LMFDB - Embedded newform 4033.2.a.f.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, 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("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$0$
Dimension:	$85$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.66354 q^{2} +1.93600 q^{3} +0.767368 q^{4} -2.27919 q^{5} -3.22061 q^{6} +0.280246 q^{7} +2.05053 q^{8} +0.748091 q^{9} +O(q^{10})$	\(q-1.66354 q^{2} +1.93600 q^{3} +0.767368 q^{4} -2.27919 q^{5} -3.22061 q^{6} +0.280246 q^{7} +2.05053 q^{8} +0.748091 q^{9} +3.79153 q^{10} -0.838736 q^{11} +1.48562 q^{12} -6.44849 q^{13} -0.466201 q^{14} -4.41251 q^{15} -4.94588 q^{16} -5.62782 q^{17} -1.24448 q^{18} +7.99234 q^{19} -1.74898 q^{20} +0.542556 q^{21} +1.39527 q^{22} +1.07829 q^{23} +3.96983 q^{24} +0.194721 q^{25} +10.7273 q^{26} -4.35969 q^{27} +0.215052 q^{28} +7.63317 q^{29} +7.34040 q^{30} -6.25208 q^{31} +4.12661 q^{32} -1.62379 q^{33} +9.36210 q^{34} -0.638735 q^{35} +0.574061 q^{36} +1.00000 q^{37} -13.2956 q^{38} -12.4843 q^{39} -4.67356 q^{40} -0.298149 q^{41} -0.902565 q^{42} -2.25887 q^{43} -0.643619 q^{44} -1.70504 q^{45} -1.79378 q^{46} +4.42223 q^{47} -9.57522 q^{48} -6.92146 q^{49} -0.323927 q^{50} -10.8954 q^{51} -4.94836 q^{52} -10.6911 q^{53} +7.25253 q^{54} +1.91164 q^{55} +0.574654 q^{56} +15.4732 q^{57} -12.6981 q^{58} +3.13251 q^{59} -3.38602 q^{60} +12.4654 q^{61} +10.4006 q^{62} +0.209650 q^{63} +3.02698 q^{64} +14.6973 q^{65} +2.70124 q^{66} +12.7046 q^{67} -4.31861 q^{68} +2.08756 q^{69} +1.06256 q^{70} +11.3068 q^{71} +1.53399 q^{72} +11.0100 q^{73} -1.66354 q^{74} +0.376980 q^{75} +6.13306 q^{76} -0.235053 q^{77} +20.7681 q^{78} -16.2743 q^{79} +11.2726 q^{80} -10.6846 q^{81} +0.495983 q^{82} +7.64634 q^{83} +0.416340 q^{84} +12.8269 q^{85} +3.75772 q^{86} +14.7778 q^{87} -1.71986 q^{88} -14.3218 q^{89} +2.83641 q^{90} -1.80716 q^{91} +0.827443 q^{92} -12.1040 q^{93} -7.35655 q^{94} -18.2161 q^{95} +7.98911 q^{96} +0.322581 q^{97} +11.5141 q^{98} -0.627450 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9}+O(q^{10}) $ 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9} + 9 q^{10} + 37 q^{11} + 44 q^{12} + 14 q^{13} + 26 q^{14} + 27 q^{15} + 85 q^{16} + 34 q^{17} + 3 q^{18} + 15 q^{19} + 15 q^{20} + 17 q^{21} + q^{22} + 72 q^{23} + 15 q^{24} + 85 q^{25} + 33 q^{26} + 69 q^{27} + 7 q^{28} + 19 q^{29} - 9 q^{30} + 23 q^{31} + 51 q^{32} + 32 q^{33} + 49 q^{34} + 40 q^{35} + 121 q^{36} + 85 q^{37} + 84 q^{38} + 39 q^{39} + 22 q^{40} + 55 q^{41} - 28 q^{42} + 78 q^{44} + 28 q^{45} + 17 q^{46} + 184 q^{47} + 97 q^{48} + 88 q^{49} + 26 q^{50} + 27 q^{51} + 73 q^{52} + 64 q^{53} + 31 q^{54} + 39 q^{55} + 68 q^{56} - 33 q^{57} + 28 q^{58} + 60 q^{59} - 22 q^{60} + 7 q^{61} + 70 q^{62} + 28 q^{63} + 102 q^{64} + 17 q^{65} - 15 q^{66} + 82 q^{67} + 92 q^{68} + 22 q^{69} - 41 q^{70} + 113 q^{71} - 19 q^{73} + 11 q^{74} + 45 q^{75} + 34 q^{76} + 64 q^{77} + 29 q^{78} + 23 q^{79} + 54 q^{80} + 149 q^{81} + 4 q^{82} + 100 q^{83} - 49 q^{84} - 5 q^{85} - 24 q^{86} + 65 q^{87} + 14 q^{88} + 84 q^{89} - 21 q^{90} + 32 q^{91} + 95 q^{92} + 19 q^{93} - 47 q^{94} + 102 q^{95} + 29 q^{96} + 7 q^{97} + 26 q^{98} + 107 q^{99}+O(q^{100}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9 + 9 * q^10 + 37 * q^11 + 44 * q^12 + 14 * q^13 + 26 * q^14 + 27 * q^15 + 85 * q^16 + 34 * q^17 + 3 * q^18 + 15 * q^19 + 15 * q^20 + 17 * q^21 + q^22 + 72 * q^23 + 15 * q^24 + 85 * q^25 + 33 * q^26 + 69 * q^27 + 7 * q^28 + 19 * q^29 - 9 * q^30 + 23 * q^31 + 51 * q^32 + 32 * q^33 + 49 * q^34 + 40 * q^35 + 121 * q^36 + 85 * q^37 + 84 * q^38 + 39 * q^39 + 22 * q^40 + 55 * q^41 - 28 * q^42 + 78 * q^44 + 28 * q^45 + 17 * q^46 + 184 * q^47 + 97 * q^48 + 88 * q^49 + 26 * q^50 + 27 * q^51 + 73 * q^52 + 64 * q^53 + 31 * q^54 + 39 * q^55 + 68 * q^56 - 33 * q^57 + 28 * q^58 + 60 * q^59 - 22 * q^60 + 7 * q^61 + 70 * q^62 + 28 * q^63 + 102 * q^64 + 17 * q^65 - 15 * q^66 + 82 * q^67 + 92 * q^68 + 22 * q^69 - 41 * q^70 + 113 * q^71 - 19 * q^73 + 11 * q^74 + 45 * q^75 + 34 * q^76 + 64 * q^77 + 29 * q^78 + 23 * q^79 + 54 * q^80 + 149 * q^81 + 4 * q^82 + 100 * q^83 - 49 * q^84 - 5 * q^85 - 24 * q^86 + 65 * q^87 + 14 * q^88 + 84 * q^89 - 21 * q^90 + 32 * q^91 + 95 * q^92 + 19 * q^93 - 47 * q^94 + 102 * q^95 + 29 * q^96 + 7 * q^97 + 26 * q^98 + 107 * 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 $

$2$	−1.66354	−1.17630	−0.588150	−	0.808752i	$-0.700144\pi$
$2$	−1.66354	−1.17630	−0.588150	+	0.808752i	$0.700144\pi$
$3$	1.93600	1.11775	0.558875	−	0.829252i	$-0.311233\pi$
$3$	1.93600	1.11775	0.558875	+	0.829252i	$0.311233\pi$
$4$	0.767368	0.383684
$5$	−2.27919	−1.01929	−0.509643	−	0.860386i	$-0.670223\pi$
$5$	−2.27919	−1.01929	−0.509643	+	0.860386i	$0.670223\pi$
$6$	−3.22061	−1.31481
$7$	0.280246	0.105923	0.0529616	−	0.998597i	$-0.483134\pi$
$7$	0.280246	0.105923	0.0529616	+	0.998597i	$0.483134\pi$
$8$	2.05053	0.724973
$9$	0.748091	0.249364
$10$	3.79153	1.19899
$11$	−0.838736	−0.252888	−0.126444	−	0.991974i	$-0.540356\pi$
$11$	−0.838736	−0.252888	−0.126444	+	0.991974i	$0.540356\pi$
$12$	1.48562	0.428862
$13$	−6.44849	−1.78849	−0.894244	−	0.447580i	$-0.852286\pi$
$13$	−6.44849	−1.78849	−0.894244	+	0.447580i	$0.852286\pi$
$14$	−0.466201	−0.124597
$15$	−4.41251	−1.13931
$16$	−4.94588	−1.23647
$17$	−5.62782	−1.36495	−0.682473	−	0.730911i	$-0.739096\pi$
$17$	−5.62782	−1.36495	−0.682473	+	0.730911i	$0.739096\pi$
$18$	−1.24448	−0.293327
$19$	7.99234	1.83357	0.916784	−	0.399383i	$-0.130776\pi$
$19$	7.99234	1.83357	0.916784	+	0.399383i	$0.130776\pi$
$20$	−1.74898	−0.391084
$21$	0.542556	0.118396
$22$	1.39527	0.297473
$23$	1.07829	0.224839	0.112419	−	0.993661i	$-0.464140\pi$
$23$	1.07829	0.224839	0.112419	+	0.993661i	$0.464140\pi$
$24$	3.96983	0.810338
$25$	0.194721	0.0389442
$26$	10.7273	2.10380
$27$	−4.35969	−0.839023
$28$	0.215052	0.0406410
$29$	7.63317	1.41744	0.708722	−	0.705488i	$-0.249272\pi$
$29$	7.63317	1.41744	0.708722	+	0.705488i	$0.249272\pi$
$30$	7.34040	1.34017
$31$	−6.25208	−1.12291	−0.561454	−	0.827508i	$-0.689758\pi$
$31$	−6.25208	−1.12291	−0.561454	+	0.827508i	$0.689758\pi$
$32$	4.12661	0.729488
$33$	−1.62379	−0.282666
$34$	9.36210	1.60559
$35$	−0.638735	−0.107966
$36$	0.574061	0.0956768
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−13.2956	−2.15683
$39$	−12.4843	−1.99908
$40$	−4.67356	−0.738955
$41$	−0.298149	−0.0465630	−0.0232815	−	0.999729i	$-0.507411\pi$
$41$	−0.298149	−0.0465630	−0.0232815	+	0.999729i	$0.507411\pi$
$42$	−0.902565	−0.139269
$43$	−2.25887	−0.344474	−0.172237	−	0.985056i	$-0.555099\pi$
$43$	−2.25887	−0.344474	−0.172237	+	0.985056i	$0.555099\pi$
$44$	−0.643619	−0.0970292
$45$	−1.70504	−0.254173
$46$	−1.79378	−0.264478
$47$	4.42223	0.645048	0.322524	−	0.946561i	$-0.395469\pi$
$47$	4.42223	0.645048	0.322524	+	0.946561i	$0.395469\pi$
$48$	−9.57522	−1.38206
$49$	−6.92146	−0.988780
$50$	−0.323927	−0.0458102
$51$	−10.8954	−1.52567
$52$	−4.94836	−0.686214
$53$	−10.6911	−1.46854	−0.734268	−	0.678859i	$-0.762475\pi$
$53$	−10.6911	−1.46854	−0.734268	+	0.678859i	$0.762475\pi$
$54$	7.25253	0.986944
$55$	1.91164	0.257766
$56$	0.574654	0.0767914
$57$	15.4732	2.04947
$58$	−12.6981	−1.66734
$59$	3.13251	0.407818	0.203909	−	0.978990i	$-0.434635\pi$
$59$	3.13251	0.407818	0.203909	+	0.978990i	$0.434635\pi$
$60$	−3.38602	−0.437134
$61$	12.4654	1.59604	0.798018	−	0.602633i	$-0.205882\pi$
$61$	12.4654	1.59604	0.798018	+	0.602633i	$0.205882\pi$
$62$	10.4006	1.32088
$63$	0.209650	0.0264134
$64$	3.02698	0.378373
$65$	14.6973	1.82298
$66$	2.70124	0.332500
$67$	12.7046	1.55211	0.776057	−	0.630663i	$-0.217217\pi$
$67$	12.7046	1.55211	0.776057	+	0.630663i	$0.217217\pi$
$68$	−4.31861	−0.523708
$69$	2.08756	0.251313
$70$	1.06256	0.127000
$71$	11.3068	1.34187	0.670933	−	0.741518i	$-0.265894\pi$
$71$	11.3068	1.34187	0.670933	+	0.741518i	$0.265894\pi$
$72$	1.53399	0.180782
$73$	11.0100	1.28863	0.644313	−	0.764762i	$-0.277144\pi$
$73$	11.0100	1.28863	0.644313	+	0.764762i	$0.277144\pi$
$74$	−1.66354	−0.193383
$75$	0.376980	0.0435299
$76$	6.13306	0.703511
$77$	−0.235053	−0.0267867
$78$	20.7681	2.35152
$79$	−16.2743	−1.83101	−0.915503	−	0.402312i	$-0.868207\pi$
$79$	−16.2743	−1.83101	−0.915503	+	0.402312i	$0.868207\pi$
$80$	11.2726	1.26032
$81$	−10.6846	−1.18718
$82$	0.495983	0.0547721
$83$	7.64634	0.839295	0.419647	−	0.907687i	$-0.362154\pi$
$83$	7.64634	0.839295	0.419647	+	0.907687i	$0.362154\pi$
$84$	0.416340	0.0454264
$85$	12.8269	1.39127
$86$	3.75772	0.405205
$87$	14.7778	1.58435
$88$	−1.71986	−0.183337
$89$	−14.3218	−1.51811	−0.759055	−	0.651026i	$-0.774339\pi$
$89$	−14.3218	−1.51811	−0.759055	+	0.651026i	$0.774339\pi$
$90$	2.83641	0.298984
$91$	−1.80716	−0.189442
$92$	0.827443	0.0862669
$93$	−12.1040	−1.25513
$94$	−7.35655	−0.758771
$95$	−18.2161	−1.86893
$96$	7.98911	0.815385
$97$	0.322581	0.0327531	0.0163765	−	0.999866i	$-0.494787\pi$
$97$	0.322581	0.0327531	0.0163765	+	0.999866i	$0.494787\pi$
$98$	11.5141	1.16310
$99$	−0.627450	−0.0630611
$100$	0.149423	0.0149423
$101$	2.90172	0.288732	0.144366	−	0.989524i	$-0.453886\pi$
$101$	2.90172	0.288732	0.144366	+	0.989524i	$0.453886\pi$
$102$	18.1250	1.79464
$103$	17.9316	1.76685	0.883426	−	0.468571i	$-0.155231\pi$
$103$	17.9316	1.76685	0.883426	+	0.468571i	$0.155231\pi$
$104$	−13.2228	−1.29661
$105$	−1.23659	−0.120679
$106$	17.7851	1.72744
$107$	15.8842	1.53559	0.767793	−	0.640698i	$-0.221355\pi$
$107$	15.8842	1.53559	0.767793	+	0.640698i	$0.221355\pi$
$108$	−3.34549	−0.321920
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−3.18009	−0.303210
$111$	1.93600	0.183757
$112$	−1.38606	−0.130971
$113$	−18.6792	−1.75719	−0.878596	−	0.477565i	$-0.841519\pi$
$113$	−18.6792	−1.75719	−0.878596	+	0.477565i	$0.841519\pi$
$114$	−25.7402	−2.41079
$115$	−2.45763	−0.229175
$116$	5.85744	0.543850
$117$	−4.82405	−0.445984
$118$	−5.21106	−0.479717
$119$	−1.57717	−0.144579
$120$	−9.04801	−0.825967
$121$	−10.2965	−0.936047
$122$	−20.7368	−1.87742
$123$	−0.577216	−0.0520458
$124$	−4.79765	−0.430842
$125$	10.9522	0.979591
$126$	−0.348761	−0.0310701
$127$	5.55628	0.493040	0.246520	−	0.969138i	$-0.420713\pi$
$127$	5.55628	0.493040	0.246520	+	0.969138i	$0.420713\pi$
$128$	−13.2887	−1.17457
$129$	−4.37316	−0.385036
$130$	−24.4496	−2.14437
$131$	18.1781	1.58822	0.794112	−	0.607772i	$-0.207936\pi$
$131$	18.1781	1.58822	0.794112	+	0.607772i	$0.207936\pi$
$132$	−1.24605	−0.108454
$133$	2.23982	0.194217
$134$	−21.1346	−1.82575
$135$	9.93658	0.855205
$136$	−11.5400	−0.989549
$137$	6.57044	0.561351	0.280675	−	0.959803i	$-0.409442\pi$
$137$	6.57044	0.561351	0.280675	+	0.959803i	$0.409442\pi$
$138$	−3.47275	−0.295620
$139$	−14.8864	−1.26264	−0.631322	−	0.775521i	$-0.717487\pi$
$139$	−14.8864	−1.26264	−0.631322	+	0.775521i	$0.717487\pi$
$140$	−0.490145	−0.0414248
$141$	8.56142	0.721002
$142$	−18.8093	−1.57844
$143$	5.40858	0.452288
$144$	−3.69997	−0.308331
$145$	−17.3975	−1.44478
$146$	−18.3156	−1.51581
$147$	−13.3999	−1.10521
$148$	0.767368	0.0630772
$149$	19.0624	1.56165	0.780827	−	0.624748i	$-0.214798\pi$
$149$	19.0624	1.56165	0.780827	+	0.624748i	$0.214798\pi$
$150$	−0.627122	−0.0512043
$151$	−2.24853	−0.182983	−0.0914914	−	0.995806i	$-0.529163\pi$
$151$	−2.24853	−0.182983	−0.0914914	+	0.995806i	$0.529163\pi$
$152$	16.3886	1.32929
$153$	−4.21012	−0.340368
$154$	0.391020	0.0315092
$155$	14.2497	1.14456
$156$	−9.58002	−0.767015
$157$	−11.6346	−0.928546	−0.464273	−	0.885692i	$-0.653684\pi$
$157$	−11.6346	−0.928546	−0.464273	+	0.885692i	$0.653684\pi$
$158$	27.0730	2.15381
$159$	−20.6980	−1.64146
$160$	−9.40534	−0.743557
$161$	0.302186	0.0238156
$162$	17.7743	1.39648
$163$	−3.04285	−0.238335	−0.119167	−	0.992874i	$-0.538023\pi$
$163$	−3.04285	−0.238335	−0.119167	+	0.992874i	$0.538023\pi$
$164$	−0.228790	−0.0178655
$165$	3.70093	0.288117
$166$	−12.7200	−0.987263
$167$	7.23086	0.559540	0.279770	−	0.960067i	$-0.409742\pi$
$167$	7.23086	0.559540	0.279770	+	0.960067i	$0.409742\pi$
$168$	1.11253	0.0858336
$169$	28.5830	2.19869
$170$	−21.3380	−1.63655
$171$	5.97899	0.457225
$172$	−1.73338	−0.132169
$173$	21.0233	1.59837	0.799187	−	0.601083i	$-0.205264\pi$
$173$	21.0233	1.59837	0.799187	+	0.601083i	$0.205264\pi$
$174$	−24.5835	−1.86367
$175$	0.0545699	0.00412510
$176$	4.14829	0.312689
$177$	6.06454	0.455838
$178$	23.8249	1.78575
$179$	−11.3923	−0.851501	−0.425751	−	0.904841i	$-0.639990\pi$
$179$	−11.3923	−0.851501	−0.425751	+	0.904841i	$0.639990\pi$
$180$	−1.30840	−0.0975220
$181$	8.47716	0.630102	0.315051	−	0.949075i	$-0.397978\pi$
$181$	8.47716	0.630102	0.315051	+	0.949075i	$0.397978\pi$
$182$	3.00629	0.222841
$183$	24.1331	1.78397
$184$	2.21107	0.163002
$185$	−2.27919	−0.167570
$186$	20.1355	1.47641
$187$	4.72025	0.345179
$188$	3.39347	0.247495
$189$	−1.22179	−0.0888720
$190$	30.3032	2.19843
$191$	11.8817	0.859727	0.429864	−	0.902894i	$-0.358562\pi$
$191$	11.8817	0.859727	0.429864	+	0.902894i	$0.358562\pi$
$192$	5.86023	0.422926
$193$	6.04742	0.435303	0.217651	−	0.976027i	$-0.430160\pi$
$193$	6.04742	0.435303	0.217651	+	0.976027i	$0.430160\pi$
$194$	−0.536626	−0.0385275
$195$	28.4540	2.03764
$196$	−5.31131	−0.379379
$197$	17.0340	1.21363	0.606813	−	0.794845i	$-0.292448\pi$
$197$	17.0340	1.21363	0.606813	+	0.794845i	$0.292448\pi$
$198$	1.04379	0.0741789
$199$	−18.3588	−1.30142	−0.650712	−	0.759325i	$-0.725529\pi$
$199$	−18.3588	−1.30142	−0.650712	+	0.759325i	$0.725529\pi$
$200$	0.399283	0.0282335
$201$	24.5961	1.73487
$202$	−4.82713	−0.339636
$203$	2.13917	0.150140
$204$	−8.36081	−0.585374
$205$	0.679539	0.0474611
$206$	−29.8299	−2.07835
$207$	0.806657	0.0560665
$208$	31.8934	2.21141
$209$	−6.70346	−0.463688
$210$	2.05712	0.141955
$211$	−22.1723	−1.52640	−0.763202	−	0.646160i	$-0.776374\pi$
$211$	−22.1723	−1.52640	−0.763202	+	0.646160i	$0.776374\pi$
$212$	−8.20401	−0.563454
$213$	21.8899	1.49987
$214$	−26.4241	−1.80631
$215$	5.14839	0.351118
$216$	−8.93970	−0.608269
$217$	−1.75212	−0.118942
$218$	1.66354	0.112669
$219$	21.3154	1.44036
$220$	1.46693	0.0989005
$221$	36.2909	2.44119
$222$	−3.22061	−0.216153
$223$	4.62064	0.309421	0.154711	−	0.987960i	$-0.450555\pi$
$223$	4.62064	0.309421	0.154711	+	0.987960i	$0.450555\pi$
$224$	1.15647	0.0772697
$225$	0.145669	0.00971128
$226$	31.0736	2.06699
$227$	−3.67592	−0.243979	−0.121990	−	0.992531i	$-0.538927\pi$
$227$	−3.67592	−0.243979	−0.121990	+	0.992531i	$0.538927\pi$
$228$	11.8736	0.786349
$229$	−15.1612	−1.00188	−0.500940	−	0.865482i	$-0.667012\pi$
$229$	−15.1612	−1.00188	−0.500940	+	0.865482i	$0.667012\pi$
$230$	4.08836	0.269579
$231$	−0.455061	−0.0299408
$232$	15.6521	1.02761
$233$	11.8018	0.773164	0.386582	−	0.922255i	$-0.373656\pi$
$233$	11.8018	0.773164	0.386582	+	0.922255i	$0.373656\pi$
$234$	8.02501	0.524611
$235$	−10.0791	−0.657489
$236$	2.40379	0.156473
$237$	−31.5071	−2.04661
$238$	2.62369	0.170069
$239$	−6.27461	−0.405871	−0.202935	−	0.979192i	$-0.565048\pi$
$239$	−6.27461	−0.405871	−0.202935	+	0.979192i	$0.565048\pi$
$240$	21.8238	1.40872
$241$	−12.3768	−0.797257	−0.398628	−	0.917113i	$-0.630514\pi$
$241$	−12.3768	−0.797257	−0.398628	+	0.917113i	$0.630514\pi$
$242$	17.1287	1.10107
$243$	−7.60635	−0.487948
$244$	9.56558	0.612373
$245$	15.7753	1.00785
$246$	0.960222	0.0612215
$247$	−51.5385	−3.27932
$248$	−12.8201	−0.814078
$249$	14.8033	0.938121
$250$	−18.2194	−1.15229
$251$	−13.6941	−0.864365	−0.432183	−	0.901786i	$-0.642256\pi$
$251$	−13.6941	−0.864365	−0.432183	+	0.901786i	$0.642256\pi$
$252$	0.160878	0.0101344
$253$	−0.904399	−0.0568591
$254$	−9.24310	−0.579964
$255$	24.8328	1.55509
$256$	16.0524	1.00327
$257$	−4.62370	−0.288418	−0.144209	−	0.989547i	$-0.546064\pi$
$257$	−4.62370	−0.288418	−0.144209	+	0.989547i	$0.546064\pi$
$258$	7.27494	0.452918
$259$	0.280246	0.0174137
$260$	11.2783	0.699448
$261$	5.71030	0.353459
$262$	−30.2399	−1.86823
$263$	11.8481	0.730587	0.365293	−	0.930892i	$-0.380969\pi$
$263$	11.8481	0.730587	0.365293	+	0.930892i	$0.380969\pi$
$264$	−3.32964	−0.204925
$265$	24.3671	1.49686
$266$	−3.72604	−0.228458
$267$	−27.7270	−1.69687
$268$	9.74910	0.595521
$269$	25.5005	1.55480	0.777398	−	0.629010i	$-0.216539\pi$
$269$	25.5005	1.55480	0.777398	+	0.629010i	$0.216539\pi$
$270$	−16.5299	−1.00598
$271$	−20.1831	−1.22603	−0.613017	−	0.790069i	$-0.710044\pi$
$271$	−20.1831	−1.22603	−0.613017	+	0.790069i	$0.710044\pi$
$272$	27.8345	1.68772
$273$	−3.49867	−0.211749
$274$	−10.9302	−0.660317
$275$	−0.163320	−0.00984855
$276$	1.60193	0.0964248
$277$	8.63800	0.519007	0.259504	−	0.965742i	$-0.416441\pi$
$277$	8.63800	0.519007	0.259504	+	0.965742i	$0.416441\pi$
$278$	24.7641	1.48525
$279$	−4.67713	−0.280012
$280$	−1.30975	−0.0782724
$281$	4.95819	0.295781	0.147890	−	0.989004i	$-0.452752\pi$
$281$	4.95819	0.295781	0.147890	+	0.989004i	$0.452752\pi$
$282$	−14.2423	−0.848115
$283$	28.2083	1.67681	0.838405	−	0.545047i	$-0.183488\pi$
$283$	28.2083	1.67681	0.838405	+	0.545047i	$0.183488\pi$
$284$	8.67645	0.514853
$285$	−35.2663	−2.08900
$286$	−8.99739	−0.532027
$287$	−0.0835551	−0.00493210
$288$	3.08708	0.181908
$289$	14.6723	0.863078
$290$	28.9414	1.69950
$291$	0.624516	0.0366098
$292$	8.44873	0.494425
$293$	−6.78686	−0.396493	−0.198246	−	0.980152i	$-0.563525\pi$
$293$	−6.78686	−0.396493	−0.198246	+	0.980152i	$0.563525\pi$
$294$	22.2913	1.30006
$295$	−7.13960	−0.415683
$296$	2.05053	0.119185
$297$	3.65663	0.212179
$298$	−31.7111	−1.83697
$299$	−6.95332	−0.402121
$300$	0.289282	0.0167017
$301$	−0.633039	−0.0364878
$302$	3.74052	0.215243
$303$	5.61773	0.322730
$304$	−39.5292	−2.26715
$305$	−28.4112	−1.62682
$306$	7.00370	0.400375
$307$	23.6448	1.34948	0.674739	−	0.738057i	$-0.264256\pi$
$307$	23.6448	1.34948	0.674739	+	0.738057i	$0.264256\pi$
$308$	−0.180372	−0.0102776
$309$	34.7155	1.97490
$310$	−23.7050	−1.34635
$311$	18.4730	1.04751	0.523755	−	0.851869i	$-0.324531\pi$
$311$	18.4730	1.04751	0.523755	+	0.851869i	$0.324531\pi$
$312$	−25.5994	−1.44928
$313$	10.9631	0.619671	0.309836	−	0.950790i	$-0.399726\pi$
$313$	10.9631	0.619671	0.309836	+	0.950790i	$0.399726\pi$
$314$	19.3547	1.09225
$315$	−0.477832	−0.0269228
$316$	−12.4884	−0.702527
$317$	18.3449	1.03035	0.515176	−	0.857085i	$-0.327727\pi$
$317$	18.3449	1.03035	0.515176	+	0.857085i	$0.327727\pi$
$318$	34.4319	1.93085
$319$	−6.40221	−0.358455
$320$	−6.89908	−0.385670
$321$	30.7518	1.71640
$322$	−0.502699	−0.0280143
$323$	−44.9794	−2.50272
$324$	−8.19904	−0.455502
$325$	−1.25566	−0.0696513
$326$	5.06191	0.280353
$327$	−1.93600	−0.107061
$328$	−0.611364	−0.0337569
$329$	1.23931	0.0683255
$330$	−6.15665	−0.338913
$331$	−9.73247	−0.534945	−0.267473	−	0.963565i	$-0.586188\pi$
$331$	−9.73247	−0.534945	−0.267473	+	0.963565i	$0.586188\pi$
$332$	5.86755	0.322024
$333$	0.748091	0.0409951
$334$	−12.0288	−0.658188
$335$	−28.9562	−1.58205
$336$	−2.68342	−0.146393
$337$	−4.65652	−0.253657	−0.126828	−	0.991925i	$-0.540480\pi$
$337$	−4.65652	−0.253657	−0.126828	+	0.991925i	$0.540480\pi$
$338$	−47.5489	−2.58632
$339$	−36.1629	−1.96410
$340$	9.84294	0.533808
$341$	5.24385	0.283970
$342$	−9.94630	−0.537834
$343$	−3.90144	−0.210658
$344$	−4.63188	−0.249734
$345$	−4.75796	−0.256160
$346$	−34.9731	−1.88017
$347$	−16.7576	−0.899595	−0.449797	−	0.893131i	$-0.648504\pi$
$347$	−16.7576	−0.899595	−0.449797	+	0.893131i	$0.648504\pi$
$348$	11.3400	0.607888
$349$	8.47731	0.453780	0.226890	−	0.973920i	$-0.427144\pi$
$349$	8.47731	0.453780	0.226890	+	0.973920i	$0.427144\pi$
$350$	−0.0907793	−0.00485236
$351$	28.1134	1.50058
$352$	−3.46113	−0.184479
$353$	−1.59783	−0.0850438	−0.0425219	−	0.999096i	$-0.513539\pi$
$353$	−1.59783	−0.0850438	−0.0425219	+	0.999096i	$0.513539\pi$
$354$	−10.0886	−0.536203
$355$	−25.7703	−1.36775
$356$	−10.9901	−0.582474
$357$	−3.05341	−0.161603
$358$	18.9516	1.00162
$359$	13.0006	0.686145	0.343073	−	0.939309i	$-0.388532\pi$
$359$	13.0006	0.686145	0.343073	+	0.939309i	$0.388532\pi$
$360$	−3.49625	−0.184268
$361$	44.8775	2.36197
$362$	−14.1021	−0.741190
$363$	−19.9341	−1.04627
$364$	−1.38676	−0.0726859
$365$	−25.0940	−1.31348
$366$	−40.1464	−2.09848
$367$	20.5598	1.07322	0.536608	−	0.843832i	$-0.319706\pi$
$367$	20.5598	1.07322	0.536608	+	0.843832i	$0.319706\pi$
$368$	−5.33308	−0.278006
$369$	−0.223042	−0.0116111
$370$	3.79153	0.197112
$371$	−2.99614	−0.155552
$372$	−9.28824	−0.481573
$373$	29.3613	1.52027	0.760134	−	0.649766i	$-0.225133\pi$
$373$	29.3613	1.52027	0.760134	+	0.649766i	$0.225133\pi$
$374$	−7.85233	−0.406034
$375$	21.2034	1.09494
$376$	9.06793	0.467643
$377$	−49.2224	−2.53508
$378$	2.03249	0.104540
$379$	19.6145	1.00753	0.503765	−	0.863841i	$-0.331948\pi$
$379$	19.6145	1.00753	0.503765	+	0.863841i	$0.331948\pi$
$380$	−13.9784	−0.717079
$381$	10.7570	0.551095
$382$	−19.7656	−1.01130
$383$	2.75677	0.140864	0.0704321	−	0.997517i	$-0.477562\pi$
$383$	2.75677	0.140864	0.0704321	+	0.997517i	$0.477562\pi$
$384$	−25.7270	−1.31287
$385$	0.535730	0.0273033
$386$	−10.0601	−0.512047
$387$	−1.68984	−0.0858993
$388$	0.247538	0.0125668
$389$	34.9851	1.77381	0.886907	−	0.461949i	$-0.152850\pi$
$389$	34.9851	1.77381	0.886907	+	0.461949i	$0.152850\pi$
$390$	−47.3344	−2.39687
$391$	−6.06841	−0.306893
$392$	−14.1927	−0.716839
$393$	35.1927	1.77524
$394$	−28.3368	−1.42759
$395$	37.0923	1.86632
$396$	−0.481485	−0.0241955
$397$	−4.70489	−0.236132	−0.118066	−	0.993006i	$-0.537669\pi$
$397$	−4.70489	−0.236132	−0.118066	+	0.993006i	$0.537669\pi$
$398$	30.5407	1.53087
$399$	4.33629	0.217086
$400$	−0.963068	−0.0481534
$401$	17.4936	0.873590	0.436795	−	0.899561i	$-0.356114\pi$
$401$	17.4936	0.873590	0.436795	+	0.899561i	$0.356114\pi$
$402$	−40.9166	−2.04073
$403$	40.3165	2.00831
$404$	2.22669	0.110782
$405$	24.3523	1.21008
$406$	−3.55859	−0.176610
$407$	−0.838736	−0.0415746
$408$	−22.3415	−1.10607
$409$	16.3741	0.809649	0.404824	−	0.914394i	$-0.367333\pi$
$409$	16.3741	0.809649	0.404824	+	0.914394i	$0.367333\pi$
$410$	−1.13044	−0.0558285
$411$	12.7204	0.627449
$412$	13.7601	0.677912
$413$	0.877874	0.0431974
$414$	−1.34191	−0.0659511
$415$	−17.4275	−0.855481
$416$	−26.6104	−1.30468
$417$	−28.8200	−1.41132
$418$	11.1515	0.545437
$419$	−12.1757	−0.594821	−0.297411	−	0.954750i	$-0.596123\pi$
$419$	−12.1757	−0.594821	−0.297411	+	0.954750i	$0.596123\pi$
$420$	−0.948920	−0.0463025
$421$	0.0221456	0.00107931	0.000539655	−	1.00000i	$-0.499828\pi$
$421$	0.0221456	0.00107931	0.000539655		1.00000i	$0.499828\pi$
$422$	36.8845	1.79551
$423$	3.30823	0.160851
$424$	−21.9225	−1.06465
$425$	−1.09586	−0.0531568
$426$	−36.4147	−1.76430
$427$	3.49339	0.169057
$428$	12.1890	0.589180
$429$	10.4710	0.505544
$430$	−8.56456	−0.413020
$431$	−13.2466	−0.638067	−0.319034	−	0.947743i	$-0.603358\pi$
$431$	−13.2466	−0.638067	−0.319034	+	0.947743i	$0.603358\pi$
$432$	21.5625	1.03743
$433$	−8.04356	−0.386549	−0.193274	−	0.981145i	$-0.561911\pi$
$433$	−8.04356	−0.386549	−0.193274	+	0.981145i	$0.561911\pi$
$434$	2.91473	0.139911
$435$	−33.6815	−1.61490
$436$	−0.767368	−0.0367503
$437$	8.61804	0.412257
$438$	−35.4590	−1.69430
$439$	−15.7492	−0.751666	−0.375833	−	0.926687i	$-0.622643\pi$
$439$	−15.7492	−0.751666	−0.375833	+	0.926687i	$0.622643\pi$
$440$	3.91988	0.186873
$441$	−5.17788	−0.246566
$442$	−60.3714	−2.87157
$443$	7.49477	0.356087	0.178044	−	0.984023i	$-0.443023\pi$
$443$	7.49477	0.356087	0.178044	+	0.984023i	$0.443023\pi$
$444$	1.48562	0.0705045
$445$	32.6422	1.54739
$446$	−7.68663	−0.363972
$447$	36.9048	1.74554
$448$	0.848301	0.0400784
$449$	11.2197	0.529489	0.264744	−	0.964319i	$-0.414712\pi$
$449$	11.2197	0.529489	0.264744	+	0.964319i	$0.414712\pi$
$450$	−0.242327	−0.0114234
$451$	0.250068	0.0117752
$452$	−14.3338	−0.674206
$453$	−4.35315	−0.204529
$454$	6.11504	0.286993
$455$	4.11888	0.193096
$456$	31.7282	1.48581
$457$	−13.7712	−0.644189	−0.322095	−	0.946707i	$-0.604387\pi$
$457$	−13.7712	−0.644189	−0.322095	+	0.946707i	$0.604387\pi$
$458$	25.2212	1.17851
$459$	24.5356	1.14522
$460$	−1.88590	−0.0879307
$461$	−36.5579	−1.70267	−0.851335	−	0.524622i	$-0.824207\pi$
$461$	−36.5579	−1.70267	−0.851335	+	0.524622i	$0.824207\pi$
$462$	0.757013	0.0352194
$463$	−21.5275	−1.00047	−0.500233	−	0.865891i	$-0.666752\pi$
$463$	−21.5275	−1.00047	−0.500233	+	0.865891i	$0.666752\pi$
$464$	−37.7527	−1.75263
$465$	27.5874	1.27934
$466$	−19.6328	−0.909473
$467$	−30.2345	−1.39909	−0.699543	−	0.714591i	$-0.746613\pi$
$467$	−30.2345	−1.39909	−0.699543	+	0.714591i	$0.746613\pi$
$468$	−3.70182	−0.171117
$469$	3.56042	0.164405
$470$	16.7670	0.773404
$471$	−22.5247	−1.03788
$472$	6.42332	0.295657
$473$	1.89459	0.0871135
$474$	52.4133	2.40742
$475$	1.55628	0.0714069
$476$	−1.21027	−0.0554728
$477$	−7.99792	−0.366200
$478$	10.4381	0.477426
$479$	17.9662	0.820895	0.410447	−	0.911884i	$-0.365373\pi$
$479$	17.9662	0.820895	0.410447	+	0.911884i	$0.365373\pi$
$480$	−18.2087	−0.831111
$481$	−6.44849	−0.294026
$482$	20.5892	0.937814
$483$	0.585032	0.0266199
$484$	−7.90122	−0.359146
$485$	−0.735224	−0.0333848
$486$	12.6535	0.573973
$487$	5.06597	0.229561	0.114781	−	0.993391i	$-0.463384\pi$
$487$	5.06597	0.229561	0.114781	+	0.993391i	$0.463384\pi$
$488$	25.5608	1.15708
$489$	−5.89096	−0.266398
$490$	−26.2429	−1.18553
$491$	−12.8341	−0.579194	−0.289597	−	0.957149i	$-0.593521\pi$
$491$	−12.8341	−0.579194	−0.289597	+	0.957149i	$0.593521\pi$
$492$	−0.442937	−0.0199691
$493$	−42.9581	−1.93473
$494$	85.7364	3.85746
$495$	1.43008	0.0642773
$496$	30.9221	1.38844
$497$	3.16868	0.142135
$498$	−24.6259	−1.10351
$499$	−38.1852	−1.70940	−0.854702	−	0.519119i	$-0.826260\pi$
$499$	−38.1852	−1.70940	−0.854702	+	0.519119i	$0.826260\pi$
$500$	8.40433	0.375853
$501$	13.9989	0.625426
$502$	22.7807	1.01675
$503$	15.9093	0.709358	0.354679	−	0.934988i	$-0.384590\pi$
$503$	15.9093	0.709358	0.354679	+	0.934988i	$0.384590\pi$
$504$	0.429894	0.0191490
$505$	−6.61359	−0.294301
$506$	1.50450	0.0668834
$507$	55.3366	2.45758
$508$	4.26371	0.189172
$509$	36.1965	1.60438	0.802191	−	0.597067i	$-0.203667\pi$
$509$	36.1965	1.60438	0.802191	+	0.597067i	$0.203667\pi$
$510$	−41.3104	−1.82926
$511$	3.08552	0.136495
$512$	−0.126323	−0.00558272
$513$	−34.8441	−1.53841
$514$	7.69171	0.339267
$515$	−40.8695	−1.80093
$516$	−3.35582	−0.147732
$517$	−3.70908	−0.163125
$518$	−0.466201	−0.0204837
$519$	40.7011	1.78658
$520$	30.1374	1.32161
$521$	−7.59295	−0.332653	−0.166327	−	0.986071i	$-0.553191\pi$
$521$	−7.59295	−0.332653	−0.166327	+	0.986071i	$0.553191\pi$
$522$	−9.49932	−0.415774
$523$	−5.89319	−0.257691	−0.128846	−	0.991665i	$-0.541127\pi$
$523$	−5.89319	−0.257691	−0.128846	+	0.991665i	$0.541127\pi$
$524$	13.9493	0.609376
$525$	0.105647	0.00461082
$526$	−19.7098	−0.859390
$527$	35.1856	1.53271
$528$	8.03108	0.349508
$529$	−21.8373	−0.949448
$530$	−40.5357	−1.76076
$531$	2.34340	0.101695
$532$	1.71877	0.0745180
$533$	1.92261	0.0832774
$534$	46.1250	1.99603
$535$	−36.2032	−1.56520
$536$	26.0512	1.12524
$537$	−22.0555	−0.951765
$538$	−42.4212	−1.82891
$539$	5.80528	0.250051
$540$	7.62501	0.328128
$541$	−24.5930	−1.05733	−0.528667	−	0.848829i	$-0.677308\pi$
$541$	−24.5930	−1.05733	−0.528667	+	0.848829i	$0.677308\pi$
$542$	33.5754	1.44219
$543$	16.4118	0.704297
$544$	−23.2238	−0.995712
$545$	2.27919	0.0976299
$546$	5.82017	0.249080
$547$	−14.2064	−0.607423	−0.303711	−	0.952764i	$-0.598226\pi$
$547$	−14.2064	−0.607423	−0.303711	+	0.952764i	$0.598226\pi$
$548$	5.04195	0.215381
$549$	9.32528	0.397993
$550$	0.271689	0.0115849
$551$	61.0068	2.59898
$552$	4.28062	0.182195
$553$	−4.56082	−0.193946
$554$	−14.3697	−0.610509
$555$	−4.41251	−0.187301
$556$	−11.4233	−0.484456
$557$	29.8773	1.26594	0.632972	−	0.774175i	$-0.281835\pi$
$557$	29.8773	1.26594	0.632972	+	0.774175i	$0.281835\pi$
$558$	7.78059	0.329379
$559$	14.5663	0.616088
$560$	3.15911	0.133497
$561$	9.13840	0.385824
$562$	−8.24814	−0.347927
$563$	32.9464	1.38852	0.694262	−	0.719722i	$-0.255731\pi$
$563$	32.9464	1.38852	0.694262	+	0.719722i	$0.255731\pi$
$564$	6.56976	0.276637
$565$	42.5735	1.79108
$566$	−46.9257	−1.97243
$567$	−2.99433	−0.125750
$568$	23.1849	0.972817
$569$	−15.8391	−0.664012	−0.332006	−	0.943277i	$-0.607725\pi$
$569$	−15.8391	−0.664012	−0.332006	+	0.943277i	$0.607725\pi$
$570$	58.6670	2.45729
$571$	24.5961	1.02931	0.514656	−	0.857397i	$-0.327920\pi$
$571$	24.5961	1.02931	0.514656	+	0.857397i	$0.327920\pi$
$572$	4.15037	0.173536
$573$	23.0029	0.960960
$574$	0.138997	0.00580164
$575$	0.209966	0.00875617
$576$	2.26446	0.0943524
$577$	−12.3499	−0.514133	−0.257066	−	0.966394i	$-0.582756\pi$
$577$	−12.3499	−0.514133	−0.257066	+	0.966394i	$0.582756\pi$
$578$	−24.4080	−1.01524
$579$	11.7078	0.486559
$580$	−13.3502	−0.554339
$581$	2.14286	0.0889007
$582$	−1.03891	−0.0430641
$583$	8.96702	0.371376
$584$	22.5764	0.934219
$585$	10.9949	0.454585
$586$	11.2902	0.466395
$587$	3.61984	0.149407	0.0747034	−	0.997206i	$-0.476199\pi$
$587$	3.61984	0.149407	0.0747034	+	0.997206i	$0.476199\pi$
$588$	−10.2827	−0.424051
$589$	−49.9688	−2.05893
$590$	11.8770	0.488969
$591$	32.9779	1.35653
$592$	−4.94588	−0.203275
$593$	7.64434	0.313915	0.156958	−	0.987605i	$-0.449831\pi$
$593$	7.64434	0.313915	0.156958	+	0.987605i	$0.449831\pi$
$594$	−6.08295	−0.249587
$595$	3.59469	0.147368
$596$	14.6279	0.599181
$597$	−35.5427	−1.45467
$598$	11.5671	0.473015
$599$	−16.9673	−0.693263	−0.346632	−	0.938001i	$-0.612675\pi$
$599$	−16.9673	−0.693263	−0.346632	+	0.938001i	$0.612675\pi$
$600$	0.773010	0.0315580
$601$	25.8925	1.05618	0.528089	−	0.849189i	$-0.322909\pi$
$601$	25.8925	1.05618	0.528089	+	0.849189i	$0.322909\pi$
$602$	1.05309	0.0429206
$603$	9.50419	0.387041
$604$	−1.72545	−0.0702075
$605$	23.4678	0.954100
$606$	−9.34532	−0.379628
$607$	11.0903	0.450140	0.225070	−	0.974343i	$-0.427739\pi$
$607$	11.0903	0.450140	0.225070	+	0.974343i	$0.427739\pi$
$608$	32.9813	1.33757
$609$	4.14142	0.167819
$610$	47.2631	1.91363
$611$	−28.5167	−1.15366
$612$	−3.23071	−0.130594
$613$	27.3252	1.10365	0.551827	−	0.833958i	$-0.313931\pi$
$613$	27.3252	1.10365	0.551827	+	0.833958i	$0.313931\pi$
$614$	−39.3340	−1.58739
$615$	1.31559	0.0530496
$616$	−0.481983	−0.0194197
$617$	17.2199	0.693249	0.346624	−	0.938004i	$-0.387328\pi$
$617$	17.2199	0.693249	0.346624	+	0.938004i	$0.387328\pi$
$618$	−57.7507	−2.32307
$619$	11.9350	0.479709	0.239855	−	0.970809i	$-0.422900\pi$
$619$	11.9350	0.479709	0.239855	+	0.970809i	$0.422900\pi$
$620$	10.9348	0.439151
$621$	−4.70100	−0.188645
$622$	−30.7306	−1.23219
$623$	−4.01364	−0.160803
$624$	61.7457	2.47181
$625$	−25.9357	−1.03743
$626$	−18.2376	−0.728920
$627$	−12.9779	−0.518287
$628$	−8.92805	−0.356268
$629$	−5.62782	−0.224396
$630$	0.794893	0.0316693
$631$	−10.1591	−0.404427	−0.202213	−	0.979341i	$-0.564813\pi$
$631$	−10.1591	−0.404427	−0.202213	+	0.979341i	$0.564813\pi$
$632$	−33.3711	−1.32743
$633$	−42.9255	−1.70614
$634$	−30.5175	−1.21200
$635$	−12.6638	−0.502549
$636$	−15.8830	−0.629800
$637$	44.6329	1.76842
$638$	10.6503	0.421651
$639$	8.45849	0.334613
$640$	30.2876	1.19722
$641$	40.5582	1.60195	0.800977	−	0.598695i	$-0.204314\pi$
$641$	40.5582	1.60195	0.800977	+	0.598695i	$0.204314\pi$
$642$	−51.1569	−2.01900
$643$	−29.2228	−1.15243	−0.576217	−	0.817297i	$-0.695472\pi$
$643$	−29.2228	−1.15243	−0.576217	+	0.817297i	$0.695472\pi$
$644$	0.231888	0.00913766
$645$	9.96728	0.392461
$646$	74.8251	2.94395
$647$	21.9980	0.864830	0.432415	−	0.901675i	$-0.357662\pi$
$647$	21.9980	0.864830	0.432415	+	0.901675i	$0.357662\pi$
$648$	−21.9092	−0.860675
$649$	−2.62735	−0.103132
$650$	2.08884	0.0819309
$651$	−3.39211	−0.132947
$652$	−2.33499	−0.0914452
$653$	42.7225	1.67186	0.835930	−	0.548836i	$-0.184929\pi$
$653$	42.7225	1.67186	0.835930	+	0.548836i	$0.184929\pi$
$654$	3.22061	0.125936
$655$	−41.4313	−1.61885
$656$	1.47461	0.0575738
$657$	8.23649	0.321336
$658$	−2.06165	−0.0803714
$659$	−6.12509	−0.238600	−0.119300	−	0.992858i	$-0.538065\pi$
$659$	−6.12509	−0.238600	−0.119300	+	0.992858i	$0.538065\pi$
$660$	2.83998	0.110546
$661$	11.5308	0.448496	0.224248	−	0.974532i	$-0.428007\pi$
$661$	11.5308	0.448496	0.224248	+	0.974532i	$0.428007\pi$
$662$	16.1904	0.629256
$663$	70.2591	2.72864
$664$	15.6791	0.608466
$665$	−5.10499	−0.197963
$666$	−1.24448	−0.0482226
$667$	8.23075	0.318696
$668$	5.54873	0.214687
$669$	8.94556	0.345855
$670$	48.1699	1.86096
$671$	−10.4552	−0.403619
$672$	2.23892	0.0863681
$673$	14.3009	0.551258	0.275629	−	0.961264i	$-0.411114\pi$
$673$	14.3009	0.551258	0.275629	+	0.961264i	$0.411114\pi$
$674$	7.74631	0.298377
$675$	−0.848925	−0.0326751
$676$	21.9336	0.843602
$677$	−9.51420	−0.365660	−0.182830	−	0.983145i	$-0.558526\pi$
$677$	−9.51420	−0.365660	−0.182830	+	0.983145i	$0.558526\pi$
$678$	60.1585	2.31037
$679$	0.0904020	0.00346931
$680$	26.3020	1.00863
$681$	−7.11657	−0.272707
$682$	−8.72335	−0.334034
$683$	33.5549	1.28394	0.641971	−	0.766729i	$-0.278117\pi$
$683$	33.5549	1.28394	0.641971	+	0.766729i	$0.278117\pi$
$684$	4.58809	0.175430
$685$	−14.9753	−0.572177
$686$	6.49020	0.247797
$687$	−29.3520	−1.11985
$688$	11.1721	0.425932
$689$	68.9415	2.62646
$690$	7.91506	0.301321
$691$	43.7734	1.66522	0.832610	−	0.553860i	$-0.186846\pi$
$691$	43.7734	1.66522	0.832610	+	0.553860i	$0.186846\pi$
$692$	16.1326	0.613270
$693$	−0.175841	−0.00667963
$694$	27.8769	1.05819
$695$	33.9289	1.28700
$696$	30.3024	1.14861
$697$	1.67793	0.0635560
$698$	−14.1023	−0.533782
$699$	22.8483	0.864203
$700$	0.0418752	0.00158273
$701$	−30.7993	−1.16327	−0.581637	−	0.813448i	$-0.697588\pi$
$701$	−30.7993	−1.16327	−0.581637	+	0.813448i	$0.697588\pi$
$702$	−46.7678	−1.76514
$703$	7.99234	0.301437
$704$	−2.53884	−0.0956861
$705$	−19.5131	−0.734907
$706$	2.65805	0.100037
$707$	0.813197	0.0305834
$708$	4.65373	0.174898
$709$	−11.5682	−0.434451	−0.217226	−	0.976121i	$-0.569701\pi$
$709$	−11.5682	−0.434451	−0.217226	+	0.976121i	$0.569701\pi$
$710$	42.8700	1.60888
$711$	−12.1747	−0.456586
$712$	−29.3674	−1.10059
$713$	−6.74155	−0.252473
$714$	5.07947	0.190094
$715$	−12.3272	−0.461011
$716$	−8.74209	−0.326707
$717$	−12.1476	−0.453662
$718$	−21.6270	−0.807113
$719$	−44.7252	−1.66797	−0.833985	−	0.551787i	$-0.813946\pi$
$719$	−44.7252	−1.66797	−0.833985	+	0.551787i	$0.813946\pi$
$720$	8.43294	0.314277
$721$	5.02526	0.187150
$722$	−74.6555	−2.77839
$723$	−23.9614	−0.891133
$724$	6.50510	0.241760
$725$	1.48634	0.0552013
$726$	33.1611	1.23072
$727$	−34.3694	−1.27469	−0.637345	−	0.770579i	$-0.719967\pi$
$727$	−34.3694	−1.27469	−0.637345	+	0.770579i	$0.719967\pi$
$728$	−3.70565	−0.137341
$729$	17.3280	0.641778
$730$	41.7448	1.54505
$731$	12.7125	0.470189
$732$	18.5189	0.684480
$733$	21.6862	0.801000	0.400500	−	0.916297i	$-0.368836\pi$
$733$	21.6862	0.801000	0.400500	+	0.916297i	$0.368836\pi$
$734$	−34.2021	−1.26242
$735$	30.5411	1.12652
$736$	4.44967	0.164017
$737$	−10.6558	−0.392512
$738$	0.371040	0.0136582
$739$	49.7361	1.82957	0.914787	−	0.403937i	$-0.132358\pi$
$739$	49.7361	1.82957	0.914787	+	0.403937i	$0.132358\pi$
$740$	−1.74898	−0.0642938
$741$	−99.7784	−3.66545
$742$	4.98421	0.182976
$743$	−16.4574	−0.603762	−0.301881	−	0.953346i	$-0.597614\pi$
$743$	−16.4574	−0.603762	−0.301881	+	0.953346i	$0.597614\pi$
$744$	−24.8197	−0.909935
$745$	−43.4469	−1.59177
$746$	−48.8436	−1.78829
$747$	5.72015	0.209289
$748$	3.62217	0.132440
$749$	4.45149	0.162654
$750$	−35.2727	−1.28798
$751$	−15.0153	−0.547917	−0.273958	−	0.961742i	$-0.588333\pi$
$751$	−15.0153	−0.547917	−0.273958	+	0.961742i	$0.588333\pi$
$752$	−21.8718	−0.797583
$753$	−26.5118	−0.966144
$754$	81.8834	2.98202
$755$	5.12483	0.186512
$756$	−0.937561	−0.0340987
$757$	−3.76004	−0.136661	−0.0683305	−	0.997663i	$-0.521767\pi$
$757$	−3.76004	−0.136661	−0.0683305	+	0.997663i	$0.521767\pi$
$758$	−32.6295	−1.18516
$759$	−1.75091	−0.0635542
$760$	−37.3527	−1.35492
$761$	−13.2940	−0.481908	−0.240954	−	0.970537i	$-0.577460\pi$
$761$	−13.2940	−0.481908	−0.240954	+	0.970537i	$0.577460\pi$
$762$	−17.8946	−0.648254
$763$	−0.280246	−0.0101456
$764$	9.11761	0.329864
$765$	9.59567	0.346932
$766$	−4.58599	−0.165699
$767$	−20.2000	−0.729378
$768$	31.0774	1.12141
$769$	−20.6511	−0.744697	−0.372349	−	0.928093i	$-0.621447\pi$
$769$	−20.6511	−0.744697	−0.372349	+	0.928093i	$0.621447\pi$
$770$	−0.891209	−0.0321169
$771$	−8.95147	−0.322379
$772$	4.64059	0.167019
$773$	−51.4157	−1.84929	−0.924647	−	0.380826i	$-0.875640\pi$
$773$	−51.4157	−1.84929	−0.924647	+	0.380826i	$0.875640\pi$
$774$	2.81111	0.101043
$775$	−1.21741	−0.0437308
$776$	0.661462	0.0237451
$777$	0.542556	0.0194641
$778$	−58.1991	−2.08654
$779$	−2.38291	−0.0853765
$780$	21.8347	0.781808
$781$	−9.48339	−0.339342
$782$	10.0950	0.360998
$783$	−33.2783	−1.18927
$784$	34.2327	1.22260
$785$	26.5176	0.946454
$786$	−58.5445	−2.08821
$787$	−35.5400	−1.26686	−0.633432	−	0.773799i	$-0.718354\pi$
$787$	−35.5400	−1.26686	−0.633432	+	0.773799i	$0.718354\pi$
$788$	13.0714	0.465648
$789$	22.9380	0.816613
$790$	−61.7046	−2.19535
$791$	−5.23478	−0.186127
$792$	−1.28661	−0.0457176
$793$	−80.3832	−2.85449
$794$	7.82678	0.277762
$795$	47.1747	1.67311
$796$	−14.0880	−0.499335
$797$	−13.9000	−0.492362	−0.246181	−	0.969224i	$-0.579176\pi$
$797$	−13.9000	−0.492362	−0.246181	+	0.969224i	$0.579176\pi$
$798$	−7.21360	−0.255359
$799$	−24.8875	−0.880456
$800$	0.803538	0.0284094
$801$	−10.7140	−0.378561
$802$	−29.1013	−1.02760
$803$	−9.23450	−0.325878
$804$	18.8742	0.665643
$805$	−0.688741	−0.0242749
$806$	−67.0681	−2.36237
$807$	49.3690	1.73787
$808$	5.95008	0.209323
$809$	−22.2891	−0.783642	−0.391821	−	0.920042i	$-0.628155\pi$
$809$	−22.2891	−0.783642	−0.391821	+	0.920042i	$0.628155\pi$
$810$	−40.5111	−1.42342
$811$	−6.47918	−0.227515	−0.113757	−	0.993509i	$-0.536289\pi$
$811$	−6.47918	−0.227515	−0.113757	+	0.993509i	$0.536289\pi$
$812$	1.64153	0.0576063
$813$	−39.0744	−1.37040
$814$	1.39527	0.0489042
$815$	6.93525	0.242931
$816$	53.8876	1.88644
$817$	−18.0536	−0.631617
$818$	−27.2390	−0.952391
$819$	−1.35192	−0.0472400
$820$	0.521456	0.0182100
$821$	23.1854	0.809175	0.404587	−	0.914499i	$-0.367415\pi$
$821$	23.1854	0.809175	0.404587	+	0.914499i	$0.367415\pi$
$822$	−21.1608	−0.738069
$823$	−19.3137	−0.673233	−0.336617	−	0.941642i	$-0.609283\pi$
$823$	−19.3137	−0.673233	−0.336617	+	0.941642i	$0.609283\pi$
$824$	36.7693	1.28092
$825$	−0.316187	−0.0110082
$826$	−1.46038	−0.0508131
$827$	−18.4629	−0.642019	−0.321009	−	0.947076i	$-0.604022\pi$
$827$	−18.4629	−0.642019	−0.321009	+	0.947076i	$0.604022\pi$
$828$	0.619003	0.0215118
$829$	51.5371	1.78996	0.894979	−	0.446108i	$-0.147190\pi$
$829$	51.5371	1.78996	0.894979	+	0.446108i	$0.147190\pi$
$830$	28.9913	1.00630
$831$	16.7232	0.580120
$832$	−19.5195	−0.676715
$833$	38.9527	1.34963
$834$	47.9432	1.66014
$835$	−16.4805	−0.570332
$836$	−5.14402	−0.177910
$837$	27.2572	0.942146
$838$	20.2548	0.699689
$839$	−26.3690	−0.910358	−0.455179	−	0.890400i	$-0.650425\pi$
$839$	−26.3690	−0.910358	−0.455179	+	0.890400i	$0.650425\pi$
$840$	−2.53567	−0.0874890
$841$	29.2652	1.00915
$842$	−0.0368401	−0.00126959
$843$	9.59904	0.330609
$844$	−17.0143	−0.585656
$845$	−65.1461	−2.24109
$846$	−5.50337	−0.189210
$847$	−2.88556	−0.0991491
$848$	52.8770	1.81580
$849$	54.6113	1.87425
$850$	1.82300	0.0625284
$851$	1.07829	0.0369632
$852$	16.7976	0.575476
$853$	38.9511	1.33366	0.666830	−	0.745210i	$-0.267651\pi$
$853$	38.9511	1.33366	0.666830	+	0.745210i	$0.267651\pi$
$854$	−5.81140	−0.198862
$855$	−13.6273	−0.466043
$856$	32.5711	1.11326
$857$	−35.1996	−1.20239	−0.601197	−	0.799101i	$-0.705309\pi$
$857$	−35.1996	−1.20239	−0.601197	+	0.799101i	$0.705309\pi$
$858$	−17.4189	−0.594672
$859$	−40.2126	−1.37204	−0.686018	−	0.727584i	$-0.740643\pi$
$859$	−40.2126	−1.37204	−0.686018	+	0.727584i	$0.740643\pi$
$860$	3.95071	0.134718
$861$	−0.161763	−0.00551285
$862$	22.0363	0.750559
$863$	−28.3165	−0.963905	−0.481953	−	0.876197i	$-0.660072\pi$
$863$	−28.3165	−0.963905	−0.481953	+	0.876197i	$0.660072\pi$
$864$	−17.9907	−0.612058
$865$	−47.9162	−1.62920
$866$	13.3808	0.454698
$867$	28.4056	0.964705
$868$	−1.34452	−0.0456361
$869$	13.6499	0.463040
$870$	56.0305	1.89961
$871$	−81.9254	−2.77594
$872$	−2.05053	−0.0694398
$873$	0.241320	0.00816743
$874$	−14.3365	−0.484938
$875$	3.06930	0.103761
$876$	16.3567	0.552643
$877$	−20.1023	−0.678807	−0.339404	−	0.940641i	$-0.610225\pi$
$877$	−20.1023	−0.678807	−0.339404	+	0.940641i	$0.610225\pi$
$878$	26.1994	0.884186
$879$	−13.1393	−0.443179
$880$	−9.45475	−0.318720
$881$	−0.269412	−0.00907671	−0.00453836	−	0.999990i	$-0.501445\pi$
$881$	−0.269412	−0.00907671	−0.00453836	+	0.999990i	$0.501445\pi$
$882$	8.61362	0.290036
$883$	−27.8467	−0.937115	−0.468557	−	0.883433i	$-0.655226\pi$
$883$	−27.8467	−0.937115	−0.468557	+	0.883433i	$0.655226\pi$
$884$	27.8485	0.936645
$885$	−13.8222	−0.464630
$886$	−12.4679	−0.418866
$887$	31.6191	1.06166	0.530832	−	0.847477i	$-0.321880\pi$
$887$	31.6191	1.06166	0.530832	+	0.847477i	$0.321880\pi$
$888$	3.96983	0.133219
$889$	1.55713	0.0522244
$890$	−54.3016	−1.82019
$891$	8.96158	0.300224
$892$	3.54573	0.118720
$893$	35.3439	1.18274
$894$	−61.3926	−2.05328
$895$	25.9653	0.867924
$896$	−3.72412	−0.124414
$897$	−13.4616	−0.449471
$898$	−18.6644	−0.622838
$899$	−47.7232	−1.59166
$900$	0.111782	0.00372606
$901$	60.1676	2.00447
$902$	−0.415998	−0.0138512
$903$	−1.22556	−0.0407842
$904$	−38.3024	−1.27392
$905$	−19.3211	−0.642255
$906$	7.24164	0.240587
$907$	25.3006	0.840093	0.420047	−	0.907503i	$-0.362014\pi$
$907$	25.3006	0.840093	0.420047	+	0.907503i	$0.362014\pi$
$908$	−2.82078	−0.0936109
$909$	2.17075	0.0719993
$910$	−6.85192	−0.227139
$911$	34.9013	1.15633	0.578166	−	0.815919i	$-0.303769\pi$
$911$	34.9013	1.15633	0.578166	+	0.815919i	$0.303769\pi$
$912$	−76.5284	−2.53411
$913$	−6.41326	−0.212248
$914$	22.9089	0.757761
$915$	−55.0040	−1.81837
$916$	−11.6342	−0.384405
$917$	5.09433	0.168230
$918$	−40.8159	−1.34713
$919$	−23.2761	−0.767807	−0.383903	−	0.923373i	$-0.625420\pi$
$919$	−23.2761	−0.767807	−0.383903	+	0.923373i	$0.625420\pi$
$920$	−5.03945	−0.166146
$921$	45.7762	1.50838
$922$	60.8155	2.00285
$923$	−72.9115	−2.39991
$924$	−0.349199	−0.0114878
$925$	0.194721	0.00640240
$926$	35.8118	1.17685
$927$	13.4144	0.440588
$928$	31.4991	1.03401
$929$	−8.95774	−0.293894	−0.146947	−	0.989144i	$-0.546945\pi$
$929$	−8.95774	−0.293894	−0.146947	+	0.989144i	$0.546945\pi$
$930$	−45.8928	−1.50488
$931$	−55.3187	−1.81300
$932$	9.05635	0.296650
$933$	35.7638	1.17085
$934$	50.2963	1.64575
$935$	−10.7584	−0.351836
$936$	−9.89188	−0.323326
$937$	−1.88070	−0.0614398	−0.0307199	−	0.999528i	$-0.509780\pi$
$937$	−1.88070	−0.0614398	−0.0307199	+	0.999528i	$0.509780\pi$
$938$	−5.92290	−0.193389
$939$	21.2245	0.692637
$940$	−7.73438	−0.252268
$941$	19.2503	0.627543	0.313772	−	0.949498i	$-0.398407\pi$
$941$	19.2503	0.627543	0.313772	+	0.949498i	$0.398407\pi$
$942$	37.4707	1.22086
$943$	−0.321490	−0.0104692
$944$	−15.4930	−0.504255
$945$	2.78469	0.0905860
$946$	−3.15173	−0.102472
$947$	26.0077	0.845137	0.422569	−	0.906331i	$-0.361129\pi$
$947$	26.0077	0.845137	0.422569	+	0.906331i	$0.361129\pi$
$948$	−24.1775	−0.785249
$949$	−70.9979	−2.30469
$950$	−2.58893	−0.0839961
$951$	35.5157	1.15167
$952$	−3.23405	−0.104816
$953$	2.68314	0.0869153	0.0434576	−	0.999055i	$-0.486163\pi$
$953$	2.68314	0.0869153	0.0434576	+	0.999055i	$0.486163\pi$
$954$	13.3049	0.430761
$955$	−27.0806	−0.876308
$956$	−4.81493	−0.155726
$957$	−12.3947	−0.400663
$958$	−29.8874	−0.965619
$959$	1.84134	0.0594600
$960$	−13.3566	−0.431083
$961$	8.08856	0.260921
$962$	10.7273	0.345863
$963$	11.8828	0.382919
$964$	−9.49752	−0.305895
$965$	−13.7832	−0.443698
$966$	−0.973224	−0.0313130
$967$	9.28493	0.298583	0.149292	−	0.988793i	$-0.452301\pi$
$967$	9.28493	0.298583	0.149292	+	0.988793i	$0.452301\pi$
$968$	−21.1134	−0.678609
$969$	−87.0801	−2.79742
$970$	1.22307	0.0392705
$971$	55.7109	1.78785	0.893924	−	0.448219i	$-0.147942\pi$
$971$	55.7109	1.78785	0.893924	+	0.448219i	$0.147942\pi$
$972$	−5.83687	−0.187218
$973$	−4.17185	−0.133743
$974$	−8.42745	−0.270033
$975$	−2.43095	−0.0778527
$976$	−61.6526	−1.97345
$977$	8.36084	0.267487	0.133743	−	0.991016i	$-0.457300\pi$
$977$	8.36084	0.267487	0.133743	+	0.991016i	$0.457300\pi$
$978$	9.79985	0.313365
$979$	12.0122	0.383912
$980$	12.1055	0.386696
$981$	−0.748091	−0.0238847
$982$	21.3500	0.681307
$983$	−1.96092	−0.0625438	−0.0312719	−	0.999511i	$-0.509956\pi$
$983$	−1.96092	−0.0625438	−0.0312719	+	0.999511i	$0.509956\pi$
$984$	−1.18360	−0.0377318
$985$	−38.8239	−1.23703
$986$	71.4625	2.27583
$987$	2.39931	0.0763708
$988$	−39.5490	−1.25822
$989$	−2.43571	−0.0774510
$990$	−2.37900	−0.0756095
$991$	−30.7573	−0.977039	−0.488519	−	0.872553i	$-0.662463\pi$
$991$	−30.7573	−0.977039	−0.488519	+	0.872553i	$0.662463\pi$
$992$	−25.7999	−0.819148
$993$	−18.8421	−0.597934
$994$	−5.27123	−0.167193
$995$	41.8433	1.32652
$996$	11.3596	0.359942
$997$	15.8530	0.502069	0.251035	−	0.967978i	$-0.419229\pi$
$997$	15.8530	0.502069	0.251035	+	0.967978i	$0.419229\pi$
$998$	63.5226	2.01077
$999$	−4.35969	−0.137935

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.f.1.20	✓	85

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.f.1.20	✓	85	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-1.66354 q^{2} +1.93600 q^{3} +0.767368 q^{4} -2.27919 q^{5} -3.22061 q^{6} +0.280246 q^{7} +2.05053 q^{8} +0.748091 q^{9} +O(q^{10})\)	\(q-1.66354 q^{2} +1.93600 q^{3} +0.767368 q^{4} -2.27919 q^{5} -3.22061 q^{6} +0.280246 q^{7} +2.05053 q^{8} +0.748091 q^{9} +3.79153 q^{10} -0.838736 q^{11} +1.48562 q^{12} -6.44849 q^{13} -0.466201 q^{14} -4.41251 q^{15} -4.94588 q^{16} -5.62782 q^{17} -1.24448 q^{18} +7.99234 q^{19} -1.74898 q^{20} +0.542556 q^{21} +1.39527 q^{22} +1.07829 q^{23} +3.96983 q^{24} +0.194721 q^{25} +10.7273 q^{26} -4.35969 q^{27} +0.215052 q^{28} +7.63317 q^{29} +7.34040 q^{30} -6.25208 q^{31} +4.12661 q^{32} -1.62379 q^{33} +9.36210 q^{34} -0.638735 q^{35} +0.574061 q^{36} +1.00000 q^{37} -13.2956 q^{38} -12.4843 q^{39} -4.67356 q^{40} -0.298149 q^{41} -0.902565 q^{42} -2.25887 q^{43} -0.643619 q^{44} -1.70504 q^{45} -1.79378 q^{46} +4.42223 q^{47} -9.57522 q^{48} -6.92146 q^{49} -0.323927 q^{50} -10.8954 q^{51} -4.94836 q^{52} -10.6911 q^{53} +7.25253 q^{54} +1.91164 q^{55} +0.574654 q^{56} +15.4732 q^{57} -12.6981 q^{58} +3.13251 q^{59} -3.38602 q^{60} +12.4654 q^{61} +10.4006 q^{62} +0.209650 q^{63} +3.02698 q^{64} +14.6973 q^{65} +2.70124 q^{66} +12.7046 q^{67} -4.31861 q^{68} +2.08756 q^{69} +1.06256 q^{70} +11.3068 q^{71} +1.53399 q^{72} +11.0100 q^{73} -1.66354 q^{74} +0.376980 q^{75} +6.13306 q^{76} -0.235053 q^{77} +20.7681 q^{78} -16.2743 q^{79} +11.2726 q^{80} -10.6846 q^{81} +0.495983 q^{82} +7.64634 q^{83} +0.416340 q^{84} +12.8269 q^{85} +3.75772 q^{86} +14.7778 q^{87} -1.71986 q^{88} -14.3218 q^{89} +2.83641 q^{90} -1.80716 q^{91} +0.827443 q^{92} -12.1040 q^{93} -7.35655 q^{94} -18.2161 q^{95} +7.98911 q^{96} +0.322581 q^{97} +11.5141 q^{98} -0.627450 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9}+O(q^{10}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9} + 9 q^{10} + 37 q^{11} + 44 q^{12} + 14 q^{13} + 26 q^{14} + 27 q^{15} + 85 q^{16} + 34 q^{17} + 3 q^{18} + 15 q^{19} + 15 q^{20} + 17 q^{21} + q^{22} + 72 q^{23} + 15 q^{24} + 85 q^{25} + 33 q^{26} + 69 q^{27} + 7 q^{28} + 19 q^{29} - 9 q^{30} + 23 q^{31} + 51 q^{32} + 32 q^{33} + 49 q^{34} + 40 q^{35} + 121 q^{36} + 85 q^{37} + 84 q^{38} + 39 q^{39} + 22 q^{40} + 55 q^{41} - 28 q^{42} + 78 q^{44} + 28 q^{45} + 17 q^{46} + 184 q^{47} + 97 q^{48} + 88 q^{49} + 26 q^{50} + 27 q^{51} + 73 q^{52} + 64 q^{53} + 31 q^{54} + 39 q^{55} + 68 q^{56} - 33 q^{57} + 28 q^{58} + 60 q^{59} - 22 q^{60} + 7 q^{61} + 70 q^{62} + 28 q^{63} + 102 q^{64} + 17 q^{65} - 15 q^{66} + 82 q^{67} + 92 q^{68} + 22 q^{69} - 41 q^{70} + 113 q^{71} - 19 q^{73} + 11 q^{74} + 45 q^{75} + 34 q^{76} + 64 q^{77} + 29 q^{78} + 23 q^{79} + 54 q^{80} + 149 q^{81} + 4 q^{82} + 100 q^{83} - 49 q^{84} - 5 q^{85} - 24 q^{86} + 65 q^{87} + 14 q^{88} + 84 q^{89} - 21 q^{90} + 32 q^{91} + 95 q^{92} + 19 q^{93} - 47 q^{94} + 102 q^{95} + 29 q^{96} + 7 q^{97} + 26 q^{98} + 107 q^{99}+O(q^{100}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9 + 9 * q^10 + 37 * q^11 + 44 * q^12 + 14 * q^13 + 26 * q^14 + 27 * q^15 + 85 * q^16 + 34 * q^17 + 3 * q^18 + 15 * q^19 + 15 * q^20 + 17 * q^21 + q^22 + 72 * q^23 + 15 * q^24 + 85 * q^25 + 33 * q^26 + 69 * q^27 + 7 * q^28 + 19 * q^29 - 9 * q^30 + 23 * q^31 + 51 * q^32 + 32 * q^33 + 49 * q^34 + 40 * q^35 + 121 * q^36 + 85 * q^37 + 84 * q^38 + 39 * q^39 + 22 * q^40 + 55 * q^41 - 28 * q^42 + 78 * q^44 + 28 * q^45 + 17 * q^46 + 184 * q^47 + 97 * q^48 + 88 * q^49 + 26 * q^50 + 27 * q^51 + 73 * q^52 + 64 * q^53 + 31 * q^54 + 39 * q^55 + 68 * q^56 - 33 * q^57 + 28 * q^58 + 60 * q^59 - 22 * q^60 + 7 * q^61 + 70 * q^62 + 28 * q^63 + 102 * q^64 + 17 * q^65 - 15 * q^66 + 82 * q^67 + 92 * q^68 + 22 * q^69 - 41 * q^70 + 113 * q^71 - 19 * q^73 + 11 * q^74 + 45 * q^75 + 34 * q^76 + 64 * q^77 + 29 * q^78 + 23 * q^79 + 54 * q^80 + 149 * q^81 + 4 * q^82 + 100 * q^83 - 49 * q^84 - 5 * q^85 - 24 * q^86 + 65 * q^87 + 14 * q^88 + 84 * q^89 - 21 * q^90 + 32 * q^91 + 95 * q^92 + 19 * q^93 - 47 * q^94 + 102 * q^95 + 29 * q^96 + 7 * q^97 + 26 * q^98 + 107 * q^99

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