LMFDB - Embedded newform 570.4.a.s.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,4,Mod(1,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("570.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	570.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:	$33.6310887033$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 410x^{2} + 4362x - 12540 $ x^4 - x^3 - 410x^2 + 4362x - 12540
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$12.2089$ of defining polynomial
Character	$\chi$	$=$	570.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +6.00000 q^{6} +17.1829 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +6.00000 q^{6} +17.1829 q^{7} +8.00000 q^{8} +9.00000 q^{9} +10.0000 q^{10} +29.2349 q^{11} +12.0000 q^{12} -69.9219 q^{13} +34.3658 q^{14} +15.0000 q^{15} +16.0000 q^{16} +94.5904 q^{17} +18.0000 q^{18} +19.0000 q^{19} +20.0000 q^{20} +51.5487 q^{21} +58.4699 q^{22} -8.21713 q^{23} +24.0000 q^{24} +25.0000 q^{25} -139.844 q^{26} +27.0000 q^{27} +68.7316 q^{28} +216.520 q^{29} +30.0000 q^{30} -227.097 q^{31} +32.0000 q^{32} +87.7048 q^{33} +189.181 q^{34} +85.9144 q^{35} +36.0000 q^{36} -5.48766 q^{37} +38.0000 q^{38} -209.766 q^{39} +40.0000 q^{40} -423.214 q^{41} +103.097 q^{42} +267.242 q^{43} +116.940 q^{44} +45.0000 q^{45} -16.4343 q^{46} -6.59371 q^{47} +48.0000 q^{48} -47.7483 q^{49} +50.0000 q^{50} +283.771 q^{51} -279.688 q^{52} -206.172 q^{53} +54.0000 q^{54} +146.175 q^{55} +137.463 q^{56} +57.0000 q^{57} +433.040 q^{58} +208.532 q^{59} +60.0000 q^{60} +510.064 q^{61} -454.195 q^{62} +154.646 q^{63} +64.0000 q^{64} -349.610 q^{65} +175.410 q^{66} +1010.47 q^{67} +378.362 q^{68} -24.6514 q^{69} +171.829 q^{70} +334.247 q^{71} +72.0000 q^{72} -866.693 q^{73} -10.9753 q^{74} +75.0000 q^{75} +76.0000 q^{76} +502.341 q^{77} -419.532 q^{78} +502.538 q^{79} +80.0000 q^{80} +81.0000 q^{81} -846.428 q^{82} -478.314 q^{83} +206.195 q^{84} +472.952 q^{85} +534.485 q^{86} +649.559 q^{87} +233.879 q^{88} -1150.25 q^{89} +90.0000 q^{90} -1201.46 q^{91} -32.8685 q^{92} -681.292 q^{93} -13.1874 q^{94} +95.0000 q^{95} +96.0000 q^{96} -1394.30 q^{97} -95.4967 q^{98} +263.114 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{2} + 12 q^{3} + 16 q^{4} + 20 q^{5} + 24 q^{6} + 36 q^{7} + 32 q^{8} + 36 q^{9}+O(q^{10}) $ 4 * q + 8 * q^2 + 12 * q^3 + 16 * q^4 + 20 * q^5 + 24 * q^6 + 36 * q^7 + 32 * q^8 + 36 * q^9	\( 4 q + 8 q^{2} + 12 q^{3} + 16 q^{4} + 20 q^{5} + 24 q^{6} + 36 q^{7} + 32 q^{8} + 36 q^{9} + 40 q^{10} + 54 q^{11} + 48 q^{12} + 46 q^{13} + 72 q^{14} + 60 q^{15} + 64 q^{16} + 14 q^{17} + 72 q^{18} + 76 q^{19} + 80 q^{20} + 108 q^{21} + 108 q^{22} + 104 q^{23} + 96 q^{24} + 100 q^{25} + 92 q^{26} + 108 q^{27} + 144 q^{28} + 14 q^{29} + 120 q^{30} + 30 q^{31} + 128 q^{32} + 162 q^{33} + 28 q^{34} + 180 q^{35} + 144 q^{36} + 30 q^{37} + 152 q^{38} + 138 q^{39} + 160 q^{40} - 36 q^{41} + 216 q^{42} + 102 q^{43} + 216 q^{44} + 180 q^{45} + 208 q^{46} + 408 q^{47} + 192 q^{48} + 480 q^{49} + 200 q^{50} + 42 q^{51} + 184 q^{52} - 176 q^{53} + 216 q^{54} + 270 q^{55} + 288 q^{56} + 228 q^{57} + 28 q^{58} + 66 q^{59} + 240 q^{60} + 60 q^{61} + 60 q^{62} + 324 q^{63} + 256 q^{64} + 230 q^{65} + 324 q^{66} - 152 q^{67} + 56 q^{68} + 312 q^{69} + 360 q^{70} + 172 q^{71} + 288 q^{72} + 284 q^{73} + 60 q^{74} + 300 q^{75} + 304 q^{76} - 300 q^{77} + 276 q^{78} + 554 q^{79} + 320 q^{80} + 324 q^{81} - 72 q^{82} - 394 q^{83} + 432 q^{84} + 70 q^{85} + 204 q^{86} + 42 q^{87} + 432 q^{88} - 60 q^{89} + 360 q^{90} + 32 q^{91} + 416 q^{92} + 90 q^{93} + 816 q^{94} + 380 q^{95} + 384 q^{96} - 922 q^{97} + 960 q^{98} + 486 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 + 12 * q^3 + 16 * q^4 + 20 * q^5 + 24 * q^6 + 36 * q^7 + 32 * q^8 + 36 * q^9 + 40 * q^10 + 54 * q^11 + 48 * q^12 + 46 * q^13 + 72 * q^14 + 60 * q^15 + 64 * q^16 + 14 * q^17 + 72 * q^18 + 76 * q^19 + 80 * q^20 + 108 * q^21 + 108 * q^22 + 104 * q^23 + 96 * q^24 + 100 * q^25 + 92 * q^26 + 108 * q^27 + 144 * q^28 + 14 * q^29 + 120 * q^30 + 30 * q^31 + 128 * q^32 + 162 * q^33 + 28 * q^34 + 180 * q^35 + 144 * q^36 + 30 * q^37 + 152 * q^38 + 138 * q^39 + 160 * q^40 - 36 * q^41 + 216 * q^42 + 102 * q^43 + 216 * q^44 + 180 * q^45 + 208 * q^46 + 408 * q^47 + 192 * q^48 + 480 * q^49 + 200 * q^50 + 42 * q^51 + 184 * q^52 - 176 * q^53 + 216 * q^54 + 270 * q^55 + 288 * q^56 + 228 * q^57 + 28 * q^58 + 66 * q^59 + 240 * q^60 + 60 * q^61 + 60 * q^62 + 324 * q^63 + 256 * q^64 + 230 * q^65 + 324 * q^66 - 152 * q^67 + 56 * q^68 + 312 * q^69 + 360 * q^70 + 172 * q^71 + 288 * q^72 + 284 * q^73 + 60 * q^74 + 300 * q^75 + 304 * q^76 - 300 * q^77 + 276 * q^78 + 554 * q^79 + 320 * q^80 + 324 * q^81 - 72 * q^82 - 394 * q^83 + 432 * q^84 + 70 * q^85 + 204 * q^86 + 42 * q^87 + 432 * q^88 - 60 * q^89 + 360 * q^90 + 32 * q^91 + 416 * q^92 + 90 * q^93 + 816 * q^94 + 380 * q^95 + 384 * q^96 - 922 * q^97 + 960 * q^98 + 486 * 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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.00000	0.500000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	6.00000	0.408248
$7$	17.1829	0.927789	0.463894	−	0.885891i	$-0.346452\pi$
$7$	17.1829	0.927789	0.463894	+	0.885891i	$0.346452\pi$
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	10.0000	0.316228
$11$	29.2349	0.801333	0.400666	−	0.916224i	$-0.368779\pi$
$11$	29.2349	0.801333	0.400666	+	0.916224i	$0.368779\pi$
$12$	12.0000	0.288675
$13$	−69.9219	−1.49176	−0.745879	−	0.666082i	$-0.767970\pi$
$13$	−69.9219	−1.49176	−0.745879	+	0.666082i	$0.767970\pi$
$14$	34.3658	0.656046
$15$	15.0000	0.258199
$16$	16.0000	0.250000
$17$	94.5904	1.34950	0.674751	−	0.738045i	$-0.264251\pi$
$17$	94.5904	1.34950	0.674751	+	0.738045i	$0.264251\pi$
$18$	18.0000	0.235702
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	20.0000	0.223607
$21$	51.5487	0.535659
$22$	58.4699	0.566628
$23$	−8.21713	−0.0744952	−0.0372476	−	0.999306i	$-0.511859\pi$
$23$	−8.21713	−0.0744952	−0.0372476	+	0.999306i	$0.511859\pi$
$24$	24.0000	0.204124
$25$	25.0000	0.200000
$26$	−139.844	−1.05483
$27$	27.0000	0.192450
$28$	68.7316	0.463894
$29$	216.520	1.38644	0.693219	−	0.720727i	$-0.256192\pi$
$29$	216.520	1.38644	0.693219	+	0.720727i	$0.256192\pi$
$30$	30.0000	0.182574
$31$	−227.097	−1.31574	−0.657869	−	0.753132i	$-0.728542\pi$
$31$	−227.097	−1.31574	−0.657869	+	0.753132i	$0.728542\pi$
$32$	32.0000	0.176777
$33$	87.7048	0.462650
$34$	189.181	0.954242
$35$	85.9144	0.414920
$36$	36.0000	0.166667
$37$	−5.48766	−0.0243828	−0.0121914	−	0.999926i	$-0.503881\pi$
$37$	−5.48766	−0.0243828	−0.0121914	+	0.999926i	$0.503881\pi$
$38$	38.0000	0.162221
$39$	−209.766	−0.861267
$40$	40.0000	0.158114
$41$	−423.214	−1.61207	−0.806035	−	0.591867i	$-0.798391\pi$
$41$	−423.214	−1.61207	−0.806035	+	0.591867i	$0.798391\pi$
$42$	103.097	0.378768
$43$	267.242	0.947769	0.473885	−	0.880587i	$-0.342851\pi$
$43$	267.242	0.947769	0.473885	+	0.880587i	$0.342851\pi$
$44$	116.940	0.400666
$45$	45.0000	0.149071
$46$	−16.4343	−0.0526761
$47$	−6.59371	−0.0204636	−0.0102318	−	0.999948i	$-0.503257\pi$
$47$	−6.59371	−0.0204636	−0.0102318	+	0.999948i	$0.503257\pi$
$48$	48.0000	0.144338
$49$	−47.7483	−0.139208
$50$	50.0000	0.141421
$51$	283.771	0.779136
$52$	−279.688	−0.745879
$53$	−206.172	−0.534338	−0.267169	−	0.963650i	$-0.586088\pi$
$53$	−206.172	−0.534338	−0.267169	+	0.963650i	$0.586088\pi$
$54$	54.0000	0.136083
$55$	146.175	0.358367
$56$	137.463	0.328023
$57$	57.0000	0.132453
$58$	433.040	0.980360
$59$	208.532	0.460146	0.230073	−	0.973173i	$-0.426104\pi$
$59$	208.532	0.460146	0.230073	+	0.973173i	$0.426104\pi$
$60$	60.0000	0.129099
$61$	510.064	1.07061	0.535303	−	0.844660i	$-0.320197\pi$
$61$	510.064	1.07061	0.535303	+	0.844660i	$0.320197\pi$
$62$	−454.195	−0.930367
$63$	154.646	0.309263
$64$	64.0000	0.125000
$65$	−349.610	−0.667134
$66$	175.410	0.327143
$67$	1010.47	1.84251	0.921257	−	0.388956i	$-0.127164\pi$
$67$	1010.47	1.84251	0.921257	+	0.388956i	$0.127164\pi$
$68$	378.362	0.674751
$69$	−24.6514	−0.0430098
$70$	171.829	0.293393
$71$	334.247	0.558701	0.279351	−	0.960189i	$-0.409881\pi$
$71$	334.247	0.558701	0.279351	+	0.960189i	$0.409881\pi$
$72$	72.0000	0.117851
$73$	−866.693	−1.38957	−0.694786	−	0.719217i	$-0.744501\pi$
$73$	−866.693	−1.38957	−0.694786	+	0.719217i	$0.744501\pi$
$74$	−10.9753	−0.0172413
$75$	75.0000	0.115470
$76$	76.0000	0.114708
$77$	502.341	0.743468
$78$	−419.532	−0.609008
$79$	502.538	0.715695	0.357848	−	0.933780i	$-0.383511\pi$
$79$	502.538	0.715695	0.357848	+	0.933780i	$0.383511\pi$
$80$	80.0000	0.111803
$81$	81.0000	0.111111
$82$	−846.428	−1.13991
$83$	−478.314	−0.632551	−0.316276	−	0.948667i	$-0.602432\pi$
$83$	−478.314	−0.632551	−0.316276	+	0.948667i	$0.602432\pi$
$84$	206.195	0.267830
$85$	472.952	0.603516
$86$	534.485	0.670174
$87$	649.559	0.800461
$88$	233.879	0.283314
$89$	−1150.25	−1.36996	−0.684978	−	0.728563i	$-0.740188\pi$
$89$	−1150.25	−1.36996	−0.684978	+	0.728563i	$0.740188\pi$
$90$	90.0000	0.105409
$91$	−1201.46	−1.38404
$92$	−32.8685	−0.0372476
$93$	−681.292	−0.759642
$94$	−13.1874	−0.0144700
$95$	95.0000	0.102598
$96$	96.0000	0.102062
$97$	−1394.30	−1.45948	−0.729742	−	0.683723i	$-0.760360\pi$
$97$	−1394.30	−1.45948	−0.729742	+	0.683723i	$0.760360\pi$
$98$	−95.4967	−0.0984349
$99$	263.114	0.267111
$100$	100.000	0.100000
$101$	1962.77	1.93369	0.966847	−	0.255357i	$-0.0821931\pi$
$101$	1962.77	1.93369	0.966847	+	0.255357i	$0.0821931\pi$
$102$	567.542	0.550932
$103$	1511.69	1.44612	0.723062	−	0.690783i	$-0.242734\pi$
$103$	1511.69	1.44612	0.723062	+	0.690783i	$0.242734\pi$
$104$	−559.375	−0.527416
$105$	257.743	0.239554
$106$	−412.344	−0.377834
$107$	−1034.13	−0.934332	−0.467166	−	0.884170i	$-0.654725\pi$
$107$	−1034.13	−0.934332	−0.467166	+	0.884170i	$0.654725\pi$
$108$	108.000	0.0962250
$109$	−489.446	−0.430096	−0.215048	−	0.976603i	$-0.568991\pi$
$109$	−489.446	−0.430096	−0.215048	+	0.976603i	$0.568991\pi$
$110$	292.349	0.253404
$111$	−16.4630	−0.0140774
$112$	274.926	0.231947
$113$	598.992	0.498659	0.249329	−	0.968419i	$-0.419790\pi$
$113$	598.992	0.498659	0.249329	+	0.968419i	$0.419790\pi$
$114$	114.000	0.0936586
$115$	−41.0857	−0.0333153
$116$	866.079	0.693219
$117$	−629.297	−0.497253
$118$	417.065	0.325372
$119$	1625.34	1.25205
$120$	120.000	0.0912871
$121$	−476.319	−0.357865
$122$	1020.13	0.757033
$123$	−1269.64	−0.930730
$124$	−908.389	−0.657869
$125$	125.000	0.0894427
$126$	309.292	0.218682
$127$	−1621.31	−1.13282	−0.566411	−	0.824123i	$-0.691668\pi$
$127$	−1621.31	−1.13282	−0.566411	+	0.824123i	$0.691668\pi$
$128$	128.000	0.0883883
$129$	801.727	0.547195
$130$	−699.219	−0.471735
$131$	−2133.74	−1.42309	−0.711547	−	0.702639i	$-0.752005\pi$
$131$	−2133.74	−1.42309	−0.711547	+	0.702639i	$0.752005\pi$
$132$	350.819	0.231325
$133$	326.475	0.212849
$134$	2020.94	1.30285
$135$	135.000	0.0860663
$136$	756.723	0.477121
$137$	822.308	0.512807	0.256403	−	0.966570i	$-0.417462\pi$
$137$	822.308	0.512807	0.256403	+	0.966570i	$0.417462\pi$
$138$	−49.3028	−0.0304126
$139$	423.232	0.258259	0.129130	−	0.991628i	$-0.458782\pi$
$139$	423.232	0.258259	0.129130	+	0.991628i	$0.458782\pi$
$140$	343.658	0.207460
$141$	−19.7811	−0.0118147
$142$	668.493	0.395061
$143$	−2044.16	−1.19539
$144$	144.000	0.0833333
$145$	1082.60	0.620034
$146$	−1733.39	−0.982576
$147$	−143.245	−0.0803718
$148$	−21.9506	−0.0121914
$149$	−1387.73	−0.763003	−0.381502	−	0.924368i	$-0.624593\pi$
$149$	−1387.73	−0.763003	−0.381502	+	0.924368i	$0.624593\pi$
$150$	150.000	0.0816497
$151$	1687.63	0.909518	0.454759	−	0.890614i	$-0.349725\pi$
$151$	1687.63	0.909518	0.454759	+	0.890614i	$0.349725\pi$
$152$	152.000	0.0811107
$153$	851.313	0.449834
$154$	1004.68	0.525711
$155$	−1135.49	−0.588416
$156$	−839.063	−0.430633
$157$	−1875.67	−0.953468	−0.476734	−	0.879048i	$-0.658179\pi$
$157$	−1875.67	−0.953468	−0.476734	+	0.879048i	$0.658179\pi$
$158$	1005.08	0.506073
$159$	−618.517	−0.308500
$160$	160.000	0.0790569
$161$	−141.194	−0.0691158
$162$	162.000	0.0785674
$163$	879.526	0.422637	0.211318	−	0.977417i	$-0.432224\pi$
$163$	879.526	0.422637	0.211318	+	0.977417i	$0.432224\pi$
$164$	−1692.86	−0.806035
$165$	438.524	0.206903
$166$	−956.627	−0.447281
$167$	−3292.23	−1.52551	−0.762756	−	0.646686i	$-0.776154\pi$
$167$	−3292.23	−1.52551	−0.762756	+	0.646686i	$0.776154\pi$
$168$	412.389	0.189384
$169$	2692.07	1.22534
$170$	945.904	0.426750
$171$	171.000	0.0764719
$172$	1068.97	0.473885
$173$	−1861.03	−0.817868	−0.408934	−	0.912564i	$-0.634099\pi$
$173$	−1861.03	−0.817868	−0.408934	+	0.912564i	$0.634099\pi$
$174$	1299.12	0.566011
$175$	429.572	0.185558
$176$	467.759	0.200333
$177$	625.597	0.265665
$178$	−2300.50	−0.968706
$179$	−2869.30	−1.19811	−0.599055	−	0.800708i	$-0.704457\pi$
$179$	−2869.30	−1.19811	−0.599055	+	0.800708i	$0.704457\pi$
$180$	180.000	0.0745356
$181$	−2402.69	−0.986689	−0.493344	−	0.869834i	$-0.664226\pi$
$181$	−2402.69	−0.986689	−0.493344	+	0.869834i	$0.664226\pi$
$182$	−2402.92	−0.978661
$183$	1530.19	0.618115
$184$	−65.7371	−0.0263380
$185$	−27.4383	−0.0109043
$186$	−1362.58	−0.537148
$187$	2765.34	1.08140
$188$	−26.3748	−0.0102318
$189$	463.938	0.178553
$190$	190.000	0.0725476
$191$	−746.471	−0.282789	−0.141395	−	0.989953i	$-0.545159\pi$
$191$	−746.471	−0.282789	−0.141395	+	0.989953i	$0.545159\pi$
$192$	192.000	0.0721688
$193$	646.067	0.240958	0.120479	−	0.992716i	$-0.461557\pi$
$193$	646.067	0.240958	0.120479	+	0.992716i	$0.461557\pi$
$194$	−2788.60	−1.03201
$195$	−1048.83	−0.385170
$196$	−190.993	−0.0696040
$197$	4906.46	1.77447	0.887236	−	0.461316i	$-0.152623\pi$
$197$	4906.46	1.77447	0.887236	+	0.461316i	$0.152623\pi$
$198$	526.229	0.188876
$199$	−1166.24	−0.415438	−0.207719	−	0.978189i	$-0.566604\pi$
$199$	−1166.24	−0.415438	−0.207719	+	0.978189i	$0.566604\pi$
$200$	200.000	0.0707107
$201$	3031.41	1.06378
$202$	3925.54	1.36733
$203$	3720.44	1.28632
$204$	1135.08	0.389568
$205$	−2116.07	−0.720940
$206$	3023.37	1.02256
$207$	−73.9542	−0.0248317
$208$	−1118.75	−0.372939
$209$	555.464	0.183838
$210$	515.487	0.169390
$211$	−5519.45	−1.80083	−0.900414	−	0.435035i	$-0.856736\pi$
$211$	−5519.45	−1.80083	−0.900414	+	0.435035i	$0.856736\pi$
$212$	−824.689	−0.267169
$213$	1002.74	0.322566
$214$	−2068.27	−0.660672
$215$	1336.21	0.423855
$216$	216.000	0.0680414
$217$	−3902.19	−1.22073
$218$	−978.893	−0.304124
$219$	−2600.08	−0.802270
$220$	584.699	0.179184
$221$	−6613.94	−2.01313
$222$	−32.9259	−0.00995425
$223$	1393.07	0.418326	0.209163	−	0.977881i	$-0.432926\pi$
$223$	1393.07	0.418326	0.209163	+	0.977881i	$0.432926\pi$
$224$	549.852	0.164011
$225$	225.000	0.0666667
$226$	1197.98	0.352605
$227$	−4179.18	−1.22195	−0.610974	−	0.791651i	$-0.709222\pi$
$227$	−4179.18	−1.22195	−0.610974	+	0.791651i	$0.709222\pi$
$228$	228.000	0.0662266
$229$	2796.83	0.807074	0.403537	−	0.914963i	$-0.367781\pi$
$229$	2796.83	0.807074	0.403537	+	0.914963i	$0.367781\pi$
$230$	−82.1713	−0.0235575
$231$	1507.02	0.429241
$232$	1732.16	0.490180
$233$	−4967.60	−1.39673	−0.698365	−	0.715742i	$-0.746089\pi$
$233$	−4967.60	−1.39673	−0.698365	+	0.715742i	$0.746089\pi$
$234$	−1258.59	−0.351611
$235$	−32.9685	−0.00915162
$236$	834.129	0.230073
$237$	1507.61	0.413207
$238$	3250.67	0.885335
$239$	4698.63	1.27167	0.635835	−	0.771825i	$-0.280656\pi$
$239$	4698.63	1.27167	0.635835	+	0.771825i	$0.280656\pi$
$240$	240.000	0.0645497
$241$	−67.0326	−0.0179168	−0.00895840	−	0.999960i	$-0.502852\pi$
$241$	−67.0326	−0.0179168	−0.00895840	+	0.999960i	$0.502852\pi$
$242$	−952.638	−0.253049
$243$	243.000	0.0641500
$244$	2040.26	0.535303
$245$	−238.742	−0.0622557
$246$	−2539.28	−0.658125
$247$	−1328.52	−0.342233
$248$	−1816.78	−0.465184
$249$	−1434.94	−0.365204
$250$	250.000	0.0632456
$251$	−5378.10	−1.35244	−0.676221	−	0.736699i	$-0.736384\pi$
$251$	−5378.10	−1.35244	−0.676221	+	0.736699i	$0.736384\pi$
$252$	618.584	0.154631
$253$	−240.227	−0.0596955
$254$	−3242.63	−0.801026
$255$	1418.86	0.348440
$256$	256.000	0.0625000
$257$	−2751.52	−0.667840	−0.333920	−	0.942601i	$-0.608372\pi$
$257$	−2751.52	−0.667840	−0.333920	+	0.942601i	$0.608372\pi$
$258$	1603.45	0.386925
$259$	−94.2938	−0.0226221
$260$	−1398.44	−0.333567
$261$	1948.68	0.462146
$262$	−4267.47	−1.00628
$263$	−1557.63	−0.365201	−0.182600	−	0.983187i	$-0.558451\pi$
$263$	−1557.63	−0.365201	−0.182600	+	0.983187i	$0.558451\pi$
$264$	701.638	0.163571
$265$	−1030.86	−0.238963
$266$	652.950	0.150507
$267$	−3450.75	−0.790945
$268$	4041.87	0.921257
$269$	−1660.54	−0.376375	−0.188187	−	0.982133i	$-0.560261\pi$
$269$	−1660.54	−0.376375	−0.188187	+	0.982133i	$0.560261\pi$
$270$	270.000	0.0608581
$271$	1880.00	0.421409	0.210704	−	0.977550i	$-0.432424\pi$
$271$	1880.00	0.421409	0.210704	+	0.977550i	$0.432424\pi$
$272$	1513.45	0.337376
$273$	−3604.38	−0.799074
$274$	1644.62	0.362609
$275$	730.873	0.160267
$276$	−98.6056	−0.0215049
$277$	−8624.73	−1.87079	−0.935397	−	0.353599i	$-0.884958\pi$
$277$	−8624.73	−1.87079	−0.935397	+	0.353599i	$0.884958\pi$
$278$	846.464	0.182617
$279$	−2043.88	−0.438579
$280$	687.316	0.146696
$281$	−928.020	−0.197014	−0.0985071	−	0.995136i	$-0.531407\pi$
$281$	−928.020	−0.197014	−0.0985071	+	0.995136i	$0.531407\pi$
$282$	−39.5623	−0.00835425
$283$	−2306.23	−0.484420	−0.242210	−	0.970224i	$-0.577872\pi$
$283$	−2306.23	−0.484420	−0.242210	+	0.970224i	$0.577872\pi$
$284$	1336.99	0.279351
$285$	285.000	0.0592349
$286$	−4088.32	−0.845272
$287$	−7272.04	−1.49566
$288$	288.000	0.0589256
$289$	4034.34	0.821156
$290$	2165.20	0.438430
$291$	−4182.91	−0.842633
$292$	−3466.77	−0.694786
$293$	2760.03	0.550317	0.275158	−	0.961399i	$-0.411270\pi$
$293$	2760.03	0.550317	0.275158	+	0.961399i	$0.411270\pi$
$294$	−286.490	−0.0568314
$295$	1042.66	0.205783
$296$	−43.9012	−0.00862064
$297$	789.343	0.154217
$298$	−2775.46	−0.539525
$299$	574.558	0.111129
$300$	300.000	0.0577350
$301$	4592.00	0.879330
$302$	3375.26	0.643127
$303$	5888.31	1.11642
$304$	304.000	0.0573539
$305$	2550.32	0.478790
$306$	1702.63	0.318081
$307$	5771.80	1.07301	0.536505	−	0.843897i	$-0.319744\pi$
$307$	5771.80	1.07301	0.536505	+	0.843897i	$0.319744\pi$
$308$	2009.36	0.371734
$309$	4535.06	0.834920
$310$	−2270.97	−0.416073
$311$	−6175.04	−1.12590	−0.562949	−	0.826491i	$-0.690333\pi$
$311$	−6175.04	−1.12590	−0.562949	+	0.826491i	$0.690333\pi$
$312$	−1678.13	−0.304504
$313$	11040.3	1.99372	0.996862	−	0.0791558i	$-0.0252224\pi$
$313$	11040.3	1.99372	0.996862	+	0.0791558i	$0.0252224\pi$
$314$	−3751.33	−0.674203
$315$	773.230	0.138307
$316$	2010.15	0.357848
$317$	−1426.52	−0.252748	−0.126374	−	0.991983i	$-0.540334\pi$
$317$	−1426.52	−0.252748	−0.126374	+	0.991983i	$0.540334\pi$
$318$	−1237.03	−0.218143
$319$	6329.94	1.11100
$320$	320.000	0.0559017
$321$	−3102.40	−0.539437
$322$	−282.388	−0.0488723
$323$	1797.22	0.309597
$324$	324.000	0.0555556
$325$	−1748.05	−0.298352
$326$	1759.05	0.298849
$327$	−1468.34	−0.248316
$328$	−3385.71	−0.569953
$329$	−113.299	−0.0189859
$330$	877.048	0.146303
$331$	−900.393	−0.149517	−0.0747584	−	0.997202i	$-0.523819\pi$
$331$	−900.393	−0.149517	−0.0747584	+	0.997202i	$0.523819\pi$
$332$	−1913.25	−0.316276
$333$	−49.3889	−0.00812761
$334$	−6584.46	−1.07870
$335$	5052.34	0.823997
$336$	824.779	0.133915
$337$	7663.82	1.23880	0.619399	−	0.785076i	$-0.287376\pi$
$337$	7663.82	1.23880	0.619399	+	0.785076i	$0.287376\pi$
$338$	5384.15	0.866447
$339$	1796.98	0.287901
$340$	1891.81	0.301758
$341$	−6639.17	−1.05434
$342$	342.000	0.0540738
$343$	−6714.19	−1.05694
$344$	2137.94	0.335087
$345$	−123.257	−0.0192346
$346$	−3722.05	−0.578320
$347$	−10905.5	−1.68714	−0.843569	−	0.537021i	$-0.819549\pi$
$347$	−10905.5	−1.68714	−0.843569	+	0.537021i	$0.819549\pi$
$348$	2598.24	0.400230
$349$	−2473.62	−0.379397	−0.189699	−	0.981842i	$-0.560751\pi$
$349$	−2473.62	−0.379397	−0.189699	+	0.981842i	$0.560751\pi$
$350$	859.144	0.131209
$351$	−1887.89	−0.287089
$352$	935.518	0.141657
$353$	−4926.69	−0.742836	−0.371418	−	0.928466i	$-0.621128\pi$
$353$	−4926.69	−0.742836	−0.371418	+	0.928466i	$0.621128\pi$
$354$	1251.19	0.187854
$355$	1671.23	0.249859
$356$	−4601.00	−0.684978
$357$	4876.01	0.722873
$358$	−5738.61	−0.847192
$359$	7595.97	1.11671	0.558356	−	0.829601i	$-0.311432\pi$
$359$	7595.97	1.11671	0.558356	+	0.829601i	$0.311432\pi$
$360$	360.000	0.0527046
$361$	361.000	0.0526316
$362$	−4805.38	−0.697694
$363$	−1428.96	−0.206614
$364$	−4805.84	−0.692018
$365$	−4333.47	−0.621435
$366$	3060.38	0.437073
$367$	5177.70	0.736441	0.368221	−	0.929738i	$-0.379967\pi$
$367$	5177.70	0.736441	0.368221	+	0.929738i	$0.379967\pi$
$368$	−131.474	−0.0186238
$369$	−3808.92	−0.537357
$370$	−54.8766	−0.00771053
$371$	−3542.63	−0.495753
$372$	−2725.17	−0.379821
$373$	4912.63	0.681947	0.340974	−	0.940073i	$-0.389243\pi$
$373$	4912.63	0.681947	0.340974	+	0.940073i	$0.389243\pi$
$374$	5530.69	0.764666
$375$	375.000	0.0516398
$376$	−52.7497	−0.00723499
$377$	−15139.5	−2.06823
$378$	927.876	0.126256
$379$	−6166.88	−0.835809	−0.417904	−	0.908491i	$-0.637235\pi$
$379$	−6166.88	−0.835809	−0.417904	+	0.908491i	$0.637235\pi$
$380$	380.000	0.0512989
$381$	−4863.94	−0.654035
$382$	−1492.94	−0.199962
$383$	−6827.55	−0.910891	−0.455446	−	0.890264i	$-0.650520\pi$
$383$	−6827.55	−0.910891	−0.455446	+	0.890264i	$0.650520\pi$
$384$	384.000	0.0510310
$385$	2511.70	0.332489
$386$	1292.13	0.170383
$387$	2405.18	0.315923
$388$	−5577.21	−0.729742
$389$	1891.05	0.246479	0.123239	−	0.992377i	$-0.460672\pi$
$389$	1891.05	0.246479	0.123239	+	0.992377i	$0.460672\pi$
$390$	−2097.66	−0.272356
$391$	−777.262	−0.100531
$392$	−381.987	−0.0492175
$393$	−6401.21	−0.821624
$394$	9812.92	1.25474
$395$	2512.69	0.320069
$396$	1052.46	0.133555
$397$	9658.62	1.22104	0.610519	−	0.792001i	$-0.290961\pi$
$397$	9658.62	1.22104	0.610519	+	0.792001i	$0.290961\pi$
$398$	−2332.47	−0.293759
$399$	979.425	0.122889
$400$	400.000	0.0500000
$401$	2062.75	0.256880	0.128440	−	0.991717i	$-0.459003\pi$
$401$	2062.75	0.256880	0.128440	+	0.991717i	$0.459003\pi$
$402$	6062.81	0.752203
$403$	15879.1	1.96276
$404$	7851.08	0.966847
$405$	405.000	0.0496904
$406$	7440.87	0.909567
$407$	−160.431	−0.0195388
$408$	2270.17	0.275466
$409$	−6421.95	−0.776394	−0.388197	−	0.921576i	$-0.626902\pi$
$409$	−6421.95	−0.776394	−0.388197	+	0.921576i	$0.626902\pi$
$410$	−4232.14	−0.509782
$411$	2466.92	0.296069
$412$	6046.74	0.723062
$413$	3583.19	0.426918
$414$	−147.908	−0.0175587
$415$	−2391.57	−0.282885
$416$	−2237.50	−0.263708
$417$	1269.70	0.149106
$418$	1110.93	0.129993
$419$	3671.43	0.428070	0.214035	−	0.976826i	$-0.431339\pi$
$419$	3671.43	0.428070	0.214035	+	0.976826i	$0.431339\pi$
$420$	1030.97	0.119777
$421$	−5940.10	−0.687655	−0.343827	−	0.939033i	$-0.611723\pi$
$421$	−5940.10	−0.687655	−0.343827	+	0.939033i	$0.611723\pi$
$422$	−11038.9	−1.27338
$423$	−59.3434	−0.00682122
$424$	−1649.38	−0.188917
$425$	2364.76	0.269900
$426$	2005.48	0.228089
$427$	8764.37	0.993297
$428$	−4136.53	−0.467166
$429$	−6132.49	−0.690161
$430$	2672.42	0.299711
$431$	−17677.0	−1.97557	−0.987785	−	0.155825i	$-0.950196\pi$
$431$	−17677.0	−1.97557	−0.987785	+	0.155825i	$0.950196\pi$
$432$	432.000	0.0481125
$433$	13703.0	1.52084	0.760421	−	0.649430i	$-0.224993\pi$
$433$	13703.0	1.52084	0.760421	+	0.649430i	$0.224993\pi$
$434$	−7804.38	−0.863184
$435$	3247.80	0.357977
$436$	−1957.79	−0.215048
$437$	−156.126	−0.0170904
$438$	−5200.16	−0.567290
$439$	−2745.97	−0.298538	−0.149269	−	0.988797i	$-0.547692\pi$
$439$	−2745.97	−0.298538	−0.149269	+	0.988797i	$0.547692\pi$
$440$	1169.40	0.126702
$441$	−429.735	−0.0464027
$442$	−13227.9	−1.42350
$443$	8941.76	0.958997	0.479499	−	0.877543i	$-0.340819\pi$
$443$	8941.76	0.958997	0.479499	+	0.877543i	$0.340819\pi$
$444$	−65.8519	−0.00703872
$445$	−5751.24	−0.612663
$446$	2786.14	0.295801
$447$	−4163.20	−0.440520
$448$	1099.70	0.115974
$449$	8770.30	0.921818	0.460909	−	0.887448i	$-0.347524\pi$
$449$	8770.30	0.921818	0.460909	+	0.887448i	$0.347524\pi$
$450$	450.000	0.0471405
$451$	−12372.6	−1.29181
$452$	2395.97	0.249329
$453$	5062.89	0.525111
$454$	−8358.36	−0.864047
$455$	−6007.30	−0.618960
$456$	456.000	0.0468293
$457$	14319.3	1.46571	0.732856	−	0.680384i	$-0.238187\pi$
$457$	14319.3	1.46571	0.732856	+	0.680384i	$0.238187\pi$
$458$	5593.67	0.570688
$459$	2553.94	0.259712
$460$	−164.343	−0.0166576
$461$	2579.44	0.260599	0.130300	−	0.991475i	$-0.458406\pi$
$461$	2579.44	0.260599	0.130300	+	0.991475i	$0.458406\pi$
$462$	3014.04	0.303519
$463$	19134.6	1.92065	0.960324	−	0.278888i	$-0.0899657\pi$
$463$	19134.6	1.92065	0.960324	+	0.278888i	$0.0899657\pi$
$464$	3464.32	0.346610
$465$	−3406.46	−0.339722
$466$	−9935.20	−0.987637
$467$	12280.1	1.21682	0.608409	−	0.793624i	$-0.291808\pi$
$467$	12280.1	1.21682	0.608409	+	0.793624i	$0.291808\pi$
$468$	−2517.19	−0.248626
$469$	17362.8	1.70946
$470$	−65.9371	−0.00647117
$471$	−5627.00	−0.550485
$472$	1668.26	0.162686
$473$	7812.81	0.759479
$474$	3015.23	0.292181
$475$	475.000	0.0458831
$476$	6501.34	0.626027
$477$	−1855.55	−0.178113
$478$	9397.26	0.899206
$479$	1427.43	0.136160	0.0680802	−	0.997680i	$-0.478313\pi$
$479$	1427.43	0.136160	0.0680802	+	0.997680i	$0.478313\pi$
$480$	480.000	0.0456435
$481$	383.707	0.0363733
$482$	−134.065	−0.0126691
$483$	−423.582	−0.0399041
$484$	−1905.28	−0.178933
$485$	−6971.51	−0.652701
$486$	486.000	0.0453609
$487$	14257.2	1.32660	0.663301	−	0.748353i	$-0.269155\pi$
$487$	14257.2	1.32660	0.663301	+	0.748353i	$0.269155\pi$
$488$	4080.51	0.378517
$489$	2638.58	0.244010
$490$	−477.483	−0.0440214
$491$	−17429.3	−1.60198	−0.800990	−	0.598678i	$-0.795693\pi$
$491$	−17429.3	−1.60198	−0.800990	+	0.598678i	$0.795693\pi$
$492$	−5078.57	−0.465365
$493$	20480.7	1.87100
$494$	−2657.03	−0.241995
$495$	1315.57	0.119456
$496$	−3633.56	−0.328935
$497$	5743.32	0.518357
$498$	−2869.88	−0.258238
$499$	−6280.73	−0.563455	−0.281728	−	0.959494i	$-0.590907\pi$
$499$	−6280.73	−0.563455	−0.281728	+	0.959494i	$0.590907\pi$
$500$	500.000	0.0447214
$501$	−9876.69	−0.880755
$502$	−10756.2	−0.956321
$503$	6433.48	0.570288	0.285144	−	0.958485i	$-0.407959\pi$
$503$	6433.48	0.570288	0.285144	+	0.958485i	$0.407959\pi$
$504$	1237.17	0.109341
$505$	9813.86	0.864774
$506$	−480.455	−0.0422111
$507$	8076.22	0.707451
$508$	−6485.26	−0.566411
$509$	18989.4	1.65362	0.826808	−	0.562485i	$-0.190155\pi$
$509$	18989.4	1.65362	0.826808	+	0.562485i	$0.190155\pi$
$510$	2837.71	0.246384
$511$	−14892.3	−1.28923
$512$	512.000	0.0441942
$513$	513.000	0.0441511
$514$	−5503.03	−0.472234
$515$	7558.43	0.646726
$516$	3206.91	0.273597
$517$	−192.767	−0.0163982
$518$	−188.588	−0.0159963
$519$	−5583.08	−0.472197
$520$	−2796.88	−0.235868
$521$	7232.61	0.608189	0.304094	−	0.952642i	$-0.401646\pi$
$521$	7232.61	0.608189	0.304094	+	0.952642i	$0.401646\pi$
$522$	3897.36	0.326787
$523$	7864.04	0.657496	0.328748	−	0.944418i	$-0.393373\pi$
$523$	7864.04	0.657496	0.328748	+	0.944418i	$0.393373\pi$
$524$	−8534.94	−0.711547
$525$	1288.72	0.107132
$526$	−3115.27	−0.258236
$527$	−21481.2	−1.77559
$528$	1403.28	0.115662
$529$	−12099.5	−0.994450
$530$	−2061.72	−0.168973
$531$	1876.79	0.153382
$532$	1305.90	0.106425
$533$	29591.9	2.40482
$534$	−6901.49	−0.559282
$535$	−5170.67	−0.417846
$536$	8083.75	0.651427
$537$	−8607.91	−0.691729
$538$	−3321.08	−0.266137
$539$	−1395.92	−0.111552
$540$	540.000	0.0430331
$541$	19267.3	1.53117	0.765587	−	0.643332i	$-0.222449\pi$
$541$	19267.3	1.53117	0.765587	+	0.643332i	$0.222449\pi$
$542$	3760.00	0.297981
$543$	−7208.08	−0.569665
$544$	3026.89	0.238561
$545$	−2447.23	−0.192345
$546$	−7208.76	−0.565030
$547$	7054.21	0.551401	0.275700	−	0.961244i	$-0.411090\pi$
$547$	7054.21	0.551401	0.275700	+	0.961244i	$0.411090\pi$
$548$	3289.23	0.256403
$549$	4590.57	0.356869
$550$	1461.75	0.113326
$551$	4113.88	0.318071
$552$	−197.211	−0.0152063
$553$	8635.05	0.664014
$554$	−17249.5	−1.32285
$555$	−82.3148	−0.00629562
$556$	1692.93	0.129130
$557$	7105.83	0.540546	0.270273	−	0.962784i	$-0.412886\pi$
$557$	7105.83	0.540546	0.270273	+	0.962784i	$0.412886\pi$
$558$	−4087.75	−0.310122
$559$	−18686.1	−1.41384
$560$	1374.63	0.103730
$561$	8296.03	0.624347
$562$	−1856.04	−0.139310
$563$	1180.00	0.0883323	0.0441661	−	0.999024i	$-0.485937\pi$
$563$	1180.00	0.0883323	0.0441661	+	0.999024i	$0.485937\pi$
$564$	−79.1245	−0.00590735
$565$	2994.96	0.223007
$566$	−4612.45	−0.342537
$567$	1391.81	0.103088
$568$	2673.97	0.197531
$569$	2692.66	0.198387	0.0991936	−	0.995068i	$-0.468374\pi$
$569$	2692.66	0.198387	0.0991936	+	0.995068i	$0.468374\pi$
$570$	570.000	0.0418854
$571$	−10754.0	−0.788160	−0.394080	−	0.919076i	$-0.628937\pi$
$571$	−10754.0	−0.788160	−0.394080	+	0.919076i	$0.628937\pi$
$572$	−8176.65	−0.597697
$573$	−2239.41	−0.163268
$574$	−14544.1	−1.05759
$575$	−205.428	−0.0148990
$576$	576.000	0.0416667
$577$	16146.3	1.16495	0.582476	−	0.812848i	$-0.302084\pi$
$577$	16146.3	1.16495	0.582476	+	0.812848i	$0.302084\pi$
$578$	8068.68	0.580645
$579$	1938.20	0.139117
$580$	4330.40	0.310017
$581$	−8218.81	−0.586874
$582$	−8365.81	−0.595832
$583$	−6027.43	−0.428183
$584$	−6933.54	−0.491288
$585$	−3146.49	−0.222378
$586$	5520.06	0.389133
$587$	19339.4	1.35984	0.679918	−	0.733288i	$-0.262015\pi$
$587$	19339.4	1.35984	0.679918	+	0.733288i	$0.262015\pi$
$588$	−572.980	−0.0401859
$589$	−4314.85	−0.301851
$590$	2085.32	0.145511
$591$	14719.4	1.02449
$592$	−87.8025	−0.00609571
$593$	15453.7	1.07016	0.535082	−	0.844800i	$-0.320281\pi$
$593$	15453.7	1.07016	0.535082	+	0.844800i	$0.320281\pi$
$594$	1578.69	0.109048
$595$	8126.68	0.559935
$596$	−5550.93	−0.381502
$597$	−3498.71	−0.239853
$598$	1149.12	0.0785800
$599$	15789.0	1.07700	0.538500	−	0.842626i	$-0.318991\pi$
$599$	15789.0	1.07700	0.538500	+	0.842626i	$0.318991\pi$
$600$	600.000	0.0408248
$601$	−4673.39	−0.317191	−0.158595	−	0.987344i	$-0.550697\pi$
$601$	−4673.39	−0.317191	−0.158595	+	0.987344i	$0.550697\pi$
$602$	9183.99	0.621780
$603$	9094.22	0.614171
$604$	6750.51	0.454759
$605$	−2381.59	−0.160042
$606$	11776.6	0.789427
$607$	10101.9	0.675488	0.337744	−	0.941238i	$-0.390336\pi$
$607$	10101.9	0.675488	0.337744	+	0.941238i	$0.390336\pi$
$608$	608.000	0.0405554
$609$	11161.3	0.742658
$610$	5100.64	0.338555
$611$	461.045	0.0305268
$612$	3405.25	0.224917
$613$	−8592.15	−0.566123	−0.283062	−	0.959102i	$-0.591350\pi$
$613$	−8592.15	−0.566123	−0.283062	+	0.959102i	$0.591350\pi$
$614$	11543.6	0.758732
$615$	−6348.21	−0.416235
$616$	4018.72	0.262856
$617$	−14952.7	−0.975646	−0.487823	−	0.872943i	$-0.662209\pi$
$617$	−14952.7	−0.975646	−0.487823	+	0.872943i	$0.662209\pi$
$618$	9070.11	0.590378
$619$	−25121.9	−1.63124	−0.815618	−	0.578591i	$-0.803603\pi$
$619$	−25121.9	−1.63124	−0.815618	+	0.578591i	$0.803603\pi$
$620$	−4541.95	−0.294208
$621$	−221.863	−0.0143366
$622$	−12350.1	−0.796131
$623$	−19764.6	−1.27103
$624$	−3356.25	−0.215317
$625$	625.000	0.0400000
$626$	22080.6	1.40978
$627$	1666.39	0.106139
$628$	−7502.66	−0.476734
$629$	−519.080	−0.0329047
$630$	1546.46	0.0977975
$631$	18777.7	1.18468	0.592338	−	0.805690i	$-0.298205\pi$
$631$	18777.7	1.18468	0.592338	+	0.805690i	$0.298205\pi$
$632$	4020.30	0.253037
$633$	−16558.3	−1.03971
$634$	−2853.03	−0.178720
$635$	−8106.57	−0.506613
$636$	−2474.07	−0.154250
$637$	3338.66	0.207665
$638$	12659.9	0.785595
$639$	3008.22	0.186234
$640$	640.000	0.0395285
$641$	25392.7	1.56466	0.782332	−	0.622862i	$-0.214030\pi$
$641$	25392.7	1.56466	0.782332	+	0.622862i	$0.214030\pi$
$642$	−6204.80	−0.381439
$643$	215.451	0.0132139	0.00660696	−	0.999978i	$-0.497897\pi$
$643$	215.451	0.0132139	0.00660696	+	0.999978i	$0.497897\pi$
$644$	−564.776	−0.0345579
$645$	4008.64	0.244713
$646$	3594.43	0.218918
$647$	−19929.7	−1.21100	−0.605501	−	0.795844i	$-0.707027\pi$
$647$	−19929.7	−1.21100	−0.605501	+	0.795844i	$0.707027\pi$
$648$	648.000	0.0392837
$649$	6096.43	0.368730
$650$	−3496.10	−0.210966
$651$	−11706.6	−0.704787
$652$	3518.11	0.211318
$653$	18648.1	1.11754	0.558771	−	0.829322i	$-0.311273\pi$
$653$	18648.1	1.11754	0.558771	+	0.829322i	$0.311273\pi$
$654$	−2936.68	−0.175586
$655$	−10668.7	−0.636427
$656$	−6771.42	−0.403018
$657$	−7800.24	−0.463191
$658$	−226.598	−0.0134251
$659$	−8105.95	−0.479155	−0.239577	−	0.970877i	$-0.577009\pi$
$659$	−8105.95	−0.479155	−0.239577	+	0.970877i	$0.577009\pi$
$660$	1754.10	0.103452
$661$	−4872.33	−0.286704	−0.143352	−	0.989672i	$-0.545788\pi$
$661$	−4872.33	−0.286704	−0.143352	+	0.989672i	$0.545788\pi$
$662$	−1800.79	−0.105724
$663$	−19841.8	−1.16228
$664$	−3826.51	−0.223641
$665$	1632.37	0.0951891
$666$	−98.7778	−0.00574709
$667$	−1779.17	−0.103283
$668$	−13168.9	−0.762756
$669$	4179.20	0.241521
$670$	10104.7	0.582654
$671$	14911.7	0.857912
$672$	1649.56	0.0946920
$673$	12953.6	0.741937	0.370969	−	0.928645i	$-0.379026\pi$
$673$	12953.6	0.741937	0.370969	+	0.928645i	$0.379026\pi$
$674$	15327.6	0.875962
$675$	675.000	0.0384900
$676$	10768.3	0.612671
$677$	6098.11	0.346188	0.173094	−	0.984905i	$-0.444624\pi$
$677$	6098.11	0.346188	0.173094	+	0.984905i	$0.444624\pi$
$678$	3593.95	0.203577
$679$	−23958.1	−1.35409
$680$	3783.62	0.213375
$681$	−12537.5	−0.705491
$682$	−13278.3	−0.745534
$683$	27530.4	1.54234	0.771171	−	0.636628i	$-0.219671\pi$
$683$	27530.4	1.54234	0.771171	+	0.636628i	$0.219671\pi$
$684$	684.000	0.0382360
$685$	4111.54	0.229334
$686$	−13428.4	−0.747373
$687$	8390.50	0.465965
$688$	4275.88	0.236942
$689$	14416.0	0.797103
$690$	−246.514	−0.0136009
$691$	−26669.7	−1.46825	−0.734127	−	0.679012i	$-0.762408\pi$
$691$	−26669.7	−1.46825	−0.734127	+	0.679012i	$0.762408\pi$
$692$	−7444.11	−0.408934
$693$	4521.06	0.247823
$694$	−21811.0	−1.19299
$695$	2116.16	0.115497
$696$	5196.47	0.283006
$697$	−40032.0	−2.17549
$698$	−4947.23	−0.268274
$699$	−14902.8	−0.806403
$700$	1718.29	0.0927789
$701$	−5377.33	−0.289727	−0.144864	−	0.989452i	$-0.546274\pi$
$701$	−5377.33	−0.289727	−0.144864	+	0.989452i	$0.546274\pi$
$702$	−3775.78	−0.203003
$703$	−104.265	−0.00559381
$704$	1871.04	0.100167
$705$	−98.9056	−0.00528369
$706$	−9853.38	−0.525265
$707$	33726.1	1.79406
$708$	2502.39	0.132833
$709$	−14906.2	−0.789580	−0.394790	−	0.918771i	$-0.629183\pi$
$709$	−14906.2	−0.789580	−0.394790	+	0.918771i	$0.629183\pi$
$710$	3342.47	0.176677
$711$	4522.84	0.238565
$712$	−9201.99	−0.484353
$713$	1866.09	0.0980162
$714$	9752.02	0.511149
$715$	−10220.8	−0.534597
$716$	−11477.2	−0.599055
$717$	14095.9	0.734199
$718$	15191.9	0.789635
$719$	−17007.1	−0.882140	−0.441070	−	0.897473i	$-0.645401\pi$
$719$	−17007.1	−0.882140	−0.441070	+	0.897473i	$0.645401\pi$
$720$	720.000	0.0372678
$721$	25975.1	1.34170
$722$	722.000	0.0372161
$723$	−201.098	−0.0103443
$724$	−9610.77	−0.493344
$725$	5412.99	0.277288
$726$	−2857.91	−0.146098
$727$	25491.3	1.30044	0.650221	−	0.759745i	$-0.274676\pi$
$727$	25491.3	1.30044	0.650221	+	0.759745i	$0.274676\pi$
$728$	−9611.68	−0.489331
$729$	729.000	0.0370370
$730$	−8666.93	−0.439421
$731$	25278.6	1.27902
$732$	6120.77	0.309057
$733$	−18043.7	−0.909223	−0.454611	−	0.890690i	$-0.650222\pi$
$733$	−18043.7	−0.909223	−0.454611	+	0.890690i	$0.650222\pi$
$734$	10355.4	0.520743
$735$	−716.225	−0.0359433
$736$	−262.948	−0.0131690
$737$	29541.0	1.47647
$738$	−7617.85	−0.379969
$739$	−4482.52	−0.223129	−0.111564	−	0.993757i	$-0.535586\pi$
$739$	−4482.52	−0.223129	−0.111564	+	0.993757i	$0.535586\pi$
$740$	−109.753	−0.00545217
$741$	−3985.55	−0.197588
$742$	−7085.27	−0.350550
$743$	−1934.60	−0.0955230	−0.0477615	−	0.998859i	$-0.515209\pi$
$743$	−1934.60	−0.0955230	−0.0477615	+	0.998859i	$0.515209\pi$
$744$	−5450.34	−0.268574
$745$	−6938.66	−0.341225
$746$	9825.26	0.482210
$747$	−4304.82	−0.210850
$748$	11061.4	0.540700
$749$	−17769.4	−0.866862
$750$	750.000	0.0365148
$751$	6102.74	0.296528	0.148264	−	0.988948i	$-0.452632\pi$
$751$	6102.74	0.296528	0.148264	+	0.988948i	$0.452632\pi$
$752$	−105.499	−0.00511591
$753$	−16134.3	−0.780833
$754$	−30279.0	−1.46246
$755$	8438.14	0.406749
$756$	1855.75	0.0892765
$757$	−40052.0	−1.92301	−0.961503	−	0.274796i	$-0.911390\pi$
$757$	−40052.0	−1.92301	−0.961503	+	0.274796i	$0.911390\pi$
$758$	−12333.8	−0.591006
$759$	−720.682	−0.0344652
$760$	760.000	0.0362738
$761$	−10449.7	−0.497770	−0.248885	−	0.968533i	$-0.580064\pi$
$761$	−10449.7	−0.497770	−0.248885	+	0.968533i	$0.580064\pi$
$762$	−9727.88	−0.462472
$763$	−8410.10	−0.399038
$764$	−2985.88	−0.141395
$765$	4256.57	0.201172
$766$	−13655.1	−0.644097
$767$	−14581.0	−0.686426
$768$	768.000	0.0360844
$769$	6903.59	0.323732	0.161866	−	0.986813i	$-0.448249\pi$
$769$	6903.59	0.323732	0.161866	+	0.986813i	$0.448249\pi$
$770$	5023.41	0.235105
$771$	−8254.55	−0.385578
$772$	2584.27	0.120479
$773$	−26849.0	−1.24928	−0.624639	−	0.780914i	$-0.714754\pi$
$773$	−26849.0	−1.24928	−0.624639	+	0.780914i	$0.714754\pi$
$774$	4810.36	0.223391
$775$	−5677.43	−0.263148
$776$	−11154.4	−0.516005
$777$	−282.881	−0.0130609
$778$	3782.11	0.174287
$779$	−8041.06	−0.369834
$780$	−4195.32	−0.192585
$781$	9771.68	0.447706
$782$	−1554.52	−0.0710865
$783$	5846.03	0.266820
$784$	−763.973	−0.0348020
$785$	−9378.33	−0.426404
$786$	−12802.4	−0.580976
$787$	13804.1	0.625239	0.312620	−	0.949878i	$-0.398793\pi$
$787$	13804.1	0.625239	0.312620	+	0.949878i	$0.398793\pi$
$788$	19625.8	0.887236
$789$	−4672.90	−0.210849
$790$	5025.38	0.226323
$791$	10292.4	0.462650
$792$	2104.91	0.0944380
$793$	−35664.6	−1.59709
$794$	19317.2	0.863405
$795$	−3092.58	−0.137966
$796$	−4664.94	−0.207719
$797$	14190.6	0.630684	0.315342	−	0.948978i	$-0.397881\pi$
$797$	14190.6	0.630684	0.315342	+	0.948978i	$0.397881\pi$
$798$	1958.85	0.0868954
$799$	−623.702	−0.0276157
$800$	800.000	0.0353553
$801$	−10352.2	−0.456652
$802$	4125.50	0.181642
$803$	−25337.7	−1.11351
$804$	12125.6	0.531888
$805$	−705.970	−0.0309095
$806$	31758.2	1.38788
$807$	−4981.62	−0.217300
$808$	15702.2	0.683664
$809$	23720.0	1.03084	0.515422	−	0.856937i	$-0.327635\pi$
$809$	23720.0	1.03084	0.515422	+	0.856937i	$0.327635\pi$
$810$	810.000	0.0351364
$811$	23359.2	1.01141	0.505704	−	0.862707i	$-0.331233\pi$
$811$	23359.2	1.01141	0.505704	+	0.862707i	$0.331233\pi$
$812$	14881.7	0.643161
$813$	5639.99	0.243300
$814$	−320.862	−0.0138160
$815$	4397.63	0.189009
$816$	4540.34	0.194784
$817$	5077.61	0.217433
$818$	−12843.9	−0.548994
$819$	−10813.1	−0.461345
$820$	−8464.28	−0.360470
$821$	−13199.5	−0.561103	−0.280551	−	0.959839i	$-0.590517\pi$
$821$	−13199.5	−0.561103	−0.280551	+	0.959839i	$0.590517\pi$
$822$	4933.85	0.209352
$823$	−11817.2	−0.500513	−0.250256	−	0.968180i	$-0.580515\pi$
$823$	−11817.2	−0.500513	−0.250256	+	0.968180i	$0.580515\pi$
$824$	12093.5	0.511282
$825$	2192.62	0.0925300
$826$	7166.38	0.301877
$827$	−33124.4	−1.39280	−0.696402	−	0.717652i	$-0.745217\pi$
$827$	−33124.4	−1.39280	−0.696402	+	0.717652i	$0.745217\pi$
$828$	−295.817	−0.0124159
$829$	21452.5	0.898764	0.449382	−	0.893340i	$-0.351644\pi$
$829$	21452.5	0.898764	0.449382	+	0.893340i	$0.351644\pi$
$830$	−4783.14	−0.200030
$831$	−25874.2	−1.08010
$832$	−4475.00	−0.186470
$833$	−4516.53	−0.187862
$834$	2539.39	0.105434
$835$	−16461.2	−0.682230
$836$	2221.85	0.0919192
$837$	−6131.63	−0.253214
$838$	7342.86	0.302691
$839$	−4748.27	−0.195386	−0.0976928	−	0.995217i	$-0.531146\pi$
$839$	−4748.27	−0.195386	−0.0976928	+	0.995217i	$0.531146\pi$
$840$	2061.95	0.0846951
$841$	22491.8	0.922212
$842$	−11880.2	−0.486245
$843$	−2784.06	−0.113746
$844$	−22077.8	−0.900414
$845$	13460.4	0.547989
$846$	−118.687	−0.00482333
$847$	−8184.53	−0.332024
$848$	−3298.76	−0.133585
$849$	−6918.68	−0.279680
$850$	4729.52	0.190848
$851$	45.0928	0.00181641
$852$	4010.96	0.161283
$853$	16832.9	0.675672	0.337836	−	0.941205i	$-0.390305\pi$
$853$	16832.9	0.675672	0.337836	+	0.941205i	$0.390305\pi$
$854$	17528.7	0.702367
$855$	855.000	0.0341993
$856$	−8273.07	−0.330336
$857$	22016.2	0.877548	0.438774	−	0.898597i	$-0.355413\pi$
$857$	22016.2	0.877548	0.438774	+	0.898597i	$0.355413\pi$
$858$	−12265.0	−0.488018
$859$	−44154.2	−1.75381	−0.876904	−	0.480666i	$-0.840395\pi$
$859$	−44154.2	−1.75381	−0.876904	+	0.480666i	$0.840395\pi$
$860$	5344.85	0.211928
$861$	−21816.1	−0.863520
$862$	−35354.0	−1.39694
$863$	18091.3	0.713598	0.356799	−	0.934181i	$-0.383868\pi$
$863$	18091.3	0.713598	0.356799	+	0.934181i	$0.383868\pi$
$864$	864.000	0.0340207
$865$	−9305.13	−0.365762
$866$	27406.0	1.07540
$867$	12103.0	0.474095
$868$	−15608.8	−0.610363
$869$	14691.7	0.573510
$870$	6495.59	0.253128
$871$	−70653.9	−2.74858
$872$	−3915.57	−0.152062
$873$	−12548.7	−0.486495
$874$	−312.251	−0.0120847
$875$	2147.86	0.0829840
$876$	−10400.3	−0.401135
$877$	17188.7	0.661825	0.330913	−	0.943661i	$-0.392643\pi$
$877$	17188.7	0.661825	0.330913	+	0.943661i	$0.392643\pi$
$878$	−5491.94	−0.211098
$879$	8280.09	0.317725
$880$	2338.79	0.0895918
$881$	−36459.5	−1.39427	−0.697135	−	0.716940i	$-0.745542\pi$
$881$	−36459.5	−1.39427	−0.697135	+	0.716940i	$0.745542\pi$
$882$	−859.470	−0.0328116
$883$	−39492.5	−1.50513	−0.752565	−	0.658518i	$-0.771184\pi$
$883$	−39492.5	−1.50513	−0.752565	+	0.658518i	$0.771184\pi$
$884$	−26455.8	−1.00657
$885$	3127.98	0.118809
$886$	17883.5	0.678113
$887$	−11920.3	−0.451232	−0.225616	−	0.974216i	$-0.572439\pi$
$887$	−11920.3	−0.451232	−0.225616	+	0.974216i	$0.572439\pi$
$888$	−131.704	−0.00497713
$889$	−27858.9	−1.05102
$890$	−11502.5	−0.433218
$891$	2368.03	0.0890370
$892$	5572.27	0.209163
$893$	−125.280	−0.00469468
$894$	−8326.39	−0.311495
$895$	−14346.5	−0.535811
$896$	2199.41	0.0820057
$897$	1723.67	0.0641603
$898$	17540.6	0.651823
$899$	−49171.1	−1.82419
$900$	900.000	0.0333333
$901$	−19501.9	−0.721091
$902$	−24745.3	−0.913444
$903$	13776.0	0.507681
$904$	4791.94	0.176303
$905$	−12013.5	−0.441261
$906$	10125.8	0.371309
$907$	−45690.1	−1.67267	−0.836337	−	0.548215i	$-0.815307\pi$
$907$	−45690.1	−1.67267	−0.836337	+	0.548215i	$0.815307\pi$
$908$	−16716.7	−0.610974
$909$	17664.9	0.644564
$910$	−12014.6	−0.437671
$911$	−32444.3	−1.17994	−0.589971	−	0.807424i	$-0.700861\pi$
$911$	−32444.3	−1.17994	−0.589971	+	0.807424i	$0.700861\pi$
$912$	912.000	0.0331133
$913$	−13983.5	−0.506884
$914$	28638.7	1.03641
$915$	7650.96	0.276429
$916$	11187.3	0.403537
$917$	−36663.7	−1.32033
$918$	5107.88	0.183644
$919$	−30990.9	−1.11240	−0.556201	−	0.831048i	$-0.687741\pi$
$919$	−30990.9	−1.11240	−0.556201	+	0.831048i	$0.687741\pi$
$920$	−328.685	−0.0117787
$921$	17315.4	0.619502
$922$	5158.87	0.184272
$923$	−23371.2	−0.833447
$924$	6028.09	0.214621
$925$	−137.191	−0.00487657
$926$	38269.2	1.35810
$927$	13605.2	0.482041
$928$	6928.63	0.245090
$929$	18596.6	0.656766	0.328383	−	0.944545i	$-0.393496\pi$
$929$	18596.6	0.656766	0.328383	+	0.944545i	$0.393496\pi$
$930$	−6812.92	−0.240220
$931$	−907.218	−0.0319365
$932$	−19870.4	−0.698365
$933$	−18525.1	−0.650038
$934$	24560.1	0.860420
$935$	13826.7	0.483617
$936$	−5034.38	−0.175805
$937$	38908.0	1.35653	0.678266	−	0.734816i	$-0.262732\pi$
$937$	38908.0	1.35653	0.678266	+	0.734816i	$0.262732\pi$
$938$	34725.5	1.20877
$939$	33121.0	1.15108
$940$	−131.874	−0.00457581
$941$	−30289.8	−1.04933	−0.524665	−	0.851309i	$-0.675809\pi$
$941$	−30289.8	−1.04933	−0.524665	+	0.851309i	$0.675809\pi$
$942$	−11254.0	−0.389252
$943$	3477.60	0.120092
$944$	3336.52	0.115036
$945$	2319.69	0.0798513
$946$	15625.6	0.537033
$947$	5350.55	0.183600	0.0918002	−	0.995777i	$-0.470738\pi$
$947$	5350.55	0.183600	0.0918002	+	0.995777i	$0.470738\pi$
$948$	6030.46	0.206603
$949$	60600.8	2.07290
$950$	950.000	0.0324443
$951$	−4279.55	−0.145924
$952$	13002.7	0.442668
$953$	18445.6	0.626978	0.313489	−	0.949592i	$-0.398502\pi$
$953$	18445.6	0.626978	0.313489	+	0.949592i	$0.398502\pi$
$954$	−3711.10	−0.125945
$955$	−3732.36	−0.126467
$956$	18794.5	0.635835
$957$	18989.8	0.641435
$958$	2854.85	0.0962799
$959$	14129.6	0.475776
$960$	960.000	0.0322749
$961$	21782.2	0.731167
$962$	767.415	0.0257198
$963$	−9307.20	−0.311444
$964$	−268.130	−0.00895840
$965$	3230.33	0.107760
$966$	−847.164	−0.0282164
$967$	2251.28	0.0748670	0.0374335	−	0.999299i	$-0.488082\pi$
$967$	2251.28	0.0748670	0.0374335	+	0.999299i	$0.488082\pi$
$968$	−3810.55	−0.126525
$969$	5391.65	0.178746
$970$	−13943.0	−0.461529
$971$	−15117.4	−0.499630	−0.249815	−	0.968294i	$-0.580370\pi$
$971$	−15117.4	−0.499630	−0.249815	+	0.968294i	$0.580370\pi$
$972$	972.000	0.0320750
$973$	7272.35	0.239610
$974$	28514.4	0.938049
$975$	−5244.14	−0.172253
$976$	8161.02	0.267652
$977$	−52640.2	−1.72376	−0.861878	−	0.507116i	$-0.830712\pi$
$977$	−52640.2	−1.72376	−0.861878	+	0.507116i	$0.830712\pi$
$978$	5277.16	0.172541
$979$	−33627.4	−1.09779
$980$	−954.967	−0.0311279
$981$	−4405.02	−0.143365
$982$	−34858.5	−1.13277
$983$	−3111.24	−0.100949	−0.0504746	−	0.998725i	$-0.516073\pi$
$983$	−3111.24	−0.100949	−0.0504746	+	0.998725i	$0.516073\pi$
$984$	−10157.1	−0.329063
$985$	24532.3	0.793568
$986$	40961.4	1.32300
$987$	−339.897	−0.0109615
$988$	−5314.07	−0.171116
$989$	−2195.97	−0.0706043
$990$	2631.14	0.0844679
$991$	20100.4	0.644308	0.322154	−	0.946687i	$-0.395593\pi$
$991$	20100.4	0.644308	0.322154	+	0.946687i	$0.395593\pi$
$992$	−7267.11	−0.232592
$993$	−2701.18	−0.0863236
$994$	11486.6	0.366534
$995$	−5831.18	−0.185790
$996$	−5739.76	−0.182602
$997$	53308.1	1.69337	0.846683	−	0.532098i	$-0.178596\pi$
$997$	53308.1	1.69337	0.846683	+	0.532098i	$0.178596\pi$
$998$	−12561.5	−0.398423
$999$	−148.167	−0.00469248

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.4.a.s.1.3	✓	4
3.2	odd	2		1710.4.a.bc.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.4.a.s.1.3	✓	4	1.1	even	1	trivial
1710.4.a.bc.1.3		4	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	570.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +6.00000 q^{6} +17.1829 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +6.00000 q^{6} +17.1829 q^{7} +8.00000 q^{8} +9.00000 q^{9} +10.0000 q^{10} +29.2349 q^{11} +12.0000 q^{12} -69.9219 q^{13} +34.3658 q^{14} +15.0000 q^{15} +16.0000 q^{16} +94.5904 q^{17} +18.0000 q^{18} +19.0000 q^{19} +20.0000 q^{20} +51.5487 q^{21} +58.4699 q^{22} -8.21713 q^{23} +24.0000 q^{24} +25.0000 q^{25} -139.844 q^{26} +27.0000 q^{27} +68.7316 q^{28} +216.520 q^{29} +30.0000 q^{30} -227.097 q^{31} +32.0000 q^{32} +87.7048 q^{33} +189.181 q^{34} +85.9144 q^{35} +36.0000 q^{36} -5.48766 q^{37} +38.0000 q^{38} -209.766 q^{39} +40.0000 q^{40} -423.214 q^{41} +103.097 q^{42} +267.242 q^{43} +116.940 q^{44} +45.0000 q^{45} -16.4343 q^{46} -6.59371 q^{47} +48.0000 q^{48} -47.7483 q^{49} +50.0000 q^{50} +283.771 q^{51} -279.688 q^{52} -206.172 q^{53} +54.0000 q^{54} +146.175 q^{55} +137.463 q^{56} +57.0000 q^{57} +433.040 q^{58} +208.532 q^{59} +60.0000 q^{60} +510.064 q^{61} -454.195 q^{62} +154.646 q^{63} +64.0000 q^{64} -349.610 q^{65} +175.410 q^{66} +1010.47 q^{67} +378.362 q^{68} -24.6514 q^{69} +171.829 q^{70} +334.247 q^{71} +72.0000 q^{72} -866.693 q^{73} -10.9753 q^{74} +75.0000 q^{75} +76.0000 q^{76} +502.341 q^{77} -419.532 q^{78} +502.538 q^{79} +80.0000 q^{80} +81.0000 q^{81} -846.428 q^{82} -478.314 q^{83} +206.195 q^{84} +472.952 q^{85} +534.485 q^{86} +649.559 q^{87} +233.879 q^{88} -1150.25 q^{89} +90.0000 q^{90} -1201.46 q^{91} -32.8685 q^{92} -681.292 q^{93} -13.1874 q^{94} +95.0000 q^{95} +96.0000 q^{96} -1394.30 q^{97} -95.4967 q^{98} +263.114 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} + 12 q^{3} + 16 q^{4} + 20 q^{5} + 24 q^{6} + 36 q^{7} + 32 q^{8} + 36 q^{9}+O(q^{10}) \) 4 * q + 8 * q^2 + 12 * q^3 + 16 * q^4 + 20 * q^5 + 24 * q^6 + 36 * q^7 + 32 * q^8 + 36 * q^9	\( 4 q + 8 q^{2} + 12 q^{3} + 16 q^{4} + 20 q^{5} + 24 q^{6} + 36 q^{7} + 32 q^{8} + 36 q^{9} + 40 q^{10} + 54 q^{11} + 48 q^{12} + 46 q^{13} + 72 q^{14} + 60 q^{15} + 64 q^{16} + 14 q^{17} + 72 q^{18} + 76 q^{19} + 80 q^{20} + 108 q^{21} + 108 q^{22} + 104 q^{23} + 96 q^{24} + 100 q^{25} + 92 q^{26} + 108 q^{27} + 144 q^{28} + 14 q^{29} + 120 q^{30} + 30 q^{31} + 128 q^{32} + 162 q^{33} + 28 q^{34} + 180 q^{35} + 144 q^{36} + 30 q^{37} + 152 q^{38} + 138 q^{39} + 160 q^{40} - 36 q^{41} + 216 q^{42} + 102 q^{43} + 216 q^{44} + 180 q^{45} + 208 q^{46} + 408 q^{47} + 192 q^{48} + 480 q^{49} + 200 q^{50} + 42 q^{51} + 184 q^{52} - 176 q^{53} + 216 q^{54} + 270 q^{55} + 288 q^{56} + 228 q^{57} + 28 q^{58} + 66 q^{59} + 240 q^{60} + 60 q^{61} + 60 q^{62} + 324 q^{63} + 256 q^{64} + 230 q^{65} + 324 q^{66} - 152 q^{67} + 56 q^{68} + 312 q^{69} + 360 q^{70} + 172 q^{71} + 288 q^{72} + 284 q^{73} + 60 q^{74} + 300 q^{75} + 304 q^{76} - 300 q^{77} + 276 q^{78} + 554 q^{79} + 320 q^{80} + 324 q^{81} - 72 q^{82} - 394 q^{83} + 432 q^{84} + 70 q^{85} + 204 q^{86} + 42 q^{87} + 432 q^{88} - 60 q^{89} + 360 q^{90} + 32 q^{91} + 416 q^{92} + 90 q^{93} + 816 q^{94} + 380 q^{95} + 384 q^{96} - 922 q^{97} + 960 q^{98} + 486 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 + 12 * q^3 + 16 * q^4 + 20 * q^5 + 24 * q^6 + 36 * q^7 + 32 * q^8 + 36 * q^9 + 40 * q^10 + 54 * q^11 + 48 * q^12 + 46 * q^13 + 72 * q^14 + 60 * q^15 + 64 * q^16 + 14 * q^17 + 72 * q^18 + 76 * q^19 + 80 * q^20 + 108 * q^21 + 108 * q^22 + 104 * q^23 + 96 * q^24 + 100 * q^25 + 92 * q^26 + 108 * q^27 + 144 * q^28 + 14 * q^29 + 120 * q^30 + 30 * q^31 + 128 * q^32 + 162 * q^33 + 28 * q^34 + 180 * q^35 + 144 * q^36 + 30 * q^37 + 152 * q^38 + 138 * q^39 + 160 * q^40 - 36 * q^41 + 216 * q^42 + 102 * q^43 + 216 * q^44 + 180 * q^45 + 208 * q^46 + 408 * q^47 + 192 * q^48 + 480 * q^49 + 200 * q^50 + 42 * q^51 + 184 * q^52 - 176 * q^53 + 216 * q^54 + 270 * q^55 + 288 * q^56 + 228 * q^57 + 28 * q^58 + 66 * q^59 + 240 * q^60 + 60 * q^61 + 60 * q^62 + 324 * q^63 + 256 * q^64 + 230 * q^65 + 324 * q^66 - 152 * q^67 + 56 * q^68 + 312 * q^69 + 360 * q^70 + 172 * q^71 + 288 * q^72 + 284 * q^73 + 60 * q^74 + 300 * q^75 + 304 * q^76 - 300 * q^77 + 276 * q^78 + 554 * q^79 + 320 * q^80 + 324 * q^81 - 72 * q^82 - 394 * q^83 + 432 * q^84 + 70 * q^85 + 204 * q^86 + 42 * q^87 + 432 * q^88 - 60 * q^89 + 360 * q^90 + 32 * q^91 + 416 * q^92 + 90 * q^93 + 816 * q^94 + 380 * q^95 + 384 * q^96 - 922 * q^97 + 960 * q^98 + 486 * q^99

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