LMFDB - Embedded newform 242.6.a.m.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [242,6,Mod(1,242)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("242.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(242, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 242 = 2 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	242.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,16,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$38.8128843947$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.2103025.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 149x^{2} + 150x + 5220 $ x^4 - 2x^3 - 149x^2 + 150*x + 5220
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 11 $
Twist minimal:	no (minimal twist has level 22)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-6.92465$ of defining polynomial
Character	$\chi$	$=$	242.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.00000 q^{2} -13.9952 q^{3} +16.0000 q^{4} +34.0320 q^{5} -55.9808 q^{6} -44.8946 q^{7} +64.0000 q^{8} -47.1346 q^{9} +136.128 q^{10} -223.923 q^{12} +168.584 q^{13} -179.578 q^{14} -476.285 q^{15} +256.000 q^{16} +1007.58 q^{17} -188.538 q^{18} -1927.72 q^{19} +544.513 q^{20} +628.309 q^{21} -464.264 q^{23} -895.692 q^{24} -1966.82 q^{25} +674.336 q^{26} +4060.49 q^{27} -718.314 q^{28} -6839.56 q^{29} -1905.14 q^{30} +1981.43 q^{31} +1024.00 q^{32} +4030.32 q^{34} -1527.86 q^{35} -754.153 q^{36} -5355.14 q^{37} -7710.88 q^{38} -2359.37 q^{39} +2178.05 q^{40} -14799.9 q^{41} +2513.24 q^{42} +14097.7 q^{43} -1604.09 q^{45} -1857.06 q^{46} +16186.9 q^{47} -3582.77 q^{48} -14791.5 q^{49} -7867.28 q^{50} -14101.3 q^{51} +2697.35 q^{52} -27732.0 q^{53} +16242.0 q^{54} -2873.26 q^{56} +26978.8 q^{57} -27358.2 q^{58} -34942.5 q^{59} -7620.56 q^{60} -20765.8 q^{61} +7925.71 q^{62} +2116.09 q^{63} +4096.00 q^{64} +5737.26 q^{65} -62400.3 q^{67} +16121.3 q^{68} +6497.47 q^{69} -6111.42 q^{70} -81099.2 q^{71} -3016.61 q^{72} -55133.4 q^{73} -21420.6 q^{74} +27526.0 q^{75} -30843.5 q^{76} -9437.47 q^{78} +19236.6 q^{79} +8712.20 q^{80} -45373.6 q^{81} -59199.5 q^{82} +38934.8 q^{83} +10052.9 q^{84} +34290.0 q^{85} +56390.7 q^{86} +95720.9 q^{87} -25758.7 q^{89} -6416.34 q^{90} -7568.52 q^{91} -7428.23 q^{92} -27730.5 q^{93} +64747.5 q^{94} -65604.3 q^{95} -14331.1 q^{96} +79424.6 q^{97} -59165.9 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 16 q^{2} - 10 q^{3} + 64 q^{4} - 150 q^{5} - 40 q^{6} - 34 q^{7} + 256 q^{8} + 302 q^{9} - 600 q^{10} - 160 q^{12} + 138 q^{13} - 136 q^{14} + 206 q^{15} + 1024 q^{16} - 370 q^{17} + 1208 q^{18} - 2358 q^{19}+ \cdots - 90152 q^{98}+O(q^{100}) $ 4 * q + 16 * q^2 - 10 * q^3 + 64 * q^4 - 150 * q^5 - 40 * q^6 - 34 * q^7 + 256 * q^8 + 302 * q^9 - 600 * q^10 - 160 * q^12 + 138 * q^13 - 136 * q^14 + 206 * q^15 + 1024 * q^16 - 370 * q^17 + 1208 * q^18 - 2358 * q^19 - 2400 * q^20 - 5162 * q^21 + 820 * q^23 - 640 * q^24 + 1114 * q^25 + 552 * q^26 - 7810 * q^27 - 544 * q^28 - 11242 * q^29 + 824 * q^30 - 17096 * q^31 + 4096 * q^32 - 1480 * q^34 - 9238 * q^35 + 4832 * q^36 - 16194 * q^37 - 9432 * q^38 - 15446 * q^39 - 9600 * q^40 - 34262 * q^41 - 20648 * q^42 + 5396 * q^43 - 33940 * q^45 + 3280 * q^46 + 8898 * q^47 - 2560 * q^48 - 22538 * q^49 + 4456 * q^50 - 62378 * q^51 + 2208 * q^52 - 12274 * q^53 - 31240 * q^54 - 2176 * q^56 + 87082 * q^57 - 44968 * q^58 + 8222 * q^59 + 3296 * q^60 + 68186 * q^61 - 68384 * q^62 + 70948 * q^63 + 16384 * q^64 + 16486 * q^65 - 167868 * q^67 - 5920 * q^68 - 119656 * q^69 - 36952 * q^70 - 96324 * q^71 + 19328 * q^72 - 33278 * q^73 - 64776 * q^74 - 89830 * q^75 - 37728 * q^76 - 61784 * q^78 + 158272 * q^79 - 38400 * q^80 - 143056 * q^81 - 137048 * q^82 + 196304 * q^83 - 82592 * q^84 + 80558 * q^85 + 21584 * q^86 + 86828 * q^87 - 267400 * q^89 - 135760 * q^90 - 48850 * q^91 + 13120 * q^92 - 58944 * q^93 + 35592 * q^94 + 3038 * q^95 - 10240 * q^96 - 26738 * q^97 - 90152 * q^98

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 $

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	−13.9952	−0.897792	−0.448896	−	0.893584i	$-0.648183\pi$
$3$	−13.9952	−0.897792	−0.448896	+	0.893584i	$0.648183\pi$
$4$	16.0000	0.500000
$5$	34.0320	0.608784	0.304392	−	0.952547i	$-0.401547\pi$
$5$	34.0320	0.608784	0.304392	+	0.952547i	$0.401547\pi$
$6$	−55.9808	−0.634835
$7$	−44.8946	−0.346297	−0.173149	−	0.984896i	$-0.555394\pi$
$7$	−44.8946	−0.346297	−0.173149	+	0.984896i	$0.555394\pi$
$8$	64.0000	0.353553
$9$	−47.1346	−0.193969
$10$	136.128	0.430475
$11$	0	0
$11$	0	0
$12$	−223.923	−0.448896
$13$	168.584	0.276668	0.138334	−	0.990386i	$-0.455825\pi$
$13$	168.584	0.276668	0.138334	+	0.990386i	$0.455825\pi$
$14$	−179.578	−0.244869
$15$	−476.285	−0.546561
$16$	256.000	0.250000
$17$	1007.58	0.845585	0.422793	−	0.906226i	$-0.361050\pi$
$17$	1007.58	0.845585	0.422793	+	0.906226i	$0.361050\pi$
$18$	−188.538	−0.137157
$19$	−1927.72	−1.22507	−0.612534	−	0.790444i	$-0.709850\pi$
$19$	−1927.72	−1.22507	−0.612534	+	0.790444i	$0.709850\pi$
$20$	544.513	0.304392
$21$	628.309	0.310903
$22$	0	0
$23$	−464.264	−0.182998	−0.0914988	−	0.995805i	$-0.529166\pi$
$23$	−464.264	−0.182998	−0.0914988	+	0.995805i	$0.529166\pi$
$24$	−895.692	−0.317417
$25$	−1966.82	−0.629382
$26$	674.336	0.195634
$27$	4060.49	1.07194
$28$	−718.314	−0.173149
$29$	−6839.56	−1.51019	−0.755097	−	0.655613i	$-0.772410\pi$
$29$	−6839.56	−1.51019	−0.755097	+	0.655613i	$0.772410\pi$
$30$	−1905.14	−0.386477
$31$	1981.43	0.370317	0.185159	−	0.982709i	$-0.440720\pi$
$31$	1981.43	0.370317	0.185159	+	0.982709i	$0.440720\pi$
$32$	1024.00	0.176777
$33$	0	0
$34$	4030.32	0.597919
$35$	−1527.86	−0.210820
$36$	−754.153	−0.0969847
$37$	−5355.14	−0.643082	−0.321541	−	0.946896i	$-0.604201\pi$
$37$	−5355.14	−0.643082	−0.321541	+	0.946896i	$0.604201\pi$
$38$	−7710.88	−0.866254
$39$	−2359.37	−0.248390
$40$	2178.05	0.215238
$41$	−14799.9	−1.37499	−0.687493	−	0.726191i	$-0.741289\pi$
$41$	−14799.9	−1.37499	−0.687493	+	0.726191i	$0.741289\pi$
$42$	2513.24	0.219842
$43$	14097.7	1.16272	0.581362	−	0.813645i	$-0.302520\pi$
$43$	14097.7	1.16272	0.581362	+	0.813645i	$0.302520\pi$
$44$	0	0
$45$	−1604.09	−0.118085
$46$	−1857.06	−0.129399
$47$	16186.9	1.06885	0.534427	−	0.845215i	$-0.320528\pi$
$47$	16186.9	1.06885	0.534427	+	0.845215i	$0.320528\pi$
$48$	−3582.77	−0.224448
$49$	−14791.5	−0.880078
$50$	−7867.28	−0.445041
$51$	−14101.3	−0.759160
$52$	2697.35	0.138334
$53$	−27732.0	−1.35610	−0.678049	−	0.735017i	$-0.737174\pi$
$53$	−27732.0	−1.35610	−0.678049	+	0.735017i	$0.737174\pi$
$54$	16242.0	0.757973
$55$	0	0
$56$	−2873.26	−0.122435
$57$	26978.8	1.09986
$58$	−27358.2	−1.06787
$59$	−34942.5	−1.30685	−0.653423	−	0.756993i	$-0.726668\pi$
$59$	−34942.5	−1.30685	−0.653423	+	0.756993i	$0.726668\pi$
$60$	−7620.56	−0.273281
$61$	−20765.8	−0.714534	−0.357267	−	0.934002i	$-0.616291\pi$
$61$	−20765.8	−0.714534	−0.357267	+	0.934002i	$0.616291\pi$
$62$	7925.71	0.261854
$63$	2116.09	0.0671711
$64$	4096.00	0.125000
$65$	5737.26	0.168431
$66$	0	0
$67$	−62400.3	−1.69824	−0.849121	−	0.528198i	$-0.822868\pi$
$67$	−62400.3	−1.69824	−0.849121	+	0.528198i	$0.822868\pi$
$68$	16121.3	0.422793
$69$	6497.47	0.164294
$70$	−6111.42	−0.149072
$71$	−81099.2	−1.90929	−0.954643	−	0.297754i	$-0.903763\pi$
$71$	−81099.2	−1.90929	−0.954643	+	0.297754i	$0.903763\pi$
$72$	−3016.61	−0.0685786
$73$	−55133.4	−1.21090	−0.605450	−	0.795884i	$-0.707007\pi$
$73$	−55133.4	−1.21090	−0.605450	+	0.795884i	$0.707007\pi$
$74$	−21420.6	−0.454728
$75$	27526.0	0.565055
$76$	−30843.5	−0.612534
$77$	0	0
$78$	−9437.47	−0.175638
$79$	19236.6	0.346785	0.173392	−	0.984853i	$-0.444527\pi$
$79$	19236.6	0.346785	0.173392	+	0.984853i	$0.444527\pi$
$80$	8712.20	0.152196
$81$	−45373.6	−0.768406
$82$	−59199.5	−0.972263
$83$	38934.8	0.620359	0.310179	−	0.950678i	$-0.399611\pi$
$83$	38934.8	0.620359	0.310179	+	0.950678i	$0.399611\pi$
$84$	10052.9	0.155452
$85$	34290.0	0.514779
$86$	56390.7	0.822170
$87$	95720.9	1.35584
$88$	0	0
$89$	−25758.7	−0.344705	−0.172353	−	0.985035i	$-0.555137\pi$
$89$	−25758.7	−0.344705	−0.172353	+	0.985035i	$0.555137\pi$
$90$	−6416.34	−0.0834990
$91$	−7568.52	−0.0958093
$92$	−7428.23	−0.0914988
$93$	−27730.5	−0.332468
$94$	64747.5	0.755793
$95$	−65604.3	−0.745801
$96$	−14331.1	−0.158709
$97$	79424.6	0.857089	0.428544	−	0.903521i	$-0.359027\pi$
$97$	79424.6	0.857089	0.428544	+	0.903521i	$0.359027\pi$
$98$	−59165.9	−0.622309
$99$	0	0
$100$	−31469.1	−0.314691
$101$	89306.5	0.871124	0.435562	−	0.900159i	$-0.356550\pi$
$101$	89306.5	0.871124	0.435562	+	0.900159i	$0.356550\pi$
$102$	−56405.1	−0.536807
$103$	36916.7	0.342870	0.171435	−	0.985195i	$-0.445160\pi$
$103$	36916.7	0.342870	0.171435	+	0.985195i	$0.445160\pi$
$104$	10789.4	0.0978168
$105$	21382.6	0.189273
$106$	−110928.	−0.958906
$107$	124055.	1.04751	0.523753	−	0.851870i	$-0.324532\pi$
$107$	124055.	1.04751	0.523753	+	0.851870i	$0.324532\pi$
$108$	64967.8	0.535968
$109$	194413.	1.56733	0.783663	−	0.621186i	$-0.213349\pi$
$109$	194413.	1.56733	0.783663	+	0.621186i	$0.213349\pi$
$110$	0	0
$111$	74946.2	0.577354
$112$	−11493.0	−0.0865743
$113$	44714.6	0.329422	0.164711	−	0.986342i	$-0.447331\pi$
$113$	44714.6	0.329422	0.164711	+	0.986342i	$0.447331\pi$
$114$	107915.	0.777716
$115$	−15799.9	−0.111406
$116$	−109433.	−0.755097
$117$	−7946.14	−0.0536651
$118$	−139770.	−0.924080
$119$	−45235.0	−0.292824
$120$	−30482.2	−0.193239
$121$	0	0
$122$	−83063.0	−0.505252
$123$	207127.	1.23445
$124$	31702.8	0.185159
$125$	−173285.	−0.991941
$126$	8464.36	0.0474972
$127$	146037.	0.803439	0.401719	−	0.915763i	$-0.368413\pi$
$127$	146037.	0.803439	0.401719	+	0.915763i	$0.368413\pi$
$128$	16384.0	0.0883883
$129$	−197300.	−1.04388
$130$	22949.0	0.119098
$131$	29127.1	0.148292	0.0741462	−	0.997247i	$-0.476377\pi$
$131$	29127.1	0.148292	0.0741462	+	0.997247i	$0.476377\pi$
$132$	0	0
$133$	86544.3	0.424238
$134$	−249601.	−1.20084
$135$	138187.	0.652577
$136$	64485.2	0.298960
$137$	178353.	0.811854	0.405927	−	0.913906i	$-0.366949\pi$
$137$	178353.	0.811854	0.405927	+	0.913906i	$0.366949\pi$
$138$	25989.9	0.116173
$139$	288572.	1.26683	0.633414	−	0.773813i	$-0.281653\pi$
$139$	288572.	1.26683	0.633414	+	0.773813i	$0.281653\pi$
$140$	−24445.7	−0.105410
$141$	−226538.	−0.959608
$142$	−324397.	−1.35007
$143$	0	0
$144$	−12066.5	−0.0484924
$145$	−232764.	−0.919382
$146$	−220534.	−0.856235
$147$	207010.	0.790127
$148$	−85682.2	−0.321541
$149$	−495023.	−1.82667	−0.913335	−	0.407210i	$-0.866502\pi$
$149$	−495023.	−1.82667	−0.913335	+	0.407210i	$0.866502\pi$
$150$	110104.	0.399554
$151$	296102.	1.05681	0.528407	−	0.848991i	$-0.322789\pi$
$151$	296102.	1.05681	0.528407	+	0.848991i	$0.322789\pi$
$152$	−123374.	−0.433127
$153$	−47491.9	−0.164018
$154$	0	0
$155$	67432.0	0.225443
$156$	−37749.9	−0.124195
$157$	−115529.	−0.374062	−0.187031	−	0.982354i	$-0.559886\pi$
$157$	−115529.	−0.374062	−0.187031	+	0.982354i	$0.559886\pi$
$158$	76946.3	0.245214
$159$	388114.	1.21749
$160$	34848.8	0.107619
$161$	20843.0	0.0633716
$162$	−181495.	−0.543345
$163$	−572235.	−1.68696	−0.843482	−	0.537158i	$-0.819498\pi$
$163$	−572235.	−1.68696	−0.843482	+	0.537158i	$0.819498\pi$
$164$	−236798.	−0.687493
$165$	0	0
$166$	155739.	0.438660
$167$	−234964.	−0.651943	−0.325972	−	0.945380i	$-0.605691\pi$
$167$	−234964.	−0.651943	−0.325972	+	0.945380i	$0.605691\pi$
$168$	40211.8	0.109921
$169$	−342872.	−0.923455
$170$	137160.	0.364003
$171$	90862.3	0.237626
$172$	225563.	0.581362
$173$	439517.	1.11650	0.558252	−	0.829672i	$-0.311472\pi$
$173$	439517.	1.11650	0.558252	+	0.829672i	$0.311472\pi$
$174$	382884.	0.958724
$175$	88299.7	0.217954
$176$	0	0
$177$	489028.	1.17328
$178$	−103035.	−0.243744
$179$	343503.	0.801305	0.400652	−	0.916230i	$-0.368783\pi$
$179$	343503.	0.801305	0.400652	+	0.916230i	$0.368783\pi$
$180$	−25665.4	−0.0590427
$181$	530114.	1.20274	0.601371	−	0.798970i	$-0.294621\pi$
$181$	530114.	1.20274	0.601371	+	0.798970i	$0.294621\pi$
$182$	−30274.1	−0.0677474
$183$	290621.	0.641503
$184$	−29712.9	−0.0646994
$185$	−182246.	−0.391498
$186$	−110922.	−0.235090
$187$	0	0
$188$	258990.	0.534427
$189$	−182294.	−0.371209
$190$	−262417.	−0.527361
$191$	12559.4	0.0249106	0.0124553	−	0.999922i	$-0.496035\pi$
$191$	12559.4	0.0249106	0.0124553	+	0.999922i	$0.496035\pi$
$192$	−57324.3	−0.112224
$193$	358520.	0.692819	0.346409	−	0.938083i	$-0.387401\pi$
$193$	358520.	0.692819	0.346409	+	0.938083i	$0.387401\pi$
$194$	317699.	0.606053
$195$	−80294.1	−0.151216
$196$	−236664.	−0.440039
$197$	−660910.	−1.21332	−0.606662	−	0.794960i	$-0.707492\pi$
$197$	−660910.	−1.21332	−0.606662	+	0.794960i	$0.707492\pi$
$198$	0	0
$199$	−344066.	−0.615898	−0.307949	−	0.951403i	$-0.599643\pi$
$199$	−344066.	−0.615898	−0.307949	+	0.951403i	$0.599643\pi$
$200$	−125876.	−0.222520
$201$	873304.	1.52467
$202$	357226.	0.615978
$203$	307059.	0.522976
$204$	−225621.	−0.379580
$205$	−503670.	−0.837070
$206$	147667.	0.242446
$207$	21882.9	0.0354960
$208$	43157.5	0.0691669
$209$	0	0
$210$	85530.5	0.133836
$211$	−63996.2	−0.0989574	−0.0494787	−	0.998775i	$-0.515756\pi$
$211$	−63996.2	−0.0989574	−0.0494787	+	0.998775i	$0.515756\pi$
$212$	−443711.	−0.678049
$213$	1.13500e6	1.71414
$214$	496222.	0.740698
$215$	479773.	0.707847
$216$	259871.	0.378987
$217$	−88955.4	−0.128240
$218$	777653.	1.10827
$219$	771603.	1.08714
$220$	0	0
$221$	169862.	0.233946
$222$	299785.	0.408251
$223$	−471534.	−0.634967	−0.317484	−	0.948264i	$-0.602838\pi$
$223$	−471534.	−0.634967	−0.317484	+	0.948264i	$0.602838\pi$
$224$	−45972.1	−0.0612173
$225$	92705.2	0.122081
$226$	178858.	0.232937
$227$	62515.3	0.0805233	0.0402616	−	0.999189i	$-0.487181\pi$
$227$	62515.3	0.0805233	0.0402616	+	0.999189i	$0.487181\pi$
$228$	431661.	0.549928
$229$	304688.	0.383942	0.191971	−	0.981401i	$-0.438512\pi$
$229$	304688.	0.383942	0.191971	+	0.981401i	$0.438512\pi$
$230$	−63199.4	−0.0787759
$231$	0	0
$232$	−437732.	−0.533934
$233$	1.02310e6	1.23461	0.617305	−	0.786724i	$-0.288224\pi$
$233$	1.02310e6	1.23461	0.617305	+	0.786724i	$0.288224\pi$
$234$	−31784.6	−0.0379469
$235$	550872.	0.650700
$236$	−559081.	−0.653423
$237$	−269219.	−0.311340
$238$	−180940.	−0.207058
$239$	−113098.	−0.128074	−0.0640370	−	0.997948i	$-0.520398\pi$
$239$	−113098.	−0.128074	−0.0640370	+	0.997948i	$0.520398\pi$
$240$	−121929.	−0.136640
$241$	−745081.	−0.826344	−0.413172	−	0.910653i	$-0.635579\pi$
$241$	−745081.	−0.826344	−0.413172	+	0.910653i	$0.635579\pi$
$242$	0	0
$243$	−351686.	−0.382067
$244$	−332252.	−0.357267
$245$	−503384.	−0.535777
$246$	828509.	0.872890
$247$	−324983.	−0.338936
$248$	126811.	0.130927
$249$	−544900.	−0.556953
$250$	−693140.	−0.701408
$251$	1.12854e6	1.13066	0.565331	−	0.824864i	$-0.308748\pi$
$251$	1.12854e6	1.13066	0.565331	+	0.824864i	$0.308748\pi$
$252$	33857.4	0.0335856
$253$	0	0
$254$	584147.	0.568117
$255$	−479896.	−0.462164
$256$	65536.0	0.0625000
$257$	−1.65637e6	−1.56431	−0.782157	−	0.623081i	$-0.785881\pi$
$257$	−1.65637e6	−1.56431	−0.782157	+	0.623081i	$0.785881\pi$
$258$	−789199.	−0.738138
$259$	240417.	0.222698
$260$	91796.2	0.0842153
$261$	322380.	0.292932
$262$	116508.	0.104859
$263$	−57188.8	−0.0509825	−0.0254913	−	0.999675i	$-0.508115\pi$
$263$	−57188.8	−0.0509825	−0.0254913	+	0.999675i	$0.508115\pi$
$264$	0	0
$265$	−943775.	−0.825570
$266$	346177.	0.299981
$267$	360497.	0.309474
$268$	−998405.	−0.849121
$269$	−515767.	−0.434583	−0.217292	−	0.976107i	$-0.569722\pi$
$269$	−515767.	−0.434583	−0.217292	+	0.976107i	$0.569722\pi$
$270$	552747.	0.461442
$271$	1.55254e6	1.28416	0.642080	−	0.766638i	$-0.278072\pi$
$271$	1.55254e6	1.28416	0.642080	+	0.766638i	$0.278072\pi$
$272$	257941.	0.211396
$273$	105923.	0.0860168
$274$	713410.	0.574067
$275$	0	0
$276$	103959.	0.0821469
$277$	1.01798e6	0.797148	0.398574	−	0.917136i	$-0.369505\pi$
$277$	1.01798e6	0.797148	0.398574	+	0.917136i	$0.369505\pi$
$278$	1.15429e6	0.895782
$279$	−93393.8	−0.0718302
$280$	−97782.8	−0.0745362
$281$	88821.5	0.0671046	0.0335523	−	0.999437i	$-0.489318\pi$
$281$	88821.5	0.0671046	0.0335523	+	0.999437i	$0.489318\pi$
$282$	−906153.	−0.678545
$283$	772817.	0.573602	0.286801	−	0.957990i	$-0.407408\pi$
$283$	772817.	0.573602	0.286801	+	0.957990i	$0.407408\pi$
$284$	−1.29759e6	−0.954643
$285$	918144.	0.669574
$286$	0	0
$287$	664435.	0.476154
$288$	−48265.8	−0.0342893
$289$	−404638.	−0.284985
$290$	−931056.	−0.650101
$291$	−1.11156e6	−0.769488
$292$	−882135.	−0.605450
$293$	−2.22347e6	−1.51308	−0.756539	−	0.653948i	$-0.773111\pi$
$293$	−2.22347e6	−1.51308	−0.756539	+	0.653948i	$0.773111\pi$
$294$	828038.	0.558704
$295$	−1.18917e6	−0.795587
$296$	−342729.	−0.227364
$297$	0	0
$298$	−1.98009e6	−1.29165
$299$	−78267.6	−0.0506295
$300$	440416.	0.282527
$301$	−632910.	−0.402648
$302$	1.18441e6	0.747281
$303$	−1.24986e6	−0.782088
$304$	−493496.	−0.306267
$305$	−706701.	−0.434997
$306$	−189968.	−0.115978
$307$	572812.	0.346870	0.173435	−	0.984845i	$-0.444513\pi$
$307$	572812.	0.346870	0.173435	+	0.984845i	$0.444513\pi$
$308$	0	0
$309$	−516656.	−0.307826
$310$	269728.	0.159412
$311$	−1.38578e6	−0.812443	−0.406221	−	0.913775i	$-0.633154\pi$
$311$	−1.38578e6	−0.812443	−0.406221	+	0.913775i	$0.633154\pi$
$312$	−150999.	−0.0878191
$313$	−2.67552e6	−1.54365	−0.771824	−	0.635837i	$-0.780655\pi$
$313$	−2.67552e6	−1.54365	−0.771824	+	0.635837i	$0.780655\pi$
$314$	−462117.	−0.264502
$315$	72014.8	0.0408927
$316$	307785.	0.173392
$317$	1.16112e6	0.648976	0.324488	−	0.945890i	$-0.394808\pi$
$317$	1.16112e6	0.648976	0.324488	+	0.945890i	$0.394808\pi$
$318$	1.55246e6	0.860898
$319$	0	0
$320$	139395.	0.0760980
$321$	−1.73618e6	−0.940442
$322$	83371.9	0.0448105
$323$	−1.94233e6	−1.03590
$324$	−725978.	−0.384203
$325$	−331575.	−0.174130
$326$	−2.28894e6	−1.19286
$327$	−2.72085e6	−1.40713
$328$	−947192.	−0.486131
$329$	−726703.	−0.370141
$330$	0	0
$331$	523469.	0.262616	0.131308	−	0.991342i	$-0.458082\pi$
$331$	523469.	0.262616	0.131308	+	0.991342i	$0.458082\pi$
$332$	622957.	0.310179
$333$	252412.	0.124738
$334$	−939855.	−0.460993
$335$	−2.12361e6	−1.03386
$336$	160847.	0.0777258
$337$	2.18377e6	1.04745	0.523723	−	0.851888i	$-0.324543\pi$
$337$	2.18377e6	1.04745	0.523723	+	0.851888i	$0.324543\pi$
$338$	−1.37149e6	−0.652981
$339$	−625789.	−0.295753
$340$	548640.	0.257389
$341$	0	0
$342$	363449.	0.168027
$343$	1.41860e6	0.651066
$344$	902252.	0.411085
$345$	221122.	0.100019
$346$	1.75807e6	0.789487
$347$	−1.46113e6	−0.651426	−0.325713	−	0.945469i	$-0.605604\pi$
$347$	−1.46113e6	−0.651426	−0.325713	+	0.945469i	$0.605604\pi$
$348$	1.53153e6	0.677920
$349$	−3.85292e6	−1.69327	−0.846635	−	0.532175i	$-0.821375\pi$
$349$	−3.85292e6	−1.69327	−0.846635	+	0.532175i	$0.821375\pi$
$350$	353199.	0.154116
$351$	684534.	0.296570
$352$	0	0
$353$	−1.35757e6	−0.579864	−0.289932	−	0.957047i	$-0.593633\pi$
$353$	−1.35757e6	−0.579864	−0.289932	+	0.957047i	$0.593633\pi$
$354$	1.95611e6	0.829632
$355$	−2.75997e6	−1.16234
$356$	−412138.	−0.172353
$357$	633072.	0.262895
$358$	1.37401e6	0.566608
$359$	−1.68067e6	−0.688248	−0.344124	−	0.938924i	$-0.611824\pi$
$359$	−1.68067e6	−0.688248	−0.344124	+	0.938924i	$0.611824\pi$
$360$	−102662.	−0.0417495
$361$	1.24001e6	0.500791
$362$	2.12045e6	0.850467
$363$	0	0
$364$	−121096.	−0.0479046
$365$	−1.87630e6	−0.737176
$366$	1.16248e6	0.453611
$367$	3.47103e6	1.34522	0.672609	−	0.739998i	$-0.265174\pi$
$367$	3.47103e6	1.34522	0.672609	+	0.739998i	$0.265174\pi$
$368$	−118852.	−0.0457494
$369$	697586.	0.266705
$370$	−728985.	−0.276831
$371$	1.24502e6	0.469613
$372$	−443687.	−0.166234
$373$	−214110.	−0.0796827	−0.0398413	−	0.999206i	$-0.512685\pi$
$373$	−214110.	−0.0796827	−0.0398413	+	0.999206i	$0.512685\pi$
$374$	0	0
$375$	2.42516e6	0.890557
$376$	1.03596e6	0.377897
$377$	−1.15304e6	−0.417822
$378$	−729177.	−0.262484
$379$	−470610.	−0.168292	−0.0841459	−	0.996453i	$-0.526816\pi$
$379$	−470610.	−0.168292	−0.0841459	+	0.996453i	$0.526816\pi$
$380$	−1.04967e6	−0.372901
$381$	−2.04381e6	−0.721321
$382$	50237.5	0.0176145
$383$	5.44569e6	1.89695	0.948475	−	0.316851i	$-0.102625\pi$
$383$	5.44569e6	1.89695	0.948475	+	0.316851i	$0.102625\pi$
$384$	−229297.	−0.0793544
$385$	0	0
$386$	1.43408e6	0.489897
$387$	−664488.	−0.225533
$388$	1.27079e6	0.428544
$389$	2.90015e6	0.971732	0.485866	−	0.874033i	$-0.338504\pi$
$389$	2.90015e6	0.971732	0.485866	+	0.874033i	$0.338504\pi$
$390$	−321176.	−0.106926
$391$	−467784.	−0.154740
$392$	−946654.	−0.311155
$393$	−407639.	−0.133136
$394$	−2.64364e6	−0.857950
$395$	654660.	0.211117
$396$	0	0
$397$	−5.79367e6	−1.84492	−0.922459	−	0.386094i	$-0.873824\pi$
$397$	−5.79367e6	−1.84492	−0.922459	+	0.386094i	$0.873824\pi$
$398$	−1.37626e6	−0.435505
$399$	−1.21120e6	−0.380877
$400$	−503506.	−0.157346
$401$	4.81743e6	1.49608	0.748039	−	0.663654i	$-0.230995\pi$
$401$	4.81743e6	1.49608	0.748039	+	0.663654i	$0.230995\pi$
$402$	3.49322e6	1.07810
$403$	334037.	0.102455
$404$	1.42890e6	0.435562
$405$	−1.54416e6	−0.467793
$406$	1.22824e6	0.369800
$407$	0	0
$408$	−902482.	−0.268404
$409$	1.58399e6	0.468214	0.234107	−	0.972211i	$-0.424783\pi$
$409$	1.58399e6	0.468214	0.234107	+	0.972211i	$0.424783\pi$
$410$	−2.01468e6	−0.591898
$411$	−2.49608e6	−0.728876
$412$	590667.	0.171435
$413$	1.56873e6	0.452557
$414$	87531.6	0.0250994
$415$	1.32503e6	0.377664
$416$	172630.	0.0489084
$417$	−4.03862e6	−1.13735
$418$	0	0
$419$	5.54621e6	1.54334	0.771669	−	0.636024i	$-0.219422\pi$
$419$	5.54621e6	1.54334	0.771669	+	0.636024i	$0.219422\pi$
$420$	342122.	0.0946363
$421$	5.71372e6	1.57113	0.785567	−	0.618776i	$-0.212371\pi$
$421$	5.71372e6	1.57113	0.785567	+	0.618776i	$0.212371\pi$
$422$	−255985.	−0.0699734
$423$	−762961.	−0.207325
$424$	−1.77485e6	−0.479453
$425$	−1.98173e6	−0.532197
$426$	4.54000e6	1.21208
$427$	932271.	0.247441
$428$	1.98489e6	0.523753
$429$	0	0
$430$	1.91909e6	0.500524
$431$	−1.98415e6	−0.514494	−0.257247	−	0.966346i	$-0.582815\pi$
$431$	−1.98415e6	−0.514494	−0.257247	+	0.966346i	$0.582815\pi$
$432$	1.03949e6	0.267984
$433$	942839.	0.241667	0.120834	−	0.992673i	$-0.461443\pi$
$433$	942839.	0.241667	0.120834	+	0.992673i	$0.461443\pi$
$434$	−355822.	−0.0906793
$435$	3.25758e6	0.825414
$436$	3.11061e6	0.783663
$437$	894972.	0.224185
$438$	3.08641e6	0.768721
$439$	−5.19234e6	−1.28589	−0.642943	−	0.765914i	$-0.722287\pi$
$439$	−5.19234e6	−1.28589	−0.642943	+	0.765914i	$0.722287\pi$
$440$	0	0
$441$	697190.	0.170708
$442$	679448.	0.165425
$443$	−207343.	−0.0501974	−0.0250987	−	0.999685i	$-0.507990\pi$
$443$	−207343.	−0.0501974	−0.0250987	+	0.999685i	$0.507990\pi$
$444$	1.19914e6	0.288677
$445$	−876620.	−0.209851
$446$	−1.88614e6	−0.448989
$447$	6.92795e6	1.63997
$448$	−183888.	−0.0432872
$449$	−3.30440e6	−0.773529	−0.386764	−	0.922179i	$-0.626407\pi$
$449$	−3.30440e6	−0.773529	−0.386764	+	0.922179i	$0.626407\pi$
$450$	370821.	0.0863243
$451$	0	0
$452$	715433.	0.164711
$453$	−4.14400e6	−0.948800
$454$	250061.	0.0569386
$455$	−257572.	−0.0583271
$456$	1.72664e6	0.388858
$457$	2.41419e6	0.540731	0.270365	−	0.962758i	$-0.412855\pi$
$457$	2.41419e6	0.540731	0.270365	+	0.962758i	$0.412855\pi$
$458$	1.21875e6	0.271488
$459$	4.09127e6	0.906414
$460$	−252798.	−0.0557030
$461$	−7.38717e6	−1.61892	−0.809461	−	0.587174i	$-0.800241\pi$
$461$	−7.38717e6	−1.61892	−0.809461	+	0.587174i	$0.800241\pi$
$462$	0	0
$463$	−5.36462e6	−1.16302	−0.581509	−	0.813540i	$-0.697537\pi$
$463$	−5.36462e6	−1.16302	−0.581509	+	0.813540i	$0.697537\pi$
$464$	−1.75093e6	−0.377549
$465$	−943724.	−0.202401
$466$	4.09242e6	0.873001
$467$	334356.	0.0709441	0.0354721	−	0.999371i	$-0.488707\pi$
$467$	334356.	0.0709441	0.0354721	+	0.999371i	$0.488707\pi$
$468$	−127138.	−0.0268325
$469$	2.80144e6	0.588097
$470$	2.20349e6	0.460115
$471$	1.61686e6	0.335830
$472$	−2.23632e6	−0.462040
$473$	0	0
$474$	−1.07688e6	−0.220151
$475$	3.79148e6	0.771036
$476$	−723759.	−0.146412
$477$	1.30713e6	0.263041
$478$	−452393.	−0.0905619
$479$	−4.31661e6	−0.859615	−0.429807	−	0.902921i	$-0.641419\pi$
$479$	−4.31661e6	−0.859615	−0.429807	+	0.902921i	$0.641419\pi$
$480$	−487716.	−0.0966193
$481$	−902791.	−0.177920
$482$	−2.98032e6	−0.584313
$483$	−291701.	−0.0568945
$484$	0	0
$485$	2.70298e6	0.521782
$486$	−1.40674e6	−0.270162
$487$	−6.73620e6	−1.28704	−0.643521	−	0.765429i	$-0.722527\pi$
$487$	−6.73620e6	−1.28704	−0.643521	+	0.765429i	$0.722527\pi$
$488$	−1.32901e6	−0.252626
$489$	8.00855e6	1.51454
$490$	−2.01354e6	−0.378852
$491$	7.61747e6	1.42596	0.712980	−	0.701184i	$-0.247345\pi$
$491$	7.61747e6	1.42596	0.712980	+	0.701184i	$0.247345\pi$
$492$	3.31403e6	0.617226
$493$	−6.89140e6	−1.27700
$494$	−1.29993e6	−0.239664
$495$	0	0
$496$	507245.	0.0925793
$497$	3.64092e6	0.661181
$498$	−2.17960e6	−0.393825
$499$	6.78667e6	1.22013	0.610064	−	0.792352i	$-0.291144\pi$
$499$	6.78667e6	1.22013	0.610064	+	0.792352i	$0.291144\pi$
$500$	−2.77256e6	−0.495971
$501$	3.28836e6	0.585309
$502$	4.51416e6	0.799499
$503$	3.57940e6	0.630798	0.315399	−	0.948959i	$-0.397862\pi$
$503$	3.57940e6	0.630798	0.315399	+	0.948959i	$0.397862\pi$
$504$	135430.	0.0237486
$505$	3.03928e6	0.530326
$506$	0	0
$507$	4.79857e6	0.829071
$508$	2.33659e6	0.401719
$509$	8.82739e6	1.51021	0.755106	−	0.655603i	$-0.227585\pi$
$509$	8.82739e6	1.51021	0.755106	+	0.655603i	$0.227585\pi$
$510$	−1.91958e6	−0.326799
$511$	2.47520e6	0.419331
$512$	262144.	0.0441942
$513$	−7.82749e6	−1.31319
$514$	−6.62547e6	−1.10614
$515$	1.25635e6	0.208734
$516$	−3.15680e6	−0.521942
$517$	0	0
$518$	961668.	0.157471
$519$	−6.15112e6	−1.00239
$520$	367185.	0.0595492
$521$	2.98921e6	0.482460	0.241230	−	0.970468i	$-0.422449\pi$
$521$	2.98921e6	0.482460	0.241230	+	0.970468i	$0.422449\pi$
$522$	1.28952e6	0.207134
$523$	−1.10478e7	−1.76612	−0.883061	−	0.469259i	$-0.844521\pi$
$523$	−1.10478e7	−1.76612	−0.883061	+	0.469259i	$0.844521\pi$
$524$	466033.	0.0741462
$525$	−1.23577e6	−0.195677
$526$	−228755.	−0.0360501
$527$	1.99645e6	0.313135
$528$	0	0
$529$	−6.22080e6	−0.966512
$530$	−3.77510e6	−0.583766
$531$	1.64700e6	0.253488
$532$	1.38471e6	0.212119
$533$	−2.49502e6	−0.380414
$534$	1.44199e6	0.218831
$535$	4.22186e6	0.637704
$536$	−3.99362e6	−0.600419
$537$	−4.80739e6	−0.719405
$538$	−2.06307e6	−0.307297
$539$	0	0
$540$	2.21099e6	0.326289
$541$	−6.22056e6	−0.913769	−0.456885	−	0.889526i	$-0.651035\pi$
$541$	−6.22056e6	−0.913769	−0.456885	+	0.889526i	$0.651035\pi$
$542$	6.21015e6	0.908038
$543$	−7.41904e6	−1.07981
$544$	1.03176e6	0.149480
$545$	6.61628e6	0.954163
$546$	423692.	0.0608231
$547$	−2.34371e6	−0.334916	−0.167458	−	0.985879i	$-0.553556\pi$
$547$	−2.34371e6	−0.334916	−0.167458	+	0.985879i	$0.553556\pi$
$548$	2.85364e6	0.405927
$549$	978785.	0.138598
$550$	0	0
$551$	1.31848e7	1.85009
$552$	415838.	0.0580866
$553$	−863618.	−0.120091
$554$	4.07191e6	0.563669
$555$	2.55057e6	0.351484
$556$	4.61715e6	0.633414
$557$	−2.36041e6	−0.322366	−0.161183	−	0.986925i	$-0.551531\pi$
$557$	−2.36041e6	−0.322366	−0.161183	+	0.986925i	$0.551531\pi$
$558$	−373575.	−0.0507917
$559$	2.37665e6	0.321688
$560$	−391131.	−0.0527050
$561$	0	0
$562$	355286.	0.0474501
$563$	3.72963e6	0.495901	0.247950	−	0.968773i	$-0.420243\pi$
$563$	3.72963e6	0.495901	0.247950	+	0.968773i	$0.420243\pi$
$564$	−3.62461e6	−0.479804
$565$	1.52173e6	0.200547
$566$	3.09127e6	0.405598
$567$	2.03703e6	0.266097
$568$	−5.19035e6	−0.675034
$569$	−332049.	−0.0429954	−0.0214977	−	0.999769i	$-0.506843\pi$
$569$	−332049.	−0.0429954	−0.0214977	+	0.999769i	$0.506843\pi$
$570$	3.67258e6	0.473461
$571$	9.55352e6	1.22623	0.613117	−	0.789992i	$-0.289915\pi$
$571$	9.55352e6	1.22623	0.613117	+	0.789992i	$0.289915\pi$
$572$	0	0
$573$	−175771.	−0.0223645
$574$	2.65774e6	0.336692
$575$	913124.	0.115176
$576$	−193063.	−0.0242462
$577$	1.31593e7	1.64548	0.822741	−	0.568416i	$-0.192444\pi$
$577$	1.31593e7	1.64548	0.822741	+	0.568416i	$0.192444\pi$
$578$	−1.61855e6	−0.201515
$579$	−5.01755e6	−0.622007
$580$	−3.72422e6	−0.459691
$581$	−1.74796e6	−0.214829
$582$	−4.44625e6	−0.544110
$583$	0	0
$584$	−3.52854e6	−0.428118
$585$	−270423.	−0.0326704
$586$	−8.89386e6	−1.06991
$587$	−6.29053e6	−0.753515	−0.376757	−	0.926312i	$-0.622961\pi$
$587$	−6.29053e6	−0.753515	−0.376757	+	0.926312i	$0.622961\pi$
$588$	3.31215e6	0.395064
$589$	−3.81964e6	−0.453664
$590$	−4.75666e6	−0.562565
$591$	9.24956e6	1.08931
$592$	−1.37092e6	−0.160771
$593$	6.91154e6	0.807120	0.403560	−	0.914953i	$-0.367773\pi$
$593$	6.91154e6	0.807120	0.403560	+	0.914953i	$0.367773\pi$
$594$	0	0
$595$	−1.53944e6	−0.178266
$596$	−7.92037e6	−0.913335
$597$	4.81526e6	0.552948
$598$	−313070.	−0.0358005
$599$	−1.07235e7	−1.22115	−0.610577	−	0.791957i	$-0.709062\pi$
$599$	−1.07235e7	−1.22115	−0.610577	+	0.791957i	$0.709062\pi$
$600$	1.76167e6	0.199777
$601$	−3.75263e6	−0.423789	−0.211894	−	0.977293i	$-0.567963\pi$
$601$	−3.75263e6	−0.423789	−0.211894	+	0.977293i	$0.567963\pi$
$602$	−2.53164e6	−0.284715
$603$	2.94121e6	0.329407
$604$	4.73763e6	0.528407
$605$	0	0
$606$	−4.99945e6	−0.553020
$607$	1.17904e7	1.29885	0.649424	−	0.760427i	$-0.275010\pi$
$607$	1.17904e7	1.29885	0.649424	+	0.760427i	$0.275010\pi$
$608$	−1.97399e6	−0.216563
$609$	−4.29735e6	−0.469524
$610$	−2.82680e6	−0.307589
$611$	2.72885e6	0.295717
$612$	−759870.	−0.0820089
$613$	−1.45578e7	−1.56475	−0.782374	−	0.622808i	$-0.785992\pi$
$613$	−1.45578e7	−1.56475	−0.782374	+	0.622808i	$0.785992\pi$
$614$	2.29125e6	0.245274
$615$	7.04896e6	0.751514
$616$	0	0
$617$	726606.	0.0768398	0.0384199	−	0.999262i	$-0.487768\pi$
$617$	726606.	0.0768398	0.0384199	+	0.999262i	$0.487768\pi$
$618$	−2.06662e6	−0.217666
$619$	−8.20988e6	−0.861212	−0.430606	−	0.902540i	$-0.641700\pi$
$619$	−8.20988e6	−0.861212	−0.430606	+	0.902540i	$0.641700\pi$
$620$	1.07891e6	0.112722
$621$	−1.88514e6	−0.196162
$622$	−5.54311e6	−0.574484
$623$	1.15643e6	0.119371
$624$	−603998.	−0.0620975
$625$	249070.	0.0255047
$626$	−1.07021e7	−1.09152
$627$	0	0
$628$	−1.84847e6	−0.187031
$629$	−5.39574e6	−0.543781
$630$	288059.	0.0289155
$631$	5.07809e6	0.507724	0.253862	−	0.967241i	$-0.418299\pi$
$631$	5.07809e6	0.507724	0.253862	+	0.967241i	$0.418299\pi$
$632$	1.23114e6	0.122607
$633$	895639.	0.0888431
$634$	4.64447e6	0.458895
$635$	4.96993e6	0.489120
$636$	6.20983e6	0.608747
$637$	−2.49361e6	−0.243489
$638$	0	0
$639$	3.82258e6	0.370343
$640$	557581.	0.0538094
$641$	5.29171e6	0.508687	0.254344	−	0.967114i	$-0.418141\pi$
$641$	5.29171e6	0.508687	0.254344	+	0.967114i	$0.418141\pi$
$642$	−6.94472e6	−0.664993
$643$	−1.83185e7	−1.74728	−0.873640	−	0.486574i	$-0.838247\pi$
$643$	−1.83185e7	−1.74728	−0.873640	+	0.486574i	$0.838247\pi$
$644$	333487.	0.0316858
$645$	−6.71451e6	−0.635500
$646$	−7.76934e6	−0.732492
$647$	−1.01632e6	−0.0954483	−0.0477241	−	0.998861i	$-0.515197\pi$
$647$	−1.01632e6	−0.0954483	−0.0477241	+	0.998861i	$0.515197\pi$
$648$	−2.90391e6	−0.271673
$649$	0	0
$650$	−1.32630e6	−0.123128
$651$	1.24495e6	0.115133
$652$	−9.15577e6	−0.843482
$653$	−1.35585e7	−1.24431	−0.622156	−	0.782893i	$-0.713743\pi$
$653$	−1.35585e7	−1.24431	−0.622156	+	0.782893i	$0.713743\pi$
$654$	−1.08834e7	−0.994993
$655$	991254.	0.0902780
$656$	−3.78877e6	−0.343747
$657$	2.59869e6	0.234877
$658$	−2.90681e6	−0.261729
$659$	1.39936e7	1.25521	0.627603	−	0.778534i	$-0.284036\pi$
$659$	1.39936e7	1.25521	0.627603	+	0.778534i	$0.284036\pi$
$660$	0	0
$661$	−2.04876e7	−1.82384	−0.911921	−	0.410365i	$-0.865401\pi$
$661$	−2.04876e7	−1.82384	−0.911921	+	0.410365i	$0.865401\pi$
$662$	2.09387e6	0.185697
$663$	−2.37725e6	−0.210035
$664$	2.49183e6	0.219330
$665$	2.94528e6	0.258269
$666$	1.00965e6	0.0882033
$667$	3.17536e6	0.276362
$668$	−3.75942e6	−0.325972
$669$	6.59921e6	0.570068
$670$	−8.49444e6	−0.731051
$671$	0	0
$672$	643388.	0.0549604
$673$	1.85921e7	1.58230	0.791152	−	0.611620i	$-0.209482\pi$
$673$	1.85921e7	1.58230	0.791152	+	0.611620i	$0.209482\pi$
$674$	8.73507e6	0.740657
$675$	−7.98625e6	−0.674658
$676$	−5.48596e6	−0.461728
$677$	−714475.	−0.0599123	−0.0299561	−	0.999551i	$-0.509537\pi$
$677$	−714475.	−0.0599123	−0.0299561	+	0.999551i	$0.509537\pi$
$678$	−2.50316e6	−0.209129
$679$	−3.56574e6	−0.296808
$680$	2.19456e6	0.182002
$681$	−874913.	−0.0722932
$682$	0	0
$683$	−4.26980e6	−0.350232	−0.175116	−	0.984548i	$-0.556030\pi$
$683$	−4.26980e6	−0.350232	−0.175116	+	0.984548i	$0.556030\pi$
$684$	1.45380e6	0.118813
$685$	6.06970e6	0.494243
$686$	5.67441e6	0.460373
$687$	−4.26416e6	−0.344700
$688$	3.60901e6	0.290681
$689$	−4.67517e6	−0.375188
$690$	884488.	0.0707244
$691$	−2.22906e7	−1.77593	−0.887965	−	0.459910i	$-0.847882\pi$
$691$	−2.22906e7	−1.77593	−0.887965	+	0.459910i	$0.847882\pi$
$692$	7.03227e6	0.558252
$693$	0	0
$694$	−5.84452e6	−0.460627
$695$	9.82070e6	0.771224
$696$	6.12614e6	0.479362
$697$	−1.49121e7	−1.16267
$698$	−1.54117e7	−1.19732
$699$	−1.43185e7	−1.10842
$700$	1.41279e6	0.108977
$701$	1.98732e7	1.52747	0.763737	−	0.645528i	$-0.223363\pi$
$701$	1.98732e7	1.52747	0.763737	+	0.645528i	$0.223363\pi$
$702$	2.73814e6	0.209707
$703$	1.03232e7	0.787819
$704$	0	0
$705$	−7.70956e6	−0.584194
$706$	−5.43029e6	−0.410026
$707$	−4.00938e6	−0.301668
$708$	7.82444e6	0.586638
$709$	−1.96135e7	−1.46534	−0.732671	−	0.680583i	$-0.761726\pi$
$709$	−1.96135e7	−1.46534	−0.732671	+	0.680583i	$0.761726\pi$
$710$	−1.10399e7	−0.821900
$711$	−906707.	−0.0672656
$712$	−1.64855e6	−0.121872
$713$	−919906.	−0.0677672
$714$	2.53229e6	0.185895
$715$	0	0
$716$	5.49605e6	0.400652
$717$	1.58283e6	0.114984
$718$	−6.72266e6	−0.486665
$719$	1.07684e7	0.776839	0.388419	−	0.921483i	$-0.373021\pi$
$719$	1.07684e7	0.776839	0.388419	+	0.921483i	$0.373021\pi$
$720$	−410646.	−0.0295214
$721$	−1.65736e6	−0.118735
$722$	4.96003e6	0.354113
$723$	1.04276e7	0.741885
$724$	8.48182e6	0.601371
$725$	1.34522e7	0.950490
$726$	0	0
$727$	3.08418e6	0.216423	0.108212	−	0.994128i	$-0.465488\pi$
$727$	3.08418e6	0.216423	0.108212	+	0.994128i	$0.465488\pi$
$728$	−484385.	−0.0338737
$729$	1.59477e7	1.11142
$730$	−7.50521e6	−0.521262
$731$	1.42046e7	0.983182
$732$	4.64993e6	0.320752
$733$	−2.41098e7	−1.65742	−0.828712	−	0.559675i	$-0.810926\pi$
$733$	−2.41098e7	−1.65742	−0.828712	+	0.559675i	$0.810926\pi$
$734$	1.38841e7	0.951213
$735$	7.04496e6	0.481016
$736$	−475406.	−0.0323497
$737$	0	0
$738$	2.79034e6	0.188589
$739$	3.60334e6	0.242713	0.121357	−	0.992609i	$-0.461276\pi$
$739$	3.60334e6	0.242713	0.121357	+	0.992609i	$0.461276\pi$
$740$	−2.91594e6	−0.195749
$741$	4.54820e6	0.304294
$742$	4.98006e6	0.332066
$743$	1.97401e7	1.31183	0.655916	−	0.754834i	$-0.272283\pi$
$743$	1.97401e7	1.31183	0.655916	+	0.754834i	$0.272283\pi$
$744$	−1.77475e6	−0.117545
$745$	−1.68467e7	−1.11205
$746$	−856438.	−0.0563442
$747$	−1.83518e6	−0.120331
$748$	0	0
$749$	−5.56942e6	−0.362748
$750$	9.70063e6	0.629719
$751$	−699753.	−0.0452736	−0.0226368	−	0.999744i	$-0.507206\pi$
$751$	−699753.	−0.0452736	−0.0226368	+	0.999744i	$0.507206\pi$
$752$	4.14384e6	0.267213
$753$	−1.57941e7	−1.01510
$754$	−4.61216e6	−0.295445
$755$	1.00770e7	0.643372
$756$	−2.91671e6	−0.185604
$757$	−2.99299e6	−0.189830	−0.0949151	−	0.995485i	$-0.530258\pi$
$757$	−2.99299e6	−0.189830	−0.0949151	+	0.995485i	$0.530258\pi$
$758$	−1.88244e6	−0.119000
$759$	0	0
$760$	−4.19867e6	−0.263681
$761$	1.30835e7	0.818962	0.409481	−	0.912319i	$-0.365710\pi$
$761$	1.30835e7	0.818962	0.409481	+	0.912319i	$0.365710\pi$
$762$	−8.17525e6	−0.510051
$763$	−8.72811e6	−0.542761
$764$	200950.	0.0124553
$765$	−1.61625e6	−0.0998513
$766$	2.17828e7	1.34135
$767$	−5.89076e6	−0.361562
$768$	−917189.	−0.0561120
$769$	−1.92752e7	−1.17539	−0.587697	−	0.809081i	$-0.699965\pi$
$769$	−1.92752e7	−1.17539	−0.587697	+	0.809081i	$0.699965\pi$
$770$	0	0
$771$	2.31812e7	1.40443
$772$	5.73631e6	0.346409
$773$	4.59668e6	0.276692	0.138346	−	0.990384i	$-0.455821\pi$
$773$	4.59668e6	0.276692	0.138346	+	0.990384i	$0.455821\pi$
$774$	−2.65795e6	−0.159476
$775$	−3.89711e6	−0.233071
$776$	5.08318e6	0.303027
$777$	−3.36468e6	−0.199936
$778$	1.16006e7	0.687118
$779$	2.85300e7	1.68445
$780$	−1.28471e6	−0.0756079
$781$	0	0
$782$	−1.87113e6	−0.109418
$783$	−2.77719e7	−1.61883
$784$	−3.78662e6	−0.220020
$785$	−3.93170e6	−0.227723
$786$	−1.63056e6	−0.0941412
$787$	1.00311e7	0.577313	0.288657	−	0.957433i	$-0.406791\pi$
$787$	1.00311e7	0.577313	0.288657	+	0.957433i	$0.406791\pi$
$788$	−1.05746e7	−0.606662
$789$	800368.	0.0457717
$790$	2.61864e6	0.149282
$791$	−2.00744e6	−0.114078
$792$	0	0
$793$	−3.50078e6	−0.197688
$794$	−2.31747e7	−1.30455
$795$	1.32083e7	0.741190
$796$	−5.50505e6	−0.307949
$797$	2.24814e7	1.25365	0.626827	−	0.779159i	$-0.284353\pi$
$797$	2.24814e7	1.25365	0.626827	+	0.779159i	$0.284353\pi$
$798$	−4.84482e6	−0.269321
$799$	1.63096e7	0.903807
$800$	−2.01402e6	−0.111260
$801$	1.21412e6	0.0668623
$802$	1.92697e7	1.05789
$803$	0	0
$804$	1.39729e7	0.762334
$805$	709329.	0.0385796
$806$	1.33615e6	0.0724465
$807$	7.21826e6	0.390165
$808$	5.71562e6	0.307989
$809$	1.59748e7	0.858153	0.429077	−	0.903268i	$-0.358839\pi$
$809$	1.59748e7	0.858153	0.429077	+	0.903268i	$0.358839\pi$
$810$	−6.17663e6	−0.330780
$811$	−2.04745e6	−0.109310	−0.0546551	−	0.998505i	$-0.517406\pi$
$811$	−2.04745e6	−0.109310	−0.0546551	+	0.998505i	$0.517406\pi$
$812$	4.91295e6	0.261488
$813$	−2.17281e7	−1.15291
$814$	0	0
$815$	−1.94743e7	−1.02700
$816$	−3.60993e6	−0.189790
$817$	−2.71764e7	−1.42442
$818$	6.33596e6	0.331077
$819$	356739.	0.0185841
$820$	−8.05872e6	−0.418535
$821$	−2.23680e7	−1.15816	−0.579082	−	0.815269i	$-0.696589\pi$
$821$	−2.23680e7	−1.15816	−0.579082	+	0.815269i	$0.696589\pi$
$822$	−9.98431e6	−0.515393
$823$	−1.19039e7	−0.612616	−0.306308	−	0.951933i	$-0.599094\pi$
$823$	−1.19039e7	−0.612616	−0.306308	+	0.951933i	$0.599094\pi$
$824$	2.36267e6	0.121223
$825$	0	0
$826$	6.27493e6	0.320006
$827$	−1.28553e7	−0.653611	−0.326805	−	0.945092i	$-0.605972\pi$
$827$	−1.28553e7	−0.653611	−0.326805	+	0.945092i	$0.605972\pi$
$828$	350126.	0.0177480
$829$	3.55346e7	1.79583	0.897914	−	0.440171i	$-0.145082\pi$
$829$	3.55346e7	1.79583	0.897914	+	0.440171i	$0.145082\pi$
$830$	5.30013e6	0.267049
$831$	−1.42468e7	−0.715673
$832$	690521.	0.0345834
$833$	−1.49036e7	−0.744181
$834$	−1.61545e7	−0.804226
$835$	−7.99630e6	−0.396892
$836$	0	0
$837$	8.04557e6	0.396957
$838$	2.21848e7	1.09130
$839$	−2.40146e6	−0.117780	−0.0588899	−	0.998264i	$-0.518756\pi$
$839$	−2.40146e6	−0.117780	−0.0588899	+	0.998264i	$0.518756\pi$
$840$	1.36849e6	0.0669180
$841$	2.62684e7	1.28069
$842$	2.28549e7	1.11096
$843$	−1.24307e6	−0.0602460
$844$	−1.02394e6	−0.0494787
$845$	−1.16686e7	−0.562184
$846$	−3.05184e6	−0.146601
$847$	0	0
$848$	−7.09938e6	−0.339024
$849$	−1.08157e7	−0.514975
$850$	−7.92692e6	−0.376320
$851$	2.48620e6	0.117683
$852$	1.81600e7	0.857071
$853$	−2.60183e7	−1.22435	−0.612176	−	0.790722i	$-0.709706\pi$
$853$	−2.60183e7	−1.22435	−0.612176	+	0.790722i	$0.709706\pi$
$854$	3.72908e6	0.174967
$855$	3.09223e6	0.144663
$856$	7.93955e6	0.370349
$857$	−1.67662e7	−0.779800	−0.389900	−	0.920857i	$-0.627490\pi$
$857$	−1.67662e7	−0.779800	−0.389900	+	0.920857i	$0.627490\pi$
$858$	0	0
$859$	−1.56395e7	−0.723168	−0.361584	−	0.932340i	$-0.617764\pi$
$859$	−1.56395e7	−0.723168	−0.361584	+	0.932340i	$0.617764\pi$
$860$	7.67637e6	0.353924
$861$	−9.29890e6	−0.427488
$862$	−7.93659e6	−0.363802
$863$	2.85791e7	1.30624	0.653119	−	0.757256i	$-0.273460\pi$
$863$	2.85791e7	1.30624	0.653119	+	0.757256i	$0.273460\pi$
$864$	4.15794e6	0.189493
$865$	1.49577e7	0.679709
$866$	3.77135e6	0.170884
$867$	5.66299e6	0.255857
$868$	−1.42329e6	−0.0641200
$869$	0	0
$870$	1.30303e7	0.583656
$871$	−1.05197e7	−0.469848
$872$	1.24424e7	0.554134
$873$	−3.74365e6	−0.166249
$874$	3.57989e6	0.158522
$875$	7.77957e6	0.343507
$876$	1.23457e7	0.543568
$877$	6.33547e6	0.278150	0.139075	−	0.990282i	$-0.455587\pi$
$877$	6.33547e6	0.278150	0.139075	+	0.990282i	$0.455587\pi$
$878$	−2.07694e7	−0.909258
$879$	3.11178e7	1.35843
$880$	0	0
$881$	3.12019e7	1.35438	0.677191	−	0.735807i	$-0.263197\pi$
$881$	3.12019e7	1.35438	0.677191	+	0.735807i	$0.263197\pi$
$882$	2.78876e6	0.120709
$883$	−1.27448e7	−0.550087	−0.275044	−	0.961432i	$-0.588692\pi$
$883$	−1.27448e7	−0.550087	−0.275044	+	0.961432i	$0.588692\pi$
$884$	2.71779e6	0.116973
$885$	1.66426e7	0.714271
$886$	−829374.	−0.0354949
$887$	3.53427e7	1.50831	0.754155	−	0.656697i	$-0.228047\pi$
$887$	3.53427e7	1.50831	0.754155	+	0.656697i	$0.228047\pi$
$888$	4.79656e6	0.204125
$889$	−6.55626e6	−0.278229
$890$	−3.50648e6	−0.148387
$891$	0	0
$892$	−7.54455e6	−0.317484
$893$	−3.12037e7	−1.30942
$894$	2.77118e7	1.15963
$895$	1.16901e7	0.487821
$896$	−735553.	−0.0306087
$897$	1.09537e6	0.0454548
$898$	−1.32176e7	−0.546968
$899$	−1.35521e7	−0.559251
$900$	1.48328e6	0.0610405
$901$	−2.79422e7	−1.14670
$902$	0	0
$903$	8.85770e6	0.361494
$904$	2.86173e6	0.116468
$905$	1.80408e7	0.732210
$906$	−1.65760e7	−0.670903
$907$	3.10415e6	0.125292	0.0626462	−	0.998036i	$-0.480046\pi$
$907$	3.10415e6	0.125292	0.0626462	+	0.998036i	$0.480046\pi$
$908$	1.00024e6	0.0402616
$909$	−4.20943e6	−0.168971
$910$	−1.03029e6	−0.0412435
$911$	−1.80496e7	−0.720563	−0.360281	−	0.932844i	$-0.617319\pi$
$911$	−1.80496e7	−0.720563	−0.360281	+	0.932844i	$0.617319\pi$
$912$	6.90658e6	0.274964
$913$	0	0
$914$	9.65676e6	0.382354
$915$	9.89042e6	0.390537
$916$	4.87500e6	0.191971
$917$	−1.30765e6	−0.0513533
$918$	1.63651e7	0.640931
$919$	−1.25209e7	−0.489044	−0.244522	−	0.969644i	$-0.578631\pi$
$919$	−1.25209e7	−0.489044	−0.244522	+	0.969644i	$0.578631\pi$
$920$	−1.01119e6	−0.0393880
$921$	−8.01662e6	−0.311417
$922$	−2.95487e7	−1.14475
$923$	−1.36720e7	−0.528237
$924$	0	0
$925$	1.05326e7	0.404745
$926$	−2.14585e7	−0.822377
$927$	−1.74005e6	−0.0665063
$928$	−7.00370e6	−0.266967
$929$	−1.30954e7	−0.497826	−0.248913	−	0.968526i	$-0.580073\pi$
$929$	−1.30954e7	−0.497826	−0.248913	+	0.968526i	$0.580073\pi$
$930$	−3.77490e6	−0.143119
$931$	2.85138e7	1.07816
$932$	1.63697e7	0.617305
$933$	1.93942e7	0.729404
$934$	1.33742e6	0.0501651
$935$	0	0
$936$	−508553.	−0.0189735
$937$	1.22906e6	0.0457324	0.0228662	−	0.999739i	$-0.492721\pi$
$937$	1.22906e6	0.0457324	0.0228662	+	0.999739i	$0.492721\pi$
$938$	1.12057e7	0.415847
$939$	3.74445e7	1.38587
$940$	8.81395e6	0.325350
$941$	2.81996e6	0.103817	0.0519085	−	0.998652i	$-0.483470\pi$
$941$	2.81996e6	0.103817	0.0519085	+	0.998652i	$0.483470\pi$
$942$	6.46742e6	0.237467
$943$	6.87105e6	0.251619
$944$	−8.94529e6	−0.326712
$945$	−6.20384e6	−0.225986
$946$	0	0
$947$	4.77505e7	1.73023	0.865114	−	0.501576i	$-0.167246\pi$
$947$	4.77505e7	1.73023	0.865114	+	0.501576i	$0.167246\pi$
$948$	−4.30751e6	−0.155670
$949$	−9.29462e6	−0.335017
$950$	1.51659e7	0.545205
$951$	−1.62501e7	−0.582645
$952$	−2.89504e6	−0.103529
$953$	4.11415e7	1.46740	0.733699	−	0.679474i	$-0.237792\pi$
$953$	4.11415e7	1.46740	0.733699	+	0.679474i	$0.237792\pi$
$954$	5.22854e6	0.185998
$955$	427421.	0.0151652
$956$	−1.80957e6	−0.0640370
$957$	0	0
$958$	−1.72664e7	−0.607839
$959$	−8.00707e6	−0.281143
$960$	−1.95086e6	−0.0683201
$961$	−2.47031e7	−0.862865
$962$	−3.61117e6	−0.125808
$963$	−5.84730e6	−0.203184
$964$	−1.19213e7	−0.413172
$965$	1.22012e7	0.421777
$966$	−1.16681e6	−0.0402305
$967$	−2.71858e7	−0.934924	−0.467462	−	0.884013i	$-0.654832\pi$
$967$	−2.71858e7	−0.934924	−0.467462	+	0.884013i	$0.654832\pi$
$968$	0	0
$969$	2.71833e7	0.930022
$970$	1.08119e7	0.368955
$971$	−3.01073e7	−1.02476	−0.512382	−	0.858758i	$-0.671237\pi$
$971$	−3.01073e7	−1.02476	−0.512382	+	0.858758i	$0.671237\pi$
$972$	−5.62698e6	−0.191034
$973$	−1.29553e7	−0.438699
$974$	−2.69448e7	−0.910076
$975$	4.64045e6	0.156332
$976$	−5.31603e6	−0.178634
$977$	2.08285e7	0.698105	0.349053	−	0.937103i	$-0.386503\pi$
$977$	2.08285e7	0.698105	0.349053	+	0.937103i	$0.386503\pi$
$978$	3.20342e7	1.07094
$979$	0	0
$980$	−8.05414e6	−0.267889
$981$	−9.16358e6	−0.304013
$982$	3.04699e7	1.00831
$983$	−4.97327e6	−0.164156	−0.0820782	−	0.996626i	$-0.526156\pi$
$983$	−4.97327e6	−0.164156	−0.0820782	+	0.996626i	$0.526156\pi$
$984$	1.32561e7	0.436445
$985$	−2.24921e7	−0.738652
$986$	−2.75656e7	−0.902974
$987$	1.01704e7	0.332310
$988$	−5.19973e6	−0.169468
$989$	−6.54505e6	−0.212776
$990$	0	0
$991$	−3.93510e7	−1.27283	−0.636417	−	0.771345i	$-0.719584\pi$
$991$	−3.93510e7	−1.27283	−0.636417	+	0.771345i	$0.719584\pi$
$992$	2.02898e6	0.0654635
$993$	−7.32605e6	−0.235774
$994$	1.45637e7	0.467525
$995$	−1.17093e7	−0.374948
$996$	−8.71841e6	−0.278477
$997$	−1.00523e6	−0.0320280	−0.0160140	−	0.999872i	$-0.505098\pi$
$997$	−1.00523e6	−0.0320280	−0.0160140	+	0.999872i	$0.505098\pi$
$998$	2.71467e7	0.862761
$999$	−2.17445e7	−0.689343

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	242.6.a.m.1.2		4
11.2	odd	10		22.6.c.a.15.1	yes	8
11.6	odd	10		22.6.c.a.3.1	✓	8
11.10	odd	2		242.6.a.k.1.2		4
33.2	even	10		198.6.f.b.37.2		8
33.17	even	10		198.6.f.b.91.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.6.c.a.3.1	✓	8	11.6	odd	10
22.6.c.a.15.1	yes	8	11.2	odd	10
198.6.f.b.37.2		8	33.2	even	10
198.6.f.b.91.2		8	33.17	even	10
242.6.a.k.1.2		4	11.10	odd	2
242.6.a.m.1.2		4	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 242 = 2 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	242.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} -13.9952 q^{3} +16.0000 q^{4} +34.0320 q^{5} -55.9808 q^{6} -44.8946 q^{7} +64.0000 q^{8} -47.1346 q^{9} +136.128 q^{10} -223.923 q^{12} +168.584 q^{13} -179.578 q^{14} -476.285 q^{15} +256.000 q^{16} +1007.58 q^{17} -188.538 q^{18} -1927.72 q^{19} +544.513 q^{20} +628.309 q^{21} -464.264 q^{23} -895.692 q^{24} -1966.82 q^{25} +674.336 q^{26} +4060.49 q^{27} -718.314 q^{28} -6839.56 q^{29} -1905.14 q^{30} +1981.43 q^{31} +1024.00 q^{32} +4030.32 q^{34} -1527.86 q^{35} -754.153 q^{36} -5355.14 q^{37} -7710.88 q^{38} -2359.37 q^{39} +2178.05 q^{40} -14799.9 q^{41} +2513.24 q^{42} +14097.7 q^{43} -1604.09 q^{45} -1857.06 q^{46} +16186.9 q^{47} -3582.77 q^{48} -14791.5 q^{49} -7867.28 q^{50} -14101.3 q^{51} +2697.35 q^{52} -27732.0 q^{53} +16242.0 q^{54} -2873.26 q^{56} +26978.8 q^{57} -27358.2 q^{58} -34942.5 q^{59} -7620.56 q^{60} -20765.8 q^{61} +7925.71 q^{62} +2116.09 q^{63} +4096.00 q^{64} +5737.26 q^{65} -62400.3 q^{67} +16121.3 q^{68} +6497.47 q^{69} -6111.42 q^{70} -81099.2 q^{71} -3016.61 q^{72} -55133.4 q^{73} -21420.6 q^{74} +27526.0 q^{75} -30843.5 q^{76} -9437.47 q^{78} +19236.6 q^{79} +8712.20 q^{80} -45373.6 q^{81} -59199.5 q^{82} +38934.8 q^{83} +10052.9 q^{84} +34290.0 q^{85} +56390.7 q^{86} +95720.9 q^{87} -25758.7 q^{89} -6416.34 q^{90} -7568.52 q^{91} -7428.23 q^{92} -27730.5 q^{93} +64747.5 q^{94} -65604.3 q^{95} -14331.1 q^{96} +79424.6 q^{97} -59165.9 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 16 q^{2} - 10 q^{3} + 64 q^{4} - 150 q^{5} - 40 q^{6} - 34 q^{7} + 256 q^{8} + 302 q^{9} - 600 q^{10} - 160 q^{12} + 138 q^{13} - 136 q^{14} + 206 q^{15} + 1024 q^{16} - 370 q^{17} + 1208 q^{18} - 2358 q^{19}+ \cdots - 90152 q^{98}+O(q^{100}) \) 4 * q + 16 * q^2 - 10 * q^3 + 64 * q^4 - 150 * q^5 - 40 * q^6 - 34 * q^7 + 256 * q^8 + 302 * q^9 - 600 * q^10 - 160 * q^12 + 138 * q^13 - 136 * q^14 + 206 * q^15 + 1024 * q^16 - 370 * q^17 + 1208 * q^18 - 2358 * q^19 - 2400 * q^20 - 5162 * q^21 + 820 * q^23 - 640 * q^24 + 1114 * q^25 + 552 * q^26 - 7810 * q^27 - 544 * q^28 - 11242 * q^29 + 824 * q^30 - 17096 * q^31 + 4096 * q^32 - 1480 * q^34 - 9238 * q^35 + 4832 * q^36 - 16194 * q^37 - 9432 * q^38 - 15446 * q^39 - 9600 * q^40 - 34262 * q^41 - 20648 * q^42 + 5396 * q^43 - 33940 * q^45 + 3280 * q^46 + 8898 * q^47 - 2560 * q^48 - 22538 * q^49 + 4456 * q^50 - 62378 * q^51 + 2208 * q^52 - 12274 * q^53 - 31240 * q^54 - 2176 * q^56 + 87082 * q^57 - 44968 * q^58 + 8222 * q^59 + 3296 * q^60 + 68186 * q^61 - 68384 * q^62 + 70948 * q^63 + 16384 * q^64 + 16486 * q^65 - 167868 * q^67 - 5920 * q^68 - 119656 * q^69 - 36952 * q^70 - 96324 * q^71 + 19328 * q^72 - 33278 * q^73 - 64776 * q^74 - 89830 * q^75 - 37728 * q^76 - 61784 * q^78 + 158272 * q^79 - 38400 * q^80 - 143056 * q^81 - 137048 * q^82 + 196304 * q^83 - 82592 * q^84 + 80558 * q^85 + 21584 * q^86 + 86828 * q^87 - 267400 * q^89 - 135760 * q^90 - 48850 * q^91 + 13120 * q^92 - 58944 * q^93 + 35592 * q^94 + 3038 * q^95 - 10240 * q^96 - 26738 * q^97 - 90152 * q^98

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