LMFDB - Embedded newform 1617.4.a.bd.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,4,Mod(1,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1617.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1617.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:	$95.4060884793$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 92 x^{14} + 346 x^{13} + 3385 x^{12} - 11756 x^{11} - 63875 x^{10} + 199466 x^{9} + \cdots - 738304 $ x^16 - 4x^15 - 92x^14 + 346x^13 + 3385x^12 - 11756x^11 - 63875x^10 + 199466x^9 + 657606x^8 - 1772388x^7 - 3590705x^6 + 7831536x^5 + 8898560x^4 - 14389664x^3 - 4854640x^2 + 6896896*x - 738304
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{4}\cdot 7^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$3.30535$ of defining polynomial
Character	$\chi$	$=$	1617.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.30535 q^{2} +3.00000 q^{3} +2.92536 q^{4} -9.14781 q^{5} -9.91606 q^{6} +16.7735 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.30535 q^{2} +3.00000 q^{3} +2.92536 q^{4} -9.14781 q^{5} -9.91606 q^{6} +16.7735 q^{8} +9.00000 q^{9} +30.2367 q^{10} -11.0000 q^{11} +8.77609 q^{12} +18.9478 q^{13} -27.4434 q^{15} -78.8452 q^{16} -57.7497 q^{17} -29.7482 q^{18} +130.217 q^{19} -26.7607 q^{20} +36.3589 q^{22} -82.4674 q^{23} +50.3204 q^{24} -41.3176 q^{25} -62.6292 q^{26} +27.0000 q^{27} +169.379 q^{29} +90.7102 q^{30} -152.809 q^{31} +126.423 q^{32} -33.0000 q^{33} +190.883 q^{34} +26.3283 q^{36} +26.8593 q^{37} -430.413 q^{38} +56.8434 q^{39} -153.440 q^{40} -47.5382 q^{41} +121.614 q^{43} -32.1790 q^{44} -82.3303 q^{45} +272.584 q^{46} -269.124 q^{47} -236.535 q^{48} +136.569 q^{50} -173.249 q^{51} +55.4292 q^{52} -225.527 q^{53} -89.2445 q^{54} +100.626 q^{55} +390.651 q^{57} -559.858 q^{58} +55.0788 q^{59} -80.2820 q^{60} +942.983 q^{61} +505.089 q^{62} +212.887 q^{64} -173.331 q^{65} +109.077 q^{66} -554.922 q^{67} -168.939 q^{68} -247.402 q^{69} +1116.85 q^{71} +150.961 q^{72} -16.2814 q^{73} -88.7794 q^{74} -123.953 q^{75} +380.932 q^{76} -187.888 q^{78} +868.381 q^{79} +721.260 q^{80} +81.0000 q^{81} +157.131 q^{82} -235.602 q^{83} +528.283 q^{85} -401.976 q^{86} +508.137 q^{87} -184.508 q^{88} -631.807 q^{89} +272.131 q^{90} -241.247 q^{92} -458.428 q^{93} +889.550 q^{94} -1191.20 q^{95} +379.270 q^{96} +275.792 q^{97} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 48 q^{3} + 72 q^{4} - 12 q^{6} - 66 q^{8} + 144 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 + 48 * q^3 + 72 * q^4 - 12 * q^6 - 66 * q^8 + 144 * q^9	\( 16 q - 4 q^{2} + 48 q^{3} + 72 q^{4} - 12 q^{6} - 66 q^{8} + 144 q^{9} - 178 q^{10} - 176 q^{11} + 216 q^{12} - 104 q^{13} + 220 q^{16} - 220 q^{17} - 36 q^{18} - 152 q^{19} - 182 q^{20} + 44 q^{22} - 180 q^{23} - 198 q^{24} + 284 q^{25} - 10 q^{26} + 432 q^{27} - 604 q^{29} - 534 q^{30} - 380 q^{31} - 592 q^{32} - 528 q^{33} - 632 q^{34} + 648 q^{36} + 148 q^{37} - 266 q^{38} - 312 q^{39} - 1792 q^{40} - 60 q^{41} + 252 q^{43} - 792 q^{44} - 116 q^{46} - 1468 q^{47} + 660 q^{48} - 850 q^{50} - 660 q^{51} - 310 q^{52} - 1456 q^{53} - 108 q^{54} - 456 q^{57} - 1350 q^{58} - 1312 q^{59} - 546 q^{60} - 2880 q^{61} - 708 q^{62} + 630 q^{64} - 4064 q^{65} + 132 q^{66} + 1220 q^{67} - 4956 q^{68} - 540 q^{69} - 2040 q^{71} - 594 q^{72} - 1628 q^{73} - 3126 q^{74} + 852 q^{75} - 6286 q^{76} - 30 q^{78} - 416 q^{79} + 874 q^{80} + 1296 q^{81} - 3040 q^{82} - 3724 q^{83} + 628 q^{85} - 1608 q^{86} - 1812 q^{87} + 726 q^{88} - 752 q^{89} - 1602 q^{90} - 32 q^{92} - 1140 q^{93} - 610 q^{94} - 912 q^{95} - 1776 q^{96} - 1088 q^{97} - 1584 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 48 * q^3 + 72 * q^4 - 12 * q^6 - 66 * q^8 + 144 * q^9 - 178 * q^10 - 176 * q^11 + 216 * q^12 - 104 * q^13 + 220 * q^16 - 220 * q^17 - 36 * q^18 - 152 * q^19 - 182 * q^20 + 44 * q^22 - 180 * q^23 - 198 * q^24 + 284 * q^25 - 10 * q^26 + 432 * q^27 - 604 * q^29 - 534 * q^30 - 380 * q^31 - 592 * q^32 - 528 * q^33 - 632 * q^34 + 648 * q^36 + 148 * q^37 - 266 * q^38 - 312 * q^39 - 1792 * q^40 - 60 * q^41 + 252 * q^43 - 792 * q^44 - 116 * q^46 - 1468 * q^47 + 660 * q^48 - 850 * q^50 - 660 * q^51 - 310 * q^52 - 1456 * q^53 - 108 * q^54 - 456 * q^57 - 1350 * q^58 - 1312 * q^59 - 546 * q^60 - 2880 * q^61 - 708 * q^62 + 630 * q^64 - 4064 * q^65 + 132 * q^66 + 1220 * q^67 - 4956 * q^68 - 540 * q^69 - 2040 * q^71 - 594 * q^72 - 1628 * q^73 - 3126 * q^74 + 852 * q^75 - 6286 * q^76 - 30 * q^78 - 416 * q^79 + 874 * q^80 + 1296 * q^81 - 3040 * q^82 - 3724 * q^83 + 628 * q^85 - 1608 * q^86 - 1812 * q^87 + 726 * q^88 - 752 * q^89 - 1602 * q^90 - 32 * q^92 - 1140 * q^93 - 610 * q^94 - 912 * q^95 - 1776 * q^96 - 1088 * q^97 - 1584 * 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 $

$2$	−3.30535	−1.16862	−0.584309	−	0.811531i	$-0.698635\pi$
$2$	−3.30535	−1.16862	−0.584309	+	0.811531i	$0.698635\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	2.92536	0.365670
$5$	−9.14781	−0.818205	−0.409102	−	0.912488i	$-0.634158\pi$
$5$	−9.14781	−0.818205	−0.409102	+	0.912488i	$0.634158\pi$
$6$	−9.91606	−0.674702
$7$	0	0
$7$	0	0
$8$	16.7735	0.741290
$9$	9.00000	0.333333
$10$	30.2367	0.956170
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	8.77609	0.211120
$13$	18.9478	0.404244	0.202122	−	0.979360i	$-0.435216\pi$
$13$	18.9478	0.404244	0.202122	+	0.979360i	$0.435216\pi$
$14$	0	0
$15$	−27.4434	−0.472391
$16$	−78.8452	−1.23196
$17$	−57.7497	−0.823904	−0.411952	−	0.911206i	$-0.635153\pi$
$17$	−57.7497	−0.823904	−0.411952	+	0.911206i	$0.635153\pi$
$18$	−29.7482	−0.389540
$19$	130.217	1.57231	0.786154	−	0.618031i	$-0.212069\pi$
$19$	130.217	1.57231	0.786154	+	0.618031i	$0.212069\pi$
$20$	−26.7607	−0.299193
$21$	0	0
$22$	36.3589	0.352352
$23$	−82.4674	−0.747636	−0.373818	−	0.927502i	$-0.621952\pi$
$23$	−82.4674	−0.747636	−0.373818	+	0.927502i	$0.621952\pi$
$24$	50.3204	0.427984
$25$	−41.3176	−0.330541
$26$	−62.6292	−0.472407
$27$	27.0000	0.192450
$28$	0	0
$29$	169.379	1.08458	0.542292	−	0.840190i	$-0.317557\pi$
$29$	169.379	1.08458	0.542292	+	0.840190i	$0.317557\pi$
$30$	90.7102	0.552045
$31$	−152.809	−0.885334	−0.442667	−	0.896686i	$-0.645968\pi$
$31$	−152.809	−0.885334	−0.442667	+	0.896686i	$0.645968\pi$
$32$	126.423	0.698397
$33$	−33.0000	−0.174078
$34$	190.883	0.962830
$35$	0	0
$36$	26.3283	0.121890
$37$	26.8593	0.119342	0.0596708	−	0.998218i	$-0.480995\pi$
$37$	26.8593	0.119342	0.0596708	+	0.998218i	$0.480995\pi$
$38$	−430.413	−1.83743
$39$	56.8434	0.233390
$40$	−153.440	−0.606527
$41$	−47.5382	−0.181079	−0.0905393	−	0.995893i	$-0.528859\pi$
$41$	−47.5382	−0.181079	−0.0905393	+	0.995893i	$0.528859\pi$
$42$	0	0
$43$	121.614	0.431300	0.215650	−	0.976471i	$-0.430813\pi$
$43$	121.614	0.431300	0.215650	+	0.976471i	$0.430813\pi$
$44$	−32.1790	−0.110254
$45$	−82.3303	−0.272735
$46$	272.584	0.873702
$47$	−269.124	−0.835229	−0.417615	−	0.908624i	$-0.637134\pi$
$47$	−269.124	−0.835229	−0.417615	+	0.908624i	$0.637134\pi$
$48$	−236.535	−0.711270
$49$	0	0
$50$	136.569	0.386276
$51$	−173.249	−0.475681
$52$	55.4292	0.147820
$53$	−225.527	−0.584501	−0.292250	−	0.956342i	$-0.594404\pi$
$53$	−225.527	−0.584501	−0.292250	+	0.956342i	$0.594404\pi$
$54$	−89.2445	−0.224901
$55$	100.626	0.246698
$56$	0	0
$57$	390.651	0.907772
$58$	−559.858	−1.26746
$59$	55.0788	0.121536	0.0607682	−	0.998152i	$-0.480645\pi$
$59$	55.0788	0.121536	0.0607682	+	0.998152i	$0.480645\pi$
$60$	−80.2820	−0.172739
$61$	942.983	1.97929	0.989645	−	0.143538i	$-0.0458480\pi$
$61$	942.983	1.97929	0.989645	+	0.143538i	$0.0458480\pi$
$62$	505.089	1.03462
$63$	0	0
$64$	212.887	0.415796
$65$	−173.331	−0.330755
$66$	109.077	0.203430
$67$	−554.922	−1.01186	−0.505930	−	0.862575i	$-0.668850\pi$
$67$	−554.922	−1.01186	−0.505930	+	0.862575i	$0.668850\pi$
$68$	−168.939	−0.301277
$69$	−247.402	−0.431648
$70$	0	0
$71$	1116.85	1.86683	0.933417	−	0.358794i	$-0.116812\pi$
$71$	1116.85	1.86683	0.933417	+	0.358794i	$0.116812\pi$
$72$	150.961	0.247097
$73$	−16.2814	−0.0261041	−0.0130520	−	0.999915i	$-0.504155\pi$
$73$	−16.2814	−0.0261041	−0.0130520	+	0.999915i	$0.504155\pi$
$74$	−88.7794	−0.139465
$75$	−123.953	−0.190838
$76$	380.932	0.574946
$77$	0	0
$78$	−187.888	−0.272745
$79$	868.381	1.23671	0.618357	−	0.785897i	$-0.287798\pi$
$79$	868.381	1.23671	0.618357	+	0.785897i	$0.287798\pi$
$80$	721.260	1.00799
$81$	81.0000	0.111111
$82$	157.131	0.211612
$83$	−235.602	−0.311575	−0.155787	−	0.987791i	$-0.549792\pi$
$83$	−235.602	−0.311575	−0.155787	+	0.987791i	$0.549792\pi$
$84$	0	0
$85$	528.283	0.674122
$86$	−401.976	−0.504026
$87$	508.137	0.626184
$88$	−184.508	−0.223507
$89$	−631.807	−0.752488	−0.376244	−	0.926521i	$-0.622785\pi$
$89$	−631.807	−0.752488	−0.376244	+	0.926521i	$0.622785\pi$
$90$	272.131	0.318723
$91$	0	0
$92$	−241.247	−0.273388
$93$	−458.428	−0.511148
$94$	889.550	0.976064
$95$	−1191.20	−1.28647
$96$	379.270	0.403220
$97$	275.792	0.288685	0.144342	−	0.989528i	$-0.453893\pi$
$97$	275.792	0.288685	0.144342	+	0.989528i	$0.453893\pi$
$98$	0	0
$99$	−99.0000	−0.100504
$100$	−120.869	−0.120869
$101$	1008.33	0.993388	0.496694	−	0.867926i	$-0.334547\pi$
$101$	1008.33	0.993388	0.496694	+	0.867926i	$0.334547\pi$
$102$	572.650	0.555890
$103$	−787.247	−0.753105	−0.376552	−	0.926395i	$-0.622891\pi$
$103$	−787.247	−0.753105	−0.376552	+	0.926395i	$0.622891\pi$
$104$	317.820	0.299662
$105$	0	0
$106$	745.447	0.683059
$107$	−1306.94	−1.18081	−0.590404	−	0.807108i	$-0.701032\pi$
$107$	−1306.94	−1.18081	−0.590404	+	0.807108i	$0.701032\pi$
$108$	78.9848	0.0703733
$109$	−1461.34	−1.28414	−0.642071	−	0.766646i	$-0.721924\pi$
$109$	−1461.34	−1.28414	−0.642071	+	0.766646i	$0.721924\pi$
$110$	−332.604	−0.288296
$111$	80.5778	0.0689019
$112$	0	0
$113$	−528.487	−0.439963	−0.219982	−	0.975504i	$-0.570600\pi$
$113$	−528.487	−0.439963	−0.219982	+	0.975504i	$0.570600\pi$
$114$	−1291.24	−1.06084
$115$	754.396	0.611720
$116$	495.495	0.396600
$117$	170.530	0.134748
$118$	−182.055	−0.142030
$119$	0	0
$120$	−460.321	−0.350178
$121$	121.000	0.0909091
$122$	−3116.89	−2.31304
$123$	−142.615	−0.104546
$124$	−447.022	−0.323740
$125$	1521.44	1.08865
$126$	0	0
$127$	1250.82	0.873958	0.436979	−	0.899472i	$-0.356048\pi$
$127$	1250.82	0.873958	0.436979	+	0.899472i	$0.356048\pi$
$128$	−1715.05	−1.18430
$129$	364.841	0.249011
$130$	572.920	0.386526
$131$	462.755	0.308634	0.154317	−	0.988021i	$-0.450682\pi$
$131$	462.755	0.308634	0.154317	+	0.988021i	$0.450682\pi$
$132$	−96.5370	−0.0636550
$133$	0	0
$134$	1834.22	1.18248
$135$	−246.991	−0.157464
$136$	−968.663	−0.610751
$137$	2.81281	0.00175412	0.000877059	−	1.00000i	$-0.499721\pi$
$137$	2.81281	0.00175412	0.000877059		1.00000i	$0.499721\pi$
$138$	817.751	0.504432
$139$	−2068.90	−1.26246	−0.631230	−	0.775596i	$-0.717450\pi$
$139$	−2068.90	−1.26246	−0.631230	+	0.775596i	$0.717450\pi$
$140$	0	0
$141$	−807.372	−0.482220
$142$	−3691.57	−2.18162
$143$	−208.426	−0.121884
$144$	−709.606	−0.410652
$145$	−1549.45	−0.887411
$146$	53.8159	0.0305057
$147$	0	0
$148$	78.5731	0.0436397
$149$	−933.102	−0.513038	−0.256519	−	0.966539i	$-0.582576\pi$
$149$	−933.102	−0.513038	−0.256519	+	0.966539i	$0.582576\pi$
$150$	409.708	0.223017
$151$	2063.97	1.11234	0.556172	−	0.831067i	$-0.312270\pi$
$151$	2063.97	1.11234	0.556172	+	0.831067i	$0.312270\pi$
$152$	2184.19	1.16554
$153$	−519.747	−0.274635
$154$	0	0
$155$	1397.87	0.724384
$156$	166.288	0.0853440
$157$	2896.02	1.47215	0.736075	−	0.676900i	$-0.236677\pi$
$157$	2896.02	1.47215	0.736075	+	0.676900i	$0.236677\pi$
$158$	−2870.30	−1.44525
$159$	−676.582	−0.337462
$160$	−1156.50	−0.571432
$161$	0	0
$162$	−267.734	−0.129847
$163$	−884.052	−0.424812	−0.212406	−	0.977182i	$-0.568130\pi$
$163$	−884.052	−0.424812	−0.212406	+	0.977182i	$0.568130\pi$
$164$	−139.067	−0.0662151
$165$	301.878	0.142431
$166$	778.749	0.364112
$167$	−1949.31	−0.903245	−0.451623	−	0.892209i	$-0.649155\pi$
$167$	−1949.31	−0.903245	−0.451623	+	0.892209i	$0.649155\pi$
$168$	0	0
$169$	−1837.98	−0.836587
$170$	−1746.16	−0.787792
$171$	1171.95	0.524102
$172$	355.764	0.157714
$173$	−1677.27	−0.737114	−0.368557	−	0.929605i	$-0.620148\pi$
$173$	−1677.27	−0.737114	−0.368557	+	0.929605i	$0.620148\pi$
$174$	−1679.57	−0.731771
$175$	0	0
$176$	867.297	0.371449
$177$	165.236	0.0701691
$178$	2088.35	0.879372
$179$	−2116.92	−0.883944	−0.441972	−	0.897029i	$-0.645721\pi$
$179$	−2116.92	−0.883944	−0.441972	+	0.897029i	$0.645721\pi$
$180$	−240.846	−0.0997311
$181$	−1631.93	−0.670168	−0.335084	−	0.942188i	$-0.608765\pi$
$181$	−1631.93	−0.670168	−0.335084	+	0.942188i	$0.608765\pi$
$182$	0	0
$183$	2828.95	1.14274
$184$	−1383.26	−0.554215
$185$	−245.703	−0.0976458
$186$	1515.27	0.597337
$187$	635.247	0.248416
$188$	−787.285	−0.305418
$189$	0	0
$190$	3937.34	1.50339
$191$	357.094	0.135279	0.0676397	−	0.997710i	$-0.478453\pi$
$191$	357.094	0.135279	0.0676397	+	0.997710i	$0.478453\pi$
$192$	638.662	0.240060
$193$	4811.15	1.79437	0.897186	−	0.441653i	$-0.145608\pi$
$193$	4811.15	1.79437	0.897186	+	0.441653i	$0.145608\pi$
$194$	−911.590	−0.337363
$195$	−519.992	−0.190961
$196$	0	0
$197$	−3267.21	−1.18162	−0.590809	−	0.806811i	$-0.701191\pi$
$197$	−3267.21	−1.18162	−0.590809	+	0.806811i	$0.701191\pi$
$198$	327.230	0.117451
$199$	−3344.70	−1.19145	−0.595727	−	0.803187i	$-0.703136\pi$
$199$	−3344.70	−1.19145	−0.595727	+	0.803187i	$0.703136\pi$
$200$	−693.040	−0.245027
$201$	−1664.77	−0.584197
$202$	−3332.87	−1.16089
$203$	0	0
$204$	−506.817	−0.173942
$205$	434.870	0.148159
$206$	2602.13	0.880093
$207$	−742.206	−0.249212
$208$	−1493.94	−0.498011
$209$	−1432.39	−0.474068
$210$	0	0
$211$	3727.42	1.21614	0.608072	−	0.793882i	$-0.291943\pi$
$211$	3727.42	1.21614	0.608072	+	0.793882i	$0.291943\pi$
$212$	−659.749	−0.213735
$213$	3350.54	1.07782
$214$	4319.89	1.37991
$215$	−1112.50	−0.352892
$216$	452.884	0.142661
$217$	0	0
$218$	4830.26	1.50067
$219$	−48.8443	−0.0150712
$220$	294.367	0.0902102
$221$	−1094.23	−0.333058
$222$	−266.338	−0.0805200
$223$	1344.30	0.403681	0.201841	−	0.979418i	$-0.435308\pi$
$223$	1344.30	0.403681	0.201841	+	0.979418i	$0.435308\pi$
$224$	0	0
$225$	−371.858	−0.110180
$226$	1746.83	0.514149
$227$	−2725.27	−0.796839	−0.398420	−	0.917203i	$-0.630441\pi$
$227$	−2725.27	−0.796839	−0.398420	+	0.917203i	$0.630441\pi$
$228$	1142.80	0.331945
$229$	1159.61	0.334625	0.167313	−	0.985904i	$-0.446491\pi$
$229$	1159.61	0.334625	0.167313	+	0.985904i	$0.446491\pi$
$230$	−2493.54	−0.714867
$231$	0	0
$232$	2841.08	0.803990
$233$	−3501.98	−0.984645	−0.492323	−	0.870413i	$-0.663852\pi$
$233$	−3501.98	−0.984645	−0.492323	+	0.870413i	$0.663852\pi$
$234$	−563.663	−0.157469
$235$	2461.89	0.683388
$236$	161.125	0.0444423
$237$	2605.14	0.714017
$238$	0	0
$239$	−1227.24	−0.332148	−0.166074	−	0.986113i	$-0.553109\pi$
$239$	−1227.24	−0.332148	−0.166074	+	0.986113i	$0.553109\pi$
$240$	2163.78	0.581964
$241$	3909.42	1.04493	0.522465	−	0.852661i	$-0.325013\pi$
$241$	3909.42	1.04493	0.522465	+	0.852661i	$0.325013\pi$
$242$	−399.948	−0.106238
$243$	243.000	0.0641500
$244$	2758.57	0.723767
$245$	0	0
$246$	471.392	0.122174
$247$	2467.33	0.635596
$248$	−2563.14	−0.656289
$249$	−706.807	−0.179888
$250$	−5028.90	−1.27222
$251$	−4937.09	−1.24154	−0.620769	−	0.783993i	$-0.713180\pi$
$251$	−4937.09	−1.24154	−0.620769	+	0.783993i	$0.713180\pi$
$252$	0	0
$253$	907.141	0.225421
$254$	−4134.42	−1.02132
$255$	1584.85	0.389205
$256$	3965.76	0.968204
$257$	−3284.52	−0.797209	−0.398605	−	0.917123i	$-0.630505\pi$
$257$	−3284.52	−0.797209	−0.398605	+	0.917123i	$0.630505\pi$
$258$	−1205.93	−0.290999
$259$	0	0
$260$	−507.056	−0.120947
$261$	1524.41	0.361528
$262$	−1529.57	−0.360676
$263$	5171.89	1.21259	0.606297	−	0.795238i	$-0.292654\pi$
$263$	5171.89	1.21259	0.606297	+	0.795238i	$0.292654\pi$
$264$	−553.525	−0.129042
$265$	2063.08	0.478241
$266$	0	0
$267$	−1895.42	−0.434449
$268$	−1623.35	−0.370007
$269$	−3671.32	−0.832135	−0.416067	−	0.909334i	$-0.636592\pi$
$269$	−3671.32	−0.832135	−0.416067	+	0.909334i	$0.636592\pi$
$270$	816.392	0.184015
$271$	−502.142	−0.112557	−0.0562785	−	0.998415i	$-0.517923\pi$
$271$	−502.142	−0.112557	−0.0562785	+	0.998415i	$0.517923\pi$
$272$	4553.29	1.01501
$273$	0	0
$274$	−9.29732	−0.00204990
$275$	454.494	0.0996618
$276$	−723.741	−0.157841
$277$	−1197.56	−0.259763	−0.129882	−	0.991530i	$-0.541460\pi$
$277$	−1197.56	−0.259763	−0.129882	+	0.991530i	$0.541460\pi$
$278$	6838.45	1.47533
$279$	−1375.28	−0.295111
$280$	0	0
$281$	3442.75	0.730879	0.365440	−	0.930835i	$-0.380919\pi$
$281$	3442.75	0.730879	0.365440	+	0.930835i	$0.380919\pi$
$282$	2668.65	0.563531
$283$	−3864.68	−0.811771	−0.405886	−	0.913924i	$-0.633037\pi$
$283$	−3864.68	−0.811771	−0.405886	+	0.913924i	$0.633037\pi$
$284$	3267.18	0.682646
$285$	−3573.60	−0.742743
$286$	688.921	0.142436
$287$	0	0
$288$	1137.81	0.232799
$289$	−1577.97	−0.321183
$290$	5121.47	1.03705
$291$	827.376	0.166672
$292$	−47.6291	−0.00954549
$293$	−5350.31	−1.06679	−0.533393	−	0.845867i	$-0.679083\pi$
$293$	−5350.31	−1.06679	−0.533393	+	0.845867i	$0.679083\pi$
$294$	0	0
$295$	−503.850	−0.0994417
$296$	450.523	0.0884667
$297$	−297.000	−0.0580259
$298$	3084.23	0.599546
$299$	−1562.57	−0.302228
$300$	−362.607	−0.0697837
$301$	0	0
$302$	−6822.17	−1.29991
$303$	3024.98	0.573533
$304$	−10267.0	−1.93701
$305$	−8626.23	−1.61946
$306$	1717.95	0.320943
$307$	−3717.51	−0.691106	−0.345553	−	0.938399i	$-0.612309\pi$
$307$	−3717.51	−0.691106	−0.345553	+	0.938399i	$0.612309\pi$
$308$	0	0
$309$	−2361.74	−0.434805
$310$	−4620.45	−0.846529
$311$	−8231.82	−1.50091	−0.750456	−	0.660920i	$-0.770166\pi$
$311$	−8231.82	−1.50091	−0.750456	+	0.660920i	$0.770166\pi$
$312$	953.461	0.173010
$313$	−7851.86	−1.41793	−0.708967	−	0.705241i	$-0.750839\pi$
$313$	−7851.86	−1.41793	−0.708967	+	0.705241i	$0.750839\pi$
$314$	−9572.37	−1.72038
$315$	0	0
$316$	2540.33	0.452230
$317$	−7990.53	−1.41575	−0.707875	−	0.706338i	$-0.750346\pi$
$317$	−7990.53	−1.41575	−0.707875	+	0.706338i	$0.750346\pi$
$318$	2236.34	0.394364
$319$	−1863.17	−0.327014
$320$	−1947.45	−0.340206
$321$	−3920.81	−0.681740
$322$	0	0
$323$	−7520.00	−1.29543
$324$	236.954	0.0406300
$325$	−782.878	−0.133619
$326$	2922.11	0.496443
$327$	−4384.03	−0.741399
$328$	−797.381	−0.134232
$329$	0	0
$330$	−997.812	−0.166448
$331$	5894.84	0.978881	0.489441	−	0.872037i	$-0.337201\pi$
$331$	5894.84	0.978881	0.489441	+	0.872037i	$0.337201\pi$
$332$	−689.223	−0.113934
$333$	241.733	0.0397805
$334$	6443.15	1.05555
$335$	5076.32	0.827908
$336$	0	0
$337$	−7428.31	−1.20073	−0.600364	−	0.799727i	$-0.704978\pi$
$337$	−7428.31	−1.20073	−0.600364	+	0.799727i	$0.704978\pi$
$338$	6075.18	0.977651
$339$	−1585.46	−0.254013
$340$	1545.42	0.246506
$341$	1680.90	0.266938
$342$	−3873.72	−0.612476
$343$	0	0
$344$	2039.88	0.319719
$345$	2263.19	0.353176
$346$	5543.98	0.861405
$347$	1278.55	0.197799	0.0988996	−	0.995097i	$-0.468468\pi$
$347$	1278.55	0.197799	0.0988996	+	0.995097i	$0.468468\pi$
$348$	1486.49	0.228977
$349$	−5725.67	−0.878189	−0.439095	−	0.898441i	$-0.644701\pi$
$349$	−5725.67	−0.878189	−0.439095	+	0.898441i	$0.644701\pi$
$350$	0	0
$351$	511.591	0.0777968
$352$	−1390.66	−0.210575
$353$	−5765.04	−0.869241	−0.434621	−	0.900614i	$-0.643118\pi$
$353$	−5765.04	−0.869241	−0.434621	+	0.900614i	$0.643118\pi$
$354$	−546.165	−0.0820009
$355$	−10216.7	−1.52745
$356$	−1848.27	−0.275163
$357$	0	0
$358$	6997.17	1.03299
$359$	−11302.0	−1.66155	−0.830773	−	0.556611i	$-0.812101\pi$
$359$	−11302.0	−1.66155	−0.830773	+	0.556611i	$0.812101\pi$
$360$	−1380.96	−0.202176
$361$	10097.5	1.47215
$362$	5394.11	0.783171
$363$	363.000	0.0524864
$364$	0	0
$365$	148.939	0.0213585
$366$	−9350.68	−1.33543
$367$	−4394.68	−0.625069	−0.312534	−	0.949906i	$-0.601178\pi$
$367$	−4394.68	−0.625069	−0.312534	+	0.949906i	$0.601178\pi$
$368$	6502.15	0.921055
$369$	−427.844	−0.0603595
$370$	812.137	0.114111
$371$	0	0
$372$	−1341.07	−0.186912
$373$	3869.33	0.537122	0.268561	−	0.963263i	$-0.413452\pi$
$373$	3869.33	0.537122	0.268561	+	0.963263i	$0.413452\pi$
$374$	−2099.72	−0.290304
$375$	4564.32	0.628535
$376$	−4514.14	−0.619147
$377$	3209.36	0.438436
$378$	0	0
$379$	4961.74	0.672474	0.336237	−	0.941777i	$-0.390846\pi$
$379$	4961.74	0.672474	0.336237	+	0.941777i	$0.390846\pi$
$380$	−3484.69	−0.470424
$381$	3752.47	0.504580
$382$	−1180.32	−0.158090
$383$	3459.47	0.461542	0.230771	−	0.973008i	$-0.425875\pi$
$383$	3459.47	0.461542	0.230771	+	0.973008i	$0.425875\pi$
$384$	−5145.16	−0.683758
$385$	0	0
$386$	−15902.5	−2.09694
$387$	1094.52	0.143767
$388$	806.791	0.105563
$389$	−8055.42	−1.04994	−0.524969	−	0.851121i	$-0.675923\pi$
$389$	−8055.42	−1.04994	−0.524969	+	0.851121i	$0.675923\pi$
$390$	1718.76	0.223161
$391$	4762.47	0.615980
$392$	0	0
$393$	1388.27	0.178190
$394$	10799.3	1.38086
$395$	−7943.78	−1.01189
$396$	−289.611	−0.0367513
$397$	−15102.9	−1.90930	−0.954652	−	0.297723i	$-0.903773\pi$
$397$	−15102.9	−1.90930	−0.954652	+	0.297723i	$0.903773\pi$
$398$	11055.4	1.39236
$399$	0	0
$400$	3257.69	0.407212
$401$	6191.10	0.770994	0.385497	−	0.922709i	$-0.374030\pi$
$401$	6191.10	0.770994	0.385497	+	0.922709i	$0.374030\pi$
$402$	5502.65	0.682704
$403$	−2895.40	−0.357891
$404$	2949.72	0.363253
$405$	−740.972	−0.0909116
$406$	0	0
$407$	−295.452	−0.0359828
$408$	−2905.99	−0.352617
$409$	−8172.83	−0.988070	−0.494035	−	0.869442i	$-0.664478\pi$
$409$	−8172.83	−0.988070	−0.494035	+	0.869442i	$0.664478\pi$
$410$	−1437.40	−0.173142
$411$	8.43842	0.00101274
$412$	−2302.98	−0.275388
$413$	0	0
$414$	2453.25	0.291234
$415$	2155.25	0.254932
$416$	2395.44	0.282323
$417$	−6206.70	−0.728882
$418$	4734.55	0.554005
$419$	2327.26	0.271347	0.135673	−	0.990754i	$-0.456680\pi$
$419$	2327.26	0.271347	0.135673	+	0.990754i	$0.456680\pi$
$420$	0	0
$421$	−14308.3	−1.65640	−0.828200	−	0.560433i	$-0.810635\pi$
$421$	−14308.3	−1.65640	−0.828200	+	0.560433i	$0.810635\pi$
$422$	−12320.4	−1.42121
$423$	−2422.12	−0.278410
$424$	−3782.87	−0.433284
$425$	2386.08	0.272334
$426$	−11074.7	−1.25956
$427$	0	0
$428$	−3823.27	−0.431787
$429$	−625.277	−0.0703699
$430$	3677.20	0.412396
$431$	−6945.52	−0.776227	−0.388114	−	0.921612i	$-0.626873\pi$
$431$	−6945.52	−0.776227	−0.388114	+	0.921612i	$0.626873\pi$
$432$	−2128.82	−0.237090
$433$	1412.71	0.156791	0.0783953	−	0.996922i	$-0.475020\pi$
$433$	1412.71	0.156791	0.0783953	+	0.996922i	$0.475020\pi$
$434$	0	0
$435$	−4648.34	−0.512347
$436$	−4274.96	−0.469572
$437$	−10738.7	−1.17551
$438$	161.448	0.0176125
$439$	−12715.3	−1.38239	−0.691196	−	0.722668i	$-0.742916\pi$
$439$	−12715.3	−1.38239	−0.691196	+	0.722668i	$0.742916\pi$
$440$	1687.85	0.182875
$441$	0	0
$442$	3616.82	0.389218
$443$	−9941.76	−1.06625	−0.533123	−	0.846038i	$-0.678982\pi$
$443$	−9941.76	−1.06625	−0.533123	+	0.846038i	$0.678982\pi$
$444$	235.719	0.0251954
$445$	5779.65	0.615689
$446$	−4443.38	−0.471749
$447$	−2799.31	−0.296203
$448$	0	0
$449$	12727.7	1.33777	0.668885	−	0.743366i	$-0.266772\pi$
$449$	12727.7	1.33777	0.668885	+	0.743366i	$0.266772\pi$
$450$	1229.12	0.128759
$451$	522.920	0.0545972
$452$	−1546.01	−0.160881
$453$	6191.92	0.642212
$454$	9007.98	0.931201
$455$	0	0
$456$	6552.57	0.672922
$457$	16246.3	1.66296	0.831479	−	0.555556i	$-0.187495\pi$
$457$	16246.3	1.66296	0.831479	+	0.555556i	$0.187495\pi$
$458$	−3832.92	−0.391049
$459$	−1559.24	−0.158560
$460$	2206.88	0.223688
$461$	−16189.8	−1.63565	−0.817827	−	0.575464i	$-0.804821\pi$
$461$	−16189.8	−1.63565	−0.817827	+	0.575464i	$0.804821\pi$
$462$	0	0
$463$	−1873.41	−0.188045	−0.0940226	−	0.995570i	$-0.529973\pi$
$463$	−1873.41	−0.188045	−0.0940226	+	0.995570i	$0.529973\pi$
$464$	−13354.7	−1.33616
$465$	4193.61	0.418224
$466$	11575.3	1.15068
$467$	−3839.69	−0.380470	−0.190235	−	0.981739i	$-0.560925\pi$
$467$	−3839.69	−0.380470	−0.190235	+	0.981739i	$0.560925\pi$
$468$	498.863	0.0492734
$469$	0	0
$470$	−8137.43	−0.798621
$471$	8688.06	0.849946
$472$	923.863	0.0900937
$473$	−1337.75	−0.130042
$474$	−8610.91	−0.834414
$475$	−5380.26	−0.519712
$476$	0	0
$477$	−2029.74	−0.194834
$478$	4056.45	0.388154
$479$	−605.246	−0.0577336	−0.0288668	−	0.999583i	$-0.509190\pi$
$479$	−605.246	−0.0577336	−0.0288668	+	0.999583i	$0.509190\pi$
$480$	−3469.49	−0.329916
$481$	508.924	0.0482431
$482$	−12922.0	−1.22113
$483$	0	0
$484$	353.969	0.0332428
$485$	−2522.89	−0.236203
$486$	−803.201	−0.0749669
$487$	7771.40	0.723113	0.361556	−	0.932350i	$-0.382245\pi$
$487$	7771.40	0.723113	0.361556	+	0.932350i	$0.382245\pi$
$488$	15817.1	1.46723
$489$	−2652.16	−0.245265
$490$	0	0
$491$	−16040.4	−1.47433	−0.737164	−	0.675714i	$-0.763836\pi$
$491$	−16040.4	−1.47433	−0.737164	+	0.675714i	$0.763836\pi$
$492$	−417.200	−0.0382293
$493$	−9781.60	−0.893592
$494$	−8155.38	−0.742769
$495$	905.633	0.0822327
$496$	12048.3	1.09069
$497$	0	0
$498$	2336.25	0.210220
$499$	7341.88	0.658652	0.329326	−	0.944216i	$-0.393178\pi$
$499$	7341.88	0.658652	0.329326	+	0.944216i	$0.393178\pi$
$500$	4450.77	0.398089
$501$	−5847.92	−0.521489
$502$	16318.8	1.45089
$503$	−16856.0	−1.49417	−0.747087	−	0.664726i	$-0.768548\pi$
$503$	−16856.0	−1.49417	−0.747087	+	0.664726i	$0.768548\pi$
$504$	0	0
$505$	−9223.97	−0.812795
$506$	−2998.42	−0.263431
$507$	−5513.94	−0.483004
$508$	3659.11	0.319581
$509$	17765.4	1.54702	0.773512	−	0.633781i	$-0.218498\pi$
$509$	17765.4	1.54702	0.773512	+	0.633781i	$0.218498\pi$
$510$	−5238.49	−0.454832
$511$	0	0
$512$	612.187	0.0528420
$513$	3515.86	0.302591
$514$	10856.5	0.931634
$515$	7201.59	0.616194
$516$	1067.29	0.0910561
$517$	2960.36	0.251831
$518$	0	0
$519$	−5031.82	−0.425573
$520$	−2907.36	−0.245185
$521$	5538.25	0.465710	0.232855	−	0.972511i	$-0.425193\pi$
$521$	5538.25	0.465710	0.232855	+	0.972511i	$0.425193\pi$
$522$	−5038.72	−0.422488
$523$	−2695.27	−0.225346	−0.112673	−	0.993632i	$-0.535941\pi$
$523$	−2695.27	−0.225346	−0.112673	+	0.993632i	$0.535941\pi$
$524$	1353.73	0.112858
$525$	0	0
$526$	−17094.9	−1.41706
$527$	8824.69	0.729430
$528$	2601.89	0.214456
$529$	−5366.14	−0.441040
$530$	−6819.21	−0.558882
$531$	495.709	0.0405121
$532$	0	0
$533$	−900.744	−0.0732000
$534$	6265.04	0.507706
$535$	11955.6	0.966143
$536$	−9307.98	−0.750081
$537$	−6350.76	−0.510345
$538$	12135.0	0.972449
$539$	0	0
$540$	−722.538	−0.0575798
$541$	−7375.35	−0.586121	−0.293060	−	0.956094i	$-0.594674\pi$
$541$	−7375.35	−0.586121	−0.293060	+	0.956094i	$0.594674\pi$
$542$	1659.76	0.131536
$543$	−4895.79	−0.386922
$544$	−7300.91	−0.575412
$545$	13368.1	1.05069
$546$	0	0
$547$	22868.9	1.78757	0.893786	−	0.448494i	$-0.148039\pi$
$547$	22868.9	1.78757	0.893786	+	0.448494i	$0.148039\pi$
$548$	8.22848	0.000641429 0
$549$	8486.85	0.659763
$550$	−1502.26	−0.116467
$551$	22056.0	1.70530
$552$	−4149.79	−0.319976
$553$	0	0
$554$	3958.36	0.303564
$555$	−737.110	−0.0563758
$556$	−6052.29	−0.461644
$557$	6977.14	0.530756	0.265378	−	0.964144i	$-0.414503\pi$
$557$	6977.14	0.530756	0.265378	+	0.964144i	$0.414503\pi$
$558$	4545.80	0.344873
$559$	2304.31	0.174351
$560$	0	0
$561$	1905.74	0.143423
$562$	−11379.5	−0.854119
$563$	−8625.79	−0.645708	−0.322854	−	0.946449i	$-0.604642\pi$
$563$	−8625.79	−0.645708	−0.322854	+	0.946449i	$0.604642\pi$
$564$	−2361.86	−0.176333
$565$	4834.49	0.359980
$566$	12774.1	0.948651
$567$	0	0
$568$	18733.4	1.38386
$569$	16809.0	1.23843	0.619217	−	0.785220i	$-0.287450\pi$
$569$	16809.0	1.23843	0.619217	+	0.785220i	$0.287450\pi$
$570$	11812.0	0.867984
$571$	245.633	0.0180025	0.00900125	−	0.999959i	$-0.497135\pi$
$571$	245.633	0.0180025	0.00900125	+	0.999959i	$0.497135\pi$
$572$	−609.721	−0.0445694
$573$	1071.28	0.0781036
$574$	0	0
$575$	3407.35	0.247124
$576$	1915.99	0.138599
$577$	−1820.80	−0.131371	−0.0656855	−	0.997840i	$-0.520923\pi$
$577$	−1820.80	−0.131371	−0.0656855	+	0.997840i	$0.520923\pi$
$578$	5215.75	0.375340
$579$	14433.4	1.03598
$580$	−4532.70	−0.324500
$581$	0	0
$582$	−2734.77	−0.194776
$583$	2480.80	0.176234
$584$	−273.096	−0.0193507
$585$	−1559.98	−0.110252
$586$	17684.7	1.24667
$587$	26819.6	1.88580	0.942900	−	0.333076i	$-0.108087\pi$
$587$	26819.6	1.88580	0.942900	+	0.333076i	$0.108087\pi$
$588$	0	0
$589$	−19898.4	−1.39202
$590$	1665.40	0.116209
$591$	−9801.62	−0.682208
$592$	−2117.72	−0.147023
$593$	1675.24	0.116010	0.0580050	−	0.998316i	$-0.481526\pi$
$593$	1675.24	0.116010	0.0580050	+	0.998316i	$0.481526\pi$
$594$	981.690	0.0678102
$595$	0	0
$596$	−2729.66	−0.187603
$597$	−10034.1	−0.687887
$598$	5164.86	0.353189
$599$	−12880.5	−0.878605	−0.439302	−	0.898339i	$-0.644774\pi$
$599$	−12880.5	−0.878605	−0.439302	+	0.898339i	$0.644774\pi$
$600$	−2079.12	−0.141466
$601$	23356.7	1.58526	0.792628	−	0.609706i	$-0.208712\pi$
$601$	23356.7	1.58526	0.792628	+	0.609706i	$0.208712\pi$
$602$	0	0
$603$	−4994.30	−0.337286
$604$	6037.87	0.406751
$605$	−1106.88	−0.0743823
$606$	−9998.62	−0.670241
$607$	−1074.29	−0.0718352	−0.0359176	−	0.999355i	$-0.511435\pi$
$607$	−1074.29	−0.0718352	−0.0359176	+	0.999355i	$0.511435\pi$
$608$	16462.5	1.09809
$609$	0	0
$610$	28512.7	1.89254
$611$	−5099.31	−0.337636
$612$	−1520.45	−0.100426
$613$	−8060.89	−0.531119	−0.265560	−	0.964094i	$-0.585557\pi$
$613$	−8060.89	−0.531119	−0.265560	+	0.964094i	$0.585557\pi$
$614$	12287.7	0.807639
$615$	1304.61	0.0855398
$616$	0	0
$617$	17114.8	1.11672	0.558359	−	0.829599i	$-0.311431\pi$
$617$	17114.8	1.11672	0.558359	+	0.829599i	$0.311431\pi$
$618$	7806.39	0.508122
$619$	−11842.3	−0.768956	−0.384478	−	0.923134i	$-0.625619\pi$
$619$	−11842.3	−0.768956	−0.384478	+	0.923134i	$0.625619\pi$
$620$	4089.28	0.264886
$621$	−2226.62	−0.143883
$622$	27209.1	1.75400
$623$	0	0
$624$	−4481.83	−0.287527
$625$	−8753.15	−0.560202
$626$	25953.2	1.65703
$627$	−4297.16	−0.273704
$628$	8471.91	0.538321
$629$	−1551.12	−0.0983260
$630$	0	0
$631$	−6693.99	−0.422319	−0.211160	−	0.977452i	$-0.567724\pi$
$631$	−6693.99	−0.422319	−0.211160	+	0.977452i	$0.567724\pi$
$632$	14565.8	0.916764
$633$	11182.3	0.702141
$634$	26411.5	1.65447
$635$	−11442.3	−0.715077
$636$	−1979.25	−0.123400
$637$	0	0
$638$	6158.44	0.382155
$639$	10051.6	0.622278
$640$	15689.0	0.969003
$641$	7444.89	0.458745	0.229373	−	0.973339i	$-0.426333\pi$
$641$	7444.89	0.458745	0.229373	+	0.973339i	$0.426333\pi$
$642$	12959.7	0.796694
$643$	17092.0	1.04828	0.524140	−	0.851632i	$-0.324387\pi$
$643$	17092.0	1.04828	0.524140	+	0.851632i	$0.324387\pi$
$644$	0	0
$645$	−3337.50	−0.203742
$646$	24856.2	1.51386
$647$	1949.35	0.118450	0.0592248	−	0.998245i	$-0.481137\pi$
$647$	1949.35	0.118450	0.0592248	+	0.998245i	$0.481137\pi$
$648$	1358.65	0.0823655
$649$	−605.867	−0.0366446
$650$	2587.69	0.156150
$651$	0	0
$652$	−2586.17	−0.155341
$653$	−102.387	−0.00613585	−0.00306792	−	0.999995i	$-0.500977\pi$
$653$	−102.387	−0.00613585	−0.00306792	+	0.999995i	$0.500977\pi$
$654$	14490.8	0.866413
$655$	−4233.19	−0.252526
$656$	3748.16	0.223081
$657$	−146.533	−0.00870136
$658$	0	0
$659$	17993.7	1.06363	0.531817	−	0.846859i	$-0.321509\pi$
$659$	17993.7	1.06363	0.531817	+	0.846859i	$0.321509\pi$
$660$	883.102	0.0520829
$661$	−32394.7	−1.90622	−0.953109	−	0.302629i	$-0.902136\pi$
$661$	−32394.7	−1.90622	−0.953109	+	0.302629i	$0.902136\pi$
$662$	−19484.5	−1.14394
$663$	−3282.69	−0.192291
$664$	−3951.87	−0.230967
$665$	0	0
$666$	−799.015	−0.0464883
$667$	−13968.3	−0.810874
$668$	−5702.43	−0.330290
$669$	4032.90	0.233065
$670$	−16779.0	−0.967509
$671$	−10372.8	−0.596778
$672$	0	0
$673$	19213.6	1.10049	0.550246	−	0.835003i	$-0.314534\pi$
$673$	19213.6	1.10049	0.550246	+	0.835003i	$0.314534\pi$
$674$	24553.2	1.40319
$675$	−1115.58	−0.0636126
$676$	−5376.76	−0.305915
$677$	−19038.8	−1.08083	−0.540414	−	0.841399i	$-0.681732\pi$
$677$	−19038.8	−1.08083	−0.540414	+	0.841399i	$0.681732\pi$
$678$	5240.50	0.296844
$679$	0	0
$680$	8861.15	0.499720
$681$	−8175.81	−0.460055
$682$	−5555.97	−0.311949
$683$	−20632.0	−1.15588	−0.577938	−	0.816081i	$-0.696142\pi$
$683$	−20632.0	−1.15588	−0.577938	+	0.816081i	$0.696142\pi$
$684$	3428.39	0.191649
$685$	−25.7310	−0.00143523
$686$	0	0
$687$	3478.83	0.193196
$688$	−9588.65	−0.531343
$689$	−4273.24	−0.236281
$690$	−7480.63	−0.412729
$691$	−5210.40	−0.286849	−0.143425	−	0.989661i	$-0.545811\pi$
$691$	−5210.40	−0.286849	−0.143425	+	0.989661i	$0.545811\pi$
$692$	−4906.63	−0.269541
$693$	0	0
$694$	−4226.07	−0.231152
$695$	18925.9	1.03295
$696$	8523.23	0.464184
$697$	2745.32	0.149191
$698$	18925.4	1.02627
$699$	−10505.9	−0.568485
$700$	0	0
$701$	2718.31	0.146461	0.0732305	−	0.997315i	$-0.476669\pi$
$701$	2718.31	0.146461	0.0732305	+	0.997315i	$0.476669\pi$
$702$	−1690.99	−0.0909148
$703$	3497.53	0.187642
$704$	−2341.76	−0.125367
$705$	7385.68	0.394554
$706$	19055.5	1.01581
$707$	0	0
$708$	483.376	0.0256588
$709$	−7409.31	−0.392472	−0.196236	−	0.980557i	$-0.562872\pi$
$709$	−7409.31	−0.392472	−0.196236	+	0.980557i	$0.562872\pi$
$710$	33769.8	1.78501
$711$	7815.43	0.412238
$712$	−10597.6	−0.557812
$713$	12601.8	0.661908
$714$	0	0
$715$	1906.64	0.0997262
$716$	−6192.76	−0.323232
$717$	−3681.71	−0.191765
$718$	37357.0	1.94171
$719$	29427.0	1.52635	0.763173	−	0.646195i	$-0.223641\pi$
$719$	29427.0	1.52635	0.763173	+	0.646195i	$0.223641\pi$
$720$	6491.34	0.335997
$721$	0	0
$722$	−33375.7	−1.72038
$723$	11728.3	0.603291
$724$	−4773.99	−0.245061
$725$	−6998.34	−0.358499
$726$	−1199.84	−0.0613366
$727$	23090.9	1.17799	0.588993	−	0.808138i	$-0.299525\pi$
$727$	23090.9	1.17799	0.588993	+	0.808138i	$0.299525\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−492.298	−0.0249599
$731$	−7023.16	−0.355350
$732$	8275.71	0.417867
$733$	−15768.4	−0.794568	−0.397284	−	0.917696i	$-0.630047\pi$
$733$	−15768.4	−0.794568	−0.397284	+	0.917696i	$0.630047\pi$
$734$	14526.0	0.730467
$735$	0	0
$736$	−10425.8	−0.522147
$737$	6104.15	0.305087
$738$	1414.18	0.0705373
$739$	−5708.36	−0.284148	−0.142074	−	0.989856i	$-0.545377\pi$
$739$	−5708.36	−0.284148	−0.142074	+	0.989856i	$0.545377\pi$
$740$	−718.772	−0.0357062
$741$	7401.98	0.366961
$742$	0	0
$743$	−21278.4	−1.05065	−0.525323	−	0.850903i	$-0.676056\pi$
$743$	−21278.4	−1.05065	−0.525323	+	0.850903i	$0.676056\pi$
$744$	−7689.42	−0.378909
$745$	8535.84	0.419770
$746$	−12789.5	−0.627691
$747$	−2120.42	−0.103858
$748$	1858.33	0.0908385
$749$	0	0
$750$	−15086.7	−0.734518
$751$	26421.9	1.28382	0.641910	−	0.766780i	$-0.278142\pi$
$751$	26421.9	1.28382	0.641910	+	0.766780i	$0.278142\pi$
$752$	21219.1	1.02897
$753$	−14811.3	−0.716803
$754$	−10608.1	−0.512365
$755$	−18880.8	−0.910125
$756$	0	0
$757$	6694.06	0.321400	0.160700	−	0.987003i	$-0.448625\pi$
$757$	6694.06	0.321400	0.160700	+	0.987003i	$0.448625\pi$
$758$	−16400.3	−0.785865
$759$	2721.42	0.130147
$760$	−19980.6	−0.953646
$761$	−33080.0	−1.57576	−0.787878	−	0.615831i	$-0.788820\pi$
$761$	−33080.0	−1.57576	−0.787878	+	0.615831i	$0.788820\pi$
$762$	−12403.2	−0.589662
$763$	0	0
$764$	1044.63	0.0494677
$765$	4754.55	0.224707
$766$	−11434.8	−0.539367
$767$	1043.62	0.0491304
$768$	11897.3	0.558993
$769$	9132.94	0.428274	0.214137	−	0.976804i	$-0.431306\pi$
$769$	9132.94	0.428274	0.214137	+	0.976804i	$0.431306\pi$
$770$	0	0
$771$	−9853.56	−0.460269
$772$	14074.3	0.656149
$773$	1490.11	0.0693345	0.0346672	−	0.999399i	$-0.488963\pi$
$773$	1490.11	0.0693345	0.0346672	+	0.999399i	$0.488963\pi$
$774$	−3617.79	−0.168009
$775$	6313.71	0.292639
$776$	4625.99	0.213999
$777$	0	0
$778$	26626.0	1.22698
$779$	−6190.28	−0.284711
$780$	−1521.17	−0.0698288
$781$	−12285.3	−0.562871
$782$	−15741.6	−0.719846
$783$	4573.24	0.208728
$784$	0	0
$785$	−26492.2	−1.20452
$786$	−4588.71	−0.208236
$787$	13411.6	0.607463	0.303731	−	0.952758i	$-0.401767\pi$
$787$	13411.6	0.607463	0.303731	+	0.952758i	$0.401767\pi$
$788$	−9557.76	−0.432083
$789$	15515.7	0.700092
$790$	26257.0	1.18251
$791$	0	0
$792$	−1660.57	−0.0745024
$793$	17867.5	0.800116
$794$	49920.5	2.23125
$795$	6189.24	0.276113
$796$	−9784.46	−0.435680
$797$	−36490.1	−1.62177	−0.810883	−	0.585209i	$-0.801013\pi$
$797$	−36490.1	−1.62177	−0.810883	+	0.585209i	$0.801013\pi$
$798$	0	0
$799$	15541.8	0.688148
$800$	−5223.51	−0.230849
$801$	−5686.27	−0.250829
$802$	−20463.8	−0.900998
$803$	179.096	0.00787068
$804$	−4870.05	−0.213624
$805$	0	0
$806$	9570.32	0.418238
$807$	−11014.0	−0.480433
$808$	16913.1	0.736388
$809$	13591.6	0.590674	0.295337	−	0.955393i	$-0.404568\pi$
$809$	13591.6	0.590674	0.295337	+	0.955393i	$0.404568\pi$
$810$	2449.18	0.106241
$811$	−2789.96	−0.120800	−0.0603999	−	0.998174i	$-0.519238\pi$
$811$	−2789.96	−0.120800	−0.0603999	+	0.998174i	$0.519238\pi$
$812$	0	0
$813$	−1506.43	−0.0649848
$814$	976.573	0.0420502
$815$	8087.14	0.347583
$816$	13659.9	0.586018
$817$	15836.2	0.678137
$818$	27014.1	1.15468
$819$	0	0
$820$	1272.15	0.0541775
$821$	8241.56	0.350344	0.175172	−	0.984538i	$-0.443952\pi$
$821$	8241.56	0.350344	0.175172	+	0.984538i	$0.443952\pi$
$822$	−27.8920	−0.00118351
$823$	16971.5	0.718819	0.359409	−	0.933180i	$-0.382978\pi$
$823$	16971.5	0.718819	0.359409	+	0.933180i	$0.382978\pi$
$824$	−13204.9	−0.558269
$825$	1363.48	0.0575398
$826$	0	0
$827$	22592.5	0.949960	0.474980	−	0.879997i	$-0.342455\pi$
$827$	22592.5	0.949960	0.474980	+	0.879997i	$0.342455\pi$
$828$	−2171.22	−0.0911295
$829$	39679.6	1.66240	0.831201	−	0.555973i	$-0.187654\pi$
$829$	39679.6	1.66240	0.831201	+	0.555973i	$0.187654\pi$
$830$	−7123.85	−0.297919
$831$	−3592.68	−0.149974
$832$	4033.75	0.168083
$833$	0	0
$834$	20515.4	0.851785
$835$	17831.9	0.739040
$836$	−4190.25	−0.173353
$837$	−4125.85	−0.170383
$838$	−7692.43	−0.317101
$839$	−47296.0	−1.94617	−0.973086	−	0.230442i	$-0.925983\pi$
$839$	−47296.0	−1.94617	−0.973086	+	0.230442i	$0.925983\pi$
$840$	0	0
$841$	4300.29	0.176321
$842$	47294.0	1.93570
$843$	10328.2	0.421973
$844$	10904.1	0.444708
$845$	16813.5	0.684499
$846$	8005.95	0.325355
$847$	0	0
$848$	17781.7	0.720079
$849$	−11594.0	−0.468676
$850$	−7886.84	−0.318255
$851$	−2215.01	−0.0892241
$852$	9801.53	0.394126
$853$	86.2698	0.00346286	0.00173143	−	0.999999i	$-0.499449\pi$
$853$	86.2698	0.00346286	0.00173143	+	0.999999i	$0.499449\pi$
$854$	0	0
$855$	−10720.8	−0.428823
$856$	−21921.9	−0.875321
$857$	−15731.2	−0.627034	−0.313517	−	0.949583i	$-0.601507\pi$
$857$	−15731.2	−0.627034	−0.313517	+	0.949583i	$0.601507\pi$
$858$	2066.76	0.0822356
$859$	−31869.1	−1.26584	−0.632922	−	0.774215i	$-0.718145\pi$
$859$	−31869.1	−1.26584	−0.632922	+	0.774215i	$0.718145\pi$
$860$	−3254.46	−0.129042
$861$	0	0
$862$	22957.4	0.907114
$863$	18786.8	0.741030	0.370515	−	0.928827i	$-0.379181\pi$
$863$	18786.8	0.741030	0.370515	+	0.928827i	$0.379181\pi$
$864$	3413.43	0.134407
$865$	15343.4	0.603110
$866$	−4669.50	−0.183229
$867$	−4733.91	−0.185435
$868$	0	0
$869$	−9552.19	−0.372883
$870$	15364.4	0.598739
$871$	−10514.6	−0.409038
$872$	−24511.8	−0.951921
$873$	2482.13	0.0962283
$874$	35495.0	1.37373
$875$	0	0
$876$	−142.887	−0.00551109
$877$	39071.0	1.50437	0.752186	−	0.658951i	$-0.228999\pi$
$877$	39071.0	1.50437	0.752186	+	0.658951i	$0.228999\pi$
$878$	42028.7	1.61549
$879$	−16050.9	−0.615910
$880$	−7933.86	−0.303921
$881$	15266.2	0.583802	0.291901	−	0.956448i	$-0.405712\pi$
$881$	15266.2	0.583802	0.291901	+	0.956448i	$0.405712\pi$
$882$	0	0
$883$	7381.68	0.281329	0.140664	−	0.990057i	$-0.455076\pi$
$883$	7381.68	0.281329	0.140664	+	0.990057i	$0.455076\pi$
$884$	−3201.02	−0.121790
$885$	−1511.55	−0.0574127
$886$	32861.0	1.24604
$887$	−4971.91	−0.188208	−0.0941040	−	0.995562i	$-0.529999\pi$
$887$	−4971.91	−0.188208	−0.0941040	+	0.995562i	$0.529999\pi$
$888$	1351.57	0.0510762
$889$	0	0
$890$	−19103.8	−0.719506
$891$	−891.000	−0.0335013
$892$	3932.56	0.147614
$893$	−35044.5	−1.31324
$894$	9252.69	0.346148
$895$	19365.2	0.723247
$896$	0	0
$897$	−4687.72	−0.174491
$898$	−42069.6	−1.56334
$899$	−25882.7	−0.960218
$900$	−1087.82	−0.0402897
$901$	13024.1	0.481572
$902$	−1728.44	−0.0638034
$903$	0	0
$904$	−8864.55	−0.326140
$905$	14928.6	0.548335
$906$	−20466.5	−0.750501
$907$	16175.9	0.592185	0.296092	−	0.955159i	$-0.404316\pi$
$907$	16175.9	0.592185	0.296092	+	0.955159i	$0.404316\pi$
$908$	−7972.40	−0.291380
$909$	9074.94	0.331129
$910$	0	0
$911$	9222.15	0.335394	0.167697	−	0.985839i	$-0.446367\pi$
$911$	9222.15	0.335394	0.167697	+	0.985839i	$0.446367\pi$
$912$	−30800.9	−1.11833
$913$	2591.63	0.0939434
$914$	−53699.9	−1.94336
$915$	−25878.7	−0.934998
$916$	3392.28	0.122363
$917$	0	0
$918$	5153.85	0.185297
$919$	−17403.4	−0.624685	−0.312343	−	0.949970i	$-0.601114\pi$
$919$	−17403.4	−0.624685	−0.312343	+	0.949970i	$0.601114\pi$
$920$	12653.8	0.453461
$921$	−11152.5	−0.399010
$922$	53513.2	1.91146
$923$	21161.8	0.754656
$924$	0	0
$925$	−1109.76	−0.0394473
$926$	6192.30	0.219753
$927$	−7085.23	−0.251035
$928$	21413.5	0.757470
$929$	29925.6	1.05686	0.528431	−	0.848976i	$-0.322780\pi$
$929$	29925.6	1.05686	0.528431	+	0.848976i	$0.322780\pi$
$930$	−13861.4	−0.488744
$931$	0	0
$932$	−10244.6	−0.360056
$933$	−24695.5	−0.866552
$934$	12691.5	0.444625
$935$	−5811.12	−0.203255
$936$	2860.38	0.0998873
$937$	−13940.3	−0.486028	−0.243014	−	0.970023i	$-0.578136\pi$
$937$	−13940.3	−0.486028	−0.243014	+	0.970023i	$0.578136\pi$
$938$	0	0
$939$	−23555.6	−0.818645
$940$	7201.93	0.249895
$941$	−259.256	−0.00898140	−0.00449070	−	0.999990i	$-0.501429\pi$
$941$	−259.256	−0.00898140	−0.00449070	+	0.999990i	$0.501429\pi$
$942$	−28717.1	−0.993263
$943$	3920.35	0.135381
$944$	−4342.70	−0.149727
$945$	0	0
$946$	4421.74	0.151970
$947$	10247.8	0.351646	0.175823	−	0.984422i	$-0.443741\pi$
$947$	10247.8	0.351646	0.175823	+	0.984422i	$0.443741\pi$
$948$	7620.98	0.261095
$949$	−308.497	−0.0105524
$950$	17783.6	0.607345
$951$	−23971.6	−0.817384
$952$	0	0
$953$	−38861.8	−1.32094	−0.660471	−	0.750852i	$-0.729643\pi$
$953$	−38861.8	−1.32094	−0.660471	+	0.750852i	$0.729643\pi$
$954$	6709.02	0.227686
$955$	−3266.62	−0.110686
$956$	−3590.11	−0.121457
$957$	−5589.51	−0.188802
$958$	2000.55	0.0674686
$959$	0	0
$960$	−5842.36	−0.196418
$961$	−6440.34	−0.216184
$962$	−1682.17	−0.0563778
$963$	−11762.4	−0.393603
$964$	11436.5	0.382100
$965$	−44011.4	−1.46816
$966$	0	0
$967$	−4897.42	−0.162865	−0.0814325	−	0.996679i	$-0.525949\pi$
$967$	−4897.42	−0.162865	−0.0814325	+	0.996679i	$0.525949\pi$
$968$	2029.59	0.0673900
$969$	−22560.0	−0.747917
$970$	8339.05	0.276032
$971$	20006.8	0.661223	0.330612	−	0.943767i	$-0.392745\pi$
$971$	20006.8	0.661223	0.330612	+	0.943767i	$0.392745\pi$
$972$	710.863	0.0234578
$973$	0	0
$974$	−25687.2	−0.845043
$975$	−2348.63	−0.0771451
$976$	−74349.7	−2.43840
$977$	13353.9	0.437286	0.218643	−	0.975805i	$-0.429837\pi$
$977$	13353.9	0.437286	0.218643	+	0.975805i	$0.429837\pi$
$978$	8766.32	0.286622
$979$	6949.88	0.226884
$980$	0	0
$981$	−13152.1	−0.428047
$982$	53019.3	1.72293
$983$	19720.9	0.639877	0.319939	−	0.947438i	$-0.396338\pi$
$983$	19720.9	0.639877	0.319939	+	0.947438i	$0.396338\pi$
$984$	−2392.14	−0.0774987
$985$	29887.8	0.966806
$986$	32331.6	1.04427
$987$	0	0
$988$	7217.82	0.232419
$989$	−10029.2	−0.322456
$990$	−2993.44	−0.0960987
$991$	−52028.6	−1.66775	−0.833877	−	0.551951i	$-0.813884\pi$
$991$	−52028.6	−1.66775	−0.833877	+	0.551951i	$0.813884\pi$
$992$	−19318.7	−0.618314
$993$	17684.5	0.565157
$994$	0	0
$995$	30596.7	0.974854
$996$	−2067.67	−0.0657797
$997$	−34683.5	−1.10174	−0.550872	−	0.834590i	$-0.685705\pi$
$997$	−34683.5	−1.10174	−0.550872	+	0.834590i	$0.685705\pi$
$998$	−24267.5	−0.769714
$999$	725.200	0.0229673

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.4.a.bd.1.5	yes	16
7.6	odd	2		1617.4.a.bc.1.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1617.4.a.bc.1.5	✓	16	7.6	odd	2
1617.4.a.bd.1.5	yes	16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1617.a (trivial)

\(f(q)\)	\(=\)	\(q-3.30535 q^{2} +3.00000 q^{3} +2.92536 q^{4} -9.14781 q^{5} -9.91606 q^{6} +16.7735 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.30535 q^{2} +3.00000 q^{3} +2.92536 q^{4} -9.14781 q^{5} -9.91606 q^{6} +16.7735 q^{8} +9.00000 q^{9} +30.2367 q^{10} -11.0000 q^{11} +8.77609 q^{12} +18.9478 q^{13} -27.4434 q^{15} -78.8452 q^{16} -57.7497 q^{17} -29.7482 q^{18} +130.217 q^{19} -26.7607 q^{20} +36.3589 q^{22} -82.4674 q^{23} +50.3204 q^{24} -41.3176 q^{25} -62.6292 q^{26} +27.0000 q^{27} +169.379 q^{29} +90.7102 q^{30} -152.809 q^{31} +126.423 q^{32} -33.0000 q^{33} +190.883 q^{34} +26.3283 q^{36} +26.8593 q^{37} -430.413 q^{38} +56.8434 q^{39} -153.440 q^{40} -47.5382 q^{41} +121.614 q^{43} -32.1790 q^{44} -82.3303 q^{45} +272.584 q^{46} -269.124 q^{47} -236.535 q^{48} +136.569 q^{50} -173.249 q^{51} +55.4292 q^{52} -225.527 q^{53} -89.2445 q^{54} +100.626 q^{55} +390.651 q^{57} -559.858 q^{58} +55.0788 q^{59} -80.2820 q^{60} +942.983 q^{61} +505.089 q^{62} +212.887 q^{64} -173.331 q^{65} +109.077 q^{66} -554.922 q^{67} -168.939 q^{68} -247.402 q^{69} +1116.85 q^{71} +150.961 q^{72} -16.2814 q^{73} -88.7794 q^{74} -123.953 q^{75} +380.932 q^{76} -187.888 q^{78} +868.381 q^{79} +721.260 q^{80} +81.0000 q^{81} +157.131 q^{82} -235.602 q^{83} +528.283 q^{85} -401.976 q^{86} +508.137 q^{87} -184.508 q^{88} -631.807 q^{89} +272.131 q^{90} -241.247 q^{92} -458.428 q^{93} +889.550 q^{94} -1191.20 q^{95} +379.270 q^{96} +275.792 q^{97} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 48 q^{3} + 72 q^{4} - 12 q^{6} - 66 q^{8} + 144 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 + 48 * q^3 + 72 * q^4 - 12 * q^6 - 66 * q^8 + 144 * q^9	\( 16 q - 4 q^{2} + 48 q^{3} + 72 q^{4} - 12 q^{6} - 66 q^{8} + 144 q^{9} - 178 q^{10} - 176 q^{11} + 216 q^{12} - 104 q^{13} + 220 q^{16} - 220 q^{17} - 36 q^{18} - 152 q^{19} - 182 q^{20} + 44 q^{22} - 180 q^{23} - 198 q^{24} + 284 q^{25} - 10 q^{26} + 432 q^{27} - 604 q^{29} - 534 q^{30} - 380 q^{31} - 592 q^{32} - 528 q^{33} - 632 q^{34} + 648 q^{36} + 148 q^{37} - 266 q^{38} - 312 q^{39} - 1792 q^{40} - 60 q^{41} + 252 q^{43} - 792 q^{44} - 116 q^{46} - 1468 q^{47} + 660 q^{48} - 850 q^{50} - 660 q^{51} - 310 q^{52} - 1456 q^{53} - 108 q^{54} - 456 q^{57} - 1350 q^{58} - 1312 q^{59} - 546 q^{60} - 2880 q^{61} - 708 q^{62} + 630 q^{64} - 4064 q^{65} + 132 q^{66} + 1220 q^{67} - 4956 q^{68} - 540 q^{69} - 2040 q^{71} - 594 q^{72} - 1628 q^{73} - 3126 q^{74} + 852 q^{75} - 6286 q^{76} - 30 q^{78} - 416 q^{79} + 874 q^{80} + 1296 q^{81} - 3040 q^{82} - 3724 q^{83} + 628 q^{85} - 1608 q^{86} - 1812 q^{87} + 726 q^{88} - 752 q^{89} - 1602 q^{90} - 32 q^{92} - 1140 q^{93} - 610 q^{94} - 912 q^{95} - 1776 q^{96} - 1088 q^{97} - 1584 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 48 * q^3 + 72 * q^4 - 12 * q^6 - 66 * q^8 + 144 * q^9 - 178 * q^10 - 176 * q^11 + 216 * q^12 - 104 * q^13 + 220 * q^16 - 220 * q^17 - 36 * q^18 - 152 * q^19 - 182 * q^20 + 44 * q^22 - 180 * q^23 - 198 * q^24 + 284 * q^25 - 10 * q^26 + 432 * q^27 - 604 * q^29 - 534 * q^30 - 380 * q^31 - 592 * q^32 - 528 * q^33 - 632 * q^34 + 648 * q^36 + 148 * q^37 - 266 * q^38 - 312 * q^39 - 1792 * q^40 - 60 * q^41 + 252 * q^43 - 792 * q^44 - 116 * q^46 - 1468 * q^47 + 660 * q^48 - 850 * q^50 - 660 * q^51 - 310 * q^52 - 1456 * q^53 - 108 * q^54 - 456 * q^57 - 1350 * q^58 - 1312 * q^59 - 546 * q^60 - 2880 * q^61 - 708 * q^62 + 630 * q^64 - 4064 * q^65 + 132 * q^66 + 1220 * q^67 - 4956 * q^68 - 540 * q^69 - 2040 * q^71 - 594 * q^72 - 1628 * q^73 - 3126 * q^74 + 852 * q^75 - 6286 * q^76 - 30 * q^78 - 416 * q^79 + 874 * q^80 + 1296 * q^81 - 3040 * q^82 - 3724 * q^83 + 628 * q^85 - 1608 * q^86 - 1812 * q^87 + 726 * q^88 - 752 * q^89 - 1602 * q^90 - 32 * q^92 - 1140 * q^93 - 610 * q^94 - 912 * q^95 - 1776 * q^96 - 1088 * q^97 - 1584 * q^99

Introduction

L-functions

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