LMFDB - Embedded newform 2009.4.a.h.1.14

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:	$1$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-0.941072 q^{2} -8.32984 q^{3} -7.11438 q^{4} +21.2675 q^{5} +7.83898 q^{6} +14.2237 q^{8} +42.3862 q^{9} +O(q^{10})$	\(q-0.941072 q^{2} -8.32984 q^{3} -7.11438 q^{4} +21.2675 q^{5} +7.83898 q^{6} +14.2237 q^{8} +42.3862 q^{9} -20.0142 q^{10} -58.7410 q^{11} +59.2617 q^{12} +82.5683 q^{13} -177.155 q^{15} +43.5295 q^{16} +60.3684 q^{17} -39.8885 q^{18} +26.1230 q^{19} -151.305 q^{20} +55.2795 q^{22} -175.460 q^{23} -118.481 q^{24} +327.306 q^{25} -77.7027 q^{26} -128.165 q^{27} -221.315 q^{29} +166.715 q^{30} -11.5046 q^{31} -154.754 q^{32} +489.303 q^{33} -56.8110 q^{34} -301.552 q^{36} +110.335 q^{37} -24.5836 q^{38} -687.781 q^{39} +302.503 q^{40} -41.0000 q^{41} -482.674 q^{43} +417.906 q^{44} +901.448 q^{45} +165.121 q^{46} -68.7291 q^{47} -362.594 q^{48} -308.018 q^{50} -502.859 q^{51} -587.423 q^{52} -182.340 q^{53} +120.612 q^{54} -1249.27 q^{55} -217.600 q^{57} +208.273 q^{58} +413.591 q^{59} +1260.35 q^{60} -637.602 q^{61} +10.8266 q^{62} -202.601 q^{64} +1756.02 q^{65} -460.469 q^{66} -137.845 q^{67} -429.484 q^{68} +1461.56 q^{69} +41.1462 q^{71} +602.890 q^{72} -154.274 q^{73} -103.834 q^{74} -2726.41 q^{75} -185.849 q^{76} +647.251 q^{78} +627.920 q^{79} +925.764 q^{80} -76.8363 q^{81} +38.5839 q^{82} +1131.89 q^{83} +1283.89 q^{85} +454.231 q^{86} +1843.52 q^{87} -835.515 q^{88} -34.4338 q^{89} -848.328 q^{90} +1248.29 q^{92} +95.8312 q^{93} +64.6790 q^{94} +555.570 q^{95} +1289.08 q^{96} -198.518 q^{97} -2489.81 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.941072	−0.332719	−0.166360	−	0.986065i	$-0.553201\pi$
$2$	−0.941072	−0.332719	−0.166360	+	0.986065i	$0.553201\pi$
$3$	−8.32984	−1.60308	−0.801539	−	0.597942i	$-0.795985\pi$
$3$	−8.32984	−1.60308	−0.801539	+	0.597942i	$0.795985\pi$
$4$	−7.11438	−0.889298
$5$	21.2675	1.90222	0.951111	−	0.308849i	$-0.0999439\pi$
$5$	21.2675	1.90222	0.951111	+	0.308849i	$0.0999439\pi$
$6$	7.83898	0.533375
$7$	0	0
$7$	0	0
$8$	14.2237	0.628606
$9$	42.3862	1.56986
$10$	−20.0142	−0.632906
$11$	−58.7410	−1.61010	−0.805049	−	0.593208i	$-0.797861\pi$
$11$	−58.7410	−1.61010	−0.805049	+	0.593208i	$0.797861\pi$
$12$	59.2617	1.42561
$13$	82.5683	1.76156	0.880782	−	0.473522i	$-0.157018\pi$
$13$	82.5683	1.76156	0.880782	+	0.473522i	$0.157018\pi$
$14$	0	0
$15$	−177.155	−3.04941
$16$	43.5295	0.680149
$17$	60.3684	0.861265	0.430632	−	0.902527i	$-0.358291\pi$
$17$	60.3684	0.861265	0.430632	+	0.902527i	$0.358291\pi$
$18$	−39.8885	−0.522322
$19$	26.1230	0.315422	0.157711	−	0.987485i	$-0.449589\pi$
$19$	26.1230	0.315422	0.157711	+	0.987485i	$0.449589\pi$
$20$	−151.305	−1.69164
$21$	0	0
$22$	55.2795	0.535710
$23$	−175.460	−1.59069	−0.795347	−	0.606154i	$-0.792712\pi$
$23$	−175.460	−1.59069	−0.795347	+	0.606154i	$0.792712\pi$
$24$	−118.481	−1.00770
$25$	327.306	2.61845
$26$	−77.7027	−0.586106
$27$	−128.165	−0.913530
$28$	0	0
$29$	−221.315	−1.41714	−0.708572	−	0.705639i	$-0.750660\pi$
$29$	−221.315	−1.41714	−0.708572	+	0.705639i	$0.750660\pi$
$30$	166.715	1.01460
$31$	−11.5046	−0.0666543	−0.0333271	−	0.999444i	$-0.510610\pi$
$31$	−11.5046	−0.0666543	−0.0333271	+	0.999444i	$0.510610\pi$
$32$	−154.754	−0.854904
$33$	489.303	2.58111
$34$	−56.8110	−0.286559
$35$	0	0
$36$	−301.552	−1.39607
$37$	110.335	0.490244	0.245122	−	0.969492i	$-0.421172\pi$
$37$	110.335	0.490244	0.245122	+	0.969492i	$0.421172\pi$
$38$	−24.5836	−0.104947
$39$	−687.781	−2.82392
$40$	302.503	1.19575
$41$	−41.0000	−0.156174
$41$	−41.0000	−0.156174
$42$	0	0
$43$	−482.674	−1.71179	−0.855896	−	0.517148i	$-0.826994\pi$
$43$	−482.674	−1.71179	−0.855896	+	0.517148i	$0.826994\pi$
$44$	417.906	1.43186
$45$	901.448	2.98622
$46$	165.121	0.529255
$47$	−68.7291	−0.213302	−0.106651	−	0.994297i	$-0.534013\pi$
$47$	−68.7291	−0.213302	−0.106651	+	0.994297i	$0.534013\pi$
$48$	−362.594	−1.09033
$49$	0	0
$50$	−308.018	−0.871208
$51$	−502.859	−1.38067
$52$	−587.423	−1.56655
$53$	−182.340	−0.472572	−0.236286	−	0.971684i	$-0.575930\pi$
$53$	−182.340	−0.472572	−0.236286	+	0.971684i	$0.575930\pi$
$54$	120.612	0.303949
$55$	−1249.27	−3.06276
$56$	0	0
$57$	−217.600	−0.505646
$58$	208.273	0.471511
$59$	413.591	0.912627	0.456313	−	0.889819i	$-0.349170\pi$
$59$	413.591	0.912627	0.456313	+	0.889819i	$0.349170\pi$
$60$	1260.35	2.71183
$61$	−637.602	−1.33830	−0.669152	−	0.743125i	$-0.733343\pi$
$61$	−637.602	−1.33830	−0.669152	+	0.743125i	$0.733343\pi$
$62$	10.8266	0.0221771
$63$	0	0
$64$	−202.601	−0.395706
$65$	1756.02	3.35088
$66$	−460.469	−0.858786
$67$	−137.845	−0.251350	−0.125675	−	0.992071i	$-0.540110\pi$
$67$	−137.845	−0.251350	−0.125675	+	0.992071i	$0.540110\pi$
$68$	−429.484	−0.765921
$69$	1461.56	2.55001
$70$	0	0
$71$	41.1462	0.0687769	0.0343884	−	0.999409i	$-0.489052\pi$
$71$	41.1462	0.0687769	0.0343884	+	0.999409i	$0.489052\pi$
$72$	602.890	0.986823
$73$	−154.274	−0.247348	−0.123674	−	0.992323i	$-0.539468\pi$
$73$	−154.274	−0.247348	−0.123674	+	0.992323i	$0.539468\pi$
$74$	−103.834	−0.163114
$75$	−2726.41	−4.19758
$76$	−185.849	−0.280504
$77$	0	0
$78$	647.251	0.939574
$79$	627.920	0.894259	0.447130	−	0.894469i	$-0.352446\pi$
$79$	627.920	0.894259	0.447130	+	0.894469i	$0.352446\pi$
$80$	925.764	1.29379
$81$	−76.8363	−0.105400
$82$	38.5839	0.0519620
$83$	1131.89	1.49689	0.748443	−	0.663199i	$-0.230802\pi$
$83$	1131.89	1.49689	0.748443	+	0.663199i	$0.230802\pi$
$84$	0	0
$85$	1283.89	1.63832
$86$	454.231	0.569546
$87$	1843.52	2.27179
$88$	−835.515	−1.01212
$89$	−34.4338	−0.0410110	−0.0205055	−	0.999790i	$-0.506528\pi$
$89$	−34.4338	−0.0410110	−0.0205055	+	0.999790i	$0.506528\pi$
$90$	−848.328	−0.993573
$91$	0	0
$92$	1248.29	1.41460
$93$	95.8312	0.106852
$94$	64.6790	0.0709695
$95$	555.570	0.600003
$96$	1289.08	1.37048
$97$	−198.518	−0.207798	−0.103899	−	0.994588i	$-0.533132\pi$
$97$	−198.518	−0.207798	−0.103899	+	0.994588i	$0.533132\pi$
$98$	0	0
$99$	−2489.81	−2.52763
$100$	−2328.58	−2.32858
$101$	447.163	0.440539	0.220269	−	0.975439i	$-0.429306\pi$
$101$	447.163	0.440539	0.220269	+	0.975439i	$0.429306\pi$
$102$	473.227	0.459377
$103$	736.949	0.704988	0.352494	−	0.935814i	$-0.385334\pi$
$103$	736.949	0.704988	0.352494	+	0.935814i	$0.385334\pi$
$104$	1174.43	1.10733
$105$	0	0
$106$	171.595	0.157234
$107$	449.690	0.406291	0.203146	−	0.979149i	$-0.434883\pi$
$107$	449.690	0.406291	0.203146	+	0.979149i	$0.434883\pi$
$108$	911.813	0.812401
$109$	−526.050	−0.462261	−0.231131	−	0.972923i	$-0.574242\pi$
$109$	−526.050	−0.462261	−0.231131	+	0.972923i	$0.574242\pi$
$110$	1175.66	1.01904
$111$	−919.077	−0.785900
$112$	0	0
$113$	−1923.14	−1.60100	−0.800502	−	0.599330i	$-0.795434\pi$
$113$	−1923.14	−1.60100	−0.800502	+	0.599330i	$0.795434\pi$
$114$	204.777	0.168238
$115$	−3731.60	−3.02585
$116$	1574.52	1.26026
$117$	3499.76	2.76541
$118$	−389.219	−0.303648
$119$	0	0
$120$	−2519.80	−1.91688
$121$	2119.50	1.59241
$122$	600.029	0.445279
$123$	341.523	0.250359
$124$	81.8480	0.0592755
$125$	4302.54	3.07865
$126$	0	0
$127$	715.633	0.500017	0.250008	−	0.968244i	$-0.419567\pi$
$127$	715.633	0.500017	0.250008	+	0.968244i	$0.419567\pi$
$128$	1428.70	0.986563
$129$	4020.59	2.74414
$130$	−1652.54	−1.11490
$131$	999.428	0.666568	0.333284	−	0.942827i	$-0.391843\pi$
$131$	999.428	0.666568	0.333284	+	0.942827i	$0.391843\pi$
$132$	−3481.09	−2.29538
$133$	0	0
$134$	129.722	0.0836290
$135$	−2725.74	−1.73774
$136$	858.664	0.541396
$137$	591.434	0.368829	0.184415	−	0.982849i	$-0.440961\pi$
$137$	591.434	0.368829	0.184415	+	0.982849i	$0.440961\pi$
$138$	−1375.43	−0.848436
$139$	81.9138	0.0499844	0.0249922	−	0.999688i	$-0.492044\pi$
$139$	81.9138	0.0499844	0.0249922	+	0.999688i	$0.492044\pi$
$140$	0	0
$141$	572.503	0.341939
$142$	−38.7216	−0.0228834
$143$	−4850.14	−2.83629
$144$	1845.05	1.06774
$145$	−4706.81	−2.69572
$146$	145.183	0.0822975
$147$	0	0
$148$	−784.969	−0.435973
$149$	2083.73	1.14568	0.572838	−	0.819668i	$-0.305842\pi$
$149$	2083.73	1.14568	0.572838	+	0.819668i	$0.305842\pi$
$150$	2565.74	1.39661
$151$	−449.677	−0.242346	−0.121173	−	0.992631i	$-0.538666\pi$
$151$	−449.677	−0.242346	−0.121173	+	0.992631i	$0.538666\pi$
$152$	371.566	0.198276
$153$	2558.79	1.35206
$154$	0	0
$155$	−244.673	−0.126791
$156$	4893.14	2.51131
$157$	−85.4788	−0.0434519	−0.0217259	−	0.999764i	$-0.506916\pi$
$157$	−85.4788	−0.0434519	−0.0217259	+	0.999764i	$0.506916\pi$
$158$	−590.917	−0.297537
$159$	1518.86	0.757570
$160$	−3291.23	−1.62622
$161$	0	0
$162$	72.3084	0.0350684
$163$	−3330.22	−1.60026	−0.800131	−	0.599825i	$-0.795237\pi$
$163$	−3330.22	−1.60026	−0.800131	+	0.599825i	$0.795237\pi$
$164$	291.690	0.138885
$165$	10406.2	4.90985
$166$	−1065.19	−0.498042
$167$	−1876.30	−0.869415	−0.434708	−	0.900572i	$-0.643148\pi$
$167$	−1876.30	−0.869415	−0.434708	+	0.900572i	$0.643148\pi$
$168$	0	0
$169$	4620.52	2.10311
$170$	−1208.23	−0.545099
$171$	1107.25	0.495169
$172$	3433.93	1.52229
$173$	−2573.22	−1.13086	−0.565429	−	0.824797i	$-0.691289\pi$
$173$	−2573.22	−1.13086	−0.565429	+	0.824797i	$0.691289\pi$
$174$	−1734.88	−0.755868
$175$	0	0
$176$	−2556.97	−1.09511
$177$	−3445.15	−1.46301
$178$	32.4047	0.0136451
$179$	−2945.25	−1.22982	−0.614911	−	0.788596i	$-0.710808\pi$
$179$	−2945.25	−1.22982	−0.614911	+	0.788596i	$0.710808\pi$
$180$	−6413.25	−2.65564
$181$	2523.72	1.03639	0.518195	−	0.855263i	$-0.326604\pi$
$181$	2523.72	1.03639	0.518195	+	0.855263i	$0.326604\pi$
$182$	0	0
$183$	5311.12	2.14541
$184$	−2495.70	−0.999920
$185$	2346.56	0.932553
$186$	−90.1841	−0.0355517
$187$	−3546.10	−1.38672
$188$	488.965	0.189689
$189$	0	0
$190$	−522.831	−0.199632
$191$	4914.37	1.86174	0.930868	−	0.365356i	$-0.119053\pi$
$191$	4914.37	1.86174	0.930868	+	0.365356i	$0.119053\pi$
$192$	1687.64	0.634348
$193$	−3229.37	−1.20443	−0.602215	−	0.798334i	$-0.705715\pi$
$193$	−3229.37	−1.20443	−0.602215	+	0.798334i	$0.705715\pi$
$194$	186.819	0.0691384
$195$	−14627.4	−5.37173
$196$	0	0
$197$	−2564.27	−0.927396	−0.463698	−	0.885993i	$-0.653478\pi$
$197$	−2564.27	−0.927396	−0.463698	+	0.885993i	$0.653478\pi$
$198$	2343.09	0.840990
$199$	−4732.23	−1.68572	−0.842861	−	0.538131i	$-0.819131\pi$
$199$	−4732.23	−1.68572	−0.842861	+	0.538131i	$0.819131\pi$
$200$	4655.51	1.64597
$201$	1148.23	0.402934
$202$	−420.813	−0.146576
$203$	0	0
$204$	3577.54	1.22783
$205$	−871.967	−0.297077
$206$	−693.522	−0.234563
$207$	−7437.09	−2.49717
$208$	3594.16	1.19813
$209$	−1534.49	−0.507861
$210$	0	0
$211$	1242.08	0.405252	0.202626	−	0.979256i	$-0.435052\pi$
$211$	1242.08	0.405252	0.202626	+	0.979256i	$0.435052\pi$
$212$	1297.24	0.420257
$213$	−342.741	−0.110255
$214$	−423.191	−0.135181
$215$	−10265.3	−3.25621
$216$	−1822.98	−0.574250
$217$	0	0
$218$	495.051	0.153803
$219$	1285.08	0.396519
$220$	8887.81	2.72371
$221$	4984.52	1.51717
$222$	864.917	0.261484
$223$	−1405.02	−0.421917	−0.210958	−	0.977495i	$-0.567658\pi$
$223$	−1405.02	−0.421917	−0.210958	+	0.977495i	$0.567658\pi$
$224$	0	0
$225$	13873.3	4.11060
$226$	1809.81	0.532685
$227$	5636.19	1.64796	0.823980	−	0.566619i	$-0.191749\pi$
$227$	5636.19	1.64796	0.823980	+	0.566619i	$0.191749\pi$
$228$	1548.09	0.449670
$229$	−1168.82	−0.337283	−0.168641	−	0.985677i	$-0.553938\pi$
$229$	−1168.82	−0.337283	−0.168641	+	0.985677i	$0.553938\pi$
$230$	3511.70	1.00676
$231$	0	0
$232$	−3147.92	−0.890824
$233$	−1743.14	−0.490116	−0.245058	−	0.969508i	$-0.578807\pi$
$233$	−1743.14	−0.490116	−0.245058	+	0.969508i	$0.578807\pi$
$234$	−3293.52	−0.920104
$235$	−1461.70	−0.405747
$236$	−2942.45	−0.811597
$237$	−5230.47	−1.43357
$238$	0	0
$239$	−1550.40	−0.419612	−0.209806	−	0.977743i	$-0.567283\pi$
$239$	−1550.40	−0.419612	−0.209806	+	0.977743i	$0.567283\pi$
$240$	−7711.46	−2.07405
$241$	−1061.60	−0.283749	−0.141875	−	0.989885i	$-0.545313\pi$
$241$	−1061.60	−0.283749	−0.141875	+	0.989885i	$0.545313\pi$
$242$	−1994.61	−0.529827
$243$	4100.48	1.08249
$244$	4536.14	1.19015
$245$	0	0
$246$	−321.398	−0.0832991
$247$	2156.93	0.555636
$248$	−163.638	−0.0418992
$249$	−9428.49	−2.39962
$250$	−4049.00	−1.02432
$251$	3319.69	0.834808	0.417404	−	0.908721i	$-0.362940\pi$
$251$	3319.69	0.834808	0.417404	+	0.908721i	$0.362940\pi$
$252$	0	0
$253$	10306.7	2.56117
$254$	−673.462	−0.166365
$255$	−10694.6	−2.62635
$256$	276.307	0.0674577
$257$	2564.82	0.622527	0.311263	−	0.950324i	$-0.399248\pi$
$257$	2564.82	0.622527	0.311263	+	0.950324i	$0.399248\pi$
$258$	−3783.67	−0.913026
$259$	0	0
$260$	−12493.0	−2.97994
$261$	−9380.70	−2.22472
$262$	−940.533	−0.221780
$263$	459.341	0.107697	0.0538483	−	0.998549i	$-0.482851\pi$
$263$	459.341	0.107697	0.0538483	+	0.998549i	$0.482851\pi$
$264$	6959.71	1.62250
$265$	−3877.91	−0.898937
$266$	0	0
$267$	286.828	0.0657438
$268$	980.683	0.223525
$269$	−6374.88	−1.44492	−0.722459	−	0.691414i	$-0.756988\pi$
$269$	−6374.88	−1.44492	−0.722459	+	0.691414i	$0.756988\pi$
$270$	2565.12	0.578178
$271$	−7163.13	−1.60564	−0.802821	−	0.596220i	$-0.796669\pi$
$271$	−7163.13	−1.60564	−0.802821	+	0.596220i	$0.796669\pi$
$272$	2627.81	0.585788
$273$	0	0
$274$	−556.582	−0.122717
$275$	−19226.3	−4.21596
$276$	−10398.1	−2.26772
$277$	−3028.30	−0.656870	−0.328435	−	0.944527i	$-0.606521\pi$
$277$	−3028.30	−0.656870	−0.328435	+	0.944527i	$0.606521\pi$
$278$	−77.0868	−0.0166308
$279$	−487.635	−0.104638
$280$	0	0
$281$	2587.58	0.549331	0.274666	−	0.961540i	$-0.411433\pi$
$281$	2587.58	0.549331	0.274666	+	0.961540i	$0.411433\pi$
$282$	−538.766	−0.113770
$283$	−1739.52	−0.365384	−0.182692	−	0.983170i	$-0.558481\pi$
$283$	−1739.52	−0.365384	−0.182692	+	0.983170i	$0.558481\pi$
$284$	−292.730	−0.0611632
$285$	−4627.81	−0.961852
$286$	4564.33	0.943688
$287$	0	0
$288$	−6559.44	−1.34208
$289$	−1268.65	−0.258223
$290$	4429.45	0.896918
$291$	1653.62	0.333117
$292$	1097.57	0.219966
$293$	−8500.05	−1.69481	−0.847403	−	0.530950i	$-0.821835\pi$
$293$	−8500.05	−1.69481	−0.847403	+	0.530950i	$0.821835\pi$
$294$	0	0
$295$	8796.04	1.73602
$296$	1569.38	0.308170
$297$	7528.52	1.47087
$298$	−1960.94	−0.381189
$299$	−14487.5	−2.80211
$300$	19396.7	3.73290
$301$	0	0
$302$	423.179	0.0806331
$303$	−3724.80	−0.706218
$304$	1137.12	0.214534
$305$	−13560.2	−2.54575
$306$	−2408.01	−0.449858
$307$	2951.05	0.548617	0.274308	−	0.961642i	$-0.411551\pi$
$307$	2951.05	0.548617	0.274308	+	0.961642i	$0.411551\pi$
$308$	0	0
$309$	−6138.66	−1.13015
$310$	230.255	0.0421859
$311$	−5854.97	−1.06754	−0.533770	−	0.845630i	$-0.679225\pi$
$311$	−5854.97	−1.06754	−0.533770	+	0.845630i	$0.679225\pi$
$312$	−9782.80	−1.77513
$313$	3664.01	0.661668	0.330834	−	0.943689i	$-0.392670\pi$
$313$	3664.01	0.661668	0.330834	+	0.943689i	$0.392670\pi$
$314$	80.4416	0.0144573
$315$	0	0
$316$	−4467.26	−0.795263
$317$	−1687.07	−0.298913	−0.149457	−	0.988768i	$-0.547752\pi$
$317$	−1687.07	−0.298913	−0.149457	+	0.988768i	$0.547752\pi$
$318$	−1429.36	−0.252058
$319$	13000.3	2.28174
$320$	−4308.82	−0.752721
$321$	−3745.85	−0.651317
$322$	0	0
$323$	1577.00	0.271662
$324$	546.643	0.0937316
$325$	27025.1	4.61256
$326$	3133.97	0.532438
$327$	4381.91	0.741041
$328$	−583.172	−0.0981717
$329$	0	0
$330$	−9793.02	−1.63360
$331$	−6625.02	−1.10013	−0.550067	−	0.835121i	$-0.685398\pi$
$331$	−6625.02	−1.10013	−0.550067	+	0.835121i	$0.685398\pi$
$332$	−8052.73	−1.33118
$333$	4676.70	0.769615
$334$	1765.73	0.289271
$335$	−2931.62	−0.478124
$336$	0	0
$337$	−8744.28	−1.41345	−0.706723	−	0.707490i	$-0.749827\pi$
$337$	−8744.28	−1.41345	−0.706723	+	0.707490i	$0.749827\pi$
$338$	−4348.25	−0.699744
$339$	16019.4	2.56653
$340$	−9134.05	−1.45695
$341$	675.790	0.107320
$342$	−1042.01	−0.164752
$343$	0	0
$344$	−6865.41	−1.07604
$345$	31083.6	4.85068
$346$	2421.59	0.376258
$347$	−647.891	−0.100232	−0.0501162	−	0.998743i	$-0.515959\pi$
$347$	−647.891	−0.100232	−0.0501162	+	0.998743i	$0.515959\pi$
$348$	−13115.5	−2.02030
$349$	5702.35	0.874612	0.437306	−	0.899313i	$-0.355933\pi$
$349$	5702.35	0.874612	0.437306	+	0.899313i	$0.355933\pi$
$350$	0	0
$351$	−10582.3	−1.60924
$352$	9090.41	1.37648
$353$	8148.67	1.22864	0.614320	−	0.789057i	$-0.289430\pi$
$353$	8148.67	1.22864	0.614320	+	0.789057i	$0.289430\pi$
$354$	3242.13	0.486772
$355$	875.077	0.130829
$356$	244.976	0.0364710
$357$	0	0
$358$	2771.69	0.409186
$359$	7149.56	1.05109	0.525543	−	0.850767i	$-0.323862\pi$
$359$	7149.56	1.05109	0.525543	+	0.850767i	$0.323862\pi$
$360$	12821.9	1.87716
$361$	−6176.59	−0.900509
$362$	−2375.00	−0.344826
$363$	−17655.1	−2.55277
$364$	0	0
$365$	−3281.02	−0.470511
$366$	−4998.15	−0.713818
$367$	−9732.62	−1.38430	−0.692151	−	0.721753i	$-0.743337\pi$
$367$	−9732.62	−1.38430	−0.692151	+	0.721753i	$0.743337\pi$
$368$	−7637.70	−1.08191
$369$	−1737.84	−0.245171
$370$	−2208.28	−0.310278
$371$	0	0
$372$	−681.780	−0.0950233
$373$	−13289.7	−1.84482	−0.922408	−	0.386216i	$-0.873782\pi$
$373$	−13289.7	−1.84482	−0.922408	+	0.386216i	$0.873782\pi$
$374$	3337.14	0.461388
$375$	−35839.5	−4.93531
$376$	−977.584	−0.134083
$377$	−18273.6	−2.49639
$378$	0	0
$379$	1759.15	0.238421	0.119211	−	0.992869i	$-0.461964\pi$
$379$	1759.15	0.238421	0.119211	+	0.992869i	$0.461964\pi$
$380$	−3952.54	−0.533581
$381$	−5961.10	−0.801566
$382$	−4624.78	−0.619435
$383$	2416.82	0.322438	0.161219	−	0.986919i	$-0.448457\pi$
$383$	2416.82	0.322438	0.161219	+	0.986919i	$0.448457\pi$
$384$	−11900.8	−1.58154
$385$	0	0
$386$	3039.07	0.400737
$387$	−20458.7	−2.68727
$388$	1412.33	0.184794
$389$	−11967.1	−1.55979	−0.779895	−	0.625911i	$-0.784727\pi$
$389$	−11967.1	−1.55979	−0.779895	+	0.625911i	$0.784727\pi$
$390$	13765.4	1.78728
$391$	−10592.3	−1.37001
$392$	0	0
$393$	−8325.07	−1.06856
$394$	2413.17	0.308562
$395$	13354.3	1.70108
$396$	17713.5	2.24781
$397$	10350.0	1.30844	0.654222	−	0.756303i	$-0.272996\pi$
$397$	10350.0	1.30844	0.654222	+	0.756303i	$0.272996\pi$
$398$	4453.37	0.560872
$399$	0	0
$400$	14247.5	1.78093
$401$	−6887.96	−0.857777	−0.428888	−	0.903358i	$-0.641095\pi$
$401$	−6887.96	−0.857777	−0.428888	+	0.903358i	$0.641095\pi$
$402$	−1080.56	−0.134064
$403$	−949.913	−0.117416
$404$	−3181.29	−0.391770
$405$	−1634.11	−0.200493
$406$	0	0
$407$	−6481.21	−0.789341
$408$	−7152.53	−0.867900
$409$	−10080.9	−1.21875	−0.609377	−	0.792880i	$-0.708580\pi$
$409$	−10080.9	−1.21875	−0.609377	+	0.792880i	$0.708580\pi$
$410$	820.583	0.0988432
$411$	−4926.55	−0.591263
$412$	−5242.94	−0.626944
$413$	0	0
$414$	6998.84	0.830856
$415$	24072.5	2.84741
$416$	−12777.8	−1.50597
$417$	−682.329	−0.0801290
$418$	1444.06	0.168975
$419$	1387.29	0.161750	0.0808752	−	0.996724i	$-0.474228\pi$
$419$	1387.29	0.161750	0.0808752	+	0.996724i	$0.474228\pi$
$420$	0	0
$421$	8208.08	0.950207	0.475104	−	0.879930i	$-0.342411\pi$
$421$	8208.08	0.950207	0.475104	+	0.879930i	$0.342411\pi$
$422$	−1168.88	−0.134835
$423$	−2913.17	−0.334854
$424$	−2593.55	−0.297061
$425$	19759.0	2.25518
$426$	322.544	0.0366839
$427$	0	0
$428$	−3199.27	−0.361314
$429$	40400.9	4.54679
$430$	9660.34	1.08340
$431$	4442.18	0.496456	0.248228	−	0.968702i	$-0.420152\pi$
$431$	4442.18	0.496456	0.248228	+	0.968702i	$0.420152\pi$
$432$	−5578.95	−0.621337
$433$	3732.36	0.414240	0.207120	−	0.978316i	$-0.433591\pi$
$433$	3732.36	0.414240	0.207120	+	0.978316i	$0.433591\pi$
$434$	0	0
$435$	39207.0	4.32145
$436$	3742.52	0.411088
$437$	−4583.54	−0.501740
$438$	−1209.35	−0.131929
$439$	−9098.30	−0.989153	−0.494576	−	0.869134i	$-0.664677\pi$
$439$	−9098.30	−0.989153	−0.494576	+	0.869134i	$0.664677\pi$
$440$	−17769.3	−1.92527
$441$	0	0
$442$	−4690.79	−0.504792
$443$	5495.91	0.589433	0.294716	−	0.955585i	$-0.404775\pi$
$443$	5495.91	0.589433	0.294716	+	0.955585i	$0.404775\pi$
$444$	6538.66	0.698899
$445$	−732.321	−0.0780120
$446$	1322.23	0.140380
$447$	−17357.1	−1.83661
$448$	0	0
$449$	9534.29	1.00212	0.501059	−	0.865413i	$-0.332944\pi$
$449$	9534.29	1.00212	0.501059	+	0.865413i	$0.332944\pi$
$450$	−13055.7	−1.36767
$451$	2408.38	0.251455
$452$	13681.9	1.42377
$453$	3745.74	0.388499
$454$	−5304.06	−0.548308
$455$	0	0
$456$	−3095.08	−0.317852
$457$	970.014	0.0992895	0.0496448	−	0.998767i	$-0.484191\pi$
$457$	970.014	0.0992895	0.0496448	+	0.998767i	$0.484191\pi$
$458$	1099.94	0.112220
$459$	−7737.11	−0.786791
$460$	26548.0	2.69089
$461$	8892.14	0.898369	0.449185	−	0.893439i	$-0.351715\pi$
$461$	8892.14	0.898369	0.449185	+	0.893439i	$0.351715\pi$
$462$	0	0
$463$	−17353.8	−1.74190	−0.870952	−	0.491368i	$-0.836497\pi$
$463$	−17353.8	−1.74190	−0.870952	+	0.491368i	$0.836497\pi$
$464$	−9633.74	−0.963869
$465$	2038.09	0.203256
$466$	1640.42	0.163071
$467$	12755.8	1.26396	0.631979	−	0.774985i	$-0.282243\pi$
$467$	12755.8	1.26396	0.631979	+	0.774985i	$0.282243\pi$
$468$	−24898.6	−2.45927
$469$	0	0
$470$	1375.56	0.135000
$471$	712.024	0.0696568
$472$	5882.80	0.573682
$473$	28352.7	2.75615
$474$	4922.25	0.476975
$475$	8550.21	0.825917
$476$	0	0
$477$	−7728.70	−0.741872
$478$	1459.04	0.139613
$479$	−1232.39	−0.117556	−0.0587781	−	0.998271i	$-0.518720\pi$
$479$	−1232.39	−0.117556	−0.0587781	+	0.998271i	$0.518720\pi$
$480$	27415.4	2.60695
$481$	9110.21	0.863596
$482$	999.041	0.0944089
$483$	0	0
$484$	−15079.0	−1.41613
$485$	−4221.97	−0.395278
$486$	−3858.85	−0.360166
$487$	−9774.17	−0.909465	−0.454733	−	0.890628i	$-0.650265\pi$
$487$	−9774.17	−0.909465	−0.454733	+	0.890628i	$0.650265\pi$
$488$	−9069.07	−0.841265
$489$	27740.2	2.56535
$490$	0	0
$491$	10172.9	0.935024	0.467512	−	0.883987i	$-0.345150\pi$
$491$	10172.9	0.935024	0.467512	+	0.883987i	$0.345150\pi$
$492$	−2429.73	−0.222644
$493$	−13360.4	−1.22054
$494$	−2029.83	−0.184871
$495$	−52952.0	−4.80811
$496$	−500.789	−0.0453348
$497$	0	0
$498$	8872.89	0.798401
$499$	15766.7	1.41445	0.707227	−	0.706986i	$-0.249946\pi$
$499$	15766.7	1.41445	0.707227	+	0.706986i	$0.249946\pi$
$500$	−30609.9	−2.73783
$501$	15629.3	1.39374
$502$	−3124.06	−0.277757
$503$	9804.31	0.869091	0.434545	−	0.900650i	$-0.356909\pi$
$503$	9804.31	0.869091	0.434545	+	0.900650i	$0.356909\pi$
$504$	0	0
$505$	9510.04	0.838002
$506$	−9699.35	−0.852152
$507$	−38488.2	−3.37144
$508$	−5091.29	−0.444664
$509$	6656.85	0.579685	0.289842	−	0.957074i	$-0.406397\pi$
$509$	6656.85	0.579685	0.289842	+	0.957074i	$0.406397\pi$
$510$	10064.3	0.873837
$511$	0	0
$512$	−11689.6	−1.00901
$513$	−3348.04	−0.288148
$514$	−2413.68	−0.207127
$515$	15673.0	1.34104
$516$	−28604.0	−2.44035
$517$	4037.22	0.343436
$518$	0	0
$519$	21434.5	1.81285
$520$	24977.1	2.10638
$521$	5425.86	0.456260	0.228130	−	0.973631i	$-0.426739\pi$
$521$	5425.86	0.456260	0.228130	+	0.973631i	$0.426739\pi$
$522$	8827.92	0.740206
$523$	650.605	0.0543957	0.0271979	−	0.999630i	$-0.491342\pi$
$523$	650.605	0.0543957	0.0271979	+	0.999630i	$0.491342\pi$
$524$	−7110.31	−0.592777
$525$	0	0
$526$	−432.273	−0.0358327
$527$	−694.513	−0.0574070
$528$	21299.1	1.75554
$529$	18619.3	1.53031
$530$	3649.39	0.299094
$531$	17530.6	1.43270
$532$	0	0
$533$	−3385.30	−0.275110
$534$	−269.926	−0.0218742
$535$	9563.78	0.772856
$536$	−1960.67	−0.158000
$537$	24533.5	1.97150
$538$	5999.22	0.480752
$539$	0	0
$540$	19392.0	1.54537
$541$	−16051.5	−1.27561	−0.637806	−	0.770197i	$-0.720158\pi$
$541$	−16051.5	−1.27561	−0.637806	+	0.770197i	$0.720158\pi$
$542$	6741.02	0.534228
$543$	−21022.2	−1.66141
$544$	−9342.27	−0.736299
$545$	−11187.8	−0.879323
$546$	0	0
$547$	−16087.1	−1.25747	−0.628734	−	0.777620i	$-0.716427\pi$
$547$	−16087.1	−1.25747	−0.628734	+	0.777620i	$0.716427\pi$
$548$	−4207.69	−0.327999
$549$	−27025.5	−2.10095
$550$	18093.3	1.40273
$551$	−5781.41	−0.446998
$552$	20788.8	1.60295
$553$	0	0
$554$	2849.85	0.218553
$555$	−19546.5	−1.49496
$556$	−582.766	−0.0444511
$557$	−18847.5	−1.43374	−0.716871	−	0.697206i	$-0.754426\pi$
$557$	−18847.5	−1.43374	−0.716871	+	0.697206i	$0.754426\pi$
$558$	458.900	0.0348150
$559$	−39853.5	−3.01543
$560$	0	0
$561$	29538.5	2.22302
$562$	−2435.10	−0.182773
$563$	7324.74	0.548314	0.274157	−	0.961685i	$-0.411601\pi$
$563$	7324.74	0.548314	0.274157	+	0.961685i	$0.411601\pi$
$564$	−4073.00	−0.304086
$565$	−40900.3	−3.04546
$566$	1637.01	0.121570
$567$	0	0
$568$	585.252	0.0432335
$569$	11184.4	0.824034	0.412017	−	0.911176i	$-0.364824\pi$
$569$	11184.4	0.824034	0.412017	+	0.911176i	$0.364824\pi$
$570$	4355.10	0.320026
$571$	−7888.73	−0.578166	−0.289083	−	0.957304i	$-0.593350\pi$
$571$	−7888.73	−0.578166	−0.289083	+	0.957304i	$0.593350\pi$
$572$	34505.8	2.52231
$573$	−40935.9	−2.98451
$574$	0	0
$575$	−57429.2	−4.16515
$576$	−8587.51	−0.621203
$577$	−3002.16	−0.216606	−0.108303	−	0.994118i	$-0.534542\pi$
$577$	−3002.16	−0.216606	−0.108303	+	0.994118i	$0.534542\pi$
$578$	1193.89	0.0859158
$579$	26900.1	1.93080
$580$	33486.1	2.39730
$581$	0	0
$582$	−1556.18	−0.110834
$583$	10710.8	0.760887
$584$	−2194.35	−0.155485
$585$	74431.1	5.26042
$586$	7999.16	0.563894
$587$	6016.80	0.423067	0.211533	−	0.977371i	$-0.432154\pi$
$587$	6016.80	0.423067	0.211533	+	0.977371i	$0.432154\pi$
$588$	0	0
$589$	−300.534	−0.0210242
$590$	−8277.71	−0.577606
$591$	21360.0	1.48669
$592$	4802.85	0.333439
$593$	14810.7	1.02564	0.512818	−	0.858497i	$-0.328602\pi$
$593$	14810.7	1.02564	0.512818	+	0.858497i	$0.328602\pi$
$594$	−7084.88	−0.489388
$595$	0	0
$596$	−14824.5	−1.01885
$597$	39418.7	2.70234
$598$	13633.7	0.932316
$599$	−17394.6	−1.18652	−0.593260	−	0.805011i	$-0.702159\pi$
$599$	−17394.6	−1.18652	−0.593260	+	0.805011i	$0.702159\pi$
$600$	−38779.6	−2.63862
$601$	22742.5	1.54357	0.771786	−	0.635882i	$-0.219363\pi$
$601$	22742.5	1.54357	0.771786	+	0.635882i	$0.219363\pi$
$602$	0	0
$603$	−5842.73	−0.394585
$604$	3199.18	0.215518
$605$	45076.5	3.02913
$606$	3505.30	0.234972
$607$	15336.4	1.02551	0.512756	−	0.858534i	$-0.328624\pi$
$607$	15336.4	1.02551	0.512756	+	0.858534i	$0.328624\pi$
$608$	−4042.64	−0.269656
$609$	0	0
$610$	12761.1	0.847020
$611$	−5674.85	−0.375744
$612$	−18204.2	−1.20239
$613$	−2333.58	−0.153756	−0.0768781	−	0.997041i	$-0.524495\pi$
$613$	−2333.58	−0.153756	−0.0768781	+	0.997041i	$0.524495\pi$
$614$	−2777.15	−0.182535
$615$	7263.34	0.476238
$616$	0	0
$617$	−13983.5	−0.912405	−0.456202	−	0.889876i	$-0.650791\pi$
$617$	−13983.5	−0.912405	−0.456202	+	0.889876i	$0.650791\pi$
$618$	5776.92	0.376023
$619$	−4861.99	−0.315702	−0.157851	−	0.987463i	$-0.550457\pi$
$619$	−4861.99	−0.315702	−0.157851	+	0.987463i	$0.550457\pi$
$620$	1740.70	0.112755
$621$	22487.8	1.45315
$622$	5509.95	0.355191
$623$	0	0
$624$	−29938.8	−1.92069
$625$	50591.0	3.23782
$626$	−3448.09	−0.220149
$627$	12782.1	0.814140
$628$	608.129	0.0386417
$629$	6660.78	0.422230
$630$	0	0
$631$	−5433.52	−0.342797	−0.171399	−	0.985202i	$-0.554829\pi$
$631$	−5433.52	−0.342797	−0.171399	+	0.985202i	$0.554829\pi$
$632$	8931.35	0.562136
$633$	−10346.3	−0.649650
$634$	1587.66	0.0994541
$635$	15219.7	0.951143
$636$	−10805.8	−0.673706
$637$	0	0
$638$	−12234.2	−0.759178
$639$	1744.03	0.107970
$640$	30384.8	1.87666
$641$	2287.08	0.140927	0.0704636	−	0.997514i	$-0.477552\pi$
$641$	2287.08	0.140927	0.0704636	+	0.997514i	$0.477552\pi$
$642$	3525.11	0.216706
$643$	−15214.6	−0.933136	−0.466568	−	0.884485i	$-0.654510\pi$
$643$	−15214.6	−0.933136	−0.466568	+	0.884485i	$0.654510\pi$
$644$	0	0
$645$	85507.9	5.21996
$646$	−1484.07	−0.0903871
$647$	22373.8	1.35951	0.679757	−	0.733438i	$-0.262085\pi$
$647$	22373.8	1.35951	0.679757	+	0.733438i	$0.262085\pi$
$648$	−1092.90	−0.0662547
$649$	−24294.8	−1.46942
$650$	−25432.6	−1.53469
$651$	0	0
$652$	23692.5	1.42311
$653$	−16760.2	−1.00441	−0.502204	−	0.864749i	$-0.667478\pi$
$653$	−16760.2	−1.00441	−0.502204	+	0.864749i	$0.667478\pi$
$654$	−4123.69	−0.246558
$655$	21255.3	1.26796
$656$	−1784.71	−0.106221
$657$	−6539.10	−0.388302
$658$	0	0
$659$	4392.75	0.259662	0.129831	−	0.991536i	$-0.458557\pi$
$659$	4392.75	0.259662	0.129831	+	0.991536i	$0.458557\pi$
$660$	−74034.0	−4.36632
$661$	−29967.5	−1.76339	−0.881696	−	0.471817i	$-0.843598\pi$
$661$	−29967.5	−1.76339	−0.881696	+	0.471817i	$0.843598\pi$
$662$	6234.62	0.366035
$663$	−41520.3	−2.43215
$664$	16099.7	0.940951
$665$	0	0
$666$	−4401.11	−0.256066
$667$	38832.0	2.25424
$668$	13348.7	0.773169
$669$	11703.6	0.676365
$670$	2758.86	0.159081
$671$	37453.4	2.15480
$672$	0	0
$673$	−16552.8	−0.948090	−0.474045	−	0.880501i	$-0.657207\pi$
$673$	−16552.8	−0.948090	−0.474045	+	0.880501i	$0.657207\pi$
$674$	8229.00	0.470281
$675$	−41949.1	−2.39203
$676$	−32872.2	−1.87029
$677$	−23545.0	−1.33664	−0.668321	−	0.743873i	$-0.732987\pi$
$677$	−23545.0	−1.33664	−0.668321	+	0.743873i	$0.732987\pi$
$678$	−15075.4	−0.853935
$679$	0	0
$680$	18261.6	1.02985
$681$	−46948.5	−2.64181
$682$	−635.967	−0.0357074
$683$	22381.6	1.25389	0.626947	−	0.779062i	$-0.284304\pi$
$683$	22381.6	1.25389	0.626947	+	0.779062i	$0.284304\pi$
$684$	−7877.43	−0.440353
$685$	12578.3	0.701595
$686$	0	0
$687$	9736.07	0.540690
$688$	−21010.6	−1.16427
$689$	−15055.5	−0.832466
$690$	−29251.9	−1.61391
$691$	−12486.8	−0.687436	−0.343718	−	0.939073i	$-0.611686\pi$
$691$	−12486.8	−0.687436	−0.343718	+	0.939073i	$0.611686\pi$
$692$	18306.9	1.00567
$693$	0	0
$694$	609.712	0.0333492
$695$	1742.10	0.0950815
$696$	26221.7	1.42806
$697$	−2475.11	−0.134507
$698$	−5366.32	−0.291000
$699$	14520.1	0.785694
$700$	0	0
$701$	−30002.2	−1.61650	−0.808250	−	0.588840i	$-0.799585\pi$
$701$	−30002.2	−1.61650	−0.808250	+	0.588840i	$0.799585\pi$
$702$	9958.75	0.535425
$703$	2882.29	0.154634
$704$	11901.0	0.637125
$705$	12175.7	0.650444
$706$	−7668.48	−0.408792
$707$	0	0
$708$	24510.1	1.30105
$709$	19374.5	1.02627	0.513135	−	0.858308i	$-0.328484\pi$
$709$	19374.5	1.02627	0.513135	+	0.858308i	$0.328484\pi$
$710$	−823.510	−0.0435293
$711$	26615.1	1.40386
$712$	−489.777	−0.0257797
$713$	2018.59	0.106027
$714$	0	0
$715$	−103150.	−5.39525
$716$	20953.6	1.09368
$717$	12914.6	0.672671
$718$	−6728.25	−0.349716
$719$	22060.8	1.14427	0.572135	−	0.820159i	$-0.306115\pi$
$719$	22060.8	1.14427	0.572135	+	0.820159i	$0.306115\pi$
$720$	39239.6	2.03108
$721$	0	0
$722$	5812.61	0.299616
$723$	8842.95	0.454873
$724$	−17954.7	−0.921659
$725$	−72437.7	−3.71072
$726$	16614.7	0.849354
$727$	11896.6	0.606908	0.303454	−	0.952846i	$-0.401860\pi$
$727$	11896.6	0.606908	0.303454	+	0.952846i	$0.401860\pi$
$728$	0	0
$729$	−32081.8	−1.62992
$730$	3087.68	0.156548
$731$	−29138.3	−1.47431
$732$	−37785.4	−1.90791
$733$	−21405.1	−1.07860	−0.539302	−	0.842112i	$-0.681312\pi$
$733$	−21405.1	−1.07860	−0.539302	+	0.842112i	$0.681312\pi$
$734$	9159.09	0.460584
$735$	0	0
$736$	27153.2	1.35989
$737$	8097.16	0.404698
$738$	1635.43	0.0815731
$739$	−3158.70	−0.157232	−0.0786161	−	0.996905i	$-0.525050\pi$
$739$	−3158.70	−0.157232	−0.0786161	+	0.996905i	$0.525050\pi$
$740$	−16694.3	−0.829318
$741$	−17966.9	−0.890728
$742$	0	0
$743$	−8239.41	−0.406830	−0.203415	−	0.979093i	$-0.565204\pi$
$743$	−8239.41	−0.406830	−0.203415	+	0.979093i	$0.565204\pi$
$744$	1363.08	0.0671678
$745$	44315.7	2.17933
$746$	12506.6	0.613806
$747$	47976.7	2.34990
$748$	25228.3	1.23321
$749$	0	0
$750$	33727.5	1.64207
$751$	−4894.04	−0.237798	−0.118899	−	0.992906i	$-0.537936\pi$
$751$	−4894.04	−0.237798	−0.118899	+	0.992906i	$0.537936\pi$
$752$	−2991.75	−0.145077
$753$	−27652.5	−1.33826
$754$	17196.8	0.830596
$755$	−9563.51	−0.460996
$756$	0	0
$757$	13377.1	0.642272	0.321136	−	0.947033i	$-0.395935\pi$
$757$	13377.1	0.642272	0.321136	+	0.947033i	$0.395935\pi$
$758$	−1655.49	−0.0793274
$759$	−85853.2	−4.10576
$760$	7902.27	0.377165
$761$	29091.1	1.38574	0.692872	−	0.721061i	$-0.256345\pi$
$761$	29091.1	1.38574	0.692872	+	0.721061i	$0.256345\pi$
$762$	5609.83	0.266696
$763$	0	0
$764$	−34962.7	−1.65564
$765$	54419.0	2.57193
$766$	−2274.40	−0.107281
$767$	34149.5	1.60765
$768$	−2301.59	−0.108140
$769$	4119.15	0.193160	0.0965801	−	0.995325i	$-0.469210\pi$
$769$	4119.15	0.193160	0.0965801	+	0.995325i	$0.469210\pi$
$770$	0	0
$771$	−21364.6	−0.997959
$772$	22975.0	1.07110
$773$	−32823.2	−1.52726	−0.763628	−	0.645656i	$-0.776584\pi$
$773$	−32823.2	−1.52726	−0.763628	+	0.645656i	$0.776584\pi$
$774$	19253.1	0.894107
$775$	−3765.52	−0.174531
$776$	−2823.66	−0.130623
$777$	0	0
$778$	11261.9	0.518972
$779$	−1071.04	−0.0492607
$780$	104065.	4.77707
$781$	−2416.97	−0.110738
$782$	9968.08	0.455828
$783$	28364.8	1.29460
$784$	0	0
$785$	−1817.92	−0.0826551
$786$	7834.49	0.355530
$787$	19397.6	0.878590	0.439295	−	0.898343i	$-0.355228\pi$
$787$	19397.6	0.878590	0.439295	+	0.898343i	$0.355228\pi$
$788$	18243.2	0.824731
$789$	−3826.24	−0.172646
$790$	−12567.3	−0.565982
$791$	0	0
$792$	−35414.3	−1.58888
$793$	−52645.7	−2.35751
$794$	−9740.10	−0.435344
$795$	32302.4	1.44107
$796$	33666.9	1.49911
$797$	−36278.0	−1.61234	−0.806169	−	0.591686i	$-0.798463\pi$
$797$	−36278.0	−1.61234	−0.806169	+	0.591686i	$0.798463\pi$
$798$	0	0
$799$	−4149.07	−0.183709
$800$	−50652.0	−2.23852
$801$	−1459.52	−0.0643815
$802$	6482.07	0.285399
$803$	9062.22	0.398255
$804$	−8168.93	−0.358328
$805$	0	0
$806$	893.936	0.0390665
$807$	53101.7	2.31632
$808$	6360.32	0.276925
$809$	12367.7	0.537486	0.268743	−	0.963212i	$-0.413392\pi$
$809$	12367.7	0.537486	0.268743	+	0.963212i	$0.413392\pi$
$810$	1537.82	0.0667079
$811$	16260.6	0.704052	0.352026	−	0.935990i	$-0.385493\pi$
$811$	16260.6	0.704052	0.352026	+	0.935990i	$0.385493\pi$
$812$	0	0
$813$	59667.7	2.57397
$814$	6099.29	0.262629
$815$	−70825.4	−3.04405
$816$	−21889.2	−0.939064
$817$	−12608.9	−0.539937
$818$	9486.89	0.405503
$819$	0	0
$820$	6203.51	0.264190
$821$	−42428.1	−1.80360	−0.901798	−	0.432159i	$-0.857752\pi$
$821$	−42428.1	−1.80360	−0.901798	+	0.432159i	$0.857752\pi$
$822$	4636.24	0.196724
$823$	−23206.1	−0.982883	−0.491442	−	0.870910i	$-0.663530\pi$
$823$	−23206.1	−0.982883	−0.491442	+	0.870910i	$0.663530\pi$
$824$	10482.2	0.443159
$825$	160152.	6.75851
$826$	0	0
$827$	15963.0	0.671206	0.335603	−	0.942003i	$-0.391060\pi$
$827$	15963.0	0.671206	0.335603	+	0.942003i	$0.391060\pi$
$828$	52910.3	2.22073
$829$	−17882.4	−0.749194	−0.374597	−	0.927188i	$-0.622219\pi$
$829$	−17882.4	−0.749194	−0.374597	+	0.927188i	$0.622219\pi$
$830$	−22654.0	−0.947387
$831$	25225.3	1.05301
$832$	−16728.5	−0.697061
$833$	0	0
$834$	642.120	0.0266604
$835$	−39904.2	−1.65382
$836$	10916.9	0.451639
$837$	1474.48	0.0608907
$838$	−1305.54	−0.0538174
$839$	−33423.7	−1.37534	−0.687672	−	0.726021i	$-0.741367\pi$
$839$	−33423.7	−1.37534	−0.687672	+	0.726021i	$0.741367\pi$
$840$	0	0
$841$	24591.3	1.00830
$842$	−7724.39	−0.316152
$843$	−21554.1	−0.880621
$844$	−8836.61	−0.360389
$845$	98266.9	4.00057
$846$	2741.50	0.111412
$847$	0	0
$848$	−7937.17	−0.321419
$849$	14489.9	0.585739
$850$	−18594.6	−0.750340
$851$	−19359.5	−0.779829
$852$	2438.39	0.0980493
$853$	3314.68	0.133051	0.0665255	−	0.997785i	$-0.478809\pi$
$853$	3314.68	0.133051	0.0665255	+	0.997785i	$0.478809\pi$
$854$	0	0
$855$	23548.5	0.941921
$856$	6396.26	0.255397
$857$	−27819.3	−1.10885	−0.554427	−	0.832232i	$-0.687063\pi$
$857$	−27819.3	−1.10885	−0.554427	+	0.832232i	$0.687063\pi$
$858$	−38020.2	−1.51281
$859$	−46348.7	−1.84097	−0.920487	−	0.390774i	$-0.872208\pi$
$859$	−46348.7	−1.84097	−0.920487	+	0.390774i	$0.872208\pi$
$860$	73031.0	2.89574
$861$	0	0
$862$	−4180.41	−0.165180
$863$	−12402.2	−0.489195	−0.244598	−	0.969625i	$-0.578656\pi$
$863$	−12402.2	−0.489195	−0.244598	+	0.969625i	$0.578656\pi$
$864$	19834.0	0.780981
$865$	−54726.0	−2.15114
$866$	−3512.42	−0.137826
$867$	10567.7	0.413952
$868$	0	0
$869$	−36884.6	−1.43984
$870$	−36896.6	−1.43783
$871$	−11381.6	−0.442769
$872$	−7482.39	−0.290580
$873$	−8414.42	−0.326214
$874$	4313.44	0.166939
$875$	0	0
$876$	−9142.55	−0.352623
$877$	−28319.3	−1.09039	−0.545196	−	0.838308i	$-0.683545\pi$
$877$	−28319.3	−1.09039	−0.545196	+	0.838308i	$0.683545\pi$
$878$	8562.15	0.329110
$879$	70804.1	2.71691
$880$	−54380.3	−2.08314
$881$	−50471.1	−1.93010	−0.965048	−	0.262075i	$-0.915593\pi$
$881$	−50471.1	−1.93010	−0.965048	+	0.262075i	$0.915593\pi$
$882$	0	0
$883$	−40941.9	−1.56037	−0.780184	−	0.625551i	$-0.784874\pi$
$883$	−40941.9	−1.56037	−0.780184	+	0.625551i	$0.784874\pi$
$884$	−35461.8	−1.34922
$885$	−73269.6	−2.78297
$886$	−5172.05	−0.196115
$887$	−3617.89	−0.136953	−0.0684763	−	0.997653i	$-0.521814\pi$
$887$	−3617.89	−0.136953	−0.0684763	+	0.997653i	$0.521814\pi$
$888$	−13072.7	−0.494021
$889$	0	0
$890$	689.167	0.0259561
$891$	4513.44	0.169704
$892$	9995.88	0.375210
$893$	−1795.41	−0.0672800
$894$	16334.3	0.611075
$895$	−62638.1	−2.33940
$896$	0	0
$897$	120678.	4.49200
$898$	−8972.45	−0.333424
$899$	2546.13	0.0944587
$900$	−98699.7	−3.65555
$901$	−11007.6	−0.407010
$902$	−2266.46	−0.0836639
$903$	0	0
$904$	−27354.1	−1.00640
$905$	53673.1	1.97144
$906$	−3525.01	−0.129261
$907$	−4749.78	−0.173885	−0.0869426	−	0.996213i	$-0.527710\pi$
$907$	−4749.78	−0.173885	−0.0869426	+	0.996213i	$0.527710\pi$
$908$	−40098.0	−1.46553
$909$	18953.6	0.691584
$910$	0	0
$911$	−29998.8	−1.09100	−0.545502	−	0.838109i	$-0.683661\pi$
$911$	−29998.8	−1.09100	−0.545502	+	0.838109i	$0.683661\pi$
$912$	−9472.03	−0.343915
$913$	−66488.6	−2.41013
$914$	−912.852	−0.0330355
$915$	112954.	4.08104
$916$	8315.42	0.299945
$917$	0	0
$918$	7281.17	0.261780
$919$	−51092.6	−1.83394	−0.916970	−	0.398957i	$-0.869372\pi$
$919$	−51092.6	−1.83394	−0.916970	+	0.398957i	$0.869372\pi$
$920$	−53077.2	−1.90207
$921$	−24581.8	−0.879476
$922$	−8368.14	−0.298905
$923$	3397.37	0.121155
$924$	0	0
$925$	36113.5	1.28368
$926$	16331.2	0.579565
$927$	31236.5	1.10673
$928$	34249.4	1.21152
$929$	−43429.8	−1.53379	−0.766893	−	0.641775i	$-0.778198\pi$
$929$	−43429.8	−1.53379	−0.766893	+	0.641775i	$0.778198\pi$
$930$	−1917.99	−0.0676272
$931$	0	0
$932$	12401.4	0.435859
$933$	48771.0	1.71135
$934$	−12004.1	−0.420543
$935$	−75416.7	−2.63785
$936$	49779.6	1.73835
$937$	16515.9	0.575826	0.287913	−	0.957656i	$-0.407039\pi$
$937$	16515.9	0.575826	0.287913	+	0.957656i	$0.407039\pi$
$938$	0	0
$939$	−30520.6	−1.06070
$940$	10399.1	0.360830
$941$	8499.25	0.294440	0.147220	−	0.989104i	$-0.452968\pi$
$941$	8499.25	0.294440	0.147220	+	0.989104i	$0.452968\pi$
$942$	−670.066	−0.0231761
$943$	7193.87	0.248425
$944$	18003.4	0.620722
$945$	0	0
$946$	−26682.0	−0.917024
$947$	38271.8	1.31327	0.656636	−	0.754208i	$-0.271979\pi$
$947$	38271.8	1.31327	0.656636	+	0.754208i	$0.271979\pi$
$948$	37211.6	1.27487
$949$	−12738.2	−0.435720
$950$	−8046.36	−0.274798
$951$	14053.1	0.479181
$952$	0	0
$953$	14015.9	0.476410	0.238205	−	0.971215i	$-0.423441\pi$
$953$	14015.9	0.476410	0.238205	+	0.971215i	$0.423441\pi$
$954$	7273.26	0.246835
$955$	104516.	3.54143
$956$	11030.2	0.373160
$957$	−108290.	−3.65781
$958$	1159.77	0.0391132
$959$	0	0
$960$	35891.8	1.20667
$961$	−29658.6	−0.995557
$962$	−8573.36	−0.287335
$963$	19060.7	0.637821
$964$	7552.62	0.252338
$965$	−68680.6	−2.29109
$966$	0	0
$967$	−52047.4	−1.73085	−0.865425	−	0.501039i	$-0.832951\pi$
$967$	−52047.4	−1.73085	−0.865425	+	0.501039i	$0.832951\pi$
$968$	30147.2	1.00100
$969$	−13136.2	−0.435495
$970$	3973.18	0.131517
$971$	−4985.98	−0.164787	−0.0823933	−	0.996600i	$-0.526256\pi$
$971$	−4985.98	−0.164787	−0.0823933	+	0.996600i	$0.526256\pi$
$972$	−29172.4	−0.962660
$973$	0	0
$974$	9198.19	0.302597
$975$	−225115.	−7.39430
$976$	−27754.5	−0.910246
$977$	−23828.2	−0.780279	−0.390140	−	0.920756i	$-0.627573\pi$
$977$	−23828.2	−0.780279	−0.390140	+	0.920756i	$0.627573\pi$
$978$	−26105.5	−0.853540
$979$	2022.68	0.0660317
$980$	0	0
$981$	−22297.3	−0.725685
$982$	−9573.44	−0.311100
$983$	43241.6	1.40304	0.701522	−	0.712647i	$-0.252504\pi$
$983$	43241.6	1.40304	0.701522	+	0.712647i	$0.252504\pi$
$984$	4857.73	0.157377
$985$	−54535.7	−1.76411
$986$	12573.1	0.406095
$987$	0	0
$988$	−15345.2	−0.494126
$989$	84690.0	2.72294
$990$	49831.6	1.59975
$991$	−12305.0	−0.394430	−0.197215	−	0.980360i	$-0.563190\pi$
$991$	−12305.0	−0.394430	−0.197215	+	0.980360i	$0.563190\pi$
$992$	1780.38	0.0569830
$993$	55185.4	1.76360
$994$	0	0
$995$	−100643.	−3.20662
$996$	67077.9	2.13398
$997$	36570.2	1.16167	0.580837	−	0.814020i	$-0.302725\pi$
$997$	36570.2	1.16167	0.580837	+	0.814020i	$0.302725\pi$
$998$	−14837.6	−0.470616
$999$	−14141.1	−0.447853

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.4.a.h.1.14	✓	30
7.6	odd	2		2009.4.a.i.1.14	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2009.4.a.h.1.14	✓	30	1.1	even	1	trivial
2009.4.a.i.1.14	yes	30	7.6	odd	2

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)

\(f(q)\)	\(=\)	\(q-0.941072 q^{2} -8.32984 q^{3} -7.11438 q^{4} +21.2675 q^{5} +7.83898 q^{6} +14.2237 q^{8} +42.3862 q^{9} +O(q^{10})\)	\(q-0.941072 q^{2} -8.32984 q^{3} -7.11438 q^{4} +21.2675 q^{5} +7.83898 q^{6} +14.2237 q^{8} +42.3862 q^{9} -20.0142 q^{10} -58.7410 q^{11} +59.2617 q^{12} +82.5683 q^{13} -177.155 q^{15} +43.5295 q^{16} +60.3684 q^{17} -39.8885 q^{18} +26.1230 q^{19} -151.305 q^{20} +55.2795 q^{22} -175.460 q^{23} -118.481 q^{24} +327.306 q^{25} -77.7027 q^{26} -128.165 q^{27} -221.315 q^{29} +166.715 q^{30} -11.5046 q^{31} -154.754 q^{32} +489.303 q^{33} -56.8110 q^{34} -301.552 q^{36} +110.335 q^{37} -24.5836 q^{38} -687.781 q^{39} +302.503 q^{40} -41.0000 q^{41} -482.674 q^{43} +417.906 q^{44} +901.448 q^{45} +165.121 q^{46} -68.7291 q^{47} -362.594 q^{48} -308.018 q^{50} -502.859 q^{51} -587.423 q^{52} -182.340 q^{53} +120.612 q^{54} -1249.27 q^{55} -217.600 q^{57} +208.273 q^{58} +413.591 q^{59} +1260.35 q^{60} -637.602 q^{61} +10.8266 q^{62} -202.601 q^{64} +1756.02 q^{65} -460.469 q^{66} -137.845 q^{67} -429.484 q^{68} +1461.56 q^{69} +41.1462 q^{71} +602.890 q^{72} -154.274 q^{73} -103.834 q^{74} -2726.41 q^{75} -185.849 q^{76} +647.251 q^{78} +627.920 q^{79} +925.764 q^{80} -76.8363 q^{81} +38.5839 q^{82} +1131.89 q^{83} +1283.89 q^{85} +454.231 q^{86} +1843.52 q^{87} -835.515 q^{88} -34.4338 q^{89} -848.328 q^{90} +1248.29 q^{92} +95.8312 q^{93} +64.6790 q^{94} +555.570 q^{95} +1289.08 q^{96} -198.518 q^{97} -2489.81 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + q^{2} - 12 q^{3} + 103 q^{4} - 20 q^{5} - 36 q^{6} - 9 q^{8} + 318 q^{9}+O(q^{10}) \) 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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