LMFDB - Embedded newform 6005.2.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$1$
Dimension:	$88$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69778 q^{2} -3.22929 q^{3} +5.27799 q^{4} +1.00000 q^{5} +8.71190 q^{6} +2.27707 q^{7} -8.84328 q^{8} +7.42831 q^{9} +O(q^{10})$	\(q-2.69778 q^{2} -3.22929 q^{3} +5.27799 q^{4} +1.00000 q^{5} +8.71190 q^{6} +2.27707 q^{7} -8.84328 q^{8} +7.42831 q^{9} -2.69778 q^{10} +0.682522 q^{11} -17.0442 q^{12} -2.19601 q^{13} -6.14303 q^{14} -3.22929 q^{15} +13.3012 q^{16} -1.66218 q^{17} -20.0399 q^{18} -8.68627 q^{19} +5.27799 q^{20} -7.35333 q^{21} -1.84129 q^{22} +5.21881 q^{23} +28.5575 q^{24} +1.00000 q^{25} +5.92434 q^{26} -14.3003 q^{27} +12.0184 q^{28} +6.11215 q^{29} +8.71190 q^{30} +5.46205 q^{31} -18.1971 q^{32} -2.20406 q^{33} +4.48419 q^{34} +2.27707 q^{35} +39.2066 q^{36} +4.88360 q^{37} +23.4336 q^{38} +7.09155 q^{39} -8.84328 q^{40} +7.22181 q^{41} +19.8376 q^{42} -9.03233 q^{43} +3.60234 q^{44} +7.42831 q^{45} -14.0792 q^{46} -3.05473 q^{47} -42.9535 q^{48} -1.81494 q^{49} -2.69778 q^{50} +5.36766 q^{51} -11.5905 q^{52} -10.6721 q^{53} +38.5790 q^{54} +0.682522 q^{55} -20.1368 q^{56} +28.0505 q^{57} -16.4892 q^{58} +5.66531 q^{59} -17.0442 q^{60} +5.32959 q^{61} -14.7354 q^{62} +16.9148 q^{63} +22.4893 q^{64} -2.19601 q^{65} +5.94606 q^{66} -9.69371 q^{67} -8.77297 q^{68} -16.8530 q^{69} -6.14303 q^{70} -6.87699 q^{71} -65.6907 q^{72} +11.1368 q^{73} -13.1748 q^{74} -3.22929 q^{75} -45.8461 q^{76} +1.55415 q^{77} -19.1314 q^{78} -14.3650 q^{79} +13.3012 q^{80} +23.8949 q^{81} -19.4828 q^{82} +12.5182 q^{83} -38.8108 q^{84} -1.66218 q^{85} +24.3672 q^{86} -19.7379 q^{87} -6.03573 q^{88} -0.592090 q^{89} -20.0399 q^{90} -5.00048 q^{91} +27.5448 q^{92} -17.6385 q^{93} +8.24097 q^{94} -8.68627 q^{95} +58.7637 q^{96} -9.42198 q^{97} +4.89630 q^{98} +5.06999 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9}+O(q^{10}) $ 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9} - 14 q^{10} - 26 q^{11} - 64 q^{12} - 31 q^{13} - 17 q^{14} - 34 q^{15} + 34 q^{16} - 31 q^{17} - 42 q^{18} - 56 q^{19} + 66 q^{20} - q^{21} - 49 q^{22} - 74 q^{23} - 3 q^{24} + 88 q^{25} - q^{26} - 130 q^{27} - 57 q^{28} - 6 q^{29} - q^{30} - 37 q^{31} - 87 q^{32} - 43 q^{33} - 35 q^{34} - 35 q^{35} + 53 q^{36} - 67 q^{37} - 40 q^{38} - 21 q^{39} - 39 q^{40} + 2 q^{41} - 15 q^{42} - 136 q^{43} - 15 q^{44} + 72 q^{45} - 16 q^{46} - 139 q^{47} - 71 q^{48} + 41 q^{49} - 14 q^{50} - 71 q^{51} - 71 q^{52} - 75 q^{53} + 26 q^{54} - 26 q^{55} - 22 q^{56} - 34 q^{57} - 65 q^{58} - 41 q^{59} - 64 q^{60} - 11 q^{61} - 30 q^{62} - 114 q^{63} - 33 q^{64} - 31 q^{65} + 24 q^{66} - 209 q^{67} - 42 q^{68} - 22 q^{69} - 17 q^{70} - 43 q^{71} - 80 q^{72} - 50 q^{73} + 9 q^{74} - 34 q^{75} - 62 q^{76} - 49 q^{77} - 19 q^{78} - 77 q^{79} + 34 q^{80} + 72 q^{81} - 107 q^{82} - 113 q^{83} + 19 q^{84} - 31 q^{85} + 14 q^{86} - 87 q^{87} - 107 q^{88} - 5 q^{89} - 42 q^{90} - 159 q^{91} - 100 q^{92} - 82 q^{93} - 31 q^{94} - 56 q^{95} + 58 q^{96} - 105 q^{97} - 29 q^{98} - 68 q^{99}+O(q^{100}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9 - 14 * q^10 - 26 * q^11 - 64 * q^12 - 31 * q^13 - 17 * q^14 - 34 * q^15 + 34 * q^16 - 31 * q^17 - 42 * q^18 - 56 * q^19 + 66 * q^20 - q^21 - 49 * q^22 - 74 * q^23 - 3 * q^24 + 88 * q^25 - q^26 - 130 * q^27 - 57 * q^28 - 6 * q^29 - q^30 - 37 * q^31 - 87 * q^32 - 43 * q^33 - 35 * q^34 - 35 * q^35 + 53 * q^36 - 67 * q^37 - 40 * q^38 - 21 * q^39 - 39 * q^40 + 2 * q^41 - 15 * q^42 - 136 * q^43 - 15 * q^44 + 72 * q^45 - 16 * q^46 - 139 * q^47 - 71 * q^48 + 41 * q^49 - 14 * q^50 - 71 * q^51 - 71 * q^52 - 75 * q^53 + 26 * q^54 - 26 * q^55 - 22 * q^56 - 34 * q^57 - 65 * q^58 - 41 * q^59 - 64 * q^60 - 11 * q^61 - 30 * q^62 - 114 * q^63 - 33 * q^64 - 31 * q^65 + 24 * q^66 - 209 * q^67 - 42 * q^68 - 22 * q^69 - 17 * q^70 - 43 * q^71 - 80 * q^72 - 50 * q^73 + 9 * q^74 - 34 * q^75 - 62 * q^76 - 49 * q^77 - 19 * q^78 - 77 * q^79 + 34 * q^80 + 72 * q^81 - 107 * q^82 - 113 * q^83 + 19 * q^84 - 31 * q^85 + 14 * q^86 - 87 * q^87 - 107 * q^88 - 5 * q^89 - 42 * q^90 - 159 * q^91 - 100 * q^92 - 82 * q^93 - 31 * q^94 - 56 * q^95 + 58 * q^96 - 105 * q^97 - 29 * q^98 - 68 * 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 $

$2$	−2.69778	−1.90762	−0.953808	−	0.300418i	$-0.902874\pi$
$2$	−2.69778	−1.90762	−0.953808	+	0.300418i	$0.902874\pi$
$3$	−3.22929	−1.86443	−0.932216	−	0.361903i	$-0.882127\pi$
$3$	−3.22929	−1.86443	−0.932216	+	0.361903i	$0.882127\pi$
$4$	5.27799	2.63900
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	8.71190	3.55662
$7$	2.27707	0.860653	0.430326	−	0.902673i	$-0.358398\pi$
$7$	2.27707	0.860653	0.430326	+	0.902673i	$0.358398\pi$
$8$	−8.84328	−3.12657
$9$	7.42831	2.47610
$10$	−2.69778	−0.853111
$11$	0.682522	0.205788	0.102894	−	0.994692i	$-0.467190\pi$
$11$	0.682522	0.205788	0.102894	+	0.994692i	$0.467190\pi$
$12$	−17.0442	−4.92023
$13$	−2.19601	−0.609064	−0.304532	−	0.952502i	$-0.598500\pi$
$13$	−2.19601	−0.609064	−0.304532	+	0.952502i	$0.598500\pi$
$14$	−6.14303	−1.64179
$15$	−3.22929	−0.833799
$16$	13.3012	3.32530
$17$	−1.66218	−0.403138	−0.201569	−	0.979474i	$-0.564604\pi$
$17$	−1.66218	−0.403138	−0.201569	+	0.979474i	$0.564604\pi$
$18$	−20.0399	−4.72346
$19$	−8.68627	−1.99277	−0.996384	−	0.0849644i	$-0.972922\pi$
$19$	−8.68627	−1.99277	−0.996384	+	0.0849644i	$0.972922\pi$
$20$	5.27799	1.18019
$21$	−7.35333	−1.60463
$22$	−1.84129	−0.392565
$23$	5.21881	1.08820	0.544098	−	0.839021i	$-0.316872\pi$
$23$	5.21881	1.08820	0.544098	+	0.839021i	$0.316872\pi$
$24$	28.5575	5.82928
$25$	1.00000	0.200000
$26$	5.92434	1.16186
$27$	−14.3003	−2.75210
$28$	12.0184	2.27126
$29$	6.11215	1.13500	0.567499	−	0.823374i	$-0.307911\pi$
$29$	6.11215	1.13500	0.567499	+	0.823374i	$0.307911\pi$
$30$	8.71190	1.59057
$31$	5.46205	0.981013	0.490506	−	0.871438i	$-0.336812\pi$
$31$	5.46205	0.981013	0.490506	+	0.871438i	$0.336812\pi$
$32$	−18.1971	−3.21682
$33$	−2.20406	−0.383678
$34$	4.48419	0.769031
$35$	2.27707	0.384896
$36$	39.2066	6.53443
$37$	4.88360	0.802858	0.401429	−	0.915890i	$-0.368514\pi$
$37$	4.88360	0.802858	0.401429	+	0.915890i	$0.368514\pi$
$38$	23.4336	3.80143
$39$	7.09155	1.13556
$40$	−8.84328	−1.39825
$41$	7.22181	1.12786	0.563928	−	0.825824i	$-0.309289\pi$
$41$	7.22181	1.12786	0.563928	+	0.825824i	$0.309289\pi$
$42$	19.8376	3.06101
$43$	−9.03233	−1.37742	−0.688709	−	0.725038i	$-0.741822\pi$
$43$	−9.03233	−1.37742	−0.688709	+	0.725038i	$0.741822\pi$
$44$	3.60234	0.543074
$45$	7.42831	1.10735
$46$	−14.0792	−2.07586
$47$	−3.05473	−0.445578	−0.222789	−	0.974867i	$-0.571516\pi$
$47$	−3.05473	−0.445578	−0.222789	+	0.974867i	$0.571516\pi$
$48$	−42.9535	−6.19980
$49$	−1.81494	−0.259277
$50$	−2.69778	−0.381523
$51$	5.36766	0.751623
$52$	−11.5905	−1.60732
$53$	−10.6721	−1.46593	−0.732965	−	0.680266i	$-0.761864\pi$
$53$	−10.6721	−1.46593	−0.732965	+	0.680266i	$0.761864\pi$
$54$	38.5790	5.24994
$55$	0.682522	0.0920313
$56$	−20.1368	−2.69089
$57$	28.0505	3.71538
$58$	−16.4892	−2.16514
$59$	5.66531	0.737561	0.368780	−	0.929517i	$-0.379775\pi$
$59$	5.66531	0.737561	0.368780	+	0.929517i	$0.379775\pi$
$60$	−17.0442	−2.20039
$61$	5.32959	0.682384	0.341192	−	0.939994i	$-0.389169\pi$
$61$	5.32959	0.682384	0.341192	+	0.939994i	$0.389169\pi$
$62$	−14.7354	−1.87139
$63$	16.9148	2.13107
$64$	22.4893	2.81116
$65$	−2.19601	−0.272382
$66$	5.94606	0.731910
$67$	−9.69371	−1.18427	−0.592137	−	0.805837i	$-0.701716\pi$
$67$	−9.69371	−1.18427	−0.592137	+	0.805837i	$0.701716\pi$
$68$	−8.77297	−1.06388
$69$	−16.8530	−2.02887
$70$	−6.14303	−0.734233
$71$	−6.87699	−0.816149	−0.408074	−	0.912949i	$-0.633800\pi$
$71$	−6.87699	−0.816149	−0.408074	+	0.912949i	$0.633800\pi$
$72$	−65.6907	−7.74172
$73$	11.1368	1.30346	0.651731	−	0.758450i	$-0.274043\pi$
$73$	11.1368	1.30346	0.651731	+	0.758450i	$0.274043\pi$
$74$	−13.1748	−1.53154
$75$	−3.22929	−0.372886
$76$	−45.8461	−5.25891
$77$	1.55415	0.177112
$78$	−19.1314	−2.16621
$79$	−14.3650	−1.61619	−0.808095	−	0.589052i	$-0.799501\pi$
$79$	−14.3650	−1.61619	−0.808095	+	0.589052i	$0.799501\pi$
$80$	13.3012	1.48712
$81$	23.8949	2.65499
$82$	−19.4828	−2.15152
$83$	12.5182	1.37405	0.687027	−	0.726632i	$-0.258915\pi$
$83$	12.5182	1.37405	0.687027	+	0.726632i	$0.258915\pi$
$84$	−38.8108	−4.23461
$85$	−1.66218	−0.180289
$86$	24.3672	2.62758
$87$	−19.7379	−2.11612
$88$	−6.03573	−0.643411
$89$	−0.592090	−0.0627614	−0.0313807	−	0.999508i	$-0.509990\pi$
$89$	−0.592090	−0.0627614	−0.0313807	+	0.999508i	$0.509990\pi$
$90$	−20.0399	−2.11239
$91$	−5.00048	−0.524192
$92$	27.5448	2.87175
$93$	−17.6385	−1.82903
$94$	8.24097	0.849991
$95$	−8.68627	−0.891193
$96$	58.7637	5.99755
$97$	−9.42198	−0.956657	−0.478328	−	0.878181i	$-0.658757\pi$
$97$	−9.42198	−0.956657	−0.478328	+	0.878181i	$0.658757\pi$
$98$	4.89630	0.494601
$99$	5.06999	0.509553
$100$	5.27799	0.527799
$101$	−3.94287	−0.392330	−0.196165	−	0.980571i	$-0.562849\pi$
$101$	−3.94287	−0.392330	−0.196165	+	0.980571i	$0.562849\pi$
$102$	−14.4807	−1.43381
$103$	13.3421	1.31464	0.657320	−	0.753611i	$-0.271690\pi$
$103$	13.3421	1.31464	0.657320	+	0.753611i	$0.271690\pi$
$104$	19.4199	1.90428
$105$	−7.35333	−0.717611
$106$	28.7910	2.79643
$107$	−11.2186	−1.08455	−0.542273	−	0.840202i	$-0.682436\pi$
$107$	−11.2186	−1.08455	−0.542273	+	0.840202i	$0.682436\pi$
$108$	−75.4769	−7.26277
$109$	−4.33864	−0.415567	−0.207783	−	0.978175i	$-0.566625\pi$
$109$	−4.33864	−0.415567	−0.207783	+	0.978175i	$0.566625\pi$
$110$	−1.84129	−0.175560
$111$	−15.7705	−1.49687
$112$	30.2878	2.86193
$113$	3.37402	0.317401	0.158700	−	0.987327i	$-0.449270\pi$
$113$	3.37402	0.317401	0.158700	+	0.987327i	$0.449270\pi$
$114$	−75.6739	−7.08751
$115$	5.21881	0.486656
$116$	32.2599	2.99525
$117$	−16.3127	−1.50811
$118$	−15.2837	−1.40698
$119$	−3.78490	−0.346961
$120$	28.5575	2.60693
$121$	−10.5342	−0.957651
$122$	−14.3780	−1.30173
$123$	−23.3213	−2.10281
$124$	28.8286	2.58889
$125$	1.00000	0.0894427
$126$	−45.6324	−4.06525
$127$	−8.19663	−0.727333	−0.363667	−	0.931529i	$-0.618475\pi$
$127$	−8.19663	−0.727333	−0.363667	+	0.931529i	$0.618475\pi$
$128$	−24.2768	−2.14579
$129$	29.1680	2.56810
$130$	5.92434	0.519599
$131$	−13.5780	−1.18632	−0.593159	−	0.805085i	$-0.702119\pi$
$131$	−13.5780	−1.18632	−0.593159	+	0.805085i	$0.702119\pi$
$132$	−11.6330	−1.01252
$133$	−19.7793	−1.71508
$134$	26.1514	2.25914
$135$	−14.3003	−1.23078
$136$	14.6991	1.26044
$137$	−9.53950	−0.815014	−0.407507	−	0.913202i	$-0.633602\pi$
$137$	−9.53950	−0.815014	−0.407507	+	0.913202i	$0.633602\pi$
$138$	45.4657	3.87030
$139$	13.6454	1.15739	0.578694	−	0.815545i	$-0.303562\pi$
$139$	13.6454	1.15739	0.578694	+	0.815545i	$0.303562\pi$
$140$	12.0184	1.01574
$141$	9.86460	0.830750
$142$	18.5526	1.55690
$143$	−1.49883	−0.125338
$144$	98.8055	8.23379
$145$	6.11215	0.507586
$146$	−30.0445	−2.48650
$147$	5.86096	0.483404
$148$	25.7756	2.11874
$149$	16.8330	1.37901	0.689507	−	0.724279i	$-0.257827\pi$
$149$	16.8330	1.37901	0.689507	+	0.724279i	$0.257827\pi$
$150$	8.71190	0.711324
$151$	1.82819	0.148776	0.0743880	−	0.997229i	$-0.476300\pi$
$151$	1.82819	0.148776	0.0743880	+	0.997229i	$0.476300\pi$
$152$	76.8152	6.23053
$153$	−12.3472	−0.998211
$154$	−4.19275	−0.337862
$155$	5.46205	0.438722
$156$	37.4292	2.99673
$157$	−6.77127	−0.540406	−0.270203	−	0.962803i	$-0.587091\pi$
$157$	−6.77127	−0.540406	−0.270203	+	0.962803i	$0.587091\pi$
$158$	38.7536	3.08307
$159$	34.4634	2.73313
$160$	−18.1971	−1.43861
$161$	11.8836	0.936559
$162$	−64.4631	−5.06470
$163$	0.836560	0.0655245	0.0327622	−	0.999463i	$-0.489570\pi$
$163$	0.836560	0.0655245	0.0327622	+	0.999463i	$0.489570\pi$
$164$	38.1166	2.97641
$165$	−2.20406	−0.171586
$166$	−33.7714	−2.62117
$167$	1.90309	0.147266	0.0736328	−	0.997285i	$-0.476541\pi$
$167$	1.90309	0.147266	0.0736328	+	0.997285i	$0.476541\pi$
$168$	65.0276	5.01699
$169$	−8.17754	−0.629041
$170$	4.48419	0.343921
$171$	−64.5244	−4.93430
$172$	−47.6726	−3.63500
$173$	14.0642	1.06928	0.534640	−	0.845080i	$-0.320447\pi$
$173$	14.0642	1.06928	0.534640	+	0.845080i	$0.320447\pi$
$174$	53.2484	4.03675
$175$	2.27707	0.172131
$176$	9.07837	0.684308
$177$	−18.2949	−1.37513
$178$	1.59733	0.119725
$179$	−0.479896	−0.0358691	−0.0179345	−	0.999839i	$-0.505709\pi$
$179$	−0.479896	−0.0358691	−0.0179345	+	0.999839i	$0.505709\pi$
$180$	39.2066	2.92229
$181$	−13.7118	−1.01919	−0.509596	−	0.860414i	$-0.670205\pi$
$181$	−13.7118	−1.01919	−0.509596	+	0.860414i	$0.670205\pi$
$182$	13.4902	0.999957
$183$	−17.2108	−1.27226
$184$	−46.1514	−3.40233
$185$	4.88360	0.359049
$186$	47.5848	3.48909
$187$	−1.13447	−0.0829609
$188$	−16.1228	−1.17588
$189$	−32.5629	−2.36860
$190$	23.4336	1.70005
$191$	−0.282345	−0.0204298	−0.0102149	−	0.999948i	$-0.503252\pi$
$191$	−0.282345	−0.0204298	−0.0102149	+	0.999948i	$0.503252\pi$
$192$	−72.6244	−5.24121
$193$	−1.08963	−0.0784332	−0.0392166	−	0.999231i	$-0.512486\pi$
$193$	−1.08963	−0.0784332	−0.0392166	+	0.999231i	$0.512486\pi$
$194$	25.4184	1.82493
$195$	7.09155	0.507837
$196$	−9.57923	−0.684231
$197$	10.3187	0.735180	0.367590	−	0.929988i	$-0.380183\pi$
$197$	10.3187	0.735180	0.367590	+	0.929988i	$0.380183\pi$
$198$	−13.6777	−0.972031
$199$	14.4952	1.02754	0.513770	−	0.857928i	$-0.328248\pi$
$199$	14.4952	1.02754	0.513770	+	0.857928i	$0.328248\pi$
$200$	−8.84328	−0.625314
$201$	31.3038	2.20800
$202$	10.6370	0.748416
$203$	13.9178	0.976839
$204$	28.3305	1.98353
$205$	7.22181	0.504393
$206$	−35.9941	−2.50783
$207$	38.7669	2.69449
$208$	−29.2096	−2.02532
$209$	−5.92857	−0.410088
$210$	19.8376	1.36893
$211$	−8.05143	−0.554283	−0.277142	−	0.960829i	$-0.589387\pi$
$211$	−8.05143	−0.554283	−0.277142	+	0.960829i	$0.589387\pi$
$212$	−56.3274	−3.86858
$213$	22.2078	1.52165
$214$	30.2654	2.06890
$215$	−9.03233	−0.616000
$216$	126.462	8.60463
$217$	12.4375	0.844311
$218$	11.7047	0.792742
$219$	−35.9639	−2.43022
$220$	3.60234	0.242870
$221$	3.65016	0.245536
$222$	42.5454	2.85546
$223$	−23.5370	−1.57615	−0.788077	−	0.615576i	$-0.788923\pi$
$223$	−23.5370	−1.57615	−0.788077	+	0.615576i	$0.788923\pi$
$224$	−41.4361	−2.76857
$225$	7.42831	0.495221
$226$	−9.10234	−0.605479
$227$	−10.3519	−0.687079	−0.343539	−	0.939138i	$-0.611626\pi$
$227$	−10.3519	−0.687079	−0.343539	+	0.939138i	$0.611626\pi$
$228$	148.050	9.80487
$229$	−22.4625	−1.48436	−0.742181	−	0.670200i	$-0.766208\pi$
$229$	−22.4625	−1.48436	−0.742181	+	0.670200i	$0.766208\pi$
$230$	−14.0792	−0.928353
$231$	−5.01881	−0.330213
$232$	−54.0514	−3.54865
$233$	28.1451	1.84385	0.921923	−	0.387373i	$-0.126618\pi$
$233$	28.1451	1.84385	0.921923	+	0.387373i	$0.126618\pi$
$234$	44.0079	2.87689
$235$	−3.05473	−0.199269
$236$	29.9015	1.94642
$237$	46.3888	3.01328
$238$	10.2108	0.661869
$239$	9.87520	0.638773	0.319387	−	0.947624i	$-0.396523\pi$
$239$	9.87520	0.638773	0.319387	+	0.947624i	$0.396523\pi$
$240$	−42.9535	−2.77263
$241$	−24.6935	−1.59065	−0.795323	−	0.606186i	$-0.792699\pi$
$241$	−24.6935	−1.59065	−0.795323	+	0.606186i	$0.792699\pi$
$242$	28.4188	1.82683
$243$	−34.2627	−2.19795
$244$	28.1295	1.80081
$245$	−1.81494	−0.115952
$246$	62.9156	4.01136
$247$	19.0751	1.21372
$248$	−48.3024	−3.06721
$249$	−40.4250	−2.56183
$250$	−2.69778	−0.170622
$251$	−10.2926	−0.649661	−0.324831	−	0.945772i	$-0.605307\pi$
$251$	−10.2926	−0.649661	−0.324831	+	0.945772i	$0.605307\pi$
$252$	89.2762	5.62387
$253$	3.56195	0.223938
$254$	22.1127	1.38747
$255$	5.36766	0.336136
$256$	20.5148	1.28217
$257$	12.0198	0.749772	0.374886	−	0.927071i	$-0.377682\pi$
$257$	12.0198	0.749772	0.374886	+	0.927071i	$0.377682\pi$
$258$	−78.6888	−4.89895
$259$	11.1203	0.690982
$260$	−11.5905	−0.718814
$261$	45.4030	2.81037
$262$	36.6305	2.26304
$263$	8.14399	0.502180	0.251090	−	0.967964i	$-0.419211\pi$
$263$	8.14399	0.502180	0.251090	+	0.967964i	$0.419211\pi$
$264$	19.4911	1.19960
$265$	−10.6721	−0.655584
$266$	53.3600	3.27171
$267$	1.91203	0.117014
$268$	−51.1633	−3.12530
$269$	12.4595	0.759671	0.379835	−	0.925054i	$-0.375981\pi$
$269$	12.4595	0.759671	0.379835	+	0.925054i	$0.375981\pi$
$270$	38.5790	2.34785
$271$	4.83072	0.293446	0.146723	−	0.989178i	$-0.453127\pi$
$271$	4.83072	0.293446	0.146723	+	0.989178i	$0.453127\pi$
$272$	−22.1090	−1.34055
$273$	16.1480	0.977321
$274$	25.7354	1.55473
$275$	0.682522	0.0411576
$276$	−88.9502	−5.35417
$277$	2.33713	0.140424	0.0702121	−	0.997532i	$-0.477632\pi$
$277$	2.33713	0.140424	0.0702121	+	0.997532i	$0.477632\pi$
$278$	−36.8122	−2.20785
$279$	40.5738	2.42909
$280$	−20.1368	−1.20340
$281$	−26.2383	−1.56524	−0.782622	−	0.622498i	$-0.786118\pi$
$281$	−26.2383	−1.56524	−0.782622	+	0.622498i	$0.786118\pi$
$282$	−26.6125	−1.58475
$283$	−2.94802	−0.175242	−0.0876209	−	0.996154i	$-0.527926\pi$
$283$	−2.94802	−0.175242	−0.0876209	+	0.996154i	$0.527926\pi$
$284$	−36.2967	−2.15381
$285$	28.0505	1.66157
$286$	4.04349	0.239097
$287$	16.4446	0.970693
$288$	−135.174	−7.96519
$289$	−14.2372	−0.837480
$290$	−16.4892	−0.968279
$291$	30.4263	1.78362
$292$	58.7799	3.43983
$293$	24.2168	1.41476	0.707380	−	0.706834i	$-0.249877\pi$
$293$	24.2168	1.41476	0.707380	+	0.706834i	$0.249877\pi$
$294$	−15.8116	−0.922149
$295$	5.66531	0.329847
$296$	−43.1870	−2.51019
$297$	−9.76028	−0.566349
$298$	−45.4117	−2.63063
$299$	−11.4606	−0.662781
$300$	−17.0442	−0.984045
$301$	−20.5673	−1.18548
$302$	−4.93204	−0.283807
$303$	12.7327	0.731473
$304$	−115.538	−6.62655
$305$	5.32959	0.305171
$306$	33.3099	1.90420
$307$	−16.9762	−0.968884	−0.484442	−	0.874823i	$-0.660977\pi$
$307$	−16.9762	−0.968884	−0.484442	+	0.874823i	$0.660977\pi$
$308$	8.20280	0.467398
$309$	−43.0857	−2.45106
$310$	−14.7354	−0.836913
$311$	29.4794	1.67162	0.835811	−	0.549018i	$-0.184998\pi$
$311$	29.4794	1.67162	0.835811	+	0.549018i	$0.184998\pi$
$312$	−62.7126	−3.55040
$313$	0.0366464	0.00207138	0.00103569	−	0.999999i	$-0.499670\pi$
$313$	0.0366464	0.00207138	0.00103569	+	0.999999i	$0.499670\pi$
$314$	18.2674	1.03089
$315$	16.9148	0.953042
$316$	−75.8184	−4.26512
$317$	−19.5590	−1.09854	−0.549272	−	0.835644i	$-0.685095\pi$
$317$	−19.5590	−1.09854	−0.549272	+	0.835644i	$0.685095\pi$
$318$	−92.9746	−5.21375
$319$	4.17168	0.233569
$320$	22.4893	1.25719
$321$	36.2282	2.02206
$322$	−32.0593	−1.78659
$323$	14.4381	0.803360
$324$	126.117	7.00651
$325$	−2.19601	−0.121813
$326$	−2.25685	−0.124995
$327$	14.0107	0.774796
$328$	−63.8645	−3.52633
$329$	−6.95584	−0.383488
$330$	5.94606	0.327320
$331$	−32.8905	−1.80783	−0.903913	−	0.427717i	$-0.859318\pi$
$331$	−32.8905	−1.80783	−0.903913	+	0.427717i	$0.859318\pi$
$332$	66.0711	3.62612
$333$	36.2769	1.98796
$334$	−5.13411	−0.280926
$335$	−9.69371	−0.529624
$336$	−97.8081	−5.33587
$337$	4.06418	0.221390	0.110695	−	0.993854i	$-0.464692\pi$
$337$	4.06418	0.221390	0.110695	+	0.993854i	$0.464692\pi$
$338$	22.0612	1.19997
$339$	−10.8957	−0.591772
$340$	−8.77297	−0.475781
$341$	3.72797	0.201881
$342$	174.072	9.41275
$343$	−20.0723	−1.08380
$344$	79.8755	4.30660
$345$	−16.8530	−0.907337
$346$	−37.9420	−2.03978
$347$	20.3102	1.09031	0.545155	−	0.838335i	$-0.316471\pi$
$347$	20.3102	1.09031	0.545155	+	0.838335i	$0.316471\pi$
$348$	−104.176	−5.58444
$349$	25.3932	1.35927	0.679633	−	0.733553i	$-0.262139\pi$
$349$	25.3932	1.35927	0.679633	+	0.733553i	$0.262139\pi$
$350$	−6.14303	−0.328359
$351$	31.4036	1.67620
$352$	−12.4199	−0.661984
$353$	−11.4440	−0.609104	−0.304552	−	0.952496i	$-0.598507\pi$
$353$	−11.4440	−0.609104	−0.304552	+	0.952496i	$0.598507\pi$
$354$	49.3556	2.62322
$355$	−6.87699	−0.364993
$356$	−3.12505	−0.165627
$357$	12.2225	0.646886
$358$	1.29465	0.0684244
$359$	24.9922	1.31904	0.659519	−	0.751688i	$-0.270760\pi$
$359$	24.9922	1.31904	0.659519	+	0.751688i	$0.270760\pi$
$360$	−65.6907	−3.46220
$361$	56.4514	2.97112
$362$	36.9914	1.94422
$363$	34.0179	1.78548
$364$	−26.3925	−1.38334
$365$	11.1368	0.582926
$366$	46.4308	2.42698
$367$	6.20719	0.324013	0.162006	−	0.986790i	$-0.448203\pi$
$367$	6.20719	0.324013	0.162006	+	0.986790i	$0.448203\pi$
$368$	69.4164	3.61858
$369$	53.6459	2.79269
$370$	−13.1748	−0.684928
$371$	−24.3012	−1.26166
$372$	−93.0960	−4.82680
$373$	32.6206	1.68903	0.844516	−	0.535530i	$-0.179888\pi$
$373$	32.6206	1.68903	0.844516	+	0.535530i	$0.179888\pi$
$374$	3.06056	0.158258
$375$	−3.22929	−0.166760
$376$	27.0138	1.39313
$377$	−13.4223	−0.691286
$378$	87.8473	4.51838
$379$	4.89980	0.251686	0.125843	−	0.992050i	$-0.459836\pi$
$379$	4.89980	0.251686	0.125843	+	0.992050i	$0.459836\pi$
$380$	−45.8461	−2.35185
$381$	26.4693	1.35606
$382$	0.761703	0.0389721
$383$	−16.1779	−0.826650	−0.413325	−	0.910584i	$-0.635633\pi$
$383$	−16.1779	−0.826650	−0.413325	+	0.910584i	$0.635633\pi$
$384$	78.3968	4.00067
$385$	1.55415	0.0792069
$386$	2.93957	0.149620
$387$	−67.0950	−3.41063
$388$	−49.7291	−2.52461
$389$	−23.9219	−1.21289	−0.606443	−	0.795127i	$-0.707404\pi$
$389$	−23.9219	−1.21289	−0.606443	+	0.795127i	$0.707404\pi$
$390$	−19.1314	−0.968757
$391$	−8.67459	−0.438693
$392$	16.0500	0.810648
$393$	43.8474	2.21181
$394$	−27.8377	−1.40244
$395$	−14.3650	−0.722782
$396$	26.7594	1.34471
$397$	−16.8632	−0.846342	−0.423171	−	0.906050i	$-0.639083\pi$
$397$	−16.8632	−0.846342	−0.423171	+	0.906050i	$0.639083\pi$
$398$	−39.1049	−1.96015
$399$	63.8730	3.19765
$400$	13.3012	0.665060
$401$	10.3008	0.514395	0.257198	−	0.966359i	$-0.417201\pi$
$401$	10.3008	0.514395	0.257198	+	0.966359i	$0.417201\pi$
$402$	−84.4506	−4.21201
$403$	−11.9947	−0.597499
$404$	−20.8104	−1.03536
$405$	23.8949	1.18735
$406$	−37.5471	−1.86343
$407$	3.33316	0.165219
$408$	−47.4677	−2.35000
$409$	36.3376	1.79678	0.898389	−	0.439200i	$-0.144738\pi$
$409$	36.3376	1.79678	0.898389	+	0.439200i	$0.144738\pi$
$410$	−19.4828	−0.962187
$411$	30.8058	1.51954
$412$	70.4197	3.46933
$413$	12.9003	0.634783
$414$	−104.585	−5.14005
$415$	12.5182	0.614496
$416$	39.9610	1.95925
$417$	−44.0650	−2.15787
$418$	15.9940	0.782290
$419$	−30.0032	−1.46575	−0.732877	−	0.680362i	$-0.761823\pi$
$419$	−30.0032	−1.46575	−0.732877	+	0.680362i	$0.761823\pi$
$420$	−38.8108	−1.89377
$421$	−25.3595	−1.23595	−0.617974	−	0.786199i	$-0.712046\pi$
$421$	−25.3595	−1.23595	−0.617974	+	0.786199i	$0.712046\pi$
$422$	21.7209	1.05736
$423$	−22.6915	−1.10330
$424$	94.3767	4.58334
$425$	−1.66218	−0.0806275
$426$	−59.9116	−2.90273
$427$	12.1359	0.587296
$428$	−59.2119	−2.86211
$429$	4.84014	0.233684
$430$	24.3672	1.17509
$431$	−31.9665	−1.53977	−0.769887	−	0.638181i	$-0.779687\pi$
$431$	−31.9665	−1.53977	−0.769887	+	0.638181i	$0.779687\pi$
$432$	−190.211	−9.15155
$433$	26.0053	1.24973	0.624867	−	0.780731i	$-0.285153\pi$
$433$	26.0053	1.24973	0.624867	+	0.780731i	$0.285153\pi$
$434$	−33.5535	−1.61062
$435$	−19.7379	−0.946360
$436$	−22.8993	−1.09668
$437$	−45.3320	−2.16852
$438$	97.0226	4.63592
$439$	25.3741	1.21104	0.605519	−	0.795831i	$-0.292966\pi$
$439$	25.3741	1.21104	0.605519	+	0.795831i	$0.292966\pi$
$440$	−6.03573	−0.287742
$441$	−13.4819	−0.641997
$442$	−9.84732	−0.468389
$443$	−14.8863	−0.707271	−0.353636	−	0.935383i	$-0.615055\pi$
$443$	−14.8863	−0.707271	−0.353636	+	0.935383i	$0.615055\pi$
$444$	−83.2368	−3.95024
$445$	−0.592090	−0.0280678
$446$	63.4975	3.00670
$447$	−54.3587	−2.57108
$448$	51.2097	2.41943
$449$	22.0412	1.04019	0.520094	−	0.854109i	$-0.325897\pi$
$449$	22.0412	1.04019	0.520094	+	0.854109i	$0.325897\pi$
$450$	−20.0399	−0.944691
$451$	4.92904	0.232100
$452$	17.8080	0.837619
$453$	−5.90375	−0.277383
$454$	27.9271	1.31068
$455$	−5.00048	−0.234426
$456$	−248.058	−11.6164
$457$	9.20109	0.430409	0.215204	−	0.976569i	$-0.430958\pi$
$457$	9.20109	0.430409	0.215204	+	0.976569i	$0.430958\pi$
$458$	60.5987	2.83159
$459$	23.7697	1.10947
$460$	27.5448	1.28428
$461$	−25.8509	−1.20400	−0.601999	−	0.798497i	$-0.705629\pi$
$461$	−25.8509	−1.20400	−0.601999	+	0.798497i	$0.705629\pi$
$462$	13.5396	0.629920
$463$	32.0074	1.48751	0.743754	−	0.668453i	$-0.233043\pi$
$463$	32.0074	1.48751	0.743754	+	0.668453i	$0.233043\pi$
$464$	81.2989	3.77421
$465$	−17.6385	−0.817967
$466$	−75.9291	−3.51735
$467$	22.5957	1.04560	0.522801	−	0.852455i	$-0.324887\pi$
$467$	22.5957	1.04560	0.522801	+	0.852455i	$0.324887\pi$
$468$	−86.0981	−3.97988
$469$	−22.0733	−1.01925
$470$	8.24097	0.380128
$471$	21.8664	1.00755
$472$	−50.0999	−2.30604
$473$	−6.16477	−0.283456
$474$	−125.147	−5.74817
$475$	−8.68627	−0.398554
$476$	−19.9767	−0.915630
$477$	−79.2760	−3.62980
$478$	−26.6411	−1.21853
$479$	−7.24064	−0.330833	−0.165417	−	0.986224i	$-0.552897\pi$
$479$	−7.24064	−0.330833	−0.165417	+	0.986224i	$0.552897\pi$
$480$	58.7637	2.68218
$481$	−10.7244	−0.488992
$482$	66.6174	3.03434
$483$	−38.3756	−1.74615
$484$	−55.5992	−2.52724
$485$	−9.42198	−0.427830
$486$	92.4330	4.19285
$487$	−39.6994	−1.79895	−0.899476	−	0.436970i	$-0.856052\pi$
$487$	−39.6994	−1.79895	−0.899476	+	0.436970i	$0.856052\pi$
$488$	−47.1311	−2.13352
$489$	−2.70150	−0.122166
$490$	4.89630	0.221192
$491$	−17.5070	−0.790079	−0.395040	−	0.918664i	$-0.629269\pi$
$491$	−17.5070	−0.790079	−0.395040	+	0.918664i	$0.629269\pi$
$492$	−123.090	−5.54931
$493$	−10.1595	−0.457560
$494$	−51.4605	−2.31532
$495$	5.06999	0.227879
$496$	72.6518	3.26216
$497$	−15.6594	−0.702421
$498$	109.058	4.88699
$499$	0.338564	0.0151562	0.00757810	−	0.999971i	$-0.497588\pi$
$499$	0.338564	0.0151562	0.00757810	+	0.999971i	$0.497588\pi$
$500$	5.27799	0.236039
$501$	−6.14563	−0.274567
$502$	27.7670	1.23930
$503$	13.8798	0.618869	0.309434	−	0.950921i	$-0.399860\pi$
$503$	13.8798	0.618869	0.309434	+	0.950921i	$0.399860\pi$
$504$	−149.582	−6.66293
$505$	−3.94287	−0.175456
$506$	−9.60934	−0.427187
$507$	26.4076	1.17280
$508$	−43.2617	−1.91943
$509$	−0.823771	−0.0365130	−0.0182565	−	0.999833i	$-0.505812\pi$
$509$	−0.823771	−0.0365130	−0.0182565	+	0.999833i	$0.505812\pi$
$510$	−14.4807	−0.641218
$511$	25.3593	1.12183
$512$	−6.79070	−0.300109
$513$	124.216	5.48429
$514$	−32.4266	−1.43028
$515$	13.3421	0.587925
$516$	153.949	6.77721
$517$	−2.08492	−0.0916947
$518$	−30.0001	−1.31813
$519$	−45.4173	−1.99360
$520$	19.4199	0.851621
$521$	17.1121	0.749696	0.374848	−	0.927086i	$-0.377695\pi$
$521$	17.1121	0.749696	0.374848	+	0.927086i	$0.377695\pi$
$522$	−122.487	−5.36111
$523$	−15.0549	−0.658304	−0.329152	−	0.944277i	$-0.606763\pi$
$523$	−15.0549	−0.658304	−0.329152	+	0.944277i	$0.606763\pi$
$524$	−71.6647	−3.13069
$525$	−7.35333	−0.320926
$526$	−21.9706	−0.957966
$527$	−9.07890	−0.395483
$528$	−29.3167	−1.27584
$529$	4.23595	0.184172
$530$	28.7910	1.25060
$531$	42.0837	1.82628
$532$	−104.395	−4.52609
$533$	−15.8592	−0.686937
$534$	−5.15823	−0.223218
$535$	−11.2186	−0.485024
$536$	85.7242	3.70272
$537$	1.54972	0.0668754
$538$	−33.6130	−1.44916
$539$	−1.23874	−0.0533561
$540$	−75.4769	−3.24801
$541$	2.75325	0.118371	0.0591857	−	0.998247i	$-0.481150\pi$
$541$	2.75325	0.118371	0.0591857	+	0.998247i	$0.481150\pi$
$542$	−13.0322	−0.559781
$543$	44.2794	1.90021
$544$	30.2468	1.29682
$545$	−4.33864	−0.185847
$546$	−43.5636	−1.86435
$547$	37.2803	1.59399	0.796996	−	0.603984i	$-0.206421\pi$
$547$	37.2803	1.59399	0.796996	+	0.603984i	$0.206421\pi$
$548$	−50.3494	−2.15082
$549$	39.5899	1.68965
$550$	−1.84129	−0.0785129
$551$	−53.0918	−2.26179
$552$	149.036	6.34340
$553$	−32.7102	−1.39098
$554$	−6.30504	−0.267875
$555$	−15.7705	−0.669423
$556$	72.0203	3.05434
$557$	−2.15744	−0.0914135	−0.0457068	−	0.998955i	$-0.514554\pi$
$557$	−2.15744	−0.0914135	−0.0457068	+	0.998955i	$0.514554\pi$
$558$	−109.459	−4.63377
$559$	19.8351	0.838935
$560$	30.2878	1.27989
$561$	3.66355	0.154675
$562$	70.7849	2.98588
$563$	34.9758	1.47405	0.737027	−	0.675863i	$-0.236229\pi$
$563$	34.9758	1.47405	0.737027	+	0.675863i	$0.236229\pi$
$564$	52.0653	2.19234
$565$	3.37402	0.141946
$566$	7.95310	0.334294
$567$	54.4105	2.28502
$568$	60.8152	2.55175
$569$	−26.0510	−1.09211	−0.546057	−	0.837748i	$-0.683872\pi$
$569$	−26.0510	−1.09211	−0.546057	+	0.837748i	$0.683872\pi$
$570$	−75.6739	−3.16963
$571$	−38.1126	−1.59496	−0.797482	−	0.603342i	$-0.793835\pi$
$571$	−38.1126	−1.59496	−0.797482	+	0.603342i	$0.793835\pi$
$572$	−7.91079	−0.330767
$573$	0.911774	0.0380899
$574$	−44.3638	−1.85171
$575$	5.21881	0.217639
$576$	167.057	6.96072
$577$	13.1585	0.547796	0.273898	−	0.961759i	$-0.411687\pi$
$577$	13.1585	0.547796	0.273898	+	0.961759i	$0.411687\pi$
$578$	38.4087	1.59759
$579$	3.51873	0.146233
$580$	32.2599	1.33952
$581$	28.5049	1.18258
$582$	−82.0833	−3.40246
$583$	−7.28397	−0.301671
$584$	−98.4858	−4.07537
$585$	−16.3127	−0.674445
$586$	−65.3314	−2.69882
$587$	−33.8401	−1.39673	−0.698366	−	0.715741i	$-0.746089\pi$
$587$	−33.8401	−1.39673	−0.698366	+	0.715741i	$0.746089\pi$
$588$	30.9341	1.27570
$589$	−47.4448	−1.95493
$590$	−15.2837	−0.629221
$591$	−33.3222	−1.37069
$592$	64.9577	2.66975
$593$	40.4334	1.66040	0.830200	−	0.557465i	$-0.188226\pi$
$593$	40.4334	1.66040	0.830200	+	0.557465i	$0.188226\pi$
$594$	26.3310	1.08038
$595$	−3.78490	−0.155166
$596$	88.8445	3.63921
$597$	−46.8094	−1.91578
$598$	30.9180	1.26433
$599$	−29.4933	−1.20507	−0.602533	−	0.798094i	$-0.705842\pi$
$599$	−29.4933	−1.20507	−0.602533	+	0.798094i	$0.705842\pi$
$600$	28.5575	1.16586
$601$	−12.7342	−0.519441	−0.259720	−	0.965684i	$-0.583630\pi$
$601$	−12.7342	−0.519441	−0.259720	+	0.965684i	$0.583630\pi$
$602$	55.4859	2.26144
$603$	−72.0079	−2.93239
$604$	9.64917	0.392619
$605$	−10.5342	−0.428275
$606$	−34.3499	−1.39537
$607$	−13.0203	−0.528478	−0.264239	−	0.964457i	$-0.585121\pi$
$607$	−13.0203	−0.528478	−0.264239	+	0.964457i	$0.585121\pi$
$608$	158.065	6.41038
$609$	−44.9446	−1.82125
$610$	−14.3780	−0.582150
$611$	6.70822	0.271385
$612$	−65.1684	−2.63427
$613$	7.99106	0.322756	0.161378	−	0.986893i	$-0.448406\pi$
$613$	7.99106	0.322756	0.161378	+	0.986893i	$0.448406\pi$
$614$	45.7980	1.84826
$615$	−23.3213	−0.940406
$616$	−13.7438	−0.553754
$617$	−39.1202	−1.57492	−0.787460	−	0.616366i	$-0.788604\pi$
$617$	−39.1202	−1.57492	−0.787460	+	0.616366i	$0.788604\pi$
$618$	116.235	4.67567
$619$	−32.2295	−1.29541	−0.647706	−	0.761891i	$-0.724271\pi$
$619$	−32.2295	−1.29541	−0.647706	+	0.761891i	$0.724271\pi$
$620$	28.8286	1.15779
$621$	−74.6306	−2.99482
$622$	−79.5287	−3.18881
$623$	−1.34823	−0.0540158
$624$	94.3262	3.77607
$625$	1.00000	0.0400000
$626$	−0.0988637	−0.00395139
$627$	19.1451	0.764581
$628$	−35.7387	−1.42613
$629$	−8.11741	−0.323662
$630$	−45.6324	−1.81804
$631$	−0.283330	−0.0112792	−0.00563960	−	0.999984i	$-0.501795\pi$
$631$	−0.283330	−0.0112792	−0.00563960	+	0.999984i	$0.501795\pi$
$632$	127.034	5.05314
$633$	26.0004	1.03342
$634$	52.7658	2.09560
$635$	−8.19663	−0.325273
$636$	181.898	7.21271
$637$	3.98562	0.157916
$638$	−11.2542	−0.445560
$639$	−51.0845	−2.02087
$640$	−24.2768	−0.959624
$641$	3.58533	0.141612	0.0708061	−	0.997490i	$-0.477443\pi$
$641$	3.58533	0.141612	0.0708061	+	0.997490i	$0.477443\pi$
$642$	−97.7357	−3.85732
$643$	−30.1575	−1.18929	−0.594647	−	0.803987i	$-0.702708\pi$
$643$	−30.1575	−1.18929	−0.594647	+	0.803987i	$0.702708\pi$
$644$	62.7216	2.47158
$645$	29.1680	1.14849
$646$	−38.9509	−1.53250
$647$	6.47946	0.254734	0.127367	−	0.991856i	$-0.459347\pi$
$647$	6.47946	0.254734	0.127367	+	0.991856i	$0.459347\pi$
$648$	−211.309	−8.30102
$649$	3.86670	0.151781
$650$	5.92434	0.232372
$651$	−40.1642	−1.57416
$652$	4.41536	0.172919
$653$	−36.4372	−1.42590	−0.712948	−	0.701217i	$-0.752640\pi$
$653$	−36.4372	−1.42590	−0.712948	+	0.701217i	$0.752640\pi$
$654$	−37.7978	−1.47801
$655$	−13.5780	−0.530537
$656$	96.0587	3.75046
$657$	82.7276	3.22751
$658$	18.7653	0.731547
$659$	−17.7927	−0.693106	−0.346553	−	0.938030i	$-0.612648\pi$
$659$	−17.7927	−0.693106	−0.346553	+	0.938030i	$0.612648\pi$
$660$	−11.6330	−0.452815
$661$	40.3614	1.56988	0.784938	−	0.619574i	$-0.212695\pi$
$661$	40.3614	1.56988	0.784938	+	0.619574i	$0.212695\pi$
$662$	88.7312	3.44863
$663$	−11.7874	−0.457786
$664$	−110.702	−4.29608
$665$	−19.7793	−0.767008
$666$	−97.8669	−3.79227
$667$	31.8981	1.23510
$668$	10.0445	0.388633
$669$	76.0078	2.93863
$670$	26.1514	1.01032
$671$	3.63756	0.140427
$672$	133.809	5.16180
$673$	2.92665	0.112814	0.0564071	−	0.998408i	$-0.482036\pi$
$673$	2.92665	0.112814	0.0564071	+	0.998408i	$0.482036\pi$
$674$	−10.9642	−0.422327
$675$	−14.3003	−0.550419
$676$	−43.1610	−1.66004
$677$	4.99896	0.192126	0.0960628	−	0.995375i	$-0.469375\pi$
$677$	4.99896	0.192126	0.0960628	+	0.995375i	$0.469375\pi$
$678$	29.3941	1.12887
$679$	−21.4545	−0.823349
$680$	14.6991	0.563685
$681$	33.4292	1.28101
$682$	−10.0572	−0.385111
$683$	33.6509	1.28762	0.643808	−	0.765187i	$-0.277353\pi$
$683$	33.6509	1.28762	0.643808	+	0.765187i	$0.277353\pi$
$684$	−340.559	−13.0216
$685$	−9.53950	−0.364485
$686$	54.1504	2.06747
$687$	72.5378	2.76749
$688$	−120.141	−4.58033
$689$	23.4361	0.892845
$690$	45.4657	1.73085
$691$	−7.51183	−0.285764	−0.142882	−	0.989740i	$-0.545637\pi$
$691$	−7.51183	−0.285764	−0.142882	+	0.989740i	$0.545637\pi$
$692$	74.2306	2.82183
$693$	11.5447	0.438548
$694$	−54.7924	−2.07989
$695$	13.6454	0.517600
$696$	174.548	6.61622
$697$	−12.0039	−0.454681
$698$	−68.5051	−2.59296
$699$	−90.8886	−3.43772
$700$	12.0184	0.454252
$701$	3.19592	0.120708	0.0603541	−	0.998177i	$-0.480777\pi$
$701$	3.19592	0.120708	0.0603541	+	0.998177i	$0.480777\pi$
$702$	−84.7200	−3.19755
$703$	−42.4203	−1.59991
$704$	15.3494	0.578503
$705$	9.86460	0.371522
$706$	30.8734	1.16194
$707$	−8.97821	−0.337660
$708$	−96.5605	−3.62896
$709$	−41.2262	−1.54828	−0.774142	−	0.633013i	$-0.781818\pi$
$709$	−41.2262	−1.54828	−0.774142	+	0.633013i	$0.781818\pi$
$710$	18.5526	0.696266
$711$	−106.708	−4.00186
$712$	5.23602	0.196228
$713$	28.5054	1.06753
$714$	−32.9737	−1.23401
$715$	−1.49883	−0.0560529
$716$	−2.53288	−0.0946583
$717$	−31.8899	−1.19095
$718$	−67.4234	−2.51622
$719$	16.1980	0.604083	0.302041	−	0.953295i	$-0.402332\pi$
$719$	16.1980	0.604083	0.302041	+	0.953295i	$0.402332\pi$
$720$	98.8055	3.68227
$721$	30.3810	1.13145
$722$	−152.293	−5.66776
$723$	79.7424	2.96565
$724$	−72.3708	−2.68964
$725$	6.11215	0.226999
$726$	−91.7726	−3.40600
$727$	−43.5895	−1.61665	−0.808323	−	0.588739i	$-0.799625\pi$
$727$	−43.5895	−1.61665	−0.808323	+	0.588739i	$0.799625\pi$
$728$	44.2206	1.63893
$729$	38.9594	1.44294
$730$	−30.0445	−1.11200
$731$	15.0134	0.555289
$732$	−90.8384	−3.35748
$733$	23.8020	0.879149	0.439574	−	0.898206i	$-0.355129\pi$
$733$	23.8020	0.879149	0.439574	+	0.898206i	$0.355129\pi$
$734$	−16.7456	−0.618092
$735$	5.86096	0.216185
$736$	−94.9671	−3.50054
$737$	−6.61617	−0.243710
$738$	−144.724	−5.32738
$739$	41.8822	1.54066	0.770331	−	0.637644i	$-0.220091\pi$
$739$	41.8822	1.54066	0.770331	+	0.637644i	$0.220091\pi$
$740$	25.7756	0.947529
$741$	−61.5992	−2.26290
$742$	65.5592	2.40676
$743$	−30.1728	−1.10693	−0.553467	−	0.832871i	$-0.686696\pi$
$743$	−30.1728	−1.10693	−0.553467	+	0.832871i	$0.686696\pi$
$744$	155.983	5.71860
$745$	16.8330	0.616714
$746$	−88.0031	−3.22202
$747$	92.9894	3.40230
$748$	−5.98774	−0.218934
$749$	−25.5457	−0.933418
$750$	8.71190	0.318114
$751$	−12.9241	−0.471605	−0.235803	−	0.971801i	$-0.575772\pi$
$751$	−12.9241	−0.471605	−0.235803	+	0.971801i	$0.575772\pi$
$752$	−40.6316	−1.48168
$753$	33.2377	1.21125
$754$	36.2105	1.31871
$755$	1.82819	0.0665346
$756$	−171.866	−6.25072
$757$	−25.2857	−0.919024	−0.459512	−	0.888172i	$-0.651976\pi$
$757$	−25.2857	−0.919024	−0.459512	+	0.888172i	$0.651976\pi$
$758$	−13.2186	−0.480120
$759$	−11.5026	−0.417517
$760$	76.8152	2.78638
$761$	−41.9105	−1.51925	−0.759627	−	0.650359i	$-0.774619\pi$
$761$	−41.9105	−1.51925	−0.759627	+	0.650359i	$0.774619\pi$
$762$	−71.4082	−2.58685
$763$	−9.87941	−0.357659
$764$	−1.49021	−0.0539141
$765$	−12.3472	−0.446414
$766$	43.6442	1.57693
$767$	−12.4411	−0.449221
$768$	−66.2482	−2.39053
$769$	52.5695	1.89570	0.947852	−	0.318711i	$-0.103250\pi$
$769$	52.5695	1.89570	0.947852	+	0.318711i	$0.103250\pi$
$770$	−4.19275	−0.151096
$771$	−38.8153	−1.39790
$772$	−5.75105	−0.206985
$773$	−29.4290	−1.05849	−0.529244	−	0.848470i	$-0.677524\pi$
$773$	−29.4290	−1.05849	−0.529244	+	0.848470i	$0.677524\pi$
$774$	181.007	6.50617
$775$	5.46205	0.196203
$776$	83.3212	2.99106
$777$	−35.9107	−1.28829
$778$	64.5358	2.31372
$779$	−62.7306	−2.24756
$780$	37.4292	1.34018
$781$	−4.69370	−0.167954
$782$	23.4021	0.836857
$783$	−87.4056	−3.12362
$784$	−24.1409	−0.862174
$785$	−6.77127	−0.241677
$786$	−118.290	−4.21928
$787$	−47.9155	−1.70800	−0.854002	−	0.520269i	$-0.825832\pi$
$787$	−47.9155	−1.70800	−0.854002	+	0.520269i	$0.825832\pi$
$788$	54.4623	1.94014
$789$	−26.2993	−0.936280
$790$	38.7536	1.37879
$791$	7.68288	0.273172
$792$	−44.8353	−1.59315
$793$	−11.7038	−0.415615
$794$	45.4932	1.61449
$795$	34.4634	1.22229
$796$	76.5058	2.71168
$797$	29.5805	1.04780	0.523898	−	0.851781i	$-0.324477\pi$
$797$	29.5805	1.04780	0.523898	+	0.851781i	$0.324477\pi$
$798$	−172.315	−6.09989
$799$	5.07751	0.179629
$800$	−18.1971	−0.643365
$801$	−4.39823	−0.155404
$802$	−27.7891	−0.981268
$803$	7.60110	0.268237
$804$	165.221	5.82690
$805$	11.8836	0.418842
$806$	32.3590	1.13980
$807$	−40.2354	−1.41635
$808$	34.8679	1.22665
$809$	8.36989	0.294269	0.147135	−	0.989116i	$-0.452995\pi$
$809$	8.36989	0.294269	0.147135	+	0.989116i	$0.452995\pi$
$810$	−64.4631	−2.26500
$811$	−0.0571751	−0.00200769	−0.00100385	−	0.999999i	$-0.500320\pi$
$811$	−0.0571751	−0.00200769	−0.00100385	+	0.999999i	$0.500320\pi$
$812$	73.4581	2.57787
$813$	−15.5998	−0.547109
$814$	−8.99212	−0.315174
$815$	0.836560	0.0293034
$816$	71.3963	2.49937
$817$	78.4573	2.74487
$818$	−98.0307	−3.42756
$819$	−37.1451	−1.29796
$820$	38.1166	1.33109
$821$	20.2421	0.706455	0.353227	−	0.935538i	$-0.385084\pi$
$821$	20.2421	0.706455	0.353227	+	0.935538i	$0.385084\pi$
$822$	−83.1071	−2.89869
$823$	17.9848	0.626912	0.313456	−	0.949603i	$-0.398513\pi$
$823$	17.9848	0.626912	0.313456	+	0.949603i	$0.398513\pi$
$824$	−117.988	−4.11032
$825$	−2.20406	−0.0767356
$826$	−34.8022	−1.21092
$827$	−13.2984	−0.462432	−0.231216	−	0.972902i	$-0.574270\pi$
$827$	−13.2984	−0.462432	−0.231216	+	0.972902i	$0.574270\pi$
$828$	204.612	7.11074
$829$	2.63713	0.0915915	0.0457957	−	0.998951i	$-0.485418\pi$
$829$	2.63713	0.0915915	0.0457957	+	0.998951i	$0.485418\pi$
$830$	−33.7714	−1.17222
$831$	−7.54726	−0.261811
$832$	−49.3867	−1.71217
$833$	3.01675	0.104524
$834$	118.877	4.11639
$835$	1.90309	0.0658592
$836$	−31.2910	−1.08222
$837$	−78.1090	−2.69984
$838$	80.9419	2.79609
$839$	22.5237	0.777603	0.388802	−	0.921321i	$-0.372889\pi$
$839$	22.5237	0.777603	0.388802	+	0.921321i	$0.372889\pi$
$840$	65.0276	2.24366
$841$	8.35835	0.288219
$842$	68.4143	2.35771
$843$	84.7309	2.91829
$844$	−42.4954	−1.46275
$845$	−8.17754	−0.281316
$846$	61.2165	2.10467
$847$	−23.9871	−0.824205
$848$	−141.952	−4.87466
$849$	9.52002	0.326726
$850$	4.48419	0.153806
$851$	25.4865	0.873668
$852$	117.213	4.01564
$853$	55.6020	1.90377	0.951887	−	0.306448i	$-0.0991406\pi$
$853$	55.6020	1.90377	0.951887	+	0.306448i	$0.0991406\pi$
$854$	−32.7398	−1.12033
$855$	−64.5244	−2.20669
$856$	99.2096	3.39091
$857$	−8.78381	−0.300049	−0.150025	−	0.988682i	$-0.547935\pi$
$857$	−8.78381	−0.300049	−0.150025	+	0.988682i	$0.547935\pi$
$858$	−13.0576	−0.445780
$859$	−34.4838	−1.17657	−0.588286	−	0.808653i	$-0.700197\pi$
$859$	−34.4838	−1.17657	−0.588286	+	0.808653i	$0.700197\pi$
$860$	−47.6726	−1.62562
$861$	−53.1043	−1.80979
$862$	86.2385	2.93729
$863$	−21.8324	−0.743183	−0.371591	−	0.928396i	$-0.621188\pi$
$863$	−21.8324	−0.743183	−0.371591	+	0.928396i	$0.621188\pi$
$864$	260.224	8.85301
$865$	14.0642	0.478197
$866$	−70.1565	−2.38401
$867$	45.9759	1.56142
$868$	65.6449	2.22813
$869$	−9.80444	−0.332593
$870$	53.2484	1.80529
$871$	21.2875	0.721299
$872$	38.3679	1.29930
$873$	−69.9894	−2.36878
$874$	122.296	4.13671
$875$	2.27707	0.0769791
$876$	−189.817	−6.41333
$877$	−4.58924	−0.154968	−0.0774838	−	0.996994i	$-0.524689\pi$
$877$	−4.58924	−0.154968	−0.0774838	+	0.996994i	$0.524689\pi$
$878$	−68.4535	−2.31019
$879$	−78.2030	−2.63772
$880$	9.07837	0.306032
$881$	32.8899	1.10809	0.554044	−	0.832487i	$-0.313084\pi$
$881$	32.8899	1.10809	0.554044	+	0.832487i	$0.313084\pi$
$882$	36.3712	1.22468
$883$	0.111512	0.00375269	0.00187635	−	0.999998i	$-0.499403\pi$
$883$	0.111512	0.00375269	0.00187635	+	0.999998i	$0.499403\pi$
$884$	19.2655	0.647970
$885$	−18.2949	−0.614977
$886$	40.1600	1.34920
$887$	−10.1267	−0.340020	−0.170010	−	0.985442i	$-0.554380\pi$
$887$	−10.1267	−0.340020	−0.170010	+	0.985442i	$0.554380\pi$
$888$	139.463	4.68009
$889$	−18.6643	−0.625981
$890$	1.59733	0.0535425
$891$	16.3088	0.546366
$892$	−124.228	−4.15946
$893$	26.5342	0.887933
$894$	146.648	4.90463
$895$	−0.479896	−0.0160411
$896$	−55.2800	−1.84678
$897$	37.0095	1.23571
$898$	−59.4622	−1.98428
$899$	33.3848	1.11345
$900$	39.2066	1.30689
$901$	17.7390	0.590972
$902$	−13.2974	−0.442757
$903$	66.4177	2.21024
$904$	−29.8374	−0.992377
$905$	−13.7118	−0.455796
$906$	15.9270	0.529139
$907$	−55.8501	−1.85447	−0.927236	−	0.374478i	$-0.877822\pi$
$907$	−55.8501	−1.85447	−0.927236	+	0.374478i	$0.877822\pi$
$908$	−54.6372	−1.81320
$909$	−29.2889	−0.971451
$910$	13.4902	0.447194
$911$	−42.3249	−1.40229	−0.701144	−	0.713020i	$-0.747327\pi$
$911$	−42.3249	−1.40229	−0.701144	+	0.713020i	$0.747327\pi$
$912$	373.105	12.3548
$913$	8.54397	0.282764
$914$	−24.8225	−0.821054
$915$	−17.2108	−0.568971
$916$	−118.557	−3.91722
$917$	−30.9182	−1.02101
$918$	−64.1253	−2.11645
$919$	−21.6927	−0.715575	−0.357788	−	0.933803i	$-0.616469\pi$
$919$	−21.6927	−0.715575	−0.357788	+	0.933803i	$0.616469\pi$
$920$	−46.1514	−1.52157
$921$	54.8212	1.80642
$922$	69.7400	2.29676
$923$	15.1019	0.497087
$924$	−26.4892	−0.871432
$925$	4.88360	0.160572
$926$	−86.3487	−2.83759
$927$	99.1096	3.25519
$928$	−111.223	−3.65109
$929$	−18.9869	−0.622940	−0.311470	−	0.950256i	$-0.600821\pi$
$929$	−18.9869	−0.622940	−0.311470	+	0.950256i	$0.600821\pi$
$930$	47.5848	1.56037
$931$	15.7651	0.516679
$932$	148.549	4.86590
$933$	−95.1974	−3.11662
$934$	−60.9580	−1.99461
$935$	−1.13447	−0.0371013
$936$	144.257	4.71520
$937$	40.1203	1.31067	0.655337	−	0.755337i	$-0.272527\pi$
$937$	40.1203	1.31067	0.655337	+	0.755337i	$0.272527\pi$
$938$	59.5487	1.94434
$939$	−0.118342	−0.00386194
$940$	−16.1228	−0.525869
$941$	−1.79466	−0.0585043	−0.0292521	−	0.999572i	$-0.509313\pi$
$941$	−1.79466	−0.0585043	−0.0292521	+	0.999572i	$0.509313\pi$
$942$	−58.9906	−1.92202
$943$	37.6892	1.22733
$944$	75.3555	2.45261
$945$	−32.5629	−1.05927
$946$	16.6312	0.540725
$947$	−4.21548	−0.136985	−0.0684924	−	0.997652i	$-0.521819\pi$
$947$	−4.21548	−0.136985	−0.0684924	+	0.997652i	$0.521819\pi$
$948$	244.840	7.95202
$949$	−24.4565	−0.793892
$950$	23.4336	0.760287
$951$	63.1617	2.04816
$952$	33.4710	1.08480
$953$	−15.5195	−0.502725	−0.251362	−	0.967893i	$-0.580879\pi$
$953$	−15.5195	−0.502725	−0.251362	+	0.967893i	$0.580879\pi$
$954$	213.869	6.92426
$955$	−0.282345	−0.00913647
$956$	52.1212	1.68572
$957$	−13.4716	−0.435473
$958$	19.5336	0.631102
$959$	−21.7221	−0.701444
$960$	−72.6244	−2.34394
$961$	−1.16604	−0.0376142
$962$	28.9321	0.932808
$963$	−83.3356	−2.68545
$964$	−130.332	−4.19771
$965$	−1.08963	−0.0350764
$966$	103.529	3.33098
$967$	1.91655	0.0616322	0.0308161	−	0.999525i	$-0.490189\pi$
$967$	1.91655	0.0616322	0.0308161	+	0.999525i	$0.490189\pi$
$968$	93.1566	2.99417
$969$	−46.6250	−1.49781
$970$	25.4184	0.816135
$971$	−54.7200	−1.75605	−0.878024	−	0.478616i	$-0.841139\pi$
$971$	−54.7200	−1.75605	−0.878024	+	0.478616i	$0.841139\pi$
$972$	−180.838	−5.80039
$973$	31.0716	0.996109
$974$	107.100	3.43171
$975$	7.09155	0.227112
$976$	70.8900	2.26913
$977$	18.2733	0.584614	0.292307	−	0.956325i	$-0.405577\pi$
$977$	18.2733	0.584614	0.292307	+	0.956325i	$0.405577\pi$
$978$	7.28803	0.233045
$979$	−0.404115	−0.0129156
$980$	−9.57923	−0.305997
$981$	−32.2288	−1.02899
$982$	47.2299	1.50717
$983$	10.7052	0.341444	0.170722	−	0.985319i	$-0.445390\pi$
$983$	10.7052	0.341444	0.170722	+	0.985319i	$0.445390\pi$
$984$	206.237	6.57459
$985$	10.3187	0.328783
$986$	27.4080	0.872849
$987$	22.4624	0.714987
$988$	100.678	3.20301
$989$	−47.1380	−1.49890
$990$	−13.6777	−0.434705
$991$	25.0154	0.794639	0.397320	−	0.917680i	$-0.369940\pi$
$991$	25.0154	0.794639	0.397320	+	0.917680i	$0.369940\pi$
$992$	−99.3934	−3.15574
$993$	106.213	3.37057
$994$	42.2456	1.33995
$995$	14.4952	0.459530
$996$	−213.363	−6.76066
$997$	−49.4383	−1.56573	−0.782863	−	0.622194i	$-0.786242\pi$
$997$	−49.4383	−1.56573	−0.782863	+	0.622194i	$0.786242\pi$
$998$	−0.913369	−0.0289122
$999$	−69.8370	−2.20954

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.e.1.4	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.e.1.4	✓	88	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69778 q^{2} -3.22929 q^{3} +5.27799 q^{4} +1.00000 q^{5} +8.71190 q^{6} +2.27707 q^{7} -8.84328 q^{8} +7.42831 q^{9} +O(q^{10})\)	\(q-2.69778 q^{2} -3.22929 q^{3} +5.27799 q^{4} +1.00000 q^{5} +8.71190 q^{6} +2.27707 q^{7} -8.84328 q^{8} +7.42831 q^{9} -2.69778 q^{10} +0.682522 q^{11} -17.0442 q^{12} -2.19601 q^{13} -6.14303 q^{14} -3.22929 q^{15} +13.3012 q^{16} -1.66218 q^{17} -20.0399 q^{18} -8.68627 q^{19} +5.27799 q^{20} -7.35333 q^{21} -1.84129 q^{22} +5.21881 q^{23} +28.5575 q^{24} +1.00000 q^{25} +5.92434 q^{26} -14.3003 q^{27} +12.0184 q^{28} +6.11215 q^{29} +8.71190 q^{30} +5.46205 q^{31} -18.1971 q^{32} -2.20406 q^{33} +4.48419 q^{34} +2.27707 q^{35} +39.2066 q^{36} +4.88360 q^{37} +23.4336 q^{38} +7.09155 q^{39} -8.84328 q^{40} +7.22181 q^{41} +19.8376 q^{42} -9.03233 q^{43} +3.60234 q^{44} +7.42831 q^{45} -14.0792 q^{46} -3.05473 q^{47} -42.9535 q^{48} -1.81494 q^{49} -2.69778 q^{50} +5.36766 q^{51} -11.5905 q^{52} -10.6721 q^{53} +38.5790 q^{54} +0.682522 q^{55} -20.1368 q^{56} +28.0505 q^{57} -16.4892 q^{58} +5.66531 q^{59} -17.0442 q^{60} +5.32959 q^{61} -14.7354 q^{62} +16.9148 q^{63} +22.4893 q^{64} -2.19601 q^{65} +5.94606 q^{66} -9.69371 q^{67} -8.77297 q^{68} -16.8530 q^{69} -6.14303 q^{70} -6.87699 q^{71} -65.6907 q^{72} +11.1368 q^{73} -13.1748 q^{74} -3.22929 q^{75} -45.8461 q^{76} +1.55415 q^{77} -19.1314 q^{78} -14.3650 q^{79} +13.3012 q^{80} +23.8949 q^{81} -19.4828 q^{82} +12.5182 q^{83} -38.8108 q^{84} -1.66218 q^{85} +24.3672 q^{86} -19.7379 q^{87} -6.03573 q^{88} -0.592090 q^{89} -20.0399 q^{90} -5.00048 q^{91} +27.5448 q^{92} -17.6385 q^{93} +8.24097 q^{94} -8.68627 q^{95} +58.7637 q^{96} -9.42198 q^{97} +4.89630 q^{98} +5.06999 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9}+O(q^{10}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9} - 14 q^{10} - 26 q^{11} - 64 q^{12} - 31 q^{13} - 17 q^{14} - 34 q^{15} + 34 q^{16} - 31 q^{17} - 42 q^{18} - 56 q^{19} + 66 q^{20} - q^{21} - 49 q^{22} - 74 q^{23} - 3 q^{24} + 88 q^{25} - q^{26} - 130 q^{27} - 57 q^{28} - 6 q^{29} - q^{30} - 37 q^{31} - 87 q^{32} - 43 q^{33} - 35 q^{34} - 35 q^{35} + 53 q^{36} - 67 q^{37} - 40 q^{38} - 21 q^{39} - 39 q^{40} + 2 q^{41} - 15 q^{42} - 136 q^{43} - 15 q^{44} + 72 q^{45} - 16 q^{46} - 139 q^{47} - 71 q^{48} + 41 q^{49} - 14 q^{50} - 71 q^{51} - 71 q^{52} - 75 q^{53} + 26 q^{54} - 26 q^{55} - 22 q^{56} - 34 q^{57} - 65 q^{58} - 41 q^{59} - 64 q^{60} - 11 q^{61} - 30 q^{62} - 114 q^{63} - 33 q^{64} - 31 q^{65} + 24 q^{66} - 209 q^{67} - 42 q^{68} - 22 q^{69} - 17 q^{70} - 43 q^{71} - 80 q^{72} - 50 q^{73} + 9 q^{74} - 34 q^{75} - 62 q^{76} - 49 q^{77} - 19 q^{78} - 77 q^{79} + 34 q^{80} + 72 q^{81} - 107 q^{82} - 113 q^{83} + 19 q^{84} - 31 q^{85} + 14 q^{86} - 87 q^{87} - 107 q^{88} - 5 q^{89} - 42 q^{90} - 159 q^{91} - 100 q^{92} - 82 q^{93} - 31 q^{94} - 56 q^{95} + 58 q^{96} - 105 q^{97} - 29 q^{98} - 68 q^{99}+O(q^{100}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9 - 14 * q^10 - 26 * q^11 - 64 * q^12 - 31 * q^13 - 17 * q^14 - 34 * q^15 + 34 * q^16 - 31 * q^17 - 42 * q^18 - 56 * q^19 + 66 * q^20 - q^21 - 49 * q^22 - 74 * q^23 - 3 * q^24 + 88 * q^25 - q^26 - 130 * q^27 - 57 * q^28 - 6 * q^29 - q^30 - 37 * q^31 - 87 * q^32 - 43 * q^33 - 35 * q^34 - 35 * q^35 + 53 * q^36 - 67 * q^37 - 40 * q^38 - 21 * q^39 - 39 * q^40 + 2 * q^41 - 15 * q^42 - 136 * q^43 - 15 * q^44 + 72 * q^45 - 16 * q^46 - 139 * q^47 - 71 * q^48 + 41 * q^49 - 14 * q^50 - 71 * q^51 - 71 * q^52 - 75 * q^53 + 26 * q^54 - 26 * q^55 - 22 * q^56 - 34 * q^57 - 65 * q^58 - 41 * q^59 - 64 * q^60 - 11 * q^61 - 30 * q^62 - 114 * q^63 - 33 * q^64 - 31 * q^65 + 24 * q^66 - 209 * q^67 - 42 * q^68 - 22 * q^69 - 17 * q^70 - 43 * q^71 - 80 * q^72 - 50 * q^73 + 9 * q^74 - 34 * q^75 - 62 * q^76 - 49 * q^77 - 19 * q^78 - 77 * q^79 + 34 * q^80 + 72 * q^81 - 107 * q^82 - 113 * q^83 + 19 * q^84 - 31 * q^85 + 14 * q^86 - 87 * q^87 - 107 * q^88 - 5 * q^89 - 42 * q^90 - 159 * q^91 - 100 * q^92 - 82 * q^93 - 31 * q^94 - 56 * q^95 + 58 * q^96 - 105 * q^97 - 29 * q^98 - 68 * q^99

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