LMFDB - Embedded newform 177.6.a.b.1.7

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$28.3879361069$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
Defining polynomial:	$x^{12} - 4 x^{11} - 283 x^{10} + 1045 x^{9} + 27968 x^{8} - 94393 x^{7} - 1130486 x^{6} + 3566264 x^{5} + 15496192 x^{4} - 53008480 x^{3} - 16576192 x^{2} + 120303168 x - 50564480$
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.501674$ of defining polynomial
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q-0.501674 q^{2} -9.00000 q^{3} -31.7483 q^{4} -14.0506 q^{5} +4.51506 q^{6} +117.234 q^{7} +31.9809 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-0.501674 q^{2} -9.00000 q^{3} -31.7483 q^{4} -14.0506 q^{5} +4.51506 q^{6} +117.234 q^{7} +31.9809 q^{8} +81.0000 q^{9} +7.04881 q^{10} +53.5537 q^{11} +285.735 q^{12} -471.768 q^{13} -58.8130 q^{14} +126.455 q^{15} +999.902 q^{16} +1164.87 q^{17} -40.6356 q^{18} +1826.16 q^{19} +446.082 q^{20} -1055.10 q^{21} -26.8665 q^{22} +254.207 q^{23} -287.828 q^{24} -2927.58 q^{25} +236.673 q^{26} -729.000 q^{27} -3721.97 q^{28} -6598.12 q^{29} -63.4393 q^{30} +1104.44 q^{31} -1525.01 q^{32} -481.983 q^{33} -584.382 q^{34} -1647.20 q^{35} -2571.61 q^{36} -7748.51 q^{37} -916.136 q^{38} +4245.91 q^{39} -449.350 q^{40} -5824.87 q^{41} +529.317 q^{42} -6404.30 q^{43} -1700.24 q^{44} -1138.10 q^{45} -127.529 q^{46} -2856.66 q^{47} -8999.12 q^{48} -3063.28 q^{49} +1468.69 q^{50} -10483.8 q^{51} +14977.8 q^{52} -16675.9 q^{53} +365.720 q^{54} -752.461 q^{55} +3749.23 q^{56} -16435.4 q^{57} +3310.10 q^{58} -3481.00 q^{59} -4014.74 q^{60} +37099.5 q^{61} -554.070 q^{62} +9495.92 q^{63} -31231.8 q^{64} +6628.61 q^{65} +241.798 q^{66} +10974.2 q^{67} -36982.5 q^{68} -2287.86 q^{69} +826.357 q^{70} -15478.9 q^{71} +2590.45 q^{72} -42171.4 q^{73} +3887.22 q^{74} +26348.2 q^{75} -57977.5 q^{76} +6278.29 q^{77} -2130.06 q^{78} -89645.3 q^{79} -14049.2 q^{80} +6561.00 q^{81} +2922.18 q^{82} +58689.8 q^{83} +33497.7 q^{84} -16367.0 q^{85} +3212.87 q^{86} +59383.1 q^{87} +1712.69 q^{88} +61752.2 q^{89} +570.953 q^{90} -55307.0 q^{91} -8070.64 q^{92} -9939.99 q^{93} +1433.11 q^{94} -25658.6 q^{95} +13725.1 q^{96} -13874.8 q^{97} +1536.77 q^{98} +4337.85 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12q - 4q^{2} - 108q^{3} + 198q^{4} + 36q^{5} + 36q^{6} - 411q^{7} - 69q^{8} + 972q^{9} + O(q^{10}) $	\( 12q - 4q^{2} - 108q^{3} + 198q^{4} + 36q^{5} + 36q^{6} - 411q^{7} - 69q^{8} + 972q^{9} - 863q^{10} + 492q^{11} - 1782q^{12} - 974q^{13} - 967q^{14} - 324q^{15} + 6370q^{16} - 1463q^{17} - 324q^{18} - 3189q^{19} - 835q^{20} + 3699q^{21} - 2726q^{22} - 2617q^{23} + 621q^{24} + 8642q^{25} + 2414q^{26} - 8748q^{27} - 20458q^{28} - 1963q^{29} + 7767q^{30} - 11929q^{31} - 14382q^{32} - 4428q^{33} - 20744q^{34} + 1829q^{35} + 16038q^{36} - 28105q^{37} - 23475q^{38} + 8766q^{39} - 100576q^{40} - 7585q^{41} + 8703q^{42} - 33146q^{43} + 26014q^{44} + 2916q^{45} - 142851q^{46} - 79215q^{47} - 57330q^{48} - 32569q^{49} - 136019q^{50} + 13167q^{51} - 248218q^{52} - 12220q^{53} + 2916q^{54} - 117770q^{55} - 186728q^{56} + 28701q^{57} - 188072q^{58} - 41772q^{59} + 7515q^{60} - 54195q^{61} + 36230q^{62} - 33291q^{63} + 45197q^{64} + 42368q^{65} + 24534q^{66} + 24224q^{67} - 209639q^{68} + 23553q^{69} - 35684q^{70} + 60254q^{71} - 5589q^{72} - 15385q^{73} + 214638q^{74} - 77778q^{75} - 167504q^{76} - 17169q^{77} - 21726q^{78} - 27054q^{79} + 216899q^{80} + 78732q^{81} + 37917q^{82} - 117595q^{83} + 184122q^{84} - 121585q^{85} + 306756q^{86} + 17667q^{87} - 105799q^{88} - 36033q^{89} - 69903q^{90} - 32217q^{91} - 30906q^{92} + 107361q^{93} + 128392q^{94} - 50721q^{95} + 129438q^{96} - 196914q^{97} + 574100q^{98} + 39852q^{99} + O(q^{100}) \)

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 $

$2$	−0.501674	−0.0886842	−0.0443421	−	0.999016i	$-0.514119\pi$
$2$	−0.501674	−0.0886842	−0.0443421	+	0.999016i	$0.514119\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−31.7483	−0.992135
$5$	−14.0506	−0.251344	−0.125672	−	0.992072i	$-0.540109\pi$
$5$	−14.0506	−0.251344	−0.125672	+	0.992072i	$0.540109\pi$
$6$	4.51506	0.0512019
$7$	117.234	0.904288	0.452144	−	0.891945i	$-0.350659\pi$
$7$	117.234	0.904288	0.452144	+	0.891945i	$0.350659\pi$
$8$	31.9809	0.176671
$9$	81.0000	0.333333
$10$	7.04881	0.0222903
$11$	53.5537	0.133447	0.0667233	−	0.997772i	$-0.478746\pi$
$11$	53.5537	0.133447	0.0667233	+	0.997772i	$0.478746\pi$
$12$	285.735	0.572809
$13$	−471.768	−0.774230	−0.387115	−	0.922031i	$-0.626528\pi$
$13$	−471.768	−0.774230	−0.387115	+	0.922031i	$0.626528\pi$
$14$	−58.8130	−0.0801961
$15$	126.455	0.145114
$16$	999.902	0.976467
$17$	1164.87	0.977582	0.488791	−	0.872401i	$-0.337438\pi$
$17$	1164.87	0.977582	0.488791	+	0.872401i	$0.337438\pi$
$18$	−40.6356	−0.0295614
$19$	1826.16	1.16053	0.580263	−	0.814429i	$-0.302950\pi$
$19$	1826.16	1.16053	0.580263	+	0.814429i	$0.302950\pi$
$20$	446.082	0.249368
$21$	−1055.10	−0.522091
$22$	−26.8665	−0.0118346
$23$	254.207	0.100200	0.0501000	−	0.998744i	$-0.484046\pi$
$23$	254.207	0.100200	0.0501000	+	0.998744i	$0.484046\pi$
$24$	−287.828	−0.102001
$25$	−2927.58	−0.936826
$26$	236.673	0.0686620
$27$	−729.000	−0.192450
$28$	−3721.97	−0.897176
$29$	−6598.12	−1.45689	−0.728443	−	0.685107i	$-0.759755\pi$
$29$	−6598.12	−1.45689	−0.728443	+	0.685107i	$0.759755\pi$
$30$	−63.4393	−0.0128693
$31$	1104.44	0.206414	0.103207	−	0.994660i	$-0.467090\pi$
$31$	1104.44	0.206414	0.103207	+	0.994660i	$0.467090\pi$
$32$	−1525.01	−0.263268
$33$	−481.983	−0.0770455
$34$	−584.382	−0.0866961
$35$	−1647.20	−0.227288
$36$	−2571.61	−0.330712
$37$	−7748.51	−0.930494	−0.465247	−	0.885181i	$-0.654035\pi$
$37$	−7748.51	−0.930494	−0.465247	+	0.885181i	$0.654035\pi$
$38$	−916.136	−0.102920
$39$	4245.91	0.447002
$40$	−449.350	−0.0444053
$41$	−5824.87	−0.541161	−0.270581	−	0.962697i	$-0.587216\pi$
$41$	−5824.87	−0.541161	−0.270581	+	0.962697i	$0.587216\pi$
$42$	529.317	0.0463012
$43$	−6404.30	−0.528203	−0.264101	−	0.964495i	$-0.585075\pi$
$43$	−6404.30	−0.528203	−0.264101	+	0.964495i	$0.585075\pi$
$44$	−1700.24	−0.132397
$45$	−1138.10	−0.0837815
$46$	−127.529	−0.00888616
$47$	−2856.66	−0.188632	−0.0943158	−	0.995542i	$-0.530066\pi$
$47$	−2856.66	−0.188632	−0.0943158	+	0.995542i	$0.530066\pi$
$48$	−8999.12	−0.563764
$49$	−3063.28	−0.182262
$50$	1468.69	0.0830817
$51$	−10483.8	−0.564407
$52$	14977.8	0.768141
$53$	−16675.9	−0.815452	−0.407726	−	0.913104i	$-0.633678\pi$
$53$	−16675.9	−0.815452	−0.407726	+	0.913104i	$0.633678\pi$
$54$	365.720	0.0170673
$55$	−752.461	−0.0335411
$56$	3749.23	0.159761
$57$	−16435.4	−0.670030
$58$	3310.10	0.129203
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	−4014.74	−0.143972
$61$	37099.5	1.27657	0.638284	−	0.769801i	$-0.279645\pi$
$61$	37099.5	1.27657	0.638284	+	0.769801i	$0.279645\pi$
$62$	−554.070	−0.0183057
$63$	9495.92	0.301429
$64$	−31231.8	−0.953119
$65$	6628.61	0.194598
$66$	241.798	0.00683272
$67$	10974.2	0.298665	0.149332	−	0.988787i	$-0.452288\pi$
$67$	10974.2	0.298665	0.149332	+	0.988787i	$0.452288\pi$
$68$	−36982.5	−0.969894
$69$	−2287.86	−0.0578505
$70$	826.357	0.0201568
$71$	−15478.9	−0.364414	−0.182207	−	0.983260i	$-0.558324\pi$
$71$	−15478.9	−0.364414	−0.182207	+	0.983260i	$0.558324\pi$
$72$	2590.45	0.0588903
$73$	−42171.4	−0.926214	−0.463107	−	0.886302i	$-0.653265\pi$
$73$	−42171.4	−0.926214	−0.463107	+	0.886302i	$0.653265\pi$
$74$	3887.22	0.0825202
$75$	26348.2	0.540877
$76$	−57977.5	−1.15140
$77$	6278.29	0.120674
$78$	−2130.06	−0.0396420
$79$	−89645.3	−1.61607	−0.808034	−	0.589136i	$-0.799468\pi$
$79$	−89645.3	−1.61607	−0.808034	+	0.589136i	$0.799468\pi$
$80$	−14049.2	−0.245430
$81$	6561.00	0.111111
$82$	2922.18	0.0479924
$83$	58689.8	0.935120	0.467560	−	0.883961i	$-0.345133\pi$
$83$	58689.8	0.935120	0.467560	+	0.883961i	$0.345133\pi$
$84$	33497.7	0.517985
$85$	−16367.0	−0.245710
$86$	3212.87	0.0468433
$87$	59383.1	0.841133
$88$	1712.69	0.0235761
$89$	61752.2	0.826376	0.413188	−	0.910646i	$-0.364415\pi$
$89$	61752.2	0.826376	0.413188	+	0.910646i	$0.364415\pi$
$90$	570.953	0.00743010
$91$	−55307.0	−0.700127
$92$	−8070.64	−0.0994119
$93$	−9939.99	−0.119173
$94$	1433.11	0.0167286
$95$	−25658.6	−0.291692
$96$	13725.1	0.151998
$97$	−13874.8	−0.149726	−0.0748630	−	0.997194i	$-0.523852\pi$
$97$	−13874.8	−0.149726	−0.0748630	+	0.997194i	$0.523852\pi$
$98$	1536.77	0.0161638
$99$	4337.85	0.0444822
$100$	92945.8	0.929458
$101$	101934.	0.994293	0.497146	−	0.867667i	$-0.334381\pi$
$101$	101934.	0.994293	0.497146	+	0.867667i	$0.334381\pi$
$102$	5259.44	0.0500540
$103$	−176131.	−1.63585	−0.817925	−	0.575325i	$-0.804875\pi$
$103$	−176131.	−1.63585	−0.817925	+	0.575325i	$0.804875\pi$
$104$	−15087.5	−0.136784
$105$	14824.8	0.131225
$106$	8365.84	0.0723177
$107$	140675.	1.18783	0.593917	−	0.804526i	$-0.297581\pi$
$107$	140675.	1.18783	0.593917	+	0.804526i	$0.297581\pi$
$108$	23144.5	0.190936
$109$	−87074.8	−0.701982	−0.350991	−	0.936379i	$-0.614155\pi$
$109$	−87074.8	−0.701982	−0.350991	+	0.936379i	$0.614155\pi$
$110$	377.490	0.00297456
$111$	69736.6	0.537221
$112$	117222.	0.883008
$113$	−257288.	−1.89550	−0.947748	−	0.319019i	$-0.896647\pi$
$113$	−257288.	−1.89550	−0.947748	+	0.319019i	$0.896647\pi$
$114$	8245.23	0.0594211
$115$	−3571.75	−0.0251847
$116$	209479.	1.44543
$117$	−38213.2	−0.258077
$118$	1746.33	0.0115457
$119$	136561.	0.884016
$120$	4044.15	0.0256374
$121$	−158183.	−0.982192
$122$	−18611.9	−0.113211
$123$	52423.8	0.312439
$124$	−35064.2	−0.204791
$125$	85042.3	0.486810
$126$	−4763.85	−0.0267320
$127$	−60712.0	−0.334014	−0.167007	−	0.985956i	$-0.553410\pi$
$127$	−60712.0	−0.334014	−0.167007	+	0.985956i	$0.553410\pi$
$128$	64468.6	0.347795
$129$	57638.7	0.304958
$130$	−3325.40	−0.0172578
$131$	191296.	0.973928	0.486964	−	0.873422i	$-0.338104\pi$
$131$	191296.	0.973928	0.486964	+	0.873422i	$0.338104\pi$
$132$	15302.2	0.0764395
$133$	214087.	1.04945
$134$	−5505.44	−0.0264869
$135$	10242.9	0.0483713
$136$	37253.4	0.172710
$137$	262613.	1.19541	0.597703	−	0.801718i	$-0.296080\pi$
$137$	262613.	1.19541	0.597703	+	0.801718i	$0.296080\pi$
$138$	1147.76	0.00513043
$139$	−149545.	−0.656502	−0.328251	−	0.944590i	$-0.606459\pi$
$139$	−149545.	−0.656502	−0.328251	+	0.944590i	$0.606459\pi$
$140$	52295.8	0.225500
$141$	25710.0	0.108906
$142$	7765.38	0.0323178
$143$	−25264.9	−0.103318
$144$	80992.1	0.325489
$145$	92707.4	0.366180
$146$	21156.3	0.0821406
$147$	27569.6	0.105229
$148$	246002.	0.923176
$149$	−356966.	−1.31723	−0.658614	−	0.752481i	$-0.728857\pi$
$149$	−356966.	−1.31723	−0.658614	+	0.752481i	$0.728857\pi$
$150$	−13218.2	−0.0479672
$151$	−236793.	−0.845135	−0.422568	−	0.906331i	$-0.638871\pi$
$151$	−236793.	−0.845135	−0.422568	+	0.906331i	$0.638871\pi$
$152$	58402.2	0.205031
$153$	94354.1	0.325861
$154$	−3149.65	−0.0107019
$155$	−15518.1	−0.0518810
$156$	−134801.	−0.443486
$157$	13948.1	0.0451613	0.0225807	−	0.999745i	$-0.492812\pi$
$157$	13948.1	0.0451613	0.0225807	+	0.999745i	$0.492812\pi$
$158$	44972.7	0.143320
$159$	150083.	0.470802
$160$	21427.3	0.0661710
$161$	29801.6	0.0906097
$162$	−3291.48	−0.00985380
$163$	119894.	0.353450	0.176725	−	0.984260i	$-0.443450\pi$
$163$	119894.	0.353450	0.176725	+	0.984260i	$0.443450\pi$
$164$	184930.	0.536905
$165$	6772.15	0.0193650
$166$	−29443.1	−0.0829304
$167$	−6906.10	−0.0191620	−0.00958102	−	0.999954i	$-0.503050\pi$
$167$	−6906.10	−0.0191620	−0.00958102	+	0.999954i	$0.503050\pi$
$168$	−33743.1	−0.0922383
$169$	−148728.	−0.400568
$170$	8210.91	0.0217906
$171$	147919.	0.386842
$172$	203326.	0.524049
$173$	−394688.	−1.00263	−0.501313	−	0.865266i	$-0.667149\pi$
$173$	−394688.	−1.00263	−0.501313	+	0.865266i	$0.667149\pi$
$174$	−29790.9	−0.0745952
$175$	−343211.	−0.847161
$176$	53548.5	0.130306
$177$	31329.0	0.0751646
$178$	−30979.5	−0.0732865
$179$	728867.	1.70026	0.850130	−	0.526572i	$-0.176523\pi$
$179$	728867.	1.70026	0.850130	+	0.526572i	$0.176523\pi$
$180$	36132.7	0.0831225
$181$	−409033.	−0.928030	−0.464015	−	0.885827i	$-0.653592\pi$
$181$	−409033.	−0.928030	−0.464015	+	0.885827i	$0.653592\pi$
$182$	27746.1	0.0620902
$183$	−333896.	−0.737026
$184$	8129.75	0.0177024
$185$	108871.	0.233875
$186$	4986.63	0.0105688
$187$	62382.8	0.130455
$188$	90694.3	0.187148
$189$	−85463.3	−0.174030
$190$	12872.2	0.0258685
$191$	−549926.	−1.09074	−0.545369	−	0.838196i	$-0.683611\pi$
$191$	−549926.	−1.09074	−0.545369	+	0.838196i	$0.683611\pi$
$192$	281086.	0.550284
$193$	272527.	0.526644	0.263322	−	0.964708i	$-0.415182\pi$
$193$	272527.	0.526644	0.263322	+	0.964708i	$0.415182\pi$
$194$	6960.61	0.0132783
$195$	−59657.5	−0.112351
$196$	97254.1	0.180829
$197$	−196950.	−0.361569	−0.180784	−	0.983523i	$-0.557864\pi$
$197$	−196950.	−0.361569	−0.180784	+	0.983523i	$0.557864\pi$
$198$	−2176.18	−0.00394487
$199$	−573962.	−1.02743	−0.513713	−	0.857962i	$-0.671730\pi$
$199$	−573962.	−1.02743	−0.513713	+	0.857962i	$0.671730\pi$
$200$	−93626.6	−0.165510
$201$	−98767.4	−0.172434
$202$	−51137.4	−0.0881781
$203$	−773522.	−1.31744
$204$	332843.	0.559968
$205$	81842.8	0.136018
$206$	88360.4	0.145074
$207$	20590.8	0.0334000
$208$	−471722.	−0.756010
$209$	97797.6	0.154868
$210$	−7437.21	−0.0116376
$211$	−812952.	−1.25707	−0.628534	−	0.777782i	$-0.716345\pi$
$211$	−812952.	−1.25707	−0.628534	+	0.777782i	$0.716345\pi$
$212$	529431.	0.809039
$213$	139311.	0.210395
$214$	−70572.7	−0.105342
$215$	89984.2	0.132761
$216$	−23314.0	−0.0340003
$217$	129478.	0.186658
$218$	43683.1	0.0622548
$219$	379543.	0.534750
$220$	23889.4	0.0332773
$221$	−549546.	−0.756873
$222$	−34985.0	−0.0476430
$223$	−211386.	−0.284652	−0.142326	−	0.989820i	$-0.545458\pi$
$223$	−211386.	−0.284652	−0.142326	+	0.989820i	$0.545458\pi$
$224$	−178783.	−0.238070
$225$	−237134.	−0.312275
$226$	129074.	0.168101
$227$	−383490.	−0.493958	−0.246979	−	0.969021i	$-0.579438\pi$
$227$	−383490.	−0.493958	−0.246979	+	0.969021i	$0.579438\pi$
$228$	521798.	0.664760
$229$	−67560.6	−0.0851344	−0.0425672	−	0.999094i	$-0.513554\pi$
$229$	−67560.6	−0.0851344	−0.0425672	+	0.999094i	$0.513554\pi$
$230$	1791.86	0.00223349
$231$	−56504.6	−0.0696713
$232$	−211014.	−0.257389
$233$	592445.	0.714922	0.357461	−	0.933928i	$-0.383643\pi$
$233$	592445.	0.714922	0.357461	+	0.933928i	$0.383643\pi$
$234$	19170.6	0.0228873
$235$	40137.8	0.0474115
$236$	110516.	0.129165
$237$	806807.	0.933037
$238$	−68509.2	−0.0783983
$239$	45816.0	0.0518827	0.0259413	−	0.999663i	$-0.491742\pi$
$239$	45816.0	0.0518827	0.0259413	+	0.999663i	$0.491742\pi$
$240$	126443.	0.141699
$241$	−1.56926e6	−1.74041	−0.870204	−	0.492691i	$-0.836013\pi$
$241$	−1.56926e6	−1.74041	−0.870204	+	0.492691i	$0.836013\pi$
$242$	79356.3	0.0871049
$243$	−59049.0	−0.0641500
$244$	−1.17785e6	−1.26653
$245$	43040.9	0.0458106
$246$	−26299.7	−0.0277085
$247$	−861523.	−0.898514
$248$	35321.0	0.0364673
$249$	−528208.	−0.539892
$250$	−42663.5	−0.0431724
$251$	−36553.8	−0.0366225	−0.0183113	−	0.999832i	$-0.505829\pi$
$251$	−36553.8	−0.0366225	−0.0183113	+	0.999832i	$0.505829\pi$
$252$	−301480.	−0.299059
$253$	13613.7	0.0133714
$254$	30457.6	0.0296218
$255$	147303.	0.141861
$256$	967076.	0.922276
$257$	−821929.	−0.776250	−0.388125	−	0.921607i	$-0.626877\pi$
$257$	−821929.	−0.776250	−0.388125	+	0.921607i	$0.626877\pi$
$258$	−28915.8	−0.0270450
$259$	−908385.	−0.841435
$260$	−210447.	−0.193068
$261$	−534448.	−0.485628
$262$	−95968.0	−0.0863721
$263$	−242612.	−0.216283	−0.108141	−	0.994136i	$-0.534490\pi$
$263$	−242612.	−0.216283	−0.108141	+	0.994136i	$0.534490\pi$
$264$	−15414.2	−0.0136117
$265$	234306.	0.204959
$266$	−107402.	−0.0930697
$267$	−555770.	−0.477108
$268$	−348411.	−0.296316
$269$	−1.06646e6	−0.898596	−0.449298	−	0.893382i	$-0.648326\pi$
$269$	−1.06646e6	−0.898596	−0.449298	+	0.893382i	$0.648326\pi$
$270$	−5138.58	−0.00428977
$271$	202507.	0.167501	0.0837505	−	0.996487i	$-0.473310\pi$
$271$	202507.	0.167501	0.0837505	+	0.996487i	$0.473310\pi$
$272$	1.16475e6	0.954577
$273$	497763.	0.404219
$274$	−131746.	−0.106014
$275$	−156783.	−0.125016
$276$	72635.8	0.0573955
$277$	1.26102e6	0.987469	0.493735	−	0.869613i	$-0.335631\pi$
$277$	1.26102e6	0.987469	0.493735	+	0.869613i	$0.335631\pi$
$278$	75023.0	0.0582214
$279$	89459.9	0.0688047
$280$	−52678.9	−0.0401552
$281$	1.93346e6	1.46072	0.730362	−	0.683060i	$-0.239351\pi$
$281$	1.93346e6	1.46072	0.730362	+	0.683060i	$0.239351\pi$
$282$	−12898.0	−0.00965829
$283$	−502495.	−0.372963	−0.186482	−	0.982458i	$-0.559708\pi$
$283$	−502495.	−0.372963	−0.186482	+	0.982458i	$0.559708\pi$
$284$	491431.	0.361548
$285$	230927.	0.168408
$286$	12674.7	0.00916271
$287$	−682870.	−0.489366
$288$	−123526.	−0.0877561
$289$	−62946.4	−0.0443329
$290$	−46508.9	−0.0324744
$291$	124873.	0.0864443
$292$	1.33887e6	0.918929
$293$	−86625.1	−0.0589487	−0.0294744	−	0.999566i	$-0.509383\pi$
$293$	−86625.1	−0.0589487	−0.0294744	+	0.999566i	$0.509383\pi$
$294$	−13830.9	−0.00933217
$295$	48910.1	0.0327223
$296$	−247804.	−0.164391
$297$	−39040.6	−0.0256818
$298$	179080.	0.116817
$299$	−119927.	−0.0775778
$300$	−836512.	−0.536623
$301$	−750800.	−0.477648
$302$	118793.	0.0749502
$303$	−917403.	−0.574055
$304$	1.82598e6	1.13322
$305$	−521270.	−0.320858
$306$	−47335.0	−0.0288987
$307$	630671.	0.381907	0.190953	−	0.981599i	$-0.438842\pi$
$307$	630671.	0.381907	0.190953	+	0.981599i	$0.438842\pi$
$308$	−199325.	−0.119725
$309$	1.58518e6	0.944458
$310$	7785.01	0.00460103
$311$	−828845.	−0.485929	−0.242964	−	0.970035i	$-0.578120\pi$
$311$	−828845.	−0.485929	−0.242964	+	0.970035i	$0.578120\pi$
$312$	135788.	0.0789722
$313$	1.64437e6	0.948724	0.474362	−	0.880330i	$-0.342679\pi$
$313$	1.64437e6	0.948724	0.474362	+	0.880330i	$0.342679\pi$
$314$	−6997.40	−0.00400510
$315$	−133423.	−0.0757626
$316$	2.84609e6	1.60336
$317$	2.66630e6	1.49025	0.745127	−	0.666923i	$-0.232389\pi$
$317$	2.66630e6	1.49025	0.745127	+	0.666923i	$0.232389\pi$
$318$	−75292.6	−0.0417527
$319$	−353354.	−0.194416
$320$	438825.	0.239561
$321$	−1.26607e6	−0.685797
$322$	−14950.7	−0.00803565
$323$	2.12723e6	1.13451
$324$	−208301.	−0.110237
$325$	1.38114e6	0.725319
$326$	−60147.6	−0.0313454
$327$	783673.	0.405290
$328$	−186284.	−0.0956074
$329$	−334897.	−0.170577
$330$	−3397.41	−0.00171737
$331$	1.09024e6	0.546955	0.273477	−	0.961878i	$-0.411826\pi$
$331$	1.09024e6	0.546955	0.273477	+	0.961878i	$0.411826\pi$
$332$	−1.86330e6	−0.927765
$333$	−627629.	−0.310165
$334$	3464.61	0.00169937
$335$	−154193.	−0.0750677
$336$	−1.05500e6	−0.509805
$337$	−1.37111e6	−0.657654	−0.328827	−	0.944390i	$-0.606653\pi$
$337$	−1.37111e6	−0.657654	−0.328827	+	0.944390i	$0.606653\pi$
$338$	74613.0	0.0355241
$339$	2.31559e6	1.09437
$340$	519626.	0.243777
$341$	59147.0	0.0275453
$342$	−74207.0	−0.0343068
$343$	−2.32946e6	−1.06911
$344$	−204815.	−0.0933181
$345$	32145.8	0.0145404
$346$	198005.	0.0889170
$347$	−2.35316e6	−1.04913	−0.524564	−	0.851371i	$-0.675772\pi$
$347$	−2.35316e6	−1.04913	−0.524564	+	0.851371i	$0.675772\pi$
$348$	−1.88531e6	−0.834518
$349$	844331.	0.371064	0.185532	−	0.982638i	$-0.440599\pi$
$349$	844331.	0.371064	0.185532	+	0.982638i	$0.440599\pi$
$350$	172180.	0.0751298
$351$	343919.	0.149001
$352$	−81670.0	−0.0351323
$353$	1.07476e6	0.459066	0.229533	−	0.973301i	$-0.426280\pi$
$353$	1.07476e6	0.459066	0.229533	+	0.973301i	$0.426280\pi$
$354$	−15716.9	−0.00666591
$355$	217488.	0.0915935
$356$	−1.96053e6	−0.819877
$357$	−1.22905e6	−0.510387
$358$	−365653.	−0.150786
$359$	1.95175e6	0.799259	0.399629	−	0.916677i	$-0.369139\pi$
$359$	1.95175e6	0.799259	0.399629	+	0.916677i	$0.369139\pi$
$360$	−36397.3	−0.0148018
$361$	858761.	0.346820
$362$	205201.	0.0823016
$363$	1.42365e6	0.567069
$364$	1.75591e6	0.694621
$365$	592533.	0.232799
$366$	167507.	0.0653626
$367$	1.56632e6	0.607036	0.303518	−	0.952826i	$-0.401839\pi$
$367$	1.56632e6	0.607036	0.303518	+	0.952826i	$0.401839\pi$
$368$	254182.	0.0978420
$369$	−471814.	−0.180387
$370$	−54617.7	−0.0207410
$371$	−1.95497e6	−0.737404
$372$	315578.	0.118236
$373$	2.85853e6	1.06382	0.531912	−	0.846799i	$-0.321474\pi$
$373$	2.85853e6	1.06382	0.531912	+	0.846799i	$0.321474\pi$
$374$	−31295.8	−0.0115693
$375$	−765381.	−0.281060
$376$	−91358.5	−0.0333257
$377$	3.11278e6	1.12796
$378$	42874.7	0.0154337
$379$	1.66138e6	0.594116	0.297058	−	0.954859i	$-0.403995\pi$
$379$	1.66138e6	0.594116	0.297058	+	0.954859i	$0.403995\pi$
$380$	814618.	0.289398
$381$	546408.	0.192843
$382$	275883.	0.0967313
$383$	−4.91425e6	−1.71183	−0.855914	−	0.517118i	$-0.827005\pi$
$383$	−4.91425e6	−1.71183	−0.855914	+	0.517118i	$0.827005\pi$
$384$	−580217.	−0.200799
$385$	−88213.7	−0.0303308
$386$	−136720.	−0.0467050
$387$	−518749.	−0.176068
$388$	440501.	0.148548
$389$	4.04295e6	1.35464	0.677320	−	0.735688i	$-0.263141\pi$
$389$	4.04295e6	1.35464	0.677320	+	0.735688i	$0.263141\pi$
$390$	29928.6	0.00996380
$391$	296117.	0.0979538
$392$	−97966.4	−0.0322005
$393$	−1.72166e6	−0.562298
$394$	98804.7	0.0320654
$395$	1.25957e6	0.406190
$396$	−137719.	−0.0441324
$397$	2.31593e6	0.737477	0.368738	−	0.929533i	$-0.379790\pi$
$397$	2.31593e6	0.737477	0.368738	+	0.929533i	$0.379790\pi$
$398$	287942.	0.0911164
$399$	−1.92679e6	−0.605900
$400$	−2.92730e6	−0.914780
$401$	−3.24006e6	−1.00622	−0.503110	−	0.864223i	$-0.667811\pi$
$401$	−3.24006e6	−1.00622	−0.503110	+	0.864223i	$0.667811\pi$
$402$	49549.0	0.0152922
$403$	−521041.	−0.159812
$404$	−3.23622e6	−0.986473
$405$	−92185.9	−0.0279272
$406$	388055.	0.116837
$407$	−414961.	−0.124171
$408$	−335280.	−0.0997144
$409$	2.30082e6	0.680101	0.340051	−	0.940407i	$-0.389556\pi$
$409$	2.30082e6	0.680101	0.340051	+	0.940407i	$0.389556\pi$
$410$	−41058.4	−0.0120626
$411$	−2.36352e6	−0.690168
$412$	5.59187e6	1.62298
$413$	−408090.	−0.117728
$414$	−10329.8	−0.00296205
$415$	−824626.	−0.235037
$416$	719452.	0.203830
$417$	1.34591e6	0.379032
$418$	−49062.5	−0.0137344
$419$	4.71896e6	1.31314	0.656570	−	0.754265i	$-0.272007\pi$
$419$	4.71896e6	1.31314	0.656570	+	0.754265i	$0.272007\pi$
$420$	−470663.	−0.130193
$421$	1.59180e6	0.437708	0.218854	−	0.975758i	$-0.429768\pi$
$421$	1.59180e6	0.437708	0.218854	+	0.975758i	$0.429768\pi$
$422$	407837.	0.111482
$423$	−231390.	−0.0628772
$424$	−533308.	−0.144067
$425$	−3.41024e6	−0.915824
$426$	−69888.4	−0.0186587
$427$	4.34931e6	1.15438
$428$	−4.46618e6	−1.17849
$429$	227384.	0.0596509
$430$	−45142.7	−0.0117738
$431$	−3.84179e6	−0.996186	−0.498093	−	0.867124i	$-0.665966\pi$
$431$	−3.84179e6	−0.996186	−0.498093	+	0.867124i	$0.665966\pi$
$432$	−728929.	−0.187921
$433$	−97620.0	−0.0250218	−0.0125109	−	0.999922i	$-0.503982\pi$
$433$	−97620.0	−0.0250218	−0.0125109	+	0.999922i	$0.503982\pi$
$434$	−64955.6	−0.0165536
$435$	−834367.	−0.211414
$436$	2.76448e6	0.696461
$437$	464222.	0.116285
$438$	−190407.	−0.0474239
$439$	4.43043e6	1.09720	0.548599	−	0.836086i	$-0.315161\pi$
$439$	4.43043e6	1.09720	0.548599	+	0.836086i	$0.315161\pi$
$440$	−24064.3	−0.00592573
$441$	−248126.	−0.0607541
$442$	275693.	0.0671227
$443$	−6.14299e6	−1.48720	−0.743602	−	0.668623i	$-0.766884\pi$
$443$	−6.14299e6	−1.48720	−0.743602	+	0.668623i	$0.766884\pi$
$444$	−2.21402e6	−0.532996
$445$	−867655.	−0.207705
$446$	106047.	0.0252441
$447$	3.21269e6	0.760502
$448$	−3.66142e6	−0.861895
$449$	5.39476e6	1.26286	0.631431	−	0.775432i	$-0.282468\pi$
$449$	5.39476e6	1.26286	0.631431	+	0.775432i	$0.282468\pi$
$450$	118964.	0.0276939
$451$	−311943.	−0.0722161
$452$	8.16845e6	1.88059
$453$	2.13114e6	0.487939
$454$	192387.	0.0438063
$455$	777096.	0.175973
$456$	−525619.	−0.118375
$457$	−1.53312e6	−0.343388	−0.171694	−	0.985150i	$-0.554924\pi$
$457$	−1.53312e6	−0.343388	−0.171694	+	0.985150i	$0.554924\pi$
$458$	33893.4	0.00755008
$459$	−849187.	−0.188136
$460$	113397.	0.0249866
$461$	2.69249e6	0.590067	0.295033	−	0.955487i	$-0.404669\pi$
$461$	2.69249e6	0.590067	0.295033	+	0.955487i	$0.404669\pi$
$462$	28346.9	0.00617875
$463$	−2.40113e6	−0.520550	−0.260275	−	0.965535i	$-0.583813\pi$
$463$	−2.40113e6	−0.520550	−0.260275	+	0.965535i	$0.583813\pi$
$464$	−6.59748e6	−1.42260
$465$	139663.	0.0299535
$466$	−297214.	−0.0634023
$467$	−7.70828e6	−1.63556	−0.817778	−	0.575534i	$-0.804794\pi$
$467$	−7.70828e6	−1.63556	−0.817778	+	0.575534i	$0.804794\pi$
$468$	1.21320e6	0.256047
$469$	1.28654e6	0.270079
$470$	−20136.1	−0.00420465
$471$	−125533.	−0.0260739
$472$	−111325.	−0.0230006
$473$	−342974.	−0.0704869
$474$	−404754.	−0.0827457
$475$	−5.34623e6	−1.08721
$476$	−4.33559e6	−0.877064
$477$	−1.35074e6	−0.271817
$478$	−22984.7	−0.00460118
$479$	4.29567e6	0.855445	0.427723	−	0.903910i	$-0.359316\pi$
$479$	4.29567e6	0.855445	0.427723	+	0.903910i	$0.359316\pi$
$480$	−192846.	−0.0382038
$481$	3.65550e6	0.720416
$482$	787254.	0.154347
$483$	−268214.	−0.0523135
$484$	5.02205e6	0.974467
$485$	194949.	0.0376328
$486$	29623.3	0.00568910
$487$	−9.17052e6	−1.75215	−0.876076	−	0.482173i	$-0.839848\pi$
$487$	−9.17052e6	−1.75215	−0.876076	+	0.482173i	$0.839848\pi$
$488$	1.18647e6	0.225532
$489$	−1.07904e6	−0.204064
$490$	−21592.5	−0.00406268
$491$	−1.90208e6	−0.356062	−0.178031	−	0.984025i	$-0.556973\pi$
$491$	−1.90208e6	−0.356062	−0.178031	+	0.984025i	$0.556973\pi$
$492$	−1.66437e6	−0.309982
$493$	−7.68592e6	−1.42423
$494$	432204.	0.0796840
$495$	−60949.3	−0.0111804
$496$	1.10434e6	0.201556
$497$	−1.81465e6	−0.329536
$498$	264988.	0.0478799
$499$	−5.54825e6	−0.997482	−0.498741	−	0.866751i	$-0.666204\pi$
$499$	−5.54825e6	−0.997482	−0.498741	+	0.866751i	$0.666204\pi$
$500$	−2.69995e6	−0.482982
$501$	62154.9	0.0110632
$502$	18338.1	0.00324784
$503$	5.18973e6	0.914587	0.457294	−	0.889316i	$-0.348819\pi$
$503$	5.18973e6	0.914587	0.457294	+	0.889316i	$0.348819\pi$
$504$	303688.	0.0532538
$505$	−1.43223e6	−0.249910
$506$	−6829.65	−0.00118583
$507$	1.33855e6	0.231268
$508$	1.92750e6	0.331387
$509$	2.94232e6	0.503379	0.251689	−	0.967808i	$-0.419014\pi$
$509$	2.94232e6	0.503379	0.251689	+	0.967808i	$0.419014\pi$
$510$	−73898.2	−0.0125808
$511$	−4.94391e6	−0.837565
$512$	−2.54815e6	−0.429586
$513$	−1.33127e6	−0.223343
$514$	412340.	0.0688411
$515$	2.47475e6	0.411162
$516$	−1.82993e6	−0.302560
$517$	−152985.	−0.0251723
$518$	455713.	0.0746220
$519$	3.55219e6	0.578866
$520$	211989.	0.0343799
$521$	−3.27821e6	−0.529106	−0.264553	−	0.964371i	$-0.585224\pi$
$521$	−3.27821e6	−0.529106	−0.264553	+	0.964371i	$0.585224\pi$
$522$	268118.	0.0430676
$523$	−890700.	−0.142389	−0.0711946	−	0.997462i	$-0.522681\pi$
$523$	−890700.	−0.142389	−0.0711946	+	0.997462i	$0.522681\pi$
$524$	−6.07332e6	−0.966268
$525$	3.08890e6	0.489109
$526$	121712.	0.0191809
$527$	1.28653e6	0.201787
$528$	−481936.	−0.0752324
$529$	−6.37172e6	−0.989960
$530$	−117545.	−0.0181767
$531$	−281961.	−0.0433963
$532$	−6.79691e6	−1.04120
$533$	2.74799e6	0.418983
$534$	278815.	0.0423120
$535$	−1.97656e6	−0.298556
$536$	350963.	0.0527654
$537$	−6.55980e6	−0.981646
$538$	535016.	0.0796913
$539$	−164050.	−0.0243223
$540$	−325194.	−0.0479908
$541$	5.79897e6	0.851839	0.425920	−	0.904761i	$-0.359951\pi$
$541$	5.79897e6	0.851839	0.425920	+	0.904761i	$0.359951\pi$
$542$	−101593.	−0.0148547
$543$	3.68130e6	0.535799
$544$	−1.77643e6	−0.257366
$545$	1.22345e6	0.176439
$546$	−249715.	−0.0358478
$547$	2.82959e6	0.404348	0.202174	−	0.979350i	$-0.435199\pi$
$547$	2.82959e6	0.404348	0.202174	+	0.979350i	$0.435199\pi$
$548$	−8.33753e6	−1.18600
$549$	3.00506e6	0.425522
$550$	78653.8	0.0110870
$551$	−1.20492e7	−1.69075
$552$	−73167.8	−0.0102205
$553$	−1.05094e7	−1.46139
$554$	−632622.	−0.0875729
$555$	−979839.	−0.135028
$556$	4.74782e6	0.651339
$557$	−9.20725e6	−1.25745	−0.628726	−	0.777627i	$-0.716423\pi$
$557$	−9.20725e6	−1.25745	−0.628726	+	0.777627i	$0.716423\pi$
$558$	−44879.7	−0.00610189
$559$	3.02134e6	0.408950
$560$	−1.64704e6	−0.221939
$561$	−561445.	−0.0753183
$562$	−969964.	−0.129543
$563$	4.99478e6	0.664118	0.332059	−	0.943259i	$-0.392257\pi$
$563$	4.99478e6	0.664118	0.332059	+	0.943259i	$0.392257\pi$
$564$	−816248.	−0.108050
$565$	3.61504e6	0.476423
$566$	252089.	0.0330759
$567$	769170.	0.100476
$568$	−495030.	−0.0643814
$569$	1.02729e6	0.133018	0.0665092	−	0.997786i	$-0.478814\pi$
$569$	1.02729e6	0.133018	0.0665092	+	0.997786i	$0.478814\pi$
$570$	−115850.	−0.0149352
$571$	7.08898e6	0.909900	0.454950	−	0.890517i	$-0.349657\pi$
$571$	7.08898e6	0.909900	0.454950	+	0.890517i	$0.349657\pi$
$572$	802118.	0.102506
$573$	4.94933e6	0.629738
$574$	342578.	0.0433990
$575$	−744211.	−0.0938700
$576$	−2.52978e6	−0.317706
$577$	−4.15153e6	−0.519121	−0.259561	−	0.965727i	$-0.583578\pi$
$577$	−4.15153e6	−0.519121	−0.259561	+	0.965727i	$0.583578\pi$
$578$	31578.6	0.00393163
$579$	−2.45275e6	−0.304058
$580$	−2.94331e6	−0.363300
$581$	6.88042e6	0.845618
$582$	−62645.5	−0.00766624
$583$	−893054.	−0.108819
$584$	−1.34868e6	−0.163635
$585$	536918.	0.0648661
$586$	43457.5	0.00522782
$587$	1.65158e7	1.97835	0.989176	−	0.146737i	$-0.0468771\pi$
$587$	1.65158e7	1.97835	0.989176	+	0.146737i	$0.0468771\pi$
$588$	−875287.	−0.104402
$589$	2.01689e6	0.239549
$590$	−24536.9	−0.00290195
$591$	1.77255e6	0.208752
$592$	−7.74775e6	−0.908597
$593$	7.04831e6	0.823092	0.411546	−	0.911389i	$-0.364989\pi$
$593$	7.04831e6	0.823092	0.411546	+	0.911389i	$0.364989\pi$
$594$	19585.7	0.00227757
$595$	−1.91877e6	−0.222193
$596$	1.13331e7	1.30687
$597$	5.16566e6	0.593184
$598$	60164.0	0.00687993
$599$	1.26382e7	1.43919	0.719594	−	0.694395i	$-0.244328\pi$
$599$	1.26382e7	1.43919	0.719594	+	0.694395i	$0.244328\pi$
$600$	842639.	0.0955572
$601$	6.61706e6	0.747272	0.373636	−	0.927575i	$-0.378111\pi$
$601$	6.61706e6	0.747272	0.373636	+	0.927575i	$0.378111\pi$
$602$	376656.	0.0423598
$603$	888906.	0.0995549
$604$	7.51778e6	0.838489
$605$	2.22256e6	0.246868
$606$	460237.	0.0509096
$607$	−2.10068e6	−0.231413	−0.115707	−	0.993283i	$-0.536913\pi$
$607$	−2.10068e6	−0.231413	−0.115707	+	0.993283i	$0.536913\pi$
$608$	−2.78492e6	−0.305529
$609$	6.96169e6	0.760627
$610$	261507.	0.0284550
$611$	1.34768e6	0.146044
$612$	−2.99558e6	−0.323298
$613$	1.51680e7	1.63034	0.815168	−	0.579225i	$-0.196645\pi$
$613$	1.51680e7	1.63034	0.815168	+	0.579225i	$0.196645\pi$
$614$	−316391.	−0.0338691
$615$	−736585.	−0.0785299
$616$	200785.	0.0213196
$617$	−1.74862e6	−0.184920	−0.0924600	−	0.995716i	$-0.529473\pi$
$617$	−1.74862e6	−0.184920	−0.0924600	+	0.995716i	$0.529473\pi$
$618$	−795244.	−0.0837585
$619$	−1.06999e7	−1.12241	−0.561206	−	0.827676i	$-0.689662\pi$
$619$	−1.06999e7	−1.12241	−0.561206	+	0.827676i	$0.689662\pi$
$620$	492673.	0.0514730
$621$	−185317.	−0.0192835
$622$	415810.	0.0430942
$623$	7.23944e6	0.747282
$624$	4.24550e6	0.436483
$625$	7.95380e6	0.814469
$626$	−824939.	−0.0841368
$627$	−880179.	−0.0894133
$628$	−442829.	−0.0448061
$629$	−9.02597e6	−0.909635
$630$	66934.9	0.00671895
$631$	1.06482e7	1.06464	0.532322	−	0.846542i	$-0.321319\pi$
$631$	1.06482e7	1.06464	0.532322	+	0.846542i	$0.321319\pi$
$632$	−2.86693e6	−0.285512
$633$	7.31657e6	0.725769
$634$	−1.33761e6	−0.132162
$635$	853038.	0.0839526
$636$	−4.76488e6	−0.467099
$637$	1.44516e6	0.141113
$638$	177268.	0.0172417
$639$	−1.25379e6	−0.121471
$640$	−905821.	−0.0874163
$641$	1.71884e7	1.65231	0.826155	−	0.563443i	$-0.190523\pi$
$641$	1.71884e7	1.65231	0.826155	+	0.563443i	$0.190523\pi$
$642$	635155.	0.0608194
$643$	9.90174e6	0.944461	0.472230	−	0.881475i	$-0.343449\pi$
$643$	9.90174e6	0.944461	0.472230	+	0.881475i	$0.343449\pi$
$644$	−946151.	−0.0898971
$645$	−809858.	−0.0766495
$646$	−1.06718e6	−0.100613
$647$	4.53741e6	0.426136	0.213068	−	0.977037i	$-0.431654\pi$
$647$	4.53741e6	0.426136	0.213068	+	0.977037i	$0.431654\pi$
$648$	209826.	0.0196301
$649$	−186420.	−0.0173733
$650$	−692881.	−0.0643243
$651$	−1.16530e6	−0.107767
$652$	−3.80643e6	−0.350670
$653$	−5.46204e6	−0.501270	−0.250635	−	0.968082i	$-0.580639\pi$
$653$	−5.46204e6	−0.501270	−0.250635	+	0.968082i	$0.580639\pi$
$654$	−393148.	−0.0359428
$655$	−2.68782e6	−0.244791
$656$	−5.82430e6	−0.528426
$657$	−3.41589e6	−0.308738
$658$	168009.	0.0151275
$659$	1.36246e6	0.122211	0.0611056	−	0.998131i	$-0.480537\pi$
$659$	1.36246e6	0.122211	0.0611056	+	0.998131i	$0.480537\pi$
$660$	−215004.	−0.0192126
$661$	1.11826e7	0.995497	0.497748	−	0.867321i	$-0.334160\pi$
$661$	1.11826e7	0.995497	0.497748	+	0.867321i	$0.334160\pi$
$662$	−546944.	−0.0485062
$663$	4.94591e6	0.436981
$664$	1.87695e6	0.165209
$665$	−3.00805e6	−0.263773
$666$	314865.	0.0275067
$667$	−1.67729e6	−0.145980
$668$	219257.	0.0190113
$669$	1.90247e6	0.164344
$670$	77354.7	0.00665732
$671$	1.98682e6	0.170354
$672$	1.60904e6	0.137450
$673$	−2.22259e7	−1.89157	−0.945785	−	0.324794i	$-0.894705\pi$
$673$	−2.22259e7	−1.89157	−0.945785	+	0.324794i	$0.894705\pi$
$674$	687850.	0.0583235
$675$	2.13421e6	0.180292
$676$	4.72187e6	0.397418
$677$	−7.09861e6	−0.595253	−0.297627	−	0.954682i	$-0.596195\pi$
$677$	−7.09861e6	−0.595253	−0.297627	+	0.954682i	$0.596195\pi$
$678$	−1.16167e6	−0.0970529
$679$	−1.62659e6	−0.135395
$680$	−523432.	−0.0434098
$681$	3.45141e6	0.285187
$682$	−29672.5	−0.00244283
$683$	−2.04470e7	−1.67717	−0.838585	−	0.544771i	$-0.816616\pi$
$683$	−2.04470e7	−1.67717	−0.838585	+	0.544771i	$0.816616\pi$
$684$	−4.69618e6	−0.383799
$685$	−3.68987e6	−0.300458
$686$	1.16863e6	0.0948128
$687$	608046.	0.0491524
$688$	−6.40368e6	−0.515773
$689$	7.86713e6	0.631347
$690$	−16126.7	−0.00128950
$691$	7.78175e6	0.619987	0.309993	−	0.950739i	$-0.399673\pi$
$691$	7.78175e6	0.619987	0.309993	+	0.950739i	$0.399673\pi$
$692$	1.25307e7	0.994740
$693$	508542.	0.0402248
$694$	1.18052e6	0.0930411
$695$	2.10120e6	0.165008
$696$	1.89912e6	0.148604
$697$	−6.78519e6	−0.529029
$698$	−423579.	−0.0329075
$699$	−5.33201e6	−0.412760
$700$	1.08964e7	0.840498
$701$	−1.01109e7	−0.777136	−0.388568	−	0.921420i	$-0.627030\pi$
$701$	−1.01109e7	−0.777136	−0.388568	+	0.921420i	$0.627030\pi$
$702$	−172535.	−0.0132140
$703$	−1.41500e7	−1.07986
$704$	−1.67258e6	−0.127191
$705$	−361240.	−0.0273730
$706$	−539179.	−0.0407119
$707$	1.19500e7	0.899127
$708$	−994643.	−0.0745734
$709$	5.55179e6	0.414780	0.207390	−	0.978258i	$-0.433503\pi$
$709$	5.55179e6	0.414780	0.207390	+	0.978258i	$0.433503\pi$
$710$	−109108.	−0.00812290
$711$	−7.26127e6	−0.538689
$712$	1.97489e6	0.145997
$713$	280757.	0.0206827
$714$	616583.	0.0452633
$715$	354987.	0.0259685
$716$	−2.31403e7	−1.68689
$717$	−412344.	−0.0299545
$718$	−979140.	−0.0708816
$719$	1.36153e7	0.982215	0.491107	−	0.871099i	$-0.336592\pi$
$719$	1.36153e7	0.982215	0.491107	+	0.871099i	$0.336592\pi$
$720$	−1.13799e6	−0.0818099
$721$	−2.06485e7	−1.47928
$722$	−430818.	−0.0307575
$723$	1.41233e7	1.00483
$724$	1.29861e7	0.920731
$725$	1.93165e7	1.36485
$726$	−714206.	−0.0502901
$727$	7.71813e6	0.541597	0.270798	−	0.962636i	$-0.412712\pi$
$727$	7.71813e6	0.541597	0.270798	+	0.962636i	$0.412712\pi$
$728$	−1.76877e6	−0.123692
$729$	531441.	0.0370370
$730$	−297258.	−0.0206456
$731$	−7.46015e6	−0.516362
$732$	1.06006e7	0.731230
$733$	−2.00055e7	−1.37527	−0.687636	−	0.726056i	$-0.741351\pi$
$733$	−2.00055e7	−1.37527	−0.687636	+	0.726056i	$0.741351\pi$
$734$	−785779.	−0.0538345
$735$	−387368.	−0.0264488
$736$	−387669.	−0.0263795
$737$	587706.	0.0398558
$738$	236697.	0.0159975
$739$	−1.40919e7	−0.949204	−0.474602	−	0.880201i	$-0.657408\pi$
$739$	−1.40919e7	−0.949204	−0.474602	+	0.880201i	$0.657408\pi$
$740$	−3.45647e6	−0.232035
$741$	7.75371e6	0.518757
$742$	980758.	0.0653961
$743$	1.01829e7	0.676706	0.338353	−	0.941019i	$-0.390130\pi$
$743$	1.01829e7	0.676706	0.338353	+	0.941019i	$0.390130\pi$
$744$	−317889.	−0.0210544
$745$	5.01558e6	0.331078
$746$	−1.43405e6	−0.0943444
$747$	4.75387e6	0.311707
$748$	−1.98055e6	−0.129429
$749$	1.64918e7	1.07415
$750$	383971.	0.0249256
$751$	−2.24603e7	−1.45317	−0.726583	−	0.687079i	$-0.758893\pi$
$751$	−2.24603e7	−1.45317	−0.726583	+	0.687079i	$0.758893\pi$
$752$	−2.85638e6	−0.184193
$753$	328984.	0.0211440
$754$	−1.56160e6	−0.100033
$755$	3.32708e6	0.212420
$756$	2.71332e6	0.172662
$757$	−2.42736e7	−1.53955	−0.769777	−	0.638313i	$-0.779633\pi$
$757$	−2.42736e7	−1.53955	−0.769777	+	0.638313i	$0.779633\pi$
$758$	−833471.	−0.0526887
$759$	−122523.	−0.00771996
$760$	−820584.	−0.0515334
$761$	2.19171e7	1.37190	0.685948	−	0.727651i	$-0.259388\pi$
$761$	2.19171e7	1.37190	0.685948	+	0.727651i	$0.259388\pi$
$762$	−274118.	−0.0171021
$763$	−1.02081e7	−0.634795
$764$	1.74592e7	1.08216
$765$	−1.32573e6	−0.0819033
$766$	2.46535e6	0.151812
$767$	1.64222e6	0.100796
$768$	−8.70368e6	−0.532476
$769$	1.95692e7	1.19332	0.596660	−	0.802494i	$-0.296494\pi$
$769$	1.95692e7	1.19332	0.596660	+	0.802494i	$0.296494\pi$
$770$	44254.5	0.00268986
$771$	7.39736e6	0.448168
$772$	−8.65229e6	−0.522502
$773$	2.41099e7	1.45127	0.725634	−	0.688081i	$-0.241547\pi$
$773$	2.41099e7	1.45127	0.725634	+	0.688081i	$0.241547\pi$
$774$	260243.	0.0156144
$775$	−3.23335e6	−0.193374
$776$	−443728.	−0.0264522
$777$	8.17547e6	0.485803
$778$	−2.02824e6	−0.120135
$779$	−1.06371e7	−0.628031
$780$	1.89403e6	0.111468
$781$	−828955.	−0.0486299
$782$	−148554.	−0.00868695
$783$	4.81003e6	0.280378
$784$	−3.06298e6	−0.177973
$785$	−195979.	−0.0113510
$786$	863712.	0.0498669
$787$	−3.33270e7	−1.91805	−0.959025	−	0.283321i	$-0.908564\pi$
$787$	−3.33270e7	−1.91805	−0.959025	+	0.283321i	$0.908564\pi$
$788$	6.25284e6	0.358725
$789$	2.18351e6	0.124871
$790$	−631892.	−0.0360226
$791$	−3.01628e7	−1.71408
$792$	138728.	0.00785872
$793$	−1.75024e7	−0.988356
$794$	−1.16184e6	−0.0654026
$795$	−2.10875e6	−0.118333
$796$	1.82223e7	1.01935
$797$	−864232.	−0.0481930	−0.0240965	−	0.999710i	$-0.507671\pi$
$797$	−864232.	−0.0481930	−0.0240965	+	0.999710i	$0.507671\pi$
$798$	966618.	0.0537338
$799$	−3.32763e6	−0.184403
$800$	4.46460e6	0.246636
$801$	5.00193e6	0.275459
$802$	1.62545e6	0.0892358
$803$	−2.25844e6	−0.123600
$804$	3.13570e6	0.171078
$805$	−418730.	−0.0227742
$806$	261392.	0.0141728
$807$	9.59815e6	0.518805
$808$	3.25993e6	0.175663
$809$	1.13424e7	0.609303	0.304651	−	0.952464i	$-0.401460\pi$
$809$	1.13424e7	0.609303	0.304651	+	0.952464i	$0.401460\pi$
$810$	46247.2	0.00247670
$811$	3.43446e6	0.183361	0.0916805	−	0.995788i	$-0.470776\pi$
$811$	3.43446e6	0.183361	0.0916805	+	0.995788i	$0.470776\pi$
$812$	2.45580e7	1.30708
$813$	−1.82256e6	−0.0967067
$814$	208175.	0.0110120
$815$	−1.68458e6	−0.0888376
$816$	−1.04828e7	−0.551125
$817$	−1.16953e7	−0.612993
$818$	−1.15426e6	−0.0603142
$819$	−4.47987e6	−0.233376
$820$	−2.59837e6	−0.134948
$821$	1.81504e7	0.939782	0.469891	−	0.882724i	$-0.344293\pi$
$821$	1.81504e7	0.939782	0.469891	+	0.882724i	$0.344293\pi$
$822$	1.18572e6	0.0612070
$823$	−1.63665e6	−0.0842281	−0.0421141	−	0.999113i	$-0.513409\pi$
$823$	−1.63665e6	−0.0842281	−0.0421141	+	0.999113i	$0.513409\pi$
$824$	−5.63283e6	−0.289007
$825$	1.41105e6	0.0721782
$826$	204728.	0.0104406
$827$	−1.28654e7	−0.654125	−0.327063	−	0.945003i	$-0.606059\pi$
$827$	−1.28654e7	−0.654125	−0.327063	+	0.945003i	$0.606059\pi$
$828$	−653722.	−0.0331373
$829$	−8.03655e6	−0.406147	−0.203073	−	0.979164i	$-0.565093\pi$
$829$	−8.03655e6	−0.406147	−0.203073	+	0.979164i	$0.565093\pi$
$830$	413693.	0.0208441
$831$	−1.13492e7	−0.570116
$832$	1.47342e7	0.737933
$833$	−3.56831e6	−0.178176
$834$	−675207.	−0.0336141
$835$	97034.7	0.00481627
$836$	−3.10491e6	−0.153650
$837$	−805139.	−0.0397244
$838$	−2.36738e6	−0.116455
$839$	−3.59741e7	−1.76435	−0.882176	−	0.470920i	$-0.843922\pi$
$839$	−3.59741e7	−1.76435	−0.882176	+	0.470920i	$0.843922\pi$
$840$	474110.	0.0231836
$841$	2.30241e7	1.12251
$842$	−798566.	−0.0388178
$843$	−1.74011e7	−0.843350
$844$	2.58099e7	1.24718
$845$	2.08972e6	0.100681
$846$	116082.	0.00557621
$847$	−1.85444e7	−0.888185
$848$	−1.66742e7	−0.796262
$849$	4.52246e6	0.215330
$850$	1.71083e6	0.0812192
$851$	−1.96972e6	−0.0932355
$852$	−4.42287e6	−0.208740
$853$	−2.61300e7	−1.22961	−0.614803	−	0.788680i	$-0.710765\pi$
$853$	−2.61300e7	−1.22961	−0.614803	+	0.788680i	$0.710765\pi$
$854$	−2.18193e6	−0.102376
$855$	−2.07835e6	−0.0972306
$856$	4.49889e6	0.209856
$857$	−2.58354e7	−1.20161	−0.600804	−	0.799396i	$-0.705153\pi$
$857$	−2.58354e7	−1.20161	−0.600804	+	0.799396i	$0.705153\pi$
$858$	−114073.	−0.00529009
$859$	−2.85214e7	−1.31883	−0.659415	−	0.751779i	$-0.729196\pi$
$859$	−2.85214e7	−1.31883	−0.659415	+	0.751779i	$0.729196\pi$
$860$	−2.85685e6	−0.131717
$861$	6.14583e6	0.282535
$862$	1.92732e6	0.0883460
$863$	−2.80905e7	−1.28390	−0.641952	−	0.766745i	$-0.721875\pi$
$863$	−2.80905e7	−1.28390	−0.641952	+	0.766745i	$0.721875\pi$
$864$	1.11173e6	0.0506660
$865$	5.54560e6	0.252004
$866$	48973.4	0.00221904
$867$	566518.	0.0255956
$868$	−4.11070e6	−0.185190
$869$	−4.80083e6	−0.215659
$870$	418580.	0.0187491
$871$	−5.17725e6	−0.231235
$872$	−2.78473e6	−0.124020
$873$	−1.12386e6	−0.0499086
$874$	−232888.	−0.0103126
$875$	9.96981e6	0.440217
$876$	−1.20499e7	−0.530544
$877$	1.23614e7	0.542712	0.271356	−	0.962479i	$-0.412528\pi$
$877$	1.23614e7	0.542712	0.271356	+	0.962479i	$0.412528\pi$
$878$	−2.22263e6	−0.0973041
$879$	779626.	0.0340341
$880$	−752387.	−0.0327518
$881$	−1.44013e7	−0.625119	−0.312560	−	0.949898i	$-0.601186\pi$
$881$	−1.44013e7	−0.625119	−0.312560	+	0.949898i	$0.601186\pi$
$882$	124478.	0.00538793
$883$	76484.3	0.00330119	0.00165059	−	0.999999i	$-0.499475\pi$
$883$	76484.3	0.00330119	0.00165059	+	0.999999i	$0.499475\pi$
$884$	1.74472e7	0.750921
$885$	−440191.	−0.0188922
$886$	3.08178e6	0.131891
$887$	−4.12317e7	−1.75963	−0.879817	−	0.475312i	$-0.842335\pi$
$887$	−4.12317e7	−1.75963	−0.879817	+	0.475312i	$0.842335\pi$
$888$	2.23024e6	0.0949114
$889$	−7.11748e6	−0.302045
$890$	435280.	0.0184202
$891$	351366.	0.0148274
$892$	6.71115e6	0.282413
$893$	−5.21672e6	−0.218912
$894$	−1.61172e6	−0.0674445
$895$	−1.02410e7	−0.427351
$896$	7.55788e6	0.314507
$897$	1.07934e6	0.0447896
$898$	−2.70641e6	−0.111996
$899$	−7.28725e6	−0.300721
$900$	7.52861e6	0.309819
$901$	−1.94251e7	−0.797172
$902$	156494.	0.00640443
$903$	6.75720e6	0.275770
$904$	−8.22828e6	−0.334879
$905$	5.74715e6	0.233255
$906$	−1.06913e6	−0.0432725
$907$	3.00251e7	1.21190	0.605950	−	0.795503i	$-0.292793\pi$
$907$	3.00251e7	1.21190	0.605950	+	0.795503i	$0.292793\pi$
$908$	1.21752e7	0.490073
$909$	8.25663e6	0.331431
$910$	−389849.	−0.0156060
$911$	−7.61632e6	−0.304053	−0.152026	−	0.988376i	$-0.548580\pi$
$911$	−7.61632e6	−0.304053	−0.152026	+	0.988376i	$0.548580\pi$
$912$	−1.64338e7	−0.654262
$913$	3.14306e6	0.124789
$914$	769124.	0.0304531
$915$	4.69143e6	0.185247
$916$	2.14494e6	0.0844648
$917$	2.24263e7	0.880712
$918$	426015.	0.0166847
$919$	1.41234e7	0.551634	0.275817	−	0.961210i	$-0.411052\pi$
$919$	1.41234e7	0.551634	0.275817	+	0.961210i	$0.411052\pi$
$920$	−114228.	−0.00444941
$921$	−5.67604e6	−0.220494
$922$	−1.35075e6	−0.0523296
$923$	7.30247e6	0.282140
$924$	1.79393e6	0.0691234
$925$	2.26844e7	0.871711
$926$	1.20458e6	0.0461646
$927$	−1.42666e7	−0.545283
$928$	1.00622e7	0.383551
$929$	−2.95615e7	−1.12380	−0.561898	−	0.827206i	$-0.689929\pi$
$929$	−2.95615e7	−1.12380	−0.561898	+	0.827206i	$0.689929\pi$
$930$	−70065.0	−0.00265640
$931$	−5.59405e6	−0.211520
$932$	−1.88091e7	−0.709299
$933$	7.45961e6	0.280551
$934$	3.86704e6	0.145048
$935$	−876515.	−0.0327892
$936$	−1.22209e6	−0.0455946
$937$	3.40344e7	1.26639	0.633197	−	0.773990i	$-0.281742\pi$
$937$	3.40344e7	1.26639	0.633197	+	0.773990i	$0.281742\pi$
$938$	−645423.	−0.0239518
$939$	−1.47994e7	−0.547746
$940$	−1.27431e6	−0.0470386
$941$	2.51116e7	0.924485	0.462242	−	0.886754i	$-0.347045\pi$
$941$	2.51116e7	0.924485	0.462242	+	0.886754i	$0.347045\pi$
$942$	62976.6	0.00231234
$943$	−1.48072e6	−0.0542243
$944$	−3.48066e6	−0.127125
$945$	1.20081e6	0.0437416
$946$	172061.	0.00625108
$947$	−2.02733e7	−0.734599	−0.367300	−	0.930103i	$-0.619718\pi$
$947$	−2.02733e7	−0.734599	−0.367300	+	0.930103i	$0.619718\pi$
$948$	−2.56148e7	−0.925699
$949$	1.98951e7	0.717102
$950$	2.68206e6	0.0964184
$951$	−2.39967e7	−0.860398
$952$	4.36735e6	0.156180
$953$	1.24755e7	0.444965	0.222483	−	0.974937i	$-0.428584\pi$
$953$	1.24755e7	0.444965	0.222483	+	0.974937i	$0.428584\pi$
$954$	677633.	0.0241059
$955$	7.72678e6	0.274151
$956$	−1.45458e6	−0.0514746
$957$	3.18018e6	0.112246
$958$	−2.15503e6	−0.0758645
$959$	3.07871e7	1.08099
$960$	−3.94943e6	−0.138311
$961$	−2.74094e7	−0.957393
$962$	−1.83387e6	−0.0638896
$963$	1.13946e7	0.395945
$964$	4.98212e7	1.72672
$965$	−3.82917e6	−0.132369
$966$	134556.	0.00463939
$967$	3.79545e7	1.30526	0.652630	−	0.757677i	$-0.273666\pi$
$967$	3.79545e7	1.30526	0.652630	+	0.757677i	$0.273666\pi$
$968$	−5.05883e6	−0.173525
$969$	−1.91451e7	−0.655009
$970$	−97800.7	−0.00333743
$971$	−5.56592e6	−0.189447	−0.0947237	−	0.995504i	$-0.530197\pi$
$971$	−5.56592e6	−0.189447	−0.0947237	+	0.995504i	$0.530197\pi$
$972$	1.87471e6	0.0636455
$973$	−1.75318e7	−0.593667
$974$	4.60061e6	0.155388
$975$	−1.24302e7	−0.418763
$976$	3.70959e7	1.24653
$977$	−4.95886e7	−1.66206	−0.831028	−	0.556230i	$-0.812247\pi$
$977$	−4.95886e7	−1.66206	−0.831028	+	0.556230i	$0.812247\pi$
$978$	541328.	0.0180973
$979$	3.30706e6	0.110277
$980$	−1.36648e6	−0.0454503
$981$	−7.05306e6	−0.233994
$982$	954224.	0.0315771
$983$	1.16536e7	0.384660	0.192330	−	0.981330i	$-0.438396\pi$
$983$	1.16536e7	0.384660	0.192330	+	0.981330i	$0.438396\pi$
$984$	1.67656e6	0.0551990
$985$	2.76726e6	0.0908783
$986$	3.85582e6	0.126306
$987$	3.01407e6	0.0984829
$988$	2.73519e7	0.891447
$989$	−1.62802e6	−0.0529259
$990$	30576.7	0.000991521 0
$991$	−1.62828e7	−0.526679	−0.263340	−	0.964703i	$-0.584824\pi$
$991$	−1.62828e7	−0.526679	−0.263340	+	0.964703i	$0.584824\pi$
$992$	−1.68429e6	−0.0543422
$993$	−9.81214e6	−0.315784
$994$	910363.	0.0292246
$995$	8.06450e6	0.258238
$996$	1.67697e7	0.535646
$997$	1.47322e7	0.469386	0.234693	−	0.972070i	$-0.424592\pi$
$997$	1.47322e7	0.469386	0.234693	+	0.972070i	$0.424592\pi$
$998$	2.78341e6	0.0884609
$999$	5.64866e6	0.179074

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.b.1.7	✓	12
3.2	odd	2		531.6.a.d.1.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.b.1.7	✓	12	1.1	even	1	trivial
531.6.a.d.1.6		12	3.2	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-0.501674 q^{2} -9.00000 q^{3} -31.7483 q^{4} -14.0506 q^{5} +4.51506 q^{6} +117.234 q^{7} +31.9809 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-0.501674 q^{2} -9.00000 q^{3} -31.7483 q^{4} -14.0506 q^{5} +4.51506 q^{6} +117.234 q^{7} +31.9809 q^{8} +81.0000 q^{9} +7.04881 q^{10} +53.5537 q^{11} +285.735 q^{12} -471.768 q^{13} -58.8130 q^{14} +126.455 q^{15} +999.902 q^{16} +1164.87 q^{17} -40.6356 q^{18} +1826.16 q^{19} +446.082 q^{20} -1055.10 q^{21} -26.8665 q^{22} +254.207 q^{23} -287.828 q^{24} -2927.58 q^{25} +236.673 q^{26} -729.000 q^{27} -3721.97 q^{28} -6598.12 q^{29} -63.4393 q^{30} +1104.44 q^{31} -1525.01 q^{32} -481.983 q^{33} -584.382 q^{34} -1647.20 q^{35} -2571.61 q^{36} -7748.51 q^{37} -916.136 q^{38} +4245.91 q^{39} -449.350 q^{40} -5824.87 q^{41} +529.317 q^{42} -6404.30 q^{43} -1700.24 q^{44} -1138.10 q^{45} -127.529 q^{46} -2856.66 q^{47} -8999.12 q^{48} -3063.28 q^{49} +1468.69 q^{50} -10483.8 q^{51} +14977.8 q^{52} -16675.9 q^{53} +365.720 q^{54} -752.461 q^{55} +3749.23 q^{56} -16435.4 q^{57} +3310.10 q^{58} -3481.00 q^{59} -4014.74 q^{60} +37099.5 q^{61} -554.070 q^{62} +9495.92 q^{63} -31231.8 q^{64} +6628.61 q^{65} +241.798 q^{66} +10974.2 q^{67} -36982.5 q^{68} -2287.86 q^{69} +826.357 q^{70} -15478.9 q^{71} +2590.45 q^{72} -42171.4 q^{73} +3887.22 q^{74} +26348.2 q^{75} -57977.5 q^{76} +6278.29 q^{77} -2130.06 q^{78} -89645.3 q^{79} -14049.2 q^{80} +6561.00 q^{81} +2922.18 q^{82} +58689.8 q^{83} +33497.7 q^{84} -16367.0 q^{85} +3212.87 q^{86} +59383.1 q^{87} +1712.69 q^{88} +61752.2 q^{89} +570.953 q^{90} -55307.0 q^{91} -8070.64 q^{92} -9939.99 q^{93} +1433.11 q^{94} -25658.6 q^{95} +13725.1 q^{96} -13874.8 q^{97} +1536.77 q^{98} +4337.85 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12q - 4q^{2} - 108q^{3} + 198q^{4} + 36q^{5} + 36q^{6} - 411q^{7} - 69q^{8} + 972q^{9} + O(q^{10}) \)	\( 12q - 4q^{2} - 108q^{3} + 198q^{4} + 36q^{5} + 36q^{6} - 411q^{7} - 69q^{8} + 972q^{9} - 863q^{10} + 492q^{11} - 1782q^{12} - 974q^{13} - 967q^{14} - 324q^{15} + 6370q^{16} - 1463q^{17} - 324q^{18} - 3189q^{19} - 835q^{20} + 3699q^{21} - 2726q^{22} - 2617q^{23} + 621q^{24} + 8642q^{25} + 2414q^{26} - 8748q^{27} - 20458q^{28} - 1963q^{29} + 7767q^{30} - 11929q^{31} - 14382q^{32} - 4428q^{33} - 20744q^{34} + 1829q^{35} + 16038q^{36} - 28105q^{37} - 23475q^{38} + 8766q^{39} - 100576q^{40} - 7585q^{41} + 8703q^{42} - 33146q^{43} + 26014q^{44} + 2916q^{45} - 142851q^{46} - 79215q^{47} - 57330q^{48} - 32569q^{49} - 136019q^{50} + 13167q^{51} - 248218q^{52} - 12220q^{53} + 2916q^{54} - 117770q^{55} - 186728q^{56} + 28701q^{57} - 188072q^{58} - 41772q^{59} + 7515q^{60} - 54195q^{61} + 36230q^{62} - 33291q^{63} + 45197q^{64} + 42368q^{65} + 24534q^{66} + 24224q^{67} - 209639q^{68} + 23553q^{69} - 35684q^{70} + 60254q^{71} - 5589q^{72} - 15385q^{73} + 214638q^{74} - 77778q^{75} - 167504q^{76} - 17169q^{77} - 21726q^{78} - 27054q^{79} + 216899q^{80} + 78732q^{81} + 37917q^{82} - 117595q^{83} + 184122q^{84} - 121585q^{85} + 306756q^{86} + 17667q^{87} - 105799q^{88} - 36033q^{89} - 69903q^{90} - 32217q^{91} - 30906q^{92} + 107361q^{93} + 128392q^{94} - 50721q^{95} + 129438q^{96} - 196914q^{97} + 574100q^{98} + 39852q^{99} + O(q^{100}) \)

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