LMFDB - Embedded newform 1859.4.a.f.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:	$1$
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} - 4 x^{16} - 99 x^{15} + 375 x^{14} + 3949 x^{13} - 13998 x^{12} - 81750 x^{11} + 267574 x^{10} + \cdots + 2596992 $ x^17 - 4x^16 - 99x^15 + 375x^14 + 3949x^13 - 13998x^12 - 81750x^11 + 267574x^10 + 941923x^9 - 2799440x^8 - 6021311x^7 + 15765187x^6 + 20197463x^5 - 42560950x^4 - 32766128x^3 + 37775816x^2 + 27375104x + 2596992
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 3\cdot 5 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-0.549217$ 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)

$f(q)$	$=$	$q+0.549217 q^{2} -0.561969 q^{3} -7.69836 q^{4} -16.1600 q^{5} -0.308643 q^{6} -31.1335 q^{7} -8.62181 q^{8} -26.6842 q^{9} +O(q^{10})$	\(q+0.549217 q^{2} -0.561969 q^{3} -7.69836 q^{4} -16.1600 q^{5} -0.308643 q^{6} -31.1335 q^{7} -8.62181 q^{8} -26.6842 q^{9} -8.87537 q^{10} +11.0000 q^{11} +4.32624 q^{12} -17.0990 q^{14} +9.08144 q^{15} +56.8516 q^{16} +76.3225 q^{17} -14.6554 q^{18} +95.5779 q^{19} +124.406 q^{20} +17.4960 q^{21} +6.04139 q^{22} -119.887 q^{23} +4.84518 q^{24} +136.147 q^{25} +30.1688 q^{27} +239.677 q^{28} -48.3831 q^{29} +4.98768 q^{30} -210.428 q^{31} +100.198 q^{32} -6.18165 q^{33} +41.9176 q^{34} +503.119 q^{35} +205.425 q^{36} -249.123 q^{37} +52.4930 q^{38} +139.329 q^{40} -271.764 q^{41} +9.60912 q^{42} +512.404 q^{43} -84.6820 q^{44} +431.218 q^{45} -65.8439 q^{46} +623.311 q^{47} -31.9488 q^{48} +626.294 q^{49} +74.7743 q^{50} -42.8908 q^{51} +213.689 q^{53} +16.5692 q^{54} -177.761 q^{55} +268.427 q^{56} -53.7118 q^{57} -26.5728 q^{58} +34.2545 q^{59} -69.9122 q^{60} +497.737 q^{61} -115.571 q^{62} +830.772 q^{63} -399.782 q^{64} -3.39507 q^{66} -107.068 q^{67} -587.558 q^{68} +67.3726 q^{69} +276.321 q^{70} +21.5024 q^{71} +230.066 q^{72} +748.611 q^{73} -136.823 q^{74} -76.5104 q^{75} -735.793 q^{76} -342.468 q^{77} -991.434 q^{79} -918.725 q^{80} +703.519 q^{81} -149.258 q^{82} -459.023 q^{83} -134.691 q^{84} -1233.38 q^{85} +281.421 q^{86} +27.1898 q^{87} -94.8399 q^{88} +688.450 q^{89} +236.832 q^{90} +922.932 q^{92} +118.254 q^{93} +342.333 q^{94} -1544.54 q^{95} -56.3083 q^{96} -1624.23 q^{97} +343.971 q^{98} -293.526 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 4 q^{2} - 6 q^{3} + 78 q^{4} - 16 q^{5} - 14 q^{6} + 6 q^{7} - 63 q^{8} + 135 q^{9}+O(q^{10}) $ 17 * q - 4 * q^2 - 6 * q^3 + 78 * q^4 - 16 * q^5 - 14 * q^6 + 6 * q^7 - 63 * q^8 + 135 * q^9	\( 17 q - 4 q^{2} - 6 q^{3} + 78 q^{4} - 16 q^{5} - 14 q^{6} + 6 q^{7} - 63 q^{8} + 135 q^{9} + 2 q^{10} + 187 q^{11} - 95 q^{12} - 60 q^{14} + 28 q^{15} + 350 q^{16} + 118 q^{17} - 478 q^{18} - 403 q^{19} - 98 q^{20} - 220 q^{21} - 44 q^{22} - 215 q^{23} - 26 q^{24} + 319 q^{25} - 384 q^{27} + 396 q^{28} - 7 q^{29} - 1269 q^{30} - 682 q^{31} - 813 q^{32} - 66 q^{33} - 738 q^{34} + 10 q^{35} + 560 q^{36} - 1084 q^{37} + 410 q^{38} + 95 q^{40} - 240 q^{41} + 393 q^{42} - 435 q^{43} + 858 q^{44} - 1242 q^{45} - 1671 q^{46} - 549 q^{47} + 894 q^{48} + 403 q^{49} + 651 q^{50} + 1552 q^{51} - 566 q^{53} - 311 q^{54} - 176 q^{55} - 1925 q^{56} + 534 q^{57} - 618 q^{58} - 2010 q^{59} + 411 q^{60} + 460 q^{61} - 823 q^{62} - 820 q^{63} + 3171 q^{64} - 154 q^{66} + 232 q^{67} + 1795 q^{68} - 1608 q^{69} - 207 q^{70} - 489 q^{71} - 2556 q^{72} - 290 q^{73} + 2653 q^{74} - 2852 q^{75} - 2421 q^{76} + 66 q^{77} - 732 q^{79} - 4915 q^{80} + 2393 q^{81} - 1772 q^{82} + 117 q^{83} - 4161 q^{84} - 4858 q^{85} - 1034 q^{86} + 3032 q^{87} - 693 q^{88} - 4113 q^{89} + 15145 q^{90} - 3554 q^{92} - 802 q^{93} + 2325 q^{94} - 3924 q^{95} - 2601 q^{96} - 2793 q^{97} - 533 q^{98} + 1485 q^{99}+O(q^{100}) \) 17 * q - 4 * q^2 - 6 * q^3 + 78 * q^4 - 16 * q^5 - 14 * q^6 + 6 * q^7 - 63 * q^8 + 135 * q^9 + 2 * q^10 + 187 * q^11 - 95 * q^12 - 60 * q^14 + 28 * q^15 + 350 * q^16 + 118 * q^17 - 478 * q^18 - 403 * q^19 - 98 * q^20 - 220 * q^21 - 44 * q^22 - 215 * q^23 - 26 * q^24 + 319 * q^25 - 384 * q^27 + 396 * q^28 - 7 * q^29 - 1269 * q^30 - 682 * q^31 - 813 * q^32 - 66 * q^33 - 738 * q^34 + 10 * q^35 + 560 * q^36 - 1084 * q^37 + 410 * q^38 + 95 * q^40 - 240 * q^41 + 393 * q^42 - 435 * q^43 + 858 * q^44 - 1242 * q^45 - 1671 * q^46 - 549 * q^47 + 894 * q^48 + 403 * q^49 + 651 * q^50 + 1552 * q^51 - 566 * q^53 - 311 * q^54 - 176 * q^55 - 1925 * q^56 + 534 * q^57 - 618 * q^58 - 2010 * q^59 + 411 * q^60 + 460 * q^61 - 823 * q^62 - 820 * q^63 + 3171 * q^64 - 154 * q^66 + 232 * q^67 + 1795 * q^68 - 1608 * q^69 - 207 * q^70 - 489 * q^71 - 2556 * q^72 - 290 * q^73 + 2653 * q^74 - 2852 * q^75 - 2421 * q^76 + 66 * q^77 - 732 * q^79 - 4915 * q^80 + 2393 * q^81 - 1772 * q^82 + 117 * q^83 - 4161 * q^84 - 4858 * q^85 - 1034 * q^86 + 3032 * q^87 - 693 * q^88 - 4113 * q^89 + 15145 * q^90 - 3554 * q^92 - 802 * q^93 + 2325 * q^94 - 3924 * q^95 - 2601 * q^96 - 2793 * q^97 - 533 * 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 $

$2$	0.549217	0.194178	0.0970888	−	0.995276i	$-0.469047\pi$
$2$	0.549217	0.194178	0.0970888	+	0.995276i	$0.469047\pi$
$3$	−0.561969	−0.108151	−0.0540754	−	0.998537i	$-0.517221\pi$
$3$	−0.561969	−0.108151	−0.0540754	+	0.998537i	$0.517221\pi$
$4$	−7.69836	−0.962295
$5$	−16.1600	−1.44540	−0.722699	−	0.691163i	$-0.757099\pi$
$5$	−16.1600	−1.44540	−0.722699	+	0.691163i	$0.757099\pi$
$6$	−0.308643	−0.0210005
$7$	−31.1335	−1.68105	−0.840525	−	0.541773i	$-0.817753\pi$
$7$	−31.1335	−1.68105	−0.840525	+	0.541773i	$0.817753\pi$
$8$	−8.62181	−0.381034
$9$	−26.6842	−0.988303
$10$	−8.87537	−0.280664
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	4.32624	0.104073
$13$	0	0
$13$	0	0
$14$	−17.0990	−0.326422
$15$	9.08144	0.156321
$16$	56.8516	0.888307
$17$	76.3225	1.08888	0.544439	−	0.838801i	$-0.316743\pi$
$17$	76.3225	1.08888	0.544439	+	0.838801i	$0.316743\pi$
$18$	−14.6554	−0.191906
$19$	95.5779	1.15406	0.577028	−	0.816724i	$-0.304212\pi$
$19$	95.5779	1.15406	0.577028	+	0.816724i	$0.304212\pi$
$20$	124.406	1.39090
$21$	17.4960	0.181807
$22$	6.04139	0.0585467
$23$	−119.887	−1.08688	−0.543438	−	0.839450i	$-0.682878\pi$
$23$	−119.887	−1.08688	−0.543438	+	0.839450i	$0.682878\pi$
$24$	4.84518	0.0412091
$25$	136.147	1.08918
$26$	0	0
$27$	30.1688	0.215037
$28$	239.677	1.61767
$29$	−48.3831	−0.309811	−0.154905	−	0.987929i	$-0.549507\pi$
$29$	−48.3831	−0.309811	−0.154905	+	0.987929i	$0.549507\pi$
$30$	4.98768	0.0303541
$31$	−210.428	−1.21916	−0.609581	−	0.792724i	$-0.708662\pi$
$31$	−210.428	−1.21916	−0.609581	+	0.792724i	$0.708662\pi$
$32$	100.198	0.553523
$33$	−6.18165	−0.0326087
$34$	41.9176	0.211436
$35$	503.119	2.42979
$36$	205.425	0.951039
$37$	−249.123	−1.10691	−0.553454	−	0.832880i	$-0.686691\pi$
$37$	−249.123	−1.10691	−0.553454	+	0.832880i	$0.686691\pi$
$38$	52.4930	0.224092
$39$	0	0
$40$	139.329	0.550746
$41$	−271.764	−1.03518	−0.517591	−	0.855628i	$-0.673171\pi$
$41$	−271.764	−1.03518	−0.517591	+	0.855628i	$0.673171\pi$
$42$	9.60912	0.0353029
$43$	512.404	1.81723	0.908615	−	0.417636i	$-0.137141\pi$
$43$	512.404	1.81723	0.908615	+	0.417636i	$0.137141\pi$
$44$	−84.6820	−0.290143
$45$	431.218	1.42849
$46$	−65.8439	−0.211047
$47$	623.311	1.93445	0.967226	−	0.253918i	$-0.0817192\pi$
$47$	623.311	1.93445	0.967226	+	0.253918i	$0.0817192\pi$
$48$	−31.9488	−0.0960712
$49$	626.294	1.82593
$50$	74.7743	0.211494
$51$	−42.8908	−0.117763
$52$	0	0
$53$	213.689	0.553819	0.276909	−	0.960896i	$-0.410690\pi$
$53$	213.689	0.553819	0.276909	+	0.960896i	$0.410690\pi$
$54$	16.5692	0.0417553
$55$	−177.761	−0.435804
$56$	268.427	0.640537
$57$	−53.7118	−0.124812
$58$	−26.5728	−0.0601583
$59$	34.2545	0.0755856	0.0377928	−	0.999286i	$-0.487967\pi$
$59$	34.2545	0.0755856	0.0377928	+	0.999286i	$0.487967\pi$
$60$	−69.9122	−0.150427
$61$	497.737	1.04473	0.522366	−	0.852721i	$-0.325049\pi$
$61$	497.737	1.04473	0.522366	+	0.852721i	$0.325049\pi$
$62$	−115.571	−0.236734
$63$	830.772	1.66139
$64$	−399.782	−0.780825
$65$	0	0
$66$	−3.39507	−0.00633188
$67$	−107.068	−0.195230	−0.0976148	−	0.995224i	$-0.531121\pi$
$67$	−107.068	−0.195230	−0.0976148	+	0.995224i	$0.531121\pi$
$68$	−587.558	−1.04782
$69$	67.3726	0.117547
$70$	276.321	0.471810
$71$	21.5024	0.0359418	0.0179709	−	0.999839i	$-0.494279\pi$
$71$	21.5024	0.0359418	0.0179709	+	0.999839i	$0.494279\pi$
$72$	230.066	0.376577
$73$	748.611	1.20025	0.600126	−	0.799906i	$-0.295117\pi$
$73$	748.611	1.20025	0.600126	+	0.799906i	$0.295117\pi$
$74$	−136.823	−0.214937
$75$	−76.5104	−0.117795
$76$	−735.793	−1.11054
$77$	−342.468	−0.506856
$78$	0	0
$79$	−991.434	−1.41196	−0.705981	−	0.708231i	$-0.749494\pi$
$79$	−991.434	−1.41196	−0.705981	+	0.708231i	$0.749494\pi$
$80$	−918.725	−1.28396
$81$	703.519	0.965047
$82$	−149.258	−0.201009
$83$	−459.023	−0.607041	−0.303520	−	0.952825i	$-0.598162\pi$
$83$	−459.023	−0.607041	−0.303520	+	0.952825i	$0.598162\pi$
$84$	−134.691	−0.174952
$85$	−1233.38	−1.57386
$86$	281.421	0.352865
$87$	27.1898	0.0335063
$88$	−94.8399	−0.114886
$89$	688.450	0.819951	0.409975	−	0.912097i	$-0.365537\pi$
$89$	688.450	0.819951	0.409975	+	0.912097i	$0.365537\pi$
$90$	236.832	0.277381
$91$	0	0
$92$	922.932	1.04589
$93$	118.254	0.131853
$94$	342.333	0.375627
$95$	−1544.54	−1.66807
$96$	−56.3083	−0.0598640
$97$	−1624.23	−1.70016	−0.850081	−	0.526652i	$-0.823447\pi$
$97$	−1624.23	−1.70016	−0.850081	+	0.526652i	$0.823447\pi$
$98$	343.971	0.354554
$99$	−293.526	−0.297985
$100$	−1048.11	−1.04811
$101$	823.240	0.811044	0.405522	−	0.914085i	$-0.367090\pi$
$101$	823.240	0.811044	0.405522	+	0.914085i	$0.367090\pi$
$102$	−23.5564	−0.0228670
$103$	−262.534	−0.251148	−0.125574	−	0.992084i	$-0.540077\pi$
$103$	−262.534	−0.251148	−0.125574	+	0.992084i	$0.540077\pi$
$104$	0	0
$105$	−282.737	−0.262784
$106$	117.361	0.107539
$107$	−1423.48	−1.28610	−0.643050	−	0.765824i	$-0.722331\pi$
$107$	−1423.48	−1.28610	−0.643050	+	0.765824i	$0.722331\pi$
$108$	−232.251	−0.206929
$109$	−873.349	−0.767446	−0.383723	−	0.923448i	$-0.625358\pi$
$109$	−873.349	−0.767446	−0.383723	+	0.923448i	$0.625358\pi$
$110$	−97.6291	−0.0846234
$111$	139.999	0.119713
$112$	−1769.99	−1.49329
$113$	2.00364	0.00166802	0.000834010	−	1.00000i	$-0.499735\pi$
$113$	2.00364	0.00166802	0.000834010		1.00000i	$0.499735\pi$
$114$	−29.4994	−0.0242357
$115$	1937.38	1.57097
$116$	372.471	0.298130
$117$	0	0
$118$	18.8131	0.0146770
$119$	−2376.18	−1.83046
$120$	−78.2984	−0.0595636
$121$	121.000	0.0909091
$122$	273.366	0.202864
$123$	152.723	0.111956
$124$	1619.95	1.17319
$125$	−180.138	−0.128896
$126$	456.274	0.322604
$127$	1405.39	0.981952	0.490976	−	0.871173i	$-0.336640\pi$
$127$	1405.39	0.981952	0.490976	+	0.871173i	$0.336640\pi$
$128$	−1021.15	−0.705142
$129$	−287.955	−0.196535
$130$	0	0
$131$	377.327	0.251658	0.125829	−	0.992052i	$-0.459841\pi$
$131$	377.327	0.251658	0.125829	+	0.992052i	$0.459841\pi$
$132$	47.5886	0.0313792
$133$	−2975.67	−1.94003
$134$	−58.8033	−0.0379092
$135$	−487.530	−0.310814
$136$	−658.038	−0.414899
$137$	−1186.33	−0.739817	−0.369909	−	0.929068i	$-0.620611\pi$
$137$	−1186.33	−0.739817	−0.369909	+	0.929068i	$0.620611\pi$
$138$	37.0022	0.0228249
$139$	583.423	0.356009	0.178005	−	0.984030i	$-0.443036\pi$
$139$	583.423	0.356009	0.178005	+	0.984030i	$0.443036\pi$
$140$	−3873.19	−2.33817
$141$	−350.281	−0.209213
$142$	11.8095	0.00697909
$143$	0	0
$144$	−1517.04	−0.877917
$145$	781.873	0.447800
$146$	411.150	0.233062
$147$	−351.957	−0.197476
$148$	1917.84	1.06517
$149$	1672.99	0.919842	0.459921	−	0.887960i	$-0.347878\pi$
$149$	1672.99	0.919842	0.459921	+	0.887960i	$0.347878\pi$
$150$	−42.0208	−0.0228732
$151$	−1198.39	−0.645849	−0.322925	−	0.946425i	$-0.604666\pi$
$151$	−1198.39	−0.645849	−0.322925	+	0.946425i	$0.604666\pi$
$152$	−824.054	−0.439734
$153$	−2036.60	−1.07614
$154$	−188.089	−0.0984200
$155$	3400.53	1.76217
$156$	0	0
$157$	−592.287	−0.301081	−0.150540	−	0.988604i	$-0.548101\pi$
$157$	−592.287	−0.301081	−0.150540	+	0.988604i	$0.548101\pi$
$158$	−544.512	−0.274171
$159$	−120.086	−0.0598960
$160$	−1619.21	−0.800061
$161$	3732.49	1.82709
$162$	386.385	0.187390
$163$	1858.31	0.892968	0.446484	−	0.894792i	$-0.352676\pi$
$163$	1858.31	0.892968	0.446484	+	0.894792i	$0.352676\pi$
$164$	2092.14	0.996151
$165$	99.8958	0.0471326
$166$	−252.104	−0.117874
$167$	−1425.31	−0.660440	−0.330220	−	0.943904i	$-0.607123\pi$
$167$	−1425.31	−0.660440	−0.330220	+	0.943904i	$0.607123\pi$
$168$	−150.847	−0.0692746
$169$	0	0
$170$	−677.391	−0.305609
$171$	−2550.42	−1.14056
$172$	−3944.67	−1.74871
$173$	−2615.89	−1.14961	−0.574804	−	0.818291i	$-0.694922\pi$
$173$	−2615.89	−1.14961	−0.574804	+	0.818291i	$0.694922\pi$
$174$	14.9331	0.00650618
$175$	−4238.73	−1.83096
$176$	625.368	0.267835
$177$	−19.2499	−0.00817466
$178$	378.109	0.159216
$179$	8.43939	0.00352397	0.00176198	−	0.999998i	$-0.499439\pi$
$179$	8.43939	0.00352397	0.00176198	+	0.999998i	$0.499439\pi$
$180$	−3319.67	−1.37463
$181$	4206.54	1.72746	0.863728	−	0.503958i	$-0.168123\pi$
$181$	4206.54	1.72746	0.863728	+	0.503958i	$0.168123\pi$
$182$	0	0
$183$	−279.713	−0.112989
$184$	1033.64	0.414136
$185$	4025.84	1.59992
$186$	64.9471	0.0256030
$187$	839.547	0.328309
$188$	−4798.47	−1.86151
$189$	−939.261	−0.361488
$190$	−848.290	−0.323902
$191$	−1547.25	−0.586151	−0.293076	−	0.956089i	$-0.594679\pi$
$191$	−1547.25	−0.586151	−0.293076	+	0.956089i	$0.594679\pi$
$192$	224.665	0.0844469
$193$	−952.426	−0.355218	−0.177609	−	0.984101i	$-0.556836\pi$
$193$	−952.426	−0.355218	−0.177609	+	0.984101i	$0.556836\pi$
$194$	−892.056	−0.330133
$195$	0	0
$196$	−4821.43	−1.75708
$197$	729.394	0.263793	0.131896	−	0.991264i	$-0.457893\pi$
$197$	729.394	0.263793	0.131896	+	0.991264i	$0.457893\pi$
$198$	−161.210	−0.0578619
$199$	4564.82	1.62609	0.813044	−	0.582202i	$-0.197809\pi$
$199$	4564.82	1.62609	0.813044	+	0.582202i	$0.197809\pi$
$200$	−1173.83	−0.415013
$201$	60.1686	0.0211143
$202$	452.137	0.157487
$203$	1506.33	0.520808
$204$	330.189	0.113323
$205$	4391.73	1.49625
$206$	−144.188	−0.0487673
$207$	3199.08	1.07416
$208$	0	0
$209$	1051.36	0.347961
$210$	−155.284	−0.0510267
$211$	−1248.85	−0.407461	−0.203731	−	0.979027i	$-0.565307\pi$
$211$	−1248.85	−0.407461	−0.203731	+	0.979027i	$0.565307\pi$
$212$	−1645.05	−0.532937
$213$	−12.0837	−0.00388714
$214$	−781.798	−0.249732
$215$	−8280.47	−2.62662
$216$	−260.110	−0.0819363
$217$	6551.36	2.04947
$218$	−479.658	−0.149021
$219$	−420.696	−0.129808
$220$	1368.46	0.419372
$221$	0	0
$222$	76.8901	0.0232456
$223$	−3583.12	−1.07598	−0.537990	−	0.842951i	$-0.680816\pi$
$223$	−3583.12	−1.07598	−0.537990	+	0.842951i	$0.680816\pi$
$224$	−3119.52	−0.930500
$225$	−3632.98	−1.07644
$226$	1.10043	0.000323892 0
$227$	4379.55	1.28053	0.640266	−	0.768153i	$-0.278824\pi$
$227$	4379.55	1.28053	0.640266	+	0.768153i	$0.278824\pi$
$228$	413.493	0.120106
$229$	−1460.32	−0.421401	−0.210701	−	0.977551i	$-0.567575\pi$
$229$	−1460.32	−0.421401	−0.210701	+	0.977551i	$0.567575\pi$
$230$	1064.04	0.305047
$231$	192.456	0.0548169
$232$	417.150	0.118048
$233$	512.812	0.144186	0.0720932	−	0.997398i	$-0.477032\pi$
$233$	512.812	0.144186	0.0720932	+	0.997398i	$0.477032\pi$
$234$	0	0
$235$	−10072.7	−2.79605
$236$	−263.703	−0.0727357
$237$	557.155	0.152705
$238$	−1305.04	−0.355434
$239$	−4506.95	−1.21979	−0.609896	−	0.792481i	$-0.708789\pi$
$239$	−4506.95	−1.21979	−0.609896	+	0.792481i	$0.708789\pi$
$240$	516.295	0.138861
$241$	−523.128	−0.139824	−0.0699121	−	0.997553i	$-0.522272\pi$
$241$	−523.128	−0.139824	−0.0699121	+	0.997553i	$0.522272\pi$
$242$	66.4553	0.0176525
$243$	−1209.91	−0.319407
$244$	−3831.76	−1.00534
$245$	−10120.9	−2.63920
$246$	83.8781	0.0217393
$247$	0	0
$248$	1814.27	0.464542
$249$	257.957	0.0656520
$250$	−98.9349	−0.0250288
$251$	5145.03	1.29383	0.646915	−	0.762562i	$-0.276059\pi$
$251$	5145.03	1.29383	0.646915	+	0.762562i	$0.276059\pi$
$252$	−6395.58	−1.59874
$253$	−1318.75	−0.327705
$254$	771.862	0.190673
$255$	693.118	0.170215
$256$	2637.42	0.643902
$257$	1309.87	0.317928	0.158964	−	0.987284i	$-0.449185\pi$
$257$	1309.87	0.317928	0.158964	+	0.987284i	$0.449185\pi$
$258$	−158.150	−0.0381627
$259$	7756.07	1.86077
$260$	0	0
$261$	1291.06	0.306187
$262$	207.234	0.0488663
$263$	2860.57	0.670685	0.335343	−	0.942096i	$-0.391148\pi$
$263$	2860.57	0.670685	0.335343	+	0.942096i	$0.391148\pi$
$264$	53.2970	0.0124250
$265$	−3453.22	−0.800489
$266$	−1634.29	−0.376710
$267$	−386.887	−0.0886784
$268$	824.245	0.187868
$269$	2008.87	0.455327	0.227664	−	0.973740i	$-0.426891\pi$
$269$	2008.87	0.455327	0.227664	+	0.973740i	$0.426891\pi$
$270$	−267.760	−0.0603531
$271$	3730.89	0.836294	0.418147	−	0.908379i	$-0.362680\pi$
$271$	3730.89	0.836294	0.418147	+	0.908379i	$0.362680\pi$
$272$	4339.06	0.967258
$273$	0	0
$274$	−651.553	−0.143656
$275$	1497.62	0.328399
$276$	−518.659	−0.113114
$277$	2007.44	0.435435	0.217718	−	0.976012i	$-0.430139\pi$
$277$	2007.44	0.435435	0.217718	+	0.976012i	$0.430139\pi$
$278$	320.426	0.0691290
$279$	5615.10	1.20490
$280$	−4337.79	−0.925831
$281$	−2917.39	−0.619348	−0.309674	−	0.950843i	$-0.600220\pi$
$281$	−2917.39	−0.619348	−0.309674	+	0.950843i	$0.600220\pi$
$282$	−192.380	−0.0406244
$283$	1686.35	0.354216	0.177108	−	0.984191i	$-0.443326\pi$
$283$	1686.35	0.354216	0.177108	+	0.984191i	$0.443326\pi$
$284$	−165.533	−0.0345866
$285$	867.985	0.180403
$286$	0	0
$287$	8460.97	1.74019
$288$	−2673.71	−0.547049
$289$	912.122	0.185655
$290$	429.418	0.0869528
$291$	912.767	0.183874
$292$	−5763.08	−1.15500
$293$	5146.27	1.02610	0.513052	−	0.858358i	$-0.328515\pi$
$293$	5146.27	1.02610	0.513052	+	0.858358i	$0.328515\pi$
$294$	−193.301	−0.0383454
$295$	−553.554	−0.109251
$296$	2147.89	0.421769
$297$	331.857	0.0648360
$298$	918.834	0.178613
$299$	0	0
$300$	589.005	0.113354
$301$	−15952.9	−3.05485
$302$	−658.174	−0.125409
$303$	−462.635	−0.0877151
$304$	5433.76	1.02516
$305$	−8043.45	−1.51005
$306$	−1118.54	−0.208963
$307$	−7.10672	−0.00132118	−0.000660590	−	1.00000i	$-0.500210\pi$
$307$	−7.10672	−0.00132118	−0.000660590		1.00000i	$0.500210\pi$
$308$	2636.44	0.487745
$309$	147.536	0.0271619
$310$	1867.63	0.342175
$311$	2323.48	0.423642	0.211821	−	0.977309i	$-0.432061\pi$
$311$	2323.48	0.423642	0.211821	+	0.977309i	$0.432061\pi$
$312$	0	0
$313$	7622.82	1.37657	0.688287	−	0.725439i	$-0.258363\pi$
$313$	7622.82	1.37657	0.688287	+	0.725439i	$0.258363\pi$
$314$	−325.294	−0.0584631
$315$	−13425.3	−2.40137
$316$	7632.42	1.35872
$317$	−10587.7	−1.87591	−0.937957	−	0.346753i	$-0.887284\pi$
$317$	−10587.7	−1.87591	−0.937957	+	0.346753i	$0.887284\pi$
$318$	−65.9535	−0.0116305
$319$	−532.214	−0.0934115
$320$	6460.50	1.12860
$321$	799.949	0.139093
$322$	2049.95	0.354780
$323$	7294.74	1.25663
$324$	−5415.94	−0.928660
$325$	0	0
$326$	1020.61	0.173394
$327$	490.794	0.0830000
$328$	2343.10	0.394439
$329$	−19405.8	−3.25191
$330$	54.8645	0.00915209
$331$	1313.03	0.218038	0.109019	−	0.994040i	$-0.465229\pi$
$331$	1313.03	0.218038	0.109019	+	0.994040i	$0.465229\pi$
$332$	3533.73	0.584152
$333$	6647.65	1.09396
$334$	−782.803	−0.128243
$335$	1730.22	0.282185
$336$	994.678	0.161500
$337$	−6444.92	−1.04177	−0.520886	−	0.853626i	$-0.674398\pi$
$337$	−6444.92	−1.04177	−0.520886	+	0.853626i	$0.674398\pi$
$338$	0	0
$339$	−1.12598	−0.000180398 0
$340$	9494.97	1.51452
$341$	−2314.71	−0.367591
$342$	−1400.73	−0.221471
$343$	−8819.92	−1.38843
$344$	−4417.85	−0.692426
$345$	−1088.74	−0.169902
$346$	−1436.69	−0.223228
$347$	3094.87	0.478793	0.239396	−	0.970922i	$-0.423050\pi$
$347$	3094.87	0.478793	0.239396	+	0.970922i	$0.423050\pi$
$348$	−209.317	−0.0322430
$349$	4461.70	0.684324	0.342162	−	0.939641i	$-0.388841\pi$
$349$	4461.70	0.684324	0.342162	+	0.939641i	$0.388841\pi$
$350$	−2327.99	−0.355532
$351$	0	0
$352$	1102.18	0.166893
$353$	−9734.23	−1.46771	−0.733854	−	0.679308i	$-0.762280\pi$
$353$	−9734.23	−1.46771	−0.733854	+	0.679308i	$0.762280\pi$
$354$	−10.5724	−0.00158733
$355$	−347.480	−0.0519502
$356$	−5299.94	−0.789034
$357$	1335.34	0.197966
$358$	4.63506	0.000684275 0
$359$	7988.89	1.17448	0.587239	−	0.809413i	$-0.300215\pi$
$359$	7988.89	1.17448	0.587239	+	0.809413i	$0.300215\pi$
$360$	−3717.88	−0.544304
$361$	2276.13	0.331846
$362$	2310.30	0.335433
$363$	−67.9982	−0.00983190
$364$	0	0
$365$	−12097.6	−1.73484
$366$	−153.623	−0.0219399
$367$	5436.07	0.773189	0.386595	−	0.922250i	$-0.373651\pi$
$367$	5436.07	0.773189	0.386595	+	0.922250i	$0.373651\pi$
$368$	−6815.76	−0.965479
$369$	7251.82	1.02307
$370$	2211.06	0.310669
$371$	−6652.87	−0.930997
$372$	−910.362	−0.126882
$373$	6898.89	0.957671	0.478835	−	0.877905i	$-0.341059\pi$
$373$	6898.89	0.957671	0.478835	+	0.877905i	$0.341059\pi$
$374$	461.094	0.0637502
$375$	101.232	0.0139403
$376$	−5374.07	−0.737091
$377$	0	0
$378$	−515.858	−0.0701928
$379$	4398.18	0.596094	0.298047	−	0.954551i	$-0.403665\pi$
$379$	4398.18	0.596094	0.298047	+	0.954551i	$0.403665\pi$
$380$	11890.5	1.60518
$381$	−789.783	−0.106199
$382$	−849.775	−0.113817
$383$	−12903.6	−1.72153	−0.860763	−	0.509006i	$-0.830013\pi$
$383$	−12903.6	−1.72153	−0.860763	+	0.509006i	$0.830013\pi$
$384$	573.857	0.0762617
$385$	5534.30	0.732608
$386$	−523.088	−0.0689754
$387$	−13673.1	−1.79597
$388$	12503.9	1.63606
$389$	1963.45	0.255915	0.127957	−	0.991780i	$-0.459158\pi$
$389$	1963.45	0.255915	0.127957	+	0.991780i	$0.459158\pi$
$390$	0	0
$391$	−9150.06	−1.18347
$392$	−5399.78	−0.695740
$393$	−212.046	−0.0272170
$394$	400.595	0.0512226
$395$	16021.6	2.04085
$396$	2259.67	0.286749
$397$	7227.93	0.913752	0.456876	−	0.889530i	$-0.348968\pi$
$397$	7227.93	0.913752	0.456876	+	0.889530i	$0.348968\pi$
$398$	2507.08	0.315750
$399$	1672.23	0.209816
$400$	7740.19	0.967523
$401$	−11289.1	−1.40587	−0.702933	−	0.711256i	$-0.748127\pi$
$401$	−11289.1	−1.40587	−0.702933	+	0.711256i	$0.748127\pi$
$402$	33.0456	0.00409991
$403$	0	0
$404$	−6337.60	−0.780464
$405$	−11368.9	−1.39488
$406$	827.305	0.101129
$407$	−2740.36	−0.333745
$408$	369.797	0.0448717
$409$	−430.371	−0.0520304	−0.0260152	−	0.999662i	$-0.508282\pi$
$409$	−430.371	−0.0520304	−0.0260152	+	0.999662i	$0.508282\pi$
$410$	2412.01	0.290538
$411$	666.680	0.0800119
$412$	2021.08	0.241678
$413$	−1066.46	−0.127063
$414$	1756.99	0.208578
$415$	7417.84	0.877416
$416$	0	0
$417$	−327.865	−0.0385027
$418$	577.423	0.0675662
$419$	−13080.0	−1.52506	−0.762532	−	0.646950i	$-0.776044\pi$
$419$	−13080.0	−1.52506	−0.762532	+	0.646950i	$0.776044\pi$
$420$	2176.61	0.252875
$421$	8124.94	0.940583	0.470292	−	0.882511i	$-0.344149\pi$
$421$	8124.94	0.940583	0.470292	+	0.882511i	$0.344149\pi$
$422$	−685.889	−0.0791198
$423$	−16632.5	−1.91183
$424$	−1842.38	−0.211024
$425$	10391.1	1.18598
$426$	−6.63657	−0.000754795 0
$427$	−15496.3	−1.75625
$428$	10958.4	1.23761
$429$	0	0
$430$	−4547.78	−0.510031
$431$	−6068.30	−0.678189	−0.339095	−	0.940752i	$-0.610121\pi$
$431$	−6068.30	−0.678189	−0.339095	+	0.940752i	$0.610121\pi$
$432$	1715.15	0.191019
$433$	12145.1	1.34793	0.673966	−	0.738762i	$-0.264589\pi$
$433$	12145.1	1.34793	0.673966	+	0.738762i	$0.264589\pi$
$434$	3598.12	0.397961
$435$	−439.388	−0.0484300
$436$	6723.35	0.738510
$437$	−11458.5	−1.25432
$438$	−231.053	−0.0252058
$439$	1499.48	0.163022	0.0815108	−	0.996672i	$-0.474025\pi$
$439$	1499.48	0.163022	0.0815108	+	0.996672i	$0.474025\pi$
$440$	1532.62	0.166056
$441$	−16712.1	−1.80457
$442$	0	0
$443$	15934.0	1.70892	0.854458	−	0.519521i	$-0.173890\pi$
$443$	15934.0	1.70892	0.854458	+	0.519521i	$0.173890\pi$
$444$	−1077.77	−0.115199
$445$	−11125.4	−1.18516
$446$	−1967.91	−0.208931
$447$	−940.167	−0.0994818
$448$	12446.6	1.31261
$449$	16474.3	1.73156	0.865782	−	0.500421i	$-0.166822\pi$
$449$	16474.3	1.73156	0.865782	+	0.500421i	$0.166822\pi$
$450$	−1995.29	−0.209020
$451$	−2989.41	−0.312119
$452$	−15.4247	−0.00160513
$453$	673.455	0.0698492
$454$	2405.32	0.248651
$455$	0	0
$456$	463.093	0.0475577
$457$	10464.5	1.07114	0.535569	−	0.844491i	$-0.320097\pi$
$457$	10464.5	1.07114	0.535569	+	0.844491i	$0.320097\pi$
$458$	−802.034	−0.0818267
$459$	2302.56	0.234149
$460$	−14914.6	−1.51173
$461$	−14850.3	−1.50032	−0.750159	−	0.661257i	$-0.770023\pi$
$461$	−14850.3	−1.50032	−0.750159	+	0.661257i	$0.770023\pi$
$462$	105.700	0.0106442
$463$	−5176.15	−0.519559	−0.259780	−	0.965668i	$-0.583650\pi$
$463$	−5176.15	−0.519559	−0.259780	+	0.965668i	$0.583650\pi$
$464$	−2750.66	−0.275207
$465$	−1910.99	−0.190581
$466$	281.645	0.0279978
$467$	7920.85	0.784867	0.392434	−	0.919780i	$-0.371633\pi$
$467$	7920.85	0.784867	0.392434	+	0.919780i	$0.371633\pi$
$468$	0	0
$469$	3333.39	0.328191
$470$	−5532.12	−0.542931
$471$	332.847	0.0325621
$472$	−295.336	−0.0288007
$473$	5636.44	0.547915
$474$	305.999	0.0296519
$475$	13012.7	1.25697
$476$	18292.7	1.76144
$477$	−5702.11	−0.547341
$478$	−2475.30	−0.236856
$479$	−6533.79	−0.623250	−0.311625	−	0.950205i	$-0.600873\pi$
$479$	−6533.79	−0.623250	−0.311625	+	0.950205i	$0.600873\pi$
$480$	909.945	0.0865273
$481$	0	0
$482$	−287.311	−0.0271507
$483$	−2097.54	−0.197602
$484$	−931.502	−0.0874814
$485$	26247.7	2.45741
$486$	−664.505	−0.0620218
$487$	462.581	0.0430422	0.0215211	−	0.999768i	$-0.493149\pi$
$487$	462.581	0.0430422	0.0215211	+	0.999768i	$0.493149\pi$
$488$	−4291.39	−0.398078
$489$	−1044.31	−0.0965753
$490$	−5558.59	−0.512473
$491$	10095.4	0.927904	0.463952	−	0.885860i	$-0.346431\pi$
$491$	10095.4	0.927904	0.463952	+	0.885860i	$0.346431\pi$
$492$	−1175.72	−0.107735
$493$	−3692.72	−0.337346
$494$	0	0
$495$	4743.40	0.430707
$496$	−11963.2	−1.08299
$497$	−669.445	−0.0604200
$498$	141.674	0.0127481
$499$	4759.63	0.426995	0.213497	−	0.976944i	$-0.431514\pi$
$499$	4759.63	0.426995	0.213497	+	0.976944i	$0.431514\pi$
$500$	1386.77	0.124036
$501$	800.977	0.0714272
$502$	2825.74	0.251233
$503$	−9461.21	−0.838677	−0.419338	−	0.907830i	$-0.637738\pi$
$503$	−9461.21	−0.838677	−0.419338	+	0.907830i	$0.637738\pi$
$504$	−7162.75	−0.633045
$505$	−13303.6	−1.17228
$506$	−724.283	−0.0636330
$507$	0	0
$508$	−10819.2	−0.944928
$509$	19775.1	1.72204	0.861019	−	0.508573i	$-0.169827\pi$
$509$	19775.1	1.72204	0.861019	+	0.508573i	$0.169827\pi$
$510$	380.672	0.0330519
$511$	−23306.9	−2.01768
$512$	9617.75	0.830173
$513$	2883.47	0.248165
$514$	719.403	0.0617345
$515$	4242.56	0.363009
$516$	2216.78	0.189125
$517$	6856.42	0.583259
$518$	4259.77	0.361319
$519$	1470.05	0.124331
$520$	0	0
$521$	7861.93	0.661108	0.330554	−	0.943787i	$-0.392764\pi$
$521$	7861.93	0.661108	0.330554	+	0.943787i	$0.392764\pi$
$522$	709.074	0.0594547
$523$	1121.91	0.0938010	0.0469005	−	0.998900i	$-0.485066\pi$
$523$	1121.91	0.0938010	0.0469005	+	0.998900i	$0.485066\pi$
$524$	−2904.80	−0.242169
$525$	2382.04	0.198020
$526$	1571.07	0.130232
$527$	−16060.4	−1.32752
$528$	−351.437	−0.0289666
$529$	2205.85	0.181298
$530$	−1896.57	−0.155437
$531$	−914.053	−0.0747016
$532$	22907.8	1.86688
$533$	0	0
$534$	−212.485	−0.0172194
$535$	23003.5	1.85893
$536$	923.116	0.0743890
$537$	−4.74267	−0.000381120 0
$538$	1103.31	0.0884144
$539$	6889.23	0.550538
$540$	3753.18	0.299095
$541$	−8332.51	−0.662186	−0.331093	−	0.943598i	$-0.607417\pi$
$541$	−8332.51	−0.662186	−0.331093	+	0.943598i	$0.607417\pi$
$542$	2049.07	0.162390
$543$	−2363.94	−0.186826
$544$	7647.39	0.602719
$545$	14113.4	1.10927
$546$	0	0
$547$	−12910.2	−1.00914	−0.504569	−	0.863371i	$-0.668349\pi$
$547$	−12910.2	−1.00914	−0.504569	+	0.863371i	$0.668349\pi$
$548$	9132.79	0.711923
$549$	−13281.7	−1.03251
$550$	822.518	0.0637678
$551$	−4624.36	−0.357539
$552$	−580.874	−0.0447892
$553$	30866.8	2.37358
$554$	1102.52	0.0845518
$555$	−2262.40	−0.173033
$556$	−4491.40	−0.342586
$557$	−4348.77	−0.330814	−0.165407	−	0.986225i	$-0.552894\pi$
$557$	−4348.77	−0.330814	−0.165407	+	0.986225i	$0.552894\pi$
$558$	3083.91	0.233965
$559$	0	0
$560$	28603.1	2.15840
$561$	−471.799	−0.0355069
$562$	−1602.28	−0.120263
$563$	11077.6	0.829246	0.414623	−	0.909993i	$-0.363913\pi$
$563$	11077.6	0.829246	0.414623	+	0.909993i	$0.363913\pi$
$564$	2696.59	0.201324
$565$	−32.3788	−0.00241095
$566$	926.172	0.0687808
$567$	−21903.0	−1.62229
$568$	−185.390	−0.0136950
$569$	−14716.8	−1.08429	−0.542143	−	0.840286i	$-0.682387\pi$
$569$	−14716.8	−1.08429	−0.542143	+	0.840286i	$0.682387\pi$
$570$	476.712	0.0350303
$571$	−13302.9	−0.974973	−0.487486	−	0.873131i	$-0.662086\pi$
$571$	−13302.9	−0.974973	−0.487486	+	0.873131i	$0.662086\pi$
$572$	0	0
$573$	869.505	0.0633928
$574$	4646.91	0.337907
$575$	−16322.2	−1.18380
$576$	10667.9	0.771692
$577$	−7178.88	−0.517956	−0.258978	−	0.965883i	$-0.583386\pi$
$577$	−7178.88	−0.517956	−0.258978	+	0.965883i	$0.583386\pi$
$578$	500.953	0.0360500
$579$	535.233	0.0384172
$580$	−6019.14	−0.430916
$581$	14291.0	1.02047
$582$	501.307	0.0357042
$583$	2350.58	0.166983
$584$	−6454.38	−0.457336
$585$	0	0
$586$	2826.42	0.199246
$587$	1350.70	0.0949732	0.0474866	−	0.998872i	$-0.484879\pi$
$587$	1350.70	0.0949732	0.0474866	+	0.998872i	$0.484879\pi$
$588$	2709.49	0.190030
$589$	−20112.3	−1.40698
$590$	−304.021	−0.0212142
$591$	−409.896	−0.0285294
$592$	−14163.1	−0.983274
$593$	−7312.10	−0.506361	−0.253180	−	0.967419i	$-0.581477\pi$
$593$	−7312.10	−0.506361	−0.253180	+	0.967419i	$0.581477\pi$
$594$	182.262	0.0125897
$595$	38399.3	2.64574
$596$	−12879.3	−0.885160
$597$	−2565.29	−0.175863
$598$	0	0
$599$	−16153.4	−1.10185	−0.550926	−	0.834554i	$-0.685725\pi$
$599$	−16153.4	−1.10185	−0.550926	+	0.834554i	$0.685725\pi$
$600$	659.658	0.0448840
$601$	−15562.0	−1.05622	−0.528111	−	0.849176i	$-0.677099\pi$
$601$	−15562.0	−1.05622	−0.528111	+	0.849176i	$0.677099\pi$
$602$	−8761.61	−0.593184
$603$	2857.01	0.192946
$604$	9225.61	0.621498
$605$	−1955.37	−0.131400
$606$	−254.087	−0.0170323
$607$	−22025.2	−1.47278	−0.736389	−	0.676559i	$-0.763470\pi$
$607$	−22025.2	−1.47278	−0.736389	+	0.676559i	$0.763470\pi$
$608$	9576.75	0.638797
$609$	−846.513	−0.0563258
$610$	−4417.60	−0.293219
$611$	0	0
$612$	15678.5	1.03557
$613$	−20235.2	−1.33326	−0.666632	−	0.745387i	$-0.732265\pi$
$613$	−20235.2	−1.33326	−0.666632	+	0.745387i	$0.732265\pi$
$614$	−3.90313	−0.000256543 0
$615$	−2468.01	−0.161821
$616$	2952.70	0.193129
$617$	17664.4	1.15258	0.576291	−	0.817245i	$-0.304499\pi$
$617$	17664.4	1.15258	0.576291	+	0.817245i	$0.304499\pi$
$618$	81.0291	0.00527422
$619$	−4501.45	−0.292291	−0.146146	−	0.989263i	$-0.546687\pi$
$619$	−4501.45	−0.292291	−0.146146	+	0.989263i	$0.546687\pi$
$620$	−26178.5	−1.69573
$621$	−3616.84	−0.233718
$622$	1276.10	0.0822617
$623$	−21433.9	−1.37838
$624$	0	0
$625$	−14107.4	−0.902870
$626$	4186.58	0.267300
$627$	−590.829	−0.0376323
$628$	4559.64	0.289728
$629$	−19013.7	−1.20529
$630$	−7373.41	−0.466292
$631$	−21587.0	−1.36191	−0.680956	−	0.732324i	$-0.738435\pi$
$631$	−21587.0	−1.36191	−0.680956	+	0.732324i	$0.738435\pi$
$632$	8547.95	0.538005
$633$	701.814	0.0440673
$634$	−5814.95	−0.364260
$635$	−22711.1	−1.41931
$636$	924.468	0.0576376
$637$	0	0
$638$	−292.301	−0.0181384
$639$	−573.775	−0.0355214
$640$	16501.9	1.01921
$641$	−3319.01	−0.204513	−0.102257	−	0.994758i	$-0.532606\pi$
$641$	−3319.01	−0.204513	−0.102257	+	0.994758i	$0.532606\pi$
$642$	439.346	0.0270087
$643$	−8597.35	−0.527288	−0.263644	−	0.964620i	$-0.584924\pi$
$643$	−8597.35	−0.527288	−0.263644	+	0.964620i	$0.584924\pi$
$644$	−28734.1	−1.75820
$645$	4653.36	0.284071
$646$	4006.40	0.244009
$647$	−22369.0	−1.35922	−0.679612	−	0.733572i	$-0.737852\pi$
$647$	−22369.0	−1.35922	−0.679612	+	0.733572i	$0.737852\pi$
$648$	−6065.61	−0.367715
$649$	376.799	0.0227899
$650$	0	0
$651$	−3681.66	−0.221652
$652$	−14305.9	−0.859299
$653$	13644.5	0.817689	0.408845	−	0.912604i	$-0.365932\pi$
$653$	13644.5	0.817689	0.408845	+	0.912604i	$0.365932\pi$
$654$	269.553	0.0161167
$655$	−6097.62	−0.363746
$656$	−15450.3	−0.919560
$657$	−19976.1	−1.18621
$658$	−10658.0	−0.631448
$659$	−11044.4	−0.652851	−0.326425	−	0.945223i	$-0.605844\pi$
$659$	−11044.4	−0.652851	−0.326425	+	0.945223i	$0.605844\pi$
$660$	−769.034	−0.0453555
$661$	3807.34	0.224037	0.112018	−	0.993706i	$-0.464268\pi$
$661$	3807.34	0.224037	0.112018	+	0.993706i	$0.464268\pi$
$662$	721.139	0.0423381
$663$	0	0
$664$	3957.61	0.231303
$665$	48087.0	2.80411
$666$	3651.00	0.212423
$667$	5800.50	0.336726
$668$	10972.5	0.635538
$669$	2013.60	0.116368
$670$	950.265	0.0547939
$671$	5475.11	0.314999
$672$	1753.07	0.100634
$673$	−4905.06	−0.280945	−0.140473	−	0.990085i	$-0.544862\pi$
$673$	−4905.06	−0.280945	−0.140473	+	0.990085i	$0.544862\pi$
$674$	−3539.66	−0.202289
$675$	4107.40	0.234213
$676$	0	0
$677$	24704.2	1.40245	0.701227	−	0.712938i	$-0.252636\pi$
$677$	24704.2	1.40245	0.701227	+	0.712938i	$0.252636\pi$
$678$	−0.618408	−3.50292e−5 0
$679$	50568.0	2.85806
$680$	10633.9	0.599695
$681$	−2461.17	−0.138491
$682$	−1271.28	−0.0713779
$683$	29349.6	1.64427	0.822133	−	0.569296i	$-0.192784\pi$
$683$	29349.6	1.64427	0.822133	+	0.569296i	$0.192784\pi$
$684$	19634.0	1.09755
$685$	19171.1	1.06933
$686$	−4844.05	−0.269602
$687$	820.656	0.0455749
$688$	29131.0	1.61426
$689$	0	0
$690$	−597.957	−0.0329911
$691$	17054.6	0.938909	0.469454	−	0.882957i	$-0.344451\pi$
$691$	17054.6	0.938909	0.469454	+	0.882957i	$0.344451\pi$
$692$	20138.0	1.10626
$693$	9138.49	0.500927
$694$	1699.75	0.0929709
$695$	−9428.14	−0.514575
$696$	−234.425	−0.0127670
$697$	−20741.7	−1.12719
$698$	2450.44	0.132880
$699$	−288.184	−0.0155939
$700$	32631.3	1.76192
$701$	−30796.6	−1.65930	−0.829651	−	0.558282i	$-0.811461\pi$
$701$	−30796.6	−1.65930	−0.829651	+	0.558282i	$0.811461\pi$
$702$	0	0
$703$	−23810.7	−1.27743
$704$	−4397.61	−0.235428
$705$	5660.56	0.302396
$706$	−5346.20	−0.284996
$707$	−25630.3	−1.36341
$708$	148.193	0.00786643
$709$	4408.37	0.233512	0.116756	−	0.993161i	$-0.462751\pi$
$709$	4408.37	0.233512	0.116756	+	0.993161i	$0.462751\pi$
$710$	−190.842	−0.0100876
$711$	26455.6	1.39545
$712$	−5935.69	−0.312429
$713$	25227.6	1.32508
$714$	733.392	0.0384405
$715$	0	0
$716$	−64.9695	−0.00339110
$717$	2532.77	0.131922
$718$	4387.64	0.228057
$719$	9072.44	0.470577	0.235288	−	0.971926i	$-0.424397\pi$
$719$	9072.44	0.470577	0.235288	+	0.971926i	$0.424397\pi$
$720$	24515.4	1.26894
$721$	8173.59	0.422192
$722$	1250.09	0.0644371
$723$	293.981	0.0151221
$724$	−32383.5	−1.66232
$725$	−6587.22	−0.337439
$726$	−37.3458	−0.00190913
$727$	−3456.15	−0.176316	−0.0881578	−	0.996107i	$-0.528098\pi$
$727$	−3456.15	−0.176316	−0.0881578	+	0.996107i	$0.528098\pi$
$728$	0	0
$729$	−18315.1	−0.930503
$730$	−6644.20	−0.336867
$731$	39107.9	1.97874
$732$	2153.33	0.108729
$733$	6830.00	0.344163	0.172082	−	0.985083i	$-0.444951\pi$
$733$	6830.00	0.344163	0.172082	+	0.985083i	$0.444951\pi$
$734$	2985.58	0.150136
$735$	5687.65	0.285431
$736$	−12012.5	−0.601610
$737$	−1177.74	−0.0588639
$738$	3982.82	0.198658
$739$	−17055.9	−0.849001	−0.424501	−	0.905428i	$-0.639550\pi$
$739$	−17055.9	−0.849001	−0.424501	+	0.905428i	$0.639550\pi$
$740$	−30992.4	−1.53960
$741$	0	0
$742$	−3653.87	−0.180779
$743$	−28651.8	−1.41471	−0.707357	−	0.706857i	$-0.750113\pi$
$743$	−28651.8	−1.41471	−0.707357	+	0.706857i	$0.750113\pi$
$744$	−1019.56	−0.0502406
$745$	−27035.6	−1.32954
$746$	3788.99	0.185958
$747$	12248.7	0.599940
$748$	−6463.14	−0.315930
$749$	44317.8	2.16200
$750$	55.5983	0.00270688
$751$	−30809.3	−1.49700	−0.748501	−	0.663134i	$-0.769226\pi$
$751$	−30809.3	−1.49700	−0.748501	+	0.663134i	$0.769226\pi$
$752$	35436.2	1.71839
$753$	−2891.34	−0.139929
$754$	0	0
$755$	19366.0	0.933510
$756$	7230.77	0.347858
$757$	4403.83	0.211440	0.105720	−	0.994396i	$-0.466285\pi$
$757$	4403.83	0.211440	0.105720	+	0.994396i	$0.466285\pi$
$758$	2415.56	0.115748
$759$	741.099	0.0354416
$760$	13316.8	0.635591
$761$	12880.1	0.613537	0.306768	−	0.951784i	$-0.400752\pi$
$761$	12880.1	0.613537	0.306768	+	0.951784i	$0.400752\pi$
$762$	−433.762	−0.0206215
$763$	27190.4	1.29012
$764$	11911.3	0.564051
$765$	32911.6	1.55545
$766$	−7086.89	−0.334282
$767$	0	0
$768$	−1482.15	−0.0696386
$769$	11410.1	0.535057	0.267528	−	0.963550i	$-0.413793\pi$
$769$	11410.1	0.535057	0.267528	+	0.963550i	$0.413793\pi$
$770$	3039.53	0.142256
$771$	−736.106	−0.0343842
$772$	7332.12	0.341825
$773$	29422.0	1.36900	0.684499	−	0.729014i	$-0.260021\pi$
$773$	29422.0	1.36900	0.684499	+	0.729014i	$0.260021\pi$
$774$	−7509.49	−0.348738
$775$	−28649.2	−1.32788
$776$	14003.8	0.647819
$777$	−4358.67	−0.201244
$778$	1078.36	0.0496929
$779$	−25974.7	−1.19466
$780$	0	0
$781$	236.527	0.0108369
$782$	−5025.37	−0.229804
$783$	−1459.66	−0.0666207
$784$	35605.8	1.62199
$785$	9571.39	0.435182
$786$	−116.459	−0.00528494
$787$	−24492.6	−1.10936	−0.554680	−	0.832064i	$-0.687159\pi$
$787$	−24492.6	−1.10936	−0.554680	+	0.832064i	$0.687159\pi$
$788$	−5615.13	−0.253846
$789$	−1607.55	−0.0725352
$790$	8799.35	0.396287
$791$	−62.3802	−0.00280402
$792$	2530.73	0.113542
$793$	0	0
$794$	3969.70	0.177430
$795$	1940.60	0.0865736
$796$	−35141.6	−1.56478
$797$	−26556.2	−1.18026	−0.590132	−	0.807307i	$-0.700924\pi$
$797$	−26556.2	−1.18026	−0.590132	+	0.807307i	$0.700924\pi$
$798$	918.420	0.0407415
$799$	47572.6	2.10638
$800$	13641.7	0.602884
$801$	−18370.7	−0.810360
$802$	−6200.18	−0.272988
$803$	8234.72	0.361889
$804$	−463.200	−0.0203181
$805$	−60317.3	−2.64088
$806$	0	0
$807$	−1128.92	−0.0492441
$808$	−7097.82	−0.309035
$809$	17140.7	0.744911	0.372456	−	0.928050i	$-0.378516\pi$
$809$	17140.7	0.744911	0.372456	+	0.928050i	$0.378516\pi$
$810$	−6244.00	−0.270854
$811$	13024.5	0.563935	0.281967	−	0.959424i	$-0.409013\pi$
$811$	13024.5	0.563935	0.281967	+	0.959424i	$0.409013\pi$
$812$	−11596.3	−0.501171
$813$	−2096.65	−0.0904460
$814$	−1505.05	−0.0648059
$815$	−30030.3	−1.29069
$816$	−2438.41	−0.104610
$817$	48974.5	2.09719
$818$	−236.367	−0.0101031
$819$	0	0
$820$	−33809.1	−1.43984
$821$	−623.522	−0.0265056	−0.0132528	−	0.999912i	$-0.504219\pi$
$821$	−623.522	−0.0265056	−0.0132528	+	0.999912i	$0.504219\pi$
$822$	366.152	0.0155365
$823$	−10196.1	−0.431851	−0.215925	−	0.976410i	$-0.569277\pi$
$823$	−10196.1	−0.431851	−0.215925	+	0.976410i	$0.569277\pi$
$824$	2263.52	0.0956958
$825$	−841.614	−0.0355167
$826$	−585.719	−0.0246728
$827$	−16337.2	−0.686939	−0.343470	−	0.939164i	$-0.611602\pi$
$827$	−16337.2	−0.686939	−0.343470	+	0.939164i	$0.611602\pi$
$828$	−24627.7	−1.03366
$829$	26859.9	1.12531	0.562655	−	0.826692i	$-0.309780\pi$
$829$	26859.9	1.12531	0.562655	+	0.826692i	$0.309780\pi$
$830$	4074.00	0.170374
$831$	−1128.12	−0.0470927
$832$	0	0
$833$	47800.3	1.98821
$834$	−180.069	−0.00747636
$835$	23033.0	0.954599
$836$	−8093.72	−0.334841
$837$	−6348.37	−0.262165
$838$	−7183.79	−0.296133
$839$	−29845.6	−1.22811	−0.614056	−	0.789263i	$-0.710463\pi$
$839$	−29845.6	−1.22811	−0.614056	+	0.789263i	$0.710463\pi$
$840$	2437.70	0.100129
$841$	−22048.1	−0.904017
$842$	4462.36	0.182640
$843$	1639.48	0.0669830
$844$	9614.09	0.392098
$845$	0	0
$846$	−9134.88	−0.371234
$847$	−3767.15	−0.152823
$848$	12148.6	0.491961
$849$	−947.676	−0.0383088
$850$	5706.96	0.230291
$851$	29866.6	1.20307
$852$	93.0246	0.00374057
$853$	−11863.5	−0.476201	−0.238101	−	0.971240i	$-0.576525\pi$
$853$	−11863.5	−0.476201	−0.238101	+	0.971240i	$0.576525\pi$
$854$	−8510.82	−0.341024
$855$	41214.9	1.64856
$856$	12272.9	0.490047
$857$	−7802.07	−0.310984	−0.155492	−	0.987837i	$-0.549696\pi$
$857$	−7802.07	−0.310984	−0.155492	+	0.987837i	$0.549696\pi$
$858$	0	0
$859$	37222.6	1.47849	0.739243	−	0.673438i	$-0.235183\pi$
$859$	37222.6	1.47849	0.739243	+	0.673438i	$0.235183\pi$
$860$	63746.1	2.52758
$861$	−4754.80	−0.188203
$862$	−3332.81	−0.131689
$863$	−20010.5	−0.789299	−0.394650	−	0.918832i	$-0.629134\pi$
$863$	−20010.5	−0.789299	−0.394650	+	0.918832i	$0.629134\pi$
$864$	3022.87	0.119028
$865$	42272.8	1.66164
$866$	6670.28	0.261738
$867$	−512.584	−0.0200787
$868$	−50434.7	−1.97220
$869$	−10905.8	−0.425723
$870$	−241.319	−0.00940402
$871$	0	0
$872$	7529.84	0.292423
$873$	43341.3	1.68028
$874$	−6293.22	−0.243560
$875$	5608.33	0.216681
$876$	3238.67	0.124914
$877$	−33535.2	−1.29122	−0.645612	−	0.763666i	$-0.723397\pi$
$877$	−33535.2	−1.29122	−0.645612	+	0.763666i	$0.723397\pi$
$878$	823.542	0.0316551
$879$	−2892.04	−0.110974
$880$	−10106.0	−0.387128
$881$	−18597.0	−0.711178	−0.355589	−	0.934642i	$-0.615720\pi$
$881$	−18597.0	−0.711178	−0.355589	+	0.934642i	$0.615720\pi$
$882$	−9178.59	−0.350407
$883$	−5381.17	−0.205086	−0.102543	−	0.994729i	$-0.532698\pi$
$883$	−5381.17	−0.205086	−0.102543	+	0.994729i	$0.532698\pi$
$884$	0	0
$885$	311.080	0.0118156
$886$	8751.25	0.331833
$887$	−21789.7	−0.824831	−0.412415	−	0.910996i	$-0.635315\pi$
$887$	−21789.7	−0.824831	−0.412415	+	0.910996i	$0.635315\pi$
$888$	−1207.05	−0.0456147
$889$	−43754.6	−1.65071
$890$	−6110.25	−0.230131
$891$	7738.71	0.290973
$892$	27584.2	1.03541
$893$	59574.7	2.23247
$894$	−516.356	−0.0193171
$895$	−136.381	−0.00509354
$896$	31792.1	1.18538
$897$	0	0
$898$	9047.99	0.336231
$899$	10181.2	0.377710
$900$	27968.0	1.03585
$901$	16309.3	0.603041
$902$	−1641.83	−0.0606066
$903$	8965.04	0.330385
$904$	−17.2750	−0.000635572 0
$905$	−67977.9	−2.49686
$906$	369.873	0.0135631
$907$	21457.4	0.785538	0.392769	−	0.919637i	$-0.371517\pi$
$907$	21457.4	0.785538	0.392769	+	0.919637i	$0.371517\pi$
$908$	−33715.4	−1.23225
$909$	−21967.5	−0.801557
$910$	0	0
$911$	−15579.2	−0.566588	−0.283294	−	0.959033i	$-0.591427\pi$
$911$	−15579.2	−0.566588	−0.283294	+	0.959033i	$0.591427\pi$
$912$	−3053.60	−0.110872
$913$	−5049.26	−0.183030
$914$	5747.30	0.207991
$915$	4520.17	0.163314
$916$	11242.1	0.405512
$917$	−11747.5	−0.423050
$918$	1264.61	0.0454664
$919$	−26711.8	−0.958804	−0.479402	−	0.877596i	$-0.659146\pi$
$919$	−26711.8	−0.958804	−0.479402	+	0.877596i	$0.659146\pi$
$920$	−16703.7	−0.598592
$921$	3.99376	0.000142887 0
$922$	−8156.03	−0.291328
$923$	0	0
$924$	−1481.60	−0.0527500
$925$	−33917.4	−1.20562
$926$	−2842.83	−0.100887
$927$	7005.50	0.248210
$928$	−4847.91	−0.171487
$929$	16736.9	0.591086	0.295543	−	0.955329i	$-0.404499\pi$
$929$	16736.9	0.591086	0.295543	+	0.955329i	$0.404499\pi$
$930$	−1049.55	−0.0370065
$931$	59859.8	2.10723
$932$	−3947.81	−0.138750
$933$	−1305.72	−0.0458172
$934$	4350.26	0.152404
$935$	−13567.1	−0.474537
$936$	0	0
$937$	26868.9	0.936786	0.468393	−	0.883520i	$-0.344833\pi$
$937$	26868.9	0.936786	0.468393	+	0.883520i	$0.344833\pi$
$938$	1830.75	0.0637273
$939$	−4283.79	−0.148878
$940$	77543.5	2.69063
$941$	36995.2	1.28163	0.640813	−	0.767697i	$-0.278598\pi$
$941$	36995.2	1.28163	0.640813	+	0.767697i	$0.278598\pi$
$942$	182.805	0.00632284
$943$	32581.0	1.12511
$944$	1947.42	0.0671433
$945$	15178.5	0.522494
$946$	3095.63	0.106393
$947$	−15638.3	−0.536616	−0.268308	−	0.963333i	$-0.586464\pi$
$947$	−15638.3	−0.536616	−0.268308	+	0.963333i	$0.586464\pi$
$948$	−4289.18	−0.146947
$949$	0	0
$950$	7146.77	0.244076
$951$	5949.95	0.202882
$952$	20487.0	0.697466
$953$	29168.9	0.991474	0.495737	−	0.868473i	$-0.334898\pi$
$953$	29168.9	0.991474	0.495737	+	0.868473i	$0.334898\pi$
$954$	−3131.70	−0.106281
$955$	25003.6	0.847222
$956$	34696.1	1.17380
$957$	299.088	0.0101025
$958$	−3588.47	−0.121021
$959$	36934.6	1.24367
$960$	−3630.60	−0.122059
$961$	14489.0	0.486355
$962$	0	0
$963$	37984.3	1.27106
$964$	4027.23	0.134552
$965$	15391.2	0.513432
$966$	−1152.01	−0.0383698
$967$	−49221.6	−1.63688	−0.818438	−	0.574595i	$-0.805160\pi$
$967$	−49221.6	−1.63688	−0.818438	+	0.574595i	$0.805160\pi$
$968$	−1043.24	−0.0346394
$969$	−4099.42	−0.135905
$970$	14415.7	0.477174
$971$	4185.21	0.138321	0.0691605	−	0.997606i	$-0.477968\pi$
$971$	4185.21	0.138321	0.0691605	+	0.997606i	$0.477968\pi$
$972$	9314.35	0.307364
$973$	−18164.0	−0.598469
$974$	254.057	0.00835783
$975$	0	0
$976$	28297.2	0.928043
$977$	7647.93	0.250439	0.125219	−	0.992129i	$-0.460036\pi$
$977$	7647.93	0.250439	0.125219	+	0.992129i	$0.460036\pi$
$978$	−573.553	−0.0187528
$979$	7572.95	0.247224
$980$	77914.6	2.53968
$981$	23304.6	0.758470
$982$	5544.59	0.180178
$983$	34985.2	1.13515	0.567577	−	0.823321i	$-0.307881\pi$
$983$	34985.2	1.13515	0.567577	+	0.823321i	$0.307881\pi$
$984$	−1316.75	−0.0426590
$985$	−11787.0	−0.381285
$986$	−2028.10	−0.0655051
$987$	10905.5	0.351697
$988$	0	0
$989$	−61430.5	−1.97510
$990$	2605.15	0.0836336
$991$	−28942.6	−0.927741	−0.463871	−	0.885903i	$-0.653540\pi$
$991$	−28942.6	−0.927741	−0.463871	+	0.885903i	$0.653540\pi$
$992$	−21084.6	−0.674834
$993$	−737.882	−0.0235810
$994$	−367.671	−0.0117322
$995$	−73767.7	−2.35035
$996$	−1985.84	−0.0631766
$997$	−25092.8	−0.797088	−0.398544	−	0.917149i	$-0.630484\pi$
$997$	−25092.8	−0.797088	−0.398544	+	0.917149i	$0.630484\pi$
$998$	2614.07	0.0829128
$999$	−7515.75	−0.238026

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.f.1.10		17
13.4	even	6		143.4.e.a.133.10	yes	34
13.10	even	6		143.4.e.a.100.10	✓	34
13.12	even	2		1859.4.a.i.1.8		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.a.100.10	✓	34	13.10	even	6
143.4.e.a.133.10	yes	34	13.4	even	6
1859.4.a.f.1.10		17	1.1	even	1	trivial
1859.4.a.i.1.8		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)

\(f(q)\)	\(=\)	\(q+0.549217 q^{2} -0.561969 q^{3} -7.69836 q^{4} -16.1600 q^{5} -0.308643 q^{6} -31.1335 q^{7} -8.62181 q^{8} -26.6842 q^{9} +O(q^{10})\)	\(q+0.549217 q^{2} -0.561969 q^{3} -7.69836 q^{4} -16.1600 q^{5} -0.308643 q^{6} -31.1335 q^{7} -8.62181 q^{8} -26.6842 q^{9} -8.87537 q^{10} +11.0000 q^{11} +4.32624 q^{12} -17.0990 q^{14} +9.08144 q^{15} +56.8516 q^{16} +76.3225 q^{17} -14.6554 q^{18} +95.5779 q^{19} +124.406 q^{20} +17.4960 q^{21} +6.04139 q^{22} -119.887 q^{23} +4.84518 q^{24} +136.147 q^{25} +30.1688 q^{27} +239.677 q^{28} -48.3831 q^{29} +4.98768 q^{30} -210.428 q^{31} +100.198 q^{32} -6.18165 q^{33} +41.9176 q^{34} +503.119 q^{35} +205.425 q^{36} -249.123 q^{37} +52.4930 q^{38} +139.329 q^{40} -271.764 q^{41} +9.60912 q^{42} +512.404 q^{43} -84.6820 q^{44} +431.218 q^{45} -65.8439 q^{46} +623.311 q^{47} -31.9488 q^{48} +626.294 q^{49} +74.7743 q^{50} -42.8908 q^{51} +213.689 q^{53} +16.5692 q^{54} -177.761 q^{55} +268.427 q^{56} -53.7118 q^{57} -26.5728 q^{58} +34.2545 q^{59} -69.9122 q^{60} +497.737 q^{61} -115.571 q^{62} +830.772 q^{63} -399.782 q^{64} -3.39507 q^{66} -107.068 q^{67} -587.558 q^{68} +67.3726 q^{69} +276.321 q^{70} +21.5024 q^{71} +230.066 q^{72} +748.611 q^{73} -136.823 q^{74} -76.5104 q^{75} -735.793 q^{76} -342.468 q^{77} -991.434 q^{79} -918.725 q^{80} +703.519 q^{81} -149.258 q^{82} -459.023 q^{83} -134.691 q^{84} -1233.38 q^{85} +281.421 q^{86} +27.1898 q^{87} -94.8399 q^{88} +688.450 q^{89} +236.832 q^{90} +922.932 q^{92} +118.254 q^{93} +342.333 q^{94} -1544.54 q^{95} -56.3083 q^{96} -1624.23 q^{97} +343.971 q^{98} -293.526 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 4 q^{2} - 6 q^{3} + 78 q^{4} - 16 q^{5} - 14 q^{6} + 6 q^{7} - 63 q^{8} + 135 q^{9}+O(q^{10}) \) 17 * q - 4 * q^2 - 6 * q^3 + 78 * q^4 - 16 * q^5 - 14 * q^6 + 6 * q^7 - 63 * q^8 + 135 * q^9	\( 17 q - 4 q^{2} - 6 q^{3} + 78 q^{4} - 16 q^{5} - 14 q^{6} + 6 q^{7} - 63 q^{8} + 135 q^{9} + 2 q^{10} + 187 q^{11} - 95 q^{12} - 60 q^{14} + 28 q^{15} + 350 q^{16} + 118 q^{17} - 478 q^{18} - 403 q^{19} - 98 q^{20} - 220 q^{21} - 44 q^{22} - 215 q^{23} - 26 q^{24} + 319 q^{25} - 384 q^{27} + 396 q^{28} - 7 q^{29} - 1269 q^{30} - 682 q^{31} - 813 q^{32} - 66 q^{33} - 738 q^{34} + 10 q^{35} + 560 q^{36} - 1084 q^{37} + 410 q^{38} + 95 q^{40} - 240 q^{41} + 393 q^{42} - 435 q^{43} + 858 q^{44} - 1242 q^{45} - 1671 q^{46} - 549 q^{47} + 894 q^{48} + 403 q^{49} + 651 q^{50} + 1552 q^{51} - 566 q^{53} - 311 q^{54} - 176 q^{55} - 1925 q^{56} + 534 q^{57} - 618 q^{58} - 2010 q^{59} + 411 q^{60} + 460 q^{61} - 823 q^{62} - 820 q^{63} + 3171 q^{64} - 154 q^{66} + 232 q^{67} + 1795 q^{68} - 1608 q^{69} - 207 q^{70} - 489 q^{71} - 2556 q^{72} - 290 q^{73} + 2653 q^{74} - 2852 q^{75} - 2421 q^{76} + 66 q^{77} - 732 q^{79} - 4915 q^{80} + 2393 q^{81} - 1772 q^{82} + 117 q^{83} - 4161 q^{84} - 4858 q^{85} - 1034 q^{86} + 3032 q^{87} - 693 q^{88} - 4113 q^{89} + 15145 q^{90} - 3554 q^{92} - 802 q^{93} + 2325 q^{94} - 3924 q^{95} - 2601 q^{96} - 2793 q^{97} - 533 q^{98} + 1485 q^{99}+O(q^{100}) \) 17 * q - 4 * q^2 - 6 * q^3 + 78 * q^4 - 16 * q^5 - 14 * q^6 + 6 * q^7 - 63 * q^8 + 135 * q^9 + 2 * q^10 + 187 * q^11 - 95 * q^12 - 60 * q^14 + 28 * q^15 + 350 * q^16 + 118 * q^17 - 478 * q^18 - 403 * q^19 - 98 * q^20 - 220 * q^21 - 44 * q^22 - 215 * q^23 - 26 * q^24 + 319 * q^25 - 384 * q^27 + 396 * q^28 - 7 * q^29 - 1269 * q^30 - 682 * q^31 - 813 * q^32 - 66 * q^33 - 738 * q^34 + 10 * q^35 + 560 * q^36 - 1084 * q^37 + 410 * q^38 + 95 * q^40 - 240 * q^41 + 393 * q^42 - 435 * q^43 + 858 * q^44 - 1242 * q^45 - 1671 * q^46 - 549 * q^47 + 894 * q^48 + 403 * q^49 + 651 * q^50 + 1552 * q^51 - 566 * q^53 - 311 * q^54 - 176 * q^55 - 1925 * q^56 + 534 * q^57 - 618 * q^58 - 2010 * q^59 + 411 * q^60 + 460 * q^61 - 823 * q^62 - 820 * q^63 + 3171 * q^64 - 154 * q^66 + 232 * q^67 + 1795 * q^68 - 1608 * q^69 - 207 * q^70 - 489 * q^71 - 2556 * q^72 - 290 * q^73 + 2653 * q^74 - 2852 * q^75 - 2421 * q^76 + 66 * q^77 - 732 * q^79 - 4915 * q^80 + 2393 * q^81 - 1772 * q^82 + 117 * q^83 - 4161 * q^84 - 4858 * q^85 - 1034 * q^86 + 3032 * q^87 - 693 * q^88 - 4113 * q^89 + 15145 * q^90 - 3554 * q^92 - 802 * q^93 + 2325 * q^94 - 3924 * q^95 - 2601 * q^96 - 2793 * q^97 - 533 * q^98 + 1485 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more