LMFDB - Embedded newform 33.6.a.c.1.2

Newspace parameters

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	33.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$5.29266605383$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{177}) $
Defining polynomial:	$x^{2} - x - 44$
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-6.15207$ of defining polynomial
Character	$\chi$	$=$	33.1

$q$-expansion

$f(q)$	$=$	$q+4.15207 q^{2} -9.00000 q^{3} -14.7603 q^{4} -37.5207 q^{5} -37.3686 q^{6} -76.4793 q^{7} -194.152 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+4.15207 q^{2} -9.00000 q^{3} -14.7603 q^{4} -37.5207 q^{5} -37.3686 q^{6} -76.4793 q^{7} -194.152 q^{8} +81.0000 q^{9} -155.788 q^{10} -121.000 q^{11} +132.843 q^{12} +169.779 q^{13} -317.547 q^{14} +337.686 q^{15} -333.802 q^{16} -0.875959 q^{17} +336.317 q^{18} -817.825 q^{19} +553.818 q^{20} +688.314 q^{21} -502.400 q^{22} +749.657 q^{23} +1747.37 q^{24} -1717.20 q^{25} +704.932 q^{26} -729.000 q^{27} +1128.86 q^{28} +6040.65 q^{29} +1402.10 q^{30} -1475.69 q^{31} +4826.90 q^{32} +1089.00 q^{33} -3.63704 q^{34} +2869.56 q^{35} -1195.59 q^{36} -15862.7 q^{37} -3395.66 q^{38} -1528.01 q^{39} +7284.72 q^{40} -7626.27 q^{41} +2857.93 q^{42} -18279.5 q^{43} +1786.00 q^{44} -3039.17 q^{45} +3112.62 q^{46} -12878.1 q^{47} +3004.22 q^{48} -10957.9 q^{49} -7129.93 q^{50} +7.88363 q^{51} -2505.99 q^{52} +21763.5 q^{53} -3026.86 q^{54} +4540.00 q^{55} +14848.6 q^{56} +7360.42 q^{57} +25081.2 q^{58} -1168.45 q^{59} -4984.36 q^{60} +14026.3 q^{61} -6127.16 q^{62} -6194.83 q^{63} +30723.3 q^{64} -6370.21 q^{65} +4521.60 q^{66} +36954.6 q^{67} +12.9295 q^{68} -6746.91 q^{69} +11914.6 q^{70} -37513.1 q^{71} -15726.3 q^{72} +80452.0 q^{73} -65862.9 q^{74} +15454.8 q^{75} +12071.4 q^{76} +9254.00 q^{77} -6344.39 q^{78} -62139.9 q^{79} +12524.5 q^{80} +6561.00 q^{81} -31664.8 q^{82} -11905.8 q^{83} -10159.7 q^{84} +32.8666 q^{85} -75897.7 q^{86} -54365.9 q^{87} +23492.4 q^{88} +146348. q^{89} -12618.9 q^{90} -12984.5 q^{91} -11065.2 q^{92} +13281.2 q^{93} -53470.8 q^{94} +30685.3 q^{95} -43442.1 q^{96} -138129. q^{97} -45498.0 q^{98} -9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2q - 5q^{2} - 18q^{3} + 37q^{4} + 58q^{5} + 45q^{6} - 286q^{7} - 375q^{8} + 162q^{9} + O(q^{10}) $	\( 2q - 5q^{2} - 18q^{3} + 37q^{4} + 58q^{5} + 45q^{6} - 286q^{7} - 375q^{8} + 162q^{9} - 1030q^{10} - 242q^{11} - 333q^{12} - 166q^{13} + 1600q^{14} - 522q^{15} - 335q^{16} - 800q^{17} - 405q^{18} - 1476q^{19} + 5498q^{20} + 2574q^{21} + 605q^{22} - 3370q^{23} + 3375q^{24} + 4282q^{25} + 3778q^{26} - 1458q^{27} - 9716q^{28} + 6600q^{29} + 9270q^{30} - 7528q^{31} + 10625q^{32} + 2178q^{33} + 7310q^{34} - 17144q^{35} + 2997q^{36} - 29916q^{37} + 2628q^{38} + 1494q^{39} - 9990q^{40} - 5780q^{41} - 14400q^{42} - 16656q^{43} - 4477q^{44} + 4698q^{45} + 40816q^{46} + 7850q^{47} + 3015q^{48} + 16134q^{49} - 62035q^{50} + 7200q^{51} - 19886q^{52} + 14178q^{53} + 3645q^{54} - 7018q^{55} + 52740q^{56} + 13284q^{57} + 19962q^{58} + 17300q^{59} - 49482q^{60} - 2946q^{61} + 49264q^{62} - 23166q^{63} - 22303q^{64} - 38444q^{65} - 5445q^{66} + 31336q^{67} - 41350q^{68} + 30330q^{69} + 195080q^{70} - 33810q^{71} - 30375q^{72} + 60644q^{73} + 62754q^{74} - 38538q^{75} - 21996q^{76} + 34606q^{77} - 34002q^{78} + 1870q^{79} + 12410q^{80} + 13122q^{81} - 48562q^{82} - 58296q^{83} + 87444q^{84} - 76300q^{85} - 90756q^{86} - 59400q^{87} + 45375q^{88} + 92388q^{89} - 83430q^{90} + 57368q^{91} - 224300q^{92} + 67752q^{93} - 243176q^{94} - 32184q^{95} - 95625q^{96} + 7120q^{97} - 293445q^{98} - 19602q^{99} + O(q^{100}) \)

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 $

$2$	4.15207	0.733989	0.366994	−	0.930223i	$-0.380387\pi$
$2$	4.15207	0.733989	0.366994	+	0.930223i	$0.380387\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−14.7603	−0.461261
$5$	−37.5207	−0.671190	−0.335595	−	0.942006i	$-0.608937\pi$
$5$	−37.5207	−0.671190	−0.335595	+	0.942006i	$0.608937\pi$
$6$	−37.3686	−0.423769
$7$	−76.4793	−0.589928	−0.294964	−	0.955508i	$-0.595308\pi$
$7$	−76.4793	−0.589928	−0.294964	+	0.955508i	$0.595308\pi$
$8$	−194.152	−1.07255
$9$	81.0000	0.333333
$10$	−155.788	−0.492646
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	132.843	0.266309
$13$	169.779	0.278628	0.139314	−	0.990248i	$-0.455510\pi$
$13$	169.779	0.278628	0.139314	+	0.990248i	$0.455510\pi$
$14$	−317.547	−0.433000
$15$	337.686	0.387512
$16$	−333.802	−0.325978
$17$	−0.875959	−0.000735126 0	−0.000367563	−	1.00000i	$-0.500117\pi$
$17$	−0.875959	−0.000735126 0	−0.000367563		1.00000i	$0.500117\pi$
$18$	336.317	0.244663
$19$	−817.825	−0.519728	−0.259864	−	0.965645i	$-0.583678\pi$
$19$	−817.825	−0.519728	−0.259864	+	0.965645i	$0.583678\pi$
$20$	553.818	0.309594
$21$	688.314	0.340595
$22$	−502.400	−0.221306
$23$	749.657	0.295490	0.147745	−	0.989025i	$-0.452799\pi$
$23$	749.657	0.295490	0.147745	+	0.989025i	$0.452799\pi$
$24$	1747.37	0.619236
$25$	−1717.20	−0.549504
$26$	704.932	0.204510
$27$	−729.000	−0.192450
$28$	1128.86	0.272110
$29$	6040.65	1.33379	0.666897	−	0.745150i	$-0.267622\pi$
$29$	6040.65	1.33379	0.666897	+	0.745150i	$0.267622\pi$
$30$	1402.10	0.284429
$31$	−1475.69	−0.275798	−0.137899	−	0.990446i	$-0.544035\pi$
$31$	−1475.69	−0.275798	−0.137899	+	0.990446i	$0.544035\pi$
$32$	4826.90	0.833284
$33$	1089.00	0.174078
$34$	−3.63704	−0.000539574 0
$35$	2869.56	0.395954
$36$	−1195.59	−0.153754
$37$	−15862.7	−1.90490	−0.952450	−	0.304694i	$-0.901446\pi$
$37$	−15862.7	−1.90490	−0.952450	+	0.304694i	$0.901446\pi$
$38$	−3395.66	−0.381475
$39$	−1528.01	−0.160866
$40$	7284.72	0.719884
$41$	−7626.27	−0.708521	−0.354260	−	0.935147i	$-0.615267\pi$
$41$	−7626.27	−0.708521	−0.354260	+	0.935147i	$0.615267\pi$
$42$	2857.93	0.249993
$43$	−18279.5	−1.50762	−0.753812	−	0.657090i	$-0.771787\pi$
$43$	−18279.5	−1.50762	−0.753812	+	0.657090i	$0.771787\pi$
$44$	1786.00	0.139075
$45$	−3039.17	−0.223730
$46$	3112.62	0.216886
$47$	−12878.1	−0.850370	−0.425185	−	0.905106i	$-0.639791\pi$
$47$	−12878.1	−0.850370	−0.425185	+	0.905106i	$0.639791\pi$
$48$	3004.22	0.188204
$49$	−10957.9	−0.651985
$50$	−7129.93	−0.403330
$51$	7.88363	0.000424425 0
$52$	−2505.99	−0.128520
$53$	21763.5	1.06424	0.532118	−	0.846670i	$-0.321396\pi$
$53$	21763.5	1.06424	0.532118	+	0.846670i	$0.321396\pi$
$54$	−3026.86	−0.141256
$55$	4540.00	0.202371
$56$	14848.6	0.632726
$57$	7360.42	0.300065
$58$	25081.2	0.978990
$59$	−1168.45	−0.0436999	−0.0218500	−	0.999761i	$-0.506956\pi$
$59$	−1168.45	−0.0436999	−0.0218500	+	0.999761i	$0.506956\pi$
$60$	−4984.36	−0.178744
$61$	14026.3	0.482635	0.241318	−	0.970446i	$-0.422420\pi$
$61$	14026.3	0.482635	0.241318	+	0.970446i	$0.422420\pi$
$62$	−6127.16	−0.202432
$63$	−6194.83	−0.196643
$64$	30723.3	0.937600
$65$	−6370.21	−0.187012
$66$	4521.60	0.127771
$67$	36954.6	1.00573	0.502865	−	0.864365i	$-0.332279\pi$
$67$	36954.6	1.00573	0.502865	+	0.864365i	$0.332279\pi$
$68$	12.9295	0.000339084 0
$69$	−6746.91	−0.170601
$70$	11914.6	0.290626
$71$	−37513.1	−0.883155	−0.441578	−	0.897223i	$-0.645581\pi$
$71$	−37513.1	−0.883155	−0.441578	+	0.897223i	$0.645581\pi$
$72$	−15726.3	−0.357516
$73$	80452.0	1.76697	0.883486	−	0.468458i	$-0.155190\pi$
$73$	80452.0	1.76697	0.883486	+	0.468458i	$0.155190\pi$
$74$	−65862.9	−1.39818
$75$	15454.8	0.317256
$76$	12071.4	0.239730
$77$	9254.00	0.177870
$78$	−6344.39	−0.118074
$79$	−62139.9	−1.12022	−0.560109	−	0.828419i	$-0.689241\pi$
$79$	−62139.9	−1.12022	−0.560109	+	0.828419i	$0.689241\pi$
$80$	12524.5	0.218793
$81$	6561.00	0.111111
$82$	−31664.8	−0.520046
$83$	−11905.8	−0.189699	−0.0948495	−	0.995492i	$-0.530237\pi$
$83$	−11905.8	−0.189699	−0.0948495	+	0.995492i	$0.530237\pi$
$84$	−10159.7	−0.157103
$85$	32.8666	0.000493409 0
$86$	−75897.7	−1.10658
$87$	−54365.9	−0.770066
$88$	23492.4	0.323386
$89$	146348.	1.95844	0.979220	−	0.202800i	$-0.0650041\pi$
$89$	146348.	1.95844	0.979220	+	0.202800i	$0.0650041\pi$
$90$	−12618.9	−0.164215
$91$	−12984.5	−0.164370
$92$	−11065.2	−0.136298
$93$	13281.2	0.159232
$94$	−53470.8	−0.624162
$95$	30685.3	0.348836
$96$	−43442.1	−0.481097
$97$	−138129.	−1.49058	−0.745291	−	0.666740i	$-0.767689\pi$
$97$	−138129.	−1.49058	−0.745291	+	0.666740i	$0.767689\pi$
$98$	−45498.0	−0.478550
$99$	−9801.00	−0.100504
$100$	25346.4	0.253464
$101$	36615.1	0.357155	0.178577	−	0.983926i	$-0.442850\pi$
$101$	36615.1	0.357155	0.178577	+	0.983926i	$0.442850\pi$
$102$	32.7334	0.000311523 0
$103$	45198.5	0.419789	0.209895	−	0.977724i	$-0.432688\pi$
$103$	45198.5	0.419789	0.209895	+	0.977724i	$0.432688\pi$
$104$	−32962.9	−0.298842
$105$	−25826.0	−0.228604
$106$	90363.4	0.781138
$107$	−28086.8	−0.237161	−0.118580	−	0.992944i	$-0.537834\pi$
$107$	−28086.8	−0.237161	−0.118580	+	0.992944i	$0.537834\pi$
$108$	10760.3	0.0887696
$109$	−33852.9	−0.272916	−0.136458	−	0.990646i	$-0.543572\pi$
$109$	−33852.9	−0.272916	−0.136458	+	0.990646i	$0.543572\pi$
$110$	18850.4	0.148538
$111$	142764.	1.09979
$112$	25528.9	0.192304
$113$	168559.	1.24181	0.620904	−	0.783886i	$-0.286766\pi$
$113$	168559.	1.24181	0.620904	+	0.783886i	$0.286766\pi$
$114$	30561.0	0.220244
$115$	−28127.6	−0.198330
$116$	−89162.1	−0.615227
$117$	13752.1	0.0928759
$118$	−4851.49	−0.0320752
$119$	66.9928	0.000433671 0
$120$	−65562.4	−0.415625
$121$	14641.0	0.0909091
$122$	58238.2	0.354249
$123$	68636.4	0.409065
$124$	21781.7	0.127215
$125$	181683.	1.04001
$126$	−25721.3	−0.144333
$127$	−336859.	−1.85327	−0.926636	−	0.375960i	$-0.877313\pi$
$127$	−336859.	−1.85327	−0.926636	+	0.375960i	$0.877313\pi$
$128$	−26895.7	−0.145097
$129$	164515.	0.870427
$130$	−26449.5	−0.137265
$131$	−83896.5	−0.427135	−0.213568	−	0.976928i	$-0.568508\pi$
$131$	−83896.5	−0.427135	−0.213568	+	0.976928i	$0.568508\pi$
$132$	−16074.0	−0.0802952
$133$	62546.7	0.306602
$134$	153438.	0.738195
$135$	27352.6	0.129171
$136$	170.069	0.000788458 0
$137$	−196507.	−0.894492	−0.447246	−	0.894411i	$-0.647595\pi$
$137$	−196507.	−0.894492	−0.447246	+	0.894411i	$0.647595\pi$
$138$	−28013.6	−0.125219
$139$	263232.	1.15559	0.577793	−	0.816183i	$-0.303914\pi$
$139$	263232.	1.15559	0.577793	+	0.816183i	$0.303914\pi$
$140$	−42355.6	−0.182638
$141$	115903.	0.490961
$142$	−155757.	−0.648226
$143$	−20543.2	−0.0840094
$144$	−27037.9	−0.108659
$145$	−226649.	−0.895230
$146$	334042.	1.29694
$147$	98621.2	0.376424
$148$	234139.	0.878655
$149$	−337412.	−1.24507	−0.622536	−	0.782591i	$-0.713898\pi$
$149$	−337412.	−1.24507	−0.622536	+	0.782591i	$0.713898\pi$
$150$	64169.3	0.232862
$151$	−157583.	−0.562428	−0.281214	−	0.959645i	$-0.590737\pi$
$151$	−157583.	−0.562428	−0.281214	+	0.959645i	$0.590737\pi$
$152$	158782.	0.557434
$153$	−70.9527	−0.000245042 0
$154$	38423.2	0.130555
$155$	55368.8	0.185113
$156$	22553.9	0.0742011
$157$	5369.59	0.0173857	0.00869285	−	0.999962i	$-0.497233\pi$
$157$	5369.59	0.0173857	0.00869285	+	0.999962i	$0.497233\pi$
$158$	−258009.	−0.822228
$159$	−195871.	−0.614437
$160$	−181109.	−0.559292
$161$	−57333.2	−0.174318
$162$	27241.7	0.0815543
$163$	−503102.	−1.48316	−0.741579	−	0.670866i	$-0.765923\pi$
$163$	−503102.	−1.48316	−0.741579	+	0.670866i	$0.765923\pi$
$164$	112566.	0.326813
$165$	−40860.0	−0.116839
$166$	−49433.9	−0.139237
$167$	−584523.	−1.62185	−0.810924	−	0.585151i	$-0.801035\pi$
$167$	−584523.	−1.62185	−0.810924	+	0.585151i	$0.801035\pi$
$168$	−133638.	−0.365305
$169$	−342468.	−0.922367
$170$	136.464	0.000362157 0
$171$	−66243.8	−0.173243
$172$	269811.	0.695407
$173$	−55544.0	−0.141098	−0.0705491	−	0.997508i	$-0.522475\pi$
$173$	−55544.0	−0.141098	−0.0705491	+	0.997508i	$0.522475\pi$
$174$	−225731.	−0.565220
$175$	131330.	0.324168
$176$	40390.0	0.0982861
$177$	10516.1	0.0252302
$178$	607645.	1.43747
$179$	215136.	0.501858	0.250929	−	0.968006i	$-0.419264\pi$
$179$	215136.	0.501858	0.250929	+	0.968006i	$0.419264\pi$
$180$	44859.2	0.103198
$181$	682113.	1.54761	0.773803	−	0.633427i	$-0.218352\pi$
$181$	682113.	1.54761	0.773803	+	0.633427i	$0.218352\pi$
$182$	−53912.7	−0.120646
$183$	−126237.	−0.278650
$184$	−145547.	−0.316927
$185$	595178.	1.27855
$186$	55144.4	0.116874
$187$	105.991	0.000221649 0
$188$	190085.	0.392242
$189$	55753.4	0.113532
$190$	127408.	0.256042
$191$	−89697.4	−0.177908	−0.0889542	−	0.996036i	$-0.528352\pi$
$191$	−89697.4	−0.177908	−0.0889542	+	0.996036i	$0.528352\pi$
$192$	−276509.	−0.541323
$193$	657062.	1.26973	0.634867	−	0.772621i	$-0.281055\pi$
$193$	657062.	1.26973	0.634867	+	0.772621i	$0.281055\pi$
$194$	−573521.	−1.09407
$195$	57331.9	0.107972
$196$	161742.	0.300735
$197$	720419.	1.32257	0.661286	−	0.750134i	$-0.270011\pi$
$197$	720419.	1.32257	0.661286	+	0.750134i	$0.270011\pi$
$198$	−40694.4	−0.0737686
$199$	140848.	0.252127	0.126063	−	0.992022i	$-0.459766\pi$
$199$	140848.	0.252127	0.126063	+	0.992022i	$0.459766\pi$
$200$	333398.	0.589370
$201$	−332592.	−0.580659
$202$	152028.	0.262148
$203$	−461985.	−0.786842
$204$	−116.365	−0.000195770 0
$205$	286143.	0.475552
$206$	187667.	0.308121
$207$	60722.2	0.0984967
$208$	−56672.4	−0.0908266
$209$	98956.8	0.156704
$210$	−107231.	−0.167793
$211$	−111929.	−0.173075	−0.0865377	−	0.996249i	$-0.527580\pi$
$211$	−111929.	−0.173075	−0.0865377	+	0.996249i	$0.527580\pi$
$212$	−321236.	−0.490890
$213$	337618.	0.509890
$214$	−116618.	−0.174073
$215$	685859.	1.01190
$216$	141537.	0.206412
$217$	112860.	0.162701
$218$	−140559.	−0.200317
$219$	−724068.	−1.02016
$220$	−67012.0	−0.0933460
$221$	−148.719	−0.000204826 0
$222$	592766.	0.807237
$223$	−906826.	−1.22113	−0.610565	−	0.791966i	$-0.709058\pi$
$223$	−906826.	−1.22113	−0.610565	+	0.791966i	$0.709058\pi$
$224$	−369158.	−0.491578
$225$	−139093.	−0.183168
$226$	699867.	0.911474
$227$	−1.35715e6	−1.74809	−0.874046	−	0.485844i	$-0.838512\pi$
$227$	−1.35715e6	−1.74809	−0.874046	+	0.485844i	$0.838512\pi$
$228$	−108642.	−0.138408
$229$	−344956.	−0.434685	−0.217342	−	0.976095i	$-0.569739\pi$
$229$	−344956.	−0.434685	−0.217342	+	0.976095i	$0.569739\pi$
$230$	−116788.	−0.145572
$231$	−83286.0	−0.102693
$232$	−1.17281e6	−1.43056
$233$	−1.18163e6	−1.42591	−0.712955	−	0.701210i	$-0.752643\pi$
$233$	−1.18163e6	−1.42591	−0.712955	+	0.701210i	$0.752643\pi$
$234$	57099.5	0.0681699
$235$	483196.	0.570760
$236$	17246.7	0.0201570
$237$	559259.	0.646759
$238$	278.158	0.000318310 0
$239$	−723612.	−0.819429	−0.409714	−	0.912214i	$-0.634372\pi$
$239$	−723612.	−0.819429	−0.409714	+	0.912214i	$0.634372\pi$
$240$	−112720.	−0.126320
$241$	394322.	0.437329	0.218664	−	0.975800i	$-0.429830\pi$
$241$	394322.	0.437329	0.218664	+	0.975800i	$0.429830\pi$
$242$	60790.4	0.0667262
$243$	−59049.0	−0.0641500
$244$	−207033.	−0.222621
$245$	411148.	0.437606
$246$	284983.	0.300249
$247$	−138849.	−0.144811
$248$	286508.	0.295806
$249$	107153.	0.109523
$250$	754358.	0.763357
$251$	1.49884e6	1.50165	0.750827	−	0.660499i	$-0.229655\pi$
$251$	1.49884e6	1.50165	0.750827	+	0.660499i	$0.229655\pi$
$252$	91437.7	0.0907035
$253$	−90708.5	−0.0890936
$254$	−1.39866e6	−1.36028
$255$	−295.799	−0.000284870 0
$256$	−1.09482e6	−1.04410
$257$	−512138.	−0.483676	−0.241838	−	0.970317i	$-0.577750\pi$
$257$	−512138.	−0.483676	−0.241838	+	0.970317i	$0.577750\pi$
$258$	683079.	0.638884
$259$	1.21317e6	1.12375
$260$	94026.4	0.0862614
$261$	489293.	0.444598
$262$	−348344.	−0.313513
$263$	154350.	0.137600	0.0687998	−	0.997630i	$-0.478083\pi$
$263$	154350.	0.137600	0.0687998	+	0.997630i	$0.478083\pi$
$264$	−211432.	−0.186707
$265$	−816580.	−0.714305
$266$	259698.	0.225043
$267$	−1.31713e6	−1.13071
$268$	−545463.	−0.463904
$269$	2.27104e6	1.91357	0.956783	−	0.290802i	$-0.0939221\pi$
$269$	2.27104e6	1.91357	0.956783	+	0.290802i	$0.0939221\pi$
$270$	113570.	0.0948098
$271$	304916.	0.252207	0.126103	−	0.992017i	$-0.459753\pi$
$271$	304916.	0.252207	0.126103	+	0.992017i	$0.459753\pi$
$272$	292.397	0.000239635 0
$273$	116861.	0.0948993
$274$	−815910.	−0.656547
$275$	207781.	0.165682
$276$	99586.7	0.0786916
$277$	−884418.	−0.692561	−0.346280	−	0.938131i	$-0.612555\pi$
$277$	−884418.	−0.692561	−0.346280	+	0.938131i	$0.612555\pi$
$278$	1.09296e6	0.848187
$279$	−119531.	−0.0919325
$280$	−557130.	−0.424680
$281$	2.03032e6	1.53391	0.766955	−	0.641701i	$-0.221771\pi$
$281$	2.03032e6	1.53391	0.766955	+	0.641701i	$0.221771\pi$
$282$	481237.	0.360360
$283$	1.32361e6	0.982415	0.491207	−	0.871043i	$-0.336556\pi$
$283$	1.32361e6	0.982415	0.491207	+	0.871043i	$0.336556\pi$
$284$	553706.	0.407365
$285$	−276168.	−0.201401
$286$	−85296.8	−0.0616620
$287$	583252.	0.417976
$288$	390979.	0.277761
$289$	−1.41986e6	−0.999999
$290$	−941063.	−0.657088
$291$	1.24316e6	0.860587
$292$	−1.18750e6	−0.815034
$293$	−2.50642e6	−1.70563	−0.852816	−	0.522211i	$-0.825107\pi$
$293$	−2.50642e6	−1.70563	−0.852816	+	0.522211i	$0.825107\pi$
$294$	409482.	0.276291
$295$	43841.1	0.0293310
$296$	3.07977e6	2.04310
$297$	88209.0	0.0580259
$298$	−1.40096e6	−0.913869
$299$	127276.	0.0823317
$300$	−228118.	−0.146338
$301$	1.39800e6	0.889389
$302$	−654295.	−0.412816
$303$	−329536.	−0.206203
$304$	272991.	0.169420
$305$	−526277.	−0.323940
$306$	−294.600	−0.000179858 0
$307$	871198.	0.527559	0.263779	−	0.964583i	$-0.415031\pi$
$307$	871198.	0.527559	0.263779	+	0.964583i	$0.415031\pi$
$308$	−136592.	−0.0820444
$309$	−406787.	−0.242365
$310$	229895.	0.135871
$311$	1.26077e6	0.739156	0.369578	−	0.929200i	$-0.379502\pi$
$311$	1.26077e6	0.739156	0.369578	+	0.929200i	$0.379502\pi$
$312$	296666.	0.172536
$313$	326948.	0.188633	0.0943164	−	0.995542i	$-0.469933\pi$
$313$	326948.	0.188633	0.0943164	+	0.995542i	$0.469933\pi$
$314$	22294.9	0.0127609
$315$	232434.	0.131985
$316$	917206.	0.516713
$317$	−969525.	−0.541890	−0.270945	−	0.962595i	$-0.587336\pi$
$317$	−969525.	−0.541890	−0.270945	+	0.962595i	$0.587336\pi$
$318$	−813270.	−0.450990
$319$	−730919.	−0.402154
$320$	−1.15276e6	−0.629308
$321$	252781.	0.136925
$322$	−238051.	−0.127947
$323$	716.381	0.000382065 0
$324$	−96842.6	−0.0512512
$325$	−291544.	−0.153107
$326$	−2.08891e6	−1.08862
$327$	304676.	0.157568
$328$	1.48066e6	0.759923
$329$	984910.	0.501657
$330$	−169654.	−0.0857587
$331$	2.06283e6	1.03489	0.517444	−	0.855717i	$-0.326884\pi$
$331$	2.06283e6	1.03489	0.517444	+	0.855717i	$0.326884\pi$
$332$	175734.	0.0875006
$333$	−1.28488e6	−0.634967
$334$	−2.42698e6	−1.19042
$335$	−1.38656e6	−0.675037
$336$	−229760.	−0.111027
$337$	−2.86366e6	−1.37356	−0.686778	−	0.726867i	$-0.740976\pi$
$337$	−2.86366e6	−1.37356	−0.686778	+	0.726867i	$0.740976\pi$
$338$	−1.42195e6	−0.677007
$339$	−1.51703e6	−0.716959
$340$	−485.122	−0.000227590 0
$341$	178558.	0.0831561
$342$	−275049.	−0.127158
$343$	2.12344e6	0.974552
$344$	3.54900e6	1.61700
$345$	253149.	0.114506
$346$	−230622.	−0.103565
$347$	−2.33015e6	−1.03887	−0.519434	−	0.854511i	$-0.673857\pi$
$347$	−2.33015e6	−1.03887	−0.519434	+	0.854511i	$0.673857\pi$
$348$	802458.	0.355201
$349$	949067.	0.417094	0.208547	−	0.978012i	$-0.433127\pi$
$349$	949067.	0.417094	0.208547	+	0.978012i	$0.433127\pi$
$350$	545292.	0.237935
$351$	−123769.	−0.0536219
$352$	−584055.	−0.251245
$353$	−2.05584e6	−0.878119	−0.439059	−	0.898458i	$-0.644688\pi$
$353$	−2.05584e6	−0.878119	−0.439059	+	0.898458i	$0.644688\pi$
$354$	43663.4	0.0185187
$355$	1.40752e6	0.592765
$356$	−2.16014e6	−0.903351
$357$	−602.935	−0.000250380 0
$358$	893259.	0.368358
$359$	−1.11901e6	−0.458244	−0.229122	−	0.973398i	$-0.573585\pi$
$359$	−1.11901e6	−0.458244	−0.229122	+	0.973398i	$0.573585\pi$
$360$	590062.	0.239961
$361$	−1.80726e6	−0.729883
$362$	2.83218e6	1.13592
$363$	−131769.	−0.0524864
$364$	191656.	0.0758175
$365$	−3.01861e6	−1.18597
$366$	−524144.	−0.204526
$367$	4.10134e6	1.58950	0.794749	−	0.606938i	$-0.207602\pi$
$367$	4.10134e6	1.58950	0.794749	+	0.606938i	$0.207602\pi$
$368$	−250237.	−0.0963233
$369$	−617728.	−0.236174
$370$	2.47122e6	0.938442
$371$	−1.66445e6	−0.627823
$372$	−196035.	−0.0734474
$373$	−3.54538e6	−1.31945	−0.659723	−	0.751509i	$-0.729326\pi$
$373$	−3.54538e6	−1.31945	−0.659723	+	0.751509i	$0.729326\pi$
$374$	440.082	0.000162688 0
$375$	−1.63514e6	−0.600451
$376$	2.50031e6	0.912063
$377$	1.02557e6	0.371632
$378$	231492.	0.0833310
$379$	3.23295e6	1.15612	0.578058	−	0.815996i	$-0.303811\pi$
$379$	3.23295e6	1.15612	0.578058	+	0.815996i	$0.303811\pi$
$380$	−452926.	−0.160904
$381$	3.03173e6	1.06999
$382$	−372430.	−0.130583
$383$	−3.72375e6	−1.29713	−0.648565	−	0.761159i	$-0.724631\pi$
$383$	−3.72375e6	−1.29713	−0.648565	+	0.761159i	$0.724631\pi$
$384$	242061.	0.0837717
$385$	−347216.	−0.119385
$386$	2.72817e6	0.931971
$387$	−1.48064e6	−0.502541
$388$	2.03883e6	0.687546
$389$	−1.00909e6	−0.338108	−0.169054	−	0.985607i	$-0.554071\pi$
$389$	−1.00909e6	−0.338108	−0.169054	+	0.985607i	$0.554071\pi$
$390$	238046.	0.0792499
$391$	−656.669	−0.000217222 0
$392$	2.12750e6	0.699286
$393$	755068.	0.246607
$394$	2.99123e6	0.970753
$395$	2.33153e6	0.751880
$396$	144666.	0.0463584
$397$	−366919.	−0.116841	−0.0584203	−	0.998292i	$-0.518606\pi$
$397$	−366919.	−0.116841	−0.0584203	+	0.998292i	$0.518606\pi$
$398$	584811.	0.185058
$399$	−562920.	−0.177017
$400$	573204.	0.179126
$401$	1.21086e6	0.376038	0.188019	−	0.982165i	$-0.439793\pi$
$401$	1.21086e6	0.376038	0.188019	+	0.982165i	$0.439793\pi$
$402$	−1.38094e6	−0.426197
$403$	−250540.	−0.0768449
$404$	−540451.	−0.164741
$405$	−246173.	−0.0745767
$406$	−1.91819e6	−0.577533
$407$	1.91938e6	0.574349
$408$	−1530.62	−0.000455216 0
$409$	314741.	0.0930346	0.0465173	−	0.998917i	$-0.485188\pi$
$409$	314741.	0.0930346	0.0465173	+	0.998917i	$0.485188\pi$
$410$	1.18808e6	0.349050
$411$	1.76856e6	0.516435
$412$	−667145.	−0.193632
$413$	89362.4	0.0257798
$414$	252123.	0.0722954
$415$	446715.	0.127324
$416$	819504.	0.232176
$417$	−2.36909e6	−0.667178
$418$	410875.	0.115019
$419$	5.98987e6	1.66679	0.833397	−	0.552674i	$-0.186393\pi$
$419$	5.98987e6	1.66679	0.833397	+	0.552674i	$0.186393\pi$
$420$	381200.	0.105446
$421$	−3.19815e6	−0.879414	−0.439707	−	0.898141i	$-0.644918\pi$
$421$	−3.19815e6	−0.879414	−0.439707	+	0.898141i	$0.644918\pi$
$422$	−464735.	−0.127035
$423$	−1.04313e6	−0.283457
$424$	−4.22542e6	−1.14145
$425$	1504.20	0.000403954 0
$426$	1.40181e6	0.374254
$427$	−1.07272e6	−0.284720
$428$	414571.	0.109393
$429$	184889.	0.0485029
$430$	2.84773e6	0.742725
$431$	−5.24498e6	−1.36004	−0.680019	−	0.733195i	$-0.738028\pi$
$431$	−5.24498e6	−1.36004	−0.680019	+	0.733195i	$0.738028\pi$
$432$	243341.	0.0627345
$433$	5.44629e6	1.39599	0.697993	−	0.716105i	$-0.254077\pi$
$433$	5.44629e6	1.39599	0.697993	+	0.716105i	$0.254077\pi$
$434$	468601.	0.119421
$435$	2.03984e6	0.516861
$436$	499680.	0.125885
$437$	−613088.	−0.153574
$438$	−3.00638e6	−0.748787
$439$	−6.38391e6	−1.58098	−0.790488	−	0.612477i	$-0.790173\pi$
$439$	−6.38391e6	−1.58098	−0.790488	+	0.612477i	$0.790173\pi$
$440$	−881451.	−0.217053
$441$	−887591.	−0.217328
$442$	−617.492	−0.000150340 0
$443$	2.26340e6	0.547964	0.273982	−	0.961735i	$-0.411659\pi$
$443$	2.26340e6	0.547964	0.273982	+	0.961735i	$0.411659\pi$
$444$	−2.10725e6	−0.507292
$445$	−5.49106e6	−1.31449
$446$	−3.76520e6	−0.896296
$447$	3.03671e6	0.718843
$448$	−2.34969e6	−0.553116
$449$	4.05102e6	0.948306	0.474153	−	0.880442i	$-0.342754\pi$
$449$	4.05102e6	0.948306	0.474153	+	0.880442i	$0.342754\pi$
$450$	−577524.	−0.134443
$451$	922779.	0.213627
$452$	−2.48798e6	−0.572797
$453$	1.41825e6	0.324718
$454$	−5.63499e6	−1.28308
$455$	487189.	0.110324
$456$	−1.42904e6	−0.321835
$457$	−5.07731e6	−1.13722	−0.568608	−	0.822609i	$-0.692518\pi$
$457$	−5.07731e6	−1.13722	−0.568608	+	0.822609i	$0.692518\pi$
$458$	−1.43228e6	−0.319054
$459$	638.574	0.000141475 0
$460$	415173.	0.0914818
$461$	−3.81197e6	−0.835405	−0.417702	−	0.908584i	$-0.637165\pi$
$461$	−3.81197e6	−0.835405	−0.417702	+	0.908584i	$0.637165\pi$
$462$	−345809.	−0.0753757
$463$	6.00414e6	1.30166	0.650832	−	0.759222i	$-0.274420\pi$
$463$	6.00414e6	1.30166	0.650832	+	0.759222i	$0.274420\pi$
$464$	−2.01638e6	−0.434788
$465$	−498320.	−0.106875
$466$	−4.90621e6	−1.04660
$467$	−3.29877e6	−0.699939	−0.349969	−	0.936761i	$-0.613808\pi$
$467$	−3.29877e6	−0.699939	−0.349969	+	0.936761i	$0.613808\pi$
$468$	−202985.	−0.0428400
$469$	−2.82626e6	−0.593309
$470$	2.00626e6	0.418931
$471$	−48326.3	−0.0100376
$472$	226857.	0.0468703
$473$	2.21182e6	0.454566
$474$	2.32208e6	0.474714
$475$	1.40437e6	0.285593
$476$	−988.836	−0.000200035 0
$477$	1.76284e6	0.354746
$478$	−3.00449e6	−0.601452
$479$	5.86911e6	1.16878	0.584391	−	0.811472i	$-0.301333\pi$
$479$	5.86911e6	1.16878	0.584391	+	0.811472i	$0.301333\pi$
$480$	1.62998e6	0.322908
$481$	−2.69314e6	−0.530758
$482$	1.63725e6	0.320995
$483$	515999.	0.100642
$484$	−216106.	−0.0419328
$485$	5.18269e6	1.00046
$486$	−245175.	−0.0470854
$487$	981038.	0.187441	0.0937203	−	0.995599i	$-0.470124\pi$
$487$	981038.	0.187441	0.0937203	+	0.995599i	$0.470124\pi$
$488$	−2.72324e6	−0.517650
$489$	4.52792e6	0.856301
$490$	1.70712e6	0.321198
$491$	5.94395e6	1.11268	0.556342	−	0.830954i	$-0.312205\pi$
$491$	5.94395e6	1.11268	0.556342	+	0.830954i	$0.312205\pi$
$492$	−1.01310e6	−0.188685
$493$	−5291.36	−0.000980506 0
$494$	−576511.	−0.106289
$495$	367740.	0.0674572
$496$	492587.	0.0899040
$497$	2.86898e6	0.520998
$498$	444905.	0.0803884
$499$	6.59714e6	1.18605	0.593027	−	0.805183i	$-0.297933\pi$
$499$	6.59714e6	1.18605	0.593027	+	0.805183i	$0.297933\pi$
$500$	−2.68170e6	−0.479716
$501$	5.26070e6	0.936374
$502$	6.22327e6	1.10220
$503$	−7.55854e6	−1.33204	−0.666021	−	0.745933i	$-0.732004\pi$
$503$	−7.55854e6	−1.33204	−0.666021	+	0.745933i	$0.732004\pi$
$504$	1.20274e6	0.210909
$505$	−1.37382e6	−0.239719
$506$	−376628.	−0.0653937
$507$	3.08221e6	0.532529
$508$	4.97216e6	0.854841
$509$	4.67934e6	0.800553	0.400276	−	0.916394i	$-0.368914\pi$
$509$	4.67934e6	0.800553	0.400276	+	0.916394i	$0.368914\pi$
$510$	−1228.18	−0.000209091 0
$511$	−6.15291e6	−1.04239
$512$	−3.68509e6	−0.621260
$513$	596194.	0.100022
$514$	−2.12643e6	−0.355013
$515$	−1.69588e6	−0.281758
$516$	−2.42830e6	−0.401494
$517$	1.55825e6	0.256396
$518$	5.03715e6	0.824823
$519$	499896.	0.0814631
$520$	1.23679e6	0.200580
$521$	557794.	0.0900284	0.0450142	−	0.998986i	$-0.485667\pi$
$521$	557794.	0.0900284	0.0450142	+	0.998986i	$0.485667\pi$
$522$	2.03158e6	0.326330
$523$	3.87401e6	0.619308	0.309654	−	0.950849i	$-0.399787\pi$
$523$	3.87401e6	0.619308	0.309654	+	0.950849i	$0.399787\pi$
$524$	1.23834e6	0.197021
$525$	−1.18197e6	−0.187158
$526$	640871.	0.100997
$527$	1292.64	0.000202746 0
$528$	−363510.	−0.0567455
$529$	−5.87436e6	−0.912686
$530$	−3.39049e6	−0.524292
$531$	−94644.6	−0.0145666
$532$	−923210.	−0.141423
$533$	−1.29478e6	−0.197414
$534$	−5.46880e6	−0.829926
$535$	1.05384e6	0.159180
$536$	−7.17481e6	−1.07870
$537$	−1.93622e6	−0.289748
$538$	9.42950e6	1.40454
$539$	1.32591e6	0.196581
$540$	−403733.	−0.0595813
$541$	−5.42985e6	−0.797618	−0.398809	−	0.917034i	$-0.630576\pi$
$541$	−5.42985e6	−0.797618	−0.398809	+	0.917034i	$0.630576\pi$
$542$	1.26603e6	0.185117
$543$	−6.13902e6	−0.893510
$544$	−4228.17	−0.000612569 0
$545$	1.27018e6	0.183179
$546$	485215.	0.0696550
$547$	−853295.	−0.121936	−0.0609679	−	0.998140i	$-0.519419\pi$
$547$	−853295.	−0.121936	−0.0609679	+	0.998140i	$0.519419\pi$
$548$	2.90051e6	0.412594
$549$	1.13613e6	0.160878
$550$	862721.	0.121608
$551$	−4.94019e6	−0.693210
$552$	1.30993e6	0.182978
$553$	4.75242e6	0.660848
$554$	−3.67216e6	−0.508332
$555$	−5.35661e6	−0.738171
$556$	−3.88540e6	−0.533026
$557$	1.08605e6	0.148324	0.0741618	−	0.997246i	$-0.476372\pi$
$557$	1.08605e6	0.148324	0.0741618	+	0.997246i	$0.476372\pi$
$558$	−496300.	−0.0674775
$559$	−3.10347e6	−0.420066
$560$	−957863.	−0.129072
$561$	−953.919	−0.000127969 0
$562$	8.43005e6	1.12587
$563$	6.05610e6	0.805235	0.402617	−	0.915368i	$-0.368101\pi$
$563$	6.05610e6	0.805235	0.402617	+	0.915368i	$0.368101\pi$
$564$	−1.71077e6	−0.226461
$565$	−6.32443e6	−0.833490
$566$	5.49573e6	0.721081
$567$	−501781.	−0.0655475
$568$	7.28325e6	0.947227
$569$	4.03513e6	0.522489	0.261245	−	0.965273i	$-0.415867\pi$
$569$	4.03513e6	0.522489	0.261245	+	0.965273i	$0.415867\pi$
$570$	−1.14667e6	−0.147826
$571$	597325.	0.0766691	0.0383345	−	0.999265i	$-0.487795\pi$
$571$	597325.	0.0766691	0.0383345	+	0.999265i	$0.487795\pi$
$572$	303225.	0.0387502
$573$	807277.	0.102715
$574$	2.42170e6	0.306790
$575$	−1.28731e6	−0.162373
$576$	2.48858e6	0.312533
$577$	4.08910e6	0.511315	0.255657	−	0.966767i	$-0.417708\pi$
$577$	4.08910e6	0.511315	0.255657	+	0.966767i	$0.417708\pi$
$578$	−5.89534e6	−0.733988
$579$	−5.91356e6	−0.733082
$580$	3.34542e6	0.412934
$581$	910551.	0.111909
$582$	5.16169e6	0.631662
$583$	−2.63338e6	−0.320879
$584$	−1.56199e7	−1.89516
$585$	−515987.	−0.0623374
$586$	−1.04068e7	−1.25191
$587$	1.56181e6	0.187082	0.0935409	−	0.995615i	$-0.470181\pi$
$587$	1.56181e6	0.187082	0.0935409	+	0.995615i	$0.470181\pi$
$588$	−1.45568e6	−0.173629
$589$	1.20685e6	0.143340
$590$	182031.	0.0215286
$591$	−6.48377e6	−0.763587
$592$	5.29499e6	0.620956
$593$	−8.87674e6	−1.03661	−0.518307	−	0.855195i	$-0.673437\pi$
$593$	−8.87674e6	−1.03661	−0.518307	+	0.855195i	$0.673437\pi$
$594$	366250.	0.0425903
$595$	−2513.61	−0.000291076 0
$596$	4.98031e6	0.574303
$597$	−1.26763e6	−0.145565
$598$	528457.	0.0604306
$599$	−7.17157e6	−0.816671	−0.408336	−	0.912832i	$-0.633891\pi$
$599$	−7.17157e6	−0.816671	−0.408336	+	0.912832i	$0.633891\pi$
$600$	−3.00058e6	−0.340273
$601$	−4.79599e6	−0.541617	−0.270809	−	0.962633i	$-0.587291\pi$
$601$	−4.79599e6	−0.541617	−0.270809	+	0.962633i	$0.587291\pi$
$602$	5.80460e6	0.652802
$603$	2.99332e6	0.335244
$604$	2.32598e6	0.259426
$605$	−549340.	−0.0610173
$606$	−1.36825e6	−0.151351
$607$	−8.49023e6	−0.935293	−0.467646	−	0.883916i	$-0.654898\pi$
$607$	−8.49023e6	−0.935293	−0.467646	+	0.883916i	$0.654898\pi$
$608$	−3.94756e6	−0.433081
$609$	4.15786e6	0.454284
$610$	−2.18514e6	−0.237768
$611$	−2.18643e6	−0.236937
$612$	1047.29	0.000113028 0
$613$	6.52329e6	0.701158	0.350579	−	0.936533i	$-0.385985\pi$
$613$	6.52329e6	0.701158	0.350579	+	0.936533i	$0.385985\pi$
$614$	3.61727e6	0.387222
$615$	−2.57529e6	−0.274560
$616$	−1.79668e6	−0.190774
$617$	1.20215e7	1.27129	0.635647	−	0.771980i	$-0.280733\pi$
$617$	1.20215e7	1.27129	0.635647	+	0.771980i	$0.280733\pi$
$618$	−1.68901e6	−0.177893
$619$	1.34686e7	1.41285	0.706424	−	0.707789i	$-0.250307\pi$
$619$	1.34686e7	1.41285	0.706424	+	0.707789i	$0.250307\pi$
$620$	−817263.	−0.0853852
$621$	−546500.	−0.0568671
$622$	5.23482e6	0.542532
$623$	−1.11926e7	−1.15534
$624$	510051.	0.0524388
$625$	−1.45061e6	−0.148542
$626$	1.35751e6	0.138454
$627$	−890611.	−0.0904731
$628$	−79257.0	−0.00801934
$629$	13895.1	0.00140034
$630$	965082.	0.0968752
$631$	−1.08509e7	−1.08490	−0.542452	−	0.840087i	$-0.682504\pi$
$631$	−1.08509e7	−1.08490	−0.542452	+	0.840087i	$0.682504\pi$
$632$	1.20646e7	1.20149
$633$	1.00736e6	0.0999251
$634$	−4.02554e6	−0.397741
$635$	1.26392e7	1.24390
$636$	2.89112e6	0.283416
$637$	−1.86042e6	−0.181661
$638$	−3.03482e6	−0.295177
$639$	−3.03856e6	−0.294385
$640$	1.00915e6	0.0973876
$641$	−9.31338e6	−0.895287	−0.447643	−	0.894212i	$-0.647737\pi$
$641$	−9.31338e6	−0.895287	−0.447643	+	0.894212i	$0.647737\pi$
$642$	1.04956e6	0.100501
$643$	1.35760e7	1.29493	0.647464	−	0.762096i	$-0.275830\pi$
$643$	1.35760e7	1.29493	0.647464	+	0.762096i	$0.275830\pi$
$644$	846258.	0.0804059
$645$	−6.17273e6	−0.584222
$646$	2974.46	0.000280432 0
$647$	−1.18628e7	−1.11411	−0.557053	−	0.830477i	$-0.688068\pi$
$647$	−1.18628e7	−1.11411	−0.557053	+	0.830477i	$0.688068\pi$
$648$	−1.27383e6	−0.119172
$649$	141383.	0.0131760
$650$	−1.21051e6	−0.112379
$651$	−1.01574e6	−0.0939353
$652$	7.42596e6	0.684122
$653$	1.22670e7	1.12579	0.562893	−	0.826530i	$-0.309688\pi$
$653$	1.22670e7	1.12579	0.562893	+	0.826530i	$0.309688\pi$
$654$	1.26503e6	0.115653
$655$	3.14785e6	0.286689
$656$	2.54566e6	0.230962
$657$	6.51661e6	0.588991
$658$	4.08941e6	0.368211
$659$	4.60998e6	0.413509	0.206755	−	0.978393i	$-0.433710\pi$
$659$	4.60998e6	0.413509	0.206755	+	0.978393i	$0.433710\pi$
$660$	603108.	0.0538933
$661$	−1.04708e7	−0.932130	−0.466065	−	0.884750i	$-0.654329\pi$
$661$	−1.04708e7	−0.932130	−0.466065	+	0.884750i	$0.654329\pi$
$662$	8.56500e6	0.759596
$663$	1338.47	0.000118257 0
$664$	2.31154e6	0.203461
$665$	−2.34679e6	−0.205788
$666$	−5.33490e6	−0.466058
$667$	4.52841e6	0.394123
$668$	8.62775e6	0.748094
$669$	8.16143e6	0.705020
$670$	−5.75710e6	−0.495469
$671$	−1.69718e6	−0.145520
$672$	3.32242e6	0.283813
$673$	−5.32923e6	−0.453552	−0.226776	−	0.973947i	$-0.572819\pi$
$673$	−5.32923e6	−0.453552	−0.226776	+	0.973947i	$0.572819\pi$
$674$	−1.18901e7	−1.00818
$675$	1.25184e6	0.105752
$676$	5.05495e6	0.425451
$677$	1.75693e6	0.147327	0.0736634	−	0.997283i	$-0.476531\pi$
$677$	1.75693e6	0.147327	0.0736634	+	0.997283i	$0.476531\pi$
$678$	−6.29880e6	−0.526240
$679$	1.05640e7	0.879335
$680$	−6381.11	−0.000529205 0
$681$	1.22144e7	1.00926
$682$	741386.	0.0610357
$683$	−1.42170e7	−1.16615	−0.583077	−	0.812417i	$-0.698152\pi$
$683$	−1.42170e7	−1.16615	−0.583077	+	0.812417i	$0.698152\pi$
$684$	977781.	0.0799100
$685$	7.37307e6	0.600374
$686$	8.81667e6	0.715310
$687$	3.10460e6	0.250965
$688$	6.10173e6	0.491453
$689$	3.69497e6	0.296526
$690$	1.05109e6	0.0840460
$691$	−2.40296e7	−1.91448	−0.957240	−	0.289294i	$-0.906579\pi$
$691$	−2.40296e7	−1.91448	−0.957240	+	0.289294i	$0.906579\pi$
$692$	819848.	0.0650831
$693$	749574.	0.0592900
$694$	−9.67494e6	−0.762517
$695$	−9.87665e6	−0.775618
$696$	1.05552e7	0.825934
$697$	6680.30	0.000520852 0
$698$	3.94059e6	0.306142
$699$	1.06347e7	0.823249
$700$	−1.93848e6	−0.149526
$701$	−5.04194e6	−0.387528	−0.193764	−	0.981048i	$-0.562070\pi$
$701$	−5.04194e6	−0.387528	−0.193764	+	0.981048i	$0.562070\pi$
$702$	−513895.	−0.0393579
$703$	1.29729e7	0.990030
$704$	−3.71751e6	−0.282697
$705$	−4.34876e6	−0.329528
$706$	−8.53600e6	−0.644529
$707$	−2.80030e6	−0.210696
$708$	−155221.	−0.0116377
$709$	1.87351e7	1.39972	0.699860	−	0.714280i	$-0.253246\pi$
$709$	1.87351e7	1.39972	0.699860	+	0.714280i	$0.253246\pi$
$710$	5.84411e6	0.435083
$711$	−5.03333e6	−0.373406
$712$	−2.84137e7	−2.10052
$713$	−1.10626e6	−0.0814955
$714$	−2503.43	−0.000183776 0
$715$	770795.	0.0563863
$716$	−3.17548e6	−0.231487
$717$	6.51251e6	0.473097
$718$	−4.64619e6	−0.336346
$719$	9.84863e6	0.710483	0.355242	−	0.934775i	$-0.384399\pi$
$719$	9.84863e6	0.710483	0.355242	+	0.934775i	$0.384399\pi$
$720$	1.01448e6	0.0729311
$721$	−3.45675e6	−0.247645
$722$	−7.50387e6	−0.535726
$723$	−3.54890e6	−0.252492
$724$	−1.00682e7	−0.713849
$725$	−1.03730e7	−0.732925
$726$	−547114.	−0.0385244
$727$	−1.76700e7	−1.23994	−0.619968	−	0.784627i	$-0.712854\pi$
$727$	−1.76700e7	−1.23994	−0.619968	+	0.784627i	$0.712854\pi$
$728$	2.52098e6	0.176295
$729$	531441.	0.0370370
$730$	−1.25335e7	−0.870492
$731$	16012.1	0.00110829
$732$	1.86330e6	0.128530
$733$	−1.72881e7	−1.18847	−0.594235	−	0.804291i	$-0.702545\pi$
$733$	−1.72881e7	−1.18847	−0.594235	+	0.804291i	$0.702545\pi$
$734$	1.70290e7	1.16667
$735$	−3.70033e6	−0.252652
$736$	3.61852e6	0.246227
$737$	−4.47151e6	−0.303239
$738$	−2.56485e6	−0.173349
$739$	−5.26063e6	−0.354345	−0.177172	−	0.984180i	$-0.556695\pi$
$739$	−5.26063e6	−0.354345	−0.177172	+	0.984180i	$0.556695\pi$
$740$	−8.78503e6	−0.589745
$741$	1.24964e6	0.0836065
$742$	−6.91093e6	−0.460815
$743$	5.40803e6	0.359391	0.179695	−	0.983722i	$-0.442489\pi$
$743$	5.40803e6	0.359391	0.179695	+	0.983722i	$0.442489\pi$
$744$	−2.57857e6	−0.170784
$745$	1.26599e7	0.835681
$746$	−1.47207e7	−0.968458
$747$	−964373.	−0.0632330
$748$	−1564.46	−0.000102238 0
$749$	2.14806e6	0.139908
$750$	−6.78922e6	−0.440724
$751$	−1.50076e7	−0.970980	−0.485490	−	0.874242i	$-0.661359\pi$
$751$	−1.50076e7	−0.970980	−0.485490	+	0.874242i	$0.661359\pi$
$752$	4.29874e6	0.277202
$753$	−1.34895e7	−0.866980
$754$	4.25825e6	0.272774
$755$	5.91262e6	0.377496
$756$	−822939.	−0.0523677
$757$	5.65482e6	0.358657	0.179328	−	0.983789i	$-0.442608\pi$
$757$	5.65482e6	0.358657	0.179328	+	0.983789i	$0.442608\pi$
$758$	1.34234e7	0.848576
$759$	816376.	0.0514382
$760$	−5.95762e6	−0.374144
$761$	1.90760e7	1.19406	0.597030	−	0.802219i	$-0.296347\pi$
$761$	1.90760e7	1.19406	0.597030	+	0.802219i	$0.296347\pi$
$762$	1.25880e7	0.785358
$763$	2.58904e6	0.161001
$764$	1.32396e6	0.0820621
$765$	2662.19	0.000164470 0
$766$	−1.54613e7	−0.952079
$767$	−198378.	−0.0121760
$768$	9.85336e6	0.602811
$769$	2.03557e7	1.24128	0.620639	−	0.784096i	$-0.286873\pi$
$769$	2.03557e7	1.24128	0.620639	+	0.784096i	$0.286873\pi$
$770$	−1.44167e6	−0.0876269
$771$	4.60925e6	0.279250
$772$	−9.69845e6	−0.585678
$773$	−9.29224e6	−0.559334	−0.279667	−	0.960097i	$-0.590224\pi$
$773$	−9.29224e6	−0.559334	−0.279667	+	0.960097i	$0.590224\pi$
$774$	−6.14771e6	−0.368860
$775$	2.53405e6	0.151552
$776$	2.68180e7	1.59872
$777$	−1.09185e7	−0.648800
$778$	−4.18981e6	−0.248168
$779$	6.23695e6	0.368238
$780$	−846237.	−0.0498030
$781$	4.53909e6	0.266281
$782$	−2726.53	−0.000159439 0
$783$	−4.40364e6	−0.256689
$784$	3.65777e6	0.212533
$785$	−201471.	−0.0116691
$786$	3.13509e6	0.181007
$787$	1.28703e7	0.740716	0.370358	−	0.928889i	$-0.379235\pi$
$787$	1.28703e7	0.740716	0.370358	+	0.928889i	$0.379235\pi$
$788$	−1.06336e7	−0.610050
$789$	−1.38915e6	−0.0794431
$790$	9.68067e6	0.551871
$791$	−1.28912e7	−0.732578
$792$	1.90288e6	0.107795
$793$	2.38137e6	0.134476
$794$	−1.52347e6	−0.0857597
$795$	7.34922e6	0.412404
$796$	−2.07897e6	−0.116296
$797$	8.82772e6	0.492269	0.246135	−	0.969236i	$-0.420839\pi$
$797$	8.82772e6	0.492269	0.246135	+	0.969236i	$0.420839\pi$
$798$	−2.33728e6	−0.129928
$799$	11280.7	0.000625129 0
$800$	−8.28875e6	−0.457893
$801$	1.18541e7	0.652813
$802$	5.02756e6	0.276008
$803$	−9.73469e6	−0.532762
$804$	4.90916e6	0.267835
$805$	2.15118e6	0.117000
$806$	−1.04026e6	−0.0564033
$807$	−2.04393e7	−1.10480
$808$	−7.10890e6	−0.383066
$809$	640426.	0.0344031	0.0172016	−	0.999852i	$-0.494524\pi$
$809$	640426.	0.0344031	0.0172016	+	0.999852i	$0.494524\pi$
$810$	−1.02213e6	−0.0547385
$811$	1.30571e7	0.697099	0.348550	−	0.937290i	$-0.386674\pi$
$811$	1.30571e7	0.697099	0.348550	+	0.937290i	$0.386674\pi$
$812$	6.81905e6	0.362939
$813$	−2.74424e6	−0.145612
$814$	7.96941e6	0.421566
$815$	1.88767e7	0.995481
$816$	−2631.57	−0.000138353 0
$817$	1.49494e7	0.783555
$818$	1.30682e6	0.0682864
$819$	−1.05175e6	−0.0547901
$820$	−4.22356e6	−0.219353
$821$	3.01122e7	1.55914	0.779570	−	0.626315i	$-0.215438\pi$
$821$	3.01122e7	1.55914	0.779570	+	0.626315i	$0.215438\pi$
$822$	7.34319e6	0.379057
$823$	1.95327e7	1.00523	0.502613	−	0.864512i	$-0.332372\pi$
$823$	1.95327e7	1.00523	0.502613	+	0.864512i	$0.332372\pi$
$824$	−8.77539e6	−0.450244
$825$	−1.87003e6	−0.0956563
$826$	371039.	0.0189221
$827$	6.83832e6	0.347685	0.173842	−	0.984773i	$-0.444382\pi$
$827$	6.83832e6	0.347685	0.173842	+	0.984773i	$0.444382\pi$
$828$	−896280.	−0.0454326
$829$	7.34516e6	0.371206	0.185603	−	0.982625i	$-0.440576\pi$
$829$	7.34516e6	0.371206	0.185603	+	0.982625i	$0.440576\pi$
$830$	1.85479e6	0.0934544
$831$	7.95976e6	0.399850
$832$	5.21615e6	0.261241
$833$	9598.68	0.000479291 0
$834$	−9.83662e6	−0.489701
$835$	2.19317e7	1.08857
$836$	−1.46064e6	−0.0722813
$837$	1.07578e6	0.0530773
$838$	2.48703e7	1.22341
$839$	−3.88085e7	−1.90336	−0.951682	−	0.307084i	$-0.900647\pi$
$839$	−3.88085e7	−1.90336	−0.951682	+	0.307084i	$0.900647\pi$
$840$	5.01417e6	0.245189
$841$	1.59783e7	0.779007
$842$	−1.32789e7	−0.645480
$843$	−1.82729e7	−0.885603
$844$	1.65211e6	0.0798328
$845$	1.28496e7	0.619083
$846$	−4.33114e6	−0.208054
$847$	−1.11973e6	−0.0536298
$848$	−7.26468e6	−0.346918
$849$	−1.19125e7	−0.567197
$850$	6245.52	0.000296498 0
$851$	−1.18916e7	−0.562879
$852$	−4.98335e6	−0.235192
$853$	−1.11803e7	−0.526115	−0.263058	−	0.964780i	$-0.584731\pi$
$853$	−1.11803e7	−0.526115	−0.263058	+	0.964780i	$0.584731\pi$
$854$	−4.45402e6	−0.208981
$855$	2.48551e6	0.116279
$856$	5.45311e6	0.254367
$857$	−2.30926e7	−1.07404	−0.537020	−	0.843569i	$-0.680450\pi$
$857$	−2.30926e7	−1.07404	−0.537020	+	0.843569i	$0.680450\pi$
$858$	767671.	0.0356006
$859$	−1.28419e7	−0.593809	−0.296904	−	0.954907i	$-0.595954\pi$
$859$	−1.28419e7	−0.593809	−0.296904	+	0.954907i	$0.595954\pi$
$860$	−1.01235e7	−0.466751
$861$	−5.24927e6	−0.241319
$862$	−2.17775e7	−0.998252
$863$	−2.98309e7	−1.36345	−0.681725	−	0.731608i	$-0.738770\pi$
$863$	−2.98309e7	−1.36345	−0.681725	+	0.731608i	$0.738770\pi$
$864$	−3.51881e6	−0.160366
$865$	2.08405e6	0.0947038
$866$	2.26134e7	1.02464
$867$	1.27787e7	0.577350
$868$	−1.66585e6	−0.0750474
$869$	7.51893e6	0.337759
$870$	8.46957e6	0.379370
$871$	6.27410e6	0.280225
$872$	6.57260e6	0.292716
$873$	−1.11885e7	−0.496860
$874$	−2.54558e6	−0.112722
$875$	−1.38950e7	−0.613532
$876$	1.06875e7	0.470560
$877$	−3.85241e7	−1.69135	−0.845674	−	0.533700i	$-0.820801\pi$
$877$	−3.85241e7	−1.69135	−0.845674	+	0.533700i	$0.820801\pi$
$878$	−2.65064e7	−1.16042
$879$	2.25578e7	0.984747
$880$	−1.51546e6	−0.0659687
$881$	−3.12023e7	−1.35440	−0.677200	−	0.735799i	$-0.736807\pi$
$881$	−3.12023e7	−1.35440	−0.677200	+	0.735799i	$0.736807\pi$
$882$	−3.68534e6	−0.159517
$883$	−1.08832e7	−0.469738	−0.234869	−	0.972027i	$-0.575466\pi$
$883$	−1.08832e7	−0.469738	−0.234869	+	0.972027i	$0.575466\pi$
$884$	2195.14	9.44783e−5 0
$885$	−394570.	−0.0169342
$886$	9.39779e6	0.402199
$887$	4.34842e7	1.85576	0.927882	−	0.372875i	$-0.121628\pi$
$887$	4.34842e7	1.85576	0.927882	+	0.372875i	$0.121628\pi$
$888$	−2.77180e7	−1.17958
$889$	2.57628e7	1.09330
$890$	−2.27992e7	−0.964818
$891$	−793881.	−0.0335013
$892$	1.33851e7	0.563259
$893$	1.05320e7	0.441961
$894$	1.26086e7	0.527623
$895$	−8.07205e6	−0.336842
$896$	2.05697e6	0.0855967
$897$	−1.14548e6	−0.0475342
$898$	1.68201e7	0.696046
$899$	−8.91412e6	−0.367857
$900$	2.05306e6	0.0844881
$901$	−19063.9	−0.000782348 0
$902$	3.83144e6	0.156800
$903$	−1.25820e7	−0.513489
$904$	−3.27260e7	−1.33190
$905$	−2.55934e7	−1.03874
$906$	5.88866e6	0.238339
$907$	−9.01861e6	−0.364017	−0.182008	−	0.983297i	$-0.558260\pi$
$907$	−9.01861e6	−0.364017	−0.182008	+	0.983297i	$0.558260\pi$
$908$	2.00320e7	0.806326
$909$	2.96582e6	0.119052
$910$	2.02284e6	0.0809764
$911$	−6.69826e6	−0.267403	−0.133701	−	0.991022i	$-0.542686\pi$
$911$	−6.69826e6	−0.267403	−0.133701	+	0.991022i	$0.542686\pi$
$912$	−2.45692e6	−0.0978147
$913$	1.44061e6	0.0571964
$914$	−2.10813e7	−0.834704
$915$	4.73649e6	0.187027
$916$	5.09166e6	0.200503
$917$	6.41635e6	0.251979
$918$	2651.40	0.000103841 0
$919$	−1.01836e7	−0.397753	−0.198877	−	0.980025i	$-0.563729\pi$
$919$	−1.01836e7	−0.397753	−0.198877	+	0.980025i	$0.563729\pi$
$920$	5.46104e6	0.212719
$921$	−7.84078e6	−0.304586
$922$	−1.58275e7	−0.613178
$923$	−6.36892e6	−0.246072
$924$	1.22933e6	0.0473684
$925$	2.72394e7	1.04675
$926$	2.49296e7	0.955406
$927$	3.66108e6	0.139930
$928$	2.91576e7	1.11143
$929$	7.05588e6	0.268233	0.134116	−	0.990966i	$-0.457180\pi$
$929$	7.05588e6	0.268233	0.134116	+	0.990966i	$0.457180\pi$
$930$	−2.06906e6	−0.0784449
$931$	8.96165e6	0.338855
$932$	1.74413e7	0.657716
$933$	−1.13470e7	−0.426752
$934$	−1.36967e7	−0.513747
$935$	−3976.86	−0.000148768 0
$936$	−2.66999e6	−0.0996140
$937$	1.62634e6	0.0605150	0.0302575	−	0.999542i	$-0.490367\pi$
$937$	1.62634e6	0.0605150	0.0302575	+	0.999542i	$0.490367\pi$
$938$	−1.17348e7	−0.435482
$939$	−2.94253e6	−0.108907
$940$	−7.13213e6	−0.263269
$941$	−2.73619e7	−1.00733	−0.503665	−	0.863899i	$-0.668015\pi$
$941$	−2.73619e7	−1.00733	−0.503665	+	0.863899i	$0.668015\pi$
$942$	−200654.	−0.00736752
$943$	−5.71709e6	−0.209361
$944$	390031.	0.0142452
$945$	−2.09191e6	−0.0762014
$946$	9.18362e6	0.333646
$947$	4.28329e7	1.55204	0.776019	−	0.630709i	$-0.217236\pi$
$947$	4.28329e7	1.55204	0.776019	+	0.630709i	$0.217236\pi$
$948$	−8.25485e6	−0.298324
$949$	1.36590e7	0.492327
$950$	5.83103e6	0.209622
$951$	8.72573e6	0.312860
$952$	−13006.8	−0.000465133 0
$953$	2.80611e7	1.00086	0.500429	−	0.865777i	$-0.333176\pi$
$953$	2.80611e7	1.00086	0.500429	+	0.865777i	$0.333176\pi$
$954$	7.31943e6	0.260379
$955$	3.36551e6	0.119410
$956$	1.06808e7	0.377970
$957$	6.57827e6	0.232184
$958$	2.43690e7	0.857873
$959$	1.50287e7	0.527686
$960$	1.03748e7	0.363331
$961$	−2.64515e7	−0.923936
$962$	−1.11821e7	−0.389571
$963$	−2.27503e6	−0.0790536
$964$	−5.82032e6	−0.201723
$965$	−2.46534e7	−0.852233
$966$	2.14246e6	0.0738704
$967$	−3.20738e7	−1.10302	−0.551512	−	0.834167i	$-0.685949\pi$
$967$	−3.20738e7	−1.10302	−0.551512	+	0.834167i	$0.685949\pi$
$968$	−2.84258e6	−0.0975044
$969$	−6447.43	−0.000220586 0
$970$	2.15189e7	0.734329
$971$	4.92583e7	1.67661	0.838304	−	0.545203i	$-0.183548\pi$
$971$	4.92583e7	1.67661	0.838304	+	0.545203i	$0.183548\pi$
$972$	871583.	0.0295899
$973$	−2.01318e7	−0.681712
$974$	4.07334e6	0.137579
$975$	2.62389e6	0.0883964
$976$	−4.68201e6	−0.157329
$977$	−1.26363e7	−0.423530	−0.211765	−	0.977321i	$-0.567921\pi$
$977$	−1.26363e7	−0.423530	−0.211765	+	0.977321i	$0.567921\pi$
$978$	1.88002e7	0.628516
$979$	−1.77081e7	−0.590492
$980$	−6.06869e6	−0.201850
$981$	−2.74208e6	−0.0909720
$982$	2.46797e7	0.816697
$983$	6.52333e6	0.215321	0.107660	−	0.994188i	$-0.465664\pi$
$983$	6.52333e6	0.215321	0.107660	+	0.994188i	$0.465664\pi$
$984$	−1.33259e7	−0.438742
$985$	−2.70306e7	−0.887697
$986$	−21970.1	−0.000719681 0
$987$	−8.86419e6	−0.289632
$988$	2.04946e6	0.0667955
$989$	−1.37033e7	−0.445488
$990$	1.52688e6	0.0495128
$991$	2.28897e7	0.740382	0.370191	−	0.928956i	$-0.379292\pi$
$991$	2.28897e7	0.740382	0.370191	+	0.928956i	$0.379292\pi$
$992$	−7.12300e6	−0.229818
$993$	−1.85655e7	−0.597492
$994$	1.19122e7	0.382407
$995$	−5.28472e6	−0.169225
$996$	−1.58161e6	−0.0505185
$997$	−1.82397e7	−0.581138	−0.290569	−	0.956854i	$-0.593845\pi$
$997$	−1.82397e7	−0.581138	−0.290569	+	0.956854i	$0.593845\pi$
$998$	2.73918e7	0.870550
$999$	1.15639e7	0.366598

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.6.a.c.1.2	✓	2
3.2	odd	2		99.6.a.f.1.1		2
4.3	odd	2		528.6.a.s.1.1		2
5.4	even	2		825.6.a.e.1.1		2
11.10	odd	2		363.6.a.j.1.1		2
33.32	even	2		1089.6.a.j.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.6.a.c.1.2	✓	2	1.1	even	1	trivial
99.6.a.f.1.1		2	3.2	odd	2
363.6.a.j.1.1		2	11.10	odd	2
528.6.a.s.1.1		2	4.3	odd	2
825.6.a.e.1.1		2	5.4	even	2
1089.6.a.j.1.2		2	33.32	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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	33.a (trivial)

\(f(q)\)	\(=\)	\(q+4.15207 q^{2} -9.00000 q^{3} -14.7603 q^{4} -37.5207 q^{5} -37.3686 q^{6} -76.4793 q^{7} -194.152 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+4.15207 q^{2} -9.00000 q^{3} -14.7603 q^{4} -37.5207 q^{5} -37.3686 q^{6} -76.4793 q^{7} -194.152 q^{8} +81.0000 q^{9} -155.788 q^{10} -121.000 q^{11} +132.843 q^{12} +169.779 q^{13} -317.547 q^{14} +337.686 q^{15} -333.802 q^{16} -0.875959 q^{17} +336.317 q^{18} -817.825 q^{19} +553.818 q^{20} +688.314 q^{21} -502.400 q^{22} +749.657 q^{23} +1747.37 q^{24} -1717.20 q^{25} +704.932 q^{26} -729.000 q^{27} +1128.86 q^{28} +6040.65 q^{29} +1402.10 q^{30} -1475.69 q^{31} +4826.90 q^{32} +1089.00 q^{33} -3.63704 q^{34} +2869.56 q^{35} -1195.59 q^{36} -15862.7 q^{37} -3395.66 q^{38} -1528.01 q^{39} +7284.72 q^{40} -7626.27 q^{41} +2857.93 q^{42} -18279.5 q^{43} +1786.00 q^{44} -3039.17 q^{45} +3112.62 q^{46} -12878.1 q^{47} +3004.22 q^{48} -10957.9 q^{49} -7129.93 q^{50} +7.88363 q^{51} -2505.99 q^{52} +21763.5 q^{53} -3026.86 q^{54} +4540.00 q^{55} +14848.6 q^{56} +7360.42 q^{57} +25081.2 q^{58} -1168.45 q^{59} -4984.36 q^{60} +14026.3 q^{61} -6127.16 q^{62} -6194.83 q^{63} +30723.3 q^{64} -6370.21 q^{65} +4521.60 q^{66} +36954.6 q^{67} +12.9295 q^{68} -6746.91 q^{69} +11914.6 q^{70} -37513.1 q^{71} -15726.3 q^{72} +80452.0 q^{73} -65862.9 q^{74} +15454.8 q^{75} +12071.4 q^{76} +9254.00 q^{77} -6344.39 q^{78} -62139.9 q^{79} +12524.5 q^{80} +6561.00 q^{81} -31664.8 q^{82} -11905.8 q^{83} -10159.7 q^{84} +32.8666 q^{85} -75897.7 q^{86} -54365.9 q^{87} +23492.4 q^{88} +146348. q^{89} -12618.9 q^{90} -12984.5 q^{91} -11065.2 q^{92} +13281.2 q^{93} -53470.8 q^{94} +30685.3 q^{95} -43442.1 q^{96} -138129. q^{97} -45498.0 q^{98} -9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2q - 5q^{2} - 18q^{3} + 37q^{4} + 58q^{5} + 45q^{6} - 286q^{7} - 375q^{8} + 162q^{9} + O(q^{10}) \)	\( 2q - 5q^{2} - 18q^{3} + 37q^{4} + 58q^{5} + 45q^{6} - 286q^{7} - 375q^{8} + 162q^{9} - 1030q^{10} - 242q^{11} - 333q^{12} - 166q^{13} + 1600q^{14} - 522q^{15} - 335q^{16} - 800q^{17} - 405q^{18} - 1476q^{19} + 5498q^{20} + 2574q^{21} + 605q^{22} - 3370q^{23} + 3375q^{24} + 4282q^{25} + 3778q^{26} - 1458q^{27} - 9716q^{28} + 6600q^{29} + 9270q^{30} - 7528q^{31} + 10625q^{32} + 2178q^{33} + 7310q^{34} - 17144q^{35} + 2997q^{36} - 29916q^{37} + 2628q^{38} + 1494q^{39} - 9990q^{40} - 5780q^{41} - 14400q^{42} - 16656q^{43} - 4477q^{44} + 4698q^{45} + 40816q^{46} + 7850q^{47} + 3015q^{48} + 16134q^{49} - 62035q^{50} + 7200q^{51} - 19886q^{52} + 14178q^{53} + 3645q^{54} - 7018q^{55} + 52740q^{56} + 13284q^{57} + 19962q^{58} + 17300q^{59} - 49482q^{60} - 2946q^{61} + 49264q^{62} - 23166q^{63} - 22303q^{64} - 38444q^{65} - 5445q^{66} + 31336q^{67} - 41350q^{68} + 30330q^{69} + 195080q^{70} - 33810q^{71} - 30375q^{72} + 60644q^{73} + 62754q^{74} - 38538q^{75} - 21996q^{76} + 34606q^{77} - 34002q^{78} + 1870q^{79} + 12410q^{80} + 13122q^{81} - 48562q^{82} - 58296q^{83} + 87444q^{84} - 76300q^{85} - 90756q^{86} - 59400q^{87} + 45375q^{88} + 92388q^{89} - 83430q^{90} + 57368q^{91} - 224300q^{92} + 67752q^{93} - 243176q^{94} - 32184q^{95} - 95625q^{96} + 7120q^{97} - 293445q^{98} - 19602q^{99} + O(q^{100}) \)

Introduction

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