LMFDB - Embedded newform 2883.2.a.n.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2883,2,Mod(1,2883)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2883, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("2883.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2883 = 3 \cdot 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2883.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:	$23.0208709027$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	8.8.1697203125.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 5x^{6} + 12x^{5} + 9x^{4} - 12x^{3} - 5x^{2} + 3x + 1 $ x^8 - 3x^7 - 5x^6 + 12x^5 + 9x^4 - 12x^3 - 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 93)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.18333$ of defining polynomial
Character	$\chi$	$=$	2883.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.18333 q^{2} +1.00000 q^{3} +2.76694 q^{4} +0.544022 q^{5} -2.18333 q^{6} +0.576411 q^{7} -1.67449 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.18333 q^{2} +1.00000 q^{3} +2.76694 q^{4} +0.544022 q^{5} -2.18333 q^{6} +0.576411 q^{7} -1.67449 q^{8} +1.00000 q^{9} -1.18778 q^{10} -4.32207 q^{11} +2.76694 q^{12} -4.29252 q^{13} -1.25850 q^{14} +0.544022 q^{15} -1.87792 q^{16} -0.120217 q^{17} -2.18333 q^{18} +0.624627 q^{19} +1.50528 q^{20} +0.576411 q^{21} +9.43652 q^{22} +9.35012 q^{23} -1.67449 q^{24} -4.70404 q^{25} +9.37200 q^{26} +1.00000 q^{27} +1.59489 q^{28} +6.59414 q^{29} -1.18778 q^{30} +7.44910 q^{32} -4.32207 q^{33} +0.262473 q^{34} +0.313580 q^{35} +2.76694 q^{36} -1.98547 q^{37} -1.36377 q^{38} -4.29252 q^{39} -0.910956 q^{40} -5.55223 q^{41} -1.25850 q^{42} +3.54647 q^{43} -11.9589 q^{44} +0.544022 q^{45} -20.4144 q^{46} -3.31459 q^{47} -1.87792 q^{48} -6.66775 q^{49} +10.2705 q^{50} -0.120217 q^{51} -11.8771 q^{52} +5.16382 q^{53} -2.18333 q^{54} -2.35130 q^{55} -0.965191 q^{56} +0.624627 q^{57} -14.3972 q^{58} -9.47321 q^{59} +1.50528 q^{60} -12.2514 q^{61} +0.576411 q^{63} -12.5080 q^{64} -2.33522 q^{65} +9.43652 q^{66} -3.96505 q^{67} -0.332633 q^{68} +9.35012 q^{69} -0.684649 q^{70} +0.560054 q^{71} -1.67449 q^{72} +12.6639 q^{73} +4.33495 q^{74} -4.70404 q^{75} +1.72830 q^{76} -2.49129 q^{77} +9.37200 q^{78} -13.3591 q^{79} -1.02163 q^{80} +1.00000 q^{81} +12.1224 q^{82} -6.79053 q^{83} +1.59489 q^{84} -0.0654006 q^{85} -7.74312 q^{86} +6.59414 q^{87} +7.23725 q^{88} +16.8177 q^{89} -1.18778 q^{90} -2.47425 q^{91} +25.8712 q^{92} +7.23684 q^{94} +0.339811 q^{95} +7.44910 q^{96} -11.2255 q^{97} +14.5579 q^{98} -4.32207 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{2} + 8 q^{3} + 5 q^{4} - 6 q^{5} - 5 q^{6} - 6 q^{7} + 8 q^{9}+O(q^{10}) $ 8 * q - 5 * q^2 + 8 * q^3 + 5 * q^4 - 6 * q^5 - 5 * q^6 - 6 * q^7 + 8 * q^9	$ 8 q - 5 q^{2} + 8 q^{3} + 5 q^{4} - 6 q^{5} - 5 q^{6} - 6 q^{7} + 8 q^{9} + q^{10} + 5 q^{12} - 12 q^{13} - 3 q^{14} - 6 q^{15} + 3 q^{16} - 2 q^{17} - 5 q^{18} - 8 q^{19} - 5 q^{20} - 6 q^{21} - 4 q^{22} - 4 q^{23} - 12 q^{25} + 18 q^{26} + 8 q^{27} - 15 q^{28} + 6 q^{29} + q^{30} - 17 q^{34} + 9 q^{35} + 5 q^{36} - 8 q^{37} - 7 q^{38} - 12 q^{39} + 13 q^{40} - 20 q^{41} - 3 q^{42} - 14 q^{43} - 25 q^{44} - 6 q^{45} - 9 q^{46} + 6 q^{47} + 3 q^{48} - 20 q^{49} + 6 q^{50} - 2 q^{51} - 30 q^{52} + 30 q^{53} - 5 q^{54} - 19 q^{55} + 6 q^{56} - 8 q^{57} - 19 q^{58} - 20 q^{59} - 5 q^{60} - 13 q^{61} - 6 q^{63} - 26 q^{64} + 27 q^{65} - 4 q^{66} + 32 q^{67} + 15 q^{68} - 4 q^{69} - 6 q^{70} - 17 q^{71} + 12 q^{73} + 10 q^{74} - 12 q^{75} - 20 q^{76} - 18 q^{77} + 18 q^{78} - 30 q^{79} - 21 q^{80} + 8 q^{81} - 23 q^{82} - 12 q^{83} - 15 q^{84} - 28 q^{85} + 46 q^{86} + 6 q^{87} - 22 q^{88} - 6 q^{89} + q^{90} + 15 q^{91} + 70 q^{92} + 44 q^{94} - 36 q^{95} - 39 q^{97} + 32 q^{98}+O(q^{100}) $ 8 * q - 5 * q^2 + 8 * q^3 + 5 * q^4 - 6 * q^5 - 5 * q^6 - 6 * q^7 + 8 * q^9 + q^10 + 5 * q^12 - 12 * q^13 - 3 * q^14 - 6 * q^15 + 3 * q^16 - 2 * q^17 - 5 * q^18 - 8 * q^19 - 5 * q^20 - 6 * q^21 - 4 * q^22 - 4 * q^23 - 12 * q^25 + 18 * q^26 + 8 * q^27 - 15 * q^28 + 6 * q^29 + q^30 - 17 * q^34 + 9 * q^35 + 5 * q^36 - 8 * q^37 - 7 * q^38 - 12 * q^39 + 13 * q^40 - 20 * q^41 - 3 * q^42 - 14 * q^43 - 25 * q^44 - 6 * q^45 - 9 * q^46 + 6 * q^47 + 3 * q^48 - 20 * q^49 + 6 * q^50 - 2 * q^51 - 30 * q^52 + 30 * q^53 - 5 * q^54 - 19 * q^55 + 6 * q^56 - 8 * q^57 - 19 * q^58 - 20 * q^59 - 5 * q^60 - 13 * q^61 - 6 * q^63 - 26 * q^64 + 27 * q^65 - 4 * q^66 + 32 * q^67 + 15 * q^68 - 4 * q^69 - 6 * q^70 - 17 * q^71 + 12 * q^73 + 10 * q^74 - 12 * q^75 - 20 * q^76 - 18 * q^77 + 18 * q^78 - 30 * q^79 - 21 * q^80 + 8 * q^81 - 23 * q^82 - 12 * q^83 - 15 * q^84 - 28 * q^85 + 46 * q^86 + 6 * q^87 - 22 * q^88 - 6 * q^89 + q^90 + 15 * q^91 + 70 * q^92 + 44 * q^94 - 36 * q^95 - 39 * q^97 + 32 * q^98

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 $

$2$	−2.18333	−1.54385	−0.771925	−	0.635714i	$-0.780706\pi$
$2$	−2.18333	−1.54385	−0.771925	+	0.635714i	$0.780706\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.76694	1.38347
$5$	0.544022	0.243294	0.121647	−	0.992573i	$-0.461182\pi$
$5$	0.544022	0.243294	0.121647	+	0.992573i	$0.461182\pi$
$6$	−2.18333	−0.891342
$7$	0.576411	0.217863	0.108931	−	0.994049i	$-0.465257\pi$
$7$	0.576411	0.217863	0.108931	+	0.994049i	$0.465257\pi$
$8$	−1.67449	−0.592020
$9$	1.00000	0.333333
$10$	−1.18778	−0.375609
$11$	−4.32207	−1.30315	−0.651577	−	0.758582i	$-0.725892\pi$
$11$	−4.32207	−1.30315	−0.651577	+	0.758582i	$0.725892\pi$
$12$	2.76694	0.798747
$13$	−4.29252	−1.19053	−0.595265	−	0.803529i	$-0.702953\pi$
$13$	−4.29252	−1.19053	−0.595265	+	0.803529i	$0.702953\pi$
$14$	−1.25850	−0.336347
$15$	0.544022	0.140466
$16$	−1.87792	−0.469481
$17$	−0.120217	−0.0291569	−0.0145784	−	0.999894i	$-0.504641\pi$
$17$	−0.120217	−0.0291569	−0.0145784	+	0.999894i	$0.504641\pi$
$18$	−2.18333	−0.514616
$19$	0.624627	0.143299	0.0716496	−	0.997430i	$-0.477174\pi$
$19$	0.624627	0.143299	0.0716496	+	0.997430i	$0.477174\pi$
$20$	1.50528	0.336590
$21$	0.576411	0.125783
$22$	9.43652	2.01187
$23$	9.35012	1.94963	0.974817	−	0.223006i	$-0.0715868\pi$
$23$	9.35012	1.94963	0.974817	+	0.223006i	$0.0715868\pi$
$24$	−1.67449	−0.341803
$25$	−4.70404	−0.940808
$26$	9.37200	1.83800
$27$	1.00000	0.192450
$28$	1.59489	0.301407
$29$	6.59414	1.22450	0.612251	−	0.790664i	$-0.290264\pi$
$29$	6.59414	1.22450	0.612251	+	0.790664i	$0.290264\pi$
$30$	−1.18778	−0.216858
$31$	0	0
$31$	0	0
$32$	7.44910	1.31683
$33$	−4.32207	−0.752377
$34$	0.262473	0.0450138
$35$	0.313580	0.0530047
$36$	2.76694	0.461157
$37$	−1.98547	−0.326410	−0.163205	−	0.986592i	$-0.552183\pi$
$37$	−1.98547	−0.326410	−0.163205	+	0.986592i	$0.552183\pi$
$38$	−1.36377	−0.221232
$39$	−4.29252	−0.687353
$40$	−0.910956	−0.144035
$41$	−5.55223	−0.867112	−0.433556	−	0.901127i	$-0.642741\pi$
$41$	−5.55223	−0.867112	−0.433556	+	0.901127i	$0.642741\pi$
$42$	−1.25850	−0.194190
$43$	3.54647	0.540832	0.270416	−	0.962744i	$-0.412839\pi$
$43$	3.54647	0.540832	0.270416	+	0.962744i	$0.412839\pi$
$44$	−11.9589	−1.80288
$45$	0.544022	0.0810980
$46$	−20.4144	−3.00994
$47$	−3.31459	−0.483482	−0.241741	−	0.970341i	$-0.577718\pi$
$47$	−3.31459	−0.483482	−0.241741	+	0.970341i	$0.577718\pi$
$48$	−1.87792	−0.271055
$49$	−6.66775	−0.952536
$50$	10.2705	1.45247
$51$	−0.120217	−0.0168337
$52$	−11.8771	−1.64706
$53$	5.16382	0.709305	0.354653	−	0.934998i	$-0.384599\pi$
$53$	5.16382	0.709305	0.354653	+	0.934998i	$0.384599\pi$
$54$	−2.18333	−0.297114
$55$	−2.35130	−0.317050
$56$	−0.965191	−0.128979
$57$	0.624627	0.0827338
$58$	−14.3972	−1.89045
$59$	−9.47321	−1.23331	−0.616654	−	0.787234i	$-0.711512\pi$
$59$	−9.47321	−1.23331	−0.616654	+	0.787234i	$0.711512\pi$
$60$	1.50528	0.194330
$61$	−12.2514	−1.56863	−0.784314	−	0.620365i	$-0.786985\pi$
$61$	−12.2514	−1.56863	−0.784314	+	0.620365i	$0.786985\pi$
$62$	0	0
$63$	0.576411	0.0726209
$64$	−12.5080	−1.56350
$65$	−2.33522	−0.289649
$66$	9.43652	1.16156
$67$	−3.96505	−0.484408	−0.242204	−	0.970225i	$-0.577870\pi$
$67$	−3.96505	−0.484408	−0.242204	+	0.970225i	$0.577870\pi$
$68$	−0.332633	−0.0403376
$69$	9.35012	1.12562
$70$	−0.684649	−0.0818312
$71$	0.560054	0.0664662	0.0332331	−	0.999448i	$-0.489420\pi$
$71$	0.560054	0.0664662	0.0332331	+	0.999448i	$0.489420\pi$
$72$	−1.67449	−0.197340
$73$	12.6639	1.48220	0.741098	−	0.671397i	$-0.234305\pi$
$73$	12.6639	1.48220	0.741098	+	0.671397i	$0.234305\pi$
$74$	4.33495	0.503927
$75$	−4.70404	−0.543176
$76$	1.72830	0.198250
$77$	−2.49129	−0.283909
$78$	9.37200	1.06117
$79$	−13.3591	−1.50302	−0.751509	−	0.659723i	$-0.770674\pi$
$79$	−13.3591	−1.50302	−0.751509	+	0.659723i	$0.770674\pi$
$80$	−1.02163	−0.114222
$81$	1.00000	0.111111
$82$	12.1224	1.33869
$83$	−6.79053	−0.745358	−0.372679	−	0.927960i	$-0.621561\pi$
$83$	−6.79053	−0.745358	−0.372679	+	0.927960i	$0.621561\pi$
$84$	1.59489	0.174017
$85$	−0.0654006	−0.00709369
$86$	−7.74312	−0.834963
$87$	6.59414	0.706966
$88$	7.23725	0.771493
$89$	16.8177	1.78267	0.891334	−	0.453346i	$-0.149770\pi$
$89$	16.8177	1.78267	0.891334	+	0.453346i	$0.149770\pi$
$90$	−1.18778	−0.125203
$91$	−2.47425	−0.259372
$92$	25.8712	2.69726
$93$	0	0
$94$	7.23684	0.746423
$95$	0.339811	0.0348638
$96$	7.44910	0.760271
$97$	−11.2255	−1.13978	−0.569888	−	0.821723i	$-0.693013\pi$
$97$	−11.2255	−1.13978	−0.569888	+	0.821723i	$0.693013\pi$
$98$	14.5579	1.47057
$99$	−4.32207	−0.434385
$100$	−13.0158	−1.30158
$101$	−1.42232	−0.141526	−0.0707632	−	0.997493i	$-0.522543\pi$
$101$	−1.42232	−0.141526	−0.0707632	+	0.997493i	$0.522543\pi$
$102$	0.262473	0.0259887
$103$	−4.20372	−0.414205	−0.207102	−	0.978319i	$-0.566403\pi$
$103$	−4.20372	−0.414205	−0.207102	+	0.978319i	$0.566403\pi$
$104$	7.18776	0.704818
$105$	0.313580	0.0306023
$106$	−11.2743	−1.09506
$107$	−19.3808	−1.87361	−0.936804	−	0.349855i	$-0.886231\pi$
$107$	−19.3808	−1.87361	−0.936804	+	0.349855i	$0.886231\pi$
$108$	2.76694	0.266249
$109$	13.2471	1.26884	0.634420	−	0.772989i	$-0.281239\pi$
$109$	13.2471	1.26884	0.634420	+	0.772989i	$0.281239\pi$
$110$	5.13367	0.489477
$111$	−1.98547	−0.188453
$112$	−1.08245	−0.102282
$113$	−4.30175	−0.404674	−0.202337	−	0.979316i	$-0.564854\pi$
$113$	−4.30175	−0.404674	−0.202337	+	0.979316i	$0.564854\pi$
$114$	−1.36377	−0.127729
$115$	5.08667	0.474334
$116$	18.2456	1.69406
$117$	−4.29252	−0.396844
$118$	20.6832	1.90404
$119$	−0.0692943	−0.00635219
$120$	−0.910956	−0.0831586
$121$	7.68033	0.698211
$122$	26.7488	2.42172
$123$	−5.55223	−0.500628
$124$	0	0
$125$	−5.27921	−0.472187
$126$	−1.25850	−0.112116
$127$	−14.0071	−1.24293	−0.621463	−	0.783443i	$-0.713461\pi$
$127$	−14.0071	−1.24293	−0.621463	+	0.783443i	$0.713461\pi$
$128$	12.4110	1.09698
$129$	3.54647	0.312249
$130$	5.09857	0.447174
$131$	−3.14033	−0.274372	−0.137186	−	0.990545i	$-0.543806\pi$
$131$	−3.14033	−0.274372	−0.137186	+	0.990545i	$0.543806\pi$
$132$	−11.9589	−1.04089
$133$	0.360042	0.0312196
$134$	8.65702	0.747852
$135$	0.544022	0.0468219
$136$	0.201301	0.0172614
$137$	−2.28941	−0.195598	−0.0977988	−	0.995206i	$-0.531180\pi$
$137$	−2.28941	−0.195598	−0.0977988	+	0.995206i	$0.531180\pi$
$138$	−20.4144	−1.73779
$139$	−16.9536	−1.43799	−0.718994	−	0.695016i	$-0.755397\pi$
$139$	−16.9536	−1.43799	−0.718994	+	0.695016i	$0.755397\pi$
$140$	0.867657	0.0733304
$141$	−3.31459	−0.279139
$142$	−1.22278	−0.102614
$143$	18.5526	1.55145
$144$	−1.87792	−0.156494
$145$	3.58736	0.297914
$146$	−27.6495	−2.28829
$147$	−6.66775	−0.549947
$148$	−5.49368	−0.451578
$149$	10.0105	0.820094	0.410047	−	0.912064i	$-0.365512\pi$
$149$	10.0105	0.820094	0.410047	+	0.912064i	$0.365512\pi$
$150$	10.2705	0.838581
$151$	6.24617	0.508306	0.254153	−	0.967164i	$-0.418203\pi$
$151$	6.24617	0.508306	0.254153	+	0.967164i	$0.418203\pi$
$152$	−1.04593	−0.0848360
$153$	−0.120217	−0.00971895
$154$	5.43931	0.438312
$155$	0	0
$156$	−11.8771	−0.950933
$157$	−7.72952	−0.616883	−0.308441	−	0.951243i	$-0.599807\pi$
$157$	−7.72952	−0.616883	−0.308441	+	0.951243i	$0.599807\pi$
$158$	29.1674	2.32043
$159$	5.16382	0.409518
$160$	4.05247	0.320376
$161$	5.38951	0.424753
$162$	−2.18333	−0.171539
$163$	10.6504	0.834202	0.417101	−	0.908860i	$-0.363046\pi$
$163$	10.6504	0.834202	0.417101	+	0.908860i	$0.363046\pi$
$164$	−15.3627	−1.19962
$165$	−2.35130	−0.183049
$166$	14.8260	1.15072
$167$	−12.9868	−1.00495	−0.502473	−	0.864593i	$-0.667576\pi$
$167$	−12.9868	−1.00495	−0.502473	+	0.864593i	$0.667576\pi$
$168$	−0.965191	−0.0744661
$169$	5.42572	0.417363
$170$	0.142791	0.0109516
$171$	0.624627	0.0477664
$172$	9.81287	0.748224
$173$	2.71703	0.206572	0.103286	−	0.994652i	$-0.467064\pi$
$173$	2.71703	0.206572	0.103286	+	0.994652i	$0.467064\pi$
$174$	−14.3972	−1.09145
$175$	−2.71146	−0.204967
$176$	8.11652	0.611806
$177$	−9.47321	−0.712050
$178$	−36.7185	−2.75217
$179$	7.20605	0.538605	0.269303	−	0.963056i	$-0.413207\pi$
$179$	7.20605	0.538605	0.269303	+	0.963056i	$0.413207\pi$
$180$	1.50528	0.112197
$181$	−20.3446	−1.51220	−0.756102	−	0.654454i	$-0.772899\pi$
$181$	−20.3446	−1.51220	−0.756102	+	0.654454i	$0.772899\pi$
$182$	5.40212	0.400432
$183$	−12.2514	−0.905647
$184$	−15.6566	−1.15422
$185$	−1.08014	−0.0794135
$186$	0	0
$187$	0.519586	0.0379959
$188$	−9.17126	−0.668883
$189$	0.576411	0.0419277
$190$	−0.741919	−0.0538245
$191$	−12.7837	−0.924996	−0.462498	−	0.886620i	$-0.653047\pi$
$191$	−12.7837	−0.924996	−0.462498	+	0.886620i	$0.653047\pi$
$192$	−12.5080	−0.902688
$193$	−16.5833	−1.19369	−0.596845	−	0.802357i	$-0.703579\pi$
$193$	−16.5833	−1.19369	−0.596845	+	0.802357i	$0.703579\pi$
$194$	24.5090	1.75964
$195$	−2.33522	−0.167229
$196$	−18.4493	−1.31780
$197$	3.15873	0.225050	0.112525	−	0.993649i	$-0.464106\pi$
$197$	3.15873	0.225050	0.112525	+	0.993649i	$0.464106\pi$
$198$	9.43652	0.670625
$199$	8.77662	0.622158	0.311079	−	0.950384i	$-0.399310\pi$
$199$	8.77662	0.622158	0.311079	+	0.950384i	$0.399310\pi$
$200$	7.87685	0.556977
$201$	−3.96505	−0.279673
$202$	3.10540	0.218496
$203$	3.80093	0.266773
$204$	−0.332633	−0.0232889
$205$	−3.02053	−0.210963
$206$	9.17812	0.639470
$207$	9.35012	0.649878
$208$	8.06102	0.558931
$209$	−2.69968	−0.186741
$210$	−0.684649	−0.0472453
$211$	12.3493	0.850163	0.425082	−	0.905155i	$-0.360245\pi$
$211$	12.3493	0.850163	0.425082	+	0.905155i	$0.360245\pi$
$212$	14.2880	0.981303
$213$	0.560054	0.0383743
$214$	42.3146	2.89257
$215$	1.92936	0.131581
$216$	−1.67449	−0.113934
$217$	0	0
$218$	−28.9228	−1.95890
$219$	12.6639	0.855746
$220$	−6.50591	−0.438629
$221$	0.516033	0.0347121
$222$	4.33495	0.290943
$223$	23.5264	1.57544	0.787721	−	0.616032i	$-0.211261\pi$
$223$	23.5264	1.57544	0.787721	+	0.616032i	$0.211261\pi$
$224$	4.29374	0.286888
$225$	−4.70404	−0.313603
$226$	9.39214	0.624756
$227$	−3.71655	−0.246676	−0.123338	−	0.992365i	$-0.539360\pi$
$227$	−3.71655	−0.246676	−0.123338	+	0.992365i	$0.539360\pi$
$228$	1.72830	0.114460
$229$	5.16875	0.341561	0.170780	−	0.985309i	$-0.445371\pi$
$229$	5.16875	0.341561	0.170780	+	0.985309i	$0.445371\pi$
$230$	−11.1059	−0.732300
$231$	−2.49129	−0.163915
$232$	−11.0418	−0.724929
$233$	−16.5272	−1.08273	−0.541365	−	0.840787i	$-0.682092\pi$
$233$	−16.5272	−1.08273	−0.541365	+	0.840787i	$0.682092\pi$
$234$	9.37200	0.612667
$235$	−1.80321	−0.117628
$236$	−26.2118	−1.70624
$237$	−13.3591	−0.867768
$238$	0.151292	0.00980683
$239$	−13.5984	−0.879607	−0.439804	−	0.898094i	$-0.644952\pi$
$239$	−13.5984	−0.879607	−0.439804	+	0.898094i	$0.644952\pi$
$240$	−1.02163	−0.0659460
$241$	−7.03693	−0.453289	−0.226644	−	0.973978i	$-0.572776\pi$
$241$	−7.03693	−0.453289	−0.226644	+	0.973978i	$0.572776\pi$
$242$	−16.7687	−1.07793
$243$	1.00000	0.0641500
$244$	−33.8988	−2.17015
$245$	−3.62740	−0.231746
$246$	12.1224	0.772893
$247$	−2.68122	−0.170602
$248$	0	0
$249$	−6.79053	−0.430332
$250$	11.5263	0.728985
$251$	−0.846434	−0.0534264	−0.0267132	−	0.999643i	$-0.508504\pi$
$251$	−0.846434	−0.0534264	−0.0267132	+	0.999643i	$0.508504\pi$
$252$	1.59489	0.100469
$253$	−40.4119	−2.54067
$254$	30.5821	1.91889
$255$	−0.0654006	−0.00409554
$256$	−2.08121	−0.130075
$257$	−24.5489	−1.53132	−0.765659	−	0.643247i	$-0.777587\pi$
$257$	−24.5489	−1.53132	−0.765659	+	0.643247i	$0.777587\pi$
$258$	−7.74312	−0.482066
$259$	−1.14445	−0.0711125
$260$	−6.46142	−0.400721
$261$	6.59414	0.408167
$262$	6.85638	0.423589
$263$	6.45614	0.398103	0.199051	−	0.979989i	$-0.436214\pi$
$263$	6.45614	0.398103	0.199051	+	0.979989i	$0.436214\pi$
$264$	7.23725	0.445422
$265$	2.80923	0.172570
$266$	−0.786090	−0.0481983
$267$	16.8177	1.02922
$268$	−10.9710	−0.670163
$269$	16.8062	1.02469	0.512345	−	0.858780i	$-0.328777\pi$
$269$	16.8062	1.02469	0.512345	+	0.858780i	$0.328777\pi$
$270$	−1.18778	−0.0722860
$271$	18.4133	1.11853	0.559263	−	0.828990i	$-0.311084\pi$
$271$	18.4133	1.11853	0.559263	+	0.828990i	$0.311084\pi$
$272$	0.225758	0.0136886
$273$	−2.47425	−0.149749
$274$	4.99855	0.301973
$275$	20.3312	1.22602
$276$	25.8712	1.55726
$277$	−12.5398	−0.753442	−0.376721	−	0.926327i	$-0.622948\pi$
$277$	−12.5398	−0.753442	−0.376721	+	0.926327i	$0.622948\pi$
$278$	37.0154	2.22004
$279$	0	0
$280$	−0.525085	−0.0313798
$281$	−1.40927	−0.0840702	−0.0420351	−	0.999116i	$-0.513384\pi$
$281$	−1.40927	−0.0840702	−0.0420351	+	0.999116i	$0.513384\pi$
$282$	7.23684	0.430948
$283$	−31.9676	−1.90027	−0.950137	−	0.311832i	$-0.899057\pi$
$283$	−31.9676	−1.90027	−0.950137	+	0.311832i	$0.899057\pi$
$284$	1.54964	0.0919539
$285$	0.339811	0.0201286
$286$	−40.5065	−2.39520
$287$	−3.20036	−0.188912
$288$	7.44910	0.438942
$289$	−16.9855	−0.999150
$290$	−7.83239	−0.459934
$291$	−11.2255	−0.658050
$292$	35.0402	2.05057
$293$	28.2321	1.64934	0.824669	−	0.565616i	$-0.191361\pi$
$293$	28.2321	1.64934	0.824669	+	0.565616i	$0.191361\pi$
$294$	14.5579	0.849035
$295$	−5.15364	−0.300056
$296$	3.32464	0.193241
$297$	−4.32207	−0.250792
$298$	−21.8563	−1.26610
$299$	−40.1356	−2.32110
$300$	−13.0158	−0.751467
$301$	2.04422	0.117827
$302$	−13.6375	−0.784748
$303$	−1.42232	−0.0817103
$304$	−1.17300	−0.0672762
$305$	−6.66501	−0.381638
$306$	0.262473	0.0150046
$307$	8.71221	0.497232	0.248616	−	0.968602i	$-0.420024\pi$
$307$	8.71221	0.497232	0.248616	+	0.968602i	$0.420024\pi$
$308$	−6.89325	−0.392779
$309$	−4.20372	−0.239141
$310$	0	0
$311$	26.5726	1.50679	0.753396	−	0.657567i	$-0.228414\pi$
$311$	26.5726	1.50679	0.753396	+	0.657567i	$0.228414\pi$
$312$	7.18776	0.406927
$313$	−0.629741	−0.0355950	−0.0177975	−	0.999842i	$-0.505665\pi$
$313$	−0.629741	−0.0355950	−0.0177975	+	0.999842i	$0.505665\pi$
$314$	16.8761	0.952374
$315$	0.313580	0.0176682
$316$	−36.9639	−2.07938
$317$	17.5567	0.986083	0.493041	−	0.870006i	$-0.335885\pi$
$317$	17.5567	0.986083	0.493041	+	0.870006i	$0.335885\pi$
$318$	−11.2743	−0.632234
$319$	−28.5004	−1.59571
$320$	−6.80463	−0.380391
$321$	−19.3808	−1.08173
$322$	−11.7671	−0.655754
$323$	−0.0750906	−0.00417815
$324$	2.76694	0.153719
$325$	20.1922	1.12006
$326$	−23.2533	−1.28788
$327$	13.2471	0.732565
$328$	9.29712	0.513348
$329$	−1.91056	−0.105333
$330$	5.13367	0.282600
$331$	−26.2073	−1.44049	−0.720243	−	0.693722i	$-0.755970\pi$
$331$	−26.2073	−1.44049	−0.720243	+	0.693722i	$0.755970\pi$
$332$	−18.7890	−1.03118
$333$	−1.98547	−0.108803
$334$	28.3544	1.55148
$335$	−2.15707	−0.117853
$336$	−1.08245	−0.0590527
$337$	−1.81989	−0.0991355	−0.0495678	−	0.998771i	$-0.515784\pi$
$337$	−1.81989	−0.0991355	−0.0495678	+	0.998771i	$0.515784\pi$
$338$	−11.8462	−0.644346
$339$	−4.30175	−0.233639
$340$	−0.180959	−0.00981390
$341$	0	0
$342$	−1.36377	−0.0737441
$343$	−7.87824	−0.425385
$344$	−5.93851	−0.320183
$345$	5.08667	0.273857
$346$	−5.93219	−0.318916
$347$	−21.4887	−1.15357	−0.576787	−	0.816894i	$-0.695694\pi$
$347$	−21.4887	−1.15357	−0.576787	+	0.816894i	$0.695694\pi$
$348$	18.2456	0.978067
$349$	4.71128	0.252189	0.126095	−	0.992018i	$-0.459756\pi$
$349$	4.71128	0.252189	0.126095	+	0.992018i	$0.459756\pi$
$350$	5.92002	0.316438
$351$	−4.29252	−0.229118
$352$	−32.1956	−1.71603
$353$	9.95610	0.529910	0.264955	−	0.964261i	$-0.414643\pi$
$353$	9.95610	0.529910	0.264955	+	0.964261i	$0.414643\pi$
$354$	20.6832	1.09930
$355$	0.304681	0.0161708
$356$	46.5335	2.46627
$357$	−0.0692943	−0.00366744
$358$	−15.7332	−0.831525
$359$	−23.9868	−1.26597	−0.632987	−	0.774163i	$-0.718171\pi$
$359$	−23.9868	−1.26597	−0.632987	+	0.774163i	$0.718171\pi$
$360$	−0.910956	−0.0480116
$361$	−18.6098	−0.979465
$362$	44.4191	2.33462
$363$	7.68033	0.403113
$364$	−6.84611	−0.358834
$365$	6.88943	0.360609
$366$	26.7488	1.39818
$367$	−16.5078	−0.861698	−0.430849	−	0.902424i	$-0.641786\pi$
$367$	−16.5078	−0.861698	−0.430849	+	0.902424i	$0.641786\pi$
$368$	−17.5588	−0.915316
$369$	−5.55223	−0.289037
$370$	2.35831	0.122602
$371$	2.97648	0.154531
$372$	0	0
$373$	−33.4166	−1.73024	−0.865122	−	0.501561i	$-0.832759\pi$
$373$	−33.4166	−1.73024	−0.865122	+	0.501561i	$0.832759\pi$
$374$	−1.13443	−0.0586599
$375$	−5.27921	−0.272617
$376$	5.55023	0.286231
$377$	−28.3055	−1.45781
$378$	−1.25850	−0.0647301
$379$	28.2904	1.45318	0.726591	−	0.687070i	$-0.241104\pi$
$379$	28.2904	1.45318	0.726591	+	0.687070i	$0.241104\pi$
$380$	0.940235	0.0482331
$381$	−14.0071	−0.717604
$382$	27.9111	1.42805
$383$	19.4604	0.994379	0.497189	−	0.867642i	$-0.334365\pi$
$383$	19.4604	0.994379	0.497189	+	0.867642i	$0.334365\pi$
$384$	12.4110	0.633344
$385$	−1.35532	−0.0690733
$386$	36.2068	1.84288
$387$	3.54647	0.180277
$388$	−31.0602	−1.57684
$389$	−25.0170	−1.26841	−0.634207	−	0.773163i	$-0.718673\pi$
$389$	−25.0170	−1.26841	−0.634207	+	0.773163i	$0.718673\pi$
$390$	5.09857	0.258176
$391$	−1.12404	−0.0568452
$392$	11.1650	0.563920
$393$	−3.14033	−0.158409
$394$	−6.89655	−0.347443
$395$	−7.26765	−0.365675
$396$	−11.9589	−0.600958
$397$	−21.6868	−1.08843	−0.544214	−	0.838947i	$-0.683172\pi$
$397$	−21.6868	−1.08843	−0.544214	+	0.838947i	$0.683172\pi$
$398$	−19.1623	−0.960518
$399$	0.360042	0.0180246
$400$	8.83382	0.441691
$401$	−19.2004	−0.958821	−0.479411	−	0.877591i	$-0.659150\pi$
$401$	−19.2004	−0.958821	−0.479411	+	0.877591i	$0.659150\pi$
$402$	8.65702	0.431773
$403$	0	0
$404$	−3.93548	−0.195798
$405$	0.544022	0.0270327
$406$	−8.29870	−0.411858
$407$	8.58136	0.425362
$408$	0.201301	0.00996590
$409$	−5.46664	−0.270308	−0.135154	−	0.990825i	$-0.543153\pi$
$409$	−5.46664	−0.270308	−0.135154	+	0.990825i	$0.543153\pi$
$410$	6.59483	0.325695
$411$	−2.28941	−0.112928
$412$	−11.6314	−0.573040
$413$	−5.46046	−0.268692
$414$	−20.4144	−1.00331
$415$	−3.69420	−0.181341
$416$	−31.9754	−1.56772
$417$	−16.9536	−0.830223
$418$	5.89431	0.288300
$419$	25.0648	1.22450	0.612248	−	0.790666i	$-0.290265\pi$
$419$	25.0648	1.22450	0.612248	+	0.790666i	$0.290265\pi$
$420$	0.867657	0.0423373
$421$	−28.9642	−1.41163	−0.705813	−	0.708398i	$-0.749418\pi$
$421$	−28.9642	−1.41163	−0.705813	+	0.708398i	$0.749418\pi$
$422$	−26.9627	−1.31252
$423$	−3.31459	−0.161161
$424$	−8.64674	−0.419923
$425$	0.565505	0.0274310
$426$	−1.22278	−0.0592441
$427$	−7.06182	−0.341746
$428$	−53.6254	−2.59208
$429$	18.5526	0.895727
$430$	−4.21243	−0.203141
$431$	−27.6733	−1.33298	−0.666489	−	0.745515i	$-0.732204\pi$
$431$	−27.6733	−1.33298	−0.666489	+	0.745515i	$0.732204\pi$
$432$	−1.87792	−0.0903516
$433$	3.15532	0.151635	0.0758174	−	0.997122i	$-0.475843\pi$
$433$	3.15532	0.151635	0.0758174	+	0.997122i	$0.475843\pi$
$434$	0	0
$435$	3.58736	0.172001
$436$	36.6539	1.75540
$437$	5.84033	0.279381
$438$	−27.6495	−1.32114
$439$	19.7961	0.944817	0.472408	−	0.881380i	$-0.343385\pi$
$439$	19.7961	0.944817	0.472408	+	0.881380i	$0.343385\pi$
$440$	3.93722	0.187700
$441$	−6.66775	−0.317512
$442$	−1.12667	−0.0535903
$443$	15.1602	0.720282	0.360141	−	0.932898i	$-0.382729\pi$
$443$	15.1602	0.720282	0.360141	+	0.932898i	$0.382729\pi$
$444$	−5.49368	−0.260719
$445$	9.14918	0.433713
$446$	−51.3659	−2.43224
$447$	10.0105	0.473481
$448$	−7.20975	−0.340629
$449$	14.0884	0.664873	0.332437	−	0.943126i	$-0.392129\pi$
$449$	14.0884	0.664873	0.332437	+	0.943126i	$0.392129\pi$
$450$	10.2705	0.484155
$451$	23.9971	1.12998
$452$	−11.9027	−0.559855
$453$	6.24617	0.293471
$454$	8.11446	0.380830
$455$	−1.34605	−0.0631037
$456$	−1.04593	−0.0489801
$457$	10.1726	0.475856	0.237928	−	0.971283i	$-0.423532\pi$
$457$	10.1726	0.475856	0.237928	+	0.971283i	$0.423532\pi$
$458$	−11.2851	−0.527318
$459$	−0.120217	−0.00561124
$460$	14.0745	0.656227
$461$	−1.89542	−0.0882787	−0.0441394	−	0.999025i	$-0.514055\pi$
$461$	−1.89542	−0.0882787	−0.0441394	+	0.999025i	$0.514055\pi$
$462$	5.43931	0.253060
$463$	24.1745	1.12348	0.561742	−	0.827313i	$-0.310131\pi$
$463$	24.1745	1.12348	0.561742	+	0.827313i	$0.310131\pi$
$464$	−12.3833	−0.574880
$465$	0	0
$466$	36.0843	1.67157
$467$	−21.8646	−1.01177	−0.505886	−	0.862600i	$-0.668834\pi$
$467$	−21.8646	−1.01177	−0.505886	+	0.862600i	$0.668834\pi$
$468$	−11.8771	−0.549021
$469$	−2.28550	−0.105534
$470$	3.93700	0.181600
$471$	−7.72952	−0.356157
$472$	15.8628	0.730143
$473$	−15.3281	−0.704787
$474$	29.1674	1.33970
$475$	−2.93827	−0.134817
$476$	−0.191733	−0.00878807
$477$	5.16382	0.236435
$478$	29.6898	1.35798
$479$	13.5003	0.616843	0.308421	−	0.951250i	$-0.400199\pi$
$479$	13.5003	0.616843	0.308421	+	0.951250i	$0.400199\pi$
$480$	4.05247	0.184969
$481$	8.52268	0.388601
$482$	15.3640	0.699809
$483$	5.38951	0.245231
$484$	21.2510	0.965955
$485$	−6.10691	−0.277300
$486$	−2.18333	−0.0990380
$487$	30.7196	1.39204	0.696019	−	0.718024i	$-0.254953\pi$
$487$	30.7196	1.39204	0.696019	+	0.718024i	$0.254953\pi$
$488$	20.5147	0.928659
$489$	10.6504	0.481627
$490$	7.91982	0.357781
$491$	−4.15277	−0.187412	−0.0937060	−	0.995600i	$-0.529871\pi$
$491$	−4.15277	−0.187412	−0.0937060	+	0.995600i	$0.529871\pi$
$492$	−15.3627	−0.692603
$493$	−0.792727	−0.0357026
$494$	5.85400	0.263384
$495$	−2.35130	−0.105683
$496$	0	0
$497$	0.322821	0.0144805
$498$	14.8260	0.664368
$499$	−20.1359	−0.901405	−0.450703	−	0.892674i	$-0.648827\pi$
$499$	−20.1359	−0.901405	−0.450703	+	0.892674i	$0.648827\pi$
$500$	−14.6073	−0.653256
$501$	−12.9868	−0.580206
$502$	1.84805	0.0824823
$503$	7.78865	0.347279	0.173639	−	0.984809i	$-0.444447\pi$
$503$	7.78865	0.347279	0.173639	+	0.984809i	$0.444447\pi$
$504$	−0.965191	−0.0429930
$505$	−0.773775	−0.0344325
$506$	88.2326	3.92242
$507$	5.42572	0.240965
$508$	−38.7567	−1.71955
$509$	19.4723	0.863095	0.431547	−	0.902090i	$-0.357968\pi$
$509$	19.4723	0.863095	0.431547	+	0.902090i	$0.357968\pi$
$510$	0.142791	0.00632290
$511$	7.29960	0.322915
$512$	−20.2779	−0.896167
$513$	0.624627	0.0275779
$514$	53.5984	2.36412
$515$	−2.28692	−0.100774
$516$	9.81287	0.431988
$517$	14.3259	0.630052
$518$	2.49871	0.109787
$519$	2.71703	0.119264
$520$	3.91030	0.171478
$521$	18.5057	0.810748	0.405374	−	0.914151i	$-0.367141\pi$
$521$	18.5057	0.810748	0.405374	+	0.914151i	$0.367141\pi$
$522$	−14.3972	−0.630149
$523$	−7.37737	−0.322590	−0.161295	−	0.986906i	$-0.551567\pi$
$523$	−7.37737	−0.322590	−0.161295	+	0.986906i	$0.551567\pi$
$524$	−8.68910	−0.379585
$525$	−2.71146	−0.118338
$526$	−14.0959	−0.614611
$527$	0	0
$528$	8.11652	0.353226
$529$	64.4247	2.80107
$530$	−6.13349	−0.266422
$531$	−9.47321	−0.411102
$532$	0.996213	0.0431913
$533$	23.8330	1.03232
$534$	−36.7185	−1.58897
$535$	−10.5436	−0.455837
$536$	6.63941	0.286779
$537$	7.20605	0.310964
$538$	−36.6934	−1.58197
$539$	28.8185	1.24130
$540$	1.50528	0.0647768
$541$	−18.5224	−0.796342	−0.398171	−	0.917311i	$-0.630355\pi$
$541$	−18.5224	−0.796342	−0.398171	+	0.917311i	$0.630355\pi$
$542$	−40.2023	−1.72684
$543$	−20.3446	−0.873071
$544$	−0.895507	−0.0383945
$545$	7.20670	0.308701
$546$	5.40212	0.231189
$547$	33.5340	1.43381	0.716906	−	0.697170i	$-0.245558\pi$
$547$	33.5340	1.43381	0.716906	+	0.697170i	$0.245558\pi$
$548$	−6.33467	−0.270603
$549$	−12.2514	−0.522876
$550$	−44.3898	−1.89279
$551$	4.11888	0.175470
$552$	−15.6566	−0.666391
$553$	−7.70034	−0.327452
$554$	27.3785	1.16320
$555$	−1.08014	−0.0458494
$556$	−46.9097	−1.98941
$557$	−3.07109	−0.130126	−0.0650631	−	0.997881i	$-0.520725\pi$
$557$	−3.07109	−0.130126	−0.0650631	+	0.997881i	$0.520725\pi$
$558$	0	0
$559$	−15.2233	−0.643877
$560$	−0.588879	−0.0248847
$561$	0.519586	0.0219369
$562$	3.07691	0.129792
$563$	15.2851	0.644188	0.322094	−	0.946708i	$-0.395613\pi$
$563$	15.2851	0.644188	0.322094	+	0.946708i	$0.395613\pi$
$564$	−9.17126	−0.386180
$565$	−2.34024	−0.0984548
$566$	69.7958	2.93374
$567$	0.576411	0.0242070
$568$	−0.937802	−0.0393493
$569$	−19.5827	−0.820950	−0.410475	−	0.911872i	$-0.634637\pi$
$569$	−19.5827	−0.820950	−0.410475	+	0.911872i	$0.634637\pi$
$570$	−0.741919	−0.0310756
$571$	−16.6778	−0.697946	−0.348973	−	0.937133i	$-0.613470\pi$
$571$	−16.6778	−0.697946	−0.348973	+	0.937133i	$0.613470\pi$
$572$	51.3339	2.14638
$573$	−12.7837	−0.534047
$574$	6.98746	0.291651
$575$	−43.9833	−1.83423
$576$	−12.5080	−0.521167
$577$	21.8376	0.909113	0.454556	−	0.890718i	$-0.349798\pi$
$577$	21.8376	0.909113	0.454556	+	0.890718i	$0.349798\pi$
$578$	37.0851	1.54254
$579$	−16.5833	−0.689177
$580$	9.92600	0.412155
$581$	−3.91414	−0.162386
$582$	24.5090	1.01593
$583$	−22.3184	−0.924335
$584$	−21.2055	−0.877489
$585$	−2.33522	−0.0965496
$586$	−61.6401	−2.54633
$587$	−23.8666	−0.985079	−0.492539	−	0.870290i	$-0.663931\pi$
$587$	−23.8666	−0.985079	−0.492539	+	0.870290i	$0.663931\pi$
$588$	−18.4493	−0.760835
$589$	0	0
$590$	11.2521	0.463242
$591$	3.15873	0.129933
$592$	3.72856	0.153243
$593$	−7.96657	−0.327148	−0.163574	−	0.986531i	$-0.552302\pi$
$593$	−7.96657	−0.327148	−0.163574	+	0.986531i	$0.552302\pi$
$594$	9.43652	0.387185
$595$	−0.0376976	−0.00154545
$596$	27.6985	1.13458
$597$	8.77662	0.359203
$598$	87.6293	3.58343
$599$	26.3636	1.07719	0.538594	−	0.842565i	$-0.318956\pi$
$599$	26.3636	1.07719	0.538594	+	0.842565i	$0.318956\pi$
$600$	7.87685	0.321571
$601$	35.7363	1.45771	0.728856	−	0.684667i	$-0.240052\pi$
$601$	35.7363	1.45771	0.728856	+	0.684667i	$0.240052\pi$
$602$	−4.46322	−0.181907
$603$	−3.96505	−0.161469
$604$	17.2828	0.703226
$605$	4.17826	0.169871
$606$	3.10540	0.126148
$607$	11.7150	0.475497	0.237748	−	0.971327i	$-0.423591\pi$
$607$	11.7150	0.475497	0.237748	+	0.971327i	$0.423591\pi$
$608$	4.65291	0.188700
$609$	3.80093	0.154022
$610$	14.5519	0.589191
$611$	14.2279	0.575600
$612$	−0.332633	−0.0134459
$613$	−7.96337	−0.321637	−0.160819	−	0.986984i	$-0.551413\pi$
$613$	−7.96337	−0.321637	−0.160819	+	0.986984i	$0.551413\pi$
$614$	−19.0217	−0.767652
$615$	−3.02053	−0.121800
$616$	4.17163	0.168080
$617$	12.7408	0.512924	0.256462	−	0.966554i	$-0.417443\pi$
$617$	12.7408	0.512924	0.256462	+	0.966554i	$0.417443\pi$
$618$	9.17812	0.369198
$619$	−20.9025	−0.840142	−0.420071	−	0.907491i	$-0.637995\pi$
$619$	−20.9025	−0.840142	−0.420071	+	0.907491i	$0.637995\pi$
$620$	0	0
$621$	9.35012	0.375207
$622$	−58.0167	−2.32626
$623$	9.69388	0.388377
$624$	8.06102	0.322699
$625$	20.6482	0.825928
$626$	1.37493	0.0549534
$627$	−2.69968	−0.107815
$628$	−21.3871	−0.853439
$629$	0.238687	0.00951708
$630$	−0.684649	−0.0272771
$631$	34.3198	1.36625	0.683126	−	0.730301i	$-0.260620\pi$
$631$	34.3198	1.36625	0.683126	+	0.730301i	$0.260620\pi$
$632$	22.3697	0.889817
$633$	12.3493	0.490842
$634$	−38.3321	−1.52236
$635$	−7.62015	−0.302396
$636$	14.2880	0.566555
$637$	28.6214	1.13402
$638$	62.2258	2.46354
$639$	0.560054	0.0221554
$640$	6.75183	0.266889
$641$	−30.9177	−1.22118	−0.610588	−	0.791949i	$-0.709067\pi$
$641$	−30.9177	−1.22118	−0.610588	+	0.791949i	$0.709067\pi$
$642$	42.3146	1.67002
$643$	28.7356	1.13322	0.566611	−	0.823985i	$-0.308254\pi$
$643$	28.7356	1.13322	0.566611	+	0.823985i	$0.308254\pi$
$644$	14.9124	0.587633
$645$	1.92936	0.0759684
$646$	0.163948	0.00645044
$647$	28.0895	1.10431	0.552156	−	0.833741i	$-0.313805\pi$
$647$	28.0895	1.10431	0.552156	+	0.833741i	$0.313805\pi$
$648$	−1.67449	−0.0657800
$649$	40.9439	1.60719
$650$	−44.0862	−1.72920
$651$	0	0
$652$	29.4690	1.15409
$653$	−39.7006	−1.55360	−0.776801	−	0.629746i	$-0.783159\pi$
$653$	−39.7006	−1.55360	−0.776801	+	0.629746i	$0.783159\pi$
$654$	−28.9228	−1.13097
$655$	−1.70841	−0.0667530
$656$	10.4267	0.407093
$657$	12.6639	0.494065
$658$	4.17139	0.162618
$659$	−13.3952	−0.521803	−0.260901	−	0.965365i	$-0.584020\pi$
$659$	−13.3952	−0.521803	−0.260901	+	0.965365i	$0.584020\pi$
$660$	−6.50591	−0.253242
$661$	−4.94835	−0.192468	−0.0962342	−	0.995359i	$-0.530680\pi$
$661$	−4.94835	−0.192468	−0.0962342	+	0.995359i	$0.530680\pi$
$662$	57.2193	2.22389
$663$	0.516033	0.0200411
$664$	11.3706	0.441267
$665$	0.195870	0.00759553
$666$	4.33495	0.167976
$667$	61.6560	2.38733
$668$	−35.9336	−1.39031
$669$	23.5264	0.909582
$670$	4.70960	0.181948
$671$	52.9513	2.04416
$672$	4.29374	0.165635
$673$	−39.4412	−1.52035	−0.760173	−	0.649721i	$-0.774886\pi$
$673$	−39.4412	−1.52035	−0.760173	+	0.649721i	$0.774886\pi$
$674$	3.97342	0.153050
$675$	−4.70404	−0.181059
$676$	15.0126	0.577409
$677$	−30.5491	−1.17410	−0.587050	−	0.809551i	$-0.699711\pi$
$677$	−30.5491	−1.17410	−0.587050	+	0.809551i	$0.699711\pi$
$678$	9.39214	0.360703
$679$	−6.47049	−0.248315
$680$	0.109512	0.00419960
$681$	−3.71655	−0.142418
$682$	0	0
$683$	4.13533	0.158234	0.0791170	−	0.996865i	$-0.474790\pi$
$683$	4.13533	0.158234	0.0791170	+	0.996865i	$0.474790\pi$
$684$	1.72830	0.0660834
$685$	−1.24549	−0.0475877
$686$	17.2008	0.656730
$687$	5.16875	0.197200
$688$	−6.66000	−0.253910
$689$	−22.1658	−0.844450
$690$	−11.1059	−0.422794
$691$	−2.76822	−0.105308	−0.0526541	−	0.998613i	$-0.516768\pi$
$691$	−2.76822	−0.105308	−0.0526541	+	0.998613i	$0.516768\pi$
$692$	7.51787	0.285786
$693$	−2.49129	−0.0946363
$694$	46.9170	1.78095
$695$	−9.22315	−0.349854
$696$	−11.0418	−0.418538
$697$	0.667471	0.0252823
$698$	−10.2863	−0.389342
$699$	−16.5272	−0.625115
$700$	−7.50245	−0.283566
$701$	20.1059	0.759388	0.379694	−	0.925112i	$-0.376029\pi$
$701$	20.1059	0.759388	0.379694	+	0.925112i	$0.376029\pi$
$702$	9.37200	0.353723
$703$	−1.24018	−0.0467742
$704$	54.0606	2.03748
$705$	−1.80321	−0.0679127
$706$	−21.7375	−0.818101
$707$	−0.819843	−0.0308334
$708$	−26.2118	−0.985100
$709$	48.8536	1.83474	0.917369	−	0.398039i	$-0.130309\pi$
$709$	48.8536	1.83474	0.917369	+	0.398039i	$0.130309\pi$
$710$	−0.665221	−0.0249653
$711$	−13.3591	−0.501006
$712$	−28.1609	−1.05538
$713$	0	0
$714$	0.151292	0.00566198
$715$	10.0930	0.377457
$716$	19.9387	0.745144
$717$	−13.5984	−0.507841
$718$	52.3711	1.95447
$719$	9.32895	0.347911	0.173956	−	0.984753i	$-0.444345\pi$
$719$	9.32895	0.347911	0.173956	+	0.984753i	$0.444345\pi$
$720$	−1.02163	−0.0380739
$721$	−2.42307	−0.0902398
$722$	40.6315	1.51215
$723$	−7.03693	−0.261706
$724$	−56.2924	−2.09209
$725$	−31.0191	−1.15202
$726$	−16.7687	−0.622345
$727$	−6.82088	−0.252972	−0.126486	−	0.991968i	$-0.540370\pi$
$727$	−6.82088	−0.252972	−0.126486	+	0.991968i	$0.540370\pi$
$728$	4.14310	0.153554
$729$	1.00000	0.0370370
$730$	−15.0419	−0.556726
$731$	−0.426345	−0.0157690
$732$	−33.8988	−1.25294
$733$	−7.63027	−0.281831	−0.140915	−	0.990022i	$-0.545005\pi$
$733$	−7.63027	−0.281831	−0.140915	+	0.990022i	$0.545005\pi$
$734$	36.0419	1.33033
$735$	−3.62740	−0.133799
$736$	69.6500	2.56733
$737$	17.1372	0.631258
$738$	12.1224	0.446230
$739$	1.07504	0.0395459	0.0197730	−	0.999804i	$-0.493706\pi$
$739$	1.07504	0.0395459	0.0197730	+	0.999804i	$0.493706\pi$
$740$	−2.98868	−0.109866
$741$	−2.68122	−0.0984972
$742$	−6.49865	−0.238573
$743$	−1.15865	−0.0425069	−0.0212535	−	0.999774i	$-0.506766\pi$
$743$	−1.15865	−0.0425069	−0.0212535	+	0.999774i	$0.506766\pi$
$744$	0	0
$745$	5.44594	0.199524
$746$	72.9595	2.67124
$747$	−6.79053	−0.248453
$748$	1.43766	0.0525662
$749$	−11.1713	−0.408189
$750$	11.5263	0.420880
$751$	51.3022	1.87204	0.936022	−	0.351941i	$-0.114478\pi$
$751$	51.3022	1.87204	0.936022	+	0.351941i	$0.114478\pi$
$752$	6.22454	0.226986
$753$	−0.846434	−0.0308458
$754$	61.8003	2.25063
$755$	3.39805	0.123668
$756$	1.59489	0.0580057
$757$	−1.60827	−0.0584535	−0.0292267	−	0.999573i	$-0.509304\pi$
$757$	−1.60827	−0.0584535	−0.0292267	+	0.999573i	$0.509304\pi$
$758$	−61.7674	−2.24349
$759$	−40.4119	−1.46686
$760$	−0.569008	−0.0206401
$761$	54.0239	1.95836	0.979182	−	0.202986i	$-0.0650647\pi$
$761$	54.0239	1.95836	0.979182	+	0.202986i	$0.0650647\pi$
$762$	30.5821	1.10787
$763$	7.63576	0.276433
$764$	−35.3717	−1.27970
$765$	−0.0654006	−0.00236456
$766$	−42.4885	−1.53517
$767$	40.6640	1.46829
$768$	−2.08121	−0.0750991
$769$	−33.3564	−1.20286	−0.601431	−	0.798924i	$-0.705403\pi$
$769$	−33.3564	−1.20286	−0.601431	+	0.798924i	$0.705403\pi$
$770$	2.95911	0.106639
$771$	−24.5489	−0.884106
$772$	−45.8849	−1.65143
$773$	−24.7577	−0.890471	−0.445235	−	0.895414i	$-0.646880\pi$
$773$	−24.7577	−0.890471	−0.445235	+	0.895414i	$0.646880\pi$
$774$	−7.74312	−0.278321
$775$	0	0
$776$	18.7969	0.674770
$777$	−1.14445	−0.0410568
$778$	54.6205	1.95824
$779$	−3.46807	−0.124257
$780$	−6.46142	−0.231356
$781$	−2.42059	−0.0866157
$782$	2.45416	0.0877604
$783$	6.59414	0.235655
$784$	12.5215	0.447197
$785$	−4.20503	−0.150084
$786$	6.85638	0.244559
$787$	32.1264	1.14518	0.572590	−	0.819842i	$-0.305939\pi$
$787$	32.1264	1.14518	0.572590	+	0.819842i	$0.305939\pi$
$788$	8.74001	0.311350
$789$	6.45614	0.229845
$790$	15.8677	0.564547
$791$	−2.47957	−0.0881635
$792$	7.23725	0.257164
$793$	52.5892	1.86750
$794$	47.3494	1.68037
$795$	2.80923	0.0996332
$796$	24.2844	0.860737
$797$	6.23641	0.220905	0.110452	−	0.993881i	$-0.464770\pi$
$797$	6.23641	0.220905	0.110452	+	0.993881i	$0.464770\pi$
$798$	−0.786090	−0.0278273
$799$	0.398469	0.0140968
$800$	−35.0409	−1.23888
$801$	16.8177	0.594223
$802$	41.9208	1.48028
$803$	−54.7343	−1.93153
$804$	−10.9710	−0.386919
$805$	2.93201	0.103340
$806$	0	0
$807$	16.8062	0.591605
$808$	2.38166	0.0837865
$809$	−30.1620	−1.06044	−0.530219	−	0.847861i	$-0.677890\pi$
$809$	−30.1620	−1.06044	−0.530219	+	0.847861i	$0.677890\pi$
$810$	−1.18778	−0.0417343
$811$	20.6553	0.725306	0.362653	−	0.931924i	$-0.381871\pi$
$811$	20.6553	0.725306	0.362653	+	0.931924i	$0.381871\pi$
$812$	10.5170	0.369073
$813$	18.4133	0.645781
$814$	−18.7360	−0.656695
$815$	5.79404	0.202956
$816$	0.225758	0.00790311
$817$	2.21522	0.0775007
$818$	11.9355	0.417315
$819$	−2.47425	−0.0864574
$820$	−8.35763	−0.291861
$821$	−32.3545	−1.12918	−0.564591	−	0.825371i	$-0.690966\pi$
$821$	−32.3545	−1.12918	−0.564591	+	0.825371i	$0.690966\pi$
$822$	4.99855	0.174344
$823$	−16.0570	−0.559712	−0.279856	−	0.960042i	$-0.590287\pi$
$823$	−16.0570	−0.559712	−0.279856	+	0.960042i	$0.590287\pi$
$824$	7.03907	0.245218
$825$	20.3312	0.707842
$826$	11.9220	0.414820
$827$	−15.3522	−0.533848	−0.266924	−	0.963718i	$-0.586007\pi$
$827$	−15.3522	−0.533848	−0.266924	+	0.963718i	$0.586007\pi$
$828$	25.8712	0.899087
$829$	−14.9407	−0.518913	−0.259457	−	0.965755i	$-0.583543\pi$
$829$	−14.9407	−0.518913	−0.259457	+	0.965755i	$0.583543\pi$
$830$	8.06566	0.279963
$831$	−12.5398	−0.435000
$832$	53.6909	1.86140
$833$	0.801576	0.0277729
$834$	37.0154	1.28174
$835$	−7.06508	−0.244497
$836$	−7.46986	−0.258351
$837$	0	0
$838$	−54.7248	−1.89044
$839$	3.64605	0.125876	0.0629378	−	0.998017i	$-0.479953\pi$
$839$	3.64605	0.125876	0.0629378	+	0.998017i	$0.479953\pi$
$840$	−0.525085	−0.0181172
$841$	14.4827	0.499404
$842$	63.2384	2.17934
$843$	−1.40927	−0.0485379
$844$	34.1699	1.17618
$845$	2.95171	0.101542
$846$	7.23684	0.248808
$847$	4.42702	0.152114
$848$	−9.69726	−0.333005
$849$	−31.9676	−1.09712
$850$	−1.23468	−0.0423493
$851$	−18.5644	−0.636380
$852$	1.54964	0.0530896
$853$	−32.3809	−1.10870	−0.554351	−	0.832283i	$-0.687033\pi$
$853$	−32.3809	−1.10870	−0.554351	+	0.832283i	$0.687033\pi$
$854$	15.4183	0.527603
$855$	0.339811	0.0116213
$856$	32.4528	1.10921
$857$	2.54593	0.0869674	0.0434837	−	0.999054i	$-0.486154\pi$
$857$	2.54593	0.0869674	0.0434837	+	0.999054i	$0.486154\pi$
$858$	−40.5065	−1.38287
$859$	18.3533	0.626208	0.313104	−	0.949719i	$-0.398631\pi$
$859$	18.3533	0.626208	0.313104	+	0.949719i	$0.398631\pi$
$860$	5.33842	0.182038
$861$	−3.20036	−0.109068
$862$	60.4201	2.05792
$863$	8.12883	0.276709	0.138354	−	0.990383i	$-0.455819\pi$
$863$	8.12883	0.276709	0.138354	+	0.990383i	$0.455819\pi$
$864$	7.44910	0.253424
$865$	1.47812	0.0502578
$866$	−6.88910	−0.234101
$867$	−16.9855	−0.576859
$868$	0	0
$869$	57.7391	1.95867
$870$	−7.83239	−0.265543
$871$	17.0200	0.576702
$872$	−22.1820	−0.751178
$873$	−11.2255	−0.379925
$874$	−12.7514	−0.431322
$875$	−3.04299	−0.102872
$876$	35.0402	1.18390
$877$	−13.0175	−0.439569	−0.219784	−	0.975548i	$-0.570535\pi$
$877$	−13.0175	−0.439569	−0.219784	+	0.975548i	$0.570535\pi$
$878$	−43.2215	−1.45865
$879$	28.2321	0.952246
$880$	4.41556	0.148849
$881$	45.2077	1.52309	0.761544	−	0.648113i	$-0.224442\pi$
$881$	45.2077	1.52309	0.761544	+	0.648113i	$0.224442\pi$
$882$	14.5579	0.490191
$883$	27.4674	0.924351	0.462175	−	0.886789i	$-0.347069\pi$
$883$	27.4674	0.924351	0.462175	+	0.886789i	$0.347069\pi$
$884$	1.42783	0.0480232
$885$	−5.15364	−0.173238
$886$	−33.0997	−1.11201
$887$	−39.6805	−1.33234	−0.666170	−	0.745800i	$-0.732068\pi$
$887$	−39.6805	−1.33234	−0.666170	+	0.745800i	$0.732068\pi$
$888$	3.32464	0.111568
$889$	−8.07383	−0.270787
$890$	−19.9757	−0.669587
$891$	−4.32207	−0.144795
$892$	65.0960	2.17958
$893$	−2.07038	−0.0692826
$894$	−21.8563	−0.730984
$895$	3.92025	0.131039
$896$	7.15381	0.238992
$897$	−40.1356	−1.34009
$898$	−30.7597	−1.02646
$899$	0	0
$900$	−13.0158	−0.433860
$901$	−0.620778	−0.0206811
$902$	−52.3937	−1.74452
$903$	2.04422	0.0680275
$904$	7.20321	0.239575
$905$	−11.0679	−0.367910
$906$	−13.6375	−0.453074
$907$	−33.1919	−1.10212	−0.551060	−	0.834466i	$-0.685777\pi$
$907$	−33.1919	−1.10212	−0.551060	+	0.834466i	$0.685777\pi$
$908$	−10.2835	−0.341269
$909$	−1.42232	−0.0471755
$910$	2.93887	0.0974226
$911$	26.0807	0.864092	0.432046	−	0.901852i	$-0.357792\pi$
$911$	26.0807	0.864092	0.432046	+	0.901852i	$0.357792\pi$
$912$	−1.17300	−0.0388419
$913$	29.3492	0.971316
$914$	−22.2102	−0.734650
$915$	−6.66501	−0.220339
$916$	14.3016	0.472539
$917$	−1.81012	−0.0597754
$918$	0.262473	0.00866291
$919$	37.7669	1.24582	0.622908	−	0.782295i	$-0.285951\pi$
$919$	37.7669	1.24582	0.622908	+	0.782295i	$0.285951\pi$
$920$	−8.51755	−0.280815
$921$	8.71221	0.287077
$922$	4.13834	0.136289
$923$	−2.40404	−0.0791300
$924$	−6.89325	−0.226771
$925$	9.33974	0.307089
$926$	−52.7809	−1.73449
$927$	−4.20372	−0.138068
$928$	49.1204	1.61246
$929$	28.8820	0.947588	0.473794	−	0.880636i	$-0.342884\pi$
$929$	28.8820	0.947588	0.473794	+	0.880636i	$0.342884\pi$
$930$	0	0
$931$	−4.16486	−0.136498
$932$	−45.7297	−1.49793
$933$	26.5726	0.869947
$934$	47.7376	1.56202
$935$	0.282666	0.00924417
$936$	7.18776	0.234939
$937$	38.0976	1.24460	0.622298	−	0.782781i	$-0.286199\pi$
$937$	38.0976	1.24460	0.622298	+	0.782781i	$0.286199\pi$
$938$	4.99000	0.162929
$939$	−0.629741	−0.0205508
$940$	−4.98937	−0.162735
$941$	15.9792	0.520907	0.260454	−	0.965486i	$-0.416128\pi$
$941$	15.9792	0.520907	0.260454	+	0.965486i	$0.416128\pi$
$942$	16.8761	0.549853
$943$	−51.9140	−1.69055
$944$	17.7900	0.579014
$945$	0.313580	0.0102008
$946$	33.4664	1.08809
$947$	−21.9867	−0.714472	−0.357236	−	0.934014i	$-0.616281\pi$
$947$	−21.9867	−0.714472	−0.357236	+	0.934014i	$0.616281\pi$
$948$	−36.9639	−1.20053
$949$	−54.3600	−1.76460
$950$	6.41522	0.208137
$951$	17.5567	0.569315
$952$	0.116032	0.00376063
$953$	−4.65753	−0.150872	−0.0754361	−	0.997151i	$-0.524035\pi$
$953$	−4.65753	−0.150872	−0.0754361	+	0.997151i	$0.524035\pi$
$954$	−11.2743	−0.365020
$955$	−6.95461	−0.225046
$956$	−37.6259	−1.21691
$957$	−28.5004	−0.921286
$958$	−29.4756	−0.952312
$959$	−1.31964	−0.0426134
$960$	−6.80463	−0.219619
$961$	0	0
$962$	−18.6078	−0.599941
$963$	−19.3808	−0.624536
$964$	−19.4708	−0.627111
$965$	−9.02165	−0.290417
$966$	−11.7671	−0.378600
$967$	−15.5017	−0.498500	−0.249250	−	0.968439i	$-0.580184\pi$
$967$	−15.5017	−0.498500	−0.249250	+	0.968439i	$0.580184\pi$
$968$	−12.8606	−0.413355
$969$	−0.0750906	−0.00241226
$970$	13.3334	0.428110
$971$	7.64833	0.245447	0.122723	−	0.992441i	$-0.460837\pi$
$971$	7.64833	0.245447	0.122723	+	0.992441i	$0.460837\pi$
$972$	2.76694	0.0887496
$973$	−9.77226	−0.313284
$974$	−67.0711	−2.14910
$975$	20.1922	0.646667
$976$	23.0071	0.736440
$977$	−33.9074	−1.08480	−0.542398	−	0.840122i	$-0.682483\pi$
$977$	−33.9074	−1.08480	−0.542398	+	0.840122i	$0.682483\pi$
$978$	−23.2533	−0.743559
$979$	−72.6872	−2.32309
$980$	−10.0368	−0.320614
$981$	13.2471	0.422947
$982$	9.06688	0.289336
$983$	−2.47069	−0.0788027	−0.0394014	−	0.999223i	$-0.512545\pi$
$983$	−2.47069	−0.0788027	−0.0394014	+	0.999223i	$0.512545\pi$
$984$	9.29712	0.296382
$985$	1.71842	0.0547533
$986$	1.73079	0.0551195
$987$	−1.91056	−0.0608139
$988$	−7.41878	−0.236023
$989$	33.1599	1.05442
$990$	5.13367	0.163159
$991$	3.74762	0.119047	0.0595235	−	0.998227i	$-0.481042\pi$
$991$	3.74762	0.119047	0.0595235	+	0.998227i	$0.481042\pi$
$992$	0	0
$993$	−26.2073	−0.831665
$994$	−0.704826	−0.0223557
$995$	4.77467	0.151367
$996$	−18.7890	−0.595352
$997$	19.0516	0.603372	0.301686	−	0.953407i	$-0.402451\pi$
$997$	19.0516	0.603372	0.301686	+	0.953407i	$0.402451\pi$
$998$	43.9633	1.39163
$999$	−1.98547	−0.0628176

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2883.2.a.n.1.2		8
3.2	odd	2		8649.2.a.bi.1.7		8
31.22	odd	30		93.2.m.a.19.2	✓	16
31.24	odd	30		93.2.m.a.49.2	yes	16
31.30	odd	2		2883.2.a.m.1.2		8
93.53	even	30		279.2.y.b.19.1		16
93.86	even	30		279.2.y.b.235.1		16
93.92	even	2		8649.2.a.bj.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.m.a.19.2	✓	16	31.22	odd	30
93.2.m.a.49.2	yes	16	31.24	odd	30
279.2.y.b.19.1		16	93.53	even	30
279.2.y.b.235.1		16	93.86	even	30
2883.2.a.m.1.2		8	31.30	odd	2
2883.2.a.n.1.2		8	1.1	even	1	trivial
8649.2.a.bi.1.7		8	3.2	odd	2
8649.2.a.bj.1.7		8	93.92	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2883 = 3 \cdot 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2883.a (trivial)

\(f(q)\)	\(=\)	\(q-2.18333 q^{2} +1.00000 q^{3} +2.76694 q^{4} +0.544022 q^{5} -2.18333 q^{6} +0.576411 q^{7} -1.67449 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.18333 q^{2} +1.00000 q^{3} +2.76694 q^{4} +0.544022 q^{5} -2.18333 q^{6} +0.576411 q^{7} -1.67449 q^{8} +1.00000 q^{9} -1.18778 q^{10} -4.32207 q^{11} +2.76694 q^{12} -4.29252 q^{13} -1.25850 q^{14} +0.544022 q^{15} -1.87792 q^{16} -0.120217 q^{17} -2.18333 q^{18} +0.624627 q^{19} +1.50528 q^{20} +0.576411 q^{21} +9.43652 q^{22} +9.35012 q^{23} -1.67449 q^{24} -4.70404 q^{25} +9.37200 q^{26} +1.00000 q^{27} +1.59489 q^{28} +6.59414 q^{29} -1.18778 q^{30} +7.44910 q^{32} -4.32207 q^{33} +0.262473 q^{34} +0.313580 q^{35} +2.76694 q^{36} -1.98547 q^{37} -1.36377 q^{38} -4.29252 q^{39} -0.910956 q^{40} -5.55223 q^{41} -1.25850 q^{42} +3.54647 q^{43} -11.9589 q^{44} +0.544022 q^{45} -20.4144 q^{46} -3.31459 q^{47} -1.87792 q^{48} -6.66775 q^{49} +10.2705 q^{50} -0.120217 q^{51} -11.8771 q^{52} +5.16382 q^{53} -2.18333 q^{54} -2.35130 q^{55} -0.965191 q^{56} +0.624627 q^{57} -14.3972 q^{58} -9.47321 q^{59} +1.50528 q^{60} -12.2514 q^{61} +0.576411 q^{63} -12.5080 q^{64} -2.33522 q^{65} +9.43652 q^{66} -3.96505 q^{67} -0.332633 q^{68} +9.35012 q^{69} -0.684649 q^{70} +0.560054 q^{71} -1.67449 q^{72} +12.6639 q^{73} +4.33495 q^{74} -4.70404 q^{75} +1.72830 q^{76} -2.49129 q^{77} +9.37200 q^{78} -13.3591 q^{79} -1.02163 q^{80} +1.00000 q^{81} +12.1224 q^{82} -6.79053 q^{83} +1.59489 q^{84} -0.0654006 q^{85} -7.74312 q^{86} +6.59414 q^{87} +7.23725 q^{88} +16.8177 q^{89} -1.18778 q^{90} -2.47425 q^{91} +25.8712 q^{92} +7.23684 q^{94} +0.339811 q^{95} +7.44910 q^{96} -11.2255 q^{97} +14.5579 q^{98} -4.32207 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{2} + 8 q^{3} + 5 q^{4} - 6 q^{5} - 5 q^{6} - 6 q^{7} + 8 q^{9}+O(q^{10}) \) 8 * q - 5 * q^2 + 8 * q^3 + 5 * q^4 - 6 * q^5 - 5 * q^6 - 6 * q^7 + 8 * q^9	\( 8 q - 5 q^{2} + 8 q^{3} + 5 q^{4} - 6 q^{5} - 5 q^{6} - 6 q^{7} + 8 q^{9} + q^{10} + 5 q^{12} - 12 q^{13} - 3 q^{14} - 6 q^{15} + 3 q^{16} - 2 q^{17} - 5 q^{18} - 8 q^{19} - 5 q^{20} - 6 q^{21} - 4 q^{22} - 4 q^{23} - 12 q^{25} + 18 q^{26} + 8 q^{27} - 15 q^{28} + 6 q^{29} + q^{30} - 17 q^{34} + 9 q^{35} + 5 q^{36} - 8 q^{37} - 7 q^{38} - 12 q^{39} + 13 q^{40} - 20 q^{41} - 3 q^{42} - 14 q^{43} - 25 q^{44} - 6 q^{45} - 9 q^{46} + 6 q^{47} + 3 q^{48} - 20 q^{49} + 6 q^{50} - 2 q^{51} - 30 q^{52} + 30 q^{53} - 5 q^{54} - 19 q^{55} + 6 q^{56} - 8 q^{57} - 19 q^{58} - 20 q^{59} - 5 q^{60} - 13 q^{61} - 6 q^{63} - 26 q^{64} + 27 q^{65} - 4 q^{66} + 32 q^{67} + 15 q^{68} - 4 q^{69} - 6 q^{70} - 17 q^{71} + 12 q^{73} + 10 q^{74} - 12 q^{75} - 20 q^{76} - 18 q^{77} + 18 q^{78} - 30 q^{79} - 21 q^{80} + 8 q^{81} - 23 q^{82} - 12 q^{83} - 15 q^{84} - 28 q^{85} + 46 q^{86} + 6 q^{87} - 22 q^{88} - 6 q^{89} + q^{90} + 15 q^{91} + 70 q^{92} + 44 q^{94} - 36 q^{95} - 39 q^{97} + 32 q^{98}+O(q^{100}) \) 8 * q - 5 * q^2 + 8 * q^3 + 5 * q^4 - 6 * q^5 - 5 * q^6 - 6 * q^7 + 8 * q^9 + q^10 + 5 * q^12 - 12 * q^13 - 3 * q^14 - 6 * q^15 + 3 * q^16 - 2 * q^17 - 5 * q^18 - 8 * q^19 - 5 * q^20 - 6 * q^21 - 4 * q^22 - 4 * q^23 - 12 * q^25 + 18 * q^26 + 8 * q^27 - 15 * q^28 + 6 * q^29 + q^30 - 17 * q^34 + 9 * q^35 + 5 * q^36 - 8 * q^37 - 7 * q^38 - 12 * q^39 + 13 * q^40 - 20 * q^41 - 3 * q^42 - 14 * q^43 - 25 * q^44 - 6 * q^45 - 9 * q^46 + 6 * q^47 + 3 * q^48 - 20 * q^49 + 6 * q^50 - 2 * q^51 - 30 * q^52 + 30 * q^53 - 5 * q^54 - 19 * q^55 + 6 * q^56 - 8 * q^57 - 19 * q^58 - 20 * q^59 - 5 * q^60 - 13 * q^61 - 6 * q^63 - 26 * q^64 + 27 * q^65 - 4 * q^66 + 32 * q^67 + 15 * q^68 - 4 * q^69 - 6 * q^70 - 17 * q^71 + 12 * q^73 + 10 * q^74 - 12 * q^75 - 20 * q^76 - 18 * q^77 + 18 * q^78 - 30 * q^79 - 21 * q^80 + 8 * q^81 - 23 * q^82 - 12 * q^83 - 15 * q^84 - 28 * q^85 + 46 * q^86 + 6 * q^87 - 22 * q^88 - 6 * q^89 + q^90 + 15 * q^91 + 70 * q^92 + 44 * q^94 - 36 * q^95 - 39 * q^97 + 32 * q^98

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