LMFDB - Embedded newform 4029.2.a.l.1.13

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:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q-0.857766 q^{2} -1.00000 q^{3} -1.26424 q^{4} -4.41756 q^{5} +0.857766 q^{6} +0.00991750 q^{7} +2.79995 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.857766 q^{2} -1.00000 q^{3} -1.26424 q^{4} -4.41756 q^{5} +0.857766 q^{6} +0.00991750 q^{7} +2.79995 q^{8} +1.00000 q^{9} +3.78923 q^{10} -3.26684 q^{11} +1.26424 q^{12} +2.70187 q^{13} -0.00850689 q^{14} +4.41756 q^{15} +0.126774 q^{16} -1.00000 q^{17} -0.857766 q^{18} -4.27554 q^{19} +5.58484 q^{20} -0.00991750 q^{21} +2.80218 q^{22} -8.57091 q^{23} -2.79995 q^{24} +14.5148 q^{25} -2.31757 q^{26} -1.00000 q^{27} -0.0125381 q^{28} +2.58015 q^{29} -3.78923 q^{30} -3.29810 q^{31} -5.70865 q^{32} +3.26684 q^{33} +0.857766 q^{34} -0.0438111 q^{35} -1.26424 q^{36} -5.23127 q^{37} +3.66741 q^{38} -2.70187 q^{39} -12.3689 q^{40} -10.5143 q^{41} +0.00850689 q^{42} +1.43416 q^{43} +4.13006 q^{44} -4.41756 q^{45} +7.35183 q^{46} -1.69597 q^{47} -0.126774 q^{48} -6.99990 q^{49} -12.4503 q^{50} +1.00000 q^{51} -3.41581 q^{52} -4.25127 q^{53} +0.857766 q^{54} +14.4314 q^{55} +0.0277685 q^{56} +4.27554 q^{57} -2.21316 q^{58} +0.575912 q^{59} -5.58484 q^{60} -3.22241 q^{61} +2.82900 q^{62} +0.00991750 q^{63} +4.64313 q^{64} -11.9357 q^{65} -2.80218 q^{66} -7.36295 q^{67} +1.26424 q^{68} +8.57091 q^{69} +0.0375797 q^{70} -15.6371 q^{71} +2.79995 q^{72} -6.91670 q^{73} +4.48720 q^{74} -14.5148 q^{75} +5.40530 q^{76} -0.0323988 q^{77} +2.31757 q^{78} +1.00000 q^{79} -0.560033 q^{80} +1.00000 q^{81} +9.01881 q^{82} +0.651310 q^{83} +0.0125381 q^{84} +4.41756 q^{85} -1.23017 q^{86} -2.58015 q^{87} -9.14698 q^{88} -7.54867 q^{89} +3.78923 q^{90} +0.0267958 q^{91} +10.8357 q^{92} +3.29810 q^{93} +1.45475 q^{94} +18.8875 q^{95} +5.70865 q^{96} -11.4421 q^{97} +6.00428 q^{98} -3.26684 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9} + 17 q^{10} + 8 q^{11} - 41 q^{12} + 17 q^{13} + q^{14} + q^{15} + 55 q^{16} - 32 q^{17} - q^{18} + 48 q^{19} - 7 q^{20} - 4 q^{21} - 4 q^{22} - 19 q^{23} + 3 q^{24} + 63 q^{25} + 27 q^{26} - 32 q^{27} + 17 q^{28} - 15 q^{29} - 17 q^{30} + 20 q^{31} + 13 q^{32} - 8 q^{33} + q^{34} + 22 q^{35} + 41 q^{36} + 6 q^{37} + 11 q^{38} - 17 q^{39} + 47 q^{40} + q^{41} - q^{42} + 40 q^{43} + 22 q^{44} - q^{45} + 5 q^{46} - 5 q^{47} - 55 q^{48} + 88 q^{49} + 17 q^{50} + 32 q^{51} + 23 q^{52} - 34 q^{53} + q^{54} + 48 q^{55} - 48 q^{57} - 9 q^{58} + 41 q^{59} + 7 q^{60} + 20 q^{61} + 15 q^{62} + 4 q^{63} + 93 q^{64} - 58 q^{65} + 4 q^{66} + 52 q^{67} - 41 q^{68} + 19 q^{69} + 25 q^{70} + q^{71} - 3 q^{72} + 19 q^{73} + 12 q^{74} - 63 q^{75} + 128 q^{76} - 20 q^{77} - 27 q^{78} + 32 q^{79} - 16 q^{80} + 32 q^{81} - 5 q^{82} + 31 q^{83} - 17 q^{84} + q^{85} - 62 q^{86} + 15 q^{87} + 35 q^{88} + 18 q^{89} + 17 q^{90} + 48 q^{91} - 75 q^{92} - 20 q^{93} + 29 q^{94} + 5 q^{95} - 13 q^{96} + 17 q^{97} + 30 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9 + 17 * q^10 + 8 * q^11 - 41 * q^12 + 17 * q^13 + q^14 + q^15 + 55 * q^16 - 32 * q^17 - q^18 + 48 * q^19 - 7 * q^20 - 4 * q^21 - 4 * q^22 - 19 * q^23 + 3 * q^24 + 63 * q^25 + 27 * q^26 - 32 * q^27 + 17 * q^28 - 15 * q^29 - 17 * q^30 + 20 * q^31 + 13 * q^32 - 8 * q^33 + q^34 + 22 * q^35 + 41 * q^36 + 6 * q^37 + 11 * q^38 - 17 * q^39 + 47 * q^40 + q^41 - q^42 + 40 * q^43 + 22 * q^44 - q^45 + 5 * q^46 - 5 * q^47 - 55 * q^48 + 88 * q^49 + 17 * q^50 + 32 * q^51 + 23 * q^52 - 34 * q^53 + q^54 + 48 * q^55 - 48 * q^57 - 9 * q^58 + 41 * q^59 + 7 * q^60 + 20 * q^61 + 15 * q^62 + 4 * q^63 + 93 * q^64 - 58 * q^65 + 4 * q^66 + 52 * q^67 - 41 * q^68 + 19 * q^69 + 25 * q^70 + q^71 - 3 * q^72 + 19 * q^73 + 12 * q^74 - 63 * q^75 + 128 * q^76 - 20 * q^77 - 27 * q^78 + 32 * q^79 - 16 * q^80 + 32 * q^81 - 5 * q^82 + 31 * q^83 - 17 * q^84 + q^85 - 62 * q^86 + 15 * q^87 + 35 * q^88 + 18 * q^89 + 17 * q^90 + 48 * q^91 - 75 * q^92 - 20 * q^93 + 29 * q^94 + 5 * q^95 - 13 * q^96 + 17 * q^97 + 30 * q^98 + 8 * 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 $

$2$	−0.857766	−0.606532	−0.303266	−	0.952906i	$-0.598077\pi$
$2$	−0.857766	−0.606532	−0.303266	+	0.952906i	$0.598077\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.26424	−0.632119
$5$	−4.41756	−1.97559	−0.987796	−	0.155754i	$-0.950219\pi$
$5$	−4.41756	−1.97559	−0.987796	+	0.155754i	$0.950219\pi$
$6$	0.857766	0.350181
$7$	0.00991750	0.00374846	0.00187423	−	0.999998i	$-0.499403\pi$
$7$	0.00991750	0.00374846	0.00187423	+	0.999998i	$0.499403\pi$
$8$	2.79995	0.989932
$9$	1.00000	0.333333
$10$	3.78923	1.19826
$11$	−3.26684	−0.984988	−0.492494	−	0.870316i	$-0.663915\pi$
$11$	−3.26684	−0.984988	−0.492494	+	0.870316i	$0.663915\pi$
$12$	1.26424	0.364954
$13$	2.70187	0.749365	0.374682	−	0.927153i	$-0.377752\pi$
$13$	2.70187	0.749365	0.374682	+	0.927153i	$0.377752\pi$
$14$	−0.00850689	−0.00227356
$15$	4.41756	1.14061
$16$	0.126774	0.0316936
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−0.857766	−0.202177
$19$	−4.27554	−0.980877	−0.490438	−	0.871476i	$-0.663163\pi$
$19$	−4.27554	−0.980877	−0.490438	+	0.871476i	$0.663163\pi$
$20$	5.58484	1.24881
$21$	−0.00991750	−0.00216418
$22$	2.80218	0.597427
$23$	−8.57091	−1.78716	−0.893579	−	0.448907i	$-0.851814\pi$
$23$	−8.57091	−1.78716	−0.893579	+	0.448907i	$0.851814\pi$
$24$	−2.79995	−0.571538
$25$	14.5148	2.90296
$26$	−2.31757	−0.454514
$27$	−1.00000	−0.192450
$28$	−0.0125381	−0.00236947
$29$	2.58015	0.479121	0.239561	−	0.970881i	$-0.422997\pi$
$29$	2.58015	0.479121	0.239561	+	0.970881i	$0.422997\pi$
$30$	−3.78923	−0.691815
$31$	−3.29810	−0.592356	−0.296178	−	0.955133i	$-0.595712\pi$
$31$	−3.29810	−0.592356	−0.296178	+	0.955133i	$0.595712\pi$
$32$	−5.70865	−1.00916
$33$	3.26684	0.568683
$34$	0.857766	0.147106
$35$	−0.0438111	−0.00740543
$36$	−1.26424	−0.210706
$37$	−5.23127	−0.860015	−0.430008	−	0.902825i	$-0.641489\pi$
$37$	−5.23127	−0.860015	−0.430008	+	0.902825i	$0.641489\pi$
$38$	3.66741	0.594933
$39$	−2.70187	−0.432646
$40$	−12.3689	−1.95570
$41$	−10.5143	−1.64206	−0.821030	−	0.570886i	$-0.806600\pi$
$41$	−10.5143	−1.64206	−0.821030	+	0.570886i	$0.806600\pi$
$42$	0.00850689	0.00131264
$43$	1.43416	0.218707	0.109353	−	0.994003i	$-0.465122\pi$
$43$	1.43416	0.218707	0.109353	+	0.994003i	$0.465122\pi$
$44$	4.13006	0.622630
$45$	−4.41756	−0.658531
$46$	7.35183	1.08397
$47$	−1.69597	−0.247383	−0.123692	−	0.992321i	$-0.539473\pi$
$47$	−1.69597	−0.247383	−0.123692	+	0.992321i	$0.539473\pi$
$48$	−0.126774	−0.0182983
$49$	−6.99990	−0.999986
$50$	−12.4503	−1.76074
$51$	1.00000	0.140028
$52$	−3.41581	−0.473688
$53$	−4.25127	−0.583957	−0.291978	−	0.956425i	$-0.594314\pi$
$53$	−4.25127	−0.583957	−0.291978	+	0.956425i	$0.594314\pi$
$54$	0.857766	0.116727
$55$	14.4314	1.94593
$56$	0.0277685	0.00371072
$57$	4.27554	0.566309
$58$	−2.21316	−0.290602
$59$	0.575912	0.0749773	0.0374887	−	0.999297i	$-0.488064\pi$
$59$	0.575912	0.0749773	0.0374887	+	0.999297i	$0.488064\pi$
$60$	−5.58484	−0.721000
$61$	−3.22241	−0.412587	−0.206294	−	0.978490i	$-0.566140\pi$
$61$	−3.22241	−0.412587	−0.206294	+	0.978490i	$0.566140\pi$
$62$	2.82900	0.359283
$63$	0.00991750	0.00124949
$64$	4.64313	0.580391
$65$	−11.9357	−1.48044
$66$	−2.80218	−0.344925
$67$	−7.36295	−0.899528	−0.449764	−	0.893147i	$-0.648492\pi$
$67$	−7.36295	−0.899528	−0.449764	+	0.893147i	$0.648492\pi$
$68$	1.26424	0.153311
$69$	8.57091	1.03182
$70$	0.0375797	0.00449163
$71$	−15.6371	−1.85578	−0.927889	−	0.372857i	$-0.878378\pi$
$71$	−15.6371	−1.85578	−0.927889	+	0.372857i	$0.878378\pi$
$72$	2.79995	0.329977
$73$	−6.91670	−0.809538	−0.404769	−	0.914419i	$-0.632648\pi$
$73$	−6.91670	−0.809538	−0.404769	+	0.914419i	$0.632648\pi$
$74$	4.48720	0.521627
$75$	−14.5148	−1.67603
$76$	5.40530	0.620031
$77$	−0.0323988	−0.00369219
$78$	2.31757	0.262414
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	−0.560033	−0.0626136
$81$	1.00000	0.111111
$82$	9.01881	0.995961
$83$	0.651310	0.0714906	0.0357453	−	0.999361i	$-0.488619\pi$
$83$	0.651310	0.0714906	0.0357453	+	0.999361i	$0.488619\pi$
$84$	0.0125381	0.00136802
$85$	4.41756	0.479151
$86$	−1.23017	−0.132653
$87$	−2.58015	−0.276621
$88$	−9.14698	−0.975072
$89$	−7.54867	−0.800157	−0.400079	−	0.916481i	$-0.631017\pi$
$89$	−7.54867	−0.800157	−0.400079	+	0.916481i	$0.631017\pi$
$90$	3.78923	0.399420
$91$	0.0267958	0.00280896
$92$	10.8357	1.12970
$93$	3.29810	0.341997
$94$	1.45475	0.150046
$95$	18.8875	1.93781
$96$	5.70865	0.582636
$97$	−11.4421	−1.16177	−0.580886	−	0.813985i	$-0.697294\pi$
$97$	−11.4421	−1.16177	−0.580886	+	0.813985i	$0.697294\pi$
$98$	6.00428	0.606523
$99$	−3.26684	−0.328329
$100$	−18.3502	−1.83502
$101$	−12.3316	−1.22704	−0.613521	−	0.789679i	$-0.710247\pi$
$101$	−12.3316	−1.22704	−0.613521	+	0.789679i	$0.710247\pi$
$102$	−0.857766	−0.0849315
$103$	13.9114	1.37073	0.685364	−	0.728201i	$-0.259643\pi$
$103$	13.9114	1.37073	0.685364	+	0.728201i	$0.259643\pi$
$104$	7.56511	0.741820
$105$	0.0438111	0.00427553
$106$	3.64659	0.354188
$107$	−0.872179	−0.0843167	−0.0421584	−	0.999111i	$-0.513423\pi$
$107$	−0.872179	−0.0843167	−0.0421584	+	0.999111i	$0.513423\pi$
$108$	1.26424	0.121651
$109$	−12.5345	−1.20059	−0.600295	−	0.799779i	$-0.704950\pi$
$109$	−12.5345	−1.20059	−0.600295	+	0.799779i	$0.704950\pi$
$110$	−12.3788	−1.18027
$111$	5.23127	0.496530
$112$	0.00125728	0.000118802 0
$113$	6.28218	0.590977	0.295489	−	0.955346i	$-0.404518\pi$
$113$	6.28218	0.590977	0.295489	+	0.955346i	$0.404518\pi$
$114$	−3.66741	−0.343485
$115$	37.8625	3.53069
$116$	−3.26192	−0.302862
$117$	2.70187	0.249788
$118$	−0.493997	−0.0454761
$119$	−0.00991750	−0.000909135 0
$120$	12.3689	1.12913
$121$	−0.327777	−0.0297979
$122$	2.76407	0.250247
$123$	10.5143	0.948043
$124$	4.16958	0.374440
$125$	−42.0322	−3.75948
$126$	−0.00850689	−0.000757854 0
$127$	−12.2427	−1.08637	−0.543184	−	0.839614i	$-0.682781\pi$
$127$	−12.2427	−1.08637	−0.543184	+	0.839614i	$0.682781\pi$
$128$	7.43457	0.657130
$129$	−1.43416	−0.126271
$130$	10.2380	0.897933
$131$	11.7426	1.02596	0.512978	−	0.858402i	$-0.328542\pi$
$131$	11.7426	1.02596	0.512978	+	0.858402i	$0.328542\pi$
$132$	−4.13006	−0.359476
$133$	−0.0424027	−0.00367678
$134$	6.31569	0.545592
$135$	4.41756	0.380203
$136$	−2.79995	−0.240094
$137$	−4.44600	−0.379848	−0.189924	−	0.981799i	$-0.560824\pi$
$137$	−4.44600	−0.379848	−0.189924	+	0.981799i	$0.560824\pi$
$138$	−7.35183	−0.625829
$139$	9.97488	0.846058	0.423029	−	0.906116i	$-0.360967\pi$
$139$	9.97488	0.846058	0.423029	+	0.906116i	$0.360967\pi$
$140$	0.0553877	0.00468111
$141$	1.69597	0.142827
$142$	13.4129	1.12559
$143$	−8.82658	−0.738115
$144$	0.126774	0.0105645
$145$	−11.3980	−0.946548
$146$	5.93290	0.491011
$147$	6.99990	0.577342
$148$	6.61357	0.543632
$149$	−11.3655	−0.931098	−0.465549	−	0.885022i	$-0.654143\pi$
$149$	−11.3655	−0.931098	−0.465549	+	0.885022i	$0.654143\pi$
$150$	12.4503	1.01656
$151$	−0.599460	−0.0487834	−0.0243917	−	0.999702i	$-0.507765\pi$
$151$	−0.599460	−0.0487834	−0.0243917	+	0.999702i	$0.507765\pi$
$152$	−11.9713	−0.971002
$153$	−1.00000	−0.0808452
$154$	0.0277906	0.00223943
$155$	14.5696	1.17025
$156$	3.41581	0.273484
$157$	16.2588	1.29759	0.648796	−	0.760962i	$-0.275273\pi$
$157$	16.2588	1.29759	0.648796	+	0.760962i	$0.275273\pi$
$158$	−0.857766	−0.0682402
$159$	4.25127	0.337148
$160$	25.2183	1.99368
$161$	−0.0850019	−0.00669909
$162$	−0.857766	−0.0673924
$163$	−10.9405	−0.856923	−0.428461	−	0.903560i	$-0.640944\pi$
$163$	−10.9405	−0.856923	−0.428461	+	0.903560i	$0.640944\pi$
$164$	13.2926	1.03798
$165$	−14.4314	−1.12349
$166$	−0.558671	−0.0433613
$167$	10.1964	0.789021	0.394511	−	0.918891i	$-0.370914\pi$
$167$	10.1964	0.789021	0.394511	+	0.918891i	$0.370914\pi$
$168$	−0.0277685	−0.00214239
$169$	−5.69988	−0.438453
$170$	−3.78923	−0.290621
$171$	−4.27554	−0.326959
$172$	−1.81312	−0.138249
$173$	−15.1014	−1.14814	−0.574071	−	0.818806i	$-0.694637\pi$
$173$	−15.1014	−1.14814	−0.574071	+	0.818806i	$0.694637\pi$
$174$	2.21316	0.167779
$175$	0.143951	0.0108816
$176$	−0.414151	−0.0312178
$177$	−0.575912	−0.0432882
$178$	6.47499	0.485321
$179$	12.1907	0.911178	0.455589	−	0.890190i	$-0.349429\pi$
$179$	12.1907	0.911178	0.455589	+	0.890190i	$0.349429\pi$
$180$	5.58484	0.416270
$181$	−12.8454	−0.954791	−0.477396	−	0.878688i	$-0.658419\pi$
$181$	−12.8454	−0.954791	−0.477396	+	0.878688i	$0.658419\pi$
$182$	−0.0229845	−0.00170373
$183$	3.22241	0.238207
$184$	−23.9981	−1.76916
$185$	23.1094	1.69904
$186$	−2.82900	−0.207432
$187$	3.26684	0.238895
$188$	2.14412	0.156376
$189$	−0.00991750	−0.000721392 0
$190$	−16.2010	−1.17534
$191$	6.07241	0.439384	0.219692	−	0.975569i	$-0.429495\pi$
$191$	6.07241	0.439384	0.219692	+	0.975569i	$0.429495\pi$
$192$	−4.64313	−0.335089
$193$	−3.69134	−0.265709	−0.132854	−	0.991136i	$-0.542414\pi$
$193$	−3.69134	−0.265709	−0.132854	+	0.991136i	$0.542414\pi$
$194$	9.81467	0.704652
$195$	11.9357	0.854732
$196$	8.84954	0.632110
$197$	23.9789	1.70842	0.854211	−	0.519926i	$-0.174040\pi$
$197$	23.9789	1.70842	0.854211	+	0.519926i	$0.174040\pi$
$198$	2.80218	0.199142
$199$	−5.53090	−0.392075	−0.196038	−	0.980596i	$-0.562807\pi$
$199$	−5.53090	−0.392075	−0.196038	+	0.980596i	$0.562807\pi$
$200$	40.6408	2.87374
$201$	7.36295	0.519343
$202$	10.5776	0.744240
$203$	0.0255886	0.00179597
$204$	−1.26424	−0.0885144
$205$	46.4476	3.24404
$206$	−11.9327	−0.831390
$207$	−8.57091	−0.595719
$208$	0.342528	0.0237500
$209$	13.9675	0.966152
$210$	−0.0375797	−0.00259324
$211$	21.4352	1.47566	0.737830	−	0.674986i	$-0.235850\pi$
$211$	21.4352	1.47566	0.737830	+	0.674986i	$0.235850\pi$
$212$	5.37462	0.369130
$213$	15.6371	1.07143
$214$	0.748125	0.0511408
$215$	−6.33547	−0.432076
$216$	−2.79995	−0.190513
$217$	−0.0327089	−0.00222043
$218$	10.7517	0.728196
$219$	6.91670	0.467387
$220$	−18.2448	−1.23006
$221$	−2.70187	−0.181748
$222$	−4.48720	−0.301161
$223$	26.2867	1.76029	0.880145	−	0.474706i	$-0.157446\pi$
$223$	26.2867	1.76029	0.880145	+	0.474706i	$0.157446\pi$
$224$	−0.0566155	−0.00378278
$225$	14.5148	0.967654
$226$	−5.38863	−0.358447
$227$	−0.621313	−0.0412380	−0.0206190	−	0.999787i	$-0.506564\pi$
$227$	−0.621313	−0.0412380	−0.0206190	+	0.999787i	$0.506564\pi$
$228$	−5.40530	−0.357975
$229$	6.55118	0.432914	0.216457	−	0.976292i	$-0.430550\pi$
$229$	6.55118	0.432914	0.216457	+	0.976292i	$0.430550\pi$
$230$	−32.4771	−2.14148
$231$	0.0323988	0.00213169
$232$	7.22429	0.474298
$233$	−24.9995	−1.63777	−0.818885	−	0.573958i	$-0.805407\pi$
$233$	−24.9995	−1.63777	−0.818885	+	0.573958i	$0.805407\pi$
$234$	−2.31757	−0.151505
$235$	7.49206	0.488728
$236$	−0.728090	−0.0473946
$237$	−1.00000	−0.0649570
$238$	0.00850689	0.000551420 0
$239$	−17.5256	−1.13364	−0.566819	−	0.823842i	$-0.691826\pi$
$239$	−17.5256	−1.13364	−0.566819	+	0.823842i	$0.691826\pi$
$240$	0.560033	0.0361500
$241$	18.4610	1.18918	0.594588	−	0.804030i	$-0.297315\pi$
$241$	18.4610	1.18918	0.594588	+	0.804030i	$0.297315\pi$
$242$	0.281156	0.0180734
$243$	−1.00000	−0.0641500
$244$	4.07389	0.260804
$245$	30.9225	1.97556
$246$	−9.01881	−0.575019
$247$	−11.5520	−0.735034
$248$	−9.23452	−0.586393
$249$	−0.651310	−0.0412751
$250$	36.0538	2.28024
$251$	29.5254	1.86363	0.931814	−	0.362935i	$-0.118225\pi$
$251$	29.5254	1.86363	0.931814	+	0.362935i	$0.118225\pi$
$252$	−0.0125381	−0.000789825 0
$253$	27.9998	1.76033
$254$	10.5014	0.658917
$255$	−4.41756	−0.276638
$256$	−15.6634	−0.978961
$257$	−10.8979	−0.679792	−0.339896	−	0.940463i	$-0.610392\pi$
$257$	−10.8979	−0.679792	−0.339896	+	0.940463i	$0.610392\pi$
$258$	1.23017	0.0765871
$259$	−0.0518811	−0.00322373
$260$	15.0895	0.935814
$261$	2.58015	0.159707
$262$	−10.0724	−0.622275
$263$	−19.4022	−1.19639	−0.598196	−	0.801350i	$-0.704116\pi$
$263$	−19.4022	−1.19639	−0.598196	+	0.801350i	$0.704116\pi$
$264$	9.14698	0.562958
$265$	18.7802	1.15366
$266$	0.0363716	0.00223008
$267$	7.54867	0.461971
$268$	9.30853	0.568609
$269$	10.6240	0.647756	0.323878	−	0.946099i	$-0.395013\pi$
$269$	10.6240	0.647756	0.323878	+	0.946099i	$0.395013\pi$
$270$	−3.78923	−0.230605
$271$	−11.1895	−0.679715	−0.339857	−	0.940477i	$-0.610379\pi$
$271$	−11.1895	−0.679715	−0.339857	+	0.940477i	$0.610379\pi$
$272$	−0.126774	−0.00768682
$273$	−0.0267958	−0.00162176
$274$	3.81363	0.230390
$275$	−47.4175	−2.85938
$276$	−10.8357	−0.652230
$277$	23.7002	1.42401	0.712003	−	0.702176i	$-0.247788\pi$
$277$	23.7002	1.42401	0.712003	+	0.702176i	$0.247788\pi$
$278$	−8.55611	−0.513161
$279$	−3.29810	−0.197452
$280$	−0.122669	−0.00733087
$281$	−4.90376	−0.292534	−0.146267	−	0.989245i	$-0.546726\pi$
$281$	−4.90376	−0.292534	−0.146267	+	0.989245i	$0.546726\pi$
$282$	−1.45475	−0.0866290
$283$	12.2940	0.730803	0.365402	−	0.930850i	$-0.380932\pi$
$283$	12.2940	0.730803	0.365402	+	0.930850i	$0.380932\pi$
$284$	19.7690	1.17307
$285$	−18.8875	−1.11880
$286$	7.57113	0.447691
$287$	−0.104276	−0.00615520
$288$	−5.70865	−0.336385
$289$	1.00000	0.0588235
$290$	9.77677	0.574112
$291$	11.4421	0.670750
$292$	8.74435	0.511724
$293$	−1.55549	−0.0908726	−0.0454363	−	0.998967i	$-0.514468\pi$
$293$	−1.55549	−0.0908726	−0.0454363	+	0.998967i	$0.514468\pi$
$294$	−6.00428	−0.350176
$295$	−2.54412	−0.148125
$296$	−14.6473	−0.851357
$297$	3.26684	0.189561
$298$	9.74894	0.564741
$299$	−23.1575	−1.33923
$300$	18.3502	1.05945
$301$	0.0142232	0.000819814 0
$302$	0.514196	0.0295887
$303$	12.3316	0.708433
$304$	−0.542029	−0.0310875
$305$	14.2352	0.815104
$306$	0.857766	0.0490352
$307$	−24.0461	−1.37238	−0.686191	−	0.727422i	$-0.740718\pi$
$307$	−24.0461	−1.37238	−0.686191	+	0.727422i	$0.740718\pi$
$308$	0.0409599	0.00233390
$309$	−13.9114	−0.791390
$310$	−12.4973	−0.709797
$311$	−23.4847	−1.33170	−0.665848	−	0.746088i	$-0.731930\pi$
$311$	−23.4847	−1.33170	−0.665848	+	0.746088i	$0.731930\pi$
$312$	−7.56511	−0.428290
$313$	−21.3568	−1.20716	−0.603578	−	0.797304i	$-0.706259\pi$
$313$	−21.3568	−1.20716	−0.603578	+	0.797304i	$0.706259\pi$
$314$	−13.9462	−0.787031
$315$	−0.0438111	−0.00246848
$316$	−1.26424	−0.0711190
$317$	−0.835900	−0.0469488	−0.0234744	−	0.999724i	$-0.507473\pi$
$317$	−0.835900	−0.0469488	−0.0234744	+	0.999724i	$0.507473\pi$
$318$	−3.64659	−0.204491
$319$	−8.42892	−0.471929
$320$	−20.5113	−1.14662
$321$	0.872179	0.0486803
$322$	0.0729117	0.00406321
$323$	4.27554	0.237898
$324$	−1.26424	−0.0702355
$325$	39.2172	2.17538
$326$	9.38435	0.519751
$327$	12.5345	0.693161
$328$	−29.4396	−1.62553
$329$	−0.0168198	−0.000927307 0
$330$	12.3788	0.681430
$331$	−15.9837	−0.878544	−0.439272	−	0.898354i	$-0.644764\pi$
$331$	−15.9837	−0.878544	−0.439272	+	0.898354i	$0.644764\pi$
$332$	−0.823411	−0.0451906
$333$	−5.23127	−0.286672
$334$	−8.74612	−0.478567
$335$	32.5263	1.77710
$336$	−0.00125728	−6.85904e−5 0
$337$	3.24657	0.176852	0.0884259	−	0.996083i	$-0.471816\pi$
$337$	3.24657	0.176852	0.0884259	+	0.996083i	$0.471816\pi$
$338$	4.88916	0.265935
$339$	−6.28218	−0.341201
$340$	−5.58484	−0.302881
$341$	10.7744	0.583464
$342$	3.66741	0.198311
$343$	−0.138844	−0.00749687
$344$	4.01557	0.216505
$345$	−37.8625	−2.03845
$346$	12.9535	0.696384
$347$	13.9015	0.746274	0.373137	−	0.927776i	$-0.378282\pi$
$347$	13.9015	0.746274	0.373137	+	0.927776i	$0.378282\pi$
$348$	3.26192	0.174857
$349$	9.91279	0.530620	0.265310	−	0.964163i	$-0.414526\pi$
$349$	9.91279	0.530620	0.265310	+	0.964163i	$0.414526\pi$
$350$	−0.123476	−0.00660007
$351$	−2.70187	−0.144215
$352$	18.6492	0.994006
$353$	−26.0400	−1.38597	−0.692985	−	0.720952i	$-0.743705\pi$
$353$	−26.0400	−1.38597	−0.692985	+	0.720952i	$0.743705\pi$
$354$	0.493997	0.0262557
$355$	69.0776	3.66626
$356$	9.54332	0.505795
$357$	0.00991750	0.000524890 0
$358$	−10.4568	−0.552659
$359$	22.3216	1.17809	0.589044	−	0.808101i	$-0.299504\pi$
$359$	22.3216	1.17809	0.589044	+	0.808101i	$0.299504\pi$
$360$	−12.3689	−0.651901
$361$	−0.719734	−0.0378807
$362$	11.0183	0.579111
$363$	0.327777	0.0172038
$364$	−0.0338763	−0.00177560
$365$	30.5549	1.59932
$366$	−2.76407	−0.144480
$367$	4.93974	0.257852	0.128926	−	0.991654i	$-0.458847\pi$
$367$	4.93974	0.257852	0.128926	+	0.991654i	$0.458847\pi$
$368$	−1.08657	−0.0566414
$369$	−10.5143	−0.547353
$370$	−19.8225	−1.03052
$371$	−0.0421619	−0.00218894
$372$	−4.16958	−0.216183
$373$	−6.95263	−0.359993	−0.179997	−	0.983667i	$-0.557609\pi$
$373$	−6.95263	−0.359993	−0.179997	+	0.983667i	$0.557609\pi$
$374$	−2.80218	−0.144897
$375$	42.0322	2.17054
$376$	−4.74865	−0.244893
$377$	6.97123	0.359037
$378$	0.00850689	0.000437547 0
$379$	−33.1311	−1.70183	−0.850915	−	0.525303i	$-0.823952\pi$
$379$	−33.1311	−1.70183	−0.850915	+	0.525303i	$0.823952\pi$
$380$	−23.8782	−1.22493
$381$	12.2427	0.627215
$382$	−5.20871	−0.266501
$383$	6.90333	0.352744	0.176372	−	0.984324i	$-0.443564\pi$
$383$	6.90333	0.352744	0.176372	+	0.984324i	$0.443564\pi$
$384$	−7.43457	−0.379394
$385$	0.143124	0.00729426
$386$	3.16631	0.161161
$387$	1.43416	0.0729023
$388$	14.4656	0.734379
$389$	−34.4429	−1.74633	−0.873163	−	0.487428i	$-0.837935\pi$
$389$	−34.4429	−1.74633	−0.873163	+	0.487428i	$0.837935\pi$
$390$	−10.2380	−0.518422
$391$	8.57091	0.433449
$392$	−19.5994	−0.989918
$393$	−11.7426	−0.592335
$394$	−20.5682	−1.03621
$395$	−4.41756	−0.222271
$396$	4.13006	0.207543
$397$	−8.38591	−0.420877	−0.210438	−	0.977607i	$-0.567489\pi$
$397$	−8.38591	−0.420877	−0.210438	+	0.977607i	$0.567489\pi$
$398$	4.74422	0.237806
$399$	0.0424027	0.00212279
$400$	1.84011	0.0920053
$401$	−25.0140	−1.24914	−0.624571	−	0.780968i	$-0.714726\pi$
$401$	−25.0140	−1.24914	−0.624571	+	0.780968i	$0.714726\pi$
$402$	−6.31569	−0.314998
$403$	−8.91105	−0.443891
$404$	15.5901	0.775636
$405$	−4.41756	−0.219510
$406$	−0.0219490	−0.00108931
$407$	17.0897	0.847105
$408$	2.79995	0.138618
$409$	−2.21531	−0.109540	−0.0547699	−	0.998499i	$-0.517443\pi$
$409$	−2.21531	−0.109540	−0.0547699	+	0.998499i	$0.517443\pi$
$410$	−39.8411	−1.96761
$411$	4.44600	0.219305
$412$	−17.5873	−0.866463
$413$	0.00571160	0.000281050 0
$414$	7.35183	0.361323
$415$	−2.87720	−0.141236
$416$	−15.4240	−0.756225
$417$	−9.97488	−0.488472
$418$	−11.9808	−0.586002
$419$	24.0544	1.17514	0.587568	−	0.809175i	$-0.300086\pi$
$419$	24.0544	1.17514	0.587568	+	0.809175i	$0.300086\pi$
$420$	−0.0553877	−0.00270264
$421$	−8.23853	−0.401521	−0.200761	−	0.979640i	$-0.564341\pi$
$421$	−8.23853	−0.401521	−0.200761	+	0.979640i	$0.564341\pi$
$422$	−18.3864	−0.895035
$423$	−1.69597	−0.0824611
$424$	−11.9033	−0.578078
$425$	−14.5148	−0.704072
$426$	−13.4129	−0.649859
$427$	−0.0319582	−0.00154657
$428$	1.10264	0.0532982
$429$	8.82658	0.426151
$430$	5.43435	0.262068
$431$	−2.57171	−0.123875	−0.0619375	−	0.998080i	$-0.519728\pi$
$431$	−2.57171	−0.123875	−0.0619375	+	0.998080i	$0.519728\pi$
$432$	−0.126774	−0.00609943
$433$	7.05674	0.339125	0.169563	−	0.985519i	$-0.445765\pi$
$433$	7.05674	0.339125	0.169563	+	0.985519i	$0.445765\pi$
$434$	0.0280566	0.00134676
$435$	11.3980	0.546490
$436$	15.8466	0.758916
$437$	36.6453	1.75298
$438$	−5.93290	−0.283485
$439$	−15.8385	−0.755928	−0.377964	−	0.925820i	$-0.623376\pi$
$439$	−15.8385	−0.755928	−0.377964	+	0.925820i	$0.623376\pi$
$440$	40.4073	1.92634
$441$	−6.99990	−0.333329
$442$	2.31757	0.110236
$443$	−18.4791	−0.877969	−0.438984	−	0.898495i	$-0.644662\pi$
$443$	−18.4791	−0.877969	−0.438984	+	0.898495i	$0.644662\pi$
$444$	−6.61357	−0.313866
$445$	33.3467	1.58078
$446$	−22.5478	−1.06767
$447$	11.3655	0.537570
$448$	0.0460482	0.00217557
$449$	20.1196	0.949505	0.474752	−	0.880119i	$-0.342538\pi$
$449$	20.1196	0.949505	0.474752	+	0.880119i	$0.342538\pi$
$450$	−12.4503	−0.586913
$451$	34.3485	1.61741
$452$	−7.94217	−0.373568
$453$	0.599460	0.0281651
$454$	0.532941	0.0250121
$455$	−0.118372	−0.00554937
$456$	11.9713	0.560608
$457$	7.98977	0.373746	0.186873	−	0.982384i	$-0.440165\pi$
$457$	7.98977	0.373746	0.186873	+	0.982384i	$0.440165\pi$
$458$	−5.61938	−0.262576
$459$	1.00000	0.0466760
$460$	−47.8672	−2.23182
$461$	2.18374	0.101707	0.0508534	−	0.998706i	$-0.483806\pi$
$461$	2.18374	0.101707	0.0508534	+	0.998706i	$0.483806\pi$
$462$	−0.0277906	−0.00129294
$463$	−14.6319	−0.680002	−0.340001	−	0.940425i	$-0.610427\pi$
$463$	−14.6319	−0.680002	−0.340001	+	0.940425i	$0.610427\pi$
$464$	0.327096	0.0151851
$465$	−14.5696	−0.675647
$466$	21.4437	0.993359
$467$	31.2841	1.44765	0.723827	−	0.689982i	$-0.242381\pi$
$467$	31.2841	1.44765	0.723827	+	0.689982i	$0.242381\pi$
$468$	−3.41581	−0.157896
$469$	−0.0730221	−0.00337185
$470$	−6.42644	−0.296429
$471$	−16.2588	−0.749166
$472$	1.61252	0.0742225
$473$	−4.68516	−0.215424
$474$	0.857766	0.0393985
$475$	−62.0587	−2.84745
$476$	0.0125381	0.000574682 0
$477$	−4.25127	−0.194652
$478$	15.0329	0.687588
$479$	−18.7553	−0.856953	−0.428477	−	0.903553i	$-0.640950\pi$
$479$	−18.7553	−0.856953	−0.428477	+	0.903553i	$0.640950\pi$
$480$	−25.2183	−1.15105
$481$	−14.1342	−0.644465
$482$	−15.8352	−0.721273
$483$	0.0850019	0.00386772
$484$	0.414388	0.0188358
$485$	50.5463	2.29519
$486$	0.857766	0.0389090
$487$	30.8510	1.39799	0.698997	−	0.715125i	$-0.253630\pi$
$487$	30.8510	1.39799	0.698997	+	0.715125i	$0.253630\pi$
$488$	−9.02259	−0.408433
$489$	10.9405	0.494744
$490$	−26.5242	−1.19824
$491$	−2.19111	−0.0988832	−0.0494416	−	0.998777i	$-0.515744\pi$
$491$	−2.19111	−0.0988832	−0.0494416	+	0.998777i	$0.515744\pi$
$492$	−13.2926	−0.599276
$493$	−2.58015	−0.116204
$494$	9.90888	0.445822
$495$	14.4314	0.648645
$496$	−0.418114	−0.0187739
$497$	−0.155080	−0.00695631
$498$	0.558671	0.0250347
$499$	−37.8977	−1.69653	−0.848267	−	0.529569i	$-0.822354\pi$
$499$	−37.8977	−1.69653	−0.848267	+	0.529569i	$0.822354\pi$
$500$	53.1388	2.37644
$501$	−10.1964	−0.455542
$502$	−25.3259	−1.13035
$503$	15.0939	0.673002	0.336501	−	0.941683i	$-0.390756\pi$
$503$	15.0939	0.673002	0.336501	+	0.941683i	$0.390756\pi$
$504$	0.0277685	0.00123691
$505$	54.4756	2.42413
$506$	−24.0172	−1.06770
$507$	5.69988	0.253141
$508$	15.4777	0.686714
$509$	−40.5887	−1.79906	−0.899531	−	0.436857i	$-0.856092\pi$
$509$	−40.5887	−1.79906	−0.899531	+	0.436857i	$0.856092\pi$
$510$	3.78923	0.167790
$511$	−0.0685963	−0.00303452
$512$	−1.43363	−0.0633582
$513$	4.27554	0.188770
$514$	9.34784	0.412315
$515$	−61.4543	−2.70800
$516$	1.81312	0.0798180
$517$	5.54047	0.243670
$518$	0.0445018	0.00195530
$519$	15.1014	0.662880
$520$	−33.4193	−1.46553
$521$	1.49204	0.0653673	0.0326836	−	0.999466i	$-0.489595\pi$
$521$	1.49204	0.0653673	0.0326836	+	0.999466i	$0.489595\pi$
$522$	−2.21316	−0.0968675
$523$	−21.3629	−0.934135	−0.467068	−	0.884222i	$-0.654690\pi$
$523$	−21.3629	−0.934135	−0.467068	+	0.884222i	$0.654690\pi$
$524$	−14.8454	−0.648526
$525$	−0.143951	−0.00628252
$526$	16.6426	0.725650
$527$	3.29810	0.143668
$528$	0.414151	0.0180236
$529$	50.4604	2.19393
$530$	−16.1090	−0.699732
$531$	0.575912	0.0249924
$532$	0.0536071	0.00232416
$533$	−28.4083	−1.23050
$534$	−6.47499	−0.280200
$535$	3.85290	0.166575
$536$	−20.6159	−0.890472
$537$	−12.1907	−0.526069
$538$	−9.11290	−0.392885
$539$	22.8675	0.984975
$540$	−5.58484	−0.240333
$541$	−2.34046	−0.100624	−0.0503121	−	0.998734i	$-0.516022\pi$
$541$	−2.34046	−0.100624	−0.0503121	+	0.998734i	$0.516022\pi$
$542$	9.59798	0.412269
$543$	12.8454	0.551249
$544$	5.70865	0.244756
$545$	55.3720	2.37188
$546$	0.0229845	0.000983647 0
$547$	23.2535	0.994247	0.497124	−	0.867680i	$-0.334390\pi$
$547$	23.2535	0.994247	0.497124	+	0.867680i	$0.334390\pi$
$548$	5.62081	0.240109
$549$	−3.22241	−0.137529
$550$	40.6731	1.73431
$551$	−11.0315	−0.469959
$552$	23.9981	1.02143
$553$	0.00991750	0.000421735 0
$554$	−20.3292	−0.863706
$555$	−23.1094	−0.980941
$556$	−12.6106	−0.534809
$557$	−37.6487	−1.59523	−0.797613	−	0.603170i	$-0.793904\pi$
$557$	−37.6487	−1.59523	−0.797613	+	0.603170i	$0.793904\pi$
$558$	2.82900	0.119761
$559$	3.87491	0.163891
$560$	−0.00555412	−0.000234704 0
$561$	−3.26684	−0.137926
$562$	4.20628	0.177431
$563$	28.2094	1.18888	0.594442	−	0.804138i	$-0.297373\pi$
$563$	28.2094	1.18888	0.594442	+	0.804138i	$0.297373\pi$
$564$	−2.14412	−0.0902835
$565$	−27.7519	−1.16753
$566$	−10.5454	−0.443255
$567$	0.00991750	0.000416496 0
$568$	−43.7830	−1.83709
$569$	18.3588	0.769643	0.384821	−	0.922991i	$-0.374263\pi$
$569$	18.3588	0.769643	0.384821	+	0.922991i	$0.374263\pi$
$570$	16.2010	0.678586
$571$	−33.4017	−1.39782	−0.698909	−	0.715211i	$-0.746331\pi$
$571$	−33.4017	−1.39782	−0.698909	+	0.715211i	$0.746331\pi$
$572$	11.1589	0.466577
$573$	−6.07241	−0.253679
$574$	0.0894440	0.00373332
$575$	−124.405	−5.18805
$576$	4.64313	0.193464
$577$	−34.2634	−1.42640	−0.713202	−	0.700958i	$-0.752756\pi$
$577$	−34.2634	−1.42640	−0.713202	+	0.700958i	$0.752756\pi$
$578$	−0.857766	−0.0356783
$579$	3.69134	0.153407
$580$	14.4097	0.598331
$581$	0.00645937	0.000267980 0
$582$	−9.81467	−0.406831
$583$	13.8882	0.575191
$584$	−19.3664	−0.801388
$585$	−11.9357	−0.493480
$586$	1.33425	0.0551172
$587$	45.0220	1.85826	0.929128	−	0.369758i	$-0.120559\pi$
$587$	45.0220	1.85826	0.929128	+	0.369758i	$0.120559\pi$
$588$	−8.84954	−0.364949
$589$	14.1012	0.581029
$590$	2.18226	0.0898423
$591$	−23.9789	−0.986358
$592$	−0.663190	−0.0272570
$593$	−6.50436	−0.267102	−0.133551	−	0.991042i	$-0.542638\pi$
$593$	−6.50436	−0.267102	−0.133551	+	0.991042i	$0.542638\pi$
$594$	−2.80218	−0.114975
$595$	0.0438111	0.00179608
$596$	14.3687	0.588565
$597$	5.53090	0.226365
$598$	19.8637	0.812287
$599$	−17.2141	−0.703349	−0.351674	−	0.936122i	$-0.614388\pi$
$599$	−17.2141	−0.703349	−0.351674	+	0.936122i	$0.614388\pi$
$600$	−40.6408	−1.65915
$601$	30.1513	1.22990	0.614948	−	0.788568i	$-0.289177\pi$
$601$	30.1513	1.22990	0.614948	+	0.788568i	$0.289177\pi$
$602$	−0.0122002	−0.000497244 0
$603$	−7.36295	−0.299843
$604$	0.757860	0.0308369
$605$	1.44797	0.0588685
$606$	−10.5776	−0.429687
$607$	0.868578	0.0352545	0.0176272	−	0.999845i	$-0.494389\pi$
$607$	0.868578	0.0352545	0.0176272	+	0.999845i	$0.494389\pi$
$608$	24.4076	0.989857
$609$	−0.0255886	−0.00103690
$610$	−12.2104	−0.494387
$611$	−4.58231	−0.185380
$612$	1.26424	0.0511038
$613$	−2.99176	−0.120836	−0.0604180	−	0.998173i	$-0.519243\pi$
$613$	−2.99176	−0.120836	−0.0604180	+	0.998173i	$0.519243\pi$
$614$	20.6259	0.832393
$615$	−46.4476	−1.87295
$616$	−0.0907152	−0.00365502
$617$	−34.1943	−1.37661	−0.688306	−	0.725420i	$-0.741645\pi$
$617$	−34.1943	−1.37661	−0.688306	+	0.725420i	$0.741645\pi$
$618$	11.9327	0.480003
$619$	26.9489	1.08317	0.541585	−	0.840646i	$-0.317825\pi$
$619$	26.9489	1.08317	0.541585	+	0.840646i	$0.317825\pi$
$620$	−18.4194	−0.739740
$621$	8.57091	0.343939
$622$	20.1444	0.807716
$623$	−0.0748639	−0.00299936
$624$	−0.342528	−0.0137121
$625$	113.106	4.52423
$626$	18.3191	0.732179
$627$	−13.9675	−0.557808
$628$	−20.5550	−0.820233
$629$	5.23127	0.208584
$630$	0.0375797	0.00149721
$631$	21.9961	0.875651	0.437826	−	0.899060i	$-0.355749\pi$
$631$	21.9961	0.875651	0.437826	+	0.899060i	$0.355749\pi$
$632$	2.79995	0.111376
$633$	−21.4352	−0.851973
$634$	0.717006	0.0284760
$635$	54.0830	2.14622
$636$	−5.37462	−0.213117
$637$	−18.9128	−0.749354
$638$	7.23004	0.286240
$639$	−15.6371	−0.618592
$640$	−32.8427	−1.29822
$641$	15.1640	0.598940	0.299470	−	0.954106i	$-0.403190\pi$
$641$	15.1640	0.598940	0.299470	+	0.954106i	$0.403190\pi$
$642$	−0.748125	−0.0295261
$643$	−3.34319	−0.131842	−0.0659212	−	0.997825i	$-0.520999\pi$
$643$	−3.34319	−0.131842	−0.0659212	+	0.997825i	$0.520999\pi$
$644$	0.107463	0.00423462
$645$	6.33547	0.249459
$646$	−3.66741	−0.144292
$647$	−11.0469	−0.434297	−0.217149	−	0.976139i	$-0.569676\pi$
$647$	−11.0469	−0.434297	−0.217149	+	0.976139i	$0.569676\pi$
$648$	2.79995	0.109992
$649$	−1.88141	−0.0738518
$650$	−33.6392	−1.31944
$651$	0.0327089	0.00128196
$652$	13.8313	0.541677
$653$	−19.2944	−0.755048	−0.377524	−	0.926000i	$-0.623225\pi$
$653$	−19.2944	−0.755048	−0.377524	+	0.926000i	$0.623225\pi$
$654$	−10.7517	−0.420424
$655$	−51.8736	−2.02687
$656$	−1.33294	−0.0520427
$657$	−6.91670	−0.269846
$658$	0.0144275	0.000562441 0
$659$	5.68747	0.221552	0.110776	−	0.993845i	$-0.464666\pi$
$659$	5.68747	0.221552	0.110776	+	0.993845i	$0.464666\pi$
$660$	18.2448	0.710177
$661$	−16.5678	−0.644411	−0.322205	−	0.946670i	$-0.604424\pi$
$661$	−16.5678	−0.644411	−0.322205	+	0.946670i	$0.604424\pi$
$662$	13.7103	0.532865
$663$	2.70187	0.104932
$664$	1.82364	0.0707708
$665$	0.187316	0.00726381
$666$	4.48720	0.173876
$667$	−22.1142	−0.856265
$668$	−12.8907	−0.498755
$669$	−26.2867	−1.01630
$670$	−27.8999	−1.07787
$671$	10.5271	0.406394
$672$	0.0566155	0.00218399
$673$	32.5610	1.25513	0.627567	−	0.778563i	$-0.284051\pi$
$673$	32.5610	1.25513	0.627567	+	0.778563i	$0.284051\pi$
$674$	−2.78479	−0.107266
$675$	−14.5148	−0.558676
$676$	7.20601	0.277154
$677$	11.0341	0.424074	0.212037	−	0.977262i	$-0.431990\pi$
$677$	11.0341	0.424074	0.212037	+	0.977262i	$0.431990\pi$
$678$	5.38863	0.206949
$679$	−0.113477	−0.00435486
$680$	12.3689	0.474327
$681$	0.621313	0.0238088
$682$	−9.24187	−0.353890
$683$	37.3675	1.42983	0.714913	−	0.699213i	$-0.246466\pi$
$683$	37.3675	1.42983	0.714913	+	0.699213i	$0.246466\pi$
$684$	5.40530	0.206677
$685$	19.6405	0.750424
$686$	0.119096	0.00454709
$687$	−6.55118	−0.249943
$688$	0.181814	0.00693160
$689$	−11.4864	−0.437597
$690$	32.4771	1.23638
$691$	18.7953	0.715008	0.357504	−	0.933912i	$-0.383628\pi$
$691$	18.7953	0.715008	0.357504	+	0.933912i	$0.383628\pi$
$692$	19.0918	0.725762
$693$	−0.0323988	−0.00123073
$694$	−11.9243	−0.452639
$695$	−44.0646	−1.67147
$696$	−7.22429	−0.273836
$697$	10.5143	0.398258
$698$	−8.50285	−0.321838
$699$	24.9995	0.945567
$700$	−0.181988	−0.00687850
$701$	−16.1476	−0.609888	−0.304944	−	0.952370i	$-0.598638\pi$
$701$	−16.1476	−0.609888	−0.304944	+	0.952370i	$0.598638\pi$
$702$	2.31757	0.0874712
$703$	22.3665	0.843569
$704$	−15.1684	−0.571679
$705$	−7.49206	−0.282167
$706$	22.3362	0.840635
$707$	−0.122299	−0.00459952
$708$	0.728090	0.0273633
$709$	29.4719	1.10684	0.553420	−	0.832902i	$-0.313322\pi$
$709$	29.4719	1.10684	0.553420	+	0.832902i	$0.313322\pi$
$710$	−59.2524	−2.22370
$711$	1.00000	0.0375029
$712$	−21.1359	−0.792102
$713$	28.2677	1.05863
$714$	−0.00850689	−0.000318362 0
$715$	38.9919	1.45821
$716$	−15.4120	−0.575973
$717$	17.5256	0.654506
$718$	−19.1467	−0.714548
$719$	−31.4919	−1.17445	−0.587224	−	0.809424i	$-0.699779\pi$
$719$	−31.4919	−1.17445	−0.587224	+	0.809424i	$0.699779\pi$
$720$	−0.560033	−0.0208712
$721$	0.137966	0.00513812
$722$	0.617363	0.0229759
$723$	−18.4610	−0.686571
$724$	16.2396	0.603542
$725$	37.4504	1.39087
$726$	−0.281156	−0.0104347
$727$	−4.27714	−0.158630	−0.0793152	−	0.996850i	$-0.525273\pi$
$727$	−4.27714	−0.158630	−0.0793152	+	0.996850i	$0.525273\pi$
$728$	0.0750270	0.00278068
$729$	1.00000	0.0370370
$730$	−26.2089	−0.970036
$731$	−1.43416	−0.0530442
$732$	−4.07389	−0.150575
$733$	8.09488	0.298991	0.149496	−	0.988762i	$-0.452235\pi$
$733$	8.09488	0.298991	0.149496	+	0.988762i	$0.452235\pi$
$734$	−4.23714	−0.156396
$735$	−30.9225	−1.14059
$736$	48.9283	1.80352
$737$	24.0536	0.886025
$738$	9.01881	0.331987
$739$	19.8278	0.729376	0.364688	−	0.931130i	$-0.381176\pi$
$739$	19.8278	0.729376	0.364688	+	0.931130i	$0.381176\pi$
$740$	−29.2158	−1.07399
$741$	11.5520	0.424372
$742$	0.0361651	0.00132766
$743$	−6.79768	−0.249383	−0.124691	−	0.992196i	$-0.539794\pi$
$743$	−6.79768	−0.249383	−0.124691	+	0.992196i	$0.539794\pi$
$744$	9.23452	0.338554
$745$	50.2078	1.83947
$746$	5.96373	0.218348
$747$	0.651310	0.0238302
$748$	−4.13006	−0.151010
$749$	−0.00864983	−0.000316058 0
$750$	−36.0538	−1.31650
$751$	3.60740	0.131636	0.0658179	−	0.997832i	$-0.479034\pi$
$751$	3.60740	0.131636	0.0658179	+	0.997832i	$0.479034\pi$
$752$	−0.215006	−0.00784046
$753$	−29.5254	−1.07597
$754$	−5.97968	−0.217767
$755$	2.64815	0.0963760
$756$	0.0125381	0.000456005 0
$757$	34.9771	1.27126	0.635631	−	0.771993i	$-0.280740\pi$
$757$	34.9771	1.27126	0.635631	+	0.771993i	$0.280740\pi$
$758$	28.4187	1.03221
$759$	−27.9998	−1.01633
$760$	52.8840	1.91830
$761$	−34.2736	−1.24242	−0.621209	−	0.783645i	$-0.713358\pi$
$761$	−34.2736	−1.24242	−0.621209	+	0.783645i	$0.713358\pi$
$762$	−10.5014	−0.380426
$763$	−0.124311	−0.00450036
$764$	−7.67697	−0.277743
$765$	4.41756	0.159717
$766$	−5.92144	−0.213950
$767$	1.55604	0.0561854
$768$	15.6634	0.565204
$769$	49.2191	1.77489	0.887443	−	0.460917i	$-0.152479\pi$
$769$	49.2191	1.77489	0.887443	+	0.460917i	$0.152479\pi$
$770$	−0.122767	−0.00442420
$771$	10.8979	0.392478
$772$	4.66674	0.167960
$773$	−11.2742	−0.405504	−0.202752	−	0.979230i	$-0.564989\pi$
$773$	−11.2742	−0.405504	−0.202752	+	0.979230i	$0.564989\pi$
$774$	−1.23017	−0.0442176
$775$	−47.8713	−1.71959
$776$	−32.0374	−1.15008
$777$	0.0518811	0.00186122
$778$	29.5440	1.05920
$779$	44.9544	1.61066
$780$	−15.0895	−0.540292
$781$	51.0837	1.82792
$782$	−7.35183	−0.262901
$783$	−2.58015	−0.0922070
$784$	−0.887407	−0.0316931
$785$	−71.8242	−2.56351
$786$	10.0724	0.359270
$787$	33.2404	1.18489	0.592447	−	0.805610i	$-0.298162\pi$
$787$	33.2404	1.18489	0.592447	+	0.805610i	$0.298162\pi$
$788$	−30.3150	−1.07993
$789$	19.4022	0.690738
$790$	3.78923	0.134815
$791$	0.0623035	0.00221526
$792$	−9.14698	−0.325024
$793$	−8.70654	−0.309178
$794$	7.19314	0.255275
$795$	−18.7802	−0.666066
$796$	6.99238	0.247838
$797$	41.8772	1.48337	0.741683	−	0.670750i	$-0.234028\pi$
$797$	41.8772	1.48337	0.741683	+	0.670750i	$0.234028\pi$
$798$	−0.0363716	−0.00128754
$799$	1.69597	0.0599993
$800$	−82.8599	−2.92954
$801$	−7.54867	−0.266719
$802$	21.4562	0.757644
$803$	22.5957	0.797385
$804$	−9.30853	−0.328286
$805$	0.375501	0.0132347
$806$	7.64359	0.269234
$807$	−10.6240	−0.373982
$808$	−34.5279	−1.21469
$809$	−17.9758	−0.631997	−0.315998	−	0.948760i	$-0.602339\pi$
$809$	−17.9758	−0.631997	−0.315998	+	0.948760i	$0.602339\pi$
$810$	3.78923	0.133140
$811$	36.5068	1.28193	0.640963	−	0.767572i	$-0.278535\pi$
$811$	36.5068	1.28193	0.640963	+	0.767572i	$0.278535\pi$
$812$	−0.0323501	−0.00113527
$813$	11.1895	0.392433
$814$	−14.6590	−0.513796
$815$	48.3301	1.69293
$816$	0.126774	0.00443799
$817$	−6.13180	−0.214525
$818$	1.90021	0.0664394
$819$	0.0267958	0.000936322 0
$820$	−58.7208	−2.05062
$821$	52.0985	1.81825	0.909125	−	0.416524i	$-0.136752\pi$
$821$	52.0985	1.81825	0.909125	+	0.416524i	$0.136752\pi$
$822$	−3.81363	−0.133016
$823$	−46.9992	−1.63829	−0.819144	−	0.573587i	$-0.805551\pi$
$823$	−46.9992	−1.63829	−0.819144	+	0.573587i	$0.805551\pi$
$824$	38.9512	1.35693
$825$	47.4175	1.65087
$826$	−0.00489922	−0.000170466 0
$827$	−12.3299	−0.428751	−0.214376	−	0.976751i	$-0.568772\pi$
$827$	−12.3299	−0.428751	−0.214376	+	0.976751i	$0.568772\pi$
$828$	10.8357	0.376565
$829$	19.5307	0.678329	0.339165	−	0.940727i	$-0.389856\pi$
$829$	19.5307	0.678329	0.339165	+	0.940727i	$0.389856\pi$
$830$	2.46796	0.0856643
$831$	−23.7002	−0.822151
$832$	12.5451	0.434925
$833$	6.99990	0.242532
$834$	8.55611	0.296274
$835$	−45.0432	−1.55878
$836$	−17.6582	−0.610723
$837$	3.29810	0.113999
$838$	−20.6331	−0.712757
$839$	9.68676	0.334424	0.167212	−	0.985921i	$-0.446524\pi$
$839$	9.68676	0.334424	0.167212	+	0.985921i	$0.446524\pi$
$840$	0.122669	0.00423248
$841$	−22.3428	−0.770443
$842$	7.06672	0.243535
$843$	4.90376	0.168894
$844$	−27.0992	−0.932793
$845$	25.1796	0.866203
$846$	1.45475	0.0500153
$847$	−0.00325073	−0.000111696 0
$848$	−0.538952	−0.0185077
$849$	−12.2940	−0.421929
$850$	12.4503	0.427042
$851$	44.8367	1.53698
$852$	−19.7690	−0.677274
$853$	37.1292	1.27128	0.635640	−	0.771986i	$-0.280736\pi$
$853$	37.1292	1.27128	0.635640	+	0.771986i	$0.280736\pi$
$854$	0.0274127	0.000938042 0
$855$	18.8875	0.645937
$856$	−2.44206	−0.0834678
$857$	−6.38603	−0.218143	−0.109071	−	0.994034i	$-0.534788\pi$
$857$	−6.38603	−0.218143	−0.109071	+	0.994034i	$0.534788\pi$
$858$	−7.57113	−0.258474
$859$	−42.3549	−1.44513	−0.722565	−	0.691303i	$-0.757037\pi$
$859$	−42.3549	−1.44513	−0.722565	+	0.691303i	$0.757037\pi$
$860$	8.00955	0.273123
$861$	0.104276	0.00355370
$862$	2.20593	0.0751341
$863$	20.2052	0.687792	0.343896	−	0.939008i	$-0.388253\pi$
$863$	20.2052	0.687792	0.343896	+	0.939008i	$0.388253\pi$
$864$	5.70865	0.194212
$865$	66.7115	2.26826
$866$	−6.05303	−0.205690
$867$	−1.00000	−0.0339618
$868$	0.0413518	0.00140357
$869$	−3.26684	−0.110820
$870$	−9.77677	−0.331464
$871$	−19.8938	−0.674075
$872$	−35.0961	−1.18850
$873$	−11.4421	−0.387257
$874$	−31.4331	−1.06324
$875$	−0.416855	−0.0140923
$876$	−8.74435	−0.295444
$877$	−44.1906	−1.49221	−0.746105	−	0.665829i	$-0.768078\pi$
$877$	−44.1906	−1.49221	−0.746105	+	0.665829i	$0.768078\pi$
$878$	13.5857	0.458495
$879$	1.55549	0.0524653
$880$	1.82954	0.0616736
$881$	8.73368	0.294245	0.147123	−	0.989118i	$-0.452999\pi$
$881$	8.73368	0.294245	0.147123	+	0.989118i	$0.452999\pi$
$882$	6.00428	0.202174
$883$	−36.5034	−1.22844	−0.614219	−	0.789135i	$-0.710529\pi$
$883$	−36.5034	−1.22844	−0.614219	+	0.789135i	$0.710529\pi$
$884$	3.41581	0.114886
$885$	2.54412	0.0855198
$886$	15.8507	0.532516
$887$	−0.247086	−0.00829633	−0.00414816	−	0.999991i	$-0.501320\pi$
$887$	−0.247086	−0.00829633	−0.00414816	+	0.999991i	$0.501320\pi$
$888$	14.6473	0.491531
$889$	−0.121417	−0.00407221
$890$	−28.6036	−0.958796
$891$	−3.26684	−0.109443
$892$	−33.2327	−1.11271
$893$	7.25121	0.242653
$894$	−9.74894	−0.326053
$895$	−53.8533	−1.80012
$896$	0.0737323	0.00246322
$897$	23.1575	0.773206
$898$	−17.2579	−0.575905
$899$	−8.50959	−0.283811
$900$	−18.3502	−0.611673
$901$	4.25127	0.141630
$902$	−29.4630	−0.981010
$903$	−0.0142232	−0.000473320 0
$904$	17.5898	0.585028
$905$	56.7453	1.88628
$906$	−0.514196	−0.0170830
$907$	−6.74409	−0.223934	−0.111967	−	0.993712i	$-0.535715\pi$
$907$	−6.74409	−0.223934	−0.111967	+	0.993712i	$0.535715\pi$
$908$	0.785487	0.0260673
$909$	−12.3316	−0.409014
$910$	0.101535	0.00336587
$911$	−29.3567	−0.972630	−0.486315	−	0.873784i	$-0.661659\pi$
$911$	−29.3567	−0.972630	−0.486315	+	0.873784i	$0.661659\pi$
$912$	0.542029	0.0179484
$913$	−2.12772	−0.0704174
$914$	−6.85335	−0.226689
$915$	−14.2352	−0.470601
$916$	−8.28225	−0.273653
$917$	0.116457	0.00384575
$918$	−0.857766	−0.0283105
$919$	32.1337	1.05999	0.529996	−	0.848000i	$-0.322193\pi$
$919$	32.1337	1.05999	0.529996	+	0.848000i	$0.322193\pi$
$920$	106.013	3.49515
$921$	24.0461	0.792345
$922$	−1.87314	−0.0616885
$923$	−42.2493	−1.39065
$924$	−0.0409599	−0.00134748
$925$	−75.9309	−2.49659
$926$	12.5507	0.412443
$927$	13.9114	0.456909
$928$	−14.7291	−0.483508
$929$	6.48527	0.212775	0.106387	−	0.994325i	$-0.466072\pi$
$929$	6.48527	0.212775	0.106387	+	0.994325i	$0.466072\pi$
$930$	12.4973	0.409801
$931$	29.9284	0.980863
$932$	31.6053	1.03527
$933$	23.4847	0.768855
$934$	−26.8344	−0.878048
$935$	−14.4314	−0.471959
$936$	7.56511	0.247273
$937$	−8.72439	−0.285013	−0.142507	−	0.989794i	$-0.545516\pi$
$937$	−8.72439	−0.285013	−0.142507	+	0.989794i	$0.545516\pi$
$938$	0.0626358	0.00204513
$939$	21.3568	0.696952
$940$	−9.47175	−0.308935
$941$	34.5477	1.12622	0.563112	−	0.826381i	$-0.309604\pi$
$941$	34.5477	1.12622	0.563112	+	0.826381i	$0.309604\pi$
$942$	13.9462	0.454393
$943$	90.1172	2.93462
$944$	0.0730108	0.00237630
$945$	0.0438111	0.00142518
$946$	4.01877	0.130661
$947$	−20.9258	−0.679996	−0.339998	−	0.940426i	$-0.610426\pi$
$947$	−20.9258	−0.679996	−0.339998	+	0.940426i	$0.610426\pi$
$948$	1.26424	0.0410605
$949$	−18.6880	−0.606639
$950$	53.2318	1.72707
$951$	0.835900	0.0271059
$952$	−0.0277685	−0.000899982 0
$953$	−7.28422	−0.235959	−0.117979	−	0.993016i	$-0.537642\pi$
$953$	−7.28422	−0.235959	−0.117979	+	0.993016i	$0.537642\pi$
$954$	3.64659	0.118063
$955$	−26.8252	−0.868044
$956$	22.1566	0.716594
$957$	8.42892	0.272468
$958$	16.0877	0.519769
$959$	−0.0440932	−0.00142384
$960$	20.5113	0.661999
$961$	−20.1225	−0.649114
$962$	12.1238	0.390889
$963$	−0.872179	−0.0281056
$964$	−23.3391	−0.751701
$965$	16.3067	0.524932
$966$	−0.0729117	−0.00234590
$967$	−39.6715	−1.27575	−0.637874	−	0.770140i	$-0.720186\pi$
$967$	−39.6715	−1.27575	−0.637874	+	0.770140i	$0.720186\pi$
$968$	−0.917760	−0.0294979
$969$	−4.27554	−0.137350
$970$	−43.3569	−1.39210
$971$	27.4482	0.880856	0.440428	−	0.897788i	$-0.354827\pi$
$971$	27.4482	0.880856	0.440428	+	0.897788i	$0.354827\pi$
$972$	1.26424	0.0405505
$973$	0.0989258	0.00317142
$974$	−26.4629	−0.847928
$975$	−39.2172	−1.25596
$976$	−0.408519	−0.0130764
$977$	−2.02254	−0.0647069	−0.0323534	−	0.999476i	$-0.510300\pi$
$977$	−2.02254	−0.0647069	−0.0323534	+	0.999476i	$0.510300\pi$
$978$	−9.38435	−0.300078
$979$	24.6603	0.788146
$980$	−39.0934	−1.24879
$981$	−12.5345	−0.400197
$982$	1.87946	0.0599758
$983$	−5.48224	−0.174856	−0.0874282	−	0.996171i	$-0.527865\pi$
$983$	−5.48224	−0.174856	−0.0874282	+	0.996171i	$0.527865\pi$
$984$	29.4396	0.938499
$985$	−105.928	−3.37515
$986$	2.21316	0.0704814
$987$	0.0168198	0.000535381 0
$988$	14.6044	0.464629
$989$	−12.2920	−0.390864
$990$	−12.3788	−0.393424
$991$	41.8540	1.32954	0.664769	−	0.747049i	$-0.268530\pi$
$991$	41.8540	1.32954	0.664769	+	0.747049i	$0.268530\pi$
$992$	18.8277	0.597780
$993$	15.9837	0.507227
$994$	0.133023	0.00421922
$995$	24.4331	0.774581
$996$	0.823411	0.0260908
$997$	−38.2656	−1.21188	−0.605941	−	0.795509i	$-0.707203\pi$
$997$	−38.2656	−1.21188	−0.605941	+	0.795509i	$0.707203\pi$
$998$	32.5073	1.02900
$999$	5.23127	0.165510

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.l.1.13	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.l.1.13	✓	32	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)

\(f(q)\)	\(=\)	\(q-0.857766 q^{2} -1.00000 q^{3} -1.26424 q^{4} -4.41756 q^{5} +0.857766 q^{6} +0.00991750 q^{7} +2.79995 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.857766 q^{2} -1.00000 q^{3} -1.26424 q^{4} -4.41756 q^{5} +0.857766 q^{6} +0.00991750 q^{7} +2.79995 q^{8} +1.00000 q^{9} +3.78923 q^{10} -3.26684 q^{11} +1.26424 q^{12} +2.70187 q^{13} -0.00850689 q^{14} +4.41756 q^{15} +0.126774 q^{16} -1.00000 q^{17} -0.857766 q^{18} -4.27554 q^{19} +5.58484 q^{20} -0.00991750 q^{21} +2.80218 q^{22} -8.57091 q^{23} -2.79995 q^{24} +14.5148 q^{25} -2.31757 q^{26} -1.00000 q^{27} -0.0125381 q^{28} +2.58015 q^{29} -3.78923 q^{30} -3.29810 q^{31} -5.70865 q^{32} +3.26684 q^{33} +0.857766 q^{34} -0.0438111 q^{35} -1.26424 q^{36} -5.23127 q^{37} +3.66741 q^{38} -2.70187 q^{39} -12.3689 q^{40} -10.5143 q^{41} +0.00850689 q^{42} +1.43416 q^{43} +4.13006 q^{44} -4.41756 q^{45} +7.35183 q^{46} -1.69597 q^{47} -0.126774 q^{48} -6.99990 q^{49} -12.4503 q^{50} +1.00000 q^{51} -3.41581 q^{52} -4.25127 q^{53} +0.857766 q^{54} +14.4314 q^{55} +0.0277685 q^{56} +4.27554 q^{57} -2.21316 q^{58} +0.575912 q^{59} -5.58484 q^{60} -3.22241 q^{61} +2.82900 q^{62} +0.00991750 q^{63} +4.64313 q^{64} -11.9357 q^{65} -2.80218 q^{66} -7.36295 q^{67} +1.26424 q^{68} +8.57091 q^{69} +0.0375797 q^{70} -15.6371 q^{71} +2.79995 q^{72} -6.91670 q^{73} +4.48720 q^{74} -14.5148 q^{75} +5.40530 q^{76} -0.0323988 q^{77} +2.31757 q^{78} +1.00000 q^{79} -0.560033 q^{80} +1.00000 q^{81} +9.01881 q^{82} +0.651310 q^{83} +0.0125381 q^{84} +4.41756 q^{85} -1.23017 q^{86} -2.58015 q^{87} -9.14698 q^{88} -7.54867 q^{89} +3.78923 q^{90} +0.0267958 q^{91} +10.8357 q^{92} +3.29810 q^{93} +1.45475 q^{94} +18.8875 q^{95} +5.70865 q^{96} -11.4421 q^{97} +6.00428 q^{98} -3.26684 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9} + 17 q^{10} + 8 q^{11} - 41 q^{12} + 17 q^{13} + q^{14} + q^{15} + 55 q^{16} - 32 q^{17} - q^{18} + 48 q^{19} - 7 q^{20} - 4 q^{21} - 4 q^{22} - 19 q^{23} + 3 q^{24} + 63 q^{25} + 27 q^{26} - 32 q^{27} + 17 q^{28} - 15 q^{29} - 17 q^{30} + 20 q^{31} + 13 q^{32} - 8 q^{33} + q^{34} + 22 q^{35} + 41 q^{36} + 6 q^{37} + 11 q^{38} - 17 q^{39} + 47 q^{40} + q^{41} - q^{42} + 40 q^{43} + 22 q^{44} - q^{45} + 5 q^{46} - 5 q^{47} - 55 q^{48} + 88 q^{49} + 17 q^{50} + 32 q^{51} + 23 q^{52} - 34 q^{53} + q^{54} + 48 q^{55} - 48 q^{57} - 9 q^{58} + 41 q^{59} + 7 q^{60} + 20 q^{61} + 15 q^{62} + 4 q^{63} + 93 q^{64} - 58 q^{65} + 4 q^{66} + 52 q^{67} - 41 q^{68} + 19 q^{69} + 25 q^{70} + q^{71} - 3 q^{72} + 19 q^{73} + 12 q^{74} - 63 q^{75} + 128 q^{76} - 20 q^{77} - 27 q^{78} + 32 q^{79} - 16 q^{80} + 32 q^{81} - 5 q^{82} + 31 q^{83} - 17 q^{84} + q^{85} - 62 q^{86} + 15 q^{87} + 35 q^{88} + 18 q^{89} + 17 q^{90} + 48 q^{91} - 75 q^{92} - 20 q^{93} + 29 q^{94} + 5 q^{95} - 13 q^{96} + 17 q^{97} + 30 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9 + 17 * q^10 + 8 * q^11 - 41 * q^12 + 17 * q^13 + q^14 + q^15 + 55 * q^16 - 32 * q^17 - q^18 + 48 * q^19 - 7 * q^20 - 4 * q^21 - 4 * q^22 - 19 * q^23 + 3 * q^24 + 63 * q^25 + 27 * q^26 - 32 * q^27 + 17 * q^28 - 15 * q^29 - 17 * q^30 + 20 * q^31 + 13 * q^32 - 8 * q^33 + q^34 + 22 * q^35 + 41 * q^36 + 6 * q^37 + 11 * q^38 - 17 * q^39 + 47 * q^40 + q^41 - q^42 + 40 * q^43 + 22 * q^44 - q^45 + 5 * q^46 - 5 * q^47 - 55 * q^48 + 88 * q^49 + 17 * q^50 + 32 * q^51 + 23 * q^52 - 34 * q^53 + q^54 + 48 * q^55 - 48 * q^57 - 9 * q^58 + 41 * q^59 + 7 * q^60 + 20 * q^61 + 15 * q^62 + 4 * q^63 + 93 * q^64 - 58 * q^65 + 4 * q^66 + 52 * q^67 - 41 * q^68 + 19 * q^69 + 25 * q^70 + q^71 - 3 * q^72 + 19 * q^73 + 12 * q^74 - 63 * q^75 + 128 * q^76 - 20 * q^77 - 27 * q^78 + 32 * q^79 - 16 * q^80 + 32 * q^81 - 5 * q^82 + 31 * q^83 - 17 * q^84 + q^85 - 62 * q^86 + 15 * q^87 + 35 * q^88 + 18 * q^89 + 17 * q^90 + 48 * q^91 - 75 * q^92 - 20 * q^93 + 29 * q^94 + 5 * q^95 - 13 * q^96 + 17 * q^97 + 30 * q^98 + 8 * q^99

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