LMFDB - Embedded newform 4029.2.a.k.1.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.29
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.54629 q^{2} +1.00000 q^{3} +4.48362 q^{4} +0.532500 q^{5} +2.54629 q^{6} +0.266076 q^{7} +6.32402 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.54629 q^{2} +1.00000 q^{3} +4.48362 q^{4} +0.532500 q^{5} +2.54629 q^{6} +0.266076 q^{7} +6.32402 q^{8} +1.00000 q^{9} +1.35590 q^{10} +3.13784 q^{11} +4.48362 q^{12} +4.93220 q^{13} +0.677507 q^{14} +0.532500 q^{15} +7.13559 q^{16} +1.00000 q^{17} +2.54629 q^{18} -4.75227 q^{19} +2.38753 q^{20} +0.266076 q^{21} +7.98988 q^{22} -4.73927 q^{23} +6.32402 q^{24} -4.71644 q^{25} +12.5588 q^{26} +1.00000 q^{27} +1.19298 q^{28} +1.01931 q^{29} +1.35590 q^{30} -5.44937 q^{31} +5.52127 q^{32} +3.13784 q^{33} +2.54629 q^{34} +0.141685 q^{35} +4.48362 q^{36} +5.22931 q^{37} -12.1007 q^{38} +4.93220 q^{39} +3.36754 q^{40} +2.21952 q^{41} +0.677507 q^{42} +7.57029 q^{43} +14.0689 q^{44} +0.532500 q^{45} -12.0676 q^{46} -3.64587 q^{47} +7.13559 q^{48} -6.92920 q^{49} -12.0095 q^{50} +1.00000 q^{51} +22.1141 q^{52} -8.29840 q^{53} +2.54629 q^{54} +1.67090 q^{55} +1.68267 q^{56} -4.75227 q^{57} +2.59545 q^{58} +7.56905 q^{59} +2.38753 q^{60} -2.77205 q^{61} -13.8757 q^{62} +0.266076 q^{63} -0.212391 q^{64} +2.62640 q^{65} +7.98988 q^{66} +5.37953 q^{67} +4.48362 q^{68} -4.73927 q^{69} +0.360773 q^{70} -6.65160 q^{71} +6.32402 q^{72} +1.86363 q^{73} +13.3154 q^{74} -4.71644 q^{75} -21.3074 q^{76} +0.834904 q^{77} +12.5588 q^{78} +1.00000 q^{79} +3.79970 q^{80} +1.00000 q^{81} +5.65154 q^{82} +7.57960 q^{83} +1.19298 q^{84} +0.532500 q^{85} +19.2762 q^{86} +1.01931 q^{87} +19.8438 q^{88} -12.5833 q^{89} +1.35590 q^{90} +1.31234 q^{91} -21.2491 q^{92} -5.44937 q^{93} -9.28346 q^{94} -2.53058 q^{95} +5.52127 q^{96} +7.15649 q^{97} -17.6438 q^{98} +3.13784 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * 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 $

$2$	2.54629	1.80050	0.900251	−	0.435371i	$-0.143383\pi$
$2$	2.54629	1.80050	0.900251	+	0.435371i	$0.143383\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.48362	2.24181
$5$	0.532500	0.238141	0.119071	−	0.992886i	$-0.462009\pi$
$5$	0.532500	0.238141	0.119071	+	0.992886i	$0.462009\pi$
$6$	2.54629	1.03952
$7$	0.266076	0.100567	0.0502836	−	0.998735i	$-0.483987\pi$
$7$	0.266076	0.100567	0.0502836	+	0.998735i	$0.483987\pi$
$8$	6.32402	2.23588
$9$	1.00000	0.333333
$10$	1.35590	0.428774
$11$	3.13784	0.946095	0.473048	−	0.881037i	$-0.343154\pi$
$11$	3.13784	0.946095	0.473048	+	0.881037i	$0.343154\pi$
$12$	4.48362	1.29431
$13$	4.93220	1.36795	0.683973	−	0.729507i	$-0.260250\pi$
$13$	4.93220	1.36795	0.683973	+	0.729507i	$0.260250\pi$
$14$	0.677507	0.181071
$15$	0.532500	0.137491
$16$	7.13559	1.78390
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.54629	0.600167
$19$	−4.75227	−1.09024	−0.545122	−	0.838356i	$-0.683517\pi$
$19$	−4.75227	−1.09024	−0.545122	+	0.838356i	$0.683517\pi$
$20$	2.38753	0.533867
$21$	0.266076	0.0580625
$22$	7.98988	1.70345
$23$	−4.73927	−0.988207	−0.494103	−	0.869403i	$-0.664504\pi$
$23$	−4.73927	−0.988207	−0.494103	+	0.869403i	$0.664504\pi$
$24$	6.32402	1.29089
$25$	−4.71644	−0.943289
$26$	12.5588	2.46299
$27$	1.00000	0.192450
$28$	1.19298	0.225452
$29$	1.01931	0.189280	0.0946402	−	0.995512i	$-0.469830\pi$
$29$	1.01931	0.189280	0.0946402	+	0.995512i	$0.469830\pi$
$30$	1.35590	0.247553
$31$	−5.44937	−0.978736	−0.489368	−	0.872077i	$-0.662773\pi$
$31$	−5.44937	−0.978736	−0.489368	+	0.872077i	$0.662773\pi$
$32$	5.52127	0.976032
$33$	3.13784	0.546228
$34$	2.54629	0.436686
$35$	0.141685	0.0239492
$36$	4.48362	0.747270
$37$	5.22931	0.859693	0.429847	−	0.902902i	$-0.358568\pi$
$37$	5.22931	0.859693	0.429847	+	0.902902i	$0.358568\pi$
$38$	−12.1007	−1.96299
$39$	4.93220	0.789784
$40$	3.36754	0.532455
$41$	2.21952	0.346630	0.173315	−	0.984866i	$-0.444552\pi$
$41$	2.21952	0.346630	0.173315	+	0.984866i	$0.444552\pi$
$42$	0.677507	0.104542
$43$	7.57029	1.15446	0.577229	−	0.816582i	$-0.304134\pi$
$43$	7.57029	1.15446	0.577229	+	0.816582i	$0.304134\pi$
$44$	14.0689	2.12097
$45$	0.532500	0.0793804
$46$	−12.0676	−1.77927
$47$	−3.64587	−0.531805	−0.265902	−	0.964000i	$-0.585670\pi$
$47$	−3.64587	−0.531805	−0.265902	+	0.964000i	$0.585670\pi$
$48$	7.13559	1.02993
$49$	−6.92920	−0.989886
$50$	−12.0095	−1.69839
$51$	1.00000	0.140028
$52$	22.1141	3.06667
$53$	−8.29840	−1.13987	−0.569936	−	0.821689i	$-0.693032\pi$
$53$	−8.29840	−1.13987	−0.569936	+	0.821689i	$0.693032\pi$
$54$	2.54629	0.346507
$55$	1.67090	0.225304
$56$	1.68267	0.224856
$57$	−4.75227	−0.629453
$58$	2.59545	0.340800
$59$	7.56905	0.985407	0.492703	−	0.870197i	$-0.336009\pi$
$59$	7.56905	0.985407	0.492703	+	0.870197i	$0.336009\pi$
$60$	2.38753	0.308228
$61$	−2.77205	−0.354924	−0.177462	−	0.984128i	$-0.556789\pi$
$61$	−2.77205	−0.354924	−0.177462	+	0.984128i	$0.556789\pi$
$62$	−13.8757	−1.76222
$63$	0.266076	0.0335224
$64$	−0.212391	−0.0265489
$65$	2.62640	0.325764
$66$	7.98988	0.983486
$67$	5.37953	0.657214	0.328607	−	0.944467i	$-0.393421\pi$
$67$	5.37953	0.657214	0.328607	+	0.944467i	$0.393421\pi$
$68$	4.48362	0.543718
$69$	−4.73927	−0.570542
$70$	0.360773	0.0431206
$71$	−6.65160	−0.789399	−0.394700	−	0.918810i	$-0.629151\pi$
$71$	−6.65160	−0.789399	−0.394700	+	0.918810i	$0.629151\pi$
$72$	6.32402	0.745293
$73$	1.86363	0.218121	0.109061	−	0.994035i	$-0.465216\pi$
$73$	1.86363	0.218121	0.109061	+	0.994035i	$0.465216\pi$
$74$	13.3154	1.54788
$75$	−4.71644	−0.544608
$76$	−21.3074	−2.44412
$77$	0.834904	0.0951462
$78$	12.5588	1.42201
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	3.79970	0.424820
$81$	1.00000	0.111111
$82$	5.65154	0.624108
$83$	7.57960	0.831969	0.415984	−	0.909372i	$-0.363437\pi$
$83$	7.57960	0.831969	0.415984	+	0.909372i	$0.363437\pi$
$84$	1.19298	0.130165
$85$	0.532500	0.0577577
$86$	19.2762	2.07860
$87$	1.01931	0.109281
$88$	19.8438	2.11536
$89$	−12.5833	−1.33383	−0.666914	−	0.745134i	$-0.732385\pi$
$89$	−12.5833	−1.33383	−0.666914	+	0.745134i	$0.732385\pi$
$90$	1.35590	0.142925
$91$	1.31234	0.137571
$92$	−21.2491	−2.21537
$93$	−5.44937	−0.565074
$94$	−9.28346	−0.957516
$95$	−2.53058	−0.259632
$96$	5.52127	0.563513
$97$	7.15649	0.726631	0.363316	−	0.931666i	$-0.381645\pi$
$97$	7.15649	0.726631	0.363316	+	0.931666i	$0.381645\pi$
$98$	−17.6438	−1.78229
$99$	3.13784	0.315365
$100$	−21.1467	−2.11467
$101$	4.72685	0.470339	0.235170	−	0.971954i	$-0.424435\pi$
$101$	4.72685	0.470339	0.235170	+	0.971954i	$0.424435\pi$
$102$	2.54629	0.252121
$103$	−5.44652	−0.536662	−0.268331	−	0.963327i	$-0.586472\pi$
$103$	−5.44652	−0.536662	−0.268331	+	0.963327i	$0.586472\pi$
$104$	31.1914	3.05856
$105$	0.141685	0.0138271
$106$	−21.1302	−2.05234
$107$	−17.5629	−1.69787	−0.848936	−	0.528496i	$-0.822756\pi$
$107$	−17.5629	−1.69787	−0.848936	+	0.528496i	$0.822756\pi$
$108$	4.48362	0.431436
$109$	−8.96015	−0.858227	−0.429113	−	0.903251i	$-0.641174\pi$
$109$	−8.96015	−0.858227	−0.429113	+	0.903251i	$0.641174\pi$
$110$	4.25461	0.405661
$111$	5.22931	0.496344
$112$	1.89861	0.179402
$113$	20.5070	1.92914	0.964570	−	0.263827i	$-0.0849848\pi$
$113$	20.5070	1.92914	0.964570	+	0.263827i	$0.0849848\pi$
$114$	−12.1007	−1.13333
$115$	−2.52366	−0.235333
$116$	4.57018	0.424331
$117$	4.93220	0.455982
$118$	19.2730	1.77423
$119$	0.266076	0.0243911
$120$	3.36754	0.307413
$121$	−1.15394	−0.104903
$122$	−7.05845	−0.639042
$123$	2.21952	0.200127
$124$	−24.4329	−2.19414
$125$	−5.17401	−0.462777
$126$	0.677507	0.0603571
$127$	11.9350	1.05906	0.529530	−	0.848291i	$-0.322368\pi$
$127$	11.9350	1.05906	0.529530	+	0.848291i	$0.322368\pi$
$128$	−11.5834	−1.02383
$129$	7.57029	0.666527
$130$	6.68758	0.586540
$131$	11.0287	0.963578	0.481789	−	0.876287i	$-0.339987\pi$
$131$	11.0287	0.963578	0.481789	+	0.876287i	$0.339987\pi$
$132$	14.0689	1.22454
$133$	−1.26446	−0.109643
$134$	13.6979	1.18332
$135$	0.532500	0.0458303
$136$	6.32402	0.542280
$137$	−8.22942	−0.703087	−0.351543	−	0.936172i	$-0.614343\pi$
$137$	−8.22942	−0.703087	−0.351543	+	0.936172i	$0.614343\pi$
$138$	−12.0676	−1.02726
$139$	−15.1225	−1.28267	−0.641335	−	0.767261i	$-0.721619\pi$
$139$	−15.1225	−1.28267	−0.641335	+	0.767261i	$0.721619\pi$
$140$	0.635263	0.0536895
$141$	−3.64587	−0.307038
$142$	−16.9369	−1.42132
$143$	15.4765	1.29421
$144$	7.13559	0.594633
$145$	0.542781	0.0450755
$146$	4.74534	0.392727
$147$	−6.92920	−0.571511
$148$	23.4462	1.92727
$149$	−12.0319	−0.985694	−0.492847	−	0.870116i	$-0.664044\pi$
$149$	−12.0319	−0.985694	−0.492847	+	0.870116i	$0.664044\pi$
$150$	−12.0095	−0.980568
$151$	−0.498704	−0.0405840	−0.0202920	−	0.999794i	$-0.506460\pi$
$151$	−0.498704	−0.0405840	−0.0202920	+	0.999794i	$0.506460\pi$
$152$	−30.0534	−2.43766
$153$	1.00000	0.0808452
$154$	2.12591	0.171311
$155$	−2.90179	−0.233077
$156$	22.1141	1.77055
$157$	−1.15865	−0.0924704	−0.0462352	−	0.998931i	$-0.514722\pi$
$157$	−1.15865	−0.0924704	−0.0462352	+	0.998931i	$0.514722\pi$
$158$	2.54629	0.202572
$159$	−8.29840	−0.658106
$160$	2.94008	0.232434
$161$	−1.26101	−0.0993812
$162$	2.54629	0.200056
$163$	21.5949	1.69144	0.845721	−	0.533626i	$-0.179171\pi$
$163$	21.5949	1.69144	0.845721	+	0.533626i	$0.179171\pi$
$164$	9.95146	0.777078
$165$	1.67090	0.130080
$166$	19.2999	1.49796
$167$	7.63979	0.591185	0.295592	−	0.955314i	$-0.404483\pi$
$167$	7.63979	0.591185	0.295592	+	0.955314i	$0.404483\pi$
$168$	1.68267	0.129821
$169$	11.3266	0.871278
$170$	1.35590	0.103993
$171$	−4.75227	−0.363415
$172$	33.9423	2.58807
$173$	0.769937	0.0585372	0.0292686	−	0.999572i	$-0.490682\pi$
$173$	0.769937	0.0585372	0.0292686	+	0.999572i	$0.490682\pi$
$174$	2.59545	0.196761
$175$	−1.25493	−0.0948639
$176$	22.3904	1.68774
$177$	7.56905	0.568925
$178$	−32.0408	−2.40156
$179$	−6.31991	−0.472372	−0.236186	−	0.971708i	$-0.575897\pi$
$179$	−6.31991	−0.472372	−0.236186	+	0.971708i	$0.575897\pi$
$180$	2.38753	0.177956
$181$	−6.23690	−0.463585	−0.231793	−	0.972765i	$-0.574459\pi$
$181$	−6.23690	−0.463585	−0.231793	+	0.972765i	$0.574459\pi$
$182$	3.34160	0.247696
$183$	−2.77205	−0.204916
$184$	−29.9713	−2.20951
$185$	2.78461	0.204728
$186$	−13.8757	−1.01742
$187$	3.13784	0.229462
$188$	−16.3467	−1.19220
$189$	0.266076	0.0193542
$190$	−6.44361	−0.467469
$191$	13.3151	0.963444	0.481722	−	0.876324i	$-0.340012\pi$
$191$	13.3151	0.963444	0.481722	+	0.876324i	$0.340012\pi$
$192$	−0.212391	−0.0153280
$193$	−11.3117	−0.814236	−0.407118	−	0.913376i	$-0.633466\pi$
$193$	−11.3117	−0.814236	−0.407118	+	0.913376i	$0.633466\pi$
$194$	18.2225	1.30830
$195$	2.62640	0.188080
$196$	−31.0679	−2.21914
$197$	−2.70415	−0.192663	−0.0963314	−	0.995349i	$-0.530711\pi$
$197$	−2.70415	−0.192663	−0.0963314	+	0.995349i	$0.530711\pi$
$198$	7.98988	0.567816
$199$	25.6820	1.82055	0.910276	−	0.414002i	$-0.135869\pi$
$199$	25.6820	1.82055	0.910276	+	0.414002i	$0.135869\pi$
$200$	−29.8269	−2.10908
$201$	5.37953	0.379443
$202$	12.0360	0.846847
$203$	0.271213	0.0190354
$204$	4.48362	0.313916
$205$	1.18189	0.0825469
$206$	−13.8684	−0.966261
$207$	−4.73927	−0.329402
$208$	35.1942	2.44028
$209$	−14.9119	−1.03148
$210$	0.360773	0.0248957
$211$	10.2352	0.704621	0.352311	−	0.935883i	$-0.385396\pi$
$211$	10.2352	0.704621	0.352311	+	0.935883i	$0.385396\pi$
$212$	−37.2068	−2.55538
$213$	−6.65160	−0.455760
$214$	−44.7204	−3.05702
$215$	4.03118	0.274924
$216$	6.32402	0.430295
$217$	−1.44995	−0.0984287
$218$	−22.8152	−1.54524
$219$	1.86363	0.125932
$220$	7.49168	0.505089
$221$	4.93220	0.331776
$222$	13.3154	0.893669
$223$	−3.80056	−0.254504	−0.127252	−	0.991870i	$-0.540616\pi$
$223$	−3.80056	−0.254504	−0.127252	+	0.991870i	$0.540616\pi$
$224$	1.46908	0.0981568
$225$	−4.71644	−0.314430
$226$	52.2170	3.47342
$227$	23.9153	1.58732	0.793658	−	0.608364i	$-0.208174\pi$
$227$	23.9153	1.58732	0.793658	+	0.608364i	$0.208174\pi$
$228$	−21.3074	−1.41111
$229$	−9.14353	−0.604221	−0.302111	−	0.953273i	$-0.597691\pi$
$229$	−9.14353	−0.604221	−0.302111	+	0.953273i	$0.597691\pi$
$230$	−6.42599	−0.423717
$231$	0.834904	0.0549327
$232$	6.44612	0.423208
$233$	1.97637	0.129476	0.0647381	−	0.997902i	$-0.479379\pi$
$233$	1.97637	0.129476	0.0647381	+	0.997902i	$0.479379\pi$
$234$	12.5588	0.820997
$235$	−1.94143	−0.126645
$236$	33.9367	2.20909
$237$	1.00000	0.0649570
$238$	0.677507	0.0439163
$239$	−5.44367	−0.352122	−0.176061	−	0.984379i	$-0.556336\pi$
$239$	−5.44367	−0.352122	−0.176061	+	0.984379i	$0.556336\pi$
$240$	3.79970	0.245270
$241$	−1.13651	−0.0732090	−0.0366045	−	0.999330i	$-0.511654\pi$
$241$	−1.13651	−0.0732090	−0.0366045	+	0.999330i	$0.511654\pi$
$242$	−2.93826	−0.188879
$243$	1.00000	0.0641500
$244$	−12.4288	−0.795673
$245$	−3.68980	−0.235733
$246$	5.65154	0.360329
$247$	−23.4391	−1.49140
$248$	−34.4620	−2.18834
$249$	7.57960	0.480337
$250$	−13.1745	−0.833231
$251$	−7.29987	−0.460764	−0.230382	−	0.973100i	$-0.573998\pi$
$251$	−7.29987	−0.460764	−0.230382	+	0.973100i	$0.573998\pi$
$252$	1.19298	0.0751508
$253$	−14.8711	−0.934938
$254$	30.3900	1.90684
$255$	0.532500	0.0333464
$256$	−29.0699	−1.81687
$257$	19.2233	1.19911	0.599557	−	0.800332i	$-0.295343\pi$
$257$	19.2233	1.19911	0.599557	+	0.800332i	$0.295343\pi$
$258$	19.2762	1.20008
$259$	1.39139	0.0864569
$260$	11.7758	0.730302
$261$	1.01931	0.0630935
$262$	28.0822	1.73492
$263$	30.5167	1.88174	0.940871	−	0.338766i	$-0.110010\pi$
$263$	30.5167	1.88174	0.940871	+	0.338766i	$0.110010\pi$
$264$	19.8438	1.22130
$265$	−4.41890	−0.271451
$266$	−3.21970	−0.197412
$267$	−12.5833	−0.770086
$268$	24.1198	1.47335
$269$	12.7976	0.780283	0.390142	−	0.920755i	$-0.372426\pi$
$269$	12.7976	0.780283	0.390142	+	0.920755i	$0.372426\pi$
$270$	1.35590	0.0825176
$271$	3.20825	0.194887	0.0974436	−	0.995241i	$-0.468933\pi$
$271$	3.20825	0.194887	0.0974436	+	0.995241i	$0.468933\pi$
$272$	7.13559	0.432659
$273$	1.31234	0.0794264
$274$	−20.9545	−1.26591
$275$	−14.7995	−0.892441
$276$	−21.2491	−1.27904
$277$	−18.1532	−1.09072	−0.545361	−	0.838202i	$-0.683607\pi$
$277$	−18.1532	−1.09072	−0.545361	+	0.838202i	$0.683607\pi$
$278$	−38.5062	−2.30945
$279$	−5.44937	−0.326245
$280$	0.896021	0.0535475
$281$	−23.6350	−1.40995	−0.704973	−	0.709234i	$-0.749041\pi$
$281$	−23.6350	−1.40995	−0.704973	+	0.709234i	$0.749041\pi$
$282$	−9.28346	−0.552822
$283$	−1.03820	−0.0617146	−0.0308573	−	0.999524i	$-0.509824\pi$
$283$	−1.03820	−0.0617146	−0.0308573	+	0.999524i	$0.509824\pi$
$284$	−29.8232	−1.76968
$285$	−2.53058	−0.149899
$286$	39.4077	2.33022
$287$	0.590559	0.0348596
$288$	5.52127	0.325344
$289$	1.00000	0.0588235
$290$	1.38208	0.0811585
$291$	7.15649	0.419521
$292$	8.35579	0.488986
$293$	−31.9923	−1.86901	−0.934506	−	0.355948i	$-0.884158\pi$
$293$	−31.9923	−1.86901	−0.934506	+	0.355948i	$0.884158\pi$
$294$	−17.6438	−1.02901
$295$	4.03052	0.234666
$296$	33.0703	1.92217
$297$	3.13784	0.182076
$298$	−30.6369	−1.77475
$299$	−23.3751	−1.35181
$300$	−21.1467	−1.22091
$301$	2.01427	0.116101
$302$	−1.26985	−0.0730715
$303$	4.72685	0.271551
$304$	−33.9102	−1.94489
$305$	−1.47612	−0.0845222
$306$	2.54629	0.145562
$307$	−23.4550	−1.33865	−0.669323	−	0.742972i	$-0.733416\pi$
$307$	−23.4550	−1.33865	−0.669323	+	0.742972i	$0.733416\pi$
$308$	3.74339	0.213299
$309$	−5.44652	−0.309842
$310$	−7.38882	−0.419657
$311$	−24.8917	−1.41148	−0.705739	−	0.708472i	$-0.749385\pi$
$311$	−24.8917	−1.41148	−0.705739	+	0.708472i	$0.749385\pi$
$312$	31.1914	1.76586
$313$	6.96133	0.393478	0.196739	−	0.980456i	$-0.436965\pi$
$313$	6.96133	0.393478	0.196739	+	0.980456i	$0.436965\pi$
$314$	−2.95027	−0.166493
$315$	0.141685	0.00798306
$316$	4.48362	0.252223
$317$	4.35777	0.244757	0.122378	−	0.992484i	$-0.460948\pi$
$317$	4.35777	0.244757	0.122378	+	0.992484i	$0.460948\pi$
$318$	−21.1302	−1.18492
$319$	3.19842	0.179077
$320$	−0.113098	−0.00632239
$321$	−17.5629	−0.980267
$322$	−3.21089	−0.178936
$323$	−4.75227	−0.264423
$324$	4.48362	0.249090
$325$	−23.2625	−1.29037
$326$	54.9869	3.04544
$327$	−8.96015	−0.495498
$328$	14.0363	0.775023
$329$	−0.970078	−0.0534821
$330$	4.25461	0.234208
$331$	0.621633	0.0341681	0.0170840	−	0.999854i	$-0.494562\pi$
$331$	0.621633	0.0341681	0.0170840	+	0.999854i	$0.494562\pi$
$332$	33.9840	1.86512
$333$	5.22931	0.286564
$334$	19.4532	1.06443
$335$	2.86460	0.156510
$336$	1.89861	0.103578
$337$	−33.7404	−1.83796	−0.918979	−	0.394307i	$-0.870985\pi$
$337$	−33.7404	−1.83796	−0.918979	+	0.394307i	$0.870985\pi$
$338$	28.8409	1.56874
$339$	20.5070	1.11379
$340$	2.38753	0.129482
$341$	−17.0993	−0.925978
$342$	−12.1007	−0.654330
$343$	−3.70622	−0.200117
$344$	47.8747	2.58123
$345$	−2.52366	−0.135869
$346$	1.96049	0.105396
$347$	24.0234	1.28964	0.644821	−	0.764334i	$-0.276932\pi$
$347$	24.0234	1.28964	0.644821	+	0.764334i	$0.276932\pi$
$348$	4.57018	0.244987
$349$	−16.9522	−0.907429	−0.453714	−	0.891147i	$-0.649901\pi$
$349$	−16.9522	−0.907429	−0.453714	+	0.891147i	$0.649901\pi$
$350$	−3.19543	−0.170803
$351$	4.93220	0.263261
$352$	17.3249	0.923420
$353$	−0.0456906	−0.00243187	−0.00121593	−	0.999999i	$-0.500387\pi$
$353$	−0.0456906	−0.00243187	−0.00121593	+	0.999999i	$0.500387\pi$
$354$	19.2730	1.02435
$355$	−3.54198	−0.187989
$356$	−56.4188	−2.99019
$357$	0.266076	0.0140822
$358$	−16.0923	−0.850507
$359$	−30.9851	−1.63533	−0.817665	−	0.575694i	$-0.804732\pi$
$359$	−30.9851	−1.63533	−0.817665	+	0.575694i	$0.804732\pi$
$360$	3.36754	0.177485
$361$	3.58405	0.188634
$362$	−15.8810	−0.834687
$363$	−1.15394	−0.0605660
$364$	5.88403	0.308407
$365$	0.992381	0.0519436
$366$	−7.05845	−0.368951
$367$	9.21672	0.481109	0.240554	−	0.970636i	$-0.422671\pi$
$367$	9.21672	0.481109	0.240554	+	0.970636i	$0.422671\pi$
$368$	−33.8175	−1.76286
$369$	2.21952	0.115543
$370$	7.09043	0.368614
$371$	−2.20800	−0.114634
$372$	−24.4329	−1.26679
$373$	−37.9091	−1.96286	−0.981430	−	0.191820i	$-0.938561\pi$
$373$	−37.9091	−1.96286	−0.981430	+	0.191820i	$0.938561\pi$
$374$	7.98988	0.413147
$375$	−5.17401	−0.267185
$376$	−23.0566	−1.18905
$377$	5.02742	0.258926
$378$	0.677507	0.0348472
$379$	−37.1249	−1.90698	−0.953489	−	0.301428i	$-0.902537\pi$
$379$	−37.1249	−1.90698	−0.953489	+	0.301428i	$0.902537\pi$
$380$	−11.3462	−0.582046
$381$	11.9350	0.611448
$382$	33.9041	1.73468
$383$	28.2467	1.44334	0.721668	−	0.692239i	$-0.243376\pi$
$383$	28.2467	1.44334	0.721668	+	0.692239i	$0.243376\pi$
$384$	−11.5834	−0.591111
$385$	0.444586	0.0226582
$386$	−28.8030	−1.46603
$387$	7.57029	0.384819
$388$	32.0870	1.62897
$389$	16.7415	0.848826	0.424413	−	0.905469i	$-0.360481\pi$
$389$	16.7415	0.848826	0.424413	+	0.905469i	$0.360481\pi$
$390$	6.68758	0.338639
$391$	−4.73927	−0.239675
$392$	−43.8204	−2.21327
$393$	11.0287	0.556322
$394$	−6.88557	−0.346890
$395$	0.532500	0.0267930
$396$	14.0689	0.706988
$397$	11.2822	0.566239	0.283119	−	0.959085i	$-0.408631\pi$
$397$	11.2822	0.566239	0.283119	+	0.959085i	$0.408631\pi$
$398$	65.3940	3.27791
$399$	−1.26446	−0.0633023
$400$	−33.6546	−1.68273
$401$	−0.435557	−0.0217507	−0.0108754	−	0.999941i	$-0.503462\pi$
$401$	−0.435557	−0.0217507	−0.0108754	+	0.999941i	$0.503462\pi$
$402$	13.6979	0.683188
$403$	−26.8774	−1.33886
$404$	21.1934	1.05441
$405$	0.532500	0.0264601
$406$	0.690587	0.0342733
$407$	16.4088	0.813352
$408$	6.32402	0.313086
$409$	34.6394	1.71281	0.856405	−	0.516305i	$-0.172693\pi$
$409$	34.6394	1.71281	0.856405	+	0.516305i	$0.172693\pi$
$410$	3.00945	0.148626
$411$	−8.22942	−0.405927
$412$	−24.4201	−1.20309
$413$	2.01394	0.0990996
$414$	−12.0676	−0.593090
$415$	4.03614	0.198126
$416$	27.2320	1.33516
$417$	−15.1225	−0.740550
$418$	−37.9700	−1.85717
$419$	4.12171	0.201359	0.100679	−	0.994919i	$-0.467898\pi$
$419$	4.12171	0.201359	0.100679	+	0.994919i	$0.467898\pi$
$420$	0.635263	0.0309977
$421$	−19.7188	−0.961034	−0.480517	−	0.876985i	$-0.659551\pi$
$421$	−19.7188	−0.961034	−0.480517	+	0.876985i	$0.659551\pi$
$422$	26.0619	1.26867
$423$	−3.64587	−0.177268
$424$	−52.4792	−2.54862
$425$	−4.71644	−0.228781
$426$	−16.9369	−0.820597
$427$	−0.737575	−0.0356938
$428$	−78.7454	−3.80630
$429$	15.4765	0.747211
$430$	10.2646	0.495001
$431$	36.5800	1.76199	0.880997	−	0.473122i	$-0.156873\pi$
$431$	36.5800	1.76199	0.880997	+	0.473122i	$0.156873\pi$
$432$	7.13559	0.343311
$433$	−20.7728	−0.998276	−0.499138	−	0.866522i	$-0.666350\pi$
$433$	−20.7728	−0.998276	−0.499138	+	0.866522i	$0.666350\pi$
$434$	−3.69199	−0.177221
$435$	0.542781	0.0260243
$436$	−40.1739	−1.92398
$437$	22.5223	1.07739
$438$	4.74534	0.226741
$439$	12.7905	0.610458	0.305229	−	0.952279i	$-0.401267\pi$
$439$	12.7905	0.610458	0.305229	+	0.952279i	$0.401267\pi$
$440$	10.5668	0.503753
$441$	−6.92920	−0.329962
$442$	12.5588	0.597363
$443$	−28.2539	−1.34238	−0.671192	−	0.741283i	$-0.734218\pi$
$443$	−28.2539	−1.34238	−0.671192	+	0.741283i	$0.734218\pi$
$444$	23.4462	1.11271
$445$	−6.70061	−0.317640
$446$	−9.67734	−0.458235
$447$	−12.0319	−0.569091
$448$	−0.0565122	−0.00266995
$449$	11.0406	0.521039	0.260519	−	0.965469i	$-0.416106\pi$
$449$	11.0406	0.521039	0.260519	+	0.965469i	$0.416106\pi$
$450$	−12.0095	−0.566131
$451$	6.96449	0.327945
$452$	91.9457	4.32476
$453$	−0.498704	−0.0234312
$454$	60.8955	2.85797
$455$	0.698821	0.0327612
$456$	−30.0534	−1.40738
$457$	26.5340	1.24121	0.620604	−	0.784124i	$-0.286887\pi$
$457$	26.5340	1.24121	0.620604	+	0.784124i	$0.286887\pi$
$458$	−23.2821	−1.08790
$459$	1.00000	0.0466760
$460$	−11.3151	−0.527571
$461$	−13.9112	−0.647909	−0.323954	−	0.946073i	$-0.605012\pi$
$461$	−13.9112	−0.647909	−0.323954	+	0.946073i	$0.605012\pi$
$462$	2.12591	0.0989064
$463$	−19.9407	−0.926722	−0.463361	−	0.886170i	$-0.653357\pi$
$463$	−19.9407	−0.926722	−0.463361	+	0.886170i	$0.653357\pi$
$464$	7.27335	0.337657
$465$	−2.90179	−0.134567
$466$	5.03242	0.233122
$467$	−30.7089	−1.42104	−0.710519	−	0.703678i	$-0.751540\pi$
$467$	−30.7089	−1.42104	−0.710519	+	0.703678i	$0.751540\pi$
$468$	22.1141	1.02222
$469$	1.43136	0.0660942
$470$	−4.94344	−0.228024
$471$	−1.15865	−0.0533878
$472$	47.8669	2.20325
$473$	23.7544	1.09223
$474$	2.54629	0.116955
$475$	22.4138	1.02842
$476$	1.19298	0.0546802
$477$	−8.29840	−0.379957
$478$	−13.8612	−0.633996
$479$	−34.9934	−1.59889	−0.799444	−	0.600741i	$-0.794872\pi$
$479$	−34.9934	−1.59889	−0.799444	+	0.600741i	$0.794872\pi$
$480$	2.94008	0.134196
$481$	25.7920	1.17601
$482$	−2.89389	−0.131813
$483$	−1.26101	−0.0573778
$484$	−5.17381	−0.235173
$485$	3.81083	0.173041
$486$	2.54629	0.115502
$487$	26.6198	1.20626	0.603128	−	0.797644i	$-0.293921\pi$
$487$	26.6198	1.20626	0.603128	+	0.797644i	$0.293921\pi$
$488$	−17.5305	−0.793568
$489$	21.5949	0.976554
$490$	−9.39532	−0.424437
$491$	−4.65724	−0.210178	−0.105089	−	0.994463i	$-0.533513\pi$
$491$	−4.65724	−0.210178	−0.105089	+	0.994463i	$0.533513\pi$
$492$	9.95146	0.448646
$493$	1.01931	0.0459072
$494$	−59.6830	−2.68526
$495$	1.67090	0.0751015
$496$	−38.8845	−1.74597
$497$	−1.76983	−0.0793877
$498$	19.2999	0.864849
$499$	−26.0271	−1.16513	−0.582566	−	0.812784i	$-0.697951\pi$
$499$	−26.0271	−1.16513	−0.582566	+	0.812784i	$0.697951\pi$
$500$	−23.1983	−1.03746
$501$	7.63979	0.341321
$502$	−18.5876	−0.829606
$503$	−3.91322	−0.174482	−0.0872410	−	0.996187i	$-0.527805\pi$
$503$	−3.91322	−0.174482	−0.0872410	+	0.996187i	$0.527805\pi$
$504$	1.68267	0.0749520
$505$	2.51705	0.112007
$506$	−37.8662	−1.68336
$507$	11.3266	0.503033
$508$	53.5120	2.37421
$509$	3.89517	0.172650	0.0863251	−	0.996267i	$-0.472488\pi$
$509$	3.89517	0.172650	0.0863251	+	0.996267i	$0.472488\pi$
$510$	1.35590	0.0600403
$511$	0.495866	0.0219358
$512$	−50.8537	−2.24744
$513$	−4.75227	−0.209818
$514$	48.9481	2.15901
$515$	−2.90027	−0.127801
$516$	33.9423	1.49423
$517$	−11.4402	−0.503138
$518$	3.54290	0.155666
$519$	0.769937	0.0337965
$520$	16.6094	0.728370
$521$	5.83210	0.255509	0.127754	−	0.991806i	$-0.459223\pi$
$521$	5.83210	0.255509	0.127754	+	0.991806i	$0.459223\pi$
$522$	2.59545	0.113600
$523$	34.7993	1.52167	0.760834	−	0.648947i	$-0.224790\pi$
$523$	34.7993	1.52167	0.760834	+	0.648947i	$0.224790\pi$
$524$	49.4483	2.16016
$525$	−1.25493	−0.0547697
$526$	77.7046	3.38808
$527$	−5.44937	−0.237378
$528$	22.3904	0.974416
$529$	−0.539283	−0.0234471
$530$	−11.2518	−0.488747
$531$	7.56905	0.328469
$532$	−5.66937	−0.245798
$533$	10.9471	0.474171
$534$	−32.0408	−1.38654
$535$	−9.35225	−0.404333
$536$	34.0203	1.46945
$537$	−6.31991	−0.272724
$538$	32.5865	1.40490
$539$	−21.7428	−0.936527
$540$	2.38753	0.102743
$541$	−3.48984	−0.150040	−0.0750200	−	0.997182i	$-0.523902\pi$
$541$	−3.48984	−0.150040	−0.0750200	+	0.997182i	$0.523902\pi$
$542$	8.16915	0.350895
$543$	−6.23690	−0.267651
$544$	5.52127	0.236723
$545$	−4.77128	−0.204379
$546$	3.34160	0.143007
$547$	−13.1718	−0.563184	−0.281592	−	0.959534i	$-0.590862\pi$
$547$	−13.1718	−0.563184	−0.281592	+	0.959534i	$0.590862\pi$
$548$	−36.8976	−1.57619
$549$	−2.77205	−0.118308
$550$	−37.6838	−1.60684
$551$	−4.84402	−0.206362
$552$	−29.9713	−1.27566
$553$	0.266076	0.0113147
$554$	−46.2234	−1.96385
$555$	2.78461	0.118200
$556$	−67.8033	−2.87550
$557$	26.0947	1.10567	0.552833	−	0.833292i	$-0.313547\pi$
$557$	26.0947	1.10567	0.552833	+	0.833292i	$0.313547\pi$
$558$	−13.8757	−0.587406
$559$	37.3382	1.57924
$560$	1.01101	0.0427229
$561$	3.13784	0.132480
$562$	−60.1817	−2.53861
$563$	−13.0124	−0.548408	−0.274204	−	0.961672i	$-0.588414\pi$
$563$	−13.0124	−0.548408	−0.274204	+	0.961672i	$0.588414\pi$
$564$	−16.3467	−0.688320
$565$	10.9200	0.459408
$566$	−2.64356	−0.111117
$567$	0.266076	0.0111741
$568$	−42.0649	−1.76500
$569$	27.0617	1.13448	0.567242	−	0.823551i	$-0.308010\pi$
$569$	27.0617	1.13448	0.567242	+	0.823551i	$0.308010\pi$
$570$	−6.44361	−0.269893
$571$	−3.04008	−0.127224	−0.0636118	−	0.997975i	$-0.520262\pi$
$571$	−3.04008	−0.127224	−0.0636118	+	0.997975i	$0.520262\pi$
$572$	69.3906	2.90137
$573$	13.3151	0.556245
$574$	1.50374	0.0627648
$575$	22.3525	0.932164
$576$	−0.212391	−0.00884964
$577$	11.0398	0.459592	0.229796	−	0.973239i	$-0.426194\pi$
$577$	11.0398	0.459592	0.229796	+	0.973239i	$0.426194\pi$
$578$	2.54629	0.105912
$579$	−11.3117	−0.470099
$580$	2.43362	0.101051
$581$	2.01675	0.0836688
$582$	18.2225	0.755348
$583$	−26.0391	−1.07843
$584$	11.7856	0.487692
$585$	2.62640	0.108588
$586$	−81.4619	−3.36516
$587$	−7.25957	−0.299634	−0.149817	−	0.988714i	$-0.547869\pi$
$587$	−7.25957	−0.299634	−0.149817	+	0.988714i	$0.547869\pi$
$588$	−31.0679	−1.28122
$589$	25.8969	1.06706
$590$	10.2629	0.422517
$591$	−2.70415	−0.111234
$592$	37.3142	1.53360
$593$	−6.79346	−0.278974	−0.139487	−	0.990224i	$-0.544545\pi$
$593$	−6.79346	−0.278974	−0.139487	+	0.990224i	$0.544545\pi$
$594$	7.98988	0.327829
$595$	0.141685	0.00580853
$596$	−53.9466	−2.20974
$597$	25.6820	1.05110
$598$	−59.5198	−2.43394
$599$	11.8384	0.483702	0.241851	−	0.970313i	$-0.422245\pi$
$599$	11.8384	0.483702	0.241851	+	0.970313i	$0.422245\pi$
$600$	−29.8269	−1.21768
$601$	0.997576	0.0406920	0.0203460	−	0.999793i	$-0.493523\pi$
$601$	0.997576	0.0406920	0.0203460	+	0.999793i	$0.493523\pi$
$602$	5.12892	0.209039
$603$	5.37953	0.219071
$604$	−2.23600	−0.0909815
$605$	−0.614471	−0.0249818
$606$	12.0360	0.488927
$607$	6.05430	0.245736	0.122868	−	0.992423i	$-0.460791\pi$
$607$	6.05430	0.245736	0.122868	+	0.992423i	$0.460791\pi$
$608$	−26.2386	−1.06411
$609$	0.271213	0.0109901
$610$	−3.75863	−0.152182
$611$	−17.9822	−0.727481
$612$	4.48362	0.181239
$613$	12.8654	0.519627	0.259813	−	0.965659i	$-0.416339\pi$
$613$	12.8654	0.519627	0.259813	+	0.965659i	$0.416339\pi$
$614$	−59.7232	−2.41023
$615$	1.18189	0.0476585
$616$	5.27995	0.212735
$617$	19.1878	0.772473	0.386237	−	0.922400i	$-0.373775\pi$
$617$	19.1878	0.772473	0.386237	+	0.922400i	$0.373775\pi$
$618$	−13.8684	−0.557871
$619$	20.4353	0.821365	0.410683	−	0.911778i	$-0.365290\pi$
$619$	20.4353	0.821365	0.410683	+	0.911778i	$0.365290\pi$
$620$	−13.0105	−0.522515
$621$	−4.73927	−0.190181
$622$	−63.3815	−2.54137
$623$	−3.34811	−0.134139
$624$	35.1942	1.40889
$625$	20.8271	0.833082
$626$	17.7256	0.708458
$627$	−14.9119	−0.595523
$628$	−5.19495	−0.207301
$629$	5.22931	0.208506
$630$	0.360773	0.0143735
$631$	20.3028	0.808244	0.404122	−	0.914705i	$-0.367577\pi$
$631$	20.3028	0.808244	0.404122	+	0.914705i	$0.367577\pi$
$632$	6.32402	0.251556
$633$	10.2352	0.406813
$634$	11.0962	0.440685
$635$	6.35539	0.252206
$636$	−37.2068	−1.47535
$637$	−34.1762	−1.35411
$638$	8.14413	0.322429
$639$	−6.65160	−0.263133
$640$	−6.16814	−0.243817
$641$	−9.11411	−0.359986	−0.179993	−	0.983668i	$-0.557607\pi$
$641$	−9.11411	−0.359986	−0.179993	+	0.983668i	$0.557607\pi$
$642$	−44.7204	−1.76497
$643$	14.0882	0.555586	0.277793	−	0.960641i	$-0.410397\pi$
$643$	14.0882	0.555586	0.277793	+	0.960641i	$0.410397\pi$
$644$	−5.65387	−0.222794
$645$	4.03118	0.158727
$646$	−12.1007	−0.476095
$647$	9.24543	0.363475	0.181738	−	0.983347i	$-0.441828\pi$
$647$	9.24543	0.363475	0.181738	+	0.983347i	$0.441828\pi$
$648$	6.32402	0.248431
$649$	23.7505	0.932289
$650$	−59.2331	−2.32331
$651$	−1.44995	−0.0568279
$652$	96.8232	3.79189
$653$	17.0409	0.666864	0.333432	−	0.942774i	$-0.391793\pi$
$653$	17.0409	0.666864	0.333432	+	0.942774i	$0.391793\pi$
$654$	−22.8152	−0.892144
$655$	5.87276	0.229468
$656$	15.8376	0.618353
$657$	1.86363	0.0727070
$658$	−2.47010	−0.0962947
$659$	16.4264	0.639883	0.319941	−	0.947437i	$-0.396337\pi$
$659$	16.4264	0.639883	0.319941	+	0.947437i	$0.396337\pi$
$660$	7.49168	0.291613
$661$	−1.19839	−0.0466121	−0.0233060	−	0.999728i	$-0.507419\pi$
$661$	−1.19839	−0.0466121	−0.0233060	+	0.999728i	$0.507419\pi$
$662$	1.58286	0.0615197
$663$	4.93220	0.191551
$664$	47.9335	1.86018
$665$	−0.673327	−0.0261105
$666$	13.3154	0.515960
$667$	−4.83077	−0.187048
$668$	34.2539	1.32532
$669$	−3.80056	−0.146938
$670$	7.29412	0.281796
$671$	−8.69826	−0.335792
$672$	1.46908	0.0566709
$673$	36.3529	1.40130	0.700650	−	0.713505i	$-0.252893\pi$
$673$	36.3529	1.40130	0.700650	+	0.713505i	$0.252893\pi$
$674$	−85.9130	−3.30925
$675$	−4.71644	−0.181536
$676$	50.7842	1.95324
$677$	−5.81728	−0.223576	−0.111788	−	0.993732i	$-0.535658\pi$
$677$	−5.81728	−0.223576	−0.111788	+	0.993732i	$0.535658\pi$
$678$	52.2170	2.00538
$679$	1.90417	0.0730753
$680$	3.36754	0.129139
$681$	23.9153	0.916437
$682$	−43.5398	−1.66723
$683$	21.2952	0.814837	0.407418	−	0.913242i	$-0.366429\pi$
$683$	21.2952	0.814837	0.407418	+	0.913242i	$0.366429\pi$
$684$	−21.3074	−0.814707
$685$	−4.38217	−0.167434
$686$	−9.43714	−0.360312
$687$	−9.14353	−0.348847
$688$	54.0185	2.05943
$689$	−40.9294	−1.55928
$690$	−6.42599	−0.244633
$691$	31.9276	1.21458	0.607291	−	0.794479i	$-0.292256\pi$
$691$	31.9276	1.21458	0.607291	+	0.794479i	$0.292256\pi$
$692$	3.45210	0.131229
$693$	0.834904	0.0317154
$694$	61.1705	2.32200
$695$	−8.05271	−0.305457
$696$	6.44612	0.244339
$697$	2.21952	0.0840701
$698$	−43.1652	−1.63383
$699$	1.97637	0.0747531
$700$	−5.62663	−0.212667
$701$	−9.48551	−0.358263	−0.179131	−	0.983825i	$-0.557329\pi$
$701$	−9.48551	−0.358263	−0.179131	+	0.983825i	$0.557329\pi$
$702$	12.5588	0.474003
$703$	−24.8511	−0.937276
$704$	−0.666451	−0.0251178
$705$	−1.94143	−0.0731183
$706$	−0.116342	−0.00437858
$707$	1.25770	0.0473007
$708$	33.9367	1.27542
$709$	−16.1248	−0.605581	−0.302790	−	0.953057i	$-0.597918\pi$
$709$	−16.1248	−0.605581	−0.302790	+	0.953057i	$0.597918\pi$
$710$	−9.01892	−0.338474
$711$	1.00000	0.0375029
$712$	−79.5772	−2.98228
$713$	25.8261	0.967194
$714$	0.677507	0.0253551
$715$	8.24122	0.308204
$716$	−28.3360	−1.05897
$717$	−5.44367	−0.203298
$718$	−78.8972	−2.94442
$719$	42.5806	1.58799	0.793995	−	0.607924i	$-0.207998\pi$
$719$	42.5806	1.58799	0.793995	+	0.607924i	$0.207998\pi$
$720$	3.79970	0.141607
$721$	−1.44919	−0.0539705
$722$	9.12604	0.339636
$723$	−1.13651	−0.0422672
$724$	−27.9639	−1.03927
$725$	−4.80750	−0.178546
$726$	−2.93826	−0.109049
$727$	8.74471	0.324323	0.162162	−	0.986764i	$-0.448153\pi$
$727$	8.74471	0.324323	0.162162	+	0.986764i	$0.448153\pi$
$728$	8.29926	0.307591
$729$	1.00000	0.0370370
$730$	2.52690	0.0935246
$731$	7.57029	0.279997
$732$	−12.4288	−0.459382
$733$	49.9317	1.84427	0.922135	−	0.386869i	$-0.126444\pi$
$733$	49.9317	1.84427	0.922135	+	0.386869i	$0.126444\pi$
$734$	23.4685	0.866238
$735$	−3.68980	−0.136100
$736$	−26.1668	−0.964522
$737$	16.8801	0.621788
$738$	5.65154	0.208036
$739$	−34.0590	−1.25288	−0.626439	−	0.779470i	$-0.715488\pi$
$739$	−34.0590	−1.25288	−0.626439	+	0.779470i	$0.715488\pi$
$740$	12.4851	0.458962
$741$	−23.4391	−0.861058
$742$	−5.62222	−0.206398
$743$	−8.04545	−0.295159	−0.147579	−	0.989050i	$-0.547148\pi$
$743$	−8.04545	−0.295159	−0.147579	+	0.989050i	$0.547148\pi$
$744$	−34.4620	−1.26344
$745$	−6.40700	−0.234734
$746$	−96.5278	−3.53413
$747$	7.57960	0.277323
$748$	14.0689	0.514410
$749$	−4.67307	−0.170750
$750$	−13.1745	−0.481066
$751$	−17.3578	−0.633396	−0.316698	−	0.948526i	$-0.602574\pi$
$751$	−17.3578	−0.633396	−0.316698	+	0.948526i	$0.602574\pi$
$752$	−26.0154	−0.948685
$753$	−7.29987	−0.266022
$754$	12.8013	0.466196
$755$	−0.265560	−0.00966472
$756$	1.19298	0.0433883
$757$	−1.01355	−0.0368383	−0.0184191	−	0.999830i	$-0.505863\pi$
$757$	−1.01355	−0.0368383	−0.0184191	+	0.999830i	$0.505863\pi$
$758$	−94.5309	−3.43352
$759$	−14.8711	−0.539787
$760$	−16.0035	−0.580507
$761$	15.5347	0.563131	0.281566	−	0.959542i	$-0.409146\pi$
$761$	15.5347	0.563131	0.281566	+	0.959542i	$0.409146\pi$
$762$	30.3900	1.10091
$763$	−2.38408	−0.0863095
$764$	59.6996	2.15986
$765$	0.532500	0.0192526
$766$	71.9243	2.59873
$767$	37.3321	1.34798
$768$	−29.0699	−1.04897
$769$	−33.5545	−1.21001	−0.605004	−	0.796223i	$-0.706828\pi$
$769$	−33.5545	−1.21001	−0.605004	+	0.796223i	$0.706828\pi$
$770$	1.13205	0.0407962
$771$	19.2233	0.692309
$772$	−50.7175	−1.82536
$773$	44.4944	1.60035	0.800176	−	0.599766i	$-0.204740\pi$
$773$	44.4944	1.60035	0.800176	+	0.599766i	$0.204740\pi$
$774$	19.2762	0.692868
$775$	25.7017	0.923231
$776$	45.2578	1.62466
$777$	1.39139	0.0499159
$778$	42.6287	1.52831
$779$	−10.5477	−0.377912
$780$	11.7758	0.421640
$781$	−20.8717	−0.746847
$782$	−12.0676	−0.431536
$783$	1.01931	0.0364270
$784$	−49.4440	−1.76586
$785$	−0.616982	−0.0220210
$786$	28.0822	1.00166
$787$	32.7740	1.16827	0.584134	−	0.811657i	$-0.301434\pi$
$787$	32.7740	1.16827	0.584134	+	0.811657i	$0.301434\pi$
$788$	−12.1244	−0.431913
$789$	30.5167	1.08642
$790$	1.35590	0.0482408
$791$	5.45643	0.194008
$792$	19.8438	0.705119
$793$	−13.6723	−0.485518
$794$	28.7279	1.01951
$795$	−4.41890	−0.156722
$796$	115.148	4.08133
$797$	35.7702	1.26705	0.633523	−	0.773724i	$-0.281608\pi$
$797$	35.7702	1.26705	0.633523	+	0.773724i	$0.281608\pi$
$798$	−3.21970	−0.113976
$799$	−3.64587	−0.128982
$800$	−26.0408	−0.920680
$801$	−12.5833	−0.444610
$802$	−1.10906	−0.0391622
$803$	5.84777	0.206363
$804$	24.1198	0.850638
$805$	−0.671486	−0.0236668
$806$	−68.4378	−2.41062
$807$	12.7976	0.450497
$808$	29.8927	1.05162
$809$	4.58045	0.161040	0.0805200	−	0.996753i	$-0.474342\pi$
$809$	4.58045	0.161040	0.0805200	+	0.996753i	$0.474342\pi$
$810$	1.35590	0.0476415
$811$	25.5650	0.897709	0.448854	−	0.893605i	$-0.351832\pi$
$811$	25.5650	0.897709	0.448854	+	0.893605i	$0.351832\pi$
$812$	1.21601	0.0426737
$813$	3.20825	0.112518
$814$	41.7815	1.46444
$815$	11.4993	0.402802
$816$	7.13559	0.249796
$817$	−35.9760	−1.25864
$818$	88.2022	3.08392
$819$	1.31234	0.0458568
$820$	5.29915	0.185054
$821$	28.5176	0.995271	0.497635	−	0.867386i	$-0.334202\pi$
$821$	28.5176	0.995271	0.497635	+	0.867386i	$0.334202\pi$
$822$	−20.9545	−0.730873
$823$	39.3369	1.37120	0.685600	−	0.727979i	$-0.259540\pi$
$823$	39.3369	1.37120	0.685600	+	0.727979i	$0.259540\pi$
$824$	−34.4439	−1.19991
$825$	−14.7995	−0.515251
$826$	5.12809	0.178429
$827$	−13.9764	−0.486007	−0.243003	−	0.970025i	$-0.578133\pi$
$827$	−13.9764	−0.486007	−0.243003	+	0.970025i	$0.578133\pi$
$828$	−21.2491	−0.738457
$829$	5.36858	0.186459	0.0932293	−	0.995645i	$-0.470281\pi$
$829$	5.36858	0.186459	0.0932293	+	0.995645i	$0.470281\pi$
$830$	10.2772	0.356726
$831$	−18.1532	−0.629728
$832$	−1.04756	−0.0363175
$833$	−6.92920	−0.240083
$834$	−38.5062	−1.33336
$835$	4.06819	0.140785
$836$	−66.8591	−2.31237
$837$	−5.44937	−0.188358
$838$	10.4951	0.362547
$839$	−21.6746	−0.748291	−0.374145	−	0.927370i	$-0.622064\pi$
$839$	−21.6746	−0.748291	−0.374145	+	0.927370i	$0.622064\pi$
$840$	0.896021	0.0309157
$841$	−27.9610	−0.964173
$842$	−50.2098	−1.73034
$843$	−23.6350	−0.814033
$844$	45.8908	1.57963
$845$	6.03142	0.207487
$846$	−9.28346	−0.319172
$847$	−0.307034	−0.0105498
$848$	−59.2140	−2.03342
$849$	−1.03820	−0.0356309
$850$	−12.0095	−0.411921
$851$	−24.7831	−0.849555
$852$	−29.8232	−1.02173
$853$	20.2172	0.692222	0.346111	−	0.938194i	$-0.387502\pi$
$853$	20.2172	0.692222	0.346111	+	0.938194i	$0.387502\pi$
$854$	−1.87808	−0.0642667
$855$	−2.53058	−0.0865441
$856$	−111.068	−3.79624
$857$	−5.27738	−0.180272	−0.0901359	−	0.995929i	$-0.528730\pi$
$857$	−5.27738	−0.180272	−0.0901359	+	0.995929i	$0.528730\pi$
$858$	39.4077	1.34536
$859$	−9.58449	−0.327019	−0.163509	−	0.986542i	$-0.552281\pi$
$859$	−9.58449	−0.327019	−0.163509	+	0.986542i	$0.552281\pi$
$860$	18.0743	0.616327
$861$	0.590559	0.0201262
$862$	93.1433	3.17247
$863$	5.78061	0.196774	0.0983871	−	0.995148i	$-0.468632\pi$
$863$	5.78061	0.196774	0.0983871	+	0.995148i	$0.468632\pi$
$864$	5.52127	0.187838
$865$	0.409991	0.0139401
$866$	−52.8936	−1.79740
$867$	1.00000	0.0339618
$868$	−6.50100	−0.220658
$869$	3.13784	0.106444
$870$	1.38208	0.0468569
$871$	26.5329	0.899034
$872$	−56.6642	−1.91889
$873$	7.15649	0.242210
$874$	57.3484	1.93984
$875$	−1.37668	−0.0465402
$876$	8.35579	0.282316
$877$	−46.6190	−1.57421	−0.787106	−	0.616818i	$-0.788421\pi$
$877$	−46.6190	−1.57421	−0.787106	+	0.616818i	$0.788421\pi$
$878$	32.5684	1.09913
$879$	−31.9923	−1.07907
$880$	11.9229	0.401920
$881$	41.3130	1.39187	0.695935	−	0.718105i	$-0.254990\pi$
$881$	41.3130	1.39187	0.695935	+	0.718105i	$0.254990\pi$
$882$	−17.6438	−0.594098
$883$	−52.7142	−1.77397	−0.886986	−	0.461795i	$-0.847205\pi$
$883$	−52.7142	−1.77397	−0.886986	+	0.461795i	$0.847205\pi$
$884$	22.1141	0.743778
$885$	4.03052	0.135484
$886$	−71.9428	−2.41697
$887$	−13.4105	−0.450280	−0.225140	−	0.974326i	$-0.572284\pi$
$887$	−13.4105	−0.450280	−0.225140	+	0.974326i	$0.572284\pi$
$888$	33.0703	1.10977
$889$	3.17561	0.106507
$890$	−17.0617	−0.571911
$891$	3.13784	0.105122
$892$	−17.0403	−0.570550
$893$	17.3261	0.579797
$894$	−30.6369	−1.02465
$895$	−3.36535	−0.112491
$896$	−3.08205	−0.102964
$897$	−23.3751	−0.780470
$898$	28.1127	0.938131
$899$	−5.55458	−0.185256
$900$	−21.1467	−0.704891
$901$	−8.29840	−0.276460
$902$	17.7337	0.590466
$903$	2.01427	0.0670307
$904$	129.687	4.31332
$905$	−3.32115	−0.110399
$906$	−1.26985	−0.0421879
$907$	49.8213	1.65429	0.827144	−	0.561990i	$-0.189964\pi$
$907$	49.8213	1.65429	0.827144	+	0.561990i	$0.189964\pi$
$908$	107.227	3.55846
$909$	4.72685	0.156780
$910$	1.77940	0.0589866
$911$	16.8623	0.558674	0.279337	−	0.960193i	$-0.409885\pi$
$911$	16.8623	0.558674	0.279337	+	0.960193i	$0.409885\pi$
$912$	−33.9102	−1.12288
$913$	23.7836	0.787122
$914$	67.5634	2.23480
$915$	−1.47612	−0.0487989
$916$	−40.9961	−1.35455
$917$	2.93446	0.0969043
$918$	2.54629	0.0840403
$919$	−20.4249	−0.673756	−0.336878	−	0.941548i	$-0.609371\pi$
$919$	−20.4249	−0.673756	−0.336878	+	0.941548i	$0.609371\pi$
$920$	−15.9597	−0.526176
$921$	−23.4550	−0.772867
$922$	−35.4220	−1.16656
$923$	−32.8070	−1.07986
$924$	3.74339	0.123149
$925$	−24.6637	−0.810939
$926$	−50.7748	−1.66856
$927$	−5.44652	−0.178887
$928$	5.62787	0.184744
$929$	−31.1567	−1.02222	−0.511109	−	0.859516i	$-0.670765\pi$
$929$	−31.1567	−1.02222	−0.511109	+	0.859516i	$0.670765\pi$
$930$	−7.38882	−0.242289
$931$	32.9294	1.07922
$932$	8.86128	0.290261
$933$	−24.8917	−0.814917
$934$	−78.1939	−2.55858
$935$	1.67090	0.0546443
$936$	31.1914	1.01952
$937$	−27.2102	−0.888919	−0.444459	−	0.895799i	$-0.646604\pi$
$937$	−27.2102	−0.888919	−0.444459	+	0.895799i	$0.646604\pi$
$938$	3.64467	0.119003
$939$	6.96133	0.227174
$940$	−8.70461	−0.283913
$941$	20.9837	0.684049	0.342024	−	0.939691i	$-0.388887\pi$
$941$	20.9837	0.684049	0.342024	+	0.939691i	$0.388887\pi$
$942$	−2.95027	−0.0961249
$943$	−10.5189	−0.342542
$944$	54.0097	1.75786
$945$	0.141685	0.00460902
$946$	60.4857	1.96656
$947$	22.4148	0.728384	0.364192	−	0.931324i	$-0.381345\pi$
$947$	22.4148	0.728384	0.364192	+	0.931324i	$0.381345\pi$
$948$	4.48362	0.145621
$949$	9.19178	0.298378
$950$	57.0722	1.85167
$951$	4.35777	0.141310
$952$	1.68267	0.0545356
$953$	−43.8000	−1.41882	−0.709410	−	0.704796i	$-0.751039\pi$
$953$	−43.8000	−1.41882	−0.709410	+	0.704796i	$0.751039\pi$
$954$	−21.1302	−0.684114
$955$	7.09027	0.229436
$956$	−24.4074	−0.789390
$957$	3.19842	0.103390
$958$	−89.1034	−2.87880
$959$	−2.18965	−0.0707074
$960$	−0.113098	−0.00365024
$961$	−1.30434	−0.0420754
$962$	65.6741	2.11742
$963$	−17.5629	−0.565957
$964$	−5.09567	−0.164120
$965$	−6.02349	−0.193903
$966$	−3.21089	−0.103309
$967$	5.08385	0.163486	0.0817428	−	0.996653i	$-0.473951\pi$
$967$	5.08385	0.163486	0.0817428	+	0.996653i	$0.473951\pi$
$968$	−7.29752	−0.234551
$969$	−4.75227	−0.152665
$970$	9.70350	0.311561
$971$	−27.7885	−0.891775	−0.445887	−	0.895089i	$-0.647112\pi$
$971$	−27.7885	−0.891775	−0.445887	+	0.895089i	$0.647112\pi$
$972$	4.48362	0.143812
$973$	−4.02372	−0.128995
$974$	67.7818	2.17187
$975$	−23.2625	−0.744995
$976$	−19.7802	−0.633149
$977$	−0.925263	−0.0296018	−0.0148009	−	0.999890i	$-0.504711\pi$
$977$	−0.925263	−0.0296018	−0.0148009	+	0.999890i	$0.504711\pi$
$978$	54.9869	1.75829
$979$	−39.4845	−1.26193
$980$	−16.5437	−0.528468
$981$	−8.96015	−0.286076
$982$	−11.8587	−0.378426
$983$	−21.6061	−0.689126	−0.344563	−	0.938763i	$-0.611973\pi$
$983$	−21.6061	−0.689126	−0.344563	+	0.938763i	$0.611973\pi$
$984$	14.0363	0.447460
$985$	−1.43996	−0.0458810
$986$	2.59545	0.0826561
$987$	−0.970078	−0.0308779
$988$	−105.092	−3.34343
$989$	−35.8777	−1.14084
$990$	4.25461	0.135220
$991$	−47.5661	−1.51099	−0.755493	−	0.655156i	$-0.772603\pi$
$991$	−47.5661	−1.51099	−0.755493	+	0.655156i	$0.772603\pi$
$992$	−30.0875	−0.955278
$993$	0.621633	0.0197269
$994$	−4.50651	−0.142938
$995$	13.6757	0.433548
$996$	33.9840	1.07682
$997$	−12.8729	−0.407688	−0.203844	−	0.979003i	$-0.565344\pi$
$997$	−12.8729	−0.407688	−0.203844	+	0.979003i	$0.565344\pi$
$998$	−66.2726	−2.09782
$999$	5.22931	0.165448

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.k.1.29	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.k.1.29	✓	31	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q+2.54629 q^{2} +1.00000 q^{3} +4.48362 q^{4} +0.532500 q^{5} +2.54629 q^{6} +0.266076 q^{7} +6.32402 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.54629 q^{2} +1.00000 q^{3} +4.48362 q^{4} +0.532500 q^{5} +2.54629 q^{6} +0.266076 q^{7} +6.32402 q^{8} +1.00000 q^{9} +1.35590 q^{10} +3.13784 q^{11} +4.48362 q^{12} +4.93220 q^{13} +0.677507 q^{14} +0.532500 q^{15} +7.13559 q^{16} +1.00000 q^{17} +2.54629 q^{18} -4.75227 q^{19} +2.38753 q^{20} +0.266076 q^{21} +7.98988 q^{22} -4.73927 q^{23} +6.32402 q^{24} -4.71644 q^{25} +12.5588 q^{26} +1.00000 q^{27} +1.19298 q^{28} +1.01931 q^{29} +1.35590 q^{30} -5.44937 q^{31} +5.52127 q^{32} +3.13784 q^{33} +2.54629 q^{34} +0.141685 q^{35} +4.48362 q^{36} +5.22931 q^{37} -12.1007 q^{38} +4.93220 q^{39} +3.36754 q^{40} +2.21952 q^{41} +0.677507 q^{42} +7.57029 q^{43} +14.0689 q^{44} +0.532500 q^{45} -12.0676 q^{46} -3.64587 q^{47} +7.13559 q^{48} -6.92920 q^{49} -12.0095 q^{50} +1.00000 q^{51} +22.1141 q^{52} -8.29840 q^{53} +2.54629 q^{54} +1.67090 q^{55} +1.68267 q^{56} -4.75227 q^{57} +2.59545 q^{58} +7.56905 q^{59} +2.38753 q^{60} -2.77205 q^{61} -13.8757 q^{62} +0.266076 q^{63} -0.212391 q^{64} +2.62640 q^{65} +7.98988 q^{66} +5.37953 q^{67} +4.48362 q^{68} -4.73927 q^{69} +0.360773 q^{70} -6.65160 q^{71} +6.32402 q^{72} +1.86363 q^{73} +13.3154 q^{74} -4.71644 q^{75} -21.3074 q^{76} +0.834904 q^{77} +12.5588 q^{78} +1.00000 q^{79} +3.79970 q^{80} +1.00000 q^{81} +5.65154 q^{82} +7.57960 q^{83} +1.19298 q^{84} +0.532500 q^{85} +19.2762 q^{86} +1.01931 q^{87} +19.8438 q^{88} -12.5833 q^{89} +1.35590 q^{90} +1.31234 q^{91} -21.2491 q^{92} -5.44937 q^{93} -9.28346 q^{94} -2.53058 q^{95} +5.52127 q^{96} +7.15649 q^{97} -17.6438 q^{98} +3.13784 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * q^99

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