LMFDB - Embedded newform 1617.4.a.bd.1.8

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			1.8
Root			$0.626276$ 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)

$f(q)$	$=$	$q-0.626276 q^{2} +3.00000 q^{3} -7.60778 q^{4} +4.84903 q^{5} -1.87883 q^{6} +9.77478 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-0.626276 q^{2} +3.00000 q^{3} -7.60778 q^{4} +4.84903 q^{5} -1.87883 q^{6} +9.77478 q^{8} +9.00000 q^{9} -3.03683 q^{10} -11.0000 q^{11} -22.8233 q^{12} -28.0184 q^{13} +14.5471 q^{15} +54.7405 q^{16} +117.229 q^{17} -5.63648 q^{18} -38.9320 q^{19} -36.8904 q^{20} +6.88904 q^{22} -125.398 q^{23} +29.3243 q^{24} -101.487 q^{25} +17.5473 q^{26} +27.0000 q^{27} +108.820 q^{29} -9.11050 q^{30} -274.167 q^{31} -112.481 q^{32} -33.0000 q^{33} -73.4179 q^{34} -68.4700 q^{36} +257.219 q^{37} +24.3822 q^{38} -84.0553 q^{39} +47.3982 q^{40} +178.284 q^{41} -169.552 q^{43} +83.6856 q^{44} +43.6413 q^{45} +78.5338 q^{46} +342.829 q^{47} +164.222 q^{48} +63.5588 q^{50} +351.688 q^{51} +213.158 q^{52} -249.783 q^{53} -16.9095 q^{54} -53.3394 q^{55} -116.796 q^{57} -68.1513 q^{58} +367.871 q^{59} -110.671 q^{60} +309.236 q^{61} +171.704 q^{62} -367.480 q^{64} -135.862 q^{65} +20.6671 q^{66} -732.854 q^{67} -891.854 q^{68} -376.194 q^{69} -683.141 q^{71} +87.9730 q^{72} +589.145 q^{73} -161.090 q^{74} -304.461 q^{75} +296.186 q^{76} +52.6418 q^{78} -929.114 q^{79} +265.439 q^{80} +81.0000 q^{81} -111.655 q^{82} -561.203 q^{83} +568.449 q^{85} +106.186 q^{86} +326.460 q^{87} -107.523 q^{88} +1172.75 q^{89} -27.3315 q^{90} +954.001 q^{92} -822.500 q^{93} -214.705 q^{94} -188.782 q^{95} -337.443 q^{96} -1089.65 q^{97} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.626276	−0.221422	−0.110711	−	0.993853i	$-0.535313\pi$
$2$	−0.626276	−0.221422	−0.110711	+	0.993853i	$0.535313\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−7.60778	−0.950972
$5$	4.84903	0.433711	0.216855	−	0.976204i	$-0.430420\pi$
$5$	4.84903	0.433711	0.216855	+	0.976204i	$0.430420\pi$
$6$	−1.87883	−0.127838
$7$	0	0
$7$	0	0
$8$	9.77478	0.431988
$9$	9.00000	0.333333
$10$	−3.03683	−0.0960331
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−22.8233	−0.549044
$13$	−28.0184	−0.597763	−0.298881	−	0.954290i	$-0.596613\pi$
$13$	−28.0184	−0.597763	−0.298881	+	0.954290i	$0.596613\pi$
$14$	0	0
$15$	14.5471	0.250403
$16$	54.7405	0.855321
$17$	117.229	1.67249	0.836244	−	0.548358i	$-0.184747\pi$
$17$	117.229	1.67249	0.836244	+	0.548358i	$0.184747\pi$
$18$	−5.63648	−0.0738073
$19$	−38.9320	−0.470085	−0.235042	−	0.971985i	$-0.575523\pi$
$19$	−38.9320	−0.470085	−0.235042	+	0.971985i	$0.575523\pi$
$20$	−36.8904	−0.412447
$21$	0	0
$22$	6.88904	0.0667612
$23$	−125.398	−1.13684	−0.568420	−	0.822739i	$-0.692445\pi$
$23$	−125.398	−1.13684	−0.568420	+	0.822739i	$0.692445\pi$
$24$	29.3243	0.249409
$25$	−101.487	−0.811895
$26$	17.5473	0.132358
$27$	27.0000	0.192450
$28$	0	0
$29$	108.820	0.696806	0.348403	−	0.937345i	$-0.386724\pi$
$29$	108.820	0.696806	0.348403	+	0.937345i	$0.386724\pi$
$30$	−9.11050	−0.0554447
$31$	−274.167	−1.58845	−0.794223	−	0.607627i	$-0.792122\pi$
$31$	−274.167	−1.58845	−0.794223	+	0.607627i	$0.792122\pi$
$32$	−112.481	−0.621375
$33$	−33.0000	−0.174078
$34$	−73.4179	−0.370325
$35$	0	0
$36$	−68.4700	−0.316991
$37$	257.219	1.14288	0.571439	−	0.820644i	$-0.306385\pi$
$37$	257.219	1.14288	0.571439	+	0.820644i	$0.306385\pi$
$38$	24.3822	0.104087
$39$	−84.0553	−0.345118
$40$	47.3982	0.187358
$41$	178.284	0.679104	0.339552	−	0.940587i	$-0.389724\pi$
$41$	178.284	0.679104	0.339552	+	0.940587i	$0.389724\pi$
$42$	0	0
$43$	−169.552	−0.601311	−0.300656	−	0.953733i	$-0.597205\pi$
$43$	−169.552	−0.601311	−0.300656	+	0.953733i	$0.597205\pi$
$44$	83.6856	0.286729
$45$	43.6413	0.144570
$46$	78.5338	0.251721
$47$	342.829	1.06397	0.531986	−	0.846753i	$-0.321446\pi$
$47$	342.829	1.06397	0.531986	+	0.846753i	$0.321446\pi$
$48$	164.222	0.493820
$49$	0	0
$50$	63.5588	0.179771
$51$	351.688	0.965611
$52$	213.158	0.568456
$53$	−249.783	−0.647365	−0.323683	−	0.946166i	$-0.604921\pi$
$53$	−249.783	−0.647365	−0.323683	+	0.946166i	$0.604921\pi$
$54$	−16.9095	−0.0426127
$55$	−53.3394	−0.130769
$56$	0	0
$57$	−116.796	−0.271403
$58$	−68.1513	−0.154288
$59$	367.871	0.811741	0.405871	−	0.913931i	$-0.366968\pi$
$59$	367.871	0.811741	0.405871	+	0.913931i	$0.366968\pi$
$60$	−110.671	−0.238126
$61$	309.236	0.649075	0.324538	−	0.945873i	$-0.394791\pi$
$61$	309.236	0.649075	0.324538	+	0.945873i	$0.394791\pi$
$62$	171.704	0.351717
$63$	0	0
$64$	−367.480	−0.717735
$65$	−135.862	−0.259256
$66$	20.6671	0.0385446
$67$	−732.854	−1.33630	−0.668152	−	0.744025i	$-0.732914\pi$
$67$	−732.854	−1.33630	−0.668152	+	0.744025i	$0.732914\pi$
$68$	−891.854	−1.59049
$69$	−376.194	−0.656355
$70$	0	0
$71$	−683.141	−1.14189	−0.570943	−	0.820990i	$-0.693422\pi$
$71$	−683.141	−1.14189	−0.570943	+	0.820990i	$0.693422\pi$
$72$	87.9730	0.143996
$73$	589.145	0.944579	0.472289	−	0.881444i	$-0.343428\pi$
$73$	589.145	0.944579	0.472289	+	0.881444i	$0.343428\pi$
$74$	−161.090	−0.253058
$75$	−304.461	−0.468748
$76$	296.186	0.447037
$77$	0	0
$78$	52.6418	0.0764168
$79$	−929.114	−1.32321	−0.661604	−	0.749853i	$-0.730124\pi$
$79$	−929.114	−1.32321	−0.661604	+	0.749853i	$0.730124\pi$
$80$	265.439	0.370962
$81$	81.0000	0.111111
$82$	−111.655	−0.150369
$83$	−561.203	−0.742169	−0.371084	−	0.928599i	$-0.621014\pi$
$83$	−561.203	−0.742169	−0.371084	+	0.928599i	$0.621014\pi$
$84$	0	0
$85$	568.449	0.725375
$86$	106.186	0.133144
$87$	326.460	0.402301
$88$	−107.523	−0.130249
$89$	1172.75	1.39675	0.698375	−	0.715732i	$-0.253907\pi$
$89$	1172.75	1.39675	0.698375	+	0.715732i	$0.253907\pi$
$90$	−27.3315	−0.0320110
$91$	0	0
$92$	954.001	1.08110
$93$	−822.500	−0.917090
$94$	−214.705	−0.235587
$95$	−188.782	−0.203881
$96$	−337.443	−0.358751
$97$	−1089.65	−1.14059	−0.570295	−	0.821440i	$-0.693171\pi$
$97$	−1089.65	−1.14059	−0.570295	+	0.821440i	$0.693171\pi$
$98$	0	0
$99$	−99.0000	−0.100504
$100$	772.090	0.772090
$101$	538.595	0.530616	0.265308	−	0.964164i	$-0.414526\pi$
$101$	538.595	0.530616	0.265308	+	0.964164i	$0.414526\pi$
$102$	−220.254	−0.213807
$103$	−1442.22	−1.37968	−0.689838	−	0.723964i	$-0.742318\pi$
$103$	−1442.22	−1.37968	−0.689838	+	0.723964i	$0.742318\pi$
$104$	−273.874	−0.258226
$105$	0	0
$106$	156.433	0.143341
$107$	2051.96	1.85393	0.926965	−	0.375147i	$-0.122408\pi$
$107$	2051.96	1.85393	0.926965	+	0.375147i	$0.122408\pi$
$108$	−205.410	−0.183015
$109$	309.157	0.271669	0.135834	−	0.990732i	$-0.456628\pi$
$109$	309.157	0.271669	0.135834	+	0.990732i	$0.456628\pi$
$110$	33.4052	0.0289551
$111$	771.656	0.659841
$112$	0	0
$113$	−1224.30	−1.01923	−0.509613	−	0.860404i	$-0.670211\pi$
$113$	−1224.30	−1.01923	−0.509613	+	0.860404i	$0.670211\pi$
$114$	73.1465	0.0600947
$115$	−608.060	−0.493060
$116$	−827.878	−0.662643
$117$	−252.166	−0.199254
$118$	−230.389	−0.179737
$119$	0	0
$120$	142.195	0.108171
$121$	121.000	0.0909091
$122$	−193.667	−0.143720
$123$	534.852	0.392081
$124$	2085.80	1.51057
$125$	−1098.24	−0.785838
$126$	0	0
$127$	−2052.59	−1.43415	−0.717077	−	0.696994i	$-0.754520\pi$
$127$	−2052.59	−1.43415	−0.717077	+	0.696994i	$0.754520\pi$
$128$	1129.99	0.780297
$129$	−508.655	−0.347167
$130$	85.0873	0.0574050
$131$	−1783.82	−1.18972	−0.594860	−	0.803830i	$-0.702792\pi$
$131$	−1783.82	−1.18972	−0.594860	+	0.803830i	$0.702792\pi$
$132$	251.057	0.165543
$133$	0	0
$134$	458.969	0.295887
$135$	130.924	0.0834677
$136$	1145.89	0.722495
$137$	1514.84	0.944685	0.472343	−	0.881415i	$-0.343409\pi$
$137$	1514.84	0.944685	0.472343	+	0.881415i	$0.343409\pi$
$138$	235.602	0.145331
$139$	−1493.97	−0.911633	−0.455816	−	0.890074i	$-0.650653\pi$
$139$	−1493.97	−0.911633	−0.455816	+	0.890074i	$0.650653\pi$
$140$	0	0
$141$	1028.49	0.614285
$142$	427.835	0.252839
$143$	308.203	0.180232
$144$	492.665	0.285107
$145$	527.672	0.302212
$146$	−368.968	−0.209151
$147$	0	0
$148$	−1956.86	−1.08685
$149$	136.181	0.0748750	0.0374375	−	0.999299i	$-0.488080\pi$
$149$	136.181	0.0748750	0.0374375	+	0.999299i	$0.488080\pi$
$150$	190.676	0.103791
$151$	−697.821	−0.376079	−0.188039	−	0.982161i	$-0.560213\pi$
$151$	−697.821	−0.376079	−0.188039	+	0.982161i	$0.560213\pi$
$152$	−380.551	−0.203071
$153$	1055.06	0.557496
$154$	0	0
$155$	−1329.44	−0.688926
$156$	639.474	0.328198
$157$	−63.1395	−0.0320961	−0.0160480	−	0.999871i	$-0.505108\pi$
$157$	−63.1395	−0.0320961	−0.0160480	+	0.999871i	$0.505108\pi$
$158$	581.882	0.292988
$159$	−749.350	−0.373757
$160$	−545.423	−0.269497
$161$	0	0
$162$	−50.7284	−0.0246024
$163$	801.913	0.385341	0.192671	−	0.981263i	$-0.438285\pi$
$163$	801.913	0.385341	0.192671	+	0.981263i	$0.438285\pi$
$164$	−1356.34	−0.645809
$165$	−160.018	−0.0754993
$166$	351.468	0.164332
$167$	−251.070	−0.116337	−0.0581687	−	0.998307i	$-0.518526\pi$
$167$	−251.070	−0.116337	−0.0581687	+	0.998307i	$0.518526\pi$
$168$	0	0
$169$	−1411.97	−0.642680
$170$	−356.006	−0.160614
$171$	−350.388	−0.156695
$172$	1289.91	0.571830
$173$	−3834.70	−1.68524	−0.842621	−	0.538507i	$-0.818988\pi$
$173$	−3834.70	−1.68524	−0.842621	+	0.538507i	$0.818988\pi$
$174$	−204.454	−0.0890783
$175$	0	0
$176$	−602.146	−0.257889
$177$	1103.61	0.468659
$178$	−734.463	−0.309271
$179$	−2420.32	−1.01063	−0.505317	−	0.862934i	$-0.668625\pi$
$179$	−2420.32	−1.01063	−0.505317	+	0.862934i	$0.668625\pi$
$180$	−332.013	−0.137482
$181$	−4554.98	−1.87055	−0.935274	−	0.353925i	$-0.884847\pi$
$181$	−4554.98	−1.87055	−0.935274	+	0.353925i	$0.884847\pi$
$182$	0	0
$183$	927.708	0.374744
$184$	−1225.74	−0.491101
$185$	1247.26	0.495679
$186$	515.112	0.203064
$187$	−1289.52	−0.504274
$188$	−2608.16	−1.01181
$189$	0	0
$190$	118.230	0.0451437
$191$	2272.43	0.860874	0.430437	−	0.902621i	$-0.358359\pi$
$191$	2272.43	0.860874	0.430437	+	0.902621i	$0.358359\pi$
$192$	−1102.44	−0.414384
$193$	3317.36	1.23725	0.618624	−	0.785687i	$-0.287690\pi$
$193$	3317.36	1.23725	0.618624	+	0.785687i	$0.287690\pi$
$194$	682.421	0.252552
$195$	−407.587	−0.149682
$196$	0	0
$197$	3804.76	1.37603	0.688014	−	0.725697i	$-0.258483\pi$
$197$	3804.76	1.37603	0.688014	+	0.725697i	$0.258483\pi$
$198$	62.0013	0.0222537
$199$	−4411.32	−1.57141	−0.785704	−	0.618603i	$-0.787699\pi$
$199$	−4411.32	−1.57141	−0.785704	+	0.618603i	$0.787699\pi$
$200$	−992.012	−0.350729
$201$	−2198.56	−0.771515
$202$	−337.309	−0.117490
$203$	0	0
$204$	−2675.56	−0.918269
$205$	864.505	0.294535
$206$	903.231	0.305491
$207$	−1128.58	−0.378947
$208$	−1533.74	−0.511279
$209$	428.252	0.141736
$210$	0	0
$211$	−4881.08	−1.59255	−0.796274	−	0.604936i	$-0.793199\pi$
$211$	−4881.08	−1.59255	−0.796274	+	0.604936i	$0.793199\pi$
$212$	1900.30	0.615627
$213$	−2049.42	−0.659268
$214$	−1285.09	−0.410501
$215$	−822.161	−0.260795
$216$	263.919	0.0831362
$217$	0	0
$218$	−193.618	−0.0601535
$219$	1767.44	0.545353
$220$	405.794	0.124357
$221$	−3284.58	−0.999750
$222$	−483.270	−0.146103
$223$	−362.206	−0.108767	−0.0543837	−	0.998520i	$-0.517319\pi$
$223$	−362.206	−0.108767	−0.0543837	+	0.998520i	$0.517319\pi$
$224$	0	0
$225$	−913.382	−0.270632
$226$	766.750	0.225679
$227$	−3154.96	−0.922477	−0.461238	−	0.887276i	$-0.652595\pi$
$227$	−3154.96	−0.922477	−0.461238	+	0.887276i	$0.652595\pi$
$228$	888.558	0.258097
$229$	1094.43	0.315817	0.157909	−	0.987454i	$-0.449525\pi$
$229$	1094.43	0.315817	0.157909	+	0.987454i	$0.449525\pi$
$230$	380.813	0.109174
$231$	0	0
$232$	1063.69	0.301012
$233$	−1474.49	−0.414579	−0.207290	−	0.978280i	$-0.566464\pi$
$233$	−1474.49	−0.414579	−0.207290	+	0.978280i	$0.566464\pi$
$234$	157.925	0.0441193
$235$	1662.39	0.461456
$236$	−2798.68	−0.771943
$237$	−2787.34	−0.763955
$238$	0	0
$239$	−5476.68	−1.48225	−0.741123	−	0.671370i	$-0.765706\pi$
$239$	−5476.68	−1.48225	−0.741123	+	0.671370i	$0.765706\pi$
$240$	796.316	0.214175
$241$	1402.57	0.374886	0.187443	−	0.982276i	$-0.439980\pi$
$241$	1402.57	0.374886	0.187443	+	0.982276i	$0.439980\pi$
$242$	−75.7794	−0.0201293
$243$	243.000	0.0641500
$244$	−2352.60	−0.617253
$245$	0	0
$246$	−334.965	−0.0868154
$247$	1090.81	0.280999
$248$	−2679.92	−0.686190
$249$	−1683.61	−0.428491
$250$	687.803	0.174002
$251$	2111.96	0.531100	0.265550	−	0.964097i	$-0.414447\pi$
$251$	2111.96	0.531100	0.265550	+	0.964097i	$0.414447\pi$
$252$	0	0
$253$	1379.38	0.342770
$254$	1285.49	0.317553
$255$	1705.35	0.418796
$256$	2232.15	0.544960
$257$	−3608.25	−0.875783	−0.437892	−	0.899028i	$-0.644275\pi$
$257$	−3608.25	−0.875783	−0.437892	+	0.899028i	$0.644275\pi$
$258$	318.558	0.0768704
$259$	0	0
$260$	1033.61	0.246545
$261$	979.380	0.232269
$262$	1117.16	0.263430
$263$	−2928.22	−0.686547	−0.343273	−	0.939236i	$-0.611536\pi$
$263$	−2928.22	−0.686547	−0.343273	+	0.939236i	$0.611536\pi$
$264$	−322.568	−0.0751995
$265$	−1211.21	−0.280769
$266$	0	0
$267$	3518.24	0.806414
$268$	5575.39	1.27079
$269$	3413.73	0.773751	0.386876	−	0.922132i	$-0.373554\pi$
$269$	3413.73	0.773751	0.386876	+	0.922132i	$0.373554\pi$
$270$	−81.9945	−0.0184816
$271$	5706.36	1.27910	0.639552	−	0.768748i	$-0.279120\pi$
$271$	5706.36	1.27910	0.639552	+	0.768748i	$0.279120\pi$
$272$	6417.19	1.43051
$273$	0	0
$274$	−948.711	−0.209174
$275$	1116.36	0.244796
$276$	2862.00	0.624175
$277$	−1091.85	−0.236833	−0.118416	−	0.992964i	$-0.537782\pi$
$277$	−1091.85	−0.236833	−0.118416	+	0.992964i	$0.537782\pi$
$278$	935.638	0.201856
$279$	−2467.50	−0.529482
$280$	0	0
$281$	−580.580	−0.123254	−0.0616272	−	0.998099i	$-0.519629\pi$
$281$	−580.580	−0.123254	−0.0616272	+	0.998099i	$0.519629\pi$
$282$	−644.116	−0.136016
$283$	−7585.39	−1.59330	−0.796651	−	0.604439i	$-0.793397\pi$
$283$	−7585.39	−1.59330	−0.796651	+	0.604439i	$0.793397\pi$
$284$	5197.19	1.08590
$285$	−566.347	−0.117711
$286$	−193.020	−0.0399074
$287$	0	0
$288$	−1012.33	−0.207125
$289$	8829.71	1.79721
$290$	−330.468	−0.0669164
$291$	−3268.95	−0.658520
$292$	−4482.09	−0.898268
$293$	964.871	0.192383	0.0961917	−	0.995363i	$-0.469334\pi$
$293$	964.871	0.192383	0.0961917	+	0.995363i	$0.469334\pi$
$294$	0	0
$295$	1783.82	0.352061
$296$	2514.26	0.493710
$297$	−297.000	−0.0580259
$298$	−85.2868	−0.0165790
$299$	3513.46	0.679561
$300$	2316.27	0.445766
$301$	0	0
$302$	437.029	0.0832721
$303$	1615.79	0.306351
$304$	−2131.16	−0.402073
$305$	1499.49	0.281511
$306$	−660.761	−0.123442
$307$	−6866.63	−1.27654	−0.638272	−	0.769811i	$-0.720351\pi$
$307$	−6866.63	−1.27654	−0.638272	+	0.769811i	$0.720351\pi$
$308$	0	0
$309$	−4326.67	−0.796556
$310$	832.599	0.152543
$311$	−2268.64	−0.413642	−0.206821	−	0.978379i	$-0.566312\pi$
$311$	−2268.64	−0.413642	−0.206821	+	0.978379i	$0.566312\pi$
$312$	−821.622	−0.149087
$313$	4077.40	0.736321	0.368161	−	0.929762i	$-0.379988\pi$
$313$	4077.40	0.736321	0.368161	+	0.929762i	$0.379988\pi$
$314$	39.5428	0.00710678
$315$	0	0
$316$	7068.49	1.25833
$317$	−1037.38	−0.183802	−0.0919011	−	0.995768i	$-0.529294\pi$
$317$	−1037.38	−0.183802	−0.0919011	+	0.995768i	$0.529294\pi$
$318$	469.300	0.0827579
$319$	−1197.02	−0.210095
$320$	−1781.92	−0.311289
$321$	6155.88	1.07037
$322$	0	0
$323$	−4563.97	−0.786210
$324$	−616.230	−0.105664
$325$	2843.50	0.485321
$326$	−502.219	−0.0853231
$327$	927.472	0.156848
$328$	1742.69	0.293365
$329$	0	0
$330$	100.215	0.0167172
$331$	3362.37	0.558347	0.279173	−	0.960241i	$-0.409940\pi$
$331$	3362.37	0.558347	0.279173	+	0.960241i	$0.409940\pi$
$332$	4269.51	0.705782
$333$	2314.97	0.380960
$334$	157.239	0.0257597
$335$	−3553.63	−0.579569
$336$	0	0
$337$	−3818.71	−0.617266	−0.308633	−	0.951181i	$-0.599871\pi$
$337$	−3818.71	−0.617266	−0.308633	+	0.951181i	$0.599871\pi$
$338$	884.281	0.142303
$339$	−3672.90	−0.588450
$340$	−4324.63	−0.689812
$341$	3015.83	0.478934
$342$	219.439	0.0346957
$343$	0	0
$344$	−1657.33	−0.259759
$345$	−1824.18	−0.284668
$346$	2401.58	0.373150
$347$	−8848.14	−1.36886	−0.684428	−	0.729080i	$-0.739948\pi$
$347$	−8848.14	−1.36886	−0.684428	+	0.729080i	$0.739948\pi$
$348$	−2483.64	−0.382577
$349$	−9595.49	−1.47173	−0.735866	−	0.677127i	$-0.763225\pi$
$349$	−9595.49	−1.47173	−0.735866	+	0.677127i	$0.763225\pi$
$350$	0	0
$351$	−756.498	−0.115039
$352$	1237.29	0.187352
$353$	−7728.29	−1.16526	−0.582628	−	0.812739i	$-0.697975\pi$
$353$	−7728.29	−1.16526	−0.582628	+	0.812739i	$0.697975\pi$
$354$	−691.166	−0.103771
$355$	−3312.57	−0.495248
$356$	−8921.99	−1.32827
$357$	0	0
$358$	1515.79	0.223777
$359$	−3081.42	−0.453012	−0.226506	−	0.974010i	$-0.572730\pi$
$359$	−3081.42	−0.453012	−0.226506	+	0.974010i	$0.572730\pi$
$360$	426.584	0.0624526
$361$	−5343.30	−0.779020
$362$	2852.68	0.414180
$363$	363.000	0.0524864
$364$	0	0
$365$	2856.78	0.409674
$366$	−581.001	−0.0829765
$367$	8280.38	1.17774	0.588872	−	0.808226i	$-0.299572\pi$
$367$	8280.38	1.17774	0.588872	+	0.808226i	$0.299572\pi$
$368$	−6864.36	−0.972363
$369$	1604.56	0.226368
$370$	−781.130	−0.109754
$371$	0	0
$372$	6257.40	0.872127
$373$	−10112.0	−1.40369	−0.701847	−	0.712327i	$-0.747641\pi$
$373$	−10112.0	−1.40369	−0.701847	+	0.712327i	$0.747641\pi$
$374$	807.597	0.111657
$375$	−3294.73	−0.453704
$376$	3351.07	0.459623
$377$	−3048.97	−0.416524
$378$	0	0
$379$	12259.2	1.66151	0.830754	−	0.556639i	$-0.187909\pi$
$379$	12259.2	1.66151	0.830754	+	0.556639i	$0.187909\pi$
$380$	1436.21	0.193885
$381$	−6157.76	−0.828009
$382$	−1423.17	−0.190617
$383$	−3317.39	−0.442587	−0.221293	−	0.975207i	$-0.571028\pi$
$383$	−3317.39	−0.442587	−0.221293	+	0.975207i	$0.571028\pi$
$384$	3389.97	0.450505
$385$	0	0
$386$	−2077.58	−0.273954
$387$	−1525.96	−0.200437
$388$	8289.81	1.08467
$389$	−14101.2	−1.83794	−0.918972	−	0.394323i	$-0.870979\pi$
$389$	−14101.2	−1.83794	−0.918972	+	0.394323i	$0.870979\pi$
$390$	255.262	0.0331428
$391$	−14700.3	−1.90135
$392$	0	0
$393$	−5351.46	−0.686885
$394$	−2382.83	−0.304683
$395$	−4505.30	−0.573890
$396$	753.170	0.0955763
$397$	−5175.17	−0.654243	−0.327122	−	0.944982i	$-0.606079\pi$
$397$	−5175.17	−0.654243	−0.327122	+	0.944982i	$0.606079\pi$
$398$	2762.70	0.347944
$399$	0	0
$400$	−5555.44	−0.694431
$401$	5098.23	0.634896	0.317448	−	0.948276i	$-0.397174\pi$
$401$	5098.23	0.634896	0.317448	+	0.948276i	$0.397174\pi$
$402$	1376.91	0.170830
$403$	7681.73	0.949514
$404$	−4097.51	−0.504601
$405$	392.772	0.0481901
$406$	0	0
$407$	−2829.41	−0.344591
$408$	3437.67	0.417132
$409$	−3268.16	−0.395110	−0.197555	−	0.980292i	$-0.563300\pi$
$409$	−3268.16	−0.395110	−0.197555	+	0.980292i	$0.563300\pi$
$410$	−541.419	−0.0652165
$411$	4544.53	0.545414
$412$	10972.1	1.31203
$413$	0	0
$414$	706.805	0.0839071
$415$	−2721.29	−0.321886
$416$	3151.54	0.371435
$417$	−4481.91	−0.526331
$418$	−268.204	−0.0313834
$419$	−874.425	−0.101953	−0.0509767	−	0.998700i	$-0.516233\pi$
$419$	−874.425	−0.101953	−0.0509767	+	0.998700i	$0.516233\pi$
$420$	0	0
$421$	860.976	0.0996708	0.0498354	−	0.998757i	$-0.484130\pi$
$421$	860.976	0.0996708	0.0498354	+	0.998757i	$0.484130\pi$
$422$	3056.91	0.352625
$423$	3085.46	0.354657
$424$	−2441.58	−0.279654
$425$	−11897.2	−1.35788
$426$	1283.50	0.145977
$427$	0	0
$428$	−15610.9	−1.76304
$429$	924.608	0.104057
$430$	514.900	0.0577458
$431$	7387.28	0.825598	0.412799	−	0.910822i	$-0.364551\pi$
$431$	7387.28	0.825598	0.412799	+	0.910822i	$0.364551\pi$
$432$	1477.99	0.164607
$433$	1522.04	0.168925	0.0844625	−	0.996427i	$-0.473083\pi$
$433$	1522.04	0.168925	0.0844625	+	0.996427i	$0.473083\pi$
$434$	0	0
$435$	1583.01	0.174482
$436$	−2352.00	−0.258350
$437$	4882.00	0.534411
$438$	−1106.90	−0.120753
$439$	14551.7	1.58204	0.791018	−	0.611792i	$-0.209551\pi$
$439$	14551.7	1.58204	0.791018	+	0.611792i	$0.209551\pi$
$440$	−521.380	−0.0564905
$441$	0	0
$442$	2057.05	0.221367
$443$	−5998.77	−0.643364	−0.321682	−	0.946848i	$-0.604248\pi$
$443$	−5998.77	−0.643364	−0.321682	+	0.946848i	$0.604248\pi$
$444$	−5870.59	−0.627491
$445$	5686.68	0.605786
$446$	226.841	0.0240835
$447$	408.543	0.0432291
$448$	0	0
$449$	5163.35	0.542702	0.271351	−	0.962480i	$-0.412530\pi$
$449$	5163.35	0.542702	0.271351	+	0.962480i	$0.412530\pi$
$450$	572.029	0.0599238
$451$	−1961.12	−0.204758
$452$	9314.20	0.969255
$453$	−2093.46	−0.217129
$454$	1975.88	0.204257
$455$	0	0
$456$	−1141.65	−0.117243
$457$	13208.0	1.35195	0.675977	−	0.736923i	$-0.263722\pi$
$457$	13208.0	1.35195	0.675977	+	0.736923i	$0.263722\pi$
$458$	−685.417	−0.0699289
$459$	3165.19	0.321870
$460$	4625.98	0.468886
$461$	−6649.36	−0.671782	−0.335891	−	0.941901i	$-0.609037\pi$
$461$	−6649.36	−0.671782	−0.335891	+	0.941901i	$0.609037\pi$
$462$	0	0
$463$	12514.9	1.25619	0.628094	−	0.778138i	$-0.283835\pi$
$463$	12514.9	1.25619	0.628094	+	0.778138i	$0.283835\pi$
$464$	5956.86	0.595992
$465$	−3988.33	−0.397751
$466$	923.437	0.0917970
$467$	−9962.34	−0.987157	−0.493578	−	0.869701i	$-0.664311\pi$
$467$	−9962.34	−0.987157	−0.493578	+	0.869701i	$0.664311\pi$
$468$	1918.42	0.189485
$469$	0	0
$470$	−1041.11	−0.102177
$471$	−189.419	−0.0185307
$472$	3595.86	0.350663
$473$	1865.07	0.181302
$474$	1745.65	0.169156
$475$	3951.09	0.381659
$476$	0	0
$477$	−2248.05	−0.215788
$478$	3429.91	0.328202
$479$	1649.36	0.157331	0.0786653	−	0.996901i	$-0.474934\pi$
$479$	1649.36	0.157331	0.0786653	+	0.996901i	$0.474934\pi$
$480$	−1636.27	−0.155594
$481$	−7206.87	−0.683170
$482$	−878.396	−0.0830079
$483$	0	0
$484$	−920.541	−0.0864520
$485$	−5283.75	−0.494686
$486$	−152.185	−0.0142042
$487$	14291.4	1.32979	0.664894	−	0.746938i	$-0.268477\pi$
$487$	14291.4	1.32979	0.664894	+	0.746938i	$0.268477\pi$
$488$	3022.71	0.280393
$489$	2405.74	0.222477
$490$	0	0
$491$	13384.0	1.23017	0.615084	−	0.788462i	$-0.289122\pi$
$491$	13384.0	1.23017	0.615084	+	0.788462i	$0.289122\pi$
$492$	−4069.03	−0.372858
$493$	12756.9	1.16540
$494$	−683.150	−0.0622194
$495$	−480.054	−0.0435896
$496$	−15008.0	−1.35863
$497$	0	0
$498$	1054.40	0.0948774
$499$	10153.2	0.910865	0.455433	−	0.890270i	$-0.349485\pi$
$499$	10153.2	0.910865	0.455433	+	0.890270i	$0.349485\pi$
$500$	8355.18	0.747310
$501$	−753.209	−0.0671674
$502$	−1322.67	−0.117597
$503$	−566.682	−0.0502328	−0.0251164	−	0.999685i	$-0.507996\pi$
$503$	−566.682	−0.0502328	−0.0251164	+	0.999685i	$0.507996\pi$
$504$	0	0
$505$	2611.67	0.230134
$506$	−863.872	−0.0758969
$507$	−4235.90	−0.371051
$508$	15615.6	1.36384
$509$	10536.0	0.917488	0.458744	−	0.888569i	$-0.348300\pi$
$509$	10536.0	0.917488	0.458744	+	0.888569i	$0.348300\pi$
$510$	−1068.02	−0.0927306
$511$	0	0
$512$	−10437.9	−0.900963
$513$	−1051.16	−0.0904678
$514$	2259.76	0.193918
$515$	−6993.39	−0.598380
$516$	3869.73	0.330146
$517$	−3771.12	−0.320800
$518$	0	0
$519$	−11504.1	−0.972975
$520$	−1328.02	−0.111996
$521$	−18566.0	−1.56121	−0.780605	−	0.625025i	$-0.785089\pi$
$521$	−18566.0	−1.56121	−0.780605	+	0.625025i	$0.785089\pi$
$522$	−613.362	−0.0514294
$523$	−5435.12	−0.454419	−0.227210	−	0.973846i	$-0.572960\pi$
$523$	−5435.12	−0.454419	−0.227210	+	0.973846i	$0.572960\pi$
$524$	13570.9	1.13139
$525$	0	0
$526$	1833.87	0.152017
$527$	−32140.4	−2.65665
$528$	−1806.44	−0.148892
$529$	3557.69	0.292405
$530$	758.550	0.0621685
$531$	3310.84	0.270580
$532$	0	0
$533$	−4995.24	−0.405943
$534$	−2203.39	−0.178558
$535$	9950.03	0.804069
$536$	−7163.48	−0.577267
$537$	−7260.97	−0.583490
$538$	−2137.94	−0.171326
$539$	0	0
$540$	−996.040	−0.0793754
$541$	−23130.2	−1.83816	−0.919082	−	0.394067i	$-0.871068\pi$
$541$	−23130.2	−1.83816	−0.919082	+	0.394067i	$0.871068\pi$
$542$	−3573.76	−0.283222
$543$	−13664.9	−1.07996
$544$	−13186.1	−1.03924
$545$	1499.11	0.117826
$546$	0	0
$547$	21414.3	1.67387	0.836937	−	0.547299i	$-0.184344\pi$
$547$	21414.3	1.67387	0.836937	+	0.547299i	$0.184344\pi$
$548$	−11524.6	−0.898370
$549$	2783.12	0.216358
$550$	−699.147	−0.0542031
$551$	−4236.58	−0.327558
$552$	−3677.22	−0.283538
$553$	0	0
$554$	683.797	0.0524399
$555$	3741.79	0.286180
$556$	11365.8	0.866937
$557$	14779.4	1.12428	0.562141	−	0.827042i	$-0.309978\pi$
$557$	14779.4	1.12428	0.562141	+	0.827042i	$0.309978\pi$
$558$	1545.34	0.117239
$559$	4750.57	0.359441
$560$	0	0
$561$	−3868.57	−0.291143
$562$	363.603	0.0272912
$563$	6220.76	0.465673	0.232837	−	0.972516i	$-0.425199\pi$
$563$	6220.76	0.465673	0.232837	+	0.972516i	$0.425199\pi$
$564$	−7824.49	−0.584168
$565$	−5936.67	−0.442049
$566$	4750.55	0.352792
$567$	0	0
$568$	−6677.55	−0.493281
$569$	−7479.44	−0.551062	−0.275531	−	0.961292i	$-0.588854\pi$
$569$	−7479.44	−0.551062	−0.275531	+	0.961292i	$0.588854\pi$
$570$	354.690	0.0260637
$571$	16296.9	1.19440	0.597200	−	0.802092i	$-0.296280\pi$
$571$	16296.9	1.19440	0.597200	+	0.802092i	$0.296280\pi$
$572$	−2344.74	−0.171396
$573$	6817.28	0.497026
$574$	0	0
$575$	12726.3	0.922995
$576$	−3307.32	−0.239245
$577$	10963.1	0.790985	0.395492	−	0.918469i	$-0.370574\pi$
$577$	10963.1	0.790985	0.395492	+	0.918469i	$0.370574\pi$
$578$	−5529.83	−0.397943
$579$	9952.09	0.714326
$580$	−4014.41	−0.287395
$581$	0	0
$582$	2047.26	0.145811
$583$	2747.62	0.195188
$584$	5758.76	0.408047
$585$	−1222.76	−0.0864187
$586$	−604.275	−0.0425979
$587$	624.141	0.0438859	0.0219430	−	0.999759i	$-0.493015\pi$
$587$	624.141	0.0438859	0.0219430	+	0.999759i	$0.493015\pi$
$588$	0	0
$589$	10673.9	0.746704
$590$	−1117.16	−0.0779540
$591$	11414.3	0.794450
$592$	14080.3	0.977528
$593$	25820.4	1.78806	0.894028	−	0.448011i	$-0.147867\pi$
$593$	25820.4	1.78806	0.894028	+	0.448011i	$0.147867\pi$
$594$	186.004	0.0128482
$595$	0	0
$596$	−1036.03	−0.0712040
$597$	−13234.0	−0.907252
$598$	−2200.40	−0.150470
$599$	11280.7	0.769479	0.384740	−	0.923025i	$-0.374291\pi$
$599$	11280.7	0.769479	0.384740	+	0.923025i	$0.374291\pi$
$600$	−2976.04	−0.202494
$601$	10771.6	0.731087	0.365544	−	0.930794i	$-0.380883\pi$
$601$	10771.6	0.731087	0.365544	+	0.930794i	$0.380883\pi$
$602$	0	0
$603$	−6595.69	−0.445435
$604$	5308.87	0.357641
$605$	586.733	0.0394282
$606$	−1011.93	−0.0678329
$607$	16788.0	1.12258	0.561289	−	0.827620i	$-0.310306\pi$
$607$	16788.0	1.12258	0.561289	+	0.827620i	$0.310306\pi$
$608$	4379.10	0.292099
$609$	0	0
$610$	−939.097	−0.0623327
$611$	−9605.52	−0.636003
$612$	−8026.69	−0.530163
$613$	−3934.86	−0.259262	−0.129631	−	0.991562i	$-0.541379\pi$
$613$	−3934.86	−0.259262	−0.129631	+	0.991562i	$0.541379\pi$
$614$	4300.40	0.282655
$615$	2593.51	0.170050
$616$	0	0
$617$	−6018.59	−0.392706	−0.196353	−	0.980533i	$-0.562910\pi$
$617$	−6018.59	−0.392706	−0.196353	+	0.980533i	$0.562910\pi$
$618$	2709.69	0.176375
$619$	−10587.5	−0.687473	−0.343737	−	0.939066i	$-0.611693\pi$
$619$	−10587.5	−0.687473	−0.343737	+	0.939066i	$0.611693\pi$
$620$	10114.1	0.655149
$621$	−3385.75	−0.218785
$622$	1420.79	0.0915894
$623$	0	0
$624$	−4601.23	−0.295187
$625$	7360.45	0.471069
$626$	−2553.58	−0.163038
$627$	1284.76	0.0818312
$628$	480.352	0.0305225
$629$	30153.6	1.91145
$630$	0	0
$631$	−13078.4	−0.825108	−0.412554	−	0.910933i	$-0.635363\pi$
$631$	−13078.4	−0.825108	−0.412554	+	0.910933i	$0.635363\pi$
$632$	−9081.88	−0.571611
$633$	−14643.3	−0.919458
$634$	649.689	0.0406978
$635$	−9953.06	−0.622008
$636$	5700.89	0.355432
$637$	0	0
$638$	749.665	0.0465196
$639$	−6148.27	−0.380629
$640$	5479.36	0.338423
$641$	−19163.3	−1.18082	−0.590410	−	0.807104i	$-0.701034\pi$
$641$	−19163.3	−1.18082	−0.590410	+	0.807104i	$0.701034\pi$
$642$	−3855.28	−0.237003
$643$	−9112.25	−0.558868	−0.279434	−	0.960165i	$-0.590147\pi$
$643$	−9112.25	−0.558868	−0.279434	+	0.960165i	$0.590147\pi$
$644$	0	0
$645$	−2466.48	−0.150570
$646$	2858.30	0.174084
$647$	−26821.5	−1.62977	−0.814885	−	0.579622i	$-0.803200\pi$
$647$	−26821.5	−1.62977	−0.814885	+	0.579622i	$0.803200\pi$
$648$	791.757	0.0479987
$649$	−4046.58	−0.244749
$650$	−1780.82	−0.107461
$651$	0	0
$652$	−6100.77	−0.366449
$653$	3246.51	0.194557	0.0972784	−	0.995257i	$-0.468986\pi$
$653$	3246.51	0.194557	0.0972784	+	0.995257i	$0.468986\pi$
$654$	−580.854	−0.0347296
$655$	−8649.81	−0.515994
$656$	9759.36	0.580852
$657$	5302.31	0.314860
$658$	0	0
$659$	−11756.7	−0.694957	−0.347479	−	0.937688i	$-0.612962\pi$
$659$	−11756.7	−0.694957	−0.347479	+	0.937688i	$0.612962\pi$
$660$	1217.38	0.0717978
$661$	−22376.9	−1.31673	−0.658366	−	0.752698i	$-0.728752\pi$
$661$	−22376.9	−1.31673	−0.658366	+	0.752698i	$0.728752\pi$
$662$	−2105.77	−0.123630
$663$	−9853.74	−0.577206
$664$	−5485.63	−0.320608
$665$	0	0
$666$	−1449.81	−0.0843528
$667$	−13645.8	−0.792157
$668$	1910.08	0.110634
$669$	−1086.62	−0.0627969
$670$	2225.55	0.128329
$671$	−3401.59	−0.195704
$672$	0	0
$673$	23234.0	1.33076	0.665381	−	0.746504i	$-0.268269\pi$
$673$	23234.0	1.33076	0.665381	+	0.746504i	$0.268269\pi$
$674$	2391.57	0.136676
$675$	−2740.15	−0.156249
$676$	10741.9	0.611171
$677$	−1002.81	−0.0569293	−0.0284647	−	0.999595i	$-0.509062\pi$
$677$	−1002.81	−0.0569293	−0.0284647	+	0.999595i	$0.509062\pi$
$678$	2300.25	0.130296
$679$	0	0
$680$	5556.46	0.313354
$681$	−9464.89	−0.532592
$682$	−1888.75	−0.106047
$683$	26255.7	1.47093	0.735467	−	0.677561i	$-0.236963\pi$
$683$	26255.7	1.47093	0.735467	+	0.677561i	$0.236963\pi$
$684$	2665.67	0.149012
$685$	7345.53	0.409720
$686$	0	0
$687$	3283.30	0.182337
$688$	−9281.34	−0.514314
$689$	6998.54	0.386971
$690$	1142.44	0.0630318
$691$	−10233.6	−0.563393	−0.281696	−	0.959504i	$-0.590897\pi$
$691$	−10233.6	−0.563393	−0.281696	+	0.959504i	$0.590897\pi$
$692$	29173.5	1.60262
$693$	0	0
$694$	5541.38	0.303095
$695$	−7244.31	−0.395385
$696$	3191.07	0.173789
$697$	20900.1	1.13579
$698$	6009.42	0.325874
$699$	−4423.47	−0.239357
$700$	0	0
$701$	20918.6	1.12708	0.563542	−	0.826087i	$-0.309438\pi$
$701$	20918.6	1.12708	0.563542	+	0.826087i	$0.309438\pi$
$702$	473.776	0.0254723
$703$	−10014.0	−0.537250
$704$	4042.28	0.216405
$705$	4987.16	0.266422
$706$	4840.04	0.258013
$707$	0	0
$708$	−8396.05	−0.445682
$709$	10297.5	0.545458	0.272729	−	0.962091i	$-0.412074\pi$
$709$	10297.5	0.545458	0.272729	+	0.962091i	$0.412074\pi$
$710$	2074.58	0.109659
$711$	−8362.03	−0.441070
$712$	11463.3	0.603380
$713$	34380.0	1.80581
$714$	0	0
$715$	1494.49	0.0781686
$716$	18413.3	0.961085
$717$	−16430.0	−0.855775
$718$	1929.82	0.100307
$719$	−19778.4	−1.02588	−0.512942	−	0.858423i	$-0.671444\pi$
$719$	−19778.4	−1.02588	−0.512942	+	0.858423i	$0.671444\pi$
$720$	2388.95	0.123654
$721$	0	0
$722$	3346.38	0.172492
$723$	4207.71	0.216440
$724$	34653.3	1.77884
$725$	−11043.8	−0.565733
$726$	−227.338	−0.0116216
$727$	−9273.88	−0.473108	−0.236554	−	0.971618i	$-0.576018\pi$
$727$	−9273.88	−0.473108	−0.236554	+	0.971618i	$0.576018\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−1789.14	−0.0907108
$731$	−19876.4	−1.00568
$732$	−7057.79	−0.356371
$733$	28112.8	1.41660	0.708301	−	0.705911i	$-0.249462\pi$
$733$	28112.8	1.41660	0.708301	+	0.705911i	$0.249462\pi$
$734$	−5185.80	−0.260779
$735$	0	0
$736$	14104.9	0.706404
$737$	8061.39	0.402911
$738$	−1004.89	−0.0501229
$739$	23681.4	1.17880	0.589402	−	0.807840i	$-0.299363\pi$
$739$	23681.4	1.17880	0.589402	+	0.807840i	$0.299363\pi$
$740$	−9488.89	−0.471377
$741$	3272.44	0.162235
$742$	0	0
$743$	−4720.06	−0.233058	−0.116529	−	0.993187i	$-0.537177\pi$
$743$	−4720.06	−0.233058	−0.116529	+	0.993187i	$0.537177\pi$
$744$	−8039.76	−0.396172
$745$	660.346	0.0324741
$746$	6332.89	0.310809
$747$	−5050.82	−0.247390
$748$	9810.40	0.479550
$749$	0	0
$750$	2063.41	0.100460
$751$	3319.60	0.161297	0.0806484	−	0.996743i	$-0.474301\pi$
$751$	3319.60	0.161297	0.0806484	+	0.996743i	$0.474301\pi$
$752$	18766.6	0.910037
$753$	6335.89	0.306631
$754$	1909.49	0.0922277
$755$	−3383.76	−0.163109
$756$	0	0
$757$	19026.0	0.913487	0.456744	−	0.889598i	$-0.349016\pi$
$757$	19026.0	0.913487	0.456744	+	0.889598i	$0.349016\pi$
$758$	−7677.63	−0.367895
$759$	4138.14	0.197898
$760$	−1845.31	−0.0880741
$761$	26227.5	1.24934	0.624669	−	0.780890i	$-0.285234\pi$
$761$	26227.5	1.24934	0.624669	+	0.780890i	$0.285234\pi$
$762$	3856.46	0.183339
$763$	0	0
$764$	−17288.1	−0.818668
$765$	5116.04	0.241792
$766$	2077.60	0.0979985
$767$	−10307.2	−0.485229
$768$	6696.46	0.314633
$769$	4812.62	0.225680	0.112840	−	0.993613i	$-0.464005\pi$
$769$	4812.62	0.225680	0.112840	+	0.993613i	$0.464005\pi$
$770$	0	0
$771$	−10824.7	−0.505634
$772$	−25237.8	−1.17659
$773$	9251.58	0.430474	0.215237	−	0.976562i	$-0.430948\pi$
$773$	9251.58	0.430474	0.215237	+	0.976562i	$0.430948\pi$
$774$	955.675	0.0443812
$775$	27824.3	1.28965
$776$	−10651.1	−0.492721
$777$	0	0
$778$	8831.25	0.406961
$779$	−6940.95	−0.319237
$780$	3100.83	0.142343
$781$	7514.55	0.344292
$782$	9206.47	0.421001
$783$	2938.14	0.134100
$784$	0	0
$785$	−306.166	−0.0139204
$786$	3351.49	0.152091
$787$	7698.38	0.348688	0.174344	−	0.984685i	$-0.444219\pi$
$787$	7698.38	0.348688	0.174344	+	0.984685i	$0.444219\pi$
$788$	−28945.7	−1.30856
$789$	−8784.66	−0.396378
$790$	2821.56	0.127072
$791$	0	0
$792$	−967.703	−0.0434164
$793$	−8664.30	−0.387993
$794$	3241.09	0.144864
$795$	−3633.62	−0.162102
$796$	33560.3	1.49436
$797$	22747.5	1.01099	0.505493	−	0.862830i	$-0.331311\pi$
$797$	22747.5	1.01099	0.505493	+	0.862830i	$0.331311\pi$
$798$	0	0
$799$	40189.6	1.77948
$800$	11415.3	0.504491
$801$	10554.7	0.465584
$802$	−3192.90	−0.140580
$803$	−6480.60	−0.284801
$804$	16726.2	0.733690
$805$	0	0
$806$	−4810.88	−0.210243
$807$	10241.2	0.446725
$808$	5264.65	0.229220
$809$	−15275.5	−0.663853	−0.331926	−	0.943305i	$-0.607699\pi$
$809$	−15275.5	−0.663853	−0.331926	+	0.943305i	$0.607699\pi$
$810$	−245.983	−0.0106703
$811$	−8082.83	−0.349971	−0.174986	−	0.984571i	$-0.555988\pi$
$811$	−8082.83	−0.349971	−0.174986	+	0.984571i	$0.555988\pi$
$812$	0	0
$813$	17119.1	0.738491
$814$	1771.99	0.0763000
$815$	3888.50	0.167127
$816$	19251.6	0.825907
$817$	6600.98	0.282667
$818$	2046.77	0.0874860
$819$	0	0
$820$	−6576.96	−0.280094
$821$	−2876.74	−0.122288	−0.0611442	−	0.998129i	$-0.519475\pi$
$821$	−2876.74	−0.122288	−0.0611442	+	0.998129i	$0.519475\pi$
$822$	−2846.13	−0.120767
$823$	15389.9	0.651834	0.325917	−	0.945398i	$-0.394327\pi$
$823$	15389.9	0.651834	0.325917	+	0.945398i	$0.394327\pi$
$824$	−14097.4	−0.596004
$825$	3349.07	0.141333
$826$	0	0
$827$	−23739.0	−0.998169	−0.499084	−	0.866553i	$-0.666330\pi$
$827$	−23739.0	−0.998169	−0.499084	+	0.866553i	$0.666330\pi$
$828$	8586.01	0.360368
$829$	−3090.24	−0.129467	−0.0647337	−	0.997903i	$-0.520620\pi$
$829$	−3090.24	−0.129467	−0.0647337	+	0.997903i	$0.520620\pi$
$830$	1704.28	0.0712727
$831$	−3275.54	−0.136735
$832$	10296.2	0.429035
$833$	0	0
$834$	2806.91	0.116541
$835$	−1217.44	−0.0504568
$836$	−3258.04	−0.134787
$837$	−7402.50	−0.305697
$838$	547.632	0.0225747
$839$	−3466.70	−0.142651	−0.0713253	−	0.997453i	$-0.522723\pi$
$839$	−3466.70	−0.142651	−0.0713253	+	0.997453i	$0.522723\pi$
$840$	0	0
$841$	−12547.2	−0.514462
$842$	−539.208	−0.0220693
$843$	−1741.74	−0.0711610
$844$	37134.2	1.51447
$845$	−6846.68	−0.278737
$846$	−1932.35	−0.0785290
$847$	0	0
$848$	−13673.3	−0.553705
$849$	−22756.2	−0.919894
$850$	7450.95	0.300665
$851$	−32254.8	−1.29927
$852$	15591.6	0.626946
$853$	−40500.2	−1.62568	−0.812838	−	0.582490i	$-0.802079\pi$
$853$	−40500.2	−1.62568	−0.812838	+	0.582490i	$0.802079\pi$
$854$	0	0
$855$	−1699.04	−0.0679602
$856$	20057.5	0.800876
$857$	25580.8	1.01963	0.509814	−	0.860284i	$-0.329714\pi$
$857$	25580.8	1.01963	0.509814	+	0.860284i	$0.329714\pi$
$858$	−579.060	−0.0230405
$859$	41957.8	1.66657	0.833283	−	0.552846i	$-0.186458\pi$
$859$	41957.8	1.66657	0.833283	+	0.552846i	$0.186458\pi$
$860$	6254.82	0.248009
$861$	0	0
$862$	−4626.47	−0.182805
$863$	11126.2	0.438863	0.219432	−	0.975628i	$-0.429580\pi$
$863$	11126.2	0.438863	0.219432	+	0.975628i	$0.429580\pi$
$864$	−3036.98	−0.119584
$865$	−18594.6	−0.730907
$866$	−953.216	−0.0374037
$867$	26489.1	1.03762
$868$	0	0
$869$	10220.3	0.398962
$870$	−991.404	−0.0386342
$871$	20533.4	0.798793
$872$	3021.95	0.117358
$873$	−9806.85	−0.380196
$874$	−3057.48	−0.118330
$875$	0	0
$876$	−13446.3	−0.518615
$877$	−23041.5	−0.887179	−0.443589	−	0.896230i	$-0.646295\pi$
$877$	−23041.5	−0.887179	−0.443589	+	0.896230i	$0.646295\pi$
$878$	−9113.37	−0.350298
$879$	2894.61	0.111073
$880$	−2919.82	−0.111849
$881$	−6875.19	−0.262918	−0.131459	−	0.991322i	$-0.541966\pi$
$881$	−6875.19	−0.262918	−0.131459	+	0.991322i	$0.541966\pi$
$882$	0	0
$883$	38869.1	1.48137	0.740684	−	0.671854i	$-0.234502\pi$
$883$	38869.1	1.48137	0.740684	+	0.671854i	$0.234502\pi$
$884$	24988.4	0.950735
$885$	5351.46	0.203262
$886$	3756.89	0.142455
$887$	28577.0	1.08176	0.540881	−	0.841099i	$-0.318091\pi$
$887$	28577.0	1.08176	0.540881	+	0.841099i	$0.318091\pi$
$888$	7542.77	0.285044
$889$	0	0
$890$	−3561.43	−0.134134
$891$	−891.000	−0.0335013
$892$	2755.58	0.103435
$893$	−13347.0	−0.500157
$894$	−255.860	−0.00957187
$895$	−11736.2	−0.438323
$896$	0	0
$897$	10540.4	0.392344
$898$	−3233.68	−0.120166
$899$	−29834.8	−1.10684
$900$	6948.81	0.257363
$901$	−29281.9	−1.08271
$902$	1228.20	0.0453379
$903$	0	0
$904$	−11967.3	−0.440293
$905$	−22087.3	−0.811276
$906$	1311.09	0.0480772
$907$	25317.3	0.926842	0.463421	−	0.886138i	$-0.346622\pi$
$907$	25317.3	0.926842	0.463421	+	0.886138i	$0.346622\pi$
$908$	24002.3	0.877250
$909$	4847.36	0.176872
$910$	0	0
$911$	39660.8	1.44240	0.721198	−	0.692729i	$-0.243592\pi$
$911$	39660.8	1.44240	0.721198	+	0.692729i	$0.243592\pi$
$912$	−6393.47	−0.232137
$913$	6173.23	0.223772
$914$	−8271.84	−0.299352
$915$	4498.48	0.162530
$916$	−8326.20	−0.300333
$917$	0	0
$918$	−1982.28	−0.0712692
$919$	−42697.0	−1.53258	−0.766291	−	0.642494i	$-0.777900\pi$
$919$	−42697.0	−1.53258	−0.766291	+	0.642494i	$0.777900\pi$
$920$	−5943.65	−0.212996
$921$	−20599.9	−0.737013
$922$	4164.34	0.148747
$923$	19140.5	0.682577
$924$	0	0
$925$	−26104.3	−0.927898
$926$	−7837.75	−0.278147
$927$	−12980.0	−0.459892
$928$	−12240.2	−0.432978
$929$	−11991.9	−0.423509	−0.211755	−	0.977323i	$-0.567918\pi$
$929$	−11991.9	−0.423509	−0.211755	+	0.977323i	$0.567918\pi$
$930$	2497.80	0.0880709
$931$	0	0
$932$	11217.6	0.394253
$933$	−6805.91	−0.238816
$934$	6239.17	0.218578
$935$	−6252.94	−0.218709
$936$	−2464.87	−0.0860755
$937$	−23223.4	−0.809686	−0.404843	−	0.914386i	$-0.632674\pi$
$937$	−23223.4	−0.809686	−0.404843	+	0.914386i	$0.632674\pi$
$938$	0	0
$939$	12232.2	0.425115
$940$	−12647.1	−0.438832
$941$	−46308.9	−1.60428	−0.802140	−	0.597136i	$-0.796305\pi$
$941$	−46308.9	−1.60428	−0.802140	+	0.597136i	$0.796305\pi$
$942$	118.628	0.00410310
$943$	−22356.5	−0.772033
$944$	20137.5	0.694299
$945$	0	0
$946$	−1168.05	−0.0401443
$947$	−4598.73	−0.157802	−0.0789011	−	0.996882i	$-0.525141\pi$
$947$	−4598.73	−0.157802	−0.0789011	+	0.996882i	$0.525141\pi$
$948$	21205.5	0.726500
$949$	−16506.9	−0.564634
$950$	−2474.47	−0.0845078
$951$	−3112.15	−0.106118
$952$	0	0
$953$	45607.9	1.55025	0.775124	−	0.631810i	$-0.217688\pi$
$953$	45607.9	1.55025	0.775124	+	0.631810i	$0.217688\pi$
$954$	1407.90	0.0477803
$955$	11019.1	0.373370
$956$	41665.3	1.40957
$957$	−3591.06	−0.121298
$958$	−1032.96	−0.0348364
$959$	0	0
$960$	−5345.77	−0.179723
$961$	45376.4	1.52316
$962$	4513.49	0.151269
$963$	18467.6	0.617977
$964$	−10670.4	−0.356506
$965$	16086.0	0.536608
$966$	0	0
$967$	−5076.95	−0.168835	−0.0844176	−	0.996430i	$-0.526903\pi$
$967$	−5076.95	−0.168835	−0.0844176	+	0.996430i	$0.526903\pi$
$968$	1182.75	0.0392717
$969$	−13691.9	−0.453919
$970$	3309.08	0.109534
$971$	39616.4	1.30932	0.654660	−	0.755923i	$-0.272812\pi$
$971$	39616.4	1.30932	0.654660	+	0.755923i	$0.272812\pi$
$972$	−1848.69	−0.0610049
$973$	0	0
$974$	−8950.38	−0.294444
$975$	8530.51	0.280200
$976$	16927.7	0.555167
$977$	−4297.81	−0.140736	−0.0703680	−	0.997521i	$-0.522417\pi$
$977$	−4297.81	−0.140736	−0.0703680	+	0.997521i	$0.522417\pi$
$978$	−1506.66	−0.0492613
$979$	−12900.2	−0.421136
$980$	0	0
$981$	2782.42	0.0905563
$982$	−8382.09	−0.272386
$983$	45085.3	1.46287	0.731433	−	0.681914i	$-0.238852\pi$
$983$	45085.3	1.46287	0.731433	+	0.681914i	$0.238852\pi$
$984$	5228.06	0.169374
$985$	18449.4	0.596798
$986$	−7989.33	−0.258045
$987$	0	0
$988$	−8298.66	−0.267222
$989$	21261.5	0.683594
$990$	300.646	0.00965169
$991$	−19332.2	−0.619685	−0.309843	−	0.950788i	$-0.600276\pi$
$991$	−19332.2	−0.619685	−0.309843	+	0.950788i	$0.600276\pi$
$992$	30838.5	0.987020
$993$	10087.1	0.322362
$994$	0	0
$995$	−21390.6	−0.681536
$996$	12808.5	0.407483
$997$	−27910.6	−0.886597	−0.443299	−	0.896374i	$-0.646192\pi$
$997$	−27910.6	−0.886597	−0.443299	+	0.896374i	$0.646192\pi$
$998$	−6358.73	−0.201686
$999$	6944.91	0.219947

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.4.a.bd.1.8	yes	16
7.6	odd	2		1617.4.a.bc.1.8	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1617.4.a.bc.1.8	✓	16	7.6	odd	2
1617.4.a.bd.1.8	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)

\(f(q)\)	\(=\)	\(q-0.626276 q^{2} +3.00000 q^{3} -7.60778 q^{4} +4.84903 q^{5} -1.87883 q^{6} +9.77478 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-0.626276 q^{2} +3.00000 q^{3} -7.60778 q^{4} +4.84903 q^{5} -1.87883 q^{6} +9.77478 q^{8} +9.00000 q^{9} -3.03683 q^{10} -11.0000 q^{11} -22.8233 q^{12} -28.0184 q^{13} +14.5471 q^{15} +54.7405 q^{16} +117.229 q^{17} -5.63648 q^{18} -38.9320 q^{19} -36.8904 q^{20} +6.88904 q^{22} -125.398 q^{23} +29.3243 q^{24} -101.487 q^{25} +17.5473 q^{26} +27.0000 q^{27} +108.820 q^{29} -9.11050 q^{30} -274.167 q^{31} -112.481 q^{32} -33.0000 q^{33} -73.4179 q^{34} -68.4700 q^{36} +257.219 q^{37} +24.3822 q^{38} -84.0553 q^{39} +47.3982 q^{40} +178.284 q^{41} -169.552 q^{43} +83.6856 q^{44} +43.6413 q^{45} +78.5338 q^{46} +342.829 q^{47} +164.222 q^{48} +63.5588 q^{50} +351.688 q^{51} +213.158 q^{52} -249.783 q^{53} -16.9095 q^{54} -53.3394 q^{55} -116.796 q^{57} -68.1513 q^{58} +367.871 q^{59} -110.671 q^{60} +309.236 q^{61} +171.704 q^{62} -367.480 q^{64} -135.862 q^{65} +20.6671 q^{66} -732.854 q^{67} -891.854 q^{68} -376.194 q^{69} -683.141 q^{71} +87.9730 q^{72} +589.145 q^{73} -161.090 q^{74} -304.461 q^{75} +296.186 q^{76} +52.6418 q^{78} -929.114 q^{79} +265.439 q^{80} +81.0000 q^{81} -111.655 q^{82} -561.203 q^{83} +568.449 q^{85} +106.186 q^{86} +326.460 q^{87} -107.523 q^{88} +1172.75 q^{89} -27.3315 q^{90} +954.001 q^{92} -822.500 q^{93} -214.705 q^{94} -188.782 q^{95} -337.443 q^{96} -1089.65 q^{97} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 48 q^{3} + 72 q^{4} - 12 q^{6} - 66 q^{8} + 144 q^{9}+O(q^{10}) \) 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

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