LMFDB - Embedded newform 8045.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8045,2,Mod(1,8045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8045, 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("8045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8045 = 5 \cdot 1609 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8045.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:	$64.2396484261$
Analytic rank:	$1$
Dimension:	$126$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.77015 q^{2} +2.48053 q^{3} +5.67370 q^{4} -1.00000 q^{5} -6.87144 q^{6} +2.38067 q^{7} -10.1767 q^{8} +3.15305 q^{9} +O(q^{10})$	\(q-2.77015 q^{2} +2.48053 q^{3} +5.67370 q^{4} -1.00000 q^{5} -6.87144 q^{6} +2.38067 q^{7} -10.1767 q^{8} +3.15305 q^{9} +2.77015 q^{10} -1.97879 q^{11} +14.0738 q^{12} -6.77441 q^{13} -6.59481 q^{14} -2.48053 q^{15} +16.8435 q^{16} +3.17128 q^{17} -8.73441 q^{18} -4.54698 q^{19} -5.67370 q^{20} +5.90534 q^{21} +5.48154 q^{22} +8.28236 q^{23} -25.2436 q^{24} +1.00000 q^{25} +18.7661 q^{26} +0.379647 q^{27} +13.5072 q^{28} +3.91792 q^{29} +6.87144 q^{30} -3.80735 q^{31} -26.3056 q^{32} -4.90846 q^{33} -8.78490 q^{34} -2.38067 q^{35} +17.8895 q^{36} -4.57104 q^{37} +12.5958 q^{38} -16.8042 q^{39} +10.1767 q^{40} +2.39260 q^{41} -16.3587 q^{42} +1.37719 q^{43} -11.2271 q^{44} -3.15305 q^{45} -22.9433 q^{46} +3.19009 q^{47} +41.7809 q^{48} -1.33239 q^{49} -2.77015 q^{50} +7.86646 q^{51} -38.4360 q^{52} -1.49210 q^{53} -1.05168 q^{54} +1.97879 q^{55} -24.2274 q^{56} -11.2789 q^{57} -10.8532 q^{58} -1.68098 q^{59} -14.0738 q^{60} +1.99074 q^{61} +10.5469 q^{62} +7.50639 q^{63} +39.1833 q^{64} +6.77441 q^{65} +13.5972 q^{66} -0.0168755 q^{67} +17.9929 q^{68} +20.5447 q^{69} +6.59481 q^{70} +2.85933 q^{71} -32.0876 q^{72} -11.5054 q^{73} +12.6625 q^{74} +2.48053 q^{75} -25.7982 q^{76} -4.71086 q^{77} +46.5499 q^{78} -3.69254 q^{79} -16.8435 q^{80} -8.51742 q^{81} -6.62784 q^{82} -11.6758 q^{83} +33.5052 q^{84} -3.17128 q^{85} -3.81501 q^{86} +9.71854 q^{87} +20.1376 q^{88} +15.4217 q^{89} +8.73441 q^{90} -16.1277 q^{91} +46.9917 q^{92} -9.44426 q^{93} -8.83701 q^{94} +4.54698 q^{95} -65.2519 q^{96} -4.34119 q^{97} +3.69092 q^{98} -6.23923 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 126 q + 5 q^{2} - 9 q^{3} + 109 q^{4} - 126 q^{5} - 21 q^{6} - 23 q^{7} + 12 q^{8} + 109 q^{9}+O(q^{10}) $ 126 * q + 5 * q^2 - 9 * q^3 + 109 * q^4 - 126 * q^5 - 21 * q^6 - 23 * q^7 + 12 * q^8 + 109 * q^9	\( 126 q + 5 q^{2} - 9 q^{3} + 109 q^{4} - 126 q^{5} - 21 q^{6} - 23 q^{7} + 12 q^{8} + 109 q^{9} - 5 q^{10} - 44 q^{11} - 11 q^{12} - 35 q^{13} - 14 q^{14} + 9 q^{15} + 75 q^{16} + 11 q^{17} - 15 q^{18} - 130 q^{19} - 109 q^{20} - 44 q^{21} - 14 q^{22} + 75 q^{23} - 63 q^{24} + 126 q^{25} - 43 q^{26} - 42 q^{27} - 77 q^{28} - 24 q^{29} + 21 q^{30} - 78 q^{31} + 24 q^{32} - 29 q^{33} - 57 q^{34} + 23 q^{35} + 50 q^{36} - 31 q^{37} - 3 q^{38} - 57 q^{39} - 12 q^{40} - 38 q^{41} - 10 q^{42} - 100 q^{43} - 90 q^{44} - 109 q^{45} - 96 q^{46} + 12 q^{47} - 22 q^{48} + 65 q^{49} + 5 q^{50} - 74 q^{51} - 112 q^{52} + 20 q^{53} - 90 q^{54} + 44 q^{55} - 57 q^{56} + 6 q^{57} - 35 q^{58} - 97 q^{59} + 11 q^{60} - 102 q^{61} - 16 q^{62} - 15 q^{63} + 4 q^{64} + 35 q^{65} - 83 q^{66} - 121 q^{67} + 41 q^{68} - 71 q^{69} + 14 q^{70} - 32 q^{71} - 32 q^{72} - 85 q^{73} - 42 q^{74} - 9 q^{75} - 275 q^{76} + 13 q^{77} + 10 q^{78} - 97 q^{79} - 75 q^{80} + 86 q^{81} - 55 q^{82} - 73 q^{83} - 111 q^{84} - 11 q^{85} - 56 q^{86} - q^{87} - 37 q^{88} - 67 q^{89} + 15 q^{90} - 180 q^{91} + 98 q^{92} - 44 q^{93} - 86 q^{94} + 130 q^{95} - 179 q^{96} - 50 q^{97} + 18 q^{98} - 217 q^{99}+O(q^{100}) \) 126 * q + 5 * q^2 - 9 * q^3 + 109 * q^4 - 126 * q^5 - 21 * q^6 - 23 * q^7 + 12 * q^8 + 109 * q^9 - 5 * q^10 - 44 * q^11 - 11 * q^12 - 35 * q^13 - 14 * q^14 + 9 * q^15 + 75 * q^16 + 11 * q^17 - 15 * q^18 - 130 * q^19 - 109 * q^20 - 44 * q^21 - 14 * q^22 + 75 * q^23 - 63 * q^24 + 126 * q^25 - 43 * q^26 - 42 * q^27 - 77 * q^28 - 24 * q^29 + 21 * q^30 - 78 * q^31 + 24 * q^32 - 29 * q^33 - 57 * q^34 + 23 * q^35 + 50 * q^36 - 31 * q^37 - 3 * q^38 - 57 * q^39 - 12 * q^40 - 38 * q^41 - 10 * q^42 - 100 * q^43 - 90 * q^44 - 109 * q^45 - 96 * q^46 + 12 * q^47 - 22 * q^48 + 65 * q^49 + 5 * q^50 - 74 * q^51 - 112 * q^52 + 20 * q^53 - 90 * q^54 + 44 * q^55 - 57 * q^56 + 6 * q^57 - 35 * q^58 - 97 * q^59 + 11 * q^60 - 102 * q^61 - 16 * q^62 - 15 * q^63 + 4 * q^64 + 35 * q^65 - 83 * q^66 - 121 * q^67 + 41 * q^68 - 71 * q^69 + 14 * q^70 - 32 * q^71 - 32 * q^72 - 85 * q^73 - 42 * q^74 - 9 * q^75 - 275 * q^76 + 13 * q^77 + 10 * q^78 - 97 * q^79 - 75 * q^80 + 86 * q^81 - 55 * q^82 - 73 * q^83 - 111 * q^84 - 11 * q^85 - 56 * q^86 - q^87 - 37 * q^88 - 67 * q^89 + 15 * q^90 - 180 * q^91 + 98 * q^92 - 44 * q^93 - 86 * q^94 + 130 * q^95 - 179 * q^96 - 50 * q^97 + 18 * q^98 - 217 * 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 $

$2$	−2.77015	−1.95879	−0.979394	−	0.201958i	$-0.935270\pi$
$2$	−2.77015	−1.95879	−0.979394	+	0.201958i	$0.935270\pi$
$3$	2.48053	1.43214	0.716069	−	0.698030i	$-0.245940\pi$
$3$	2.48053	1.43214	0.716069	+	0.698030i	$0.245940\pi$
$4$	5.67370	2.83685
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−6.87144	−2.80525
$7$	2.38067	0.899810	0.449905	−	0.893076i	$-0.351458\pi$
$7$	2.38067	0.899810	0.449905	+	0.893076i	$0.351458\pi$
$8$	−10.1767	−3.59801
$9$	3.15305	1.05102
$10$	2.77015	0.875997
$11$	−1.97879	−0.596628	−0.298314	−	0.954468i	$-0.596424\pi$
$11$	−1.97879	−0.596628	−0.298314	+	0.954468i	$0.596424\pi$
$12$	14.0738	4.06276
$13$	−6.77441	−1.87888	−0.939441	−	0.342709i	$-0.888655\pi$
$13$	−6.77441	−1.87888	−0.939441	+	0.342709i	$0.888655\pi$
$14$	−6.59481	−1.76254
$15$	−2.48053	−0.640471
$16$	16.8435	4.21088
$17$	3.17128	0.769148	0.384574	−	0.923094i	$-0.374348\pi$
$17$	3.17128	0.769148	0.384574	+	0.923094i	$0.374348\pi$
$18$	−8.73441	−2.05872
$19$	−4.54698	−1.04315	−0.521575	−	0.853206i	$-0.674655\pi$
$19$	−4.54698	−1.04315	−0.521575	+	0.853206i	$0.674655\pi$
$20$	−5.67370	−1.26868
$21$	5.90534	1.28865
$22$	5.48154	1.16867
$23$	8.28236	1.72699	0.863496	−	0.504356i	$-0.168270\pi$
$23$	8.28236	1.72699	0.863496	+	0.504356i	$0.168270\pi$
$24$	−25.2436	−5.15284
$25$	1.00000	0.200000
$26$	18.7661	3.68033
$27$	0.379647	0.0730632
$28$	13.5072	2.55263
$29$	3.91792	0.727540	0.363770	−	0.931489i	$-0.381489\pi$
$29$	3.91792	0.727540	0.363770	+	0.931489i	$0.381489\pi$
$30$	6.87144	1.25455
$31$	−3.80735	−0.683820	−0.341910	−	0.939733i	$-0.611074\pi$
$31$	−3.80735	−0.683820	−0.341910	+	0.939733i	$0.611074\pi$
$32$	−26.3056	−4.65022
$33$	−4.90846	−0.854454
$34$	−8.78490	−1.50660
$35$	−2.38067	−0.402407
$36$	17.8895	2.98158
$37$	−4.57104	−0.751475	−0.375737	−	0.926726i	$-0.622611\pi$
$37$	−4.57104	−0.751475	−0.375737	+	0.926726i	$0.622611\pi$
$38$	12.5958	2.04331
$39$	−16.8042	−2.69082
$40$	10.1767	1.60908
$41$	2.39260	0.373661	0.186831	−	0.982392i	$-0.440178\pi$
$41$	2.39260	0.373661	0.186831	+	0.982392i	$0.440178\pi$
$42$	−16.3587	−2.52420
$43$	1.37719	0.210019	0.105009	−	0.994471i	$-0.466513\pi$
$43$	1.37719	0.210019	0.105009	+	0.994471i	$0.466513\pi$
$44$	−11.2271	−1.69255
$45$	−3.15305	−0.470029
$46$	−22.9433	−3.38281
$47$	3.19009	0.465323	0.232661	−	0.972558i	$-0.425257\pi$
$47$	3.19009	0.465323	0.232661	+	0.972558i	$0.425257\pi$
$48$	41.7809	6.03056
$49$	−1.33239	−0.190342
$50$	−2.77015	−0.391758
$51$	7.86646	1.10152
$52$	−38.4360	−5.33011
$53$	−1.49210	−0.204956	−0.102478	−	0.994735i	$-0.532677\pi$
$53$	−1.49210	−0.204956	−0.102478	+	0.994735i	$0.532677\pi$
$54$	−1.05168	−0.143115
$55$	1.97879	0.266820
$56$	−24.2274	−3.23752
$57$	−11.2789	−1.49393
$58$	−10.8532	−1.42510
$59$	−1.68098	−0.218845	−0.109422	−	0.993995i	$-0.534900\pi$
$59$	−1.68098	−0.218845	−0.109422	+	0.993995i	$0.534900\pi$
$60$	−14.0738	−1.81692
$61$	1.99074	0.254888	0.127444	−	0.991846i	$-0.459323\pi$
$61$	1.99074	0.254888	0.127444	+	0.991846i	$0.459323\pi$
$62$	10.5469	1.33946
$63$	7.50639	0.945716
$64$	39.1833	4.89791
$65$	6.77441	0.840262
$66$	13.5972	1.67369
$67$	−0.0168755	−0.00206168	−0.00103084	−	0.999999i	$-0.500328\pi$
$67$	−0.0168755	−0.00206168	−0.00103084	+	0.999999i	$0.500328\pi$
$68$	17.9929	2.18196
$69$	20.5447	2.47329
$70$	6.59481	0.788231
$71$	2.85933	0.339340	0.169670	−	0.985501i	$-0.445730\pi$
$71$	2.85933	0.339340	0.169670	+	0.985501i	$0.445730\pi$
$72$	−32.0876	−3.78156
$73$	−11.5054	−1.34660	−0.673301	−	0.739369i	$-0.735124\pi$
$73$	−11.5054	−1.34660	−0.673301	+	0.739369i	$0.735124\pi$
$74$	12.6625	1.47198
$75$	2.48053	0.286427
$76$	−25.7982	−2.95926
$77$	−4.71086	−0.536852
$78$	46.5499	5.27074
$79$	−3.69254	−0.415443	−0.207721	−	0.978188i	$-0.566605\pi$
$79$	−3.69254	−0.415443	−0.207721	+	0.978188i	$0.566605\pi$
$80$	−16.8435	−1.88316
$81$	−8.51742	−0.946380
$82$	−6.62784	−0.731923
$83$	−11.6758	−1.28159	−0.640794	−	0.767713i	$-0.721395\pi$
$83$	−11.6758	−1.28159	−0.640794	+	0.767713i	$0.721395\pi$
$84$	33.5052	3.65571
$85$	−3.17128	−0.343973
$86$	−3.81501	−0.411383
$87$	9.71854	1.04194
$88$	20.1376	2.14667
$89$	15.4217	1.63470	0.817348	−	0.576145i	$-0.195444\pi$
$89$	15.4217	1.63470	0.817348	+	0.576145i	$0.195444\pi$
$90$	8.73441	0.920687
$91$	−16.1277	−1.69064
$92$	46.9917	4.89922
$93$	−9.44426	−0.979324
$94$	−8.83701	−0.911468
$95$	4.54698	0.466511
$96$	−65.2519	−6.65975
$97$	−4.34119	−0.440781	−0.220390	−	0.975412i	$-0.570733\pi$
$97$	−4.34119	−0.440781	−0.220390	+	0.975412i	$0.570733\pi$
$98$	3.69092	0.372839
$99$	−6.23923	−0.627067
$100$	5.67370	0.567370
$101$	−12.7246	−1.26614	−0.633071	−	0.774093i	$-0.718206\pi$
$101$	−12.7246	−1.26614	−0.633071	+	0.774093i	$0.718206\pi$
$102$	−21.7912	−2.15765
$103$	13.8579	1.36546	0.682729	−	0.730672i	$-0.260793\pi$
$103$	13.8579	1.36546	0.682729	+	0.730672i	$0.260793\pi$
$104$	68.9411	6.76023
$105$	−5.90534	−0.576302
$106$	4.13335	0.401466
$107$	1.83765	0.177652	0.0888262	−	0.996047i	$-0.471688\pi$
$107$	1.83765	0.177652	0.0888262	+	0.996047i	$0.471688\pi$
$108$	2.15401	0.207269
$109$	−0.179736	−0.0172156	−0.00860780	−	0.999963i	$-0.502740\pi$
$109$	−0.179736	−0.0172156	−0.00860780	+	0.999963i	$0.502740\pi$
$110$	−5.48154	−0.522645
$111$	−11.3386	−1.07621
$112$	40.0989	3.78899
$113$	18.5499	1.74503	0.872513	−	0.488590i	$-0.162489\pi$
$113$	18.5499	1.74503	0.872513	+	0.488590i	$0.162489\pi$
$114$	31.2443	2.92630
$115$	−8.28236	−0.772334
$116$	22.2291	2.06392
$117$	−21.3601	−1.97474
$118$	4.65655	0.428670
$119$	7.54978	0.692087
$120$	25.2436	2.30442
$121$	−7.08438	−0.644034
$122$	−5.51463	−0.499271
$123$	5.93492	0.535134
$124$	−21.6018	−1.93990
$125$	−1.00000	−0.0894427
$126$	−20.7938	−1.85246
$127$	−5.83282	−0.517579	−0.258789	−	0.965934i	$-0.583324\pi$
$127$	−5.83282	−0.517579	−0.258789	+	0.965934i	$0.583324\pi$
$128$	−55.9322	−4.94376
$129$	3.41616	0.300776
$130$	−18.7661	−1.64590
$131$	−14.0478	−1.22736	−0.613680	−	0.789555i	$-0.710311\pi$
$131$	−14.0478	−1.22736	−0.613680	+	0.789555i	$0.710311\pi$
$132$	−27.8492	−2.42396
$133$	−10.8249	−0.938637
$134$	0.0467477	0.00403839
$135$	−0.379647	−0.0326748
$136$	−32.2731	−2.76740
$137$	−10.4254	−0.890700	−0.445350	−	0.895357i	$-0.646921\pi$
$137$	−10.4254	−0.890700	−0.445350	+	0.895357i	$0.646921\pi$
$138$	−56.9118	−4.84465
$139$	−2.31047	−0.195971	−0.0979856	−	0.995188i	$-0.531240\pi$
$139$	−2.31047	−0.195971	−0.0979856	+	0.995188i	$0.531240\pi$
$140$	−13.5072	−1.14157
$141$	7.91313	0.666406
$142$	−7.92077	−0.664696
$143$	13.4052	1.12100
$144$	53.1085	4.42571
$145$	−3.91792	−0.325366
$146$	31.8716	2.63771
$147$	−3.30504	−0.272595
$148$	−25.9347	−2.13182
$149$	−20.4647	−1.67653	−0.838266	−	0.545261i	$-0.816431\pi$
$149$	−20.4647	−1.67653	−0.838266	+	0.545261i	$0.816431\pi$
$150$	−6.87144	−0.561051
$151$	0.257502	0.0209552	0.0104776	−	0.999945i	$-0.496665\pi$
$151$	0.257502	0.0209552	0.0104776	+	0.999945i	$0.496665\pi$
$152$	46.2733	3.75326
$153$	9.99920	0.808387
$154$	13.0498	1.05158
$155$	3.80735	0.305814
$156$	−95.3418	−7.63345
$157$	−19.8268	−1.58235	−0.791177	−	0.611587i	$-0.790531\pi$
$157$	−19.8268	−1.58235	−0.791177	+	0.611587i	$0.790531\pi$
$158$	10.2289	0.813765
$159$	−3.70122	−0.293525
$160$	26.3056	2.07964
$161$	19.7176	1.55396
$162$	23.5945	1.85376
$163$	11.3063	0.885577	0.442788	−	0.896626i	$-0.353989\pi$
$163$	11.3063	0.885577	0.442788	+	0.896626i	$0.353989\pi$
$164$	13.5749	1.06002
$165$	4.90846	0.382123
$166$	32.3437	2.51036
$167$	16.4971	1.27658	0.638292	−	0.769795i	$-0.279641\pi$
$167$	16.4971	1.27658	0.638292	+	0.769795i	$0.279641\pi$
$168$	−60.0969	−4.63658
$169$	32.8926	2.53020
$170$	8.78490	0.673771
$171$	−14.3369	−1.09637
$172$	7.81375	0.595793
$173$	12.3097	0.935888	0.467944	−	0.883758i	$-0.344995\pi$
$173$	12.3097	0.935888	0.467944	+	0.883758i	$0.344995\pi$
$174$	−26.9218	−2.04093
$175$	2.38067	0.179962
$176$	−33.3298	−2.51233
$177$	−4.16972	−0.313415
$178$	−42.7203	−3.20202
$179$	−16.8216	−1.25730	−0.628652	−	0.777687i	$-0.716393\pi$
$179$	−16.8216	−1.25730	−0.628652	+	0.777687i	$0.716393\pi$
$180$	−17.8895	−1.33340
$181$	−4.28506	−0.318506	−0.159253	−	0.987238i	$-0.550909\pi$
$181$	−4.28506	−0.318506	−0.159253	+	0.987238i	$0.550909\pi$
$182$	44.6760	3.31160
$183$	4.93809	0.365034
$184$	−84.2871	−6.21373
$185$	4.57104	0.336070
$186$	26.1620	1.91829
$187$	−6.27530	−0.458895
$188$	18.0996	1.32005
$189$	0.903817	0.0657430
$190$	−12.5958	−0.913796
$191$	−9.54896	−0.690938	−0.345469	−	0.938430i	$-0.612280\pi$
$191$	−9.54896	−0.690938	−0.345469	+	0.938430i	$0.612280\pi$
$192$	97.1955	7.01448
$193$	12.7703	0.919224	0.459612	−	0.888120i	$-0.347988\pi$
$193$	12.7703	0.919224	0.459612	+	0.888120i	$0.347988\pi$
$194$	12.0257	0.863396
$195$	16.8042	1.20337
$196$	−7.55960	−0.539971
$197$	6.15966	0.438858	0.219429	−	0.975629i	$-0.429581\pi$
$197$	6.15966	0.438858	0.219429	+	0.975629i	$0.429581\pi$
$198$	17.2836	1.22829
$199$	−16.0629	−1.13867	−0.569336	−	0.822105i	$-0.692800\pi$
$199$	−16.0629	−1.13867	−0.569336	+	0.822105i	$0.692800\pi$
$200$	−10.1767	−0.719601
$201$	−0.0418604	−0.00295260
$202$	35.2489	2.48011
$203$	9.32729	0.654648
$204$	44.6320	3.12486
$205$	−2.39260	−0.167106
$206$	−38.3883	−2.67464
$207$	26.1147	1.81510
$208$	−114.105	−7.91175
$209$	8.99754	0.622373
$210$	16.3587	1.12885
$211$	11.5872	0.797697	0.398849	−	0.917017i	$-0.369410\pi$
$211$	11.5872	0.797697	0.398849	+	0.917017i	$0.369410\pi$
$212$	−8.46576	−0.581431
$213$	7.09267	0.485982
$214$	−5.09056	−0.347983
$215$	−1.37719	−0.0939233
$216$	−3.86356	−0.262882
$217$	−9.06405	−0.615308
$218$	0.497895	0.0337217
$219$	−28.5395	−1.92852
$220$	11.2271	0.756930
$221$	−21.4835	−1.44514
$222$	31.4096	2.10808
$223$	−14.8905	−0.997141	−0.498570	−	0.866849i	$-0.666141\pi$
$223$	−14.8905	−0.997141	−0.498570	+	0.866849i	$0.666141\pi$
$224$	−62.6251	−4.18431
$225$	3.15305	0.210203
$226$	−51.3859	−3.41814
$227$	−15.1694	−1.00683	−0.503415	−	0.864045i	$-0.667923\pi$
$227$	−15.1694	−1.00683	−0.503415	+	0.864045i	$0.667923\pi$
$228$	−63.9934	−4.23807
$229$	−19.2679	−1.27326	−0.636630	−	0.771169i	$-0.719672\pi$
$229$	−19.2679	−1.27326	−0.636630	+	0.771169i	$0.719672\pi$
$230$	22.9433	1.51284
$231$	−11.6855	−0.768846
$232$	−39.8715	−2.61769
$233$	10.4541	0.684873	0.342437	−	0.939541i	$-0.388748\pi$
$233$	10.4541	0.684873	0.342437	+	0.939541i	$0.388748\pi$
$234$	59.1705	3.86809
$235$	−3.19009	−0.208099
$236$	−9.53737	−0.620830
$237$	−9.15947	−0.594971
$238$	−20.9140	−1.35565
$239$	−30.2820	−1.95878	−0.979389	−	0.201982i	$-0.935262\pi$
$239$	−30.2820	−1.95878	−0.979389	+	0.201982i	$0.935262\pi$
$240$	−41.7809	−2.69695
$241$	−6.33134	−0.407837	−0.203919	−	0.978988i	$-0.565368\pi$
$241$	−6.33134	−0.407837	−0.203919	+	0.978988i	$0.565368\pi$
$242$	19.6248	1.26153
$243$	−22.2667	−1.42841
$244$	11.2949	0.723079
$245$	1.33239	0.0851234
$246$	−16.4406	−1.04821
$247$	30.8031	1.95996
$248$	38.7462	2.46039
$249$	−28.9623	−1.83541
$250$	2.77015	0.175199
$251$	−9.25885	−0.584413	−0.292207	−	0.956355i	$-0.594390\pi$
$251$	−9.25885	−0.584413	−0.292207	+	0.956355i	$0.594390\pi$
$252$	42.5890	2.68286
$253$	−16.3891	−1.03037
$254$	16.1578	1.01383
$255$	−7.86646	−0.492617
$256$	76.5738	4.78586
$257$	24.3963	1.52180	0.760898	−	0.648871i	$-0.224759\pi$
$257$	24.3963	1.52180	0.760898	+	0.648871i	$0.224759\pi$
$258$	−9.46326	−0.589157
$259$	−10.8822	−0.676185
$260$	38.4360	2.38370
$261$	12.3534	0.764657
$262$	38.9144	2.40414
$263$	−23.0019	−1.41836	−0.709178	−	0.705030i	$-0.750934\pi$
$263$	−23.0019	−1.41836	−0.709178	+	0.705030i	$0.750934\pi$
$264$	49.9519	3.07433
$265$	1.49210	0.0916592
$266$	29.9865	1.83859
$267$	38.2540	2.34111
$268$	−0.0957468	−0.00584867
$269$	−14.2922	−0.871412	−0.435706	−	0.900089i	$-0.643501\pi$
$269$	−14.2922	−0.871412	−0.435706	+	0.900089i	$0.643501\pi$
$270$	1.05168	0.0640031
$271$	18.4251	1.11925	0.559623	−	0.828747i	$-0.310946\pi$
$271$	18.4251	1.11925	0.559623	+	0.828747i	$0.310946\pi$
$272$	53.4155	3.23879
$273$	−40.0052	−2.42123
$274$	28.8798	1.74469
$275$	−1.97879	−0.119326
$276$	116.564	7.01636
$277$	−8.36681	−0.502713	−0.251356	−	0.967895i	$-0.580877\pi$
$277$	−8.36681	−0.502713	−0.251356	+	0.967895i	$0.580877\pi$
$278$	6.40033	0.383866
$279$	−12.0048	−0.718706
$280$	24.2274	1.44786
$281$	14.2453	0.849805	0.424902	−	0.905239i	$-0.360308\pi$
$281$	14.2453	0.849805	0.424902	+	0.905239i	$0.360308\pi$
$282$	−21.9205	−1.30535
$283$	−23.4113	−1.39166	−0.695828	−	0.718209i	$-0.744962\pi$
$283$	−23.4113	−1.39166	−0.695828	+	0.718209i	$0.744962\pi$
$284$	16.2230	0.962658
$285$	11.2789	0.668107
$286$	−37.1342	−2.19579
$287$	5.69600	0.336224
$288$	−82.9429	−4.88746
$289$	−6.94300	−0.408412
$290$	10.8532	0.637323
$291$	−10.7685	−0.631258
$292$	−65.2781	−3.82011
$293$	−27.4831	−1.60558	−0.802791	−	0.596260i	$-0.796653\pi$
$293$	−27.4831	−1.60558	−0.802791	+	0.596260i	$0.796653\pi$
$294$	9.15545	0.533957
$295$	1.68098	0.0978702
$296$	46.5181	2.70381
$297$	−0.751244	−0.0435916
$298$	56.6902	3.28397
$299$	−56.1081	−3.24482
$300$	14.0738	0.812552
$301$	3.27863	0.188977
$302$	−0.713317	−0.0410468
$303$	−31.5637	−1.81329
$304$	−76.5872	−4.39258
$305$	−1.99074	−0.113989
$306$	−27.6992	−1.58346
$307$	−15.5925	−0.889910	−0.444955	−	0.895553i	$-0.646780\pi$
$307$	−15.5925	−0.889910	−0.444955	+	0.895553i	$0.646780\pi$
$308$	−26.7280	−1.52297
$309$	34.3749	1.95552
$310$	−10.5469	−0.599024
$311$	−33.1009	−1.87698	−0.938489	−	0.345310i	$-0.887774\pi$
$311$	−33.1009	−1.87698	−0.938489	+	0.345310i	$0.887774\pi$
$312$	171.011	9.68158
$313$	−6.77160	−0.382753	−0.191377	−	0.981517i	$-0.561295\pi$
$313$	−6.77160	−0.382753	−0.191377	+	0.981517i	$0.561295\pi$
$314$	54.9232	3.09950
$315$	−7.50639	−0.422937
$316$	−20.9504	−1.17855
$317$	−15.6010	−0.876239	−0.438119	−	0.898917i	$-0.644355\pi$
$317$	−15.6010	−0.876239	−0.438119	+	0.898917i	$0.644355\pi$
$318$	10.2529	0.574954
$319$	−7.75276	−0.434071
$320$	−39.1833	−2.19041
$321$	4.55836	0.254423
$322$	−54.6206	−3.04389
$323$	−14.4197	−0.802336
$324$	−48.3253	−2.68474
$325$	−6.77441	−0.375777
$326$	−31.3201	−1.73466
$327$	−0.445842	−0.0246551
$328$	−24.3487	−1.34443
$329$	7.59457	0.418702
$330$	−13.5972	−0.748499
$331$	16.3408	0.898174	0.449087	−	0.893488i	$-0.351749\pi$
$331$	16.3408	0.898174	0.449087	+	0.893488i	$0.351749\pi$
$332$	−66.2452	−3.63568
$333$	−14.4127	−0.789813
$334$	−45.6993	−2.50056
$335$	0.0168755	0.000922009 0
$336$	99.4668	5.42636
$337$	−1.34315	−0.0731662	−0.0365831	−	0.999331i	$-0.511647\pi$
$337$	−1.34315	−0.0731662	−0.0365831	+	0.999331i	$0.511647\pi$
$338$	−91.1173	−4.95613
$339$	46.0136	2.49912
$340$	−17.9929	−0.975801
$341$	7.53395	0.407986
$342$	39.7152	2.14755
$343$	−19.8367	−1.07108
$344$	−14.0152	−0.755649
$345$	−20.5447	−1.10609
$346$	−34.0996	−1.83321
$347$	−2.36591	−0.127009	−0.0635043	−	0.997982i	$-0.520228\pi$
$347$	−2.36591	−0.127009	−0.0635043	+	0.997982i	$0.520228\pi$
$348$	55.1401	2.95582
$349$	−29.0982	−1.55759	−0.778795	−	0.627279i	$-0.784169\pi$
$349$	−29.0982	−1.55759	−0.778795	+	0.627279i	$0.784169\pi$
$350$	−6.59481	−0.352508
$351$	−2.57189	−0.137277
$352$	52.0533	2.77445
$353$	4.80667	0.255833	0.127917	−	0.991785i	$-0.459171\pi$
$353$	4.80667	0.255833	0.127917	+	0.991785i	$0.459171\pi$
$354$	11.5507	0.613914
$355$	−2.85933	−0.151758
$356$	87.4981	4.63739
$357$	18.7275	0.991163
$358$	46.5982	2.46279
$359$	21.7096	1.14579	0.572895	−	0.819629i	$-0.305820\pi$
$359$	21.7096	1.14579	0.572895	+	0.819629i	$0.305820\pi$
$360$	32.0876	1.69117
$361$	1.67506	0.0881612
$362$	11.8702	0.623886
$363$	−17.5730	−0.922346
$364$	−91.5036	−4.79609
$365$	11.5054	0.602219
$366$	−13.6792	−0.715025
$367$	−1.14012	−0.0595139	−0.0297569	−	0.999557i	$-0.509473\pi$
$367$	−1.14012	−0.0595139	−0.0297569	+	0.999557i	$0.509473\pi$
$368$	139.504	7.27215
$369$	7.54398	0.392724
$370$	−12.6625	−0.658290
$371$	−3.55221	−0.184422
$372$	−53.5839	−2.77820
$373$	12.4362	0.643920	0.321960	−	0.946753i	$-0.395658\pi$
$373$	12.4362	0.643920	0.321960	+	0.946753i	$0.395658\pi$
$374$	17.3835	0.898879
$375$	−2.48053	−0.128094
$376$	−32.4646	−1.67423
$377$	−26.5416	−1.36696
$378$	−2.50370	−0.128777
$379$	−28.0844	−1.44260	−0.721300	−	0.692623i	$-0.756455\pi$
$379$	−28.0844	−1.44260	−0.721300	+	0.692623i	$0.756455\pi$
$380$	25.7982	1.32342
$381$	−14.4685	−0.741244
$382$	26.4520	1.35340
$383$	10.2244	0.522443	0.261221	−	0.965279i	$-0.415875\pi$
$383$	10.2244	0.522443	0.261221	+	0.965279i	$0.415875\pi$
$384$	−138.742	−7.08014
$385$	4.71086	0.240088
$386$	−35.3755	−1.80057
$387$	4.34234	0.220733
$388$	−24.6306	−1.25043
$389$	29.5925	1.50040	0.750201	−	0.661210i	$-0.229957\pi$
$389$	29.5925	1.50040	0.750201	+	0.661210i	$0.229957\pi$
$390$	−46.5499	−2.35715
$391$	26.2657	1.32831
$392$	13.5593	0.684851
$393$	−34.8460	−1.75775
$394$	−17.0632	−0.859629
$395$	3.69254	0.185792
$396$	−35.3996	−1.77890
$397$	20.0507	1.00632	0.503159	−	0.864194i	$-0.332171\pi$
$397$	20.0507	1.00632	0.503159	+	0.864194i	$0.332171\pi$
$398$	44.4967	2.23042
$399$	−26.8515	−1.34426
$400$	16.8435	0.842176
$401$	−3.53538	−0.176548	−0.0882742	−	0.996096i	$-0.528135\pi$
$401$	−3.53538	−0.176548	−0.0882742	+	0.996096i	$0.528135\pi$
$402$	0.115959	0.00578352
$403$	25.7925	1.28482
$404$	−72.1955	−3.59186
$405$	8.51742	0.423234
$406$	−25.8380	−1.28232
$407$	9.04515	0.448351
$408$	−80.0546	−3.96329
$409$	−15.0442	−0.743887	−0.371944	−	0.928255i	$-0.621309\pi$
$409$	−15.0442	−0.743887	−0.371944	+	0.928255i	$0.621309\pi$
$410$	6.62784	0.327326
$411$	−25.8605	−1.27560
$412$	78.6255	3.87360
$413$	−4.00186	−0.196919
$414$	−72.3415	−3.55539
$415$	11.6758	0.573143
$416$	178.205	8.73721
$417$	−5.73119	−0.280658
$418$	−24.9245	−1.21910
$419$	26.4211	1.29075	0.645377	−	0.763864i	$-0.276700\pi$
$419$	26.4211	1.29075	0.645377	+	0.763864i	$0.276700\pi$
$420$	−33.5052	−1.63489
$421$	−27.3541	−1.33316	−0.666578	−	0.745435i	$-0.732242\pi$
$421$	−27.3541	−1.33316	−0.666578	+	0.745435i	$0.732242\pi$
$422$	−32.0983	−1.56252
$423$	10.0585	0.489062
$424$	15.1847	0.737434
$425$	3.17128	0.153830
$426$	−19.6477	−0.951936
$427$	4.73929	0.229350
$428$	10.4263	0.503974
$429$	33.2519	1.60542
$430$	3.81501	0.183976
$431$	16.5938	0.799297	0.399649	−	0.916668i	$-0.369132\pi$
$431$	16.5938	0.799297	0.399649	+	0.916668i	$0.369132\pi$
$432$	6.39460	0.307660
$433$	−22.6371	−1.08787	−0.543934	−	0.839128i	$-0.683066\pi$
$433$	−22.6371	−1.08787	−0.543934	+	0.839128i	$0.683066\pi$
$434$	25.1087	1.20526
$435$	−9.71854	−0.465968
$436$	−1.01977	−0.0488381
$437$	−37.6598	−1.80151
$438$	79.0585	3.77756
$439$	21.7273	1.03699	0.518494	−	0.855081i	$-0.326493\pi$
$439$	21.7273	1.03699	0.518494	+	0.855081i	$0.326493\pi$
$440$	−20.1376	−0.960021
$441$	−4.20110	−0.200052
$442$	59.5125	2.83072
$443$	17.4194	0.827619	0.413809	−	0.910364i	$-0.364198\pi$
$443$	17.4194	0.827619	0.413809	+	0.910364i	$0.364198\pi$
$444$	−64.3320	−3.05306
$445$	−15.4217	−0.731058
$446$	41.2488	1.95319
$447$	−50.7634	−2.40103
$448$	93.2826	4.40719
$449$	−24.2152	−1.14279	−0.571393	−	0.820676i	$-0.693597\pi$
$449$	−24.2152	−1.14279	−0.571393	+	0.820676i	$0.693597\pi$
$450$	−8.73441	−0.411744
$451$	−4.73446	−0.222937
$452$	105.247	4.95038
$453$	0.638742	0.0300107
$454$	42.0215	1.97217
$455$	16.1277	0.756076
$456$	114.782	5.37518
$457$	−2.04451	−0.0956380	−0.0478190	−	0.998856i	$-0.515227\pi$
$457$	−2.04451	−0.0956380	−0.0478190	+	0.998856i	$0.515227\pi$
$458$	53.3749	2.49405
$459$	1.20397	0.0561964
$460$	−46.9917	−2.19100
$461$	−11.2781	−0.525271	−0.262636	−	0.964895i	$-0.584592\pi$
$461$	−11.2781	−0.525271	−0.262636	+	0.964895i	$0.584592\pi$
$462$	32.3704	1.50601
$463$	−2.40556	−0.111796	−0.0558980	−	0.998436i	$-0.517802\pi$
$463$	−2.40556	−0.111796	−0.0558980	+	0.998436i	$0.517802\pi$
$464$	65.9916	3.06358
$465$	9.44426	0.437967
$466$	−28.9595	−1.34152
$467$	−0.604952	−0.0279939	−0.0139969	−	0.999902i	$-0.504456\pi$
$467$	−0.604952	−0.0279939	−0.0139969	+	0.999902i	$0.504456\pi$
$468$	−121.191	−5.60204
$469$	−0.0401752	−0.00185512
$470$	8.83701	0.407621
$471$	−49.1811	−2.26615
$472$	17.1068	0.787404
$473$	−2.72517	−0.125303
$474$	25.3731	1.16542
$475$	−4.54698	−0.208630
$476$	42.8352	1.96335
$477$	−4.70468	−0.215412
$478$	83.8855	3.83683
$479$	−16.7293	−0.764380	−0.382190	−	0.924084i	$-0.624830\pi$
$479$	−16.7293	−0.764380	−0.382190	+	0.924084i	$0.624830\pi$
$480$	65.2519	2.97833
$481$	30.9661	1.41193
$482$	17.5387	0.798867
$483$	48.9102	2.22549
$484$	−40.1947	−1.82703
$485$	4.34119	0.197123
$486$	61.6820	2.79795
$487$	26.5383	1.20257	0.601284	−	0.799036i	$-0.294656\pi$
$487$	26.5383	1.20257	0.601284	+	0.799036i	$0.294656\pi$
$488$	−20.2591	−0.917087
$489$	28.0456	1.26827
$490$	−3.69092	−0.166739
$491$	−21.7069	−0.979617	−0.489808	−	0.871830i	$-0.662933\pi$
$491$	−21.7069	−0.979617	−0.489808	+	0.871830i	$0.662933\pi$
$492$	33.6730	1.51810
$493$	12.4248	0.559586
$494$	−85.3291	−3.83914
$495$	6.23923	0.280433
$496$	−64.1291	−2.87948
$497$	6.80714	0.305342
$498$	80.2297	3.59518
$499$	−20.3396	−0.910524	−0.455262	−	0.890358i	$-0.650454\pi$
$499$	−20.3396	−0.910524	−0.455262	+	0.890358i	$0.650454\pi$
$500$	−5.67370	−0.253736
$501$	40.9216	1.82824
$502$	25.6484	1.14474
$503$	29.5414	1.31719	0.658593	−	0.752499i	$-0.271152\pi$
$503$	29.5414	1.31719	0.658593	+	0.752499i	$0.271152\pi$
$504$	−76.3902	−3.40269
$505$	12.7246	0.566236
$506$	45.4001	2.01828
$507$	81.5913	3.62359
$508$	−33.0937	−1.46829
$509$	19.9132	0.882637	0.441318	−	0.897351i	$-0.354511\pi$
$509$	19.9132	0.882637	0.441318	+	0.897351i	$0.354511\pi$
$510$	21.7912	0.964932
$511$	−27.3905	−1.21169
$512$	−100.256	−4.43074
$513$	−1.72625	−0.0762158
$514$	−67.5812	−2.98088
$515$	−13.8579	−0.610651
$516$	19.3823	0.853257
$517$	−6.31253	−0.277625
$518$	30.1452	1.32450
$519$	30.5346	1.34032
$520$	−68.9411	−3.02327
$521$	36.5961	1.60331	0.801653	−	0.597790i	$-0.203954\pi$
$521$	36.5961	1.60331	0.801653	+	0.597790i	$0.203954\pi$
$522$	−34.2207	−1.49780
$523$	−12.1500	−0.531284	−0.265642	−	0.964072i	$-0.585584\pi$
$523$	−12.1500	−0.531284	−0.265642	+	0.964072i	$0.585584\pi$
$524$	−79.7029	−3.48184
$525$	5.90534	0.257730
$526$	63.7185	2.77826
$527$	−12.0742	−0.525958
$528$	−82.6758	−3.59800
$529$	45.5975	1.98250
$530$	−4.13335	−0.179541
$531$	−5.30020	−0.230009
$532$	−61.4172	−2.66277
$533$	−16.2084	−0.702065
$534$	−105.969	−4.58574
$535$	−1.83765	−0.0794486
$536$	0.171737	0.00741792
$537$	−41.7265	−1.80063
$538$	39.5915	1.70691
$539$	2.63653	0.113563
$540$	−2.15401	−0.0926937
$541$	29.0187	1.24761	0.623806	−	0.781579i	$-0.285586\pi$
$541$	29.0187	1.24761	0.623806	+	0.781579i	$0.285586\pi$
$542$	−51.0402	−2.19237
$543$	−10.6292	−0.456144
$544$	−83.4223	−3.57670
$545$	0.179736	0.00769905
$546$	110.820	4.74267
$547$	32.6747	1.39707	0.698535	−	0.715576i	$-0.253836\pi$
$547$	32.6747	1.39707	0.698535	+	0.715576i	$0.253836\pi$
$548$	−59.1505	−2.52678
$549$	6.27689	0.267891
$550$	5.48154	0.233734
$551$	−17.8147	−0.758933
$552$	−209.077	−8.89891
$553$	−8.79073	−0.373820
$554$	23.1773	0.984708
$555$	11.3386	0.481298
$556$	−13.1089	−0.555941
$557$	42.2640	1.79078	0.895391	−	0.445280i	$-0.146896\pi$
$557$	42.2640	1.79078	0.895391	+	0.445280i	$0.146896\pi$
$558$	33.2549	1.40779
$559$	−9.32962	−0.394601
$560$	−40.0989	−1.69449
$561$	−15.5661	−0.657201
$562$	−39.4616	−1.66459
$563$	−20.0956	−0.846928	−0.423464	−	0.905913i	$-0.639186\pi$
$563$	−20.0956	−0.846928	−0.423464	+	0.905913i	$0.639186\pi$
$564$	44.8968	1.89049
$565$	−18.5499	−0.780400
$566$	64.8526	2.72596
$567$	−20.2772	−0.851563
$568$	−29.0986	−1.22095
$569$	−42.3773	−1.77655	−0.888274	−	0.459313i	$-0.848096\pi$
$569$	−42.3773	−1.77655	−0.888274	+	0.459313i	$0.848096\pi$
$570$	−31.2443	−1.30868
$571$	−16.5979	−0.694601	−0.347301	−	0.937754i	$-0.612902\pi$
$571$	−16.5979	−0.694601	−0.347301	+	0.937754i	$0.612902\pi$
$572$	76.0569	3.18010
$573$	−23.6865	−0.989519
$574$	−15.7787	−0.658592
$575$	8.28236	0.345398
$576$	123.547	5.14779
$577$	−37.7018	−1.56955	−0.784774	−	0.619782i	$-0.787221\pi$
$577$	−37.7018	−1.56955	−0.784774	+	0.619782i	$0.787221\pi$
$578$	19.2331	0.799993
$579$	31.6771	1.31646
$580$	−22.2291	−0.923015
$581$	−27.7963	−1.15319
$582$	29.8302	1.23650
$583$	2.95256	0.122283
$584$	117.087	4.84508
$585$	21.3601	0.883130
$586$	76.1323	3.14500
$587$	33.7110	1.39140	0.695700	−	0.718332i	$-0.255094\pi$
$587$	33.7110	1.39140	0.695700	+	0.718332i	$0.255094\pi$
$588$	−18.7518	−0.773313
$589$	17.3120	0.713327
$590$	−4.65655	−0.191707
$591$	15.2792	0.628504
$592$	−76.9924	−3.16437
$593$	−12.1204	−0.497727	−0.248863	−	0.968539i	$-0.580057\pi$
$593$	−12.1204	−0.497727	−0.248863	+	0.968539i	$0.580057\pi$
$594$	2.08105	0.0853867
$595$	−7.54978	−0.309511
$596$	−116.111	−4.75608
$597$	−39.8447	−1.63073
$598$	155.428	6.35591
$599$	45.5959	1.86300	0.931500	−	0.363742i	$-0.118501\pi$
$599$	45.5959	1.86300	0.931500	+	0.363742i	$0.118501\pi$
$600$	−25.2436	−1.03057
$601$	−11.4408	−0.466679	−0.233340	−	0.972395i	$-0.574965\pi$
$601$	−11.4408	−0.466679	−0.233340	+	0.972395i	$0.574965\pi$
$602$	−9.08229	−0.370166
$603$	−0.0532094	−0.00216686
$604$	1.46099	0.0594468
$605$	7.08438	0.288021
$606$	87.4362	3.55185
$607$	22.9024	0.929581	0.464791	−	0.885421i	$-0.346130\pi$
$607$	22.9024	0.929581	0.464791	+	0.885421i	$0.346130\pi$
$608$	119.611	4.85087
$609$	23.1367	0.937545
$610$	5.51463	0.223281
$611$	−21.6110	−0.874287
$612$	56.7325	2.29328
$613$	−7.66349	−0.309525	−0.154763	−	0.987952i	$-0.549461\pi$
$613$	−7.66349	−0.309525	−0.154763	+	0.987952i	$0.549461\pi$
$614$	43.1934	1.74315
$615$	−5.93492	−0.239319
$616$	47.9410	1.93160
$617$	16.5138	0.664822	0.332411	−	0.943135i	$-0.392138\pi$
$617$	16.5138	0.664822	0.332411	+	0.943135i	$0.392138\pi$
$618$	−95.2236	−3.83045
$619$	7.13053	0.286600	0.143300	−	0.989679i	$-0.454229\pi$
$619$	7.13053	0.286600	0.143300	+	0.989679i	$0.454229\pi$
$620$	21.6018	0.867548
$621$	3.14438	0.126180
$622$	91.6942	3.67660
$623$	36.7140	1.47092
$624$	−283.041	−11.3307
$625$	1.00000	0.0400000
$626$	18.7583	0.749733
$627$	22.3187	0.891323
$628$	−112.492	−4.48890
$629$	−14.4960	−0.577995
$630$	20.7938	0.828444
$631$	−29.1972	−1.16232	−0.581161	−	0.813788i	$-0.697401\pi$
$631$	−29.1972	−1.16232	−0.581161	+	0.813788i	$0.697401\pi$
$632$	37.5778	1.49477
$633$	28.7425	1.14241
$634$	43.2170	1.71637
$635$	5.83282	0.231468
$636$	−20.9996	−0.832688
$637$	9.02617	0.357630
$638$	21.4763	0.850253
$639$	9.01562	0.356652
$640$	55.9322	2.21092
$641$	23.5727	0.931064	0.465532	−	0.885031i	$-0.345863\pi$
$641$	23.5727	0.931064	0.465532	+	0.885031i	$0.345863\pi$
$642$	−12.6273	−0.498360
$643$	11.8691	0.468073	0.234036	−	0.972228i	$-0.424807\pi$
$643$	11.8691	0.468073	0.234036	+	0.972228i	$0.424807\pi$
$644$	111.872	4.40837
$645$	−3.41616	−0.134511
$646$	39.9448	1.57161
$647$	23.2248	0.913061	0.456530	−	0.889708i	$-0.349092\pi$
$647$	23.2248	0.913061	0.456530	+	0.889708i	$0.349092\pi$
$648$	86.6792	3.40508
$649$	3.32630	0.130569
$650$	18.7661	0.736067
$651$	−22.4837	−0.881206
$652$	64.1485	2.51225
$653$	29.7439	1.16397	0.581985	−	0.813200i	$-0.302276\pi$
$653$	29.7439	1.16397	0.581985	+	0.813200i	$0.302276\pi$
$654$	1.23505	0.0482941
$655$	14.0478	0.548892
$656$	40.2998	1.57344
$657$	−36.2770	−1.41530
$658$	−21.0380	−0.820149
$659$	−23.9510	−0.932997	−0.466498	−	0.884522i	$-0.654485\pi$
$659$	−23.9510	−0.932997	−0.466498	+	0.884522i	$0.654485\pi$
$660$	27.8492	1.08403
$661$	29.3024	1.13973	0.569865	−	0.821738i	$-0.306995\pi$
$661$	29.3024	1.13973	0.569865	+	0.821738i	$0.306995\pi$
$662$	−45.2665	−1.75933
$663$	−53.2906	−2.06964
$664$	118.821	4.61116
$665$	10.8249	0.419771
$666$	39.9254	1.54708
$667$	32.4497	1.25646
$668$	93.5996	3.62148
$669$	−36.9364	−1.42804
$670$	−0.0467477	−0.00180602
$671$	−3.93925	−0.152073
$672$	−155.344	−5.99251
$673$	−1.42634	−0.0549814	−0.0274907	−	0.999622i	$-0.508752\pi$
$673$	−1.42634	−0.0549814	−0.0274907	+	0.999622i	$0.508752\pi$
$674$	3.72073	0.143317
$675$	0.379647	0.0146126
$676$	186.623	7.17781
$677$	13.8237	0.531289	0.265644	−	0.964071i	$-0.414415\pi$
$677$	13.8237	0.531289	0.265644	+	0.964071i	$0.414415\pi$
$678$	−127.464	−4.89524
$679$	−10.3349	−0.396619
$680$	32.2731	1.23762
$681$	−37.6283	−1.44192
$682$	−20.8701	−0.799159
$683$	−0.158715	−0.00607304	−0.00303652	−	0.999995i	$-0.500967\pi$
$683$	−0.158715	−0.00607304	−0.00303652	+	0.999995i	$0.500967\pi$
$684$	−81.3432	−3.11023
$685$	10.4254	0.398333
$686$	54.9506	2.09802
$687$	−47.7947	−1.82348
$688$	23.1967	0.884365
$689$	10.1081	0.385089
$690$	56.9118	2.16659
$691$	36.2388	1.37859	0.689295	−	0.724481i	$-0.257921\pi$
$691$	36.2388	1.37859	0.689295	+	0.724481i	$0.257921\pi$
$692$	69.8415	2.65498
$693$	−14.8536	−0.564241
$694$	6.55391	0.248783
$695$	2.31047	0.0876410
$696$	−98.9026	−3.74889
$697$	7.58759	0.287401
$698$	80.6062	3.05099
$699$	25.9319	0.980833
$700$	13.5072	0.510526
$701$	−49.7503	−1.87904	−0.939521	−	0.342492i	$-0.888729\pi$
$701$	−49.7503	−1.87904	−0.939521	+	0.342492i	$0.888729\pi$
$702$	7.12450	0.268897
$703$	20.7845	0.783901
$704$	−77.5356	−2.92223
$705$	−7.91313	−0.298026
$706$	−13.3152	−0.501123
$707$	−30.2931	−1.13929
$708$	−23.6578	−0.889113
$709$	−26.4094	−0.991824	−0.495912	−	0.868373i	$-0.665166\pi$
$709$	−26.4094	−0.991824	−0.495912	+	0.868373i	$0.665166\pi$
$710$	7.92077	0.297261
$711$	−11.6428	−0.436638
$712$	−156.942	−5.88164
$713$	−31.5338	−1.18095
$714$	−51.8778	−1.94148
$715$	−13.4052	−0.501324
$716$	−95.4407	−3.56679
$717$	−75.1155	−2.80524
$718$	−60.1388	−2.24436
$719$	−30.0815	−1.12185	−0.560925	−	0.827867i	$-0.689554\pi$
$719$	−30.0815	−1.12185	−0.560925	+	0.827867i	$0.689554\pi$
$720$	−53.1085	−1.97924
$721$	32.9911	1.22865
$722$	−4.64017	−0.172689
$723$	−15.7051	−0.584079
$724$	−24.3122	−0.903555
$725$	3.91792	0.145508
$726$	48.6799	1.80668
$727$	0.789016	0.0292630	0.0146315	−	0.999893i	$-0.495342\pi$
$727$	0.789016	0.0292630	0.0146315	+	0.999893i	$0.495342\pi$
$728$	164.126	6.08292
$729$	−29.6811	−1.09930
$730$	−31.8716	−1.17962
$731$	4.36744	0.161536
$732$	28.0173	1.03555
$733$	−2.67601	−0.0988407	−0.0494204	−	0.998778i	$-0.515737\pi$
$733$	−2.67601	−0.0988407	−0.0494204	+	0.998778i	$0.515737\pi$
$734$	3.15830	0.116575
$735$	3.30504	0.121908
$736$	−217.872	−8.03089
$737$	0.0333932	0.00123005
$738$	−20.8979	−0.769263
$739$	34.9717	1.28646	0.643228	−	0.765675i	$-0.277595\pi$
$739$	34.9717	1.28646	0.643228	+	0.765675i	$0.277595\pi$
$740$	25.9347	0.953380
$741$	76.4082	2.80693
$742$	9.84015	0.361243
$743$	−34.6218	−1.27015	−0.635076	−	0.772450i	$-0.719031\pi$
$743$	−34.6218	−1.27015	−0.635076	+	0.772450i	$0.719031\pi$
$744$	96.1114	3.52361
$745$	20.4647	0.749768
$746$	−34.4500	−1.26130
$747$	−36.8144	−1.34697
$748$	−35.6042	−1.30182
$749$	4.37485	0.159853
$750$	6.87144	0.250910
$751$	−33.4632	−1.22109	−0.610545	−	0.791982i	$-0.709049\pi$
$751$	−33.4632	−1.22109	−0.610545	+	0.791982i	$0.709049\pi$
$752$	53.7323	1.95942
$753$	−22.9669	−0.836960
$754$	73.5241	2.67759
$755$	−0.257502	−0.00937145
$756$	5.12799	0.186503
$757$	−1.85381	−0.0673780	−0.0336890	−	0.999432i	$-0.510726\pi$
$757$	−1.85381	−0.0673780	−0.0336890	+	0.999432i	$0.510726\pi$
$758$	77.7979	2.82575
$759$	−40.6537	−1.47563
$760$	−46.2733	−1.67851
$761$	28.6350	1.03802	0.519009	−	0.854769i	$-0.326301\pi$
$761$	28.6350	1.03802	0.519009	+	0.854769i	$0.326301\pi$
$762$	40.0799	1.45194
$763$	−0.427893	−0.0154908
$764$	−54.1780	−1.96009
$765$	−9.99920	−0.361522
$766$	−28.3231	−1.02335
$767$	11.3876	0.411183
$768$	189.944	6.85401
$769$	2.57172	0.0927387	0.0463694	−	0.998924i	$-0.485235\pi$
$769$	2.57172	0.0927387	0.0463694	+	0.998924i	$0.485235\pi$
$770$	−13.0498	−0.470281
$771$	60.5157	2.17942
$772$	72.4548	2.60770
$773$	21.0729	0.757939	0.378969	−	0.925409i	$-0.376279\pi$
$773$	21.0729	0.757939	0.378969	+	0.925409i	$0.376279\pi$
$774$	−12.0289	−0.432370
$775$	−3.80735	−0.136764
$776$	44.1789	1.58593
$777$	−26.9936	−0.968389
$778$	−81.9756	−2.93897
$779$	−10.8791	−0.389784
$780$	95.3418	3.41378
$781$	−5.65803	−0.202460
$782$	−72.7597	−2.60188
$783$	1.48743	0.0531564
$784$	−22.4422	−0.801506
$785$	19.8268	0.707650
$786$	96.5284	3.44305
$787$	50.6015	1.80375	0.901875	−	0.431997i	$-0.142191\pi$
$787$	50.6015	1.80375	0.901875	+	0.431997i	$0.142191\pi$
$788$	34.9481	1.24497
$789$	−57.0569	−2.03128
$790$	−10.2289	−0.363927
$791$	44.1612	1.57019
$792$	63.4948	2.25619
$793$	−13.4861	−0.478904
$794$	−55.5435	−1.97116
$795$	3.70122	0.131269
$796$	−91.1364	−3.23024
$797$	−16.1877	−0.573399	−0.286699	−	0.958021i	$-0.592558\pi$
$797$	−16.1877	−0.573399	−0.286699	+	0.958021i	$0.592558\pi$
$798$	74.3826	2.63311
$799$	10.1167	0.357902
$800$	−26.3056	−0.930043
$801$	48.6254	1.71809
$802$	9.79351	0.345821
$803$	22.7667	0.803421
$804$	−0.237503	−0.00837609
$805$	−19.7176	−0.694954
$806$	−71.4491	−2.51669
$807$	−35.4523	−1.24798
$808$	129.494	4.55559
$809$	0.598481	0.0210415	0.0105207	−	0.999945i	$-0.496651\pi$
$809$	0.598481	0.0210415	0.0105207	+	0.999945i	$0.496651\pi$
$810$	−23.5945	−0.829026
$811$	−40.1155	−1.40865	−0.704324	−	0.709879i	$-0.748750\pi$
$811$	−40.1155	−1.40865	−0.704324	+	0.709879i	$0.748750\pi$
$812$	52.9203	1.85714
$813$	45.7041	1.60291
$814$	−25.0564	−0.878225
$815$	−11.3063	−0.396042
$816$	132.499	4.63839
$817$	−6.26204	−0.219081
$818$	41.6746	1.45712
$819$	−50.8513	−1.77689
$820$	−13.5749	−0.474056
$821$	−11.4225	−0.398648	−0.199324	−	0.979934i	$-0.563875\pi$
$821$	−11.4225	−0.398648	−0.199324	+	0.979934i	$0.563875\pi$
$822$	71.6373	2.49864
$823$	−30.7626	−1.07232	−0.536159	−	0.844117i	$-0.680125\pi$
$823$	−30.7626	−1.07232	−0.536159	+	0.844117i	$0.680125\pi$
$824$	−141.027	−4.91292
$825$	−4.90846	−0.170891
$826$	11.0857	0.385722
$827$	−36.9746	−1.28573	−0.642867	−	0.765978i	$-0.722255\pi$
$827$	−36.9746	−1.28573	−0.642867	+	0.765978i	$0.722255\pi$
$828$	148.167	5.14916
$829$	−20.9965	−0.729238	−0.364619	−	0.931157i	$-0.618801\pi$
$829$	−20.9965	−0.729238	−0.364619	+	0.931157i	$0.618801\pi$
$830$	−32.3437	−1.12267
$831$	−20.7542	−0.719954
$832$	−265.444	−9.20260
$833$	−4.22538	−0.146401
$834$	15.8762	0.549749
$835$	−16.4971	−0.570905
$836$	51.0494	1.76558
$837$	−1.44545	−0.0499621
$838$	−73.1902	−2.52831
$839$	−48.9326	−1.68934	−0.844671	−	0.535286i	$-0.820204\pi$
$839$	−48.9326	−1.68934	−0.844671	+	0.535286i	$0.820204\pi$
$840$	60.0969	2.07354
$841$	−13.6499	−0.470686
$842$	75.7747	2.61137
$843$	35.3360	1.21704
$844$	65.7425	2.26295
$845$	−32.8926	−1.13154
$846$	−27.8636	−0.957969
$847$	−16.8656	−0.579509
$848$	−25.1323	−0.863046
$849$	−58.0724	−1.99304
$850$	−8.78490	−0.301320
$851$	−37.8590	−1.29779
$852$	40.2417	1.37866
$853$	49.4639	1.69361	0.846805	−	0.531903i	$-0.178523\pi$
$853$	49.4639	1.69361	0.846805	+	0.531903i	$0.178523\pi$
$854$	−13.1285	−0.449249
$855$	14.3369	0.490311
$856$	−18.7012	−0.639194
$857$	−40.7636	−1.39246	−0.696229	−	0.717820i	$-0.745140\pi$
$857$	−40.7636	−1.39246	−0.696229	+	0.717820i	$0.745140\pi$
$858$	−92.1127	−3.14468
$859$	22.6019	0.771168	0.385584	−	0.922673i	$-0.374000\pi$
$859$	22.6019	0.771168	0.385584	+	0.922673i	$0.374000\pi$
$860$	−7.81375	−0.266447
$861$	14.1291	0.481519
$862$	−45.9674	−1.56565
$863$	−1.87536	−0.0638382	−0.0319191	−	0.999490i	$-0.510162\pi$
$863$	−1.87536	−0.0638382	−0.0319191	+	0.999490i	$0.510162\pi$
$864$	−9.98685	−0.339760
$865$	−12.3097	−0.418542
$866$	62.7080	2.13090
$867$	−17.2224	−0.584902
$868$	−51.4268	−1.74554
$869$	7.30677	0.247865
$870$	26.9218	0.912733
$871$	0.114322	0.00387365
$872$	1.82912	0.0619418
$873$	−13.6880	−0.463268
$874$	104.323	3.52878
$875$	−2.38067	−0.0804815
$876$	−161.925	−5.47092
$877$	33.4379	1.12912	0.564559	−	0.825392i	$-0.309046\pi$
$877$	33.4379	1.12912	0.564559	+	0.825392i	$0.309046\pi$
$878$	−60.1878	−2.03124
$879$	−68.1729	−2.29941
$880$	33.3298	1.12355
$881$	−3.81964	−0.128687	−0.0643434	−	0.997928i	$-0.520495\pi$
$881$	−3.81964	−0.128687	−0.0643434	+	0.997928i	$0.520495\pi$
$882$	11.6377	0.391860
$883$	−16.1217	−0.542537	−0.271268	−	0.962504i	$-0.587443\pi$
$883$	−16.1217	−0.542537	−0.271268	+	0.962504i	$0.587443\pi$
$884$	−121.891	−4.09964
$885$	4.16972	0.140164
$886$	−48.2542	−1.62113
$887$	51.1623	1.71786	0.858931	−	0.512091i	$-0.171129\pi$
$887$	51.1623	1.71786	0.858931	+	0.512091i	$0.171129\pi$
$888$	115.390	3.87223
$889$	−13.8860	−0.465723
$890$	42.7203	1.43199
$891$	16.8542	0.564637
$892$	−84.4842	−2.82874
$893$	−14.5053	−0.485401
$894$	140.622	4.70310
$895$	16.8216	0.562284
$896$	−133.156	−4.44844
$897$	−139.178	−4.64702
$898$	67.0797	2.23848
$899$	−14.9169	−0.497506
$900$	17.8895	0.596316
$901$	−4.73188	−0.157642
$902$	13.1151	0.436686
$903$	8.13276	0.270641
$904$	−188.777	−6.27862
$905$	4.28506	0.142440
$906$	−1.76941	−0.0587846
$907$	−0.254635	−0.00845501	−0.00422750	−	0.999991i	$-0.501346\pi$
$907$	−0.254635	−0.00845501	−0.00422750	+	0.999991i	$0.501346\pi$
$908$	−86.0669	−2.85623
$909$	−40.1212	−1.33074
$910$	−44.6760	−1.48099
$911$	17.1786	0.569153	0.284576	−	0.958653i	$-0.408147\pi$
$911$	17.1786	0.569153	0.284576	+	0.958653i	$0.408147\pi$
$912$	−189.977	−6.29077
$913$	23.1040	0.764632
$914$	5.66358	0.187335
$915$	−4.93809	−0.163248
$916$	−109.320	−3.61205
$917$	−33.4432	−1.10439
$918$	−3.33516	−0.110077
$919$	21.5409	0.710570	0.355285	−	0.934758i	$-0.384384\pi$
$919$	21.5409	0.710570	0.355285	+	0.934758i	$0.384384\pi$
$920$	84.2871	2.77886
$921$	−38.6777	−1.27447
$922$	31.2419	1.02890
$923$	−19.3703	−0.637581
$924$	−66.2998	−2.18110
$925$	−4.57104	−0.150295
$926$	6.66376	0.218985
$927$	43.6946	1.43512
$928$	−103.063	−3.38322
$929$	−52.1539	−1.71111	−0.855557	−	0.517709i	$-0.826785\pi$
$929$	−52.1539	−1.71111	−0.855557	+	0.517709i	$0.826785\pi$
$930$	−26.1620	−0.857885
$931$	6.05837	0.198555
$932$	59.3137	1.94289
$933$	−82.1078	−2.68809
$934$	1.67581	0.0548340
$935$	6.27530	0.205224
$936$	217.375	7.10512
$937$	7.06185	0.230701	0.115350	−	0.993325i	$-0.463201\pi$
$937$	7.06185	0.230701	0.115350	+	0.993325i	$0.463201\pi$
$938$	0.111291	0.00363378
$939$	−16.7972	−0.548156
$940$	−18.0996	−0.590345
$941$	50.9877	1.66215	0.831076	−	0.556159i	$-0.187725\pi$
$941$	50.9877	1.66215	0.831076	+	0.556159i	$0.187725\pi$
$942$	136.239	4.43890
$943$	19.8164	0.645310
$944$	−28.3136	−0.921528
$945$	−0.903817	−0.0294012
$946$	7.54911	0.245443
$947$	36.5578	1.18797	0.593984	−	0.804477i	$-0.297554\pi$
$947$	36.5578	1.18797	0.593984	+	0.804477i	$0.297554\pi$
$948$	−51.9681	−1.68785
$949$	77.9421	2.53011
$950$	12.5958	0.408662
$951$	−38.6988	−1.25489
$952$	−76.8318	−2.49013
$953$	−45.4880	−1.47350	−0.736751	−	0.676164i	$-0.763641\pi$
$953$	−45.4880	−1.47350	−0.736751	+	0.676164i	$0.763641\pi$
$954$	13.0326	0.421948
$955$	9.54896	0.308997
$956$	−171.811	−5.55677
$957$	−19.2310	−0.621649
$958$	46.3425	1.49726
$959$	−24.8194	−0.801461
$960$	−97.1955	−3.13697
$961$	−16.5041	−0.532390
$962$	−85.7806	−2.76568
$963$	5.79421	0.186716
$964$	−35.9221	−1.15697
$965$	−12.7703	−0.411090
$966$	−135.488	−4.35927
$967$	27.1257	0.872304	0.436152	−	0.899873i	$-0.356341\pi$
$967$	27.1257	0.872304	0.436152	+	0.899873i	$0.356341\pi$
$968$	72.0956	2.31724
$969$	−35.7687	−1.14906
$970$	−12.0257	−0.386123
$971$	11.9384	0.383121	0.191561	−	0.981481i	$-0.438645\pi$
$971$	11.9384	0.383121	0.191561	+	0.981481i	$0.438645\pi$
$972$	−126.335	−4.05219
$973$	−5.50047	−0.176337
$974$	−73.5151	−2.35557
$975$	−16.8042	−0.538164
$976$	33.5310	1.07330
$977$	0.902354	0.0288689	0.0144344	−	0.999896i	$-0.495405\pi$
$977$	0.902354	0.0288689	0.0144344	+	0.999896i	$0.495405\pi$
$978$	−77.6905	−2.48427
$979$	−30.5163	−0.975306
$980$	7.55960	0.241483
$981$	−0.566717	−0.0180939
$982$	60.1311	1.91886
$983$	−31.0962	−0.991815	−0.495907	−	0.868375i	$-0.665164\pi$
$983$	−31.0962	−0.991815	−0.495907	+	0.868375i	$0.665164\pi$
$984$	−60.3979	−1.92541
$985$	−6.15966	−0.196263
$986$	−34.4185	−1.09611
$987$	18.8386	0.599639
$988$	174.768	5.56011
$989$	11.4064	0.362701
$990$	−17.2836	−0.549308
$991$	−22.8034	−0.724374	−0.362187	−	0.932106i	$-0.617970\pi$
$991$	−22.8034	−0.724374	−0.362187	+	0.932106i	$0.617970\pi$
$992$	100.155	3.17991
$993$	40.5340	1.28631
$994$	−18.8568	−0.598100
$995$	16.0629	0.509230
$996$	−164.323	−5.20679
$997$	15.2085	0.481659	0.240829	−	0.970567i	$-0.422581\pi$
$997$	15.2085	0.481659	0.240829	+	0.970567i	$0.422581\pi$
$998$	56.3435	1.78352
$999$	−1.73538	−0.0549051

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8045.2.a.b.1.1	✓	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8045.2.a.b.1.1	✓	126	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:	\( N \)	\(=\)	\( 8045 = 5 \cdot 1609 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8045.a (trivial)

\(f(q)\)	\(=\)	\(q-2.77015 q^{2} +2.48053 q^{3} +5.67370 q^{4} -1.00000 q^{5} -6.87144 q^{6} +2.38067 q^{7} -10.1767 q^{8} +3.15305 q^{9} +O(q^{10})\)	\(q-2.77015 q^{2} +2.48053 q^{3} +5.67370 q^{4} -1.00000 q^{5} -6.87144 q^{6} +2.38067 q^{7} -10.1767 q^{8} +3.15305 q^{9} +2.77015 q^{10} -1.97879 q^{11} +14.0738 q^{12} -6.77441 q^{13} -6.59481 q^{14} -2.48053 q^{15} +16.8435 q^{16} +3.17128 q^{17} -8.73441 q^{18} -4.54698 q^{19} -5.67370 q^{20} +5.90534 q^{21} +5.48154 q^{22} +8.28236 q^{23} -25.2436 q^{24} +1.00000 q^{25} +18.7661 q^{26} +0.379647 q^{27} +13.5072 q^{28} +3.91792 q^{29} +6.87144 q^{30} -3.80735 q^{31} -26.3056 q^{32} -4.90846 q^{33} -8.78490 q^{34} -2.38067 q^{35} +17.8895 q^{36} -4.57104 q^{37} +12.5958 q^{38} -16.8042 q^{39} +10.1767 q^{40} +2.39260 q^{41} -16.3587 q^{42} +1.37719 q^{43} -11.2271 q^{44} -3.15305 q^{45} -22.9433 q^{46} +3.19009 q^{47} +41.7809 q^{48} -1.33239 q^{49} -2.77015 q^{50} +7.86646 q^{51} -38.4360 q^{52} -1.49210 q^{53} -1.05168 q^{54} +1.97879 q^{55} -24.2274 q^{56} -11.2789 q^{57} -10.8532 q^{58} -1.68098 q^{59} -14.0738 q^{60} +1.99074 q^{61} +10.5469 q^{62} +7.50639 q^{63} +39.1833 q^{64} +6.77441 q^{65} +13.5972 q^{66} -0.0168755 q^{67} +17.9929 q^{68} +20.5447 q^{69} +6.59481 q^{70} +2.85933 q^{71} -32.0876 q^{72} -11.5054 q^{73} +12.6625 q^{74} +2.48053 q^{75} -25.7982 q^{76} -4.71086 q^{77} +46.5499 q^{78} -3.69254 q^{79} -16.8435 q^{80} -8.51742 q^{81} -6.62784 q^{82} -11.6758 q^{83} +33.5052 q^{84} -3.17128 q^{85} -3.81501 q^{86} +9.71854 q^{87} +20.1376 q^{88} +15.4217 q^{89} +8.73441 q^{90} -16.1277 q^{91} +46.9917 q^{92} -9.44426 q^{93} -8.83701 q^{94} +4.54698 q^{95} -65.2519 q^{96} -4.34119 q^{97} +3.69092 q^{98} -6.23923 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q + 5 q^{2} - 9 q^{3} + 109 q^{4} - 126 q^{5} - 21 q^{6} - 23 q^{7} + 12 q^{8} + 109 q^{9}+O(q^{10}) \) 126 * q + 5 * q^2 - 9 * q^3 + 109 * q^4 - 126 * q^5 - 21 * q^6 - 23 * q^7 + 12 * q^8 + 109 * q^9	\( 126 q + 5 q^{2} - 9 q^{3} + 109 q^{4} - 126 q^{5} - 21 q^{6} - 23 q^{7} + 12 q^{8} + 109 q^{9} - 5 q^{10} - 44 q^{11} - 11 q^{12} - 35 q^{13} - 14 q^{14} + 9 q^{15} + 75 q^{16} + 11 q^{17} - 15 q^{18} - 130 q^{19} - 109 q^{20} - 44 q^{21} - 14 q^{22} + 75 q^{23} - 63 q^{24} + 126 q^{25} - 43 q^{26} - 42 q^{27} - 77 q^{28} - 24 q^{29} + 21 q^{30} - 78 q^{31} + 24 q^{32} - 29 q^{33} - 57 q^{34} + 23 q^{35} + 50 q^{36} - 31 q^{37} - 3 q^{38} - 57 q^{39} - 12 q^{40} - 38 q^{41} - 10 q^{42} - 100 q^{43} - 90 q^{44} - 109 q^{45} - 96 q^{46} + 12 q^{47} - 22 q^{48} + 65 q^{49} + 5 q^{50} - 74 q^{51} - 112 q^{52} + 20 q^{53} - 90 q^{54} + 44 q^{55} - 57 q^{56} + 6 q^{57} - 35 q^{58} - 97 q^{59} + 11 q^{60} - 102 q^{61} - 16 q^{62} - 15 q^{63} + 4 q^{64} + 35 q^{65} - 83 q^{66} - 121 q^{67} + 41 q^{68} - 71 q^{69} + 14 q^{70} - 32 q^{71} - 32 q^{72} - 85 q^{73} - 42 q^{74} - 9 q^{75} - 275 q^{76} + 13 q^{77} + 10 q^{78} - 97 q^{79} - 75 q^{80} + 86 q^{81} - 55 q^{82} - 73 q^{83} - 111 q^{84} - 11 q^{85} - 56 q^{86} - q^{87} - 37 q^{88} - 67 q^{89} + 15 q^{90} - 180 q^{91} + 98 q^{92} - 44 q^{93} - 86 q^{94} + 130 q^{95} - 179 q^{96} - 50 q^{97} + 18 q^{98} - 217 q^{99}+O(q^{100}) \) 126 * q + 5 * q^2 - 9 * q^3 + 109 * q^4 - 126 * q^5 - 21 * q^6 - 23 * q^7 + 12 * q^8 + 109 * q^9 - 5 * q^10 - 44 * q^11 - 11 * q^12 - 35 * q^13 - 14 * q^14 + 9 * q^15 + 75 * q^16 + 11 * q^17 - 15 * q^18 - 130 * q^19 - 109 * q^20 - 44 * q^21 - 14 * q^22 + 75 * q^23 - 63 * q^24 + 126 * q^25 - 43 * q^26 - 42 * q^27 - 77 * q^28 - 24 * q^29 + 21 * q^30 - 78 * q^31 + 24 * q^32 - 29 * q^33 - 57 * q^34 + 23 * q^35 + 50 * q^36 - 31 * q^37 - 3 * q^38 - 57 * q^39 - 12 * q^40 - 38 * q^41 - 10 * q^42 - 100 * q^43 - 90 * q^44 - 109 * q^45 - 96 * q^46 + 12 * q^47 - 22 * q^48 + 65 * q^49 + 5 * q^50 - 74 * q^51 - 112 * q^52 + 20 * q^53 - 90 * q^54 + 44 * q^55 - 57 * q^56 + 6 * q^57 - 35 * q^58 - 97 * q^59 + 11 * q^60 - 102 * q^61 - 16 * q^62 - 15 * q^63 + 4 * q^64 + 35 * q^65 - 83 * q^66 - 121 * q^67 + 41 * q^68 - 71 * q^69 + 14 * q^70 - 32 * q^71 - 32 * q^72 - 85 * q^73 - 42 * q^74 - 9 * q^75 - 275 * q^76 + 13 * q^77 + 10 * q^78 - 97 * q^79 - 75 * q^80 + 86 * q^81 - 55 * q^82 - 73 * q^83 - 111 * q^84 - 11 * q^85 - 56 * q^86 - q^87 - 37 * q^88 - 67 * q^89 + 15 * q^90 - 180 * q^91 + 98 * q^92 - 44 * q^93 - 86 * q^94 + 130 * q^95 - 179 * q^96 - 50 * q^97 + 18 * q^98 - 217 * q^99

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