LMFDB - Embedded newform 6043.2.a.c.1.4

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			1.4
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)

$f(q)$	$=$	$q-2.66716 q^{2} +0.658905 q^{3} +5.11375 q^{4} -0.783297 q^{5} -1.75741 q^{6} -0.338104 q^{7} -8.30489 q^{8} -2.56584 q^{9} +O(q^{10})$	\(q-2.66716 q^{2} +0.658905 q^{3} +5.11375 q^{4} -0.783297 q^{5} -1.75741 q^{6} -0.338104 q^{7} -8.30489 q^{8} -2.56584 q^{9} +2.08918 q^{10} +4.66349 q^{11} +3.36948 q^{12} +0.840231 q^{13} +0.901779 q^{14} -0.516119 q^{15} +11.9230 q^{16} -1.70019 q^{17} +6.84352 q^{18} -5.80164 q^{19} -4.00559 q^{20} -0.222779 q^{21} -12.4383 q^{22} -1.82105 q^{23} -5.47214 q^{24} -4.38645 q^{25} -2.24103 q^{26} -3.66736 q^{27} -1.72898 q^{28} -7.54922 q^{29} +1.37657 q^{30} -3.98375 q^{31} -15.1907 q^{32} +3.07280 q^{33} +4.53469 q^{34} +0.264836 q^{35} -13.1211 q^{36} -5.81485 q^{37} +15.4739 q^{38} +0.553633 q^{39} +6.50520 q^{40} +1.65231 q^{41} +0.594187 q^{42} +8.44116 q^{43} +23.8479 q^{44} +2.00982 q^{45} +4.85702 q^{46} +6.97850 q^{47} +7.85611 q^{48} -6.88569 q^{49} +11.6994 q^{50} -1.12027 q^{51} +4.29673 q^{52} -2.68221 q^{53} +9.78146 q^{54} -3.65290 q^{55} +2.80792 q^{56} -3.82273 q^{57} +20.1350 q^{58} -0.307295 q^{59} -2.63930 q^{60} +11.5060 q^{61} +10.6253 q^{62} +0.867523 q^{63} +16.6702 q^{64} -0.658150 q^{65} -8.19565 q^{66} +5.64993 q^{67} -8.69438 q^{68} -1.19990 q^{69} -0.706361 q^{70} +10.9328 q^{71} +21.3090 q^{72} -9.17667 q^{73} +15.5092 q^{74} -2.89025 q^{75} -29.6682 q^{76} -1.57675 q^{77} -1.47663 q^{78} -2.76935 q^{79} -9.33923 q^{80} +5.28108 q^{81} -4.40699 q^{82} +6.69087 q^{83} -1.13924 q^{84} +1.33176 q^{85} -22.5139 q^{86} -4.97422 q^{87} -38.7298 q^{88} +6.43339 q^{89} -5.36051 q^{90} -0.284086 q^{91} -9.31238 q^{92} -2.62492 q^{93} -18.6128 q^{94} +4.54441 q^{95} -10.0093 q^{96} -14.3260 q^{97} +18.3652 q^{98} -11.9658 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.66716	−1.88597	−0.942984	−	0.332837i	$-0.891994\pi$
$2$	−2.66716	−1.88597	−0.942984	+	0.332837i	$0.891994\pi$
$3$	0.658905	0.380419	0.190210	−	0.981743i	$-0.439083\pi$
$3$	0.658905	0.380419	0.190210	+	0.981743i	$0.439083\pi$
$4$	5.11375	2.55688
$5$	−0.783297	−0.350301	−0.175151	−	0.984542i	$-0.556041\pi$
$5$	−0.783297	−0.350301	−0.175151	+	0.984542i	$0.556041\pi$
$6$	−1.75741	−0.717459
$7$	−0.338104	−0.127791	−0.0638957	−	0.997957i	$-0.520352\pi$
$7$	−0.338104	−0.127791	−0.0638957	+	0.997957i	$0.520352\pi$
$8$	−8.30489	−2.93622
$9$	−2.56584	−0.855281
$10$	2.08918	0.660657
$11$	4.66349	1.40610	0.703048	−	0.711143i	$-0.251822\pi$
$11$	4.66349	1.40610	0.703048	+	0.711143i	$0.251822\pi$
$12$	3.36948	0.972685
$13$	0.840231	0.233038	0.116519	−	0.993188i	$-0.462826\pi$
$13$	0.840231	0.233038	0.116519	+	0.993188i	$0.462826\pi$
$14$	0.901779	0.241011
$15$	−0.516119	−0.133261
$16$	11.9230	2.98074
$17$	−1.70019	−0.412358	−0.206179	−	0.978514i	$-0.566103\pi$
$17$	−1.70019	−0.412358	−0.206179	+	0.978514i	$0.566103\pi$
$18$	6.84352	1.61303
$19$	−5.80164	−1.33099	−0.665494	−	0.746404i	$-0.731779\pi$
$19$	−5.80164	−1.33099	−0.665494	+	0.746404i	$0.731779\pi$
$20$	−4.00559	−0.895677
$21$	−0.222779	−0.0486143
$22$	−12.4383	−2.65185
$23$	−1.82105	−0.379714	−0.189857	−	0.981812i	$-0.560802\pi$
$23$	−1.82105	−0.379714	−0.189857	+	0.981812i	$0.560802\pi$
$24$	−5.47214	−1.11700
$25$	−4.38645	−0.877289
$26$	−2.24103	−0.439502
$27$	−3.66736	−0.705785
$28$	−1.72898	−0.326747
$29$	−7.54922	−1.40186	−0.700928	−	0.713232i	$-0.747230\pi$
$29$	−7.54922	−1.40186	−0.700928	+	0.713232i	$0.747230\pi$
$30$	1.37657	0.251327
$31$	−3.98375	−0.715503	−0.357751	−	0.933817i	$-0.616456\pi$
$31$	−3.98375	−0.715503	−0.357751	+	0.933817i	$0.616456\pi$
$32$	−15.1907	−2.68537
$33$	3.07280	0.534906
$34$	4.53469	0.777694
$35$	0.264836	0.0447655
$36$	−13.1211	−2.18685
$37$	−5.81485	−0.955956	−0.477978	−	0.878372i	$-0.658630\pi$
$37$	−5.81485	−0.955956	−0.477978	+	0.878372i	$0.658630\pi$
$38$	15.4739	2.51020
$39$	0.553633	0.0886522
$40$	6.50520	1.02856
$41$	1.65231	0.258048	0.129024	−	0.991641i	$-0.458816\pi$
$41$	1.65231	0.258048	0.129024	+	0.991641i	$0.458816\pi$
$42$	0.594187	0.0916850
$43$	8.44116	1.28726	0.643632	−	0.765335i	$-0.277427\pi$
$43$	8.44116	1.28726	0.643632	+	0.765335i	$0.277427\pi$
$44$	23.8479	3.59521
$45$	2.00982	0.299606
$46$	4.85702	0.716129
$47$	6.97850	1.01792	0.508959	−	0.860791i	$-0.330030\pi$
$47$	6.97850	1.01792	0.508959	+	0.860791i	$0.330030\pi$
$48$	7.85611	1.13393
$49$	−6.88569	−0.983669
$50$	11.6994	1.65454
$51$	−1.12027	−0.156869
$52$	4.29673	0.595850
$53$	−2.68221	−0.368430	−0.184215	−	0.982886i	$-0.558974\pi$
$53$	−2.68221	−0.368430	−0.184215	+	0.982886i	$0.558974\pi$
$54$	9.78146	1.33109
$55$	−3.65290	−0.492557
$56$	2.80792	0.375224
$57$	−3.82273	−0.506333
$58$	20.1350	2.64386
$59$	−0.307295	−0.0400064	−0.0200032	−	0.999800i	$-0.506368\pi$
$59$	−0.307295	−0.0400064	−0.0200032	+	0.999800i	$0.506368\pi$
$60$	−2.63930	−0.340733
$61$	11.5060	1.47319	0.736595	−	0.676334i	$-0.236432\pi$
$61$	11.5060	1.47319	0.736595	+	0.676334i	$0.236432\pi$
$62$	10.6253	1.34942
$63$	0.867523	0.109298
$64$	16.6702	2.08377
$65$	−0.658150	−0.0816335
$66$	−8.19565	−1.00882
$67$	5.64993	0.690248	0.345124	−	0.938557i	$-0.387837\pi$
$67$	5.64993	0.690248	0.345124	+	0.938557i	$0.387837\pi$
$68$	−8.69438	−1.05435
$69$	−1.19990	−0.144451
$70$	−0.706361	−0.0844263
$71$	10.9328	1.29748	0.648742	−	0.761009i	$-0.275296\pi$
$71$	10.9328	1.29748	0.648742	+	0.761009i	$0.275296\pi$
$72$	21.3090	2.51129
$73$	−9.17667	−1.07405	−0.537024	−	0.843567i	$-0.680452\pi$
$73$	−9.17667	−1.07405	−0.537024	+	0.843567i	$0.680452\pi$
$74$	15.5092	1.80290
$75$	−2.89025	−0.333738
$76$	−29.6682	−3.40317
$77$	−1.57675	−0.179687
$78$	−1.47663	−0.167195
$79$	−2.76935	−0.311576	−0.155788	−	0.987790i	$-0.549792\pi$
$79$	−2.76935	−0.311576	−0.155788	+	0.987790i	$0.549792\pi$
$80$	−9.33923	−1.04416
$81$	5.28108	0.586787
$82$	−4.40699	−0.486670
$83$	6.69087	0.734418	0.367209	−	0.930138i	$-0.380313\pi$
$83$	6.69087	0.734418	0.367209	+	0.930138i	$0.380313\pi$
$84$	−1.13924	−0.124301
$85$	1.33176	0.144449
$86$	−22.5139	−2.42774
$87$	−4.97422	−0.533293
$88$	−38.7298	−4.12861
$89$	6.43339	0.681938	0.340969	−	0.940075i	$-0.389245\pi$
$89$	6.43339	0.681938	0.340969	+	0.940075i	$0.389245\pi$
$90$	−5.36051	−0.565047
$91$	−0.284086	−0.0297803
$92$	−9.31238	−0.970883
$93$	−2.62492	−0.272191
$94$	−18.6128	−1.91976
$95$	4.54441	0.466246
$96$	−10.0093	−1.02157
$97$	−14.3260	−1.45458	−0.727291	−	0.686330i	$-0.759221\pi$
$97$	−14.3260	−1.45458	−0.727291	+	0.686330i	$0.759221\pi$
$98$	18.3652	1.85517
$99$	−11.9658	−1.20261
$100$	−22.4312	−2.24312
$101$	6.51742	0.648508	0.324254	−	0.945970i	$-0.394887\pi$
$101$	6.51742	0.648508	0.324254	+	0.945970i	$0.394887\pi$
$102$	2.98794	0.295850
$103$	14.5790	1.43651	0.718257	−	0.695778i	$-0.244940\pi$
$103$	14.5790	1.43651	0.718257	+	0.695778i	$0.244940\pi$
$104$	−6.97802	−0.684251
$105$	0.174502	0.0170296
$106$	7.15390	0.694848
$107$	5.88326	0.568757	0.284378	−	0.958712i	$-0.408213\pi$
$107$	5.88326	0.568757	0.284378	+	0.958712i	$0.408213\pi$
$108$	−18.7540	−1.80460
$109$	−18.8375	−1.80430	−0.902151	−	0.431420i	$-0.858013\pi$
$109$	−18.8375	−1.80430	−0.902151	+	0.431420i	$0.858013\pi$
$110$	9.74287	0.928947
$111$	−3.83144	−0.363664
$112$	−4.03121	−0.380913
$113$	19.7823	1.86097	0.930483	−	0.366335i	$-0.119388\pi$
$113$	19.7823	1.86097	0.930483	+	0.366335i	$0.119388\pi$
$114$	10.1958	0.954928
$115$	1.42642	0.133014
$116$	−38.6049	−3.58437
$117$	−2.15590	−0.199313
$118$	0.819606	0.0754508
$119$	0.574843	0.0526958
$120$	4.28631	0.391285
$121$	10.7481	0.977103
$122$	−30.6883	−2.77839
$123$	1.08872	0.0981664
$124$	−20.3719	−1.82945
$125$	7.35238	0.657617
$126$	−2.31382	−0.206132
$127$	1.54761	0.137328	0.0686641	−	0.997640i	$-0.478126\pi$
$127$	1.54761	0.137328	0.0686641	+	0.997640i	$0.478126\pi$
$128$	−14.0807	−1.24457
$129$	5.56192	0.489700
$130$	1.75539	0.153958
$131$	−0.567558	−0.0495878	−0.0247939	−	0.999693i	$-0.507893\pi$
$131$	−0.567558	−0.0495878	−0.0247939	+	0.999693i	$0.507893\pi$
$132$	15.7135	1.36769
$133$	1.96156	0.170089
$134$	−15.0693	−1.30179
$135$	2.87264	0.247237
$136$	14.1199	1.21077
$137$	−14.0557	−1.20086	−0.600430	−	0.799677i	$-0.705004\pi$
$137$	−14.0557	−1.20086	−0.600430	+	0.799677i	$0.705004\pi$
$138$	3.20032	0.272429
$139$	−1.08081	−0.0916734	−0.0458367	−	0.998949i	$-0.514595\pi$
$139$	−1.08081	−0.0916734	−0.0458367	+	0.998949i	$0.514595\pi$
$140$	1.35431	0.114460
$141$	4.59817	0.387236
$142$	−29.1595	−2.44701
$143$	3.91841	0.327674
$144$	−30.5925	−2.54937
$145$	5.91328	0.491072
$146$	24.4757	2.02562
$147$	−4.53702	−0.374207
$148$	−29.7357	−2.44426
$149$	13.5882	1.11319	0.556596	−	0.830783i	$-0.312107\pi$
$149$	13.5882	1.11319	0.556596	+	0.830783i	$0.312107\pi$
$150$	7.70877	0.629419
$151$	7.33710	0.597084	0.298542	−	0.954396i	$-0.403500\pi$
$151$	7.33710	0.597084	0.298542	+	0.954396i	$0.403500\pi$
$152$	48.1820	3.90807
$153$	4.36243	0.352682
$154$	4.20544	0.338884
$155$	3.12046	0.250642
$156$	2.83114	0.226673
$157$	9.04328	0.721733	0.360866	−	0.932618i	$-0.382481\pi$
$157$	9.04328	0.721733	0.360866	+	0.932618i	$0.382481\pi$
$158$	7.38631	0.587623
$159$	−1.76733	−0.140158
$160$	11.8989	0.940687
$161$	0.615703	0.0485242
$162$	−14.0855	−1.10666
$163$	16.7719	1.31368	0.656839	−	0.754031i	$-0.271893\pi$
$163$	16.7719	1.31368	0.656839	+	0.754031i	$0.271893\pi$
$164$	8.44953	0.659797
$165$	−2.40691	−0.187378
$166$	−17.8456	−1.38509
$167$	14.9991	1.16067	0.580333	−	0.814379i	$-0.302922\pi$
$167$	14.9991	1.16067	0.580333	+	0.814379i	$0.302922\pi$
$168$	1.85015	0.142742
$169$	−12.2940	−0.945693
$170$	−3.55201	−0.272427
$171$	14.8861	1.13837
$172$	43.1660	3.29138
$173$	−7.11361	−0.540838	−0.270419	−	0.962743i	$-0.587162\pi$
$173$	−7.11361	−0.540838	−0.270419	+	0.962743i	$0.587162\pi$
$174$	13.2671	1.00577
$175$	1.48308	0.112110
$176$	55.6027	4.19121
$177$	−0.202478	−0.0152192
$178$	−17.1589	−1.28611
$179$	4.15683	0.310696	0.155348	−	0.987860i	$-0.450350\pi$
$179$	4.15683	0.310696	0.155348	+	0.987860i	$0.450350\pi$
$180$	10.2777	0.766056
$181$	4.11016	0.305506	0.152753	−	0.988264i	$-0.451186\pi$
$181$	4.11016	0.305506	0.152753	+	0.988264i	$0.451186\pi$
$182$	0.757702	0.0561646
$183$	7.58135	0.560430
$184$	15.1236	1.11493
$185$	4.55476	0.334872
$186$	7.00108	0.513344
$187$	−7.92884	−0.579814
$188$	35.6863	2.60269
$189$	1.23995	0.0901932
$190$	−12.1207	−0.879326
$191$	−15.1417	−1.09561	−0.547807	−	0.836605i	$-0.684537\pi$
$191$	−15.1417	−1.09561	−0.547807	+	0.836605i	$0.684537\pi$
$192$	10.9841	0.792708
$193$	12.9098	0.929266	0.464633	−	0.885503i	$-0.346186\pi$
$193$	12.9098	0.929266	0.464633	+	0.885503i	$0.346186\pi$
$194$	38.2097	2.74329
$195$	−0.433659	−0.0310550
$196$	−35.2117	−2.51512
$197$	−24.0649	−1.71455	−0.857277	−	0.514855i	$-0.827846\pi$
$197$	−24.0649	−1.71455	−0.857277	+	0.514855i	$0.827846\pi$
$198$	31.9147	2.26808
$199$	−13.0942	−0.928220	−0.464110	−	0.885778i	$-0.653626\pi$
$199$	−13.0942	−0.928220	−0.464110	+	0.885778i	$0.653626\pi$
$200$	36.4289	2.57591
$201$	3.72277	0.262584
$202$	−17.3830	−1.22307
$203$	2.55242	0.179145
$204$	−5.72877	−0.401094
$205$	−1.29425	−0.0903945
$206$	−38.8846	−2.70922
$207$	4.67252	0.324763
$208$	10.0181	0.694627
$209$	−27.0559	−1.87149
$210$	−0.465425	−0.0321174
$211$	22.7148	1.56375	0.781875	−	0.623436i	$-0.214264\pi$
$211$	22.7148	1.56375	0.781875	+	0.623436i	$0.214264\pi$
$212$	−13.7162	−0.942031
$213$	7.20367	0.493588
$214$	−15.6916	−1.07266
$215$	−6.61193	−0.450930
$216$	30.4571	2.07234
$217$	1.34692	0.0914351
$218$	50.2426	3.40286
$219$	−6.04656	−0.408589
$220$	−18.6800	−1.25941
$221$	−1.42856	−0.0960951
$222$	10.2191	0.685859
$223$	1.44039	0.0964559	0.0482279	−	0.998836i	$-0.484643\pi$
$223$	1.44039	0.0964559	0.0482279	+	0.998836i	$0.484643\pi$
$224$	5.13605	0.343167
$225$	11.2549	0.750329
$226$	−52.7627	−3.50972
$227$	−15.4980	−1.02864	−0.514318	−	0.857599i	$-0.671955\pi$
$227$	−15.4980	−1.02864	−0.514318	+	0.857599i	$0.671955\pi$
$228$	−19.5485	−1.29463
$229$	6.00576	0.396872	0.198436	−	0.980114i	$-0.436414\pi$
$229$	6.00576	0.396872	0.198436	+	0.980114i	$0.436414\pi$
$230$	−3.80449	−0.250861
$231$	−1.03893	−0.0683563
$232$	62.6954	4.11616
$233$	19.6645	1.28827	0.644133	−	0.764913i	$-0.277218\pi$
$233$	19.6645	1.28827	0.644133	+	0.764913i	$0.277218\pi$
$234$	5.75014	0.375898
$235$	−5.46624	−0.356578
$236$	−1.57143	−0.102291
$237$	−1.82474	−0.118530
$238$	−1.53320	−0.0993826
$239$	30.4487	1.96956	0.984781	−	0.173800i	$-0.0556047\pi$
$239$	30.4487	1.96956	0.984781	+	0.173800i	$0.0556047\pi$
$240$	−6.15367	−0.397218
$241$	−13.7247	−0.884085	−0.442043	−	0.896994i	$-0.645746\pi$
$241$	−13.7247	−0.884085	−0.442043	+	0.896994i	$0.645746\pi$
$242$	−28.6670	−1.84279
$243$	14.4818	0.929010
$244$	58.8388	3.76677
$245$	5.39354	0.344581
$246$	−2.90379	−0.185139
$247$	−4.87471	−0.310171
$248$	33.0846	2.10087
$249$	4.40865	0.279387
$250$	−19.6100	−1.24024
$251$	5.14687	0.324868	0.162434	−	0.986719i	$-0.448066\pi$
$251$	5.14687	0.324868	0.162434	+	0.986719i	$0.448066\pi$
$252$	4.43630	0.279460
$253$	−8.49243	−0.533914
$254$	−4.12772	−0.258996
$255$	0.877502	0.0549513
$256$	4.21500	0.263437
$257$	24.4557	1.52551	0.762753	−	0.646690i	$-0.223847\pi$
$257$	24.4557	1.52551	0.762753	+	0.646690i	$0.223847\pi$
$258$	−14.8346	−0.923559
$259$	1.96603	0.122163
$260$	−3.36562	−0.208727
$261$	19.3701	1.19898
$262$	1.51377	0.0935210
$263$	1.30307	0.0803506	0.0401753	−	0.999193i	$-0.487208\pi$
$263$	1.30307	0.0803506	0.0401753	+	0.999193i	$0.487208\pi$
$264$	−25.5193	−1.57060
$265$	2.10097	0.129062
$266$	−5.23179	−0.320782
$267$	4.23900	0.259422
$268$	28.8923	1.76488
$269$	4.66565	0.284470	0.142235	−	0.989833i	$-0.454571\pi$
$269$	4.66565	0.284470	0.142235	+	0.989833i	$0.454571\pi$
$270$	−7.66179	−0.466282
$271$	−13.7281	−0.833923	−0.416962	−	0.908924i	$-0.636905\pi$
$271$	−13.7281	−0.833923	−0.416962	+	0.908924i	$0.636905\pi$
$272$	−20.2714	−1.22913
$273$	−0.187186	−0.0113290
$274$	37.4889	2.26478
$275$	−20.4561	−1.23355
$276$	−6.13598	−0.369343
$277$	2.03111	0.122038	0.0610189	−	0.998137i	$-0.480565\pi$
$277$	2.03111	0.122038	0.0610189	+	0.998137i	$0.480565\pi$
$278$	2.88271	0.172893
$279$	10.2217	0.611956
$280$	−2.19943	−0.131441
$281$	−9.57763	−0.571353	−0.285677	−	0.958326i	$-0.592218\pi$
$281$	−9.57763	−0.571353	−0.285677	+	0.958326i	$0.592218\pi$
$282$	−12.2641	−0.730315
$283$	−33.1514	−1.97065	−0.985323	−	0.170702i	$-0.945396\pi$
$283$	−33.1514	−1.97065	−0.985323	+	0.170702i	$0.945396\pi$
$284$	55.9076	3.31750
$285$	2.99433	0.177369
$286$	−10.4510	−0.617982
$287$	−0.558654	−0.0329763
$288$	38.9770	2.29674
$289$	−14.1093	−0.829961
$290$	−15.7717	−0.926146
$291$	−9.43945	−0.553351
$292$	−46.9272	−2.74621
$293$	−4.48756	−0.262166	−0.131083	−	0.991371i	$-0.541845\pi$
$293$	−4.48756	−0.262166	−0.131083	+	0.991371i	$0.541845\pi$
$294$	12.1010	0.705742
$295$	0.240703	0.0140143
$296$	48.2917	2.80690
$297$	−17.1027	−0.992400
$298$	−36.2420	−2.09944
$299$	−1.53010	−0.0884879
$300$	−14.7800	−0.853326
$301$	−2.85399	−0.164501
$302$	−19.5692	−1.12608
$303$	4.29437	0.246705
$304$	−69.1728	−3.96733
$305$	−9.01260	−0.516060
$306$	−11.6353	−0.665147
$307$	32.7166	1.86723	0.933617	−	0.358273i	$-0.116634\pi$
$307$	32.7166	1.86723	0.933617	+	0.358273i	$0.116634\pi$
$308$	−8.06309	−0.459437
$309$	9.60619	0.546477
$310$	−8.32278	−0.472702
$311$	−9.79968	−0.555689	−0.277844	−	0.960626i	$-0.589620\pi$
$311$	−9.79968	−0.555689	−0.277844	+	0.960626i	$0.589620\pi$
$312$	−4.59786	−0.260302
$313$	4.98240	0.281622	0.140811	−	0.990036i	$-0.455029\pi$
$313$	4.98240	0.281622	0.140811	+	0.990036i	$0.455029\pi$
$314$	−24.1199	−1.36116
$315$	−0.679528	−0.0382871
$316$	−14.1618	−0.796663
$317$	−17.8350	−1.00171	−0.500856	−	0.865531i	$-0.666981\pi$
$317$	−17.8350	−1.00171	−0.500856	+	0.865531i	$0.666981\pi$
$318$	4.71374	0.264334
$319$	−35.2057	−1.97114
$320$	−13.0577	−0.729949
$321$	3.87652	0.216366
$322$	−1.64218	−0.0915151
$323$	9.86391	0.548843
$324$	27.0062	1.50034
$325$	−3.68563	−0.204442
$326$	−44.7334	−2.47756
$327$	−12.4121	−0.686391
$328$	−13.7223	−0.757686
$329$	−2.35946	−0.130081
$330$	6.41963	0.353389
$331$	8.74743	0.480802	0.240401	−	0.970674i	$-0.422721\pi$
$331$	8.74743	0.480802	0.240401	+	0.970674i	$0.422721\pi$
$332$	34.2155	1.87782
$333$	14.9200	0.817611
$334$	−40.0051	−2.18898
$335$	−4.42557	−0.241795
$336$	−2.65619	−0.144907
$337$	−8.97010	−0.488632	−0.244316	−	0.969696i	$-0.578563\pi$
$337$	−8.97010	−0.488632	−0.244316	+	0.969696i	$0.578563\pi$
$338$	32.7901	1.78355
$339$	13.0347	0.707947
$340$	6.81028	0.369339
$341$	−18.5782	−1.00607
$342$	−39.7036	−2.14693
$343$	4.69481	0.253496
$344$	−70.1028	−3.77969
$345$	0.939876	0.0506012
$346$	18.9732	1.02000
$347$	22.6667	1.21681	0.608406	−	0.793626i	$-0.291809\pi$
$347$	22.6667	1.21681	0.608406	+	0.793626i	$0.291809\pi$
$348$	−25.4370	−1.36356
$349$	−25.3419	−1.35652	−0.678261	−	0.734821i	$-0.737266\pi$
$349$	−25.3419	−1.35652	−0.678261	+	0.734821i	$0.737266\pi$
$350$	−3.95560	−0.211436
$351$	−3.08143	−0.164475
$352$	−70.8418	−3.77588
$353$	32.5598	1.73298	0.866492	−	0.499191i	$-0.166370\pi$
$353$	32.5598	1.73298	0.866492	+	0.499191i	$0.166370\pi$
$354$	0.540043	0.0287029
$355$	−8.56362	−0.454510
$356$	32.8988	1.74363
$357$	0.378767	0.0200465
$358$	−11.0869	−0.585963
$359$	−16.0245	−0.845739	−0.422870	−	0.906191i	$-0.638977\pi$
$359$	−16.0245	−0.845739	−0.422870	+	0.906191i	$0.638977\pi$
$360$	−16.6913	−0.879710
$361$	14.6590	0.771527
$362$	−10.9625	−0.576175
$363$	7.08201	0.371709
$364$	−1.45274	−0.0761445
$365$	7.18806	0.376240
$366$	−20.2207	−1.05695
$367$	16.9357	0.884034	0.442017	−	0.897007i	$-0.354263\pi$
$367$	16.9357	0.884034	0.442017	+	0.897007i	$0.354263\pi$
$368$	−21.7123	−1.13183
$369$	−4.23958	−0.220704
$370$	−12.1483	−0.631559
$371$	0.906868	0.0470822
$372$	−13.4232	−0.695959
$373$	−6.66990	−0.345354	−0.172677	−	0.984978i	$-0.555242\pi$
$373$	−6.66990	−0.345354	−0.172677	+	0.984978i	$0.555242\pi$
$374$	21.1475	1.09351
$375$	4.84452	0.250170
$376$	−57.9556	−2.98883
$377$	−6.34309	−0.326686
$378$	−3.30715	−0.170102
$379$	6.15599	0.316212	0.158106	−	0.987422i	$-0.449461\pi$
$379$	6.15599	0.316212	0.158106	+	0.987422i	$0.449461\pi$
$380$	23.2390	1.19213
$381$	1.01973	0.0522423
$382$	40.3853	2.06629
$383$	32.0748	1.63894	0.819472	−	0.573120i	$-0.194267\pi$
$383$	32.0748	1.63894	0.819472	+	0.573120i	$0.194267\pi$
$384$	−9.27782	−0.473457
$385$	1.23506	0.0629445
$386$	−34.4325	−1.75257
$387$	−21.6587	−1.10097
$388$	−73.2594	−3.71919
$389$	−15.7346	−0.797777	−0.398889	−	0.916999i	$-0.630604\pi$
$389$	−15.7346	−0.797777	−0.398889	+	0.916999i	$0.630604\pi$
$390$	1.15664	0.0585687
$391$	3.09613	0.156578
$392$	57.1848	2.88827
$393$	−0.373967	−0.0188641
$394$	64.1850	3.23360
$395$	2.16923	0.109146
$396$	−61.1901	−3.07492
$397$	31.4175	1.57680	0.788400	−	0.615164i	$-0.210910\pi$
$397$	31.4175	1.57680	0.788400	+	0.615164i	$0.210910\pi$
$398$	34.9242	1.75059
$399$	1.29248	0.0647050
$400$	−52.2995	−2.61497
$401$	−30.8159	−1.53887	−0.769435	−	0.638725i	$-0.779462\pi$
$401$	−30.8159	−1.53887	−0.769435	+	0.638725i	$0.779462\pi$
$402$	−9.92922	−0.495225
$403$	−3.34727	−0.166739
$404$	33.3285	1.65815
$405$	−4.13666	−0.205552
$406$	−6.80773	−0.337862
$407$	−27.1175	−1.34416
$408$	9.30370	0.460602
$409$	0.790454	0.0390854	0.0195427	−	0.999809i	$-0.493779\pi$
$409$	0.790454	0.0390854	0.0195427	+	0.999809i	$0.493779\pi$
$410$	3.45198	0.170481
$411$	−9.26138	−0.456830
$412$	74.5535	3.67299
$413$	0.103898	0.00511247
$414$	−12.4624	−0.612492
$415$	−5.24094	−0.257268
$416$	−12.7637	−0.625793
$417$	−0.712154	−0.0348743
$418$	72.1624	3.52958
$419$	3.01651	0.147366	0.0736830	−	0.997282i	$-0.476525\pi$
$419$	3.01651	0.147366	0.0736830	+	0.997282i	$0.476525\pi$
$420$	0.892360	0.0435427
$421$	−0.396298	−0.0193144	−0.00965719	−	0.999953i	$-0.503074\pi$
$421$	−0.396298	−0.0193144	−0.00965719	+	0.999953i	$0.503074\pi$
$422$	−60.5840	−2.94918
$423$	−17.9057	−0.870607
$424$	22.2755	1.08179
$425$	7.45781	0.361757
$426$	−19.2134	−0.930891
$427$	−3.89022	−0.188261
$428$	30.0856	1.45424
$429$	2.58186	0.124653
$430$	17.6351	0.850440
$431$	29.8848	1.43950	0.719751	−	0.694232i	$-0.244256\pi$
$431$	29.8848	1.43950	0.719751	+	0.694232i	$0.244256\pi$
$432$	−43.7259	−2.10376
$433$	−6.20389	−0.298140	−0.149070	−	0.988827i	$-0.547628\pi$
$433$	−6.20389	−0.298140	−0.149070	+	0.988827i	$0.547628\pi$
$434$	−3.59246	−0.172444
$435$	3.89630	0.186813
$436$	−96.3302	−4.61338
$437$	10.5650	0.505395
$438$	16.1272	0.770585
$439$	13.6075	0.649450	0.324725	−	0.945808i	$-0.394728\pi$
$439$	13.6075	0.649450	0.324725	+	0.945808i	$0.394728\pi$
$440$	30.3369	1.44626
$441$	17.6676	0.841314
$442$	3.81019	0.181232
$443$	−24.2713	−1.15317	−0.576583	−	0.817038i	$-0.695614\pi$
$443$	−24.2713	−1.15317	−0.576583	+	0.817038i	$0.695614\pi$
$444$	−19.5930	−0.929844
$445$	−5.03926	−0.238884
$446$	−3.84176	−0.181913
$447$	8.95336	0.423480
$448$	−5.63626	−0.266288
$449$	16.5839	0.782641	0.391321	−	0.920254i	$-0.372018\pi$
$449$	16.5839	0.782641	0.391321	+	0.920254i	$0.372018\pi$
$450$	−30.0187	−1.41510
$451$	7.70555	0.362840
$452$	101.162	4.75826
$453$	4.83445	0.227142
$454$	41.3356	1.93998
$455$	0.222523	0.0104321
$456$	31.7474	1.48671
$457$	−3.45205	−0.161480	−0.0807401	−	0.996735i	$-0.525728\pi$
$457$	−3.45205	−0.161480	−0.0807401	+	0.996735i	$0.525728\pi$
$458$	−16.0183	−0.748488
$459$	6.23523	0.291036
$460$	7.29436	0.340101
$461$	−18.3585	−0.855040	−0.427520	−	0.904006i	$-0.640613\pi$
$461$	−18.3585	−0.855040	−0.427520	+	0.904006i	$0.640613\pi$
$462$	2.77098	0.128918
$463$	7.11049	0.330453	0.165226	−	0.986256i	$-0.447165\pi$
$463$	7.11049	0.330453	0.165226	+	0.986256i	$0.447165\pi$
$464$	−90.0092	−4.17857
$465$	2.05609	0.0953489
$466$	−52.4485	−2.42963
$467$	−5.21192	−0.241179	−0.120589	−	0.992702i	$-0.538478\pi$
$467$	−5.21192	−0.241179	−0.120589	+	0.992702i	$0.538478\pi$
$468$	−11.0247	−0.509619
$469$	−1.91026	−0.0882078
$470$	14.5793	0.672495
$471$	5.95867	0.274561
$472$	2.55205	0.117468
$473$	39.3652	1.81002
$474$	4.86688	0.223543
$475$	25.4486	1.16766
$476$	2.93961	0.134737
$477$	6.88214	0.315112
$478$	−81.2116	−3.71453
$479$	15.2102	0.694972	0.347486	−	0.937685i	$-0.387035\pi$
$479$	15.2102	0.694972	0.347486	+	0.937685i	$0.387035\pi$
$480$	7.84022	0.357856
$481$	−4.88582	−0.222774
$482$	36.6060	1.66736
$483$	0.405690	0.0184595
$484$	54.9633	2.49833
$485$	11.2215	0.509541
$486$	−38.6254	−1.75208
$487$	23.8701	1.08166	0.540828	−	0.841133i	$-0.318111\pi$
$487$	23.8701	1.08166	0.540828	+	0.841133i	$0.318111\pi$
$488$	−95.5559	−4.32561
$489$	11.0511	0.499748
$490$	−14.3854	−0.649868
$491$	26.0327	1.17484	0.587420	−	0.809282i	$-0.300144\pi$
$491$	26.0327	1.17484	0.587420	+	0.809282i	$0.300144\pi$
$492$	5.56744	0.251000
$493$	12.8351	0.578066
$494$	13.0017	0.584972
$495$	9.37277	0.421275
$496$	−47.4982	−2.13273
$497$	−3.69642	−0.165807
$498$	−11.7586	−0.526915
$499$	−37.5991	−1.68317	−0.841583	−	0.540128i	$-0.818376\pi$
$499$	−37.5991	−1.68317	−0.841583	+	0.540128i	$0.818376\pi$
$500$	37.5982	1.68144
$501$	9.88300	0.441540
$502$	−13.7275	−0.612690
$503$	−25.9909	−1.15887	−0.579437	−	0.815017i	$-0.696728\pi$
$503$	−25.9909	−1.15887	−0.579437	+	0.815017i	$0.696728\pi$
$504$	−7.20468	−0.320922
$505$	−5.10508	−0.227173
$506$	22.6507	1.00695
$507$	−8.10059	−0.359760
$508$	7.91409	0.351131
$509$	39.9172	1.76930	0.884650	−	0.466256i	$-0.154397\pi$
$509$	39.9172	1.76930	0.884650	+	0.466256i	$0.154397\pi$
$510$	−2.34044	−0.103636
$511$	3.10267	0.137254
$512$	16.9192	0.747731
$513$	21.2767	0.939390
$514$	−65.2274	−2.87706
$515$	−11.4197	−0.503212
$516$	28.4423	1.25210
$517$	32.5442	1.43129
$518$	−5.24371	−0.230395
$519$	−4.68720	−0.205745
$520$	5.46587	0.239694
$521$	−41.9531	−1.83800	−0.918999	−	0.394260i	$-0.871001\pi$
$521$	−41.9531	−1.83800	−0.918999	+	0.394260i	$0.871001\pi$
$522$	−51.6633	−2.26124
$523$	20.4098	0.892459	0.446230	−	0.894919i	$-0.352766\pi$
$523$	20.4098	0.892459	0.446230	+	0.894919i	$0.352766\pi$
$524$	−2.90235	−0.126790
$525$	0.977207	0.0426488
$526$	−3.47549	−0.151539
$527$	6.77315	0.295043
$528$	36.6369	1.59442
$529$	−19.6838	−0.855817
$530$	−5.60363	−0.243406
$531$	0.788471	0.0342167
$532$	10.0309	0.434896
$533$	1.38832	0.0601350
$534$	−11.3061	−0.489262
$535$	−4.60834	−0.199236
$536$	−46.9220	−2.02672
$537$	2.73896	0.118195
$538$	−12.4441	−0.536501
$539$	−32.1113	−1.38313
$540$	14.6900	0.632155
$541$	10.6155	0.456395	0.228197	−	0.973615i	$-0.426717\pi$
$541$	10.6155	0.456395	0.228197	+	0.973615i	$0.426717\pi$
$542$	36.6151	1.57275
$543$	2.70821	0.116220
$544$	25.8272	1.10733
$545$	14.7553	0.632049
$546$	0.499254	0.0213661
$547$	4.14173	0.177088	0.0885438	−	0.996072i	$-0.471779\pi$
$547$	4.14173	0.177088	0.0885438	+	0.996072i	$0.471779\pi$
$548$	−71.8774	−3.07045
$549$	−29.5225	−1.25999
$550$	54.5599	2.32644
$551$	43.7979	1.86585
$552$	9.96501	0.424139
$553$	0.936330	0.0398168
$554$	−5.41731	−0.230159
$555$	3.00116	0.127392
$556$	−5.52702	−0.234398
$557$	23.1200	0.979627	0.489814	−	0.871827i	$-0.337065\pi$
$557$	23.1200	0.979627	0.489814	+	0.871827i	$0.337065\pi$
$558$	−27.2629	−1.15413
$559$	7.09252	0.299982
$560$	3.15763	0.133434
$561$	−5.22436	−0.220572
$562$	25.5451	1.07755
$563$	1.11215	0.0468714	0.0234357	−	0.999725i	$-0.492539\pi$
$563$	1.11215	0.0468714	0.0234357	+	0.999725i	$0.492539\pi$
$564$	23.5139	0.990114
$565$	−15.4955	−0.651899
$566$	88.4201	3.71658
$567$	−1.78556	−0.0749863
$568$	−90.7956	−3.80970
$569$	37.3755	1.56686	0.783431	−	0.621479i	$-0.213468\pi$
$569$	37.3755	1.56686	0.783431	+	0.621479i	$0.213468\pi$
$570$	−7.98638	−0.334513
$571$	10.9105	0.456592	0.228296	−	0.973592i	$-0.426685\pi$
$571$	10.9105	0.456592	0.228296	+	0.973592i	$0.426685\pi$
$572$	20.0378	0.837821
$573$	−9.97694	−0.416793
$574$	1.49002	0.0621923
$575$	7.98792	0.333119
$576$	−42.7731	−1.78221
$577$	−36.5277	−1.52067	−0.760334	−	0.649533i	$-0.774965\pi$
$577$	−36.5277	−1.52067	−0.760334	+	0.649533i	$0.774965\pi$
$578$	37.6319	1.56528
$579$	8.50632	0.353511
$580$	30.2391	1.25561
$581$	−2.26221	−0.0938523
$582$	25.1766	1.04360
$583$	−12.5085	−0.518048
$584$	76.2112	3.15364
$585$	1.68871	0.0698196
$586$	11.9690	0.494437
$587$	30.6482	1.26499	0.632494	−	0.774565i	$-0.282031\pi$
$587$	30.6482	1.26499	0.632494	+	0.774565i	$0.282031\pi$
$588$	−23.2012	−0.956801
$589$	23.1123	0.952325
$590$	−0.641995	−0.0264305
$591$	−15.8565	−0.652250
$592$	−69.3303	−2.84946
$593$	41.4959	1.70403	0.852016	−	0.523515i	$-0.175380\pi$
$593$	41.4959	1.70403	0.852016	+	0.523515i	$0.175380\pi$
$594$	45.6157	1.87164
$595$	−0.450273	−0.0184594
$596$	69.4869	2.84629
$597$	−8.62781	−0.353113
$598$	4.08102	0.166885
$599$	−11.2225	−0.458538	−0.229269	−	0.973363i	$-0.573634\pi$
$599$	−11.2225	−0.458538	−0.229269	+	0.973363i	$0.573634\pi$
$600$	24.0032	0.979928
$601$	−15.3837	−0.627515	−0.313757	−	0.949503i	$-0.601588\pi$
$601$	−15.3837	−0.627515	−0.313757	+	0.949503i	$0.601588\pi$
$602$	7.61205	0.310244
$603$	−14.4968	−0.590356
$604$	37.5201	1.52667
$605$	−8.41899	−0.342280
$606$	−11.4538	−0.465278
$607$	−1.20035	−0.0487205	−0.0243603	−	0.999703i	$-0.507755\pi$
$607$	−1.20035	−0.0487205	−0.0243603	+	0.999703i	$0.507755\pi$
$608$	88.1311	3.57419
$609$	1.68181	0.0681502
$610$	24.0381	0.973273
$611$	5.86355	0.237214
$612$	22.3084	0.901764
$613$	−28.9911	−1.17094	−0.585470	−	0.810694i	$-0.699090\pi$
$613$	−28.9911	−1.17094	−0.585470	+	0.810694i	$0.699090\pi$
$614$	−87.2604	−3.52154
$615$	−0.852790	−0.0343878
$616$	13.0947	0.527600
$617$	24.0305	0.967433	0.483717	−	0.875225i	$-0.339287\pi$
$617$	24.0305	0.967433	0.483717	+	0.875225i	$0.339287\pi$
$618$	−25.6213	−1.03064
$619$	−1.52246	−0.0611929	−0.0305964	−	0.999532i	$-0.509741\pi$
$619$	−1.52246	−0.0611929	−0.0305964	+	0.999532i	$0.509741\pi$
$620$	15.9573	0.640860
$621$	6.67844	0.267997
$622$	26.1373	1.04801
$623$	−2.17516	−0.0871458
$624$	6.60095	0.264249
$625$	16.1731	0.646925
$626$	−13.2889	−0.531130
$627$	−17.8273	−0.711953
$628$	46.2451	1.84538
$629$	9.88638	0.394196
$630$	1.81241	0.0722082
$631$	6.44483	0.256564	0.128282	−	0.991738i	$-0.459054\pi$
$631$	6.44483	0.256564	0.128282	+	0.991738i	$0.459054\pi$
$632$	22.9992	0.914858
$633$	14.9669	0.594880
$634$	47.5688	1.88920
$635$	−1.21224	−0.0481062
$636$	−9.03767	−0.358367
$637$	−5.78556	−0.229232
$638$	93.8994	3.71751
$639$	−28.0518	−1.10971
$640$	11.0293	0.435973
$641$	−18.0724	−0.713817	−0.356908	−	0.934139i	$-0.616169\pi$
$641$	−18.0724	−0.713817	−0.356908	+	0.934139i	$0.616169\pi$
$642$	−10.3393	−0.408059
$643$	−39.9559	−1.57571	−0.787854	−	0.615862i	$-0.788808\pi$
$643$	−39.9559	−1.57571	−0.787854	+	0.615862i	$0.788808\pi$
$644$	3.14856	0.124070
$645$	−4.35664	−0.171543
$646$	−26.3087	−1.03510
$647$	2.90440	0.114184	0.0570920	−	0.998369i	$-0.481817\pi$
$647$	2.90440	0.114184	0.0570920	+	0.998369i	$0.481817\pi$
$648$	−43.8588	−1.72294
$649$	−1.43307	−0.0562528
$650$	9.83016	0.385571
$651$	0.887495	0.0347837
$652$	85.7675	3.35891
$653$	−21.4532	−0.839527	−0.419763	−	0.907634i	$-0.637887\pi$
$653$	−21.4532	−0.839527	−0.419763	+	0.907634i	$0.637887\pi$
$654$	33.1051	1.29451
$655$	0.444567	0.0173707
$656$	19.7005	0.769175
$657$	23.5459	0.918613
$658$	6.29306	0.245329
$659$	31.1338	1.21280	0.606401	−	0.795159i	$-0.292613\pi$
$659$	31.1338	1.21280	0.606401	+	0.795159i	$0.292613\pi$
$660$	−12.3084	−0.479103
$661$	−29.2519	−1.13777	−0.568883	−	0.822418i	$-0.692624\pi$
$661$	−29.2519	−1.13777	−0.568883	+	0.822418i	$0.692624\pi$
$662$	−23.3308	−0.906778
$663$	−0.941283	−0.0365564
$664$	−55.5669	−2.15641
$665$	−1.53648	−0.0595823
$666$	−39.7941	−1.54199
$667$	13.7475	0.532305
$668$	76.7018	2.96768
$669$	0.949083	0.0366937
$670$	11.8037	0.456017
$671$	53.6580	2.07145
$672$	3.38417	0.130547
$673$	36.2871	1.39877	0.699383	−	0.714747i	$-0.253458\pi$
$673$	36.2871	1.39877	0.699383	+	0.714747i	$0.253458\pi$
$674$	23.9247	0.921545
$675$	16.0867	0.619177
$676$	−62.8686	−2.41802
$677$	7.88088	0.302887	0.151443	−	0.988466i	$-0.451608\pi$
$677$	7.88088	0.302887	0.151443	+	0.988466i	$0.451608\pi$
$678$	−34.7656	−1.33517
$679$	4.84367	0.185883
$680$	−11.0601	−0.424135
$681$	−10.2117	−0.391313
$682$	49.5510	1.89741
$683$	2.54041	0.0972061	0.0486031	−	0.998818i	$-0.484523\pi$
$683$	2.54041	0.0972061	0.0486031	+	0.998818i	$0.484523\pi$
$684$	76.1238	2.91067
$685$	11.0098	0.420663
$686$	−12.5218	−0.478085
$687$	3.95723	0.150978
$688$	100.644	3.83700
$689$	−2.25368	−0.0858583
$690$	−2.50680	−0.0954323
$691$	4.47391	0.170195	0.0850977	−	0.996373i	$-0.472880\pi$
$691$	4.47391	0.170195	0.0850977	+	0.996373i	$0.472880\pi$
$692$	−36.3773	−1.38286
$693$	4.04568	0.153683
$694$	−60.4557	−2.29487
$695$	0.846599	0.0321133
$696$	41.3104	1.56587
$697$	−2.80925	−0.106408
$698$	67.5910	2.55836
$699$	12.9571	0.490081
$700$	7.58408	0.286651
$701$	−39.9123	−1.50747	−0.753733	−	0.657181i	$-0.771749\pi$
$701$	−39.9123	−1.50747	−0.753733	+	0.657181i	$0.771749\pi$
$702$	8.21868	0.310194
$703$	33.7357	1.27237
$704$	77.7413	2.92999
$705$	−3.60173	−0.135649
$706$	−86.8423	−3.26835
$707$	−2.20357	−0.0828737
$708$	−1.03542	−0.0389136
$709$	5.14595	0.193260	0.0966300	−	0.995320i	$-0.469194\pi$
$709$	5.14595	0.193260	0.0966300	+	0.995320i	$0.469194\pi$
$710$	22.8406	0.857191
$711$	7.10573	0.266486
$712$	−53.4286	−2.00232
$713$	7.25459	0.271687
$714$	−1.01023	−0.0378070
$715$	−3.06928	−0.114784
$716$	21.2570	0.794411
$717$	20.0628	0.749259
$718$	42.7399	1.59504
$719$	41.1369	1.53415	0.767074	−	0.641559i	$-0.221712\pi$
$719$	41.1369	1.53415	0.767074	+	0.641559i	$0.221712\pi$
$720$	23.9630	0.893049
$721$	−4.92923	−0.183574
$722$	−39.0979	−1.45507
$723$	−9.04327	−0.336323
$724$	21.0184	0.781142
$725$	33.1143	1.22983
$726$	−18.8889	−0.701031
$727$	13.0398	0.483619	0.241810	−	0.970324i	$-0.422259\pi$
$727$	13.0398	0.483619	0.241810	+	0.970324i	$0.422259\pi$
$728$	2.35930	0.0874414
$729$	−6.30109	−0.233374
$730$	−19.1717	−0.709577
$731$	−14.3516	−0.530813
$732$	38.7692	1.43295
$733$	−1.85333	−0.0684541	−0.0342271	−	0.999414i	$-0.510897\pi$
$733$	−1.85333	−0.0684541	−0.0342271	+	0.999414i	$0.510897\pi$
$734$	−45.1702	−1.66726
$735$	3.55383	0.131085
$736$	27.6630	1.01967
$737$	26.3484	0.970555
$738$	11.3076	0.416240
$739$	25.8555	0.951111	0.475556	−	0.879686i	$-0.342247\pi$
$739$	25.8555	0.951111	0.475556	+	0.879686i	$0.342247\pi$
$740$	23.2919	0.856228
$741$	−3.21198	−0.117995
$742$	−2.41876	−0.0887956
$743$	39.4269	1.44643	0.723217	−	0.690621i	$-0.242663\pi$
$743$	39.4269	1.44643	0.723217	+	0.690621i	$0.242663\pi$
$744$	21.7996	0.799213
$745$	−10.6436	−0.389952
$746$	17.7897	0.651327
$747$	−17.1677	−0.628134
$748$	−40.5461	−1.48251
$749$	−1.98916	−0.0726822
$750$	−12.9211	−0.471813
$751$	−7.85358	−0.286581	−0.143291	−	0.989681i	$-0.545768\pi$
$751$	−7.85358	−0.286581	−0.143291	+	0.989681i	$0.545768\pi$
$752$	83.2045	3.03415
$753$	3.39130	0.123586
$754$	16.9180	0.616119
$755$	−5.74713	−0.209159
$756$	6.34081	0.230613
$757$	−21.1649	−0.769251	−0.384626	−	0.923073i	$-0.625669\pi$
$757$	−21.1649	−0.769251	−0.384626	+	0.923073i	$0.625669\pi$
$758$	−16.4190	−0.596366
$759$	−5.59571	−0.203111
$760$	−37.7408	−1.36900
$761$	−17.0686	−0.618738	−0.309369	−	0.950942i	$-0.600118\pi$
$761$	−17.0686	−0.618738	−0.309369	+	0.950942i	$0.600118\pi$
$762$	−2.71978	−0.0985272
$763$	6.36903	0.230574
$764$	−77.4308	−2.80135
$765$	−3.41708	−0.123545
$766$	−85.5486	−3.09100
$767$	−0.258199	−0.00932302
$768$	2.77729	0.100217
$769$	−3.26523	−0.117747	−0.0588736	−	0.998265i	$-0.518751\pi$
$769$	−3.26523	−0.117747	−0.0588736	+	0.998265i	$0.518751\pi$
$770$	−3.29411	−0.118711
$771$	16.1140	0.580332
$772$	66.0174	2.37602
$773$	−51.1621	−1.84017	−0.920086	−	0.391715i	$-0.871882\pi$
$773$	−51.1621	−1.84017	−0.920086	+	0.391715i	$0.871882\pi$
$774$	57.7672	2.07640
$775$	17.4745	0.627703
$776$	118.976	4.27097
$777$	1.29543	0.0464731
$778$	41.9668	1.50458
$779$	−9.58613	−0.343459
$780$	−2.21763	−0.0794037
$781$	50.9849	1.82438
$782$	−8.25789	−0.295301
$783$	27.6858	0.989408
$784$	−82.0979	−2.93207
$785$	−7.08358	−0.252824
$786$	0.997431	0.0355772
$787$	25.7064	0.916334	0.458167	−	0.888866i	$-0.348506\pi$
$787$	25.7064	0.916334	0.458167	+	0.888866i	$0.348506\pi$
$788$	−123.062	−4.38391
$789$	0.858599	0.0305669
$790$	−5.78568	−0.205845
$791$	−6.68849	−0.237815
$792$	99.3745	3.53112
$793$	9.66768	0.343309
$794$	−83.7956	−2.97379
$795$	1.38434	0.0490975
$796$	−66.9603	−2.37334
$797$	39.3099	1.39243	0.696214	−	0.717834i	$-0.254866\pi$
$797$	39.3099	1.39243	0.696214	+	0.717834i	$0.254866\pi$
$798$	−3.44726	−0.122032
$799$	−11.8648	−0.419747
$800$	66.6333	2.35584
$801$	−16.5071	−0.583249
$802$	82.1909	2.90226
$803$	−42.7953	−1.51021
$804$	19.0373	0.671394
$805$	−0.482279	−0.0169981
$806$	8.92771	0.314465
$807$	3.07422	0.108218
$808$	−54.1265	−1.90416
$809$	−10.9338	−0.384412	−0.192206	−	0.981355i	$-0.561564\pi$
$809$	−10.9338	−0.384412	−0.192206	+	0.981355i	$0.561564\pi$
$810$	11.0331	0.387665
$811$	37.9895	1.33399	0.666995	−	0.745062i	$-0.267580\pi$
$811$	37.9895	1.33399	0.666995	+	0.745062i	$0.267580\pi$
$812$	13.0525	0.458052
$813$	−9.04553	−0.317241
$814$	72.3268	2.53505
$815$	−13.1374	−0.460183
$816$	−13.3569	−0.467586
$817$	−48.9725	−1.71333
$818$	−2.10827	−0.0737139
$819$	0.728919	0.0254705
$820$	−6.61849	−0.231128
$821$	38.8748	1.35674	0.678370	−	0.734720i	$-0.262686\pi$
$821$	38.8748	1.35674	0.678370	+	0.734720i	$0.262686\pi$
$822$	24.7016	0.861568
$823$	54.0363	1.88359	0.941794	−	0.336190i	$-0.109138\pi$
$823$	54.0363	1.88359	0.941794	+	0.336190i	$0.109138\pi$
$824$	−121.077	−4.21792
$825$	−13.4787	−0.469267
$826$	−0.277112	−0.00964196
$827$	46.3264	1.61093	0.805463	−	0.592646i	$-0.201917\pi$
$827$	46.3264	1.61093	0.805463	+	0.592646i	$0.201917\pi$
$828$	23.8941	0.830378
$829$	−19.8963	−0.691027	−0.345513	−	0.938414i	$-0.612295\pi$
$829$	−19.8963	−0.691027	−0.345513	+	0.938414i	$0.612295\pi$
$830$	13.9784	0.485199
$831$	1.33831	0.0464255
$832$	14.0068	0.485599
$833$	11.7070	0.405624
$834$	1.89943	0.0657719
$835$	−11.7488	−0.406583
$836$	−138.357	−4.78518
$837$	14.6099	0.504991
$838$	−8.04551	−0.277928
$839$	−26.7054	−0.921973	−0.460987	−	0.887407i	$-0.652504\pi$
$839$	−26.7054	−0.921973	−0.460987	+	0.887407i	$0.652504\pi$
$840$	−1.44922	−0.0500028
$841$	27.9908	0.965198
$842$	1.05699	0.0364263
$843$	−6.31075	−0.217354
$844$	116.158	3.99832
$845$	9.62987	0.331277
$846$	47.7575	1.64194
$847$	−3.63399	−0.124865
$848$	−31.9800	−1.09820
$849$	−21.8436	−0.749671
$850$	−19.8912	−0.682262
$851$	10.5891	0.362990
$852$	36.8378	1.26204
$853$	7.29645	0.249826	0.124913	−	0.992168i	$-0.460135\pi$
$853$	7.29645	0.249826	0.124913	+	0.992168i	$0.460135\pi$
$854$	10.3759	0.355054
$855$	−11.6602	−0.398772
$856$	−48.8599	−1.67000
$857$	−33.7955	−1.15443	−0.577216	−	0.816592i	$-0.695861\pi$
$857$	−33.7955	−1.15443	−0.577216	+	0.816592i	$0.695861\pi$
$858$	−6.88624	−0.235092
$859$	−48.7499	−1.66333	−0.831663	−	0.555281i	$-0.812611\pi$
$859$	−48.7499	−1.66333	−0.831663	+	0.555281i	$0.812611\pi$
$860$	−33.8118	−1.15297
$861$	−0.368100	−0.0125448
$862$	−79.7077	−2.71486
$863$	0.778138	0.0264881	0.0132441	−	0.999912i	$-0.495784\pi$
$863$	0.778138	0.0264881	0.0132441	+	0.999912i	$0.495784\pi$
$864$	55.7100	1.89529
$865$	5.57207	0.189456
$866$	16.5468	0.562283
$867$	−9.29672	−0.315733
$868$	6.88783	0.233788
$869$	−12.9148	−0.438106
$870$	−10.3921	−0.352324
$871$	4.74724	0.160854
$872$	156.443	5.29783
$873$	36.7582	1.24408
$874$	−28.1787	−0.953159
$875$	−2.48587	−0.0840377
$876$	−30.9206	−1.04471
$877$	45.5552	1.53829	0.769144	−	0.639075i	$-0.220683\pi$
$877$	45.5552	1.53829	0.769144	+	0.639075i	$0.220683\pi$
$878$	−36.2934	−1.22484
$879$	−2.95688	−0.0997330
$880$	−43.5534	−1.46819
$881$	−35.2520	−1.18767	−0.593835	−	0.804587i	$-0.702387\pi$
$881$	−35.2520	−1.18767	−0.593835	+	0.804587i	$0.702387\pi$
$882$	−47.1223	−1.58669
$883$	24.5755	0.827030	0.413515	−	0.910497i	$-0.364301\pi$
$883$	24.5755	0.827030	0.413515	+	0.910497i	$0.364301\pi$
$884$	−7.30528	−0.245703
$885$	0.158601	0.00533131
$886$	64.7356	2.17484
$887$	−42.5525	−1.42877	−0.714387	−	0.699751i	$-0.753294\pi$
$887$	−42.5525	−1.42877	−0.714387	+	0.699751i	$0.753294\pi$
$888$	31.8197	1.06780
$889$	−0.523253	−0.0175493
$890$	13.4405	0.450527
$891$	24.6283	0.825078
$892$	7.36582	0.246626
$893$	−40.4867	−1.35484
$894$	−23.8801	−0.798669
$895$	−3.25603	−0.108837
$896$	4.76073	0.159045
$897$	−1.00819	−0.0336625
$898$	−44.2319	−1.47604
$899$	30.0742	1.00303
$900$	57.5550	1.91850
$901$	4.56029	0.151925
$902$	−20.5519	−0.684305
$903$	−1.88051	−0.0625794
$904$	−164.290	−5.46421
$905$	−3.21948	−0.107019
$906$	−12.8943	−0.428383
$907$	−31.8406	−1.05725	−0.528625	−	0.848855i	$-0.677292\pi$
$907$	−31.8406	−1.05725	−0.528625	+	0.848855i	$0.677292\pi$
$908$	−79.2528	−2.63010
$909$	−16.7227	−0.554657
$910$	−0.593506	−0.0196745
$911$	53.3020	1.76597	0.882986	−	0.469399i	$-0.155529\pi$
$911$	53.3020	1.76597	0.882986	+	0.469399i	$0.155529\pi$
$912$	−45.5783	−1.50925
$913$	31.2028	1.03266
$914$	9.20718	0.304547
$915$	−5.93845	−0.196319
$916$	30.7120	1.01475
$917$	0.191894	0.00633689
$918$	−16.6304	−0.548884
$919$	2.20502	0.0727370	0.0363685	−	0.999338i	$-0.488421\pi$
$919$	2.20502	0.0727370	0.0363685	+	0.999338i	$0.488421\pi$
$920$	−11.8463	−0.390560
$921$	21.5571	0.710332
$922$	48.9651	1.61258
$923$	9.18606	0.302363
$924$	−5.31281	−0.174779
$925$	25.5065	0.838650
$926$	−18.9648	−0.623223
$927$	−37.4075	−1.22862
$928$	114.678	3.76450
$929$	−32.5888	−1.06920	−0.534602	−	0.845104i	$-0.679538\pi$
$929$	−32.5888	−1.06920	−0.534602	+	0.845104i	$0.679538\pi$
$930$	−5.48392	−0.179825
$931$	39.9483	1.30925
$932$	100.560	3.29394
$933$	−6.45706	−0.211395
$934$	13.9010	0.454856
$935$	6.21064	0.203110
$936$	17.9045	0.585227
$937$	34.8932	1.13991	0.569956	−	0.821675i	$-0.306960\pi$
$937$	34.8932	1.13991	0.569956	+	0.821675i	$0.306960\pi$
$938$	5.09498	0.166357
$939$	3.28293	0.107134
$940$	−27.9530	−0.911726
$941$	18.8006	0.612882	0.306441	−	0.951890i	$-0.400862\pi$
$941$	18.8006	0.612882	0.306441	+	0.951890i	$0.400862\pi$
$942$	−15.8927	−0.517813
$943$	−3.00894	−0.0979845
$944$	−3.66387	−0.119249
$945$	−0.971251	−0.0315948
$946$	−104.993	−3.41363
$947$	−41.2510	−1.34048	−0.670238	−	0.742146i	$-0.733808\pi$
$947$	−41.2510	−1.34048	−0.670238	+	0.742146i	$0.733808\pi$
$948$	−9.33128	−0.303066
$949$	−7.71052	−0.250294
$950$	−67.8755	−2.20217
$951$	−11.7516	−0.381071
$952$	−4.77401	−0.154726
$953$	−15.0306	−0.486888	−0.243444	−	0.969915i	$-0.578277\pi$
$953$	−15.0306	−0.486888	−0.243444	+	0.969915i	$0.578277\pi$
$954$	−18.3558	−0.594291
$955$	11.8604	0.383795
$956$	155.707	5.03593
$957$	−23.1972	−0.749860
$958$	−40.5681	−1.31070
$959$	4.75229	0.153460
$960$	−8.60380	−0.277687
$961$	−15.1297	−0.488056
$962$	13.0313	0.420145
$963$	−15.0955	−0.486447
$964$	−70.1847	−2.26050
$965$	−10.1122	−0.325523
$966$	−1.08204	−0.0348141
$967$	26.1840	0.842020	0.421010	−	0.907056i	$-0.361676\pi$
$967$	26.1840	0.842020	0.421010	+	0.907056i	$0.361676\pi$
$968$	−89.2621	−2.86899
$969$	6.49939	0.208790
$970$	−29.9295	−0.960979
$971$	10.2956	0.330402	0.165201	−	0.986260i	$-0.447173\pi$
$971$	10.2956	0.330402	0.165201	+	0.986260i	$0.447173\pi$
$972$	74.0565	2.37536
$973$	0.365428	0.0117151
$974$	−63.6653	−2.03997
$975$	−2.42848	−0.0777736
$976$	137.186	4.39120
$977$	13.5033	0.432008	0.216004	−	0.976392i	$-0.430698\pi$
$977$	13.5033	0.432008	0.216004	+	0.976392i	$0.430698\pi$
$978$	−29.4751	−0.942510
$979$	30.0021	0.958870
$980$	27.5812	0.881050
$981$	48.3340	1.54319
$982$	−69.4334	−2.21571
$983$	33.8510	1.07968	0.539840	−	0.841768i	$-0.318485\pi$
$983$	33.8510	1.07968	0.539840	+	0.841768i	$0.318485\pi$
$984$	−9.04169	−0.288238
$985$	18.8500	0.600610
$986$	−34.2334	−1.09021
$987$	−1.55466	−0.0494854
$988$	−24.9281	−0.793068
$989$	−15.3717	−0.488793
$990$	−24.9987	−0.794510
$991$	39.6661	1.26004	0.630018	−	0.776581i	$-0.283048\pi$
$991$	39.6661	1.26004	0.630018	+	0.776581i	$0.283048\pi$
$992$	60.5161	1.92139
$993$	5.76373	0.182906
$994$	9.85895	0.312707
$995$	10.2566	0.325157
$996$	22.5448	0.714358
$997$	1.15607	0.0366131	0.0183065	−	0.999832i	$-0.494173\pi$
$997$	1.15607	0.0366131	0.0183065	+	0.999832i	$0.494173\pi$
$998$	100.283	3.17440
$999$	21.3252	0.674699

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6043.2.a.c.1.4	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6043.2.a.c.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-2.66716 q^{2} +0.658905 q^{3} +5.11375 q^{4} -0.783297 q^{5} -1.75741 q^{6} -0.338104 q^{7} -8.30489 q^{8} -2.56584 q^{9} +O(q^{10})\)	\(q-2.66716 q^{2} +0.658905 q^{3} +5.11375 q^{4} -0.783297 q^{5} -1.75741 q^{6} -0.338104 q^{7} -8.30489 q^{8} -2.56584 q^{9} +2.08918 q^{10} +4.66349 q^{11} +3.36948 q^{12} +0.840231 q^{13} +0.901779 q^{14} -0.516119 q^{15} +11.9230 q^{16} -1.70019 q^{17} +6.84352 q^{18} -5.80164 q^{19} -4.00559 q^{20} -0.222779 q^{21} -12.4383 q^{22} -1.82105 q^{23} -5.47214 q^{24} -4.38645 q^{25} -2.24103 q^{26} -3.66736 q^{27} -1.72898 q^{28} -7.54922 q^{29} +1.37657 q^{30} -3.98375 q^{31} -15.1907 q^{32} +3.07280 q^{33} +4.53469 q^{34} +0.264836 q^{35} -13.1211 q^{36} -5.81485 q^{37} +15.4739 q^{38} +0.553633 q^{39} +6.50520 q^{40} +1.65231 q^{41} +0.594187 q^{42} +8.44116 q^{43} +23.8479 q^{44} +2.00982 q^{45} +4.85702 q^{46} +6.97850 q^{47} +7.85611 q^{48} -6.88569 q^{49} +11.6994 q^{50} -1.12027 q^{51} +4.29673 q^{52} -2.68221 q^{53} +9.78146 q^{54} -3.65290 q^{55} +2.80792 q^{56} -3.82273 q^{57} +20.1350 q^{58} -0.307295 q^{59} -2.63930 q^{60} +11.5060 q^{61} +10.6253 q^{62} +0.867523 q^{63} +16.6702 q^{64} -0.658150 q^{65} -8.19565 q^{66} +5.64993 q^{67} -8.69438 q^{68} -1.19990 q^{69} -0.706361 q^{70} +10.9328 q^{71} +21.3090 q^{72} -9.17667 q^{73} +15.5092 q^{74} -2.89025 q^{75} -29.6682 q^{76} -1.57675 q^{77} -1.47663 q^{78} -2.76935 q^{79} -9.33923 q^{80} +5.28108 q^{81} -4.40699 q^{82} +6.69087 q^{83} -1.13924 q^{84} +1.33176 q^{85} -22.5139 q^{86} -4.97422 q^{87} -38.7298 q^{88} +6.43339 q^{89} -5.36051 q^{90} -0.284086 q^{91} -9.31238 q^{92} -2.62492 q^{93} -18.6128 q^{94} +4.54441 q^{95} -10.0093 q^{96} -14.3260 q^{97} +18.3652 q^{98} -11.9658 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9}+O(q^{10}) \) 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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