LMFDB - Embedded newform 6029.2.a.b.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6029,2,Mod(1,6029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6029, 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("6029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6029 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6029.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:	$48.1418073786$
Analytic rank:	$0$
Dimension:	$268$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.50934 q^{2} -1.29295 q^{3} +4.29679 q^{4} -2.86314 q^{5} +3.24445 q^{6} +3.23051 q^{7} -5.76344 q^{8} -1.32829 q^{9} +O(q^{10})$	\(q-2.50934 q^{2} -1.29295 q^{3} +4.29679 q^{4} -2.86314 q^{5} +3.24445 q^{6} +3.23051 q^{7} -5.76344 q^{8} -1.32829 q^{9} +7.18460 q^{10} -0.163813 q^{11} -5.55553 q^{12} -3.11485 q^{13} -8.10644 q^{14} +3.70189 q^{15} +5.86886 q^{16} -0.924070 q^{17} +3.33312 q^{18} -0.559171 q^{19} -12.3023 q^{20} -4.17688 q^{21} +0.411063 q^{22} -3.51087 q^{23} +7.45183 q^{24} +3.19757 q^{25} +7.81623 q^{26} +5.59625 q^{27} +13.8808 q^{28} -7.35734 q^{29} -9.28931 q^{30} -11.0585 q^{31} -3.20008 q^{32} +0.211802 q^{33} +2.31881 q^{34} -9.24939 q^{35} -5.70737 q^{36} -0.273151 q^{37} +1.40315 q^{38} +4.02734 q^{39} +16.5015 q^{40} -10.7763 q^{41} +10.4812 q^{42} +9.53331 q^{43} -0.703871 q^{44} +3.80307 q^{45} +8.80997 q^{46} +1.48887 q^{47} -7.58812 q^{48} +3.43617 q^{49} -8.02380 q^{50} +1.19477 q^{51} -13.3839 q^{52} -5.48181 q^{53} -14.0429 q^{54} +0.469020 q^{55} -18.6188 q^{56} +0.722979 q^{57} +18.4621 q^{58} -8.16820 q^{59} +15.9063 q^{60} +6.37058 q^{61} +27.7496 q^{62} -4.29104 q^{63} -3.70762 q^{64} +8.91826 q^{65} -0.531483 q^{66} -8.65926 q^{67} -3.97054 q^{68} +4.53937 q^{69} +23.2099 q^{70} +14.0143 q^{71} +7.65550 q^{72} -11.0128 q^{73} +0.685428 q^{74} -4.13430 q^{75} -2.40264 q^{76} -0.529199 q^{77} -10.1060 q^{78} -2.09210 q^{79} -16.8034 q^{80} -3.25080 q^{81} +27.0413 q^{82} -16.7782 q^{83} -17.9472 q^{84} +2.64574 q^{85} -23.9223 q^{86} +9.51265 q^{87} +0.944127 q^{88} -5.64577 q^{89} -9.54320 q^{90} -10.0626 q^{91} -15.0855 q^{92} +14.2981 q^{93} -3.73607 q^{94} +1.60099 q^{95} +4.13753 q^{96} +13.5714 q^{97} -8.62253 q^{98} +0.217591 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9}+O(q^{10}) $ 268 * q + 8 * q^2 + 43 * q^3 + 300 * q^4 + 18 * q^5 + 34 * q^6 + 59 * q^7 + 21 * q^8 + 295 * q^9	\( 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9} + 91 q^{10} + 49 q^{11} + 77 q^{12} + 45 q^{13} + 42 q^{14} + 37 q^{15} + 356 q^{16} + 40 q^{17} + 36 q^{18} + 245 q^{19} + 40 q^{20} + 66 q^{21} + 51 q^{22} + 26 q^{23} + 90 q^{24} + 314 q^{25} + 24 q^{26} + 160 q^{27} + 117 q^{28} + 54 q^{29} + 25 q^{30} + 181 q^{31} + 35 q^{32} + 49 q^{33} + 84 q^{34} + 73 q^{35} + 348 q^{36} + 77 q^{37} + 20 q^{38} + 96 q^{39} + 257 q^{40} + 62 q^{41} + 22 q^{42} + 199 q^{43} + 59 q^{44} + 60 q^{45} + 116 q^{46} + 41 q^{47} + 106 q^{48} + 381 q^{49} + 21 q^{50} + 248 q^{51} + 101 q^{52} + 4 q^{53} + 98 q^{54} + 136 q^{55} + 79 q^{56} + 47 q^{57} + 14 q^{58} + 170 q^{59} + 31 q^{60} + 247 q^{61} + 17 q^{62} + 143 q^{63} + 437 q^{64} + 29 q^{65} + 38 q^{66} + 114 q^{67} + 62 q^{68} + 101 q^{69} + 48 q^{70} + 64 q^{71} + 54 q^{72} + 115 q^{73} + 22 q^{74} + 250 q^{75} + 448 q^{76} + 8 q^{77} - 50 q^{78} + 271 q^{79} + 39 q^{80} + 336 q^{81} + 132 q^{82} + 74 q^{83} + 122 q^{84} + 58 q^{85} + 27 q^{86} + 105 q^{87} + 127 q^{88} + 63 q^{89} + 179 q^{90} + 406 q^{91} + 13 q^{92} + q^{93} + 263 q^{94} + 76 q^{95} + 161 q^{96} + 123 q^{97} - 7 q^{98} + 180 q^{99}+O(q^{100}) \) 268 * q + 8 * q^2 + 43 * q^3 + 300 * q^4 + 18 * q^5 + 34 * q^6 + 59 * q^7 + 21 * q^8 + 295 * q^9 + 91 * q^10 + 49 * q^11 + 77 * q^12 + 45 * q^13 + 42 * q^14 + 37 * q^15 + 356 * q^16 + 40 * q^17 + 36 * q^18 + 245 * q^19 + 40 * q^20 + 66 * q^21 + 51 * q^22 + 26 * q^23 + 90 * q^24 + 314 * q^25 + 24 * q^26 + 160 * q^27 + 117 * q^28 + 54 * q^29 + 25 * q^30 + 181 * q^31 + 35 * q^32 + 49 * q^33 + 84 * q^34 + 73 * q^35 + 348 * q^36 + 77 * q^37 + 20 * q^38 + 96 * q^39 + 257 * q^40 + 62 * q^41 + 22 * q^42 + 199 * q^43 + 59 * q^44 + 60 * q^45 + 116 * q^46 + 41 * q^47 + 106 * q^48 + 381 * q^49 + 21 * q^50 + 248 * q^51 + 101 * q^52 + 4 * q^53 + 98 * q^54 + 136 * q^55 + 79 * q^56 + 47 * q^57 + 14 * q^58 + 170 * q^59 + 31 * q^60 + 247 * q^61 + 17 * q^62 + 143 * q^63 + 437 * q^64 + 29 * q^65 + 38 * q^66 + 114 * q^67 + 62 * q^68 + 101 * q^69 + 48 * q^70 + 64 * q^71 + 54 * q^72 + 115 * q^73 + 22 * q^74 + 250 * q^75 + 448 * q^76 + 8 * q^77 - 50 * q^78 + 271 * q^79 + 39 * q^80 + 336 * q^81 + 132 * q^82 + 74 * q^83 + 122 * q^84 + 58 * q^85 + 27 * q^86 + 105 * q^87 + 127 * q^88 + 63 * q^89 + 179 * q^90 + 406 * q^91 + 13 * q^92 + q^93 + 263 * q^94 + 76 * q^95 + 161 * q^96 + 123 * q^97 - 7 * q^98 + 180 * 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 $

$2$	−2.50934	−1.77437	−0.887186	−	0.461412i	$-0.847343\pi$
$2$	−2.50934	−1.77437	−0.887186	+	0.461412i	$0.847343\pi$
$3$	−1.29295	−0.746484	−0.373242	−	0.927734i	$-0.621754\pi$
$3$	−1.29295	−0.746484	−0.373242	+	0.927734i	$0.621754\pi$
$4$	4.29679	2.14840
$5$	−2.86314	−1.28044	−0.640218	−	0.768194i	$-0.721156\pi$
$5$	−2.86314	−1.28044	−0.640218	+	0.768194i	$0.721156\pi$
$6$	3.24445	1.32454
$7$	3.23051	1.22102	0.610508	−	0.792010i	$-0.290965\pi$
$7$	3.23051	1.22102	0.610508	+	0.792010i	$0.290965\pi$
$8$	−5.76344	−2.03768
$9$	−1.32829	−0.442762
$10$	7.18460	2.27197
$11$	−0.163813	−0.0493915	−0.0246957	−	0.999695i	$-0.507862\pi$
$11$	−0.163813	−0.0493915	−0.0246957	+	0.999695i	$0.507862\pi$
$12$	−5.55553	−1.60374
$13$	−3.11485	−0.863905	−0.431952	−	0.901896i	$-0.642175\pi$
$13$	−3.11485	−0.863905	−0.431952	+	0.901896i	$0.642175\pi$
$14$	−8.10644	−2.16654
$15$	3.70189	0.955824
$16$	5.86886	1.46721
$17$	−0.924070	−0.224120	−0.112060	−	0.993701i	$-0.535745\pi$
$17$	−0.924070	−0.224120	−0.112060	+	0.993701i	$0.535745\pi$
$18$	3.33312	0.785625
$19$	−0.559171	−0.128283	−0.0641413	−	0.997941i	$-0.520431\pi$
$19$	−0.559171	−0.128283	−0.0641413	+	0.997941i	$0.520431\pi$
$20$	−12.3023	−2.75088
$21$	−4.17688	−0.911469
$22$	0.411063	0.0876389
$23$	−3.51087	−0.732067	−0.366033	−	0.930602i	$-0.619284\pi$
$23$	−3.51087	−0.732067	−0.366033	+	0.930602i	$0.619284\pi$
$24$	7.45183	1.52110
$25$	3.19757	0.639515
$26$	7.81623	1.53289
$27$	5.59625	1.07700
$28$	13.8808	2.62323
$29$	−7.35734	−1.36622	−0.683112	−	0.730314i	$-0.739374\pi$
$29$	−7.35734	−1.36622	−0.683112	+	0.730314i	$0.739374\pi$
$30$	−9.28931	−1.69599
$31$	−11.0585	−1.98617	−0.993084	−	0.117405i	$-0.962542\pi$
$31$	−11.0585	−1.98617	−0.993084	+	0.117405i	$0.962542\pi$
$32$	−3.20008	−0.565699
$33$	0.211802	0.0368699
$34$	2.31881	0.397672
$35$	−9.24939	−1.56343
$36$	−5.70737	−0.951229
$37$	−0.273151	−0.0449057	−0.0224528	−	0.999748i	$-0.507148\pi$
$37$	−0.273151	−0.0449057	−0.0224528	+	0.999748i	$0.507148\pi$
$38$	1.40315	0.227621
$39$	4.02734	0.644891
$40$	16.5015	2.60912
$41$	−10.7763	−1.68297	−0.841485	−	0.540281i	$-0.818318\pi$
$41$	−10.7763	−1.68297	−0.841485	+	0.540281i	$0.818318\pi$
$42$	10.4812	1.61729
$43$	9.53331	1.45382	0.726908	−	0.686734i	$-0.240956\pi$
$43$	9.53331	1.45382	0.726908	+	0.686734i	$0.240956\pi$
$44$	−0.703871	−0.106113
$45$	3.80307	0.566928
$46$	8.80997	1.29896
$47$	1.48887	0.217173	0.108587	−	0.994087i	$-0.465368\pi$
$47$	1.48887	0.217173	0.108587	+	0.994087i	$0.465368\pi$
$48$	−7.58812	−1.09525
$49$	3.43617	0.490882
$50$	−8.02380	−1.13474
$51$	1.19477	0.167302
$52$	−13.3839	−1.85601
$53$	−5.48181	−0.752984	−0.376492	−	0.926420i	$-0.622870\pi$
$53$	−5.48181	−0.752984	−0.376492	+	0.926420i	$0.622870\pi$
$54$	−14.0429	−1.91100
$55$	0.469020	0.0632426
$56$	−18.6188	−2.48805
$57$	0.722979	0.0957609
$58$	18.4621	2.42419
$59$	−8.16820	−1.06341	−0.531704	−	0.846930i	$-0.678448\pi$
$59$	−8.16820	−1.06341	−0.531704	+	0.846930i	$0.678448\pi$
$60$	15.9063	2.05349
$61$	6.37058	0.815669	0.407834	−	0.913056i	$-0.366284\pi$
$61$	6.37058	0.815669	0.407834	+	0.913056i	$0.366284\pi$
$62$	27.7496	3.52420
$63$	−4.29104	−0.540620
$64$	−3.70762	−0.463453
$65$	8.91826	1.10617
$66$	−0.531483	−0.0654210
$67$	−8.65926	−1.05790	−0.528949	−	0.848654i	$-0.677414\pi$
$67$	−8.65926	−1.05790	−0.528949	+	0.848654i	$0.677414\pi$
$68$	−3.97054	−0.481499
$69$	4.53937	0.546476
$70$	23.2099	2.77411
$71$	14.0143	1.66319	0.831597	−	0.555379i	$-0.187427\pi$
$71$	14.0143	1.66319	0.831597	+	0.555379i	$0.187427\pi$
$72$	7.65550	0.902209
$73$	−11.0128	−1.28895	−0.644477	−	0.764624i	$-0.722925\pi$
$73$	−11.0128	−1.28895	−0.644477	+	0.764624i	$0.722925\pi$
$74$	0.685428	0.0796794
$75$	−4.13430	−0.477387
$76$	−2.40264	−0.275602
$77$	−0.529199	−0.0603078
$78$	−10.1060	−1.14428
$79$	−2.09210	−0.235380	−0.117690	−	0.993050i	$-0.537549\pi$
$79$	−2.09210	−0.235380	−0.117690	+	0.993050i	$0.537549\pi$
$80$	−16.8034	−1.87867
$81$	−3.25080	−0.361200
$82$	27.0413	2.98621
$83$	−16.7782	−1.84164	−0.920821	−	0.389985i	$-0.872480\pi$
$83$	−16.7782	−1.84164	−0.920821	+	0.389985i	$0.872480\pi$
$84$	−17.9472	−1.95820
$85$	2.64574	0.286971
$86$	−23.9223	−2.57961
$87$	9.51265	1.01986
$88$	0.944127	0.100644
$89$	−5.64577	−0.598450	−0.299225	−	0.954183i	$-0.596728\pi$
$89$	−5.64577	−0.598450	−0.299225	+	0.954183i	$0.596728\pi$
$90$	−9.54320	−1.00594
$91$	−10.0626	−1.05484
$92$	−15.0855	−1.57277
$93$	14.2981	1.48264
$94$	−3.73607	−0.385346
$95$	1.60099	0.164258
$96$	4.13753	0.422285
$97$	13.5714	1.37797	0.688983	−	0.724778i	$-0.258058\pi$
$97$	13.5714	1.37797	0.688983	+	0.724778i	$0.258058\pi$
$98$	−8.62253	−0.871007
$99$	0.217591	0.0218687
$100$	13.7393	1.37393
$101$	17.5392	1.74521	0.872606	−	0.488425i	$-0.162429\pi$
$101$	17.5392	1.74521	0.872606	+	0.488425i	$0.162429\pi$
$102$	−2.99810	−0.296856
$103$	6.35488	0.626165	0.313082	−	0.949726i	$-0.398638\pi$
$103$	6.35488	0.626165	0.313082	+	0.949726i	$0.398638\pi$
$104$	17.9523	1.76037
$105$	11.9590	1.16708
$106$	13.7557	1.33607
$107$	−3.80198	−0.367551	−0.183776	−	0.982968i	$-0.558832\pi$
$107$	−3.80198	−0.367551	−0.183776	+	0.982968i	$0.558832\pi$
$108$	24.0459	2.31382
$109$	13.6079	1.30340	0.651699	−	0.758478i	$-0.274057\pi$
$109$	13.6079	1.30340	0.651699	+	0.758478i	$0.274057\pi$
$110$	−1.17693	−0.112216
$111$	0.353169	0.0335214
$112$	18.9594	1.79149
$113$	−7.93592	−0.746549	−0.373274	−	0.927721i	$-0.621765\pi$
$113$	−7.93592	−0.746549	−0.373274	+	0.927721i	$0.621765\pi$
$114$	−1.81420	−0.169916
$115$	10.0521	0.937364
$116$	−31.6130	−2.93519
$117$	4.13742	0.382504
$118$	20.4968	1.88688
$119$	−2.98522	−0.273654
$120$	−21.3356	−1.94767
$121$	−10.9732	−0.997560
$122$	−15.9859	−1.44730
$123$	13.9331	1.25631
$124$	−47.5162	−4.26708
$125$	5.16060	0.461578
$126$	10.7677	0.959261
$127$	−8.44718	−0.749566	−0.374783	−	0.927113i	$-0.622283\pi$
$127$	−8.44718	−0.749566	−0.374783	+	0.927113i	$0.622283\pi$
$128$	15.7038	1.38804
$129$	−12.3261	−1.08525
$130$	−22.3790	−1.96276
$131$	−14.6381	−1.27894	−0.639468	−	0.768818i	$-0.720845\pi$
$131$	−14.6381	−1.27894	−0.639468	+	0.768818i	$0.720845\pi$
$132$	0.910068	0.0792113
$133$	−1.80641	−0.156635
$134$	21.7290	1.87710
$135$	−16.0228	−1.37903
$136$	5.32583	0.456686
$137$	−9.15192	−0.781902	−0.390951	−	0.920412i	$-0.627854\pi$
$137$	−9.15192	−0.781902	−0.390951	+	0.920412i	$0.627854\pi$
$138$	−11.3908	−0.969652
$139$	9.47319	0.803505	0.401753	−	0.915748i	$-0.368401\pi$
$139$	9.47319	0.803505	0.401753	+	0.915748i	$0.368401\pi$
$140$	−39.7427	−3.35888
$141$	−1.92502	−0.162116
$142$	−35.1667	−2.95113
$143$	0.510254	0.0426695
$144$	−7.79552	−0.649627
$145$	21.0651	1.74936
$146$	27.6349	2.28708
$147$	−4.44279	−0.366435
$148$	−1.17367	−0.0964752
$149$	−15.3365	−1.25641	−0.628207	−	0.778046i	$-0.716211\pi$
$149$	−15.3365	−1.25641	−0.628207	+	0.778046i	$0.716211\pi$
$150$	10.3744	0.847063
$151$	21.6345	1.76059	0.880295	−	0.474427i	$-0.157345\pi$
$151$	21.6345	1.76059	0.880295	+	0.474427i	$0.157345\pi$
$152$	3.22275	0.261400
$153$	1.22743	0.0992318
$154$	1.32794	0.107009
$155$	31.6621	2.54316
$156$	17.3047	1.38548
$157$	−13.3892	−1.06858	−0.534289	−	0.845302i	$-0.679421\pi$
$157$	−13.3892	−1.06858	−0.534289	+	0.845302i	$0.679421\pi$
$158$	5.24980	0.417651
$159$	7.08769	0.562090
$160$	9.16228	0.724341
$161$	−11.3419	−0.893866
$162$	8.15736	0.640903
$163$	−22.5243	−1.76424	−0.882119	−	0.471027i	$-0.843883\pi$
$163$	−22.5243	−1.76424	−0.882119	+	0.471027i	$0.843883\pi$
$164$	−46.3034	−3.61569
$165$	−0.606418	−0.0472096
$166$	42.1021	3.26776
$167$	−9.81058	−0.759165	−0.379583	−	0.925158i	$-0.623932\pi$
$167$	−9.81058	−0.759165	−0.379583	+	0.925158i	$0.623932\pi$
$168$	24.0732	1.85729
$169$	−3.29769	−0.253669
$170$	−6.63907	−0.509194
$171$	0.742739	0.0567987
$172$	40.9627	3.12338
$173$	12.6620	0.962672	0.481336	−	0.876536i	$-0.340152\pi$
$173$	12.6620	0.962672	0.481336	+	0.876536i	$0.340152\pi$
$174$	−23.8705	−1.80962
$175$	10.3298	0.780858
$176$	−0.961395	−0.0724679
$177$	10.5611	0.793817
$178$	14.1672	1.06187
$179$	−6.07771	−0.454269	−0.227135	−	0.973863i	$-0.572936\pi$
$179$	−6.07771	−0.454269	−0.227135	+	0.973863i	$0.572936\pi$
$180$	16.3410	1.21799
$181$	15.1049	1.12274	0.561371	−	0.827564i	$-0.310274\pi$
$181$	15.1049	1.12274	0.561371	+	0.827564i	$0.310274\pi$
$182$	25.2504	1.87168
$183$	−8.23682	−0.608883
$184$	20.2347	1.49172
$185$	0.782068	0.0574988
$186$	−35.8788	−2.63076
$187$	0.151375	0.0110696
$188$	6.39735	0.466575
$189$	18.0787	1.31503
$190$	−4.01742	−0.291454
$191$	−1.64721	−0.119188	−0.0595939	−	0.998223i	$-0.518981\pi$
$191$	−1.64721	−0.119188	−0.0595939	+	0.998223i	$0.518981\pi$
$192$	4.79376	0.345960
$193$	−14.7815	−1.06400	−0.531999	−	0.846745i	$-0.678559\pi$
$193$	−14.7815	−1.06400	−0.531999	+	0.846745i	$0.678559\pi$
$194$	−34.0552	−2.44502
$195$	−11.5308	−0.825741
$196$	14.7645	1.05461
$197$	−14.1902	−1.01101	−0.505505	−	0.862824i	$-0.668694\pi$
$197$	−14.1902	−1.01101	−0.505505	+	0.862824i	$0.668694\pi$
$198$	−0.546009	−0.0388032
$199$	4.04594	0.286809	0.143405	−	0.989664i	$-0.454195\pi$
$199$	4.04594	0.286809	0.143405	+	0.989664i	$0.454195\pi$
$200$	−18.4290	−1.30313
$201$	11.1960	0.789703
$202$	−44.0117	−3.09665
$203$	−23.7679	−1.66818
$204$	5.13370	0.359431
$205$	30.8539	2.15493
$206$	−15.9466	−1.11105
$207$	4.66344	0.324131
$208$	−18.2806	−1.26753
$209$	0.0915995	0.00633607
$210$	−30.0092	−2.07083
$211$	−15.8689	−1.09246	−0.546229	−	0.837636i	$-0.683937\pi$
$211$	−15.8689	−1.09246	−0.546229	+	0.837636i	$0.683937\pi$
$212$	−23.5542	−1.61771
$213$	−18.1198	−1.24155
$214$	9.54047	0.652173
$215$	−27.2952	−1.86152
$216$	−32.2537	−2.19458
$217$	−35.7246	−2.42514
$218$	−34.1468	−2.31271
$219$	14.2390	0.962183
$220$	2.01528	0.135870
$221$	2.87834	0.193618
$222$	−0.886223	−0.0594794
$223$	−23.2475	−1.55677	−0.778384	−	0.627789i	$-0.783960\pi$
$223$	−23.2475	−1.55677	−0.778384	+	0.627789i	$0.783960\pi$
$224$	−10.3379	−0.690728
$225$	−4.24729	−0.283153
$226$	19.9139	1.32466
$227$	6.21833	0.412725	0.206363	−	0.978476i	$-0.433837\pi$
$227$	6.21833	0.412725	0.206363	+	0.978476i	$0.433837\pi$
$228$	3.10649	0.205733
$229$	5.31004	0.350897	0.175449	−	0.984489i	$-0.443862\pi$
$229$	5.31004	0.350897	0.175449	+	0.984489i	$0.443862\pi$
$230$	−25.2242	−1.66323
$231$	0.684227	0.0450188
$232$	42.4036	2.78393
$233$	−8.31997	−0.545059	−0.272530	−	0.962147i	$-0.587860\pi$
$233$	−8.31997	−0.545059	−0.272530	+	0.962147i	$0.587860\pi$
$234$	−10.3822	−0.678705
$235$	−4.26283	−0.278076
$236$	−35.0971	−2.28462
$237$	2.70498	0.175707
$238$	7.49092	0.485565
$239$	5.99454	0.387755	0.193877	−	0.981026i	$-0.437894\pi$
$239$	5.99454	0.387755	0.193877	+	0.981026i	$0.437894\pi$
$240$	21.7259	1.40240
$241$	2.78214	0.179213	0.0896067	−	0.995977i	$-0.471439\pi$
$241$	2.78214	0.179213	0.0896067	+	0.995977i	$0.471439\pi$
$242$	27.5354	1.77004
$243$	−12.5856	−0.807369
$244$	27.3731	1.75238
$245$	−9.83824	−0.628542
$246$	−34.9630	−2.22916
$247$	1.74174	0.110824
$248$	63.7351	4.04718
$249$	21.6933	1.37476
$250$	−12.9497	−0.819011
$251$	3.62912	0.229068	0.114534	−	0.993419i	$-0.463463\pi$
$251$	3.62912	0.229068	0.114534	+	0.993419i	$0.463463\pi$
$252$	−18.4377	−1.16147
$253$	0.575126	0.0361579
$254$	21.1968	1.33001
$255$	−3.42081	−0.214219
$256$	−31.9911	−1.99944
$257$	10.7342	0.669578	0.334789	−	0.942293i	$-0.391335\pi$
$257$	10.7342	0.669578	0.334789	+	0.942293i	$0.391335\pi$
$258$	30.9303	1.92564
$259$	−0.882415	−0.0548306
$260$	38.3199	2.37650
$261$	9.77265	0.604912
$262$	36.7320	2.26931
$263$	−19.7144	−1.21564	−0.607821	−	0.794074i	$-0.707956\pi$
$263$	−19.7144	−1.21564	−0.607821	+	0.794074i	$0.707956\pi$
$264$	−1.22071	−0.0751293
$265$	15.6952	0.964148
$266$	4.53289	0.277929
$267$	7.29968	0.446733
$268$	−37.2071	−2.27278
$269$	10.0446	0.612433	0.306216	−	0.951962i	$-0.400937\pi$
$269$	10.0446	0.612433	0.306216	+	0.951962i	$0.400937\pi$
$270$	40.2068	2.44691
$271$	−3.09015	−0.187713	−0.0938567	−	0.995586i	$-0.529920\pi$
$271$	−3.09015	−0.187713	−0.0938567	+	0.995586i	$0.529920\pi$
$272$	−5.42324	−0.328832
$273$	13.0104	0.787423
$274$	22.9653	1.38738
$275$	−0.523804	−0.0315866
$276$	19.5047	1.17405
$277$	−24.6192	−1.47923	−0.739613	−	0.673032i	$-0.764992\pi$
$277$	−24.6192	−1.47923	−0.739613	+	0.673032i	$0.764992\pi$
$278$	−23.7715	−1.42572
$279$	14.6889	0.879400
$280$	53.3084	3.18578
$281$	14.0358	0.837308	0.418654	−	0.908146i	$-0.362502\pi$
$281$	14.0358	0.837308	0.418654	+	0.908146i	$0.362502\pi$
$282$	4.83054	0.287655
$283$	−27.4258	−1.63030	−0.815149	−	0.579252i	$-0.803345\pi$
$283$	−27.4258	−1.63030	−0.815149	+	0.579252i	$0.803345\pi$
$284$	60.2167	3.57320
$285$	−2.06999	−0.122616
$286$	−1.28040	−0.0757117
$287$	−34.8128	−2.05493
$288$	4.25062	0.250470
$289$	−16.1461	−0.949770
$290$	−52.8595	−3.10402
$291$	−17.5471	−1.02863
$292$	−47.3199	−2.76919
$293$	12.5035	0.730459	0.365230	−	0.930917i	$-0.380990\pi$
$293$	12.5035	0.730459	0.365230	+	0.930917i	$0.380990\pi$
$294$	11.1485	0.650193
$295$	23.3867	1.36163
$296$	1.57429	0.0915036
$297$	−0.916738	−0.0531946
$298$	38.4845	2.22935
$299$	10.9358	0.632436
$300$	−17.7642	−1.02562
$301$	30.7974	1.77513
$302$	−54.2883	−3.12394
$303$	−22.6772	−1.30277
$304$	−3.28169	−0.188218
$305$	−18.2399	−1.04441
$306$	−3.08004	−0.176074
$307$	3.30503	0.188628	0.0943139	−	0.995543i	$-0.469934\pi$
$307$	3.30503	0.188628	0.0943139	+	0.995543i	$0.469934\pi$
$308$	−2.27386	−0.129565
$309$	−8.21652	−0.467422
$310$	−79.4510	−4.51251
$311$	15.0199	0.851703	0.425852	−	0.904793i	$-0.359975\pi$
$311$	15.0199	0.851703	0.425852	+	0.904793i	$0.359975\pi$
$312$	−23.2114	−1.31408
$313$	10.3320	0.584000	0.292000	−	0.956418i	$-0.405679\pi$
$313$	10.3320	0.584000	0.292000	+	0.956418i	$0.405679\pi$
$314$	33.5982	1.89605
$315$	12.2858	0.692229
$316$	−8.98933	−0.505689
$317$	−5.24391	−0.294527	−0.147264	−	0.989097i	$-0.547047\pi$
$317$	−5.24391	−0.294527	−0.147264	+	0.989097i	$0.547047\pi$
$318$	−17.7854	−0.997358
$319$	1.20523	0.0674798
$320$	10.6154	0.593421
$321$	4.91576	0.274371
$322$	28.4607	1.58605
$323$	0.516714	0.0287507
$324$	−13.9680	−0.776001
$325$	−9.95997	−0.552480
$326$	56.5211	3.13041
$327$	−17.5943	−0.972965
$328$	62.1084	3.42936
$329$	4.80979	0.265172
$330$	1.52171	0.0837674
$331$	11.1948	0.615322	0.307661	−	0.951496i	$-0.400454\pi$
$331$	11.1948	0.615322	0.307661	+	0.951496i	$0.400454\pi$
$332$	−72.0923	−3.95658
$333$	0.362822	0.0198825
$334$	24.6181	1.34704
$335$	24.7927	1.35457
$336$	−24.5135	−1.33732
$337$	20.0997	1.09490	0.547451	−	0.836838i	$-0.315598\pi$
$337$	20.0997	1.09490	0.547451	+	0.836838i	$0.315598\pi$
$338$	8.27503	0.450102
$339$	10.2607	0.557287
$340$	11.3682	0.616528
$341$	1.81153	0.0980998
$342$	−1.86379	−0.100782
$343$	−11.5130	−0.621642
$344$	−54.9447	−2.96242
$345$	−12.9969	−0.699727
$346$	−31.7732	−1.70814
$347$	11.6576	0.625811	0.312905	−	0.949784i	$-0.398698\pi$
$347$	11.6576	0.625811	0.312905	+	0.949784i	$0.398698\pi$
$348$	40.8739	2.19107
$349$	16.1306	0.863450	0.431725	−	0.902005i	$-0.357905\pi$
$349$	16.1306	0.863450	0.431725	+	0.902005i	$0.357905\pi$
$350$	−25.9210	−1.38553
$351$	−17.4315	−0.930424
$352$	0.524215	0.0279407
$353$	−15.2749	−0.812999	−0.406499	−	0.913651i	$-0.633251\pi$
$353$	−15.2749	−0.812999	−0.406499	+	0.913651i	$0.633251\pi$
$354$	−26.5013	−1.40853
$355$	−40.1250	−2.12961
$356$	−24.2587	−1.28571
$357$	3.85973	0.204278
$358$	15.2511	0.806043
$359$	−30.4788	−1.60861	−0.804304	−	0.594218i	$-0.797462\pi$
$359$	−30.4788	−1.60861	−0.804304	+	0.594218i	$0.797462\pi$
$360$	−21.9188	−1.15522
$361$	−18.6873	−0.983544
$362$	−37.9035	−1.99216
$363$	14.1877	0.744663
$364$	−43.2367	−2.26622
$365$	31.5313	1.65042
$366$	20.6690	1.08039
$367$	−6.70797	−0.350153	−0.175076	−	0.984555i	$-0.556017\pi$
$367$	−6.70797	−0.350153	−0.175076	+	0.984555i	$0.556017\pi$
$368$	−20.6048	−1.07410
$369$	14.3140	0.745155
$370$	−1.96248	−0.102024
$371$	−17.7090	−0.919406
$372$	61.4359	3.18530
$373$	11.9253	0.617469	0.308734	−	0.951148i	$-0.400095\pi$
$373$	11.9253	0.617469	0.308734	+	0.951148i	$0.400095\pi$
$374$	−0.379851	−0.0196416
$375$	−6.67239	−0.344561
$376$	−8.58099	−0.442531
$377$	22.9170	1.18029
$378$	−45.3657	−2.33336
$379$	28.1709	1.44704	0.723520	−	0.690303i	$-0.242523\pi$
$379$	28.1709	1.44704	0.723520	+	0.690303i	$0.242523\pi$
$380$	6.87911	0.352891
$381$	10.9218	0.559539
$382$	4.13341	0.211484
$383$	−33.0567	−1.68912	−0.844559	−	0.535463i	$-0.820137\pi$
$383$	−33.0567	−1.68912	−0.844559	+	0.535463i	$0.820137\pi$
$384$	−20.3043	−1.03615
$385$	1.51517	0.0772203
$386$	37.0919	1.88793
$387$	−12.6630	−0.643695
$388$	58.3135	2.96042
$389$	18.5860	0.942349	0.471174	−	0.882040i	$-0.343830\pi$
$389$	18.5860	0.942349	0.471174	+	0.882040i	$0.343830\pi$
$390$	28.9348	1.46517
$391$	3.24429	0.164071
$392$	−19.8042	−1.00026
$393$	18.9263	0.954705
$394$	35.6081	1.79391
$395$	5.98998	0.301389
$396$	0.934942	0.0469826
$397$	−15.6975	−0.787837	−0.393918	−	0.919145i	$-0.628881\pi$
$397$	−15.6975	−0.787837	−0.393918	+	0.919145i	$0.628881\pi$
$398$	−10.1527	−0.508907
$399$	2.33559	0.116926
$400$	18.7661	0.938305
$401$	32.3398	1.61497	0.807487	−	0.589886i	$-0.200827\pi$
$401$	32.3398	1.61497	0.807487	+	0.589886i	$0.200827\pi$
$402$	−28.0945	−1.40123
$403$	34.4457	1.71586
$404$	75.3622	3.74941
$405$	9.30749	0.462493
$406$	59.6418	2.95997
$407$	0.0447456	0.00221796
$408$	−6.88602	−0.340909
$409$	−27.4380	−1.35672	−0.678361	−	0.734729i	$-0.737309\pi$
$409$	−27.4380	−1.35672	−0.678361	+	0.734729i	$0.737309\pi$
$410$	−77.4231	−3.82365
$411$	11.8330	0.583677
$412$	27.3056	1.34525
$413$	−26.3874	−1.29844
$414$	−11.7022	−0.575130
$415$	48.0382	2.35810
$416$	9.96777	0.488710
$417$	−12.2483	−0.599804
$418$	−0.229854	−0.0112426
$419$	−14.4651	−0.706664	−0.353332	−	0.935498i	$-0.614951\pi$
$419$	−14.4651	−0.706664	−0.353332	+	0.935498i	$0.614951\pi$
$420$	51.3853	2.50735
$421$	−8.80106	−0.428938	−0.214469	−	0.976731i	$-0.568802\pi$
$421$	−8.80106	−0.428938	−0.214469	+	0.976731i	$0.568802\pi$
$422$	39.8204	1.93843
$423$	−1.97764	−0.0961561
$424$	31.5941	1.53434
$425$	−2.95478	−0.143328
$426$	45.4688	2.20297
$427$	20.5802	0.995945
$428$	−16.3363	−0.789646
$429$	−0.659731	−0.0318521
$430$	68.4930	3.30303
$431$	−16.7995	−0.809202	−0.404601	−	0.914493i	$-0.632590\pi$
$431$	−16.7995	−0.809202	−0.404601	+	0.914493i	$0.632590\pi$
$432$	32.8436	1.58019
$433$	27.6901	1.33070	0.665351	−	0.746531i	$-0.268282\pi$
$433$	27.6901	1.33070	0.665351	+	0.746531i	$0.268282\pi$
$434$	89.6452	4.30311
$435$	−27.2361	−1.30587
$436$	58.4702	2.80022
$437$	1.96318	0.0939115
$438$	−35.7305	−1.70727
$439$	31.6781	1.51191	0.755957	−	0.654621i	$-0.227172\pi$
$439$	31.6781	1.51191	0.755957	+	0.654621i	$0.227172\pi$
$440$	−2.70317	−0.128868
$441$	−4.56422	−0.217344
$442$	−7.22275	−0.343551
$443$	−24.0322	−1.14181	−0.570903	−	0.821018i	$-0.693407\pi$
$443$	−24.0322	−1.14181	−0.570903	+	0.821018i	$0.693407\pi$
$444$	1.51750	0.0720172
$445$	16.1646	0.766276
$446$	58.3359	2.76228
$447$	19.8293	0.937893
$448$	−11.9775	−0.565883
$449$	−31.6034	−1.49146	−0.745728	−	0.666250i	$-0.767898\pi$
$449$	−31.6034	−1.49146	−0.745728	+	0.666250i	$0.767898\pi$
$450$	10.6579	0.502419
$451$	1.76529	0.0831243
$452$	−34.0990	−1.60388
$453$	−27.9723	−1.31425
$454$	−15.6039	−0.732328
$455$	28.8105	1.35066
$456$	−4.16685	−0.195131
$457$	12.8000	0.598760	0.299380	−	0.954134i	$-0.403220\pi$
$457$	12.8000	0.598760	0.299380	+	0.954134i	$0.403220\pi$
$458$	−13.3247	−0.622622
$459$	−5.17133	−0.241377
$460$	43.1919	2.01383
$461$	30.7694	1.43307	0.716537	−	0.697549i	$-0.245726\pi$
$461$	30.7694	1.43307	0.716537	+	0.697549i	$0.245726\pi$
$462$	−1.71696	−0.0798801
$463$	−26.3809	−1.22602	−0.613011	−	0.790074i	$-0.710042\pi$
$463$	−26.3809	−1.22602	−0.613011	+	0.790074i	$0.710042\pi$
$464$	−43.1791	−2.00454
$465$	−40.9374	−1.89843
$466$	20.8776	0.967138
$467$	12.4651	0.576818	0.288409	−	0.957507i	$-0.406874\pi$
$467$	12.4651	0.576818	0.288409	+	0.957507i	$0.406874\pi$
$468$	17.7776	0.821771
$469$	−27.9738	−1.29171
$470$	10.6969	0.493411
$471$	17.3116	0.797676
$472$	47.0769	2.16689
$473$	−1.56168	−0.0718062
$474$	−6.78771	−0.311770
$475$	−1.78799	−0.0820386
$476$	−12.8269	−0.587918
$477$	7.28141	0.333393
$478$	−15.0423	−0.688021
$479$	−15.6696	−0.715963	−0.357982	−	0.933729i	$-0.616535\pi$
$479$	−15.6696	−0.715963	−0.357982	+	0.933729i	$0.616535\pi$
$480$	−11.8463	−0.540709
$481$	0.850824	0.0387942
$482$	−6.98134	−0.317991
$483$	14.6645	0.667256
$484$	−47.1494	−2.14316
$485$	−38.8568	−1.76440
$486$	31.5816	1.43257
$487$	15.1152	0.684936	0.342468	−	0.939529i	$-0.388737\pi$
$487$	15.1152	0.684936	0.342468	+	0.939529i	$0.388737\pi$
$488$	−36.7164	−1.66208
$489$	29.1227	1.31697
$490$	24.6875	1.11527
$491$	6.07639	0.274224	0.137112	−	0.990556i	$-0.456218\pi$
$491$	6.07639	0.274224	0.137112	+	0.990556i	$0.456218\pi$
$492$	59.8679	2.69905
$493$	6.79870	0.306198
$494$	−4.37061	−0.196643
$495$	−0.622992	−0.0280014
$496$	−64.9008	−2.91413
$497$	45.2734	2.03079
$498$	−54.4359	−2.43933
$499$	−31.2213	−1.39766	−0.698829	−	0.715288i	$-0.746295\pi$
$499$	−31.2213	−1.39766	−0.698829	+	0.715288i	$0.746295\pi$
$500$	22.1740	0.991653
$501$	12.6846	0.566705
$502$	−9.10669	−0.406451
$503$	−21.7349	−0.969110	−0.484555	−	0.874761i	$-0.661018\pi$
$503$	−21.7349	−0.969110	−0.484555	+	0.874761i	$0.661018\pi$
$504$	24.7311	1.10161
$505$	−50.2171	−2.23463
$506$	−1.44319	−0.0641575
$507$	4.26374	0.189359
$508$	−36.2958	−1.61036
$509$	20.8270	0.923139	0.461569	−	0.887104i	$-0.347287\pi$
$509$	20.8270	0.923139	0.461569	+	0.887104i	$0.347287\pi$
$510$	8.58398	0.380105
$511$	−35.5770	−1.57383
$512$	48.8688	2.15972
$513$	−3.12926	−0.138160
$514$	−26.9357	−1.18808
$515$	−18.1949	−0.801763
$516$	−52.9626	−2.33155
$517$	−0.243896	−0.0107265
$518$	2.21428	0.0972899
$519$	−16.3713	−0.718619
$520$	−51.3999	−2.25403
$521$	20.2559	0.887429	0.443715	−	0.896168i	$-0.353660\pi$
$521$	20.2559	0.887429	0.443715	+	0.896168i	$0.353660\pi$
$522$	−24.5229	−1.07334
$523$	14.7323	0.644199	0.322099	−	0.946706i	$-0.395611\pi$
$523$	14.7323	0.644199	0.322099	+	0.946706i	$0.395611\pi$
$524$	−62.8969	−2.74766
$525$	−13.3559	−0.582898
$526$	49.4702	2.15700
$527$	10.2188	0.445140
$528$	1.24303	0.0540961
$529$	−10.6738	−0.464078
$530$	−39.3846	−1.71076
$531$	10.8497	0.470837
$532$	−7.76176	−0.336515
$533$	33.5665	1.45393
$534$	−18.3174	−0.792671
$535$	10.8856	0.470626
$536$	49.9072	2.15566
$537$	7.85816	0.339105
$538$	−25.2054	−1.08668
$539$	−0.562890	−0.0242454
$540$	−68.8469	−2.96270
$541$	−1.84350	−0.0792581	−0.0396291	−	0.999214i	$-0.512618\pi$
$541$	−1.84350	−0.0792581	−0.0396291	+	0.999214i	$0.512618\pi$
$542$	7.75425	0.333073
$543$	−19.5299	−0.838109
$544$	2.95710	0.126785
$545$	−38.9612	−1.66892
$546$	−32.6474	−1.39718
$547$	21.3997	0.914986	0.457493	−	0.889213i	$-0.348747\pi$
$547$	21.3997	0.914986	0.457493	+	0.889213i	$0.348747\pi$
$548$	−39.3239	−1.67984
$549$	−8.46195	−0.361147
$550$	1.31440	0.0560464
$551$	4.11401	0.175263
$552$	−26.1624	−1.11355
$553$	−6.75855	−0.287403
$554$	61.7781	2.62470
$555$	−1.01117	−0.0429219
$556$	40.7043	1.72625
$557$	−0.130409	−0.00552561	−0.00276280	−	0.999996i	$-0.500879\pi$
$557$	−0.130409	−0.00552561	−0.00276280	+	0.999996i	$0.500879\pi$
$558$	−36.8594	−1.56038
$559$	−29.6949	−1.25596
$560$	−54.2834	−2.29389
$561$	−0.195720	−0.00826329
$562$	−35.2207	−1.48570
$563$	46.3199	1.95215	0.976076	−	0.217430i	$-0.0697673\pi$
$563$	46.3199	1.95215	0.976076	+	0.217430i	$0.0697673\pi$
$564$	−8.27144	−0.348290
$565$	22.7217	0.955908
$566$	68.8208	2.89275
$567$	−10.5017	−0.441031
$568$	−80.7708	−3.38907
$569$	13.7850	0.577896	0.288948	−	0.957345i	$-0.406695\pi$
$569$	13.7850	0.577896	0.288948	+	0.957345i	$0.406695\pi$
$570$	5.19431	0.217566
$571$	−38.8825	−1.62718	−0.813591	−	0.581438i	$-0.802490\pi$
$571$	−38.8825	−1.62718	−0.813591	+	0.581438i	$0.802490\pi$
$572$	2.19245	0.0916711
$573$	2.12975	0.0889718
$574$	87.3572	3.64622
$575$	−11.2263	−0.468168
$576$	4.92478	0.205199
$577$	13.7898	0.574078	0.287039	−	0.957919i	$-0.407329\pi$
$577$	13.7898	0.574078	0.287039	+	0.957919i	$0.407329\pi$
$578$	40.5161	1.68525
$579$	19.1118	0.794258
$580$	90.5124	3.75832
$581$	−54.2019	−2.24868
$582$	44.0317	1.82517
$583$	0.897992	0.0371910
$584$	63.4718	2.62648
$585$	−11.8460	−0.489772
$586$	−31.3754	−1.29611
$587$	43.2967	1.78704	0.893522	−	0.449018i	$-0.148226\pi$
$587$	43.2967	1.78704	0.893522	+	0.449018i	$0.148226\pi$
$588$	−19.0898	−0.787249
$589$	6.18360	0.254791
$590$	−58.6852	−2.41603
$591$	18.3472	0.754703
$592$	−1.60308	−0.0658862
$593$	−18.5331	−0.761064	−0.380532	−	0.924768i	$-0.624259\pi$
$593$	−18.5331	−0.761064	−0.380532	+	0.924768i	$0.624259\pi$
$594$	2.30041	0.0943869
$595$	8.54709	0.350397
$596$	−65.8978	−2.69928
$597$	−5.23120	−0.214099
$598$	−27.4418	−1.12218
$599$	2.75983	0.112764	0.0563819	−	0.998409i	$-0.482044\pi$
$599$	2.75983	0.112764	0.0563819	+	0.998409i	$0.482044\pi$
$600$	23.8278	0.972765
$601$	−11.3059	−0.461178	−0.230589	−	0.973051i	$-0.574065\pi$
$601$	−11.3059	−0.461178	−0.230589	+	0.973051i	$0.574065\pi$
$602$	−77.2813	−3.14975
$603$	11.5020	0.468397
$604$	92.9589	3.78245
$605$	31.4177	1.27731
$606$	56.9049	2.31160
$607$	37.7519	1.53230	0.766151	−	0.642660i	$-0.222169\pi$
$607$	37.7519	1.53230	0.766151	+	0.642660i	$0.222169\pi$
$608$	1.78939	0.0725694
$609$	30.7307	1.24527
$610$	45.7700	1.85317
$611$	−4.63760	−0.187617
$612$	5.27401	0.213189
$613$	39.9266	1.61262	0.806310	−	0.591493i	$-0.201461\pi$
$613$	39.9266	1.61262	0.806310	+	0.591493i	$0.201461\pi$
$614$	−8.29344	−0.334696
$615$	−39.8925	−1.60862
$616$	3.05001	0.122888
$617$	−3.50635	−0.141161	−0.0705803	−	0.997506i	$-0.522485\pi$
$617$	−3.50635	−0.141161	−0.0705803	+	0.997506i	$0.522485\pi$
$618$	20.6181	0.829380
$619$	26.0803	1.04826	0.524129	−	0.851639i	$-0.324391\pi$
$619$	26.0803	1.04826	0.524129	+	0.851639i	$0.324391\pi$
$620$	136.045	5.46372
$621$	−19.6477	−0.788435
$622$	−37.6902	−1.51124
$623$	−18.2387	−0.730717
$624$	23.6359	0.946193
$625$	−30.7634	−1.23054
$626$	−25.9266	−1.03623
$627$	−0.118433	−0.00472977
$628$	−57.5308	−2.29573
$629$	0.252410	0.0100643
$630$	−30.8294	−1.22827
$631$	44.1554	1.75780	0.878899	−	0.477007i	$-0.158278\pi$
$631$	44.1554	1.75780	0.878899	+	0.477007i	$0.158278\pi$
$632$	12.0577	0.479630
$633$	20.5176	0.815503
$634$	13.1588	0.522601
$635$	24.1855	0.959770
$636$	30.4544	1.20759
$637$	−10.7032	−0.424075
$638$	−3.02433	−0.119734
$639$	−18.6150	−0.736399
$640$	−44.9623	−1.77729
$641$	44.3860	1.75314	0.876571	−	0.481273i	$-0.159825\pi$
$641$	44.3860	1.75314	0.876571	+	0.481273i	$0.159825\pi$
$642$	−12.3353	−0.486837
$643$	22.9109	0.903518	0.451759	−	0.892140i	$-0.350797\pi$
$643$	22.9109	0.903518	0.451759	+	0.892140i	$0.350797\pi$
$644$	−48.7338	−1.92038
$645$	35.2913	1.38959
$646$	−1.29661	−0.0510145
$647$	41.1369	1.61726	0.808629	−	0.588318i	$-0.200210\pi$
$647$	41.1369	1.61726	0.808629	+	0.588318i	$0.200210\pi$
$648$	18.7358	0.736011
$649$	1.33806	0.0525233
$650$	24.9930	0.980305
$651$	46.1901	1.81033
$652$	−96.7822	−3.79028
$653$	−45.3144	−1.77329	−0.886644	−	0.462453i	$-0.846970\pi$
$653$	−45.3144	−1.77329	−0.886644	+	0.462453i	$0.846970\pi$
$654$	44.1500	1.72640
$655$	41.9109	1.63759
$656$	−63.2443	−2.46928
$657$	14.6282	0.570700
$658$	−12.0694	−0.470514
$659$	−18.2261	−0.709989	−0.354995	−	0.934868i	$-0.615517\pi$
$659$	−18.2261	−0.709989	−0.354995	+	0.934868i	$0.615517\pi$
$660$	−2.60565	−0.101425
$661$	34.7371	1.35112	0.675558	−	0.737307i	$-0.263903\pi$
$661$	34.7371	1.35112	0.675558	+	0.737307i	$0.263903\pi$
$662$	−28.0916	−1.09181
$663$	−3.72155	−0.144533
$664$	96.6999	3.75269
$665$	5.17199	0.200561
$666$	−0.910445	−0.0352790
$667$	25.8306	1.00017
$668$	−42.1540	−1.63099
$669$	30.0578	1.16210
$670$	−62.2133	−2.40351
$671$	−1.04358	−0.0402871
$672$	13.3663	0.515617
$673$	−11.2892	−0.435166	−0.217583	−	0.976042i	$-0.569817\pi$
$673$	−11.2892	−0.435166	−0.217583	+	0.976042i	$0.569817\pi$
$674$	−50.4371	−1.94276
$675$	17.8944	0.688756
$676$	−14.1695	−0.544981
$677$	−13.6990	−0.526496	−0.263248	−	0.964728i	$-0.584794\pi$
$677$	−13.6990	−0.526496	−0.263248	+	0.964728i	$0.584794\pi$
$678$	−25.7477	−0.988834
$679$	43.8425	1.68252
$680$	−15.2486	−0.584757
$681$	−8.03998	−0.308093
$682$	−4.54574	−0.174066
$683$	21.6109	0.826918	0.413459	−	0.910523i	$-0.364320\pi$
$683$	21.6109	0.826918	0.413459	+	0.910523i	$0.364320\pi$
$684$	3.19140	0.122026
$685$	26.2032	1.00117
$686$	28.8900	1.10302
$687$	−6.86560	−0.261939
$688$	55.9496	2.13306
$689$	17.0750	0.650507
$690$	32.6136	1.24158
$691$	37.4593	1.42502	0.712509	−	0.701663i	$-0.247559\pi$
$691$	37.4593	1.42502	0.712509	+	0.701663i	$0.247559\pi$
$692$	54.4059	2.06820
$693$	0.702928	0.0267020
$694$	−29.2528	−1.11042
$695$	−27.1231	−1.02884
$696$	−54.8256	−2.07816
$697$	9.95802	0.377187
$698$	−40.4771	−1.53208
$699$	10.7573	0.406878
$700$	44.3850	1.67759
$701$	9.58853	0.362154	0.181077	−	0.983469i	$-0.442042\pi$
$701$	9.58853	0.362154	0.181077	+	0.983469i	$0.442042\pi$
$702$	43.7416	1.65092
$703$	0.152738	0.00576062
$704$	0.607357	0.0228906
$705$	5.51162	0.207579
$706$	38.3298	1.44256
$707$	56.6604	2.13093
$708$	45.3787	1.70544
$709$	−35.2991	−1.32569	−0.662843	−	0.748759i	$-0.730650\pi$
$709$	−35.2991	−1.32569	−0.662843	+	0.748759i	$0.730650\pi$
$710$	100.687	3.77873
$711$	2.77891	0.104217
$712$	32.5390	1.21945
$713$	38.8250	1.45401
$714$	−9.68537	−0.362466
$715$	−1.46093	−0.0546356
$716$	−26.1147	−0.975951
$717$	−7.75063	−0.289452
$718$	76.4816	2.85427
$719$	−14.3086	−0.533621	−0.266811	−	0.963749i	$-0.585970\pi$
$719$	−14.3086	−0.533621	−0.266811	+	0.963749i	$0.585970\pi$
$720$	22.3197	0.831805
$721$	20.5295	0.764557
$722$	46.8929	1.74517
$723$	−3.59716	−0.133780
$724$	64.9029	2.41210
$725$	−23.5256	−0.873720
$726$	−35.6019	−1.32131
$727$	−38.3133	−1.42096	−0.710480	−	0.703717i	$-0.751522\pi$
$727$	−38.3133	−1.42096	−0.710480	+	0.703717i	$0.751522\pi$
$728$	57.9949	2.14944
$729$	26.0250	0.963887
$730$	−79.1227	−2.92846
$731$	−8.80945	−0.325829
$732$	−35.3919	−1.30812
$733$	−9.43115	−0.348348	−0.174174	−	0.984715i	$-0.555725\pi$
$733$	−9.43115	−0.348348	−0.174174	+	0.984715i	$0.555725\pi$
$734$	16.8326	0.621302
$735$	12.7203	0.469197
$736$	11.2351	0.414130
$737$	1.41850	0.0522511
$738$	−35.9186	−1.32218
$739$	13.4781	0.495800	0.247900	−	0.968786i	$-0.420260\pi$
$739$	13.4781	0.495800	0.247900	+	0.968786i	$0.420260\pi$
$740$	3.36039	0.123530
$741$	−2.25197	−0.0827283
$742$	44.4380	1.63137
$743$	51.0013	1.87106	0.935529	−	0.353250i	$-0.114923\pi$
$743$	51.0013	1.87106	0.935529	+	0.353250i	$0.114923\pi$
$744$	−82.4062	−3.02116
$745$	43.9105	1.60876
$746$	−29.9247	−1.09562
$747$	22.2862	0.815409
$748$	0.650426	0.0237819
$749$	−12.2823	−0.448786
$750$	16.7433	0.611379
$751$	−18.2002	−0.664133	−0.332067	−	0.943256i	$-0.607746\pi$
$751$	−18.2002	−0.664133	−0.332067	+	0.943256i	$0.607746\pi$
$752$	8.73793	0.318640
$753$	−4.69226	−0.170995
$754$	−57.5066	−2.09427
$755$	−61.9426	−2.25432
$756$	77.6805	2.82521
$757$	42.9009	1.55926	0.779630	−	0.626240i	$-0.215407\pi$
$757$	42.9009	1.55926	0.779630	+	0.626240i	$0.215407\pi$
$758$	−70.6904	−2.56759
$759$	−0.743608	−0.0269913
$760$	−9.22719	−0.334705
$761$	−21.6162	−0.783587	−0.391793	−	0.920053i	$-0.628145\pi$
$761$	−21.6162	−0.783587	−0.391793	+	0.920053i	$0.628145\pi$
$762$	−27.4064	−0.992830
$763$	43.9603	1.59147
$764$	−7.07772	−0.256063
$765$	−3.51430	−0.127060
$766$	82.9505	2.99712
$767$	25.4427	0.918684
$768$	41.3628	1.49255
$769$	41.2256	1.48663	0.743316	−	0.668941i	$-0.233252\pi$
$769$	41.2256	1.48663	0.743316	+	0.668941i	$0.233252\pi$
$770$	−3.80208	−0.137018
$771$	−13.8787	−0.499829
$772$	−63.5133	−2.28589
$773$	12.4493	0.447769	0.223884	−	0.974616i	$-0.428126\pi$
$773$	12.4493	0.447769	0.223884	+	0.974616i	$0.428126\pi$
$774$	31.7757	1.14215
$775$	−35.3604	−1.27018
$776$	−78.2179	−2.80786
$777$	1.14092	0.0409301
$778$	−46.6387	−1.67208
$779$	6.02577	0.215896
$780$	−49.5457	−1.77402
$781$	−2.29573	−0.0821477
$782$	−8.14103	−0.291123
$783$	−41.1735	−1.47142
$784$	20.1664	0.720229
$785$	38.3353	1.36824
$786$	−47.4925	−1.69400
$787$	−41.2236	−1.46946	−0.734731	−	0.678359i	$-0.762691\pi$
$787$	−41.2236	−1.46946	−0.734731	+	0.678359i	$0.762691\pi$
$788$	−60.9724	−2.17205
$789$	25.4897	0.907458
$790$	−15.0309	−0.534776
$791$	−25.6371	−0.911549
$792$	−1.25407	−0.0445615
$793$	−19.8434	−0.704660
$794$	39.3905	1.39792
$795$	−20.2931	−0.719721
$796$	17.3846	0.616181
$797$	45.8627	1.62454	0.812270	−	0.583281i	$-0.198231\pi$
$797$	45.8627	1.62454	0.812270	+	0.583281i	$0.198231\pi$
$798$	−5.86079	−0.207470
$799$	−1.37582	−0.0486729
$800$	−10.2325	−0.361773
$801$	7.49919	0.264971
$802$	−81.1517	−2.86556
$803$	1.80404	0.0636633
$804$	48.1068	1.69660
$805$	32.4734	1.14454
$806$	−86.4359	−3.04457
$807$	−12.9872	−0.457171
$808$	−101.086	−3.55619
$809$	33.0979	1.16366	0.581831	−	0.813310i	$-0.302337\pi$
$809$	33.0979	1.16366	0.581831	+	0.813310i	$0.302337\pi$
$810$	−23.3557	−0.820635
$811$	7.26574	0.255135	0.127567	−	0.991830i	$-0.459283\pi$
$811$	7.26574	0.255135	0.127567	+	0.991830i	$0.459283\pi$
$812$	−102.126	−3.58392
$813$	3.99541	0.140125
$814$	−0.112282	−0.00393548
$815$	64.4902	2.25899
$816$	7.01196	0.245468
$817$	−5.33075	−0.186499
$818$	68.8513	2.40733
$819$	13.3659	0.467044
$820$	132.573	4.62965
$821$	−0.337702	−0.0117859	−0.00589295	−	0.999983i	$-0.501876\pi$
$821$	−0.337702	−0.0117859	−0.00589295	+	0.999983i	$0.501876\pi$
$822$	−29.6929	−1.03566
$823$	38.6426	1.34700	0.673499	−	0.739188i	$-0.264791\pi$
$823$	38.6426	1.34700	0.673499	+	0.739188i	$0.264791\pi$
$824$	−36.6260	−1.27593
$825$	0.677251	0.0235789
$826$	66.2150	2.30392
$827$	39.6551	1.37894	0.689472	−	0.724313i	$-0.257843\pi$
$827$	39.6551	1.37894	0.689472	+	0.724313i	$0.257843\pi$
$828$	20.0378	0.696363
$829$	11.6416	0.404328	0.202164	−	0.979352i	$-0.435203\pi$
$829$	11.6416	0.404328	0.202164	+	0.979352i	$0.435203\pi$
$830$	−120.544	−4.18415
$831$	31.8314	1.10422
$832$	11.5487	0.400379
$833$	−3.17527	−0.110016
$834$	30.7353	1.06428
$835$	28.0891	0.972062
$836$	0.393584	0.0136124
$837$	−61.8862	−2.13910
$838$	36.2978	1.25389
$839$	−19.8923	−0.686758	−0.343379	−	0.939197i	$-0.611571\pi$
$839$	−19.8923	−0.686758	−0.343379	+	0.939197i	$0.611571\pi$
$840$	−68.9249	−2.37814
$841$	25.1304	0.866565
$842$	22.0849	0.761095
$843$	−18.1476	−0.625037
$844$	−68.1853	−2.34704
$845$	9.44175	0.324806
$846$	4.96257	0.170617
$847$	−35.4489	−1.21804
$848$	−32.1719	−1.10479
$849$	35.4602	1.21699
$850$	7.41456	0.254317
$851$	0.958996	0.0328740
$852$	−77.8570	−2.66734
$853$	5.57752	0.190971	0.0954853	−	0.995431i	$-0.469560\pi$
$853$	5.57752	0.190971	0.0954853	+	0.995431i	$0.469560\pi$
$854$	−51.6427	−1.76718
$855$	−2.12657	−0.0727271
$856$	21.9125	0.748954
$857$	49.8657	1.70338	0.851691	−	0.524045i	$-0.175578\pi$
$857$	49.8657	1.70338	0.851691	+	0.524045i	$0.175578\pi$
$858$	1.65549	0.0565175
$859$	20.5409	0.700846	0.350423	−	0.936592i	$-0.386038\pi$
$859$	20.5409	0.700846	0.350423	+	0.936592i	$0.386038\pi$
$860$	−117.282	−3.99928
$861$	45.0111	1.53397
$862$	42.1556	1.43583
$863$	−13.2325	−0.450438	−0.225219	−	0.974308i	$-0.572310\pi$
$863$	−13.2325	−0.450438	−0.225219	+	0.974308i	$0.572310\pi$
$864$	−17.9084	−0.609257
$865$	−36.2530	−1.23264
$866$	−69.4839	−2.36116
$867$	20.8761	0.708988
$868$	−153.501	−5.21017
$869$	0.342713	0.0116258
$870$	68.3446	2.31710
$871$	26.9723	0.913922
$872$	−78.4282	−2.65591
$873$	−18.0267	−0.610111
$874$	−4.92628	−0.166634
$875$	16.6714	0.563595
$876$	61.1821	2.06715
$877$	−56.9530	−1.92317	−0.961583	−	0.274515i	$-0.911483\pi$
$877$	−56.9530	−1.92317	−0.961583	+	0.274515i	$0.911483\pi$
$878$	−79.4912	−2.68270
$879$	−16.1663	−0.545276
$880$	2.75261	0.0927904
$881$	−52.3819	−1.76479	−0.882395	−	0.470509i	$-0.844070\pi$
$881$	−52.3819	−1.76479	−0.882395	+	0.470509i	$0.844070\pi$
$882$	11.4532	0.385649
$883$	−13.0096	−0.437808	−0.218904	−	0.975746i	$-0.570248\pi$
$883$	−13.0096	−0.437808	−0.218904	+	0.975746i	$0.570248\pi$
$884$	12.3677	0.415969
$885$	−30.2378	−1.01643
$886$	60.3051	2.02599
$887$	−35.0352	−1.17637	−0.588184	−	0.808727i	$-0.700157\pi$
$887$	−35.0352	−1.17637	−0.588184	+	0.808727i	$0.700157\pi$
$888$	−2.03547	−0.0683060
$889$	−27.2887	−0.915232
$890$	−40.5626	−1.35966
$891$	0.532523	0.0178402
$892$	−99.8897	−3.34455
$893$	−0.832530	−0.0278596
$894$	−49.7584	−1.66417
$895$	17.4013	0.581663
$896$	50.7314	1.69482
$897$	−14.1395	−0.472103
$898$	79.3037	2.64640
$899$	81.3612	2.71355
$900$	−18.2497	−0.608325
$901$	5.06558	0.168759
$902$	−4.42972	−0.147494
$903$	−39.8195	−1.32511
$904$	45.7382	1.52123
$905$	−43.2476	−1.43760
$906$	70.1919	2.33197
$907$	−5.95374	−0.197691	−0.0988454	−	0.995103i	$-0.531515\pi$
$907$	−5.95374	−0.197691	−0.0988454	+	0.995103i	$0.531515\pi$
$908$	26.7189	0.886697
$909$	−23.2970	−0.772713
$910$	−72.2954	−2.39657
$911$	−7.94120	−0.263104	−0.131552	−	0.991309i	$-0.541996\pi$
$911$	−7.94120	−0.263104	−0.131552	+	0.991309i	$0.541996\pi$
$912$	4.24306	0.140502
$913$	2.74848	0.0909614
$914$	−32.1196	−1.06242
$915$	23.5832	0.779636
$916$	22.8161	0.753866
$917$	−47.2884	−1.56160
$918$	12.9766	0.428292
$919$	−36.4422	−1.20212	−0.601059	−	0.799205i	$-0.705254\pi$
$919$	−36.4422	−1.20212	−0.601059	+	0.799205i	$0.705254\pi$
$920$	−57.9348	−1.91005
$921$	−4.27323	−0.140808
$922$	−77.2110	−2.54281
$923$	−43.6526	−1.43684
$924$	2.93998	0.0967183
$925$	−0.873419	−0.0287178
$926$	66.1986	2.17542
$927$	−8.44109	−0.277242
$928$	23.5441	0.772871
$929$	−26.5933	−0.872498	−0.436249	−	0.899826i	$-0.643693\pi$
$929$	−26.5933	−0.872498	−0.436249	+	0.899826i	$0.643693\pi$
$930$	102.726	3.36852
$931$	−1.92141	−0.0629716
$932$	−35.7492	−1.17100
$933$	−19.4200	−0.635783
$934$	−31.2793	−1.02349
$935$	−0.433407	−0.0141739
$936$	−23.8458	−0.779423
$937$	−10.7660	−0.351711	−0.175855	−	0.984416i	$-0.556269\pi$
$937$	−10.7660	−0.351711	−0.175855	+	0.984416i	$0.556269\pi$
$938$	70.1958	2.29197
$939$	−13.3588	−0.435947
$940$	−18.3165	−0.597419
$941$	13.9752	0.455578	0.227789	−	0.973711i	$-0.426850\pi$
$941$	13.9752	0.455578	0.227789	+	0.973711i	$0.426850\pi$
$942$	−43.4407	−1.41537
$943$	37.8340	1.23205
$944$	−47.9380	−1.56025
$945$	−51.7619	−1.68381
$946$	3.91879	0.127411
$947$	10.5098	0.341522	0.170761	−	0.985313i	$-0.445377\pi$
$947$	10.5098	0.341522	0.170761	+	0.985313i	$0.445377\pi$
$948$	11.6227	0.377489
$949$	34.3033	1.11353
$950$	4.48668	0.145567
$951$	6.78010	0.219860
$952$	17.2051	0.557621
$953$	54.8893	1.77804	0.889019	−	0.457870i	$-0.151388\pi$
$953$	54.8893	1.77804	0.889019	+	0.457870i	$0.151388\pi$
$954$	−18.2715	−0.591563
$955$	4.71619	0.152612
$956$	25.7573	0.833051
$957$	−1.55830	−0.0503726
$958$	39.3204	1.27039
$959$	−29.5654	−0.954715
$960$	−13.7252	−0.442979
$961$	91.2908	2.94486
$962$	−2.13501	−0.0688354
$963$	5.05012	0.162738
$964$	11.9543	0.385022
$965$	42.3216	1.36238
$966$	−36.7982	−1.18396
$967$	−50.7638	−1.63245	−0.816226	−	0.577732i	$-0.803938\pi$
$967$	−50.7638	−1.63245	−0.816226	+	0.577732i	$0.803938\pi$
$968$	63.2432	2.03271
$969$	−0.668084	−0.0214619
$970$	97.5050	3.13070
$971$	14.2416	0.457034	0.228517	−	0.973540i	$-0.426612\pi$
$971$	14.2416	0.457034	0.228517	+	0.973540i	$0.426612\pi$
$972$	−54.0779	−1.73455
$973$	30.6032	0.981094
$974$	−37.9293	−1.21533
$975$	12.8777	0.412417
$976$	37.3880	1.19676
$977$	23.0523	0.737508	0.368754	−	0.929527i	$-0.379785\pi$
$977$	23.0523	0.737508	0.368754	+	0.929527i	$0.379785\pi$
$978$	−73.0788	−2.33680
$979$	0.924850	0.0295583
$980$	−42.2729	−1.35036
$981$	−18.0751	−0.577095
$982$	−15.2477	−0.486575
$983$	−2.94466	−0.0939200	−0.0469600	−	0.998897i	$-0.514953\pi$
$983$	−2.94466	−0.0939200	−0.0469600	+	0.998897i	$0.514953\pi$
$984$	−80.3029	−2.55996
$985$	40.6286	1.29453
$986$	−17.0603	−0.543309
$987$	−6.21881	−0.197947
$988$	7.48388	0.238094
$989$	−33.4702	−1.06429
$990$	1.56330	0.0496850
$991$	5.95963	0.189314	0.0946569	−	0.995510i	$-0.469825\pi$
$991$	5.95963	0.189314	0.0946569	+	0.995510i	$0.469825\pi$
$992$	35.3881	1.12357
$993$	−14.4743	−0.459328
$994$	−113.606	−3.60338
$995$	−11.5841	−0.367241
$996$	93.2116	2.95352
$997$	50.9814	1.61460	0.807298	−	0.590144i	$-0.200929\pi$
$997$	50.9814	1.61460	0.807298	+	0.590144i	$0.200929\pi$
$998$	78.3450	2.47997
$999$	−1.52862	−0.0483633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6029.2.a.b.1.20	✓	268

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6029.2.a.b.1.20	✓	268	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:	\( N \)	\(=\)	\( 6029 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.50934 q^{2} -1.29295 q^{3} +4.29679 q^{4} -2.86314 q^{5} +3.24445 q^{6} +3.23051 q^{7} -5.76344 q^{8} -1.32829 q^{9} +O(q^{10})\)	\(q-2.50934 q^{2} -1.29295 q^{3} +4.29679 q^{4} -2.86314 q^{5} +3.24445 q^{6} +3.23051 q^{7} -5.76344 q^{8} -1.32829 q^{9} +7.18460 q^{10} -0.163813 q^{11} -5.55553 q^{12} -3.11485 q^{13} -8.10644 q^{14} +3.70189 q^{15} +5.86886 q^{16} -0.924070 q^{17} +3.33312 q^{18} -0.559171 q^{19} -12.3023 q^{20} -4.17688 q^{21} +0.411063 q^{22} -3.51087 q^{23} +7.45183 q^{24} +3.19757 q^{25} +7.81623 q^{26} +5.59625 q^{27} +13.8808 q^{28} -7.35734 q^{29} -9.28931 q^{30} -11.0585 q^{31} -3.20008 q^{32} +0.211802 q^{33} +2.31881 q^{34} -9.24939 q^{35} -5.70737 q^{36} -0.273151 q^{37} +1.40315 q^{38} +4.02734 q^{39} +16.5015 q^{40} -10.7763 q^{41} +10.4812 q^{42} +9.53331 q^{43} -0.703871 q^{44} +3.80307 q^{45} +8.80997 q^{46} +1.48887 q^{47} -7.58812 q^{48} +3.43617 q^{49} -8.02380 q^{50} +1.19477 q^{51} -13.3839 q^{52} -5.48181 q^{53} -14.0429 q^{54} +0.469020 q^{55} -18.6188 q^{56} +0.722979 q^{57} +18.4621 q^{58} -8.16820 q^{59} +15.9063 q^{60} +6.37058 q^{61} +27.7496 q^{62} -4.29104 q^{63} -3.70762 q^{64} +8.91826 q^{65} -0.531483 q^{66} -8.65926 q^{67} -3.97054 q^{68} +4.53937 q^{69} +23.2099 q^{70} +14.0143 q^{71} +7.65550 q^{72} -11.0128 q^{73} +0.685428 q^{74} -4.13430 q^{75} -2.40264 q^{76} -0.529199 q^{77} -10.1060 q^{78} -2.09210 q^{79} -16.8034 q^{80} -3.25080 q^{81} +27.0413 q^{82} -16.7782 q^{83} -17.9472 q^{84} +2.64574 q^{85} -23.9223 q^{86} +9.51265 q^{87} +0.944127 q^{88} -5.64577 q^{89} -9.54320 q^{90} -10.0626 q^{91} -15.0855 q^{92} +14.2981 q^{93} -3.73607 q^{94} +1.60099 q^{95} +4.13753 q^{96} +13.5714 q^{97} -8.62253 q^{98} +0.217591 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9}+O(q^{10}) \) 268 * q + 8 * q^2 + 43 * q^3 + 300 * q^4 + 18 * q^5 + 34 * q^6 + 59 * q^7 + 21 * q^8 + 295 * q^9	\( 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9} + 91 q^{10} + 49 q^{11} + 77 q^{12} + 45 q^{13} + 42 q^{14} + 37 q^{15} + 356 q^{16} + 40 q^{17} + 36 q^{18} + 245 q^{19} + 40 q^{20} + 66 q^{21} + 51 q^{22} + 26 q^{23} + 90 q^{24} + 314 q^{25} + 24 q^{26} + 160 q^{27} + 117 q^{28} + 54 q^{29} + 25 q^{30} + 181 q^{31} + 35 q^{32} + 49 q^{33} + 84 q^{34} + 73 q^{35} + 348 q^{36} + 77 q^{37} + 20 q^{38} + 96 q^{39} + 257 q^{40} + 62 q^{41} + 22 q^{42} + 199 q^{43} + 59 q^{44} + 60 q^{45} + 116 q^{46} + 41 q^{47} + 106 q^{48} + 381 q^{49} + 21 q^{50} + 248 q^{51} + 101 q^{52} + 4 q^{53} + 98 q^{54} + 136 q^{55} + 79 q^{56} + 47 q^{57} + 14 q^{58} + 170 q^{59} + 31 q^{60} + 247 q^{61} + 17 q^{62} + 143 q^{63} + 437 q^{64} + 29 q^{65} + 38 q^{66} + 114 q^{67} + 62 q^{68} + 101 q^{69} + 48 q^{70} + 64 q^{71} + 54 q^{72} + 115 q^{73} + 22 q^{74} + 250 q^{75} + 448 q^{76} + 8 q^{77} - 50 q^{78} + 271 q^{79} + 39 q^{80} + 336 q^{81} + 132 q^{82} + 74 q^{83} + 122 q^{84} + 58 q^{85} + 27 q^{86} + 105 q^{87} + 127 q^{88} + 63 q^{89} + 179 q^{90} + 406 q^{91} + 13 q^{92} + q^{93} + 263 q^{94} + 76 q^{95} + 161 q^{96} + 123 q^{97} - 7 q^{98} + 180 q^{99}+O(q^{100}) \) 268 * q + 8 * q^2 + 43 * q^3 + 300 * q^4 + 18 * q^5 + 34 * q^6 + 59 * q^7 + 21 * q^8 + 295 * q^9 + 91 * q^10 + 49 * q^11 + 77 * q^12 + 45 * q^13 + 42 * q^14 + 37 * q^15 + 356 * q^16 + 40 * q^17 + 36 * q^18 + 245 * q^19 + 40 * q^20 + 66 * q^21 + 51 * q^22 + 26 * q^23 + 90 * q^24 + 314 * q^25 + 24 * q^26 + 160 * q^27 + 117 * q^28 + 54 * q^29 + 25 * q^30 + 181 * q^31 + 35 * q^32 + 49 * q^33 + 84 * q^34 + 73 * q^35 + 348 * q^36 + 77 * q^37 + 20 * q^38 + 96 * q^39 + 257 * q^40 + 62 * q^41 + 22 * q^42 + 199 * q^43 + 59 * q^44 + 60 * q^45 + 116 * q^46 + 41 * q^47 + 106 * q^48 + 381 * q^49 + 21 * q^50 + 248 * q^51 + 101 * q^52 + 4 * q^53 + 98 * q^54 + 136 * q^55 + 79 * q^56 + 47 * q^57 + 14 * q^58 + 170 * q^59 + 31 * q^60 + 247 * q^61 + 17 * q^62 + 143 * q^63 + 437 * q^64 + 29 * q^65 + 38 * q^66 + 114 * q^67 + 62 * q^68 + 101 * q^69 + 48 * q^70 + 64 * q^71 + 54 * q^72 + 115 * q^73 + 22 * q^74 + 250 * q^75 + 448 * q^76 + 8 * q^77 - 50 * q^78 + 271 * q^79 + 39 * q^80 + 336 * q^81 + 132 * q^82 + 74 * q^83 + 122 * q^84 + 58 * q^85 + 27 * q^86 + 105 * q^87 + 127 * q^88 + 63 * q^89 + 179 * q^90 + 406 * q^91 + 13 * q^92 + q^93 + 263 * q^94 + 76 * q^95 + 161 * q^96 + 123 * q^97 - 7 * q^98 + 180 * q^99

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