LMFDB - Embedded newform 294.6.a.n.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,6,Mod(1,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("294.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	294.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:	$47.1528430250$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 7 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	294.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -4.50253 q^{5} +36.0000 q^{6} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -4.50253 q^{5} +36.0000 q^{6} -64.0000 q^{8} +81.0000 q^{9} +18.0101 q^{10} -116.191 q^{11} -144.000 q^{12} +85.4773 q^{13} +40.5227 q^{15} +256.000 q^{16} -33.2662 q^{17} -324.000 q^{18} -635.377 q^{19} -72.0404 q^{20} +464.764 q^{22} +2727.43 q^{23} +576.000 q^{24} -3104.73 q^{25} -341.909 q^{26} -729.000 q^{27} +5860.48 q^{29} -162.091 q^{30} -279.136 q^{31} -1024.00 q^{32} +1045.72 q^{33} +133.065 q^{34} +1296.00 q^{36} +3038.49 q^{37} +2541.51 q^{38} -769.295 q^{39} +288.162 q^{40} -819.415 q^{41} +11100.2 q^{43} -1859.05 q^{44} -364.705 q^{45} -10909.7 q^{46} +7407.40 q^{47} -2304.00 q^{48} +12418.9 q^{50} +299.395 q^{51} +1367.64 q^{52} -13698.8 q^{53} +2916.00 q^{54} +523.153 q^{55} +5718.39 q^{57} -23441.9 q^{58} -22375.7 q^{59} +648.364 q^{60} +12692.1 q^{61} +1116.55 q^{62} +4096.00 q^{64} -384.864 q^{65} -4182.87 q^{66} -52303.3 q^{67} -532.259 q^{68} -24546.8 q^{69} +60230.2 q^{71} -5184.00 q^{72} -76958.4 q^{73} -12154.0 q^{74} +27942.5 q^{75} -10166.0 q^{76} +3077.18 q^{78} -33596.0 q^{79} -1152.65 q^{80} +6561.00 q^{81} +3277.66 q^{82} -60574.9 q^{83} +149.782 q^{85} -44400.9 q^{86} -52744.3 q^{87} +7436.22 q^{88} -92190.1 q^{89} +1458.82 q^{90} +43638.8 q^{92} +2512.23 q^{93} -29629.6 q^{94} +2860.80 q^{95} +9216.00 q^{96} -152287. q^{97} -9411.46 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{2} - 18 q^{3} + 32 q^{4} - 108 q^{5} + 72 q^{6} - 128 q^{8} + 162 q^{9}+O(q^{10}) $ 2 * q - 8 * q^2 - 18 * q^3 + 32 * q^4 - 108 * q^5 + 72 * q^6 - 128 * q^8 + 162 * q^9	\( 2 q - 8 q^{2} - 18 q^{3} + 32 q^{4} - 108 q^{5} + 72 q^{6} - 128 q^{8} + 162 q^{9} + 432 q^{10} + 124 q^{11} - 288 q^{12} - 720 q^{13} + 972 q^{15} + 512 q^{16} + 1260 q^{17} - 648 q^{18} - 360 q^{19} - 1728 q^{20} - 496 q^{22} + 6524 q^{23} + 1152 q^{24} + 4482 q^{25} + 2880 q^{26} - 1458 q^{27} + 7088 q^{29} - 3888 q^{30} - 5904 q^{31} - 2048 q^{32} - 1116 q^{33} - 5040 q^{34} + 2592 q^{36} - 6040 q^{37} + 1440 q^{38} + 6480 q^{39} + 6912 q^{40} + 17388 q^{41} - 608 q^{43} + 1984 q^{44} - 8748 q^{45} - 26096 q^{46} + 30456 q^{47} - 4608 q^{48} - 17928 q^{50} - 11340 q^{51} - 11520 q^{52} + 3964 q^{53} + 5832 q^{54} - 24336 q^{55} + 3240 q^{57} - 28352 q^{58} - 40752 q^{59} + 15552 q^{60} + 1368 q^{61} + 23616 q^{62} + 8192 q^{64} + 82980 q^{65} + 4464 q^{66} - 16224 q^{67} + 20160 q^{68} - 58716 q^{69} - 3204 q^{71} - 10368 q^{72} - 23976 q^{73} + 24160 q^{74} - 40338 q^{75} - 5760 q^{76} - 25920 q^{78} - 82160 q^{79} - 27648 q^{80} + 13122 q^{81} - 69552 q^{82} - 173736 q^{83} - 133700 q^{85} + 2432 q^{86} - 63792 q^{87} - 7936 q^{88} - 200556 q^{89} + 34992 q^{90} + 104384 q^{92} + 53136 q^{93} - 121824 q^{94} - 25640 q^{95} + 18432 q^{96} - 251928 q^{97} + 10044 q^{99}+O(q^{100}) \) 2 * q - 8 * q^2 - 18 * q^3 + 32 * q^4 - 108 * q^5 + 72 * q^6 - 128 * q^8 + 162 * q^9 + 432 * q^10 + 124 * q^11 - 288 * q^12 - 720 * q^13 + 972 * q^15 + 512 * q^16 + 1260 * q^17 - 648 * q^18 - 360 * q^19 - 1728 * q^20 - 496 * q^22 + 6524 * q^23 + 1152 * q^24 + 4482 * q^25 + 2880 * q^26 - 1458 * q^27 + 7088 * q^29 - 3888 * q^30 - 5904 * q^31 - 2048 * q^32 - 1116 * q^33 - 5040 * q^34 + 2592 * q^36 - 6040 * q^37 + 1440 * q^38 + 6480 * q^39 + 6912 * q^40 + 17388 * q^41 - 608 * q^43 + 1984 * q^44 - 8748 * q^45 - 26096 * q^46 + 30456 * q^47 - 4608 * q^48 - 17928 * q^50 - 11340 * q^51 - 11520 * q^52 + 3964 * q^53 + 5832 * q^54 - 24336 * q^55 + 3240 * q^57 - 28352 * q^58 - 40752 * q^59 + 15552 * q^60 + 1368 * q^61 + 23616 * q^62 + 8192 * q^64 + 82980 * q^65 + 4464 * q^66 - 16224 * q^67 + 20160 * q^68 - 58716 * q^69 - 3204 * q^71 - 10368 * q^72 - 23976 * q^73 + 24160 * q^74 - 40338 * q^75 - 5760 * q^76 - 25920 * q^78 - 82160 * q^79 - 27648 * q^80 + 13122 * q^81 - 69552 * q^82 - 173736 * q^83 - 133700 * q^85 + 2432 * q^86 - 63792 * q^87 - 7936 * q^88 - 200556 * q^89 + 34992 * q^90 + 104384 * q^92 + 53136 * q^93 - 121824 * q^94 - 25640 * q^95 + 18432 * q^96 - 251928 * q^97 + 10044 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	16.0000	0.500000
$5$	−4.50253	−0.0805436	−0.0402718	−	0.999189i	$-0.512822\pi$
$5$	−4.50253	−0.0805436	−0.0402718	+	0.999189i	$0.512822\pi$
$6$	36.0000	0.408248
$7$	0	0
$7$	0	0
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	18.0101	0.0569529
$11$	−116.191	−0.289528	−0.144764	−	0.989466i	$-0.546242\pi$
$11$	−116.191	−0.289528	−0.144764	+	0.989466i	$0.546242\pi$
$12$	−144.000	−0.288675
$13$	85.4773	0.140279	0.0701394	−	0.997537i	$-0.477656\pi$
$13$	85.4773	0.140279	0.0701394	+	0.997537i	$0.477656\pi$
$14$	0	0
$15$	40.5227	0.0465019
$16$	256.000	0.250000
$17$	−33.2662	−0.0279177	−0.0139589	−	0.999903i	$-0.504443\pi$
$17$	−33.2662	−0.0279177	−0.0139589	+	0.999903i	$0.504443\pi$
$18$	−324.000	−0.235702
$19$	−635.377	−0.403782	−0.201891	−	0.979408i	$-0.564709\pi$
$19$	−635.377	−0.403782	−0.201891	+	0.979408i	$0.564709\pi$
$20$	−72.0404	−0.0402718
$21$	0	0
$22$	464.764	0.204727
$23$	2727.43	1.07506	0.537531	−	0.843244i	$-0.319357\pi$
$23$	2727.43	1.07506	0.537531	+	0.843244i	$0.319357\pi$
$24$	576.000	0.204124
$25$	−3104.73	−0.993513
$26$	−341.909	−0.0991921
$27$	−729.000	−0.192450
$28$	0	0
$29$	5860.48	1.29401	0.647006	−	0.762485i	$-0.276021\pi$
$29$	5860.48	1.29401	0.647006	+	0.762485i	$0.276021\pi$
$30$	−162.091	−0.0328818
$31$	−279.136	−0.0521690	−0.0260845	−	0.999660i	$-0.508304\pi$
$31$	−279.136	−0.0521690	−0.0260845	+	0.999660i	$0.508304\pi$
$32$	−1024.00	−0.176777
$33$	1045.72	0.167159
$34$	133.065	0.0197408
$35$	0	0
$36$	1296.00	0.166667
$37$	3038.49	0.364883	0.182442	−	0.983217i	$-0.441600\pi$
$37$	3038.49	0.364883	0.182442	+	0.983217i	$0.441600\pi$
$38$	2541.51	0.285517
$39$	−769.295	−0.0809900
$40$	288.162	0.0284765
$41$	−819.415	−0.0761279	−0.0380640	−	0.999275i	$-0.512119\pi$
$41$	−819.415	−0.0761279	−0.0380640	+	0.999275i	$0.512119\pi$
$42$	0	0
$43$	11100.2	0.915504	0.457752	−	0.889080i	$-0.348655\pi$
$43$	11100.2	0.915504	0.457752	+	0.889080i	$0.348655\pi$
$44$	−1859.05	−0.144764
$45$	−364.705	−0.0268479
$46$	−10909.7	−0.760184
$47$	7407.40	0.489126	0.244563	−	0.969633i	$-0.421355\pi$
$47$	7407.40	0.489126	0.244563	+	0.969633i	$0.421355\pi$
$48$	−2304.00	−0.144338
$49$	0	0
$50$	12418.9	0.702520
$51$	299.395	0.0161183
$52$	1367.64	0.0701394
$53$	−13698.8	−0.669874	−0.334937	−	0.942241i	$-0.608715\pi$
$53$	−13698.8	−0.669874	−0.334937	+	0.942241i	$0.608715\pi$
$54$	2916.00	0.136083
$55$	523.153	0.0233196
$56$	0	0
$57$	5718.39	0.233124
$58$	−23441.9	−0.915005
$59$	−22375.7	−0.836848	−0.418424	−	0.908252i	$-0.637417\pi$
$59$	−22375.7	−0.836848	−0.418424	+	0.908252i	$0.637417\pi$
$60$	648.364	0.0232509
$61$	12692.1	0.436725	0.218363	−	0.975868i	$-0.429928\pi$
$61$	12692.1	0.436725	0.218363	+	0.975868i	$0.429928\pi$
$62$	1116.55	0.0368890
$63$	0	0
$64$	4096.00	0.125000
$65$	−384.864	−0.0112986
$66$	−4182.87	−0.118199
$67$	−52303.3	−1.42345	−0.711725	−	0.702458i	$-0.752086\pi$
$67$	−52303.3	−1.42345	−0.711725	+	0.702458i	$0.752086\pi$
$68$	−532.259	−0.0139589
$69$	−24546.8	−0.620687
$70$	0	0
$71$	60230.2	1.41798	0.708988	−	0.705221i	$-0.249152\pi$
$71$	60230.2	1.41798	0.708988	+	0.705221i	$0.249152\pi$
$72$	−5184.00	−0.117851
$73$	−76958.4	−1.69024	−0.845121	−	0.534575i	$-0.820472\pi$
$73$	−76958.4	−1.69024	−0.845121	+	0.534575i	$0.820472\pi$
$74$	−12154.0	−0.258011
$75$	27942.5	0.573605
$76$	−10166.0	−0.201891
$77$	0	0
$78$	3077.18	0.0572686
$79$	−33596.0	−0.605647	−0.302824	−	0.953047i	$-0.597929\pi$
$79$	−33596.0	−0.605647	−0.302824	+	0.953047i	$0.597929\pi$
$80$	−1152.65	−0.0201359
$81$	6561.00	0.111111
$82$	3277.66	0.0538306
$83$	−60574.9	−0.965157	−0.482578	−	0.875853i	$-0.660300\pi$
$83$	−60574.9	−0.965157	−0.482578	+	0.875853i	$0.660300\pi$
$84$	0	0
$85$	149.782	0.00224860
$86$	−44400.9	−0.647359
$87$	−52744.3	−0.747098
$88$	7436.22	0.102364
$89$	−92190.1	−1.23370	−0.616850	−	0.787081i	$-0.711591\pi$
$89$	−92190.1	−1.23370	−0.616850	+	0.787081i	$0.711591\pi$
$90$	1458.82	0.0189843
$91$	0	0
$92$	43638.8	0.537531
$93$	2512.23	0.0301198
$94$	−29629.6	−0.345865
$95$	2860.80	0.0325221
$96$	9216.00	0.102062
$97$	−152287.	−1.64336	−0.821680	−	0.569949i	$-0.806963\pi$
$97$	−152287.	−1.64336	−0.821680	+	0.569949i	$0.806963\pi$
$98$	0	0
$99$	−9411.46	−0.0965093
$100$	−49675.6	−0.496756
$101$	−107644.	−1.04999	−0.524997	−	0.851104i	$-0.675934\pi$
$101$	−107644.	−1.04999	−0.524997	+	0.851104i	$0.675934\pi$
$102$	−1197.58	−0.0113974
$103$	−120639.	−1.12046	−0.560229	−	0.828338i	$-0.689287\pi$
$103$	−120639.	−1.12046	−0.560229	+	0.828338i	$0.689287\pi$
$104$	−5470.55	−0.0495961
$105$	0	0
$106$	54795.2	0.473672
$107$	86114.3	0.727136	0.363568	−	0.931568i	$-0.381558\pi$
$107$	86114.3	0.727136	0.363568	+	0.931568i	$0.381558\pi$
$108$	−11664.0	−0.0962250
$109$	−66139.2	−0.533203	−0.266602	−	0.963807i	$-0.585901\pi$
$109$	−66139.2	−0.533203	−0.266602	+	0.963807i	$0.585901\pi$
$110$	−2092.61	−0.0164895
$111$	−27346.4	−0.210665
$112$	0	0
$113$	131608.	0.969588	0.484794	−	0.874628i	$-0.338895\pi$
$113$	131608.	0.969588	0.484794	+	0.874628i	$0.338895\pi$
$114$	−22873.6	−0.164843
$115$	−12280.3	−0.0865894
$116$	93767.7	0.647006
$117$	6923.66	0.0467596
$118$	89502.8	0.591741
$119$	0	0
$120$	−2593.45	−0.0164409
$121$	−147551.	−0.916174
$122$	−50768.3	−0.308812
$123$	7374.73	0.0439525
$124$	−4466.18	−0.0260845
$125$	28049.5	0.160565
$126$	0	0
$127$	14437.3	0.0794284	0.0397142	−	0.999211i	$-0.487355\pi$
$127$	14437.3	0.0794284	0.0397142	+	0.999211i	$0.487355\pi$
$128$	−16384.0	−0.0883883
$129$	−99902.0	−0.528567
$130$	1539.45	0.00798929
$131$	−319216.	−1.62520	−0.812600	−	0.582821i	$-0.801949\pi$
$131$	−319216.	−1.62520	−0.812600	+	0.582821i	$0.801949\pi$
$132$	16731.5	0.0835795
$133$	0	0
$134$	209213.	1.00653
$135$	3282.34	0.0155006
$136$	2129.03	0.00987041
$137$	−50534.0	−0.230029	−0.115014	−	0.993364i	$-0.536691\pi$
$137$	−50534.0	−0.230029	−0.115014	+	0.993364i	$0.536691\pi$
$138$	98187.4	0.438892
$139$	−223787.	−0.982422	−0.491211	−	0.871041i	$-0.663446\pi$
$139$	−223787.	−0.982422	−0.491211	+	0.871041i	$0.663446\pi$
$140$	0	0
$141$	−66666.6	−0.282397
$142$	−240921.	−1.00266
$143$	−9931.68	−0.0406146
$144$	20736.0	0.0833333
$145$	−26387.0	−0.104224
$146$	307834.	1.19518
$147$	0	0
$148$	48615.9	0.182442
$149$	259521.	0.957651	0.478825	−	0.877910i	$-0.341063\pi$
$149$	259521.	0.957651	0.478825	+	0.877910i	$0.341063\pi$
$150$	−111770.	−0.405600
$151$	−110893.	−0.395786	−0.197893	−	0.980224i	$-0.563410\pi$
$151$	−110893.	−0.395786	−0.197893	+	0.980224i	$0.563410\pi$
$152$	40664.1	0.142759
$153$	−2694.56	−0.00930592
$154$	0	0
$155$	1256.82	0.00420188
$156$	−12308.7	−0.0404950
$157$	405385.	1.31256	0.656280	−	0.754518i	$-0.272129\pi$
$157$	405385.	1.31256	0.656280	+	0.754518i	$0.272129\pi$
$158$	134384.	0.428257
$159$	123289.	0.386752
$160$	4610.59	0.0142382
$161$	0	0
$162$	−26244.0	−0.0785674
$163$	38618.7	0.113849	0.0569244	−	0.998378i	$-0.481871\pi$
$163$	38618.7	0.113849	0.0569244	+	0.998378i	$0.481871\pi$
$164$	−13110.6	−0.0380640
$165$	−4708.37	−0.0134636
$166$	242300.	0.682469
$167$	207255.	0.575060	0.287530	−	0.957772i	$-0.407166\pi$
$167$	207255.	0.575060	0.287530	+	0.957772i	$0.407166\pi$
$168$	0	0
$169$	−363987.	−0.980322
$170$	−599.127	−0.00159000
$171$	−51465.5	−0.134594
$172$	177603.	0.457752
$173$	128257.	0.325812	0.162906	−	0.986642i	$-0.447913\pi$
$173$	128257.	0.325812	0.162906	+	0.986642i	$0.447913\pi$
$174$	210977.	0.528278
$175$	0	0
$176$	−29744.9	−0.0723820
$177$	201381.	0.483154
$178$	368760.	0.872357
$179$	−98599.5	−0.230007	−0.115004	−	0.993365i	$-0.536688\pi$
$179$	−98599.5	−0.230007	−0.115004	+	0.993365i	$0.536688\pi$
$180$	−5835.27	−0.0134239
$181$	−599225.	−1.35954	−0.679772	−	0.733423i	$-0.737921\pi$
$181$	−599225.	−1.35954	−0.679772	+	0.733423i	$0.737921\pi$
$182$	0	0
$183$	−114229.	−0.252144
$184$	−174555.	−0.380092
$185$	−13680.9	−0.0293890
$186$	−10048.9	−0.0212979
$187$	3865.23	0.00808297
$188$	118518.	0.244563
$189$	0	0
$190$	−11443.2	−0.0229966
$191$	829216.	1.64469	0.822346	−	0.568988i	$-0.192665\pi$
$191$	829216.	1.64469	0.822346	+	0.568988i	$0.192665\pi$
$192$	−36864.0	−0.0721688
$193$	−416385.	−0.804641	−0.402320	−	0.915499i	$-0.631796\pi$
$193$	−416385.	−0.804641	−0.402320	+	0.915499i	$0.631796\pi$
$194$	609147.	1.16203
$195$	3463.77	0.00652323
$196$	0	0
$197$	−592061.	−1.08693	−0.543464	−	0.839433i	$-0.682887\pi$
$197$	−592061.	−1.08693	−0.543464	+	0.839433i	$0.682887\pi$
$198$	37645.9	0.0682424
$199$	1.06608e6	1.90835	0.954173	−	0.299255i	$-0.0967380\pi$
$199$	1.06608e6	1.90835	0.954173	+	0.299255i	$0.0967380\pi$
$200$	198703.	0.351260
$201$	470730.	0.821830
$202$	430577.	0.742458
$203$	0	0
$204$	4790.33	0.00805916
$205$	3689.44	0.00613162
$206$	482557.	0.792283
$207$	220922.	0.358354
$208$	21882.2	0.0350697
$209$	73825.0	0.116906
$210$	0	0
$211$	−846029.	−1.30822	−0.654108	−	0.756401i	$-0.726956\pi$
$211$	−846029.	−1.30822	−0.654108	+	0.756401i	$0.726956\pi$
$212$	−219181.	−0.334937
$213$	−542072.	−0.818669
$214$	−344457.	−0.514163
$215$	−49979.0	−0.0737380
$216$	46656.0	0.0680414
$217$	0	0
$218$	264557.	0.377032
$219$	692625.	0.975861
$220$	8370.44	0.0116598
$221$	−2843.50	−0.00391627
$222$	109386.	0.148963
$223$	−112299.	−0.151222	−0.0756109	−	0.997137i	$-0.524091\pi$
$223$	−112299.	−0.151222	−0.0756109	+	0.997137i	$0.524091\pi$
$224$	0	0
$225$	−251483.	−0.331171
$226$	−526433.	−0.685602
$227$	178477.	0.229889	0.114944	−	0.993372i	$-0.463331\pi$
$227$	178477.	0.229889	0.114944	+	0.993372i	$0.463331\pi$
$228$	91494.3	0.116562
$229$	−459753.	−0.579344	−0.289672	−	0.957126i	$-0.593546\pi$
$229$	−459753.	−0.579344	−0.289672	+	0.957126i	$0.593546\pi$
$230$	49121.2	0.0612280
$231$	0	0
$232$	−375071.	−0.457502
$233$	748667.	0.903440	0.451720	−	0.892160i	$-0.350811\pi$
$233$	748667.	0.903440	0.451720	+	0.892160i	$0.350811\pi$
$234$	−27694.6	−0.0330640
$235$	−33352.0	−0.0393960
$236$	−358011.	−0.418424
$237$	302364.	0.349670
$238$	0	0
$239$	−814752.	−0.922637	−0.461319	−	0.887235i	$-0.652623\pi$
$239$	−814752.	−0.922637	−0.461319	+	0.887235i	$0.652623\pi$
$240$	10373.8	0.0116255
$241$	1.04763e6	1.16189	0.580947	−	0.813942i	$-0.302682\pi$
$241$	1.04763e6	1.16189	0.580947	+	0.813942i	$0.302682\pi$
$242$	590203.	0.647833
$243$	−59049.0	−0.0641500
$244$	203073.	0.218363
$245$	0	0
$246$	−29498.9	−0.0310791
$247$	−54310.3	−0.0566421
$248$	17864.7	0.0184445
$249$	545174.	0.557233
$250$	−112198.	−0.113536
$251$	1.09401e6	1.09607	0.548034	−	0.836456i	$-0.315377\pi$
$251$	1.09401e6	1.09607	0.548034	+	0.836456i	$0.315377\pi$
$252$	0	0
$253$	−316902.	−0.311261
$254$	−57749.1	−0.0561644
$255$	−1348.04	−0.00129823
$256$	65536.0	0.0625000
$257$	778391.	0.735131	0.367566	−	0.929998i	$-0.380191\pi$
$257$	778391.	0.735131	0.367566	+	0.929998i	$0.380191\pi$
$258$	399608.	0.373753
$259$	0	0
$260$	−6157.82	−0.00564928
$261$	474699.	0.431337
$262$	1.27687e6	1.14919
$263$	1.10976e6	0.989329	0.494664	−	0.869084i	$-0.335291\pi$
$263$	1.10976e6	0.989329	0.494664	+	0.869084i	$0.335291\pi$
$264$	−66926.0	−0.0590996
$265$	61679.2	0.0539540
$266$	0	0
$267$	829711.	0.712277
$268$	−836854.	−0.711725
$269$	−1.33640e6	−1.12605	−0.563024	−	0.826440i	$-0.690362\pi$
$269$	−1.33640e6	−1.12605	−0.563024	+	0.826440i	$0.690362\pi$
$270$	−13129.4	−0.0109606
$271$	−1.79201e6	−1.48224	−0.741118	−	0.671375i	$-0.765704\pi$
$271$	−1.79201e6	−1.48224	−0.741118	+	0.671375i	$0.765704\pi$
$272$	−8516.14	−0.00697944
$273$	0	0
$274$	202136.	0.162655
$275$	360741.	0.287650
$276$	−392750.	−0.310344
$277$	57577.6	0.0450873	0.0225436	−	0.999746i	$-0.492824\pi$
$277$	57577.6	0.0450873	0.0225436	+	0.999746i	$0.492824\pi$
$278$	895148.	0.694677
$279$	−22610.0	−0.0173897
$280$	0	0
$281$	−550257.	−0.415719	−0.207860	−	0.978159i	$-0.566650\pi$
$281$	−550257.	−0.415719	−0.207860	+	0.978159i	$0.566650\pi$
$282$	266666.	0.199685
$283$	1.17788e6	0.874249	0.437125	−	0.899401i	$-0.355997\pi$
$283$	1.17788e6	0.874249	0.437125	+	0.899401i	$0.355997\pi$
$284$	963684.	0.708988
$285$	−25747.2	−0.0187766
$286$	39726.7	0.0287189
$287$	0	0
$288$	−82944.0	−0.0589256
$289$	−1.41875e6	−0.999221
$290$	105548.	0.0736978
$291$	1.37058e6	0.948795
$292$	−1.23133e6	−0.845121
$293$	−300762.	−0.204670	−0.102335	−	0.994750i	$-0.532631\pi$
$293$	−300762.	−0.204670	−0.102335	+	0.994750i	$0.532631\pi$
$294$	0	0
$295$	100747.	0.0674028
$296$	−194463.	−0.129006
$297$	84703.2	0.0557197
$298$	−1.03808e6	−0.677161
$299$	233133.	0.150809
$300$	447081.	0.286802
$301$	0	0
$302$	443571.	0.279863
$303$	968798.	0.606215
$304$	−162656.	−0.100946
$305$	−57146.4	−0.0351754
$306$	10778.2	0.00658028
$307$	−146787.	−0.0888874	−0.0444437	−	0.999012i	$-0.514152\pi$
$307$	−146787.	−0.0888874	−0.0444437	+	0.999012i	$0.514152\pi$
$308$	0	0
$309$	1.08575e6	0.646896
$310$	−5027.27	−0.00297118
$311$	−1.70311e6	−0.998484	−0.499242	−	0.866462i	$-0.666388\pi$
$311$	−1.70311e6	−0.998484	−0.499242	+	0.866462i	$0.666388\pi$
$312$	49234.9	0.0286343
$313$	−1.11695e6	−0.644424	−0.322212	−	0.946668i	$-0.604426\pi$
$313$	−1.11695e6	−0.644424	−0.322212	+	0.946668i	$0.604426\pi$
$314$	−1.62154e6	−0.928120
$315$	0	0
$316$	−537536.	−0.302824
$317$	−962894.	−0.538184	−0.269092	−	0.963115i	$-0.586724\pi$
$317$	−962894.	−0.538184	−0.269092	+	0.963115i	$0.586724\pi$
$318$	−493157.	−0.273475
$319$	−680935.	−0.374653
$320$	−18442.3	−0.0100680
$321$	−775029.	−0.419812
$322$	0	0
$323$	21136.5	0.0112727
$324$	104976.	0.0555556
$325$	−265384.	−0.139369
$326$	−154475.	−0.0805032
$327$	595253.	0.307845
$328$	52442.5	0.0269153
$329$	0	0
$330$	18833.5	0.00952020
$331$	−2.25995e6	−1.13378	−0.566891	−	0.823793i	$-0.691854\pi$
$331$	−2.25995e6	−1.13378	−0.566891	+	0.823793i	$0.691854\pi$
$332$	−969199.	−0.482578
$333$	246118.	0.121628
$334$	−829019.	−0.406629
$335$	235497.	0.114650
$336$	0	0
$337$	1.33338e6	0.639557	0.319778	−	0.947492i	$-0.396392\pi$
$337$	1.33338e6	0.639557	0.319778	+	0.947492i	$0.396392\pi$
$338$	1.45595e6	0.693192
$339$	−1.18447e6	−0.559792
$340$	2396.51	0.00112430
$341$	32433.1	0.0151044
$342$	205862.	0.0951724
$343$	0	0
$344$	−710414.	−0.323680
$345$	110523.	0.0499924
$346$	−513029.	−0.230384
$347$	−1.43486e6	−0.639715	−0.319857	−	0.947466i	$-0.603635\pi$
$347$	−1.43486e6	−0.639715	−0.319857	+	0.947466i	$0.603635\pi$
$348$	−843909.	−0.373549
$349$	−3.34711e6	−1.47098	−0.735489	−	0.677536i	$-0.763048\pi$
$349$	−3.34711e6	−1.47098	−0.735489	+	0.677536i	$0.763048\pi$
$350$	0	0
$351$	−62312.9	−0.0269967
$352$	118979.	0.0511818
$353$	−4.00418e6	−1.71032	−0.855160	−	0.518365i	$-0.826541\pi$
$353$	−4.00418e6	−1.71032	−0.855160	+	0.518365i	$0.826541\pi$
$354$	−805525.	−0.341642
$355$	−271188.	−0.114209
$356$	−1.47504e6	−0.616850
$357$	0	0
$358$	394398.	0.162640
$359$	−595986.	−0.244062	−0.122031	−	0.992526i	$-0.538941\pi$
$359$	−595986.	−0.244062	−0.122031	+	0.992526i	$0.538941\pi$
$360$	23341.1	0.00949216
$361$	−2.07240e6	−0.836960
$362$	2.39690e6	0.961343
$363$	1.32796e6	0.528953
$364$	0	0
$365$	346507.	0.136138
$366$	456915.	0.178292
$367$	3.30390e6	1.28045	0.640224	−	0.768188i	$-0.278842\pi$
$367$	3.30390e6	1.28045	0.640224	+	0.768188i	$0.278842\pi$
$368$	698221.	0.268766
$369$	−66372.6	−0.0253760
$370$	54723.5	0.0207812
$371$	0	0
$372$	40195.6	0.0150599
$373$	−2.83063e6	−1.05344	−0.526722	−	0.850038i	$-0.676579\pi$
$373$	−2.83063e6	−1.05344	−0.526722	+	0.850038i	$0.676579\pi$
$374$	−15460.9	−0.00571552
$375$	−252446.	−0.0927021
$376$	−474074.	−0.172932
$377$	500938.	0.181523
$378$	0	0
$379$	2.45025e6	0.876218	0.438109	−	0.898922i	$-0.355648\pi$
$379$	2.45025e6	0.876218	0.438109	+	0.898922i	$0.355648\pi$
$380$	45772.8	0.0162610
$381$	−129935.	−0.0458580
$382$	−3.31687e6	−1.16297
$383$	3.38405e6	1.17880	0.589399	−	0.807842i	$-0.299364\pi$
$383$	3.38405e6	1.17880	0.589399	+	0.807842i	$0.299364\pi$
$384$	147456.	0.0510310
$385$	0	0
$386$	1.66554e6	0.568967
$387$	899118.	0.305168
$388$	−2.43659e6	−0.821680
$389$	−4.14961e6	−1.39038	−0.695189	−	0.718827i	$-0.744679\pi$
$389$	−4.14961e6	−1.39038	−0.695189	+	0.718827i	$0.744679\pi$
$390$	−13855.1	−0.00461262
$391$	−90731.0	−0.0300133
$392$	0	0
$393$	2.87295e6	0.938310
$394$	2.36824e6	0.768574
$395$	151267.	0.0487810
$396$	−150583.	−0.0482547
$397$	1.64666e6	0.524358	0.262179	−	0.965019i	$-0.415559\pi$
$397$	1.64666e6	0.524358	0.262179	+	0.965019i	$0.415559\pi$
$398$	−4.26432e6	−1.34940
$399$	0	0
$400$	−794810.	−0.248378
$401$	−4.38664e6	−1.36229	−0.681147	−	0.732147i	$-0.738519\pi$
$401$	−4.38664e6	−1.36229	−0.681147	+	0.732147i	$0.738519\pi$
$402$	−1.88292e6	−0.581121
$403$	−23859.8	−0.00731820
$404$	−1.72231e6	−0.524997
$405$	−29541.1	−0.00894929
$406$	0	0
$407$	−353045.	−0.105644
$408$	−19161.3	−0.00569869
$409$	−354592.	−0.104814	−0.0524072	−	0.998626i	$-0.516689\pi$
$409$	−354592.	−0.104814	−0.0524072	+	0.998626i	$0.516689\pi$
$410$	−14757.7	−0.00433571
$411$	454806.	0.132807
$412$	−1.93023e6	−0.560229
$413$	0	0
$414$	−883686.	−0.253395
$415$	272740.	0.0777372
$416$	−87528.7	−0.0247980
$417$	2.01408e6	0.567202
$418$	−295300.	−0.0826652
$419$	1.79802e6	0.500335	0.250167	−	0.968203i	$-0.419514\pi$
$419$	1.79802e6	0.500335	0.250167	+	0.968203i	$0.419514\pi$
$420$	0	0
$421$	6.10881e6	1.67978	0.839888	−	0.542760i	$-0.182621\pi$
$421$	6.10881e6	1.67978	0.839888	+	0.542760i	$0.182621\pi$
$422$	3.38412e6	0.925048
$423$	599999.	0.163042
$424$	876723.	0.236836
$425$	103282.	0.0277366
$426$	2.16829e6	0.578886
$427$	0	0
$428$	1.37783e6	0.363568
$429$	89385.1	0.0234489
$430$	199916.	0.0521407
$431$	−1.91176e6	−0.495724	−0.247862	−	0.968795i	$-0.579728\pi$
$431$	−1.91176e6	−0.495724	−0.247862	+	0.968795i	$0.579728\pi$
$432$	−186624.	−0.0481125
$433$	−385530.	−0.0988186	−0.0494093	−	0.998779i	$-0.515734\pi$
$433$	−385530.	−0.0988186	−0.0494093	+	0.998779i	$0.515734\pi$
$434$	0	0
$435$	237483.	0.0601740
$436$	−1.05823e6	−0.266602
$437$	−1.73294e6	−0.434091
$438$	−2.77050e6	−0.690038
$439$	1.83382e6	0.454146	0.227073	−	0.973878i	$-0.427084\pi$
$439$	1.83382e6	0.454146	0.227073	+	0.973878i	$0.427084\pi$
$440$	−33481.8	−0.00824473
$441$	0	0
$442$	11374.0	0.00276922
$443$	−1.93392e6	−0.468198	−0.234099	−	0.972213i	$-0.575214\pi$
$443$	−1.93392e6	−0.468198	−0.234099	+	0.972213i	$0.575214\pi$
$444$	−437543.	−0.105333
$445$	415088.	0.0993666
$446$	449197.	0.106930
$447$	−2.33569e6	−0.552900
$448$	0	0
$449$	6.76354e6	1.58328	0.791641	−	0.610987i	$-0.209227\pi$
$449$	6.76354e6	1.58328	0.791641	+	0.610987i	$0.209227\pi$
$450$	1.00593e6	0.234173
$451$	95208.5	0.0220412
$452$	2.10573e6	0.484794
$453$	998035.	0.228507
$454$	−713907.	−0.162556
$455$	0	0
$456$	−365977.	−0.0824217
$457$	−2.39492e6	−0.536414	−0.268207	−	0.963361i	$-0.586431\pi$
$457$	−2.39492e6	−0.536414	−0.268207	+	0.963361i	$0.586431\pi$
$458$	1.83901e6	0.409658
$459$	24251.0	0.00537277
$460$	−196485.	−0.0432947
$461$	6.42949e6	1.40904	0.704522	−	0.709682i	$-0.251162\pi$
$461$	6.42949e6	1.40904	0.704522	+	0.709682i	$0.251162\pi$
$462$	0	0
$463$	1.36524e6	0.295976	0.147988	−	0.988989i	$-0.452720\pi$
$463$	1.36524e6	0.295976	0.147988	+	0.988989i	$0.452720\pi$
$464$	1.50028e6	0.323503
$465$	−11311.4	−0.00242595
$466$	−2.99467e6	−0.638828
$467$	−4.36362e6	−0.925880	−0.462940	−	0.886390i	$-0.653205\pi$
$467$	−4.36362e6	−0.925880	−0.462940	+	0.886390i	$0.653205\pi$
$468$	110779.	0.0233798
$469$	0	0
$470$	133408.	0.0278572
$471$	−3.64847e6	−0.757807
$472$	1.43204e6	0.295870
$473$	−1.28974e6	−0.265064
$474$	−1.20946e6	−0.247254
$475$	1.97267e6	0.401163
$476$	0	0
$477$	−1.10960e6	−0.223291
$478$	3.25901e6	0.652403
$479$	1.39250e6	0.277303	0.138652	−	0.990341i	$-0.455723\pi$
$479$	1.39250e6	0.277303	0.138652	+	0.990341i	$0.455723\pi$
$480$	−41495.3	−0.00822045
$481$	259722.	0.0511854
$482$	−4.19053e6	−0.821583
$483$	0	0
$484$	−2.36081e6	−0.458087
$485$	685675.	0.132362
$486$	236196.	0.0453609
$487$	9.82919e6	1.87800	0.939000	−	0.343918i	$-0.111754\pi$
$487$	9.82919e6	1.87800	0.939000	+	0.343918i	$0.111754\pi$
$488$	−812294.	−0.154406
$489$	−347568.	−0.0657306
$490$	0	0
$491$	−7.67255e6	−1.43627	−0.718135	−	0.695904i	$-0.755004\pi$
$491$	−7.67255e6	−1.43627	−0.718135	+	0.695904i	$0.755004\pi$
$492$	117996.	0.0219762
$493$	−194956.	−0.0361259
$494$	217241.	0.0400520
$495$	42375.4	0.00777321
$496$	−71458.9	−0.0130422
$497$	0	0
$498$	−2.18070e6	−0.394024
$499$	3.39383e6	0.610152	0.305076	−	0.952328i	$-0.401318\pi$
$499$	3.39383e6	0.610152	0.305076	+	0.952328i	$0.401318\pi$
$500$	448792.	0.0802824
$501$	−1.86529e6	−0.332011
$502$	−4.37604e6	−0.775037
$503$	8.36268e6	1.47376	0.736878	−	0.676026i	$-0.236299\pi$
$503$	8.36268e6	1.47376	0.736878	+	0.676026i	$0.236299\pi$
$504$	0	0
$505$	484671.	0.0845704
$506$	1.26761e6	0.220094
$507$	3.27588e6	0.565989
$508$	230996.	0.0397142
$509$	−3.87324e6	−0.662643	−0.331322	−	0.943518i	$-0.607494\pi$
$509$	−3.87324e6	−0.662643	−0.331322	+	0.943518i	$0.607494\pi$
$510$	5392.14	0.000917986 0
$511$	0	0
$512$	−262144.	−0.0441942
$513$	463190.	0.0777079
$514$	−3.11356e6	−0.519816
$515$	543181.	0.0902457
$516$	−1.59843e6	−0.264283
$517$	−860672.	−0.141616
$518$	0	0
$519$	−1.15432e6	−0.188108
$520$	24631.3	0.00399465
$521$	−731064.	−0.117994	−0.0589971	−	0.998258i	$-0.518790\pi$
$521$	−731064.	−0.117994	−0.0589971	+	0.998258i	$0.518790\pi$
$522$	−1.89880e6	−0.305002
$523$	7.10854e6	1.13639	0.568193	−	0.822895i	$-0.307643\pi$
$523$	7.10854e6	1.13639	0.568193	+	0.822895i	$0.307643\pi$
$524$	−5.10746e6	−0.812600
$525$	0	0
$526$	−4.43905e6	−0.699561
$527$	9285.80	0.00145644
$528$	267704.	0.0417898
$529$	1.00252e6	0.155759
$530$	−246717.	−0.0381513
$531$	−1.81243e6	−0.278949
$532$	0	0
$533$	−70041.3	−0.0106791
$534$	−3.31884e6	−0.503656
$535$	−387732.	−0.0585662
$536$	3.34741e6	0.503266
$537$	887395.	0.132795
$538$	5.34562e6	0.796237
$539$	0	0
$540$	52517.5	0.00775031
$541$	3.79514e6	0.557487	0.278743	−	0.960366i	$-0.410082\pi$
$541$	3.79514e6	0.557487	0.278743	+	0.960366i	$0.410082\pi$
$542$	7.16804e6	1.04810
$543$	5.39302e6	0.784933
$544$	34064.5	0.00493521
$545$	297793.	0.0429461
$546$	0	0
$547$	−1.34686e7	−1.92466	−0.962332	−	0.271879i	$-0.912355\pi$
$547$	−1.34686e7	−1.92466	−0.962332	+	0.271879i	$0.912355\pi$
$548$	−808543.	−0.115014
$549$	1.02806e6	0.145575
$550$	−1.44296e6	−0.203399
$551$	−3.72361e6	−0.522499
$552$	1.57100e6	0.219446
$553$	0	0
$554$	−230310.	−0.0318815
$555$	123128.	0.0169677
$556$	−3.58059e6	−0.491211
$557$	4.89487e6	0.668503	0.334251	−	0.942484i	$-0.391517\pi$
$557$	4.89487e6	0.668503	0.334251	+	0.942484i	$0.391517\pi$
$558$	90440.2	0.0122963
$559$	948816.	0.128426
$560$	0	0
$561$	−34787.0	−0.00466670
$562$	2.20103e6	0.293958
$563$	6.25606e6	0.831821	0.415910	−	0.909406i	$-0.363463\pi$
$563$	6.25606e6	0.831821	0.415910	+	0.909406i	$0.363463\pi$
$564$	−1.06667e6	−0.141199
$565$	−592569.	−0.0780941
$566$	−4.71152e6	−0.618188
$567$	0	0
$568$	−3.85474e6	−0.501330
$569$	1.42825e6	0.184937	0.0924685	−	0.995716i	$-0.470524\pi$
$569$	1.42825e6	0.184937	0.0924685	+	0.995716i	$0.470524\pi$
$570$	102989.	0.0132771
$571$	9.05147e6	1.16179	0.580897	−	0.813977i	$-0.302702\pi$
$571$	9.05147e6	1.16179	0.580897	+	0.813977i	$0.302702\pi$
$572$	−158907.	−0.0203073
$573$	−7.46295e6	−0.949563
$574$	0	0
$575$	−8.46792e6	−1.06809
$576$	331776.	0.0416667
$577$	−8.01919e6	−1.00275	−0.501373	−	0.865231i	$-0.667172\pi$
$577$	−8.01919e6	−1.00275	−0.501373	+	0.865231i	$0.667172\pi$
$578$	5.67500e6	0.706556
$579$	3.74747e6	0.464559
$580$	−422191.	−0.0521122
$581$	0	0
$582$	−5.48232e6	−0.670899
$583$	1.59168e6	0.193947
$584$	4.92534e6	0.597591
$585$	−31174.0	−0.00376619
$586$	1.20305e6	0.144723
$587$	8.28470e6	0.992388	0.496194	−	0.868212i	$-0.334730\pi$
$587$	8.28470e6	0.992388	0.496194	+	0.868212i	$0.334730\pi$
$588$	0	0
$589$	177357.	0.0210649
$590$	−402989.	−0.0476610
$591$	5.32855e6	0.627538
$592$	777854.	0.0912208
$593$	−5.91443e6	−0.690679	−0.345340	−	0.938478i	$-0.612236\pi$
$593$	−5.91443e6	−0.690679	−0.345340	+	0.938478i	$0.612236\pi$
$594$	−338813.	−0.0393998
$595$	0	0
$596$	4.15234e6	0.478825
$597$	−9.59472e6	−1.10178
$598$	−932532.	−0.106638
$599$	3.32897e6	0.379091	0.189545	−	0.981872i	$-0.439299\pi$
$599$	3.32897e6	0.379091	0.189545	+	0.981872i	$0.439299\pi$
$600$	−1.78832e6	−0.202800
$601$	4.87081e6	0.550066	0.275033	−	0.961435i	$-0.411311\pi$
$601$	4.87081e6	0.550066	0.275033	+	0.961435i	$0.411311\pi$
$602$	0	0
$603$	−4.23657e6	−0.474484
$604$	−1.77428e6	−0.197893
$605$	664351.	0.0737919
$606$	−3.87519e6	−0.428659
$607$	1.51701e7	1.67115	0.835577	−	0.549374i	$-0.185134\pi$
$607$	1.51701e7	1.67115	0.835577	+	0.549374i	$0.185134\pi$
$608$	650626.	0.0713793
$609$	0	0
$610$	228586.	0.0248728
$611$	633164.	0.0686141
$612$	−43112.9	−0.00465296
$613$	5.18156e6	0.556941	0.278471	−	0.960445i	$-0.410173\pi$
$613$	5.18156e6	0.556941	0.278471	+	0.960445i	$0.410173\pi$
$614$	587146.	0.0628529
$615$	−33204.9	−0.00354009
$616$	0	0
$617$	1.55854e6	0.164818	0.0824092	−	0.996599i	$-0.473739\pi$
$617$	1.55854e6	0.164818	0.0824092	+	0.996599i	$0.473739\pi$
$618$	−4.34301e6	−0.457425
$619$	1.40751e6	0.147647	0.0738236	−	0.997271i	$-0.476480\pi$
$619$	1.40751e6	0.147647	0.0738236	+	0.997271i	$0.476480\pi$
$620$	20109.1	0.00210094
$621$	−1.98829e6	−0.206896
$622$	6.81243e6	0.706035
$623$	0	0
$624$	−196940.	−0.0202475
$625$	9.57598e6	0.980580
$626$	4.46779e6	0.455677
$627$	−664425.	−0.0674959
$628$	6.48617e6	0.656280
$629$	−101079.	−0.0101867
$630$	0	0
$631$	−1.09643e7	−1.09624	−0.548120	−	0.836399i	$-0.684656\pi$
$631$	−1.09643e7	−1.09624	−0.548120	+	0.836399i	$0.684656\pi$
$632$	2.15014e6	0.214129
$633$	7.61426e6	0.755298
$634$	3.85158e6	0.380553
$635$	−65004.2	−0.00639745
$636$	1.97263e6	0.193376
$637$	0	0
$638$	2.72374e6	0.264919
$639$	4.87865e6	0.472659
$640$	73769.4	0.00711912
$641$	−1.42122e7	−1.36621	−0.683103	−	0.730322i	$-0.739370\pi$
$641$	−1.42122e7	−1.36621	−0.683103	+	0.730322i	$0.739370\pi$
$642$	3.10012e6	0.296852
$643$	9.13928e6	0.871735	0.435868	−	0.900011i	$-0.356442\pi$
$643$	9.13928e6	0.871735	0.435868	+	0.900011i	$0.356442\pi$
$644$	0	0
$645$	449811.	0.0425727
$646$	−84546.2	−0.00797100
$647$	1.89272e7	1.77757	0.888785	−	0.458324i	$-0.151550\pi$
$647$	1.89272e7	1.77757	0.888785	+	0.458324i	$0.151550\pi$
$648$	−419904.	−0.0392837
$649$	2.59985e6	0.242291
$650$	1.06153e6	0.0985487
$651$	0	0
$652$	617899.	0.0569244
$653$	−4.29983e6	−0.394610	−0.197305	−	0.980342i	$-0.563219\pi$
$653$	−4.29983e6	−0.394610	−0.197305	+	0.980342i	$0.563219\pi$
$654$	−2.38101e6	−0.217679
$655$	1.43728e6	0.130900
$656$	−209770.	−0.0190320
$657$	−6.23363e6	−0.563414
$658$	0	0
$659$	−1.15303e7	−1.03425	−0.517126	−	0.855909i	$-0.672998\pi$
$659$	−1.15303e7	−1.03425	−0.517126	+	0.855909i	$0.672998\pi$
$660$	−75334.0	−0.00673180
$661$	−1.47047e7	−1.30904	−0.654521	−	0.756044i	$-0.727130\pi$
$661$	−1.47047e7	−1.30904	−0.654521	+	0.756044i	$0.727130\pi$
$662$	9.03981e6	0.801704
$663$	25591.5	0.00226106
$664$	3.87680e6	0.341234
$665$	0	0
$666$	−984471.	−0.0860037
$667$	1.59840e7	1.39114
$668$	3.31608e6	0.287530
$669$	1.01069e6	0.0873080
$670$	−941989.	−0.0810697
$671$	−1.47471e6	−0.126444
$672$	0	0
$673$	1.42971e7	1.21678	0.608389	−	0.793639i	$-0.291816\pi$
$673$	1.42971e7	1.21678	0.608389	+	0.793639i	$0.291816\pi$
$674$	−5.33352e6	−0.452235
$675$	2.26335e6	0.191202
$676$	−5.82379e6	−0.490161
$677$	−9.12025e6	−0.764777	−0.382389	−	0.924002i	$-0.624898\pi$
$677$	−9.12025e6	−0.764777	−0.382389	+	0.924002i	$0.624898\pi$
$678$	4.73790e6	0.395832
$679$	0	0
$680$	−9586.03	−0.000794999 0
$681$	−1.60629e6	−0.132726
$682$	−129732.	−0.0106804
$683$	−1.45152e7	−1.19062	−0.595309	−	0.803497i	$-0.702970\pi$
$683$	−1.45152e7	−1.19062	−0.595309	+	0.803497i	$0.702970\pi$
$684$	−823448.	−0.0672971
$685$	227530.	0.0185273
$686$	0	0
$687$	4.13778e6	0.334484
$688$	2.84166e6	0.228876
$689$	−1.17094e6	−0.0939691
$690$	−442091.	−0.0353500
$691$	−2.08507e6	−0.166122	−0.0830608	−	0.996544i	$-0.526470\pi$
$691$	−2.08507e6	−0.166122	−0.0830608	+	0.996544i	$0.526470\pi$
$692$	2.05212e6	0.162906
$693$	0	0
$694$	5.73945e6	0.452347
$695$	1.00761e6	0.0791278
$696$	3.37564e6	0.264139
$697$	27258.8	0.00212532
$698$	1.33884e7	1.04014
$699$	−6.73801e6	−0.521601
$700$	0	0
$701$	9.96513e6	0.765928	0.382964	−	0.923763i	$-0.374903\pi$
$701$	9.96513e6	0.765928	0.382964	+	0.923763i	$0.374903\pi$
$702$	249252.	0.0190895
$703$	−1.93059e6	−0.147333
$704$	−475918.	−0.0361910
$705$	300168.	0.0227453
$706$	1.60167e7	1.20938
$707$	0	0
$708$	3.22210e6	0.241577
$709$	7.09035e6	0.529727	0.264864	−	0.964286i	$-0.414673\pi$
$709$	7.09035e6	0.529727	0.264864	+	0.964286i	$0.414673\pi$
$710$	1.08475e6	0.0807579
$711$	−2.72127e6	−0.201882
$712$	5.90017e6	0.436179
$713$	−761324.	−0.0560849
$714$	0	0
$715$	44717.6	0.00327125
$716$	−1.57759e6	−0.115004
$717$	7.33277e6	0.532685
$718$	2.38394e6	0.172578
$719$	−1.20167e7	−0.866886	−0.433443	−	0.901181i	$-0.642701\pi$
$719$	−1.20167e7	−0.866886	−0.433443	+	0.901181i	$0.642701\pi$
$720$	−93364.4	−0.00671197
$721$	0	0
$722$	8.28958e6	0.591820
$723$	−9.42869e6	−0.670820
$724$	−9.58760e6	−0.679772
$725$	−1.81952e7	−1.28562
$726$	−5.31182e6	−0.374026
$727$	−1.32577e7	−0.930318	−0.465159	−	0.885227i	$-0.654003\pi$
$727$	−1.32577e7	−0.930318	−0.465159	+	0.885227i	$0.654003\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	−1.38603e6	−0.0962642
$731$	−369262.	−0.0255588
$732$	−1.82766e6	−0.126072
$733$	909303.	0.0625099	0.0312549	−	0.999511i	$-0.490050\pi$
$733$	909303.	0.0625099	0.0312549	+	0.999511i	$0.490050\pi$
$734$	−1.32156e7	−0.905413
$735$	0	0
$736$	−2.79289e6	−0.190046
$737$	6.07717e6	0.412129
$738$	265490.	0.0179435
$739$	−286851.	−0.0193217	−0.00966086	−	0.999953i	$-0.503075\pi$
$739$	−286851.	−0.0193217	−0.00966086	+	0.999953i	$0.503075\pi$
$740$	−218894.	−0.0146945
$741$	488792.	0.0327024
$742$	0	0
$743$	−1.35906e6	−0.0903163	−0.0451582	−	0.998980i	$-0.514379\pi$
$743$	−1.35906e6	−0.0903163	−0.0451582	+	0.998980i	$0.514379\pi$
$744$	−160783.	−0.0106489
$745$	−1.16850e6	−0.0771327
$746$	1.13225e7	0.744897
$747$	−4.90657e6	−0.321719
$748$	61843.6	0.00404148
$749$	0	0
$750$	1.00978e6	0.0655503
$751$	1.54404e7	0.998982	0.499491	−	0.866319i	$-0.333520\pi$
$751$	1.54404e7	0.998982	0.499491	+	0.866319i	$0.333520\pi$
$752$	1.89629e6	0.122282
$753$	−9.84610e6	−0.632815
$754$	−2.00375e6	−0.128356
$755$	499298.	0.0318781
$756$	0	0
$757$	1.70683e7	1.08256	0.541279	−	0.840843i	$-0.317940\pi$
$757$	1.70683e7	1.08256	0.541279	+	0.840843i	$0.317940\pi$
$758$	−9.80100e6	−0.619580
$759$	2.85212e6	0.179706
$760$	−183091.	−0.0114983
$761$	−3.08345e6	−0.193008	−0.0965041	−	0.995333i	$-0.530766\pi$
$761$	−3.08345e6	−0.193008	−0.0965041	+	0.995333i	$0.530766\pi$
$762$	519742.	0.0324265
$763$	0	0
$764$	1.32675e7	0.822346
$765$	12132.3	0.000749532 0
$766$	−1.35362e7	−0.833537
$767$	−1.91261e6	−0.117392
$768$	−589824.	−0.0360844
$769$	−3.00821e7	−1.83439	−0.917195	−	0.398439i	$-0.869552\pi$
$769$	−3.00821e7	−1.83439	−0.917195	+	0.398439i	$0.869552\pi$
$770$	0	0
$771$	−7.00552e6	−0.424428
$772$	−6.66216e6	−0.402320
$773$	−2.16914e7	−1.30569	−0.652843	−	0.757494i	$-0.726424\pi$
$773$	−2.16914e7	−1.30569	−0.652843	+	0.757494i	$0.726424\pi$
$774$	−3.59647e6	−0.215786
$775$	866642.	0.0518305
$776$	9.74635e6	0.581016
$777$	0	0
$778$	1.65984e7	0.983146
$779$	520637.	0.0307391
$780$	55420.4	0.00326162
$781$	−6.99821e6	−0.410544
$782$	362924.	0.0212226
$783$	−4.27229e6	−0.249033
$784$	0	0
$785$	−1.82526e6	−0.105718
$786$	−1.14918e7	−0.663485
$787$	−1.21019e6	−0.0696490	−0.0348245	−	0.999393i	$-0.511087\pi$
$787$	−1.21019e6	−0.0696490	−0.0348245	+	0.999393i	$0.511087\pi$
$788$	−9.47297e6	−0.543464
$789$	−9.98786e6	−0.571189
$790$	−605067.	−0.0344934
$791$	0	0
$792$	602334.	0.0341212
$793$	1.08489e6	0.0612633
$794$	−6.58664e6	−0.370777
$795$	−555113.	−0.0311504
$796$	1.70573e7	0.954173
$797$	−2.44457e7	−1.36319	−0.681596	−	0.731728i	$-0.738714\pi$
$797$	−2.44457e7	−1.36319	−0.681596	+	0.731728i	$0.738714\pi$
$798$	0	0
$799$	−246416.	−0.0136553
$800$	3.17924e6	0.175630
$801$	−7.46740e6	−0.411233
$802$	1.75466e7	0.963288
$803$	8.94186e6	0.489372
$804$	7.53168e6	0.410915
$805$	0	0
$806$	95439.3	0.00517475
$807$	1.20276e7	0.650124
$808$	6.88923e6	0.371229
$809$	−1.18645e7	−0.637352	−0.318676	−	0.947864i	$-0.603238\pi$
$809$	−1.18645e7	−0.637352	−0.318676	+	0.947864i	$0.603238\pi$
$810$	118164.	0.00632810
$811$	1.63289e7	0.871778	0.435889	−	0.900000i	$-0.356434\pi$
$811$	1.63289e7	0.871778	0.435889	+	0.900000i	$0.356434\pi$
$812$	0	0
$813$	1.61281e7	0.855769
$814$	1.41218e6	0.0747015
$815$	−173882.	−0.00916979
$816$	76645.2	0.00402958
$817$	−7.05282e6	−0.369664
$818$	1.41837e6	0.0741150
$819$	0	0
$820$	59031.0	0.00306581
$821$	−2.20202e7	−1.14015	−0.570077	−	0.821591i	$-0.693087\pi$
$821$	−2.20202e7	−1.14015	−0.570077	+	0.821591i	$0.693087\pi$
$822$	−1.81922e6	−0.0939088
$823$	9.43220e6	0.485415	0.242708	−	0.970099i	$-0.421964\pi$
$823$	9.43220e6	0.485415	0.242708	+	0.970099i	$0.421964\pi$
$824$	7.72091e6	0.396142
$825$	−3.24667e6	−0.166075
$826$	0	0
$827$	−1.93147e7	−0.982027	−0.491014	−	0.871152i	$-0.663374\pi$
$827$	−1.93147e7	−0.982027	−0.491014	+	0.871152i	$0.663374\pi$
$828$	3.53475e6	0.179177
$829$	−3.26260e7	−1.64883	−0.824417	−	0.565982i	$-0.808497\pi$
$829$	−3.26260e7	−1.64883	−0.824417	+	0.565982i	$0.808497\pi$
$830$	−1.09096e6	−0.0549685
$831$	−518198.	−0.0260311
$832$	350115.	0.0175349
$833$	0	0
$834$	−8.05634e6	−0.401072
$835$	−933170.	−0.0463174
$836$	1.18120e6	0.0584531
$837$	203490.	0.0100399
$838$	−7.19210e6	−0.353790
$839$	−2.39890e7	−1.17654	−0.588272	−	0.808663i	$-0.700191\pi$
$839$	−2.39890e7	−1.17654	−0.588272	+	0.808663i	$0.700191\pi$
$840$	0	0
$841$	1.38341e7	0.674467
$842$	−2.44352e7	−1.18778
$843$	4.95231e6	0.240015
$844$	−1.35365e7	−0.654108
$845$	1.63886e6	0.0789587
$846$	−2.40000e6	−0.115288
$847$	0	0
$848$	−3.50689e6	−0.167468
$849$	−1.06009e7	−0.504748
$850$	−413129.	−0.0196128
$851$	8.28726e6	0.392272
$852$	−8.67316e6	−0.409334
$853$	−1.36214e7	−0.640988	−0.320494	−	0.947251i	$-0.603849\pi$
$853$	−1.36214e7	−0.640988	−0.320494	+	0.947251i	$0.603849\pi$
$854$	0	0
$855$	231725.	0.0108407
$856$	−5.51132e6	−0.257082
$857$	−3.97793e7	−1.85014	−0.925071	−	0.379793i	$-0.875995\pi$
$857$	−3.97793e7	−1.85014	−0.925071	+	0.379793i	$0.875995\pi$
$858$	−357541.	−0.0165809
$859$	−1.88973e7	−0.873807	−0.436904	−	0.899508i	$-0.643925\pi$
$859$	−1.88973e7	−0.873807	−0.436904	+	0.899508i	$0.643925\pi$
$860$	−799664.	−0.0368690
$861$	0	0
$862$	7.64704e6	0.350530
$863$	−1.81214e7	−0.828256	−0.414128	−	0.910219i	$-0.635913\pi$
$863$	−1.81214e7	−0.828256	−0.414128	+	0.910219i	$0.635913\pi$
$864$	746496.	0.0340207
$865$	−577482.	−0.0262421
$866$	1.54212e6	0.0698753
$867$	1.27688e7	0.576900
$868$	0	0
$869$	3.90355e6	0.175352
$870$	−949931.	−0.0425494
$871$	−4.47075e6	−0.199680
$872$	4.23291e6	0.188516
$873$	−1.23352e7	−0.547787
$874$	6.93178e6	0.306949
$875$	0	0
$876$	1.10820e7	0.487931
$877$	−2.38248e7	−1.04600	−0.522999	−	0.852333i	$-0.675187\pi$
$877$	−2.38248e7	−1.04600	−0.522999	+	0.852333i	$0.675187\pi$
$878$	−7.33528e6	−0.321129
$879$	2.70686e6	0.118166
$880$	133927.	0.00582991
$881$	6.59299e6	0.286182	0.143091	−	0.989710i	$-0.454296\pi$
$881$	6.59299e6	0.286182	0.143091	+	0.989710i	$0.454296\pi$
$882$	0	0
$883$	1.13391e7	0.489413	0.244707	−	0.969597i	$-0.421308\pi$
$883$	1.13391e7	0.489413	0.244707	+	0.969597i	$0.421308\pi$
$884$	−45496.0	−0.00195814
$885$	−906724.	−0.0389150
$886$	7.73568e6	0.331066
$887$	1.16981e7	0.499237	0.249619	−	0.968344i	$-0.419695\pi$
$887$	1.16981e7	0.499237	0.249619	+	0.968344i	$0.419695\pi$
$888$	1.75017e6	0.0744814
$889$	0	0
$890$	−1.66035e6	−0.0702628
$891$	−762329.	−0.0321698
$892$	−1.79679e6	−0.0756109
$893$	−4.70649e6	−0.197501
$894$	9.34276e6	0.390959
$895$	443947.	0.0185256
$896$	0	0
$897$	−2.09820e6	−0.0870693
$898$	−2.70542e7	−1.11955
$899$	−1.63587e6	−0.0675073
$900$	−4.02373e6	−0.165585
$901$	455706.	0.0187014
$902$	−380834.	−0.0155855
$903$	0	0
$904$	−8.42293e6	−0.342801
$905$	2.69803e6	0.109503
$906$	−3.99214e6	−0.161579
$907$	2.74600e6	0.110837	0.0554183	−	0.998463i	$-0.482351\pi$
$907$	2.74600e6	0.110837	0.0554183	+	0.998463i	$0.482351\pi$
$908$	2.85563e6	0.114944
$909$	−8.71918e6	−0.349998
$910$	0	0
$911$	−8.70382e6	−0.347467	−0.173734	−	0.984793i	$-0.555583\pi$
$911$	−8.70382e6	−0.347467	−0.173734	+	0.984793i	$0.555583\pi$
$912$	1.46391e6	0.0582810
$913$	7.03826e6	0.279440
$914$	9.57967e6	0.379302
$915$	514318.	0.0203086
$916$	−7.35606e6	−0.289672
$917$	0	0
$918$	−97004.1	−0.00379912
$919$	3.65884e7	1.42907	0.714536	−	0.699598i	$-0.246638\pi$
$919$	3.65884e7	1.42907	0.714536	+	0.699598i	$0.246638\pi$
$920$	785940.	0.0306140
$921$	1.32108e6	0.0513192
$922$	−2.57180e7	−0.996344
$923$	5.14832e6	0.198912
$924$	0	0
$925$	−9.43369e6	−0.362516
$926$	−5.46097e6	−0.209287
$927$	−9.77177e6	−0.373486
$928$	−6.00113e6	−0.228751
$929$	3.19411e6	0.121426	0.0607128	−	0.998155i	$-0.480663\pi$
$929$	3.19411e6	0.121426	0.0607128	+	0.998155i	$0.480663\pi$
$930$	45245.5	0.00171541
$931$	0	0
$932$	1.19787e7	0.451720
$933$	1.53280e7	0.576475
$934$	1.74545e7	0.654696
$935$	−17403.3	−0.000651031 0
$936$	−443114.	−0.0165320
$937$	−1.53039e7	−0.569447	−0.284724	−	0.958610i	$-0.591902\pi$
$937$	−1.53039e7	−0.569447	−0.284724	+	0.958610i	$0.591902\pi$
$938$	0	0
$939$	1.00525e7	0.372058
$940$	−533632.	−0.0196980
$941$	−1.23623e7	−0.455121	−0.227560	−	0.973764i	$-0.573075\pi$
$941$	−1.23623e7	−0.455121	−0.227560	+	0.973764i	$0.573075\pi$
$942$	1.45939e7	0.535850
$943$	−2.23489e6	−0.0818423
$944$	−5.72818e6	−0.209212
$945$	0	0
$946$	5.15898e6	0.187429
$947$	5.83773e6	0.211528	0.105764	−	0.994391i	$-0.466271\pi$
$947$	5.83773e6	0.211528	0.105764	+	0.994391i	$0.466271\pi$
$948$	4.83782e6	0.174835
$949$	−6.57819e6	−0.237105
$950$	−7.89069e6	−0.283665
$951$	8.66605e6	0.310720
$952$	0	0
$953$	1.59935e7	0.570443	0.285222	−	0.958462i	$-0.407933\pi$
$953$	1.59935e7	0.570443	0.285222	+	0.958462i	$0.407933\pi$
$954$	4.43841e6	0.157891
$955$	−3.73357e6	−0.132469
$956$	−1.30360e7	−0.461319
$957$	6.12841e6	0.216306
$958$	−5.56998e6	−0.196083
$959$	0	0
$960$	165981.	0.00581274
$961$	−2.85512e7	−0.997278
$962$	−1.03889e6	−0.0361935
$963$	6.97526e6	0.242379
$964$	1.67621e7	0.580947
$965$	1.87478e6	0.0648087
$966$	0	0
$967$	−4.65279e6	−0.160010	−0.0800050	−	0.996794i	$-0.525494\pi$
$967$	−4.65279e6	−0.160010	−0.0800050	+	0.996794i	$0.525494\pi$
$968$	9.44324e6	0.323916
$969$	−190229.	−0.00650829
$970$	−2.74270e6	−0.0935942
$971$	−2.17271e7	−0.739528	−0.369764	−	0.929126i	$-0.620561\pi$
$971$	−2.17271e7	−0.739528	−0.369764	+	0.929126i	$0.620561\pi$
$972$	−944784.	−0.0320750
$973$	0	0
$974$	−3.93168e7	−1.32795
$975$	2.38845e6	0.0804646
$976$	3.24917e6	0.109181
$977$	2.27382e7	0.762113	0.381056	−	0.924552i	$-0.375560\pi$
$977$	2.27382e7	0.762113	0.381056	+	0.924552i	$0.375560\pi$
$978$	1.39027e6	0.0464786
$979$	1.07117e7	0.357190
$980$	0	0
$981$	−5.35728e6	−0.177734
$982$	3.06902e7	1.01560
$983$	4.40870e7	1.45521	0.727607	−	0.685994i	$-0.240632\pi$
$983$	4.40870e7	1.45521	0.727607	+	0.685994i	$0.240632\pi$
$984$	−471983.	−0.0155396
$985$	2.66577e6	0.0875451
$986$	779823.	0.0255449
$987$	0	0
$988$	−868964.	−0.0283211
$989$	3.02750e7	0.984224
$990$	−169501.	−0.00549649
$991$	2.80292e7	0.906623	0.453312	−	0.891352i	$-0.350242\pi$
$991$	2.80292e7	0.906623	0.453312	+	0.891352i	$0.350242\pi$
$992$	285836.	0.00922226
$993$	2.03396e7	0.654589
$994$	0	0
$995$	−4.80005e6	−0.153705
$996$	8.72279e6	0.278617
$997$	4.46315e7	1.42201	0.711006	−	0.703186i	$-0.248240\pi$
$997$	4.46315e7	1.42201	0.711006	+	0.703186i	$0.248240\pi$
$998$	−1.35753e7	−0.431443
$999$	−2.21506e6	−0.0702218

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.6.a.n.1.2	✓	2
3.2	odd	2		882.6.a.bu.1.1		2
7.2	even	3		294.6.e.z.67.1		4
7.3	odd	6		294.6.e.x.79.2		4
7.4	even	3		294.6.e.z.79.1		4
7.5	odd	6		294.6.e.x.67.2		4
7.6	odd	2		294.6.a.q.1.1	yes	2
21.20	even	2		882.6.a.bk.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.6.a.n.1.2	✓	2	1.1	even	1	trivial
294.6.a.q.1.1	yes	2	7.6	odd	2
294.6.e.x.67.2		4	7.5	odd	6
294.6.e.x.79.2		4	7.3	odd	6
294.6.e.z.67.1		4	7.2	even	3
294.6.e.z.79.1		4	7.4	even	3
882.6.a.bk.1.2		2	21.20	even	2
882.6.a.bu.1.1		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	294.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -4.50253 q^{5} +36.0000 q^{6} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -4.50253 q^{5} +36.0000 q^{6} -64.0000 q^{8} +81.0000 q^{9} +18.0101 q^{10} -116.191 q^{11} -144.000 q^{12} +85.4773 q^{13} +40.5227 q^{15} +256.000 q^{16} -33.2662 q^{17} -324.000 q^{18} -635.377 q^{19} -72.0404 q^{20} +464.764 q^{22} +2727.43 q^{23} +576.000 q^{24} -3104.73 q^{25} -341.909 q^{26} -729.000 q^{27} +5860.48 q^{29} -162.091 q^{30} -279.136 q^{31} -1024.00 q^{32} +1045.72 q^{33} +133.065 q^{34} +1296.00 q^{36} +3038.49 q^{37} +2541.51 q^{38} -769.295 q^{39} +288.162 q^{40} -819.415 q^{41} +11100.2 q^{43} -1859.05 q^{44} -364.705 q^{45} -10909.7 q^{46} +7407.40 q^{47} -2304.00 q^{48} +12418.9 q^{50} +299.395 q^{51} +1367.64 q^{52} -13698.8 q^{53} +2916.00 q^{54} +523.153 q^{55} +5718.39 q^{57} -23441.9 q^{58} -22375.7 q^{59} +648.364 q^{60} +12692.1 q^{61} +1116.55 q^{62} +4096.00 q^{64} -384.864 q^{65} -4182.87 q^{66} -52303.3 q^{67} -532.259 q^{68} -24546.8 q^{69} +60230.2 q^{71} -5184.00 q^{72} -76958.4 q^{73} -12154.0 q^{74} +27942.5 q^{75} -10166.0 q^{76} +3077.18 q^{78} -33596.0 q^{79} -1152.65 q^{80} +6561.00 q^{81} +3277.66 q^{82} -60574.9 q^{83} +149.782 q^{85} -44400.9 q^{86} -52744.3 q^{87} +7436.22 q^{88} -92190.1 q^{89} +1458.82 q^{90} +43638.8 q^{92} +2512.23 q^{93} -29629.6 q^{94} +2860.80 q^{95} +9216.00 q^{96} -152287. q^{97} -9411.46 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{2} - 18 q^{3} + 32 q^{4} - 108 q^{5} + 72 q^{6} - 128 q^{8} + 162 q^{9}+O(q^{10}) \) 2 * q - 8 * q^2 - 18 * q^3 + 32 * q^4 - 108 * q^5 + 72 * q^6 - 128 * q^8 + 162 * q^9	\( 2 q - 8 q^{2} - 18 q^{3} + 32 q^{4} - 108 q^{5} + 72 q^{6} - 128 q^{8} + 162 q^{9} + 432 q^{10} + 124 q^{11} - 288 q^{12} - 720 q^{13} + 972 q^{15} + 512 q^{16} + 1260 q^{17} - 648 q^{18} - 360 q^{19} - 1728 q^{20} - 496 q^{22} + 6524 q^{23} + 1152 q^{24} + 4482 q^{25} + 2880 q^{26} - 1458 q^{27} + 7088 q^{29} - 3888 q^{30} - 5904 q^{31} - 2048 q^{32} - 1116 q^{33} - 5040 q^{34} + 2592 q^{36} - 6040 q^{37} + 1440 q^{38} + 6480 q^{39} + 6912 q^{40} + 17388 q^{41} - 608 q^{43} + 1984 q^{44} - 8748 q^{45} - 26096 q^{46} + 30456 q^{47} - 4608 q^{48} - 17928 q^{50} - 11340 q^{51} - 11520 q^{52} + 3964 q^{53} + 5832 q^{54} - 24336 q^{55} + 3240 q^{57} - 28352 q^{58} - 40752 q^{59} + 15552 q^{60} + 1368 q^{61} + 23616 q^{62} + 8192 q^{64} + 82980 q^{65} + 4464 q^{66} - 16224 q^{67} + 20160 q^{68} - 58716 q^{69} - 3204 q^{71} - 10368 q^{72} - 23976 q^{73} + 24160 q^{74} - 40338 q^{75} - 5760 q^{76} - 25920 q^{78} - 82160 q^{79} - 27648 q^{80} + 13122 q^{81} - 69552 q^{82} - 173736 q^{83} - 133700 q^{85} + 2432 q^{86} - 63792 q^{87} - 7936 q^{88} - 200556 q^{89} + 34992 q^{90} + 104384 q^{92} + 53136 q^{93} - 121824 q^{94} - 25640 q^{95} + 18432 q^{96} - 251928 q^{97} + 10044 q^{99}+O(q^{100}) \) 2 * q - 8 * q^2 - 18 * q^3 + 32 * q^4 - 108 * q^5 + 72 * q^6 - 128 * q^8 + 162 * q^9 + 432 * q^10 + 124 * q^11 - 288 * q^12 - 720 * q^13 + 972 * q^15 + 512 * q^16 + 1260 * q^17 - 648 * q^18 - 360 * q^19 - 1728 * q^20 - 496 * q^22 + 6524 * q^23 + 1152 * q^24 + 4482 * q^25 + 2880 * q^26 - 1458 * q^27 + 7088 * q^29 - 3888 * q^30 - 5904 * q^31 - 2048 * q^32 - 1116 * q^33 - 5040 * q^34 + 2592 * q^36 - 6040 * q^37 + 1440 * q^38 + 6480 * q^39 + 6912 * q^40 + 17388 * q^41 - 608 * q^43 + 1984 * q^44 - 8748 * q^45 - 26096 * q^46 + 30456 * q^47 - 4608 * q^48 - 17928 * q^50 - 11340 * q^51 - 11520 * q^52 + 3964 * q^53 + 5832 * q^54 - 24336 * q^55 + 3240 * q^57 - 28352 * q^58 - 40752 * q^59 + 15552 * q^60 + 1368 * q^61 + 23616 * q^62 + 8192 * q^64 + 82980 * q^65 + 4464 * q^66 - 16224 * q^67 + 20160 * q^68 - 58716 * q^69 - 3204 * q^71 - 10368 * q^72 - 23976 * q^73 + 24160 * q^74 - 40338 * q^75 - 5760 * q^76 - 25920 * q^78 - 82160 * q^79 - 27648 * q^80 + 13122 * q^81 - 69552 * q^82 - 173736 * q^83 - 133700 * q^85 + 2432 * q^86 - 63792 * q^87 - 7936 * q^88 - 200556 * q^89 + 34992 * q^90 + 104384 * q^92 + 53136 * q^93 - 121824 * q^94 - 25640 * q^95 + 18432 * q^96 - 251928 * q^97 + 10044 * q^99

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