LMFDB - Embedded newform 5077.2.a.b.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5077,2,Mod(1,5077)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5077, 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("5077.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5077 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5077.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:	$40.5400491062$
Analytic rank:	$1$
Dimension:	$205$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	5077.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58762 q^{2} +0.766219 q^{3} +4.69576 q^{4} +1.84822 q^{5} -1.98268 q^{6} -5.04954 q^{7} -6.97561 q^{8} -2.41291 q^{9} +O(q^{10})$	\(q-2.58762 q^{2} +0.766219 q^{3} +4.69576 q^{4} +1.84822 q^{5} -1.98268 q^{6} -5.04954 q^{7} -6.97561 q^{8} -2.41291 q^{9} -4.78248 q^{10} -4.49504 q^{11} +3.59798 q^{12} +5.95124 q^{13} +13.0663 q^{14} +1.41614 q^{15} +8.65867 q^{16} +5.94585 q^{17} +6.24368 q^{18} -2.59001 q^{19} +8.67880 q^{20} -3.86906 q^{21} +11.6314 q^{22} +5.07878 q^{23} -5.34484 q^{24} -1.58409 q^{25} -15.3995 q^{26} -4.14747 q^{27} -23.7115 q^{28} +6.37999 q^{29} -3.66443 q^{30} -1.63544 q^{31} -8.45412 q^{32} -3.44418 q^{33} -15.3856 q^{34} -9.33266 q^{35} -11.3304 q^{36} -0.397533 q^{37} +6.70195 q^{38} +4.55995 q^{39} -12.8924 q^{40} -6.87961 q^{41} +10.0116 q^{42} -3.03051 q^{43} -21.1076 q^{44} -4.45958 q^{45} -13.1419 q^{46} +1.80977 q^{47} +6.63444 q^{48} +18.4979 q^{49} +4.09902 q^{50} +4.55582 q^{51} +27.9456 q^{52} -2.78340 q^{53} +10.7321 q^{54} -8.30781 q^{55} +35.2236 q^{56} -1.98451 q^{57} -16.5090 q^{58} -4.71105 q^{59} +6.64986 q^{60} +11.2088 q^{61} +4.23189 q^{62} +12.1841 q^{63} +4.55869 q^{64} +10.9992 q^{65} +8.91223 q^{66} +11.8469 q^{67} +27.9203 q^{68} +3.89146 q^{69} +24.1494 q^{70} -5.94805 q^{71} +16.8315 q^{72} -5.36688 q^{73} +1.02866 q^{74} -1.21376 q^{75} -12.1621 q^{76} +22.6979 q^{77} -11.7994 q^{78} -16.0823 q^{79} +16.0031 q^{80} +4.06085 q^{81} +17.8018 q^{82} -0.0257040 q^{83} -18.1682 q^{84} +10.9892 q^{85} +7.84181 q^{86} +4.88847 q^{87} +31.3556 q^{88} -2.46316 q^{89} +11.5397 q^{90} -30.0510 q^{91} +23.8488 q^{92} -1.25310 q^{93} -4.68299 q^{94} -4.78690 q^{95} -6.47771 q^{96} +11.7916 q^{97} -47.8655 q^{98} +10.8461 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9}+O(q^{10}) $ 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9} - 28 q^{10} - 83 q^{11} - 108 q^{12} - 36 q^{13} - 67 q^{14} - 63 q^{15} + 187 q^{16} - 72 q^{17} - 57 q^{18} - 47 q^{19} - 132 q^{20} - 35 q^{21} - 40 q^{22} - 97 q^{23} - 49 q^{24} + 175 q^{25} - 78 q^{26} - 227 q^{27} - 59 q^{28} - 46 q^{29} + 30 q^{30} - 77 q^{31} - 175 q^{32} - 74 q^{33} - 28 q^{34} - 171 q^{35} + 171 q^{36} - 52 q^{37} - 144 q^{38} - 54 q^{39} - 49 q^{40} - 107 q^{41} + 7 q^{42} - 58 q^{43} - 139 q^{44} - 89 q^{45} - 33 q^{46} - 255 q^{47} - 202 q^{48} + 171 q^{49} - 74 q^{50} - 63 q^{51} - 90 q^{52} - 82 q^{53} - 51 q^{54} - 70 q^{55} - 180 q^{56} - 70 q^{57} - 50 q^{58} - 289 q^{59} - 105 q^{60} - 20 q^{61} - 143 q^{62} - 119 q^{63} + 201 q^{64} - 92 q^{65} - 3 q^{66} - 138 q^{67} - 177 q^{68} - 67 q^{69} + 4 q^{70} - 141 q^{71} - 138 q^{72} - 71 q^{73} - 26 q^{74} - 251 q^{75} - 42 q^{76} - 149 q^{77} - 6 q^{78} - 47 q^{79} - 294 q^{80} + 193 q^{81} - 70 q^{82} - 329 q^{83} - 40 q^{84} - 45 q^{85} - 83 q^{86} - 139 q^{87} - 45 q^{88} - 163 q^{89} - 116 q^{90} - 141 q^{91} - 204 q^{92} - 91 q^{93} - 8 q^{94} - 173 q^{95} - 53 q^{96} - 147 q^{97} - 156 q^{98} - 157 q^{99}+O(q^{100}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9 - 28 * q^10 - 83 * q^11 - 108 * q^12 - 36 * q^13 - 67 * q^14 - 63 * q^15 + 187 * q^16 - 72 * q^17 - 57 * q^18 - 47 * q^19 - 132 * q^20 - 35 * q^21 - 40 * q^22 - 97 * q^23 - 49 * q^24 + 175 * q^25 - 78 * q^26 - 227 * q^27 - 59 * q^28 - 46 * q^29 + 30 * q^30 - 77 * q^31 - 175 * q^32 - 74 * q^33 - 28 * q^34 - 171 * q^35 + 171 * q^36 - 52 * q^37 - 144 * q^38 - 54 * q^39 - 49 * q^40 - 107 * q^41 + 7 * q^42 - 58 * q^43 - 139 * q^44 - 89 * q^45 - 33 * q^46 - 255 * q^47 - 202 * q^48 + 171 * q^49 - 74 * q^50 - 63 * q^51 - 90 * q^52 - 82 * q^53 - 51 * q^54 - 70 * q^55 - 180 * q^56 - 70 * q^57 - 50 * q^58 - 289 * q^59 - 105 * q^60 - 20 * q^61 - 143 * q^62 - 119 * q^63 + 201 * q^64 - 92 * q^65 - 3 * q^66 - 138 * q^67 - 177 * q^68 - 67 * q^69 + 4 * q^70 - 141 * q^71 - 138 * q^72 - 71 * q^73 - 26 * q^74 - 251 * q^75 - 42 * q^76 - 149 * q^77 - 6 * q^78 - 47 * q^79 - 294 * q^80 + 193 * q^81 - 70 * q^82 - 329 * q^83 - 40 * q^84 - 45 * q^85 - 83 * q^86 - 139 * q^87 - 45 * q^88 - 163 * q^89 - 116 * q^90 - 141 * q^91 - 204 * q^92 - 91 * q^93 - 8 * q^94 - 173 * q^95 - 53 * q^96 - 147 * q^97 - 156 * q^98 - 157 * 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 $

$2$	−2.58762	−1.82972	−0.914861	−	0.403769i	$-0.867700\pi$
$2$	−2.58762	−1.82972	−0.914861	+	0.403769i	$0.867700\pi$
$3$	0.766219	0.442377	0.221188	−	0.975231i	$-0.429006\pi$
$3$	0.766219	0.442377	0.221188	+	0.975231i	$0.429006\pi$
$4$	4.69576	2.34788
$5$	1.84822	0.826548	0.413274	−	0.910607i	$-0.364385\pi$
$5$	1.84822	0.826548	0.413274	+	0.910607i	$0.364385\pi$
$6$	−1.98268	−0.809426
$7$	−5.04954	−1.90855	−0.954274	−	0.298933i	$-0.903369\pi$
$7$	−5.04954	−1.90855	−0.954274	+	0.298933i	$0.903369\pi$
$8$	−6.97561	−2.46625
$9$	−2.41291	−0.804303
$10$	−4.78248	−1.51235
$11$	−4.49504	−1.35530	−0.677652	−	0.735382i	$-0.737003\pi$
$11$	−4.49504	−1.35530	−0.677652	+	0.735382i	$0.737003\pi$
$12$	3.59798	1.03865
$13$	5.95124	1.65058	0.825288	−	0.564711i	$-0.191013\pi$
$13$	5.95124	1.65058	0.825288	+	0.564711i	$0.191013\pi$
$14$	13.0663	3.49211
$15$	1.41614	0.365646
$16$	8.65867	2.16467
$17$	5.94585	1.44208	0.721040	−	0.692893i	$-0.243664\pi$
$17$	5.94585	1.44208	0.721040	+	0.692893i	$0.243664\pi$
$18$	6.24368	1.47165
$19$	−2.59001	−0.594189	−0.297094	−	0.954848i	$-0.596018\pi$
$19$	−2.59001	−0.594189	−0.297094	+	0.954848i	$0.596018\pi$
$20$	8.67880	1.94064
$21$	−3.86906	−0.844297
$22$	11.6314	2.47983
$23$	5.07878	1.05900	0.529499	−	0.848310i	$-0.322380\pi$
$23$	5.07878	1.05900	0.529499	+	0.848310i	$0.322380\pi$
$24$	−5.34484	−1.09101
$25$	−1.58409	−0.316818
$26$	−15.3995	−3.02010
$27$	−4.14747	−0.798182
$28$	−23.7115	−4.48105
$29$	6.37999	1.18474	0.592368	−	0.805668i	$-0.298193\pi$
$29$	6.37999	1.18474	0.592368	+	0.805668i	$0.298193\pi$
$30$	−3.66443	−0.669030
$31$	−1.63544	−0.293733	−0.146867	−	0.989156i	$-0.546919\pi$
$31$	−1.63544	−0.293733	−0.146867	+	0.989156i	$0.546919\pi$
$32$	−8.45412	−1.49449
$33$	−3.44418	−0.599555
$34$	−15.3856	−2.63861
$35$	−9.33266	−1.57751
$36$	−11.3304	−1.88841
$37$	−0.397533	−0.0653541	−0.0326770	−	0.999466i	$-0.510403\pi$
$37$	−0.397533	−0.0653541	−0.0326770	+	0.999466i	$0.510403\pi$
$38$	6.70195	1.08720
$39$	4.55995	0.730177
$40$	−12.8924	−2.03847
$41$	−6.87961	−1.07442	−0.537208	−	0.843450i	$-0.680521\pi$
$41$	−6.87961	−1.07442	−0.537208	+	0.843450i	$0.680521\pi$
$42$	10.0116	1.54483
$43$	−3.03051	−0.462149	−0.231075	−	0.972936i	$-0.574224\pi$
$43$	−3.03051	−0.462149	−0.231075	+	0.972936i	$0.574224\pi$
$44$	−21.1076	−3.18210
$45$	−4.45958	−0.664795
$46$	−13.1419	−1.93767
$47$	1.80977	0.263982	0.131991	−	0.991251i	$-0.457863\pi$
$47$	1.80977	0.263982	0.131991	+	0.991251i	$0.457863\pi$
$48$	6.63444	0.957599
$49$	18.4979	2.64256
$50$	4.09902	0.579688
$51$	4.55582	0.637943
$52$	27.9456	3.87536
$53$	−2.78340	−0.382330	−0.191165	−	0.981558i	$-0.561226\pi$
$53$	−2.78340	−0.382330	−0.191165	+	0.981558i	$0.561226\pi$
$54$	10.7321	1.46045
$55$	−8.30781	−1.12023
$56$	35.2236	4.70696
$57$	−1.98451	−0.262855
$58$	−16.5090	−2.16774
$59$	−4.71105	−0.613327	−0.306663	−	0.951818i	$-0.599213\pi$
$59$	−4.71105	−0.613327	−0.306663	+	0.951818i	$0.599213\pi$
$60$	6.64986	0.858493
$61$	11.2088	1.43514	0.717568	−	0.696488i	$-0.245255\pi$
$61$	11.2088	1.43514	0.717568	+	0.696488i	$0.245255\pi$
$62$	4.23189	0.537450
$63$	12.1841	1.53505
$64$	4.55869	0.569836
$65$	10.9992	1.36428
$66$	8.91223	1.09702
$67$	11.8469	1.44733	0.723665	−	0.690151i	$-0.242456\pi$
$67$	11.8469	1.44733	0.723665	+	0.690151i	$0.242456\pi$
$68$	27.9203	3.38584
$69$	3.89146	0.468476
$70$	24.1494	2.88640
$71$	−5.94805	−0.705904	−0.352952	−	0.935642i	$-0.614822\pi$
$71$	−5.94805	−0.705904	−0.352952	+	0.935642i	$0.614822\pi$
$72$	16.8315	1.98361
$73$	−5.36688	−0.628145	−0.314073	−	0.949399i	$-0.601694\pi$
$73$	−5.36688	−0.628145	−0.314073	+	0.949399i	$0.601694\pi$
$74$	1.02866	0.119580
$75$	−1.21376	−0.140153
$76$	−12.1621	−1.39508
$77$	22.6979	2.58666
$78$	−11.7994	−1.33602
$79$	−16.0823	−1.80940	−0.904698	−	0.426054i	$-0.859903\pi$
$79$	−16.0823	−1.80940	−0.904698	+	0.426054i	$0.859903\pi$
$80$	16.0031	1.78920
$81$	4.06085	0.451206
$82$	17.8018	1.96588
$83$	−0.0257040	−0.00282138	−0.00141069	−	0.999999i	$-0.500449\pi$
$83$	−0.0257040	−0.00282138	−0.00141069	+	0.999999i	$0.500449\pi$
$84$	−18.1682	−1.98231
$85$	10.9892	1.19195
$86$	7.84181	0.845604
$87$	4.88847	0.524099
$88$	31.3556	3.34252
$89$	−2.46316	−0.261094	−0.130547	−	0.991442i	$-0.541673\pi$
$89$	−2.46316	−0.261094	−0.130547	+	0.991442i	$0.541673\pi$
$90$	11.5397	1.21639
$91$	−30.0510	−3.15021
$92$	23.8488	2.48640
$93$	−1.25310	−0.129941
$94$	−4.68299	−0.483014
$95$	−4.78690	−0.491126
$96$	−6.47771	−0.661129
$97$	11.7916	1.19725	0.598626	−	0.801028i	$-0.295713\pi$
$97$	11.7916	1.19725	0.598626	+	0.801028i	$0.295713\pi$
$98$	−47.8655	−4.83514
$99$	10.8461	1.09008
$100$	−7.43851	−0.743851
$101$	10.2893	1.02383	0.511914	−	0.859037i	$-0.328937\pi$
$101$	10.2893	1.02383	0.511914	+	0.859037i	$0.328937\pi$
$102$	−11.7887	−1.16726
$103$	−8.38960	−0.826652	−0.413326	−	0.910583i	$-0.635633\pi$
$103$	−8.38960	−0.826652	−0.413326	+	0.910583i	$0.635633\pi$
$104$	−41.5135	−4.07073
$105$	−7.15086	−0.697853
$106$	7.20238	0.699557
$107$	2.89861	0.280219	0.140110	−	0.990136i	$-0.455254\pi$
$107$	2.89861	0.280219	0.140110	+	0.990136i	$0.455254\pi$
$108$	−19.4756	−1.87404
$109$	8.51618	0.815702	0.407851	−	0.913049i	$-0.366278\pi$
$109$	8.51618	0.815702	0.407851	+	0.913049i	$0.366278\pi$
$110$	21.4974	2.04970
$111$	−0.304598	−0.0289111
$112$	−43.7224	−4.13137
$113$	−20.3099	−1.91059	−0.955296	−	0.295650i	$-0.904464\pi$
$113$	−20.3099	−1.91059	−0.955296	+	0.295650i	$0.904464\pi$
$114$	5.13516	0.480952
$115$	9.38669	0.875314
$116$	29.9590	2.78162
$117$	−14.3598	−1.32756
$118$	12.1904	1.12222
$119$	−30.0238	−2.75228
$120$	−9.87844	−0.901774
$121$	9.20537	0.836852
$122$	−29.0040	−2.62590
$123$	−5.27129	−0.475296
$124$	−7.67963	−0.689651
$125$	−12.1688	−1.08841
$126$	−31.5278	−2.80872
$127$	4.52126	0.401197	0.200598	−	0.979674i	$-0.435711\pi$
$127$	4.52126	0.401197	0.200598	+	0.979674i	$0.435711\pi$
$128$	5.11210	0.451850
$129$	−2.32204	−0.204444
$130$	−28.4617	−2.49626
$131$	5.51783	0.482095	0.241048	−	0.970513i	$-0.422509\pi$
$131$	5.51783	0.482095	0.241048	+	0.970513i	$0.422509\pi$
$132$	−16.1731	−1.40769
$133$	13.0784	1.13404
$134$	−30.6553	−2.64821
$135$	−7.66544	−0.659736
$136$	−41.4759	−3.55653
$137$	−2.64880	−0.226302	−0.113151	−	0.993578i	$-0.536094\pi$
$137$	−2.64880	−0.226302	−0.113151	+	0.993578i	$0.536094\pi$
$138$	−10.0696	−0.857182
$139$	14.4666	1.22704	0.613521	−	0.789678i	$-0.289752\pi$
$139$	14.4666	1.22704	0.613521	+	0.789678i	$0.289752\pi$
$140$	−43.8240	−3.70380
$141$	1.38668	0.116779
$142$	15.3913	1.29161
$143$	−26.7510	−2.23703
$144$	−20.8926	−1.74105
$145$	11.7916	0.979241
$146$	13.8874	1.14933
$147$	14.1734	1.16901
$148$	−1.86672	−0.153444
$149$	−2.95291	−0.241912	−0.120956	−	0.992658i	$-0.538596\pi$
$149$	−2.95291	−0.241912	−0.120956	+	0.992658i	$0.538596\pi$
$150$	3.14074	0.256441
$151$	3.33749	0.271601	0.135801	−	0.990736i	$-0.456639\pi$
$151$	3.33749	0.271601	0.135801	+	0.990736i	$0.456639\pi$
$152$	18.0669	1.46542
$153$	−14.3468	−1.15987
$154$	−58.7335	−4.73288
$155$	−3.02265	−0.242785
$156$	21.4125	1.71437
$157$	−12.6950	−1.01317	−0.506585	−	0.862190i	$-0.669093\pi$
$157$	−12.6950	−1.01317	−0.506585	+	0.862190i	$0.669093\pi$
$158$	41.6147	3.31069
$159$	−2.13269	−0.169134
$160$	−15.6251	−1.23527
$161$	−25.6455	−2.02115
$162$	−10.5079	−0.825581
$163$	11.8635	0.929223	0.464611	−	0.885515i	$-0.346194\pi$
$163$	11.8635	0.929223	0.464611	+	0.885515i	$0.346194\pi$
$164$	−32.3050	−2.52260
$165$	−6.36560	−0.495562
$166$	0.0665120	0.00516233
$167$	−24.0347	−1.85986	−0.929930	−	0.367736i	$-0.880133\pi$
$167$	−24.0347	−1.85986	−0.929930	+	0.367736i	$0.880133\pi$
$168$	26.9890	2.08225
$169$	22.4172	1.72440
$170$	−28.4359	−2.18094
$171$	6.24945	0.477908
$172$	−14.2306	−1.08507
$173$	−10.4947	−0.797899	−0.398950	−	0.916973i	$-0.630625\pi$
$173$	−10.4947	−0.797899	−0.398950	+	0.916973i	$0.630625\pi$
$174$	−12.6495	−0.958956
$175$	7.99893	0.604662
$176$	−38.9211	−2.93379
$177$	−3.60970	−0.271321
$178$	6.37370	0.477729
$179$	−9.95085	−0.743762	−0.371881	−	0.928280i	$-0.621287\pi$
$179$	−9.95085	−0.743762	−0.371881	+	0.928280i	$0.621287\pi$
$180$	−20.9411	−1.56086
$181$	−23.0790	−1.71545	−0.857723	−	0.514112i	$-0.828122\pi$
$181$	−23.0790	−1.71545	−0.857723	+	0.514112i	$0.828122\pi$
$182$	77.7606	5.76400
$183$	8.58837	0.634871
$184$	−35.4276	−2.61176
$185$	−0.734729	−0.0540183
$186$	3.24255	0.237755
$187$	−26.7268	−1.95446
$188$	8.49825	0.619799
$189$	20.9428	1.52337
$190$	12.3867	0.898623
$191$	23.8289	1.72420	0.862100	−	0.506737i	$-0.169149\pi$
$191$	23.8289	1.72420	0.862100	+	0.506737i	$0.169149\pi$
$192$	3.49295	0.252082
$193$	−19.2071	−1.38256	−0.691279	−	0.722588i	$-0.742952\pi$
$193$	−19.2071	−1.38256	−0.691279	+	0.722588i	$0.742952\pi$
$194$	−30.5121	−2.19064
$195$	8.42779	0.603526
$196$	86.8618	6.20441
$197$	−7.10233	−0.506020	−0.253010	−	0.967464i	$-0.581421\pi$
$197$	−7.10233	−0.506020	−0.253010	+	0.967464i	$0.581421\pi$
$198$	−28.0656	−1.99454
$199$	13.2520	0.939406	0.469703	−	0.882825i	$-0.344361\pi$
$199$	13.2520	0.939406	0.469703	+	0.882825i	$0.344361\pi$
$200$	11.0500	0.781352
$201$	9.07733	0.640266
$202$	−26.6249	−1.87332
$203$	−32.2161	−2.26112
$204$	21.3931	1.49781
$205$	−12.7150	−0.888056
$206$	21.7091	1.51254
$207$	−12.2546	−0.851756
$208$	51.5298	3.57295
$209$	11.6422	0.805307
$210$	18.5037	1.27688
$211$	16.1986	1.11516	0.557578	−	0.830125i	$-0.311731\pi$
$211$	16.1986	1.11516	0.557578	+	0.830125i	$0.311731\pi$
$212$	−13.0702	−0.897665
$213$	−4.55751	−0.312275
$214$	−7.50050	−0.512723
$215$	−5.60105	−0.381989
$216$	28.9311	1.96852
$217$	8.25821	0.560604
$218$	−22.0366	−1.49251
$219$	−4.11220	−0.277877
$220$	−39.0115	−2.63016
$221$	35.3852	2.38026
$222$	0.788182	0.0528993
$223$	−23.5131	−1.57456	−0.787278	−	0.616599i	$-0.788510\pi$
$223$	−23.5131	−1.57456	−0.787278	+	0.616599i	$0.788510\pi$
$224$	42.6895	2.85231
$225$	3.82226	0.254817
$226$	52.5542	3.49585
$227$	−9.57054	−0.635219	−0.317609	−	0.948222i	$-0.602880\pi$
$227$	−9.57054	−0.635219	−0.317609	+	0.948222i	$0.602880\pi$
$228$	−9.31881	−0.617153
$229$	9.91149	0.654970	0.327485	−	0.944856i	$-0.393799\pi$
$229$	9.91149	0.654970	0.327485	+	0.944856i	$0.393799\pi$
$230$	−24.2892	−1.60158
$231$	17.3916	1.14428
$232$	−44.5043	−2.92185
$233$	6.39402	0.418886	0.209443	−	0.977821i	$-0.432835\pi$
$233$	6.39402	0.418886	0.209443	+	0.977821i	$0.432835\pi$
$234$	37.1577	2.42907
$235$	3.34485	0.218194
$236$	−22.1220	−1.44002
$237$	−12.3225	−0.800434
$238$	77.6902	5.03591
$239$	−19.3926	−1.25440	−0.627201	−	0.778857i	$-0.715800\pi$
$239$	−19.3926	−1.25440	−0.627201	+	0.778857i	$0.715800\pi$
$240$	12.2619	0.791502
$241$	−10.5814	−0.681608	−0.340804	−	0.940134i	$-0.610699\pi$
$241$	−10.5814	−0.681608	−0.340804	+	0.940134i	$0.610699\pi$
$242$	−23.8200	−1.53121
$243$	15.5539	0.997785
$244$	52.6337	3.36953
$245$	34.1881	2.18420
$246$	13.6401	0.869660
$247$	−15.4138	−0.980754
$248$	11.4082	0.724419
$249$	−0.0196949	−0.00124811
$250$	31.4883	1.99149
$251$	−16.8151	−1.06136	−0.530681	−	0.847572i	$-0.678064\pi$
$251$	−16.8151	−1.06136	−0.530681	+	0.847572i	$0.678064\pi$
$252$	57.2136	3.60412
$253$	−22.8293	−1.43527
$254$	−11.6993	−0.734079
$255$	8.42016	0.527291
$256$	−22.3455	−1.39660
$257$	−8.44417	−0.526733	−0.263366	−	0.964696i	$-0.584833\pi$
$257$	−8.44417	−0.526733	−0.263366	+	0.964696i	$0.584833\pi$
$258$	6.00855	0.374076
$259$	2.00736	0.124731
$260$	51.6496	3.20317
$261$	−15.3943	−0.952886
$262$	−14.2780	−0.882101
$263$	4.55204	0.280691	0.140345	−	0.990103i	$-0.455179\pi$
$263$	4.55204	0.280691	0.140345	+	0.990103i	$0.455179\pi$
$264$	24.0253	1.47865
$265$	−5.14433	−0.316014
$266$	−33.8418	−2.07497
$267$	−1.88732	−0.115502
$268$	55.6303	3.39816
$269$	−31.9921	−1.95059	−0.975297	−	0.220898i	$-0.929101\pi$
$269$	−31.9921	−1.95059	−0.975297	+	0.220898i	$0.929101\pi$
$270$	19.8352	1.20713
$271$	−19.1585	−1.16380	−0.581899	−	0.813261i	$-0.697690\pi$
$271$	−19.1585	−1.16380	−0.581899	+	0.813261i	$0.697690\pi$
$272$	51.4832	3.12163
$273$	−23.0257	−1.39358
$274$	6.85408	0.414070
$275$	7.12054	0.429385
$276$	18.2734	1.09993
$277$	−4.98781	−0.299688	−0.149844	−	0.988710i	$-0.547877\pi$
$277$	−4.98781	−0.299688	−0.149844	+	0.988710i	$0.547877\pi$
$278$	−37.4341	−2.24515
$279$	3.94616	0.236250
$280$	65.1010	3.89053
$281$	24.3252	1.45112	0.725560	−	0.688159i	$-0.241581\pi$
$281$	24.3252	1.45112	0.725560	+	0.688159i	$0.241581\pi$
$282$	−3.58820	−0.213674
$283$	0.750252	0.0445979	0.0222989	−	0.999751i	$-0.492901\pi$
$283$	0.750252	0.0445979	0.0222989	+	0.999751i	$0.492901\pi$
$284$	−27.9306	−1.65738
$285$	−3.66781	−0.217263
$286$	69.2215	4.09315
$287$	34.7389	2.05057
$288$	20.3990	1.20202
$289$	18.3531	1.07960
$290$	−30.5122	−1.79174
$291$	9.03493	0.529637
$292$	−25.2016	−1.47481
$293$	13.9289	0.813737	0.406869	−	0.913487i	$-0.366621\pi$
$293$	13.9289	0.813737	0.406869	+	0.913487i	$0.366621\pi$
$294$	−36.6754	−2.13895
$295$	−8.70705	−0.506944
$296$	2.77304	0.161179
$297$	18.6431	1.08178
$298$	7.64100	0.442631
$299$	30.2250	1.74796
$300$	−5.69953	−0.329062
$301$	15.3027	0.882034
$302$	−8.63615	−0.496954
$303$	7.88389	0.452918
$304$	−22.4260	−1.28622
$305$	20.7163	1.18621
$306$	37.1240	2.12224
$307$	−4.03565	−0.230327	−0.115163	−	0.993347i	$-0.536739\pi$
$307$	−4.03565	−0.230327	−0.115163	+	0.993347i	$0.536739\pi$
$308$	106.584	6.07318
$309$	−6.42827	−0.365692
$310$	7.82145	0.444229
$311$	−16.1657	−0.916671	−0.458336	−	0.888779i	$-0.651554\pi$
$311$	−16.1657	−0.916671	−0.458336	+	0.888779i	$0.651554\pi$
$312$	−31.8084	−1.80080
$313$	−11.4098	−0.644922	−0.322461	−	0.946583i	$-0.604510\pi$
$313$	−11.4098	−0.644922	−0.322461	+	0.946583i	$0.604510\pi$
$314$	32.8498	1.85382
$315$	22.5189	1.26879
$316$	−75.5185	−4.24825
$317$	−21.5803	−1.21207	−0.606036	−	0.795437i	$-0.707241\pi$
$317$	−21.5803	−1.21207	−0.606036	+	0.795437i	$0.707241\pi$
$318$	5.51860	0.309468
$319$	−28.6783	−1.60568
$320$	8.42545	0.470997
$321$	2.22097	0.123963
$322$	66.3608	3.69814
$323$	−15.3998	−0.856868
$324$	19.0688	1.05938
$325$	−9.42729	−0.522932
$326$	−30.6982	−1.70022
$327$	6.52526	0.360848
$328$	47.9895	2.64978
$329$	−9.13851	−0.503822
$330$	16.4717	0.906740
$331$	19.4107	1.06691	0.533453	−	0.845830i	$-0.320894\pi$
$331$	19.4107	1.06691	0.533453	+	0.845830i	$0.320894\pi$
$332$	−0.120700	−0.00662426
$333$	0.959212	0.0525645
$334$	62.1926	3.40303
$335$	21.8957	1.19629
$336$	−33.5009	−1.82762
$337$	14.9979	0.816987	0.408494	−	0.912761i	$-0.366054\pi$
$337$	14.9979	0.816987	0.408494	+	0.912761i	$0.366054\pi$
$338$	−58.0073	−3.15518
$339$	−15.5618	−0.845202
$340$	51.6028	2.79856
$341$	7.35135	0.398098
$342$	−16.1712	−0.874438
$343$	−58.0591	−3.13490
$344$	21.1397	1.13978
$345$	7.19226	0.387218
$346$	27.1563	1.45993
$347$	−21.1969	−1.13791	−0.568955	−	0.822369i	$-0.692652\pi$
$347$	−21.1969	−1.13791	−0.568955	+	0.822369i	$0.692652\pi$
$348$	22.9551	1.23052
$349$	−23.6881	−1.26800	−0.633998	−	0.773335i	$-0.718587\pi$
$349$	−23.6881	−1.26800	−0.633998	+	0.773335i	$0.718587\pi$
$350$	−20.6982	−1.10636
$351$	−24.6826	−1.31746
$352$	38.0016	2.02549
$353$	−11.5168	−0.612976	−0.306488	−	0.951875i	$-0.599154\pi$
$353$	−11.5168	−0.612976	−0.306488	+	0.951875i	$0.599154\pi$
$354$	9.34052	0.496443
$355$	−10.9933	−0.583463
$356$	−11.5664	−0.613018
$357$	−23.0048	−1.21754
$358$	25.7490	1.36088
$359$	−8.13803	−0.429509	−0.214754	−	0.976668i	$-0.568895\pi$
$359$	−8.13803	−0.429509	−0.214754	+	0.976668i	$0.568895\pi$
$360$	31.1083	1.63955
$361$	−12.2919	−0.646940
$362$	59.7195	3.13879
$363$	7.05333	0.370204
$364$	−141.113	−7.39631
$365$	−9.91916	−0.519192
$366$	−22.2234	−1.16164
$367$	−3.28415	−0.171431	−0.0857156	−	0.996320i	$-0.527318\pi$
$367$	−3.28415	−0.171431	−0.0857156	+	0.996320i	$0.527318\pi$
$368$	43.9755	2.29238
$369$	16.5999	0.864155
$370$	1.90120	0.0988385
$371$	14.0549	0.729694
$372$	−5.88428	−0.305086
$373$	20.7088	1.07226	0.536131	−	0.844135i	$-0.319885\pi$
$373$	20.7088	1.07226	0.536131	+	0.844135i	$0.319885\pi$
$374$	69.1588	3.57612
$375$	−9.32399	−0.481489
$376$	−12.6242	−0.651045
$377$	37.9689	1.95550
$378$	−54.1921	−2.78734
$379$	−6.08202	−0.312412	−0.156206	−	0.987724i	$-0.549926\pi$
$379$	−6.08202	−0.312412	−0.156206	+	0.987724i	$0.549926\pi$
$380$	−22.4782	−1.15311
$381$	3.46428	0.177480
$382$	−61.6602	−3.15481
$383$	−31.1342	−1.59088	−0.795441	−	0.606031i	$-0.792761\pi$
$383$	−31.1342	−1.59088	−0.795441	+	0.606031i	$0.792761\pi$
$384$	3.91699	0.199888
$385$	41.9507	2.13800
$386$	49.7006	2.52970
$387$	7.31235	0.371708
$388$	55.3705	2.81101
$389$	13.6895	0.694087	0.347044	−	0.937849i	$-0.387186\pi$
$389$	13.6895	0.694087	0.347044	+	0.937849i	$0.387186\pi$
$390$	−21.8079	−1.10429
$391$	30.1977	1.52716
$392$	−129.034	−6.51720
$393$	4.22787	0.213268
$394$	18.3781	0.925876
$395$	−29.7235	−1.49555
$396$	50.9308	2.55937
$397$	12.8676	0.645805	0.322903	−	0.946432i	$-0.395341\pi$
$397$	12.8676	0.645805	0.322903	+	0.946432i	$0.395341\pi$
$398$	−34.2910	−1.71885
$399$	10.0209	0.501672
$400$	−13.7161	−0.685806
$401$	−22.9024	−1.14369	−0.571846	−	0.820361i	$-0.693772\pi$
$401$	−22.9024	−1.14369	−0.571846	+	0.820361i	$0.693772\pi$
$402$	−23.4887	−1.17151
$403$	−9.73288	−0.484829
$404$	48.3163	2.40383
$405$	7.50534	0.372943
$406$	83.3628	4.13723
$407$	1.78693	0.0885747
$408$	−31.7796	−1.57333
$409$	4.74393	0.234572	0.117286	−	0.993098i	$-0.462581\pi$
$409$	4.74393	0.234572	0.117286	+	0.993098i	$0.462581\pi$
$410$	32.9016	1.62490
$411$	−2.02956	−0.100111
$412$	−39.3956	−1.94088
$413$	23.7887	1.17056
$414$	31.7103	1.55848
$415$	−0.0475065	−0.00233200
$416$	−50.3125	−2.46677
$417$	11.0846	0.542815
$418$	−30.1255	−1.47349
$419$	−14.7035	−0.718314	−0.359157	−	0.933277i	$-0.616936\pi$
$419$	−14.7035	−0.718314	−0.359157	+	0.933277i	$0.616936\pi$
$420$	−33.5788	−1.63848
$421$	−24.5200	−1.19503	−0.597517	−	0.801857i	$-0.703846\pi$
$421$	−24.5200	−1.19503	−0.597517	+	0.801857i	$0.703846\pi$
$422$	−41.9157	−2.04042
$423$	−4.36681	−0.212321
$424$	19.4159	0.942920
$425$	−9.41876	−0.456877
$426$	11.7931	0.571377
$427$	−56.5992	−2.73903
$428$	13.6112	0.657922
$429$	−20.4972	−0.989612
$430$	14.4934	0.698933
$431$	26.4517	1.27414	0.637068	−	0.770808i	$-0.280147\pi$
$431$	26.4517	1.27414	0.637068	+	0.770808i	$0.280147\pi$
$432$	−35.9116	−1.72780
$433$	−22.5495	−1.08366	−0.541829	−	0.840489i	$-0.682268\pi$
$433$	−22.5495	−1.08366	−0.541829	+	0.840489i	$0.682268\pi$
$434$	−21.3691	−1.02575
$435$	9.03497	0.433193
$436$	39.9900	1.91517
$437$	−13.1541	−0.629245
$438$	10.6408	0.508437
$439$	−23.6058	−1.12664	−0.563321	−	0.826238i	$-0.690477\pi$
$439$	−23.6058	−1.12664	−0.563321	+	0.826238i	$0.690477\pi$
$440$	57.9520	2.76275
$441$	−44.6337	−2.12542
$442$	−91.5633	−4.35522
$443$	−33.9437	−1.61271	−0.806356	−	0.591430i	$-0.798563\pi$
$443$	−33.9437	−1.61271	−0.806356	+	0.591430i	$0.798563\pi$
$444$	−1.43032	−0.0678799
$445$	−4.55245	−0.215807
$446$	60.8430	2.88100
$447$	−2.26258	−0.107016
$448$	−23.0193	−1.08756
$449$	15.4000	0.726770	0.363385	−	0.931639i	$-0.381621\pi$
$449$	15.4000	0.726770	0.363385	+	0.931639i	$0.381621\pi$
$450$	−9.89055	−0.466245
$451$	30.9241	1.45616
$452$	−95.3704	−4.48585
$453$	2.55725	0.120150
$454$	24.7649	1.16227
$455$	−55.5409	−2.60380
$456$	13.8432	0.648267
$457$	−3.99425	−0.186843	−0.0934215	−	0.995627i	$-0.529780\pi$
$457$	−3.99425	−0.186843	−0.0934215	+	0.995627i	$0.529780\pi$
$458$	−25.6471	−1.19841
$459$	−24.6603	−1.15104
$460$	44.0777	2.05513
$461$	−29.3465	−1.36680	−0.683401	−	0.730044i	$-0.739500\pi$
$461$	−29.3465	−1.36680	−0.683401	+	0.730044i	$0.739500\pi$
$462$	−45.0027	−2.09371
$463$	42.1482	1.95879	0.979396	−	0.201948i	$-0.0647273\pi$
$463$	42.1482	1.95879	0.979396	+	0.201948i	$0.0647273\pi$
$464$	55.2423	2.56456
$465$	−2.31601	−0.107402
$466$	−16.5453	−0.766445
$467$	−34.7270	−1.60697	−0.803487	−	0.595323i	$-0.797024\pi$
$467$	−34.7270	−1.60697	−0.803487	+	0.595323i	$0.797024\pi$
$468$	−67.4302	−3.11696
$469$	−59.8215	−2.76230
$470$	−8.65519	−0.399234
$471$	−9.72715	−0.448203
$472$	32.8624	1.51262
$473$	13.6223	0.626353
$474$	31.8860	1.46457
$475$	4.10280	0.188249
$476$	−140.985	−6.46203
$477$	6.71609	0.307509
$478$	50.1806	2.29521
$479$	−1.66170	−0.0759252	−0.0379626	−	0.999279i	$-0.512087\pi$
$479$	−1.66170	−0.0759252	−0.0379626	+	0.999279i	$0.512087\pi$
$480$	−11.9722	−0.546455
$481$	−2.36582	−0.107872
$482$	27.3806	1.24715
$483$	−19.6501	−0.894110
$484$	43.2262	1.96483
$485$	21.7934	0.989587
$486$	−40.2476	−1.82567
$487$	−6.63744	−0.300771	−0.150385	−	0.988627i	$-0.548051\pi$
$487$	−6.63744	−0.300771	−0.150385	+	0.988627i	$0.548051\pi$
$488$	−78.1880	−3.53940
$489$	9.09005	0.411066
$490$	−88.4659	−3.99648
$491$	−17.7654	−0.801743	−0.400871	−	0.916134i	$-0.631293\pi$
$491$	−17.7654	−0.801743	−0.400871	+	0.916134i	$0.631293\pi$
$492$	−24.7527	−1.11594
$493$	37.9345	1.70848
$494$	39.8849	1.79451
$495$	20.0460	0.901000
$496$	−14.1607	−0.635835
$497$	30.0349	1.34725
$498$	0.0509628	0.00228370
$499$	−13.1513	−0.588734	−0.294367	−	0.955692i	$-0.595109\pi$
$499$	−13.1513	−0.588734	−0.294367	+	0.955692i	$0.595109\pi$
$500$	−57.1420	−2.55547
$501$	−18.4158	−0.822759
$502$	43.5111	1.94200
$503$	−12.7272	−0.567477	−0.283739	−	0.958902i	$-0.591575\pi$
$503$	−12.7272	−0.567477	−0.283739	+	0.958902i	$0.591575\pi$
$504$	−84.9914	−3.78582
$505$	19.0170	0.846243
$506$	59.0735	2.62614
$507$	17.1765	0.762836
$508$	21.2308	0.941963
$509$	18.4125	0.816118	0.408059	−	0.912955i	$-0.366206\pi$
$509$	18.4125	0.816118	0.408059	+	0.912955i	$0.366206\pi$
$510$	−21.7881	−0.964795
$511$	27.1003	1.19885
$512$	47.5975	2.10353
$513$	10.7420	0.474270
$514$	21.8503	0.963774
$515$	−15.5058	−0.683268
$516$	−10.9037	−0.480011
$517$	−8.13498	−0.357776
$518$	−5.19429	−0.228224
$519$	−8.04126	−0.352972
$520$	−76.7260	−3.36466
$521$	39.5624	1.73326	0.866630	−	0.498952i	$-0.166282\pi$
$521$	39.5624	1.73326	0.866630	+	0.498952i	$0.166282\pi$
$522$	39.8347	1.74352
$523$	−30.7335	−1.34388	−0.671941	−	0.740605i	$-0.734539\pi$
$523$	−30.7335	−1.34388	−0.671941	+	0.740605i	$0.734539\pi$
$524$	25.9104	1.13190
$525$	6.12893	0.267488
$526$	−11.7789	−0.513586
$527$	−9.72407	−0.423587
$528$	−29.8221	−1.29784
$529$	2.79400	0.121478
$530$	13.3116	0.578217
$531$	11.3673	0.493300
$532$	61.4129	2.66259
$533$	−40.9422	−1.77340
$534$	4.88365	0.211336
$535$	5.35727	0.231615
$536$	−82.6394	−3.56948
$537$	−7.62453	−0.329023
$538$	82.7834	3.56904
$539$	−83.1487	−3.58147
$540$	−35.9951	−1.54898
$541$	3.56507	0.153274	0.0766371	−	0.997059i	$-0.475582\pi$
$541$	3.56507	0.153274	0.0766371	+	0.997059i	$0.475582\pi$
$542$	49.5750	2.12943
$543$	−17.6835	−0.758874
$544$	−50.2670	−2.15518
$545$	15.7398	0.674217
$546$	59.5817	2.54986
$547$	19.7788	0.845678	0.422839	−	0.906205i	$-0.361034\pi$
$547$	19.7788	0.845678	0.422839	+	0.906205i	$0.361034\pi$
$548$	−12.4381	−0.531331
$549$	−27.0457	−1.15428
$550$	−18.4252	−0.785655
$551$	−16.5242	−0.703956
$552$	−27.1453	−1.15538
$553$	81.2081	3.45332
$554$	12.9065	0.548346
$555$	−0.562963	−0.0238964
$556$	67.9318	2.88095
$557$	−19.7703	−0.837694	−0.418847	−	0.908057i	$-0.637566\pi$
$557$	−19.7703	−0.837694	−0.418847	+	0.908057i	$0.637566\pi$
$558$	−10.2112	−0.432273
$559$	−18.0353	−0.762813
$560$	−80.8085	−3.41478
$561$	−20.4786	−0.864607
$562$	−62.9443	−2.65515
$563$	−5.67918	−0.239349	−0.119674	−	0.992813i	$-0.538185\pi$
$563$	−5.67918	−0.239349	−0.119674	+	0.992813i	$0.538185\pi$
$564$	6.51152	0.274184
$565$	−37.5371	−1.57920
$566$	−1.94137	−0.0816017
$567$	−20.5055	−0.861148
$568$	41.4913	1.74093
$569$	18.0978	0.758701	0.379350	−	0.925253i	$-0.376147\pi$
$569$	18.0978	0.758701	0.379350	+	0.925253i	$0.376147\pi$
$570$	9.49090	0.397530
$571$	43.1172	1.80440	0.902200	−	0.431318i	$-0.141951\pi$
$571$	43.1172	1.80440	0.902200	+	0.431318i	$0.141951\pi$
$572$	−125.617	−5.25229
$573$	18.2582	0.762746
$574$	−89.8910	−3.75198
$575$	−8.04524	−0.335510
$576$	−10.9997	−0.458321
$577$	21.7848	0.906914	0.453457	−	0.891278i	$-0.350191\pi$
$577$	21.7848	0.906914	0.453457	+	0.891278i	$0.350191\pi$
$578$	−47.4909	−1.97536
$579$	−14.7168	−0.611611
$580$	55.3707	2.29914
$581$	0.129793	0.00538473
$582$	−23.3789	−0.969088
$583$	12.5115	0.518173
$584$	37.4372	1.54916
$585$	−26.5400	−1.09730
$586$	−36.0428	−1.48891
$587$	22.6747	0.935886	0.467943	−	0.883759i	$-0.344995\pi$
$587$	22.6747	0.935886	0.467943	+	0.883759i	$0.344995\pi$
$588$	66.5551	2.74469
$589$	4.23580	0.174533
$590$	22.5305	0.927567
$591$	−5.44194	−0.223851
$592$	−3.44211	−0.141470
$593$	−18.9771	−0.779296	−0.389648	−	0.920964i	$-0.627403\pi$
$593$	−18.9771	−0.779296	−0.389648	+	0.920964i	$0.627403\pi$
$594$	−48.2411	−1.97936
$595$	−55.4906	−2.27489
$596$	−13.8662	−0.567980
$597$	10.1539	0.415571
$598$	−78.2108	−3.19828
$599$	−25.6169	−1.04668	−0.523339	−	0.852125i	$-0.675314\pi$
$599$	−25.6169	−1.04668	−0.523339	+	0.852125i	$0.675314\pi$
$600$	8.46671	0.345652
$601$	12.9796	0.529449	0.264724	−	0.964324i	$-0.414719\pi$
$601$	12.9796	0.529449	0.264724	+	0.964324i	$0.414719\pi$
$602$	−39.5976	−1.61388
$603$	−28.5855	−1.16409
$604$	15.6721	0.637687
$605$	17.0135	0.691698
$606$	−20.4005	−0.828713
$607$	13.2246	0.536768	0.268384	−	0.963312i	$-0.413510\pi$
$607$	13.2246	0.536768	0.268384	+	0.963312i	$0.413510\pi$
$608$	21.8962	0.888010
$609$	−24.6846	−1.00027
$610$	−53.6057	−2.17043
$611$	10.7704	0.435723
$612$	−67.3692	−2.72324
$613$	42.9124	1.73322	0.866608	−	0.498989i	$-0.166295\pi$
$613$	42.9124	1.73322	0.866608	+	0.498989i	$0.166295\pi$
$614$	10.4427	0.421433
$615$	−9.74250	−0.392855
$616$	−158.332	−6.37936
$617$	−28.5801	−1.15059	−0.575295	−	0.817946i	$-0.695113\pi$
$617$	−28.5801	−1.15059	−0.575295	+	0.817946i	$0.695113\pi$
$618$	16.6339	0.669114
$619$	45.8167	1.84153	0.920764	−	0.390120i	$-0.127567\pi$
$619$	45.8167	1.84153	0.920764	+	0.390120i	$0.127567\pi$
$620$	−14.1936	−0.570030
$621$	−21.0641	−0.845273
$622$	41.8306	1.67725
$623$	12.4378	0.498310
$624$	39.4831	1.58059
$625$	−14.5702	−0.582809
$626$	29.5243	1.18003
$627$	8.92046	0.356249
$628$	−59.6127	−2.37881
$629$	−2.36367	−0.0942459
$630$	−58.2702	−2.32154
$631$	−24.9912	−0.994883	−0.497441	−	0.867498i	$-0.665727\pi$
$631$	−24.9912	−0.994883	−0.497441	+	0.867498i	$0.665727\pi$
$632$	112.184	4.46242
$633$	12.4117	0.493319
$634$	55.8416	2.21775
$635$	8.35628	0.331609
$636$	−10.0146	−0.397106
$637$	110.085	4.36174
$638$	74.2085	2.93794
$639$	14.3521	0.567760
$640$	9.44828	0.373476
$641$	−13.6363	−0.538600	−0.269300	−	0.963056i	$-0.586792\pi$
$641$	−13.6363	−0.538600	−0.269300	+	0.963056i	$0.586792\pi$
$642$	−5.74702	−0.226817
$643$	19.4148	0.765646	0.382823	−	0.923822i	$-0.374952\pi$
$643$	19.4148	0.765646	0.382823	+	0.923822i	$0.374952\pi$
$644$	−120.425	−4.74542
$645$	−4.29163	−0.168983
$646$	39.8488	1.56783
$647$	−33.1636	−1.30380	−0.651898	−	0.758307i	$-0.726027\pi$
$647$	−33.1636	−1.30380	−0.651898	+	0.758307i	$0.726027\pi$
$648$	−28.3269	−1.11279
$649$	21.1764	0.831245
$650$	24.3942	0.956820
$651$	6.32760	0.247998
$652$	55.7083	2.18171
$653$	32.6631	1.27821	0.639104	−	0.769120i	$-0.279305\pi$
$653$	32.6631	1.27821	0.639104	+	0.769120i	$0.279305\pi$
$654$	−16.8849	−0.660251
$655$	10.1982	0.398475
$656$	−59.5683	−2.32575
$657$	12.9498	0.505219
$658$	23.6470	0.921855
$659$	29.2818	1.14066	0.570329	−	0.821417i	$-0.306816\pi$
$659$	29.2818	1.14066	0.570329	+	0.821417i	$0.306816\pi$
$660$	−29.8914	−1.16352
$661$	−12.1162	−0.471264	−0.235632	−	0.971842i	$-0.575716\pi$
$661$	−12.1162	−0.471264	−0.235632	+	0.971842i	$0.575716\pi$
$662$	−50.2274	−1.95214
$663$	27.1128	1.05297
$664$	0.179301	0.00695822
$665$	24.1717	0.937337
$666$	−2.48207	−0.0961784
$667$	32.4026	1.25463
$668$	−112.861	−4.36673
$669$	−18.0162	−0.696547
$670$	−56.6577	−2.18888
$671$	−50.3838	−1.94505
$672$	32.7095	1.26180
$673$	−19.7654	−0.761901	−0.380950	−	0.924596i	$-0.624403\pi$
$673$	−19.7654	−0.761901	−0.380950	+	0.924596i	$0.624403\pi$
$674$	−38.8088	−1.49486
$675$	6.56997	0.252878
$676$	105.266	4.04870
$677$	−5.95906	−0.229025	−0.114513	−	0.993422i	$-0.536531\pi$
$677$	−5.95906	−0.229025	−0.114513	+	0.993422i	$0.536531\pi$
$678$	40.2680	1.54648
$679$	−59.5421	−2.28501
$680$	−76.6566	−2.93964
$681$	−7.33313	−0.281006
$682$	−19.0225	−0.728409
$683$	−29.3246	−1.12208	−0.561038	−	0.827790i	$-0.689598\pi$
$683$	−29.3246	−1.12208	−0.561038	+	0.827790i	$0.689598\pi$
$684$	29.3460	1.12207
$685$	−4.89556	−0.187050
$686$	150.235	5.73599
$687$	7.59437	0.289743
$688$	−26.2402	−1.00040
$689$	−16.5647	−0.631064
$690$	−18.6108	−0.708502
$691$	14.6338	0.556697	0.278349	−	0.960480i	$-0.410213\pi$
$691$	14.6338	0.556697	0.278349	+	0.960480i	$0.410213\pi$
$692$	−49.2808	−1.87337
$693$	−54.7679	−2.08046
$694$	54.8495	2.08206
$695$	26.7375	1.01421
$696$	−34.1001	−1.29256
$697$	−40.9052	−1.54939
$698$	61.2958	2.32008
$699$	4.89922	0.185305
$700$	37.5611	1.41968
$701$	31.4420	1.18755	0.593773	−	0.804632i	$-0.297638\pi$
$701$	31.4420	1.18755	0.593773	+	0.804632i	$0.297638\pi$
$702$	63.8691	2.41059
$703$	1.02961	0.0388327
$704$	−20.4915	−0.772302
$705$	2.56289	0.0965239
$706$	29.8010	1.12158
$707$	−51.9565	−1.95402
$708$	−16.9503	−0.637031
$709$	−15.3996	−0.578345	−0.289172	−	0.957277i	$-0.593380\pi$
$709$	−15.3996	−0.578345	−0.289172	+	0.957277i	$0.593380\pi$
$710$	28.4464	1.06758
$711$	38.8050	1.45530
$712$	17.1820	0.643923
$713$	−8.30603	−0.311063
$714$	59.5277	2.22777
$715$	−49.4418	−1.84902
$716$	−46.7269	−1.74627
$717$	−14.8590	−0.554918
$718$	21.0581	0.785882
$719$	−20.4106	−0.761186	−0.380593	−	0.924743i	$-0.624280\pi$
$719$	−20.4106	−0.761186	−0.380593	+	0.924743i	$0.624280\pi$
$720$	−38.6141	−1.43906
$721$	42.3637	1.57771
$722$	31.8066	1.18372
$723$	−8.10768	−0.301528
$724$	−108.373	−4.02767
$725$	−10.1065	−0.375345
$726$	−18.2513	−0.677370
$727$	−43.4520	−1.61154	−0.805772	−	0.592226i	$-0.798249\pi$
$727$	−43.4520	−1.61154	−0.805772	+	0.592226i	$0.798249\pi$
$728$	209.624	7.76919
$729$	−0.264847	−0.00980915
$730$	25.6670	0.949978
$731$	−18.0190	−0.666456
$732$	40.3290	1.49060
$733$	−22.9809	−0.848818	−0.424409	−	0.905471i	$-0.639518\pi$
$733$	−22.9809	−0.848818	−0.424409	+	0.905471i	$0.639518\pi$
$734$	8.49812	0.313671
$735$	26.1956	0.966240
$736$	−42.9366	−1.58267
$737$	−53.2523	−1.96157
$738$	−42.9541	−1.58116
$739$	−14.9032	−0.548224	−0.274112	−	0.961698i	$-0.588384\pi$
$739$	−14.9032	−0.548224	−0.274112	+	0.961698i	$0.588384\pi$
$740$	−3.45011	−0.126829
$741$	−11.8103	−0.433863
$742$	−36.3687	−1.33514
$743$	4.41987	0.162149	0.0810747	−	0.996708i	$-0.474165\pi$
$743$	4.41987	0.162149	0.0810747	+	0.996708i	$0.474165\pi$
$744$	8.74116	0.320466
$745$	−5.45762	−0.199952
$746$	−53.5865	−1.96194
$747$	0.0620213	0.00226924
$748$	−125.503	−4.58884
$749$	−14.6367	−0.534812
$750$	24.1269	0.880991
$751$	15.2773	0.557478	0.278739	−	0.960367i	$-0.410084\pi$
$751$	15.2773	0.557478	0.278739	+	0.960367i	$0.410084\pi$
$752$	15.6702	0.571434
$753$	−12.8841	−0.469521
$754$	−98.2489	−3.57801
$755$	6.16841	0.224491
$756$	98.3427	3.57669
$757$	17.8436	0.648538	0.324269	−	0.945965i	$-0.394882\pi$
$757$	17.8436	0.648538	0.324269	+	0.945965i	$0.394882\pi$
$758$	15.7379	0.571628
$759$	−17.4922	−0.634928
$760$	33.3915	1.21124
$761$	36.3083	1.31617	0.658087	−	0.752942i	$-0.271366\pi$
$761$	36.3083	1.31617	0.658087	+	0.752942i	$0.271366\pi$
$762$	−8.96422	−0.324739
$763$	−43.0028	−1.55681
$764$	111.895	4.04822
$765$	−26.5160	−0.958688
$766$	80.5633	2.91087
$767$	−28.0366	−1.01234
$768$	−17.1216	−0.617822
$769$	−11.8439	−0.427101	−0.213551	−	0.976932i	$-0.568503\pi$
$769$	−11.8439	−0.427101	−0.213551	+	0.976932i	$0.568503\pi$
$770$	−108.552	−3.91195
$771$	−6.47008	−0.233014
$772$	−90.1920	−3.24608
$773$	−40.8618	−1.46970	−0.734849	−	0.678231i	$-0.762747\pi$
$773$	−40.8618	−1.46970	−0.734849	+	0.678231i	$0.762747\pi$
$774$	−18.9216	−0.680122
$775$	2.59068	0.0930599
$776$	−82.2534	−2.95272
$777$	1.53808	0.0551783
$778$	−35.4233	−1.26999
$779$	17.8183	0.638405
$780$	39.5749	1.41701
$781$	26.7367	0.956715
$782$	−78.1400	−2.79428
$783$	−26.4609	−0.945634
$784$	160.167	5.72026
$785$	−23.4631	−0.837435
$786$	−10.9401	−0.390221
$787$	50.9887	1.81755	0.908776	−	0.417284i	$-0.137018\pi$
$787$	50.9887	1.81755	0.908776	+	0.417284i	$0.137018\pi$
$788$	−33.3509	−1.18808
$789$	3.48786	0.124171
$790$	76.9131	2.73645
$791$	102.556	3.64646
$792$	−75.6582	−2.68840
$793$	66.7061	2.36880
$794$	−33.2964	−1.18164
$795$	−3.94169	−0.139797
$796$	62.2280	2.20561
$797$	1.67963	0.0594955	0.0297477	−	0.999557i	$-0.490530\pi$
$797$	1.67963	0.0594955	0.0297477	+	0.999557i	$0.490530\pi$
$798$	−25.9302	−0.917920
$799$	10.7606	0.380683
$800$	13.3921	0.473482
$801$	5.94337	0.209999
$802$	59.2627	2.09264
$803$	24.1243	0.851328
$804$	42.6250	1.50327
$805$	−47.3985	−1.67058
$806$	25.1850	0.887103
$807$	−24.5130	−0.862897
$808$	−71.7744	−2.52501
$809$	−36.7198	−1.29100	−0.645500	−	0.763760i	$-0.723351\pi$
$809$	−36.7198	−1.29100	−0.645500	+	0.763760i	$0.723351\pi$
$810$	−19.4210	−0.682383
$811$	43.2016	1.51701	0.758507	−	0.651665i	$-0.225929\pi$
$811$	43.2016	1.51701	0.758507	+	0.651665i	$0.225929\pi$
$812$	−151.279	−5.30885
$813$	−14.6796	−0.514837
$814$	−4.62389	−0.162067
$815$	21.9264	0.768047
$816$	39.4474	1.38094
$817$	7.84906	0.274604
$818$	−12.2755	−0.429202
$819$	72.5104	2.53372
$820$	−59.7068	−2.08505
$821$	6.10920	0.213212	0.106606	−	0.994301i	$-0.466002\pi$
$821$	6.10920	0.213212	0.106606	+	0.994301i	$0.466002\pi$
$822$	5.25172	0.183175
$823$	−3.82763	−0.133423	−0.0667113	−	0.997772i	$-0.521251\pi$
$823$	−3.82763	−0.133423	−0.0667113	+	0.997772i	$0.521251\pi$
$824$	58.5226	2.03873
$825$	5.45589	0.189950
$826$	−61.5560	−2.14181
$827$	−5.27275	−0.183352	−0.0916758	−	0.995789i	$-0.529222\pi$
$827$	−5.27275	−0.183352	−0.0916758	+	0.995789i	$0.529222\pi$
$828$	−57.5449	−1.99982
$829$	−22.5151	−0.781982	−0.390991	−	0.920395i	$-0.627868\pi$
$829$	−22.5151	−0.781982	−0.390991	+	0.920395i	$0.627868\pi$
$830$	0.122929	0.00426692
$831$	−3.82175	−0.132575
$832$	27.1299	0.940558
$833$	109.986	3.81078
$834$	−28.6827	−0.993201
$835$	−44.4214	−1.53726
$836$	54.6690	1.89077
$837$	6.78293	0.234452
$838$	38.0471	1.31432
$839$	−34.3175	−1.18477	−0.592386	−	0.805654i	$-0.701814\pi$
$839$	−34.3175	−1.18477	−0.592386	+	0.805654i	$0.701814\pi$
$840$	49.8816	1.72108
$841$	11.7043	0.403598
$842$	63.4485	2.18658
$843$	18.6384	0.641942
$844$	76.0647	2.61825
$845$	41.4320	1.42530
$846$	11.2996	0.388489
$847$	−46.4829	−1.59717
$848$	−24.1006	−0.827617
$849$	0.574858	0.0197291
$850$	24.3721	0.835957
$851$	−2.01898	−0.0692099
$852$	−21.4010	−0.733186
$853$	−17.1442	−0.587008	−0.293504	−	0.955958i	$-0.594821\pi$
$853$	−17.1442	−0.587008	−0.293504	+	0.955958i	$0.594821\pi$
$854$	146.457	5.01166
$855$	11.5504	0.395014
$856$	−20.2196	−0.691091
$857$	18.4468	0.630130	0.315065	−	0.949070i	$-0.397974\pi$
$857$	18.4468	0.630130	0.315065	+	0.949070i	$0.397974\pi$
$858$	53.0388	1.81072
$859$	22.8708	0.780341	0.390171	−	0.920743i	$-0.372416\pi$
$859$	22.8708	0.780341	0.390171	+	0.920743i	$0.372416\pi$
$860$	−26.3012	−0.896864
$861$	26.6176	0.907126
$862$	−68.4470	−2.33131
$863$	29.9703	1.02020	0.510101	−	0.860115i	$-0.329608\pi$
$863$	29.9703	1.02020	0.510101	+	0.860115i	$0.329608\pi$
$864$	35.0633	1.19288
$865$	−19.3965	−0.659502
$866$	58.3494	1.98279
$867$	14.0625	0.477588
$868$	38.7786	1.31623
$869$	72.2904	2.45228
$870$	−23.3790	−0.792624
$871$	70.5038	2.38893
$872$	−59.4055	−2.01172
$873$	−28.4520	−0.962954
$874$	34.0377	1.15134
$875$	61.4471	2.07729
$876$	−19.3099	−0.652422
$877$	−1.15505	−0.0390031	−0.0195016	−	0.999810i	$-0.506208\pi$
$877$	−1.15505	−0.0390031	−0.0195016	+	0.999810i	$0.506208\pi$
$878$	61.0828	2.06144
$879$	10.6726	0.359979
$880$	−71.9346	−2.42492
$881$	−34.2596	−1.15424	−0.577118	−	0.816661i	$-0.695823\pi$
$881$	−34.2596	−1.15424	−0.577118	+	0.816661i	$0.695823\pi$
$882$	115.495	3.88892
$883$	50.3106	1.69309	0.846543	−	0.532320i	$-0.178680\pi$
$883$	50.3106	1.69309	0.846543	+	0.532320i	$0.178680\pi$
$884$	166.160	5.58858
$885$	−6.67151	−0.224260
$886$	87.8332	2.95081
$887$	51.3685	1.72478	0.862392	−	0.506240i	$-0.168965\pi$
$887$	51.3685	1.72478	0.862392	+	0.506240i	$0.168965\pi$
$888$	2.12475	0.0713021
$889$	−22.8303	−0.765704
$890$	11.7800	0.394866
$891$	−18.2537	−0.611522
$892$	−110.412	−3.69687
$893$	−4.68732	−0.156855
$894$	5.85468	0.195810
$895$	−18.3914	−0.614755
$896$	−25.8138	−0.862378
$897$	23.1590	0.773256
$898$	−39.8492	−1.32979
$899$	−10.4341	−0.347996
$900$	17.9484	0.598281
$901$	−16.5497	−0.551350
$902$	−80.0198	−2.66437
$903$	11.7252	0.390191
$904$	141.674	4.71200
$905$	−42.6550	−1.41790
$906$	−6.61718	−0.219841
$907$	−16.7231	−0.555282	−0.277641	−	0.960685i	$-0.589553\pi$
$907$	−16.7231	−0.555282	−0.277641	+	0.960685i	$0.589553\pi$
$908$	−44.9410	−1.49142
$909$	−24.8272	−0.823468
$910$	143.719	4.76422
$911$	37.5732	1.24486	0.622428	−	0.782677i	$-0.286146\pi$
$911$	37.5732	1.24486	0.622428	+	0.782677i	$0.286146\pi$
$912$	−17.1833	−0.568994
$913$	0.115540	0.00382383
$914$	10.3356	0.341871
$915$	15.8732	0.524751
$916$	46.5420	1.53779
$917$	−27.8625	−0.920102
$918$	63.8113	2.10609
$919$	49.0002	1.61637	0.808184	−	0.588931i	$-0.200451\pi$
$919$	49.0002	1.61637	0.808184	+	0.588931i	$0.200451\pi$
$920$	−65.4779	−2.15874
$921$	−3.09219	−0.101891
$922$	75.9374	2.50087
$923$	−35.3983	−1.16515
$924$	81.6667	2.68664
$925$	0.629728	0.0207053
$926$	−109.063	−3.58405
$927$	20.2433	0.664879
$928$	−53.9373	−1.77058
$929$	−19.4990	−0.639741	−0.319870	−	0.947461i	$-0.603639\pi$
$929$	−19.4990	−0.639741	−0.319870	+	0.947461i	$0.603639\pi$
$930$	5.99294	0.196516
$931$	−47.9097	−1.57018
$932$	30.0248	0.983495
$933$	−12.3864	−0.405514
$934$	89.8602	2.94031
$935$	−49.3970	−1.61546
$936$	100.168	3.27410
$937$	−56.5182	−1.84637	−0.923185	−	0.384355i	$-0.874424\pi$
$937$	−56.5182	−1.84637	−0.923185	+	0.384355i	$0.874424\pi$
$938$	154.795	5.05424
$939$	−8.74243	−0.285298
$940$	15.7066	0.512294
$941$	30.8643	1.00615	0.503074	−	0.864243i	$-0.332202\pi$
$941$	30.8643	1.00615	0.503074	+	0.864243i	$0.332202\pi$
$942$	25.1701	0.820087
$943$	−34.9400	−1.13780
$944$	−40.7915	−1.32765
$945$	38.7070	1.25914
$946$	−35.2492	−1.14605
$947$	−14.2544	−0.463205	−0.231602	−	0.972811i	$-0.574397\pi$
$947$	−14.2544	−0.463205	−0.231602	+	0.972811i	$0.574397\pi$
$948$	−57.8637	−1.87933
$949$	−31.9396	−1.03680
$950$	−10.6165	−0.344444
$951$	−16.5353	−0.536192
$952$	209.434	6.78781
$953$	2.97643	0.0964159	0.0482079	−	0.998837i	$-0.484649\pi$
$953$	2.97643	0.0964159	0.0482079	+	0.998837i	$0.484649\pi$
$954$	−17.3787	−0.562655
$955$	44.0411	1.42514
$956$	−91.0630	−2.94519
$957$	−21.9739	−0.710314
$958$	4.29986	0.138922
$959$	13.3752	0.431909
$960$	6.45574	0.208358
$961$	−28.3253	−0.913721
$962$	6.12183	0.197376
$963$	−6.99408	−0.225381
$964$	−49.6878	−1.60034
$965$	−35.4989	−1.14275
$966$	50.8469	1.63597
$967$	16.6289	0.534751	0.267375	−	0.963592i	$-0.413844\pi$
$967$	16.6289	0.534751	0.267375	+	0.963592i	$0.413844\pi$
$968$	−64.2130	−2.06388
$969$	−11.7996	−0.379058
$970$	−56.3930	−1.81067
$971$	−58.6271	−1.88143	−0.940717	−	0.339193i	$-0.889846\pi$
$971$	−58.6271	−1.88143	−0.940717	+	0.339193i	$0.889846\pi$
$972$	73.0376	2.34268
$973$	−73.0498	−2.34187
$974$	17.1751	0.550327
$975$	−7.22337	−0.231333
$976$	97.0531	3.10659
$977$	−8.58363	−0.274615	−0.137307	−	0.990528i	$-0.543845\pi$
$977$	−8.58363	−0.274615	−0.137307	+	0.990528i	$0.543845\pi$
$978$	−23.5216	−0.752137
$979$	11.0720	0.353862
$980$	160.539	5.12825
$981$	−20.5488	−0.656071
$982$	45.9701	1.46697
$983$	−48.9536	−1.56138	−0.780689	−	0.624919i	$-0.785132\pi$
$983$	−48.9536	−1.56138	−0.780689	+	0.624919i	$0.785132\pi$
$984$	36.7705	1.17220
$985$	−13.1267	−0.418250
$986$	−98.1600	−3.12605
$987$	−7.00210	−0.222879
$988$	−72.3794	−2.30269
$989$	−15.3913	−0.489415
$990$	−51.8714	−1.64858
$991$	16.9560	0.538625	0.269313	−	0.963053i	$-0.413203\pi$
$991$	16.9560	0.538625	0.269313	+	0.963053i	$0.413203\pi$
$992$	13.8262	0.438982
$993$	14.8728	0.471975
$994$	−77.7189	−2.46509
$995$	24.4925	0.776464
$996$	−0.0924824	−0.00293042
$997$	28.6720	0.908052	0.454026	−	0.890988i	$-0.349987\pi$
$997$	28.6720	0.908052	0.454026	+	0.890988i	$0.349987\pi$
$998$	34.0306	1.07722
$999$	1.64876	0.0521644

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5077.2.a.b.1.15	✓	205

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5077.2.a.b.1.15	✓	205	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:	\( N \)	\(=\)	\( 5077 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5077.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58762 q^{2} +0.766219 q^{3} +4.69576 q^{4} +1.84822 q^{5} -1.98268 q^{6} -5.04954 q^{7} -6.97561 q^{8} -2.41291 q^{9} +O(q^{10})\)	\(q-2.58762 q^{2} +0.766219 q^{3} +4.69576 q^{4} +1.84822 q^{5} -1.98268 q^{6} -5.04954 q^{7} -6.97561 q^{8} -2.41291 q^{9} -4.78248 q^{10} -4.49504 q^{11} +3.59798 q^{12} +5.95124 q^{13} +13.0663 q^{14} +1.41614 q^{15} +8.65867 q^{16} +5.94585 q^{17} +6.24368 q^{18} -2.59001 q^{19} +8.67880 q^{20} -3.86906 q^{21} +11.6314 q^{22} +5.07878 q^{23} -5.34484 q^{24} -1.58409 q^{25} -15.3995 q^{26} -4.14747 q^{27} -23.7115 q^{28} +6.37999 q^{29} -3.66443 q^{30} -1.63544 q^{31} -8.45412 q^{32} -3.44418 q^{33} -15.3856 q^{34} -9.33266 q^{35} -11.3304 q^{36} -0.397533 q^{37} +6.70195 q^{38} +4.55995 q^{39} -12.8924 q^{40} -6.87961 q^{41} +10.0116 q^{42} -3.03051 q^{43} -21.1076 q^{44} -4.45958 q^{45} -13.1419 q^{46} +1.80977 q^{47} +6.63444 q^{48} +18.4979 q^{49} +4.09902 q^{50} +4.55582 q^{51} +27.9456 q^{52} -2.78340 q^{53} +10.7321 q^{54} -8.30781 q^{55} +35.2236 q^{56} -1.98451 q^{57} -16.5090 q^{58} -4.71105 q^{59} +6.64986 q^{60} +11.2088 q^{61} +4.23189 q^{62} +12.1841 q^{63} +4.55869 q^{64} +10.9992 q^{65} +8.91223 q^{66} +11.8469 q^{67} +27.9203 q^{68} +3.89146 q^{69} +24.1494 q^{70} -5.94805 q^{71} +16.8315 q^{72} -5.36688 q^{73} +1.02866 q^{74} -1.21376 q^{75} -12.1621 q^{76} +22.6979 q^{77} -11.7994 q^{78} -16.0823 q^{79} +16.0031 q^{80} +4.06085 q^{81} +17.8018 q^{82} -0.0257040 q^{83} -18.1682 q^{84} +10.9892 q^{85} +7.84181 q^{86} +4.88847 q^{87} +31.3556 q^{88} -2.46316 q^{89} +11.5397 q^{90} -30.0510 q^{91} +23.8488 q^{92} -1.25310 q^{93} -4.68299 q^{94} -4.78690 q^{95} -6.47771 q^{96} +11.7916 q^{97} -47.8655 q^{98} +10.8461 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9}+O(q^{10}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9} - 28 q^{10} - 83 q^{11} - 108 q^{12} - 36 q^{13} - 67 q^{14} - 63 q^{15} + 187 q^{16} - 72 q^{17} - 57 q^{18} - 47 q^{19} - 132 q^{20} - 35 q^{21} - 40 q^{22} - 97 q^{23} - 49 q^{24} + 175 q^{25} - 78 q^{26} - 227 q^{27} - 59 q^{28} - 46 q^{29} + 30 q^{30} - 77 q^{31} - 175 q^{32} - 74 q^{33} - 28 q^{34} - 171 q^{35} + 171 q^{36} - 52 q^{37} - 144 q^{38} - 54 q^{39} - 49 q^{40} - 107 q^{41} + 7 q^{42} - 58 q^{43} - 139 q^{44} - 89 q^{45} - 33 q^{46} - 255 q^{47} - 202 q^{48} + 171 q^{49} - 74 q^{50} - 63 q^{51} - 90 q^{52} - 82 q^{53} - 51 q^{54} - 70 q^{55} - 180 q^{56} - 70 q^{57} - 50 q^{58} - 289 q^{59} - 105 q^{60} - 20 q^{61} - 143 q^{62} - 119 q^{63} + 201 q^{64} - 92 q^{65} - 3 q^{66} - 138 q^{67} - 177 q^{68} - 67 q^{69} + 4 q^{70} - 141 q^{71} - 138 q^{72} - 71 q^{73} - 26 q^{74} - 251 q^{75} - 42 q^{76} - 149 q^{77} - 6 q^{78} - 47 q^{79} - 294 q^{80} + 193 q^{81} - 70 q^{82} - 329 q^{83} - 40 q^{84} - 45 q^{85} - 83 q^{86} - 139 q^{87} - 45 q^{88} - 163 q^{89} - 116 q^{90} - 141 q^{91} - 204 q^{92} - 91 q^{93} - 8 q^{94} - 173 q^{95} - 53 q^{96} - 147 q^{97} - 156 q^{98} - 157 q^{99}+O(q^{100}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9 - 28 * q^10 - 83 * q^11 - 108 * q^12 - 36 * q^13 - 67 * q^14 - 63 * q^15 + 187 * q^16 - 72 * q^17 - 57 * q^18 - 47 * q^19 - 132 * q^20 - 35 * q^21 - 40 * q^22 - 97 * q^23 - 49 * q^24 + 175 * q^25 - 78 * q^26 - 227 * q^27 - 59 * q^28 - 46 * q^29 + 30 * q^30 - 77 * q^31 - 175 * q^32 - 74 * q^33 - 28 * q^34 - 171 * q^35 + 171 * q^36 - 52 * q^37 - 144 * q^38 - 54 * q^39 - 49 * q^40 - 107 * q^41 + 7 * q^42 - 58 * q^43 - 139 * q^44 - 89 * q^45 - 33 * q^46 - 255 * q^47 - 202 * q^48 + 171 * q^49 - 74 * q^50 - 63 * q^51 - 90 * q^52 - 82 * q^53 - 51 * q^54 - 70 * q^55 - 180 * q^56 - 70 * q^57 - 50 * q^58 - 289 * q^59 - 105 * q^60 - 20 * q^61 - 143 * q^62 - 119 * q^63 + 201 * q^64 - 92 * q^65 - 3 * q^66 - 138 * q^67 - 177 * q^68 - 67 * q^69 + 4 * q^70 - 141 * q^71 - 138 * q^72 - 71 * q^73 - 26 * q^74 - 251 * q^75 - 42 * q^76 - 149 * q^77 - 6 * q^78 - 47 * q^79 - 294 * q^80 + 193 * q^81 - 70 * q^82 - 329 * q^83 - 40 * q^84 - 45 * q^85 - 83 * q^86 - 139 * q^87 - 45 * q^88 - 163 * q^89 - 116 * q^90 - 141 * q^91 - 204 * q^92 - 91 * q^93 - 8 * q^94 - 173 * q^95 - 53 * q^96 - 147 * q^97 - 156 * q^98 - 157 * q^99

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