LMFDB - Embedded newform 8033.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8033,2,Mod(1,8033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8033, 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("8033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8033 = 29 \cdot 277 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8033.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:	$64.1438279437$
Analytic rank:	$1$
Dimension:	$154$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.80099 q^{2} -1.33349 q^{3} +5.84554 q^{4} +0.375260 q^{5} +3.73510 q^{6} +1.86520 q^{7} -10.7713 q^{8} -1.22179 q^{9} +O(q^{10})$	\(q-2.80099 q^{2} -1.33349 q^{3} +5.84554 q^{4} +0.375260 q^{5} +3.73510 q^{6} +1.86520 q^{7} -10.7713 q^{8} -1.22179 q^{9} -1.05110 q^{10} +1.91622 q^{11} -7.79499 q^{12} -6.19977 q^{13} -5.22442 q^{14} -0.500407 q^{15} +18.4792 q^{16} -1.94389 q^{17} +3.42223 q^{18} +0.740570 q^{19} +2.19360 q^{20} -2.48724 q^{21} -5.36731 q^{22} +0.635052 q^{23} +14.3635 q^{24} -4.85918 q^{25} +17.3655 q^{26} +5.62974 q^{27} +10.9031 q^{28} +1.00000 q^{29} +1.40163 q^{30} -2.38553 q^{31} -30.2175 q^{32} -2.55527 q^{33} +5.44480 q^{34} +0.699937 q^{35} -7.14205 q^{36} -4.54331 q^{37} -2.07433 q^{38} +8.26736 q^{39} -4.04204 q^{40} +6.66433 q^{41} +6.96673 q^{42} -6.09280 q^{43} +11.2013 q^{44} -0.458491 q^{45} -1.77877 q^{46} -6.05344 q^{47} -24.6419 q^{48} -3.52101 q^{49} +13.6105 q^{50} +2.59216 q^{51} -36.2410 q^{52} +9.23915 q^{53} -15.7688 q^{54} +0.719081 q^{55} -20.0907 q^{56} -0.987545 q^{57} -2.80099 q^{58} +10.4335 q^{59} -2.92515 q^{60} +10.8729 q^{61} +6.68183 q^{62} -2.27890 q^{63} +47.6804 q^{64} -2.32653 q^{65} +7.15727 q^{66} +10.7183 q^{67} -11.3631 q^{68} -0.846837 q^{69} -1.96052 q^{70} +9.56498 q^{71} +13.1603 q^{72} +8.50736 q^{73} +12.7258 q^{74} +6.47969 q^{75} +4.32903 q^{76} +3.57414 q^{77} -23.1568 q^{78} +3.50484 q^{79} +6.93452 q^{80} -3.84183 q^{81} -18.6667 q^{82} +10.4785 q^{83} -14.5392 q^{84} -0.729464 q^{85} +17.0659 q^{86} -1.33349 q^{87} -20.6402 q^{88} +16.6318 q^{89} +1.28423 q^{90} -11.5638 q^{91} +3.71222 q^{92} +3.18109 q^{93} +16.9556 q^{94} +0.277906 q^{95} +40.2948 q^{96} -16.8015 q^{97} +9.86232 q^{98} -2.34123 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9}+O(q^{10}) $ 154 * q - 12 * q^2 - 36 * q^3 + 142 * q^4 - 9 * q^5 - 11 * q^6 - 68 * q^7 - 33 * q^8 + 146 * q^9	\( 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9} - 40 q^{10} - 36 q^{11} - 67 q^{12} - 51 q^{13} - 19 q^{14} - 48 q^{15} + 122 q^{16} - 54 q^{17} - 46 q^{18} - 73 q^{19} - 21 q^{20} - 8 q^{21} - 23 q^{22} - 38 q^{23} - 17 q^{24} + 133 q^{25} - 20 q^{26} - 129 q^{27} - 99 q^{28} + 154 q^{29} - 10 q^{30} - 91 q^{31} - 88 q^{32} - 39 q^{33} - 42 q^{34} - 36 q^{35} + 101 q^{36} - 50 q^{37} - 17 q^{38} - 33 q^{39} - 92 q^{40} - 31 q^{41} - 62 q^{42} - 154 q^{43} - 42 q^{44} - 14 q^{45} - 24 q^{46} - 140 q^{47} - 118 q^{48} + 126 q^{49} - 5 q^{50} - 16 q^{51} - 133 q^{52} - 40 q^{53} + 14 q^{54} - 203 q^{55} - 44 q^{56} - 16 q^{57} - 12 q^{58} + 5 q^{59} - 28 q^{60} - 106 q^{61} - 30 q^{62} - 145 q^{63} + 111 q^{64} - 15 q^{65} - 49 q^{66} - 78 q^{67} - 118 q^{68} - 32 q^{69} - 43 q^{70} - 4 q^{71} - 152 q^{72} - 137 q^{73} + 9 q^{74} - 129 q^{75} - 204 q^{76} - 76 q^{77} + 15 q^{78} - 141 q^{79} - 44 q^{80} + 122 q^{81} - 71 q^{82} - 90 q^{83} + 92 q^{84} - 41 q^{85} + 9 q^{86} - 36 q^{87} - 109 q^{88} - 51 q^{89} - 82 q^{90} - 22 q^{91} - 8 q^{92} - 10 q^{93} - 106 q^{94} - 55 q^{95} - 49 q^{96} - 140 q^{97} - 4 q^{98} - 101 q^{99}+O(q^{100}) \) 154 * q - 12 * q^2 - 36 * q^3 + 142 * q^4 - 9 * q^5 - 11 * q^6 - 68 * q^7 - 33 * q^8 + 146 * q^9 - 40 * q^10 - 36 * q^11 - 67 * q^12 - 51 * q^13 - 19 * q^14 - 48 * q^15 + 122 * q^16 - 54 * q^17 - 46 * q^18 - 73 * q^19 - 21 * q^20 - 8 * q^21 - 23 * q^22 - 38 * q^23 - 17 * q^24 + 133 * q^25 - 20 * q^26 - 129 * q^27 - 99 * q^28 + 154 * q^29 - 10 * q^30 - 91 * q^31 - 88 * q^32 - 39 * q^33 - 42 * q^34 - 36 * q^35 + 101 * q^36 - 50 * q^37 - 17 * q^38 - 33 * q^39 - 92 * q^40 - 31 * q^41 - 62 * q^42 - 154 * q^43 - 42 * q^44 - 14 * q^45 - 24 * q^46 - 140 * q^47 - 118 * q^48 + 126 * q^49 - 5 * q^50 - 16 * q^51 - 133 * q^52 - 40 * q^53 + 14 * q^54 - 203 * q^55 - 44 * q^56 - 16 * q^57 - 12 * q^58 + 5 * q^59 - 28 * q^60 - 106 * q^61 - 30 * q^62 - 145 * q^63 + 111 * q^64 - 15 * q^65 - 49 * q^66 - 78 * q^67 - 118 * q^68 - 32 * q^69 - 43 * q^70 - 4 * q^71 - 152 * q^72 - 137 * q^73 + 9 * q^74 - 129 * q^75 - 204 * q^76 - 76 * q^77 + 15 * q^78 - 141 * q^79 - 44 * q^80 + 122 * q^81 - 71 * q^82 - 90 * q^83 + 92 * q^84 - 41 * q^85 + 9 * q^86 - 36 * q^87 - 109 * q^88 - 51 * q^89 - 82 * q^90 - 22 * q^91 - 8 * q^92 - 10 * q^93 - 106 * q^94 - 55 * q^95 - 49 * q^96 - 140 * q^97 - 4 * q^98 - 101 * 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 $

$2$	−2.80099	−1.98060	−0.990299	−	0.138953i	$-0.955626\pi$
$2$	−2.80099	−1.98060	−0.990299	+	0.138953i	$0.955626\pi$
$3$	−1.33349	−0.769893	−0.384946	−	0.922939i	$-0.625780\pi$
$3$	−1.33349	−0.769893	−0.384946	+	0.922939i	$0.625780\pi$
$4$	5.84554	2.92277
$5$	0.375260	0.167822	0.0839108	−	0.996473i	$-0.473259\pi$
$5$	0.375260	0.167822	0.0839108	+	0.996473i	$0.473259\pi$
$6$	3.73510	1.52485
$7$	1.86520	0.704981	0.352491	−	0.935815i	$-0.385335\pi$
$7$	1.86520	0.704981	0.352491	+	0.935815i	$0.385335\pi$
$8$	−10.7713	−3.80823
$9$	−1.22179	−0.407265
$10$	−1.05110	−0.332387
$11$	1.91622	0.577762	0.288881	−	0.957365i	$-0.406717\pi$
$11$	1.91622	0.577762	0.288881	+	0.957365i	$0.406717\pi$
$12$	−7.79499	−2.25022
$13$	−6.19977	−1.71951	−0.859754	−	0.510709i	$-0.829383\pi$
$13$	−6.19977	−1.71951	−0.859754	+	0.510709i	$0.829383\pi$
$14$	−5.22442	−1.39628
$15$	−0.500407	−0.129205
$16$	18.4792	4.61981
$17$	−1.94389	−0.471462	−0.235731	−	0.971818i	$-0.575748\pi$
$17$	−1.94389	−0.471462	−0.235731	+	0.971818i	$0.575748\pi$
$18$	3.42223	0.806628
$19$	0.740570	0.169898	0.0849492	−	0.996385i	$-0.472927\pi$
$19$	0.740570	0.169898	0.0849492	+	0.996385i	$0.472927\pi$
$20$	2.19360	0.490503
$21$	−2.48724	−0.542760
$22$	−5.36731	−1.14431
$23$	0.635052	0.132417	0.0662087	−	0.997806i	$-0.478910\pi$
$23$	0.635052	0.132417	0.0662087	+	0.997806i	$0.478910\pi$
$24$	14.3635	2.93193
$25$	−4.85918	−0.971836
$26$	17.3655	3.40565
$27$	5.62974	1.08344
$28$	10.9031	2.06050
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	1.40163	0.255902
$31$	−2.38553	−0.428453	−0.214227	−	0.976784i	$-0.568723\pi$
$31$	−2.38553	−0.428453	−0.214227	+	0.976784i	$0.568723\pi$
$32$	−30.2175	−5.34175
$33$	−2.55527	−0.444815
$34$	5.44480	0.933776
$35$	0.699937	0.118311
$36$	−7.14205	−1.19034
$37$	−4.54331	−0.746915	−0.373458	−	0.927647i	$-0.621828\pi$
$37$	−4.54331	−0.746915	−0.373458	+	0.927647i	$0.621828\pi$
$38$	−2.07433	−0.336500
$39$	8.26736	1.32384
$40$	−4.04204	−0.639103
$41$	6.66433	1.04079	0.520397	−	0.853924i	$-0.325784\pi$
$41$	6.66433	1.04079	0.520397	+	0.853924i	$0.325784\pi$
$42$	6.96673	1.07499
$43$	−6.09280	−0.929144	−0.464572	−	0.885535i	$-0.653792\pi$
$43$	−6.09280	−0.929144	−0.464572	+	0.885535i	$0.653792\pi$
$44$	11.2013	1.68866
$45$	−0.458491	−0.0683478
$46$	−1.77877	−0.262266
$47$	−6.05344	−0.882985	−0.441493	−	0.897265i	$-0.645551\pi$
$47$	−6.05344	−0.882985	−0.441493	+	0.897265i	$0.645551\pi$
$48$	−24.6419	−3.55676
$49$	−3.52101	−0.503002
$50$	13.6105	1.92482
$51$	2.59216	0.362975
$52$	−36.2410	−5.02572
$53$	9.23915	1.26910	0.634548	−	0.772884i	$-0.281186\pi$
$53$	9.23915	1.26910	0.634548	+	0.772884i	$0.281186\pi$
$54$	−15.7688	−2.14587
$55$	0.719081	0.0969609
$56$	−20.0907	−2.68473
$57$	−0.987545	−0.130804
$58$	−2.80099	−0.367788
$59$	10.4335	1.35832	0.679162	−	0.733988i	$-0.262343\pi$
$59$	10.4335	1.35832	0.679162	+	0.733988i	$0.262343\pi$
$60$	−2.92515	−0.377635
$61$	10.8729	1.39214	0.696068	−	0.717976i	$-0.254931\pi$
$61$	10.8729	1.39214	0.696068	+	0.717976i	$0.254931\pi$
$62$	6.68183	0.848594
$63$	−2.27890	−0.287114
$64$	47.6804	5.96005
$65$	−2.32653	−0.288570
$66$	7.15727	0.881000
$67$	10.7183	1.30944	0.654722	−	0.755870i	$-0.272786\pi$
$67$	10.7183	1.30944	0.654722	+	0.755870i	$0.272786\pi$
$68$	−11.3631	−1.37797
$69$	−0.846837	−0.101947
$70$	−1.96052	−0.234326
$71$	9.56498	1.13515	0.567577	−	0.823320i	$-0.307881\pi$
$71$	9.56498	1.13515	0.567577	+	0.823320i	$0.307881\pi$
$72$	13.1603	1.55096
$73$	8.50736	0.995711	0.497855	−	0.867260i	$-0.334121\pi$
$73$	8.50736	0.995711	0.497855	+	0.867260i	$0.334121\pi$
$74$	12.7258	1.47934
$75$	6.47969	0.748210
$76$	4.32903	0.496573
$77$	3.57414	0.407311
$78$	−23.1568	−2.62199
$79$	3.50484	0.394325	0.197162	−	0.980371i	$-0.436827\pi$
$79$	3.50484	0.394325	0.197162	+	0.980371i	$0.436827\pi$
$80$	6.93452	0.775303
$81$	−3.84183	−0.426870
$82$	−18.6667	−2.06139
$83$	10.4785	1.15017	0.575084	−	0.818095i	$-0.304970\pi$
$83$	10.4785	1.15017	0.575084	+	0.818095i	$0.304970\pi$
$84$	−14.5392	−1.58636
$85$	−0.729464	−0.0791214
$86$	17.0659	1.84026
$87$	−1.33349	−0.142966
$88$	−20.6402	−2.20025
$89$	16.6318	1.76297	0.881486	−	0.472210i	$-0.156544\pi$
$89$	16.6318	1.76297	0.881486	+	0.472210i	$0.156544\pi$
$90$	1.28423	0.135370
$91$	−11.5638	−1.21222
$92$	3.71222	0.387025
$93$	3.18109	0.329863
$94$	16.9556	1.74884
$95$	0.277906	0.0285126
$96$	40.2948	4.11258
$97$	−16.8015	−1.70593	−0.852967	−	0.521966i	$-0.825199\pi$
$97$	−16.8015	−1.70593	−0.852967	+	0.521966i	$0.825199\pi$
$98$	9.86232	0.996244
$99$	−2.34123	−0.235302
$100$	−28.4045	−2.84045
$101$	−16.2244	−1.61439	−0.807196	−	0.590284i	$-0.799016\pi$
$101$	−16.2244	−1.61439	−0.807196	+	0.590284i	$0.799016\pi$
$102$	−7.26061	−0.718908
$103$	16.9104	1.66623	0.833114	−	0.553101i	$-0.186556\pi$
$103$	16.9104	1.66623	0.833114	+	0.553101i	$0.186556\pi$
$104$	66.7796	6.54828
$105$	−0.933362	−0.0910868
$106$	−25.8788	−2.51357
$107$	0.704484	0.0681050	0.0340525	−	0.999420i	$-0.489159\pi$
$107$	0.704484	0.0681050	0.0340525	+	0.999420i	$0.489159\pi$
$108$	32.9088	3.16665
$109$	−13.2756	−1.27157	−0.635784	−	0.771867i	$-0.719323\pi$
$109$	−13.2756	−1.27157	−0.635784	+	0.771867i	$0.719323\pi$
$110$	−2.01414	−0.192041
$111$	6.05847	0.575045
$112$	34.4675	3.25688
$113$	−13.3859	−1.25924	−0.629618	−	0.776905i	$-0.716788\pi$
$113$	−13.3859	−1.25924	−0.629618	+	0.776905i	$0.716788\pi$
$114$	2.76610	0.259069
$115$	0.238310	0.0222225
$116$	5.84554	0.542744
$117$	7.57485	0.700295
$118$	−29.2241	−2.69029
$119$	−3.62575	−0.332372
$120$	5.39004	0.492041
$121$	−7.32810	−0.666191
$122$	−30.4550	−2.75726
$123$	−8.88685	−0.801300
$124$	−13.9447	−1.25227
$125$	−3.69976	−0.330916
$126$	6.38316	0.568657
$127$	7.95555	0.705941	0.352971	−	0.935634i	$-0.385172\pi$
$127$	7.95555	0.705941	0.352971	+	0.935634i	$0.385172\pi$
$128$	−73.1173	−6.46272
$129$	8.12472	0.715341
$130$	6.51658	0.571542
$131$	17.1390	1.49744	0.748719	−	0.662887i	$-0.230669\pi$
$131$	17.1390	1.49744	0.748719	+	0.662887i	$0.230669\pi$
$132$	−14.9369	−1.30009
$133$	1.38131	0.119775
$134$	−30.0217	−2.59348
$135$	2.11262	0.181825
$136$	20.9382	1.79544
$137$	−15.7470	−1.34536	−0.672678	−	0.739935i	$-0.734856\pi$
$137$	−15.7470	−1.34536	−0.672678	+	0.739935i	$0.734856\pi$
$138$	2.37198	0.201916
$139$	−7.16425	−0.607664	−0.303832	−	0.952726i	$-0.598266\pi$
$139$	−7.16425	−0.607664	−0.303832	+	0.952726i	$0.598266\pi$
$140$	4.09151	0.345796
$141$	8.07223	0.679804
$142$	−26.7914	−2.24828
$143$	−11.8801	−0.993466
$144$	−22.5778	−1.88149
$145$	0.375260	0.0311637
$146$	−23.8290	−1.97210
$147$	4.69525	0.387257
$148$	−26.5581	−2.18306
$149$	−12.5606	−1.02900	−0.514501	−	0.857490i	$-0.672023\pi$
$149$	−12.5606	−1.02900	−0.514501	+	0.857490i	$0.672023\pi$
$150$	−18.1495	−1.48190
$151$	−6.50580	−0.529435	−0.264717	−	0.964326i	$-0.585279\pi$
$151$	−6.50580	−0.529435	−0.264717	+	0.964326i	$0.585279\pi$
$152$	−7.97690	−0.647012
$153$	2.37503	0.192010
$154$	−10.0111	−0.806720
$155$	−0.895194	−0.0719037
$156$	48.3271	3.86927
$157$	−11.5159	−0.919071	−0.459536	−	0.888159i	$-0.651984\pi$
$157$	−11.5159	−0.919071	−0.459536	+	0.888159i	$0.651984\pi$
$158$	−9.81701	−0.780999
$159$	−12.3204	−0.977068
$160$	−11.3394	−0.896461
$161$	1.18450	0.0933518
$162$	10.7609	0.845459
$163$	−2.39657	−0.187714	−0.0938569	−	0.995586i	$-0.529920\pi$
$163$	−2.39657	−0.187714	−0.0938569	+	0.995586i	$0.529920\pi$
$164$	38.9566	3.04200
$165$	−0.958890	−0.0746495
$166$	−29.3502	−2.27802
$167$	20.6583	1.59859	0.799295	−	0.600939i	$-0.205206\pi$
$167$	20.6583	1.59859	0.799295	+	0.600939i	$0.205206\pi$
$168$	26.7908	2.06696
$169$	25.4372	1.95671
$170$	2.04322	0.156708
$171$	−0.904824	−0.0691936
$172$	−35.6157	−2.71567
$173$	−11.9269	−0.906788	−0.453394	−	0.891310i	$-0.649787\pi$
$173$	−11.9269	−0.906788	−0.453394	+	0.891310i	$0.649787\pi$
$174$	3.73510	0.283157
$175$	−9.06336	−0.685126
$176$	35.4103	2.66915
$177$	−13.9130	−1.04576
$178$	−46.5856	−3.49174
$179$	20.6713	1.54504	0.772521	−	0.634989i	$-0.218995\pi$
$179$	20.6713	1.54504	0.772521	+	0.634989i	$0.218995\pi$
$180$	−2.68013	−0.199765
$181$	−2.15917	−0.160490	−0.0802449	−	0.996775i	$-0.525570\pi$
$181$	−2.15917	−0.160490	−0.0802449	+	0.996775i	$0.525570\pi$
$182$	32.3902	2.40092
$183$	−14.4990	−1.07180
$184$	−6.84033	−0.504276
$185$	−1.70492	−0.125348
$186$	−8.91018	−0.653326
$187$	−3.72491	−0.272393
$188$	−35.3856	−2.58076
$189$	10.5006	0.763807
$190$	−0.778413	−0.0564720
$191$	9.46489	0.684856	0.342428	−	0.939544i	$-0.388751\pi$
$191$	9.46489	0.684856	0.342428	+	0.939544i	$0.388751\pi$
$192$	−63.5815	−4.58860
$193$	−12.5350	−0.902287	−0.451144	−	0.892451i	$-0.648984\pi$
$193$	−12.5350	−0.902287	−0.451144	+	0.892451i	$0.648984\pi$
$194$	47.0608	3.37877
$195$	3.10241	0.222168
$196$	−20.5822	−1.47016
$197$	2.31309	0.164801	0.0824003	−	0.996599i	$-0.473741\pi$
$197$	2.31309	0.164801	0.0824003	+	0.996599i	$0.473741\pi$
$198$	6.55775	0.466039
$199$	−4.14141	−0.293577	−0.146789	−	0.989168i	$-0.546894\pi$
$199$	−4.14141	−0.293577	−0.146789	+	0.989168i	$0.546894\pi$
$200$	52.3397	3.70098
$201$	−14.2927	−1.00813
$202$	45.4445	3.19746
$203$	1.86520	0.130912
$204$	15.1526	1.06089
$205$	2.50086	0.174668
$206$	−47.3658	−3.30013
$207$	−0.775903	−0.0539290
$208$	−114.567	−7.94379
$209$	1.41909	0.0981608
$210$	2.61434	0.180406
$211$	−2.82836	−0.194713	−0.0973563	−	0.995250i	$-0.531039\pi$
$211$	−2.82836	−0.194713	−0.0973563	+	0.995250i	$0.531039\pi$
$212$	54.0078	3.70927
$213$	−12.7548	−0.873947
$214$	−1.97325	−0.134889
$215$	−2.28639	−0.155930
$216$	−60.6396	−4.12600
$217$	−4.44950	−0.302051
$218$	37.1847	2.51847
$219$	−11.3445	−0.766591
$220$	4.20342	0.283394
$221$	12.0517	0.810682
$222$	−16.9697	−1.13893
$223$	−4.20119	−0.281333	−0.140666	−	0.990057i	$-0.544924\pi$
$223$	−4.20119	−0.281333	−0.140666	+	0.990057i	$0.544924\pi$
$224$	−56.3618	−3.76583
$225$	5.93692	0.395795
$226$	37.4936	2.49404
$227$	4.37989	0.290704	0.145352	−	0.989380i	$-0.453569\pi$
$227$	4.37989	0.290704	0.145352	+	0.989380i	$0.453569\pi$
$228$	−5.77273	−0.382308
$229$	−1.05704	−0.0698512	−0.0349256	−	0.999390i	$-0.511119\pi$
$229$	−1.05704	−0.0698512	−0.0349256	+	0.999390i	$0.511119\pi$
$230$	−0.667503	−0.0440138
$231$	−4.76610	−0.313586
$232$	−10.7713	−0.707171
$233$	9.04169	0.592341	0.296170	−	0.955135i	$-0.404290\pi$
$233$	9.04169	0.592341	0.296170	+	0.955135i	$0.404290\pi$
$234$	−21.2171	−1.38700
$235$	−2.27162	−0.148184
$236$	60.9893	3.97007
$237$	−4.67368	−0.303588
$238$	10.1557	0.658295
$239$	−17.6012	−1.13853	−0.569264	−	0.822155i	$-0.692772\pi$
$239$	−17.6012	−1.13853	−0.569264	+	0.822155i	$0.692772\pi$
$240$	−9.24714	−0.596900
$241$	0.326914	0.0210584	0.0105292	−	0.999945i	$-0.496648\pi$
$241$	0.326914	0.0210584	0.0105292	+	0.999945i	$0.496648\pi$
$242$	20.5259	1.31946
$243$	−11.7661	−0.754799
$244$	63.5581	4.06889
$245$	−1.32130	−0.0844145
$246$	24.8920	1.58705
$247$	−4.59136	−0.292141
$248$	25.6952	1.63165
$249$	−13.9730	−0.885506
$250$	10.3630	0.655413
$251$	−24.5611	−1.55028	−0.775140	−	0.631789i	$-0.782321\pi$
$251$	−24.5611	−1.55028	−0.775140	+	0.631789i	$0.782321\pi$
$252$	−13.3214	−0.839168
$253$	1.21690	0.0765057
$254$	−22.2834	−1.39819
$255$	0.972735	0.0609150
$256$	109.440	6.83999
$257$	18.0050	1.12312	0.561559	−	0.827437i	$-0.310202\pi$
$257$	18.0050	1.12312	0.561559	+	0.827437i	$0.310202\pi$
$258$	−22.7572	−1.41680
$259$	−8.47420	−0.526561
$260$	−13.5998	−0.843424
$261$	−1.22179	−0.0756272
$262$	−48.0060	−2.96582
$263$	18.2511	1.12541	0.562705	−	0.826658i	$-0.309761\pi$
$263$	18.2511	1.12541	0.562705	+	0.826658i	$0.309761\pi$
$264$	27.5236	1.69396
$265$	3.46709	0.212982
$266$	−3.86904	−0.237226
$267$	−22.1785	−1.35730
$268$	62.6540	3.82720
$269$	−17.9745	−1.09592	−0.547962	−	0.836503i	$-0.684596\pi$
$269$	−17.9745	−1.09592	−0.547962	+	0.836503i	$0.684596\pi$
$270$	−5.91742	−0.360122
$271$	−24.6050	−1.49465	−0.747323	−	0.664461i	$-0.768661\pi$
$271$	−24.6050	−1.49465	−0.747323	+	0.664461i	$0.768661\pi$
$272$	−35.9215	−2.17806
$273$	15.4203	0.933280
$274$	44.1071	2.66461
$275$	−9.31126	−0.561490
$276$	−4.95022	−0.297968
$277$	1.00000	0.0600842
$277$	1.00000	0.0600842
$278$	20.0670	1.20354
$279$	2.91462	0.174494
$280$	−7.53924	−0.450556
$281$	−5.73878	−0.342347	−0.171173	−	0.985241i	$-0.554756\pi$
$281$	−5.73878	−0.342347	−0.171173	+	0.985241i	$0.554756\pi$
$282$	−22.6102	−1.34642
$283$	−3.11377	−0.185094	−0.0925472	−	0.995708i	$-0.529501\pi$
$283$	−3.11377	−0.185094	−0.0925472	+	0.995708i	$0.529501\pi$
$284$	55.9125	3.31779
$285$	−0.370586	−0.0219516
$286$	33.2761	1.96766
$287$	12.4303	0.733740
$288$	36.9196	2.17551
$289$	−13.2213	−0.777724
$290$	−1.05110	−0.0617227
$291$	22.4047	1.31339
$292$	49.7301	2.91023
$293$	−20.1807	−1.17897	−0.589486	−	0.807779i	$-0.700670\pi$
$293$	−20.1807	−1.17897	−0.589486	+	0.807779i	$0.700670\pi$
$294$	−13.1513	−0.767001
$295$	3.91527	0.227956
$296$	48.9374	2.84443
$297$	10.7878	0.625972
$298$	35.1820	2.03804
$299$	−3.93717	−0.227693
$300$	37.8772	2.18684
$301$	−11.3643	−0.655029
$302$	18.2227	1.04860
$303$	21.6352	1.24291
$304$	13.6852	0.784898
$305$	4.08018	0.233630
$306$	−6.65243	−0.380294
$307$	4.65917	0.265913	0.132956	−	0.991122i	$-0.457553\pi$
$307$	4.65917	0.265913	0.132956	+	0.991122i	$0.457553\pi$
$308$	20.8928	1.19048
$309$	−22.5499	−1.28282
$310$	2.50743	0.142412
$311$	31.5303	1.78792	0.893959	−	0.448148i	$-0.147916\pi$
$311$	31.5303	1.78792	0.893959	+	0.448148i	$0.147916\pi$
$312$	−89.0502	−5.04148
$313$	29.1084	1.64530	0.822652	−	0.568545i	$-0.192494\pi$
$313$	29.1084	1.64530	0.822652	+	0.568545i	$0.192494\pi$
$314$	32.2560	1.82031
$315$	−0.855180	−0.0481839
$316$	20.4877	1.15252
$317$	−29.8273	−1.67527	−0.837634	−	0.546232i	$-0.816062\pi$
$317$	−29.8273	−1.67527	−0.837634	+	0.546232i	$0.816062\pi$
$318$	34.5092	1.93518
$319$	1.91622	0.107288
$320$	17.8926	1.00022
$321$	−0.939425	−0.0524336
$322$	−3.31777	−0.184892
$323$	−1.43958	−0.0801006
$324$	−22.4576	−1.24764
$325$	30.1258	1.67108
$326$	6.71276	0.371786
$327$	17.7029	0.978971
$328$	−71.7836	−3.96358
$329$	−11.2909	−0.622488
$330$	2.68584	0.147851
$331$	−34.3910	−1.89030	−0.945151	−	0.326633i	$-0.894086\pi$
$331$	−34.3910	−1.89030	−0.945151	+	0.326633i	$0.894086\pi$
$332$	61.2526	3.36167
$333$	5.55099	0.304192
$334$	−57.8638	−3.16616
$335$	4.02214	0.219753
$336$	−45.9622	−2.50745
$337$	15.8284	0.862229	0.431114	−	0.902297i	$-0.358121\pi$
$337$	15.8284	0.862229	0.431114	+	0.902297i	$0.358121\pi$
$338$	−71.2492	−3.87545
$339$	17.8500	0.969476
$340$	−4.26411	−0.231254
$341$	−4.57119	−0.247544
$342$	2.53440	0.137045
$343$	−19.6238	−1.05959
$344$	65.6275	3.53840
$345$	−0.317784	−0.0171089
$346$	33.4072	1.79598
$347$	−13.1817	−0.707630	−0.353815	−	0.935315i	$-0.615116\pi$
$347$	−13.1817	−0.707630	−0.353815	+	0.935315i	$0.615116\pi$
$348$	−7.79499	−0.417855
$349$	−22.4185	−1.20004	−0.600018	−	0.799986i	$-0.704840\pi$
$349$	−22.4185	−1.20004	−0.600018	+	0.799986i	$0.704840\pi$
$350$	25.3864	1.35696
$351$	−34.9031	−1.86299
$352$	−57.9034	−3.08626
$353$	−16.7721	−0.892690	−0.446345	−	0.894861i	$-0.647275\pi$
$353$	−16.7721	−0.892690	−0.446345	+	0.894861i	$0.647275\pi$
$354$	38.9701	2.07124
$355$	3.58936	0.190503
$356$	97.2221	5.15276
$357$	4.83491	0.255891
$358$	−57.9000	−3.06011
$359$	−7.27221	−0.383813	−0.191906	−	0.981413i	$-0.561467\pi$
$359$	−7.27221	−0.383813	−0.191906	+	0.981413i	$0.561467\pi$
$360$	4.93855	0.260284
$361$	−18.4516	−0.971135
$362$	6.04781	0.317866
$363$	9.77198	0.512896
$364$	−67.5969	−3.54304
$365$	3.19247	0.167102
$366$	40.6115	2.12280
$367$	−11.9757	−0.625127	−0.312564	−	0.949897i	$-0.601188\pi$
$367$	−11.9757	−0.625127	−0.312564	+	0.949897i	$0.601188\pi$
$368$	11.7353	0.611743
$369$	−8.14245	−0.423879
$370$	4.77547	0.248265
$371$	17.2329	0.894688
$372$	18.5952	0.964114
$373$	−24.1099	−1.24836	−0.624182	−	0.781279i	$-0.714568\pi$
$373$	−24.1099	−1.24836	−0.624182	+	0.781279i	$0.714568\pi$
$374$	10.4334	0.539500
$375$	4.93360	0.254770
$376$	65.2035	3.36261
$377$	−6.19977	−0.319305
$378$	−29.4121	−1.51279
$379$	0.630235	0.0323730	0.0161865	−	0.999869i	$-0.494847\pi$
$379$	0.630235	0.0323730	0.0161865	+	0.999869i	$0.494847\pi$
$380$	1.62451	0.0833357
$381$	−10.6087	−0.543499
$382$	−26.5111	−1.35642
$383$	19.9064	1.01717	0.508585	−	0.861012i	$-0.330169\pi$
$383$	19.9064	1.01717	0.508585	+	0.861012i	$0.330169\pi$
$384$	97.5015	4.97560
$385$	1.34123	0.0683556
$386$	35.1103	1.78707
$387$	7.44416	0.378408
$388$	−98.2137	−4.98605
$389$	−6.86612	−0.348126	−0.174063	−	0.984735i	$-0.555690\pi$
$389$	−6.86612	−0.348126	−0.174063	+	0.984735i	$0.555690\pi$
$390$	−8.68982	−0.440026
$391$	−1.23447	−0.0624297
$392$	37.9259	1.91555
$393$	−22.8547	−1.15287
$394$	−6.47893	−0.326404
$395$	1.31523	0.0661762
$396$	−13.6857	−0.687734
$397$	11.5458	0.579468	0.289734	−	0.957107i	$-0.406433\pi$
$397$	11.5458	0.579468	0.289734	+	0.957107i	$0.406433\pi$
$398$	11.6001	0.581458
$399$	−1.84197	−0.0922140
$400$	−89.7939	−4.48969
$401$	−13.6942	−0.683857	−0.341929	−	0.939726i	$-0.611080\pi$
$401$	−13.6942	−0.683857	−0.341929	+	0.939726i	$0.611080\pi$
$402$	40.0338	1.99670
$403$	14.7897	0.736729
$404$	−94.8405	−4.71849
$405$	−1.44169	−0.0716380
$406$	−5.22442	−0.259283
$407$	−8.70598	−0.431539
$408$	−27.9210	−1.38229
$409$	−32.0109	−1.58284	−0.791419	−	0.611274i	$-0.790657\pi$
$409$	−32.0109	−1.58284	−0.791419	+	0.611274i	$0.790657\pi$
$410$	−7.00488	−0.345946
$411$	20.9985	1.03578
$412$	98.8502	4.87000
$413$	19.4606	0.957593
$414$	2.17329	0.106812
$415$	3.93217	0.193023
$416$	187.342	9.18518
$417$	9.55348	0.467836
$418$	−3.97487	−0.194417
$419$	19.8456	0.969521	0.484760	−	0.874647i	$-0.338907\pi$
$419$	19.8456	0.969521	0.484760	+	0.874647i	$0.338907\pi$
$420$	−5.45600	−0.266226
$421$	38.1122	1.85748	0.928738	−	0.370738i	$-0.120895\pi$
$421$	38.1122	1.85748	0.928738	+	0.370738i	$0.120895\pi$
$422$	7.92221	0.385647
$423$	7.39606	0.359609
$424$	−99.5177	−4.83301
$425$	9.44569	0.458183
$426$	35.7262	1.73094
$427$	20.2802	0.981430
$428$	4.11809	0.199055
$429$	15.8421	0.764863
$430$	6.40415	0.308835
$431$	29.2729	1.41002	0.705012	−	0.709195i	$-0.250942\pi$
$431$	29.2729	1.41002	0.705012	+	0.709195i	$0.250942\pi$
$432$	104.033	5.00530
$433$	29.0534	1.39622	0.698109	−	0.715992i	$-0.254025\pi$
$433$	29.0534	1.39622	0.698109	+	0.715992i	$0.254025\pi$
$434$	12.4630	0.598242
$435$	−0.500407	−0.0239927
$436$	−77.6028	−3.71650
$437$	0.470300	0.0224975
$438$	31.7758	1.51831
$439$	−6.44850	−0.307770	−0.153885	−	0.988089i	$-0.549179\pi$
$439$	−6.44850	−0.307770	−0.153885	+	0.988089i	$0.549179\pi$
$440$	−7.74544	−0.369250
$441$	4.30195	0.204855
$442$	−33.7565	−1.60564
$443$	−31.6805	−1.50519	−0.752593	−	0.658486i	$-0.771197\pi$
$443$	−31.6805	−1.50519	−0.752593	+	0.658486i	$0.771197\pi$
$444$	35.4150	1.68072
$445$	6.24127	0.295865
$446$	11.7675	0.557207
$447$	16.7494	0.792221
$448$	88.9337	4.20172
$449$	39.9921	1.88734	0.943672	−	0.330882i	$-0.107346\pi$
$449$	39.9921	1.88734	0.943672	+	0.330882i	$0.107346\pi$
$450$	−16.6292	−0.783910
$451$	12.7703	0.601331
$452$	−78.2475	−3.68045
$453$	8.67545	0.407608
$454$	−12.2680	−0.575767
$455$	−4.33945	−0.203437
$456$	10.6371	0.498130
$457$	29.8214	1.39499	0.697494	−	0.716591i	$-0.254299\pi$
$457$	29.8214	1.39499	0.697494	+	0.716591i	$0.254299\pi$
$458$	2.96076	0.138347
$459$	−10.9436	−0.510802
$460$	1.39305	0.0649512
$461$	38.4637	1.79143	0.895716	−	0.444626i	$-0.146663\pi$
$461$	38.4637	1.79143	0.895716	+	0.444626i	$0.146663\pi$
$462$	13.3498	0.621088
$463$	−1.43040	−0.0664761	−0.0332381	−	0.999447i	$-0.510582\pi$
$463$	−1.43040	−0.0664761	−0.0332381	+	0.999447i	$0.510582\pi$
$464$	18.4792	0.857877
$465$	1.19373	0.0553581
$466$	−25.3257	−1.17319
$467$	−9.01260	−0.417053	−0.208527	−	0.978017i	$-0.566867\pi$
$467$	−9.01260	−0.417053	−0.208527	+	0.978017i	$0.566867\pi$
$468$	44.2791	2.04680
$469$	19.9917	0.923133
$470$	6.36277	0.293493
$471$	15.3564	0.707586
$472$	−112.382	−5.17281
$473$	−11.6752	−0.536824
$474$	13.0909	0.601286
$475$	−3.59856	−0.165113
$476$	−21.1944	−0.971445
$477$	−11.2883	−0.516858
$478$	49.3008	2.25496
$479$	15.1082	0.690313	0.345157	−	0.938545i	$-0.387826\pi$
$479$	15.1082	0.690313	0.345157	+	0.938545i	$0.387826\pi$
$480$	15.1211	0.690179
$481$	28.1675	1.28433
$482$	−0.915681	−0.0417081
$483$	−1.57952	−0.0718709
$484$	−42.8367	−1.94712
$485$	−6.30493	−0.286292
$486$	32.9568	1.49495
$487$	12.7018	0.575572	0.287786	−	0.957695i	$-0.407081\pi$
$487$	12.7018	0.575572	0.287786	+	0.957695i	$0.407081\pi$
$488$	−117.116	−5.30158
$489$	3.19581	0.144520
$490$	3.70094	0.167191
$491$	10.9198	0.492801	0.246401	−	0.969168i	$-0.420752\pi$
$491$	10.9198	0.492801	0.246401	+	0.969168i	$0.420752\pi$
$492$	−51.9484	−2.34201
$493$	−1.94389	−0.0875483
$494$	12.8604	0.578615
$495$	−0.878570	−0.0394888
$496$	−44.0827	−1.97937
$497$	17.8406	0.800262
$498$	39.1383	1.75383
$499$	8.73375	0.390976	0.195488	−	0.980706i	$-0.437371\pi$
$499$	8.73375	0.390976	0.195488	+	0.980706i	$0.437371\pi$
$500$	−21.6271	−0.967192
$501$	−27.5478	−1.23074
$502$	68.7953	3.07048
$503$	−28.2885	−1.26132	−0.630661	−	0.776058i	$-0.717216\pi$
$503$	−28.2885	−1.26132	−0.630661	+	0.776058i	$0.717216\pi$
$504$	24.5467	1.09340
$505$	−6.08839	−0.270930
$506$	−3.40852	−0.151527
$507$	−33.9203	−1.50645
$508$	46.5045	2.06330
$509$	23.8054	1.05515	0.527577	−	0.849507i	$-0.323100\pi$
$509$	23.8054	1.05515	0.527577	+	0.849507i	$0.323100\pi$
$510$	−2.72462	−0.120648
$511$	15.8680	0.701957
$512$	−160.305	−7.08456
$513$	4.16921	0.184075
$514$	−50.4317	−2.22445
$515$	6.34579	0.279629
$516$	47.4933	2.09078
$517$	−11.5997	−0.510155
$518$	23.7361	1.04291
$519$	15.9045	0.698130
$520$	25.0597	1.09894
$521$	−29.7085	−1.30155	−0.650777	−	0.759269i	$-0.725557\pi$
$521$	−29.7085	−1.30155	−0.650777	+	0.759269i	$0.725557\pi$
$522$	3.42223	0.149787
$523$	22.2108	0.971211	0.485605	−	0.874178i	$-0.338599\pi$
$523$	22.2108	0.971211	0.485605	+	0.874178i	$0.338599\pi$
$524$	100.186	4.37666
$525$	12.0859	0.527474
$526$	−51.1211	−2.22898
$527$	4.63719	0.201999
$528$	−47.2194	−2.05496
$529$	−22.5967	−0.982466
$530$	−9.71127	−0.421831
$531$	−12.7476	−0.553198
$532$	8.07452	0.350075
$533$	−41.3174	−1.78965
$534$	62.1216	2.68827
$535$	0.264365	0.0114295
$536$	−115.450	−4.98666
$537$	−27.5650	−1.18952
$538$	50.3463	2.17058
$539$	−6.74703	−0.290615
$540$	12.3494	0.531433
$541$	−31.6308	−1.35991	−0.679956	−	0.733253i	$-0.738001\pi$
$541$	−31.6308	−1.35991	−0.679956	+	0.733253i	$0.738001\pi$
$542$	68.9182	2.96029
$543$	2.87924	0.123560
$544$	58.7394	2.51843
$545$	−4.98179	−0.213396
$546$	−43.1921	−1.84845
$547$	18.1147	0.774529	0.387264	−	0.921969i	$-0.373420\pi$
$547$	18.1147	0.774529	0.387264	+	0.921969i	$0.373420\pi$
$548$	−92.0496	−3.93217
$549$	−13.2845	−0.566968
$550$	26.0807	1.11209
$551$	0.740570	0.0315493
$552$	9.12154	0.388239
$553$	6.53724	0.277992
$554$	−2.80099	−0.119003
$555$	2.27350	0.0965049
$556$	−41.8789	−1.77606
$557$	−13.5792	−0.575369	−0.287684	−	0.957725i	$-0.592885\pi$
$557$	−13.5792	−0.575369	−0.287684	+	0.957725i	$0.592885\pi$
$558$	−8.16383	−0.345602
$559$	37.7740	1.59767
$560$	12.9343	0.546574
$561$	4.96715	0.209713
$562$	16.0743	0.678051
$563$	−11.1216	−0.468719	−0.234359	−	0.972150i	$-0.575299\pi$
$563$	−11.1216	−0.468719	−0.234359	+	0.972150i	$0.575299\pi$
$564$	47.1865	1.98691
$565$	−5.02318	−0.211327
$566$	8.72163	0.366598
$567$	−7.16581	−0.300936
$568$	−103.027	−4.32293
$569$	−28.3485	−1.18843	−0.594216	−	0.804306i	$-0.702538\pi$
$569$	−28.3485	−1.18843	−0.594216	+	0.804306i	$0.702538\pi$
$570$	1.03801	0.0434774
$571$	2.91136	0.121837	0.0609183	−	0.998143i	$-0.480597\pi$
$571$	2.91136	0.121837	0.0609183	+	0.998143i	$0.480597\pi$
$572$	−69.4457	−2.90367
$573$	−12.6214	−0.527266
$574$	−34.8173	−1.45324
$575$	−3.08583	−0.128688
$576$	−58.2557	−2.42732
$577$	−45.0163	−1.87405	−0.937027	−	0.349258i	$-0.886434\pi$
$577$	−45.0163	−1.87405	−0.937027	+	0.349258i	$0.886434\pi$
$578$	37.0327	1.54036
$579$	16.7153	0.694665
$580$	2.19360	0.0910842
$581$	19.5446	0.810846
$582$	−62.7553	−2.60129
$583$	17.7043	0.733235
$584$	−91.6353	−3.79190
$585$	2.84254	0.117525
$586$	56.5260	2.33507
$587$	−6.17879	−0.255026	−0.127513	−	0.991837i	$-0.540699\pi$
$587$	−6.17879	−0.255026	−0.127513	+	0.991837i	$0.540699\pi$
$588$	27.4462	1.13186
$589$	−1.76665	−0.0727935
$590$	−10.9666	−0.451489
$591$	−3.08449	−0.126879
$592$	−83.9568	−3.45060
$593$	−32.5067	−1.33489	−0.667446	−	0.744658i	$-0.732613\pi$
$593$	−32.5067	−1.33489	−0.667446	+	0.744658i	$0.732613\pi$
$594$	−30.2165	−1.23980
$595$	−1.36060	−0.0557791
$596$	−73.4233	−3.00754
$597$	5.52255	0.226023
$598$	11.0280	0.450968
$599$	−21.0144	−0.858626	−0.429313	−	0.903156i	$-0.641244\pi$
$599$	−21.0144	−0.858626	−0.429313	+	0.903156i	$0.641244\pi$
$600$	−69.7947	−2.84936
$601$	−34.8526	−1.42167	−0.710834	−	0.703359i	$-0.751682\pi$
$601$	−34.8526	−1.42167	−0.710834	+	0.703359i	$0.751682\pi$
$602$	31.8313	1.29735
$603$	−13.0955	−0.533290
$604$	−38.0299	−1.54742
$605$	−2.74995	−0.111801
$606$	−60.5999	−2.46170
$607$	2.88450	0.117078	0.0585391	−	0.998285i	$-0.481356\pi$
$607$	2.88450	0.117078	0.0585391	+	0.998285i	$0.481356\pi$
$608$	−22.3782	−0.907554
$609$	−2.48724	−0.100788
$610$	−11.4285	−0.462728
$611$	37.5300	1.51830
$612$	13.8833	0.561200
$613$	−18.6390	−0.752821	−0.376410	−	0.926453i	$-0.622842\pi$
$613$	−18.6390	−0.752821	−0.376410	+	0.926453i	$0.622842\pi$
$614$	−13.0503	−0.526666
$615$	−3.33488	−0.134475
$616$	−38.4982	−1.55114
$617$	0.764294	0.0307693	0.0153847	−	0.999882i	$-0.495103\pi$
$617$	0.764294	0.0307693	0.0153847	+	0.999882i	$0.495103\pi$
$618$	63.1620	2.54075
$619$	36.9566	1.48541	0.742705	−	0.669618i	$-0.233542\pi$
$619$	36.9566	1.48541	0.742705	+	0.669618i	$0.233542\pi$
$620$	−5.23289	−0.210158
$621$	3.57517	0.143467
$622$	−88.3160	−3.54115
$623$	31.0218	1.24286
$624$	152.774	6.11587
$625$	22.9075	0.916301
$626$	−81.5323	−3.25869
$627$	−1.89235	−0.0755733
$628$	−67.3168	−2.68623
$629$	8.83168	0.352142
$630$	2.39535	0.0954330
$631$	39.2792	1.56368	0.781840	−	0.623479i	$-0.214281\pi$
$631$	39.2792	1.56368	0.781840	+	0.623479i	$0.214281\pi$
$632$	−37.7517	−1.50168
$633$	3.77161	0.149908
$634$	83.5459	3.31803
$635$	2.98540	0.118472
$636$	−72.0191	−2.85574
$637$	21.8295	0.864915
$638$	−5.36731	−0.212494
$639$	−11.6864	−0.462309
$640$	−27.4380	−1.08458
$641$	28.6683	1.13233	0.566164	−	0.824293i	$-0.308427\pi$
$641$	28.6683	1.13233	0.566164	+	0.824293i	$0.308427\pi$
$642$	2.63132	0.103850
$643$	−17.1399	−0.675930	−0.337965	−	0.941159i	$-0.609739\pi$
$643$	−17.1399	−0.675930	−0.337965	+	0.941159i	$0.609739\pi$
$644$	6.92404	0.272846
$645$	3.04888	0.120050
$646$	4.03226	0.158647
$647$	6.85644	0.269555	0.134777	−	0.990876i	$-0.456968\pi$
$647$	6.85644	0.269555	0.134777	+	0.990876i	$0.456968\pi$
$648$	41.3816	1.62562
$649$	19.9929	0.784788
$650$	−84.3820	−3.30974
$651$	5.93337	0.232547
$652$	−14.0092	−0.548644
$653$	−13.2042	−0.516721	−0.258360	−	0.966049i	$-0.583182\pi$
$653$	−13.2042	−0.516721	−0.258360	+	0.966049i	$0.583182\pi$
$654$	−49.5856	−1.93895
$655$	6.43157	0.251302
$656$	123.152	4.80827
$657$	−10.3942	−0.405518
$658$	31.6257	1.23290
$659$	−13.3552	−0.520246	−0.260123	−	0.965575i	$-0.583763\pi$
$659$	−13.3552	−0.520246	−0.260123	+	0.965575i	$0.583763\pi$
$660$	−5.60523	−0.218183
$661$	−19.1857	−0.746237	−0.373119	−	0.927784i	$-0.621712\pi$
$661$	−19.1857	−0.746237	−0.373119	+	0.927784i	$0.621712\pi$
$662$	96.3289	3.74393
$663$	−16.0708	−0.624138
$664$	−112.867	−4.38010
$665$	0.518352	0.0201008
$666$	−15.5483	−0.602483
$667$	0.635052	0.0245893
$668$	120.759	4.67231
$669$	5.60226	0.216596
$670$	−11.2660	−0.435242
$671$	20.8349	0.804324
$672$	75.1581	2.89929
$673$	25.6209	0.987614	0.493807	−	0.869572i	$-0.335605\pi$
$673$	25.6209	0.987614	0.493807	+	0.869572i	$0.335605\pi$
$674$	−44.3352	−1.70773
$675$	−27.3559	−1.05293
$676$	148.694	5.71900
$677$	−24.3544	−0.936014	−0.468007	−	0.883725i	$-0.655028\pi$
$677$	−24.3544	−0.936014	−0.468007	+	0.883725i	$0.655028\pi$
$678$	−49.9975	−1.92014
$679$	−31.3382	−1.20265
$680$	7.85727	0.301313
$681$	−5.84056	−0.223811
$682$	12.8039	0.490285
$683$	−29.6057	−1.13283	−0.566415	−	0.824120i	$-0.691670\pi$
$683$	−29.6057	−1.13283	−0.566415	+	0.824120i	$0.691670\pi$
$684$	−5.28918	−0.202237
$685$	−5.90922	−0.225780
$686$	54.9661	2.09862
$687$	1.40956	0.0537780
$688$	−112.590	−4.29247
$689$	−57.2807	−2.18222
$690$	0.890110	0.0338859
$691$	36.1178	1.37399	0.686993	−	0.726664i	$-0.258930\pi$
$691$	36.1178	1.37399	0.686993	+	0.726664i	$0.258930\pi$
$692$	−69.7193	−2.65033
$693$	−4.36687	−0.165884
$694$	36.9218	1.40153
$695$	−2.68846	−0.101979
$696$	14.3635	0.544446
$697$	−12.9547	−0.490695
$698$	62.7941	2.37679
$699$	−12.0570	−0.456039
$700$	−52.9802	−2.00246
$701$	−5.05867	−0.191063	−0.0955317	−	0.995426i	$-0.530455\pi$
$701$	−5.05867	−0.191063	−0.0955317	+	0.995426i	$0.530455\pi$
$702$	97.7631	3.68983
$703$	−3.36464	−0.126900
$704$	91.3662	3.44349
$705$	3.02919	0.114086
$706$	46.9785	1.76806
$707$	−30.2619	−1.13812
$708$	−81.3289	−3.05653
$709$	−24.0990	−0.905055	−0.452528	−	0.891750i	$-0.649478\pi$
$709$	−24.0990	−0.905055	−0.452528	+	0.891750i	$0.649478\pi$
$710$	−10.0538	−0.377311
$711$	−4.28219	−0.160595
$712$	−179.147	−6.71381
$713$	−1.51493	−0.0567347
$714$	−13.5425	−0.506816
$715$	−4.45814	−0.166725
$716$	120.835	4.51580
$717$	23.4711	0.876544
$718$	20.3694	0.760179
$719$	−42.9476	−1.60167	−0.800837	−	0.598882i	$-0.795612\pi$
$719$	−42.9476	−1.60167	−0.800837	+	0.598882i	$0.795612\pi$
$720$	−8.47256	−0.315754
$721$	31.5413	1.17466
$722$	51.6826	1.92343
$723$	−0.435937	−0.0162127
$724$	−12.6215	−0.469074
$725$	−4.85918	−0.180465
$726$	−27.3712	−1.01584
$727$	−15.0916	−0.559718	−0.279859	−	0.960041i	$-0.590288\pi$
$727$	−15.0916	−0.559718	−0.279859	+	0.960041i	$0.590288\pi$
$728$	124.558	4.61642
$729$	27.2156	1.00798
$730$	−8.94208	−0.330961
$731$	11.8437	0.438056
$732$	−84.7544	−3.13261
$733$	−36.5087	−1.34848	−0.674239	−	0.738513i	$-0.735528\pi$
$733$	−36.5087	−1.34848	−0.674239	+	0.738513i	$0.735528\pi$
$734$	33.5438	1.23813
$735$	1.76194	0.0649901
$736$	−19.1897	−0.707341
$737$	20.5385	0.756547
$738$	22.8069	0.839534
$739$	−3.11875	−0.114725	−0.0573625	−	0.998353i	$-0.518269\pi$
$739$	−3.11875	−0.114725	−0.0573625	+	0.998353i	$0.518269\pi$
$740$	−9.96619	−0.366365
$741$	6.12255	0.224918
$742$	−48.2692	−1.77202
$743$	−9.05617	−0.332239	−0.166119	−	0.986106i	$-0.553124\pi$
$743$	−9.05617	−0.332239	−0.166119	+	0.986106i	$0.553124\pi$
$744$	−34.2644	−1.25620
$745$	−4.71348	−0.172689
$746$	67.5316	2.47251
$747$	−12.8026	−0.468423
$748$	−21.7741	−0.796141
$749$	1.31401	0.0480128
$750$	−13.8190	−0.504597
$751$	10.4658	0.381901	0.190950	−	0.981600i	$-0.438843\pi$
$751$	10.4658	0.381901	0.190950	+	0.981600i	$0.438843\pi$
$752$	−111.863	−4.07922
$753$	32.7520	1.19355
$754$	17.3655	0.632414
$755$	−2.44137	−0.0888505
$756$	61.3817	2.23243
$757$	−21.1230	−0.767728	−0.383864	−	0.923390i	$-0.625407\pi$
$757$	−21.1230	−0.767728	−0.383864	+	0.923390i	$0.625407\pi$
$758$	−1.76528	−0.0641179
$759$	−1.62273	−0.0589012
$760$	−2.99341	−0.108583
$761$	20.8184	0.754668	0.377334	−	0.926077i	$-0.376841\pi$
$761$	20.8184	0.754668	0.377334	+	0.926077i	$0.376841\pi$
$762$	29.7148	1.07645
$763$	−24.7616	−0.896431
$764$	55.3274	2.00167
$765$	0.891255	0.0322234
$766$	−55.7576	−2.01461
$767$	−64.6852	−2.33565
$768$	−145.937	−5.26606
$769$	−40.2036	−1.44978	−0.724889	−	0.688866i	$-0.758109\pi$
$769$	−40.2036	−1.44978	−0.724889	+	0.688866i	$0.758109\pi$
$770$	−3.75678	−0.135385
$771$	−24.0095	−0.864681
$772$	−73.2737	−2.63718
$773$	24.8786	0.894823	0.447411	−	0.894328i	$-0.352346\pi$
$773$	24.8786	0.894823	0.447411	+	0.894328i	$0.352346\pi$
$774$	−20.8510	−0.749474
$775$	11.5917	0.416386
$776$	180.974	6.49659
$777$	11.3003	0.405396
$778$	19.2319	0.689498
$779$	4.93540	0.176829
$780$	18.1353	0.649346
$781$	18.3286	0.655849
$782$	3.45773	0.123648
$783$	5.62974	0.201190
$784$	−65.0656	−2.32377
$785$	−4.32147	−0.154240
$786$	64.0157	2.28337
$787$	34.7655	1.23926	0.619628	−	0.784896i	$-0.287283\pi$
$787$	34.7655	1.23926	0.619628	+	0.784896i	$0.287283\pi$
$788$	13.5212	0.481674
$789$	−24.3377	−0.866445
$790$	−3.68393	−0.131068
$791$	−24.9674	−0.887737
$792$	25.2181	0.896085
$793$	−67.4097	−2.39379
$794$	−32.3397	−1.14769
$795$	−4.62334	−0.163973
$796$	−24.2088	−0.858058
$797$	12.7231	0.450676	0.225338	−	0.974281i	$-0.427651\pi$
$797$	12.7231	0.450676	0.225338	+	0.974281i	$0.427651\pi$
$798$	5.15935	0.182639
$799$	11.7672	0.416294
$800$	146.832	5.19130
$801$	−20.3207	−0.717997
$802$	38.3574	1.35445
$803$	16.3020	0.575284
$804$	−83.5487	−2.94653
$805$	0.444496	0.0156664
$806$	−41.4258	−1.45916
$807$	23.9689	0.843744
$808$	174.758	6.14798
$809$	25.3200	0.890202	0.445101	−	0.895480i	$-0.353168\pi$
$809$	25.3200	0.890202	0.445101	+	0.895480i	$0.353168\pi$
$810$	4.03815	0.141886
$811$	−11.0864	−0.389295	−0.194648	−	0.980873i	$-0.562356\pi$
$811$	−11.0864	−0.389295	−0.194648	+	0.980873i	$0.562356\pi$
$812$	10.9031	0.382625
$813$	32.8106	1.15072
$814$	24.3853	0.854706
$815$	−0.899337	−0.0315024
$816$	47.9011	1.67687
$817$	−4.51215	−0.157860
$818$	89.6622	3.13497
$819$	14.1286	0.493695
$820$	14.6189	0.510513
$821$	10.0852	0.351976	0.175988	−	0.984392i	$-0.443688\pi$
$821$	10.0852	0.351976	0.175988	+	0.984392i	$0.443688\pi$
$822$	−58.8166	−2.05146
$823$	1.34836	0.0470010	0.0235005	−	0.999724i	$-0.492519\pi$
$823$	1.34836	0.0470010	0.0235005	+	0.999724i	$0.492519\pi$
$824$	−182.147	−6.34539
$825$	12.4165	0.432287
$826$	−54.5089	−1.89661
$827$	5.21415	0.181314	0.0906569	−	0.995882i	$-0.471103\pi$
$827$	5.21415	0.181314	0.0906569	+	0.995882i	$0.471103\pi$
$828$	−4.53557	−0.157622
$829$	29.6204	1.02876	0.514380	−	0.857562i	$-0.328022\pi$
$829$	29.6204	1.02876	0.514380	+	0.857562i	$0.328022\pi$
$830$	−11.0140	−0.382301
$831$	−1.33349	−0.0462584
$832$	−295.608	−10.2484
$833$	6.84445	0.237146
$834$	−26.7592	−0.926595
$835$	7.75225	0.268278
$836$	8.29537	0.286901
$837$	−13.4299	−0.464205
$838$	−55.5873	−1.92023
$839$	−49.0644	−1.69389	−0.846946	−	0.531679i	$-0.821561\pi$
$839$	−49.0644	−1.69389	−0.846946	+	0.531679i	$0.821561\pi$
$840$	10.0535	0.346880
$841$	1.00000	0.0344828
$842$	−106.752	−3.67891
$843$	7.65262	0.263570
$844$	−16.5333	−0.569100
$845$	9.54556	0.328377
$846$	−20.7163	−0.712241
$847$	−13.6684	−0.469652
$848$	170.732	5.86298
$849$	4.15219	0.142503
$850$	−26.4573	−0.907477
$851$	−2.88523	−0.0989046
$852$	−74.5589	−2.55435
$853$	19.9548	0.683240	0.341620	−	0.939838i	$-0.389024\pi$
$853$	19.9548	0.683240	0.341620	+	0.939838i	$0.389024\pi$
$854$	−56.8047	−1.94382
$855$	−0.339545	−0.0116122
$856$	−7.58821	−0.259360
$857$	−23.5484	−0.804399	−0.402200	−	0.915552i	$-0.631754\pi$
$857$	−23.5484	−0.804399	−0.402200	+	0.915552i	$0.631754\pi$
$858$	−44.3735	−1.51489
$859$	−49.3302	−1.68312	−0.841562	−	0.540161i	$-0.818363\pi$
$859$	−49.3302	−1.68312	−0.841562	+	0.540161i	$0.818363\pi$
$860$	−13.3652	−0.455748
$861$	−16.5758	−0.564901
$862$	−81.9929	−2.79269
$863$	−36.9859	−1.25902	−0.629508	−	0.776994i	$-0.716744\pi$
$863$	−36.9859	−1.25902	−0.629508	+	0.776994i	$0.716744\pi$
$864$	−170.117	−5.78748
$865$	−4.47570	−0.152179
$866$	−81.3782	−2.76535
$867$	17.6305	0.598764
$868$	−26.0097	−0.882826
$869$	6.71604	0.227826
$870$	1.40163	0.0475199
$871$	−66.4508	−2.25160
$872$	142.995	4.84243
$873$	20.5280	0.694767
$874$	−1.31730	−0.0445585
$875$	−6.90081	−0.233290
$876$	−66.3147	−2.24057
$877$	−31.5007	−1.06370	−0.531852	−	0.846837i	$-0.678504\pi$
$877$	−31.5007	−1.06370	−0.531852	+	0.846837i	$0.678504\pi$
$878$	18.0622	0.609569
$879$	26.9109	0.907682
$880$	13.2881	0.447941
$881$	44.7806	1.50870	0.754349	−	0.656473i	$-0.227953\pi$
$881$	44.7806	1.50870	0.754349	+	0.656473i	$0.227953\pi$
$882$	−12.0497	−0.405735
$883$	−32.8679	−1.10609	−0.553046	−	0.833151i	$-0.686535\pi$
$883$	−32.8679	−1.10609	−0.553046	+	0.833151i	$0.686535\pi$
$884$	70.4484	2.36944
$885$	−5.22099	−0.175502
$886$	88.7368	2.98117
$887$	−41.6216	−1.39752	−0.698759	−	0.715357i	$-0.746264\pi$
$887$	−41.6216	−1.39752	−0.698759	+	0.715357i	$0.746264\pi$
$888$	−65.2577	−2.18990
$889$	14.8387	0.497675
$890$	−17.4817	−0.585989
$891$	−7.36180	−0.246630
$892$	−24.5582	−0.822270
$893$	−4.48300	−0.150018
$894$	−46.9150	−1.56907
$895$	7.75710	0.259291
$896$	−136.379	−4.55609
$897$	5.25020	0.175299
$898$	−112.017	−3.73807
$899$	−2.38553	−0.0795618
$900$	34.7045	1.15682
$901$	−17.9599	−0.598330
$902$	−35.7695	−1.19100
$903$	15.1543	0.504302
$904$	144.183	4.79546
$905$	−0.810250	−0.0269336
$906$	−24.2998	−0.807308
$907$	32.0906	1.06555	0.532775	−	0.846257i	$-0.321149\pi$
$907$	32.0906	1.06555	0.532775	+	0.846257i	$0.321149\pi$
$908$	25.6028	0.849659
$909$	19.8229	0.657485
$910$	12.1548	0.402926
$911$	−19.2220	−0.636854	−0.318427	−	0.947947i	$-0.603155\pi$
$911$	−19.2220	−0.636854	−0.318427	+	0.947947i	$0.603155\pi$
$912$	−18.2491	−0.604287
$913$	20.0792	0.664523
$914$	−83.5295	−2.76291
$915$	−5.44089	−0.179870
$916$	−6.17897	−0.204159
$917$	31.9677	1.05567
$918$	30.6528	1.01169
$919$	24.8686	0.820341	0.410170	−	0.912009i	$-0.365469\pi$
$919$	24.8686	0.820341	0.410170	+	0.912009i	$0.365469\pi$
$920$	−2.56691	−0.0846284
$921$	−6.21297	−0.204724
$922$	−107.736	−3.54811
$923$	−59.3007	−1.95191
$924$	−27.8604	−0.916540
$925$	22.0768	0.725879
$926$	4.00652	0.131662
$927$	−20.6610	−0.678596
$928$	−30.2175	−0.991938
$929$	3.91896	0.128577	0.0642884	−	0.997931i	$-0.479522\pi$
$929$	3.91896	0.128577	0.0642884	+	0.997931i	$0.479522\pi$
$930$	−3.34364	−0.109642
$931$	−2.60755	−0.0854592
$932$	52.8536	1.73128
$933$	−42.0454	−1.37651
$934$	25.2442	0.826015
$935$	−1.39781	−0.0457134
$936$	−81.5910	−2.66689
$937$	−30.4995	−0.996375	−0.498187	−	0.867069i	$-0.666001\pi$
$937$	−30.4995	−0.996375	−0.498187	+	0.867069i	$0.666001\pi$
$938$	−55.9966	−1.82836
$939$	−38.8159	−1.26671
$940$	−13.2788	−0.433107
$941$	18.5620	0.605105	0.302553	−	0.953133i	$-0.402161\pi$
$941$	18.5620	0.605105	0.302553	+	0.953133i	$0.402161\pi$
$942$	−43.0131	−1.40144
$943$	4.23220	0.137819
$944$	192.803	6.27520
$945$	3.94046	0.128183
$946$	32.7020	1.06323
$947$	−16.8906	−0.548869	−0.274435	−	0.961606i	$-0.588491\pi$
$947$	−16.8906	−0.548869	−0.274435	+	0.961606i	$0.588491\pi$
$948$	−27.3202	−0.887317
$949$	−52.7437	−1.71213
$950$	10.0795	0.327023
$951$	39.7745	1.28978
$952$	39.0540	1.26575
$953$	−7.22687	−0.234101	−0.117051	−	0.993126i	$-0.537344\pi$
$953$	−7.22687	−0.234101	−0.117051	+	0.993126i	$0.537344\pi$
$954$	31.6185	1.02369
$955$	3.55180	0.114934
$956$	−102.888	−3.32765
$957$	−2.55527	−0.0826001
$958$	−42.3180	−1.36723
$959$	−29.3714	−0.948451
$960$	−23.8596	−0.770066
$961$	−25.3093	−0.816428
$962$	−78.8968	−2.54373
$963$	−0.860735	−0.0277368
$964$	1.91099	0.0615487
$965$	−4.70388	−0.151423
$966$	4.42423	0.142347
$967$	−22.4252	−0.721146	−0.360573	−	0.932731i	$-0.617419\pi$
$967$	−22.4252	−0.721146	−0.360573	+	0.932731i	$0.617419\pi$
$968$	78.9332	2.53701
$969$	1.91968	0.0616689
$970$	17.6600	0.567030
$971$	47.2480	1.51626	0.758130	−	0.652104i	$-0.226113\pi$
$971$	47.2480	1.51626	0.758130	+	0.652104i	$0.226113\pi$
$972$	−68.7795	−2.20610
$973$	−13.3628	−0.428391
$974$	−35.5775	−1.13998
$975$	−40.1726	−1.28655
$976$	200.923	6.43140
$977$	−10.4506	−0.334346	−0.167173	−	0.985928i	$-0.553464\pi$
$977$	−10.4506	−0.334346	−0.167173	+	0.985928i	$0.553464\pi$
$978$	−8.95143	−0.286235
$979$	31.8703	1.01858
$980$	−7.72369	−0.246724
$981$	16.2200	0.517865
$982$	−30.5861	−0.976042
$983$	−13.1962	−0.420894	−0.210447	−	0.977605i	$-0.567492\pi$
$983$	−13.1962	−0.420894	−0.210447	+	0.977605i	$0.567492\pi$
$984$	95.7229	3.05154
$985$	0.868010	0.0276571
$986$	5.44480	0.173398
$987$	15.0564	0.479249
$988$	−26.8390	−0.853862
$989$	−3.86924	−0.123035
$990$	2.46086	0.0782114
$991$	41.0450	1.30384	0.651919	−	0.758288i	$-0.273964\pi$
$991$	41.0450	1.30384	0.651919	+	0.758288i	$0.273964\pi$
$992$	72.0847	2.28869
$993$	45.8602	1.45533
$994$	−49.9715	−1.58500
$995$	−1.55411	−0.0492686
$996$	−81.6799	−2.58813
$997$	−0.795622	−0.0251976	−0.0125988	−	0.999921i	$-0.504010\pi$
$997$	−0.795622	−0.0251976	−0.0125988	+	0.999921i	$0.504010\pi$
$998$	−24.4631	−0.774367
$999$	−25.5776	−0.809240

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.c.1.2	✓	154

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.c.1.2	✓	154	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:	\( N \)	\(=\)	\( 8033 = 29 \cdot 277 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.80099 q^{2} -1.33349 q^{3} +5.84554 q^{4} +0.375260 q^{5} +3.73510 q^{6} +1.86520 q^{7} -10.7713 q^{8} -1.22179 q^{9} +O(q^{10})\)	\(q-2.80099 q^{2} -1.33349 q^{3} +5.84554 q^{4} +0.375260 q^{5} +3.73510 q^{6} +1.86520 q^{7} -10.7713 q^{8} -1.22179 q^{9} -1.05110 q^{10} +1.91622 q^{11} -7.79499 q^{12} -6.19977 q^{13} -5.22442 q^{14} -0.500407 q^{15} +18.4792 q^{16} -1.94389 q^{17} +3.42223 q^{18} +0.740570 q^{19} +2.19360 q^{20} -2.48724 q^{21} -5.36731 q^{22} +0.635052 q^{23} +14.3635 q^{24} -4.85918 q^{25} +17.3655 q^{26} +5.62974 q^{27} +10.9031 q^{28} +1.00000 q^{29} +1.40163 q^{30} -2.38553 q^{31} -30.2175 q^{32} -2.55527 q^{33} +5.44480 q^{34} +0.699937 q^{35} -7.14205 q^{36} -4.54331 q^{37} -2.07433 q^{38} +8.26736 q^{39} -4.04204 q^{40} +6.66433 q^{41} +6.96673 q^{42} -6.09280 q^{43} +11.2013 q^{44} -0.458491 q^{45} -1.77877 q^{46} -6.05344 q^{47} -24.6419 q^{48} -3.52101 q^{49} +13.6105 q^{50} +2.59216 q^{51} -36.2410 q^{52} +9.23915 q^{53} -15.7688 q^{54} +0.719081 q^{55} -20.0907 q^{56} -0.987545 q^{57} -2.80099 q^{58} +10.4335 q^{59} -2.92515 q^{60} +10.8729 q^{61} +6.68183 q^{62} -2.27890 q^{63} +47.6804 q^{64} -2.32653 q^{65} +7.15727 q^{66} +10.7183 q^{67} -11.3631 q^{68} -0.846837 q^{69} -1.96052 q^{70} +9.56498 q^{71} +13.1603 q^{72} +8.50736 q^{73} +12.7258 q^{74} +6.47969 q^{75} +4.32903 q^{76} +3.57414 q^{77} -23.1568 q^{78} +3.50484 q^{79} +6.93452 q^{80} -3.84183 q^{81} -18.6667 q^{82} +10.4785 q^{83} -14.5392 q^{84} -0.729464 q^{85} +17.0659 q^{86} -1.33349 q^{87} -20.6402 q^{88} +16.6318 q^{89} +1.28423 q^{90} -11.5638 q^{91} +3.71222 q^{92} +3.18109 q^{93} +16.9556 q^{94} +0.277906 q^{95} +40.2948 q^{96} -16.8015 q^{97} +9.86232 q^{98} -2.34123 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9}+O(q^{10}) \) 154 * q - 12 * q^2 - 36 * q^3 + 142 * q^4 - 9 * q^5 - 11 * q^6 - 68 * q^7 - 33 * q^8 + 146 * q^9	\( 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9} - 40 q^{10} - 36 q^{11} - 67 q^{12} - 51 q^{13} - 19 q^{14} - 48 q^{15} + 122 q^{16} - 54 q^{17} - 46 q^{18} - 73 q^{19} - 21 q^{20} - 8 q^{21} - 23 q^{22} - 38 q^{23} - 17 q^{24} + 133 q^{25} - 20 q^{26} - 129 q^{27} - 99 q^{28} + 154 q^{29} - 10 q^{30} - 91 q^{31} - 88 q^{32} - 39 q^{33} - 42 q^{34} - 36 q^{35} + 101 q^{36} - 50 q^{37} - 17 q^{38} - 33 q^{39} - 92 q^{40} - 31 q^{41} - 62 q^{42} - 154 q^{43} - 42 q^{44} - 14 q^{45} - 24 q^{46} - 140 q^{47} - 118 q^{48} + 126 q^{49} - 5 q^{50} - 16 q^{51} - 133 q^{52} - 40 q^{53} + 14 q^{54} - 203 q^{55} - 44 q^{56} - 16 q^{57} - 12 q^{58} + 5 q^{59} - 28 q^{60} - 106 q^{61} - 30 q^{62} - 145 q^{63} + 111 q^{64} - 15 q^{65} - 49 q^{66} - 78 q^{67} - 118 q^{68} - 32 q^{69} - 43 q^{70} - 4 q^{71} - 152 q^{72} - 137 q^{73} + 9 q^{74} - 129 q^{75} - 204 q^{76} - 76 q^{77} + 15 q^{78} - 141 q^{79} - 44 q^{80} + 122 q^{81} - 71 q^{82} - 90 q^{83} + 92 q^{84} - 41 q^{85} + 9 q^{86} - 36 q^{87} - 109 q^{88} - 51 q^{89} - 82 q^{90} - 22 q^{91} - 8 q^{92} - 10 q^{93} - 106 q^{94} - 55 q^{95} - 49 q^{96} - 140 q^{97} - 4 q^{98} - 101 q^{99}+O(q^{100}) \) 154 * q - 12 * q^2 - 36 * q^3 + 142 * q^4 - 9 * q^5 - 11 * q^6 - 68 * q^7 - 33 * q^8 + 146 * q^9 - 40 * q^10 - 36 * q^11 - 67 * q^12 - 51 * q^13 - 19 * q^14 - 48 * q^15 + 122 * q^16 - 54 * q^17 - 46 * q^18 - 73 * q^19 - 21 * q^20 - 8 * q^21 - 23 * q^22 - 38 * q^23 - 17 * q^24 + 133 * q^25 - 20 * q^26 - 129 * q^27 - 99 * q^28 + 154 * q^29 - 10 * q^30 - 91 * q^31 - 88 * q^32 - 39 * q^33 - 42 * q^34 - 36 * q^35 + 101 * q^36 - 50 * q^37 - 17 * q^38 - 33 * q^39 - 92 * q^40 - 31 * q^41 - 62 * q^42 - 154 * q^43 - 42 * q^44 - 14 * q^45 - 24 * q^46 - 140 * q^47 - 118 * q^48 + 126 * q^49 - 5 * q^50 - 16 * q^51 - 133 * q^52 - 40 * q^53 + 14 * q^54 - 203 * q^55 - 44 * q^56 - 16 * q^57 - 12 * q^58 + 5 * q^59 - 28 * q^60 - 106 * q^61 - 30 * q^62 - 145 * q^63 + 111 * q^64 - 15 * q^65 - 49 * q^66 - 78 * q^67 - 118 * q^68 - 32 * q^69 - 43 * q^70 - 4 * q^71 - 152 * q^72 - 137 * q^73 + 9 * q^74 - 129 * q^75 - 204 * q^76 - 76 * q^77 + 15 * q^78 - 141 * q^79 - 44 * q^80 + 122 * q^81 - 71 * q^82 - 90 * q^83 + 92 * q^84 - 41 * q^85 + 9 * q^86 - 36 * q^87 - 109 * q^88 - 51 * q^89 - 82 * q^90 - 22 * q^91 - 8 * q^92 - 10 * q^93 - 106 * q^94 - 55 * q^95 - 49 * q^96 - 140 * q^97 - 4 * q^98 - 101 * q^99

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