LMFDB - Embedded newform 6029.2.a.a.1.13

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:	$1$
Dimension:	$234$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q-2.56265 q^{2} +1.36912 q^{3} +4.56717 q^{4} +2.03853 q^{5} -3.50857 q^{6} -0.777924 q^{7} -6.57875 q^{8} -1.12552 q^{9} +O(q^{10})$	\(q-2.56265 q^{2} +1.36912 q^{3} +4.56717 q^{4} +2.03853 q^{5} -3.50857 q^{6} -0.777924 q^{7} -6.57875 q^{8} -1.12552 q^{9} -5.22404 q^{10} -0.297037 q^{11} +6.25299 q^{12} +1.93278 q^{13} +1.99355 q^{14} +2.79099 q^{15} +7.72468 q^{16} -6.33169 q^{17} +2.88430 q^{18} +0.351257 q^{19} +9.31031 q^{20} -1.06507 q^{21} +0.761201 q^{22} +5.59820 q^{23} -9.00708 q^{24} -0.844396 q^{25} -4.95304 q^{26} -5.64832 q^{27} -3.55291 q^{28} +2.29728 q^{29} -7.15232 q^{30} +0.765413 q^{31} -6.63815 q^{32} -0.406678 q^{33} +16.2259 q^{34} -1.58582 q^{35} -5.14042 q^{36} -1.44876 q^{37} -0.900148 q^{38} +2.64620 q^{39} -13.4110 q^{40} -6.35448 q^{41} +2.72940 q^{42} -2.37300 q^{43} -1.35662 q^{44} -2.29440 q^{45} -14.3462 q^{46} -0.966087 q^{47} +10.5760 q^{48} -6.39483 q^{49} +2.16389 q^{50} -8.66883 q^{51} +8.82733 q^{52} +5.66352 q^{53} +14.4747 q^{54} -0.605518 q^{55} +5.11776 q^{56} +0.480912 q^{57} -5.88713 q^{58} +10.4690 q^{59} +12.7469 q^{60} -8.48678 q^{61} -1.96149 q^{62} +0.875565 q^{63} +1.56189 q^{64} +3.94003 q^{65} +1.04217 q^{66} +5.65108 q^{67} -28.9179 q^{68} +7.66460 q^{69} +4.06390 q^{70} +8.76208 q^{71} +7.40448 q^{72} -13.5513 q^{73} +3.71266 q^{74} -1.15608 q^{75} +1.60425 q^{76} +0.231072 q^{77} -6.78129 q^{78} +13.8112 q^{79} +15.7470 q^{80} -4.35667 q^{81} +16.2843 q^{82} -2.67248 q^{83} -4.86435 q^{84} -12.9073 q^{85} +6.08117 q^{86} +3.14525 q^{87} +1.95413 q^{88} -9.51972 q^{89} +5.87973 q^{90} -1.50356 q^{91} +25.5679 q^{92} +1.04794 q^{93} +2.47574 q^{94} +0.716048 q^{95} -9.08842 q^{96} +9.97900 q^{97} +16.3877 q^{98} +0.334320 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9}+O(q^{10}) $ 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9	\( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9} - 89 q^{10} - 55 q^{11} - 75 q^{12} - 49 q^{13} - 42 q^{14} - 43 q^{15} + 142 q^{16} - 40 q^{17} - 30 q^{18} - 235 q^{19} - 62 q^{20} - 62 q^{21} - 63 q^{22} - 30 q^{23} - 108 q^{24} + 170 q^{25} - 44 q^{26} - 160 q^{27} - 147 q^{28} - 76 q^{29} - 15 q^{30} - 175 q^{31} - 49 q^{32} - 43 q^{33} - 104 q^{34} - 87 q^{35} + 124 q^{36} - 77 q^{37} - 18 q^{38} - 104 q^{39} - 247 q^{40} - 60 q^{41} - 6 q^{42} - 201 q^{43} - 89 q^{44} - 102 q^{45} - 128 q^{46} - 27 q^{47} - 130 q^{48} + 123 q^{49} - 33 q^{50} - 220 q^{51} - 125 q^{52} - 34 q^{53} - 126 q^{54} - 176 q^{55} - 125 q^{56} - 17 q^{57} - 46 q^{58} - 172 q^{59} - 61 q^{60} - 243 q^{61} - 37 q^{62} - 137 q^{63} + 39 q^{64} - 31 q^{65} - 142 q^{66} - 132 q^{67} - 106 q^{68} - 115 q^{69} - 60 q^{70} - 68 q^{71} - 66 q^{72} - 109 q^{73} - 74 q^{74} - 256 q^{75} - 412 q^{76} - 32 q^{77} - 38 q^{78} - 297 q^{79} - 111 q^{80} + 142 q^{81} - 94 q^{82} - 100 q^{83} - 134 q^{84} - 90 q^{85} + q^{86} - 103 q^{87} - 143 q^{88} - 77 q^{89} - 181 q^{90} - 418 q^{91} - 19 q^{92} + 5 q^{93} - 231 q^{94} - 92 q^{95} - 189 q^{96} - 141 q^{97} - 25 q^{98} - 244 q^{99}+O(q^{100}) \) 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9 - 89 * q^10 - 55 * q^11 - 75 * q^12 - 49 * q^13 - 42 * q^14 - 43 * q^15 + 142 * q^16 - 40 * q^17 - 30 * q^18 - 235 * q^19 - 62 * q^20 - 62 * q^21 - 63 * q^22 - 30 * q^23 - 108 * q^24 + 170 * q^25 - 44 * q^26 - 160 * q^27 - 147 * q^28 - 76 * q^29 - 15 * q^30 - 175 * q^31 - 49 * q^32 - 43 * q^33 - 104 * q^34 - 87 * q^35 + 124 * q^36 - 77 * q^37 - 18 * q^38 - 104 * q^39 - 247 * q^40 - 60 * q^41 - 6 * q^42 - 201 * q^43 - 89 * q^44 - 102 * q^45 - 128 * q^46 - 27 * q^47 - 130 * q^48 + 123 * q^49 - 33 * q^50 - 220 * q^51 - 125 * q^52 - 34 * q^53 - 126 * q^54 - 176 * q^55 - 125 * q^56 - 17 * q^57 - 46 * q^58 - 172 * q^59 - 61 * q^60 - 243 * q^61 - 37 * q^62 - 137 * q^63 + 39 * q^64 - 31 * q^65 - 142 * q^66 - 132 * q^67 - 106 * q^68 - 115 * q^69 - 60 * q^70 - 68 * q^71 - 66 * q^72 - 109 * q^73 - 74 * q^74 - 256 * q^75 - 412 * q^76 - 32 * q^77 - 38 * q^78 - 297 * q^79 - 111 * q^80 + 142 * q^81 - 94 * q^82 - 100 * q^83 - 134 * q^84 - 90 * q^85 + q^86 - 103 * q^87 - 143 * q^88 - 77 * q^89 - 181 * q^90 - 418 * q^91 - 19 * q^92 + 5 * q^93 - 231 * q^94 - 92 * q^95 - 189 * q^96 - 141 * q^97 - 25 * q^98 - 244 * 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 $

$2$	−2.56265	−1.81207	−0.906033	−	0.423207i	$-0.860904\pi$
$2$	−2.56265	−1.81207	−0.906033	+	0.423207i	$0.860904\pi$
$3$	1.36912	0.790461	0.395230	−	0.918582i	$-0.370665\pi$
$3$	1.36912	0.790461	0.395230	+	0.918582i	$0.370665\pi$
$4$	4.56717	2.28358
$5$	2.03853	0.911658	0.455829	−	0.890067i	$-0.349343\pi$
$5$	2.03853	0.911658	0.455829	+	0.890067i	$0.349343\pi$
$6$	−3.50857	−1.43237
$7$	−0.777924	−0.294028	−0.147014	−	0.989134i	$-0.546966\pi$
$7$	−0.777924	−0.294028	−0.147014	+	0.989134i	$0.546966\pi$
$8$	−6.57875	−2.32594
$9$	−1.12552	−0.375172
$10$	−5.22404	−1.65199
$11$	−0.297037	−0.0895600	−0.0447800	−	0.998997i	$-0.514259\pi$
$11$	−0.297037	−0.0895600	−0.0447800	+	0.998997i	$0.514259\pi$
$12$	6.25299	1.80508
$13$	1.93278	0.536057	0.268028	−	0.963411i	$-0.413628\pi$
$13$	1.93278	0.536057	0.268028	+	0.963411i	$0.413628\pi$
$14$	1.99355	0.532797
$15$	2.79099	0.720630
$16$	7.72468	1.93117
$17$	−6.33169	−1.53566	−0.767830	−	0.640653i	$-0.778664\pi$
$17$	−6.33169	−1.53566	−0.767830	+	0.640653i	$0.778664\pi$
$18$	2.88430	0.679836
$19$	0.351257	0.0805839	0.0402920	−	0.999188i	$-0.487171\pi$
$19$	0.351257	0.0805839	0.0402920	+	0.999188i	$0.487171\pi$
$20$	9.31031	2.08185
$21$	−1.06507	−0.232417
$22$	0.761201	0.162289
$23$	5.59820	1.16731	0.583653	−	0.812003i	$-0.301623\pi$
$23$	5.59820	1.16731	0.583653	+	0.812003i	$0.301623\pi$
$24$	−9.00708	−1.83856
$25$	−0.844396	−0.168879
$26$	−4.95304	−0.971370
$27$	−5.64832	−1.08702
$28$	−3.55291	−0.671437
$29$	2.29728	0.426595	0.213297	−	0.976987i	$-0.431580\pi$
$29$	2.29728	0.426595	0.213297	+	0.976987i	$0.431580\pi$
$30$	−7.15232	−1.30583
$31$	0.765413	0.137472	0.0687361	−	0.997635i	$-0.478103\pi$
$31$	0.765413	0.137472	0.0687361	+	0.997635i	$0.478103\pi$
$32$	−6.63815	−1.17347
$33$	−0.406678	−0.0707936
$34$	16.2259	2.78272
$35$	−1.58582	−0.268053
$36$	−5.14042	−0.856736
$37$	−1.44876	−0.238175	−0.119087	−	0.992884i	$-0.537997\pi$
$37$	−1.44876	−0.238175	−0.119087	+	0.992884i	$0.537997\pi$
$38$	−0.900148	−0.146023
$39$	2.64620	0.423732
$40$	−13.4110	−2.12046
$41$	−6.35448	−0.992404	−0.496202	−	0.868207i	$-0.665272\pi$
$41$	−6.35448	−0.992404	−0.496202	+	0.868207i	$0.665272\pi$
$42$	2.72940	0.421155
$43$	−2.37300	−0.361879	−0.180940	−	0.983494i	$-0.557914\pi$
$43$	−2.37300	−0.361879	−0.180940	+	0.983494i	$0.557914\pi$
$44$	−1.35662	−0.204518
$45$	−2.29440	−0.342029
$46$	−14.3462	−2.11524
$47$	−0.966087	−0.140918	−0.0704592	−	0.997515i	$-0.522446\pi$
$47$	−0.966087	−0.140918	−0.0704592	+	0.997515i	$0.522446\pi$
$48$	10.5760	1.52651
$49$	−6.39483	−0.913548
$50$	2.16389	0.306020
$51$	−8.66883	−1.21388
$52$	8.82733	1.22413
$53$	5.66352	0.777945	0.388972	−	0.921249i	$-0.372830\pi$
$53$	5.66352	0.777945	0.388972	+	0.921249i	$0.372830\pi$
$54$	14.4747	1.96975
$55$	−0.605518	−0.0816481
$56$	5.11776	0.683890
$57$	0.480912	0.0636984
$58$	−5.88713	−0.773018
$59$	10.4690	1.36294	0.681471	−	0.731845i	$-0.261340\pi$
$59$	10.4690	1.36294	0.681471	+	0.731845i	$0.261340\pi$
$60$	12.7469	1.64562
$61$	−8.48678	−1.08662	−0.543310	−	0.839532i	$-0.682829\pi$
$61$	−8.48678	−1.08662	−0.543310	+	0.839532i	$0.682829\pi$
$62$	−1.96149	−0.249109
$63$	0.875565	0.110311
$64$	1.56189	0.195236
$65$	3.94003	0.488701
$66$	1.04217	0.128283
$67$	5.65108	0.690390	0.345195	−	0.938531i	$-0.387813\pi$
$67$	5.65108	0.690390	0.345195	+	0.938531i	$0.387813\pi$
$68$	−28.9179	−3.50681
$69$	7.66460	0.922710
$70$	4.06390	0.485729
$71$	8.76208	1.03987	0.519934	−	0.854206i	$-0.325957\pi$
$71$	8.76208	1.03987	0.519934	+	0.854206i	$0.325957\pi$
$72$	7.40448	0.872627
$73$	−13.5513	−1.58605	−0.793027	−	0.609186i	$-0.791496\pi$
$73$	−13.5513	−1.58605	−0.793027	+	0.609186i	$0.791496\pi$
$74$	3.71266	0.431588
$75$	−1.15608	−0.133492
$76$	1.60425	0.184020
$77$	0.231072	0.0263331
$78$	−6.78129	−0.767830
$79$	13.8112	1.55388	0.776938	−	0.629577i	$-0.216772\pi$
$79$	13.8112	1.55388	0.776938	+	0.629577i	$0.216772\pi$
$80$	15.7470	1.76057
$81$	−4.35667	−0.484074
$82$	16.2843	1.79830
$83$	−2.67248	−0.293343	−0.146672	−	0.989185i	$-0.546856\pi$
$83$	−2.67248	−0.293343	−0.146672	+	0.989185i	$0.546856\pi$
$84$	−4.86435	−0.530744
$85$	−12.9073	−1.40000
$86$	6.08117	0.655749
$87$	3.14525	0.337206
$88$	1.95413	0.208311
$89$	−9.51972	−1.00909	−0.504544	−	0.863386i	$-0.668339\pi$
$89$	−9.51972	−1.00909	−0.504544	+	0.863386i	$0.668339\pi$
$90$	5.87973	0.619778
$91$	−1.50356	−0.157615
$92$	25.5679	2.66564
$93$	1.04794	0.108666
$94$	2.47574	0.255353
$95$	0.716048	0.0734650
$96$	−9.08842	−0.927583
$97$	9.97900	1.01321	0.506607	−	0.862177i	$-0.330899\pi$
$97$	9.97900	1.01321	0.506607	+	0.862177i	$0.330899\pi$
$98$	16.3877	1.65541
$99$	0.334320	0.0336004
$100$	−3.85650	−0.385650
$101$	−13.9209	−1.38518	−0.692592	−	0.721330i	$-0.743531\pi$
$101$	−13.9209	−1.38518	−0.692592	+	0.721330i	$0.743531\pi$
$102$	22.2152	2.19963
$103$	−1.18065	−0.116333	−0.0581667	−	0.998307i	$-0.518525\pi$
$103$	−1.18065	−0.116333	−0.0581667	+	0.998307i	$0.518525\pi$
$104$	−12.7153	−1.24684
$105$	−2.17118	−0.211885
$106$	−14.5136	−1.40969
$107$	6.34452	0.613348	0.306674	−	0.951815i	$-0.400784\pi$
$107$	6.34452	0.613348	0.306674	+	0.951815i	$0.400784\pi$
$108$	−25.7968	−2.48230
$109$	−13.0703	−1.25190	−0.625952	−	0.779862i	$-0.715289\pi$
$109$	−13.0703	−1.25190	−0.625952	+	0.779862i	$0.715289\pi$
$110$	1.55173	0.147952
$111$	−1.98352	−0.188268
$112$	−6.00922	−0.567817
$113$	11.3442	1.06717	0.533587	−	0.845745i	$-0.320844\pi$
$113$	11.3442	1.06717	0.533587	+	0.845745i	$0.320844\pi$
$114$	−1.23241	−0.115426
$115$	11.4121	1.06418
$116$	10.4921	0.974164
$117$	−2.17537	−0.201113
$118$	−26.8283	−2.46974
$119$	4.92557	0.451527
$120$	−18.3612	−1.67614
$121$	−10.9118	−0.991979
$122$	21.7486	1.96903
$123$	−8.70004	−0.784456
$124$	3.49577	0.313929
$125$	−11.9140	−1.06562
$126$	−2.24377	−0.199891
$127$	−9.31073	−0.826194	−0.413097	−	0.910687i	$-0.635553\pi$
$127$	−9.31073	−0.826194	−0.413097	+	0.910687i	$0.635553\pi$
$128$	9.27374	0.819690
$129$	−3.24892	−0.286051
$130$	−10.0969	−0.885558
$131$	10.3557	0.904778	0.452389	−	0.891821i	$-0.350572\pi$
$131$	10.3557	0.904778	0.452389	+	0.891821i	$0.350572\pi$
$132$	−1.85737	−0.161663
$133$	−0.273251	−0.0236939
$134$	−14.4817	−1.25103
$135$	−11.5143	−0.990990
$136$	41.6546	3.57185
$137$	−18.0759	−1.54433	−0.772164	−	0.635423i	$-0.780826\pi$
$137$	−18.0759	−1.54433	−0.772164	+	0.635423i	$0.780826\pi$
$138$	−19.6417	−1.67201
$139$	9.28727	0.787736	0.393868	−	0.919167i	$-0.371137\pi$
$139$	9.28727	0.787736	0.393868	+	0.919167i	$0.371137\pi$
$140$	−7.24271	−0.612121
$141$	−1.32269	−0.111390
$142$	−22.4541	−1.88431
$143$	−0.574107	−0.0480092
$144$	−8.69425	−0.724521
$145$	4.68308	0.388908
$146$	34.7271	2.87404
$147$	−8.75528	−0.722124
$148$	−6.61673	−0.543891
$149$	5.74437	0.470598	0.235299	−	0.971923i	$-0.424393\pi$
$149$	5.74437	0.470598	0.235299	+	0.971923i	$0.424393\pi$
$150$	2.96262	0.241897
$151$	−23.8516	−1.94102	−0.970508	−	0.241070i	$-0.922502\pi$
$151$	−23.8516	−1.94102	−0.970508	+	0.241070i	$0.922502\pi$
$152$	−2.31083	−0.187433
$153$	7.12642	0.576137
$154$	−0.592156	−0.0477173
$155$	1.56032	0.125328
$156$	12.0857	0.967627
$157$	17.7182	1.41406	0.707032	−	0.707181i	$-0.250034\pi$
$157$	17.7182	1.41406	0.707032	+	0.707181i	$0.250034\pi$
$158$	−35.3931	−2.81573
$159$	7.75403	0.614935
$160$	−13.5321	−1.06980
$161$	−4.35497	−0.343220
$162$	11.1646	0.877174
$163$	−24.1431	−1.89104	−0.945518	−	0.325569i	$-0.894444\pi$
$163$	−24.1431	−1.89104	−0.945518	+	0.325569i	$0.894444\pi$
$164$	−29.0220	−2.26624
$165$	−0.829026	−0.0645396
$166$	6.84864	0.531557
$167$	−4.02783	−0.311683	−0.155842	−	0.987782i	$-0.549809\pi$
$167$	−4.02783	−0.311683	−0.155842	+	0.987782i	$0.549809\pi$
$168$	7.00682	0.540588
$169$	−9.26436	−0.712643
$170$	33.0770	2.53689
$171$	−0.395345	−0.0302328
$172$	−10.8379	−0.826382
$173$	−9.62218	−0.731561	−0.365781	−	0.930701i	$-0.619198\pi$
$173$	−9.62218	−0.731561	−0.365781	+	0.930701i	$0.619198\pi$
$174$	−8.06017	−0.611040
$175$	0.656876	0.0496551
$176$	−2.29452	−0.172956
$177$	14.3332	1.07735
$178$	24.3957	1.82853
$179$	−22.6038	−1.68949	−0.844745	−	0.535170i	$-0.820248\pi$
$179$	−22.6038	−1.68949	−0.844745	+	0.535170i	$0.820248\pi$
$180$	−10.4789	−0.781051
$181$	−2.72804	−0.202773	−0.101387	−	0.994847i	$-0.532328\pi$
$181$	−2.72804	−0.202773	−0.101387	+	0.994847i	$0.532328\pi$
$182$	3.85308	0.285610
$183$	−11.6194	−0.858931
$184$	−36.8292	−2.71508
$185$	−2.95334	−0.217134
$186$	−2.68551	−0.196911
$187$	1.88074	0.137534
$188$	−4.41228	−0.321799
$189$	4.39396	0.319614
$190$	−1.83498	−0.133123
$191$	−1.84102	−0.133211	−0.0666057	−	0.997779i	$-0.521217\pi$
$191$	−1.84102	−0.133211	−0.0666057	+	0.997779i	$0.521217\pi$
$192$	2.13841	0.154326
$193$	−8.31896	−0.598812	−0.299406	−	0.954126i	$-0.596789\pi$
$193$	−8.31896	−0.598812	−0.299406	+	0.954126i	$0.596789\pi$
$194$	−25.5727	−1.83601
$195$	5.39437	0.386299
$196$	−29.2063	−2.08616
$197$	−12.2150	−0.870282	−0.435141	−	0.900362i	$-0.643302\pi$
$197$	−12.2150	−0.870282	−0.435141	+	0.900362i	$0.643302\pi$
$198$	−0.856743	−0.0608861
$199$	−21.9905	−1.55887	−0.779434	−	0.626485i	$-0.784493\pi$
$199$	−21.9905	−1.55887	−0.779434	+	0.626485i	$0.784493\pi$
$200$	5.55507	0.392803
$201$	7.73700	0.545726
$202$	35.6744	2.51004
$203$	−1.78711	−0.125431
$204$	−39.5920	−2.77200
$205$	−12.9538	−0.904733
$206$	3.02560	0.210804
$207$	−6.30086	−0.437940
$208$	14.9301	1.03522
$209$	−0.104336	−0.00721709
$210$	5.56396	0.383950
$211$	−0.927057	−0.0638212	−0.0319106	−	0.999491i	$-0.510159\pi$
$211$	−0.927057	−0.0638212	−0.0319106	+	0.999491i	$0.510159\pi$
$212$	25.8663	1.77650
$213$	11.9963	0.821975
$214$	−16.2588	−1.11143
$215$	−4.83743	−0.329910
$216$	37.1589	2.52834
$217$	−0.595433	−0.0404206
$218$	33.4945	2.26853
$219$	−18.5533	−1.25371
$220$	−2.76550	−0.186450
$221$	−12.2378	−0.823201
$222$	5.08307	0.341153
$223$	−5.95890	−0.399038	−0.199519	−	0.979894i	$-0.563938\pi$
$223$	−5.95890	−0.399038	−0.199519	+	0.979894i	$0.563938\pi$
$224$	5.16398	0.345033
$225$	0.950381	0.0633587
$226$	−29.0712	−1.93379
$227$	−0.0304621	−0.00202184	−0.00101092	−	0.999999i	$-0.500322\pi$
$227$	−0.0304621	−0.00202184	−0.00101092	+	0.999999i	$0.500322\pi$
$228$	2.19641	0.145461
$229$	2.18312	0.144264	0.0721322	−	0.997395i	$-0.477020\pi$
$229$	2.18312	0.144264	0.0721322	+	0.997395i	$0.477020\pi$
$230$	−29.2452	−1.92837
$231$	0.316365	0.0208153
$232$	−15.1132	−0.992233
$233$	−6.56680	−0.430205	−0.215103	−	0.976591i	$-0.569009\pi$
$233$	−6.56680	−0.430205	−0.215103	+	0.976591i	$0.569009\pi$
$234$	5.57472	0.364431
$235$	−1.96940	−0.128469
$236$	47.8135	3.11239
$237$	18.9091	1.22828
$238$	−12.6225	−0.818196
$239$	−10.7107	−0.692818	−0.346409	−	0.938084i	$-0.612599\pi$
$239$	−10.7107	−0.692818	−0.346409	+	0.938084i	$0.612599\pi$
$240$	21.5595	1.39166
$241$	21.2608	1.36953	0.684765	−	0.728764i	$-0.259905\pi$
$241$	21.2608	1.36953	0.684765	+	0.728764i	$0.259905\pi$
$242$	27.9630	1.79753
$243$	10.9802	0.704378
$244$	−38.7605	−2.48139
$245$	−13.0361	−0.832843
$246$	22.2951	1.42149
$247$	0.678903	0.0431975
$248$	−5.03546	−0.319752
$249$	−3.65895	−0.231876
$250$	30.5313	1.93097
$251$	6.40148	0.404058	0.202029	−	0.979380i	$-0.435247\pi$
$251$	6.40148	0.404058	0.202029	+	0.979380i	$0.435247\pi$
$252$	3.99885	0.251904
$253$	−1.66287	−0.104544
$254$	23.8601	1.49712
$255$	−17.6717	−1.10664
$256$	−26.8891	−1.68057
$257$	29.0302	1.81086	0.905428	−	0.424500i	$-0.139550\pi$
$257$	29.0302	1.81086	0.905428	+	0.424500i	$0.139550\pi$
$258$	8.32584	0.518344
$259$	1.12702	0.0700299
$260$	17.9948	1.11599
$261$	−2.58563	−0.160046
$262$	−26.5379	−1.63952
$263$	−5.42119	−0.334285	−0.167143	−	0.985933i	$-0.553454\pi$
$263$	−5.42119	−0.334285	−0.167143	+	0.985933i	$0.553454\pi$
$264$	2.67543	0.164662
$265$	11.5453	0.709220
$266$	0.700247	0.0429349
$267$	−13.0336	−0.797645
$268$	25.8094	1.57656
$269$	−13.7910	−0.840851	−0.420425	−	0.907327i	$-0.638119\pi$
$269$	−13.7910	−0.840851	−0.420425	+	0.907327i	$0.638119\pi$
$270$	29.5070	1.79574
$271$	−24.7998	−1.50648	−0.753239	−	0.657747i	$-0.771510\pi$
$271$	−24.7998	−1.50648	−0.753239	+	0.657747i	$0.771510\pi$
$272$	−48.9103	−2.96562
$273$	−2.05854	−0.124589
$274$	46.3222	2.79842
$275$	0.250817	0.0151248
$276$	35.0055	2.10708
$277$	−19.4627	−1.16940	−0.584699	−	0.811250i	$-0.698787\pi$
$277$	−19.4627	−1.16940	−0.584699	+	0.811250i	$0.698787\pi$
$278$	−23.8000	−1.42743
$279$	−0.861485	−0.0515757
$280$	10.4327	0.623474
$281$	12.1253	0.723332	0.361666	−	0.932308i	$-0.382208\pi$
$281$	12.1253	0.723332	0.361666	+	0.932308i	$0.382208\pi$
$282$	3.38958	0.201847
$283$	−2.49606	−0.148376	−0.0741878	−	0.997244i	$-0.523636\pi$
$283$	−2.49606	−0.148376	−0.0741878	+	0.997244i	$0.523636\pi$
$284$	40.0179	2.37463
$285$	0.980354	0.0580712
$286$	1.47123	0.0869959
$287$	4.94330	0.291794
$288$	7.47135	0.440253
$289$	23.0903	1.35825
$290$	−12.0011	−0.704728
$291$	13.6624	0.800906
$292$	−61.8909	−3.62189
$293$	−23.2755	−1.35977	−0.679885	−	0.733318i	$-0.737970\pi$
$293$	−23.2755	−1.35977	−0.679885	+	0.733318i	$0.737970\pi$
$294$	22.4367	1.30854
$295$	21.3413	1.24254
$296$	9.53102	0.553979
$297$	1.67776	0.0973534
$298$	−14.7208	−0.852754
$299$	10.8201	0.625742
$300$	−5.28000	−0.304841
$301$	1.84601	0.106402
$302$	61.1233	3.51725
$303$	−19.0594	−1.09493
$304$	2.71335	0.155621
$305$	−17.3006	−0.990627
$306$	−18.2625	−1.04400
$307$	21.5105	1.22767	0.613835	−	0.789435i	$-0.289626\pi$
$307$	21.5105	1.22767	0.613835	+	0.789435i	$0.289626\pi$
$308$	1.05534	0.0601338
$309$	−1.61645	−0.0919569
$310$	−3.99855	−0.227102
$311$	−10.8566	−0.615623	−0.307811	−	0.951447i	$-0.599597\pi$
$311$	−10.8566	−0.615623	−0.307811	+	0.951447i	$0.599597\pi$
$312$	−17.4087	−0.985574
$313$	−4.87300	−0.275438	−0.137719	−	0.990471i	$-0.543977\pi$
$313$	−4.87300	−0.275438	−0.137719	+	0.990471i	$0.543977\pi$
$314$	−45.4055	−2.56238
$315$	1.78487	0.100566
$316$	63.0779	3.54841
$317$	13.0380	0.732288	0.366144	−	0.930558i	$-0.380678\pi$
$317$	13.0380	0.732288	0.366144	+	0.930558i	$0.380678\pi$
$318$	−19.8709	−1.11430
$319$	−0.682377	−0.0382058
$320$	3.18396	0.177989
$321$	8.68639	0.484827
$322$	11.1603	0.621938
$323$	−2.22405	−0.123750
$324$	−19.8976	−1.10542
$325$	−1.63203	−0.0905288
$326$	61.8704	3.42668
$327$	−17.8947	−0.989580
$328$	41.8046	2.30827
$329$	0.751542	0.0414339
$330$	2.12450	0.116950
$331$	4.90424	0.269561	0.134781	−	0.990875i	$-0.456967\pi$
$331$	4.90424	0.269561	0.134781	+	0.990875i	$0.456967\pi$
$332$	−12.2057	−0.669874
$333$	1.63060	0.0893564
$334$	10.3219	0.564791
$335$	11.5199	0.629399
$336$	−8.22733	−0.448837
$337$	5.63218	0.306804	0.153402	−	0.988164i	$-0.450977\pi$
$337$	5.63218	0.306804	0.153402	+	0.988164i	$0.450977\pi$
$338$	23.7413	1.29136
$339$	15.5316	0.843558
$340$	−58.9500	−3.19701
$341$	−0.227356	−0.0123120
$342$	1.01313	0.0547839
$343$	10.4202	0.562636
$344$	15.6114	0.841709
$345$	15.6245	0.841196
$346$	24.6583	1.32564
$347$	22.8541	1.22687	0.613437	−	0.789744i	$-0.289787\pi$
$347$	22.8541	1.22687	0.613437	+	0.789744i	$0.289787\pi$
$348$	14.3649	0.770039
$349$	−31.5557	−1.68914	−0.844569	−	0.535447i	$-0.820143\pi$
$349$	−31.5557	−1.68914	−0.844569	+	0.535447i	$0.820143\pi$
$350$	−1.68334	−0.0899784
$351$	−10.9170	−0.582704
$352$	1.97178	0.105096
$353$	32.7284	1.74196	0.870980	−	0.491319i	$-0.163485\pi$
$353$	32.7284	1.74196	0.870980	+	0.491319i	$0.163485\pi$
$354$	−36.7311	−1.95223
$355$	17.8618	0.948004
$356$	−43.4782	−2.30434
$357$	6.74369	0.356914
$358$	57.9257	3.06147
$359$	−15.5431	−0.820331	−0.410165	−	0.912011i	$-0.634529\pi$
$359$	−15.5431	−0.820331	−0.410165	+	0.912011i	$0.634529\pi$
$360$	15.0943	0.795537
$361$	−18.8766	−0.993506
$362$	6.99100	0.367439
$363$	−14.9395	−0.784120
$364$	−6.86699	−0.359928
$365$	−27.6246	−1.44594
$366$	29.7764	1.55644
$367$	−26.8430	−1.40119	−0.700595	−	0.713559i	$-0.747082\pi$
$367$	−26.8430	−1.40119	−0.700595	+	0.713559i	$0.747082\pi$
$368$	43.2443	2.25427
$369$	7.15207	0.372322
$370$	7.56837	0.393461
$371$	−4.40579	−0.228737
$372$	4.78612	0.248149
$373$	27.7419	1.43642	0.718211	−	0.695825i	$-0.244961\pi$
$373$	27.7419	1.43642	0.718211	+	0.695825i	$0.244961\pi$
$374$	−4.81969	−0.249220
$375$	−16.3116	−0.842329
$376$	6.35564	0.327767
$377$	4.44014	0.228679
$378$	−11.2602	−0.579161
$379$	34.0919	1.75118	0.875592	−	0.483051i	$-0.160471\pi$
$379$	34.0919	1.75118	0.875592	+	0.483051i	$0.160471\pi$
$380$	3.27031	0.167763
$381$	−12.7475	−0.653074
$382$	4.71788	0.241388
$383$	−9.52646	−0.486780	−0.243390	−	0.969929i	$-0.578259\pi$
$383$	−9.52646	−0.486780	−0.243390	+	0.969929i	$0.578259\pi$
$384$	12.6968	0.647933
$385$	0.471047	0.0240068
$386$	21.3186	1.08509
$387$	2.67085	0.135767
$388$	45.5758	2.31376
$389$	24.2135	1.22768	0.613838	−	0.789432i	$-0.289625\pi$
$389$	24.2135	1.22768	0.613838	+	0.789432i	$0.289625\pi$
$390$	−13.8239	−0.699999
$391$	−35.4461	−1.79259
$392$	42.0700	2.12486
$393$	14.1781	0.715191
$394$	31.3027	1.57701
$395$	28.1545	1.41660
$396$	1.52689	0.0767293
$397$	−5.64425	−0.283277	−0.141638	−	0.989918i	$-0.545237\pi$
$397$	−5.64425	−0.283277	−0.141638	+	0.989918i	$0.545237\pi$
$398$	56.3540	2.82477
$399$	−0.374113	−0.0187291
$400$	−6.52269	−0.326135
$401$	16.1754	0.807763	0.403881	−	0.914811i	$-0.367661\pi$
$401$	16.1754	0.807763	0.403881	+	0.914811i	$0.367661\pi$
$402$	−19.8272	−0.988891
$403$	1.47938	0.0736929
$404$	−63.5792	−3.16318
$405$	−8.88120	−0.441310
$406$	4.57974	0.227288
$407$	0.430335	0.0213309
$408$	57.0301	2.82341
$409$	30.1008	1.48839	0.744195	−	0.667962i	$-0.232833\pi$
$409$	30.1008	1.48839	0.744195	+	0.667962i	$0.232833\pi$
$410$	33.1961	1.63944
$411$	−24.7480	−1.22073
$412$	−5.39225	−0.265657
$413$	−8.14405	−0.400743
$414$	16.1469	0.793577
$415$	−5.44794	−0.267429
$416$	−12.8301	−0.629047
$417$	12.7154	0.622675
$418$	0.267377	0.0130778
$419$	20.5320	1.00305	0.501527	−	0.865142i	$-0.332772\pi$
$419$	20.5320	1.00305	0.501527	+	0.865142i	$0.332772\pi$
$420$	−9.91612	−0.483857
$421$	−10.8894	−0.530715	−0.265357	−	0.964150i	$-0.585490\pi$
$421$	−10.8894	−0.530715	−0.265357	+	0.964150i	$0.585490\pi$
$422$	2.37572	0.115648
$423$	1.08735	0.0528686
$424$	−37.2589	−1.80945
$425$	5.34646	0.259341
$426$	−30.7424	−1.48947
$427$	6.60207	0.319496
$428$	28.9765	1.40063
$429$	−0.786020	−0.0379494
$430$	12.3966	0.597819
$431$	24.9473	1.20167	0.600833	−	0.799374i	$-0.294835\pi$
$431$	24.9473	1.20167	0.600833	+	0.799374i	$0.294835\pi$
$432$	−43.6315	−2.09922
$433$	−25.1146	−1.20693	−0.603466	−	0.797389i	$-0.706214\pi$
$433$	−25.1146	−1.20693	−0.603466	+	0.797389i	$0.706214\pi$
$434$	1.52589	0.0732449
$435$	6.41169	0.307417
$436$	−59.6940	−2.85883
$437$	1.96641	0.0940661
$438$	47.5455	2.27181
$439$	24.3824	1.16371	0.581855	−	0.813293i	$-0.302327\pi$
$439$	24.3824	1.16371	0.581855	+	0.813293i	$0.302327\pi$
$440$	3.98355	0.189908
$441$	7.19749	0.342737
$442$	31.3611	1.49169
$443$	7.01874	0.333470	0.166735	−	0.986002i	$-0.446678\pi$
$443$	7.01874	0.333470	0.166735	+	0.986002i	$0.446678\pi$
$444$	−9.05908	−0.429925
$445$	−19.4062	−0.919944
$446$	15.2706	0.723083
$447$	7.86473	0.371989
$448$	−1.21503	−0.0574048
$449$	−19.3912	−0.915129	−0.457565	−	0.889176i	$-0.651278\pi$
$449$	−19.3912	−0.915129	−0.457565	+	0.889176i	$0.651278\pi$
$450$	−2.43549	−0.114810
$451$	1.88752	0.0888796
$452$	51.8109	2.43698
$453$	−32.6557	−1.53430
$454$	0.0780636	0.00366371
$455$	−3.06504	−0.143691
$456$	−3.16380	−0.148159
$457$	4.54128	0.212432	0.106216	−	0.994343i	$-0.466127\pi$
$457$	4.54128	0.212432	0.106216	+	0.994343i	$0.466127\pi$
$458$	−5.59456	−0.261417
$459$	35.7634	1.66929
$460$	52.1210	2.43015
$461$	−15.0497	−0.700935	−0.350468	−	0.936575i	$-0.613977\pi$
$461$	−15.0497	−0.700935	−0.350468	+	0.936575i	$0.613977\pi$
$462$	−0.810732	−0.0377187
$463$	7.48495	0.347855	0.173927	−	0.984758i	$-0.444354\pi$
$463$	7.48495	0.347855	0.173927	+	0.984758i	$0.444354\pi$
$464$	17.7458	0.823827
$465$	2.13626	0.0990667
$466$	16.8284	0.779560
$467$	−33.8238	−1.56518	−0.782589	−	0.622539i	$-0.786101\pi$
$467$	−33.8238	−1.56518	−0.782589	+	0.622539i	$0.786101\pi$
$468$	−9.93530	−0.459259
$469$	−4.39611	−0.202994
$470$	5.04687	0.232795
$471$	24.2583	1.11776
$472$	−68.8726	−3.17012
$473$	0.704869	0.0324099
$474$	−48.4574	−2.22572
$475$	−0.296600	−0.0136089
$476$	22.4959	1.03110
$477$	−6.37438	−0.291863
$478$	27.4478	1.25543
$479$	41.8492	1.91214	0.956070	−	0.293139i	$-0.0946998\pi$
$479$	41.8492	1.91214	0.956070	+	0.293139i	$0.0946998\pi$
$480$	−18.5270	−0.845638
$481$	−2.80013	−0.127675
$482$	−54.4840	−2.48168
$483$	−5.96248	−0.271302
$484$	−49.8359	−2.26527
$485$	20.3425	0.923705
$486$	−28.1383	−1.27638
$487$	−30.5560	−1.38462	−0.692312	−	0.721599i	$-0.743408\pi$
$487$	−30.5560	−1.38462	−0.692312	+	0.721599i	$0.743408\pi$
$488$	55.8324	2.52741
$489$	−33.0548	−1.49479
$490$	33.4068	1.50917
$491$	−13.5895	−0.613285	−0.306642	−	0.951825i	$-0.599206\pi$
$491$	−13.5895	−0.613285	−0.306642	+	0.951825i	$0.599206\pi$
$492$	−39.7345	−1.79137
$493$	−14.5457	−0.655104
$494$	−1.73979	−0.0782768
$495$	0.681520	0.0306321
$496$	5.91258	0.265483
$497$	−6.81623	−0.305750
$498$	9.37659	0.420175
$499$	−32.7234	−1.46490	−0.732450	−	0.680821i	$-0.761623\pi$
$499$	−32.7234	−1.46490	−0.732450	+	0.680821i	$0.761623\pi$
$500$	−54.4131	−2.43343
$501$	−5.51458	−0.246373
$502$	−16.4047	−0.732179
$503$	−20.1982	−0.900594	−0.450297	−	0.892879i	$-0.648682\pi$
$503$	−20.1982	−0.900594	−0.450297	+	0.892879i	$0.648682\pi$
$504$	−5.76012	−0.256576
$505$	−28.3782	−1.26281
$506$	4.26136	0.189440
$507$	−12.6840	−0.563316
$508$	−42.5237	−1.88668
$509$	−17.4507	−0.773488	−0.386744	−	0.922187i	$-0.626400\pi$
$509$	−17.4507	−0.773488	−0.386744	+	0.922187i	$0.626400\pi$
$510$	45.2863	2.00531
$511$	10.5418	0.466344
$512$	50.3599	2.22561
$513$	−1.98401	−0.0875963
$514$	−74.3943	−3.28139
$515$	−2.40680	−0.106056
$516$	−14.8384	−0.653222
$517$	0.286963	0.0126206
$518$	−2.88817	−0.126899
$519$	−13.1739	−0.578270
$520$	−25.9205	−1.13669
$521$	0.562284	0.0246341	0.0123171	−	0.999924i	$-0.496079\pi$
$521$	0.562284	0.0246341	0.0123171	+	0.999924i	$0.496079\pi$
$522$	6.62605	0.290014
$523$	−31.9713	−1.39801	−0.699004	−	0.715118i	$-0.746373\pi$
$523$	−31.9713	−1.39801	−0.699004	+	0.715118i	$0.746373\pi$
$524$	47.2960	2.06614
$525$	0.899341	0.0392504
$526$	13.8926	0.605747
$527$	−4.84636	−0.211111
$528$	−3.14146	−0.136715
$529$	8.33988	0.362603
$530$	−29.5864	−1.28515
$531$	−11.7830	−0.511338
$532$	−1.24798	−0.0541070
$533$	−12.2818	−0.531985
$534$	33.4006	1.44538
$535$	12.9335	0.559163
$536$	−37.1771	−1.60580
$537$	−30.9473	−1.33547
$538$	35.3414	1.52368
$539$	1.89950	0.0818173
$540$	−52.5876	−2.26301
$541$	−28.5704	−1.22834	−0.614168	−	0.789176i	$-0.710508\pi$
$541$	−28.5704	−1.22834	−0.614168	+	0.789176i	$0.710508\pi$
$542$	63.5530	2.72984
$543$	−3.73501	−0.160284
$544$	42.0307	1.80205
$545$	−26.6441	−1.14131
$546$	5.27533	0.225763
$547$	−0.266931	−0.0114131	−0.00570657	−	0.999984i	$-0.501816\pi$
$547$	−0.266931	−0.0114131	−0.00570657	+	0.999984i	$0.501816\pi$
$548$	−82.5557	−3.52660
$549$	9.55200	0.407670
$550$	−0.642755	−0.0274072
$551$	0.806937	0.0343767
$552$	−50.4235	−2.14617
$553$	−10.7440	−0.456883
$554$	49.8759	2.11903
$555$	−4.04347	−0.171636
$556$	42.4165	1.79886
$557$	43.0131	1.82252	0.911262	−	0.411827i	$-0.135109\pi$
$557$	43.0131	1.82252	0.911262	+	0.411827i	$0.135109\pi$
$558$	2.20768	0.0934586
$559$	−4.58649	−0.193988
$560$	−12.2500	−0.517655
$561$	2.57496	0.108715
$562$	−31.0728	−1.31073
$563$	−19.2540	−0.811458	−0.405729	−	0.913993i	$-0.632982\pi$
$563$	−19.2540	−0.811458	−0.405729	+	0.913993i	$0.632982\pi$
$564$	−6.04094	−0.254369
$565$	23.1255	0.972897
$566$	6.39654	0.268866
$567$	3.38916	0.142331
$568$	−57.6435	−2.41867
$569$	1.40943	0.0590863	0.0295431	−	0.999564i	$-0.490595\pi$
$569$	1.40943	0.0590863	0.0295431	+	0.999564i	$0.490595\pi$
$570$	−2.51230	−0.105229
$571$	4.59809	0.192424	0.0962121	−	0.995361i	$-0.469327\pi$
$571$	4.59809	0.192424	0.0962121	+	0.995361i	$0.469327\pi$
$572$	−2.62204	−0.109633
$573$	−2.52057	−0.105298
$574$	−12.6680	−0.528750
$575$	−4.72710	−0.197134
$576$	−1.75793	−0.0732471
$577$	−24.0753	−1.00227	−0.501133	−	0.865370i	$-0.667083\pi$
$577$	−24.0753	−1.00227	−0.501133	+	0.865370i	$0.667083\pi$
$578$	−59.1724	−2.46125
$579$	−11.3896	−0.473337
$580$	21.3884	0.888105
$581$	2.07899	0.0862510
$582$	−35.0120	−1.45129
$583$	−1.68227	−0.0696727
$584$	89.1503	3.68907
$585$	−4.43456	−0.183347
$586$	59.6470	2.46399
$587$	−5.38680	−0.222337	−0.111168	−	0.993802i	$-0.535459\pi$
$587$	−5.38680	−0.222337	−0.111168	+	0.993802i	$0.535459\pi$
$588$	−39.9868	−1.64903
$589$	0.268857	0.0110781
$590$	−54.6902	−2.25156
$591$	−16.7238	−0.687924
$592$	−11.1912	−0.459956
$593$	−2.00428	−0.0823057	−0.0411529	−	0.999153i	$-0.513103\pi$
$593$	−2.00428	−0.0823057	−0.0411529	+	0.999153i	$0.513103\pi$
$594$	−4.29950	−0.176411
$595$	10.0409	0.411638
$596$	26.2355	1.07465
$597$	−30.1076	−1.23222
$598$	−27.7281	−1.13389
$599$	−14.8533	−0.606889	−0.303445	−	0.952849i	$-0.598137\pi$
$599$	−14.8533	−0.606889	−0.303445	+	0.952849i	$0.598137\pi$
$600$	7.60555	0.310495
$601$	−35.4653	−1.44666	−0.723330	−	0.690503i	$-0.757389\pi$
$601$	−35.4653	−1.44666	−0.723330	+	0.690503i	$0.757389\pi$
$602$	−4.73068	−0.192808
$603$	−6.36038	−0.259015
$604$	−108.934	−4.43247
$605$	−22.2440	−0.904346
$606$	48.8425	1.98409
$607$	13.9084	0.564526	0.282263	−	0.959337i	$-0.408915\pi$
$607$	13.9084	0.564526	0.282263	+	0.959337i	$0.408915\pi$
$608$	−2.33170	−0.0945629
$609$	−2.44676	−0.0991479
$610$	44.3352	1.79508
$611$	−1.86723	−0.0755402
$612$	32.5475	1.31566
$613$	45.1039	1.82173	0.910866	−	0.412703i	$-0.135415\pi$
$613$	45.1039	1.82173	0.910866	+	0.412703i	$0.135415\pi$
$614$	−55.1239	−2.22462
$615$	−17.7353	−0.715156
$616$	−1.52016	−0.0612492
$617$	27.2118	1.09551	0.547753	−	0.836640i	$-0.315483\pi$
$617$	27.2118	1.09551	0.547753	+	0.836640i	$0.315483\pi$
$618$	4.14241	0.166632
$619$	−45.9643	−1.84746	−0.923731	−	0.383041i	$-0.874877\pi$
$619$	−45.9643	−1.84746	−0.923731	+	0.383041i	$0.874877\pi$
$620$	7.12623	0.286196
$621$	−31.6204	−1.26888
$622$	27.8217	1.11555
$623$	7.40562	0.296700
$624$	20.4411	0.818298
$625$	−20.0650	−0.802601
$626$	12.4878	0.499112
$627$	−0.142849	−0.00570483
$628$	80.9219	3.22913
$629$	9.17309	0.365755
$630$	−4.57398	−0.182232
$631$	18.1288	0.721695	0.360847	−	0.932625i	$-0.382488\pi$
$631$	18.1288	0.721695	0.360847	+	0.932625i	$0.382488\pi$
$632$	−90.8601	−3.61422
$633$	−1.26925	−0.0504482
$634$	−33.4118	−1.32695
$635$	−18.9802	−0.753207
$636$	35.4140	1.40425
$637$	−12.3598	−0.489713
$638$	1.74869	0.0692314
$639$	−9.86186	−0.390129
$640$	18.9048	0.747278
$641$	−23.0487	−0.910368	−0.455184	−	0.890398i	$-0.650426\pi$
$641$	−23.0487	−0.910368	−0.455184	+	0.890398i	$0.650426\pi$
$642$	−22.2602	−0.878539
$643$	31.0084	1.22285	0.611425	−	0.791302i	$-0.290596\pi$
$643$	31.0084	1.22285	0.611425	+	0.791302i	$0.290596\pi$
$644$	−19.8899	−0.783772
$645$	−6.62302	−0.260781
$646$	5.69946	0.224242
$647$	38.4526	1.51173	0.755864	−	0.654728i	$-0.227217\pi$
$647$	38.4526	1.51173	0.755864	+	0.654728i	$0.227217\pi$
$648$	28.6614	1.12593
$649$	−3.10967	−0.122065
$650$	4.18232	0.164044
$651$	−0.815218	−0.0319509
$652$	−110.266	−4.31834
$653$	16.4496	0.643723	0.321862	−	0.946787i	$-0.395691\pi$
$653$	16.4496	0.643723	0.321862	+	0.946787i	$0.395691\pi$
$654$	45.8579	1.79318
$655$	21.1103	0.824848
$656$	−49.0864	−1.91650
$657$	15.2521	0.595043
$658$	−1.92594	−0.0750809
$659$	19.0860	0.743486	0.371743	−	0.928336i	$-0.378760\pi$
$659$	19.0860	0.743486	0.371743	+	0.928336i	$0.378760\pi$
$660$	−3.78630	−0.147382
$661$	38.7804	1.50838	0.754192	−	0.656654i	$-0.228029\pi$
$661$	38.7804	1.50838	0.754192	+	0.656654i	$0.228029\pi$
$662$	−12.5678	−0.488463
$663$	−16.7549	−0.650708
$664$	17.5816	0.682298
$665$	−0.557031	−0.0216007
$666$	−4.17866	−0.161920
$667$	12.8607	0.497966
$668$	−18.3958	−0.711755
$669$	−8.15844	−0.315424
$670$	−29.5215	−1.14051
$671$	2.52089	0.0973177
$672$	7.07010	0.272735
$673$	−23.7059	−0.913795	−0.456898	−	0.889519i	$-0.651039\pi$
$673$	−23.7059	−0.913795	−0.456898	+	0.889519i	$0.651039\pi$
$674$	−14.4333	−0.555950
$675$	4.76942	0.183575
$676$	−42.3119	−1.62738
$677$	20.5531	0.789920	0.394960	−	0.918698i	$-0.370758\pi$
$677$	20.5531	0.789920	0.394960	+	0.918698i	$0.370758\pi$
$678$	−39.8019	−1.52858
$679$	−7.76290	−0.297913
$680$	84.9141	3.25631
$681$	−0.0417062	−0.00159819
$682$	0.582633	0.0223102
$683$	25.7747	0.986240	0.493120	−	0.869961i	$-0.335856\pi$
$683$	25.7747	0.986240	0.493120	+	0.869961i	$0.335856\pi$
$684$	−1.80561	−0.0690392
$685$	−36.8483	−1.40790
$686$	−26.7032	−1.01953
$687$	2.98894	0.114035
$688$	−18.3307	−0.698851
$689$	10.9463	0.417022
$690$	−40.0401	−1.52430
$691$	−8.87040	−0.337446	−0.168723	−	0.985664i	$-0.553964\pi$
$691$	−8.87040	−0.337446	−0.168723	+	0.985664i	$0.553964\pi$
$692$	−43.9461	−1.67058
$693$	−0.260075	−0.00987944
$694$	−58.5671	−2.22318
$695$	18.9324	0.718146
$696$	−20.6918	−0.784321
$697$	40.2346	1.52400
$698$	80.8662	3.06083
$699$	−8.99072	−0.340060
$700$	3.00006	0.113392
$701$	−38.3681	−1.44914	−0.724571	−	0.689200i	$-0.757962\pi$
$701$	−38.3681	−1.44914	−0.724571	+	0.689200i	$0.757962\pi$
$702$	27.9763	1.05590
$703$	−0.508887	−0.0191930
$704$	−0.463938	−0.0174853
$705$	−2.69634	−0.101550
$706$	−83.8715	−3.15655
$707$	10.8294	0.407282
$708$	65.4623	2.46022
$709$	14.0459	0.527504	0.263752	−	0.964591i	$-0.415040\pi$
$709$	14.0459	0.527504	0.263752	+	0.964591i	$0.415040\pi$
$710$	−45.7734	−1.71785
$711$	−15.5447	−0.582971
$712$	62.6278	2.34708
$713$	4.28494	0.160472
$714$	−17.2817	−0.646752
$715$	−1.17033	−0.0437680
$716$	−103.235	−3.85809
$717$	−14.6642	−0.547645
$718$	39.8314	1.48649
$719$	−45.8032	−1.70817	−0.854085	−	0.520134i	$-0.825882\pi$
$719$	−45.8032	−1.70817	−0.854085	+	0.520134i	$0.825882\pi$
$720$	−17.7235	−0.660516
$721$	0.918459	0.0342052
$722$	48.3741	1.80030
$723$	29.1086	1.08256
$724$	−12.4594	−0.463050
$725$	−1.93982	−0.0720430
$726$	38.2847	1.42088
$727$	−24.7935	−0.919540	−0.459770	−	0.888038i	$-0.652068\pi$
$727$	−24.7935	−0.919540	−0.459770	+	0.888038i	$0.652068\pi$
$728$	9.89151	0.366604
$729$	28.1031	1.04086
$730$	70.7922	2.62014
$731$	15.0251	0.555724
$732$	−53.0678	−1.96144
$733$	34.3404	1.26839	0.634196	−	0.773172i	$-0.281331\pi$
$733$	34.3404	1.26839	0.634196	+	0.773172i	$0.281331\pi$
$734$	68.7891	2.53905
$735$	−17.8479	−0.658330
$736$	−37.1617	−1.36980
$737$	−1.67858	−0.0618313
$738$	−18.3282	−0.674672
$739$	−40.4813	−1.48913	−0.744565	−	0.667550i	$-0.767343\pi$
$739$	−40.4813	−1.48913	−0.744565	+	0.667550i	$0.767343\pi$
$740$	−13.4884	−0.495843
$741$	0.929498	0.0341460
$742$	11.2905	0.414487
$743$	0.510035	0.0187114	0.00935568	−	0.999956i	$-0.497022\pi$
$743$	0.510035	0.0187114	0.00935568	+	0.999956i	$0.497022\pi$
$744$	−6.89414	−0.252751
$745$	11.7101	0.429024
$746$	−71.0928	−2.60289
$747$	3.00792	0.110054
$748$	8.58968	0.314070
$749$	−4.93555	−0.180341
$750$	41.8010	1.52636
$751$	−12.3043	−0.448991	−0.224496	−	0.974475i	$-0.572073\pi$
$751$	−12.3043	−0.448991	−0.224496	+	0.974475i	$0.572073\pi$
$752$	−7.46272	−0.272137
$753$	8.76438	0.319392
$754$	−11.3785	−0.414381
$755$	−48.6222	−1.76954
$756$	20.0680	0.729864
$757$	46.7279	1.69835	0.849177	−	0.528109i	$-0.177099\pi$
$757$	46.7279	1.69835	0.849177	+	0.528109i	$0.177099\pi$
$758$	−87.3656	−3.17326
$759$	−2.27667	−0.0826378
$760$	−4.71070	−0.170875
$761$	−30.9804	−1.12304	−0.561519	−	0.827464i	$-0.689783\pi$
$761$	−30.9804	−1.12304	−0.561519	+	0.827464i	$0.689783\pi$
$762$	32.6674	1.18341
$763$	10.1677	0.368094
$764$	−8.40824	−0.304199
$765$	14.5274	0.525240
$766$	24.4130	0.882077
$767$	20.2342	0.730614
$768$	−36.8144	−1.32842
$769$	−30.2062	−1.08926	−0.544632	−	0.838675i	$-0.683331\pi$
$769$	−30.2062	−1.08926	−0.544632	+	0.838675i	$0.683331\pi$
$770$	−1.20713	−0.0435019
$771$	39.7458	1.43141
$772$	−37.9941	−1.36744
$773$	12.8130	0.460852	0.230426	−	0.973090i	$-0.425988\pi$
$773$	12.8130	0.460852	0.230426	+	0.973090i	$0.425988\pi$
$774$	−6.84445	−0.246019
$775$	−0.646312	−0.0232162
$776$	−65.6493	−2.35667
$777$	1.54303	0.0553559
$778$	−62.0508	−2.22463
$779$	−2.23206	−0.0799718
$780$	24.6370	0.882145
$781$	−2.60266	−0.0931305
$782$	90.8359	3.24828
$783$	−12.9758	−0.463717
$784$	−49.3981	−1.76422
$785$	36.1190	1.28914
$786$	−36.3335	−1.29597
$787$	−34.3230	−1.22348	−0.611741	−	0.791058i	$-0.709531\pi$
$787$	−34.3230	−1.22348	−0.611741	+	0.791058i	$0.709531\pi$
$788$	−55.7879	−1.98736
$789$	−7.42225	−0.264239
$790$	−72.1500	−2.56698
$791$	−8.82493	−0.313778
$792$	−2.19940	−0.0781524
$793$	−16.4031	−0.582490
$794$	14.4642	0.513316
$795$	15.8068	0.560610
$796$	−100.434	−3.55980
$797$	24.8441	0.880024	0.440012	−	0.897992i	$-0.354974\pi$
$797$	24.8441	0.880024	0.440012	+	0.897992i	$0.354974\pi$
$798$	0.958721	0.0339383
$799$	6.11697	0.216403
$800$	5.60523	0.198175
$801$	10.7146	0.378582
$802$	−41.4520	−1.46372
$803$	4.02522	0.142047
$804$	35.3362	1.24621
$805$	−8.87775	−0.312899
$806$	−3.79112	−0.133536
$807$	−18.8815	−0.664660
$808$	91.5823	3.22185
$809$	−33.3377	−1.17209	−0.586046	−	0.810278i	$-0.699316\pi$
$809$	−33.3377	−1.17209	−0.586046	+	0.810278i	$0.699316\pi$
$810$	22.7594	0.799683
$811$	−29.4240	−1.03322	−0.516608	−	0.856222i	$-0.672806\pi$
$811$	−29.4240	−1.03322	−0.516608	+	0.856222i	$0.672806\pi$
$812$	−8.16203	−0.286431
$813$	−33.9538	−1.19081
$814$	−1.10280	−0.0386530
$815$	−49.2165	−1.72398
$816$	−66.9640	−2.34421
$817$	−0.833533	−0.0291616
$818$	−77.1379	−2.69706
$819$	1.69228	0.0591329
$820$	−59.1622	−2.06603
$821$	4.10076	0.143118	0.0715588	−	0.997436i	$-0.477203\pi$
$821$	4.10076	0.143118	0.0715588	+	0.997436i	$0.477203\pi$
$822$	63.4205	2.21204
$823$	16.0587	0.559772	0.279886	−	0.960033i	$-0.409703\pi$
$823$	16.0587	0.559772	0.279886	+	0.960033i	$0.409703\pi$
$824$	7.76723	0.270584
$825$	0.343398	0.0119556
$826$	20.8703	0.726172
$827$	−6.84205	−0.237921	−0.118961	−	0.992899i	$-0.537956\pi$
$827$	−6.84205	−0.237921	−0.118961	+	0.992899i	$0.537956\pi$
$828$	−28.7771	−1.00007
$829$	30.4630	1.05803	0.529013	−	0.848614i	$-0.322562\pi$
$829$	30.4630	1.05803	0.529013	+	0.848614i	$0.322562\pi$
$830$	13.9612	0.484599
$831$	−26.6467	−0.924363
$832$	3.01879	0.104658
$833$	40.4901	1.40290
$834$	−32.5850	−1.12833
$835$	−8.21086	−0.284149
$836$	−0.476521	−0.0164808
$837$	−4.32330	−0.149435
$838$	−52.6163	−1.81760
$839$	12.2655	0.423453	0.211726	−	0.977329i	$-0.432091\pi$
$839$	12.2655	0.423453	0.211726	+	0.977329i	$0.432091\pi$
$840$	14.2836	0.492832
$841$	−23.7225	−0.818017
$842$	27.9056	0.961690
$843$	16.6009	0.571765
$844$	−4.23402	−0.145741
$845$	−18.8857	−0.649687
$846$	−2.78649	−0.0958014
$847$	8.48852	0.291669
$848$	43.7489	1.50234
$849$	−3.41741	−0.117285
$850$	−13.7011	−0.469943
$851$	−8.11045	−0.278023
$852$	54.7892	1.87705
$853$	−7.36757	−0.252261	−0.126130	−	0.992014i	$-0.540256\pi$
$853$	−7.36757	−0.252261	−0.126130	+	0.992014i	$0.540256\pi$
$854$	−16.9188	−0.578949
$855$	−0.805923	−0.0275620
$856$	−41.7390	−1.42661
$857$	42.4630	1.45051	0.725254	−	0.688482i	$-0.241723\pi$
$857$	42.4630	1.45051	0.725254	+	0.688482i	$0.241723\pi$
$858$	2.01429	0.0687668
$859$	19.0692	0.650633	0.325316	−	0.945605i	$-0.394529\pi$
$859$	19.0692	0.650633	0.325316	+	0.945605i	$0.394529\pi$
$860$	−22.0934	−0.753378
$861$	6.76797	0.230652
$862$	−63.9310	−2.17750
$863$	−33.7118	−1.14756	−0.573782	−	0.819008i	$-0.694524\pi$
$863$	−33.7118	−1.14756	−0.573782	+	0.819008i	$0.694524\pi$
$864$	37.4944	1.27559
$865$	−19.6151	−0.666934
$866$	64.3600	2.18704
$867$	31.6134	1.07365
$868$	−2.71944	−0.0923039
$869$	−4.10242	−0.139165
$870$	−16.4309	−0.557060
$871$	10.9223	0.370088
$872$	85.9859	2.91185
$873$	−11.2315	−0.380129
$874$	−5.03921	−0.170454
$875$	9.26816	0.313321
$876$	−84.7359	−2.86296
$877$	28.5806	0.965097	0.482548	−	0.875869i	$-0.339711\pi$
$877$	28.5806	0.965097	0.482548	+	0.875869i	$0.339711\pi$
$878$	−62.4836	−2.10872
$879$	−31.8669	−1.07485
$880$	−4.67744	−0.157676
$881$	57.2982	1.93043	0.965214	−	0.261463i	$-0.0842049\pi$
$881$	57.2982	1.93043	0.965214	+	0.261463i	$0.0842049\pi$
$882$	−18.4446	−0.621063
$883$	3.91166	0.131638	0.0658189	−	0.997832i	$-0.479034\pi$
$883$	3.91166	0.131638	0.0658189	+	0.997832i	$0.479034\pi$
$884$	−55.8919	−1.87985
$885$	29.2187	0.982177
$886$	−17.9866	−0.604270
$887$	−31.2502	−1.04928	−0.524640	−	0.851324i	$-0.675800\pi$
$887$	−31.2502	−1.04928	−0.524640	+	0.851324i	$0.675800\pi$
$888$	13.0491	0.437899
$889$	7.24304	0.242924
$890$	49.7314	1.66700
$891$	1.29409	0.0433537
$892$	−27.2153	−0.911236
$893$	−0.339345	−0.0113557
$894$	−20.1545	−0.674068
$895$	−46.0786	−1.54024
$896$	−7.21426	−0.241012
$897$	14.8140	0.494625
$898$	49.6929	1.65827
$899$	1.75837	0.0586449
$900$	4.34055	0.144685
$901$	−35.8597	−1.19466
$902$	−4.83704	−0.161056
$903$	2.52741	0.0841070
$904$	−74.6307	−2.48218
$905$	−5.56119	−0.184860
$906$	83.6850	2.78025
$907$	7.11169	0.236140	0.118070	−	0.993005i	$-0.462329\pi$
$907$	7.11169	0.236140	0.118070	+	0.993005i	$0.462329\pi$
$908$	−0.139125	−0.00461704
$909$	15.6682	0.519682
$910$	7.85463	0.260378
$911$	−7.00586	−0.232115	−0.116057	−	0.993243i	$-0.537026\pi$
$911$	−7.00586	−0.232115	−0.116057	+	0.993243i	$0.537026\pi$
$912$	3.71490	0.123013
$913$	0.793826	0.0262718
$914$	−11.6377	−0.384941
$915$	−23.6865	−0.783052
$916$	9.97066	0.329440
$917$	−8.05591	−0.266030
$918$	−91.6490	−3.02487
$919$	14.0570	0.463698	0.231849	−	0.972752i	$-0.425523\pi$
$919$	14.0570	0.463698	0.231849	+	0.972752i	$0.425523\pi$
$920$	−75.0774	−2.47523
$921$	29.4504	0.970424
$922$	38.5671	1.27014
$923$	16.9352	0.557428
$924$	1.44489	0.0475334
$925$	1.22333	0.0402227
$926$	−19.1813	−0.630336
$927$	1.32884	0.0436450
$928$	−15.2497	−0.500596
$929$	−1.90645	−0.0625487	−0.0312744	−	0.999511i	$-0.509957\pi$
$929$	−1.90645	−0.0625487	−0.0312744	+	0.999511i	$0.509957\pi$
$930$	−5.47448	−0.179515
$931$	−2.24623	−0.0736172
$932$	−29.9917	−0.982409
$933$	−14.8640	−0.486626
$934$	86.6784	2.83620
$935$	3.83395	0.125384
$936$	14.3112	0.467777
$937$	−7.87885	−0.257391	−0.128695	−	0.991684i	$-0.541079\pi$
$937$	−7.87885	−0.257391	−0.128695	+	0.991684i	$0.541079\pi$
$938$	11.2657	0.367838
$939$	−6.67171	−0.217723
$940$	−8.99457	−0.293370
$941$	12.4629	0.406278	0.203139	−	0.979150i	$-0.434886\pi$
$941$	12.4629	0.406278	0.203139	+	0.979150i	$0.434886\pi$
$942$	−62.1654	−2.02546
$943$	−35.5737	−1.15844
$944$	80.8694	2.63208
$945$	8.95722	0.291378
$946$	−1.80633	−0.0587289
$947$	30.9683	1.00634	0.503168	−	0.864189i	$-0.332168\pi$
$947$	30.9683	1.00634	0.503168	+	0.864189i	$0.332168\pi$
$948$	86.3611	2.80488
$949$	−26.1916	−0.850215
$950$	0.760082	0.0246603
$951$	17.8506	0.578845
$952$	−32.4041	−1.05022
$953$	−2.25404	−0.0730155	−0.0365077	−	0.999333i	$-0.511623\pi$
$953$	−2.25404	−0.0730155	−0.0365077	+	0.999333i	$0.511623\pi$
$954$	16.3353	0.528875
$955$	−3.75297	−0.121443
$956$	−48.9176	−1.58211
$957$	−0.934255	−0.0302002
$958$	−107.245	−3.46492
$959$	14.0617	0.454075
$960$	4.35921	0.140693
$961$	−30.4141	−0.981101
$962$	7.17576	0.231356
$963$	−7.14085	−0.230111
$964$	97.1017	3.12744
$965$	−16.9585	−0.545912
$966$	15.2797	0.491617
$967$	−42.6844	−1.37264	−0.686320	−	0.727300i	$-0.740775\pi$
$967$	−42.6844	−1.37264	−0.686320	+	0.727300i	$0.740775\pi$
$968$	71.7858	2.30728
$969$	−3.04499	−0.0978191
$970$	−52.1307	−1.67381
$971$	52.8503	1.69605	0.848023	−	0.529959i	$-0.177793\pi$
$971$	52.8503	1.69605	0.848023	+	0.529959i	$0.177793\pi$
$972$	50.1482	1.60851
$973$	−7.22479	−0.231616
$974$	78.3042	2.50903
$975$	−2.23444	−0.0715595
$976$	−65.5577	−2.09845
$977$	18.0463	0.577353	0.288676	−	0.957427i	$-0.406785\pi$
$977$	18.0463	0.577353	0.288676	+	0.957427i	$0.406785\pi$
$978$	84.7078	2.70866
$979$	2.82771	0.0903739
$980$	−59.5379	−1.90187
$981$	14.7108	0.469679
$982$	34.8251	1.11131
$983$	−3.56262	−0.113630	−0.0568150	−	0.998385i	$-0.518095\pi$
$983$	−3.56262	−0.113630	−0.0568150	+	0.998385i	$0.518095\pi$
$984$	57.2354	1.82460
$985$	−24.9006	−0.793400
$986$	37.2755	1.18709
$987$	1.02895	0.0327518
$988$	3.10066	0.0986452
$989$	−13.2845	−0.422424
$990$	−1.74650	−0.0555073
$991$	0.887033	0.0281775	0.0140888	−	0.999901i	$-0.495515\pi$
$991$	0.887033	0.0281775	0.0140888	+	0.999901i	$0.495515\pi$
$992$	−5.08093	−0.161320
$993$	6.71448	0.213078
$994$	17.4676	0.554039
$995$	−44.8283	−1.42115
$996$	−16.7110	−0.529509
$997$	17.2883	0.547524	0.273762	−	0.961797i	$-0.411732\pi$
$997$	17.2883	0.547524	0.273762	+	0.961797i	$0.411732\pi$
$998$	83.8586	2.65450
$999$	8.18305	0.258900

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6029.2.a.a.1.13	✓	234

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6029.2.a.a.1.13	✓	234	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)

\(f(q)\)	\(=\)	\(q-2.56265 q^{2} +1.36912 q^{3} +4.56717 q^{4} +2.03853 q^{5} -3.50857 q^{6} -0.777924 q^{7} -6.57875 q^{8} -1.12552 q^{9} +O(q^{10})\)	\(q-2.56265 q^{2} +1.36912 q^{3} +4.56717 q^{4} +2.03853 q^{5} -3.50857 q^{6} -0.777924 q^{7} -6.57875 q^{8} -1.12552 q^{9} -5.22404 q^{10} -0.297037 q^{11} +6.25299 q^{12} +1.93278 q^{13} +1.99355 q^{14} +2.79099 q^{15} +7.72468 q^{16} -6.33169 q^{17} +2.88430 q^{18} +0.351257 q^{19} +9.31031 q^{20} -1.06507 q^{21} +0.761201 q^{22} +5.59820 q^{23} -9.00708 q^{24} -0.844396 q^{25} -4.95304 q^{26} -5.64832 q^{27} -3.55291 q^{28} +2.29728 q^{29} -7.15232 q^{30} +0.765413 q^{31} -6.63815 q^{32} -0.406678 q^{33} +16.2259 q^{34} -1.58582 q^{35} -5.14042 q^{36} -1.44876 q^{37} -0.900148 q^{38} +2.64620 q^{39} -13.4110 q^{40} -6.35448 q^{41} +2.72940 q^{42} -2.37300 q^{43} -1.35662 q^{44} -2.29440 q^{45} -14.3462 q^{46} -0.966087 q^{47} +10.5760 q^{48} -6.39483 q^{49} +2.16389 q^{50} -8.66883 q^{51} +8.82733 q^{52} +5.66352 q^{53} +14.4747 q^{54} -0.605518 q^{55} +5.11776 q^{56} +0.480912 q^{57} -5.88713 q^{58} +10.4690 q^{59} +12.7469 q^{60} -8.48678 q^{61} -1.96149 q^{62} +0.875565 q^{63} +1.56189 q^{64} +3.94003 q^{65} +1.04217 q^{66} +5.65108 q^{67} -28.9179 q^{68} +7.66460 q^{69} +4.06390 q^{70} +8.76208 q^{71} +7.40448 q^{72} -13.5513 q^{73} +3.71266 q^{74} -1.15608 q^{75} +1.60425 q^{76} +0.231072 q^{77} -6.78129 q^{78} +13.8112 q^{79} +15.7470 q^{80} -4.35667 q^{81} +16.2843 q^{82} -2.67248 q^{83} -4.86435 q^{84} -12.9073 q^{85} +6.08117 q^{86} +3.14525 q^{87} +1.95413 q^{88} -9.51972 q^{89} +5.87973 q^{90} -1.50356 q^{91} +25.5679 q^{92} +1.04794 q^{93} +2.47574 q^{94} +0.716048 q^{95} -9.08842 q^{96} +9.97900 q^{97} +16.3877 q^{98} +0.334320 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9}+O(q^{10}) \) 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9	\( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9} - 89 q^{10} - 55 q^{11} - 75 q^{12} - 49 q^{13} - 42 q^{14} - 43 q^{15} + 142 q^{16} - 40 q^{17} - 30 q^{18} - 235 q^{19} - 62 q^{20} - 62 q^{21} - 63 q^{22} - 30 q^{23} - 108 q^{24} + 170 q^{25} - 44 q^{26} - 160 q^{27} - 147 q^{28} - 76 q^{29} - 15 q^{30} - 175 q^{31} - 49 q^{32} - 43 q^{33} - 104 q^{34} - 87 q^{35} + 124 q^{36} - 77 q^{37} - 18 q^{38} - 104 q^{39} - 247 q^{40} - 60 q^{41} - 6 q^{42} - 201 q^{43} - 89 q^{44} - 102 q^{45} - 128 q^{46} - 27 q^{47} - 130 q^{48} + 123 q^{49} - 33 q^{50} - 220 q^{51} - 125 q^{52} - 34 q^{53} - 126 q^{54} - 176 q^{55} - 125 q^{56} - 17 q^{57} - 46 q^{58} - 172 q^{59} - 61 q^{60} - 243 q^{61} - 37 q^{62} - 137 q^{63} + 39 q^{64} - 31 q^{65} - 142 q^{66} - 132 q^{67} - 106 q^{68} - 115 q^{69} - 60 q^{70} - 68 q^{71} - 66 q^{72} - 109 q^{73} - 74 q^{74} - 256 q^{75} - 412 q^{76} - 32 q^{77} - 38 q^{78} - 297 q^{79} - 111 q^{80} + 142 q^{81} - 94 q^{82} - 100 q^{83} - 134 q^{84} - 90 q^{85} + q^{86} - 103 q^{87} - 143 q^{88} - 77 q^{89} - 181 q^{90} - 418 q^{91} - 19 q^{92} + 5 q^{93} - 231 q^{94} - 92 q^{95} - 189 q^{96} - 141 q^{97} - 25 q^{98} - 244 q^{99}+O(q^{100}) \) 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9 - 89 * q^10 - 55 * q^11 - 75 * q^12 - 49 * q^13 - 42 * q^14 - 43 * q^15 + 142 * q^16 - 40 * q^17 - 30 * q^18 - 235 * q^19 - 62 * q^20 - 62 * q^21 - 63 * q^22 - 30 * q^23 - 108 * q^24 + 170 * q^25 - 44 * q^26 - 160 * q^27 - 147 * q^28 - 76 * q^29 - 15 * q^30 - 175 * q^31 - 49 * q^32 - 43 * q^33 - 104 * q^34 - 87 * q^35 + 124 * q^36 - 77 * q^37 - 18 * q^38 - 104 * q^39 - 247 * q^40 - 60 * q^41 - 6 * q^42 - 201 * q^43 - 89 * q^44 - 102 * q^45 - 128 * q^46 - 27 * q^47 - 130 * q^48 + 123 * q^49 - 33 * q^50 - 220 * q^51 - 125 * q^52 - 34 * q^53 - 126 * q^54 - 176 * q^55 - 125 * q^56 - 17 * q^57 - 46 * q^58 - 172 * q^59 - 61 * q^60 - 243 * q^61 - 37 * q^62 - 137 * q^63 + 39 * q^64 - 31 * q^65 - 142 * q^66 - 132 * q^67 - 106 * q^68 - 115 * q^69 - 60 * q^70 - 68 * q^71 - 66 * q^72 - 109 * q^73 - 74 * q^74 - 256 * q^75 - 412 * q^76 - 32 * q^77 - 38 * q^78 - 297 * q^79 - 111 * q^80 + 142 * q^81 - 94 * q^82 - 100 * q^83 - 134 * q^84 - 90 * q^85 + q^86 - 103 * q^87 - 143 * q^88 - 77 * q^89 - 181 * q^90 - 418 * q^91 - 19 * q^92 + 5 * q^93 - 231 * q^94 - 92 * q^95 - 189 * q^96 - 141 * q^97 - 25 * q^98 - 244 * q^99

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