LMFDB - Embedded newform 1859.4.a.g.1.7

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			1.7
Root			$1.06843$ 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)

$f(q)$	$=$	$q-1.06843 q^{2} -9.85108 q^{3} -6.85846 q^{4} +2.35929 q^{5} +10.5252 q^{6} +12.2506 q^{7} +15.8752 q^{8} +70.0437 q^{9} +O(q^{10})$	\(q-1.06843 q^{2} -9.85108 q^{3} -6.85846 q^{4} +2.35929 q^{5} +10.5252 q^{6} +12.2506 q^{7} +15.8752 q^{8} +70.0437 q^{9} -2.52073 q^{10} +11.0000 q^{11} +67.5632 q^{12} -13.0888 q^{14} -23.2415 q^{15} +37.9062 q^{16} -21.2126 q^{17} -74.8367 q^{18} -33.3247 q^{19} -16.1811 q^{20} -120.681 q^{21} -11.7527 q^{22} -111.274 q^{23} -156.388 q^{24} -119.434 q^{25} -424.027 q^{27} -84.0200 q^{28} +212.777 q^{29} +24.8319 q^{30} +177.548 q^{31} -167.502 q^{32} -108.362 q^{33} +22.6641 q^{34} +28.9026 q^{35} -480.392 q^{36} +181.734 q^{37} +35.6050 q^{38} +37.4542 q^{40} -181.556 q^{41} +128.939 q^{42} -364.873 q^{43} -75.4431 q^{44} +165.253 q^{45} +118.888 q^{46} +180.081 q^{47} -373.417 q^{48} -192.924 q^{49} +127.606 q^{50} +208.967 q^{51} -290.575 q^{53} +453.043 q^{54} +25.9522 q^{55} +194.480 q^{56} +328.284 q^{57} -227.337 q^{58} -357.844 q^{59} +159.401 q^{60} -570.427 q^{61} -189.697 q^{62} +858.075 q^{63} -124.286 q^{64} +115.777 q^{66} +1082.30 q^{67} +145.486 q^{68} +1096.17 q^{69} -30.8804 q^{70} +880.042 q^{71} +1111.96 q^{72} +709.422 q^{73} -194.170 q^{74} +1176.55 q^{75} +228.556 q^{76} +134.756 q^{77} -93.0294 q^{79} +89.4317 q^{80} +2285.94 q^{81} +193.980 q^{82} +1231.90 q^{83} +827.687 q^{84} -50.0467 q^{85} +389.841 q^{86} -2096.08 q^{87} +174.627 q^{88} -988.442 q^{89} -176.562 q^{90} +763.167 q^{92} -1749.04 q^{93} -192.404 q^{94} -78.6226 q^{95} +1650.07 q^{96} -108.162 q^{97} +206.125 q^{98} +770.481 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.06843	−0.377746	−0.188873	−	0.982001i	$-0.560484\pi$
$2$	−1.06843	−0.377746	−0.188873	+	0.982001i	$0.560484\pi$
$3$	−9.85108	−1.89584	−0.947920	−	0.318507i	$-0.896818\pi$
$3$	−9.85108	−1.89584	−0.947920	+	0.318507i	$0.896818\pi$
$4$	−6.85846	−0.857308
$5$	2.35929	0.211021	0.105511	−	0.994418i	$-0.466352\pi$
$5$	2.35929	0.211021	0.105511	+	0.994418i	$0.466352\pi$
$6$	10.5252	0.716147
$7$	12.2506	0.661468	0.330734	−	0.943724i	$-0.392704\pi$
$7$	12.2506	0.661468	0.330734	+	0.943724i	$0.392704\pi$
$8$	15.8752	0.701591
$9$	70.0437	2.59421
$10$	−2.52073	−0.0797126
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	67.5632	1.62532
$13$	0	0
$13$	0	0
$14$	−13.0888	−0.249867
$15$	−23.2415	−0.400063
$16$	37.9062	0.592284
$17$	−21.2126	−0.302636	−0.151318	−	0.988485i	$-0.548352\pi$
$17$	−21.2126	−0.302636	−0.151318	+	0.988485i	$0.548352\pi$
$18$	−74.8367	−0.979955
$19$	−33.3247	−0.402379	−0.201190	−	0.979552i	$-0.564481\pi$
$19$	−33.3247	−0.402379	−0.201190	+	0.979552i	$0.564481\pi$
$20$	−16.1811	−0.180910
$21$	−120.681	−1.25404
$22$	−11.7527	−0.113895
$23$	−111.274	−1.00879	−0.504395	−	0.863473i	$-0.668285\pi$
$23$	−111.274	−1.00879	−0.504395	+	0.863473i	$0.668285\pi$
$24$	−156.388	−1.33011
$25$	−119.434	−0.955470
$26$	0	0
$27$	−424.027	−3.02237
$28$	−84.0200	−0.567082
$29$	212.777	1.36247	0.681237	−	0.732063i	$-0.261442\pi$
$29$	212.777	1.36247	0.681237	+	0.732063i	$0.261442\pi$
$30$	24.8319	0.151122
$31$	177.548	1.02866	0.514331	−	0.857592i	$-0.328040\pi$
$31$	177.548	1.02866	0.514331	+	0.857592i	$0.328040\pi$
$32$	−167.502	−0.925325
$33$	−108.362	−0.571618
$34$	22.6641	0.114320
$35$	28.9026	0.139584
$36$	−480.392	−2.22404
$37$	181.734	0.807485	0.403743	−	0.914873i	$-0.367709\pi$
$37$	181.734	0.807485	0.403743	+	0.914873i	$0.367709\pi$
$38$	35.6050	0.151997
$39$	0	0
$40$	37.4542	0.148051
$41$	−181.556	−0.691569	−0.345784	−	0.938314i	$-0.612387\pi$
$41$	−181.556	−0.691569	−0.345784	+	0.938314i	$0.612387\pi$
$42$	128.939	0.473708
$43$	−364.873	−1.29402	−0.647008	−	0.762483i	$-0.723980\pi$
$43$	−364.873	−1.29402	−0.647008	+	0.762483i	$0.723980\pi$
$44$	−75.4431	−0.258488
$45$	165.253	0.547434
$46$	118.888	0.381067
$47$	180.081	0.558883	0.279442	−	0.960163i	$-0.409851\pi$
$47$	180.081	0.558883	0.279442	+	0.960163i	$0.409851\pi$
$48$	−373.417	−1.12288
$49$	−192.924	−0.562460
$50$	127.606	0.360925
$51$	208.967	0.573750
$52$	0	0
$53$	−290.575	−0.753085	−0.376543	−	0.926399i	$-0.622887\pi$
$53$	−290.575	−0.753085	−0.376543	+	0.926399i	$0.622887\pi$
$54$	453.043	1.14169
$55$	25.9522	0.0636253
$56$	194.480	0.464080
$57$	328.284	0.762847
$58$	−227.337	−0.514670
$59$	−357.844	−0.789616	−0.394808	−	0.918764i	$-0.629189\pi$
$59$	−357.844	−0.789616	−0.394808	+	0.918764i	$0.629189\pi$
$60$	159.401	0.342977
$61$	−570.427	−1.19731	−0.598653	−	0.801009i	$-0.704297\pi$
$61$	−570.427	−1.19731	−0.598653	+	0.801009i	$0.704297\pi$
$62$	−189.697	−0.388574
$63$	858.075	1.71599
$64$	−124.286	−0.242746
$65$	0	0
$66$	115.777	0.215926
$67$	1082.30	1.97349	0.986744	−	0.162283i	$-0.0518858\pi$
$67$	1082.30	1.97349	0.986744	+	0.162283i	$0.0518858\pi$
$68$	145.486	0.259452
$69$	1096.17	1.91251
$70$	−30.8804	−0.0527273
$71$	880.042	1.47101	0.735506	−	0.677519i	$-0.236945\pi$
$71$	880.042	1.47101	0.735506	+	0.677519i	$0.236945\pi$
$72$	1111.96	1.82008
$73$	709.422	1.13742	0.568709	−	0.822539i	$-0.307443\pi$
$73$	709.422	1.13742	0.568709	+	0.822539i	$0.307443\pi$
$74$	−194.170	−0.305025
$75$	1176.55	1.81142
$76$	228.556	0.344963
$77$	134.756	0.199440
$78$	0	0
$79$	−93.0294	−0.132489	−0.0662444	−	0.997803i	$-0.521102\pi$
$79$	−93.0294	−0.132489	−0.0662444	+	0.997803i	$0.521102\pi$
$80$	89.4317	0.124985
$81$	2285.94	3.13573
$82$	193.980	0.261238
$83$	1231.90	1.62914	0.814569	−	0.580067i	$-0.196974\pi$
$83$	1231.90	1.62914	0.814569	+	0.580067i	$0.196974\pi$
$84$	827.687	1.07510
$85$	−50.0467	−0.0638627
$86$	389.841	0.488810
$87$	−2096.08	−2.58303
$88$	174.627	0.211538
$89$	−988.442	−1.17724	−0.588622	−	0.808409i	$-0.700329\pi$
$89$	−988.442	−1.17724	−0.588622	+	0.808409i	$0.700329\pi$
$90$	−176.562	−0.206791
$91$	0	0
$92$	763.167	0.864844
$93$	−1749.04	−1.95018
$94$	−192.404	−0.211116
$95$	−78.6226	−0.0849106
$96$	1650.07	1.75427
$97$	−108.162	−0.113219	−0.0566093	−	0.998396i	$-0.518029\pi$
$97$	−108.162	−0.113219	−0.0566093	+	0.998396i	$0.518029\pi$
$98$	206.125	0.212467
$99$	770.481	0.782184
$100$	819.132	0.819132
$101$	−747.321	−0.736249	−0.368125	−	0.929776i	$-0.620000\pi$
$101$	−747.321	−0.736249	−0.368125	+	0.929776i	$0.620000\pi$
$102$	−223.266	−0.216732
$103$	−995.178	−0.952018	−0.476009	−	0.879441i	$-0.657917\pi$
$103$	−995.178	−0.952018	−0.476009	+	0.879441i	$0.657917\pi$
$104$	0	0
$105$	−284.722	−0.264629
$106$	310.458	0.284475
$107$	1007.38	0.910156	0.455078	−	0.890452i	$-0.349611\pi$
$107$	1007.38	0.910156	0.455078	+	0.890452i	$0.349611\pi$
$108$	2908.17	2.59110
$109$	558.653	0.490910	0.245455	−	0.969408i	$-0.421063\pi$
$109$	558.653	0.490910	0.245455	+	0.969408i	$0.421063\pi$
$110$	−27.7281	−0.0240342
$111$	−1790.28	−1.53086
$112$	464.372	0.391777
$113$	1145.39	0.953533	0.476767	−	0.879030i	$-0.341809\pi$
$113$	1145.39	0.953533	0.476767	+	0.879030i	$0.341809\pi$
$114$	−350.748	−0.288163
$115$	−262.527	−0.212876
$116$	−1459.32	−1.16806
$117$	0	0
$118$	382.331	0.298275
$119$	−259.866	−0.200184
$120$	−368.964	−0.280681
$121$	121.000	0.0909091
$122$	609.460	0.452278
$123$	1788.53	1.31110
$124$	−1217.71	−0.881880
$125$	−576.690	−0.412646
$126$	−916.791	−0.648209
$127$	1067.54	0.745894	0.372947	−	0.927853i	$-0.378347\pi$
$127$	1067.54	0.745894	0.372947	+	0.927853i	$0.378347\pi$
$128$	1472.80	1.01702
$129$	3594.40	2.45325
$130$	0	0
$131$	−2231.55	−1.48833	−0.744165	−	0.667996i	$-0.767152\pi$
$131$	−2231.55	−1.48833	−0.744165	+	0.667996i	$0.767152\pi$
$132$	743.196	0.490052
$133$	−408.246	−0.266161
$134$	−1156.36	−0.745478
$135$	−1000.40	−0.637785
$136$	−336.754	−0.212327
$137$	522.005	0.325532	0.162766	−	0.986665i	$-0.447958\pi$
$137$	522.005	0.325532	0.162766	+	0.986665i	$0.447958\pi$
$138$	−1171.18	−0.722442
$139$	1272.17	0.776288	0.388144	−	0.921599i	$-0.373116\pi$
$139$	1272.17	0.776288	0.388144	+	0.921599i	$0.373116\pi$
$140$	−198.227	−0.119666
$141$	−1773.99	−1.05955
$142$	−940.262	−0.555669
$143$	0	0
$144$	2655.09	1.53651
$145$	502.003	0.287511
$146$	−757.966	−0.429656
$147$	1900.51	1.06633
$148$	−1246.42	−0.692263
$149$	−601.025	−0.330456	−0.165228	−	0.986255i	$-0.552836\pi$
$149$	−601.025	−0.330456	−0.165228	+	0.986255i	$0.552836\pi$
$150$	−1257.06	−0.684257
$151$	−2338.76	−1.26044	−0.630218	−	0.776418i	$-0.717035\pi$
$151$	−2338.76	−1.26044	−0.630218	+	0.776418i	$0.717035\pi$
$152$	−529.036	−0.282306
$153$	−1485.81	−0.785102
$154$	−143.977	−0.0753378
$155$	418.887	0.217070
$156$	0	0
$157$	−3307.95	−1.68155	−0.840774	−	0.541386i	$-0.817900\pi$
$157$	−3307.95	−1.68155	−0.840774	+	0.541386i	$0.817900\pi$
$158$	99.3952	0.0500472
$159$	2862.47	1.42773
$160$	−395.185	−0.195263
$161$	−1363.17	−0.667283
$162$	−2442.37	−1.18451
$163$	289.961	0.139334	0.0696672	−	0.997570i	$-0.477806\pi$
$163$	289.961	0.139334	0.0696672	+	0.997570i	$0.477806\pi$
$164$	1245.20	0.592887
$165$	−255.657	−0.120623
$166$	−1316.19	−0.615401
$167$	44.0906	0.0204301	0.0102151	−	0.999948i	$-0.496748\pi$
$167$	44.0906	0.0204301	0.0102151	+	0.999948i	$0.496748\pi$
$168$	−1915.84	−0.879822
$169$	0	0
$170$	53.4713	0.0241239
$171$	−2334.19	−1.04386
$172$	2502.47	1.10937
$173$	411.991	0.181058	0.0905292	−	0.995894i	$-0.471144\pi$
$173$	411.991	0.181058	0.0905292	+	0.995894i	$0.471144\pi$
$174$	2239.52	0.975732
$175$	−1463.13	−0.632013
$176$	416.968	0.178580
$177$	3525.15	1.49699
$178$	1056.08	0.444700
$179$	−1019.88	−0.425862	−0.212931	−	0.977067i	$-0.568301\pi$
$179$	−1019.88	−0.425862	−0.212931	+	0.977067i	$0.568301\pi$
$180$	−1133.38	−0.469319
$181$	−1211.88	−0.497670	−0.248835	−	0.968546i	$-0.580048\pi$
$181$	−1211.88	−0.497670	−0.248835	+	0.968546i	$0.580048\pi$
$182$	0	0
$183$	5619.32	2.26990
$184$	−1766.49	−0.707759
$185$	428.764	0.170397
$186$	1868.72	0.736674
$187$	−233.339	−0.0912482
$188$	−1235.08	−0.479135
$189$	−5194.57	−1.99920
$190$	84.0026	0.0320747
$191$	314.472	0.119133	0.0595665	−	0.998224i	$-0.481028\pi$
$191$	314.472	0.119133	0.0595665	+	0.998224i	$0.481028\pi$
$192$	1224.35	0.460208
$193$	3376.39	1.25926	0.629631	−	0.776894i	$-0.283206\pi$
$193$	3376.39	1.25926	0.629631	+	0.776894i	$0.283206\pi$
$194$	115.564	0.0427679
$195$	0	0
$196$	1323.16	0.482201
$197$	−3447.73	−1.24691	−0.623454	−	0.781860i	$-0.714271\pi$
$197$	−3447.73	−1.24691	−0.623454	+	0.781860i	$0.714271\pi$
$198$	−823.204	−0.295467
$199$	−253.878	−0.0904369	−0.0452184	−	0.998977i	$-0.514398\pi$
$199$	−253.878	−0.0904369	−0.0452184	+	0.998977i	$0.514398\pi$
$200$	−1896.03	−0.670350
$201$	−10661.8	−3.74142
$202$	798.458	0.278116
$203$	2606.64	0.901233
$204$	−1433.19	−0.491880
$205$	−428.344	−0.145936
$206$	1063.28	0.359621
$207$	−7794.03	−2.61702
$208$	0	0
$209$	−366.571	−0.121322
$210$	304.205	0.0999626
$211$	4014.97	1.30996	0.654980	−	0.755646i	$-0.272677\pi$
$211$	4014.97	1.30996	0.654980	+	0.755646i	$0.272677\pi$
$212$	1992.90	0.645626
$213$	−8669.37	−2.78880
$214$	−1076.31	−0.343808
$215$	−860.842	−0.273065
$216$	−6731.52	−2.12047
$217$	2175.06	0.680427
$218$	−596.880	−0.185440
$219$	−6988.57	−2.15636
$220$	−177.992	−0.0545465
$221$	0	0
$222$	1912.79	0.578278
$223$	1012.17	0.303947	0.151973	−	0.988385i	$-0.451437\pi$
$223$	1012.17	0.303947	0.151973	+	0.988385i	$0.451437\pi$
$224$	−2051.99	−0.612073
$225$	−8365.59	−2.47869
$226$	−1223.77	−0.360194
$227$	4359.53	1.27468	0.637339	−	0.770583i	$-0.280035\pi$
$227$	4359.53	1.27468	0.637339	+	0.770583i	$0.280035\pi$
$228$	−2251.52	−0.653995
$229$	−4087.21	−1.17943	−0.589717	−	0.807610i	$-0.700761\pi$
$229$	−4087.21	−1.17943	−0.589717	+	0.807610i	$0.700761\pi$
$230$	280.491	0.0804133
$231$	−1327.49	−0.378107
$232$	3377.88	0.955900
$233$	−3417.59	−0.960916	−0.480458	−	0.877018i	$-0.659530\pi$
$233$	−3417.59	−0.960916	−0.480458	+	0.877018i	$0.659530\pi$
$234$	0	0
$235$	424.863	0.117936
$236$	2454.26	0.676944
$237$	916.440	0.251178
$238$	277.648	0.0756188
$239$	3900.66	1.05570	0.527850	−	0.849337i	$-0.322998\pi$
$239$	3900.66	1.05570	0.527850	+	0.849337i	$0.322998\pi$
$240$	−880.998	−0.236951
$241$	5547.65	1.48280	0.741401	−	0.671062i	$-0.234162\pi$
$241$	5547.65	1.48280	0.741401	+	0.671062i	$0.234162\pi$
$242$	−129.280	−0.0343406
$243$	−11070.3	−2.92246
$244$	3912.25	1.02646
$245$	−455.163	−0.118691
$246$	−1910.91	−0.495265
$247$	0	0
$248$	2818.61	0.721701
$249$	−12135.5	−3.08858
$250$	616.152	0.155876
$251$	−2045.51	−0.514387	−0.257194	−	0.966360i	$-0.582798\pi$
$251$	−2045.51	−0.514387	−0.257194	+	0.966360i	$0.582798\pi$
$252$	−5885.07	−1.47113
$253$	−1224.01	−0.304162
$254$	−1140.59	−0.281759
$255$	493.014	0.121073
$256$	−579.298	−0.141430
$257$	2728.40	0.662230	0.331115	−	0.943590i	$-0.392575\pi$
$257$	2728.40	0.662230	0.331115	+	0.943590i	$0.392575\pi$
$258$	−3840.36	−0.926706
$259$	2226.35	0.534126
$260$	0	0
$261$	14903.7	3.53455
$262$	2384.25	0.562211
$263$	−5588.07	−1.31017	−0.655086	−	0.755555i	$-0.727367\pi$
$263$	−5588.07	−1.31017	−0.655086	+	0.755555i	$0.727367\pi$
$264$	−1720.27	−0.401042
$265$	−685.550	−0.158917
$266$	436.182	0.100541
$267$	9737.22	2.23187
$268$	−7422.90	−1.69189
$269$	2853.09	0.646677	0.323338	−	0.946283i	$-0.395195\pi$
$269$	2853.09	0.646677	0.323338	+	0.946283i	$0.395195\pi$
$270$	1068.86	0.240921
$271$	3246.20	0.727648	0.363824	−	0.931468i	$-0.381471\pi$
$271$	3246.20	0.727648	0.363824	+	0.931468i	$0.381471\pi$
$272$	−804.089	−0.179246
$273$	0	0
$274$	−557.725	−0.122969
$275$	−1313.77	−0.288085
$276$	−7518.01	−1.63961
$277$	−5994.73	−1.30032	−0.650160	−	0.759798i	$-0.725298\pi$
$277$	−5994.73	−1.30032	−0.650160	+	0.759798i	$0.725298\pi$
$278$	−1359.22	−0.293240
$279$	12436.1	2.66857
$280$	458.835	0.0979308
$281$	7043.43	1.49529	0.747644	−	0.664100i	$-0.231185\pi$
$281$	7043.43	1.49529	0.747644	+	0.664100i	$0.231185\pi$
$282$	1895.38	0.400243
$283$	−1637.69	−0.343996	−0.171998	−	0.985097i	$-0.555022\pi$
$283$	−1637.69	−0.343996	−0.171998	+	0.985097i	$0.555022\pi$
$284$	−6035.74	−1.26111
$285$	774.517	0.160977
$286$	0	0
$287$	−2224.17	−0.457451
$288$	−11732.4	−2.40049
$289$	−4463.03	−0.908411
$290$	−536.354	−0.108606
$291$	1065.51	0.214644
$292$	−4865.54	−0.975117
$293$	−624.066	−0.124431	−0.0622155	−	0.998063i	$-0.519817\pi$
$293$	−624.066	−0.124431	−0.0622155	+	0.998063i	$0.519817\pi$
$294$	−2030.56	−0.402804
$295$	−844.259	−0.166626
$296$	2885.07	0.566525
$297$	−4664.30	−0.911280
$298$	642.152	0.124828
$299$	0	0
$300$	−8069.33	−1.55294
$301$	−4469.90	−0.855950
$302$	2498.80	0.476125
$303$	7361.91	1.39581
$304$	−1263.21	−0.238323
$305$	−1345.80	−0.252657
$306$	1587.48	0.296570
$307$	7433.53	1.38193	0.690967	−	0.722886i	$-0.257185\pi$
$307$	7433.53	1.38193	0.690967	+	0.722886i	$0.257185\pi$
$308$	−924.220	−0.170982
$309$	9803.58	1.80487
$310$	−447.551	−0.0819973
$311$	−4377.50	−0.798152	−0.399076	−	0.916918i	$-0.630669\pi$
$311$	−4377.50	−0.798152	−0.399076	+	0.916918i	$0.630669\pi$
$312$	0	0
$313$	10948.3	1.97712	0.988558	−	0.150842i	$-0.0481983\pi$
$313$	10948.3	1.97712	0.988558	+	0.150842i	$0.0481983\pi$
$314$	3534.31	0.635199
$315$	2024.45	0.362110
$316$	638.038	0.113584
$317$	1588.82	0.281505	0.140752	−	0.990045i	$-0.455048\pi$
$317$	1588.82	0.281505	0.140752	+	0.990045i	$0.455048\pi$
$318$	−3058.35	−0.539320
$319$	2340.55	0.410801
$320$	−293.227	−0.0512246
$321$	−9923.74	−1.72551
$322$	1456.44	0.252064
$323$	706.903	0.121774
$324$	−15678.1	−2.68828
$325$	0	0
$326$	−309.803	−0.0526331
$327$	−5503.33	−0.930688
$328$	−2882.24	−0.485199
$329$	2206.09	0.369684
$330$	273.151	0.0455651
$331$	−3082.31	−0.511840	−0.255920	−	0.966698i	$-0.582378\pi$
$331$	−3082.31	−0.511840	−0.255920	+	0.966698i	$0.582378\pi$
$332$	−8448.92	−1.39667
$333$	12729.4	2.09479
$334$	−47.1076	−0.00771741
$335$	2553.45	0.416448
$336$	−4574.56	−0.742747
$337$	−1631.13	−0.263660	−0.131830	−	0.991272i	$-0.542085\pi$
$337$	−1631.13	−0.263660	−0.131830	+	0.991272i	$0.542085\pi$
$338$	0	0
$339$	−11283.3	−1.80775
$340$	343.243	0.0547499
$341$	1953.03	0.310153
$342$	2493.91	0.394313
$343$	−6565.37	−1.03352
$344$	−5792.44	−0.907870
$345$	2586.17	0.403580
$346$	−440.183	−0.0683942
$347$	11356.6	1.75693	0.878464	−	0.477808i	$-0.158569\pi$
$347$	11356.6	1.75693	0.878464	+	0.477808i	$0.158569\pi$
$348$	14375.9	2.21445
$349$	−521.265	−0.0799503	−0.0399752	−	0.999201i	$-0.512728\pi$
$349$	−521.265	−0.0799503	−0.0399752	+	0.999201i	$0.512728\pi$
$350$	1563.25	0.238741
$351$	0	0
$352$	−1842.52	−0.278996
$353$	−12864.3	−1.93966	−0.969830	−	0.243783i	$-0.921612\pi$
$353$	−12864.3	−1.93966	−0.969830	+	0.243783i	$0.921612\pi$
$354$	−3766.37	−0.565481
$355$	2076.28	0.310415
$356$	6779.19	1.00926
$357$	2559.96	0.379517
$358$	1089.67	0.160868
$359$	−13151.0	−1.93339	−0.966693	−	0.255939i	$-0.917615\pi$
$359$	−13151.0	−1.93339	−0.966693	+	0.255939i	$0.917615\pi$
$360$	2623.43	0.384075
$361$	−5748.47	−0.838091
$362$	1294.81	0.187993
$363$	−1191.98	−0.172349
$364$	0	0
$365$	1673.73	0.240019
$366$	−6003.84	−0.857447
$367$	13004.3	1.84964	0.924819	−	0.380407i	$-0.124216\pi$
$367$	13004.3	1.84964	0.924819	+	0.380407i	$0.124216\pi$
$368$	−4217.96	−0.597490
$369$	−12716.9	−1.79408
$370$	−458.104	−0.0643667
$371$	−3559.70	−0.498142
$372$	11995.7	1.67190
$373$	−10770.9	−1.49516	−0.747582	−	0.664170i	$-0.768785\pi$
$373$	−10770.9	−1.49516	−0.747582	+	0.664170i	$0.768785\pi$
$374$	249.306	0.0344687
$375$	5681.02	0.782311
$376$	2858.82	0.392108
$377$	0	0
$378$	5550.03	0.755192
$379$	3871.68	0.524736	0.262368	−	0.964968i	$-0.415497\pi$
$379$	3871.68	0.524736	0.262368	+	0.964968i	$0.415497\pi$
$380$	539.230	0.0727945
$381$	−10516.4	−1.41410
$382$	−335.991	−0.0450020
$383$	−8526.19	−1.13751	−0.568757	−	0.822505i	$-0.692576\pi$
$383$	−8526.19	−1.13751	−0.568757	+	0.822505i	$0.692576\pi$
$384$	−14508.7	−1.92811
$385$	317.929	0.0420861
$386$	−3607.43	−0.475682
$387$	−25557.1	−3.35695
$388$	741.826	0.0970632
$389$	12613.5	1.64403	0.822016	−	0.569464i	$-0.192849\pi$
$389$	12613.5	1.64403	0.822016	+	0.569464i	$0.192849\pi$
$390$	0	0
$391$	2360.41	0.305296
$392$	−3062.70	−0.394617
$393$	21983.1	2.82164
$394$	3683.66	0.471015
$395$	−219.483	−0.0279580
$396$	−5284.31	−0.670573
$397$	8429.93	1.06571	0.532854	−	0.846207i	$-0.321119\pi$
$397$	8429.93	1.06571	0.532854	+	0.846207i	$0.321119\pi$
$398$	271.250	0.0341622
$399$	4021.66	0.504599
$400$	−4527.28	−0.565910
$401$	−8148.57	−1.01476	−0.507382	−	0.861721i	$-0.669387\pi$
$401$	−8148.57	−1.01476	−0.507382	+	0.861721i	$0.669387\pi$
$402$	11391.4	1.41331
$403$	0	0
$404$	5125.47	0.631192
$405$	5393.20	0.661705
$406$	−2785.01	−0.340437
$407$	1999.08	0.243466
$408$	3317.39	0.402538
$409$	−275.792	−0.0333424	−0.0166712	−	0.999861i	$-0.505307\pi$
$409$	−275.792	−0.0333424	−0.0166712	+	0.999861i	$0.505307\pi$
$410$	457.655	0.0551267
$411$	−5142.32	−0.617157
$412$	6825.39	0.816172
$413$	−4383.79	−0.522306
$414$	8327.36	0.988569
$415$	2906.40	0.343783
$416$	0	0
$417$	−12532.2	−1.47172
$418$	391.655	0.0458289
$419$	818.395	0.0954206	0.0477103	−	0.998861i	$-0.484808\pi$
$419$	818.395	0.0954206	0.0477103	+	0.998861i	$0.484808\pi$
$420$	1952.75	0.226868
$421$	1200.57	0.138984	0.0694918	−	0.997583i	$-0.477862\pi$
$421$	1200.57	0.138984	0.0694918	+	0.997583i	$0.477862\pi$
$422$	−4289.70	−0.494833
$423$	12613.6	1.44986
$424$	−4612.93	−0.528358
$425$	2533.50	0.289160
$426$	9262.60	1.05346
$427$	−6988.04	−0.791979
$428$	−6909.05	−0.780284
$429$	0	0
$430$	919.748	0.103149
$431$	9298.10	1.03915	0.519575	−	0.854425i	$-0.326090\pi$
$431$	9298.10	1.03915	0.519575	+	0.854425i	$0.326090\pi$
$432$	−16073.2	−1.79010
$433$	705.472	0.0782975	0.0391488	−	0.999233i	$-0.487535\pi$
$433$	705.472	0.0782975	0.0391488	+	0.999233i	$0.487535\pi$
$434$	−2323.90	−0.257029
$435$	−4945.27	−0.545075
$436$	−3831.50	−0.420861
$437$	3708.16	0.405916
$438$	7466.78	0.814559
$439$	−16024.8	−1.74220	−0.871098	−	0.491109i	$-0.836592\pi$
$439$	−16024.8	−1.74220	−0.871098	+	0.491109i	$0.836592\pi$
$440$	411.996	0.0446390
$441$	−13513.1	−1.45914
$442$	0	0
$443$	−12527.4	−1.34356	−0.671779	−	0.740751i	$-0.734470\pi$
$443$	−12527.4	−1.34356	−0.671779	+	0.740751i	$0.734470\pi$
$444$	12278.6	1.31242
$445$	−2332.02	−0.248424
$446$	−1081.44	−0.114815
$447$	5920.75	0.626491
$448$	−1522.57	−0.160569
$449$	6411.85	0.673928	0.336964	−	0.941517i	$-0.390600\pi$
$449$	6411.85	0.673928	0.336964	+	0.941517i	$0.390600\pi$
$450$	8938.03	0.936317
$451$	−1997.12	−0.208516
$452$	−7855.62	−0.817472
$453$	23039.3	2.38959
$454$	−4657.84	−0.481505
$455$	0	0
$456$	5211.57	0.535207
$457$	−6493.23	−0.664640	−0.332320	−	0.943167i	$-0.607831\pi$
$457$	−6493.23	−0.664640	−0.332320	+	0.943167i	$0.607831\pi$
$458$	4366.89	0.445527
$459$	8994.72	0.914679
$460$	1800.53	0.182500
$461$	−12691.3	−1.28220	−0.641100	−	0.767458i	$-0.721522\pi$
$461$	−12691.3	−1.28220	−0.641100	+	0.767458i	$0.721522\pi$
$462$	1418.33	0.142828
$463$	16605.5	1.66679	0.833396	−	0.552677i	$-0.186394\pi$
$463$	16605.5	1.66679	0.833396	+	0.552677i	$0.186394\pi$
$464$	8065.57	0.806971
$465$	−4126.49	−0.411530
$466$	3651.45	0.362983
$467$	5952.63	0.589839	0.294919	−	0.955522i	$-0.404707\pi$
$467$	5952.63	0.589839	0.294919	+	0.955522i	$0.404707\pi$
$468$	0	0
$469$	13258.8	1.30540
$470$	−453.936	−0.0445500
$471$	32586.9	3.18795
$472$	−5680.85	−0.553988
$473$	−4013.61	−0.390160
$474$	−979.150	−0.0948815
$475$	3980.09	0.384461
$476$	1782.28	0.171619
$477$	−20352.9	−1.95366
$478$	−4167.57	−0.398787
$479$	12772.9	1.21839	0.609197	−	0.793019i	$-0.291492\pi$
$479$	12772.9	1.21839	0.609197	+	0.793019i	$0.291492\pi$
$480$	3893.00	0.370188
$481$	0	0
$482$	−5927.26	−0.560123
$483$	13428.6	1.26506
$484$	−829.874	−0.0779371
$485$	−255.186	−0.0238915
$486$	11827.8	1.10395
$487$	−4399.95	−0.409406	−0.204703	−	0.978824i	$-0.565623\pi$
$487$	−4399.95	−0.409406	−0.204703	+	0.978824i	$0.565623\pi$
$488$	−9055.64	−0.840019
$489$	−2856.43	−0.264156
$490$	486.309	0.0448351
$491$	−14199.1	−1.30508	−0.652541	−	0.757754i	$-0.726297\pi$
$491$	−14199.1	−1.30508	−0.652541	+	0.757754i	$0.726297\pi$
$492$	−12266.5	−1.12402
$493$	−4513.56	−0.412334
$494$	0	0
$495$	1817.79	0.165058
$496$	6730.16	0.609260
$497$	10781.0	0.973027
$498$	12965.9	1.16670
$499$	−3982.56	−0.357283	−0.178641	−	0.983914i	$-0.557170\pi$
$499$	−3982.56	−0.357283	−0.178641	+	0.983914i	$0.557170\pi$
$500$	3955.21	0.353764
$501$	−434.340	−0.0387323
$502$	2185.48	0.194308
$503$	2406.84	0.213351	0.106676	−	0.994294i	$-0.465979\pi$
$503$	2406.84	0.213351	0.106676	+	0.994294i	$0.465979\pi$
$504$	13622.1	1.20392
$505$	−1763.15	−0.155364
$506$	1307.77	0.114896
$507$	0	0
$508$	−7321.65	−0.639460
$509$	19571.5	1.70430	0.852151	−	0.523296i	$-0.175298\pi$
$509$	19571.5	1.70430	0.852151	+	0.523296i	$0.175298\pi$
$510$	−526.750	−0.0457351
$511$	8690.81	0.752366
$512$	−11163.5	−0.963596
$513$	14130.6	1.21614
$514$	−2915.10	−0.250155
$515$	−2347.91	−0.200896
$516$	−24652.0	−2.10319
$517$	1980.89	0.168510
$518$	−2378.69	−0.201764
$519$	−4058.56	−0.343258
$520$	0	0
$521$	−9383.29	−0.789039	−0.394520	−	0.918888i	$-0.629089\pi$
$521$	−9383.29	−0.789039	−0.394520	+	0.918888i	$0.629089\pi$
$522$	−15923.5	−1.33516
$523$	−8917.02	−0.745533	−0.372767	−	0.927925i	$-0.621591\pi$
$523$	−8917.02	−0.745533	−0.372767	+	0.927925i	$0.621591\pi$
$524$	15305.0	1.27596
$525$	14413.4	1.19820
$526$	5970.45	0.494913
$527$	−3766.25	−0.311310
$528$	−4107.58	−0.338560
$529$	214.846	0.0176581
$530$	732.461	0.0600303
$531$	−25064.8	−2.04843
$532$	2799.94	0.228182
$533$	0	0
$534$	−10403.5	−0.843080
$535$	2376.69	0.192062
$536$	17181.7	1.38458
$537$	10046.9	0.807366
$538$	−3048.32	−0.244280
$539$	−2122.16	−0.169588
$540$	6861.23	0.546778
$541$	−10673.0	−0.848187	−0.424094	−	0.905618i	$-0.639407\pi$
$541$	−10673.0	−0.848187	−0.424094	+	0.905618i	$0.639407\pi$
$542$	−3468.33	−0.274866
$543$	11938.3	0.943503
$544$	3553.15	0.280037
$545$	1318.02	0.103593
$546$	0	0
$547$	−11642.2	−0.910029	−0.455014	−	0.890484i	$-0.650366\pi$
$547$	−11642.2	−0.910029	−0.455014	+	0.890484i	$0.650366\pi$
$548$	−3580.15	−0.279081
$549$	−39954.8	−3.10606
$550$	1403.67	0.108823
$551$	−7090.73	−0.548231
$552$	17401.9	1.34180
$553$	−1139.66	−0.0876372
$554$	6404.94	0.491191
$555$	−4223.79	−0.323045
$556$	−8725.13	−0.665518
$557$	−13698.5	−1.04206	−0.521028	−	0.853539i	$-0.674451\pi$
$557$	−13698.5	−1.04206	−0.521028	+	0.853539i	$0.674451\pi$
$558$	−13287.1	−1.00804
$559$	0	0
$560$	1095.59	0.0826733
$561$	2298.64	0.172992
$562$	−7525.40	−0.564839
$563$	−2021.94	−0.151358	−0.0756790	−	0.997132i	$-0.524112\pi$
$563$	−2021.94	−0.151358	−0.0756790	+	0.997132i	$0.524112\pi$
$564$	12166.9	0.908364
$565$	2702.31	0.201216
$566$	1749.76	0.129943
$567$	28004.1	2.07418
$568$	13970.8	1.03205
$569$	−1246.96	−0.0918722	−0.0459361	−	0.998944i	$-0.514627\pi$
$569$	−1246.96	−0.0918722	−0.0459361	+	0.998944i	$0.514627\pi$
$570$	−827.516	−0.0608085
$571$	8377.50	0.613988	0.306994	−	0.951711i	$-0.400677\pi$
$571$	8377.50	0.613988	0.306994	+	0.951711i	$0.400677\pi$
$572$	0	0
$573$	−3097.89	−0.225857
$574$	2376.36	0.172800
$575$	13289.8	0.963869
$576$	−8705.45	−0.629734
$577$	21869.2	1.57786	0.788930	−	0.614483i	$-0.210636\pi$
$577$	21869.2	1.57786	0.788930	+	0.614483i	$0.210636\pi$
$578$	4768.42	0.343149
$579$	−33261.0	−2.38736
$580$	−3442.97	−0.246485
$581$	15091.4	1.07762
$582$	−1138.43	−0.0810812
$583$	−3196.32	−0.227064
$584$	11262.2	0.798003
$585$	0	0
$586$	666.769	0.0470034
$587$	−4157.12	−0.292305	−0.146152	−	0.989262i	$-0.546689\pi$
$587$	−4157.12	−0.292305	−0.146152	+	0.989262i	$0.546689\pi$
$588$	−13034.6	−0.914177
$589$	−5916.73	−0.413913
$590$	902.030	0.0629423
$591$	33963.9	2.36394
$592$	6888.86	0.478261
$593$	−23811.5	−1.64894	−0.824469	−	0.565908i	$-0.808526\pi$
$593$	−23811.5	−1.64894	−0.824469	+	0.565908i	$0.808526\pi$
$594$	4983.47	0.344233
$595$	−613.100	−0.0422431
$596$	4122.11	0.283302
$597$	2500.97	0.171454
$598$	0	0
$599$	−22974.4	−1.56712	−0.783562	−	0.621314i	$-0.786599\pi$
$599$	−22974.4	−1.56712	−0.783562	+	0.621314i	$0.786599\pi$
$600$	18678.0	1.27088
$601$	−1763.44	−0.119688	−0.0598439	−	0.998208i	$-0.519060\pi$
$601$	−1763.44	−0.119688	−0.0598439	+	0.998208i	$0.519060\pi$
$602$	4775.77	0.323332
$603$	75808.2	5.11965
$604$	16040.3	1.08058
$605$	285.474	0.0191838
$606$	−7865.68	−0.527263
$607$	−4733.12	−0.316494	−0.158247	−	0.987400i	$-0.550584\pi$
$607$	−4733.12	−0.316494	−0.158247	+	0.987400i	$0.550584\pi$
$608$	5581.94	0.372331
$609$	−25678.2	−1.70859
$610$	1437.89	0.0954403
$611$	0	0
$612$	10190.4	0.673074
$613$	5699.99	0.375563	0.187782	−	0.982211i	$-0.439870\pi$
$613$	5699.99	0.375563	0.187782	+	0.982211i	$0.439870\pi$
$614$	−7942.19	−0.522021
$615$	4219.65	0.276671
$616$	2139.28	0.139925
$617$	18224.6	1.18913	0.594566	−	0.804047i	$-0.297324\pi$
$617$	18224.6	1.18913	0.594566	+	0.804047i	$0.297324\pi$
$618$	−10474.4	−0.681785
$619$	−10254.3	−0.665840	−0.332920	−	0.942955i	$-0.608034\pi$
$619$	−10254.3	−0.665840	−0.332920	+	0.942955i	$0.608034\pi$
$620$	−2872.92	−0.186096
$621$	47183.1	3.04894
$622$	4677.05	0.301499
$623$	−12109.0	−0.778709
$624$	0	0
$625$	13568.6	0.868393
$626$	−11697.5	−0.746849
$627$	3611.12	0.230007
$628$	22687.4	1.44160
$629$	−3855.06	−0.244374
$630$	−2162.98	−0.136786
$631$	4554.62	0.287348	0.143674	−	0.989625i	$-0.454108\pi$
$631$	4554.62	0.287348	0.143674	+	0.989625i	$0.454108\pi$
$632$	−1476.86	−0.0929531
$633$	−39551.7	−2.48348
$634$	−1697.54	−0.106337
$635$	2518.63	0.157399
$636$	−19632.2	−1.22400
$637$	0	0
$638$	−2500.71	−0.155179
$639$	61641.4	3.81612
$640$	3474.77	0.214613
$641$	−19042.4	−1.17337	−0.586683	−	0.809817i	$-0.699567\pi$
$641$	−19042.4	−1.17337	−0.586683	+	0.809817i	$0.699567\pi$
$642$	10602.8	0.651806
$643$	−21140.9	−1.29660	−0.648301	−	0.761384i	$-0.724520\pi$
$643$	−21140.9	−1.29660	−0.648301	+	0.761384i	$0.724520\pi$
$644$	9349.22	0.572066
$645$	8480.23	0.517688
$646$	−755.276	−0.0459999
$647$	−5671.51	−0.344621	−0.172311	−	0.985043i	$-0.555123\pi$
$647$	−5671.51	−0.344621	−0.172311	+	0.985043i	$0.555123\pi$
$648$	36289.8	2.20000
$649$	−3936.29	−0.238078
$650$	0	0
$651$	−21426.7	−1.28998
$652$	−1988.69	−0.119452
$653$	6776.24	0.406087	0.203043	−	0.979170i	$-0.434917\pi$
$653$	6776.24	0.406087	0.203043	+	0.979170i	$0.434917\pi$
$654$	5879.91	0.351564
$655$	−5264.87	−0.314069
$656$	−6882.10	−0.409605
$657$	49690.5	2.95070
$658$	−2357.05	−0.139647
$659$	−10321.9	−0.610143	−0.305071	−	0.952330i	$-0.598680\pi$
$659$	−10321.9	−0.610143	−0.305071	+	0.952330i	$0.598680\pi$
$660$	1753.41	0.103411
$661$	−20694.7	−1.21775	−0.608874	−	0.793267i	$-0.708379\pi$
$661$	−20694.7	−1.21775	−0.608874	+	0.793267i	$0.708379\pi$
$662$	3293.23	0.193346
$663$	0	0
$664$	19556.6	1.14299
$665$	−963.171	−0.0561656
$666$	−13600.4	−0.791299
$667$	−23676.5	−1.37445
$668$	−302.393	−0.0175149
$669$	−9971.00	−0.576235
$670$	−2728.18	−0.157312
$671$	−6274.69	−0.361001
$672$	20214.3	1.16039
$673$	−9767.56	−0.559453	−0.279726	−	0.960080i	$-0.590244\pi$
$673$	−9767.56	−0.559453	−0.279726	+	0.960080i	$0.590244\pi$
$674$	1742.75	0.0995967
$675$	50643.2	2.88779
$676$	0	0
$677$	−16919.3	−0.960506	−0.480253	−	0.877130i	$-0.659455\pi$
$677$	−16919.3	−0.960506	−0.480253	+	0.877130i	$0.659455\pi$
$678$	12055.4	0.682870
$679$	−1325.05	−0.0748905
$680$	−794.501	−0.0448055
$681$	−42946.1	−2.41659
$682$	−2086.67	−0.117159
$683$	−29013.0	−1.62540	−0.812702	−	0.582680i	$-0.802004\pi$
$683$	−29013.0	−1.62540	−0.812702	+	0.582680i	$0.802004\pi$
$684$	16008.9	0.894907
$685$	1231.56	0.0686943
$686$	7014.62	0.390408
$687$	40263.4	2.23602
$688$	−13831.0	−0.766425
$689$	0	0
$690$	−2763.14	−0.152451
$691$	−20339.0	−1.11973	−0.559863	−	0.828585i	$-0.689146\pi$
$691$	−20339.0	−1.11973	−0.559863	+	0.828585i	$0.689146\pi$
$692$	−2825.63	−0.155223
$693$	9438.82	0.517390
$694$	−12133.7	−0.663673
$695$	3001.42	0.163813
$696$	−33275.8	−1.81223
$697$	3851.28	0.209294
$698$	556.934	0.0302009
$699$	33666.9	1.82174
$700$	10034.8	0.541829
$701$	−496.855	−0.0267702	−0.0133851	−	0.999910i	$-0.504261\pi$
$701$	−496.855	−0.0267702	−0.0133851	+	0.999910i	$0.504261\pi$
$702$	0	0
$703$	−6056.24	−0.324915
$704$	−1367.14	−0.0731906
$705$	−4185.36	−0.223588
$706$	13744.6	0.732700
$707$	−9155.09	−0.487005
$708$	−24177.1	−1.28338
$709$	−2803.53	−0.148503	−0.0742515	−	0.997240i	$-0.523657\pi$
$709$	−2803.53	−0.148503	−0.0742515	+	0.997240i	$0.523657\pi$
$710$	−2218.35	−0.117258
$711$	−6516.12	−0.343704
$712$	−15691.7	−0.825944
$713$	−19756.4	−1.03771
$714$	−2735.14	−0.143361
$715$	0	0
$716$	6994.80	0.365095
$717$	−38425.7	−2.00144
$718$	14050.9	0.730330
$719$	29926.2	1.55224	0.776118	−	0.630588i	$-0.217186\pi$
$719$	29926.2	1.55224	0.776118	+	0.630588i	$0.217186\pi$
$720$	6264.13	0.324236
$721$	−12191.5	−0.629729
$722$	6141.82	0.316586
$723$	−54650.3	−2.81116
$724$	8311.62	0.426656
$725$	−25412.8	−1.30180
$726$	1273.55	0.0651043
$727$	11850.0	0.604528	0.302264	−	0.953224i	$-0.402258\pi$
$727$	11850.0	0.604528	0.302264	+	0.953224i	$0.402258\pi$
$728$	0	0
$729$	47333.7	2.40480
$730$	−1788.26	−0.0906665
$731$	7739.92	0.391616
$732$	−38539.9	−1.94600
$733$	−28928.4	−1.45770	−0.728850	−	0.684674i	$-0.759945\pi$
$733$	−28928.4	−1.45770	−0.728850	+	0.684674i	$0.759945\pi$
$734$	−13894.1	−0.698694
$735$	4483.85	0.225019
$736$	18638.5	0.933459
$737$	11905.3	0.595029
$738$	13587.1	0.677706
$739$	33785.0	1.68173	0.840867	−	0.541242i	$-0.182046\pi$
$739$	33785.0	1.68173	0.840867	+	0.541242i	$0.182046\pi$
$740$	−2940.66	−0.146082
$741$	0	0
$742$	3803.29	0.188171
$743$	−1642.09	−0.0810800	−0.0405400	−	0.999178i	$-0.512908\pi$
$743$	−1642.09	−0.0810800	−0.0405400	+	0.999178i	$0.512908\pi$
$744$	−27766.3	−1.36823
$745$	−1417.99	−0.0697332
$746$	11507.9	0.564793
$747$	86286.7	4.22633
$748$	1600.34	0.0782278
$749$	12340.9	0.602039
$750$	−6069.76	−0.295515
$751$	−1494.90	−0.0726360	−0.0363180	−	0.999340i	$-0.511563\pi$
$751$	−1494.90	−0.0726360	−0.0363180	+	0.999340i	$0.511563\pi$
$752$	6826.18	0.331018
$753$	20150.4	0.975196
$754$	0	0
$755$	−5517.82	−0.265979
$756$	35626.8	1.71393
$757$	22740.5	1.09183	0.545917	−	0.837839i	$-0.316181\pi$
$757$	22740.5	1.09183	0.545917	+	0.837839i	$0.316181\pi$
$758$	−4136.61	−0.198217
$759$	12057.8	0.576642
$760$	−1248.15	−0.0595725
$761$	−22650.7	−1.07896	−0.539479	−	0.841999i	$-0.681379\pi$
$761$	−22650.7	−1.07896	−0.539479	+	0.841999i	$0.681379\pi$
$762$	11236.0	0.534170
$763$	6843.81	0.324721
$764$	−2156.79	−0.102134
$765$	−3505.46	−0.165673
$766$	9109.63	0.429692
$767$	0	0
$768$	5706.71	0.268129
$769$	−39078.0	−1.83250	−0.916249	−	0.400610i	$-0.868798\pi$
$769$	−39078.0	−1.83250	−0.916249	+	0.400610i	$0.868798\pi$
$770$	−339.684	−0.0158979
$771$	−26877.7	−1.25548
$772$	−23156.8	−1.07958
$773$	−2252.40	−0.104804	−0.0524018	−	0.998626i	$-0.516688\pi$
$773$	−2252.40	−0.104804	−0.0524018	+	0.998626i	$0.516688\pi$
$774$	27305.9	1.26808
$775$	−21205.2	−0.982856
$776$	−1717.10	−0.0794332
$777$	−21931.9	−1.01262
$778$	−13476.6	−0.621028
$779$	6050.31	0.278273
$780$	0	0
$781$	9680.47	0.443527
$782$	−2521.92	−0.115325
$783$	−90223.3	−4.11790
$784$	−7313.00	−0.333136
$785$	−7804.41	−0.354843
$786$	−23487.4	−1.06586
$787$	−24858.5	−1.12593	−0.562967	−	0.826479i	$-0.690340\pi$
$787$	−24858.5	−1.12593	−0.562967	+	0.826479i	$0.690340\pi$
$788$	23646.2	1.06898
$789$	55048.5	2.48388
$790$	234.502	0.0105610
$791$	14031.7	0.630732
$792$	12231.5	0.548774
$793$	0	0
$794$	−9006.78	−0.402568
$795$	6753.41	0.301281
$796$	1741.21	0.0775322
$797$	−14061.3	−0.624937	−0.312469	−	0.949928i	$-0.601156\pi$
$797$	−14061.3	−0.624937	−0.312469	+	0.949928i	$0.601156\pi$
$798$	−4296.86	−0.190610
$799$	−3819.99	−0.169138
$800$	20005.3	0.884120
$801$	−69234.2	−3.05402
$802$	8706.17	0.383323
$803$	7803.64	0.342945
$804$	73123.5	3.20755
$805$	−3216.10	−0.140811
$806$	0	0
$807$	−28106.0	−1.22600
$808$	−11863.9	−0.516546
$809$	−12440.6	−0.540652	−0.270326	−	0.962769i	$-0.587132\pi$
$809$	−12440.6	−0.540652	−0.270326	+	0.962769i	$0.587132\pi$
$810$	−5762.25	−0.249957
$811$	−3110.40	−0.134674	−0.0673371	−	0.997730i	$-0.521450\pi$
$811$	−3110.40	−0.134674	−0.0673371	+	0.997730i	$0.521450\pi$
$812$	−17877.5	−0.772634
$813$	−31978.6	−1.37950
$814$	−2135.87	−0.0919684
$815$	684.102	0.0294025
$816$	7921.14	0.339823
$817$	12159.3	0.520685
$818$	294.664	0.0125950
$819$	0	0
$820$	2937.78	0.125112
$821$	20890.6	0.888048	0.444024	−	0.896015i	$-0.353551\pi$
$821$	20890.6	0.888048	0.444024	+	0.896015i	$0.353551\pi$
$822$	5494.20	0.233129
$823$	−17299.9	−0.732730	−0.366365	−	0.930471i	$-0.619398\pi$
$823$	−17299.9	−0.732730	−0.366365	+	0.930471i	$0.619398\pi$
$824$	−15798.7	−0.667927
$825$	12942.1	0.546163
$826$	4683.77	0.197299
$827$	7394.58	0.310925	0.155462	−	0.987842i	$-0.450313\pi$
$827$	7394.58	0.310925	0.155462	+	0.987842i	$0.450313\pi$
$828$	53455.0	2.24359
$829$	−22770.6	−0.953987	−0.476994	−	0.878907i	$-0.658274\pi$
$829$	−22770.6	−0.953987	−0.476994	+	0.878907i	$0.658274\pi$
$830$	−3105.29	−0.129863
$831$	59054.6	2.46520
$832$	0	0
$833$	4092.42	0.170221
$834$	13389.8	0.555937
$835$	104.022	0.00431119
$836$	2514.12	0.104010
$837$	−75285.1	−3.10900
$838$	−874.397	−0.0360448
$839$	−4960.27	−0.204109	−0.102055	−	0.994779i	$-0.532542\pi$
$839$	−4960.27	−0.204109	−0.102055	+	0.994779i	$0.532542\pi$
$840$	−4520.02	−0.185661
$841$	20885.1	0.856335
$842$	−1282.72	−0.0525005
$843$	−69385.4	−2.83483
$844$	−27536.5	−1.12304
$845$	0	0
$846$	−13476.7	−0.547680
$847$	1482.32	0.0601335
$848$	−11014.6	−0.446040
$849$	16133.0	0.652161
$850$	−2706.86	−0.109229
$851$	−20222.3	−0.814584
$852$	59458.5	2.39086
$853$	−26084.7	−1.04704	−0.523518	−	0.852015i	$-0.675381\pi$
$853$	−26084.7	−1.04704	−0.523518	+	0.852015i	$0.675381\pi$
$854$	7466.22	0.299167
$855$	−5507.02	−0.220276
$856$	15992.3	0.638558
$857$	42203.7	1.68221	0.841104	−	0.540873i	$-0.181906\pi$
$857$	42203.7	1.68221	0.841104	+	0.540873i	$0.181906\pi$
$858$	0	0
$859$	−6608.73	−0.262499	−0.131250	−	0.991349i	$-0.541899\pi$
$859$	−6608.73	−0.262499	−0.131250	+	0.991349i	$0.541899\pi$
$860$	5904.05	0.234101
$861$	21910.4	0.867254
$862$	−9934.35	−0.392535
$863$	23816.7	0.939431	0.469716	−	0.882818i	$-0.344356\pi$
$863$	23816.7	0.939431	0.469716	+	0.882818i	$0.344356\pi$
$864$	71025.2	2.79668
$865$	972.007	0.0382072
$866$	−753.747	−0.0295766
$867$	43965.6	1.72220
$868$	−14917.6	−0.583336
$869$	−1023.32	−0.0399469
$870$	5283.67	0.205900
$871$	0	0
$872$	8868.72	0.344418
$873$	−7576.08	−0.293713
$874$	−3961.91	−0.153333
$875$	−7064.78	−0.272952
$876$	47930.8	1.84867
$877$	−40806.0	−1.57118	−0.785588	−	0.618749i	$-0.787640\pi$
$877$	−40806.0	−1.57118	−0.785588	+	0.618749i	$0.787640\pi$
$878$	17121.4	0.658109
$879$	6147.72	0.235902
$880$	983.748	0.0376843
$881$	−13567.4	−0.518838	−0.259419	−	0.965765i	$-0.583531\pi$
$881$	−13567.4	−0.518838	−0.259419	+	0.965765i	$0.583531\pi$
$882$	14437.8	0.551185
$883$	34415.4	1.31163	0.655816	−	0.754921i	$-0.272325\pi$
$883$	34415.4	1.31163	0.655816	+	0.754921i	$0.272325\pi$
$884$	0	0
$885$	8316.86	0.315896
$886$	13384.7	0.507524
$887$	−4694.42	−0.177704	−0.0888520	−	0.996045i	$-0.528320\pi$
$887$	−4694.42	−0.177704	−0.0888520	+	0.996045i	$0.528320\pi$
$888$	−28421.1	−1.07404
$889$	13077.9	0.493385
$890$	2491.60	0.0938411
$891$	25145.4	0.945457
$892$	−6941.95	−0.260576
$893$	−6001.14	−0.224883
$894$	−6325.89	−0.236655
$895$	−2406.19	−0.0898659
$896$	18042.7	0.672727
$897$	0	0
$898$	−6850.60	−0.254574
$899$	37778.1	1.40153
$900$	57375.0	2.12500
$901$	6163.85	0.227911
$902$	2133.78	0.0787661
$903$	44033.4	1.62275
$904$	18183.3	0.668991
$905$	−2859.17	−0.105019
$906$	−24615.9	−0.902658
$907$	−10414.2	−0.381253	−0.190627	−	0.981663i	$-0.561052\pi$
$907$	−10414.2	−0.381253	−0.190627	+	0.981663i	$0.561052\pi$
$908$	−29899.7	−1.09279
$909$	−52345.1	−1.90999
$910$	0	0
$911$	45611.2	1.65880	0.829400	−	0.558656i	$-0.188683\pi$
$911$	45611.2	1.65880	0.829400	+	0.558656i	$0.188683\pi$
$912$	12444.0	0.451822
$913$	13550.9	0.491203
$914$	6937.55	0.251065
$915$	13257.6	0.478997
$916$	28032.0	1.01114
$917$	−27337.7	−0.984482
$918$	−9610.22	−0.345517
$919$	−7509.13	−0.269536	−0.134768	−	0.990877i	$-0.543029\pi$
$919$	−7509.13	−0.269536	−0.134768	+	0.990877i	$0.543029\pi$
$920$	−4167.67	−0.149352
$921$	−73228.3	−2.61993
$922$	13559.8	0.484346
$923$	0	0
$924$	9104.56	0.324154
$925$	−21705.2	−0.771528
$926$	−17741.8	−0.629625
$927$	−69706.0	−2.46974
$928$	−35640.5	−1.26073
$929$	−17185.9	−0.606945	−0.303473	−	0.952840i	$-0.598146\pi$
$929$	−17185.9	−0.606945	−0.303473	+	0.952840i	$0.598146\pi$
$930$	4408.86	0.155454
$931$	6429.12	0.226322
$932$	23439.4	0.823801
$933$	43123.1	1.51317
$934$	−6359.95	−0.222809
$935$	−550.514	−0.0192553
$936$	0	0
$937$	−11342.3	−0.395449	−0.197725	−	0.980258i	$-0.563355\pi$
$937$	−11342.3	−0.395449	−0.197725	+	0.980258i	$0.563355\pi$
$938$	−14166.0	−0.493110
$939$	−107853.	−3.74830
$940$	−2913.91	−0.101108
$941$	−50673.1	−1.75547	−0.877734	−	0.479148i	$-0.840946\pi$
$941$	−50673.1	−1.75547	−0.877734	+	0.479148i	$0.840946\pi$
$942$	−34816.7	−1.20424
$943$	20202.4	0.697648
$944$	−13564.5	−0.467677
$945$	−12255.5	−0.421874
$946$	4288.25	0.147382
$947$	10395.8	0.356725	0.178362	−	0.983965i	$-0.442920\pi$
$947$	10395.8	0.356725	0.178362	+	0.983965i	$0.442920\pi$
$948$	−6285.37	−0.215337
$949$	0	0
$950$	−4252.44	−0.145229
$951$	−15651.6	−0.533688
$952$	−4125.43	−0.140447
$953$	−4987.43	−0.169526	−0.0847632	−	0.996401i	$-0.527013\pi$
$953$	−4987.43	−0.169526	−0.0847632	+	0.996401i	$0.527013\pi$
$954$	21745.7	0.737989
$955$	741.930	0.0251396
$956$	−26752.5	−0.905060
$957$	−23056.9	−0.778814
$958$	−13647.0	−0.460244
$959$	6394.86	0.215329
$960$	2888.60	0.0971136
$961$	1732.25	0.0581469
$962$	0	0
$963$	70560.4	2.36114
$964$	−38048.3	−1.27122
$965$	7965.88	0.265731
$966$	−14347.5	−0.477873
$967$	−20072.0	−0.667498	−0.333749	−	0.942662i	$-0.608314\pi$
$967$	−20072.0	−0.667498	−0.333749	+	0.942662i	$0.608314\pi$
$968$	1920.90	0.0637810
$969$	−6963.76	−0.230865
$970$	272.648	0.00902494
$971$	−880.709	−0.0291074	−0.0145537	−	0.999894i	$-0.504633\pi$
$971$	−880.709	−0.0291074	−0.0145537	+	0.999894i	$0.504633\pi$
$972$	75925.1	2.50545
$973$	15584.8	0.513490
$974$	4701.03	0.154652
$975$	0	0
$976$	−21622.7	−0.709145
$977$	−12187.0	−0.399075	−0.199537	−	0.979890i	$-0.563944\pi$
$977$	−12187.0	−0.399075	−0.199537	+	0.979890i	$0.563944\pi$
$978$	3051.89	0.0997839
$979$	−10872.9	−0.354952
$980$	3121.72	0.101755
$981$	39130.1	1.27353
$982$	15170.7	0.492990
$983$	26378.0	0.855877	0.427938	−	0.903808i	$-0.359240\pi$
$983$	26378.0	0.855877	0.427938	+	0.903808i	$0.359240\pi$
$984$	28393.2	0.919860
$985$	−8134.21	−0.263124
$986$	4822.41	0.155758
$987$	−21732.4	−0.700861
$988$	0	0
$989$	40600.8	1.30539
$990$	−1942.18	−0.0623499
$991$	−58359.4	−1.87068	−0.935342	−	0.353744i	$-0.884909\pi$
$991$	−58359.4	−1.87068	−0.935342	+	0.353744i	$0.884909\pi$
$992$	−29739.6	−0.951847
$993$	30364.1	0.970367
$994$	−11518.7	−0.367557
$995$	−598.972	−0.0190841
$996$	83231.0	2.64787
$997$	−18837.2	−0.598376	−0.299188	−	0.954194i	$-0.596716\pi$
$997$	−18837.2	−0.598376	−0.299188	+	0.954194i	$0.596716\pi$
$998$	4255.08	0.134962
$999$	−77060.4	−2.44052

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.g.1.7		17
13.3	even	3		143.4.e.b.100.11	✓	34
13.9	even	3		143.4.e.b.133.11	yes	34
13.12	even	2		1859.4.a.h.1.11		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.b.100.11	✓	34	13.3	even	3
143.4.e.b.133.11	yes	34	13.9	even	3
1859.4.a.g.1.7		17	1.1	even	1	trivial
1859.4.a.h.1.11		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)

\(f(q)\)	\(=\)	\(q-1.06843 q^{2} -9.85108 q^{3} -6.85846 q^{4} +2.35929 q^{5} +10.5252 q^{6} +12.2506 q^{7} +15.8752 q^{8} +70.0437 q^{9} +O(q^{10})\)	\(q-1.06843 q^{2} -9.85108 q^{3} -6.85846 q^{4} +2.35929 q^{5} +10.5252 q^{6} +12.2506 q^{7} +15.8752 q^{8} +70.0437 q^{9} -2.52073 q^{10} +11.0000 q^{11} +67.5632 q^{12} -13.0888 q^{14} -23.2415 q^{15} +37.9062 q^{16} -21.2126 q^{17} -74.8367 q^{18} -33.3247 q^{19} -16.1811 q^{20} -120.681 q^{21} -11.7527 q^{22} -111.274 q^{23} -156.388 q^{24} -119.434 q^{25} -424.027 q^{27} -84.0200 q^{28} +212.777 q^{29} +24.8319 q^{30} +177.548 q^{31} -167.502 q^{32} -108.362 q^{33} +22.6641 q^{34} +28.9026 q^{35} -480.392 q^{36} +181.734 q^{37} +35.6050 q^{38} +37.4542 q^{40} -181.556 q^{41} +128.939 q^{42} -364.873 q^{43} -75.4431 q^{44} +165.253 q^{45} +118.888 q^{46} +180.081 q^{47} -373.417 q^{48} -192.924 q^{49} +127.606 q^{50} +208.967 q^{51} -290.575 q^{53} +453.043 q^{54} +25.9522 q^{55} +194.480 q^{56} +328.284 q^{57} -227.337 q^{58} -357.844 q^{59} +159.401 q^{60} -570.427 q^{61} -189.697 q^{62} +858.075 q^{63} -124.286 q^{64} +115.777 q^{66} +1082.30 q^{67} +145.486 q^{68} +1096.17 q^{69} -30.8804 q^{70} +880.042 q^{71} +1111.96 q^{72} +709.422 q^{73} -194.170 q^{74} +1176.55 q^{75} +228.556 q^{76} +134.756 q^{77} -93.0294 q^{79} +89.4317 q^{80} +2285.94 q^{81} +193.980 q^{82} +1231.90 q^{83} +827.687 q^{84} -50.0467 q^{85} +389.841 q^{86} -2096.08 q^{87} +174.627 q^{88} -988.442 q^{89} -176.562 q^{90} +763.167 q^{92} -1749.04 q^{93} -192.404 q^{94} -78.6226 q^{95} +1650.07 q^{96} -108.162 q^{97} +206.125 q^{98} +770.481 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9}+O(q^{10}) \) 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

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Database

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