LMFDB - Embedded newform 2009.4.a.h.1.15

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			1.15
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)

$f(q)$	$=$	$q-0.208351 q^{2} -3.07702 q^{3} -7.95659 q^{4} +2.07481 q^{5} +0.641101 q^{6} +3.32458 q^{8} -17.5319 q^{9} +O(q^{10})$	\(q-0.208351 q^{2} -3.07702 q^{3} -7.95659 q^{4} +2.07481 q^{5} +0.641101 q^{6} +3.32458 q^{8} -17.5319 q^{9} -0.432289 q^{10} -38.9328 q^{11} +24.4826 q^{12} -73.0514 q^{13} -6.38423 q^{15} +62.9600 q^{16} +83.6320 q^{17} +3.65280 q^{18} +48.6959 q^{19} -16.5084 q^{20} +8.11170 q^{22} +20.7593 q^{23} -10.2298 q^{24} -120.695 q^{25} +15.2203 q^{26} +137.026 q^{27} +134.071 q^{29} +1.33016 q^{30} +159.615 q^{31} -39.7144 q^{32} +119.797 q^{33} -17.4248 q^{34} +139.494 q^{36} +155.189 q^{37} -10.1458 q^{38} +224.781 q^{39} +6.89786 q^{40} -41.0000 q^{41} -397.813 q^{43} +309.772 q^{44} -36.3754 q^{45} -4.32523 q^{46} -83.7629 q^{47} -193.729 q^{48} +25.1470 q^{50} -257.337 q^{51} +581.240 q^{52} +203.758 q^{53} -28.5495 q^{54} -80.7782 q^{55} -149.838 q^{57} -27.9338 q^{58} +227.030 q^{59} +50.7967 q^{60} +391.924 q^{61} -33.2560 q^{62} -495.406 q^{64} -151.568 q^{65} -24.9599 q^{66} +627.351 q^{67} -665.425 q^{68} -63.8769 q^{69} -330.480 q^{71} -58.2862 q^{72} +519.291 q^{73} -32.3339 q^{74} +371.382 q^{75} -387.453 q^{76} -46.8333 q^{78} +101.300 q^{79} +130.630 q^{80} +51.7310 q^{81} +8.54240 q^{82} +5.89149 q^{83} +173.520 q^{85} +82.8848 q^{86} -412.539 q^{87} -129.435 q^{88} +599.027 q^{89} +7.57887 q^{90} -165.173 q^{92} -491.139 q^{93} +17.4521 q^{94} +101.035 q^{95} +122.202 q^{96} -538.109 q^{97} +682.568 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.208351	−0.0736633	−0.0368316	−	0.999321i	$-0.511727\pi$
$2$	−0.208351	−0.0736633	−0.0368316	+	0.999321i	$0.511727\pi$
$3$	−3.07702	−0.592173	−0.296087	−	0.955161i	$-0.595682\pi$
$3$	−3.07702	−0.592173	−0.296087	+	0.955161i	$0.595682\pi$
$4$	−7.95659	−0.994574
$5$	2.07481	0.185577	0.0927883	−	0.995686i	$-0.470422\pi$
$5$	2.07481	0.185577	0.0927883	+	0.995686i	$0.470422\pi$
$6$	0.641101	0.0436214
$7$	0	0
$7$	0	0
$8$	3.32458	0.146927
$9$	−17.5319	−0.649331
$10$	−0.432289	−0.0136702
$11$	−38.9328	−1.06715	−0.533577	−	0.845752i	$-0.679152\pi$
$11$	−38.9328	−1.06715	−0.533577	+	0.845752i	$0.679152\pi$
$12$	24.4826	0.588960
$13$	−73.0514	−1.55852	−0.779262	−	0.626698i	$-0.784406\pi$
$13$	−73.0514	−1.55852	−0.779262	+	0.626698i	$0.784406\pi$
$14$	0	0
$15$	−6.38423	−0.109893
$16$	62.9600	0.983751
$17$	83.6320	1.19316	0.596580	−	0.802553i	$-0.296526\pi$
$17$	83.6320	1.19316	0.596580	+	0.802553i	$0.296526\pi$
$18$	3.65280	0.0478319
$19$	48.6959	0.587979	0.293989	−	0.955809i	$-0.405017\pi$
$19$	48.6959	0.587979	0.293989	+	0.955809i	$0.405017\pi$
$20$	−16.5084	−0.184570
$21$	0	0
$22$	8.11170	0.0786100
$23$	20.7593	0.188201	0.0941004	−	0.995563i	$-0.470003\pi$
$23$	20.7593	0.188201	0.0941004	+	0.995563i	$0.470003\pi$
$24$	−10.2298	−0.0870062
$25$	−120.695	−0.965561
$26$	15.2203	0.114806
$27$	137.026	0.976690
$28$	0	0
$29$	134.071	0.858493	0.429247	−	0.903187i	$-0.358779\pi$
$29$	134.071	0.858493	0.429247	+	0.903187i	$0.358779\pi$
$30$	1.33016	0.00809512
$31$	159.615	0.924765	0.462382	−	0.886681i	$-0.346995\pi$
$31$	159.615	0.924765	0.462382	+	0.886681i	$0.346995\pi$
$32$	−39.7144	−0.219393
$33$	119.797	0.631940
$34$	−17.4248	−0.0878922
$35$	0	0
$36$	139.494	0.645807
$37$	155.189	0.689539	0.344770	−	0.938687i	$-0.387957\pi$
$37$	155.189	0.689539	0.344770	+	0.938687i	$0.387957\pi$
$38$	−10.1458	−0.0433125
$39$	224.781	0.922916
$40$	6.89786	0.0272662
$41$	−41.0000	−0.156174
$41$	−41.0000	−0.156174
$42$	0	0
$43$	−397.813	−1.41083	−0.705417	−	0.708792i	$-0.749240\pi$
$43$	−397.813	−1.41083	−0.705417	+	0.708792i	$0.749240\pi$
$44$	309.772	1.06136
$45$	−36.3754	−0.120501
$46$	−4.32523	−0.0138635
$47$	−83.7629	−0.259959	−0.129980	−	0.991517i	$-0.541491\pi$
$47$	−83.7629	−0.259959	−0.129980	+	0.991517i	$0.541491\pi$
$48$	−193.729	−0.582551
$49$	0	0
$50$	25.1470	0.0711264
$51$	−257.337	−0.706558
$52$	581.240	1.55007
$53$	203.758	0.528081	0.264041	−	0.964512i	$-0.414945\pi$
$53$	203.758	0.528081	0.264041	+	0.964512i	$0.414945\pi$
$54$	−28.5495	−0.0719462
$55$	−80.7782	−0.198039
$56$	0	0
$57$	−149.838	−0.348185
$58$	−27.9338	−0.0632394
$59$	227.030	0.500963	0.250482	−	0.968121i	$-0.419411\pi$
$59$	227.030	0.500963	0.250482	+	0.968121i	$0.419411\pi$
$60$	50.7967	0.109297
$61$	391.924	0.822634	0.411317	−	0.911492i	$-0.365069\pi$
$61$	391.924	0.822634	0.411317	+	0.911492i	$0.365069\pi$
$62$	−33.2560	−0.0681212
$63$	0	0
$64$	−495.406	−0.967589
$65$	−151.568	−0.289226
$66$	−24.9599	−0.0465507
$67$	627.351	1.14393	0.571964	−	0.820279i	$-0.306182\pi$
$67$	627.351	1.14393	0.571964	+	0.820279i	$0.306182\pi$
$68$	−665.425	−1.18669
$69$	−63.8769	−0.111447
$70$	0	0
$71$	−330.480	−0.552406	−0.276203	−	0.961099i	$-0.589076\pi$
$71$	−330.480	−0.552406	−0.276203	+	0.961099i	$0.589076\pi$
$72$	−58.2862	−0.0954042
$73$	519.291	0.832581	0.416290	−	0.909232i	$-0.363330\pi$
$73$	519.291	0.832581	0.416290	+	0.909232i	$0.363330\pi$
$74$	−32.3339	−0.0507937
$75$	371.382	0.571780
$76$	−387.453	−0.584788
$77$	0	0
$78$	−46.8333	−0.0679850
$79$	101.300	0.144267	0.0721335	−	0.997395i	$-0.477019\pi$
$79$	101.300	0.144267	0.0721335	+	0.997395i	$0.477019\pi$
$80$	130.630	0.182561
$81$	51.7310	0.0709615
$82$	8.54240	0.0115043
$83$	5.89149	0.00779126	0.00389563	−	0.999992i	$-0.498760\pi$
$83$	5.89149	0.00779126	0.00389563	+	0.999992i	$0.498760\pi$
$84$	0	0
$85$	173.520	0.221423
$86$	82.8848	0.103927
$87$	−412.539	−0.508377
$88$	−129.435	−0.156793
$89$	599.027	0.713446	0.356723	−	0.934210i	$-0.383894\pi$
$89$	599.027	0.713446	0.356723	+	0.934210i	$0.383894\pi$
$90$	7.57887	0.00887647
$91$	0	0
$92$	−165.173	−0.187180
$93$	−491.139	−0.547621
$94$	17.4521	0.0191494
$95$	101.035	0.109115
$96$	122.202	0.129919
$97$	−538.109	−0.563265	−0.281633	−	0.959522i	$-0.590876\pi$
$97$	−538.109	−0.563265	−0.281633	+	0.959522i	$0.590876\pi$
$98$	0	0
$99$	682.568	0.692936
$100$	960.322	0.960322
$101$	−909.093	−0.895625	−0.447813	−	0.894127i	$-0.647797\pi$
$101$	−909.093	−0.895625	−0.447813	+	0.894127i	$0.647797\pi$
$102$	53.6166	0.0520474
$103$	−732.445	−0.700679	−0.350339	−	0.936623i	$-0.613934\pi$
$103$	−732.445	−0.700679	−0.350339	+	0.936623i	$0.613934\pi$
$104$	−242.865	−0.228989
$105$	0	0
$106$	−42.4532	−0.0389002
$107$	734.745	0.663836	0.331918	−	0.943308i	$-0.392304\pi$
$107$	734.745	0.663836	0.331918	+	0.943308i	$0.392304\pi$
$108$	−1090.26	−0.971390
$109$	403.000	0.354132	0.177066	−	0.984199i	$-0.443339\pi$
$109$	403.000	0.354132	0.177066	+	0.984199i	$0.443339\pi$
$110$	16.8302	0.0145882
$111$	−477.521	−0.408327
$112$	0	0
$113$	95.9394	0.0798692	0.0399346	−	0.999202i	$-0.487285\pi$
$113$	95.9394	0.0798692	0.0399346	+	0.999202i	$0.487285\pi$
$114$	31.2190	0.0256485
$115$	43.0716	0.0349257
$116$	−1066.75	−0.853835
$117$	1280.73	1.01200
$118$	−47.3020	−0.0369026
$119$	0	0
$120$	−21.2249	−0.0161463
$121$	184.764	0.138816
$122$	−81.6578	−0.0605980
$123$	126.158	0.0924819
$124$	−1269.99	−0.919746
$125$	−509.771	−0.364762
$126$	0	0
$127$	860.764	0.601421	0.300711	−	0.953715i	$-0.402776\pi$
$127$	860.764	0.601421	0.300711	+	0.953715i	$0.402776\pi$
$128$	420.934	0.290669
$129$	1224.08	0.835458
$130$	31.5793	0.0213053
$131$	−1365.43	−0.910672	−0.455336	−	0.890320i	$-0.650481\pi$
$131$	−1365.43	−0.910672	−0.455336	+	0.890320i	$0.650481\pi$
$132$	−953.177	−0.628510
$133$	0	0
$134$	−130.709	−0.0842655
$135$	284.302	0.181251
$136$	278.041	0.175307
$137$	−690.524	−0.430624	−0.215312	−	0.976545i	$-0.569077\pi$
$137$	−690.524	−0.430624	−0.215312	+	0.976545i	$0.569077\pi$
$138$	13.3088	0.00820958
$139$	−977.605	−0.596542	−0.298271	−	0.954481i	$-0.596410\pi$
$139$	−977.605	−0.596542	−0.298271	+	0.954481i	$0.596410\pi$
$140$	0	0
$141$	257.740	0.153941
$142$	68.8560	0.0406920
$143$	2844.10	1.66318
$144$	−1103.81	−0.638780
$145$	278.171	0.159316
$146$	−108.195	−0.0613306
$147$	0	0
$148$	−1234.78	−0.685798
$149$	43.0310	0.0236593	0.0118297	−	0.999930i	$-0.496234\pi$
$149$	43.0310	0.0236593	0.0118297	+	0.999930i	$0.496234\pi$
$150$	−77.3778	−0.0421192
$151$	1146.31	0.617783	0.308892	−	0.951097i	$-0.400042\pi$
$151$	1146.31	0.617783	0.308892	+	0.951097i	$0.400042\pi$
$152$	161.893	0.0863899
$153$	−1466.23	−0.774756
$154$	0	0
$155$	331.171	0.171615
$156$	−1788.49	−0.917908
$157$	2435.28	1.23794	0.618969	−	0.785416i	$-0.287551\pi$
$157$	2435.28	1.23794	0.618969	+	0.785416i	$0.287551\pi$
$158$	−21.1059	−0.0106272
$159$	−626.968	−0.312716
$160$	−82.3998	−0.0407142
$161$	0	0
$162$	−10.7782	−0.00522726
$163$	3804.62	1.82823	0.914113	−	0.405460i	$-0.132889\pi$
$163$	3804.62	1.82823	0.914113	+	0.405460i	$0.132889\pi$
$164$	326.220	0.155326
$165$	248.556	0.117273
$166$	−1.22750	−0.000573930 0
$167$	1124.92	0.521251	0.260625	−	0.965440i	$-0.416071\pi$
$167$	1124.92	0.521251	0.260625	+	0.965440i	$0.416071\pi$
$168$	0	0
$169$	3139.50	1.42900
$170$	−36.1532	−0.0163107
$171$	−853.733	−0.381793
$172$	3165.23	1.40318
$173$	−328.958	−0.144568	−0.0722839	−	0.997384i	$-0.523029\pi$
$173$	−328.958	−0.144568	−0.0722839	+	0.997384i	$0.523029\pi$
$174$	85.9529	0.0374487
$175$	0	0
$176$	−2451.21	−1.04981
$177$	−698.577	−0.296657
$178$	−124.808	−0.0525548
$179$	1515.59	0.632851	0.316426	−	0.948617i	$-0.397517\pi$
$179$	1515.59	0.632851	0.316426	+	0.948617i	$0.397517\pi$
$180$	289.424	0.119847
$181$	−1251.03	−0.513747	−0.256873	−	0.966445i	$-0.582692\pi$
$181$	−1251.03	−0.513747	−0.256873	+	0.966445i	$0.582692\pi$
$182$	0	0
$183$	−1205.96	−0.487142
$184$	69.0159	0.0276517
$185$	321.988	0.127962
$186$	102.329	0.0403395
$187$	−3256.03	−1.27329
$188$	666.467	0.258549
$189$	0	0
$190$	−21.0507	−0.00803778
$191$	1366.21	0.517569	0.258785	−	0.965935i	$-0.416678\pi$
$191$	1366.21	0.517569	0.258785	+	0.965935i	$0.416678\pi$
$192$	1524.37	0.572980
$193$	672.198	0.250704	0.125352	−	0.992112i	$-0.459994\pi$
$193$	672.198	0.250704	0.125352	+	0.992112i	$0.459994\pi$
$194$	112.116	0.0414920
$195$	466.377	0.171272
$196$	0	0
$197$	−1181.83	−0.427422	−0.213711	−	0.976897i	$-0.568555\pi$
$197$	−1181.83	−0.427422	−0.213711	+	0.976897i	$0.568555\pi$
$198$	−142.214	−0.0510439
$199$	−1896.24	−0.675482	−0.337741	−	0.941239i	$-0.609663\pi$
$199$	−1896.24	−0.675482	−0.337741	+	0.941239i	$0.609663\pi$
$200$	−401.260	−0.141867
$201$	−1930.37	−0.677403
$202$	189.411	0.0659747
$203$	0	0
$204$	2047.53	0.702724
$205$	−85.0672	−0.0289822
$206$	152.606	0.0516143
$207$	−363.951	−0.122205
$208$	−4599.32	−1.53320
$209$	−1895.87	−0.627464
$210$	0	0
$211$	−5125.22	−1.67220	−0.836101	−	0.548576i	$-0.815170\pi$
$211$	−5125.22	−1.67220	−0.836101	+	0.548576i	$0.815170\pi$
$212$	−1621.22	−0.525216
$213$	1016.90	0.327120
$214$	−153.085	−0.0489003
$215$	−825.386	−0.261818
$216$	455.552	0.143502
$217$	0	0
$218$	−83.9656	−0.0260866
$219$	−1597.87	−0.493032
$220$	642.719	0.196964
$221$	−6109.43	−1.85957
$222$	99.4920	0.0300787
$223$	−2673.84	−0.802931	−0.401466	−	0.915874i	$-0.631499\pi$
$223$	−2673.84	−0.802931	−0.401466	+	0.915874i	$0.631499\pi$
$224$	0	0
$225$	2116.02	0.626969
$226$	−19.9891	−0.00588343
$227$	316.875	0.0926508	0.0463254	−	0.998926i	$-0.485249\pi$
$227$	316.875	0.0926508	0.0463254	+	0.998926i	$0.485249\pi$
$228$	1192.20	0.346296
$229$	−6455.34	−1.86280	−0.931399	−	0.364001i	$-0.881411\pi$
$229$	−6455.34	−1.86280	−0.931399	+	0.364001i	$0.881411\pi$
$230$	−8.97403	−0.00257274
$231$	0	0
$232$	445.728	0.126136
$233$	−4890.45	−1.37504	−0.687520	−	0.726166i	$-0.741300\pi$
$233$	−4890.45	−1.37504	−0.687520	+	0.726166i	$0.741300\pi$
$234$	−266.842	−0.0745471
$235$	−173.792	−0.0482423
$236$	−1806.39	−0.498245
$237$	−311.701	−0.0854311
$238$	0	0
$239$	5131.66	1.38887	0.694434	−	0.719556i	$-0.255655\pi$
$239$	5131.66	1.38887	0.694434	+	0.719556i	$0.255655\pi$
$240$	−401.952	−0.108108
$241$	−3654.00	−0.976659	−0.488330	−	0.872659i	$-0.662394\pi$
$241$	−3654.00	−0.976659	−0.488330	+	0.872659i	$0.662394\pi$
$242$	−38.4959	−0.0102257
$243$	−3858.87	−1.01871
$244$	−3118.38	−0.818171
$245$	0	0
$246$	−26.2852	−0.00681252
$247$	−3557.30	−0.916379
$248$	530.652	0.135873
$249$	−18.1282	−0.00461378
$250$	106.211	0.0268696
$251$	−3486.76	−0.876821	−0.438411	−	0.898775i	$-0.644458\pi$
$251$	−3486.76	−0.876821	−0.438411	+	0.898775i	$0.644458\pi$
$252$	0	0
$253$	−808.219	−0.200839
$254$	−179.341	−0.0443027
$255$	−533.926	−0.131121
$256$	3875.54	0.946178
$257$	−7220.87	−1.75263	−0.876314	−	0.481740i	$-0.840005\pi$
$257$	−7220.87	−1.75263	−0.876314	+	0.481740i	$0.840005\pi$
$258$	−255.038	−0.0615426
$259$	0	0
$260$	1205.96	0.287656
$261$	−2350.52	−0.557446
$262$	284.489	0.0670831
$263$	−6520.33	−1.52875	−0.764375	−	0.644773i	$-0.776952\pi$
$263$	−6520.33	−1.52875	−0.764375	+	0.644773i	$0.776952\pi$
$264$	398.275	0.0928489
$265$	422.759	0.0979995
$266$	0	0
$267$	−1843.22	−0.422484
$268$	−4991.57	−1.13772
$269$	−259.076	−0.0587217	−0.0293609	−	0.999569i	$-0.509347\pi$
$269$	−259.076	−0.0587217	−0.0293609	+	0.999569i	$0.509347\pi$
$270$	−59.2347	−0.0133515
$271$	4993.55	1.11932	0.559661	−	0.828722i	$-0.310931\pi$
$271$	4993.55	1.11932	0.559661	+	0.828722i	$0.310931\pi$
$272$	5265.47	1.17377
$273$	0	0
$274$	143.872	0.0317212
$275$	4699.00	1.03040
$276$	508.242	0.110843
$277$	−487.474	−0.105738	−0.0528691	−	0.998601i	$-0.516837\pi$
$277$	−487.474	−0.105738	−0.0528691	+	0.998601i	$0.516837\pi$
$278$	203.685	0.0439433
$279$	−2798.36	−0.600478
$280$	0	0
$281$	−2311.78	−0.490781	−0.245391	−	0.969424i	$-0.578916\pi$
$281$	−2311.78	−0.490781	−0.245391	+	0.969424i	$0.578916\pi$
$282$	−53.7005	−0.0113398
$283$	−5080.55	−1.06716	−0.533582	−	0.845748i	$-0.679154\pi$
$283$	−5080.55	−1.06716	−0.533582	+	0.845748i	$0.679154\pi$
$284$	2629.50	0.549408
$285$	−310.886	−0.0646151
$286$	−592.571	−0.122516
$287$	0	0
$288$	696.270	0.142459
$289$	2081.31	0.423633
$290$	−57.9573	−0.0117358
$291$	1655.77	0.333551
$292$	−4131.78	−0.828063
$293$	−7011.41	−1.39799	−0.698995	−	0.715126i	$-0.746369\pi$
$293$	−7011.41	−1.39799	−0.698995	+	0.715126i	$0.746369\pi$
$294$	0	0
$295$	471.045	0.0929670
$296$	515.938	0.101312
$297$	−5334.80	−1.04228
$298$	−8.96556	−0.00174282
$299$	−1516.50	−0.293315
$300$	−2954.93	−0.568677
$301$	0	0
$302$	−238.835	−0.0455080
$303$	2797.30	0.530365
$304$	3065.89	0.578425
$305$	813.167	0.152662
$306$	305.491	0.0570711
$307$	−5277.60	−0.981135	−0.490567	−	0.871403i	$-0.663210\pi$
$307$	−5277.60	−0.981135	−0.490567	+	0.871403i	$0.663210\pi$
$308$	0	0
$309$	2253.75	0.414923
$310$	−68.9998	−0.0126417
$311$	−1005.14	−0.183267	−0.0916336	−	0.995793i	$-0.529209\pi$
$311$	−1005.14	−0.183267	−0.0916336	+	0.995793i	$0.529209\pi$
$312$	747.301	0.135601
$313$	1447.74	0.261440	0.130720	−	0.991419i	$-0.458271\pi$
$313$	1447.74	0.261440	0.130720	+	0.991419i	$0.458271\pi$
$314$	−507.393	−0.0911905
$315$	0	0
$316$	−806.000	−0.143484
$317$	−5578.05	−0.988310	−0.494155	−	0.869374i	$-0.664523\pi$
$317$	−5578.05	−0.988310	−0.494155	+	0.869374i	$0.664523\pi$
$318$	130.629	0.0230357
$319$	−5219.75	−0.916144
$320$	−1027.87	−0.179562
$321$	−2260.83	−0.393106
$322$	0	0
$323$	4072.53	0.701554
$324$	−411.602	−0.0705765
$325$	8816.95	1.50485
$326$	−792.697	−0.134673
$327$	−1240.04	−0.209708
$328$	−136.308	−0.0229461
$329$	0	0
$330$	−51.7870	−0.00863873
$331$	10774.1	1.78911	0.894557	−	0.446953i	$-0.147491\pi$
$331$	10774.1	1.78911	0.894557	+	0.446953i	$0.147491\pi$
$332$	−46.8761	−0.00774898
$333$	−2720.77	−0.447739
$334$	−234.378	−0.0383971
$335$	1301.63	0.212286
$336$	0	0
$337$	10050.7	1.62462	0.812311	−	0.583224i	$-0.198209\pi$
$337$	10050.7	1.62462	0.812311	+	0.583224i	$0.198209\pi$
$338$	−654.120	−0.105265
$339$	−295.208	−0.0472964
$340$	−1380.63	−0.220221
$341$	−6214.26	−0.986865
$342$	177.876	0.0281241
$343$	0	0
$344$	−1322.56	−0.207289
$345$	−132.532	−0.0206820
$346$	68.5388	0.0106493
$347$	−1300.10	−0.201133	−0.100567	−	0.994930i	$-0.532066\pi$
$347$	−1300.10	−0.201133	−0.100567	+	0.994930i	$0.532066\pi$
$348$	3282.40	0.505618
$349$	−3067.36	−0.470465	−0.235232	−	0.971939i	$-0.575585\pi$
$349$	−3067.36	−0.470465	−0.235232	+	0.971939i	$0.575585\pi$
$350$	0	0
$351$	−10009.9	−1.52219
$352$	1546.19	0.234126
$353$	12705.0	1.91563	0.957816	−	0.287383i	$-0.0927852\pi$
$353$	12705.0	1.91563	0.957816	+	0.287383i	$0.0927852\pi$
$354$	145.549	0.0218527
$355$	−685.684	−0.102514
$356$	−4766.21	−0.709575
$357$	0	0
$358$	−315.775	−0.0466179
$359$	2009.26	0.295388	0.147694	−	0.989033i	$-0.452815\pi$
$359$	2009.26	0.295388	0.147694	+	0.989033i	$0.452815\pi$
$360$	−120.933	−0.0177048
$361$	−4487.71	−0.654281
$362$	260.653	0.0378443
$363$	−568.524	−0.0822032
$364$	0	0
$365$	1077.43	0.154508
$366$	251.263	0.0358845
$367$	3687.62	0.524502	0.262251	−	0.965000i	$-0.415535\pi$
$367$	3687.62	0.524502	0.262251	+	0.965000i	$0.415535\pi$
$368$	1307.01	0.185143
$369$	718.809	0.101408
$370$	−67.0866	−0.00942613
$371$	0	0
$372$	3907.79	0.544649
$373$	63.7217	0.00884554	0.00442277	−	0.999990i	$-0.498592\pi$
$373$	63.7217	0.00884554	0.00442277	+	0.999990i	$0.498592\pi$
$374$	678.398	0.0937944
$375$	1568.58	0.216002
$376$	−278.476	−0.0381950
$377$	−9794.05	−1.33798
$378$	0	0
$379$	1745.13	0.236520	0.118260	−	0.992983i	$-0.462268\pi$
$379$	1745.13	0.236520	0.118260	+	0.992983i	$0.462268\pi$
$380$	−803.891	−0.108523
$381$	−2648.59	−0.356145
$382$	−284.652	−0.0381259
$383$	6348.80	0.847020	0.423510	−	0.905891i	$-0.360798\pi$
$383$	6348.80	0.847020	0.423510	+	0.905891i	$0.360798\pi$
$384$	−1295.22	−0.172126
$385$	0	0
$386$	−140.053	−0.0184677
$387$	6974.43	0.916098
$388$	4281.51	0.560209
$389$	6466.16	0.842795	0.421398	−	0.906876i	$-0.361540\pi$
$389$	6466.16	0.842795	0.421398	+	0.906876i	$0.361540\pi$
$390$	−97.1703	−0.0126164
$391$	1736.14	0.224554
$392$	0	0
$393$	4201.46	0.539276
$394$	246.237	0.0314853
$395$	210.177	0.0267726
$396$	−5430.91	−0.689176
$397$	−2197.69	−0.277831	−0.138915	−	0.990304i	$-0.544362\pi$
$397$	−2197.69	−0.277831	−0.138915	+	0.990304i	$0.544362\pi$
$398$	395.084	0.0497582
$399$	0	0
$400$	−7598.97	−0.949872
$401$	−7819.89	−0.973832	−0.486916	−	0.873449i	$-0.661878\pi$
$401$	−7819.89	−0.973832	−0.486916	+	0.873449i	$0.661878\pi$
$402$	402.196	0.0498997
$403$	−11660.1	−1.44127
$404$	7233.28	0.890765
$405$	107.332	0.0131688
$406$	0	0
$407$	−6041.95	−0.735844
$408$	−855.538	−0.103812
$409$	7340.34	0.887424	0.443712	−	0.896169i	$-0.353661\pi$
$409$	7340.34	0.887424	0.443712	+	0.896169i	$0.353661\pi$
$410$	17.7239	0.00213492
$411$	2124.76	0.255004
$412$	5827.76	0.696877
$413$	0	0
$414$	75.8296	0.00900199
$415$	12.2237	0.00144588
$416$	2901.19	0.341929
$417$	3008.11	0.353256
$418$	395.006	0.0462210
$419$	−12437.2	−1.45011	−0.725057	−	0.688688i	$-0.758187\pi$
$419$	−12437.2	−1.45011	−0.725057	+	0.688688i	$0.758187\pi$
$420$	0	0
$421$	−4617.61	−0.534557	−0.267279	−	0.963619i	$-0.586124\pi$
$421$	−4617.61	−0.534557	−0.267279	+	0.963619i	$0.586124\pi$
$422$	1067.85	0.123180
$423$	1468.53	0.168799
$424$	677.409	0.0775893
$425$	−10094.0	−1.15207
$426$	−211.871	−0.0240967
$427$	0	0
$428$	−5846.06	−0.660234
$429$	−8751.35	−0.984893
$430$	171.970	0.0192864
$431$	−4151.57	−0.463977	−0.231989	−	0.972718i	$-0.574523\pi$
$431$	−4151.57	−0.463977	−0.231989	+	0.972718i	$0.574523\pi$
$432$	8627.15	0.960819
$433$	−9091.16	−1.00899	−0.504496	−	0.863414i	$-0.668322\pi$
$433$	−9091.16	−1.00899	−0.504496	+	0.863414i	$0.668322\pi$
$434$	0	0
$435$	−855.939	−0.0943428
$436$	−3206.51	−0.352211
$437$	1010.89	0.110658
$438$	332.918	0.0363184
$439$	1988.87	0.216227	0.108114	−	0.994139i	$-0.465519\pi$
$439$	1988.87	0.216227	0.108114	+	0.994139i	$0.465519\pi$
$440$	−268.553	−0.0290972
$441$	0	0
$442$	1272.91	0.136982
$443$	−14229.0	−1.52605	−0.763025	−	0.646369i	$-0.776287\pi$
$443$	−14229.0	−1.52605	−0.763025	+	0.646369i	$0.776287\pi$
$444$	3799.44	0.406111
$445$	1242.87	0.132399
$446$	557.098	0.0591466
$447$	−132.407	−0.0140104
$448$	0	0
$449$	2976.66	0.312867	0.156434	−	0.987688i	$-0.450000\pi$
$449$	2976.66	0.312867	0.156434	+	0.987688i	$0.450000\pi$
$450$	−440.875	−0.0461846
$451$	1596.25	0.166661
$452$	−763.351	−0.0794358
$453$	−3527.22	−0.365835
$454$	−66.0213	−0.00682496
$455$	0	0
$456$	−498.149	−0.0511578
$457$	−3459.67	−0.354128	−0.177064	−	0.984199i	$-0.556660\pi$
$457$	−3459.67	−0.354128	−0.177064	+	0.984199i	$0.556660\pi$
$458$	1344.98	0.137220
$459$	11459.7	1.16535
$460$	−342.703	−0.0347361
$461$	17389.6	1.75687	0.878433	−	0.477865i	$-0.158589\pi$
$461$	17389.6	1.75687	0.878433	+	0.477865i	$0.158589\pi$
$462$	0	0
$463$	2354.65	0.236350	0.118175	−	0.992993i	$-0.462296\pi$
$463$	2354.65	0.236350	0.118175	+	0.992993i	$0.462296\pi$
$464$	8441.10	0.844543
$465$	−1019.02	−0.101626
$466$	1018.93	0.101290
$467$	−7133.15	−0.706816	−0.353408	−	0.935469i	$-0.614977\pi$
$467$	−7133.15	−0.706816	−0.353408	+	0.935469i	$0.614977\pi$
$468$	−10190.3	−1.00651
$469$	0	0
$470$	36.2098	0.00355369
$471$	−7493.40	−0.733073
$472$	754.779	0.0736049
$473$	15488.0	1.50558
$474$	64.9433	0.00629314
$475$	−5877.36	−0.567730
$476$	0	0
$477$	−3572.27	−0.342899
$478$	−1069.19	−0.102309
$479$	−7113.39	−0.678537	−0.339268	−	0.940690i	$-0.610179\pi$
$479$	−7113.39	−0.678537	−0.339268	+	0.940690i	$0.610179\pi$
$480$	253.546	0.0241099
$481$	−11336.8	−1.07466
$482$	761.316	0.0719439
$483$	0	0
$484$	−1470.09	−0.138063
$485$	−1116.47	−0.104529
$486$	804.001	0.0750416
$487$	12638.1	1.17595	0.587976	−	0.808878i	$-0.299925\pi$
$487$	12638.1	1.17595	0.587976	+	0.808878i	$0.299925\pi$
$488$	1302.98	0.120867
$489$	−11706.9	−1.08263
$490$	0	0
$491$	4514.41	0.414934	0.207467	−	0.978242i	$-0.433478\pi$
$491$	4514.41	0.414934	0.207467	+	0.978242i	$0.433478\pi$
$492$	−1003.79	−0.0919801
$493$	11212.6	1.02432
$494$	741.168	0.0675035
$495$	1416.20	0.128593
$496$	10049.4	0.909738
$497$	0	0
$498$	3.77704	0.000339866 0
$499$	6947.03	0.623230	0.311615	−	0.950208i	$-0.399130\pi$
$499$	6947.03	0.623230	0.311615	+	0.950208i	$0.399130\pi$
$500$	4056.04	0.362783
$501$	−3461.40	−0.308671
$502$	726.470	0.0645895
$503$	−21669.0	−1.92082	−0.960410	−	0.278590i	$-0.910133\pi$
$503$	−21669.0	−1.92082	−0.960410	+	0.278590i	$0.910133\pi$
$504$	0	0
$505$	−1886.19	−0.166207
$506$	168.393	0.0147945
$507$	−9660.33	−0.846213
$508$	−6848.75	−0.598158
$509$	19613.1	1.70793	0.853966	−	0.520329i	$-0.174191\pi$
$509$	19613.1	1.70793	0.853966	+	0.520329i	$0.174191\pi$
$510$	111.244	0.00965878
$511$	0	0
$512$	−4174.94	−0.360368
$513$	6672.59	0.574273
$514$	1504.48	0.129104
$515$	−1519.68	−0.130030
$516$	−9739.49	−0.830925
$517$	3261.13	0.277416
$518$	0	0
$519$	1012.21	0.0856091
$520$	−503.898	−0.0424950
$521$	−6322.62	−0.531668	−0.265834	−	0.964019i	$-0.585647\pi$
$521$	−6322.62	−0.531668	−0.265834	+	0.964019i	$0.585647\pi$
$522$	489.734	0.0410633
$523$	17218.7	1.43962	0.719811	−	0.694171i	$-0.244229\pi$
$523$	17218.7	1.43962	0.719811	+	0.694171i	$0.244229\pi$
$524$	10864.2	0.905731
$525$	0	0
$526$	1358.52	0.112613
$527$	13348.9	1.10339
$528$	7542.43	0.621671
$529$	−11736.1	−0.964580
$530$	−88.0823	−0.00721897
$531$	−3980.28	−0.325291
$532$	0	0
$533$	2995.11	0.243401
$534$	384.037	0.0311216
$535$	1524.46	0.123192
$536$	2085.68	0.168074
$537$	−4663.50	−0.374758
$538$	53.9788	0.00432564
$539$	0	0
$540$	−2262.08	−0.180267
$541$	8460.91	0.672390	0.336195	−	0.941792i	$-0.390860\pi$
$541$	8460.91	0.672390	0.336195	+	0.941792i	$0.390860\pi$
$542$	−1040.41	−0.0824530
$543$	3849.44	0.304227
$544$	−3321.39	−0.261771
$545$	836.149	0.0657187
$546$	0	0
$547$	11005.8	0.860283	0.430141	−	0.902762i	$-0.358464\pi$
$547$	11005.8	0.860283	0.430141	+	0.902762i	$0.358464\pi$
$548$	5494.21	0.428287
$549$	−6871.18	−0.534162
$550$	−979.043	−0.0759028
$551$	6528.69	0.504776
$552$	−212.364	−0.0163746
$553$	0	0
$554$	101.566	0.00778902
$555$	−990.764	−0.0757759
$556$	7778.40	0.593305
$557$	20339.1	1.54721	0.773604	−	0.633670i	$-0.218452\pi$
$557$	20339.1	1.54721	0.773604	+	0.633670i	$0.218452\pi$
$558$	583.042	0.0442332
$559$	29060.8	2.19882
$560$	0	0
$561$	10018.9	0.754006
$562$	481.663	0.0361525
$563$	−13097.0	−0.980412	−0.490206	−	0.871606i	$-0.663079\pi$
$563$	−13097.0	−0.980412	−0.490206	+	0.871606i	$0.663079\pi$
$564$	−2050.73	−0.153105
$565$	199.056	0.0148219
$566$	1058.54	0.0786108
$567$	0	0
$568$	−1098.71	−0.0811632
$569$	12743.8	0.938922	0.469461	−	0.882953i	$-0.344448\pi$
$569$	12743.8	0.938922	0.469461	+	0.882953i	$0.344448\pi$
$570$	64.7735	0.00475976
$571$	−5113.34	−0.374758	−0.187379	−	0.982288i	$-0.559999\pi$
$571$	−5113.34	−0.374758	−0.187379	+	0.982288i	$0.559999\pi$
$572$	−22629.3	−1.65416
$573$	−4203.87	−0.306491
$574$	0	0
$575$	−2505.55	−0.181719
$576$	8685.42	0.628286
$577$	−23689.0	−1.70916	−0.854580	−	0.519320i	$-0.826185\pi$
$577$	−23689.0	−1.70916	−0.854580	+	0.519320i	$0.826185\pi$
$578$	−433.643	−0.0312062
$579$	−2068.37	−0.148460
$580$	−2213.29	−0.158452
$581$	0	0
$582$	−344.983	−0.0245704
$583$	−7932.87	−0.563544
$584$	1726.42	0.122329
$585$	2657.28	0.187803
$586$	1460.84	0.102981
$587$	−14857.0	−1.04466	−0.522330	−	0.852744i	$-0.674937\pi$
$587$	−14857.0	−1.04466	−0.522330	+	0.852744i	$0.674937\pi$
$588$	0	0
$589$	7772.59	0.543742
$590$	−98.1427	−0.00684826
$591$	3636.53	0.253108
$592$	9770.72	0.678335
$593$	6021.37	0.416978	0.208489	−	0.978025i	$-0.433145\pi$
$593$	6021.37	0.416978	0.208489	+	0.978025i	$0.433145\pi$
$594$	1111.51	0.0767776
$595$	0	0
$596$	−342.380	−0.0235309
$597$	5834.77	0.400002
$598$	315.964	0.0216066
$599$	−1594.48	−0.108762	−0.0543812	−	0.998520i	$-0.517319\pi$
$599$	−1594.48	−0.108762	−0.0543812	+	0.998520i	$0.517319\pi$
$600$	1234.69	0.0840098
$601$	21627.1	1.46787	0.733934	−	0.679221i	$-0.237682\pi$
$601$	21627.1	1.46787	0.733934	+	0.679221i	$0.237682\pi$
$602$	0	0
$603$	−10998.7	−0.742787
$604$	−9120.71	−0.614431
$605$	383.351	0.0257610
$606$	−582.821	−0.0390684
$607$	−20559.2	−1.37474	−0.687372	−	0.726305i	$-0.741236\pi$
$607$	−20559.2	−1.37474	−0.687372	+	0.726305i	$0.741236\pi$
$608$	−1933.93	−0.128999
$609$	0	0
$610$	−169.424	−0.0112456
$611$	6119.00	0.405152
$612$	11666.2	0.770552
$613$	−5721.94	−0.377010	−0.188505	−	0.982072i	$-0.560364\pi$
$613$	−5721.94	−0.377010	−0.188505	+	0.982072i	$0.560364\pi$
$614$	1099.59	0.0722736
$615$	261.754	0.0171625
$616$	0	0
$617$	13423.3	0.875851	0.437925	−	0.899011i	$-0.355713\pi$
$617$	13423.3	0.875851	0.437925	+	0.899011i	$0.355713\pi$
$618$	−469.571	−0.0305646
$619$	−15775.5	−1.02434	−0.512172	−	0.858883i	$-0.671159\pi$
$619$	−15775.5	−1.02434	−0.512172	+	0.858883i	$0.671159\pi$
$620$	−2634.99	−0.170683
$621$	2844.56	0.183814
$622$	209.422	0.0135001
$623$	0	0
$624$	14152.2	0.907919
$625$	14029.2	0.897870
$626$	−301.637	−0.0192586
$627$	5833.63	0.371567
$628$	−19376.5	−1.23122
$629$	12978.8	0.822731
$630$	0	0
$631$	−11004.1	−0.694244	−0.347122	−	0.937820i	$-0.612841\pi$
$631$	−11004.1	−0.694244	−0.347122	+	0.937820i	$0.612841\pi$
$632$	336.778	0.0211967
$633$	15770.4	0.990233
$634$	1162.19	0.0728022
$635$	1785.92	0.111610
$636$	4988.52	0.311019
$637$	0	0
$638$	1087.54	0.0674862
$639$	5793.96	0.358694
$640$	873.357	0.0539414
$641$	−17985.2	−1.10822	−0.554112	−	0.832442i	$-0.686942\pi$
$641$	−17985.2	−1.10822	−0.554112	+	0.832442i	$0.686942\pi$
$642$	471.046	0.0289575
$643$	7600.79	0.466168	0.233084	−	0.972457i	$-0.425118\pi$
$643$	7600.79	0.466168	0.233084	+	0.972457i	$0.425118\pi$
$644$	0	0
$645$	2539.73	0.155041
$646$	−848.517	−0.0516787
$647$	−18716.7	−1.13730	−0.568648	−	0.822581i	$-0.692533\pi$
$647$	−18716.7	−1.13730	−0.568648	+	0.822581i	$0.692533\pi$
$648$	171.983	0.0104262
$649$	−8838.93	−0.534605
$650$	−1837.02	−0.110852
$651$	0	0
$652$	−30271.8	−1.81830
$653$	12110.3	0.725749	0.362875	−	0.931838i	$-0.381795\pi$
$653$	12110.3	0.725749	0.362875	+	0.931838i	$0.381795\pi$
$654$	258.364	0.0154478
$655$	−2833.01	−0.168999
$656$	−2581.36	−0.153636
$657$	−9104.17	−0.540621
$658$	0	0
$659$	−13536.0	−0.800132	−0.400066	−	0.916486i	$-0.631013\pi$
$659$	−13536.0	−0.800132	−0.400066	+	0.916486i	$0.631013\pi$
$660$	−1977.66	−0.116637
$661$	24708.6	1.45394	0.726970	−	0.686670i	$-0.240928\pi$
$661$	24708.6	1.45394	0.726970	+	0.686670i	$0.240928\pi$
$662$	−2244.79	−0.131792
$663$	18798.9	1.10119
$664$	19.5867	0.00114475
$665$	0	0
$666$	566.875	0.0329819
$667$	2783.22	0.161569
$668$	−8950.53	−0.518423
$669$	8227.47	0.475474
$670$	−271.197	−0.0156377
$671$	−15258.7	−0.877877
$672$	0	0
$673$	−8457.56	−0.484420	−0.242210	−	0.970224i	$-0.577872\pi$
$673$	−8457.56	−0.484420	−0.242210	+	0.970224i	$0.577872\pi$
$674$	−2094.08	−0.119675
$675$	−16538.3	−0.943054
$676$	−24979.8	−1.42124
$677$	24800.8	1.40794	0.703968	−	0.710231i	$-0.251410\pi$
$677$	24800.8	1.40794	0.703968	+	0.710231i	$0.251410\pi$
$678$	61.5069	0.00348401
$679$	0	0
$680$	576.882	0.0325330
$681$	−975.031	−0.0548653
$682$	1294.75	0.0726958
$683$	29550.8	1.65554	0.827768	−	0.561070i	$-0.189610\pi$
$683$	29550.8	1.65554	0.827768	+	0.561070i	$0.189610\pi$
$684$	6792.80	0.379721
$685$	−1432.71	−0.0799137
$686$	0	0
$687$	19863.2	1.10310
$688$	−25046.3	−1.38791
$689$	−14884.8	−0.823027
$690$	27.6133	0.00152351
$691$	16037.8	0.882930	0.441465	−	0.897278i	$-0.354459\pi$
$691$	16037.8	0.882930	0.441465	+	0.897278i	$0.354459\pi$
$692$	2617.38	0.143783
$693$	0	0
$694$	270.878	0.0148161
$695$	−2028.34	−0.110704
$696$	−1371.52	−0.0746942
$697$	−3428.91	−0.186340
$698$	639.089	0.0346560
$699$	15048.0	0.814261
$700$	0	0
$701$	−33266.4	−1.79237	−0.896187	−	0.443677i	$-0.853674\pi$
$701$	−33266.4	−1.79237	−0.896187	+	0.443677i	$0.853674\pi$
$702$	2085.58	0.112130
$703$	7557.08	0.405435
$704$	19287.5	1.03257
$705$	534.762	0.0285678
$706$	−2647.10	−0.141112
$707$	0	0
$708$	5558.29	0.295047
$709$	11780.9	0.624034	0.312017	−	0.950076i	$-0.398995\pi$
$709$	11780.9	0.624034	0.312017	+	0.950076i	$0.398995\pi$
$710$	142.863	0.00755149
$711$	−1775.98	−0.0936771
$712$	1991.51	0.104824
$713$	3313.50	0.174041
$714$	0	0
$715$	5900.96	0.308648
$716$	−12058.9	−0.629417
$717$	−15790.2	−0.822450
$718$	−418.631	−0.0217593
$719$	31223.2	1.61951	0.809757	−	0.586765i	$-0.199599\pi$
$719$	31223.2	1.61951	0.809757	+	0.586765i	$0.199599\pi$
$720$	−2290.20	−0.118543
$721$	0	0
$722$	935.020	0.0481965
$723$	11243.4	0.578351
$724$	9953.92	0.510959
$725$	−16181.7	−0.828928
$726$	118.453	0.00605536
$727$	11523.1	0.587850	0.293925	−	0.955829i	$-0.405038\pi$
$727$	11523.1	0.587850	0.293925	+	0.955829i	$0.405038\pi$
$728$	0	0
$729$	10477.1	0.532292
$730$	−224.484	−0.0113815
$731$	−33269.9	−1.68335
$732$	9595.31	0.484499
$733$	5401.79	0.272196	0.136098	−	0.990695i	$-0.456544\pi$
$733$	5401.79	0.272196	0.136098	+	0.990695i	$0.456544\pi$
$734$	−768.320	−0.0386365
$735$	0	0
$736$	−824.444	−0.0412900
$737$	−24424.5	−1.22075
$738$	−149.765	−0.00747008
$739$	−6517.18	−0.324409	−0.162204	−	0.986757i	$-0.551860\pi$
$739$	−6517.18	−0.324409	−0.162204	+	0.986757i	$0.551860\pi$
$740$	−2561.93	−0.127268
$741$	10945.9	0.542655
$742$	0	0
$743$	−25033.6	−1.23606	−0.618031	−	0.786154i	$-0.712069\pi$
$743$	−25033.6	−1.23606	−0.618031	+	0.786154i	$0.712069\pi$
$744$	−1632.83	−0.0804602
$745$	89.2811	0.00439061
$746$	−13.2765	−0.000651591 0
$747$	−103.289	−0.00505911
$748$	25906.9	1.26638
$749$	0	0
$750$	−326.815	−0.0159114
$751$	−24652.0	−1.19782	−0.598911	−	0.800816i	$-0.704400\pi$
$751$	−24652.0	−1.19782	−0.598911	+	0.800816i	$0.704400\pi$
$752$	−5273.72	−0.255735
$753$	10728.8	0.519230
$754$	2040.60	0.0985602
$755$	2378.37	0.114646
$756$	0	0
$757$	20964.7	1.00657	0.503287	−	0.864119i	$-0.332124\pi$
$757$	20964.7	1.00657	0.503287	+	0.864119i	$0.332124\pi$
$758$	−363.600	−0.0174229
$759$	2486.91	0.118931
$760$	335.897	0.0160319
$761$	9537.17	0.454300	0.227150	−	0.973860i	$-0.427059\pi$
$761$	9537.17	0.454300	0.227150	+	0.973860i	$0.427059\pi$
$762$	551.837	0.0262348
$763$	0	0
$764$	−10870.4	−0.514761
$765$	−3042.15	−0.143777
$766$	−1322.78	−0.0623943
$767$	−16584.9	−0.780763
$768$	−11925.1	−0.560301
$769$	35417.4	1.66084	0.830418	−	0.557141i	$-0.188102\pi$
$769$	35417.4	1.66084	0.830418	+	0.557141i	$0.188102\pi$
$770$	0	0
$771$	22218.8	1.03786
$772$	−5348.41	−0.249344
$773$	−12434.1	−0.578554	−0.289277	−	0.957245i	$-0.593415\pi$
$773$	−12434.1	−0.578554	−0.289277	+	0.957245i	$0.593415\pi$
$774$	−1453.13	−0.0674828
$775$	−19264.8	−0.892917
$776$	−1788.98	−0.0827588
$777$	0	0
$778$	−1347.23	−0.0620831
$779$	−1996.53	−0.0918269
$780$	−3710.77	−0.170342
$781$	12866.5	0.589502
$782$	−361.728	−0.0165414
$783$	18371.1	0.838482
$784$	0	0
$785$	5052.73	0.229732
$786$	−875.378	−0.0397248
$787$	−6613.15	−0.299534	−0.149767	−	0.988721i	$-0.547852\pi$
$787$	−6613.15	−0.299534	−0.149767	+	0.988721i	$0.547852\pi$
$788$	9403.37	0.425103
$789$	20063.2	0.905284
$790$	−43.7907	−0.00197216
$791$	0	0
$792$	2269.25	0.101811
$793$	−28630.6	−1.28210
$794$	457.891	0.0204659
$795$	−1300.84	−0.0580327
$796$	15087.6	0.671816
$797$	−35782.2	−1.59030	−0.795152	−	0.606410i	$-0.792609\pi$
$797$	−35782.2	−1.59030	−0.795152	+	0.606410i	$0.792609\pi$
$798$	0	0
$799$	−7005.26	−0.310173
$800$	4793.34	0.211838
$801$	−10502.1	−0.463263
$802$	1629.28	0.0717357
$803$	−20217.5	−0.888491
$804$	15359.2	0.673727
$805$	0	0
$806$	2429.40	0.106169
$807$	797.183	0.0347734
$808$	−3022.35	−0.131591
$809$	−33634.9	−1.46173	−0.730866	−	0.682521i	$-0.760884\pi$
$809$	−33634.9	−1.46173	−0.730866	+	0.682521i	$0.760884\pi$
$810$	−22.3627	−0.000970057 0
$811$	34937.1	1.51271	0.756356	−	0.654161i	$-0.226978\pi$
$811$	34937.1	1.51271	0.756356	+	0.654161i	$0.226978\pi$
$812$	0	0
$813$	−15365.3	−0.662833
$814$	1258.85	0.0542047
$815$	7893.86	0.339276
$816$	−16202.0	−0.695077
$817$	−19371.8	−0.829541
$818$	−1529.37	−0.0653706
$819$	0	0
$820$	676.845	0.0288249
$821$	31535.2	1.34054	0.670271	−	0.742117i	$-0.266178\pi$
$821$	31535.2	1.34054	0.670271	+	0.742117i	$0.266178\pi$
$822$	−442.696	−0.0187844
$823$	−3812.83	−0.161491	−0.0807455	−	0.996735i	$-0.525730\pi$
$823$	−3812.83	−0.161491	−0.0807455	+	0.996735i	$0.525730\pi$
$824$	−2435.07	−0.102949
$825$	−14458.9	−0.610176
$826$	0	0
$827$	−149.578	−0.00628941	−0.00314470	−	0.999995i	$-0.501001\pi$
$827$	−149.578	−0.00628941	−0.00314470	+	0.999995i	$0.501001\pi$
$828$	2895.81	0.121541
$829$	8950.69	0.374994	0.187497	−	0.982265i	$-0.439962\pi$
$829$	8950.69	0.374994	0.187497	+	0.982265i	$0.439962\pi$
$830$	−2.54683	−0.000106508 0
$831$	1499.97	0.0626153
$832$	36190.1	1.50801
$833$	0	0
$834$	−626.744	−0.0260220
$835$	2333.99	0.0967320
$836$	15084.6	0.624059
$837$	21871.4	0.903208
$838$	2591.31	0.106820
$839$	2140.17	0.0880655	0.0440328	−	0.999030i	$-0.485979\pi$
$839$	2140.17	0.0880655	0.0440328	+	0.999030i	$0.485979\pi$
$840$	0	0
$841$	−6414.04	−0.262989
$842$	962.085	0.0393773
$843$	7113.41	0.290627
$844$	40779.3	1.66313
$845$	6513.87	0.265188
$846$	−305.969	−0.0124343
$847$	0	0
$848$	12828.6	0.519500
$849$	15633.0	0.631946
$850$	2103.09	0.0848653
$851$	3221.62	0.129772
$852$	−8091.02	−0.325345
$853$	−24549.7	−0.985422	−0.492711	−	0.870193i	$-0.663994\pi$
$853$	−24549.7	−0.985422	−0.492711	+	0.870193i	$0.663994\pi$
$854$	0	0
$855$	−1771.33	−0.0708518
$856$	2442.71	0.0975353
$857$	−29035.7	−1.15734	−0.578669	−	0.815562i	$-0.696428\pi$
$857$	−29035.7	−1.15734	−0.578669	+	0.815562i	$0.696428\pi$
$858$	1823.35	0.0725504
$859$	−48099.2	−1.91050	−0.955252	−	0.295793i	$-0.904416\pi$
$859$	−48099.2	−1.91050	−0.955252	+	0.295793i	$0.904416\pi$
$860$	6567.25	0.260397
$861$	0	0
$862$	864.985	0.0341781
$863$	−44794.9	−1.76690	−0.883452	−	0.468522i	$-0.844787\pi$
$863$	−44794.9	−1.76690	−0.883452	+	0.468522i	$0.844787\pi$
$864$	−5441.90	−0.214279
$865$	−682.525	−0.0268284
$866$	1894.15	0.0743256
$867$	−6404.23	−0.250864
$868$	0	0
$869$	−3943.88	−0.153955
$870$	178.336	0.00694960
$871$	−45828.9	−1.78284
$872$	1339.80	0.0520316
$873$	9434.10	0.365745
$874$	−210.621	−0.00815144
$875$	0	0
$876$	12713.6	0.490357
$877$	−488.442	−0.0188068	−0.00940338	−	0.999956i	$-0.502993\pi$
$877$	−488.442	−0.0188068	−0.00940338	+	0.999956i	$0.502993\pi$
$878$	−414.384	−0.0159280
$879$	21574.3	0.827853
$880$	−5085.80	−0.194821
$881$	38640.4	1.47767	0.738836	−	0.673886i	$-0.235376\pi$
$881$	38640.4	1.47767	0.738836	+	0.673886i	$0.235376\pi$
$882$	0	0
$883$	33779.0	1.28738	0.643688	−	0.765288i	$-0.277404\pi$
$883$	33779.0	1.28738	0.643688	+	0.765288i	$0.277404\pi$
$884$	48610.2	1.84948
$885$	−1449.41	−0.0550526
$886$	2964.63	0.112414
$887$	40980.4	1.55128	0.775641	−	0.631174i	$-0.217427\pi$
$887$	40980.4	1.55128	0.775641	+	0.631174i	$0.217427\pi$
$888$	−1587.55	−0.0599942
$889$	0	0
$890$	−258.953	−0.00975294
$891$	−2014.03	−0.0757268
$892$	21274.7	0.798574
$893$	−4078.91	−0.152850
$894$	27.5872	0.00103205
$895$	3144.56	0.117442
$896$	0	0
$897$	4666.29	0.173693
$898$	−620.192	−0.0230468
$899$	21399.7	0.793904
$900$	−16836.3	−0.623567
$901$	17040.7	0.630086
$902$	−332.580	−0.0122768
$903$	0	0
$904$	318.958	0.0117349
$905$	−2595.64	−0.0953394
$906$	734.900	0.0269486
$907$	−26198.0	−0.959084	−0.479542	−	0.877519i	$-0.659197\pi$
$907$	−26198.0	−0.959084	−0.479542	+	0.877519i	$0.659197\pi$
$908$	−2521.24	−0.0921480
$909$	15938.2	0.581557
$910$	0	0
$911$	−38426.2	−1.39749	−0.698746	−	0.715369i	$-0.746258\pi$
$911$	−38426.2	−1.39749	−0.698746	+	0.715369i	$0.746258\pi$
$912$	−9433.82	−0.342528
$913$	−229.372	−0.00831447
$914$	720.827	0.0260863
$915$	−2502.13	−0.0904022
$916$	51362.5	1.85269
$917$	0	0
$918$	−2387.65	−0.0858434
$919$	23104.3	0.829315	0.414657	−	0.909978i	$-0.363901\pi$
$919$	23104.3	0.829315	0.414657	+	0.909978i	$0.363901\pi$
$920$	143.195	0.00513152
$921$	16239.3	0.581002
$922$	−3623.15	−0.129417
$923$	24142.0	0.860937
$924$	0	0
$925$	−18730.6	−0.665792
$926$	−490.595	−0.0174103
$927$	12841.2	0.454972
$928$	−5324.54	−0.188348
$929$	32996.9	1.16533	0.582665	−	0.812712i	$-0.302010\pi$
$929$	32996.9	1.16533	0.582665	+	0.812712i	$0.302010\pi$
$930$	212.314	0.00748608
$931$	0	0
$932$	38911.3	1.36758
$933$	3092.83	0.108526
$934$	1486.20	0.0520664
$935$	−6755.64	−0.236292
$936$	4257.89	0.148690
$937$	−1975.64	−0.0688810	−0.0344405	−	0.999407i	$-0.510965\pi$
$937$	−1975.64	−0.0688810	−0.0344405	+	0.999407i	$0.510965\pi$
$938$	0	0
$939$	−4454.71	−0.154818
$940$	1382.79	0.0479806
$941$	−19625.1	−0.679871	−0.339935	−	0.940449i	$-0.610405\pi$
$941$	−19625.1	−0.679871	−0.339935	+	0.940449i	$0.610405\pi$
$942$	1561.26	0.0540006
$943$	−851.132	−0.0293920
$944$	14293.8	0.492823
$945$	0	0
$946$	−3226.94	−0.110906
$947$	12144.8	0.416739	0.208369	−	0.978050i	$-0.433184\pi$
$947$	12144.8	0.416739	0.208369	+	0.978050i	$0.433184\pi$
$948$	2480.08	0.0849675
$949$	−37934.9	−1.29760
$950$	1224.55	0.0418208
$951$	17163.8	0.585251
$952$	0	0
$953$	3869.66	0.131533	0.0657663	−	0.997835i	$-0.479051\pi$
$953$	3869.66	0.131533	0.0657663	+	0.997835i	$0.479051\pi$
$954$	744.287	0.0252591
$955$	2834.63	0.0960488
$956$	−40830.5	−1.38133
$957$	16061.3	0.542516
$958$	1482.08	0.0499833
$959$	0	0
$960$	3162.79	0.106332
$961$	−4314.05	−0.144811
$962$	2362.03	0.0791632
$963$	−12881.5	−0.431049
$964$	29073.4	0.971360
$965$	1394.68	0.0465248
$966$	0	0
$967$	−4830.47	−0.160638	−0.0803192	−	0.996769i	$-0.525594\pi$
$967$	−4830.47	−0.160638	−0.0803192	+	0.996769i	$0.525594\pi$
$968$	614.263	0.0203958
$969$	−12531.3	−0.415441
$970$	232.619	0.00769994
$971$	44365.5	1.46628	0.733140	−	0.680078i	$-0.238054\pi$
$971$	44365.5	1.46628	0.733140	+	0.680078i	$0.238054\pi$
$972$	30703.5	1.01318
$973$	0	0
$974$	−2633.17	−0.0866245
$975$	−27129.9	−0.891132
$976$	24675.5	0.809267
$977$	−42622.9	−1.39573	−0.697865	−	0.716230i	$-0.745866\pi$
$977$	−42622.9	−1.39573	−0.697865	+	0.716230i	$0.745866\pi$
$978$	2439.15	0.0797498
$979$	−23321.8	−0.761357
$980$	0	0
$981$	−7065.37	−0.229949
$982$	−940.583	−0.0305654
$983$	44221.3	1.43483	0.717417	−	0.696644i	$-0.245324\pi$
$983$	44221.3	1.43483	0.717417	+	0.696644i	$0.245324\pi$
$984$	419.421	0.0135881
$985$	−2452.08	−0.0793196
$986$	−2336.16	−0.0754548
$987$	0	0
$988$	28304.0	0.911407
$989$	−8258.32	−0.265520
$990$	−295.067	−0.00947256
$991$	−11795.6	−0.378101	−0.189051	−	0.981967i	$-0.560541\pi$
$991$	−11795.6	−0.378101	−0.189051	+	0.981967i	$0.560541\pi$
$992$	−6339.01	−0.202887
$993$	−33152.1	−1.05947
$994$	0	0
$995$	−3934.34	−0.125354
$996$	144.239	0.00458874
$997$	3534.26	0.112268	0.0561340	−	0.998423i	$-0.482123\pi$
$997$	3534.26	0.112268	0.0561340	+	0.998423i	$0.482123\pi$
$998$	−1447.42	−0.0459092
$999$	21264.9	0.673466

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.4.a.h.1.15	✓	30
7.6	odd	2		2009.4.a.i.1.15	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2009.4.a.h.1.15	✓	30	1.1	even	1	trivial
2009.4.a.i.1.15	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)

\(f(q)\)	\(=\)	\(q-0.208351 q^{2} -3.07702 q^{3} -7.95659 q^{4} +2.07481 q^{5} +0.641101 q^{6} +3.32458 q^{8} -17.5319 q^{9} +O(q^{10})\)	\(q-0.208351 q^{2} -3.07702 q^{3} -7.95659 q^{4} +2.07481 q^{5} +0.641101 q^{6} +3.32458 q^{8} -17.5319 q^{9} -0.432289 q^{10} -38.9328 q^{11} +24.4826 q^{12} -73.0514 q^{13} -6.38423 q^{15} +62.9600 q^{16} +83.6320 q^{17} +3.65280 q^{18} +48.6959 q^{19} -16.5084 q^{20} +8.11170 q^{22} +20.7593 q^{23} -10.2298 q^{24} -120.695 q^{25} +15.2203 q^{26} +137.026 q^{27} +134.071 q^{29} +1.33016 q^{30} +159.615 q^{31} -39.7144 q^{32} +119.797 q^{33} -17.4248 q^{34} +139.494 q^{36} +155.189 q^{37} -10.1458 q^{38} +224.781 q^{39} +6.89786 q^{40} -41.0000 q^{41} -397.813 q^{43} +309.772 q^{44} -36.3754 q^{45} -4.32523 q^{46} -83.7629 q^{47} -193.729 q^{48} +25.1470 q^{50} -257.337 q^{51} +581.240 q^{52} +203.758 q^{53} -28.5495 q^{54} -80.7782 q^{55} -149.838 q^{57} -27.9338 q^{58} +227.030 q^{59} +50.7967 q^{60} +391.924 q^{61} -33.2560 q^{62} -495.406 q^{64} -151.568 q^{65} -24.9599 q^{66} +627.351 q^{67} -665.425 q^{68} -63.8769 q^{69} -330.480 q^{71} -58.2862 q^{72} +519.291 q^{73} -32.3339 q^{74} +371.382 q^{75} -387.453 q^{76} -46.8333 q^{78} +101.300 q^{79} +130.630 q^{80} +51.7310 q^{81} +8.54240 q^{82} +5.89149 q^{83} +173.520 q^{85} +82.8848 q^{86} -412.539 q^{87} -129.435 q^{88} +599.027 q^{89} +7.57887 q^{90} -165.173 q^{92} -491.139 q^{93} +17.4521 q^{94} +101.035 q^{95} +122.202 q^{96} -538.109 q^{97} +682.568 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + q^{2} - 12 q^{3} + 103 q^{4} - 20 q^{5} - 36 q^{6} - 9 q^{8} + 318 q^{9}+O(q^{10}) \) 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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