LMFDB - Embedded newform 6005.2.a.d.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, 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("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$1$
Dimension:	$83$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.30347 q^{2} +2.77237 q^{3} +3.30599 q^{4} -1.00000 q^{5} -6.38609 q^{6} +3.31837 q^{7} -3.00832 q^{8} +4.68605 q^{9} +O(q^{10})$	\(q-2.30347 q^{2} +2.77237 q^{3} +3.30599 q^{4} -1.00000 q^{5} -6.38609 q^{6} +3.31837 q^{7} -3.00832 q^{8} +4.68605 q^{9} +2.30347 q^{10} -4.78443 q^{11} +9.16544 q^{12} -5.36185 q^{13} -7.64379 q^{14} -2.77237 q^{15} +0.317593 q^{16} +6.64336 q^{17} -10.7942 q^{18} +0.701256 q^{19} -3.30599 q^{20} +9.19977 q^{21} +11.0208 q^{22} -6.30358 q^{23} -8.34017 q^{24} +1.00000 q^{25} +12.3509 q^{26} +4.67436 q^{27} +10.9705 q^{28} +1.72202 q^{29} +6.38609 q^{30} -4.29381 q^{31} +5.28506 q^{32} -13.2642 q^{33} -15.3028 q^{34} -3.31837 q^{35} +15.4920 q^{36} -8.18973 q^{37} -1.61533 q^{38} -14.8650 q^{39} +3.00832 q^{40} -0.923697 q^{41} -21.1914 q^{42} -10.4999 q^{43} -15.8173 q^{44} -4.68605 q^{45} +14.5201 q^{46} +7.56478 q^{47} +0.880487 q^{48} +4.01161 q^{49} -2.30347 q^{50} +18.4179 q^{51} -17.7262 q^{52} +7.33934 q^{53} -10.7673 q^{54} +4.78443 q^{55} -9.98272 q^{56} +1.94414 q^{57} -3.96663 q^{58} +2.18196 q^{59} -9.16544 q^{60} +3.91134 q^{61} +9.89069 q^{62} +15.5501 q^{63} -12.8092 q^{64} +5.36185 q^{65} +30.5538 q^{66} -0.158853 q^{67} +21.9629 q^{68} -17.4759 q^{69} +7.64379 q^{70} +6.65980 q^{71} -14.0971 q^{72} -10.5639 q^{73} +18.8648 q^{74} +2.77237 q^{75} +2.31835 q^{76} -15.8765 q^{77} +34.2412 q^{78} -10.7091 q^{79} -0.317593 q^{80} -1.09908 q^{81} +2.12771 q^{82} -13.3681 q^{83} +30.4144 q^{84} -6.64336 q^{85} +24.1863 q^{86} +4.77409 q^{87} +14.3931 q^{88} +7.36489 q^{89} +10.7942 q^{90} -17.7926 q^{91} -20.8396 q^{92} -11.9041 q^{93} -17.4253 q^{94} -0.701256 q^{95} +14.6522 q^{96} +10.2571 q^{97} -9.24064 q^{98} -22.4201 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9}+O(q^{10}) $ 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9	\( 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9} - q^{10} - 26 q^{11} - 12 q^{12} - 15 q^{13} - 21 q^{14} + 4 q^{15} + 5 q^{16} + 8 q^{17} - 12 q^{18} - 79 q^{19} - 61 q^{20} - 34 q^{21} - 25 q^{22} + 31 q^{23} - 42 q^{24} + 83 q^{25} - 13 q^{26} - 25 q^{27} - 16 q^{28} - 16 q^{29} + 6 q^{30} - 40 q^{31} + 15 q^{32} - 33 q^{33} - 54 q^{34} - 2 q^{35} + 11 q^{36} - 45 q^{37} + 10 q^{38} - 54 q^{39} + 3 q^{40} - 27 q^{41} - 28 q^{42} - 101 q^{43} - 51 q^{44} - 61 q^{45} - 46 q^{46} + 71 q^{47} - 14 q^{48} + 23 q^{49} + q^{50} - 71 q^{51} - 34 q^{52} - 49 q^{53} - 25 q^{54} + 26 q^{55} - 41 q^{56} - 20 q^{57} - 43 q^{58} - 60 q^{59} + 12 q^{60} - 38 q^{61} - 2 q^{62} + 36 q^{63} - 113 q^{64} + 15 q^{65} - 42 q^{66} - 164 q^{67} + 10 q^{68} - 93 q^{69} + 21 q^{70} - 78 q^{71} + q^{72} - 18 q^{73} - 23 q^{74} - 4 q^{75} - 112 q^{76} - 35 q^{77} - 44 q^{78} - 124 q^{79} - 5 q^{80} - 45 q^{81} - 34 q^{82} + 5 q^{83} - 60 q^{84} - 8 q^{85} - 25 q^{86} + 12 q^{87} - 149 q^{88} - 44 q^{89} + 12 q^{90} - 192 q^{91} + 35 q^{92} - 13 q^{93} - 32 q^{94} + 79 q^{95} - 59 q^{96} - 31 q^{97} + 25 q^{98} - 134 q^{99}+O(q^{100}) \) 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9 - q^10 - 26 * q^11 - 12 * q^12 - 15 * q^13 - 21 * q^14 + 4 * q^15 + 5 * q^16 + 8 * q^17 - 12 * q^18 - 79 * q^19 - 61 * q^20 - 34 * q^21 - 25 * q^22 + 31 * q^23 - 42 * q^24 + 83 * q^25 - 13 * q^26 - 25 * q^27 - 16 * q^28 - 16 * q^29 + 6 * q^30 - 40 * q^31 + 15 * q^32 - 33 * q^33 - 54 * q^34 - 2 * q^35 + 11 * q^36 - 45 * q^37 + 10 * q^38 - 54 * q^39 + 3 * q^40 - 27 * q^41 - 28 * q^42 - 101 * q^43 - 51 * q^44 - 61 * q^45 - 46 * q^46 + 71 * q^47 - 14 * q^48 + 23 * q^49 + q^50 - 71 * q^51 - 34 * q^52 - 49 * q^53 - 25 * q^54 + 26 * q^55 - 41 * q^56 - 20 * q^57 - 43 * q^58 - 60 * q^59 + 12 * q^60 - 38 * q^61 - 2 * q^62 + 36 * q^63 - 113 * q^64 + 15 * q^65 - 42 * q^66 - 164 * q^67 + 10 * q^68 - 93 * q^69 + 21 * q^70 - 78 * q^71 + q^72 - 18 * q^73 - 23 * q^74 - 4 * q^75 - 112 * q^76 - 35 * q^77 - 44 * q^78 - 124 * q^79 - 5 * q^80 - 45 * q^81 - 34 * q^82 + 5 * q^83 - 60 * q^84 - 8 * q^85 - 25 * q^86 + 12 * q^87 - 149 * q^88 - 44 * q^89 + 12 * q^90 - 192 * q^91 + 35 * q^92 - 13 * q^93 - 32 * q^94 + 79 * q^95 - 59 * q^96 - 31 * q^97 + 25 * q^98 - 134 * 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 $

$2$	−2.30347	−1.62880	−0.814401	−	0.580303i	$-0.802934\pi$
$2$	−2.30347	−1.62880	−0.814401	+	0.580303i	$0.802934\pi$
$3$	2.77237	1.60063	0.800315	−	0.599580i	$-0.204666\pi$
$3$	2.77237	1.60063	0.800315	+	0.599580i	$0.204666\pi$
$4$	3.30599	1.65300
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−6.38609	−2.60711
$7$	3.31837	1.25423	0.627114	−	0.778928i	$-0.284236\pi$
$7$	3.31837	1.25423	0.627114	+	0.778928i	$0.284236\pi$
$8$	−3.00832	−1.06360
$9$	4.68605	1.56202
$10$	2.30347	0.728422
$11$	−4.78443	−1.44256	−0.721280	−	0.692644i	$-0.756446\pi$
$11$	−4.78443	−1.44256	−0.721280	+	0.692644i	$0.756446\pi$
$12$	9.16544	2.64583
$13$	−5.36185	−1.48711	−0.743555	−	0.668675i	$-0.766862\pi$
$13$	−5.36185	−1.48711	−0.743555	+	0.668675i	$0.766862\pi$
$14$	−7.64379	−2.04289
$15$	−2.77237	−0.715824
$16$	0.317593	0.0793983
$17$	6.64336	1.61125	0.805626	−	0.592424i	$-0.201829\pi$
$17$	6.64336	1.61125	0.805626	+	0.592424i	$0.201829\pi$
$18$	−10.7942	−2.54422
$19$	0.701256	0.160879	0.0804396	−	0.996759i	$-0.474368\pi$
$19$	0.701256	0.160879	0.0804396	+	0.996759i	$0.474368\pi$
$20$	−3.30599	−0.739242
$21$	9.19977	2.00755
$22$	11.0208	2.34964
$23$	−6.30358	−1.31439	−0.657194	−	0.753722i	$-0.728257\pi$
$23$	−6.30358	−1.31439	−0.657194	+	0.753722i	$0.728257\pi$
$24$	−8.34017	−1.70243
$25$	1.00000	0.200000
$26$	12.3509	2.42221
$27$	4.67436	0.899581
$28$	10.9705	2.07323
$29$	1.72202	0.319772	0.159886	−	0.987136i	$-0.448887\pi$
$29$	1.72202	0.319772	0.159886	+	0.987136i	$0.448887\pi$
$30$	6.38609	1.16593
$31$	−4.29381	−0.771192	−0.385596	−	0.922668i	$-0.626004\pi$
$31$	−4.29381	−0.771192	−0.385596	+	0.922668i	$0.626004\pi$
$32$	5.28506	0.934276
$33$	−13.2642	−2.30901
$34$	−15.3028	−2.62441
$35$	−3.31837	−0.560908
$36$	15.4920	2.58201
$37$	−8.18973	−1.34638	−0.673192	−	0.739468i	$-0.735077\pi$
$37$	−8.18973	−1.34638	−0.673192	+	0.739468i	$0.735077\pi$
$38$	−1.61533	−0.262040
$39$	−14.8650	−2.38031
$40$	3.00832	0.475656
$41$	−0.923697	−0.144257	−0.0721286	−	0.997395i	$-0.522979\pi$
$41$	−0.923697	−0.144257	−0.0721286	+	0.997395i	$0.522979\pi$
$42$	−21.1914	−3.26991
$43$	−10.4999	−1.60122	−0.800611	−	0.599185i	$-0.795491\pi$
$43$	−10.4999	−1.60122	−0.800611	+	0.599185i	$0.795491\pi$
$44$	−15.8173	−2.38455
$45$	−4.68605	−0.698555
$46$	14.5201	2.14088
$47$	7.56478	1.10344	0.551718	−	0.834031i	$-0.313972\pi$
$47$	7.56478	1.10344	0.551718	+	0.834031i	$0.313972\pi$
$48$	0.880487	0.127087
$49$	4.01161	0.573087
$50$	−2.30347	−0.325760
$51$	18.4179	2.57902
$52$	−17.7262	−2.45819
$53$	7.33934	1.00814	0.504068	−	0.863664i	$-0.331836\pi$
$53$	7.33934	1.00814	0.504068	+	0.863664i	$0.331836\pi$
$54$	−10.7673	−1.46524
$55$	4.78443	0.645132
$56$	−9.98272	−1.33400
$57$	1.94414	0.257508
$58$	−3.96663	−0.520845
$59$	2.18196	0.284067	0.142033	−	0.989862i	$-0.454636\pi$
$59$	2.18196	0.284067	0.142033	+	0.989862i	$0.454636\pi$
$60$	−9.16544	−1.18325
$61$	3.91134	0.500796	0.250398	−	0.968143i	$-0.419438\pi$
$61$	3.91134	0.500796	0.250398	+	0.968143i	$0.419438\pi$
$62$	9.89069	1.25612
$63$	15.5501	1.95912
$64$	−12.8092	−1.60115
$65$	5.36185	0.665056
$66$	30.5538	3.76091
$67$	−0.158853	−0.0194070	−0.00970350	−	0.999953i	$-0.503089\pi$
$67$	−0.158853	−0.0194070	−0.00970350	+	0.999953i	$0.503089\pi$
$68$	21.9629	2.66339
$69$	−17.4759	−2.10385
$70$	7.64379	0.913607
$71$	6.65980	0.790373	0.395186	−	0.918601i	$-0.370680\pi$
$71$	6.65980	0.790373	0.395186	+	0.918601i	$0.370680\pi$
$72$	−14.0971	−1.66136
$73$	−10.5639	−1.23642	−0.618208	−	0.786014i	$-0.712141\pi$
$73$	−10.5639	−1.23642	−0.618208	+	0.786014i	$0.712141\pi$
$74$	18.8648	2.19299
$75$	2.77237	0.320126
$76$	2.31835	0.265933
$77$	−15.8765	−1.80930
$78$	34.2412	3.87706
$79$	−10.7091	−1.20487	−0.602435	−	0.798168i	$-0.705803\pi$
$79$	−10.7091	−1.20487	−0.602435	+	0.798168i	$0.705803\pi$
$80$	−0.317593	−0.0355080
$81$	−1.09908	−0.122120
$82$	2.12771	0.234967
$83$	−13.3681	−1.46734	−0.733671	−	0.679505i	$-0.762195\pi$
$83$	−13.3681	−1.46734	−0.733671	+	0.679505i	$0.762195\pi$
$84$	30.4144	3.31848
$85$	−6.64336	−0.720574
$86$	24.1863	2.60807
$87$	4.77409	0.511836
$88$	14.3931	1.53431
$89$	7.36489	0.780677	0.390339	−	0.920671i	$-0.372358\pi$
$89$	7.36489	0.780677	0.390339	+	0.920671i	$0.372358\pi$
$90$	10.7942	1.13781
$91$	−17.7926	−1.86517
$92$	−20.8396	−2.17268
$93$	−11.9041	−1.23439
$94$	−17.4253	−1.79728
$95$	−0.701256	−0.0719474
$96$	14.6522	1.49543
$97$	10.2571	1.04145	0.520726	−	0.853724i	$-0.325661\pi$
$97$	10.2571	1.04145	0.520726	+	0.853724i	$0.325661\pi$
$98$	−9.24064	−0.933445
$99$	−22.4201	−2.25330
$100$	3.30599	0.330599
$101$	−7.71466	−0.767637	−0.383818	−	0.923409i	$-0.625391\pi$
$101$	−7.71466	−0.767637	−0.383818	+	0.923409i	$0.625391\pi$
$102$	−42.4251	−4.20071
$103$	−6.91141	−0.681001	−0.340501	−	0.940244i	$-0.610597\pi$
$103$	−6.91141	−0.681001	−0.340501	+	0.940244i	$0.610597\pi$
$104$	16.1301	1.58169
$105$	−9.19977	−0.897806
$106$	−16.9060	−1.64205
$107$	3.62052	0.350009	0.175005	−	0.984568i	$-0.444006\pi$
$107$	3.62052	0.350009	0.175005	+	0.984568i	$0.444006\pi$
$108$	15.4534	1.48700
$109$	7.59906	0.727858	0.363929	−	0.931427i	$-0.381435\pi$
$109$	7.59906	0.727858	0.363929	+	0.931427i	$0.381435\pi$
$110$	−11.0208	−1.05079
$111$	−22.7050	−2.15506
$112$	1.05389	0.0995835
$113$	0.611188	0.0574957	0.0287478	−	0.999587i	$-0.490848\pi$
$113$	0.611188	0.0574957	0.0287478	+	0.999587i	$0.490848\pi$
$114$	−4.47828	−0.419430
$115$	6.30358	0.587812
$116$	5.69299	0.528581
$117$	−25.1259	−2.32289
$118$	−5.02609	−0.462689
$119$	22.0452	2.02088
$120$	8.34017	0.761350
$121$	11.8908	1.08098
$122$	−9.00968	−0.815698
$123$	−2.56083	−0.230903
$124$	−14.1953	−1.27478
$125$	−1.00000	−0.0894427
$126$	−35.8192	−3.19103
$127$	−17.0888	−1.51638	−0.758191	−	0.652033i	$-0.773916\pi$
$127$	−17.0888	−1.51638	−0.758191	+	0.652033i	$0.773916\pi$
$128$	18.9355	1.67368
$129$	−29.1097	−2.56296
$130$	−12.3509	−1.08324
$131$	−17.7248	−1.54862	−0.774311	−	0.632806i	$-0.781903\pi$
$131$	−17.7248	−1.54862	−0.774311	+	0.632806i	$0.781903\pi$
$132$	−43.8514	−3.81677
$133$	2.32703	0.201779
$134$	0.365914	0.0316102
$135$	−4.67436	−0.402305
$136$	−19.9853	−1.71373
$137$	−2.27439	−0.194315	−0.0971573	−	0.995269i	$-0.530975\pi$
$137$	−2.27439	−0.194315	−0.0971573	+	0.995269i	$0.530975\pi$
$138$	40.2552	3.42675
$139$	−14.0418	−1.19101	−0.595505	−	0.803351i	$-0.703048\pi$
$139$	−14.0418	−1.19101	−0.595505	+	0.803351i	$0.703048\pi$
$140$	−10.9705	−0.927178
$141$	20.9724	1.76619
$142$	−15.3407	−1.28736
$143$	25.6534	2.14525
$144$	1.48826	0.124021
$145$	−1.72202	−0.143006
$146$	24.3338	2.01388
$147$	11.1217	0.917300
$148$	−27.0752	−2.22557
$149$	19.4320	1.59193	0.795966	−	0.605341i	$-0.206963\pi$
$149$	19.4320	1.59193	0.795966	+	0.605341i	$0.206963\pi$
$150$	−6.38609	−0.521422
$151$	5.88601	0.478997	0.239498	−	0.970897i	$-0.423017\pi$
$151$	5.88601	0.478997	0.239498	+	0.970897i	$0.423017\pi$
$152$	−2.10960	−0.171111
$153$	31.1311	2.51680
$154$	36.5712	2.94699
$155$	4.29381	0.344887
$156$	−49.1437	−3.93465
$157$	−12.4018	−0.989772	−0.494886	−	0.868958i	$-0.664790\pi$
$157$	−12.4018	−0.989772	−0.494886	+	0.868958i	$0.664790\pi$
$158$	24.6682	1.96249
$159$	20.3474	1.61365
$160$	−5.28506	−0.417821
$161$	−20.9176	−1.64854
$162$	2.53171	0.198910
$163$	−19.9402	−1.56184	−0.780919	−	0.624633i	$-0.785249\pi$
$163$	−19.9402	−1.56184	−0.780919	+	0.624633i	$0.785249\pi$
$164$	−3.05373	−0.238457
$165$	13.2642	1.03262
$166$	30.7931	2.39001
$167$	−3.76440	−0.291298	−0.145649	−	0.989336i	$-0.546527\pi$
$167$	−3.76440	−0.291298	−0.145649	+	0.989336i	$0.546527\pi$
$168$	−27.6758	−2.13524
$169$	15.7494	1.21150
$170$	15.3028	1.17367
$171$	3.28612	0.251296
$172$	−34.7126	−2.64681
$173$	−4.67373	−0.355337	−0.177669	−	0.984090i	$-0.556856\pi$
$173$	−4.67373	−0.355337	−0.177669	+	0.984090i	$0.556856\pi$
$174$	−10.9970	−0.833680
$175$	3.31837	0.250846
$176$	−1.51950	−0.114537
$177$	6.04921	0.454686
$178$	−16.9648	−1.27157
$179$	−14.5329	−1.08624	−0.543121	−	0.839655i	$-0.682757\pi$
$179$	−14.5329	−1.08624	−0.543121	+	0.839655i	$0.682757\pi$
$180$	−15.4920	−1.15471
$181$	−8.83962	−0.657044	−0.328522	−	0.944496i	$-0.606550\pi$
$181$	−8.83962	−0.657044	−0.328522	+	0.944496i	$0.606550\pi$
$182$	40.9848	3.03800
$183$	10.8437	0.801589
$184$	18.9632	1.39798
$185$	8.18973	0.602121
$186$	27.4207	2.01058
$187$	−31.7847	−2.32433
$188$	25.0091	1.82397
$189$	15.5113	1.12828
$190$	1.61533	0.117188
$191$	−1.12128	−0.0811331	−0.0405666	−	0.999177i	$-0.512916\pi$
$191$	−1.12128	−0.0811331	−0.0405666	+	0.999177i	$0.512916\pi$
$192$	−35.5118	−2.56285
$193$	−4.52236	−0.325526	−0.162763	−	0.986665i	$-0.552041\pi$
$193$	−4.52236	−0.325526	−0.162763	+	0.986665i	$0.552041\pi$
$194$	−23.6270	−1.69632
$195$	14.8650	1.06451
$196$	13.2623	0.947310
$197$	−2.90175	−0.206741	−0.103371	−	0.994643i	$-0.532963\pi$
$197$	−2.90175	−0.206741	−0.103371	+	0.994643i	$0.532963\pi$
$198$	51.6441	3.67018
$199$	15.2805	1.08321	0.541604	−	0.840634i	$-0.317817\pi$
$199$	15.2805	1.08321	0.541604	+	0.840634i	$0.317817\pi$
$200$	−3.00832	−0.212720
$201$	−0.440400	−0.0310634
$202$	17.7705	1.25033
$203$	5.71432	0.401066
$204$	60.8893	4.26311
$205$	0.923697	0.0645138
$206$	15.9202	1.10922
$207$	−29.5389	−2.05309
$208$	−1.70289	−0.118074
$209$	−3.35511	−0.232078
$210$	21.1914	1.46235
$211$	−25.7715	−1.77419	−0.887093	−	0.461590i	$-0.847279\pi$
$211$	−25.7715	−1.77419	−0.887093	+	0.461590i	$0.847279\pi$
$212$	24.2638	1.66644
$213$	18.4634	1.26509
$214$	−8.33978	−0.570096
$215$	10.4999	0.716088
$216$	−14.0619	−0.956794
$217$	−14.2485	−0.967250
$218$	−17.5042	−1.18554
$219$	−29.2872	−1.97905
$220$	15.8173	1.06640
$221$	−35.6207	−2.39611
$222$	52.3004	3.51017
$223$	8.39688	0.562296	0.281148	−	0.959664i	$-0.409285\pi$
$223$	8.39688	0.562296	0.281148	+	0.959664i	$0.409285\pi$
$224$	17.5378	1.17179
$225$	4.68605	0.312403
$226$	−1.40785	−0.0936491
$227$	21.7037	1.44053	0.720264	−	0.693700i	$-0.244021\pi$
$227$	21.7037	1.44053	0.720264	+	0.693700i	$0.244021\pi$
$228$	6.42732	0.425660
$229$	−8.27280	−0.546682	−0.273341	−	0.961917i	$-0.588129\pi$
$229$	−8.27280	−0.546682	−0.273341	+	0.961917i	$0.588129\pi$
$230$	−14.5201	−0.957429
$231$	−44.0157	−2.89602
$232$	−5.18039	−0.340109
$233$	−14.8694	−0.974126	−0.487063	−	0.873367i	$-0.661932\pi$
$233$	−14.8694	−0.974126	−0.487063	+	0.873367i	$0.661932\pi$
$234$	57.8768	3.78353
$235$	−7.56478	−0.493472
$236$	7.21354	0.469561
$237$	−29.6897	−1.92855
$238$	−50.7805	−3.29161
$239$	−7.78648	−0.503666	−0.251833	−	0.967771i	$-0.581033\pi$
$239$	−7.78648	−0.503666	−0.251833	+	0.967771i	$0.581033\pi$
$240$	−0.880487	−0.0568352
$241$	25.5103	1.64326	0.821632	−	0.570018i	$-0.193064\pi$
$241$	25.5103	1.64326	0.821632	+	0.570018i	$0.193064\pi$
$242$	−27.3901	−1.76070
$243$	−17.0701	−1.09505
$244$	12.9309	0.827814
$245$	−4.01161	−0.256292
$246$	5.89881	0.376094
$247$	−3.76003	−0.239245
$248$	12.9171	0.820239
$249$	−37.0614	−2.34867
$250$	2.30347	0.145684
$251$	−30.7489	−1.94085	−0.970427	−	0.241395i	$-0.922395\pi$
$251$	−30.7489	−1.94085	−0.970427	+	0.241395i	$0.922395\pi$
$252$	51.4084	3.23842
$253$	30.1590	1.89608
$254$	39.3635	2.46988
$255$	−18.4179	−1.15337
$256$	−17.9991	−1.12494
$257$	8.30948	0.518331	0.259166	−	0.965833i	$-0.416552\pi$
$257$	8.30948	0.518331	0.259166	+	0.965833i	$0.416552\pi$
$258$	67.0533	4.17456
$259$	−27.1766	−1.68867
$260$	17.7262	1.09933
$261$	8.06949	0.499489
$262$	40.8286	2.52240
$263$	7.62409	0.470121	0.235061	−	0.971981i	$-0.424471\pi$
$263$	7.62409	0.470121	0.235061	+	0.971981i	$0.424471\pi$
$264$	39.9030	2.45586
$265$	−7.33934	−0.450852
$266$	−5.36025	−0.328658
$267$	20.4182	1.24958
$268$	−0.525167	−0.0320797
$269$	−9.74237	−0.594003	−0.297001	−	0.954877i	$-0.595987\pi$
$269$	−9.74237	−0.594003	−0.297001	+	0.954877i	$0.595987\pi$
$270$	10.7673	0.655275
$271$	8.25126	0.501228	0.250614	−	0.968087i	$-0.419367\pi$
$271$	8.25126	0.501228	0.250614	+	0.968087i	$0.419367\pi$
$272$	2.10989	0.127931
$273$	−49.3278	−2.98545
$274$	5.23900	0.316500
$275$	−4.78443	−0.288512
$276$	−57.7751	−3.47765
$277$	22.3066	1.34027	0.670136	−	0.742239i	$-0.266236\pi$
$277$	22.3066	1.34027	0.670136	+	0.742239i	$0.266236\pi$
$278$	32.3449	1.93992
$279$	−20.1210	−1.20461
$280$	9.98272	0.596581
$281$	19.4175	1.15835	0.579176	−	0.815203i	$-0.303374\pi$
$281$	19.4175	1.15835	0.579176	+	0.815203i	$0.303374\pi$
$282$	−48.3093	−2.87678
$283$	5.40518	0.321304	0.160652	−	0.987011i	$-0.448640\pi$
$283$	5.40518	0.321304	0.160652	+	0.987011i	$0.448640\pi$
$284$	22.0172	1.30648
$285$	−1.94414	−0.115161
$286$	−59.0919	−3.49418
$287$	−3.06517	−0.180931
$288$	24.7661	1.45935
$289$	27.1343	1.59613
$290$	3.96663	0.232929
$291$	28.4365	1.66698
$292$	−34.9243	−2.04379
$293$	−11.2488	−0.657160	−0.328580	−	0.944476i	$-0.606570\pi$
$293$	−11.2488	−0.657160	−0.328580	+	0.944476i	$0.606570\pi$
$294$	−25.6185	−1.49410
$295$	−2.18196	−0.127039
$296$	24.6373	1.43201
$297$	−22.3642	−1.29770
$298$	−44.7611	−2.59294
$299$	33.7988	1.95464
$300$	9.16544	0.529167
$301$	−34.8426	−2.00830
$302$	−13.5583	−0.780191
$303$	−21.3879	−1.22870
$304$	0.222714	0.0127735
$305$	−3.91134	−0.223963
$306$	−71.7097	−4.09937
$307$	−24.4968	−1.39811	−0.699054	−	0.715069i	$-0.746395\pi$
$307$	−24.4968	−1.39811	−0.699054	+	0.715069i	$0.746395\pi$
$308$	−52.4877	−2.99076
$309$	−19.1610	−1.09003
$310$	−9.89069	−0.561753
$311$	−18.5502	−1.05189	−0.525944	−	0.850519i	$-0.676288\pi$
$311$	−18.5502	−1.05189	−0.525944	+	0.850519i	$0.676288\pi$
$312$	44.7187	2.53170
$313$	18.8776	1.06703	0.533514	−	0.845791i	$-0.320871\pi$
$313$	18.8776	1.06703	0.533514	+	0.845791i	$0.320871\pi$
$314$	28.5672	1.61214
$315$	−15.5501	−0.876147
$316$	−35.4042	−1.99164
$317$	9.59395	0.538850	0.269425	−	0.963021i	$-0.413166\pi$
$317$	9.59395	0.538850	0.269425	+	0.963021i	$0.413166\pi$
$318$	−46.8697	−2.62832
$319$	−8.23890	−0.461290
$320$	12.8092	0.716055
$321$	10.0374	0.560235
$322$	48.1832	2.68515
$323$	4.65870	0.259217
$324$	−3.63356	−0.201864
$325$	−5.36185	−0.297422
$326$	45.9317	2.54392
$327$	21.0674	1.16503
$328$	2.77877	0.153432
$329$	25.1028	1.38396
$330$	−30.5538	−1.68193
$331$	−33.8681	−1.86156	−0.930780	−	0.365581i	$-0.880870\pi$
$331$	−33.8681	−1.86156	−0.930780	+	0.365581i	$0.880870\pi$
$332$	−44.1949	−2.42551
$333$	−38.3775	−2.10307
$334$	8.67119	0.474467
$335$	0.158853	0.00867908
$336$	2.92178	0.159396
$337$	25.6996	1.39994	0.699972	−	0.714170i	$-0.253196\pi$
$337$	25.6996	1.39994	0.699972	+	0.714170i	$0.253196\pi$
$338$	−36.2784	−1.97329
$339$	1.69444	0.0920293
$340$	−21.9629	−1.19111
$341$	20.5435	1.11249
$342$	−7.56950	−0.409312
$343$	−9.91660	−0.535446
$344$	31.5870	1.70306
$345$	17.4759	0.940869
$346$	10.7658	0.578774
$347$	−10.5870	−0.568340	−0.284170	−	0.958774i	$-0.591718\pi$
$347$	−10.5870	−0.568340	−0.284170	+	0.958774i	$0.591718\pi$
$348$	15.7831	0.846063
$349$	16.3282	0.874030	0.437015	−	0.899454i	$-0.356036\pi$
$349$	16.3282	0.874030	0.437015	+	0.899454i	$0.356036\pi$
$350$	−7.64379	−0.408578
$351$	−25.0632	−1.33778
$352$	−25.2860	−1.34775
$353$	12.7662	0.679477	0.339739	−	0.940520i	$-0.389661\pi$
$353$	12.7662	0.679477	0.339739	+	0.940520i	$0.389661\pi$
$354$	−13.9342	−0.740594
$355$	−6.65980	−0.353465
$356$	24.3483	1.29046
$357$	61.1174	3.23468
$358$	33.4762	1.76927
$359$	−20.4949	−1.08168	−0.540841	−	0.841125i	$-0.681894\pi$
$359$	−20.4949	−1.08168	−0.540841	+	0.841125i	$0.681894\pi$
$360$	14.0971	0.742983
$361$	−18.5082	−0.974118
$362$	20.3618	1.07019
$363$	32.9657	1.73025
$364$	−58.8223	−3.08312
$365$	10.5639	0.552942
$366$	−24.9782	−1.30563
$367$	13.4936	0.704362	0.352181	−	0.935932i	$-0.385440\pi$
$367$	13.4936	0.704362	0.352181	+	0.935932i	$0.385440\pi$
$368$	−2.00197	−0.104360
$369$	−4.32849	−0.225332
$370$	−18.8648	−0.980736
$371$	24.3547	1.26443
$372$	−39.3547	−2.04045
$373$	28.3625	1.46856	0.734278	−	0.678849i	$-0.237521\pi$
$373$	28.3625	1.46856	0.734278	+	0.678849i	$0.237521\pi$
$374$	73.2152	3.78587
$375$	−2.77237	−0.143165
$376$	−22.7572	−1.17361
$377$	−9.23323	−0.475536
$378$	−35.7298	−1.83774
$379$	1.94104	0.0997047	0.0498524	−	0.998757i	$-0.484125\pi$
$379$	1.94104	0.0997047	0.0498524	+	0.998757i	$0.484125\pi$
$380$	−2.31835	−0.118929
$381$	−47.3764	−2.42717
$382$	2.58284	0.132150
$383$	4.68515	0.239400	0.119700	−	0.992810i	$-0.461807\pi$
$383$	4.68515	0.239400	0.119700	+	0.992810i	$0.461807\pi$
$384$	52.4963	2.67894
$385$	15.8765	0.809143
$386$	10.4171	0.530218
$387$	−49.2031	−2.50113
$388$	33.9099	1.72151
$389$	5.91265	0.299783	0.149892	−	0.988702i	$-0.452108\pi$
$389$	5.91265	0.299783	0.149892	+	0.988702i	$0.452108\pi$
$390$	−34.2412	−1.73387
$391$	−41.8770	−2.11781
$392$	−12.0682	−0.609535
$393$	−49.1397	−2.47877
$394$	6.68411	0.336741
$395$	10.7091	0.538834
$396$	−74.1206	−3.72470
$397$	−3.77675	−0.189550	−0.0947749	−	0.995499i	$-0.530213\pi$
$397$	−3.77675	−0.189550	−0.0947749	+	0.995499i	$0.530213\pi$
$398$	−35.1983	−1.76433
$399$	6.45140	0.322974
$400$	0.317593	0.0158797
$401$	9.72526	0.485656	0.242828	−	0.970069i	$-0.421925\pi$
$401$	9.72526	0.485656	0.242828	+	0.970069i	$0.421925\pi$
$402$	1.01445	0.0505962
$403$	23.0228	1.14685
$404$	−25.5046	−1.26890
$405$	1.09908	0.0546139
$406$	−13.1628	−0.653258
$407$	39.1832	1.94224
$408$	−55.4068	−2.74304
$409$	−1.77474	−0.0877553	−0.0438777	−	0.999037i	$-0.513971\pi$
$409$	−1.77474	−0.0877553	−0.0438777	+	0.999037i	$0.513971\pi$
$410$	−2.12771	−0.105080
$411$	−6.30547	−0.311026
$412$	−22.8491	−1.12569
$413$	7.24056	0.356285
$414$	68.0421	3.34408
$415$	13.3681	0.656215
$416$	−28.3377	−1.38937
$417$	−38.9291	−1.90637
$418$	7.72841	0.378009
$419$	−28.2325	−1.37925	−0.689624	−	0.724167i	$-0.742224\pi$
$419$	−28.2325	−1.37925	−0.689624	+	0.724167i	$0.742224\pi$
$420$	−30.4144	−1.48407
$421$	7.90202	0.385121	0.192560	−	0.981285i	$-0.438321\pi$
$421$	7.90202	0.385121	0.192560	+	0.981285i	$0.438321\pi$
$422$	59.3641	2.88980
$423$	35.4489	1.72359
$424$	−22.0790	−1.07225
$425$	6.64336	0.322250
$426$	−42.5300	−2.06059
$427$	12.9793	0.628112
$428$	11.9694	0.578564
$429$	71.1208	3.43374
$430$	−24.1863	−1.16637
$431$	23.5229	1.13306	0.566530	−	0.824041i	$-0.308286\pi$
$431$	23.5229	1.13306	0.566530	+	0.824041i	$0.308286\pi$
$432$	1.48454	0.0714252
$433$	12.7656	0.613475	0.306737	−	0.951794i	$-0.400763\pi$
$433$	12.7656	0.613475	0.306737	+	0.951794i	$0.400763\pi$
$434$	32.8210	1.57546
$435$	−4.77409	−0.228900
$436$	25.1224	1.20315
$437$	−4.42042	−0.211458
$438$	67.4623	3.22347
$439$	11.3322	0.540855	0.270428	−	0.962740i	$-0.412835\pi$
$439$	11.3322	0.540855	0.270428	+	0.962740i	$0.412835\pi$
$440$	−14.3931	−0.686163
$441$	18.7986	0.895172
$442$	82.0514	3.90279
$443$	−22.4059	−1.06454	−0.532268	−	0.846576i	$-0.678660\pi$
$443$	−22.4059	−1.06454	−0.532268	+	0.846576i	$0.678660\pi$
$444$	−75.0625	−3.56231
$445$	−7.36489	−0.349129
$446$	−19.3420	−0.915869
$447$	53.8728	2.54809
$448$	−42.5057	−2.00820
$449$	−31.5420	−1.48856	−0.744280	−	0.667868i	$-0.767207\pi$
$449$	−31.5420	−1.48856	−0.744280	+	0.667868i	$0.767207\pi$
$450$	−10.7942	−0.508843
$451$	4.41937	0.208100
$452$	2.02058	0.0950401
$453$	16.3182	0.766697
$454$	−49.9940	−2.34633
$455$	17.7926	0.834131
$456$	−5.84860	−0.273886
$457$	−5.16747	−0.241724	−0.120862	−	0.992669i	$-0.538566\pi$
$457$	−5.16747	−0.241724	−0.120862	+	0.992669i	$0.538566\pi$
$458$	19.0562	0.890437
$459$	31.0535	1.44945
$460$	20.8396	0.971650
$461$	41.0974	1.91410	0.957048	−	0.289930i	$-0.0936320\pi$
$461$	41.0974	1.91410	0.957048	+	0.289930i	$0.0936320\pi$
$462$	101.389	4.71704
$463$	25.7699	1.19763	0.598814	−	0.800888i	$-0.295639\pi$
$463$	25.7699	1.19763	0.598814	+	0.800888i	$0.295639\pi$
$464$	0.546903	0.0253893
$465$	11.9041	0.552037
$466$	34.2513	1.58666
$467$	31.4853	1.45697	0.728484	−	0.685063i	$-0.240225\pi$
$467$	31.4853	1.45697	0.728484	+	0.685063i	$0.240225\pi$
$468$	−83.0660	−3.83973
$469$	−0.527134	−0.0243408
$470$	17.4253	0.803768
$471$	−34.3824	−1.58426
$472$	−6.56402	−0.302134
$473$	50.2361	2.30986
$474$	68.3893	3.14123
$475$	0.701256	0.0321758
$476$	72.8811	3.34050
$477$	34.3925	1.57473
$478$	17.9360	0.820371
$479$	−15.1361	−0.691587	−0.345794	−	0.938311i	$-0.612390\pi$
$479$	−15.1361	−0.691587	−0.345794	+	0.938311i	$0.612390\pi$
$480$	−14.6522	−0.668777
$481$	43.9121	2.00222
$482$	−58.7623	−2.67655
$483$	−57.9915	−2.63870
$484$	39.3108	1.78685
$485$	−10.2571	−0.465751
$486$	39.3206	1.78362
$487$	22.2424	1.00790	0.503950	−	0.863733i	$-0.331880\pi$
$487$	22.2424	1.00790	0.503950	+	0.863733i	$0.331880\pi$
$488$	−11.7666	−0.532647
$489$	−55.2817	−2.49992
$490$	9.24064	0.417449
$491$	−15.2653	−0.688913	−0.344457	−	0.938802i	$-0.611937\pi$
$491$	−15.2653	−0.688913	−0.344457	+	0.938802i	$0.611937\pi$
$492$	−8.46609	−0.381681
$493$	11.4400	0.515233
$494$	8.66113	0.389683
$495$	22.4201	1.00771
$496$	−1.36369	−0.0612313
$497$	22.0997	0.991307
$498$	85.3700	3.82552
$499$	16.9979	0.760931	0.380465	−	0.924795i	$-0.375764\pi$
$499$	16.9979	0.760931	0.380465	+	0.924795i	$0.375764\pi$
$500$	−3.30599	−0.147848
$501$	−10.4363	−0.466260
$502$	70.8293	3.16127
$503$	1.00998	0.0450327	0.0225164	−	0.999746i	$-0.492832\pi$
$503$	1.00998	0.0450327	0.0225164	+	0.999746i	$0.492832\pi$
$504$	−46.7795	−2.08373
$505$	7.71466	0.343298
$506$	−69.4705	−3.08834
$507$	43.6633	1.93916
$508$	−56.4953	−2.50657
$509$	12.7980	0.567259	0.283630	−	0.958934i	$-0.408461\pi$
$509$	12.7980	0.567259	0.283630	+	0.958934i	$0.408461\pi$
$510$	42.4251	1.87861
$511$	−35.0551	−1.55075
$512$	3.58934	0.158628
$513$	3.27792	0.144724
$514$	−19.1407	−0.844259
$515$	6.91141	0.304553
$516$	−96.2363	−4.23657
$517$	−36.1931	−1.59177
$518$	62.6006	2.75051
$519$	−12.9573	−0.568763
$520$	−16.1301	−0.707353
$521$	9.67882	0.424037	0.212018	−	0.977266i	$-0.431996\pi$
$521$	9.67882	0.424037	0.212018	+	0.977266i	$0.431996\pi$
$522$	−18.5878	−0.813568
$523$	33.9385	1.48403	0.742013	−	0.670385i	$-0.233871\pi$
$523$	33.9385	1.48403	0.742013	+	0.670385i	$0.233871\pi$
$524$	−58.5980	−2.55986
$525$	9.19977	0.401511
$526$	−17.5619	−0.765735
$527$	−28.5254	−1.24258
$528$	−4.21263	−0.183331
$529$	16.7351	0.727613
$530$	16.9060	0.734349
$531$	10.2248	0.443717
$532$	7.69314	0.333540
$533$	4.95273	0.214526
$534$	−47.0329	−2.03531
$535$	−3.62052	−0.156529
$536$	0.477880	0.0206413
$537$	−40.2907	−1.73867
$538$	22.4413	0.967512
$539$	−19.1933	−0.826713
$540$	−15.4534	−0.665008
$541$	−32.1891	−1.38392	−0.691958	−	0.721938i	$-0.743252\pi$
$541$	−32.1891	−1.38392	−0.691958	+	0.721938i	$0.743252\pi$
$542$	−19.0066	−0.816402
$543$	−24.5067	−1.05168
$544$	35.1106	1.50535
$545$	−7.59906	−0.325508
$546$	113.625	4.86271
$547$	−22.8301	−0.976143	−0.488071	−	0.872804i	$-0.662299\pi$
$547$	−22.8301	−0.976143	−0.488071	+	0.872804i	$0.662299\pi$
$548$	−7.51912	−0.321201
$549$	18.3288	0.782252
$550$	11.0208	0.469929
$551$	1.20758	0.0514446
$552$	52.5729	2.23765
$553$	−35.5368	−1.51118
$554$	−51.3826	−2.18304
$555$	22.7050	0.963773
$556$	−46.4221	−1.96873
$557$	44.5518	1.88772	0.943860	−	0.330345i	$-0.107165\pi$
$557$	44.5518	1.88772	0.943860	+	0.330345i	$0.107165\pi$
$558$	46.3483	1.96208
$559$	56.2989	2.38119
$560$	−1.05389	−0.0445351
$561$	−88.1191	−3.72039
$562$	−44.7277	−1.88673
$563$	−7.51554	−0.316742	−0.158371	−	0.987380i	$-0.550624\pi$
$563$	−7.51554	−0.316742	−0.158371	+	0.987380i	$0.550624\pi$
$564$	69.3345	2.91951
$565$	−0.611188	−0.0257129
$566$	−12.4507	−0.523341
$567$	−3.64717	−0.153167
$568$	−20.0348	−0.840640
$569$	36.6577	1.53677	0.768386	−	0.639986i	$-0.221060\pi$
$569$	36.6577	1.53677	0.768386	+	0.639986i	$0.221060\pi$
$570$	4.47828	0.187575
$571$	7.56728	0.316681	0.158340	−	0.987385i	$-0.449386\pi$
$571$	7.56728	0.316681	0.158340	+	0.987385i	$0.449386\pi$
$572$	84.8099	3.54608
$573$	−3.10861	−0.129864
$574$	7.06055	0.294702
$575$	−6.30358	−0.262877
$576$	−60.0245	−2.50102
$577$	−41.5854	−1.73122	−0.865612	−	0.500715i	$-0.833071\pi$
$577$	−41.5854	−1.73122	−0.865612	+	0.500715i	$0.833071\pi$
$578$	−62.5031	−2.59979
$579$	−12.5377	−0.521048
$580$	−5.69299	−0.236389
$581$	−44.3604	−1.84038
$582$	−65.5028	−2.71518
$583$	−35.1146	−1.45430
$584$	31.7797	1.31505
$585$	25.1259	1.03883
$586$	25.9112	1.07038
$587$	−30.0021	−1.23832	−0.619159	−	0.785266i	$-0.712526\pi$
$587$	−30.0021	−1.23832	−0.619159	+	0.785266i	$0.712526\pi$
$588$	36.7682	1.51629
$589$	−3.01106	−0.124069
$590$	5.02609	0.206921
$591$	−8.04474	−0.330917
$592$	−2.60100	−0.106901
$593$	−25.5891	−1.05082	−0.525409	−	0.850850i	$-0.676088\pi$
$593$	−25.5891	−1.05082	−0.525409	+	0.850850i	$0.676088\pi$
$594$	51.5152	2.11370
$595$	−22.0452	−0.903764
$596$	64.2420	2.63146
$597$	42.3634	1.73382
$598$	−77.8547	−3.18372
$599$	−7.63434	−0.311931	−0.155965	−	0.987763i	$-0.549849\pi$
$599$	−7.63434	−0.311931	−0.155965	+	0.987763i	$0.549849\pi$
$600$	−8.34017	−0.340486
$601$	−35.9546	−1.46662	−0.733310	−	0.679895i	$-0.762026\pi$
$601$	−35.9546	−1.46662	−0.733310	+	0.679895i	$0.762026\pi$
$602$	80.2591	3.27112
$603$	−0.744394	−0.0303141
$604$	19.4591	0.791780
$605$	−11.8908	−0.483429
$606$	49.2665	2.00131
$607$	2.61430	0.106111	0.0530556	−	0.998592i	$-0.483104\pi$
$607$	2.61430	0.106111	0.0530556	+	0.998592i	$0.483104\pi$
$608$	3.70618	0.150306
$609$	15.8422	0.641959
$610$	9.00968	0.364791
$611$	−40.5612	−1.64093
$612$	102.919	4.16026
$613$	−19.8409	−0.801366	−0.400683	−	0.916217i	$-0.631227\pi$
$613$	−19.8409	−0.801366	−0.400683	+	0.916217i	$0.631227\pi$
$614$	56.4278	2.27724
$615$	2.56083	0.103263
$616$	47.7616	1.92437
$617$	−48.1259	−1.93748	−0.968739	−	0.248083i	$-0.920199\pi$
$617$	−48.1259	−1.93748	−0.968739	+	0.248083i	$0.920199\pi$
$618$	44.1369	1.77544
$619$	−12.0900	−0.485939	−0.242970	−	0.970034i	$-0.578122\pi$
$619$	−12.0900	−0.485939	−0.242970	+	0.970034i	$0.578122\pi$
$620$	14.1953	0.570097
$621$	−29.4652	−1.18240
$622$	42.7300	1.71332
$623$	24.4395	0.979147
$624$	−4.72104	−0.188993
$625$	1.00000	0.0400000
$626$	−43.4842	−1.73798
$627$	−9.30162	−0.371471
$628$	−41.0003	−1.63609
$629$	−54.4074	−2.16936
$630$	35.8192	1.42707
$631$	9.78533	0.389548	0.194774	−	0.980848i	$-0.437603\pi$
$631$	9.78533	0.389548	0.194774	+	0.980848i	$0.437603\pi$
$632$	32.2164	1.28150
$633$	−71.4483	−2.83982
$634$	−22.0994	−0.877679
$635$	17.0888	0.678146
$636$	67.2683	2.66736
$637$	−21.5096	−0.852243
$638$	18.9781	0.751350
$639$	31.2081	1.23458
$640$	−18.9355	−0.748491
$641$	−29.4059	−1.16146	−0.580732	−	0.814095i	$-0.697234\pi$
$641$	−29.4059	−1.16146	−0.580732	+	0.814095i	$0.697234\pi$
$642$	−23.1210	−0.912513
$643$	36.4353	1.43687	0.718434	−	0.695595i	$-0.244859\pi$
$643$	36.4353	1.43687	0.718434	+	0.695595i	$0.244859\pi$
$644$	−69.1535	−2.72503
$645$	29.1097	1.14619
$646$	−10.7312	−0.422213
$647$	19.7770	0.777513	0.388756	−	0.921341i	$-0.372905\pi$
$647$	19.7770	0.777513	0.388756	+	0.921341i	$0.372905\pi$
$648$	3.30639	0.129887
$649$	−10.4394	−0.409784
$650$	12.3509	0.484441
$651$	−39.5021	−1.54821
$652$	−65.9221	−2.58171
$653$	−20.3367	−0.795838	−0.397919	−	0.917421i	$-0.630267\pi$
$653$	−20.3367	−0.795838	−0.397919	+	0.917421i	$0.630267\pi$
$654$	−48.5283	−1.89760
$655$	17.7248	0.692564
$656$	−0.293360	−0.0114538
$657$	−49.5032	−1.93130
$658$	−57.8236	−2.25420
$659$	−47.6265	−1.85527	−0.927633	−	0.373492i	$-0.878160\pi$
$659$	−47.6265	−1.85527	−0.927633	+	0.373492i	$0.878160\pi$
$660$	43.8514	1.70691
$661$	1.47935	0.0575399	0.0287699	−	0.999586i	$-0.490841\pi$
$661$	1.47935	0.0575399	0.0287699	+	0.999586i	$0.490841\pi$
$662$	78.0143	3.03211
$663$	−98.7539	−3.83528
$664$	40.2155	1.56067
$665$	−2.32703	−0.0902384
$666$	88.4016	3.42549
$667$	−10.8549	−0.420304
$668$	−12.4451	−0.481514
$669$	23.2793	0.900029
$670$	−0.365914	−0.0141365
$671$	−18.7135	−0.722429
$672$	48.6214	1.87561
$673$	−16.2992	−0.628290	−0.314145	−	0.949375i	$-0.601718\pi$
$673$	−16.2992	−0.628290	−0.314145	+	0.949375i	$0.601718\pi$
$674$	−59.1983	−2.28023
$675$	4.67436	0.179916
$676$	52.0675	2.00260
$677$	47.4920	1.82527	0.912633	−	0.408779i	$-0.134045\pi$
$677$	47.4920	1.82527	0.912633	+	0.408779i	$0.134045\pi$
$678$	−3.90310	−0.149898
$679$	34.0369	1.30622
$680$	19.9853	0.766402
$681$	60.1708	2.30575
$682$	−47.3213	−1.81203
$683$	25.8716	0.989948	0.494974	−	0.868908i	$-0.335178\pi$
$683$	25.8716	0.989948	0.494974	+	0.868908i	$0.335178\pi$
$684$	10.8639	0.415391
$685$	2.27439	0.0869001
$686$	22.8426	0.872135
$687$	−22.9353	−0.875036
$688$	−3.33470	−0.127134
$689$	−39.3524	−1.49921
$690$	−40.2552	−1.53249
$691$	11.6869	0.444589	0.222295	−	0.974980i	$-0.428645\pi$
$691$	11.6869	0.444589	0.222295	+	0.974980i	$0.428645\pi$
$692$	−15.4513	−0.587371
$693$	−74.3982	−2.82616
$694$	24.3869	0.925712
$695$	14.0418	0.532636
$696$	−14.3620	−0.544389
$697$	−6.13646	−0.232435
$698$	−37.6116	−1.42362
$699$	−41.2235	−1.55922
$700$	10.9705	0.414647
$701$	−10.2028	−0.385354	−0.192677	−	0.981262i	$-0.561717\pi$
$701$	−10.2028	−0.385354	−0.192677	+	0.981262i	$0.561717\pi$
$702$	57.7325	2.17897
$703$	−5.74310	−0.216605
$704$	61.2847	2.30975
$705$	−20.9724	−0.789866
$706$	−29.4066	−1.10673
$707$	−25.6001	−0.962791
$708$	19.9986	0.751594
$709$	46.1367	1.73270	0.866351	−	0.499436i	$-0.166459\pi$
$709$	46.1367	1.73270	0.866351	+	0.499436i	$0.166459\pi$
$710$	15.3407	0.575725
$711$	−50.1834	−1.88203
$712$	−22.1559	−0.830328
$713$	27.0664	1.01364
$714$	−140.782	−5.26865
$715$	−25.6534	−0.959383
$716$	−48.0457	−1.79555
$717$	−21.5870	−0.806182
$718$	47.2095	1.76184
$719$	10.1662	0.379135	0.189567	−	0.981868i	$-0.439291\pi$
$719$	10.1662	0.379135	0.189567	+	0.981868i	$0.439291\pi$
$720$	−1.48826	−0.0554641
$721$	−22.9346	−0.854131
$722$	42.6332	1.58664
$723$	70.7241	2.63026
$724$	−29.2237	−1.08609
$725$	1.72202	0.0639543
$726$	−75.9355	−2.81823
$727$	11.7198	0.434662	0.217331	−	0.976098i	$-0.430265\pi$
$727$	11.7198	0.434662	0.217331	+	0.976098i	$0.430265\pi$
$728$	53.5258	1.98380
$729$	−44.0276	−1.63065
$730$	−24.3338	−0.900633
$731$	−69.7547	−2.57997
$732$	35.8492	1.32502
$733$	−14.6585	−0.541423	−0.270711	−	0.962661i	$-0.587259\pi$
$733$	−14.6585	−0.541423	−0.270711	+	0.962661i	$0.587259\pi$
$734$	−31.0822	−1.14727
$735$	−11.1217	−0.410229
$736$	−33.3148	−1.22800
$737$	0.760022	0.0279958
$738$	9.97057	0.367022
$739$	−18.7515	−0.689784	−0.344892	−	0.938642i	$-0.612084\pi$
$739$	−18.7515	−0.689784	−0.344892	+	0.938642i	$0.612084\pi$
$740$	27.0752	0.995303
$741$	−10.4242	−0.382943
$742$	−56.1004	−2.05951
$743$	2.45753	0.0901582	0.0450791	−	0.998983i	$-0.485646\pi$
$743$	2.45753	0.0901582	0.0450791	+	0.998983i	$0.485646\pi$
$744$	35.8111	1.31290
$745$	−19.4320	−0.711934
$746$	−65.3323	−2.39199
$747$	−62.6437	−2.29201
$748$	−105.080	−3.84210
$749$	12.0143	0.438991
$750$	6.38609	0.233187
$751$	−18.3187	−0.668461	−0.334230	−	0.942491i	$-0.608476\pi$
$751$	−18.3187	−0.668461	−0.334230	+	0.942491i	$0.608476\pi$
$752$	2.40252	0.0876109
$753$	−85.2474	−3.10659
$754$	21.2685	0.774553
$755$	−5.88601	−0.214214
$756$	51.2801	1.86504
$757$	−31.1381	−1.13173	−0.565866	−	0.824497i	$-0.691458\pi$
$757$	−31.1381	−1.13173	−0.565866	+	0.824497i	$0.691458\pi$
$758$	−4.47114	−0.162399
$759$	83.6121	3.03493
$760$	2.10960	0.0765232
$761$	34.9351	1.26640	0.633198	−	0.773990i	$-0.281742\pi$
$761$	34.9351	1.26640	0.633198	+	0.773990i	$0.281742\pi$
$762$	109.130	3.95337
$763$	25.2165	0.912899
$764$	−3.70695	−0.134113
$765$	−31.1311	−1.12555
$766$	−10.7921	−0.389935
$767$	−11.6993	−0.422439
$768$	−49.9001	−1.80061
$769$	2.80356	0.101099	0.0505496	−	0.998722i	$-0.483903\pi$
$769$	2.80356	0.101099	0.0505496	+	0.998722i	$0.483903\pi$
$770$	−36.5712	−1.31793
$771$	23.0370	0.829657
$772$	−14.9509	−0.538094
$773$	−20.4050	−0.733917	−0.366959	−	0.930237i	$-0.619601\pi$
$773$	−20.4050	−0.733917	−0.366959	+	0.930237i	$0.619601\pi$
$774$	113.338	4.07385
$775$	−4.29381	−0.154238
$776$	−30.8566	−1.10769
$777$	−75.3437	−2.70294
$778$	−13.6196	−0.488287
$779$	−0.647749	−0.0232080
$780$	49.1437	1.75963
$781$	−31.8633	−1.14016
$782$	96.4625	3.44949
$783$	8.04936	0.287661
$784$	1.27406	0.0455021
$785$	12.4018	0.442640
$786$	113.192	4.03742
$787$	34.4193	1.22691	0.613457	−	0.789728i	$-0.289778\pi$
$787$	34.4193	1.22691	0.613457	+	0.789728i	$0.289778\pi$
$788$	−9.59317	−0.341743
$789$	21.1368	0.752491
$790$	−24.6682	−0.877654
$791$	2.02815	0.0721127
$792$	67.4467	2.39661
$793$	−20.9720	−0.744739
$794$	8.69965	0.308739
$795$	−20.3474	−0.721647
$796$	50.5173	1.79054
$797$	39.8220	1.41057	0.705283	−	0.708925i	$-0.250820\pi$
$797$	39.8220	1.41057	0.705283	+	0.708925i	$0.250820\pi$
$798$	−14.8606	−0.526060
$799$	50.2556	1.77791
$800$	5.28506	0.186855
$801$	34.5123	1.21943
$802$	−22.4019	−0.791038
$803$	50.5425	1.78360
$804$	−1.45596	−0.0513477
$805$	20.9176	0.737250
$806$	−53.0324	−1.86799
$807$	−27.0095	−0.950778
$808$	23.2081	0.816459
$809$	−40.8345	−1.43566	−0.717832	−	0.696217i	$-0.754865\pi$
$809$	−40.8345	−1.43566	−0.717832	+	0.696217i	$0.754865\pi$
$810$	−2.53171	−0.0889551
$811$	24.6016	0.863878	0.431939	−	0.901903i	$-0.357830\pi$
$811$	24.6016	0.863878	0.431939	+	0.901903i	$0.357830\pi$
$812$	18.8915	0.662961
$813$	22.8756	0.802281
$814$	−90.2575	−3.16352
$815$	19.9402	0.698475
$816$	5.84939	0.204770
$817$	−7.36313	−0.257603
$818$	4.08807	0.142936
$819$	−83.3771	−2.91343
$820$	3.05373	0.106641
$821$	26.3190	0.918541	0.459270	−	0.888297i	$-0.348111\pi$
$821$	26.3190	0.918541	0.459270	+	0.888297i	$0.348111\pi$
$822$	14.5245	0.506599
$823$	3.15195	0.109870	0.0549350	−	0.998490i	$-0.482505\pi$
$823$	3.15195	0.109870	0.0549350	+	0.998490i	$0.482505\pi$
$824$	20.7917	0.724313
$825$	−13.2642	−0.461801
$826$	−16.6784	−0.580317
$827$	11.6283	0.404356	0.202178	−	0.979349i	$-0.435198\pi$
$827$	11.6283	0.404356	0.202178	+	0.979349i	$0.435198\pi$
$828$	−97.6553	−3.39376
$829$	−35.6257	−1.23733	−0.618665	−	0.785655i	$-0.712326\pi$
$829$	−35.6257	−1.23733	−0.618665	+	0.785655i	$0.712326\pi$
$830$	−30.7931	−1.06884
$831$	61.8421	2.14528
$832$	68.6810	2.38108
$833$	26.6506	0.923388
$834$	89.6722	3.10509
$835$	3.76440	0.130272
$836$	−11.0920	−0.383624
$837$	−20.0708	−0.693749
$838$	65.0328	2.24652
$839$	−50.4799	−1.74276	−0.871379	−	0.490610i	$-0.836774\pi$
$839$	−50.4799	−1.74276	−0.871379	+	0.490610i	$0.836774\pi$
$840$	27.6758	0.954906
$841$	−26.0346	−0.897746
$842$	−18.2021	−0.627286
$843$	53.8326	1.85409
$844$	−85.2005	−2.93272
$845$	−15.7494	−0.541797
$846$	−81.6557	−2.80738
$847$	39.4580	1.35579
$848$	2.33092	0.0800443
$849$	14.9852	0.514290
$850$	−15.3028	−0.524882
$851$	51.6246	1.76967
$852$	61.0400	2.09119
$853$	−7.35589	−0.251861	−0.125930	−	0.992039i	$-0.540192\pi$
$853$	−7.35589	−0.251861	−0.125930	+	0.992039i	$0.540192\pi$
$854$	−29.8975	−1.02307
$855$	−3.28612	−0.112383
$856$	−10.8917	−0.372270
$857$	31.7429	1.08432	0.542159	−	0.840276i	$-0.317607\pi$
$857$	31.7429	1.08432	0.542159	+	0.840276i	$0.317607\pi$
$858$	−163.825	−5.59289
$859$	−24.7812	−0.845523	−0.422761	−	0.906241i	$-0.638939\pi$
$859$	−24.7812	−0.845523	−0.422761	+	0.906241i	$0.638939\pi$
$860$	34.7126	1.18369
$861$	−8.49780	−0.289604
$862$	−54.1844	−1.84553
$863$	−34.5147	−1.17489	−0.587447	−	0.809263i	$-0.699867\pi$
$863$	−34.5147	−1.17489	−0.587447	+	0.809263i	$0.699867\pi$
$864$	24.7043	0.840457
$865$	4.67373	0.158912
$866$	−29.4052	−0.999229
$867$	75.2263	2.55482
$868$	−47.1053	−1.59886
$869$	51.2370	1.73810
$870$	10.9970	0.372833
$871$	0.851747	0.0288603
$872$	−22.8604	−0.774150
$873$	48.0653	1.62676
$874$	10.1823	0.344423
$875$	−3.31837	−0.112182
$876$	−96.8232	−3.27135
$877$	−37.0331	−1.25052	−0.625259	−	0.780417i	$-0.715007\pi$
$877$	−37.0331	−1.25052	−0.625259	+	0.780417i	$0.715007\pi$
$878$	−26.1034	−0.880946
$879$	−31.1858	−1.05187
$880$	1.51950	0.0512224
$881$	5.72772	0.192972	0.0964859	−	0.995334i	$-0.469240\pi$
$881$	5.72772	0.192972	0.0964859	+	0.995334i	$0.469240\pi$
$882$	−43.3021	−1.45806
$883$	30.6392	1.03109	0.515546	−	0.856862i	$-0.327589\pi$
$883$	30.6392	1.03109	0.515546	+	0.856862i	$0.327589\pi$
$884$	−117.762	−3.96076
$885$	−6.04921	−0.203342
$886$	51.6114	1.73392
$887$	15.7427	0.528587	0.264294	−	0.964442i	$-0.414861\pi$
$887$	15.7427	0.528587	0.264294	+	0.964442i	$0.414861\pi$
$888$	68.3038	2.29212
$889$	−56.7069	−1.90189
$890$	16.9648	0.568663
$891$	5.25848	0.176166
$892$	27.7600	0.929473
$893$	5.30485	0.177520
$894$	−124.095	−4.15034
$895$	14.5329	0.485782
$896$	62.8351	2.09917
$897$	93.7030	3.12865
$898$	72.6562	2.42457
$899$	−7.39405	−0.246605
$900$	15.4920	0.516401
$901$	48.7579	1.62436
$902$	−10.1799	−0.338953
$903$	−96.5968	−3.21454
$904$	−1.83864	−0.0611524
$905$	8.83962	0.293839
$906$	−37.5886	−1.24880
$907$	−47.7148	−1.58435	−0.792173	−	0.610297i	$-0.791050\pi$
$907$	−47.7148	−1.58435	−0.792173	+	0.610297i	$0.791050\pi$
$908$	71.7523	2.38118
$909$	−36.1513	−1.19906
$910$	−40.9848	−1.35863
$911$	25.0776	0.830858	0.415429	−	0.909626i	$-0.363632\pi$
$911$	25.0776	0.830858	0.415429	+	0.909626i	$0.363632\pi$
$912$	0.617447	0.0204457
$913$	63.9589	2.11673
$914$	11.9031	0.393720
$915$	−10.8437	−0.358482
$916$	−27.3498	−0.903663
$917$	−58.8175	−1.94232
$918$	−71.5309	−2.36087
$919$	−23.0098	−0.759024	−0.379512	−	0.925187i	$-0.623908\pi$
$919$	−23.0098	−0.759024	−0.379512	+	0.925187i	$0.623908\pi$
$920$	−18.9632	−0.625197
$921$	−67.9143	−2.23785
$922$	−94.6667	−3.11768
$923$	−35.7088	−1.17537
$924$	−145.515	−4.78710
$925$	−8.18973	−0.269277
$926$	−59.3602	−1.95070
$927$	−32.3872	−1.06374
$928$	9.10100	0.298755
$929$	−11.8965	−0.390312	−0.195156	−	0.980772i	$-0.562521\pi$
$929$	−11.8965	−0.390312	−0.195156	+	0.980772i	$0.562521\pi$
$930$	−27.4207	−0.899159
$931$	2.81317	0.0921978
$932$	−49.1581	−1.61023
$933$	−51.4282	−1.68368
$934$	−72.5257	−2.37311
$935$	31.7847	1.03947
$936$	75.5866	2.47063
$937$	−9.04262	−0.295409	−0.147705	−	0.989032i	$-0.547189\pi$
$937$	−9.04262	−0.295409	−0.147705	+	0.989032i	$0.547189\pi$
$938$	1.21424	0.0396463
$939$	52.3359	1.70792
$940$	−25.0091	−0.815706
$941$	−16.6494	−0.542754	−0.271377	−	0.962473i	$-0.587479\pi$
$941$	−16.6494	−0.542754	−0.271377	+	0.962473i	$0.587479\pi$
$942$	79.1990	2.58044
$943$	5.82260	0.189610
$944$	0.692975	0.0225544
$945$	−15.5113	−0.504582
$946$	−115.718	−3.76230
$947$	28.3038	0.919749	0.459875	−	0.887984i	$-0.347894\pi$
$947$	28.3038	0.919749	0.459875	+	0.887984i	$0.347894\pi$
$948$	−98.1537	−3.18788
$949$	56.6423	1.83869
$950$	−1.61533	−0.0524081
$951$	26.5980	0.862499
$952$	−66.3188	−2.14940
$953$	−0.724689	−0.0234750	−0.0117375	−	0.999931i	$-0.503736\pi$
$953$	−0.724689	−0.0234750	−0.0117375	+	0.999931i	$0.503736\pi$
$954$	−79.2223	−2.56492
$955$	1.12128	0.0362838
$956$	−25.7420	−0.832557
$957$	−22.8413	−0.738354
$958$	34.8657	1.12646
$959$	−7.54729	−0.243715
$960$	35.5118	1.14614
$961$	−12.5632	−0.405263
$962$	−101.150	−3.26122
$963$	16.9660	0.546720
$964$	84.3369	2.71631
$965$	4.52236	0.145580
$966$	133.582	4.29793
$967$	49.0402	1.57703	0.788513	−	0.615018i	$-0.210851\pi$
$967$	49.0402	1.57703	0.788513	+	0.615018i	$0.210851\pi$
$968$	−35.7712	−1.14973
$969$	12.9157	0.414911
$970$	23.6270	0.758617
$971$	−8.69375	−0.278996	−0.139498	−	0.990222i	$-0.544549\pi$
$971$	−8.69375	−0.278996	−0.139498	+	0.990222i	$0.544549\pi$
$972$	−56.4337	−1.81011
$973$	−46.5960	−1.49380
$974$	−51.2348	−1.64167
$975$	−14.8650	−0.476063
$976$	1.24222	0.0397624
$977$	−23.7584	−0.760097	−0.380049	−	0.924967i	$-0.624093\pi$
$977$	−23.7584	−0.760097	−0.380049	+	0.924967i	$0.624093\pi$
$978$	127.340	4.07188
$979$	−35.2368	−1.12617
$980$	−13.2623	−0.423650
$981$	35.6096	1.13693
$982$	35.1632	1.12210
$983$	41.8666	1.33534	0.667668	−	0.744459i	$-0.267293\pi$
$983$	41.8666	1.33534	0.667668	+	0.744459i	$0.267293\pi$
$984$	7.70379	0.245588
$985$	2.90175	0.0924576
$986$	−26.3518	−0.839212
$987$	69.5942	2.21521
$988$	−12.4306	−0.395471
$989$	66.1870	2.10462
$990$	−51.6441	−1.64136
$991$	28.9430	0.919404	0.459702	−	0.888073i	$-0.347956\pi$
$991$	28.9430	0.919404	0.459702	+	0.888073i	$0.347956\pi$
$992$	−22.6931	−0.720506
$993$	−93.8950	−2.97967
$994$	−50.9061	−1.61464
$995$	−15.2805	−0.484426
$996$	−122.525	−3.88234
$997$	8.47935	0.268544	0.134272	−	0.990945i	$-0.457130\pi$
$997$	8.47935	0.268544	0.134272	+	0.990945i	$0.457130\pi$
$998$	−39.1542	−1.23941
$999$	−38.2818	−1.21118

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.d.1.9	✓	83

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.d.1.9	✓	83	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.30347 q^{2} +2.77237 q^{3} +3.30599 q^{4} -1.00000 q^{5} -6.38609 q^{6} +3.31837 q^{7} -3.00832 q^{8} +4.68605 q^{9} +O(q^{10})\)	\(q-2.30347 q^{2} +2.77237 q^{3} +3.30599 q^{4} -1.00000 q^{5} -6.38609 q^{6} +3.31837 q^{7} -3.00832 q^{8} +4.68605 q^{9} +2.30347 q^{10} -4.78443 q^{11} +9.16544 q^{12} -5.36185 q^{13} -7.64379 q^{14} -2.77237 q^{15} +0.317593 q^{16} +6.64336 q^{17} -10.7942 q^{18} +0.701256 q^{19} -3.30599 q^{20} +9.19977 q^{21} +11.0208 q^{22} -6.30358 q^{23} -8.34017 q^{24} +1.00000 q^{25} +12.3509 q^{26} +4.67436 q^{27} +10.9705 q^{28} +1.72202 q^{29} +6.38609 q^{30} -4.29381 q^{31} +5.28506 q^{32} -13.2642 q^{33} -15.3028 q^{34} -3.31837 q^{35} +15.4920 q^{36} -8.18973 q^{37} -1.61533 q^{38} -14.8650 q^{39} +3.00832 q^{40} -0.923697 q^{41} -21.1914 q^{42} -10.4999 q^{43} -15.8173 q^{44} -4.68605 q^{45} +14.5201 q^{46} +7.56478 q^{47} +0.880487 q^{48} +4.01161 q^{49} -2.30347 q^{50} +18.4179 q^{51} -17.7262 q^{52} +7.33934 q^{53} -10.7673 q^{54} +4.78443 q^{55} -9.98272 q^{56} +1.94414 q^{57} -3.96663 q^{58} +2.18196 q^{59} -9.16544 q^{60} +3.91134 q^{61} +9.89069 q^{62} +15.5501 q^{63} -12.8092 q^{64} +5.36185 q^{65} +30.5538 q^{66} -0.158853 q^{67} +21.9629 q^{68} -17.4759 q^{69} +7.64379 q^{70} +6.65980 q^{71} -14.0971 q^{72} -10.5639 q^{73} +18.8648 q^{74} +2.77237 q^{75} +2.31835 q^{76} -15.8765 q^{77} +34.2412 q^{78} -10.7091 q^{79} -0.317593 q^{80} -1.09908 q^{81} +2.12771 q^{82} -13.3681 q^{83} +30.4144 q^{84} -6.64336 q^{85} +24.1863 q^{86} +4.77409 q^{87} +14.3931 q^{88} +7.36489 q^{89} +10.7942 q^{90} -17.7926 q^{91} -20.8396 q^{92} -11.9041 q^{93} -17.4253 q^{94} -0.701256 q^{95} +14.6522 q^{96} +10.2571 q^{97} -9.24064 q^{98} -22.4201 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9}+O(q^{10}) \) 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9	\( 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9} - q^{10} - 26 q^{11} - 12 q^{12} - 15 q^{13} - 21 q^{14} + 4 q^{15} + 5 q^{16} + 8 q^{17} - 12 q^{18} - 79 q^{19} - 61 q^{20} - 34 q^{21} - 25 q^{22} + 31 q^{23} - 42 q^{24} + 83 q^{25} - 13 q^{26} - 25 q^{27} - 16 q^{28} - 16 q^{29} + 6 q^{30} - 40 q^{31} + 15 q^{32} - 33 q^{33} - 54 q^{34} - 2 q^{35} + 11 q^{36} - 45 q^{37} + 10 q^{38} - 54 q^{39} + 3 q^{40} - 27 q^{41} - 28 q^{42} - 101 q^{43} - 51 q^{44} - 61 q^{45} - 46 q^{46} + 71 q^{47} - 14 q^{48} + 23 q^{49} + q^{50} - 71 q^{51} - 34 q^{52} - 49 q^{53} - 25 q^{54} + 26 q^{55} - 41 q^{56} - 20 q^{57} - 43 q^{58} - 60 q^{59} + 12 q^{60} - 38 q^{61} - 2 q^{62} + 36 q^{63} - 113 q^{64} + 15 q^{65} - 42 q^{66} - 164 q^{67} + 10 q^{68} - 93 q^{69} + 21 q^{70} - 78 q^{71} + q^{72} - 18 q^{73} - 23 q^{74} - 4 q^{75} - 112 q^{76} - 35 q^{77} - 44 q^{78} - 124 q^{79} - 5 q^{80} - 45 q^{81} - 34 q^{82} + 5 q^{83} - 60 q^{84} - 8 q^{85} - 25 q^{86} + 12 q^{87} - 149 q^{88} - 44 q^{89} + 12 q^{90} - 192 q^{91} + 35 q^{92} - 13 q^{93} - 32 q^{94} + 79 q^{95} - 59 q^{96} - 31 q^{97} + 25 q^{98} - 134 q^{99}+O(q^{100}) \) 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9 - q^10 - 26 * q^11 - 12 * q^12 - 15 * q^13 - 21 * q^14 + 4 * q^15 + 5 * q^16 + 8 * q^17 - 12 * q^18 - 79 * q^19 - 61 * q^20 - 34 * q^21 - 25 * q^22 + 31 * q^23 - 42 * q^24 + 83 * q^25 - 13 * q^26 - 25 * q^27 - 16 * q^28 - 16 * q^29 + 6 * q^30 - 40 * q^31 + 15 * q^32 - 33 * q^33 - 54 * q^34 - 2 * q^35 + 11 * q^36 - 45 * q^37 + 10 * q^38 - 54 * q^39 + 3 * q^40 - 27 * q^41 - 28 * q^42 - 101 * q^43 - 51 * q^44 - 61 * q^45 - 46 * q^46 + 71 * q^47 - 14 * q^48 + 23 * q^49 + q^50 - 71 * q^51 - 34 * q^52 - 49 * q^53 - 25 * q^54 + 26 * q^55 - 41 * q^56 - 20 * q^57 - 43 * q^58 - 60 * q^59 + 12 * q^60 - 38 * q^61 - 2 * q^62 + 36 * q^63 - 113 * q^64 + 15 * q^65 - 42 * q^66 - 164 * q^67 + 10 * q^68 - 93 * q^69 + 21 * q^70 - 78 * q^71 + q^72 - 18 * q^73 - 23 * q^74 - 4 * q^75 - 112 * q^76 - 35 * q^77 - 44 * q^78 - 124 * q^79 - 5 * q^80 - 45 * q^81 - 34 * q^82 + 5 * q^83 - 60 * q^84 - 8 * q^85 - 25 * q^86 + 12 * q^87 - 149 * q^88 - 44 * q^89 + 12 * q^90 - 192 * q^91 + 35 * q^92 - 13 * q^93 - 32 * q^94 + 79 * q^95 - 59 * q^96 - 31 * q^97 + 25 * q^98 - 134 * q^99

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