LMFDB - Embedded newform 8018.2.a.e.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.43969 q^{3} +1.00000 q^{4} -3.67207 q^{5} -1.43969 q^{6} -3.77033 q^{7} +1.00000 q^{8} -0.927290 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.43969 q^{3} +1.00000 q^{4} -3.67207 q^{5} -1.43969 q^{6} -3.77033 q^{7} +1.00000 q^{8} -0.927290 q^{9} -3.67207 q^{10} +0.629962 q^{11} -1.43969 q^{12} +4.53130 q^{13} -3.77033 q^{14} +5.28665 q^{15} +1.00000 q^{16} -3.06397 q^{17} -0.927290 q^{18} -1.00000 q^{19} -3.67207 q^{20} +5.42811 q^{21} +0.629962 q^{22} +3.55770 q^{23} -1.43969 q^{24} +8.48410 q^{25} +4.53130 q^{26} +5.65408 q^{27} -3.77033 q^{28} -9.36074 q^{29} +5.28665 q^{30} +0.222431 q^{31} +1.00000 q^{32} -0.906951 q^{33} -3.06397 q^{34} +13.8449 q^{35} -0.927290 q^{36} +7.87426 q^{37} -1.00000 q^{38} -6.52367 q^{39} -3.67207 q^{40} +8.51533 q^{41} +5.42811 q^{42} +0.278877 q^{43} +0.629962 q^{44} +3.40507 q^{45} +3.55770 q^{46} +7.11842 q^{47} -1.43969 q^{48} +7.21538 q^{49} +8.48410 q^{50} +4.41117 q^{51} +4.53130 q^{52} +2.27143 q^{53} +5.65408 q^{54} -2.31326 q^{55} -3.77033 q^{56} +1.43969 q^{57} -9.36074 q^{58} -6.76683 q^{59} +5.28665 q^{60} -2.24982 q^{61} +0.222431 q^{62} +3.49619 q^{63} +1.00000 q^{64} -16.6393 q^{65} -0.906951 q^{66} -10.4124 q^{67} -3.06397 q^{68} -5.12199 q^{69} +13.8449 q^{70} +0.0542548 q^{71} -0.927290 q^{72} +1.62278 q^{73} +7.87426 q^{74} -12.2145 q^{75} -1.00000 q^{76} -2.37516 q^{77} -6.52367 q^{78} +12.1272 q^{79} -3.67207 q^{80} -5.35826 q^{81} +8.51533 q^{82} +11.8520 q^{83} +5.42811 q^{84} +11.2511 q^{85} +0.278877 q^{86} +13.4766 q^{87} +0.629962 q^{88} +0.484681 q^{89} +3.40507 q^{90} -17.0845 q^{91} +3.55770 q^{92} -0.320232 q^{93} +7.11842 q^{94} +3.67207 q^{95} -1.43969 q^{96} -1.38783 q^{97} +7.21538 q^{98} -0.584158 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9}+O(q^{10}) $ 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9} - 6 q^{10} - 21 q^{11} - 7 q^{12} - 19 q^{13} - 5 q^{14} - 14 q^{15} + 32 q^{16} - 14 q^{17} + 15 q^{18} - 32 q^{19} - 6 q^{20} - 26 q^{21} - 21 q^{22} - 13 q^{23} - 7 q^{24} - 10 q^{25} - 19 q^{26} - 25 q^{27} - 5 q^{28} - 42 q^{29} - 14 q^{30} - 15 q^{31} + 32 q^{32} - 32 q^{33} - 14 q^{34} - 22 q^{35} + 15 q^{36} - 54 q^{37} - 32 q^{38} - 32 q^{39} - 6 q^{40} - 16 q^{41} - 26 q^{42} - 37 q^{43} - 21 q^{44} - 46 q^{45} - 13 q^{46} - 9 q^{47} - 7 q^{48} - 7 q^{49} - 10 q^{50} - 32 q^{51} - 19 q^{52} - 53 q^{53} - 25 q^{54} - 17 q^{55} - 5 q^{56} + 7 q^{57} - 42 q^{58} - 34 q^{59} - 14 q^{60} - 33 q^{61} - 15 q^{62} + 18 q^{63} + 32 q^{64} - 50 q^{65} - 32 q^{66} - 53 q^{67} - 14 q^{68} - 40 q^{69} - 22 q^{70} - 27 q^{71} + 15 q^{72} - 43 q^{73} - 54 q^{74} + 5 q^{75} - 32 q^{76} - 56 q^{77} - 32 q^{78} - 11 q^{79} - 6 q^{80} - 8 q^{81} - 16 q^{82} - 17 q^{83} - 26 q^{84} - 30 q^{85} - 37 q^{86} + 3 q^{87} - 21 q^{88} - 21 q^{89} - 46 q^{90} - 67 q^{91} - 13 q^{92} - 31 q^{93} - 9 q^{94} + 6 q^{95} - 7 q^{96} - 51 q^{97} - 7 q^{98} - 32 q^{99}+O(q^{100}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9 - 6 * q^10 - 21 * q^11 - 7 * q^12 - 19 * q^13 - 5 * q^14 - 14 * q^15 + 32 * q^16 - 14 * q^17 + 15 * q^18 - 32 * q^19 - 6 * q^20 - 26 * q^21 - 21 * q^22 - 13 * q^23 - 7 * q^24 - 10 * q^25 - 19 * q^26 - 25 * q^27 - 5 * q^28 - 42 * q^29 - 14 * q^30 - 15 * q^31 + 32 * q^32 - 32 * q^33 - 14 * q^34 - 22 * q^35 + 15 * q^36 - 54 * q^37 - 32 * q^38 - 32 * q^39 - 6 * q^40 - 16 * q^41 - 26 * q^42 - 37 * q^43 - 21 * q^44 - 46 * q^45 - 13 * q^46 - 9 * q^47 - 7 * q^48 - 7 * q^49 - 10 * q^50 - 32 * q^51 - 19 * q^52 - 53 * q^53 - 25 * q^54 - 17 * q^55 - 5 * q^56 + 7 * q^57 - 42 * q^58 - 34 * q^59 - 14 * q^60 - 33 * q^61 - 15 * q^62 + 18 * q^63 + 32 * q^64 - 50 * q^65 - 32 * q^66 - 53 * q^67 - 14 * q^68 - 40 * q^69 - 22 * q^70 - 27 * q^71 + 15 * q^72 - 43 * q^73 - 54 * q^74 + 5 * q^75 - 32 * q^76 - 56 * q^77 - 32 * q^78 - 11 * q^79 - 6 * q^80 - 8 * q^81 - 16 * q^82 - 17 * q^83 - 26 * q^84 - 30 * q^85 - 37 * q^86 + 3 * q^87 - 21 * q^88 - 21 * q^89 - 46 * q^90 - 67 * q^91 - 13 * q^92 - 31 * q^93 - 9 * q^94 + 6 * q^95 - 7 * q^96 - 51 * q^97 - 7 * q^98 - 32 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.43969	−0.831206	−0.415603	−	0.909546i	$-0.636429\pi$
$3$	−1.43969	−0.831206	−0.415603	+	0.909546i	$0.636429\pi$
$4$	1.00000	0.500000
$5$	−3.67207	−1.64220	−0.821100	−	0.570785i	$-0.806639\pi$
$5$	−3.67207	−1.64220	−0.821100	+	0.570785i	$0.806639\pi$
$6$	−1.43969	−0.587751
$7$	−3.77033	−1.42505	−0.712525	−	0.701646i	$-0.752449\pi$
$7$	−3.77033	−1.42505	−0.712525	+	0.701646i	$0.752449\pi$
$8$	1.00000	0.353553
$9$	−0.927290	−0.309097
$10$	−3.67207	−1.16121
$11$	0.629962	0.189941	0.0949703	−	0.995480i	$-0.469724\pi$
$11$	0.629962	0.189941	0.0949703	+	0.995480i	$0.469724\pi$
$12$	−1.43969	−0.415603
$13$	4.53130	1.25676	0.628379	−	0.777908i	$-0.283719\pi$
$13$	4.53130	1.25676	0.628379	+	0.777908i	$0.283719\pi$
$14$	−3.77033	−1.00766
$15$	5.28665	1.36501
$16$	1.00000	0.250000
$17$	−3.06397	−0.743122	−0.371561	−	0.928408i	$-0.621177\pi$
$17$	−3.06397	−0.743122	−0.371561	+	0.928408i	$0.621177\pi$
$18$	−0.927290	−0.218564
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−3.67207	−0.821100
$21$	5.42811	1.18451
$22$	0.629962	0.134308
$23$	3.55770	0.741832	0.370916	−	0.928666i	$-0.379044\pi$
$23$	3.55770	0.741832	0.370916	+	0.928666i	$0.379044\pi$
$24$	−1.43969	−0.293876
$25$	8.48410	1.69682
$26$	4.53130	0.888661
$27$	5.65408	1.08813
$28$	−3.77033	−0.712525
$29$	−9.36074	−1.73825	−0.869123	−	0.494596i	$-0.835316\pi$
$29$	−9.36074	−1.73825	−0.869123	+	0.494596i	$0.835316\pi$
$30$	5.28665	0.965205
$31$	0.222431	0.0399498	0.0199749	−	0.999800i	$-0.493641\pi$
$31$	0.222431	0.0399498	0.0199749	+	0.999800i	$0.493641\pi$
$32$	1.00000	0.176777
$33$	−0.906951	−0.157880
$34$	−3.06397	−0.525467
$35$	13.8449	2.34022
$36$	−0.927290	−0.154548
$37$	7.87426	1.29452	0.647260	−	0.762269i	$-0.275915\pi$
$37$	7.87426	1.29452	0.647260	+	0.762269i	$0.275915\pi$
$38$	−1.00000	−0.162221
$39$	−6.52367	−1.04462
$40$	−3.67207	−0.580605
$41$	8.51533	1.32987	0.664935	−	0.746901i	$-0.268459\pi$
$41$	8.51533	1.32987	0.664935	+	0.746901i	$0.268459\pi$
$42$	5.42811	0.837575
$43$	0.278877	0.0425283	0.0212642	−	0.999774i	$-0.493231\pi$
$43$	0.278877	0.0425283	0.0212642	+	0.999774i	$0.493231\pi$
$44$	0.629962	0.0949703
$45$	3.40507	0.507598
$46$	3.55770	0.524554
$47$	7.11842	1.03833	0.519164	−	0.854675i	$-0.326243\pi$
$47$	7.11842	1.03833	0.519164	+	0.854675i	$0.326243\pi$
$48$	−1.43969	−0.207801
$49$	7.21538	1.03077
$50$	8.48410	1.19983
$51$	4.41117	0.617688
$52$	4.53130	0.628379
$53$	2.27143	0.312005	0.156003	−	0.987757i	$-0.450139\pi$
$53$	2.27143	0.312005	0.156003	+	0.987757i	$0.450139\pi$
$54$	5.65408	0.769423
$55$	−2.31326	−0.311921
$56$	−3.77033	−0.503831
$57$	1.43969	0.190692
$58$	−9.36074	−1.22913
$59$	−6.76683	−0.880966	−0.440483	−	0.897761i	$-0.645193\pi$
$59$	−6.76683	−0.880966	−0.440483	+	0.897761i	$0.645193\pi$
$60$	5.28665	0.682503
$61$	−2.24982	−0.288060	−0.144030	−	0.989573i	$-0.546006\pi$
$61$	−2.24982	−0.288060	−0.144030	+	0.989573i	$0.546006\pi$
$62$	0.222431	0.0282488
$63$	3.49619	0.440478
$64$	1.00000	0.125000
$65$	−16.6393	−2.06385
$66$	−0.906951	−0.111638
$67$	−10.4124	−1.27208	−0.636041	−	0.771655i	$-0.719429\pi$
$67$	−10.4124	−1.27208	−0.636041	+	0.771655i	$0.719429\pi$
$68$	−3.06397	−0.371561
$69$	−5.12199	−0.616615
$70$	13.8449	1.65478
$71$	0.0542548	0.00643886	0.00321943	−	0.999995i	$-0.498975\pi$
$71$	0.0542548	0.00643886	0.00321943	+	0.999995i	$0.498975\pi$
$72$	−0.927290	−0.109282
$73$	1.62278	0.189933	0.0949663	−	0.995480i	$-0.469726\pi$
$73$	1.62278	0.189933	0.0949663	+	0.995480i	$0.469726\pi$
$74$	7.87426	0.915364
$75$	−12.2145	−1.41041
$76$	−1.00000	−0.114708
$77$	−2.37516	−0.270675
$78$	−6.52367	−0.738661
$79$	12.1272	1.36441	0.682207	−	0.731159i	$-0.261020\pi$
$79$	12.1272	1.36441	0.682207	+	0.731159i	$0.261020\pi$
$80$	−3.67207	−0.410550
$81$	−5.35826	−0.595363
$82$	8.51533	0.940361
$83$	11.8520	1.30092	0.650461	−	0.759540i	$-0.274576\pi$
$83$	11.8520	1.30092	0.650461	+	0.759540i	$0.274576\pi$
$84$	5.42811	0.592255
$85$	11.2511	1.22036
$86$	0.278877	0.0300721
$87$	13.4766	1.44484
$88$	0.629962	0.0671542
$89$	0.484681	0.0513761	0.0256880	−	0.999670i	$-0.491822\pi$
$89$	0.484681	0.0513761	0.0256880	+	0.999670i	$0.491822\pi$
$90$	3.40507	0.358926
$91$	−17.0845	−1.79094
$92$	3.55770	0.370916
$93$	−0.320232	−0.0332065
$94$	7.11842	0.734209
$95$	3.67207	0.376746
$96$	−1.43969	−0.146938
$97$	−1.38783	−0.140913	−0.0704566	−	0.997515i	$-0.522446\pi$
$97$	−1.38783	−0.140913	−0.0704566	+	0.997515i	$0.522446\pi$
$98$	7.21538	0.728864
$99$	−0.584158	−0.0587100
$100$	8.48410	0.848410
$101$	13.5355	1.34683	0.673415	−	0.739265i	$-0.264827\pi$
$101$	13.5355	1.34683	0.673415	+	0.739265i	$0.264827\pi$
$102$	4.41117	0.436771
$103$	−4.84547	−0.477438	−0.238719	−	0.971089i	$-0.576727\pi$
$103$	−4.84547	−0.477438	−0.238719	+	0.971089i	$0.576727\pi$
$104$	4.53130	0.444331
$105$	−19.9324	−1.94520
$106$	2.27143	0.220621
$107$	−4.01343	−0.387993	−0.193997	−	0.981002i	$-0.562145\pi$
$107$	−4.01343	−0.387993	−0.193997	+	0.981002i	$0.562145\pi$
$108$	5.65408	0.544064
$109$	−15.8730	−1.52036	−0.760180	−	0.649713i	$-0.774889\pi$
$109$	−15.8730	−1.52036	−0.760180	+	0.649713i	$0.774889\pi$
$110$	−2.31326	−0.220561
$111$	−11.3365	−1.07601
$112$	−3.77033	−0.356263
$113$	4.35116	0.409322	0.204661	−	0.978833i	$-0.434391\pi$
$113$	4.35116	0.409322	0.204661	+	0.978833i	$0.434391\pi$
$114$	1.43969	0.134839
$115$	−13.0641	−1.21824
$116$	−9.36074	−0.869123
$117$	−4.20183	−0.388459
$118$	−6.76683	−0.622937
$119$	11.5522	1.05899
$120$	5.28665	0.482603
$121$	−10.6031	−0.963923
$122$	−2.24982	−0.203689
$123$	−12.2594	−1.10540
$124$	0.222431	0.0199749
$125$	−12.7939	−1.14432
$126$	3.49619	0.311465
$127$	−11.4501	−1.01603	−0.508015	−	0.861348i	$-0.669621\pi$
$127$	−11.4501	−1.01603	−0.508015	+	0.861348i	$0.669621\pi$
$128$	1.00000	0.0883883
$129$	−0.401497	−0.0353498
$130$	−16.6393	−1.45936
$131$	5.10803	0.446291	0.223145	−	0.974785i	$-0.428368\pi$
$131$	5.10803	0.446291	0.223145	+	0.974785i	$0.428368\pi$
$132$	−0.906951	−0.0789399
$133$	3.77033	0.326929
$134$	−10.4124	−0.899498
$135$	−20.7622	−1.78692
$136$	−3.06397	−0.262733
$137$	−9.26670	−0.791708	−0.395854	−	0.918313i	$-0.629551\pi$
$137$	−9.26670	−0.791708	−0.395854	+	0.918313i	$0.629551\pi$
$138$	−5.12199	−0.436013
$139$	−22.0397	−1.86939	−0.934693	−	0.355457i	$-0.884325\pi$
$139$	−22.0397	−1.86939	−0.934693	+	0.355457i	$0.884325\pi$
$140$	13.8449	1.17011
$141$	−10.2483	−0.863064
$142$	0.0542548	0.00455296
$143$	2.85455	0.238709
$144$	−0.927290	−0.0772742
$145$	34.3733	2.85455
$146$	1.62278	0.134303
$147$	−10.3879	−0.856781
$148$	7.87426	0.647260
$149$	15.7406	1.28952	0.644760	−	0.764385i	$-0.276957\pi$
$149$	15.7406	1.28952	0.644760	+	0.764385i	$0.276957\pi$
$150$	−12.2145	−0.997308
$151$	2.75455	0.224162	0.112081	−	0.993699i	$-0.464248\pi$
$151$	2.75455	0.224162	0.112081	+	0.993699i	$0.464248\pi$
$152$	−1.00000	−0.0811107
$153$	2.84119	0.229697
$154$	−2.37516	−0.191396
$155$	−0.816782	−0.0656055
$156$	−6.52367	−0.522312
$157$	−4.20120	−0.335292	−0.167646	−	0.985847i	$-0.553617\pi$
$157$	−4.20120	−0.335292	−0.167646	+	0.985847i	$0.553617\pi$
$158$	12.1272	0.964786
$159$	−3.27016	−0.259341
$160$	−3.67207	−0.290303
$161$	−13.4137	−1.05715
$162$	−5.35826	−0.420985
$163$	7.02538	0.550271	0.275135	−	0.961406i	$-0.411277\pi$
$163$	7.02538	0.550271	0.275135	+	0.961406i	$0.411277\pi$
$164$	8.51533	0.664935
$165$	3.33039	0.259270
$166$	11.8520	0.919890
$167$	−16.1367	−1.24869	−0.624347	−	0.781147i	$-0.714635\pi$
$167$	−16.1367	−1.24869	−0.624347	+	0.781147i	$0.714635\pi$
$168$	5.42811	0.418788
$169$	7.53270	0.579438
$170$	11.2511	0.862922
$171$	0.927290	0.0709116
$172$	0.278877	0.0212642
$173$	−8.72026	−0.662989	−0.331495	−	0.943457i	$-0.607553\pi$
$173$	−8.72026	−0.662989	−0.331495	+	0.943457i	$0.607553\pi$
$174$	13.4766	1.02166
$175$	−31.9878	−2.41805
$176$	0.629962	0.0474852
$177$	9.74214	0.732264
$178$	0.484681	0.0363284
$179$	13.2823	0.992764	0.496382	−	0.868104i	$-0.334662\pi$
$179$	13.2823	0.992764	0.496382	+	0.868104i	$0.334662\pi$
$180$	3.40507	0.253799
$181$	20.1230	1.49573	0.747866	−	0.663850i	$-0.231078\pi$
$181$	20.1230	1.49573	0.747866	+	0.663850i	$0.231078\pi$
$182$	−17.0845	−1.26639
$183$	3.23904	0.239437
$184$	3.55770	0.262277
$185$	−28.9148	−2.12586
$186$	−0.320232	−0.0234805
$187$	−1.93019	−0.141149
$188$	7.11842	0.519164
$189$	−21.3178	−1.55064
$190$	3.67207	0.266400
$191$	−5.29050	−0.382807	−0.191404	−	0.981511i	$-0.561304\pi$
$191$	−5.29050	−0.382807	−0.191404	+	0.981511i	$0.561304\pi$
$192$	−1.43969	−0.103901
$193$	2.82001	0.202989	0.101494	−	0.994836i	$-0.467638\pi$
$193$	2.82001	0.202989	0.101494	+	0.994836i	$0.467638\pi$
$194$	−1.38783	−0.0996407
$195$	23.9554	1.71548
$196$	7.21538	0.515385
$197$	−23.0321	−1.64097	−0.820486	−	0.571667i	$-0.806297\pi$
$197$	−23.0321	−1.64097	−0.820486	+	0.571667i	$0.806297\pi$
$198$	−0.584158	−0.0415143
$199$	−0.551348	−0.0390840	−0.0195420	−	0.999809i	$-0.506221\pi$
$199$	−0.551348	−0.0390840	−0.0195420	+	0.999809i	$0.506221\pi$
$200$	8.48410	0.599916
$201$	14.9907	1.05736
$202$	13.5355	0.952353
$203$	35.2931	2.47709
$204$	4.41117	0.308844
$205$	−31.2689	−2.18391
$206$	−4.84547	−0.337600
$207$	−3.29902	−0.229298
$208$	4.53130	0.314189
$209$	−0.629962	−0.0435754
$210$	−19.9324	−1.37547
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	2.27143	0.156003
$213$	−0.0781101	−0.00535202
$214$	−4.01343	−0.274353
$215$	−1.02406	−0.0698400
$216$	5.65408	0.384712
$217$	−0.838638	−0.0569305
$218$	−15.8730	−1.07506
$219$	−2.33631	−0.157873
$220$	−2.31326	−0.155960
$221$	−13.8838	−0.933924
$222$	−11.3365	−0.760856
$223$	−11.0832	−0.742183	−0.371092	−	0.928596i	$-0.621016\pi$
$223$	−11.0832	−0.742183	−0.371092	+	0.928596i	$0.621016\pi$
$224$	−3.77033	−0.251916
$225$	−7.86722	−0.524481
$226$	4.35116	0.289435
$227$	21.4624	1.42451	0.712255	−	0.701921i	$-0.247674\pi$
$227$	21.4624	1.42451	0.712255	+	0.701921i	$0.247674\pi$
$228$	1.43969	0.0953459
$229$	−9.85306	−0.651109	−0.325554	−	0.945523i	$-0.605551\pi$
$229$	−9.85306	−0.651109	−0.325554	+	0.945523i	$0.605551\pi$
$230$	−13.0641	−0.861423
$231$	3.41950	0.224987
$232$	−9.36074	−0.614563
$233$	25.3018	1.65758	0.828788	−	0.559562i	$-0.189031\pi$
$233$	25.3018	1.65758	0.828788	+	0.559562i	$0.189031\pi$
$234$	−4.20183	−0.274682
$235$	−26.1393	−1.70514
$236$	−6.76683	−0.440483
$237$	−17.4594	−1.13411
$238$	11.5522	0.748817
$239$	7.16014	0.463151	0.231575	−	0.972817i	$-0.425612\pi$
$239$	7.16014	0.463151	0.231575	+	0.972817i	$0.425612\pi$
$240$	5.28665	0.341252
$241$	−15.4863	−0.997559	−0.498779	−	0.866729i	$-0.666218\pi$
$241$	−15.4863	−0.997559	−0.498779	+	0.866729i	$0.666218\pi$
$242$	−10.6031	−0.681596
$243$	−9.24801	−0.593260
$244$	−2.24982	−0.144030
$245$	−26.4954	−1.69273
$246$	−12.2594	−0.781633
$247$	−4.53130	−0.288320
$248$	0.222431	0.0141244
$249$	−17.0632	−1.08133
$250$	−12.7939	−0.809154
$251$	25.2963	1.59669	0.798345	−	0.602201i	$-0.205709\pi$
$251$	25.2963	1.59669	0.798345	+	0.602201i	$0.205709\pi$
$252$	3.49619	0.220239
$253$	2.24122	0.140904
$254$	−11.4501	−0.718442
$255$	−16.1981	−1.01437
$256$	1.00000	0.0625000
$257$	−1.74501	−0.108851	−0.0544253	−	0.998518i	$-0.517333\pi$
$257$	−1.74501	−0.108851	−0.0544253	+	0.998518i	$0.517333\pi$
$258$	−0.401497	−0.0249961
$259$	−29.6885	−1.84476
$260$	−16.6393	−1.03192
$261$	8.68012	0.537286
$262$	5.10803	0.315575
$263$	−0.142995	−0.00881745	−0.00440872	−	0.999990i	$-0.501403\pi$
$263$	−0.142995	−0.00881745	−0.00440872	+	0.999990i	$0.501403\pi$
$264$	−0.906951	−0.0558189
$265$	−8.34086	−0.512375
$266$	3.77033	0.231174
$267$	−0.697791	−0.0427041
$268$	−10.4124	−0.636041
$269$	−30.0017	−1.82924	−0.914618	−	0.404319i	$-0.867509\pi$
$269$	−30.0017	−1.82924	−0.914618	+	0.404319i	$0.867509\pi$
$270$	−20.7622	−1.26355
$271$	−25.5111	−1.54969	−0.774844	−	0.632153i	$-0.782172\pi$
$271$	−25.5111	−1.54969	−0.774844	+	0.632153i	$0.782172\pi$
$272$	−3.06397	−0.185781
$273$	24.5964	1.48864
$274$	−9.26670	−0.559822
$275$	5.34466	0.322295
$276$	−5.12199	−0.308308
$277$	−13.9064	−0.835553	−0.417777	−	0.908550i	$-0.637191\pi$
$277$	−13.9064	−0.835553	−0.417777	+	0.908550i	$0.637191\pi$
$278$	−22.0397	−1.32186
$279$	−0.206258	−0.0123483
$280$	13.8449	0.827392
$281$	−17.3610	−1.03567	−0.517835	−	0.855481i	$-0.673262\pi$
$281$	−17.3610	−1.03567	−0.517835	+	0.855481i	$0.673262\pi$
$282$	−10.2483	−0.610279
$283$	−11.9563	−0.710729	−0.355365	−	0.934728i	$-0.615643\pi$
$283$	−11.9563	−0.710729	−0.355365	+	0.934728i	$0.615643\pi$
$284$	0.0542548	0.00321943
$285$	−5.28665	−0.313154
$286$	2.85455	0.168793
$287$	−32.1056	−1.89513
$288$	−0.927290	−0.0546411
$289$	−7.61207	−0.447769
$290$	34.3733	2.01847
$291$	1.99805	0.117128
$292$	1.62278	0.0949663
$293$	15.1912	0.887477	0.443739	−	0.896156i	$-0.353652\pi$
$293$	15.1912	0.887477	0.443739	+	0.896156i	$0.353652\pi$
$294$	−10.3879	−0.605836
$295$	24.8483	1.44672
$296$	7.87426	0.457682
$297$	3.56186	0.206680
$298$	15.7406	0.911828
$299$	16.1210	0.932303
$300$	−12.2145	−0.705203
$301$	−1.05146	−0.0606050
$302$	2.75455	0.158506
$303$	−19.4869	−1.11949
$304$	−1.00000	−0.0573539
$305$	8.26149	0.473051
$306$	2.84119	0.162420
$307$	7.76159	0.442978	0.221489	−	0.975163i	$-0.428908\pi$
$307$	7.76159	0.442978	0.221489	+	0.975163i	$0.428908\pi$
$308$	−2.37516	−0.135338
$309$	6.97598	0.396849
$310$	−0.816782	−0.0463901
$311$	1.38305	0.0784256	0.0392128	−	0.999231i	$-0.487515\pi$
$311$	1.38305	0.0784256	0.0392128	+	0.999231i	$0.487515\pi$
$312$	−6.52367	−0.369330
$313$	−27.0758	−1.53042	−0.765209	−	0.643783i	$-0.777364\pi$
$313$	−27.0758	−1.53042	−0.765209	+	0.643783i	$0.777364\pi$
$314$	−4.20120	−0.237087
$315$	−12.8383	−0.723354
$316$	12.1272	0.682207
$317$	−8.32248	−0.467437	−0.233718	−	0.972304i	$-0.575089\pi$
$317$	−8.32248	−0.467437	−0.233718	+	0.972304i	$0.575089\pi$
$318$	−3.27016	−0.183382
$319$	−5.89691	−0.330164
$320$	−3.67207	−0.205275
$321$	5.77811	0.322502
$322$	−13.4137	−0.747517
$323$	3.06397	0.170484
$324$	−5.35826	−0.297681
$325$	38.4440	2.13249
$326$	7.02538	0.389100
$327$	22.8522	1.26373
$328$	8.51533	0.470180
$329$	−26.8388	−1.47967
$330$	3.33039	0.183332
$331$	−1.32550	−0.0728558	−0.0364279	−	0.999336i	$-0.511598\pi$
$331$	−1.32550	−0.0728558	−0.0364279	+	0.999336i	$0.511598\pi$
$332$	11.8520	0.650461
$333$	−7.30172	−0.400132
$334$	−16.1367	−0.882960
$335$	38.2352	2.08901
$336$	5.42811	0.296128
$337$	23.8777	1.30070	0.650349	−	0.759635i	$-0.274623\pi$
$337$	23.8777	1.30070	0.650349	+	0.759635i	$0.274623\pi$
$338$	7.53270	0.409725
$339$	−6.26432	−0.340231
$340$	11.2511	0.610178
$341$	0.140123	0.00758809
$342$	0.927290	0.0501421
$343$	−0.812069	−0.0438476
$344$	0.278877	0.0150360
$345$	18.8083	1.01261
$346$	−8.72026	−0.468804
$347$	−17.7032	−0.950357	−0.475178	−	0.879890i	$-0.657616\pi$
$347$	−17.7032	−0.950357	−0.475178	+	0.879890i	$0.657616\pi$
$348$	13.4766	0.722420
$349$	4.75557	0.254560	0.127280	−	0.991867i	$-0.459375\pi$
$349$	4.75557	0.254560	0.127280	+	0.991867i	$0.459375\pi$
$350$	−31.9878	−1.70982
$351$	25.6204	1.36751
$352$	0.629962	0.0335771
$353$	20.3949	1.08551	0.542756	−	0.839891i	$-0.317381\pi$
$353$	20.3949	1.08551	0.542756	+	0.839891i	$0.317381\pi$
$354$	9.74214	0.517789
$355$	−0.199227	−0.0105739
$356$	0.484681	0.0256880
$357$	−16.6316	−0.880236
$358$	13.2823	0.701990
$359$	−35.2921	−1.86265	−0.931324	−	0.364192i	$-0.881345\pi$
$359$	−35.2921	−1.86265	−0.931324	+	0.364192i	$0.881345\pi$
$360$	3.40507	0.179463
$361$	1.00000	0.0526316
$362$	20.1230	1.05764
$363$	15.2653	0.801218
$364$	−17.0845	−0.895471
$365$	−5.95898	−0.311907
$366$	3.23904	0.169307
$367$	0.727242	0.0379617	0.0189809	−	0.999820i	$-0.493958\pi$
$367$	0.727242	0.0379617	0.0189809	+	0.999820i	$0.493958\pi$
$368$	3.55770	0.185458
$369$	−7.89618	−0.411059
$370$	−28.9148	−1.50321
$371$	−8.56405	−0.444623
$372$	−0.320232	−0.0166033
$373$	12.8575	0.665735	0.332868	−	0.942974i	$-0.391984\pi$
$373$	12.8575	0.665735	0.332868	+	0.942974i	$0.391984\pi$
$374$	−1.93019	−0.0998075
$375$	18.4192	0.951163
$376$	7.11842	0.367104
$377$	−42.4164	−2.18455
$378$	−21.3178	−1.09647
$379$	−4.59838	−0.236203	−0.118102	−	0.993002i	$-0.537681\pi$
$379$	−4.59838	−0.236203	−0.118102	+	0.993002i	$0.537681\pi$
$380$	3.67207	0.188373
$381$	16.4846	0.844530
$382$	−5.29050	−0.270686
$383$	21.4746	1.09730	0.548651	−	0.836051i	$-0.315141\pi$
$383$	21.4746	1.09730	0.548651	+	0.836051i	$0.315141\pi$
$384$	−1.43969	−0.0734689
$385$	8.72177	0.444503
$386$	2.82001	0.143535
$387$	−0.258600	−0.0131454
$388$	−1.38783	−0.0704566
$389$	−15.1628	−0.768786	−0.384393	−	0.923169i	$-0.625589\pi$
$389$	−15.1628	−0.768786	−0.384393	+	0.923169i	$0.625589\pi$
$390$	23.9554	1.21303
$391$	−10.9007	−0.551272
$392$	7.21538	0.364432
$393$	−7.35398	−0.370959
$394$	−23.0321	−1.16034
$395$	−44.5318	−2.24064
$396$	−0.584158	−0.0293550
$397$	−15.3128	−0.768526	−0.384263	−	0.923224i	$-0.625544\pi$
$397$	−15.3128	−0.768526	−0.384263	+	0.923224i	$0.625544\pi$
$398$	−0.551348	−0.0276366
$399$	−5.42811	−0.271745
$400$	8.48410	0.424205
$401$	8.33909	0.416434	0.208217	−	0.978083i	$-0.433234\pi$
$401$	8.33909	0.416434	0.208217	+	0.978083i	$0.433234\pi$
$402$	14.9907	0.747668
$403$	1.00790	0.0502072
$404$	13.5355	0.673415
$405$	19.6759	0.977704
$406$	35.2931	1.75157
$407$	4.96048	0.245882
$408$	4.41117	0.218386
$409$	17.1374	0.847391	0.423695	−	0.905805i	$-0.360733\pi$
$409$	17.1374	0.847391	0.423695	+	0.905805i	$0.360733\pi$
$410$	−31.2689	−1.54426
$411$	13.3412	0.658072
$412$	−4.84547	−0.238719
$413$	25.5132	1.25542
$414$	−3.29902	−0.162138
$415$	−43.5212	−2.13637
$416$	4.53130	0.222165
$417$	31.7304	1.55384
$418$	−0.629962	−0.0308124
$419$	−10.9632	−0.535588	−0.267794	−	0.963476i	$-0.586295\pi$
$419$	−10.9632	−0.535588	−0.267794	+	0.963476i	$0.586295\pi$
$420$	−19.9324	−0.972601
$421$	−8.48415	−0.413492	−0.206746	−	0.978395i	$-0.566287\pi$
$421$	−8.48415	−0.413492	−0.206746	+	0.978395i	$0.566287\pi$
$422$	1.00000	0.0486792
$423$	−6.60084	−0.320944
$424$	2.27143	0.110311
$425$	−25.9950	−1.26094
$426$	−0.0781101	−0.00378445
$427$	8.48255	0.410500
$428$	−4.01343	−0.193997
$429$	−4.10967	−0.198417
$430$	−1.02406	−0.0493843
$431$	9.48471	0.456863	0.228431	−	0.973560i	$-0.426640\pi$
$431$	9.48471	0.456863	0.228431	+	0.973560i	$0.426640\pi$
$432$	5.65408	0.272032
$433$	−31.6704	−1.52198	−0.760992	−	0.648761i	$-0.775287\pi$
$433$	−31.6704	−1.52198	−0.760992	+	0.648761i	$0.775287\pi$
$434$	−0.838638	−0.0402559
$435$	−49.4869	−2.37272
$436$	−15.8730	−0.760180
$437$	−3.55770	−0.170188
$438$	−2.33631	−0.111633
$439$	5.50508	0.262743	0.131372	−	0.991333i	$-0.458062\pi$
$439$	5.50508	0.262743	0.131372	+	0.991333i	$0.458062\pi$
$440$	−2.31326	−0.110281
$441$	−6.69075	−0.318607
$442$	−13.8838	−0.660384
$443$	2.71519	0.129002	0.0645012	−	0.997918i	$-0.479454\pi$
$443$	2.71519	0.129002	0.0645012	+	0.997918i	$0.479454\pi$
$444$	−11.3365	−0.538006
$445$	−1.77978	−0.0843698
$446$	−11.0832	−0.524803
$447$	−22.6616	−1.07186
$448$	−3.77033	−0.178131
$449$	3.99752	0.188655	0.0943273	−	0.995541i	$-0.469930\pi$
$449$	3.99752	0.188655	0.0943273	+	0.995541i	$0.469930\pi$
$450$	−7.86722	−0.370864
$451$	5.36433	0.252597
$452$	4.35116	0.204661
$453$	−3.96570	−0.186325
$454$	21.4624	1.00728
$455$	62.7355	2.94108
$456$	1.43969	0.0674197
$457$	−27.3564	−1.27968	−0.639838	−	0.768509i	$-0.720999\pi$
$457$	−27.3564	−1.27968	−0.639838	+	0.768509i	$0.720999\pi$
$458$	−9.85306	−0.460403
$459$	−17.3240	−0.808613
$460$	−13.0641	−0.609118
$461$	−13.3011	−0.619492	−0.309746	−	0.950819i	$-0.600244\pi$
$461$	−13.3011	−0.619492	−0.309746	+	0.950819i	$0.600244\pi$
$462$	3.41950	0.159090
$463$	0.389921	0.0181212	0.00906059	−	0.999959i	$-0.497116\pi$
$463$	0.389921	0.0181212	0.00906059	+	0.999959i	$0.497116\pi$
$464$	−9.36074	−0.434562
$465$	1.17591	0.0545317
$466$	25.3018	1.17208
$467$	32.3122	1.49523	0.747615	−	0.664132i	$-0.231199\pi$
$467$	32.3122	1.49523	0.747615	+	0.664132i	$0.231199\pi$
$468$	−4.20183	−0.194230
$469$	39.2583	1.81278
$470$	−26.1393	−1.20572
$471$	6.04843	0.278697
$472$	−6.76683	−0.311469
$473$	0.175682	0.00807786
$474$	−17.4594	−0.801936
$475$	−8.48410	−0.389277
$476$	11.5522	0.529494
$477$	−2.10628	−0.0964398
$478$	7.16014	0.327497
$479$	−1.67908	−0.0767190	−0.0383595	−	0.999264i	$-0.512213\pi$
$479$	−1.67908	−0.0767190	−0.0383595	+	0.999264i	$0.512213\pi$
$480$	5.28665	0.241301
$481$	35.6806	1.62690
$482$	−15.4863	−0.705381
$483$	19.3116	0.878708
$484$	−10.6031	−0.481961
$485$	5.09622	0.231408
$486$	−9.24801	−0.419498
$487$	−11.7935	−0.534416	−0.267208	−	0.963639i	$-0.586101\pi$
$487$	−11.7935	−0.534416	−0.267208	+	0.963639i	$0.586101\pi$
$488$	−2.24982	−0.101844
$489$	−10.1144	−0.457388
$490$	−26.4954	−1.19694
$491$	−20.1838	−0.910881	−0.455440	−	0.890266i	$-0.650518\pi$
$491$	−20.1838	−0.910881	−0.455440	+	0.890266i	$0.650518\pi$
$492$	−12.2594	−0.552698
$493$	28.6811	1.29173
$494$	−4.53130	−0.203873
$495$	2.14507	0.0964136
$496$	0.222431	0.00998745
$497$	−0.204558	−0.00917570
$498$	−17.0632	−0.764618
$499$	−24.2607	−1.08606	−0.543030	−	0.839713i	$-0.682723\pi$
$499$	−24.2607	−1.08606	−0.543030	+	0.839713i	$0.682723\pi$
$500$	−12.7939	−0.572158
$501$	23.2318	1.03792
$502$	25.2963	1.12903
$503$	2.87789	0.128319	0.0641594	−	0.997940i	$-0.479563\pi$
$503$	2.87789	0.128319	0.0641594	+	0.997940i	$0.479563\pi$
$504$	3.49619	0.155733
$505$	−49.7032	−2.21176
$506$	2.24122	0.0996342
$507$	−10.8448	−0.481633
$508$	−11.4501	−0.508015
$509$	−1.62924	−0.0722148	−0.0361074	−	0.999348i	$-0.511496\pi$
$509$	−1.62924	−0.0722148	−0.0361074	+	0.999348i	$0.511496\pi$
$510$	−16.1981	−0.717265
$511$	−6.11843	−0.270663
$512$	1.00000	0.0441942
$513$	−5.65408	−0.249634
$514$	−1.74501	−0.0769689
$515$	17.7929	0.784049
$516$	−0.401497	−0.0176749
$517$	4.48433	0.197221
$518$	−29.6885	−1.30444
$519$	12.5545	0.551081
$520$	−16.6393	−0.729680
$521$	39.1957	1.71719	0.858597	−	0.512651i	$-0.171336\pi$
$521$	39.1957	1.71719	0.858597	+	0.512651i	$0.171336\pi$
$522$	8.68012	0.379919
$523$	15.8464	0.692915	0.346458	−	0.938066i	$-0.387384\pi$
$523$	15.8464	0.692915	0.346458	+	0.938066i	$0.387384\pi$
$524$	5.10803	0.223145
$525$	46.0526	2.00990
$526$	−0.142995	−0.00623488
$527$	−0.681523	−0.0296876
$528$	−0.906951	−0.0394700
$529$	−10.3428	−0.449685
$530$	−8.34086	−0.362304
$531$	6.27481	0.272304
$532$	3.77033	0.163465
$533$	38.5855	1.67132
$534$	−0.697791	−0.0301964
$535$	14.7376	0.637163
$536$	−10.4124	−0.449749
$537$	−19.1224	−0.825191
$538$	−30.0017	−1.29347
$539$	4.54542	0.195785
$540$	−20.7622	−0.893462
$541$	−5.96987	−0.256665	−0.128332	−	0.991731i	$-0.540962\pi$
$541$	−5.96987	−0.256665	−0.128332	+	0.991731i	$0.540962\pi$
$542$	−25.5111	−1.09579
$543$	−28.9709	−1.24326
$544$	−3.06397	−0.131367
$545$	58.2868	2.49673
$546$	24.5964	1.05263
$547$	15.1922	0.649571	0.324786	−	0.945788i	$-0.394708\pi$
$547$	15.1922	0.649571	0.324786	+	0.945788i	$0.394708\pi$
$548$	−9.26670	−0.395854
$549$	2.08623	0.0890383
$550$	5.34466	0.227897
$551$	9.36074	0.398781
$552$	−5.12199	−0.218006
$553$	−45.7234	−1.94436
$554$	−13.9064	−0.590825
$555$	41.6284	1.76703
$556$	−22.0397	−0.934693
$557$	8.00895	0.339350	0.169675	−	0.985500i	$-0.445728\pi$
$557$	8.00895	0.339350	0.169675	+	0.985500i	$0.445728\pi$
$558$	−0.206258	−0.00873160
$559$	1.26368	0.0534478
$560$	13.8449	0.585054
$561$	2.77887	0.117324
$562$	−17.3610	−0.732329
$563$	−20.7468	−0.874374	−0.437187	−	0.899371i	$-0.644025\pi$
$563$	−20.7468	−0.874374	−0.437187	+	0.899371i	$0.644025\pi$
$564$	−10.2483	−0.431532
$565$	−15.9777	−0.672189
$566$	−11.9563	−0.502562
$567$	20.2024	0.848422
$568$	0.0542548	0.00227648
$569$	32.2125	1.35042	0.675209	−	0.737627i	$-0.264054\pi$
$569$	32.2125	1.35042	0.675209	+	0.737627i	$0.264054\pi$
$570$	−5.28665	−0.221433
$571$	31.0150	1.29794	0.648968	−	0.760816i	$-0.275201\pi$
$571$	31.0150	1.29794	0.648968	+	0.760816i	$0.275201\pi$
$572$	2.85455	0.119355
$573$	7.61669	0.318192
$574$	−32.1056	−1.34006
$575$	30.1839	1.25875
$576$	−0.927290	−0.0386371
$577$	−14.3000	−0.595317	−0.297658	−	0.954672i	$-0.596206\pi$
$577$	−14.3000	−0.595317	−0.297658	+	0.954672i	$0.596206\pi$
$578$	−7.61207	−0.316621
$579$	−4.05995	−0.168726
$580$	34.3733	1.42727
$581$	−44.6858	−1.85388
$582$	1.99805	0.0828219
$583$	1.43092	0.0592625
$584$	1.62278	0.0671513
$585$	15.4294	0.637928
$586$	15.1912	0.627541
$587$	9.87256	0.407484	0.203742	−	0.979025i	$-0.434690\pi$
$587$	9.87256	0.407484	0.203742	+	0.979025i	$0.434690\pi$
$588$	−10.3879	−0.428391
$589$	−0.222431	−0.00916511
$590$	24.8483	1.02299
$591$	33.1592	1.36399
$592$	7.87426	0.323630
$593$	5.64281	0.231723	0.115861	−	0.993265i	$-0.463037\pi$
$593$	5.64281	0.231723	0.115861	+	0.993265i	$0.463037\pi$
$594$	3.56186	0.146145
$595$	−42.4204	−1.73907
$596$	15.7406	0.644760
$597$	0.793771	0.0324869
$598$	16.1210	0.659237
$599$	16.7223	0.683255	0.341628	−	0.939835i	$-0.389022\pi$
$599$	16.7223	0.683255	0.341628	+	0.939835i	$0.389022\pi$
$600$	−12.2145	−0.498654
$601$	−30.9579	−1.26280	−0.631400	−	0.775457i	$-0.717520\pi$
$601$	−30.9579	−1.26280	−0.631400	+	0.775457i	$0.717520\pi$
$602$	−1.05146	−0.0428542
$603$	9.65535	0.393196
$604$	2.75455	0.112081
$605$	38.9355	1.58295
$606$	−19.4869	−0.791601
$607$	45.7954	1.85878	0.929389	−	0.369102i	$-0.120335\pi$
$607$	45.7954	1.85878	0.929389	+	0.369102i	$0.120335\pi$
$608$	−1.00000	−0.0405554
$609$	−50.8111	−2.05897
$610$	8.26149	0.334498
$611$	32.2557	1.30493
$612$	2.84119	0.114848
$613$	14.3832	0.580931	0.290466	−	0.956885i	$-0.406190\pi$
$613$	14.3832	0.580931	0.290466	+	0.956885i	$0.406190\pi$
$614$	7.76159	0.313232
$615$	45.0175	1.81528
$616$	−2.37516	−0.0956981
$617$	7.26922	0.292648	0.146324	−	0.989237i	$-0.453256\pi$
$617$	7.26922	0.292648	0.146324	+	0.989237i	$0.453256\pi$
$618$	6.97598	0.280615
$619$	24.5426	0.986450	0.493225	−	0.869902i	$-0.335818\pi$
$619$	24.5426	0.986450	0.493225	+	0.869902i	$0.335818\pi$
$620$	−0.816782	−0.0328028
$621$	20.1155	0.807209
$622$	1.38305	0.0554553
$623$	−1.82741	−0.0732135
$624$	−6.52367	−0.261156
$625$	4.55942	0.182377
$626$	−27.0758	−1.08217
$627$	0.906951	0.0362201
$628$	−4.20120	−0.167646
$629$	−24.1265	−0.961987
$630$	−12.8383	−0.511488
$631$	12.4390	0.495188	0.247594	−	0.968864i	$-0.420360\pi$
$631$	12.4390	0.495188	0.247594	+	0.968864i	$0.420360\pi$
$632$	12.1272	0.482393
$633$	−1.43969	−0.0572226
$634$	−8.32248	−0.330528
$635$	42.0455	1.66852
$636$	−3.27016	−0.129670
$637$	32.6951	1.29543
$638$	−5.89691	−0.233461
$639$	−0.0503099	−0.00199023
$640$	−3.67207	−0.145151
$641$	−36.2406	−1.43142	−0.715708	−	0.698399i	$-0.753896\pi$
$641$	−36.2406	−1.43142	−0.715708	+	0.698399i	$0.753896\pi$
$642$	5.77811	0.228044
$643$	−3.07577	−0.121297	−0.0606483	−	0.998159i	$-0.519317\pi$
$643$	−3.07577	−0.121297	−0.0606483	+	0.998159i	$0.519317\pi$
$644$	−13.4137	−0.528574
$645$	1.47432	0.0580514
$646$	3.06397	0.120550
$647$	33.3747	1.31210	0.656048	−	0.754719i	$-0.272227\pi$
$647$	33.3747	1.31210	0.656048	+	0.754719i	$0.272227\pi$
$648$	−5.35826	−0.210492
$649$	−4.26285	−0.167331
$650$	38.4440	1.50790
$651$	1.20738	0.0473210
$652$	7.02538	0.275135
$653$	−32.1590	−1.25848	−0.629240	−	0.777211i	$-0.716634\pi$
$653$	−32.1590	−1.25848	−0.629240	+	0.777211i	$0.716634\pi$
$654$	22.8522	0.893593
$655$	−18.7570	−0.732898
$656$	8.51533	0.332468
$657$	−1.50479	−0.0587075
$658$	−26.8388	−1.04628
$659$	−5.20755	−0.202857	−0.101429	−	0.994843i	$-0.532341\pi$
$659$	−5.20755	−0.202857	−0.101429	+	0.994843i	$0.532341\pi$
$660$	3.33039	0.129635
$661$	32.7283	1.27298	0.636491	−	0.771284i	$-0.280385\pi$
$661$	32.7283	1.27298	0.636491	+	0.771284i	$0.280385\pi$
$662$	−1.32550	−0.0515168
$663$	19.9884	0.776283
$664$	11.8520	0.459945
$665$	−13.8449	−0.536883
$666$	−7.30172	−0.282936
$667$	−33.3027	−1.28949
$668$	−16.1367	−0.624347
$669$	15.9563	0.616907
$670$	38.2352	1.47716
$671$	−1.41730	−0.0547142
$672$	5.42811	0.209394
$673$	−47.4706	−1.82986	−0.914929	−	0.403616i	$-0.867753\pi$
$673$	−47.4706	−1.82986	−0.914929	+	0.403616i	$0.867753\pi$
$674$	23.8777	0.919733
$675$	47.9698	1.84636
$676$	7.53270	0.289719
$677$	2.08942	0.0803029	0.0401515	−	0.999194i	$-0.487216\pi$
$677$	2.08942	0.0803029	0.0401515	+	0.999194i	$0.487216\pi$
$678$	−6.26432	−0.240580
$679$	5.23259	0.200808
$680$	11.2511	0.431461
$681$	−30.8992	−1.18406
$682$	0.140123	0.00536559
$683$	−23.1012	−0.883945	−0.441972	−	0.897029i	$-0.645721\pi$
$683$	−23.1012	−0.883945	−0.441972	+	0.897029i	$0.645721\pi$
$684$	0.927290	0.0354558
$685$	34.0280	1.30014
$686$	−0.812069	−0.0310050
$687$	14.1854	0.541205
$688$	0.278877	0.0106321
$689$	10.2925	0.392115
$690$	18.8083	0.716020
$691$	8.40732	0.319830	0.159915	−	0.987131i	$-0.448878\pi$
$691$	8.40732	0.319830	0.159915	+	0.987131i	$0.448878\pi$
$692$	−8.72026	−0.331495
$693$	2.20247	0.0836648
$694$	−17.7032	−0.672004
$695$	80.9314	3.06990
$696$	13.4766	0.510828
$697$	−26.0907	−0.988257
$698$	4.75557	0.180001
$699$	−36.4268	−1.37779
$700$	−31.9878	−1.20903
$701$	10.3082	0.389333	0.194667	−	0.980869i	$-0.437637\pi$
$701$	10.3082	0.389333	0.194667	+	0.980869i	$0.437637\pi$
$702$	25.6204	0.966978
$703$	−7.87426	−0.296983
$704$	0.629962	0.0237426
$705$	37.6325	1.41732
$706$	20.3949	0.767572
$707$	−51.0332	−1.91930
$708$	9.74214	0.366132
$709$	−22.5776	−0.847918	−0.423959	−	0.905681i	$-0.639360\pi$
$709$	−22.5776	−0.847918	−0.423959	+	0.905681i	$0.639360\pi$
$710$	−0.199227	−0.00747687
$711$	−11.2454	−0.421736
$712$	0.484681	0.0181642
$713$	0.791343	0.0296360
$714$	−16.6316	−0.622421
$715$	−10.4821	−0.392008
$716$	13.2823	0.496382
$717$	−10.3084	−0.384974
$718$	−35.2921	−1.31709
$719$	16.4743	0.614387	0.307194	−	0.951647i	$-0.400610\pi$
$719$	16.4743	0.614387	0.307194	+	0.951647i	$0.400610\pi$
$720$	3.40507	0.126900
$721$	18.2690	0.680373
$722$	1.00000	0.0372161
$723$	22.2954	0.829177
$724$	20.1230	0.747866
$725$	−79.4175	−2.94949
$726$	15.2653	0.566547
$727$	45.6712	1.69385	0.846926	−	0.531710i	$-0.178451\pi$
$727$	45.6712	1.69385	0.846926	+	0.531710i	$0.178451\pi$
$728$	−17.0845	−0.633194
$729$	29.3891	1.08848
$730$	−5.95898	−0.220552
$731$	−0.854471	−0.0316038
$732$	3.23904	0.119718
$733$	46.1813	1.70575	0.852873	−	0.522118i	$-0.174858\pi$
$733$	46.1813	1.70575	0.852873	+	0.522118i	$0.174858\pi$
$734$	0.727242	0.0268430
$735$	38.1452	1.40701
$736$	3.55770	0.131139
$737$	−6.55944	−0.241620
$738$	−7.89618	−0.290662
$739$	−5.76193	−0.211956	−0.105978	−	0.994368i	$-0.533797\pi$
$739$	−5.76193	−0.211956	−0.105978	+	0.994368i	$0.533797\pi$
$740$	−28.9148	−1.06293
$741$	6.52367	0.239653
$742$	−8.56405	−0.314396
$743$	−32.7478	−1.20140	−0.600700	−	0.799475i	$-0.705111\pi$
$743$	−32.7478	−1.20140	−0.600700	+	0.799475i	$0.705111\pi$
$744$	−0.320232	−0.0117403
$745$	−57.8006	−2.11765
$746$	12.8575	0.470746
$747$	−10.9902	−0.402111
$748$	−1.93019	−0.0705746
$749$	15.1320	0.552910
$750$	18.4192	0.672574
$751$	21.8403	0.796966	0.398483	−	0.917176i	$-0.369537\pi$
$751$	21.8403	0.796966	0.398483	+	0.917176i	$0.369537\pi$
$752$	7.11842	0.259582
$753$	−36.4189	−1.32718
$754$	−42.4164	−1.54471
$755$	−10.1149	−0.368119
$756$	−21.3178	−0.775319
$757$	−3.82330	−0.138960	−0.0694801	−	0.997583i	$-0.522134\pi$
$757$	−3.82330	−0.138960	−0.0694801	+	0.997583i	$0.522134\pi$
$758$	−4.59838	−0.167021
$759$	−3.22666	−0.117120
$760$	3.67207	0.133200
$761$	22.5992	0.819221	0.409611	−	0.912260i	$-0.365665\pi$
$761$	22.5992	0.819221	0.409611	+	0.912260i	$0.365665\pi$
$762$	16.4846	0.597173
$763$	59.8465	2.16659
$764$	−5.29050	−0.191404
$765$	−10.4331	−0.377208
$766$	21.4746	0.775910
$767$	−30.6625	−1.10716
$768$	−1.43969	−0.0519504
$769$	−32.7724	−1.18180	−0.590902	−	0.806743i	$-0.701228\pi$
$769$	−32.7724	−1.18180	−0.590902	+	0.806743i	$0.701228\pi$
$770$	8.72177	0.314311
$771$	2.51227	0.0904772
$772$	2.82001	0.101494
$773$	−1.15693	−0.0416118	−0.0208059	−	0.999784i	$-0.506623\pi$
$773$	−1.15693	−0.0416118	−0.0208059	+	0.999784i	$0.506623\pi$
$774$	−0.258600	−0.00929518
$775$	1.88713	0.0677876
$776$	−1.38783	−0.0498203
$777$	42.7423	1.53337
$778$	−15.1628	−0.543614
$779$	−8.51533	−0.305093
$780$	23.9554	0.857740
$781$	0.0341784	0.00122300
$782$	−10.9007	−0.389808
$783$	−52.9264	−1.89144
$784$	7.21538	0.257692
$785$	15.4271	0.550617
$786$	−7.35398	−0.262308
$787$	5.07152	0.180780	0.0903901	−	0.995906i	$-0.471189\pi$
$787$	5.07152	0.180780	0.0903901	+	0.995906i	$0.471189\pi$
$788$	−23.0321	−0.820486
$789$	0.205869	0.00732912
$790$	−44.5318	−1.58437
$791$	−16.4053	−0.583305
$792$	−0.584158	−0.0207571
$793$	−10.1946	−0.362021
$794$	−15.3128	−0.543430
$795$	12.0083	0.425889
$796$	−0.551348	−0.0195420
$797$	13.1633	0.466269	0.233134	−	0.972445i	$-0.425102\pi$
$797$	13.1633	0.466269	0.233134	+	0.972445i	$0.425102\pi$
$798$	−5.42811	−0.192153
$799$	−21.8106	−0.771605
$800$	8.48410	0.299958
$801$	−0.449440	−0.0158802
$802$	8.33909	0.294463
$803$	1.02229	0.0360759
$804$	14.9907	0.528681
$805$	49.2561	1.73605
$806$	1.00790	0.0355018
$807$	43.1932	1.52047
$808$	13.5355	0.476176
$809$	−41.9335	−1.47430	−0.737152	−	0.675727i	$-0.763830\pi$
$809$	−41.9335	−1.47430	−0.737152	+	0.675727i	$0.763830\pi$
$810$	19.6759	0.691341
$811$	−27.3896	−0.961780	−0.480890	−	0.876781i	$-0.659686\pi$
$811$	−27.3896	−0.961780	−0.480890	+	0.876781i	$0.659686\pi$
$812$	35.2931	1.23854
$813$	36.7281	1.28811
$814$	4.96048	0.173865
$815$	−25.7977	−0.903654
$816$	4.41117	0.154422
$817$	−0.278877	−0.00975667
$818$	17.1374	0.599196
$819$	15.8423	0.553574
$820$	−31.2689	−1.09196
$821$	−28.6562	−1.00011	−0.500055	−	0.865994i	$-0.666687\pi$
$821$	−28.6562	−1.00011	−0.500055	+	0.865994i	$0.666687\pi$
$822$	13.3412	0.465327
$823$	−8.01972	−0.279550	−0.139775	−	0.990183i	$-0.544638\pi$
$823$	−8.01972	−0.279550	−0.139775	+	0.990183i	$0.544638\pi$
$824$	−4.84547	−0.168800
$825$	−7.69466	−0.267894
$826$	25.5132	0.887717
$827$	−33.4730	−1.16397	−0.581985	−	0.813200i	$-0.697724\pi$
$827$	−33.4730	−1.16397	−0.581985	+	0.813200i	$0.697724\pi$
$828$	−3.29902	−0.114649
$829$	47.3182	1.64343	0.821714	−	0.569901i	$-0.193018\pi$
$829$	47.3182	1.64343	0.821714	+	0.569901i	$0.193018\pi$
$830$	−43.5212	−1.51064
$831$	20.0209	0.694517
$832$	4.53130	0.157095
$833$	−22.1077	−0.765988
$834$	31.7304	1.09873
$835$	59.2550	2.05060
$836$	−0.629962	−0.0217877
$837$	1.25764	0.0434705
$838$	−10.9632	−0.378718
$839$	8.96043	0.309348	0.154674	−	0.987966i	$-0.450567\pi$
$839$	8.96043	0.309348	0.154674	+	0.987966i	$0.450567\pi$
$840$	−19.9324	−0.687733
$841$	58.6235	2.02150
$842$	−8.48415	−0.292383
$843$	24.9945	0.860855
$844$	1.00000	0.0344214
$845$	−27.6606	−0.951553
$846$	−6.60084	−0.226941
$847$	39.9774	1.37364
$848$	2.27143	0.0780013
$849$	17.2134	0.590762
$850$	−25.9950	−0.891622
$851$	28.0143	0.960316
$852$	−0.0781101	−0.00267601
$853$	−4.85212	−0.166133	−0.0830667	−	0.996544i	$-0.526471\pi$
$853$	−4.85212	−0.166133	−0.0830667	+	0.996544i	$0.526471\pi$
$854$	8.48255	0.290267
$855$	−3.40507	−0.116451
$856$	−4.01343	−0.137176
$857$	−3.49197	−0.119283	−0.0596417	−	0.998220i	$-0.518996\pi$
$857$	−3.49197	−0.119283	−0.0596417	+	0.998220i	$0.518996\pi$
$858$	−4.10967	−0.140302
$859$	−12.9895	−0.443198	−0.221599	−	0.975138i	$-0.571128\pi$
$859$	−12.9895	−0.443198	−0.221599	+	0.975138i	$0.571128\pi$
$860$	−1.02406	−0.0349200
$861$	46.2221	1.57525
$862$	9.48471	0.323051
$863$	14.1973	0.483281	0.241641	−	0.970366i	$-0.422315\pi$
$863$	14.1973	0.483281	0.241641	+	0.970366i	$0.422315\pi$
$864$	5.65408	0.192356
$865$	32.0214	1.08876
$866$	−31.6704	−1.07620
$867$	10.9590	0.372188
$868$	−0.838638	−0.0284652
$869$	7.63966	0.259158
$870$	−49.4869	−1.67776
$871$	−47.1819	−1.59870
$872$	−15.8730	−0.537528
$873$	1.28692	0.0435558
$874$	−3.55770	−0.120341
$875$	48.2370	1.63071
$876$	−2.33631	−0.0789365
$877$	6.34579	0.214282	0.107141	−	0.994244i	$-0.465830\pi$
$877$	6.34579	0.214282	0.107141	+	0.994244i	$0.465830\pi$
$878$	5.50508	0.185787
$879$	−21.8706	−0.737677
$880$	−2.31326	−0.0779801
$881$	−35.3711	−1.19168	−0.595842	−	0.803102i	$-0.703182\pi$
$881$	−35.3711	−1.19168	−0.595842	+	0.803102i	$0.703182\pi$
$882$	−6.69075	−0.225289
$883$	−41.2524	−1.38825	−0.694126	−	0.719853i	$-0.744209\pi$
$883$	−41.2524	−1.38825	−0.694126	+	0.719853i	$0.744209\pi$
$884$	−13.8838	−0.466962
$885$	−35.7738	−1.20252
$886$	2.71519	0.0912185
$887$	−23.3461	−0.783886	−0.391943	−	0.919989i	$-0.628197\pi$
$887$	−23.3461	−0.783886	−0.391943	+	0.919989i	$0.628197\pi$
$888$	−11.3365	−0.380428
$889$	43.1705	1.44789
$890$	−1.77978	−0.0596584
$891$	−3.37550	−0.113084
$892$	−11.0832	−0.371092
$893$	−7.11842	−0.238209
$894$	−22.6616	−0.757917
$895$	−48.7734	−1.63032
$896$	−3.77033	−0.125958
$897$	−23.2093	−0.774935
$898$	3.99752	0.133399
$899$	−2.08212	−0.0694426
$900$	−7.86722	−0.262241
$901$	−6.95961	−0.231858
$902$	5.36433	0.178613
$903$	1.51377	0.0503753
$904$	4.35116	0.144717
$905$	−73.8931	−2.45629
$906$	−3.96570	−0.131751
$907$	−36.8880	−1.22485	−0.612424	−	0.790530i	$-0.709805\pi$
$907$	−36.8880	−1.22485	−0.612424	+	0.790530i	$0.709805\pi$
$908$	21.4624	0.712255
$909$	−12.5513	−0.416301
$910$	62.7355	2.07966
$911$	28.3934	0.940716	0.470358	−	0.882476i	$-0.344125\pi$
$911$	28.3934	0.940716	0.470358	+	0.882476i	$0.344125\pi$
$912$	1.43969	0.0476729
$913$	7.46628	0.247098
$914$	−27.3564	−0.904868
$915$	−11.8940	−0.393203
$916$	−9.85306	−0.325554
$917$	−19.2590	−0.635987
$918$	−17.3240	−0.571776
$919$	11.2879	0.372352	0.186176	−	0.982516i	$-0.440391\pi$
$919$	11.2879	0.372352	0.186176	+	0.982516i	$0.440391\pi$
$920$	−13.0641	−0.430712
$921$	−11.1743	−0.368206
$922$	−13.3011	−0.438047
$923$	0.245845	0.00809208
$924$	3.41950	0.112493
$925$	66.8060	2.19657
$926$	0.389921	0.0128136
$927$	4.49315	0.147575
$928$	−9.36074	−0.307281
$929$	−23.2103	−0.761505	−0.380753	−	0.924677i	$-0.624335\pi$
$929$	−23.2103	−0.761505	−0.380753	+	0.924677i	$0.624335\pi$
$930$	1.17591	0.0385597
$931$	−7.21538	−0.236475
$932$	25.3018	0.828788
$933$	−1.99117	−0.0651878
$934$	32.3122	1.05729
$935$	7.08778	0.231795
$936$	−4.20183	−0.137341
$937$	28.2536	0.923006	0.461503	−	0.887139i	$-0.347310\pi$
$937$	28.2536	0.923006	0.461503	+	0.887139i	$0.347310\pi$
$938$	39.2583	1.28183
$939$	38.9808	1.27209
$940$	−26.1393	−0.852571
$941$	−22.2667	−0.725873	−0.362937	−	0.931814i	$-0.618226\pi$
$941$	−22.2667	−0.725873	−0.362937	+	0.931814i	$0.618226\pi$
$942$	6.04843	0.197068
$943$	30.2950	0.986541
$944$	−6.76683	−0.220242
$945$	78.2803	2.54646
$946$	0.175682	0.00571191
$947$	−54.8506	−1.78240	−0.891202	−	0.453606i	$-0.850137\pi$
$947$	−54.8506	−1.78240	−0.891202	+	0.453606i	$0.850137\pi$
$948$	−17.4594	−0.567054
$949$	7.35333	0.238699
$950$	−8.48410	−0.275260
$951$	11.9818	0.388536
$952$	11.5522	0.374408
$953$	−4.35790	−0.141166	−0.0705831	−	0.997506i	$-0.522486\pi$
$953$	−4.35790	−0.141166	−0.0705831	+	0.997506i	$0.522486\pi$
$954$	−2.10628	−0.0681932
$955$	19.4271	0.628646
$956$	7.16014	0.231575
$957$	8.48973	0.274434
$958$	−1.67908	−0.0542485
$959$	34.9385	1.12822
$960$	5.28665	0.170626
$961$	−30.9505	−0.998404
$962$	35.6806	1.15039
$963$	3.72162	0.119927
$964$	−15.4863	−0.498779
$965$	−10.3553	−0.333348
$966$	19.3116	0.621340
$967$	8.04741	0.258787	0.129394	−	0.991593i	$-0.458697\pi$
$967$	8.04741	0.258787	0.129394	+	0.991593i	$0.458697\pi$
$968$	−10.6031	−0.340798
$969$	−4.41117	−0.141707
$970$	5.09622	0.163630
$971$	−17.2713	−0.554261	−0.277131	−	0.960832i	$-0.589384\pi$
$971$	−17.2713	−0.554261	−0.277131	+	0.960832i	$0.589384\pi$
$972$	−9.24801	−0.296630
$973$	83.0970	2.66397
$974$	−11.7935	−0.377889
$975$	−55.3475	−1.77254
$976$	−2.24982	−0.0720149
$977$	2.60980	0.0834948	0.0417474	−	0.999128i	$-0.486708\pi$
$977$	2.60980	0.0834948	0.0417474	+	0.999128i	$0.486708\pi$
$978$	−10.1144	−0.323422
$979$	0.305331	0.00975841
$980$	−26.4954	−0.846364
$981$	14.7189	0.469938
$982$	−20.1838	−0.644090
$983$	46.1033	1.47047	0.735234	−	0.677814i	$-0.237072\pi$
$983$	46.1033	1.47047	0.735234	+	0.677814i	$0.237072\pi$
$984$	−12.2594	−0.390817
$985$	84.5756	2.69480
$986$	28.6811	0.913391
$987$	38.6395	1.22991
$988$	−4.53130	−0.144160
$989$	0.992161	0.0315489
$990$	2.14507	0.0681747
$991$	−16.4351	−0.522079	−0.261039	−	0.965328i	$-0.584065\pi$
$991$	−16.4351	−0.522079	−0.261039	+	0.965328i	$0.584065\pi$
$992$	0.222431	0.00706219
$993$	1.90830	0.0605582
$994$	−0.204558	−0.00648820
$995$	2.02459	0.0641838
$996$	−17.0632	−0.540667
$997$	−43.3317	−1.37233	−0.686164	−	0.727446i	$-0.740707\pi$
$997$	−43.3317	−1.37233	−0.686164	+	0.727446i	$0.740707\pi$
$998$	−24.2607	−0.767961
$999$	44.5217	1.40860

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.e.1.11	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.e.1.11	✓	32	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.43969 q^{3} +1.00000 q^{4} -3.67207 q^{5} -1.43969 q^{6} -3.77033 q^{7} +1.00000 q^{8} -0.927290 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.43969 q^{3} +1.00000 q^{4} -3.67207 q^{5} -1.43969 q^{6} -3.77033 q^{7} +1.00000 q^{8} -0.927290 q^{9} -3.67207 q^{10} +0.629962 q^{11} -1.43969 q^{12} +4.53130 q^{13} -3.77033 q^{14} +5.28665 q^{15} +1.00000 q^{16} -3.06397 q^{17} -0.927290 q^{18} -1.00000 q^{19} -3.67207 q^{20} +5.42811 q^{21} +0.629962 q^{22} +3.55770 q^{23} -1.43969 q^{24} +8.48410 q^{25} +4.53130 q^{26} +5.65408 q^{27} -3.77033 q^{28} -9.36074 q^{29} +5.28665 q^{30} +0.222431 q^{31} +1.00000 q^{32} -0.906951 q^{33} -3.06397 q^{34} +13.8449 q^{35} -0.927290 q^{36} +7.87426 q^{37} -1.00000 q^{38} -6.52367 q^{39} -3.67207 q^{40} +8.51533 q^{41} +5.42811 q^{42} +0.278877 q^{43} +0.629962 q^{44} +3.40507 q^{45} +3.55770 q^{46} +7.11842 q^{47} -1.43969 q^{48} +7.21538 q^{49} +8.48410 q^{50} +4.41117 q^{51} +4.53130 q^{52} +2.27143 q^{53} +5.65408 q^{54} -2.31326 q^{55} -3.77033 q^{56} +1.43969 q^{57} -9.36074 q^{58} -6.76683 q^{59} +5.28665 q^{60} -2.24982 q^{61} +0.222431 q^{62} +3.49619 q^{63} +1.00000 q^{64} -16.6393 q^{65} -0.906951 q^{66} -10.4124 q^{67} -3.06397 q^{68} -5.12199 q^{69} +13.8449 q^{70} +0.0542548 q^{71} -0.927290 q^{72} +1.62278 q^{73} +7.87426 q^{74} -12.2145 q^{75} -1.00000 q^{76} -2.37516 q^{77} -6.52367 q^{78} +12.1272 q^{79} -3.67207 q^{80} -5.35826 q^{81} +8.51533 q^{82} +11.8520 q^{83} +5.42811 q^{84} +11.2511 q^{85} +0.278877 q^{86} +13.4766 q^{87} +0.629962 q^{88} +0.484681 q^{89} +3.40507 q^{90} -17.0845 q^{91} +3.55770 q^{92} -0.320232 q^{93} +7.11842 q^{94} +3.67207 q^{95} -1.43969 q^{96} -1.38783 q^{97} +7.21538 q^{98} -0.584158 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9}+O(q^{10}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9} - 6 q^{10} - 21 q^{11} - 7 q^{12} - 19 q^{13} - 5 q^{14} - 14 q^{15} + 32 q^{16} - 14 q^{17} + 15 q^{18} - 32 q^{19} - 6 q^{20} - 26 q^{21} - 21 q^{22} - 13 q^{23} - 7 q^{24} - 10 q^{25} - 19 q^{26} - 25 q^{27} - 5 q^{28} - 42 q^{29} - 14 q^{30} - 15 q^{31} + 32 q^{32} - 32 q^{33} - 14 q^{34} - 22 q^{35} + 15 q^{36} - 54 q^{37} - 32 q^{38} - 32 q^{39} - 6 q^{40} - 16 q^{41} - 26 q^{42} - 37 q^{43} - 21 q^{44} - 46 q^{45} - 13 q^{46} - 9 q^{47} - 7 q^{48} - 7 q^{49} - 10 q^{50} - 32 q^{51} - 19 q^{52} - 53 q^{53} - 25 q^{54} - 17 q^{55} - 5 q^{56} + 7 q^{57} - 42 q^{58} - 34 q^{59} - 14 q^{60} - 33 q^{61} - 15 q^{62} + 18 q^{63} + 32 q^{64} - 50 q^{65} - 32 q^{66} - 53 q^{67} - 14 q^{68} - 40 q^{69} - 22 q^{70} - 27 q^{71} + 15 q^{72} - 43 q^{73} - 54 q^{74} + 5 q^{75} - 32 q^{76} - 56 q^{77} - 32 q^{78} - 11 q^{79} - 6 q^{80} - 8 q^{81} - 16 q^{82} - 17 q^{83} - 26 q^{84} - 30 q^{85} - 37 q^{86} + 3 q^{87} - 21 q^{88} - 21 q^{89} - 46 q^{90} - 67 q^{91} - 13 q^{92} - 31 q^{93} - 9 q^{94} + 6 q^{95} - 7 q^{96} - 51 q^{97} - 7 q^{98} - 32 q^{99}+O(q^{100}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9 - 6 * q^10 - 21 * q^11 - 7 * q^12 - 19 * q^13 - 5 * q^14 - 14 * q^15 + 32 * q^16 - 14 * q^17 + 15 * q^18 - 32 * q^19 - 6 * q^20 - 26 * q^21 - 21 * q^22 - 13 * q^23 - 7 * q^24 - 10 * q^25 - 19 * q^26 - 25 * q^27 - 5 * q^28 - 42 * q^29 - 14 * q^30 - 15 * q^31 + 32 * q^32 - 32 * q^33 - 14 * q^34 - 22 * q^35 + 15 * q^36 - 54 * q^37 - 32 * q^38 - 32 * q^39 - 6 * q^40 - 16 * q^41 - 26 * q^42 - 37 * q^43 - 21 * q^44 - 46 * q^45 - 13 * q^46 - 9 * q^47 - 7 * q^48 - 7 * q^49 - 10 * q^50 - 32 * q^51 - 19 * q^52 - 53 * q^53 - 25 * q^54 - 17 * q^55 - 5 * q^56 + 7 * q^57 - 42 * q^58 - 34 * q^59 - 14 * q^60 - 33 * q^61 - 15 * q^62 + 18 * q^63 + 32 * q^64 - 50 * q^65 - 32 * q^66 - 53 * q^67 - 14 * q^68 - 40 * q^69 - 22 * q^70 - 27 * q^71 + 15 * q^72 - 43 * q^73 - 54 * q^74 + 5 * q^75 - 32 * q^76 - 56 * q^77 - 32 * q^78 - 11 * q^79 - 6 * q^80 - 8 * q^81 - 16 * q^82 - 17 * q^83 - 26 * q^84 - 30 * q^85 - 37 * q^86 + 3 * q^87 - 21 * q^88 - 21 * q^89 - 46 * q^90 - 67 * q^91 - 13 * q^92 - 31 * q^93 - 9 * q^94 + 6 * q^95 - 7 * q^96 - 51 * q^97 - 7 * q^98 - 32 * q^99

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