LMFDB - Embedded newform 165.6.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,6,Mod(1,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("165.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	165.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$26.4633302691$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.307532.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 76x + 168 $ x^3 - x^2 - 76*x + 168
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-9.21967$ of defining polynomial
Character	$\chi$	$=$	165.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-7.21967 q^{2} -9.00000 q^{3} +20.1236 q^{4} -25.0000 q^{5} +64.9770 q^{6} +147.570 q^{7} +85.7438 q^{8} +81.0000 q^{9} +180.492 q^{10} +121.000 q^{11} -181.112 q^{12} -1124.39 q^{13} -1065.40 q^{14} +225.000 q^{15} -1263.00 q^{16} +1019.99 q^{17} -584.793 q^{18} -13.7131 q^{19} -503.090 q^{20} -1328.13 q^{21} -873.580 q^{22} -2116.94 q^{23} -771.694 q^{24} +625.000 q^{25} +8117.69 q^{26} -729.000 q^{27} +2969.63 q^{28} +3120.98 q^{29} -1624.42 q^{30} -9628.99 q^{31} +6374.61 q^{32} -1089.00 q^{33} -7363.96 q^{34} -3689.24 q^{35} +1630.01 q^{36} -3121.52 q^{37} +99.0039 q^{38} +10119.5 q^{39} -2143.59 q^{40} -5884.38 q^{41} +9588.63 q^{42} +20522.3 q^{43} +2434.95 q^{44} -2025.00 q^{45} +15283.6 q^{46} +24718.5 q^{47} +11367.0 q^{48} +4969.81 q^{49} -4512.29 q^{50} -9179.87 q^{51} -22626.7 q^{52} +22761.1 q^{53} +5263.14 q^{54} -3025.00 q^{55} +12653.2 q^{56} +123.418 q^{57} -22532.4 q^{58} -14533.5 q^{59} +4527.81 q^{60} +43984.9 q^{61} +69518.1 q^{62} +11953.1 q^{63} -5606.68 q^{64} +28109.6 q^{65} +7862.22 q^{66} -31488.3 q^{67} +20525.8 q^{68} +19052.5 q^{69} +26635.1 q^{70} -29173.2 q^{71} +6945.24 q^{72} +49583.0 q^{73} +22536.3 q^{74} -5625.00 q^{75} -275.956 q^{76} +17855.9 q^{77} -73059.2 q^{78} -85075.4 q^{79} +31574.9 q^{80} +6561.00 q^{81} +42483.3 q^{82} +77321.9 q^{83} -26726.7 q^{84} -25499.6 q^{85} -148164. q^{86} -28088.8 q^{87} +10375.0 q^{88} +70217.7 q^{89} +14619.8 q^{90} -165925. q^{91} -42600.5 q^{92} +86660.9 q^{93} -178459. q^{94} +342.827 q^{95} -57371.5 q^{96} -21080.0 q^{97} -35880.4 q^{98} +9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 7 q^{2} - 27 q^{3} + 73 q^{4} - 75 q^{5} - 63 q^{6} + 92 q^{7} + 231 q^{8} + 243 q^{9} - 175 q^{10} + 363 q^{11} - 657 q^{12} - 90 q^{13} - 784 q^{14} + 675 q^{15} - 415 q^{16} + 1934 q^{17} + 567 q^{18}+ \cdots + 29403 q^{99}+O(q^{100}) $ 3 * q + 7 * q^2 - 27 * q^3 + 73 * q^4 - 75 * q^5 - 63 * q^6 + 92 * q^7 + 231 * q^8 + 243 * q^9 - 175 * q^10 + 363 * q^11 - 657 * q^12 - 90 * q^13 - 784 * q^14 + 675 * q^15 - 415 * q^16 + 1934 * q^17 + 567 * q^18 + 2084 * q^19 - 1825 * q^20 - 828 * q^21 + 847 * q^22 + 1220 * q^23 - 2079 * q^24 + 1875 * q^25 + 17062 * q^26 - 2187 * q^27 + 11120 * q^28 + 4402 * q^29 + 1575 * q^30 - 10688 * q^31 + 12439 * q^32 - 3267 * q^33 - 4094 * q^34 - 2300 * q^35 + 5913 * q^36 - 8190 * q^37 + 13792 * q^38 + 810 * q^39 - 5775 * q^40 + 5974 * q^41 + 7056 * q^42 + 18868 * q^43 + 8833 * q^44 - 6075 * q^45 + 46220 * q^46 + 55500 * q^47 + 3735 * q^48 + 1907 * q^49 + 4375 * q^50 - 17406 * q^51 + 27330 * q^52 + 9206 * q^53 - 5103 * q^54 - 9075 * q^55 + 73248 * q^56 - 18756 * q^57 + 15366 * q^58 - 59196 * q^59 + 16425 * q^60 + 79902 * q^61 + 64616 * q^62 + 7452 * q^63 + 2129 * q^64 + 2250 * q^65 - 7623 * q^66 + 4468 * q^67 - 1218 * q^68 - 10980 * q^69 + 19600 * q^70 - 75164 * q^71 + 18711 * q^72 - 61290 * q^73 - 56766 * q^74 - 16875 * q^75 + 37816 * q^76 + 11132 * q^77 - 153558 * q^78 - 83564 * q^79 + 10375 * q^80 + 19683 * q^81 + 147410 * q^82 + 74764 * q^83 - 100080 * q^84 - 48350 * q^85 - 253432 * q^86 - 39618 * q^87 + 27951 * q^88 + 37342 * q^89 - 14175 * q^90 - 126488 * q^91 + 148164 * q^92 + 96192 * q^93 + 59252 * q^94 - 52100 * q^95 - 111951 * q^96 + 33486 * q^97 - 95249 * q^98 + 29403 * q^99

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 $

$2$	−7.21967	−1.27627	−0.638134	−	0.769925i	$-0.720294\pi$
$2$	−7.21967	−1.27627	−0.638134	+	0.769925i	$0.720294\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	20.1236	0.628862
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	64.9770	0.736854
$7$	147.570	1.13829	0.569144	−	0.822238i	$-0.307275\pi$
$7$	147.570	1.13829	0.569144	+	0.822238i	$0.307275\pi$
$8$	85.7438	0.473672
$9$	81.0000	0.333333
$10$	180.492	0.570765
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−181.112	−0.363074
$13$	−1124.39	−1.84526	−0.922628	−	0.385690i	$-0.873963\pi$
$13$	−1124.39	−1.84526	−0.922628	+	0.385690i	$0.873963\pi$
$14$	−1065.40	−1.45276
$15$	225.000	0.258199
$16$	−1263.00	−1.23339
$17$	1019.99	0.855996	0.427998	−	0.903780i	$-0.359219\pi$
$17$	1019.99	0.855996	0.427998	+	0.903780i	$0.359219\pi$
$18$	−584.793	−0.425423
$19$	−13.7131	−0.00871467	−0.00435734	−	0.999991i	$-0.501387\pi$
$19$	−13.7131	−0.00871467	−0.00435734	+	0.999991i	$0.501387\pi$
$20$	−503.090	−0.281236
$21$	−1328.13	−0.657191
$22$	−873.580	−0.384810
$23$	−2116.94	−0.834430	−0.417215	−	0.908808i	$-0.636994\pi$
$23$	−2116.94	−0.834430	−0.417215	+	0.908808i	$0.636994\pi$
$24$	−771.694	−0.273475
$25$	625.000	0.200000
$26$	8117.69	2.35504
$27$	−729.000	−0.192450
$28$	2969.63	0.715826
$29$	3120.98	0.689122	0.344561	−	0.938764i	$-0.388028\pi$
$29$	3120.98	0.689122	0.344561	+	0.938764i	$0.388028\pi$
$30$	−1624.42	−0.329531
$31$	−9628.99	−1.79960	−0.899801	−	0.436301i	$-0.856288\pi$
$31$	−9628.99	−1.79960	−0.899801	+	0.436301i	$0.856288\pi$
$32$	6374.61	1.10047
$33$	−1089.00	−0.174078
$34$	−7363.96	−1.09248
$35$	−3689.24	−0.509058
$36$	1630.01	0.209621
$37$	−3121.52	−0.374854	−0.187427	−	0.982279i	$-0.560015\pi$
$37$	−3121.52	−0.374854	−0.187427	+	0.982279i	$0.560015\pi$
$38$	99.0039	0.0111223
$39$	10119.5	1.06536
$40$	−2143.59	−0.211832
$41$	−5884.38	−0.546690	−0.273345	−	0.961916i	$-0.588130\pi$
$41$	−5884.38	−0.546690	−0.273345	+	0.961916i	$0.588130\pi$
$42$	9588.63	0.838752
$43$	20522.3	1.69260	0.846302	−	0.532704i	$-0.178824\pi$
$43$	20522.3	1.69260	0.846302	+	0.532704i	$0.178824\pi$
$44$	2434.95	0.189609
$45$	−2025.00	−0.149071
$46$	15283.6	1.06496
$47$	24718.5	1.63222	0.816108	−	0.577899i	$-0.196127\pi$
$47$	24718.5	1.63222	0.816108	+	0.577899i	$0.196127\pi$
$48$	11367.0	0.712101
$49$	4969.81	0.295699
$50$	−4512.29	−0.255254
$51$	−9179.87	−0.494210
$52$	−22626.7	−1.16041
$53$	22761.1	1.11302	0.556511	−	0.830840i	$-0.312140\pi$
$53$	22761.1	1.11302	0.556511	+	0.830840i	$0.312140\pi$
$54$	5263.14	0.245618
$55$	−3025.00	−0.134840
$56$	12653.2	0.539175
$57$	123.418	0.00503142
$58$	−22532.4	−0.879505
$59$	−14533.5	−0.543553	−0.271776	−	0.962360i	$-0.587611\pi$
$59$	−14533.5	−0.543553	−0.271776	+	0.962360i	$0.587611\pi$
$60$	4527.81	0.162371
$61$	43984.9	1.51349	0.756743	−	0.653712i	$-0.226789\pi$
$61$	43984.9	1.51349	0.756743	+	0.653712i	$0.226789\pi$
$62$	69518.1	2.29677
$63$	11953.1	0.379429
$64$	−5606.68	−0.171102
$65$	28109.6	0.825224
$66$	7862.22	0.222170
$67$	−31488.3	−0.856964	−0.428482	−	0.903550i	$-0.640951\pi$
$67$	−31488.3	−0.856964	−0.428482	+	0.903550i	$0.640951\pi$
$68$	20525.8	0.538303
$69$	19052.5	0.481758
$70$	26635.1	0.649694
$71$	−29173.2	−0.686812	−0.343406	−	0.939187i	$-0.611581\pi$
$71$	−29173.2	−0.686812	−0.343406	+	0.939187i	$0.611581\pi$
$72$	6945.24	0.157891
$73$	49583.0	1.08899	0.544497	−	0.838763i	$-0.316721\pi$
$73$	49583.0	1.08899	0.544497	+	0.838763i	$0.316721\pi$
$74$	22536.3	0.478414
$75$	−5625.00	−0.115470
$76$	−275.956	−0.00548033
$77$	17855.9	0.343207
$78$	−73059.2	−1.35968
$79$	−85075.4	−1.53369	−0.766843	−	0.641835i	$-0.778174\pi$
$79$	−85075.4	−1.53369	−0.766843	+	0.641835i	$0.778174\pi$
$80$	31574.9	0.551591
$81$	6561.00	0.111111
$82$	42483.3	0.697724
$83$	77321.9	1.23199	0.615995	−	0.787750i	$-0.288754\pi$
$83$	77321.9	1.23199	0.615995	+	0.787750i	$0.288754\pi$
$84$	−26726.7	−0.413282
$85$	−25499.6	−0.382813
$86$	−148164.	−2.16022
$87$	−28088.8	−0.397865
$88$	10375.0	0.142817
$89$	70217.7	0.939661	0.469831	−	0.882757i	$-0.344315\pi$
$89$	70217.7	0.939661	0.469831	+	0.882757i	$0.344315\pi$
$90$	14619.8	0.190255
$91$	−165925.	−2.10043
$92$	−42600.5	−0.524741
$93$	86660.9	1.03900
$94$	−178459.	−2.08315
$95$	342.827	0.00389732
$96$	−57371.5	−0.635357
$97$	−21080.0	−0.227479	−0.113739	−	0.993511i	$-0.536283\pi$
$97$	−21080.0	−0.227479	−0.113739	+	0.993511i	$0.536283\pi$
$98$	−35880.4	−0.377391
$99$	9801.00	0.100504
$100$	12577.2	0.125772
$101$	−60279.4	−0.587984	−0.293992	−	0.955808i	$-0.594984\pi$
$101$	−60279.4	−0.587984	−0.293992	+	0.955808i	$0.594984\pi$
$102$	66275.6	0.630744
$103$	83535.5	0.775851	0.387925	−	0.921691i	$-0.373192\pi$
$103$	83535.5	0.775851	0.387925	+	0.921691i	$0.373192\pi$
$104$	−96409.0	−0.874046
$105$	33203.2	0.293905
$106$	−164328.	−1.42052
$107$	159288.	1.34500	0.672502	−	0.740095i	$-0.265219\pi$
$107$	159288.	1.34500	0.672502	+	0.740095i	$0.265219\pi$
$108$	−14670.1	−0.121025
$109$	−31166.3	−0.251258	−0.125629	−	0.992077i	$-0.540095\pi$
$109$	−31166.3	−0.251258	−0.125629	+	0.992077i	$0.540095\pi$
$110$	21839.5	0.172092
$111$	28093.7	0.216422
$112$	−186380.	−1.40396
$113$	141850.	1.04504	0.522521	−	0.852626i	$-0.324992\pi$
$113$	141850.	1.04504	0.522521	+	0.852626i	$0.324992\pi$
$114$	−891.035	−0.00642144
$115$	52923.6	0.373168
$116$	62805.3	0.433363
$117$	−91075.2	−0.615086
$118$	104927.	0.693719
$119$	150519.	0.974370
$120$	19292.3	0.122302
$121$	14641.0	0.0909091
$122$	−317556.	−1.93162
$123$	52959.5	0.315632
$124$	−193770.	−1.13170
$125$	−15625.0	−0.0894427
$126$	−86297.7	−0.484254
$127$	−92350.0	−0.508075	−0.254037	−	0.967194i	$-0.581759\pi$
$127$	−92350.0	−0.508075	−0.254037	+	0.967194i	$0.581759\pi$
$128$	−163509.	−0.882098
$129$	−184701.	−0.977225
$130$	−202942.	−1.05321
$131$	210539.	1.07190	0.535949	−	0.844250i	$-0.319954\pi$
$131$	210539.	1.07190	0.535949	+	0.844250i	$0.319954\pi$
$132$	−21914.6	−0.109471
$133$	−2023.64	−0.00991981
$134$	227335.	1.09372
$135$	18225.0	0.0860663
$136$	87457.4	0.405461
$137$	23859.0	0.108605	0.0543027	−	0.998525i	$-0.482706\pi$
$137$	23859.0	0.108605	0.0543027	+	0.998525i	$0.482706\pi$
$138$	−137553.	−0.614853
$139$	292430.	1.28377	0.641883	−	0.766803i	$-0.278154\pi$
$139$	292430.	1.28377	0.641883	+	0.766803i	$0.278154\pi$
$140$	−74240.8	−0.320127
$141$	−222467.	−0.942361
$142$	210621.	0.876557
$143$	−136051.	−0.556366
$144$	−102303.	−0.411132
$145$	−78024.5	−0.308185
$146$	−357973.	−1.38985
$147$	−44728.3	−0.170722
$148$	−62816.2	−0.235731
$149$	350530.	1.29348	0.646740	−	0.762710i	$-0.276132\pi$
$149$	350530.	1.29348	0.646740	+	0.762710i	$0.276132\pi$
$150$	40610.6	0.147371
$151$	−513284.	−1.83196	−0.915979	−	0.401225i	$-0.868584\pi$
$151$	−513284.	−1.83196	−0.915979	+	0.401225i	$0.868584\pi$
$152$	−1175.81	−0.00412790
$153$	82618.8	0.285332
$154$	−128914.	−0.438024
$155$	240725.	0.804806
$156$	203640.	0.669964
$157$	154810.	0.501244	0.250622	−	0.968085i	$-0.419365\pi$
$157$	154810.	0.501244	0.250622	+	0.968085i	$0.419365\pi$
$158$	614216.	1.95740
$159$	−204850.	−0.642604
$160$	−159365.	−0.492146
$161$	−312397.	−0.949821
$162$	−47368.2	−0.141808
$163$	184152.	0.542883	0.271442	−	0.962455i	$-0.412500\pi$
$163$	184152.	0.542883	0.271442	+	0.962455i	$0.412500\pi$
$164$	−118415.	−0.343793
$165$	27225.0	0.0778499
$166$	−558238.	−1.57235
$167$	−72082.3	−0.200003	−0.100002	−	0.994987i	$-0.531885\pi$
$167$	−72082.3	−0.200003	−0.100002	+	0.994987i	$0.531885\pi$
$168$	−113879.	−0.311293
$169$	892949.	2.40497
$170$	184099.	0.488572
$171$	−1110.76	−0.00290489
$172$	412983.	1.06441
$173$	−374895.	−0.952345	−0.476173	−	0.879352i	$-0.657976\pi$
$173$	−374895.	−0.952345	−0.476173	+	0.879352i	$0.657976\pi$
$174$	202792.	0.507782
$175$	92231.0	0.227658
$176$	−152823.	−0.371882
$177$	130802.	0.313820
$178$	−506948.	−1.19926
$179$	354545.	0.827064	0.413532	−	0.910490i	$-0.364295\pi$
$179$	354545.	0.827064	0.413532	+	0.910490i	$0.364295\pi$
$180$	−40750.3	−0.0937452
$181$	403999.	0.916609	0.458305	−	0.888795i	$-0.348457\pi$
$181$	403999.	0.916609	0.458305	+	0.888795i	$0.348457\pi$
$182$	1.19792e6	2.68072
$183$	−395864.	−0.873812
$184$	−181515.	−0.395246
$185$	78038.0	0.167640
$186$	−625663.	−1.32604
$187$	123418.	0.258093
$188$	497425.	1.02644
$189$	−107578.	−0.219064
$190$	−2475.10	−0.00497403
$191$	181282.	0.359560	0.179780	−	0.983707i	$-0.442461\pi$
$191$	181282.	0.359560	0.179780	+	0.983707i	$0.442461\pi$
$192$	50460.2	0.0987860
$193$	683762.	1.32133	0.660665	−	0.750681i	$-0.270274\pi$
$193$	683762.	1.32133	0.660665	+	0.750681i	$0.270274\pi$
$194$	152190.	0.290324
$195$	−252987.	−0.476443
$196$	100010.	0.185954
$197$	−442098.	−0.811620	−0.405810	−	0.913958i	$-0.633010\pi$
$197$	−442098.	−0.811620	−0.405810	+	0.913958i	$0.633010\pi$
$198$	−70760.0	−0.128270
$199$	925615.	1.65691	0.828453	−	0.560059i	$-0.189222\pi$
$199$	925615.	1.65691	0.828453	+	0.560059i	$0.189222\pi$
$200$	53589.8	0.0947344
$201$	283395.	0.494768
$202$	435197.	0.750425
$203$	460562.	0.784419
$204$	−184732.	−0.310790
$205$	147110.	0.244487
$206$	−603099.	−0.990194
$207$	−171472.	−0.278143
$208$	1.42009e6	2.27593
$209$	−1659.28	−0.00262757
$210$	−239716.	−0.375101
$211$	605880.	0.936873	0.468436	−	0.883497i	$-0.344818\pi$
$211$	605880.	0.936873	0.468436	+	0.883497i	$0.344818\pi$
$212$	458035.	0.699938
$213$	262559.	0.396531
$214$	−1.15001e6	−1.71659
$215$	−513058.	−0.756955
$216$	−62507.2	−0.0911582
$217$	−1.42095e6	−2.04846
$218$	225011.	0.320673
$219$	−446247.	−0.628731
$220$	−60873.8	−0.0847957
$221$	−1.14686e6	−1.57953
$222$	−202827.	−0.276213
$223$	581147.	0.782571	0.391286	−	0.920269i	$-0.372030\pi$
$223$	581147.	0.782571	0.391286	+	0.920269i	$0.372030\pi$
$224$	940699.	1.25265
$225$	50625.0	0.0666667
$226$	−1.02411e6	−1.33376
$227$	1.51651e6	1.95335	0.976674	−	0.214726i	$-0.0688859\pi$
$227$	1.51651e6	1.95335	0.976674	+	0.214726i	$0.0688859\pi$
$228$	2483.61	0.00316407
$229$	916540.	1.15495	0.577474	−	0.816409i	$-0.304038\pi$
$229$	916540.	1.15495	0.577474	+	0.816409i	$0.304038\pi$
$230$	−382091.	−0.476263
$231$	−160703.	−0.198150
$232$	267605.	0.326418
$233$	−650940.	−0.785509	−0.392755	−	0.919643i	$-0.628478\pi$
$233$	−650940.	−0.785509	−0.392755	+	0.919643i	$0.628478\pi$
$234$	657533.	0.785014
$235$	−617963.	−0.729950
$236$	−292467.	−0.341820
$237$	765679.	0.885474
$238$	−1.08670e6	−1.24356
$239$	−1.06473e6	−1.20572	−0.602860	−	0.797847i	$-0.705972\pi$
$239$	−1.06473e6	−1.20572	−0.602860	+	0.797847i	$0.705972\pi$
$240$	−284174.	−0.318461
$241$	−1.21958e6	−1.35259	−0.676297	−	0.736629i	$-0.736417\pi$
$241$	−1.21958e6	−1.35259	−0.676297	+	0.736629i	$0.736417\pi$
$242$	−105703.	−0.116024
$243$	−59049.0	−0.0641500
$244$	885133.	0.951774
$245$	−124245.	−0.132240
$246$	−382350.	−0.402831
$247$	15418.8	0.0160808
$248$	−825625.	−0.852420
$249$	−695897.	−0.711290
$250$	112807.	0.114153
$251$	1.82454e6	1.82797	0.913987	−	0.405743i	$-0.132987\pi$
$251$	1.82454e6	1.82797	0.913987	+	0.405743i	$0.132987\pi$
$252$	240540.	0.238609
$253$	−256150.	−0.251590
$254$	666736.	0.648440
$255$	229497.	0.221017
$256$	1.35990e6	1.29690
$257$	−475038.	−0.448637	−0.224319	−	0.974516i	$-0.572016\pi$
$257$	−475038.	−0.448637	−0.224319	+	0.974516i	$0.572016\pi$
$258$	1.33348e6	1.24720
$259$	−460642.	−0.426691
$260$	565667.	0.518952
$261$	252799.	0.229707
$262$	−1.52002e6	−1.36803
$263$	−1.07504e6	−0.958376	−0.479188	−	0.877712i	$-0.659069\pi$
$263$	−1.07504e6	−0.958376	−0.479188	+	0.877712i	$0.659069\pi$
$264$	−93375.0	−0.0824557
$265$	−569028.	−0.497759
$266$	14610.0	0.0126603
$267$	−631959.	−0.542514
$268$	−633658.	−0.538912
$269$	180662.	0.152225	0.0761126	−	0.997099i	$-0.475749\pi$
$269$	180662.	0.152225	0.0761126	+	0.997099i	$0.475749\pi$
$270$	−131578.	−0.109844
$271$	302884.	0.250526	0.125263	−	0.992124i	$-0.460023\pi$
$271$	302884.	0.250526	0.125263	+	0.992124i	$0.460023\pi$
$272$	−1.28824e6	−1.05578
$273$	1.49333e6	1.21269
$274$	−172254.	−0.138610
$275$	75625.0	0.0603023
$276$	383404.	0.302959
$277$	1.08898e6	0.852745	0.426372	−	0.904548i	$-0.359791\pi$
$277$	1.08898e6	0.852745	0.426372	+	0.904548i	$0.359791\pi$
$278$	−2.11125e6	−1.63843
$279$	−779948.	−0.599867
$280$	−316329.	−0.241126
$281$	−942590.	−0.712127	−0.356063	−	0.934462i	$-0.615881\pi$
$281$	−942590.	−0.712127	−0.356063	+	0.934462i	$0.615881\pi$
$282$	1.60614e6	1.20271
$283$	848952.	0.630111	0.315055	−	0.949073i	$-0.397977\pi$
$283$	848952.	0.630111	0.315055	+	0.949073i	$0.397977\pi$
$284$	−587069.	−0.431910
$285$	−3085.44	−0.00225012
$286$	982240.	0.710072
$287$	−868357.	−0.622291
$288$	516343.	0.366824
$289$	−379486.	−0.267271
$290$	563311.	0.393327
$291$	189720.	0.131335
$292$	997788.	0.684827
$293$	628367.	0.427606	0.213803	−	0.976877i	$-0.431415\pi$
$293$	628367.	0.427606	0.213803	+	0.976877i	$0.431415\pi$
$294$	322923.	0.217887
$295$	363339.	0.243084
$296$	−267651.	−0.177558
$297$	−88209.0	−0.0580259
$298$	−2.53071e6	−1.65083
$299$	2.38026e6	1.53974
$300$	−113195.	−0.0726147
$301$	3.02847e6	1.92667
$302$	3.70574e6	2.33807
$303$	542514.	0.339473
$304$	17319.6	0.0107486
$305$	−1.09962e6	−0.676852
$306$	−596480.	−0.364160
$307$	1.88248e6	1.13994	0.569972	−	0.821664i	$-0.306954\pi$
$307$	1.88248e6	1.13994	0.569972	+	0.821664i	$0.306954\pi$
$308$	359325.	0.215830
$309$	−751820.	−0.447938
$310$	−1.73795e6	−1.02715
$311$	−1.53497e6	−0.899908	−0.449954	−	0.893052i	$-0.648560\pi$
$311$	−1.53497e6	−0.899908	−0.449954	+	0.893052i	$0.648560\pi$
$312$	867681.	0.504631
$313$	−2.22901e6	−1.28603	−0.643015	−	0.765854i	$-0.722317\pi$
$313$	−2.22901e6	−1.28603	−0.643015	+	0.765854i	$0.722317\pi$
$314$	−1.11767e6	−0.639722
$315$	−298829.	−0.169686
$316$	−1.71202e6	−0.964477
$317$	1.00659e6	0.562605	0.281303	−	0.959619i	$-0.409234\pi$
$317$	1.00659e6	0.562605	0.281303	+	0.959619i	$0.409234\pi$
$318$	1.47895e6	0.820135
$319$	377639.	0.207778
$320$	140167.	0.0765193
$321$	−1.43359e6	−0.776539
$322$	2.25540e6	1.21223
$323$	−13987.2	−0.00745973
$324$	132031.	0.0698736
$325$	−702741.	−0.369051
$326$	−1.32951e6	−0.692865
$327$	280497.	0.145064
$328$	−504549.	−0.258952
$329$	3.64770e6	1.85793
$330$	−196555.	−0.0993574
$331$	−2.96963e6	−1.48982	−0.744908	−	0.667167i	$-0.767507\pi$
$331$	−2.96963e6	−1.48982	−0.744908	+	0.667167i	$0.767507\pi$
$332$	1.55599e6	0.774752
$333$	−252843.	−0.124951
$334$	520410.	0.255258
$335$	787208.	0.383246
$336$	1.67742e6	0.810575
$337$	69782.5	0.0334712	0.0167356	−	0.999860i	$-0.494673\pi$
$337$	69782.5	0.0334712	0.0167356	+	0.999860i	$0.494673\pi$
$338$	−6.44680e6	−3.06939
$339$	−1.27665e6	−0.603356
$340$	−513144.	−0.240737
$341$	−1.16511e6	−0.542600
$342$	8019.32	0.00370742
$343$	−1.74681e6	−0.801697
$344$	1.75966e6	0.801739
$345$	−476312.	−0.215449
$346$	2.70662e6	1.21545
$347$	−1.04233e6	−0.464708	−0.232354	−	0.972631i	$-0.574643\pi$
$347$	−1.04233e6	−0.464708	−0.232354	+	0.972631i	$0.574643\pi$
$348$	−565248.	−0.250202
$349$	−3.75012e6	−1.64809	−0.824047	−	0.566522i	$-0.808289\pi$
$349$	−3.75012e6	−1.64809	−0.824047	+	0.566522i	$0.808289\pi$
$350$	−665877.	−0.290552
$351$	819677.	0.355120
$352$	771328.	0.331805
$353$	800792.	0.342045	0.171022	−	0.985267i	$-0.445293\pi$
$353$	800792.	0.342045	0.171022	+	0.985267i	$0.445293\pi$
$354$	−944346.	−0.400519
$355$	729330.	0.307152
$356$	1.41303e6	0.590917
$357$	−1.35467e6	−0.562553
$358$	−2.55970e6	−1.05556
$359$	267422.	0.109512	0.0547559	−	0.998500i	$-0.482562\pi$
$359$	267422.	0.109512	0.0547559	+	0.998500i	$0.482562\pi$
$360$	−173631.	−0.0706108
$361$	−2.47591e6	−0.999924
$362$	−2.91674e6	−1.16984
$363$	−131769.	−0.0524864
$364$	−3.33901e6	−1.32088
$365$	−1.23957e6	−0.487013
$366$	2.85800e6	1.11522
$367$	2.63334e6	1.02057	0.510283	−	0.860007i	$-0.329541\pi$
$367$	2.63334e6	1.02057	0.510283	+	0.860007i	$0.329541\pi$
$368$	2.67369e6	1.02918
$369$	−476635.	−0.182230
$370$	−563408.	−0.213953
$371$	3.35885e6	1.26694
$372$	1.74393e6	0.653388
$373$	−3.93389e6	−1.46403	−0.732015	−	0.681289i	$-0.761420\pi$
$373$	−3.93389e6	−1.46403	−0.732015	+	0.681289i	$0.761420\pi$
$374$	−891039.	−0.329395
$375$	140625.	0.0516398
$376$	2.11946e6	0.773135
$377$	−3.50918e6	−1.27161
$378$	776679.	0.279584
$379$	−1.80355e6	−0.644956	−0.322478	−	0.946577i	$-0.604516\pi$
$379$	−1.80355e6	−0.644956	−0.322478	+	0.946577i	$0.604516\pi$
$380$	6898.91	0.00245088
$381$	831150.	0.293337
$382$	−1.30880e6	−0.458895
$383$	2.19398e6	0.764252	0.382126	−	0.924110i	$-0.375192\pi$
$383$	2.19398e6	0.764252	0.382126	+	0.924110i	$0.375192\pi$
$384$	1.47158e6	0.509280
$385$	−446398.	−0.153487
$386$	−4.93653e6	−1.68637
$387$	1.66231e6	0.564201
$388$	−424204.	−0.143053
$389$	354221.	0.118686	0.0593430	−	0.998238i	$-0.481099\pi$
$389$	354221.	0.118686	0.0593430	+	0.998238i	$0.481099\pi$
$390$	1.82648e6	0.608070
$391$	−2.15925e6	−0.714268
$392$	426130.	0.140064
$393$	−1.89485e6	−0.618861
$394$	3.19180e6	1.03584
$395$	2.12689e6	0.685885
$396$	197231.	0.0632030
$397$	168373.	0.0536162	0.0268081	−	0.999641i	$-0.491466\pi$
$397$	168373.	0.0536162	0.0268081	+	0.999641i	$0.491466\pi$
$398$	−6.68263e6	−2.11466
$399$	18212.7	0.00572720
$400$	−789373.	−0.246679
$401$	−4.59458e6	−1.42687	−0.713436	−	0.700721i	$-0.752862\pi$
$401$	−4.59458e6	−1.42687	−0.713436	+	0.700721i	$0.752862\pi$
$402$	−2.04602e6	−0.631457
$403$	1.08267e7	3.32073
$404$	−1.21304e6	−0.369761
$405$	−164025.	−0.0496904
$406$	−3.32510e6	−1.00113
$407$	−377704.	−0.113023
$408$	−787117.	−0.234093
$409$	3.59299e6	1.06206	0.531028	−	0.847354i	$-0.321806\pi$
$409$	3.59299e6	1.06206	0.531028	+	0.847354i	$0.321806\pi$
$410$	−1.06208e6	−0.312032
$411$	−214731.	−0.0627033
$412$	1.68103e6	0.487903
$413$	−2.14471e6	−0.618719
$414$	1.23797e6	0.354986
$415$	−1.93305e6	−0.550963
$416$	−7.16752e6	−2.03065
$417$	−2.63187e6	−0.741182
$418$	11979.5	0.00335349
$419$	−4.10701e6	−1.14285	−0.571427	−	0.820653i	$-0.693610\pi$
$419$	−4.10701e6	−1.14285	−0.571427	+	0.820653i	$0.693610\pi$
$420$	668167.	0.184825
$421$	5.36278e6	1.47464	0.737318	−	0.675546i	$-0.236092\pi$
$421$	5.36278e6	1.47464	0.737318	+	0.675546i	$0.236092\pi$
$422$	−4.37425e6	−1.19570
$423$	2.00220e6	0.544072
$424$	1.95162e6	0.527208
$425$	637491.	0.171199
$426$	−1.89559e6	−0.506081
$427$	6.49083e6	1.72278
$428$	3.20545e6	0.845822
$429$	1.22446e6	0.321218
$430$	3.70411e6	0.966078
$431$	2.52160e6	0.653857	0.326929	−	0.945049i	$-0.393986\pi$
$431$	2.52160e6	0.653857	0.326929	+	0.945049i	$0.393986\pi$
$432$	920724.	0.237367
$433$	2.99694e6	0.768171	0.384085	−	0.923298i	$-0.374517\pi$
$433$	2.99694e6	0.768171	0.384085	+	0.923298i	$0.374517\pi$
$434$	1.02588e7	2.61439
$435$	702221.	0.177931
$436$	−627179.	−0.158007
$437$	29029.8	0.00727178
$438$	3.22175e6	0.802430
$439$	1.93618e6	0.479495	0.239748	−	0.970835i	$-0.422935\pi$
$439$	1.93618e6	0.479495	0.239748	+	0.970835i	$0.422935\pi$
$440$	−259375.	−0.0638699
$441$	402554.	0.0985662
$442$	8.27992e6	2.01591
$443$	−7.28132e6	−1.76279	−0.881395	−	0.472380i	$-0.843395\pi$
$443$	−7.28132e6	−1.76279	−0.881395	+	0.472380i	$0.843395\pi$
$444$	565346.	0.136100
$445$	−1.75544e6	−0.420229
$446$	−4.19569e6	−0.998771
$447$	−3.15477e6	−0.746791
$448$	−827377.	−0.194764
$449$	6.15007e6	1.43967	0.719837	−	0.694143i	$-0.244216\pi$
$449$	6.15007e6	1.43967	0.719837	+	0.694143i	$0.244216\pi$
$450$	−365496.	−0.0850846
$451$	−712011.	−0.164833
$452$	2.85454e6	0.657188
$453$	4.61956e6	1.05768
$454$	−1.09487e7	−2.49300
$455$	4.14813e6	0.939342
$456$	10582.3	0.00238324
$457$	−5.60231e6	−1.25481	−0.627403	−	0.778695i	$-0.715882\pi$
$457$	−5.60231e6	−1.25481	−0.627403	+	0.778695i	$0.715882\pi$
$458$	−6.61711e6	−1.47402
$459$	−743570.	−0.164737
$460$	1.06501e6	0.234671
$461$	2.85697e6	0.626113	0.313057	−	0.949734i	$-0.398647\pi$
$461$	2.85697e6	0.626113	0.313057	+	0.949734i	$0.398647\pi$
$462$	1.16022e6	0.252893
$463$	2.42615e6	0.525976	0.262988	−	0.964799i	$-0.415292\pi$
$463$	2.42615e6	0.525976	0.262988	+	0.964799i	$0.415292\pi$
$464$	−3.94179e6	−0.849959
$465$	−2.16652e6	−0.464655
$466$	4.69957e6	1.00252
$467$	167522.	0.0355451	0.0177726	−	0.999842i	$-0.494343\pi$
$467$	167522.	0.0355451	0.0177726	+	0.999842i	$0.494343\pi$
$468$	−1.83276e6	−0.386804
$469$	−4.64672e6	−0.975471
$470$	4.46149e6	0.931612
$471$	−1.39329e6	−0.289393
$472$	−1.24616e6	−0.257466
$473$	2.48320e6	0.510339
$474$	−5.52795e6	−1.13010
$475$	−8570.68	−0.00174293
$476$	3.02898e6	0.612744
$477$	1.84365e6	0.371008
$478$	7.68702e6	1.53882
$479$	5.39034e6	1.07344	0.536719	−	0.843761i	$-0.319663\pi$
$479$	5.39034e6	1.07344	0.536719	+	0.843761i	$0.319663\pi$
$480$	1.43429e6	0.284140
$481$	3.50979e6	0.691701
$482$	8.80496e6	1.72627
$483$	2.81157e6	0.548379
$484$	294629.	0.0571693
$485$	526999.	0.101732
$486$	426314.	0.0818727
$487$	1.38574e6	0.264764	0.132382	−	0.991199i	$-0.457737\pi$
$487$	1.38574e6	0.264764	0.132382	+	0.991199i	$0.457737\pi$
$488$	3.77143e6	0.716896
$489$	−1.65736e6	−0.313434
$490$	897009.	0.168774
$491$	−3.39592e6	−0.635703	−0.317851	−	0.948141i	$-0.602961\pi$
$491$	−3.39592e6	−0.635703	−0.317851	+	0.948141i	$0.602961\pi$
$492$	1.06573e6	0.198489
$493$	3.18336e6	0.589886
$494$	−111319.	−0.0205234
$495$	−245025.	−0.0449467
$496$	1.21614e7	2.21962
$497$	−4.30508e6	−0.781790
$498$	5.02414e6	0.907797
$499$	2.83293e6	0.509313	0.254657	−	0.967032i	$-0.418038\pi$
$499$	2.83293e6	0.509313	0.254657	+	0.967032i	$0.418038\pi$
$500$	−314431.	−0.0562471
$501$	648741.	0.115472
$502$	−1.31726e7	−2.33299
$503$	9.23328e6	1.62718	0.813591	−	0.581437i	$-0.197509\pi$
$503$	9.23328e6	1.62718	0.813591	+	0.581437i	$0.197509\pi$
$504$	1.02491e6	0.179725
$505$	1.50698e6	0.262954
$506$	1.84932e6	0.321096
$507$	−8.03654e6	−1.38851
$508$	−1.85841e6	−0.319509
$509$	−5.70039e6	−0.975238	−0.487619	−	0.873057i	$-0.662134\pi$
$509$	−5.70039e6	−0.975238	−0.487619	+	0.873057i	$0.662134\pi$
$510$	−1.65689e6	−0.282077
$511$	7.31695e6	1.23959
$512$	−4.58570e6	−0.773091
$513$	9996.84	0.00167714
$514$	3.42961e6	0.572582
$515$	−2.08839e6	−0.346971
$516$	−3.71684e6	−0.614540
$517$	2.99094e6	0.492132
$518$	3.32568e6	0.544573
$519$	3.37406e6	0.549837
$520$	2.41023e6	0.390885
$521$	−1.35063e6	−0.217994	−0.108997	−	0.994042i	$-0.534764\pi$
$521$	−1.35063e6	−0.217994	−0.108997	+	0.994042i	$0.534764\pi$
$522$	−1.82513e6	−0.293168
$523$	440837.	0.0704731	0.0352366	−	0.999379i	$-0.488782\pi$
$523$	440837.	0.0704731	0.0352366	+	0.999379i	$0.488782\pi$
$524$	4.23679e6	0.674076
$525$	−830079.	−0.131438
$526$	7.76144e6	1.22314
$527$	−9.82143e6	−1.54045
$528$	1.37540e6	0.214706
$529$	−1.95489e6	−0.303727
$530$	4.10819e6	0.635274
$531$	−1.17722e6	−0.181184
$532$	−40722.8	−0.00623819
$533$	6.61632e6	1.00878
$534$	4.56253e6	0.692393
$535$	−3.98220e6	−0.601504
$536$	−2.69993e6	−0.405919
$537$	−3.19091e6	−0.477506
$538$	−1.30432e6	−0.194280
$539$	601347.	0.0891565
$540$	366752.	0.0541238
$541$	7.01375e6	1.03028	0.515142	−	0.857105i	$-0.327739\pi$
$541$	7.01375e6	1.03028	0.515142	+	0.857105i	$0.327739\pi$
$542$	−2.18672e6	−0.319738
$543$	−3.63599e6	−0.529205
$544$	6.50201e6	0.941999
$545$	779159.	0.112366
$546$	−1.07813e7	−1.54771
$547$	−1.01822e7	−1.45503	−0.727517	−	0.686090i	$-0.759326\pi$
$547$	−1.01822e7	−1.45503	−0.727517	+	0.686090i	$0.759326\pi$
$548$	480129.	0.0682978
$549$	3.56277e6	0.504496
$550$	−545987.	−0.0769619
$551$	−42798.3	−0.00600547
$552$	1.63363e6	0.228195
$553$	−1.25546e7	−1.74578
$554$	−7.86205e6	−1.08833
$555$	−702342.	−0.0967868
$556$	5.88475e6	0.807311
$557$	−1.09154e7	−1.49074	−0.745371	−	0.666650i	$-0.767728\pi$
$557$	−1.09154e7	−1.49074	−0.745371	+	0.666650i	$0.767728\pi$
$558$	5.63096e6	0.765592
$559$	−2.30750e7	−3.12329
$560$	4.65950e6	0.627869
$561$	−1.11076e6	−0.149010
$562$	6.80519e6	0.908865
$563$	1.25187e6	0.166452	0.0832261	−	0.996531i	$-0.473478\pi$
$563$	1.25187e6	0.166452	0.0832261	+	0.996531i	$0.473478\pi$
$564$	−4.47683e6	−0.592615
$565$	−3.54626e6	−0.467357
$566$	−6.12915e6	−0.804191
$567$	968205.	0.126476
$568$	−2.50142e6	−0.325324
$569$	3.75381e6	0.486061	0.243031	−	0.970019i	$-0.421858\pi$
$569$	3.75381e6	0.486061	0.243031	+	0.970019i	$0.421858\pi$
$570$	22275.9	0.00287176
$571$	−7.39573e6	−0.949273	−0.474636	−	0.880182i	$-0.657420\pi$
$571$	−7.39573e6	−0.949273	−0.474636	+	0.880182i	$0.657420\pi$
$572$	−2.73783e6	−0.349877
$573$	−1.63154e6	−0.207592
$574$	6.26925e6	0.794210
$575$	−1.32309e6	−0.166886
$576$	−454141.	−0.0570341
$577$	−6.45181e6	−0.806755	−0.403378	−	0.915034i	$-0.632164\pi$
$577$	−6.45181e6	−0.806755	−0.403378	+	0.915034i	$0.632164\pi$
$578$	2.73976e6	0.341109
$579$	−6.15386e6	−0.762871
$580$	−1.57013e6	−0.193806
$581$	1.14104e7	1.40236
$582$	−1.36971e6	−0.167619
$583$	2.75410e6	0.335589
$584$	4.25143e6	0.515826
$585$	2.27688e6	0.275075
$586$	−4.53660e6	−0.545741
$587$	5.91956e6	0.709078	0.354539	−	0.935041i	$-0.384638\pi$
$587$	5.91956e6	0.709078	0.354539	+	0.935041i	$0.384638\pi$
$588$	−900093.	−0.107360
$589$	132043.	0.0156829
$590$	−2.62318e6	−0.310241
$591$	3.97888e6	0.468589
$592$	3.94247e6	0.462343
$593$	−2.54171e6	−0.296817	−0.148409	−	0.988926i	$-0.547415\pi$
$593$	−2.54171e6	−0.296817	−0.148409	+	0.988926i	$0.547415\pi$
$594$	636840.	0.0740566
$595$	−3.76297e6	−0.435751
$596$	7.05393e6	0.813421
$597$	−8.33053e6	−0.956615
$598$	−1.71847e7	−1.96512
$599$	1.17309e7	1.33587	0.667935	−	0.744220i	$-0.267179\pi$
$599$	1.17309e7	1.33587	0.667935	+	0.744220i	$0.267179\pi$
$600$	−482309.	−0.0546949
$601$	−2.88018e6	−0.325262	−0.162631	−	0.986687i	$-0.551998\pi$
$601$	−2.88018e6	−0.325262	−0.162631	+	0.986687i	$0.551998\pi$
$602$	−2.18646e7	−2.45895
$603$	−2.55055e6	−0.285655
$604$	−1.03291e7	−1.15205
$605$	−366025.	−0.0406558
$606$	−3.91677e6	−0.433258
$607$	−1.33207e7	−1.46742	−0.733712	−	0.679460i	$-0.762214\pi$
$607$	−1.33207e7	−1.46742	−0.733712	+	0.679460i	$0.762214\pi$
$608$	−87415.6	−0.00959025
$609$	−4.14506e6	−0.452885
$610$	7.93890e6	0.863845
$611$	−2.77931e7	−3.01186
$612$	1.66259e6	0.179434
$613$	−8.85926e6	−0.952239	−0.476120	−	0.879381i	$-0.657957\pi$
$613$	−8.85926e6	−0.952239	−0.476120	+	0.879381i	$0.657957\pi$
$614$	−1.35908e7	−1.45487
$615$	−1.32399e6	−0.141155
$616$	1.53103e6	0.162567
$617$	1.75148e7	1.85222	0.926110	−	0.377253i	$-0.123131\pi$
$617$	1.75148e7	1.85222	0.926110	+	0.377253i	$0.123131\pi$
$618$	5.42789e6	0.571689
$619$	3.94768e6	0.414109	0.207055	−	0.978329i	$-0.433612\pi$
$619$	3.94768e6	0.414109	0.207055	+	0.978329i	$0.433612\pi$
$620$	4.84424e6	0.506112
$621$	1.54325e6	0.160586
$622$	1.10820e7	1.14852
$623$	1.03620e7	1.06960
$624$	−1.27808e7	−1.31401
$625$	390625.	0.0400000
$626$	1.60927e7	1.64132
$627$	14933.6	0.00151703
$628$	3.11533e6	0.315213
$629$	−3.18391e6	−0.320873
$630$	2.15744e6	0.216565
$631$	−5.78181e6	−0.578083	−0.289042	−	0.957317i	$-0.593337\pi$
$631$	−5.78181e6	−0.578083	−0.289042	+	0.957317i	$0.593337\pi$
$632$	−7.29469e6	−0.726464
$633$	−5.45292e6	−0.540904
$634$	−7.26723e6	−0.718035
$635$	2.30875e6	0.227218
$636$	−4.12232e6	−0.404109
$637$	−5.58798e6	−0.545640
$638$	−2.72643e6	−0.265181
$639$	−2.36303e6	−0.228937
$640$	4.08773e6	0.394486
$641$	−4.31966e6	−0.415245	−0.207623	−	0.978209i	$-0.566573\pi$
$641$	−4.31966e6	−0.415245	−0.207623	+	0.978209i	$0.566573\pi$
$642$	1.03501e7	0.991072
$643$	1.95083e7	1.86076	0.930381	−	0.366593i	$-0.119476\pi$
$643$	1.95083e7	1.86076	0.930381	+	0.366593i	$0.119476\pi$
$644$	−6.28654e6	−0.597306
$645$	4.61752e6	0.437028
$646$	100983.	0.00952062
$647$	−1.08322e7	−1.01732	−0.508660	−	0.860967i	$-0.669859\pi$
$647$	−1.08322e7	−1.01732	−0.508660	+	0.860967i	$0.669859\pi$
$648$	562565.	0.0526302
$649$	−1.75856e6	−0.163887
$650$	5.07355e6	0.471009
$651$	1.27885e7	1.18268
$652$	3.70579e6	0.341399
$653$	1.83320e6	0.168239	0.0841197	−	0.996456i	$-0.473192\pi$
$653$	1.83320e6	0.168239	0.0841197	+	0.996456i	$0.473192\pi$
$654$	−2.02510e6	−0.185140
$655$	−5.26346e6	−0.479367
$656$	7.43195e6	0.674285
$657$	4.01622e6	0.362998
$658$	−2.63352e7	−2.37122
$659$	1.77259e7	1.58999	0.794994	−	0.606618i	$-0.207474\pi$
$659$	1.77259e7	1.58999	0.794994	+	0.606618i	$0.207474\pi$
$660$	547865.	0.0489568
$661$	−5.89810e6	−0.525060	−0.262530	−	0.964924i	$-0.584557\pi$
$661$	−5.89810e6	−0.525060	−0.262530	+	0.964924i	$0.584557\pi$
$662$	2.14398e7	1.90141
$663$	1.03217e7	0.911943
$664$	6.62987e6	0.583559
$665$	50590.9	0.00443627
$666$	1.82544e6	0.159471
$667$	−6.60694e6	−0.575024
$668$	−1.45055e6	−0.125775
$669$	−5.23032e6	−0.451818
$670$	−5.68338e6	−0.489125
$671$	5.32217e6	0.456333
$672$	−8.46629e6	−0.723219
$673$	−6.98177e6	−0.594193	−0.297097	−	0.954847i	$-0.596018\pi$
$673$	−6.98177e6	−0.594193	−0.297097	+	0.954847i	$0.596018\pi$
$674$	−503806.	−0.0427183
$675$	−455625.	−0.0384900
$676$	1.79693e7	1.51240
$677$	5.68896e6	0.477047	0.238524	−	0.971137i	$-0.423337\pi$
$677$	5.68896e6	0.477047	0.238524	+	0.971137i	$0.423337\pi$
$678$	9.21700e6	0.770044
$679$	−3.11076e6	−0.258936
$680$	−2.18644e6	−0.181328
$681$	−1.36486e7	−1.12777
$682$	8.41169e6	0.692504
$683$	1.65539e6	0.135784	0.0678920	−	0.997693i	$-0.478373\pi$
$683$	1.65539e6	0.135784	0.0678920	+	0.997693i	$0.478373\pi$
$684$	−22352.5	−0.00182678
$685$	−596475.	−0.0485698
$686$	1.26114e7	1.02318
$687$	−8.24886e6	−0.666810
$688$	−2.59196e7	−2.08765
$689$	−2.55923e7	−2.05381
$690$	3.43882e6	0.274971
$691$	−8.36041e6	−0.666090	−0.333045	−	0.942911i	$-0.608076\pi$
$691$	−8.36041e6	−0.666090	−0.333045	+	0.942911i	$0.608076\pi$
$692$	−7.54423e6	−0.598894
$693$	1.44633e6	0.114402
$694$	7.52524e6	0.593092
$695$	−7.31076e6	−0.574117
$696$	−2.40844e6	−0.188457
$697$	−6.00199e6	−0.467965
$698$	2.70746e7	2.10341
$699$	5.85846e6	0.453514
$700$	1.85602e6	0.143165
$701$	1.07851e7	0.828948	0.414474	−	0.910061i	$-0.363966\pi$
$701$	1.07851e7	0.828948	0.414474	+	0.910061i	$0.363966\pi$
$702$	−5.91779e6	−0.453228
$703$	42805.7	0.00326673
$704$	−678409.	−0.0515893
$705$	5.56167e6	0.421437
$706$	−5.78145e6	−0.436541
$707$	−8.89541e6	−0.669295
$708$	2.63220e6	0.197350
$709$	−1.37457e7	−1.02695	−0.513476	−	0.858104i	$-0.671642\pi$
$709$	−1.37457e7	−1.02695	−0.513476	+	0.858104i	$0.671642\pi$
$710$	−5.26552e6	−0.392008
$711$	−6.89111e6	−0.511229
$712$	6.02073e6	0.445091
$713$	2.03840e7	1.50164
$714$	9.78027e6	0.717968
$715$	3.40127e6	0.248814
$716$	7.13472e6	0.520109
$717$	9.58260e6	0.696122
$718$	−1.93070e6	−0.139767
$719$	2.23290e6	0.161082	0.0805409	−	0.996751i	$-0.474335\pi$
$719$	2.23290e6	0.161082	0.0805409	+	0.996751i	$0.474335\pi$
$720$	2.55757e6	0.183864
$721$	1.23273e7	0.883141
$722$	1.78753e7	1.27617
$723$	1.09762e7	0.780921
$724$	8.12991e6	0.576421
$725$	1.95061e6	0.137824
$726$	951328.	0.0669867
$727$	7.70500e6	0.540675	0.270338	−	0.962766i	$-0.412865\pi$
$727$	7.70500e6	0.540675	0.270338	+	0.962766i	$0.412865\pi$
$728$	−1.42270e7	−0.994916
$729$	531441.	0.0370370
$730$	8.94932e6	0.621560
$731$	2.09325e7	1.44886
$732$	−7.96620e6	−0.549507
$733$	−5.23205e6	−0.359676	−0.179838	−	0.983696i	$-0.557557\pi$
$733$	−5.23205e6	−0.359676	−0.179838	+	0.983696i	$0.557557\pi$
$734$	−1.90118e7	−1.30252
$735$	1.11821e6	0.0763491
$736$	−1.34947e7	−0.918266
$737$	−3.81009e6	−0.258384
$738$	3.44115e6	0.232575
$739$	1.90698e7	1.28450	0.642252	−	0.766494i	$-0.278000\pi$
$739$	1.90698e7	1.28450	0.642252	+	0.766494i	$0.278000\pi$
$740$	1.57040e6	0.105422
$741$	−138769.	−0.00928426
$742$	−2.42498e7	−1.61696
$743$	2.31407e7	1.53781	0.768907	−	0.639361i	$-0.220801\pi$
$743$	2.31407e7	1.53781	0.768907	+	0.639361i	$0.220801\pi$
$744$	7.43063e6	0.492145
$745$	−8.76326e6	−0.578462
$746$	2.84013e7	1.86849
$747$	6.26307e6	0.410663
$748$	2.48362e6	0.162305
$749$	2.35061e7	1.53100
$750$	−1.01527e6	−0.0659062
$751$	1.96879e7	1.27380	0.636898	−	0.770948i	$-0.280217\pi$
$751$	1.96879e7	1.27380	0.636898	+	0.770948i	$0.280217\pi$
$752$	−3.12194e7	−2.01317
$753$	−1.64209e7	−1.05538
$754$	2.53351e7	1.62291
$755$	1.28321e7	0.819277
$756$	−2.16486e6	−0.137761
$757$	−8.22162e6	−0.521456	−0.260728	−	0.965412i	$-0.583963\pi$
$757$	−8.22162e6	−0.521456	−0.260728	+	0.965412i	$0.583963\pi$
$758$	1.30210e7	0.823137
$759$	2.30535e6	0.145256
$760$	29395.3	0.00184605
$761$	2.18719e6	0.136907	0.0684534	−	0.997654i	$-0.478194\pi$
$761$	2.18719e6	0.136907	0.0684534	+	0.997654i	$0.478194\pi$
$762$	−6.00063e6	−0.374377
$763$	−4.59921e6	−0.286004
$764$	3.64805e6	0.226114
$765$	−2.06547e6	−0.127604
$766$	−1.58398e7	−0.975391
$767$	1.63413e7	1.00299
$768$	−1.22391e7	−0.748764
$769$	3.97950e6	0.242668	0.121334	−	0.992612i	$-0.461283\pi$
$769$	3.97950e6	0.242668	0.121334	+	0.992612i	$0.461283\pi$
$770$	3.22285e6	0.195890
$771$	4.27534e6	0.259021
$772$	1.37597e7	0.830935
$773$	−1.92979e7	−1.16161	−0.580807	−	0.814042i	$-0.697263\pi$
$773$	−1.92979e7	−1.16161	−0.580807	+	0.814042i	$0.697263\pi$
$774$	−1.20013e7	−0.720072
$775$	−6.01812e6	−0.359920
$776$	−1.80748e6	−0.107750
$777$	4.14578e6	0.246350
$778$	−2.55735e6	−0.151475
$779$	80693.1	0.00476423
$780$	−5.09100e6	−0.299617
$781$	−3.52996e6	−0.207082
$782$	1.55891e7	0.911599
$783$	−2.27519e6	−0.132622
$784$	−6.27685e6	−0.364713
$785$	−3.87024e6	−0.224163
$786$	1.36802e7	0.789832
$787$	−1.54391e7	−0.888556	−0.444278	−	0.895889i	$-0.646540\pi$
$787$	−1.54391e7	−0.888556	−0.444278	+	0.895889i	$0.646540\pi$
$788$	−8.89659e6	−0.510397
$789$	9.67537e6	0.553318
$790$	−1.53554e7	−0.875374
$791$	2.09328e7	1.18956
$792$	840375.	0.0476058
$793$	−4.94559e7	−2.79277
$794$	−1.21560e6	−0.0684287
$795$	5.12125e6	0.287381
$796$	1.86267e7	1.04196
$797$	2.66071e7	1.48372	0.741860	−	0.670555i	$-0.233944\pi$
$797$	2.66071e7	1.48372	0.741860	+	0.670555i	$0.233944\pi$
$798$	−131490.	−0.00730945
$799$	2.52125e7	1.39717
$800$	3.98413e6	0.220094
$801$	5.68763e6	0.313220
$802$	3.31713e7	1.82107
$803$	5.99954e6	0.328344
$804$	5.70292e6	0.311141
$805$	7.80992e6	0.424773
$806$	−7.81651e7	−4.23814
$807$	−1.62596e6	−0.0878872
$808$	−5.16858e6	−0.278511
$809$	−3.15651e7	−1.69565	−0.847825	−	0.530276i	$-0.822088\pi$
$809$	−3.15651e7	−1.69565	−0.847825	+	0.530276i	$0.822088\pi$
$810$	1.18421e6	0.0634183
$811$	3.50230e7	1.86982	0.934912	−	0.354880i	$-0.115478\pi$
$811$	3.50230e7	1.86982	0.934912	+	0.354880i	$0.115478\pi$
$812$	9.26816e6	0.493291
$813$	−2.72595e6	−0.144641
$814$	2.72690e6	0.144247
$815$	−4.60379e6	−0.242785
$816$	1.15941e7	0.609555
$817$	−281424.	−0.0147505
$818$	−2.59402e7	−1.35547
$819$	−1.34399e7	−0.700144
$820$	2.96037e6	0.153749
$821$	−6.00202e6	−0.310770	−0.155385	−	0.987854i	$-0.549662\pi$
$821$	−6.00202e6	−0.310770	−0.155385	+	0.987854i	$0.549662\pi$
$822$	1.55029e6	0.0800263
$823$	−2.98462e7	−1.53599	−0.767996	−	0.640455i	$-0.778746\pi$
$823$	−2.98462e7	−1.53599	−0.767996	+	0.640455i	$0.778746\pi$
$824$	7.16265e6	0.367499
$825$	−680625.	−0.0348155
$826$	1.54841e7	0.789652
$827$	−3.81477e6	−0.193956	−0.0969782	−	0.995287i	$-0.530918\pi$
$827$	−3.81477e6	−0.193956	−0.0969782	+	0.995287i	$0.530918\pi$
$828$	−3.45064e6	−0.174914
$829$	7.23404e6	0.365590	0.182795	−	0.983151i	$-0.441486\pi$
$829$	7.23404e6	0.365590	0.182795	+	0.983151i	$0.441486\pi$
$830$	1.39560e7	0.703177
$831$	−9.80079e6	−0.492332
$832$	6.30407e6	0.315728
$833$	5.06913e6	0.253117
$834$	1.90013e7	0.945948
$835$	1.80206e6	0.0894442
$836$	−33390.7	−0.00165238
$837$	7.01953e6	0.346333
$838$	2.96512e7	1.45859
$839$	−2.18515e6	−0.107171	−0.0535853	−	0.998563i	$-0.517065\pi$
$839$	−2.18515e6	−0.107171	−0.0535853	+	0.998563i	$0.517065\pi$
$840$	2.84697e6	0.139214
$841$	−1.07706e7	−0.525111
$842$	−3.87175e7	−1.88203
$843$	8.48331e6	0.411146
$844$	1.21925e7	0.589164
$845$	−2.23237e7	−1.07554
$846$	−1.44552e7	−0.694383
$847$	2.16057e6	0.103481
$848$	−2.87472e7	−1.37280
$849$	−7.64056e6	−0.363795
$850$	−4.60247e6	−0.218496
$851$	6.60808e6	0.312789
$852$	5.28362e6	0.249363
$853$	−1.41107e7	−0.664014	−0.332007	−	0.943277i	$-0.607726\pi$
$853$	−1.41107e7	−0.664014	−0.332007	+	0.943277i	$0.607726\pi$
$854$	−4.68616e7	−2.19873
$855$	27769.0	0.00129911
$856$	1.36580e7	0.637091
$857$	3.50068e7	1.62817	0.814087	−	0.580743i	$-0.197238\pi$
$857$	3.50068e7	1.62817	0.814087	+	0.580743i	$0.197238\pi$
$858$	−8.84016e6	−0.409960
$859$	2.72242e6	0.125885	0.0629423	−	0.998017i	$-0.479952\pi$
$859$	2.72242e6	0.125885	0.0629423	+	0.998017i	$0.479952\pi$
$860$	−1.03246e7	−0.476020
$861$	7.81521e6	0.359280
$862$	−1.82051e7	−0.834498
$863$	976336.	0.0446244	0.0223122	−	0.999751i	$-0.492897\pi$
$863$	976336.	0.0446244	0.0223122	+	0.999751i	$0.492897\pi$
$864$	−4.64709e6	−0.211786
$865$	9.37238e6	0.425902
$866$	−2.16369e7	−0.980392
$867$	3.41538e6	0.154309
$868$	−2.85945e7	−1.28820
$869$	−1.02941e7	−0.462424
$870$	−5.06980e6	−0.227087
$871$	3.54050e7	1.58132
$872$	−2.67232e6	−0.119014
$873$	−1.70748e6	−0.0758262
$874$	−209586.	−0.00928075
$875$	−2.30578e6	−0.101812
$876$	−8.98009e6	−0.395385
$877$	3.04885e7	1.33856	0.669279	−	0.743011i	$-0.266603\pi$
$877$	3.04885e7	1.33856	0.669279	+	0.743011i	$0.266603\pi$
$878$	−1.39786e7	−0.611965
$879$	−5.65530e6	−0.246879
$880$	3.82056e6	0.166311
$881$	3.54112e7	1.53710	0.768548	−	0.639792i	$-0.220980\pi$
$881$	3.54112e7	1.53710	0.768548	+	0.639792i	$0.220980\pi$
$882$	−2.90631e6	−0.125797
$883$	7.34069e6	0.316836	0.158418	−	0.987372i	$-0.449361\pi$
$883$	7.34069e6	0.316836	0.158418	+	0.987372i	$0.449361\pi$
$884$	−2.30789e7	−0.993308
$885$	−3.27005e6	−0.140345
$886$	5.25687e7	2.24979
$887$	8.51565e6	0.363420	0.181710	−	0.983352i	$-0.441837\pi$
$887$	8.51565e6	0.363420	0.181710	+	0.983352i	$0.441837\pi$
$888$	2.40886e6	0.102513
$889$	−1.36281e7	−0.578335
$890$	1.26737e7	0.536326
$891$	793881.	0.0335013
$892$	1.16948e7	0.492129
$893$	−338967.	−0.0142242
$894$	2.27764e7	0.953107
$895$	−8.86363e6	−0.369874
$896$	−2.41290e7	−1.00408
$897$	−2.14223e7	−0.888967
$898$	−4.44015e7	−1.83741
$899$	−3.00519e7	−1.24014
$900$	1.01876e6	0.0419241
$901$	2.32160e7	0.952743
$902$	5.14048e6	0.210372
$903$	−2.72562e7	−1.11236
$904$	1.21628e7	0.495007
$905$	−1.01000e7	−0.409920
$906$	−3.33517e7	−1.34989
$907$	1.84383e7	0.744224	0.372112	−	0.928188i	$-0.378634\pi$
$907$	1.84383e7	0.744224	0.372112	+	0.928188i	$0.378634\pi$
$908$	3.05176e7	1.22839
$909$	−4.88263e6	−0.195995
$910$	−2.99481e7	−1.19885
$911$	3.20540e7	1.27964	0.639819	−	0.768526i	$-0.279009\pi$
$911$	3.20540e7	1.27964	0.639819	+	0.768526i	$0.279009\pi$
$912$	−155876.	−0.00620573
$913$	9.35595e6	0.371459
$914$	4.04468e7	1.60147
$915$	9.89659e6	0.390781
$916$	1.84441e7	0.726303
$917$	3.10691e7	1.22013
$918$	5.36832e6	0.210248
$919$	2.41323e7	0.942563	0.471282	−	0.881983i	$-0.343792\pi$
$919$	2.41323e7	0.942563	0.471282	+	0.881983i	$0.343792\pi$
$920$	4.53787e6	0.176759
$921$	−1.69423e7	−0.658147
$922$	−2.06264e7	−0.799089
$923$	3.28019e7	1.26735
$924$	−3.23393e6	−0.124609
$925$	−1.95095e6	−0.0749708
$926$	−1.75160e7	−0.671287
$927$	6.76638e6	0.258617
$928$	1.98950e7	0.758359
$929$	−2.12500e7	−0.807828	−0.403914	−	0.914797i	$-0.632350\pi$
$929$	−2.12500e7	−0.807828	−0.403914	+	0.914797i	$0.632350\pi$
$930$	1.56416e7	0.593025
$931$	−68151.4	−0.00257692
$932$	−1.30993e7	−0.493977
$933$	1.38147e7	0.519562
$934$	−1.20945e6	−0.0453652
$935$	−3.08546e6	−0.115422
$936$	−7.80913e6	−0.291349
$937$	−2.96484e7	−1.10320	−0.551598	−	0.834110i	$-0.685982\pi$
$937$	−2.96484e7	−1.10320	−0.551598	+	0.834110i	$0.685982\pi$
$938$	3.35478e7	1.24496
$939$	2.00611e7	0.742490
$940$	−1.24356e7	−0.459038
$941$	−4.32235e7	−1.59128	−0.795638	−	0.605772i	$-0.792864\pi$
$941$	−4.32235e7	−1.59128	−0.795638	+	0.605772i	$0.792864\pi$
$942$	1.00591e7	0.369344
$943$	1.24569e7	0.456175
$944$	1.83558e7	0.670415
$945$	2.68946e6	0.0979682
$946$	−1.79279e7	−0.651330
$947$	1.03051e7	0.373402	0.186701	−	0.982417i	$-0.440220\pi$
$947$	1.03051e7	0.373402	0.186701	+	0.982417i	$0.440220\pi$
$948$	1.54082e7	0.556841
$949$	−5.57504e7	−2.00947
$950$	61877.4	0.00222445
$951$	−9.05929e6	−0.324820
$952$	1.29061e7	0.461531
$953$	2.76302e7	0.985488	0.492744	−	0.870174i	$-0.335994\pi$
$953$	2.76302e7	0.985488	0.492744	+	0.870174i	$0.335994\pi$
$954$	−1.33105e7	−0.473505
$955$	−4.53205e6	−0.160800
$956$	−2.14263e7	−0.758231
$957$	−3.39875e6	−0.119961
$958$	−3.89164e7	−1.37000
$959$	3.52087e6	0.123624
$960$	−1.26150e6	−0.0441785
$961$	6.40882e7	2.23856
$962$	−2.53395e7	−0.882797
$963$	1.29023e7	0.448335
$964$	−2.45423e7	−0.850596
$965$	−1.70940e7	−0.590917
$966$	−2.02986e7	−0.699879
$967$	−1.92779e7	−0.662968	−0.331484	−	0.943461i	$-0.607549\pi$
$967$	−1.92779e7	−0.662968	−0.331484	+	0.943461i	$0.607549\pi$
$968$	1.25537e6	0.0430611
$969$	125884.	0.00430688
$970$	−3.80476e6	−0.129837
$971$	−2.79869e7	−0.952592	−0.476296	−	0.879285i	$-0.658021\pi$
$971$	−2.79869e7	−0.952592	−0.476296	+	0.879285i	$0.658021\pi$
$972$	−1.18828e6	−0.0403415
$973$	4.31539e7	1.46129
$974$	−1.00046e7	−0.337910
$975$	6.32467e6	0.213072
$976$	−5.55527e7	−1.86673
$977$	3.40783e7	1.14220	0.571099	−	0.820881i	$-0.306517\pi$
$977$	3.40783e7	1.14220	0.571099	+	0.820881i	$0.306517\pi$
$978$	1.19656e7	0.400026
$979$	8.49634e6	0.283319
$980$	−2.50026e6	−0.0831610
$981$	−2.52447e6	−0.0837526
$982$	2.45174e7	0.811328
$983$	−5.50760e7	−1.81794	−0.908968	−	0.416866i	$-0.863128\pi$
$983$	−5.50760e7	−1.81794	−0.908968	+	0.416866i	$0.863128\pi$
$984$	4.54094e6	0.149506
$985$	1.10524e7	0.362967
$986$	−2.29828e7	−0.752853
$987$	−3.28293e7	−1.07268
$988$	310281.	0.0101126
$989$	−4.34446e7	−1.41236
$990$	1.76900e6	0.0573640
$991$	−6.15387e6	−0.199051	−0.0995255	−	0.995035i	$-0.531732\pi$
$991$	−6.15387e6	−0.199051	−0.0995255	+	0.995035i	$0.531732\pi$
$992$	−6.13810e7	−1.98041
$993$	2.67267e7	0.860146
$994$	3.10812e7	0.997774
$995$	−2.31404e7	−0.740990
$996$	−1.40039e7	−0.447303
$997$	1.41497e7	0.450828	0.225414	−	0.974263i	$-0.427627\pi$
$997$	1.41497e7	0.450828	0.225414	+	0.974263i	$0.427627\pi$
$998$	−2.04528e7	−0.650021
$999$	2.27559e6	0.0721406

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.6.a.e.1.1	✓	3
3.2	odd	2		495.6.a.a.1.3		3
5.4	even	2		825.6.a.f.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.a.e.1.1	✓	3	1.1	even	1	trivial
495.6.a.a.1.3		3	3.2	odd	2
825.6.a.f.1.3		3	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	165.a (trivial)

\(f(q)\)	\(=\)	\(q-7.21967 q^{2} -9.00000 q^{3} +20.1236 q^{4} -25.0000 q^{5} +64.9770 q^{6} +147.570 q^{7} +85.7438 q^{8} +81.0000 q^{9} +180.492 q^{10} +121.000 q^{11} -181.112 q^{12} -1124.39 q^{13} -1065.40 q^{14} +225.000 q^{15} -1263.00 q^{16} +1019.99 q^{17} -584.793 q^{18} -13.7131 q^{19} -503.090 q^{20} -1328.13 q^{21} -873.580 q^{22} -2116.94 q^{23} -771.694 q^{24} +625.000 q^{25} +8117.69 q^{26} -729.000 q^{27} +2969.63 q^{28} +3120.98 q^{29} -1624.42 q^{30} -9628.99 q^{31} +6374.61 q^{32} -1089.00 q^{33} -7363.96 q^{34} -3689.24 q^{35} +1630.01 q^{36} -3121.52 q^{37} +99.0039 q^{38} +10119.5 q^{39} -2143.59 q^{40} -5884.38 q^{41} +9588.63 q^{42} +20522.3 q^{43} +2434.95 q^{44} -2025.00 q^{45} +15283.6 q^{46} +24718.5 q^{47} +11367.0 q^{48} +4969.81 q^{49} -4512.29 q^{50} -9179.87 q^{51} -22626.7 q^{52} +22761.1 q^{53} +5263.14 q^{54} -3025.00 q^{55} +12653.2 q^{56} +123.418 q^{57} -22532.4 q^{58} -14533.5 q^{59} +4527.81 q^{60} +43984.9 q^{61} +69518.1 q^{62} +11953.1 q^{63} -5606.68 q^{64} +28109.6 q^{65} +7862.22 q^{66} -31488.3 q^{67} +20525.8 q^{68} +19052.5 q^{69} +26635.1 q^{70} -29173.2 q^{71} +6945.24 q^{72} +49583.0 q^{73} +22536.3 q^{74} -5625.00 q^{75} -275.956 q^{76} +17855.9 q^{77} -73059.2 q^{78} -85075.4 q^{79} +31574.9 q^{80} +6561.00 q^{81} +42483.3 q^{82} +77321.9 q^{83} -26726.7 q^{84} -25499.6 q^{85} -148164. q^{86} -28088.8 q^{87} +10375.0 q^{88} +70217.7 q^{89} +14619.8 q^{90} -165925. q^{91} -42600.5 q^{92} +86660.9 q^{93} -178459. q^{94} +342.827 q^{95} -57371.5 q^{96} -21080.0 q^{97} -35880.4 q^{98} +9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 7 q^{2} - 27 q^{3} + 73 q^{4} - 75 q^{5} - 63 q^{6} + 92 q^{7} + 231 q^{8} + 243 q^{9} - 175 q^{10} + 363 q^{11} - 657 q^{12} - 90 q^{13} - 784 q^{14} + 675 q^{15} - 415 q^{16} + 1934 q^{17} + 567 q^{18}+ \cdots + 29403 q^{99}+O(q^{100}) \) 3 * q + 7 * q^2 - 27 * q^3 + 73 * q^4 - 75 * q^5 - 63 * q^6 + 92 * q^7 + 231 * q^8 + 243 * q^9 - 175 * q^10 + 363 * q^11 - 657 * q^12 - 90 * q^13 - 784 * q^14 + 675 * q^15 - 415 * q^16 + 1934 * q^17 + 567 * q^18 + 2084 * q^19 - 1825 * q^20 - 828 * q^21 + 847 * q^22 + 1220 * q^23 - 2079 * q^24 + 1875 * q^25 + 17062 * q^26 - 2187 * q^27 + 11120 * q^28 + 4402 * q^29 + 1575 * q^30 - 10688 * q^31 + 12439 * q^32 - 3267 * q^33 - 4094 * q^34 - 2300 * q^35 + 5913 * q^36 - 8190 * q^37 + 13792 * q^38 + 810 * q^39 - 5775 * q^40 + 5974 * q^41 + 7056 * q^42 + 18868 * q^43 + 8833 * q^44 - 6075 * q^45 + 46220 * q^46 + 55500 * q^47 + 3735 * q^48 + 1907 * q^49 + 4375 * q^50 - 17406 * q^51 + 27330 * q^52 + 9206 * q^53 - 5103 * q^54 - 9075 * q^55 + 73248 * q^56 - 18756 * q^57 + 15366 * q^58 - 59196 * q^59 + 16425 * q^60 + 79902 * q^61 + 64616 * q^62 + 7452 * q^63 + 2129 * q^64 + 2250 * q^65 - 7623 * q^66 + 4468 * q^67 - 1218 * q^68 - 10980 * q^69 + 19600 * q^70 - 75164 * q^71 + 18711 * q^72 - 61290 * q^73 - 56766 * q^74 - 16875 * q^75 + 37816 * q^76 + 11132 * q^77 - 153558 * q^78 - 83564 * q^79 + 10375 * q^80 + 19683 * q^81 + 147410 * q^82 + 74764 * q^83 - 100080 * q^84 - 48350 * q^85 - 253432 * q^86 - 39618 * q^87 + 27951 * q^88 + 37342 * q^89 - 14175 * q^90 - 126488 * q^91 + 148164 * q^92 + 96192 * q^93 + 59252 * q^94 - 52100 * q^95 - 111951 * q^96 + 33486 * q^97 - 95249 * q^98 + 29403 * q^99

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