LMFDB - Embedded newform 6043.2.a.c.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6043,2,Mod(1,6043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6043, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6043 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6043.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:	$48.2535979415$
Analytic rank:	$0$
Dimension:	$259$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.45883 q^{2} +0.759848 q^{3} +4.04584 q^{4} +3.80282 q^{5} -1.86834 q^{6} +2.58562 q^{7} -5.03037 q^{8} -2.42263 q^{9} +O(q^{10})$	\(q-2.45883 q^{2} +0.759848 q^{3} +4.04584 q^{4} +3.80282 q^{5} -1.86834 q^{6} +2.58562 q^{7} -5.03037 q^{8} -2.42263 q^{9} -9.35049 q^{10} +2.74028 q^{11} +3.07422 q^{12} -1.61816 q^{13} -6.35760 q^{14} +2.88957 q^{15} +4.27714 q^{16} -1.32081 q^{17} +5.95684 q^{18} +2.92381 q^{19} +15.3856 q^{20} +1.96468 q^{21} -6.73788 q^{22} +0.302229 q^{23} -3.82232 q^{24} +9.46146 q^{25} +3.97878 q^{26} -4.12038 q^{27} +10.4610 q^{28} +6.91718 q^{29} -7.10495 q^{30} +10.2950 q^{31} -0.456020 q^{32} +2.08220 q^{33} +3.24765 q^{34} +9.83265 q^{35} -9.80158 q^{36} -3.37370 q^{37} -7.18914 q^{38} -1.22956 q^{39} -19.1296 q^{40} -4.58569 q^{41} -4.83081 q^{42} +4.12481 q^{43} +11.0867 q^{44} -9.21283 q^{45} -0.743131 q^{46} +0.130187 q^{47} +3.24998 q^{48} -0.314567 q^{49} -23.2641 q^{50} -1.00362 q^{51} -6.54682 q^{52} +5.53006 q^{53} +10.1313 q^{54} +10.4208 q^{55} -13.0066 q^{56} +2.22165 q^{57} -17.0082 q^{58} -12.1047 q^{59} +11.6907 q^{60} -9.24210 q^{61} -25.3137 q^{62} -6.26400 q^{63} -7.43301 q^{64} -6.15357 q^{65} -5.11976 q^{66} +1.49512 q^{67} -5.34380 q^{68} +0.229648 q^{69} -24.1768 q^{70} +12.0008 q^{71} +12.1867 q^{72} +10.6074 q^{73} +8.29535 q^{74} +7.18927 q^{75} +11.8293 q^{76} +7.08532 q^{77} +3.02327 q^{78} -11.5212 q^{79} +16.2652 q^{80} +4.13703 q^{81} +11.2754 q^{82} +12.4974 q^{83} +7.94878 q^{84} -5.02282 q^{85} -10.1422 q^{86} +5.25600 q^{87} -13.7846 q^{88} +3.66988 q^{89} +22.6528 q^{90} -4.18395 q^{91} +1.22277 q^{92} +7.82265 q^{93} -0.320106 q^{94} +11.1187 q^{95} -0.346506 q^{96} -2.60710 q^{97} +0.773465 q^{98} -6.63869 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9}+O(q^{10}) $ 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9} + 36 q^{10} + 35 q^{11} + 58 q^{12} + 109 q^{13} + 31 q^{14} + 30 q^{15} + 287 q^{16} + 124 q^{17} + 97 q^{18} + 42 q^{19} + 149 q^{20} + 99 q^{21} + 22 q^{22} + 63 q^{23} + 53 q^{24} + 308 q^{25} + 86 q^{26} + 82 q^{27} + 52 q^{28} + 131 q^{29} + 6 q^{30} + 29 q^{31} + 251 q^{32} + 147 q^{33} + 24 q^{34} + 79 q^{35} + 315 q^{36} + 108 q^{37} + 124 q^{38} + 48 q^{39} + 87 q^{40} + 190 q^{41} + 28 q^{42} + 36 q^{43} + 70 q^{44} + 211 q^{45} + 19 q^{46} + 186 q^{47} + 103 q^{48} + 297 q^{49} + 161 q^{50} + 20 q^{51} + 173 q^{52} + 213 q^{53} + 56 q^{54} + 35 q^{55} + 99 q^{56} + 80 q^{57} + 32 q^{58} + 135 q^{59} + 23 q^{60} + 83 q^{61} + 172 q^{62} + 85 q^{63} + 297 q^{64} + 177 q^{65} + 41 q^{66} + 30 q^{67} + 271 q^{68} + 168 q^{69} + 24 q^{70} + 63 q^{71} + 241 q^{72} + 152 q^{73} + 32 q^{74} + 36 q^{75} + 92 q^{76} + 396 q^{77} + 21 q^{78} - 2 q^{79} + 242 q^{80} + 343 q^{81} + 40 q^{82} + 236 q^{83} + 92 q^{84} + 124 q^{85} + 55 q^{86} + 113 q^{87} + 7 q^{88} + 214 q^{89} + 100 q^{90} + 2 q^{91} + 176 q^{92} + 228 q^{93} + 51 q^{94} + 96 q^{95} + 48 q^{96} + 135 q^{97} + 261 q^{98} + 26 q^{99}+O(q^{100}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9 + 36 * q^10 + 35 * q^11 + 58 * q^12 + 109 * q^13 + 31 * q^14 + 30 * q^15 + 287 * q^16 + 124 * q^17 + 97 * q^18 + 42 * q^19 + 149 * q^20 + 99 * q^21 + 22 * q^22 + 63 * q^23 + 53 * q^24 + 308 * q^25 + 86 * q^26 + 82 * q^27 + 52 * q^28 + 131 * q^29 + 6 * q^30 + 29 * q^31 + 251 * q^32 + 147 * q^33 + 24 * q^34 + 79 * q^35 + 315 * q^36 + 108 * q^37 + 124 * q^38 + 48 * q^39 + 87 * q^40 + 190 * q^41 + 28 * q^42 + 36 * q^43 + 70 * q^44 + 211 * q^45 + 19 * q^46 + 186 * q^47 + 103 * q^48 + 297 * q^49 + 161 * q^50 + 20 * q^51 + 173 * q^52 + 213 * q^53 + 56 * q^54 + 35 * q^55 + 99 * q^56 + 80 * q^57 + 32 * q^58 + 135 * q^59 + 23 * q^60 + 83 * q^61 + 172 * q^62 + 85 * q^63 + 297 * q^64 + 177 * q^65 + 41 * q^66 + 30 * q^67 + 271 * q^68 + 168 * q^69 + 24 * q^70 + 63 * q^71 + 241 * q^72 + 152 * q^73 + 32 * q^74 + 36 * q^75 + 92 * q^76 + 396 * q^77 + 21 * q^78 - 2 * q^79 + 242 * q^80 + 343 * q^81 + 40 * q^82 + 236 * q^83 + 92 * q^84 + 124 * q^85 + 55 * q^86 + 113 * q^87 + 7 * q^88 + 214 * q^89 + 100 * q^90 + 2 * q^91 + 176 * q^92 + 228 * q^93 + 51 * q^94 + 96 * q^95 + 48 * q^96 + 135 * q^97 + 261 * q^98 + 26 * 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 $

$2$	−2.45883	−1.73865	−0.869327	−	0.494237i	$-0.835448\pi$
$2$	−2.45883	−1.73865	−0.869327	+	0.494237i	$0.835448\pi$
$3$	0.759848	0.438698	0.219349	−	0.975646i	$-0.429607\pi$
$3$	0.759848	0.438698	0.219349	+	0.975646i	$0.429607\pi$
$4$	4.04584	2.02292
$5$	3.80282	1.70067	0.850337	−	0.526239i	$-0.176398\pi$
$5$	3.80282	1.70067	0.850337	+	0.526239i	$0.176398\pi$
$6$	−1.86834	−0.762745
$7$	2.58562	0.977273	0.488636	−	0.872488i	$-0.337494\pi$
$7$	2.58562	0.977273	0.488636	+	0.872488i	$0.337494\pi$
$8$	−5.03037	−1.77850
$9$	−2.42263	−0.807544
$10$	−9.35049	−2.95688
$11$	2.74028	0.826225	0.413113	−	0.910680i	$-0.364442\pi$
$11$	2.74028	0.826225	0.413113	+	0.910680i	$0.364442\pi$
$12$	3.07422	0.887452
$13$	−1.61816	−0.448797	−0.224398	−	0.974497i	$-0.572042\pi$
$13$	−1.61816	−0.448797	−0.224398	+	0.974497i	$0.572042\pi$
$14$	−6.35760	−1.69914
$15$	2.88957	0.746083
$16$	4.27714	1.06929
$17$	−1.32081	−0.320344	−0.160172	−	0.987089i	$-0.551205\pi$
$17$	−1.32081	−0.320344	−0.160172	+	0.987089i	$0.551205\pi$
$18$	5.95684	1.40404
$19$	2.92381	0.670767	0.335383	−	0.942082i	$-0.391134\pi$
$19$	2.92381	0.670767	0.335383	+	0.942082i	$0.391134\pi$
$20$	15.3856	3.44033
$21$	1.96468	0.428728
$22$	−6.73788	−1.43652
$23$	0.302229	0.0630192	0.0315096	−	0.999503i	$-0.489969\pi$
$23$	0.302229	0.0630192	0.0315096	+	0.999503i	$0.489969\pi$
$24$	−3.82232	−0.780227
$25$	9.46146	1.89229
$26$	3.97878	0.780303
$27$	−4.12038	−0.792967
$28$	10.4610	1.97694
$29$	6.91718	1.28449	0.642244	−	0.766500i	$-0.278004\pi$
$29$	6.91718	1.28449	0.642244	+	0.766500i	$0.278004\pi$
$30$	−7.10495	−1.29718
$31$	10.2950	1.84904	0.924520	−	0.381135i	$-0.124467\pi$
$31$	10.2950	1.84904	0.924520	+	0.381135i	$0.124467\pi$
$32$	−0.456020	−0.0806137
$33$	2.08220	0.362464
$34$	3.24765	0.556968
$35$	9.83265	1.66202
$36$	−9.80158	−1.63360
$37$	−3.37370	−0.554633	−0.277316	−	0.960779i	$-0.589445\pi$
$37$	−3.37370	−0.554633	−0.277316	+	0.960779i	$0.589445\pi$
$38$	−7.18914	−1.16623
$39$	−1.22956	−0.196886
$40$	−19.1296	−3.02466
$41$	−4.58569	−0.716165	−0.358083	−	0.933690i	$-0.616569\pi$
$41$	−4.58569	−0.716165	−0.358083	+	0.933690i	$0.616569\pi$
$42$	−4.83081	−0.745410
$43$	4.12481	0.629028	0.314514	−	0.949253i	$-0.398159\pi$
$43$	4.12481	0.629028	0.314514	+	0.949253i	$0.398159\pi$
$44$	11.0867	1.67139
$45$	−9.21283	−1.37337
$46$	−0.743131	−0.109569
$47$	0.130187	0.0189897	0.00949483	−	0.999955i	$-0.496978\pi$
$47$	0.130187	0.0189897	0.00949483	+	0.999955i	$0.496978\pi$
$48$	3.24998	0.469094
$49$	−0.314567	−0.0449381
$50$	−23.2641	−3.29004
$51$	−1.00362	−0.140535
$52$	−6.54682	−0.907880
$53$	5.53006	0.759612	0.379806	−	0.925066i	$-0.375991\pi$
$53$	5.53006	0.759612	0.379806	+	0.925066i	$0.375991\pi$
$54$	10.1313	1.37870
$55$	10.4208	1.40514
$56$	−13.0066	−1.73808
$57$	2.22165	0.294264
$58$	−17.0082	−2.23328
$59$	−12.1047	−1.57590	−0.787948	−	0.615741i	$-0.788857\pi$
$59$	−12.1047	−1.57590	−0.787948	+	0.615741i	$0.788857\pi$
$60$	11.6907	1.50927
$61$	−9.24210	−1.18333	−0.591665	−	0.806184i	$-0.701529\pi$
$61$	−9.24210	−1.18333	−0.591665	+	0.806184i	$0.701529\pi$
$62$	−25.3137	−3.21484
$63$	−6.26400	−0.789190
$64$	−7.43301	−0.929126
$65$	−6.15357	−0.763257
$66$	−5.11976	−0.630199
$67$	1.49512	0.182658	0.0913292	−	0.995821i	$-0.470888\pi$
$67$	1.49512	0.182658	0.0913292	+	0.995821i	$0.470888\pi$
$68$	−5.34380	−0.648031
$69$	0.229648	0.0276464
$70$	−24.1768	−2.88968
$71$	12.0008	1.42423	0.712115	−	0.702063i	$-0.247737\pi$
$71$	12.0008	1.42423	0.712115	+	0.702063i	$0.247737\pi$
$72$	12.1867	1.43622
$73$	10.6074	1.24151	0.620753	−	0.784006i	$-0.286827\pi$
$73$	10.6074	1.24151	0.620753	+	0.784006i	$0.286827\pi$
$74$	8.29535	0.964315
$75$	7.18927	0.830145
$76$	11.8293	1.35691
$77$	7.08532	0.807447
$78$	3.02327	0.342318
$79$	−11.5212	−1.29624	−0.648118	−	0.761540i	$-0.724444\pi$
$79$	−11.5212	−1.29624	−0.648118	+	0.761540i	$0.724444\pi$
$80$	16.2652	1.81851
$81$	4.13703	0.459670
$82$	11.2754	1.24516
$83$	12.4974	1.37177	0.685885	−	0.727710i	$-0.259415\pi$
$83$	12.4974	1.37177	0.685885	+	0.727710i	$0.259415\pi$
$84$	7.94878	0.867283
$85$	−5.02282	−0.544801
$86$	−10.1422	−1.09366
$87$	5.25600	0.563503
$88$	−13.7846	−1.46945
$89$	3.66988	0.389007	0.194503	−	0.980902i	$-0.437690\pi$
$89$	3.66988	0.389007	0.194503	+	0.980902i	$0.437690\pi$
$90$	22.6528	2.38781
$91$	−4.18395	−0.438597
$92$	1.22277	0.127483
$93$	7.82265	0.811171
$94$	−0.320106	−0.0330165
$95$	11.1187	1.14076
$96$	−0.346506	−0.0353651
$97$	−2.60710	−0.264710	−0.132355	−	0.991202i	$-0.542254\pi$
$97$	−2.60710	−0.264710	−0.132355	+	0.991202i	$0.542254\pi$
$98$	0.773465	0.0781318
$99$	−6.63869	−0.667213
$100$	38.2795	3.82795
$101$	−0.738371	−0.0734707	−0.0367353	−	0.999325i	$-0.511696\pi$
$101$	−0.738371	−0.0734707	−0.0367353	+	0.999325i	$0.511696\pi$
$102$	2.46772	0.244341
$103$	0.346954	0.0341864	0.0170932	−	0.999854i	$-0.494559\pi$
$103$	0.346954	0.0341864	0.0170932	+	0.999854i	$0.494559\pi$
$104$	8.13995	0.798187
$105$	7.47132	0.729126
$106$	−13.5975	−1.32070
$107$	−1.37351	−0.132782	−0.0663912	−	0.997794i	$-0.521149\pi$
$107$	−1.37351	−0.132782	−0.0663912	+	0.997794i	$0.521149\pi$
$108$	−16.6704	−1.60411
$109$	−8.72664	−0.835861	−0.417930	−	0.908479i	$-0.637244\pi$
$109$	−8.72664	−0.835861	−0.417930	+	0.908479i	$0.637244\pi$
$110$	−25.6230	−2.44305
$111$	−2.56350	−0.243316
$112$	11.0591	1.04498
$113$	−0.231431	−0.0217712	−0.0108856	−	0.999941i	$-0.503465\pi$
$113$	−0.231431	−0.0217712	−0.0108856	+	0.999941i	$0.503465\pi$
$114$	−5.46265	−0.511624
$115$	1.14932	0.107175
$116$	27.9858	2.59842
$117$	3.92020	0.362423
$118$	29.7634	2.73994
$119$	−3.41512	−0.313064
$120$	−14.5356	−1.32691
$121$	−3.49087	−0.317352
$122$	22.7248	2.05740
$123$	−3.48443	−0.314181
$124$	41.6520	3.74046
$125$	16.9661	1.51750
$126$	15.4021	1.37213
$127$	14.6679	1.30156	0.650782	−	0.759265i	$-0.274441\pi$
$127$	14.6679	1.30156	0.650782	+	0.759265i	$0.274441\pi$
$128$	19.1885	1.69604
$129$	3.13423	0.275953
$130$	15.1306	1.32704
$131$	−9.79248	−0.855573	−0.427787	−	0.903880i	$-0.640707\pi$
$131$	−9.79248	−0.855573	−0.427787	+	0.903880i	$0.640707\pi$
$132$	8.42423	0.733235
$133$	7.55985	0.655522
$134$	−3.67625	−0.317580
$135$	−15.6691	−1.34858
$136$	6.64418	0.569734
$137$	−6.51257	−0.556407	−0.278203	−	0.960522i	$-0.589739\pi$
$137$	−6.51257	−0.556407	−0.278203	+	0.960522i	$0.589739\pi$
$138$	−0.564666	−0.0480676
$139$	−1.48078	−0.125598	−0.0627991	−	0.998026i	$-0.520003\pi$
$139$	−1.48078	−0.125598	−0.0627991	+	0.998026i	$0.520003\pi$
$140$	39.7814	3.36214
$141$	0.0989220	0.00833073
$142$	−29.5079	−2.47624
$143$	−4.43421	−0.370807
$144$	−10.3619	−0.863495
$145$	26.3048	2.18449
$146$	−26.0819	−2.15855
$147$	−0.239023	−0.0197143
$148$	−13.6494	−1.12198
$149$	−1.04065	−0.0852531	−0.0426266	−	0.999091i	$-0.513573\pi$
$149$	−1.04065	−0.0852531	−0.0426266	+	0.999091i	$0.513573\pi$
$150$	−17.6772	−1.44334
$151$	17.2895	1.40700	0.703498	−	0.710697i	$-0.251620\pi$
$151$	17.2895	1.40700	0.703498	+	0.710697i	$0.251620\pi$
$152$	−14.7078	−1.19296
$153$	3.19984	0.258692
$154$	−17.4216	−1.40387
$155$	39.1501	3.14461
$156$	−4.97459	−0.398286
$157$	−14.1823	−1.13187	−0.565934	−	0.824450i	$-0.691484\pi$
$157$	−14.1823	−1.13187	−0.565934	+	0.824450i	$0.691484\pi$
$158$	28.3287	2.25371
$159$	4.20201	0.333241
$160$	−1.73416	−0.137098
$161$	0.781451	0.0615869
$162$	−10.1723	−0.799208
$163$	12.7799	1.00100	0.500498	−	0.865738i	$-0.333150\pi$
$163$	12.7799	1.00100	0.500498	+	0.865738i	$0.333150\pi$
$164$	−18.5530	−1.44874
$165$	7.91822	0.616433
$166$	−30.7290	−2.38504
$167$	−0.647826	−0.0501303	−0.0250651	−	0.999686i	$-0.507979\pi$
$167$	−0.647826	−0.0501303	−0.0250651	+	0.999686i	$0.507979\pi$
$168$	−9.88306	−0.762495
$169$	−10.3816	−0.798581
$170$	12.3502	0.947221
$171$	−7.08330	−0.541674
$172$	16.6883	1.27247
$173$	11.0300	0.838593	0.419296	−	0.907849i	$-0.362277\pi$
$173$	11.0300	0.838593	0.419296	+	0.907849i	$0.362277\pi$
$174$	−12.9236	−0.979737
$175$	24.4637	1.84928
$176$	11.7206	0.883471
$177$	−9.19773	−0.691343
$178$	−9.02361	−0.676349
$179$	7.27829	0.544005	0.272002	−	0.962297i	$-0.412314\pi$
$179$	7.27829	0.544005	0.272002	+	0.962297i	$0.412314\pi$
$180$	−37.2737	−2.77821
$181$	23.5176	1.74805	0.874025	−	0.485881i	$-0.161501\pi$
$181$	23.5176	1.74805	0.874025	+	0.485881i	$0.161501\pi$
$182$	10.2876	0.762569
$183$	−7.02259	−0.519125
$184$	−1.52033	−0.112080
$185$	−12.8296	−0.943249
$186$	−19.2345	−1.41035
$187$	−3.61940	−0.264677
$188$	0.526714	0.0384146
$189$	−10.6537	−0.774945
$190$	−27.3390	−1.98338
$191$	−8.53300	−0.617426	−0.308713	−	0.951155i	$-0.599898\pi$
$191$	−8.53300	−0.617426	−0.308713	+	0.951155i	$0.599898\pi$
$192$	−5.64796	−0.407606
$193$	−9.04731	−0.651240	−0.325620	−	0.945501i	$-0.605573\pi$
$193$	−9.04731	−0.651240	−0.325620	+	0.945501i	$0.605573\pi$
$194$	6.41040	0.460240
$195$	−4.67578	−0.334840
$196$	−1.27269	−0.0909062
$197$	0.516188	0.0367769	0.0183884	−	0.999831i	$-0.494146\pi$
$197$	0.516188	0.0367769	0.0183884	+	0.999831i	$0.494146\pi$
$198$	16.3234	1.16005
$199$	4.07048	0.288548	0.144274	−	0.989538i	$-0.453915\pi$
$199$	4.07048	0.288548	0.144274	+	0.989538i	$0.453915\pi$
$200$	−47.5946	−3.36545
$201$	1.13607	0.0801320
$202$	1.81553	0.127740
$203$	17.8852	1.25529
$204$	−4.06048	−0.284290
$205$	−17.4386	−1.21796
$206$	−0.853102	−0.0594384
$207$	−0.732191	−0.0508908
$208$	−6.92110	−0.479892
$209$	8.01204	0.554205
$210$	−18.3707	−1.26770
$211$	22.6689	1.56059	0.780295	−	0.625411i	$-0.215069\pi$
$211$	22.6689	1.56059	0.780295	+	0.625411i	$0.215069\pi$
$212$	22.3737	1.53664
$213$	9.11876	0.624807
$214$	3.37723	0.230863
$215$	15.6859	1.06977
$216$	20.7270	1.41029
$217$	26.6190	1.80702
$218$	21.4573	1.45327
$219$	8.06004	0.544647
$220$	42.1609	2.84249
$221$	2.13729	0.143769
$222$	6.30320	0.423043
$223$	−2.08582	−0.139677	−0.0698385	−	0.997558i	$-0.522248\pi$
$223$	−2.08582	−0.139677	−0.0698385	+	0.997558i	$0.522248\pi$
$224$	−1.17909	−0.0787816
$225$	−22.9216	−1.52811
$226$	0.569050	0.0378526
$227$	15.5345	1.03106	0.515530	−	0.856872i	$-0.327595\pi$
$227$	15.5345	1.03106	0.515530	+	0.856872i	$0.327595\pi$
$228$	8.98843	0.595273
$229$	6.59957	0.436112	0.218056	−	0.975936i	$-0.430029\pi$
$229$	6.59957	0.436112	0.218056	+	0.975936i	$0.430029\pi$
$230$	−2.82599	−0.186340
$231$	5.38377	0.354226
$232$	−34.7960	−2.28447
$233$	−0.534727	−0.0350311	−0.0175156	−	0.999847i	$-0.505576\pi$
$233$	−0.534727	−0.0350311	−0.0175156	+	0.999847i	$0.505576\pi$
$234$	−9.63911	−0.630129
$235$	0.495076	0.0322952
$236$	−48.9736	−3.18791
$237$	−8.75436	−0.568657
$238$	8.39720	0.544310
$239$	9.90235	0.640530	0.320265	−	0.947328i	$-0.396228\pi$
$239$	9.90235	0.640530	0.320265	+	0.947328i	$0.396228\pi$
$240$	12.3591	0.797776
$241$	−9.64531	−0.621309	−0.310655	−	0.950523i	$-0.600548\pi$
$241$	−9.64531	−0.621309	−0.310655	+	0.950523i	$0.600548\pi$
$242$	8.58345	0.551765
$243$	15.5046	0.994623
$244$	−37.3921	−2.39378
$245$	−1.19624	−0.0764250
$246$	8.56762	0.546251
$247$	−4.73119	−0.301038
$248$	−51.7877	−3.28853
$249$	9.49615	0.601794
$250$	−41.7168	−2.63840
$251$	10.1477	0.640515	0.320258	−	0.947330i	$-0.396230\pi$
$251$	10.1477	0.640515	0.320258	+	0.947330i	$0.396230\pi$
$252$	−25.3432	−1.59647
$253$	0.828193	0.0520681
$254$	−36.0658	−2.26297
$255$	−3.81658	−0.239003
$256$	−32.3153	−2.01971
$257$	−28.4163	−1.77256	−0.886280	−	0.463151i	$-0.846719\pi$
$257$	−28.4163	−1.77256	−0.886280	+	0.463151i	$0.846719\pi$
$258$	−7.70653	−0.479788
$259$	−8.72310	−0.542027
$260$	−24.8964	−1.54401
$261$	−16.7578	−1.03728
$262$	24.0780	1.48755
$263$	8.17960	0.504376	0.252188	−	0.967678i	$-0.418850\pi$
$263$	8.17960	0.504376	0.252188	+	0.967678i	$0.418850\pi$
$264$	−10.4742	−0.644644
$265$	21.0298	1.29185
$266$	−18.5884	−1.13973
$267$	2.78855	0.170657
$268$	6.04903	0.369504
$269$	−12.6396	−0.770650	−0.385325	−	0.922781i	$-0.625911\pi$
$269$	−12.6396	−0.770650	−0.385325	+	0.922781i	$0.625911\pi$
$270$	38.5275	2.34471
$271$	−6.42236	−0.390131	−0.195065	−	0.980790i	$-0.562492\pi$
$271$	−6.42236	−0.390131	−0.195065	+	0.980790i	$0.562492\pi$
$272$	−5.64931	−0.342540
$273$	−3.17916	−0.192412
$274$	16.0133	0.967399
$275$	25.9270	1.56346
$276$	0.929121	0.0559265
$277$	0.157811	0.00948197	0.00474099	−	0.999989i	$-0.498491\pi$
$277$	0.157811	0.00948197	0.00474099	+	0.999989i	$0.498491\pi$
$278$	3.64098	0.218372
$279$	−24.9410	−1.49318
$280$	−49.4619	−2.95591
$281$	15.0858	0.899946	0.449973	−	0.893042i	$-0.351434\pi$
$281$	15.0858	0.899946	0.449973	+	0.893042i	$0.351434\pi$
$282$	−0.243232	−0.0144843
$283$	−23.3756	−1.38953	−0.694766	−	0.719236i	$-0.744492\pi$
$283$	−23.3756	−1.38953	−0.694766	+	0.719236i	$0.744492\pi$
$284$	48.5532	2.88110
$285$	8.44853	0.500448
$286$	10.9030	0.644706
$287$	−11.8569	−0.699889
$288$	1.10477	0.0650991
$289$	−15.2555	−0.897380
$290$	−64.6790	−3.79808
$291$	−1.98100	−0.116128
$292$	42.9160	2.51147
$293$	−5.53109	−0.323130	−0.161565	−	0.986862i	$-0.551654\pi$
$293$	−5.53109	−0.323130	−0.161565	+	0.986862i	$0.551654\pi$
$294$	0.587716	0.0342763
$295$	−46.0320	−2.68009
$296$	16.9710	0.986417
$297$	−11.2910	−0.655169
$298$	2.55877	0.148226
$299$	−0.489056	−0.0282828
$300$	29.0866	1.67932
$301$	10.6652	0.614731
$302$	−42.5118	−2.44628
$303$	−0.561050	−0.0322315
$304$	12.5055	0.717242
$305$	−35.1461	−2.01246
$306$	−7.86787	−0.449776
$307$	−0.219919	−0.0125514	−0.00627571	−	0.999980i	$-0.501998\pi$
$307$	−0.219919	−0.0125514	−0.00627571	+	0.999980i	$0.501998\pi$
$308$	28.6661	1.63340
$309$	0.263633	0.0149975
$310$	−96.2634	−5.46740
$311$	−11.2775	−0.639489	−0.319744	−	0.947504i	$-0.603597\pi$
$311$	−11.2775	−0.639489	−0.319744	+	0.947504i	$0.603597\pi$
$312$	6.18512	0.350164
$313$	−7.38728	−0.417554	−0.208777	−	0.977963i	$-0.566948\pi$
$313$	−7.38728	−0.417554	−0.208777	+	0.977963i	$0.566948\pi$
$314$	34.8718	1.96793
$315$	−23.8209	−1.34216
$316$	−46.6129	−2.62218
$317$	10.2725	0.576962	0.288481	−	0.957486i	$-0.406850\pi$
$317$	10.2725	0.576962	0.288481	+	0.957486i	$0.406850\pi$
$318$	−10.3320	−0.579391
$319$	18.9550	1.06128
$320$	−28.2664	−1.58014
$321$	−1.04366	−0.0582514
$322$	−1.92145	−0.107078
$323$	−3.86180	−0.214876
$324$	16.7378	0.929877
$325$	−15.3102	−0.849254
$326$	−31.4235	−1.74038
$327$	−6.63092	−0.366691
$328$	23.0677	1.27370
$329$	0.336613	0.0185581
$330$	−19.4696	−1.07176
$331$	−17.4929	−0.961498	−0.480749	−	0.876858i	$-0.659635\pi$
$331$	−17.4929	−0.961498	−0.480749	+	0.876858i	$0.659635\pi$
$332$	50.5626	2.77498
$333$	8.17323	0.447890
$334$	1.59289	0.0871593
$335$	5.68569	0.310643
$336$	8.40321	0.458433
$337$	12.4530	0.678357	0.339178	−	0.940722i	$-0.389851\pi$
$337$	12.4530	0.678357	0.339178	+	0.940722i	$0.389851\pi$
$338$	25.5265	1.38846
$339$	−0.175852	−0.00955100
$340$	−20.3215	−1.10209
$341$	28.2112	1.52772
$342$	17.4166	0.941783
$343$	−18.9127	−1.02119
$344$	−20.7493	−1.11873
$345$	0.873312	0.0470176
$346$	−27.1208	−1.45802
$347$	6.73453	0.361528	0.180764	−	0.983526i	$-0.442143\pi$
$347$	6.73453	0.361528	0.180764	+	0.983526i	$0.442143\pi$
$348$	21.2649	1.13992
$349$	−26.5202	−1.41959	−0.709797	−	0.704406i	$-0.751214\pi$
$349$	−26.5202	−1.41959	−0.709797	+	0.704406i	$0.751214\pi$
$350$	−60.1521	−3.21527
$351$	6.66743	0.355881
$352$	−1.24962	−0.0666051
$353$	7.79103	0.414675	0.207337	−	0.978270i	$-0.433520\pi$
$353$	7.79103	0.414675	0.207337	+	0.978270i	$0.433520\pi$
$354$	22.6156	1.20201
$355$	45.6368	2.42215
$356$	14.8478	0.786930
$357$	−2.59497	−0.137341
$358$	−17.8961	−0.945837
$359$	11.3670	0.599928	0.299964	−	0.953950i	$-0.403025\pi$
$359$	11.3670	0.599928	0.299964	+	0.953950i	$0.403025\pi$
$360$	46.3440	2.44254
$361$	−10.4514	−0.550072
$362$	−57.8258	−3.03926
$363$	−2.65253	−0.139222
$364$	−16.9276	−0.887247
$365$	40.3382	2.11140
$366$	17.2674	0.902579
$367$	0.688355	0.0359318	0.0179659	−	0.999839i	$-0.494281\pi$
$367$	0.688355	0.0359318	0.0179659	+	0.999839i	$0.494281\pi$
$368$	1.29268	0.0673855
$369$	11.1094	0.578335
$370$	31.5457	1.63998
$371$	14.2986	0.742348
$372$	31.6492	1.64093
$373$	11.0594	0.572636	0.286318	−	0.958135i	$-0.407569\pi$
$373$	11.0594	0.572636	0.286318	+	0.958135i	$0.407569\pi$
$374$	8.89948	0.460181
$375$	12.8917	0.665723
$376$	−0.654887	−0.0337732
$377$	−11.1931	−0.576474
$378$	26.1957	1.34736
$379$	2.12859	0.109338	0.0546691	−	0.998505i	$-0.482590\pi$
$379$	2.12859	0.109338	0.0546691	+	0.998505i	$0.482590\pi$
$380$	44.9845	2.30766
$381$	11.1454	0.570994
$382$	20.9812	1.07349
$383$	−11.6383	−0.594687	−0.297343	−	0.954771i	$-0.596101\pi$
$383$	−11.6383	−0.594687	−0.297343	+	0.954771i	$0.596101\pi$
$384$	14.5804	0.744052
$385$	26.9442	1.37320
$386$	22.2458	1.13228
$387$	−9.99289	−0.507967
$388$	−10.5479	−0.535488
$389$	15.8990	0.806112	0.403056	−	0.915175i	$-0.367948\pi$
$389$	15.8990	0.806112	0.403056	+	0.915175i	$0.367948\pi$
$390$	11.4969	0.582171
$391$	−0.399189	−0.0201878
$392$	1.58239	0.0799226
$393$	−7.44080	−0.375339
$394$	−1.26922	−0.0639423
$395$	−43.8131	−2.20448
$396$	−26.8591	−1.34972
$397$	−29.6093	−1.48605	−0.743025	−	0.669264i	$-0.766610\pi$
$397$	−29.6093	−1.48605	−0.743025	+	0.669264i	$0.766610\pi$
$398$	−10.0086	−0.501686
$399$	5.74434	0.287577
$400$	40.4680	2.02340
$401$	4.18649	0.209064	0.104532	−	0.994522i	$-0.466666\pi$
$401$	4.18649	0.209064	0.104532	+	0.994522i	$0.466666\pi$
$402$	−2.79339	−0.139322
$403$	−16.6590	−0.829843
$404$	−2.98733	−0.148625
$405$	15.7324	0.781749
$406$	−43.9766	−2.18252
$407$	−9.24488	−0.458252
$408$	5.04857	0.249941
$409$	−17.5784	−0.869195	−0.434597	−	0.900625i	$-0.643109\pi$
$409$	−17.5784	−0.869195	−0.434597	+	0.900625i	$0.643109\pi$
$410$	42.8785	2.11762
$411$	−4.94856	−0.244095
$412$	1.40372	0.0691564
$413$	−31.2981	−1.54008
$414$	1.80033	0.0884815
$415$	47.5255	2.33293
$416$	0.737914	0.0361792
$417$	−1.12517	−0.0550997
$418$	−19.7002	−0.963571
$419$	6.67256	0.325976	0.162988	−	0.986628i	$-0.447887\pi$
$419$	6.67256	0.325976	0.162988	+	0.986628i	$0.447887\pi$
$420$	30.2278	1.47496
$421$	−22.7856	−1.11050	−0.555252	−	0.831682i	$-0.687378\pi$
$421$	−22.7856	−1.11050	−0.555252	+	0.831682i	$0.687378\pi$
$422$	−55.7389	−2.71333
$423$	−0.315394	−0.0153350
$424$	−27.8183	−1.35097
$425$	−12.4968	−0.606185
$426$	−22.4215	−1.08632
$427$	−23.8966	−1.15644
$428$	−5.55701	−0.268608
$429$	−3.36933	−0.162673
$430$	−38.5690	−1.85996
$431$	−36.8506	−1.77503	−0.887516	−	0.460778i	$-0.847571\pi$
$431$	−36.8506	−1.77503	−0.887516	+	0.460778i	$0.847571\pi$
$432$	−17.6234	−0.847908
$433$	35.1062	1.68710	0.843549	−	0.537052i	$-0.180462\pi$
$433$	35.1062	1.68710	0.843549	+	0.537052i	$0.180462\pi$
$434$	−65.4516	−3.14178
$435$	19.9876	0.958334
$436$	−35.3066	−1.69088
$437$	0.883660	0.0422712
$438$	−19.8183	−0.946953
$439$	5.30061	0.252985	0.126492	−	0.991968i	$-0.459628\pi$
$439$	5.30061	0.252985	0.126492	+	0.991968i	$0.459628\pi$
$440$	−52.4205	−2.49905
$441$	0.762079	0.0362895
$442$	−5.25522	−0.249966
$443$	−10.9748	−0.521429	−0.260714	−	0.965416i	$-0.583958\pi$
$443$	−10.9748	−0.521429	−0.260714	+	0.965416i	$0.583958\pi$
$444$	−10.3715	−0.492210
$445$	13.9559	0.661574
$446$	5.12868	0.242850
$447$	−0.790733	−0.0374004
$448$	−19.2189	−0.908010
$449$	34.1549	1.61187	0.805935	−	0.592004i	$-0.201663\pi$
$449$	34.1549	1.61187	0.805935	+	0.592004i	$0.201663\pi$
$450$	56.3603	2.65685
$451$	−12.5661	−0.591714
$452$	−0.936333	−0.0440414
$453$	13.1374	0.617247
$454$	−38.1966	−1.79266
$455$	−15.9108	−0.745910
$456$	−11.1757	−0.523351
$457$	34.1781	1.59878	0.799392	−	0.600809i	$-0.205155\pi$
$457$	34.1781	1.59878	0.799392	+	0.600809i	$0.205155\pi$
$458$	−16.2272	−0.758247
$459$	5.44225	0.254022
$460$	4.64999	0.216807
$461$	13.2409	0.616692	0.308346	−	0.951274i	$-0.400225\pi$
$461$	13.2409	0.616692	0.308346	+	0.951274i	$0.400225\pi$
$462$	−13.2378	−0.615877
$463$	−28.5568	−1.32715	−0.663573	−	0.748112i	$-0.730961\pi$
$463$	−28.5568	−1.32715	−0.663573	+	0.748112i	$0.730961\pi$
$464$	29.5858	1.37348
$465$	29.7481	1.37954
$466$	1.31480	0.0609070
$467$	16.2567	0.752268	0.376134	−	0.926565i	$-0.377253\pi$
$467$	16.2567	0.752268	0.376134	+	0.926565i	$0.377253\pi$
$468$	15.8605	0.733153
$469$	3.86582	0.178507
$470$	−1.21731	−0.0561502
$471$	−10.7764	−0.496549
$472$	60.8911	2.80274
$473$	11.3031	0.519718
$474$	21.5255	0.988698
$475$	27.6635	1.26929
$476$	−13.8170	−0.633303
$477$	−13.3973	−0.613420
$478$	−24.3482	−1.11366
$479$	11.2030	0.511876	0.255938	−	0.966693i	$-0.417616\pi$
$479$	11.2030	0.511876	0.255938	+	0.966693i	$0.417616\pi$
$480$	−1.31770	−0.0601445
$481$	5.45918	0.248917
$482$	23.7162	1.08024
$483$	0.593784	0.0270181
$484$	−14.1235	−0.641977
$485$	−9.91432	−0.450186
$486$	−38.1233	−1.72931
$487$	−21.4942	−0.973997	−0.486999	−	0.873403i	$-0.661908\pi$
$487$	−21.4942	−0.973997	−0.486999	+	0.873403i	$0.661908\pi$
$488$	46.4912	2.10456
$489$	9.71074	0.439135
$490$	2.94135	0.132877
$491$	15.4584	0.697629	0.348814	−	0.937192i	$-0.386584\pi$
$491$	15.4584	0.697629	0.348814	+	0.937192i	$0.386584\pi$
$492$	−14.0974	−0.635562
$493$	−9.13630	−0.411478
$494$	11.6332	0.523401
$495$	−25.2457	−1.13471
$496$	44.0332	1.97715
$497$	31.0294	1.39186
$498$	−23.3494	−1.04631
$499$	−3.07922	−0.137845	−0.0689224	−	0.997622i	$-0.521956\pi$
$499$	−3.07922	−0.137845	−0.0689224	+	0.997622i	$0.521956\pi$
$500$	68.6422	3.06977
$501$	−0.492249	−0.0219921
$502$	−24.9514	−1.11364
$503$	29.8425	1.33061	0.665307	−	0.746570i	$-0.268301\pi$
$503$	29.8425	1.33061	0.665307	+	0.746570i	$0.268301\pi$
$504$	31.5103	1.40358
$505$	−2.80789	−0.124950
$506$	−2.03639	−0.0905284
$507$	−7.88841	−0.350336
$508$	59.3439	2.63296
$509$	26.7337	1.18495	0.592475	−	0.805589i	$-0.298151\pi$
$509$	26.7337	1.18495	0.592475	+	0.805589i	$0.298151\pi$
$510$	9.38431	0.415544
$511$	27.4268	1.21329
$512$	41.0808	1.81553
$513$	−12.0472	−0.531896
$514$	69.8708	3.08187
$515$	1.31941	0.0581400
$516$	12.6806	0.558232
$517$	0.356747	0.0156897
$518$	21.4486	0.942398
$519$	8.38110	0.367889
$520$	30.9548	1.35746
$521$	1.47105	0.0644479	0.0322239	−	0.999481i	$-0.489741\pi$
$521$	1.47105	0.0644479	0.0322239	+	0.999481i	$0.489741\pi$
$522$	41.2045	1.80347
$523$	5.33226	0.233163	0.116582	−	0.993181i	$-0.462806\pi$
$523$	5.33226	0.233163	0.116582	+	0.993181i	$0.462806\pi$
$524$	−39.6188	−1.73076
$525$	18.5887	0.811278
$526$	−20.1122	−0.876936
$527$	−13.5978	−0.592329
$528$	8.90585	0.387577
$529$	−22.9087	−0.996029
$530$	−51.7088	−2.24609
$531$	29.3252	1.27261
$532$	30.5860	1.32607
$533$	7.42039	0.321413
$534$	−6.85658	−0.296713
$535$	−5.22322	−0.225819
$536$	−7.52103	−0.324859
$537$	5.53039	0.238654
$538$	31.0786	1.33989
$539$	−0.862000	−0.0371290
$540$	−63.3945	−2.72806
$541$	−31.3587	−1.34821	−0.674107	−	0.738634i	$-0.735471\pi$
$541$	−31.3587	−1.34821	−0.674107	+	0.738634i	$0.735471\pi$
$542$	15.7915	0.678303
$543$	17.8698	0.766867
$544$	0.602317	0.0258241
$545$	−33.1859	−1.42153
$546$	7.81702	0.334538
$547$	8.69646	0.371834	0.185917	−	0.982565i	$-0.440475\pi$
$547$	8.69646	0.371834	0.185917	+	0.982565i	$0.440475\pi$
$548$	−26.3488	−1.12557
$549$	22.3902	0.955591
$550$	−63.7501	−2.71832
$551$	20.2245	0.861592
$552$	−1.15522	−0.0491693
$553$	−29.7895	−1.26678
$554$	−0.388031	−0.0164859
$555$	−9.74853	−0.413802
$556$	−5.99100	−0.254075
$557$	12.5182	0.530413	0.265206	−	0.964192i	$-0.414560\pi$
$557$	12.5182	0.530413	0.265206	+	0.964192i	$0.414560\pi$
$558$	61.3257	2.59612
$559$	−6.67460	−0.282306
$560$	42.0557	1.77718
$561$	−2.75019	−0.116113
$562$	−37.0935	−1.56470
$563$	−17.7645	−0.748684	−0.374342	−	0.927291i	$-0.622131\pi$
$563$	−17.7645	−0.748684	−0.374342	+	0.927291i	$0.622131\pi$
$564$	0.400222	0.0168524
$565$	−0.880091	−0.0370257
$566$	57.4765	2.41592
$567$	10.6968	0.449223
$568$	−60.3684	−2.53300
$569$	9.29099	0.389499	0.194749	−	0.980853i	$-0.437611\pi$
$569$	9.29099	0.389499	0.194749	+	0.980853i	$0.437611\pi$
$570$	−20.7735	−0.870106
$571$	6.30240	0.263747	0.131874	−	0.991267i	$-0.457901\pi$
$571$	6.30240	0.263747	0.131874	+	0.991267i	$0.457901\pi$
$572$	−17.9401	−0.750114
$573$	−6.48378	−0.270864
$574$	29.1540	1.21686
$575$	2.85953	0.119251
$576$	18.0074	0.750310
$577$	−32.8758	−1.36864	−0.684318	−	0.729183i	$-0.739900\pi$
$577$	−32.8758	−1.36864	−0.684318	+	0.729183i	$0.739900\pi$
$578$	37.5105	1.56023
$579$	−6.87458	−0.285698
$580$	106.425	4.41906
$581$	32.3136	1.34059
$582$	4.87093	0.201907
$583$	15.1539	0.627611
$584$	−53.3593	−2.20803
$585$	14.9078	0.616363
$586$	13.6000	0.561811
$587$	45.3044	1.86991	0.934955	−	0.354765i	$-0.115439\pi$
$587$	45.3044	1.86991	0.934955	+	0.354765i	$0.115439\pi$
$588$	−0.967048	−0.0398804
$589$	30.1006	1.24027
$590$	113.185	4.65974
$591$	0.392224	0.0161340
$592$	−14.4298	−0.593061
$593$	22.9166	0.941071	0.470535	−	0.882381i	$-0.344061\pi$
$593$	22.9166	0.941071	0.470535	+	0.882381i	$0.344061\pi$
$594$	27.7626	1.13911
$595$	−12.9871	−0.532419
$596$	−4.21029	−0.172460
$597$	3.09294	0.126586
$598$	1.20250	0.0491741
$599$	37.0670	1.51452	0.757258	−	0.653116i	$-0.226539\pi$
$599$	37.0670	1.51452	0.757258	+	0.653116i	$0.226539\pi$
$600$	−36.1647	−1.47642
$601$	−14.9265	−0.608865	−0.304433	−	0.952534i	$-0.598467\pi$
$601$	−14.9265	−0.608865	−0.304433	+	0.952534i	$0.598467\pi$
$602$	−26.2239	−1.06881
$603$	−3.62213	−0.147505
$604$	69.9504	2.84624
$605$	−13.2752	−0.539712
$606$	1.37953	0.0560394
$607$	−11.4525	−0.464841	−0.232420	−	0.972615i	$-0.574665\pi$
$607$	−11.4525	−0.464841	−0.232420	+	0.972615i	$0.574665\pi$
$608$	−1.33331	−0.0540730
$609$	13.5900	0.550696
$610$	86.4182	3.49897
$611$	−0.210663	−0.00852250
$612$	12.9461	0.523313
$613$	2.78653	0.112547	0.0562734	−	0.998415i	$-0.482078\pi$
$613$	2.78653	0.112547	0.0562734	+	0.998415i	$0.482078\pi$
$614$	0.540742	0.0218226
$615$	−13.2507	−0.534319
$616$	−35.6418	−1.43605
$617$	−26.0902	−1.05035	−0.525177	−	0.850993i	$-0.676001\pi$
$617$	−26.0902	−1.05035	−0.525177	+	0.850993i	$0.676001\pi$
$618$	−0.648228	−0.0260755
$619$	13.3086	0.534917	0.267459	−	0.963569i	$-0.413816\pi$
$619$	13.3086	0.534917	0.267459	+	0.963569i	$0.413816\pi$
$620$	158.395	6.36130
$621$	−1.24530	−0.0499721
$622$	27.7295	1.11185
$623$	9.48892	0.380166
$624$	−5.25899	−0.210528
$625$	17.2119	0.688475
$626$	18.1641	0.725982
$627$	6.08794	0.243129
$628$	−57.3792	−2.28968
$629$	4.45603	0.177673
$630$	58.5715	2.33354
$631$	−31.8014	−1.26599	−0.632997	−	0.774154i	$-0.718175\pi$
$631$	−31.8014	−1.26599	−0.632997	+	0.774154i	$0.718175\pi$
$632$	57.9559	2.30536
$633$	17.2249	0.684629
$634$	−25.2584	−1.00314
$635$	55.7793	2.21353
$636$	17.0006	0.674119
$637$	0.509019	0.0201681
$638$	−46.6071	−1.84519
$639$	−29.0734	−1.15013
$640$	72.9706	2.88442
$641$	−30.8602	−1.21891	−0.609453	−	0.792822i	$-0.708611\pi$
$641$	−30.8602	−1.21891	−0.609453	+	0.792822i	$0.708611\pi$
$642$	2.56618	0.101279
$643$	11.7058	0.461633	0.230817	−	0.972997i	$-0.425860\pi$
$643$	11.7058	0.461633	0.230817	+	0.972997i	$0.425860\pi$
$644$	3.16162	0.124585
$645$	11.9189	0.469307
$646$	9.49551	0.373596
$647$	26.8854	1.05698	0.528488	−	0.848941i	$-0.322759\pi$
$647$	26.8854	1.05698	0.528488	+	0.848941i	$0.322759\pi$
$648$	−20.8108	−0.817526
$649$	−33.1702	−1.30205
$650$	37.6450	1.47656
$651$	20.2264	0.792735
$652$	51.7052	2.02493
$653$	−31.9335	−1.24965	−0.624827	−	0.780763i	$-0.714831\pi$
$653$	−31.9335	−1.24965	−0.624827	+	0.780763i	$0.714831\pi$
$654$	16.3043	0.637549
$655$	−37.2391	−1.45505
$656$	−19.6137	−0.765785
$657$	−25.6979	−1.00257
$658$	−0.827674	−0.0322661
$659$	−28.4095	−1.10668	−0.553339	−	0.832956i	$-0.686647\pi$
$659$	−28.4095	−1.10668	−0.553339	+	0.832956i	$0.686647\pi$
$660$	32.0359	1.24699
$661$	−7.53349	−0.293019	−0.146509	−	0.989209i	$-0.546804\pi$
$661$	−7.53349	−0.293019	−0.146509	+	0.989209i	$0.546804\pi$
$662$	43.0121	1.67171
$663$	1.62401	0.0630715
$664$	−62.8667	−2.43970
$665$	28.7488	1.11483
$666$	−20.0966	−0.778726
$667$	2.09057	0.0809474
$668$	−2.62100	−0.101410
$669$	−1.58491	−0.0612760
$670$	−13.9801	−0.540100
$671$	−25.3259	−0.977697
$672$	−0.895933	−0.0345614
$673$	10.6212	0.409419	0.204710	−	0.978823i	$-0.434375\pi$
$673$	10.6212	0.409419	0.204710	+	0.978823i	$0.434375\pi$
$674$	−30.6197	−1.17943
$675$	−38.9848	−1.50052
$676$	−42.0021	−1.61547
$677$	43.9583	1.68945	0.844727	−	0.535198i	$-0.179763\pi$
$677$	43.9583	1.68945	0.844727	+	0.535198i	$0.179763\pi$
$678$	0.432391	0.0166059
$679$	−6.74096	−0.258694
$680$	25.2666	0.968931
$681$	11.8038	0.452324
$682$	−69.3666	−2.65618
$683$	17.1556	0.656441	0.328221	−	0.944601i	$-0.393551\pi$
$683$	17.1556	0.656441	0.328221	+	0.944601i	$0.393551\pi$
$684$	−28.6579	−1.09576
$685$	−24.7662	−0.946266
$686$	46.5031	1.77550
$687$	5.01467	0.191321
$688$	17.6424	0.672610
$689$	−8.94853	−0.340912
$690$	−2.14733	−0.0817473
$691$	−24.7451	−0.941348	−0.470674	−	0.882307i	$-0.655989\pi$
$691$	−24.7451	−0.941348	−0.470674	+	0.882307i	$0.655989\pi$
$692$	44.6255	1.69641
$693$	−17.1651	−0.652049
$694$	−16.5591	−0.628573
$695$	−5.63114	−0.213601
$696$	−26.4396	−1.00219
$697$	6.05685	0.229419
$698$	65.2087	2.46819
$699$	−0.406311	−0.0153681
$700$	98.9764	3.74095
$701$	43.8721	1.65702	0.828512	−	0.559971i	$-0.189188\pi$
$701$	43.8721	1.65702	0.828512	+	0.559971i	$0.189188\pi$
$702$	−16.3941	−0.618754
$703$	−9.86404	−0.372029
$704$	−20.3685	−0.767668
$705$	0.376183	0.0141679
$706$	−19.1568	−0.720976
$707$	−1.90915	−0.0718009
$708$	−37.2125	−1.39853
$709$	12.2289	0.459266	0.229633	−	0.973277i	$-0.426247\pi$
$709$	12.2289	0.459266	0.229633	+	0.973277i	$0.426247\pi$
$710$	−112.213	−4.21128
$711$	27.9116	1.04677
$712$	−18.4609	−0.691851
$713$	3.11146	0.116525
$714$	6.38060	0.238788
$715$	−16.8625	−0.630622
$716$	29.4468	1.10048
$717$	7.52428	0.280999
$718$	−27.9496	−1.04307
$719$	17.5133	0.653134	0.326567	−	0.945174i	$-0.394108\pi$
$719$	17.5133	0.653134	0.326567	+	0.945174i	$0.394108\pi$
$720$	−39.4046	−1.46852
$721$	0.897093	0.0334095
$722$	25.6981	0.956385
$723$	−7.32897	−0.272567
$724$	95.1485	3.53617
$725$	65.4466	2.43062
$726$	6.52212	0.242058
$727$	38.1696	1.41563	0.707816	−	0.706397i	$-0.249681\pi$
$727$	38.1696	1.41563	0.707816	+	0.706397i	$0.249681\pi$
$728$	21.0468	0.780047
$729$	−0.629930	−0.0233308
$730$	−99.1847	−3.67099
$731$	−5.44810	−0.201505
$732$	−28.4123	−1.05015
$733$	−21.4558	−0.792488	−0.396244	−	0.918145i	$-0.629687\pi$
$733$	−21.4558	−0.792488	−0.396244	+	0.918145i	$0.629687\pi$
$734$	−1.69255	−0.0624731
$735$	−0.908961	−0.0335275
$736$	−0.137823	−0.00508021
$737$	4.09706	0.150917
$738$	−27.3162	−1.00552
$739$	−32.3844	−1.19128	−0.595639	−	0.803252i	$-0.703101\pi$
$739$	−32.3844	−1.19128	−0.595639	+	0.803252i	$0.703101\pi$
$740$	−51.9064	−1.90812
$741$	−3.59498	−0.132065
$742$	−35.1579	−1.29069
$743$	26.8416	0.984722	0.492361	−	0.870391i	$-0.336134\pi$
$743$	26.8416	0.984722	0.492361	+	0.870391i	$0.336134\pi$
$744$	−39.3508	−1.44267
$745$	−3.95740	−0.144988
$746$	−27.1933	−0.995617
$747$	−30.2767	−1.10776
$748$	−14.6435	−0.535419
$749$	−3.55138	−0.129765
$750$	−31.6984	−1.15746
$751$	34.4509	1.25713	0.628565	−	0.777757i	$-0.283643\pi$
$751$	34.4509	1.25713	0.628565	+	0.777757i	$0.283643\pi$
$752$	0.556826	0.0203054
$753$	7.71069	0.280993
$754$	27.5219	1.00229
$755$	65.7487	2.39284
$756$	−43.1033	−1.56765
$757$	−22.7034	−0.825169	−0.412585	−	0.910919i	$-0.635374\pi$
$757$	−22.7034	−0.825169	−0.412585	+	0.910919i	$0.635374\pi$
$758$	−5.23384	−0.190102
$759$	0.629301	0.0228422
$760$	−55.9313	−2.02884
$761$	12.4779	0.452325	0.226162	−	0.974090i	$-0.427382\pi$
$761$	12.4779	0.452325	0.226162	+	0.974090i	$0.427382\pi$
$762$	−27.4045	−0.992761
$763$	−22.5638	−0.816864
$764$	−34.5231	−1.24900
$765$	12.1684	0.439951
$766$	28.6165	1.03396
$767$	19.5873	0.707257
$768$	−24.5547	−0.886043
$769$	−6.07987	−0.219246	−0.109623	−	0.993973i	$-0.534964\pi$
$769$	−6.07987	−0.219246	−0.109623	+	0.993973i	$0.534964\pi$
$770$	−66.2512	−2.38753
$771$	−21.5921	−0.777619
$772$	−36.6040	−1.31741
$773$	−40.2221	−1.44669	−0.723344	−	0.690488i	$-0.757396\pi$
$773$	−40.2221	−1.44669	−0.723344	+	0.690488i	$0.757396\pi$
$774$	24.5708	0.883180
$775$	97.4058	3.49892
$776$	13.1147	0.470789
$777$	−6.62823	−0.237787
$778$	−39.0930	−1.40155
$779$	−13.4077	−0.480380
$780$	−18.9175	−0.677354
$781$	32.8855	1.17673
$782$	0.981537	0.0350997
$783$	−28.5014	−1.01856
$784$	−1.34545	−0.0480517
$785$	−53.9326	−1.92494
$786$	18.2957	0.652584
$787$	19.4228	0.692349	0.346175	−	0.938170i	$-0.387480\pi$
$787$	19.4228	0.692349	0.346175	+	0.938170i	$0.387480\pi$
$788$	2.08841	0.0743967
$789$	6.21526	0.221269
$790$	107.729	3.83282
$791$	−0.598393	−0.0212764
$792$	33.3951	1.18664
$793$	14.9552	0.531075
$794$	72.8043	2.58373
$795$	15.9795	0.566734
$796$	16.4685	0.583710
$797$	−3.09265	−0.109547	−0.0547736	−	0.998499i	$-0.517444\pi$
$797$	−3.09265	−0.109547	−0.0547736	+	0.998499i	$0.517444\pi$
$798$	−14.1243	−0.499996
$799$	−0.171952	−0.00608323
$800$	−4.31461	−0.152545
$801$	−8.89077	−0.314140
$802$	−10.2939	−0.363489
$803$	29.0673	1.02576
$804$	4.59635	0.162101
$805$	2.97172	0.104739
$806$	40.9616	1.44281
$807$	−9.60417	−0.338083
$808$	3.71428	0.130668
$809$	−30.6359	−1.07710	−0.538551	−	0.842593i	$-0.681028\pi$
$809$	−30.6359	−1.07710	−0.538551	+	0.842593i	$0.681028\pi$
$810$	−38.6833	−1.35919
$811$	−33.0176	−1.15940	−0.579702	−	0.814828i	$-0.696831\pi$
$811$	−33.0176	−1.15940	−0.579702	+	0.814828i	$0.696831\pi$
$812$	72.3606	2.53936
$813$	−4.88002	−0.171150
$814$	22.7316	0.796741
$815$	48.5995	1.70237
$816$	−4.29261	−0.150272
$817$	12.0601	0.421931
$818$	43.2222	1.51123
$819$	10.1362	0.354186
$820$	−70.5537	−2.46384
$821$	−51.6336	−1.80202	−0.901012	−	0.433795i	$-0.857174\pi$
$821$	−51.6336	−1.80202	−0.901012	+	0.433795i	$0.857174\pi$
$822$	12.1677	0.424396
$823$	−39.3764	−1.37257	−0.686287	−	0.727331i	$-0.740760\pi$
$823$	−39.3764	−1.37257	−0.686287	+	0.727331i	$0.740760\pi$
$824$	−1.74531	−0.0608007
$825$	19.7006	0.685887
$826$	76.9568	2.67767
$827$	15.6265	0.543387	0.271693	−	0.962384i	$-0.412416\pi$
$827$	15.6265	0.543387	0.271693	+	0.962384i	$0.412416\pi$
$828$	−2.96233	−0.102948
$829$	−17.9401	−0.623086	−0.311543	−	0.950232i	$-0.600846\pi$
$829$	−17.9401	−0.623086	−0.311543	+	0.950232i	$0.600846\pi$
$830$	−116.857	−4.05617
$831$	0.119913	0.00415973
$832$	12.0278	0.416989
$833$	0.415484	0.0143957
$834$	2.76659	0.0957993
$835$	−2.46357	−0.0852553
$836$	32.4155	1.12111
$837$	−42.4193	−1.46623
$838$	−16.4067	−0.566759
$839$	−9.00570	−0.310911	−0.155456	−	0.987843i	$-0.549685\pi$
$839$	−9.00570	−0.310911	−0.155456	+	0.987843i	$0.549685\pi$
$840$	−37.5835	−1.29675
$841$	18.8473	0.649908
$842$	56.0259	1.93078
$843$	11.4629	0.394805
$844$	91.7147	3.15695
$845$	−39.4792	−1.35813
$846$	0.775500	0.0266622
$847$	−9.02606	−0.310139
$848$	23.6529	0.812243
$849$	−17.7619	−0.609586
$850$	30.7275	1.05395
$851$	−1.01963	−0.0349525
$852$	36.8931	1.26394
$853$	6.72608	0.230296	0.115148	−	0.993348i	$-0.463266\pi$
$853$	6.72608	0.230296	0.115148	+	0.993348i	$0.463266\pi$
$854$	58.7576	2.01064
$855$	−26.9365	−0.921210
$856$	6.90927	0.236154
$857$	4.96351	0.169550	0.0847752	−	0.996400i	$-0.472983\pi$
$857$	4.96351	0.169550	0.0847752	+	0.996400i	$0.472983\pi$
$858$	8.28460	0.282831
$859$	−33.6736	−1.14893	−0.574465	−	0.818529i	$-0.694790\pi$
$859$	−33.6736	−1.14893	−0.574465	+	0.818529i	$0.694790\pi$
$860$	63.4627	2.16406
$861$	−9.00941	−0.307040
$862$	90.6093	3.08617
$863$	−18.5210	−0.630462	−0.315231	−	0.949015i	$-0.602082\pi$
$863$	−18.5210	−0.630462	−0.315231	+	0.949015i	$0.602082\pi$
$864$	1.87897	0.0639240
$865$	41.9450	1.42617
$866$	−86.3202	−2.93328
$867$	−11.5918	−0.393679
$868$	107.696	3.65545
$869$	−31.5713	−1.07098
$870$	−49.1462	−1.66621
$871$	−2.41935	−0.0819766
$872$	43.8983	1.48658
$873$	6.31603	0.213765
$874$	−2.17277	−0.0734950
$875$	43.8680	1.48301
$876$	32.6096	1.10178
$877$	−36.0220	−1.21638	−0.608188	−	0.793793i	$-0.708103\pi$
$877$	−36.0220	−1.21638	−0.608188	+	0.793793i	$0.708103\pi$
$878$	−13.0333	−0.439853
$879$	−4.20279	−0.141757
$880$	44.5712	1.50250
$881$	35.6953	1.20260	0.601302	−	0.799022i	$-0.294649\pi$
$881$	35.6953	1.20260	0.601302	+	0.799022i	$0.294649\pi$
$882$	−1.87382	−0.0630949
$883$	−1.79869	−0.0605307	−0.0302653	−	0.999542i	$-0.509635\pi$
$883$	−1.79869	−0.0605307	−0.0302653	+	0.999542i	$0.509635\pi$
$884$	8.64712	0.290834
$885$	−34.9773	−1.17575
$886$	26.9852	0.906584
$887$	43.7290	1.46827	0.734137	−	0.679001i	$-0.237587\pi$
$887$	43.7290	1.46827	0.734137	+	0.679001i	$0.237587\pi$
$888$	12.8953	0.432740
$889$	37.9255	1.27198
$890$	−34.3152	−1.15025
$891$	11.3366	0.379791
$892$	−8.43890	−0.282555
$893$	0.380640	0.0127376
$894$	1.94428	0.0650264
$895$	27.6780	0.925175
$896$	49.6143	1.65750
$897$	−0.371608	−0.0124076
$898$	−83.9811	−2.80249
$899$	71.2124	2.37507
$900$	−92.7372	−3.09124
$901$	−7.30418	−0.243337
$902$	30.8979	1.02879
$903$	8.10392	0.269682
$904$	1.16418	0.0387202
$905$	89.4333	2.97286
$906$	−32.3025	−1.07318
$907$	15.8476	0.526210	0.263105	−	0.964767i	$-0.415253\pi$
$907$	15.8476	0.526210	0.263105	+	0.964767i	$0.415253\pi$
$908$	62.8500	2.08575
$909$	1.78880	0.0593308
$910$	39.1220	1.29688
$911$	−32.9637	−1.09214	−0.546068	−	0.837741i	$-0.683876\pi$
$911$	−32.9637	−1.09214	−0.546068	+	0.837741i	$0.683876\pi$
$912$	9.50230	0.314653
$913$	34.2464	1.13339
$914$	−84.0381	−2.77973
$915$	−26.7057	−0.882862
$916$	26.7008	0.882219
$917$	−25.3196	−0.836128
$918$	−13.3816	−0.441657
$919$	−32.4007	−1.06880	−0.534400	−	0.845232i	$-0.679462\pi$
$919$	−32.4007	−1.06880	−0.534400	+	0.845232i	$0.679462\pi$
$920$	−5.78153	−0.190611
$921$	−0.167105	−0.00550629
$922$	−32.5572	−1.07221
$923$	−19.4192	−0.639190
$924$	21.7819	0.716571
$925$	−31.9201	−1.04953
$926$	70.2162	2.30745
$927$	−0.840543	−0.0276070
$928$	−3.15437	−0.103547
$929$	−2.79822	−0.0918068	−0.0459034	−	0.998946i	$-0.514617\pi$
$929$	−2.79822	−0.0918068	−0.0459034	+	0.998946i	$0.514617\pi$
$930$	−73.1456	−2.39854
$931$	−0.919732	−0.0301430
$932$	−2.16342	−0.0708651
$933$	−8.56919	−0.280543
$934$	−39.9723	−1.30793
$935$	−13.7639	−0.450128
$936$	−19.7201	−0.644571
$937$	57.3985	1.87513	0.937564	−	0.347813i	$-0.113076\pi$
$937$	57.3985	1.87513	0.937564	+	0.347813i	$0.113076\pi$
$938$	−9.50540	−0.310362
$939$	−5.61321	−0.183180
$940$	2.00300	0.0653306
$941$	−5.74982	−0.187439	−0.0937194	−	0.995599i	$-0.529876\pi$
$941$	−5.74982	−0.187439	−0.0937194	+	0.995599i	$0.529876\pi$
$942$	26.4972	0.863327
$943$	−1.38593	−0.0451322
$944$	−51.7735	−1.68508
$945$	−40.5142	−1.31793
$946$	−27.7925	−0.903611
$947$	−21.3282	−0.693072	−0.346536	−	0.938037i	$-0.612642\pi$
$947$	−21.3282	−0.693072	−0.346536	+	0.938037i	$0.612642\pi$
$948$	−35.4188	−1.15035
$949$	−17.1645	−0.557184
$950$	−68.0197	−2.20685
$951$	7.80555	0.253112
$952$	17.1793	0.556785
$953$	−7.83944	−0.253945	−0.126972	−	0.991906i	$-0.540526\pi$
$953$	−7.83944	−0.253945	−0.126972	+	0.991906i	$0.540526\pi$
$954$	32.9417	1.06653
$955$	−32.4495	−1.05004
$956$	40.0633	1.29574
$957$	14.4029	0.465580
$958$	−27.5462	−0.889976
$959$	−16.8390	−0.543761
$960$	−21.4782	−0.693205
$961$	74.9873	2.41895
$962$	−13.4232	−0.432781
$963$	3.32751	0.107228
$964$	−39.0234	−1.25686
$965$	−34.4053	−1.10755
$966$	−1.46001	−0.0469751
$967$	−48.4900	−1.55933	−0.779666	−	0.626195i	$-0.784611\pi$
$967$	−48.4900	−1.55933	−0.779666	+	0.626195i	$0.784611\pi$
$968$	17.5604	0.564412
$969$	−2.93438	−0.0942659
$970$	24.3776	0.782718
$971$	−30.1821	−0.968589	−0.484295	−	0.874905i	$-0.660924\pi$
$971$	−30.1821	−0.968589	−0.484295	+	0.874905i	$0.660924\pi$
$972$	62.7293	2.01204
$973$	−3.82873	−0.122744
$974$	52.8507	1.69344
$975$	−11.6334	−0.372567
$976$	−39.5298	−1.26532
$977$	−6.73424	−0.215447	−0.107724	−	0.994181i	$-0.534356\pi$
$977$	−6.73424	−0.215447	−0.107724	+	0.994181i	$0.534356\pi$
$978$	−23.8771	−0.763504
$979$	10.0565	0.321407
$980$	−4.83980	−0.154602
$981$	21.1414	0.674994
$982$	−38.0096	−1.21294
$983$	−26.5742	−0.847586	−0.423793	−	0.905759i	$-0.639302\pi$
$983$	−26.5742	−0.847586	−0.423793	+	0.905759i	$0.639302\pi$
$984$	17.5280	0.558772
$985$	1.96297	0.0625455
$986$	22.4646	0.715419
$987$	0.255775	0.00814140
$988$	−19.1416	−0.608976
$989$	1.24664	0.0396408
$990$	62.0750	1.97287
$991$	−28.5022	−0.905402	−0.452701	−	0.891662i	$-0.649540\pi$
$991$	−28.5022	−0.905402	−0.452701	+	0.891662i	$0.649540\pi$
$992$	−4.69473	−0.149058
$993$	−13.2920	−0.421808
$994$	−76.2961	−2.41997
$995$	15.4793	0.490727
$996$	38.4199	1.21738
$997$	22.9556	0.727012	0.363506	−	0.931592i	$-0.381580\pi$
$997$	22.9556	0.727012	0.363506	+	0.931592i	$0.381580\pi$
$998$	7.57128	0.239665
$999$	13.9009	0.439805

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6043.2.a.c.1.17	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6043.2.a.c.1.17	✓	259	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:	\( N \)	\(=\)	\( 6043 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6043.a (trivial)

\(f(q)\)	\(=\)	\(q-2.45883 q^{2} +0.759848 q^{3} +4.04584 q^{4} +3.80282 q^{5} -1.86834 q^{6} +2.58562 q^{7} -5.03037 q^{8} -2.42263 q^{9} +O(q^{10})\)	\(q-2.45883 q^{2} +0.759848 q^{3} +4.04584 q^{4} +3.80282 q^{5} -1.86834 q^{6} +2.58562 q^{7} -5.03037 q^{8} -2.42263 q^{9} -9.35049 q^{10} +2.74028 q^{11} +3.07422 q^{12} -1.61816 q^{13} -6.35760 q^{14} +2.88957 q^{15} +4.27714 q^{16} -1.32081 q^{17} +5.95684 q^{18} +2.92381 q^{19} +15.3856 q^{20} +1.96468 q^{21} -6.73788 q^{22} +0.302229 q^{23} -3.82232 q^{24} +9.46146 q^{25} +3.97878 q^{26} -4.12038 q^{27} +10.4610 q^{28} +6.91718 q^{29} -7.10495 q^{30} +10.2950 q^{31} -0.456020 q^{32} +2.08220 q^{33} +3.24765 q^{34} +9.83265 q^{35} -9.80158 q^{36} -3.37370 q^{37} -7.18914 q^{38} -1.22956 q^{39} -19.1296 q^{40} -4.58569 q^{41} -4.83081 q^{42} +4.12481 q^{43} +11.0867 q^{44} -9.21283 q^{45} -0.743131 q^{46} +0.130187 q^{47} +3.24998 q^{48} -0.314567 q^{49} -23.2641 q^{50} -1.00362 q^{51} -6.54682 q^{52} +5.53006 q^{53} +10.1313 q^{54} +10.4208 q^{55} -13.0066 q^{56} +2.22165 q^{57} -17.0082 q^{58} -12.1047 q^{59} +11.6907 q^{60} -9.24210 q^{61} -25.3137 q^{62} -6.26400 q^{63} -7.43301 q^{64} -6.15357 q^{65} -5.11976 q^{66} +1.49512 q^{67} -5.34380 q^{68} +0.229648 q^{69} -24.1768 q^{70} +12.0008 q^{71} +12.1867 q^{72} +10.6074 q^{73} +8.29535 q^{74} +7.18927 q^{75} +11.8293 q^{76} +7.08532 q^{77} +3.02327 q^{78} -11.5212 q^{79} +16.2652 q^{80} +4.13703 q^{81} +11.2754 q^{82} +12.4974 q^{83} +7.94878 q^{84} -5.02282 q^{85} -10.1422 q^{86} +5.25600 q^{87} -13.7846 q^{88} +3.66988 q^{89} +22.6528 q^{90} -4.18395 q^{91} +1.22277 q^{92} +7.82265 q^{93} -0.320106 q^{94} +11.1187 q^{95} -0.346506 q^{96} -2.60710 q^{97} +0.773465 q^{98} -6.63869 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9}+O(q^{10}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9} + 36 q^{10} + 35 q^{11} + 58 q^{12} + 109 q^{13} + 31 q^{14} + 30 q^{15} + 287 q^{16} + 124 q^{17} + 97 q^{18} + 42 q^{19} + 149 q^{20} + 99 q^{21} + 22 q^{22} + 63 q^{23} + 53 q^{24} + 308 q^{25} + 86 q^{26} + 82 q^{27} + 52 q^{28} + 131 q^{29} + 6 q^{30} + 29 q^{31} + 251 q^{32} + 147 q^{33} + 24 q^{34} + 79 q^{35} + 315 q^{36} + 108 q^{37} + 124 q^{38} + 48 q^{39} + 87 q^{40} + 190 q^{41} + 28 q^{42} + 36 q^{43} + 70 q^{44} + 211 q^{45} + 19 q^{46} + 186 q^{47} + 103 q^{48} + 297 q^{49} + 161 q^{50} + 20 q^{51} + 173 q^{52} + 213 q^{53} + 56 q^{54} + 35 q^{55} + 99 q^{56} + 80 q^{57} + 32 q^{58} + 135 q^{59} + 23 q^{60} + 83 q^{61} + 172 q^{62} + 85 q^{63} + 297 q^{64} + 177 q^{65} + 41 q^{66} + 30 q^{67} + 271 q^{68} + 168 q^{69} + 24 q^{70} + 63 q^{71} + 241 q^{72} + 152 q^{73} + 32 q^{74} + 36 q^{75} + 92 q^{76} + 396 q^{77} + 21 q^{78} - 2 q^{79} + 242 q^{80} + 343 q^{81} + 40 q^{82} + 236 q^{83} + 92 q^{84} + 124 q^{85} + 55 q^{86} + 113 q^{87} + 7 q^{88} + 214 q^{89} + 100 q^{90} + 2 q^{91} + 176 q^{92} + 228 q^{93} + 51 q^{94} + 96 q^{95} + 48 q^{96} + 135 q^{97} + 261 q^{98} + 26 q^{99}+O(q^{100}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9 + 36 * q^10 + 35 * q^11 + 58 * q^12 + 109 * q^13 + 31 * q^14 + 30 * q^15 + 287 * q^16 + 124 * q^17 + 97 * q^18 + 42 * q^19 + 149 * q^20 + 99 * q^21 + 22 * q^22 + 63 * q^23 + 53 * q^24 + 308 * q^25 + 86 * q^26 + 82 * q^27 + 52 * q^28 + 131 * q^29 + 6 * q^30 + 29 * q^31 + 251 * q^32 + 147 * q^33 + 24 * q^34 + 79 * q^35 + 315 * q^36 + 108 * q^37 + 124 * q^38 + 48 * q^39 + 87 * q^40 + 190 * q^41 + 28 * q^42 + 36 * q^43 + 70 * q^44 + 211 * q^45 + 19 * q^46 + 186 * q^47 + 103 * q^48 + 297 * q^49 + 161 * q^50 + 20 * q^51 + 173 * q^52 + 213 * q^53 + 56 * q^54 + 35 * q^55 + 99 * q^56 + 80 * q^57 + 32 * q^58 + 135 * q^59 + 23 * q^60 + 83 * q^61 + 172 * q^62 + 85 * q^63 + 297 * q^64 + 177 * q^65 + 41 * q^66 + 30 * q^67 + 271 * q^68 + 168 * q^69 + 24 * q^70 + 63 * q^71 + 241 * q^72 + 152 * q^73 + 32 * q^74 + 36 * q^75 + 92 * q^76 + 396 * q^77 + 21 * q^78 - 2 * q^79 + 242 * q^80 + 343 * q^81 + 40 * q^82 + 236 * q^83 + 92 * q^84 + 124 * q^85 + 55 * q^86 + 113 * q^87 + 7 * q^88 + 214 * q^89 + 100 * q^90 + 2 * q^91 + 176 * q^92 + 228 * q^93 + 51 * q^94 + 96 * q^95 + 48 * q^96 + 135 * q^97 + 261 * q^98 + 26 * q^99

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