LMFDB - Embedded newform 6023.2.a.a.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0938971374$
Analytic rank:	$1$
Dimension:	$98$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51046 q^{2} +3.07291 q^{3} +4.30243 q^{4} +0.528149 q^{5} -7.71443 q^{6} -0.975247 q^{7} -5.78017 q^{8} +6.44278 q^{9} +O(q^{10})$	\(q-2.51046 q^{2} +3.07291 q^{3} +4.30243 q^{4} +0.528149 q^{5} -7.71443 q^{6} -0.975247 q^{7} -5.78017 q^{8} +6.44278 q^{9} -1.32590 q^{10} -3.81720 q^{11} +13.2210 q^{12} -0.802444 q^{13} +2.44832 q^{14} +1.62295 q^{15} +5.90605 q^{16} -0.448012 q^{17} -16.1744 q^{18} +1.00000 q^{19} +2.27232 q^{20} -2.99685 q^{21} +9.58294 q^{22} -7.34982 q^{23} -17.7619 q^{24} -4.72106 q^{25} +2.01451 q^{26} +10.5793 q^{27} -4.19593 q^{28} +6.25449 q^{29} -4.07437 q^{30} +0.0764409 q^{31} -3.26658 q^{32} -11.7299 q^{33} +1.12472 q^{34} -0.515075 q^{35} +27.7196 q^{36} -0.482533 q^{37} -2.51046 q^{38} -2.46584 q^{39} -3.05279 q^{40} +11.5019 q^{41} +7.52348 q^{42} -8.70290 q^{43} -16.4232 q^{44} +3.40274 q^{45} +18.4515 q^{46} -8.23605 q^{47} +18.1488 q^{48} -6.04889 q^{49} +11.8520 q^{50} -1.37670 q^{51} -3.45246 q^{52} +0.760072 q^{53} -26.5591 q^{54} -2.01605 q^{55} +5.63709 q^{56} +3.07291 q^{57} -15.7017 q^{58} +3.26961 q^{59} +6.98264 q^{60} -4.86450 q^{61} -0.191902 q^{62} -6.28330 q^{63} -3.61146 q^{64} -0.423810 q^{65} +29.4475 q^{66} -3.94794 q^{67} -1.92754 q^{68} -22.5853 q^{69} +1.29308 q^{70} +4.76213 q^{71} -37.2403 q^{72} -11.4716 q^{73} +1.21138 q^{74} -14.5074 q^{75} +4.30243 q^{76} +3.72271 q^{77} +6.19040 q^{78} +0.693842 q^{79} +3.11927 q^{80} +13.1810 q^{81} -28.8752 q^{82} +3.44637 q^{83} -12.8937 q^{84} -0.236617 q^{85} +21.8483 q^{86} +19.2195 q^{87} +22.0641 q^{88} +10.1700 q^{89} -8.54246 q^{90} +0.782582 q^{91} -31.6221 q^{92} +0.234896 q^{93} +20.6763 q^{94} +0.528149 q^{95} -10.0379 q^{96} +3.80144 q^{97} +15.1855 q^{98} -24.5934 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9}+O(q^{10}) $ 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9	\( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9} - 24 q^{10} - 12 q^{11} - 51 q^{12} - 58 q^{13} - 15 q^{14} - 18 q^{15} + 58 q^{16} - 25 q^{17} - 40 q^{18} + 98 q^{19} - 12 q^{20} - 24 q^{21} - 59 q^{22} - 38 q^{23} - 9 q^{24} - 12 q^{25} - 3 q^{26} - 85 q^{27} - 33 q^{28} - 24 q^{29} - 22 q^{30} - 56 q^{31} - 29 q^{32} - 51 q^{33} - 38 q^{34} - 10 q^{35} + 50 q^{36} - 124 q^{37} - 8 q^{38} - 4 q^{39} - 80 q^{40} - 28 q^{41} - 37 q^{42} - 63 q^{43} - 7 q^{44} - 32 q^{45} - 47 q^{46} - 10 q^{47} - 88 q^{48} + 6 q^{49} - 17 q^{50} - 22 q^{51} - 119 q^{52} - 65 q^{53} + 24 q^{54} - 30 q^{55} - 39 q^{56} - 25 q^{57} - 91 q^{58} - 26 q^{59} - 60 q^{60} - 60 q^{61} + 6 q^{62} - 26 q^{63} + 50 q^{64} - 40 q^{65} + 57 q^{66} - 108 q^{67} - 41 q^{68} - 15 q^{69} - 36 q^{70} - 19 q^{71} - 47 q^{72} - 136 q^{73} + 22 q^{74} - 48 q^{75} + 82 q^{76} - 35 q^{77} - 56 q^{78} - 98 q^{79} - 42 q^{80} + 6 q^{81} - 37 q^{82} - 31 q^{83} - 24 q^{84} - 71 q^{85} - 24 q^{86} + 7 q^{87} - 166 q^{88} - 38 q^{89} + 26 q^{90} - 100 q^{91} - 59 q^{92} - 21 q^{93} - 48 q^{94} - 10 q^{95} - 16 q^{96} - 190 q^{97} - 80 q^{98} - 17 q^{99}+O(q^{100}) \) 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9 - 24 * q^10 - 12 * q^11 - 51 * q^12 - 58 * q^13 - 15 * q^14 - 18 * q^15 + 58 * q^16 - 25 * q^17 - 40 * q^18 + 98 * q^19 - 12 * q^20 - 24 * q^21 - 59 * q^22 - 38 * q^23 - 9 * q^24 - 12 * q^25 - 3 * q^26 - 85 * q^27 - 33 * q^28 - 24 * q^29 - 22 * q^30 - 56 * q^31 - 29 * q^32 - 51 * q^33 - 38 * q^34 - 10 * q^35 + 50 * q^36 - 124 * q^37 - 8 * q^38 - 4 * q^39 - 80 * q^40 - 28 * q^41 - 37 * q^42 - 63 * q^43 - 7 * q^44 - 32 * q^45 - 47 * q^46 - 10 * q^47 - 88 * q^48 + 6 * q^49 - 17 * q^50 - 22 * q^51 - 119 * q^52 - 65 * q^53 + 24 * q^54 - 30 * q^55 - 39 * q^56 - 25 * q^57 - 91 * q^58 - 26 * q^59 - 60 * q^60 - 60 * q^61 + 6 * q^62 - 26 * q^63 + 50 * q^64 - 40 * q^65 + 57 * q^66 - 108 * q^67 - 41 * q^68 - 15 * q^69 - 36 * q^70 - 19 * q^71 - 47 * q^72 - 136 * q^73 + 22 * q^74 - 48 * q^75 + 82 * q^76 - 35 * q^77 - 56 * q^78 - 98 * q^79 - 42 * q^80 + 6 * q^81 - 37 * q^82 - 31 * q^83 - 24 * q^84 - 71 * q^85 - 24 * q^86 + 7 * q^87 - 166 * q^88 - 38 * q^89 + 26 * q^90 - 100 * q^91 - 59 * q^92 - 21 * q^93 - 48 * q^94 - 10 * q^95 - 16 * q^96 - 190 * q^97 - 80 * q^98 - 17 * 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 $

$2$	−2.51046	−1.77517	−0.887583	−	0.460648i	$-0.847617\pi$
$2$	−2.51046	−1.77517	−0.887583	+	0.460648i	$0.847617\pi$
$3$	3.07291	1.77415	0.887073	−	0.461630i	$-0.152735\pi$
$3$	3.07291	1.77415	0.887073	+	0.461630i	$0.152735\pi$
$4$	4.30243	2.15122
$5$	0.528149	0.236195	0.118098	−	0.993002i	$-0.462320\pi$
$5$	0.528149	0.236195	0.118098	+	0.993002i	$0.462320\pi$
$6$	−7.71443	−3.14940
$7$	−0.975247	−0.368609	−0.184304	−	0.982869i	$-0.559003\pi$
$7$	−0.975247	−0.368609	−0.184304	+	0.982869i	$0.559003\pi$
$8$	−5.78017	−2.04360
$9$	6.44278	2.14759
$10$	−1.32590	−0.419286
$11$	−3.81720	−1.15093	−0.575464	−	0.817827i	$-0.695179\pi$
$11$	−3.81720	−1.15093	−0.575464	+	0.817827i	$0.695179\pi$
$12$	13.2210	3.81657
$13$	−0.802444	−0.222558	−0.111279	−	0.993789i	$-0.535495\pi$
$13$	−0.802444	−0.222558	−0.111279	+	0.993789i	$0.535495\pi$
$14$	2.44832	0.654342
$15$	1.62295	0.419045
$16$	5.90605	1.47651
$17$	−0.448012	−0.108659	−0.0543294	−	0.998523i	$-0.517302\pi$
$17$	−0.448012	−0.108659	−0.0543294	+	0.998523i	$0.517302\pi$
$18$	−16.1744	−3.81233
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	2.27232	0.508107
$21$	−2.99685	−0.653966
$22$	9.58294	2.04309
$23$	−7.34982	−1.53254	−0.766271	−	0.642517i	$-0.777890\pi$
$23$	−7.34982	−1.53254	−0.766271	+	0.642517i	$0.777890\pi$
$24$	−17.7619	−3.62564
$25$	−4.72106	−0.944212
$26$	2.01451	0.395077
$27$	10.5793	2.03599
$28$	−4.19593	−0.792957
$29$	6.25449	1.16143	0.580715	−	0.814107i	$-0.302773\pi$
$29$	6.25449	1.16143	0.580715	+	0.814107i	$0.302773\pi$
$30$	−4.07437	−0.743874
$31$	0.0764409	0.0137292	0.00686459	−	0.999976i	$-0.497815\pi$
$31$	0.0764409	0.0137292	0.00686459	+	0.999976i	$0.497815\pi$
$32$	−3.26658	−0.577456
$33$	−11.7299	−2.04192
$34$	1.12472	0.192887
$35$	−0.515075	−0.0870636
$36$	27.7196	4.61993
$37$	−0.482533	−0.0793279	−0.0396640	−	0.999213i	$-0.512629\pi$
$37$	−0.482533	−0.0793279	−0.0396640	+	0.999213i	$0.512629\pi$
$38$	−2.51046	−0.407251
$39$	−2.46584	−0.394850
$40$	−3.05279	−0.482688
$41$	11.5019	1.79630	0.898151	−	0.439688i	$-0.144911\pi$
$41$	11.5019	1.79630	0.898151	+	0.439688i	$0.144911\pi$
$42$	7.52348	1.16090
$43$	−8.70290	−1.32718	−0.663590	−	0.748096i	$-0.730968\pi$
$43$	−8.70290	−1.32718	−0.663590	+	0.748096i	$0.730968\pi$
$44$	−16.4232	−2.47590
$45$	3.40274	0.507251
$46$	18.4515	2.72052
$47$	−8.23605	−1.20135	−0.600676	−	0.799493i	$-0.705102\pi$
$47$	−8.23605	−1.20135	−0.600676	+	0.799493i	$0.705102\pi$
$48$	18.1488	2.61955
$49$	−6.04889	−0.864128
$50$	11.8520	1.67613
$51$	−1.37670	−0.192777
$52$	−3.45246	−0.478770
$53$	0.760072	0.104404	0.0522019	−	0.998637i	$-0.483376\pi$
$53$	0.760072	0.104404	0.0522019	+	0.998637i	$0.483376\pi$
$54$	−26.5591	−3.61423
$55$	−2.01605	−0.271844
$56$	5.63709	0.753288
$57$	3.07291	0.407017
$58$	−15.7017	−2.06173
$59$	3.26961	0.425667	0.212834	−	0.977088i	$-0.431731\pi$
$59$	3.26961	0.425667	0.212834	+	0.977088i	$0.431731\pi$
$60$	6.98264	0.901455
$61$	−4.86450	−0.622835	−0.311417	−	0.950273i	$-0.600804\pi$
$61$	−4.86450	−0.622835	−0.311417	+	0.950273i	$0.600804\pi$
$62$	−0.191902	−0.0243716
$63$	−6.28330	−0.791621
$64$	−3.61146	−0.451432
$65$	−0.423810	−0.0525671
$66$	29.4475	3.62474
$67$	−3.94794	−0.482318	−0.241159	−	0.970486i	$-0.577528\pi$
$67$	−3.94794	−0.482318	−0.241159	+	0.970486i	$0.577528\pi$
$68$	−1.92754	−0.233748
$69$	−22.5853	−2.71895
$70$	1.29308	0.154552
$71$	4.76213	0.565160	0.282580	−	0.959244i	$-0.408810\pi$
$71$	4.76213	0.565160	0.282580	+	0.959244i	$0.408810\pi$
$72$	−37.2403	−4.38882
$73$	−11.4716	−1.34265	−0.671327	−	0.741161i	$-0.734275\pi$
$73$	−11.4716	−1.34265	−0.671327	+	0.741161i	$0.734275\pi$
$74$	1.21138	0.140820
$75$	−14.5074	−1.67517
$76$	4.30243	0.493523
$77$	3.72271	0.424242
$78$	6.19040	0.700925
$79$	0.693842	0.0780633	0.0390316	−	0.999238i	$-0.487573\pi$
$79$	0.693842	0.0780633	0.0390316	+	0.999238i	$0.487573\pi$
$80$	3.11927	0.348745
$81$	13.1810	1.46456
$82$	−28.8752	−3.18873
$83$	3.44637	0.378289	0.189144	−	0.981949i	$-0.439429\pi$
$83$	3.44637	0.378289	0.189144	+	0.981949i	$0.439429\pi$
$84$	−12.8937	−1.40682
$85$	−0.236617	−0.0256647
$86$	21.8483	2.35597
$87$	19.2195	2.06055
$88$	22.0641	2.35204
$89$	10.1700	1.07802	0.539009	−	0.842300i	$-0.318799\pi$
$89$	10.1700	1.07802	0.539009	+	0.842300i	$0.318799\pi$
$90$	−8.54246	−0.900455
$91$	0.782582	0.0820368
$92$	−31.6221	−3.29683
$93$	0.234896	0.0243576
$94$	20.6763	2.13260
$95$	0.528149	0.0541869
$96$	−10.0379	−1.02449
$97$	3.80144	0.385978	0.192989	−	0.981201i	$-0.438182\pi$
$97$	3.80144	0.385978	0.192989	+	0.981201i	$0.438182\pi$
$98$	15.1855	1.53397
$99$	−24.5934	−2.47173
$100$	−20.3120	−2.03120
$101$	−4.51906	−0.449664	−0.224832	−	0.974398i	$-0.572183\pi$
$101$	−4.51906	−0.449664	−0.224832	+	0.974398i	$0.572183\pi$
$102$	3.45616	0.342210
$103$	4.69036	0.462155	0.231078	−	0.972935i	$-0.425775\pi$
$103$	4.69036	0.462155	0.231078	+	0.972935i	$0.425775\pi$
$104$	4.63826	0.454819
$105$	−1.58278	−0.154464
$106$	−1.90813	−0.185334
$107$	−3.74156	−0.361710	−0.180855	−	0.983510i	$-0.557887\pi$
$107$	−3.74156	−0.361710	−0.180855	+	0.983510i	$0.557887\pi$
$108$	45.5169	4.37986
$109$	−6.40794	−0.613769	−0.306884	−	0.951747i	$-0.599287\pi$
$109$	−6.40794	−0.613769	−0.306884	+	0.951747i	$0.599287\pi$
$110$	5.06122	0.482568
$111$	−1.48278	−0.140739
$112$	−5.75986	−0.544255
$113$	−14.8154	−1.39371	−0.696857	−	0.717210i	$-0.745419\pi$
$113$	−14.8154	−1.39371	−0.696857	+	0.717210i	$0.745419\pi$
$114$	−7.71443	−0.722523
$115$	−3.88180	−0.361979
$116$	26.9095	2.49849
$117$	−5.16997	−0.477964
$118$	−8.20825	−0.755630
$119$	0.436922	0.0400526
$120$	−9.38094	−0.856359
$121$	3.57101	0.324637
$122$	12.2121	1.10564
$123$	35.3444	3.18690
$124$	0.328882	0.0295344
$125$	−5.13416	−0.459214
$126$	15.7740	1.40526
$127$	−9.12735	−0.809921	−0.404961	−	0.914334i	$-0.632715\pi$
$127$	−9.12735	−0.809921	−0.404961	+	0.914334i	$0.632715\pi$
$128$	15.5996	1.37882
$129$	−26.7432	−2.35461
$130$	1.06396	0.0933154
$131$	3.82514	0.334204	0.167102	−	0.985940i	$-0.446559\pi$
$131$	3.82514	0.334204	0.167102	+	0.985940i	$0.446559\pi$
$132$	−50.4671	−4.39260
$133$	−0.975247	−0.0845647
$134$	9.91117	0.856195
$135$	5.58746	0.480892
$136$	2.58958	0.222055
$137$	−9.66167	−0.825452	−0.412726	−	0.910855i	$-0.635423\pi$
$137$	−9.66167	−0.825452	−0.412726	+	0.910855i	$0.635423\pi$
$138$	56.6996	4.82659
$139$	−2.09079	−0.177338	−0.0886691	−	0.996061i	$-0.528261\pi$
$139$	−2.09079	−0.177338	−0.0886691	+	0.996061i	$0.528261\pi$
$140$	−2.21608	−0.187293
$141$	−25.3086	−2.13137
$142$	−11.9551	−1.00325
$143$	3.06309	0.256148
$144$	38.0513	3.17094
$145$	3.30330	0.274324
$146$	28.7991	2.38343
$147$	−18.5877	−1.53309
$148$	−2.07606	−0.170651
$149$	2.26369	0.185448	0.0927242	−	0.995692i	$-0.470443\pi$
$149$	2.26369	0.185448	0.0927242	+	0.995692i	$0.470443\pi$
$150$	36.4203	2.97370
$151$	12.9373	1.05282	0.526409	−	0.850231i	$-0.323538\pi$
$151$	12.9373	1.05282	0.526409	+	0.850231i	$0.323538\pi$
$152$	−5.78017	−0.468834
$153$	−2.88644	−0.233355
$154$	−9.34574	−0.753101
$155$	0.0403721	0.00324277
$156$	−10.6091	−0.849408
$157$	−7.80410	−0.622835	−0.311418	−	0.950273i	$-0.600804\pi$
$157$	−7.80410	−0.622835	−0.311418	+	0.950273i	$0.600804\pi$
$158$	−1.74186	−0.138575
$159$	2.33563	0.185228
$160$	−1.72524	−0.136392
$161$	7.16789	0.564909
$162$	−33.0905	−2.59984
$163$	−1.68599	−0.132057	−0.0660284	−	0.997818i	$-0.521033\pi$
$163$	−1.68599	−0.132057	−0.0660284	+	0.997818i	$0.521033\pi$
$164$	49.4863	3.86423
$165$	−6.19514	−0.482291
$166$	−8.65200	−0.671525
$167$	−14.7485	−1.14127	−0.570636	−	0.821203i	$-0.693303\pi$
$167$	−14.7485	−1.14127	−0.570636	+	0.821203i	$0.693303\pi$
$168$	17.3223	1.33644
$169$	−12.3561	−0.950468
$170$	0.594018	0.0455591
$171$	6.44278	0.492691
$172$	−37.4436	−2.85505
$173$	12.4868	0.949351	0.474676	−	0.880161i	$-0.342565\pi$
$173$	12.4868	0.949351	0.474676	+	0.880161i	$0.342565\pi$
$174$	−48.2499	−3.65781
$175$	4.60420	0.348045
$176$	−22.5446	−1.69936
$177$	10.0472	0.755196
$178$	−25.5314	−1.91366
$179$	8.99859	0.672586	0.336293	−	0.941757i	$-0.390827\pi$
$179$	8.99859	0.672586	0.336293	+	0.941757i	$0.390827\pi$
$180$	14.6401	1.09121
$181$	−7.89530	−0.586853	−0.293427	−	0.955982i	$-0.594796\pi$
$181$	−7.89530	−0.586853	−0.293427	+	0.955982i	$0.594796\pi$
$182$	−1.96464	−0.145629
$183$	−14.9482	−1.10500
$184$	42.4832	3.13190
$185$	−0.254849	−0.0187369
$186$	−0.589698	−0.0432387
$187$	1.71015	0.125059
$188$	−35.4350	−2.58437
$189$	−10.3175	−0.750486
$190$	−1.32590	−0.0961908
$191$	−1.52661	−0.110461	−0.0552307	−	0.998474i	$-0.517589\pi$
$191$	−1.52661	−0.110461	−0.0552307	+	0.998474i	$0.517589\pi$
$192$	−11.0977	−0.800907
$193$	−3.85694	−0.277628	−0.138814	−	0.990318i	$-0.544329\pi$
$193$	−3.85694	−0.277628	−0.138814	+	0.990318i	$0.544329\pi$
$194$	−9.54339	−0.685175
$195$	−1.30233	−0.0932617
$196$	−26.0249	−1.85892
$197$	−9.02660	−0.643118	−0.321559	−	0.946889i	$-0.604207\pi$
$197$	−9.02660	−0.643118	−0.321559	+	0.946889i	$0.604207\pi$
$198$	61.7407	4.38772
$199$	−8.91923	−0.632267	−0.316134	−	0.948715i	$-0.602385\pi$
$199$	−8.91923	−0.632267	−0.316134	+	0.948715i	$0.602385\pi$
$200$	27.2885	1.92959
$201$	−12.1317	−0.855703
$202$	11.3449	0.798228
$203$	−6.09968	−0.428113
$204$	−5.92315	−0.414704
$205$	6.07473	0.424278
$206$	−11.7750	−0.820402
$207$	−47.3532	−3.29128
$208$	−4.73927	−0.328610
$209$	−3.81720	−0.264041
$210$	3.97351	0.274199
$211$	−9.98666	−0.687510	−0.343755	−	0.939059i	$-0.611699\pi$
$211$	−9.98666	−0.687510	−0.343755	+	0.939059i	$0.611699\pi$
$212$	3.27016	0.224595
$213$	14.6336	1.00268
$214$	9.39305	0.642096
$215$	−4.59643	−0.313474
$216$	−61.1504	−4.16076
$217$	−0.0745487	−0.00506070
$218$	16.0869	1.08954
$219$	−35.2513	−2.38206
$220$	−8.67391	−0.584795
$221$	0.359504	0.0241829
$222$	3.72247	0.249836
$223$	−18.7769	−1.25740	−0.628698	−	0.777649i	$-0.716412\pi$
$223$	−18.7769	−1.25740	−0.628698	+	0.777649i	$0.716412\pi$
$224$	3.18572	0.212855
$225$	−30.4167	−2.02778
$226$	37.1935	2.47407
$227$	−12.4791	−0.828268	−0.414134	−	0.910216i	$-0.635916\pi$
$227$	−12.4791	−0.828268	−0.414134	+	0.910216i	$0.635916\pi$
$228$	13.2210	0.875581
$229$	−13.7163	−0.906399	−0.453199	−	0.891409i	$-0.649717\pi$
$229$	−13.7163	−0.906399	−0.453199	+	0.891409i	$0.649717\pi$
$230$	9.74511	0.642573
$231$	11.4396	0.752668
$232$	−36.1520	−2.37350
$233$	−26.7612	−1.75318	−0.876592	−	0.481235i	$-0.840188\pi$
$233$	−26.7612	−1.75318	−0.876592	+	0.481235i	$0.840188\pi$
$234$	12.9790	0.848465
$235$	−4.34986	−0.283753
$236$	14.0673	0.915702
$237$	2.13211	0.138496
$238$	−1.09688	−0.0711000
$239$	16.6922	1.07973	0.539864	−	0.841753i	$-0.318476\pi$
$239$	16.6922	1.07973	0.539864	+	0.841753i	$0.318476\pi$
$240$	9.58524	0.618724
$241$	−13.5351	−0.871873	−0.435937	−	0.899977i	$-0.643583\pi$
$241$	−13.5351	−0.871873	−0.435937	+	0.899977i	$0.643583\pi$
$242$	−8.96489	−0.576285
$243$	8.76610	0.562346
$244$	−20.9292	−1.33985
$245$	−3.19471	−0.204103
$246$	−88.7309	−5.65728
$247$	−0.802444	−0.0510583
$248$	−0.441841	−0.0280569
$249$	10.5904	0.671139
$250$	12.8891	0.815180
$251$	−21.9968	−1.38842	−0.694212	−	0.719771i	$-0.744247\pi$
$251$	−21.9968	−1.38842	−0.694212	+	0.719771i	$0.744247\pi$
$252$	−27.0335	−1.70295
$253$	28.0557	1.76385
$254$	22.9139	1.43774
$255$	−0.727102	−0.0455329
$256$	−31.9393	−1.99621
$257$	−15.7522	−0.982594	−0.491297	−	0.870992i	$-0.663477\pi$
$257$	−15.7522	−0.982594	−0.491297	+	0.870992i	$0.663477\pi$
$258$	67.1379	4.17983
$259$	0.470589	0.0292410
$260$	−1.82341	−0.113083
$261$	40.2963	2.49428
$262$	−9.60287	−0.593268
$263$	18.0776	1.11471	0.557357	−	0.830273i	$-0.311815\pi$
$263$	18.0776	1.11471	0.557357	+	0.830273i	$0.311815\pi$
$264$	67.8009	4.17285
$265$	0.401431	0.0246597
$266$	2.44832	0.150116
$267$	31.2515	1.91256
$268$	−16.9858	−1.03757
$269$	−21.2219	−1.29392	−0.646962	−	0.762522i	$-0.723961\pi$
$269$	−21.2219	−1.29392	−0.646962	+	0.762522i	$0.723961\pi$
$270$	−14.0271	−0.853664
$271$	15.3188	0.930548	0.465274	−	0.885167i	$-0.345956\pi$
$271$	15.3188	0.930548	0.465274	+	0.885167i	$0.345956\pi$
$272$	−2.64598	−0.160436
$273$	2.40480	0.145545
$274$	24.2553	1.46531
$275$	18.0212	1.08672
$276$	−97.1718	−5.84905
$277$	−7.59733	−0.456479	−0.228240	−	0.973605i	$-0.573297\pi$
$277$	−7.59733	−0.456479	−0.228240	+	0.973605i	$0.573297\pi$
$278$	5.24884	0.314805
$279$	0.492491	0.0294847
$280$	2.97722	0.177923
$281$	−2.14889	−0.128192	−0.0640959	−	0.997944i	$-0.520416\pi$
$281$	−2.14889	−0.128192	−0.0640959	+	0.997944i	$0.520416\pi$
$282$	63.5364	3.78354
$283$	4.32750	0.257243	0.128621	−	0.991694i	$-0.458945\pi$
$283$	4.32750	0.257243	0.128621	+	0.991694i	$0.458945\pi$
$284$	20.4887	1.21578
$285$	1.62295	0.0961354
$286$	−7.68978	−0.454706
$287$	−11.2172	−0.662132
$288$	−21.0459	−1.24014
$289$	−16.7993	−0.988193
$290$	−8.29282	−0.486971
$291$	11.6815	0.684781
$292$	−49.3559	−2.88834
$293$	5.17495	0.302324	0.151162	−	0.988509i	$-0.451699\pi$
$293$	5.17495	0.302324	0.151162	+	0.988509i	$0.451699\pi$
$294$	46.6638	2.72149
$295$	1.72684	0.100541
$296$	2.78912	0.162114
$297$	−40.3834	−2.34329
$298$	−5.68290	−0.329202
$299$	5.89782	0.341080
$300$	−62.4170	−3.60365
$301$	8.48748	0.489210
$302$	−32.4785	−1.86893
$303$	−13.8867	−0.797769
$304$	5.90605	0.338735
$305$	−2.56918	−0.147111
$306$	7.24630	0.414244
$307$	24.1264	1.37697	0.688484	−	0.725252i	$-0.258277\pi$
$307$	24.1264	1.37697	0.688484	+	0.725252i	$0.258277\pi$
$308$	16.0167	0.912637
$309$	14.4131	0.819930
$310$	−0.101353	−0.00575645
$311$	18.1670	1.03016	0.515078	−	0.857144i	$-0.327763\pi$
$311$	18.1670	1.03016	0.515078	+	0.857144i	$0.327763\pi$
$312$	14.2530	0.806915
$313$	21.2003	1.19831	0.599155	−	0.800633i	$-0.295503\pi$
$313$	21.2003	1.19831	0.599155	+	0.800633i	$0.295503\pi$
$314$	19.5919	1.10564
$315$	−3.31852	−0.186977
$316$	2.98521	0.167931
$317$	1.00000	0.0561656
$317$	1.00000	0.0561656
$318$	−5.86352	−0.328810
$319$	−23.8746	−1.33672
$320$	−1.90739	−0.106626
$321$	−11.4975	−0.641726
$322$	−17.9947	−1.00281
$323$	−0.448012	−0.0249280
$324$	56.7105	3.15058
$325$	3.78839	0.210142
$326$	4.23262	0.234423
$327$	−19.6910	−1.08892
$328$	−66.4832	−3.67092
$329$	8.03218	0.442829
$330$	15.5527	0.856146
$331$	17.2893	0.950307	0.475153	−	0.879903i	$-0.342393\pi$
$331$	17.2893	0.950307	0.475153	+	0.879903i	$0.342393\pi$
$332$	14.8278	0.813780
$333$	−3.10885	−0.170364
$334$	37.0256	2.02595
$335$	−2.08510	−0.113921
$336$	−17.6995	−0.965588
$337$	−33.9112	−1.84726	−0.923631	−	0.383282i	$-0.874794\pi$
$337$	−33.9112	−1.84726	−0.923631	+	0.383282i	$0.874794\pi$
$338$	31.0195	1.68724
$339$	−45.5263	−2.47265
$340$	−1.01803	−0.0552103
$341$	−0.291790	−0.0158013
$342$	−16.1744	−0.874609
$343$	12.7259	0.687134
$344$	50.3043	2.71222
$345$	−11.9284	−0.642204
$346$	−31.3476	−1.68526
$347$	16.1523	0.867102	0.433551	−	0.901129i	$-0.357260\pi$
$347$	16.1523	0.867102	0.433551	+	0.901129i	$0.357260\pi$
$348$	82.6905	4.43268
$349$	21.7455	1.16401	0.582004	−	0.813186i	$-0.302269\pi$
$349$	21.7455	1.16401	0.582004	+	0.813186i	$0.302269\pi$
$350$	−11.5587	−0.617837
$351$	−8.48933	−0.453127
$352$	12.4692	0.664610
$353$	−6.83121	−0.363589	−0.181794	−	0.983337i	$-0.558190\pi$
$353$	−6.83121	−0.363589	−0.181794	+	0.983337i	$0.558190\pi$
$354$	−25.2232	−1.34060
$355$	2.51511	0.133488
$356$	43.7557	2.31905
$357$	1.34262	0.0710591
$358$	−22.5906	−1.19395
$359$	25.9033	1.36712	0.683562	−	0.729892i	$-0.260430\pi$
$359$	25.9033	1.36712	0.683562	+	0.729892i	$0.260430\pi$
$360$	−19.6684	−1.03662
$361$	1.00000	0.0526316
$362$	19.8209	1.04176
$363$	10.9734	0.575953
$364$	3.36700	0.176479
$365$	−6.05873	−0.317129
$366$	37.5268	1.96156
$367$	21.3506	1.11449	0.557247	−	0.830347i	$-0.311858\pi$
$367$	21.3506	1.11449	0.557247	+	0.830347i	$0.311858\pi$
$368$	−43.4084	−2.26282
$369$	74.1044	3.85772
$370$	0.639790	0.0332611
$371$	−0.741258	−0.0384842
$372$	1.01062	0.0523984
$373$	20.4144	1.05702	0.528509	−	0.848928i	$-0.322751\pi$
$373$	20.4144	1.05702	0.528509	+	0.848928i	$0.322751\pi$
$374$	−4.29327	−0.222000
$375$	−15.7768	−0.814712
$376$	47.6058	2.45508
$377$	−5.01888	−0.258486
$378$	25.9016	1.33224
$379$	−22.3061	−1.14579	−0.572894	−	0.819629i	$-0.694179\pi$
$379$	−22.3061	−1.14579	−0.572894	+	0.819629i	$0.694179\pi$
$380$	2.27232	0.116568
$381$	−28.0475	−1.43692
$382$	3.83249	0.196087
$383$	38.7885	1.98200	0.991000	−	0.133860i	$-0.0427373\pi$
$383$	38.7885	1.98200	0.991000	+	0.133860i	$0.0427373\pi$
$384$	47.9362	2.44623
$385$	1.96615	0.100204
$386$	9.68270	0.492836
$387$	−56.0708	−2.85024
$388$	16.3554	0.830322
$389$	2.42847	0.123128	0.0615642	−	0.998103i	$-0.480391\pi$
$389$	2.42847	0.123128	0.0615642	+	0.998103i	$0.480391\pi$
$390$	3.26945	0.165555
$391$	3.29280	0.166524
$392$	34.9636	1.76593
$393$	11.7543	0.592926
$394$	22.6610	1.14164
$395$	0.366452	0.0184382
$396$	−105.811	−5.31721
$397$	1.38675	0.0695992	0.0347996	−	0.999394i	$-0.488921\pi$
$397$	1.38675	0.0695992	0.0347996	+	0.999394i	$0.488921\pi$
$398$	22.3914	1.12238
$399$	−2.99685	−0.150030
$400$	−27.8828	−1.39414
$401$	−29.9560	−1.49593	−0.747966	−	0.663737i	$-0.768969\pi$
$401$	−29.9560	−1.49593	−0.747966	+	0.663737i	$0.768969\pi$
$402$	30.4561	1.51901
$403$	−0.0613395	−0.00305554
$404$	−19.4430	−0.967323
$405$	6.96154	0.345922
$406$	15.3130	0.759972
$407$	1.84192	0.0913008
$408$	7.95756	0.393958
$409$	13.9386	0.689217	0.344609	−	0.938746i	$-0.388012\pi$
$409$	13.9386	0.689217	0.344609	+	0.938746i	$0.388012\pi$
$410$	−15.2504	−0.753164
$411$	−29.6894	−1.46447
$412$	20.1800	0.994195
$413$	−3.18868	−0.156905
$414$	118.879	5.84256
$415$	1.82020	0.0893500
$416$	2.62125	0.128517
$417$	−6.42480	−0.314624
$418$	9.58294	0.468717
$419$	20.4840	1.00071	0.500355	−	0.865820i	$-0.333203\pi$
$419$	20.4840	1.00071	0.500355	+	0.865820i	$0.333203\pi$
$420$	−6.80980	−0.332284
$421$	−22.0026	−1.07234	−0.536171	−	0.844109i	$-0.680130\pi$
$421$	−22.0026	−1.07234	−0.536171	+	0.844109i	$0.680130\pi$
$422$	25.0712	1.22044
$423$	−53.0630	−2.58001
$424$	−4.39334	−0.213360
$425$	2.11509	0.102597
$426$	−36.7371	−1.77992
$427$	4.74409	0.229582
$428$	−16.0978	−0.778116
$429$	9.41260	0.454445
$430$	11.5392	0.556468
$431$	32.6974	1.57498	0.787490	−	0.616327i	$-0.211380\pi$
$431$	32.6974	1.57498	0.787490	+	0.616327i	$0.211380\pi$
$432$	62.4821	3.00617
$433$	22.7085	1.09130	0.545649	−	0.838014i	$-0.316283\pi$
$433$	22.7085	1.09130	0.545649	+	0.838014i	$0.316283\pi$
$434$	0.187152	0.00898358
$435$	10.1507	0.486691
$436$	−27.5697	−1.32035
$437$	−7.34982	−0.351589
$438$	88.4972	4.22856
$439$	−38.4834	−1.83671	−0.918356	−	0.395755i	$-0.870483\pi$
$439$	−38.4834	−1.83671	−0.918356	+	0.395755i	$0.870483\pi$
$440$	11.6531	0.555540
$441$	−38.9717	−1.85579
$442$	−0.902523	−0.0429286
$443$	−9.90745	−0.470717	−0.235359	−	0.971909i	$-0.575626\pi$
$443$	−9.90745	−0.470717	−0.235359	+	0.971909i	$0.575626\pi$
$444$	−6.37956	−0.302761
$445$	5.37127	0.254623
$446$	47.1388	2.23209
$447$	6.95611	0.329013
$448$	3.52206	0.166402
$449$	−33.6287	−1.58704	−0.793518	−	0.608547i	$-0.791753\pi$
$449$	−33.6287	−1.58704	−0.793518	+	0.608547i	$0.791753\pi$
$450$	76.3601	3.59965
$451$	−43.9052	−2.06741
$452$	−63.7421	−2.99818
$453$	39.7550	1.86785
$454$	31.3284	1.47031
$455$	0.413319	0.0193767
$456$	−17.7619	−0.831779
$457$	27.9995	1.30976	0.654881	−	0.755732i	$-0.272719\pi$
$457$	27.9995	1.30976	0.654881	+	0.755732i	$0.272719\pi$
$458$	34.4343	1.60901
$459$	−4.73967	−0.221229
$460$	−16.7012	−0.778695
$461$	4.83836	0.225345	0.112673	−	0.993632i	$-0.464059\pi$
$461$	4.83836	0.225345	0.112673	+	0.993632i	$0.464059\pi$
$462$	−28.7186	−1.33611
$463$	5.50966	0.256056	0.128028	−	0.991771i	$-0.459135\pi$
$463$	5.50966	0.256056	0.128028	+	0.991771i	$0.459135\pi$
$464$	36.9393	1.71487
$465$	0.124060	0.00575314
$466$	67.1830	3.11219
$467$	−16.1881	−0.749097	−0.374549	−	0.927207i	$-0.622202\pi$
$467$	−16.1881	−0.749097	−0.374549	+	0.927207i	$0.622202\pi$
$468$	−22.2434	−1.02820
$469$	3.85022	0.177787
$470$	10.9202	0.503710
$471$	−23.9813	−1.10500
$472$	−18.8989	−0.869893
$473$	33.2207	1.52749
$474$	−5.35259	−0.245853
$475$	−4.72106	−0.216617
$476$	1.87983	0.0861617
$477$	4.89697	0.224217
$478$	−41.9051	−1.91670
$479$	14.2572	0.651430	0.325715	−	0.945468i	$-0.394395\pi$
$479$	14.2572	0.651430	0.325715	+	0.945468i	$0.394395\pi$
$480$	−5.30151	−0.241980
$481$	0.387206	0.0176551
$482$	33.9794	1.54772
$483$	22.0263	1.00223
$484$	15.3640	0.698364
$485$	2.00773	0.0911662
$486$	−22.0070	−0.998257
$487$	−6.25357	−0.283376	−0.141688	−	0.989911i	$-0.545253\pi$
$487$	−6.25357	−0.283376	−0.141688	+	0.989911i	$0.545253\pi$
$488$	28.1176	1.27282
$489$	−5.18089	−0.234288
$490$	8.02022	0.362316
$491$	25.8103	1.16480	0.582401	−	0.812901i	$-0.302113\pi$
$491$	25.8103	1.16480	0.582401	+	0.812901i	$0.302113\pi$
$492$	152.067	6.85571
$493$	−2.80209	−0.126200
$494$	2.01451	0.0906370
$495$	−12.9889	−0.583810
$496$	0.451463	0.0202713
$497$	−4.64425	−0.208323
$498$	−26.5868	−1.19138
$499$	−37.8634	−1.69500	−0.847500	−	0.530796i	$-0.821893\pi$
$499$	−37.8634	−1.69500	−0.847500	+	0.530796i	$0.821893\pi$
$500$	−22.0894	−0.987867
$501$	−45.3208	−2.02478
$502$	55.2221	2.46468
$503$	−21.8943	−0.976219	−0.488110	−	0.872782i	$-0.662313\pi$
$503$	−21.8943	−0.976219	−0.488110	+	0.872782i	$0.662313\pi$
$504$	36.3185	1.61776
$505$	−2.38674	−0.106208
$506$	−70.4329	−3.13112
$507$	−37.9691	−1.68627
$508$	−39.2698	−1.74231
$509$	−10.6974	−0.474152	−0.237076	−	0.971491i	$-0.576189\pi$
$509$	−10.6974	−0.474152	−0.237076	+	0.971491i	$0.576189\pi$
$510$	1.82536	0.0808285
$511$	11.1877	0.494914
$512$	48.9833	2.16478
$513$	10.5793	0.467089
$514$	39.5453	1.74427
$515$	2.47721	0.109159
$516$	−115.061	−5.06527
$517$	31.4386	1.38267
$518$	−1.18140	−0.0519076
$519$	38.3707	1.68429
$520$	2.44969	0.107426
$521$	4.77036	0.208993	0.104497	−	0.994525i	$-0.466677\pi$
$521$	4.77036	0.208993	0.104497	+	0.994525i	$0.466677\pi$
$522$	−101.162	−4.42776
$523$	27.0751	1.18391	0.591956	−	0.805970i	$-0.298356\pi$
$523$	27.0751	1.18391	0.591956	+	0.805970i	$0.298356\pi$
$524$	16.4574	0.718945
$525$	14.1483	0.617482
$526$	−45.3832	−1.97880
$527$	−0.0342464	−0.00149180
$528$	−69.2774	−3.01491
$529$	31.0198	1.34869
$530$	−1.00778	−0.0437751
$531$	21.0654	0.914160
$532$	−4.19593	−0.181917
$533$	−9.22967	−0.399781
$534$	−78.4558	−3.39511
$535$	−1.97610	−0.0854342
$536$	22.8198	0.985665
$537$	27.6518	1.19327
$538$	53.2769	2.29693
$539$	23.0898	0.994549
$540$	24.0397	1.03450
$541$	10.2189	0.439345	0.219673	−	0.975574i	$-0.429501\pi$
$541$	10.2189	0.439345	0.219673	+	0.975574i	$0.429501\pi$
$542$	−38.4572	−1.65188
$543$	−24.2616	−1.04116
$544$	1.46347	0.0627456
$545$	−3.38434	−0.144969
$546$	−6.03717	−0.258367
$547$	22.1686	0.947859	0.473930	−	0.880563i	$-0.342835\pi$
$547$	22.1686	0.947859	0.473930	+	0.880563i	$0.342835\pi$
$548$	−41.5686	−1.77572
$549$	−31.3409	−1.33760
$550$	−45.2416	−1.92911
$551$	6.25449	0.266450
$552$	130.547	5.55645
$553$	−0.676667	−0.0287748
$554$	19.0728	0.810326
$555$	−0.783128	−0.0332420
$556$	−8.99546	−0.381493
$557$	−4.46210	−0.189065	−0.0945325	−	0.995522i	$-0.530136\pi$
$557$	−4.46210	−0.189065	−0.0945325	+	0.995522i	$0.530136\pi$
$558$	−1.23638	−0.0523402
$559$	6.98359	0.295375
$560$	−3.04206	−0.128551
$561$	5.25514	0.221872
$562$	5.39470	0.227562
$563$	−12.8633	−0.542122	−0.271061	−	0.962562i	$-0.587375\pi$
$563$	−12.8633	−0.542122	−0.271061	+	0.962562i	$0.587375\pi$
$564$	−108.889	−4.58504
$565$	−7.82472	−0.329188
$566$	−10.8640	−0.456649
$567$	−12.8548	−0.539849
$568$	−27.5259	−1.15496
$569$	11.5682	0.484964	0.242482	−	0.970156i	$-0.422039\pi$
$569$	11.5682	0.484964	0.242482	+	0.970156i	$0.422039\pi$
$570$	−4.07437	−0.170656
$571$	8.50118	0.355763	0.177882	−	0.984052i	$-0.443076\pi$
$571$	8.50118	0.355763	0.177882	+	0.984052i	$0.443076\pi$
$572$	13.1787	0.551030
$573$	−4.69112	−0.195974
$574$	28.1605	1.17540
$575$	34.6989	1.44704
$576$	−23.2678	−0.969492
$577$	−13.3586	−0.556125	−0.278063	−	0.960563i	$-0.589692\pi$
$577$	−13.3586	−0.556125	−0.278063	+	0.960563i	$0.589692\pi$
$578$	42.1740	1.75421
$579$	−11.8520	−0.492553
$580$	14.2122	0.590131
$581$	−3.36107	−0.139440
$582$	−29.3260	−1.21560
$583$	−2.90135	−0.120161
$584$	66.3080	2.74385
$585$	−2.73051	−0.112893
$586$	−12.9915	−0.536675
$587$	25.9421	1.07074	0.535372	−	0.844616i	$-0.320171\pi$
$587$	25.9421	1.07074	0.535372	+	0.844616i	$0.320171\pi$
$588$	−79.9723	−3.29800
$589$	0.0764409	0.00314969
$590$	−4.33517	−0.178476
$591$	−27.7379	−1.14099
$592$	−2.84986	−0.117129
$593$	−30.1567	−1.23839	−0.619193	−	0.785238i	$-0.712540\pi$
$593$	−30.1567	−1.23839	−0.619193	+	0.785238i	$0.712540\pi$
$594$	101.381	4.15972
$595$	0.230760	0.00946023
$596$	9.73936	0.398940
$597$	−27.4080	−1.12173
$598$	−14.8063	−0.605473
$599$	12.9185	0.527836	0.263918	−	0.964545i	$-0.414985\pi$
$599$	12.9185	0.527836	0.263918	+	0.964545i	$0.414985\pi$
$600$	83.8552	3.42337
$601$	22.2170	0.906250	0.453125	−	0.891447i	$-0.350309\pi$
$601$	22.2170	0.906250	0.453125	+	0.891447i	$0.350309\pi$
$602$	−21.3075	−0.868430
$603$	−25.4357	−1.03582
$604$	55.6616	2.26484
$605$	1.88602	0.0766777
$606$	34.8620	1.41617
$607$	31.0738	1.26125	0.630624	−	0.776089i	$-0.282799\pi$
$607$	31.0738	1.26125	0.630624	+	0.776089i	$0.282799\pi$
$608$	−3.26658	−0.132477
$609$	−18.7438	−0.759535
$610$	6.44983	0.261146
$611$	6.60897	0.267370
$612$	−12.4187	−0.501996
$613$	−12.6272	−0.510006	−0.255003	−	0.966940i	$-0.582077\pi$
$613$	−12.6272	−0.510006	−0.255003	+	0.966940i	$0.582077\pi$
$614$	−60.5685	−2.44435
$615$	18.6671	0.752731
$616$	−21.5179	−0.866981
$617$	25.4413	1.02423	0.512115	−	0.858917i	$-0.328862\pi$
$617$	25.4413	1.02423	0.512115	+	0.858917i	$0.328862\pi$
$618$	−36.1835	−1.45551
$619$	14.2554	0.572973	0.286486	−	0.958084i	$-0.407513\pi$
$619$	14.2554	0.572973	0.286486	+	0.958084i	$0.407513\pi$
$620$	0.173698	0.00697589
$621$	−77.7562	−3.12025
$622$	−45.6076	−1.82870
$623$	−9.91826	−0.397367
$624$	−14.5634	−0.583001
$625$	20.8937	0.835748
$626$	−53.2225	−2.12720
$627$	−11.7299	−0.468447
$628$	−33.5766	−1.33985
$629$	0.216180	0.00861968
$630$	8.33101	0.331916
$631$	22.1461	0.881622	0.440811	−	0.897600i	$-0.354691\pi$
$631$	22.1461	0.881622	0.440811	+	0.897600i	$0.354691\pi$
$632$	−4.01052	−0.159530
$633$	−30.6881	−1.21974
$634$	−2.51046	−0.0997033
$635$	−4.82060	−0.191299
$636$	10.0489	0.398465
$637$	4.85390	0.192318
$638$	59.9364	2.37291
$639$	30.6813	1.21373
$640$	8.23891	0.325671
$641$	5.76283	0.227618	0.113809	−	0.993503i	$-0.463695\pi$
$641$	5.76283	0.227618	0.113809	+	0.993503i	$0.463695\pi$
$642$	28.8640	1.13917
$643$	20.6733	0.815274	0.407637	−	0.913144i	$-0.366353\pi$
$643$	20.6733	0.815274	0.407637	+	0.913144i	$0.366353\pi$
$644$	30.8393	1.21524
$645$	−14.1244	−0.556148
$646$	1.12472	0.0442514
$647$	17.8505	0.701777	0.350889	−	0.936417i	$-0.385880\pi$
$647$	17.8505	0.701777	0.350889	+	0.936417i	$0.385880\pi$
$648$	−76.1886	−2.99297
$649$	−12.4808	−0.489913
$650$	−9.51061	−0.373037
$651$	−0.229082	−0.00897841
$652$	−7.25385	−0.284083
$653$	−35.5754	−1.39217	−0.696086	−	0.717958i	$-0.745077\pi$
$653$	−35.5754	−1.39217	−0.696086	+	0.717958i	$0.745077\pi$
$654$	49.4336	1.93301
$655$	2.02024	0.0789374
$656$	67.9310	2.65226
$657$	−73.9092	−2.88347
$658$	−20.1645	−0.786094
$659$	2.01164	0.0783623	0.0391812	−	0.999232i	$-0.487525\pi$
$659$	2.01164	0.0783623	0.0391812	+	0.999232i	$0.487525\pi$
$660$	−26.6541	−1.03751
$661$	22.5543	0.877260	0.438630	−	0.898668i	$-0.355464\pi$
$661$	22.5543	0.877260	0.438630	+	0.898668i	$0.355464\pi$
$662$	−43.4042	−1.68695
$663$	1.10472	0.0429040
$664$	−19.9206	−0.773070
$665$	−0.515075	−0.0199738
$666$	7.80466	0.302424
$667$	−45.9694	−1.77994
$668$	−63.4544	−2.45512
$669$	−57.6998	−2.23080
$670$	5.23457	0.202229
$671$	18.5687	0.716839
$672$	9.78945	0.377636
$673$	−14.8482	−0.572355	−0.286178	−	0.958177i	$-0.592385\pi$
$673$	−14.8482	−0.572355	−0.286178	+	0.958177i	$0.592385\pi$
$674$	85.1329	3.27920
$675$	−49.9457	−1.92241
$676$	−53.1612	−2.04466
$677$	23.3371	0.896918	0.448459	−	0.893803i	$-0.351973\pi$
$677$	23.3371	0.896918	0.448459	+	0.893803i	$0.351973\pi$
$678$	114.292	4.38937
$679$	−3.70735	−0.142275
$680$	1.36769	0.0524483
$681$	−38.3472	−1.46947
$682$	0.732528	0.0280500
$683$	29.8785	1.14327	0.571634	−	0.820508i	$-0.306310\pi$
$683$	29.8785	1.14327	0.571634	+	0.820508i	$0.306310\pi$
$684$	27.7196	1.05989
$685$	−5.10280	−0.194968
$686$	−31.9479	−1.21978
$687$	−42.1490	−1.60808
$688$	−51.3998	−1.95960
$689$	−0.609915	−0.0232359
$690$	29.9458	1.14002
$691$	12.2791	0.467120	0.233560	−	0.972342i	$-0.424962\pi$
$691$	12.2791	0.467120	0.233560	+	0.972342i	$0.424962\pi$
$692$	53.7234	2.04226
$693$	23.9846	0.911100
$694$	−40.5498	−1.53925
$695$	−1.10425	−0.0418864
$696$	−111.092	−4.21093
$697$	−5.15300	−0.195184
$698$	−54.5912	−2.06631
$699$	−82.2347	−3.11040
$700$	19.8092	0.748719
$701$	−19.8622	−0.750186	−0.375093	−	0.926987i	$-0.622389\pi$
$701$	−19.8622	−0.750186	−0.375093	+	0.926987i	$0.622389\pi$
$702$	21.3122	0.804376
$703$	−0.482533	−0.0181991
$704$	13.7857	0.519566
$705$	−13.3667	−0.503420
$706$	17.1495	0.645430
$707$	4.40721	0.165750
$708$	43.2275	1.62459
$709$	−49.7860	−1.86975	−0.934876	−	0.354974i	$-0.884490\pi$
$709$	−49.7860	−1.86975	−0.934876	+	0.354974i	$0.884490\pi$
$710$	−6.31409	−0.236964
$711$	4.47027	0.167648
$712$	−58.7843	−2.20304
$713$	−0.561826	−0.0210406
$714$	−3.37061	−0.126142
$715$	1.61777	0.0605010
$716$	38.7158	1.44688
$717$	51.2936	1.91559
$718$	−65.0294	−2.42687
$719$	−17.3516	−0.647106	−0.323553	−	0.946210i	$-0.604877\pi$
$719$	−17.3516	−0.647106	−0.323553	+	0.946210i	$0.604877\pi$
$720$	20.0968	0.748962
$721$	−4.57426	−0.170354
$722$	−2.51046	−0.0934298
$723$	−41.5922	−1.54683
$724$	−33.9690	−1.26245
$725$	−29.5278	−1.09664
$726$	−27.5483	−1.02241
$727$	−35.6048	−1.32051	−0.660255	−	0.751042i	$-0.729552\pi$
$727$	−35.6048	−1.32051	−0.660255	+	0.751042i	$0.729552\pi$
$728$	−4.52345	−0.167650
$729$	−12.6056	−0.466876
$730$	15.2102	0.562956
$731$	3.89900	0.144210
$732$	−64.3134	−2.37709
$733$	−25.1275	−0.928106	−0.464053	−	0.885807i	$-0.653605\pi$
$733$	−25.1275	−0.928106	−0.464053	+	0.885807i	$0.653605\pi$
$734$	−53.6000	−1.97841
$735$	−9.81707	−0.362108
$736$	24.0088	0.884975
$737$	15.0701	0.555114
$738$	−186.036	−6.84810
$739$	−21.1708	−0.778782	−0.389391	−	0.921073i	$-0.627314\pi$
$739$	−21.1708	−0.778782	−0.389391	+	0.921073i	$0.627314\pi$
$740$	−1.09647	−0.0403071
$741$	−2.46584	−0.0905849
$742$	1.86090	0.0683158
$743$	−3.27894	−0.120293	−0.0601463	−	0.998190i	$-0.519157\pi$
$743$	−3.27894	−0.120293	−0.0601463	+	0.998190i	$0.519157\pi$
$744$	−1.35774	−0.0497771
$745$	1.19556	0.0438020
$746$	−51.2497	−1.87638
$747$	22.2042	0.812409
$748$	7.35780	0.269028
$749$	3.64895	0.133330
$750$	39.6072	1.44625
$751$	28.8103	1.05130	0.525651	−	0.850701i	$-0.323822\pi$
$751$	28.8103	1.05130	0.525651	+	0.850701i	$0.323822\pi$
$752$	−48.6425	−1.77381
$753$	−67.5941	−2.46326
$754$	12.5997	0.458855
$755$	6.83279	0.248671
$756$	−44.3902	−1.61446
$757$	−30.6068	−1.11242	−0.556211	−	0.831041i	$-0.687745\pi$
$757$	−30.6068	−1.11242	−0.556211	+	0.831041i	$0.687745\pi$
$758$	55.9987	2.03397
$759$	86.2127	3.12932
$760$	−3.05279	−0.110736
$761$	2.43352	0.0882149	0.0441074	−	0.999027i	$-0.485956\pi$
$761$	2.43352	0.0882149	0.0441074	+	0.999027i	$0.485956\pi$
$762$	70.4123	2.55077
$763$	6.24932	0.226241
$764$	−6.56812	−0.237626
$765$	−1.52447	−0.0551173
$766$	−97.3772	−3.51838
$767$	−2.62368	−0.0947357
$768$	−98.1467	−3.54156
$769$	−40.2801	−1.45254	−0.726270	−	0.687410i	$-0.758748\pi$
$769$	−40.2801	−1.45254	−0.726270	+	0.687410i	$0.758748\pi$
$770$	−4.93594	−0.177879
$771$	−48.4050	−1.74326
$772$	−16.5942	−0.597238
$773$	−14.7564	−0.530752	−0.265376	−	0.964145i	$-0.585496\pi$
$773$	−14.7564	−0.530752	−0.265376	+	0.964145i	$0.585496\pi$
$774$	140.764	5.05965
$775$	−0.360882	−0.0129633
$776$	−21.9730	−0.788784
$777$	1.44608	0.0518777
$778$	−6.09659	−0.218573
$779$	11.5019	0.412100
$780$	−5.60318	−0.200626
$781$	−18.1780	−0.650459
$782$	−8.26647	−0.295608
$783$	66.1684	2.36467
$784$	−35.7250	−1.27589
$785$	−4.12173	−0.147111
$786$	−29.5088	−1.05254
$787$	36.7310	1.30932	0.654659	−	0.755925i	$-0.272812\pi$
$787$	36.7310	1.30932	0.654659	+	0.755925i	$0.272812\pi$
$788$	−38.8363	−1.38349
$789$	55.5509	1.97767
$790$	−0.919963	−0.0327308
$791$	14.4487	0.513735
$792$	142.154	5.05121
$793$	3.90349	0.138617
$794$	−3.48140	−0.123550
$795$	1.23356	0.0437499
$796$	−38.3744	−1.36014
$797$	−14.4798	−0.512902	−0.256451	−	0.966557i	$-0.582553\pi$
$797$	−14.4798	−0.512902	−0.256451	+	0.966557i	$0.582553\pi$
$798$	7.52348	0.266328
$799$	3.68985	0.130537
$800$	15.4217	0.545240
$801$	65.5230	2.31514
$802$	75.2035	2.65553
$803$	43.7895	1.54530
$804$	−52.1957	−1.84080
$805$	3.78571	0.133429
$806$	0.153991	0.00542409
$807$	−65.2131	−2.29561
$808$	26.1210	0.918932
$809$	40.4116	1.42080	0.710398	−	0.703801i	$-0.248515\pi$
$809$	40.4116	1.42080	0.710398	+	0.703801i	$0.248515\pi$
$810$	−17.4767	−0.614069
$811$	−27.9307	−0.980781	−0.490391	−	0.871503i	$-0.663146\pi$
$811$	−27.9307	−0.980781	−0.490391	+	0.871503i	$0.663146\pi$
$812$	−26.2434	−0.920964
$813$	47.0732	1.65093
$814$	−4.62409	−0.162074
$815$	−0.890453	−0.0311912
$816$	−8.13085	−0.284637
$817$	−8.70290	−0.304476
$818$	−34.9923	−1.22348
$819$	5.04200	0.176182
$820$	26.1361	0.912713
$821$	−41.4342	−1.44606	−0.723031	−	0.690815i	$-0.757252\pi$
$821$	−41.4342	−1.44606	−0.723031	+	0.690815i	$0.757252\pi$
$822$	74.5342	2.59968
$823$	16.0473	0.559375	0.279688	−	0.960091i	$-0.409769\pi$
$823$	16.0473	0.559375	0.279688	+	0.960091i	$0.409769\pi$
$824$	−27.1111	−0.944459
$825$	55.3776	1.92800
$826$	8.00507	0.278532
$827$	36.3085	1.26257	0.631284	−	0.775551i	$-0.282528\pi$
$827$	36.3085	1.26257	0.631284	+	0.775551i	$0.282528\pi$
$828$	−203.734	−7.08024
$829$	−30.8493	−1.07144	−0.535721	−	0.844395i	$-0.679960\pi$
$829$	−30.8493	−1.07144	−0.535721	+	0.844395i	$0.679960\pi$
$830$	−4.56954	−0.158611
$831$	−23.3459	−0.809860
$832$	2.89799	0.100470
$833$	2.70997	0.0938951
$834$	16.1292	0.558509
$835$	−7.78939	−0.269563
$836$	−16.4232	−0.568009
$837$	0.808694	0.0279525
$838$	−51.4244	−1.77643
$839$	33.5196	1.15722	0.578612	−	0.815603i	$-0.303594\pi$
$839$	33.5196	1.15722	0.578612	+	0.815603i	$0.303594\pi$
$840$	9.14874	0.315662
$841$	10.1187	0.348920
$842$	55.2368	1.90359
$843$	−6.60333	−0.227431
$844$	−42.9669	−1.47898
$845$	−6.52585	−0.224496
$846$	133.213	4.57995
$847$	−3.48262	−0.119664
$848$	4.48902	0.154154
$849$	13.2980	0.456386
$850$	−5.30986	−0.182127
$851$	3.54653	0.121573
$852$	62.9600	2.15697
$853$	−5.66746	−0.194050	−0.0970251	−	0.995282i	$-0.530933\pi$
$853$	−5.66746	−0.194050	−0.0970251	+	0.995282i	$0.530933\pi$
$854$	−11.9099	−0.407547
$855$	3.40274	0.116371
$856$	21.6268	0.739190
$857$	−36.0279	−1.23069	−0.615345	−	0.788258i	$-0.710983\pi$
$857$	−36.0279	−1.23069	−0.615345	+	0.788258i	$0.710983\pi$
$858$	−23.6300	−0.806715
$859$	−4.30629	−0.146929	−0.0734644	−	0.997298i	$-0.523406\pi$
$859$	−4.30629	−0.146929	−0.0734644	+	0.997298i	$0.523406\pi$
$860$	−19.7758	−0.674349
$861$	−34.4696	−1.17472
$862$	−82.0858	−2.79585
$863$	−0.628396	−0.0213908	−0.0106954	−	0.999943i	$-0.503405\pi$
$863$	−0.628396	−0.0213908	−0.0106954	+	0.999943i	$0.503405\pi$
$864$	−34.5583	−1.17570
$865$	6.59487	0.224232
$866$	−57.0088	−1.93724
$867$	−51.6227	−1.75320
$868$	−0.320741	−0.0108867
$869$	−2.64853	−0.0898453
$870$	−25.4831	−0.863958
$871$	3.16801	0.107344
$872$	37.0390	1.25430
$873$	24.4918	0.828923
$874$	18.4515	0.624130
$875$	5.00708	0.169270
$876$	−151.666	−5.12433
$877$	−26.5056	−0.895029	−0.447515	−	0.894277i	$-0.647691\pi$
$877$	−26.5056	−0.895029	−0.447515	+	0.894277i	$0.647691\pi$
$878$	96.6112	3.26047
$879$	15.9021	0.536366
$880$	−11.9069	−0.401381
$881$	−20.9908	−0.707198	−0.353599	−	0.935397i	$-0.615042\pi$
$881$	−20.9908	−0.707198	−0.353599	+	0.935397i	$0.615042\pi$
$882$	97.8370	3.29434
$883$	−7.96317	−0.267982	−0.133991	−	0.990983i	$-0.542779\pi$
$883$	−7.96317	−0.267982	−0.133991	+	0.990983i	$0.542779\pi$
$884$	1.54674	0.0520226
$885$	5.30643	0.178374
$886$	24.8723	0.835601
$887$	−8.33341	−0.279809	−0.139904	−	0.990165i	$-0.544679\pi$
$887$	−8.33341	−0.279809	−0.139904	+	0.990165i	$0.544679\pi$
$888$	8.57072	0.287615
$889$	8.90142	0.298544
$890$	−13.4844	−0.451998
$891$	−50.3146	−1.68560
$892$	−80.7864	−2.70493
$893$	−8.23605	−0.275609
$894$	−17.4631	−0.584052
$895$	4.75259	0.158862
$896$	−15.2135	−0.508246
$897$	18.1235	0.605125
$898$	84.4236	2.81725
$899$	0.478099	0.0159455
$900$	−130.866	−4.36219
$901$	−0.340521	−0.0113444
$902$	110.222	3.67001
$903$	26.0813	0.867930
$904$	85.6354	2.84819
$905$	−4.16989	−0.138612
$906$	−99.8035	−3.31575
$907$	30.6186	1.01667	0.508337	−	0.861158i	$-0.330260\pi$
$907$	30.6186	1.01667	0.508337	+	0.861158i	$0.330260\pi$
$908$	−53.6905	−1.78178
$909$	−29.1153	−0.965694
$910$	−1.03762	−0.0343969
$911$	31.2272	1.03460	0.517302	−	0.855803i	$-0.326937\pi$
$911$	31.2272	1.03460	0.517302	+	0.855803i	$0.326937\pi$
$912$	18.1488	0.600965
$913$	−13.1555	−0.435383
$914$	−70.2918	−2.32505
$915$	−7.89485	−0.260996
$916$	−59.0134	−1.94986
$917$	−3.73046	−0.123191
$918$	11.8988	0.392718
$919$	−2.10731	−0.0695136	−0.0347568	−	0.999396i	$-0.511066\pi$
$919$	−2.10731	−0.0695136	−0.0347568	+	0.999396i	$0.511066\pi$
$920$	22.4374	0.739740
$921$	74.1383	2.44294
$922$	−12.1465	−0.400025
$923$	−3.82134	−0.125781
$924$	49.2179	1.61915
$925$	2.27807	0.0749024
$926$	−13.8318	−0.454542
$927$	30.2190	0.992521
$928$	−20.4308	−0.670674
$929$	−10.0729	−0.330483	−0.165241	−	0.986253i	$-0.552840\pi$
$929$	−10.0729	−0.330483	−0.165241	+	0.986253i	$0.552840\pi$
$930$	−0.311448	−0.0102128
$931$	−6.04889	−0.198244
$932$	−115.138	−3.77148
$933$	55.8255	1.82765
$934$	40.6397	1.32977
$935$	0.903213	0.0295382
$936$	29.8833	0.976766
$937$	12.3205	0.402492	0.201246	−	0.979541i	$-0.435501\pi$
$937$	12.3205	0.402492	0.201246	+	0.979541i	$0.435501\pi$
$938$	−9.66584	−0.315601
$939$	65.1466	2.12598
$940$	−18.7150	−0.610415
$941$	33.7869	1.10142	0.550711	−	0.834696i	$-0.314357\pi$
$941$	33.7869	1.10142	0.550711	+	0.834696i	$0.314357\pi$
$942$	60.2042	1.96156
$943$	−84.5371	−2.75291
$944$	19.3105	0.628503
$945$	−5.44916	−0.177261
$946$	−83.3994	−2.71155
$947$	−45.2016	−1.46885	−0.734427	−	0.678688i	$-0.762549\pi$
$947$	−45.2016	−1.46885	−0.734427	+	0.678688i	$0.762549\pi$
$948$	9.17327	0.297934
$949$	9.20535	0.298818
$950$	11.8520	0.384531
$951$	3.07291	0.0996459
$952$	−2.52548	−0.0818514
$953$	−1.15814	−0.0375159	−0.0187579	−	0.999824i	$-0.505971\pi$
$953$	−1.15814	−0.0375159	−0.0187579	+	0.999824i	$0.505971\pi$
$954$	−12.2937	−0.398022
$955$	−0.806275	−0.0260904
$956$	71.8169	2.32273
$957$	−73.3646	−2.37154
$958$	−35.7923	−1.15640
$959$	9.42251	0.304269
$960$	−5.86123	−0.189170
$961$	−30.9942	−0.999812
$962$	−0.972066	−0.0313407
$963$	−24.1060	−0.776806
$964$	−58.2339	−1.87559
$965$	−2.03704	−0.0655745
$966$	−55.2962	−1.77913
$967$	14.1460	0.454904	0.227452	−	0.973789i	$-0.426960\pi$
$967$	14.1460	0.454904	0.227452	+	0.973789i	$0.426960\pi$
$968$	−20.6410	−0.663428
$969$	−1.37670	−0.0442260
$970$	−5.04033	−0.161835
$971$	−9.72324	−0.312034	−0.156017	−	0.987754i	$-0.549865\pi$
$971$	−9.72324	−0.312034	−0.156017	+	0.987754i	$0.549865\pi$
$972$	37.7155	1.20973
$973$	2.03903	0.0653684
$974$	15.6994	0.503040
$975$	11.6414	0.372822
$976$	−28.7299	−0.919623
$977$	56.4277	1.80528	0.902640	−	0.430396i	$-0.141626\pi$
$977$	56.4277	1.80528	0.902640	+	0.430396i	$0.141626\pi$
$978$	13.0064	0.415900
$979$	−38.8209	−1.24072
$980$	−13.7450	−0.439069
$981$	−41.2849	−1.31813
$982$	−64.7958	−2.06772
$983$	18.1756	0.579711	0.289856	−	0.957070i	$-0.406393\pi$
$983$	18.1756	0.579711	0.289856	+	0.957070i	$0.406393\pi$
$984$	−204.297	−6.51274
$985$	−4.76739	−0.151902
$986$	7.03454	0.224025
$987$	24.6822	0.785642
$988$	−3.45246	−0.109837
$989$	63.9647	2.03396
$990$	32.6083	1.03636
$991$	−58.3138	−1.85240	−0.926200	−	0.377033i	$-0.876944\pi$
$991$	−58.3138	−1.85240	−0.926200	+	0.377033i	$0.876944\pi$
$992$	−0.249700	−0.00792799
$993$	53.1285	1.68598
$994$	11.6592	0.369808
$995$	−4.71068	−0.149339
$996$	45.5644	1.44376
$997$	−59.4040	−1.88134	−0.940672	−	0.339317i	$-0.889804\pi$
$997$	−59.4040	−1.88134	−0.940672	+	0.339317i	$0.889804\pi$
$998$	95.0548	3.00891
$999$	−5.10488	−0.161511

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.a.1.9	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.a.1.9	✓	98	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.51046 q^{2} +3.07291 q^{3} +4.30243 q^{4} +0.528149 q^{5} -7.71443 q^{6} -0.975247 q^{7} -5.78017 q^{8} +6.44278 q^{9} +O(q^{10})\)	\(q-2.51046 q^{2} +3.07291 q^{3} +4.30243 q^{4} +0.528149 q^{5} -7.71443 q^{6} -0.975247 q^{7} -5.78017 q^{8} +6.44278 q^{9} -1.32590 q^{10} -3.81720 q^{11} +13.2210 q^{12} -0.802444 q^{13} +2.44832 q^{14} +1.62295 q^{15} +5.90605 q^{16} -0.448012 q^{17} -16.1744 q^{18} +1.00000 q^{19} +2.27232 q^{20} -2.99685 q^{21} +9.58294 q^{22} -7.34982 q^{23} -17.7619 q^{24} -4.72106 q^{25} +2.01451 q^{26} +10.5793 q^{27} -4.19593 q^{28} +6.25449 q^{29} -4.07437 q^{30} +0.0764409 q^{31} -3.26658 q^{32} -11.7299 q^{33} +1.12472 q^{34} -0.515075 q^{35} +27.7196 q^{36} -0.482533 q^{37} -2.51046 q^{38} -2.46584 q^{39} -3.05279 q^{40} +11.5019 q^{41} +7.52348 q^{42} -8.70290 q^{43} -16.4232 q^{44} +3.40274 q^{45} +18.4515 q^{46} -8.23605 q^{47} +18.1488 q^{48} -6.04889 q^{49} +11.8520 q^{50} -1.37670 q^{51} -3.45246 q^{52} +0.760072 q^{53} -26.5591 q^{54} -2.01605 q^{55} +5.63709 q^{56} +3.07291 q^{57} -15.7017 q^{58} +3.26961 q^{59} +6.98264 q^{60} -4.86450 q^{61} -0.191902 q^{62} -6.28330 q^{63} -3.61146 q^{64} -0.423810 q^{65} +29.4475 q^{66} -3.94794 q^{67} -1.92754 q^{68} -22.5853 q^{69} +1.29308 q^{70} +4.76213 q^{71} -37.2403 q^{72} -11.4716 q^{73} +1.21138 q^{74} -14.5074 q^{75} +4.30243 q^{76} +3.72271 q^{77} +6.19040 q^{78} +0.693842 q^{79} +3.11927 q^{80} +13.1810 q^{81} -28.8752 q^{82} +3.44637 q^{83} -12.8937 q^{84} -0.236617 q^{85} +21.8483 q^{86} +19.2195 q^{87} +22.0641 q^{88} +10.1700 q^{89} -8.54246 q^{90} +0.782582 q^{91} -31.6221 q^{92} +0.234896 q^{93} +20.6763 q^{94} +0.528149 q^{95} -10.0379 q^{96} +3.80144 q^{97} +15.1855 q^{98} -24.5934 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9}+O(q^{10}) \) 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9	\( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9} - 24 q^{10} - 12 q^{11} - 51 q^{12} - 58 q^{13} - 15 q^{14} - 18 q^{15} + 58 q^{16} - 25 q^{17} - 40 q^{18} + 98 q^{19} - 12 q^{20} - 24 q^{21} - 59 q^{22} - 38 q^{23} - 9 q^{24} - 12 q^{25} - 3 q^{26} - 85 q^{27} - 33 q^{28} - 24 q^{29} - 22 q^{30} - 56 q^{31} - 29 q^{32} - 51 q^{33} - 38 q^{34} - 10 q^{35} + 50 q^{36} - 124 q^{37} - 8 q^{38} - 4 q^{39} - 80 q^{40} - 28 q^{41} - 37 q^{42} - 63 q^{43} - 7 q^{44} - 32 q^{45} - 47 q^{46} - 10 q^{47} - 88 q^{48} + 6 q^{49} - 17 q^{50} - 22 q^{51} - 119 q^{52} - 65 q^{53} + 24 q^{54} - 30 q^{55} - 39 q^{56} - 25 q^{57} - 91 q^{58} - 26 q^{59} - 60 q^{60} - 60 q^{61} + 6 q^{62} - 26 q^{63} + 50 q^{64} - 40 q^{65} + 57 q^{66} - 108 q^{67} - 41 q^{68} - 15 q^{69} - 36 q^{70} - 19 q^{71} - 47 q^{72} - 136 q^{73} + 22 q^{74} - 48 q^{75} + 82 q^{76} - 35 q^{77} - 56 q^{78} - 98 q^{79} - 42 q^{80} + 6 q^{81} - 37 q^{82} - 31 q^{83} - 24 q^{84} - 71 q^{85} - 24 q^{86} + 7 q^{87} - 166 q^{88} - 38 q^{89} + 26 q^{90} - 100 q^{91} - 59 q^{92} - 21 q^{93} - 48 q^{94} - 10 q^{95} - 16 q^{96} - 190 q^{97} - 80 q^{98} - 17 q^{99}+O(q^{100}) \) 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9 - 24 * q^10 - 12 * q^11 - 51 * q^12 - 58 * q^13 - 15 * q^14 - 18 * q^15 + 58 * q^16 - 25 * q^17 - 40 * q^18 + 98 * q^19 - 12 * q^20 - 24 * q^21 - 59 * q^22 - 38 * q^23 - 9 * q^24 - 12 * q^25 - 3 * q^26 - 85 * q^27 - 33 * q^28 - 24 * q^29 - 22 * q^30 - 56 * q^31 - 29 * q^32 - 51 * q^33 - 38 * q^34 - 10 * q^35 + 50 * q^36 - 124 * q^37 - 8 * q^38 - 4 * q^39 - 80 * q^40 - 28 * q^41 - 37 * q^42 - 63 * q^43 - 7 * q^44 - 32 * q^45 - 47 * q^46 - 10 * q^47 - 88 * q^48 + 6 * q^49 - 17 * q^50 - 22 * q^51 - 119 * q^52 - 65 * q^53 + 24 * q^54 - 30 * q^55 - 39 * q^56 - 25 * q^57 - 91 * q^58 - 26 * q^59 - 60 * q^60 - 60 * q^61 + 6 * q^62 - 26 * q^63 + 50 * q^64 - 40 * q^65 + 57 * q^66 - 108 * q^67 - 41 * q^68 - 15 * q^69 - 36 * q^70 - 19 * q^71 - 47 * q^72 - 136 * q^73 + 22 * q^74 - 48 * q^75 + 82 * q^76 - 35 * q^77 - 56 * q^78 - 98 * q^79 - 42 * q^80 + 6 * q^81 - 37 * q^82 - 31 * q^83 - 24 * q^84 - 71 * q^85 - 24 * q^86 + 7 * q^87 - 166 * q^88 - 38 * q^89 + 26 * q^90 - 100 * q^91 - 59 * q^92 - 21 * q^93 - 48 * q^94 - 10 * q^95 - 16 * q^96 - 190 * q^97 - 80 * q^98 - 17 * q^99

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