LMFDB - Embedded newform 6005.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$47.9501664138$
Analytic rank:	$1$
Dimension:	$83$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62595 q^{2} +0.137720 q^{3} +4.89563 q^{4} -1.00000 q^{5} -0.361646 q^{6} +0.826916 q^{7} -7.60380 q^{8} -2.98103 q^{9} +O(q^{10})$	\(q-2.62595 q^{2} +0.137720 q^{3} +4.89563 q^{4} -1.00000 q^{5} -0.361646 q^{6} +0.826916 q^{7} -7.60380 q^{8} -2.98103 q^{9} +2.62595 q^{10} +2.70784 q^{11} +0.674225 q^{12} +0.500142 q^{13} -2.17144 q^{14} -0.137720 q^{15} +10.1759 q^{16} +7.50110 q^{17} +7.82805 q^{18} +2.49891 q^{19} -4.89563 q^{20} +0.113883 q^{21} -7.11068 q^{22} +0.239295 q^{23} -1.04719 q^{24} +1.00000 q^{25} -1.31335 q^{26} -0.823706 q^{27} +4.04828 q^{28} -1.00264 q^{29} +0.361646 q^{30} -6.17352 q^{31} -11.5140 q^{32} +0.372924 q^{33} -19.6975 q^{34} -0.826916 q^{35} -14.5940 q^{36} -8.27630 q^{37} -6.56203 q^{38} +0.0688794 q^{39} +7.60380 q^{40} -4.43879 q^{41} -0.299051 q^{42} -8.42918 q^{43} +13.2566 q^{44} +2.98103 q^{45} -0.628378 q^{46} +9.46750 q^{47} +1.40143 q^{48} -6.31621 q^{49} -2.62595 q^{50} +1.03305 q^{51} +2.44851 q^{52} -8.05395 q^{53} +2.16301 q^{54} -2.70784 q^{55} -6.28770 q^{56} +0.344150 q^{57} +2.63290 q^{58} -0.712100 q^{59} -0.674225 q^{60} -11.3305 q^{61} +16.2114 q^{62} -2.46506 q^{63} +9.88327 q^{64} -0.500142 q^{65} -0.979280 q^{66} +1.02370 q^{67} +36.7226 q^{68} +0.0329557 q^{69} +2.17144 q^{70} -4.24101 q^{71} +22.6672 q^{72} +6.22964 q^{73} +21.7332 q^{74} +0.137720 q^{75} +12.2338 q^{76} +2.23916 q^{77} -0.180874 q^{78} +13.3179 q^{79} -10.1759 q^{80} +8.82966 q^{81} +11.6561 q^{82} -8.08006 q^{83} +0.557528 q^{84} -7.50110 q^{85} +22.1346 q^{86} -0.138084 q^{87} -20.5899 q^{88} +2.62740 q^{89} -7.82805 q^{90} +0.413575 q^{91} +1.17150 q^{92} -0.850215 q^{93} -24.8612 q^{94} -2.49891 q^{95} -1.58570 q^{96} +4.56286 q^{97} +16.5861 q^{98} -8.07218 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9}+O(q^{10}) $ 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9	\( 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9} - q^{10} - 26 q^{11} - 12 q^{12} - 15 q^{13} - 21 q^{14} + 4 q^{15} + 5 q^{16} + 8 q^{17} - 12 q^{18} - 79 q^{19} - 61 q^{20} - 34 q^{21} - 25 q^{22} + 31 q^{23} - 42 q^{24} + 83 q^{25} - 13 q^{26} - 25 q^{27} - 16 q^{28} - 16 q^{29} + 6 q^{30} - 40 q^{31} + 15 q^{32} - 33 q^{33} - 54 q^{34} - 2 q^{35} + 11 q^{36} - 45 q^{37} + 10 q^{38} - 54 q^{39} + 3 q^{40} - 27 q^{41} - 28 q^{42} - 101 q^{43} - 51 q^{44} - 61 q^{45} - 46 q^{46} + 71 q^{47} - 14 q^{48} + 23 q^{49} + q^{50} - 71 q^{51} - 34 q^{52} - 49 q^{53} - 25 q^{54} + 26 q^{55} - 41 q^{56} - 20 q^{57} - 43 q^{58} - 60 q^{59} + 12 q^{60} - 38 q^{61} - 2 q^{62} + 36 q^{63} - 113 q^{64} + 15 q^{65} - 42 q^{66} - 164 q^{67} + 10 q^{68} - 93 q^{69} + 21 q^{70} - 78 q^{71} + q^{72} - 18 q^{73} - 23 q^{74} - 4 q^{75} - 112 q^{76} - 35 q^{77} - 44 q^{78} - 124 q^{79} - 5 q^{80} - 45 q^{81} - 34 q^{82} + 5 q^{83} - 60 q^{84} - 8 q^{85} - 25 q^{86} + 12 q^{87} - 149 q^{88} - 44 q^{89} + 12 q^{90} - 192 q^{91} + 35 q^{92} - 13 q^{93} - 32 q^{94} + 79 q^{95} - 59 q^{96} - 31 q^{97} + 25 q^{98} - 134 q^{99}+O(q^{100}) \) 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9 - q^10 - 26 * q^11 - 12 * q^12 - 15 * q^13 - 21 * q^14 + 4 * q^15 + 5 * q^16 + 8 * q^17 - 12 * q^18 - 79 * q^19 - 61 * q^20 - 34 * q^21 - 25 * q^22 + 31 * q^23 - 42 * q^24 + 83 * q^25 - 13 * q^26 - 25 * q^27 - 16 * q^28 - 16 * q^29 + 6 * q^30 - 40 * q^31 + 15 * q^32 - 33 * q^33 - 54 * q^34 - 2 * q^35 + 11 * q^36 - 45 * q^37 + 10 * q^38 - 54 * q^39 + 3 * q^40 - 27 * q^41 - 28 * q^42 - 101 * q^43 - 51 * q^44 - 61 * q^45 - 46 * q^46 + 71 * q^47 - 14 * q^48 + 23 * q^49 + q^50 - 71 * q^51 - 34 * q^52 - 49 * q^53 - 25 * q^54 + 26 * q^55 - 41 * q^56 - 20 * q^57 - 43 * q^58 - 60 * q^59 + 12 * q^60 - 38 * q^61 - 2 * q^62 + 36 * q^63 - 113 * q^64 + 15 * q^65 - 42 * q^66 - 164 * q^67 + 10 * q^68 - 93 * q^69 + 21 * q^70 - 78 * q^71 + q^72 - 18 * q^73 - 23 * q^74 - 4 * q^75 - 112 * q^76 - 35 * q^77 - 44 * q^78 - 124 * q^79 - 5 * q^80 - 45 * q^81 - 34 * q^82 + 5 * q^83 - 60 * q^84 - 8 * q^85 - 25 * q^86 + 12 * q^87 - 149 * q^88 - 44 * q^89 + 12 * q^90 - 192 * q^91 + 35 * q^92 - 13 * q^93 - 32 * q^94 + 79 * q^95 - 59 * q^96 - 31 * q^97 + 25 * q^98 - 134 * 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 $

$2$	−2.62595	−1.85683	−0.928415	−	0.371545i	$-0.878828\pi$
$2$	−2.62595	−1.85683	−0.928415	+	0.371545i	$0.878828\pi$
$3$	0.137720	0.0795125	0.0397563	−	0.999209i	$-0.487342\pi$
$3$	0.137720	0.0795125	0.0397563	+	0.999209i	$0.487342\pi$
$4$	4.89563	2.44782
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.361646	−0.147641
$7$	0.826916	0.312545	0.156272	−	0.987714i	$-0.450052\pi$
$7$	0.826916	0.312545	0.156272	+	0.987714i	$0.450052\pi$
$8$	−7.60380	−2.68835
$9$	−2.98103	−0.993678
$10$	2.62595	0.830399
$11$	2.70784	0.816446	0.408223	−	0.912882i	$-0.366149\pi$
$11$	2.70784	0.816446	0.408223	+	0.912882i	$0.366149\pi$
$12$	0.674225	0.194632
$13$	0.500142	0.138714	0.0693572	−	0.997592i	$-0.477905\pi$
$13$	0.500142	0.138714	0.0693572	+	0.997592i	$0.477905\pi$
$14$	−2.17144	−0.580343
$15$	−0.137720	−0.0355591
$16$	10.1759	2.54399
$17$	7.50110	1.81928	0.909642	−	0.415394i	$-0.136356\pi$
$17$	7.50110	1.81928	0.909642	+	0.415394i	$0.136356\pi$
$18$	7.82805	1.84509
$19$	2.49891	0.573290	0.286645	−	0.958037i	$-0.407460\pi$
$19$	2.49891	0.573290	0.286645	+	0.958037i	$0.407460\pi$
$20$	−4.89563	−1.09470
$21$	0.113883	0.0248512
$22$	−7.11068	−1.51600
$23$	0.239295	0.0498965	0.0249482	−	0.999689i	$-0.492058\pi$
$23$	0.239295	0.0498965	0.0249482	+	0.999689i	$0.492058\pi$
$24$	−1.04719	−0.213757
$25$	1.00000	0.200000
$26$	−1.31335	−0.257569
$27$	−0.823706	−0.158522
$28$	4.04828	0.765052
$29$	−1.00264	−0.186186	−0.0930932	−	0.995657i	$-0.529675\pi$
$29$	−1.00264	−0.186186	−0.0930932	+	0.995657i	$0.529675\pi$
$30$	0.361646	0.0660272
$31$	−6.17352	−1.10880	−0.554398	−	0.832252i	$-0.687052\pi$
$31$	−6.17352	−1.10880	−0.554398	+	0.832252i	$0.687052\pi$
$32$	−11.5140	−2.03540
$33$	0.372924	0.0649177
$34$	−19.6975	−3.37810
$35$	−0.826916	−0.139774
$36$	−14.5940	−2.43234
$37$	−8.27630	−1.36061	−0.680307	−	0.732927i	$-0.738154\pi$
$37$	−8.27630	−1.36061	−0.680307	+	0.732927i	$0.738154\pi$
$38$	−6.56203	−1.06450
$39$	0.0688794	0.0110295
$40$	7.60380	1.20227
$41$	−4.43879	−0.693223	−0.346611	−	0.938009i	$-0.612668\pi$
$41$	−4.43879	−0.693223	−0.346611	+	0.938009i	$0.612668\pi$
$42$	−0.299051	−0.0461445
$43$	−8.42918	−1.28544	−0.642719	−	0.766102i	$-0.722194\pi$
$43$	−8.42918	−1.28544	−0.642719	+	0.766102i	$0.722194\pi$
$44$	13.2566	1.99851
$45$	2.98103	0.444386
$46$	−0.628378	−0.0926492
$47$	9.46750	1.38098	0.690488	−	0.723344i	$-0.257396\pi$
$47$	9.46750	1.38098	0.690488	+	0.723344i	$0.257396\pi$
$48$	1.40143	0.202279
$49$	−6.31621	−0.902316
$50$	−2.62595	−0.371366
$51$	1.03305	0.144656
$52$	2.44851	0.339547
$53$	−8.05395	−1.10630	−0.553148	−	0.833083i	$-0.686573\pi$
$53$	−8.05395	−1.10630	−0.553148	+	0.833083i	$0.686573\pi$
$54$	2.16301	0.294349
$55$	−2.70784	−0.365126
$56$	−6.28770	−0.840229
$57$	0.344150	0.0455838
$58$	2.63290	0.345716
$59$	−0.712100	−0.0927075	−0.0463538	−	0.998925i	$-0.514760\pi$
$59$	−0.712100	−0.0927075	−0.0463538	+	0.998925i	$0.514760\pi$
$60$	−0.674225	−0.0870421
$61$	−11.3305	−1.45072	−0.725359	−	0.688371i	$-0.758326\pi$
$61$	−11.3305	−1.45072	−0.725359	+	0.688371i	$0.758326\pi$
$62$	16.2114	2.05885
$63$	−2.46506	−0.310569
$64$	9.88327	1.23541
$65$	−0.500142	−0.0620350
$66$	−0.979280	−0.120541
$67$	1.02370	0.125065	0.0625323	−	0.998043i	$-0.480082\pi$
$67$	1.02370	0.125065	0.0625323	+	0.998043i	$0.480082\pi$
$68$	36.7226	4.45327
$69$	0.0329557	0.00396739
$70$	2.17144	0.259537
$71$	−4.24101	−0.503315	−0.251658	−	0.967816i	$-0.580976\pi$
$71$	−4.24101	−0.503315	−0.251658	+	0.967816i	$0.580976\pi$
$72$	22.6672	2.67135
$73$	6.22964	0.729124	0.364562	−	0.931179i	$-0.381219\pi$
$73$	6.22964	0.729124	0.364562	+	0.931179i	$0.381219\pi$
$74$	21.7332	2.52643
$75$	0.137720	0.0159025
$76$	12.2338	1.40331
$77$	2.23916	0.255176
$78$	−0.180874	−0.0204800
$79$	13.3179	1.49838	0.749190	−	0.662355i	$-0.230443\pi$
$79$	13.3179	1.49838	0.749190	+	0.662355i	$0.230443\pi$
$80$	−10.1759	−1.13771
$81$	8.82966	0.981073
$82$	11.6561	1.28720
$83$	−8.08006	−0.886902	−0.443451	−	0.896299i	$-0.646246\pi$
$83$	−8.08006	−0.886902	−0.443451	+	0.896299i	$0.646246\pi$
$84$	0.557528	0.0608313
$85$	−7.50110	−0.813608
$86$	22.1346	2.38684
$87$	−0.138084	−0.0148042
$88$	−20.5899	−2.19489
$89$	2.62740	0.278504	0.139252	−	0.990257i	$-0.455530\pi$
$89$	2.62740	0.278504	0.139252	+	0.990257i	$0.455530\pi$
$90$	−7.82805	−0.825149
$91$	0.413575	0.0433545
$92$	1.17150	0.122137
$93$	−0.850215	−0.0881632
$94$	−24.8612	−2.56424
$95$	−2.49891	−0.256383
$96$	−1.58570	−0.161840
$97$	4.56286	0.463288	0.231644	−	0.972801i	$-0.425590\pi$
$97$	4.56286	0.463288	0.231644	+	0.972801i	$0.425590\pi$
$98$	16.5861	1.67545
$99$	−8.07218	−0.811284
$100$	4.89563	0.489563
$101$	1.09992	0.109446	0.0547231	−	0.998502i	$-0.482572\pi$
$101$	1.09992	0.109446	0.0547231	+	0.998502i	$0.482572\pi$
$102$	−2.71274	−0.268601
$103$	5.92283	0.583594	0.291797	−	0.956480i	$-0.405747\pi$
$103$	5.92283	0.583594	0.291797	+	0.956480i	$0.405747\pi$
$104$	−3.80298	−0.372912
$105$	−0.113883	−0.0111138
$106$	21.1493	2.05420
$107$	−11.3924	−1.10134	−0.550672	−	0.834722i	$-0.685629\pi$
$107$	−11.3924	−1.10134	−0.550672	+	0.834722i	$0.685629\pi$
$108$	−4.03256	−0.388034
$109$	−9.28195	−0.889049	−0.444525	−	0.895767i	$-0.646627\pi$
$109$	−9.28195	−0.889049	−0.444525	+	0.895767i	$0.646627\pi$
$110$	7.11068	0.677976
$111$	−1.13981	−0.108186
$112$	8.41466	0.795110
$113$	19.2313	1.80912	0.904562	−	0.426342i	$-0.140198\pi$
$113$	19.2313	1.80912	0.904562	+	0.426342i	$0.140198\pi$
$114$	−0.903722	−0.0846413
$115$	−0.239295	−0.0223144
$116$	−4.90858	−0.455750
$117$	−1.49094	−0.137837
$118$	1.86994	0.172142
$119$	6.20278	0.568608
$120$	1.04719	0.0955952
$121$	−3.66758	−0.333416
$122$	29.7533	2.69373
$123$	−0.611309	−0.0551199
$124$	−30.2233	−2.71413
$125$	−1.00000	−0.0894427
$126$	6.47314	0.576674
$127$	10.3207	0.915818	0.457909	−	0.888999i	$-0.348598\pi$
$127$	10.3207	0.915818	0.457909	+	0.888999i	$0.348598\pi$
$128$	−2.92506	−0.258542
$129$	−1.16086	−0.102208
$130$	1.31335	0.115188
$131$	−6.00751	−0.524879	−0.262439	−	0.964948i	$-0.584527\pi$
$131$	−6.00751	−0.524879	−0.262439	+	0.964948i	$0.584527\pi$
$132$	1.82570	0.158907
$133$	2.06639	0.179179
$134$	−2.68818	−0.232224
$135$	0.823706	0.0708934
$136$	−57.0368	−4.89087
$137$	6.94293	0.593175	0.296587	−	0.955006i	$-0.404151\pi$
$137$	6.94293	0.593175	0.296587	+	0.955006i	$0.404151\pi$
$138$	−0.0865400	−0.00736677
$139$	−11.6968	−0.992113	−0.496056	−	0.868290i	$-0.665219\pi$
$139$	−11.6968	−0.992113	−0.496056	+	0.868290i	$0.665219\pi$
$140$	−4.04828	−0.342142
$141$	1.30386	0.109805
$142$	11.1367	0.934571
$143$	1.35431	0.113253
$144$	−30.3348	−2.52790
$145$	1.00264	0.0832651
$146$	−16.3587	−1.35386
$147$	−0.869867	−0.0717454
$148$	−40.5177	−3.33053
$149$	−1.63880	−0.134256	−0.0671278	−	0.997744i	$-0.521384\pi$
$149$	−1.63880	−0.134256	−0.0671278	+	0.997744i	$0.521384\pi$
$150$	−0.361646	−0.0295282
$151$	−8.33273	−0.678108	−0.339054	−	0.940767i	$-0.610107\pi$
$151$	−8.33273	−0.678108	−0.339054	+	0.940767i	$0.610107\pi$
$152$	−19.0012	−1.54120
$153$	−22.3610	−1.80778
$154$	−5.87993	−0.473818
$155$	6.17352	0.495869
$156$	0.337208	0.0269983
$157$	8.37599	0.668477	0.334239	−	0.942489i	$-0.391521\pi$
$157$	8.37599	0.668477	0.334239	+	0.942489i	$0.391521\pi$
$158$	−34.9722	−2.78224
$159$	−1.10919	−0.0879643
$160$	11.5140	0.910260
$161$	0.197877	0.0155949
$162$	−23.1863	−1.82169
$163$	5.27830	0.413428	0.206714	−	0.978401i	$-0.433723\pi$
$163$	5.27830	0.413428	0.206714	+	0.978401i	$0.433723\pi$
$164$	−21.7307	−1.69688
$165$	−0.372924	−0.0290321
$166$	21.2179	1.64683
$167$	9.62525	0.744824	0.372412	−	0.928067i	$-0.378531\pi$
$167$	9.62525	0.744824	0.372412	+	0.928067i	$0.378531\pi$
$168$	−0.865941	−0.0668088
$169$	−12.7499	−0.980758
$170$	19.6975	1.51073
$171$	−7.44935	−0.569666
$172$	−41.2661	−3.14651
$173$	−1.06808	−0.0812049	−0.0406025	−	0.999175i	$-0.512928\pi$
$173$	−1.06808	−0.0812049	−0.0406025	+	0.999175i	$0.512928\pi$
$174$	0.362602	0.0274888
$175$	0.826916	0.0625090
$176$	27.5549	2.07703
$177$	−0.0980703	−0.00737141
$178$	−6.89944	−0.517135
$179$	9.90704	0.740487	0.370243	−	0.928935i	$-0.379274\pi$
$179$	9.90704	0.740487	0.370243	+	0.928935i	$0.379274\pi$
$180$	14.5940	1.08778
$181$	−5.51339	−0.409807	−0.204904	−	0.978782i	$-0.565688\pi$
$181$	−5.51339	−0.409807	−0.204904	+	0.978782i	$0.565688\pi$
$182$	−1.08603	−0.0805019
$183$	−1.56043	−0.115350
$184$	−1.81955	−0.134139
$185$	8.27630	0.608485
$186$	2.23263	0.163704
$187$	20.3118	1.48535
$188$	46.3494	3.38038
$189$	−0.681136	−0.0495454
$190$	6.56203	0.476060
$191$	18.1361	1.31228	0.656141	−	0.754638i	$-0.272188\pi$
$191$	18.1361	1.31228	0.656141	+	0.754638i	$0.272188\pi$
$192$	1.36112	0.0982305
$193$	−14.7387	−1.06092	−0.530459	−	0.847711i	$-0.677980\pi$
$193$	−14.7387	−1.06092	−0.530459	+	0.847711i	$0.677980\pi$
$194$	−11.9819	−0.860247
$195$	−0.0688794	−0.00493256
$196$	−30.9218	−2.20870
$197$	−9.01948	−0.642611	−0.321306	−	0.946976i	$-0.604122\pi$
$197$	−9.01948	−0.642611	−0.321306	+	0.946976i	$0.604122\pi$
$198$	21.1972	1.50642
$199$	−20.3258	−1.44086	−0.720429	−	0.693529i	$-0.756055\pi$
$199$	−20.3258	−1.44086	−0.720429	+	0.693529i	$0.756055\pi$
$200$	−7.60380	−0.537670
$201$	0.140983	0.00994420
$202$	−2.88834	−0.203223
$203$	−0.829103	−0.0581916
$204$	5.05743	0.354091
$205$	4.43879	0.310019
$206$	−15.5531	−1.08363
$207$	−0.713346	−0.0495810
$208$	5.08942	0.352888
$209$	6.76667	0.468061
$210$	0.299051	0.0206365
$211$	−12.7105	−0.875029	−0.437515	−	0.899211i	$-0.644141\pi$
$211$	−12.7105	−0.875029	−0.437515	+	0.899211i	$0.644141\pi$
$212$	−39.4292	−2.70801
$213$	−0.584071	−0.0400199
$214$	29.9159	2.04501
$215$	8.42918	0.574865
$216$	6.26330	0.426163
$217$	−5.10498	−0.346549
$218$	24.3740	1.65081
$219$	0.857944	0.0579745
$220$	−13.2566	−0.893761
$221$	3.75161	0.252361
$222$	2.99309	0.200883
$223$	16.0857	1.07717	0.538587	−	0.842570i	$-0.318958\pi$
$223$	16.0857	1.07717	0.538587	+	0.842570i	$0.318958\pi$
$224$	−9.52109	−0.636155
$225$	−2.98103	−0.198736
$226$	−50.5004	−3.35924
$227$	7.66664	0.508853	0.254426	−	0.967092i	$-0.418113\pi$
$227$	7.66664	0.508853	0.254426	+	0.967092i	$0.418113\pi$
$228$	1.68483	0.111581
$229$	−12.5118	−0.826801	−0.413400	−	0.910549i	$-0.635659\pi$
$229$	−12.5118	−0.826801	−0.413400	+	0.910549i	$0.635659\pi$
$230$	0.628378	0.0414340
$231$	0.308377	0.0202897
$232$	7.62390	0.500534
$233$	27.6905	1.81407	0.907033	−	0.421060i	$-0.138342\pi$
$233$	27.6905	1.81407	0.907033	+	0.421060i	$0.138342\pi$
$234$	3.91514	0.255941
$235$	−9.46750	−0.617591
$236$	−3.48618	−0.226931
$237$	1.83414	0.119140
$238$	−16.2882	−1.05581
$239$	14.4831	0.936832	0.468416	−	0.883508i	$-0.344825\pi$
$239$	14.4831	0.936832	0.468416	+	0.883508i	$0.344825\pi$
$240$	−1.40143	−0.0904619
$241$	−19.7687	−1.27341	−0.636707	−	0.771106i	$-0.719704\pi$
$241$	−19.7687	−1.27341	−0.636707	+	0.771106i	$0.719704\pi$
$242$	9.63088	0.619097
$243$	3.68714	0.236530
$244$	−55.4698	−3.55109
$245$	6.31621	0.403528
$246$	1.60527	0.102348
$247$	1.24981	0.0795236
$248$	46.9422	2.98083
$249$	−1.11278	−0.0705198
$250$	2.62595	0.166080
$251$	−20.1587	−1.27241	−0.636204	−	0.771520i	$-0.719497\pi$
$251$	−20.1587	−1.27241	−0.636204	+	0.771520i	$0.719497\pi$
$252$	−12.0680	−0.760216
$253$	0.647974	0.0407378
$254$	−27.1018	−1.70052
$255$	−1.03305	−0.0646921
$256$	−12.0855	−0.755342
$257$	−20.8891	−1.30303	−0.651515	−	0.758636i	$-0.725866\pi$
$257$	−20.8891	−1.30303	−0.651515	+	0.758636i	$0.725866\pi$
$258$	3.04838	0.189784
$259$	−6.84380	−0.425253
$260$	−2.44851	−0.151850
$261$	2.98892	0.185009
$262$	15.7754	0.974610
$263$	−9.35741	−0.577003	−0.288501	−	0.957479i	$-0.593157\pi$
$263$	−9.35741	−0.577003	−0.288501	+	0.957479i	$0.593157\pi$
$264$	−2.83564	−0.174521
$265$	8.05395	0.494750
$266$	−5.42625	−0.332705
$267$	0.361845	0.0221446
$268$	5.01165	0.306135
$269$	6.01730	0.366881	0.183441	−	0.983031i	$-0.441276\pi$
$269$	6.01730	0.366881	0.183441	+	0.983031i	$0.441276\pi$
$270$	−2.16301	−0.131637
$271$	−1.29640	−0.0787508	−0.0393754	−	0.999224i	$-0.512537\pi$
$271$	−1.29640	−0.0787508	−0.0393754	+	0.999224i	$0.512537\pi$
$272$	76.3308	4.62823
$273$	0.0569575	0.00344722
$274$	−18.2318	−1.10142
$275$	2.70784	0.163289
$276$	0.161339	0.00971145
$277$	−18.2638	−1.09736	−0.548681	−	0.836032i	$-0.684870\pi$
$277$	−18.2638	−1.09736	−0.548681	+	0.836032i	$0.684870\pi$
$278$	30.7153	1.84218
$279$	18.4035	1.10179
$280$	6.28770	0.375762
$281$	−22.3528	−1.33346	−0.666729	−	0.745300i	$-0.732306\pi$
$281$	−22.3528	−1.33346	−0.666729	+	0.745300i	$0.732306\pi$
$282$	−3.42388	−0.203889
$283$	−16.7858	−0.997814	−0.498907	−	0.866656i	$-0.666265\pi$
$283$	−16.7858	−0.997814	−0.498907	+	0.866656i	$0.666265\pi$
$284$	−20.7624	−1.23202
$285$	−0.344150	−0.0203857
$286$	−3.55635	−0.210291
$287$	−3.67051	−0.216663
$288$	34.3236	2.02253
$289$	39.2665	2.30979
$290$	−2.63290	−0.154609
$291$	0.628396	0.0368372
$292$	30.4980	1.78476
$293$	30.2122	1.76502	0.882508	−	0.470298i	$-0.155854\pi$
$293$	30.2122	1.76502	0.882508	+	0.470298i	$0.155854\pi$
$294$	2.28423	0.133219
$295$	0.712100	0.0414601
$296$	62.9313	3.65781
$297$	−2.23047	−0.129425
$298$	4.30341	0.249290
$299$	0.119681	0.00692136
$300$	0.674225	0.0389264
$301$	−6.97022	−0.401757
$302$	21.8814	1.25913
$303$	0.151481	0.00870235
$304$	25.4288	1.45844
$305$	11.3305	0.648780
$306$	58.7190	3.35674
$307$	−14.7966	−0.844489	−0.422244	−	0.906482i	$-0.638758\pi$
$307$	−14.7966	−0.844489	−0.422244	+	0.906482i	$0.638758\pi$
$308$	10.9621	0.624624
$309$	0.815691	0.0464031
$310$	−16.2114	−0.920744
$311$	24.2886	1.37728	0.688641	−	0.725103i	$-0.258208\pi$
$311$	24.2886	1.37728	0.688641	+	0.725103i	$0.258208\pi$
$312$	−0.523745	−0.0296512
$313$	18.1924	1.02829	0.514146	−	0.857702i	$-0.328109\pi$
$313$	18.1924	1.02829	0.514146	+	0.857702i	$0.328109\pi$
$314$	−21.9950	−1.24125
$315$	2.46506	0.138891
$316$	65.1995	3.66776
$317$	−15.9014	−0.893114	−0.446557	−	0.894755i	$-0.647350\pi$
$317$	−15.9014	−0.893114	−0.446557	+	0.894755i	$0.647350\pi$
$318$	2.91268	0.163335
$319$	−2.71501	−0.152011
$320$	−9.88327	−0.552492
$321$	−1.56896	−0.0875707
$322$	−0.519616	−0.0289570
$323$	18.7446	1.04298
$324$	43.2268	2.40149
$325$	0.500142	0.0277429
$326$	−13.8606	−0.767666
$327$	−1.27831	−0.0706906
$328$	33.7517	1.86362
$329$	7.82883	0.431617
$330$	0.979280	0.0539076
$331$	2.24248	0.123258	0.0616289	−	0.998099i	$-0.480370\pi$
$331$	2.24248	0.123258	0.0616289	+	0.998099i	$0.480370\pi$
$332$	−39.5570	−2.17097
$333$	24.6719	1.35201
$334$	−25.2755	−1.38301
$335$	−1.02370	−0.0559306
$336$	1.15886	0.0632212
$337$	−14.0374	−0.764666	−0.382333	−	0.924025i	$-0.624879\pi$
$337$	−14.0374	−0.764666	−0.382333	+	0.924025i	$0.624879\pi$
$338$	33.4805	1.82110
$339$	2.64852	0.143848
$340$	−36.7226	−1.99156
$341$	−16.7169	−0.905272
$342$	19.5616	1.05777
$343$	−11.0114	−0.594559
$344$	64.0937	3.45570
$345$	−0.0329557	−0.00177427
$346$	2.80474	0.150784
$347$	−32.9453	−1.76860	−0.884298	−	0.466922i	$-0.845363\pi$
$347$	−32.9453	−1.76860	−0.884298	+	0.466922i	$0.845363\pi$
$348$	−0.676008	−0.0362378
$349$	9.95473	0.532865	0.266432	−	0.963854i	$-0.414155\pi$
$349$	9.95473	0.532865	0.266432	+	0.963854i	$0.414155\pi$
$350$	−2.17144	−0.116069
$351$	−0.411970	−0.0219893
$352$	−31.1781	−1.66180
$353$	−5.82662	−0.310120	−0.155060	−	0.987905i	$-0.549557\pi$
$353$	−5.82662	−0.310120	−0.155060	+	0.987905i	$0.549557\pi$
$354$	0.257528	0.0136875
$355$	4.24101	0.225089
$356$	12.8628	0.681727
$357$	0.854245	0.0452115
$358$	−26.0154	−1.37496
$359$	19.7274	1.04117	0.520585	−	0.853810i	$-0.325714\pi$
$359$	19.7274	1.04117	0.520585	+	0.853810i	$0.325714\pi$
$360$	−22.6672	−1.19466
$361$	−12.7554	−0.671338
$362$	14.4779	0.760942
$363$	−0.505098	−0.0265108
$364$	2.02471	0.106124
$365$	−6.22964	−0.326074
$366$	4.09761	0.214186
$367$	17.2120	0.898460	0.449230	−	0.893416i	$-0.351698\pi$
$367$	17.2120	0.898460	0.449230	+	0.893416i	$0.351698\pi$
$368$	2.43505	0.126936
$369$	13.2322	0.688840
$370$	−21.7332	−1.12985
$371$	−6.65994	−0.345767
$372$	−4.16234	−0.215807
$373$	−4.94471	−0.256027	−0.128014	−	0.991772i	$-0.540860\pi$
$373$	−4.94471	−0.256027	−0.128014	+	0.991772i	$0.540860\pi$
$374$	−53.3379	−2.75804
$375$	−0.137720	−0.00711182
$376$	−71.9889	−3.71254
$377$	−0.501464	−0.0258267
$378$	1.78863	0.0919973
$379$	13.4500	0.690880	0.345440	−	0.938441i	$-0.387730\pi$
$379$	13.4500	0.690880	0.345440	+	0.938441i	$0.387730\pi$
$380$	−12.2338	−0.627579
$381$	1.42137	0.0728190
$382$	−47.6245	−2.43668
$383$	−22.8898	−1.16962	−0.584808	−	0.811172i	$-0.698830\pi$
$383$	−22.8898	−1.16962	−0.584808	+	0.811172i	$0.698830\pi$
$384$	−0.402839	−0.0205573
$385$	−2.23916	−0.114118
$386$	38.7033	1.96994
$387$	25.1277	1.27731
$388$	22.3381	1.13404
$389$	−4.14239	−0.210027	−0.105014	−	0.994471i	$-0.533489\pi$
$389$	−4.14239	−0.210027	−0.105014	+	0.994471i	$0.533489\pi$
$390$	0.180874	0.00915892
$391$	1.79498	0.0907758
$392$	48.0272	2.42574
$393$	−0.827353	−0.0417344
$394$	23.6847	1.19322
$395$	−13.3179	−0.670096
$396$	−39.5184	−1.98587
$397$	−22.7843	−1.14351	−0.571756	−	0.820424i	$-0.693738\pi$
$397$	−22.7843	−1.14351	−0.571756	+	0.820424i	$0.693738\pi$
$398$	53.3746	2.67543
$399$	0.284583	0.0142470
$400$	10.1759	0.508797
$401$	−36.3613	−1.81579	−0.907897	−	0.419193i	$-0.862313\pi$
$401$	−36.3613	−1.81579	−0.907897	+	0.419193i	$0.862313\pi$
$402$	−0.370216	−0.0184647
$403$	−3.08763	−0.153806
$404$	5.38481	0.267904
$405$	−8.82966	−0.438749
$406$	2.17719	0.108052
$407$	−22.4109	−1.11087
$408$	−7.85510	−0.388885
$409$	−16.6633	−0.823949	−0.411974	−	0.911195i	$-0.635161\pi$
$409$	−16.6633	−0.823949	−0.411974	+	0.911195i	$0.635161\pi$
$410$	−11.6561	−0.575652
$411$	0.956179	0.0471648
$412$	28.9960	1.42853
$413$	−0.588847	−0.0289753
$414$	1.87321	0.0920635
$415$	8.08006	0.396635
$416$	−5.75862	−0.282340
$417$	−1.61089	−0.0788854
$418$	−17.7690	−0.869109
$419$	−8.96558	−0.437997	−0.218999	−	0.975725i	$-0.570279\pi$
$419$	−8.96558	−0.437997	−0.218999	+	0.975725i	$0.570279\pi$
$420$	−0.557528	−0.0272046
$421$	−7.92305	−0.386146	−0.193073	−	0.981184i	$-0.561845\pi$
$421$	−7.92305	−0.386146	−0.193073	+	0.981184i	$0.561845\pi$
$422$	33.3773	1.62478
$423$	−28.2229	−1.37225
$424$	61.2406	2.97411
$425$	7.50110	0.363857
$426$	1.53374	0.0743101
$427$	−9.36934	−0.453414
$428$	−55.7730	−2.69589
$429$	0.186515	0.00900502
$430$	−22.1346	−1.06743
$431$	−18.8185	−0.906457	−0.453229	−	0.891394i	$-0.649728\pi$
$431$	−18.8185	−0.906457	−0.453229	+	0.891394i	$0.649728\pi$
$432$	−8.38199	−0.403279
$433$	−4.91678	−0.236285	−0.118143	−	0.992997i	$-0.537694\pi$
$433$	−4.91678	−0.236285	−0.118143	+	0.992997i	$0.537694\pi$
$434$	13.4054	0.643482
$435$	0.138084	0.00662062
$436$	−45.4410	−2.17623
$437$	0.597978	0.0286052
$438$	−2.25292	−0.107649
$439$	32.3657	1.54473	0.772364	−	0.635180i	$-0.219074\pi$
$439$	32.3657	1.54473	0.772364	+	0.635180i	$0.219074\pi$
$440$	20.5899	0.981585
$441$	18.8288	0.896611
$442$	−9.85156	−0.468591
$443$	25.5301	1.21297	0.606487	−	0.795094i	$-0.292578\pi$
$443$	25.5301	1.21297	0.606487	+	0.795094i	$0.292578\pi$
$444$	−5.58009	−0.264819
$445$	−2.62740	−0.124551
$446$	−42.2402	−2.00013
$447$	−0.225695	−0.0106750
$448$	8.17264	0.386121
$449$	10.0096	0.472381	0.236190	−	0.971707i	$-0.424101\pi$
$449$	10.0096	0.472381	0.236190	+	0.971707i	$0.424101\pi$
$450$	7.82805	0.369018
$451$	−12.0196	−0.565979
$452$	94.1491	4.42840
$453$	−1.14758	−0.0539181
$454$	−20.1322	−0.944853
$455$	−0.413575	−0.0193887
$456$	−2.61685	−0.122545
$457$	39.5787	1.85141	0.925707	−	0.378242i	$-0.123471\pi$
$457$	39.5787	1.85141	0.925707	+	0.378242i	$0.123471\pi$
$458$	32.8553	1.53523
$459$	−6.17870	−0.288397
$460$	−1.17150	−0.0546215
$461$	−16.1071	−0.750182	−0.375091	−	0.926988i	$-0.622389\pi$
$461$	−16.1071	−0.750182	−0.375091	+	0.926988i	$0.622389\pi$
$462$	−0.809783	−0.0376745
$463$	−15.8863	−0.738298	−0.369149	−	0.929370i	$-0.620351\pi$
$463$	−15.8863	−0.738298	−0.369149	+	0.929370i	$0.620351\pi$
$464$	−10.2029	−0.473656
$465$	0.850215	0.0394278
$466$	−72.7140	−3.36841
$467$	−33.1507	−1.53403	−0.767016	−	0.641628i	$-0.778259\pi$
$467$	−33.1507	−1.53403	−0.767016	+	0.641628i	$0.778259\pi$
$468$	−7.29909	−0.337401
$469$	0.846512	0.0390883
$470$	24.8612	1.14676
$471$	1.15354	0.0531523
$472$	5.41466	0.249230
$473$	−22.8249	−1.04949
$474$	−4.81636	−0.221223
$475$	2.49891	0.114658
$476$	30.3665	1.39185
$477$	24.0091	1.09930
$478$	−38.0319	−1.73954
$479$	−29.2480	−1.33637	−0.668187	−	0.743994i	$-0.732929\pi$
$479$	−29.2480	−1.33637	−0.668187	+	0.743994i	$0.732929\pi$
$480$	1.58570	0.0723771
$481$	−4.13932	−0.188737
$482$	51.9117	2.36451
$483$	0.0272516	0.00123999
$484$	−17.9551	−0.816141
$485$	−4.56286	−0.207189
$486$	−9.68225	−0.439196
$487$	25.1367	1.13905	0.569526	−	0.821973i	$-0.307127\pi$
$487$	25.1367	1.13905	0.569526	+	0.821973i	$0.307127\pi$
$488$	86.1545	3.90003
$489$	0.726926	0.0328727
$490$	−16.5861	−0.749282
$491$	−16.5916	−0.748770	−0.374385	−	0.927273i	$-0.622146\pi$
$491$	−16.5916	−0.748770	−0.374385	+	0.927273i	$0.622146\pi$
$492$	−2.99275	−0.134923
$493$	−7.52093	−0.338726
$494$	−3.28195	−0.147662
$495$	8.07218	0.362817
$496$	−62.8214	−2.82076
$497$	−3.50696	−0.157309
$498$	2.92212	0.130943
$499$	−5.10274	−0.228430	−0.114215	−	0.993456i	$-0.536435\pi$
$499$	−5.10274	−0.228430	−0.114215	+	0.993456i	$0.536435\pi$
$500$	−4.89563	−0.218939
$501$	1.32559	0.0592229
$502$	52.9359	2.36265
$503$	25.5323	1.13843	0.569214	−	0.822190i	$-0.307248\pi$
$503$	25.5323	1.13843	0.569214	+	0.822190i	$0.307248\pi$
$504$	18.7438	0.834917
$505$	−1.09992	−0.0489459
$506$	−1.70155	−0.0756431
$507$	−1.75591	−0.0779826
$508$	50.5266	2.24175
$509$	38.6902	1.71491	0.857457	−	0.514556i	$-0.172043\pi$
$509$	38.6902	1.71491	0.857457	+	0.514556i	$0.172043\pi$
$510$	2.71274	0.120122
$511$	5.15139	0.227884
$512$	37.5860	1.66108
$513$	−2.05837	−0.0908793
$514$	54.8539	2.41950
$515$	−5.92283	−0.260991
$516$	−5.68316	−0.250187
$517$	25.6365	1.12749
$518$	17.9715	0.789623
$519$	−0.147096	−0.00645681
$520$	3.80298	0.166772
$521$	−20.7884	−0.910758	−0.455379	−	0.890298i	$-0.650496\pi$
$521$	−20.7884	−0.910758	−0.455379	+	0.890298i	$0.650496\pi$
$522$	−7.84876	−0.343531
$523$	−39.9997	−1.74906	−0.874531	−	0.484969i	$-0.838831\pi$
$523$	−39.9997	−1.74906	−0.874531	+	0.484969i	$0.838831\pi$
$524$	−29.4106	−1.28481
$525$	0.113883	0.00497025
$526$	24.5721	1.07140
$527$	−46.3082	−2.01721
$528$	3.79485	0.165150
$529$	−22.9427	−0.997510
$530$	−21.1493	−0.918667
$531$	2.12279	0.0921214
$532$	10.1163	0.438597
$533$	−2.22003	−0.0961600
$534$	−0.950189	−0.0411187
$535$	11.3924	0.492536
$536$	−7.78399	−0.336217
$537$	1.36439	0.0588780
$538$	−15.8012	−0.681236
$539$	−17.1033	−0.736692
$540$	4.03256	0.173534
$541$	20.4267	0.878214	0.439107	−	0.898435i	$-0.355295\pi$
$541$	20.4267	0.878214	0.439107	+	0.898435i	$0.355295\pi$
$542$	3.40429	0.146227
$543$	−0.759303	−0.0325848
$544$	−86.3675	−3.70298
$545$	9.28195	0.397595
$546$	−0.149568	−0.00640091
$547$	−37.2374	−1.59216	−0.796079	−	0.605193i	$-0.793096\pi$
$547$	−37.2374	−1.59216	−0.796079	+	0.605193i	$0.793096\pi$
$548$	33.9901	1.45198
$549$	33.7765	1.44155
$550$	−7.11068	−0.303200
$551$	−2.50552	−0.106739
$552$	−0.250588	−0.0106657
$553$	11.0128	0.468311
$554$	47.9598	2.03762
$555$	1.13981	0.0483822
$556$	−57.2634	−2.42851
$557$	10.3705	0.439414	0.219707	−	0.975566i	$-0.429490\pi$
$557$	10.3705	0.439414	0.219707	+	0.975566i	$0.429490\pi$
$558$	−48.3266	−2.04583
$559$	−4.21578	−0.178309
$560$	−8.41466	−0.355584
$561$	2.79734	0.118104
$562$	58.6975	2.47600
$563$	−27.7634	−1.17009	−0.585044	−	0.811002i	$-0.698923\pi$
$563$	−27.7634	−1.17009	−0.585044	+	0.811002i	$0.698923\pi$
$564$	6.38323	0.268782
$565$	−19.2313	−0.809065
$566$	44.0788	1.85277
$567$	7.30139	0.306629
$568$	32.2478	1.35309
$569$	−26.2882	−1.10206	−0.551030	−	0.834486i	$-0.685765\pi$
$569$	−26.2882	−1.10206	−0.551030	+	0.834486i	$0.685765\pi$
$570$	0.903722	0.0378527
$571$	20.3837	0.853032	0.426516	−	0.904480i	$-0.359741\pi$
$571$	20.3837	0.853032	0.426516	+	0.904480i	$0.359741\pi$
$572$	6.63019	0.277222
$573$	2.49770	0.104343
$574$	9.63859	0.402307
$575$	0.239295	0.00997929
$576$	−29.4624	−1.22760
$577$	−5.67310	−0.236174	−0.118087	−	0.993003i	$-0.537676\pi$
$577$	−5.67310	−0.236174	−0.118087	+	0.993003i	$0.537676\pi$
$578$	−103.112	−4.28889
$579$	−2.02982	−0.0843563
$580$	4.90858	0.203818
$581$	−6.68153	−0.277197
$582$	−1.65014	−0.0684004
$583$	−21.8088	−0.903230
$584$	−47.3689	−1.96014
$585$	1.49094	0.0616428
$586$	−79.3358	−3.27733
$587$	7.80895	0.322310	0.161155	−	0.986929i	$-0.448478\pi$
$587$	7.80895	0.322310	0.161155	+	0.986929i	$0.448478\pi$
$588$	−4.25855	−0.175620
$589$	−15.4271	−0.635662
$590$	−1.86994	−0.0769843
$591$	−1.24216	−0.0510956
$592$	−84.2192	−3.46139
$593$	−1.03853	−0.0426475	−0.0213237	−	0.999773i	$-0.506788\pi$
$593$	−1.03853	−0.0426475	−0.0213237	+	0.999773i	$0.506788\pi$
$594$	5.85711	0.240320
$595$	−6.20278	−0.254289
$596$	−8.02296	−0.328633
$597$	−2.79926	−0.114566
$598$	−0.314278	−0.0128518
$599$	12.3214	0.503440	0.251720	−	0.967800i	$-0.419004\pi$
$599$	12.3214	0.503440	0.251720	+	0.967800i	$0.419004\pi$
$600$	−1.04719	−0.0427515
$601$	−9.03930	−0.368721	−0.184360	−	0.982859i	$-0.559021\pi$
$601$	−9.03930	−0.368721	−0.184360	+	0.982859i	$0.559021\pi$
$602$	18.3035	0.745994
$603$	−3.05168	−0.124274
$604$	−40.7940	−1.65988
$605$	3.66758	0.149108
$606$	−0.397782	−0.0161588
$607$	4.91846	0.199634	0.0998170	−	0.995006i	$-0.468174\pi$
$607$	4.91846	0.199634	0.0998170	+	0.995006i	$0.468174\pi$
$608$	−28.7724	−1.16688
$609$	−0.114184	−0.00462696
$610$	−29.7533	−1.20467
$611$	4.73509	0.191561
$612$	−109.471	−4.42512
$613$	40.7848	1.64728	0.823641	−	0.567111i	$-0.191939\pi$
$613$	40.7848	1.64728	0.823641	+	0.567111i	$0.191939\pi$
$614$	38.8553	1.56807
$615$	0.611309	0.0246504
$616$	−17.0261	−0.686002
$617$	−16.9401	−0.681981	−0.340991	−	0.940067i	$-0.610762\pi$
$617$	−16.9401	−0.681981	−0.340991	+	0.940067i	$0.610762\pi$
$618$	−2.14197	−0.0861626
$619$	9.22618	0.370831	0.185416	−	0.982660i	$-0.440637\pi$
$619$	9.22618	0.370831	0.185416	+	0.982660i	$0.440637\pi$
$620$	30.2233	1.21380
$621$	−0.197109	−0.00790971
$622$	−63.7808	−2.55738
$623$	2.17264	0.0870450
$624$	0.700913	0.0280590
$625$	1.00000	0.0400000
$626$	−47.7723	−1.90936
$627$	0.931905	0.0372167
$628$	41.0058	1.63631
$629$	−62.0813	−2.47534
$630$	−6.47314	−0.257896
$631$	−1.80482	−0.0718487	−0.0359244	−	0.999355i	$-0.511438\pi$
$631$	−1.80482	−0.0718487	−0.0359244	+	0.999355i	$0.511438\pi$
$632$	−101.267	−4.02817
$633$	−1.75049	−0.0695758
$634$	41.7564	1.65836
$635$	−10.3207	−0.409566
$636$	−5.43018	−0.215320
$637$	−3.15900	−0.125164
$638$	7.12948	0.282259
$639$	12.6426	0.500133
$640$	2.92506	0.115623
$641$	−3.99645	−0.157850	−0.0789251	−	0.996881i	$-0.525149\pi$
$641$	−3.99645	−0.157850	−0.0789251	+	0.996881i	$0.525149\pi$
$642$	4.12001	0.162604
$643$	24.1168	0.951075	0.475538	−	0.879695i	$-0.342254\pi$
$643$	24.1168	0.951075	0.475538	+	0.879695i	$0.342254\pi$
$644$	0.968733	0.0381734
$645$	1.16086	0.0457090
$646$	−49.2225	−1.93663
$647$	−4.36655	−0.171667	−0.0858334	−	0.996310i	$-0.527355\pi$
$647$	−4.36655	−0.171667	−0.0858334	+	0.996310i	$0.527355\pi$
$648$	−67.1389	−2.63747
$649$	−1.92826	−0.0756907
$650$	−1.31335	−0.0515138
$651$	−0.703057	−0.0275550
$652$	25.8406	1.01200
$653$	−3.02307	−0.118302	−0.0591509	−	0.998249i	$-0.518839\pi$
$653$	−3.02307	−0.118302	−0.0591509	+	0.998249i	$0.518839\pi$
$654$	3.35678	0.131260
$655$	6.00751	0.234733
$656$	−45.1689	−1.76355
$657$	−18.5708	−0.724514
$658$	−20.5581	−0.801440
$659$	39.4029	1.53492	0.767459	−	0.641098i	$-0.221521\pi$
$659$	39.4029	1.53492	0.767459	+	0.641098i	$0.221521\pi$
$660$	−1.82570	−0.0710652
$661$	−39.0218	−1.51777	−0.758886	−	0.651223i	$-0.774256\pi$
$661$	−39.0218	−1.51777	−0.758886	+	0.651223i	$0.774256\pi$
$662$	−5.88865	−0.228869
$663$	0.516671	0.0200659
$664$	61.4391	2.38430
$665$	−2.06639	−0.0801313
$666$	−64.7873	−2.51046
$667$	−0.239928	−0.00929004
$668$	47.1217	1.82319
$669$	2.21531	0.0856489
$670$	2.68818	0.103854
$671$	−30.6811	−1.18443
$672$	−1.31124	−0.0505823
$673$	−42.6904	−1.64559	−0.822797	−	0.568336i	$-0.807588\pi$
$673$	−42.6904	−1.64559	−0.822797	+	0.568336i	$0.807588\pi$
$674$	36.8616	1.41985
$675$	−0.823706	−0.0317045
$676$	−62.4186	−2.40072
$677$	−34.8219	−1.33831	−0.669156	−	0.743122i	$-0.733344\pi$
$677$	−34.8219	−1.33831	−0.669156	+	0.743122i	$0.733344\pi$
$678$	−6.95490	−0.267101
$679$	3.77310	0.144798
$680$	57.0368	2.18726
$681$	1.05585	0.0404602
$682$	43.8979	1.68094
$683$	−19.5247	−0.747093	−0.373546	−	0.927611i	$-0.621858\pi$
$683$	−19.5247	−0.747093	−0.373546	+	0.927611i	$0.621858\pi$
$684$	−36.4693	−1.39444
$685$	−6.94293	−0.265276
$686$	28.9154	1.10399
$687$	−1.72312	−0.0657410
$688$	−85.7749	−3.27014
$689$	−4.02812	−0.153459
$690$	0.0865400	0.00329452
$691$	3.81186	0.145010	0.0725051	−	0.997368i	$-0.476901\pi$
$691$	3.81186	0.145010	0.0725051	+	0.997368i	$0.476901\pi$
$692$	−5.22895	−0.198775
$693$	−6.67501	−0.253563
$694$	86.5129	3.28398
$695$	11.6968	0.443686
$696$	1.04996	0.0397987
$697$	−33.2958	−1.26117
$698$	−26.1407	−0.989439
$699$	3.81353	0.144241
$700$	4.04828	0.153010
$701$	3.21274	0.121343	0.0606717	−	0.998158i	$-0.480676\pi$
$701$	3.21274	0.121343	0.0606717	+	0.998158i	$0.480676\pi$
$702$	1.08181	0.0408304
$703$	−20.6818	−0.780027
$704$	26.7624	1.00865
$705$	−1.30386	−0.0491063
$706$	15.3004	0.575839
$707$	0.909543	0.0342069
$708$	−0.480116	−0.0180439
$709$	−10.7104	−0.402237	−0.201118	−	0.979567i	$-0.564458\pi$
$709$	−10.7104	−0.402237	−0.201118	+	0.979567i	$0.564458\pi$
$710$	−11.1367	−0.417953
$711$	−39.7011	−1.48891
$712$	−19.9782	−0.748716
$713$	−1.47729	−0.0553250
$714$	−2.24321	−0.0839500
$715$	−1.35431	−0.0506482
$716$	48.5012	1.81257
$717$	1.99460	0.0744899
$718$	−51.8031	−1.93328
$719$	−34.2576	−1.27759	−0.638796	−	0.769376i	$-0.720567\pi$
$719$	−34.2576	−1.27759	−0.638796	+	0.769376i	$0.720567\pi$
$720$	30.3348	1.13051
$721$	4.89769	0.182399
$722$	33.4952	1.24656
$723$	−2.72254	−0.101252
$724$	−26.9915	−1.00313
$725$	−1.00264	−0.0372373
$726$	1.32636	0.0492259
$727$	−47.8193	−1.77352	−0.886759	−	0.462231i	$-0.847049\pi$
$727$	−47.8193	−1.77352	−0.886759	+	0.462231i	$0.847049\pi$
$728$	−3.14474	−0.116552
$729$	−25.9812	−0.962266
$730$	16.3587	0.605464
$731$	−63.2281	−2.33857
$732$	−7.63928	−0.282356
$733$	−7.44679	−0.275053	−0.137527	−	0.990498i	$-0.543915\pi$
$733$	−7.44679	−0.275053	−0.137527	+	0.990498i	$0.543915\pi$
$734$	−45.1980	−1.66829
$735$	0.869867	0.0320855
$736$	−2.75524	−0.101559
$737$	2.77201	0.102108
$738$	−34.7471	−1.27906
$739$	28.2760	1.04015	0.520074	−	0.854121i	$-0.325904\pi$
$739$	28.2760	1.04015	0.520074	+	0.854121i	$0.325904\pi$
$740$	40.5177	1.48946
$741$	0.172124	0.00632312
$742$	17.4887	0.642030
$743$	42.4803	1.55845	0.779226	−	0.626743i	$-0.215612\pi$
$743$	42.4803	1.55845	0.779226	+	0.626743i	$0.215612\pi$
$744$	6.46486	0.237013
$745$	1.63880	0.0600410
$746$	12.9846	0.475399
$747$	24.0869	0.881295
$748$	99.4392	3.63586
$749$	−9.42055	−0.344220
$750$	0.361646	0.0132054
$751$	29.8029	1.08752	0.543761	−	0.839240i	$-0.317000\pi$
$751$	29.8029	1.08752	0.543761	+	0.839240i	$0.317000\pi$
$752$	96.3408	3.51319
$753$	−2.77626	−0.101172
$754$	1.31682	0.0479558
$755$	8.33273	0.303259
$756$	−3.33459	−0.121278
$757$	−29.2873	−1.06446	−0.532232	−	0.846598i	$-0.678647\pi$
$757$	−29.2873	−1.06446	−0.532232	+	0.846598i	$0.678647\pi$
$758$	−35.3191	−1.28285
$759$	0.0892388	0.00323916
$760$	19.0012	0.689247
$761$	−18.6342	−0.675491	−0.337745	−	0.941237i	$-0.609664\pi$
$761$	−18.6342	−0.675491	−0.337745	+	0.941237i	$0.609664\pi$
$762$	−3.73245	−0.135213
$763$	−7.67539	−0.277868
$764$	88.7877	3.21222
$765$	22.3610	0.808465
$766$	60.1077	2.17178
$767$	−0.356151	−0.0128599
$768$	−1.66441	−0.0600591
$769$	−7.98368	−0.287899	−0.143949	−	0.989585i	$-0.545980\pi$
$769$	−7.98368	−0.287899	−0.143949	+	0.989585i	$0.545980\pi$
$770$	5.87993	0.211898
$771$	−2.87685	−0.103607
$772$	−72.1555	−2.59693
$773$	−34.0879	−1.22606	−0.613029	−	0.790060i	$-0.710049\pi$
$773$	−34.0879	−1.22606	−0.613029	+	0.790060i	$0.710049\pi$
$774$	−65.9841	−2.37175
$775$	−6.17352	−0.221759
$776$	−34.6950	−1.24548
$777$	−0.942527	−0.0338130
$778$	10.8777	0.389985
$779$	−11.0922	−0.397418
$780$	−0.337208	−0.0120740
$781$	−11.4840	−0.410930
$782$	−4.71352	−0.168555
$783$	0.825885	0.0295147
$784$	−64.2734	−2.29548
$785$	−8.37599	−0.298952
$786$	2.17259	0.0774937
$787$	21.6960	0.773378	0.386689	−	0.922210i	$-0.373619\pi$
$787$	21.6960	0.773378	0.386689	+	0.922210i	$0.373619\pi$
$788$	−44.1560	−1.57299
$789$	−1.28870	−0.0458790
$790$	34.9722	1.24425
$791$	15.9026	0.565433
$792$	61.3792	2.18101
$793$	−5.66684	−0.201235
$794$	59.8305	2.12331
$795$	1.10919	0.0393388
$796$	−99.5077	−3.52696
$797$	0.601924	0.0213212	0.0106606	−	0.999943i	$-0.496607\pi$
$797$	0.601924	0.0213212	0.0106606	+	0.999943i	$0.496607\pi$
$798$	−0.747302	−0.0264542
$799$	71.0166	2.51239
$800$	−11.5140	−0.407081
$801$	−7.83237	−0.276743
$802$	95.4830	3.37162
$803$	16.8689	0.595290
$804$	0.690203	0.0243416
$805$	−0.197877	−0.00697424
$806$	8.10798	0.285592
$807$	0.828701	0.0291717
$808$	−8.36358	−0.294230
$809$	23.0480	0.810324	0.405162	−	0.914245i	$-0.367215\pi$
$809$	23.0480	0.810324	0.405162	+	0.914245i	$0.367215\pi$
$810$	23.1863	0.814683
$811$	−11.4090	−0.400624	−0.200312	−	0.979732i	$-0.564196\pi$
$811$	−11.4090	−0.400624	−0.200312	+	0.979732i	$0.564196\pi$
$812$	−4.05898	−0.142442
$813$	−0.178540	−0.00626167
$814$	58.8501	2.06269
$815$	−5.27830	−0.184891
$816$	10.5123	0.368003
$817$	−21.0638	−0.736929
$818$	43.7571	1.52993
$819$	−1.23288	−0.0430804
$820$	21.7307	0.758869
$821$	−30.1471	−1.05214	−0.526071	−	0.850440i	$-0.676336\pi$
$821$	−30.1471	−1.05214	−0.526071	+	0.850440i	$0.676336\pi$
$822$	−2.51088	−0.0875771
$823$	16.1542	0.563100	0.281550	−	0.959547i	$-0.409151\pi$
$823$	16.1542	0.563100	0.281550	+	0.959547i	$0.409151\pi$
$824$	−45.0360	−1.56890
$825$	0.372924	0.0129835
$826$	1.54629	0.0538021
$827$	−14.2770	−0.496460	−0.248230	−	0.968701i	$-0.579849\pi$
$827$	−14.2770	−0.496460	−0.248230	+	0.968701i	$0.579849\pi$
$828$	−3.49228	−0.121365
$829$	−14.4862	−0.503127	−0.251563	−	0.967841i	$-0.580945\pi$
$829$	−14.4862	−0.503127	−0.251563	+	0.967841i	$0.580945\pi$
$830$	−21.2179	−0.736483
$831$	−2.51528	−0.0872541
$832$	4.94304	0.171369
$833$	−47.3785	−1.64157
$834$	4.23011	0.146477
$835$	−9.62525	−0.333096
$836$	33.1271	1.14573
$837$	5.08517	0.175769
$838$	23.5432	0.813286
$839$	28.3018	0.977088	0.488544	−	0.872539i	$-0.337528\pi$
$839$	28.3018	0.977088	0.488544	+	0.872539i	$0.337528\pi$
$840$	0.865941	0.0298778
$841$	−27.9947	−0.965335
$842$	20.8056	0.717007
$843$	−3.07843	−0.106027
$844$	−62.2261	−2.14191
$845$	12.7499	0.438608
$846$	74.1121	2.54803
$847$	−3.03278	−0.104207
$848$	−81.9566	−2.81440
$849$	−2.31174	−0.0793387
$850$	−19.6975	−0.675620
$851$	−1.98048	−0.0678899
$852$	−2.85940	−0.0979613
$853$	28.7636	0.984846	0.492423	−	0.870356i	$-0.336111\pi$
$853$	28.7636	0.984846	0.492423	+	0.870356i	$0.336111\pi$
$854$	24.6035	0.841913
$855$	7.44935	0.254762
$856$	86.6254	2.96080
$857$	6.53005	0.223062	0.111531	−	0.993761i	$-0.464424\pi$
$857$	6.53005	0.223062	0.111531	+	0.993761i	$0.464424\pi$
$858$	−0.489779	−0.0167208
$859$	1.24820	0.0425880	0.0212940	−	0.999773i	$-0.493221\pi$
$859$	1.24820	0.0425880	0.0212940	+	0.999773i	$0.493221\pi$
$860$	41.2661	1.40716
$861$	−0.505502	−0.0172274
$862$	49.4166	1.68314
$863$	−18.6600	−0.635195	−0.317598	−	0.948226i	$-0.602876\pi$
$863$	−18.6600	−0.635195	−0.317598	+	0.948226i	$0.602876\pi$
$864$	9.48414	0.322657
$865$	1.06808	0.0363159
$866$	12.9112	0.438742
$867$	5.40777	0.183658
$868$	−24.9921	−0.848287
$869$	36.0628	1.22335
$870$	−0.362602	−0.0122934
$871$	0.511994	0.0173483
$872$	70.5780	2.39007
$873$	−13.6020	−0.460359
$874$	−1.57026	−0.0531149
$875$	−0.826916	−0.0279549
$876$	4.20018	0.141911
$877$	5.88903	0.198858	0.0994292	−	0.995045i	$-0.468298\pi$
$877$	5.88903	0.198858	0.0994292	+	0.995045i	$0.468298\pi$
$878$	−84.9907	−2.86830
$879$	4.16082	0.140341
$880$	−27.5549	−0.928875
$881$	20.6380	0.695312	0.347656	−	0.937622i	$-0.386978\pi$
$881$	20.6380	0.695312	0.347656	+	0.937622i	$0.386978\pi$
$882$	−49.4436	−1.66485
$883$	−35.8903	−1.20781	−0.603903	−	0.797058i	$-0.706389\pi$
$883$	−35.8903	−1.20781	−0.603903	+	0.797058i	$0.706389\pi$
$884$	18.3665	0.617733
$885$	0.0980703	0.00329660
$886$	−67.0409	−2.25228
$887$	−1.16595	−0.0391486	−0.0195743	−	0.999808i	$-0.506231\pi$
$887$	−1.16595	−0.0391486	−0.0195743	+	0.999808i	$0.506231\pi$
$888$	8.66688	0.290841
$889$	8.53439	0.286234
$890$	6.89944	0.231270
$891$	23.9093	0.800993
$892$	78.7494	2.63673
$893$	23.6585	0.791700
$894$	0.592665	0.0198217
$895$	−9.90704	−0.331156
$896$	−2.41878	−0.0808059
$897$	0.0164825	0.000550335 0
$898$	−26.2847	−0.877131
$899$	6.18984	0.206443
$900$	−14.5940	−0.486468
$901$	−60.4135	−2.01266
$902$	31.5628	1.05093
$903$	−0.959937	−0.0319447
$904$	−146.231	−4.86355
$905$	5.51339	0.183271
$906$	3.01350	0.100117
$907$	−29.3349	−0.974051	−0.487025	−	0.873388i	$-0.661918\pi$
$907$	−29.3349	−0.974051	−0.487025	+	0.873388i	$0.661918\pi$
$908$	37.5330	1.24558
$909$	−3.27890	−0.108754
$910$	1.08603	0.0360015
$911$	−34.3007	−1.13643	−0.568217	−	0.822879i	$-0.692366\pi$
$911$	−34.3007	−1.13643	−0.568217	+	0.822879i	$0.692366\pi$
$912$	3.50205	0.115965
$913$	−21.8796	−0.724108
$914$	−103.932	−3.43776
$915$	1.56043	0.0515862
$916$	−61.2530	−2.02386
$917$	−4.96771	−0.164048
$918$	16.2250	0.535504
$919$	11.9624	0.394603	0.197301	−	0.980343i	$-0.436782\pi$
$919$	11.9624	0.394603	0.197301	+	0.980343i	$0.436782\pi$
$920$	1.81955	0.0599888
$921$	−2.03779	−0.0671474
$922$	42.2965	1.39296
$923$	−2.12111	−0.0698171
$924$	1.50970	0.0496654
$925$	−8.27630	−0.272123
$926$	41.7166	1.37089
$927$	−17.6562	−0.579905
$928$	11.5444	0.378964
$929$	−39.5244	−1.29675	−0.648377	−	0.761320i	$-0.724552\pi$
$929$	−39.5244	−1.29675	−0.648377	+	0.761320i	$0.724552\pi$
$930$	−2.23263	−0.0732107
$931$	−15.7837	−0.517289
$932$	135.563	4.44050
$933$	3.34502	0.109511
$934$	87.0522	2.84844
$935$	−20.3118	−0.664267
$936$	11.3368	0.370555
$937$	9.44399	0.308522	0.154261	−	0.988030i	$-0.450700\pi$
$937$	9.44399	0.308522	0.154261	+	0.988030i	$0.450700\pi$
$938$	−2.22290	−0.0725803
$939$	2.50545	0.0817622
$940$	−46.3494	−1.51175
$941$	−26.5121	−0.864270	−0.432135	−	0.901809i	$-0.642240\pi$
$941$	−26.5121	−0.864270	−0.432135	+	0.901809i	$0.642240\pi$
$942$	−3.02914	−0.0986948
$943$	−1.06218	−0.0345894
$944$	−7.24629	−0.235847
$945$	0.681136	0.0221574
$946$	59.9371	1.94872
$947$	59.0275	1.91814	0.959068	−	0.283177i	$-0.0913884\pi$
$947$	59.0275	1.91814	0.959068	+	0.283177i	$0.0913884\pi$
$948$	8.97926	0.291633
$949$	3.11570	0.101140
$950$	−6.56203	−0.212900
$951$	−2.18994	−0.0710138
$952$	−47.1647	−1.52862
$953$	49.5708	1.60576	0.802878	−	0.596144i	$-0.203301\pi$
$953$	49.5708	1.60576	0.802878	+	0.596144i	$0.203301\pi$
$954$	−63.0468	−2.04121
$955$	−18.1361	−0.586870
$956$	70.9038	2.29319
$957$	−0.373910	−0.0120868
$958$	76.8038	2.48142
$959$	5.74122	0.185394
$960$	−1.36112	−0.0439300
$961$	7.11231	0.229429
$962$	10.8697	0.350452
$963$	33.9611	1.09438
$964$	−96.7802	−3.11708
$965$	14.7387	0.474457
$966$	−0.0715613	−0.00230245
$967$	−18.9494	−0.609372	−0.304686	−	0.952453i	$-0.598551\pi$
$967$	−18.9494	−0.609372	−0.304686	+	0.952453i	$0.598551\pi$
$968$	27.8875	0.896338
$969$	2.58150	0.0829298
$970$	11.9819	0.384714
$971$	37.2208	1.19447	0.597236	−	0.802065i	$-0.296265\pi$
$971$	37.2208	1.19447	0.597236	+	0.802065i	$0.296265\pi$
$972$	18.0509	0.578982
$973$	−9.67230	−0.310080
$974$	−66.0078	−2.11503
$975$	0.0688794	0.00220591
$976$	−115.298	−3.69061
$977$	−24.6722	−0.789334	−0.394667	−	0.918824i	$-0.629140\pi$
$977$	−24.6722	−0.789334	−0.394667	+	0.918824i	$0.629140\pi$
$978$	−1.90887	−0.0610390
$979$	7.11460	0.227384
$980$	30.9218	0.987762
$981$	27.6698	0.883429
$982$	43.5689	1.39034
$983$	−27.8167	−0.887214	−0.443607	−	0.896221i	$-0.646301\pi$
$983$	−27.8167	−0.887214	−0.443607	+	0.896221i	$0.646301\pi$
$984$	4.64827	0.148181
$985$	9.01948	0.287384
$986$	19.7496	0.628956
$987$	1.07818	0.0343190
$988$	6.11862	0.194659
$989$	−2.01706	−0.0641388
$990$	−21.1972	−0.673690
$991$	−24.4889	−0.777914	−0.388957	−	0.921256i	$-0.627165\pi$
$991$	−24.4889	−0.777914	−0.388957	+	0.921256i	$0.627165\pi$
$992$	71.0817	2.25685
$993$	0.308834	0.00980054
$994$	9.20911	0.292095
$995$	20.3258	0.644371
$996$	−5.44778	−0.172620
$997$	55.8418	1.76853	0.884265	−	0.466986i	$-0.154660\pi$
$997$	55.8418	1.76853	0.884265	+	0.466986i	$0.154660\pi$
$998$	13.3996	0.424156
$999$	6.81724	0.215688

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.d.1.2	✓	83

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.d.1.2	✓	83	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.62595 q^{2} +0.137720 q^{3} +4.89563 q^{4} -1.00000 q^{5} -0.361646 q^{6} +0.826916 q^{7} -7.60380 q^{8} -2.98103 q^{9} +O(q^{10})\)	\(q-2.62595 q^{2} +0.137720 q^{3} +4.89563 q^{4} -1.00000 q^{5} -0.361646 q^{6} +0.826916 q^{7} -7.60380 q^{8} -2.98103 q^{9} +2.62595 q^{10} +2.70784 q^{11} +0.674225 q^{12} +0.500142 q^{13} -2.17144 q^{14} -0.137720 q^{15} +10.1759 q^{16} +7.50110 q^{17} +7.82805 q^{18} +2.49891 q^{19} -4.89563 q^{20} +0.113883 q^{21} -7.11068 q^{22} +0.239295 q^{23} -1.04719 q^{24} +1.00000 q^{25} -1.31335 q^{26} -0.823706 q^{27} +4.04828 q^{28} -1.00264 q^{29} +0.361646 q^{30} -6.17352 q^{31} -11.5140 q^{32} +0.372924 q^{33} -19.6975 q^{34} -0.826916 q^{35} -14.5940 q^{36} -8.27630 q^{37} -6.56203 q^{38} +0.0688794 q^{39} +7.60380 q^{40} -4.43879 q^{41} -0.299051 q^{42} -8.42918 q^{43} +13.2566 q^{44} +2.98103 q^{45} -0.628378 q^{46} +9.46750 q^{47} +1.40143 q^{48} -6.31621 q^{49} -2.62595 q^{50} +1.03305 q^{51} +2.44851 q^{52} -8.05395 q^{53} +2.16301 q^{54} -2.70784 q^{55} -6.28770 q^{56} +0.344150 q^{57} +2.63290 q^{58} -0.712100 q^{59} -0.674225 q^{60} -11.3305 q^{61} +16.2114 q^{62} -2.46506 q^{63} +9.88327 q^{64} -0.500142 q^{65} -0.979280 q^{66} +1.02370 q^{67} +36.7226 q^{68} +0.0329557 q^{69} +2.17144 q^{70} -4.24101 q^{71} +22.6672 q^{72} +6.22964 q^{73} +21.7332 q^{74} +0.137720 q^{75} +12.2338 q^{76} +2.23916 q^{77} -0.180874 q^{78} +13.3179 q^{79} -10.1759 q^{80} +8.82966 q^{81} +11.6561 q^{82} -8.08006 q^{83} +0.557528 q^{84} -7.50110 q^{85} +22.1346 q^{86} -0.138084 q^{87} -20.5899 q^{88} +2.62740 q^{89} -7.82805 q^{90} +0.413575 q^{91} +1.17150 q^{92} -0.850215 q^{93} -24.8612 q^{94} -2.49891 q^{95} -1.58570 q^{96} +4.56286 q^{97} +16.5861 q^{98} -8.07218 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9}+O(q^{10}) \) 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9	\( 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9} - q^{10} - 26 q^{11} - 12 q^{12} - 15 q^{13} - 21 q^{14} + 4 q^{15} + 5 q^{16} + 8 q^{17} - 12 q^{18} - 79 q^{19} - 61 q^{20} - 34 q^{21} - 25 q^{22} + 31 q^{23} - 42 q^{24} + 83 q^{25} - 13 q^{26} - 25 q^{27} - 16 q^{28} - 16 q^{29} + 6 q^{30} - 40 q^{31} + 15 q^{32} - 33 q^{33} - 54 q^{34} - 2 q^{35} + 11 q^{36} - 45 q^{37} + 10 q^{38} - 54 q^{39} + 3 q^{40} - 27 q^{41} - 28 q^{42} - 101 q^{43} - 51 q^{44} - 61 q^{45} - 46 q^{46} + 71 q^{47} - 14 q^{48} + 23 q^{49} + q^{50} - 71 q^{51} - 34 q^{52} - 49 q^{53} - 25 q^{54} + 26 q^{55} - 41 q^{56} - 20 q^{57} - 43 q^{58} - 60 q^{59} + 12 q^{60} - 38 q^{61} - 2 q^{62} + 36 q^{63} - 113 q^{64} + 15 q^{65} - 42 q^{66} - 164 q^{67} + 10 q^{68} - 93 q^{69} + 21 q^{70} - 78 q^{71} + q^{72} - 18 q^{73} - 23 q^{74} - 4 q^{75} - 112 q^{76} - 35 q^{77} - 44 q^{78} - 124 q^{79} - 5 q^{80} - 45 q^{81} - 34 q^{82} + 5 q^{83} - 60 q^{84} - 8 q^{85} - 25 q^{86} + 12 q^{87} - 149 q^{88} - 44 q^{89} + 12 q^{90} - 192 q^{91} + 35 q^{92} - 13 q^{93} - 32 q^{94} + 79 q^{95} - 59 q^{96} - 31 q^{97} + 25 q^{98} - 134 q^{99}+O(q^{100}) \) 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9 - q^10 - 26 * q^11 - 12 * q^12 - 15 * q^13 - 21 * q^14 + 4 * q^15 + 5 * q^16 + 8 * q^17 - 12 * q^18 - 79 * q^19 - 61 * q^20 - 34 * q^21 - 25 * q^22 + 31 * q^23 - 42 * q^24 + 83 * q^25 - 13 * q^26 - 25 * q^27 - 16 * q^28 - 16 * q^29 + 6 * q^30 - 40 * q^31 + 15 * q^32 - 33 * q^33 - 54 * q^34 - 2 * q^35 + 11 * q^36 - 45 * q^37 + 10 * q^38 - 54 * q^39 + 3 * q^40 - 27 * q^41 - 28 * q^42 - 101 * q^43 - 51 * q^44 - 61 * q^45 - 46 * q^46 + 71 * q^47 - 14 * q^48 + 23 * q^49 + q^50 - 71 * q^51 - 34 * q^52 - 49 * q^53 - 25 * q^54 + 26 * q^55 - 41 * q^56 - 20 * q^57 - 43 * q^58 - 60 * q^59 + 12 * q^60 - 38 * q^61 - 2 * q^62 + 36 * q^63 - 113 * q^64 + 15 * q^65 - 42 * q^66 - 164 * q^67 + 10 * q^68 - 93 * q^69 + 21 * q^70 - 78 * q^71 + q^72 - 18 * q^73 - 23 * q^74 - 4 * q^75 - 112 * q^76 - 35 * q^77 - 44 * q^78 - 124 * q^79 - 5 * q^80 - 45 * q^81 - 34 * q^82 + 5 * q^83 - 60 * q^84 - 8 * q^85 - 25 * q^86 + 12 * q^87 - 149 * q^88 - 44 * q^89 + 12 * q^90 - 192 * q^91 + 35 * q^92 - 13 * q^93 - 32 * q^94 + 79 * q^95 - 59 * q^96 - 31 * q^97 + 25 * q^98 - 134 * q^99

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