LMFDB - Embedded newform 6015.2.a.h.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.05828 q^{2} +1.00000 q^{3} +2.23653 q^{4} -1.00000 q^{5} -2.05828 q^{6} +4.53201 q^{7} -0.486836 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.05828 q^{2} +1.00000 q^{3} +2.23653 q^{4} -1.00000 q^{5} -2.05828 q^{6} +4.53201 q^{7} -0.486836 q^{8} +1.00000 q^{9} +2.05828 q^{10} -4.65017 q^{11} +2.23653 q^{12} +3.76144 q^{13} -9.32815 q^{14} -1.00000 q^{15} -3.47100 q^{16} +0.549685 q^{17} -2.05828 q^{18} +3.90641 q^{19} -2.23653 q^{20} +4.53201 q^{21} +9.57137 q^{22} -8.60454 q^{23} -0.486836 q^{24} +1.00000 q^{25} -7.74211 q^{26} +1.00000 q^{27} +10.1359 q^{28} +3.52781 q^{29} +2.05828 q^{30} +5.03276 q^{31} +8.11798 q^{32} -4.65017 q^{33} -1.13141 q^{34} -4.53201 q^{35} +2.23653 q^{36} -6.40736 q^{37} -8.04049 q^{38} +3.76144 q^{39} +0.486836 q^{40} +4.59733 q^{41} -9.32815 q^{42} -2.99691 q^{43} -10.4002 q^{44} -1.00000 q^{45} +17.7106 q^{46} +3.72948 q^{47} -3.47100 q^{48} +13.5391 q^{49} -2.05828 q^{50} +0.549685 q^{51} +8.41256 q^{52} -10.5446 q^{53} -2.05828 q^{54} +4.65017 q^{55} -2.20635 q^{56} +3.90641 q^{57} -7.26122 q^{58} -0.100553 q^{59} -2.23653 q^{60} -8.78757 q^{61} -10.3588 q^{62} +4.53201 q^{63} -9.76708 q^{64} -3.76144 q^{65} +9.57137 q^{66} +8.30450 q^{67} +1.22938 q^{68} -8.60454 q^{69} +9.32815 q^{70} +8.49868 q^{71} -0.486836 q^{72} +10.4281 q^{73} +13.1882 q^{74} +1.00000 q^{75} +8.73678 q^{76} -21.0746 q^{77} -7.74211 q^{78} +0.619163 q^{79} +3.47100 q^{80} +1.00000 q^{81} -9.46260 q^{82} +11.0832 q^{83} +10.1359 q^{84} -0.549685 q^{85} +6.16849 q^{86} +3.52781 q^{87} +2.26387 q^{88} +3.59089 q^{89} +2.05828 q^{90} +17.0469 q^{91} -19.2443 q^{92} +5.03276 q^{93} -7.67633 q^{94} -3.90641 q^{95} +8.11798 q^{96} +12.2871 q^{97} -27.8672 q^{98} -4.65017 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9}+O(q^{10}) $ 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9} - q^{11} + 48 q^{12} + 30 q^{13} + 8 q^{14} - 39 q^{15} + 58 q^{16} + 32 q^{17} + 27 q^{19} - 48 q^{20} + 22 q^{21} + 23 q^{22} - 8 q^{23} + 3 q^{24} + 39 q^{25} - 4 q^{26} + 39 q^{27} + 60 q^{28} - 9 q^{29} + 19 q^{31} + q^{32} - q^{33} + 26 q^{34} - 22 q^{35} + 48 q^{36} + 44 q^{37} + 14 q^{38} + 30 q^{39} - 3 q^{40} + 31 q^{41} + 8 q^{42} + 75 q^{43} + q^{44} - 39 q^{45} + 19 q^{46} - 16 q^{47} + 58 q^{48} + 91 q^{49} + 32 q^{51} + 94 q^{52} + 17 q^{53} + q^{55} + 27 q^{56} + 27 q^{57} + 26 q^{58} - q^{59} - 48 q^{60} + 55 q^{61} + 11 q^{62} + 22 q^{63} + 77 q^{64} - 30 q^{65} + 23 q^{66} + 84 q^{67} + 36 q^{68} - 8 q^{69} - 8 q^{70} - 2 q^{71} + 3 q^{72} + 79 q^{73} + 20 q^{74} + 39 q^{75} + 58 q^{76} + 32 q^{77} - 4 q^{78} + 29 q^{79} - 58 q^{80} + 39 q^{81} + 53 q^{82} + 9 q^{83} + 60 q^{84} - 32 q^{85} - 17 q^{86} - 9 q^{87} + 57 q^{88} + 37 q^{89} + 71 q^{91} + 7 q^{92} + 19 q^{93} + 32 q^{94} - 27 q^{95} + q^{96} + 91 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9 - q^11 + 48 * q^12 + 30 * q^13 + 8 * q^14 - 39 * q^15 + 58 * q^16 + 32 * q^17 + 27 * q^19 - 48 * q^20 + 22 * q^21 + 23 * q^22 - 8 * q^23 + 3 * q^24 + 39 * q^25 - 4 * q^26 + 39 * q^27 + 60 * q^28 - 9 * q^29 + 19 * q^31 + q^32 - q^33 + 26 * q^34 - 22 * q^35 + 48 * q^36 + 44 * q^37 + 14 * q^38 + 30 * q^39 - 3 * q^40 + 31 * q^41 + 8 * q^42 + 75 * q^43 + q^44 - 39 * q^45 + 19 * q^46 - 16 * q^47 + 58 * q^48 + 91 * q^49 + 32 * q^51 + 94 * q^52 + 17 * q^53 + q^55 + 27 * q^56 + 27 * q^57 + 26 * q^58 - q^59 - 48 * q^60 + 55 * q^61 + 11 * q^62 + 22 * q^63 + 77 * q^64 - 30 * q^65 + 23 * q^66 + 84 * q^67 + 36 * q^68 - 8 * q^69 - 8 * q^70 - 2 * q^71 + 3 * q^72 + 79 * q^73 + 20 * q^74 + 39 * q^75 + 58 * q^76 + 32 * q^77 - 4 * q^78 + 29 * q^79 - 58 * q^80 + 39 * q^81 + 53 * q^82 + 9 * q^83 + 60 * q^84 - 32 * q^85 - 17 * q^86 - 9 * q^87 + 57 * q^88 + 37 * q^89 + 71 * q^91 + 7 * q^92 + 19 * q^93 + 32 * q^94 - 27 * q^95 + q^96 + 91 * q^97 - 9 * q^98 - 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 $

$2$	−2.05828	−1.45543	−0.727713	−	0.685882i	$-0.759417\pi$
$2$	−2.05828	−1.45543	−0.727713	+	0.685882i	$0.759417\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.23653	1.11826
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.05828	−0.840290
$7$	4.53201	1.71294	0.856469	−	0.516199i	$-0.172654\pi$
$7$	4.53201	1.71294	0.856469	+	0.516199i	$0.172654\pi$
$8$	−0.486836	−0.172123
$9$	1.00000	0.333333
$10$	2.05828	0.650886
$11$	−4.65017	−1.40208	−0.701040	−	0.713122i	$-0.747281\pi$
$11$	−4.65017	−1.40208	−0.701040	+	0.713122i	$0.747281\pi$
$12$	2.23653	0.645629
$13$	3.76144	1.04324	0.521618	−	0.853179i	$-0.325329\pi$
$13$	3.76144	1.04324	0.521618	+	0.853179i	$0.325329\pi$
$14$	−9.32815	−2.49305
$15$	−1.00000	−0.258199
$16$	−3.47100	−0.867751
$17$	0.549685	0.133318	0.0666591	−	0.997776i	$-0.478766\pi$
$17$	0.549685	0.133318	0.0666591	+	0.997776i	$0.478766\pi$
$18$	−2.05828	−0.485142
$19$	3.90641	0.896191	0.448096	−	0.893986i	$-0.352102\pi$
$19$	3.90641	0.896191	0.448096	+	0.893986i	$0.352102\pi$
$20$	−2.23653	−0.500102
$21$	4.53201	0.988965
$22$	9.57137	2.04062
$23$	−8.60454	−1.79417	−0.897086	−	0.441856i	$-0.854320\pi$
$23$	−8.60454	−1.79417	−0.897086	+	0.441856i	$0.854320\pi$
$24$	−0.486836	−0.0993751
$25$	1.00000	0.200000
$26$	−7.74211	−1.51835
$27$	1.00000	0.192450
$28$	10.1359	1.91551
$29$	3.52781	0.655097	0.327549	−	0.944834i	$-0.393777\pi$
$29$	3.52781	0.655097	0.327549	+	0.944834i	$0.393777\pi$
$30$	2.05828	0.375789
$31$	5.03276	0.903910	0.451955	−	0.892041i	$-0.350727\pi$
$31$	5.03276	0.903910	0.451955	+	0.892041i	$0.350727\pi$
$32$	8.11798	1.43507
$33$	−4.65017	−0.809491
$34$	−1.13141	−0.194035
$35$	−4.53201	−0.766049
$36$	2.23653	0.372754
$37$	−6.40736	−1.05336	−0.526682	−	0.850062i	$-0.676564\pi$
$37$	−6.40736	−1.05336	−0.526682	+	0.850062i	$0.676564\pi$
$38$	−8.04049	−1.30434
$39$	3.76144	0.602312
$40$	0.486836	0.0769756
$41$	4.59733	0.717982	0.358991	−	0.933341i	$-0.383121\pi$
$41$	4.59733	0.717982	0.358991	+	0.933341i	$0.383121\pi$
$42$	−9.32815	−1.43936
$43$	−2.99691	−0.457025	−0.228512	−	0.973541i	$-0.573386\pi$
$43$	−2.99691	−0.457025	−0.228512	+	0.973541i	$0.573386\pi$
$44$	−10.4002	−1.56789
$45$	−1.00000	−0.149071
$46$	17.7106	2.61128
$47$	3.72948	0.544001	0.272001	−	0.962297i	$-0.412315\pi$
$47$	3.72948	0.544001	0.272001	+	0.962297i	$0.412315\pi$
$48$	−3.47100	−0.500996
$49$	13.5391	1.93415
$50$	−2.05828	−0.291085
$51$	0.549685	0.0769713
$52$	8.41256	1.16661
$53$	−10.5446	−1.44841	−0.724204	−	0.689586i	$-0.757793\pi$
$53$	−10.5446	−1.44841	−0.724204	+	0.689586i	$0.757793\pi$
$54$	−2.05828	−0.280097
$55$	4.65017	0.627029
$56$	−2.20635	−0.294835
$57$	3.90641	0.517416
$58$	−7.26122	−0.953445
$59$	−0.100553	−0.0130909	−0.00654546	−	0.999979i	$-0.502083\pi$
$59$	−0.100553	−0.0130909	−0.00654546	+	0.999979i	$0.502083\pi$
$60$	−2.23653	−0.288734
$61$	−8.78757	−1.12513	−0.562567	−	0.826752i	$-0.690186\pi$
$61$	−8.78757	−1.12513	−0.562567	+	0.826752i	$0.690186\pi$
$62$	−10.3588	−1.31557
$63$	4.53201	0.570979
$64$	−9.76708	−1.22089
$65$	−3.76144	−0.466549
$66$	9.57137	1.17815
$67$	8.30450	1.01456	0.507278	−	0.861783i	$-0.330652\pi$
$67$	8.30450	1.01456	0.507278	+	0.861783i	$0.330652\pi$
$68$	1.22938	0.149085
$69$	−8.60454	−1.03587
$70$	9.32815	1.11493
$71$	8.49868	1.00861	0.504304	−	0.863526i	$-0.331749\pi$
$71$	8.49868	1.00861	0.504304	+	0.863526i	$0.331749\pi$
$72$	−0.486836	−0.0573742
$73$	10.4281	1.22052	0.610260	−	0.792201i	$-0.291065\pi$
$73$	10.4281	1.22052	0.610260	+	0.792201i	$0.291065\pi$
$74$	13.1882	1.53309
$75$	1.00000	0.115470
$76$	8.73678	1.00218
$77$	−21.0746	−2.40167
$78$	−7.74211	−0.876621
$79$	0.619163	0.0696613	0.0348307	−	0.999393i	$-0.488911\pi$
$79$	0.619163	0.0696613	0.0348307	+	0.999393i	$0.488911\pi$
$80$	3.47100	0.388070
$81$	1.00000	0.111111
$82$	−9.46260	−1.04497
$83$	11.0832	1.21654	0.608268	−	0.793732i	$-0.291864\pi$
$83$	11.0832	1.21654	0.608268	+	0.793732i	$0.291864\pi$
$84$	10.1359	1.10592
$85$	−0.549685	−0.0596217
$86$	6.16849	0.665165
$87$	3.52781	0.378221
$88$	2.26387	0.241330
$89$	3.59089	0.380634	0.190317	−	0.981723i	$-0.439048\pi$
$89$	3.59089	0.380634	0.190317	+	0.981723i	$0.439048\pi$
$90$	2.05828	0.216962
$91$	17.0469	1.78700
$92$	−19.2443	−2.00636
$93$	5.03276	0.521873
$94$	−7.67633	−0.791753
$95$	−3.90641	−0.400789
$96$	8.11798	0.828538
$97$	12.2871	1.24757	0.623783	−	0.781598i	$-0.285595\pi$
$97$	12.2871	1.24757	0.623783	+	0.781598i	$0.285595\pi$
$98$	−27.8672	−2.81502
$99$	−4.65017	−0.467360
$100$	2.23653	0.223653
$101$	4.00962	0.398972	0.199486	−	0.979901i	$-0.436073\pi$
$101$	4.00962	0.398972	0.199486	+	0.979901i	$0.436073\pi$
$102$	−1.13141	−0.112026
$103$	−16.5053	−1.62631	−0.813156	−	0.582045i	$-0.802253\pi$
$103$	−16.5053	−1.62631	−0.813156	+	0.582045i	$0.802253\pi$
$104$	−1.83121	−0.179565
$105$	−4.53201	−0.442278
$106$	21.7037	2.10805
$107$	5.92247	0.572547	0.286274	−	0.958148i	$-0.407583\pi$
$107$	5.92247	0.572547	0.286274	+	0.958148i	$0.407583\pi$
$108$	2.23653	0.215210
$109$	−9.31913	−0.892611	−0.446306	−	0.894881i	$-0.647261\pi$
$109$	−9.31913	−0.892611	−0.446306	+	0.894881i	$0.647261\pi$
$110$	−9.57137	−0.912594
$111$	−6.40736	−0.608160
$112$	−15.7306	−1.48640
$113$	20.7630	1.95322	0.976610	−	0.215021i	$-0.0689818\pi$
$113$	20.7630	1.95322	0.976610	+	0.215021i	$0.0689818\pi$
$114$	−8.04049	−0.753061
$115$	8.60454	0.802378
$116$	7.89003	0.732571
$117$	3.76144	0.347745
$118$	0.206967	0.0190529
$119$	2.49118	0.228366
$120$	0.486836	0.0444419
$121$	10.6241	0.965828
$122$	18.0873	1.63755
$123$	4.59733	0.414527
$124$	11.2559	1.01081
$125$	−1.00000	−0.0894427
$126$	−9.32815	−0.831017
$127$	−4.12572	−0.366099	−0.183049	−	0.983104i	$-0.558597\pi$
$127$	−4.12572	−0.366099	−0.183049	+	0.983104i	$0.558597\pi$
$128$	3.86746	0.341838
$129$	−2.99691	−0.263863
$130$	7.74211	0.679028
$131$	4.04648	0.353542	0.176771	−	0.984252i	$-0.443435\pi$
$131$	4.04648	0.353542	0.176771	+	0.984252i	$0.443435\pi$
$132$	−10.4002	−0.905224
$133$	17.7039	1.53512
$134$	−17.0930	−1.47661
$135$	−1.00000	−0.0860663
$136$	−0.267607	−0.0229471
$137$	19.3007	1.64897	0.824486	−	0.565883i	$-0.191465\pi$
$137$	19.3007	1.64897	0.824486	+	0.565883i	$0.191465\pi$
$138$	17.7106	1.50762
$139$	14.5532	1.23439	0.617194	−	0.786811i	$-0.288269\pi$
$139$	14.5532	1.23439	0.617194	+	0.786811i	$0.288269\pi$
$140$	−10.1359	−0.856644
$141$	3.72948	0.314079
$142$	−17.4927	−1.46795
$143$	−17.4913	−1.46270
$144$	−3.47100	−0.289250
$145$	−3.52781	−0.292968
$146$	−21.4640	−1.77638
$147$	13.5391	1.11668
$148$	−14.3302	−1.17794
$149$	18.5314	1.51815	0.759074	−	0.651004i	$-0.225652\pi$
$149$	18.5314	1.51815	0.759074	+	0.651004i	$0.225652\pi$
$150$	−2.05828	−0.168058
$151$	11.0693	0.900808	0.450404	−	0.892825i	$-0.351280\pi$
$151$	11.0693	0.900808	0.450404	+	0.892825i	$0.351280\pi$
$152$	−1.90178	−0.154255
$153$	0.549685	0.0444394
$154$	43.3775	3.49546
$155$	−5.03276	−0.404241
$156$	8.41256	0.673544
$157$	−17.1457	−1.36837	−0.684187	−	0.729307i	$-0.739843\pi$
$157$	−17.1457	−1.36837	−0.684187	+	0.729307i	$0.739843\pi$
$158$	−1.27441	−0.101387
$159$	−10.5446	−0.836239
$160$	−8.11798	−0.641783
$161$	−38.9958	−3.07330
$162$	−2.05828	−0.161714
$163$	−13.4185	−1.05102	−0.525509	−	0.850788i	$-0.676125\pi$
$163$	−13.4185	−1.05102	−0.525509	+	0.850788i	$0.676125\pi$
$164$	10.2820	0.802893
$165$	4.65017	0.362015
$166$	−22.8123	−1.77058
$167$	6.86819	0.531476	0.265738	−	0.964045i	$-0.414384\pi$
$167$	6.86819	0.531476	0.265738	+	0.964045i	$0.414384\pi$
$168$	−2.20635	−0.170223
$169$	1.14843	0.0883410
$170$	1.13141	0.0867749
$171$	3.90641	0.298730
$172$	−6.70267	−0.511074
$173$	−11.3727	−0.864650	−0.432325	−	0.901718i	$-0.642307\pi$
$173$	−11.3727	−0.864650	−0.432325	+	0.901718i	$0.642307\pi$
$174$	−7.26122	−0.550472
$175$	4.53201	0.342587
$176$	16.1408	1.21666
$177$	−0.100553	−0.00755805
$178$	−7.39107	−0.553984
$179$	−5.70756	−0.426603	−0.213302	−	0.976986i	$-0.568422\pi$
$179$	−5.70756	−0.426603	−0.213302	+	0.976986i	$0.568422\pi$
$180$	−2.23653	−0.166701
$181$	8.77631	0.652338	0.326169	−	0.945311i	$-0.394242\pi$
$181$	8.77631	0.652338	0.326169	+	0.945311i	$0.394242\pi$
$182$	−35.0873	−2.60084
$183$	−8.78757	−0.649596
$184$	4.18901	0.308818
$185$	6.40736	0.471079
$186$	−10.3588	−0.759547
$187$	−2.55613	−0.186923
$188$	8.34109	0.608336
$189$	4.53201	0.329655
$190$	8.04049	0.583318
$191$	−17.9291	−1.29731	−0.648653	−	0.761085i	$-0.724667\pi$
$191$	−17.9291	−1.29731	−0.648653	+	0.761085i	$0.724667\pi$
$192$	−9.76708	−0.704879
$193$	−3.21424	−0.231366	−0.115683	−	0.993286i	$-0.536906\pi$
$193$	−3.21424	−0.231366	−0.115683	+	0.993286i	$0.536906\pi$
$194$	−25.2903	−1.81574
$195$	−3.76144	−0.269362
$196$	30.2805	2.16289
$197$	−15.1374	−1.07849	−0.539246	−	0.842148i	$-0.681291\pi$
$197$	−15.1374	−1.07849	−0.539246	+	0.842148i	$0.681291\pi$
$198$	9.57137	0.680207
$199$	1.95101	0.138303	0.0691517	−	0.997606i	$-0.477971\pi$
$199$	1.95101	0.138303	0.0691517	+	0.997606i	$0.477971\pi$
$200$	−0.486836	−0.0344245
$201$	8.30450	0.585754
$202$	−8.25292	−0.580674
$203$	15.9880	1.12214
$204$	1.22938	0.0860741
$205$	−4.59733	−0.321091
$206$	33.9725	2.36698
$207$	−8.60454	−0.598057
$208$	−13.0560	−0.905269
$209$	−18.1655	−1.25653
$210$	9.32815	0.643703
$211$	−26.5016	−1.82444	−0.912222	−	0.409697i	$-0.865635\pi$
$211$	−26.5016	−1.82444	−0.912222	+	0.409697i	$0.865635\pi$
$212$	−23.5832	−1.61970
$213$	8.49868	0.582320
$214$	−12.1901	−0.833299
$215$	2.99691	0.204388
$216$	−0.486836	−0.0331250
$217$	22.8085	1.54834
$218$	19.1814	1.29913
$219$	10.4281	0.704668
$220$	10.4002	0.701183
$221$	2.06761	0.139082
$222$	13.1882	0.885131
$223$	10.0347	0.671971	0.335985	−	0.941867i	$-0.390931\pi$
$223$	10.0347	0.671971	0.335985	+	0.941867i	$0.390931\pi$
$224$	36.7907	2.45818
$225$	1.00000	0.0666667
$226$	−42.7361	−2.84276
$227$	14.5009	0.962459	0.481230	−	0.876595i	$-0.340190\pi$
$227$	14.5009	0.962459	0.481230	+	0.876595i	$0.340190\pi$
$228$	8.73678	0.578607
$229$	4.77368	0.315453	0.157727	−	0.987483i	$-0.449584\pi$
$229$	4.77368	0.315453	0.157727	+	0.987483i	$0.449584\pi$
$230$	−17.7106	−1.16780
$231$	−21.0746	−1.38661
$232$	−1.71746	−0.112757
$233$	19.2958	1.26411	0.632056	−	0.774923i	$-0.282211\pi$
$233$	19.2958	1.26411	0.632056	+	0.774923i	$0.282211\pi$
$234$	−7.74211	−0.506117
$235$	−3.72948	−0.243285
$236$	−0.224890	−0.0146391
$237$	0.619163	0.0402190
$238$	−5.12754	−0.332369
$239$	−27.6868	−1.79091	−0.895454	−	0.445153i	$-0.853149\pi$
$239$	−27.6868	−1.79091	−0.895454	+	0.445153i	$0.853149\pi$
$240$	3.47100	0.224052
$241$	−3.32943	−0.214468	−0.107234	−	0.994234i	$-0.534199\pi$
$241$	−3.32943	−0.214468	−0.107234	+	0.994234i	$0.534199\pi$
$242$	−21.8674	−1.40569
$243$	1.00000	0.0641500
$244$	−19.6536	−1.25819
$245$	−13.5391	−0.864980
$246$	−9.46260	−0.603313
$247$	14.6937	0.934939
$248$	−2.45013	−0.155583
$249$	11.0832	0.702368
$250$	2.05828	0.130177
$251$	3.16235	0.199606	0.0998028	−	0.995007i	$-0.468179\pi$
$251$	3.16235	0.199606	0.0998028	+	0.995007i	$0.468179\pi$
$252$	10.1359	0.638505
$253$	40.0126	2.51557
$254$	8.49190	0.532829
$255$	−0.549685	−0.0344226
$256$	11.5739	0.723366
$257$	−28.2845	−1.76434	−0.882168	−	0.470934i	$-0.843917\pi$
$257$	−28.2845	−1.76434	−0.882168	+	0.470934i	$0.843917\pi$
$258$	6.16849	0.384033
$259$	−29.0382	−1.80435
$260$	−8.41256	−0.521725
$261$	3.52781	0.218366
$262$	−8.32879	−0.514554
$263$	13.0463	0.804467	0.402233	−	0.915537i	$-0.368234\pi$
$263$	13.0463	0.804467	0.402233	+	0.915537i	$0.368234\pi$
$264$	2.26387	0.139332
$265$	10.5446	0.647748
$266$	−36.4395	−2.23425
$267$	3.59089	0.219759
$268$	18.5732	1.13454
$269$	30.9689	1.88821	0.944103	−	0.329651i	$-0.106931\pi$
$269$	30.9689	1.88821	0.944103	+	0.329651i	$0.106931\pi$
$270$	2.05828	0.125263
$271$	−14.6210	−0.888162	−0.444081	−	0.895987i	$-0.646470\pi$
$271$	−14.6210	−0.888162	−0.444081	+	0.895987i	$0.646470\pi$
$272$	−1.90796	−0.115687
$273$	17.0469	1.03172
$274$	−39.7263	−2.39995
$275$	−4.65017	−0.280416
$276$	−19.2443	−1.15837
$277$	18.5363	1.11374	0.556869	−	0.830600i	$-0.312002\pi$
$277$	18.5363	1.11374	0.556869	+	0.830600i	$0.312002\pi$
$278$	−29.9546	−1.79656
$279$	5.03276	0.301303
$280$	2.20635	0.131854
$281$	10.3235	0.615848	0.307924	−	0.951411i	$-0.400366\pi$
$281$	10.3235	0.615848	0.307924	+	0.951411i	$0.400366\pi$
$282$	−7.67633	−0.457119
$283$	−20.4879	−1.21788	−0.608941	−	0.793215i	$-0.708405\pi$
$283$	−20.4879	−1.21788	−0.608941	+	0.793215i	$0.708405\pi$
$284$	19.0075	1.12789
$285$	−3.90641	−0.231396
$286$	36.0021	2.12885
$287$	20.8351	1.22986
$288$	8.11798	0.478357
$289$	−16.6978	−0.982226
$290$	7.26122	0.426394
$291$	12.2871	0.720283
$292$	23.3228	1.36486
$293$	2.15250	0.125750	0.0628751	−	0.998021i	$-0.479973\pi$
$293$	2.15250	0.125750	0.0628751	+	0.998021i	$0.479973\pi$
$294$	−27.8672	−1.62525
$295$	0.100553	0.00585444
$296$	3.11934	0.181308
$297$	−4.65017	−0.269830
$298$	−38.1428	−2.20955
$299$	−32.3655	−1.87174
$300$	2.23653	0.129126
$301$	−13.5820	−0.782854
$302$	−22.7838	−1.31106
$303$	4.00962	0.230346
$304$	−13.5592	−0.777671
$305$	8.78757	0.503175
$306$	−1.13141	−0.0646782
$307$	0.540118	0.0308262	0.0154131	−	0.999881i	$-0.495094\pi$
$307$	0.540118	0.0308262	0.0154131	+	0.999881i	$0.495094\pi$
$308$	−47.1339	−2.68570
$309$	−16.5053	−0.938952
$310$	10.3588	0.588343
$311$	23.7619	1.34741	0.673707	−	0.738999i	$-0.264701\pi$
$311$	23.7619	1.34741	0.673707	+	0.738999i	$0.264701\pi$
$312$	−1.83121	−0.103672
$313$	23.4440	1.32513	0.662566	−	0.749003i	$-0.269467\pi$
$313$	23.4440	1.32513	0.662566	+	0.749003i	$0.269467\pi$
$314$	35.2906	1.99157
$315$	−4.53201	−0.255350
$316$	1.38477	0.0778997
$317$	1.59661	0.0896748	0.0448374	−	0.998994i	$-0.485723\pi$
$317$	1.59661	0.0896748	0.0448374	+	0.998994i	$0.485723\pi$
$318$	21.7037	1.21708
$319$	−16.4049	−0.918498
$320$	9.76708	0.545997
$321$	5.92247	0.330560
$322$	80.2645	4.47296
$323$	2.14729	0.119479
$324$	2.23653	0.124251
$325$	3.76144	0.208647
$326$	27.6191	1.52968
$327$	−9.31913	−0.515349
$328$	−2.23815	−0.123581
$329$	16.9020	0.931840
$330$	−9.57137	−0.526886
$331$	21.3912	1.17577	0.587884	−	0.808945i	$-0.299961\pi$
$331$	21.3912	1.17577	0.587884	+	0.808945i	$0.299961\pi$
$332$	24.7878	1.36041
$333$	−6.40736	−0.351121
$334$	−14.1367	−0.773524
$335$	−8.30450	−0.453723
$336$	−15.7306	−0.858175
$337$	−1.39259	−0.0758591	−0.0379296	−	0.999280i	$-0.512076\pi$
$337$	−1.39259	−0.0758591	−0.0379296	+	0.999280i	$0.512076\pi$
$338$	−2.36380	−0.128574
$339$	20.7630	1.12769
$340$	−1.22938	−0.0666727
$341$	−23.4032	−1.26735
$342$	−8.04049	−0.434780
$343$	29.6351	1.60015
$344$	1.45901	0.0786643
$345$	8.60454	0.463253
$346$	23.4082	1.25843
$347$	−5.13533	−0.275679	−0.137840	−	0.990455i	$-0.544016\pi$
$347$	−5.13533	−0.275679	−0.137840	+	0.990455i	$0.544016\pi$
$348$	7.89003	0.422950
$349$	4.05445	0.217029	0.108515	−	0.994095i	$-0.465391\pi$
$349$	4.05445	0.217029	0.108515	+	0.994095i	$0.465391\pi$
$350$	−9.32815	−0.498610
$351$	3.76144	0.200771
$352$	−37.7500	−2.01208
$353$	26.7715	1.42490	0.712452	−	0.701721i	$-0.247585\pi$
$353$	26.7715	1.42490	0.712452	+	0.701721i	$0.247585\pi$
$354$	0.206967	0.0110002
$355$	−8.49868	−0.451063
$356$	8.03112	0.425649
$357$	2.49118	0.131847
$358$	11.7478	0.620889
$359$	19.0512	1.00549	0.502743	−	0.864436i	$-0.332324\pi$
$359$	19.0512	1.00549	0.502743	+	0.864436i	$0.332324\pi$
$360$	0.486836	0.0256585
$361$	−3.73998	−0.196841
$362$	−18.0641	−0.949429
$363$	10.6241	0.557621
$364$	38.1258	1.99833
$365$	−10.4281	−0.545834
$366$	18.0873	0.945439
$367$	−21.2215	−1.10775	−0.553877	−	0.832598i	$-0.686852\pi$
$367$	−21.2215	−1.10775	−0.553877	+	0.832598i	$0.686852\pi$
$368$	29.8664	1.55689
$369$	4.59733	0.239327
$370$	−13.1882	−0.685620
$371$	−47.7881	−2.48103
$372$	11.2559	0.583591
$373$	−10.6449	−0.551172	−0.275586	−	0.961276i	$-0.588872\pi$
$373$	−10.6449	−0.551172	−0.275586	+	0.961276i	$0.588872\pi$
$374$	5.26124	0.272052
$375$	−1.00000	−0.0516398
$376$	−1.81565	−0.0936349
$377$	13.2696	0.683421
$378$	−9.32815	−0.479788
$379$	21.7388	1.11665	0.558324	−	0.829623i	$-0.311445\pi$
$379$	21.7388	1.11665	0.558324	+	0.829623i	$0.311445\pi$
$380$	−8.73678	−0.448187
$381$	−4.12572	−0.211367
$382$	36.9032	1.88813
$383$	14.4631	0.739028	0.369514	−	0.929225i	$-0.379524\pi$
$383$	14.4631	0.739028	0.369514	+	0.929225i	$0.379524\pi$
$384$	3.86746	0.197360
$385$	21.0746	1.07406
$386$	6.61582	0.336736
$387$	−2.99691	−0.152342
$388$	27.4804	1.39511
$389$	−20.2574	−1.02709	−0.513545	−	0.858062i	$-0.671668\pi$
$389$	−20.2574	−1.02709	−0.513545	+	0.858062i	$0.671668\pi$
$390$	7.74211	0.392037
$391$	−4.72979	−0.239196
$392$	−6.59131	−0.332912
$393$	4.04648	0.204118
$394$	31.1570	1.56967
$395$	−0.619163	−0.0311535
$396$	−10.4002	−0.522631
$397$	23.9762	1.20333	0.601666	−	0.798748i	$-0.294504\pi$
$397$	23.9762	1.20333	0.601666	+	0.798748i	$0.294504\pi$
$398$	−4.01573	−0.201290
$399$	17.7039	0.886302
$400$	−3.47100	−0.173550
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−17.0930	−0.852521
$403$	18.9304	0.942992
$404$	8.96761	0.446155
$405$	−1.00000	−0.0496904
$406$	−32.9079	−1.63319
$407$	29.7953	1.47690
$408$	−0.267607	−0.0132485
$409$	−8.22370	−0.406636	−0.203318	−	0.979113i	$-0.565173\pi$
$409$	−8.22370	−0.406636	−0.203318	+	0.979113i	$0.565173\pi$
$410$	9.46260	0.467325
$411$	19.3007	0.952034
$412$	−36.9145	−1.81865
$413$	−0.455708	−0.0224239
$414$	17.7106	0.870428
$415$	−11.0832	−0.544052
$416$	30.5353	1.49712
$417$	14.5532	0.712675
$418$	37.3897	1.82879
$419$	−11.7841	−0.575692	−0.287846	−	0.957677i	$-0.592939\pi$
$419$	−11.7841	−0.575692	−0.287846	+	0.957677i	$0.592939\pi$
$420$	−10.1359	−0.494584
$421$	−20.4893	−0.998586	−0.499293	−	0.866433i	$-0.666407\pi$
$421$	−20.4893	−0.998586	−0.499293	+	0.866433i	$0.666407\pi$
$422$	54.5477	2.65534
$423$	3.72948	0.181334
$424$	5.13348	0.249304
$425$	0.549685	0.0266636
$426$	−17.4927	−0.847523
$427$	−39.8253	−1.92728
$428$	13.2458	0.640258
$429$	−17.4913	−0.844490
$430$	−6.16849	−0.297471
$431$	−11.4338	−0.550746	−0.275373	−	0.961337i	$-0.588801\pi$
$431$	−11.4338	−0.550746	−0.275373	+	0.961337i	$0.588801\pi$
$432$	−3.47100	−0.166999
$433$	36.4103	1.74977	0.874884	−	0.484333i	$-0.160938\pi$
$433$	36.4103	1.74977	0.874884	+	0.484333i	$0.160938\pi$
$434$	−46.9463	−2.25350
$435$	−3.52781	−0.169145
$436$	−20.8425	−0.998174
$437$	−33.6129	−1.60792
$438$	−21.4640	−1.02559
$439$	−15.4581	−0.737773	−0.368887	−	0.929474i	$-0.620261\pi$
$439$	−15.4581	−0.737773	−0.368887	+	0.929474i	$0.620261\pi$
$440$	−2.26387	−0.107926
$441$	13.5391	0.644718
$442$	−4.25572	−0.202424
$443$	11.3816	0.540757	0.270379	−	0.962754i	$-0.412851\pi$
$443$	11.3816	0.540757	0.270379	+	0.962754i	$0.412851\pi$
$444$	−14.3302	−0.680083
$445$	−3.59089	−0.170225
$446$	−20.6542	−0.978003
$447$	18.5314	0.876503
$448$	−44.2645	−2.09130
$449$	−21.6686	−1.02260	−0.511302	−	0.859401i	$-0.670836\pi$
$449$	−21.6686	−1.02260	−0.511302	+	0.859401i	$0.670836\pi$
$450$	−2.05828	−0.0970284
$451$	−21.3784	−1.00667
$452$	46.4370	2.18421
$453$	11.0693	0.520082
$454$	−29.8470	−1.40079
$455$	−17.0469	−0.799170
$456$	−1.90178	−0.0890591
$457$	40.8123	1.90912	0.954560	−	0.298020i	$-0.0963262\pi$
$457$	40.8123	1.90912	0.954560	+	0.298020i	$0.0963262\pi$
$458$	−9.82557	−0.459119
$459$	0.549685	0.0256571
$460$	19.2443	0.897269
$461$	−24.9334	−1.16127	−0.580633	−	0.814166i	$-0.697195\pi$
$461$	−24.9334	−1.16127	−0.580633	+	0.814166i	$0.697195\pi$
$462$	43.3775	2.01810
$463$	−16.2529	−0.755337	−0.377668	−	0.925941i	$-0.623274\pi$
$463$	−16.2529	−0.755337	−0.377668	+	0.925941i	$0.623274\pi$
$464$	−12.2450	−0.568461
$465$	−5.03276	−0.233389
$466$	−39.7163	−1.83982
$467$	−33.3109	−1.54145	−0.770723	−	0.637170i	$-0.780105\pi$
$467$	−33.3109	−1.54145	−0.770723	+	0.637170i	$0.780105\pi$
$468$	8.41256	0.388871
$469$	37.6360	1.73787
$470$	7.67633	0.354083
$471$	−17.1457	−0.790031
$472$	0.0489530	0.00225324
$473$	13.9362	0.640785
$474$	−1.27441	−0.0585357
$475$	3.90641	0.179238
$476$	5.57158	0.255373
$477$	−10.5446	−0.482803
$478$	56.9872	2.60653
$479$	0.924498	0.0422414	0.0211207	−	0.999777i	$-0.493277\pi$
$479$	0.924498	0.0422414	0.0211207	+	0.999777i	$0.493277\pi$
$480$	−8.11798	−0.370533
$481$	−24.1009	−1.09891
$482$	6.85291	0.312141
$483$	−38.9958	−1.77437
$484$	23.7611	1.08005
$485$	−12.2871	−0.557929
$486$	−2.05828	−0.0933656
$487$	30.4383	1.37929	0.689645	−	0.724148i	$-0.257767\pi$
$487$	30.4383	1.37929	0.689645	+	0.724148i	$0.257767\pi$
$488$	4.27811	0.193661
$489$	−13.4185	−0.606805
$490$	27.8672	1.25891
$491$	−1.92288	−0.0867782	−0.0433891	−	0.999058i	$-0.513816\pi$
$491$	−1.92288	−0.0867782	−0.0433891	+	0.999058i	$0.513816\pi$
$492$	10.2820	0.463550
$493$	1.93918	0.0873364
$494$	−30.2438	−1.36073
$495$	4.65017	0.209010
$496$	−17.4687	−0.784369
$497$	38.5161	1.72768
$498$	−22.8123	−1.02224
$499$	29.4586	1.31875	0.659374	−	0.751815i	$-0.270821\pi$
$499$	29.4586	1.31875	0.659374	+	0.751815i	$0.270821\pi$
$500$	−2.23653	−0.100020
$501$	6.86819	0.306848
$502$	−6.50900	−0.290511
$503$	7.85818	0.350379	0.175190	−	0.984535i	$-0.443946\pi$
$503$	7.85818	0.350379	0.175190	+	0.984535i	$0.443946\pi$
$504$	−2.20635	−0.0982784
$505$	−4.00962	−0.178426
$506$	−82.3573	−3.66123
$507$	1.14843	0.0510037
$508$	−9.22729	−0.409395
$509$	−14.6565	−0.649640	−0.324820	−	0.945776i	$-0.605304\pi$
$509$	−14.6565	−0.649640	−0.324820	+	0.945776i	$0.605304\pi$
$510$	1.13141	0.0500995
$511$	47.2604	2.09068
$512$	−31.5572	−1.39464
$513$	3.90641	0.172472
$514$	58.2174	2.56786
$515$	16.5053	0.727309
$516$	−6.70267	−0.295069
$517$	−17.3427	−0.762733
$518$	59.7688	2.62609
$519$	−11.3727	−0.499206
$520$	1.83121	0.0803037
$521$	−8.42572	−0.369137	−0.184569	−	0.982820i	$-0.559089\pi$
$521$	−8.42572	−0.369137	−0.184569	+	0.982820i	$0.559089\pi$
$522$	−7.26122	−0.317815
$523$	27.4720	1.20127	0.600633	−	0.799525i	$-0.294915\pi$
$523$	27.4720	1.20127	0.600633	+	0.799525i	$0.294915\pi$
$524$	9.05005	0.395353
$525$	4.53201	0.197793
$526$	−26.8529	−1.17084
$527$	2.76643	0.120508
$528$	16.1408	0.702437
$529$	51.0382	2.21905
$530$	−21.7037	−0.942749
$531$	−0.100553	−0.00436364
$532$	39.5951	1.71667
$533$	17.2926	0.749025
$534$	−7.39107	−0.319843
$535$	−5.92247	−0.256051
$536$	−4.04293	−0.174628
$537$	−5.70756	−0.246300
$538$	−63.7427	−2.74814
$539$	−62.9590	−2.71184
$540$	−2.23653	−0.0962447
$541$	−13.1306	−0.564528	−0.282264	−	0.959337i	$-0.591085\pi$
$541$	−13.1306	−0.564528	−0.282264	+	0.959337i	$0.591085\pi$
$542$	30.0941	1.29265
$543$	8.77631	0.376628
$544$	4.46233	0.191321
$545$	9.31913	0.399188
$546$	−35.0873	−1.50160
$547$	11.8767	0.507810	0.253905	−	0.967229i	$-0.418285\pi$
$547$	11.8767	0.507810	0.253905	+	0.967229i	$0.418285\pi$
$548$	43.1665	1.84398
$549$	−8.78757	−0.375045
$550$	9.57137	0.408124
$551$	13.7810	0.587092
$552$	4.18901	0.178296
$553$	2.80605	0.119325
$554$	−38.1529	−1.62096
$555$	6.40736	0.271977
$556$	32.5487	1.38037
$557$	−39.7529	−1.68438	−0.842192	−	0.539177i	$-0.818735\pi$
$557$	−39.7529	−1.68438	−0.842192	+	0.539177i	$0.818735\pi$
$558$	−10.3588	−0.438525
$559$	−11.2727	−0.476784
$560$	15.7306	0.664740
$561$	−2.55613	−0.107920
$562$	−21.2486	−0.896320
$563$	−3.96109	−0.166940	−0.0834700	−	0.996510i	$-0.526600\pi$
$563$	−3.96109	−0.166940	−0.0834700	+	0.996510i	$0.526600\pi$
$564$	8.34109	0.351223
$565$	−20.7630	−0.873506
$566$	42.1700	1.77254
$567$	4.53201	0.190326
$568$	−4.13747	−0.173604
$569$	−30.8127	−1.29173	−0.645867	−	0.763450i	$-0.723504\pi$
$569$	−30.8127	−1.29173	−0.645867	+	0.763450i	$0.723504\pi$
$570$	8.04049	0.336779
$571$	6.87192	0.287581	0.143790	−	0.989608i	$-0.454071\pi$
$571$	6.87192	0.287581	0.143790	+	0.989608i	$0.454071\pi$
$572$	−39.1198	−1.63568
$573$	−17.9291	−0.749000
$574$	−42.8846	−1.78997
$575$	−8.60454	−0.358834
$576$	−9.76708	−0.406962
$577$	8.79214	0.366021	0.183011	−	0.983111i	$-0.441416\pi$
$577$	8.79214	0.366021	0.183011	+	0.983111i	$0.441416\pi$
$578$	34.3689	1.42956
$579$	−3.21424	−0.133579
$580$	−7.89003	−0.327616
$581$	50.2290	2.08385
$582$	−25.2903	−1.04832
$583$	49.0341	2.03078
$584$	−5.07680	−0.210079
$585$	−3.76144	−0.155516
$586$	−4.43045	−0.183020
$587$	−5.87975	−0.242683	−0.121342	−	0.992611i	$-0.538720\pi$
$587$	−5.87975	−0.242683	−0.121342	+	0.992611i	$0.538720\pi$
$588$	30.2805	1.24875
$589$	19.6600	0.810077
$590$	−0.206967	−0.00852070
$591$	−15.1374	−0.622668
$592$	22.2400	0.914058
$593$	32.4246	1.33152	0.665759	−	0.746167i	$-0.268108\pi$
$593$	32.4246	1.33152	0.665759	+	0.746167i	$0.268108\pi$
$594$	9.57137	0.392718
$595$	−2.49118	−0.102128
$596$	41.4459	1.69769
$597$	1.95101	0.0798495
$598$	66.6173	2.72418
$599$	−5.93374	−0.242446	−0.121223	−	0.992625i	$-0.538682\pi$
$599$	−5.93374	−0.242446	−0.121223	+	0.992625i	$0.538682\pi$
$600$	−0.486836	−0.0198750
$601$	24.3657	0.993900	0.496950	−	0.867779i	$-0.334453\pi$
$601$	24.3657	0.993900	0.496950	+	0.867779i	$0.334453\pi$
$602$	27.9556	1.13939
$603$	8.30450	0.338185
$604$	24.7568	1.00734
$605$	−10.6241	−0.431931
$606$	−8.25292	−0.335252
$607$	−29.3895	−1.19288	−0.596442	−	0.802657i	$-0.703419\pi$
$607$	−29.3895	−1.19288	−0.596442	+	0.802657i	$0.703419\pi$
$608$	31.7121	1.28610
$609$	15.9880	0.647868
$610$	−18.0873	−0.732334
$611$	14.0282	0.567522
$612$	1.22938	0.0496949
$613$	−0.467795	−0.0188940	−0.00944702	−	0.999955i	$-0.503007\pi$
$613$	−0.467795	−0.0188940	−0.00944702	+	0.999955i	$0.503007\pi$
$614$	−1.11172	−0.0448652
$615$	−4.59733	−0.185382
$616$	10.2599	0.413383
$617$	−41.5759	−1.67378	−0.836891	−	0.547369i	$-0.815629\pi$
$617$	−41.5759	−1.67378	−0.836891	+	0.547369i	$0.815629\pi$
$618$	33.9725	1.36657
$619$	25.0666	1.00751	0.503755	−	0.863847i	$-0.331951\pi$
$619$	25.0666	1.00751	0.503755	+	0.863847i	$0.331951\pi$
$620$	−11.2559	−0.452048
$621$	−8.60454	−0.345288
$622$	−48.9087	−1.96106
$623$	16.2739	0.652002
$624$	−13.0560	−0.522657
$625$	1.00000	0.0400000
$626$	−48.2543	−1.92863
$627$	−18.1655	−0.725459
$628$	−38.3467	−1.53020
$629$	−3.52203	−0.140433
$630$	9.32815	0.371642
$631$	37.5322	1.49413	0.747066	−	0.664750i	$-0.231462\pi$
$631$	37.5322	1.49413	0.747066	+	0.664750i	$0.231462\pi$
$632$	−0.301431	−0.0119903
$633$	−26.5016	−1.05334
$634$	−3.28628	−0.130515
$635$	4.12572	0.163724
$636$	−23.5832	−0.935135
$637$	50.9264	2.01778
$638$	33.7659	1.33681
$639$	8.49868	0.336203
$640$	−3.86746	−0.152875
$641$	40.2913	1.59141	0.795705	−	0.605685i	$-0.207101\pi$
$641$	40.2913	1.59141	0.795705	+	0.605685i	$0.207101\pi$
$642$	−12.1901	−0.481106
$643$	−6.80604	−0.268404	−0.134202	−	0.990954i	$-0.542847\pi$
$643$	−6.80604	−0.268404	−0.134202	+	0.990954i	$0.542847\pi$
$644$	−87.2152	−3.43676
$645$	2.99691	0.118003
$646$	−4.41974	−0.173892
$647$	9.06380	0.356335	0.178167	−	0.984000i	$-0.442983\pi$
$647$	9.06380	0.356335	0.178167	+	0.984000i	$0.442983\pi$
$648$	−0.486836	−0.0191247
$649$	0.467590	0.0183545
$650$	−7.74211	−0.303670
$651$	22.8085	0.893935
$652$	−30.0108	−1.17531
$653$	12.5899	0.492682	0.246341	−	0.969183i	$-0.420772\pi$
$653$	12.5899	0.492682	0.246341	+	0.969183i	$0.420772\pi$
$654$	19.1814	0.750052
$655$	−4.04648	−0.158109
$656$	−15.9574	−0.623030
$657$	10.4281	0.406840
$658$	−34.7892	−1.35622
$659$	19.3771	0.754824	0.377412	−	0.926045i	$-0.376814\pi$
$659$	19.3771	0.754824	0.377412	+	0.926045i	$0.376814\pi$
$660$	10.4002	0.404828
$661$	28.7465	1.11811	0.559055	−	0.829131i	$-0.311164\pi$
$661$	28.7465	1.11811	0.559055	+	0.829131i	$0.311164\pi$
$662$	−44.0292	−1.71124
$663$	2.06761	0.0802992
$664$	−5.39569	−0.209393
$665$	−17.7039	−0.686526
$666$	13.1882	0.511031
$667$	−30.3552	−1.17536
$668$	15.3609	0.594330
$669$	10.0347	0.387962
$670$	17.0930	0.660360
$671$	40.8637	1.57753
$672$	36.7907	1.41923
$673$	−26.2648	−1.01243	−0.506217	−	0.862406i	$-0.668956\pi$
$673$	−26.2648	−1.01243	−0.506217	+	0.862406i	$0.668956\pi$
$674$	2.86634	0.110407
$675$	1.00000	0.0384900
$676$	2.56850	0.0987884
$677$	7.92869	0.304724	0.152362	−	0.988325i	$-0.451312\pi$
$677$	7.92869	0.304724	0.152362	+	0.988325i	$0.451312\pi$
$678$	−42.7361	−1.64127
$679$	55.6852	2.13700
$680$	0.267607	0.0102622
$681$	14.5009	0.555676
$682$	48.1704	1.84454
$683$	37.6589	1.44098	0.720490	−	0.693466i	$-0.243917\pi$
$683$	37.6589	1.44098	0.720490	+	0.693466i	$0.243917\pi$
$684$	8.73678	0.334059
$685$	−19.3007	−0.737442
$686$	−60.9975	−2.32889
$687$	4.77368	0.182127
$688$	10.4023	0.396584
$689$	−39.6628	−1.51103
$690$	−17.7106	−0.674230
$691$	−19.2721	−0.733145	−0.366572	−	0.930390i	$-0.619469\pi$
$691$	−19.2721	−0.733145	−0.366572	+	0.930390i	$0.619469\pi$
$692$	−25.4353	−0.966906
$693$	−21.0746	−0.800558
$694$	10.5700	0.401230
$695$	−14.5532	−0.552035
$696$	−1.71746	−0.0651003
$697$	2.52708	0.0957201
$698$	−8.34519	−0.315870
$699$	19.2958	0.729835
$700$	10.1359	0.383103
$701$	30.7176	1.16019	0.580093	−	0.814550i	$-0.303016\pi$
$701$	30.7176	1.16019	0.580093	+	0.814550i	$0.303016\pi$
$702$	−7.74211	−0.292207
$703$	−25.0298	−0.944016
$704$	45.4186	1.71178
$705$	−3.72948	−0.140461
$706$	−55.1033	−2.07384
$707$	18.1716	0.683414
$708$	−0.224890	−0.00845188
$709$	28.4431	1.06820	0.534102	−	0.845420i	$-0.320650\pi$
$709$	28.4431	1.06820	0.534102	+	0.845420i	$0.320650\pi$
$710$	17.4927	0.656489
$711$	0.619163	0.0232204
$712$	−1.74818	−0.0655157
$713$	−43.3046	−1.62177
$714$	−5.12754	−0.191893
$715$	17.4913	0.654139
$716$	−12.7651	−0.477055
$717$	−27.6868	−1.03398
$718$	−39.2128	−1.46341
$719$	47.4335	1.76897	0.884486	−	0.466567i	$-0.154509\pi$
$719$	47.4335	1.76897	0.884486	+	0.466567i	$0.154509\pi$
$720$	3.47100	0.129357
$721$	−74.8020	−2.78577
$722$	7.69793	0.286487
$723$	−3.32943	−0.123823
$724$	19.6284	0.729485
$725$	3.52781	0.131019
$726$	−21.8674	−0.811575
$727$	2.71646	0.100748	0.0503739	−	0.998730i	$-0.483959\pi$
$727$	2.71646	0.100748	0.0503739	+	0.998730i	$0.483959\pi$
$728$	−8.29904	−0.307583
$729$	1.00000	0.0370370
$730$	21.4640	0.794420
$731$	−1.64736	−0.0609297
$732$	−19.6536	−0.726419
$733$	24.6875	0.911854	0.455927	−	0.890017i	$-0.349308\pi$
$733$	24.6875	0.911854	0.455927	+	0.890017i	$0.349308\pi$
$734$	43.6799	1.61225
$735$	−13.5391	−0.499396
$736$	−69.8515	−2.57476
$737$	−38.6173	−1.42249
$738$	−9.46260	−0.348323
$739$	−51.0989	−1.87970	−0.939852	−	0.341583i	$-0.889037\pi$
$739$	−51.0989	−1.87970	−0.939852	+	0.341583i	$0.889037\pi$
$740$	14.3302	0.526790
$741$	14.6937	0.539787
$742$	98.3613	3.61096
$743$	53.2472	1.95345	0.976724	−	0.214498i	$-0.0688114\pi$
$743$	53.2472	1.95345	0.976724	+	0.214498i	$0.0688114\pi$
$744$	−2.45013	−0.0898261
$745$	−18.5314	−0.678937
$746$	21.9102	0.802190
$747$	11.0832	0.405512
$748$	−5.71685	−0.209029
$749$	26.8407	0.980737
$750$	2.05828	0.0751578
$751$	6.42701	0.234525	0.117262	−	0.993101i	$-0.462588\pi$
$751$	6.42701	0.234525	0.117262	+	0.993101i	$0.462588\pi$
$752$	−12.9451	−0.472058
$753$	3.16235	0.115242
$754$	−27.3126	−0.994668
$755$	−11.0693	−0.402854
$756$	10.1359	0.368641
$757$	−29.7268	−1.08044	−0.540220	−	0.841524i	$-0.681659\pi$
$757$	−29.7268	−1.08044	−0.540220	+	0.841524i	$0.681659\pi$
$758$	−44.7446	−1.62520
$759$	40.0126	1.45237
$760$	1.90178	0.0689849
$761$	−20.0426	−0.726545	−0.363273	−	0.931683i	$-0.618341\pi$
$761$	−20.0426	−0.726545	−0.363273	+	0.931683i	$0.618341\pi$
$762$	8.49190	0.307629
$763$	−42.2344	−1.52899
$764$	−40.0989	−1.45073
$765$	−0.549685	−0.0198739
$766$	−29.7691	−1.07560
$767$	−0.378225	−0.0136569
$768$	11.5739	0.417635
$769$	16.6261	0.599553	0.299777	−	0.954009i	$-0.403088\pi$
$769$	16.6261	0.599553	0.299777	+	0.954009i	$0.403088\pi$
$770$	−43.3775	−1.56322
$771$	−28.2845	−1.01864
$772$	−7.18873	−0.258728
$773$	31.0470	1.11668	0.558342	−	0.829611i	$-0.311438\pi$
$773$	31.0470	1.11668	0.558342	+	0.829611i	$0.311438\pi$
$774$	6.16849	0.221722
$775$	5.03276	0.180782
$776$	−5.98181	−0.214734
$777$	−29.0382	−1.04174
$778$	41.6954	1.49485
$779$	17.9590	0.643450
$780$	−8.41256	−0.301218
$781$	−39.5203	−1.41415
$782$	9.73524	0.348131
$783$	3.52781	0.126074
$784$	−46.9942	−1.67836
$785$	17.1457	0.611956
$786$	−8.32879	−0.297078
$787$	46.6483	1.66283	0.831415	−	0.555651i	$-0.187531\pi$
$787$	46.6483	1.66283	0.831415	+	0.555651i	$0.187531\pi$
$788$	−33.8551	−1.20604
$789$	13.0463	0.464459
$790$	1.27441	0.0453416
$791$	94.0980	3.34574
$792$	2.26387	0.0804432
$793$	−33.0539	−1.17378
$794$	−49.3498	−1.75136
$795$	10.5446	0.373977
$796$	4.36348	0.154660
$797$	2.66376	0.0943553	0.0471777	−	0.998887i	$-0.484977\pi$
$797$	2.66376	0.0943553	0.0471777	+	0.998887i	$0.484977\pi$
$798$	−36.4395	−1.28995
$799$	2.05004	0.0725253
$800$	8.11798	0.287014
$801$	3.59089	0.126878
$802$	2.05828	0.0726805
$803$	−48.4926	−1.71127
$804$	18.5732	0.655027
$805$	38.9958	1.37442
$806$	−38.9642	−1.37245
$807$	30.9689	1.09016
$808$	−1.95203	−0.0686721
$809$	−35.8977	−1.26210	−0.631048	−	0.775744i	$-0.717375\pi$
$809$	−35.8977	−1.26210	−0.631048	+	0.775744i	$0.717375\pi$
$810$	2.05828	0.0723207
$811$	−55.5353	−1.95011	−0.975053	−	0.221971i	$-0.928751\pi$
$811$	−55.5353	−1.95011	−0.975053	+	0.221971i	$0.928751\pi$
$812$	35.7577	1.25485
$813$	−14.6210	−0.512781
$814$	−61.3272	−2.14952
$815$	13.4185	0.470029
$816$	−1.90796	−0.0667919
$817$	−11.7072	−0.409582
$818$	16.9267	0.591828
$819$	17.0469	0.595666
$820$	−10.2820	−0.359065
$821$	−14.6480	−0.511220	−0.255610	−	0.966780i	$-0.582276\pi$
$821$	−14.6480	−0.511220	−0.255610	+	0.966780i	$0.582276\pi$
$822$	−39.7263	−1.38561
$823$	−23.6621	−0.824810	−0.412405	−	0.911001i	$-0.635311\pi$
$823$	−23.6621	−0.824810	−0.412405	+	0.911001i	$0.635311\pi$
$824$	8.03537	0.279925
$825$	−4.65017	−0.161898
$826$	0.937976	0.0326363
$827$	25.8946	0.900444	0.450222	−	0.892917i	$-0.351345\pi$
$827$	25.8946	0.900444	0.450222	+	0.892917i	$0.351345\pi$
$828$	−19.2443	−0.668785
$829$	53.0102	1.84112	0.920561	−	0.390599i	$-0.127732\pi$
$829$	53.0102	1.84112	0.920561	+	0.390599i	$0.127732\pi$
$830$	22.8123	0.791827
$831$	18.5363	0.643017
$832$	−36.7383	−1.27367
$833$	7.44223	0.257858
$834$	−29.9546	−1.03724
$835$	−6.86819	−0.237683
$836$	−40.6275	−1.40513
$837$	5.03276	0.173958
$838$	24.2551	0.837877
$839$	22.1558	0.764902	0.382451	−	0.923976i	$-0.375080\pi$
$839$	22.1558	0.764902	0.382451	+	0.923976i	$0.375080\pi$
$840$	2.20635	0.0761261
$841$	−16.5546	−0.570848
$842$	42.1727	1.45337
$843$	10.3235	0.355560
$844$	−59.2714	−2.04021
$845$	−1.14843	−0.0395073
$846$	−7.67633	−0.263918
$847$	48.1485	1.65440
$848$	36.6003	1.25686
$849$	−20.4879	−0.703145
$850$	−1.13141	−0.0388069
$851$	55.1324	1.88992
$852$	19.0075	0.651187
$853$	8.71613	0.298435	0.149217	−	0.988804i	$-0.452325\pi$
$853$	8.71613	0.298435	0.149217	+	0.988804i	$0.452325\pi$
$854$	81.9718	2.80502
$855$	−3.90641	−0.133596
$856$	−2.88328	−0.0985483
$857$	24.2012	0.826697	0.413348	−	0.910573i	$-0.364359\pi$
$857$	24.2012	0.826697	0.413348	+	0.910573i	$0.364359\pi$
$858$	36.0021	1.22909
$859$	45.8017	1.56273	0.781367	−	0.624072i	$-0.214523\pi$
$859$	45.8017	1.56273	0.781367	+	0.624072i	$0.214523\pi$
$860$	6.70267	0.228559
$861$	20.8351	0.710059
$862$	23.5340	0.801570
$863$	−3.76293	−0.128092	−0.0640458	−	0.997947i	$-0.520400\pi$
$863$	−3.76293	−0.128092	−0.0640458	+	0.997947i	$0.520400\pi$
$864$	8.11798	0.276179
$865$	11.3727	0.386683
$866$	−74.9427	−2.54666
$867$	−16.6978	−0.567089
$868$	51.0118	1.73145
$869$	−2.87922	−0.0976707
$870$	7.26122	0.246178
$871$	31.2369	1.05842
$872$	4.53689	0.153639
$873$	12.2871	0.415855
$874$	69.1848	2.34021
$875$	−4.53201	−0.153210
$876$	23.3228	0.788004
$877$	39.9250	1.34817	0.674086	−	0.738653i	$-0.264538\pi$
$877$	39.9250	1.34817	0.674086	+	0.738653i	$0.264538\pi$
$878$	31.8171	1.07377
$879$	2.15250	0.0726020
$880$	−16.1408	−0.544105
$881$	12.9991	0.437949	0.218975	−	0.975731i	$-0.429729\pi$
$881$	12.9991	0.437949	0.218975	+	0.975731i	$0.429729\pi$
$882$	−27.8672	−0.938339
$883$	39.4058	1.32611	0.663055	−	0.748571i	$-0.269260\pi$
$883$	39.4058	1.32611	0.663055	+	0.748571i	$0.269260\pi$
$884$	4.62426	0.155531
$885$	0.100553	0.00338006
$886$	−23.4266	−0.787032
$887$	−26.6731	−0.895596	−0.447798	−	0.894135i	$-0.647792\pi$
$887$	−26.6731	−0.895596	−0.447798	+	0.894135i	$0.647792\pi$
$888$	3.11934	0.104678
$889$	−18.6978	−0.627104
$890$	7.39107	0.247749
$891$	−4.65017	−0.155787
$892$	22.4428	0.751440
$893$	14.5689	0.487529
$894$	−38.1428	−1.27569
$895$	5.70756	0.190783
$896$	17.5273	0.585547
$897$	−32.3655	−1.08065
$898$	44.6000	1.48832
$899$	17.7546	0.592149
$900$	2.23653	0.0745509
$901$	−5.79619	−0.193099
$902$	44.0027	1.46513
$903$	−13.5820	−0.451981
$904$	−10.1082	−0.336193
$905$	−8.77631	−0.291734
$906$	−22.7838	−0.756940
$907$	−43.2902	−1.43743	−0.718715	−	0.695305i	$-0.755269\pi$
$907$	−43.2902	−1.43743	−0.718715	+	0.695305i	$0.755269\pi$
$908$	32.4317	1.07628
$909$	4.00962	0.132991
$910$	35.0873	1.16313
$911$	38.5844	1.27836	0.639180	−	0.769058i	$-0.279274\pi$
$911$	38.5844	1.27836	0.639180	+	0.769058i	$0.279274\pi$
$912$	−13.5592	−0.448989
$913$	−51.5387	−1.70568
$914$	−84.0032	−2.77858
$915$	8.78757	0.290508
$916$	10.6764	0.352760
$917$	18.3387	0.605596
$918$	−1.13141	−0.0373420
$919$	28.2533	0.931989	0.465995	−	0.884788i	$-0.345697\pi$
$919$	28.2533	0.931989	0.465995	+	0.884788i	$0.345697\pi$
$920$	−4.18901	−0.138107
$921$	0.540118	0.0177975
$922$	51.3200	1.69013
$923$	31.9673	1.05222
$924$	−47.1339	−1.55059
$925$	−6.40736	−0.210673
$926$	33.4531	1.09934
$927$	−16.5053	−0.542104
$928$	28.6387	0.940110
$929$	8.20408	0.269167	0.134584	−	0.990902i	$-0.457030\pi$
$929$	8.20408	0.269167	0.134584	+	0.990902i	$0.457030\pi$
$930$	10.3588	0.339680
$931$	52.8892	1.73337
$932$	43.1556	1.41361
$933$	23.7619	0.777930
$934$	68.5633	2.24346
$935$	2.55613	0.0835944
$936$	−1.83121	−0.0598548
$937$	46.3566	1.51440	0.757202	−	0.653180i	$-0.226566\pi$
$937$	46.3566	1.51440	0.757202	+	0.653180i	$0.226566\pi$
$938$	−77.4656	−2.52934
$939$	23.4440	0.765065
$940$	−8.34109	−0.272056
$941$	−42.4876	−1.38506	−0.692528	−	0.721391i	$-0.743503\pi$
$941$	−42.4876	−1.38506	−0.692528	+	0.721391i	$0.743503\pi$
$942$	35.2906	1.14983
$943$	−39.5579	−1.28818
$944$	0.349021	0.0113597
$945$	−4.53201	−0.147426
$946$	−28.6845	−0.932615
$947$	31.6805	1.02948	0.514740	−	0.857347i	$-0.327889\pi$
$947$	31.6805	1.02948	0.514740	+	0.857347i	$0.327889\pi$
$948$	1.38477	0.0449754
$949$	39.2248	1.27329
$950$	−8.04049	−0.260868
$951$	1.59661	0.0517738
$952$	−1.21279	−0.0393069
$953$	2.08532	0.0675500	0.0337750	−	0.999429i	$-0.489247\pi$
$953$	2.08532	0.0675500	0.0337750	+	0.999429i	$0.489247\pi$
$954$	21.7037	0.702683
$955$	17.9291	0.580173
$956$	−61.9222	−2.00271
$957$	−16.4049	−0.530295
$958$	−1.90288	−0.0614792
$959$	87.4710	2.82458
$960$	9.76708	0.315231
$961$	−5.67133	−0.182946
$962$	49.6065	1.59938
$963$	5.92247	0.190849
$964$	−7.44636	−0.239831
$965$	3.21424	0.103470
$966$	80.2645	2.58247
$967$	7.54381	0.242592	0.121296	−	0.992616i	$-0.461295\pi$
$967$	7.54381	0.242592	0.121296	+	0.992616i	$0.461295\pi$
$968$	−5.17220	−0.166241
$969$	2.14729	0.0689810
$970$	25.2903	0.812023
$971$	−42.0592	−1.34974	−0.674872	−	0.737935i	$-0.735801\pi$
$971$	−42.0592	−1.34974	−0.674872	+	0.737935i	$0.735801\pi$
$972$	2.23653	0.0717366
$973$	65.9553	2.11443
$974$	−62.6505	−2.00745
$975$	3.76144	0.120462
$976$	30.5017	0.976336
$977$	−54.8792	−1.75574	−0.877870	−	0.478898i	$-0.841036\pi$
$977$	−54.8792	−1.75574	−0.877870	+	0.478898i	$0.841036\pi$
$978$	27.6191	0.883160
$979$	−16.6983	−0.533679
$980$	−30.2805	−0.967275
$981$	−9.31913	−0.297537
$982$	3.95782	0.126299
$983$	−44.8389	−1.43014	−0.715070	−	0.699053i	$-0.753605\pi$
$983$	−44.8389	−1.43014	−0.715070	+	0.699053i	$0.753605\pi$
$984$	−2.23815	−0.0713495
$985$	15.1374	0.482317
$986$	−3.99138	−0.127112
$987$	16.9020	0.537998
$988$	32.8629	1.04551
$989$	25.7871	0.819981
$990$	−9.57137	−0.304198
$991$	13.0238	0.413715	0.206858	−	0.978371i	$-0.433676\pi$
$991$	13.0238	0.413715	0.206858	+	0.978371i	$0.433676\pi$
$992$	40.8558	1.29717
$993$	21.3912	0.678830
$994$	−79.2769	−2.51451
$995$	−1.95101	−0.0618512
$996$	24.7878	0.785432
$997$	−15.5372	−0.492069	−0.246034	−	0.969261i	$-0.579128\pi$
$997$	−15.5372	−0.492069	−0.246034	+	0.969261i	$0.579128\pi$
$998$	−60.6341	−1.91934
$999$	−6.40736	−0.202720

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.h.1.8	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.h.1.8	✓	39	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.05828 q^{2} +1.00000 q^{3} +2.23653 q^{4} -1.00000 q^{5} -2.05828 q^{6} +4.53201 q^{7} -0.486836 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.05828 q^{2} +1.00000 q^{3} +2.23653 q^{4} -1.00000 q^{5} -2.05828 q^{6} +4.53201 q^{7} -0.486836 q^{8} +1.00000 q^{9} +2.05828 q^{10} -4.65017 q^{11} +2.23653 q^{12} +3.76144 q^{13} -9.32815 q^{14} -1.00000 q^{15} -3.47100 q^{16} +0.549685 q^{17} -2.05828 q^{18} +3.90641 q^{19} -2.23653 q^{20} +4.53201 q^{21} +9.57137 q^{22} -8.60454 q^{23} -0.486836 q^{24} +1.00000 q^{25} -7.74211 q^{26} +1.00000 q^{27} +10.1359 q^{28} +3.52781 q^{29} +2.05828 q^{30} +5.03276 q^{31} +8.11798 q^{32} -4.65017 q^{33} -1.13141 q^{34} -4.53201 q^{35} +2.23653 q^{36} -6.40736 q^{37} -8.04049 q^{38} +3.76144 q^{39} +0.486836 q^{40} +4.59733 q^{41} -9.32815 q^{42} -2.99691 q^{43} -10.4002 q^{44} -1.00000 q^{45} +17.7106 q^{46} +3.72948 q^{47} -3.47100 q^{48} +13.5391 q^{49} -2.05828 q^{50} +0.549685 q^{51} +8.41256 q^{52} -10.5446 q^{53} -2.05828 q^{54} +4.65017 q^{55} -2.20635 q^{56} +3.90641 q^{57} -7.26122 q^{58} -0.100553 q^{59} -2.23653 q^{60} -8.78757 q^{61} -10.3588 q^{62} +4.53201 q^{63} -9.76708 q^{64} -3.76144 q^{65} +9.57137 q^{66} +8.30450 q^{67} +1.22938 q^{68} -8.60454 q^{69} +9.32815 q^{70} +8.49868 q^{71} -0.486836 q^{72} +10.4281 q^{73} +13.1882 q^{74} +1.00000 q^{75} +8.73678 q^{76} -21.0746 q^{77} -7.74211 q^{78} +0.619163 q^{79} +3.47100 q^{80} +1.00000 q^{81} -9.46260 q^{82} +11.0832 q^{83} +10.1359 q^{84} -0.549685 q^{85} +6.16849 q^{86} +3.52781 q^{87} +2.26387 q^{88} +3.59089 q^{89} +2.05828 q^{90} +17.0469 q^{91} -19.2443 q^{92} +5.03276 q^{93} -7.67633 q^{94} -3.90641 q^{95} +8.11798 q^{96} +12.2871 q^{97} -27.8672 q^{98} -4.65017 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9}+O(q^{10}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9} - q^{11} + 48 q^{12} + 30 q^{13} + 8 q^{14} - 39 q^{15} + 58 q^{16} + 32 q^{17} + 27 q^{19} - 48 q^{20} + 22 q^{21} + 23 q^{22} - 8 q^{23} + 3 q^{24} + 39 q^{25} - 4 q^{26} + 39 q^{27} + 60 q^{28} - 9 q^{29} + 19 q^{31} + q^{32} - q^{33} + 26 q^{34} - 22 q^{35} + 48 q^{36} + 44 q^{37} + 14 q^{38} + 30 q^{39} - 3 q^{40} + 31 q^{41} + 8 q^{42} + 75 q^{43} + q^{44} - 39 q^{45} + 19 q^{46} - 16 q^{47} + 58 q^{48} + 91 q^{49} + 32 q^{51} + 94 q^{52} + 17 q^{53} + q^{55} + 27 q^{56} + 27 q^{57} + 26 q^{58} - q^{59} - 48 q^{60} + 55 q^{61} + 11 q^{62} + 22 q^{63} + 77 q^{64} - 30 q^{65} + 23 q^{66} + 84 q^{67} + 36 q^{68} - 8 q^{69} - 8 q^{70} - 2 q^{71} + 3 q^{72} + 79 q^{73} + 20 q^{74} + 39 q^{75} + 58 q^{76} + 32 q^{77} - 4 q^{78} + 29 q^{79} - 58 q^{80} + 39 q^{81} + 53 q^{82} + 9 q^{83} + 60 q^{84} - 32 q^{85} - 17 q^{86} - 9 q^{87} + 57 q^{88} + 37 q^{89} + 71 q^{91} + 7 q^{92} + 19 q^{93} + 32 q^{94} - 27 q^{95} + q^{96} + 91 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9 - q^11 + 48 * q^12 + 30 * q^13 + 8 * q^14 - 39 * q^15 + 58 * q^16 + 32 * q^17 + 27 * q^19 - 48 * q^20 + 22 * q^21 + 23 * q^22 - 8 * q^23 + 3 * q^24 + 39 * q^25 - 4 * q^26 + 39 * q^27 + 60 * q^28 - 9 * q^29 + 19 * q^31 + q^32 - q^33 + 26 * q^34 - 22 * q^35 + 48 * q^36 + 44 * q^37 + 14 * q^38 + 30 * q^39 - 3 * q^40 + 31 * q^41 + 8 * q^42 + 75 * q^43 + q^44 - 39 * q^45 + 19 * q^46 - 16 * q^47 + 58 * q^48 + 91 * q^49 + 32 * q^51 + 94 * q^52 + 17 * q^53 + q^55 + 27 * q^56 + 27 * q^57 + 26 * q^58 - q^59 - 48 * q^60 + 55 * q^61 + 11 * q^62 + 22 * q^63 + 77 * q^64 - 30 * q^65 + 23 * q^66 + 84 * q^67 + 36 * q^68 - 8 * q^69 - 8 * q^70 - 2 * q^71 + 3 * q^72 + 79 * q^73 + 20 * q^74 + 39 * q^75 + 58 * q^76 + 32 * q^77 - 4 * q^78 + 29 * q^79 - 58 * q^80 + 39 * q^81 + 53 * q^82 + 9 * q^83 + 60 * q^84 - 32 * q^85 - 17 * q^86 - 9 * q^87 + 57 * q^88 + 37 * q^89 + 71 * q^91 + 7 * q^92 + 19 * q^93 + 32 * q^94 - 27 * q^95 + q^96 + 91 * q^97 - 9 * q^98 - q^99

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