LMFDB - Embedded newform 8031.2.a.a.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8031,2,Mod(1,8031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8031, 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("8031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8031 = 3 \cdot 2677 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8031.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.1278578633$
Analytic rank:	$1$
Dimension:	$92$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.38249 q^{2} +1.00000 q^{3} +3.67627 q^{4} -1.60383 q^{5} -2.38249 q^{6} -3.97189 q^{7} -3.99371 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.38249 q^{2} +1.00000 q^{3} +3.67627 q^{4} -1.60383 q^{5} -2.38249 q^{6} -3.97189 q^{7} -3.99371 q^{8} +1.00000 q^{9} +3.82111 q^{10} -0.782665 q^{11} +3.67627 q^{12} +2.85905 q^{13} +9.46301 q^{14} -1.60383 q^{15} +2.16244 q^{16} -1.64931 q^{17} -2.38249 q^{18} -6.47342 q^{19} -5.89611 q^{20} -3.97189 q^{21} +1.86469 q^{22} -0.534132 q^{23} -3.99371 q^{24} -2.42774 q^{25} -6.81167 q^{26} +1.00000 q^{27} -14.6018 q^{28} +1.22394 q^{29} +3.82111 q^{30} +4.16047 q^{31} +2.83542 q^{32} -0.782665 q^{33} +3.92948 q^{34} +6.37023 q^{35} +3.67627 q^{36} +0.0774709 q^{37} +15.4229 q^{38} +2.85905 q^{39} +6.40522 q^{40} +6.59043 q^{41} +9.46301 q^{42} +3.42992 q^{43} -2.87729 q^{44} -1.60383 q^{45} +1.27257 q^{46} +9.82247 q^{47} +2.16244 q^{48} +8.77593 q^{49} +5.78408 q^{50} -1.64931 q^{51} +10.5107 q^{52} -5.58000 q^{53} -2.38249 q^{54} +1.25526 q^{55} +15.8626 q^{56} -6.47342 q^{57} -2.91604 q^{58} +13.4543 q^{59} -5.89611 q^{60} +7.96449 q^{61} -9.91229 q^{62} -3.97189 q^{63} -11.0802 q^{64} -4.58542 q^{65} +1.86469 q^{66} +2.02759 q^{67} -6.06333 q^{68} -0.534132 q^{69} -15.1770 q^{70} -2.25830 q^{71} -3.99371 q^{72} +3.30362 q^{73} -0.184574 q^{74} -2.42774 q^{75} -23.7981 q^{76} +3.10866 q^{77} -6.81167 q^{78} -6.84083 q^{79} -3.46818 q^{80} +1.00000 q^{81} -15.7017 q^{82} -6.67770 q^{83} -14.6018 q^{84} +2.64521 q^{85} -8.17177 q^{86} +1.22394 q^{87} +3.12574 q^{88} +3.35493 q^{89} +3.82111 q^{90} -11.3558 q^{91} -1.96362 q^{92} +4.16047 q^{93} -23.4020 q^{94} +10.3822 q^{95} +2.83542 q^{96} -1.34841 q^{97} -20.9086 q^{98} -0.782665 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q - 6 q^{2} + 92 q^{3} + 70 q^{4} - 18 q^{5} - 6 q^{6} - 42 q^{7} - 15 q^{8} + 92 q^{9}+O(q^{10}) $ 92 * q - 6 * q^2 + 92 * q^3 + 70 * q^4 - 18 * q^5 - 6 * q^6 - 42 * q^7 - 15 * q^8 + 92 * q^9	\( 92 q - 6 q^{2} + 92 q^{3} + 70 q^{4} - 18 q^{5} - 6 q^{6} - 42 q^{7} - 15 q^{8} + 92 q^{9} - 44 q^{10} - 24 q^{11} + 70 q^{12} - 48 q^{13} - 29 q^{14} - 18 q^{15} + 26 q^{16} - 69 q^{17} - 6 q^{18} - 74 q^{19} - 42 q^{20} - 42 q^{21} - 62 q^{22} - 19 q^{23} - 15 q^{24} + 16 q^{25} - 27 q^{26} + 92 q^{27} - 101 q^{28} - 54 q^{29} - 44 q^{30} - 67 q^{31} - 36 q^{32} - 24 q^{33} - 63 q^{34} - 31 q^{35} + 70 q^{36} - 70 q^{37} - 18 q^{38} - 48 q^{39} - 125 q^{40} - 98 q^{41} - 29 q^{42} - 159 q^{43} - 52 q^{44} - 18 q^{45} - 68 q^{46} - 15 q^{47} + 26 q^{48} - 28 q^{49} - 7 q^{50} - 69 q^{51} - 98 q^{52} - 23 q^{53} - 6 q^{54} - 93 q^{55} - 48 q^{56} - 74 q^{57} - 37 q^{58} - 36 q^{59} - 42 q^{60} - 172 q^{61} - 26 q^{62} - 42 q^{63} - 23 q^{64} - 66 q^{65} - 62 q^{66} - 143 q^{67} - 74 q^{68} - 19 q^{69} - 30 q^{70} - 9 q^{71} - 15 q^{72} - 134 q^{73} - 19 q^{74} + 16 q^{75} - 157 q^{76} - 25 q^{77} - 27 q^{78} - 138 q^{79} - 29 q^{80} + 92 q^{81} - 61 q^{82} - 24 q^{83} - 101 q^{84} - 84 q^{85} + 14 q^{86} - 54 q^{87} - 140 q^{88} - 148 q^{89} - 44 q^{90} - 115 q^{91} - 12 q^{92} - 67 q^{93} - 79 q^{94} - 10 q^{95} - 36 q^{96} - 165 q^{97} + 36 q^{98} - 24 q^{99}+O(q^{100}) \) 92 * q - 6 * q^2 + 92 * q^3 + 70 * q^4 - 18 * q^5 - 6 * q^6 - 42 * q^7 - 15 * q^8 + 92 * q^9 - 44 * q^10 - 24 * q^11 + 70 * q^12 - 48 * q^13 - 29 * q^14 - 18 * q^15 + 26 * q^16 - 69 * q^17 - 6 * q^18 - 74 * q^19 - 42 * q^20 - 42 * q^21 - 62 * q^22 - 19 * q^23 - 15 * q^24 + 16 * q^25 - 27 * q^26 + 92 * q^27 - 101 * q^28 - 54 * q^29 - 44 * q^30 - 67 * q^31 - 36 * q^32 - 24 * q^33 - 63 * q^34 - 31 * q^35 + 70 * q^36 - 70 * q^37 - 18 * q^38 - 48 * q^39 - 125 * q^40 - 98 * q^41 - 29 * q^42 - 159 * q^43 - 52 * q^44 - 18 * q^45 - 68 * q^46 - 15 * q^47 + 26 * q^48 - 28 * q^49 - 7 * q^50 - 69 * q^51 - 98 * q^52 - 23 * q^53 - 6 * q^54 - 93 * q^55 - 48 * q^56 - 74 * q^57 - 37 * q^58 - 36 * q^59 - 42 * q^60 - 172 * q^61 - 26 * q^62 - 42 * q^63 - 23 * q^64 - 66 * q^65 - 62 * q^66 - 143 * q^67 - 74 * q^68 - 19 * q^69 - 30 * q^70 - 9 * q^71 - 15 * q^72 - 134 * q^73 - 19 * q^74 + 16 * q^75 - 157 * q^76 - 25 * q^77 - 27 * q^78 - 138 * q^79 - 29 * q^80 + 92 * q^81 - 61 * q^82 - 24 * q^83 - 101 * q^84 - 84 * q^85 + 14 * q^86 - 54 * q^87 - 140 * q^88 - 148 * q^89 - 44 * q^90 - 115 * q^91 - 12 * q^92 - 67 * q^93 - 79 * q^94 - 10 * q^95 - 36 * q^96 - 165 * q^97 + 36 * q^98 - 24 * 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 $

$2$	−2.38249	−1.68468	−0.842339	−	0.538949i	$-0.818822\pi$
$2$	−2.38249	−1.68468	−0.842339	+	0.538949i	$0.818822\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.67627	1.83814
$5$	−1.60383	−0.717253	−0.358627	−	0.933481i	$-0.616755\pi$
$5$	−1.60383	−0.717253	−0.358627	+	0.933481i	$0.616755\pi$
$6$	−2.38249	−0.972649
$7$	−3.97189	−1.50123	−0.750617	−	0.660737i	$-0.770244\pi$
$7$	−3.97189	−1.50123	−0.750617	+	0.660737i	$0.770244\pi$
$8$	−3.99371	−1.41199
$9$	1.00000	0.333333
$10$	3.82111	1.20834
$11$	−0.782665	−0.235982	−0.117991	−	0.993015i	$-0.537645\pi$
$11$	−0.782665	−0.235982	−0.117991	+	0.993015i	$0.537645\pi$
$12$	3.67627	1.06125
$13$	2.85905	0.792958	0.396479	−	0.918044i	$-0.370232\pi$
$13$	2.85905	0.792958	0.396479	+	0.918044i	$0.370232\pi$
$14$	9.46301	2.52910
$15$	−1.60383	−0.414106
$16$	2.16244	0.540611
$17$	−1.64931	−0.400018	−0.200009	−	0.979794i	$-0.564097\pi$
$17$	−1.64931	−0.400018	−0.200009	+	0.979794i	$0.564097\pi$
$18$	−2.38249	−0.561559
$19$	−6.47342	−1.48510	−0.742552	−	0.669788i	$-0.766385\pi$
$19$	−6.47342	−1.48510	−0.742552	+	0.669788i	$0.766385\pi$
$20$	−5.89611	−1.31841
$21$	−3.97189	−0.866738
$22$	1.86469	0.397554
$23$	−0.534132	−0.111374	−0.0556872	−	0.998448i	$-0.517735\pi$
$23$	−0.534132	−0.111374	−0.0556872	+	0.998448i	$0.517735\pi$
$24$	−3.99371	−0.815213
$25$	−2.42774	−0.485548
$26$	−6.81167	−1.33588
$27$	1.00000	0.192450
$28$	−14.6018	−2.75947
$29$	1.22394	0.227281	0.113640	−	0.993522i	$-0.463749\pi$
$29$	1.22394	0.227281	0.113640	+	0.993522i	$0.463749\pi$
$30$	3.82111	0.697635
$31$	4.16047	0.747242	0.373621	−	0.927581i	$-0.378116\pi$
$31$	4.16047	0.747242	0.373621	+	0.927581i	$0.378116\pi$
$32$	2.83542	0.501236
$33$	−0.782665	−0.136244
$34$	3.92948	0.673901
$35$	6.37023	1.07676
$36$	3.67627	0.612712
$37$	0.0774709	0.0127361	0.00636807	−	0.999980i	$-0.497973\pi$
$37$	0.0774709	0.0127361	0.00636807	+	0.999980i	$0.497973\pi$
$38$	15.4229	2.50192
$39$	2.85905	0.457815
$40$	6.40522	1.01275
$41$	6.59043	1.02925	0.514626	−	0.857415i	$-0.327931\pi$
$41$	6.59043	1.02925	0.514626	+	0.857415i	$0.327931\pi$
$42$	9.46301	1.46017
$43$	3.42992	0.523058	0.261529	−	0.965196i	$-0.415773\pi$
$43$	3.42992	0.523058	0.261529	+	0.965196i	$0.415773\pi$
$44$	−2.87729	−0.433768
$45$	−1.60383	−0.239084
$46$	1.27257	0.187630
$47$	9.82247	1.43276	0.716378	−	0.697713i	$-0.245799\pi$
$47$	9.82247	1.43276	0.716378	+	0.697713i	$0.245799\pi$
$48$	2.16244	0.312122
$49$	8.77593	1.25370
$50$	5.78408	0.817992
$51$	−1.64931	−0.230950
$52$	10.5107	1.45757
$53$	−5.58000	−0.766472	−0.383236	−	0.923651i	$-0.625190\pi$
$53$	−5.58000	−0.766472	−0.383236	+	0.923651i	$0.625190\pi$
$54$	−2.38249	−0.324216
$55$	1.25526	0.169259
$56$	15.8626	2.11973
$57$	−6.47342	−0.857425
$58$	−2.91604	−0.382894
$59$	13.4543	1.75160	0.875799	−	0.482676i	$-0.160335\pi$
$59$	13.4543	1.75160	0.875799	+	0.482676i	$0.160335\pi$
$60$	−5.89611	−0.761184
$61$	7.96449	1.01975	0.509874	−	0.860249i	$-0.329692\pi$
$61$	7.96449	1.01975	0.509874	+	0.860249i	$0.329692\pi$
$62$	−9.91229	−1.25886
$63$	−3.97189	−0.500411
$64$	−11.0802	−1.38503
$65$	−4.58542	−0.568752
$66$	1.86469	0.229528
$67$	2.02759	0.247709	0.123855	−	0.992300i	$-0.460474\pi$
$67$	2.02759	0.247709	0.123855	+	0.992300i	$0.460474\pi$
$68$	−6.06333	−0.735287
$69$	−0.534132	−0.0643020
$70$	−15.1770	−1.81400
$71$	−2.25830	−0.268011	−0.134006	−	0.990981i	$-0.542784\pi$
$71$	−2.25830	−0.268011	−0.134006	+	0.990981i	$0.542784\pi$
$72$	−3.99371	−0.470663
$73$	3.30362	0.386659	0.193329	−	0.981134i	$-0.438071\pi$
$73$	3.30362	0.386659	0.193329	+	0.981134i	$0.438071\pi$
$74$	−0.184574	−0.0214563
$75$	−2.42774	−0.280331
$76$	−23.7981	−2.72983
$77$	3.10866	0.354265
$78$	−6.81167	−0.771270
$79$	−6.84083	−0.769654	−0.384827	−	0.922989i	$-0.625739\pi$
$79$	−6.84083	−0.769654	−0.384827	+	0.922989i	$0.625739\pi$
$80$	−3.46818	−0.387755
$81$	1.00000	0.111111
$82$	−15.7017	−1.73396
$83$	−6.67770	−0.732973	−0.366486	−	0.930423i	$-0.619439\pi$
$83$	−6.67770	−0.732973	−0.366486	+	0.930423i	$0.619439\pi$
$84$	−14.6018	−1.59318
$85$	2.64521	0.286914
$86$	−8.17177	−0.881185
$87$	1.22394	0.131220
$88$	3.12574	0.333205
$89$	3.35493	0.355622	0.177811	−	0.984065i	$-0.443098\pi$
$89$	3.35493	0.355622	0.177811	+	0.984065i	$0.443098\pi$
$90$	3.82111	0.402780
$91$	−11.3558	−1.19042
$92$	−1.96362	−0.204721
$93$	4.16047	0.431420
$94$	−23.4020	−2.41373
$95$	10.3822	1.06520
$96$	2.83542	0.289388
$97$	−1.34841	−0.136911	−0.0684553	−	0.997654i	$-0.521807\pi$
$97$	−1.34841	−0.136911	−0.0684553	+	0.997654i	$0.521807\pi$
$98$	−20.9086	−2.11209
$99$	−0.782665	−0.0786608
$100$	−8.92504	−0.892504
$101$	3.84316	0.382409	0.191204	−	0.981550i	$-0.438761\pi$
$101$	3.84316	0.382409	0.191204	+	0.981550i	$0.438761\pi$
$102$	3.92948	0.389077
$103$	6.32855	0.623570	0.311785	−	0.950153i	$-0.399073\pi$
$103$	6.32855	0.623570	0.311785	+	0.950153i	$0.399073\pi$
$104$	−11.4182	−1.11965
$105$	6.37023	0.621670
$106$	13.2943	1.29126
$107$	5.32464	0.514752	0.257376	−	0.966311i	$-0.417142\pi$
$107$	5.32464	0.514752	0.257376	+	0.966311i	$0.417142\pi$
$108$	3.67627	0.353750
$109$	−15.4966	−1.48431	−0.742153	−	0.670230i	$-0.766195\pi$
$109$	−15.4966	−1.48431	−0.742153	+	0.670230i	$0.766195\pi$
$110$	−2.99065	−0.285147
$111$	0.0774709	0.00735321
$112$	−8.58899	−0.811584
$113$	−12.9838	−1.22142	−0.610708	−	0.791856i	$-0.709115\pi$
$113$	−12.9838	−1.22142	−0.610708	+	0.791856i	$0.709115\pi$
$114$	15.4229	1.44448
$115$	0.856656	0.0798836
$116$	4.49955	0.417773
$117$	2.85905	0.264319
$118$	−32.0547	−2.95088
$119$	6.55090	0.600520
$120$	6.40522	0.584714
$121$	−10.3874	−0.944312
$122$	−18.9753	−1.71795
$123$	6.59043	0.594239
$124$	15.2950	1.37353
$125$	11.9128	1.06551
$126$	9.46301	0.843032
$127$	−3.27817	−0.290891	−0.145445	−	0.989366i	$-0.546461\pi$
$127$	−3.27817	−0.290891	−0.145445	+	0.989366i	$0.546461\pi$
$128$	20.7278	1.83209
$129$	3.42992	0.301988
$130$	10.9247	0.958163
$131$	12.3457	1.07865	0.539326	−	0.842097i	$-0.318679\pi$
$131$	12.3457	1.07865	0.539326	+	0.842097i	$0.318679\pi$
$132$	−2.87729	−0.250436
$133$	25.7117	2.22949
$134$	−4.83071	−0.417310
$135$	−1.60383	−0.138035
$136$	6.58689	0.564821
$137$	15.3081	1.30786	0.653928	−	0.756556i	$-0.273120\pi$
$137$	15.3081	1.30786	0.653928	+	0.756556i	$0.273120\pi$
$138$	1.27257	0.108328
$139$	−22.8119	−1.93488	−0.967438	−	0.253107i	$-0.918547\pi$
$139$	−22.8119	−1.93488	−0.967438	+	0.253107i	$0.918547\pi$
$140$	23.4187	1.97924
$141$	9.82247	0.827201
$142$	5.38039	0.451512
$143$	−2.23768	−0.187124
$144$	2.16244	0.180204
$145$	−1.96299	−0.163018
$146$	−7.87084	−0.651396
$147$	8.77593	0.723826
$148$	0.284804	0.0234108
$149$	−11.8399	−0.969959	−0.484979	−	0.874526i	$-0.661173\pi$
$149$	−11.8399	−0.969959	−0.484979	+	0.874526i	$0.661173\pi$
$150$	5.78408	0.472268
$151$	−9.31073	−0.757696	−0.378848	−	0.925459i	$-0.623680\pi$
$151$	−9.31073	−0.757696	−0.378848	+	0.925459i	$0.623680\pi$
$152$	25.8530	2.09695
$153$	−1.64931	−0.133339
$154$	−7.40636	−0.596822
$155$	−6.67267	−0.535962
$156$	10.5107	0.841526
$157$	−6.52865	−0.521043	−0.260521	−	0.965468i	$-0.583894\pi$
$157$	−6.52865	−0.521043	−0.260521	+	0.965468i	$0.583894\pi$
$158$	16.2982	1.29662
$159$	−5.58000	−0.442523
$160$	−4.54752	−0.359513
$161$	2.12152	0.167199
$162$	−2.38249	−0.187186
$163$	17.7718	1.39199	0.695997	−	0.718044i	$-0.254962\pi$
$163$	17.7718	1.39199	0.695997	+	0.718044i	$0.254962\pi$
$164$	24.2282	1.89191
$165$	1.25526	0.0977218
$166$	15.9096	1.23482
$167$	0.915741	0.0708621	0.0354311	−	0.999372i	$-0.488720\pi$
$167$	0.915741	0.0708621	0.0354311	+	0.999372i	$0.488720\pi$
$168$	15.8626	1.22383
$169$	−4.82582	−0.371217
$170$	−6.30221	−0.483357
$171$	−6.47342	−0.495035
$172$	12.6093	0.961453
$173$	13.9763	1.06260	0.531300	−	0.847184i	$-0.321704\pi$
$173$	13.9763	1.06260	0.531300	+	0.847184i	$0.321704\pi$
$174$	−2.91604	−0.221064
$175$	9.64272	0.728921
$176$	−1.69247	−0.127575
$177$	13.4543	1.01129
$178$	−7.99309	−0.599108
$179$	23.3690	1.74668	0.873340	−	0.487112i	$-0.161950\pi$
$179$	23.3690	1.74668	0.873340	+	0.487112i	$0.161950\pi$
$180$	−5.89611	−0.439470
$181$	15.9037	1.18211	0.591055	−	0.806631i	$-0.298712\pi$
$181$	15.9037	1.18211	0.591055	+	0.806631i	$0.298712\pi$
$182$	27.0552	2.00547
$183$	7.96449	0.588752
$184$	2.13317	0.157259
$185$	−0.124250	−0.00913503
$186$	−9.91229	−0.726804
$187$	1.29086	0.0943971
$188$	36.1101	2.63360
$189$	−3.97189	−0.288913
$190$	−24.7356	−1.79451
$191$	−10.5171	−0.760994	−0.380497	−	0.924782i	$-0.624247\pi$
$191$	−10.5171	−0.760994	−0.380497	+	0.924782i	$0.624247\pi$
$192$	−11.0802	−0.799648
$193$	−0.842217	−0.0606241	−0.0303120	−	0.999540i	$-0.509650\pi$
$193$	−0.842217	−0.0606241	−0.0303120	+	0.999540i	$0.509650\pi$
$194$	3.21259	0.230650
$195$	−4.58542	−0.328369
$196$	32.2627	2.30448
$197$	−13.5649	−0.966461	−0.483231	−	0.875493i	$-0.660537\pi$
$197$	−13.5649	−0.966461	−0.483231	+	0.875493i	$0.660537\pi$
$198$	1.86469	0.132518
$199$	−18.9156	−1.34089	−0.670447	−	0.741957i	$-0.733898\pi$
$199$	−18.9156	−1.34089	−0.670447	+	0.741957i	$0.733898\pi$
$200$	9.69570	0.685589
$201$	2.02759	0.143015
$202$	−9.15630	−0.644235
$203$	−4.86137	−0.341201
$204$	−6.06333	−0.424518
$205$	−10.5699	−0.738235
$206$	−15.0777	−1.05051
$207$	−0.534132	−0.0371248
$208$	6.18254	0.428682
$209$	5.06652	0.350458
$210$	−15.1770	−1.04731
$211$	−25.5228	−1.75707	−0.878533	−	0.477682i	$-0.841477\pi$
$211$	−25.5228	−1.75707	−0.878533	+	0.477682i	$0.841477\pi$
$212$	−20.5136	−1.40888
$213$	−2.25830	−0.154736
$214$	−12.6859	−0.867192
$215$	−5.50100	−0.375165
$216$	−3.99371	−0.271738
$217$	−16.5249	−1.12179
$218$	36.9206	2.50058
$219$	3.30362	0.223238
$220$	4.61468	0.311121
$221$	−4.71548	−0.317197
$222$	−0.184574	−0.0123878
$223$	28.2877	1.89428	0.947142	−	0.320816i	$-0.103957\pi$
$223$	28.2877	1.89428	0.947142	+	0.320816i	$0.103957\pi$
$224$	−11.2620	−0.752472
$225$	−2.42774	−0.161849
$226$	30.9339	2.05769
$227$	1.50123	0.0996403	0.0498201	−	0.998758i	$-0.484135\pi$
$227$	1.50123	0.0996403	0.0498201	+	0.998758i	$0.484135\pi$
$228$	−23.7981	−1.57607
$229$	−4.96690	−0.328222	−0.164111	−	0.986442i	$-0.552476\pi$
$229$	−4.96690	−0.328222	−0.164111	+	0.986442i	$0.552476\pi$
$230$	−2.04098	−0.134578
$231$	3.10866	0.204535
$232$	−4.88808	−0.320918
$233$	−1.77844	−0.116509	−0.0582546	−	0.998302i	$-0.518554\pi$
$233$	−1.77844	−0.116509	−0.0582546	+	0.998302i	$0.518554\pi$
$234$	−6.81167	−0.445293
$235$	−15.7535	−1.02765
$236$	49.4616	3.21968
$237$	−6.84083	−0.444360
$238$	−15.6075	−1.01168
$239$	11.5048	0.744184	0.372092	−	0.928196i	$-0.378641\pi$
$239$	11.5048	0.744184	0.372092	+	0.928196i	$0.378641\pi$
$240$	−3.46818	−0.223870
$241$	8.66129	0.557923	0.278961	−	0.960302i	$-0.410010\pi$
$241$	8.66129	0.557923	0.278961	+	0.960302i	$0.410010\pi$
$242$	24.7480	1.59086
$243$	1.00000	0.0641500
$244$	29.2797	1.87444
$245$	−14.0751	−0.899223
$246$	−15.7017	−1.00110
$247$	−18.5078	−1.17763
$248$	−16.6157	−1.05510
$249$	−6.67770	−0.423182
$250$	−28.3822	−1.79505
$251$	−24.4940	−1.54605	−0.773024	−	0.634377i	$-0.781257\pi$
$251$	−24.4940	−1.54605	−0.773024	+	0.634377i	$0.781257\pi$
$252$	−14.6018	−0.919825
$253$	0.418047	0.0262824
$254$	7.81022	0.490057
$255$	2.64521	0.165650
$256$	−27.2233	−1.70146
$257$	6.24597	0.389613	0.194806	−	0.980842i	$-0.437592\pi$
$257$	6.24597	0.389613	0.194806	+	0.980842i	$0.437592\pi$
$258$	−8.17177	−0.508752
$259$	−0.307706	−0.0191199
$260$	−16.8573	−1.04544
$261$	1.22394	0.0757602
$262$	−29.4137	−1.81718
$263$	−4.26912	−0.263245	−0.131623	−	0.991300i	$-0.542019\pi$
$263$	−4.26912	−0.263245	−0.131623	+	0.991300i	$0.542019\pi$
$264$	3.12574	0.192376
$265$	8.94935	0.549754
$266$	−61.2580	−3.75597
$267$	3.35493	0.205318
$268$	7.45397	0.455323
$269$	−23.7432	−1.44765	−0.723825	−	0.689984i	$-0.757618\pi$
$269$	−23.7432	−1.44765	−0.723825	+	0.689984i	$0.757618\pi$
$270$	3.82111	0.232545
$271$	−14.7332	−0.894976	−0.447488	−	0.894290i	$-0.647681\pi$
$271$	−14.7332	−0.894976	−0.447488	+	0.894290i	$0.647681\pi$
$272$	−3.56655	−0.216254
$273$	−11.3558	−0.687287
$274$	−36.4714	−2.20332
$275$	1.90011	0.114581
$276$	−1.96362	−0.118196
$277$	−16.2587	−0.976893	−0.488447	−	0.872594i	$-0.662436\pi$
$277$	−16.2587	−0.976893	−0.488447	+	0.872594i	$0.662436\pi$
$278$	54.3491	3.25964
$279$	4.16047	0.249081
$280$	−25.4408	−1.52038
$281$	17.0559	1.01747	0.508736	−	0.860923i	$-0.330113\pi$
$281$	17.0559	1.01747	0.508736	+	0.860923i	$0.330113\pi$
$282$	−23.4020	−1.39357
$283$	−5.46412	−0.324808	−0.162404	−	0.986724i	$-0.551925\pi$
$283$	−5.46412	−0.324808	−0.162404	+	0.986724i	$0.551925\pi$
$284$	−8.30213	−0.492641
$285$	10.3822	0.614991
$286$	5.33126	0.315244
$287$	−26.1765	−1.54515
$288$	2.83542	0.167079
$289$	−14.2798	−0.839986
$290$	4.67682	0.274632
$291$	−1.34841	−0.0790454
$292$	12.1450	0.710732
$293$	−13.6191	−0.795638	−0.397819	−	0.917464i	$-0.630233\pi$
$293$	−13.6191	−0.795638	−0.397819	+	0.917464i	$0.630233\pi$
$294$	−20.9086	−1.21941
$295$	−21.5783	−1.25634
$296$	−0.309396	−0.0179833
$297$	−0.782665	−0.0454148
$298$	28.2084	1.63407
$299$	−1.52711	−0.0883152
$300$	−8.92504	−0.515287
$301$	−13.6233	−0.785233
$302$	22.1827	1.27647
$303$	3.84316	0.220784
$304$	−13.9984	−0.802864
$305$	−12.7737	−0.731418
$306$	3.92948	0.224634
$307$	−14.8956	−0.850139	−0.425069	−	0.905161i	$-0.639750\pi$
$307$	−14.8956	−0.850139	−0.425069	+	0.905161i	$0.639750\pi$
$308$	11.4283	0.651187
$309$	6.32855	0.360018
$310$	15.8976	0.902922
$311$	14.3607	0.814320	0.407160	−	0.913357i	$-0.366519\pi$
$311$	14.3607	0.814320	0.407160	+	0.913357i	$0.366519\pi$
$312$	−11.4182	−0.646430
$313$	1.10533	0.0624772	0.0312386	−	0.999512i	$-0.490055\pi$
$313$	1.10533	0.0624772	0.0312386	+	0.999512i	$0.490055\pi$
$314$	15.5545	0.877789
$315$	6.37023	0.358922
$316$	−25.1488	−1.41473
$317$	20.6007	1.15705	0.578525	−	0.815665i	$-0.303629\pi$
$317$	20.6007	1.15705	0.578525	+	0.815665i	$0.303629\pi$
$318$	13.2943	0.745508
$319$	−0.957938	−0.0536342
$320$	17.7708	0.993418
$321$	5.32464	0.297192
$322$	−5.05450	−0.281676
$323$	10.6767	0.594068
$324$	3.67627	0.204237
$325$	−6.94104	−0.385019
$326$	−42.3412	−2.34506
$327$	−15.4966	−0.856965
$328$	−26.3203	−1.45330
$329$	−39.0138	−2.15090
$330$	−2.99065	−0.164630
$331$	24.5677	1.35036	0.675181	−	0.737652i	$-0.264065\pi$
$331$	24.5677	1.35036	0.675181	+	0.737652i	$0.264065\pi$
$332$	−24.5490	−1.34730
$333$	0.0774709	0.00424538
$334$	−2.18175	−0.119380
$335$	−3.25190	−0.177670
$336$	−8.58899	−0.468568
$337$	0.219952	0.0119816	0.00599079	−	0.999982i	$-0.498093\pi$
$337$	0.219952	0.0119816	0.00599079	+	0.999982i	$0.498093\pi$
$338$	11.4975	0.625381
$339$	−12.9838	−0.705185
$340$	9.72454	0.527387
$341$	−3.25625	−0.176336
$342$	15.4229	0.833974
$343$	−7.05380	−0.380869
$344$	−13.6981	−0.738554
$345$	0.856656	0.0461208
$346$	−33.2985	−1.79014
$347$	11.4598	0.615192	0.307596	−	0.951517i	$-0.400475\pi$
$347$	11.4598	0.615192	0.307596	+	0.951517i	$0.400475\pi$
$348$	4.49955	0.241201
$349$	−4.83248	−0.258677	−0.129338	−	0.991601i	$-0.541285\pi$
$349$	−4.83248	−0.258677	−0.129338	+	0.991601i	$0.541285\pi$
$350$	−22.9737	−1.22800
$351$	2.85905	0.152605
$352$	−2.21918	−0.118283
$353$	−33.0160	−1.75727	−0.878633	−	0.477498i	$-0.841544\pi$
$353$	−33.0160	−1.75727	−0.878633	+	0.477498i	$0.841544\pi$
$354$	−32.0547	−1.70369
$355$	3.62192	0.192232
$356$	12.3336	0.653681
$357$	6.55090	0.346710
$358$	−55.6764	−2.94259
$359$	24.0363	1.26858	0.634292	−	0.773093i	$-0.281292\pi$
$359$	24.0363	1.26858	0.634292	+	0.773093i	$0.281292\pi$
$360$	6.40522	0.337585
$361$	22.9052	1.20553
$362$	−37.8904	−1.99147
$363$	−10.3874	−0.545199
$364$	−41.7472	−2.18815
$365$	−5.29843	−0.277332
$366$	−18.9753	−0.991857
$367$	0.593968	0.0310049	0.0155024	−	0.999880i	$-0.495065\pi$
$367$	0.593968	0.0310049	0.0155024	+	0.999880i	$0.495065\pi$
$368$	−1.15503	−0.0602102
$369$	6.59043	0.343084
$370$	0.296024	0.0153896
$371$	22.1632	1.15065
$372$	15.2950	0.793010
$373$	−15.8277	−0.819528	−0.409764	−	0.912192i	$-0.634389\pi$
$373$	−15.8277	−0.819528	−0.409764	+	0.912192i	$0.634389\pi$
$374$	−3.07547	−0.159029
$375$	11.9128	0.615175
$376$	−39.2281	−2.02304
$377$	3.49932	0.180224
$378$	9.46301	0.486725
$379$	−0.990626	−0.0508850	−0.0254425	−	0.999676i	$-0.508099\pi$
$379$	−0.990626	−0.0508850	−0.0254425	+	0.999676i	$0.508099\pi$
$380$	38.1680	1.95798
$381$	−3.27817	−0.167946
$382$	25.0570	1.28203
$383$	−10.9663	−0.560352	−0.280176	−	0.959949i	$-0.590393\pi$
$383$	−10.9663	−0.560352	−0.280176	+	0.959949i	$0.590393\pi$
$384$	20.7278	1.05776
$385$	−4.98575	−0.254098
$386$	2.00658	0.102132
$387$	3.42992	0.174353
$388$	−4.95714	−0.251661
$389$	−1.66381	−0.0843587	−0.0421793	−	0.999110i	$-0.513430\pi$
$389$	−1.66381	−0.0843587	−0.0421793	+	0.999110i	$0.513430\pi$
$390$	10.9247	0.553196
$391$	0.880953	0.0445517
$392$	−35.0485	−1.77022
$393$	12.3457	0.622761
$394$	32.3184	1.62818
$395$	10.9715	0.552036
$396$	−2.87729	−0.144589
$397$	19.3146	0.969373	0.484686	−	0.874688i	$-0.338934\pi$
$397$	19.3146	0.969373	0.484686	+	0.874688i	$0.338934\pi$
$398$	45.0664	2.25897
$399$	25.7117	1.28720
$400$	−5.24985	−0.262493
$401$	−19.1127	−0.954445	−0.477222	−	0.878783i	$-0.658356\pi$
$401$	−19.1127	−0.954445	−0.477222	+	0.878783i	$0.658356\pi$
$402$	−4.83071	−0.240934
$403$	11.8950	0.592532
$404$	14.1285	0.702920
$405$	−1.60383	−0.0796948
$406$	11.5822	0.574814
$407$	−0.0606338	−0.00300550
$408$	6.58689	0.326100
$409$	13.8480	0.684741	0.342370	−	0.939565i	$-0.388770\pi$
$409$	13.8480	0.684741	0.342370	+	0.939565i	$0.388770\pi$
$410$	25.1827	1.24369
$411$	15.3081	0.755092
$412$	23.2655	1.14621
$413$	−53.4389	−2.62956
$414$	1.27257	0.0625433
$415$	10.7099	0.525727
$416$	8.10660	0.397459
$417$	−22.8119	−1.11710
$418$	−12.0709	−0.590409
$419$	−18.1193	−0.885185	−0.442592	−	0.896723i	$-0.645941\pi$
$419$	−18.1193	−0.885185	−0.442592	+	0.896723i	$0.645941\pi$
$420$	23.4187	1.14272
$421$	−27.5853	−1.34442	−0.672212	−	0.740358i	$-0.734656\pi$
$421$	−27.5853	−1.34442	−0.672212	+	0.740358i	$0.734656\pi$
$422$	60.8080	2.96009
$423$	9.82247	0.477585
$424$	22.2849	1.08225
$425$	4.00411	0.194228
$426$	5.38039	0.260681
$427$	−31.6341	−1.53088
$428$	19.5748	0.946185
$429$	−2.23768	−0.108036
$430$	13.1061	0.632032
$431$	14.9951	0.722287	0.361144	−	0.932510i	$-0.382386\pi$
$431$	14.9951	0.722287	0.361144	+	0.932510i	$0.382386\pi$
$432$	2.16244	0.104041
$433$	24.4764	1.17626	0.588131	−	0.808765i	$-0.299864\pi$
$433$	24.4764	1.17626	0.588131	+	0.808765i	$0.299864\pi$
$434$	39.3705	1.88985
$435$	−1.96299	−0.0941183
$436$	−56.9698	−2.72836
$437$	3.45766	0.165402
$438$	−7.87084	−0.376083
$439$	−3.67024	−0.175171	−0.0875855	−	0.996157i	$-0.527915\pi$
$439$	−3.67024	−0.175171	−0.0875855	+	0.996157i	$0.527915\pi$
$440$	−5.01314	−0.238992
$441$	8.77593	0.417901
$442$	11.2346	0.534375
$443$	−36.6659	−1.74205	−0.871026	−	0.491238i	$-0.836545\pi$
$443$	−36.6659	−1.74205	−0.871026	+	0.491238i	$0.836545\pi$
$444$	0.284804	0.0135162
$445$	−5.38072	−0.255071
$446$	−67.3952	−3.19126
$447$	−11.8399	−0.560006
$448$	44.0096	2.07926
$449$	−37.4488	−1.76732	−0.883659	−	0.468131i	$-0.844927\pi$
$449$	−37.4488	−1.76732	−0.883659	+	0.468131i	$0.844927\pi$
$450$	5.78408	0.272664
$451$	−5.15810	−0.242886
$452$	−47.7322	−2.24513
$453$	−9.31073	−0.437456
$454$	−3.57668	−0.167862
$455$	18.2128	0.853829
$456$	25.8530	1.21068
$457$	13.1468	0.614982	0.307491	−	0.951551i	$-0.400511\pi$
$457$	13.1468	0.614982	0.307491	+	0.951551i	$0.400511\pi$
$458$	11.8336	0.552949
$459$	−1.64931	−0.0769834
$460$	3.14930	0.146837
$461$	29.4502	1.37163	0.685817	−	0.727774i	$-0.259445\pi$
$461$	29.4502	1.37163	0.685817	+	0.727774i	$0.259445\pi$
$462$	−7.40636	−0.344575
$463$	−3.85811	−0.179302	−0.0896508	−	0.995973i	$-0.528575\pi$
$463$	−3.85811	−0.179302	−0.0896508	+	0.995973i	$0.528575\pi$
$464$	2.64671	0.122870
$465$	−6.67267	−0.309438
$466$	4.23711	0.196280
$467$	−27.5302	−1.27395	−0.636974	−	0.770886i	$-0.719814\pi$
$467$	−27.5302	−1.27395	−0.636974	+	0.770886i	$0.719814\pi$
$468$	10.5107	0.485855
$469$	−8.05336	−0.371869
$470$	37.5327	1.73125
$471$	−6.52865	−0.300824
$472$	−53.7325	−2.47324
$473$	−2.68448	−0.123433
$474$	16.2982	0.748603
$475$	15.7158	0.721090
$476$	24.0829	1.10384
$477$	−5.58000	−0.255491
$478$	−27.4101	−1.25371
$479$	35.7976	1.63564	0.817818	−	0.575478i	$-0.195184\pi$
$479$	35.7976	1.63564	0.817818	+	0.575478i	$0.195184\pi$
$480$	−4.54752	−0.207565
$481$	0.221493	0.0100992
$482$	−20.6355	−0.939919
$483$	2.12152	0.0965323
$484$	−38.1871	−1.73578
$485$	2.16262	0.0981996
$486$	−2.38249	−0.108072
$487$	−15.0844	−0.683540	−0.341770	−	0.939784i	$-0.611026\pi$
$487$	−15.0844	−0.683540	−0.341770	+	0.939784i	$0.611026\pi$
$488$	−31.8079	−1.43988
$489$	17.7718	0.803669
$490$	33.5338	1.51490
$491$	14.0279	0.633070	0.316535	−	0.948581i	$-0.397481\pi$
$491$	14.0279	0.633070	0.316535	+	0.948581i	$0.397481\pi$
$492$	24.2282	1.09229
$493$	−2.01867	−0.0909162
$494$	44.0948	1.98392
$495$	1.25526	0.0564197
$496$	8.99678	0.403967
$497$	8.96973	0.402347
$498$	15.9096	0.712925
$499$	31.6683	1.41767	0.708834	−	0.705376i	$-0.249222\pi$
$499$	31.6683	1.41767	0.708834	+	0.705376i	$0.249222\pi$
$500$	43.7947	1.95856
$501$	0.915741	0.0409123
$502$	58.3568	2.60459
$503$	−15.9165	−0.709680	−0.354840	−	0.934927i	$-0.615465\pi$
$503$	−15.9165	−0.709680	−0.354840	+	0.934927i	$0.615465\pi$
$504$	15.8626	0.706576
$505$	−6.16376	−0.274284
$506$	−0.995994	−0.0442773
$507$	−4.82582	−0.214322
$508$	−12.0515	−0.534697
$509$	11.2165	0.497162	0.248581	−	0.968611i	$-0.420036\pi$
$509$	11.2165	0.497162	0.248581	+	0.968611i	$0.420036\pi$
$510$	−6.30221	−0.279066
$511$	−13.1216	−0.580466
$512$	23.4038	1.03431
$513$	−6.47342	−0.285808
$514$	−14.8810	−0.656372
$515$	−10.1499	−0.447258
$516$	12.6093	0.555095
$517$	−7.68771	−0.338105
$518$	0.733108	0.0322109
$519$	13.9763	0.613492
$520$	18.3129	0.803072
$521$	3.86151	0.169176	0.0845879	−	0.996416i	$-0.473043\pi$
$521$	3.86151	0.169176	0.0845879	+	0.996416i	$0.473043\pi$
$522$	−2.91604	−0.127631
$523$	35.4905	1.55189	0.775945	−	0.630800i	$-0.217273\pi$
$523$	35.4905	1.55189	0.775945	+	0.630800i	$0.217273\pi$
$524$	45.3864	1.98271
$525$	9.64272	0.420843
$526$	10.1711	0.443483
$527$	−6.86192	−0.298910
$528$	−1.69247	−0.0736553
$529$	−22.7147	−0.987596
$530$	−21.3218	−0.926158
$531$	13.4543	0.583866
$532$	94.5234	4.09811
$533$	18.8424	0.816154
$534$	−7.99309	−0.345895
$535$	−8.53980	−0.369208
$536$	−8.09760	−0.349763
$537$	23.3690	1.00845
$538$	56.5680	2.43882
$539$	−6.86861	−0.295852
$540$	−5.89611	−0.253728
$541$	−7.52578	−0.323559	−0.161779	−	0.986827i	$-0.551723\pi$
$541$	−7.52578	−0.323559	−0.161779	+	0.986827i	$0.551723\pi$
$542$	35.1017	1.50775
$543$	15.9037	0.682492
$544$	−4.67649	−0.200503
$545$	24.8539	1.06462
$546$	27.0552	1.15786
$547$	−14.3309	−0.612746	−0.306373	−	0.951912i	$-0.599115\pi$
$547$	−14.3309	−0.612746	−0.306373	+	0.951912i	$0.599115\pi$
$548$	56.2767	2.40402
$549$	7.96449	0.339916
$550$	−4.52699	−0.193032
$551$	−7.92310	−0.337535
$552$	2.13317	0.0907938
$553$	27.1710	1.15543
$554$	38.7363	1.64575
$555$	−0.124250	−0.00527411
$556$	−83.8626	−3.55657
$557$	−45.3748	−1.92259	−0.961295	−	0.275521i	$-0.911150\pi$
$557$	−45.3748	−1.92259	−0.961295	+	0.275521i	$0.911150\pi$
$558$	−9.91229	−0.419621
$559$	9.80633	0.414764
$560$	13.7753	0.582111
$561$	1.29086	0.0545002
$562$	−40.6356	−1.71411
$563$	8.56272	0.360876	0.180438	−	0.983586i	$-0.442249\pi$
$563$	8.56272	0.360876	0.180438	+	0.983586i	$0.442249\pi$
$564$	36.1101	1.52051
$565$	20.8238	0.876065
$566$	13.0182	0.547197
$567$	−3.97189	−0.166804
$568$	9.01900	0.378429
$569$	−24.5464	−1.02904	−0.514519	−	0.857479i	$-0.672029\pi$
$569$	−24.5464	−1.02904	−0.514519	+	0.857479i	$0.672029\pi$
$570$	−24.7356	−1.03606
$571$	−0.301120	−0.0126015	−0.00630075	−	0.999980i	$-0.502006\pi$
$571$	−0.301120	−0.0126015	−0.00630075	+	0.999980i	$0.502006\pi$
$572$	−8.22632	−0.343960
$573$	−10.5171	−0.439360
$574$	62.3653	2.60308
$575$	1.29674	0.0540776
$576$	−11.0802	−0.461677
$577$	9.28600	0.386581	0.193291	−	0.981142i	$-0.438084\pi$
$577$	9.28600	0.386581	0.193291	+	0.981142i	$0.438084\pi$
$578$	34.0214	1.41511
$579$	−0.842217	−0.0350013
$580$	−7.21650	−0.299649
$581$	26.5231	1.10036
$582$	3.21259	0.133166
$583$	4.36727	0.180874
$584$	−13.1937	−0.545959
$585$	−4.58542	−0.189584
$586$	32.4475	1.34039
$587$	0.964063	0.0397911	0.0198956	−	0.999802i	$-0.493667\pi$
$587$	0.964063	0.0397911	0.0198956	+	0.999802i	$0.493667\pi$
$588$	32.2627	1.33049
$589$	−26.9325	−1.10973
$590$	51.4102	2.11653
$591$	−13.5649	−0.557987
$592$	0.167526	0.00688529
$593$	−27.1547	−1.11511	−0.557556	−	0.830140i	$-0.688261\pi$
$593$	−27.1547	−1.11511	−0.557556	+	0.830140i	$0.688261\pi$
$594$	1.86469	0.0765093
$595$	−10.5065	−0.430725
$596$	−43.5265	−1.78292
$597$	−18.9156	−0.774166
$598$	3.63833	0.148783
$599$	11.3166	0.462385	0.231192	−	0.972908i	$-0.425737\pi$
$599$	11.3166	0.462385	0.231192	+	0.972908i	$0.425737\pi$
$600$	9.69570	0.395825
$601$	−17.4101	−0.710171	−0.355086	−	0.934834i	$-0.615548\pi$
$601$	−17.4101	−0.710171	−0.355086	+	0.934834i	$0.615548\pi$
$602$	32.4574	1.32286
$603$	2.02759	0.0825697
$604$	−34.2288	−1.39275
$605$	16.6596	0.677311
$606$	−9.15630	−0.371949
$607$	−22.5247	−0.914250	−0.457125	−	0.889402i	$-0.651121\pi$
$607$	−22.5247	−0.914250	−0.457125	+	0.889402i	$0.651121\pi$
$608$	−18.3548	−0.744387
$609$	−4.86137	−0.196993
$610$	30.4332	1.23220
$611$	28.0830	1.13611
$612$	−6.06333	−0.245096
$613$	14.3613	0.580047	0.290024	−	0.957019i	$-0.406337\pi$
$613$	14.3613	0.580047	0.290024	+	0.957019i	$0.406337\pi$
$614$	35.4888	1.43221
$615$	−10.5699	−0.426220
$616$	−12.4151	−0.500219
$617$	−34.1761	−1.37588	−0.687938	−	0.725769i	$-0.741484\pi$
$617$	−34.1761	−1.37588	−0.687938	+	0.725769i	$0.741484\pi$
$618$	−15.0777	−0.606515
$619$	−27.6806	−1.11258	−0.556288	−	0.830990i	$-0.687775\pi$
$619$	−27.6806	−1.11258	−0.556288	+	0.830990i	$0.687775\pi$
$620$	−24.5306	−0.985171
$621$	−0.534132	−0.0214340
$622$	−34.2142	−1.37187
$623$	−13.3254	−0.533871
$624$	6.18254	0.247500
$625$	−6.96737	−0.278695
$626$	−2.63345	−0.105254
$627$	5.06652	0.202337
$628$	−24.0011	−0.957748
$629$	−0.127774	−0.00509468
$630$	−15.1770	−0.604667
$631$	−5.50731	−0.219243	−0.109621	−	0.993973i	$-0.534964\pi$
$631$	−5.50731	−0.219243	−0.109621	+	0.993973i	$0.534964\pi$
$632$	27.3203	1.08674
$633$	−25.5228	−1.01444
$634$	−49.0810	−1.94926
$635$	5.25762	0.208642
$636$	−20.5136	−0.813417
$637$	25.0908	0.994135
$638$	2.28228	0.0903563
$639$	−2.25830	−0.0893370
$640$	−33.2438	−1.31408
$641$	−30.4170	−1.20140	−0.600699	−	0.799475i	$-0.705111\pi$
$641$	−30.4170	−1.20140	−0.600699	+	0.799475i	$0.705111\pi$
$642$	−12.6859	−0.500673
$643$	0.805700	0.0317737	0.0158869	−	0.999874i	$-0.494943\pi$
$643$	0.805700	0.0317737	0.0158869	+	0.999874i	$0.494943\pi$
$644$	7.79928	0.307335
$645$	−5.50100	−0.216602
$646$	−25.4372	−1.00081
$647$	49.4121	1.94259	0.971294	−	0.237880i	$-0.0764526\pi$
$647$	49.4121	1.94259	0.971294	+	0.237880i	$0.0764526\pi$
$648$	−3.99371	−0.156888
$649$	−10.5302	−0.413346
$650$	16.5370	0.648633
$651$	−16.5249	−0.647663
$652$	65.3340	2.55868
$653$	5.00085	0.195699	0.0978493	−	0.995201i	$-0.468804\pi$
$653$	5.00085	0.195699	0.0978493	+	0.995201i	$0.468804\pi$
$654$	36.9206	1.44371
$655$	−19.8004	−0.773667
$656$	14.2514	0.556425
$657$	3.30362	0.128886
$658$	92.9501	3.62357
$659$	−24.3975	−0.950391	−0.475195	−	0.879880i	$-0.657623\pi$
$659$	−24.3975	−0.950391	−0.475195	+	0.879880i	$0.657623\pi$
$660$	4.61468	0.179626
$661$	−3.61129	−0.140463	−0.0702314	−	0.997531i	$-0.522374\pi$
$661$	−3.61129	−0.140463	−0.0702314	+	0.997531i	$0.522374\pi$
$662$	−58.5324	−2.27493
$663$	−4.71548	−0.183134
$664$	26.6688	1.03495
$665$	−41.2371	−1.59911
$666$	−0.184574	−0.00715209
$667$	−0.653748	−0.0253132
$668$	3.36651	0.130254
$669$	28.2877	1.09366
$670$	7.74762	0.299317
$671$	−6.23353	−0.240643
$672$	−11.2620	−0.434440
$673$	−34.4719	−1.32880	−0.664398	−	0.747379i	$-0.731312\pi$
$673$	−34.4719	−1.32880	−0.664398	+	0.747379i	$0.731312\pi$
$674$	−0.524035	−0.0201851
$675$	−2.42774	−0.0934438
$676$	−17.7411	−0.682348
$677$	6.24778	0.240122	0.120061	−	0.992767i	$-0.461691\pi$
$677$	6.24778	0.240122	0.120061	+	0.992767i	$0.461691\pi$
$678$	30.9339	1.18801
$679$	5.35575	0.205535
$680$	−10.5642	−0.405120
$681$	1.50123	0.0575273
$682$	7.75800	0.297069
$683$	50.7216	1.94081	0.970403	−	0.241491i	$-0.0776363\pi$
$683$	50.7216	1.94081	0.970403	+	0.241491i	$0.0776363\pi$
$684$	−23.7981	−0.909942
$685$	−24.5515	−0.938064
$686$	16.8056	0.641642
$687$	−4.96690	−0.189499
$688$	7.41702	0.282771
$689$	−15.9535	−0.607780
$690$	−2.04098	−0.0776986
$691$	−17.2859	−0.657588	−0.328794	−	0.944402i	$-0.606642\pi$
$691$	−17.2859	−0.657588	−0.328794	+	0.944402i	$0.606642\pi$
$692$	51.3808	1.95320
$693$	3.10866	0.118088
$694$	−27.3028	−1.03640
$695$	36.5863	1.38780
$696$	−4.88808	−0.185282
$697$	−10.8697	−0.411719
$698$	11.5134	0.435787
$699$	−1.77844	−0.0672666
$700$	35.4493	1.33986
$701$	−45.2412	−1.70874	−0.854369	−	0.519667i	$-0.826056\pi$
$701$	−45.2412	−1.70874	−0.854369	+	0.519667i	$0.826056\pi$
$702$	−6.81167	−0.257090
$703$	−0.501502	−0.0189145
$704$	8.67212	0.326843
$705$	−15.7535	−0.593313
$706$	78.6604	2.96042
$707$	−15.2646	−0.574085
$708$	49.4616	1.85888
$709$	−41.0950	−1.54336	−0.771678	−	0.636013i	$-0.780582\pi$
$709$	−41.0950	−1.54336	−0.771678	+	0.636013i	$0.780582\pi$
$710$	−8.62921	−0.323848
$711$	−6.84083	−0.256551
$712$	−13.3986	−0.502134
$713$	−2.22224	−0.0832236
$714$	−15.6075	−0.584095
$715$	3.58885	0.134215
$716$	85.9108	3.21064
$717$	11.5048	0.429655
$718$	−57.2662	−2.13716
$719$	4.88014	0.181998	0.0909992	−	0.995851i	$-0.470994\pi$
$719$	4.88014	0.181998	0.0909992	+	0.995851i	$0.470994\pi$
$720$	−3.46818	−0.129252
$721$	−25.1363	−0.936125
$722$	−54.5714	−2.03094
$723$	8.66129	0.322117
$724$	58.4662	2.17288
$725$	−2.97142	−0.110356
$726$	24.7480	0.918484
$727$	−22.9431	−0.850911	−0.425455	−	0.904979i	$-0.639886\pi$
$727$	−22.9431	−0.850911	−0.425455	+	0.904979i	$0.639886\pi$
$728$	45.3520	1.68086
$729$	1.00000	0.0370370
$730$	12.6235	0.467215
$731$	−5.65702	−0.209233
$732$	29.2797	1.08221
$733$	11.4549	0.423096	0.211548	−	0.977368i	$-0.432150\pi$
$733$	11.4549	0.423096	0.211548	+	0.977368i	$0.432150\pi$
$734$	−1.41513	−0.0522332
$735$	−14.0751	−0.519167
$736$	−1.51449	−0.0558248
$737$	−1.58692	−0.0584550
$738$	−15.7017	−0.577986
$739$	32.3109	1.18858	0.594288	−	0.804252i	$-0.297434\pi$
$739$	32.3109	1.18858	0.594288	+	0.804252i	$0.297434\pi$
$740$	−0.456777	−0.0167914
$741$	−18.5078	−0.679903
$742$	−52.8036	−1.93848
$743$	−3.53783	−0.129790	−0.0648952	−	0.997892i	$-0.520671\pi$
$743$	−3.53783	−0.129790	−0.0648952	+	0.997892i	$0.520671\pi$
$744$	−16.6157	−0.609161
$745$	18.9891	0.695706
$746$	37.7094	1.38064
$747$	−6.67770	−0.244324
$748$	4.74556	0.173515
$749$	−21.1489	−0.772764
$750$	−28.3822	−1.03637
$751$	−42.6268	−1.55547	−0.777737	−	0.628589i	$-0.783633\pi$
$751$	−42.6268	−1.55547	−0.777737	+	0.628589i	$0.783633\pi$
$752$	21.2405	0.774563
$753$	−24.4940	−0.892611
$754$	−8.33710	−0.303619
$755$	14.9328	0.543460
$756$	−14.6018	−0.531061
$757$	−20.7653	−0.754726	−0.377363	−	0.926065i	$-0.623169\pi$
$757$	−20.7653	−0.754726	−0.377363	+	0.926065i	$0.623169\pi$
$758$	2.36016	0.0857249
$759$	0.418047	0.0151741
$760$	−41.4637	−1.50405
$761$	−8.41002	−0.304863	−0.152432	−	0.988314i	$-0.548710\pi$
$761$	−8.41002	−0.304863	−0.152432	+	0.988314i	$0.548710\pi$
$762$	7.81022	0.282934
$763$	61.5509	2.22829
$764$	−38.6639	−1.39881
$765$	2.64521	0.0956379
$766$	26.1271	0.944012
$767$	38.4665	1.38894
$768$	−27.2233	−0.982337
$769$	−1.15232	−0.0415537	−0.0207769	−	0.999784i	$-0.506614\pi$
$769$	−1.15232	−0.0415537	−0.0207769	+	0.999784i	$0.506614\pi$
$770$	11.8785	0.428072
$771$	6.24597	0.224943
$772$	−3.09622	−0.111435
$773$	26.8464	0.965598	0.482799	−	0.875731i	$-0.339620\pi$
$773$	26.8464	0.965598	0.482799	+	0.875731i	$0.339620\pi$
$774$	−8.17177	−0.293728
$775$	−10.1005	−0.362822
$776$	5.38518	0.193317
$777$	−0.307706	−0.0110389
$778$	3.96402	0.142117
$779$	−42.6626	−1.52855
$780$	−16.8573	−0.603587
$781$	1.76749	0.0632459
$782$	−2.09886	−0.0750552
$783$	1.22394	0.0437402
$784$	18.9775	0.677766
$785$	10.4708	0.373720
$786$	−29.4137	−1.04915
$787$	12.3295	0.439498	0.219749	−	0.975556i	$-0.429476\pi$
$787$	12.3295	0.439498	0.219749	+	0.975556i	$0.429476\pi$
$788$	−49.8684	−1.77649
$789$	−4.26912	−0.151985
$790$	−26.1395	−0.930003
$791$	51.5704	1.83363
$792$	3.12574	0.111068
$793$	22.7709	0.808618
$794$	−46.0169	−1.63308
$795$	8.94935	0.317401
$796$	−69.5391	−2.46475
$797$	39.8796	1.41261	0.706304	−	0.707909i	$-0.250361\pi$
$797$	39.8796	1.41261	0.706304	+	0.707909i	$0.250361\pi$
$798$	−61.2580	−2.16851
$799$	−16.2004	−0.573127
$800$	−6.88366	−0.243374
$801$	3.35493	0.118541
$802$	45.5360	1.60793
$803$	−2.58562	−0.0912447
$804$	7.45397	0.262881
$805$	−3.40254	−0.119924
$806$	−28.3397	−0.998225
$807$	−23.7432	−0.835801
$808$	−15.3485	−0.539957
$809$	−5.54535	−0.194964	−0.0974821	−	0.995237i	$-0.531079\pi$
$809$	−5.54535	−0.194964	−0.0974821	+	0.995237i	$0.531079\pi$
$810$	3.82111	0.134260
$811$	−45.0905	−1.58334	−0.791671	−	0.610947i	$-0.790789\pi$
$811$	−45.0905	−1.58334	−0.791671	+	0.610947i	$0.790789\pi$
$812$	−17.8717	−0.627175
$813$	−14.7332	−0.516715
$814$	0.144460	0.00506330
$815$	−28.5029	−0.998412
$816$	−3.56655	−0.124854
$817$	−22.2033	−0.776796
$818$	−32.9928	−1.15357
$819$	−11.3558	−0.396805
$820$	−38.8579	−1.35698
$821$	29.1780	1.01832	0.509160	−	0.860672i	$-0.329956\pi$
$821$	29.1780	1.01832	0.509160	+	0.860672i	$0.329956\pi$
$822$	−36.4714	−1.27209
$823$	23.3006	0.812209	0.406104	−	0.913827i	$-0.366887\pi$
$823$	23.3006	0.812209	0.406104	+	0.913827i	$0.366887\pi$
$824$	−25.2744	−0.880475
$825$	1.90011	0.0661533
$826$	127.318	4.42996
$827$	0.453334	0.0157640	0.00788199	−	0.999969i	$-0.497491\pi$
$827$	0.453334	0.0157640	0.00788199	+	0.999969i	$0.497491\pi$
$828$	−1.96362	−0.0682404
$829$	−18.8258	−0.653849	−0.326924	−	0.945051i	$-0.606012\pi$
$829$	−18.8258	−0.653849	−0.326924	+	0.945051i	$0.606012\pi$
$830$	−25.5162	−0.885680
$831$	−16.2587	−0.564010
$832$	−31.6790	−1.09827
$833$	−14.4743	−0.501504
$834$	54.3491	1.88196
$835$	−1.46869	−0.0508261
$836$	18.6259	0.644191
$837$	4.16047	0.143807
$838$	43.1691	1.49125
$839$	19.2264	0.663768	0.331884	−	0.943320i	$-0.392316\pi$
$839$	19.2264	0.663768	0.331884	+	0.943320i	$0.392316\pi$
$840$	−25.4408	−0.877793
$841$	−27.5020	−0.948344
$842$	65.7218	2.26492
$843$	17.0559	0.587437
$844$	−93.8290	−3.22973
$845$	7.73978	0.266257
$846$	−23.4020	−0.804577
$847$	41.2578	1.41763
$848$	−12.0664	−0.414363
$849$	−5.46412	−0.187528
$850$	−9.53976	−0.327211
$851$	−0.0413797	−0.00141848
$852$	−8.30213	−0.284426
$853$	9.76849	0.334467	0.167233	−	0.985917i	$-0.446517\pi$
$853$	9.76849	0.334467	0.167233	+	0.985917i	$0.446517\pi$
$854$	75.3680	2.57904
$855$	10.3822	0.355065
$856$	−21.2651	−0.726825
$857$	−17.0865	−0.583665	−0.291832	−	0.956469i	$-0.594265\pi$
$857$	−17.0865	−0.583665	−0.291832	+	0.956469i	$0.594265\pi$
$858$	5.33126	0.182006
$859$	43.0767	1.46976	0.734879	−	0.678198i	$-0.237239\pi$
$859$	43.0767	1.46976	0.734879	+	0.678198i	$0.237239\pi$
$860$	−20.2232	−0.689605
$861$	−26.1765	−0.892092
$862$	−35.7257	−1.21682
$863$	−42.2814	−1.43928	−0.719638	−	0.694350i	$-0.755692\pi$
$863$	−42.2814	−1.43928	−0.719638	+	0.694350i	$0.755692\pi$
$864$	2.83542	0.0964628
$865$	−22.4156	−0.762153
$866$	−58.3150	−1.98162
$867$	−14.2798	−0.484966
$868$	−60.7502	−2.06200
$869$	5.35408	0.181625
$870$	4.67682	0.158559
$871$	5.79698	0.196423
$872$	61.8890	2.09583
$873$	−1.34841	−0.0456369
$874$	−8.23786	−0.278650
$875$	−47.3164	−1.59959
$876$	12.1450	0.410341
$877$	−8.30941	−0.280589	−0.140294	−	0.990110i	$-0.544805\pi$
$877$	−8.30941	−0.280589	−0.140294	+	0.990110i	$0.544805\pi$
$878$	8.74432	0.295107
$879$	−13.6191	−0.459362
$880$	2.71443	0.0915033
$881$	11.7603	0.396214	0.198107	−	0.980180i	$-0.436521\pi$
$881$	11.7603	0.396214	0.198107	+	0.980180i	$0.436521\pi$
$882$	−20.9086	−0.704029
$883$	−12.4844	−0.420134	−0.210067	−	0.977687i	$-0.567368\pi$
$883$	−12.4844	−0.420134	−0.210067	+	0.977687i	$0.567368\pi$
$884$	−17.3354	−0.583052
$885$	−21.5783	−0.725348
$886$	87.3563	2.93479
$887$	12.4542	0.418170	0.209085	−	0.977898i	$-0.432952\pi$
$887$	12.4542	0.418170	0.209085	+	0.977898i	$0.432952\pi$
$888$	−0.309396	−0.0103827
$889$	13.0205	0.436695
$890$	12.8195	0.429712
$891$	−0.782665	−0.0262203
$892$	103.993	3.48195
$893$	−63.5850	−2.12779
$894$	28.2084	0.943429
$895$	−37.4798	−1.25281
$896$	−82.3285	−2.75040
$897$	−1.52711	−0.0509888
$898$	89.2215	2.97736
$899$	5.09218	0.169834
$900$	−8.92504	−0.297501
$901$	9.20317	0.306602
$902$	12.2891	0.409184
$903$	−13.6233	−0.453355
$904$	51.8537	1.72463
$905$	−25.5067	−0.847872
$906$	22.1827	0.736972
$907$	−28.3248	−0.940510	−0.470255	−	0.882531i	$-0.655838\pi$
$907$	−28.3248	−0.940510	−0.470255	+	0.882531i	$0.655838\pi$
$908$	5.51894	0.183153
$909$	3.84316	0.127470
$910$	−43.3919	−1.43843
$911$	−17.1258	−0.567404	−0.283702	−	0.958913i	$-0.591563\pi$
$911$	−17.1258	−0.567404	−0.283702	+	0.958913i	$0.591563\pi$
$912$	−13.9984	−0.463534
$913$	5.22640	0.172969
$914$	−31.3222	−1.03605
$915$	−12.7737	−0.422284
$916$	−18.2597	−0.603318
$917$	−49.0360	−1.61931
$918$	3.92948	0.129692
$919$	−17.1079	−0.564337	−0.282169	−	0.959365i	$-0.591054\pi$
$919$	−17.1079	−0.564337	−0.282169	+	0.959365i	$0.591054\pi$
$920$	−3.42124	−0.112795
$921$	−14.8956	−0.490828
$922$	−70.1650	−2.31076
$923$	−6.45660	−0.212522
$924$	11.4283	0.375963
$925$	−0.188079	−0.00618401
$926$	9.19192	0.302065
$927$	6.32855	0.207857
$928$	3.47039	0.113921
$929$	−0.203485	−0.00667611	−0.00333806	−	0.999994i	$-0.501063\pi$
$929$	−0.203485	−0.00667611	−0.00333806	+	0.999994i	$0.501063\pi$
$930$	15.8976	0.521302
$931$	−56.8103	−1.86188
$932$	−6.53802	−0.214160
$933$	14.3607	0.470148
$934$	65.5906	2.14619
$935$	−2.07032	−0.0677066
$936$	−11.4182	−0.373216
$937$	−32.2230	−1.05268	−0.526340	−	0.850274i	$-0.676436\pi$
$937$	−32.2230	−1.05268	−0.526340	+	0.850274i	$0.676436\pi$
$938$	19.1871	0.626480
$939$	1.10533	0.0360712
$940$	−57.9143	−1.88896
$941$	−20.0505	−0.653629	−0.326815	−	0.945088i	$-0.605975\pi$
$941$	−20.0505	−0.653629	−0.326815	+	0.945088i	$0.605975\pi$
$942$	15.5545	0.506792
$943$	−3.52016	−0.114632
$944$	29.0941	0.946933
$945$	6.37023	0.207223
$946$	6.39576	0.207944
$947$	−46.9165	−1.52458	−0.762291	−	0.647234i	$-0.775926\pi$
$947$	−46.9165	−1.52458	−0.762291	+	0.647234i	$0.775926\pi$
$948$	−25.1488	−0.816794
$949$	9.44521	0.306604
$950$	−37.4428	−1.21480
$951$	20.6007	0.668023
$952$	−26.1624	−0.847929
$953$	35.8142	1.16014	0.580069	−	0.814568i	$-0.303026\pi$
$953$	35.8142	1.16014	0.580069	+	0.814568i	$0.303026\pi$
$954$	13.2943	0.430419
$955$	16.8677	0.545825
$956$	42.2948	1.36791
$957$	−0.957938	−0.0309657
$958$	−85.2876	−2.75552
$959$	−60.8020	−1.96340
$960$	17.7708	0.573550
$961$	−13.6905	−0.441629
$962$	−0.527706	−0.0170139
$963$	5.32464	0.171584
$964$	31.8413	1.02554
$965$	1.35077	0.0434828
$966$	−5.05450	−0.162626
$967$	22.4533	0.722050	0.361025	−	0.932556i	$-0.382427\pi$
$967$	22.4533	0.722050	0.361025	+	0.932556i	$0.382427\pi$
$968$	41.4844	1.33336
$969$	10.6767	0.342985
$970$	−5.15243	−0.165435
$971$	−3.97335	−0.127511	−0.0637555	−	0.997966i	$-0.520308\pi$
$971$	−3.97335	−0.127511	−0.0637555	+	0.997966i	$0.520308\pi$
$972$	3.67627	0.117917
$973$	90.6062	2.90470
$974$	35.9385	1.15154
$975$	−6.94104	−0.222291
$976$	17.2228	0.551287
$977$	−43.9699	−1.40672	−0.703361	−	0.710832i	$-0.748318\pi$
$977$	−43.9699	−1.40672	−0.703361	+	0.710832i	$0.748318\pi$
$978$	−42.3412	−1.35392
$979$	−2.62578	−0.0839204
$980$	−51.7438	−1.65290
$981$	−15.4966	−0.494769
$982$	−33.4213	−1.06652
$983$	32.1694	1.02604	0.513022	−	0.858375i	$-0.328526\pi$
$983$	32.1694	1.02604	0.513022	+	0.858375i	$0.328526\pi$
$984$	−26.3203	−0.839060
$985$	21.7558	0.693197
$986$	4.80946	0.153164
$987$	−39.0138	−1.24182
$988$	−68.0399	−2.16464
$989$	−1.83203	−0.0582553
$990$	−2.99065	−0.0950490
$991$	−17.7739	−0.564605	−0.282303	−	0.959325i	$-0.591098\pi$
$991$	−17.7739	−0.564605	−0.282303	+	0.959325i	$0.591098\pi$
$992$	11.7967	0.374544
$993$	24.5677	0.779632
$994$	−21.3703	−0.677825
$995$	30.3374	0.961761
$996$	−24.5490	−0.777866
$997$	−0.640020	−0.0202696	−0.0101348	−	0.999949i	$-0.503226\pi$
$997$	−0.640020	−0.0202696	−0.0101348	+	0.999949i	$0.503226\pi$
$998$	−75.4495	−2.38831
$999$	0.0774709	0.00245107

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8031.2.a.a.1.9	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8031.2.a.a.1.9	✓	92	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:	\( N \)	\(=\)	\( 8031 = 3 \cdot 2677 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.38249 q^{2} +1.00000 q^{3} +3.67627 q^{4} -1.60383 q^{5} -2.38249 q^{6} -3.97189 q^{7} -3.99371 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.38249 q^{2} +1.00000 q^{3} +3.67627 q^{4} -1.60383 q^{5} -2.38249 q^{6} -3.97189 q^{7} -3.99371 q^{8} +1.00000 q^{9} +3.82111 q^{10} -0.782665 q^{11} +3.67627 q^{12} +2.85905 q^{13} +9.46301 q^{14} -1.60383 q^{15} +2.16244 q^{16} -1.64931 q^{17} -2.38249 q^{18} -6.47342 q^{19} -5.89611 q^{20} -3.97189 q^{21} +1.86469 q^{22} -0.534132 q^{23} -3.99371 q^{24} -2.42774 q^{25} -6.81167 q^{26} +1.00000 q^{27} -14.6018 q^{28} +1.22394 q^{29} +3.82111 q^{30} +4.16047 q^{31} +2.83542 q^{32} -0.782665 q^{33} +3.92948 q^{34} +6.37023 q^{35} +3.67627 q^{36} +0.0774709 q^{37} +15.4229 q^{38} +2.85905 q^{39} +6.40522 q^{40} +6.59043 q^{41} +9.46301 q^{42} +3.42992 q^{43} -2.87729 q^{44} -1.60383 q^{45} +1.27257 q^{46} +9.82247 q^{47} +2.16244 q^{48} +8.77593 q^{49} +5.78408 q^{50} -1.64931 q^{51} +10.5107 q^{52} -5.58000 q^{53} -2.38249 q^{54} +1.25526 q^{55} +15.8626 q^{56} -6.47342 q^{57} -2.91604 q^{58} +13.4543 q^{59} -5.89611 q^{60} +7.96449 q^{61} -9.91229 q^{62} -3.97189 q^{63} -11.0802 q^{64} -4.58542 q^{65} +1.86469 q^{66} +2.02759 q^{67} -6.06333 q^{68} -0.534132 q^{69} -15.1770 q^{70} -2.25830 q^{71} -3.99371 q^{72} +3.30362 q^{73} -0.184574 q^{74} -2.42774 q^{75} -23.7981 q^{76} +3.10866 q^{77} -6.81167 q^{78} -6.84083 q^{79} -3.46818 q^{80} +1.00000 q^{81} -15.7017 q^{82} -6.67770 q^{83} -14.6018 q^{84} +2.64521 q^{85} -8.17177 q^{86} +1.22394 q^{87} +3.12574 q^{88} +3.35493 q^{89} +3.82111 q^{90} -11.3558 q^{91} -1.96362 q^{92} +4.16047 q^{93} -23.4020 q^{94} +10.3822 q^{95} +2.83542 q^{96} -1.34841 q^{97} -20.9086 q^{98} -0.782665 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q - 6 q^{2} + 92 q^{3} + 70 q^{4} - 18 q^{5} - 6 q^{6} - 42 q^{7} - 15 q^{8} + 92 q^{9}+O(q^{10}) \) 92 * q - 6 * q^2 + 92 * q^3 + 70 * q^4 - 18 * q^5 - 6 * q^6 - 42 * q^7 - 15 * q^8 + 92 * q^9	\( 92 q - 6 q^{2} + 92 q^{3} + 70 q^{4} - 18 q^{5} - 6 q^{6} - 42 q^{7} - 15 q^{8} + 92 q^{9} - 44 q^{10} - 24 q^{11} + 70 q^{12} - 48 q^{13} - 29 q^{14} - 18 q^{15} + 26 q^{16} - 69 q^{17} - 6 q^{18} - 74 q^{19} - 42 q^{20} - 42 q^{21} - 62 q^{22} - 19 q^{23} - 15 q^{24} + 16 q^{25} - 27 q^{26} + 92 q^{27} - 101 q^{28} - 54 q^{29} - 44 q^{30} - 67 q^{31} - 36 q^{32} - 24 q^{33} - 63 q^{34} - 31 q^{35} + 70 q^{36} - 70 q^{37} - 18 q^{38} - 48 q^{39} - 125 q^{40} - 98 q^{41} - 29 q^{42} - 159 q^{43} - 52 q^{44} - 18 q^{45} - 68 q^{46} - 15 q^{47} + 26 q^{48} - 28 q^{49} - 7 q^{50} - 69 q^{51} - 98 q^{52} - 23 q^{53} - 6 q^{54} - 93 q^{55} - 48 q^{56} - 74 q^{57} - 37 q^{58} - 36 q^{59} - 42 q^{60} - 172 q^{61} - 26 q^{62} - 42 q^{63} - 23 q^{64} - 66 q^{65} - 62 q^{66} - 143 q^{67} - 74 q^{68} - 19 q^{69} - 30 q^{70} - 9 q^{71} - 15 q^{72} - 134 q^{73} - 19 q^{74} + 16 q^{75} - 157 q^{76} - 25 q^{77} - 27 q^{78} - 138 q^{79} - 29 q^{80} + 92 q^{81} - 61 q^{82} - 24 q^{83} - 101 q^{84} - 84 q^{85} + 14 q^{86} - 54 q^{87} - 140 q^{88} - 148 q^{89} - 44 q^{90} - 115 q^{91} - 12 q^{92} - 67 q^{93} - 79 q^{94} - 10 q^{95} - 36 q^{96} - 165 q^{97} + 36 q^{98} - 24 q^{99}+O(q^{100}) \) 92 * q - 6 * q^2 + 92 * q^3 + 70 * q^4 - 18 * q^5 - 6 * q^6 - 42 * q^7 - 15 * q^8 + 92 * q^9 - 44 * q^10 - 24 * q^11 + 70 * q^12 - 48 * q^13 - 29 * q^14 - 18 * q^15 + 26 * q^16 - 69 * q^17 - 6 * q^18 - 74 * q^19 - 42 * q^20 - 42 * q^21 - 62 * q^22 - 19 * q^23 - 15 * q^24 + 16 * q^25 - 27 * q^26 + 92 * q^27 - 101 * q^28 - 54 * q^29 - 44 * q^30 - 67 * q^31 - 36 * q^32 - 24 * q^33 - 63 * q^34 - 31 * q^35 + 70 * q^36 - 70 * q^37 - 18 * q^38 - 48 * q^39 - 125 * q^40 - 98 * q^41 - 29 * q^42 - 159 * q^43 - 52 * q^44 - 18 * q^45 - 68 * q^46 - 15 * q^47 + 26 * q^48 - 28 * q^49 - 7 * q^50 - 69 * q^51 - 98 * q^52 - 23 * q^53 - 6 * q^54 - 93 * q^55 - 48 * q^56 - 74 * q^57 - 37 * q^58 - 36 * q^59 - 42 * q^60 - 172 * q^61 - 26 * q^62 - 42 * q^63 - 23 * q^64 - 66 * q^65 - 62 * q^66 - 143 * q^67 - 74 * q^68 - 19 * q^69 - 30 * q^70 - 9 * q^71 - 15 * q^72 - 134 * q^73 - 19 * q^74 + 16 * q^75 - 157 * q^76 - 25 * q^77 - 27 * q^78 - 138 * q^79 - 29 * q^80 + 92 * q^81 - 61 * q^82 - 24 * q^83 - 101 * q^84 - 84 * q^85 + 14 * q^86 - 54 * q^87 - 140 * q^88 - 148 * q^89 - 44 * q^90 - 115 * q^91 - 12 * q^92 - 67 * q^93 - 79 * q^94 - 10 * q^95 - 36 * q^96 - 165 * q^97 + 36 * q^98 - 24 * q^99

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