LMFDB - Embedded newform 8021.2.a.a.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, 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("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.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:	$64.0480074613$
Analytic rank:	$1$
Dimension:	$134$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.45973 q^{2} -2.31536 q^{3} +4.05029 q^{4} -2.20524 q^{5} +5.69516 q^{6} -0.890619 q^{7} -5.04316 q^{8} +2.36088 q^{9} +O(q^{10})$	\(q-2.45973 q^{2} -2.31536 q^{3} +4.05029 q^{4} -2.20524 q^{5} +5.69516 q^{6} -0.890619 q^{7} -5.04316 q^{8} +2.36088 q^{9} +5.42429 q^{10} -1.81246 q^{11} -9.37786 q^{12} +1.00000 q^{13} +2.19069 q^{14} +5.10591 q^{15} +4.30426 q^{16} -2.96099 q^{17} -5.80714 q^{18} -7.45390 q^{19} -8.93184 q^{20} +2.06210 q^{21} +4.45818 q^{22} -8.54775 q^{23} +11.6767 q^{24} -0.136930 q^{25} -2.45973 q^{26} +1.47979 q^{27} -3.60726 q^{28} +10.0296 q^{29} -12.5592 q^{30} -7.75715 q^{31} -0.500998 q^{32} +4.19650 q^{33} +7.28324 q^{34} +1.96403 q^{35} +9.56225 q^{36} +7.12117 q^{37} +18.3346 q^{38} -2.31536 q^{39} +11.1214 q^{40} +1.41132 q^{41} -5.07222 q^{42} +4.26646 q^{43} -7.34100 q^{44} -5.20630 q^{45} +21.0252 q^{46} +8.74552 q^{47} -9.96589 q^{48} -6.20680 q^{49} +0.336812 q^{50} +6.85575 q^{51} +4.05029 q^{52} +2.66520 q^{53} -3.63989 q^{54} +3.99691 q^{55} +4.49153 q^{56} +17.2585 q^{57} -24.6702 q^{58} -4.22538 q^{59} +20.6804 q^{60} -15.1537 q^{61} +19.0805 q^{62} -2.10265 q^{63} -7.37619 q^{64} -2.20524 q^{65} -10.3223 q^{66} -12.7596 q^{67} -11.9929 q^{68} +19.7911 q^{69} -4.83098 q^{70} +15.0852 q^{71} -11.9063 q^{72} +9.95574 q^{73} -17.5162 q^{74} +0.317043 q^{75} -30.1905 q^{76} +1.61421 q^{77} +5.69516 q^{78} -6.85303 q^{79} -9.49190 q^{80} -10.5089 q^{81} -3.47147 q^{82} -5.19063 q^{83} +8.35210 q^{84} +6.52968 q^{85} -10.4943 q^{86} -23.2221 q^{87} +9.14055 q^{88} +9.77411 q^{89} +12.8061 q^{90} -0.890619 q^{91} -34.6209 q^{92} +17.9606 q^{93} -21.5116 q^{94} +16.4376 q^{95} +1.15999 q^{96} +1.22167 q^{97} +15.2671 q^{98} -4.27901 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) $ 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9} - 33 q^{10} - 47 q^{11} - 53 q^{12} + 134 q^{13} - 28 q^{14} - 30 q^{15} + 30 q^{16} - 17 q^{17} - 14 q^{18} - 87 q^{19} - 12 q^{20} - 24 q^{21} - 52 q^{22} - 44 q^{23} - 36 q^{24} + 58 q^{25} - 6 q^{26} - 117 q^{27} - 71 q^{28} - 42 q^{29} - 21 q^{30} - 82 q^{31} - 31 q^{32} + 12 q^{33} - 30 q^{34} - 54 q^{35} + 32 q^{36} - 55 q^{37} - 12 q^{38} - 33 q^{39} - 86 q^{40} - 16 q^{41} + 6 q^{42} - 148 q^{43} - 54 q^{44} - 24 q^{45} - 57 q^{46} - 21 q^{47} - 82 q^{48} + 12 q^{49} - 17 q^{50} - 123 q^{51} + 98 q^{52} - 17 q^{53} - 10 q^{54} - 148 q^{55} - 47 q^{56} - q^{57} - 58 q^{58} - 64 q^{59} - 16 q^{60} - 112 q^{61} - 15 q^{62} - 58 q^{63} - 65 q^{64} - 8 q^{65} - 20 q^{66} - 110 q^{67} - 8 q^{68} - 57 q^{69} - 40 q^{70} - 78 q^{71} - 28 q^{72} - 43 q^{73} - 52 q^{74} - 150 q^{75} - 96 q^{76} - 24 q^{77} - 16 q^{78} - 228 q^{79} + 20 q^{80} + 54 q^{81} - 89 q^{82} - 12 q^{83} + 6 q^{84} - 77 q^{85} + 29 q^{86} - 77 q^{87} - 95 q^{88} - 32 q^{89} - 46 q^{90} - 32 q^{91} - 62 q^{92} - 9 q^{93} - 87 q^{94} - 61 q^{95} - 54 q^{96} - 38 q^{97} + 6 q^{98} - 193 q^{99}+O(q^{100}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9 - 33 * q^10 - 47 * q^11 - 53 * q^12 + 134 * q^13 - 28 * q^14 - 30 * q^15 + 30 * q^16 - 17 * q^17 - 14 * q^18 - 87 * q^19 - 12 * q^20 - 24 * q^21 - 52 * q^22 - 44 * q^23 - 36 * q^24 + 58 * q^25 - 6 * q^26 - 117 * q^27 - 71 * q^28 - 42 * q^29 - 21 * q^30 - 82 * q^31 - 31 * q^32 + 12 * q^33 - 30 * q^34 - 54 * q^35 + 32 * q^36 - 55 * q^37 - 12 * q^38 - 33 * q^39 - 86 * q^40 - 16 * q^41 + 6 * q^42 - 148 * q^43 - 54 * q^44 - 24 * q^45 - 57 * q^46 - 21 * q^47 - 82 * q^48 + 12 * q^49 - 17 * q^50 - 123 * q^51 + 98 * q^52 - 17 * q^53 - 10 * q^54 - 148 * q^55 - 47 * q^56 - q^57 - 58 * q^58 - 64 * q^59 - 16 * q^60 - 112 * q^61 - 15 * q^62 - 58 * q^63 - 65 * q^64 - 8 * q^65 - 20 * q^66 - 110 * q^67 - 8 * q^68 - 57 * q^69 - 40 * q^70 - 78 * q^71 - 28 * q^72 - 43 * q^73 - 52 * q^74 - 150 * q^75 - 96 * q^76 - 24 * q^77 - 16 * q^78 - 228 * q^79 + 20 * q^80 + 54 * q^81 - 89 * q^82 - 12 * q^83 + 6 * q^84 - 77 * q^85 + 29 * q^86 - 77 * q^87 - 95 * q^88 - 32 * q^89 - 46 * q^90 - 32 * q^91 - 62 * q^92 - 9 * q^93 - 87 * q^94 - 61 * q^95 - 54 * q^96 - 38 * q^97 + 6 * q^98 - 193 * 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 $

$2$	−2.45973	−1.73929	−0.869647	−	0.493674i	$-0.835654\pi$
$2$	−2.45973	−1.73929	−0.869647	+	0.493674i	$0.835654\pi$
$3$	−2.31536	−1.33677	−0.668386	−	0.743814i	$-0.733015\pi$
$3$	−2.31536	−1.33677	−0.668386	+	0.743814i	$0.733015\pi$
$4$	4.05029	2.02514
$5$	−2.20524	−0.986212	−0.493106	−	0.869969i	$-0.664139\pi$
$5$	−2.20524	−0.986212	−0.493106	+	0.869969i	$0.664139\pi$
$6$	5.69516	2.32504
$7$	−0.890619	−0.336622	−0.168311	−	0.985734i	$-0.553831\pi$
$7$	−0.890619	−0.336622	−0.168311	+	0.985734i	$0.553831\pi$
$8$	−5.04316	−1.78303
$9$	2.36088	0.786960
$10$	5.42429	1.71531
$11$	−1.81246	−0.546478	−0.273239	−	0.961946i	$-0.588095\pi$
$11$	−1.81246	−0.546478	−0.273239	+	0.961946i	$0.588095\pi$
$12$	−9.37786	−2.70716
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	2.19069	0.585485
$15$	5.10591	1.31834
$16$	4.30426	1.07606
$17$	−2.96099	−0.718145	−0.359073	−	0.933310i	$-0.616907\pi$
$17$	−2.96099	−0.718145	−0.359073	+	0.933310i	$0.616907\pi$
$18$	−5.80714	−1.36876
$19$	−7.45390	−1.71004	−0.855021	−	0.518593i	$-0.826456\pi$
$19$	−7.45390	−1.71004	−0.855021	+	0.518593i	$0.826456\pi$
$20$	−8.93184	−1.99722
$21$	2.06210	0.449987
$22$	4.45818	0.950487
$23$	−8.54775	−1.78233	−0.891165	−	0.453679i	$-0.850111\pi$
$23$	−8.54775	−1.78233	−0.891165	+	0.453679i	$0.850111\pi$
$24$	11.6767	2.38350
$25$	−0.136930	−0.0273861
$26$	−2.45973	−0.482393
$27$	1.47979	0.284786
$28$	−3.60726	−0.681709
$29$	10.0296	1.86245	0.931226	−	0.364443i	$-0.118741\pi$
$29$	10.0296	1.86245	0.931226	+	0.364443i	$0.118741\pi$
$30$	−12.5592	−2.29298
$31$	−7.75715	−1.39322	−0.696612	−	0.717448i	$-0.745310\pi$
$31$	−7.75715	−1.39322	−0.696612	+	0.717448i	$0.745310\pi$
$32$	−0.500998	−0.0885647
$33$	4.19650	0.730517
$34$	7.28324	1.24907
$35$	1.96403	0.331981
$36$	9.56225	1.59371
$37$	7.12117	1.17071	0.585356	−	0.810776i	$-0.300955\pi$
$37$	7.12117	1.17071	0.585356	+	0.810776i	$0.300955\pi$
$38$	18.3346	2.97427
$39$	−2.31536	−0.370754
$40$	11.1214	1.75844
$41$	1.41132	0.220411	0.110206	−	0.993909i	$-0.464849\pi$
$41$	1.41132	0.220411	0.110206	+	0.993909i	$0.464849\pi$
$42$	−5.07222	−0.782660
$43$	4.26646	0.650628	0.325314	−	0.945606i	$-0.394530\pi$
$43$	4.26646	0.650628	0.325314	+	0.945606i	$0.394530\pi$
$44$	−7.34100	−1.10670
$45$	−5.20630	−0.776110
$46$	21.0252	3.10000
$47$	8.74552	1.27566	0.637832	−	0.770175i	$-0.279831\pi$
$47$	8.74552	1.27566	0.637832	+	0.770175i	$0.279831\pi$
$48$	−9.96589	−1.43845
$49$	−6.20680	−0.886685
$50$	0.336812	0.0476324
$51$	6.85575	0.959997
$52$	4.05029	0.561674
$53$	2.66520	0.366093	0.183047	−	0.983104i	$-0.441404\pi$
$53$	2.66520	0.366093	0.183047	+	0.983104i	$0.441404\pi$
$54$	−3.63989	−0.495326
$55$	3.99691	0.538943
$56$	4.49153	0.600207
$57$	17.2585	2.28594
$58$	−24.6702	−3.23935
$59$	−4.22538	−0.550097	−0.275049	−	0.961430i	$-0.588694\pi$
$59$	−4.22538	−0.550097	−0.275049	+	0.961430i	$0.588694\pi$
$60$	20.6804	2.66983
$61$	−15.1537	−1.94023	−0.970117	−	0.242636i	$-0.921988\pi$
$61$	−15.1537	−1.94023	−0.970117	+	0.242636i	$0.921988\pi$
$62$	19.0805	2.42323
$63$	−2.10265	−0.264908
$64$	−7.37619	−0.922024
$65$	−2.20524	−0.273526
$66$	−10.3223	−1.27058
$67$	−12.7596	−1.55883	−0.779415	−	0.626508i	$-0.784483\pi$
$67$	−12.7596	−1.55883	−0.779415	+	0.626508i	$0.784483\pi$
$68$	−11.9929	−1.45435
$69$	19.7911	2.38257
$70$	−4.83098	−0.577413
$71$	15.0852	1.79028	0.895142	−	0.445781i	$-0.147074\pi$
$71$	15.0852	1.79028	0.895142	+	0.445781i	$0.147074\pi$
$72$	−11.9063	−1.40317
$73$	9.95574	1.16523	0.582616	−	0.812748i	$-0.302029\pi$
$73$	9.95574	1.16523	0.582616	+	0.812748i	$0.302029\pi$
$74$	−17.5162	−2.03621
$75$	0.317043	0.0366089
$76$	−30.1905	−3.46308
$77$	1.61421	0.183957
$78$	5.69516	0.644850
$79$	−6.85303	−0.771027	−0.385513	−	0.922702i	$-0.625976\pi$
$79$	−6.85303	−0.771027	−0.385513	+	0.922702i	$0.625976\pi$
$80$	−9.49190	−1.06123
$81$	−10.5089	−1.16765
$82$	−3.47147	−0.383360
$83$	−5.19063	−0.569745	−0.284873	−	0.958565i	$-0.591951\pi$
$83$	−5.19063	−0.569745	−0.284873	+	0.958565i	$0.591951\pi$
$84$	8.35210	0.911289
$85$	6.52968	0.708243
$86$	−10.4943	−1.13163
$87$	−23.2221	−2.48967
$88$	9.14055	0.974385
$89$	9.77411	1.03605	0.518027	−	0.855365i	$-0.326667\pi$
$89$	9.77411	1.03605	0.518027	+	0.855365i	$0.326667\pi$
$90$	12.8061	1.34988
$91$	−0.890619	−0.0933622
$92$	−34.6209	−3.60947
$93$	17.9606	1.86242
$94$	−21.5116	−2.21876
$95$	16.4376	1.68646
$96$	1.15999	0.118391
$97$	1.22167	0.124041	0.0620206	−	0.998075i	$-0.480246\pi$
$97$	1.22167	0.124041	0.0620206	+	0.998075i	$0.480246\pi$
$98$	15.2671	1.54221
$99$	−4.27901	−0.430057
$100$	−0.554607	−0.0554607
$101$	17.0169	1.69325	0.846625	−	0.532190i	$-0.178631\pi$
$101$	17.0169	1.69325	0.846625	+	0.532190i	$0.178631\pi$
$102$	−16.8633	−1.66972
$103$	−12.2122	−1.20331	−0.601653	−	0.798758i	$-0.705491\pi$
$103$	−12.2122	−1.20331	−0.601653	+	0.798758i	$0.705491\pi$
$104$	−5.04316	−0.494523
$105$	−4.54742	−0.443783
$106$	−6.55568	−0.636744
$107$	−6.94824	−0.671712	−0.335856	−	0.941913i	$-0.609025\pi$
$107$	−6.94824	−0.671712	−0.335856	+	0.941913i	$0.609025\pi$
$108$	5.99358	0.576732
$109$	−3.21713	−0.308145	−0.154073	−	0.988060i	$-0.549239\pi$
$109$	−3.21713	−0.308145	−0.154073	+	0.988060i	$0.549239\pi$
$110$	−9.83134	−0.937381
$111$	−16.4880	−1.56498
$112$	−3.83345	−0.362227
$113$	−10.1700	−0.956714	−0.478357	−	0.878165i	$-0.658768\pi$
$113$	−10.1700	−0.956714	−0.478357	+	0.878165i	$0.658768\pi$
$114$	−42.4512	−3.97592
$115$	18.8498	1.75776
$116$	40.6228	3.77173
$117$	2.36088	0.218263
$118$	10.3933	0.956781
$119$	2.63711	0.241744
$120$	−25.7499	−2.35064
$121$	−7.71498	−0.701361
$122$	37.2741	3.37464
$123$	−3.26771	−0.294639
$124$	−31.4187	−2.82148
$125$	11.3281	1.01322
$126$	5.17195	0.460754
$127$	−3.24902	−0.288304	−0.144152	−	0.989556i	$-0.546045\pi$
$127$	−3.24902	−0.288304	−0.144152	+	0.989556i	$0.546045\pi$
$128$	19.1455	1.69224
$129$	−9.87837	−0.869742
$130$	5.42429	0.475742
$131$	0.584395	0.0510588	0.0255294	−	0.999674i	$-0.491873\pi$
$131$	0.584395	0.0510588	0.0255294	+	0.999674i	$0.491873\pi$
$132$	16.9970	1.47940
$133$	6.63859	0.575639
$134$	31.3851	2.71126
$135$	−3.26329	−0.280859
$136$	14.9327	1.28047
$137$	18.6969	1.59739	0.798693	−	0.601739i	$-0.205525\pi$
$137$	18.6969	1.59739	0.798693	+	0.601739i	$0.205525\pi$
$138$	−48.6808	−4.14399
$139$	10.6147	0.900330	0.450165	−	0.892945i	$-0.351365\pi$
$139$	10.6147	0.900330	0.450165	+	0.892945i	$0.351365\pi$
$140$	7.95487	0.672309
$141$	−20.2490	−1.70527
$142$	−37.1056	−3.11383
$143$	−1.81246	−0.151566
$144$	10.1618	0.846819
$145$	−22.1177	−1.83677
$146$	−24.4885	−2.02668
$147$	14.3710	1.18530
$148$	28.8428	2.37086
$149$	7.38236	0.604787	0.302393	−	0.953183i	$-0.402214\pi$
$149$	7.38236	0.604787	0.302393	+	0.953183i	$0.402214\pi$
$150$	−0.779841	−0.0636737
$151$	−2.15205	−0.175131	−0.0875655	−	0.996159i	$-0.527909\pi$
$151$	−2.15205	−0.175131	−0.0875655	+	0.996159i	$0.527909\pi$
$152$	37.5912	3.04905
$153$	−6.99054	−0.565152
$154$	−3.97054	−0.319955
$155$	17.1063	1.37401
$156$	−9.37786	−0.750830
$157$	15.1555	1.20954	0.604771	−	0.796399i	$-0.293264\pi$
$157$	15.1555	1.20954	0.604771	+	0.796399i	$0.293264\pi$
$158$	16.8566	1.34104
$159$	−6.17089	−0.489383
$160$	1.10482	0.0873436
$161$	7.61279	0.599972
$162$	25.8491	2.03089
$163$	17.5376	1.37365	0.686824	−	0.726824i	$-0.259004\pi$
$163$	17.5376	1.37365	0.686824	+	0.726824i	$0.259004\pi$
$164$	5.71625	0.446364
$165$	−9.25428	−0.720445
$166$	12.7676	0.990955
$167$	−11.8794	−0.919254	−0.459627	−	0.888112i	$-0.652017\pi$
$167$	−11.8794	−0.919254	−0.459627	+	0.888112i	$0.652017\pi$
$168$	−10.3995	−0.802340
$169$	1.00000	0.0769231
$170$	−16.0613	−1.23184
$171$	−17.5978	−1.34574
$172$	17.2804	1.31762
$173$	5.65748	0.430130	0.215065	−	0.976600i	$-0.431004\pi$
$173$	5.65748	0.430130	0.215065	+	0.976600i	$0.431004\pi$
$174$	57.1202	4.33027
$175$	0.121953	0.00921877
$176$	−7.80131	−0.588046
$177$	9.78326	0.735355
$178$	−24.0417	−1.80200
$179$	−18.0100	−1.34613	−0.673065	−	0.739583i	$-0.735023\pi$
$179$	−18.0100	−1.34613	−0.673065	+	0.739583i	$0.735023\pi$
$180$	−21.0870	−1.57173
$181$	−9.24275	−0.687008	−0.343504	−	0.939151i	$-0.611614\pi$
$181$	−9.24275	−0.687008	−0.343504	+	0.939151i	$0.611614\pi$
$182$	2.19069	0.162384
$183$	35.0863	2.59365
$184$	43.1077	3.17794
$185$	−15.7039	−1.15457
$186$	−44.1782	−3.23930
$187$	5.36668	0.392451
$188$	35.4219	2.58340
$189$	−1.31793	−0.0958652
$190$	−40.4322	−2.93326
$191$	7.75719	0.561291	0.280645	−	0.959812i	$-0.409451\pi$
$191$	7.75719	0.561291	0.280645	+	0.959812i	$0.409451\pi$
$192$	17.0785	1.23254
$193$	2.77310	0.199612	0.0998060	−	0.995007i	$-0.468178\pi$
$193$	2.77310	0.199612	0.0998060	+	0.995007i	$0.468178\pi$
$194$	−3.00497	−0.215744
$195$	5.10591	0.365642
$196$	−25.1393	−1.79567
$197$	26.4317	1.88318	0.941590	−	0.336762i	$-0.109332\pi$
$197$	26.4317	1.88318	0.941590	+	0.336762i	$0.109332\pi$
$198$	10.5252	0.747995
$199$	7.12132	0.504817	0.252409	−	0.967621i	$-0.418777\pi$
$199$	7.12132	0.504817	0.252409	+	0.967621i	$0.418777\pi$
$200$	0.690562	0.0488301
$201$	29.5430	2.08380
$202$	−41.8571	−2.94506
$203$	−8.93256	−0.626943
$204$	27.7677	1.94413
$205$	−3.11229	−0.217372
$206$	30.0388	2.09290
$207$	−20.1802	−1.40262
$208$	4.30426	0.298446
$209$	13.5099	0.934501
$210$	11.1854	0.771869
$211$	−8.40753	−0.578798	−0.289399	−	0.957209i	$-0.593455\pi$
$211$	−8.40753	−0.578798	−0.289399	+	0.957209i	$0.593455\pi$
$212$	10.7948	0.741392
$213$	−34.9276	−2.39320
$214$	17.0908	1.16830
$215$	−9.40855	−0.641657
$216$	−7.46282	−0.507781
$217$	6.90866	0.468990
$218$	7.91329	0.535955
$219$	−23.0511	−1.55765
$220$	16.1886	1.09144
$221$	−2.96099	−0.199178
$222$	40.5562	2.72195
$223$	20.2523	1.35619	0.678096	−	0.734974i	$-0.262805\pi$
$223$	20.2523	1.35619	0.678096	+	0.734974i	$0.262805\pi$
$224$	0.446198	0.0298129
$225$	−0.323276	−0.0215518
$226$	25.0155	1.66401
$227$	15.2853	1.01452	0.507261	−	0.861792i	$-0.330658\pi$
$227$	15.2853	1.01452	0.507261	+	0.861792i	$0.330658\pi$
$228$	69.9017	4.62935
$229$	−8.46059	−0.559092	−0.279546	−	0.960132i	$-0.590184\pi$
$229$	−8.46059	−0.559092	−0.279546	+	0.960132i	$0.590184\pi$
$230$	−46.3655	−3.05725
$231$	−3.73748	−0.245908
$232$	−50.5809	−3.32080
$233$	−10.9903	−0.719997	−0.359999	−	0.932953i	$-0.617223\pi$
$233$	−10.9903	−0.719997	−0.359999	+	0.932953i	$0.617223\pi$
$234$	−5.80714	−0.379624
$235$	−19.2859	−1.25808
$236$	−17.1140	−1.11403
$237$	15.8672	1.03069
$238$	−6.48659	−0.420463
$239$	−28.6596	−1.85383	−0.926917	−	0.375267i	$-0.877551\pi$
$239$	−28.6596	−1.85383	−0.926917	+	0.375267i	$0.877551\pi$
$240$	21.9771	1.41862
$241$	29.7098	1.91378	0.956889	−	0.290452i	$-0.0938058\pi$
$241$	29.7098	1.91378	0.956889	+	0.290452i	$0.0938058\pi$
$242$	18.9768	1.21987
$243$	19.8925	1.27610
$244$	−61.3769	−3.92925
$245$	13.6875	0.874460
$246$	8.03769	0.512465
$247$	−7.45390	−0.474281
$248$	39.1205	2.48416
$249$	12.0182	0.761620
$250$	−27.8642	−1.76229
$251$	13.9902	0.883054	0.441527	−	0.897248i	$-0.354437\pi$
$251$	13.9902	0.883054	0.441527	+	0.897248i	$0.354437\pi$
$252$	−8.51632	−0.536478
$253$	15.4925	0.974005
$254$	7.99173	0.501446
$255$	−15.1185	−0.946760
$256$	−32.3403	−2.02127
$257$	−4.79895	−0.299350	−0.149675	−	0.988735i	$-0.547823\pi$
$257$	−4.79895	−0.299350	−0.149675	+	0.988735i	$0.547823\pi$
$258$	24.2982	1.51274
$259$	−6.34225	−0.394088
$260$	−8.93184	−0.553929
$261$	23.6787	1.46567
$262$	−1.43746	−0.0888063
$263$	−6.88841	−0.424758	−0.212379	−	0.977187i	$-0.568121\pi$
$263$	−6.88841	−0.424758	−0.212379	+	0.977187i	$0.568121\pi$
$264$	−21.1636	−1.30253
$265$	−5.87740	−0.361046
$266$	−16.3292	−1.00120
$267$	−22.6305	−1.38497
$268$	−51.6799	−3.15685
$269$	−2.83799	−0.173036	−0.0865178	−	0.996250i	$-0.527574\pi$
$269$	−2.83799	−0.173036	−0.0865178	+	0.996250i	$0.527574\pi$
$270$	8.02682	0.488497
$271$	14.8386	0.901384	0.450692	−	0.892680i	$-0.351177\pi$
$271$	14.8386	0.901384	0.450692	+	0.892680i	$0.351177\pi$
$272$	−12.7448	−0.772770
$273$	2.06210	0.124804
$274$	−45.9894	−2.77832
$275$	0.248181	0.0149659
$276$	80.1597	4.82505
$277$	−10.6353	−0.639012	−0.319506	−	0.947584i	$-0.603517\pi$
$277$	−10.6353	−0.639012	−0.319506	+	0.947584i	$0.603517\pi$
$278$	−26.1094	−1.56594
$279$	−18.3137	−1.09641
$280$	−9.90490	−0.591931
$281$	4.98660	0.297475	0.148738	−	0.988877i	$-0.452479\pi$
$281$	4.98660	0.297475	0.148738	+	0.988877i	$0.452479\pi$
$282$	49.8071	2.96597
$283$	6.45551	0.383740	0.191870	−	0.981420i	$-0.438545\pi$
$283$	6.45551	0.383740	0.191870	+	0.981420i	$0.438545\pi$
$284$	61.0994	3.62558
$285$	−38.0590	−2.25442
$286$	4.45818	0.263618
$287$	−1.25695	−0.0741953
$288$	−1.18280	−0.0696969
$289$	−8.23255	−0.484267
$290$	54.4035	3.19469
$291$	−2.82859	−0.165815
$292$	40.3236	2.35976
$293$	7.30332	0.426664	0.213332	−	0.976980i	$-0.431568\pi$
$293$	7.30332	0.426664	0.213332	+	0.976980i	$0.431568\pi$
$294$	−35.3487	−2.06158
$295$	9.31796	0.542513
$296$	−35.9132	−2.08741
$297$	−2.68207	−0.155629
$298$	−18.1586	−1.05190
$299$	−8.54775	−0.494329
$300$	1.28411	0.0741384
$301$	−3.79979	−0.219016
$302$	5.29346	0.304604
$303$	−39.4003	−2.26349
$304$	−32.0835	−1.84012
$305$	33.4175	1.91348
$306$	17.1949	0.982965
$307$	18.6079	1.06201	0.531005	−	0.847369i	$-0.321814\pi$
$307$	18.6079	1.06201	0.531005	+	0.847369i	$0.321814\pi$
$308$	6.53803	0.372539
$309$	28.2756	1.60855
$310$	−42.0770	−2.38982
$311$	11.9235	0.676122	0.338061	−	0.941124i	$-0.390229\pi$
$311$	11.9235	0.676122	0.338061	+	0.941124i	$0.390229\pi$
$312$	11.6767	0.661064
$313$	31.3740	1.77336	0.886681	−	0.462381i	$-0.153005\pi$
$313$	31.3740	1.77336	0.886681	+	0.462381i	$0.153005\pi$
$314$	−37.2786	−2.10375
$315$	4.63683	0.261256
$316$	−27.7568	−1.56144
$317$	−21.2251	−1.19212	−0.596059	−	0.802940i	$-0.703268\pi$
$317$	−21.2251	−1.19212	−0.596059	+	0.802940i	$0.703268\pi$
$318$	15.1787	0.851182
$319$	−18.1783	−1.01779
$320$	16.2662	0.909311
$321$	16.0877	0.897926
$322$	−18.7254	−1.04353
$323$	22.0709	1.22806
$324$	−42.5640	−2.36467
$325$	−0.136930	−0.00759553
$326$	−43.1377	−2.38918
$327$	7.44881	0.411920
$328$	−7.11751	−0.392999
$329$	−7.78892	−0.429417
$330$	22.7631	1.25307
$331$	8.37205	0.460170	0.230085	−	0.973171i	$-0.426100\pi$
$331$	8.37205	0.460170	0.230085	+	0.973171i	$0.426100\pi$
$332$	−21.0235	−1.15382
$333$	16.8122	0.921304
$334$	29.2201	1.59885
$335$	28.1379	1.53734
$336$	8.87581	0.484215
$337$	15.8145	0.861472	0.430736	−	0.902478i	$-0.358254\pi$
$337$	15.8145	0.861472	0.430736	+	0.902478i	$0.358254\pi$
$338$	−2.45973	−0.133792
$339$	23.5472	1.27891
$340$	26.4471	1.43429
$341$	14.0595	0.761367
$342$	43.2858	2.34063
$343$	11.7622	0.635100
$344$	−21.5164	−1.16009
$345$	−43.6441	−2.34972
$346$	−13.9159	−0.748123
$347$	16.8612	0.905156	0.452578	−	0.891725i	$-0.350504\pi$
$347$	16.8612	0.905156	0.452578	+	0.891725i	$0.350504\pi$
$348$	−94.0563	−5.04195
$349$	−4.53306	−0.242649	−0.121325	−	0.992613i	$-0.538714\pi$
$349$	−4.53306	−0.242649	−0.121325	+	0.992613i	$0.538714\pi$
$350$	−0.299971	−0.0160341
$351$	1.47979	0.0789853
$352$	0.908040	0.0483987
$353$	−16.4652	−0.876352	−0.438176	−	0.898889i	$-0.644375\pi$
$353$	−16.4652	−0.876352	−0.438176	+	0.898889i	$0.644375\pi$
$354$	−24.0642	−1.27900
$355$	−33.2664	−1.76560
$356$	39.5879	2.09816
$357$	−6.10586	−0.323156
$358$	44.2998	2.34132
$359$	−27.4609	−1.44933	−0.724666	−	0.689100i	$-0.758006\pi$
$359$	−27.4609	−1.44933	−0.724666	+	0.689100i	$0.758006\pi$
$360$	26.2562	1.38382
$361$	36.5607	1.92425
$362$	22.7347	1.19491
$363$	17.8629	0.937560
$364$	−3.60726	−0.189072
$365$	−21.9548	−1.14917
$366$	−86.3029	−4.51112
$367$	17.8711	0.932866	0.466433	−	0.884557i	$-0.345539\pi$
$367$	17.8711	0.932866	0.466433	+	0.884557i	$0.345539\pi$
$368$	−36.7917	−1.91790
$369$	3.33196	0.173455
$370$	38.6273	2.00814
$371$	−2.37368	−0.123235
$372$	72.7455	3.77168
$373$	4.28436	0.221836	0.110918	−	0.993830i	$-0.464621\pi$
$373$	4.28436	0.221836	0.110918	+	0.993830i	$0.464621\pi$
$374$	−13.2006	−0.682587
$375$	−26.2287	−1.35444
$376$	−44.1051	−2.27454
$377$	10.0296	0.516551
$378$	3.24175	0.166738
$379$	3.97270	0.204064	0.102032	−	0.994781i	$-0.467466\pi$
$379$	3.97270	0.204064	0.102032	+	0.994781i	$0.467466\pi$
$380$	66.5771	3.41533
$381$	7.52265	0.385397
$382$	−19.0806	−0.976250
$383$	22.0070	1.12450	0.562252	−	0.826966i	$-0.309935\pi$
$383$	22.0070	1.12450	0.562252	+	0.826966i	$0.309935\pi$
$384$	−44.3286	−2.26213
$385$	−3.55973	−0.181420
$386$	−6.82108	−0.347184
$387$	10.0726	0.512019
$388$	4.94810	0.251201
$389$	−24.4752	−1.24094	−0.620470	−	0.784230i	$-0.713058\pi$
$389$	−24.4752	−1.24094	−0.620470	+	0.784230i	$0.713058\pi$
$390$	−12.5592	−0.635959
$391$	25.3098	1.27997
$392$	31.3019	1.58098
$393$	−1.35308	−0.0682540
$394$	−65.0149	−3.27540
$395$	15.1126	0.760396
$396$	−17.3312	−0.870927
$397$	−27.6171	−1.38606	−0.693030	−	0.720909i	$-0.743725\pi$
$397$	−27.6171	−1.38606	−0.693030	+	0.720909i	$0.743725\pi$
$398$	−17.5165	−0.878025
$399$	−15.3707	−0.769498
$400$	−0.589383	−0.0294692
$401$	5.75345	0.287313	0.143657	−	0.989628i	$-0.454114\pi$
$401$	5.75345	0.287313	0.143657	+	0.989628i	$0.454114\pi$
$402$	−72.6678	−3.62434
$403$	−7.75715	−0.386411
$404$	68.9235	3.42907
$405$	23.1746	1.15155
$406$	21.9717	1.09044
$407$	−12.9069	−0.639769
$408$	−34.5746	−1.71170
$409$	5.05537	0.249972	0.124986	−	0.992159i	$-0.460111\pi$
$409$	5.05537	0.249972	0.124986	+	0.992159i	$0.460111\pi$
$410$	7.65541	0.378074
$411$	−43.2900	−2.13534
$412$	−49.4630	−2.43687
$413$	3.76320	0.185175
$414$	49.6380	2.43957
$415$	11.4466	0.561890
$416$	−0.500998	−0.0245634
$417$	−24.5769	−1.20354
$418$	−33.2308	−1.62537
$419$	6.58860	0.321874	0.160937	−	0.986965i	$-0.448548\pi$
$419$	6.58860	0.321874	0.160937	+	0.986965i	$0.448548\pi$
$420$	−18.4184	−0.898724
$421$	−10.2150	−0.497848	−0.248924	−	0.968523i	$-0.580077\pi$
$421$	−10.2150	−0.497848	−0.248924	+	0.968523i	$0.580077\pi$
$422$	20.6803	1.00670
$423$	20.6471	1.00390
$424$	−13.4410	−0.652754
$425$	0.405449	0.0196672
$426$	85.9127	4.16248
$427$	13.4962	0.653126
$428$	−28.1424	−1.36031
$429$	4.19650	0.202609
$430$	23.1425	1.11603
$431$	−17.3046	−0.833531	−0.416765	−	0.909014i	$-0.636836\pi$
$431$	−17.3046	−0.833531	−0.416765	+	0.909014i	$0.636836\pi$
$432$	6.36939	0.306448
$433$	30.5560	1.46843	0.734214	−	0.678918i	$-0.237551\pi$
$433$	30.5560	1.46843	0.734214	+	0.678918i	$0.237551\pi$
$434$	−16.9935	−0.815712
$435$	51.2103	2.45535
$436$	−13.0303	−0.624039
$437$	63.7141	3.04786
$438$	56.6996	2.70921
$439$	17.1881	0.820342	0.410171	−	0.912009i	$-0.365469\pi$
$439$	17.1881	0.820342	0.410171	+	0.912009i	$0.365469\pi$
$440$	−20.1571	−0.960951
$441$	−14.6535	−0.697786
$442$	7.28324	0.346428
$443$	28.0979	1.33497	0.667486	−	0.744622i	$-0.267370\pi$
$443$	28.0979	1.33497	0.667486	+	0.744622i	$0.267370\pi$
$444$	−66.7813	−3.16930
$445$	−21.5542	−1.02177
$446$	−49.8152	−2.35882
$447$	−17.0928	−0.808462
$448$	6.56937	0.310374
$449$	−2.46234	−0.116205	−0.0581024	−	0.998311i	$-0.518505\pi$
$449$	−2.46234	−0.116205	−0.0581024	+	0.998311i	$0.518505\pi$
$450$	0.795173	0.0374848
$451$	−2.55797	−0.120450
$452$	−41.1915	−1.93748
$453$	4.98276	0.234110
$454$	−37.5978	−1.76455
$455$	1.96403	0.0920749
$456$	−87.0372	−4.07589
$457$	31.5335	1.47507	0.737537	−	0.675307i	$-0.235989\pi$
$457$	31.5335	1.47507	0.737537	+	0.675307i	$0.235989\pi$
$458$	20.8108	0.972425
$459$	−4.38164	−0.204517
$460$	76.3472	3.55971
$461$	−6.25599	−0.291371	−0.145685	−	0.989331i	$-0.546539\pi$
$461$	−6.25599	−0.291371	−0.145685	+	0.989331i	$0.546539\pi$
$462$	9.19321	0.427707
$463$	2.24515	0.104341	0.0521706	−	0.998638i	$-0.483386\pi$
$463$	2.24515	0.104341	0.0521706	+	0.998638i	$0.483386\pi$
$464$	43.1700	2.00412
$465$	−39.6073	−1.83674
$466$	27.0332	1.25229
$467$	27.4655	1.27095	0.635477	−	0.772120i	$-0.280804\pi$
$467$	27.4655	1.27095	0.635477	+	0.772120i	$0.280804\pi$
$468$	9.56225	0.442015
$469$	11.3639	0.524737
$470$	47.4383	2.18816
$471$	−35.0905	−1.61688
$472$	21.3093	0.980838
$473$	−7.73280	−0.355554
$474$	−39.0291	−1.79267
$475$	1.02067	0.0468314
$476$	10.6811	0.489566
$477$	6.29222	0.288101
$478$	70.4949	3.22436
$479$	21.8531	0.998493	0.499246	−	0.866460i	$-0.333610\pi$
$479$	21.8531	0.998493	0.499246	+	0.866460i	$0.333610\pi$
$480$	−2.55805	−0.116759
$481$	7.12117	0.324697
$482$	−73.0783	−3.32862
$483$	−17.6263	−0.802026
$484$	−31.2479	−1.42036
$485$	−2.69406	−0.122331
$486$	−48.9301	−2.21952
$487$	38.2254	1.73216	0.866078	−	0.499909i	$-0.166633\pi$
$487$	38.2254	1.73216	0.866078	+	0.499909i	$0.166633\pi$
$488$	76.4226	3.45949
$489$	−40.6057	−1.83625
$490$	−33.6675	−1.52094
$491$	4.63653	0.209244	0.104622	−	0.994512i	$-0.466637\pi$
$491$	4.63653	0.209244	0.104622	+	0.994512i	$0.466637\pi$
$492$	−13.2352	−0.596687
$493$	−29.6975	−1.33751
$494$	18.3346	0.824913
$495$	9.43623	0.424127
$496$	−33.3887	−1.49920
$497$	−13.4352	−0.602650
$498$	−29.5615	−1.32468
$499$	−40.0348	−1.79220	−0.896101	−	0.443850i	$-0.853612\pi$
$499$	−40.0348	−1.79220	−0.896101	+	0.443850i	$0.853612\pi$
$500$	45.8823	2.05192
$501$	27.5050	1.22883
$502$	−34.4122	−1.53589
$503$	−36.6435	−1.63385	−0.816926	−	0.576743i	$-0.804323\pi$
$503$	−36.6435	−1.63385	−0.816926	+	0.576743i	$0.804323\pi$
$504$	10.6040	0.472339
$505$	−37.5264	−1.66990
$506$	−38.1074	−1.69408
$507$	−2.31536	−0.102829
$508$	−13.1595	−0.583857
$509$	4.76700	0.211294	0.105647	−	0.994404i	$-0.466309\pi$
$509$	4.76700	0.211294	0.105647	+	0.994404i	$0.466309\pi$
$510$	37.1876	1.64669
$511$	−8.86677	−0.392243
$512$	41.2577	1.82335
$513$	−11.0302	−0.486996
$514$	11.8041	0.520658
$515$	26.9308	1.18671
$516$	−40.0102	−1.76135
$517$	−15.8509	−0.697123
$518$	15.6002	0.685435
$519$	−13.0991	−0.574986
$520$	11.1214	0.487704
$521$	−21.6942	−0.950441	−0.475221	−	0.879867i	$-0.657632\pi$
$521$	−21.6942	−0.950441	−0.475221	+	0.879867i	$0.657632\pi$
$522$	−58.2433	−2.54924
$523$	0.412057	0.0180180	0.00900900	−	0.999959i	$-0.497132\pi$
$523$	0.412057	0.0180180	0.00900900	+	0.999959i	$0.497132\pi$
$524$	2.36697	0.103401
$525$	−0.282364	−0.0123234
$526$	16.9437	0.738778
$527$	22.9688	1.00054
$528$	18.0628	0.786083
$529$	50.0641	2.17670
$530$	14.4568	0.627965
$531$	−9.97561	−0.432905
$532$	26.8882	1.16575
$533$	1.41132	0.0611310
$534$	55.6651	2.40887
$535$	15.3225	0.662450
$536$	64.3486	2.77943
$537$	41.6996	1.79947
$538$	6.98071	0.300960
$539$	11.2496	0.484554
$540$	−13.2173	−0.568780
$541$	−40.5964	−1.74538	−0.872688	−	0.488278i	$-0.837625\pi$
$541$	−40.5964	−1.74538	−0.872688	+	0.488278i	$0.837625\pi$
$542$	−36.4991	−1.56777
$543$	21.4003	0.918374
$544$	1.48345	0.0636023
$545$	7.09454	0.303897
$546$	−5.07222	−0.217071
$547$	−32.2489	−1.37886	−0.689432	−	0.724351i	$-0.742140\pi$
$547$	−32.2489	−1.37886	−0.689432	+	0.724351i	$0.742140\pi$
$548$	75.7279	3.23493
$549$	−35.7761	−1.52689
$550$	−0.610460	−0.0260301
$551$	−74.7597	−3.18487
$552$	−99.8097	−4.24818
$553$	6.10344	0.259545
$554$	26.1599	1.11143
$555$	36.3600	1.54340
$556$	42.9927	1.82330
$557$	22.9535	0.972572	0.486286	−	0.873800i	$-0.338351\pi$
$557$	22.9535	0.972572	0.486286	+	0.873800i	$0.338351\pi$
$558$	45.0468	1.90698
$559$	4.26646	0.180452
$560$	8.45367	0.357233
$561$	−12.4258	−0.524617
$562$	−12.2657	−0.517397
$563$	33.7985	1.42444	0.712218	−	0.701958i	$-0.247691\pi$
$563$	33.7985	1.42444	0.712218	+	0.701958i	$0.247691\pi$
$564$	−82.0143	−3.45342
$565$	22.4273	0.943523
$566$	−15.8788	−0.667437
$567$	9.35941	0.393058
$568$	−76.0771	−3.19212
$569$	33.4822	1.40365	0.701824	−	0.712350i	$-0.252369\pi$
$569$	33.4822	1.40365	0.701824	+	0.712350i	$0.252369\pi$
$570$	93.6149	3.92110
$571$	−20.0288	−0.838178	−0.419089	−	0.907945i	$-0.637651\pi$
$571$	−20.0288	−0.838178	−0.419089	+	0.907945i	$0.637651\pi$
$572$	−7.34100	−0.306943
$573$	−17.9607	−0.750318
$574$	3.09176	0.129047
$575$	1.17045	0.0488110
$576$	−17.4143	−0.725596
$577$	4.19287	0.174551	0.0872757	−	0.996184i	$-0.472184\pi$
$577$	4.19287	0.174551	0.0872757	+	0.996184i	$0.472184\pi$
$578$	20.2499	0.842284
$579$	−6.42072	−0.266836
$580$	−89.5829	−3.71973
$581$	4.62287	0.191789
$582$	6.95758	0.288401
$583$	−4.83058	−0.200062
$584$	−50.2084	−2.07764
$585$	−5.20630	−0.215254
$586$	−17.9642	−0.742095
$587$	−16.1367	−0.666034	−0.333017	−	0.942921i	$-0.608067\pi$
$587$	−16.1367	−0.666034	−0.333017	+	0.942921i	$0.608067\pi$
$588$	58.2065	2.40040
$589$	57.8210	2.38247
$590$	−22.9197	−0.943589
$591$	−61.1988	−2.51738
$592$	30.6513	1.25976
$593$	6.91404	0.283926	0.141963	−	0.989872i	$-0.454659\pi$
$593$	6.91404	0.283926	0.141963	+	0.989872i	$0.454659\pi$
$594$	6.59717	0.270685
$595$	−5.81546	−0.238411
$596$	29.9007	1.22478
$597$	−16.4884	−0.674825
$598$	21.0252	0.859784
$599$	−25.3985	−1.03776	−0.518878	−	0.854849i	$-0.673650\pi$
$599$	−25.3985	−1.03776	−0.518878	+	0.854849i	$0.673650\pi$
$600$	−1.59890	−0.0652747
$601$	−40.6374	−1.65763	−0.828816	−	0.559521i	$-0.810985\pi$
$601$	−40.6374	−1.65763	−0.828816	+	0.559521i	$0.810985\pi$
$602$	9.34646	0.380933
$603$	−30.1238	−1.22674
$604$	−8.71640	−0.354665
$605$	17.0133	0.691691
$606$	96.9143	3.93687
$607$	−13.3117	−0.540304	−0.270152	−	0.962818i	$-0.587074\pi$
$607$	−13.3117	−0.540304	−0.270152	+	0.962818i	$0.587074\pi$
$608$	3.73439	0.151449
$609$	20.6821	0.838080
$610$	−82.1982	−3.32811
$611$	8.74552	0.353806
$612$	−28.3137	−1.14451
$613$	−19.2654	−0.778121	−0.389061	−	0.921212i	$-0.627200\pi$
$613$	−19.2654	−0.778121	−0.389061	+	0.921212i	$0.627200\pi$
$614$	−45.7705	−1.84715
$615$	7.20607	0.290577
$616$	−8.14074	−0.328000
$617$	1.00000	0.0402585
$617$	1.00000	0.0402585
$618$	−69.5506	−2.79773
$619$	−24.7192	−0.993548	−0.496774	−	0.867880i	$-0.665482\pi$
$619$	−24.7192	−0.993548	−0.496774	+	0.867880i	$0.665482\pi$
$620$	69.2856	2.78258
$621$	−12.6489	−0.507582
$622$	−29.3287	−1.17597
$623$	−8.70500	−0.348759
$624$	−9.96589	−0.398955
$625$	−24.2966	−0.971864
$626$	−77.1716	−3.08440
$627$	−31.2803	−1.24922
$628$	61.3843	2.44950
$629$	−21.0857	−0.840742
$630$	−11.4054	−0.454401
$631$	−2.30893	−0.0919172	−0.0459586	−	0.998943i	$-0.514634\pi$
$631$	−2.30893	−0.0919172	−0.0459586	+	0.998943i	$0.514634\pi$
$632$	34.5610	1.37476
$633$	19.4664	0.773722
$634$	52.2080	2.07345
$635$	7.16487	0.284329
$636$	−24.9939	−0.991072
$637$	−6.20680	−0.245922
$638$	44.7138	1.77023
$639$	35.6144	1.40888
$640$	−42.2203	−1.66890
$641$	3.14795	0.124337	0.0621683	−	0.998066i	$-0.480198\pi$
$641$	3.14795	0.124337	0.0621683	+	0.998066i	$0.480198\pi$
$642$	−39.5713	−1.56176
$643$	29.8323	1.17647	0.588236	−	0.808689i	$-0.299823\pi$
$643$	29.8323	1.17647	0.588236	+	0.808689i	$0.299823\pi$
$644$	30.8340	1.21503
$645$	21.7841	0.857750
$646$	−54.2886	−2.13596
$647$	−19.8551	−0.780583	−0.390292	−	0.920691i	$-0.627626\pi$
$647$	−19.8551	−0.780583	−0.390292	+	0.920691i	$0.627626\pi$
$648$	52.9980	2.08196
$649$	7.65834	0.300616
$650$	0.336812	0.0132109
$651$	−15.9960	−0.626933
$652$	71.0322	2.78184
$653$	−41.3645	−1.61872	−0.809360	−	0.587313i	$-0.800186\pi$
$653$	−41.3645	−1.61872	−0.809360	+	0.587313i	$0.800186\pi$
$654$	−18.3221	−0.716450
$655$	−1.28873	−0.0503548
$656$	6.07468	0.237176
$657$	23.5043	0.916991
$658$	19.1587	0.746883
$659$	−32.9092	−1.28196	−0.640980	−	0.767558i	$-0.721472\pi$
$659$	−32.9092	−1.28196	−0.640980	+	0.767558i	$0.721472\pi$
$660$	−37.4825	−1.45900
$661$	0.619072	0.0240791	0.0120395	−	0.999928i	$-0.496168\pi$
$661$	0.619072	0.0240791	0.0120395	+	0.999928i	$0.496168\pi$
$662$	−20.5930	−0.800370
$663$	6.85575	0.266255
$664$	26.1772	1.01587
$665$	−14.6397	−0.567702
$666$	−41.3536	−1.60242
$667$	−85.7306	−3.31950
$668$	−48.1149	−1.86162
$669$	−46.8912	−1.81292
$670$	−69.2117	−2.67388
$671$	27.4656	1.06030
$672$	−1.03311	−0.0398530
$673$	−41.2780	−1.59115	−0.795575	−	0.605855i	$-0.792831\pi$
$673$	−41.2780	−1.59115	−0.795575	+	0.605855i	$0.792831\pi$
$674$	−38.8995	−1.49835
$675$	−0.202628	−0.00779916
$676$	4.05029	0.155780
$677$	−19.0264	−0.731244	−0.365622	−	0.930763i	$-0.619144\pi$
$677$	−19.0264	−0.731244	−0.365622	+	0.930763i	$0.619144\pi$
$678$	−57.9199	−2.22440
$679$	−1.08804	−0.0417551
$680$	−32.9302	−1.26282
$681$	−35.3910	−1.35619
$682$	−34.5827	−1.32424
$683$	−15.9486	−0.610255	−0.305128	−	0.952311i	$-0.598699\pi$
$683$	−15.9486	−0.610255	−0.305128	+	0.952311i	$0.598699\pi$
$684$	−71.2761	−2.72531
$685$	−41.2311	−1.57536
$686$	−28.9319	−1.10463
$687$	19.5893	0.747378
$688$	18.3639	0.700118
$689$	2.66520	0.101536
$690$	107.353	4.08685
$691$	2.57120	0.0978132	0.0489066	−	0.998803i	$-0.484426\pi$
$691$	2.57120	0.0978132	0.0489066	+	0.998803i	$0.484426\pi$
$692$	22.9144	0.871075
$693$	3.81097	0.144767
$694$	−41.4740	−1.57433
$695$	−23.4080	−0.887916
$696$	117.113	4.43915
$697$	−4.17890	−0.158287
$698$	11.1501	0.422038
$699$	25.4464	0.962472
$700$	0.493944	0.0186693
$701$	−1.16647	−0.0440569	−0.0220285	−	0.999757i	$-0.507012\pi$
$701$	−1.16647	−0.0440569	−0.0220285	+	0.999757i	$0.507012\pi$
$702$	−3.63989	−0.137379
$703$	−53.0805	−2.00197
$704$	13.3691	0.503866
$705$	44.6538	1.68176
$706$	40.4999	1.52423
$707$	−15.1556	−0.569986
$708$	39.6250	1.48920
$709$	23.0279	0.864831	0.432416	−	0.901674i	$-0.357661\pi$
$709$	23.0279	0.864831	0.432416	+	0.901674i	$0.357661\pi$
$710$	81.8266	3.07090
$711$	−16.1792	−0.606767
$712$	−49.2924	−1.84731
$713$	66.3062	2.48319
$714$	15.0188	0.562064
$715$	3.99691	0.149476
$716$	−72.9457	−2.72611
$717$	66.3571	2.47815
$718$	67.5466	2.52082
$719$	51.4729	1.91962	0.959808	−	0.280657i	$-0.0905522\pi$
$719$	51.4729	1.91962	0.959808	+	0.280657i	$0.0905522\pi$
$720$	−22.4092	−0.835143
$721$	10.8764	0.405059
$722$	−89.9295	−3.34683
$723$	−68.7889	−2.55829
$724$	−37.4358	−1.39129
$725$	−1.37336	−0.0510052
$726$	−43.9380	−1.63069
$727$	10.8698	0.403138	0.201569	−	0.979474i	$-0.435396\pi$
$727$	10.8698	0.403138	0.201569	+	0.979474i	$0.435396\pi$
$728$	4.49153	0.166467
$729$	−14.5315	−0.538203
$730$	54.0029	1.99874
$731$	−12.6329	−0.467246
$732$	142.109	5.25252
$733$	6.00526	0.221809	0.110905	−	0.993831i	$-0.464625\pi$
$733$	6.00526	0.221809	0.110905	+	0.993831i	$0.464625\pi$
$734$	−43.9582	−1.62253
$735$	−31.6914	−1.16895
$736$	4.28241	0.157852
$737$	23.1263	0.851867
$738$	−8.19573	−0.301689
$739$	−18.0170	−0.662767	−0.331383	−	0.943496i	$-0.607515\pi$
$739$	−18.0170	−0.662767	−0.331383	+	0.943496i	$0.607515\pi$
$740$	−63.6051	−2.33817
$741$	17.2585	0.634005
$742$	5.83861	0.214342
$743$	−41.0540	−1.50613	−0.753063	−	0.657948i	$-0.771425\pi$
$743$	−41.0540	−1.50613	−0.753063	+	0.657948i	$0.771425\pi$
$744$	−90.5780	−3.32075
$745$	−16.2799	−0.596448
$746$	−10.5384	−0.385838
$747$	−12.2544	−0.448367
$748$	21.7366	0.794769
$749$	6.18823	0.226113
$750$	64.5156	2.35578
$751$	31.7225	1.15757	0.578784	−	0.815481i	$-0.303527\pi$
$751$	31.7225	1.15757	0.578784	+	0.815481i	$0.303527\pi$
$752$	37.6429	1.37270
$753$	−32.3923	−1.18044
$754$	−24.6702	−0.898434
$755$	4.74577	0.172716
$756$	−5.33799	−0.194141
$757$	31.7079	1.15244	0.576221	−	0.817294i	$-0.304527\pi$
$757$	31.7079	1.15244	0.576221	+	0.817294i	$0.304527\pi$
$758$	−9.77177	−0.354927
$759$	−35.8707	−1.30202
$760$	−82.8976	−3.00701
$761$	−31.1860	−1.13049	−0.565246	−	0.824923i	$-0.691219\pi$
$761$	−31.1860	−1.13049	−0.565246	+	0.824923i	$0.691219\pi$
$762$	−18.5037	−0.670319
$763$	2.86524	0.103729
$764$	31.4189	1.13669
$765$	15.4158	0.557359
$766$	−54.1313	−1.95584
$767$	−4.22538	−0.152570
$768$	74.8794	2.70198
$769$	32.8316	1.18394	0.591969	−	0.805960i	$-0.298351\pi$
$769$	32.8316	1.18394	0.591969	+	0.805960i	$0.298351\pi$
$770$	8.75598	0.315543
$771$	11.1113	0.400163
$772$	11.2318	0.404243
$773$	15.3649	0.552636	0.276318	−	0.961066i	$-0.410886\pi$
$773$	15.3649	0.552636	0.276318	+	0.961066i	$0.410886\pi$
$774$	−24.7759	−0.890551
$775$	1.06219	0.0381550
$776$	−6.16105	−0.221169
$777$	14.6846	0.526806
$778$	60.2024	2.15836
$779$	−10.5198	−0.376912
$780$	20.6804	0.740478
$781$	−27.3414	−0.978352
$782$	−62.2554	−2.22625
$783$	14.8417	0.530399
$784$	−26.7156	−0.954130
$785$	−33.4215	−1.19287
$786$	3.32822	0.118714
$787$	12.8898	0.459472	0.229736	−	0.973253i	$-0.426214\pi$
$787$	12.8898	0.459472	0.229736	+	0.973253i	$0.426214\pi$
$788$	107.056	3.81371
$789$	15.9491	0.567804
$790$	−37.1729	−1.32255
$791$	9.05761	0.322051
$792$	21.5797	0.766803
$793$	−15.1537	−0.538124
$794$	67.9306	2.41077
$795$	13.6083	0.482636
$796$	28.8434	1.02233
$797$	12.2711	0.434665	0.217333	−	0.976098i	$-0.430264\pi$
$797$	12.2711	0.434665	0.217333	+	0.976098i	$0.430264\pi$
$798$	37.8078	1.33838
$799$	−25.8954	−0.916113
$800$	0.0686018	0.00242544
$801$	23.0755	0.815333
$802$	−14.1519	−0.499723
$803$	−18.0444	−0.636774
$804$	119.658	4.21999
$805$	−16.7880	−0.591700
$806$	19.0805	0.672082
$807$	6.57097	0.231309
$808$	−85.8192	−3.01911
$809$	−36.3989	−1.27972	−0.639858	−	0.768493i	$-0.721007\pi$
$809$	−36.3989	−1.27972	−0.639858	+	0.768493i	$0.721007\pi$
$810$	−57.0033	−2.00289
$811$	14.2993	0.502117	0.251059	−	0.967972i	$-0.419221\pi$
$811$	14.2993	0.502117	0.251059	+	0.967972i	$0.419221\pi$
$812$	−36.1794	−1.26965
$813$	−34.3568	−1.20494
$814$	31.7474	1.11275
$815$	−38.6745	−1.35471
$816$	29.5089	1.03302
$817$	−31.8018	−1.11260
$818$	−12.4349	−0.434775
$819$	−2.10265	−0.0734724
$820$	−12.6057	−0.440210
$821$	−2.40556	−0.0839547	−0.0419773	−	0.999119i	$-0.513366\pi$
$821$	−2.40556	−0.0839547	−0.0419773	+	0.999119i	$0.513366\pi$
$822$	106.482	3.71398
$823$	−3.90643	−0.136170	−0.0680849	−	0.997680i	$-0.521689\pi$
$823$	−3.90643	−0.136170	−0.0680849	+	0.997680i	$0.521689\pi$
$824$	61.5882	2.14553
$825$	−0.574629	−0.0200060
$826$	−9.25647	−0.322074
$827$	−9.73334	−0.338461	−0.169231	−	0.985576i	$-0.554128\pi$
$827$	−9.73334	−0.338461	−0.169231	+	0.985576i	$0.554128\pi$
$828$	−81.7357	−2.84051
$829$	−35.7167	−1.24049	−0.620246	−	0.784407i	$-0.712967\pi$
$829$	−35.7167	−1.24049	−0.620246	+	0.784407i	$0.712967\pi$
$830$	−28.1555	−0.977291
$831$	24.6245	0.854213
$832$	−7.37619	−0.255723
$833$	18.3783	0.636769
$834$	60.4526	2.09330
$835$	26.1969	0.906580
$836$	54.7191	1.89250
$837$	−11.4789	−0.396770
$838$	−16.2062	−0.559834
$839$	−17.3033	−0.597377	−0.298688	−	0.954351i	$-0.596549\pi$
$839$	−17.3033	−0.597377	−0.298688	+	0.954351i	$0.596549\pi$
$840$	22.9334	0.791277
$841$	71.5930	2.46872
$842$	25.1261	0.865904
$843$	−11.5458	−0.397657
$844$	−34.0529	−1.17215
$845$	−2.20524	−0.0758625
$846$	−50.7864	−1.74607
$847$	6.87110	0.236094
$848$	11.4717	0.393940
$849$	−14.9468	−0.512973
$850$	−0.997297	−0.0342070
$851$	−60.8700	−2.08660
$852$	−141.467	−4.84658
$853$	41.2758	1.41326	0.706628	−	0.707585i	$-0.250215\pi$
$853$	41.2758	1.41326	0.706628	+	0.707585i	$0.250215\pi$
$854$	−33.1970	−1.13598
$855$	38.8073	1.32718
$856$	35.0411	1.19768
$857$	−6.77866	−0.231554	−0.115777	−	0.993275i	$-0.536936\pi$
$857$	−6.77866	−0.231554	−0.115777	+	0.993275i	$0.536936\pi$
$858$	−10.3223	−0.352397
$859$	10.1715	0.347049	0.173524	−	0.984830i	$-0.444484\pi$
$859$	10.1715	0.347049	0.173524	+	0.984830i	$0.444484\pi$
$860$	−38.1073	−1.29945
$861$	2.91028	0.0991822
$862$	42.5646	1.44976
$863$	4.42072	0.150483	0.0752415	−	0.997165i	$-0.476027\pi$
$863$	4.42072	0.150483	0.0752415	+	0.997165i	$0.476027\pi$
$864$	−0.741372	−0.0252220
$865$	−12.4761	−0.424199
$866$	−75.1596	−2.55403
$867$	19.0613	0.647355
$868$	27.9821	0.949773
$869$	12.4209	0.421349
$870$	−125.964	−4.27057
$871$	−12.7596	−0.432341
$872$	16.2245	0.549431
$873$	2.88421	0.0976156
$874$	−156.720	−5.30113
$875$	−10.0891	−0.341073
$876$	−93.3636	−3.15446
$877$	−49.1833	−1.66080	−0.830400	−	0.557167i	$-0.811888\pi$
$877$	−49.1833	−1.66080	−0.830400	+	0.557167i	$0.811888\pi$
$878$	−42.2781	−1.42682
$879$	−16.9098	−0.570353
$880$	17.2037	0.579938
$881$	18.1714	0.612209	0.306104	−	0.951998i	$-0.400974\pi$
$881$	18.1714	0.612209	0.306104	+	0.951998i	$0.400974\pi$
$882$	36.0437	1.21366
$883$	−47.9800	−1.61466	−0.807328	−	0.590103i	$-0.799087\pi$
$883$	−47.9800	−1.61466	−0.807328	+	0.590103i	$0.799087\pi$
$884$	−11.9929	−0.403363
$885$	−21.5744	−0.725216
$886$	−69.1134	−2.32191
$887$	12.8607	0.431820	0.215910	−	0.976413i	$-0.430728\pi$
$887$	12.8607	0.431820	0.215910	+	0.976413i	$0.430728\pi$
$888$	83.1519	2.79039
$889$	2.89364	0.0970496
$890$	53.0176	1.77715
$891$	19.0470	0.638098
$892$	82.0275	2.74648
$893$	−65.1883	−2.18144
$894$	42.0437	1.40615
$895$	39.7163	1.32757
$896$	−17.0513	−0.569644
$897$	19.7911	0.660806
$898$	6.05669	0.202114
$899$	−77.8011	−2.59481
$900$	−1.30936	−0.0436454
$901$	−7.89163	−0.262908
$902$	6.29191	0.209498
$903$	8.79786	0.292775
$904$	51.2890	1.70585
$905$	20.3825	0.677536
$906$	−12.2562	−0.407187
$907$	14.9157	0.495267	0.247633	−	0.968854i	$-0.420347\pi$
$907$	14.9157	0.495267	0.247633	+	0.968854i	$0.420347\pi$
$908$	61.9099	2.05455
$909$	40.1750	1.33252
$910$	−4.83098	−0.160145
$911$	3.64159	0.120651	0.0603257	−	0.998179i	$-0.480786\pi$
$911$	3.64159	0.120651	0.0603257	+	0.998179i	$0.480786\pi$
$912$	74.2848	2.45982
$913$	9.40782	0.311353
$914$	−77.5639	−2.56559
$915$	−77.3735	−2.55789
$916$	−34.2678	−1.13224
$917$	−0.520473	−0.0171875
$918$	10.7777	0.355716
$919$	−53.4146	−1.76199	−0.880993	−	0.473130i	$-0.843124\pi$
$919$	−53.4146	−1.76199	−0.880993	+	0.473130i	$0.843124\pi$
$920$	−95.0627	−3.13412
$921$	−43.0840	−1.41967
$922$	15.3881	0.506779
$923$	15.0852	0.496535
$924$	−15.1379	−0.498000
$925$	−0.975104	−0.0320612
$926$	−5.52248	−0.181480
$927$	−28.8316	−0.946953
$928$	−5.02481	−0.164947
$929$	7.09091	0.232645	0.116323	−	0.993211i	$-0.462889\pi$
$929$	7.09091	0.232645	0.116323	+	0.993211i	$0.462889\pi$
$930$	97.4234	3.19464
$931$	46.2649	1.51627
$932$	−44.5138	−1.45810
$933$	−27.6073	−0.903821
$934$	−67.5579	−2.21056
$935$	−11.8348	−0.387040
$936$	−11.9063	−0.389170
$937$	−20.9720	−0.685124	−0.342562	−	0.939495i	$-0.611295\pi$
$937$	−20.9720	−0.685124	−0.342562	+	0.939495i	$0.611295\pi$
$938$	−27.9522	−0.912672
$939$	−72.6420	−2.37058
$940$	−78.1136	−2.54778
$941$	−6.76739	−0.220611	−0.110305	−	0.993898i	$-0.535183\pi$
$941$	−6.76739	−0.220611	−0.110305	+	0.993898i	$0.535183\pi$
$942$	86.3132	2.81224
$943$	−12.0636	−0.392845
$944$	−18.1871	−0.591940
$945$	2.90635	0.0945434
$946$	19.0206	0.618414
$947$	33.1589	1.07752	0.538760	−	0.842459i	$-0.318893\pi$
$947$	33.1589	1.07752	0.538760	+	0.842459i	$0.318893\pi$
$948$	64.2668	2.08729
$949$	9.95574	0.323177
$950$	−2.51057	−0.0814535
$951$	49.1436	1.59359
$952$	−13.2994	−0.431035
$953$	−10.8799	−0.352434	−0.176217	−	0.984351i	$-0.556386\pi$
$953$	−10.8799	−0.352434	−0.176217	+	0.984351i	$0.556386\pi$
$954$	−15.4772	−0.501092
$955$	−17.1065	−0.553552
$956$	−116.079	−3.75428
$957$	42.0893	1.36055
$958$	−53.7527	−1.73667
$959$	−16.6518	−0.537716
$960$	−37.6622	−1.21554
$961$	29.1733	0.941074
$962$	−17.5162	−0.564744
$963$	−16.4040	−0.528610
$964$	120.333	3.87568
$965$	−6.11534	−0.196860
$966$	43.3561	1.39496
$967$	−37.2375	−1.19748	−0.598738	−	0.800945i	$-0.704331\pi$
$967$	−37.2375	−1.19748	−0.598738	+	0.800945i	$0.704331\pi$
$968$	38.9079	1.25055
$969$	−51.1021	−1.64164
$970$	6.62667	0.212770
$971$	54.8554	1.76039	0.880197	−	0.474609i	$-0.157411\pi$
$971$	54.8554	1.76039	0.880197	+	0.474609i	$0.157411\pi$
$972$	80.5702	2.58429
$973$	−9.45368	−0.303071
$974$	−94.0242	−3.01273
$975$	0.317043	0.0101535
$976$	−65.2255	−2.08782
$977$	14.8009	0.473523	0.236762	−	0.971568i	$-0.423914\pi$
$977$	14.8009	0.473523	0.236762	+	0.971568i	$0.423914\pi$
$978$	99.8793	3.19379
$979$	−17.7152	−0.566181
$980$	55.4381	1.77091
$981$	−7.59526	−0.242498
$982$	−11.4046	−0.363936
$983$	−18.8218	−0.600322	−0.300161	−	0.953889i	$-0.597040\pi$
$983$	−18.8218	−0.600322	−0.300161	+	0.953889i	$0.597040\pi$
$984$	16.4796	0.525350
$985$	−58.2881	−1.85721
$986$	73.0480	2.32632
$987$	18.0341	0.574033
$988$	−30.1905	−0.960486
$989$	−36.4686	−1.15963
$990$	−23.2106	−0.737682
$991$	−36.1415	−1.14807	−0.574036	−	0.818830i	$-0.694623\pi$
$991$	−36.1415	−1.14807	−0.574036	+	0.818830i	$0.694623\pi$
$992$	3.88631	0.123391
$993$	−19.3843	−0.615142
$994$	33.0469	1.04818
$995$	−15.7042	−0.497857
$996$	48.6770	1.54239
$997$	27.0461	0.856559	0.428279	−	0.903646i	$-0.359120\pi$
$997$	27.0461	0.856559	0.428279	+	0.903646i	$0.359120\pi$
$998$	98.4748	3.11717
$999$	10.5378	0.333402

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.a.1.10	✓	134

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.a.1.10	✓	134	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.45973 q^{2} -2.31536 q^{3} +4.05029 q^{4} -2.20524 q^{5} +5.69516 q^{6} -0.890619 q^{7} -5.04316 q^{8} +2.36088 q^{9} +O(q^{10})\)	\(q-2.45973 q^{2} -2.31536 q^{3} +4.05029 q^{4} -2.20524 q^{5} +5.69516 q^{6} -0.890619 q^{7} -5.04316 q^{8} +2.36088 q^{9} +5.42429 q^{10} -1.81246 q^{11} -9.37786 q^{12} +1.00000 q^{13} +2.19069 q^{14} +5.10591 q^{15} +4.30426 q^{16} -2.96099 q^{17} -5.80714 q^{18} -7.45390 q^{19} -8.93184 q^{20} +2.06210 q^{21} +4.45818 q^{22} -8.54775 q^{23} +11.6767 q^{24} -0.136930 q^{25} -2.45973 q^{26} +1.47979 q^{27} -3.60726 q^{28} +10.0296 q^{29} -12.5592 q^{30} -7.75715 q^{31} -0.500998 q^{32} +4.19650 q^{33} +7.28324 q^{34} +1.96403 q^{35} +9.56225 q^{36} +7.12117 q^{37} +18.3346 q^{38} -2.31536 q^{39} +11.1214 q^{40} +1.41132 q^{41} -5.07222 q^{42} +4.26646 q^{43} -7.34100 q^{44} -5.20630 q^{45} +21.0252 q^{46} +8.74552 q^{47} -9.96589 q^{48} -6.20680 q^{49} +0.336812 q^{50} +6.85575 q^{51} +4.05029 q^{52} +2.66520 q^{53} -3.63989 q^{54} +3.99691 q^{55} +4.49153 q^{56} +17.2585 q^{57} -24.6702 q^{58} -4.22538 q^{59} +20.6804 q^{60} -15.1537 q^{61} +19.0805 q^{62} -2.10265 q^{63} -7.37619 q^{64} -2.20524 q^{65} -10.3223 q^{66} -12.7596 q^{67} -11.9929 q^{68} +19.7911 q^{69} -4.83098 q^{70} +15.0852 q^{71} -11.9063 q^{72} +9.95574 q^{73} -17.5162 q^{74} +0.317043 q^{75} -30.1905 q^{76} +1.61421 q^{77} +5.69516 q^{78} -6.85303 q^{79} -9.49190 q^{80} -10.5089 q^{81} -3.47147 q^{82} -5.19063 q^{83} +8.35210 q^{84} +6.52968 q^{85} -10.4943 q^{86} -23.2221 q^{87} +9.14055 q^{88} +9.77411 q^{89} +12.8061 q^{90} -0.890619 q^{91} -34.6209 q^{92} +17.9606 q^{93} -21.5116 q^{94} +16.4376 q^{95} +1.15999 q^{96} +1.22167 q^{97} +15.2671 q^{98} -4.27901 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9} - 33 q^{10} - 47 q^{11} - 53 q^{12} + 134 q^{13} - 28 q^{14} - 30 q^{15} + 30 q^{16} - 17 q^{17} - 14 q^{18} - 87 q^{19} - 12 q^{20} - 24 q^{21} - 52 q^{22} - 44 q^{23} - 36 q^{24} + 58 q^{25} - 6 q^{26} - 117 q^{27} - 71 q^{28} - 42 q^{29} - 21 q^{30} - 82 q^{31} - 31 q^{32} + 12 q^{33} - 30 q^{34} - 54 q^{35} + 32 q^{36} - 55 q^{37} - 12 q^{38} - 33 q^{39} - 86 q^{40} - 16 q^{41} + 6 q^{42} - 148 q^{43} - 54 q^{44} - 24 q^{45} - 57 q^{46} - 21 q^{47} - 82 q^{48} + 12 q^{49} - 17 q^{50} - 123 q^{51} + 98 q^{52} - 17 q^{53} - 10 q^{54} - 148 q^{55} - 47 q^{56} - q^{57} - 58 q^{58} - 64 q^{59} - 16 q^{60} - 112 q^{61} - 15 q^{62} - 58 q^{63} - 65 q^{64} - 8 q^{65} - 20 q^{66} - 110 q^{67} - 8 q^{68} - 57 q^{69} - 40 q^{70} - 78 q^{71} - 28 q^{72} - 43 q^{73} - 52 q^{74} - 150 q^{75} - 96 q^{76} - 24 q^{77} - 16 q^{78} - 228 q^{79} + 20 q^{80} + 54 q^{81} - 89 q^{82} - 12 q^{83} + 6 q^{84} - 77 q^{85} + 29 q^{86} - 77 q^{87} - 95 q^{88} - 32 q^{89} - 46 q^{90} - 32 q^{91} - 62 q^{92} - 9 q^{93} - 87 q^{94} - 61 q^{95} - 54 q^{96} - 38 q^{97} + 6 q^{98} - 193 q^{99}+O(q^{100}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9 - 33 * q^10 - 47 * q^11 - 53 * q^12 + 134 * q^13 - 28 * q^14 - 30 * q^15 + 30 * q^16 - 17 * q^17 - 14 * q^18 - 87 * q^19 - 12 * q^20 - 24 * q^21 - 52 * q^22 - 44 * q^23 - 36 * q^24 + 58 * q^25 - 6 * q^26 - 117 * q^27 - 71 * q^28 - 42 * q^29 - 21 * q^30 - 82 * q^31 - 31 * q^32 + 12 * q^33 - 30 * q^34 - 54 * q^35 + 32 * q^36 - 55 * q^37 - 12 * q^38 - 33 * q^39 - 86 * q^40 - 16 * q^41 + 6 * q^42 - 148 * q^43 - 54 * q^44 - 24 * q^45 - 57 * q^46 - 21 * q^47 - 82 * q^48 + 12 * q^49 - 17 * q^50 - 123 * q^51 + 98 * q^52 - 17 * q^53 - 10 * q^54 - 148 * q^55 - 47 * q^56 - q^57 - 58 * q^58 - 64 * q^59 - 16 * q^60 - 112 * q^61 - 15 * q^62 - 58 * q^63 - 65 * q^64 - 8 * q^65 - 20 * q^66 - 110 * q^67 - 8 * q^68 - 57 * q^69 - 40 * q^70 - 78 * q^71 - 28 * q^72 - 43 * q^73 - 52 * q^74 - 150 * q^75 - 96 * q^76 - 24 * q^77 - 16 * q^78 - 228 * q^79 + 20 * q^80 + 54 * q^81 - 89 * q^82 - 12 * q^83 + 6 * q^84 - 77 * q^85 + 29 * q^86 - 77 * q^87 - 95 * q^88 - 32 * q^89 - 46 * q^90 - 32 * q^91 - 62 * q^92 - 9 * q^93 - 87 * q^94 - 61 * q^95 - 54 * q^96 - 38 * q^97 + 6 * q^98 - 193 * q^99

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