LMFDB - Embedded newform 2005.2.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2005,2,Mod(1,2005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2005, 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("2005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2005 = 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2005.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:	$16.0100056053$
Analytic rank:	$1$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	2005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.27234 q^{2} +1.15962 q^{3} +3.16351 q^{4} -1.00000 q^{5} -2.63504 q^{6} -2.94936 q^{7} -2.64390 q^{8} -1.65529 q^{9} +O(q^{10})$	\(q-2.27234 q^{2} +1.15962 q^{3} +3.16351 q^{4} -1.00000 q^{5} -2.63504 q^{6} -2.94936 q^{7} -2.64390 q^{8} -1.65529 q^{9} +2.27234 q^{10} +0.860635 q^{11} +3.66847 q^{12} +3.83171 q^{13} +6.70193 q^{14} -1.15962 q^{15} -0.319205 q^{16} -0.946558 q^{17} +3.76137 q^{18} -1.79254 q^{19} -3.16351 q^{20} -3.42013 q^{21} -1.95565 q^{22} +5.58835 q^{23} -3.06591 q^{24} +1.00000 q^{25} -8.70695 q^{26} -5.39835 q^{27} -9.33033 q^{28} +0.817083 q^{29} +2.63504 q^{30} +5.15664 q^{31} +6.01313 q^{32} +0.998008 q^{33} +2.15090 q^{34} +2.94936 q^{35} -5.23652 q^{36} +5.31018 q^{37} +4.07325 q^{38} +4.44333 q^{39} +2.64390 q^{40} +2.85479 q^{41} +7.77168 q^{42} +5.48786 q^{43} +2.72263 q^{44} +1.65529 q^{45} -12.6986 q^{46} -10.3775 q^{47} -0.370156 q^{48} +1.69870 q^{49} -2.27234 q^{50} -1.09765 q^{51} +12.1217 q^{52} -11.2158 q^{53} +12.2669 q^{54} -0.860635 q^{55} +7.79779 q^{56} -2.07866 q^{57} -1.85669 q^{58} -9.07241 q^{59} -3.66847 q^{60} -13.6177 q^{61} -11.7176 q^{62} +4.88203 q^{63} -13.0255 q^{64} -3.83171 q^{65} -2.26781 q^{66} +3.16450 q^{67} -2.99445 q^{68} +6.48035 q^{69} -6.70193 q^{70} -12.7629 q^{71} +4.37640 q^{72} +5.09894 q^{73} -12.0665 q^{74} +1.15962 q^{75} -5.67073 q^{76} -2.53832 q^{77} -10.0967 q^{78} -4.37254 q^{79} +0.319205 q^{80} -1.29417 q^{81} -6.48705 q^{82} +6.92010 q^{83} -10.8196 q^{84} +0.946558 q^{85} -12.4703 q^{86} +0.947504 q^{87} -2.27543 q^{88} -8.17530 q^{89} -3.76137 q^{90} -11.3011 q^{91} +17.6788 q^{92} +5.97973 q^{93} +23.5812 q^{94} +1.79254 q^{95} +6.97294 q^{96} -2.47287 q^{97} -3.86002 q^{98} -1.42460 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q - 5 q^{2} - 3 q^{3} + 19 q^{4} - 29 q^{5} - 6 q^{6} + 12 q^{7} - 15 q^{8} + 14 q^{9}+O(q^{10}) $ 29 * q - 5 * q^2 - 3 * q^3 + 19 * q^4 - 29 * q^5 - 6 * q^6 + 12 * q^7 - 15 * q^8 + 14 * q^9	\( 29 q - 5 q^{2} - 3 q^{3} + 19 q^{4} - 29 q^{5} - 6 q^{6} + 12 q^{7} - 15 q^{8} + 14 q^{9} + 5 q^{10} - 38 q^{11} - 6 q^{12} + 5 q^{13} - 18 q^{14} + 3 q^{15} + 7 q^{16} - 16 q^{17} - 2 q^{18} - 18 q^{19} - 19 q^{20} - 20 q^{21} - 2 q^{22} - 19 q^{23} - 19 q^{24} + 29 q^{25} - 21 q^{26} - 21 q^{27} + 26 q^{28} - 31 q^{29} + 6 q^{30} - 13 q^{31} - 30 q^{32} + 2 q^{33} - 14 q^{34} - 12 q^{35} - 29 q^{36} - q^{37} - 23 q^{38} - 39 q^{39} + 15 q^{40} - 24 q^{41} - 20 q^{42} - 27 q^{43} - 76 q^{44} - 14 q^{45} - 11 q^{46} - 5 q^{47} - 2 q^{48} - 11 q^{49} - 5 q^{50} - 58 q^{51} + 11 q^{52} - 37 q^{53} - 18 q^{54} + 38 q^{55} - 50 q^{56} - 6 q^{57} + 31 q^{58} - 67 q^{59} + 6 q^{60} - 31 q^{61} - 19 q^{62} - 2 q^{63} - 13 q^{64} - 5 q^{65} + 6 q^{66} - 17 q^{67} - 16 q^{68} - 48 q^{69} + 18 q^{70} - 53 q^{71} + 9 q^{72} + 29 q^{73} - 59 q^{74} - 3 q^{75} - 21 q^{76} - 62 q^{77} - 12 q^{78} - 13 q^{79} - 7 q^{80} - 11 q^{81} + 32 q^{82} - 72 q^{83} - 58 q^{84} + 16 q^{85} - 43 q^{86} + 4 q^{87} + 12 q^{88} - 38 q^{89} + 2 q^{90} - 45 q^{91} - 37 q^{92} - 27 q^{93} - 44 q^{94} + 18 q^{95} - 21 q^{96} + 32 q^{97} - 32 q^{98} - 107 q^{99}+O(q^{100}) \) 29 * q - 5 * q^2 - 3 * q^3 + 19 * q^4 - 29 * q^5 - 6 * q^6 + 12 * q^7 - 15 * q^8 + 14 * q^9 + 5 * q^10 - 38 * q^11 - 6 * q^12 + 5 * q^13 - 18 * q^14 + 3 * q^15 + 7 * q^16 - 16 * q^17 - 2 * q^18 - 18 * q^19 - 19 * q^20 - 20 * q^21 - 2 * q^22 - 19 * q^23 - 19 * q^24 + 29 * q^25 - 21 * q^26 - 21 * q^27 + 26 * q^28 - 31 * q^29 + 6 * q^30 - 13 * q^31 - 30 * q^32 + 2 * q^33 - 14 * q^34 - 12 * q^35 - 29 * q^36 - q^37 - 23 * q^38 - 39 * q^39 + 15 * q^40 - 24 * q^41 - 20 * q^42 - 27 * q^43 - 76 * q^44 - 14 * q^45 - 11 * q^46 - 5 * q^47 - 2 * q^48 - 11 * q^49 - 5 * q^50 - 58 * q^51 + 11 * q^52 - 37 * q^53 - 18 * q^54 + 38 * q^55 - 50 * q^56 - 6 * q^57 + 31 * q^58 - 67 * q^59 + 6 * q^60 - 31 * q^61 - 19 * q^62 - 2 * q^63 - 13 * q^64 - 5 * q^65 + 6 * q^66 - 17 * q^67 - 16 * q^68 - 48 * q^69 + 18 * q^70 - 53 * q^71 + 9 * q^72 + 29 * q^73 - 59 * q^74 - 3 * q^75 - 21 * q^76 - 62 * q^77 - 12 * q^78 - 13 * q^79 - 7 * q^80 - 11 * q^81 + 32 * q^82 - 72 * q^83 - 58 * q^84 + 16 * q^85 - 43 * q^86 + 4 * q^87 + 12 * q^88 - 38 * q^89 + 2 * q^90 - 45 * q^91 - 37 * q^92 - 27 * q^93 - 44 * q^94 + 18 * q^95 - 21 * q^96 + 32 * q^97 - 32 * q^98 - 107 * 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 $

$2$	−2.27234	−1.60678	−0.803392	−	0.595450i	$-0.796974\pi$
$2$	−2.27234	−1.60678	−0.803392	+	0.595450i	$0.796974\pi$
$3$	1.15962	0.669506	0.334753	−	0.942306i	$-0.391347\pi$
$3$	1.15962	0.669506	0.334753	+	0.942306i	$0.391347\pi$
$4$	3.16351	1.58176
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.63504	−1.07575
$7$	−2.94936	−1.11475	−0.557376	−	0.830260i	$-0.688192\pi$
$7$	−2.94936	−1.11475	−0.557376	+	0.830260i	$0.688192\pi$
$8$	−2.64390	−0.934759
$9$	−1.65529	−0.551762
$10$	2.27234	0.718576
$11$	0.860635	0.259491	0.129746	−	0.991547i	$-0.458584\pi$
$11$	0.860635	0.259491	0.129746	+	0.991547i	$0.458584\pi$
$12$	3.66847	1.05900
$13$	3.83171	1.06273	0.531363	−	0.847144i	$-0.321680\pi$
$13$	3.83171	1.06273	0.531363	+	0.847144i	$0.321680\pi$
$14$	6.70193	1.79117
$15$	−1.15962	−0.299412
$16$	−0.319205	−0.0798012
$17$	−0.946558	−0.229574	−0.114787	−	0.993390i	$-0.536619\pi$
$17$	−0.946558	−0.229574	−0.114787	+	0.993390i	$0.536619\pi$
$18$	3.76137	0.886563
$19$	−1.79254	−0.411237	−0.205618	−	0.978632i	$-0.565921\pi$
$19$	−1.79254	−0.411237	−0.205618	+	0.978632i	$0.565921\pi$
$20$	−3.16351	−0.707383
$21$	−3.42013	−0.746333
$22$	−1.95565	−0.416947
$23$	5.58835	1.16525	0.582626	−	0.812741i	$-0.302025\pi$
$23$	5.58835	1.16525	0.582626	+	0.812741i	$0.302025\pi$
$24$	−3.06591	−0.625826
$25$	1.00000	0.200000
$26$	−8.70695	−1.70757
$27$	−5.39835	−1.03891
$28$	−9.33033	−1.76327
$29$	0.817083	0.151729	0.0758643	−	0.997118i	$-0.475828\pi$
$29$	0.817083	0.151729	0.0758643	+	0.997118i	$0.475828\pi$
$30$	2.63504	0.481091
$31$	5.15664	0.926159	0.463080	−	0.886317i	$-0.346744\pi$
$31$	5.15664	0.926159	0.463080	+	0.886317i	$0.346744\pi$
$32$	6.01313	1.06298
$33$	0.998008	0.173731
$34$	2.15090	0.368876
$35$	2.94936	0.498532
$36$	−5.23652	−0.872753
$37$	5.31018	0.872988	0.436494	−	0.899707i	$-0.356220\pi$
$37$	5.31018	0.872988	0.436494	+	0.899707i	$0.356220\pi$
$38$	4.07325	0.660769
$39$	4.44333	0.711501
$40$	2.64390	0.418037
$41$	2.85479	0.445843	0.222922	−	0.974836i	$-0.428441\pi$
$41$	2.85479	0.445843	0.222922	+	0.974836i	$0.428441\pi$
$42$	7.77168	1.19920
$43$	5.48786	0.836890	0.418445	−	0.908242i	$-0.362575\pi$
$43$	5.48786	0.836890	0.418445	+	0.908242i	$0.362575\pi$
$44$	2.72263	0.410452
$45$	1.65529	0.246755
$46$	−12.6986	−1.87231
$47$	−10.3775	−1.51371	−0.756856	−	0.653581i	$-0.773266\pi$
$47$	−10.3775	−1.51371	−0.756856	+	0.653581i	$0.773266\pi$
$48$	−0.370156	−0.0534274
$49$	1.69870	0.242672
$50$	−2.27234	−0.321357
$51$	−1.09765	−0.153701
$52$	12.1217	1.68098
$53$	−11.2158	−1.54061	−0.770304	−	0.637677i	$-0.779895\pi$
$53$	−11.2158	−1.54061	−0.770304	+	0.637677i	$0.779895\pi$
$54$	12.2669	1.66931
$55$	−0.860635	−0.116048
$56$	7.79779	1.04202
$57$	−2.07866	−0.275325
$58$	−1.85669	−0.243795
$59$	−9.07241	−1.18113	−0.590563	−	0.806991i	$-0.701094\pi$
$59$	−9.07241	−1.18113	−0.590563	+	0.806991i	$0.701094\pi$
$60$	−3.66847	−0.473597
$61$	−13.6177	−1.74357	−0.871785	−	0.489889i	$-0.837037\pi$
$61$	−13.6177	−1.74357	−0.871785	+	0.489889i	$0.837037\pi$
$62$	−11.7176	−1.48814
$63$	4.88203	0.615078
$64$	−13.0255	−1.62818
$65$	−3.83171	−0.475266
$66$	−2.26781	−0.279148
$67$	3.16450	0.386605	0.193303	−	0.981139i	$-0.438080\pi$
$67$	3.16450	0.386605	0.193303	+	0.981139i	$0.438080\pi$
$68$	−2.99445	−0.363130
$69$	6.48035	0.780142
$70$	−6.70193	−0.801034
$71$	−12.7629	−1.51468	−0.757341	−	0.653020i	$-0.773502\pi$
$71$	−12.7629	−1.51468	−0.757341	+	0.653020i	$0.773502\pi$
$72$	4.37640	0.515764
$73$	5.09894	0.596786	0.298393	−	0.954443i	$-0.403549\pi$
$73$	5.09894	0.596786	0.298393	+	0.954443i	$0.403549\pi$
$74$	−12.0665	−1.40270
$75$	1.15962	0.133901
$76$	−5.67073	−0.650477
$77$	−2.53832	−0.289268
$78$	−10.0967	−1.14323
$79$	−4.37254	−0.491949	−0.245975	−	0.969276i	$-0.579108\pi$
$79$	−4.37254	−0.491949	−0.245975	+	0.969276i	$0.579108\pi$
$80$	0.319205	0.0356882
$81$	−1.29417	−0.143797
$82$	−6.48705	−0.716374
$83$	6.92010	0.759580	0.379790	−	0.925073i	$-0.375996\pi$
$83$	6.92010	0.759580	0.379790	+	0.925073i	$0.375996\pi$
$84$	−10.8196	−1.18052
$85$	0.946558	0.102669
$86$	−12.4703	−1.34470
$87$	0.947504	0.101583
$88$	−2.27543	−0.242562
$89$	−8.17530	−0.866580	−0.433290	−	0.901254i	$-0.642647\pi$
$89$	−8.17530	−0.866580	−0.433290	+	0.901254i	$0.642647\pi$
$90$	−3.76137	−0.396483
$91$	−11.3011	−1.18468
$92$	17.6788	1.84314
$93$	5.97973	0.620069
$94$	23.5812	2.43221
$95$	1.79254	0.183911
$96$	6.97294	0.711673
$97$	−2.47287	−0.251082	−0.125541	−	0.992088i	$-0.540067\pi$
$97$	−2.47287	−0.251082	−0.125541	+	0.992088i	$0.540067\pi$
$98$	−3.86002	−0.389921
$99$	−1.42460	−0.143177
$100$	3.16351	0.316351
$101$	−7.85336	−0.781439	−0.390719	−	0.920510i	$-0.627774\pi$
$101$	−7.85336	−0.781439	−0.390719	+	0.920510i	$0.627774\pi$
$102$	2.49422	0.246965
$103$	5.06965	0.499527	0.249764	−	0.968307i	$-0.419647\pi$
$103$	5.06965	0.499527	0.249764	+	0.968307i	$0.419647\pi$
$104$	−10.1307	−0.993393
$105$	3.42013	0.333770
$106$	25.4861	2.47542
$107$	−15.2975	−1.47887	−0.739434	−	0.673229i	$-0.764907\pi$
$107$	−15.2975	−1.47887	−0.739434	+	0.673229i	$0.764907\pi$
$108$	−17.0778	−1.64331
$109$	3.33001	0.318957	0.159478	−	0.987201i	$-0.449019\pi$
$109$	3.33001	0.318957	0.159478	+	0.987201i	$0.449019\pi$
$110$	1.95565	0.186464
$111$	6.15778	0.584471
$112$	0.941449	0.0889586
$113$	19.0472	1.79181	0.895903	−	0.444249i	$-0.146530\pi$
$113$	19.0472	1.79181	0.895903	+	0.444249i	$0.146530\pi$
$114$	4.72342	0.442389
$115$	−5.58835	−0.521116
$116$	2.58485	0.239998
$117$	−6.34258	−0.586372
$118$	20.6156	1.89782
$119$	2.79174	0.255918
$120$	3.06591	0.279878
$121$	−10.2593	−0.932664
$122$	30.9440	2.80154
$123$	3.31047	0.298495
$124$	16.3131	1.46496
$125$	−1.00000	−0.0894427
$126$	−11.0936	−0.988297
$127$	−1.68960	−0.149928	−0.0749640	−	0.997186i	$-0.523884\pi$
$127$	−1.68960	−0.149928	−0.0749640	+	0.997186i	$0.523884\pi$
$128$	17.5720	1.55316
$129$	6.36382	0.560303
$130$	8.70695	0.763650
$131$	−12.9797	−1.13404	−0.567020	−	0.823704i	$-0.691904\pi$
$131$	−12.9797	−1.13404	−0.567020	+	0.823704i	$0.691904\pi$
$132$	3.15721	0.274800
$133$	5.28684	0.458427
$134$	−7.19081	−0.621192
$135$	5.39835	0.464616
$136$	2.50260	0.214596
$137$	2.04729	0.174912	0.0874558	−	0.996168i	$-0.472126\pi$
$137$	2.04729	0.174912	0.0874558	+	0.996168i	$0.472126\pi$
$138$	−14.7255	−1.25352
$139$	6.80337	0.577055	0.288527	−	0.957472i	$-0.406834\pi$
$139$	6.80337	0.577055	0.288527	+	0.957472i	$0.406834\pi$
$140$	9.33033	0.788557
$141$	−12.0339	−1.01344
$142$	29.0017	2.43377
$143$	3.29771	0.275768
$144$	0.528375	0.0440313
$145$	−0.817083	−0.0678551
$146$	−11.5865	−0.958907
$147$	1.96984	0.162470
$148$	16.7988	1.38086
$149$	−20.1410	−1.65002	−0.825008	−	0.565121i	$-0.808829\pi$
$149$	−20.1410	−1.65002	−0.825008	+	0.565121i	$0.808829\pi$
$150$	−2.63504	−0.215150
$151$	13.4562	1.09505	0.547524	−	0.836790i	$-0.315570\pi$
$151$	13.4562	1.09505	0.547524	+	0.836790i	$0.315570\pi$
$152$	4.73929	0.384407
$153$	1.56682	0.126670
$154$	5.76792	0.464792
$155$	−5.15664	−0.414191
$156$	14.0565	1.12542
$157$	2.07178	0.165346	0.0826729	−	0.996577i	$-0.473654\pi$
$157$	2.07178	0.165346	0.0826729	+	0.996577i	$0.473654\pi$
$158$	9.93589	0.790457
$159$	−13.0060	−1.03145
$160$	−6.01313	−0.475380
$161$	−16.4820	−1.29897
$162$	2.94079	0.231051
$163$	−19.9378	−1.56165	−0.780826	−	0.624749i	$-0.785201\pi$
$163$	−19.9378	−1.56165	−0.780826	+	0.624749i	$0.785201\pi$
$164$	9.03117	0.705216
$165$	−0.998008	−0.0776948
$166$	−15.7248	−1.22048
$167$	−19.6461	−1.52026	−0.760131	−	0.649770i	$-0.774865\pi$
$167$	−19.6461	−1.52026	−0.760131	+	0.649770i	$0.774865\pi$
$168$	9.04246	0.697641
$169$	1.68203	0.129387
$170$	−2.15090	−0.164966
$171$	2.96717	0.226905
$172$	17.3609	1.32376
$173$	−15.3964	−1.17057	−0.585284	−	0.810828i	$-0.699017\pi$
$173$	−15.3964	−1.17057	−0.585284	+	0.810828i	$0.699017\pi$
$174$	−2.15305	−0.163222
$175$	−2.94936	−0.222950
$176$	−0.274719	−0.0207077
$177$	−10.5205	−0.790771
$178$	18.5770	1.39241
$179$	−3.40342	−0.254384	−0.127192	−	0.991878i	$-0.540596\pi$
$179$	−3.40342	−0.254384	−0.127192	+	0.991878i	$0.540596\pi$
$180$	5.23652	0.390307
$181$	22.2631	1.65480	0.827400	−	0.561613i	$-0.189819\pi$
$181$	22.2631	1.65480	0.827400	+	0.561613i	$0.189819\pi$
$182$	25.6799	1.90352
$183$	−15.7913	−1.16733
$184$	−14.7750	−1.08923
$185$	−5.31018	−0.390412
$186$	−13.5880	−0.996318
$187$	−0.814641	−0.0595724
$188$	−32.8294	−2.39433
$189$	15.9217	1.15813
$190$	−4.07325	−0.295505
$191$	−5.96007	−0.431256	−0.215628	−	0.976476i	$-0.569180\pi$
$191$	−5.96007	−0.431256	−0.215628	+	0.976476i	$0.569180\pi$
$192$	−15.1046	−1.09008
$193$	−11.2798	−0.811935	−0.405967	−	0.913888i	$-0.633065\pi$
$193$	−11.2798	−0.811935	−0.405967	+	0.913888i	$0.633065\pi$
$194$	5.61919	0.403434
$195$	−4.44333	−0.318193
$196$	5.37387	0.383848
$197$	21.2211	1.51194	0.755969	−	0.654607i	$-0.227166\pi$
$197$	21.2211	1.51194	0.755969	+	0.654607i	$0.227166\pi$
$198$	3.23716	0.230055
$199$	−7.73438	−0.548275	−0.274138	−	0.961690i	$-0.588392\pi$
$199$	−7.73438	−0.548275	−0.274138	+	0.961690i	$0.588392\pi$
$200$	−2.64390	−0.186952
$201$	3.66961	0.258835
$202$	17.8455	1.25560
$203$	−2.40987	−0.169140
$204$	−3.47242	−0.243118
$205$	−2.85479	−0.199387
$206$	−11.5200	−0.802633
$207$	−9.25031	−0.642941
$208$	−1.22310	−0.0848069
$209$	−1.54272	−0.106712
$210$	−7.77168	−0.536297
$211$	4.05250	0.278985	0.139493	−	0.990223i	$-0.455453\pi$
$211$	4.05250	0.278985	0.139493	+	0.990223i	$0.455453\pi$
$212$	−35.4813	−2.43687
$213$	−14.8001	−1.01409
$214$	34.7611	2.37622
$215$	−5.48786	−0.374269
$216$	14.2727	0.971134
$217$	−15.2088	−1.03244
$218$	−7.56690	−0.512495
$219$	5.91283	0.399552
$220$	−2.72263	−0.183560
$221$	−3.62694	−0.243974
$222$	−13.9926	−0.939119
$223$	24.9791	1.67272	0.836361	−	0.548178i	$-0.184679\pi$
$223$	24.9791	1.67272	0.836361	+	0.548178i	$0.184679\pi$
$224$	−17.7349	−1.18496
$225$	−1.65529	−0.110352
$226$	−43.2816	−2.87905
$227$	11.2744	0.748311	0.374156	−	0.927366i	$-0.377933\pi$
$227$	11.2744	0.748311	0.374156	+	0.927366i	$0.377933\pi$
$228$	−6.57588	−0.435498
$229$	22.2787	1.47222	0.736110	−	0.676862i	$-0.236661\pi$
$229$	22.2787	1.47222	0.736110	+	0.676862i	$0.236661\pi$
$230$	12.6986	0.837321
$231$	−2.94348	−0.193667
$232$	−2.16028	−0.141830
$233$	−15.6982	−1.02842	−0.514210	−	0.857664i	$-0.671915\pi$
$233$	−15.6982	−1.02842	−0.514210	+	0.857664i	$0.671915\pi$
$234$	14.4125	0.942173
$235$	10.3775	0.676953
$236$	−28.7007	−1.86826
$237$	−5.07048	−0.329363
$238$	−6.34376	−0.411205
$239$	−6.46620	−0.418263	−0.209132	−	0.977887i	$-0.567064\pi$
$239$	−6.46620	−0.418263	−0.209132	+	0.977887i	$0.567064\pi$
$240$	0.370156	0.0238935
$241$	−29.9554	−1.92959	−0.964797	−	0.262995i	$-0.915290\pi$
$241$	−29.9554	−1.92959	−0.964797	+	0.262995i	$0.915290\pi$
$242$	23.3126	1.49859
$243$	14.6943	0.942641
$244$	−43.0798	−2.75790
$245$	−1.69870	−0.108526
$246$	−7.52250	−0.479617
$247$	−6.86850	−0.437032
$248$	−13.6336	−0.865735
$249$	8.02467	0.508543
$250$	2.27234	0.143715
$251$	−17.9497	−1.13298	−0.566488	−	0.824070i	$-0.691698\pi$
$251$	−17.9497	−1.13298	−0.566488	+	0.824070i	$0.691698\pi$
$252$	15.4444	0.972903
$253$	4.80953	0.302372
$254$	3.83935	0.240902
$255$	1.09765	0.0687372
$256$	−13.8785	−0.867406
$257$	26.5783	1.65791	0.828954	−	0.559317i	$-0.188937\pi$
$257$	26.5783	1.65791	0.828954	+	0.559317i	$0.188937\pi$
$258$	−14.4607	−0.900286
$259$	−15.6616	−0.973165
$260$	−12.1217	−0.751755
$261$	−1.35251	−0.0837180
$262$	29.4942	1.82216
$263$	−30.1510	−1.85919	−0.929596	−	0.368581i	$-0.879844\pi$
$263$	−30.1510	−1.85919	−0.929596	+	0.368581i	$0.879844\pi$
$264$	−2.63863	−0.162396
$265$	11.2158	0.688981
$266$	−12.0135	−0.736594
$267$	−9.48023	−0.580181
$268$	10.0109	0.611516
$269$	−10.9938	−0.670303	−0.335151	−	0.942164i	$-0.608787\pi$
$269$	−10.9938	−0.670303	−0.335151	+	0.942164i	$0.608787\pi$
$270$	−12.2669	−0.746538
$271$	14.4912	0.880278	0.440139	−	0.897930i	$-0.354929\pi$
$271$	14.4912	0.880278	0.440139	+	0.897930i	$0.354929\pi$
$272$	0.302146	0.0183203
$273$	−13.1049	−0.793148
$274$	−4.65213	−0.281045
$275$	0.860635	0.0518983
$276$	20.5007	1.23400
$277$	−28.1743	−1.69283	−0.846414	−	0.532526i	$-0.821243\pi$
$277$	−28.1743	−1.69283	−0.846414	+	0.532526i	$0.821243\pi$
$278$	−15.4596	−0.927203
$279$	−8.53571	−0.511019
$280$	−7.79779	−0.466007
$281$	−2.25166	−0.134323	−0.0671614	−	0.997742i	$-0.521394\pi$
$281$	−2.25166	−0.134323	−0.0671614	+	0.997742i	$0.521394\pi$
$282$	27.3451	1.62838
$283$	−24.1402	−1.43499	−0.717493	−	0.696566i	$-0.754711\pi$
$283$	−24.1402	−1.43499	−0.717493	+	0.696566i	$0.754711\pi$
$284$	−40.3757	−2.39586
$285$	2.07866	0.123129
$286$	−7.49350	−0.443100
$287$	−8.41979	−0.497005
$288$	−9.95346	−0.586513
$289$	−16.1040	−0.947296
$290$	1.85669	0.109028
$291$	−2.86758	−0.168101
$292$	16.1306	0.943971
$293$	−10.5119	−0.614113	−0.307056	−	0.951691i	$-0.599344\pi$
$293$	−10.5119	−0.614113	−0.307056	+	0.951691i	$0.599344\pi$
$294$	−4.47615	−0.261054
$295$	9.07241	0.528216
$296$	−14.0396	−0.816033
$297$	−4.64601	−0.269589
$298$	45.7672	2.65122
$299$	21.4130	1.23834
$300$	3.66847	0.211799
$301$	−16.1856	−0.932925
$302$	−30.5770	−1.75951
$303$	−9.10690	−0.523178
$304$	0.572188	0.0328172
$305$	13.6177	0.779748
$306$	−3.56035	−0.203532
$307$	−22.2913	−1.27223	−0.636115	−	0.771594i	$-0.719460\pi$
$307$	−22.2913	−1.27223	−0.636115	+	0.771594i	$0.719460\pi$
$308$	−8.03001	−0.457552
$309$	5.87886	0.334437
$310$	11.7176	0.665516
$311$	−12.3943	−0.702814	−0.351407	−	0.936223i	$-0.614297\pi$
$311$	−12.3943	−0.702814	−0.351407	+	0.936223i	$0.614297\pi$
$312$	−11.7477	−0.665082
$313$	1.40814	0.0795929	0.0397964	−	0.999208i	$-0.487329\pi$
$313$	1.40814	0.0795929	0.0397964	+	0.999208i	$0.487329\pi$
$314$	−4.70777	−0.265675
$315$	−4.88203	−0.275071
$316$	−13.8326	−0.778145
$317$	14.3883	0.808127	0.404064	−	0.914731i	$-0.367597\pi$
$317$	14.3883	0.808127	0.404064	+	0.914731i	$0.367597\pi$
$318$	29.5541	1.65731
$319$	0.703210	0.0393722
$320$	13.0255	0.728145
$321$	−17.7393	−0.990111
$322$	37.4527	2.08716
$323$	1.69674	0.0944092
$324$	−4.09413	−0.227452
$325$	3.83171	0.212545
$326$	45.3055	2.50924
$327$	3.86154	0.213543
$328$	−7.54777	−0.416756
$329$	30.6069	1.68741
$330$	2.26781	0.124839
$331$	−1.80945	−0.0994564	−0.0497282	−	0.998763i	$-0.515836\pi$
$331$	−1.80945	−0.0994564	−0.0497282	+	0.998763i	$0.515836\pi$
$332$	21.8918	1.20147
$333$	−8.78987	−0.481682
$334$	44.6426	2.44273
$335$	−3.16450	−0.172895
$336$	1.09172	0.0595583
$337$	7.79002	0.424349	0.212175	−	0.977232i	$-0.431945\pi$
$337$	7.79002	0.424349	0.212175	+	0.977232i	$0.431945\pi$
$338$	−3.82215	−0.207897
$339$	22.0874	1.19962
$340$	2.99445	0.162397
$341$	4.43798	0.240330
$342$	−6.74240	−0.364587
$343$	15.6354	0.844233
$344$	−14.5093	−0.782290
$345$	−6.48035	−0.348890
$346$	34.9858	1.88085
$347$	18.9858	1.01921	0.509605	−	0.860409i	$-0.329792\pi$
$347$	18.9858	1.01921	0.509605	+	0.860409i	$0.329792\pi$
$348$	2.99744	0.160680
$349$	7.85804	0.420631	0.210316	−	0.977634i	$-0.432551\pi$
$349$	7.85804	0.420631	0.210316	+	0.977634i	$0.432551\pi$
$350$	6.70193	0.358233
$351$	−20.6849	−1.10408
$352$	5.17512	0.275835
$353$	12.7244	0.677252	0.338626	−	0.940921i	$-0.390038\pi$
$353$	12.7244	0.677252	0.338626	+	0.940921i	$0.390038\pi$
$354$	23.9062	1.27060
$355$	12.7629	0.677386
$356$	−25.8627	−1.37072
$357$	3.23735	0.171339
$358$	7.73372	0.408740
$359$	−12.5951	−0.664746	−0.332373	−	0.943148i	$-0.607849\pi$
$359$	−12.5951	−0.664746	−0.332373	+	0.943148i	$0.607849\pi$
$360$	−4.37640	−0.230657
$361$	−15.7868	−0.830884
$362$	−50.5892	−2.65891
$363$	−11.8969	−0.624424
$364$	−35.7512	−1.87387
$365$	−5.09894	−0.266891
$366$	35.8833	1.87565
$367$	8.18485	0.427245	0.213623	−	0.976916i	$-0.431474\pi$
$367$	8.18485	0.427245	0.213623	+	0.976916i	$0.431474\pi$
$368$	−1.78383	−0.0929885
$369$	−4.72549	−0.245999
$370$	12.0665	0.627308
$371$	33.0794	1.71739
$372$	18.9170	0.980799
$373$	−20.5412	−1.06358	−0.531792	−	0.846875i	$-0.678481\pi$
$373$	−20.5412	−1.06358	−0.531792	+	0.846875i	$0.678481\pi$
$374$	1.85114	0.0957201
$375$	−1.15962	−0.0598824
$376$	27.4370	1.41496
$377$	3.13083	0.161246
$378$	−36.1794	−1.86087
$379$	−15.0116	−0.771096	−0.385548	−	0.922688i	$-0.625988\pi$
$379$	−15.0116	−0.771096	−0.385548	+	0.922688i	$0.625988\pi$
$380$	5.67073	0.290902
$381$	−1.95929	−0.100378
$382$	13.5433	0.692935
$383$	13.4326	0.686372	0.343186	−	0.939267i	$-0.388494\pi$
$383$	13.4326	0.686372	0.343186	+	0.939267i	$0.388494\pi$
$384$	20.3768	1.03985
$385$	2.53832	0.129365
$386$	25.6314	1.30460
$387$	−9.08397	−0.461764
$388$	−7.82296	−0.397150
$389$	5.28850	0.268137	0.134069	−	0.990972i	$-0.457196\pi$
$389$	5.28850	0.268137	0.134069	+	0.990972i	$0.457196\pi$
$390$	10.0967	0.511268
$391$	−5.28969	−0.267511
$392$	−4.49119	−0.226839
$393$	−15.0515	−0.759246
$394$	−48.2214	−2.42936
$395$	4.37254	0.220006
$396$	−4.50673	−0.226472
$397$	19.7559	0.991519	0.495759	−	0.868460i	$-0.334890\pi$
$397$	19.7559	0.991519	0.495759	+	0.868460i	$0.334890\pi$
$398$	17.5751	0.880961
$399$	6.13071	0.306920
$400$	−0.319205	−0.0159602
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−8.33860	−0.415891
$403$	19.7588	0.984254
$404$	−24.8442	−1.23605
$405$	1.29417	0.0643079
$406$	5.47603	0.271771
$407$	4.57013	0.226533
$408$	2.90206	0.143673
$409$	1.37292	0.0678863	0.0339432	−	0.999424i	$-0.489193\pi$
$409$	1.37292	0.0678863	0.0339432	+	0.999424i	$0.489193\pi$
$410$	6.48705	0.320372
$411$	2.37407	0.117104
$412$	16.0379	0.790131
$413$	26.7578	1.31666
$414$	21.0198	1.03307
$415$	−6.92010	−0.339694
$416$	23.0406	1.12966
$417$	7.88932	0.386341
$418$	3.50559	0.171464
$419$	8.29523	0.405249	0.202624	−	0.979257i	$-0.435053\pi$
$419$	8.29523	0.405249	0.202624	+	0.979257i	$0.435053\pi$
$420$	10.8196	0.527943
$421$	−6.88282	−0.335448	−0.167724	−	0.985834i	$-0.553642\pi$
$421$	−6.88282	−0.335448	−0.167724	+	0.985834i	$0.553642\pi$
$422$	−9.20863	−0.448269
$423$	17.1777	0.835209
$424$	29.6534	1.44010
$425$	−0.946558	−0.0459148
$426$	33.6309	1.62942
$427$	40.1635	1.94365
$428$	−48.3940	−2.33921
$429$	3.82408	0.184628
$430$	12.4703	0.601369
$431$	9.08335	0.437529	0.218765	−	0.975778i	$-0.429797\pi$
$431$	9.08335	0.437529	0.218765	+	0.975778i	$0.429797\pi$
$432$	1.72318	0.0829066
$433$	21.5236	1.03436	0.517178	−	0.855878i	$-0.326982\pi$
$433$	21.5236	1.03436	0.517178	+	0.855878i	$0.326982\pi$
$434$	34.5594	1.65891
$435$	−0.947504	−0.0454294
$436$	10.5345	0.504512
$437$	−10.0173	−0.479194
$438$	−13.4359	−0.641994
$439$	−3.42660	−0.163542	−0.0817712	−	0.996651i	$-0.526058\pi$
$439$	−3.42660	−0.163542	−0.0817712	+	0.996651i	$0.526058\pi$
$440$	2.27543	0.108477
$441$	−2.81184	−0.133897
$442$	8.24162	0.392014
$443$	−18.4628	−0.877196	−0.438598	−	0.898683i	$-0.644525\pi$
$443$	−18.4628	−0.877196	−0.438598	+	0.898683i	$0.644525\pi$
$444$	19.4802	0.924491
$445$	8.17530	0.387546
$446$	−56.7609	−2.68771
$447$	−23.3559	−1.10470
$448$	38.4167	1.81502
$449$	−35.7563	−1.68745	−0.843723	−	0.536779i	$-0.819641\pi$
$449$	−35.7563	−1.68745	−0.843723	+	0.536779i	$0.819641\pi$
$450$	3.76137	0.177313
$451$	2.45693	0.115692
$452$	60.2560	2.83420
$453$	15.6040	0.733141
$454$	−25.6193	−1.20237
$455$	11.3011	0.529803
$456$	5.49577	0.257363
$457$	4.53910	0.212330	0.106165	−	0.994349i	$-0.466143\pi$
$457$	4.53910	0.212330	0.106165	+	0.994349i	$0.466143\pi$
$458$	−50.6248	−2.36554
$459$	5.10985	0.238507
$460$	−17.6788	−0.824279
$461$	26.4277	1.23086	0.615429	−	0.788192i	$-0.288983\pi$
$461$	26.4277	1.23086	0.615429	+	0.788192i	$0.288983\pi$
$462$	6.68858	0.311181
$463$	16.4574	0.764841	0.382421	−	0.923988i	$-0.375091\pi$
$463$	16.4574	0.764841	0.382421	+	0.923988i	$0.375091\pi$
$464$	−0.260817	−0.0121081
$465$	−5.97973	−0.277303
$466$	35.6715	1.65245
$467$	−0.0517131	−0.00239300	−0.00119650	−	0.999999i	$-0.500381\pi$
$467$	−0.0517131	−0.00239300	−0.00119650	+	0.999999i	$0.500381\pi$
$468$	−20.0649	−0.927498
$469$	−9.33324	−0.430969
$470$	−23.5812	−1.08772
$471$	2.40247	0.110700
$472$	23.9865	1.10407
$473$	4.72304	0.217166
$474$	11.5218	0.529215
$475$	−1.79254	−0.0822474
$476$	8.83169	0.404800
$477$	18.5653	0.850049
$478$	14.6934	0.672059
$479$	−10.4735	−0.478545	−0.239273	−	0.970952i	$-0.576909\pi$
$479$	−10.4735	−0.478545	−0.239273	+	0.970952i	$0.576909\pi$
$480$	−6.97294	−0.318270
$481$	20.3471	0.927748
$482$	68.0687	3.10044
$483$	−19.1129	−0.869665
$484$	−32.4555	−1.47525
$485$	2.47287	0.112287
$486$	−33.3904	−1.51462
$487$	−16.7751	−0.760152	−0.380076	−	0.924955i	$-0.624102\pi$
$487$	−16.7751	−0.760152	−0.380076	+	0.924955i	$0.624102\pi$
$488$	36.0038	1.62982
$489$	−23.1203	−1.04553
$490$	3.86002	0.174378
$491$	12.6487	0.570828	0.285414	−	0.958404i	$-0.407869\pi$
$491$	12.6487	0.570828	0.285414	+	0.958404i	$0.407869\pi$
$492$	10.4727	0.472146
$493$	−0.773416	−0.0348329
$494$	15.6075	0.702217
$495$	1.42460	0.0640309
$496$	−1.64602	−0.0739087
$497$	37.6424	1.68849
$498$	−18.2348	−0.817119
$499$	−16.0861	−0.720111	−0.360056	−	0.932931i	$-0.617242\pi$
$499$	−16.0861	−0.720111	−0.360056	+	0.932931i	$0.617242\pi$
$500$	−3.16351	−0.141477
$501$	−22.7820	−1.01782
$502$	40.7878	1.82045
$503$	−13.5918	−0.606028	−0.303014	−	0.952986i	$-0.597993\pi$
$503$	−13.5918	−0.606028	−0.303014	+	0.952986i	$0.597993\pi$
$504$	−12.9076	−0.574949
$505$	7.85336	0.349470
$506$	−10.9289	−0.485847
$507$	1.95052	0.0866255
$508$	−5.34508	−0.237150
$509$	−1.06541	−0.0472234	−0.0236117	−	0.999721i	$-0.507517\pi$
$509$	−1.06541	−0.0472234	−0.0236117	+	0.999721i	$0.507517\pi$
$510$	−2.49422	−0.110446
$511$	−15.0386	−0.665268
$512$	−3.60731	−0.159422
$513$	9.67676	0.427240
$514$	−60.3948	−2.66390
$515$	−5.06965	−0.223395
$516$	20.1320	0.886263
$517$	−8.93124	−0.392795
$518$	35.5885	1.56367
$519$	−17.8540	−0.783702
$520$	10.1307	0.444259
$521$	11.6528	0.510519	0.255259	−	0.966873i	$-0.417839\pi$
$521$	11.6528	0.510519	0.255259	+	0.966873i	$0.417839\pi$
$522$	3.07335	0.134517
$523$	−23.4744	−1.02646	−0.513231	−	0.858250i	$-0.671552\pi$
$523$	−23.4744	−1.02646	−0.513231	+	0.858250i	$0.671552\pi$
$524$	−41.0614	−1.79377
$525$	−3.42013	−0.149267
$526$	68.5133	2.98732
$527$	−4.88105	−0.212622
$528$	−0.318569	−0.0138639
$529$	8.22963	0.357810
$530$	−25.4861	−1.10704
$531$	15.0174	0.651701
$532$	16.7250	0.725120
$533$	10.9387	0.473810
$534$	21.5423	0.932225
$535$	15.2975	0.661370
$536$	−8.36661	−0.361383
$537$	−3.94667	−0.170311
$538$	24.9816	1.07703
$539$	1.46196	0.0629712
$540$	17.0778	0.734910
$541$	34.5444	1.48518	0.742591	−	0.669745i	$-0.233597\pi$
$541$	34.5444	1.48518	0.742591	+	0.669745i	$0.233597\pi$
$542$	−32.9289	−1.41442
$543$	25.8166	1.10790
$544$	−5.69178	−0.244033
$545$	−3.33001	−0.142642
$546$	29.7789	1.27442
$547$	3.18775	0.136298	0.0681491	−	0.997675i	$-0.478291\pi$
$547$	3.18775	0.136298	0.0681491	+	0.997675i	$0.478291\pi$
$548$	6.47662	0.276668
$549$	22.5412	0.962035
$550$	−1.95565	−0.0833893
$551$	−1.46465	−0.0623964
$552$	−17.1334	−0.729245
$553$	12.8962	0.548401
$554$	64.0214	2.72001
$555$	−6.15778	−0.261383
$556$	21.5226	0.912760
$557$	−30.8835	−1.30857	−0.654287	−	0.756246i	$-0.727031\pi$
$557$	−30.8835	−1.30857	−0.654287	+	0.756246i	$0.727031\pi$
$558$	19.3960	0.821098
$559$	21.0279	0.889385
$560$	−0.941449	−0.0397835
$561$	−0.944672	−0.0398841
$562$	5.11653	0.215828
$563$	−24.0390	−1.01312	−0.506561	−	0.862204i	$-0.669084\pi$
$563$	−24.0390	−1.01312	−0.506561	+	0.862204i	$0.669084\pi$
$564$	−38.0695	−1.60302
$565$	−19.0472	−0.801320
$566$	54.8547	2.30571
$567$	3.81697	0.160298
$568$	33.7439	1.41586
$569$	−18.0572	−0.756998	−0.378499	−	0.925602i	$-0.623560\pi$
$569$	−18.0572	−0.756998	−0.378499	+	0.925602i	$0.623560\pi$
$570$	−4.72342	−0.197842
$571$	36.9402	1.54590	0.772950	−	0.634467i	$-0.218780\pi$
$571$	36.9402	1.54590	0.772950	+	0.634467i	$0.218780\pi$
$572$	10.4323	0.436198
$573$	−6.91141	−0.288728
$574$	19.1326	0.798580
$575$	5.58835	0.233050
$576$	21.5609	0.898369
$577$	34.7777	1.44781	0.723907	−	0.689898i	$-0.242345\pi$
$577$	34.7777	1.44781	0.723907	+	0.689898i	$0.242345\pi$
$578$	36.5938	1.52210
$579$	−13.0802	−0.543595
$580$	−2.58485	−0.107330
$581$	−20.4098	−0.846743
$582$	6.51611	0.270102
$583$	−9.65270	−0.399774
$584$	−13.4811	−0.557851
$585$	6.34258	0.262233
$586$	23.8866	0.986747
$587$	21.1750	0.873987	0.436993	−	0.899465i	$-0.356043\pi$
$587$	21.1750	0.873987	0.436993	+	0.899465i	$0.356043\pi$
$588$	6.23163	0.256988
$589$	−9.24348	−0.380871
$590$	−20.6156	−0.848729
$591$	24.6083	1.01225
$592$	−1.69504	−0.0696655
$593$	2.77687	0.114032	0.0570162	−	0.998373i	$-0.481841\pi$
$593$	2.77687	0.114032	0.0570162	+	0.998373i	$0.481841\pi$
$594$	10.5573	0.433172
$595$	−2.79174	−0.114450
$596$	−63.7164	−2.60992
$597$	−8.96892	−0.367074
$598$	−48.6574	−1.98975
$599$	24.7455	1.01107	0.505536	−	0.862805i	$-0.331295\pi$
$599$	24.7455	1.01107	0.505536	+	0.862805i	$0.331295\pi$
$600$	−3.06591	−0.125165
$601$	−12.3648	−0.504369	−0.252185	−	0.967679i	$-0.581149\pi$
$601$	−12.3648	−0.504369	−0.252185	+	0.967679i	$0.581149\pi$
$602$	36.7792	1.49901
$603$	−5.23815	−0.213314
$604$	42.5688	1.73210
$605$	10.2593	0.417100
$606$	20.6939	0.840634
$607$	−11.2256	−0.455633	−0.227816	−	0.973704i	$-0.573159\pi$
$607$	−11.2256	−0.455633	−0.227816	+	0.973704i	$0.573159\pi$
$608$	−10.7788	−0.437137
$609$	−2.79453	−0.113240
$610$	−30.9440	−1.25289
$611$	−39.7636	−1.60866
$612$	4.95667	0.200361
$613$	35.5738	1.43681	0.718406	−	0.695624i	$-0.244872\pi$
$613$	35.5738	1.43681	0.718406	+	0.695624i	$0.244872\pi$
$614$	50.6533	2.04420
$615$	−3.31047	−0.133491
$616$	6.71105	0.270396
$617$	−11.0244	−0.443827	−0.221914	−	0.975066i	$-0.571230\pi$
$617$	−11.0244	−0.443827	−0.221914	+	0.975066i	$0.571230\pi$
$618$	−13.3587	−0.537368
$619$	18.6424	0.749300	0.374650	−	0.927166i	$-0.377763\pi$
$619$	18.6424	0.749300	0.374650	+	0.927166i	$0.377763\pi$
$620$	−16.3131	−0.655150
$621$	−30.1679	−1.21060
$622$	28.1639	1.12927
$623$	24.1119	0.966022
$624$	−1.41833	−0.0567787
$625$	1.00000	0.0400000
$626$	−3.19977	−0.127889
$627$	−1.78897	−0.0714445
$628$	6.55409	0.261537
$629$	−5.02639	−0.200415
$630$	11.0936	0.441980
$631$	15.1824	0.604402	0.302201	−	0.953244i	$-0.402279\pi$
$631$	15.1824	0.604402	0.302201	+	0.953244i	$0.402279\pi$
$632$	11.5605	0.459854
$633$	4.69935	0.186782
$634$	−32.6950	−1.29849
$635$	1.68960	0.0670499
$636$	−41.1448	−1.63150
$637$	6.50894	0.257894
$638$	−1.59793	−0.0632627
$639$	21.1263	0.835743
$640$	−17.5720	−0.694593
$641$	28.6785	1.13273	0.566367	−	0.824153i	$-0.308349\pi$
$641$	28.6785	1.13273	0.566367	+	0.824153i	$0.308349\pi$
$642$	40.3097	1.59090
$643$	−22.1881	−0.875015	−0.437507	−	0.899215i	$-0.644139\pi$
$643$	−22.1881	−0.875015	−0.437507	+	0.899215i	$0.644139\pi$
$644$	−52.1411	−2.05465
$645$	−6.36382	−0.250575
$646$	−3.85557	−0.151695
$647$	−6.74724	−0.265261	−0.132631	−	0.991166i	$-0.542342\pi$
$647$	−6.74724	−0.265261	−0.132631	+	0.991166i	$0.542342\pi$
$648$	3.42166	0.134415
$649$	−7.80803	−0.306492
$650$	−8.70695	−0.341514
$651$	−17.6364	−0.691223
$652$	−63.0736	−2.47015
$653$	16.4770	0.644796	0.322398	−	0.946604i	$-0.395511\pi$
$653$	16.4770	0.644796	0.322398	+	0.946604i	$0.395511\pi$
$654$	−8.77471	−0.343118
$655$	12.9797	0.507158
$656$	−0.911263	−0.0355789
$657$	−8.44021	−0.329284
$658$	−69.5492	−2.71131
$659$	−9.48638	−0.369537	−0.184769	−	0.982782i	$-0.559154\pi$
$659$	−9.48638	−0.369537	−0.184769	+	0.982782i	$0.559154\pi$
$660$	−3.15721	−0.122894
$661$	−29.2460	−1.13754	−0.568769	−	0.822497i	$-0.692580\pi$
$661$	−29.2460	−1.13754	−0.568769	+	0.822497i	$0.692580\pi$
$662$	4.11168	0.159805
$663$	−4.20586	−0.163342
$664$	−18.2960	−0.710024
$665$	−5.28684	−0.205015
$666$	19.9735	0.773959
$667$	4.56614	0.176802
$668$	−62.1507	−2.40468
$669$	28.9662	1.11990
$670$	7.19081	0.277805
$671$	−11.7199	−0.452441
$672$	−20.5657	−0.793338
$673$	−32.0421	−1.23513	−0.617566	−	0.786519i	$-0.711881\pi$
$673$	−32.0421	−1.23513	−0.617566	+	0.786519i	$0.711881\pi$
$674$	−17.7015	−0.681838
$675$	−5.39835	−0.207783
$676$	5.32114	0.204659
$677$	3.82153	0.146873	0.0734367	−	0.997300i	$-0.476603\pi$
$677$	3.82153	0.146873	0.0734367	+	0.997300i	$0.476603\pi$
$678$	−50.1901	−1.92754
$679$	7.29337	0.279894
$680$	−2.50260	−0.0959703
$681$	13.0740	0.500999
$682$	−10.0846	−0.386159
$683$	27.1293	1.03807	0.519036	−	0.854752i	$-0.326291\pi$
$683$	27.1293	1.03807	0.519036	+	0.854752i	$0.326291\pi$
$684$	9.38667	0.358908
$685$	−2.04729	−0.0782228
$686$	−35.5289	−1.35650
$687$	25.8348	0.985659
$688$	−1.75175	−0.0667849
$689$	−42.9757	−1.63724
$690$	14.7255	0.560592
$691$	41.3427	1.57275	0.786375	−	0.617749i	$-0.211955\pi$
$691$	41.3427	1.57275	0.786375	+	0.617749i	$0.211955\pi$
$692$	−48.7068	−1.85155
$693$	4.20164	0.159607
$694$	−43.1421	−1.63765
$695$	−6.80337	−0.258067
$696$	−2.50510	−0.0949557
$697$	−2.70222	−0.102354
$698$	−17.8561	−0.675864
$699$	−18.2039	−0.688533
$700$	−9.33033	−0.352653
$701$	30.2199	1.14139	0.570694	−	0.821163i	$-0.306674\pi$
$701$	30.2199	1.14139	0.570694	+	0.821163i	$0.306674\pi$
$702$	47.0032	1.77402
$703$	−9.51871	−0.359005
$704$	−11.2102	−0.422499
$705$	12.0339	0.453224
$706$	−28.9141	−1.08820
$707$	23.1624	0.871110
$708$	−33.2818	−1.25081
$709$	−18.6525	−0.700508	−0.350254	−	0.936655i	$-0.613905\pi$
$709$	−18.6525	−0.700508	−0.350254	+	0.936655i	$0.613905\pi$
$710$	−29.0017	−1.08841
$711$	7.23781	0.271439
$712$	21.6147	0.810043
$713$	28.8171	1.07921
$714$	−7.35634	−0.275304
$715$	−3.29771	−0.123327
$716$	−10.7668	−0.402373
$717$	−7.49832	−0.280030
$718$	28.6204	1.06810
$719$	32.5520	1.21398	0.606992	−	0.794708i	$-0.292376\pi$
$719$	32.5520	1.21398	0.606992	+	0.794708i	$0.292376\pi$
$720$	−0.528375	−0.0196914
$721$	−14.9522	−0.556849
$722$	35.8729	1.33505
$723$	−34.7368	−1.29187
$724$	70.4295	2.61749
$725$	0.817083	0.0303457
$726$	27.0337	1.00332
$727$	19.7964	0.734209	0.367104	−	0.930180i	$-0.380349\pi$
$727$	19.7964	0.734209	0.367104	+	0.930180i	$0.380349\pi$
$728$	29.8789	1.10739
$729$	20.9223	0.774900
$730$	11.5865	0.428836
$731$	−5.19457	−0.192128
$732$	−49.9562	−1.84643
$733$	−25.3827	−0.937533	−0.468766	−	0.883322i	$-0.655301\pi$
$733$	−25.3827	−0.937533	−0.468766	+	0.883322i	$0.655301\pi$
$734$	−18.5987	−0.686492
$735$	−1.96984	−0.0726588
$736$	33.6035	1.23864
$737$	2.72348	0.100321
$738$	10.7379	0.395268
$739$	52.7037	1.93874	0.969368	−	0.245614i	$-0.0789895\pi$
$739$	52.7037	1.93874	0.969368	+	0.245614i	$0.0789895\pi$
$740$	−16.7988	−0.617537
$741$	−7.96484	−0.292596
$742$	−75.1675	−2.75948
$743$	19.7203	0.723468	0.361734	−	0.932281i	$-0.382185\pi$
$743$	19.7203	0.723468	0.361734	+	0.932281i	$0.382185\pi$
$744$	−15.8098	−0.579615
$745$	20.1410	0.737909
$746$	46.6765	1.70895
$747$	−11.4547	−0.419107
$748$	−2.57713	−0.0942291
$749$	45.1179	1.64857
$750$	2.63504	0.0962182
$751$	9.22891	0.336768	0.168384	−	0.985721i	$-0.446145\pi$
$751$	9.22891	0.336768	0.168384	+	0.985721i	$0.446145\pi$
$752$	3.31255	0.120796
$753$	−20.8148	−0.758534
$754$	−7.11430	−0.259087
$755$	−13.4562	−0.489720
$756$	50.3684	1.83188
$757$	27.4807	0.998803	0.499402	−	0.866371i	$-0.333553\pi$
$757$	27.4807	0.998803	0.499402	+	0.866371i	$0.333553\pi$
$758$	34.1115	1.23899
$759$	5.57722	0.202440
$760$	−4.73929	−0.171912
$761$	−2.21139	−0.0801630	−0.0400815	−	0.999196i	$-0.512762\pi$
$761$	−2.21139	−0.0801630	−0.0400815	+	0.999196i	$0.512762\pi$
$762$	4.45218	0.161285
$763$	−9.82138	−0.355558
$764$	−18.8548	−0.682142
$765$	−1.56682	−0.0566486
$766$	−30.5233	−1.10285
$767$	−34.7629	−1.25521
$768$	−16.0937	−0.580733
$769$	−12.0547	−0.434703	−0.217352	−	0.976093i	$-0.569742\pi$
$769$	−12.0547	−0.434703	−0.217352	+	0.976093i	$0.569742\pi$
$770$	−5.76792	−0.207861
$771$	30.8206	1.10998
$772$	−35.6837	−1.28428
$773$	7.61303	0.273822	0.136911	−	0.990583i	$-0.456283\pi$
$773$	7.61303	0.273822	0.136911	+	0.990583i	$0.456283\pi$
$774$	20.6418	0.741956
$775$	5.15664	0.185232
$776$	6.53801	0.234701
$777$	−18.1615	−0.651540
$778$	−12.0172	−0.430839
$779$	−5.11733	−0.183347
$780$	−14.0565	−0.503304
$781$	−10.9842	−0.393047
$782$	12.0200	0.429833
$783$	−4.41090	−0.157633
$784$	−0.542234	−0.0193655
$785$	−2.07178	−0.0739449
$786$	34.2020	1.21994
$787$	25.0020	0.891224	0.445612	−	0.895226i	$-0.352986\pi$
$787$	25.0020	0.891224	0.445612	+	0.895226i	$0.352986\pi$
$788$	67.1331	2.39152
$789$	−34.9637	−1.24474
$790$	−9.93589	−0.353503
$791$	−56.1769	−1.99742
$792$	3.76649	0.133836
$793$	−52.1792	−1.85294
$794$	−44.8920	−1.59316
$795$	13.0060	0.461277
$796$	−24.4678	−0.867239
$797$	4.72578	0.167396	0.0836979	−	0.996491i	$-0.473327\pi$
$797$	4.72578	0.167396	0.0836979	+	0.996491i	$0.473327\pi$
$798$	−13.9310	−0.493154
$799$	9.82289	0.347509
$800$	6.01313	0.212596
$801$	13.5325	0.478146
$802$	2.27234	0.0802390
$803$	4.38833	0.154861
$804$	11.6089	0.409413
$805$	16.4820	0.580915
$806$	−44.8986	−1.58148
$807$	−12.7486	−0.448772
$808$	20.7635	0.730457
$809$	21.7497	0.764680	0.382340	−	0.924022i	$-0.375118\pi$
$809$	21.7497	0.764680	0.382340	+	0.924022i	$0.375118\pi$
$810$	−2.94079	−0.103329
$811$	−28.9632	−1.01703	−0.508517	−	0.861052i	$-0.669806\pi$
$811$	−28.9632	−1.01703	−0.508517	+	0.861052i	$0.669806\pi$
$812$	−7.62366	−0.267538
$813$	16.8043	0.589351
$814$	−10.3849	−0.363989
$815$	19.9378	0.698392
$816$	0.350374	0.0122655
$817$	−9.83720	−0.344160
$818$	−3.11973	−0.109079
$819$	18.7065	0.653659
$820$	−9.03117	−0.315382
$821$	46.1739	1.61148	0.805740	−	0.592269i	$-0.201768\pi$
$821$	46.1739	1.61148	0.805740	+	0.592269i	$0.201768\pi$
$822$	−5.39469	−0.188161
$823$	−54.8322	−1.91133	−0.955665	−	0.294456i	$-0.904862\pi$
$823$	−54.8322	−1.91133	−0.955665	+	0.294456i	$0.904862\pi$
$824$	−13.4036	−0.466938
$825$	0.998008	0.0347462
$826$	−60.8026	−2.11559
$827$	−34.3466	−1.19435	−0.597174	−	0.802112i	$-0.703710\pi$
$827$	−34.3466	−1.19435	−0.597174	+	0.802112i	$0.703710\pi$
$828$	−29.2635	−1.01698
$829$	26.2771	0.912641	0.456320	−	0.889816i	$-0.349167\pi$
$829$	26.2771	0.912641	0.456320	+	0.889816i	$0.349167\pi$
$830$	15.7248	0.545816
$831$	−32.6714	−1.13336
$832$	−49.9098	−1.73031
$833$	−1.60792	−0.0557111
$834$	−17.9272	−0.620768
$835$	19.6461	0.679881
$836$	−4.88043	−0.168793
$837$	−27.8374	−0.962200
$838$	−18.8496	−0.651147
$839$	−27.1719	−0.938078	−0.469039	−	0.883177i	$-0.655400\pi$
$839$	−27.1719	−0.938078	−0.469039	+	0.883177i	$0.655400\pi$
$840$	−9.04246	−0.311995
$841$	−28.3324	−0.976978
$842$	15.6401	0.538993
$843$	−2.61107	−0.0899299
$844$	12.8201	0.441287
$845$	−1.68203	−0.0578637
$846$	−39.0336	−1.34200
$847$	30.2584	1.03969
$848$	3.58014	0.122942
$849$	−27.9934	−0.960732
$850$	2.15090	0.0737752
$851$	29.6751	1.01725
$852$	−46.8204	−1.60404
$853$	45.1506	1.54593	0.772964	−	0.634450i	$-0.218773\pi$
$853$	45.1506	1.54593	0.772964	+	0.634450i	$0.218773\pi$
$854$	−91.2650	−3.12302
$855$	−2.96717	−0.101475
$856$	40.4451	1.38238
$857$	−42.5916	−1.45490	−0.727451	−	0.686160i	$-0.759295\pi$
$857$	−42.5916	−1.45490	−0.727451	+	0.686160i	$0.759295\pi$
$858$	−8.68960	−0.296658
$859$	−22.5821	−0.770493	−0.385246	−	0.922814i	$-0.625883\pi$
$859$	−22.5821	−0.770493	−0.385246	+	0.922814i	$0.625883\pi$
$860$	−17.3609	−0.592002
$861$	−9.76375	−0.332748
$862$	−20.6404	−0.703016
$863$	−21.1328	−0.719369	−0.359685	−	0.933074i	$-0.617116\pi$
$863$	−21.1328	−0.719369	−0.359685	+	0.933074i	$0.617116\pi$
$864$	−32.4610	−1.10435
$865$	15.3964	0.523494
$866$	−48.9088	−1.66199
$867$	−18.6745	−0.634220
$868$	−48.1131	−1.63307
$869$	−3.76316	−0.127657
$870$	2.15305	0.0729952
$871$	12.1255	0.410856
$872$	−8.80420	−0.298148
$873$	4.09330	0.138537
$874$	22.7628	0.769962
$875$	2.94936	0.0997064
$876$	18.7053	0.631994
$877$	−3.80209	−0.128387	−0.0641937	−	0.997937i	$-0.520448\pi$
$877$	−3.80209	−0.128387	−0.0641937	+	0.997937i	$0.520448\pi$
$878$	7.78638	0.262778
$879$	−12.1898	−0.411152
$880$	0.274719	0.00926077
$881$	24.6924	0.831908	0.415954	−	0.909386i	$-0.363448\pi$
$881$	24.6924	0.831908	0.415954	+	0.909386i	$0.363448\pi$
$882$	6.38944	0.215144
$883$	−41.2698	−1.38884	−0.694420	−	0.719570i	$-0.744339\pi$
$883$	−41.2698	−1.38884	−0.694420	+	0.719570i	$0.744339\pi$
$884$	−11.4739	−0.385908
$885$	10.5205	0.353644
$886$	41.9538	1.40946
$887$	−31.4347	−1.05547	−0.527737	−	0.849408i	$-0.676959\pi$
$887$	−31.4347	−1.05547	−0.527737	+	0.849408i	$0.676959\pi$
$888$	−16.2805	−0.546339
$889$	4.98324	0.167133
$890$	−18.5770	−0.622704
$891$	−1.11381	−0.0373140
$892$	79.0217	2.64584
$893$	18.6021	0.622495
$894$	53.0724	1.77501
$895$	3.40342	0.113764
$896$	−51.8260	−1.73138
$897$	24.8308	0.829078
$898$	81.2504	2.71136
$899$	4.21340	0.140525
$900$	−5.23652	−0.174551
$901$	10.6164	0.353683
$902$	−5.58298	−0.185893
$903$	−18.7692	−0.624599
$904$	−50.3587	−1.67491
$905$	−22.2631	−0.740049
$906$	−35.4576	−1.17800
$907$	13.8354	0.459398	0.229699	−	0.973262i	$-0.426226\pi$
$907$	13.8354	0.459398	0.229699	+	0.973262i	$0.426226\pi$
$908$	35.6669	1.18365
$909$	12.9996	0.431168
$910$	−25.6799	−0.851280
$911$	−26.0663	−0.863616	−0.431808	−	0.901966i	$-0.642124\pi$
$911$	−26.0663	−0.863616	−0.431808	+	0.901966i	$0.642124\pi$
$912$	0.663519	0.0219713
$913$	5.95568	0.197104
$914$	−10.3144	−0.341169
$915$	15.7913	0.522046
$916$	70.4791	2.32869
$917$	38.2817	1.26417
$918$	−11.6113	−0.383230
$919$	6.07602	0.200429	0.100215	−	0.994966i	$-0.468047\pi$
$919$	6.07602	0.200429	0.100215	+	0.994966i	$0.468047\pi$
$920$	14.7750	0.487118
$921$	−25.8494	−0.851765
$922$	−60.0525	−1.97772
$923$	−48.9039	−1.60969
$924$	−9.31175	−0.306334
$925$	5.31018	0.174598
$926$	−37.3968	−1.22893
$927$	−8.39172	−0.275620
$928$	4.91323	0.161285
$929$	−45.5392	−1.49409	−0.747046	−	0.664772i	$-0.768529\pi$
$929$	−45.5392	−1.49409	−0.747046	+	0.664772i	$0.768529\pi$
$930$	13.5880	0.445567
$931$	−3.04499	−0.0997955
$932$	−49.6613	−1.62671
$933$	−14.3726	−0.470538
$934$	0.117510	0.00384503
$935$	0.814641	0.0266416
$936$	16.7691	0.548116
$937$	−13.5060	−0.441221	−0.220611	−	0.975362i	$-0.570805\pi$
$937$	−13.5060	−0.441221	−0.220611	+	0.975362i	$0.570805\pi$
$938$	21.2083	0.692474
$939$	1.63291	0.0532879
$940$	32.8294	1.07078
$941$	56.4906	1.84154	0.920770	−	0.390107i	$-0.127562\pi$
$941$	56.4906	1.84154	0.920770	+	0.390107i	$0.127562\pi$
$942$	−5.45922	−0.177871
$943$	15.9536	0.519520
$944$	2.89596	0.0942554
$945$	−15.9217	−0.517932
$946$	−10.7323	−0.348939
$947$	8.51565	0.276721	0.138361	−	0.990382i	$-0.455817\pi$
$947$	8.51565	0.276721	0.138361	+	0.990382i	$0.455817\pi$
$948$	−16.0405	−0.520972
$949$	19.5377	0.634220
$950$	4.07325	0.132154
$951$	16.6849	0.541046
$952$	−7.38106	−0.239222
$953$	−18.5546	−0.601042	−0.300521	−	0.953775i	$-0.597161\pi$
$953$	−18.5546	−0.601042	−0.300521	+	0.953775i	$0.597161\pi$
$954$	−42.1867	−1.36585
$955$	5.96007	0.192863
$956$	−20.4559	−0.661591
$957$	0.815456	0.0263599
$958$	23.7993	0.768919
$959$	−6.03818	−0.194983
$960$	15.1046	0.487497
$961$	−4.40910	−0.142229
$962$	−46.2354	−1.49069
$963$	25.3218	0.815983
$964$	−94.7642	−3.05215
$965$	11.2798	0.363108
$966$	43.4308	1.39736
$967$	−9.12954	−0.293586	−0.146793	−	0.989167i	$-0.546895\pi$
$967$	−9.12954	−0.293586	−0.146793	+	0.989167i	$0.546895\pi$
$968$	27.1245	0.871816
$969$	1.96757	0.0632075
$970$	−5.61919	−0.180421
$971$	−47.4595	−1.52305	−0.761523	−	0.648137i	$-0.775548\pi$
$971$	−47.4595	−1.52305	−0.761523	+	0.648137i	$0.775548\pi$
$972$	46.4857	1.49103
$973$	−20.0656	−0.643273
$974$	38.1187	1.22140
$975$	4.44333	0.142300
$976$	4.34684	0.139139
$977$	−13.5631	−0.433921	−0.216961	−	0.976180i	$-0.569614\pi$
$977$	−13.5631	−0.433921	−0.216961	+	0.976180i	$0.569614\pi$
$978$	52.5370	1.67995
$979$	−7.03595	−0.224870
$980$	−5.37387	−0.171662
$981$	−5.51211	−0.175988
$982$	−28.7421	−0.917198
$983$	−12.3532	−0.394007	−0.197004	−	0.980403i	$-0.563121\pi$
$983$	−12.3532	−0.394007	−0.197004	+	0.980403i	$0.563121\pi$
$984$	−8.75253	−0.279021
$985$	−21.2211	−0.676159
$986$	1.75746	0.0559690
$987$	35.4923	1.12973
$988$	−21.7286	−0.691279
$989$	30.6680	0.975187
$990$	−3.23716	−0.102884
$991$	−17.4033	−0.552833	−0.276416	−	0.961038i	$-0.589147\pi$
$991$	−17.4033	−0.552833	−0.276416	+	0.961038i	$0.589147\pi$
$992$	31.0076	0.984491
$993$	−2.09827	−0.0665866
$994$	−85.5363	−2.71305
$995$	7.73438	0.245196
$996$	25.3862	0.804392
$997$	−8.24130	−0.261005	−0.130502	−	0.991448i	$-0.541659\pi$
$997$	−8.24130	−0.261005	−0.130502	+	0.991448i	$0.541659\pi$
$998$	36.5530	1.15706
$999$	−28.6662	−0.906959

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2005.2.a.e.1.4	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2005.2.a.e.1.4	✓	29	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:	\( N \)	\(=\)	\( 2005 = 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.27234 q^{2} +1.15962 q^{3} +3.16351 q^{4} -1.00000 q^{5} -2.63504 q^{6} -2.94936 q^{7} -2.64390 q^{8} -1.65529 q^{9} +O(q^{10})\)	\(q-2.27234 q^{2} +1.15962 q^{3} +3.16351 q^{4} -1.00000 q^{5} -2.63504 q^{6} -2.94936 q^{7} -2.64390 q^{8} -1.65529 q^{9} +2.27234 q^{10} +0.860635 q^{11} +3.66847 q^{12} +3.83171 q^{13} +6.70193 q^{14} -1.15962 q^{15} -0.319205 q^{16} -0.946558 q^{17} +3.76137 q^{18} -1.79254 q^{19} -3.16351 q^{20} -3.42013 q^{21} -1.95565 q^{22} +5.58835 q^{23} -3.06591 q^{24} +1.00000 q^{25} -8.70695 q^{26} -5.39835 q^{27} -9.33033 q^{28} +0.817083 q^{29} +2.63504 q^{30} +5.15664 q^{31} +6.01313 q^{32} +0.998008 q^{33} +2.15090 q^{34} +2.94936 q^{35} -5.23652 q^{36} +5.31018 q^{37} +4.07325 q^{38} +4.44333 q^{39} +2.64390 q^{40} +2.85479 q^{41} +7.77168 q^{42} +5.48786 q^{43} +2.72263 q^{44} +1.65529 q^{45} -12.6986 q^{46} -10.3775 q^{47} -0.370156 q^{48} +1.69870 q^{49} -2.27234 q^{50} -1.09765 q^{51} +12.1217 q^{52} -11.2158 q^{53} +12.2669 q^{54} -0.860635 q^{55} +7.79779 q^{56} -2.07866 q^{57} -1.85669 q^{58} -9.07241 q^{59} -3.66847 q^{60} -13.6177 q^{61} -11.7176 q^{62} +4.88203 q^{63} -13.0255 q^{64} -3.83171 q^{65} -2.26781 q^{66} +3.16450 q^{67} -2.99445 q^{68} +6.48035 q^{69} -6.70193 q^{70} -12.7629 q^{71} +4.37640 q^{72} +5.09894 q^{73} -12.0665 q^{74} +1.15962 q^{75} -5.67073 q^{76} -2.53832 q^{77} -10.0967 q^{78} -4.37254 q^{79} +0.319205 q^{80} -1.29417 q^{81} -6.48705 q^{82} +6.92010 q^{83} -10.8196 q^{84} +0.946558 q^{85} -12.4703 q^{86} +0.947504 q^{87} -2.27543 q^{88} -8.17530 q^{89} -3.76137 q^{90} -11.3011 q^{91} +17.6788 q^{92} +5.97973 q^{93} +23.5812 q^{94} +1.79254 q^{95} +6.97294 q^{96} -2.47287 q^{97} -3.86002 q^{98} -1.42460 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q - 5 q^{2} - 3 q^{3} + 19 q^{4} - 29 q^{5} - 6 q^{6} + 12 q^{7} - 15 q^{8} + 14 q^{9}+O(q^{10}) \) 29 * q - 5 * q^2 - 3 * q^3 + 19 * q^4 - 29 * q^5 - 6 * q^6 + 12 * q^7 - 15 * q^8 + 14 * q^9	\( 29 q - 5 q^{2} - 3 q^{3} + 19 q^{4} - 29 q^{5} - 6 q^{6} + 12 q^{7} - 15 q^{8} + 14 q^{9} + 5 q^{10} - 38 q^{11} - 6 q^{12} + 5 q^{13} - 18 q^{14} + 3 q^{15} + 7 q^{16} - 16 q^{17} - 2 q^{18} - 18 q^{19} - 19 q^{20} - 20 q^{21} - 2 q^{22} - 19 q^{23} - 19 q^{24} + 29 q^{25} - 21 q^{26} - 21 q^{27} + 26 q^{28} - 31 q^{29} + 6 q^{30} - 13 q^{31} - 30 q^{32} + 2 q^{33} - 14 q^{34} - 12 q^{35} - 29 q^{36} - q^{37} - 23 q^{38} - 39 q^{39} + 15 q^{40} - 24 q^{41} - 20 q^{42} - 27 q^{43} - 76 q^{44} - 14 q^{45} - 11 q^{46} - 5 q^{47} - 2 q^{48} - 11 q^{49} - 5 q^{50} - 58 q^{51} + 11 q^{52} - 37 q^{53} - 18 q^{54} + 38 q^{55} - 50 q^{56} - 6 q^{57} + 31 q^{58} - 67 q^{59} + 6 q^{60} - 31 q^{61} - 19 q^{62} - 2 q^{63} - 13 q^{64} - 5 q^{65} + 6 q^{66} - 17 q^{67} - 16 q^{68} - 48 q^{69} + 18 q^{70} - 53 q^{71} + 9 q^{72} + 29 q^{73} - 59 q^{74} - 3 q^{75} - 21 q^{76} - 62 q^{77} - 12 q^{78} - 13 q^{79} - 7 q^{80} - 11 q^{81} + 32 q^{82} - 72 q^{83} - 58 q^{84} + 16 q^{85} - 43 q^{86} + 4 q^{87} + 12 q^{88} - 38 q^{89} + 2 q^{90} - 45 q^{91} - 37 q^{92} - 27 q^{93} - 44 q^{94} + 18 q^{95} - 21 q^{96} + 32 q^{97} - 32 q^{98} - 107 q^{99}+O(q^{100}) \) 29 * q - 5 * q^2 - 3 * q^3 + 19 * q^4 - 29 * q^5 - 6 * q^6 + 12 * q^7 - 15 * q^8 + 14 * q^9 + 5 * q^10 - 38 * q^11 - 6 * q^12 + 5 * q^13 - 18 * q^14 + 3 * q^15 + 7 * q^16 - 16 * q^17 - 2 * q^18 - 18 * q^19 - 19 * q^20 - 20 * q^21 - 2 * q^22 - 19 * q^23 - 19 * q^24 + 29 * q^25 - 21 * q^26 - 21 * q^27 + 26 * q^28 - 31 * q^29 + 6 * q^30 - 13 * q^31 - 30 * q^32 + 2 * q^33 - 14 * q^34 - 12 * q^35 - 29 * q^36 - q^37 - 23 * q^38 - 39 * q^39 + 15 * q^40 - 24 * q^41 - 20 * q^42 - 27 * q^43 - 76 * q^44 - 14 * q^45 - 11 * q^46 - 5 * q^47 - 2 * q^48 - 11 * q^49 - 5 * q^50 - 58 * q^51 + 11 * q^52 - 37 * q^53 - 18 * q^54 + 38 * q^55 - 50 * q^56 - 6 * q^57 + 31 * q^58 - 67 * q^59 + 6 * q^60 - 31 * q^61 - 19 * q^62 - 2 * q^63 - 13 * q^64 - 5 * q^65 + 6 * q^66 - 17 * q^67 - 16 * q^68 - 48 * q^69 + 18 * q^70 - 53 * q^71 + 9 * q^72 + 29 * q^73 - 59 * q^74 - 3 * q^75 - 21 * q^76 - 62 * q^77 - 12 * q^78 - 13 * q^79 - 7 * q^80 - 11 * q^81 + 32 * q^82 - 72 * q^83 - 58 * q^84 + 16 * q^85 - 43 * q^86 + 4 * q^87 + 12 * q^88 - 38 * q^89 + 2 * q^90 - 45 * q^91 - 37 * q^92 - 27 * q^93 - 44 * q^94 + 18 * q^95 - 21 * q^96 + 32 * q^97 - 32 * q^98 - 107 * q^99

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