LMFDB - Embedded newform 1617.4.a.bd.1.2

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			1.2
Root			$5.02984$ 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)

$f(q)$	$=$	$q-5.02984 q^{2} +3.00000 q^{3} +17.2993 q^{4} +20.5790 q^{5} -15.0895 q^{6} -46.7737 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-5.02984 q^{2} +3.00000 q^{3} +17.2993 q^{4} +20.5790 q^{5} -15.0895 q^{6} -46.7737 q^{8} +9.00000 q^{9} -103.509 q^{10} -11.0000 q^{11} +51.8978 q^{12} -18.2899 q^{13} +61.7371 q^{15} +96.8701 q^{16} -86.6276 q^{17} -45.2685 q^{18} -143.051 q^{19} +356.002 q^{20} +55.3282 q^{22} -12.1189 q^{23} -140.321 q^{24} +298.497 q^{25} +91.9952 q^{26} +27.0000 q^{27} +28.5844 q^{29} -310.527 q^{30} -162.953 q^{31} -113.051 q^{32} -33.0000 q^{33} +435.723 q^{34} +155.693 q^{36} +207.547 q^{37} +719.522 q^{38} -54.8697 q^{39} -962.557 q^{40} +183.705 q^{41} -45.4598 q^{43} -190.292 q^{44} +185.211 q^{45} +60.9562 q^{46} -149.035 q^{47} +290.610 q^{48} -1501.39 q^{50} -259.883 q^{51} -316.402 q^{52} +521.651 q^{53} -135.806 q^{54} -226.369 q^{55} -429.152 q^{57} -143.775 q^{58} -765.965 q^{59} +1068.01 q^{60} -42.4367 q^{61} +819.629 q^{62} -206.333 q^{64} -376.389 q^{65} +165.985 q^{66} +92.3880 q^{67} -1498.59 q^{68} -36.3568 q^{69} -906.634 q^{71} -420.963 q^{72} +1023.29 q^{73} -1043.93 q^{74} +895.490 q^{75} -2474.67 q^{76} +275.986 q^{78} -130.380 q^{79} +1993.49 q^{80} +81.0000 q^{81} -924.008 q^{82} -1204.49 q^{83} -1782.71 q^{85} +228.655 q^{86} +85.7532 q^{87} +514.511 q^{88} +358.416 q^{89} -931.582 q^{90} -209.648 q^{92} -488.860 q^{93} +749.620 q^{94} -2943.85 q^{95} -339.153 q^{96} -1453.73 q^{97} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.02984	−1.77832	−0.889158	−	0.457601i	$-0.848709\pi$
$2$	−5.02984	−1.77832	−0.889158	+	0.457601i	$0.848709\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	17.2993	2.16241
$5$	20.5790	1.84064	0.920322	−	0.391161i	$-0.127926\pi$
$5$	20.5790	1.84064	0.920322	+	0.391161i	$0.127926\pi$
$6$	−15.0895	−1.02671
$7$	0	0
$7$	0	0
$8$	−46.7737	−2.06713
$9$	9.00000	0.333333
$10$	−103.509	−3.27325
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	51.8978	1.24847
$13$	−18.2899	−0.390208	−0.195104	−	0.980783i	$-0.562504\pi$
$13$	−18.2899	−0.390208	−0.195104	+	0.980783i	$0.562504\pi$
$14$	0	0
$15$	61.7371	1.06270
$16$	96.8701	1.51359
$17$	−86.6276	−1.23590	−0.617950	−	0.786218i	$-0.712036\pi$
$17$	−86.6276	−1.23590	−0.617950	+	0.786218i	$0.712036\pi$
$18$	−45.2685	−0.592772
$19$	−143.051	−1.72727	−0.863634	−	0.504120i	$-0.831817\pi$
$19$	−143.051	−1.72727	−0.863634	+	0.504120i	$0.831817\pi$
$20$	356.002	3.98022
$21$	0	0
$22$	55.3282	0.536182
$23$	−12.1189	−0.109868	−0.0549341	−	0.998490i	$-0.517495\pi$
$23$	−12.1189	−0.109868	−0.0549341	+	0.998490i	$0.517495\pi$
$24$	−140.321	−1.19346
$25$	298.497	2.38797
$26$	91.9952	0.693914
$27$	27.0000	0.192450
$28$	0	0
$29$	28.5844	0.183034	0.0915171	−	0.995804i	$-0.470828\pi$
$29$	28.5844	0.183034	0.0915171	+	0.995804i	$0.470828\pi$
$30$	−310.527	−1.88981
$31$	−162.953	−0.944107	−0.472053	−	0.881570i	$-0.656487\pi$
$31$	−162.953	−0.944107	−0.472053	+	0.881570i	$0.656487\pi$
$32$	−113.051	−0.624524
$33$	−33.0000	−0.174078
$34$	435.723	2.19782
$35$	0	0
$36$	155.693	0.720802
$37$	207.547	0.922175	0.461088	−	0.887355i	$-0.347459\pi$
$37$	207.547	0.922175	0.461088	+	0.887355i	$0.347459\pi$
$38$	719.522	3.07163
$39$	−54.8697	−0.225287
$40$	−962.557	−3.80484
$41$	183.705	0.699755	0.349878	−	0.936795i	$-0.386223\pi$
$41$	183.705	0.699755	0.349878	+	0.936795i	$0.386223\pi$
$42$	0	0
$43$	−45.4598	−0.161222	−0.0806111	−	0.996746i	$-0.525687\pi$
$43$	−45.4598	−0.161222	−0.0806111	+	0.996746i	$0.525687\pi$
$44$	−190.292	−0.651990
$45$	185.211	0.613548
$46$	60.9562	0.195380
$47$	−149.035	−0.462531	−0.231265	−	0.972891i	$-0.574287\pi$
$47$	−149.035	−0.462531	−0.231265	+	0.972891i	$0.574287\pi$
$48$	290.610	0.873874
$49$	0	0
$50$	−1501.39	−4.24657
$51$	−259.883	−0.713547
$52$	−316.402	−0.843789
$53$	521.651	1.35197	0.675984	−	0.736917i	$-0.263719\pi$
$53$	521.651	1.35197	0.675984	+	0.736917i	$0.263719\pi$
$54$	−135.806	−0.342237
$55$	−226.369	−0.554975
$56$	0	0
$57$	−429.152	−0.997238
$58$	−143.775	−0.325493
$59$	−765.965	−1.69017	−0.845086	−	0.534630i	$-0.820451\pi$
$59$	−765.965	−1.69017	−0.845086	+	0.534630i	$0.820451\pi$
$60$	1068.01	2.29798
$61$	−42.4367	−0.0890732	−0.0445366	−	0.999008i	$-0.514181\pi$
$61$	−42.4367	−0.0890732	−0.0445366	+	0.999008i	$0.514181\pi$
$62$	819.629	1.67892
$63$	0	0
$64$	−206.333	−0.402994
$65$	−376.389	−0.718235
$66$	165.985	0.309565
$67$	92.3880	0.168463	0.0842313	−	0.996446i	$-0.473157\pi$
$67$	92.3880	0.168463	0.0842313	+	0.996446i	$0.473157\pi$
$68$	−1498.59	−2.67252
$69$	−36.3568	−0.0634325
$70$	0	0
$71$	−906.634	−1.51546	−0.757730	−	0.652568i	$-0.773692\pi$
$71$	−906.634	−1.51546	−0.757730	+	0.652568i	$0.773692\pi$
$72$	−420.963	−0.689042
$73$	1023.29	1.64064	0.820321	−	0.571904i	$-0.193795\pi$
$73$	1023.29	1.64064	0.820321	+	0.571904i	$0.193795\pi$
$74$	−1043.93	−1.63992
$75$	895.490	1.37870
$76$	−2474.67	−3.73505
$77$	0	0
$78$	275.986	0.400631
$79$	−130.380	−0.185682	−0.0928410	−	0.995681i	$-0.529595\pi$
$79$	−130.380	−0.185682	−0.0928410	+	0.995681i	$0.529595\pi$
$80$	1993.49	2.78599
$81$	81.0000	0.111111
$82$	−924.008	−1.24439
$83$	−1204.49	−1.59289	−0.796447	−	0.604709i	$-0.793290\pi$
$83$	−1204.49	−1.59289	−0.796447	+	0.604709i	$0.793290\pi$
$84$	0	0
$85$	−1782.71	−2.27485
$86$	228.655	0.286704
$87$	85.7532	0.105675
$88$	514.511	0.623262
$89$	358.416	0.426877	0.213439	−	0.976956i	$-0.431534\pi$
$89$	358.416	0.426877	0.213439	+	0.976956i	$0.431534\pi$
$90$	−931.582	−1.09108
$91$	0	0
$92$	−209.648	−0.237580
$93$	−488.860	−0.545080
$94$	749.620	0.822526
$95$	−2943.85	−3.17929
$96$	−339.153	−0.360569
$97$	−1453.73	−1.52169	−0.760846	−	0.648932i	$-0.775216\pi$
$97$	−1453.73	−1.52169	−0.760846	+	0.648932i	$0.775216\pi$
$98$	0	0
$99$	−99.0000	−0.100504
$100$	5163.77	5.16377
$101$	−1151.04	−1.13398	−0.566992	−	0.823723i	$-0.691893\pi$
$101$	−1151.04	−1.13398	−0.566992	+	0.823723i	$0.691893\pi$
$102$	1307.17	1.26891
$103$	−1476.37	−1.41234	−0.706169	−	0.708043i	$-0.749578\pi$
$103$	−1476.37	−1.41234	−0.706169	+	0.708043i	$0.749578\pi$
$104$	855.487	0.806609
$105$	0	0
$106$	−2623.82	−2.40422
$107$	−2082.25	−1.88130	−0.940650	−	0.339379i	$-0.889783\pi$
$107$	−2082.25	−1.88130	−0.940650	+	0.339379i	$0.889783\pi$
$108$	467.080	0.416155
$109$	798.053	0.701281	0.350641	−	0.936510i	$-0.385964\pi$
$109$	798.053	0.701281	0.350641	+	0.936510i	$0.385964\pi$
$110$	1138.60	0.986921
$111$	622.640	0.532418
$112$	0	0
$113$	1394.94	1.16128	0.580642	−	0.814159i	$-0.302801\pi$
$113$	1394.94	1.16128	0.580642	+	0.814159i	$0.302801\pi$
$114$	2158.56	1.77340
$115$	−249.396	−0.202228
$116$	494.489	0.395794
$117$	−164.609	−0.130069
$118$	3852.68	3.00566
$119$	0	0
$120$	−2887.67	−2.19673
$121$	121.000	0.0909091
$122$	213.450	0.158400
$123$	551.116	0.404004
$124$	−2818.97	−2.04154
$125$	3570.39	2.55476
$126$	0	0
$127$	−82.0168	−0.0573056	−0.0286528	−	0.999589i	$-0.509122\pi$
$127$	−82.0168	−0.0573056	−0.0286528	+	0.999589i	$0.509122\pi$
$128$	1942.23	1.34117
$129$	−136.379	−0.0930817
$130$	1893.17	1.27725
$131$	2314.70	1.54379	0.771894	−	0.635751i	$-0.219309\pi$
$131$	2314.70	1.54379	0.771894	+	0.635751i	$0.219309\pi$
$132$	−570.875	−0.376427
$133$	0	0
$134$	−464.696	−0.299580
$135$	555.634	0.354232
$136$	4051.89	2.55476
$137$	−823.763	−0.513714	−0.256857	−	0.966449i	$-0.582687\pi$
$137$	−823.763	−0.513714	−0.256857	+	0.966449i	$0.582687\pi$
$138$	182.869	0.112803
$139$	157.067	0.0958433	0.0479216	−	0.998851i	$-0.484740\pi$
$139$	157.067	0.0958433	0.0479216	+	0.998851i	$0.484740\pi$
$140$	0	0
$141$	−447.104	−0.267042
$142$	4560.22	2.69497
$143$	201.189	0.117652
$144$	871.830	0.504532
$145$	588.239	0.336901
$146$	−5146.97	−2.91758
$147$	0	0
$148$	3590.40	1.99412
$149$	−2552.91	−1.40364	−0.701821	−	0.712353i	$-0.747629\pi$
$149$	−2552.91	−1.40364	−0.701821	+	0.712353i	$0.747629\pi$
$150$	−4504.17	−2.45176
$151$	2284.71	1.23131	0.615653	−	0.788018i	$-0.288892\pi$
$151$	2284.71	1.23131	0.615653	+	0.788018i	$0.288892\pi$
$152$	6691.01	3.57048
$153$	−779.649	−0.411966
$154$	0	0
$155$	−3353.42	−1.73776
$156$	−949.205	−0.487162
$157$	3428.57	1.74286	0.871431	−	0.490518i	$-0.163192\pi$
$157$	3428.57	1.74286	0.871431	+	0.490518i	$0.163192\pi$
$158$	655.789	0.330201
$159$	1564.95	0.780559
$160$	−2326.48	−1.14953
$161$	0	0
$162$	−407.417	−0.197591
$163$	−2074.07	−0.996648	−0.498324	−	0.866991i	$-0.666051\pi$
$163$	−2074.07	−0.996648	−0.498324	+	0.866991i	$0.666051\pi$
$164$	3177.97	1.51316
$165$	−679.108	−0.320415
$166$	6058.40	2.83267
$167$	−2579.55	−1.19528	−0.597640	−	0.801764i	$-0.703895\pi$
$167$	−2579.55	−1.19528	−0.597640	+	0.801764i	$0.703895\pi$
$168$	0	0
$169$	−1862.48	−0.847737
$170$	8966.75	4.04540
$171$	−1287.46	−0.575756
$172$	−786.421	−0.348628
$173$	−3757.33	−1.65124	−0.825620	−	0.564227i	$-0.809174\pi$
$173$	−3757.33	−1.65124	−0.825620	+	0.564227i	$0.809174\pi$
$174$	−431.325	−0.187923
$175$	0	0
$176$	−1065.57	−0.456366
$177$	−2297.90	−0.975822
$178$	−1802.78	−0.759122
$179$	−485.487	−0.202721	−0.101360	−	0.994850i	$-0.532319\pi$
$179$	−485.487	−0.202721	−0.101360	+	0.994850i	$0.532319\pi$
$180$	3204.02	1.32674
$181$	3548.76	1.45733	0.728666	−	0.684869i	$-0.240141\pi$
$181$	3548.76	1.45733	0.728666	+	0.684869i	$0.240141\pi$
$182$	0	0
$183$	−127.310	−0.0514264
$184$	566.847	0.227111
$185$	4271.11	1.69740
$186$	2458.89	0.969325
$187$	952.904	0.372638
$188$	−2578.19	−1.00018
$189$	0	0
$190$	14807.1	5.65377
$191$	−3096.85	−1.17320	−0.586598	−	0.809879i	$-0.699533\pi$
$191$	−3096.85	−1.17320	−0.586598	+	0.809879i	$0.699533\pi$
$192$	−618.999	−0.232669
$193$	−833.551	−0.310882	−0.155441	−	0.987845i	$-0.549680\pi$
$193$	−833.551	−0.310882	−0.155441	+	0.987845i	$0.549680\pi$
$194$	7312.04	2.70605
$195$	−1129.17	−0.414673
$196$	0	0
$197$	−3560.13	−1.28756	−0.643778	−	0.765212i	$-0.722634\pi$
$197$	−3560.13	−1.28756	−0.643778	+	0.765212i	$0.722634\pi$
$198$	497.954	0.178727
$199$	2897.85	1.03228	0.516138	−	0.856506i	$-0.327369\pi$
$199$	2897.85	1.03228	0.516138	+	0.856506i	$0.327369\pi$
$200$	−13961.8	−4.93624
$201$	277.164	0.0972619
$202$	5789.52	2.01658
$203$	0	0
$204$	−4495.78	−1.54298
$205$	3780.48	1.28800
$206$	7425.89	2.51158
$207$	−109.070	−0.0366227
$208$	−1771.74	−0.590617
$209$	1573.56	0.520791
$210$	0	0
$211$	1504.70	0.490938	0.245469	−	0.969404i	$-0.421058\pi$
$211$	1504.70	0.490938	0.245469	+	0.969404i	$0.421058\pi$
$212$	9024.17	2.92350
$213$	−2719.90	−0.874952
$214$	10473.4	3.34554
$215$	−935.519	−0.296753
$216$	−1262.89	−0.397818
$217$	0	0
$218$	−4014.08	−1.24710
$219$	3069.86	0.947225
$220$	−3916.02	−1.20008
$221$	1584.41	0.482258
$222$	−3131.78	−0.946807
$223$	−4158.67	−1.24881	−0.624406	−	0.781100i	$-0.714659\pi$
$223$	−4158.67	−1.24881	−0.624406	+	0.781100i	$0.714659\pi$
$224$	0	0
$225$	2686.47	0.795991
$226$	−7016.33	−2.06513
$227$	476.653	0.139368	0.0696840	−	0.997569i	$-0.477801\pi$
$227$	476.653	0.139368	0.0696840	+	0.997569i	$0.477801\pi$
$228$	−7424.01	−2.15643
$229$	−6692.61	−1.93127	−0.965633	−	0.259909i	$-0.916308\pi$
$229$	−6692.61	−1.93127	−0.965633	+	0.259909i	$0.916308\pi$
$230$	1254.42	0.359626
$231$	0	0
$232$	−1337.00	−0.378355
$233$	−2383.77	−0.670240	−0.335120	−	0.942175i	$-0.608777\pi$
$233$	−2383.77	−0.670240	−0.335120	+	0.942175i	$0.608777\pi$
$234$	827.957	0.231305
$235$	−3066.99	−0.851355
$236$	−13250.6	−3.65484
$237$	−391.139	−0.107204
$238$	0	0
$239$	7096.75	1.92071	0.960357	−	0.278774i	$-0.0899282\pi$
$239$	7096.75	1.92071	0.960357	+	0.278774i	$0.0899282\pi$
$240$	5980.48	1.60849
$241$	82.4722	0.0220436	0.0110218	−	0.999939i	$-0.496492\pi$
$241$	82.4722	0.0220436	0.0110218	+	0.999939i	$0.496492\pi$
$242$	−608.610	−0.161665
$243$	243.000	0.0641500
$244$	−734.123	−0.192612
$245$	0	0
$246$	−2772.02	−0.718446
$247$	2616.38	0.673994
$248$	7621.94	1.95159
$249$	−3613.48	−0.919657
$250$	−17958.5	−4.54318
$251$	−5840.60	−1.46875	−0.734373	−	0.678746i	$-0.762524\pi$
$251$	−5840.60	−1.46875	−0.734373	+	0.678746i	$0.762524\pi$
$252$	0	0
$253$	133.308	0.0331265
$254$	412.531	0.101907
$255$	−5348.14	−1.31339
$256$	−8118.43	−1.98204
$257$	−7094.46	−1.72195	−0.860973	−	0.508650i	$-0.830145\pi$
$257$	−7094.46	−1.72195	−0.860973	+	0.508650i	$0.830145\pi$
$258$	685.966	0.165529
$259$	0	0
$260$	−6511.24	−1.55312
$261$	257.260	0.0610114
$262$	−11642.6	−2.74534
$263$	2435.01	0.570909	0.285454	−	0.958392i	$-0.407856\pi$
$263$	2435.01	0.570909	0.285454	+	0.958392i	$0.407856\pi$
$264$	1543.53	0.359840
$265$	10735.1	2.48849
$266$	0	0
$267$	1075.25	0.246458
$268$	1598.24	0.364284
$269$	1533.28	0.347532	0.173766	−	0.984787i	$-0.444406\pi$
$269$	1533.28	0.347532	0.173766	+	0.984787i	$0.444406\pi$
$270$	−2794.75	−0.629937
$271$	4518.93	1.01294	0.506468	−	0.862259i	$-0.330951\pi$
$271$	4518.93	1.01294	0.506468	+	0.862259i	$0.330951\pi$
$272$	−8391.62	−1.87065
$273$	0	0
$274$	4143.40	0.913546
$275$	−3283.46	−0.720001
$276$	−628.945	−0.137167
$277$	1098.94	0.238370	0.119185	−	0.992872i	$-0.461972\pi$
$277$	1098.94	0.238370	0.119185	+	0.992872i	$0.461972\pi$
$278$	−790.019	−0.170440
$279$	−1466.58	−0.314702
$280$	0	0
$281$	−1401.09	−0.297444	−0.148722	−	0.988879i	$-0.547516\pi$
$281$	−1401.09	−0.297444	−0.148722	+	0.988879i	$0.547516\pi$
$282$	2248.86	0.474885
$283$	−3317.26	−0.696787	−0.348393	−	0.937348i	$-0.613273\pi$
$283$	−3317.26	−0.696787	−0.348393	+	0.937348i	$0.613273\pi$
$284$	−15684.1	−3.27704
$285$	−8831.54	−1.83556
$286$	−1011.95	−0.209223
$287$	0	0
$288$	−1017.46	−0.208175
$289$	2591.35	0.527447
$290$	−2958.75	−0.599116
$291$	−4361.20	−0.878549
$292$	17702.1	3.54773
$293$	−6312.79	−1.25869	−0.629347	−	0.777124i	$-0.716678\pi$
$293$	−6312.79	−1.25869	−0.629347	+	0.777124i	$0.716678\pi$
$294$	0	0
$295$	−15762.8	−3.11101
$296$	−9707.73	−1.90625
$297$	−297.000	−0.0580259
$298$	12840.7	2.49612
$299$	221.654	0.0428715
$300$	15491.3	2.98130
$301$	0	0
$302$	−11491.7	−2.18965
$303$	−3453.11	−0.654706
$304$	−13857.3	−2.61438
$305$	−873.306	−0.163952
$306$	3921.50	0.732606
$307$	6448.97	1.19890	0.599450	−	0.800412i	$-0.295386\pi$
$307$	6448.97	1.19890	0.599450	+	0.800412i	$0.295386\pi$
$308$	0	0
$309$	−4429.10	−0.815414
$310$	16867.2	3.09029
$311$	−2884.59	−0.525948	−0.262974	−	0.964803i	$-0.584703\pi$
$311$	−2884.59	−0.525948	−0.262974	+	0.964803i	$0.584703\pi$
$312$	2566.46	0.465696
$313$	−3689.24	−0.666224	−0.333112	−	0.942887i	$-0.608099\pi$
$313$	−3689.24	−0.666224	−0.333112	+	0.942887i	$0.608099\pi$
$314$	−17245.1	−3.09936
$315$	0	0
$316$	−2255.47	−0.401520
$317$	−2177.66	−0.385835	−0.192918	−	0.981215i	$-0.561795\pi$
$317$	−2177.66	−0.385835	−0.192918	+	0.981215i	$0.561795\pi$
$318$	−7871.46	−1.38808
$319$	−314.428	−0.0551869
$320$	−4246.14	−0.741769
$321$	−6246.76	−1.08617
$322$	0	0
$323$	12392.1	2.13473
$324$	1401.24	0.240267
$325$	−5459.47	−0.931807
$326$	10432.2	1.77235
$327$	2394.16	0.404885
$328$	−8592.58	−1.44648
$329$	0	0
$330$	3415.80	0.569799
$331$	5184.27	0.860886	0.430443	−	0.902618i	$-0.358357\pi$
$331$	5184.27	0.860886	0.430443	+	0.902618i	$0.358357\pi$
$332$	−20836.8	−3.44448
$333$	1867.92	0.307392
$334$	12974.7	2.12559
$335$	1901.26	0.310080
$336$	0	0
$337$	3138.19	0.507265	0.253633	−	0.967301i	$-0.418375\pi$
$337$	3138.19	0.507265	0.253633	+	0.967301i	$0.418375\pi$
$338$	9367.96	1.50754
$339$	4184.83	0.670468
$340$	−30839.6	−4.91915
$341$	1792.49	0.284659
$342$	6475.69	1.02388
$343$	0	0
$344$	2126.32	0.333267
$345$	−748.187	−0.116757
$346$	18898.8	2.93643
$347$	7443.34	1.15153	0.575763	−	0.817617i	$-0.304705\pi$
$347$	7443.34	1.15153	0.575763	+	0.817617i	$0.304705\pi$
$348$	1483.47	0.228512
$349$	−7219.51	−1.10731	−0.553656	−	0.832746i	$-0.686768\pi$
$349$	−7219.51	−1.10731	−0.553656	+	0.832746i	$0.686768\pi$
$350$	0	0
$351$	−493.828	−0.0750956
$352$	1243.56	0.188301
$353$	−11342.1	−1.71014	−0.855072	−	0.518509i	$-0.826487\pi$
$353$	−11342.1	−1.71014	−0.855072	+	0.518509i	$0.826487\pi$
$354$	11558.0	1.73532
$355$	−18657.7	−2.78942
$356$	6200.34	0.923082
$357$	0	0
$358$	2441.92	0.360501
$359$	−1723.67	−0.253404	−0.126702	−	0.991941i	$-0.540439\pi$
$359$	−1723.67	−0.253404	−0.126702	+	0.991941i	$0.540439\pi$
$360$	−8663.02	−1.26828
$361$	13604.5	1.98345
$362$	−17849.7	−2.59160
$363$	363.000	0.0524864
$364$	0	0
$365$	21058.3	3.01984
$366$	640.349	0.0914524
$367$	145.376	0.0206772	0.0103386	−	0.999947i	$-0.496709\pi$
$367$	145.376	0.0206772	0.0103386	+	0.999947i	$0.496709\pi$
$368$	−1173.96	−0.166296
$369$	1653.35	0.233252
$370$	−21483.0	−3.01851
$371$	0	0
$372$	−8456.92	−1.17868
$373$	−1998.45	−0.277415	−0.138708	−	0.990333i	$-0.544295\pi$
$373$	−1998.45	−0.277415	−0.138708	+	0.990333i	$0.544295\pi$
$374$	−4792.95	−0.662667
$375$	10711.2	1.47499
$376$	6970.91	0.956109
$377$	−522.806	−0.0714215
$378$	0	0
$379$	2233.44	0.302702	0.151351	−	0.988480i	$-0.451638\pi$
$379$	2233.44	0.302702	0.151351	+	0.988480i	$0.451638\pi$
$380$	−50926.3	−6.87491
$381$	−246.050	−0.0330854
$382$	15576.7	2.08631
$383$	2747.22	0.366517	0.183259	−	0.983065i	$-0.441335\pi$
$383$	2747.22	0.366517	0.183259	+	0.983065i	$0.441335\pi$
$384$	5826.69	0.774328
$385$	0	0
$386$	4192.62	0.552847
$387$	−409.138	−0.0537408
$388$	−25148.5	−3.29052
$389$	−896.312	−0.116825	−0.0584124	−	0.998293i	$-0.518604\pi$
$389$	−896.312	−0.116825	−0.0584124	+	0.998293i	$0.518604\pi$
$390$	5679.52	0.737420
$391$	1049.83	0.135786
$392$	0	0
$393$	6944.10	0.891307
$394$	17906.9	2.28968
$395$	−2683.09	−0.341774
$396$	−1712.63	−0.217330
$397$	2449.67	0.309686	0.154843	−	0.987939i	$-0.450513\pi$
$397$	2449.67	0.309686	0.154843	+	0.987939i	$0.450513\pi$
$398$	−14575.7	−1.83571
$399$	0	0
$400$	28915.4	3.61442
$401$	−8110.23	−1.00999	−0.504994	−	0.863123i	$-0.668505\pi$
$401$	−8110.23	−1.00999	−0.504994	+	0.863123i	$0.668505\pi$
$402$	−1394.09	−0.172962
$403$	2980.40	0.368398
$404$	−19912.1	−2.45213
$405$	1666.90	0.204516
$406$	0	0
$407$	−2283.01	−0.278046
$408$	12155.7	1.47499
$409$	−4907.08	−0.593250	−0.296625	−	0.954994i	$-0.595861\pi$
$409$	−4907.08	−0.593250	−0.296625	+	0.954994i	$0.595861\pi$
$410$	−19015.2	−2.29047
$411$	−2471.29	−0.296593
$412$	−25540.1	−3.05405
$413$	0	0
$414$	548.606	0.0651268
$415$	−24787.3	−2.93195
$416$	2067.69	0.243694
$417$	471.200	0.0553351
$418$	−7914.74	−0.926130
$419$	6291.63	0.733571	0.366785	−	0.930306i	$-0.380458\pi$
$419$	6291.63	0.733571	0.366785	+	0.930306i	$0.380458\pi$
$420$	0	0
$421$	4847.20	0.561136	0.280568	−	0.959834i	$-0.409477\pi$
$421$	4847.20	0.561136	0.280568	+	0.959834i	$0.409477\pi$
$422$	−7568.40	−0.873043
$423$	−1341.31	−0.154177
$424$	−24399.5	−2.79469
$425$	−25858.0	−2.95129
$426$	13680.7	1.55594
$427$	0	0
$428$	−36021.4	−4.06813
$429$	603.567	0.0679266
$430$	4705.51	0.527720
$431$	13021.6	1.45529	0.727646	−	0.685953i	$-0.240614\pi$
$431$	13021.6	1.45529	0.727646	+	0.685953i	$0.240614\pi$
$432$	2615.49	0.291291
$433$	1744.24	0.193586	0.0967932	−	0.995305i	$-0.469141\pi$
$433$	1744.24	0.193586	0.0967932	+	0.995305i	$0.469141\pi$
$434$	0	0
$435$	1764.72	0.194510
$436$	13805.7	1.51645
$437$	1733.62	0.189772
$438$	−15440.9	−1.68446
$439$	13365.1	1.45303	0.726514	−	0.687151i	$-0.241139\pi$
$439$	13365.1	1.45303	0.726514	+	0.687151i	$0.241139\pi$
$440$	10588.1	1.14720
$441$	0	0
$442$	−7969.33	−0.857607
$443$	−3746.03	−0.401759	−0.200879	−	0.979616i	$-0.564380\pi$
$443$	−3746.03	−0.401759	−0.200879	+	0.979616i	$0.564380\pi$
$444$	10771.2	1.15130
$445$	7375.86	0.785729
$446$	20917.4	2.22078
$447$	−7658.73	−0.810393
$448$	0	0
$449$	1043.37	0.109665	0.0548326	−	0.998496i	$-0.482537\pi$
$449$	1043.37	0.109665	0.0548326	+	0.998496i	$0.482537\pi$
$450$	−13512.5	−1.41552
$451$	−2020.76	−0.210984
$452$	24131.5	2.51117
$453$	6854.13	0.710894
$454$	−2397.48	−0.247840
$455$	0	0
$456$	20073.0	2.06142
$457$	8375.86	0.857344	0.428672	−	0.903460i	$-0.358982\pi$
$457$	8375.86	0.857344	0.428672	+	0.903460i	$0.358982\pi$
$458$	33662.7	3.43440
$459$	−2338.95	−0.237849
$460$	−4314.36	−0.437300
$461$	3960.34	0.400112	0.200056	−	0.979784i	$-0.435888\pi$
$461$	3960.34	0.400112	0.200056	+	0.979784i	$0.435888\pi$
$462$	0	0
$463$	−5845.21	−0.586717	−0.293359	−	0.956002i	$-0.594773\pi$
$463$	−5845.21	−0.586717	−0.293359	+	0.956002i	$0.594773\pi$
$464$	2768.97	0.277040
$465$	−10060.3	−1.00330
$466$	11990.0	1.19190
$467$	11879.2	1.17710	0.588550	−	0.808461i	$-0.299699\pi$
$467$	11879.2	1.17710	0.588550	+	0.808461i	$0.299699\pi$
$468$	−2847.62	−0.281263
$469$	0	0
$470$	15426.5	1.51398
$471$	10285.7	1.00624
$472$	35827.0	3.49380
$473$	500.058	0.0486104
$474$	1967.37	0.190642
$475$	−42700.1	−4.12467
$476$	0	0
$477$	4694.86	0.450656
$478$	−35695.5	−3.41563
$479$	740.548	0.0706399	0.0353199	−	0.999376i	$-0.488755\pi$
$479$	740.548	0.0706399	0.0353199	+	0.999376i	$0.488755\pi$
$480$	−6979.43	−0.663679
$481$	−3796.01	−0.359840
$482$	−414.822	−0.0392005
$483$	0	0
$484$	2093.21	0.196582
$485$	−29916.4	−2.80089
$486$	−1222.25	−0.114079
$487$	6885.87	0.640716	0.320358	−	0.947297i	$-0.396197\pi$
$487$	6885.87	0.640716	0.320358	+	0.947297i	$0.396197\pi$
$488$	1984.92	0.184125
$489$	−6222.21	−0.575415
$490$	0	0
$491$	−10559.5	−0.970560	−0.485280	−	0.874359i	$-0.661282\pi$
$491$	−10559.5	−0.970560	−0.485280	+	0.874359i	$0.661282\pi$
$492$	9533.90	0.873621
$493$	−2476.20	−0.226212
$494$	−13160.0	−1.19857
$495$	−2037.32	−0.184992
$496$	−15785.3	−1.42899
$497$	0	0
$498$	18175.2	1.63544
$499$	−11854.8	−1.06351	−0.531757	−	0.846897i	$-0.678468\pi$
$499$	−11854.8	−1.06351	−0.531757	+	0.846897i	$0.678468\pi$
$500$	61765.1	5.52444
$501$	−7738.66	−0.690096
$502$	29377.2	2.61189
$503$	−8185.46	−0.725590	−0.362795	−	0.931869i	$-0.618177\pi$
$503$	−8185.46	−0.725590	−0.362795	+	0.931869i	$0.618177\pi$
$504$	0	0
$505$	−23687.2	−2.08726
$506$	−670.518	−0.0589094
$507$	−5587.44	−0.489441
$508$	−1418.83	−0.123918
$509$	11068.0	0.963811	0.481905	−	0.876223i	$-0.339945\pi$
$509$	11068.0	0.963811	0.481905	+	0.876223i	$0.339945\pi$
$510$	26900.3	2.33561
$511$	0	0
$512$	25296.5	2.18351
$513$	−3862.37	−0.332413
$514$	35684.0	3.06216
$515$	−30382.2	−2.59961
$516$	−2359.26	−0.201281
$517$	1639.38	0.139458
$518$	0	0
$519$	−11272.0	−0.953344
$520$	17605.1	1.48468
$521$	5800.83	0.487791	0.243895	−	0.969802i	$-0.421575\pi$
$521$	5800.83	0.487791	0.243895	+	0.969802i	$0.421575\pi$
$522$	−1293.97	−0.108498
$523$	11203.0	0.936662	0.468331	−	0.883553i	$-0.344855\pi$
$523$	11203.0	0.936662	0.468331	+	0.883553i	$0.344855\pi$
$524$	40042.6	3.33830
$525$	0	0
$526$	−12247.7	−1.01526
$527$	14116.3	1.16682
$528$	−3196.71	−0.263483
$529$	−12020.1	−0.987929
$530$	−53995.6	−4.42532
$531$	−6893.69	−0.563391
$532$	0	0
$533$	−3359.96	−0.273050
$534$	−5408.33	−0.438279
$535$	−42850.8	−3.46280
$536$	−4321.33	−0.348233
$537$	−1456.46	−0.117041
$538$	−7712.17	−0.618021
$539$	0	0
$540$	9612.05	0.765994
$541$	3991.68	0.317219	0.158610	−	0.987341i	$-0.449299\pi$
$541$	3991.68	0.317219	0.158610	+	0.987341i	$0.449299\pi$
$542$	−22729.5	−1.80132
$543$	10646.3	0.841391
$544$	9793.33	0.771848
$545$	16423.2	1.29081
$546$	0	0
$547$	−15237.0	−1.19102	−0.595508	−	0.803349i	$-0.703049\pi$
$547$	−15237.0	−1.19102	−0.595508	+	0.803349i	$0.703049\pi$
$548$	−14250.5	−1.11086
$549$	−381.930	−0.0296911
$550$	16515.3	1.28039
$551$	−4089.02	−0.316149
$552$	1700.54	0.131123
$553$	0	0
$554$	−5527.46	−0.423898
$555$	12813.3	0.979992
$556$	2717.13	0.207252
$557$	10758.7	0.818420	0.409210	−	0.912440i	$-0.365804\pi$
$557$	10758.7	0.818420	0.409210	+	0.912440i	$0.365804\pi$
$558$	7376.66	0.559640
$559$	831.456	0.0629103
$560$	0	0
$561$	2858.71	0.215142
$562$	7047.24	0.528950
$563$	35.4950	0.00265708	0.00132854	−	0.999999i	$-0.499577\pi$
$563$	35.4950	0.00265708	0.00132854	+	0.999999i	$0.499577\pi$
$564$	−7734.57	−0.577454
$565$	28706.6	2.13751
$566$	16685.3	1.23911
$567$	0	0
$568$	42406.7	3.13265
$569$	4495.23	0.331195	0.165598	−	0.986193i	$-0.447045\pi$
$569$	4495.23	0.331195	0.165598	+	0.986193i	$0.447045\pi$
$570$	44421.2	3.26421
$571$	−15173.6	−1.11208	−0.556040	−	0.831156i	$-0.687680\pi$
$571$	−15173.6	−1.11208	−0.556040	+	0.831156i	$0.687680\pi$
$572$	3480.42	0.254412
$573$	−9290.55	−0.677345
$574$	0	0
$575$	−3617.46	−0.262362
$576$	−1857.00	−0.134331
$577$	−21476.0	−1.54949	−0.774747	−	0.632271i	$-0.782123\pi$
$577$	−21476.0	−1.54949	−0.774747	+	0.632271i	$0.782123\pi$
$578$	−13034.0	−0.937967
$579$	−2500.65	−0.179488
$580$	10176.1	0.728517
$581$	0	0
$582$	21936.1	1.56234
$583$	−5738.16	−0.407633
$584$	−47863.0	−3.39141
$585$	−3387.50	−0.239412
$586$	31752.3	2.23835
$587$	13378.3	0.940683	0.470341	−	0.882485i	$-0.344131\pi$
$587$	13378.3	0.940683	0.470341	+	0.882485i	$0.344131\pi$
$588$	0	0
$589$	23310.6	1.63072
$590$	79284.4	5.53235
$591$	−10680.4	−0.743371
$592$	20105.1	1.39580
$593$	−15295.0	−1.05917	−0.529586	−	0.848256i	$-0.677653\pi$
$593$	−15295.0	−1.05917	−0.529586	+	0.848256i	$0.677653\pi$
$594$	1493.86	0.103188
$595$	0	0
$596$	−44163.5	−3.03524
$597$	8693.54	0.595985
$598$	−1114.88	−0.0762391
$599$	3886.77	0.265124	0.132562	−	0.991175i	$-0.457680\pi$
$599$	3886.77	0.265124	0.132562	+	0.991175i	$0.457680\pi$
$600$	−41885.4	−2.84994
$601$	11062.6	0.750839	0.375420	−	0.926855i	$-0.377499\pi$
$601$	11062.6	0.750839	0.375420	+	0.926855i	$0.377499\pi$
$602$	0	0
$603$	831.492	0.0561542
$604$	39523.8	2.66258
$605$	2490.06	0.167331
$606$	17368.6	1.16427
$607$	6965.63	0.465776	0.232888	−	0.972504i	$-0.425182\pi$
$607$	6965.63	0.465776	0.232888	+	0.972504i	$0.425182\pi$
$608$	16172.0	1.07872
$609$	0	0
$610$	4392.59	0.291558
$611$	2725.83	0.180483
$612$	−13487.3	−0.890839
$613$	16966.2	1.11788	0.558939	−	0.829209i	$-0.311208\pi$
$613$	16966.2	1.11788	0.558939	+	0.829209i	$0.311208\pi$
$614$	−32437.3	−2.13202
$615$	11341.4	0.743628
$616$	0	0
$617$	3240.58	0.211444	0.105722	−	0.994396i	$-0.466285\pi$
$617$	3240.58	0.211444	0.105722	+	0.994396i	$0.466285\pi$
$618$	22277.7	1.45006
$619$	21880.3	1.42075	0.710373	−	0.703825i	$-0.248526\pi$
$619$	21880.3	1.42075	0.710373	+	0.703825i	$0.248526\pi$
$620$	−58011.7	−3.75775
$621$	−327.211	−0.0211442
$622$	14509.0	0.935302
$623$	0	0
$624$	−5315.23	−0.340993
$625$	36163.1	2.31444
$626$	18556.3	1.18476
$627$	4720.67	0.300679
$628$	59311.6	3.76878
$629$	−17979.3	−1.13972
$630$	0	0
$631$	12341.8	0.778636	0.389318	−	0.921103i	$-0.372711\pi$
$631$	12341.8	0.778636	0.389318	+	0.921103i	$0.372711\pi$
$632$	6098.35	0.383828
$633$	4514.10	0.283443
$634$	10953.3	0.686137
$635$	−1687.83	−0.105479
$636$	27072.5	1.68789
$637$	0	0
$638$	1581.52	0.0981397
$639$	−8159.71	−0.505154
$640$	39969.2	2.46863
$641$	23591.4	1.45367	0.726836	−	0.686811i	$-0.240990\pi$
$641$	23591.4	1.45367	0.726836	+	0.686811i	$0.240990\pi$
$642$	31420.2	1.93155
$643$	−4244.40	−0.260315	−0.130158	−	0.991493i	$-0.541548\pi$
$643$	−4244.40	−0.260315	−0.130158	+	0.991493i	$0.541548\pi$
$644$	0	0
$645$	−2806.56	−0.171330
$646$	−62330.5	−3.79622
$647$	4563.11	0.277271	0.138636	−	0.990343i	$-0.455728\pi$
$647$	4563.11	0.277271	0.138636	+	0.990343i	$0.455728\pi$
$648$	−3788.67	−0.229681
$649$	8425.62	0.509606
$650$	27460.3	1.65705
$651$	0	0
$652$	−35879.8	−2.15516
$653$	4275.28	0.256209	0.128105	−	0.991761i	$-0.459111\pi$
$653$	4275.28	0.256209	0.128105	+	0.991761i	$0.459111\pi$
$654$	−12042.2	−0.720013
$655$	47634.3	2.84157
$656$	17795.6	1.05915
$657$	9209.59	0.546880
$658$	0	0
$659$	−12612.4	−0.745535	−0.372768	−	0.927925i	$-0.621591\pi$
$659$	−12612.4	−0.745535	−0.372768	+	0.927925i	$0.621591\pi$
$660$	−11748.1	−0.692868
$661$	6969.36	0.410101	0.205051	−	0.978751i	$-0.434264\pi$
$661$	6969.36	0.410101	0.205051	+	0.978751i	$0.434264\pi$
$662$	−26076.0	−1.53093
$663$	4753.23	0.278432
$664$	56338.5	3.29271
$665$	0	0
$666$	−9395.34	−0.546639
$667$	−346.412	−0.0201096
$668$	−44624.4	−2.58468
$669$	−12476.0	−0.721002
$670$	−9563.00	−0.551419
$671$	466.804	0.0268566
$672$	0	0
$673$	−9711.61	−0.556248	−0.278124	−	0.960545i	$-0.589713\pi$
$673$	−9711.61	−0.556248	−0.278124	+	0.960545i	$0.589713\pi$
$674$	−15784.6	−0.902078
$675$	8059.41	0.459565
$676$	−32219.5	−1.83315
$677$	−9285.46	−0.527133	−0.263567	−	0.964641i	$-0.584899\pi$
$677$	−9285.46	−0.527133	−0.263567	+	0.964641i	$0.584899\pi$
$678$	−21049.0	−1.19230
$679$	0	0
$680$	83384.1	4.70240
$681$	1429.96	0.0804642
$682$	−9015.92	−0.506213
$683$	7487.86	0.419495	0.209747	−	0.977756i	$-0.432736\pi$
$683$	7487.86	0.419495	0.209747	+	0.977756i	$0.432736\pi$
$684$	−22272.0	−1.24502
$685$	−16952.3	−0.945565
$686$	0	0
$687$	−20077.8	−1.11502
$688$	−4403.70	−0.244025
$689$	−9540.95	−0.527549
$690$	3763.26	0.207630
$691$	10128.6	0.557613	0.278806	−	0.960347i	$-0.410061\pi$
$691$	10128.6	0.557613	0.278806	+	0.960347i	$0.410061\pi$
$692$	−64999.0	−3.57065
$693$	0	0
$694$	−37438.8	−2.04778
$695$	3232.28	0.176413
$696$	−4011.00	−0.218443
$697$	−15914.0	−0.864827
$698$	36313.0	1.96915
$699$	−7151.31	−0.386963
$700$	0	0
$701$	−12073.7	−0.650522	−0.325261	−	0.945624i	$-0.605452\pi$
$701$	−12073.7	−0.650522	−0.325261	+	0.945624i	$0.605452\pi$
$702$	2483.87	0.133544
$703$	−29689.7	−1.59284
$704$	2269.66	0.121507
$705$	−9200.97	−0.491530
$706$	57049.1	3.04118
$707$	0	0
$708$	−39751.9	−2.11012
$709$	−11799.6	−0.625028	−0.312514	−	0.949913i	$-0.601171\pi$
$709$	−11799.6	−0.625028	−0.312514	+	0.949913i	$0.601171\pi$
$710$	93845.0	4.96048
$711$	−1173.42	−0.0618940
$712$	−16764.5	−0.882409
$713$	1974.82	0.103727
$714$	0	0
$715$	4140.27	0.216556
$716$	−8398.55	−0.438364
$717$	21290.2	1.10892
$718$	8669.79	0.450632
$719$	−6756.80	−0.350467	−0.175234	−	0.984527i	$-0.556068\pi$
$719$	−6756.80	−0.350467	−0.175234	+	0.984527i	$0.556068\pi$
$720$	17941.4	0.928663
$721$	0	0
$722$	−68428.4	−3.52721
$723$	247.417	0.0127269
$724$	61390.9	3.15134
$725$	8532.35	0.437081
$726$	−1825.83	−0.0933374
$727$	−8176.31	−0.417115	−0.208557	−	0.978010i	$-0.566877\pi$
$727$	−8176.31	−0.417115	−0.208557	+	0.978010i	$0.566877\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−105920.	−5.37022
$731$	3938.08	0.199254
$732$	−2202.37	−0.111205
$733$	2128.17	0.107238	0.0536191	−	0.998561i	$-0.482924\pi$
$733$	2128.17	0.107238	0.0536191	+	0.998561i	$0.482924\pi$
$734$	−731.216	−0.0367707
$735$	0	0
$736$	1370.05	0.0686153
$737$	−1016.27	−0.0507934
$738$	−8316.07	−0.414795
$739$	−19301.7	−0.960790	−0.480395	−	0.877052i	$-0.659507\pi$
$739$	−19301.7	−0.960790	−0.480395	+	0.877052i	$0.659507\pi$
$740$	73887.0	3.67046
$741$	7849.15	0.389131
$742$	0	0
$743$	30054.6	1.48398	0.741989	−	0.670412i	$-0.233883\pi$
$743$	30054.6	1.48398	0.741989	+	0.670412i	$0.233883\pi$
$744$	22865.8	1.12675
$745$	−52536.4	−2.58361
$746$	10051.9	0.493332
$747$	−10840.4	−0.530964
$748$	16484.5	0.805794
$749$	0	0
$750$	−53875.4	−2.62300
$751$	−11870.9	−0.576796	−0.288398	−	0.957511i	$-0.593123\pi$
$751$	−11870.9	−0.576796	−0.288398	+	0.957511i	$0.593123\pi$
$752$	−14437.0	−0.700084
$753$	−17521.8	−0.847981
$754$	2629.63	0.127010
$755$	47017.1	2.26640
$756$	0	0
$757$	17218.4	0.826701	0.413350	−	0.910572i	$-0.364358\pi$
$757$	17218.4	0.826701	0.413350	+	0.910572i	$0.364358\pi$
$758$	−11233.8	−0.538300
$759$	399.924	0.0191256
$760$	137695.	6.57198
$761$	16285.2	0.775738	0.387869	−	0.921715i	$-0.373211\pi$
$761$	16285.2	0.775738	0.387869	+	0.921715i	$0.373211\pi$
$762$	1237.59	0.0588363
$763$	0	0
$764$	−53573.2	−2.53692
$765$	−16044.4	−0.758284
$766$	−13818.0	−0.651784
$767$	14009.4	0.659519
$768$	−24355.3	−1.14433
$769$	−27740.1	−1.30082	−0.650412	−	0.759582i	$-0.725404\pi$
$769$	−27740.1	−1.30082	−0.650412	+	0.759582i	$0.725404\pi$
$770$	0	0
$771$	−21283.4	−0.994166
$772$	−14419.8	−0.672254
$773$	9991.40	0.464897	0.232449	−	0.972609i	$-0.425326\pi$
$773$	9991.40	0.464897	0.232449	+	0.972609i	$0.425326\pi$
$774$	2057.90	0.0955680
$775$	−48641.0	−2.25450
$776$	67996.4	3.14553
$777$	0	0
$778$	4508.30	0.207751
$779$	−26279.2	−1.20866
$780$	−19533.7	−0.896692
$781$	9972.98	0.456929
$782$	−5280.49	−0.241470
$783$	771.779	0.0352249
$784$	0	0
$785$	70556.6	3.20799
$786$	−34927.7	−1.58502
$787$	−1674.98	−0.0758663	−0.0379331	−	0.999280i	$-0.512077\pi$
$787$	−1674.98	−0.0758663	−0.0379331	+	0.999280i	$0.512077\pi$
$788$	−61587.5	−2.78422
$789$	7305.02	0.329614
$790$	13495.5	0.607783
$791$	0	0
$792$	4630.60	0.207754
$793$	776.163	0.0347571
$794$	−12321.4	−0.550719
$795$	32205.2	1.43673
$796$	50130.6	2.23220
$797$	35593.4	1.58191	0.790955	−	0.611874i	$-0.209584\pi$
$797$	35593.4	1.58191	0.790955	+	0.611874i	$0.209584\pi$
$798$	0	0
$799$	12910.5	0.571641
$800$	−33745.3	−1.49135
$801$	3225.75	0.142292
$802$	40793.1	1.79608
$803$	−11256.2	−0.494672
$804$	4794.73	0.210320
$805$	0	0
$806$	−14990.9	−0.655128
$807$	4599.85	0.200647
$808$	53838.2	2.34409
$809$	40430.5	1.75706	0.878529	−	0.477688i	$-0.158525\pi$
$809$	40430.5	1.75706	0.878529	+	0.477688i	$0.158525\pi$
$810$	−8384.24	−0.363694
$811$	−2957.37	−0.128049	−0.0640243	−	0.997948i	$-0.520394\pi$
$811$	−2957.37	−0.128049	−0.0640243	+	0.997948i	$0.520394\pi$
$812$	0	0
$813$	13556.8	0.584818
$814$	11483.2	0.494454
$815$	−42682.3	−1.83447
$816$	−25174.9	−1.08002
$817$	6503.06	0.278474
$818$	24681.8	1.05499
$819$	0	0
$820$	65399.5	2.78518
$821$	18486.9	0.785867	0.392934	−	0.919567i	$-0.371460\pi$
$821$	18486.9	0.785867	0.392934	+	0.919567i	$0.371460\pi$
$822$	12430.2	0.527436
$823$	−6977.98	−0.295549	−0.147775	−	0.989021i	$-0.547211\pi$
$823$	−6977.98	−0.295549	−0.147775	+	0.989021i	$0.547211\pi$
$824$	69055.2	2.91948
$825$	−9850.38	−0.415693
$826$	0	0
$827$	−24365.1	−1.02449	−0.512247	−	0.858838i	$-0.671187\pi$
$827$	−24365.1	−1.02449	−0.512247	+	0.858838i	$0.671187\pi$
$828$	−1886.83	−0.0791933
$829$	39485.7	1.65428	0.827139	−	0.561997i	$-0.189967\pi$
$829$	39485.7	1.65428	0.827139	+	0.561997i	$0.189967\pi$
$830$	124676.	5.21393
$831$	3296.81	0.137623
$832$	3773.81	0.157252
$833$	0	0
$834$	−2370.06	−0.0984033
$835$	−53084.7	−2.20009
$836$	27221.4	1.12616
$837$	−4399.74	−0.181693
$838$	−31645.9	−1.30452
$839$	−40778.2	−1.67797	−0.838987	−	0.544152i	$-0.816852\pi$
$839$	−40778.2	−1.67797	−0.838987	+	0.544152i	$0.816852\pi$
$840$	0	0
$841$	−23571.9	−0.966498
$842$	−24380.6	−0.997877
$843$	−4203.26	−0.171730
$844$	26030.2	1.06161
$845$	−38328.0	−1.56038
$846$	6746.58	0.274175
$847$	0	0
$848$	50532.4	2.04633
$849$	−9951.78	−0.402290
$850$	130062.	5.24833
$851$	−2515.24	−0.101318
$852$	−47052.3	−1.89200
$853$	24529.8	0.984625	0.492312	−	0.870419i	$-0.336152\pi$
$853$	24529.8	0.984625	0.492312	+	0.870419i	$0.336152\pi$
$854$	0	0
$855$	−26494.6	−1.05976
$856$	97394.7	3.88888
$857$	−7037.02	−0.280490	−0.140245	−	0.990117i	$-0.544789\pi$
$857$	−7037.02	−0.280490	−0.140245	+	0.990117i	$0.544789\pi$
$858$	−3035.84	−0.120795
$859$	−20246.7	−0.804199	−0.402099	−	0.915596i	$-0.631719\pi$
$859$	−20246.7	−0.804199	−0.402099	+	0.915596i	$0.631719\pi$
$860$	−16183.8	−0.641700
$861$	0	0
$862$	−65496.7	−2.58797
$863$	−4057.26	−0.160036	−0.0800178	−	0.996793i	$-0.525498\pi$
$863$	−4057.26	−0.160036	−0.0800178	+	0.996793i	$0.525498\pi$
$864$	−3052.37	−0.120190
$865$	−77322.2	−3.03935
$866$	−8773.25	−0.344258
$867$	7774.04	0.304521
$868$	0	0
$869$	1434.18	0.0559852
$870$	−8876.24	−0.345900
$871$	−1689.77	−0.0657355
$872$	−37327.9	−1.44964
$873$	−13083.6	−0.507231
$874$	−8719.83	−0.337474
$875$	0	0
$876$	53106.4	2.04828
$877$	−2179.48	−0.0839177	−0.0419589	−	0.999119i	$-0.513360\pi$
$877$	−2179.48	−0.0839177	−0.0419589	+	0.999119i	$0.513360\pi$
$878$	−67224.1	−2.58394
$879$	−18938.4	−0.726707
$880$	−21928.4	−0.840007
$881$	39549.0	1.51242	0.756209	−	0.654331i	$-0.227049\pi$
$881$	39549.0	1.51242	0.756209	+	0.654331i	$0.227049\pi$
$882$	0	0
$883$	43732.4	1.66672	0.833360	−	0.552731i	$-0.186414\pi$
$883$	43732.4	1.66672	0.833360	+	0.552731i	$0.186414\pi$
$884$	27409.1	1.04284
$885$	−47288.5	−1.79614
$886$	18841.9	0.714454
$887$	−41883.3	−1.58546	−0.792730	−	0.609573i	$-0.791341\pi$
$887$	−41883.3	−1.58546	−0.792730	+	0.609573i	$0.791341\pi$
$888$	−29123.2	−1.10057
$889$	0	0
$890$	−37099.4	−1.39727
$891$	−891.000	−0.0335013
$892$	−71941.8	−2.70044
$893$	21319.5	0.798915
$894$	38522.2	1.44113
$895$	−9990.84	−0.373136
$896$	0	0
$897$	664.962	0.0247519
$898$	−5247.98	−0.195019
$899$	−4657.93	−0.172804
$900$	46473.9	1.72126
$901$	−45189.4	−1.67090
$902$	10164.1	0.375196
$903$	0	0
$904$	−65246.7	−2.40052
$905$	73030.0	2.68243
$906$	−34475.2	−1.26419
$907$	−45206.2	−1.65496	−0.827479	−	0.561497i	$-0.810226\pi$
$907$	−45206.2	−1.65496	−0.827479	+	0.561497i	$0.810226\pi$
$908$	8245.73	0.301370
$909$	−10359.3	−0.377995
$910$	0	0
$911$	35088.5	1.27611	0.638054	−	0.769992i	$-0.279740\pi$
$911$	35088.5	1.27611	0.638054	+	0.769992i	$0.279740\pi$
$912$	−41572.0	−1.50941
$913$	13249.4	0.480275
$914$	−42129.2	−1.52463
$915$	−2619.92	−0.0946577
$916$	−115777.	−4.17618
$917$	0	0
$918$	11764.5	0.422970
$919$	7292.72	0.261768	0.130884	−	0.991398i	$-0.458218\pi$
$919$	7292.72	0.261768	0.130884	+	0.991398i	$0.458218\pi$
$920$	11665.2	0.418031
$921$	19346.9	0.692185
$922$	−19919.9	−0.711525
$923$	16582.3	0.591345
$924$	0	0
$925$	61952.0	2.20213
$926$	29400.5	1.04337
$927$	−13287.3	−0.470779
$928$	−3231.49	−0.114309
$929$	1504.76	0.0531429	0.0265714	−	0.999647i	$-0.491541\pi$
$929$	1504.76	0.0531429	0.0265714	+	0.999647i	$0.491541\pi$
$930$	50601.5	1.78418
$931$	0	0
$932$	−41237.4	−1.44933
$933$	−8653.76	−0.303656
$934$	−59750.6	−2.09325
$935$	19609.8	0.685893
$936$	7699.38	0.268870
$937$	−17524.7	−0.611000	−0.305500	−	0.952192i	$-0.598824\pi$
$937$	−17524.7	−0.611000	−0.305500	+	0.952192i	$0.598824\pi$
$938$	0	0
$939$	−11067.7	−0.384644
$940$	−53056.6	−1.84097
$941$	42617.6	1.47640	0.738200	−	0.674582i	$-0.235676\pi$
$941$	42617.6	1.47640	0.738200	+	0.674582i	$0.235676\pi$
$942$	−51735.4	−1.78942
$943$	−2226.31	−0.0768809
$944$	−74199.1	−2.55824
$945$	0	0
$946$	−2515.21	−0.0864445
$947$	−3290.30	−0.112904	−0.0564521	−	0.998405i	$-0.517979\pi$
$947$	−3290.30	−0.112904	−0.0564521	+	0.998405i	$0.517979\pi$
$948$	−6766.42	−0.231818
$949$	−18715.8	−0.640192
$950$	214775.	7.33496
$951$	−6532.99	−0.222762
$952$	0	0
$953$	−19389.8	−0.659073	−0.329537	−	0.944143i	$-0.606893\pi$
$953$	−19389.8	−0.659073	−0.329537	+	0.944143i	$0.606893\pi$
$954$	−23614.4	−0.801408
$955$	−63730.2	−2.15944
$956$	122768.	4.15336
$957$	−943.285	−0.0318622
$958$	−3724.84	−0.125620
$959$	0	0
$960$	−12738.4	−0.428261
$961$	−3237.17	−0.108663
$962$	19093.3	0.639910
$963$	−18740.3	−0.627100
$964$	1426.71	0.0476672
$965$	−17153.7	−0.572224
$966$	0	0
$967$	−36919.7	−1.22777	−0.613887	−	0.789394i	$-0.710395\pi$
$967$	−36919.7	−1.22777	−0.613887	+	0.789394i	$0.710395\pi$
$968$	−5659.62	−0.187920
$969$	37176.4	1.23249
$970$	150475.	4.98087
$971$	54039.7	1.78601	0.893005	−	0.450047i	$-0.148593\pi$
$971$	54039.7	1.78601	0.893005	+	0.450047i	$0.148593\pi$
$972$	4203.72	0.138718
$973$	0	0
$974$	−34634.8	−1.13939
$975$	−16378.4	−0.537979
$976$	−4110.85	−0.134821
$977$	−16087.5	−0.526801	−0.263401	−	0.964687i	$-0.584844\pi$
$977$	−16087.5	−0.526801	−0.263401	+	0.964687i	$0.584844\pi$
$978$	31296.7	1.02327
$979$	−3942.58	−0.128708
$980$	0	0
$981$	7182.48	0.233760
$982$	53112.7	1.72596
$983$	−3158.93	−0.102497	−0.0512484	−	0.998686i	$-0.516320\pi$
$983$	−3158.93	−0.102497	−0.0512484	+	0.998686i	$0.516320\pi$
$984$	−25777.7	−0.835127
$985$	−73264.0	−2.36993
$986$	12454.9	0.402276
$987$	0	0
$988$	45261.5	1.45745
$989$	550.924	0.0177132
$990$	10247.4	0.328974
$991$	13798.6	0.442309	0.221154	−	0.975239i	$-0.429018\pi$
$991$	13798.6	0.442309	0.221154	+	0.975239i	$0.429018\pi$
$992$	18422.0	0.589617
$993$	15552.8	0.497033
$994$	0	0
$995$	59634.9	1.90005
$996$	−62510.4	−1.98867
$997$	33220.3	1.05526	0.527632	−	0.849473i	$-0.323080\pi$
$997$	33220.3	1.05526	0.527632	+	0.849473i	$0.323080\pi$
$998$	59627.7	1.89126
$999$	5603.76	0.177473

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.4.a.bd.1.2	yes	16
7.6	odd	2		1617.4.a.bc.1.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1617.4.a.bc.1.2	✓	16	7.6	odd	2
1617.4.a.bd.1.2	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)

\(f(q)\)	\(=\)	\(q-5.02984 q^{2} +3.00000 q^{3} +17.2993 q^{4} +20.5790 q^{5} -15.0895 q^{6} -46.7737 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-5.02984 q^{2} +3.00000 q^{3} +17.2993 q^{4} +20.5790 q^{5} -15.0895 q^{6} -46.7737 q^{8} +9.00000 q^{9} -103.509 q^{10} -11.0000 q^{11} +51.8978 q^{12} -18.2899 q^{13} +61.7371 q^{15} +96.8701 q^{16} -86.6276 q^{17} -45.2685 q^{18} -143.051 q^{19} +356.002 q^{20} +55.3282 q^{22} -12.1189 q^{23} -140.321 q^{24} +298.497 q^{25} +91.9952 q^{26} +27.0000 q^{27} +28.5844 q^{29} -310.527 q^{30} -162.953 q^{31} -113.051 q^{32} -33.0000 q^{33} +435.723 q^{34} +155.693 q^{36} +207.547 q^{37} +719.522 q^{38} -54.8697 q^{39} -962.557 q^{40} +183.705 q^{41} -45.4598 q^{43} -190.292 q^{44} +185.211 q^{45} +60.9562 q^{46} -149.035 q^{47} +290.610 q^{48} -1501.39 q^{50} -259.883 q^{51} -316.402 q^{52} +521.651 q^{53} -135.806 q^{54} -226.369 q^{55} -429.152 q^{57} -143.775 q^{58} -765.965 q^{59} +1068.01 q^{60} -42.4367 q^{61} +819.629 q^{62} -206.333 q^{64} -376.389 q^{65} +165.985 q^{66} +92.3880 q^{67} -1498.59 q^{68} -36.3568 q^{69} -906.634 q^{71} -420.963 q^{72} +1023.29 q^{73} -1043.93 q^{74} +895.490 q^{75} -2474.67 q^{76} +275.986 q^{78} -130.380 q^{79} +1993.49 q^{80} +81.0000 q^{81} -924.008 q^{82} -1204.49 q^{83} -1782.71 q^{85} +228.655 q^{86} +85.7532 q^{87} +514.511 q^{88} +358.416 q^{89} -931.582 q^{90} -209.648 q^{92} -488.860 q^{93} +749.620 q^{94} -2943.85 q^{95} -339.153 q^{96} -1453.73 q^{97} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 48 q^{3} + 72 q^{4} - 12 q^{6} - 66 q^{8} + 144 q^{9}+O(q^{10}) \) 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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