LMFDB - Embedded newform 1617.4.a.bd.1.15

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			1.15
Root			$-4.70685$ 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)

$f(q)$	$=$	$q+4.70685 q^{2} +3.00000 q^{3} +14.1544 q^{4} -15.5088 q^{5} +14.1205 q^{6} +28.9678 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+4.70685 q^{2} +3.00000 q^{3} +14.1544 q^{4} -15.5088 q^{5} +14.1205 q^{6} +28.9678 q^{8} +9.00000 q^{9} -72.9976 q^{10} -11.0000 q^{11} +42.4632 q^{12} +67.8445 q^{13} -46.5264 q^{15} +23.1117 q^{16} -132.347 q^{17} +42.3616 q^{18} -44.2156 q^{19} -219.518 q^{20} -51.7753 q^{22} +44.9111 q^{23} +86.9033 q^{24} +115.523 q^{25} +319.334 q^{26} +27.0000 q^{27} -99.9738 q^{29} -218.993 q^{30} -275.285 q^{31} -122.959 q^{32} -33.0000 q^{33} -622.937 q^{34} +127.390 q^{36} +438.156 q^{37} -208.116 q^{38} +203.534 q^{39} -449.256 q^{40} -295.629 q^{41} -233.446 q^{43} -155.698 q^{44} -139.579 q^{45} +211.390 q^{46} -294.218 q^{47} +69.3350 q^{48} +543.751 q^{50} -397.041 q^{51} +960.298 q^{52} +247.527 q^{53} +127.085 q^{54} +170.597 q^{55} -132.647 q^{57} -470.561 q^{58} -406.059 q^{59} -658.554 q^{60} -201.329 q^{61} -1295.72 q^{62} -763.643 q^{64} -1052.19 q^{65} -155.326 q^{66} -400.197 q^{67} -1873.29 q^{68} +134.733 q^{69} +342.922 q^{71} +260.710 q^{72} +602.782 q^{73} +2062.33 q^{74} +346.570 q^{75} -625.845 q^{76} +958.001 q^{78} -254.581 q^{79} -358.434 q^{80} +81.0000 q^{81} -1391.48 q^{82} -1388.38 q^{83} +2052.54 q^{85} -1098.79 q^{86} -299.921 q^{87} -318.645 q^{88} +1246.54 q^{89} -656.978 q^{90} +635.690 q^{92} -825.854 q^{93} -1384.84 q^{94} +685.732 q^{95} -368.877 q^{96} +604.540 q^{97} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	4.70685	1.66412	0.832061	−	0.554685i	$-0.187161\pi$
$2$	4.70685	1.66412	0.832061	+	0.554685i	$0.187161\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	14.1544	1.76930
$5$	−15.5088	−1.38715	−0.693575	−	0.720384i	$-0.743966\pi$
$5$	−15.5088	−1.38715	−0.693575	+	0.720384i	$0.743966\pi$
$6$	14.1205	0.960781
$7$	0	0
$7$	0	0
$8$	28.9678	1.28021
$9$	9.00000	0.333333
$10$	−72.9976	−2.30839
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	42.4632	1.02151
$13$	67.8445	1.44744	0.723719	−	0.690095i	$-0.242431\pi$
$13$	67.8445	1.44744	0.723719	+	0.690095i	$0.242431\pi$
$14$	0	0
$15$	−46.5264	−0.800872
$16$	23.1117	0.361120
$17$	−132.347	−1.88817	−0.944084	−	0.329706i	$-0.893050\pi$
$17$	−132.347	−1.88817	−0.944084	+	0.329706i	$0.893050\pi$
$18$	42.3616	0.554707
$19$	−44.2156	−0.533882	−0.266941	−	0.963713i	$-0.586013\pi$
$19$	−44.2156	−0.533882	−0.266941	+	0.963713i	$0.586013\pi$
$20$	−219.518	−2.45428
$21$	0	0
$22$	−51.7753	−0.501751
$23$	44.9111	0.407157	0.203579	−	0.979059i	$-0.434743\pi$
$23$	44.9111	0.407157	0.203579	+	0.979059i	$0.434743\pi$
$24$	86.9033	0.739128
$25$	115.523	0.924187
$26$	319.334	2.40871
$27$	27.0000	0.192450
$28$	0	0
$29$	−99.9738	−0.640161	−0.320080	−	0.947390i	$-0.603710\pi$
$29$	−99.9738	−0.640161	−0.320080	+	0.947390i	$0.603710\pi$
$30$	−218.993	−1.33275
$31$	−275.285	−1.59492	−0.797461	−	0.603370i	$-0.793824\pi$
$31$	−275.285	−1.59492	−0.797461	+	0.603370i	$0.793824\pi$
$32$	−122.959	−0.679260
$33$	−33.0000	−0.174078
$34$	−622.937	−3.14214
$35$	0	0
$36$	127.390	0.589766
$37$	438.156	1.94682	0.973410	−	0.229071i	$-0.0735687\pi$
$37$	438.156	1.94682	0.973410	+	0.229071i	$0.0735687\pi$
$38$	−208.116	−0.888444
$39$	203.534	0.835678
$40$	−449.256	−1.77584
$41$	−295.629	−1.12608	−0.563042	−	0.826428i	$-0.690369\pi$
$41$	−295.629	−1.12608	−0.563042	+	0.826428i	$0.690369\pi$
$42$	0	0
$43$	−233.446	−0.827911	−0.413956	−	0.910297i	$-0.635853\pi$
$43$	−233.446	−0.827911	−0.413956	+	0.910297i	$0.635853\pi$
$44$	−155.698	−0.533464
$45$	−139.579	−0.462384
$46$	211.390	0.677559
$47$	−294.218	−0.913109	−0.456555	−	0.889695i	$-0.650917\pi$
$47$	−294.218	−0.913109	−0.456555	+	0.889695i	$0.650917\pi$
$48$	69.3350	0.208493
$49$	0	0
$50$	543.751	1.53796
$51$	−397.041	−1.09013
$52$	960.298	2.56095
$53$	247.527	0.641519	0.320759	−	0.947161i	$-0.396062\pi$
$53$	247.527	0.641519	0.320759	+	0.947161i	$0.396062\pi$
$54$	127.085	0.320260
$55$	170.597	0.418242
$56$	0	0
$57$	−132.647	−0.308237
$58$	−470.561	−1.06531
$59$	−406.059	−0.896007	−0.448004	−	0.894032i	$-0.647865\pi$
$59$	−406.059	−0.896007	−0.448004	+	0.894032i	$0.647865\pi$
$60$	−658.554	−1.41698
$61$	−201.329	−0.422583	−0.211291	−	0.977423i	$-0.567767\pi$
$61$	−201.329	−0.422583	−0.211291	+	0.977423i	$0.567767\pi$
$62$	−1295.72	−2.65414
$63$	0	0
$64$	−763.643	−1.49149
$65$	−1052.19	−2.00781
$66$	−155.326	−0.289686
$67$	−400.197	−0.729730	−0.364865	−	0.931061i	$-0.618885\pi$
$67$	−400.197	−0.729730	−0.364865	+	0.931061i	$0.618885\pi$
$68$	−1873.29	−3.34073
$69$	134.733	0.235072
$70$	0	0
$71$	342.922	0.573202	0.286601	−	0.958050i	$-0.407475\pi$
$71$	342.922	0.573202	0.286601	+	0.958050i	$0.407475\pi$
$72$	260.710	0.426735
$73$	602.782	0.966442	0.483221	−	0.875498i	$-0.339467\pi$
$73$	602.782	0.966442	0.483221	+	0.875498i	$0.339467\pi$
$74$	2062.33	3.23974
$75$	346.570	0.533580
$76$	−625.845	−0.944597
$77$	0	0
$78$	958.001	1.39067
$79$	−254.581	−0.362565	−0.181282	−	0.983431i	$-0.558025\pi$
$79$	−254.581	−0.362565	−0.181282	+	0.983431i	$0.558025\pi$
$80$	−358.434	−0.500927
$81$	81.0000	0.111111
$82$	−1391.48	−1.87394
$83$	−1388.38	−1.83608	−0.918039	−	0.396489i	$-0.870228\pi$
$83$	−1388.38	−1.83608	−0.918039	+	0.396489i	$0.870228\pi$
$84$	0	0
$85$	2052.54	2.61917
$86$	−1098.79	−1.37774
$87$	−299.921	−0.369597
$88$	−318.645	−0.385997
$89$	1246.54	1.48464	0.742318	−	0.670048i	$-0.233727\pi$
$89$	1246.54	1.48464	0.742318	+	0.670048i	$0.233727\pi$
$90$	−656.978	−0.769462
$91$	0	0
$92$	635.690	0.720383
$93$	−825.854	−0.920829
$94$	−1384.84	−1.51952
$95$	685.732	0.740575
$96$	−368.877	−0.392171
$97$	604.540	0.632801	0.316401	−	0.948626i	$-0.397526\pi$
$97$	604.540	0.632801	0.316401	+	0.948626i	$0.397526\pi$
$98$	0	0
$99$	−99.0000	−0.100504
$100$	1635.16	1.63516
$101$	−641.954	−0.632444	−0.316222	−	0.948685i	$-0.602414\pi$
$101$	−641.954	−0.632444	−0.316222	+	0.948685i	$0.602414\pi$
$102$	−1868.81	−1.81411
$103$	482.581	0.461652	0.230826	−	0.972995i	$-0.425857\pi$
$103$	482.581	0.461652	0.230826	+	0.972995i	$0.425857\pi$
$104$	1965.30	1.85302
$105$	0	0
$106$	1165.07	1.06757
$107$	846.581	0.764879	0.382440	−	0.923981i	$-0.375084\pi$
$107$	846.581	0.764879	0.382440	+	0.923981i	$0.375084\pi$
$108$	382.169	0.340502
$109$	−1179.62	−1.03658	−0.518291	−	0.855204i	$-0.673431\pi$
$109$	−1179.62	−1.03658	−0.518291	+	0.855204i	$0.673431\pi$
$110$	802.974	0.696005
$111$	1314.47	1.12400
$112$	0	0
$113$	−2295.37	−1.91088	−0.955442	−	0.295179i	$-0.904621\pi$
$113$	−2295.37	−1.91088	−0.955442	+	0.295179i	$0.904621\pi$
$114$	−624.348	−0.512943
$115$	−696.518	−0.564788
$116$	−1415.07	−1.13264
$117$	610.601	0.482479
$118$	−1911.26	−1.49106
$119$	0	0
$120$	−1347.77	−1.02528
$121$	121.000	0.0909091
$122$	−947.624	−0.703229
$123$	−886.886	−0.650145
$124$	−3896.49	−2.82189
$125$	146.972	0.105164
$126$	0	0
$127$	−949.334	−0.663305	−0.331653	−	0.943402i	$-0.607606\pi$
$127$	−949.334	−0.663305	−0.331653	+	0.943402i	$0.607606\pi$
$128$	−2610.68	−1.80276
$129$	−700.338	−0.477995
$130$	−4952.49	−3.34124
$131$	277.579	0.185131	0.0925657	−	0.995707i	$-0.470493\pi$
$131$	277.579	0.185131	0.0925657	+	0.995707i	$0.470493\pi$
$132$	−467.095	−0.307995
$133$	0	0
$134$	−1883.67	−1.21436
$135$	−418.738	−0.266957
$136$	−3833.80	−2.41724
$137$	290.054	0.180883	0.0904415	−	0.995902i	$-0.471172\pi$
$137$	290.054	0.180883	0.0904415	+	0.995902i	$0.471172\pi$
$138$	634.169	0.391189
$139$	−2721.80	−1.66086	−0.830432	−	0.557120i	$-0.811906\pi$
$139$	−2721.80	−1.66086	−0.830432	+	0.557120i	$0.811906\pi$
$140$	0	0
$141$	−882.655	−0.527184
$142$	1614.08	0.953878
$143$	−746.290	−0.436419
$144$	208.005	0.120373
$145$	1550.47	0.887999
$146$	2837.20	1.60828
$147$	0	0
$148$	6201.82	3.44451
$149$	1031.90	0.567362	0.283681	−	0.958919i	$-0.408444\pi$
$149$	1031.90	0.567362	0.283681	+	0.958919i	$0.408444\pi$
$150$	1631.25	0.887941
$151$	−918.700	−0.495117	−0.247559	−	0.968873i	$-0.579628\pi$
$151$	−918.700	−0.495117	−0.247559	+	0.968873i	$0.579628\pi$
$152$	−1280.83	−0.683479
$153$	−1191.12	−0.629389
$154$	0	0
$155$	4269.34	2.21240
$156$	2880.89	1.47856
$157$	1841.11	0.935904	0.467952	−	0.883754i	$-0.344992\pi$
$157$	1841.11	0.935904	0.467952	+	0.883754i	$0.344992\pi$
$158$	−1198.27	−0.603352
$159$	742.582	0.370381
$160$	1906.95	0.942235
$161$	0	0
$162$	381.254	0.184902
$163$	1965.48	0.944466	0.472233	−	0.881474i	$-0.343448\pi$
$163$	1965.48	0.944466	0.472233	+	0.881474i	$0.343448\pi$
$164$	−4184.44	−1.99238
$165$	511.791	0.241472
$166$	−6534.89	−3.05546
$167$	−3480.72	−1.61285	−0.806425	−	0.591336i	$-0.798601\pi$
$167$	−3480.72	−1.61285	−0.806425	+	0.591336i	$0.798601\pi$
$168$	0	0
$169$	2405.88	1.09507
$170$	9661.01	4.35862
$171$	−397.940	−0.177961
$172$	−3304.29	−1.46482
$173$	−294.151	−0.129271	−0.0646355	−	0.997909i	$-0.520588\pi$
$173$	−294.151	−0.129271	−0.0646355	+	0.997909i	$0.520588\pi$
$174$	−1411.68	−0.615054
$175$	0	0
$176$	−254.228	−0.108882
$177$	−1218.18	−0.517310
$178$	5867.25	2.47061
$179$	−2118.80	−0.884729	−0.442364	−	0.896835i	$-0.645860\pi$
$179$	−2118.80	−0.884729	−0.442364	+	0.896835i	$0.645860\pi$
$180$	−1975.66	−0.818095
$181$	2048.84	0.841374	0.420687	−	0.907206i	$-0.361789\pi$
$181$	2048.84	0.841374	0.420687	+	0.907206i	$0.361789\pi$
$182$	0	0
$183$	−603.987	−0.243978
$184$	1300.98	0.521245
$185$	−6795.27	−2.70053
$186$	−3887.17	−1.53237
$187$	1455.82	0.569304
$188$	−4164.48	−1.61556
$189$	0	0
$190$	3227.63	1.23241
$191$	444.559	0.168414	0.0842072	−	0.996448i	$-0.473164\pi$
$191$	444.559	0.168414	0.0842072	+	0.996448i	$0.473164\pi$
$192$	−2290.93	−0.861112
$193$	1744.37	0.650582	0.325291	−	0.945614i	$-0.394538\pi$
$193$	1744.37	0.650582	0.325291	+	0.945614i	$0.394538\pi$
$194$	2845.48	1.05306
$195$	−3156.56	−1.15921
$196$	0	0
$197$	719.118	0.260076	0.130038	−	0.991509i	$-0.458490\pi$
$197$	719.118	0.260076	0.130038	+	0.991509i	$0.458490\pi$
$198$	−465.978	−0.167250
$199$	3367.80	1.19968	0.599842	−	0.800118i	$-0.295230\pi$
$199$	3367.80	1.19968	0.599842	+	0.800118i	$0.295230\pi$
$200$	3346.45	1.18315
$201$	−1200.59	−0.421310
$202$	−3021.58	−1.05246
$203$	0	0
$204$	−5619.87	−1.92877
$205$	4584.85	1.56205
$206$	2271.43	0.768244
$207$	404.200	0.135719
$208$	1568.00	0.522698
$209$	486.372	0.160971
$210$	0	0
$211$	−2047.66	−0.668090	−0.334045	−	0.942557i	$-0.608414\pi$
$211$	−2047.66	−0.668090	−0.334045	+	0.942557i	$0.608414\pi$
$212$	3503.60	1.13504
$213$	1028.77	0.330938
$214$	3984.73	1.27285
$215$	3620.47	1.14844
$216$	782.130	0.246376
$217$	0	0
$218$	−5552.30	−1.72500
$219$	1808.34	0.557975
$220$	2414.70	0.739994
$221$	−8979.01	−2.73300
$222$	6186.99	1.87047
$223$	6025.91	1.80953	0.904764	−	0.425913i	$-0.140047\pi$
$223$	6025.91	1.80953	0.904764	+	0.425913i	$0.140047\pi$
$224$	0	0
$225$	1039.71	0.308062
$226$	−10803.9	−3.17994
$227$	−4303.18	−1.25820	−0.629102	−	0.777323i	$-0.716577\pi$
$227$	−4303.18	−1.25820	−0.629102	+	0.777323i	$0.716577\pi$
$228$	−1877.53	−0.545363
$229$	5390.34	1.55548	0.777738	−	0.628589i	$-0.216367\pi$
$229$	5390.34	1.55548	0.777738	+	0.628589i	$0.216367\pi$
$230$	−3278.40	−0.939876
$231$	0	0
$232$	−2896.02	−0.819538
$233$	3848.24	1.08200	0.541001	−	0.841022i	$-0.318045\pi$
$233$	3848.24	1.08200	0.541001	+	0.841022i	$0.318045\pi$
$234$	2874.00	0.802904
$235$	4562.98	1.26662
$236$	−5747.52	−1.58530
$237$	−763.743	−0.209327
$238$	0	0
$239$	3082.41	0.834244	0.417122	−	0.908850i	$-0.363039\pi$
$239$	3082.41	0.834244	0.417122	+	0.908850i	$0.363039\pi$
$240$	−1075.30	−0.289211
$241$	41.2975	0.0110382	0.00551910	−	0.999985i	$-0.498243\pi$
$241$	41.2975	0.0110382	0.00551910	+	0.999985i	$0.498243\pi$
$242$	569.528	0.151284
$243$	243.000	0.0641500
$244$	−2849.69	−0.747675
$245$	0	0
$246$	−4174.43	−1.08192
$247$	−2999.79	−0.772760
$248$	−7974.38	−2.04183
$249$	−4165.14	−1.06006
$250$	691.772	0.175006
$251$	−4336.80	−1.09058	−0.545291	−	0.838247i	$-0.683581\pi$
$251$	−4336.80	−1.09058	−0.545291	+	0.838247i	$0.683581\pi$
$252$	0	0
$253$	−494.022	−0.122763
$254$	−4468.37	−1.10382
$255$	6157.63	1.51218
$256$	−6178.90	−1.50852
$257$	3470.77	0.842416	0.421208	−	0.906964i	$-0.361606\pi$
$257$	3470.77	0.842416	0.421208	+	0.906964i	$0.361606\pi$
$258$	−3296.38	−0.795441
$259$	0	0
$260$	−14893.1	−3.55242
$261$	−899.764	−0.213387
$262$	1306.52	0.308081
$263$	1366.58	0.320407	0.160203	−	0.987084i	$-0.448785\pi$
$263$	1366.58	0.320407	0.160203	+	0.987084i	$0.448785\pi$
$264$	−955.936	−0.222855
$265$	−3838.86	−0.889883
$266$	0	0
$267$	3739.61	0.857155
$268$	−5664.55	−1.29111
$269$	−4215.86	−0.955560	−0.477780	−	0.878480i	$-0.658558\pi$
$269$	−4215.86	−0.955560	−0.477780	+	0.878480i	$0.658558\pi$
$270$	−1970.93	−0.444249
$271$	−6604.67	−1.48046	−0.740231	−	0.672353i	$-0.765284\pi$
$271$	−6604.67	−1.48046	−0.740231	+	0.672353i	$0.765284\pi$
$272$	−3058.76	−0.681854
$273$	0	0
$274$	1365.24	0.301011
$275$	−1270.76	−0.278653
$276$	1907.07	0.415913
$277$	4259.60	0.923952	0.461976	−	0.886893i	$-0.347141\pi$
$277$	4259.60	0.923952	0.461976	+	0.886893i	$0.347141\pi$
$278$	−12811.1	−2.76388
$279$	−2477.56	−0.531641
$280$	0	0
$281$	−996.366	−0.211524	−0.105762	−	0.994391i	$-0.533728\pi$
$281$	−996.366	−0.211524	−0.105762	+	0.994391i	$0.533728\pi$
$282$	−4154.52	−0.877298
$283$	6837.05	1.43611	0.718057	−	0.695984i	$-0.245032\pi$
$283$	6837.05	1.43611	0.718057	+	0.695984i	$0.245032\pi$
$284$	4853.85	1.01417
$285$	2057.19	0.427571
$286$	−3512.67	−0.726254
$287$	0	0
$288$	−1106.63	−0.226420
$289$	12602.7	2.56518
$290$	7297.84	1.47774
$291$	1813.62	0.365348
$292$	8532.01	1.70992
$293$	8625.69	1.71986	0.859928	−	0.510415i	$-0.170508\pi$
$293$	8625.69	1.71986	0.859928	+	0.510415i	$0.170508\pi$
$294$	0	0
$295$	6297.50	1.24290
$296$	12692.4	2.49233
$297$	−297.000	−0.0580259
$298$	4857.01	0.944158
$299$	3046.97	0.589335
$300$	4905.49	0.944062
$301$	0	0
$302$	−4324.18	−0.823935
$303$	−1925.86	−0.365141
$304$	−1021.90	−0.192795
$305$	3122.37	0.586186
$306$	−5606.43	−1.04738
$307$	−1676.51	−0.311672	−0.155836	−	0.987783i	$-0.549807\pi$
$307$	−1676.51	−0.311672	−0.155836	+	0.987783i	$0.549807\pi$
$308$	0	0
$309$	1447.74	0.266535
$310$	20095.1	3.68170
$311$	8070.72	1.47154	0.735769	−	0.677233i	$-0.236821\pi$
$311$	8070.72	1.47154	0.735769	+	0.677233i	$0.236821\pi$
$312$	5895.91	1.06984
$313$	3967.96	0.716557	0.358279	−	0.933615i	$-0.383364\pi$
$313$	3967.96	0.716557	0.358279	+	0.933615i	$0.383364\pi$
$314$	8665.84	1.55746
$315$	0	0
$316$	−3603.44	−0.641485
$317$	6055.16	1.07284	0.536422	−	0.843950i	$-0.319776\pi$
$317$	6055.16	1.07284	0.536422	+	0.843950i	$0.319776\pi$
$318$	3495.22	0.616359
$319$	1099.71	0.193016
$320$	11843.2	2.06892
$321$	2539.74	0.441603
$322$	0	0
$323$	5851.80	1.00806
$324$	1146.51	0.196589
$325$	7837.63	1.33770
$326$	9251.19	1.57171
$327$	−3538.87	−0.598471
$328$	−8563.70	−1.44162
$329$	0	0
$330$	2408.92	0.401839
$331$	−10324.3	−1.71443	−0.857216	−	0.514957i	$-0.827808\pi$
$331$	−10324.3	−1.71443	−0.857216	+	0.514957i	$0.827808\pi$
$332$	−19651.7	−3.24857
$333$	3943.40	0.648940
$334$	−16383.2	−2.68398
$335$	6206.59	1.01224
$336$	0	0
$337$	−5222.68	−0.844206	−0.422103	−	0.906548i	$-0.638708\pi$
$337$	−5222.68	−0.844206	−0.422103	+	0.906548i	$0.638708\pi$
$338$	11324.1	1.82234
$339$	−6886.10	−1.10325
$340$	29052.5	4.63410
$341$	3028.13	0.480887
$342$	−1873.04	−0.296148
$343$	0	0
$344$	−6762.41	−1.05990
$345$	−2089.56	−0.326081
$346$	−1384.52	−0.215123
$347$	−10.3940	−0.00160801	−0.000804003	−	1.00000i	$-0.500256\pi$
$347$	−10.3940	−0.00160801	−0.000804003		1.00000i	$0.500256\pi$
$348$	−4245.20	−0.653928
$349$	12095.3	1.85514	0.927571	−	0.373647i	$-0.121893\pi$
$349$	12095.3	1.85514	0.927571	+	0.373647i	$0.121893\pi$
$350$	0	0
$351$	1831.80	0.278559
$352$	1352.55	0.204804
$353$	−6473.30	−0.976031	−0.488016	−	0.872835i	$-0.662279\pi$
$353$	−6473.30	−0.976031	−0.488016	+	0.872835i	$0.662279\pi$
$354$	−5733.78	−0.860867
$355$	−5318.31	−0.795118
$356$	17644.0	2.62676
$357$	0	0
$358$	−9972.86	−1.47230
$359$	2393.30	0.351848	0.175924	−	0.984404i	$-0.443709\pi$
$359$	2393.30	0.351848	0.175924	+	0.984404i	$0.443709\pi$
$360$	−4043.30	−0.591946
$361$	−4903.98	−0.714970
$362$	9643.55	1.40015
$363$	363.000	0.0524864
$364$	0	0
$365$	−9348.43	−1.34060
$366$	−2842.87	−0.406009
$367$	1483.86	0.211054	0.105527	−	0.994416i	$-0.466347\pi$
$367$	1483.86	0.211054	0.105527	+	0.994416i	$0.466347\pi$
$368$	1037.97	0.147033
$369$	−2660.66	−0.375361
$370$	−31984.3	−4.49401
$371$	0	0
$372$	−11689.5	−1.62922
$373$	−5078.43	−0.704962	−0.352481	−	0.935819i	$-0.614662\pi$
$373$	−5078.43	−0.704962	−0.352481	+	0.935819i	$0.614662\pi$
$374$	6852.30	0.947391
$375$	440.915	0.0607166
$376$	−8522.85	−1.16897
$377$	−6782.67	−0.926593
$378$	0	0
$379$	−2353.93	−0.319032	−0.159516	−	0.987195i	$-0.550993\pi$
$379$	−2353.93	−0.319032	−0.159516	+	0.987195i	$0.550993\pi$
$380$	9706.11	1.31030
$381$	−2848.00	−0.382959
$382$	2092.47	0.280262
$383$	1423.41	0.189903	0.0949516	−	0.995482i	$-0.469730\pi$
$383$	1423.41	0.189903	0.0949516	+	0.995482i	$0.469730\pi$
$384$	−7832.03	−1.04082
$385$	0	0
$386$	8210.47	1.08265
$387$	−2101.01	−0.275970
$388$	8556.90	1.11961
$389$	−1126.71	−0.146854	−0.0734270	−	0.997301i	$-0.523394\pi$
$389$	−1126.71	−0.146854	−0.0734270	+	0.997301i	$0.523394\pi$
$390$	−14857.5	−1.92907
$391$	−5943.85	−0.768781
$392$	0	0
$393$	832.738	0.106886
$394$	3384.78	0.432799
$395$	3948.25	0.502932
$396$	−1401.28	−0.177821
$397$	−1670.34	−0.211163	−0.105582	−	0.994411i	$-0.533670\pi$
$397$	−1670.34	−0.211163	−0.105582	+	0.994411i	$0.533670\pi$
$398$	15851.7	1.99642
$399$	0	0
$400$	2669.94	0.333742
$401$	2113.35	0.263182	0.131591	−	0.991304i	$-0.457992\pi$
$401$	2113.35	0.263182	0.131591	+	0.991304i	$0.457992\pi$
$402$	−5651.00	−0.701110
$403$	−18676.6	−2.30855
$404$	−9086.47	−1.11898
$405$	−1256.21	−0.154128
$406$	0	0
$407$	−4819.71	−0.586988
$408$	−11501.4	−1.39560
$409$	−2155.59	−0.260604	−0.130302	−	0.991474i	$-0.541595\pi$
$409$	−2155.59	−0.260604	−0.130302	+	0.991474i	$0.541595\pi$
$410$	21580.2	2.59944
$411$	870.161	0.104433
$412$	6830.64	0.816800
$413$	0	0
$414$	1902.51	0.225853
$415$	21532.1	2.54692
$416$	−8342.10	−0.983186
$417$	−8165.40	−0.958900
$418$	2289.28	0.267876
$419$	9026.67	1.05246	0.526231	−	0.850341i	$-0.323605\pi$
$419$	9026.67	1.05246	0.526231	+	0.850341i	$0.323605\pi$
$420$	0	0
$421$	−5135.07	−0.594461	−0.297231	−	0.954806i	$-0.596063\pi$
$421$	−5135.07	−0.594461	−0.297231	+	0.954806i	$0.596063\pi$
$422$	−9638.04	−1.11178
$423$	−2647.96	−0.304370
$424$	7170.31	0.821277
$425$	−15289.2	−1.74502
$426$	4842.24	0.550722
$427$	0	0
$428$	11982.8	1.35330
$429$	−2238.87	−0.251966
$430$	17041.0	1.91114
$431$	−978.548	−0.109362	−0.0546810	−	0.998504i	$-0.517414\pi$
$431$	−978.548	−0.109362	−0.0546810	+	0.998504i	$0.517414\pi$
$432$	624.015	0.0694975
$433$	10647.8	1.18175	0.590877	−	0.806762i	$-0.298782\pi$
$433$	10647.8	1.18175	0.590877	+	0.806762i	$0.298782\pi$
$434$	0	0
$435$	4651.42	0.512687
$436$	−16696.8	−1.83402
$437$	−1985.77	−0.217374
$438$	8511.60	0.928539
$439$	−14551.4	−1.58200	−0.791000	−	0.611816i	$-0.790439\pi$
$439$	−14551.4	−1.58200	−0.791000	+	0.611816i	$0.790439\pi$
$440$	4941.81	0.535436
$441$	0	0
$442$	−42262.8	−4.54805
$443$	−1269.53	−0.136156	−0.0680781	−	0.997680i	$-0.521687\pi$
$443$	−1269.53	−0.136156	−0.0680781	+	0.997680i	$0.521687\pi$
$444$	18605.5	1.98869
$445$	−19332.3	−2.05941
$446$	28363.0	3.01127
$447$	3095.71	0.327566
$448$	0	0
$449$	1119.27	0.117643	0.0588214	−	0.998269i	$-0.481266\pi$
$449$	1119.27	0.117643	0.0588214	+	0.998269i	$0.481266\pi$
$450$	4893.75	0.512653
$451$	3251.91	0.339527
$452$	−32489.5	−3.38093
$453$	−2756.10	−0.285856
$454$	−20254.4	−2.09380
$455$	0	0
$456$	−3842.48	−0.394607
$457$	−14452.9	−1.47938	−0.739690	−	0.672948i	$-0.765028\pi$
$457$	−14452.9	−1.47938	−0.739690	+	0.672948i	$0.765028\pi$
$458$	25371.5	2.58850
$459$	−3573.37	−0.363378
$460$	−9858.79	−0.999280
$461$	−16117.1	−1.62830	−0.814151	−	0.580653i	$-0.802797\pi$
$461$	−16117.1	−1.62830	−0.814151	+	0.580653i	$0.802797\pi$
$462$	0	0
$463$	−16129.4	−1.61900	−0.809498	−	0.587123i	$-0.800260\pi$
$463$	−16129.4	−1.61900	−0.809498	+	0.587123i	$0.800260\pi$
$464$	−2310.56	−0.231175
$465$	12808.0	1.27733
$466$	18113.1	1.80058
$467$	5449.33	0.539967	0.269984	−	0.962865i	$-0.412982\pi$
$467$	5449.33	0.539967	0.269984	+	0.962865i	$0.412982\pi$
$468$	8642.68	0.853650
$469$	0	0
$470$	21477.2	2.10781
$471$	5523.34	0.540345
$472$	−11762.6	−1.14707
$473$	2567.91	0.249625
$474$	−3594.82	−0.348345
$475$	−5107.93	−0.493407
$476$	0	0
$477$	2227.75	0.213840
$478$	14508.4	1.38828
$479$	4593.02	0.438122	0.219061	−	0.975711i	$-0.429701\pi$
$479$	4593.02	0.438122	0.219061	+	0.975711i	$0.429701\pi$
$480$	5720.85	0.544000
$481$	29726.5	2.81790
$482$	194.381	0.0183689
$483$	0	0
$484$	1712.68	0.160845
$485$	−9375.70	−0.877791
$486$	1143.76	0.106753
$487$	10416.4	0.969228	0.484614	−	0.874728i	$-0.338960\pi$
$487$	10416.4	0.969228	0.484614	+	0.874728i	$0.338960\pi$
$488$	−5832.05	−0.540993
$489$	5896.43	0.545288
$490$	0	0
$491$	173.087	0.0159090	0.00795449	−	0.999968i	$-0.497468\pi$
$491$	173.087	0.0159090	0.00795449	+	0.999968i	$0.497468\pi$
$492$	−12553.3	−1.15030
$493$	13231.2	1.20873
$494$	−14119.5	−1.28597
$495$	1535.37	0.139414
$496$	−6362.29	−0.575958
$497$	0	0
$498$	−19604.7	−1.76407
$499$	−9686.75	−0.869015	−0.434508	−	0.900668i	$-0.643078\pi$
$499$	−9686.75	−0.869015	−0.434508	+	0.900668i	$0.643078\pi$
$500$	2080.29	0.186067
$501$	−10442.2	−0.931180
$502$	−20412.6	−1.81486
$503$	968.954	0.0858917	0.0429458	−	0.999077i	$-0.486326\pi$
$503$	968.954	0.0858917	0.0429458	+	0.999077i	$0.486326\pi$
$504$	0	0
$505$	9955.94	0.877295
$506$	−2325.29	−0.204292
$507$	7217.64	0.632242
$508$	−13437.2	−1.17359
$509$	16259.5	1.41589	0.707945	−	0.706268i	$-0.249623\pi$
$509$	16259.5	1.41589	0.707945	+	0.706268i	$0.249623\pi$
$510$	28983.0	2.51645
$511$	0	0
$512$	−8197.73	−0.707602
$513$	−1193.82	−0.102746
$514$	16336.4	1.40188
$515$	−7484.26	−0.640380
$516$	−9912.86	−0.845716
$517$	3236.40	0.275313
$518$	0	0
$519$	−882.453	−0.0746346
$520$	−30479.5	−2.57042
$521$	−20227.5	−1.70093	−0.850463	−	0.526035i	$-0.823678\pi$
$521$	−20227.5	−1.70093	−0.850463	+	0.526035i	$0.823678\pi$
$522$	−4235.05	−0.355102
$523$	10064.4	0.841463	0.420732	−	0.907185i	$-0.361773\pi$
$523$	10064.4	0.841463	0.420732	+	0.907185i	$0.361773\pi$
$524$	3928.97	0.327553
$525$	0	0
$526$	6432.28	0.533196
$527$	36433.1	3.01148
$528$	−762.685	−0.0628629
$529$	−10150.0	−0.834223
$530$	−18068.9	−1.48087
$531$	−3654.54	−0.298669
$532$	0	0
$533$	−20056.8	−1.62994
$534$	17601.8	1.42641
$535$	−13129.5	−1.06100
$536$	−11592.8	−0.934204
$537$	−6356.40	−0.510799
$538$	−19843.4	−1.59017
$539$	0	0
$540$	−5926.98	−0.472327
$541$	−13584.8	−1.07958	−0.539792	−	0.841798i	$-0.681497\pi$
$541$	−13584.8	−1.07958	−0.539792	+	0.841798i	$0.681497\pi$
$542$	−31087.2	−2.46367
$543$	6146.51	0.485768
$544$	16273.3	1.28256
$545$	18294.6	1.43789
$546$	0	0
$547$	16958.9	1.32561	0.662805	−	0.748792i	$-0.269366\pi$
$547$	16958.9	1.32561	0.662805	+	0.748792i	$0.269366\pi$
$548$	4105.53	0.320036
$549$	−1811.96	−0.140861
$550$	−5981.26	−0.463712
$551$	4420.40	0.341770
$552$	3902.93	0.300941
$553$	0	0
$554$	20049.3	1.53757
$555$	−20385.8	−1.55915
$556$	−38525.4	−2.93856
$557$	−12497.4	−0.950686	−0.475343	−	0.879801i	$-0.657676\pi$
$557$	−12497.4	−0.950686	−0.475343	+	0.879801i	$0.657676\pi$
$558$	−11661.5	−0.884715
$559$	−15838.0	−1.19835
$560$	0	0
$561$	4367.45	0.328688
$562$	−4689.74	−0.352001
$563$	14687.2	1.09945	0.549725	−	0.835345i	$-0.314732\pi$
$563$	14687.2	1.09945	0.549725	+	0.835345i	$0.314732\pi$
$564$	−12493.4	−0.932746
$565$	35598.4	2.65068
$566$	32180.9	2.38987
$567$	0	0
$568$	9933.68	0.733817
$569$	−751.449	−0.0553644	−0.0276822	−	0.999617i	$-0.508813\pi$
$569$	−751.449	−0.0553644	−0.0276822	+	0.999617i	$0.508813\pi$
$570$	9682.90	0.711530
$571$	−16823.6	−1.23300	−0.616501	−	0.787354i	$-0.711450\pi$
$571$	−16823.6	−1.23300	−0.616501	+	0.787354i	$0.711450\pi$
$572$	−10563.3	−0.772155
$573$	1333.68	0.0972341
$574$	0	0
$575$	5188.28	0.376289
$576$	−6872.79	−0.497163
$577$	−10920.4	−0.787909	−0.393954	−	0.919130i	$-0.628893\pi$
$577$	−10920.4	−0.787909	−0.393954	+	0.919130i	$0.628893\pi$
$578$	59319.0	4.26876
$579$	5233.11	0.375614
$580$	21946.0	1.57114
$581$	0	0
$582$	8536.43	0.607983
$583$	−2722.80	−0.193425
$584$	17461.2	1.23725
$585$	−9469.69	−0.669271
$586$	40599.8	2.86205
$587$	−13085.5	−0.920098	−0.460049	−	0.887893i	$-0.652168\pi$
$587$	−13085.5	−0.920098	−0.460049	+	0.887893i	$0.652168\pi$
$588$	0	0
$589$	12171.9	0.851500
$590$	29641.4	2.06833
$591$	2157.36	0.150155
$592$	10126.5	0.703035
$593$	23194.7	1.60623	0.803114	−	0.595826i	$-0.203175\pi$
$593$	23194.7	1.60623	0.803114	+	0.595826i	$0.203175\pi$
$594$	−1397.93	−0.0965621
$595$	0	0
$596$	14606.0	1.00383
$597$	10103.4	0.692638
$598$	14341.6	0.980724
$599$	−18055.0	−1.23157	−0.615784	−	0.787915i	$-0.711161\pi$
$599$	−18055.0	−1.23157	−0.615784	+	0.787915i	$0.711161\pi$
$600$	10039.4	0.683092
$601$	−18915.5	−1.28383	−0.641913	−	0.766777i	$-0.721859\pi$
$601$	−18915.5	−1.28383	−0.641913	+	0.766777i	$0.721859\pi$
$602$	0	0
$603$	−3601.78	−0.243243
$604$	−13003.6	−0.876011
$605$	−1876.57	−0.126105
$606$	−9064.73	−0.607640
$607$	10475.4	0.700465	0.350233	−	0.936663i	$-0.386103\pi$
$607$	10475.4	0.700465	0.350233	+	0.936663i	$0.386103\pi$
$608$	5436.71	0.362644
$609$	0	0
$610$	14696.5	0.975484
$611$	−19961.1	−1.32167
$612$	−16859.6	−1.11358
$613$	−10608.4	−0.698969	−0.349485	−	0.936942i	$-0.613643\pi$
$613$	−10608.4	−0.698969	−0.349485	+	0.936942i	$0.613643\pi$
$614$	−7891.06	−0.518660
$615$	13754.5	0.901849
$616$	0	0
$617$	19793.4	1.29149	0.645747	−	0.763552i	$-0.276546\pi$
$617$	19793.4	1.29149	0.645747	+	0.763552i	$0.276546\pi$
$618$	6814.30	0.443546
$619$	−21162.0	−1.37411	−0.687054	−	0.726606i	$-0.741096\pi$
$619$	−21162.0	−1.37411	−0.687054	+	0.726606i	$0.741096\pi$
$620$	60429.9	3.91439
$621$	1212.60	0.0783575
$622$	37987.6	2.44882
$623$	0	0
$624$	4704.00	0.301780
$625$	−16719.8	−1.07007
$626$	18676.6	1.19244
$627$	1459.11	0.0929369
$628$	26059.9	1.65589
$629$	−57988.5	−3.67592
$630$	0	0
$631$	11547.4	0.728520	0.364260	−	0.931297i	$-0.381322\pi$
$631$	11547.4	0.728520	0.364260	+	0.931297i	$0.381322\pi$
$632$	−7374.65	−0.464158
$633$	−6142.99	−0.385722
$634$	28500.7	1.78534
$635$	14723.0	0.920104
$636$	10510.8	0.655315
$637$	0	0
$638$	5176.17	0.321202
$639$	3086.30	0.191067
$640$	40488.5	2.50070
$641$	−13892.7	−0.856052	−0.428026	−	0.903766i	$-0.640791\pi$
$641$	−13892.7	−0.856052	−0.428026	+	0.903766i	$0.640791\pi$
$642$	11954.2	0.734881
$643$	−7177.56	−0.440211	−0.220105	−	0.975476i	$-0.570640\pi$
$643$	−7177.56	−0.440211	−0.220105	+	0.975476i	$0.570640\pi$
$644$	0	0
$645$	10861.4	0.663051
$646$	27543.5	1.67753
$647$	−14038.7	−0.853040	−0.426520	−	0.904478i	$-0.640261\pi$
$647$	−14038.7	−0.853040	−0.426520	+	0.904478i	$0.640261\pi$
$648$	2346.39	0.142245
$649$	4466.65	0.270156
$650$	36890.5	2.22610
$651$	0	0
$652$	27820.1	1.67104
$653$	−20560.3	−1.23214	−0.616068	−	0.787693i	$-0.711275\pi$
$653$	−20560.3	−1.23214	−0.616068	+	0.787693i	$0.711275\pi$
$654$	−16656.9	−0.995927
$655$	−4304.93	−0.256805
$656$	−6832.47	−0.406651
$657$	5425.03	0.322147
$658$	0	0
$659$	−32943.6	−1.94734	−0.973672	−	0.227956i	$-0.926796\pi$
$659$	−32943.6	−1.94734	−0.973672	+	0.227956i	$0.926796\pi$
$660$	7244.09	0.427236
$661$	−1952.48	−0.114890	−0.0574452	−	0.998349i	$-0.518295\pi$
$661$	−1952.48	−0.114890	−0.0574452	+	0.998349i	$0.518295\pi$
$662$	−48595.1	−2.85302
$663$	−26937.0	−1.57790
$664$	−40218.3	−2.35056
$665$	0	0
$666$	18561.0	1.07991
$667$	−4489.93	−0.260646
$668$	−49267.5	−2.85362
$669$	18077.7	1.04473
$670$	29213.4	1.68450
$671$	2214.62	0.127413
$672$	0	0
$673$	26683.5	1.52834	0.764169	−	0.645016i	$-0.223149\pi$
$673$	26683.5	1.52834	0.764169	+	0.645016i	$0.223149\pi$
$674$	−24582.4	−1.40486
$675$	3119.13	0.177860
$676$	34053.8	1.93751
$677$	−2172.87	−0.123353	−0.0616766	−	0.998096i	$-0.519645\pi$
$677$	−2172.87	−0.123353	−0.0616766	+	0.998096i	$0.519645\pi$
$678$	−32411.8	−1.83594
$679$	0	0
$680$	59457.6	3.35308
$681$	−12909.5	−0.726424
$682$	14252.9	0.800254
$683$	−26411.7	−1.47967	−0.739835	−	0.672789i	$-0.765096\pi$
$683$	−26411.7	−1.47967	−0.739835	+	0.672789i	$0.765096\pi$
$684$	−5632.60	−0.314866
$685$	−4498.39	−0.250912
$686$	0	0
$687$	16171.0	0.898054
$688$	−5395.32	−0.298975
$689$	16793.4	0.928558
$690$	−9835.21	−0.542638
$691$	−32397.3	−1.78358	−0.891789	−	0.452451i	$-0.850550\pi$
$691$	−32397.3	−1.78358	−0.891789	+	0.452451i	$0.850550\pi$
$692$	−4163.53	−0.228719
$693$	0	0
$694$	−48.9229	−0.00267592
$695$	42211.9	2.30387
$696$	−8688.05	−0.473160
$697$	39125.5	2.12623
$698$	56930.5	3.08718
$699$	11544.7	0.624695
$700$	0	0
$701$	14515.2	0.782073	0.391037	−	0.920375i	$-0.372117\pi$
$701$	14515.2	0.782073	0.391037	+	0.920375i	$0.372117\pi$
$702$	8622.01	0.463557
$703$	−19373.3	−1.03937
$704$	8400.07	0.449701
$705$	13688.9	0.731284
$706$	−30468.8	−1.62423
$707$	0	0
$708$	−17242.6	−0.915276
$709$	−10941.7	−0.579584	−0.289792	−	0.957090i	$-0.593586\pi$
$709$	−10941.7	−0.579584	−0.289792	+	0.957090i	$0.593586\pi$
$710$	−25032.5	−1.32317
$711$	−2291.23	−0.120855
$712$	36109.4	1.90064
$713$	−12363.3	−0.649384
$714$	0	0
$715$	11574.1	0.605379
$716$	−29990.3	−1.56535
$717$	9247.23	0.481651
$718$	11264.9	0.585518
$719$	−23099.8	−1.19816	−0.599081	−	0.800688i	$-0.704467\pi$
$719$	−23099.8	−1.19816	−0.599081	+	0.800688i	$0.704467\pi$
$720$	−3225.91	−0.166976
$721$	0	0
$722$	−23082.3	−1.18980
$723$	123.893	0.00637291
$724$	29000.0	1.48864
$725$	−11549.3	−0.591628
$726$	1708.58	0.0873437
$727$	23308.8	1.18910	0.594549	−	0.804060i	$-0.297331\pi$
$727$	23308.8	1.18910	0.594549	+	0.804060i	$0.297331\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−44001.6	−2.23092
$731$	30895.9	1.56324
$732$	−8549.07	−0.431670
$733$	−22567.3	−1.13717	−0.568583	−	0.822626i	$-0.692508\pi$
$733$	−22567.3	−1.13717	−0.568583	+	0.822626i	$0.692508\pi$
$734$	6984.29	0.351219
$735$	0	0
$736$	−5522.23	−0.276566
$737$	4402.17	0.220022
$738$	−12523.3	−0.624647
$739$	7347.65	0.365748	0.182874	−	0.983136i	$-0.441460\pi$
$739$	7347.65	0.365748	0.182874	+	0.983136i	$0.441460\pi$
$740$	−96183.0	−4.77805
$741$	−8999.36	−0.446153
$742$	0	0
$743$	35081.4	1.73218	0.866091	−	0.499887i	$-0.166625\pi$
$743$	35081.4	1.73218	0.866091	+	0.499887i	$0.166625\pi$
$744$	−23923.1	−1.17885
$745$	−16003.6	−0.787016
$746$	−23903.4	−1.17314
$747$	−12495.4	−0.612026
$748$	20606.2	1.00727
$749$	0	0
$750$	2075.32	0.101040
$751$	−27031.2	−1.31343	−0.656713	−	0.754141i	$-0.728054\pi$
$751$	−27031.2	−1.31343	−0.656713	+	0.754141i	$0.728054\pi$
$752$	−6799.87	−0.329742
$753$	−13010.4	−0.629648
$754$	−31925.0	−1.54196
$755$	14247.9	0.686802
$756$	0	0
$757$	−13726.5	−0.659046	−0.329523	−	0.944147i	$-0.606888\pi$
$757$	−13726.5	−0.659046	−0.329523	+	0.944147i	$0.606888\pi$
$758$	−11079.6	−0.530908
$759$	−1482.07	−0.0708770
$760$	19864.1	0.948088
$761$	−5112.09	−0.243513	−0.121756	−	0.992560i	$-0.538853\pi$
$761$	−5112.09	−0.243513	−0.121756	+	0.992560i	$0.538853\pi$
$762$	−13405.1	−0.637291
$763$	0	0
$764$	6292.46	0.297976
$765$	18472.9	0.873058
$766$	6699.77	0.316022
$767$	−27548.9	−1.29691
$768$	−18536.7	−0.870945
$769$	12574.7	0.589668	0.294834	−	0.955549i	$-0.404736\pi$
$769$	12574.7	0.589668	0.294834	+	0.955549i	$0.404736\pi$
$770$	0	0
$771$	10412.3	0.486369
$772$	24690.5	1.15107
$773$	17482.9	0.813473	0.406736	−	0.913546i	$-0.366667\pi$
$773$	17482.9	0.813473	0.406736	+	0.913546i	$0.366667\pi$
$774$	−9889.15	−0.459248
$775$	−31801.8	−1.47401
$776$	17512.2	0.810116
$777$	0	0
$778$	−5303.23	−0.244383
$779$	13071.4	0.601196
$780$	−44679.2	−2.05099
$781$	−3772.14	−0.172827
$782$	−27976.8	−1.27934
$783$	−2699.29	−0.123199
$784$	0	0
$785$	−28553.5	−1.29824
$786$	3919.57	0.177871
$787$	23041.6	1.04364	0.521820	−	0.853056i	$-0.325253\pi$
$787$	23041.6	1.04364	0.521820	+	0.853056i	$0.325253\pi$
$788$	10178.7	0.460153
$789$	4099.74	0.184987
$790$	18583.8	0.836940
$791$	0	0
$792$	−2867.81	−0.128666
$793$	−13659.1	−0.611662
$794$	−7862.02	−0.351401
$795$	−11516.6	−0.513774
$796$	47669.2	2.12260
$797$	−31756.4	−1.41138	−0.705689	−	0.708521i	$-0.749363\pi$
$797$	−31756.4	−1.41138	−0.705689	+	0.708521i	$0.749363\pi$
$798$	0	0
$799$	38938.9	1.72410
$800$	−14204.7	−0.627763
$801$	11218.8	0.494878
$802$	9947.23	0.437966
$803$	−6630.60	−0.291393
$804$	−16993.6	−0.745422
$805$	0	0
$806$	−87907.7	−3.84171
$807$	−12647.6	−0.551693
$808$	−18596.0	−0.809658
$809$	20651.2	0.897474	0.448737	−	0.893664i	$-0.351874\pi$
$809$	20651.2	0.897474	0.448737	+	0.893664i	$0.351874\pi$
$810$	−5912.80	−0.256487
$811$	−20036.4	−0.867539	−0.433770	−	0.901024i	$-0.642817\pi$
$811$	−20036.4	−0.867539	−0.433770	+	0.901024i	$0.642817\pi$
$812$	0	0
$813$	−19814.0	−0.854745
$814$	−22685.6	−0.976819
$815$	−30482.2	−1.31012
$816$	−9176.27	−0.393669
$817$	10322.0	0.442007
$818$	−10146.0	−0.433677
$819$	0	0
$820$	64895.8	2.76373
$821$	−27570.0	−1.17199	−0.585993	−	0.810316i	$-0.699295\pi$
$821$	−27570.0	−1.17199	−0.585993	+	0.810316i	$0.699295\pi$
$822$	4095.71	0.173789
$823$	16937.3	0.717371	0.358686	−	0.933458i	$-0.383225\pi$
$823$	16937.3	0.717371	0.358686	+	0.933458i	$0.383225\pi$
$824$	13979.3	0.591010
$825$	−3812.27	−0.160880
$826$	0	0
$827$	34463.4	1.44911	0.724554	−	0.689219i	$-0.242046\pi$
$827$	34463.4	1.44911	0.724554	+	0.689219i	$0.242046\pi$
$828$	5721.21	0.240128
$829$	−9096.83	−0.381117	−0.190558	−	0.981676i	$-0.561030\pi$
$829$	−9096.83	−0.381117	−0.190558	+	0.981676i	$0.561030\pi$
$830$	101348.	4.23838
$831$	12778.8	0.533444
$832$	−51809.0	−2.15884
$833$	0	0
$834$	−38433.3	−1.59573
$835$	53981.8	2.23727
$836$	6884.29	0.284807
$837$	−7432.69	−0.306943
$838$	42487.2	1.75143
$839$	−2574.03	−0.105918	−0.0529591	−	0.998597i	$-0.516865\pi$
$839$	−2574.03	−0.105918	−0.0529591	+	0.998597i	$0.516865\pi$
$840$	0	0
$841$	−14394.2	−0.590194
$842$	−24170.0	−0.989255
$843$	−2989.10	−0.122123
$844$	−28983.4	−1.18205
$845$	−37312.3	−1.51903
$846$	−12463.6	−0.506508
$847$	0	0
$848$	5720.77	0.231665
$849$	20511.1	0.829141
$850$	−71963.7	−2.90392
$851$	19678.1	0.792662
$852$	14561.6	0.585529
$853$	−3474.93	−0.139483	−0.0697417	−	0.997565i	$-0.522218\pi$
$853$	−3474.93	−0.139483	−0.0697417	+	0.997565i	$0.522218\pi$
$854$	0	0
$855$	6171.58	0.246858
$856$	24523.6	0.979203
$857$	−32322.3	−1.28834	−0.644171	−	0.764882i	$-0.722797\pi$
$857$	−32322.3	−1.28834	−0.644171	+	0.764882i	$0.722797\pi$
$858$	−10538.0	−0.419303
$859$	16673.9	0.662290	0.331145	−	0.943580i	$-0.392565\pi$
$859$	16673.9	0.662290	0.331145	+	0.943580i	$0.392565\pi$
$860$	51245.6	2.03193
$861$	0	0
$862$	−4605.87	−0.181992
$863$	−24447.7	−0.964320	−0.482160	−	0.876083i	$-0.660148\pi$
$863$	−24447.7	−0.964320	−0.482160	+	0.876083i	$0.660148\pi$
$864$	−3319.90	−0.130724
$865$	4561.93	0.179318
$866$	50117.4	1.96658
$867$	37808.1	1.48101
$868$	0	0
$869$	2800.39	0.109317
$870$	21893.5	0.853173
$871$	−27151.2	−1.05624
$872$	−34171.0	−1.32704
$873$	5440.86	0.210934
$874$	−9346.72	−0.361736
$875$	0	0
$876$	25596.0	0.987225
$877$	18294.0	0.704385	0.352193	−	0.935928i	$-0.385436\pi$
$877$	18294.0	0.704385	0.352193	+	0.935928i	$0.385436\pi$
$878$	−68491.0	−2.63264
$879$	25877.1	0.992960
$880$	3942.78	0.151035
$881$	22197.8	0.848880	0.424440	−	0.905456i	$-0.360471\pi$
$881$	22197.8	0.848880	0.424440	+	0.905456i	$0.360471\pi$
$882$	0	0
$883$	35035.0	1.33525	0.667623	−	0.744499i	$-0.267312\pi$
$883$	35035.0	1.33525	0.667623	+	0.744499i	$0.267312\pi$
$884$	−127092.	−4.83550
$885$	18892.5	0.717587
$886$	−5975.48	−0.226580
$887$	−1711.90	−0.0648028	−0.0324014	−	0.999475i	$-0.510315\pi$
$887$	−1711.90	−0.0648028	−0.0324014	+	0.999475i	$0.510315\pi$
$888$	38077.2	1.43895
$889$	0	0
$890$	−90994.1	−3.42711
$891$	−891.000	−0.0335013
$892$	85293.1	3.20160
$893$	13009.0	0.487493
$894$	14571.0	0.545110
$895$	32860.1	1.22725
$896$	0	0
$897$	9140.92	0.340253
$898$	5268.23	0.195772
$899$	27521.3	1.02101
$900$	14716.5	0.545054
$901$	−32759.5	−1.21130
$902$	15306.3	0.565014
$903$	0	0
$904$	−66491.6	−2.44633
$905$	−31775.0	−1.16711
$906$	−12972.5	−0.475699
$907$	242.720	0.00888577	0.00444289	−	0.999990i	$-0.498586\pi$
$907$	242.720	0.00888577	0.00444289	+	0.999990i	$0.498586\pi$
$908$	−60908.9	−2.22614
$909$	−5777.59	−0.210815
$910$	0	0
$911$	46172.6	1.67922	0.839609	−	0.543192i	$-0.182784\pi$
$911$	46172.6	1.67922	0.839609	+	0.543192i	$0.182784\pi$
$912$	−3065.69	−0.111310
$913$	15272.2	0.553599
$914$	−68027.4	−2.46187
$915$	9367.12	0.338434
$916$	76297.0	2.75210
$917$	0	0
$918$	−16819.3	−0.604705
$919$	−9111.79	−0.327062	−0.163531	−	0.986538i	$-0.552288\pi$
$919$	−9111.79	−0.327062	−0.163531	+	0.986538i	$0.552288\pi$
$920$	−20176.6	−0.723046
$921$	−5029.52	−0.179944
$922$	−75860.6	−2.70969
$923$	23265.4	0.829674
$924$	0	0
$925$	50617.2	1.79923
$926$	−75918.4	−2.69420
$927$	4343.23	0.153884
$928$	12292.7	0.434835
$929$	−49677.7	−1.75444	−0.877219	−	0.480090i	$-0.840604\pi$
$929$	−49677.7	−1.75444	−0.877219	+	0.480090i	$0.840604\pi$
$930$	60285.4	2.12563
$931$	0	0
$932$	54469.5	1.91439
$933$	24212.1	0.849593
$934$	25649.1	0.898571
$935$	−22578.0	−0.789710
$936$	17687.7	0.617673
$937$	−50143.9	−1.74827	−0.874135	−	0.485683i	$-0.838571\pi$
$937$	−50143.9	−1.74827	−0.874135	+	0.485683i	$0.838571\pi$
$938$	0	0
$939$	11903.9	0.413705
$940$	64586.2	2.24103
$941$	−42313.9	−1.46588	−0.732940	−	0.680293i	$-0.761853\pi$
$941$	−42313.9	−1.46588	−0.732940	+	0.680293i	$0.761853\pi$
$942$	25997.5	0.899199
$943$	−13277.0	−0.458493
$944$	−9384.71	−0.323566
$945$	0	0
$946$	12086.7	0.415406
$947$	19240.2	0.660214	0.330107	−	0.943944i	$-0.392915\pi$
$947$	19240.2	0.660214	0.330107	+	0.943944i	$0.392915\pi$
$948$	−10810.3	−0.370362
$949$	40895.4	1.39886
$950$	−24042.3	−0.821088
$951$	18165.5	0.619407
$952$	0	0
$953$	−51728.5	−1.75829	−0.879145	−	0.476555i	$-0.841885\pi$
$953$	−51728.5	−1.75829	−0.879145	+	0.476555i	$0.841885\pi$
$954$	10485.7	0.355855
$955$	−6894.58	−0.233616
$956$	43629.6	1.47603
$957$	3299.13	0.111438
$958$	21618.6	0.729088
$959$	0	0
$960$	35529.6	1.19449
$961$	45990.7	1.54378
$962$	139918.	4.68933
$963$	7619.23	0.254960
$964$	584.541	0.0195299
$965$	−27053.1	−0.902456
$966$	0	0
$967$	34934.4	1.16175	0.580877	−	0.813991i	$-0.302710\pi$
$967$	34934.4	1.16175	0.580877	+	0.813991i	$0.302710\pi$
$968$	3505.10	0.116382
$969$	17555.4	0.582003
$970$	−44130.0	−1.46075
$971$	18710.6	0.618384	0.309192	−	0.951000i	$-0.399941\pi$
$971$	18710.6	0.618384	0.309192	+	0.951000i	$0.399941\pi$
$972$	3439.52	0.113501
$973$	0	0
$974$	49028.6	1.61291
$975$	23512.9	0.772323
$976$	−4653.05	−0.152603
$977$	6813.79	0.223124	0.111562	−	0.993757i	$-0.464415\pi$
$977$	6813.79	0.223124	0.111562	+	0.993757i	$0.464415\pi$
$978$	27753.6	0.907424
$979$	−13711.9	−0.447634
$980$	0	0
$981$	−10616.6	−0.345527
$982$	814.694	0.0264745
$983$	−13197.8	−0.428223	−0.214111	−	0.976809i	$-0.568686\pi$
$983$	−13197.8	−0.428223	−0.214111	+	0.976809i	$0.568686\pi$
$984$	−25691.1	−0.832320
$985$	−11152.7	−0.360765
$986$	62277.3	2.01147
$987$	0	0
$988$	−42460.2	−1.36724
$989$	−10484.3	−0.337090
$990$	7226.76	0.232002
$991$	52714.3	1.68973	0.844866	−	0.534979i	$-0.179680\pi$
$991$	52714.3	1.68973	0.844866	+	0.534979i	$0.179680\pi$
$992$	33848.8	1.08337
$993$	−30973.0	−0.989828
$994$	0	0
$995$	−52230.6	−1.66414
$996$	−58955.0	−1.87556
$997$	6459.25	0.205182	0.102591	−	0.994724i	$-0.467287\pi$
$997$	6459.25	0.205182	0.102591	+	0.994724i	$0.467287\pi$
$998$	−45594.1	−1.44615
$999$	11830.2	0.374666

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.4.a.bd.1.15	yes	16
7.6	odd	2		1617.4.a.bc.1.15	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1617.4.a.bc.1.15	✓	16	7.6	odd	2
1617.4.a.bd.1.15	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)

\(f(q)\)	\(=\)	\(q+4.70685 q^{2} +3.00000 q^{3} +14.1544 q^{4} -15.5088 q^{5} +14.1205 q^{6} +28.9678 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+4.70685 q^{2} +3.00000 q^{3} +14.1544 q^{4} -15.5088 q^{5} +14.1205 q^{6} +28.9678 q^{8} +9.00000 q^{9} -72.9976 q^{10} -11.0000 q^{11} +42.4632 q^{12} +67.8445 q^{13} -46.5264 q^{15} +23.1117 q^{16} -132.347 q^{17} +42.3616 q^{18} -44.2156 q^{19} -219.518 q^{20} -51.7753 q^{22} +44.9111 q^{23} +86.9033 q^{24} +115.523 q^{25} +319.334 q^{26} +27.0000 q^{27} -99.9738 q^{29} -218.993 q^{30} -275.285 q^{31} -122.959 q^{32} -33.0000 q^{33} -622.937 q^{34} +127.390 q^{36} +438.156 q^{37} -208.116 q^{38} +203.534 q^{39} -449.256 q^{40} -295.629 q^{41} -233.446 q^{43} -155.698 q^{44} -139.579 q^{45} +211.390 q^{46} -294.218 q^{47} +69.3350 q^{48} +543.751 q^{50} -397.041 q^{51} +960.298 q^{52} +247.527 q^{53} +127.085 q^{54} +170.597 q^{55} -132.647 q^{57} -470.561 q^{58} -406.059 q^{59} -658.554 q^{60} -201.329 q^{61} -1295.72 q^{62} -763.643 q^{64} -1052.19 q^{65} -155.326 q^{66} -400.197 q^{67} -1873.29 q^{68} +134.733 q^{69} +342.922 q^{71} +260.710 q^{72} +602.782 q^{73} +2062.33 q^{74} +346.570 q^{75} -625.845 q^{76} +958.001 q^{78} -254.581 q^{79} -358.434 q^{80} +81.0000 q^{81} -1391.48 q^{82} -1388.38 q^{83} +2052.54 q^{85} -1098.79 q^{86} -299.921 q^{87} -318.645 q^{88} +1246.54 q^{89} -656.978 q^{90} +635.690 q^{92} -825.854 q^{93} -1384.84 q^{94} +685.732 q^{95} -368.877 q^{96} +604.540 q^{97} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 48 q^{3} + 72 q^{4} - 12 q^{6} - 66 q^{8} + 144 q^{9}+O(q^{10}) \) 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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Database

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