LMFDB - Embedded newform 1075.6.a.i.1.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1075,6,Mod(1,1075)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1075, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("1075.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1075 = 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1075.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:	$172.412606299$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.32
Character	$\chi$	$=$	1075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.81448 q^{2} -28.7877 q^{3} +45.6951 q^{4} -253.749 q^{6} +98.9387 q^{7} +120.716 q^{8} +585.731 q^{9} +O(q^{10})$	\(q+8.81448 q^{2} -28.7877 q^{3} +45.6951 q^{4} -253.749 q^{6} +98.9387 q^{7} +120.716 q^{8} +585.731 q^{9} +107.295 q^{11} -1315.46 q^{12} +345.351 q^{13} +872.094 q^{14} -398.199 q^{16} +1402.60 q^{17} +5162.92 q^{18} -138.222 q^{19} -2848.22 q^{21} +945.753 q^{22} +3559.57 q^{23} -3475.12 q^{24} +3044.09 q^{26} -9866.43 q^{27} +4521.02 q^{28} -1514.73 q^{29} +1555.01 q^{31} -7372.82 q^{32} -3088.79 q^{33} +12363.2 q^{34} +26765.1 q^{36} +192.463 q^{37} -1218.35 q^{38} -9941.85 q^{39} -129.051 q^{41} -25105.6 q^{42} -1849.00 q^{43} +4902.88 q^{44} +31375.8 q^{46} -23841.8 q^{47} +11463.2 q^{48} -7018.13 q^{49} -40377.6 q^{51} +15780.9 q^{52} +4052.01 q^{53} -86967.5 q^{54} +11943.4 q^{56} +3979.08 q^{57} -13351.5 q^{58} +10145.4 q^{59} +22113.5 q^{61} +13706.6 q^{62} +57951.5 q^{63} -52245.2 q^{64} -27226.1 q^{66} -31587.3 q^{67} +64092.0 q^{68} -102472. q^{69} +54546.7 q^{71} +70706.8 q^{72} +13049.5 q^{73} +1696.46 q^{74} -6316.05 q^{76} +10615.7 q^{77} -87632.3 q^{78} +39575.9 q^{79} +141699. q^{81} -1137.52 q^{82} +66617.1 q^{83} -130150. q^{84} -16298.0 q^{86} +43605.4 q^{87} +12952.2 q^{88} +87137.6 q^{89} +34168.6 q^{91} +162655. q^{92} -44765.2 q^{93} -210154. q^{94} +212246. q^{96} -44772.4 q^{97} -61861.2 q^{98} +62846.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 630 q^{4} + 291 q^{6} - 213 q^{8} + 3535 q^{9}+O(q^{10}) $ 37 * q + 630 * q^4 + 291 * q^6 - 213 * q^8 + 3535 * q^9	\( 37 q + 630 q^{4} + 291 q^{6} - 213 q^{8} + 3535 q^{9} + 675 q^{11} + 4446 q^{12} - 1241 q^{13} + 2375 q^{14} + 10518 q^{16} - 1153 q^{17} + 6680 q^{18} + 4065 q^{19} + 9953 q^{21} - 9283 q^{22} + 360 q^{23} + 2265 q^{24} + 23695 q^{26} - 1323 q^{27} + 30375 q^{28} + 19290 q^{29} + 23291 q^{31} - 8166 q^{32} + 10388 q^{33} - 13153 q^{34} + 148705 q^{36} - 13501 q^{37} + 8127 q^{38} - 1327 q^{39} + 38345 q^{41} + 21835 q^{42} - 68413 q^{43} + 47768 q^{44} + 48755 q^{46} - 84859 q^{47} + 208720 q^{48} + 107255 q^{49} + 62027 q^{51} - 128320 q^{52} + 53559 q^{53} + 44158 q^{54} + 107538 q^{56} - 104239 q^{57} + 85186 q^{58} + 48186 q^{59} + 82364 q^{61} - 206506 q^{62} + 75269 q^{63} + 161467 q^{64} + 91969 q^{66} - 38168 q^{67} - 95991 q^{68} + 287103 q^{69} + 155302 q^{71} - 9979 q^{72} - 31927 q^{73} + 59946 q^{74} + 225407 q^{76} + 80007 q^{77} + 67815 q^{78} + 150174 q^{79} + 417489 q^{81} - 60603 q^{82} - 266568 q^{83} + 586273 q^{84} + 57554 q^{87} - 323054 q^{88} + 334356 q^{89} + 51747 q^{91} + 258529 q^{92} + 285287 q^{93} + 302744 q^{94} + 287282 q^{96} + 78640 q^{97} + 397117 q^{98} + 362152 q^{99}+O(q^{100}) \) 37 * q + 630 * q^4 + 291 * q^6 - 213 * q^8 + 3535 * q^9 + 675 * q^11 + 4446 * q^12 - 1241 * q^13 + 2375 * q^14 + 10518 * q^16 - 1153 * q^17 + 6680 * q^18 + 4065 * q^19 + 9953 * q^21 - 9283 * q^22 + 360 * q^23 + 2265 * q^24 + 23695 * q^26 - 1323 * q^27 + 30375 * q^28 + 19290 * q^29 + 23291 * q^31 - 8166 * q^32 + 10388 * q^33 - 13153 * q^34 + 148705 * q^36 - 13501 * q^37 + 8127 * q^38 - 1327 * q^39 + 38345 * q^41 + 21835 * q^42 - 68413 * q^43 + 47768 * q^44 + 48755 * q^46 - 84859 * q^47 + 208720 * q^48 + 107255 * q^49 + 62027 * q^51 - 128320 * q^52 + 53559 * q^53 + 44158 * q^54 + 107538 * q^56 - 104239 * q^57 + 85186 * q^58 + 48186 * q^59 + 82364 * q^61 - 206506 * q^62 + 75269 * q^63 + 161467 * q^64 + 91969 * q^66 - 38168 * q^67 - 95991 * q^68 + 287103 * q^69 + 155302 * q^71 - 9979 * q^72 - 31927 * q^73 + 59946 * q^74 + 225407 * q^76 + 80007 * q^77 + 67815 * q^78 + 150174 * q^79 + 417489 * q^81 - 60603 * q^82 - 266568 * q^83 + 586273 * q^84 + 57554 * q^87 - 323054 * q^88 + 334356 * q^89 + 51747 * q^91 + 258529 * q^92 + 285287 * q^93 + 302744 * q^94 + 287282 * q^96 + 78640 * q^97 + 397117 * q^98 + 362152 * 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 $

$2$	8.81448	1.55820	0.779098	−	0.626903i	$-0.215678\pi$
$2$	8.81448	1.55820	0.779098	+	0.626903i	$0.215678\pi$
$3$	−28.7877	−1.84673	−0.923366	−	0.383922i	$-0.874573\pi$
$3$	−28.7877	−1.84673	−0.923366	+	0.383922i	$0.874573\pi$
$4$	45.6951	1.42797
$5$	0	0
$5$	0	0
$6$	−253.749	−2.87757
$7$	98.9387	0.763170	0.381585	−	0.924334i	$-0.375378\pi$
$7$	98.9387	0.763170	0.381585	+	0.924334i	$0.375378\pi$
$8$	120.716	0.666865
$9$	585.731	2.41042
$10$	0	0
$11$	107.295	0.267362	0.133681	−	0.991024i	$-0.457320\pi$
$11$	107.295	0.267362	0.133681	+	0.991024i	$0.457320\pi$
$12$	−1315.46	−2.63708
$13$	345.351	0.566764	0.283382	−	0.959007i	$-0.408544\pi$
$13$	345.351	0.566764	0.283382	+	0.959007i	$0.408544\pi$
$14$	872.094	1.18917
$15$	0	0
$16$	−398.199	−0.388866
$17$	1402.60	1.17710	0.588548	−	0.808462i	$-0.299700\pi$
$17$	1402.60	1.17710	0.588548	+	0.808462i	$0.299700\pi$
$18$	5162.92	3.75590
$19$	−138.222	−0.0878399	−0.0439199	−	0.999035i	$-0.513985\pi$
$19$	−138.222	−0.0878399	−0.0439199	+	0.999035i	$0.513985\pi$
$20$	0	0
$21$	−2848.22	−1.40937
$22$	945.753	0.416602
$23$	3559.57	1.40306	0.701532	−	0.712638i	$-0.252500\pi$
$23$	3559.57	1.40306	0.701532	+	0.712638i	$0.252500\pi$
$24$	−3475.12	−1.23152
$25$	0	0
$26$	3044.09	0.883129
$27$	−9866.43	−2.60466
$28$	4521.02	1.08979
$29$	−1514.73	−0.334456	−0.167228	−	0.985918i	$-0.553482\pi$
$29$	−1514.73	−0.334456	−0.167228	+	0.985918i	$0.553482\pi$
$30$	0	0
$31$	1555.01	0.290623	0.145311	−	0.989386i	$-0.453582\pi$
$31$	1555.01	0.290623	0.145311	+	0.989386i	$0.453582\pi$
$32$	−7372.82	−1.27280
$33$	−3088.79	−0.493745
$34$	12363.2	1.83415
$35$	0	0
$36$	26765.1	3.44201
$37$	192.463	0.0231122	0.0115561	−	0.999933i	$-0.496321\pi$
$37$	192.463	0.0231122	0.0115561	+	0.999933i	$0.496321\pi$
$38$	−1218.35	−0.136872
$39$	−9941.85	−1.04666
$40$	0	0
$41$	−129.051	−0.0119895	−0.00599476	−	0.999982i	$-0.501908\pi$
$41$	−129.051	−0.0119895	−0.00599476	+	0.999982i	$0.501908\pi$
$42$	−25105.6	−2.19607
$43$	−1849.00	−0.152499
$43$	−1849.00	−0.152499
$44$	4902.88	0.381785
$45$	0	0
$46$	31375.8	2.18625
$47$	−23841.8	−1.57433	−0.787164	−	0.616744i	$-0.788452\pi$
$47$	−23841.8	−1.57433	−0.787164	+	0.616744i	$0.788452\pi$
$48$	11463.2	0.718131
$49$	−7018.13	−0.417572
$50$	0	0
$51$	−40377.6	−2.17378
$52$	15780.9	0.809323
$53$	4052.01	0.198144	0.0990721	−	0.995080i	$-0.468413\pi$
$53$	4052.01	0.198144	0.0990721	+	0.995080i	$0.468413\pi$
$54$	−86967.5	−4.05857
$55$	0	0
$56$	11943.4	0.508931
$57$	3979.08	0.162217
$58$	−13351.5	−0.521148
$59$	10145.4	0.379436	0.189718	−	0.981839i	$-0.439243\pi$
$59$	10145.4	0.379436	0.189718	+	0.981839i	$0.439243\pi$
$60$	0	0
$61$	22113.5	0.760909	0.380455	−	0.924800i	$-0.375767\pi$
$61$	22113.5	0.760909	0.380455	+	0.924800i	$0.375767\pi$
$62$	13706.6	0.452847
$63$	57951.5	1.83956
$64$	−52245.2	−1.59440
$65$	0	0
$66$	−27226.1	−0.769352
$67$	−31587.3	−0.859656	−0.429828	−	0.902911i	$-0.641426\pi$
$67$	−31587.3	−0.859656	−0.429828	+	0.902911i	$0.641426\pi$
$68$	64092.0	1.68086
$69$	−102472.	−2.59108
$70$	0	0
$71$	54546.7	1.28417	0.642085	−	0.766634i	$-0.278070\pi$
$71$	54546.7	1.28417	0.642085	+	0.766634i	$0.278070\pi$
$72$	70706.8	1.60742
$73$	13049.5	0.286608	0.143304	−	0.989679i	$-0.454227\pi$
$73$	13049.5	0.286608	0.143304	+	0.989679i	$0.454227\pi$
$74$	1696.46	0.0360134
$75$	0	0
$76$	−6316.05	−0.125433
$77$	10615.7	0.204042
$78$	−87632.3	−1.63090
$79$	39575.9	0.713448	0.356724	−	0.934210i	$-0.383894\pi$
$79$	39575.9	0.713448	0.356724	+	0.934210i	$0.383894\pi$
$80$	0	0
$81$	141699.	2.39969
$82$	−1137.52	−0.0186820
$83$	66617.1	1.06143	0.530714	−	0.847551i	$-0.321924\pi$
$83$	66617.1	1.06143	0.530714	+	0.847551i	$0.321924\pi$
$84$	−130150.	−2.01254
$85$	0	0
$86$	−16298.0	−0.237623
$87$	43605.4	0.617650
$88$	12952.2	0.178294
$89$	87137.6	1.16609	0.583043	−	0.812441i	$-0.301862\pi$
$89$	87137.6	1.16609	0.583043	+	0.812441i	$0.301862\pi$
$90$	0	0
$91$	34168.6	0.432537
$92$	162655.	2.00354
$93$	−44765.2	−0.536702
$94$	−210154.	−2.45311
$95$	0	0
$96$	212246.	2.35051
$97$	−44772.4	−0.483149	−0.241574	−	0.970382i	$-0.577664\pi$
$97$	−44772.4	−0.483149	−0.241574	+	0.970382i	$0.577664\pi$
$98$	−61861.2	−0.650659
$99$	62846.2	0.644453
$100$	0	0
$101$	21037.8	0.205209	0.102604	−	0.994722i	$-0.467282\pi$
$101$	21037.8	0.205209	0.102604	+	0.994722i	$0.467282\pi$
$102$	−355908.	−3.38717
$103$	−114899.	−1.06714	−0.533572	−	0.845754i	$-0.679151\pi$
$103$	−114899.	−1.06714	−0.533572	+	0.845754i	$0.679151\pi$
$104$	41689.2	0.377955
$105$	0	0
$106$	35716.4	0.308747
$107$	−135555.	−1.14461	−0.572305	−	0.820041i	$-0.693951\pi$
$107$	−135555.	−1.14461	−0.572305	+	0.820041i	$0.693951\pi$
$108$	−450848.	−3.71938
$109$	215276.	1.73552	0.867758	−	0.496988i	$-0.165561\pi$
$109$	215276.	1.73552	0.867758	+	0.496988i	$0.165561\pi$
$110$	0	0
$111$	−5540.55	−0.0426821
$112$	−39397.3	−0.296771
$113$	−182228.	−1.34251	−0.671256	−	0.741226i	$-0.734245\pi$
$113$	−182228.	−1.34251	−0.671256	+	0.741226i	$0.734245\pi$
$114$	35073.5	0.252765
$115$	0	0
$116$	−69215.6	−0.477594
$117$	202283.	1.36614
$118$	89426.4	0.591236
$119$	138771.	0.898324
$120$	0	0
$121$	−149539.	−0.928518
$122$	194919.	1.18565
$123$	3715.08	0.0221414
$124$	71056.5	0.415001
$125$	0	0
$126$	510812.	2.86639
$127$	−150942.	−0.830426	−0.415213	−	0.909724i	$-0.636293\pi$
$127$	−150942.	−0.830426	−0.415213	+	0.909724i	$0.636293\pi$
$128$	−224584.	−1.21159
$129$	53228.4	0.281624
$130$	0	0
$131$	63616.8	0.323887	0.161944	−	0.986800i	$-0.448224\pi$
$131$	63616.8	0.323887	0.161944	+	0.986800i	$0.448224\pi$
$132$	−141142.	−0.705055
$133$	−13675.5	−0.0670367
$134$	−278425.	−1.33951
$135$	0	0
$136$	169316.	0.784964
$137$	189444.	0.862341	0.431170	−	0.902271i	$-0.358101\pi$
$137$	189444.	0.862341	0.431170	+	0.902271i	$0.358101\pi$
$138$	−903235.	−4.03741
$139$	409077.	1.79584	0.897921	−	0.440157i	$-0.145077\pi$
$139$	409077.	1.79584	0.897921	+	0.440157i	$0.145077\pi$
$140$	0	0
$141$	686352.	2.90736
$142$	480801.	2.00099
$143$	37054.5	0.151531
$144$	−233238.	−0.937329
$145$	0	0
$146$	115025.	0.446591
$147$	202036.	0.771143
$148$	8794.61	0.0330037
$149$	−106611.	−0.393403	−0.196701	−	0.980463i	$-0.563023\pi$
$149$	−106611.	−0.393403	−0.196701	+	0.980463i	$0.563023\pi$
$150$	0	0
$151$	233165.	0.832187	0.416094	−	0.909322i	$-0.363399\pi$
$151$	233165.	0.832187	0.416094	+	0.909322i	$0.363399\pi$
$152$	−16685.5	−0.0585774
$153$	821547.	2.83729
$154$	93571.6	0.317938
$155$	0	0
$156$	−454294.	−1.49460
$157$	565393.	1.83063	0.915316	−	0.402736i	$-0.131941\pi$
$157$	565393.	1.83063	0.915316	+	0.402736i	$0.131941\pi$
$158$	348841.	1.11169
$159$	−116648.	−0.365919
$160$	0	0
$161$	352179.	1.07078
$162$	1.24901e6	3.73918
$163$	277784.	0.818914	0.409457	−	0.912329i	$-0.365718\pi$
$163$	277784.	0.818914	0.409457	+	0.912329i	$0.365718\pi$
$164$	−5897.00	−0.0171207
$165$	0	0
$166$	587196.	1.65391
$167$	−245436.	−0.681001	−0.340501	−	0.940244i	$-0.610597\pi$
$167$	−245436.	−0.681001	−0.340501	+	0.940244i	$0.610597\pi$
$168$	−343824.	−0.939860
$169$	−252026.	−0.678779
$170$	0	0
$171$	−80960.6	−0.211731
$172$	−84490.3	−0.217764
$173$	424862.	1.07928	0.539638	−	0.841897i	$-0.318561\pi$
$173$	424862.	1.07928	0.539638	+	0.841897i	$0.318561\pi$
$174$	384359.	0.962420
$175$	0	0
$176$	−42724.9	−0.103968
$177$	−292062.	−0.700717
$178$	768073.	1.81699
$179$	361763.	0.843902	0.421951	−	0.906619i	$-0.361345\pi$
$179$	361763.	0.843902	0.421951	+	0.906619i	$0.361345\pi$
$180$	0	0
$181$	625898.	1.42006	0.710030	−	0.704171i	$-0.248681\pi$
$181$	625898.	1.42006	0.710030	+	0.704171i	$0.248681\pi$
$182$	301178.	0.673977
$183$	−636597.	−1.40520
$184$	429695.	0.935655
$185$	0	0
$186$	−394582.	−0.836286
$187$	150493.	0.314710
$188$	−1.08946e6	−2.24810
$189$	−976172.	−1.98780
$190$	0	0
$191$	−381854.	−0.757381	−0.378690	−	0.925523i	$-0.623625\pi$
$191$	−381854.	−0.757381	−0.378690	+	0.925523i	$0.623625\pi$
$192$	1.50402e6	2.94442
$193$	779604.	1.50654	0.753270	−	0.657711i	$-0.228475\pi$
$193$	779604.	1.50654	0.753270	+	0.657711i	$0.228475\pi$
$194$	−394646.	−0.752841
$195$	0	0
$196$	−320695.	−0.596282
$197$	122390.	0.224688	0.112344	−	0.993669i	$-0.464164\pi$
$197$	122390.	0.224688	0.112344	+	0.993669i	$0.464164\pi$
$198$	553957.	1.00418
$199$	745476.	1.33445	0.667223	−	0.744858i	$-0.267483\pi$
$199$	745476.	1.33445	0.667223	+	0.744858i	$0.267483\pi$
$200$	0	0
$201$	909324.	1.58755
$202$	185437.	0.319755
$203$	−149865.	−0.255247
$204$	−1.84506e6	−3.10410
$205$	0	0
$206$	−1.01278e6	−1.66282
$207$	2.08495e6	3.38197
$208$	−137518.	−0.220395
$209$	−14830.5	−0.0234850
$210$	0	0
$211$	550762.	0.851644	0.425822	−	0.904807i	$-0.359985\pi$
$211$	550762.	0.851644	0.425822	+	0.904807i	$0.359985\pi$
$212$	185157.	0.282944
$213$	−1.57027e6	−2.37152
$214$	−1.19485e6	−1.78353
$215$	0	0
$216$	−1.19103e6	−1.73696
$217$	153851.	0.221794
$218$	1.89754e6	2.70427
$219$	−375666.	−0.529287
$220$	0	0
$221$	484389.	0.667135
$222$	−48837.1	−0.0665071
$223$	−725164.	−0.976504	−0.488252	−	0.872703i	$-0.662365\pi$
$223$	−725164.	−0.976504	−0.488252	+	0.872703i	$0.662365\pi$
$224$	−729457.	−0.971359
$225$	0	0
$226$	−1.60624e6	−2.09190
$227$	−649335.	−0.836381	−0.418191	−	0.908359i	$-0.637336\pi$
$227$	−649335.	−0.836381	−0.418191	+	0.908359i	$0.637336\pi$
$228$	181824.	0.231641
$229$	880377.	1.10938	0.554689	−	0.832058i	$-0.312837\pi$
$229$	880377.	1.10938	0.554689	+	0.832058i	$0.312837\pi$
$230$	0	0
$231$	−305600.	−0.376811
$232$	−182851.	−0.223037
$233$	331488.	0.400016	0.200008	−	0.979794i	$-0.435903\pi$
$233$	331488.	0.400016	0.200008	+	0.979794i	$0.435903\pi$
$234$	1.78302e6	2.12871
$235$	0	0
$236$	463595.	0.541825
$237$	−1.13930e6	−1.31755
$238$	1.22320e6	1.39976
$239$	679646.	0.769641	0.384820	−	0.922992i	$-0.374263\pi$
$239$	679646.	0.769641	0.384820	+	0.922992i	$0.374263\pi$
$240$	0	0
$241$	21306.6	0.0236304	0.0118152	−	0.999930i	$-0.496239\pi$
$241$	21306.6	0.0236304	0.0118152	+	0.999930i	$0.496239\pi$
$242$	−1.31811e6	−1.44681
$243$	−1.68165e6	−1.82692
$244$	1.01048e6	1.08656
$245$	0	0
$246$	32746.5	0.0345007
$247$	−47734.9	−0.0497844
$248$	187714.	0.193806
$249$	−1.91775e6	−1.96017
$250$	0	0
$251$	−396484.	−0.397230	−0.198615	−	0.980078i	$-0.563644\pi$
$251$	−396484.	−0.397230	−0.198615	+	0.980078i	$0.563644\pi$
$252$	2.64810e6	2.62684
$253$	381925.	0.375126
$254$	−1.33048e6	−1.29397
$255$	0	0
$256$	−307749.	−0.293493
$257$	−99434.8	−0.0939086	−0.0469543	−	0.998897i	$-0.514952\pi$
$257$	−99434.8	−0.0939086	−0.0469543	+	0.998897i	$0.514952\pi$
$258$	469181.	0.438825
$259$	19042.0	0.0176386
$260$	0	0
$261$	−887222.	−0.806178
$262$	560750.	0.504680
$263$	435284.	0.388046	0.194023	−	0.980997i	$-0.437846\pi$
$263$	435284.	0.388046	0.194023	+	0.980997i	$0.437846\pi$
$264$	−372864.	−0.329262
$265$	0	0
$266$	−120542.	−0.104456
$267$	−2.50849e6	−2.15345
$268$	−1.44338e6	−1.22757
$269$	433282.	0.365082	0.182541	−	0.983198i	$-0.441568\pi$
$269$	433282.	0.365082	0.182541	+	0.983198i	$0.441568\pi$
$270$	0	0
$271$	−1.91312e6	−1.58241	−0.791204	−	0.611552i	$-0.790546\pi$
$271$	−1.91312e6	−1.58241	−0.791204	+	0.611552i	$0.790546\pi$
$272$	−558514.	−0.457733
$273$	−983634.	−0.798779
$274$	1.66985e6	1.34370
$275$	0	0
$276$	−4.68246e6	−3.70000
$277$	−2.09495e6	−1.64049	−0.820246	−	0.572011i	$-0.806164\pi$
$277$	−2.09495e6	−1.64049	−0.820246	+	0.572011i	$0.806164\pi$
$278$	3.60580e6	2.79827
$279$	910819.	0.700521
$280$	0	0
$281$	−2.42102e6	−1.82908	−0.914540	−	0.404496i	$-0.867447\pi$
$281$	−2.42102e6	−1.82908	−0.914540	+	0.404496i	$0.867447\pi$
$282$	6.04984e6	4.53024
$283$	2.52970e6	1.87760	0.938799	−	0.344465i	$-0.111940\pi$
$283$	2.52970e6	1.87760	0.938799	+	0.344465i	$0.111940\pi$
$284$	2.49252e6	1.83376
$285$	0	0
$286$	326617.	0.236115
$287$	−12768.1	−0.00915004
$288$	−4.31849e6	−3.06797
$289$	547432.	0.385554
$290$	0	0
$291$	1.28889e6	0.892246
$292$	596300.	0.409268
$293$	2.62130e6	1.78381	0.891903	−	0.452226i	$-0.149370\pi$
$293$	2.62130e6	1.78381	0.891903	+	0.452226i	$0.149370\pi$
$294$	1.78084e6	1.20159
$295$	0	0
$296$	23233.2	0.0154128
$297$	−1.05862e6	−0.696386
$298$	−939723.	−0.612998
$299$	1.22930e6	0.795206
$300$	0	0
$301$	−182938.	−0.116382
$302$	2.05523e6	1.29671
$303$	−605628.	−0.378966
$304$	55039.7	0.0341580
$305$	0	0
$306$	7.24151e6	4.42105
$307$	1.96357e6	1.18905	0.594526	−	0.804076i	$-0.297340\pi$
$307$	1.96357e6	1.18905	0.594526	+	0.804076i	$0.297340\pi$
$308$	485084.	0.291367
$309$	3.30768e6	1.97073
$310$	0	0
$311$	952083.	0.558179	0.279090	−	0.960265i	$-0.409967\pi$
$311$	952083.	0.558179	0.279090	+	0.960265i	$0.409967\pi$
$312$	−1.20014e6	−0.697982
$313$	1.83583e6	1.05919	0.529593	−	0.848252i	$-0.322345\pi$
$313$	1.83583e6	1.05919	0.529593	+	0.848252i	$0.322345\pi$
$314$	4.98364e6	2.85248
$315$	0	0
$316$	1.80842e6	1.01878
$317$	−706548.	−0.394906	−0.197453	−	0.980312i	$-0.563267\pi$
$317$	−706548.	−0.394906	−0.197453	+	0.980312i	$0.563267\pi$
$318$	−1.02819e6	−0.570173
$319$	−162523.	−0.0894207
$320$	0	0
$321$	3.90233e6	2.11379
$322$	3.10428e6	1.66848
$323$	−193870.	−0.103396
$324$	6.47496e6	3.42669
$325$	0	0
$326$	2.44852e6	1.27603
$327$	−6.19729e6	−3.20503
$328$	−15578.5	−0.00799540
$329$	−2.35888e6	−1.20148
$330$	0	0
$331$	1.44183e6	0.723345	0.361673	−	0.932305i	$-0.382206\pi$
$331$	1.44183e6	0.723345	0.361673	+	0.932305i	$0.382206\pi$
$332$	3.04408e6	1.51569
$333$	112731.	0.0557101
$334$	−2.16340e6	−1.06113
$335$	0	0
$336$	1.13416e6	0.548056
$337$	467934.	0.224445	0.112222	−	0.993683i	$-0.464203\pi$
$337$	467934.	0.224445	0.112222	+	0.993683i	$0.464203\pi$
$338$	−2.22148e6	−1.05767
$339$	5.24591e6	2.47926
$340$	0	0
$341$	166846.	0.0777014
$342$	−713626.	−0.329918
$343$	−2.35723e6	−1.08185
$344$	−223203.	−0.101696
$345$	0	0
$346$	3.74494e6	1.68172
$347$	61290.7	0.0273257	0.0136628	−	0.999907i	$-0.495651\pi$
$347$	61290.7	0.0273257	0.0136628	+	0.999907i	$0.495651\pi$
$348$	1.99256e6	0.881988
$349$	−344529.	−0.151413	−0.0757064	−	0.997130i	$-0.524121\pi$
$349$	−344529.	−0.151413	−0.0757064	+	0.997130i	$0.524121\pi$
$350$	0	0
$351$	−3.40738e6	−1.47623
$352$	−791069.	−0.340297
$353$	−3.95186e6	−1.68797	−0.843985	−	0.536367i	$-0.819796\pi$
$353$	−3.95186e6	−1.68797	−0.843985	+	0.536367i	$0.819796\pi$
$354$	−2.57438e6	−1.09185
$355$	0	0
$356$	3.98177e6	1.66514
$357$	−3.99491e6	−1.65896
$358$	3.18876e6	1.31496
$359$	1.05008e6	0.430018	0.215009	−	0.976612i	$-0.431022\pi$
$359$	1.05008e6	0.430018	0.215009	+	0.976612i	$0.431022\pi$
$360$	0	0
$361$	−2.45699e6	−0.992284
$362$	5.51696e6	2.21273
$363$	4.30487e6	1.71472
$364$	1.56134e6	0.617651
$365$	0	0
$366$	−5.61127e6	−2.18957
$367$	−4.49024e6	−1.74022	−0.870111	−	0.492856i	$-0.835953\pi$
$367$	−4.49024e6	−1.74022	−0.870111	+	0.492856i	$0.835953\pi$
$368$	−1.41742e6	−0.545605
$369$	−75589.2	−0.0288997
$370$	0	0
$371$	400901.	0.151218
$372$	−2.04555e6	−0.766396
$373$	1.69833e6	0.632048	0.316024	−	0.948751i	$-0.397652\pi$
$373$	1.69833e6	0.632048	0.316024	+	0.948751i	$0.397652\pi$
$374$	1.32651e6	0.490380
$375$	0	0
$376$	−2.87808e6	−1.04987
$377$	−523112.	−0.189558
$378$	−8.60445e6	−3.09738
$379$	−2.77198e6	−0.991269	−0.495635	−	0.868531i	$-0.665064\pi$
$379$	−2.77198e6	−0.991269	−0.495635	+	0.868531i	$0.665064\pi$
$380$	0	0
$381$	4.34527e6	1.53357
$382$	−3.36585e6	−1.18015
$383$	−2.08424e6	−0.726023	−0.363012	−	0.931785i	$-0.618252\pi$
$383$	−2.08424e6	−0.726023	−0.363012	+	0.931785i	$0.618252\pi$
$384$	6.46527e6	2.23748
$385$	0	0
$386$	6.87181e6	2.34748
$387$	−1.08302e6	−0.367585
$388$	−2.04588e6	−0.689924
$389$	5.18546e6	1.73745	0.868727	−	0.495292i	$-0.164939\pi$
$389$	5.18546e6	1.73745	0.868727	+	0.495292i	$0.164939\pi$
$390$	0	0
$391$	4.99265e6	1.65154
$392$	−847198.	−0.278464
$393$	−1.83138e6	−0.598133
$394$	1.07880e6	0.350108
$395$	0	0
$396$	2.87177e6	0.920261
$397$	227182.	0.0723432	0.0361716	−	0.999346i	$-0.488484\pi$
$397$	227182.	0.0723432	0.0361716	+	0.999346i	$0.488484\pi$
$398$	6.57099e6	2.07933
$399$	393685.	0.123799
$400$	0	0
$401$	−1.95004e6	−0.605594	−0.302797	−	0.953055i	$-0.597920\pi$
$401$	−1.95004e6	−0.605594	−0.302797	+	0.953055i	$0.597920\pi$
$402$	8.01522e6	2.47372
$403$	537025.	0.164714
$404$	961323.	0.293033
$405$	0	0
$406$	−1.32098e6	−0.397724
$407$	20650.4	0.00617933
$408$	−4.87421e6	−1.44962
$409$	4.00237e6	1.18307	0.591533	−	0.806281i	$-0.298523\pi$
$409$	4.00237e6	1.18307	0.591533	+	0.806281i	$0.298523\pi$
$410$	0	0
$411$	−5.45365e6	−1.59251
$412$	−5.25033e6	−1.52385
$413$	1.00377e6	0.289574
$414$	1.83778e7	5.26977
$415$	0	0
$416$	−2.54621e6	−0.721374
$417$	−1.17764e7	−3.31644
$418$	−130723.	−0.0365943
$419$	2.80438e6	0.780373	0.390186	−	0.920736i	$-0.372411\pi$
$419$	2.80438e6	0.780373	0.390186	+	0.920736i	$0.372411\pi$
$420$	0	0
$421$	269945.	0.0742283	0.0371142	−	0.999311i	$-0.488183\pi$
$421$	269945.	0.0742283	0.0371142	+	0.999311i	$0.488183\pi$
$422$	4.85469e6	1.32703
$423$	−1.39649e7	−3.79479
$424$	489141.	0.132135
$425$	0	0
$426$	−1.38411e7	−3.69529
$427$	2.18788e6	0.580703
$428$	−6.19423e6	−1.63447
$429$	−1.06671e6	−0.279837
$430$	0	0
$431$	−2.69610e6	−0.699105	−0.349553	−	0.936917i	$-0.613666\pi$
$431$	−2.69610e6	−0.699105	−0.349553	+	0.936917i	$0.613666\pi$
$432$	3.92880e6	1.01286
$433$	2.77746e6	0.711916	0.355958	−	0.934502i	$-0.384155\pi$
$433$	2.77746e6	0.711916	0.355958	+	0.934502i	$0.384155\pi$
$434$	1.35612e6	0.345599
$435$	0	0
$436$	9.83704e6	2.47827
$437$	−492009.	−0.123245
$438$	−3.31130e6	−0.824733
$439$	−6.80231e6	−1.68459	−0.842297	−	0.539013i	$-0.818797\pi$
$439$	−6.80231e6	−1.68459	−0.842297	+	0.539013i	$0.818797\pi$
$440$	0	0
$441$	−4.11074e6	−1.00652
$442$	4.26964e6	1.03953
$443$	−3.91275e6	−0.947268	−0.473634	−	0.880722i	$-0.657058\pi$
$443$	−3.91275e6	−0.947268	−0.473634	+	0.880722i	$0.657058\pi$
$444$	−253176.	−0.0609489
$445$	0	0
$446$	−6.39195e6	−1.52158
$447$	3.06909e6	0.726509
$448$	−5.16907e6	−1.21680
$449$	−1.93825e6	−0.453727	−0.226864	−	0.973927i	$-0.572847\pi$
$449$	−1.93825e6	−0.453727	−0.226864	+	0.973927i	$0.572847\pi$
$450$	0	0
$451$	−13846.6	−0.00320554
$452$	−8.32692e6	−1.91707
$453$	−6.71228e6	−1.53683
$454$	−5.72355e6	−1.30325
$455$	0	0
$456$	480337.	0.108177
$457$	−2.68525e6	−0.601442	−0.300721	−	0.953712i	$-0.597227\pi$
$457$	−2.68525e6	−0.601442	−0.300721	+	0.953712i	$0.597227\pi$
$458$	7.76007e6	1.72863
$459$	−1.38387e7	−3.06593
$460$	0	0
$461$	−552188.	−0.121014	−0.0605068	−	0.998168i	$-0.519272\pi$
$461$	−552188.	−0.121014	−0.0605068	+	0.998168i	$0.519272\pi$
$462$	−2.69371e6	−0.587146
$463$	1.76989e6	0.383703	0.191851	−	0.981424i	$-0.438551\pi$
$463$	1.76989e6	0.383703	0.191851	+	0.981424i	$0.438551\pi$
$464$	603162.	0.130059
$465$	0	0
$466$	2.92189e6	0.623303
$467$	−6.28442e6	−1.33344	−0.666719	−	0.745309i	$-0.732302\pi$
$467$	−6.28442e6	−1.33344	−0.666719	+	0.745309i	$0.732302\pi$
$468$	9.24333e6	1.95081
$469$	−3.12520e6	−0.656064
$470$	0	0
$471$	−1.62763e7	−3.38068
$472$	1.22471e6	0.253033
$473$	−198389.	−0.0407723
$474$	−1.00423e7	−2.05300
$475$	0	0
$476$	6.34118e6	1.28278
$477$	2.37339e6	0.477610
$478$	5.99073e6	1.19925
$479$	−5.81258e6	−1.15753	−0.578763	−	0.815496i	$-0.696464\pi$
$479$	−5.81258e6	−1.15753	−0.578763	+	0.815496i	$0.696464\pi$
$480$	0	0
$481$	66467.1	0.0130992
$482$	187806.	0.0368208
$483$	−1.01384e7	−1.97744
$484$	−6.83319e6	−1.32590
$485$	0	0
$486$	−1.48229e7	−2.84670
$487$	−186384.	−0.0356111	−0.0178056	−	0.999841i	$-0.505668\pi$
$487$	−186384.	−0.0356111	−0.0178056	+	0.999841i	$0.505668\pi$
$488$	2.66944e6	0.507424
$489$	−7.99676e6	−1.51231
$490$	0	0
$491$	8.49815e6	1.59082	0.795409	−	0.606073i	$-0.207256\pi$
$491$	8.49815e6	1.59082	0.795409	+	0.606073i	$0.207256\pi$
$492$	169761.	0.0316173
$493$	−2.12455e6	−0.393687
$494$	−420759.	−0.0775739
$495$	0	0
$496$	−619204.	−0.113013
$497$	5.39678e6	0.980039
$498$	−1.69040e7	−3.05433
$499$	−6.10529e6	−1.09763	−0.548814	−	0.835945i	$-0.684920\pi$
$499$	−6.10529e6	−1.09763	−0.548814	+	0.835945i	$0.684920\pi$
$500$	0	0
$501$	7.06555e6	1.25763
$502$	−3.49480e6	−0.618961
$503$	−7.84724e6	−1.38292	−0.691460	−	0.722414i	$-0.743032\pi$
$503$	−7.84724e6	−1.38292	−0.691460	+	0.722414i	$0.743032\pi$
$504$	6.99564e6	1.22674
$505$	0	0
$506$	3.36647e6	0.584519
$507$	7.25524e6	1.25352
$508$	−6.89732e6	−1.18583
$509$	7.63811e6	1.30675	0.653374	−	0.757035i	$-0.273353\pi$
$509$	7.63811e6	1.30675	0.653374	+	0.757035i	$0.273353\pi$
$510$	0	0
$511$	1.29110e6	0.218730
$512$	4.47405e6	0.754269
$513$	1.36375e6	0.228793
$514$	−876466.	−0.146328
$515$	0	0
$516$	2.43228e6	0.402151
$517$	−2.55812e6	−0.420915
$518$	167845.	0.0274843
$519$	−1.22308e7	−1.99313
$520$	0	0
$521$	1.02237e7	1.65011	0.825056	−	0.565051i	$-0.191143\pi$
$521$	1.02237e7	1.65011	0.825056	+	0.565051i	$0.191143\pi$
$522$	−7.82040e6	−1.25618
$523$	1.78020e6	0.284587	0.142294	−	0.989824i	$-0.454552\pi$
$523$	1.78020e6	0.284587	0.142294	+	0.989824i	$0.454552\pi$
$524$	2.90698e6	0.462502
$525$	0	0
$526$	3.83680e6	0.604651
$527$	2.18106e6	0.342091
$528$	1.22995e6	0.192001
$529$	6.23418e6	0.968590
$530$	0	0
$531$	5.94247e6	0.914599
$532$	−624902.	−0.0957266
$533$	−44567.9	−0.00679523
$534$	−2.21111e7	−3.35549
$535$	0	0
$536$	−3.81307e6	−0.573275
$537$	−1.04143e7	−1.55846
$538$	3.81916e6	0.568869
$539$	−753013.	−0.111643
$540$	0	0
$541$	−4.26642e6	−0.626716	−0.313358	−	0.949635i	$-0.601454\pi$
$541$	−4.26642e6	−0.626716	−0.313358	+	0.949635i	$0.601454\pi$
$542$	−1.68632e7	−2.46570
$543$	−1.80181e7	−2.62247
$544$	−1.03411e7	−1.49820
$545$	0	0
$546$	−8.67022e6	−1.24465
$547$	4.70659e6	0.672570	0.336285	−	0.941760i	$-0.390829\pi$
$547$	4.70659e6	0.672570	0.336285	+	0.941760i	$0.390829\pi$
$548$	8.65666e6	1.23140
$549$	1.29526e7	1.83411
$550$	0	0
$551$	209368.	0.0293786
$552$	−1.23699e7	−1.72790
$553$	3.91558e6	0.544482
$554$	−1.84659e7	−2.55621
$555$	0	0
$556$	1.86928e7	2.56441
$557$	4.15823e6	0.567899	0.283949	−	0.958839i	$-0.408355\pi$
$557$	4.15823e6	0.567899	0.283949	+	0.958839i	$0.408355\pi$
$558$	8.02840e6	1.09155
$559$	−638554.	−0.0864307
$560$	0	0
$561$	−4.33233e6	−0.581185
$562$	−2.13400e7	−2.85006
$563$	448917.	0.0596891	0.0298445	−	0.999555i	$-0.490499\pi$
$563$	448917.	0.0596891	0.0298445	+	0.999555i	$0.490499\pi$
$564$	3.13629e7	4.15163
$565$	0	0
$566$	2.22980e7	2.92566
$567$	1.40195e7	1.83137
$568$	6.58463e6	0.856368
$569$	1.35275e7	1.75161	0.875805	−	0.482665i	$-0.160331\pi$
$569$	1.35275e7	1.75161	0.875805	+	0.482665i	$0.160331\pi$
$570$	0	0
$571$	−6.85678e6	−0.880096	−0.440048	−	0.897974i	$-0.645039\pi$
$571$	−6.85678e6	−0.880096	−0.440048	+	0.897974i	$0.645039\pi$
$572$	1.69321e6	0.216382
$573$	1.09927e7	1.39868
$574$	−112545.	−0.0142575
$575$	0	0
$576$	−3.06016e7	−3.84316
$577$	6.17669e6	0.772354	0.386177	−	0.922425i	$-0.373795\pi$
$577$	6.17669e6	0.772354	0.386177	+	0.922425i	$0.373795\pi$
$578$	4.82533e6	0.600769
$579$	−2.24430e7	−2.78218
$580$	0	0
$581$	6.59101e6	0.810050
$582$	1.13609e7	1.39029
$583$	434762.	0.0529762
$584$	1.57528e6	0.191129
$585$	0	0
$586$	2.31054e7	2.77952
$587$	−4.51687e6	−0.541057	−0.270528	−	0.962712i	$-0.587198\pi$
$587$	−4.51687e6	−0.541057	−0.270528	+	0.962712i	$0.587198\pi$
$588$	9.23206e6	1.10117
$589$	−214936.	−0.0255283
$590$	0	0
$591$	−3.52332e6	−0.414938
$592$	−76638.4	−0.00898757
$593$	−1.01538e7	−1.18575	−0.592874	−	0.805295i	$-0.702007\pi$
$593$	−1.01538e7	−1.18575	−0.592874	+	0.805295i	$0.702007\pi$
$594$	−9.33121e6	−1.08511
$595$	0	0
$596$	−4.87161e6	−0.561768
$597$	−2.14605e7	−2.46436
$598$	1.08356e7	1.23909
$599$	1.26835e7	1.44435	0.722175	−	0.691711i	$-0.243143\pi$
$599$	1.26835e7	1.44435	0.722175	+	0.691711i	$0.243143\pi$
$600$	0	0
$601$	418175.	0.0472250	0.0236125	−	0.999721i	$-0.492483\pi$
$601$	418175.	0.0472250	0.0236125	+	0.999721i	$0.492483\pi$
$602$	−1.61250e6	−0.181346
$603$	−1.85016e7	−2.07213
$604$	1.06545e7	1.18834
$605$	0	0
$606$	−5.33830e6	−0.590502
$607$	1.52515e7	1.68013	0.840063	−	0.542490i	$-0.182518\pi$
$607$	1.52515e7	1.68013	0.840063	+	0.542490i	$0.182518\pi$
$608$	1.01908e6	0.111802
$609$	4.31427e6	0.471372
$610$	0	0
$611$	−8.23380e6	−0.892272
$612$	3.75407e7	4.05157
$613$	−1.21680e7	−1.30788	−0.653940	−	0.756546i	$-0.726885\pi$
$613$	−1.21680e7	−1.30788	−0.653940	+	0.756546i	$0.726885\pi$
$614$	1.73079e7	1.85278
$615$	0	0
$616$	1.28148e6	0.136069
$617$	−7.82651e6	−0.827667	−0.413833	−	0.910353i	$-0.635810\pi$
$617$	−7.82651e6	−0.827667	−0.413833	+	0.910353i	$0.635810\pi$
$618$	2.91555e7	3.07078
$619$	−3.31990e6	−0.348256	−0.174128	−	0.984723i	$-0.555711\pi$
$619$	−3.31990e6	−0.348256	−0.174128	+	0.984723i	$0.555711\pi$
$620$	0	0
$621$	−3.51202e7	−3.65450
$622$	8.39212e6	0.869753
$623$	8.62128e6	0.889922
$624$	3.95884e6	0.407011
$625$	0	0
$626$	1.61819e7	1.65042
$627$	426937.	0.0433705
$628$	2.58357e7	2.61409
$629$	269948.	0.0272053
$630$	0	0
$631$	−6.47059e6	−0.646950	−0.323475	−	0.946237i	$-0.604851\pi$
$631$	−6.47059e6	−0.646950	−0.323475	+	0.946237i	$0.604851\pi$
$632$	4.77742e6	0.475774
$633$	−1.58552e7	−1.57276
$634$	−6.22786e6	−0.615341
$635$	0	0
$636$	−5.33025e6	−0.522522
$637$	−2.42372e6	−0.236665
$638$	−1.43256e6	−0.139335
$639$	3.19497e7	3.09538
$640$	0	0
$641$	4.50662e6	0.433218	0.216609	−	0.976258i	$-0.430500\pi$
$641$	4.50662e6	0.433218	0.216609	+	0.976258i	$0.430500\pi$
$642$	3.43970e7	3.29369
$643$	8.31760e6	0.793360	0.396680	−	0.917957i	$-0.370162\pi$
$643$	8.31760e6	0.793360	0.396680	+	0.917957i	$0.370162\pi$
$644$	1.60929e7	1.52904
$645$	0	0
$646$	−1.70886e6	−0.161111
$647$	3.74937e6	0.352126	0.176063	−	0.984379i	$-0.443664\pi$
$647$	3.74937e6	0.352126	0.176063	+	0.984379i	$0.443664\pi$
$648$	1.71053e7	1.60027
$649$	1.08855e6	0.101447
$650$	0	0
$651$	−4.42901e6	−0.409595
$652$	1.26934e7	1.16939
$653$	−6.42374e6	−0.589529	−0.294765	−	0.955570i	$-0.595241\pi$
$653$	−6.42374e6	−0.589529	−0.294765	+	0.955570i	$0.595241\pi$
$654$	−5.46259e7	−4.99406
$655$	0	0
$656$	51388.0	0.00466232
$657$	7.64351e6	0.690843
$658$	−2.07923e7	−1.87214
$659$	9.10681e6	0.816870	0.408435	−	0.912787i	$-0.366075\pi$
$659$	9.10681e6	0.816870	0.408435	+	0.912787i	$0.366075\pi$
$660$	0	0
$661$	1.59096e6	0.141630	0.0708150	−	0.997489i	$-0.477440\pi$
$661$	1.59096e6	0.141630	0.0708150	+	0.997489i	$0.477440\pi$
$662$	1.27090e7	1.12711
$663$	−1.39444e7	−1.23202
$664$	8.04172e6	0.707830
$665$	0	0
$666$	993669.	0.0868073
$667$	−5.39177e6	−0.469263
$668$	−1.12153e7	−0.972451
$669$	2.08758e7	1.80334
$670$	0	0
$671$	2.37268e6	0.203438
$672$	2.09994e7	1.79384
$673$	1.25318e7	1.06654	0.533270	−	0.845945i	$-0.320963\pi$
$673$	1.25318e7	1.06654	0.533270	+	0.845945i	$0.320963\pi$
$674$	4.12460e6	0.349729
$675$	0	0
$676$	−1.15164e7	−0.969278
$677$	3.63488e6	0.304802	0.152401	−	0.988319i	$-0.451299\pi$
$677$	3.63488e6	0.304802	0.152401	+	0.988319i	$0.451299\pi$
$678$	4.62400e7	3.86317
$679$	−4.42972e6	−0.368725
$680$	0	0
$681$	1.86929e7	1.54457
$682$	1.47066e6	0.121074
$683$	−6.59490e6	−0.540949	−0.270475	−	0.962727i	$-0.587181\pi$
$683$	−6.59490e6	−0.540949	−0.270475	+	0.962727i	$0.587181\pi$
$684$	−3.69951e6	−0.302346
$685$	0	0
$686$	−2.07777e7	−1.68573
$687$	−2.53440e7	−2.04872
$688$	736270.	0.0593016
$689$	1.39937e6	0.112301
$690$	0	0
$691$	2.38268e7	1.89833	0.949164	−	0.314783i	$-0.101932\pi$
$691$	2.38268e7	1.89833	0.949164	+	0.314783i	$0.101932\pi$
$692$	1.94141e7	1.54118
$693$	6.21792e6	0.491827
$694$	540246.	0.0425787
$695$	0	0
$696$	5.26385e6	0.411890
$697$	−181007.	−0.0141128
$698$	−3.03685e6	−0.235931
$699$	−9.54276e6	−0.738722
$700$	0	0
$701$	1.47090e7	1.13054	0.565272	−	0.824905i	$-0.308771\pi$
$701$	1.47090e7	1.13054	0.565272	+	0.824905i	$0.308771\pi$
$702$	−3.00343e7	−2.30025
$703$	−26602.5	−0.00203018
$704$	−5.60567e6	−0.426281
$705$	0	0
$706$	−3.48336e7	−2.63019
$707$	2.08145e6	0.156609
$708$	−1.33458e7	−1.00060
$709$	−1.76811e7	−1.32097	−0.660486	−	0.750839i	$-0.729650\pi$
$709$	−1.76811e7	−1.32097	−0.660486	+	0.750839i	$0.729650\pi$
$710$	0	0
$711$	2.31808e7	1.71971
$712$	1.05189e7	0.777623
$713$	5.53517e6	0.407762
$714$	−3.52131e7	−2.58499
$715$	0	0
$716$	1.65308e7	1.20507
$717$	−1.95654e7	−1.42132
$718$	9.25592e6	0.670052
$719$	2.50711e6	0.180864	0.0904320	−	0.995903i	$-0.471175\pi$
$719$	2.50711e6	0.180864	0.0904320	+	0.995903i	$0.471175\pi$
$720$	0	0
$721$	−1.13680e7	−0.814412
$722$	−2.16571e7	−1.54617
$723$	−613367.	−0.0436390
$724$	2.86005e7	2.02781
$725$	0	0
$726$	3.79452e7	2.67187
$727$	−1.94538e7	−1.36511	−0.682555	−	0.730834i	$-0.739131\pi$
$727$	−1.94538e7	−1.36511	−0.682555	+	0.730834i	$0.739131\pi$
$728$	4.12468e6	0.288444
$729$	1.39779e7	0.974142
$730$	0	0
$731$	−2.59341e6	−0.179505
$732$	−2.90894e7	−2.00658
$733$	7.13116e6	0.490230	0.245115	−	0.969494i	$-0.421174\pi$
$733$	7.13116e6	0.490230	0.245115	+	0.969494i	$0.421174\pi$
$734$	−3.95792e7	−2.71161
$735$	0	0
$736$	−2.62440e7	−1.78581
$737$	−3.38917e6	−0.229839
$738$	−666280.	−0.0450314
$739$	1.07719e7	0.725574	0.362787	−	0.931872i	$-0.381825\pi$
$739$	1.07719e7	0.725574	0.362787	+	0.931872i	$0.381825\pi$
$740$	0	0
$741$	1.37418e6	0.0919385
$742$	3.53374e6	0.235627
$743$	−2.76611e7	−1.83822	−0.919111	−	0.393999i	$-0.871091\pi$
$743$	−2.76611e7	−1.83822	−0.919111	+	0.393999i	$0.871091\pi$
$744$	−5.40385e6	−0.357908
$745$	0	0
$746$	1.49699e7	0.984855
$747$	3.90197e7	2.55848
$748$	6.87678e6	0.449398
$749$	−1.34117e7	−0.873532
$750$	0	0
$751$	1.91210e7	1.23712	0.618558	−	0.785739i	$-0.287717\pi$
$751$	1.91210e7	1.23712	0.618558	+	0.785739i	$0.287717\pi$
$752$	9.49380e6	0.612203
$753$	1.14139e7	0.733576
$754$	−4.61096e6	−0.295368
$755$	0	0
$756$	−4.46063e7	−2.83852
$757$	2.12222e7	1.34602	0.673009	−	0.739634i	$-0.265001\pi$
$757$	2.12222e7	1.34602	0.673009	+	0.739634i	$0.265001\pi$
$758$	−2.44335e7	−1.54459
$759$	−1.09947e7	−0.692757
$760$	0	0
$761$	2.67708e7	1.67571	0.837856	−	0.545891i	$-0.183809\pi$
$761$	2.67708e7	1.67571	0.837856	+	0.545891i	$0.183809\pi$
$762$	3.83013e7	2.38961
$763$	2.12991e7	1.32449
$764$	−1.74489e7	−1.08152
$765$	0	0
$766$	−1.83715e7	−1.13129
$767$	3.50372e6	0.215051
$768$	8.85939e6	0.542002
$769$	−4.14867e6	−0.252984	−0.126492	−	0.991968i	$-0.540372\pi$
$769$	−4.14867e6	−0.252984	−0.126492	+	0.991968i	$0.540372\pi$
$770$	0	0
$771$	2.86250e6	0.173424
$772$	3.56241e7	2.15130
$773$	6.98749e6	0.420603	0.210302	−	0.977637i	$-0.432555\pi$
$773$	6.98749e6	0.420603	0.210302	+	0.977637i	$0.432555\pi$
$774$	−9.54623e6	−0.572769
$775$	0	0
$776$	−5.40472e6	−0.322195
$777$	−548175.	−0.0325737
$778$	4.57071e7	2.70729
$779$	17837.6	0.00105316
$780$	0	0
$781$	5.85261e6	0.343338
$782$	4.40077e7	2.57342
$783$	1.49449e7	0.871143
$784$	2.79461e6	0.162380
$785$	0	0
$786$	−1.61427e7	−0.932008
$787$	2.83753e7	1.63306	0.816532	−	0.577300i	$-0.195894\pi$
$787$	2.83753e7	1.63306	0.816532	+	0.577300i	$0.195894\pi$
$788$	5.59262e6	0.320849
$789$	−1.25308e7	−0.716616
$790$	0	0
$791$	−1.80294e7	−1.02456
$792$	7.58652e6	0.429763
$793$	7.63692e6	0.431256
$794$	2.00249e6	0.112725
$795$	0	0
$796$	3.40646e7	1.90555
$797$	−2.68366e7	−1.49652	−0.748259	−	0.663407i	$-0.769110\pi$
$797$	−2.68366e7	−1.49652	−0.748259	+	0.663407i	$0.769110\pi$
$798$	3.47013e6	0.192903
$799$	−3.34406e7	−1.85313
$800$	0	0
$801$	5.10392e7	2.81075
$802$	−1.71886e7	−0.943634
$803$	1.40015e6	0.0766279
$804$	4.15517e7	2.26698
$805$	0	0
$806$	4.73359e6	0.256657
$807$	−1.24732e7	−0.674208
$808$	2.53958e6	0.136847
$809$	1.29648e7	0.696458	0.348229	−	0.937410i	$-0.386783\pi$
$809$	1.29648e7	0.696458	0.348229	+	0.937410i	$0.386783\pi$
$810$	0	0
$811$	−2.56338e7	−1.36855	−0.684276	−	0.729223i	$-0.739882\pi$
$811$	−2.56338e7	−1.36855	−0.684276	+	0.729223i	$0.739882\pi$
$812$	−6.84810e6	−0.364485
$813$	5.50743e7	2.92228
$814$	182022.	0.00962861
$815$	0	0
$816$	1.60783e7	0.845309
$817$	255572.	0.0133955
$818$	3.52788e7	1.84345
$819$	2.00136e7	1.04259
$820$	0	0
$821$	2.49277e7	1.29070	0.645349	−	0.763888i	$-0.276712\pi$
$821$	2.49277e7	1.29070	0.645349	+	0.763888i	$0.276712\pi$
$822$	−4.80711e7	−2.48144
$823$	−3.65676e7	−1.88190	−0.940951	−	0.338543i	$-0.890066\pi$
$823$	−3.65676e7	−1.88190	−0.940951	+	0.338543i	$0.890066\pi$
$824$	−1.38701e7	−0.711642
$825$	0	0
$826$	8.84773e6	0.451213
$827$	1.33864e6	0.0680611	0.0340305	−	0.999421i	$-0.489166\pi$
$827$	1.33864e6	0.0680611	0.0340305	+	0.999421i	$0.489166\pi$
$828$	9.52720e7	4.82936
$829$	2.36426e7	1.19484	0.597418	−	0.801930i	$-0.296193\pi$
$829$	2.36426e7	1.19484	0.597418	+	0.801930i	$0.296193\pi$
$830$	0	0
$831$	6.03088e7	3.02955
$832$	−1.80429e7	−0.903647
$833$	−9.84364e6	−0.491522
$834$	−1.03803e8	−5.16766
$835$	0	0
$836$	−677683.	−0.0335360
$837$	−1.53424e7	−0.756973
$838$	2.47192e7	1.21597
$839$	−2.04325e7	−1.00211	−0.501057	−	0.865414i	$-0.667055\pi$
$839$	−2.04325e7	−1.00211	−0.501057	+	0.865414i	$0.667055\pi$
$840$	0	0
$841$	−1.82168e7	−0.888139
$842$	2.37942e6	0.115662
$843$	6.96956e7	3.37782
$844$	2.51672e7	1.21612
$845$	0	0
$846$	−1.23093e8	−5.91302
$847$	−1.47952e7	−0.708617
$848$	−1.61351e6	−0.0770516
$849$	−7.28242e7	−3.46742
$850$	0	0
$851$	685084.	0.0324280
$852$	−7.17538e7	−3.38646
$853$	−7.67435e6	−0.361135	−0.180567	−	0.983563i	$-0.557793\pi$
$853$	−7.67435e6	−0.361135	−0.180567	+	0.983563i	$0.557793\pi$
$854$	1.92850e7	0.904849
$855$	0	0
$856$	−1.63637e7	−0.763301
$857$	1.75236e7	0.815024	0.407512	−	0.913200i	$-0.366396\pi$
$857$	1.75236e7	0.815024	0.407512	+	0.913200i	$0.366396\pi$
$858$	−9.40254e6	−0.436041
$859$	−6.13683e6	−0.283767	−0.141883	−	0.989883i	$-0.545316\pi$
$859$	−6.13683e6	−0.283767	−0.141883	+	0.989883i	$0.545316\pi$
$860$	0	0
$861$	367565.	0.0168977
$862$	−2.37647e7	−1.08934
$863$	3.11872e7	1.42544	0.712721	−	0.701448i	$-0.247463\pi$
$863$	3.11872e7	1.42544	0.712721	+	0.701448i	$0.247463\pi$
$864$	7.27434e7	3.31520
$865$	0	0
$866$	2.44819e7	1.10930
$867$	−1.57593e7	−0.712015
$868$	7.03023e6	0.316716
$869$	4.24631e6	0.190749
$870$	0	0
$871$	−1.09087e7	−0.487222
$872$	2.59871e7	1.15736
$873$	−2.62246e7	−1.16459
$874$	−4.33680e6	−0.192040
$875$	0	0
$876$	−1.71661e7	−0.755808
$877$	−3.50382e7	−1.53830	−0.769152	−	0.639066i	$-0.779321\pi$
$877$	−3.50382e7	−1.53830	−0.769152	+	0.639066i	$0.779321\pi$
$878$	−5.99589e7	−2.62493
$879$	−7.54612e7	−3.29421
$880$	0	0
$881$	2.62095e7	1.13768	0.568838	−	0.822449i	$-0.307393\pi$
$881$	2.62095e7	1.13768	0.568838	+	0.822449i	$0.307393\pi$
$882$	−3.62340e7	−1.56836
$883$	6.37785e6	0.275279	0.137639	−	0.990482i	$-0.456049\pi$
$883$	6.37785e6	0.275279	0.137639	+	0.990482i	$0.456049\pi$
$884$	2.21342e7	0.952651
$885$	0	0
$886$	−3.44889e7	−1.47603
$887$	3.17424e7	1.35466	0.677331	−	0.735679i	$-0.263137\pi$
$887$	3.17424e7	1.35466	0.677331	+	0.735679i	$0.263137\pi$
$888$	−668831.	−0.0284632
$889$	−1.49340e7	−0.633756
$890$	0	0
$891$	1.52037e7	0.641585
$892$	−3.31365e7	−1.39442
$893$	3.29546e6	0.138289
$894$	2.70525e7	1.13204
$895$	0	0
$896$	−2.22201e7	−0.924647
$897$	−3.53887e7	−1.46853
$898$	−1.70847e7	−0.706995
$899$	−2.35542e6	−0.0972005
$900$	0	0
$901$	5.68336e6	0.233235
$902$	−122050.	−0.00499486
$903$	5.26635e6	0.214927
$904$	−2.19977e7	−0.895275
$905$	0	0
$906$	−5.91653e7	−2.39468
$907$	−3.51574e7	−1.41905	−0.709527	−	0.704678i	$-0.751091\pi$
$907$	−3.51574e7	−1.41905	−0.709527	+	0.704678i	$0.751091\pi$
$908$	−2.96714e7	−1.19433
$909$	1.23225e7	0.494639
$910$	0	0
$911$	4.08640e7	1.63134	0.815671	−	0.578516i	$-0.196368\pi$
$911$	4.08640e7	1.63134	0.815671	+	0.578516i	$0.196368\pi$
$912$	−1.58447e6	−0.0630806
$913$	7.14771e6	0.283785
$914$	−2.36691e7	−0.937165
$915$	0	0
$916$	4.02289e7	1.58416
$917$	6.29417e6	0.247181
$918$	−1.21981e8	−4.77732
$919$	−2.61425e7	−1.02108	−0.510539	−	0.859854i	$-0.670554\pi$
$919$	−2.61425e7	−1.02108	−0.510539	+	0.859854i	$0.670554\pi$
$920$	0	0
$921$	−5.65267e7	−2.19586
$922$	−4.86725e6	−0.188563
$923$	1.88377e7	0.727821
$924$	−1.39645e7	−0.538076
$925$	0	0
$926$	1.56007e7	0.597884
$927$	−6.72999e7	−2.57226
$928$	1.11678e7	0.425694
$929$	−7.30532e6	−0.277715	−0.138858	−	0.990312i	$-0.544343\pi$
$929$	−7.30532e6	−0.277715	−0.138858	+	0.990312i	$0.544343\pi$
$930$	0	0
$931$	970057.	0.0366795
$932$	1.51474e7	0.571212
$933$	−2.74083e7	−1.03081
$934$	−5.53939e7	−2.07776
$935$	0	0
$936$	2.44187e7	0.911029
$937$	4.84108e7	1.80133	0.900665	−	0.434514i	$-0.143080\pi$
$937$	4.84108e7	1.80133	0.900665	+	0.434514i	$0.143080\pi$
$938$	−2.75470e7	−1.02228
$939$	−5.28494e7	−1.95603
$940$	0	0
$941$	−2.33895e7	−0.861087	−0.430543	−	0.902570i	$-0.641678\pi$
$941$	−2.33895e7	−0.861087	−0.430543	+	0.902570i	$0.641678\pi$
$942$	−1.43468e8	−5.26777
$943$	−459366.	−0.0168221
$944$	−4.03989e6	−0.147550
$945$	0	0
$946$	−1.74870e6	−0.0635312
$947$	−1.17475e7	−0.425666	−0.212833	−	0.977089i	$-0.568269\pi$
$947$	−1.17475e7	−0.425666	−0.212833	+	0.977089i	$0.568269\pi$
$948$	−5.20603e7	−1.88142
$949$	4.50666e6	0.162439
$950$	0	0
$951$	2.03399e7	0.729285
$952$	1.67519e7	0.599061
$953$	4.69537e7	1.67470	0.837350	−	0.546667i	$-0.184104\pi$
$953$	4.69537e7	1.67470	0.837350	+	0.546667i	$0.184104\pi$
$954$	2.09202e7	0.744209
$955$	0	0
$956$	3.10565e7	1.09903
$957$	4.67866e6	0.165136
$958$	−5.12349e7	−1.80365
$959$	1.87433e7	0.658112
$960$	0	0
$961$	−2.62111e7	−0.915538
$962$	585873.	0.0204111
$963$	−7.93990e7	−2.75899
$964$	973607.	0.0337436
$965$	0	0
$966$	−8.93649e7	−3.08123
$967$	−2.55405e7	−0.878340	−0.439170	−	0.898404i	$-0.644727\pi$
$967$	−2.55405e7	−0.878340	−0.439170	+	0.898404i	$0.644727\pi$
$968$	−1.80516e7	−0.619196
$969$	5.58106e6	0.190944
$970$	0	0
$971$	−3.58415e7	−1.21994	−0.609969	−	0.792425i	$-0.708818\pi$
$971$	−3.58415e7	−1.21994	−0.609969	+	0.792425i	$0.708818\pi$
$972$	−7.68431e7	−2.60879
$973$	4.04735e7	1.37053
$974$	−1.64288e6	−0.0554891
$975$	0	0
$976$	−8.80558e6	−0.295892
$977$	4.59942e7	1.54158	0.770791	−	0.637088i	$-0.219861\pi$
$977$	4.59942e7	1.54158	0.770791	+	0.637088i	$0.219861\pi$
$978$	−7.04873e7	−2.35648
$979$	9.34946e6	0.311767
$980$	0	0
$981$	1.26094e8	4.18331
$982$	7.49068e7	2.47881
$983$	1.72385e7	0.569004	0.284502	−	0.958675i	$-0.408172\pi$
$983$	1.72385e7	0.569004	0.284502	+	0.958675i	$0.408172\pi$
$984$	448468.	0.0147653
$985$	0	0
$986$	−1.87269e7	−0.613441
$987$	6.79067e7	2.21881
$988$	−2.18125e6	−0.0710908
$989$	−6.58164e6	−0.213965
$990$	0	0
$991$	8.93779e6	0.289098	0.144549	−	0.989498i	$-0.453827\pi$
$991$	8.93779e6	0.289098	0.144549	+	0.989498i	$0.453827\pi$
$992$	−1.14648e7	−0.369903
$993$	−4.15071e7	−1.33582
$994$	4.75698e7	1.52709
$995$	0	0
$996$	−8.76320e7	−2.79907
$997$	3.37924e7	1.07667	0.538333	−	0.842732i	$-0.319054\pi$
$997$	3.37924e7	1.07667	0.538333	+	0.842732i	$0.319054\pi$
$998$	−5.38150e7	−1.71032
$999$	−1.89892e6	−0.0601995

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.6.a.i.1.32	✓	37
5.4	even	2		1075.6.a.j.1.6	yes	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1075.6.a.i.1.32	✓	37	1.1	even	1	trivial
1075.6.a.j.1.6	yes	37	5.4	even	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:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1075.a (trivial)

\(f(q)\)	\(=\)	\(q+8.81448 q^{2} -28.7877 q^{3} +45.6951 q^{4} -253.749 q^{6} +98.9387 q^{7} +120.716 q^{8} +585.731 q^{9} +O(q^{10})\)	\(q+8.81448 q^{2} -28.7877 q^{3} +45.6951 q^{4} -253.749 q^{6} +98.9387 q^{7} +120.716 q^{8} +585.731 q^{9} +107.295 q^{11} -1315.46 q^{12} +345.351 q^{13} +872.094 q^{14} -398.199 q^{16} +1402.60 q^{17} +5162.92 q^{18} -138.222 q^{19} -2848.22 q^{21} +945.753 q^{22} +3559.57 q^{23} -3475.12 q^{24} +3044.09 q^{26} -9866.43 q^{27} +4521.02 q^{28} -1514.73 q^{29} +1555.01 q^{31} -7372.82 q^{32} -3088.79 q^{33} +12363.2 q^{34} +26765.1 q^{36} +192.463 q^{37} -1218.35 q^{38} -9941.85 q^{39} -129.051 q^{41} -25105.6 q^{42} -1849.00 q^{43} +4902.88 q^{44} +31375.8 q^{46} -23841.8 q^{47} +11463.2 q^{48} -7018.13 q^{49} -40377.6 q^{51} +15780.9 q^{52} +4052.01 q^{53} -86967.5 q^{54} +11943.4 q^{56} +3979.08 q^{57} -13351.5 q^{58} +10145.4 q^{59} +22113.5 q^{61} +13706.6 q^{62} +57951.5 q^{63} -52245.2 q^{64} -27226.1 q^{66} -31587.3 q^{67} +64092.0 q^{68} -102472. q^{69} +54546.7 q^{71} +70706.8 q^{72} +13049.5 q^{73} +1696.46 q^{74} -6316.05 q^{76} +10615.7 q^{77} -87632.3 q^{78} +39575.9 q^{79} +141699. q^{81} -1137.52 q^{82} +66617.1 q^{83} -130150. q^{84} -16298.0 q^{86} +43605.4 q^{87} +12952.2 q^{88} +87137.6 q^{89} +34168.6 q^{91} +162655. q^{92} -44765.2 q^{93} -210154. q^{94} +212246. q^{96} -44772.4 q^{97} -61861.2 q^{98} +62846.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 630 q^{4} + 291 q^{6} - 213 q^{8} + 3535 q^{9}+O(q^{10}) \) 37 * q + 630 * q^4 + 291 * q^6 - 213 * q^8 + 3535 * q^9	\( 37 q + 630 q^{4} + 291 q^{6} - 213 q^{8} + 3535 q^{9} + 675 q^{11} + 4446 q^{12} - 1241 q^{13} + 2375 q^{14} + 10518 q^{16} - 1153 q^{17} + 6680 q^{18} + 4065 q^{19} + 9953 q^{21} - 9283 q^{22} + 360 q^{23} + 2265 q^{24} + 23695 q^{26} - 1323 q^{27} + 30375 q^{28} + 19290 q^{29} + 23291 q^{31} - 8166 q^{32} + 10388 q^{33} - 13153 q^{34} + 148705 q^{36} - 13501 q^{37} + 8127 q^{38} - 1327 q^{39} + 38345 q^{41} + 21835 q^{42} - 68413 q^{43} + 47768 q^{44} + 48755 q^{46} - 84859 q^{47} + 208720 q^{48} + 107255 q^{49} + 62027 q^{51} - 128320 q^{52} + 53559 q^{53} + 44158 q^{54} + 107538 q^{56} - 104239 q^{57} + 85186 q^{58} + 48186 q^{59} + 82364 q^{61} - 206506 q^{62} + 75269 q^{63} + 161467 q^{64} + 91969 q^{66} - 38168 q^{67} - 95991 q^{68} + 287103 q^{69} + 155302 q^{71} - 9979 q^{72} - 31927 q^{73} + 59946 q^{74} + 225407 q^{76} + 80007 q^{77} + 67815 q^{78} + 150174 q^{79} + 417489 q^{81} - 60603 q^{82} - 266568 q^{83} + 586273 q^{84} + 57554 q^{87} - 323054 q^{88} + 334356 q^{89} + 51747 q^{91} + 258529 q^{92} + 285287 q^{93} + 302744 q^{94} + 287282 q^{96} + 78640 q^{97} + 397117 q^{98} + 362152 q^{99}+O(q^{100}) \) 37 * q + 630 * q^4 + 291 * q^6 - 213 * q^8 + 3535 * q^9 + 675 * q^11 + 4446 * q^12 - 1241 * q^13 + 2375 * q^14 + 10518 * q^16 - 1153 * q^17 + 6680 * q^18 + 4065 * q^19 + 9953 * q^21 - 9283 * q^22 + 360 * q^23 + 2265 * q^24 + 23695 * q^26 - 1323 * q^27 + 30375 * q^28 + 19290 * q^29 + 23291 * q^31 - 8166 * q^32 + 10388 * q^33 - 13153 * q^34 + 148705 * q^36 - 13501 * q^37 + 8127 * q^38 - 1327 * q^39 + 38345 * q^41 + 21835 * q^42 - 68413 * q^43 + 47768 * q^44 + 48755 * q^46 - 84859 * q^47 + 208720 * q^48 + 107255 * q^49 + 62027 * q^51 - 128320 * q^52 + 53559 * q^53 + 44158 * q^54 + 107538 * q^56 - 104239 * q^57 + 85186 * q^58 + 48186 * q^59 + 82364 * q^61 - 206506 * q^62 + 75269 * q^63 + 161467 * q^64 + 91969 * q^66 - 38168 * q^67 - 95991 * q^68 + 287103 * q^69 + 155302 * q^71 - 9979 * q^72 - 31927 * q^73 + 59946 * q^74 + 225407 * q^76 + 80007 * q^77 + 67815 * q^78 + 150174 * q^79 + 417489 * q^81 - 60603 * q^82 - 266568 * q^83 + 586273 * q^84 + 57554 * q^87 - 323054 * q^88 + 334356 * q^89 + 51747 * q^91 + 258529 * q^92 + 285287 * q^93 + 302744 * q^94 + 287282 * q^96 + 78640 * q^97 + 397117 * q^98 + 362152 * q^99

Introduction

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