	−0.392082	−	0.919930i	$-0.628245\pi$
$29$	−122.463	−0.784163	−0.392082	+	0.919930i	$0.628245\pi$
$30$	36.5038	0.222155
$31$	−173.561	−1.00556	−0.502781	−	0.864414i	$-0.667690\pi$
$31$	−173.561	−1.00556	−0.502781	+	0.864414i	$0.667690\pi$
$32$	259.471	1.43339
$33$	−40.9335	−0.215927
$34$	409.297	2.06453
$35$	13.0786	0.0631623
$36$	−114.028	−0.527905
$37$	−182.752	−0.812009	−0.406004	−	0.913871i	$-0.633078\pi$
$37$	−182.752	−0.812009	−0.406004	+	0.913871i	$0.633078\pi$
$38$	288.512	1.23165
$39$	0	0
$40$	−6.56902	−0.0259663
$41$	−382.742	−1.45791	−0.728954	−	0.684562i	$-0.759993\pi$
$41$	−382.742	−1.45791	−0.728954	+	0.684562i	$0.759993\pi$
$42$	82.7028	0.303841
$43$	227.455	0.806663	0.403332	−	0.915054i	$-0.367852\pi$
$43$	227.455	0.806663	0.403332	+	0.915054i	$0.367852\pi$
$44$	95.3662	0.326750
$45$	−31.6007	−0.104683
$46$	−242.043	−0.775812
$47$	327.087	1.01512	0.507560	−	0.861617i	$-0.330548\pi$
$47$	327.087	1.01512	0.507560	+	0.861617i	$0.330548\pi$
$48$	216.554	0.651186
$49$	−313.369	−0.913613
$50$	486.787	1.37684
$51$	373.045	1.02425
$52$	0	0
$53$	660.795	1.71259	0.856294	−	0.516488i	$-0.172761\pi$
$53$	660.795	1.71259	0.856294	+	0.516488i	$0.172761\pi$
$54$	−610.045	−1.53734
$55$	26.4290	0.0647944
$56$	−14.8827	−0.0355141
$57$	262.958	0.611047
$58$	499.996	1.13194
$59$	69.7551	0.153921	0.0769605	−	0.997034i	$-0.475478\pi$
$59$	69.7551	0.153921	0.0769605	+	0.997034i	$0.475478\pi$
$60$	−77.5133	−0.166782
$61$	−305.440	−0.641108	−0.320554	−	0.947230i	$-0.603869\pi$
$61$	−305.440	−0.641108	−0.320554	+	0.947230i	$0.603869\pi$
$62$	708.622	1.45153
$63$	−71.5944	−0.143175
$64$	−593.828	−1.15982
$65$	0	0
$66$	167.125	0.311692
$67$	−452.399	−0.824916	−0.412458	−	0.910977i	$-0.635330\pi$
$67$	−452.399	−0.824916	−0.412458	+	0.910977i	$0.635330\pi$
$68$	−869.115	−1.54994
$69$	−220.605	−0.384895
$70$	−53.3978	−0.0911750
$71$	−299.219	−0.500151	−0.250076	−	0.968226i	$-0.580455\pi$
$71$	−299.219	−0.500151	−0.250076	+	0.968226i	$0.580455\pi$
$72$	35.9600	0.0588601
$73$	688.583	1.10401	0.552004	−	0.833842i	$-0.313863\pi$
$73$	688.583	1.10401	0.552004	+	0.833842i	$0.313863\pi$
$74$	746.151	1.17214
$75$	443.672	0.683077
$76$	−612.636	−0.924661
$77$	59.8775	0.0886192
$78$	0	0
$79$	521.515	0.742722	0.371361	−	0.928489i	$-0.378891\pi$
$79$	521.515	0.742722	0.371361	+	0.928489i	$0.378891\pi$
$80$	−139.820	−0.195404
$81$	−200.895	−0.275576
$82$	1562.68	2.10450
$83$	−764.260	−1.01070	−0.505352	−	0.862913i	$-0.668637\pi$
$83$	−764.260	−1.01070	−0.505352	+	0.862913i	$0.668637\pi$
$84$	−175.614	−0.228108
$85$	−240.860	−0.307352
$86$	−928.663	−1.16442
$87$	455.711	0.561578
$88$	−30.0749	−0.0364318
$89$	−180.923	−0.215481	−0.107740	−	0.994179i	$-0.534362\pi$
$89$	−180.923	−0.215481	−0.107740	+	0.994179i	$0.534362\pi$
$90$	129.021	0.151111
$91$	0	0
$92$	513.963	0.582438
$93$	645.858	0.720133
$94$	−1335.45	−1.46533
$95$	−169.781	−0.183360
$96$	−965.551	−1.02652
$97$	−203.903	−0.213435	−0.106717	−	0.994289i	$-0.534034\pi$
$97$	−203.903	−0.213435	−0.106717	+	0.994289i	$0.534034\pi$
$98$	1279.44	1.31880
$99$	−144.677	−0.146875
$100$	−1033.66	−1.03366
$101$	−430.427	−0.424050	−0.212025	−	0.977264i	$-0.568006\pi$
$101$	−430.427	−0.424050	−0.212025	+	0.977264i	$0.568006\pi$
$102$	−1523.09	−1.47851
$103$	625.188	0.598073	0.299037	−	0.954242i	$-0.403335\pi$
$103$	625.188	0.598073	0.299037	+	0.954242i	$0.403335\pi$
$104$	0	0
$105$	−48.6682	−0.0452337
$106$	−2697.93	−2.47213
$107$	−1381.82	−1.24846	−0.624230	−	0.781240i	$-0.714587\pi$
$107$	−1381.82	−1.24846	−0.624230	+	0.781240i	$0.714587\pi$
$108$	1295.39	1.15416
$109$	−239.012	−0.210029	−0.105015	−	0.994471i	$-0.533489\pi$
$109$	−239.012	−0.210029	−0.105015	+	0.994471i	$0.533489\pi$
$110$	−107.906	−0.0935310
$111$	680.063	0.581520
$112$	−316.776	−0.267255
$113$	−960.789	−0.799853	−0.399927	−	0.916547i	$-0.630964\pi$
$113$	−960.789	−0.799853	−0.399927	+	0.916547i	$0.630964\pi$
$114$	−1073.62	−0.882050
$115$	142.436	0.115497
$116$	−1061.71	−0.849802
$117$	0	0
$118$	−284.800	−0.222186
$119$	−545.691	−0.420365
$120$	24.4448	0.0185958
$121$	121.000	0.0909091
$122$	1247.07	0.925443
$123$	1424.27	1.04408
$124$	−1504.71	−1.08973
$125$	−586.790	−0.419873
$126$	292.309	0.206674
$127$	2530.05	1.76776	0.883879	−	0.467716i	$-0.154923\pi$
$127$	2530.05	1.76776	0.883879	+	0.467716i	$0.154923\pi$
$128$	348.737	0.240815
$129$	−846.410	−0.577692
$130$	0	0
$131$	1167.78	0.778854	0.389427	−	0.921057i	$-0.372673\pi$
$131$	1167.78	0.778854	0.389427	+	0.921057i	$0.372673\pi$
$132$	−354.879	−0.234002
$133$	−384.656	−0.250781
$134$	1847.08	1.19077
$135$	358.994	0.228869
$136$	274.086	0.172814
$137$	−2510.21	−1.56541	−0.782705	−	0.622392i	$-0.786161\pi$
$137$	−2510.21	−1.56541	−0.782705	+	0.622392i	$0.786161\pi$
$138$	900.698	0.555598
$139$	200.562	0.122385	0.0611923	−	0.998126i	$-0.480510\pi$
$139$	200.562	0.122385	0.0611923	+	0.998126i	$0.480510\pi$
$140$	113.387	0.0684494
$141$	−1217.17	−0.726977
$142$	1221.66	0.721970
$143$	0	0
$144$	765.401	0.442940
$145$	−294.233	−0.168516
$146$	−2811.38	−1.59364
$147$	1166.12	0.654284
$148$	−1584.40	−0.879979
$149$	669.990	0.368374	0.184187	−	0.982891i	$-0.441035\pi$
$149$	669.990	0.368374	0.184187	+	0.982891i	$0.441035\pi$
$150$	−1811.44	−0.986025
$151$	−1341.20	−0.722816	−0.361408	−	0.932408i	$-0.617704\pi$
$151$	−1341.20	−0.722816	−0.361408	+	0.932408i	$0.617704\pi$
$152$	193.203	0.103097
$153$	1318.51	0.696701
$154$	−244.471	−0.127922
$155$	−417.003	−0.216094
$156$	0	0
$157$	−2310.39	−1.17445	−0.587226	−	0.809423i	$-0.699780\pi$
$157$	−2310.39	−1.17445	−0.587226	+	0.809423i	$0.699780\pi$
$158$	−2129.27	−1.07212
$159$	−2458.97	−1.22647
$160$	623.416	0.308034
$161$	322.702	0.157966
$162$	820.223	0.397795
$163$	1331.43	0.639791	0.319896	−	0.947453i	$-0.396352\pi$
$163$	1331.43	0.639791	0.319896	+	0.947453i	$0.396352\pi$
$164$	−3318.24	−1.57995
$165$	−98.3483	−0.0464025
$166$	3120.36	1.45896
$167$	−2011.79	−0.932199	−0.466100	−	0.884732i	$-0.654341\pi$
$167$	−2011.79	−0.932199	−0.466100	+	0.884732i	$0.654341\pi$
$168$	55.3820	0.0254334
$169$	0	0
$170$	983.394	0.443664
$171$	929.414	0.415638
$172$	1971.95	0.874186
$173$	−1585.76	−0.696895	−0.348447	−	0.937328i	$-0.613291\pi$
$173$	−1585.76	−0.696895	−0.348447	+	0.937328i	$0.613291\pi$
$174$	−1860.60	−0.810641
$175$	−649.003	−0.280343
$176$	−640.138	−0.274160
$177$	−259.574	−0.110231
$178$	738.681	0.311048
$179$	2233.43	0.932596	0.466298	−	0.884628i	$-0.345588\pi$
$179$	2233.43	0.932596	0.466298	+	0.884628i	$0.345588\pi$
$180$	−273.967	−0.113446
$181$	−2398.95	−0.985151	−0.492575	−	0.870270i	$-0.663944\pi$
$181$	−2398.95	−0.985151	−0.492575	+	0.870270i	$0.663944\pi$
$182$	0	0
$183$	1136.61	0.459130
$184$	−162.085	−0.0649404
$185$	−439.088	−0.174499
$186$	−2636.94	−1.03951
$187$	−1102.73	−0.431227
$188$	2835.73	1.10009
$189$	813.335	0.313023
$190$	693.191	0.264681
$191$	−1675.89	−0.634887	−0.317444	−	0.948277i	$-0.602824\pi$
$191$	−1675.89	−0.634887	−0.317444	+	0.948277i	$0.602824\pi$
$192$	2209.77	0.830605
$193$	−4860.94	−1.81294	−0.906472	−	0.422266i	$-0.861235\pi$
$193$	−4860.94	−1.81294	−0.906472	+	0.422266i	$0.861235\pi$
$194$	832.503	0.308094
$195$	0	0
$196$	−2716.80	−0.990088
$197$	−2839.16	−1.02681	−0.513406	−	0.858146i	$-0.671617\pi$
$197$	−2839.16	−1.02681	−0.513406	+	0.858146i	$0.671617\pi$
$198$	590.696	0.212015
$199$	3477.95	1.23892	0.619461	−	0.785027i	$-0.287351\pi$
$199$	3477.95	1.23892	0.619461	+	0.785027i	$0.287351\pi$
$200$	325.978	0.115250
$201$	1683.48	0.590764
$202$	1757.37	0.612119
$203$	−666.614	−0.230479
$204$	3234.17	1.10999
$205$	−919.591	−0.313303
$206$	−2552.55	−0.863322
$207$	−779.719	−0.261808
$208$	0	0
$209$	−777.309	−0.257261
$210$	198.705	0.0652950
$211$	2715.00	0.885822	0.442911	−	0.896566i	$-0.353946\pi$
$211$	2715.00	0.885822	0.442911	+	0.896566i	$0.353946\pi$
$212$	5728.86	1.85594
$213$	1113.46	0.358183
$214$	5641.75	1.80216
$215$	546.491	0.173351
$216$	−408.517	−0.128685
$217$	−944.762	−0.295551
$218$	975.850	0.303179
$219$	−2562.37	−0.790635
$220$	229.130	0.0702181
$221$	0	0
$222$	−2776.59	−0.839427
$223$	72.1313	0.0216604	0.0108302	−	0.999941i	$-0.496553\pi$
$223$	72.1313	0.0216604	0.0108302	+	0.999941i	$0.496553\pi$
$224$	1412.41	0.421297
$225$	1568.14	0.464633
$226$	3922.76	1.15459
$227$	−471.056	−0.137732	−0.0688658	−	0.997626i	$-0.521938\pi$
$227$	−471.056	−0.137732	−0.0688658	+	0.997626i	$0.521938\pi$
$228$	2279.76	0.662196
$229$	−2955.89	−0.852972	−0.426486	−	0.904494i	$-0.640249\pi$
$229$	−2955.89	−0.852972	−0.426486	+	0.904494i	$0.640249\pi$
$230$	−581.543	−0.166721
$231$	−222.818	−0.0634646
$232$	334.823	0.0947509
$233$	−4498.53	−1.26484	−0.632421	−	0.774625i	$-0.717939\pi$
$233$	−4498.53	−1.26484	−0.632421	+	0.774625i	$0.717939\pi$
$234$	0	0
$235$	785.873	0.218148
$236$	604.753	0.166805
$237$	−1940.67	−0.531900
$238$	2227.97	0.606799
$239$	6613.07	1.78981	0.894903	−	0.446260i	$-0.147244\pi$
$239$	6613.07	1.78981	0.894903	+	0.446260i	$0.147244\pi$
$240$	520.302	0.139939
$241$	3284.05	0.877777	0.438889	−	0.898541i	$-0.355372\pi$
$241$	3284.05	0.877777	0.438889	+	0.898541i	$0.355372\pi$
$242$	−494.025	−0.131228
$243$	−3286.67	−0.867654
$244$	−2648.06	−0.694773
$245$	−752.913	−0.196334
$246$	−5815.07	−1.50714
$247$	0	0
$248$	474.529	0.121503
$249$	2843.98	0.723816
$250$	2395.78	0.606088
$251$	−3051.90	−0.767466	−0.383733	−	0.923444i	$-0.625362\pi$
$251$	−3051.90	−0.767466	−0.383733	+	0.923444i	$0.625362\pi$
$252$	−620.699	−0.155160
$253$	652.113	0.162047
$254$	−10329.8	−2.55177
$255$	896.293	0.220110
$256$	3326.78	0.812203
$257$	6617.65	1.60622	0.803108	−	0.595834i	$-0.203178\pi$
$257$	6617.65	1.60622	0.803108	+	0.595834i	$0.203178\pi$
$258$	3455.76	0.833901
$259$	−994.797	−0.238663
$260$	0	0
$261$	1610.69	0.381989
$262$	−4767.89	−1.12428
$263$	2749.56	0.644659	0.322330	−	0.946627i	$-0.395534\pi$
$263$	2749.56	0.644659	0.322330	+	0.946627i	$0.395534\pi$
$264$	111.916	0.0260906
$265$	1587.65	0.368033
$266$	1570.49	0.362004
$267$	673.255	0.154317
$268$	−3922.14	−0.893967
$269$	1537.21	0.348422	0.174211	−	0.984708i	$-0.444263\pi$
$269$	1537.21	0.348422	0.174211	+	0.984708i	$0.444263\pi$
$270$	−1465.72	−0.330373
$271$	−3433.92	−0.769726	−0.384863	−	0.922974i	$-0.625751\pi$
$271$	−3433.92	−0.769726	−0.384863	+	0.922974i	$0.625751\pi$
$272$	5833.87	1.30048
$273$	0	0
$274$	10248.8	2.25968
$275$	−1311.50	−0.287587
$276$	−1912.57	−0.417113
$277$	−6354.59	−1.37838	−0.689188	−	0.724582i	$-0.742033\pi$
$277$	−6354.59	−1.37838	−0.689188	+	0.724582i	$0.742033\pi$
$278$	−818.865	−0.176663
$279$	2282.75	0.489838
$280$	−35.7579	−0.00763193
$281$	6260.96	1.32917	0.664586	−	0.747212i	$-0.268608\pi$
$281$	6260.96	1.32917	0.664586	+	0.747212i	$0.268608\pi$
$282$	4969.50	1.04940
$283$	8055.42	1.69203	0.846016	−	0.533158i	$-0.178995\pi$
$283$	8055.42	1.69203	0.846016	+	0.533158i	$0.178995\pi$
$284$	−2594.12	−0.542017
$285$	631.794	0.131313
$286$	0	0
$287$	−2083.42	−0.428504
$288$	−3412.70	−0.698247
$289$	5136.66	1.04552
$290$	1201.31	0.243253
$291$	758.767	0.152851
$292$	5969.77	1.19642
$293$	4393.84	0.876077	0.438039	−	0.898956i	$-0.355673\pi$
$293$	4393.84	0.876077	0.438039	+	0.898956i	$0.355673\pi$
$294$	−4761.08	−0.944462
$295$	167.596	0.0330774
$296$	499.661	0.0981155
$297$	1643.58	0.321112
$298$	−2735.47	−0.531750
$299$	0	0
$300$	3846.48	0.740255
$301$	1238.13	0.237092
$302$	5475.91	1.04339
$303$	1601.72	0.303684
$304$	4112.27	0.775839
$305$	−733.862	−0.137773
$306$	−5383.28	−1.00569
$307$	101.199	0.0188134	0.00940670	−	0.999956i	$-0.497006\pi$
$307$	101.199	0.0188134	0.00940670	+	0.999956i	$0.497006\pi$
$308$	519.117	0.0960372
$309$	−2326.46	−0.428310
$310$	1702.56	0.311932
$311$	5672.13	1.03420	0.517101	−	0.855924i	$-0.327011\pi$
$311$	5672.13	1.03420	0.517101	+	0.855924i	$0.327011\pi$
$312$	0	0
$313$	−6778.97	−1.22418	−0.612092	−	0.790786i	$-0.709672\pi$
$313$	−6778.97	−1.22418	−0.612092	+	0.790786i	$0.709672\pi$
$314$	9432.96	1.69533
$315$	−172.016	−0.0307682
$316$	4521.35	0.804893
$317$	7823.33	1.38613	0.693063	−	0.720877i	$-0.256261\pi$
$317$	7823.33	1.38613	0.693063	+	0.720877i	$0.256261\pi$
$318$	10039.6	1.77042
$319$	−1347.09	−0.236434
$320$	−1426.75	−0.249244
$321$	5142.05	0.894085
$322$	−1317.54	−0.228024
$323$	7083.97	1.22032
$324$	−1741.69	−0.298643
$325$	0	0
$326$	−5436.05	−0.923542
$327$	889.418	0.150413
$328$	1046.45	0.176160
$329$	1780.47	0.298360
$330$	401.541	0.0669822
$331$	−4372.87	−0.726147	−0.363073	−	0.931761i	$-0.618273\pi$
$331$	−4372.87	−0.726147	−0.363073	+	0.931761i	$0.618273\pi$
$332$	−6625.87	−1.09531
$333$	2403.65	0.395553
$334$	8213.85	1.34563
$335$	−1086.95	−0.177273
$336$	1178.79	0.191394
$337$	5052.78	0.816744	0.408372	−	0.912816i	$-0.366097\pi$
$337$	5052.78	0.816744	0.408372	+	0.912816i	$0.366097\pi$
$338$	0	0
$339$	3575.31	0.572815
$340$	−2088.17	−0.333079
$341$	−1909.17	−0.303188
$342$	−3794.66	−0.599975
$343$	−3572.89	−0.562443
$344$	−621.880	−0.0974696
$345$	−530.035	−0.0827134
$346$	6474.40	1.00597
$347$	−163.088	−0.0252306	−0.0126153	−	0.999920i	$-0.504016\pi$
$347$	−163.088	−0.0252306	−0.0126153	+	0.999920i	$0.504016\pi$
$348$	3950.85	0.608586
$349$	10421.1	1.59837	0.799185	−	0.601086i	$-0.205265\pi$
$349$	10421.1	1.59837	0.799185	+	0.601086i	$0.205265\pi$
$350$	2649.78	0.404677
$351$	0	0
$352$	2854.19	0.432184
$353$	3374.95	0.508868	0.254434	−	0.967090i	$-0.418111\pi$
$353$	3374.95	0.508868	0.254434	+	0.967090i	$0.418111\pi$
$354$	1059.80	0.159118
$355$	−718.914	−0.107482
$356$	−1568.54	−0.233518
$357$	2030.64	0.301044
$358$	−9118.77	−1.34621
$359$	−9697.39	−1.42565	−0.712825	−	0.701342i	$-0.752585\pi$
$359$	−9697.39	−1.42565	−0.712825	+	0.701342i	$0.752585\pi$
$360$	86.3989	0.0126490
$361$	−1865.53	−0.271983
$362$	9794.54	1.42207
$363$	−450.268	−0.0651045
$364$	0	0
$365$	1654.42	0.237250
$366$	−4640.61	−0.662756
$367$	10199.9	1.45076	0.725379	−	0.688349i	$-0.241664\pi$
$367$	10199.9	1.45076	0.725379	+	0.688349i	$0.241664\pi$
$368$	−3449.94	−0.488697
$369$	5034.01	0.710190
$370$	1792.73	0.251891
$371$	3596.98	0.503358
$372$	5599.36	0.780412
$373$	7652.38	1.06227	0.531133	−	0.847289i	$-0.321767\pi$
$373$	7652.38	1.06227	0.531133	+	0.847289i	$0.321767\pi$
$374$	4502.27	0.622478
$375$	2183.58	0.300692
$376$	−894.284	−0.122657
$377$	0	0
$378$	−3320.72	−0.451851
$379$	4814.28	0.652488	0.326244	−	0.945286i	$-0.394217\pi$
$379$	4814.28	0.652488	0.326244	+	0.945286i	$0.394217\pi$
$380$	−1471.94	−0.198708
$381$	−9414.87	−1.26598
$382$	6842.43	0.916463
$383$	−4925.21	−0.657092	−0.328546	−	0.944488i	$-0.606559\pi$
$383$	−4925.21	−0.657092	−0.328546	+	0.944488i	$0.606559\pi$
$384$	−1297.73	−0.172459
$385$	143.864	0.0190441
$386$	19846.5	2.61699
$387$	−2991.60	−0.392949
$388$	−1767.76	−0.231301
$389$	−356.413	−0.0464547	−0.0232273	−	0.999730i	$-0.507394\pi$
$389$	−356.413	−0.0464547	−0.0232273	+	0.999730i	$0.507394\pi$
$390$	0	0
$391$	−5943.00	−0.768671
$392$	856.778	0.110392
$393$	−4345.59	−0.557776
$394$	11591.9	1.48221
$395$	1253.01	0.159610
$396$	−1254.30	−0.159169
$397$	4423.20	0.559179	0.279590	−	0.960120i	$-0.409802\pi$
$397$	4423.20	0.559179	0.279590	+	0.960120i	$0.409802\pi$
$398$	−14200.0	−1.78839
$399$	1431.39	0.179597
$400$	6938.36	0.867295
$401$	−8057.07	−1.00337	−0.501684	−	0.865051i	$-0.667286\pi$
$401$	−8057.07	−1.00337	−0.501684	+	0.865051i	$0.667286\pi$
$402$	−6873.39	−0.852770
$403$	0	0
$404$	−3731.65	−0.459546
$405$	−482.677	−0.0592208
$406$	2721.68	0.332697
$407$	−2010.28	−0.244830
$408$	−1019.94	−0.123761
$409$	−111.831	−0.0135200	−0.00676001	−	0.999977i	$-0.502152\pi$
$409$	−111.831	−0.0135200	−0.00676001	+	0.999977i	$0.502152\pi$
$410$	3754.55	0.452254
$411$	9341.04	1.12107
$412$	5420.16	0.648136
$413$	379.706	0.0452400
$414$	3183.48	0.377921
$415$	−1836.24	−0.217199
$416$	0	0
$417$	−746.337	−0.0876458
$418$	3173.64	0.371358
$419$	−8764.79	−1.02193	−0.510964	−	0.859602i	$-0.670712\pi$
$419$	−8764.79	−1.02193	−0.510964	+	0.859602i	$0.670712\pi$
$420$	−421.937	−0.0490200
$421$	3521.87	0.407709	0.203854	−	0.979001i	$-0.434653\pi$
$421$	3521.87	0.407709	0.203854	+	0.979001i	$0.434653\pi$
$422$	−11084.9	−1.27869
$423$	−4302.01	−0.494494
$424$	−1806.67	−0.206933
$425$	11952.3	1.36417
$426$	−4546.09	−0.517039
$427$	−1662.64	−0.188432
$428$	−11979.9	−1.35297
$429$	0	0
$430$	−2231.24	−0.250233
$431$	−7973.79	−0.891146	−0.445573	−	0.895246i	$-0.647000\pi$
$431$	−7973.79	−0.891146	−0.445573	+	0.895246i	$0.647000\pi$
$432$	−8695.19	−0.968397
$433$	17120.0	1.90008	0.950041	−	0.312125i	$-0.101041\pi$
$433$	17120.0	1.90008	0.950041	+	0.312125i	$0.101041\pi$
$434$	3857.32	0.426630
$435$	1094.91	0.120682
$436$	−2072.15	−0.227610
$437$	−4189.20	−0.458574
$438$	10461.8	1.14129
$439$	9338.99	1.01532	0.507660	−	0.861557i	$-0.330510\pi$
$439$	9338.99	1.01532	0.507660	+	0.861557i	$0.330510\pi$
$440$	−72.2592	−0.00782914
$441$	4121.59	0.445048
$442$	0	0
$443$	−9812.99	−1.05244	−0.526218	−	0.850350i	$-0.676390\pi$
$443$	−9812.99	−1.05244	−0.526218	+	0.850350i	$0.676390\pi$
$444$	5895.91	0.630197
$445$	−434.693	−0.0463065
$446$	−294.501	−0.0312669
$447$	−2493.18	−0.263811
$448$	−3232.45	−0.340890
$449$	164.243	0.0172631	0.00863153	−	0.999963i	$-0.497252\pi$
$449$	164.243	0.0172631	0.00863153	+	0.999963i	$0.497252\pi$
$450$	−6402.46	−0.670700
$451$	−4210.16	−0.439576
$452$	−8329.71	−0.866806
$453$	4990.90	0.517644
$454$	1923.25	0.198816
$455$	0	0
$456$	−718.950	−0.0738332
$457$	−1243.73	−0.127306	−0.0636532	−	0.997972i	$-0.520275\pi$
$457$	−1243.73	−0.127306	−0.0636532	+	0.997972i	$0.520275\pi$
$458$	12068.4	1.23127
$459$	−14978.7	−1.52319
$460$	1234.87	0.125165
$461$	−9897.91	−0.999982	−0.499991	−	0.866031i	$-0.666663\pi$
$461$	−9897.91	−0.999982	−0.499991	+	0.866031i	$0.666663\pi$
$462$	909.731	0.0916115
$463$	9756.03	0.979269	0.489634	−	0.871928i	$-0.337130\pi$
$463$	9756.03	0.979269	0.489634	+	0.871928i	$0.337130\pi$
$464$	7126.63	0.713029
$465$	1551.76	0.154755
$466$	18366.8	1.82581
$467$	3356.38	0.332580	0.166290	−	0.986077i	$-0.446821\pi$
$467$	3356.38	0.332580	0.166290	+	0.986077i	$0.446821\pi$
$468$	0	0
$469$	−2462.60	−0.242457
$470$	−3208.60	−0.314897
$471$	8597.47	0.841084
$472$	−190.716	−0.0185984
$473$	2502.00	0.243218
$474$	7923.48	0.767801
$475$	8425.14	0.813835
$476$	−4730.95	−0.455552
$477$	−8691.10	−0.834252
$478$	−27000.2	−2.58359
$479$	14928.2	1.42398	0.711992	−	0.702188i	$-0.247793\pi$
$479$	14928.2	1.42398	0.711992	+	0.702188i	$0.247793\pi$
$480$	−2319.87	−0.220598
$481$	0	0
$482$	−13408.3	−1.26708
$483$	−1200.85	−0.113127
$484$	1049.03	0.0985188
$485$	−489.904	−0.0458668
$486$	13419.0	1.25246
$487$	4313.54	0.401366	0.200683	−	0.979656i	$-0.435684\pi$
$487$	4313.54	0.401366	0.200683	+	0.979656i	$0.435684\pi$
$488$	835.099	0.0774655
$489$	−4954.57	−0.458187
$490$	3074.03	0.283409
$491$	6023.11	0.553603	0.276801	−	0.960927i	$-0.410726\pi$
$491$	6023.11	0.553603	0.276801	+	0.960927i	$0.410726\pi$
$492$	12347.9	1.13148
$493$	12276.6	1.12152
$494$	0	0
$495$	−347.608	−0.0315632
$496$	10100.2	0.914344
$497$	−1628.77	−0.147003
$498$	−11611.6	−1.04483
$499$	5563.71	0.499130	0.249565	−	0.968358i	$-0.419712\pi$
$499$	5563.71	0.499130	0.249565	+	0.968358i	$0.419712\pi$
$500$	−5087.27	−0.455019
$501$	7486.34	0.667595
$502$	12460.4	1.10784
$503$	−7702.04	−0.682737	−0.341369	−	0.939929i	$-0.610890\pi$
$503$	−7702.04	−0.682737	−0.341369	+	0.939929i	$0.610890\pi$
$504$	195.745	0.0173000
$505$	−1034.16	−0.0911278
$506$	−2662.48	−0.233916
$507$	0	0
$508$	21934.6	1.91573
$509$	−7788.20	−0.678204	−0.339102	−	0.940750i	$-0.610123\pi$
$509$	−7788.20	−0.678204	−0.339102	+	0.940750i	$0.610123\pi$
$510$	−3659.43	−0.317730
$511$	3748.24	0.324486
$512$	−16372.6	−1.41323
$513$	−10558.4	−0.908706
$514$	−27018.8	−2.31858
$515$	1502.10	0.128525
$516$	−7338.08	−0.626048
$517$	3597.96	0.306070
$518$	4061.60	0.344511
$519$	5900.95	0.499081
$520$	0	0
$521$	9423.23	0.792398	0.396199	−	0.918165i	$-0.370329\pi$
$521$	9423.23	0.792398	0.396199	+	0.918165i	$0.370329\pi$
$522$	−6576.19	−0.551403
$523$	7344.62	0.614069	0.307034	−	0.951698i	$-0.400663\pi$
$523$	7344.62	0.614069	0.307034	+	0.951698i	$0.400663\pi$
$524$	10124.3	0.844049
$525$	2415.09	0.200768
$526$	−11226.1	−0.930569
$527$	17399.1	1.43817
$528$	2382.10	0.196340
$529$	−8652.53	−0.711147
$530$	−6482.14	−0.531257
$531$	−917.454	−0.0749795
$532$	−3334.83	−0.271773
$533$	0	0
$534$	−2748.80	−0.222757
$535$	−3320.01	−0.268292
$536$	1236.90	0.0996751
$537$	−8311.10	−0.667878
$538$	−6276.21	−0.502949
$539$	−3447.06	−0.275465
$540$	3112.35	0.248026
$541$	−2646.68	−0.210332	−0.105166	−	0.994455i	$-0.533537\pi$
$541$	−2646.68	−0.210332	−0.105166	+	0.994455i	$0.533537\pi$
$542$	14020.2	1.11110
$543$	8927.02	0.705516
$544$	−26011.5	−2.05006
$545$	−574.260	−0.0451350
$546$	0	0
$547$	−9084.19	−0.710076	−0.355038	−	0.934852i	$-0.615532\pi$
$547$	−9084.19	−0.710076	−0.355038	+	0.934852i	$0.615532\pi$
$548$	−21762.6	−1.69645
$549$	4017.30	0.312303
$550$	5354.66	0.415133
$551$	8653.75	0.669079
$552$	603.153	0.0465071
$553$	2838.82	0.218298
$554$	25944.8	1.98969
$555$	1633.95	0.124968
$556$	1738.81	0.132629
$557$	−2155.59	−0.163977	−0.0819885	−	0.996633i	$-0.526127\pi$
$557$	−2155.59	−0.163977	−0.0819885	+	0.996633i	$0.526127\pi$
$558$	−9320.14	−0.707084
$559$	0	0
$560$	−761.098	−0.0574326
$561$	4103.50	0.308823
$562$	−25562.5	−1.91867
$563$	−20793.0	−1.55652	−0.778260	−	0.627942i	$-0.783898\pi$
$563$	−20793.0	−1.55652	−0.778260	+	0.627942i	$0.783898\pi$
$564$	−10552.4	−0.787830
$565$	−2308.43	−0.171887
$566$	−32889.1	−2.44246
$567$	−1093.55	−0.0809963
$568$	818.089	0.0604335
$569$	11666.7	0.859569	0.429785	−	0.902931i	$-0.358590\pi$
$569$	11666.7	0.859569	0.429785	+	0.902931i	$0.358590\pi$
$570$	−2579.52	−0.189551
$571$	8042.95	0.589469	0.294735	−	0.955579i	$-0.404769\pi$
$571$	8042.95	0.589469	0.294735	+	0.955579i	$0.404769\pi$
$572$	0	0
$573$	6236.38	0.454675
$574$	8506.30	0.618547
$575$	−7068.15	−0.512630
$576$	7810.31	0.564982
$577$	24482.8	1.76644	0.883218	−	0.468962i	$-0.155372\pi$
$577$	24482.8	1.76644	0.883218	+	0.468962i	$0.155372\pi$
$578$	−20972.2	−1.50922
$579$	18088.7	1.29834
$580$	−2550.90	−0.182621
$581$	−4160.18	−0.297063
$582$	−3097.93	−0.220642
$583$	7268.75	0.516365
$584$	−1882.64	−0.133398
$585$	0	0
$586$	−17939.4	−1.26462
$587$	26632.0	1.87261	0.936304	−	0.351192i	$-0.114223\pi$
$587$	26632.0	1.87261	0.936304	+	0.351192i	$0.114223\pi$
$588$	10109.8	0.709052
$589$	12264.6	0.857984
$590$	−684.271	−0.0477474
$591$	10565.2	0.735352
$592$	10635.2	0.738349
$593$	−22347.4	−1.54755	−0.773775	−	0.633460i	$-0.781634\pi$
$593$	−22347.4	−1.54755	−0.773775	+	0.633460i	$0.781634\pi$
$594$	−6710.49	−0.463527
$595$	−1311.10	−0.0903358
$596$	5808.58	0.399209
$597$	−12942.2	−0.887254
$598$	0	0
$599$	−10289.7	−0.701878	−0.350939	−	0.936398i	$-0.614138\pi$
$599$	−10289.7	−0.701878	−0.350939	+	0.936398i	$0.614138\pi$
$600$	−1213.04	−0.0825366
$601$	10481.1	0.711366	0.355683	−	0.934607i	$-0.384248\pi$
$601$	10481.1	0.711366	0.355683	+	0.934607i	$0.384248\pi$
$602$	−5055.09	−0.342243
$603$	5950.18	0.401841
$604$	−11627.7	−0.783320
$605$	290.719	0.0195362
$606$	−6539.56	−0.438369
$607$	1735.60	0.116056	0.0580278	−	0.998315i	$-0.481519\pi$
$607$	1735.60	0.116056	0.0580278	+	0.998315i	$0.481519\pi$
$608$	−18335.4	−1.22303
$609$	2480.62	0.165057
$610$	2996.25	0.198876
$611$	0	0
$612$	11431.0	0.755019
$613$	−7617.89	−0.501931	−0.250966	−	0.967996i	$-0.580748\pi$
$613$	−7617.89	−0.501931	−0.250966	+	0.967996i	$0.580748\pi$
$614$	−413.179	−0.0271572
$615$	3422.00	0.224372
$616$	−163.710	−0.0107079
$617$	21555.9	1.40649	0.703247	−	0.710945i	$-0.251733\pi$
$617$	21555.9	1.40649	0.703247	+	0.710945i	$0.251733\pi$
$618$	9498.60	0.618268
$619$	−4672.82	−0.303419	−0.151710	−	0.988425i	$-0.548478\pi$
$619$	−4672.82	−0.303419	−0.151710	+	0.988425i	$0.548478\pi$
$620$	−3615.27	−0.234182
$621$	8857.85	0.572389
$622$	−23158.4	−1.49288
$623$	−984.839	−0.0633334
$624$	0	0
$625$	13493.6	0.863589
$626$	27677.5	1.76712
$627$	2892.54	0.184238
$628$	−20030.3	−1.27276
$629$	18320.6	1.16135
$630$	702.314	0.0444140
$631$	25672.3	1.61965	0.809824	−	0.586672i	$-0.199562\pi$
$631$	25672.3	1.61965	0.809824	+	0.586672i	$0.199562\pi$
$632$	−1425.87	−0.0897435
$633$	−10103.1	−0.634381
$634$	−31941.5	−2.00088
$635$	6078.79	0.379889
$636$	−21318.4	−1.32913
$637$	0	0
$638$	5499.96	0.341294
$639$	3935.47	0.243638
$640$	837.888	0.0517507
$641$	20387.6	1.25626	0.628130	−	0.778108i	$-0.283821\pi$
$641$	20387.6	1.25626	0.628130	+	0.778108i	$0.283821\pi$
$642$	−20994.2	−1.29062
$643$	8941.27	0.548382	0.274191	−	0.961675i	$-0.411590\pi$
$643$	8941.27	0.548382	0.274191	+	0.961675i	$0.411590\pi$
$644$	2797.71	0.171188
$645$	−2033.62	−0.124145
$646$	−28922.8	−1.76154
$647$	−19721.9	−1.19837	−0.599186	−	0.800610i	$-0.704509\pi$
$647$	−19721.9	−1.19837	−0.599186	+	0.800610i	$0.704509\pi$
$648$	549.263	0.0332980
$649$	767.306	0.0464090
$650$	0	0
$651$	3515.67	0.211659
$652$	11543.1	0.693346
$653$	−10054.0	−0.602514	−0.301257	−	0.953543i	$-0.597406\pi$
$653$	−10054.0	−0.602514	−0.301257	+	0.953543i	$0.597406\pi$
$654$	−3631.36	−0.217121
$655$	2805.77	0.167375
$656$	22273.4	1.32566
$657$	−9056.58	−0.537794
$658$	−7269.40	−0.430685
$659$	−26823.9	−1.58560	−0.792801	−	0.609481i	$-0.791378\pi$
$659$	−26823.9	−1.58560	−0.792801	+	0.609481i	$0.791378\pi$
$660$	−852.646	−0.0502867
$661$	−6272.06	−0.369070	−0.184535	−	0.982826i	$-0.559078\pi$
$661$	−6272.06	−0.369070	−0.184535	+	0.982826i	$0.559078\pi$
$662$	17853.8	1.04820
$663$	0	0
$664$	2089.55	0.122124
$665$	−924.189	−0.0538925
$666$	−9813.74	−0.570983
$667$	−7259.95	−0.421449
$668$	−17441.6	−1.01023
$669$	−268.417	−0.0155121
$670$	4437.86	0.255895
$671$	−3359.84	−0.193301
$672$	−5255.89	−0.301712
$673$	−8136.78	−0.466047	−0.233024	−	0.972471i	$-0.574862\pi$
$673$	−8136.78	−0.466047	−0.233024	+	0.972471i	$0.574862\pi$
$674$	−20629.7	−1.17897
$675$	−17814.5	−1.01582
$676$	0	0
$677$	−16500.6	−0.936737	−0.468369	−	0.883533i	$-0.655158\pi$
$677$	−16500.6	−0.936737	−0.468369	+	0.883533i	$0.655158\pi$
$678$	−14597.5	−0.826861
$679$	−1109.93	−0.0627320
$680$	658.531	0.0371375
$681$	1752.91	0.0986365
$682$	7794.84	0.437654
$683$	−22315.3	−1.25018	−0.625088	−	0.780554i	$-0.714937\pi$
$683$	−22315.3	−1.25018	−0.625088	+	0.780554i	$0.714937\pi$
$684$	8057.70	0.450429
$685$	−6031.12	−0.336405
$686$	14587.6	0.811889
$687$	10999.5	0.610856
$688$	−13236.6	−0.733488
$689$	0	0
$690$	2164.05	0.119397
$691$	−18892.1	−1.04007	−0.520037	−	0.854144i	$-0.674082\pi$
$691$	−18892.1	−1.04007	−0.520037	+	0.854144i	$0.674082\pi$
$692$	−13747.9	−0.755229
$693$	−787.539	−0.0431690
$694$	665.863	0.0364205
$695$	481.879	0.0263003
$696$	−1245.95	−0.0678558
$697$	38369.1	2.08513
$698$	−42547.9	−2.30725
$699$	16740.0	0.905817
$700$	−5626.63	−0.303810
$701$	1788.03	0.0963380	0.0481690	−	0.998839i	$-0.484661\pi$
$701$	1788.03	0.0963380	0.0481690	+	0.998839i	$0.484661\pi$
$702$	0	0
$703$	12914.1	0.692838
$704$	−6532.10	−0.349699
$705$	−2924.41	−0.156226
$706$	−13779.4	−0.734554
$707$	−2342.99	−0.124635
$708$	−2250.42	−0.119458
$709$	24386.5	1.29175	0.645877	−	0.763442i	$-0.276492\pi$
$709$	24386.5	1.29175	0.645877	+	0.763442i	$0.276492\pi$
$710$	2935.22	0.155150
$711$	−6859.22	−0.361802
$712$	494.659	0.0260367
$713$	−10289.2	−0.540439
$714$	−8290.79	−0.434559
$715$	0	0
$716$	19363.1	1.01066
$717$	−24608.7	−1.28177
$718$	39593.0	2.05793
$719$	33698.7	1.74791	0.873957	−	0.486004i	$-0.161546\pi$
$719$	33698.7	1.74791	0.873957	+	0.486004i	$0.161546\pi$
$720$	1838.98	0.0951872
$721$	3403.15	0.175784
$722$	7616.68	0.392609
$723$	−12220.7	−0.628620
$724$	−20798.0	−1.06761
$725$	14600.9	0.747949
$726$	1838.38	0.0939787
$727$	−10961.7	−0.559214	−0.279607	−	0.960115i	$-0.590204\pi$
$727$	−10961.7	−0.559214	−0.279607	+	0.960115i	$0.590204\pi$
$728$	0	0
$729$	17654.6	0.896946
$730$	−6754.73	−0.342471
$731$	−22801.9	−1.15370
$732$	9854.02	0.497562
$733$	−31807.6	−1.60279	−0.801393	−	0.598138i	$-0.795907\pi$
$733$	−31807.6	−1.60279	−0.801393	+	0.598138i	$0.795907\pi$
$734$	−41644.5	−2.09418
$735$	2801.76	0.140605
$736$	15382.2	0.770376
$737$	−4976.39	−0.248722
$738$	−20553.1	−1.02516
$739$	−39144.5	−1.94851	−0.974257	−	0.225440i	$-0.927618\pi$
$739$	−39144.5	−1.94851	−0.974257	+	0.225440i	$0.927618\pi$
$740$	−3806.74	−0.189106
$741$	0	0
$742$	−14685.9	−0.726600
$743$	35157.0	1.73591	0.867957	−	0.496639i	$-0.165433\pi$
$743$	35157.0	1.73591	0.867957	+	0.496639i	$0.165433\pi$
$744$	−1765.83	−0.0870140
$745$	1609.74	0.0791631
$746$	−31243.5	−1.53339
$747$	10051.9	0.492344
$748$	−9560.26	−0.467323
$749$	−7521.80	−0.366943
$750$	−8915.22	−0.434050
$751$	−18045.8	−0.876829	−0.438415	−	0.898773i	$-0.644460\pi$
$751$	−18045.8	−0.876829	−0.438415	+	0.898773i	$0.644460\pi$
$752$	−19034.6	−0.923034
$753$	11356.8	0.549621
$754$	0	0
$755$	−3222.42	−0.155332
$756$	7051.33	0.339225
$757$	37222.4	1.78715	0.893575	−	0.448915i	$-0.148189\pi$
$757$	37222.4	1.78715	0.893575	+	0.448915i	$0.148189\pi$
$758$	−19656.0	−0.941870
$759$	−2426.66	−0.116050
$760$	464.196	0.0221555
$761$	21814.7	1.03913	0.519567	−	0.854430i	$-0.326093\pi$
$761$	21814.7	1.03913	0.519567	+	0.854430i	$0.326093\pi$
$762$	38439.5	1.82745
$763$	−1301.04	−0.0617311
$764$	−14529.4	−0.688032
$765$	3167.91	0.149720
$766$	20108.9	0.948515
$767$	0	0
$768$	−12379.7	−0.581659
$769$	−23768.5	−1.11458	−0.557291	−	0.830317i	$-0.688159\pi$
$769$	−23768.5	−1.11458	−0.557291	+	0.830317i	$0.688159\pi$
$770$	−587.375	−0.0274903
$771$	−24625.7	−1.15029
$772$	−42142.7	−1.96470
$773$	−27596.8	−1.28407	−0.642036	−	0.766675i	$-0.721910\pi$
$773$	−27596.8	−1.28407	−0.642036	+	0.766675i	$0.721910\pi$
$774$	12214.2	0.567224
$775$	20693.2	0.959123
$776$	557.487	0.0257894
$777$	3701.86	0.170918
$778$	1455.18	0.0670576
$779$	27046.3	1.24394
$780$	0	0
$781$	−3291.41	−0.150801
$782$	24264.4	1.10958
$783$	−18297.9	−0.835139
$784$	18236.3	0.830736
$785$	−5551.03	−0.252388
$786$	17742.4	0.805152
$787$	−9181.10	−0.415846	−0.207923	−	0.978145i	$-0.566670\pi$
$787$	−9181.10	−0.415846	−0.207923	+	0.978145i	$0.566670\pi$
$788$	−24614.6	−1.11276
$789$	−10231.7	−0.461673
$790$	−5115.86	−0.230398
$791$	−5229.97	−0.235090
$792$	395.560	0.0177470
$793$	0	0
$794$	−18059.3	−0.807178
$795$	−5908.01	−0.263567
$796$	30152.6	1.34263
$797$	−16961.8	−0.753848	−0.376924	−	0.926244i	$-0.623018\pi$
$797$	−16961.8	−0.753848	−0.376924	+	0.926244i	$0.623018\pi$
$798$	−5844.15	−0.259249
$799$	−32789.8	−1.45184
$800$	−30936.1	−1.36719
$801$	2379.59	0.104967
$802$	32895.8	1.44837
$803$	7574.41	0.332871
$804$	14595.2	0.640214
$805$	775.336	0.0339466
$806$	0	0
$807$	−5720.31	−0.249522
$808$	1176.82	0.0512382
$809$	−42690.3	−1.85527	−0.927635	−	0.373489i	$-0.878161\pi$
$809$	−42690.3	−1.85527	−0.927635	+	0.373489i	$0.878161\pi$
$810$	1970.70	0.0854855
$811$	−4072.57	−0.176334	−0.0881672	−	0.996106i	$-0.528101\pi$
$811$	−4072.57	−0.176334	−0.0881672	+	0.996106i	$0.528101\pi$
$812$	−5779.31	−0.249771
$813$	12778.4	0.551239
$814$	8207.66	0.353413
$815$	3198.96	0.137490
$816$	−21709.1	−0.931337
$817$	−16073.0	−0.688277
$818$	456.589	0.0195162
$819$	0	0
$820$	−7972.53	−0.339528
$821$	−13865.5	−0.589414	−0.294707	−	0.955588i	$-0.595222\pi$
$821$	−13865.5	−0.589414	−0.294707	+	0.955588i	$0.595222\pi$
$822$	−38138.0	−1.61827
$823$	13795.7	0.584313	0.292156	−	0.956371i	$-0.405627\pi$
$823$	13795.7	0.584313	0.292156	+	0.956371i	$0.405627\pi$
$824$	−1709.32	−0.0722656
$825$	4880.39	0.205955
$826$	−1550.28	−0.0653041
$827$	−16858.6	−0.708864	−0.354432	−	0.935082i	$-0.615326\pi$
$827$	−16858.6	−0.708864	−0.354432	+	0.935082i	$0.615326\pi$
$828$	−6759.89	−0.283723
$829$	35950.3	1.50616	0.753079	−	0.657930i	$-0.228568\pi$
$829$	35950.3	1.50616	0.753079	+	0.657930i	$0.228568\pi$
$830$	7497.10	0.313528
$831$	23646.9	0.987124
$832$	0	0
$833$	31414.6	1.30667
$834$	3047.18	0.126517
$835$	−4833.62	−0.200328
$836$	−6739.00	−0.278796
$837$	−25932.8	−1.07093
$838$	35785.3	1.47516
$839$	12510.1	0.514777	0.257388	−	0.966308i	$-0.417138\pi$
$839$	12510.1	0.514777	0.257388	+	0.966308i	$0.417138\pi$
$840$	133.063	0.00546561
$841$	−9391.92	−0.385088
$842$	−14379.2	−0.588529
$843$	−23298.4	−0.951886
$844$	23538.1	0.959971
$845$	0	0
$846$	17564.5	0.713805
$847$	658.653	0.0267197
$848$	−38454.5	−1.55723
$849$	−29976.0	−1.21175
$850$	−48799.4	−1.96918
$851$	−10834.1	−0.436414
$852$	9653.31	0.388165
$853$	16257.7	0.652583	0.326292	−	0.945269i	$-0.394201\pi$
$853$	16257.7	0.652583	0.326292	+	0.945269i	$0.394201\pi$
$854$	6788.29	0.272003
$855$	2233.05	0.0893200
$856$	3778.00	0.150852
$857$	33519.1	1.33604	0.668022	−	0.744142i	$-0.267141\pi$
$857$	33519.1	1.33604	0.668022	+	0.744142i	$0.267141\pi$
$858$	0	0
$859$	31473.0	1.25011	0.625056	−	0.780580i	$-0.285076\pi$
$859$	31473.0	1.25011	0.625056	+	0.780580i	$0.285076\pi$
$860$	4737.89	0.187861
$861$	7752.88	0.306873
$862$	32555.8	1.28637
$863$	−43558.0	−1.71811	−0.859057	−	0.511880i	$-0.828949\pi$
$863$	−43558.0	−1.71811	−0.859057	+	0.511880i	$0.828949\pi$
$864$	38769.3	1.52657
$865$	−3810.00	−0.149762
$866$	−69898.4	−2.74278
$867$	−19114.6	−0.748751
$868$	−8190.76	−0.320291
$869$	5736.67	0.223939
$870$	−4470.34	−0.174206
$871$	0	0
$872$	653.479	0.0253780
$873$	2681.83	0.103970
$874$	17103.9	0.661953
$875$	−3194.14	−0.123408
$876$	−22214.9	−0.856816
$877$	10846.0	0.417610	0.208805	−	0.977957i	$-0.433043\pi$
$877$	10846.0	0.417610	0.208805	+	0.977957i	$0.433043\pi$
$878$	−38129.7	−1.46562
$879$	−16350.5	−0.627403
$880$	−1538.02	−0.0589167
$881$	34684.1	1.32637	0.663187	−	0.748453i	$-0.269203\pi$
$881$	34684.1	1.32637	0.663187	+	0.748453i	$0.269203\pi$
$882$	−16827.8	−0.642429
$883$	29336.1	1.11805	0.559025	−	0.829151i	$-0.311176\pi$
$883$	29336.1	1.11805	0.559025	+	0.829151i	$0.311176\pi$
$884$	0	0
$885$	−623.664	−0.0236884
$886$	40065.0	1.51920
$887$	733.924	0.0277821	0.0138911	−	0.999904i	$-0.495578\pi$
$887$	733.924	0.0277821	0.0138911	+	0.999904i	$0.495578\pi$
$888$	−1859.35	−0.0702654
$889$	13772.1	0.519573
$890$	1774.78	0.0668437
$891$	−2209.84	−0.0830892
$892$	625.353	0.0234735
$893$	−23113.5	−0.866139
$894$	10179.3	0.380813
$895$	5366.13	0.200413
$896$	1898.32	0.0707794
$897$	0	0
$898$	−670.580	−0.0249193
$899$	21254.7	0.788524
$900$	13595.2	0.503526
$901$	−66243.4	−2.44937
$902$	17189.5	0.634530
$903$	−4607.36	−0.169793
$904$	2626.88	0.0966468
$905$	−5763.80	−0.211708
$906$	−20377.1	−0.747222
$907$	44487.6	1.62865	0.814325	−	0.580409i	$-0.197107\pi$
$907$	44487.6	1.62865	0.814325	+	0.580409i	$0.197107\pi$
$908$	−4083.89	−0.149261
$909$	5661.19	0.206567
$910$	0	0
$911$	−12796.1	−0.465372	−0.232686	−	0.972552i	$-0.574751\pi$
$911$	−12796.1	−0.465372	−0.232686	+	0.972552i	$0.574751\pi$
$912$	−15302.7	−0.555617
$913$	−8406.86	−0.304739
$914$	5077.94	0.183767
$915$	2730.87	0.0986663
$916$	−25626.5	−0.924371
$917$	6356.73	0.228918
$918$	61155.7	2.19874
$919$	−1427.24	−0.0512301	−0.0256150	−	0.999672i	$-0.508154\pi$
$919$	−1427.24	−0.0512301	−0.0256150	+	0.999672i	$0.508154\pi$
$920$	−389.431	−0.0139556
$921$	−376.583	−0.0134732
$922$	40411.7	1.44348
$923$	0	0
$924$	−1931.75	−0.0687770
$925$	21789.1	0.774509
$926$	−39832.4	−1.41358
$927$	−8222.78	−0.291339
$928$	−31775.5	−1.12401
$929$	−24910.8	−0.879759	−0.439880	−	0.898057i	$-0.644979\pi$
$929$	−24910.8	−0.879759	−0.439880	+	0.898057i	$0.644979\pi$
$930$	−6335.61	−0.223390
$931$	22144.1	0.779530
$932$	−39000.7	−1.37072
$933$	−21107.3	−0.740644
$934$	−13703.6	−0.480081
$935$	−2649.46	−0.0926701
$936$	0	0
$937$	33920.4	1.18264	0.591319	−	0.806438i	$-0.298608\pi$
$937$	33920.4	1.18264	0.591319	+	0.806438i	$0.298608\pi$
$938$	10054.4	0.349987
$939$	25226.1	0.876700
$940$	6813.24	0.236408
$941$	−30573.3	−1.05915	−0.529575	−	0.848263i	$-0.677648\pi$
$941$	−30573.3	−1.05915	−0.529575	+	0.848263i	$0.677648\pi$
$942$	−35102.2	−1.21411
$943$	−22690.1	−0.783554
$944$	−4059.35	−0.139958
$945$	1954.15	0.0672683
$946$	−10215.3	−0.351086
$947$	48092.0	1.65024	0.825122	−	0.564954i	$-0.191106\pi$
$947$	48092.0	1.65024	0.825122	+	0.564954i	$0.191106\pi$
$948$	−16825.0	−0.576424
$949$	0	0
$950$	−34398.6	−1.17478
$951$	−29112.4	−0.992674
$952$	1491.97	0.0507929
$953$	42230.0	1.43543	0.717714	−	0.696338i	$-0.245188\pi$
$953$	42230.0	1.43543	0.717714	+	0.696338i	$0.245188\pi$
$954$	35484.4	1.20425
$955$	−4026.57	−0.136436
$956$	57333.0	1.93962
$957$	5012.82	0.169322
$958$	−60949.7	−2.05553
$959$	−13664.1	−0.460100
$960$	5309.27	0.178496
$961$	332.274	0.0111535
$962$	0	0
$963$	18174.3	0.608162
$964$	28471.6	0.951253
$965$	−11679.1	−0.389599
$966$	4902.87	0.163299
$967$	−30957.4	−1.02950	−0.514749	−	0.857341i	$-0.672115\pi$
$967$	−30957.4	−1.02950	−0.514749	+	0.857341i	$0.672115\pi$
$968$	−330.824	−0.0109846
$969$	−26361.0	−0.873931
$970$	2000.20	0.0662090
$971$	44686.2	1.47688	0.738439	−	0.674320i	$-0.235563\pi$
$971$	44686.2	1.47688	0.738439	+	0.674320i	$0.235563\pi$
$972$	−28494.3	−0.940282
$973$	1091.74	0.0359709
$974$	−17611.5	−0.579374
$975$	0	0
$976$	17774.9	0.582951
$977$	−38405.9	−1.25764	−0.628819	−	0.777551i	$-0.716462\pi$
$977$	−38405.9	−1.25764	−0.628819	+	0.777551i	$0.716462\pi$
$978$	20228.7	0.661394
$979$	−1990.15	−0.0649699
$980$	−6527.50	−0.212769
$981$	3143.60	0.102311
$982$	−24591.4	−0.799128
$983$	5212.52	0.169129	0.0845644	−	0.996418i	$-0.473050\pi$
$983$	5212.52	0.169129	0.0845644	+	0.996418i	$0.473050\pi$
$984$	−3894.07	−0.126157
$985$	−6821.49	−0.220661
$986$	−50123.6	−1.61893
$987$	−6625.53	−0.213671
$988$	0	0
$989$	13484.2	0.433541
$990$	1419.23	0.0455617
$991$	−15154.6	−0.485774	−0.242887	−	0.970055i	$-0.578094\pi$
$991$	−15154.6	−0.485774	−0.242887	+	0.970055i	$0.578094\pi$
$992$	−45034.0	−1.44136
$993$	16272.4	0.520030
$994$	6650.02	0.212199
$995$	8356.26	0.266243
$996$	24656.4	0.784404
$997$	30256.0	0.961100	0.480550	−	0.876967i	$-0.340437\pi$
$997$	30256.0	0.961100	0.480550	+	0.876967i	$0.340437\pi$
$998$	−22715.8	−0.720496
$999$	−27306.2	−0.864795

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.q.1.10	yes	51
13.12	even	2		1859.4.a.p.1.42	✓	51

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.p.1.42	✓	51	13.12	even	2
1859.4.a.q.1.10	yes	51	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q-4.08285 q^{2} -3.72122 q^{3} +8.66965 q^{4} +2.40264 q^{5} +15.1932 q^{6} +5.44341 q^{7} -2.73408 q^{8} -13.1525 q^{9} +O(q^{10})\)	\(q-4.08285 q^{2} -3.72122 q^{3} +8.66965 q^{4} +2.40264 q^{5} +15.1932 q^{6} +5.44341 q^{7} -2.73408 q^{8} -13.1525 q^{9} -9.80961 q^{10} +11.0000 q^{11} -32.2617 q^{12} -22.2246 q^{14} -8.94076 q^{15} -58.1944 q^{16} -100.248 q^{17} +53.6996 q^{18} -70.6645 q^{19} +20.8300 q^{20} -20.2562 q^{21} -44.9113 q^{22} +59.2830 q^{23} +10.1741 q^{24} -119.227 q^{25} +149.416 q^{27} +47.1925 q^{28} -122.463 q^{29} +36.5038 q^{30} -173.561 q^{31} +259.471 q^{32} -40.9335 q^{33} +409.297 q^{34} +13.0786 q^{35} -114.028 q^{36} -182.752 q^{37} +288.512 q^{38} -6.56902 q^{40} -382.742 q^{41} +82.7028 q^{42} +227.455 q^{43} +95.3662 q^{44} -31.6007 q^{45} -242.043 q^{46} +327.087 q^{47} +216.554 q^{48} -313.369 q^{49} +486.787 q^{50} +373.045 q^{51} +660.795 q^{53} -610.045 q^{54} +26.4290 q^{55} -14.8827 q^{56} +262.958 q^{57} +499.996 q^{58} +69.7551 q^{59} -77.5133 q^{60} -305.440 q^{61} +708.622 q^{62} -71.5944 q^{63} -593.828 q^{64} +167.125 q^{66} -452.399 q^{67} -869.115 q^{68} -220.605 q^{69} -53.3978 q^{70} -299.219 q^{71} +35.9600 q^{72} +688.583 q^{73} +746.151 q^{74} +443.672 q^{75} -612.636 q^{76} +59.8775 q^{77} +521.515 q^{79} -139.820 q^{80} -200.895 q^{81} +1562.68 q^{82} -764.260 q^{83} -175.614 q^{84} -240.860 q^{85} -928.663 q^{86} +455.711 q^{87} -30.0749 q^{88} -180.923 q^{89} +129.021 q^{90} +513.963 q^{92} +645.858 q^{93} -1335.45 q^{94} -169.781 q^{95} -965.551 q^{96} -203.903 q^{97} +1279.44 q^{98} -144.677 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9}+O(q^{10}) \) 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9} + 212 q^{10} + 561 q^{11} + 209 q^{12} + 280 q^{14} + 284 q^{15} + 1246 q^{16} + 164 q^{17} - 189 q^{18} + 26 q^{19} + 438 q^{20} + 134 q^{21} + 373 q^{23} - 354 q^{24} + 2048 q^{25} + 1470 q^{27} - 1245 q^{28} + 898 q^{29} + 427 q^{30} + 767 q^{31} + 1127 q^{32} + 231 q^{33} + 206 q^{34} + 54 q^{35} + 3415 q^{36} + 395 q^{37} + 1577 q^{38} + 3253 q^{40} - 354 q^{41} + 942 q^{42} + 484 q^{43} + 2574 q^{44} + 1452 q^{45} - 2117 q^{46} + 1925 q^{47} + 1780 q^{48} + 4535 q^{49} - 1093 q^{50} + 230 q^{51} + 1387 q^{53} - 5271 q^{54} + 451 q^{55} + 2568 q^{56} - 5738 q^{57} + 3695 q^{58} + 1145 q^{59} - 1590 q^{60} + 5382 q^{61} - 395 q^{62} + 710 q^{63} + 9839 q^{64} - 803 q^{66} - 210 q^{67} + 1742 q^{68} + 7028 q^{69} - 6747 q^{70} + 3693 q^{71} - 12481 q^{72} + 968 q^{73} + 1735 q^{74} - 727 q^{75} - 2801 q^{76} + 44 q^{77} + 4234 q^{79} + 2390 q^{80} + 7743 q^{81} + 4770 q^{82} - 2798 q^{83} + 14821 q^{84} - 1802 q^{85} + 6558 q^{86} + 1896 q^{87} - 231 q^{88} + 3927 q^{89} + 1927 q^{90} + 1984 q^{92} - 1332 q^{93} + 7590 q^{94} + 4944 q^{95} - 7280 q^{96} + 3913 q^{97} - 15201 q^{98} + 6534 q^{99}+O(q^{100}) \) 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9 + 212 * q^10 + 561 * q^11 + 209 * q^12 + 280 * q^14 + 284 * q^15 + 1246 * q^16 + 164 * q^17 - 189 * q^18 + 26 * q^19 + 438 * q^20 + 134 * q^21 + 373 * q^23 - 354 * q^24 + 2048 * q^25 + 1470 * q^27 - 1245 * q^28 + 898 * q^29 + 427 * q^30 + 767 * q^31 + 1127 * q^32 + 231 * q^33 + 206 * q^34 + 54 * q^35 + 3415 * q^36 + 395 * q^37 + 1577 * q^38 + 3253 * q^40 - 354 * q^41 + 942 * q^42 + 484 * q^43 + 2574 * q^44 + 1452 * q^45 - 2117 * q^46 + 1925 * q^47 + 1780 * q^48 + 4535 * q^49 - 1093 * q^50 + 230 * q^51 + 1387 * q^53 - 5271 * q^54 + 451 * q^55 + 2568 * q^56 - 5738 * q^57 + 3695 * q^58 + 1145 * q^59 - 1590 * q^60 + 5382 * q^61 - 395 * q^62 + 710 * q^63 + 9839 * q^64 - 803 * q^66 - 210 * q^67 + 1742 * q^68 + 7028 * q^69 - 6747 * q^70 + 3693 * q^71 - 12481 * q^72 + 968 * q^73 + 1735 * q^74 - 727 * q^75 - 2801 * q^76 + 44 * q^77 + 4234 * q^79 + 2390 * q^80 + 7743 * q^81 + 4770 * q^82 - 2798 * q^83 + 14821 * q^84 - 1802 * q^85 + 6558 * q^86 + 1896 * q^87 - 231 * q^88 + 3927 * q^89 + 1927 * q^90 + 1984 * q^92 - 1332 * q^93 + 7590 * q^94 + 4944 * q^95 - 7280 * q^96 + 3913 * q^97 - 15201 * q^98 + 6534 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more