LMFDB - Embedded newform 1849.2.a.l.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,2,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, 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("1849.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1849.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:	$14.7643393337$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.24698$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.24698 q^{2} +1.55496 q^{3} +3.04892 q^{4} +2.00000 q^{5} +3.49396 q^{6} +4.24698 q^{7} +2.35690 q^{8} -0.582105 q^{9} +O(q^{10})$	\(q+2.24698 q^{2} +1.55496 q^{3} +3.04892 q^{4} +2.00000 q^{5} +3.49396 q^{6} +4.24698 q^{7} +2.35690 q^{8} -0.582105 q^{9} +4.49396 q^{10} -4.40581 q^{11} +4.74094 q^{12} +0.307979 q^{13} +9.54288 q^{14} +3.10992 q^{15} -0.801938 q^{16} +4.49396 q^{17} -1.30798 q^{18} -5.69202 q^{19} +6.09783 q^{20} +6.60388 q^{21} -9.89977 q^{22} +2.19806 q^{23} +3.66487 q^{24} -1.00000 q^{25} +0.692021 q^{26} -5.57002 q^{27} +12.9487 q^{28} +2.93900 q^{29} +6.98792 q^{30} +3.58211 q^{31} -6.51573 q^{32} -6.85086 q^{33} +10.0978 q^{34} +8.49396 q^{35} -1.77479 q^{36} -4.87263 q^{37} -12.7899 q^{38} +0.478894 q^{39} +4.71379 q^{40} -4.02715 q^{41} +14.8388 q^{42} -13.4330 q^{44} -1.16421 q^{45} +4.93900 q^{46} -1.00000 q^{47} -1.24698 q^{48} +11.0368 q^{49} -2.24698 q^{50} +6.98792 q^{51} +0.939001 q^{52} -1.40581 q^{53} -12.5157 q^{54} -8.81163 q^{55} +10.0097 q^{56} -8.85086 q^{57} +6.60388 q^{58} -3.25906 q^{59} +9.48188 q^{60} -2.26875 q^{61} +8.04892 q^{62} -2.47219 q^{63} -13.0368 q^{64} +0.615957 q^{65} -15.3937 q^{66} +4.18598 q^{67} +13.7017 q^{68} +3.41789 q^{69} +19.0858 q^{70} +8.81163 q^{71} -1.37196 q^{72} -4.25667 q^{73} -10.9487 q^{74} -1.55496 q^{75} -17.3545 q^{76} -18.7114 q^{77} +1.07606 q^{78} +3.71379 q^{79} -1.60388 q^{80} -6.91484 q^{81} -9.04892 q^{82} +10.1642 q^{83} +20.1347 q^{84} +8.98792 q^{85} +4.57002 q^{87} -10.3840 q^{88} -4.99761 q^{89} -2.61596 q^{90} +1.30798 q^{91} +6.70171 q^{92} +5.57002 q^{93} -2.24698 q^{94} -11.3840 q^{95} -10.1317 q^{96} +18.2470 q^{97} +24.7995 q^{98} +2.56465 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} + 5 q^{3} + 6 q^{5} + q^{6} + 8 q^{7} + 3 q^{8} + 4 q^{9}+O(q^{10}) $ 3 * q + 2 * q^2 + 5 * q^3 + 6 * q^5 + q^6 + 8 * q^7 + 3 * q^8 + 4 * q^9	$ 3 q + 2 q^{2} + 5 q^{3} + 6 q^{5} + q^{6} + 8 q^{7} + 3 q^{8} + 4 q^{9} + 4 q^{10} + 6 q^{13} + 10 q^{14} + 10 q^{15} + 2 q^{16} + 4 q^{17} - 9 q^{18} - 12 q^{19} + 11 q^{21} - 7 q^{22} + 11 q^{23} + 12 q^{24} - 3 q^{25} - 3 q^{26} + 8 q^{27} + 7 q^{28} - q^{29} + 2 q^{30} + 5 q^{31} - 7 q^{32} - 7 q^{33} + 12 q^{34} + 16 q^{35} - 7 q^{36} + 2 q^{37} - 15 q^{38} + 17 q^{39} + 6 q^{40} - 6 q^{41} + 12 q^{42} - 21 q^{44} + 8 q^{45} + 5 q^{46} - 3 q^{47} + q^{48} + 5 q^{49} - 2 q^{50} + 2 q^{51} - 7 q^{52} + 9 q^{53} - 25 q^{54} + 8 q^{56} - 13 q^{57} + 11 q^{58} - 24 q^{59} + q^{61} + 15 q^{62} - q^{63} - 11 q^{64} + 12 q^{65} - 14 q^{66} - 2 q^{67} + 14 q^{68} + 16 q^{69} + 20 q^{70} + 25 q^{72} + 14 q^{73} - q^{74} - 5 q^{75} - 7 q^{76} - 7 q^{77} - 12 q^{78} + 3 q^{79} + 4 q^{80} + 27 q^{81} - 18 q^{82} + 19 q^{83} + 14 q^{84} + 8 q^{85} - 11 q^{87} - 21 q^{88} + 26 q^{89} - 18 q^{90} + 9 q^{91} - 7 q^{92} - 8 q^{93} - 2 q^{94} - 24 q^{95} - 28 q^{96} + 50 q^{97} + 29 q^{98} - 14 q^{99}+O(q^{100}) $ 3 * q + 2 * q^2 + 5 * q^3 + 6 * q^5 + q^6 + 8 * q^7 + 3 * q^8 + 4 * q^9 + 4 * q^10 + 6 * q^13 + 10 * q^14 + 10 * q^15 + 2 * q^16 + 4 * q^17 - 9 * q^18 - 12 * q^19 + 11 * q^21 - 7 * q^22 + 11 * q^23 + 12 * q^24 - 3 * q^25 - 3 * q^26 + 8 * q^27 + 7 * q^28 - q^29 + 2 * q^30 + 5 * q^31 - 7 * q^32 - 7 * q^33 + 12 * q^34 + 16 * q^35 - 7 * q^36 + 2 * q^37 - 15 * q^38 + 17 * q^39 + 6 * q^40 - 6 * q^41 + 12 * q^42 - 21 * q^44 + 8 * q^45 + 5 * q^46 - 3 * q^47 + q^48 + 5 * q^49 - 2 * q^50 + 2 * q^51 - 7 * q^52 + 9 * q^53 - 25 * q^54 + 8 * q^56 - 13 * q^57 + 11 * q^58 - 24 * q^59 + q^61 + 15 * q^62 - q^63 - 11 * q^64 + 12 * q^65 - 14 * q^66 - 2 * q^67 + 14 * q^68 + 16 * q^69 + 20 * q^70 + 25 * q^72 + 14 * q^73 - q^74 - 5 * q^75 - 7 * q^76 - 7 * q^77 - 12 * q^78 + 3 * q^79 + 4 * q^80 + 27 * q^81 - 18 * q^82 + 19 * q^83 + 14 * q^84 + 8 * q^85 - 11 * q^87 - 21 * q^88 + 26 * q^89 - 18 * q^90 + 9 * q^91 - 7 * q^92 - 8 * q^93 - 2 * q^94 - 24 * q^95 - 28 * q^96 + 50 * q^97 + 29 * q^98 - 14 * 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 $

$2$	2.24698	1.58885	0.794427	−	0.607359i	$-0.207771\pi$
$2$	2.24698	1.58885	0.794427	+	0.607359i	$0.207771\pi$
$3$	1.55496	0.897755	0.448878	−	0.893593i	$-0.351824\pi$
$3$	1.55496	0.897755	0.448878	+	0.893593i	$0.351824\pi$
$4$	3.04892	1.52446
$5$	2.00000	0.894427	0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000	0.894427	0.447214	+	0.894427i	$0.352416\pi$
$6$	3.49396	1.42640
$7$	4.24698	1.60521	0.802604	−	0.596513i	$-0.203447\pi$
$7$	4.24698	1.60521	0.802604	+	0.596513i	$0.203447\pi$
$8$	2.35690	0.833289
$9$	−0.582105	−0.194035
$10$	4.49396	1.42111
$11$	−4.40581	−1.32840	−0.664201	−	0.747554i	$-0.731228\pi$
$11$	−4.40581	−1.32840	−0.664201	+	0.747554i	$0.731228\pi$
$12$	4.74094	1.36859
$13$	0.307979	0.0854179	0.0427089	−	0.999088i	$-0.486401\pi$
$13$	0.307979	0.0854179	0.0427089	+	0.999088i	$0.486401\pi$
$14$	9.54288	2.55044
$15$	3.10992	0.802977
$16$	−0.801938	−0.200484
$17$	4.49396	1.08995	0.544973	−	0.838454i	$-0.316540\pi$
$17$	4.49396	1.08995	0.544973	+	0.838454i	$0.316540\pi$
$18$	−1.30798	−0.308293
$19$	−5.69202	−1.30584	−0.652920	−	0.757427i	$-0.726456\pi$
$19$	−5.69202	−1.30584	−0.652920	+	0.757427i	$0.726456\pi$
$20$	6.09783	1.36352
$21$	6.60388	1.44108
$22$	−9.89977	−2.11064
$23$	2.19806	0.458328	0.229164	−	0.973388i	$-0.426401\pi$
$23$	2.19806	0.458328	0.229164	+	0.973388i	$0.426401\pi$
$24$	3.66487	0.748089
$25$	−1.00000	−0.200000
$26$	0.692021	0.135717
$27$	−5.57002	−1.07195
$28$	12.9487	2.44707
$29$	2.93900	0.545759	0.272879	−	0.962048i	$-0.412024\pi$
$29$	2.93900	0.545759	0.272879	+	0.962048i	$0.412024\pi$
$30$	6.98792	1.27581
$31$	3.58211	0.643365	0.321683	−	0.946848i	$-0.395752\pi$
$31$	3.58211	0.643365	0.321683	+	0.946848i	$0.395752\pi$
$32$	−6.51573	−1.15183
$33$	−6.85086	−1.19258
$34$	10.0978	1.73176
$35$	8.49396	1.43574
$36$	−1.77479	−0.295798
$37$	−4.87263	−0.801055	−0.400527	−	0.916285i	$-0.631173\pi$
$37$	−4.87263	−0.801055	−0.400527	+	0.916285i	$0.631173\pi$
$38$	−12.7899	−2.07479
$39$	0.478894	0.0766844
$40$	4.71379	0.745316
$41$	−4.02715	−0.628935	−0.314467	−	0.949268i	$-0.601826\pi$
$41$	−4.02715	−0.628935	−0.314467	+	0.949268i	$0.601826\pi$
$42$	14.8388	2.28967
$43$	0	0
$43$	0	0
$44$	−13.4330	−2.02509
$45$	−1.16421	−0.173550
$46$	4.93900	0.728216
$47$	−1.00000	−0.145865	−0.0729325	−	0.997337i	$-0.523236\pi$
$47$	−1.00000	−0.145865	−0.0729325	+	0.997337i	$0.523236\pi$
$48$	−1.24698	−0.179986
$49$	11.0368	1.57669
$50$	−2.24698	−0.317771
$51$	6.98792	0.978504
$52$	0.939001	0.130216
$53$	−1.40581	−0.193103	−0.0965516	−	0.995328i	$-0.530781\pi$
$53$	−1.40581	−0.193103	−0.0965516	+	0.995328i	$0.530781\pi$
$54$	−12.5157	−1.70318
$55$	−8.81163	−1.18816
$56$	10.0097	1.33760
$57$	−8.85086	−1.17232
$58$	6.60388	0.867131
$59$	−3.25906	−0.424294	−0.212147	−	0.977238i	$-0.568046\pi$
$59$	−3.25906	−0.424294	−0.212147	+	0.977238i	$0.568046\pi$
$60$	9.48188	1.22411
$61$	−2.26875	−0.290484	−0.145242	−	0.989396i	$-0.546396\pi$
$61$	−2.26875	−0.290484	−0.145242	+	0.989396i	$0.546396\pi$
$62$	8.04892	1.02221
$63$	−2.47219	−0.311467
$64$	−13.0368	−1.62960
$65$	0.615957	0.0764001
$66$	−15.3937	−1.89484
$67$	4.18598	0.511399	0.255699	−	0.966756i	$-0.417694\pi$
$67$	4.18598	0.511399	0.255699	+	0.966756i	$0.417694\pi$
$68$	13.7017	1.66158
$69$	3.41789	0.411466
$70$	19.0858	2.28118
$71$	8.81163	1.04575	0.522874	−	0.852410i	$-0.324860\pi$
$71$	8.81163	1.04575	0.522874	+	0.852410i	$0.324860\pi$
$72$	−1.37196	−0.161687
$73$	−4.25667	−0.498205	−0.249103	−	0.968477i	$-0.580136\pi$
$73$	−4.25667	−0.498205	−0.249103	+	0.968477i	$0.580136\pi$
$74$	−10.9487	−1.27276
$75$	−1.55496	−0.179551
$76$	−17.3545	−1.99070
$77$	−18.7114	−2.13236
$78$	1.07606	0.121840
$79$	3.71379	0.417834	0.208917	−	0.977933i	$-0.433006\pi$
$79$	3.71379	0.417834	0.208917	+	0.977933i	$0.433006\pi$
$80$	−1.60388	−0.179319
$81$	−6.91484	−0.768315
$82$	−9.04892	−0.999286
$83$	10.1642	1.11567	0.557834	−	0.829953i	$-0.311633\pi$
$83$	10.1642	1.11567	0.557834	+	0.829953i	$0.311633\pi$
$84$	20.1347	2.19687
$85$	8.98792	0.974877
$86$	0	0
$87$	4.57002	0.489958
$88$	−10.3840	−1.10694
$89$	−4.99761	−0.529745	−0.264873	−	0.964283i	$-0.585330\pi$
$89$	−4.99761	−0.529745	−0.264873	+	0.964283i	$0.585330\pi$
$90$	−2.61596	−0.275746
$91$	1.30798	0.137113
$92$	6.70171	0.698702
$93$	5.57002	0.577585
$94$	−2.24698	−0.231758
$95$	−11.3840	−1.16798
$96$	−10.1317	−1.03406
$97$	18.2470	1.85270	0.926350	−	0.376664i	$-0.122929\pi$
$97$	18.2470	1.85270	0.926350	+	0.376664i	$0.122929\pi$
$98$	24.7995	2.50513
$99$	2.56465	0.257757
$100$	−3.04892	−0.304892
$101$	−9.21983	−0.917408	−0.458704	−	0.888589i	$-0.651686\pi$
$101$	−9.21983	−0.917408	−0.458704	+	0.888589i	$0.651686\pi$
$102$	15.7017	1.55470
$103$	−1.16421	−0.114713	−0.0573565	−	0.998354i	$-0.518267\pi$
$103$	−1.16421	−0.114713	−0.0573565	+	0.998354i	$0.518267\pi$
$104$	0.725873	0.0711777
$105$	13.2078	1.28894
$106$	−3.15883	−0.306813
$107$	−15.6407	−1.51204	−0.756022	−	0.654546i	$-0.772860\pi$
$107$	−15.6407	−1.51204	−0.756022	+	0.654546i	$0.772860\pi$
$108$	−16.9825	−1.63415
$109$	8.94869	0.857129	0.428565	−	0.903511i	$-0.359019\pi$
$109$	8.94869	0.857129	0.428565	+	0.903511i	$0.359019\pi$
$110$	−19.7995	−1.88781
$111$	−7.57673	−0.719151
$112$	−3.40581	−0.321819
$113$	−9.34481	−0.879086	−0.439543	−	0.898222i	$-0.644860\pi$
$113$	−9.34481	−0.879086	−0.439543	+	0.898222i	$0.644860\pi$
$114$	−19.8877	−1.86265
$115$	4.39612	0.409941
$116$	8.96077	0.831987
$117$	−0.179276	−0.0165741
$118$	−7.32304	−0.674141
$119$	19.0858	1.74959
$120$	7.32975	0.669111
$121$	8.41119	0.764654
$122$	−5.09783	−0.461536
$123$	−6.26205	−0.564630
$124$	10.9215	0.980783
$125$	−12.0000	−1.07331
$126$	−5.55496	−0.494875
$127$	−14.6407	−1.29915	−0.649577	−	0.760296i	$-0.725054\pi$
$127$	−14.6407	−1.29915	−0.649577	+	0.760296i	$0.725054\pi$
$128$	−16.2620	−1.43738
$129$	0	0
$130$	1.38404	0.121389
$131$	10.4940	0.916861	0.458431	−	0.888730i	$-0.348412\pi$
$131$	10.4940	0.916861	0.458431	+	0.888730i	$0.348412\pi$
$132$	−20.8877	−1.81804
$133$	−24.1739	−2.09614
$134$	9.40581	0.812539
$135$	−11.1400	−0.958783
$136$	10.5918	0.908239
$137$	8.94869	0.764538	0.382269	−	0.924051i	$-0.375143\pi$
$137$	8.94869	0.764538	0.382269	+	0.924051i	$0.375143\pi$
$138$	7.67994	0.653760
$139$	8.41789	0.713997	0.356998	−	0.934105i	$-0.383800\pi$
$139$	8.41789	0.713997	0.356998	+	0.934105i	$0.383800\pi$
$140$	25.8974	2.18873
$141$	−1.55496	−0.130951
$142$	19.7995	1.66154
$143$	−1.35690	−0.113469
$144$	0.466812	0.0389010
$145$	5.87800	0.488142
$146$	−9.56465	−0.791576
$147$	17.1618	1.41548
$148$	−14.8562	−1.22117
$149$	6.23490	0.510783	0.255391	−	0.966838i	$-0.417796\pi$
$149$	6.23490	0.510783	0.255391	+	0.966838i	$0.417796\pi$
$150$	−3.49396	−0.285281
$151$	5.60388	0.456037	0.228018	−	0.973657i	$-0.426775\pi$
$151$	5.60388	0.456037	0.228018	+	0.973657i	$0.426775\pi$
$152$	−13.4155	−1.08814
$153$	−2.61596	−0.211488
$154$	−42.0441	−3.38801
$155$	7.16421	0.575443
$156$	1.46011	0.116902
$157$	−10.5985	−0.845852	−0.422926	−	0.906164i	$-0.638997\pi$
$157$	−10.5985	−0.845852	−0.422926	+	0.906164i	$0.638997\pi$
$158$	8.34481	0.663878
$159$	−2.18598	−0.173360
$160$	−13.0315	−1.03023
$161$	9.33513	0.735711
$162$	−15.5375	−1.22074
$163$	23.4155	1.83404	0.917022	−	0.398837i	$-0.130586\pi$
$163$	23.4155	1.83404	0.917022	+	0.398837i	$0.130586\pi$
$164$	−12.2784	−0.958785
$165$	−13.7017	−1.06668
$166$	22.8388	1.77263
$167$	9.91484	0.767233	0.383617	−	0.923492i	$-0.374678\pi$
$167$	9.91484	0.767233	0.383617	+	0.923492i	$0.374678\pi$
$168$	15.5646	1.20084
$169$	−12.9051	−0.992704
$170$	20.1957	1.54894
$171$	3.31336	0.253379
$172$	0	0
$173$	−1.53319	−0.116566	−0.0582831	−	0.998300i	$-0.518563\pi$
$173$	−1.53319	−0.116566	−0.0582831	+	0.998300i	$0.518563\pi$
$174$	10.2687	0.778472
$175$	−4.24698	−0.321041
$176$	3.53319	0.266324
$177$	−5.06770	−0.380912
$178$	−11.2295	−0.841688
$179$	17.2228	1.28729	0.643647	−	0.765323i	$-0.277421\pi$
$179$	17.2228	1.28729	0.643647	+	0.765323i	$0.277421\pi$
$180$	−3.54958	−0.264570
$181$	12.1347	0.901963	0.450981	−	0.892533i	$-0.351074\pi$
$181$	12.1347	0.901963	0.450981	+	0.892533i	$0.351074\pi$
$182$	2.93900	0.217853
$183$	−3.52781	−0.260783
$184$	5.18060	0.381919
$185$	−9.74525	−0.716485
$186$	12.5157	0.917698
$187$	−19.7995	−1.44789
$188$	−3.04892	−0.222365
$189$	−23.6558	−1.72070
$190$	−25.5797	−1.85575
$191$	16.0218	1.15929	0.579647	−	0.814867i	$-0.303190\pi$
$191$	16.0218	1.15929	0.579647	+	0.814867i	$0.303190\pi$
$192$	−20.2717	−1.46299
$193$	23.7875	1.71226	0.856130	−	0.516761i	$-0.172863\pi$
$193$	23.7875	1.71226	0.856130	+	0.516761i	$0.172863\pi$
$194$	41.0006	2.94367
$195$	0.957787	0.0685886
$196$	33.6504	2.40360
$197$	15.8552	1.12963	0.564817	−	0.825216i	$-0.308947\pi$
$197$	15.8552	1.12963	0.564817	+	0.825216i	$0.308947\pi$
$198$	5.76271	0.409538
$199$	−8.75840	−0.620866	−0.310433	−	0.950595i	$-0.600474\pi$
$199$	−8.75840	−0.620866	−0.310433	+	0.950595i	$0.600474\pi$
$200$	−2.35690	−0.166658
$201$	6.50902	0.459111
$202$	−20.7168	−1.45763
$203$	12.4819	0.876056
$204$	21.3056	1.49169
$205$	−8.05429	−0.562536
$206$	−2.61596	−0.182262
$207$	−1.27950	−0.0889316
$208$	−0.246980	−0.0171250
$209$	25.0780	1.73468
$210$	29.6775	2.04795
$211$	−8.58642	−0.591113	−0.295557	−	0.955325i	$-0.595505\pi$
$211$	−8.58642	−0.591113	−0.295557	+	0.955325i	$0.595505\pi$
$212$	−4.28621	−0.294378
$213$	13.7017	0.938826
$214$	−35.1444	−2.40242
$215$	0	0
$216$	−13.1280	−0.893245
$217$	15.2131	1.03273
$218$	20.1075	1.36185
$219$	−6.61894	−0.447267
$220$	−26.8659	−1.81130
$221$	1.38404	0.0931008
$222$	−17.0248	−1.14263
$223$	7.60388	0.509193	0.254597	−	0.967047i	$-0.418057\pi$
$223$	7.60388	0.509193	0.254597	+	0.967047i	$0.418057\pi$
$224$	−27.6722	−1.84892
$225$	0.582105	0.0388070
$226$	−20.9976	−1.39674
$227$	−15.5133	−1.02966	−0.514828	−	0.857293i	$-0.672144\pi$
$227$	−15.5133	−1.02966	−0.514828	+	0.857293i	$0.672144\pi$
$228$	−26.9855	−1.78716
$229$	−23.6353	−1.56187	−0.780933	−	0.624614i	$-0.785256\pi$
$229$	−23.6353	−1.56187	−0.780933	+	0.624614i	$0.785256\pi$
$230$	9.87800	0.651336
$231$	−29.0954	−1.91434
$232$	6.92692	0.454775
$233$	21.6625	1.41916	0.709578	−	0.704627i	$-0.248886\pi$
$233$	21.6625	1.41916	0.709578	+	0.704627i	$0.248886\pi$
$234$	−0.402829	−0.0263338
$235$	−2.00000	−0.130466
$236$	−9.93661	−0.646818
$237$	5.77479	0.375113
$238$	42.8853	2.77984
$239$	−17.2010	−1.11264	−0.556322	−	0.830967i	$-0.687788\pi$
$239$	−17.2010	−1.11264	−0.556322	+	0.830967i	$0.687788\pi$
$240$	−2.49396	−0.160984
$241$	−25.2892	−1.62902	−0.814510	−	0.580149i	$-0.802994\pi$
$241$	−25.2892	−1.62902	−0.814510	+	0.580149i	$0.802994\pi$
$242$	18.8998	1.21492
$243$	5.95779	0.382192
$244$	−6.91723	−0.442830
$245$	22.0737	1.41024
$246$	−14.0707	−0.897114
$247$	−1.75302	−0.111542
$248$	8.44265	0.536109
$249$	15.8049	1.00160
$250$	−26.9638	−1.70534
$251$	−1.94139	−0.122540	−0.0612699	−	0.998121i	$-0.519515\pi$
$251$	−1.94139	−0.122540	−0.0612699	+	0.998121i	$0.519515\pi$
$252$	−7.53750	−0.474818
$253$	−9.68425	−0.608844
$254$	−32.8974	−2.06417
$255$	13.9758	0.875201
$256$	−10.4668	−0.654176
$257$	−15.7168	−0.980386	−0.490193	−	0.871614i	$-0.663074\pi$
$257$	−15.7168	−0.980386	−0.490193	+	0.871614i	$0.663074\pi$
$258$	0	0
$259$	−20.6939	−1.28586
$260$	1.87800	0.116469
$261$	−1.71081	−0.105896
$262$	23.5797	1.45676
$263$	14.6770	0.905020	0.452510	−	0.891759i	$-0.350529\pi$
$263$	14.6770	0.905020	0.452510	+	0.891759i	$0.350529\pi$
$264$	−16.1468	−0.993764
$265$	−2.81163	−0.172717
$266$	−54.3183	−3.33047
$267$	−7.77107	−0.475582
$268$	12.7627	0.779607
$269$	−15.0761	−0.919204	−0.459602	−	0.888125i	$-0.652008\pi$
$269$	−15.0761	−0.919204	−0.459602	+	0.888125i	$0.652008\pi$
$270$	−25.0315	−1.52337
$271$	−23.1347	−1.40533	−0.702666	−	0.711520i	$-0.748007\pi$
$271$	−23.1347	−1.40533	−0.702666	+	0.711520i	$0.748007\pi$
$272$	−3.60388	−0.218517
$273$	2.03385	0.123094
$274$	20.1075	1.21474
$275$	4.40581	0.265681
$276$	10.4209	0.627263
$277$	−20.7821	−1.24867	−0.624337	−	0.781155i	$-0.714631\pi$
$277$	−20.7821	−1.24867	−0.624337	+	0.781155i	$0.714631\pi$
$278$	18.9148	1.13444
$279$	−2.08516	−0.124835
$280$	20.0194	1.19639
$281$	18.8364	1.12368	0.561842	−	0.827244i	$-0.310093\pi$
$281$	18.8364	1.12368	0.561842	+	0.827244i	$0.310093\pi$
$282$	−3.49396	−0.208062
$283$	−13.0435	−0.775358	−0.387679	−	0.921794i	$-0.626723\pi$
$283$	−13.0435	−0.775358	−0.387679	+	0.921794i	$0.626723\pi$
$284$	26.8659	1.59420
$285$	−17.7017	−1.04856
$286$	−3.04892	−0.180286
$287$	−17.1032	−1.00957
$288$	3.79284	0.223495
$289$	3.19567	0.187981
$290$	13.2078	0.775586
$291$	28.3733	1.66327
$292$	−12.9782	−0.759493
$293$	26.5297	1.54988	0.774942	−	0.632033i	$-0.217779\pi$
$293$	26.5297	1.54988	0.774942	+	0.632033i	$0.217779\pi$
$294$	38.5623	2.24900
$295$	−6.51812	−0.379500
$296$	−11.4843	−0.667510
$297$	24.5405	1.42398
$298$	14.0097	0.811559
$299$	0.676956	0.0391494
$300$	−4.74094	−0.273718
$301$	0	0
$302$	12.5918	0.724576
$303$	−14.3365	−0.823608
$304$	4.56465	0.261800
$305$	−4.53750	−0.259816
$306$	−5.87800	−0.336023
$307$	−7.08277	−0.404235	−0.202117	−	0.979361i	$-0.564782\pi$
$307$	−7.08277	−0.404235	−0.202117	+	0.979361i	$0.564782\pi$
$308$	−57.0495	−3.25070
$309$	−1.81030	−0.102984
$310$	16.0978	0.914296
$311$	−18.9172	−1.07270	−0.536349	−	0.843996i	$-0.680197\pi$
$311$	−18.9172	−1.07270	−0.536349	+	0.843996i	$0.680197\pi$
$312$	1.12870	0.0639002
$313$	18.6082	1.05180	0.525898	−	0.850547i	$-0.323729\pi$
$313$	18.6082	1.05180	0.525898	+	0.850547i	$0.323729\pi$
$314$	−23.8146	−1.34394
$315$	−4.94438	−0.278584
$316$	11.3230	0.636971
$317$	−14.3110	−0.803784	−0.401892	−	0.915687i	$-0.631647\pi$
$317$	−14.3110	−0.803784	−0.401892	+	0.915687i	$0.631647\pi$
$318$	−4.91185	−0.275443
$319$	−12.9487	−0.724987
$320$	−26.0737	−1.45756
$321$	−24.3207	−1.35745
$322$	20.9758	1.16894
$323$	−25.5797	−1.42329
$324$	−21.0828	−1.17126
$325$	−0.307979	−0.0170836
$326$	52.6142	2.91403
$327$	13.9148	0.769492
$328$	−9.49157	−0.524084
$329$	−4.24698	−0.234144
$330$	−30.7875	−1.69479
$331$	−19.4668	−1.06999	−0.534996	−	0.844854i	$-0.679687\pi$
$331$	−19.4668	−1.06999	−0.534996	+	0.844854i	$0.679687\pi$
$332$	30.9898	1.70079
$333$	2.83638	0.155433
$334$	22.2784	1.21902
$335$	8.37196	0.457409
$336$	−5.29590	−0.288915
$337$	−7.66786	−0.417695	−0.208847	−	0.977948i	$-0.566971\pi$
$337$	−7.66786	−0.417695	−0.208847	+	0.977948i	$0.566971\pi$
$338$	−28.9976	−1.57726
$339$	−14.5308	−0.789204
$340$	27.4034	1.48616
$341$	−15.7821	−0.854648
$342$	7.44504	0.402582
$343$	17.1444	0.925708
$344$	0	0
$345$	6.83579	0.368027
$346$	−3.44504	−0.185207
$347$	−5.52648	−0.296677	−0.148339	−	0.988937i	$-0.547393\pi$
$347$	−5.52648	−0.296677	−0.148339	+	0.988937i	$0.547393\pi$
$348$	13.9336	0.746921
$349$	2.57673	0.137929	0.0689646	−	0.997619i	$-0.478030\pi$
$349$	2.57673	0.137929	0.0689646	+	0.997619i	$0.478030\pi$
$350$	−9.54288	−0.510088
$351$	−1.71545	−0.0915638
$352$	28.7071	1.53009
$353$	23.9758	1.27611	0.638053	−	0.769993i	$-0.279740\pi$
$353$	23.9758	1.27611	0.638053	+	0.769993i	$0.279740\pi$
$354$	−11.3870	−0.605214
$355$	17.6233	0.935345
$356$	−15.2373	−0.807575
$357$	29.6775	1.57070
$358$	38.6993	2.04532
$359$	−2.72156	−0.143639	−0.0718193	−	0.997418i	$-0.522880\pi$
$359$	−2.72156	−0.143639	−0.0718193	+	0.997418i	$0.522880\pi$
$360$	−2.74392	−0.144617
$361$	13.3991	0.705216
$362$	27.2664	1.43309
$363$	13.0790	0.686472
$364$	3.98792	0.209024
$365$	−8.51334	−0.445608
$366$	−7.92692	−0.414347
$367$	−19.4523	−1.01540	−0.507702	−	0.861533i	$-0.669505\pi$
$367$	−19.4523	−1.01540	−0.507702	+	0.861533i	$0.669505\pi$
$368$	−1.76271	−0.0918876
$369$	2.34422	0.122035
$370$	−21.8974	−1.13839
$371$	−5.97046	−0.309971
$372$	16.9825	0.880504
$373$	17.8931	0.926468	0.463234	−	0.886236i	$-0.346689\pi$
$373$	17.8931	0.926468	0.463234	+	0.886236i	$0.346689\pi$
$374$	−44.4892	−2.30048
$375$	−18.6595	−0.963572
$376$	−2.35690	−0.121548
$377$	0.905149	0.0466176
$378$	−53.1540	−2.73395
$379$	4.83877	0.248551	0.124276	−	0.992248i	$-0.460339\pi$
$379$	4.83877	0.248551	0.124276	+	0.992248i	$0.460339\pi$
$380$	−34.7090	−1.78053
$381$	−22.7657	−1.16632
$382$	36.0006	1.84195
$383$	4.32544	0.221020	0.110510	−	0.993875i	$-0.464752\pi$
$383$	4.32544	0.221020	0.110510	+	0.993875i	$0.464752\pi$
$384$	−25.2868	−1.29041
$385$	−37.4228	−1.90724
$386$	53.4499	2.72053
$387$	0	0
$388$	55.6335	2.82436
$389$	−29.6993	−1.50582	−0.752908	−	0.658126i	$-0.771349\pi$
$389$	−29.6993	−1.50582	−0.752908	+	0.658126i	$0.771349\pi$
$390$	2.15213	0.108977
$391$	9.87800	0.499552
$392$	26.0127	1.31384
$393$	16.3177	0.823117
$394$	35.6262	1.79482
$395$	7.42758	0.373722
$396$	7.81940	0.392939
$397$	8.30021	0.416576	0.208288	−	0.978068i	$-0.433211\pi$
$397$	8.30021	0.416576	0.208288	+	0.978068i	$0.433211\pi$
$398$	−19.6799	−0.986466
$399$	−37.5894	−1.88182
$400$	0.801938	0.0400969
$401$	−0.936017	−0.0467425	−0.0233712	−	0.999727i	$-0.507440\pi$
$401$	−0.936017	−0.0467425	−0.0233712	+	0.999727i	$0.507440\pi$
$402$	14.6256	0.729461
$403$	1.10321	0.0549549
$404$	−28.1105	−1.39855
$405$	−13.8297	−0.687202
$406$	28.0465	1.39193
$407$	21.4679	1.06412
$408$	16.4698	0.815376
$409$	−3.42327	−0.169270	−0.0846349	−	0.996412i	$-0.526972\pi$
$409$	−3.42327	−0.169270	−0.0846349	+	0.996412i	$0.526972\pi$
$410$	−18.0978	−0.893788
$411$	13.9148	0.686368
$412$	−3.54958	−0.174875
$413$	−13.8412	−0.681079
$414$	−2.87502	−0.141299
$415$	20.3284	0.997883
$416$	−2.00670	−0.0983868
$417$	13.0895	0.640994
$418$	56.3497	2.75615
$419$	−3.15213	−0.153992	−0.0769958	−	0.997031i	$-0.524533\pi$
$419$	−3.15213	−0.153992	−0.0769958	+	0.997031i	$0.524533\pi$
$420$	40.2693	1.96494
$421$	−32.4644	−1.58222	−0.791109	−	0.611675i	$-0.790496\pi$
$421$	−32.4644	−1.58222	−0.791109	+	0.611675i	$0.790496\pi$
$422$	−19.2935	−0.939193
$423$	0.582105	0.0283029
$424$	−3.31336	−0.160911
$425$	−4.49396	−0.217989
$426$	30.7875	1.49166
$427$	−9.63533	−0.466287
$428$	−47.6872	−2.30505
$429$	−2.10992	−0.101868
$430$	0	0
$431$	35.9148	1.72996	0.864978	−	0.501809i	$-0.167332\pi$
$431$	35.9148	1.72996	0.864978	+	0.501809i	$0.167332\pi$
$432$	4.46681	0.214910
$433$	−26.5646	−1.27662	−0.638308	−	0.769781i	$-0.720365\pi$
$433$	−26.5646	−1.27662	−0.638308	+	0.769781i	$0.720365\pi$
$434$	34.1836	1.64086
$435$	9.14005	0.438232
$436$	27.2838	1.30666
$437$	−12.5114	−0.598502
$438$	−14.8726	−0.710642
$439$	40.0006	1.90912	0.954562	−	0.298012i	$-0.0963237\pi$
$439$	40.0006	1.90912	0.954562	+	0.298012i	$0.0963237\pi$
$440$	−20.7681	−0.990080
$441$	−6.42460	−0.305933
$442$	3.10992	0.147924
$443$	15.8006	0.750710	0.375355	−	0.926881i	$-0.377521\pi$
$443$	15.8006	0.750710	0.375355	+	0.926881i	$0.377521\pi$
$444$	−23.1008	−1.09632
$445$	−9.99521	−0.473819
$446$	17.0858	0.809034
$447$	9.69501	0.458558
$448$	−55.3672	−2.61585
$449$	13.0204	0.614473	0.307236	−	0.951633i	$-0.400596\pi$
$449$	13.0204	0.614473	0.307236	+	0.951633i	$0.400596\pi$
$450$	1.30798	0.0616587
$451$	17.7429	0.835479
$452$	−28.4916	−1.34013
$453$	8.71379	0.409410
$454$	−34.8582	−1.63597
$455$	2.61596	0.122638
$456$	−20.8605	−0.976884
$457$	24.6655	1.15380	0.576901	−	0.816814i	$-0.304262\pi$
$457$	24.6655	1.15380	0.576901	+	0.816814i	$0.304262\pi$
$458$	−53.1081	−2.48158
$459$	−25.0315	−1.16837
$460$	13.4034	0.624938
$461$	10.1661	0.473484	0.236742	−	0.971573i	$-0.423920\pi$
$461$	10.1661	0.473484	0.236742	+	0.971573i	$0.423920\pi$
$462$	−65.3769	−3.04161
$463$	−14.5700	−0.677126	−0.338563	−	0.940944i	$-0.609941\pi$
$463$	−14.5700	−0.677126	−0.338563	+	0.940944i	$0.609941\pi$
$464$	−2.35690	−0.109416
$465$	11.1400	0.516607
$466$	48.6752	2.25483
$467$	−9.56704	−0.442710	−0.221355	−	0.975193i	$-0.571048\pi$
$467$	−9.56704	−0.442710	−0.221355	+	0.975193i	$0.571048\pi$
$468$	−0.546597	−0.0252665
$469$	17.7778	0.820901
$470$	−4.49396	−0.207291
$471$	−16.4802	−0.759369
$472$	−7.68127	−0.353559
$473$	0	0
$474$	12.9758	0.596000
$475$	5.69202	0.261168
$476$	58.1909	2.66717
$477$	0.818331	0.0374688
$478$	−38.6504	−1.76783
$479$	−24.7851	−1.13246	−0.566229	−	0.824248i	$-0.691598\pi$
$479$	−24.7851	−1.13246	−0.566229	+	0.824248i	$0.691598\pi$
$480$	−20.2634	−0.924892
$481$	−1.50066	−0.0684244
$482$	−56.8243	−2.58828
$483$	14.5157	0.660489
$484$	25.6450	1.16568
$485$	36.4940	1.65711
$486$	13.3870	0.607248
$487$	25.9071	1.17396	0.586981	−	0.809601i	$-0.300316\pi$
$487$	25.9071	1.17396	0.586981	+	0.809601i	$0.300316\pi$
$488$	−5.34721	−0.242057
$489$	36.4101	1.64652
$490$	49.5991	2.24066
$491$	−24.7047	−1.11491	−0.557454	−	0.830208i	$-0.688222\pi$
$491$	−24.7047	−1.11491	−0.557454	+	0.830208i	$0.688222\pi$
$492$	−19.0925	−0.860754
$493$	13.2078	0.594847
$494$	−3.93900	−0.177224
$495$	5.12929	0.230545
$496$	−2.87263	−0.128985
$497$	37.4228	1.67864
$498$	35.5133	1.59139
$499$	28.0810	1.25708	0.628538	−	0.777779i	$-0.283654\pi$
$499$	28.0810	1.25708	0.628538	+	0.777779i	$0.283654\pi$
$500$	−36.5870	−1.63622
$501$	15.4172	0.688788
$502$	−4.36227	−0.194698
$503$	28.9119	1.28912	0.644558	−	0.764555i	$-0.277041\pi$
$503$	28.9119	1.28912	0.644558	+	0.764555i	$0.277041\pi$
$504$	−5.82669	−0.259541
$505$	−18.4397	−0.820554
$506$	−21.7603	−0.967364
$507$	−20.0670	−0.891205
$508$	−44.6383	−1.98051
$509$	3.65040	0.161801	0.0809006	−	0.996722i	$-0.474220\pi$
$509$	3.65040	0.161801	0.0809006	+	0.996722i	$0.474220\pi$
$510$	31.4034	1.39057
$511$	−18.0780	−0.799723
$512$	9.00538	0.397985
$513$	31.7047	1.39980
$514$	−35.3153	−1.55769
$515$	−2.32842	−0.102602
$516$	0	0
$517$	4.40581	0.193767
$518$	−46.4989	−2.04304
$519$	−2.38404	−0.104648
$520$	1.45175	0.0636633
$521$	13.6256	0.596950	0.298475	−	0.954417i	$-0.403522\pi$
$521$	13.6256	0.596950	0.298475	+	0.954417i	$0.403522\pi$
$522$	−3.84415	−0.168254
$523$	−4.45904	−0.194980	−0.0974902	−	0.995236i	$-0.531081\pi$
$523$	−4.45904	−0.194980	−0.0974902	+	0.995236i	$0.531081\pi$
$524$	31.9952	1.39772
$525$	−6.60388	−0.288217
$526$	32.9788	1.43794
$527$	16.0978	0.701233
$528$	5.49396	0.239094
$529$	−18.1685	−0.789936
$530$	−6.31767	−0.274422
$531$	1.89712	0.0823278
$532$	−73.7042	−3.19548
$533$	−1.24027	−0.0537223
$534$	−17.4614	−0.755630
$535$	−31.2814	−1.35241
$536$	9.86592	0.426143
$537$	26.7808	1.15568
$538$	−33.8756	−1.46048
$539$	−48.6262	−2.09448
$540$	−33.9651	−1.46162
$541$	−16.8291	−0.723539	−0.361769	−	0.932268i	$-0.617827\pi$
$541$	−16.8291	−0.723539	−0.361769	+	0.932268i	$0.617827\pi$
$542$	−51.9831	−2.23287
$543$	18.8689	0.809742
$544$	−29.2814	−1.25543
$545$	17.8974	0.766640
$546$	4.57002	0.195579
$547$	−7.93661	−0.339345	−0.169672	−	0.985501i	$-0.554271\pi$
$547$	−7.93661	−0.339345	−0.169672	+	0.985501i	$0.554271\pi$
$548$	27.2838	1.16551
$549$	1.32065	0.0563640
$550$	9.89977	0.422128
$551$	−16.7289	−0.712673
$552$	8.05562	0.342870
$553$	15.7724	0.670711
$554$	−46.6969	−1.98396
$555$	−15.1535	−0.643228
$556$	25.6655	1.08846
$557$	−14.4849	−0.613743	−0.306872	−	0.951751i	$-0.599282\pi$
$557$	−14.4849	−0.613743	−0.306872	+	0.951751i	$0.599282\pi$
$558$	−4.68532	−0.198345
$559$	0	0
$560$	−6.81163	−0.287844
$561$	−30.7875	−1.29985
$562$	42.3250	1.78537
$563$	−6.72481	−0.283417	−0.141708	−	0.989908i	$-0.545260\pi$
$563$	−6.72481	−0.283417	−0.141708	+	0.989908i	$0.545260\pi$
$564$	−4.74094	−0.199630
$565$	−18.6896	−0.786279
$566$	−29.3086	−1.23193
$567$	−29.3672	−1.23331
$568$	20.7681	0.871410
$569$	−42.2392	−1.77076	−0.885380	−	0.464868i	$-0.846102\pi$
$569$	−42.2392	−1.77076	−0.885380	+	0.464868i	$0.846102\pi$
$570$	−39.7754	−1.66601
$571$	−16.2929	−0.681837	−0.340919	−	0.940093i	$-0.610738\pi$
$571$	−16.2929	−0.681837	−0.340919	+	0.940093i	$0.610738\pi$
$572$	−4.13706	−0.172979
$573$	24.9132	1.04076
$574$	−38.4306	−1.60406
$575$	−2.19806	−0.0916655
$576$	7.58881	0.316200
$577$	44.4838	1.85188	0.925942	−	0.377665i	$-0.123273\pi$
$577$	44.4838	1.85188	0.925942	+	0.377665i	$0.123273\pi$
$578$	7.18060	0.298674
$579$	36.9885	1.53719
$580$	17.9215	0.744152
$581$	43.1672	1.79088
$582$	63.7542	2.64270
$583$	6.19375	0.256519
$584$	−10.0325	−0.415149
$585$	−0.358552	−0.0148243
$586$	59.6118	2.46254
$587$	30.4155	1.25538	0.627691	−	0.778463i	$-0.284000\pi$
$587$	30.4155	1.25538	0.627691	+	0.778463i	$0.284000\pi$
$588$	52.3250	2.15785
$589$	−20.3894	−0.840131
$590$	−14.6461	−0.602970
$591$	24.6541	1.01414
$592$	3.90754	0.160599
$593$	2.27977	0.0936188	0.0468094	−	0.998904i	$-0.485095\pi$
$593$	2.27977	0.0936188	0.0468094	+	0.998904i	$0.485095\pi$
$594$	55.1420	2.26250
$595$	38.1715	1.56488
$596$	19.0097	0.778667
$597$	−13.6189	−0.557386
$598$	1.52111	0.0622027
$599$	−21.9239	−0.895788	−0.447894	−	0.894087i	$-0.647826\pi$
$599$	−21.9239	−0.895788	−0.447894	+	0.894087i	$0.647826\pi$
$600$	−3.66487	−0.149618
$601$	−8.27173	−0.337411	−0.168706	−	0.985666i	$-0.553959\pi$
$601$	−8.27173	−0.337411	−0.168706	+	0.985666i	$0.553959\pi$
$602$	0	0
$603$	−2.43668	−0.0992293
$604$	17.0858	0.695209
$605$	16.8224	0.683927
$606$	−32.2137	−1.30859
$607$	−11.9095	−0.483390	−0.241695	−	0.970352i	$-0.577703\pi$
$607$	−11.9095	−0.483390	−0.241695	+	0.970352i	$0.577703\pi$
$608$	37.0877	1.50410
$609$	19.4088	0.786484
$610$	−10.1957	−0.412811
$611$	−0.307979	−0.0124595
$612$	−7.97584	−0.322404
$613$	−1.89738	−0.0766344	−0.0383172	−	0.999266i	$-0.512200\pi$
$613$	−1.89738	−0.0766344	−0.0383172	+	0.999266i	$0.512200\pi$
$614$	−15.9148	−0.642271
$615$	−12.5241	−0.505020
$616$	−44.1008	−1.77687
$617$	48.5392	1.95411	0.977056	−	0.212981i	$-0.0683171\pi$
$617$	48.5392	1.95411	0.977056	+	0.212981i	$0.0683171\pi$
$618$	−4.06770	−0.163627
$619$	16.1062	0.647363	0.323681	−	0.946166i	$-0.395079\pi$
$619$	16.1062	0.647363	0.323681	+	0.946166i	$0.395079\pi$
$620$	21.8431	0.877239
$621$	−12.2433	−0.491305
$622$	−42.5066	−1.70436
$623$	−21.2247	−0.850351
$624$	−0.384043	−0.0153740
$625$	−19.0000	−0.760000
$626$	41.8122	1.67115
$627$	38.9952	1.55732
$628$	−32.3139	−1.28947
$629$	−21.8974	−0.873106
$630$	−11.1099	−0.442630
$631$	30.7549	1.22433	0.612167	−	0.790728i	$-0.290298\pi$
$631$	30.7549	1.22433	0.612167	+	0.790728i	$0.290298\pi$
$632$	8.75302	0.348176
$633$	−13.3515	−0.530675
$634$	−32.1564	−1.27710
$635$	−29.2814	−1.16200
$636$	−6.66487	−0.264279
$637$	3.39911	0.134678
$638$	−29.0954	−1.15190
$639$	−5.12929	−0.202912
$640$	−32.5241	−1.28563
$641$	20.9148	0.826086	0.413043	−	0.910711i	$-0.364466\pi$
$641$	20.9148	0.826086	0.413043	+	0.910711i	$0.364466\pi$
$642$	−54.6480	−2.15678
$643$	31.5991	1.24615	0.623073	−	0.782164i	$-0.285884\pi$
$643$	31.5991	1.24615	0.623073	+	0.782164i	$0.285884\pi$
$644$	28.4620	1.12156
$645$	0	0
$646$	−57.4771	−2.26141
$647$	36.9288	1.45182	0.725911	−	0.687788i	$-0.241418\pi$
$647$	36.9288	1.45182	0.725911	+	0.687788i	$0.241418\pi$
$648$	−16.2976	−0.640228
$649$	14.3588	0.563633
$650$	−0.692021	−0.0271433
$651$	23.6558	0.927143
$652$	71.3919	2.79592
$653$	4.99894	0.195623	0.0978117	−	0.995205i	$-0.468816\pi$
$653$	4.99894	0.195623	0.0978117	+	0.995205i	$0.468816\pi$
$654$	31.2664	1.22261
$655$	20.9879	0.820066
$656$	3.22952	0.126092
$657$	2.47783	0.0966693
$658$	−9.54288	−0.372020
$659$	−4.24890	−0.165514	−0.0827568	−	0.996570i	$-0.526372\pi$
$659$	−4.24890	−0.165514	−0.0827568	+	0.996570i	$0.526372\pi$
$660$	−41.7754	−1.62610
$661$	−44.1420	−1.71692	−0.858462	−	0.512878i	$-0.828579\pi$
$661$	−44.1420	−1.71692	−0.858462	+	0.512878i	$0.828579\pi$
$662$	−43.7415	−1.70006
$663$	2.15213	0.0835818
$664$	23.9560	0.929673
$665$	−48.3478	−1.87485
$666$	6.37329	0.246960
$667$	6.46011	0.250136
$668$	30.2295	1.16962
$669$	11.8237	0.457131
$670$	18.8116	0.726757
$671$	9.99569	0.385879
$672$	−43.0291	−1.65988
$673$	11.9312	0.459915	0.229958	−	0.973201i	$-0.426141\pi$
$673$	11.9312	0.459915	0.229958	+	0.973201i	$0.426141\pi$
$674$	−17.2295	−0.663656
$675$	5.57002	0.214390
$676$	−39.3467	−1.51334
$677$	35.9812	1.38287	0.691435	−	0.722438i	$-0.256979\pi$
$677$	35.9812	1.38287	0.691435	+	0.722438i	$0.256979\pi$
$678$	−32.6504	−1.25393
$679$	77.4946	2.97397
$680$	21.1836	0.812354
$681$	−24.1226	−0.924380
$682$	−35.4620	−1.35791
$683$	28.3317	1.08408	0.542041	−	0.840352i	$-0.317652\pi$
$683$	28.3317	1.08408	0.542041	+	0.840352i	$0.317652\pi$
$684$	10.1021	0.386265
$685$	17.8974	0.683824
$686$	38.5230	1.47082
$687$	−36.7520	−1.40217
$688$	0	0
$689$	−0.432960	−0.0164945
$690$	15.3599	0.584741
$691$	6.55794	0.249476	0.124738	−	0.992190i	$-0.460191\pi$
$691$	6.55794	0.249476	0.124738	+	0.992190i	$0.460191\pi$
$692$	−4.67456	−0.177700
$693$	10.8920	0.413753
$694$	−12.4179	−0.471377
$695$	16.8358	0.638618
$696$	10.7711	0.408276
$697$	−18.0978	−0.685504
$698$	5.78986	0.219149
$699$	33.6843	1.27406
$700$	−12.9487	−0.489414
$701$	35.9057	1.35614	0.678071	−	0.734997i	$-0.262816\pi$
$701$	35.9057	1.35614	0.678071	+	0.734997i	$0.262816\pi$
$702$	−3.85458	−0.145482
$703$	27.7351	1.04605
$704$	57.4379	2.16477
$705$	−3.10992	−0.117126
$706$	53.8732	2.02755
$707$	−39.1564	−1.47263
$708$	−15.4510	−0.580685
$709$	−41.8920	−1.57329	−0.786644	−	0.617407i	$-0.788183\pi$
$709$	−41.8920	−1.57329	−0.786644	+	0.617407i	$0.788183\pi$
$710$	39.5991	1.48613
$711$	−2.16182	−0.0810745
$712$	−11.7788	−0.441431
$713$	7.87369	0.294872
$714$	66.6848	2.49562
$715$	−2.71379	−0.101490
$716$	52.5109	1.96243
$717$	−26.7469	−0.998882
$718$	−6.11529	−0.228221
$719$	33.1239	1.23531	0.617657	−	0.786448i	$-0.288082\pi$
$719$	33.1239	1.23531	0.617657	+	0.786448i	$0.288082\pi$
$720$	0.933624	0.0347941
$721$	−4.94438	−0.184138
$722$	30.1075	1.12049
$723$	−39.3236	−1.46246
$724$	36.9976	1.37501
$725$	−2.93900	−0.109152
$726$	29.3884	1.09070
$727$	6.95971	0.258121	0.129061	−	0.991637i	$-0.458804\pi$
$727$	6.95971	0.258121	0.129061	+	0.991637i	$0.458804\pi$
$728$	3.08277	0.114255
$729$	30.0086	1.11143
$730$	−19.1293	−0.708007
$731$	0	0
$732$	−10.7560	−0.397553
$733$	−38.6088	−1.42605	−0.713024	−	0.701140i	$-0.752675\pi$
$733$	−38.6088	−1.42605	−0.713024	+	0.701140i	$0.752675\pi$
$734$	−43.7090	−1.61333
$735$	34.3236	1.26605
$736$	−14.3220	−0.527915
$737$	−18.4426	−0.679344
$738$	5.26742	0.193896
$739$	−34.3394	−1.26320	−0.631598	−	0.775296i	$-0.717601\pi$
$739$	−34.3394	−1.26320	−0.631598	+	0.775296i	$0.717601\pi$
$740$	−29.7125	−1.09225
$741$	−2.72587	−0.100137
$742$	−13.4155	−0.492499
$743$	12.3797	0.454168	0.227084	−	0.973875i	$-0.427081\pi$
$743$	12.3797	0.454168	0.227084	+	0.973875i	$0.427081\pi$
$744$	13.1280	0.481295
$745$	12.4698	0.456858
$746$	40.2054	1.47202
$747$	−5.91664	−0.216479
$748$	−60.3672	−2.20724
$749$	−66.4258	−2.42715
$750$	−41.9275	−1.53098
$751$	18.4222	0.672236	0.336118	−	0.941820i	$-0.390886\pi$
$751$	18.4222	0.672236	0.336118	+	0.941820i	$0.390886\pi$
$752$	0.801938	0.0292437
$753$	−3.01879	−0.110011
$754$	2.03385	0.0740685
$755$	11.2078	0.407892
$756$	−72.1245	−2.62314
$757$	−1.51706	−0.0551384	−0.0275692	−	0.999620i	$-0.508777\pi$
$757$	−1.51706	−0.0551384	−0.0275692	+	0.999620i	$0.508777\pi$
$758$	10.8726	0.394912
$759$	−15.0586	−0.546593
$760$	−26.8310	−0.973263
$761$	−5.88902	−0.213477	−0.106738	−	0.994287i	$-0.534041\pi$
$761$	−5.88902	−0.213477	−0.106738	+	0.994287i	$0.534041\pi$
$762$	−51.1540	−1.85312
$763$	38.0049	1.37587
$764$	48.8491	1.76730
$765$	−5.23191	−0.189160
$766$	9.71917	0.351168
$767$	−1.00372	−0.0362423
$768$	−16.2755	−0.587290
$769$	10.3478	0.373151	0.186576	−	0.982441i	$-0.440261\pi$
$769$	10.3478	0.373151	0.186576	+	0.982441i	$0.440261\pi$
$770$	−84.0883	−3.03033
$771$	−24.4389	−0.880146
$772$	72.5260	2.61027
$773$	−21.6601	−0.779059	−0.389530	−	0.921014i	$-0.627362\pi$
$773$	−21.6601	−0.779059	−0.389530	+	0.921014i	$0.627362\pi$
$774$	0	0
$775$	−3.58211	−0.128673
$776$	43.0062	1.54383
$777$	−32.1782	−1.15439
$778$	−66.7338	−2.39252
$779$	22.9226	0.821288
$780$	2.92021	0.104560
$781$	−38.8224	−1.38917
$782$	22.1957	0.793716
$783$	−16.3703	−0.585027
$784$	−8.85086	−0.316102
$785$	−21.1970	−0.756553
$786$	36.6655	1.30781
$787$	−33.2040	−1.18360	−0.591798	−	0.806086i	$-0.701582\pi$
$787$	−33.2040	−1.18360	−0.591798	+	0.806086i	$0.701582\pi$
$788$	48.3411	1.72208
$789$	22.8221	0.812487
$790$	16.6896	0.593790
$791$	−39.6872	−1.41112
$792$	6.04461	0.214786
$793$	−0.698726	−0.0248125
$794$	18.6504	0.661878
$795$	−4.37196	−0.155057
$796$	−26.7036	−0.946485
$797$	−10.1099	−0.358112	−0.179056	−	0.983839i	$-0.557304\pi$
$797$	−10.1099	−0.358112	−0.179056	+	0.983839i	$0.557304\pi$
$798$	−84.4626	−2.98994
$799$	−4.49396	−0.158985
$800$	6.51573	0.230366
$801$	2.90913	0.102789
$802$	−2.10321	−0.0742670
$803$	18.7541	0.661817
$804$	19.8455	0.699896
$805$	18.6703	0.658040
$806$	2.47889	0.0873153
$807$	−23.4426	−0.825220
$808$	−21.7302	−0.764465
$809$	−37.4040	−1.31506	−0.657528	−	0.753431i	$-0.728398\pi$
$809$	−37.4040	−1.31506	−0.657528	+	0.753431i	$0.728398\pi$
$810$	−31.0750	−1.09186
$811$	53.9245	1.89355	0.946773	−	0.321902i	$-0.104322\pi$
$811$	53.9245	1.89355	0.946773	+	0.321902i	$0.104322\pi$
$812$	38.0562	1.33551
$813$	−35.9734	−1.26164
$814$	48.2379	1.69074
$815$	46.8310	1.64042
$816$	−5.60388	−0.196175
$817$	0	0
$818$	−7.69202	−0.268945
$819$	−0.761381	−0.0266048
$820$	−24.5569	−0.857563
$821$	−45.9667	−1.60425	−0.802125	−	0.597156i	$-0.796297\pi$
$821$	−45.9667	−1.60425	−0.802125	+	0.597156i	$0.796297\pi$
$822$	31.2664	1.09054
$823$	17.6420	0.614963	0.307481	−	0.951554i	$-0.400514\pi$
$823$	17.6420	0.614963	0.307481	+	0.951554i	$0.400514\pi$
$824$	−2.74392	−0.0955891
$825$	6.85086	0.238516
$826$	−31.1008	−1.08214
$827$	40.5157	1.40887	0.704435	−	0.709769i	$-0.251200\pi$
$827$	40.5157	1.40887	0.704435	+	0.709769i	$0.251200\pi$
$828$	−3.90110	−0.135573
$829$	46.3846	1.61100	0.805502	−	0.592592i	$-0.201896\pi$
$829$	46.3846	1.61100	0.805502	+	0.592592i	$0.201896\pi$
$830$	45.6775	1.58549
$831$	−32.3153	−1.12100
$832$	−4.01507	−0.139197
$833$	49.5991	1.71851
$834$	29.4118	1.01845
$835$	19.8297	0.686234
$836$	76.4607	2.64445
$837$	−19.9524	−0.689656
$838$	−7.08277	−0.244670
$839$	4.55735	0.157337	0.0786686	−	0.996901i	$-0.474933\pi$
$839$	4.55735	0.157337	0.0786686	+	0.996901i	$0.474933\pi$
$840$	31.1293	1.07406
$841$	−20.3623	−0.702147
$842$	−72.9469	−2.51392
$843$	29.2898	1.00879
$844$	−26.1793	−0.901128
$845$	−25.8103	−0.887901
$846$	1.30798	0.0449692
$847$	35.7222	1.22743
$848$	1.12737	0.0387142
$849$	−20.2822	−0.696082
$850$	−10.0978	−0.346353
$851$	−10.7103	−0.367146
$852$	41.7754	1.43120
$853$	−52.9197	−1.81194	−0.905969	−	0.423345i	$-0.860856\pi$
$853$	−52.9197	−1.81194	−0.905969	+	0.423345i	$0.860856\pi$
$854$	−21.6504	−0.740861
$855$	6.62671	0.226629
$856$	−36.8635	−1.25997
$857$	17.2808	0.590302	0.295151	−	0.955451i	$-0.404630\pi$
$857$	17.2808	0.590302	0.295151	+	0.955451i	$0.404630\pi$
$858$	−4.74094	−0.161853
$859$	14.8616	0.507072	0.253536	−	0.967326i	$-0.418406\pi$
$859$	14.8616	0.507072	0.253536	+	0.967326i	$0.418406\pi$
$860$	0	0
$861$	−26.5948	−0.906348
$862$	80.6999	2.74865
$863$	−33.1734	−1.12924	−0.564618	−	0.825352i	$-0.690977\pi$
$863$	−33.1734	−1.12924	−0.564618	+	0.825352i	$0.690977\pi$
$864$	36.2928	1.23471
$865$	−3.06638	−0.104260
$866$	−59.6902	−2.02836
$867$	4.96913	0.168761
$868$	46.3836	1.57436
$869$	−16.3623	−0.555052
$870$	20.5375	0.696286
$871$	1.28919	0.0436826
$872$	21.0911	0.714236
$873$	−10.6217	−0.359489
$874$	−28.1129	−0.950933
$875$	−50.9638	−1.72289
$876$	−20.1806	−0.681839
$877$	22.0925	0.746009	0.373005	−	0.927829i	$-0.378328\pi$
$877$	22.0925	0.746009	0.373005	+	0.927829i	$0.378328\pi$
$878$	89.8805	3.03332
$879$	41.2526	1.39142
$880$	7.06638	0.238207
$881$	36.0097	1.21320	0.606599	−	0.795008i	$-0.292534\pi$
$881$	36.0097	1.21320	0.606599	+	0.795008i	$0.292534\pi$
$882$	−14.4359	−0.486084
$883$	11.9022	0.400540	0.200270	−	0.979741i	$-0.435818\pi$
$883$	11.9022	0.400540	0.200270	+	0.979741i	$0.435818\pi$
$884$	4.21983	0.141928
$885$	−10.1354	−0.340698
$886$	35.5036	1.19277
$887$	12.0905	0.405961	0.202980	−	0.979183i	$-0.434937\pi$
$887$	12.0905	0.405961	0.202980	+	0.979183i	$0.434937\pi$
$888$	−17.8576	−0.599260
$889$	−62.1788	−2.08541
$890$	−22.4590	−0.752829
$891$	30.4655	1.02063
$892$	23.1836	0.776244
$893$	5.69202	0.190476
$894$	21.7845	0.728582
$895$	34.4456	1.15139
$896$	−69.0646	−2.30729
$897$	1.05264	0.0351466
$898$	29.2567	0.976308
$899$	10.5278	0.351122
$900$	1.77479	0.0591597
$901$	−6.31767	−0.210472
$902$	39.8678	1.32745
$903$	0	0
$904$	−22.0248	−0.732532
$905$	24.2693	0.806740
$906$	19.5797	0.650492
$907$	12.7138	0.422155	0.211077	−	0.977469i	$-0.432303\pi$
$907$	12.7138	0.422155	0.211077	+	0.977469i	$0.432303\pi$
$908$	−47.2989	−1.56967
$909$	5.36691	0.178009
$910$	5.87800	0.194854
$911$	−32.8082	−1.08698	−0.543492	−	0.839415i	$-0.682898\pi$
$911$	−32.8082	−1.08698	−0.543492	+	0.839415i	$0.682898\pi$
$912$	7.09783	0.235033
$913$	−44.7816	−1.48206
$914$	55.4228	1.83322
$915$	−7.05562	−0.233252
$916$	−72.0622	−2.38100
$917$	44.5676	1.47175
$918$	−56.2452	−1.85637
$919$	8.72050	0.287663	0.143831	−	0.989602i	$-0.454058\pi$
$919$	8.72050	0.287663	0.143831	+	0.989602i	$0.454058\pi$
$920$	10.3612	0.341599
$921$	−11.0134	−0.362904
$922$	22.8431	0.752297
$923$	2.71379	0.0893255
$924$	−88.7096	−2.91833
$925$	4.87263	0.160211
$926$	−32.7385	−1.07586
$927$	0.677693	0.0222584
$928$	−19.1497	−0.628621
$929$	4.15154	0.136208	0.0681038	−	0.997678i	$-0.478305\pi$
$929$	4.15154	0.136208	0.0681038	+	0.997678i	$0.478305\pi$
$930$	25.0315	0.820814
$931$	−62.8219	−2.05890
$932$	66.0471	2.16345
$933$	−29.4155	−0.963020
$934$	−21.4969	−0.703401
$935$	−39.5991	−1.29503
$936$	−0.422535	−0.0138110
$937$	−3.78017	−0.123493	−0.0617463	−	0.998092i	$-0.519667\pi$
$937$	−3.78017	−0.123493	−0.0617463	+	0.998092i	$0.519667\pi$
$938$	39.9463	1.30429
$939$	28.9350	0.944256
$940$	−6.09783	−0.198889
$941$	58.1831	1.89672	0.948358	−	0.317203i	$-0.102744\pi$
$941$	58.1831	1.89672	0.948358	+	0.317203i	$0.102744\pi$
$942$	−37.0307	−1.20653
$943$	−8.85192	−0.288258
$944$	2.61356	0.0850643
$945$	−47.3116	−1.53904
$946$	0	0
$947$	−16.1105	−0.523521	−0.261761	−	0.965133i	$-0.584303\pi$
$947$	−16.1105	−0.523521	−0.261761	+	0.965133i	$0.584303\pi$
$948$	17.6069	0.571844
$949$	−1.31096	−0.0425556
$950$	12.7899	0.414958
$951$	−22.2529	−0.721601
$952$	44.9831	1.45791
$953$	−15.3381	−0.496850	−0.248425	−	0.968651i	$-0.579913\pi$
$953$	−15.3381	−0.496850	−0.248425	+	0.968651i	$0.579913\pi$
$954$	1.83877	0.0595325
$955$	32.0435	1.03690
$956$	−52.4446	−1.69618
$957$	−20.1347	−0.650861
$958$	−55.6915	−1.79931
$959$	38.0049	1.22724
$960$	−40.5435	−1.30853
$961$	−18.1685	−0.586081
$962$	−3.37196	−0.108716
$963$	9.10454	0.293390
$964$	−77.1047	−2.48337
$965$	47.5749	1.53149
$966$	32.6165	1.04942
$967$	−52.6093	−1.69180	−0.845900	−	0.533342i	$-0.820936\pi$
$967$	−52.6093	−1.69180	−0.845900	+	0.533342i	$0.820936\pi$
$968$	19.8243	0.637177
$969$	−39.7754	−1.27777
$970$	82.0012	2.63290
$971$	9.12690	0.292896	0.146448	−	0.989218i	$-0.453216\pi$
$971$	9.12690	0.292896	0.146448	+	0.989218i	$0.453216\pi$
$972$	18.1648	0.582636
$973$	35.7506	1.14611
$974$	58.2127	1.86525
$975$	−0.478894	−0.0153369
$976$	1.81940	0.0582375
$977$	−40.6564	−1.30071	−0.650356	−	0.759629i	$-0.725380\pi$
$977$	−40.6564	−1.30071	−0.650356	+	0.759629i	$0.725380\pi$
$978$	81.8128	2.61609
$979$	22.0185	0.703715
$980$	67.3008	2.14985
$981$	−5.20908	−0.166313
$982$	−55.5109	−1.77143
$983$	46.1135	1.47079	0.735396	−	0.677638i	$-0.236996\pi$
$983$	46.1135	1.47079	0.735396	+	0.677638i	$0.236996\pi$
$984$	−14.7590	−0.470499
$985$	31.7103	1.01038
$986$	29.6775	0.945126
$987$	−6.60388	−0.210204
$988$	−5.34481	−0.170041
$989$	0	0
$990$	11.5254	0.366302
$991$	−36.1237	−1.14751	−0.573753	−	0.819028i	$-0.694513\pi$
$991$	−36.1237	−1.14751	−0.573753	+	0.819028i	$0.694513\pi$
$992$	−23.3400	−0.741047
$993$	−30.2701	−0.960592
$994$	84.0883	2.66712
$995$	−17.5168	−0.555320
$996$	48.1879	1.52689
$997$	20.0382	0.634615	0.317308	−	0.948323i	$-0.397221\pi$
$997$	20.0382	0.634615	0.317308	+	0.948323i	$0.397221\pi$
$998$	63.0974	1.99731
$999$	27.1406	0.858692

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.l.1.3		3
43.32	odd	14		43.2.e.b.35.1	yes	6
43.39	odd	14		43.2.e.b.16.1	✓	6
43.42	odd	2		1849.2.a.i.1.1		3
129.32	even	14		387.2.u.a.379.1		6
129.125	even	14		387.2.u.a.145.1		6
172.39	even	14		688.2.u.c.145.1		6
172.75	even	14		688.2.u.c.465.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.e.b.16.1	✓	6	43.39	odd	14
43.2.e.b.35.1	yes	6	43.32	odd	14
387.2.u.a.145.1		6	129.125	even	14
387.2.u.a.379.1		6	129.32	even	14
688.2.u.c.145.1		6	172.39	even	14
688.2.u.c.465.1		6	172.75	even	14
1849.2.a.i.1.1		3	43.42	odd	2
1849.2.a.l.1.3		3	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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q+2.24698 q^{2} +1.55496 q^{3} +3.04892 q^{4} +2.00000 q^{5} +3.49396 q^{6} +4.24698 q^{7} +2.35690 q^{8} -0.582105 q^{9} +O(q^{10})\)	\(q+2.24698 q^{2} +1.55496 q^{3} +3.04892 q^{4} +2.00000 q^{5} +3.49396 q^{6} +4.24698 q^{7} +2.35690 q^{8} -0.582105 q^{9} +4.49396 q^{10} -4.40581 q^{11} +4.74094 q^{12} +0.307979 q^{13} +9.54288 q^{14} +3.10992 q^{15} -0.801938 q^{16} +4.49396 q^{17} -1.30798 q^{18} -5.69202 q^{19} +6.09783 q^{20} +6.60388 q^{21} -9.89977 q^{22} +2.19806 q^{23} +3.66487 q^{24} -1.00000 q^{25} +0.692021 q^{26} -5.57002 q^{27} +12.9487 q^{28} +2.93900 q^{29} +6.98792 q^{30} +3.58211 q^{31} -6.51573 q^{32} -6.85086 q^{33} +10.0978 q^{34} +8.49396 q^{35} -1.77479 q^{36} -4.87263 q^{37} -12.7899 q^{38} +0.478894 q^{39} +4.71379 q^{40} -4.02715 q^{41} +14.8388 q^{42} -13.4330 q^{44} -1.16421 q^{45} +4.93900 q^{46} -1.00000 q^{47} -1.24698 q^{48} +11.0368 q^{49} -2.24698 q^{50} +6.98792 q^{51} +0.939001 q^{52} -1.40581 q^{53} -12.5157 q^{54} -8.81163 q^{55} +10.0097 q^{56} -8.85086 q^{57} +6.60388 q^{58} -3.25906 q^{59} +9.48188 q^{60} -2.26875 q^{61} +8.04892 q^{62} -2.47219 q^{63} -13.0368 q^{64} +0.615957 q^{65} -15.3937 q^{66} +4.18598 q^{67} +13.7017 q^{68} +3.41789 q^{69} +19.0858 q^{70} +8.81163 q^{71} -1.37196 q^{72} -4.25667 q^{73} -10.9487 q^{74} -1.55496 q^{75} -17.3545 q^{76} -18.7114 q^{77} +1.07606 q^{78} +3.71379 q^{79} -1.60388 q^{80} -6.91484 q^{81} -9.04892 q^{82} +10.1642 q^{83} +20.1347 q^{84} +8.98792 q^{85} +4.57002 q^{87} -10.3840 q^{88} -4.99761 q^{89} -2.61596 q^{90} +1.30798 q^{91} +6.70171 q^{92} +5.57002 q^{93} -2.24698 q^{94} -11.3840 q^{95} -10.1317 q^{96} +18.2470 q^{97} +24.7995 q^{98} +2.56465 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} + 5 q^{3} + 6 q^{5} + q^{6} + 8 q^{7} + 3 q^{8} + 4 q^{9}+O(q^{10}) \) 3 * q + 2 * q^2 + 5 * q^3 + 6 * q^5 + q^6 + 8 * q^7 + 3 * q^8 + 4 * q^9	\( 3 q + 2 q^{2} + 5 q^{3} + 6 q^{5} + q^{6} + 8 q^{7} + 3 q^{8} + 4 q^{9} + 4 q^{10} + 6 q^{13} + 10 q^{14} + 10 q^{15} + 2 q^{16} + 4 q^{17} - 9 q^{18} - 12 q^{19} + 11 q^{21} - 7 q^{22} + 11 q^{23} + 12 q^{24} - 3 q^{25} - 3 q^{26} + 8 q^{27} + 7 q^{28} - q^{29} + 2 q^{30} + 5 q^{31} - 7 q^{32} - 7 q^{33} + 12 q^{34} + 16 q^{35} - 7 q^{36} + 2 q^{37} - 15 q^{38} + 17 q^{39} + 6 q^{40} - 6 q^{41} + 12 q^{42} - 21 q^{44} + 8 q^{45} + 5 q^{46} - 3 q^{47} + q^{48} + 5 q^{49} - 2 q^{50} + 2 q^{51} - 7 q^{52} + 9 q^{53} - 25 q^{54} + 8 q^{56} - 13 q^{57} + 11 q^{58} - 24 q^{59} + q^{61} + 15 q^{62} - q^{63} - 11 q^{64} + 12 q^{65} - 14 q^{66} - 2 q^{67} + 14 q^{68} + 16 q^{69} + 20 q^{70} + 25 q^{72} + 14 q^{73} - q^{74} - 5 q^{75} - 7 q^{76} - 7 q^{77} - 12 q^{78} + 3 q^{79} + 4 q^{80} + 27 q^{81} - 18 q^{82} + 19 q^{83} + 14 q^{84} + 8 q^{85} - 11 q^{87} - 21 q^{88} + 26 q^{89} - 18 q^{90} + 9 q^{91} - 7 q^{92} - 8 q^{93} - 2 q^{94} - 24 q^{95} - 28 q^{96} + 50 q^{97} + 29 q^{98} - 14 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 + 5 * q^3 + 6 * q^5 + q^6 + 8 * q^7 + 3 * q^8 + 4 * q^9 + 4 * q^10 + 6 * q^13 + 10 * q^14 + 10 * q^15 + 2 * q^16 + 4 * q^17 - 9 * q^18 - 12 * q^19 + 11 * q^21 - 7 * q^22 + 11 * q^23 + 12 * q^24 - 3 * q^25 - 3 * q^26 + 8 * q^27 + 7 * q^28 - q^29 + 2 * q^30 + 5 * q^31 - 7 * q^32 - 7 * q^33 + 12 * q^34 + 16 * q^35 - 7 * q^36 + 2 * q^37 - 15 * q^38 + 17 * q^39 + 6 * q^40 - 6 * q^41 + 12 * q^42 - 21 * q^44 + 8 * q^45 + 5 * q^46 - 3 * q^47 + q^48 + 5 * q^49 - 2 * q^50 + 2 * q^51 - 7 * q^52 + 9 * q^53 - 25 * q^54 + 8 * q^56 - 13 * q^57 + 11 * q^58 - 24 * q^59 + q^61 + 15 * q^62 - q^63 - 11 * q^64 + 12 * q^65 - 14 * q^66 - 2 * q^67 + 14 * q^68 + 16 * q^69 + 20 * q^70 + 25 * q^72 + 14 * q^73 - q^74 - 5 * q^75 - 7 * q^76 - 7 * q^77 - 12 * q^78 + 3 * q^79 + 4 * q^80 + 27 * q^81 - 18 * q^82 + 19 * q^83 + 14 * q^84 + 8 * q^85 - 11 * q^87 - 21 * q^88 + 26 * q^89 - 18 * q^90 + 9 * q^91 - 7 * q^92 - 8 * q^93 - 2 * q^94 - 24 * q^95 - 28 * q^96 + 50 * q^97 + 29 * q^98 - 14 * q^99

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