LMFDB - Embedded newform 2005.2.a.e.1.5

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			1.5
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)

$f(q)$	$=$	$q-2.13554 q^{2} +1.65605 q^{3} +2.56051 q^{4} -1.00000 q^{5} -3.53655 q^{6} +1.78297 q^{7} -1.19700 q^{8} -0.257503 q^{9} +O(q^{10})$	\(q-2.13554 q^{2} +1.65605 q^{3} +2.56051 q^{4} -1.00000 q^{5} -3.53655 q^{6} +1.78297 q^{7} -1.19700 q^{8} -0.257503 q^{9} +2.13554 q^{10} +1.00071 q^{11} +4.24034 q^{12} +1.91338 q^{13} -3.80759 q^{14} -1.65605 q^{15} -2.56480 q^{16} -4.60179 q^{17} +0.549908 q^{18} +0.868459 q^{19} -2.56051 q^{20} +2.95268 q^{21} -2.13706 q^{22} -9.35511 q^{23} -1.98229 q^{24} +1.00000 q^{25} -4.08609 q^{26} -5.39458 q^{27} +4.56532 q^{28} +0.573206 q^{29} +3.53655 q^{30} -6.48293 q^{31} +7.87121 q^{32} +1.65723 q^{33} +9.82729 q^{34} -1.78297 q^{35} -0.659341 q^{36} -4.65469 q^{37} -1.85463 q^{38} +3.16864 q^{39} +1.19700 q^{40} -4.22593 q^{41} -6.30556 q^{42} +10.6570 q^{43} +2.56234 q^{44} +0.257503 q^{45} +19.9782 q^{46} -6.38777 q^{47} -4.24743 q^{48} -3.82102 q^{49} -2.13554 q^{50} -7.62079 q^{51} +4.89923 q^{52} +6.43867 q^{53} +11.5203 q^{54} -1.00071 q^{55} -2.13421 q^{56} +1.43821 q^{57} -1.22410 q^{58} -5.73012 q^{59} -4.24034 q^{60} +8.80820 q^{61} +13.8445 q^{62} -0.459120 q^{63} -11.6797 q^{64} -1.91338 q^{65} -3.53907 q^{66} -12.9417 q^{67} -11.7830 q^{68} -15.4925 q^{69} +3.80759 q^{70} +7.25429 q^{71} +0.308231 q^{72} +7.85472 q^{73} +9.94026 q^{74} +1.65605 q^{75} +2.22370 q^{76} +1.78424 q^{77} -6.76676 q^{78} -7.28983 q^{79} +2.56480 q^{80} -8.16118 q^{81} +9.02462 q^{82} -10.1305 q^{83} +7.56038 q^{84} +4.60179 q^{85} -22.7583 q^{86} +0.949257 q^{87} -1.19785 q^{88} -2.82714 q^{89} -0.549908 q^{90} +3.41149 q^{91} -23.9539 q^{92} -10.7361 q^{93} +13.6413 q^{94} -0.868459 q^{95} +13.0351 q^{96} -3.96782 q^{97} +8.15993 q^{98} -0.257687 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.13554	−1.51005	−0.755026	−	0.655695i	$-0.772376\pi$
$2$	−2.13554	−1.51005	−0.755026	+	0.655695i	$0.772376\pi$
$3$	1.65605	0.956120	0.478060	−	0.878327i	$-0.341340\pi$
$3$	1.65605	0.956120	0.478060	+	0.878327i	$0.341340\pi$
$4$	2.56051	1.28026
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.53655	−1.44379
$7$	1.78297	0.673899	0.336949	−	0.941523i	$-0.390605\pi$
$7$	1.78297	0.673899	0.336949	+	0.941523i	$0.390605\pi$
$8$	−1.19700	−0.423203
$9$	−0.257503	−0.0858344
$10$	2.13554	0.675316
$11$	1.00071	0.301726	0.150863	−	0.988555i	$-0.451795\pi$
$11$	1.00071	0.301726	0.150863	+	0.988555i	$0.451795\pi$
$12$	4.24034	1.22408
$13$	1.91338	0.530675	0.265338	−	0.964156i	$-0.414517\pi$
$13$	1.91338	0.530675	0.265338	+	0.964156i	$0.414517\pi$
$14$	−3.80759	−1.01762
$15$	−1.65605	−0.427590
$16$	−2.56480	−0.641199
$17$	−4.60179	−1.11610	−0.558049	−	0.829808i	$-0.688450\pi$
$17$	−4.60179	−1.11610	−0.558049	+	0.829808i	$0.688450\pi$
$18$	0.549908	0.129614
$19$	0.868459	0.199238	0.0996191	−	0.995026i	$-0.468238\pi$
$19$	0.868459	0.199238	0.0996191	+	0.995026i	$0.468238\pi$
$20$	−2.56051	−0.572548
$21$	2.95268	0.644328
$22$	−2.13706	−0.455622
$23$	−9.35511	−1.95068	−0.975338	−	0.220718i	$-0.929160\pi$
$23$	−9.35511	−1.95068	−0.975338	+	0.220718i	$0.929160\pi$
$24$	−1.98229	−0.404633
$25$	1.00000	0.200000
$26$	−4.08609	−0.801347
$27$	−5.39458	−1.03819
$28$	4.56532	0.862764
$29$	0.573206	0.106442	0.0532208	−	0.998583i	$-0.483051\pi$
$29$	0.573206	0.106442	0.0532208	+	0.998583i	$0.483051\pi$
$30$	3.53655	0.645683
$31$	−6.48293	−1.16437	−0.582185	−	0.813057i	$-0.697802\pi$
$31$	−6.48293	−1.16437	−0.582185	+	0.813057i	$0.697802\pi$
$32$	7.87121	1.39145
$33$	1.65723	0.288486
$34$	9.82729	1.68537
$35$	−1.78297	−0.301377
$36$	−0.659341	−0.109890
$37$	−4.65469	−0.765227	−0.382613	−	0.923909i	$-0.624976\pi$
$37$	−4.65469	−0.765227	−0.382613	+	0.923909i	$0.624976\pi$
$38$	−1.85463	−0.300860
$39$	3.16864	0.507389
$40$	1.19700	0.189262
$41$	−4.22593	−0.659979	−0.329990	−	0.943985i	$-0.607045\pi$
$41$	−4.22593	−0.659979	−0.329990	+	0.943985i	$0.607045\pi$
$42$	−6.30556	−0.972969
$43$	10.6570	1.62517	0.812585	−	0.582843i	$-0.198060\pi$
$43$	10.6570	1.62517	0.812585	+	0.582843i	$0.198060\pi$
$44$	2.56234	0.386287
$45$	0.257503	0.0383863
$46$	19.9782	2.94562
$47$	−6.38777	−0.931753	−0.465876	−	0.884850i	$-0.654261\pi$
$47$	−6.38777	−0.931753	−0.465876	+	0.884850i	$0.654261\pi$
$48$	−4.24743	−0.613063
$49$	−3.82102	−0.545860
$50$	−2.13554	−0.302010
$51$	−7.62079	−1.06712
$52$	4.89923	0.679401
$53$	6.43867	0.884420	0.442210	−	0.896912i	$-0.354195\pi$
$53$	6.43867	0.884420	0.442210	+	0.896912i	$0.354195\pi$
$54$	11.5203	1.56772
$55$	−1.00071	−0.134936
$56$	−2.13421	−0.285196
$57$	1.43821	0.190496
$58$	−1.22410	−0.160732
$59$	−5.73012	−0.745997	−0.372999	−	0.927832i	$-0.621670\pi$
$59$	−5.73012	−0.745997	−0.372999	+	0.927832i	$0.621670\pi$
$60$	−4.24034	−0.547425
$61$	8.80820	1.12778	0.563888	−	0.825852i	$-0.309305\pi$
$61$	8.80820	1.12778	0.563888	+	0.825852i	$0.309305\pi$
$62$	13.8445	1.75826
$63$	−0.459120	−0.0578437
$64$	−11.6797	−1.45996
$65$	−1.91338	−0.237325
$66$	−3.53907	−0.435630
$67$	−12.9417	−1.58108	−0.790538	−	0.612413i	$-0.790199\pi$
$67$	−12.9417	−1.58108	−0.790538	+	0.612413i	$0.790199\pi$
$68$	−11.7830	−1.42889
$69$	−15.4925	−1.86508
$70$	3.80759	0.455094
$71$	7.25429	0.860926	0.430463	−	0.902608i	$-0.358350\pi$
$71$	7.25429	0.860926	0.430463	+	0.902608i	$0.358350\pi$
$72$	0.308231	0.0363254
$73$	7.85472	0.919325	0.459663	−	0.888094i	$-0.347970\pi$
$73$	7.85472	0.919325	0.459663	+	0.888094i	$0.347970\pi$
$74$	9.94026	1.15553
$75$	1.65605	0.191224
$76$	2.22370	0.255076
$77$	1.78424	0.203333
$78$	−6.76676	−0.766184
$79$	−7.28983	−0.820170	−0.410085	−	0.912047i	$-0.634501\pi$
$79$	−7.28983	−0.820170	−0.410085	+	0.912047i	$0.634501\pi$
$80$	2.56480	0.286753
$81$	−8.16118	−0.906798
$82$	9.02462	0.996603
$83$	−10.1305	−1.11197	−0.555983	−	0.831194i	$-0.687658\pi$
$83$	−10.1305	−1.11197	−0.555983	+	0.831194i	$0.687658\pi$
$84$	7.56038	0.824906
$85$	4.60179	0.499135
$86$	−22.7583	−2.45409
$87$	0.949257	0.101771
$88$	−1.19785	−0.127691
$89$	−2.82714	−0.299676	−0.149838	−	0.988711i	$-0.547875\pi$
$89$	−2.82714	−0.299676	−0.149838	+	0.988711i	$0.547875\pi$
$90$	−0.549908	−0.0579654
$91$	3.41149	0.357621
$92$	−23.9539	−2.49737
$93$	−10.7361	−1.11328
$94$	13.6413	1.40699
$95$	−0.868459	−0.0891020
$96$	13.0351	1.33039
$97$	−3.96782	−0.402871	−0.201436	−	0.979502i	$-0.564561\pi$
$97$	−3.96782	−0.402871	−0.201436	+	0.979502i	$0.564561\pi$
$98$	8.15993	0.824278
$99$	−0.257687	−0.0258985
$100$	2.56051	0.256051
$101$	−18.9612	−1.88671	−0.943353	−	0.331790i	$-0.892348\pi$
$101$	−18.9612	−1.88671	−0.943353	+	0.331790i	$0.892348\pi$
$102$	16.2745	1.61141
$103$	7.04277	0.693945	0.346973	−	0.937875i	$-0.387210\pi$
$103$	7.04277	0.693945	0.346973	+	0.937875i	$0.387210\pi$
$104$	−2.29031	−0.224583
$105$	−2.95268	−0.288152
$106$	−13.7500	−1.33552
$107$	15.7569	1.52328	0.761639	−	0.648001i	$-0.224395\pi$
$107$	15.7569	1.52328	0.761639	+	0.648001i	$0.224395\pi$
$108$	−13.8129	−1.32915
$109$	5.55956	0.532509	0.266255	−	0.963903i	$-0.414214\pi$
$109$	5.55956	0.532509	0.266255	+	0.963903i	$0.414214\pi$
$110$	2.13706	0.203760
$111$	−7.70839	−0.731648
$112$	−4.57295	−0.432103
$113$	−1.53574	−0.144471	−0.0722354	−	0.997388i	$-0.523013\pi$
$113$	−1.53574	−0.144471	−0.0722354	+	0.997388i	$0.523013\pi$
$114$	−3.07135	−0.287658
$115$	9.35511	0.872369
$116$	1.46770	0.136273
$117$	−0.492701	−0.0455502
$118$	12.2369	1.12649
$119$	−8.20485	−0.752138
$120$	1.98229	0.180957
$121$	−9.99857	−0.908961
$122$	−18.8102	−1.70300
$123$	−6.99834	−0.631019
$124$	−16.5996	−1.49069
$125$	−1.00000	−0.0894427
$126$	0.980468	0.0873470
$127$	13.8715	1.23090	0.615449	−	0.788176i	$-0.288975\pi$
$127$	13.8715	1.23090	0.615449	+	0.788176i	$0.288975\pi$
$128$	9.19991	0.813165
$129$	17.6484	1.55386
$130$	4.08609	0.358373
$131$	−11.5512	−1.00923	−0.504617	−	0.863343i	$-0.668366\pi$
$131$	−11.5512	−1.00923	−0.504617	+	0.863343i	$0.668366\pi$
$132$	4.24336	0.369337
$133$	1.54844	0.134266
$134$	27.6374	2.38751
$135$	5.39458	0.464292
$136$	5.50834	0.472336
$137$	6.59073	0.563084	0.281542	−	0.959549i	$-0.409154\pi$
$137$	6.59073	0.563084	0.281542	+	0.959549i	$0.409154\pi$
$138$	33.0848	2.81637
$139$	15.8955	1.34824	0.674119	−	0.738622i	$-0.264523\pi$
$139$	15.8955	1.34824	0.674119	+	0.738622i	$0.264523\pi$
$140$	−4.56532	−0.385840
$141$	−10.5785	−0.890867
$142$	−15.4918	−1.30004
$143$	1.91474	0.160119
$144$	0.660444	0.0550370
$145$	−0.573206	−0.0476022
$146$	−16.7740	−1.38823
$147$	−6.32780	−0.521908
$148$	−11.9184	−0.979687
$149$	2.06629	0.169277	0.0846387	−	0.996412i	$-0.473026\pi$
$149$	2.06629	0.169277	0.0846387	+	0.996412i	$0.473026\pi$
$150$	−3.53655	−0.288758
$151$	−14.7026	−1.19648	−0.598238	−	0.801318i	$-0.704132\pi$
$151$	−14.7026	−1.19648	−0.598238	+	0.801318i	$0.704132\pi$
$152$	−1.03954	−0.0843181
$153$	1.18498	0.0957997
$154$	−3.81031	−0.307043
$155$	6.48293	0.520722
$156$	8.11336	0.649589
$157$	15.4503	1.23307	0.616533	−	0.787329i	$-0.288537\pi$
$157$	15.4503	1.23307	0.616533	+	0.787329i	$0.288537\pi$
$158$	15.5677	1.23850
$159$	10.6628	0.845611
$160$	−7.87121	−0.622274
$161$	−16.6799	−1.31456
$162$	17.4285	1.36931
$163$	−2.72156	−0.213169	−0.106585	−	0.994304i	$-0.533991\pi$
$163$	−2.72156	−0.213169	−0.106585	+	0.994304i	$0.533991\pi$
$164$	−10.8205	−0.844943
$165$	−1.65723	−0.129015
$166$	21.6340	1.67913
$167$	−4.80665	−0.371950	−0.185975	−	0.982555i	$-0.559544\pi$
$167$	−4.80665	−0.371950	−0.185975	+	0.982555i	$0.559544\pi$
$168$	−3.53435	−0.272681
$169$	−9.33899	−0.718384
$170$	−9.82729	−0.753719
$171$	−0.223631	−0.0171015
$172$	27.2873	2.08064
$173$	17.0275	1.29458	0.647289	−	0.762245i	$-0.275903\pi$
$173$	17.0275	1.29458	0.647289	+	0.762245i	$0.275903\pi$
$174$	−2.02717	−0.153679
$175$	1.78297	0.134780
$176$	−2.56662	−0.193467
$177$	−9.48935	−0.713263
$178$	6.03746	0.452527
$179$	−0.829658	−0.0620115	−0.0310058	−	0.999519i	$-0.509871\pi$
$179$	−0.829658	−0.0620115	−0.0310058	+	0.999519i	$0.509871\pi$
$180$	0.659341	0.0491444
$181$	−23.3935	−1.73882	−0.869412	−	0.494088i	$-0.835502\pi$
$181$	−23.3935	−1.73882	−0.869412	+	0.494088i	$0.835502\pi$
$182$	−7.28536	−0.540027
$183$	14.5868	1.07829
$184$	11.1980	0.825531
$185$	4.65469	0.342220
$186$	22.9272	1.68111
$187$	−4.60507	−0.336756
$188$	−16.3560	−1.19288
$189$	−9.61837	−0.699634
$190$	1.85463	0.134549
$191$	−10.1592	−0.735091	−0.367546	−	0.930006i	$-0.619802\pi$
$191$	−10.1592	−0.735091	−0.367546	+	0.930006i	$0.619802\pi$
$192$	−19.3421	−1.39589
$193$	−13.8377	−0.996063	−0.498031	−	0.867159i	$-0.665944\pi$
$193$	−13.8377	−0.996063	−0.498031	+	0.867159i	$0.665944\pi$
$194$	8.47342	0.608356
$195$	−3.16864	−0.226911
$196$	−9.78378	−0.698842
$197$	−7.68767	−0.547724	−0.273862	−	0.961769i	$-0.588301\pi$
$197$	−7.68767	−0.547724	−0.273862	+	0.961769i	$0.588301\pi$
$198$	0.550300	0.0391081
$199$	4.69614	0.332901	0.166450	−	0.986050i	$-0.446769\pi$
$199$	4.69614	0.332901	0.166450	+	0.986050i	$0.446769\pi$
$200$	−1.19700	−0.0846405
$201$	−21.4320	−1.51170
$202$	40.4923	2.84903
$203$	1.02201	0.0717309
$204$	−19.5131	−1.36619
$205$	4.22593	0.295152
$206$	−15.0401	−1.04789
$207$	2.40897	0.167435
$208$	−4.90742	−0.340268
$209$	0.869078	0.0601154
$210$	6.30556	0.435125
$211$	−14.1568	−0.974593	−0.487297	−	0.873237i	$-0.662017\pi$
$211$	−14.1568	−0.974593	−0.487297	+	0.873237i	$0.662017\pi$
$212$	16.4863	1.13228
$213$	12.0135	0.823149
$214$	−33.6495	−2.30023
$215$	−10.6570	−0.726798
$216$	6.45730	0.439364
$217$	−11.5589	−0.784667
$218$	−11.8726	−0.804117
$219$	13.0078	0.878985
$220$	−2.56234	−0.172753
$221$	−8.80496	−0.592286
$222$	16.4616	1.10483
$223$	−13.6100	−0.911391	−0.455696	−	0.890136i	$-0.650609\pi$
$223$	−13.6100	−0.911391	−0.455696	+	0.890136i	$0.650609\pi$
$224$	14.0341	0.937694
$225$	−0.257503	−0.0171669
$226$	3.27964	0.218158
$227$	24.5925	1.63226	0.816131	−	0.577868i	$-0.196115\pi$
$227$	24.5925	1.63226	0.816131	+	0.577868i	$0.196115\pi$
$228$	3.68256	0.243883
$229$	16.3605	1.08113	0.540565	−	0.841302i	$-0.318210\pi$
$229$	16.3605	1.08113	0.540565	+	0.841302i	$0.318210\pi$
$230$	−19.9782	−1.31732
$231$	2.95479	0.194411
$232$	−0.686126	−0.0450464
$233$	−19.6560	−1.28771	−0.643853	−	0.765149i	$-0.722665\pi$
$233$	−19.6560	−1.28771	−0.643853	+	0.765149i	$0.722665\pi$
$234$	1.05218	0.0687832
$235$	6.38777	0.416692
$236$	−14.6720	−0.955068
$237$	−12.0723	−0.784181
$238$	17.5218	1.13577
$239$	−15.1616	−0.980725	−0.490363	−	0.871519i	$-0.663136\pi$
$239$	−15.1616	−0.980725	−0.490363	+	0.871519i	$0.663136\pi$
$240$	4.24743	0.274170
$241$	24.6958	1.59080	0.795398	−	0.606088i	$-0.207262\pi$
$241$	24.6958	1.59080	0.795398	+	0.606088i	$0.207262\pi$
$242$	21.3523	1.37258
$243$	2.66844	0.171180
$244$	22.5535	1.44384
$245$	3.82102	0.244116
$246$	14.9452	0.952872
$247$	1.66169	0.105731
$248$	7.76006	0.492764
$249$	−16.7766	−1.06317
$250$	2.13554	0.135063
$251$	0.822575	0.0519205	0.0259602	−	0.999663i	$-0.491736\pi$
$251$	0.822575	0.0519205	0.0259602	+	0.999663i	$0.491736\pi$
$252$	−1.17558	−0.0740548
$253$	−9.36178	−0.588570
$254$	−29.6231	−1.85872
$255$	7.62079	0.477233
$256$	3.71257	0.232036
$257$	−28.5599	−1.78152	−0.890759	−	0.454477i	$-0.849826\pi$
$257$	−28.5599	−1.78152	−0.890759	+	0.454477i	$0.849826\pi$
$258$	−37.6889	−2.34641
$259$	−8.29917	−0.515685
$260$	−4.89923	−0.303837
$261$	−0.147602	−0.00913636
$262$	24.6680	1.52400
$263$	−7.35112	−0.453290	−0.226645	−	0.973977i	$-0.572776\pi$
$263$	−7.35112	−0.453290	−0.226645	+	0.973977i	$0.572776\pi$
$264$	−1.98370	−0.122088
$265$	−6.43867	−0.395524
$266$	−3.30674	−0.202749
$267$	−4.68188	−0.286527
$268$	−33.1373	−2.02418
$269$	−27.4106	−1.67125	−0.835627	−	0.549298i	$-0.814895\pi$
$269$	−27.4106	−1.67125	−0.835627	+	0.549298i	$0.814895\pi$
$270$	−11.5203	−0.701105
$271$	−25.4480	−1.54586	−0.772929	−	0.634492i	$-0.781209\pi$
$271$	−25.4480	−1.54586	−0.772929	+	0.634492i	$0.781209\pi$
$272$	11.8027	0.715641
$273$	5.64959	0.341929
$274$	−14.0747	−0.850286
$275$	1.00071	0.0603452
$276$	−39.6688	−2.38778
$277$	3.29927	0.198234	0.0991171	−	0.995076i	$-0.468398\pi$
$277$	3.29927	0.198234	0.0991171	+	0.995076i	$0.468398\pi$
$278$	−33.9454	−2.03591
$279$	1.66938	0.0999430
$280$	2.13421	0.127543
$281$	−26.7912	−1.59823	−0.799115	−	0.601179i	$-0.794698\pi$
$281$	−26.7912	−1.59823	−0.799115	+	0.601179i	$0.794698\pi$
$282$	22.5907	1.34526
$283$	8.33197	0.495284	0.247642	−	0.968852i	$-0.420344\pi$
$283$	8.33197	0.495284	0.247642	+	0.968852i	$0.420344\pi$
$284$	18.5747	1.10221
$285$	−1.43821	−0.0851922
$286$	−4.08900	−0.241787
$287$	−7.53470	−0.444759
$288$	−2.02686	−0.119434
$289$	4.17650	0.245676
$290$	1.22410	0.0718817
$291$	−6.57090	−0.385193
$292$	20.1121	1.17697
$293$	25.7049	1.50170	0.750849	−	0.660474i	$-0.229645\pi$
$293$	25.7049	1.50170	0.750849	+	0.660474i	$0.229645\pi$
$294$	13.5132	0.788108
$295$	5.73012	0.333620
$296$	5.57166	0.323846
$297$	−5.39843	−0.313249
$298$	−4.41265	−0.255618
$299$	−17.8999	−1.03518
$300$	4.24034	0.244816
$301$	19.0010	1.09520
$302$	31.3978	1.80674
$303$	−31.4006	−1.80392
$304$	−2.22742	−0.127751
$305$	−8.80820	−0.504356
$306$	−2.53056	−0.144663
$307$	22.1910	1.26651	0.633255	−	0.773944i	$-0.281719\pi$
$307$	22.1910	1.26651	0.633255	+	0.773944i	$0.281719\pi$
$308$	4.56857	0.260318
$309$	11.6632	0.663495
$310$	−13.8445	−0.786317
$311$	−25.1597	−1.42668	−0.713338	−	0.700821i	$-0.752817\pi$
$311$	−25.1597	−1.42668	−0.713338	+	0.700821i	$0.752817\pi$
$312$	−3.79286	−0.214728
$313$	−7.81785	−0.441891	−0.220946	−	0.975286i	$-0.570914\pi$
$313$	−7.81785	−0.441891	−0.220946	+	0.975286i	$0.570914\pi$
$314$	−32.9946	−1.86199
$315$	0.459120	0.0258685
$316$	−18.6657	−1.05003
$317$	−22.0488	−1.23839	−0.619193	−	0.785239i	$-0.712540\pi$
$317$	−22.0488	−1.23839	−0.619193	+	0.785239i	$0.712540\pi$
$318$	−22.7707	−1.27692
$319$	0.573614	0.0321162
$320$	11.6797	0.652913
$321$	26.0942	1.45644
$322$	35.6205	1.98505
$323$	−3.99647	−0.222369
$324$	−20.8968	−1.16093
$325$	1.91338	0.106135
$326$	5.81199	0.321897
$327$	9.20690	0.509143
$328$	5.05843	0.279305
$329$	−11.3892	−0.627907
$330$	3.53907	0.194819
$331$	0.211470	0.0116234	0.00581171	−	0.999983i	$-0.498150\pi$
$331$	0.211470	0.0116234	0.00581171	+	0.999983i	$0.498150\pi$
$332$	−25.9393	−1.42360
$333$	1.19860	0.0656828
$334$	10.2648	0.561663
$335$	12.9417	0.707079
$336$	−7.57303	−0.413143
$337$	−7.37868	−0.401942	−0.200971	−	0.979597i	$-0.564410\pi$
$337$	−7.37868	−0.401942	−0.200971	+	0.979597i	$0.564410\pi$
$338$	19.9437	1.08480
$339$	−2.54327	−0.138131
$340$	11.7830	0.639020
$341$	−6.48755	−0.351321
$342$	0.477572	0.0258241
$343$	−19.2935	−1.04175
$344$	−12.7564	−0.687776
$345$	15.4925	0.834089
$346$	−36.3629	−1.95488
$347$	4.52534	0.242933	0.121467	−	0.992596i	$-0.461240\pi$
$347$	4.52534	0.242933	0.121467	+	0.992596i	$0.461240\pi$
$348$	2.43058	0.130293
$349$	13.4507	0.719997	0.359998	−	0.932953i	$-0.382777\pi$
$349$	13.4507	0.719997	0.359998	+	0.932953i	$0.382777\pi$
$350$	−3.80759	−0.203524
$351$	−10.3219	−0.550941
$352$	7.87682	0.419836
$353$	16.2751	0.866239	0.433119	−	0.901337i	$-0.357413\pi$
$353$	16.2751	0.866239	0.433119	+	0.901337i	$0.357413\pi$
$354$	20.2648	1.07706
$355$	−7.25429	−0.385018
$356$	−7.23894	−0.383663
$357$	−13.5876	−0.719134
$358$	1.77176	0.0936406
$359$	−5.30550	−0.280014	−0.140007	−	0.990151i	$-0.544712\pi$
$359$	−5.30550	−0.280014	−0.140007	+	0.990151i	$0.544712\pi$
$360$	−0.308231	−0.0162452
$361$	−18.2458	−0.960304
$362$	49.9576	2.62572
$363$	−16.5581	−0.869076
$364$	8.73517	0.457847
$365$	−7.85472	−0.411135
$366$	−31.1507	−1.62827
$367$	30.4686	1.59045	0.795225	−	0.606314i	$-0.207353\pi$
$367$	30.4686	1.59045	0.795225	+	0.606314i	$0.207353\pi$
$368$	23.9940	1.25077
$369$	1.08819	0.0566489
$370$	−9.94026	−0.516770
$371$	11.4799	0.596009
$372$	−27.4898	−1.42528
$373$	−5.69523	−0.294888	−0.147444	−	0.989070i	$-0.547105\pi$
$373$	−5.69523	−0.294888	−0.147444	+	0.989070i	$0.547105\pi$
$374$	9.83430	0.508519
$375$	−1.65605	−0.0855180
$376$	7.64615	0.394320
$377$	1.09676	0.0564860
$378$	20.5404	1.05648
$379$	30.8200	1.58311	0.791557	−	0.611095i	$-0.209271\pi$
$379$	30.8200	1.58311	0.791557	+	0.611095i	$0.209271\pi$
$380$	−2.22370	−0.114073
$381$	22.9719	1.17689
$382$	21.6953	1.11003
$383$	28.9052	1.47699	0.738493	−	0.674262i	$-0.235538\pi$
$383$	28.9052	1.47699	0.738493	+	0.674262i	$0.235538\pi$
$384$	15.2355	0.777484
$385$	−1.78424	−0.0909333
$386$	29.5510	1.50411
$387$	−2.74420	−0.139496
$388$	−10.1597	−0.515779
$389$	15.8695	0.804613	0.402307	−	0.915505i	$-0.368209\pi$
$389$	15.8695	0.804613	0.402307	+	0.915505i	$0.368209\pi$
$390$	6.76676	0.342648
$391$	43.0503	2.17715
$392$	4.57376	0.231010
$393$	−19.1294	−0.964949
$394$	16.4173	0.827092
$395$	7.28983	0.366791
$396$	−0.659811	−0.0331567
$397$	−4.54593	−0.228154	−0.114077	−	0.993472i	$-0.536391\pi$
$397$	−4.54593	−0.228154	−0.114077	+	0.993472i	$0.536391\pi$
$398$	−10.0288	−0.502697
$399$	2.56428	0.128375
$400$	−2.56480	−0.128240
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	45.7689	2.28274
$403$	−12.4043	−0.617902
$404$	−48.5503	−2.41547
$405$	8.16118	0.405532
$406$	−2.18253	−0.108317
$407$	−4.65801	−0.230889
$408$	9.12207	0.451610
$409$	−12.3482	−0.610581	−0.305290	−	0.952259i	$-0.598754\pi$
$409$	−12.3482	−0.610581	−0.305290	+	0.952259i	$0.598754\pi$
$410$	−9.02462	−0.445694
$411$	10.9146	0.538376
$412$	18.0331	0.888428
$413$	−10.2166	−0.502727
$414$	−5.14445	−0.252836
$415$	10.1305	0.497287
$416$	15.0606	0.738406
$417$	26.3237	1.28908
$418$	−1.85595	−0.0907773
$419$	30.0915	1.47007	0.735033	−	0.678032i	$-0.237167\pi$
$419$	30.0915	1.47007	0.735033	+	0.678032i	$0.237167\pi$
$420$	−7.56038	−0.368909
$421$	24.7457	1.20603	0.603016	−	0.797729i	$-0.293966\pi$
$421$	24.7457	1.20603	0.603016	+	0.797729i	$0.293966\pi$
$422$	30.2323	1.47169
$423$	1.64487	0.0799765
$424$	−7.70708	−0.374289
$425$	−4.60179	−0.223220
$426$	−25.6552	−1.24300
$427$	15.7048	0.760006
$428$	40.3458	1.95019
$429$	3.17090	0.153093
$430$	22.7583	1.09750
$431$	35.6067	1.71511	0.857557	−	0.514390i	$-0.171981\pi$
$431$	35.6067	1.71511	0.857557	+	0.514390i	$0.171981\pi$
$432$	13.8360	0.665685
$433$	−19.4466	−0.934542	−0.467271	−	0.884114i	$-0.654763\pi$
$433$	−19.4466	−0.934542	−0.467271	+	0.884114i	$0.654763\pi$
$434$	24.6844	1.18489
$435$	−0.949257	−0.0455134
$436$	14.2353	0.681749
$437$	−8.12453	−0.388649
$438$	−27.7786	−1.32731
$439$	−3.13800	−0.149769	−0.0748843	−	0.997192i	$-0.523859\pi$
$439$	−3.13800	−0.149769	−0.0748843	+	0.997192i	$0.523859\pi$
$440$	1.19785	0.0571053
$441$	0.983926	0.0468536
$442$	18.8033	0.894383
$443$	8.48089	0.402939	0.201470	−	0.979495i	$-0.435428\pi$
$443$	8.48089	0.402939	0.201470	+	0.979495i	$0.435428\pi$
$444$	−19.7375	−0.936698
$445$	2.82714	0.134019
$446$	29.0646	1.37625
$447$	3.42188	0.161850
$448$	−20.8245	−0.983864
$449$	24.0739	1.13612	0.568059	−	0.822988i	$-0.307695\pi$
$449$	24.0739	1.13612	0.568059	+	0.822988i	$0.307695\pi$
$450$	0.549908	0.0259229
$451$	−4.22894	−0.199133
$452$	−3.93230	−0.184960
$453$	−24.3481	−1.14398
$454$	−52.5182	−2.46480
$455$	−3.41149	−0.159933
$456$	−1.72153	−0.0806182
$457$	−11.5587	−0.540691	−0.270345	−	0.962763i	$-0.587138\pi$
$457$	−11.5587	−0.540691	−0.270345	+	0.962763i	$0.587138\pi$
$458$	−34.9384	−1.63256
$459$	24.8248	1.15872
$460$	23.9539	1.11686
$461$	33.6030	1.56505	0.782523	−	0.622621i	$-0.213932\pi$
$461$	33.6030	1.56505	0.782523	+	0.622621i	$0.213932\pi$
$462$	−6.31005	−0.293570
$463$	−1.56284	−0.0726314	−0.0363157	−	0.999340i	$-0.511562\pi$
$463$	−1.56284	−0.0726314	−0.0363157	+	0.999340i	$0.511562\pi$
$464$	−1.47016	−0.0682503
$465$	10.7361	0.497873
$466$	41.9761	1.94450
$467$	−26.3787	−1.22066	−0.610330	−	0.792147i	$-0.708963\pi$
$467$	−26.3787	−1.22066	−0.610330	+	0.792147i	$0.708963\pi$
$468$	−1.26157	−0.0583160
$469$	−23.0746	−1.06549
$470$	−13.6413	−0.629227
$471$	25.5864	1.17896
$472$	6.85894	0.315708
$473$	10.6645	0.490356
$474$	25.7809	1.18415
$475$	0.868459	0.0398476
$476$	−21.0086	−0.962929
$477$	−1.65798	−0.0759137
$478$	32.3782	1.48095
$479$	−32.6834	−1.49334	−0.746671	−	0.665194i	$-0.768349\pi$
$479$	−32.6834	−1.49334	−0.746671	+	0.665194i	$0.768349\pi$
$480$	−13.0351	−0.594968
$481$	−8.90618	−0.406087
$482$	−52.7388	−2.40218
$483$	−27.6227	−1.25688
$484$	−25.6015	−1.16370
$485$	3.96782	0.180169
$486$	−5.69854	−0.258491
$487$	−4.35294	−0.197251	−0.0986253	−	0.995125i	$-0.531445\pi$
$487$	−4.35294	−0.197251	−0.0986253	+	0.995125i	$0.531445\pi$
$488$	−10.5434	−0.477277
$489$	−4.50704	−0.203815
$490$	−8.15993	−0.368628
$491$	−10.2459	−0.462391	−0.231196	−	0.972907i	$-0.574264\pi$
$491$	−10.2459	−0.462391	−0.231196	+	0.972907i	$0.574264\pi$
$492$	−17.9194	−0.807867
$493$	−2.63777	−0.118799
$494$	−3.54860	−0.159659
$495$	0.257687	0.0115822
$496$	16.6274	0.746593
$497$	12.9342	0.580177
$498$	35.8270	1.60545
$499$	−9.72479	−0.435341	−0.217671	−	0.976022i	$-0.569846\pi$
$499$	−9.72479	−0.435341	−0.217671	+	0.976022i	$0.569846\pi$
$500$	−2.56051	−0.114510
$501$	−7.96004	−0.355628
$502$	−1.75664	−0.0784026
$503$	−4.00136	−0.178412	−0.0892060	−	0.996013i	$-0.528433\pi$
$503$	−4.00136	−0.178412	−0.0892060	+	0.996013i	$0.528433\pi$
$504$	0.549566	0.0244796
$505$	18.9612	0.843761
$506$	19.9924	0.888771
$507$	−15.4658	−0.686861
$508$	35.5182	1.57587
$509$	−1.67537	−0.0742596	−0.0371298	−	0.999310i	$-0.511822\pi$
$509$	−1.67537	−0.0742596	−0.0371298	+	0.999310i	$0.511822\pi$
$510$	−16.2745	−0.720646
$511$	14.0047	0.619532
$512$	−26.3282	−1.16355
$513$	−4.68497	−0.206847
$514$	60.9907	2.69018
$515$	−7.04277	−0.310342
$516$	45.1891	1.98934
$517$	−6.39233	−0.281134
$518$	17.7232	0.778712
$519$	28.1984	1.23777
$520$	2.29031	0.100437
$521$	−18.2565	−0.799832	−0.399916	−	0.916552i	$-0.630961\pi$
$521$	−18.2565	−0.799832	−0.399916	+	0.916552i	$0.630961\pi$
$522$	0.315210	0.0137964
$523$	29.2377	1.27848	0.639238	−	0.769009i	$-0.279250\pi$
$523$	29.2377	1.27848	0.639238	+	0.769009i	$0.279250\pi$
$524$	−29.5770	−1.29208
$525$	2.95268	0.128866
$526$	15.6986	0.684491
$527$	29.8331	1.29955
$528$	−4.25045	−0.184977
$529$	64.5181	2.80514
$530$	13.7500	0.597262
$531$	1.47552	0.0640323
$532$	3.96479	0.171895
$533$	−8.08579	−0.350235
$534$	9.99833	0.432670
$535$	−15.7569	−0.681231
$536$	15.4912	0.669116
$537$	−1.37395	−0.0592905
$538$	58.5363	2.52368
$539$	−3.82375	−0.164700
$540$	13.8129	0.594413
$541$	9.72787	0.418234	0.209117	−	0.977891i	$-0.432941\pi$
$541$	9.72787	0.418234	0.209117	+	0.977891i	$0.432941\pi$
$542$	54.3452	2.33433
$543$	−38.7408	−1.66252
$544$	−36.2217	−1.55299
$545$	−5.55956	−0.238145
$546$	−12.0649	−0.516331
$547$	−9.38469	−0.401260	−0.200630	−	0.979667i	$-0.564299\pi$
$547$	−9.38469	−0.401260	−0.200630	+	0.979667i	$0.564299\pi$
$548$	16.8756	0.720892
$549$	−2.26814	−0.0968019
$550$	−2.13706	−0.0911245
$551$	0.497806	0.0212072
$552$	18.5445	0.789307
$553$	−12.9975	−0.552712
$554$	−7.04572	−0.299344
$555$	7.70839	0.327203
$556$	40.7006	1.72609
$557$	39.7243	1.68317	0.841586	−	0.540123i	$-0.181622\pi$
$557$	39.7243	1.68317	0.841586	+	0.540123i	$0.181622\pi$
$558$	−3.56502	−0.150919
$559$	20.3908	0.862438
$560$	4.57295	0.193242
$561$	−7.62622	−0.321979
$562$	57.2136	2.41341
$563$	44.7505	1.88601	0.943005	−	0.332779i	$-0.107986\pi$
$563$	44.7505	1.88601	0.943005	+	0.332779i	$0.107986\pi$
$564$	−27.0863	−1.14054
$565$	1.53574	0.0646093
$566$	−17.7932	−0.747905
$567$	−14.5511	−0.611090
$568$	−8.68337	−0.364346
$569$	−33.3122	−1.39652	−0.698260	−	0.715844i	$-0.746042\pi$
$569$	−33.3122	−1.39652	−0.698260	+	0.715844i	$0.746042\pi$
$570$	3.07135	0.128645
$571$	5.45663	0.228353	0.114176	−	0.993461i	$-0.463577\pi$
$571$	5.45663	0.228353	0.114176	+	0.993461i	$0.463577\pi$
$572$	4.90272	0.204993
$573$	−16.8241	−0.702835
$574$	16.0906	0.671609
$575$	−9.35511	−0.390135
$576$	3.00755	0.125315
$577$	−6.71861	−0.279700	−0.139850	−	0.990173i	$-0.544662\pi$
$577$	−6.71861	−0.279700	−0.139850	+	0.990173i	$0.544662\pi$
$578$	−8.91907	−0.370984
$579$	−22.9160	−0.952356
$580$	−1.46770	−0.0609430
$581$	−18.0624	−0.749353
$582$	14.0324	0.581662
$583$	6.44326	0.266853
$584$	−9.40208	−0.389061
$585$	0.492701	0.0203707
$586$	−54.8938	−2.26764
$587$	1.89313	0.0781379	0.0390690	−	0.999237i	$-0.487561\pi$
$587$	1.89313	0.0781379	0.0390690	+	0.999237i	$0.487561\pi$
$588$	−16.2024	−0.668176
$589$	−5.63016	−0.231987
$590$	−12.2369	−0.503784
$591$	−12.7312	−0.523690
$592$	11.9383	0.490663
$593$	3.87384	0.159079	0.0795397	−	0.996832i	$-0.474655\pi$
$593$	3.87384	0.159079	0.0795397	+	0.996832i	$0.474655\pi$
$594$	11.5285	0.473022
$595$	8.20485	0.336366
$596$	5.29078	0.216719
$597$	7.77704	0.318293
$598$	38.2258	1.56317
$599$	24.0467	0.982522	0.491261	−	0.871012i	$-0.336536\pi$
$599$	24.0467	0.982522	0.491261	+	0.871012i	$0.336536\pi$
$600$	−1.98229	−0.0809265
$601$	35.1547	1.43399	0.716994	−	0.697079i	$-0.245517\pi$
$601$	35.1547	1.43399	0.716994	+	0.697079i	$0.245517\pi$
$602$	−40.5773	−1.65381
$603$	3.33252	0.135711
$604$	−37.6461	−1.53180
$605$	9.99857	0.406500
$606$	67.0571	2.72401
$607$	−27.9591	−1.13483	−0.567413	−	0.823434i	$-0.692056\pi$
$607$	−27.9591	−1.13483	−0.567413	+	0.823434i	$0.692056\pi$
$608$	6.83582	0.277229
$609$	1.69249	0.0685834
$610$	18.8102	0.761604
$611$	−12.2222	−0.494458
$612$	3.03415	0.122648
$613$	17.4201	0.703590	0.351795	−	0.936077i	$-0.385571\pi$
$613$	17.4201	0.703590	0.351795	+	0.936077i	$0.385571\pi$
$614$	−47.3898	−1.91249
$615$	6.99834	0.282200
$616$	−2.13573	−0.0860510
$617$	21.0314	0.846692	0.423346	−	0.905968i	$-0.360856\pi$
$617$	21.0314	0.846692	0.423346	+	0.905968i	$0.360856\pi$
$618$	−24.9071	−1.00191
$619$	17.4931	0.703109	0.351554	−	0.936167i	$-0.385653\pi$
$619$	17.4931	0.703109	0.351554	+	0.936167i	$0.385653\pi$
$620$	16.5996	0.666658
$621$	50.4669	2.02517
$622$	53.7294	2.15435
$623$	−5.04071	−0.201952
$624$	−8.12693	−0.325337
$625$	1.00000	0.0400000
$626$	16.6953	0.667279
$627$	1.43924	0.0574775
$628$	39.5606	1.57864
$629$	21.4199	0.854068
$630$	−0.980468	−0.0390628
$631$	−6.04328	−0.240579	−0.120290	−	0.992739i	$-0.538382\pi$
$631$	−6.04328	−0.240579	−0.120290	+	0.992739i	$0.538382\pi$
$632$	8.72591	0.347098
$633$	−23.4443	−0.931828
$634$	47.0861	1.87003
$635$	−13.8715	−0.550475
$636$	27.3021	1.08260
$637$	−7.31106	−0.289675
$638$	−1.22497	−0.0484972
$639$	−1.86800	−0.0738971
$640$	−9.19991	−0.363659
$641$	−21.4089	−0.845599	−0.422800	−	0.906223i	$-0.638953\pi$
$641$	−21.4089	−0.845599	−0.422800	+	0.906223i	$0.638953\pi$
$642$	−55.7251	−2.19930
$643$	−33.9267	−1.33794	−0.668970	−	0.743290i	$-0.733264\pi$
$643$	−33.9267	−1.33794	−0.668970	+	0.743290i	$0.733264\pi$
$644$	−42.7090	−1.68297
$645$	−17.6484	−0.694906
$646$	8.53460	0.335789
$647$	19.5804	0.769787	0.384893	−	0.922961i	$-0.374238\pi$
$647$	19.5804	0.769787	0.384893	+	0.922961i	$0.374238\pi$
$648$	9.76892	0.383759
$649$	−5.73420	−0.225087
$650$	−4.08609	−0.160269
$651$	−19.1420	−0.750236
$652$	−6.96860	−0.272911
$653$	43.9049	1.71813	0.859066	−	0.511866i	$-0.171045\pi$
$653$	43.9049	1.71813	0.859066	+	0.511866i	$0.171045\pi$
$654$	−19.6617	−0.768832
$655$	11.5512	0.451343
$656$	10.8386	0.423178
$657$	−2.02262	−0.0789098
$658$	24.3220	0.948172
$659$	−22.5726	−0.879304	−0.439652	−	0.898168i	$-0.644898\pi$
$659$	−22.5726	−0.879304	−0.439652	+	0.898168i	$0.644898\pi$
$660$	−4.24336	−0.165172
$661$	49.6148	1.92979	0.964896	−	0.262633i	$-0.0845908\pi$
$661$	49.6148	1.92979	0.964896	+	0.262633i	$0.0845908\pi$
$662$	−0.451601	−0.0175520
$663$	−14.5814	−0.566297
$664$	12.1262	0.470587
$665$	−1.54844	−0.0600457
$666$	−2.55965	−0.0991844
$667$	−5.36240	−0.207633
$668$	−12.3075	−0.476191
$669$	−22.5388	−0.871400
$670$	−27.6374	−1.06773
$671$	8.81448	0.340279
$672$	23.2412	0.896548
$673$	−20.1990	−0.778613	−0.389307	−	0.921108i	$-0.627285\pi$
$673$	−20.1990	−0.778613	−0.389307	+	0.921108i	$0.627285\pi$
$674$	15.7574	0.606953
$675$	−5.39458	−0.207638
$676$	−23.9126	−0.919716
$677$	−10.9607	−0.421255	−0.210627	−	0.977566i	$-0.567551\pi$
$677$	−10.9607	−0.421255	−0.210627	+	0.977566i	$0.567551\pi$
$678$	5.43124	0.208586
$679$	−7.07450	−0.271494
$680$	−5.50834	−0.211235
$681$	40.7264	1.56064
$682$	13.8544	0.530513
$683$	−13.6483	−0.522237	−0.261119	−	0.965307i	$-0.584091\pi$
$683$	−13.6483	−0.522237	−0.261119	+	0.965307i	$0.584091\pi$
$684$	−0.572611	−0.0218943
$685$	−6.59073	−0.251819
$686$	41.2021	1.57310
$687$	27.0937	1.03369
$688$	−27.3329	−1.04206
$689$	12.3196	0.469340
$690$	−33.0848	−1.25952
$691$	−32.0386	−1.21881	−0.609403	−	0.792861i	$-0.708591\pi$
$691$	−32.0386	−1.21881	−0.609403	+	0.792861i	$0.708591\pi$
$692$	43.5992	1.65739
$693$	−0.459448	−0.0174530
$694$	−9.66403	−0.366842
$695$	−15.8955	−0.602951
$696$	−1.13626	−0.0430698
$697$	19.4468	0.736602
$698$	−28.7244	−1.08723
$699$	−32.5513	−1.23120
$700$	4.56532	0.172553
$701$	40.2285	1.51941	0.759705	−	0.650268i	$-0.225343\pi$
$701$	40.2285	1.51941	0.759705	+	0.650268i	$0.225343\pi$
$702$	22.0427	0.831949
$703$	−4.04241	−0.152462
$704$	−11.6880	−0.440507
$705$	10.5785	0.398408
$706$	−34.7562	−1.30807
$707$	−33.8072	−1.27145
$708$	−24.2976	−0.913160
$709$	−15.5990	−0.585832	−0.292916	−	0.956138i	$-0.594626\pi$
$709$	−15.5990	−0.585832	−0.292916	+	0.956138i	$0.594626\pi$
$710$	15.4918	0.581397
$711$	1.87716	0.0703989
$712$	3.38408	0.126824
$713$	60.6486	2.27131
$714$	29.0169	1.08593
$715$	−1.91474	−0.0716072
$716$	−2.12435	−0.0793907
$717$	−25.1084	−0.937691
$718$	11.3301	0.422835
$719$	−26.2068	−0.977348	−0.488674	−	0.872466i	$-0.662519\pi$
$719$	−26.2068	−0.977348	−0.488674	+	0.872466i	$0.662519\pi$
$720$	−0.660444	−0.0246133
$721$	12.5570	0.467649
$722$	38.9645	1.45011
$723$	40.8974	1.52099
$724$	−59.8994	−2.22614
$725$	0.573206	0.0212883
$726$	35.3605	1.31235
$727$	12.7206	0.471782	0.235891	−	0.971780i	$-0.424199\pi$
$727$	12.7206	0.471782	0.235891	+	0.971780i	$0.424199\pi$
$728$	−4.08355	−0.151346
$729$	28.9026	1.07047
$730$	16.7740	0.620835
$731$	−49.0411	−1.81385
$732$	37.3497	1.38049
$733$	27.4989	1.01569	0.507847	−	0.861447i	$-0.330442\pi$
$733$	27.4989	1.01569	0.507847	+	0.861447i	$0.330442\pi$
$734$	−65.0669	−2.40166
$735$	6.32780	0.233404
$736$	−73.6360	−2.71426
$737$	−12.9509	−0.477052
$738$	−2.32387	−0.0855428
$739$	11.5420	0.424578	0.212289	−	0.977207i	$-0.431908\pi$
$739$	11.5420	0.424578	0.212289	+	0.977207i	$0.431908\pi$
$740$	11.9184	0.438129
$741$	2.75184	0.101091
$742$	−24.5158	−0.900005
$743$	−6.25111	−0.229331	−0.114666	−	0.993404i	$-0.536580\pi$
$743$	−6.25111	−0.229331	−0.114666	+	0.993404i	$0.536580\pi$
$744$	12.8510	0.471142
$745$	−2.06629	−0.0757032
$746$	12.1624	0.445296
$747$	2.60864	0.0954450
$748$	−11.7914	−0.431135
$749$	28.0941	1.02654
$750$	3.53655	0.129137
$751$	−36.4139	−1.32876	−0.664381	−	0.747394i	$-0.731305\pi$
$751$	−36.4139	−1.32876	−0.664381	+	0.747394i	$0.731305\pi$
$752$	16.3833	0.597439
$753$	1.36222	0.0496422
$754$	−2.34217	−0.0852967
$755$	14.7026	0.535081
$756$	−24.6280	−0.895711
$757$	7.56275	0.274873	0.137436	−	0.990511i	$-0.456114\pi$
$757$	7.56275	0.274873	0.137436	+	0.990511i	$0.456114\pi$
$758$	−65.8171	−2.39059
$759$	−15.5036	−0.562744
$760$	1.03954	0.0377082
$761$	−46.0510	−1.66935	−0.834673	−	0.550745i	$-0.814344\pi$
$761$	−46.0510	−1.66935	−0.834673	+	0.550745i	$0.814344\pi$
$762$	−49.0574	−1.77716
$763$	9.91252	0.358857
$764$	−26.0127	−0.941106
$765$	−1.18498	−0.0428429
$766$	−61.7280	−2.23032
$767$	−10.9639	−0.395882
$768$	6.14820	0.221854
$769$	−27.5224	−0.992482	−0.496241	−	0.868185i	$-0.665287\pi$
$769$	−27.5224	−0.992482	−0.496241	+	0.868185i	$0.665287\pi$
$770$	3.81031	0.137314
$771$	−47.2966	−1.70334
$772$	−35.4317	−1.27522
$773$	28.9256	1.04038	0.520191	−	0.854050i	$-0.325861\pi$
$773$	28.9256	1.04038	0.520191	+	0.854050i	$0.325861\pi$
$774$	5.86034	0.210646
$775$	−6.48293	−0.232874
$776$	4.74947	0.170496
$777$	−13.7438	−0.493057
$778$	−33.8898	−1.21501
$779$	−3.67005	−0.131493
$780$	−8.11336	−0.290505
$781$	7.25946	0.259764
$782$	−91.9354	−3.28760
$783$	−3.09221	−0.110506
$784$	9.80014	0.350005
$785$	−15.4503	−0.551444
$786$	40.8514	1.45712
$787$	10.9460	0.390183	0.195092	−	0.980785i	$-0.437500\pi$
$787$	10.9460	0.390183	0.195092	+	0.980785i	$0.437500\pi$
$788$	−19.6844	−0.701227
$789$	−12.1738	−0.433399
$790$	−15.5677	−0.553874
$791$	−2.73818	−0.0973586
$792$	0.308451	0.0109603
$793$	16.8534	0.598482
$794$	9.70799	0.344524
$795$	−10.6628	−0.378169
$796$	12.0245	0.426199
$797$	−42.5034	−1.50555	−0.752774	−	0.658279i	$-0.771285\pi$
$797$	−42.5034	−1.50555	−0.752774	+	0.658279i	$0.771285\pi$
$798$	−5.47612	−0.193853
$799$	29.3952	1.03993
$800$	7.87121	0.278289
$801$	0.727998	0.0257226
$802$	2.13554	0.0754084
$803$	7.86032	0.277385
$804$	−54.8770	−1.93536
$805$	16.6799	0.587888
$806$	26.4898	0.933064
$807$	−45.3933	−1.59792
$808$	22.6965	0.798459
$809$	31.0752	1.09255	0.546273	−	0.837607i	$-0.316046\pi$
$809$	31.0752	1.09255	0.546273	+	0.837607i	$0.316046\pi$
$810$	−17.4285	−0.612375
$811$	−51.0929	−1.79411	−0.897056	−	0.441916i	$-0.854299\pi$
$811$	−51.0929	−1.79411	−0.897056	+	0.441916i	$0.854299\pi$
$812$	2.61687	0.0918340
$813$	−42.1432	−1.47803
$814$	9.94735	0.348654
$815$	2.72156	0.0953322
$816$	19.5458	0.684239
$817$	9.25513	0.323796
$818$	26.3701	0.922009
$819$	−0.878470	−0.0306962
$820$	10.8205	0.377870
$821$	31.9177	1.11393	0.556967	−	0.830534i	$-0.311965\pi$
$821$	31.9177	1.11393	0.556967	+	0.830534i	$0.311965\pi$
$822$	−23.3084	−0.812975
$823$	9.40183	0.327727	0.163864	−	0.986483i	$-0.447604\pi$
$823$	9.40183	0.327727	0.163864	+	0.986483i	$0.447604\pi$
$824$	−8.43018	−0.293679
$825$	1.65723	0.0576973
$826$	21.8180	0.759144
$827$	33.4637	1.16365	0.581824	−	0.813315i	$-0.302339\pi$
$827$	33.4637	1.16365	0.581824	+	0.813315i	$0.302339\pi$
$828$	6.16821	0.214360
$829$	−15.1959	−0.527774	−0.263887	−	0.964554i	$-0.585005\pi$
$829$	−15.1959	−0.527774	−0.263887	+	0.964554i	$0.585005\pi$
$830$	−21.6340	−0.750928
$831$	5.46376	0.189536
$832$	−22.3476	−0.774763
$833$	17.5836	0.609234
$834$	−56.2152	−1.94657
$835$	4.80665	0.166341
$836$	2.22529	0.0769631
$837$	34.9727	1.20883
$838$	−64.2614	−2.21987
$839$	14.8572	0.512929	0.256464	−	0.966554i	$-0.417442\pi$
$839$	14.8572	0.512929	0.256464	+	0.966554i	$0.417442\pi$
$840$	3.53435	0.121947
$841$	−28.6714	−0.988670
$842$	−52.8453	−1.82117
$843$	−44.3675	−1.52810
$844$	−36.2486	−1.24773
$845$	9.33899	0.321271
$846$	−3.51269	−0.120769
$847$	−17.8271	−0.612548
$848$	−16.5139	−0.567089
$849$	13.7982	0.473551
$850$	9.82729	0.337073
$851$	43.5452	1.49271
$852$	30.7606	1.05384
$853$	14.0449	0.480890	0.240445	−	0.970663i	$-0.422707\pi$
$853$	14.0449	0.480890	0.240445	+	0.970663i	$0.422707\pi$
$854$	−33.5381	−1.14765
$855$	0.223631	0.00764802
$856$	−18.8610	−0.644655
$857$	32.4539	1.10860	0.554302	−	0.832315i	$-0.312985\pi$
$857$	32.4539	1.10860	0.554302	+	0.832315i	$0.312985\pi$
$858$	−6.77158	−0.231178
$859$	−18.0469	−0.615751	−0.307875	−	0.951427i	$-0.599618\pi$
$859$	−18.0469	−0.615751	−0.307875	+	0.951427i	$0.599618\pi$
$860$	−27.2873	−0.930488
$861$	−12.4778	−0.425243
$862$	−76.0393	−2.58991
$863$	29.7904	1.01408	0.507039	−	0.861923i	$-0.330740\pi$
$863$	29.7904	1.01408	0.507039	+	0.861923i	$0.330740\pi$
$864$	−42.4619	−1.44458
$865$	−17.0275	−0.578953
$866$	41.5288	1.41121
$867$	6.91649	0.234896
$868$	−29.5966	−1.00458
$869$	−7.29503	−0.247467
$870$	2.02717	0.0687276
$871$	−24.7623	−0.839038
$872$	−6.65478	−0.225359
$873$	1.02173	0.0345802
$874$	17.3502	0.586880
$875$	−1.78297	−0.0602753
$876$	33.3066	1.12533
$877$	−45.3964	−1.53293	−0.766463	−	0.642288i	$-0.777985\pi$
$877$	−45.3964	−1.53293	−0.766463	+	0.642288i	$0.777985\pi$
$878$	6.70132	0.226158
$879$	42.5686	1.43580
$880$	2.56662	0.0865209
$881$	−35.6740	−1.20189	−0.600944	−	0.799291i	$-0.705208\pi$
$881$	−35.6740	−1.20189	−0.600944	+	0.799291i	$0.705208\pi$
$882$	−2.10121	−0.0707514
$883$	53.0650	1.78578	0.892889	−	0.450276i	$-0.148675\pi$
$883$	53.0650	1.78578	0.892889	+	0.450276i	$0.148675\pi$
$884$	−22.5452	−0.758278
$885$	9.48935	0.318981
$886$	−18.1113	−0.608459
$887$	−38.0120	−1.27632	−0.638159	−	0.769905i	$-0.720304\pi$
$887$	−38.0120	−1.27632	−0.638159	+	0.769905i	$0.720304\pi$
$888$	9.22693	0.309636
$889$	24.7325	0.829501
$890$	−6.03746	−0.202376
$891$	−8.16700	−0.273605
$892$	−34.8485	−1.16682
$893$	−5.54752	−0.185641
$894$	−7.30756	−0.244401
$895$	0.829658	0.0277324
$896$	16.4032	0.547991
$897$	−29.6430	−0.989752
$898$	−51.4107	−1.71560
$899$	−3.71606	−0.123937
$900$	−0.659341	−0.0219780
$901$	−29.6294	−0.987100
$902$	9.03105	0.300701
$903$	31.4666	1.04714
$904$	1.83828	0.0611404
$905$	23.3935	0.777626
$906$	51.9963	1.72746
$907$	−40.9765	−1.36060	−0.680301	−	0.732933i	$-0.738151\pi$
$907$	−40.9765	−1.36060	−0.680301	+	0.732933i	$0.738151\pi$
$908$	62.9694	2.08971
$909$	4.88256	0.161944
$910$	7.28536	0.241507
$911$	6.99693	0.231819	0.115909	−	0.993260i	$-0.463022\pi$
$911$	6.99693	0.231819	0.115909	+	0.993260i	$0.463022\pi$
$912$	−3.68872	−0.122146
$913$	−10.1377	−0.335509
$914$	24.6839	0.816471
$915$	−14.5868	−0.482225
$916$	41.8912	1.38413
$917$	−20.5954	−0.680121
$918$	−53.0142	−1.74973
$919$	−41.1004	−1.35578	−0.677888	−	0.735165i	$-0.737104\pi$
$919$	−41.1004	−1.35578	−0.677888	+	0.735165i	$0.737104\pi$
$920$	−11.1980	−0.369189
$921$	36.7494	1.21093
$922$	−71.7604	−2.36330
$923$	13.8802	0.456872
$924$	7.56577	0.248896
$925$	−4.65469	−0.153045
$926$	3.33750	0.109677
$927$	−1.81354	−0.0595644
$928$	4.51182	0.148108
$929$	46.0636	1.51130	0.755649	−	0.654976i	$-0.227321\pi$
$929$	46.0636	1.51130	0.755649	+	0.654976i	$0.227321\pi$
$930$	−22.9272	−0.751813
$931$	−3.31840	−0.108756
$932$	−50.3294	−1.64860
$933$	−41.6657	−1.36407
$934$	56.3326	1.84326
$935$	4.60507	0.150602
$936$	0.589762	0.0192770
$937$	25.2119	0.823637	0.411819	−	0.911266i	$-0.364894\pi$
$937$	25.2119	0.823637	0.411819	+	0.911266i	$0.364894\pi$
$938$	49.2766	1.60894
$939$	−12.9467	−0.422501
$940$	16.3560	0.533473
$941$	−32.5922	−1.06248	−0.531238	−	0.847223i	$-0.678273\pi$
$941$	−32.5922	−1.06248	−0.531238	+	0.847223i	$0.678273\pi$
$942$	−54.6407	−1.78029
$943$	39.5340	1.28741
$944$	14.6966	0.478333
$945$	9.61837	0.312886
$946$	−22.7745	−0.740464
$947$	3.84258	0.124867	0.0624335	−	0.998049i	$-0.480114\pi$
$947$	3.84258	0.124867	0.0624335	+	0.998049i	$0.480114\pi$
$948$	−30.9113	−1.00395
$949$	15.0290	0.487863
$950$	−1.85463	−0.0601720
$951$	−36.5139	−1.18405
$952$	9.82119	0.318307
$953$	−43.7169	−1.41613	−0.708064	−	0.706148i	$-0.750431\pi$
$953$	−43.7169	−1.41613	−0.708064	+	0.706148i	$0.750431\pi$
$954$	3.54067	0.114634
$955$	10.1592	0.328743
$956$	−38.8216	−1.25558
$957$	0.949933	0.0307070
$958$	69.7965	2.25502
$959$	11.7511	0.379461
$960$	19.3421	0.624263
$961$	11.0284	0.355756
$962$	19.0195	0.613212
$963$	−4.05746	−0.130750
$964$	63.2339	2.03663
$965$	13.8377	0.445453
$966$	58.9892	1.89795
$967$	−33.1714	−1.06672	−0.533360	−	0.845888i	$-0.679071\pi$
$967$	−33.1714	−1.06672	−0.533360	+	0.845888i	$0.679071\pi$
$968$	11.9683	0.384675
$969$	−6.61835	−0.212612
$970$	−8.47342	−0.272065
$971$	37.6147	1.20711	0.603556	−	0.797321i	$-0.293750\pi$
$971$	37.6147	1.20711	0.603556	+	0.797321i	$0.293750\pi$
$972$	6.83257	0.219155
$973$	28.3412	0.908576
$974$	9.29587	0.297859
$975$	3.16864	0.101478
$976$	−22.5912	−0.723128
$977$	1.89309	0.0605655	0.0302827	−	0.999541i	$-0.490359\pi$
$977$	1.89309	0.0605655	0.0302827	+	0.999541i	$0.490359\pi$
$978$	9.62494	0.307772
$979$	−2.82916	−0.0904202
$980$	9.78378	0.312531
$981$	−1.43161	−0.0457076
$982$	21.8805	0.698235
$983$	−30.3144	−0.966880	−0.483440	−	0.875377i	$-0.660613\pi$
$983$	−30.3144	−0.966880	−0.483440	+	0.875377i	$0.660613\pi$
$984$	8.37700	0.267049
$985$	7.68767	0.244950
$986$	5.63306	0.179393
$987$	−18.8611	−0.600354
$988$	4.25478	0.135363
$989$	−99.6970	−3.17018
$990$	−0.550300	−0.0174897
$991$	−6.27776	−0.199420	−0.0997098	−	0.995017i	$-0.531791\pi$
$991$	−6.27776	−0.199420	−0.0997098	+	0.995017i	$0.531791\pi$
$992$	−51.0285	−1.62016
$993$	0.350204	0.0111134
$994$	−27.6214	−0.876097
$995$	−4.69614	−0.148878
$996$	−42.9567	−1.36114
$997$	3.48181	0.110270	0.0551351	−	0.998479i	$-0.482441\pi$
$997$	3.48181	0.110270	0.0551351	+	0.998479i	$0.482441\pi$
$998$	20.7676	0.657388
$999$	25.1101	0.794449

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2005.2.a.e.1.5	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2005.2.a.e.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-2.13554 q^{2} +1.65605 q^{3} +2.56051 q^{4} -1.00000 q^{5} -3.53655 q^{6} +1.78297 q^{7} -1.19700 q^{8} -0.257503 q^{9} +O(q^{10})\)	\(q-2.13554 q^{2} +1.65605 q^{3} +2.56051 q^{4} -1.00000 q^{5} -3.53655 q^{6} +1.78297 q^{7} -1.19700 q^{8} -0.257503 q^{9} +2.13554 q^{10} +1.00071 q^{11} +4.24034 q^{12} +1.91338 q^{13} -3.80759 q^{14} -1.65605 q^{15} -2.56480 q^{16} -4.60179 q^{17} +0.549908 q^{18} +0.868459 q^{19} -2.56051 q^{20} +2.95268 q^{21} -2.13706 q^{22} -9.35511 q^{23} -1.98229 q^{24} +1.00000 q^{25} -4.08609 q^{26} -5.39458 q^{27} +4.56532 q^{28} +0.573206 q^{29} +3.53655 q^{30} -6.48293 q^{31} +7.87121 q^{32} +1.65723 q^{33} +9.82729 q^{34} -1.78297 q^{35} -0.659341 q^{36} -4.65469 q^{37} -1.85463 q^{38} +3.16864 q^{39} +1.19700 q^{40} -4.22593 q^{41} -6.30556 q^{42} +10.6570 q^{43} +2.56234 q^{44} +0.257503 q^{45} +19.9782 q^{46} -6.38777 q^{47} -4.24743 q^{48} -3.82102 q^{49} -2.13554 q^{50} -7.62079 q^{51} +4.89923 q^{52} +6.43867 q^{53} +11.5203 q^{54} -1.00071 q^{55} -2.13421 q^{56} +1.43821 q^{57} -1.22410 q^{58} -5.73012 q^{59} -4.24034 q^{60} +8.80820 q^{61} +13.8445 q^{62} -0.459120 q^{63} -11.6797 q^{64} -1.91338 q^{65} -3.53907 q^{66} -12.9417 q^{67} -11.7830 q^{68} -15.4925 q^{69} +3.80759 q^{70} +7.25429 q^{71} +0.308231 q^{72} +7.85472 q^{73} +9.94026 q^{74} +1.65605 q^{75} +2.22370 q^{76} +1.78424 q^{77} -6.76676 q^{78} -7.28983 q^{79} +2.56480 q^{80} -8.16118 q^{81} +9.02462 q^{82} -10.1305 q^{83} +7.56038 q^{84} +4.60179 q^{85} -22.7583 q^{86} +0.949257 q^{87} -1.19785 q^{88} -2.82714 q^{89} -0.549908 q^{90} +3.41149 q^{91} -23.9539 q^{92} -10.7361 q^{93} +13.6413 q^{94} -0.868459 q^{95} +13.0351 q^{96} -3.96782 q^{97} +8.15993 q^{98} -0.257687 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q - 5 q^{2} - 3 q^{3} + 19 q^{4} - 29 q^{5} - 6 q^{6} + 12 q^{7} - 15 q^{8} + 14 q^{9}+O(q^{10}) \) 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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