LMFDB - Embedded newform 8033.2.a.c.1.8

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			1.8
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)

$f(q)$	$=$	$q-2.65912 q^{2} -0.292744 q^{3} +5.07094 q^{4} +3.25351 q^{5} +0.778443 q^{6} -0.266213 q^{7} -8.16600 q^{8} -2.91430 q^{9} +O(q^{10})$	\(q-2.65912 q^{2} -0.292744 q^{3} +5.07094 q^{4} +3.25351 q^{5} +0.778443 q^{6} -0.266213 q^{7} -8.16600 q^{8} -2.91430 q^{9} -8.65148 q^{10} -4.47155 q^{11} -1.48449 q^{12} +5.34766 q^{13} +0.707893 q^{14} -0.952446 q^{15} +11.5725 q^{16} +4.90544 q^{17} +7.74949 q^{18} -8.01609 q^{19} +16.4983 q^{20} +0.0779322 q^{21} +11.8904 q^{22} +2.84081 q^{23} +2.39055 q^{24} +5.58532 q^{25} -14.2201 q^{26} +1.73138 q^{27} -1.34995 q^{28} +1.00000 q^{29} +2.53267 q^{30} -5.70515 q^{31} -14.4408 q^{32} +1.30902 q^{33} -13.0442 q^{34} -0.866126 q^{35} -14.7782 q^{36} +11.1113 q^{37} +21.3158 q^{38} -1.56550 q^{39} -26.5682 q^{40} -7.74471 q^{41} -0.207231 q^{42} -5.41417 q^{43} -22.6749 q^{44} -9.48171 q^{45} -7.55407 q^{46} +3.11666 q^{47} -3.38779 q^{48} -6.92913 q^{49} -14.8521 q^{50} -1.43604 q^{51} +27.1177 q^{52} -8.92590 q^{53} -4.60394 q^{54} -14.5482 q^{55} +2.17389 q^{56} +2.34666 q^{57} -2.65912 q^{58} +1.85298 q^{59} -4.82979 q^{60} +3.20389 q^{61} +15.1707 q^{62} +0.775824 q^{63} +15.2548 q^{64} +17.3987 q^{65} -3.48084 q^{66} +8.62674 q^{67} +24.8752 q^{68} -0.831631 q^{69} +2.30314 q^{70} +1.27336 q^{71} +23.7982 q^{72} -8.03095 q^{73} -29.5464 q^{74} -1.63507 q^{75} -40.6491 q^{76} +1.19038 q^{77} +4.16285 q^{78} -5.08474 q^{79} +37.6513 q^{80} +8.23605 q^{81} +20.5941 q^{82} +12.6266 q^{83} +0.395189 q^{84} +15.9599 q^{85} +14.3969 q^{86} -0.292744 q^{87} +36.5147 q^{88} +17.0710 q^{89} +25.2130 q^{90} -1.42362 q^{91} +14.4056 q^{92} +1.67015 q^{93} -8.28759 q^{94} -26.0804 q^{95} +4.22745 q^{96} -5.81393 q^{97} +18.4254 q^{98} +13.0314 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.65912	−1.88028	−0.940142	−	0.340783i	$-0.889308\pi$
$2$	−2.65912	−1.88028	−0.940142	+	0.340783i	$0.889308\pi$
$3$	−0.292744	−0.169016	−0.0845079	−	0.996423i	$-0.526932\pi$
$3$	−0.292744	−0.169016	−0.0845079	+	0.996423i	$0.526932\pi$
$4$	5.07094	2.53547
$5$	3.25351	1.45501	0.727507	−	0.686100i	$-0.240679\pi$
$5$	3.25351	1.45501	0.727507	+	0.686100i	$0.240679\pi$
$6$	0.778443	0.317798
$7$	−0.266213	−0.100619	−0.0503095	−	0.998734i	$-0.516021\pi$
$7$	−0.266213	−0.100619	−0.0503095	+	0.998734i	$0.516021\pi$
$8$	−8.16600	−2.88712
$9$	−2.91430	−0.971434
$10$	−8.65148	−2.73584
$11$	−4.47155	−1.34822	−0.674111	−	0.738630i	$-0.735473\pi$
$11$	−4.47155	−1.34822	−0.674111	+	0.738630i	$0.735473\pi$
$12$	−1.48449	−0.428534
$13$	5.34766	1.48317	0.741587	−	0.670856i	$-0.234073\pi$
$13$	5.34766	1.48317	0.741587	+	0.670856i	$0.234073\pi$
$14$	0.707893	0.189192
$15$	−0.952446	−0.245920
$16$	11.5725	2.89313
$17$	4.90544	1.18974	0.594871	−	0.803821i	$-0.297203\pi$
$17$	4.90544	1.18974	0.594871	+	0.803821i	$0.297203\pi$
$18$	7.74949	1.82657
$19$	−8.01609	−1.83902	−0.919509	−	0.393069i	$-0.871413\pi$
$19$	−8.01609	−1.83902	−0.919509	+	0.393069i	$0.871413\pi$
$20$	16.4983	3.68914
$21$	0.0779322	0.0170062
$22$	11.8904	2.53504
$23$	2.84081	0.592350	0.296175	−	0.955134i	$-0.404289\pi$
$23$	2.84081	0.592350	0.296175	+	0.955134i	$0.404289\pi$
$24$	2.39055	0.487969
$25$	5.58532	1.11706
$26$	−14.2201	−2.78879
$27$	1.73138	0.333204
$28$	−1.34995	−0.255116
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	2.53267	0.462400
$31$	−5.70515	−1.02468	−0.512338	−	0.858784i	$-0.671220\pi$
$31$	−5.70515	−1.02468	−0.512338	+	0.858784i	$0.671220\pi$
$32$	−14.4408	−2.55279
$33$	1.30902	0.227871
$34$	−13.0442	−2.23705
$35$	−0.866126	−0.146402
$36$	−14.7782	−2.46304
$37$	11.1113	1.82669	0.913345	−	0.407187i	$-0.133490\pi$
$37$	11.1113	1.82669	0.913345	+	0.407187i	$0.133490\pi$
$38$	21.3158	3.45788
$39$	−1.56550	−0.250680
$40$	−26.5682	−4.20079
$41$	−7.74471	−1.20952	−0.604760	−	0.796408i	$-0.706731\pi$
$41$	−7.74471	−1.20952	−0.604760	+	0.796408i	$0.706731\pi$
$42$	−0.207231	−0.0319765
$43$	−5.41417	−0.825653	−0.412826	−	0.910810i	$-0.635458\pi$
$43$	−5.41417	−0.825653	−0.412826	+	0.910810i	$0.635458\pi$
$44$	−22.6749	−3.41838
$45$	−9.48171	−1.41345
$46$	−7.55407	−1.11379
$47$	3.11666	0.454612	0.227306	−	0.973823i	$-0.427008\pi$
$47$	3.11666	0.454612	0.227306	+	0.973823i	$0.427008\pi$
$48$	−3.38779	−0.488985
$49$	−6.92913	−0.989876
$50$	−14.8521	−2.10040
$51$	−1.43604	−0.201085
$52$	27.1177	3.76054
$53$	−8.92590	−1.22607	−0.613033	−	0.790057i	$-0.710051\pi$
$53$	−8.92590	−1.22607	−0.613033	+	0.790057i	$0.710051\pi$
$54$	−4.60394	−0.626517
$55$	−14.5482	−1.96168
$56$	2.17389	0.290499
$57$	2.34666	0.310823
$58$	−2.65912	−0.349160
$59$	1.85298	0.241238	0.120619	−	0.992699i	$-0.461512\pi$
$59$	1.85298	0.241238	0.120619	+	0.992699i	$0.461512\pi$
$60$	−4.82979	−0.623523
$61$	3.20389	0.410217	0.205108	−	0.978739i	$-0.434245\pi$
$61$	3.20389	0.410217	0.205108	+	0.978739i	$0.434245\pi$
$62$	15.1707	1.92668
$63$	0.775824	0.0977447
$64$	15.2548	1.90685
$65$	17.3987	2.15804
$66$	−3.48084	−0.428462
$67$	8.62674	1.05392	0.526962	−	0.849889i	$-0.323331\pi$
$67$	8.62674	1.05392	0.526962	+	0.849889i	$0.323331\pi$
$68$	24.8752	3.01656
$69$	−0.831631	−0.100117
$70$	2.30314	0.275277
$71$	1.27336	0.151120	0.0755602	−	0.997141i	$-0.475926\pi$
$71$	1.27336	0.151120	0.0755602	+	0.997141i	$0.475926\pi$
$72$	23.7982	2.80464
$73$	−8.03095	−0.939951	−0.469976	−	0.882679i	$-0.655737\pi$
$73$	−8.03095	−0.939951	−0.469976	+	0.882679i	$0.655737\pi$
$74$	−29.5464	−3.43470
$75$	−1.63507	−0.188802
$76$	−40.6491	−4.66277
$77$	1.19038	0.135657
$78$	4.16285	0.471350
$79$	−5.08474	−0.572078	−0.286039	−	0.958218i	$-0.592339\pi$
$79$	−5.08474	−0.572078	−0.286039	+	0.958218i	$0.592339\pi$
$80$	37.6513	4.20955
$81$	8.23605	0.915117
$82$	20.5941	2.27424
$83$	12.6266	1.38595	0.692975	−	0.720962i	$-0.256300\pi$
$83$	12.6266	1.38595	0.692975	+	0.720962i	$0.256300\pi$
$84$	0.395189	0.0431187
$85$	15.9599	1.73109
$86$	14.3969	1.55246
$87$	−0.292744	−0.0313855
$88$	36.5147	3.89248
$89$	17.0710	1.80952	0.904760	−	0.425921i	$-0.140050\pi$
$89$	17.0710	1.80952	0.904760	+	0.425921i	$0.140050\pi$
$90$	25.2130	2.65769
$91$	−1.42362	−0.149236
$92$	14.4056	1.50189
$93$	1.67015	0.173187
$94$	−8.28759	−0.854799
$95$	−26.0804	−2.67580
$96$	4.22745	0.431463
$97$	−5.81393	−0.590316	−0.295158	−	0.955449i	$-0.595372\pi$
$97$	−5.81393	−0.590316	−0.295158	+	0.955449i	$0.595372\pi$
$98$	18.4254	1.86125
$99$	13.0314	1.30971
$100$	28.3228	2.83228
$101$	−15.7923	−1.57139	−0.785697	−	0.618612i	$-0.787695\pi$
$101$	−15.7923	−1.57139	−0.785697	+	0.618612i	$0.787695\pi$
$102$	3.81860	0.378098
$103$	2.19563	0.216342	0.108171	−	0.994132i	$-0.465501\pi$
$103$	2.19563	0.216342	0.108171	+	0.994132i	$0.465501\pi$
$104$	−43.6690	−4.28210
$105$	0.253553	0.0247443
$106$	23.7351	2.30535
$107$	−9.92024	−0.959026	−0.479513	−	0.877535i	$-0.659187\pi$
$107$	−9.92024	−0.959026	−0.479513	+	0.877535i	$0.659187\pi$
$108$	8.77970	0.844827
$109$	−9.64430	−0.923756	−0.461878	−	0.886943i	$-0.652824\pi$
$109$	−9.64430	−0.923756	−0.461878	+	0.886943i	$0.652824\pi$
$110$	38.6855	3.68852
$111$	−3.25277	−0.308740
$112$	−3.08076	−0.291104
$113$	8.13933	0.765684	0.382842	−	0.923814i	$-0.374945\pi$
$113$	8.13933	0.765684	0.382842	+	0.923814i	$0.374945\pi$
$114$	−6.24007	−0.584436
$115$	9.24261	0.861878
$116$	5.07094	0.470825
$117$	−15.5847	−1.44081
$118$	−4.92730	−0.453595
$119$	−1.30589	−0.119711
$120$	7.77767	0.710001
$121$	8.99475	0.817705
$122$	−8.51955	−0.771324
$123$	2.26722	0.204428
$124$	−28.9305	−2.59803
$125$	1.90435	0.170331
$126$	−2.06301	−0.183788
$127$	−7.66055	−0.679764	−0.339882	−	0.940468i	$-0.610387\pi$
$127$	−7.66055	−0.679764	−0.339882	+	0.940468i	$0.610387\pi$
$128$	−11.6827	−1.03262
$129$	1.58496	0.139548
$130$	−46.2652	−4.05773
$131$	13.6840	1.19558	0.597789	−	0.801653i	$-0.296046\pi$
$131$	13.6840	1.19558	0.597789	+	0.801653i	$0.296046\pi$
$132$	6.63796	0.577760
$133$	2.13399	0.185040
$134$	−22.9396	−1.98168
$135$	5.63305	0.484816
$136$	−40.0578	−3.43493
$137$	7.14460	0.610404	0.305202	−	0.952288i	$-0.401276\pi$
$137$	7.14460	0.610404	0.305202	+	0.952288i	$0.401276\pi$
$138$	2.21141	0.188248
$139$	3.66187	0.310596	0.155298	−	0.987868i	$-0.450366\pi$
$139$	3.66187	0.310596	0.155298	+	0.987868i	$0.450366\pi$
$140$	−4.39207	−0.371198
$141$	−0.912384	−0.0768366
$142$	−3.38603	−0.284149
$143$	−23.9123	−1.99965
$144$	−33.7258	−2.81049
$145$	3.25351	0.270189
$146$	21.3553	1.76738
$147$	2.02846	0.167305
$148$	56.3448	4.63151
$149$	−6.76743	−0.554409	−0.277205	−	0.960811i	$-0.589408\pi$
$149$	−6.76743	−0.554409	−0.277205	+	0.960811i	$0.589408\pi$
$150$	4.34785	0.355001
$151$	−10.0406	−0.817089	−0.408545	−	0.912738i	$-0.633964\pi$
$151$	−10.0406	−0.817089	−0.408545	+	0.912738i	$0.633964\pi$
$152$	65.4594	5.30946
$153$	−14.2959	−1.15576
$154$	−3.16538	−0.255073
$155$	−18.5618	−1.49092
$156$	−7.93853	−0.635591
$157$	−11.5125	−0.918799	−0.459400	−	0.888230i	$-0.651935\pi$
$157$	−11.5125	−0.918799	−0.459400	+	0.888230i	$0.651935\pi$
$158$	13.5210	1.07567
$159$	2.61300	0.207225
$160$	−46.9832	−3.71435
$161$	−0.756261	−0.0596017
$162$	−21.9007	−1.72068
$163$	−1.46354	−0.114633	−0.0573165	−	0.998356i	$-0.518254\pi$
$163$	−1.46354	−0.114633	−0.0573165	+	0.998356i	$0.518254\pi$
$164$	−39.2729	−3.06670
$165$	4.25891	0.331555
$166$	−33.5757	−2.60598
$167$	−17.4298	−1.34876	−0.674381	−	0.738384i	$-0.735589\pi$
$167$	−17.4298	−1.34876	−0.674381	+	0.738384i	$0.735589\pi$
$168$	−0.636395	−0.0490989
$169$	15.5975	1.19981
$170$	−42.4393	−3.25495
$171$	23.3613	1.78648
$172$	−27.4549	−2.09342
$173$	20.0268	1.52261	0.761303	−	0.648396i	$-0.224560\pi$
$173$	20.0268	1.52261	0.761303	+	0.648396i	$0.224560\pi$
$174$	0.778443	0.0590136
$175$	−1.48688	−0.112398
$176$	−51.7471	−3.90059
$177$	−0.542449	−0.0407730
$178$	−45.3938	−3.40241
$179$	−7.52911	−0.562752	−0.281376	−	0.959598i	$-0.590791\pi$
$179$	−7.52911	−0.562752	−0.281376	+	0.959598i	$0.590791\pi$
$180$	−48.0811	−3.58376
$181$	−9.02563	−0.670870	−0.335435	−	0.942063i	$-0.608883\pi$
$181$	−9.02563	−0.670870	−0.335435	+	0.942063i	$0.608883\pi$
$182$	3.78557	0.280605
$183$	−0.937921	−0.0693331
$184$	−23.1981	−1.71019
$185$	36.1508	2.65786
$186$	−4.44114	−0.325640
$187$	−21.9349	−1.60404
$188$	15.8044	1.15265
$189$	−0.460915	−0.0335266
$190$	69.3511	5.03126
$191$	−22.3564	−1.61765	−0.808825	−	0.588049i	$-0.799896\pi$
$191$	−22.3564	−1.61765	−0.808825	+	0.588049i	$0.799896\pi$
$192$	−4.46574	−0.322287
$193$	−8.00994	−0.576568	−0.288284	−	0.957545i	$-0.593085\pi$
$193$	−8.00994	−0.576568	−0.288284	+	0.957545i	$0.593085\pi$
$194$	15.4600	1.10996
$195$	−5.09336	−0.364743
$196$	−35.1372	−2.50980
$197$	2.10018	0.149632	0.0748160	−	0.997197i	$-0.476163\pi$
$197$	2.10018	0.149632	0.0748160	+	0.997197i	$0.476163\pi$
$198$	−34.6522	−2.46263
$199$	25.4156	1.80166	0.900831	−	0.434169i	$-0.142958\pi$
$199$	25.4156	1.80166	0.900831	+	0.434169i	$0.142958\pi$
$200$	−45.6097	−3.22510
$201$	−2.52543	−0.178130
$202$	41.9937	2.95467
$203$	−0.266213	−0.0186845
$204$	−7.28205	−0.509846
$205$	−25.1975	−1.75987
$206$	−5.83846	−0.406785
$207$	−8.27898	−0.575429
$208$	61.8860	4.29102
$209$	35.8444	2.47941
$210$	−0.674229	−0.0465262
$211$	2.16778	0.149236	0.0746180	−	0.997212i	$-0.476226\pi$
$211$	2.16778	0.149236	0.0746180	+	0.997212i	$0.476226\pi$
$212$	−45.2627	−3.10865
$213$	−0.372769	−0.0255417
$214$	26.3792	1.80324
$215$	−17.6150	−1.20134
$216$	−14.1384	−0.961998
$217$	1.51879	0.103102
$218$	25.6454	1.73692
$219$	2.35101	0.158867
$220$	−73.7731	−4.97378
$221$	26.2326	1.76460
$222$	8.64952	0.580518
$223$	−19.1887	−1.28497	−0.642486	−	0.766297i	$-0.722097\pi$
$223$	−19.1887	−1.28497	−0.642486	+	0.766297i	$0.722097\pi$
$224$	3.84432	0.256860
$225$	−16.2773	−1.08515
$226$	−21.6435	−1.43970
$227$	6.58127	0.436814	0.218407	−	0.975858i	$-0.429914\pi$
$227$	6.58127	0.436814	0.218407	+	0.975858i	$0.429914\pi$
$228$	11.8998	0.788082
$229$	−21.2519	−1.40436	−0.702182	−	0.711997i	$-0.747791\pi$
$229$	−21.2519	−1.40436	−0.702182	+	0.711997i	$0.747791\pi$
$230$	−24.5772	−1.62058
$231$	−0.348478	−0.0229282
$232$	−8.16600	−0.536124
$233$	15.8714	1.03977	0.519884	−	0.854237i	$-0.325975\pi$
$233$	15.8714	1.03977	0.519884	+	0.854237i	$0.325975\pi$
$234$	41.4416	2.70912
$235$	10.1401	0.661466
$236$	9.39635	0.611650
$237$	1.48853	0.0966903
$238$	3.47252	0.225090
$239$	−23.4833	−1.51901	−0.759503	−	0.650504i	$-0.774558\pi$
$239$	−23.4833	−1.51901	−0.759503	+	0.650504i	$0.774558\pi$
$240$	−11.0222	−0.711480
$241$	−0.781343	−0.0503307	−0.0251654	−	0.999683i	$-0.508011\pi$
$241$	−0.781343	−0.0503307	−0.0251654	+	0.999683i	$0.508011\pi$
$242$	−23.9182	−1.53752
$243$	−7.60518	−0.487873
$244$	16.2467	1.04009
$245$	−22.5440	−1.44028
$246$	−6.02881	−0.384383
$247$	−42.8674	−2.72758
$248$	46.5883	2.95836
$249$	−3.69636	−0.234247
$250$	−5.06391	−0.320270
$251$	−28.5343	−1.80107	−0.900535	−	0.434783i	$-0.856825\pi$
$251$	−28.5343	−1.80107	−0.900535	+	0.434783i	$0.856825\pi$
$252$	3.93416	0.247829
$253$	−12.7028	−0.798620
$254$	20.3703	1.27815
$255$	−4.67216	−0.292582
$256$	0.556294	0.0347684
$257$	−28.5313	−1.77974	−0.889868	−	0.456219i	$-0.849203\pi$
$257$	−28.5313	−1.77974	−0.889868	+	0.456219i	$0.849203\pi$
$258$	−4.21462	−0.262391
$259$	−2.95798	−0.183800
$260$	88.2276	5.47164
$261$	−2.91430	−0.180391
$262$	−36.3875	−2.24803
$263$	23.8815	1.47260	0.736298	−	0.676657i	$-0.236572\pi$
$263$	23.8815	1.47260	0.736298	+	0.676657i	$0.236572\pi$
$264$	−10.6895	−0.657890
$265$	−29.0405	−1.78394
$266$	−5.67453	−0.347928
$267$	−4.99743	−0.305838
$268$	43.7457	2.67219
$269$	−10.5640	−0.644100	−0.322050	−	0.946723i	$-0.604372\pi$
$269$	−10.5640	−0.644100	−0.322050	+	0.946723i	$0.604372\pi$
$270$	−14.9790	−0.911591
$271$	5.63383	0.342231	0.171115	−	0.985251i	$-0.445263\pi$
$271$	5.63383	0.342231	0.171115	+	0.985251i	$0.445263\pi$
$272$	56.7683	3.44208
$273$	0.416755	0.0252232
$274$	−18.9984	−1.14773
$275$	−24.9750	−1.50605
$276$	−4.21715	−0.253843
$277$	1.00000	0.0600842
$277$	1.00000	0.0600842
$278$	−9.73736	−0.584008
$279$	16.6265	0.995405
$280$	7.07278	0.422680
$281$	12.8287	0.765297	0.382648	−	0.923894i	$-0.375012\pi$
$281$	12.8287	0.765297	0.382648	+	0.923894i	$0.375012\pi$
$282$	2.42614	0.144475
$283$	−5.90860	−0.351230	−0.175615	−	0.984459i	$-0.556191\pi$
$283$	−5.90860	−0.351230	−0.175615	+	0.984459i	$0.556191\pi$
$284$	6.45714	0.383161
$285$	7.63489	0.452252
$286$	63.5858	3.75991
$287$	2.06174	0.121701
$288$	42.0848	2.47987
$289$	7.06330	0.415488
$290$	−8.65148	−0.508033
$291$	1.70199	0.0997727
$292$	−40.7244	−2.38322
$293$	20.7442	1.21189	0.605944	−	0.795507i	$-0.292796\pi$
$293$	20.7442	1.21189	0.605944	+	0.795507i	$0.292796\pi$
$294$	−5.39393	−0.314580
$295$	6.02869	0.351004
$296$	−90.7350	−5.27387
$297$	−7.74194	−0.449233
$298$	17.9954	1.04245
$299$	15.1917	0.878559
$300$	−8.29134	−0.478701
$301$	1.44132	0.0830763
$302$	26.6991	1.53636
$303$	4.62310	0.265590
$304$	−92.7665	−5.32052
$305$	10.4239	0.596871
$306$	38.0146	2.17315
$307$	−17.6319	−1.00631	−0.503154	−	0.864197i	$-0.667827\pi$
$307$	−17.6319	−1.00631	−0.503154	+	0.864197i	$0.667827\pi$
$308$	6.03636	0.343954
$309$	−0.642759	−0.0365653
$310$	49.3580	2.80335
$311$	−4.54417	−0.257676	−0.128838	−	0.991666i	$-0.541125\pi$
$311$	−4.54417	−0.257676	−0.128838	+	0.991666i	$0.541125\pi$
$312$	12.7838	0.723743
$313$	−2.96383	−0.167526	−0.0837628	−	0.996486i	$-0.526694\pi$
$313$	−2.96383	−0.167526	−0.0837628	+	0.996486i	$0.526694\pi$
$314$	30.6132	1.72760
$315$	2.52415	0.142220
$316$	−25.7844	−1.45049
$317$	22.8222	1.28182	0.640912	−	0.767615i	$-0.278557\pi$
$317$	22.8222	1.28182	0.640912	+	0.767615i	$0.278557\pi$
$318$	−6.94830	−0.389641
$319$	−4.47155	−0.250359
$320$	49.6315	2.77449
$321$	2.90409	0.162091
$322$	2.01099	0.112068
$323$	−39.3224	−2.18796
$324$	41.7645	2.32025
$325$	29.8684	1.65680
$326$	3.89172	0.215543
$327$	2.82331	0.156129
$328$	63.2433	3.49203
$329$	−0.829695	−0.0457426
$330$	−11.3250	−0.623418
$331$	0.425080	0.0233645	0.0116823	−	0.999932i	$-0.496281\pi$
$331$	0.425080	0.0233645	0.0116823	+	0.999932i	$0.496281\pi$
$332$	64.0287	3.51403
$333$	−32.3817	−1.77451
$334$	46.3481	2.53605
$335$	28.0672	1.53347
$336$	0.901873	0.0492012
$337$	0.879694	0.0479200	0.0239600	−	0.999713i	$-0.492373\pi$
$337$	0.879694	0.0479200	0.0239600	+	0.999713i	$0.492373\pi$
$338$	−41.4757	−2.25598
$339$	−2.38274	−0.129413
$340$	80.9316	4.38913
$341$	25.5109	1.38149
$342$	−62.1206	−3.35910
$343$	3.70811	0.200219
$344$	44.2121	2.38376
$345$	−2.70572	−0.145671
$346$	−53.2536	−2.86293
$347$	−11.9030	−0.638985	−0.319492	−	0.947589i	$-0.603512\pi$
$347$	−11.9030	−0.638985	−0.319492	+	0.947589i	$0.603512\pi$
$348$	−1.48449	−0.0795768
$349$	−14.5602	−0.779392	−0.389696	−	0.920943i	$-0.627420\pi$
$349$	−14.5602	−0.779392	−0.389696	+	0.920943i	$0.627420\pi$
$350$	3.95381	0.211340
$351$	9.25882	0.494199
$352$	64.5727	3.44173
$353$	7.54430	0.401542	0.200771	−	0.979638i	$-0.435655\pi$
$353$	7.54430	0.401542	0.200771	+	0.979638i	$0.435655\pi$
$354$	1.44244	0.0766648
$355$	4.14290	0.219882
$356$	86.5659	4.58798
$357$	0.382292	0.0202330
$358$	20.0208	1.05813
$359$	−0.203929	−0.0107629	−0.00538147	−	0.999986i	$-0.501713\pi$
$359$	−0.203929	−0.0107629	−0.00538147	+	0.999986i	$0.501713\pi$
$360$	77.4276	4.08079
$361$	45.2577	2.38199
$362$	24.0003	1.26143
$363$	−2.63316	−0.138205
$364$	−7.21907	−0.378382
$365$	−26.1288	−1.36764
$366$	2.49405	0.130366
$367$	−6.06732	−0.316711	−0.158356	−	0.987382i	$-0.550619\pi$
$367$	−6.06732	−0.316711	−0.158356	+	0.987382i	$0.550619\pi$
$368$	32.8754	1.71375
$369$	22.5704	1.17497
$370$	−96.1294	−4.99753
$371$	2.37619	0.123366
$372$	8.46923	0.439109
$373$	−22.7843	−1.17972	−0.589862	−	0.807504i	$-0.700818\pi$
$373$	−22.7843	−1.17972	−0.589862	+	0.807504i	$0.700818\pi$
$374$	58.3276	3.01605
$375$	−0.557488	−0.0287886
$376$	−25.4507	−1.31252
$377$	5.34766	0.275419
$378$	1.22563	0.0630395
$379$	−18.6865	−0.959860	−0.479930	−	0.877307i	$-0.659338\pi$
$379$	−18.6865	−0.959860	−0.479930	+	0.877307i	$0.659338\pi$
$380$	−132.252	−6.78440
$381$	2.24258	0.114891
$382$	59.4484	3.04164
$383$	−18.6288	−0.951889	−0.475945	−	0.879475i	$-0.657894\pi$
$383$	−18.6288	−0.951889	−0.475945	+	0.879475i	$0.657894\pi$
$384$	3.42005	0.174529
$385$	3.87292	0.197383
$386$	21.2994	1.08411
$387$	15.7785	0.802067
$388$	−29.4821	−1.49673
$389$	22.4358	1.13754	0.568771	−	0.822496i	$-0.307419\pi$
$389$	22.4358	1.13754	0.568771	+	0.822496i	$0.307419\pi$
$390$	13.5439	0.685820
$391$	13.9354	0.704745
$392$	56.5833	2.85789
$393$	−4.00592	−0.202072
$394$	−5.58465	−0.281351
$395$	−16.5433	−0.832381
$396$	66.0816	3.32073
$397$	−17.5297	−0.879790	−0.439895	−	0.898049i	$-0.644984\pi$
$397$	−17.5297	−0.879790	−0.439895	+	0.898049i	$0.644984\pi$
$398$	−67.5832	−3.38764
$399$	−0.624712	−0.0312747
$400$	64.6363	3.23182
$401$	26.4363	1.32017	0.660083	−	0.751192i	$-0.270521\pi$
$401$	26.4363	1.32017	0.660083	+	0.751192i	$0.270521\pi$
$402$	6.71542	0.334935
$403$	−30.5092	−1.51977
$404$	−80.0818	−3.98422
$405$	26.7961	1.33151
$406$	0.707893	0.0351321
$407$	−49.6848	−2.46278
$408$	11.7267	0.580557
$409$	−25.2471	−1.24839	−0.624195	−	0.781269i	$-0.714573\pi$
$409$	−25.2471	−1.24839	−0.624195	+	0.781269i	$0.714573\pi$
$410$	67.0032	3.30905
$411$	−2.09154	−0.103168
$412$	11.1339	0.548529
$413$	−0.493287	−0.0242731
$414$	22.0148	1.08197
$415$	41.0808	2.01658
$416$	−77.2244	−3.78624
$417$	−1.07199	−0.0524956
$418$	−95.3146	−4.66199
$419$	−33.4958	−1.63638	−0.818188	−	0.574951i	$-0.805021\pi$
$419$	−33.4958	−1.63638	−0.818188	+	0.574951i	$0.805021\pi$
$420$	1.28575	0.0627383
$421$	15.3556	0.748384	0.374192	−	0.927351i	$-0.377920\pi$
$421$	15.3556	0.748384	0.374192	+	0.927351i	$0.377920\pi$
$422$	−5.76439	−0.280606
$423$	−9.08289	−0.441625
$424$	72.8889	3.53980
$425$	27.3984	1.32902
$426$	0.991240	0.0480257
$427$	−0.852918	−0.0412756
$428$	−50.3049	−2.43158
$429$	7.00019	0.337973
$430$	46.8406	2.25885
$431$	28.9113	1.39261	0.696304	−	0.717747i	$-0.254827\pi$
$431$	28.9113	1.39261	0.696304	+	0.717747i	$0.254827\pi$
$432$	20.0364	0.964002
$433$	−21.0271	−1.01050	−0.505249	−	0.862974i	$-0.668599\pi$
$433$	−21.0271	−1.01050	−0.505249	+	0.862974i	$0.668599\pi$
$434$	−4.03864	−0.193861
$435$	−0.952446	−0.0456663
$436$	−48.9056	−2.34215
$437$	−22.7722	−1.08934
$438$	−6.25163	−0.298715
$439$	−41.4613	−1.97884	−0.989421	−	0.145072i	$-0.953659\pi$
$439$	−41.4613	−1.97884	−0.989421	+	0.145072i	$0.953659\pi$
$440$	118.801	5.66361
$441$	20.1936	0.961599
$442$	−69.7558	−3.31794
$443$	13.9509	0.662825	0.331413	−	0.943486i	$-0.392475\pi$
$443$	13.9509	0.662825	0.331413	+	0.943486i	$0.392475\pi$
$444$	−16.4946	−0.782799
$445$	55.5406	2.63288
$446$	51.0252	2.41611
$447$	1.98112	0.0937039
$448$	−4.06101	−0.191865
$449$	24.4409	1.15344	0.576719	−	0.816942i	$-0.304333\pi$
$449$	24.4409	1.15344	0.576719	+	0.816942i	$0.304333\pi$
$450$	43.2834	2.04040
$451$	34.6308	1.63070
$452$	41.2740	1.94137
$453$	2.93931	0.138101
$454$	−17.5004	−0.821335
$455$	−4.63175	−0.217140
$456$	−19.1629	−0.897383
$457$	29.9501	1.40101	0.700503	−	0.713650i	$-0.252959\pi$
$457$	29.9501	1.40101	0.700503	+	0.713650i	$0.252959\pi$
$458$	56.5114	2.64060
$459$	8.49316	0.396427
$460$	46.8687	2.18526
$461$	−26.4687	−1.23277	−0.616385	−	0.787445i	$-0.711403\pi$
$461$	−26.4687	−1.23277	−0.616385	+	0.787445i	$0.711403\pi$
$462$	0.926645	0.0431114
$463$	27.8419	1.29392	0.646961	−	0.762523i	$-0.276040\pi$
$463$	27.8419	1.29392	0.646961	+	0.762523i	$0.276040\pi$
$464$	11.5725	0.537241
$465$	5.43385	0.251989
$466$	−42.2039	−1.95506
$467$	41.8184	1.93513	0.967563	−	0.252629i	$-0.0812954\pi$
$467$	41.8184	1.93513	0.967563	+	0.252629i	$0.0812954\pi$
$468$	−79.0290	−3.65312
$469$	−2.29655	−0.106045
$470$	−26.9637	−1.24374
$471$	3.37022	0.155292
$472$	−15.1314	−0.696481
$473$	24.2097	1.11316
$474$	−3.95818	−0.181805
$475$	−44.7725	−2.05430
$476$	−6.62209	−0.303523
$477$	26.0128	1.19104
$478$	62.4449	2.85616
$479$	−0.635005	−0.0290141	−0.0145071	−	0.999895i	$-0.504618\pi$
$479$	−0.635005	−0.0290141	−0.0145071	+	0.999895i	$0.504618\pi$
$480$	13.7541	0.627784
$481$	59.4196	2.70930
$482$	2.07769	0.0946361
$483$	0.221391	0.0100736
$484$	45.6118	2.07326
$485$	−18.9157	−0.858917
$486$	20.2231	0.917340
$487$	29.7437	1.34782	0.673908	−	0.738815i	$-0.264614\pi$
$487$	29.7437	1.34782	0.673908	+	0.738815i	$0.264614\pi$
$488$	−26.1630	−1.18434
$489$	0.428442	0.0193748
$490$	59.9473	2.70814
$491$	−19.5289	−0.881326	−0.440663	−	0.897673i	$-0.645257\pi$
$491$	−19.5289	−0.881326	−0.440663	+	0.897673i	$0.645257\pi$
$492$	11.4969	0.518321
$493$	4.90544	0.220930
$494$	113.990	5.12863
$495$	42.3979	1.90564
$496$	−66.0231	−2.96452
$497$	−0.338986	−0.0152056
$498$	9.82908	0.440452
$499$	−24.1760	−1.08226	−0.541132	−	0.840938i	$-0.682004\pi$
$499$	−24.1760	−1.08226	−0.541132	+	0.840938i	$0.682004\pi$
$500$	9.65686	0.431868
$501$	5.10248	0.227962
$502$	75.8763	3.38652
$503$	−23.8261	−1.06235	−0.531176	−	0.847262i	$-0.678250\pi$
$503$	−23.8261	−1.06235	−0.531176	+	0.847262i	$0.678250\pi$
$504$	−6.33538	−0.282200
$505$	−51.3804	−2.28640
$506$	33.7784	1.50163
$507$	−4.56607	−0.202786
$508$	−38.8462	−1.72352
$509$	−23.3507	−1.03500	−0.517500	−	0.855683i	$-0.673137\pi$
$509$	−23.3507	−1.03500	−0.517500	+	0.855683i	$0.673137\pi$
$510$	12.4239	0.550137
$511$	2.13794	0.0945770
$512$	21.8862	0.967243
$513$	−13.8789	−0.612767
$514$	75.8683	3.34641
$515$	7.14352	0.314781
$516$	8.03726	0.353821
$517$	−13.9363	−0.612918
$518$	7.86562	0.345596
$519$	−5.86272	−0.257345
$520$	−142.078	−6.23051
$521$	4.69787	0.205817	0.102909	−	0.994691i	$-0.467185\pi$
$521$	4.69787	0.205817	0.102909	+	0.994691i	$0.467185\pi$
$522$	7.74949	0.339186
$523$	−19.0417	−0.832634	−0.416317	−	0.909219i	$-0.636679\pi$
$523$	−19.0417	−0.832634	−0.416317	+	0.909219i	$0.636679\pi$
$524$	69.3908	3.03135
$525$	0.435277	0.0189970
$526$	−63.5039	−2.76890
$527$	−27.9863	−1.21910
$528$	15.1487	0.659261
$529$	−14.9298	−0.649121
$530$	77.2223	3.35432
$531$	−5.40014	−0.234346
$532$	10.8213	0.469163
$533$	−41.4161	−1.79393
$534$	13.2888	0.575062
$535$	−32.2756	−1.39540
$536$	−70.4460	−3.04280
$537$	2.20410	0.0951140
$538$	28.0910	1.21109
$539$	30.9839	1.33457
$540$	28.5648	1.22923
$541$	13.6809	0.588190	0.294095	−	0.955776i	$-0.404982\pi$
$541$	13.6809	0.588190	0.294095	+	0.955776i	$0.404982\pi$
$542$	−14.9810	−0.643491
$543$	2.64220	0.113388
$544$	−70.8383	−3.03717
$545$	−31.3778	−1.34408
$546$	−1.10820	−0.0474267
$547$	−29.4925	−1.26101	−0.630504	−	0.776186i	$-0.717152\pi$
$547$	−29.4925	−1.26101	−0.630504	+	0.776186i	$0.717152\pi$
$548$	36.2298	1.54766
$549$	−9.33711	−0.398498
$550$	66.4117	2.83181
$551$	−8.01609	−0.341497
$552$	6.79110	0.289048
$553$	1.35362	0.0575619
$554$	−2.65912	−0.112975
$555$	−10.5829	−0.449220
$556$	18.5691	0.787505
$557$	23.8481	1.01048	0.505239	−	0.862980i	$-0.331404\pi$
$557$	23.8481	1.01048	0.505239	+	0.862980i	$0.331404\pi$
$558$	−44.2120	−1.87164
$559$	−28.9531	−1.22459
$560$	−10.0233	−0.423560
$561$	6.42131	0.271108
$562$	−34.1131	−1.43898
$563$	−3.74693	−0.157914	−0.0789571	−	0.996878i	$-0.525159\pi$
$563$	−3.74693	−0.157914	−0.0789571	+	0.996878i	$0.525159\pi$
$564$	−4.62664	−0.194817
$565$	26.4814	1.11408
$566$	15.7117	0.660412
$567$	−2.19254	−0.0920781
$568$	−10.3983	−0.436302
$569$	9.98325	0.418520	0.209260	−	0.977860i	$-0.432895\pi$
$569$	9.98325	0.418520	0.209260	+	0.977860i	$0.432895\pi$
$570$	−20.3021	−0.850362
$571$	−12.6684	−0.530156	−0.265078	−	0.964227i	$-0.585398\pi$
$571$	−12.6684	−0.530156	−0.265078	+	0.964227i	$0.585398\pi$
$572$	−121.258	−5.07005
$573$	6.54470	0.273409
$574$	−5.48242	−0.228832
$575$	15.8669	0.661694
$576$	−44.4570	−1.85237
$577$	−9.19408	−0.382754	−0.191377	−	0.981517i	$-0.561295\pi$
$577$	−9.19408	−0.382754	−0.191377	+	0.981517i	$0.561295\pi$
$578$	−18.7822	−0.781236
$579$	2.34486	0.0974492
$580$	16.4983	0.685056
$581$	−3.36136	−0.139453
$582$	−4.52581	−0.187601
$583$	39.9126	1.65301
$584$	65.5807	2.71375
$585$	−50.7050	−2.09639
$586$	−55.1613	−2.27869
$587$	24.0949	0.994503	0.497252	−	0.867606i	$-0.334343\pi$
$587$	24.0949	0.994503	0.497252	+	0.867606i	$0.334343\pi$
$588$	10.2862	0.424196
$589$	45.7330	1.88440
$590$	−16.0310	−0.659987
$591$	−0.614817	−0.0252902
$592$	128.586	5.28485
$593$	−26.2299	−1.07713	−0.538566	−	0.842584i	$-0.681034\pi$
$593$	−26.2299	−1.07713	−0.538566	+	0.842584i	$0.681034\pi$
$594$	20.5868	0.844685
$595$	−4.24872	−0.174181
$596$	−34.3172	−1.40569
$597$	−7.44026	−0.304510
$598$	−40.3966	−1.65194
$599$	−23.7446	−0.970177	−0.485088	−	0.874465i	$-0.661213\pi$
$599$	−23.7446	−0.970177	−0.485088	+	0.874465i	$0.661213\pi$
$600$	13.3520	0.545092
$601$	−17.8560	−0.728363	−0.364181	−	0.931328i	$-0.618651\pi$
$601$	−17.8560	−0.728363	−0.364181	+	0.931328i	$0.618651\pi$
$602$	−3.83265	−0.156207
$603$	−25.1409	−1.02382
$604$	−50.9150	−2.07170
$605$	29.2645	1.18977
$606$	−12.2934	−0.499385
$607$	−23.4514	−0.951861	−0.475931	−	0.879483i	$-0.657889\pi$
$607$	−23.4514	−0.951861	−0.475931	+	0.879483i	$0.657889\pi$
$608$	115.759	4.69463
$609$	0.0779322	0.00315797
$610$	−27.7184	−1.12229
$611$	16.6669	0.674269
$612$	−72.4937	−2.93038
$613$	8.58612	0.346790	0.173395	−	0.984852i	$-0.444526\pi$
$613$	8.58612	0.346790	0.173395	+	0.984852i	$0.444526\pi$
$614$	46.8855	1.89215
$615$	7.37641	0.297446
$616$	−9.72067	−0.391657
$617$	−19.2661	−0.775622	−0.387811	−	0.921739i	$-0.626769\pi$
$617$	−19.2661	−0.775622	−0.387811	+	0.921739i	$0.626769\pi$
$618$	1.70918	0.0687531
$619$	−16.4029	−0.659286	−0.329643	−	0.944106i	$-0.606928\pi$
$619$	−16.4029	−0.659286	−0.329643	+	0.944106i	$0.606928\pi$
$620$	−94.1256	−3.78017
$621$	4.91852	0.197373
$622$	12.0835	0.484505
$623$	−4.54451	−0.182072
$624$	−18.1168	−0.725251
$625$	−21.7308	−0.869231
$626$	7.88119	0.314996
$627$	−10.4932	−0.419059
$628$	−58.3793	−2.32959
$629$	54.5059	2.17329
$630$	−6.71203	−0.267414
$631$	−4.94532	−0.196870	−0.0984350	−	0.995143i	$-0.531384\pi$
$631$	−4.94532	−0.196870	−0.0984350	+	0.995143i	$0.531384\pi$
$632$	41.5220	1.65166
$633$	−0.634604	−0.0252233
$634$	−60.6871	−2.41019
$635$	−24.9237	−0.989065
$636$	13.2504	0.525412
$637$	−37.0546	−1.46816
$638$	11.8904	0.470745
$639$	−3.71096	−0.146803
$640$	−38.0099	−1.50247
$641$	−35.3645	−1.39681	−0.698406	−	0.715702i	$-0.746107\pi$
$641$	−35.3645	−1.39681	−0.698406	+	0.715702i	$0.746107\pi$
$642$	−7.72234	−0.304776
$643$	20.7870	0.819759	0.409879	−	0.912140i	$-0.365571\pi$
$643$	20.7870	0.819759	0.409879	+	0.912140i	$0.365571\pi$
$644$	−3.83495	−0.151118
$645$	5.15670	0.203045
$646$	104.563	4.11398
$647$	−15.8322	−0.622430	−0.311215	−	0.950340i	$-0.600736\pi$
$647$	−15.8322	−0.622430	−0.311215	+	0.950340i	$0.600736\pi$
$648$	−67.2556	−2.64205
$649$	−8.28569	−0.325242
$650$	−79.4238	−3.11526
$651$	−0.444615	−0.0174259
$652$	−7.42150	−0.290648
$653$	−36.8735	−1.44297	−0.721486	−	0.692429i	$-0.756541\pi$
$653$	−36.8735	−1.44297	−0.721486	+	0.692429i	$0.756541\pi$
$654$	−7.50753	−0.293568
$655$	44.5211	1.73958
$656$	−89.6258	−3.49930
$657$	23.4046	0.913100
$658$	2.20626	0.0860090
$659$	−10.4264	−0.406155	−0.203078	−	0.979163i	$-0.565094\pi$
$659$	−10.4264	−0.406155	−0.203078	+	0.979163i	$0.565094\pi$
$660$	21.5966	0.840648
$661$	26.7926	1.04211	0.521056	−	0.853523i	$-0.325538\pi$
$661$	26.7926	1.04211	0.521056	+	0.853523i	$0.325538\pi$
$662$	−1.13034	−0.0439320
$663$	−7.67944	−0.298245
$664$	−103.109	−4.00140
$665$	6.94295	0.269236
$666$	86.1070	3.33658
$667$	2.84081	0.109997
$668$	−88.3856	−3.41974
$669$	5.61739	0.217181
$670$	−74.6341	−2.88337
$671$	−14.3264	−0.553063
$672$	−1.12540	−0.0434133
$673$	5.65011	0.217796	0.108898	−	0.994053i	$-0.465268\pi$
$673$	5.65011	0.217796	0.108898	+	0.994053i	$0.465268\pi$
$674$	−2.33922	−0.0901032
$675$	9.67030	0.372210
$676$	79.0939	3.04207
$677$	−21.1001	−0.810943	−0.405471	−	0.914108i	$-0.632893\pi$
$677$	−21.1001	−0.810943	−0.405471	+	0.914108i	$0.632893\pi$
$678$	6.33600	0.243333
$679$	1.54774	0.0593970
$680$	−130.328	−4.99787
$681$	−1.92663	−0.0738285
$682$	−67.8366	−2.59760
$683$	17.3841	0.665186	0.332593	−	0.943070i	$-0.392077\pi$
$683$	17.3841	0.665186	0.332593	+	0.943070i	$0.392077\pi$
$684$	118.464	4.52957
$685$	23.2450	0.888147
$686$	−9.86033	−0.376469
$687$	6.22136	0.237360
$688$	−62.6556	−2.38872
$689$	−47.7327	−1.81847
$690$	7.19484	0.273903
$691$	23.9782	0.912174	0.456087	−	0.889935i	$-0.349251\pi$
$691$	23.9782	0.912174	0.456087	+	0.889935i	$0.349251\pi$
$692$	101.554	3.86052
$693$	−3.46914	−0.131782
$694$	31.6515	1.20147
$695$	11.9139	0.451921
$696$	2.39055	0.0906135
$697$	−37.9912	−1.43902
$698$	38.7175	1.46548
$699$	−4.64625	−0.175737
$700$	−7.53990	−0.284981
$701$	−9.51888	−0.359523	−0.179762	−	0.983710i	$-0.557533\pi$
$701$	−9.51888	−0.359523	−0.179762	+	0.983710i	$0.557533\pi$
$702$	−24.6203	−0.929235
$703$	−89.0694	−3.35931
$704$	−68.2124	−2.57085
$705$	−2.96845	−0.111798
$706$	−20.0612	−0.755014
$707$	4.20411	0.158112
$708$	−2.75073	−0.103379
$709$	−1.91764	−0.0720185	−0.0360092	−	0.999351i	$-0.511465\pi$
$709$	−1.91764	−0.0720185	−0.0360092	+	0.999351i	$0.511465\pi$
$710$	−11.0165	−0.413441
$711$	14.8185	0.555736
$712$	−139.402	−5.22430
$713$	−16.2073	−0.606967
$714$	−1.01656	−0.0380438
$715$	−77.7990	−2.90952
$716$	−38.1796	−1.42684
$717$	6.87459	0.256736
$718$	0.542272	0.0202374
$719$	−46.5002	−1.73416	−0.867082	−	0.498166i	$-0.834007\pi$
$719$	−46.5002	−1.73416	−0.867082	+	0.498166i	$0.834007\pi$
$720$	−109.727	−4.08930
$721$	−0.584506	−0.0217681
$722$	−120.346	−4.47881
$723$	0.228734	0.00850669
$724$	−45.7684	−1.70097
$725$	5.58532	0.207434
$726$	7.00190	0.259865
$727$	−9.75843	−0.361920	−0.180960	−	0.983490i	$-0.557920\pi$
$727$	−9.75843	−0.361920	−0.180960	+	0.983490i	$0.557920\pi$
$728$	11.6253	0.430860
$729$	−22.4818	−0.832659
$730$	69.4796	2.57156
$731$	−26.5588	−0.982314
$732$	−4.75614	−0.175792
$733$	42.6577	1.57560	0.787800	−	0.615932i	$-0.211220\pi$
$733$	42.6577	1.57560	0.787800	+	0.615932i	$0.211220\pi$
$734$	16.1337	0.595507
$735$	6.59962	0.243431
$736$	−41.0236	−1.51215
$737$	−38.5749	−1.42092
$738$	−60.0175	−2.20927
$739$	48.4959	1.78395	0.891975	−	0.452084i	$-0.149319\pi$
$739$	48.4959	1.78395	0.891975	+	0.452084i	$0.149319\pi$
$740$	183.318	6.73892
$741$	12.5492	0.461005
$742$	−6.31858	−0.231962
$743$	−23.4390	−0.859894	−0.429947	−	0.902854i	$-0.641468\pi$
$743$	−23.4390	−0.859894	−0.429947	+	0.902854i	$0.641468\pi$
$744$	−13.6384	−0.500010
$745$	−22.0179	−0.806673
$746$	60.5861	2.21822
$747$	−36.7977	−1.34636
$748$	−111.230	−4.06699
$749$	2.64090	0.0964963
$750$	1.48243	0.0541307
$751$	34.8276	1.27088	0.635439	−	0.772151i	$-0.280819\pi$
$751$	34.8276	1.27088	0.635439	+	0.772151i	$0.280819\pi$
$752$	36.0677	1.31525
$753$	8.35325	0.304409
$754$	−14.2201	−0.517865
$755$	−32.6671	−1.18888
$756$	−2.33727	−0.0850057
$757$	39.9151	1.45074	0.725370	−	0.688359i	$-0.241669\pi$
$757$	39.9151	1.45074	0.725370	+	0.688359i	$0.241669\pi$
$758$	49.6897	1.80481
$759$	3.71868	0.134980
$760$	212.973	7.72534
$761$	−46.3763	−1.68114	−0.840569	−	0.541705i	$-0.817779\pi$
$761$	−46.3763	−1.68114	−0.840569	+	0.541705i	$0.817779\pi$
$762$	−5.96330	−0.216027
$763$	2.56744	0.0929474
$764$	−113.368	−4.10150
$765$	−46.5119	−1.68164
$766$	49.5364	1.78982
$767$	9.90911	0.357797
$768$	−0.162852	−0.00587641
$769$	−22.7628	−0.820847	−0.410423	−	0.911895i	$-0.634619\pi$
$769$	−22.7628	−0.820847	−0.410423	+	0.911895i	$0.634619\pi$
$770$	−10.2986	−0.371135
$771$	8.35238	0.300803
$772$	−40.6179	−1.46187
$773$	18.7041	0.672741	0.336370	−	0.941730i	$-0.390801\pi$
$773$	18.7041	0.672741	0.336370	+	0.941730i	$0.390801\pi$
$774$	−41.9570	−1.50811
$775$	−31.8651	−1.14463
$776$	47.4766	1.70431
$777$	0.865930	0.0310651
$778$	−59.6597	−2.13890
$779$	62.0823	2.22433
$780$	−25.8281	−0.924794
$781$	−5.69390	−0.203744
$782$	−37.0560	−1.32512
$783$	1.73138	0.0618743
$784$	−80.1876	−2.86384
$785$	−37.4561	−1.33687
$786$	10.6522	0.379952
$787$	−40.1886	−1.43257	−0.716285	−	0.697808i	$-0.754159\pi$
$787$	−40.1886	−1.43257	−0.716285	+	0.697808i	$0.754159\pi$
$788$	10.6499	0.379387
$789$	−6.99117	−0.248892
$790$	43.9906	1.56511
$791$	−2.16679	−0.0770423
$792$	−106.415	−3.78128
$793$	17.1333	0.608423
$794$	46.6136	1.65426
$795$	8.50143	0.301515
$796$	128.881	4.56806
$797$	27.7731	0.983772	0.491886	−	0.870660i	$-0.336308\pi$
$797$	27.7731	0.983772	0.491886	+	0.870660i	$0.336308\pi$
$798$	1.66119	0.0588054
$799$	15.2886	0.540871
$800$	−80.6564	−2.85164
$801$	−49.7500	−1.75783
$802$	−70.2974	−2.48229
$803$	35.9108	1.26726
$804$	−12.8063	−0.451643
$805$	−2.46050	−0.0867213
$806$	81.1278	2.85761
$807$	3.09256	0.108863
$808$	128.960	4.53680
$809$	−3.47547	−0.122191	−0.0610955	−	0.998132i	$-0.519459\pi$
$809$	−3.47547	−0.122191	−0.0610955	+	0.998132i	$0.519459\pi$
$810$	−71.2541	−2.50361
$811$	−38.5961	−1.35529	−0.677645	−	0.735389i	$-0.737000\pi$
$811$	−38.5961	−1.35529	−0.677645	+	0.735389i	$0.737000\pi$
$812$	−1.34995	−0.0473739
$813$	−1.64927	−0.0578424
$814$	132.118	4.63073
$815$	−4.76163	−0.166793
$816$	−16.6186	−0.581767
$817$	43.4005	1.51839
$818$	67.1352	2.34733
$819$	4.14885	0.144972
$820$	−127.775	−4.46209
$821$	−1.90023	−0.0663185	−0.0331592	−	0.999450i	$-0.510557\pi$
$821$	−1.90023	−0.0663185	−0.0331592	+	0.999450i	$0.510557\pi$
$822$	5.56166	0.193985
$823$	−19.4892	−0.679351	−0.339675	−	0.940543i	$-0.610317\pi$
$823$	−19.4892	−0.679351	−0.339675	+	0.940543i	$0.610317\pi$
$824$	−17.9296	−0.624606
$825$	7.31130	0.254547
$826$	1.31171	0.0456403
$827$	−18.2196	−0.633559	−0.316780	−	0.948499i	$-0.602602\pi$
$827$	−18.2196	−0.633559	−0.316780	+	0.948499i	$0.602602\pi$
$828$	−41.9822	−1.45898
$829$	33.0119	1.14655	0.573274	−	0.819363i	$-0.305673\pi$
$829$	33.0119	1.14655	0.573274	+	0.819363i	$0.305673\pi$
$830$	−109.239	−3.79174
$831$	−0.292744	−0.0101552
$832$	81.5773	2.82818
$833$	−33.9904	−1.17770
$834$	2.85055	0.0987066
$835$	−56.7081	−1.96247
$836$	181.764	6.28646
$837$	−9.87777	−0.341426
$838$	89.0694	3.07685
$839$	55.5560	1.91800	0.959002	−	0.283398i	$-0.0914617\pi$
$839$	55.5560	1.91800	0.959002	+	0.283398i	$0.0914617\pi$
$840$	−2.07052	−0.0714396
$841$	1.00000	0.0344828
$842$	−40.8323	−1.40718
$843$	−3.75553	−0.129347
$844$	10.9927	0.378383
$845$	50.7466	1.74574
$846$	24.1525	0.830381
$847$	−2.39452	−0.0822766
$848$	−103.295	−3.54717
$849$	1.72971	0.0593635
$850$	−72.8558	−2.49893
$851$	31.5652	1.08204
$852$	−1.89029	−0.0647603
$853$	29.7441	1.01842	0.509209	−	0.860643i	$-0.329938\pi$
$853$	29.7441	1.01842	0.509209	+	0.860643i	$0.329938\pi$
$854$	2.26801	0.0776098
$855$	76.0062	2.59936
$856$	81.0087	2.76882
$857$	33.7513	1.15292	0.576461	−	0.817125i	$-0.304433\pi$
$857$	33.7513	1.15292	0.576461	+	0.817125i	$0.304433\pi$
$858$	−18.6144	−0.635484
$859$	−17.7729	−0.606403	−0.303201	−	0.952927i	$-0.598055\pi$
$859$	−17.7729	−0.606403	−0.303201	+	0.952927i	$0.598055\pi$
$860$	−89.3248	−3.04595
$861$	−0.603562	−0.0205693
$862$	−76.8786	−2.61850
$863$	48.3758	1.64673	0.823365	−	0.567512i	$-0.192094\pi$
$863$	48.3758	1.64673	0.823365	+	0.567512i	$0.192094\pi$
$864$	−25.0024	−0.850600
$865$	65.1572	2.21541
$866$	55.9136	1.90002
$867$	−2.06774	−0.0702241
$868$	7.70166	0.261412
$869$	22.7367	0.771289
$870$	2.53267	0.0858656
$871$	46.1329	1.56315
$872$	78.7553	2.66699
$873$	16.9436	0.573452
$874$	60.5541	2.04827
$875$	−0.506963	−0.0171385
$876$	11.9218	0.402802
$877$	13.7775	0.465232	0.232616	−	0.972569i	$-0.425271\pi$
$877$	13.7775	0.465232	0.232616	+	0.972569i	$0.425271\pi$
$878$	110.251	3.72079
$879$	−6.07274	−0.204828
$880$	−168.360	−5.67541
$881$	34.7291	1.17005	0.585026	−	0.811014i	$-0.301084\pi$
$881$	34.7291	1.17005	0.585026	+	0.811014i	$0.301084\pi$
$882$	−53.6972	−1.80808
$883$	−32.3721	−1.08941	−0.544704	−	0.838628i	$-0.683358\pi$
$883$	−32.3721	−1.08941	−0.544704	+	0.838628i	$0.683358\pi$
$884$	133.024	4.47408
$885$	−1.76486	−0.0593252
$886$	−37.0970	−1.24630
$887$	14.1803	0.476129	0.238064	−	0.971249i	$-0.423487\pi$
$887$	14.1803	0.476129	0.238064	+	0.971249i	$0.423487\pi$
$888$	26.5621	0.891367
$889$	2.03934	0.0683971
$890$	−147.689	−4.95056
$891$	−36.8279	−1.23378
$892$	−97.3049	−3.25801
$893$	−24.9834	−0.836039
$894$	−5.26805	−0.176190
$895$	−24.4960	−0.818811
$896$	3.11009	0.103901
$897$	−4.44728	−0.148490
$898$	−64.9915	−2.16879
$899$	−5.70515	−0.190278
$900$	−82.5412	−2.75137
$901$	−43.7854	−1.45870
$902$	−92.0877	−3.06618
$903$	−0.421938	−0.0140412
$904$	−66.4658	−2.21062
$905$	−29.3650	−0.976125
$906$	−7.81600	−0.259669
$907$	7.84792	0.260586	0.130293	−	0.991476i	$-0.458408\pi$
$907$	7.84792	0.260586	0.130293	+	0.991476i	$0.458408\pi$
$908$	33.3732	1.10753
$909$	46.0235	1.52650
$910$	12.3164	0.408284
$911$	−38.7191	−1.28282	−0.641411	−	0.767198i	$-0.721651\pi$
$911$	−38.7191	−1.28282	−0.641411	+	0.767198i	$0.721651\pi$
$912$	27.1568	0.899253
$913$	−56.4605	−1.86857
$914$	−79.6410	−2.63429
$915$	−3.05154	−0.100881
$916$	−107.767	−3.56072
$917$	−3.64286	−0.120298
$918$	−22.5843	−0.745395
$919$	−15.8299	−0.522182	−0.261091	−	0.965314i	$-0.584082\pi$
$919$	−15.8299	−0.522182	−0.261091	+	0.965314i	$0.584082\pi$
$920$	−75.4752	−2.48834
$921$	5.16165	0.170082
$922$	70.3835	2.31796
$923$	6.80951	0.224138
$924$	−1.76711	−0.0581336
$925$	62.0603	2.04053
$926$	−74.0350	−2.43294
$927$	−6.39874	−0.210162
$928$	−14.4408	−0.474042
$929$	40.8806	1.34125	0.670625	−	0.741797i	$-0.266026\pi$
$929$	40.8806	1.34125	0.670625	+	0.741797i	$0.266026\pi$
$930$	−14.4493	−0.473810
$931$	55.5446	1.82040
$932$	80.4827	2.63630
$933$	1.33028	0.0435514
$934$	−111.200	−3.63859
$935$	−71.3654	−2.33390
$936$	127.265	4.15977
$937$	−27.9046	−0.911604	−0.455802	−	0.890081i	$-0.650648\pi$
$937$	−27.9046	−0.911604	−0.455802	+	0.890081i	$0.650648\pi$
$938$	6.10681	0.199394
$939$	0.867643	0.0283145
$940$	51.4197	1.67713
$941$	−25.9326	−0.845380	−0.422690	−	0.906274i	$-0.638914\pi$
$941$	−25.9326	−0.845380	−0.422690	+	0.906274i	$0.638914\pi$
$942$	−8.96184	−0.291992
$943$	−22.0013	−0.716460
$944$	21.4437	0.697932
$945$	−1.49959	−0.0487817
$946$	−64.3766	−2.09306
$947$	16.9648	0.551281	0.275640	−	0.961261i	$-0.411110\pi$
$947$	16.9648	0.551281	0.275640	+	0.961261i	$0.411110\pi$
$948$	7.54823	0.245155
$949$	−42.9468	−1.39411
$950$	119.056	3.86267
$951$	−6.68107	−0.216648
$952$	10.6639	0.345619
$953$	−0.407900	−0.0132132	−0.00660659	−	0.999978i	$-0.502103\pi$
$953$	−0.407900	−0.0132132	−0.00660659	+	0.999978i	$0.502103\pi$
$954$	−69.1711	−2.23950
$955$	−72.7367	−2.35370
$956$	−119.082	−3.85139
$957$	1.30902	0.0423146
$958$	1.68856	0.0545548
$959$	−1.90198	−0.0614183
$960$	−14.5293	−0.468932
$961$	1.54879	0.0499609
$962$	−158.004	−5.09425
$963$	28.9106	0.931630
$964$	−3.96214	−0.127612
$965$	−26.0604	−0.838914
$966$	−0.588706	−0.0189413
$967$	−58.2639	−1.87364	−0.936820	−	0.349811i	$-0.886246\pi$
$967$	−58.2639	−1.87364	−0.936820	+	0.349811i	$0.886246\pi$
$968$	−73.4511	−2.36081
$969$	11.5114	0.369800
$970$	50.2991	1.61501
$971$	1.62770	0.0522355	0.0261178	−	0.999659i	$-0.491686\pi$
$971$	1.62770	0.0522355	0.0261178	+	0.999659i	$0.491686\pi$
$972$	−38.5654	−1.23699
$973$	−0.974836	−0.0312518
$974$	−79.0922	−2.53428
$975$	−8.74380	−0.280026
$976$	37.0772	1.18681
$977$	49.7931	1.59302	0.796511	−	0.604624i	$-0.206677\pi$
$977$	49.7931	1.59302	0.796511	+	0.604624i	$0.206677\pi$
$978$	−1.13928	−0.0364301
$979$	−76.3337	−2.43964
$980$	−114.319	−3.65179
$981$	28.1064	0.897368
$982$	51.9297	1.65714
$983$	−41.2358	−1.31522	−0.657609	−	0.753359i	$-0.728432\pi$
$983$	−41.2358	−1.31522	−0.657609	+	0.753359i	$0.728432\pi$
$984$	−18.5141	−0.590208
$985$	6.83297	0.217717
$986$	−13.0442	−0.415411
$987$	0.242888	0.00773122
$988$	−217.378	−6.91570
$989$	−15.3806	−0.489076
$990$	−112.741	−3.58315
$991$	31.6485	1.00535	0.502674	−	0.864476i	$-0.332349\pi$
$991$	31.6485	1.00535	0.502674	+	0.864476i	$0.332349\pi$
$992$	82.3869	2.61579
$993$	−0.124440	−0.00394898
$994$	0.901404	0.0285908
$995$	82.6898	2.62144
$996$	−18.7440	−0.593927
$997$	32.5487	1.03083	0.515413	−	0.856942i	$-0.327638\pi$
$997$	32.5487	1.03083	0.515413	+	0.856942i	$0.327638\pi$
$998$	64.2868	2.03496
$999$	19.2379	0.608659

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.c.1.8	✓	154

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.c.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-2.65912 q^{2} -0.292744 q^{3} +5.07094 q^{4} +3.25351 q^{5} +0.778443 q^{6} -0.266213 q^{7} -8.16600 q^{8} -2.91430 q^{9} +O(q^{10})\)	\(q-2.65912 q^{2} -0.292744 q^{3} +5.07094 q^{4} +3.25351 q^{5} +0.778443 q^{6} -0.266213 q^{7} -8.16600 q^{8} -2.91430 q^{9} -8.65148 q^{10} -4.47155 q^{11} -1.48449 q^{12} +5.34766 q^{13} +0.707893 q^{14} -0.952446 q^{15} +11.5725 q^{16} +4.90544 q^{17} +7.74949 q^{18} -8.01609 q^{19} +16.4983 q^{20} +0.0779322 q^{21} +11.8904 q^{22} +2.84081 q^{23} +2.39055 q^{24} +5.58532 q^{25} -14.2201 q^{26} +1.73138 q^{27} -1.34995 q^{28} +1.00000 q^{29} +2.53267 q^{30} -5.70515 q^{31} -14.4408 q^{32} +1.30902 q^{33} -13.0442 q^{34} -0.866126 q^{35} -14.7782 q^{36} +11.1113 q^{37} +21.3158 q^{38} -1.56550 q^{39} -26.5682 q^{40} -7.74471 q^{41} -0.207231 q^{42} -5.41417 q^{43} -22.6749 q^{44} -9.48171 q^{45} -7.55407 q^{46} +3.11666 q^{47} -3.38779 q^{48} -6.92913 q^{49} -14.8521 q^{50} -1.43604 q^{51} +27.1177 q^{52} -8.92590 q^{53} -4.60394 q^{54} -14.5482 q^{55} +2.17389 q^{56} +2.34666 q^{57} -2.65912 q^{58} +1.85298 q^{59} -4.82979 q^{60} +3.20389 q^{61} +15.1707 q^{62} +0.775824 q^{63} +15.2548 q^{64} +17.3987 q^{65} -3.48084 q^{66} +8.62674 q^{67} +24.8752 q^{68} -0.831631 q^{69} +2.30314 q^{70} +1.27336 q^{71} +23.7982 q^{72} -8.03095 q^{73} -29.5464 q^{74} -1.63507 q^{75} -40.6491 q^{76} +1.19038 q^{77} +4.16285 q^{78} -5.08474 q^{79} +37.6513 q^{80} +8.23605 q^{81} +20.5941 q^{82} +12.6266 q^{83} +0.395189 q^{84} +15.9599 q^{85} +14.3969 q^{86} -0.292744 q^{87} +36.5147 q^{88} +17.0710 q^{89} +25.2130 q^{90} -1.42362 q^{91} +14.4056 q^{92} +1.67015 q^{93} -8.28759 q^{94} -26.0804 q^{95} +4.22745 q^{96} -5.81393 q^{97} +18.4254 q^{98} +13.0314 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9}+O(q^{10}) \) 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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