LMFDB - Embedded newform 966.4.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,4,Mod(1,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, 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("966.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	966.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:	$56.9958450655$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.9814581.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 66x^{2} + 271x - 241 $ x^4 - x^3 - 66x^2 + 271x - 241
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$5.48574$ of defining polynomial
Character	$\chi$	$=$	966.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -19.8380 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -19.8380 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -39.6760 q^{10} +26.8184 q^{11} -12.0000 q^{12} -0.965703 q^{13} +14.0000 q^{14} +59.5140 q^{15} +16.0000 q^{16} -28.5813 q^{17} +18.0000 q^{18} +47.6041 q^{19} -79.3521 q^{20} -21.0000 q^{21} +53.6368 q^{22} +23.0000 q^{23} -24.0000 q^{24} +268.547 q^{25} -1.93141 q^{26} -27.0000 q^{27} +28.0000 q^{28} +45.0314 q^{29} +119.028 q^{30} -72.4334 q^{31} +32.0000 q^{32} -80.4552 q^{33} -57.1626 q^{34} -138.866 q^{35} +36.0000 q^{36} -279.982 q^{37} +95.2082 q^{38} +2.89711 q^{39} -158.704 q^{40} -277.983 q^{41} -42.0000 q^{42} +250.463 q^{43} +107.274 q^{44} -178.542 q^{45} +46.0000 q^{46} +235.875 q^{47} -48.0000 q^{48} +49.0000 q^{49} +537.094 q^{50} +85.7438 q^{51} -3.86281 q^{52} -317.905 q^{53} -54.0000 q^{54} -532.024 q^{55} +56.0000 q^{56} -142.812 q^{57} +90.0629 q^{58} +22.3318 q^{59} +238.056 q^{60} -371.606 q^{61} -144.867 q^{62} +63.0000 q^{63} +64.0000 q^{64} +19.1576 q^{65} -160.910 q^{66} +202.163 q^{67} -114.325 q^{68} -69.0000 q^{69} -277.732 q^{70} -799.377 q^{71} +72.0000 q^{72} -679.109 q^{73} -559.963 q^{74} -805.640 q^{75} +190.416 q^{76} +187.729 q^{77} +5.79422 q^{78} -6.87196 q^{79} -317.408 q^{80} +81.0000 q^{81} -555.966 q^{82} -1156.16 q^{83} -84.0000 q^{84} +566.996 q^{85} +500.926 q^{86} -135.094 q^{87} +214.547 q^{88} -1041.59 q^{89} -357.084 q^{90} -6.75992 q^{91} +92.0000 q^{92} +217.300 q^{93} +471.750 q^{94} -944.370 q^{95} -96.0000 q^{96} -1497.29 q^{97} +98.0000 q^{98} +241.366 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{2} - 12 q^{3} + 16 q^{4} - 15 q^{5} - 24 q^{6} + 28 q^{7} + 32 q^{8} + 36 q^{9}+O(q^{10}) $ 4 * q + 8 * q^2 - 12 * q^3 + 16 * q^4 - 15 * q^5 - 24 * q^6 + 28 * q^7 + 32 * q^8 + 36 * q^9	\( 4 q + 8 q^{2} - 12 q^{3} + 16 q^{4} - 15 q^{5} - 24 q^{6} + 28 q^{7} + 32 q^{8} + 36 q^{9} - 30 q^{10} - 26 q^{11} - 48 q^{12} - 33 q^{13} + 56 q^{14} + 45 q^{15} + 64 q^{16} - 168 q^{17} + 72 q^{18} - 138 q^{19} - 60 q^{20} - 84 q^{21} - 52 q^{22} + 92 q^{23} - 96 q^{24} - 41 q^{25} - 66 q^{26} - 108 q^{27} + 112 q^{28} + 52 q^{29} + 90 q^{30} - 248 q^{31} + 128 q^{32} + 78 q^{33} - 336 q^{34} - 105 q^{35} + 144 q^{36} + 226 q^{37} - 276 q^{38} + 99 q^{39} - 120 q^{40} - 274 q^{41} - 168 q^{42} + 269 q^{43} - 104 q^{44} - 135 q^{45} + 184 q^{46} - 408 q^{47} - 192 q^{48} + 196 q^{49} - 82 q^{50} + 504 q^{51} - 132 q^{52} - 843 q^{53} - 216 q^{54} - 249 q^{55} + 224 q^{56} + 414 q^{57} + 104 q^{58} - 653 q^{59} + 180 q^{60} - 963 q^{61} - 496 q^{62} + 252 q^{63} + 256 q^{64} - 588 q^{65} + 156 q^{66} - 789 q^{67} - 672 q^{68} - 276 q^{69} - 210 q^{70} - 1697 q^{71} + 288 q^{72} - 1800 q^{73} + 452 q^{74} + 123 q^{75} - 552 q^{76} - 182 q^{77} + 198 q^{78} + 274 q^{79} - 240 q^{80} + 324 q^{81} - 548 q^{82} - 1496 q^{83} - 336 q^{84} - 435 q^{85} + 538 q^{86} - 156 q^{87} - 208 q^{88} - 1829 q^{89} - 270 q^{90} - 231 q^{91} + 368 q^{92} + 744 q^{93} - 816 q^{94} - 1767 q^{95} - 384 q^{96} - 1910 q^{97} + 392 q^{98} - 234 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 - 12 * q^3 + 16 * q^4 - 15 * q^5 - 24 * q^6 + 28 * q^7 + 32 * q^8 + 36 * q^9 - 30 * q^10 - 26 * q^11 - 48 * q^12 - 33 * q^13 + 56 * q^14 + 45 * q^15 + 64 * q^16 - 168 * q^17 + 72 * q^18 - 138 * q^19 - 60 * q^20 - 84 * q^21 - 52 * q^22 + 92 * q^23 - 96 * q^24 - 41 * q^25 - 66 * q^26 - 108 * q^27 + 112 * q^28 + 52 * q^29 + 90 * q^30 - 248 * q^31 + 128 * q^32 + 78 * q^33 - 336 * q^34 - 105 * q^35 + 144 * q^36 + 226 * q^37 - 276 * q^38 + 99 * q^39 - 120 * q^40 - 274 * q^41 - 168 * q^42 + 269 * q^43 - 104 * q^44 - 135 * q^45 + 184 * q^46 - 408 * q^47 - 192 * q^48 + 196 * q^49 - 82 * q^50 + 504 * q^51 - 132 * q^52 - 843 * q^53 - 216 * q^54 - 249 * q^55 + 224 * q^56 + 414 * q^57 + 104 * q^58 - 653 * q^59 + 180 * q^60 - 963 * q^61 - 496 * q^62 + 252 * q^63 + 256 * q^64 - 588 * q^65 + 156 * q^66 - 789 * q^67 - 672 * q^68 - 276 * q^69 - 210 * q^70 - 1697 * q^71 + 288 * q^72 - 1800 * q^73 + 452 * q^74 + 123 * q^75 - 552 * q^76 - 182 * q^77 + 198 * q^78 + 274 * q^79 - 240 * q^80 + 324 * q^81 - 548 * q^82 - 1496 * q^83 - 336 * q^84 - 435 * q^85 + 538 * q^86 - 156 * q^87 - 208 * q^88 - 1829 * q^89 - 270 * q^90 - 231 * q^91 + 368 * q^92 + 744 * q^93 - 816 * q^94 - 1767 * q^95 - 384 * q^96 - 1910 * q^97 + 392 * q^98 - 234 * 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
$5$	−19.8380	−1.77437	−0.887183	−	0.461418i	$-0.847341\pi$
$5$	−19.8380	−1.77437	−0.887183	+	0.461418i	$0.847341\pi$
$6$	−6.00000	−0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	−39.6760	−1.25467
$11$	26.8184	0.735096	0.367548	−	0.930005i	$-0.380197\pi$
$11$	26.8184	0.735096	0.367548	+	0.930005i	$0.380197\pi$
$12$	−12.0000	−0.288675
$13$	−0.965703	−0.0206029	−0.0103015	−	0.999947i	$-0.503279\pi$
$13$	−0.965703	−0.0206029	−0.0103015	+	0.999947i	$0.503279\pi$
$14$	14.0000	0.267261
$15$	59.5140	1.02443
$16$	16.0000	0.250000
$17$	−28.5813	−0.407763	−0.203882	−	0.978996i	$-0.565356\pi$
$17$	−28.5813	−0.407763	−0.203882	+	0.978996i	$0.565356\pi$
$18$	18.0000	0.235702
$19$	47.6041	0.574796	0.287398	−	0.957811i	$-0.407210\pi$
$19$	47.6041	0.574796	0.287398	+	0.957811i	$0.407210\pi$
$20$	−79.3521	−0.887183
$21$	−21.0000	−0.218218
$22$	53.6368	0.519791
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−24.0000	−0.204124
$25$	268.547	2.14837
$26$	−1.93141	−0.0145685
$27$	−27.0000	−0.192450
$28$	28.0000	0.188982
$29$	45.0314	0.288349	0.144175	−	0.989552i	$-0.453947\pi$
$29$	45.0314	0.288349	0.144175	+	0.989552i	$0.453947\pi$
$30$	119.028	0.724382
$31$	−72.4334	−0.419659	−0.209830	−	0.977738i	$-0.567291\pi$
$31$	−72.4334	−0.419659	−0.209830	+	0.977738i	$0.567291\pi$
$32$	32.0000	0.176777
$33$	−80.4552	−0.424408
$34$	−57.1626	−0.288332
$35$	−138.866	−0.670647
$36$	36.0000	0.166667
$37$	−279.982	−1.24402	−0.622009	−	0.783010i	$-0.713683\pi$
$37$	−279.982	−1.24402	−0.622009	+	0.783010i	$0.713683\pi$
$38$	95.2082	0.406442
$39$	2.89711	0.0118951
$40$	−158.704	−0.627333
$41$	−277.983	−1.05887	−0.529435	−	0.848350i	$-0.677596\pi$
$41$	−277.983	−1.05887	−0.529435	+	0.848350i	$0.677596\pi$
$42$	−42.0000	−0.154303
$43$	250.463	0.888261	0.444131	−	0.895962i	$-0.353513\pi$
$43$	250.463	0.888261	0.444131	+	0.895962i	$0.353513\pi$
$44$	107.274	0.367548
$45$	−178.542	−0.591455
$46$	46.0000	0.147442
$47$	235.875	0.732041	0.366020	−	0.930607i	$-0.380720\pi$
$47$	235.875	0.732041	0.366020	+	0.930607i	$0.380720\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	537.094	1.51913
$51$	85.7438	0.235422
$52$	−3.86281	−0.0103015
$53$	−317.905	−0.823918	−0.411959	−	0.911202i	$-0.635155\pi$
$53$	−317.905	−0.823918	−0.411959	+	0.911202i	$0.635155\pi$
$54$	−54.0000	−0.136083
$55$	−532.024	−1.30433
$56$	56.0000	0.133631
$57$	−142.812	−0.331859
$58$	90.0629	0.203894
$59$	22.3318	0.0492771	0.0246386	−	0.999696i	$-0.492157\pi$
$59$	22.3318	0.0492771	0.0246386	+	0.999696i	$0.492157\pi$
$60$	238.056	0.512215
$61$	−371.606	−0.779987	−0.389994	−	0.920818i	$-0.627523\pi$
$61$	−371.606	−0.779987	−0.389994	+	0.920818i	$0.627523\pi$
$62$	−144.867	−0.296744
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	19.1576	0.0365571
$66$	−160.910	−0.300102
$67$	202.163	0.368629	0.184315	−	0.982867i	$-0.440993\pi$
$67$	202.163	0.368629	0.184315	+	0.982867i	$0.440993\pi$
$68$	−114.325	−0.203882
$69$	−69.0000	−0.120386
$70$	−277.732	−0.474219
$71$	−799.377	−1.33618	−0.668088	−	0.744082i	$-0.732887\pi$
$71$	−799.377	−1.33618	−0.668088	+	0.744082i	$0.732887\pi$
$72$	72.0000	0.117851
$73$	−679.109	−1.08882	−0.544409	−	0.838820i	$-0.683246\pi$
$73$	−679.109	−1.08882	−0.544409	+	0.838820i	$0.683246\pi$
$74$	−559.963	−0.879654
$75$	−805.640	−1.24036
$76$	190.416	0.287398
$77$	187.729	0.277840
$78$	5.79422	0.00841110
$79$	−6.87196	−0.00978678	−0.00489339	−	0.999988i	$-0.501558\pi$
$79$	−6.87196	−0.00978678	−0.00489339	+	0.999988i	$0.501558\pi$
$80$	−317.408	−0.443591
$81$	81.0000	0.111111
$82$	−555.966	−0.748734
$83$	−1156.16	−1.52897	−0.764485	−	0.644641i	$-0.777007\pi$
$83$	−1156.16	−1.52897	−0.764485	+	0.644641i	$0.777007\pi$
$84$	−84.0000	−0.109109
$85$	566.996	0.723522
$86$	500.926	0.628096
$87$	−135.094	−0.166478
$88$	214.547	0.259896
$89$	−1041.59	−1.24055	−0.620274	−	0.784385i	$-0.712978\pi$
$89$	−1041.59	−1.24055	−0.620274	+	0.784385i	$0.712978\pi$
$90$	−357.084	−0.418222
$91$	−6.75992	−0.00778717
$92$	92.0000	0.104257
$93$	217.300	0.242290
$94$	471.750	0.517631
$95$	−944.370	−1.01990
$96$	−96.0000	−0.102062
$97$	−1497.29	−1.56728	−0.783641	−	0.621214i	$-0.786640\pi$
$97$	−1497.29	−1.56728	−0.783641	+	0.621214i	$0.786640\pi$
$98$	98.0000	0.101015
$99$	241.366	0.245032
$100$	1074.19	1.07419
$101$	−342.133	−0.337064	−0.168532	−	0.985696i	$-0.553903\pi$
$101$	−342.133	−0.337064	−0.168532	+	0.985696i	$0.553903\pi$
$102$	171.488	0.166469
$103$	1992.72	1.90629	0.953147	−	0.302507i	$-0.0978235\pi$
$103$	1992.72	1.90629	0.953147	+	0.302507i	$0.0978235\pi$
$104$	−7.72562	−0.00728423
$105$	416.598	0.387198
$106$	−635.811	−0.582598
$107$	−431.201	−0.389587	−0.194794	−	0.980844i	$-0.562404\pi$
$107$	−431.201	−0.389587	−0.194794	+	0.980844i	$0.562404\pi$
$108$	−108.000	−0.0962250
$109$	119.038	0.104603	0.0523016	−	0.998631i	$-0.483344\pi$
$109$	119.038	0.104603	0.0523016	+	0.998631i	$0.483344\pi$
$110$	−1064.05	−0.922300
$111$	839.945	0.718234
$112$	112.000	0.0944911
$113$	−2142.50	−1.78362	−0.891811	−	0.452408i	$-0.850565\pi$
$113$	−2142.50	−1.78362	−0.891811	+	0.452408i	$0.850565\pi$
$114$	−285.625	−0.234660
$115$	−456.274	−0.369981
$116$	180.126	0.144175
$117$	−8.69133	−0.00686764
$118$	44.6635	0.0348442
$119$	−200.069	−0.154120
$120$	476.112	0.362191
$121$	−611.773	−0.459634
$122$	−743.211	−0.551534
$123$	833.950	0.611339
$124$	−289.734	−0.209830
$125$	−2847.68	−2.03764
$126$	126.000	0.0890871
$127$	−350.156	−0.244656	−0.122328	−	0.992490i	$-0.539036\pi$
$127$	−350.156	−0.244656	−0.122328	+	0.992490i	$0.539036\pi$
$128$	128.000	0.0883883
$129$	−751.389	−0.512838
$130$	38.3153	0.0258498
$131$	−1783.78	−1.18969	−0.594845	−	0.803841i	$-0.702786\pi$
$131$	−1783.78	−1.18969	−0.594845	+	0.803841i	$0.702786\pi$
$132$	−321.821	−0.212204
$133$	333.229	0.217253
$134$	404.326	0.260660
$135$	535.626	0.341477
$136$	−228.650	−0.144166
$137$	−1062.99	−0.662899	−0.331449	−	0.943473i	$-0.607538\pi$
$137$	−1062.99	−0.662899	−0.331449	+	0.943473i	$0.607538\pi$
$138$	−138.000	−0.0851257
$139$	2147.46	1.31040	0.655200	−	0.755456i	$-0.272585\pi$
$139$	2147.46	1.31040	0.655200	+	0.755456i	$0.272585\pi$
$140$	−555.464	−0.335324
$141$	−707.625	−0.422644
$142$	−1598.75	−0.944820
$143$	−25.8986	−0.0151451
$144$	144.000	0.0833333
$145$	−893.334	−0.511637
$146$	−1358.22	−0.769910
$147$	−147.000	−0.0824786
$148$	−1119.93	−0.622009
$149$	1797.47	0.988287	0.494143	−	0.869380i	$-0.335482\pi$
$149$	1797.47	0.988287	0.494143	+	0.869380i	$0.335482\pi$
$150$	−1611.28	−0.877070
$151$	1471.84	0.793225	0.396612	−	0.917986i	$-0.370186\pi$
$151$	1471.84	0.793225	0.396612	+	0.917986i	$0.370186\pi$
$152$	380.833	0.203221
$153$	−257.232	−0.135921
$154$	375.458	0.196463
$155$	1436.94	0.744629
$156$	11.5884	0.00594755
$157$	2923.20	1.48597	0.742984	−	0.669309i	$-0.233410\pi$
$157$	2923.20	1.48597	0.742984	+	0.669309i	$0.233410\pi$
$158$	−13.7439	−0.00692030
$159$	953.716	0.475689
$160$	−634.816	−0.313667
$161$	161.000	0.0788110
$162$	162.000	0.0785674
$163$	3643.54	1.75082	0.875412	−	0.483378i	$-0.160590\pi$
$163$	3643.54	1.75082	0.875412	+	0.483378i	$0.160590\pi$
$164$	−1111.93	−0.529435
$165$	1596.07	0.753055
$166$	−2312.31	−1.08115
$167$	1151.88	0.533743	0.266872	−	0.963732i	$-0.414010\pi$
$167$	1151.88	0.533743	0.266872	+	0.963732i	$0.414010\pi$
$168$	−168.000	−0.0771517
$169$	−2196.07	−0.999576
$170$	1133.99	0.511607
$171$	428.437	0.191599
$172$	1001.85	0.444131
$173$	−1638.88	−0.720243	−0.360122	−	0.932905i	$-0.617265\pi$
$173$	−1638.88	−0.720243	−0.360122	+	0.932905i	$0.617265\pi$
$174$	−270.189	−0.117718
$175$	1879.83	0.812009
$176$	429.094	0.183774
$177$	−66.9953	−0.0284502
$178$	−2083.19	−0.877199
$179$	942.034	0.393357	0.196678	−	0.980468i	$-0.436984\pi$
$179$	942.034	0.393357	0.196678	+	0.980468i	$0.436984\pi$
$180$	−714.168	−0.295728
$181$	−2814.88	−1.15596	−0.577980	−	0.816051i	$-0.696159\pi$
$181$	−2814.88	−1.15596	−0.577980	+	0.816051i	$0.696159\pi$
$182$	−13.5198	−0.00550636
$183$	1114.82	0.450326
$184$	184.000	0.0737210
$185$	5554.28	2.20734
$186$	434.601	0.171325
$187$	−766.504	−0.299745
$188$	943.500	0.366020
$189$	−189.000	−0.0727393
$190$	−1888.74	−0.721177
$191$	−1388.50	−0.526011	−0.263006	−	0.964794i	$-0.584714\pi$
$191$	−1388.50	−0.526011	−0.263006	+	0.964794i	$0.584714\pi$
$192$	−192.000	−0.0721688
$193$	−1944.37	−0.725173	−0.362587	−	0.931950i	$-0.618106\pi$
$193$	−1944.37	−0.725173	−0.362587	+	0.931950i	$0.618106\pi$
$194$	−2994.57	−1.10824
$195$	−57.4729	−0.0211062
$196$	196.000	0.0714286
$197$	4896.04	1.77070	0.885351	−	0.464924i	$-0.153918\pi$
$197$	4896.04	1.77070	0.885351	+	0.464924i	$0.153918\pi$
$198$	482.731	0.173264
$199$	112.452	0.0400580	0.0200290	−	0.999799i	$-0.493624\pi$
$199$	112.452	0.0400580	0.0200290	+	0.999799i	$0.493624\pi$
$200$	2148.37	0.759565
$201$	−606.490	−0.212828
$202$	−684.265	−0.238340
$203$	315.220	0.108986
$204$	342.975	0.117711
$205$	5514.63	1.87882
$206$	3985.44	1.34795
$207$	207.000	0.0695048
$208$	−15.4512	−0.00515073
$209$	1276.67	0.422530
$210$	833.197	0.273791
$211$	−2291.68	−0.747704	−0.373852	−	0.927488i	$-0.621963\pi$
$211$	−2291.68	−0.747704	−0.373852	+	0.927488i	$0.621963\pi$
$212$	−1271.62	−0.411959
$213$	2398.13	0.771442
$214$	−862.403	−0.275480
$215$	−4968.69	−1.57610
$216$	−216.000	−0.0680414
$217$	−507.034	−0.158616
$218$	238.076	0.0739657
$219$	2037.33	0.628629
$220$	−2128.10	−0.652164
$221$	27.6010	0.00840111
$222$	1679.89	0.507868
$223$	−2838.82	−0.852474	−0.426237	−	0.904612i	$-0.640161\pi$
$223$	−2838.82	−0.852474	−0.426237	+	0.904612i	$0.640161\pi$
$224$	224.000	0.0668153
$225$	2416.92	0.716125
$226$	−4285.00	−1.26121
$227$	−313.228	−0.0915844	−0.0457922	−	0.998951i	$-0.514581\pi$
$227$	−313.228	−0.0915844	−0.0457922	+	0.998951i	$0.514581\pi$
$228$	−571.249	−0.165929
$229$	−1939.65	−0.559720	−0.279860	−	0.960041i	$-0.590288\pi$
$229$	−1939.65	−0.559720	−0.279860	+	0.960041i	$0.590288\pi$
$230$	−912.549	−0.261616
$231$	−563.186	−0.160411
$232$	360.251	0.101947
$233$	−2046.72	−0.575472	−0.287736	−	0.957710i	$-0.592903\pi$
$233$	−2046.72	−0.575472	−0.287736	+	0.957710i	$0.592903\pi$
$234$	−17.3827	−0.00485615
$235$	−4679.29	−1.29891
$236$	89.3271	0.0246386
$237$	20.6159	0.00565040
$238$	−400.138	−0.108979
$239$	−1282.24	−0.347035	−0.173517	−	0.984831i	$-0.555513\pi$
$239$	−1282.24	−0.347035	−0.173517	+	0.984831i	$0.555513\pi$
$240$	952.225	0.256108
$241$	−803.996	−0.214896	−0.107448	−	0.994211i	$-0.534268\pi$
$241$	−803.996	−0.214896	−0.107448	+	0.994211i	$0.534268\pi$
$242$	−1223.55	−0.325011
$243$	−243.000	−0.0641500
$244$	−1486.42	−0.389994
$245$	−972.063	−0.253481
$246$	1667.90	0.432282
$247$	−45.9714	−0.0118425
$248$	−579.468	−0.148372
$249$	3468.47	0.882751
$250$	−5695.37	−1.44083
$251$	2014.62	0.506621	0.253311	−	0.967385i	$-0.418481\pi$
$251$	2014.62	0.506621	0.253311	+	0.967385i	$0.418481\pi$
$252$	252.000	0.0629941
$253$	616.823	0.153278
$254$	−700.312	−0.172998
$255$	−1700.99	−0.417725
$256$	256.000	0.0625000
$257$	−3333.60	−0.809122	−0.404561	−	0.914511i	$-0.632576\pi$
$257$	−3333.60	−0.809122	−0.404561	+	0.914511i	$0.632576\pi$
$258$	−1502.78	−0.362631
$259$	−1959.87	−0.470195
$260$	76.6305	0.0182785
$261$	405.283	0.0961164
$262$	−3567.55	−0.841238
$263$	−497.356	−0.116609	−0.0583047	−	0.998299i	$-0.518570\pi$
$263$	−497.356	−0.116609	−0.0583047	+	0.998299i	$0.518570\pi$
$264$	−643.642	−0.150051
$265$	6306.61	1.46193
$266$	666.457	0.153621
$267$	3124.78	0.716230
$268$	808.653	0.184315
$269$	−4487.00	−1.01702	−0.508508	−	0.861057i	$-0.669803\pi$
$269$	−4487.00	−1.01702	−0.508508	+	0.861057i	$0.669803\pi$
$270$	1071.25	0.241461
$271$	4143.75	0.928838	0.464419	−	0.885616i	$-0.346263\pi$
$271$	4143.75	0.928838	0.464419	+	0.885616i	$0.346263\pi$
$272$	−457.300	−0.101941
$273$	20.2798	0.00449592
$274$	−2125.97	−0.468740
$275$	7202.00	1.57926
$276$	−276.000	−0.0601929
$277$	3556.41	0.771423	0.385711	−	0.922620i	$-0.373956\pi$
$277$	3556.41	0.771423	0.385711	+	0.922620i	$0.373956\pi$
$278$	4294.93	0.926592
$279$	−651.901	−0.139886
$280$	−1110.93	−0.237110
$281$	−2081.63	−0.441920	−0.220960	−	0.975283i	$-0.570919\pi$
$281$	−2081.63	−0.441920	−0.220960	+	0.975283i	$0.570919\pi$
$282$	−1415.25	−0.298854
$283$	−2866.78	−0.602165	−0.301082	−	0.953598i	$-0.597348\pi$
$283$	−2866.78	−0.602165	−0.301082	+	0.953598i	$0.597348\pi$
$284$	−3197.51	−0.668088
$285$	2833.11	0.588839
$286$	−51.7972	−0.0107092
$287$	−1945.88	−0.400215
$288$	288.000	0.0589256
$289$	−4096.11	−0.833729
$290$	−1786.67	−0.361782
$291$	4491.86	0.904870
$292$	−2716.43	−0.544409
$293$	712.314	0.142027	0.0710133	−	0.997475i	$-0.477377\pi$
$293$	712.314	0.142027	0.0710133	+	0.997475i	$0.477377\pi$
$294$	−294.000	−0.0583212
$295$	−443.018	−0.0874356
$296$	−2239.85	−0.439827
$297$	−724.097	−0.141469
$298$	3594.95	0.698824
$299$	−22.2112	−0.00429600
$300$	−3222.56	−0.620182
$301$	1753.24	0.335731
$302$	2943.69	0.560894
$303$	1026.40	0.194604
$304$	761.665	0.143699
$305$	7371.92	1.38398
$306$	−514.463	−0.0961108
$307$	−4231.30	−0.786622	−0.393311	−	0.919406i	$-0.628670\pi$
$307$	−4231.30	−0.786622	−0.393311	+	0.919406i	$0.628670\pi$
$308$	750.915	0.138920
$309$	−5978.15	−1.10060
$310$	2873.87	0.526532
$311$	−4399.78	−0.802215	−0.401107	−	0.916031i	$-0.631375\pi$
$311$	−4399.78	−0.802215	−0.401107	+	0.916031i	$0.631375\pi$
$312$	23.1769	0.00420555
$313$	1220.67	0.220435	0.110217	−	0.993907i	$-0.464845\pi$
$313$	1220.67	0.220435	0.110217	+	0.993907i	$0.464845\pi$
$314$	5846.41	1.05074
$315$	−1249.79	−0.223549
$316$	−27.4878	−0.00489339
$317$	8372.44	1.48342	0.741708	−	0.670723i	$-0.234016\pi$
$317$	8372.44	1.48342	0.741708	+	0.670723i	$0.234016\pi$
$318$	1907.43	0.336363
$319$	1207.67	0.211964
$320$	−1269.63	−0.221796
$321$	1293.60	0.224928
$322$	322.000	0.0557278
$323$	−1360.59	−0.234381
$324$	324.000	0.0555556
$325$	−259.336	−0.0442628
$326$	7287.08	1.23802
$327$	−357.113	−0.0603927
$328$	−2223.87	−0.374367
$329$	1651.13	0.276685
$330$	3192.14	0.532490
$331$	5367.71	0.891348	0.445674	−	0.895195i	$-0.352964\pi$
$331$	5367.71	0.891348	0.445674	+	0.895195i	$0.352964\pi$
$332$	−4624.62	−0.764485
$333$	−2519.83	−0.414673
$334$	2303.76	0.377414
$335$	−4010.52	−0.654083
$336$	−336.000	−0.0545545
$337$	−3472.49	−0.561301	−0.280651	−	0.959810i	$-0.590550\pi$
$337$	−3472.49	−0.561301	−0.280651	+	0.959810i	$0.590550\pi$
$338$	−4392.13	−0.706807
$339$	6427.50	1.02977
$340$	2267.98	0.361761
$341$	−1942.55	−0.308490
$342$	856.874	0.135481
$343$	343.000	0.0539949
$344$	2003.70	0.314048
$345$	1368.82	0.213609
$346$	−3277.77	−0.509289
$347$	−4689.86	−0.725547	−0.362773	−	0.931877i	$-0.618170\pi$
$347$	−4689.86	−0.725547	−0.362773	+	0.931877i	$0.618170\pi$
$348$	−540.377	−0.0832392
$349$	−640.378	−0.0982197	−0.0491098	−	0.998793i	$-0.515638\pi$
$349$	−640.378	−0.0982197	−0.0491098	+	0.998793i	$0.515638\pi$
$350$	3759.66	0.574177
$351$	26.0740	0.00396503
$352$	858.189	0.129948
$353$	9757.17	1.47117	0.735583	−	0.677435i	$-0.236908\pi$
$353$	9757.17	1.47117	0.735583	+	0.677435i	$0.236908\pi$
$354$	−133.991	−0.0201173
$355$	15858.0	2.37087
$356$	−4166.37	−0.620274
$357$	600.207	0.0889813
$358$	1884.07	0.278145
$359$	−2083.73	−0.306337	−0.153168	−	0.988200i	$-0.548948\pi$
$359$	−2083.73	−0.306337	−0.153168	+	0.988200i	$0.548948\pi$
$360$	−1428.34	−0.209111
$361$	−4592.85	−0.669609
$362$	−5629.77	−0.817387
$363$	1835.32	0.265370
$364$	−27.0397	−0.00389358
$365$	13472.2	1.93196
$366$	2229.63	0.318428
$367$	10190.5	1.44942	0.724711	−	0.689053i	$-0.241973\pi$
$367$	10190.5	1.44942	0.724711	+	0.689053i	$0.241973\pi$
$368$	368.000	0.0521286
$369$	−2501.85	−0.352957
$370$	11108.6	1.56083
$371$	−2225.34	−0.311412
$372$	869.201	0.121145
$373$	320.275	0.0444590	0.0222295	−	0.999753i	$-0.492924\pi$
$373$	320.275	0.0444590	0.0222295	+	0.999753i	$0.492924\pi$
$374$	−1533.01	−0.211952
$375$	8543.05	1.17643
$376$	1887.00	0.258816
$377$	−43.4870	−0.00594083
$378$	−378.000	−0.0514344
$379$	−13773.7	−1.86677	−0.933385	−	0.358876i	$-0.883160\pi$
$379$	−13773.7	−1.86677	−0.933385	+	0.358876i	$0.883160\pi$
$380$	−3777.48	−0.509949
$381$	1050.47	0.141252
$382$	−2776.99	−0.371946
$383$	6285.20	0.838535	0.419267	−	0.907863i	$-0.362287\pi$
$383$	6285.20	0.838535	0.419267	+	0.907863i	$0.362287\pi$
$384$	−384.000	−0.0510310
$385$	−3724.17	−0.492990
$386$	−3888.73	−0.512775
$387$	2254.17	0.296087
$388$	−5989.14	−0.783641
$389$	−12246.1	−1.59615	−0.798075	−	0.602559i	$-0.794148\pi$
$389$	−12246.1	−1.59615	−0.798075	+	0.602559i	$0.794148\pi$
$390$	−114.946	−0.0149244
$391$	−657.369	−0.0850246
$392$	392.000	0.0505076
$393$	5351.33	0.686868
$394$	9792.07	1.25208
$395$	136.326	0.0173653
$396$	965.463	0.122516
$397$	5856.50	0.740376	0.370188	−	0.928957i	$-0.379293\pi$
$397$	5856.50	0.740376	0.370188	+	0.928957i	$0.379293\pi$
$398$	224.905	0.0283253
$399$	−999.686	−0.125431
$400$	4296.75	0.537094
$401$	−6152.98	−0.766247	−0.383124	−	0.923697i	$-0.625152\pi$
$401$	−6152.98	−0.766247	−0.383124	+	0.923697i	$0.625152\pi$
$402$	−1212.98	−0.150492
$403$	69.9492	0.00864620
$404$	−1368.53	−0.168532
$405$	−1606.88	−0.197152
$406$	630.440	0.0770646
$407$	−7508.66	−0.914473
$408$	685.951	0.0832344
$409$	8734.92	1.05602	0.528012	−	0.849237i	$-0.322938\pi$
$409$	8734.92	1.05602	0.528012	+	0.849237i	$0.322938\pi$
$410$	11029.3	1.32853
$411$	3188.96	0.382725
$412$	7970.87	0.953147
$413$	156.322	0.0186250
$414$	414.000	0.0491473
$415$	22935.8	2.71295
$416$	−30.9025	−0.00364211
$417$	−6442.39	−0.756559
$418$	2553.33	0.298774
$419$	490.282	0.0571643	0.0285822	−	0.999591i	$-0.490901\pi$
$419$	490.282	0.0571643	0.0285822	+	0.999591i	$0.490901\pi$
$420$	1666.39	0.193599
$421$	1006.87	0.116560	0.0582801	−	0.998300i	$-0.481438\pi$
$421$	1006.87	0.116560	0.0582801	+	0.998300i	$0.481438\pi$
$422$	−4583.35	−0.528707
$423$	2122.88	0.244014
$424$	−2543.24	−0.291299
$425$	−7675.41	−0.876029
$426$	4796.26	0.545492
$427$	−2601.24	−0.294807
$428$	−1724.81	−0.194794
$429$	77.6958	0.00874403
$430$	−9937.37	−1.11447
$431$	1290.34	0.144208	0.0721041	−	0.997397i	$-0.477029\pi$
$431$	1290.34	0.144208	0.0721041	+	0.997397i	$0.477029\pi$
$432$	−432.000	−0.0481125
$433$	−1652.97	−0.183457	−0.0917285	−	0.995784i	$-0.529239\pi$
$433$	−1652.97	−0.183457	−0.0917285	+	0.995784i	$0.529239\pi$
$434$	−1014.07	−0.112159
$435$	2680.00	0.295394
$436$	476.151	0.0523016
$437$	1094.89	0.119853
$438$	4074.65	0.444508
$439$	9497.37	1.03254	0.516269	−	0.856426i	$-0.327320\pi$
$439$	9497.37	1.03254	0.516269	+	0.856426i	$0.327320\pi$
$440$	−4256.19	−0.461150
$441$	441.000	0.0476190
$442$	55.2020	0.00594048
$443$	−7328.21	−0.785945	−0.392973	−	0.919550i	$-0.628553\pi$
$443$	−7328.21	−0.785945	−0.392973	+	0.919550i	$0.628553\pi$
$444$	3359.78	0.359117
$445$	20663.1	2.20118
$446$	−5677.65	−0.602790
$447$	−5392.42	−0.570588
$448$	448.000	0.0472456
$449$	3041.57	0.319690	0.159845	−	0.987142i	$-0.448901\pi$
$449$	3041.57	0.319690	0.159845	+	0.987142i	$0.448901\pi$
$450$	4833.84	0.506377
$451$	−7455.07	−0.778371
$452$	−8570.00	−0.891811
$453$	−4415.53	−0.457968
$454$	−626.455	−0.0647599
$455$	134.103	0.0138173
$456$	−1142.50	−0.117330
$457$	−3099.76	−0.317288	−0.158644	−	0.987336i	$-0.550712\pi$
$457$	−3099.76	−0.317288	−0.158644	+	0.987336i	$0.550712\pi$
$458$	−3879.31	−0.395782
$459$	771.695	0.0784741
$460$	−1825.10	−0.184990
$461$	−12302.7	−1.24294	−0.621469	−	0.783439i	$-0.713464\pi$
$461$	−12302.7	−1.24294	−0.621469	+	0.783439i	$0.713464\pi$
$462$	−1126.37	−0.113428
$463$	−689.961	−0.0692553	−0.0346277	−	0.999400i	$-0.511025\pi$
$463$	−689.961	−0.0692553	−0.0346277	+	0.999400i	$0.511025\pi$
$464$	720.503	0.0720873
$465$	−4310.81	−0.429912
$466$	−4093.44	−0.406920
$467$	7621.67	0.755222	0.377611	−	0.925964i	$-0.376746\pi$
$467$	7621.67	0.755222	0.377611	+	0.925964i	$0.376746\pi$
$468$	−34.7653	−0.00343382
$469$	1415.14	0.139329
$470$	−9358.59	−0.918467
$471$	−8769.61	−0.857924
$472$	178.654	0.0174221
$473$	6717.02	0.652957
$474$	41.2318	0.00399544
$475$	12783.9	1.23488
$476$	−800.276	−0.0770600
$477$	−2861.15	−0.274639
$478$	−2564.48	−0.245391
$479$	−14314.2	−1.36541	−0.682706	−	0.730693i	$-0.739197\pi$
$479$	−14314.2	−1.36541	−0.682706	+	0.730693i	$0.739197\pi$
$480$	1904.45	0.181095
$481$	270.379	0.0256304
$482$	−1607.99	−0.151954
$483$	−483.000	−0.0455016
$484$	−2447.09	−0.229817
$485$	29703.2	2.78093
$486$	−486.000	−0.0453609
$487$	−1894.46	−0.176275	−0.0881376	−	0.996108i	$-0.528092\pi$
$487$	−1894.46	−0.176275	−0.0881376	+	0.996108i	$0.528092\pi$
$488$	−2972.84	−0.275767
$489$	−10930.6	−1.01084
$490$	−1944.13	−0.179238
$491$	11703.7	1.07573	0.537864	−	0.843031i	$-0.319231\pi$
$491$	11703.7	1.07573	0.537864	+	0.843031i	$0.319231\pi$
$492$	3335.80	0.305670
$493$	−1287.06	−0.117578
$494$	−91.9428	−0.00837389
$495$	−4788.21	−0.434776
$496$	−1158.94	−0.104915
$497$	−5595.64	−0.505027
$498$	6936.93	0.624199
$499$	468.477	0.0420279	0.0210139	−	0.999779i	$-0.493311\pi$
$499$	468.477	0.0420279	0.0210139	+	0.999779i	$0.493311\pi$
$500$	−11390.7	−1.01882
$501$	−3455.64	−0.308157
$502$	4029.25	0.358235
$503$	−16590.2	−1.47062	−0.735311	−	0.677730i	$-0.762964\pi$
$503$	−16590.2	−1.47062	−0.735311	+	0.677730i	$0.762964\pi$
$504$	504.000	0.0445435
$505$	6787.23	0.598075
$506$	1233.65	0.108384
$507$	6588.20	0.577105
$508$	−1400.62	−0.122328
$509$	−2286.85	−0.199141	−0.0995705	−	0.995031i	$-0.531747\pi$
$509$	−2286.85	−0.199141	−0.0995705	+	0.995031i	$0.531747\pi$
$510$	−3401.97	−0.295376
$511$	−4753.76	−0.411534
$512$	512.000	0.0441942
$513$	−1285.31	−0.110620
$514$	−6667.21	−0.572136
$515$	−39531.6	−3.38246
$516$	−3005.56	−0.256419
$517$	6325.79	0.538120
$518$	−3919.74	−0.332478
$519$	4916.65	0.415833
$520$	153.261	0.0129249
$521$	1616.45	0.135927	0.0679636	−	0.997688i	$-0.478350\pi$
$521$	1616.45	0.135927	0.0679636	+	0.997688i	$0.478350\pi$
$522$	810.566	0.0679646
$523$	−4492.34	−0.375596	−0.187798	−	0.982208i	$-0.560135\pi$
$523$	−4492.34	−0.375596	−0.187798	+	0.982208i	$0.560135\pi$
$524$	−7135.11	−0.594845
$525$	−5639.48	−0.468814
$526$	−994.712	−0.0824554
$527$	2070.24	0.171122
$528$	−1287.28	−0.106102
$529$	529.000	0.0434783
$530$	12613.2	1.03374
$531$	200.986	0.0164257
$532$	1332.91	0.108626
$533$	268.449	0.0218158
$534$	6249.56	0.506451
$535$	8554.18	0.691270
$536$	1617.31	0.130330
$537$	−2826.10	−0.227105
$538$	−8974.00	−0.719139
$539$	1314.10	0.105014
$540$	2142.51	0.170738
$541$	20585.1	1.63590	0.817952	−	0.575286i	$-0.195109\pi$
$541$	20585.1	1.63590	0.817952	+	0.575286i	$0.195109\pi$
$542$	8287.51	0.656788
$543$	8444.65	0.667394
$544$	−914.601	−0.0720831
$545$	−2361.47	−0.185604
$546$	40.5595	0.00317910
$547$	−8609.28	−0.672954	−0.336477	−	0.941692i	$-0.609236\pi$
$547$	−8609.28	−0.672954	−0.336477	+	0.941692i	$0.609236\pi$
$548$	−4251.95	−0.331449
$549$	−3344.45	−0.259996
$550$	14404.0	1.11671
$551$	2143.68	0.165742
$552$	−552.000	−0.0425628
$553$	−48.1037	−0.00369906
$554$	7112.82	0.545478
$555$	−16662.8	−1.27441
$556$	8589.86	0.655200
$557$	−6153.91	−0.468132	−0.234066	−	0.972221i	$-0.575203\pi$
$557$	−6153.91	−0.468132	−0.234066	+	0.972221i	$0.575203\pi$
$558$	−1303.80	−0.0989146
$559$	−241.873	−0.0183008
$560$	−2221.86	−0.167662
$561$	2299.51	0.173058
$562$	−4163.26	−0.312485
$563$	−10096.0	−0.755764	−0.377882	−	0.925854i	$-0.623347\pi$
$563$	−10096.0	−0.755764	−0.377882	+	0.925854i	$0.623347\pi$
$564$	−2830.50	−0.211322
$565$	42502.9	3.16480
$566$	−5733.57	−0.425795
$567$	567.000	0.0419961
$568$	−6395.01	−0.472410
$569$	10448.2	0.769790	0.384895	−	0.922960i	$-0.374238\pi$
$569$	10448.2	0.769790	0.384895	+	0.922960i	$0.374238\pi$
$570$	5666.22	0.416372
$571$	−13124.9	−0.961925	−0.480963	−	0.876741i	$-0.659713\pi$
$571$	−13124.9	−0.961925	−0.480963	+	0.876741i	$0.659713\pi$
$572$	−103.594	−0.00757255
$573$	4165.49	0.303693
$574$	−3891.77	−0.282995
$575$	6176.58	0.447967
$576$	576.000	0.0416667
$577$	−11549.5	−0.833296	−0.416648	−	0.909068i	$-0.636795\pi$
$577$	−11549.5	−0.833296	−0.416648	+	0.909068i	$0.636795\pi$
$578$	−8192.22	−0.589535
$579$	5833.10	0.418679
$580$	−3573.34	−0.255818
$581$	−8093.09	−0.577896
$582$	8983.71	0.639840
$583$	−8525.71	−0.605659
$584$	−5432.87	−0.384955
$585$	172.419	0.0121857
$586$	1424.63	0.100428
$587$	−7532.02	−0.529608	−0.264804	−	0.964302i	$-0.585307\pi$
$587$	−7532.02	−0.529608	−0.264804	+	0.964302i	$0.585307\pi$
$588$	−588.000	−0.0412393
$589$	−3448.13	−0.241218
$590$	−886.036	−0.0618263
$591$	−14688.1	−1.02232
$592$	−4479.70	−0.311005
$593$	17953.5	1.24327	0.621636	−	0.783306i	$-0.286468\pi$
$593$	17953.5	1.24327	0.621636	+	0.783306i	$0.286468\pi$
$594$	−1448.19	−0.100034
$595$	3968.97	0.273465
$596$	7189.89	0.494143
$597$	−337.357	−0.0231275
$598$	−44.4223	−0.00303773
$599$	−15317.9	−1.04486	−0.522432	−	0.852681i	$-0.674975\pi$
$599$	−15317.9	−1.04486	−0.522432	+	0.852681i	$0.674975\pi$
$600$	−6445.12	−0.438535
$601$	17886.6	1.21399	0.606997	−	0.794704i	$-0.292374\pi$
$601$	17886.6	1.21399	0.606997	+	0.794704i	$0.292374\pi$
$602$	3506.48	0.237398
$603$	1819.47	0.122876
$604$	5887.37	0.396612
$605$	12136.4	0.815559
$606$	2052.80	0.137606
$607$	−8400.35	−0.561713	−0.280856	−	0.959750i	$-0.590618\pi$
$607$	−8400.35	−0.561713	−0.280856	+	0.959750i	$0.590618\pi$
$608$	1523.33	0.101611
$609$	−945.660	−0.0629230
$610$	14743.8	0.978623
$611$	−227.785	−0.0150822
$612$	−1028.93	−0.0679606
$613$	10791.6	0.711043	0.355521	−	0.934668i	$-0.384303\pi$
$613$	10791.6	0.711043	0.355521	+	0.934668i	$0.384303\pi$
$614$	−8462.59	−0.556225
$615$	−16543.9	−1.08474
$616$	1501.83	0.0982313
$617$	3489.39	0.227678	0.113839	−	0.993499i	$-0.463685\pi$
$617$	3489.39	0.227678	0.113839	+	0.993499i	$0.463685\pi$
$618$	−11956.3	−0.778241
$619$	−17516.3	−1.13738	−0.568690	−	0.822552i	$-0.692550\pi$
$619$	−17516.3	−1.13738	−0.568690	+	0.822552i	$0.692550\pi$
$620$	5747.74	0.372314
$621$	−621.000	−0.0401286
$622$	−8799.56	−0.567251
$623$	−7291.16	−0.468883
$624$	46.3537	0.00297377
$625$	22924.0	1.46714
$626$	2441.33	0.155871
$627$	−3830.00	−0.243948
$628$	11692.8	0.742984
$629$	8002.23	0.507265
$630$	−2499.59	−0.158073
$631$	−5448.24	−0.343726	−0.171863	−	0.985121i	$-0.554979\pi$
$631$	−5448.24	−0.343726	−0.171863	+	0.985121i	$0.554979\pi$
$632$	−54.9757	−0.00346015
$633$	6875.03	0.431687
$634$	16744.9	1.04893
$635$	6946.40	0.434110
$636$	3814.86	0.237845
$637$	−47.3194	−0.00294327
$638$	2415.34	0.149881
$639$	−7194.39	−0.445392
$640$	−2539.27	−0.156833
$641$	−12207.0	−0.752181	−0.376091	−	0.926583i	$-0.622732\pi$
$641$	−12207.0	−0.752181	−0.376091	+	0.926583i	$0.622732\pi$
$642$	2587.21	0.159048
$643$	21385.9	1.31163	0.655815	−	0.754922i	$-0.272325\pi$
$643$	21385.9	1.31163	0.655815	+	0.754922i	$0.272325\pi$
$644$	644.000	0.0394055
$645$	14906.1	0.909962
$646$	−2721.17	−0.165732
$647$	−8976.86	−0.545466	−0.272733	−	0.962090i	$-0.587928\pi$
$647$	−8976.86	−0.545466	−0.272733	+	0.962090i	$0.587928\pi$
$648$	648.000	0.0392837
$649$	598.903	0.0362234
$650$	−518.673	−0.0312985
$651$	1521.10	0.0915771
$652$	14574.2	0.875412
$653$	27676.1	1.65858	0.829289	−	0.558820i	$-0.188746\pi$
$653$	27676.1	1.65858	0.829289	+	0.558820i	$0.188746\pi$
$654$	−714.227	−0.0427041
$655$	35386.6	2.11094
$656$	−4447.73	−0.264718
$657$	−6111.98	−0.362939
$658$	3302.25	0.195646
$659$	8535.56	0.504549	0.252275	−	0.967656i	$-0.418821\pi$
$659$	8535.56	0.504549	0.252275	+	0.967656i	$0.418821\pi$
$660$	6384.29	0.376527
$661$	−11001.6	−0.647373	−0.323686	−	0.946164i	$-0.604922\pi$
$661$	−11001.6	−0.647373	−0.323686	+	0.946164i	$0.604922\pi$
$662$	10735.4	0.630278
$663$	−82.8031	−0.00485038
$664$	−9249.24	−0.540573
$665$	−6610.59	−0.385485
$666$	−5039.67	−0.293218
$667$	1035.72	0.0601250
$668$	4607.52	0.266872
$669$	8516.47	0.492176
$670$	−8021.03	−0.462507
$671$	−9965.87	−0.573365
$672$	−672.000	−0.0385758
$673$	−14714.2	−0.842780	−0.421390	−	0.906880i	$-0.638458\pi$
$673$	−14714.2	−0.842780	−0.421390	+	0.906880i	$0.638458\pi$
$674$	−6944.98	−0.396900
$675$	−7250.76	−0.413455
$676$	−8784.27	−0.499788
$677$	−13873.0	−0.787565	−0.393783	−	0.919204i	$-0.628834\pi$
$677$	−13873.0	−0.787565	−0.393783	+	0.919204i	$0.628834\pi$
$678$	12855.0	0.728161
$679$	−10481.0	−0.592377
$680$	4535.97	0.255803
$681$	939.683	0.0528763
$682$	−3885.10	−0.218135
$683$	20421.6	1.14408	0.572042	−	0.820225i	$-0.306152\pi$
$683$	20421.6	1.14408	0.572042	+	0.820225i	$0.306152\pi$
$684$	1713.75	0.0957994
$685$	21087.6	1.17622
$686$	686.000	0.0381802
$687$	5818.96	0.323155
$688$	4007.41	0.222065
$689$	307.002	0.0169751
$690$	2737.65	0.151044
$691$	31315.9	1.72404	0.862020	−	0.506875i	$-0.169199\pi$
$691$	31315.9	1.72404	0.862020	+	0.506875i	$0.169199\pi$
$692$	−6555.54	−0.360122
$693$	1689.56	0.0926134
$694$	−9379.72	−0.513039
$695$	−42601.4	−2.32513
$696$	−1080.75	−0.0588590
$697$	7945.12	0.431769
$698$	−1280.76	−0.0694518
$699$	6140.15	0.332249
$700$	7519.31	0.406005
$701$	−1445.86	−0.0779023	−0.0389512	−	0.999241i	$-0.512402\pi$
$701$	−1445.86	−0.0779023	−0.0389512	+	0.999241i	$0.512402\pi$
$702$	52.1480	0.00280370
$703$	−13328.3	−0.715057
$704$	1716.38	0.0918870
$705$	14037.9	0.749925
$706$	19514.3	1.04027
$707$	−2394.93	−0.127398
$708$	−267.981	−0.0142251
$709$	−28250.1	−1.49641	−0.748206	−	0.663466i	$-0.769085\pi$
$709$	−28250.1	−1.49641	−0.748206	+	0.663466i	$0.769085\pi$
$710$	31716.1	1.67646
$711$	−61.8476	−0.00326226
$712$	−8332.75	−0.438600
$713$	−1665.97	−0.0875050
$714$	1200.41	0.0629193
$715$	513.777	0.0268730
$716$	3768.13	0.196678
$717$	3846.72	0.200361
$718$	−4167.46	−0.216613
$719$	33658.0	1.74580	0.872900	−	0.487899i	$-0.162237\pi$
$719$	33658.0	1.74580	0.872900	+	0.487899i	$0.162237\pi$
$720$	−2856.67	−0.147864
$721$	13949.0	0.720512
$722$	−9185.70	−0.473485
$723$	2411.99	0.124070
$724$	−11259.5	−0.577980
$725$	12093.0	0.619482
$726$	3670.64	0.187645
$727$	−6480.35	−0.330596	−0.165298	−	0.986244i	$-0.552859\pi$
$727$	−6480.35	−0.330596	−0.165298	+	0.986244i	$0.552859\pi$
$728$	−54.0794	−0.00275318
$729$	729.000	0.0370370
$730$	26944.3	1.36610
$731$	−7158.55	−0.362201
$732$	4459.27	0.225163
$733$	15752.1	0.793746	0.396873	−	0.917874i	$-0.370095\pi$
$733$	15752.1	0.793746	0.396873	+	0.917874i	$0.370095\pi$
$734$	20380.9	1.02490
$735$	2916.19	0.146347
$736$	736.000	0.0368605
$737$	5421.69	0.270978
$738$	−5003.70	−0.249578
$739$	−21764.5	−1.08338	−0.541691	−	0.840578i	$-0.682216\pi$
$739$	−21764.5	−1.08338	−0.541691	+	0.840578i	$0.682216\pi$
$740$	22217.1	1.10367
$741$	137.914	0.00683725
$742$	−4450.68	−0.220201
$743$	−21585.0	−1.06578	−0.532891	−	0.846184i	$-0.678894\pi$
$743$	−21585.0	−1.06578	−0.532891	+	0.846184i	$0.678894\pi$
$744$	1738.40	0.0856626
$745$	−35658.3	−1.75358
$746$	640.551	0.0314373
$747$	−10405.4	−0.509657
$748$	−3066.02	−0.149873
$749$	−3018.41	−0.147250
$750$	17086.1	0.831862
$751$	33961.7	1.65017	0.825087	−	0.565006i	$-0.191126\pi$
$751$	33961.7	1.65017	0.825087	+	0.565006i	$0.191126\pi$
$752$	3774.00	0.183010
$753$	−6043.87	−0.292498
$754$	−86.9740	−0.00420080
$755$	−29198.4	−1.40747
$756$	−756.000	−0.0363696
$757$	−10142.7	−0.486978	−0.243489	−	0.969904i	$-0.578292\pi$
$757$	−10142.7	−0.486978	−0.243489	+	0.969904i	$0.578292\pi$
$758$	−27547.3	−1.32001
$759$	−1850.47	−0.0884951
$760$	−7554.96	−0.360589
$761$	33164.5	1.57978	0.789889	−	0.613249i	$-0.210138\pi$
$761$	33164.5	1.57978	0.789889	+	0.613249i	$0.210138\pi$
$762$	2100.94	0.0998805
$763$	833.265	0.0395363
$764$	−5553.99	−0.263006
$765$	5102.96	0.241174
$766$	12570.4	0.592934
$767$	−21.5659	−0.00101525
$768$	−768.000	−0.0360844
$769$	36946.2	1.73253	0.866263	−	0.499589i	$-0.166515\pi$
$769$	36946.2	1.73253	0.866263	+	0.499589i	$0.166515\pi$
$770$	−7448.33	−0.348597
$771$	10000.8	0.467147
$772$	−7777.46	−0.362587
$773$	10293.7	0.478962	0.239481	−	0.970901i	$-0.423023\pi$
$773$	10293.7	0.478962	0.239481	+	0.970901i	$0.423023\pi$
$774$	4508.33	0.209365
$775$	−19451.8	−0.901585
$776$	−11978.3	−0.554118
$777$	5879.61	0.271467
$778$	−24492.2	−1.12865
$779$	−13233.1	−0.608635
$780$	−229.892	−0.0105531
$781$	−21438.0	−0.982218
$782$	−1314.74	−0.0601214
$783$	−1215.85	−0.0554928
$784$	784.000	0.0357143
$785$	−57990.6	−2.63665
$786$	10702.7	0.485689
$787$	−28119.6	−1.27364	−0.636820	−	0.771012i	$-0.719751\pi$
$787$	−28119.6	−1.27364	−0.636820	+	0.771012i	$0.719751\pi$
$788$	19584.1	0.885351
$789$	1492.07	0.0673245
$790$	272.652	0.0122791
$791$	−14997.5	−0.674146
$792$	1930.93	0.0866319
$793$	358.861	0.0160700
$794$	11713.0	0.523525
$795$	−18919.8	−0.844047
$796$	449.810	0.0200290
$797$	−15719.9	−0.698654	−0.349327	−	0.937001i	$-0.613590\pi$
$797$	−15719.9	−0.698654	−0.349327	+	0.937001i	$0.613590\pi$
$798$	−1999.37	−0.0886930
$799$	−6741.61	−0.298500
$800$	8593.50	0.379783
$801$	−9374.34	−0.413516
$802$	−12306.0	−0.541819
$803$	−18212.6	−0.800385
$804$	−2425.96	−0.106414
$805$	−3193.92	−0.139840
$806$	139.898	0.00611378
$807$	13461.0	0.587174
$808$	−2737.06	−0.119170
$809$	−23241.7	−1.01005	−0.505027	−	0.863104i	$-0.668517\pi$
$809$	−23241.7	−1.01005	−0.505027	+	0.863104i	$0.668517\pi$
$810$	−3213.76	−0.139407
$811$	12218.8	0.529050	0.264525	−	0.964379i	$-0.414785\pi$
$811$	12218.8	0.529050	0.264525	+	0.964379i	$0.414785\pi$
$812$	1260.88	0.0544929
$813$	−12431.3	−0.536265
$814$	−15017.3	−0.646630
$815$	−72280.6	−3.10660
$816$	1371.90	0.0588556
$817$	11923.1	0.510569
$818$	17469.8	0.746722
$819$	−60.8393	−0.00259572
$820$	22058.5	0.939412
$821$	41817.6	1.77764	0.888822	−	0.458253i	$-0.151525\pi$
$821$	41817.6	1.77764	0.888822	+	0.458253i	$0.151525\pi$
$822$	6377.92	0.270627
$823$	15749.3	0.667053	0.333526	−	0.942741i	$-0.391761\pi$
$823$	15749.3	0.667053	0.333526	+	0.942741i	$0.391761\pi$
$824$	15941.7	0.673977
$825$	−21606.0	−0.911787
$826$	312.645	0.0131699
$827$	−8286.79	−0.348440	−0.174220	−	0.984707i	$-0.555740\pi$
$827$	−8286.79	−0.348440	−0.174220	+	0.984707i	$0.555740\pi$
$828$	828.000	0.0347524
$829$	−45360.8	−1.90042	−0.950208	−	0.311615i	$-0.899130\pi$
$829$	−45360.8	−1.90042	−0.950208	+	0.311615i	$0.899130\pi$
$830$	45871.6	1.91835
$831$	−10669.2	−0.445381
$832$	−61.8050	−0.00257536
$833$	−1400.48	−0.0582519
$834$	−12884.8	−0.534968
$835$	−22851.0	−0.947056
$836$	5106.66	0.211265
$837$	1955.70	0.0807634
$838$	980.565	0.0404213
$839$	−885.055	−0.0364190	−0.0182095	−	0.999834i	$-0.505797\pi$
$839$	−885.055	−0.0364190	−0.0182095	+	0.999834i	$0.505797\pi$
$840$	3332.79	0.136895
$841$	−22361.2	−0.916855
$842$	2013.74	0.0824206
$843$	6244.88	0.255143
$844$	−9166.71	−0.373852
$845$	43565.6	1.77361
$846$	4245.75	0.172544
$847$	−4282.41	−0.173725
$848$	−5086.49	−0.205980
$849$	8600.35	0.347660
$850$	−15350.8	−0.619446
$851$	−6439.58	−0.259396
$852$	9592.52	0.385721
$853$	43719.4	1.75489	0.877446	−	0.479676i	$-0.159246\pi$
$853$	43719.4	1.75489	0.877446	+	0.479676i	$0.159246\pi$
$854$	−5202.48	−0.208460
$855$	−8499.33	−0.339966
$856$	−3449.61	−0.137740
$857$	−28309.4	−1.12839	−0.564196	−	0.825641i	$-0.690814\pi$
$857$	−28309.4	−1.12839	−0.564196	+	0.825641i	$0.690814\pi$
$858$	155.392	0.00618296
$859$	43509.6	1.72820	0.864102	−	0.503317i	$-0.167887\pi$
$859$	43509.6	1.72820	0.864102	+	0.503317i	$0.167887\pi$
$860$	−19874.7	−0.788050
$861$	5837.65	0.231064
$862$	2580.69	0.101971
$863$	10119.9	0.399174	0.199587	−	0.979880i	$-0.436040\pi$
$863$	10119.9	0.399174	0.199587	+	0.979880i	$0.436040\pi$
$864$	−864.000	−0.0340207
$865$	32512.2	1.27797
$866$	−3305.95	−0.129724
$867$	12288.3	0.481354
$868$	−2028.14	−0.0793081
$869$	−184.295	−0.00719422
$870$	5360.00	0.208875
$871$	−195.230	−0.00759484
$872$	952.303	0.0369828
$873$	−13475.6	−0.522427
$874$	2189.79	0.0847491
$875$	−19933.8	−0.770154
$876$	8149.30	0.314314
$877$	−37288.9	−1.43575	−0.717877	−	0.696170i	$-0.754886\pi$
$877$	−37288.9	−1.43575	−0.717877	+	0.696170i	$0.754886\pi$
$878$	18994.7	0.730115
$879$	−2136.94	−0.0819991
$880$	−8512.38	−0.326082
$881$	−26106.1	−0.998340	−0.499170	−	0.866504i	$-0.666362\pi$
$881$	−26106.1	−0.998340	−0.499170	+	0.866504i	$0.666362\pi$
$882$	882.000	0.0336718
$883$	−25866.9	−0.985835	−0.492917	−	0.870076i	$-0.664069\pi$
$883$	−25866.9	−0.985835	−0.492917	+	0.870076i	$0.664069\pi$
$884$	110.404	0.00420056
$885$	1329.05	0.0504810
$886$	−14656.4	−0.555747
$887$	−19836.2	−0.750884	−0.375442	−	0.926846i	$-0.622509\pi$
$887$	−19836.2	−0.750884	−0.375442	+	0.926846i	$0.622509\pi$
$888$	6719.56	0.253934
$889$	−2451.09	−0.0924714
$890$	41326.3	1.55647
$891$	2172.29	0.0816773
$892$	−11355.3	−0.426237
$893$	11228.6	0.420774
$894$	−10784.8	−0.403466
$895$	−18688.1	−0.697959
$896$	896.000	0.0334077
$897$	66.6335	0.00248030
$898$	6083.15	0.226055
$899$	−3261.78	−0.121008
$900$	9667.68	0.358062
$901$	9086.14	0.335964
$902$	−14910.1	−0.550391
$903$	−5259.72	−0.193835
$904$	−17140.0	−0.630606
$905$	55841.7	2.05110
$906$	−8831.06	−0.323833
$907$	26338.7	0.964237	0.482119	−	0.876106i	$-0.339867\pi$
$907$	26338.7	0.964237	0.482119	+	0.876106i	$0.339867\pi$
$908$	−1252.91	−0.0457922
$909$	−3079.19	−0.112355
$910$	268.207	0.00977029
$911$	−13703.1	−0.498358	−0.249179	−	0.968457i	$-0.580161\pi$
$911$	−13703.1	−0.498358	−0.249179	+	0.968457i	$0.580161\pi$
$912$	−2285.00	−0.0829647
$913$	−31006.2	−1.12394
$914$	−6199.51	−0.224356
$915$	−22115.7	−0.799043
$916$	−7758.62	−0.279860
$917$	−12486.4	−0.449660
$918$	1543.39	0.0554896
$919$	−46616.4	−1.67327	−0.836634	−	0.547762i	$-0.815480\pi$
$919$	−46616.4	−1.67327	−0.836634	+	0.547762i	$0.815480\pi$
$920$	−3650.19	−0.130808
$921$	12693.9	0.454156
$922$	−24605.4	−0.878890
$923$	771.960	0.0275291
$924$	−2252.75	−0.0802055
$925$	−75188.1	−2.67262
$926$	−1379.92	−0.0489709
$927$	17934.5	0.635431
$928$	1441.01	0.0509734
$929$	−42408.3	−1.49771	−0.748854	−	0.662735i	$-0.769395\pi$
$929$	−42408.3	−1.49771	−0.748854	+	0.662735i	$0.769395\pi$
$930$	−8621.61	−0.303993
$931$	2332.60	0.0821137
$932$	−8186.87	−0.287736
$933$	13199.3	0.463159
$934$	15243.3	0.534023
$935$	15205.9	0.531858
$936$	−69.5306	−0.00242808
$937$	−13304.6	−0.463865	−0.231933	−	0.972732i	$-0.574505\pi$
$937$	−13304.6	−0.463865	−0.231933	+	0.972732i	$0.574505\pi$
$938$	2830.28	0.0985203
$939$	−3662.00	−0.127268
$940$	−18717.2	−0.649454
$941$	−9194.29	−0.318518	−0.159259	−	0.987237i	$-0.550910\pi$
$941$	−9194.29	−0.318518	−0.159259	+	0.987237i	$0.550910\pi$
$942$	−17539.2	−0.606644
$943$	−6393.61	−0.220790
$944$	357.308	0.0123193
$945$	3749.38	0.129066
$946$	13434.0	0.461710
$947$	−43559.8	−1.49472	−0.747362	−	0.664417i	$-0.768680\pi$
$947$	−43559.8	−1.49472	−0.747362	+	0.664417i	$0.768680\pi$
$948$	82.4635	0.00282520
$949$	655.817	0.0224328
$950$	25567.8	0.873190
$951$	−25117.3	−0.856451
$952$	−1600.55	−0.0544897
$953$	−15758.8	−0.535654	−0.267827	−	0.963467i	$-0.586306\pi$
$953$	−15758.8	−0.535654	−0.267827	+	0.963467i	$0.586306\pi$
$954$	−5722.30	−0.194199
$955$	27545.0	0.933336
$956$	−5128.97	−0.173517
$957$	−3623.01	−0.122378
$958$	−28628.4	−0.965492
$959$	−7440.91	−0.250552
$960$	3808.90	0.128054
$961$	−24544.4	−0.823886
$962$	540.758	0.0181234
$963$	−3880.81	−0.129862
$964$	−3215.98	−0.107448
$965$	38572.3	1.28672
$966$	−966.000	−0.0321745
$967$	−16619.2	−0.552676	−0.276338	−	0.961060i	$-0.589121\pi$
$967$	−16619.2	−0.552676	−0.276338	+	0.961060i	$0.589121\pi$
$968$	−4894.19	−0.162505
$969$	4081.76	0.135320
$970$	59406.3	1.96641
$971$	−4567.13	−0.150943	−0.0754717	−	0.997148i	$-0.524046\pi$
$971$	−4567.13	−0.150943	−0.0754717	+	0.997148i	$0.524046\pi$
$972$	−972.000	−0.0320750
$973$	15032.2	0.495284
$974$	−3788.91	−0.124645
$975$	778.009	0.0255551
$976$	−5945.69	−0.194997
$977$	730.007	0.0239048	0.0119524	−	0.999929i	$-0.496195\pi$
$977$	730.007	0.0239048	0.0119524	+	0.999929i	$0.496195\pi$
$978$	−21861.2	−0.714771
$979$	−27933.9	−0.911921
$980$	−3888.25	−0.126740
$981$	1071.34	0.0348678
$982$	23407.5	0.760655
$983$	−14740.6	−0.478283	−0.239142	−	0.970985i	$-0.576866\pi$
$983$	−14740.6	−0.478283	−0.239142	+	0.970985i	$0.576866\pi$
$984$	6671.60	0.216141
$985$	−97127.7	−3.14187
$986$	−2574.11	−0.0831404
$987$	−4953.38	−0.159744
$988$	−183.886	−0.00592124
$989$	5760.65	0.185215
$990$	−9576.43	−0.307433
$991$	13166.9	0.422058	0.211029	−	0.977480i	$-0.432319\pi$
$991$	13166.9	0.422058	0.211029	+	0.977480i	$0.432319\pi$
$992$	−2317.87	−0.0741859
$993$	−16103.1	−0.514620
$994$	−11191.3	−0.357108
$995$	−2230.83	−0.0710776
$996$	13873.9	0.441376
$997$	42548.4	1.35158	0.675788	−	0.737096i	$-0.263803\pi$
$997$	42548.4	1.35158	0.675788	+	0.737096i	$0.263803\pi$
$998$	936.954	0.0297182
$999$	7559.50	0.239411

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.k.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.k.1.1	✓	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	966.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -19.8380 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -19.8380 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -39.6760 q^{10} +26.8184 q^{11} -12.0000 q^{12} -0.965703 q^{13} +14.0000 q^{14} +59.5140 q^{15} +16.0000 q^{16} -28.5813 q^{17} +18.0000 q^{18} +47.6041 q^{19} -79.3521 q^{20} -21.0000 q^{21} +53.6368 q^{22} +23.0000 q^{23} -24.0000 q^{24} +268.547 q^{25} -1.93141 q^{26} -27.0000 q^{27} +28.0000 q^{28} +45.0314 q^{29} +119.028 q^{30} -72.4334 q^{31} +32.0000 q^{32} -80.4552 q^{33} -57.1626 q^{34} -138.866 q^{35} +36.0000 q^{36} -279.982 q^{37} +95.2082 q^{38} +2.89711 q^{39} -158.704 q^{40} -277.983 q^{41} -42.0000 q^{42} +250.463 q^{43} +107.274 q^{44} -178.542 q^{45} +46.0000 q^{46} +235.875 q^{47} -48.0000 q^{48} +49.0000 q^{49} +537.094 q^{50} +85.7438 q^{51} -3.86281 q^{52} -317.905 q^{53} -54.0000 q^{54} -532.024 q^{55} +56.0000 q^{56} -142.812 q^{57} +90.0629 q^{58} +22.3318 q^{59} +238.056 q^{60} -371.606 q^{61} -144.867 q^{62} +63.0000 q^{63} +64.0000 q^{64} +19.1576 q^{65} -160.910 q^{66} +202.163 q^{67} -114.325 q^{68} -69.0000 q^{69} -277.732 q^{70} -799.377 q^{71} +72.0000 q^{72} -679.109 q^{73} -559.963 q^{74} -805.640 q^{75} +190.416 q^{76} +187.729 q^{77} +5.79422 q^{78} -6.87196 q^{79} -317.408 q^{80} +81.0000 q^{81} -555.966 q^{82} -1156.16 q^{83} -84.0000 q^{84} +566.996 q^{85} +500.926 q^{86} -135.094 q^{87} +214.547 q^{88} -1041.59 q^{89} -357.084 q^{90} -6.75992 q^{91} +92.0000 q^{92} +217.300 q^{93} +471.750 q^{94} -944.370 q^{95} -96.0000 q^{96} -1497.29 q^{97} +98.0000 q^{98} +241.366 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} - 12 q^{3} + 16 q^{4} - 15 q^{5} - 24 q^{6} + 28 q^{7} + 32 q^{8} + 36 q^{9}+O(q^{10}) \) 4 * q + 8 * q^2 - 12 * q^3 + 16 * q^4 - 15 * q^5 - 24 * q^6 + 28 * q^7 + 32 * q^8 + 36 * q^9	\( 4 q + 8 q^{2} - 12 q^{3} + 16 q^{4} - 15 q^{5} - 24 q^{6} + 28 q^{7} + 32 q^{8} + 36 q^{9} - 30 q^{10} - 26 q^{11} - 48 q^{12} - 33 q^{13} + 56 q^{14} + 45 q^{15} + 64 q^{16} - 168 q^{17} + 72 q^{18} - 138 q^{19} - 60 q^{20} - 84 q^{21} - 52 q^{22} + 92 q^{23} - 96 q^{24} - 41 q^{25} - 66 q^{26} - 108 q^{27} + 112 q^{28} + 52 q^{29} + 90 q^{30} - 248 q^{31} + 128 q^{32} + 78 q^{33} - 336 q^{34} - 105 q^{35} + 144 q^{36} + 226 q^{37} - 276 q^{38} + 99 q^{39} - 120 q^{40} - 274 q^{41} - 168 q^{42} + 269 q^{43} - 104 q^{44} - 135 q^{45} + 184 q^{46} - 408 q^{47} - 192 q^{48} + 196 q^{49} - 82 q^{50} + 504 q^{51} - 132 q^{52} - 843 q^{53} - 216 q^{54} - 249 q^{55} + 224 q^{56} + 414 q^{57} + 104 q^{58} - 653 q^{59} + 180 q^{60} - 963 q^{61} - 496 q^{62} + 252 q^{63} + 256 q^{64} - 588 q^{65} + 156 q^{66} - 789 q^{67} - 672 q^{68} - 276 q^{69} - 210 q^{70} - 1697 q^{71} + 288 q^{72} - 1800 q^{73} + 452 q^{74} + 123 q^{75} - 552 q^{76} - 182 q^{77} + 198 q^{78} + 274 q^{79} - 240 q^{80} + 324 q^{81} - 548 q^{82} - 1496 q^{83} - 336 q^{84} - 435 q^{85} + 538 q^{86} - 156 q^{87} - 208 q^{88} - 1829 q^{89} - 270 q^{90} - 231 q^{91} + 368 q^{92} + 744 q^{93} - 816 q^{94} - 1767 q^{95} - 384 q^{96} - 1910 q^{97} + 392 q^{98} - 234 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 - 12 * q^3 + 16 * q^4 - 15 * q^5 - 24 * q^6 + 28 * q^7 + 32 * q^8 + 36 * q^9 - 30 * q^10 - 26 * q^11 - 48 * q^12 - 33 * q^13 + 56 * q^14 + 45 * q^15 + 64 * q^16 - 168 * q^17 + 72 * q^18 - 138 * q^19 - 60 * q^20 - 84 * q^21 - 52 * q^22 + 92 * q^23 - 96 * q^24 - 41 * q^25 - 66 * q^26 - 108 * q^27 + 112 * q^28 + 52 * q^29 + 90 * q^30 - 248 * q^31 + 128 * q^32 + 78 * q^33 - 336 * q^34 - 105 * q^35 + 144 * q^36 + 226 * q^37 - 276 * q^38 + 99 * q^39 - 120 * q^40 - 274 * q^41 - 168 * q^42 + 269 * q^43 - 104 * q^44 - 135 * q^45 + 184 * q^46 - 408 * q^47 - 192 * q^48 + 196 * q^49 - 82 * q^50 + 504 * q^51 - 132 * q^52 - 843 * q^53 - 216 * q^54 - 249 * q^55 + 224 * q^56 + 414 * q^57 + 104 * q^58 - 653 * q^59 + 180 * q^60 - 963 * q^61 - 496 * q^62 + 252 * q^63 + 256 * q^64 - 588 * q^65 + 156 * q^66 - 789 * q^67 - 672 * q^68 - 276 * q^69 - 210 * q^70 - 1697 * q^71 + 288 * q^72 - 1800 * q^73 + 452 * q^74 + 123 * q^75 - 552 * q^76 - 182 * q^77 + 198 * q^78 + 274 * q^79 - 240 * q^80 + 324 * q^81 - 548 * q^82 - 1496 * q^83 - 336 * q^84 - 435 * q^85 + 538 * q^86 - 156 * q^87 - 208 * q^88 - 1829 * q^89 - 270 * q^90 - 231 * q^91 + 368 * q^92 + 744 * q^93 - 816 * q^94 - 1767 * q^95 - 384 * q^96 - 1910 * q^97 + 392 * q^98 - 234 * q^99

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