LMFDB - Embedded newform 6033.2.a.c.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, 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("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.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:	$48.1737475394$
Analytic rank:	$0$
Dimension:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.08527 q^{2} -1.00000 q^{3} +2.34836 q^{4} -0.259814 q^{5} +2.08527 q^{6} +3.95786 q^{7} -0.726422 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.08527 q^{2} -1.00000 q^{3} +2.34836 q^{4} -0.259814 q^{5} +2.08527 q^{6} +3.95786 q^{7} -0.726422 q^{8} +1.00000 q^{9} +0.541783 q^{10} +2.81329 q^{11} -2.34836 q^{12} -2.02574 q^{13} -8.25322 q^{14} +0.259814 q^{15} -3.18193 q^{16} +2.88257 q^{17} -2.08527 q^{18} +8.25612 q^{19} -0.610136 q^{20} -3.95786 q^{21} -5.86648 q^{22} +6.41003 q^{23} +0.726422 q^{24} -4.93250 q^{25} +4.22422 q^{26} -1.00000 q^{27} +9.29448 q^{28} -0.621250 q^{29} -0.541783 q^{30} -5.79672 q^{31} +8.08803 q^{32} -2.81329 q^{33} -6.01094 q^{34} -1.02831 q^{35} +2.34836 q^{36} -1.61193 q^{37} -17.2162 q^{38} +2.02574 q^{39} +0.188735 q^{40} +11.0031 q^{41} +8.25322 q^{42} +9.86758 q^{43} +6.60662 q^{44} -0.259814 q^{45} -13.3667 q^{46} -3.85623 q^{47} +3.18193 q^{48} +8.66466 q^{49} +10.2856 q^{50} -2.88257 q^{51} -4.75716 q^{52} +5.57227 q^{53} +2.08527 q^{54} -0.730933 q^{55} -2.87508 q^{56} -8.25612 q^{57} +1.29548 q^{58} -6.73476 q^{59} +0.610136 q^{60} +10.9500 q^{61} +12.0877 q^{62} +3.95786 q^{63} -10.5019 q^{64} +0.526315 q^{65} +5.86648 q^{66} -10.8632 q^{67} +6.76930 q^{68} -6.41003 q^{69} +2.14430 q^{70} +10.5724 q^{71} -0.726422 q^{72} -1.63692 q^{73} +3.36131 q^{74} +4.93250 q^{75} +19.3883 q^{76} +11.1346 q^{77} -4.22422 q^{78} -1.43939 q^{79} +0.826710 q^{80} +1.00000 q^{81} -22.9444 q^{82} +3.63486 q^{83} -9.29448 q^{84} -0.748931 q^{85} -20.5766 q^{86} +0.621250 q^{87} -2.04364 q^{88} +11.9354 q^{89} +0.541783 q^{90} -8.01760 q^{91} +15.0531 q^{92} +5.79672 q^{93} +8.04128 q^{94} -2.14505 q^{95} -8.08803 q^{96} +9.16399 q^{97} -18.0682 q^{98} +2.81329 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9}+O(q^{10}) $ 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9	\( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9} - 9 q^{10} + 28 q^{11} - 87 q^{12} - 14 q^{13} + 21 q^{14} - 7 q^{15} + 93 q^{16} + 25 q^{17} + 13 q^{18} - 7 q^{19} + 40 q^{20} - 30 q^{21} + 31 q^{22} + 97 q^{23} - 39 q^{24} + 83 q^{25} + 22 q^{26} - 82 q^{27} + 53 q^{28} + 45 q^{29} + 9 q^{30} - 11 q^{31} + 86 q^{32} - 28 q^{33} - 30 q^{34} + 69 q^{35} + 87 q^{36} + 8 q^{37} + 33 q^{38} + 14 q^{39} - 38 q^{40} + 12 q^{41} - 21 q^{42} + 68 q^{43} + 77 q^{44} + 7 q^{45} - 14 q^{46} + 85 q^{47} - 93 q^{48} + 68 q^{49} + 56 q^{50} - 25 q^{51} - 18 q^{52} + 58 q^{53} - 13 q^{54} + 68 q^{55} + 59 q^{56} + 7 q^{57} + 27 q^{58} + 40 q^{59} - 40 q^{60} - 116 q^{61} + 79 q^{62} + 30 q^{63} + 127 q^{64} + 66 q^{65} - 31 q^{66} + 51 q^{67} + 94 q^{68} - 97 q^{69} + q^{70} + 101 q^{71} + 39 q^{72} + 12 q^{73} + 72 q^{74} - 83 q^{75} - 3 q^{76} + 101 q^{77} - 22 q^{78} + 26 q^{79} + 61 q^{80} + 82 q^{81} + 31 q^{82} + 94 q^{83} - 53 q^{84} - 8 q^{85} + 68 q^{86} - 45 q^{87} + 91 q^{88} + 40 q^{89} - 9 q^{90} - 6 q^{91} + 180 q^{92} + 11 q^{93} - 31 q^{94} + 153 q^{95} - 86 q^{96} - 39 q^{97} + 115 q^{98} + 28 q^{99}+O(q^{100}) \) 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9 - 9 * q^10 + 28 * q^11 - 87 * q^12 - 14 * q^13 + 21 * q^14 - 7 * q^15 + 93 * q^16 + 25 * q^17 + 13 * q^18 - 7 * q^19 + 40 * q^20 - 30 * q^21 + 31 * q^22 + 97 * q^23 - 39 * q^24 + 83 * q^25 + 22 * q^26 - 82 * q^27 + 53 * q^28 + 45 * q^29 + 9 * q^30 - 11 * q^31 + 86 * q^32 - 28 * q^33 - 30 * q^34 + 69 * q^35 + 87 * q^36 + 8 * q^37 + 33 * q^38 + 14 * q^39 - 38 * q^40 + 12 * q^41 - 21 * q^42 + 68 * q^43 + 77 * q^44 + 7 * q^45 - 14 * q^46 + 85 * q^47 - 93 * q^48 + 68 * q^49 + 56 * q^50 - 25 * q^51 - 18 * q^52 + 58 * q^53 - 13 * q^54 + 68 * q^55 + 59 * q^56 + 7 * q^57 + 27 * q^58 + 40 * q^59 - 40 * q^60 - 116 * q^61 + 79 * q^62 + 30 * q^63 + 127 * q^64 + 66 * q^65 - 31 * q^66 + 51 * q^67 + 94 * q^68 - 97 * q^69 + q^70 + 101 * q^71 + 39 * q^72 + 12 * q^73 + 72 * q^74 - 83 * q^75 - 3 * q^76 + 101 * q^77 - 22 * q^78 + 26 * q^79 + 61 * q^80 + 82 * q^81 + 31 * q^82 + 94 * q^83 - 53 * q^84 - 8 * q^85 + 68 * q^86 - 45 * q^87 + 91 * q^88 + 40 * q^89 - 9 * q^90 - 6 * q^91 + 180 * q^92 + 11 * q^93 - 31 * q^94 + 153 * q^95 - 86 * q^96 - 39 * q^97 + 115 * q^98 + 28 * 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 $

$2$	−2.08527	−1.47451	−0.737255	−	0.675615i	$-0.763878\pi$
$2$	−2.08527	−1.47451	−0.737255	+	0.675615i	$0.763878\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.34836	1.17418
$5$	−0.259814	−0.116192	−0.0580962	−	0.998311i	$-0.518503\pi$
$5$	−0.259814	−0.116192	−0.0580962	+	0.998311i	$0.518503\pi$
$6$	2.08527	0.851309
$7$	3.95786	1.49593	0.747965	−	0.663738i	$-0.231031\pi$
$7$	3.95786	1.49593	0.747965	+	0.663738i	$0.231031\pi$
$8$	−0.726422	−0.256829
$9$	1.00000	0.333333
$10$	0.541783	0.171327
$11$	2.81329	0.848240	0.424120	−	0.905606i	$-0.360584\pi$
$11$	2.81329	0.848240	0.424120	+	0.905606i	$0.360584\pi$
$12$	−2.34836	−0.677913
$13$	−2.02574	−0.561839	−0.280920	−	0.959731i	$-0.590639\pi$
$13$	−2.02574	−0.561839	−0.280920	+	0.959731i	$0.590639\pi$
$14$	−8.25322	−2.20576
$15$	0.259814	0.0670837
$16$	−3.18193	−0.795482
$17$	2.88257	0.699125	0.349563	−	0.936913i	$-0.386330\pi$
$17$	2.88257	0.699125	0.349563	+	0.936913i	$0.386330\pi$
$18$	−2.08527	−0.491503
$19$	8.25612	1.89408	0.947042	−	0.321111i	$-0.104056\pi$
$19$	8.25612	1.89408	0.947042	+	0.321111i	$0.104056\pi$
$20$	−0.610136	−0.136431
$21$	−3.95786	−0.863676
$22$	−5.86648	−1.25074
$23$	6.41003	1.33658	0.668292	−	0.743899i	$-0.267026\pi$
$23$	6.41003	1.33658	0.668292	+	0.743899i	$0.267026\pi$
$24$	0.726422	0.148280
$25$	−4.93250	−0.986499
$26$	4.22422	0.828437
$27$	−1.00000	−0.192450
$28$	9.29448	1.75649
$29$	−0.621250	−0.115363	−0.0576817	−	0.998335i	$-0.518371\pi$
$29$	−0.621250	−0.115363	−0.0576817	+	0.998335i	$0.518371\pi$
$30$	−0.541783	−0.0989155
$31$	−5.79672	−1.04112	−0.520561	−	0.853824i	$-0.674277\pi$
$31$	−5.79672	−1.04112	−0.520561	+	0.853824i	$0.674277\pi$
$32$	8.08803	1.42978
$33$	−2.81329	−0.489731
$34$	−6.01094	−1.03087
$35$	−1.02831	−0.173816
$36$	2.34836	0.391393
$37$	−1.61193	−0.264999	−0.132500	−	0.991183i	$-0.542300\pi$
$37$	−1.61193	−0.264999	−0.132500	+	0.991183i	$0.542300\pi$
$38$	−17.2162	−2.79284
$39$	2.02574	0.324378
$40$	0.188735	0.0298416
$41$	11.0031	1.71839	0.859194	−	0.511649i	$-0.170965\pi$
$41$	11.0031	1.71839	0.859194	+	0.511649i	$0.170965\pi$
$42$	8.25322	1.27350
$43$	9.86758	1.50479	0.752396	−	0.658711i	$-0.228898\pi$
$43$	9.86758	1.50479	0.752396	+	0.658711i	$0.228898\pi$
$44$	6.60662	0.995985
$45$	−0.259814	−0.0387308
$46$	−13.3667	−1.97081
$47$	−3.85623	−0.562489	−0.281244	−	0.959636i	$-0.590747\pi$
$47$	−3.85623	−0.562489	−0.281244	+	0.959636i	$0.590747\pi$
$48$	3.18193	0.459272
$49$	8.66466	1.23781
$50$	10.2856	1.45460
$51$	−2.88257	−0.403640
$52$	−4.75716	−0.659700
$53$	5.57227	0.765410	0.382705	−	0.923871i	$-0.374993\pi$
$53$	5.57227	0.765410	0.382705	+	0.923871i	$0.374993\pi$
$54$	2.08527	0.283770
$55$	−0.730933	−0.0985589
$56$	−2.87508	−0.384198
$57$	−8.25612	−1.09355
$58$	1.29548	0.170104
$59$	−6.73476	−0.876791	−0.438395	−	0.898782i	$-0.644453\pi$
$59$	−6.73476	−0.876791	−0.438395	+	0.898782i	$0.644453\pi$
$60$	0.610136	0.0787683
$61$	10.9500	1.40200	0.701001	−	0.713160i	$-0.252737\pi$
$61$	10.9500	1.40200	0.701001	+	0.713160i	$0.252737\pi$
$62$	12.0877	1.53515
$63$	3.95786	0.498644
$64$	−10.5019	−1.31274
$65$	0.526315	0.0652814
$66$	5.86648	0.722114
$67$	−10.8632	−1.32715	−0.663574	−	0.748111i	$-0.730961\pi$
$67$	−10.8632	−1.32715	−0.663574	+	0.748111i	$0.730961\pi$
$68$	6.76930	0.820898
$69$	−6.41003	−0.771677
$70$	2.14430	0.256293
$71$	10.5724	1.25471	0.627356	−	0.778733i	$-0.284137\pi$
$71$	10.5724	1.25471	0.627356	+	0.778733i	$0.284137\pi$
$72$	−0.726422	−0.0856096
$73$	−1.63692	−0.191587	−0.0957933	−	0.995401i	$-0.530539\pi$
$73$	−1.63692	−0.191587	−0.0957933	+	0.995401i	$0.530539\pi$
$74$	3.36131	0.390744
$75$	4.93250	0.569556
$76$	19.3883	2.22399
$77$	11.1346	1.26891
$78$	−4.22422	−0.478298
$79$	−1.43939	−0.161945	−0.0809723	−	0.996716i	$-0.525803\pi$
$79$	−1.43939	−0.161945	−0.0809723	+	0.996716i	$0.525803\pi$
$80$	0.826710	0.0924289
$81$	1.00000	0.111111
$82$	−22.9444	−2.53378
$83$	3.63486	0.398978	0.199489	−	0.979900i	$-0.436072\pi$
$83$	3.63486	0.398978	0.199489	+	0.979900i	$0.436072\pi$
$84$	−9.29448	−1.01411
$85$	−0.748931	−0.0812330
$86$	−20.5766	−2.21883
$87$	0.621250	0.0666050
$88$	−2.04364	−0.217852
$89$	11.9354	1.26515	0.632574	−	0.774500i	$-0.281998\pi$
$89$	11.9354	1.26515	0.632574	+	0.774500i	$0.281998\pi$
$90$	0.541783	0.0571089
$91$	−8.01760	−0.840472
$92$	15.0531	1.56939
$93$	5.79672	0.601092
$94$	8.04128	0.829395
$95$	−2.14505	−0.220078
$96$	−8.08803	−0.825481
$97$	9.16399	0.930463	0.465231	−	0.885189i	$-0.345971\pi$
$97$	9.16399	0.930463	0.465231	+	0.885189i	$0.345971\pi$
$98$	−18.0682	−1.82516
$99$	2.81329	0.282747
$100$	−11.5833	−1.15833
$101$	−2.05658	−0.204637	−0.102319	−	0.994752i	$-0.532626\pi$
$101$	−2.05658	−0.204637	−0.102319	+	0.994752i	$0.532626\pi$
$102$	6.01094	0.595171
$103$	−2.12049	−0.208938	−0.104469	−	0.994528i	$-0.533314\pi$
$103$	−2.12049	−0.208938	−0.104469	+	0.994528i	$0.533314\pi$
$104$	1.47154	0.144297
$105$	1.02831	0.100353
$106$	−11.6197	−1.12860
$107$	16.0140	1.54813	0.774064	−	0.633107i	$-0.218221\pi$
$107$	16.0140	1.54813	0.774064	+	0.633107i	$0.218221\pi$
$108$	−2.34836	−0.225971
$109$	−7.14067	−0.683952	−0.341976	−	0.939709i	$-0.611096\pi$
$109$	−7.14067	−0.683952	−0.341976	+	0.939709i	$0.611096\pi$
$110$	1.52419	0.145326
$111$	1.61193	0.152997
$112$	−12.5936	−1.18999
$113$	8.33215	0.783823	0.391911	−	0.920003i	$-0.371814\pi$
$113$	8.33215	0.783823	0.391911	+	0.920003i	$0.371814\pi$
$114$	17.2162	1.61245
$115$	−1.66542	−0.155301
$116$	−1.45892	−0.135457
$117$	−2.02574	−0.187280
$118$	14.0438	1.29284
$119$	11.4088	1.04584
$120$	−0.188735	−0.0172290
$121$	−3.08539	−0.280490
$122$	−22.8337	−2.06727
$123$	−11.0031	−0.992112
$124$	−13.6128	−1.22246
$125$	2.58060	0.230816
$126$	−8.25322	−0.735255
$127$	3.73630	0.331543	0.165771	−	0.986164i	$-0.446989\pi$
$127$	3.73630	0.331543	0.165771	+	0.986164i	$0.446989\pi$
$128$	5.72322	0.505866
$129$	−9.86758	−0.868792
$130$	−1.09751	−0.0962581
$131$	5.37955	0.470013	0.235007	−	0.971994i	$-0.424489\pi$
$131$	5.37955	0.470013	0.235007	+	0.971994i	$0.424489\pi$
$132$	−6.60662	−0.575032
$133$	32.6766	2.83342
$134$	22.6527	1.95689
$135$	0.259814	0.0223612
$136$	−2.09396	−0.179556
$137$	−2.44449	−0.208847	−0.104423	−	0.994533i	$-0.533300\pi$
$137$	−2.44449	−0.208847	−0.104423	+	0.994533i	$0.533300\pi$
$138$	13.3667	1.13785
$139$	−11.5698	−0.981336	−0.490668	−	0.871347i	$-0.663247\pi$
$139$	−11.5698	−0.981336	−0.490668	+	0.871347i	$0.663247\pi$
$140$	−2.41483	−0.204091
$141$	3.85623	0.324753
$142$	−22.0463	−1.85009
$143$	−5.69900	−0.476574
$144$	−3.18193	−0.265161
$145$	0.161410	0.0134043
$146$	3.41342	0.282496
$147$	−8.66466	−0.714649
$148$	−3.78539	−0.311157
$149$	−7.25915	−0.594693	−0.297346	−	0.954770i	$-0.596102\pi$
$149$	−7.25915	−0.594693	−0.297346	+	0.954770i	$0.596102\pi$
$150$	−10.2856	−0.839815
$151$	4.54310	0.369712	0.184856	−	0.982766i	$-0.440818\pi$
$151$	4.54310	0.369712	0.184856	+	0.982766i	$0.440818\pi$
$152$	−5.99743	−0.486455
$153$	2.88257	0.233042
$154$	−23.2187	−1.87102
$155$	1.50607	0.120970
$156$	4.75716	0.380878
$157$	13.8348	1.10414	0.552068	−	0.833799i	$-0.313839\pi$
$157$	13.8348	1.10414	0.552068	+	0.833799i	$0.313839\pi$
$158$	3.00153	0.238789
$159$	−5.57227	−0.441909
$160$	−2.10138	−0.166129
$161$	25.3700	1.99944
$162$	−2.08527	−0.163834
$163$	−16.3973	−1.28434	−0.642168	−	0.766564i	$-0.721965\pi$
$163$	−16.3973	−1.28434	−0.642168	+	0.766564i	$0.721965\pi$
$164$	25.8391	2.01770
$165$	0.730933	0.0569030
$166$	−7.57967	−0.588297
$167$	−8.54532	−0.661257	−0.330628	−	0.943761i	$-0.607261\pi$
$167$	−8.54532	−0.661257	−0.330628	+	0.943761i	$0.607261\pi$
$168$	2.87508	0.221817
$169$	−8.89638	−0.684337
$170$	1.56172	0.119779
$171$	8.25612	0.631361
$172$	23.1726	1.76690
$173$	−12.3876	−0.941812	−0.470906	−	0.882183i	$-0.656073\pi$
$173$	−12.3876	−0.941812	−0.470906	+	0.882183i	$0.656073\pi$
$174$	−1.29548	−0.0982098
$175$	−19.5221	−1.47573
$176$	−8.95170	−0.674760
$177$	6.73476	0.506215
$178$	−24.8885	−1.86547
$179$	5.44764	0.407176	0.203588	−	0.979057i	$-0.434740\pi$
$179$	5.44764	0.407176	0.203588	+	0.979057i	$0.434740\pi$
$180$	−0.610136	−0.0454769
$181$	−5.06182	−0.376242	−0.188121	−	0.982146i	$-0.560240\pi$
$181$	−5.06182	−0.376242	−0.188121	+	0.982146i	$0.560240\pi$
$182$	16.7189	1.23928
$183$	−10.9500	−0.809446
$184$	−4.65639	−0.343273
$185$	0.418801	0.0307909
$186$	−12.0877	−0.886317
$187$	8.10950	0.593026
$188$	−9.05580	−0.660462
$189$	−3.95786	−0.287892
$190$	4.47302	0.324507
$191$	−25.3559	−1.83469	−0.917344	−	0.398094i	$-0.869672\pi$
$191$	−25.3559	−1.83469	−0.917344	+	0.398094i	$0.869672\pi$
$192$	10.5019	0.757908
$193$	−20.3401	−1.46411	−0.732057	−	0.681243i	$-0.761440\pi$
$193$	−20.3401	−1.46411	−0.732057	+	0.681243i	$0.761440\pi$
$194$	−19.1094	−1.37198
$195$	−0.526315	−0.0376902
$196$	20.3477	1.45341
$197$	−14.8051	−1.05482	−0.527408	−	0.849612i	$-0.676836\pi$
$197$	−14.8051	−1.05482	−0.527408	+	0.849612i	$0.676836\pi$
$198$	−5.86648	−0.416912
$199$	2.51914	0.178577	0.0892887	−	0.996006i	$-0.471541\pi$
$199$	2.51914	0.178577	0.0892887	+	0.996006i	$0.471541\pi$
$200$	3.58307	0.253362
$201$	10.8632	0.766229
$202$	4.28852	0.301739
$203$	−2.45882	−0.172576
$204$	−6.76930	−0.473946
$205$	−2.85875	−0.199664
$206$	4.42180	0.308081
$207$	6.41003	0.445528
$208$	6.44576	0.446933
$209$	23.2269	1.60664
$210$	−2.14430	−0.147971
$211$	−1.39459	−0.0960079	−0.0480039	−	0.998847i	$-0.515286\pi$
$211$	−1.39459	−0.0960079	−0.0480039	+	0.998847i	$0.515286\pi$
$212$	13.0857	0.898728
$213$	−10.5724	−0.724408
$214$	−33.3935	−2.28273
$215$	−2.56374	−0.174845
$216$	0.726422	0.0494268
$217$	−22.9426	−1.55745
$218$	14.8902	1.00849
$219$	1.63692	0.110613
$220$	−1.71649	−0.115726
$221$	−5.83933	−0.392796
$222$	−3.36131	−0.225596
$223$	−16.1343	−1.08043	−0.540215	−	0.841527i	$-0.681657\pi$
$223$	−16.1343	−1.08043	−0.540215	+	0.841527i	$0.681657\pi$
$224$	32.0113	2.13885
$225$	−4.93250	−0.328833
$226$	−17.3748	−1.15575
$227$	−19.5072	−1.29474	−0.647368	−	0.762178i	$-0.724130\pi$
$227$	−19.5072	−1.29474	−0.647368	+	0.762178i	$0.724130\pi$
$228$	−19.3883	−1.28402
$229$	11.6189	0.767798	0.383899	−	0.923375i	$-0.374581\pi$
$229$	11.6189	0.767798	0.383899	+	0.923375i	$0.374581\pi$
$230$	3.47284	0.228993
$231$	−11.1346	−0.732604
$232$	0.451290	0.0296286
$233$	20.1264	1.31853	0.659263	−	0.751913i	$-0.270869\pi$
$233$	20.1264	1.31853	0.659263	+	0.751913i	$0.270869\pi$
$234$	4.22422	0.276146
$235$	1.00190	0.0653569
$236$	−15.8156	−1.02951
$237$	1.43939	0.0934987
$238$	−23.7904	−1.54211
$239$	16.3390	1.05688	0.528442	−	0.848969i	$-0.322776\pi$
$239$	16.3390	1.05688	0.528442	+	0.848969i	$0.322776\pi$
$240$	−0.826710	−0.0533639
$241$	−20.4100	−1.31472	−0.657361	−	0.753576i	$-0.728327\pi$
$241$	−20.4100	−1.31472	−0.657361	+	0.753576i	$0.728327\pi$
$242$	6.43387	0.413585
$243$	−1.00000	−0.0641500
$244$	25.7145	1.64620
$245$	−2.25120	−0.143824
$246$	22.9444	1.46288
$247$	−16.7247	−1.06417
$248$	4.21087	0.267390
$249$	−3.63486	−0.230350
$250$	−5.38125	−0.340340
$251$	−8.87518	−0.560197	−0.280098	−	0.959971i	$-0.590367\pi$
$251$	−8.87518	−0.560197	−0.280098	+	0.959971i	$0.590367\pi$
$252$	9.29448	0.585497
$253$	18.0333	1.13374
$254$	−7.79120	−0.488863
$255$	0.748931	0.0468999
$256$	9.06930	0.566831
$257$	28.1462	1.75571	0.877856	−	0.478924i	$-0.158973\pi$
$257$	28.1462	1.75571	0.877856	+	0.478924i	$0.158973\pi$
$258$	20.5766	1.28104
$259$	−6.37979	−0.396421
$260$	1.23598	0.0766521
$261$	−0.621250	−0.0384544
$262$	−11.2178	−0.693039
$263$	−11.1115	−0.685162	−0.342581	−	0.939488i	$-0.611301\pi$
$263$	−11.1115	−0.685162	−0.342581	+	0.939488i	$0.611301\pi$
$264$	2.04364	0.125777
$265$	−1.44775	−0.0889347
$266$	−68.1395	−4.17790
$267$	−11.9354	−0.730433
$268$	−25.5106	−1.55831
$269$	−11.4451	−0.697823	−0.348911	−	0.937156i	$-0.613449\pi$
$269$	−11.4451	−0.697823	−0.348911	+	0.937156i	$0.613449\pi$
$270$	−0.541783	−0.0329718
$271$	19.7022	1.19683	0.598413	−	0.801188i	$-0.295798\pi$
$271$	19.7022	1.19683	0.598413	+	0.801188i	$0.295798\pi$
$272$	−9.17213	−0.556142
$273$	8.01760	0.485247
$274$	5.09742	0.307947
$275$	−13.8766	−0.836788
$276$	−15.0531	−0.906087
$277$	11.9946	0.720688	0.360344	−	0.932819i	$-0.382659\pi$
$277$	11.9946	0.720688	0.360344	+	0.932819i	$0.382659\pi$
$278$	24.1261	1.44699
$279$	−5.79672	−0.347041
$280$	0.746985	0.0446409
$281$	−18.1193	−1.08091	−0.540453	−	0.841374i	$-0.681747\pi$
$281$	−18.1193	−1.08091	−0.540453	+	0.841374i	$0.681747\pi$
$282$	−8.04128	−0.478851
$283$	0.458464	0.0272528	0.0136264	−	0.999907i	$-0.495662\pi$
$283$	0.458464	0.0272528	0.0136264	+	0.999907i	$0.495662\pi$
$284$	24.8278	1.47326
$285$	2.14505	0.127062
$286$	11.8840	0.702713
$287$	43.5486	2.57059
$288$	8.08803	0.476592
$289$	−8.69081	−0.511224
$290$	−0.336583	−0.0197648
$291$	−9.16399	−0.537203
$292$	−3.84407	−0.224957
$293$	1.81720	0.106162	0.0530809	−	0.998590i	$-0.483096\pi$
$293$	1.81720	0.106162	0.0530809	+	0.998590i	$0.483096\pi$
$294$	18.0682	1.05376
$295$	1.74978	0.101876
$296$	1.17094	0.0680595
$297$	−2.81329	−0.163244
$298$	15.1373	0.876880
$299$	−12.9851	−0.750945
$300$	11.5833	0.668760
$301$	39.0545	2.25106
$302$	−9.47359	−0.545144
$303$	2.05658	0.118147
$304$	−26.2704	−1.50671
$305$	−2.84496	−0.162902
$306$	−6.01094	−0.343622
$307$	−14.5092	−0.828082	−0.414041	−	0.910258i	$-0.635883\pi$
$307$	−14.5092	−0.828082	−0.414041	+	0.910258i	$0.635883\pi$
$308$	26.1481	1.48992
$309$	2.12049	0.120630
$310$	−3.14056	−0.178372
$311$	−10.5099	−0.595961	−0.297980	−	0.954572i	$-0.596313\pi$
$311$	−10.5099	−0.595961	−0.297980	+	0.954572i	$0.596313\pi$
$312$	−1.47154	−0.0833096
$313$	2.88770	0.163222	0.0816111	−	0.996664i	$-0.473993\pi$
$313$	2.88770	0.163222	0.0816111	+	0.996664i	$0.473993\pi$
$314$	−28.8493	−1.62806
$315$	−1.02831	−0.0579386
$316$	−3.38022	−0.190152
$317$	6.73333	0.378181	0.189091	−	0.981960i	$-0.439446\pi$
$317$	6.73333	0.378181	0.189091	+	0.981960i	$0.439446\pi$
$318$	11.6197	0.651600
$319$	−1.74776	−0.0978557
$320$	2.72854	0.152530
$321$	−16.0140	−0.893812
$322$	−52.9034	−2.94819
$323$	23.7988	1.32420
$324$	2.34836	0.130464
$325$	9.99195	0.554254
$326$	34.1929	1.89377
$327$	7.14067	0.394880
$328$	−7.99286	−0.441332
$329$	−15.2624	−0.841444
$330$	−1.52419	−0.0839041
$331$	−23.6743	−1.30126	−0.650628	−	0.759397i	$-0.725494\pi$
$331$	−23.6743	−1.30126	−0.650628	+	0.759397i	$0.725494\pi$
$332$	8.53595	0.468471
$333$	−1.61193	−0.0883331
$334$	17.8193	0.975030
$335$	2.82240	0.154204
$336$	12.5936	0.687039
$337$	−27.2968	−1.48695	−0.743475	−	0.668763i	$-0.766824\pi$
$337$	−27.2968	−1.48695	−0.743475	+	0.668763i	$0.766824\pi$
$338$	18.5514	1.00906
$339$	−8.33215	−0.452540
$340$	−1.75876	−0.0953821
$341$	−16.3079	−0.883121
$342$	−17.2162	−0.930948
$343$	6.58850	0.355746
$344$	−7.16803	−0.386474
$345$	1.66542	0.0896630
$346$	25.8315	1.38871
$347$	−12.9262	−0.693914	−0.346957	−	0.937881i	$-0.612785\pi$
$347$	−12.9262	−0.693914	−0.346957	+	0.937881i	$0.612785\pi$
$348$	1.45892	0.0782062
$349$	−12.4466	−0.666252	−0.333126	−	0.942882i	$-0.608103\pi$
$349$	−12.4466	−0.666252	−0.333126	+	0.942882i	$0.608103\pi$
$350$	40.7090	2.17599
$351$	2.02574	0.108126
$352$	22.7540	1.21279
$353$	13.4224	0.714400	0.357200	−	0.934028i	$-0.383731\pi$
$353$	13.4224	0.714400	0.357200	+	0.934028i	$0.383731\pi$
$354$	−14.0438	−0.746419
$355$	−2.74685	−0.145788
$356$	28.0286	1.48551
$357$	−11.4088	−0.603818
$358$	−11.3598	−0.600384
$359$	37.1888	1.96275	0.981376	−	0.192099i	$-0.0615293\pi$
$359$	37.1888	1.96275	0.981376	+	0.192099i	$0.0615293\pi$
$360$	0.188735	0.00994718
$361$	49.1635	2.58755
$362$	10.5553	0.554772
$363$	3.08539	0.161941
$364$	−18.8282	−0.986865
$365$	0.425294	0.0222609
$366$	22.8337	1.19354
$367$	18.6813	0.975158	0.487579	−	0.873079i	$-0.337880\pi$
$367$	18.6813	0.975158	0.487579	+	0.873079i	$0.337880\pi$
$368$	−20.3963	−1.06323
$369$	11.0031	0.572796
$370$	−0.873315	−0.0454015
$371$	22.0543	1.14500
$372$	13.6128	0.705790
$373$	20.9536	1.08493	0.542467	−	0.840077i	$-0.317490\pi$
$373$	20.9536	1.08493	0.542467	+	0.840077i	$0.317490\pi$
$374$	−16.9105	−0.874422
$375$	−2.58060	−0.133262
$376$	2.80125	0.144463
$377$	1.25849	0.0648156
$378$	8.25322	0.424500
$379$	−17.8104	−0.914858	−0.457429	−	0.889246i	$-0.651230\pi$
$379$	−17.8104	−0.914858	−0.457429	+	0.889246i	$0.651230\pi$
$380$	−5.03736	−0.258411
$381$	−3.73630	−0.191416
$382$	52.8740	2.70527
$383$	−9.23417	−0.471844	−0.235922	−	0.971772i	$-0.575811\pi$
$383$	−9.23417	−0.471844	−0.235922	+	0.971772i	$0.575811\pi$
$384$	−5.72322	−0.292062
$385$	−2.89293	−0.147437
$386$	42.4147	2.15885
$387$	9.86758	0.501597
$388$	21.5203	1.09253
$389$	2.03031	0.102941	0.0514704	−	0.998675i	$-0.483609\pi$
$389$	2.03031	0.102941	0.0514704	+	0.998675i	$0.483609\pi$
$390$	1.09751	0.0555746
$391$	18.4773	0.934440
$392$	−6.29420	−0.317905
$393$	−5.37955	−0.271362
$394$	30.8726	1.55534
$395$	0.373975	0.0188167
$396$	6.60662	0.331995
$397$	33.2096	1.66674	0.833370	−	0.552715i	$-0.186408\pi$
$397$	33.2096	1.66674	0.833370	+	0.552715i	$0.186408\pi$
$398$	−5.25310	−0.263314
$399$	−32.6766	−1.63587
$400$	15.6949	0.784743
$401$	−9.50941	−0.474877	−0.237439	−	0.971403i	$-0.576308\pi$
$401$	−9.50941	−0.474877	−0.237439	+	0.971403i	$0.576308\pi$
$402$	−22.6527	−1.12981
$403$	11.7427	0.584943
$404$	−4.82958	−0.240281
$405$	−0.259814	−0.0129103
$406$	5.12731	0.254464
$407$	−4.53483	−0.224783
$408$	2.09396	0.103666
$409$	11.5677	0.571988	0.285994	−	0.958231i	$-0.407676\pi$
$409$	11.5677	0.571988	0.285994	+	0.958231i	$0.407676\pi$
$410$	5.96127	0.294406
$411$	2.44449	0.120578
$412$	−4.97967	−0.245331
$413$	−26.6552	−1.31162
$414$	−13.3667	−0.656935
$415$	−0.944387	−0.0463581
$416$	−16.3842	−0.803304
$417$	11.5698	0.566575
$418$	−48.4343	−2.36900
$419$	−14.9138	−0.728589	−0.364294	−	0.931284i	$-0.618690\pi$
$419$	−14.9138	−0.728589	−0.364294	+	0.931284i	$0.618690\pi$
$420$	2.41483	0.117832
$421$	39.3784	1.91919	0.959594	−	0.281389i	$-0.0907950\pi$
$421$	39.3784	1.91919	0.959594	+	0.281389i	$0.0907950\pi$
$422$	2.90811	0.141565
$423$	−3.85623	−0.187496
$424$	−4.04782	−0.196579
$425$	−14.2183	−0.689687
$426$	22.0463	1.06815
$427$	43.3385	2.09730
$428$	37.6065	1.81778
$429$	5.69900	0.275150
$430$	5.34608	0.257811
$431$	−27.9199	−1.34486	−0.672428	−	0.740162i	$-0.734749\pi$
$431$	−27.9199	−1.34486	−0.672428	+	0.740162i	$0.734749\pi$
$432$	3.18193	0.153091
$433$	31.7365	1.52516	0.762578	−	0.646896i	$-0.223933\pi$
$433$	31.7365	1.52516	0.762578	+	0.646896i	$0.223933\pi$
$434$	47.8416	2.29647
$435$	−0.161410	−0.00773899
$436$	−16.7689	−0.803083
$437$	52.9220	2.53160
$438$	−3.41342	−0.163099
$439$	−12.3581	−0.589819	−0.294910	−	0.955525i	$-0.595290\pi$
$439$	−12.3581	−0.589819	−0.294910	+	0.955525i	$0.595290\pi$
$440$	0.530965	0.0253128
$441$	8.66466	0.412603
$442$	12.1766	0.579181
$443$	24.3068	1.15485	0.577425	−	0.816444i	$-0.304057\pi$
$443$	24.3068	1.15485	0.577425	+	0.816444i	$0.304057\pi$
$444$	3.78539	0.179646
$445$	−3.10098	−0.147000
$446$	33.6443	1.59310
$447$	7.25915	0.343346
$448$	−41.5650	−1.96376
$449$	31.0004	1.46300	0.731501	−	0.681841i	$-0.238820\pi$
$449$	31.0004	1.46300	0.731501	+	0.681841i	$0.238820\pi$
$450$	10.2856	0.484868
$451$	30.9548	1.45761
$452$	19.5669	0.920348
$453$	−4.54310	−0.213453
$454$	40.6777	1.90910
$455$	2.08308	0.0976564
$456$	5.99743	0.280855
$457$	−22.2869	−1.04254	−0.521269	−	0.853392i	$-0.674541\pi$
$457$	−22.2869	−1.04254	−0.521269	+	0.853392i	$0.674541\pi$
$458$	−24.2285	−1.13213
$459$	−2.88257	−0.134547
$460$	−3.91099	−0.182351
$461$	−22.1827	−1.03315	−0.516576	−	0.856241i	$-0.672794\pi$
$461$	−22.1827	−1.03315	−0.516576	+	0.856241i	$0.672794\pi$
$462$	23.2187	1.08023
$463$	−20.8454	−0.968770	−0.484385	−	0.874855i	$-0.660957\pi$
$463$	−20.8454	−0.968770	−0.484385	+	0.874855i	$0.660957\pi$
$464$	1.97678	0.0917695
$465$	−1.50607	−0.0698423
$466$	−41.9690	−1.94418
$467$	−16.7288	−0.774118	−0.387059	−	0.922055i	$-0.626509\pi$
$467$	−16.7288	−0.774118	−0.387059	+	0.922055i	$0.626509\pi$
$468$	−4.75716	−0.219900
$469$	−42.9949	−1.98532
$470$	−2.08924	−0.0963693
$471$	−13.8348	−0.637473
$472$	4.89228	0.225185
$473$	27.7604	1.27642
$474$	−3.00153	−0.137865
$475$	−40.7233	−1.86851
$476$	26.7919	1.22801
$477$	5.57227	0.255137
$478$	−34.0713	−1.55839
$479$	35.1021	1.60386	0.801928	−	0.597420i	$-0.203808\pi$
$479$	35.1021	1.60386	0.801928	+	0.597420i	$0.203808\pi$
$480$	2.10138	0.0959146
$481$	3.26535	0.148887
$482$	42.5603	1.93857
$483$	−25.3700	−1.15438
$484$	−7.24559	−0.329345
$485$	−2.38093	−0.108113
$486$	2.08527	0.0945898
$487$	17.5079	0.793359	0.396679	−	0.917957i	$-0.370162\pi$
$487$	17.5079	0.793359	0.396679	+	0.917957i	$0.370162\pi$
$488$	−7.95431	−0.360075
$489$	16.3973	0.741512
$490$	4.69436	0.212070
$491$	−22.8150	−1.02963	−0.514813	−	0.857303i	$-0.672139\pi$
$491$	−22.8150	−1.02963	−0.514813	+	0.857303i	$0.672139\pi$
$492$	−25.8391	−1.16492
$493$	−1.79080	−0.0806534
$494$	34.8756	1.56913
$495$	−0.730933	−0.0328530
$496$	18.4448	0.828195
$497$	41.8441	1.87696
$498$	7.57967	0.339653
$499$	−15.9139	−0.712405	−0.356203	−	0.934409i	$-0.615929\pi$
$499$	−15.9139	−0.712405	−0.356203	+	0.934409i	$0.615929\pi$
$500$	6.06018	0.271019
$501$	8.54532	0.381777
$502$	18.5072	0.826015
$503$	4.99230	0.222596	0.111298	−	0.993787i	$-0.464499\pi$
$503$	4.99230	0.222596	0.111298	+	0.993787i	$0.464499\pi$
$504$	−2.87508	−0.128066
$505$	0.534328	0.0237773
$506$	−37.6043	−1.67172
$507$	8.89638	0.395102
$508$	8.77417	0.389291
$509$	−40.4497	−1.79290	−0.896450	−	0.443144i	$-0.853863\pi$
$509$	−40.4497	−1.79290	−0.896450	+	0.443144i	$0.853863\pi$
$510$	−1.56172	−0.0691543
$511$	−6.47869	−0.286600
$512$	−30.3584	−1.34166
$513$	−8.25612	−0.364517
$514$	−58.6925	−2.58882
$515$	0.550933	0.0242770
$516$	−23.1726	−1.02012
$517$	−10.8487	−0.477125
$518$	13.3036	0.584526
$519$	12.3876	0.543756
$520$	−0.382327	−0.0167662
$521$	−24.3314	−1.06598	−0.532989	−	0.846122i	$-0.678931\pi$
$521$	−24.3314	−1.06598	−0.532989	+	0.846122i	$0.678931\pi$
$522$	1.29548	0.0567014
$523$	−28.6775	−1.25398	−0.626990	−	0.779028i	$-0.715713\pi$
$523$	−28.6775	−1.25398	−0.626990	+	0.779028i	$0.715713\pi$
$524$	12.6331	0.551880
$525$	19.5221	0.852016
$526$	23.1704	1.01028
$527$	−16.7094	−0.727875
$528$	8.95170	0.389573
$529$	18.0885	0.786457
$530$	3.01896	0.131135
$531$	−6.73476	−0.292264
$532$	76.7363	3.32694
$533$	−22.2893	−0.965458
$534$	24.8885	1.07703
$535$	−4.16065	−0.179881
$536$	7.89125	0.340850
$537$	−5.44764	−0.235083
$538$	23.8662	1.02895
$539$	24.3762	1.04996
$540$	0.610136	0.0262561
$541$	0.622594	0.0267674	0.0133837	−	0.999910i	$-0.495740\pi$
$541$	0.622594	0.0267674	0.0133837	+	0.999910i	$0.495740\pi$
$542$	−41.0845	−1.76473
$543$	5.06182	0.217223
$544$	23.3143	0.999592
$545$	1.85525	0.0794700
$546$	−16.7189	−0.715501
$547$	13.0384	0.557483	0.278742	−	0.960366i	$-0.410083\pi$
$547$	13.0384	0.557483	0.278742	+	0.960366i	$0.410083\pi$
$548$	−5.74053	−0.245223
$549$	10.9500	0.467334
$550$	28.9364	1.23385
$551$	−5.12912	−0.218508
$552$	4.65639	0.198189
$553$	−5.69692	−0.242258
$554$	−25.0121	−1.06266
$555$	−0.418801	−0.0177771
$556$	−27.1700	−1.15226
$557$	20.6789	0.876195	0.438098	−	0.898927i	$-0.355652\pi$
$557$	20.6789	0.876195	0.438098	+	0.898927i	$0.355652\pi$
$558$	12.0877	0.511715
$559$	−19.9892	−0.845451
$560$	3.27200	0.138267
$561$	−8.10950	−0.342384
$562$	37.7836	1.59381
$563$	18.3250	0.772307	0.386154	−	0.922434i	$-0.373803\pi$
$563$	18.3250	0.772307	0.386154	+	0.922434i	$0.373803\pi$
$564$	9.05580	0.381318
$565$	−2.16481	−0.0910742
$566$	−0.956022	−0.0401846
$567$	3.95786	0.166215
$568$	−7.68002	−0.322246
$569$	−13.1346	−0.550632	−0.275316	−	0.961354i	$-0.588782\pi$
$569$	−13.1346	−0.550632	−0.275316	+	0.961354i	$0.588782\pi$
$570$	−4.47302	−0.187354
$571$	−7.27426	−0.304418	−0.152209	−	0.988348i	$-0.548639\pi$
$571$	−7.27426	−0.304418	−0.152209	+	0.988348i	$0.548639\pi$
$572$	−13.3833	−0.559583
$573$	25.3559	1.05926
$574$	−90.8106	−3.79036
$575$	−31.6175	−1.31854
$576$	−10.5019	−0.437579
$577$	−1.19291	−0.0496613	−0.0248307	−	0.999692i	$-0.507905\pi$
$577$	−1.19291	−0.0496613	−0.0248307	+	0.999692i	$0.507905\pi$
$578$	18.1227	0.753805
$579$	20.3401	0.845307
$580$	0.379047	0.0157391
$581$	14.3863	0.596843
$582$	19.1094	0.792111
$583$	15.6764	0.649251
$584$	1.18909	0.0492050
$585$	0.526315	0.0217605
$586$	−3.78935	−0.156537
$587$	6.64720	0.274359	0.137180	−	0.990546i	$-0.456196\pi$
$587$	6.64720	0.274359	0.137180	+	0.990546i	$0.456196\pi$
$588$	−20.3477	−0.839126
$589$	−47.8584	−1.97197
$590$	−3.64877	−0.150218
$591$	14.8051	0.608998
$592$	5.12904	0.210802
$593$	−34.6966	−1.42482	−0.712410	−	0.701764i	$-0.752396\pi$
$593$	−34.6966	−1.42482	−0.712410	+	0.701764i	$0.752396\pi$
$594$	5.86648	0.240705
$595$	−2.96417	−0.121519
$596$	−17.0471	−0.698276
$597$	−2.51914	−0.103102
$598$	27.0774	1.10728
$599$	33.0124	1.34885	0.674425	−	0.738344i	$-0.264392\pi$
$599$	33.0124	1.34885	0.674425	+	0.738344i	$0.264392\pi$
$600$	−3.58307	−0.146278
$601$	−3.20193	−0.130609	−0.0653046	−	0.997865i	$-0.520802\pi$
$601$	−3.20193	−0.130609	−0.0653046	+	0.997865i	$0.520802\pi$
$602$	−81.4393	−3.31922
$603$	−10.8632	−0.442383
$604$	10.6688	0.434108
$605$	0.801627	0.0325908
$606$	−4.28852	−0.174209
$607$	1.38186	0.0560879	0.0280440	−	0.999607i	$-0.491072\pi$
$607$	1.38186	0.0560879	0.0280440	+	0.999607i	$0.491072\pi$
$608$	66.7757	2.70811
$609$	2.45882	0.0996365
$610$	5.93251	0.240200
$611$	7.81171	0.316028
$612$	6.76930	0.273633
$613$	−4.89166	−0.197572	−0.0987862	−	0.995109i	$-0.531496\pi$
$613$	−4.89166	−0.197572	−0.0987862	+	0.995109i	$0.531496\pi$
$614$	30.2556	1.22101
$615$	2.85875	0.115276
$616$	−8.08843	−0.325892
$617$	17.5964	0.708406	0.354203	−	0.935169i	$-0.384752\pi$
$617$	17.5964	0.708406	0.354203	+	0.935169i	$0.384752\pi$
$618$	−4.42180	−0.177871
$619$	35.4009	1.42288	0.711441	−	0.702746i	$-0.248043\pi$
$619$	35.4009	1.42288	0.711441	+	0.702746i	$0.248043\pi$
$620$	3.53679	0.142041
$621$	−6.41003	−0.257226
$622$	21.9160	0.878750
$623$	47.2386	1.89257
$624$	−6.44576	−0.258037
$625$	23.9920	0.959680
$626$	−6.02163	−0.240673
$627$	−23.2269	−0.927592
$628$	32.4890	1.29645
$629$	−4.64649	−0.185268
$630$	2.14430	0.0854310
$631$	−12.5123	−0.498107	−0.249053	−	0.968490i	$-0.580119\pi$
$631$	−12.5123	−0.498107	−0.249053	+	0.968490i	$0.580119\pi$
$632$	1.04561	0.0415921
$633$	1.39459	0.0554302
$634$	−14.0408	−0.557632
$635$	−0.970742	−0.0385227
$636$	−13.0857	−0.518881
$637$	−17.5523	−0.695449
$638$	3.64455	0.144289
$639$	10.5724	0.418237
$640$	−1.48697	−0.0587778
$641$	25.8087	1.01938	0.509692	−	0.860357i	$-0.329759\pi$
$641$	25.8087	1.01938	0.509692	+	0.860357i	$0.329759\pi$
$642$	33.3935	1.31794
$643$	9.89580	0.390252	0.195126	−	0.980778i	$-0.437488\pi$
$643$	9.89580	0.390252	0.195126	+	0.980778i	$0.437488\pi$
$644$	59.5779	2.34770
$645$	2.56374	0.100947
$646$	−49.6270	−1.95255
$647$	34.8605	1.37051	0.685254	−	0.728304i	$-0.259691\pi$
$647$	34.8605	1.37051	0.685254	+	0.728304i	$0.259691\pi$
$648$	−0.726422	−0.0285365
$649$	−18.9468	−0.743729
$650$	−20.8359	−0.817253
$651$	22.9426	0.899192
$652$	−38.5068	−1.50804
$653$	6.77845	0.265261	0.132631	−	0.991166i	$-0.457658\pi$
$653$	6.77845	0.265261	0.132631	+	0.991166i	$0.457658\pi$
$654$	−14.8902	−0.582254
$655$	−1.39768	−0.0546119
$656$	−35.0110	−1.36695
$657$	−1.63692	−0.0638622
$658$	31.8263	1.24072
$659$	17.7564	0.691690	0.345845	−	0.938292i	$-0.387592\pi$
$659$	17.7564	0.691690	0.345845	+	0.938292i	$0.387592\pi$
$660$	1.71649	0.0668143
$661$	19.2512	0.748784	0.374392	−	0.927270i	$-0.377851\pi$
$661$	19.2512	0.748784	0.374392	+	0.927270i	$0.377851\pi$
$662$	49.3673	1.91871
$663$	5.83933	0.226781
$664$	−2.64044	−0.102469
$665$	−8.48983	−0.329221
$666$	3.36131	0.130248
$667$	−3.98223	−0.154193
$668$	−20.0675	−0.776434
$669$	16.1343	0.623787
$670$	−5.88548	−0.227376
$671$	30.8055	1.18923
$672$	−32.0113	−1.23486
$673$	5.03031	0.193904	0.0969521	−	0.995289i	$-0.469091\pi$
$673$	5.03031	0.193904	0.0969521	+	0.995289i	$0.469091\pi$
$674$	56.9212	2.19252
$675$	4.93250	0.189852
$676$	−20.8919	−0.803534
$677$	−2.05290	−0.0788995	−0.0394497	−	0.999222i	$-0.512561\pi$
$677$	−2.05290	−0.0788995	−0.0394497	+	0.999222i	$0.512561\pi$
$678$	17.3748	0.667275
$679$	36.2698	1.39191
$680$	0.544040	0.0208630
$681$	19.5072	0.747516
$682$	34.0064	1.30217
$683$	3.33460	0.127595	0.0637975	−	0.997963i	$-0.479679\pi$
$683$	3.33460	0.127595	0.0637975	+	0.997963i	$0.479679\pi$
$684$	19.3883	0.741331
$685$	0.635112	0.0242664
$686$	−13.7388	−0.524550
$687$	−11.6189	−0.443288
$688$	−31.3979	−1.19704
$689$	−11.2880	−0.430037
$690$	−3.47284	−0.132209
$691$	−13.6027	−0.517471	−0.258735	−	0.965948i	$-0.583306\pi$
$691$	−13.6027	−0.517471	−0.258735	+	0.965948i	$0.583306\pi$
$692$	−29.0905	−1.10586
$693$	11.1346	0.422969
$694$	26.9546	1.02318
$695$	3.00599	0.114024
$696$	−0.451290	−0.0171061
$697$	31.7170	1.20137
$698$	25.9546	0.982395
$699$	−20.1264	−0.761251
$700$	−45.8450	−1.73278
$701$	8.86049	0.334656	0.167328	−	0.985901i	$-0.446486\pi$
$701$	8.86049	0.334656	0.167328	+	0.985901i	$0.446486\pi$
$702$	−4.22422	−0.159433
$703$	−13.3083	−0.501931
$704$	−29.5449	−1.11351
$705$	−1.00190	−0.0377338
$706$	−27.9893	−1.05339
$707$	−8.13965	−0.306123
$708$	15.8156	0.594388
$709$	−34.5722	−1.29839	−0.649193	−	0.760623i	$-0.724893\pi$
$709$	−34.5722	−1.29839	−0.649193	+	0.760623i	$0.724893\pi$
$710$	5.72794	0.214966
$711$	−1.43939	−0.0539815
$712$	−8.67012	−0.324927
$713$	−37.1572	−1.39155
$714$	23.7904	0.890335
$715$	1.48068	0.0553743
$716$	12.7930	0.478097
$717$	−16.3390	−0.610192
$718$	−77.5488	−2.89410
$719$	14.4105	0.537423	0.268711	−	0.963221i	$-0.413402\pi$
$719$	14.4105	0.537423	0.268711	+	0.963221i	$0.413402\pi$
$720$	0.826710	0.0308096
$721$	−8.39260	−0.312557
$722$	−102.519	−3.81537
$723$	20.4100	0.759055
$724$	−11.8870	−0.441775
$725$	3.06432	0.113806
$726$	−6.43387	−0.238783
$727$	−12.1611	−0.451030	−0.225515	−	0.974240i	$-0.572406\pi$
$727$	−12.1611	−0.451030	−0.225515	+	0.974240i	$0.572406\pi$
$728$	5.82416	0.215858
$729$	1.00000	0.0370370
$730$	−0.886853	−0.0328239
$731$	28.4440	1.05204
$732$	−25.7145	−0.950435
$733$	37.6067	1.38903	0.694517	−	0.719476i	$-0.255618\pi$
$733$	37.6067	1.38903	0.694517	+	0.719476i	$0.255618\pi$
$734$	−38.9557	−1.43788
$735$	2.25120	0.0830368
$736$	51.8445	1.91102
$737$	−30.5613	−1.12574
$738$	−22.9444	−0.844594
$739$	16.4296	0.604373	0.302186	−	0.953249i	$-0.402283\pi$
$739$	16.4296	0.604373	0.302186	+	0.953249i	$0.402283\pi$
$740$	0.983496	0.0361540
$741$	16.7247	0.614399
$742$	−45.9891	−1.68831
$743$	31.6114	1.15971	0.579855	−	0.814719i	$-0.303109\pi$
$743$	31.6114	1.15971	0.579855	+	0.814719i	$0.303109\pi$
$744$	−4.21087	−0.154378
$745$	1.88603	0.0690987
$746$	−43.6938	−1.59975
$747$	3.63486	0.132993
$748$	19.0440	0.696318
$749$	63.3810	2.31589
$750$	5.38125	0.196496
$751$	−46.4205	−1.69391	−0.846955	−	0.531665i	$-0.821567\pi$
$751$	−46.4205	−1.69391	−0.846955	+	0.531665i	$0.821567\pi$
$752$	12.2702	0.447450
$753$	8.87518	0.323430
$754$	−2.62430	−0.0955713
$755$	−1.18036	−0.0429577
$756$	−9.29448	−0.338037
$757$	19.6798	0.715273	0.357637	−	0.933861i	$-0.383583\pi$
$757$	19.6798	0.715273	0.357637	+	0.933861i	$0.383583\pi$
$758$	37.1395	1.34897
$759$	−18.0333	−0.654567
$760$	1.55821	0.0565224
$761$	−19.6063	−0.710727	−0.355364	−	0.934728i	$-0.615643\pi$
$761$	−19.6063	−0.710727	−0.355364	+	0.934728i	$0.615643\pi$
$762$	7.79120	0.282245
$763$	−28.2618	−1.02315
$764$	−59.5448	−2.15425
$765$	−0.748931	−0.0270777
$766$	19.2558	0.695739
$767$	13.6429	0.492615
$768$	−9.06930	−0.327260
$769$	16.2502	0.585998	0.292999	−	0.956113i	$-0.405347\pi$
$769$	16.2502	0.585998	0.292999	+	0.956113i	$0.405347\pi$
$770$	6.03254	0.217398
$771$	−28.1462	−1.01366
$772$	−47.7659	−1.71913
$773$	−15.9254	−0.572798	−0.286399	−	0.958110i	$-0.592458\pi$
$773$	−15.9254	−0.572798	−0.286399	+	0.958110i	$0.592458\pi$
$774$	−20.5766	−0.739610
$775$	28.5923	1.02707
$776$	−6.65693	−0.238970
$777$	6.37979	0.228874
$778$	−4.23375	−0.151787
$779$	90.8425	3.25477
$780$	−1.23598	−0.0442551
$781$	29.7432	1.06430
$782$	−38.5303	−1.37784
$783$	0.621250	0.0222017
$784$	−27.5703	−0.984655
$785$	−3.59447	−0.128292
$786$	11.2178	0.400126
$787$	−42.5256	−1.51588	−0.757938	−	0.652327i	$-0.773793\pi$
$787$	−42.5256	−1.51588	−0.757938	+	0.652327i	$0.773793\pi$
$788$	−34.7676	−1.23854
$789$	11.1115	0.395579
$790$	−0.779839	−0.0277454
$791$	32.9775	1.17254
$792$	−2.04364	−0.0726175
$793$	−22.1818	−0.787700
$794$	−69.2510	−2.45763
$795$	1.44775	0.0513465
$796$	5.91585	0.209682
$797$	−1.30280	−0.0461476	−0.0230738	−	0.999734i	$-0.507345\pi$
$797$	−1.30280	−0.0461476	−0.0230738	+	0.999734i	$0.507345\pi$
$798$	68.1395	2.41211
$799$	−11.1158	−0.393250
$800$	−39.8942	−1.41047
$801$	11.9354	0.421716
$802$	19.8297	0.700211
$803$	−4.60513	−0.162511
$804$	25.5106	0.899690
$805$	−6.59148	−0.232319
$806$	−24.4866	−0.862505
$807$	11.4451	0.402888
$808$	1.49394	0.0525567
$809$	41.7960	1.46947	0.734735	−	0.678354i	$-0.237307\pi$
$809$	41.7960	1.46947	0.734735	+	0.678354i	$0.237307\pi$
$810$	0.541783	0.0190363
$811$	16.8753	0.592572	0.296286	−	0.955099i	$-0.404252\pi$
$811$	16.8753	0.592572	0.296286	+	0.955099i	$0.404252\pi$
$812$	−5.77420	−0.202635
$813$	−19.7022	−0.690988
$814$	9.45634	0.331445
$815$	4.26025	0.149230
$816$	9.17213	0.321089
$817$	81.4679	2.85020
$818$	−24.1219	−0.843402
$819$	−8.01760	−0.280157
$820$	−6.71336	−0.234441
$821$	33.2519	1.16050	0.580250	−	0.814439i	$-0.302955\pi$
$821$	33.2519	1.16050	0.580250	+	0.814439i	$0.302955\pi$
$822$	−5.09742	−0.177793
$823$	33.4569	1.16623	0.583117	−	0.812388i	$-0.301833\pi$
$823$	33.4569	1.16623	0.583117	+	0.812388i	$0.301833\pi$
$824$	1.54037	0.0536614
$825$	13.8766	0.483120
$826$	55.5834	1.93399
$827$	43.7337	1.52077	0.760386	−	0.649472i	$-0.225010\pi$
$827$	43.7337	1.52077	0.760386	+	0.649472i	$0.225010\pi$
$828$	15.0531	0.523130
$829$	−29.7208	−1.03225	−0.516123	−	0.856515i	$-0.672625\pi$
$829$	−29.7208	−1.03225	−0.516123	+	0.856515i	$0.672625\pi$
$830$	1.96930	0.0683555
$831$	−11.9946	−0.416089
$832$	21.2741	0.737546
$833$	24.9765	0.865383
$834$	−24.1261	−0.835420
$835$	2.22019	0.0768330
$836$	54.5450	1.88648
$837$	5.79672	0.200364
$838$	31.0994	1.07431
$839$	5.86675	0.202543	0.101271	−	0.994859i	$-0.467709\pi$
$839$	5.86675	0.202543	0.101271	+	0.994859i	$0.467709\pi$
$840$	−0.746985	−0.0257734
$841$	−28.6140	−0.986691
$842$	−82.1148	−2.82986
$843$	18.1193	0.624061
$844$	−3.27501	−0.112730
$845$	2.31140	0.0795147
$846$	8.04128	0.276465
$847$	−12.2115	−0.419593
$848$	−17.7306	−0.608870
$849$	−0.458464	−0.0157344
$850$	29.6489	1.01695
$851$	−10.3325	−0.354194
$852$	−24.8278	−0.850585
$853$	−10.6865	−0.365898	−0.182949	−	0.983122i	$-0.558564\pi$
$853$	−10.6865	−0.365898	−0.182949	+	0.983122i	$0.558564\pi$
$854$	−90.3726	−3.09249
$855$	−2.14505	−0.0733593
$856$	−11.6329	−0.397604
$857$	−27.9548	−0.954918	−0.477459	−	0.878654i	$-0.658442\pi$
$857$	−27.9548	−0.954918	−0.477459	+	0.878654i	$0.658442\pi$
$858$	−11.8840	−0.405712
$859$	−4.57508	−0.156100	−0.0780498	−	0.996949i	$-0.524869\pi$
$859$	−4.57508	−0.156100	−0.0780498	+	0.996949i	$0.524869\pi$
$860$	−6.02057	−0.205300
$861$	−43.5486	−1.48413
$862$	58.2207	1.98300
$863$	24.9825	0.850413	0.425207	−	0.905096i	$-0.360201\pi$
$863$	24.9825	0.850413	0.425207	+	0.905096i	$0.360201\pi$
$864$	−8.08803	−0.275160
$865$	3.21847	0.109431
$866$	−66.1791	−2.24886
$867$	8.69081	0.295155
$868$	−53.8775	−1.82872
$869$	−4.04944	−0.137368
$870$	0.336583	0.0114112
$871$	22.0060	0.745643
$872$	5.18714	0.175659
$873$	9.16399	0.310154
$874$	−110.357	−3.73287
$875$	10.2137	0.345285
$876$	3.84407	0.129879
$877$	10.2277	0.345364	0.172682	−	0.984978i	$-0.444757\pi$
$877$	10.2277	0.345364	0.172682	+	0.984978i	$0.444757\pi$
$878$	25.7700	0.869694
$879$	−1.81720	−0.0612926
$880$	2.32578	0.0784019
$881$	−45.7669	−1.54193	−0.770963	−	0.636880i	$-0.780224\pi$
$881$	−45.7669	−1.54193	−0.770963	+	0.636880i	$0.780224\pi$
$882$	−18.0682	−0.608387
$883$	40.1409	1.35085	0.675425	−	0.737429i	$-0.263960\pi$
$883$	40.1409	1.35085	0.675425	+	0.737429i	$0.263960\pi$
$884$	−13.7128	−0.461213
$885$	−1.74978	−0.0588183
$886$	−50.6863	−1.70284
$887$	34.4909	1.15809	0.579046	−	0.815295i	$-0.303425\pi$
$887$	34.4909	1.15809	0.579046	+	0.815295i	$0.303425\pi$
$888$	−1.17094	−0.0392942
$889$	14.7877	0.495965
$890$	6.46638	0.216754
$891$	2.81329	0.0942488
$892$	−37.8890	−1.26862
$893$	−31.8375	−1.06540
$894$	−15.1373	−0.506267
$895$	−1.41537	−0.0473107
$896$	22.6517	0.756741
$897$	12.9851	0.433558
$898$	−64.6443	−2.15721
$899$	3.60122	0.120107
$900$	−11.5833	−0.386109
$901$	16.0624	0.535117
$902$	−64.5492	−2.14925
$903$	−39.0545	−1.29965
$904$	−6.05266	−0.201308
$905$	1.31513	0.0437164
$906$	9.47359	0.314739
$907$	11.5020	0.381917	0.190959	−	0.981598i	$-0.438840\pi$
$907$	11.5020	0.381917	0.190959	+	0.981598i	$0.438840\pi$
$908$	−45.8098	−1.52025
$909$	−2.05658	−0.0682124
$910$	−4.34379	−0.143995
$911$	−5.21326	−0.172723	−0.0863616	−	0.996264i	$-0.527524\pi$
$911$	−5.21326	−0.172723	−0.0863616	+	0.996264i	$0.527524\pi$
$912$	26.2704	0.869899
$913$	10.2259	0.338429
$914$	46.4743	1.53723
$915$	2.84496	0.0940515
$916$	27.2853	0.901532
$917$	21.2915	0.703107
$918$	6.01094	0.198390
$919$	22.0228	0.726466	0.363233	−	0.931698i	$-0.381673\pi$
$919$	22.0228	0.726466	0.363233	+	0.931698i	$0.381673\pi$
$920$	1.20979	0.0398857
$921$	14.5092	0.478093
$922$	46.2570	1.52339
$923$	−21.4169	−0.704946
$924$	−26.1481	−0.860209
$925$	7.95083	0.261422
$926$	43.4684	1.42846
$927$	−2.12049	−0.0696460
$928$	−5.02469	−0.164944
$929$	19.8875	0.652488	0.326244	−	0.945286i	$-0.394217\pi$
$929$	19.8875	0.652488	0.326244	+	0.945286i	$0.394217\pi$
$930$	3.14056	0.102983
$931$	71.5365	2.34451
$932$	47.2640	1.54818
$933$	10.5099	0.344078
$934$	34.8841	1.14144
$935$	−2.10696	−0.0689050
$936$	1.47154	0.0480988
$937$	−45.2515	−1.47830	−0.739151	−	0.673540i	$-0.764773\pi$
$937$	−45.2515	−1.47830	−0.739151	+	0.673540i	$0.764773\pi$
$938$	89.6561	2.92738
$939$	−2.88770	−0.0942364
$940$	2.35282	0.0767407
$941$	−18.6598	−0.608292	−0.304146	−	0.952625i	$-0.598371\pi$
$941$	−18.6598	−0.608292	−0.304146	+	0.952625i	$0.598371\pi$
$942$	28.8493	0.939960
$943$	70.5299	2.29677
$944$	21.4295	0.697472
$945$	1.02831	0.0334508
$946$	−57.8880	−1.88210
$947$	6.88036	0.223582	0.111791	−	0.993732i	$-0.464341\pi$
$947$	6.88036	0.223582	0.111791	+	0.993732i	$0.464341\pi$
$948$	3.38022	0.109784
$949$	3.31597	0.107641
$950$	84.9191	2.75514
$951$	−6.73333	−0.218343
$952$	−8.28760	−0.268603
$953$	−36.7572	−1.19068	−0.595341	−	0.803473i	$-0.702983\pi$
$953$	−36.7572	−1.19068	−0.595341	+	0.803473i	$0.702983\pi$
$954$	−11.6197	−0.376201
$955$	6.58782	0.213177
$956$	38.3699	1.24097
$957$	1.74776	0.0564970
$958$	−73.1974	−2.36490
$959$	−9.67494	−0.312420
$960$	−2.72854	−0.0880631
$961$	2.60201	0.0839359
$962$	−6.80914	−0.219535
$963$	16.0140	0.516043
$964$	−47.9299	−1.54372
$965$	5.28465	0.170119
$966$	52.9034	1.70214
$967$	42.1574	1.35569	0.677846	−	0.735204i	$-0.262914\pi$
$967$	42.1574	1.35569	0.677846	+	0.735204i	$0.262914\pi$
$968$	2.24129	0.0720379
$969$	−23.7988	−0.764528
$970$	4.96489	0.159413
$971$	15.0295	0.482320	0.241160	−	0.970485i	$-0.422472\pi$
$971$	15.0295	0.482320	0.241160	+	0.970485i	$0.422472\pi$
$972$	−2.34836	−0.0753236
$973$	−45.7916	−1.46801
$974$	−36.5087	−1.16982
$975$	−9.99195	−0.319999
$976$	−34.8421	−1.11527
$977$	−40.9606	−1.31045	−0.655223	−	0.755435i	$-0.727426\pi$
$977$	−40.9606	−1.31045	−0.655223	+	0.755435i	$0.727426\pi$
$978$	−34.1929	−1.09337
$979$	33.5777	1.07315
$980$	−5.28662	−0.168875
$981$	−7.14067	−0.227984
$982$	47.5754	1.51819
$983$	18.4839	0.589544	0.294772	−	0.955568i	$-0.404756\pi$
$983$	18.4839	0.589544	0.294772	+	0.955568i	$0.404756\pi$
$984$	7.99286	0.254803
$985$	3.84656	0.122562
$986$	3.73430	0.118924
$987$	15.2624	0.485808
$988$	−39.2757	−1.24953
$989$	63.2515	2.01128
$990$	1.52419	0.0484420
$991$	−30.0543	−0.954705	−0.477352	−	0.878712i	$-0.658403\pi$
$991$	−30.0543	−0.954705	−0.477352	+	0.878712i	$0.658403\pi$
$992$	−46.8841	−1.48857
$993$	23.6743	0.751281
$994$	−87.2562	−2.76760
$995$	−0.654509	−0.0207493
$996$	−8.53595	−0.270472
$997$	9.04231	0.286373	0.143186	−	0.989696i	$-0.454265\pi$
$997$	9.04231	0.286373	0.143186	+	0.989696i	$0.454265\pi$
$998$	33.1849	1.05045
$999$	1.61193	0.0509992

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.c.1.11	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.c.1.11	✓	82	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:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.08527 q^{2} -1.00000 q^{3} +2.34836 q^{4} -0.259814 q^{5} +2.08527 q^{6} +3.95786 q^{7} -0.726422 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.08527 q^{2} -1.00000 q^{3} +2.34836 q^{4} -0.259814 q^{5} +2.08527 q^{6} +3.95786 q^{7} -0.726422 q^{8} +1.00000 q^{9} +0.541783 q^{10} +2.81329 q^{11} -2.34836 q^{12} -2.02574 q^{13} -8.25322 q^{14} +0.259814 q^{15} -3.18193 q^{16} +2.88257 q^{17} -2.08527 q^{18} +8.25612 q^{19} -0.610136 q^{20} -3.95786 q^{21} -5.86648 q^{22} +6.41003 q^{23} +0.726422 q^{24} -4.93250 q^{25} +4.22422 q^{26} -1.00000 q^{27} +9.29448 q^{28} -0.621250 q^{29} -0.541783 q^{30} -5.79672 q^{31} +8.08803 q^{32} -2.81329 q^{33} -6.01094 q^{34} -1.02831 q^{35} +2.34836 q^{36} -1.61193 q^{37} -17.2162 q^{38} +2.02574 q^{39} +0.188735 q^{40} +11.0031 q^{41} +8.25322 q^{42} +9.86758 q^{43} +6.60662 q^{44} -0.259814 q^{45} -13.3667 q^{46} -3.85623 q^{47} +3.18193 q^{48} +8.66466 q^{49} +10.2856 q^{50} -2.88257 q^{51} -4.75716 q^{52} +5.57227 q^{53} +2.08527 q^{54} -0.730933 q^{55} -2.87508 q^{56} -8.25612 q^{57} +1.29548 q^{58} -6.73476 q^{59} +0.610136 q^{60} +10.9500 q^{61} +12.0877 q^{62} +3.95786 q^{63} -10.5019 q^{64} +0.526315 q^{65} +5.86648 q^{66} -10.8632 q^{67} +6.76930 q^{68} -6.41003 q^{69} +2.14430 q^{70} +10.5724 q^{71} -0.726422 q^{72} -1.63692 q^{73} +3.36131 q^{74} +4.93250 q^{75} +19.3883 q^{76} +11.1346 q^{77} -4.22422 q^{78} -1.43939 q^{79} +0.826710 q^{80} +1.00000 q^{81} -22.9444 q^{82} +3.63486 q^{83} -9.29448 q^{84} -0.748931 q^{85} -20.5766 q^{86} +0.621250 q^{87} -2.04364 q^{88} +11.9354 q^{89} +0.541783 q^{90} -8.01760 q^{91} +15.0531 q^{92} +5.79672 q^{93} +8.04128 q^{94} -2.14505 q^{95} -8.08803 q^{96} +9.16399 q^{97} -18.0682 q^{98} +2.81329 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9}+O(q^{10}) \) 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9	\( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9} - 9 q^{10} + 28 q^{11} - 87 q^{12} - 14 q^{13} + 21 q^{14} - 7 q^{15} + 93 q^{16} + 25 q^{17} + 13 q^{18} - 7 q^{19} + 40 q^{20} - 30 q^{21} + 31 q^{22} + 97 q^{23} - 39 q^{24} + 83 q^{25} + 22 q^{26} - 82 q^{27} + 53 q^{28} + 45 q^{29} + 9 q^{30} - 11 q^{31} + 86 q^{32} - 28 q^{33} - 30 q^{34} + 69 q^{35} + 87 q^{36} + 8 q^{37} + 33 q^{38} + 14 q^{39} - 38 q^{40} + 12 q^{41} - 21 q^{42} + 68 q^{43} + 77 q^{44} + 7 q^{45} - 14 q^{46} + 85 q^{47} - 93 q^{48} + 68 q^{49} + 56 q^{50} - 25 q^{51} - 18 q^{52} + 58 q^{53} - 13 q^{54} + 68 q^{55} + 59 q^{56} + 7 q^{57} + 27 q^{58} + 40 q^{59} - 40 q^{60} - 116 q^{61} + 79 q^{62} + 30 q^{63} + 127 q^{64} + 66 q^{65} - 31 q^{66} + 51 q^{67} + 94 q^{68} - 97 q^{69} + q^{70} + 101 q^{71} + 39 q^{72} + 12 q^{73} + 72 q^{74} - 83 q^{75} - 3 q^{76} + 101 q^{77} - 22 q^{78} + 26 q^{79} + 61 q^{80} + 82 q^{81} + 31 q^{82} + 94 q^{83} - 53 q^{84} - 8 q^{85} + 68 q^{86} - 45 q^{87} + 91 q^{88} + 40 q^{89} - 9 q^{90} - 6 q^{91} + 180 q^{92} + 11 q^{93} - 31 q^{94} + 153 q^{95} - 86 q^{96} - 39 q^{97} + 115 q^{98} + 28 q^{99}+O(q^{100}) \) 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9 - 9 * q^10 + 28 * q^11 - 87 * q^12 - 14 * q^13 + 21 * q^14 - 7 * q^15 + 93 * q^16 + 25 * q^17 + 13 * q^18 - 7 * q^19 + 40 * q^20 - 30 * q^21 + 31 * q^22 + 97 * q^23 - 39 * q^24 + 83 * q^25 + 22 * q^26 - 82 * q^27 + 53 * q^28 + 45 * q^29 + 9 * q^30 - 11 * q^31 + 86 * q^32 - 28 * q^33 - 30 * q^34 + 69 * q^35 + 87 * q^36 + 8 * q^37 + 33 * q^38 + 14 * q^39 - 38 * q^40 + 12 * q^41 - 21 * q^42 + 68 * q^43 + 77 * q^44 + 7 * q^45 - 14 * q^46 + 85 * q^47 - 93 * q^48 + 68 * q^49 + 56 * q^50 - 25 * q^51 - 18 * q^52 + 58 * q^53 - 13 * q^54 + 68 * q^55 + 59 * q^56 + 7 * q^57 + 27 * q^58 + 40 * q^59 - 40 * q^60 - 116 * q^61 + 79 * q^62 + 30 * q^63 + 127 * q^64 + 66 * q^65 - 31 * q^66 + 51 * q^67 + 94 * q^68 - 97 * q^69 + q^70 + 101 * q^71 + 39 * q^72 + 12 * q^73 + 72 * q^74 - 83 * q^75 - 3 * q^76 + 101 * q^77 - 22 * q^78 + 26 * q^79 + 61 * q^80 + 82 * q^81 + 31 * q^82 + 94 * q^83 - 53 * q^84 - 8 * q^85 + 68 * q^86 - 45 * q^87 + 91 * q^88 + 40 * q^89 - 9 * q^90 - 6 * q^91 + 180 * q^92 + 11 * q^93 - 31 * q^94 + 153 * q^95 - 86 * q^96 - 39 * q^97 + 115 * q^98 + 28 * q^99

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