LMFDB - Embedded newform 177.6.a.b.1.10

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			1.10
Root			$-7.32600$ of defining polynomial
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q+7.32600 q^{2} -9.00000 q^{3} +21.6702 q^{4} +46.7845 q^{5} -65.9340 q^{6} -85.8026 q^{7} -75.6759 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+7.32600 q^{2} -9.00000 q^{3} +21.6702 q^{4} +46.7845 q^{5} -65.9340 q^{6} -85.8026 q^{7} -75.6759 q^{8} +81.0000 q^{9} +342.743 q^{10} -408.472 q^{11} -195.032 q^{12} +27.9269 q^{13} -628.589 q^{14} -421.061 q^{15} -1247.85 q^{16} +1587.94 q^{17} +593.406 q^{18} -2204.29 q^{19} +1013.83 q^{20} +772.223 q^{21} -2992.47 q^{22} -3968.63 q^{23} +681.083 q^{24} -936.208 q^{25} +204.593 q^{26} -729.000 q^{27} -1859.36 q^{28} -2905.16 q^{29} -3084.69 q^{30} +4857.43 q^{31} -6720.11 q^{32} +3676.25 q^{33} +11633.3 q^{34} -4014.23 q^{35} +1755.29 q^{36} +2836.94 q^{37} -16148.6 q^{38} -251.342 q^{39} -3540.46 q^{40} +3698.67 q^{41} +5657.30 q^{42} -8798.36 q^{43} -8851.69 q^{44} +3789.55 q^{45} -29074.2 q^{46} -21002.5 q^{47} +11230.6 q^{48} -9444.92 q^{49} -6858.66 q^{50} -14291.5 q^{51} +605.183 q^{52} -11032.7 q^{53} -5340.65 q^{54} -19110.2 q^{55} +6493.18 q^{56} +19838.6 q^{57} -21283.2 q^{58} -3481.00 q^{59} -9124.48 q^{60} +45308.5 q^{61} +35585.5 q^{62} -6950.01 q^{63} -9300.32 q^{64} +1306.55 q^{65} +26932.2 q^{66} -40826.6 q^{67} +34411.1 q^{68} +35717.7 q^{69} -29408.2 q^{70} -27052.4 q^{71} -6129.75 q^{72} +70459.2 q^{73} +20783.4 q^{74} +8425.88 q^{75} -47767.4 q^{76} +35048.0 q^{77} -1841.33 q^{78} +71673.4 q^{79} -58380.0 q^{80} +6561.00 q^{81} +27096.4 q^{82} +93280.1 q^{83} +16734.2 q^{84} +74291.2 q^{85} -64456.8 q^{86} +26146.4 q^{87} +30911.5 q^{88} -116570. q^{89} +27762.2 q^{90} -2396.20 q^{91} -86001.2 q^{92} -43716.9 q^{93} -153864. q^{94} -103127. q^{95} +60481.0 q^{96} +91107.3 q^{97} -69193.5 q^{98} -33086.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	7.32600	1.29507	0.647533	−	0.762038i	$-0.275801\pi$
$2$	7.32600	1.29507	0.647533	+	0.762038i	$0.275801\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	21.6702	0.677195
$5$	46.7845	0.836907	0.418453	−	0.908238i	$-0.362572\pi$
$5$	46.7845	0.836907	0.418453	+	0.908238i	$0.362572\pi$
$6$	−65.9340	−0.747706
$7$	−85.8026	−0.661843	−0.330922	−	0.943658i	$-0.607360\pi$
$7$	−85.8026	−0.661843	−0.330922	+	0.943658i	$0.607360\pi$
$8$	−75.6759	−0.418054
$9$	81.0000	0.333333
$10$	342.743	1.08385
$11$	−408.472	−1.01784	−0.508921	−	0.860813i	$-0.669956\pi$
$11$	−408.472	−1.01784	−0.508921	+	0.860813i	$0.669956\pi$
$12$	−195.032	−0.390979
$13$	27.9269	0.0458316	0.0229158	−	0.999737i	$-0.492705\pi$
$13$	27.9269	0.0458316	0.0229158	+	0.999737i	$0.492705\pi$
$14$	−628.589	−0.857130
$15$	−421.061	−0.483188
$16$	−1247.85	−1.21860
$17$	1587.94	1.33264	0.666320	−	0.745666i	$-0.267869\pi$
$17$	1587.94	1.33264	0.666320	+	0.745666i	$0.267869\pi$
$18$	593.406	0.431688
$19$	−2204.29	−1.40083	−0.700413	−	0.713738i	$-0.747001\pi$
$19$	−2204.29	−1.40083	−0.700413	+	0.713738i	$0.747001\pi$
$20$	1013.83	0.566749
$21$	772.223	0.382115
$22$	−2992.47	−1.31817
$23$	−3968.63	−1.56430	−0.782152	−	0.623087i	$-0.785878\pi$
$23$	−3968.63	−1.56430	−0.782152	+	0.623087i	$0.785878\pi$
$24$	681.083	0.241364
$25$	−936.208	−0.299587
$26$	204.593	0.0593549
$27$	−729.000	−0.192450
$28$	−1859.36	−0.448197
$29$	−2905.16	−0.641468	−0.320734	−	0.947169i	$-0.603930\pi$
$29$	−2905.16	−0.641468	−0.320734	+	0.947169i	$0.603930\pi$
$30$	−3084.69	−0.625761
$31$	4857.43	0.907826	0.453913	−	0.891046i	$-0.350028\pi$
$31$	4857.43	0.907826	0.453913	+	0.891046i	$0.350028\pi$
$32$	−6720.11	−1.16012
$33$	3676.25	0.587652
$34$	11633.3	1.72586
$35$	−4014.23	−0.553901
$36$	1755.29	0.225732
$37$	2836.94	0.340679	0.170340	−	0.985385i	$-0.445514\pi$
$37$	2836.94	0.340679	0.170340	+	0.985385i	$0.445514\pi$
$38$	−16148.6	−1.81416
$39$	−251.342	−0.0264609
$40$	−3540.46	−0.349872
$41$	3698.67	0.343625	0.171813	−	0.985130i	$-0.445038\pi$
$41$	3698.67	0.343625	0.171813	+	0.985130i	$0.445038\pi$
$42$	5657.30	0.494864
$43$	−8798.36	−0.725656	−0.362828	−	0.931856i	$-0.618189\pi$
$43$	−8798.36	−0.725656	−0.362828	+	0.931856i	$0.618189\pi$
$44$	−8851.69	−0.689278
$45$	3789.55	0.278969
$46$	−29074.2	−2.02588
$47$	−21002.5	−1.38684	−0.693421	−	0.720533i	$-0.743897\pi$
$47$	−21002.5	−1.38684	−0.693421	+	0.720533i	$0.743897\pi$
$48$	11230.6	0.703560
$49$	−9444.92	−0.561963
$50$	−6858.66	−0.387984
$51$	−14291.5	−0.769400
$52$	605.183	0.0310369
$53$	−11032.7	−0.539499	−0.269750	−	0.962930i	$-0.586941\pi$
$53$	−11032.7	−0.539499	−0.269750	+	0.962930i	$0.586941\pi$
$54$	−5340.65	−0.249235
$55$	−19110.2	−0.851840
$56$	6493.18	0.276686
$57$	19838.6	0.808768
$58$	−21283.2	−0.830743
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	−9124.48	−0.327213
$61$	45308.5	1.55903	0.779516	−	0.626382i	$-0.215465\pi$
$61$	45308.5	1.55903	0.779516	+	0.626382i	$0.215465\pi$
$62$	35585.5	1.17569
$63$	−6950.01	−0.220614
$64$	−9300.32	−0.283823
$65$	1306.55	0.0383568
$66$	26932.2	0.761048
$67$	−40826.6	−1.11111	−0.555553	−	0.831481i	$-0.687494\pi$
$67$	−40826.6	−1.11111	−0.555553	+	0.831481i	$0.687494\pi$
$68$	34411.1	0.902456
$69$	35717.7	0.903152
$70$	−29408.2	−0.717338
$71$	−27052.4	−0.636884	−0.318442	−	0.947942i	$-0.603160\pi$
$71$	−27052.4	−0.636884	−0.318442	+	0.947942i	$0.603160\pi$
$72$	−6129.75	−0.139351
$73$	70459.2	1.54750	0.773749	−	0.633492i	$-0.218379\pi$
$73$	70459.2	1.54750	0.773749	+	0.633492i	$0.218379\pi$
$74$	20783.4	0.441202
$75$	8425.88	0.172966
$76$	−47767.4	−0.948632
$77$	35048.0	0.673653
$78$	−1841.33	−0.0342686
$79$	71673.4	1.29208	0.646042	−	0.763302i	$-0.276423\pi$
$79$	71673.4	1.29208	0.646042	+	0.763302i	$0.276423\pi$
$80$	−58380.0	−1.01986
$81$	6561.00	0.111111
$82$	27096.4	0.445018
$83$	93280.1	1.48626	0.743128	−	0.669149i	$-0.233341\pi$
$83$	93280.1	1.48626	0.743128	+	0.669149i	$0.233341\pi$
$84$	16734.2	0.258766
$85$	74291.2	1.11530
$86$	−64456.8	−0.939772
$87$	26146.4	0.370352
$88$	30911.5	0.425513
$89$	−116570.	−1.55996	−0.779978	−	0.625806i	$-0.784770\pi$
$89$	−116570.	−1.55996	−0.779978	+	0.625806i	$0.784770\pi$
$90$	27762.2	0.361283
$91$	−2396.20	−0.0303333
$92$	−86001.2	−1.05934
$93$	−43716.9	−0.524134
$94$	−153864.	−1.79605
$95$	−103127.	−1.17236
$96$	60481.0	0.669793
$97$	91107.3	0.983159	0.491579	−	0.870833i	$-0.336420\pi$
$97$	91107.3	0.983159	0.491579	+	0.870833i	$0.336420\pi$
$98$	−69193.5	−0.727780
$99$	−33086.2	−0.339281
$100$	−20287.9	−0.202879
$101$	121110.	1.18135	0.590674	−	0.806910i	$-0.298862\pi$
$101$	121110.	1.18135	0.590674	+	0.806910i	$0.298862\pi$
$102$	−104699.	−0.996423
$103$	99956.2	0.928360	0.464180	−	0.885741i	$-0.346349\pi$
$103$	99956.2	0.928360	0.464180	+	0.885741i	$0.346349\pi$
$104$	−2113.39	−0.0191601
$105$	36128.1	0.319795
$106$	−80825.3	−0.698687
$107$	191304.	1.61534	0.807669	−	0.589636i	$-0.200729\pi$
$107$	191304.	1.61534	0.807669	+	0.589636i	$0.200729\pi$
$108$	−15797.6	−0.130326
$109$	−142907.	−1.15209	−0.576046	−	0.817417i	$-0.695405\pi$
$109$	−142907.	−1.15209	−0.576046	+	0.817417i	$0.695405\pi$
$110$	−140001.	−1.10319
$111$	−25532.4	−0.196691
$112$	107069.	0.806524
$113$	−5623.98	−0.0414332	−0.0207166	−	0.999785i	$-0.506595\pi$
$113$	−5623.98	−0.0414332	−0.0207166	+	0.999785i	$0.506595\pi$
$114$	145337.	1.04741
$115$	−185671.	−1.30918
$116$	−62955.5	−0.434399
$117$	2262.08	0.0152772
$118$	−25501.8	−0.168603
$119$	−136250.	−0.881999
$120$	31864.1	0.201999
$121$	5798.53	0.0360043
$122$	331930.	2.01905
$123$	−33288.0	−0.198392
$124$	105262.	0.614775
$125$	−190002.	−1.08763
$126$	−50915.7	−0.285710
$127$	−128360.	−0.706190	−0.353095	−	0.935587i	$-0.614871\pi$
$127$	−128360.	−0.706190	−0.353095	+	0.935587i	$0.614871\pi$
$128$	146909.	0.792546
$129$	79185.2	0.418958
$130$	9571.77	0.0496745
$131$	175357.	0.892783	0.446391	−	0.894838i	$-0.352709\pi$
$131$	175357.	0.892783	0.446391	+	0.894838i	$0.352709\pi$
$132$	79665.2	0.397955
$133$	189134.	0.927128
$134$	−299095.	−1.43896
$135$	−34105.9	−0.161063
$136$	−120169.	−0.557115
$137$	−204387.	−0.930360	−0.465180	−	0.885216i	$-0.654010\pi$
$137$	−204387.	−0.930360	−0.465180	+	0.885216i	$0.654010\pi$
$138$	261668.	1.16964
$139$	2129.04	0.00934644	0.00467322	−	0.999989i	$-0.498512\pi$
$139$	2129.04	0.00934644	0.00467322	+	0.999989i	$0.498512\pi$
$140$	−86989.3	−0.375099
$141$	189023.	0.800694
$142$	−198186.	−0.824807
$143$	−11407.4	−0.0466493
$144$	−101076.	−0.406201
$145$	−135916.	−0.536849
$146$	516184.	2.00411
$147$	85004.3	0.324450
$148$	61477.1	0.230706
$149$	−1847.03	−0.00681567	−0.00340784	−	0.999994i	$-0.501085\pi$
$149$	−1847.03	−0.00681567	−0.00340784	+	0.999994i	$0.501085\pi$
$150$	61727.9	0.224003
$151$	−67707.1	−0.241653	−0.120826	−	0.992674i	$-0.538554\pi$
$151$	−67707.1	−0.241653	−0.120826	+	0.992674i	$0.538554\pi$
$152$	166811.	0.585621
$153$	128623.	0.444213
$154$	256761.	0.872424
$155$	227253.	0.759766
$156$	−5446.65	−0.0179192
$157$	−208769.	−0.675953	−0.337976	−	0.941155i	$-0.609742\pi$
$157$	−208769.	−0.675953	−0.337976	+	0.941155i	$0.609742\pi$
$158$	525079.	1.67333
$159$	99294.0	0.311480
$160$	−314397.	−0.970909
$161$	340519.	1.03532
$162$	48065.9	0.143896
$163$	19124.2	0.0563787	0.0281894	−	0.999603i	$-0.491026\pi$
$163$	19124.2	0.0563787	0.0281894	+	0.999603i	$0.491026\pi$
$164$	80150.9	0.232701
$165$	171992.	0.491810
$166$	683370.	1.92480
$167$	−313422.	−0.869638	−0.434819	−	0.900518i	$-0.643188\pi$
$167$	−313422.	−0.869638	−0.434819	+	0.900518i	$0.643188\pi$
$168$	−58438.7	−0.159745
$169$	−370513.	−0.997899
$170$	544257.	1.44438
$171$	−178547.	−0.466942
$172$	−190662.	−0.491410
$173$	620202.	1.57550	0.787750	−	0.615996i	$-0.211246\pi$
$173$	620202.	1.57550	0.787750	+	0.615996i	$0.211246\pi$
$174$	191549.	0.479630
$175$	80329.1	0.198279
$176$	509711.	1.24035
$177$	31329.0	0.0751646
$178$	−853993.	−2.02025
$179$	−402042.	−0.937861	−0.468931	−	0.883235i	$-0.655361\pi$
$179$	−402042.	−0.937861	−0.468931	+	0.883235i	$0.655361\pi$
$180$	82120.3	0.188916
$181$	326602.	0.741007	0.370503	−	0.928831i	$-0.379185\pi$
$181$	326602.	0.741007	0.370503	+	0.928831i	$0.379185\pi$
$182$	−17554.6	−0.0392836
$183$	−407776.	−0.900107
$184$	300330.	0.653964
$185$	132725.	0.285117
$186$	−320270.	−0.678787
$187$	−648631.	−1.35642
$188$	−455130.	−0.939162
$189$	62550.1	0.127372
$190$	−755505.	−1.51828
$191$	322656.	0.639964	0.319982	−	0.947424i	$-0.396323\pi$
$191$	322656.	0.639964	0.319982	+	0.947424i	$0.396323\pi$
$192$	83702.9	0.163865
$193$	−234977.	−0.454080	−0.227040	−	0.973885i	$-0.572905\pi$
$193$	−234977.	−0.454080	−0.227040	+	0.973885i	$0.572905\pi$
$194$	667451.	1.27325
$195$	−11758.9	−0.0221453
$196$	−204674.	−0.380559
$197$	−658997.	−1.20981	−0.604906	−	0.796297i	$-0.706789\pi$
$197$	−658997.	−1.20981	−0.604906	+	0.796297i	$0.706789\pi$
$198$	−242390.	−0.439391
$199$	−339500.	−0.607725	−0.303863	−	0.952716i	$-0.598276\pi$
$199$	−339500.	−0.607725	−0.303863	+	0.952716i	$0.598276\pi$
$200$	70848.4	0.125243
$201$	367439.	0.641498
$202$	887254.	1.52992
$203$	249270.	0.424551
$204$	−309700.	−0.521033
$205$	173040.	0.287583
$206$	732279.	1.20229
$207$	−321459.	−0.521435
$208$	−34848.6	−0.0558505
$209$	900390.	1.42582
$210$	264674.	0.414156
$211$	−862627.	−1.33388	−0.666940	−	0.745111i	$-0.732396\pi$
$211$	−862627.	−1.33388	−0.666940	+	0.745111i	$0.732396\pi$
$212$	−239080.	−0.365346
$213$	243472.	0.367705
$214$	1.40149e6	2.09197
$215$	−411627.	−0.607306
$216$	55167.7	0.0804545
$217$	−416780.	−0.600839
$218$	−1.04694e6	−1.49203
$219$	−634132.	−0.893449
$220$	−414122.	−0.576861
$221$	44346.4	0.0610770
$222$	−187051.	−0.254728
$223$	−1.00055e6	−1.34734	−0.673671	−	0.739032i	$-0.735283\pi$
$223$	−1.00055e6	−1.34734	−0.673671	+	0.739032i	$0.735283\pi$
$224$	576602.	0.767815
$225$	−75832.9	−0.0998622
$226$	−41201.3	−0.0536587
$227$	−39203.6	−0.0504965	−0.0252482	−	0.999681i	$-0.508038\pi$
$227$	−39203.6	−0.0504965	−0.0252482	+	0.999681i	$0.508038\pi$
$228$	429907.	0.547693
$229$	−1.53017e6	−1.92819	−0.964096	−	0.265555i	$-0.914445\pi$
$229$	−1.53017e6	−1.92819	−0.964096	+	0.265555i	$0.914445\pi$
$230$	−1.36022e6	−1.69547
$231$	−315432.	−0.388933
$232$	219850.	0.268168
$233$	−3398.03	−0.00410050	−0.00205025	−	0.999998i	$-0.500653\pi$
$233$	−3398.03	−0.00410050	−0.00205025	+	0.999998i	$0.500653\pi$
$234$	16572.0	0.0197850
$235$	−982593.	−1.16066
$236$	−75434.1	−0.0881632
$237$	−645061.	−0.745984
$238$	−998164.	−1.14225
$239$	514521.	0.582651	0.291326	−	0.956624i	$-0.405904\pi$
$239$	514521.	0.582651	0.291326	+	0.956624i	$0.405904\pi$
$240$	525420.	0.588814
$241$	−1.54065e6	−1.70868	−0.854342	−	0.519711i	$-0.826040\pi$
$241$	−1.54065e6	−1.70868	−0.854342	+	0.519711i	$0.826040\pi$
$242$	42480.0	0.0466279
$243$	−59049.0	−0.0641500
$244$	981845.	1.05577
$245$	−441876.	−0.470311
$246$	−243868.	−0.256931
$247$	−61559.0	−0.0642021
$248$	−367591.	−0.379520
$249$	−839521.	−0.858091
$250$	−1.39195e6	−1.40856
$251$	1.00599e6	1.00789	0.503943	−	0.863737i	$-0.331882\pi$
$251$	1.00599e6	1.00789	0.503943	+	0.863737i	$0.331882\pi$
$252$	−150608.	−0.149399
$253$	1.62108e6	1.59222
$254$	−940368.	−0.914563
$255$	−668621.	−0.643916
$256$	1.37387e6	1.31022
$257$	−821444.	−0.775792	−0.387896	−	0.921703i	$-0.626798\pi$
$257$	−821444.	−0.775792	−0.387896	+	0.921703i	$0.626798\pi$
$258$	580111.	0.542577
$259$	−243417.	−0.225476
$260$	28313.2	0.0259750
$261$	−235318.	−0.213823
$262$	1.28467e6	1.15621
$263$	336622.	0.300091	0.150045	−	0.988679i	$-0.452058\pi$
$263$	336622.	0.300091	0.150045	+	0.988679i	$0.452058\pi$
$264$	−278203.	−0.245670
$265$	−516158.	−0.451511
$266$	1.38559e6	1.20069
$267$	1.04913e6	0.900642
$268$	−884721.	−0.752436
$269$	−2.12624e6	−1.79156	−0.895781	−	0.444496i	$-0.853383\pi$
$269$	−2.12624e6	−1.79156	−0.895781	+	0.444496i	$0.853383\pi$
$270$	−249860.	−0.208587
$271$	−781161.	−0.646126	−0.323063	−	0.946377i	$-0.604713\pi$
$271$	−781161.	−0.646126	−0.323063	+	0.946377i	$0.604713\pi$
$272$	−1.98151e6	−1.62396
$273$	21565.8	0.0175129
$274$	−1.49734e6	−1.20488
$275$	382415.	0.304932
$276$	774011.	0.611609
$277$	−22946.2	−0.0179685	−0.00898426	−	0.999960i	$-0.502860\pi$
$277$	−22946.2	−0.0179685	−0.00898426	+	0.999960i	$0.502860\pi$
$278$	15597.3	0.0121043
$279$	393452.	0.302609
$280$	303781.	0.231561
$281$	1.46132e6	1.10403	0.552015	−	0.833834i	$-0.313859\pi$
$281$	1.46132e6	1.10403	0.552015	+	0.833834i	$0.313859\pi$
$282$	1.38478e6	1.03695
$283$	1.25766e6	0.933466	0.466733	−	0.884398i	$-0.345431\pi$
$283$	1.25766e6	0.933466	0.466733	+	0.884398i	$0.345431\pi$
$284$	−586233.	−0.431295
$285$	928139.	0.676863
$286$	−83570.4	−0.0604140
$287$	−317355.	−0.227426
$288$	−544329.	−0.386705
$289$	1.10171e6	0.775928
$290$	−995724.	−0.695255
$291$	−819965.	−0.567627
$292$	1.52687e6	1.04796
$293$	1.57391e6	1.07105	0.535525	−	0.844519i	$-0.320114\pi$
$293$	1.57391e6	1.07105	0.535525	+	0.844519i	$0.320114\pi$
$294$	622741.	0.420184
$295$	−162857.	−0.108956
$296$	−214688.	−0.142422
$297$	297776.	0.195884
$298$	−13531.4	−0.00882675
$299$	−110832.	−0.0716945
$300$	182591.	0.117132
$301$	754922.	0.480270
$302$	−496022.	−0.312956
$303$	−1.08999e6	−0.682051
$304$	2.75062e6	1.70705
$305$	2.11974e6	1.30476
$306$	942295.	0.575285
$307$	1.48288e6	0.897969	0.448985	−	0.893539i	$-0.351786\pi$
$307$	1.48288e6	0.897969	0.448985	+	0.893539i	$0.351786\pi$
$308$	759497.	0.456194
$309$	−899606.	−0.535989
$310$	1.66485e6	0.983947
$311$	762503.	0.447034	0.223517	−	0.974700i	$-0.428246\pi$
$311$	762503.	0.447034	0.223517	+	0.974700i	$0.428246\pi$
$312$	19020.6	0.0110621
$313$	−1.35503e6	−0.781786	−0.390893	−	0.920436i	$-0.627834\pi$
$313$	−1.35503e6	−0.781786	−0.390893	+	0.920436i	$0.627834\pi$
$314$	−1.52944e6	−0.875403
$315$	−325153.	−0.184634
$316$	1.55318e6	0.874992
$317$	−897102.	−0.501411	−0.250705	−	0.968063i	$-0.580663\pi$
$317$	−897102.	−0.501411	−0.250705	+	0.968063i	$0.580663\pi$
$318$	727428.	0.403387
$319$	1.18668e6	0.652914
$320$	−435111.	−0.237534
$321$	−1.72173e6	−0.932616
$322$	2.49464e6	1.34081
$323$	−3.50028e6	−1.86680
$324$	142178.	0.0752438
$325$	−26145.4	−0.0137305
$326$	140104.	0.0730141
$327$	1.28616e6	0.665160
$328$	−279900.	−0.143654
$329$	1.80207e6	0.917872
$330$	1.26001e6	0.636926
$331$	−1.45033e6	−0.727606	−0.363803	−	0.931476i	$-0.618522\pi$
$331$	−1.45033e6	−0.727606	−0.363803	+	0.931476i	$0.618522\pi$
$332$	2.02140e6	1.00648
$333$	229792.	0.113560
$334$	−2.29613e6	−1.12624
$335$	−1.91005e6	−0.929893
$336$	−963617.	−0.465647
$337$	−2.03832e6	−0.977680	−0.488840	−	0.872373i	$-0.662580\pi$
$337$	−2.03832e6	−0.977680	−0.488840	+	0.872373i	$0.662580\pi$
$338$	−2.71438e6	−1.29235
$339$	50615.9	0.0239214
$340$	1.60991e6	0.755272
$341$	−1.98413e6	−0.924024
$342$	−1.30804e6	−0.604721
$343$	2.25248e6	1.03378
$344$	665824.	0.303363
$345$	1.67104e6	0.755854
$346$	4.54360e6	2.04037
$347$	2.94852e6	1.31456	0.657280	−	0.753646i	$-0.271707\pi$
$347$	2.94852e6	1.31456	0.657280	+	0.753646i	$0.271707\pi$
$348$	566599.	0.250800
$349$	4.25738e6	1.87102	0.935511	−	0.353299i	$-0.114940\pi$
$349$	4.25738e6	1.87102	0.935511	+	0.353299i	$0.114940\pi$
$350$	588491.	0.256785
$351$	−20358.7	−0.00882029
$352$	2.74498e6	1.18082
$353$	−2.89165e6	−1.23512	−0.617560	−	0.786524i	$-0.711879\pi$
$353$	−2.89165e6	−1.23512	−0.617560	+	0.786524i	$0.711879\pi$
$354$	229516.	0.0973431
$355$	−1.26564e6	−0.533013
$356$	−2.52610e6	−1.05639
$357$	1.22625e6	0.509222
$358$	−2.94536e6	−1.21459
$359$	566386.	0.231940	0.115970	−	0.993253i	$-0.463002\pi$
$359$	566386.	0.231940	0.115970	+	0.993253i	$0.463002\pi$
$360$	−286777.	−0.116624
$361$	2.38279e6	0.962315
$362$	2.39268e6	0.959652
$363$	−52186.8	−0.0207871
$364$	−51926.2	−0.0205416
$365$	3.29640e6	1.29511
$366$	−2.98737e6	−1.16570
$367$	314932.	0.122054	0.0610270	−	0.998136i	$-0.480562\pi$
$367$	314932.	0.122054	0.0610270	+	0.998136i	$0.480562\pi$
$368$	4.95225e6	1.90626
$369$	299592.	0.114542
$370$	972341.	0.369245
$371$	946631.	0.357064
$372$	−947355.	−0.354940
$373$	−1.61192e6	−0.599891	−0.299946	−	0.953956i	$-0.596969\pi$
$373$	−1.61192e6	−0.599891	−0.299946	+	0.953956i	$0.596969\pi$
$374$	−4.75187e6	−1.75665
$375$	1.71002e6	0.627945
$376$	1.58938e6	0.579775
$377$	−81132.2	−0.0293995
$378$	458242.	0.164955
$379$	−3.46978e6	−1.24081	−0.620404	−	0.784283i	$-0.713031\pi$
$379$	−3.46978e6	−1.24081	−0.620404	+	0.784283i	$0.713031\pi$
$380$	−2.23478e6	−0.793917
$381$	1.15524e6	0.407719
$382$	2.36377e6	0.828796
$383$	−632278.	−0.220248	−0.110124	−	0.993918i	$-0.535125\pi$
$383$	−632278.	−0.220248	−0.110124	+	0.993918i	$0.535125\pi$
$384$	−1.32218e6	−0.457576
$385$	1.63970e6	0.563784
$386$	−1.72144e6	−0.588063
$387$	−712667.	−0.241885
$388$	1.97432e6	0.665790
$389$	−1.99683e6	−0.669063	−0.334531	−	0.942385i	$-0.608578\pi$
$389$	−1.99683e6	−0.669063	−0.334531	+	0.942385i	$0.608578\pi$
$390$	−86145.9	−0.0286796
$391$	−6.30196e6	−2.08465
$392$	714753.	0.234931
$393$	−1.57822e6	−0.515448
$394$	−4.82781e6	−1.56679
$395$	3.35321e6	1.08135
$396$	−716987.	−0.229759
$397$	−3.53468e6	−1.12557	−0.562787	−	0.826602i	$-0.690271\pi$
$397$	−3.53468e6	−1.12557	−0.562787	+	0.826602i	$0.690271\pi$
$398$	−2.48718e6	−0.787044
$399$	−1.70220e6	−0.535277
$400$	1.16825e6	0.365077
$401$	3.76927e6	1.17057	0.585283	−	0.810829i	$-0.300983\pi$
$401$	3.76927e6	1.17057	0.585283	+	0.810829i	$0.300983\pi$
$402$	2.69186e6	0.830782
$403$	135653.	0.0416071
$404$	2.62449e6	0.800002
$405$	306953.	0.0929897
$406$	1.82615e6	0.549822
$407$	−1.15881e6	−0.346758
$408$	1.08152e6	0.321651
$409$	−108345.	−0.0320259	−0.0160130	−	0.999872i	$-0.505097\pi$
$409$	−108345.	−0.0320259	−0.0160130	+	0.999872i	$0.505097\pi$
$410$	1.26769e6	0.372438
$411$	1.83948e6	0.537144
$412$	2.16607e6	0.628681
$413$	298679.	0.0861647
$414$	−2.35501e6	−0.675292
$415$	4.36407e6	1.24386
$416$	−187672.	−0.0531699
$417$	−19161.3	−0.00539617
$418$	6.59626e6	1.84653
$419$	−4.59866e6	−1.27966	−0.639832	−	0.768515i	$-0.720996\pi$
$419$	−4.59866e6	−1.27966	−0.639832	+	0.768515i	$0.720996\pi$
$420$	782904.	0.216563
$421$	5.27760e6	1.45121	0.725606	−	0.688110i	$-0.241560\pi$
$421$	5.27760e6	1.45121	0.725606	+	0.688110i	$0.241560\pi$
$422$	−6.31960e6	−1.72746
$423$	−1.70120e6	−0.462281
$424$	834907.	0.225540
$425$	−1.48665e6	−0.399241
$426$	1.78368e6	0.476203
$427$	−3.88758e6	−1.03183
$428$	4.14559e6	1.09390
$429$	102666.	0.0269330
$430$	−3.01558e6	−0.786502
$431$	−3.25854e6	−0.844948	−0.422474	−	0.906375i	$-0.638838\pi$
$431$	−3.25854e6	−0.844948	−0.422474	+	0.906375i	$0.638838\pi$
$432$	909682.	0.234520
$433$	2.53904e6	0.650803	0.325402	−	0.945576i	$-0.394501\pi$
$433$	2.53904e6	0.650803	0.325402	+	0.945576i	$0.394501\pi$
$434$	−3.05333e6	−0.778125
$435$	1.22325e6	0.309950
$436$	−3.09683e6	−0.780190
$437$	8.74801e6	2.19132
$438$	−4.64565e6	−1.15707
$439$	5.11072e6	1.26567	0.632835	−	0.774286i	$-0.281891\pi$
$439$	5.11072e6	1.26567	0.632835	+	0.774286i	$0.281891\pi$
$440$	1.44618e6	0.356115
$441$	−765039.	−0.187321
$442$	324881.	0.0790987
$443$	−2.08543e6	−0.504877	−0.252438	−	0.967613i	$-0.581233\pi$
$443$	−2.08543e6	−0.504877	−0.252438	+	0.967613i	$0.581233\pi$
$444$	−553294.	−0.133198
$445$	−5.45368e6	−1.30554
$446$	−7.33004e6	−1.74489
$447$	16623.3	0.00393503
$448$	797992.	0.187847
$449$	−2.92355e6	−0.684376	−0.342188	−	0.939632i	$-0.611168\pi$
$449$	−2.92355e6	−0.684376	−0.342188	+	0.939632i	$0.611168\pi$
$450$	−555551.	−0.129328
$451$	−1.51080e6	−0.349757
$452$	−121873.	−0.0280583
$453$	609364.	0.139518
$454$	−287205.	−0.0653962
$455$	−112105.	−0.0253862
$456$	−1.50130e6	−0.338109
$457$	−8.29298e6	−1.85746	−0.928731	−	0.370754i	$-0.879099\pi$
$457$	−8.29298e6	−1.85746	−0.928731	+	0.370754i	$0.879099\pi$
$458$	−1.12100e7	−2.49713
$459$	−1.15761e6	−0.256467
$460$	−4.02352e6	−0.886568
$461$	−2.53751e6	−0.556102	−0.278051	−	0.960566i	$-0.589688\pi$
$461$	−2.53751e6	−0.556102	−0.278051	+	0.960566i	$0.589688\pi$
$462$	−2.31085e6	−0.503694
$463$	3.55974e6	0.771731	0.385865	−	0.922555i	$-0.373903\pi$
$463$	3.55974e6	0.771731	0.385865	+	0.922555i	$0.373903\pi$
$464$	3.62520e6	0.781694
$465$	−2.04527e6	−0.438651
$466$	−24893.9	−0.00531042
$467$	6.73742e6	1.42956	0.714779	−	0.699351i	$-0.246527\pi$
$467$	6.73742e6	1.42956	0.714779	+	0.699351i	$0.246527\pi$
$468$	49019.8	0.0103456
$469$	3.50302e6	0.735378
$470$	−7.19848e6	−1.50313
$471$	1.87892e6	0.390261
$472$	263428.	0.0544260
$473$	3.59389e6	0.738604
$474$	−4.72571e6	−0.966099
$475$	2.06367e6	0.419669
$476$	−2.95256e6	−0.597285
$477$	−893646.	−0.179833
$478$	3.76938e6	0.754571
$479$	7.29265e6	1.45227	0.726134	−	0.687554i	$-0.241315\pi$
$479$	7.29265e6	1.45227	0.726134	+	0.687554i	$0.241315\pi$
$480$	2.82957e6	0.560554
$481$	79227.0	0.0156139
$482$	−1.12868e7	−2.21286
$483$	−3.06467e6	−0.597745
$484$	125655.	0.0243819
$485$	4.26241e6	0.822812
$486$	−432593.	−0.0830785
$487$	1.72557e6	0.329694	0.164847	−	0.986319i	$-0.447287\pi$
$487$	1.72557e6	0.329694	0.164847	+	0.986319i	$0.447287\pi$
$488$	−3.42876e6	−0.651760
$489$	−172118.	−0.0325503
$490$	−3.23718e6	−0.609084
$491$	8.06758e6	1.51022	0.755109	−	0.655599i	$-0.227584\pi$
$491$	8.06758e6	1.51022	0.755109	+	0.655599i	$0.227584\pi$
$492$	−721358.	−0.134350
$493$	−4.61323e6	−0.854846
$494$	−450981.	−0.0831459
$495$	−1.54792e6	−0.283947
$496$	−6.06134e6	−1.10628
$497$	2.32117e6	0.421518
$498$	−6.15033e6	−1.11128
$499$	−7.26673e6	−1.30644	−0.653218	−	0.757170i	$-0.726581\pi$
$499$	−7.26673e6	−1.30644	−0.653218	+	0.757170i	$0.726581\pi$
$500$	−4.11738e6	−0.736539
$501$	2.82080e6	0.502086
$502$	7.36991e6	1.30528
$503$	−6.90011e6	−1.21601	−0.608004	−	0.793934i	$-0.708029\pi$
$503$	−6.90011e6	−1.21601	−0.608004	+	0.793934i	$0.708029\pi$
$504$	525948.	0.0922288
$505$	5.66609e6	0.988678
$506$	1.18760e7	2.06202
$507$	3.33462e6	0.576138
$508$	−2.78160e6	−0.478228
$509$	2.10129e6	0.359495	0.179747	−	0.983713i	$-0.442472\pi$
$509$	2.10129e6	0.359495	0.179747	+	0.983713i	$0.442472\pi$
$510$	−4.89831e6	−0.833914
$511$	−6.04558e6	−1.02420
$512$	5.36385e6	0.904277
$513$	1.60693e6	0.269589
$514$	−6.01790e6	−1.00470
$515$	4.67640e6	0.776951
$516$	1.71596e6	0.283716
$517$	8.57895e6	1.41159
$518$	−1.78327e6	−0.292006
$519$	−5.58182e6	−0.909615
$520$	−98874.2	−0.0160352
$521$	5.71866e6	0.922996	0.461498	−	0.887141i	$-0.347312\pi$
$521$	5.71866e6	0.922996	0.461498	+	0.887141i	$0.347312\pi$
$522$	−1.72394e6	−0.276914
$523$	−548224.	−0.0876403	−0.0438202	−	0.999039i	$-0.513953\pi$
$523$	−548224.	−0.0876403	−0.0438202	+	0.999039i	$0.513953\pi$
$524$	3.80003e6	0.604588
$525$	−722962.	−0.114477
$526$	2.46609e6	0.388637
$527$	7.71333e6	1.20980
$528$	−4.58740e6	−0.716114
$529$	9.31370e6	1.44705
$530$	−3.78137e6	−0.584736
$531$	−281961.	−0.0433963
$532$	4.09857e6	0.627846
$533$	103292.	0.0157489
$534$	7.68594e6	1.16639
$535$	8.95005e6	1.35189
$536$	3.08959e6	0.464503
$537$	3.61838e6	0.541475
$538$	−1.55768e7	−2.32019
$539$	3.85799e6	0.571991
$540$	−739083.	−0.109071
$541$	−1.44297e6	−0.211965	−0.105982	−	0.994368i	$-0.533799\pi$
$541$	−1.44297e6	−0.211965	−0.105982	+	0.994368i	$0.533799\pi$
$542$	−5.72278e6	−0.836775
$543$	−2.93942e6	−0.427820
$544$	−1.06711e7	−1.54602
$545$	−6.68583e6	−0.964193
$546$	157991.	0.0226804
$547$	5.77418e6	0.825130	0.412565	−	0.910928i	$-0.364633\pi$
$547$	5.77418e6	0.825130	0.412565	+	0.910928i	$0.364633\pi$
$548$	−4.42910e6	−0.630035
$549$	3.66999e6	0.519677
$550$	2.80157e6	0.394907
$551$	6.40381e6	0.898585
$552$	−2.70297e6	−0.377566
$553$	−6.14976e6	−0.855156
$554$	−168104.	−0.0232704
$555$	−1.19452e6	−0.164612
$556$	46136.7	0.00632936
$557$	−3.90827e6	−0.533761	−0.266880	−	0.963730i	$-0.585993\pi$
$557$	−3.90827e6	−0.533761	−0.266880	+	0.963730i	$0.585993\pi$
$558$	2.88243e6	0.391898
$559$	−245711.	−0.0332579
$560$	5.00915e6	0.674985
$561$	5.83768e6	0.783128
$562$	1.07057e7	1.42979
$563$	−8.26195e6	−1.09853	−0.549264	−	0.835649i	$-0.685092\pi$
$563$	−8.26195e6	−1.09853	−0.549264	+	0.835649i	$0.685092\pi$
$564$	4.09617e6	0.542225
$565$	−263115.	−0.0346757
$566$	9.21364e6	1.20890
$567$	−562951.	−0.0735381
$568$	2.04722e6	0.266252
$569$	9.52546e6	1.23340	0.616702	−	0.787197i	$-0.288468\pi$
$569$	9.52546e6	1.23340	0.616702	+	0.787197i	$0.288468\pi$
$570$	6.79954e6	0.876582
$571$	−5.73979e6	−0.736725	−0.368363	−	0.929682i	$-0.620081\pi$
$571$	−5.73979e6	−0.736725	−0.368363	+	0.929682i	$0.620081\pi$
$572$	−247200.	−0.0315907
$573$	−2.90390e6	−0.369484
$574$	−2.32494e6	−0.294532
$575$	3.71547e6	0.468645
$576$	−753326.	−0.0946078
$577$	7.36689e6	0.921180	0.460590	−	0.887613i	$-0.347638\pi$
$577$	7.36689e6	0.921180	0.460590	+	0.887613i	$0.347638\pi$
$578$	8.07111e6	1.00488
$579$	2.11479e6	0.262163
$580$	−2.94534e6	−0.363551
$581$	−8.00367e6	−0.983669
$582$	−6.00706e6	−0.735114
$583$	4.50654e6	0.549126
$584$	−5.33206e6	−0.646938
$585$	105830.	0.0127856
$586$	1.15304e7	1.38708
$587$	−1.28494e7	−1.53918	−0.769590	−	0.638539i	$-0.779539\pi$
$587$	−1.28494e7	−1.53918	−0.769590	+	0.638539i	$0.779539\pi$
$588$	1.84206e6	0.219716
$589$	−1.07072e7	−1.27171
$590$	−1.19309e6	−0.141105
$591$	5.93098e6	0.698486
$592$	−3.54007e6	−0.415152
$593$	−1.31628e7	−1.53714	−0.768568	−	0.639768i	$-0.779031\pi$
$593$	−1.31628e7	−1.53714	−0.768568	+	0.639768i	$0.779031\pi$
$594$	2.18151e6	0.253683
$595$	−6.37437e6	−0.738151
$596$	−40025.6	−0.00461554
$597$	3.05550e6	0.350870
$598$	−811953.	−0.0928491
$599$	−9.54195e6	−1.08660	−0.543300	−	0.839538i	$-0.682825\pi$
$599$	−9.54195e6	−1.08660	−0.543300	+	0.839538i	$0.682825\pi$
$600$	−637636.	−0.0723093
$601$	−6.64300e6	−0.750201	−0.375101	−	0.926984i	$-0.622392\pi$
$601$	−6.64300e6	−0.750201	−0.375101	+	0.926984i	$0.622392\pi$
$602$	5.53056e6	0.621982
$603$	−3.30695e6	−0.370369
$604$	−1.46723e6	−0.163646
$605$	271281.	0.0301323
$606$	−7.98528e6	−0.883301
$607$	−1.26387e7	−1.39229	−0.696147	−	0.717899i	$-0.745104\pi$
$607$	−1.26387e7	−1.39229	−0.696147	+	0.717899i	$0.745104\pi$
$608$	1.48130e7	1.62512
$609$	−2.24343e6	−0.245115
$610$	1.55292e7	1.68976
$611$	−586536.	−0.0635611
$612$	2.78730e6	0.300819
$613$	−1.20014e7	−1.28997	−0.644985	−	0.764195i	$-0.723136\pi$
$613$	−1.20014e7	−1.28997	−0.644985	+	0.764195i	$0.723136\pi$
$614$	1.08636e7	1.16293
$615$	−1.55736e6	−0.166036
$616$	−2.65229e6	−0.281623
$617$	8.14931e6	0.861803	0.430901	−	0.902399i	$-0.358196\pi$
$617$	8.14931e6	0.861803	0.430901	+	0.902399i	$0.358196\pi$
$618$	−6.59051e6	−0.694141
$619$	1.19794e6	0.125663	0.0628314	−	0.998024i	$-0.479987\pi$
$619$	1.19794e6	0.125663	0.0628314	+	0.998024i	$0.479987\pi$
$620$	4.92462e6	0.514509
$621$	2.89313e6	0.301051
$622$	5.58609e6	0.578938
$623$	1.00020e7	1.03245
$624$	313637.	0.0322453
$625$	−5.96349e6	−0.610661
$626$	−9.92694e6	−1.01246
$627$	−8.10351e6	−0.823198
$628$	−4.52407e6	−0.457752
$629$	4.50490e6	0.454003
$630$	−2.38207e6	−0.239113
$631$	2.94186e6	0.294136	0.147068	−	0.989126i	$-0.453016\pi$
$631$	2.94186e6	0.294136	0.147068	+	0.989126i	$0.453016\pi$
$632$	−5.42395e6	−0.540161
$633$	7.76364e6	0.770116
$634$	−6.57217e6	−0.649360
$635$	−6.00528e6	−0.591016
$636$	2.15172e6	0.210933
$637$	−263768.	−0.0257557
$638$	8.69359e6	0.845566
$639$	−2.19125e6	−0.212295
$640$	6.87308e6	0.663287
$641$	1.94544e7	1.87014	0.935068	−	0.354469i	$-0.115339\pi$
$641$	1.94544e7	1.87014	0.935068	+	0.354469i	$0.115339\pi$
$642$	−1.26134e7	−1.20780
$643$	−1.76373e7	−1.68231	−0.841153	−	0.540797i	$-0.818123\pi$
$643$	−1.76373e7	−1.68231	−0.841153	+	0.540797i	$0.818123\pi$
$644$	7.37912e6	0.701116
$645$	3.70464e6	0.350628
$646$	−2.56431e7	−2.41762
$647$	1.72256e7	1.61776	0.808878	−	0.587976i	$-0.200075\pi$
$647$	1.72256e7	1.61776	0.808878	+	0.587976i	$0.200075\pi$
$648$	−496509.	−0.0464505
$649$	1.42189e6	0.132512
$650$	−191541.	−0.0177819
$651$	3.75102e6	0.346894
$652$	414427.	0.0381794
$653$	−4.60913e6	−0.422996	−0.211498	−	0.977378i	$-0.567834\pi$
$653$	−4.60913e6	−0.422996	−0.211498	+	0.977378i	$0.567834\pi$
$654$	9.42242e6	0.861426
$655$	8.20401e6	0.747176
$656$	−4.61537e6	−0.418743
$657$	5.70719e6	0.515833
$658$	1.32020e7	1.18870
$659$	858283.	0.0769869	0.0384935	−	0.999259i	$-0.487744\pi$
$659$	858283.	0.0769869	0.0384935	+	0.999259i	$0.487744\pi$
$660$	3.72710e6	0.333051
$661$	1.26702e7	1.12793	0.563964	−	0.825799i	$-0.309276\pi$
$661$	1.26702e7	1.12793	0.563964	+	0.825799i	$0.309276\pi$
$662$	−1.06251e7	−0.942297
$663$	−399117.	−0.0352628
$664$	−7.05905e6	−0.621336
$665$	8.84852e6	0.775920
$666$	1.68346e6	0.147067
$667$	1.15295e7	1.00345
$668$	−6.79193e6	−0.588914
$669$	9.00497e6	0.777888
$670$	−1.39930e7	−1.20427
$671$	−1.85073e7	−1.58685
$672$	−5.18942e6	−0.443298
$673$	−2.56765e6	−0.218524	−0.109262	−	0.994013i	$-0.534849\pi$
$673$	−2.56765e6	−0.218524	−0.109262	+	0.994013i	$0.534849\pi$
$674$	−1.49327e7	−1.26616
$675$	682496.	0.0576555
$676$	−8.02910e6	−0.675772
$677$	1.74857e7	1.46626	0.733131	−	0.680087i	$-0.238058\pi$
$677$	1.74857e7	1.46626	0.733131	+	0.680087i	$0.238058\pi$
$678$	370812.	0.0309798
$679$	−7.81724e6	−0.650697
$680$	−5.62205e6	−0.466254
$681$	352832.	0.0291541
$682$	−1.45357e7	−1.19667
$683$	6.06090e6	0.497147	0.248574	−	0.968613i	$-0.420038\pi$
$683$	6.06090e6	0.497147	0.248574	+	0.968613i	$0.420038\pi$
$684$	−3.86916e6	−0.316211
$685$	−9.56213e6	−0.778625
$686$	1.65017e7	1.33881
$687$	1.37715e7	1.11324
$688$	1.09790e7	0.884286
$689$	−308109.	−0.0247261
$690$	1.22420e7	0.978880
$691$	−7.50002e6	−0.597541	−0.298770	−	0.954325i	$-0.596576\pi$
$691$	−7.50002e6	−0.597541	−0.298770	+	0.954325i	$0.596576\pi$
$692$	1.34399e7	1.06692
$693$	2.83888e6	0.224551
$694$	2.16009e7	1.70244
$695$	99606.0	0.00782210
$696$	−1.97865e6	−0.154827
$697$	5.87327e6	0.457929
$698$	3.11895e7	2.42310
$699$	30582.2	0.00236743
$700$	1.74075e6	0.134274
$701$	−1.97391e7	−1.51717	−0.758583	−	0.651576i	$-0.774108\pi$
$701$	−1.97391e7	−1.51717	−0.758583	+	0.651576i	$0.774108\pi$
$702$	−149148.	−0.0114229
$703$	−6.25343e6	−0.477232
$704$	3.79892e6	0.288888
$705$	8.84334e6	0.670106
$706$	−2.11842e7	−1.59956
$707$	−1.03916e7	−0.781867
$708$	678907.	0.0509011
$709$	−2.68377e6	−0.200507	−0.100254	−	0.994962i	$-0.531965\pi$
$709$	−2.68377e6	−0.200507	−0.100254	+	0.994962i	$0.531965\pi$
$710$	−9.27204e6	−0.690287
$711$	5.80555e6	0.430694
$712$	8.82155e6	0.652146
$713$	−1.92774e7	−1.42012
$714$	8.98348e6	0.659476
$715$	−533689.	−0.0390412
$716$	−8.71234e6	−0.635115
$717$	−4.63069e6	−0.336394
$718$	4.14934e6	0.300378
$719$	−1.26395e7	−0.911816	−0.455908	−	0.890027i	$-0.650685\pi$
$719$	−1.26395e7	−0.911816	−0.455908	+	0.890027i	$0.650685\pi$
$720$	−4.72878e6	−0.339952
$721$	−8.57650e6	−0.614429
$722$	1.74563e7	1.24626
$723$	1.38659e7	0.986509
$724$	7.07753e6	0.501806
$725$	2.71983e6	0.192175
$726$	−382320.	−0.0269207
$727$	1.30124e7	0.913105	0.456552	−	0.889697i	$-0.349084\pi$
$727$	1.30124e7	0.913105	0.456552	+	0.889697i	$0.349084\pi$
$728$	181335.	0.0126810
$729$	531441.	0.0370370
$730$	2.41494e7	1.67726
$731$	−1.39713e7	−0.967038
$732$	−8.83661e6	−0.609548
$733$	−5.49665e6	−0.377866	−0.188933	−	0.981990i	$-0.560503\pi$
$733$	−5.49665e6	−0.377866	−0.188933	+	0.981990i	$0.560503\pi$
$734$	2.30719e6	0.158068
$735$	3.97688e6	0.271534
$736$	2.66696e7	1.81477
$737$	1.66765e7	1.13093
$738$	2.19481e6	0.148339
$739$	−2.85074e6	−0.192020	−0.0960101	−	0.995380i	$-0.530608\pi$
$739$	−2.85074e6	−0.192020	−0.0960101	+	0.995380i	$0.530608\pi$
$740$	2.87618e6	0.193080
$741$	554031.	0.0370671
$742$	6.93502e6	0.462421
$743$	−8.85765e6	−0.588635	−0.294318	−	0.955708i	$-0.595092\pi$
$743$	−8.85765e6	−0.588635	−0.294318	+	0.955708i	$0.595092\pi$
$744$	3.30831e6	0.219116
$745$	−86412.5	−0.00570409
$746$	−1.18090e7	−0.776899
$747$	7.55569e6	0.495419
$748$	−1.40560e7	−0.918559
$749$	−1.64143e7	−1.06910
$750$	1.25276e7	0.813230
$751$	−1.95283e7	−1.26347	−0.631733	−	0.775186i	$-0.717656\pi$
$751$	−1.95283e7	−1.26347	−0.631733	+	0.775186i	$0.717656\pi$
$752$	2.62080e7	1.69001
$753$	−9.05395e6	−0.581903
$754$	−594374.	−0.0380743
$755$	−3.16764e6	−0.202241
$756$	1.35547e6	0.0862555
$757$	2.35067e7	1.49091	0.745457	−	0.666554i	$-0.232231\pi$
$757$	2.35067e7	1.49091	0.745457	+	0.666554i	$0.232231\pi$
$758$	−2.54196e7	−1.60693
$759$	−1.45897e7	−0.919267
$760$	7.80419e6	0.490111
$761$	1.76666e7	1.10584	0.552920	−	0.833234i	$-0.313513\pi$
$761$	1.76666e7	1.10584	0.552920	+	0.833234i	$0.313513\pi$
$762$	8.46331e6	0.528023
$763$	1.22618e7	0.762504
$764$	6.99202e6	0.433380
$765$	6.01759e6	0.371765
$766$	−4.63207e6	−0.285235
$767$	−97213.6	−0.00596676
$768$	−1.23648e7	−0.756457
$769$	−6.78452e6	−0.413717	−0.206858	−	0.978371i	$-0.566324\pi$
$769$	−6.78452e6	−0.413717	−0.206858	+	0.978371i	$0.566324\pi$
$770$	1.20125e7	0.730138
$771$	7.39300e6	0.447904
$772$	−5.09201e6	−0.307501
$773$	−1.32057e7	−0.794901	−0.397451	−	0.917624i	$-0.630105\pi$
$773$	−1.32057e7	−0.794901	−0.397451	+	0.917624i	$0.630105\pi$
$774$	−5.22100e6	−0.313257
$775$	−4.54757e6	−0.271973
$776$	−6.89462e6	−0.411014
$777$	2.19075e6	0.130179
$778$	−1.46288e7	−0.866480
$779$	−8.15292e6	−0.481360
$780$	−254819.	−0.0149967
$781$	1.10502e7	0.648248
$782$	−4.61682e7	−2.69976
$783$	2.11786e6	0.123451
$784$	1.17858e7	0.684810
$785$	−9.76714e6	−0.565710
$786$	−1.15620e7	−0.667539
$787$	−5.65588e6	−0.325509	−0.162755	−	0.986667i	$-0.552038\pi$
$787$	−5.65588e6	−0.325509	−0.162755	+	0.986667i	$0.552038\pi$
$788$	−1.42806e7	−0.819279
$789$	−3.02959e6	−0.173257
$790$	2.45656e7	1.40042
$791$	482552.	0.0274223
$792$	2.50383e6	0.141838
$793$	1.26533e6	0.0714529
$794$	−2.58951e7	−1.45769
$795$	4.64542e6	0.260680
$796$	−7.35705e6	−0.411548
$797$	2.41632e6	0.134744	0.0673718	−	0.997728i	$-0.478539\pi$
$797$	2.41632e6	0.134744	0.0673718	+	0.997728i	$0.478539\pi$
$798$	−1.24703e7	−0.693219
$799$	−3.33508e7	−1.84816
$800$	6.29142e6	0.347555
$801$	−9.44219e6	−0.519986
$802$	2.76136e7	1.51596
$803$	−2.87806e7	−1.57511
$804$	7.96249e6	0.434419
$805$	1.59310e7	0.866470
$806$	993795.	0.0538839
$807$	1.91362e7	1.03436
$808$	−9.16513e6	−0.493867
$809$	1.19990e7	0.644576	0.322288	−	0.946642i	$-0.395548\pi$
$809$	1.19990e7	0.644576	0.322288	+	0.946642i	$0.395548\pi$
$810$	2.24874e6	0.120428
$811$	−1.49699e7	−0.799220	−0.399610	−	0.916685i	$-0.630854\pi$
$811$	−1.49699e7	−0.799220	−0.399610	+	0.916685i	$0.630854\pi$
$812$	5.40174e6	0.287504
$813$	7.03045e6	0.373041
$814$	−8.48944e6	−0.449074
$815$	894719.	0.0471837
$816$	1.78336e7	0.937592
$817$	1.93941e7	1.01652
$818$	−793738.	−0.0414757
$819$	−194092.	−0.0101111
$820$	3.74982e6	0.194749
$821$	2.52512e7	1.30745	0.653724	−	0.756733i	$-0.273206\pi$
$821$	2.52512e7	1.30745	0.653724	+	0.756733i	$0.273206\pi$
$822$	1.34760e7	0.695636
$823$	1.71441e6	0.0882299	0.0441150	−	0.999026i	$-0.485953\pi$
$823$	1.71441e6	0.0882299	0.0441150	+	0.999026i	$0.485953\pi$
$824$	−7.56427e6	−0.388105
$825$	−3.44174e6	−0.176053
$826$	2.18812e6	0.111589
$827$	−1.24001e7	−0.630464	−0.315232	−	0.949015i	$-0.602082\pi$
$827$	−1.24001e7	−0.630464	−0.315232	+	0.949015i	$0.602082\pi$
$828$	−6.96610e6	−0.353113
$829$	3.26664e7	1.65088	0.825439	−	0.564491i	$-0.190928\pi$
$829$	3.26664e7	1.65088	0.825439	+	0.564491i	$0.190928\pi$
$830$	3.19711e7	1.61088
$831$	206516.	0.0103741
$832$	−259729.	−0.0130081
$833$	−1.49980e7	−0.748895
$834$	−140376.	−0.00698839
$835$	−1.46633e7	−0.727806
$836$	1.95117e7	0.965559
$837$	−3.54107e6	−0.174711
$838$	−3.36897e7	−1.65725
$839$	3.43057e7	1.68252	0.841261	−	0.540629i	$-0.181814\pi$
$839$	3.43057e7	1.68252	0.841261	+	0.540629i	$0.181814\pi$
$840$	−2.73402e6	−0.133692
$841$	−1.20712e7	−0.588519
$842$	3.86636e7	1.87941
$843$	−1.31519e7	−0.637412
$844$	−1.86933e7	−0.903297
$845$	−1.73343e7	−0.835149
$846$	−1.24630e7	−0.598684
$847$	−497529.	−0.0238292
$848$	1.37671e7	0.657435
$849$	−1.13190e7	−0.538937
$850$	−1.08912e7	−0.517043
$851$	−1.12588e7	−0.532926
$852$	5.27609e6	0.249008
$853$	1.96117e6	0.0922874	0.0461437	−	0.998935i	$-0.485307\pi$
$853$	1.96117e6	0.0922874	0.0461437	+	0.998935i	$0.485307\pi$
$854$	−2.84804e7	−1.33629
$855$	−8.35325e6	−0.390787
$856$	−1.44771e7	−0.675299
$857$	−1.73109e7	−0.805134	−0.402567	−	0.915391i	$-0.631882\pi$
$857$	−1.73109e7	−0.805134	−0.402567	+	0.915391i	$0.631882\pi$
$858$	752133.	0.0348800
$859$	1.08498e7	0.501692	0.250846	−	0.968027i	$-0.419291\pi$
$859$	1.08498e7	0.501692	0.250846	+	0.968027i	$0.419291\pi$
$860$	−8.92005e6	−0.411265
$861$	2.85619e6	0.131305
$862$	−2.38721e7	−1.09426
$863$	−3.39433e6	−0.155141	−0.0775705	−	0.996987i	$-0.524716\pi$
$863$	−3.39433e6	−0.155141	−0.0775705	+	0.996987i	$0.524716\pi$
$864$	4.89896e6	0.223264
$865$	2.90159e7	1.31855
$866$	1.86010e7	0.842833
$867$	−9.91537e6	−0.447983
$868$	−9.03172e6	−0.406885
$869$	−2.92766e7	−1.31514
$870$	8.96151e6	0.401405
$871$	−1.14016e6	−0.0509238
$872$	1.08146e7	0.481637
$873$	7.37969e6	0.327720
$874$	6.40879e7	2.83790
$875$	1.63026e7	0.719843
$876$	−1.37418e7	−0.605039
$877$	−2.12843e7	−0.934460	−0.467230	−	0.884136i	$-0.654748\pi$
$877$	−2.12843e7	−0.934460	−0.467230	+	0.884136i	$0.654748\pi$
$878$	3.74411e7	1.63913
$879$	−1.41652e7	−0.618371
$880$	2.38466e7	1.03805
$881$	−4.15740e7	−1.80461	−0.902303	−	0.431103i	$-0.858124\pi$
$881$	−4.15740e7	−1.80461	−0.902303	+	0.431103i	$0.858124\pi$
$882$	−5.60467e6	−0.242593
$883$	−3.74730e6	−0.161740	−0.0808699	−	0.996725i	$-0.525770\pi$
$883$	−3.74730e6	−0.161740	−0.0808699	+	0.996725i	$0.525770\pi$
$884$	960996.	0.0413610
$885$	1.46571e6	0.0629058
$886$	−1.52778e7	−0.653849
$887$	−6.86645e6	−0.293038	−0.146519	−	0.989208i	$-0.546807\pi$
$887$	−6.86645e6	−0.293038	−0.146519	+	0.989208i	$0.546807\pi$
$888$	1.93219e6	0.0822276
$889$	1.10137e7	0.467387
$890$	−3.99537e7	−1.69076
$891$	−2.67999e6	−0.113094
$892$	−2.16822e7	−0.912412
$893$	4.62956e7	1.94272
$894$	121782.	0.00509612
$895$	−1.88093e7	−0.784903
$896$	−1.26052e7	−0.524541
$897$	997485.	0.0413929
$898$	−2.14179e7	−0.886312
$899$	−1.41116e7	−0.582341
$900$	−1.64332e6	−0.0676262
$901$	−1.75193e7	−0.718958
$902$	−1.10681e7	−0.452958
$903$	−6.79430e6	−0.277284
$904$	425600.	0.0173213
$905$	1.52799e7	0.620154
$906$	4.46420e6	0.180685
$907$	−4.68280e7	−1.89011	−0.945056	−	0.326910i	$-0.893993\pi$
$907$	−4.68280e7	−1.89011	−0.945056	+	0.326910i	$0.893993\pi$
$908$	−849550.	−0.0341959
$909$	9.80994e6	0.393783
$910$	−821282.	−0.0328767
$911$	7.20062e6	0.287458	0.143729	−	0.989617i	$-0.454091\pi$
$911$	7.20062e6	0.287458	0.143729	+	0.989617i	$0.454091\pi$
$912$	−2.47556e7	−0.985566
$913$	−3.81023e7	−1.51278
$914$	−6.07543e7	−2.40554
$915$	−1.90776e7	−0.753306
$916$	−3.31591e7	−1.30576
$917$	−1.50461e7	−0.590882
$918$	−8.48065e6	−0.332141
$919$	−3.30525e7	−1.29097	−0.645485	−	0.763773i	$-0.723345\pi$
$919$	−3.30525e7	−1.29097	−0.645485	+	0.763773i	$0.723345\pi$
$920$	1.40508e7	0.547307
$921$	−1.33460e7	−0.518443
$922$	−1.85898e7	−0.720189
$923$	−755492.	−0.0291894
$924$	−6.83548e6	−0.263384
$925$	−2.65597e6	−0.102063
$926$	2.60786e7	0.999442
$927$	8.09645e6	0.309453
$928$	1.95230e7	0.744177
$929$	2.05879e7	0.782658	0.391329	−	0.920251i	$-0.372015\pi$
$929$	2.05879e7	0.782658	0.391329	+	0.920251i	$0.372015\pi$
$930$	−1.49837e7	−0.568082
$931$	2.08193e7	0.787213
$932$	−73636.0	−0.00277684
$933$	−6.86252e6	−0.258095
$934$	4.93583e7	1.85137
$935$	−3.03459e7	−1.13520
$936$	−171185.	−0.00638669
$937$	−2.98879e7	−1.11211	−0.556054	−	0.831146i	$-0.687685\pi$
$937$	−2.98879e7	−1.11211	−0.556054	+	0.831146i	$0.687685\pi$
$938$	2.56631e7	0.952363
$939$	1.21953e7	0.451364
$940$	−2.12930e7	−0.785991
$941$	3.84112e7	1.41411	0.707056	−	0.707158i	$-0.250023\pi$
$941$	3.84112e7	1.41411	0.707056	+	0.707158i	$0.250023\pi$
$942$	1.37650e7	0.505414
$943$	−1.46786e7	−0.537535
$944$	4.34376e6	0.158648
$945$	2.92638e6	0.106598
$946$	2.63288e7	0.956540
$947$	−827143.	−0.0299713	−0.0149857	−	0.999888i	$-0.504770\pi$
$947$	−827143.	−0.0299713	−0.0149857	+	0.999888i	$0.504770\pi$
$948$	−1.39786e7	−0.505177
$949$	1.96771e6	0.0709243
$950$	1.51185e7	0.543499
$951$	8.07392e6	0.289490
$952$	1.03108e7	0.368723
$953$	−1.38653e7	−0.494535	−0.247267	−	0.968947i	$-0.579533\pi$
$953$	−1.38653e7	−0.494535	−0.247267	+	0.968947i	$0.579533\pi$
$954$	−6.54685e6	−0.232896
$955$	1.50953e7	0.535591
$956$	1.11498e7	0.394568
$957$	−1.06801e7	−0.376960
$958$	5.34259e7	1.88078
$959$	1.75369e7	0.615753
$960$	3.91600e6	0.137140
$961$	−5.03449e6	−0.175852
$962$	580417.	0.0202210
$963$	1.54956e7	0.538446
$964$	−3.33863e7	−1.15711
$965$	−1.09933e7	−0.380023
$966$	−2.24518e7	−0.774119
$967$	−1.09394e7	−0.376208	−0.188104	−	0.982149i	$-0.560234\pi$
$967$	−1.09394e7	−0.376208	−0.188104	+	0.982149i	$0.560234\pi$
$968$	−438809.	−0.0150517
$969$	3.15026e7	1.07780
$970$	3.12264e7	1.06560
$971$	4.27950e7	1.45661	0.728307	−	0.685251i	$-0.240307\pi$
$971$	4.27950e7	1.45661	0.728307	+	0.685251i	$0.240307\pi$
$972$	−1.27961e6	−0.0434421
$973$	−182677.	−0.00618588
$974$	1.26415e7	0.426975
$975$	235309.	0.00792733
$976$	−5.65381e7	−1.89984
$977$	1.09971e7	0.368590	0.184295	−	0.982871i	$-0.441000\pi$
$977$	1.09971e7	0.368590	0.184295	+	0.982871i	$0.441000\pi$
$978$	−1.26094e6	−0.0421547
$979$	4.76157e7	1.58779
$980$	−9.57556e6	−0.318492
$981$	−1.15755e7	−0.384031
$982$	5.91031e7	1.95583
$983$	2.08290e7	0.687518	0.343759	−	0.939058i	$-0.388300\pi$
$983$	2.08290e7	0.687518	0.343759	+	0.939058i	$0.388300\pi$
$984$	2.51910e6	0.0829387
$985$	−3.08309e7	−1.01250
$986$	−3.37965e7	−1.10708
$987$	−1.62186e7	−0.529934
$988$	−1.33400e6	−0.0434773
$989$	3.49175e7	1.13515
$990$	−1.13401e7	−0.367729
$991$	1.73858e7	0.562355	0.281177	−	0.959656i	$-0.409275\pi$
$991$	1.73858e7	0.562355	0.281177	+	0.959656i	$0.409275\pi$
$992$	−3.26425e7	−1.05318
$993$	1.30529e7	0.420083
$994$	1.70049e7	0.545893
$995$	−1.58834e7	−0.508610
$996$	−1.81926e7	−0.581094
$997$	−1.37910e7	−0.439397	−0.219699	−	0.975568i	$-0.570507\pi$
$997$	−1.37910e7	−0.439397	−0.219699	+	0.975568i	$0.570507\pi$
$998$	−5.32361e7	−1.69192
$999$	−2.06813e6	−0.0655637

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.b.1.10	✓	12
3.2	odd	2		531.6.a.d.1.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.b.1.10	✓	12	1.1	even	1	trivial
531.6.a.d.1.3		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)

\(f(q)\)	\(=\)	\(q+7.32600 q^{2} -9.00000 q^{3} +21.6702 q^{4} +46.7845 q^{5} -65.9340 q^{6} -85.8026 q^{7} -75.6759 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+7.32600 q^{2} -9.00000 q^{3} +21.6702 q^{4} +46.7845 q^{5} -65.9340 q^{6} -85.8026 q^{7} -75.6759 q^{8} +81.0000 q^{9} +342.743 q^{10} -408.472 q^{11} -195.032 q^{12} +27.9269 q^{13} -628.589 q^{14} -421.061 q^{15} -1247.85 q^{16} +1587.94 q^{17} +593.406 q^{18} -2204.29 q^{19} +1013.83 q^{20} +772.223 q^{21} -2992.47 q^{22} -3968.63 q^{23} +681.083 q^{24} -936.208 q^{25} +204.593 q^{26} -729.000 q^{27} -1859.36 q^{28} -2905.16 q^{29} -3084.69 q^{30} +4857.43 q^{31} -6720.11 q^{32} +3676.25 q^{33} +11633.3 q^{34} -4014.23 q^{35} +1755.29 q^{36} +2836.94 q^{37} -16148.6 q^{38} -251.342 q^{39} -3540.46 q^{40} +3698.67 q^{41} +5657.30 q^{42} -8798.36 q^{43} -8851.69 q^{44} +3789.55 q^{45} -29074.2 q^{46} -21002.5 q^{47} +11230.6 q^{48} -9444.92 q^{49} -6858.66 q^{50} -14291.5 q^{51} +605.183 q^{52} -11032.7 q^{53} -5340.65 q^{54} -19110.2 q^{55} +6493.18 q^{56} +19838.6 q^{57} -21283.2 q^{58} -3481.00 q^{59} -9124.48 q^{60} +45308.5 q^{61} +35585.5 q^{62} -6950.01 q^{63} -9300.32 q^{64} +1306.55 q^{65} +26932.2 q^{66} -40826.6 q^{67} +34411.1 q^{68} +35717.7 q^{69} -29408.2 q^{70} -27052.4 q^{71} -6129.75 q^{72} +70459.2 q^{73} +20783.4 q^{74} +8425.88 q^{75} -47767.4 q^{76} +35048.0 q^{77} -1841.33 q^{78} +71673.4 q^{79} -58380.0 q^{80} +6561.00 q^{81} +27096.4 q^{82} +93280.1 q^{83} +16734.2 q^{84} +74291.2 q^{85} -64456.8 q^{86} +26146.4 q^{87} +30911.5 q^{88} -116570. q^{89} +27762.2 q^{90} -2396.20 q^{91} -86001.2 q^{92} -43716.9 q^{93} -153864. q^{94} -103127. q^{95} +60481.0 q^{96} +91107.3 q^{97} -69193.5 q^{98} -33086.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12q - 4q^{2} - 108q^{3} + 198q^{4} + 36q^{5} + 36q^{6} - 411q^{7} - 69q^{8} + 972q^{9} + O(q^{10}) \)	\( 12q - 4q^{2} - 108q^{3} + 198q^{4} + 36q^{5} + 36q^{6} - 411q^{7} - 69q^{8} + 972q^{9} - 863q^{10} + 492q^{11} - 1782q^{12} - 974q^{13} - 967q^{14} - 324q^{15} + 6370q^{16} - 1463q^{17} - 324q^{18} - 3189q^{19} - 835q^{20} + 3699q^{21} - 2726q^{22} - 2617q^{23} + 621q^{24} + 8642q^{25} + 2414q^{26} - 8748q^{27} - 20458q^{28} - 1963q^{29} + 7767q^{30} - 11929q^{31} - 14382q^{32} - 4428q^{33} - 20744q^{34} + 1829q^{35} + 16038q^{36} - 28105q^{37} - 23475q^{38} + 8766q^{39} - 100576q^{40} - 7585q^{41} + 8703q^{42} - 33146q^{43} + 26014q^{44} + 2916q^{45} - 142851q^{46} - 79215q^{47} - 57330q^{48} - 32569q^{49} - 136019q^{50} + 13167q^{51} - 248218q^{52} - 12220q^{53} + 2916q^{54} - 117770q^{55} - 186728q^{56} + 28701q^{57} - 188072q^{58} - 41772q^{59} + 7515q^{60} - 54195q^{61} + 36230q^{62} - 33291q^{63} + 45197q^{64} + 42368q^{65} + 24534q^{66} + 24224q^{67} - 209639q^{68} + 23553q^{69} - 35684q^{70} + 60254q^{71} - 5589q^{72} - 15385q^{73} + 214638q^{74} - 77778q^{75} - 167504q^{76} - 17169q^{77} - 21726q^{78} - 27054q^{79} + 216899q^{80} + 78732q^{81} + 37917q^{82} - 117595q^{83} + 184122q^{84} - 121585q^{85} + 306756q^{86} + 17667q^{87} - 105799q^{88} - 36033q^{89} - 69903q^{90} - 32217q^{91} - 30906q^{92} + 107361q^{93} + 128392q^{94} - 50721q^{95} + 129438q^{96} - 196914q^{97} + 574100q^{98} + 39852q^{99} + O(q^{100}) \)

Introduction

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