LMFDB - Embedded newform 6023.2.a.b.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$1$
Dimension:	$99$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.31836 q^{2} -0.700819 q^{3} +3.37481 q^{4} -1.53243 q^{5} +1.62475 q^{6} +2.29352 q^{7} -3.18731 q^{8} -2.50885 q^{9} +O(q^{10})$	\(q-2.31836 q^{2} -0.700819 q^{3} +3.37481 q^{4} -1.53243 q^{5} +1.62475 q^{6} +2.29352 q^{7} -3.18731 q^{8} -2.50885 q^{9} +3.55272 q^{10} +3.05985 q^{11} -2.36513 q^{12} +4.49419 q^{13} -5.31722 q^{14} +1.07395 q^{15} +0.639730 q^{16} +5.90362 q^{17} +5.81643 q^{18} -1.00000 q^{19} -5.17165 q^{20} -1.60734 q^{21} -7.09385 q^{22} -3.12867 q^{23} +2.23373 q^{24} -2.65167 q^{25} -10.4192 q^{26} +3.86071 q^{27} +7.74020 q^{28} +6.50640 q^{29} -2.48982 q^{30} -3.82561 q^{31} +4.89150 q^{32} -2.14440 q^{33} -13.6867 q^{34} -3.51465 q^{35} -8.46690 q^{36} -11.3256 q^{37} +2.31836 q^{38} -3.14962 q^{39} +4.88433 q^{40} -2.44703 q^{41} +3.72641 q^{42} +5.67787 q^{43} +10.3264 q^{44} +3.84463 q^{45} +7.25339 q^{46} -5.21909 q^{47} -0.448335 q^{48} -1.73976 q^{49} +6.14753 q^{50} -4.13737 q^{51} +15.1671 q^{52} -3.78806 q^{53} -8.95053 q^{54} -4.68900 q^{55} -7.31017 q^{56} +0.700819 q^{57} -15.0842 q^{58} +0.392878 q^{59} +3.62439 q^{60} -10.2150 q^{61} +8.86916 q^{62} -5.75411 q^{63} -12.6197 q^{64} -6.88702 q^{65} +4.97150 q^{66} -8.40959 q^{67} +19.9236 q^{68} +2.19263 q^{69} +8.14825 q^{70} -3.94529 q^{71} +7.99650 q^{72} +10.2216 q^{73} +26.2568 q^{74} +1.85834 q^{75} -3.37481 q^{76} +7.01783 q^{77} +7.30196 q^{78} -6.51904 q^{79} -0.980340 q^{80} +4.82090 q^{81} +5.67311 q^{82} -3.59695 q^{83} -5.42448 q^{84} -9.04687 q^{85} -13.1634 q^{86} -4.55981 q^{87} -9.75271 q^{88} -5.40100 q^{89} -8.91326 q^{90} +10.3075 q^{91} -10.5587 q^{92} +2.68106 q^{93} +12.0998 q^{94} +1.53243 q^{95} -3.42806 q^{96} +6.82937 q^{97} +4.03340 q^{98} -7.67672 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9}+O(q^{10}) $ 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9} - 6 q^{10} - 9 q^{11} - 27 q^{12} - 28 q^{13} - 13 q^{14} - 10 q^{15} + 38 q^{16} - 36 q^{17} - 14 q^{18} - 99 q^{19} - 34 q^{20} - 20 q^{21} - 53 q^{22} - 38 q^{23} - 25 q^{24} - 8 q^{25} - 3 q^{26} - 3 q^{27} - 63 q^{28} - 34 q^{29} - 30 q^{30} - 16 q^{31} - 43 q^{32} - 41 q^{33} - 14 q^{34} - 25 q^{35} - 16 q^{36} - 80 q^{37} + 4 q^{38} - 48 q^{39} - 10 q^{40} - 32 q^{41} - 37 q^{42} - 76 q^{43} - 21 q^{44} - 53 q^{45} - 23 q^{46} - 31 q^{47} - 74 q^{48} - 32 q^{49} - 29 q^{50} - 30 q^{51} - 71 q^{52} - 35 q^{53} - 80 q^{54} - 45 q^{55} - 33 q^{56} + 3 q^{57} - 91 q^{58} + 12 q^{59} - 56 q^{60} - 61 q^{61} - 46 q^{62} - 43 q^{63} - 30 q^{64} - 46 q^{65} - 75 q^{66} - 26 q^{67} - 55 q^{68} - 45 q^{69} - 76 q^{70} - 41 q^{71} - 77 q^{72} - 143 q^{73} - 64 q^{74} - 8 q^{75} - 80 q^{76} - 58 q^{77} - 34 q^{78} - 22 q^{79} - 36 q^{80} - 81 q^{81} - 109 q^{82} - 7 q^{83} - 6 q^{84} - 80 q^{85} + 32 q^{86} - 57 q^{87} - 120 q^{88} - 28 q^{89} - 12 q^{90} - 30 q^{91} - 107 q^{92} - 121 q^{93} + 8 q^{94} + 15 q^{95} + 4 q^{96} - 128 q^{97} + 54 q^{98} - 34 q^{99}+O(q^{100}) \) 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9 - 6 * q^10 - 9 * q^11 - 27 * q^12 - 28 * q^13 - 13 * q^14 - 10 * q^15 + 38 * q^16 - 36 * q^17 - 14 * q^18 - 99 * q^19 - 34 * q^20 - 20 * q^21 - 53 * q^22 - 38 * q^23 - 25 * q^24 - 8 * q^25 - 3 * q^26 - 3 * q^27 - 63 * q^28 - 34 * q^29 - 30 * q^30 - 16 * q^31 - 43 * q^32 - 41 * q^33 - 14 * q^34 - 25 * q^35 - 16 * q^36 - 80 * q^37 + 4 * q^38 - 48 * q^39 - 10 * q^40 - 32 * q^41 - 37 * q^42 - 76 * q^43 - 21 * q^44 - 53 * q^45 - 23 * q^46 - 31 * q^47 - 74 * q^48 - 32 * q^49 - 29 * q^50 - 30 * q^51 - 71 * q^52 - 35 * q^53 - 80 * q^54 - 45 * q^55 - 33 * q^56 + 3 * q^57 - 91 * q^58 + 12 * q^59 - 56 * q^60 - 61 * q^61 - 46 * q^62 - 43 * q^63 - 30 * q^64 - 46 * q^65 - 75 * q^66 - 26 * q^67 - 55 * q^68 - 45 * q^69 - 76 * q^70 - 41 * q^71 - 77 * q^72 - 143 * q^73 - 64 * q^74 - 8 * q^75 - 80 * q^76 - 58 * q^77 - 34 * q^78 - 22 * q^79 - 36 * q^80 - 81 * q^81 - 109 * q^82 - 7 * q^83 - 6 * q^84 - 80 * q^85 + 32 * q^86 - 57 * q^87 - 120 * q^88 - 28 * q^89 - 12 * q^90 - 30 * q^91 - 107 * q^92 - 121 * q^93 + 8 * q^94 + 15 * q^95 + 4 * q^96 - 128 * q^97 + 54 * q^98 - 34 * 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 $

$2$	−2.31836	−1.63933	−0.819665	−	0.572843i	$-0.805841\pi$
$2$	−2.31836	−1.63933	−0.819665	+	0.572843i	$0.805841\pi$
$3$	−0.700819	−0.404618	−0.202309	−	0.979322i	$-0.564845\pi$
$3$	−0.700819	−0.404618	−0.202309	+	0.979322i	$0.564845\pi$
$4$	3.37481	1.68741
$5$	−1.53243	−0.685322	−0.342661	−	0.939459i	$-0.611328\pi$
$5$	−1.53243	−0.685322	−0.342661	+	0.939459i	$0.611328\pi$
$6$	1.62475	0.663303
$7$	2.29352	0.866870	0.433435	−	0.901185i	$-0.357301\pi$
$7$	2.29352	0.866870	0.433435	+	0.901185i	$0.357301\pi$
$8$	−3.18731	−1.12689
$9$	−2.50885	−0.836284
$10$	3.55272	1.12347
$11$	3.05985	0.922580	0.461290	−	0.887249i	$-0.347387\pi$
$11$	3.05985	0.922580	0.461290	+	0.887249i	$0.347387\pi$
$12$	−2.36513	−0.682755
$13$	4.49419	1.24646	0.623232	−	0.782037i	$-0.285819\pi$
$13$	4.49419	1.24646	0.623232	+	0.782037i	$0.285819\pi$
$14$	−5.31722	−1.42109
$15$	1.07395	0.277294
$16$	0.639730	0.159933
$17$	5.90362	1.43184	0.715919	−	0.698183i	$-0.246008\pi$
$17$	5.90362	1.43184	0.715919	+	0.698183i	$0.246008\pi$
$18$	5.81643	1.37095
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−5.17165	−1.15642
$21$	−1.60734	−0.350751
$22$	−7.09385	−1.51241
$23$	−3.12867	−0.652373	−0.326186	−	0.945306i	$-0.605764\pi$
$23$	−3.12867	−0.652373	−0.326186	+	0.945306i	$0.605764\pi$
$24$	2.23373	0.455958
$25$	−2.65167	−0.530333
$26$	−10.4192	−2.04337
$27$	3.86071	0.742994
$28$	7.74020	1.46276
$29$	6.50640	1.20821	0.604104	−	0.796906i	$-0.293531\pi$
$29$	6.50640	1.20821	0.604104	+	0.796906i	$0.293531\pi$
$30$	−2.48982	−0.454576
$31$	−3.82561	−0.687100	−0.343550	−	0.939134i	$-0.611629\pi$
$31$	−3.82561	−0.687100	−0.343550	+	0.939134i	$0.611629\pi$
$32$	4.89150	0.864703
$33$	−2.14440	−0.373292
$34$	−13.6867	−2.34726
$35$	−3.51465	−0.594085
$36$	−8.46690	−1.41115
$37$	−11.3256	−1.86192	−0.930958	−	0.365127i	$-0.881025\pi$
$37$	−11.3256	−1.86192	−0.930958	+	0.365127i	$0.881025\pi$
$38$	2.31836	0.376088
$39$	−3.14962	−0.504342
$40$	4.88433	0.772280
$41$	−2.44703	−0.382162	−0.191081	−	0.981574i	$-0.561199\pi$
$41$	−2.44703	−0.382162	−0.191081	+	0.981574i	$0.561199\pi$
$42$	3.72641	0.574997
$43$	5.67787	0.865866	0.432933	−	0.901426i	$-0.357479\pi$
$43$	5.67787	0.865866	0.432933	+	0.901426i	$0.357479\pi$
$44$	10.3264	1.55677
$45$	3.84463	0.573124
$46$	7.25339	1.06945
$47$	−5.21909	−0.761283	−0.380642	−	0.924723i	$-0.624297\pi$
$47$	−5.21909	−0.761283	−0.380642	+	0.924723i	$0.624297\pi$
$48$	−0.448335	−0.0647116
$49$	−1.73976	−0.248537
$50$	6.14753	0.869392
$51$	−4.13737	−0.579348
$52$	15.1671	2.10329
$53$	−3.78806	−0.520330	−0.260165	−	0.965564i	$-0.583777\pi$
$53$	−3.78806	−0.520330	−0.260165	+	0.965564i	$0.583777\pi$
$54$	−8.95053	−1.21801
$55$	−4.68900	−0.632264
$56$	−7.31017	−0.976863
$57$	0.700819	0.0928258
$58$	−15.0842	−1.98065
$59$	0.392878	0.0511484	0.0255742	−	0.999673i	$-0.491859\pi$
$59$	0.392878	0.0511484	0.0255742	+	0.999673i	$0.491859\pi$
$60$	3.62439	0.467907
$61$	−10.2150	−1.30789	−0.653946	−	0.756541i	$-0.726888\pi$
$61$	−10.2150	−1.30789	−0.653946	+	0.756541i	$0.726888\pi$
$62$	8.86916	1.12638
$63$	−5.75411	−0.724949
$64$	−12.6197	−1.57747
$65$	−6.88702	−0.854230
$66$	4.97150	0.611950
$67$	−8.40959	−1.02740	−0.513698	−	0.857971i	$-0.671725\pi$
$67$	−8.40959	−1.02740	−0.513698	+	0.857971i	$0.671725\pi$
$68$	19.9236	2.41609
$69$	2.19263	0.263962
$70$	8.14825	0.973902
$71$	−3.94529	−0.468220	−0.234110	−	0.972210i	$-0.575218\pi$
$71$	−3.94529	−0.468220	−0.234110	+	0.972210i	$0.575218\pi$
$72$	7.99650	0.942397
$73$	10.2216	1.19635	0.598174	−	0.801366i	$-0.295893\pi$
$73$	10.2216	1.19635	0.598174	+	0.801366i	$0.295893\pi$
$74$	26.2568	3.05229
$75$	1.85834	0.214583
$76$	−3.37481	−0.387117
$77$	7.01783	0.799756
$78$	7.30196	0.826784
$79$	−6.51904	−0.733449	−0.366724	−	0.930330i	$-0.619521\pi$
$79$	−6.51904	−0.733449	−0.366724	+	0.930330i	$0.619521\pi$
$80$	−0.980340	−0.109605
$81$	4.82090	0.535655
$82$	5.67311	0.626490
$83$	−3.59695	−0.394816	−0.197408	−	0.980321i	$-0.563252\pi$
$83$	−3.59695	−0.394816	−0.197408	+	0.980321i	$0.563252\pi$
$84$	−5.42448	−0.591859
$85$	−9.04687	−0.981271
$86$	−13.1634	−1.41944
$87$	−4.55981	−0.488863
$88$	−9.75271	−1.03964
$89$	−5.40100	−0.572505	−0.286253	−	0.958154i	$-0.592410\pi$
$89$	−5.40100	−0.572505	−0.286253	+	0.958154i	$0.592410\pi$
$90$	−8.91326	−0.939540
$91$	10.3075	1.08052
$92$	−10.5587	−1.10082
$93$	2.68106	0.278013
$94$	12.0998	1.24799
$95$	1.53243	0.157224
$96$	−3.42806	−0.349875
$97$	6.82937	0.693418	0.346709	−	0.937973i	$-0.387299\pi$
$97$	6.82937	0.693418	0.346709	+	0.937973i	$0.387299\pi$
$98$	4.03340	0.407435
$99$	−7.67672	−0.771539
$100$	−8.94888	−0.894888
$101$	−12.1014	−1.20413	−0.602067	−	0.798445i	$-0.705656\pi$
$101$	−12.1014	−1.20413	−0.602067	+	0.798445i	$0.705656\pi$
$102$	9.59193	0.949743
$103$	−2.21838	−0.218584	−0.109292	−	0.994010i	$-0.534858\pi$
$103$	−2.21838	−0.218584	−0.109292	+	0.994010i	$0.534858\pi$
$104$	−14.3244	−1.40462
$105$	2.46314	0.240378
$106$	8.78211	0.852993
$107$	9.70867	0.938573	0.469286	−	0.883046i	$-0.344511\pi$
$107$	9.70867	0.938573	0.469286	+	0.883046i	$0.344511\pi$
$108$	13.0292	1.25373
$109$	9.71772	0.930789	0.465394	−	0.885103i	$-0.345912\pi$
$109$	9.71772	0.930789	0.465394	+	0.885103i	$0.345912\pi$
$110$	10.8708	1.03649
$111$	7.93719	0.753365
$112$	1.46724	0.138641
$113$	−2.63095	−0.247499	−0.123750	−	0.992313i	$-0.539492\pi$
$113$	−2.63095	−0.247499	−0.123750	+	0.992313i	$0.539492\pi$
$114$	−1.62475	−0.152172
$115$	4.79446	0.447085
$116$	21.9579	2.03874
$117$	−11.2753	−1.04240
$118$	−0.910835	−0.0838492
$119$	13.5401	1.24122
$120$	−3.42303	−0.312478
$121$	−1.63731	−0.148847
$122$	23.6820	2.14407
$123$	1.71493	0.154630
$124$	−12.9107	−1.15942
$125$	11.7256	1.04877
$126$	13.3401	1.18843
$127$	8.42944	0.747992	0.373996	−	0.927430i	$-0.377987\pi$
$127$	8.42944	0.747992	0.373996	+	0.927430i	$0.377987\pi$
$128$	19.4741	1.72129
$129$	−3.97916	−0.350345
$130$	15.9666	1.40037
$131$	2.51858	0.220049	0.110025	−	0.993929i	$-0.464907\pi$
$131$	2.51858	0.220049	0.110025	+	0.993929i	$0.464907\pi$
$132$	−7.23695	−0.629896
$133$	−2.29352	−0.198874
$134$	19.4965	1.68424
$135$	−5.91626	−0.509190
$136$	−18.8167	−1.61352
$137$	−7.29735	−0.623455	−0.311727	−	0.950172i	$-0.600908\pi$
$137$	−7.29735	−0.623455	−0.311727	+	0.950172i	$0.600908\pi$
$138$	−5.08332	−0.432721
$139$	−13.3781	−1.13471	−0.567356	−	0.823473i	$-0.692034\pi$
$139$	−13.3781	−1.13471	−0.567356	+	0.823473i	$0.692034\pi$
$140$	−11.8613	−1.00246
$141$	3.65764	0.308029
$142$	9.14663	0.767568
$143$	13.7516	1.14996
$144$	−1.60499	−0.133749
$145$	−9.97058	−0.828012
$146$	−23.6974	−1.96121
$147$	1.21926	0.100563
$148$	−38.2217	−3.14181
$149$	−8.43854	−0.691312	−0.345656	−	0.938361i	$-0.612344\pi$
$149$	−8.43854	−0.691312	−0.345656	+	0.938361i	$0.612344\pi$
$150$	−4.30831	−0.351772
$151$	−5.81661	−0.473349	−0.236674	−	0.971589i	$-0.576057\pi$
$151$	−5.81661	−0.473349	−0.236674	+	0.971589i	$0.576057\pi$
$152$	3.18731	0.258525
$153$	−14.8113	−1.19742
$154$	−16.2699	−1.31107
$155$	5.86247	0.470885
$156$	−10.6294	−0.851030
$157$	−20.9298	−1.67038	−0.835189	−	0.549963i	$-0.814642\pi$
$157$	−20.9298	−1.67038	−0.835189	+	0.549963i	$0.814642\pi$
$158$	15.1135	1.20237
$159$	2.65475	0.210535
$160$	−7.49587	−0.592600
$161$	−7.17567	−0.565522
$162$	−11.1766	−0.878116
$163$	−4.08256	−0.319770	−0.159885	−	0.987136i	$-0.551112\pi$
$163$	−4.08256	−0.319770	−0.159885	+	0.987136i	$0.551112\pi$
$164$	−8.25827	−0.644862
$165$	3.28614	0.255826
$166$	8.33903	0.647234
$167$	6.90837	0.534586	0.267293	−	0.963615i	$-0.413871\pi$
$167$	6.90837	0.534586	0.267293	+	0.963615i	$0.413871\pi$
$168$	5.12311	0.395256
$169$	7.19777	0.553674
$170$	20.9739	1.60863
$171$	2.50885	0.191857
$172$	19.1617	1.46107
$173$	5.82970	0.443224	0.221612	−	0.975135i	$-0.428868\pi$
$173$	5.82970	0.443224	0.221612	+	0.975135i	$0.428868\pi$
$174$	10.5713	0.801408
$175$	−6.08165	−0.459730
$176$	1.95748	0.147551
$177$	−0.275337	−0.0206956
$178$	12.5215	0.938525
$179$	2.86225	0.213935	0.106967	−	0.994263i	$-0.465886\pi$
$179$	2.86225	0.213935	0.106967	+	0.994263i	$0.465886\pi$
$180$	12.9749	0.967093
$181$	−5.66425	−0.421021	−0.210510	−	0.977592i	$-0.567513\pi$
$181$	−5.66425	−0.421021	−0.210510	+	0.977592i	$0.567513\pi$
$182$	−23.8966	−1.77133
$183$	7.15885	0.529197
$184$	9.97205	0.735149
$185$	17.3556	1.27601
$186$	−6.21567	−0.455755
$187$	18.0642	1.32099
$188$	−17.6135	−1.28459
$189$	8.85462	0.644079
$190$	−3.55272	−0.257742
$191$	24.9685	1.80666	0.903328	−	0.428951i	$-0.141117\pi$
$191$	24.9685	1.80666	0.903328	+	0.428951i	$0.141117\pi$
$192$	8.84415	0.638272
$193$	−19.4338	−1.39887	−0.699437	−	0.714694i	$-0.746566\pi$
$193$	−19.4338	−1.39887	−0.699437	+	0.714694i	$0.746566\pi$
$194$	−15.8330	−1.13674
$195$	4.82656	0.345637
$196$	−5.87136	−0.419383
$197$	−2.03931	−0.145295	−0.0726476	−	0.997358i	$-0.523145\pi$
$197$	−2.03931	−0.145295	−0.0726476	+	0.997358i	$0.523145\pi$
$198$	17.7974	1.26481
$199$	−6.42980	−0.455796	−0.227898	−	0.973685i	$-0.573185\pi$
$199$	−6.42980	−0.455796	−0.227898	+	0.973685i	$0.573185\pi$
$200$	8.45170	0.597625
$201$	5.89360	0.415703
$202$	28.0555	1.97398
$203$	14.9226	1.04736
$204$	−13.9628	−0.977595
$205$	3.74990	0.261904
$206$	5.14302	0.358331
$207$	7.84937	0.545569
$208$	2.87507	0.199350
$209$	−3.05985	−0.211654
$210$	−5.71045	−0.394058
$211$	−24.2772	−1.67131	−0.835655	−	0.549254i	$-0.814912\pi$
$211$	−24.2772	−1.67131	−0.835655	+	0.549254i	$0.814912\pi$
$212$	−12.7840	−0.878008
$213$	2.76494	0.189450
$214$	−22.5082	−1.53863
$215$	−8.70092	−0.593398
$216$	−12.3053	−0.837269
$217$	−8.77412	−0.595626
$218$	−22.5292	−1.52587
$219$	−7.16350	−0.484064
$220$	−15.8245	−1.06689
$221$	26.5320	1.78474
$222$	−18.4013	−1.23501
$223$	0.762863	0.0510851	0.0255426	−	0.999674i	$-0.491869\pi$
$223$	0.762863	0.0510851	0.0255426	+	0.999674i	$0.491869\pi$
$224$	11.2188	0.749585
$225$	6.65264	0.443509
$226$	6.09951	0.405733
$227$	3.56301	0.236485	0.118243	−	0.992985i	$-0.462274\pi$
$227$	3.56301	0.236485	0.118243	+	0.992985i	$0.462274\pi$
$228$	2.36513	0.156635
$229$	12.7267	0.841003	0.420502	−	0.907292i	$-0.361854\pi$
$229$	12.7267	0.841003	0.420502	+	0.907292i	$0.361854\pi$
$230$	−11.1153	−0.732921
$231$	−4.91823	−0.323596
$232$	−20.7379	−1.36151
$233$	−6.19207	−0.405656	−0.202828	−	0.979214i	$-0.565013\pi$
$233$	−6.19207	−0.405656	−0.202828	+	0.979214i	$0.565013\pi$
$234$	26.1402	1.70884
$235$	7.99788	0.521724
$236$	1.32589	0.0863081
$237$	4.56866	0.296767
$238$	−31.3908	−2.03477
$239$	9.18512	0.594136	0.297068	−	0.954856i	$-0.403991\pi$
$239$	9.18512	0.594136	0.297068	+	0.954856i	$0.403991\pi$
$240$	0.687041	0.0443483
$241$	14.2719	0.919337	0.459668	−	0.888091i	$-0.347968\pi$
$241$	14.2719	0.919337	0.459668	+	0.888091i	$0.347968\pi$
$242$	3.79588	0.244009
$243$	−14.9607	−0.959730
$244$	−34.4736	−2.20695
$245$	2.66606	0.170328
$246$	−3.97582	−0.253489
$247$	−4.49419	−0.285959
$248$	12.1934	0.774283
$249$	2.52081	0.159750
$250$	−27.1843	−1.71928
$251$	−30.3128	−1.91332	−0.956662	−	0.291199i	$-0.905946\pi$
$251$	−30.3128	−1.91332	−0.956662	+	0.291199i	$0.905946\pi$
$252$	−19.4190	−1.22328
$253$	−9.57326	−0.601866
$254$	−19.5425	−1.22621
$255$	6.34022	0.397040
$256$	−19.9087	−1.24429
$257$	19.8252	1.23666	0.618331	−	0.785917i	$-0.287809\pi$
$257$	19.8252	1.23666	0.618331	+	0.785917i	$0.287809\pi$
$258$	9.22513	0.574332
$259$	−25.9755	−1.61404
$260$	−23.2424	−1.44143
$261$	−16.3236	−1.01040
$262$	−5.83899	−0.360734
$263$	20.4271	1.25959	0.629795	−	0.776762i	$-0.283139\pi$
$263$	20.4271	1.25959	0.629795	+	0.776762i	$0.283139\pi$
$264$	6.83488	0.420658
$265$	5.80493	0.356594
$266$	5.31722	0.326019
$267$	3.78513	0.231646
$268$	−28.3808	−1.73363
$269$	25.8858	1.57828	0.789142	−	0.614210i	$-0.210525\pi$
$269$	25.8858	1.57828	0.789142	+	0.614210i	$0.210525\pi$
$270$	13.7160	0.834731
$271$	12.4516	0.756378	0.378189	−	0.925728i	$-0.376547\pi$
$271$	12.4516	0.756378	0.378189	+	0.925728i	$0.376547\pi$
$272$	3.77673	0.228998
$273$	−7.22371	−0.437199
$274$	16.9179	1.02205
$275$	−8.11371	−0.489275
$276$	7.39972	0.445411
$277$	17.6739	1.06192	0.530960	−	0.847397i	$-0.321831\pi$
$277$	17.6739	1.06192	0.530960	+	0.847397i	$0.321831\pi$
$278$	31.0152	1.86017
$279$	9.59789	0.574611
$280$	11.2023	0.669466
$281$	−9.81644	−0.585599	−0.292800	−	0.956174i	$-0.594587\pi$
$281$	−9.81644	−0.585599	−0.292800	+	0.956174i	$0.594587\pi$
$282$	−8.47974	−0.504961
$283$	−23.5226	−1.39827	−0.699136	−	0.714988i	$-0.746432\pi$
$283$	−23.5226	−1.39827	−0.699136	+	0.714988i	$0.746432\pi$
$284$	−13.3146	−0.790078
$285$	−1.07395	−0.0636156
$286$	−31.8811	−1.88517
$287$	−5.61232	−0.331285
$288$	−12.2721	−0.723138
$289$	17.8527	1.05016
$290$	23.1154	1.35739
$291$	−4.78616	−0.280569
$292$	34.4960	2.01873
$293$	15.5363	0.907642	0.453821	−	0.891093i	$-0.350061\pi$
$293$	15.5363	0.907642	0.453821	+	0.891093i	$0.350061\pi$
$294$	−2.82668	−0.164855
$295$	−0.602057	−0.0350531
$296$	36.0982	2.09817
$297$	11.8132	0.685471
$298$	19.5636	1.13329
$299$	−14.0608	−0.813159
$300$	6.27154	0.362088
$301$	13.0223	0.750593
$302$	13.4850	0.775975
$303$	8.48090	0.487215
$304$	−0.639730	−0.0366911
$305$	15.6537	0.896328
$306$	34.3380	1.96297
$307$	13.1880	0.752680	0.376340	−	0.926482i	$-0.377182\pi$
$307$	13.1880	0.752680	0.376340	+	0.926482i	$0.377182\pi$
$308$	23.6839	1.34951
$309$	1.55469	0.0884430
$310$	−13.5913	−0.771936
$311$	27.7005	1.57075	0.785376	−	0.619019i	$-0.212470\pi$
$311$	27.7005	1.57075	0.785376	+	0.619019i	$0.212470\pi$
$312$	10.0388	0.568336
$313$	−9.85480	−0.557026	−0.278513	−	0.960432i	$-0.589842\pi$
$313$	−9.85480	−0.557026	−0.278513	+	0.960432i	$0.589842\pi$
$314$	48.5229	2.73830
$315$	8.81775	0.496824
$316$	−22.0005	−1.23763
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	−6.15467	−0.345137
$319$	19.9086	1.11467
$320$	19.3388	1.08107
$321$	−6.80402	−0.379763
$322$	16.6358	0.927077
$323$	−5.90362	−0.328486
$324$	16.2696	0.903868
$325$	−11.9171	−0.661042
$326$	9.46485	0.524210
$327$	−6.81036	−0.376614
$328$	7.79945	0.430653
$329$	−11.9701	−0.659933
$330$	−7.61847	−0.419383
$331$	−5.46716	−0.300502	−0.150251	−	0.988648i	$-0.548008\pi$
$331$	−5.46716	−0.300502	−0.150251	+	0.988648i	$0.548008\pi$
$332$	−12.1390	−0.666215
$333$	28.4142	1.55709
$334$	−16.0161	−0.876363
$335$	12.8871	0.704097
$336$	−1.02827	−0.0560965
$337$	2.32056	0.126409	0.0632045	−	0.998001i	$-0.479868\pi$
$337$	2.32056	0.126409	0.0632045	+	0.998001i	$0.479868\pi$
$338$	−16.6870	−0.907655
$339$	1.84382	0.100143
$340$	−30.5315	−1.65580
$341$	−11.7058	−0.633904
$342$	−5.81643	−0.314517
$343$	−20.0448	−1.08232
$344$	−18.0971	−0.975732
$345$	−3.36005	−0.180899
$346$	−13.5154	−0.726590
$347$	−31.1622	−1.67288	−0.836438	−	0.548061i	$-0.815366\pi$
$347$	−31.1622	−1.67288	−0.836438	+	0.548061i	$0.815366\pi$
$348$	−15.3885	−0.824910
$349$	−34.6400	−1.85424	−0.927119	−	0.374768i	$-0.877722\pi$
$349$	−34.6400	−1.85424	−0.927119	+	0.374768i	$0.877722\pi$
$350$	14.0995	0.753649
$351$	17.3508	0.926116
$352$	14.9673	0.797758
$353$	4.42746	0.235650	0.117825	−	0.993034i	$-0.462408\pi$
$353$	4.42746	0.235650	0.117825	+	0.993034i	$0.462408\pi$
$354$	0.638331	0.0339269
$355$	6.04587	0.320882
$356$	−18.2274	−0.966048
$357$	−9.48915	−0.502219
$358$	−6.63574	−0.350710
$359$	−11.6747	−0.616166	−0.308083	−	0.951359i	$-0.599688\pi$
$359$	−11.6747	−0.616166	−0.308083	+	0.951359i	$0.599688\pi$
$360$	−12.2541	−0.645845
$361$	1.00000	0.0526316
$362$	13.1318	0.690192
$363$	1.14746	0.0602260
$364$	34.7860	1.82328
$365$	−15.6639	−0.819884
$366$	−16.5968	−0.867529
$367$	−1.78932	−0.0934018	−0.0467009	−	0.998909i	$-0.514871\pi$
$367$	−1.78932	−0.0934018	−0.0467009	+	0.998909i	$0.514871\pi$
$368$	−2.00150	−0.104336
$369$	6.13924	0.319596
$370$	−40.2367	−2.09181
$371$	−8.68800	−0.451058
$372$	9.04807	0.469121
$373$	2.87610	0.148919	0.0744594	−	0.997224i	$-0.476277\pi$
$373$	2.87610	0.148919	0.0744594	+	0.997224i	$0.476277\pi$
$374$	−41.8794	−2.16553
$375$	−8.21754	−0.424352
$376$	16.6349	0.857879
$377$	29.2410	1.50599
$378$	−20.5282	−1.05586
$379$	−4.96967	−0.255275	−0.127637	−	0.991821i	$-0.540739\pi$
$379$	−4.96967	−0.255275	−0.127637	+	0.991821i	$0.540739\pi$
$380$	5.17165	0.265300
$381$	−5.90751	−0.302651
$382$	−57.8860	−2.96171
$383$	−18.7425	−0.957699	−0.478850	−	0.877897i	$-0.658946\pi$
$383$	−18.7425	−0.957699	−0.478850	+	0.877897i	$0.658946\pi$
$384$	−13.6479	−0.696464
$385$	−10.7543	−0.548091
$386$	45.0546	2.29322
$387$	−14.2449	−0.724110
$388$	23.0479	1.17008
$389$	16.8796	0.855831	0.427915	−	0.903819i	$-0.359248\pi$
$389$	16.8796	0.855831	0.427915	+	0.903819i	$0.359248\pi$
$390$	−11.1897	−0.566613
$391$	−18.4705	−0.934092
$392$	5.54516	0.280073
$393$	−1.76507	−0.0890360
$394$	4.72787	0.238187
$395$	9.98995	0.502649
$396$	−25.9075	−1.30190
$397$	−11.8596	−0.595218	−0.297609	−	0.954688i	$-0.596189\pi$
$397$	−11.8596	−0.595218	−0.297609	+	0.954688i	$0.596189\pi$
$398$	14.9066	0.747201
$399$	1.60734	0.0804678
$400$	−1.69635	−0.0848176
$401$	32.8910	1.64250	0.821249	−	0.570570i	$-0.193278\pi$
$401$	32.8910	1.64250	0.821249	+	0.570570i	$0.193278\pi$
$402$	−13.6635	−0.681474
$403$	−17.1930	−0.856446
$404$	−40.8400	−2.03186
$405$	−7.38768	−0.367097
$406$	−34.5959	−1.71697
$407$	−34.6546	−1.71777
$408$	13.1871	0.652859
$409$	−21.1017	−1.04341	−0.521707	−	0.853125i	$-0.674705\pi$
$409$	−21.1017	−1.04341	−0.521707	+	0.853125i	$0.674705\pi$
$410$	−8.69362	−0.429347
$411$	5.11412	0.252261
$412$	−7.48663	−0.368840
$413$	0.901075	0.0443390
$414$	−18.1977	−0.894368
$415$	5.51206	0.270576
$416$	21.9833	1.07782
$417$	9.37560	0.459125
$418$	7.09385	0.346971
$419$	16.0635	0.784753	0.392376	−	0.919805i	$-0.371653\pi$
$419$	16.0635	0.784753	0.392376	+	0.919805i	$0.371653\pi$
$420$	8.31262	0.405614
$421$	28.6613	1.39687	0.698433	−	0.715675i	$-0.253881\pi$
$421$	28.6613	1.39687	0.698433	+	0.715675i	$0.253881\pi$
$422$	56.2834	2.73983
$423$	13.0939	0.636649
$424$	12.0737	0.586353
$425$	−15.6544	−0.759352
$426$	−6.41013	−0.310572
$427$	−23.4282	−1.13377
$428$	32.7649	1.58375
$429$	−9.63736	−0.465296
$430$	20.1719	0.972775
$431$	−18.3345	−0.883140	−0.441570	−	0.897227i	$-0.645578\pi$
$431$	−18.3345	−0.883140	−0.441570	+	0.897227i	$0.645578\pi$
$432$	2.46981	0.118829
$433$	−31.7402	−1.52534	−0.762669	−	0.646789i	$-0.776112\pi$
$433$	−31.7402	−1.52534	−0.762669	+	0.646789i	$0.776112\pi$
$434$	20.3416	0.976428
$435$	6.98757	0.335028
$436$	32.7955	1.57062
$437$	3.12867	0.149665
$438$	16.6076	0.793542
$439$	−16.1010	−0.768461	−0.384230	−	0.923237i	$-0.625533\pi$
$439$	−16.1010	−0.768461	−0.384230	+	0.923237i	$0.625533\pi$
$440$	14.9453	0.712490
$441$	4.36480	0.207848
$442$	−61.5109	−2.92577
$443$	−23.9462	−1.13772	−0.568858	−	0.822436i	$-0.692615\pi$
$443$	−23.9462	−1.13772	−0.568858	+	0.822436i	$0.692615\pi$
$444$	26.7865	1.27123
$445$	8.27664	0.392350
$446$	−1.76859	−0.0837454
$447$	5.91389	0.279717
$448$	−28.9436	−1.36746
$449$	16.3768	0.772869	0.386435	−	0.922317i	$-0.373707\pi$
$449$	16.3768	0.772869	0.386435	+	0.922317i	$0.373707\pi$
$450$	−15.4232	−0.727059
$451$	−7.48755	−0.352575
$452$	−8.87897	−0.417632
$453$	4.07639	0.191525
$454$	−8.26035	−0.387677
$455$	−15.7955	−0.740506
$456$	−2.23373	−0.104604
$457$	19.8276	0.927496	0.463748	−	0.885967i	$-0.346504\pi$
$457$	19.8276	0.927496	0.463748	+	0.885967i	$0.346504\pi$
$458$	−29.5051	−1.37868
$459$	22.7922	1.06385
$460$	16.1804	0.754415
$461$	1.95158	0.0908943	0.0454471	−	0.998967i	$-0.485529\pi$
$461$	1.95158	0.0908943	0.0454471	+	0.998967i	$0.485529\pi$
$462$	11.4023	0.530481
$463$	−2.25967	−0.105016	−0.0525080	−	0.998621i	$-0.516721\pi$
$463$	−2.25967	−0.105016	−0.0525080	+	0.998621i	$0.516721\pi$
$464$	4.16234	0.193232
$465$	−4.10853	−0.190529
$466$	14.3555	0.665004
$467$	−30.5428	−1.41335	−0.706676	−	0.707537i	$-0.749806\pi$
$467$	−30.5428	−1.41335	−0.706676	+	0.707537i	$0.749806\pi$
$468$	−38.0519	−1.75895
$469$	−19.2876	−0.890617
$470$	−18.5420	−0.855279
$471$	14.6680	0.675865
$472$	−1.25223	−0.0576384
$473$	17.3734	0.798831
$474$	−10.5918	−0.486499
$475$	2.65167	0.121667
$476$	45.6952	2.09444
$477$	9.50369	0.435144
$478$	−21.2945	−0.973986
$479$	10.0176	0.457714	0.228857	−	0.973460i	$-0.426501\pi$
$479$	10.0176	0.457714	0.228857	+	0.973460i	$0.426501\pi$
$480$	5.25325	0.239777
$481$	−50.8994	−2.32081
$482$	−33.0876	−1.50710
$483$	5.02885	0.228820
$484$	−5.52562	−0.251164
$485$	−10.4655	−0.475215
$486$	34.6844	1.57331
$487$	16.0387	0.726784	0.363392	−	0.931636i	$-0.381619\pi$
$487$	16.0387	0.726784	0.363392	+	0.931636i	$0.381619\pi$
$488$	32.5583	1.47385
$489$	2.86113	0.129385
$490$	−6.18089	−0.279224
$491$	24.2447	1.09415	0.547074	−	0.837084i	$-0.315742\pi$
$491$	24.2447	1.09415	0.547074	+	0.837084i	$0.315742\pi$
$492$	5.78755	0.260923
$493$	38.4113	1.72996
$494$	10.4192	0.468781
$495$	11.7640	0.528753
$496$	−2.44736	−0.109890
$497$	−9.04861	−0.405886
$498$	−5.84415	−0.261883
$499$	10.2282	0.457877	0.228938	−	0.973441i	$-0.426475\pi$
$499$	10.2282	0.457877	0.228938	+	0.973441i	$0.426475\pi$
$500$	39.5718	1.76970
$501$	−4.84152	−0.216303
$502$	70.2760	3.13657
$503$	−28.2089	−1.25777	−0.628887	−	0.777497i	$-0.716489\pi$
$503$	−28.2089	−1.25777	−0.628887	+	0.777497i	$0.716489\pi$
$504$	18.3401	0.816935
$505$	18.5445	0.825220
$506$	22.1943	0.986657
$507$	−5.04433	−0.224027
$508$	28.4478	1.26217
$509$	−2.37235	−0.105153	−0.0525763	−	0.998617i	$-0.516743\pi$
$509$	−2.37235	−0.105153	−0.0525763	+	0.998617i	$0.516743\pi$
$510$	−14.6989	−0.650880
$511$	23.4435	1.03708
$512$	7.20728	0.318520
$513$	−3.86071	−0.170454
$514$	−45.9621	−2.02730
$515$	3.39951	0.149800
$516$	−13.4289	−0.591175
$517$	−15.9697	−0.702344
$518$	60.2206	2.64594
$519$	−4.08556	−0.179336
$520$	21.9511	0.962620
$521$	−19.5247	−0.855391	−0.427696	−	0.903923i	$-0.640674\pi$
$521$	−19.5247	−0.855391	−0.427696	+	0.903923i	$0.640674\pi$
$522$	37.8440	1.65639
$523$	5.16467	0.225835	0.112918	−	0.993604i	$-0.463980\pi$
$523$	5.16467	0.225835	0.112918	+	0.993604i	$0.463980\pi$
$524$	8.49974	0.371313
$525$	4.26214	0.186015
$526$	−47.3575	−2.06488
$527$	−22.5849	−0.983816
$528$	−1.37184	−0.0597016
$529$	−13.2114	−0.574410
$530$	−13.4579	−0.584575
$531$	−0.985674	−0.0427746
$532$	−7.74020	−0.335580
$533$	−10.9974	−0.476351
$534$	−8.77530	−0.379744
$535$	−14.8778	−0.643225
$536$	26.8040	1.15776
$537$	−2.00592	−0.0865619
$538$	−60.0127	−2.58733
$539$	−5.32341	−0.229295
$540$	−19.9662	−0.859211
$541$	20.6395	0.887359	0.443680	−	0.896185i	$-0.353673\pi$
$541$	20.6395	0.887359	0.443680	+	0.896185i	$0.353673\pi$
$542$	−28.8673	−1.23995
$543$	3.96962	0.170353
$544$	28.8776	1.23812
$545$	−14.8917	−0.637890
$546$	16.7472	0.716714
$547$	17.6926	0.756480	0.378240	−	0.925708i	$-0.376529\pi$
$547$	17.6926	0.756480	0.378240	+	0.925708i	$0.376529\pi$
$548$	−24.6272	−1.05202
$549$	25.6279	1.09377
$550$	18.8105	0.802083
$551$	−6.50640	−0.277182
$552$	−6.98860	−0.297455
$553$	−14.9515	−0.635804
$554$	−40.9745	−1.74084
$555$	−12.1632	−0.516297
$556$	−45.1484	−1.91472
$557$	−27.7720	−1.17674	−0.588369	−	0.808593i	$-0.700230\pi$
$557$	−27.7720	−1.17674	−0.588369	+	0.808593i	$0.700230\pi$
$558$	−22.2514	−0.941977
$559$	25.5174	1.07927
$560$	−2.24843	−0.0950136
$561$	−12.6597	−0.534494
$562$	22.7581	0.959991
$563$	−5.14822	−0.216972	−0.108486	−	0.994098i	$-0.534600\pi$
$563$	−5.14822	−0.216972	−0.108486	+	0.994098i	$0.534600\pi$
$564$	12.3438	0.519770
$565$	4.03174	0.169617
$566$	54.5339	2.29223
$567$	11.0568	0.464343
$568$	12.5749	0.527631
$569$	−30.7962	−1.29104	−0.645522	−	0.763742i	$-0.723360\pi$
$569$	−30.7962	−1.29104	−0.645522	+	0.763742i	$0.723360\pi$
$570$	2.48982	0.104287
$571$	4.82490	0.201916	0.100958	−	0.994891i	$-0.467809\pi$
$571$	4.82490	0.201916	0.100958	+	0.994891i	$0.467809\pi$
$572$	46.4089	1.94045
$573$	−17.4984	−0.731006
$574$	13.0114	0.543085
$575$	8.29619	0.345975
$576$	31.6611	1.31921
$577$	−41.3191	−1.72014	−0.860069	−	0.510177i	$-0.829580\pi$
$577$	−41.3191	−1.72014	−0.860069	+	0.510177i	$0.829580\pi$
$578$	−41.3891	−1.72156
$579$	13.6196	0.566010
$580$	−33.6488	−1.39719
$581$	−8.24967	−0.342254
$582$	11.0961	0.459946
$583$	−11.5909	−0.480046
$584$	−32.5795	−1.34815
$585$	17.2785	0.714379
$586$	−36.0189	−1.48793
$587$	−16.8767	−0.696576	−0.348288	−	0.937388i	$-0.613237\pi$
$587$	−16.8767	−0.696576	−0.348288	+	0.937388i	$0.613237\pi$
$588$	4.11476	0.169690
$589$	3.82561	0.157632
$590$	1.39579	0.0574637
$591$	1.42919	0.0587891
$592$	−7.24532	−0.297781
$593$	−6.70968	−0.275533	−0.137767	−	0.990465i	$-0.543992\pi$
$593$	−6.70968	−0.275533	−0.137767	+	0.990465i	$0.543992\pi$
$594$	−27.3873	−1.12371
$595$	−20.7492	−0.850634
$596$	−28.4785	−1.16652
$597$	4.50612	0.184423
$598$	32.5981	1.33304
$599$	−9.46843	−0.386870	−0.193435	−	0.981113i	$-0.561963\pi$
$599$	−9.46843	−0.386870	−0.193435	+	0.981113i	$0.561963\pi$
$600$	−5.92311	−0.241810
$601$	38.2634	1.56080	0.780399	−	0.625281i	$-0.215016\pi$
$601$	38.2634	1.56080	0.780399	+	0.625281i	$0.215016\pi$
$602$	−30.1904	−1.23047
$603$	21.0984	0.859194
$604$	−19.6300	−0.798731
$605$	2.50906	0.102008
$606$	−19.6618	−0.798706
$607$	6.67079	0.270759	0.135380	−	0.990794i	$-0.456775\pi$
$607$	6.67079	0.270759	0.135380	+	0.990794i	$0.456775\pi$
$608$	−4.89150	−0.198377
$609$	−10.4580	−0.423780
$610$	−36.2910	−1.46938
$611$	−23.4556	−0.948913
$612$	−49.9854	−2.02054
$613$	−39.7813	−1.60675	−0.803375	−	0.595473i	$-0.796965\pi$
$613$	−39.7813	−1.60675	−0.803375	+	0.595473i	$0.796965\pi$
$614$	−30.5746	−1.23389
$615$	−2.62800	−0.105971
$616$	−22.3680	−0.901234
$617$	−31.7927	−1.27992	−0.639962	−	0.768406i	$-0.721050\pi$
$617$	−31.7927	−1.27992	−0.639962	+	0.768406i	$0.721050\pi$
$618$	−3.60433	−0.144987
$619$	−34.1797	−1.37380	−0.686898	−	0.726754i	$-0.741028\pi$
$619$	−34.1797	−1.37380	−0.686898	+	0.726754i	$0.741028\pi$
$620$	19.7847	0.794574
$621$	−12.0789	−0.484709
$622$	−64.2199	−2.57498
$623$	−12.3873	−0.496287
$624$	−2.01491	−0.0806608
$625$	−4.71033	−0.188413
$626$	22.8470	0.913151
$627$	2.14440	0.0856392
$628$	−70.6341	−2.81861
$629$	−66.8620	−2.66596
$630$	−20.4428	−0.814459
$631$	23.8865	0.950906	0.475453	−	0.879741i	$-0.342284\pi$
$631$	23.8865	0.950906	0.475453	+	0.879741i	$0.342284\pi$
$632$	20.7782	0.826513
$633$	17.0139	0.676242
$634$	2.31836	0.0920740
$635$	−12.9175	−0.512616
$636$	8.95927	0.355258
$637$	−7.81882	−0.309793
$638$	−46.1554	−1.82731
$639$	9.89816	0.391565
$640$	−29.8427	−1.17964
$641$	−26.7229	−1.05549	−0.527745	−	0.849403i	$-0.676962\pi$
$641$	−26.7229	−1.05549	−0.527745	+	0.849403i	$0.676962\pi$
$642$	15.7742	0.622558
$643$	−19.6302	−0.774138	−0.387069	−	0.922051i	$-0.626513\pi$
$643$	−19.6302	−0.774138	−0.387069	+	0.922051i	$0.626513\pi$
$644$	−24.2165	−0.954265
$645$	6.09777	0.240099
$646$	13.6867	0.538498
$647$	7.15265	0.281200	0.140600	−	0.990067i	$-0.455097\pi$
$647$	7.15265	0.281200	0.140600	+	0.990067i	$0.455097\pi$
$648$	−15.3657	−0.603622
$649$	1.20215	0.0471885
$650$	27.6282	1.08367
$651$	6.14907	0.241001
$652$	−13.7779	−0.539582
$653$	−48.0497	−1.88033	−0.940164	−	0.340721i	$-0.889329\pi$
$653$	−48.0497	−1.88033	−0.940164	+	0.340721i	$0.889329\pi$
$654$	15.7889	0.617395
$655$	−3.85954	−0.150805
$656$	−1.56544	−0.0611201
$657$	−25.6445	−1.00049
$658$	27.7511	1.08185
$659$	−26.9418	−1.04950	−0.524752	−	0.851255i	$-0.675842\pi$
$659$	−26.9418	−1.04950	−0.524752	+	0.851255i	$0.675842\pi$
$660$	11.0901	0.431682
$661$	32.0555	1.24681	0.623407	−	0.781898i	$-0.285748\pi$
$661$	32.0555	1.24681	0.623407	+	0.781898i	$0.285748\pi$
$662$	12.6749	0.492623
$663$	−18.5941	−0.722136
$664$	11.4646	0.444913
$665$	3.51465	0.136292
$666$	−65.8745	−2.55259
$667$	−20.3564	−0.788201
$668$	23.3144	0.902063
$669$	−0.534629	−0.0206700
$670$	−29.8770	−1.15425
$671$	−31.2563	−1.20664
$672$	−7.86232	−0.303296
$673$	−18.6513	−0.718956	−0.359478	−	0.933154i	$-0.617045\pi$
$673$	−18.6513	−0.718956	−0.359478	+	0.933154i	$0.617045\pi$
$674$	−5.37990	−0.207226
$675$	−10.2373	−0.394034
$676$	24.2911	0.934273
$677$	10.4939	0.403314	0.201657	−	0.979456i	$-0.435367\pi$
$677$	10.4939	0.403314	0.201657	+	0.979456i	$0.435367\pi$
$678$	−4.27465	−0.164167
$679$	15.6633	0.601103
$680$	28.8352	1.10578
$681$	−2.49702	−0.0956861
$682$	27.1383	1.03918
$683$	42.1440	1.61260	0.806298	−	0.591510i	$-0.201468\pi$
$683$	42.1440	1.61260	0.806298	+	0.591510i	$0.201468\pi$
$684$	8.46690	0.323740
$685$	11.1827	0.427268
$686$	46.4712	1.77428
$687$	−8.91910	−0.340285
$688$	3.63230	0.138480
$689$	−17.0243	−0.648573
$690$	7.78981	0.296553
$691$	−42.1473	−1.60336	−0.801679	−	0.597755i	$-0.796060\pi$
$691$	−42.1473	−1.60336	−0.801679	+	0.597755i	$0.796060\pi$
$692$	19.6741	0.747898
$693$	−17.6067	−0.668824
$694$	72.2454	2.74240
$695$	20.5009	0.777643
$696$	14.5335	0.550892
$697$	−14.4463	−0.547194
$698$	80.3082	3.03971
$699$	4.33952	0.164136
$700$	−20.5244	−0.775751
$701$	41.2164	1.55672	0.778361	−	0.627818i	$-0.216052\pi$
$701$	41.2164	1.55672	0.778361	+	0.627818i	$0.216052\pi$
$702$	−40.2254	−1.51821
$703$	11.3256	0.427153
$704$	−38.6145	−1.45534
$705$	−5.60507	−0.211099
$706$	−10.2645	−0.386308
$707$	−27.7548	−1.04383
$708$	−0.929209	−0.0349218
$709$	−50.6508	−1.90223	−0.951115	−	0.308838i	$-0.900060\pi$
$709$	−50.6508	−1.90223	−0.951115	+	0.308838i	$0.900060\pi$
$710$	−14.0165	−0.526031
$711$	16.3553	0.613372
$712$	17.2147	0.645148
$713$	11.9691	0.448245
$714$	21.9993	0.823303
$715$	−21.0733	−0.788095
$716$	9.65956	0.360995
$717$	−6.43711	−0.240398
$718$	27.0662	1.01010
$719$	−16.4111	−0.612030	−0.306015	−	0.952027i	$-0.598996\pi$
$719$	−16.4111	−0.612030	−0.306015	+	0.952027i	$0.598996\pi$
$720$	2.45953	0.0916612
$721$	−5.08791	−0.189484
$722$	−2.31836	−0.0862806
$723$	−10.0021	−0.371980
$724$	−19.1158	−0.710433
$725$	−17.2528	−0.640753
$726$	−2.66023	−0.0987303
$727$	−51.7902	−1.92079	−0.960396	−	0.278640i	$-0.910116\pi$
$727$	−51.7902	−1.92079	−0.960396	+	0.278640i	$0.910116\pi$
$728$	−32.8533	−1.21763
$729$	−3.97795	−0.147331
$730$	36.3146	1.34406
$731$	33.5200	1.23978
$732$	24.1598	0.892970
$733$	7.24464	0.267587	0.133793	−	0.991009i	$-0.457284\pi$
$733$	7.24464	0.267587	0.133793	+	0.991009i	$0.457284\pi$
$734$	4.14830	0.153117
$735$	−1.86842	−0.0689178
$736$	−15.3039	−0.564109
$737$	−25.7321	−0.947854
$738$	−14.2330	−0.523924
$739$	8.46646	0.311444	0.155722	−	0.987801i	$-0.450230\pi$
$739$	8.46646	0.311444	0.155722	+	0.987801i	$0.450230\pi$
$740$	58.5720	2.15315
$741$	3.14962	0.115704
$742$	20.1419	0.739434
$743$	14.2262	0.521907	0.260954	−	0.965351i	$-0.415963\pi$
$743$	14.2262	0.521907	0.260954	+	0.965351i	$0.415963\pi$
$744$	−8.54538	−0.313289
$745$	12.9315	0.473772
$746$	−6.66784	−0.244127
$747$	9.02421	0.330179
$748$	60.9633	2.22904
$749$	22.2670	0.813620
$750$	19.0512	0.695653
$751$	17.9306	0.654298	0.327149	−	0.944973i	$-0.393912\pi$
$751$	17.9306	0.654298	0.327149	+	0.944973i	$0.393912\pi$
$752$	−3.33881	−0.121754
$753$	21.2438	0.774166
$754$	−67.7913	−2.46881
$755$	8.91353	0.324396
$756$	29.8827	1.08682
$757$	4.12622	0.149970	0.0749850	−	0.997185i	$-0.476109\pi$
$757$	4.12622	0.149970	0.0749850	+	0.997185i	$0.476109\pi$
$758$	11.5215	0.418480
$759$	6.70912	0.243526
$760$	−4.88433	−0.177173
$761$	−15.0894	−0.546989	−0.273494	−	0.961874i	$-0.588180\pi$
$761$	−15.0894	−0.546989	−0.273494	+	0.961874i	$0.588180\pi$
$762$	13.6958	0.496145
$763$	22.2878	0.806873
$764$	84.2639	3.04856
$765$	22.6973	0.820621
$766$	43.4520	1.56999
$767$	1.76567	0.0637547
$768$	13.9524	0.503463
$769$	20.6291	0.743903	0.371951	−	0.928252i	$-0.378689\pi$
$769$	20.6291	0.743903	0.371951	+	0.928252i	$0.378689\pi$
$770$	24.9324	0.898502
$771$	−13.8939	−0.500376
$772$	−65.5854	−2.36047
$773$	−50.6866	−1.82307	−0.911536	−	0.411221i	$-0.865102\pi$
$773$	−50.6866	−1.82307	−0.911536	+	0.411221i	$0.865102\pi$
$774$	33.0249	1.18706
$775$	10.1442	0.364392
$776$	−21.7674	−0.781403
$777$	18.2041	0.653069
$778$	−39.1331	−1.40299
$779$	2.44703	0.0876739
$780$	16.2887	0.583230
$781$	−12.0720	−0.431970
$782$	42.8213	1.53129
$783$	25.1193	0.897691
$784$	−1.11298	−0.0397492
$785$	32.0734	1.14475
$786$	4.09207	0.145959
$787$	16.2764	0.580193	0.290096	−	0.956997i	$-0.406313\pi$
$787$	16.2764	0.580193	0.290096	+	0.956997i	$0.406313\pi$
$788$	−6.88230	−0.245172
$789$	−14.3157	−0.509653
$790$	−23.1603	−0.824008
$791$	−6.03415	−0.214550
$792$	24.4681	0.869436
$793$	−45.9080	−1.63024
$794$	27.4950	0.975760
$795$	−4.06820	−0.144284
$796$	−21.6993	−0.769113
$797$	14.6502	0.518937	0.259469	−	0.965752i	$-0.416453\pi$
$797$	14.6502	0.518937	0.259469	+	0.965752i	$0.416453\pi$
$798$	−3.72641	−0.131913
$799$	−30.8116	−1.09003
$800$	−12.9706	−0.458581
$801$	13.5503	0.478777
$802$	−76.2533	−2.69260
$803$	31.2766	1.10373
$804$	19.8898	0.701459
$805$	10.9962	0.387565
$806$	39.8597	1.40400
$807$	−18.1413	−0.638602
$808$	38.5710	1.35692
$809$	34.4021	1.20951	0.604756	−	0.796411i	$-0.293271\pi$
$809$	34.4021	1.20951	0.604756	+	0.796411i	$0.293271\pi$
$810$	17.1273	0.601793
$811$	−11.2004	−0.393300	−0.196650	−	0.980474i	$-0.563006\pi$
$811$	−11.2004	−0.393300	−0.196650	+	0.980474i	$0.563006\pi$
$812$	50.3608	1.76732
$813$	−8.72629	−0.306044
$814$	80.3420	2.81599
$815$	6.25622	0.219146
$816$	−2.64680	−0.0926566
$817$	−5.67787	−0.198643
$818$	48.9215	1.71050
$819$	−25.8601	−0.903624
$820$	12.6552	0.441938
$821$	−26.1875	−0.913950	−0.456975	−	0.889479i	$-0.651067\pi$
$821$	−26.1875	−0.913950	−0.456975	+	0.889479i	$0.651067\pi$
$822$	−11.8564	−0.413540
$823$	−50.2026	−1.74995	−0.874976	−	0.484167i	$-0.839123\pi$
$823$	−50.2026	−1.74995	−0.874976	+	0.484167i	$0.839123\pi$
$824$	7.07069	0.246319
$825$	5.68624	0.197969
$826$	−2.08902	−0.0726863
$827$	18.6532	0.648637	0.324318	−	0.945948i	$-0.394865\pi$
$827$	18.6532	0.648637	0.324318	+	0.945948i	$0.394865\pi$
$828$	26.4901	0.920596
$829$	20.6627	0.717646	0.358823	−	0.933406i	$-0.383178\pi$
$829$	20.6627	0.717646	0.358823	+	0.933406i	$0.383178\pi$
$830$	−12.7790	−0.443564
$831$	−12.3862	−0.429672
$832$	−56.7155	−1.96626
$833$	−10.2709	−0.355865
$834$	−21.7360	−0.752658
$835$	−10.5866	−0.366364
$836$	−10.3264	−0.357147
$837$	−14.7696	−0.510511
$838$	−37.2410	−1.28647
$839$	−29.7914	−1.02851	−0.514257	−	0.857636i	$-0.671932\pi$
$839$	−29.7914	−1.02851	−0.514257	+	0.857636i	$0.671932\pi$
$840$	−7.85079	−0.270878
$841$	13.3332	0.459766
$842$	−66.4473	−2.28993
$843$	6.87955	0.236944
$844$	−81.9309	−2.82018
$845$	−11.0301	−0.379445
$846$	−30.3565	−1.04368
$847$	−3.75521	−0.129031
$848$	−2.42334	−0.0832178
$849$	16.4851	0.565766
$850$	36.2927	1.24483
$851$	35.4340	1.21466
$852$	9.33114	0.319680
$853$	4.32088	0.147944	0.0739720	−	0.997260i	$-0.476432\pi$
$853$	4.32088	0.147944	0.0739720	+	0.997260i	$0.476432\pi$
$854$	54.3152	1.85863
$855$	−3.84463	−0.131484
$856$	−30.9446	−1.05766
$857$	9.66184	0.330042	0.165021	−	0.986290i	$-0.447231\pi$
$857$	9.66184	0.330042	0.165021	+	0.986290i	$0.447231\pi$
$858$	22.3429	0.762774
$859$	3.61233	0.123251	0.0616256	−	0.998099i	$-0.480372\pi$
$859$	3.61233	0.123251	0.0616256	+	0.998099i	$0.480372\pi$
$860$	−29.3640	−1.00130
$861$	3.93322	0.134044
$862$	42.5059	1.44776
$863$	−41.8604	−1.42494	−0.712472	−	0.701700i	$-0.752425\pi$
$863$	−41.8604	−1.42494	−0.712472	+	0.701700i	$0.752425\pi$
$864$	18.8847	0.642469
$865$	−8.93358	−0.303751
$866$	73.5854	2.50053
$867$	−12.5115	−0.424914
$868$	−29.6110	−1.00506
$869$	−19.9473	−0.676665
$870$	−16.1997	−0.549223
$871$	−37.7943	−1.28061
$872$	−30.9734	−1.04889
$873$	−17.1339	−0.579894
$874$	−7.25339	−0.245350
$875$	26.8930	0.909148
$876$	−24.1755	−0.816813
$877$	30.1589	1.01839	0.509197	−	0.860650i	$-0.329942\pi$
$877$	30.1589	1.01839	0.509197	+	0.860650i	$0.329942\pi$
$878$	37.3281	1.25976
$879$	−10.8882	−0.367248
$880$	−2.99969	−0.101120
$881$	48.2302	1.62492	0.812458	−	0.583020i	$-0.198129\pi$
$881$	48.2302	1.62492	0.812458	+	0.583020i	$0.198129\pi$
$882$	−10.1192	−0.340731
$883$	14.2176	0.478460	0.239230	−	0.970963i	$-0.423105\pi$
$883$	14.2176	0.478460	0.239230	+	0.970963i	$0.423105\pi$
$884$	89.5405	3.01157
$885$	0.421933	0.0141831
$886$	55.5159	1.86509
$887$	−51.0269	−1.71332	−0.856658	−	0.515885i	$-0.827463\pi$
$887$	−51.0269	−1.71332	−0.856658	+	0.515885i	$0.827463\pi$
$888$	−25.2983	−0.848956
$889$	19.3331	0.648411
$890$	−19.1883	−0.643192
$891$	14.7512	0.494185
$892$	2.57452	0.0862013
$893$	5.21909	0.174650
$894$	−13.7106	−0.458550
$895$	−4.38619	−0.146614
$896$	44.6644	1.49213
$897$	9.85411	0.329019
$898$	−37.9674	−1.26699
$899$	−24.8909	−0.830159
$900$	22.4514	0.748380
$901$	−22.3633	−0.745029
$902$	17.3589	0.577987
$903$	−9.12628	−0.303704
$904$	8.38567	0.278903
$905$	8.68005	0.288535
$906$	−9.45055	−0.313974
$907$	29.6849	0.985672	0.492836	−	0.870122i	$-0.335960\pi$
$907$	29.6849	0.985672	0.492836	+	0.870122i	$0.335960\pi$
$908$	12.0245	0.399046
$909$	30.3606	1.00700
$910$	36.6198	1.21393
$911$	−20.7632	−0.687914	−0.343957	−	0.938985i	$-0.611767\pi$
$911$	−20.7632	−0.687914	−0.343957	+	0.938985i	$0.611767\pi$
$912$	0.448335	0.0148459
$913$	−11.0061	−0.364249
$914$	−45.9676	−1.52047
$915$	−10.9704	−0.362671
$916$	42.9502	1.41911
$917$	5.77642	0.190754
$918$	−52.8405	−1.74400
$919$	−33.0495	−1.09020	−0.545102	−	0.838370i	$-0.683509\pi$
$919$	−33.0495	−1.09020	−0.545102	+	0.838370i	$0.683509\pi$
$920$	−15.2814	−0.503814
$921$	−9.24242	−0.304548
$922$	−4.52448	−0.149006
$923$	−17.7309	−0.583620
$924$	−16.5981	−0.546038
$925$	30.0317	0.987436
$926$	5.23874	0.172156
$927$	5.56560	0.182798
$928$	31.8260	1.04474
$929$	−22.4774	−0.737460	−0.368730	−	0.929536i	$-0.620207\pi$
$929$	−22.4774	−0.737460	−0.368730	+	0.929536i	$0.620207\pi$
$930$	9.52507	0.312339
$931$	1.73976	0.0570183
$932$	−20.8971	−0.684506
$933$	−19.4131	−0.635555
$934$	70.8094	2.31695
$935$	−27.6821	−0.905300
$936$	35.9378	1.17466
$937$	10.4904	0.342707	0.171354	−	0.985210i	$-0.445186\pi$
$937$	10.4904	0.342707	0.171354	+	0.985210i	$0.445186\pi$
$938$	44.7156	1.46002
$939$	6.90643	0.225383
$940$	26.9913	0.880361
$941$	9.60578	0.313139	0.156570	−	0.987667i	$-0.449956\pi$
$941$	9.60578	0.313139	0.156570	+	0.987667i	$0.449956\pi$
$942$	−34.0057	−1.10797
$943$	7.65595	0.249312
$944$	0.251336	0.00818030
$945$	−13.5691	−0.441401
$946$	−40.2779	−1.30955
$947$	7.86729	0.255653	0.127826	−	0.991797i	$-0.459200\pi$
$947$	7.86729	0.255653	0.127826	+	0.991797i	$0.459200\pi$
$948$	15.4184	0.500766
$949$	45.9379	1.49121
$950$	−6.14753	−0.199452
$951$	0.700819	0.0227256
$952$	−43.1565	−1.39871
$953$	35.6790	1.15576	0.577878	−	0.816123i	$-0.303881\pi$
$953$	35.6790	1.15576	0.577878	+	0.816123i	$0.303881\pi$
$954$	−22.0330	−0.713345
$955$	−38.2624	−1.23814
$956$	30.9981	1.00255
$957$	−13.9523	−0.451015
$958$	−23.2244	−0.750345
$959$	−16.7366	−0.540454
$960$	−13.5530	−0.437422
$961$	−16.3647	−0.527894
$962$	118.003	3.80458
$963$	−24.3576	−0.784913
$964$	48.1651	1.55129
$965$	29.7809	0.958680
$966$	−11.6587	−0.375112
$967$	−38.1453	−1.22667	−0.613334	−	0.789823i	$-0.710172\pi$
$967$	−38.1453	−1.22667	−0.613334	+	0.789823i	$0.710172\pi$
$968$	5.21863	0.167733
$969$	4.13737	0.132911
$970$	24.2629	0.779034
$971$	48.9845	1.57199	0.785994	−	0.618235i	$-0.212152\pi$
$971$	48.9845	1.57199	0.785994	+	0.618235i	$0.212152\pi$
$972$	−50.4896	−1.61945
$973$	−30.6828	−0.983647
$974$	−37.1836	−1.19144
$975$	8.35173	0.267470
$976$	−6.53483	−0.209175
$977$	−37.5320	−1.20076	−0.600378	−	0.799717i	$-0.704983\pi$
$977$	−37.5320	−1.20076	−0.600378	+	0.799717i	$0.704983\pi$
$978$	−6.63315	−0.212105
$979$	−16.5263	−0.528182
$980$	8.99744	0.287413
$981$	−24.3803	−0.778404
$982$	−56.2081	−1.79367
$983$	35.8462	1.14332	0.571658	−	0.820492i	$-0.306300\pi$
$983$	35.8462	1.14332	0.571658	+	0.820492i	$0.306300\pi$
$984$	−5.46601	−0.174250
$985$	3.12510	0.0995740
$986$	−89.0514	−2.83597
$987$	8.38888	0.267021
$988$	−15.1671	−0.482528
$989$	−17.7642	−0.564867
$990$	−27.2732	−0.866801
$991$	33.3493	1.05937	0.529687	−	0.848193i	$-0.322309\pi$
$991$	33.3493	1.05937	0.529687	+	0.848193i	$0.322309\pi$
$992$	−18.7130	−0.594137
$993$	3.83149	0.121589
$994$	20.9780	0.665381
$995$	9.85319	0.312367
$996$	8.50726	0.269563
$997$	10.9816	0.347789	0.173895	−	0.984764i	$-0.444365\pi$
$997$	10.9816	0.347789	0.173895	+	0.984764i	$0.444365\pi$
$998$	−23.7127	−0.750611
$999$	−43.7248	−1.38339

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.b.1.11	✓	99

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.b.1.11	✓	99	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.31836 q^{2} -0.700819 q^{3} +3.37481 q^{4} -1.53243 q^{5} +1.62475 q^{6} +2.29352 q^{7} -3.18731 q^{8} -2.50885 q^{9} +O(q^{10})\)	\(q-2.31836 q^{2} -0.700819 q^{3} +3.37481 q^{4} -1.53243 q^{5} +1.62475 q^{6} +2.29352 q^{7} -3.18731 q^{8} -2.50885 q^{9} +3.55272 q^{10} +3.05985 q^{11} -2.36513 q^{12} +4.49419 q^{13} -5.31722 q^{14} +1.07395 q^{15} +0.639730 q^{16} +5.90362 q^{17} +5.81643 q^{18} -1.00000 q^{19} -5.17165 q^{20} -1.60734 q^{21} -7.09385 q^{22} -3.12867 q^{23} +2.23373 q^{24} -2.65167 q^{25} -10.4192 q^{26} +3.86071 q^{27} +7.74020 q^{28} +6.50640 q^{29} -2.48982 q^{30} -3.82561 q^{31} +4.89150 q^{32} -2.14440 q^{33} -13.6867 q^{34} -3.51465 q^{35} -8.46690 q^{36} -11.3256 q^{37} +2.31836 q^{38} -3.14962 q^{39} +4.88433 q^{40} -2.44703 q^{41} +3.72641 q^{42} +5.67787 q^{43} +10.3264 q^{44} +3.84463 q^{45} +7.25339 q^{46} -5.21909 q^{47} -0.448335 q^{48} -1.73976 q^{49} +6.14753 q^{50} -4.13737 q^{51} +15.1671 q^{52} -3.78806 q^{53} -8.95053 q^{54} -4.68900 q^{55} -7.31017 q^{56} +0.700819 q^{57} -15.0842 q^{58} +0.392878 q^{59} +3.62439 q^{60} -10.2150 q^{61} +8.86916 q^{62} -5.75411 q^{63} -12.6197 q^{64} -6.88702 q^{65} +4.97150 q^{66} -8.40959 q^{67} +19.9236 q^{68} +2.19263 q^{69} +8.14825 q^{70} -3.94529 q^{71} +7.99650 q^{72} +10.2216 q^{73} +26.2568 q^{74} +1.85834 q^{75} -3.37481 q^{76} +7.01783 q^{77} +7.30196 q^{78} -6.51904 q^{79} -0.980340 q^{80} +4.82090 q^{81} +5.67311 q^{82} -3.59695 q^{83} -5.42448 q^{84} -9.04687 q^{85} -13.1634 q^{86} -4.55981 q^{87} -9.75271 q^{88} -5.40100 q^{89} -8.91326 q^{90} +10.3075 q^{91} -10.5587 q^{92} +2.68106 q^{93} +12.0998 q^{94} +1.53243 q^{95} -3.42806 q^{96} +6.82937 q^{97} +4.03340 q^{98} -7.67672 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9}+O(q^{10}) \) 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9} - 6 q^{10} - 9 q^{11} - 27 q^{12} - 28 q^{13} - 13 q^{14} - 10 q^{15} + 38 q^{16} - 36 q^{17} - 14 q^{18} - 99 q^{19} - 34 q^{20} - 20 q^{21} - 53 q^{22} - 38 q^{23} - 25 q^{24} - 8 q^{25} - 3 q^{26} - 3 q^{27} - 63 q^{28} - 34 q^{29} - 30 q^{30} - 16 q^{31} - 43 q^{32} - 41 q^{33} - 14 q^{34} - 25 q^{35} - 16 q^{36} - 80 q^{37} + 4 q^{38} - 48 q^{39} - 10 q^{40} - 32 q^{41} - 37 q^{42} - 76 q^{43} - 21 q^{44} - 53 q^{45} - 23 q^{46} - 31 q^{47} - 74 q^{48} - 32 q^{49} - 29 q^{50} - 30 q^{51} - 71 q^{52} - 35 q^{53} - 80 q^{54} - 45 q^{55} - 33 q^{56} + 3 q^{57} - 91 q^{58} + 12 q^{59} - 56 q^{60} - 61 q^{61} - 46 q^{62} - 43 q^{63} - 30 q^{64} - 46 q^{65} - 75 q^{66} - 26 q^{67} - 55 q^{68} - 45 q^{69} - 76 q^{70} - 41 q^{71} - 77 q^{72} - 143 q^{73} - 64 q^{74} - 8 q^{75} - 80 q^{76} - 58 q^{77} - 34 q^{78} - 22 q^{79} - 36 q^{80} - 81 q^{81} - 109 q^{82} - 7 q^{83} - 6 q^{84} - 80 q^{85} + 32 q^{86} - 57 q^{87} - 120 q^{88} - 28 q^{89} - 12 q^{90} - 30 q^{91} - 107 q^{92} - 121 q^{93} + 8 q^{94} + 15 q^{95} + 4 q^{96} - 128 q^{97} + 54 q^{98} - 34 q^{99}+O(q^{100}) \) 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9 - 6 * q^10 - 9 * q^11 - 27 * q^12 - 28 * q^13 - 13 * q^14 - 10 * q^15 + 38 * q^16 - 36 * q^17 - 14 * q^18 - 99 * q^19 - 34 * q^20 - 20 * q^21 - 53 * q^22 - 38 * q^23 - 25 * q^24 - 8 * q^25 - 3 * q^26 - 3 * q^27 - 63 * q^28 - 34 * q^29 - 30 * q^30 - 16 * q^31 - 43 * q^32 - 41 * q^33 - 14 * q^34 - 25 * q^35 - 16 * q^36 - 80 * q^37 + 4 * q^38 - 48 * q^39 - 10 * q^40 - 32 * q^41 - 37 * q^42 - 76 * q^43 - 21 * q^44 - 53 * q^45 - 23 * q^46 - 31 * q^47 - 74 * q^48 - 32 * q^49 - 29 * q^50 - 30 * q^51 - 71 * q^52 - 35 * q^53 - 80 * q^54 - 45 * q^55 - 33 * q^56 + 3 * q^57 - 91 * q^58 + 12 * q^59 - 56 * q^60 - 61 * q^61 - 46 * q^62 - 43 * q^63 - 30 * q^64 - 46 * q^65 - 75 * q^66 - 26 * q^67 - 55 * q^68 - 45 * q^69 - 76 * q^70 - 41 * q^71 - 77 * q^72 - 143 * q^73 - 64 * q^74 - 8 * q^75 - 80 * q^76 - 58 * q^77 - 34 * q^78 - 22 * q^79 - 36 * q^80 - 81 * q^81 - 109 * q^82 - 7 * q^83 - 6 * q^84 - 80 * q^85 + 32 * q^86 - 57 * q^87 - 120 * q^88 - 28 * q^89 - 12 * q^90 - 30 * q^91 - 107 * q^92 - 121 * q^93 + 8 * q^94 + 15 * q^95 + 4 * q^96 - 128 * q^97 + 54 * q^98 - 34 * q^99

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