LMFDB - Embedded newform 2009.4.a.i.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2009,4,Mod(1,2009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2009, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2009.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2009 = 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2009.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:	$118.534837202$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	2009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.65259 q^{2} -8.44588 q^{3} -5.26896 q^{4} -2.08319 q^{5} -13.9575 q^{6} -21.9281 q^{8} +44.3328 q^{9} +O(q^{10})$	\(q+1.65259 q^{2} -8.44588 q^{3} -5.26896 q^{4} -2.08319 q^{5} -13.9575 q^{6} -21.9281 q^{8} +44.3328 q^{9} -3.44266 q^{10} +51.0654 q^{11} +44.5010 q^{12} +66.2143 q^{13} +17.5944 q^{15} +5.91356 q^{16} +80.6906 q^{17} +73.2638 q^{18} +8.13348 q^{19} +10.9763 q^{20} +84.3900 q^{22} -110.086 q^{23} +185.202 q^{24} -120.660 q^{25} +109.425 q^{26} -146.391 q^{27} +271.791 q^{29} +29.0762 q^{30} +257.908 q^{31} +185.197 q^{32} -431.292 q^{33} +133.348 q^{34} -233.588 q^{36} -294.351 q^{37} +13.4413 q^{38} -559.237 q^{39} +45.6805 q^{40} +41.0000 q^{41} -79.0014 q^{43} -269.061 q^{44} -92.3538 q^{45} -181.926 q^{46} -414.873 q^{47} -49.9452 q^{48} -199.402 q^{50} -681.503 q^{51} -348.880 q^{52} -144.638 q^{53} -241.923 q^{54} -106.379 q^{55} -68.6943 q^{57} +449.158 q^{58} +779.514 q^{59} -92.7041 q^{60} +104.405 q^{61} +426.216 q^{62} +258.746 q^{64} -137.937 q^{65} -712.747 q^{66} +635.387 q^{67} -425.156 q^{68} +929.770 q^{69} -809.701 q^{71} -972.134 q^{72} -164.897 q^{73} -486.441 q^{74} +1019.08 q^{75} -42.8549 q^{76} -924.188 q^{78} -281.287 q^{79} -12.3191 q^{80} +39.4121 q^{81} +67.7561 q^{82} +1101.70 q^{83} -168.094 q^{85} -130.557 q^{86} -2295.51 q^{87} -1119.77 q^{88} -499.219 q^{89} -152.623 q^{90} +580.037 q^{92} -2178.26 q^{93} -685.614 q^{94} -16.9436 q^{95} -1564.15 q^{96} -1267.75 q^{97} +2263.87 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + q^{2} + 12 q^{3} + 103 q^{4} + 20 q^{5} + 36 q^{6} - 9 q^{8} + 318 q^{9}+O(q^{10}) $ 30 * q + q^2 + 12 * q^3 + 103 * q^4 + 20 * q^5 + 36 * q^6 - 9 * q^8 + 318 * q^9	\( 30 q + q^{2} + 12 q^{3} + 103 q^{4} + 20 q^{5} + 36 q^{6} - 9 q^{8} + 318 q^{9} + 80 q^{10} + 38 q^{11} - 83 q^{12} + 78 q^{13} + 24 q^{15} + 287 q^{16} + 260 q^{17} - 185 q^{18} + 336 q^{19} + 240 q^{20} - 160 q^{22} - 90 q^{23} + 1112 q^{24} + 606 q^{25} - 55 q^{26} + 432 q^{27} + 130 q^{29} - 674 q^{30} + 1320 q^{31} - 331 q^{32} + 152 q^{33} + 816 q^{34} + 983 q^{36} - 4 q^{37} + 396 q^{38} - 248 q^{39} + 934 q^{40} + 1230 q^{41} - 214 q^{43} + 926 q^{44} + 804 q^{45} - 248 q^{46} + 2262 q^{47} - 568 q^{48} - 543 q^{50} + 204 q^{51} + 650 q^{52} - 522 q^{53} + 3253 q^{54} + 1328 q^{55} - 160 q^{57} + 888 q^{58} + 656 q^{59} + 994 q^{60} + 4300 q^{61} - 728 q^{62} + 1637 q^{64} + 1848 q^{65} - 744 q^{66} + 1642 q^{67} + 4860 q^{68} - 1556 q^{69} - 980 q^{71} - 2248 q^{72} + 1112 q^{73} + 1609 q^{74} + 6916 q^{75} + 3096 q^{76} + 343 q^{78} + 2068 q^{79} - 2440 q^{80} + 3130 q^{81} + 41 q^{82} + 356 q^{83} + 788 q^{85} - 514 q^{86} + 820 q^{87} - 1130 q^{88} + 5560 q^{89} + 2160 q^{90} + 1573 q^{92} + 124 q^{93} - 2377 q^{94} + 580 q^{95} + 9857 q^{96} + 3828 q^{97} - 2870 q^{99}+O(q^{100}) \) 30 * q + q^2 + 12 * q^3 + 103 * q^4 + 20 * q^5 + 36 * q^6 - 9 * q^8 + 318 * q^9 + 80 * q^10 + 38 * q^11 - 83 * q^12 + 78 * q^13 + 24 * q^15 + 287 * q^16 + 260 * q^17 - 185 * q^18 + 336 * q^19 + 240 * q^20 - 160 * q^22 - 90 * q^23 + 1112 * q^24 + 606 * q^25 - 55 * q^26 + 432 * q^27 + 130 * q^29 - 674 * q^30 + 1320 * q^31 - 331 * q^32 + 152 * q^33 + 816 * q^34 + 983 * q^36 - 4 * q^37 + 396 * q^38 - 248 * q^39 + 934 * q^40 + 1230 * q^41 - 214 * q^43 + 926 * q^44 + 804 * q^45 - 248 * q^46 + 2262 * q^47 - 568 * q^48 - 543 * q^50 + 204 * q^51 + 650 * q^52 - 522 * q^53 + 3253 * q^54 + 1328 * q^55 - 160 * q^57 + 888 * q^58 + 656 * q^59 + 994 * q^60 + 4300 * q^61 - 728 * q^62 + 1637 * q^64 + 1848 * q^65 - 744 * q^66 + 1642 * q^67 + 4860 * q^68 - 1556 * q^69 - 980 * q^71 - 2248 * q^72 + 1112 * q^73 + 1609 * q^74 + 6916 * q^75 + 3096 * q^76 + 343 * q^78 + 2068 * q^79 - 2440 * q^80 + 3130 * q^81 + 41 * q^82 + 356 * q^83 + 788 * q^85 - 514 * q^86 + 820 * q^87 - 1130 * q^88 + 5560 * q^89 + 2160 * q^90 + 1573 * q^92 + 124 * q^93 - 2377 * q^94 + 580 * q^95 + 9857 * q^96 + 3828 * q^97 - 2870 * 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 $

$2$	1.65259	0.584278	0.292139	−	0.956376i	$-0.405633\pi$
$2$	1.65259	0.584278	0.292139	+	0.956376i	$0.405633\pi$
$3$	−8.44588	−1.62541	−0.812705	−	0.582676i	$-0.802006\pi$
$3$	−8.44588	−1.62541	−0.812705	+	0.582676i	$0.802006\pi$
$4$	−5.26896	−0.658620
$5$	−2.08319	−0.186326	−0.0931632	−	0.995651i	$-0.529698\pi$
$5$	−2.08319	−0.186326	−0.0931632	+	0.995651i	$0.529698\pi$
$6$	−13.9575	−0.949690
$7$	0	0
$7$	0	0
$8$	−21.9281	−0.969094
$9$	44.3328	1.64196
$10$	−3.44266	−0.108866
$11$	51.0654	1.39971	0.699854	−	0.714286i	$-0.253248\pi$
$11$	51.0654	1.39971	0.699854	+	0.714286i	$0.253248\pi$
$12$	44.5010	1.07053
$13$	66.2143	1.41266	0.706328	−	0.707885i	$-0.250350\pi$
$13$	66.2143	1.41266	0.706328	+	0.707885i	$0.250350\pi$
$14$	0	0
$15$	17.5944	0.302857
$16$	5.91356	0.0923994
$17$	80.6906	1.15120	0.575599	−	0.817732i	$-0.304769\pi$
$17$	80.6906	1.15120	0.575599	+	0.817732i	$0.304769\pi$
$18$	73.2638	0.959358
$19$	8.13348	0.0982078	0.0491039	−	0.998794i	$-0.484363\pi$
$19$	8.13348	0.0982078	0.0491039	+	0.998794i	$0.484363\pi$
$20$	10.9763	0.122718
$21$	0	0
$22$	84.3900	0.817818
$23$	−110.086	−0.998020	−0.499010	−	0.866596i	$-0.666303\pi$
$23$	−110.086	−0.998020	−0.499010	+	0.866596i	$0.666303\pi$
$24$	185.202	1.57518
$25$	−120.660	−0.965282
$26$	109.425	0.825384
$27$	−146.391	−1.04344
$28$	0	0
$29$	271.791	1.74035	0.870177	−	0.492739i	$-0.164004\pi$
$29$	271.791	1.74035	0.870177	+	0.492739i	$0.164004\pi$
$30$	29.0762	0.176952
$31$	257.908	1.49425	0.747124	−	0.664685i	$-0.231434\pi$
$31$	257.908	1.49425	0.747124	+	0.664685i	$0.231434\pi$
$32$	185.197	1.02308
$33$	−431.292	−2.27510
$34$	133.348	0.672619
$35$	0	0
$36$	−233.588	−1.08142
$37$	−294.351	−1.30787	−0.653933	−	0.756553i	$-0.726882\pi$
$37$	−294.351	−1.30787	−0.653933	+	0.756553i	$0.726882\pi$
$38$	13.4413	0.0573806
$39$	−559.237	−2.29614
$40$	45.6805	0.180568
$41$	41.0000	0.156174
$41$	41.0000	0.156174
$42$	0	0
$43$	−79.0014	−0.280177	−0.140088	−	0.990139i	$-0.544739\pi$
$43$	−79.0014	−0.280177	−0.140088	+	0.990139i	$0.544739\pi$
$44$	−269.061	−0.921875
$45$	−92.3538	−0.305940
$46$	−181.926	−0.583121
$47$	−414.873	−1.28756	−0.643782	−	0.765209i	$-0.722636\pi$
$47$	−414.873	−1.28756	−0.643782	+	0.765209i	$0.722636\pi$
$48$	−49.9452	−0.150187
$49$	0	0
$50$	−199.402	−0.563993
$51$	−681.503	−1.87117
$52$	−348.880	−0.930403
$53$	−144.638	−0.374861	−0.187430	−	0.982278i	$-0.560016\pi$
$53$	−144.638	−0.374861	−0.187430	+	0.982278i	$0.560016\pi$
$54$	−241.923	−0.609659
$55$	−106.379	−0.260803
$56$	0	0
$57$	−68.6943	−0.159628
$58$	449.158	1.01685
$59$	779.514	1.72007	0.860034	−	0.510236i	$-0.170442\pi$
$59$	779.514	1.72007	0.860034	+	0.510236i	$0.170442\pi$
$60$	−92.7041	−0.199467
$61$	104.405	0.219142	0.109571	−	0.993979i	$-0.465052\pi$
$61$	104.405	0.219142	0.109571	+	0.993979i	$0.465052\pi$
$62$	426.216	0.873056
$63$	0	0
$64$	258.746	0.505364
$65$	−137.937	−0.263215
$66$	−712.747	−1.32929
$67$	635.387	1.15858	0.579290	−	0.815122i	$-0.303330\pi$
$67$	635.387	1.15858	0.579290	+	0.815122i	$0.303330\pi$
$68$	−425.156	−0.758201
$69$	929.770	1.62219
$70$	0	0
$71$	−809.701	−1.35343	−0.676717	−	0.736243i	$-0.736598\pi$
$71$	−809.701	−1.35343	−0.676717	+	0.736243i	$0.736598\pi$
$72$	−972.134	−1.59121
$73$	−164.897	−0.264380	−0.132190	−	0.991224i	$-0.542201\pi$
$73$	−164.897	−0.264380	−0.132190	+	0.991224i	$0.542201\pi$
$74$	−486.441	−0.764157
$75$	1019.08	1.56898
$76$	−42.8549	−0.0646816
$77$	0	0
$78$	−924.188	−1.34159
$79$	−281.287	−0.400598	−0.200299	−	0.979735i	$-0.564191\pi$
$79$	−281.287	−0.400598	−0.200299	+	0.979735i	$0.564191\pi$
$80$	−12.3191	−0.0172165
$81$	39.4121	0.0540632
$82$	67.7561	0.0912488
$83$	1101.70	1.45696	0.728478	−	0.685069i	$-0.240228\pi$
$83$	1101.70	1.45696	0.728478	+	0.685069i	$0.240228\pi$
$84$	0	0
$85$	−168.094	−0.214498
$86$	−130.557	−0.163701
$87$	−2295.51	−2.82879
$88$	−1119.77	−1.35645
$89$	−499.219	−0.594574	−0.297287	−	0.954788i	$-0.596082\pi$
$89$	−499.219	−0.594574	−0.297287	+	0.954788i	$0.596082\pi$
$90$	−152.623	−0.178754
$91$	0	0
$92$	580.037	0.657316
$93$	−2178.26	−2.42876
$94$	−685.614	−0.752295
$95$	−16.9436	−0.0182987
$96$	−1564.15	−1.66293
$97$	−1267.75	−1.32701	−0.663506	−	0.748171i	$-0.730932\pi$
$97$	−1267.75	−1.32701	−0.663506	+	0.748171i	$0.730932\pi$
$98$	0	0
$99$	2263.87	2.29826
$100$	635.754	0.635754
$101$	114.474	0.112778	0.0563892	−	0.998409i	$-0.482041\pi$
$101$	114.474	0.112778	0.0563892	+	0.998409i	$0.482041\pi$
$102$	−1126.24	−1.09328
$103$	811.776	0.776570	0.388285	−	0.921539i	$-0.373068\pi$
$103$	811.776	0.776570	0.388285	+	0.921539i	$0.373068\pi$
$104$	−1451.95	−1.36900
$105$	0	0
$106$	−239.027	−0.219023
$107$	940.209	0.849472	0.424736	−	0.905317i	$-0.360367\pi$
$107$	940.209	0.849472	0.424736	+	0.905317i	$0.360367\pi$
$108$	771.327	0.687231
$109$	483.524	0.424892	0.212446	−	0.977173i	$-0.431857\pi$
$109$	483.524	0.424892	0.212446	+	0.977173i	$0.431857\pi$
$110$	−175.801	−0.152381
$111$	2486.05	2.12582
$112$	0	0
$113$	2366.31	1.96994	0.984971	−	0.172720i	$-0.0552556\pi$
$113$	2366.31	1.96994	0.984971	+	0.172720i	$0.0552556\pi$
$114$	−113.523	−0.0932670
$115$	229.330	0.185958
$116$	−1432.05	−1.14623
$117$	2935.46	2.31952
$118$	1288.21	1.00500
$119$	0	0
$120$	−385.812	−0.293497
$121$	1276.67	0.959183
$122$	172.538	0.128040
$123$	−346.281	−0.253846
$124$	−1358.91	−0.984141
$125$	511.758	0.366184
$126$	0	0
$127$	−2241.00	−1.56580	−0.782901	−	0.622146i	$-0.786261\pi$
$127$	−2241.00	−1.56580	−0.782901	+	0.622146i	$0.786261\pi$
$128$	−1053.98	−0.727808
$129$	667.236	0.455402
$130$	−227.953	−0.153791
$131$	2027.46	1.35221	0.676106	−	0.736805i	$-0.263666\pi$
$131$	2027.46	1.35221	0.676106	+	0.736805i	$0.263666\pi$
$132$	2272.46	1.49842
$133$	0	0
$134$	1050.03	0.676932
$135$	304.960	0.194421
$136$	−1769.39	−1.11562
$137$	−2792.44	−1.74142	−0.870708	−	0.491800i	$-0.836339\pi$
$137$	−2792.44	−1.74142	−0.870708	+	0.491800i	$0.836339\pi$
$138$	1536.53	0.947810
$139$	−1130.21	−0.689665	−0.344832	−	0.938664i	$-0.612064\pi$
$139$	−1130.21	−0.689665	−0.344832	+	0.938664i	$0.612064\pi$
$140$	0	0
$141$	3503.97	2.09282
$142$	−1338.10	−0.790781
$143$	3381.26	1.97731
$144$	262.165	0.151716
$145$	−566.193	−0.324274
$146$	−272.507	−0.154471
$147$	0	0
$148$	1550.92	0.861386
$149$	−1069.31	−0.587930	−0.293965	−	0.955816i	$-0.594975\pi$
$149$	−1069.31	−0.587930	−0.293965	+	0.955816i	$0.594975\pi$
$150$	1684.12	0.916719
$151$	2512.18	1.35389	0.676947	−	0.736032i	$-0.263303\pi$
$151$	2512.18	1.35389	0.676947	+	0.736032i	$0.263303\pi$
$152$	−178.352	−0.0951726
$153$	3577.24	1.89022
$154$	0	0
$155$	−537.273	−0.278418
$156$	2946.60	1.51229
$157$	−1133.35	−0.576122	−0.288061	−	0.957612i	$-0.593011\pi$
$157$	−1133.35	−0.576122	−0.288061	+	0.957612i	$0.593011\pi$
$158$	−464.851	−0.234061
$159$	1221.60	0.609302
$160$	−385.802	−0.190627
$161$	0	0
$162$	65.1319	0.0315879
$163$	−1465.18	−0.704061	−0.352030	−	0.935989i	$-0.614509\pi$
$163$	−1465.18	−0.704061	−0.352030	+	0.935989i	$0.614509\pi$
$164$	−216.027	−0.102859
$165$	898.464	0.423911
$166$	1820.66	0.851267
$167$	4172.16	1.93324	0.966621	−	0.256212i	$-0.0824745\pi$
$167$	4172.16	1.93324	0.966621	+	0.256212i	$0.0824745\pi$
$168$	0	0
$169$	2187.33	0.995598
$170$	−277.790	−0.125327
$171$	360.580	0.161253
$172$	416.255	0.184530
$173$	−2265.82	−0.995762	−0.497881	−	0.867245i	$-0.665888\pi$
$173$	−2265.82	−0.995762	−0.497881	+	0.867245i	$0.665888\pi$
$174$	−3793.53	−1.65280
$175$	0	0
$176$	301.978	0.129332
$177$	−6583.68	−2.79582
$178$	−825.002	−0.347396
$179$	3109.91	1.29858	0.649290	−	0.760541i	$-0.275066\pi$
$179$	3109.91	1.29858	0.649290	+	0.760541i	$0.275066\pi$
$180$	486.608	0.201498
$181$	1542.38	0.633393	0.316696	−	0.948527i	$-0.397426\pi$
$181$	1542.38	0.633393	0.316696	+	0.948527i	$0.397426\pi$
$182$	0	0
$183$	−881.791	−0.356196
$184$	2413.97	0.967176
$185$	613.190	0.243690
$186$	−3599.77	−1.41907
$187$	4120.50	1.61134
$188$	2185.95	0.848015
$189$	0	0
$190$	−28.0008	−0.0106915
$191$	−67.4801	−0.0255638	−0.0127819	−	0.999918i	$-0.504069\pi$
$191$	−67.4801	−0.0255638	−0.0127819	+	0.999918i	$0.504069\pi$
$192$	−2185.34	−0.821424
$193$	−709.526	−0.264626	−0.132313	−	0.991208i	$-0.542240\pi$
$193$	−709.526	−0.264626	−0.132313	+	0.991208i	$0.542240\pi$
$194$	−2095.06	−0.775344
$195$	1165.00	0.427832
$196$	0	0
$197$	−1191.21	−0.430814	−0.215407	−	0.976524i	$-0.569108\pi$
$197$	−1191.21	−0.430814	−0.215407	+	0.976524i	$0.569108\pi$
$198$	3741.24	1.34282
$199$	3789.87	1.35003	0.675016	−	0.737803i	$-0.264137\pi$
$199$	3789.87	1.35003	0.675016	+	0.737803i	$0.264137\pi$
$200$	2645.85	0.935450
$201$	−5366.40	−1.88317
$202$	189.179	0.0658940
$203$	0	0
$204$	3590.81	1.23239
$205$	−85.4109	−0.0290993
$206$	1341.53	0.453732
$207$	−4880.41	−1.63870
$208$	391.562	0.130529
$209$	415.339	0.137462
$210$	0	0
$211$	−1529.00	−0.498865	−0.249433	−	0.968392i	$-0.580244\pi$
$211$	−1529.00	−0.498865	−0.249433	+	0.968392i	$0.580244\pi$
$212$	762.093	0.246891
$213$	6838.63	2.19988
$214$	1553.78	0.496327
$215$	164.575	0.0522043
$216$	3210.07	1.01119
$217$	0	0
$218$	799.065	0.248255
$219$	1392.70	0.429726
$220$	560.507	0.171770
$221$	5342.87	1.62625
$222$	4108.42	1.24207
$223$	−3679.37	−1.10488	−0.552442	−	0.833551i	$-0.686304\pi$
$223$	−3679.37	−1.10488	−0.552442	+	0.833551i	$0.686304\pi$
$224$	0	0
$225$	−5349.21	−1.58495
$226$	3910.53	1.15099
$227$	−5597.91	−1.63677	−0.818384	−	0.574672i	$-0.805130\pi$
$227$	−5597.91	−1.63677	−0.818384	+	0.574672i	$0.805130\pi$
$228$	361.948	0.105134
$229$	4274.13	1.23337	0.616687	−	0.787209i	$-0.288474\pi$
$229$	4274.13	1.23337	0.616687	+	0.787209i	$0.288474\pi$
$230$	378.987	0.108651
$231$	0	0
$232$	−5959.86	−1.68657
$233$	−756.841	−0.212800	−0.106400	−	0.994323i	$-0.533932\pi$
$233$	−756.841	−0.212800	−0.106400	+	0.994323i	$0.533932\pi$
$234$	4851.11	1.35524
$235$	864.261	0.239907
$236$	−4107.22	−1.13287
$237$	2375.72	0.651136
$238$	0	0
$239$	−4427.58	−1.19831	−0.599155	−	0.800633i	$-0.704497\pi$
$239$	−4427.58	−1.19831	−0.599155	+	0.800633i	$0.704497\pi$
$240$	104.046	0.0279838
$241$	3615.95	0.966489	0.483245	−	0.875485i	$-0.339458\pi$
$241$	3615.95	0.966489	0.483245	+	0.875485i	$0.339458\pi$
$242$	2109.81	0.560429
$243$	3619.68	0.955566
$244$	−550.105	−0.144331
$245$	0	0
$246$	−572.259	−0.148317
$247$	538.552	0.138734
$248$	−5655.44	−1.44807
$249$	−9304.83	−2.36815
$250$	845.724	0.213953
$251$	−583.331	−0.146691	−0.0733457	−	0.997307i	$-0.523368\pi$
$251$	−583.331	−0.146691	−0.0733457	+	0.997307i	$0.523368\pi$
$252$	0	0
$253$	−5621.57	−1.39694
$254$	−3703.45	−0.914863
$255$	1419.70	0.348648
$256$	−3811.76	−0.930606
$257$	594.144	0.144209	0.0721044	−	0.997397i	$-0.477029\pi$
$257$	594.144	0.144209	0.0721044	+	0.997397i	$0.477029\pi$
$258$	1102.67	0.266081
$259$	0	0
$260$	726.785	0.173359
$261$	12049.2	2.85758
$262$	3350.55	0.790067
$263$	6544.19	1.53434	0.767172	−	0.641442i	$-0.221664\pi$
$263$	6544.19	1.53434	0.767172	+	0.641442i	$0.221664\pi$
$264$	9457.41	2.20479
$265$	301.310	0.0698464
$266$	0	0
$267$	4216.34	0.966426
$268$	−3347.83	−0.763063
$269$	−781.797	−0.177201	−0.0886004	−	0.996067i	$-0.528239\pi$
$269$	−781.797	−0.177201	−0.0886004	+	0.996067i	$0.528239\pi$
$270$	503.973	0.113596
$271$	2283.59	0.511876	0.255938	−	0.966693i	$-0.417616\pi$
$271$	2283.59	0.511876	0.255938	+	0.966693i	$0.417616\pi$
$272$	477.169	0.106370
$273$	0	0
$274$	−4614.75	−1.01747
$275$	−6161.56	−1.35111
$276$	−4898.92	−1.06841
$277$	4477.16	0.971142	0.485571	−	0.874197i	$-0.338612\pi$
$277$	4477.16	0.971142	0.485571	+	0.874197i	$0.338612\pi$
$278$	−1867.78	−0.402956
$279$	11433.8	2.45349
$280$	0	0
$281$	−5551.05	−1.17846	−0.589231	−	0.807965i	$-0.700569\pi$
$281$	−5551.05	−1.17846	−0.589231	+	0.807965i	$0.700569\pi$
$282$	5790.61	1.22279
$283$	−7887.98	−1.65686	−0.828431	−	0.560091i	$-0.810766\pi$
$283$	−7887.98	−1.65686	−0.828431	+	0.560091i	$0.810766\pi$
$284$	4266.28	0.891398
$285$	143.104	0.0297429
$286$	5587.82	1.15530
$287$	0	0
$288$	8210.33	1.67985
$289$	1597.98	0.325255
$290$	−935.682	−0.189466
$291$	10707.2	2.15694
$292$	868.836	0.174126
$293$	6473.30	1.29070	0.645349	−	0.763888i	$-0.276712\pi$
$293$	6473.30	1.29070	0.645349	+	0.763888i	$0.276712\pi$
$294$	0	0
$295$	−1623.88	−0.320494
$296$	6454.56	1.26745
$297$	−7475.50	−1.46051
$298$	−1767.13	−0.343514
$299$	−7289.25	−1.40986
$300$	−5369.50	−1.03336
$301$	0	0
$302$	4151.59	0.791050
$303$	−966.836	−0.183311
$304$	48.0978	0.00907434
$305$	−217.496	−0.0408320
$306$	5911.70	1.10441
$307$	4663.68	0.867004	0.433502	−	0.901153i	$-0.357278\pi$
$307$	4663.68	0.867004	0.433502	+	0.901153i	$0.357278\pi$
$308$	0	0
$309$	−6856.16	−1.26224
$310$	−887.890	−0.162673
$311$	−2471.84	−0.450692	−0.225346	−	0.974279i	$-0.572351\pi$
$311$	−2471.84	−0.450692	−0.225346	+	0.974279i	$0.572351\pi$
$312$	12263.0	2.22518
$313$	−9220.30	−1.66506	−0.832528	−	0.553983i	$-0.813107\pi$
$313$	−9220.30	−1.66506	−0.832528	+	0.553983i	$0.813107\pi$
$314$	−1872.96	−0.336615
$315$	0	0
$316$	1482.09	0.263842
$317$	−4311.09	−0.763833	−0.381917	−	0.924197i	$-0.624736\pi$
$317$	−4311.09	−0.763833	−0.381917	+	0.924197i	$0.624736\pi$
$318$	2018.80	0.356001
$319$	13879.1	2.43599
$320$	−539.019	−0.0941627
$321$	−7940.89	−1.38074
$322$	0	0
$323$	656.296	0.113057
$324$	−207.661	−0.0356071
$325$	−7989.43	−1.36361
$326$	−2421.34	−0.411367
$327$	−4083.78	−0.690623
$328$	−899.052	−0.151347
$329$	0	0
$330$	1484.79	0.247682
$331$	5750.29	0.954877	0.477439	−	0.878665i	$-0.341565\pi$
$331$	5750.29	0.954877	0.477439	+	0.878665i	$0.341565\pi$
$332$	−5804.82	−0.959580
$333$	−13049.4	−2.14746
$334$	6894.85	1.12955
$335$	−1323.63	−0.215874
$336$	0	0
$337$	230.327	0.0372306	0.0186153	−	0.999827i	$-0.494074\pi$
$337$	230.327	0.0372306	0.0186153	+	0.999827i	$0.494074\pi$
$338$	3614.75	0.581706
$339$	−19985.5	−3.20196
$340$	885.681	0.141273
$341$	13170.2	2.09151
$342$	595.890	0.0942164
$343$	0	0
$344$	1732.35	0.271518
$345$	−1936.89	−0.302257
$346$	−3744.46	−0.581802
$347$	−1333.95	−0.206370	−0.103185	−	0.994662i	$-0.532903\pi$
$347$	−1333.95	−0.206370	−0.103185	+	0.994662i	$0.532903\pi$
$348$	12094.9	1.86310
$349$	−4435.15	−0.680252	−0.340126	−	0.940380i	$-0.610470\pi$
$349$	−4435.15	−0.680252	−0.340126	+	0.940380i	$0.610470\pi$
$350$	0	0
$351$	−9693.16	−1.47402
$352$	9457.18	1.43202
$353$	1682.46	0.253677	0.126839	−	0.991923i	$-0.459517\pi$
$353$	1682.46	0.253677	0.126839	+	0.991923i	$0.459517\pi$
$354$	−10880.1	−1.63353
$355$	1686.76	0.252181
$356$	2630.36	0.391598
$357$	0	0
$358$	5139.40	0.758732
$359$	−5313.11	−0.781101	−0.390550	−	0.920582i	$-0.627715\pi$
$359$	−5313.11	−0.781101	−0.390550	+	0.920582i	$0.627715\pi$
$360$	2025.14	0.296485
$361$	−6792.85	−0.990355
$362$	2548.91	0.370077
$363$	−10782.6	−1.55907
$364$	0	0
$365$	343.513	0.0492610
$366$	−1457.24	−0.208117
$367$	−4146.74	−0.589804	−0.294902	−	0.955527i	$-0.595287\pi$
$367$	−4146.74	−0.589804	−0.294902	+	0.955527i	$0.595287\pi$
$368$	−650.999	−0.0922165
$369$	1817.65	0.256430
$370$	1013.35	0.142383
$371$	0	0
$372$	11477.2	1.59963
$373$	9697.99	1.34623	0.673114	−	0.739539i	$-0.264956\pi$
$373$	9697.99	1.34623	0.673114	+	0.739539i	$0.264956\pi$
$374$	6809.48	0.941470
$375$	−4322.24	−0.595199
$376$	9097.39	1.24777
$377$	17996.4	2.45852
$378$	0	0
$379$	9838.65	1.33345	0.666725	−	0.745304i	$-0.267696\pi$
$379$	9838.65	1.33345	0.666725	+	0.745304i	$0.267696\pi$
$380$	89.2751	0.0120519
$381$	18927.2	2.54507
$382$	−111.517	−0.0149364
$383$	3926.10	0.523797	0.261899	−	0.965095i	$-0.415651\pi$
$383$	3926.10	0.523797	0.261899	+	0.965095i	$0.415651\pi$
$384$	8901.78	1.18299
$385$	0	0
$386$	−1172.55	−0.154615
$387$	−3502.35	−0.460038
$388$	6679.70	0.873996
$389$	11980.0	1.56146	0.780732	−	0.624866i	$-0.214846\pi$
$389$	11980.0	1.56146	0.780732	+	0.624866i	$0.214846\pi$
$390$	1925.26	0.249973
$391$	−8882.89	−1.14892
$392$	0	0
$393$	−17123.6	−2.19790
$394$	−1968.58	−0.251715
$395$	585.975	0.0746421
$396$	−11928.2	−1.51368
$397$	−2182.43	−0.275901	−0.137951	−	0.990439i	$-0.544052\pi$
$397$	−2182.43	−0.275901	−0.137951	+	0.990439i	$0.544052\pi$
$398$	6263.08	0.788794
$399$	0	0
$400$	−713.533	−0.0891916
$401$	9066.64	1.12909	0.564547	−	0.825401i	$-0.309051\pi$
$401$	9066.64	1.12909	0.564547	+	0.825401i	$0.309051\pi$
$402$	−8868.44	−1.10029
$403$	17077.2	2.11086
$404$	−603.161	−0.0742781
$405$	−82.1030	−0.0100734
$406$	0	0
$407$	−15031.2	−1.83063
$408$	14944.1	1.81334
$409$	3841.04	0.464369	0.232185	−	0.972672i	$-0.425413\pi$
$409$	3841.04	0.464369	0.232185	+	0.972672i	$0.425413\pi$
$410$	−141.149	−0.0170021
$411$	23584.6	2.83051
$412$	−4277.21	−0.511464
$413$	0	0
$414$	−8065.30	−0.957459
$415$	−2295.06	−0.271470
$416$	12262.7	1.44526
$417$	9545.64	1.12099
$418$	686.384	0.0803161
$419$	15847.9	1.84778	0.923889	−	0.382661i	$-0.124992\pi$
$419$	15847.9	1.84778	0.923889	+	0.382661i	$0.124992\pi$
$420$	0	0
$421$	11598.3	1.34267	0.671337	−	0.741152i	$-0.265720\pi$
$421$	11598.3	1.34267	0.671337	+	0.741152i	$0.265720\pi$
$422$	−2526.80	−0.291476
$423$	−18392.5	−2.11412
$424$	3171.65	0.363275
$425$	−9736.16	−1.11123
$426$	11301.4	1.28534
$427$	0	0
$428$	−4953.92	−0.559479
$429$	−28557.7	−3.21393
$430$	271.975	0.0305018
$431$	5175.90	0.578455	0.289228	−	0.957260i	$-0.406602\pi$
$431$	5175.90	0.578455	0.289228	+	0.957260i	$0.406602\pi$
$432$	−865.691	−0.0964134
$433$	4108.82	0.456022	0.228011	−	0.973659i	$-0.426778\pi$
$433$	4108.82	0.456022	0.228011	+	0.973659i	$0.426778\pi$
$434$	0	0
$435$	4781.99	0.527078
$436$	−2547.67	−0.279842
$437$	−895.380	−0.0980133
$438$	2301.56	0.251079
$439$	−3409.20	−0.370643	−0.185322	−	0.982678i	$-0.559333\pi$
$439$	−3409.20	−0.370643	−0.185322	+	0.982678i	$0.559333\pi$
$440$	2332.69	0.252742
$441$	0	0
$442$	8829.56	0.950179
$443$	9770.23	1.04785	0.523925	−	0.851764i	$-0.324467\pi$
$443$	9770.23	1.04785	0.523925	+	0.851764i	$0.324467\pi$
$444$	−13098.9	−1.40011
$445$	1039.97	0.110785
$446$	−6080.49	−0.645559
$447$	9031.29	0.955627
$448$	0	0
$449$	13309.7	1.39894	0.699468	−	0.714663i	$-0.253420\pi$
$449$	13309.7	1.39894	0.699468	+	0.714663i	$0.253420\pi$
$450$	−8840.03	−0.926052
$451$	2093.68	0.218598
$452$	−12468.0	−1.29744
$453$	−21217.5	−2.20063
$454$	−9251.03	−0.956327
$455$	0	0
$456$	1506.34	0.154694
$457$	−13848.7	−1.41754	−0.708771	−	0.705438i	$-0.750750\pi$
$457$	−13848.7	−1.41754	−0.708771	+	0.705438i	$0.750750\pi$
$458$	7063.37	0.720633
$459$	−11812.4	−1.20121
$460$	−1208.33	−0.122475
$461$	−13762.7	−1.39044	−0.695222	−	0.718795i	$-0.744694\pi$
$461$	−13762.7	−1.39044	−0.695222	+	0.718795i	$0.744694\pi$
$462$	0	0
$463$	258.482	0.0259454	0.0129727	−	0.999916i	$-0.495871\pi$
$463$	258.482	0.0259454	0.0129727	+	0.999916i	$0.495871\pi$
$464$	1607.25	0.160808
$465$	4537.74	0.452543
$466$	−1250.75	−0.124334
$467$	4941.16	0.489614	0.244807	−	0.969572i	$-0.421275\pi$
$467$	4941.16	0.489614	0.244807	+	0.969572i	$0.421275\pi$
$468$	−15466.8	−1.52768
$469$	0	0
$470$	1428.27	0.140172
$471$	9572.12	0.936434
$472$	−17093.3	−1.66691
$473$	−4034.24	−0.392166
$474$	3926.08	0.380444
$475$	−981.388	−0.0947982
$476$	0	0
$477$	−6412.23	−0.615505
$478$	−7316.95	−0.700146
$479$	−9081.68	−0.866290	−0.433145	−	0.901324i	$-0.642596\pi$
$479$	−9081.68	−0.866290	−0.433145	+	0.901324i	$0.642596\pi$
$480$	3258.44	0.309847
$481$	−19490.2	−1.84756
$482$	5975.67	0.564698
$483$	0	0
$484$	−6726.73	−0.631737
$485$	2640.96	0.247257
$486$	5981.84	0.558316
$487$	−630.903	−0.0587042	−0.0293521	−	0.999569i	$-0.509344\pi$
$487$	−630.903	−0.0587042	−0.0293521	+	0.999569i	$0.509344\pi$
$488$	−2289.40	−0.212370
$489$	12374.7	1.14439
$490$	0	0
$491$	514.741	0.0473115	0.0236558	−	0.999720i	$-0.492469\pi$
$491$	514.741	0.0473115	0.0236558	+	0.999720i	$0.492469\pi$
$492$	1824.54	0.167188
$493$	21931.0	2.00349
$494$	890.004	0.0810591
$495$	−4716.08	−0.428226
$496$	1525.16	0.138068
$497$	0	0
$498$	−15377.0	−1.38366
$499$	4452.24	0.399418	0.199709	−	0.979855i	$-0.436000\pi$
$499$	4452.24	0.399418	0.199709	+	0.979855i	$0.436000\pi$
$500$	−2696.43	−0.241176
$501$	−35237.5	−3.14231
$502$	−964.005	−0.0857085
$503$	1555.27	0.137865	0.0689324	−	0.997621i	$-0.478041\pi$
$503$	1555.27	0.137865	0.0689324	+	0.997621i	$0.478041\pi$
$504$	0	0
$505$	−238.472	−0.0210136
$506$	−9290.13	−0.816199
$507$	−18473.9	−1.61825
$508$	11807.7	1.03127
$509$	5731.72	0.499124	0.249562	−	0.968359i	$-0.419713\pi$
$509$	5731.72	0.499124	0.249562	+	0.968359i	$0.419713\pi$
$510$	2346.18	0.203707
$511$	0	0
$512$	2132.56	0.184076
$513$	−1190.67	−0.102474
$514$	981.874	0.0842580
$515$	−1691.09	−0.144695
$516$	−3515.64	−0.299937
$517$	−21185.7	−1.80221
$518$	0	0
$519$	19136.8	1.61852
$520$	3024.70	0.255080
$521$	−16876.7	−1.41916	−0.709581	−	0.704624i	$-0.751116\pi$
$521$	−16876.7	−1.41916	−0.709581	+	0.704624i	$0.751116\pi$
$522$	19912.4	1.66962
$523$	−8326.80	−0.696186	−0.348093	−	0.937460i	$-0.613171\pi$
$523$	−8326.80	−0.696186	−0.348093	+	0.937460i	$0.613171\pi$
$524$	−10682.6	−0.890593
$525$	0	0
$526$	10814.8	0.896482
$527$	20810.8	1.72017
$528$	−2550.47	−0.210218
$529$	−48.1334	−0.00395606
$530$	497.940	0.0408097
$531$	34558.0	2.82428
$532$	0	0
$533$	2714.78	0.220620
$534$	6967.86	0.564661
$535$	−1958.64	−0.158279
$536$	−13932.8	−1.12277
$537$	−26265.9	−2.11072
$538$	−1291.99	−0.103534
$539$	0	0
$540$	−1606.82	−0.128049
$541$	−11242.5	−0.893440	−0.446720	−	0.894674i	$-0.647408\pi$
$541$	−11242.5	−0.893440	−0.446720	+	0.894674i	$0.647408\pi$
$542$	3773.84	0.299078
$543$	−13026.7	−1.02952
$544$	14943.7	1.17777
$545$	−1007.27	−0.0791686
$546$	0	0
$547$	1235.77	0.0965956	0.0482978	−	0.998833i	$-0.484620\pi$
$547$	1235.77	0.0965956	0.0482978	+	0.998833i	$0.484620\pi$
$548$	14713.2	1.14693
$549$	4628.56	0.359822
$550$	−10182.5	−0.789426
$551$	2210.60	0.170916
$552$	−20388.1	−1.57206
$553$	0	0
$554$	7398.89	0.567417
$555$	−5178.93	−0.396096
$556$	5955.04	0.454227
$557$	−6401.25	−0.486947	−0.243474	−	0.969908i	$-0.578287\pi$
$557$	−6401.25	−0.486947	−0.243474	+	0.969908i	$0.578287\pi$
$558$	18895.3	1.43352
$559$	−5231.02	−0.395793
$560$	0	0
$561$	−34801.2	−2.61909
$562$	−9173.58	−0.688549
$563$	12301.9	0.920895	0.460448	−	0.887687i	$-0.347689\pi$
$563$	12301.9	0.920895	0.460448	+	0.887687i	$0.347689\pi$
$564$	−18462.3	−1.37837
$565$	−4929.47	−0.367052
$566$	−13035.6	−0.968067
$567$	0	0
$568$	17755.2	1.31161
$569$	−10674.9	−0.786495	−0.393248	−	0.919433i	$-0.628649\pi$
$569$	−10674.9	−0.786495	−0.393248	+	0.919433i	$0.628649\pi$
$570$	236.491	0.0173781
$571$	−4217.15	−0.309075	−0.154538	−	0.987987i	$-0.549389\pi$
$571$	−4217.15	−0.309075	−0.154538	+	0.987987i	$0.549389\pi$
$572$	−17815.7	−1.30229
$573$	569.929	0.0415517
$574$	0	0
$575$	13283.0	0.963371
$576$	11471.0	0.829786
$577$	−19395.5	−1.39938	−0.699691	−	0.714446i	$-0.746679\pi$
$577$	−19395.5	−1.39938	−0.699691	+	0.714446i	$0.746679\pi$
$578$	2640.80	0.190039
$579$	5992.57	0.430126
$580$	2983.24	0.213573
$581$	0	0
$582$	17694.6	1.26025
$583$	−7386.01	−0.524695
$584$	3615.88	0.256209
$585$	−6115.14	−0.432188
$586$	10697.7	0.754126
$587$	15286.8	1.07488	0.537440	−	0.843302i	$-0.319392\pi$
$587$	15286.8	1.07488	0.537440	+	0.843302i	$0.319392\pi$
$588$	0	0
$589$	2097.69	0.146747
$590$	−2683.60	−0.187258
$591$	10060.8	0.700250
$592$	−1740.66	−0.120846
$593$	15420.8	1.06789	0.533944	−	0.845520i	$-0.320709\pi$
$593$	15420.8	1.06789	0.533944	+	0.845520i	$0.320709\pi$
$594$	−12353.9	−0.853345
$595$	0	0
$596$	5634.17	0.387222
$597$	−32008.7	−2.19436
$598$	−12046.1	−0.823749
$599$	−7568.12	−0.516235	−0.258118	−	0.966113i	$-0.583102\pi$
$599$	−7568.12	−0.516235	−0.258118	+	0.966113i	$0.583102\pi$
$600$	−22346.5	−1.52049
$601$	28331.8	1.92292	0.961461	−	0.274940i	$-0.0886580\pi$
$601$	28331.8	1.92292	0.961461	+	0.274940i	$0.0886580\pi$
$602$	0	0
$603$	28168.5	1.90234
$604$	−13236.5	−0.891701
$605$	−2659.56	−0.178721
$606$	−1597.78	−0.107105
$607$	1687.41	0.112834	0.0564168	−	0.998407i	$-0.482032\pi$
$607$	1687.41	0.112834	0.0564168	+	0.998407i	$0.482032\pi$
$608$	1506.30	0.100475
$609$	0	0
$610$	−359.430	−0.0238572
$611$	−27470.5	−1.81889
$612$	−18848.3	−1.24493
$613$	20369.5	1.34212	0.671058	−	0.741405i	$-0.265840\pi$
$613$	20369.5	1.34212	0.671058	+	0.741405i	$0.265840\pi$
$614$	7707.13	0.506571
$615$	721.370	0.0472983
$616$	0	0
$617$	−2656.87	−0.173357	−0.0866786	−	0.996236i	$-0.527625\pi$
$617$	−2656.87	−0.173357	−0.0866786	+	0.996236i	$0.527625\pi$
$618$	−11330.4	−0.737501
$619$	2877.98	0.186875	0.0934377	−	0.995625i	$-0.470214\pi$
$619$	2877.98	0.186875	0.0934377	+	0.995625i	$0.470214\pi$
$620$	2830.87	0.183371
$621$	16115.5	1.04138
$622$	−4084.93	−0.263329
$623$	0	0
$624$	−3307.09	−0.212163
$625$	14016.4	0.897053
$626$	−15237.4	−0.972855
$627$	−3507.90	−0.223432
$628$	5971.57	0.379445
$629$	−23751.4	−1.50561
$630$	0	0
$631$	12208.3	0.770213	0.385107	−	0.922872i	$-0.374165\pi$
$631$	12208.3	0.770213	0.385107	+	0.922872i	$0.374165\pi$
$632$	6168.09	0.388218
$633$	12913.7	0.810860
$634$	−7124.46	−0.446291
$635$	4668.44	0.291750
$636$	−6436.55	−0.401298
$637$	0	0
$638$	22936.4	1.42329
$639$	−35896.3	−2.22228
$640$	2195.64	0.135610
$641$	1293.77	0.0797204	0.0398602	−	0.999205i	$-0.487309\pi$
$641$	1293.77	0.0797204	0.0398602	+	0.999205i	$0.487309\pi$
$642$	−13123.0	−0.806735
$643$	−17187.6	−1.05414	−0.527071	−	0.849821i	$-0.676710\pi$
$643$	−17187.6	−1.05414	−0.527071	+	0.849821i	$0.676710\pi$
$644$	0	0
$645$	−1389.98	−0.0848534
$646$	1084.59	0.0660564
$647$	14987.2	0.910674	0.455337	−	0.890319i	$-0.349519\pi$
$647$	14987.2	0.910674	0.455337	+	0.890319i	$0.349519\pi$
$648$	−864.233	−0.0523924
$649$	39806.2	2.40759
$650$	−13203.2	−0.796728
$651$	0	0
$652$	7719.98	0.463708
$653$	−4882.88	−0.292621	−0.146311	−	0.989239i	$-0.546740\pi$
$653$	−4882.88	−0.292621	−0.146311	+	0.989239i	$0.546740\pi$
$654$	−6748.81	−0.403516
$655$	−4223.58	−0.251953
$656$	242.456	0.0144304
$657$	−7310.36	−0.434101
$658$	0	0
$659$	−24187.1	−1.42974	−0.714869	−	0.699259i	$-0.753514\pi$
$659$	−24187.1	−1.42974	−0.714869	+	0.699259i	$0.753514\pi$
$660$	−4733.97	−0.279196
$661$	−2817.57	−0.165795	−0.0828977	−	0.996558i	$-0.526417\pi$
$661$	−2817.57	−0.165795	−0.0828977	+	0.996558i	$0.526417\pi$
$662$	9502.85	0.557913
$663$	−45125.2	−2.64332
$664$	−24158.2	−1.41193
$665$	0	0
$666$	−21565.3	−1.25471
$667$	−29920.3	−1.73691
$668$	−21982.9	−1.27327
$669$	31075.5	1.79589
$670$	−2187.42	−0.126130
$671$	5331.48	0.306735
$672$	0	0
$673$	11983.2	0.686359	0.343179	−	0.939270i	$-0.388496\pi$
$673$	11983.2	0.686359	0.343179	+	0.939270i	$0.388496\pi$
$674$	380.635	0.0217530
$675$	17663.6	1.00722
$676$	−11524.9	−0.655720
$677$	13317.5	0.756029	0.378015	−	0.925800i	$-0.376607\pi$
$677$	13317.5	0.756029	0.378015	+	0.925800i	$0.376607\pi$
$678$	−33027.8	−1.87083
$679$	0	0
$680$	3685.99	0.207869
$681$	47279.3	2.66042
$682$	21764.9	1.22202
$683$	29157.2	1.63349	0.816743	−	0.577002i	$-0.195777\pi$
$683$	29157.2	1.63349	0.816743	+	0.577002i	$0.195777\pi$
$684$	−1899.88	−0.106204
$685$	5817.19	0.324472
$686$	0	0
$687$	−36098.8	−2.00474
$688$	−467.180	−0.0258882
$689$	−9577.12	−0.529549
$690$	−3200.88	−0.176602
$691$	−7725.56	−0.425317	−0.212659	−	0.977127i	$-0.568212\pi$
$691$	−7725.56	−0.425317	−0.212659	+	0.977127i	$0.568212\pi$
$692$	11938.5	0.655829
$693$	0	0
$694$	−2204.48	−0.120577
$695$	2354.45	0.128503
$696$	50336.2	2.74136
$697$	3308.32	0.179787
$698$	−7329.47	−0.397456
$699$	6392.19	0.345887
$700$	0	0
$701$	−11126.0	−0.599461	−0.299731	−	0.954024i	$-0.596897\pi$
$701$	−11126.0	−0.599461	−0.299731	+	0.954024i	$0.596897\pi$
$702$	−16018.8	−0.861239
$703$	−2394.10	−0.128443
$704$	13213.0	0.707362
$705$	−7299.44	−0.389947
$706$	2780.40	0.148218
$707$	0	0
$708$	34689.1	1.84138
$709$	−6722.88	−0.356112	−0.178056	−	0.984020i	$-0.556981\pi$
$709$	−6722.88	−0.356112	−0.178056	+	0.984020i	$0.556981\pi$
$710$	2787.52	0.147343
$711$	−12470.2	−0.657765
$712$	10946.9	0.576198
$713$	−28392.0	−1.49129
$714$	0	0
$715$	−7043.81	−0.368425
$716$	−16386.0	−0.855271
$717$	37394.8	1.94774
$718$	−8780.37	−0.456380
$719$	12498.1	0.648260	0.324130	−	0.946012i	$-0.394928\pi$
$719$	12498.1	0.648260	0.324130	+	0.946012i	$0.394928\pi$
$720$	−546.140	−0.0282687
$721$	0	0
$722$	−11225.8	−0.578642
$723$	−30539.9	−1.57094
$724$	−8126.73	−0.417165
$725$	−32794.4	−1.67993
$726$	−17819.2	−0.910927
$727$	14790.5	0.754538	0.377269	−	0.926104i	$-0.376863\pi$
$727$	14790.5	0.754538	0.377269	+	0.926104i	$0.376863\pi$
$728$	0	0
$729$	−31635.5	−1.60725
$730$	567.684	0.0287821
$731$	−6374.67	−0.322539
$732$	4646.12	0.234598
$733$	26068.8	1.31361	0.656803	−	0.754062i	$-0.271908\pi$
$733$	26068.8	1.31361	0.656803	+	0.754062i	$0.271908\pi$
$734$	−6852.85	−0.344610
$735$	0	0
$736$	−20387.6	−1.02106
$737$	32446.3	1.62167
$738$	3003.82	0.149827
$739$	−28843.0	−1.43574	−0.717868	−	0.696179i	$-0.754882\pi$
$739$	−28843.0	−1.43574	−0.717868	+	0.696179i	$0.754882\pi$
$740$	−3230.87	−0.160499
$741$	−4548.55	−0.225499
$742$	0	0
$743$	12274.5	0.606069	0.303034	−	0.952980i	$-0.402000\pi$
$743$	12274.5	0.606069	0.303034	+	0.952980i	$0.402000\pi$
$744$	47765.1	2.35370
$745$	2227.59	0.109547
$746$	16026.8	0.786571
$747$	48841.5	2.39226
$748$	−21710.7	−1.06126
$749$	0	0
$750$	−7142.88	−0.347761
$751$	26569.3	1.29098	0.645492	−	0.763767i	$-0.276652\pi$
$751$	26569.3	1.29098	0.645492	+	0.763767i	$0.276652\pi$
$752$	−2453.38	−0.118970
$753$	4926.74	0.238433
$754$	29740.7	1.43646
$755$	−5233.35	−0.252266
$756$	0	0
$757$	−24166.4	−1.16029	−0.580147	−	0.814512i	$-0.697005\pi$
$757$	−24166.4	−1.16029	−0.580147	+	0.814512i	$0.697005\pi$
$758$	16259.2	0.779105
$759$	47479.1	2.27059
$760$	371.541	0.0177332
$761$	153.282	0.00730154	0.00365077	−	0.999993i	$-0.498838\pi$
$761$	153.282	0.00730154	0.00365077	+	0.999993i	$0.498838\pi$
$762$	31278.9	1.48703
$763$	0	0
$764$	355.550	0.0168368
$765$	−7452.09	−0.352197
$766$	6488.22	0.306043
$767$	51614.9	2.42987
$768$	32193.7	1.51262
$769$	−18138.4	−0.850571	−0.425285	−	0.905059i	$-0.639826\pi$
$769$	−18138.4	−0.850571	−0.425285	+	0.905059i	$0.639826\pi$
$770$	0	0
$771$	−5018.06	−0.234398
$772$	3738.46	0.174288
$773$	985.822	0.0458700	0.0229350	−	0.999737i	$-0.492699\pi$
$773$	985.822	0.0458700	0.0229350	+	0.999737i	$0.492699\pi$
$774$	−5787.94	−0.268790
$775$	−31119.3	−1.44237
$776$	27799.3	1.28600
$777$	0	0
$778$	19798.0	0.912329
$779$	333.473	0.0153375
$780$	−6138.33	−0.281779
$781$	−41347.7	−1.89441
$782$	−14679.7	−0.671287
$783$	−39787.6	−1.81596
$784$	0	0
$785$	2360.98	0.107347
$786$	−28298.3	−1.28418
$787$	−37336.9	−1.69113	−0.845564	−	0.533874i	$-0.820736\pi$
$787$	−37336.9	−1.69113	−0.845564	+	0.533874i	$0.820736\pi$
$788$	6276.45	0.283743
$789$	−55271.4	−2.49394
$790$	968.375	0.0436117
$791$	0	0
$792$	−49642.4	−2.22723
$793$	6913.09	0.309573
$794$	−3606.65	−0.161203
$795$	−2544.82	−0.113529
$796$	−19968.6	−0.889158
$797$	7089.29	0.315076	0.157538	−	0.987513i	$-0.449644\pi$
$797$	7089.29	0.315076	0.157538	+	0.987513i	$0.449644\pi$
$798$	0	0
$799$	−33476.4	−1.48224
$800$	−22346.0	−0.987562
$801$	−22131.8	−0.976264
$802$	14983.4	0.659704
$803$	−8420.54	−0.370055
$804$	28275.3	1.24029
$805$	0	0
$806$	28221.6	1.23333
$807$	6602.96	0.288024
$808$	−2510.21	−0.109293
$809$	25235.6	1.09671	0.548355	−	0.836246i	$-0.315254\pi$
$809$	25235.6	1.09671	0.548355	+	0.836246i	$0.315254\pi$
$810$	−135.682	−0.00588567
$811$	4819.07	0.208656	0.104328	−	0.994543i	$-0.466731\pi$
$811$	4819.07	0.208656	0.104328	+	0.994543i	$0.466731\pi$
$812$	0	0
$813$	−19286.9	−0.832008
$814$	−24840.3	−1.06960
$815$	3052.26	0.131185
$816$	−4030.11	−0.172895
$817$	−642.556	−0.0275155
$818$	6347.64	0.271321
$819$	0	0
$820$	450.026	0.0191654
$821$	−29926.4	−1.27216	−0.636078	−	0.771625i	$-0.719444\pi$
$821$	−29926.4	−1.27216	−0.636078	+	0.771625i	$0.719444\pi$
$822$	38975.6	1.65381
$823$	42834.5	1.81424	0.907119	−	0.420874i	$-0.138276\pi$
$823$	42834.5	1.81424	0.907119	+	0.420874i	$0.138276\pi$
$824$	−17800.7	−0.752569
$825$	52039.8	2.19611
$826$	0	0
$827$	3196.46	0.134403	0.0672017	−	0.997739i	$-0.478593\pi$
$827$	3196.46	0.134403	0.0672017	+	0.997739i	$0.478593\pi$
$828$	25714.7	1.07928
$829$	9614.63	0.402811	0.201405	−	0.979508i	$-0.435449\pi$
$829$	9614.63	0.402811	0.201405	+	0.979508i	$0.435449\pi$
$830$	−3792.78	−0.158614
$831$	−37813.5	−1.57850
$832$	17132.7	0.713906
$833$	0	0
$834$	15775.0	0.654968
$835$	−8691.41	−0.360214
$836$	−2188.40	−0.0905353
$837$	−37755.4	−1.55916
$838$	26190.0	1.07962
$839$	14386.4	0.591983	0.295991	−	0.955191i	$-0.404350\pi$
$839$	14386.4	0.591983	0.295991	+	0.955191i	$0.404350\pi$
$840$	0	0
$841$	49481.2	2.02883
$842$	19167.2	0.784495
$843$	46883.4	1.91548
$844$	8056.22	0.328562
$845$	−4556.63	−0.185506
$846$	−30395.2	−1.23523
$847$	0	0
$848$	−855.328	−0.0346369
$849$	66620.9	2.69308
$850$	−16089.8	−0.649267
$851$	32403.9	1.30528
$852$	−36032.5	−1.44889
$853$	29263.5	1.17463	0.587317	−	0.809357i	$-0.300184\pi$
$853$	29263.5	1.17463	0.587317	+	0.809357i	$0.300184\pi$
$854$	0	0
$855$	−751.157	−0.0300457
$856$	−20617.0	−0.823218
$857$	−17964.4	−0.716047	−0.358024	−	0.933713i	$-0.616549\pi$
$857$	−17964.4	−0.716047	−0.358024	+	0.933713i	$0.616549\pi$
$858$	−47194.0	−1.87783
$859$	−19043.7	−0.756418	−0.378209	−	0.925720i	$-0.623460\pi$
$859$	−19043.7	−0.756418	−0.378209	+	0.925720i	$0.623460\pi$
$860$	−867.139	−0.0343828
$861$	0	0
$862$	8553.62	0.337978
$863$	22526.2	0.888530	0.444265	−	0.895895i	$-0.353465\pi$
$863$	22526.2	0.888530	0.444265	+	0.895895i	$0.353465\pi$
$864$	−27111.2	−1.06753
$865$	4720.13	0.185537
$866$	6790.19	0.266443
$867$	−13496.3	−0.528673
$868$	0	0
$869$	−14364.0	−0.560721
$870$	7902.66	0.307960
$871$	42071.7	1.63668
$872$	−10602.8	−0.411760
$873$	−56202.8	−2.17890
$874$	−1479.69	−0.0572670
$875$	0	0
$876$	−7338.08	−0.283026
$877$	23854.6	0.918485	0.459242	−	0.888311i	$-0.348121\pi$
$877$	23854.6	0.918485	0.459242	+	0.888311i	$0.348121\pi$
$878$	−5634.01	−0.216559
$879$	−54672.7	−2.09791
$880$	−629.079	−0.0240980
$881$	4096.20	0.156645	0.0783227	−	0.996928i	$-0.475044\pi$
$881$	4096.20	0.156645	0.0783227	+	0.996928i	$0.475044\pi$
$882$	0	0
$883$	−6459.56	−0.246185	−0.123093	−	0.992395i	$-0.539281\pi$
$883$	−6459.56	−0.246185	−0.123093	+	0.992395i	$0.539281\pi$
$884$	−28151.4	−1.07108
$885$	13715.1	0.520934
$886$	16146.2	0.612236
$887$	−11982.2	−0.453579	−0.226789	−	0.973944i	$-0.572823\pi$
$887$	−11982.2	−0.453579	−0.226789	+	0.973944i	$0.572823\pi$
$888$	−54514.4	−2.06012
$889$	0	0
$890$	1718.64	0.0647291
$891$	2012.59	0.0756728
$892$	19386.5	0.727698
$893$	−3374.36	−0.126449
$894$	14925.0	0.558351
$895$	−6478.55	−0.241960
$896$	0	0
$897$	61564.1	2.29160
$898$	21995.4	0.817368
$899$	70097.1	2.60052
$900$	28184.8	1.04388
$901$	−11671.0	−0.431538
$902$	3459.99	0.127722
$903$	0	0
$904$	−51888.6	−1.90906
$905$	−3213.07	−0.118018
$906$	−35063.8	−1.28578
$907$	−10729.9	−0.392811	−0.196405	−	0.980523i	$-0.562927\pi$
$907$	−10729.9	−0.392811	−0.196405	+	0.980523i	$0.562927\pi$
$908$	29495.2	1.07801
$909$	5074.97	0.185177
$910$	0	0
$911$	−54085.6	−1.96700	−0.983500	−	0.180910i	$-0.942096\pi$
$911$	−54085.6	−1.96700	−0.983500	+	0.180910i	$0.942096\pi$
$912$	−406.228	−0.0147495
$913$	56258.8	2.03931
$914$	−22886.3	−0.828239
$915$	1836.94	0.0663687
$916$	−22520.2	−0.812324
$917$	0	0
$918$	−19521.0	−0.701838
$919$	−21573.8	−0.774380	−0.387190	−	0.922000i	$-0.626554\pi$
$919$	−21573.8	−0.774380	−0.387190	+	0.922000i	$0.626554\pi$
$920$	−5028.77	−0.180210
$921$	−39388.8	−1.40924
$922$	−22744.1	−0.812405
$923$	−53613.8	−1.91194
$924$	0	0
$925$	35516.5	1.26246
$926$	427.165	0.0151593
$927$	35988.3	1.27509
$928$	50335.0	1.78052
$929$	−22762.2	−0.803878	−0.401939	−	0.915666i	$-0.631664\pi$
$929$	−22762.2	−0.803878	−0.401939	+	0.915666i	$0.631664\pi$
$930$	7499.00	0.264411
$931$	0	0
$932$	3987.76	0.140154
$933$	20876.9	0.732560
$934$	8165.70	0.286070
$935$	−8583.79	−0.300235
$936$	−64369.2	−2.24783
$937$	−26661.7	−0.929561	−0.464780	−	0.885426i	$-0.653867\pi$
$937$	−26661.7	−0.929561	−0.464780	+	0.885426i	$0.653867\pi$
$938$	0	0
$939$	77873.5	2.70640
$940$	−4553.76	−0.158008
$941$	−20373.7	−0.705805	−0.352903	−	0.935660i	$-0.614805\pi$
$941$	−20373.7	−0.705805	−0.352903	+	0.935660i	$0.614805\pi$
$942$	15818.8	0.547137
$943$	−4513.51	−0.155865
$944$	4609.71	0.158933
$945$	0	0
$946$	−6666.92	−0.229134
$947$	15725.1	0.539597	0.269799	−	0.962917i	$-0.413043\pi$
$947$	15725.1	0.539597	0.269799	+	0.962917i	$0.413043\pi$
$948$	−12517.5	−0.428851
$949$	−10918.5	−0.373478
$950$	−1621.83	−0.0553885
$951$	36411.0	1.24154
$952$	0	0
$953$	22926.4	0.779286	0.389643	−	0.920966i	$-0.372598\pi$
$953$	22926.4	0.779286	0.389643	+	0.920966i	$0.372598\pi$
$954$	−10596.8	−0.359626
$955$	140.574	0.00476322
$956$	23328.7	0.789231
$957$	−117221.	−3.95948
$958$	−15008.3	−0.506154
$959$	0	0
$960$	4552.48	0.153053
$961$	36725.7	1.23278
$962$	−32209.3	−1.07949
$963$	41682.1	1.39480
$964$	−19052.3	−0.636549
$965$	1478.08	0.0493068
$966$	0	0
$967$	45015.6	1.49700	0.748502	−	0.663132i	$-0.230773\pi$
$967$	45015.6	1.49700	0.748502	+	0.663132i	$0.230773\pi$
$968$	−27995.0	−0.929539
$969$	−5542.99	−0.183763
$970$	4364.42	0.144467
$971$	7837.73	0.259037	0.129518	−	0.991577i	$-0.458657\pi$
$971$	7837.73	0.259037	0.129518	+	0.991577i	$0.458657\pi$
$972$	−19071.9	−0.629355
$973$	0	0
$974$	−1042.62	−0.0342996
$975$	67477.8	2.21643
$976$	617.405	0.0202486
$977$	49114.9	1.60831	0.804157	−	0.594416i	$-0.202617\pi$
$977$	49114.9	1.60831	0.804157	+	0.594416i	$0.202617\pi$
$978$	20450.3	0.668640
$979$	−25492.8	−0.832230
$980$	0	0
$981$	21436.0	0.697653
$982$	850.655	0.0276431
$983$	6170.81	0.200222	0.100111	−	0.994976i	$-0.468080\pi$
$983$	6170.81	0.200222	0.100111	+	0.994976i	$0.468080\pi$
$984$	7593.28	0.246001
$985$	2481.53	0.0802721
$986$	36242.8	1.17060
$987$	0	0
$988$	−2837.61	−0.0913728
$989$	8696.93	0.279622
$990$	−7793.73	−0.250203
$991$	−1169.63	−0.0374919	−0.0187460	−	0.999824i	$-0.505967\pi$
$991$	−1169.63	−0.0374919	−0.0187460	+	0.999824i	$0.505967\pi$
$992$	47764.0	1.52874
$993$	−48566.2	−1.55207
$994$	0	0
$995$	−7895.02	−0.251547
$996$	49026.8	1.55971
$997$	25286.1	0.803229	0.401614	−	0.915809i	$-0.368449\pi$
$997$	25286.1	0.803229	0.401614	+	0.915809i	$0.368449\pi$
$998$	7357.70	0.233371
$999$	43090.3	1.36468

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.4.a.i.1.20	yes	30
7.6	odd	2		2009.4.a.h.1.20	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2009.4.a.h.1.20	✓	30	7.6	odd	2
2009.4.a.i.1.20	yes	30	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:	\( N \)	\(=\)	\( 2009 = 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2009.a (trivial)

\(f(q)\)	\(=\)	\(q+1.65259 q^{2} -8.44588 q^{3} -5.26896 q^{4} -2.08319 q^{5} -13.9575 q^{6} -21.9281 q^{8} +44.3328 q^{9} +O(q^{10})\)	\(q+1.65259 q^{2} -8.44588 q^{3} -5.26896 q^{4} -2.08319 q^{5} -13.9575 q^{6} -21.9281 q^{8} +44.3328 q^{9} -3.44266 q^{10} +51.0654 q^{11} +44.5010 q^{12} +66.2143 q^{13} +17.5944 q^{15} +5.91356 q^{16} +80.6906 q^{17} +73.2638 q^{18} +8.13348 q^{19} +10.9763 q^{20} +84.3900 q^{22} -110.086 q^{23} +185.202 q^{24} -120.660 q^{25} +109.425 q^{26} -146.391 q^{27} +271.791 q^{29} +29.0762 q^{30} +257.908 q^{31} +185.197 q^{32} -431.292 q^{33} +133.348 q^{34} -233.588 q^{36} -294.351 q^{37} +13.4413 q^{38} -559.237 q^{39} +45.6805 q^{40} +41.0000 q^{41} -79.0014 q^{43} -269.061 q^{44} -92.3538 q^{45} -181.926 q^{46} -414.873 q^{47} -49.9452 q^{48} -199.402 q^{50} -681.503 q^{51} -348.880 q^{52} -144.638 q^{53} -241.923 q^{54} -106.379 q^{55} -68.6943 q^{57} +449.158 q^{58} +779.514 q^{59} -92.7041 q^{60} +104.405 q^{61} +426.216 q^{62} +258.746 q^{64} -137.937 q^{65} -712.747 q^{66} +635.387 q^{67} -425.156 q^{68} +929.770 q^{69} -809.701 q^{71} -972.134 q^{72} -164.897 q^{73} -486.441 q^{74} +1019.08 q^{75} -42.8549 q^{76} -924.188 q^{78} -281.287 q^{79} -12.3191 q^{80} +39.4121 q^{81} +67.7561 q^{82} +1101.70 q^{83} -168.094 q^{85} -130.557 q^{86} -2295.51 q^{87} -1119.77 q^{88} -499.219 q^{89} -152.623 q^{90} +580.037 q^{92} -2178.26 q^{93} -685.614 q^{94} -16.9436 q^{95} -1564.15 q^{96} -1267.75 q^{97} +2263.87 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + q^{2} + 12 q^{3} + 103 q^{4} + 20 q^{5} + 36 q^{6} - 9 q^{8} + 318 q^{9}+O(q^{10}) \) 30 * q + q^2 + 12 * q^3 + 103 * q^4 + 20 * q^5 + 36 * q^6 - 9 * q^8 + 318 * q^9	\( 30 q + q^{2} + 12 q^{3} + 103 q^{4} + 20 q^{5} + 36 q^{6} - 9 q^{8} + 318 q^{9} + 80 q^{10} + 38 q^{11} - 83 q^{12} + 78 q^{13} + 24 q^{15} + 287 q^{16} + 260 q^{17} - 185 q^{18} + 336 q^{19} + 240 q^{20} - 160 q^{22} - 90 q^{23} + 1112 q^{24} + 606 q^{25} - 55 q^{26} + 432 q^{27} + 130 q^{29} - 674 q^{30} + 1320 q^{31} - 331 q^{32} + 152 q^{33} + 816 q^{34} + 983 q^{36} - 4 q^{37} + 396 q^{38} - 248 q^{39} + 934 q^{40} + 1230 q^{41} - 214 q^{43} + 926 q^{44} + 804 q^{45} - 248 q^{46} + 2262 q^{47} - 568 q^{48} - 543 q^{50} + 204 q^{51} + 650 q^{52} - 522 q^{53} + 3253 q^{54} + 1328 q^{55} - 160 q^{57} + 888 q^{58} + 656 q^{59} + 994 q^{60} + 4300 q^{61} - 728 q^{62} + 1637 q^{64} + 1848 q^{65} - 744 q^{66} + 1642 q^{67} + 4860 q^{68} - 1556 q^{69} - 980 q^{71} - 2248 q^{72} + 1112 q^{73} + 1609 q^{74} + 6916 q^{75} + 3096 q^{76} + 343 q^{78} + 2068 q^{79} - 2440 q^{80} + 3130 q^{81} + 41 q^{82} + 356 q^{83} + 788 q^{85} - 514 q^{86} + 820 q^{87} - 1130 q^{88} + 5560 q^{89} + 2160 q^{90} + 1573 q^{92} + 124 q^{93} - 2377 q^{94} + 580 q^{95} + 9857 q^{96} + 3828 q^{97} - 2870 q^{99}+O(q^{100}) \) 30 * q + q^2 + 12 * q^3 + 103 * q^4 + 20 * q^5 + 36 * q^6 - 9 * q^8 + 318 * q^9 + 80 * q^10 + 38 * q^11 - 83 * q^12 + 78 * q^13 + 24 * q^15 + 287 * q^16 + 260 * q^17 - 185 * q^18 + 336 * q^19 + 240 * q^20 - 160 * q^22 - 90 * q^23 + 1112 * q^24 + 606 * q^25 - 55 * q^26 + 432 * q^27 + 130 * q^29 - 674 * q^30 + 1320 * q^31 - 331 * q^32 + 152 * q^33 + 816 * q^34 + 983 * q^36 - 4 * q^37 + 396 * q^38 - 248 * q^39 + 934 * q^40 + 1230 * q^41 - 214 * q^43 + 926 * q^44 + 804 * q^45 - 248 * q^46 + 2262 * q^47 - 568 * q^48 - 543 * q^50 + 204 * q^51 + 650 * q^52 - 522 * q^53 + 3253 * q^54 + 1328 * q^55 - 160 * q^57 + 888 * q^58 + 656 * q^59 + 994 * q^60 + 4300 * q^61 - 728 * q^62 + 1637 * q^64 + 1848 * q^65 - 744 * q^66 + 1642 * q^67 + 4860 * q^68 - 1556 * q^69 - 980 * q^71 - 2248 * q^72 + 1112 * q^73 + 1609 * q^74 + 6916 * q^75 + 3096 * q^76 + 343 * q^78 + 2068 * q^79 - 2440 * q^80 + 3130 * q^81 + 41 * q^82 + 356 * q^83 + 788 * q^85 - 514 * q^86 + 820 * q^87 - 1130 * q^88 + 5560 * q^89 + 2160 * q^90 + 1573 * q^92 + 124 * q^93 - 2377 * q^94 + 580 * q^95 + 9857 * q^96 + 3828 * q^97 - 2870 * q^99

Introduction

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