LMFDB - Embedded newform 8018.2.a.e.1.15

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			1.15
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.474859 q^{3} +1.00000 q^{4} +1.84074 q^{5} -0.474859 q^{6} +4.63773 q^{7} +1.00000 q^{8} -2.77451 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.474859 q^{3} +1.00000 q^{4} +1.84074 q^{5} -0.474859 q^{6} +4.63773 q^{7} +1.00000 q^{8} -2.77451 q^{9} +1.84074 q^{10} -5.62455 q^{11} -0.474859 q^{12} -3.04428 q^{13} +4.63773 q^{14} -0.874093 q^{15} +1.00000 q^{16} +7.21625 q^{17} -2.77451 q^{18} -1.00000 q^{19} +1.84074 q^{20} -2.20227 q^{21} -5.62455 q^{22} -8.22996 q^{23} -0.474859 q^{24} -1.61167 q^{25} -3.04428 q^{26} +2.74208 q^{27} +4.63773 q^{28} -8.57223 q^{29} -0.874093 q^{30} +0.266541 q^{31} +1.00000 q^{32} +2.67087 q^{33} +7.21625 q^{34} +8.53686 q^{35} -2.77451 q^{36} -10.8238 q^{37} -1.00000 q^{38} +1.44560 q^{39} +1.84074 q^{40} -3.55163 q^{41} -2.20227 q^{42} -10.1625 q^{43} -5.62455 q^{44} -5.10716 q^{45} -8.22996 q^{46} -7.87966 q^{47} -0.474859 q^{48} +14.5085 q^{49} -1.61167 q^{50} -3.42670 q^{51} -3.04428 q^{52} +3.45091 q^{53} +2.74208 q^{54} -10.3533 q^{55} +4.63773 q^{56} +0.474859 q^{57} -8.57223 q^{58} +2.72563 q^{59} -0.874093 q^{60} +3.87962 q^{61} +0.266541 q^{62} -12.8674 q^{63} +1.00000 q^{64} -5.60373 q^{65} +2.67087 q^{66} +7.13383 q^{67} +7.21625 q^{68} +3.90807 q^{69} +8.53686 q^{70} +9.28774 q^{71} -2.77451 q^{72} -2.70600 q^{73} -10.8238 q^{74} +0.765315 q^{75} -1.00000 q^{76} -26.0851 q^{77} +1.44560 q^{78} +4.17114 q^{79} +1.84074 q^{80} +7.02143 q^{81} -3.55163 q^{82} -8.39468 q^{83} -2.20227 q^{84} +13.2833 q^{85} -10.1625 q^{86} +4.07060 q^{87} -5.62455 q^{88} -5.02122 q^{89} -5.10716 q^{90} -14.1185 q^{91} -8.22996 q^{92} -0.126570 q^{93} -7.87966 q^{94} -1.84074 q^{95} -0.474859 q^{96} -8.87450 q^{97} +14.5085 q^{98} +15.6054 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.474859	−0.274160	−0.137080	−	0.990560i	$-0.543772\pi$
$3$	−0.474859	−0.274160	−0.137080	+	0.990560i	$0.543772\pi$
$4$	1.00000	0.500000
$5$	1.84074	0.823205	0.411603	−	0.911363i	$-0.364969\pi$
$5$	1.84074	0.823205	0.411603	+	0.911363i	$0.364969\pi$
$6$	−0.474859	−0.193860
$7$	4.63773	1.75290	0.876448	−	0.481496i	$-0.159906\pi$
$7$	4.63773	1.75290	0.876448	+	0.481496i	$0.159906\pi$
$8$	1.00000	0.353553
$9$	−2.77451	−0.924836
$10$	1.84074	0.582094
$11$	−5.62455	−1.69587	−0.847933	−	0.530104i	$-0.822153\pi$
$11$	−5.62455	−1.69587	−0.847933	+	0.530104i	$0.822153\pi$
$12$	−0.474859	−0.137080
$13$	−3.04428	−0.844331	−0.422166	−	0.906519i	$-0.638730\pi$
$13$	−3.04428	−0.844331	−0.422166	+	0.906519i	$0.638730\pi$
$14$	4.63773	1.23948
$15$	−0.874093	−0.225690
$16$	1.00000	0.250000
$17$	7.21625	1.75020	0.875099	−	0.483944i	$-0.160796\pi$
$17$	7.21625	1.75020	0.875099	+	0.483944i	$0.160796\pi$
$18$	−2.77451	−0.653958
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	1.84074	0.411603
$21$	−2.20227	−0.480574
$22$	−5.62455	−1.19916
$23$	−8.22996	−1.71606	−0.858032	−	0.513596i	$-0.828313\pi$
$23$	−8.22996	−1.71606	−0.858032	+	0.513596i	$0.828313\pi$
$24$	−0.474859	−0.0969302
$25$	−1.61167	−0.322333
$26$	−3.04428	−0.597032
$27$	2.74208	0.527713
$28$	4.63773	0.876448
$29$	−8.57223	−1.59182	−0.795912	−	0.605413i	$-0.793008\pi$
$29$	−8.57223	−1.59182	−0.795912	+	0.605413i	$0.793008\pi$
$30$	−0.874093	−0.159587
$31$	0.266541	0.0478722	0.0239361	−	0.999713i	$-0.492380\pi$
$31$	0.266541	0.0478722	0.0239361	+	0.999713i	$0.492380\pi$
$32$	1.00000	0.176777
$33$	2.67087	0.464939
$34$	7.21625	1.23758
$35$	8.53686	1.44299
$36$	−2.77451	−0.462418
$37$	−10.8238	−1.77942	−0.889712	−	0.456522i	$-0.849095\pi$
$37$	−10.8238	−1.77942	−0.889712	+	0.456522i	$0.849095\pi$
$38$	−1.00000	−0.162221
$39$	1.44560	0.231482
$40$	1.84074	0.291047
$41$	−3.55163	−0.554672	−0.277336	−	0.960773i	$-0.589451\pi$
$41$	−3.55163	−0.554672	−0.277336	+	0.960773i	$0.589451\pi$
$42$	−2.20227	−0.339817
$43$	−10.1625	−1.54977	−0.774884	−	0.632103i	$-0.782192\pi$
$43$	−10.1625	−1.54977	−0.774884	+	0.632103i	$0.782192\pi$
$44$	−5.62455	−0.847933
$45$	−5.10716	−0.761330
$46$	−8.22996	−1.21344
$47$	−7.87966	−1.14937	−0.574683	−	0.818376i	$-0.694875\pi$
$47$	−7.87966	−1.14937	−0.574683	+	0.818376i	$0.694875\pi$
$48$	−0.474859	−0.0685400
$49$	14.5085	2.07265
$50$	−1.61167	−0.227924
$51$	−3.42670	−0.479834
$52$	−3.04428	−0.422166
$53$	3.45091	0.474019	0.237010	−	0.971507i	$-0.423833\pi$
$53$	3.45091	0.474019	0.237010	+	0.971507i	$0.423833\pi$
$54$	2.74208	0.373150
$55$	−10.3533	−1.39605
$56$	4.63773	0.619742
$57$	0.474859	0.0628966
$58$	−8.57223	−1.12559
$59$	2.72563	0.354847	0.177423	−	0.984135i	$-0.443224\pi$
$59$	2.72563	0.354847	0.177423	+	0.984135i	$0.443224\pi$
$60$	−0.874093	−0.112845
$61$	3.87962	0.496735	0.248367	−	0.968666i	$-0.420106\pi$
$61$	3.87962	0.496735	0.248367	+	0.968666i	$0.420106\pi$
$62$	0.266541	0.0338508
$63$	−12.8674	−1.62114
$64$	1.00000	0.125000
$65$	−5.60373	−0.695058
$66$	2.67087	0.328761
$67$	7.13383	0.871536	0.435768	−	0.900059i	$-0.356477\pi$
$67$	7.13383	0.871536	0.435768	+	0.900059i	$0.356477\pi$
$68$	7.21625	0.875099
$69$	3.90807	0.470476
$70$	8.53686	1.02035
$71$	9.28774	1.10225	0.551126	−	0.834422i	$-0.314198\pi$
$71$	9.28774	1.10225	0.551126	+	0.834422i	$0.314198\pi$
$72$	−2.77451	−0.326979
$73$	−2.70600	−0.316713	−0.158357	−	0.987382i	$-0.550620\pi$
$73$	−2.70600	−0.316713	−0.158357	+	0.987382i	$0.550620\pi$
$74$	−10.8238	−1.25824
$75$	0.765315	0.0883709
$76$	−1.00000	−0.114708
$77$	−26.0851	−2.97268
$78$	1.44560	0.163682
$79$	4.17114	0.469290	0.234645	−	0.972081i	$-0.424607\pi$
$79$	4.17114	0.469290	0.234645	+	0.972081i	$0.424607\pi$
$80$	1.84074	0.205801
$81$	7.02143	0.780158
$82$	−3.55163	−0.392212
$83$	−8.39468	−0.921436	−0.460718	−	0.887547i	$-0.652408\pi$
$83$	−8.39468	−0.921436	−0.460718	+	0.887547i	$0.652408\pi$
$84$	−2.20227	−0.240287
$85$	13.2833	1.44077
$86$	−10.1625	−1.09585
$87$	4.07060	0.436414
$88$	−5.62455	−0.599579
$89$	−5.02122	−0.532248	−0.266124	−	0.963939i	$-0.585743\pi$
$89$	−5.02122	−0.532248	−0.266124	+	0.963939i	$0.585743\pi$
$90$	−5.10716	−0.538342
$91$	−14.1185	−1.48002
$92$	−8.22996	−0.858032
$93$	−0.126570	−0.0131247
$94$	−7.87966	−0.812724
$95$	−1.84074	−0.188856
$96$	−0.474859	−0.0484651
$97$	−8.87450	−0.901069	−0.450535	−	0.892759i	$-0.648767\pi$
$97$	−8.87450	−0.901069	−0.450535	+	0.892759i	$0.648767\pi$
$98$	14.5085	1.46558
$99$	15.6054	1.56840
$100$	−1.61167	−0.161167
$101$	0.474978	0.0472621	0.0236310	−	0.999721i	$-0.492477\pi$
$101$	0.474978	0.0472621	0.0236310	+	0.999721i	$0.492477\pi$
$102$	−3.42670	−0.339294
$103$	−12.5444	−1.23604	−0.618018	−	0.786164i	$-0.712064\pi$
$103$	−12.5444	−1.23604	−0.618018	+	0.786164i	$0.712064\pi$
$104$	−3.04428	−0.298516
$105$	−4.05381	−0.395611
$106$	3.45091	0.335182
$107$	13.8275	1.33676	0.668378	−	0.743821i	$-0.266989\pi$
$107$	13.8275	1.33676	0.668378	+	0.743821i	$0.266989\pi$
$108$	2.74208	0.263857
$109$	−16.8871	−1.61749	−0.808747	−	0.588157i	$-0.799854\pi$
$109$	−16.8871	−1.61749	−0.808747	+	0.588157i	$0.799854\pi$
$110$	−10.3533	−0.987153
$111$	5.13979	0.487847
$112$	4.63773	0.438224
$113$	−13.0647	−1.22902	−0.614511	−	0.788908i	$-0.710647\pi$
$113$	−13.0647	−1.22902	−0.614511	+	0.788908i	$0.710647\pi$
$114$	0.474859	0.0444746
$115$	−15.1492	−1.41267
$116$	−8.57223	−0.795912
$117$	8.44638	0.780868
$118$	2.72563	0.250915
$119$	33.4670	3.06792
$120$	−0.874093	−0.0797934
$121$	20.6356	1.87596
$122$	3.87962	0.351244
$123$	1.68653	0.152069
$124$	0.266541	0.0239361
$125$	−12.1704	−1.08855
$126$	−12.8674	−1.14632
$127$	−15.6739	−1.39084	−0.695419	−	0.718605i	$-0.744781\pi$
$127$	−15.6739	−1.39084	−0.695419	+	0.718605i	$0.744781\pi$
$128$	1.00000	0.0883883
$129$	4.82576	0.424885
$130$	−5.60373	−0.491480
$131$	4.99131	0.436093	0.218046	−	0.975938i	$-0.430032\pi$
$131$	4.99131	0.436093	0.218046	+	0.975938i	$0.430032\pi$
$132$	2.67087	0.232469
$133$	−4.63773	−0.402142
$134$	7.13383	0.616269
$135$	5.04746	0.434416
$136$	7.21625	0.618788
$137$	2.85260	0.243714	0.121857	−	0.992548i	$-0.461115\pi$
$137$	2.85260	0.243714	0.121857	+	0.992548i	$0.461115\pi$
$138$	3.90807	0.332677
$139$	8.04923	0.682727	0.341363	−	0.939931i	$-0.389111\pi$
$139$	8.04923	0.682727	0.341363	+	0.939931i	$0.389111\pi$
$140$	8.53686	0.721497
$141$	3.74173	0.315110
$142$	9.28774	0.779410
$143$	17.1227	1.43187
$144$	−2.77451	−0.231209
$145$	−15.7793	−1.31040
$146$	−2.70600	−0.223950
$147$	−6.88950	−0.568237
$148$	−10.8238	−0.889712
$149$	13.8500	1.13463	0.567316	−	0.823500i	$-0.307982\pi$
$149$	13.8500	1.13463	0.567316	+	0.823500i	$0.307982\pi$
$150$	0.765315	0.0624877
$151$	−14.4959	−1.17966	−0.589830	−	0.807528i	$-0.700805\pi$
$151$	−14.4959	−1.17966	−0.589830	+	0.807528i	$0.700805\pi$
$152$	−1.00000	−0.0811107
$153$	−20.0215	−1.61865
$154$	−26.0851	−2.10200
$155$	0.490634	0.0394087
$156$	1.44560	0.115741
$157$	−16.0173	−1.27832	−0.639160	−	0.769074i	$-0.720718\pi$
$157$	−16.0173	−1.27832	−0.639160	+	0.769074i	$0.720718\pi$
$158$	4.17114	0.331838
$159$	−1.63870	−0.129957
$160$	1.84074	0.145523
$161$	−38.1683	−3.00808
$162$	7.02143	0.551655
$163$	13.1324	1.02861	0.514305	−	0.857607i	$-0.328050\pi$
$163$	13.1324	1.02861	0.514305	+	0.857607i	$0.328050\pi$
$164$	−3.55163	−0.277336
$165$	4.91638	0.382740
$166$	−8.39468	−0.651553
$167$	18.8778	1.46081	0.730405	−	0.683014i	$-0.239331\pi$
$167$	18.8778	1.46081	0.730405	+	0.683014i	$0.239331\pi$
$168$	−2.20227	−0.169909
$169$	−3.73237	−0.287105
$170$	13.2833	1.01878
$171$	2.77451	0.212172
$172$	−10.1625	−0.774884
$173$	13.7005	1.04163	0.520814	−	0.853670i	$-0.325629\pi$
$173$	13.7005	1.04163	0.520814	+	0.853670i	$0.325629\pi$
$174$	4.07060	0.308592
$175$	−7.47447	−0.565017
$176$	−5.62455	−0.423966
$177$	−1.29429	−0.0972848
$178$	−5.02122	−0.376356
$179$	−13.0348	−0.974266	−0.487133	−	0.873328i	$-0.661957\pi$
$179$	−13.0348	−0.974266	−0.487133	+	0.873328i	$0.661957\pi$
$180$	−5.10716	−0.380665
$181$	22.4363	1.66768	0.833839	−	0.552008i	$-0.186138\pi$
$181$	22.4363	1.66768	0.833839	+	0.552008i	$0.186138\pi$
$182$	−14.1185	−1.04654
$183$	−1.84227	−0.136185
$184$	−8.22996	−0.606721
$185$	−19.9239	−1.46483
$186$	−0.126570	−0.00928053
$187$	−40.5882	−2.96810
$188$	−7.87966	−0.574683
$189$	12.7170	0.925027
$190$	−1.84074	−0.133541
$191$	27.2025	1.96830	0.984151	−	0.177333i	$-0.0567471\pi$
$191$	27.2025	1.96830	0.984151	+	0.177333i	$0.0567471\pi$
$192$	−0.474859	−0.0342700
$193$	23.3976	1.68420	0.842098	−	0.539325i	$-0.181320\pi$
$193$	23.3976	1.68420	0.842098	+	0.539325i	$0.181320\pi$
$194$	−8.87450	−0.637152
$195$	2.66098	0.190557
$196$	14.5085	1.03632
$197$	5.21838	0.371794	0.185897	−	0.982569i	$-0.440481\pi$
$197$	5.21838	0.371794	0.185897	+	0.982569i	$0.440481\pi$
$198$	15.6054	1.10903
$199$	11.6337	0.824693	0.412346	−	0.911027i	$-0.364709\pi$
$199$	11.6337	0.824693	0.412346	+	0.911027i	$0.364709\pi$
$200$	−1.61167	−0.113962
$201$	−3.38756	−0.238940
$202$	0.474978	0.0334193
$203$	−39.7557	−2.79030
$204$	−3.42670	−0.239917
$205$	−6.53764	−0.456609
$206$	−12.5444	−0.874010
$207$	22.8341	1.58708
$208$	−3.04428	−0.211083
$209$	5.62455	0.389058
$210$	−4.05381	−0.279739
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	3.45091	0.237010
$213$	−4.41037	−0.302193
$214$	13.8275	0.945230
$215$	−18.7066	−1.27578
$216$	2.74208	0.186575
$217$	1.23615	0.0839151
$218$	−16.8871	−1.14374
$219$	1.28497	0.0868301
$220$	−10.3533	−0.698023
$221$	−21.9683	−1.47775
$222$	5.13979	0.344960
$223$	20.3324	1.36156	0.680779	−	0.732489i	$-0.261641\pi$
$223$	20.3324	1.36156	0.680779	+	0.732489i	$0.261641\pi$
$224$	4.63773	0.309871
$225$	4.47158	0.298106
$226$	−13.0647	−0.869049
$227$	7.82695	0.519493	0.259746	−	0.965677i	$-0.416361\pi$
$227$	7.82695	0.519493	0.259746	+	0.965677i	$0.416361\pi$
$228$	0.474859	0.0314483
$229$	8.63885	0.570872	0.285436	−	0.958398i	$-0.407862\pi$
$229$	8.63885	0.570872	0.285436	+	0.958398i	$0.407862\pi$
$230$	−15.1492	−0.998911
$231$	12.3868	0.814989
$232$	−8.57223	−0.562795
$233$	−6.16404	−0.403820	−0.201910	−	0.979404i	$-0.564715\pi$
$233$	−6.16404	−0.403820	−0.201910	+	0.979404i	$0.564715\pi$
$234$	8.44638	0.552157
$235$	−14.5044	−0.946164
$236$	2.72563	0.177423
$237$	−1.98070	−0.128660
$238$	33.4670	2.16934
$239$	12.5027	0.808736	0.404368	−	0.914596i	$-0.367492\pi$
$239$	12.5027	0.808736	0.404368	+	0.914596i	$0.367492\pi$
$240$	−0.874093	−0.0564225
$241$	12.0167	0.774064	0.387032	−	0.922066i	$-0.373500\pi$
$241$	12.0167	0.774064	0.387032	+	0.922066i	$0.373500\pi$
$242$	20.6356	1.32650
$243$	−11.5604	−0.741601
$244$	3.87962	0.248367
$245$	26.7064	1.70621
$246$	1.68653	0.107529
$247$	3.04428	0.193703
$248$	0.266541	0.0169254
$249$	3.98629	0.252621
$250$	−12.1704	−0.769722
$251$	−20.5673	−1.29820	−0.649098	−	0.760705i	$-0.724854\pi$
$251$	−20.5673	−1.29820	−0.649098	+	0.760705i	$0.724854\pi$
$252$	−12.8674	−0.810571
$253$	46.2898	2.91022
$254$	−15.6739	−0.983471
$255$	−6.30768	−0.395002
$256$	1.00000	0.0625000
$257$	16.6036	1.03570	0.517852	−	0.855470i	$-0.326732\pi$
$257$	16.6036	1.03570	0.517852	+	0.855470i	$0.326732\pi$
$258$	4.82576	0.300439
$259$	−50.1979	−3.11915
$260$	−5.60373	−0.347529
$261$	23.7837	1.47218
$262$	4.99131	0.308364
$263$	−8.25358	−0.508938	−0.254469	−	0.967081i	$-0.581901\pi$
$263$	−8.25358	−0.508938	−0.254469	+	0.967081i	$0.581901\pi$
$264$	2.67087	0.164381
$265$	6.35224	0.390215
$266$	−4.63773	−0.284357
$267$	2.38437	0.145921
$268$	7.13383	0.435768
$269$	10.2263	0.623511	0.311755	−	0.950162i	$-0.399083\pi$
$269$	10.2263	0.623511	0.311755	+	0.950162i	$0.399083\pi$
$270$	5.04746	0.307179
$271$	−10.8910	−0.661581	−0.330791	−	0.943704i	$-0.607315\pi$
$271$	−10.8910	−0.661581	−0.330791	+	0.943704i	$0.607315\pi$
$272$	7.21625	0.437549
$273$	6.70432	0.405764
$274$	2.85260	0.172332
$275$	9.06490	0.546634
$276$	3.90807	0.235238
$277$	18.9909	1.14105	0.570525	−	0.821280i	$-0.306740\pi$
$277$	18.9909	1.14105	0.570525	+	0.821280i	$0.306740\pi$
$278$	8.04923	0.482761
$279$	−0.739521	−0.0442740
$280$	8.53686	0.510175
$281$	2.41816	0.144255	0.0721277	−	0.997395i	$-0.477021\pi$
$281$	2.41816	0.144255	0.0721277	+	0.997395i	$0.477021\pi$
$282$	3.74173	0.222817
$283$	9.57999	0.569472	0.284736	−	0.958606i	$-0.408094\pi$
$283$	9.57999	0.569472	0.284736	+	0.958606i	$0.408094\pi$
$284$	9.28774	0.551126
$285$	0.874093	0.0517768
$286$	17.1227	1.01249
$287$	−16.4715	−0.972282
$288$	−2.77451	−0.163489
$289$	35.0743	2.06319
$290$	−15.7793	−0.926591
$291$	4.21414	0.247037
$292$	−2.70600	−0.158357
$293$	−24.5624	−1.43495	−0.717475	−	0.696584i	$-0.754702\pi$
$293$	−24.5624	−1.43495	−0.717475	+	0.696584i	$0.754702\pi$
$294$	−6.88950	−0.401804
$295$	5.01718	0.292112
$296$	−10.8238	−0.629121
$297$	−15.4230	−0.894931
$298$	13.8500	0.802306
$299$	25.0543	1.44893
$300$	0.765315	0.0441855
$301$	−47.1310	−2.71658
$302$	−14.4959	−0.834145
$303$	−0.225548	−0.0129574
$304$	−1.00000	−0.0573539
$305$	7.14139	0.408915
$306$	−20.0215	−1.14456
$307$	−28.5751	−1.63086	−0.815432	−	0.578852i	$-0.803501\pi$
$307$	−28.5751	−1.63086	−0.815432	+	0.578852i	$0.803501\pi$
$308$	−26.0851	−1.48634
$309$	5.95682	0.338872
$310$	0.490634	0.0278661
$311$	−22.8418	−1.29524	−0.647620	−	0.761964i	$-0.724235\pi$
$311$	−22.8418	−1.29524	−0.647620	+	0.761964i	$0.724235\pi$
$312$	1.44560	0.0818412
$313$	−21.7080	−1.22701	−0.613505	−	0.789690i	$-0.710241\pi$
$313$	−21.7080	−1.22701	−0.613505	+	0.789690i	$0.710241\pi$
$314$	−16.0173	−0.903908
$315$	−23.6856	−1.33453
$316$	4.17114	0.234645
$317$	−13.6236	−0.765180	−0.382590	−	0.923918i	$-0.624968\pi$
$317$	−13.6236	−0.765180	−0.382590	+	0.923918i	$0.624968\pi$
$318$	−1.63870	−0.0918935
$319$	48.2149	2.69952
$320$	1.84074	0.102901
$321$	−6.56612	−0.366485
$322$	−38.1683	−2.12704
$323$	−7.21625	−0.401523
$324$	7.02143	0.390079
$325$	4.90636	0.272156
$326$	13.1324	0.727338
$327$	8.01901	0.443452
$328$	−3.55163	−0.196106
$329$	−36.5437	−2.01472
$330$	4.91638	0.270638
$331$	−12.3996	−0.681544	−0.340772	−	0.940146i	$-0.610688\pi$
$331$	−12.3996	−0.681544	−0.340772	+	0.940146i	$0.610688\pi$
$332$	−8.39468	−0.460718
$333$	30.0308	1.64568
$334$	18.8778	1.03295
$335$	13.1315	0.717453
$336$	−2.20227	−0.120144
$337$	−19.9941	−1.08915	−0.544575	−	0.838712i	$-0.683309\pi$
$337$	−19.9941	−1.08915	−0.544575	+	0.838712i	$0.683309\pi$
$338$	−3.73237	−0.203014
$339$	6.20388	0.336949
$340$	13.2833	0.720386
$341$	−1.49918	−0.0811849
$342$	2.77451	0.150028
$343$	34.8225	1.88024
$344$	−10.1625	−0.547926
$345$	7.19375	0.387299
$346$	13.7005	0.736542
$347$	10.2909	0.552446	0.276223	−	0.961094i	$-0.410917\pi$
$347$	10.2909	0.552446	0.276223	+	0.961094i	$0.410917\pi$
$348$	4.07060	0.218207
$349$	−1.73012	−0.0926110	−0.0463055	−	0.998927i	$-0.514745\pi$
$349$	−1.73012	−0.0926110	−0.0463055	+	0.998927i	$0.514745\pi$
$350$	−7.47447	−0.399527
$351$	−8.34765	−0.445565
$352$	−5.62455	−0.299790
$353$	−25.7575	−1.37093	−0.685467	−	0.728103i	$-0.740402\pi$
$353$	−25.7575	−1.37093	−0.685467	+	0.728103i	$0.740402\pi$
$354$	−1.29429	−0.0687907
$355$	17.0963	0.907380
$356$	−5.02122	−0.266124
$357$	−15.8921	−0.841100
$358$	−13.0348	−0.688910
$359$	28.6419	1.51166	0.755831	−	0.654767i	$-0.227233\pi$
$359$	28.6419	1.51166	0.755831	+	0.654767i	$0.227233\pi$
$360$	−5.10716	−0.269171
$361$	1.00000	0.0526316
$362$	22.4363	1.17923
$363$	−9.79899	−0.514314
$364$	−14.1185	−0.740012
$365$	−4.98105	−0.260720
$366$	−1.84227	−0.0962972
$367$	−8.44469	−0.440809	−0.220404	−	0.975409i	$-0.570738\pi$
$367$	−8.44469	−0.440809	−0.220404	+	0.975409i	$0.570738\pi$
$368$	−8.22996	−0.429016
$369$	9.85404	0.512981
$370$	−19.9239	−1.03579
$371$	16.0044	0.830906
$372$	−0.126570	−0.00656233
$373$	−14.7138	−0.761850	−0.380925	−	0.924606i	$-0.624394\pi$
$373$	−14.7138	−0.761850	−0.380925	+	0.924606i	$0.624394\pi$
$374$	−40.5882	−2.09876
$375$	5.77921	0.298437
$376$	−7.87966	−0.406362
$377$	26.0963	1.34403
$378$	12.7170	0.654093
$379$	−3.36003	−0.172593	−0.0862965	−	0.996270i	$-0.527503\pi$
$379$	−3.36003	−0.172593	−0.0862965	+	0.996270i	$0.527503\pi$
$380$	−1.84074	−0.0944281
$381$	7.44292	0.381312
$382$	27.2025	1.39180
$383$	−11.7152	−0.598621	−0.299310	−	0.954156i	$-0.596757\pi$
$383$	−11.7152	−0.598621	−0.299310	+	0.954156i	$0.596757\pi$
$384$	−0.474859	−0.0242326
$385$	−48.0160	−2.44712
$386$	23.3976	1.19091
$387$	28.1960	1.43328
$388$	−8.87450	−0.450535
$389$	23.3322	1.18299	0.591495	−	0.806309i	$-0.298538\pi$
$389$	23.3322	1.18299	0.591495	+	0.806309i	$0.298538\pi$
$390$	2.66098	0.134744
$391$	−59.3894	−3.00345
$392$	14.5085	0.732791
$393$	−2.37017	−0.119559
$394$	5.21838	0.262898
$395$	7.67799	0.386322
$396$	15.6054	0.784199
$397$	−23.9570	−1.20237	−0.601185	−	0.799110i	$-0.705304\pi$
$397$	−23.9570	−1.20237	−0.601185	+	0.799110i	$0.705304\pi$
$398$	11.6337	0.583146
$399$	2.20227	0.110251
$400$	−1.61167	−0.0805834
$401$	7.99248	0.399125	0.199563	−	0.979885i	$-0.436048\pi$
$401$	7.99248	0.399125	0.199563	+	0.979885i	$0.436048\pi$
$402$	−3.38756	−0.168956
$403$	−0.811426	−0.0404200
$404$	0.474978	0.0236310
$405$	12.9246	0.642230
$406$	−39.7557	−1.97304
$407$	60.8791	3.01766
$408$	−3.42670	−0.169647
$409$	−22.2432	−1.09986	−0.549928	−	0.835212i	$-0.685345\pi$
$409$	−22.2432	−1.09986	−0.549928	+	0.835212i	$0.685345\pi$
$410$	−6.53764	−0.322871
$411$	−1.35458	−0.0668166
$412$	−12.5444	−0.618018
$413$	12.6407	0.622010
$414$	22.8341	1.12223
$415$	−15.4524	−0.758530
$416$	−3.04428	−0.149258
$417$	−3.82225	−0.187176
$418$	5.62455	0.275106
$419$	0.431663	0.0210881	0.0105441	−	0.999944i	$-0.496644\pi$
$419$	0.431663	0.0210881	0.0105441	+	0.999944i	$0.496644\pi$
$420$	−4.05381	−0.197806
$421$	−14.1620	−0.690216	−0.345108	−	0.938563i	$-0.612158\pi$
$421$	−14.1620	−0.690216	−0.345108	+	0.938563i	$0.612158\pi$
$422$	1.00000	0.0486792
$423$	21.8622	1.06298
$424$	3.45091	0.167591
$425$	−11.6302	−0.564147
$426$	−4.41037	−0.213683
$427$	17.9926	0.870725
$428$	13.8275	0.668378
$429$	−8.13087	−0.392562
$430$	−18.7066	−0.902111
$431$	−0.833087	−0.0401284	−0.0200642	−	0.999799i	$-0.506387\pi$
$431$	−0.833087	−0.0401284	−0.0200642	+	0.999799i	$0.506387\pi$
$432$	2.74208	0.131928
$433$	3.06801	0.147439	0.0737195	−	0.997279i	$-0.476513\pi$
$433$	3.06801	0.147439	0.0737195	+	0.997279i	$0.476513\pi$
$434$	1.23615	0.0593369
$435$	7.49293	0.359259
$436$	−16.8871	−0.808747
$437$	8.22996	0.393692
$438$	1.28497	0.0613981
$439$	5.17116	0.246806	0.123403	−	0.992357i	$-0.460619\pi$
$439$	5.17116	0.246806	0.123403	+	0.992357i	$0.460619\pi$
$440$	−10.3533	−0.493577
$441$	−40.2540	−1.91686
$442$	−21.9683	−1.04492
$443$	14.0193	0.666076	0.333038	−	0.942913i	$-0.391926\pi$
$443$	14.0193	0.666076	0.333038	+	0.942913i	$0.391926\pi$
$444$	5.13979	0.243924
$445$	−9.24277	−0.438149
$446$	20.3324	0.962767
$447$	−6.57678	−0.311071
$448$	4.63773	0.219112
$449$	−20.7436	−0.978952	−0.489476	−	0.872017i	$-0.662812\pi$
$449$	−20.7436	−0.978952	−0.489476	+	0.872017i	$0.662812\pi$
$450$	4.47158	0.210793
$451$	19.9763	0.940649
$452$	−13.0647	−0.614511
$453$	6.88351	0.323416
$454$	7.82695	0.367337
$455$	−25.9886	−1.21836
$456$	0.474859	0.0222373
$457$	11.4729	0.536679	0.268339	−	0.963324i	$-0.413525\pi$
$457$	11.4729	0.536679	0.268339	+	0.963324i	$0.413525\pi$
$458$	8.63885	0.403667
$459$	19.7875	0.923602
$460$	−15.1492	−0.706337
$461$	−0.0925437	−0.00431019	−0.00215510	−	0.999998i	$-0.500686\pi$
$461$	−0.0925437	−0.00431019	−0.00215510	+	0.999998i	$0.500686\pi$
$462$	12.3868	0.576284
$463$	24.2909	1.12890	0.564448	−	0.825469i	$-0.309089\pi$
$463$	24.2909	1.12890	0.564448	+	0.825469i	$0.309089\pi$
$464$	−8.57223	−0.397956
$465$	−0.232982	−0.0108043
$466$	−6.16404	−0.285544
$467$	−5.00099	−0.231418	−0.115709	−	0.993283i	$-0.536914\pi$
$467$	−5.00099	−0.231418	−0.115709	+	0.993283i	$0.536914\pi$
$468$	8.44638	0.390434
$469$	33.0847	1.52771
$470$	−14.5044	−0.669039
$471$	7.60596	0.350464
$472$	2.72563	0.125457
$473$	57.1596	2.62820
$474$	−1.98070	−0.0909767
$475$	1.61167	0.0739484
$476$	33.4670	1.53396
$477$	−9.57458	−0.438390
$478$	12.5027	0.571862
$479$	−13.9462	−0.637219	−0.318609	−	0.947886i	$-0.603216\pi$
$479$	−13.9462	−0.637219	−0.318609	+	0.947886i	$0.603216\pi$
$480$	−0.874093	−0.0398967
$481$	32.9507	1.50242
$482$	12.0167	0.547346
$483$	18.1246	0.824696
$484$	20.6356	0.937981
$485$	−16.3357	−0.741765
$486$	−11.5604	−0.524391
$487$	−11.7107	−0.530662	−0.265331	−	0.964157i	$-0.585481\pi$
$487$	−11.7107	−0.530662	−0.265331	+	0.964157i	$0.585481\pi$
$488$	3.87962	0.175622
$489$	−6.23605	−0.282004
$490$	26.7064	1.20647
$491$	−36.8859	−1.66464	−0.832319	−	0.554296i	$-0.812987\pi$
$491$	−36.8859	−1.66464	−0.832319	+	0.554296i	$0.812987\pi$
$492$	1.68653	0.0760344
$493$	−61.8594	−2.78601
$494$	3.04428	0.136969
$495$	28.7255	1.29111
$496$	0.266541	0.0119681
$497$	43.0740	1.93213
$498$	3.98629	0.178630
$499$	−36.5176	−1.63475	−0.817377	−	0.576103i	$-0.804573\pi$
$499$	−36.5176	−1.63475	−0.817377	+	0.576103i	$0.804573\pi$
$500$	−12.1704	−0.544276
$501$	−8.96431	−0.400496
$502$	−20.5673	−0.917963
$503$	44.4440	1.98166	0.990831	−	0.135109i	$-0.0431386\pi$
$503$	44.4440	1.98166	0.990831	+	0.135109i	$0.0431386\pi$
$504$	−12.8674	−0.573160
$505$	0.874312	0.0389064
$506$	46.2898	2.05783
$507$	1.77235	0.0787127
$508$	−15.6739	−0.695419
$509$	11.3506	0.503105	0.251552	−	0.967844i	$-0.419059\pi$
$509$	11.3506	0.503105	0.251552	+	0.967844i	$0.419059\pi$
$510$	−6.30768	−0.279309
$511$	−12.5497	−0.555165
$512$	1.00000	0.0441942
$513$	−2.74208	−0.121066
$514$	16.6036	0.732353
$515$	−23.0910	−1.01751
$516$	4.82576	0.212442
$517$	44.3195	1.94917
$518$	−50.1979	−2.20557
$519$	−6.50579	−0.285573
$520$	−5.60373	−0.245740
$521$	16.0813	0.704533	0.352266	−	0.935900i	$-0.385411\pi$
$521$	16.0813	0.704533	0.352266	+	0.935900i	$0.385411\pi$
$522$	23.7837	1.04099
$523$	12.2566	0.535944	0.267972	−	0.963427i	$-0.413646\pi$
$523$	12.2566	0.535944	0.267972	+	0.963427i	$0.413646\pi$
$524$	4.99131	0.218046
$525$	3.54932	0.154905
$526$	−8.25358	−0.359873
$527$	1.92343	0.0837859
$528$	2.67087	0.116235
$529$	44.7322	1.94488
$530$	6.35224	0.275924
$531$	−7.56228	−0.328175
$532$	−4.63773	−0.201071
$533$	10.8122	0.468327
$534$	2.38437	0.103182
$535$	25.4529	1.10043
$536$	7.13383	0.308134
$537$	6.18969	0.267105
$538$	10.2263	0.440889
$539$	−81.6039	−3.51493
$540$	5.04746	0.217208
$541$	−20.8960	−0.898391	−0.449195	−	0.893433i	$-0.648289\pi$
$541$	−20.8960	−0.898391	−0.449195	+	0.893433i	$0.648289\pi$
$542$	−10.8910	−0.467809
$543$	−10.6541	−0.457211
$544$	7.21625	0.309394
$545$	−31.0849	−1.33153
$546$	6.70432	0.286918
$547$	−42.8298	−1.83127	−0.915635	−	0.402010i	$-0.868312\pi$
$547$	−42.8298	−1.83127	−0.915635	+	0.402010i	$0.868312\pi$
$548$	2.85260	0.121857
$549$	−10.7640	−0.459398
$550$	9.06490	0.386529
$551$	8.57223	0.365189
$552$	3.90807	0.166339
$553$	19.3446	0.822616
$554$	18.9909	0.806844
$555$	9.46103	0.401598
$556$	8.04923	0.341363
$557$	−20.1463	−0.853628	−0.426814	−	0.904339i	$-0.640364\pi$
$557$	−20.1463	−0.853628	−0.426814	+	0.904339i	$0.640364\pi$
$558$	−0.739521	−0.0313064
$559$	30.9375	1.30852
$560$	8.53686	0.360748
$561$	19.2737	0.813735
$562$	2.41816	0.102004
$563$	−8.22702	−0.346727	−0.173364	−	0.984858i	$-0.555464\pi$
$563$	−8.22702	−0.346727	−0.173364	+	0.984858i	$0.555464\pi$
$564$	3.74173	0.157555
$565$	−24.0487	−1.01174
$566$	9.57999	0.402677
$567$	32.5635	1.36754
$568$	9.28774	0.389705
$569$	−27.7801	−1.16460	−0.582301	−	0.812973i	$-0.697847\pi$
$569$	−27.7801	−1.16460	−0.582301	+	0.812973i	$0.697847\pi$
$570$	0.874093	0.0366117
$571$	31.9001	1.33498	0.667490	−	0.744619i	$-0.267369\pi$
$571$	31.9001	1.33498	0.667490	+	0.744619i	$0.267369\pi$
$572$	17.1227	0.715936
$573$	−12.9173	−0.539630
$574$	−16.4715	−0.687507
$575$	13.2640	0.553145
$576$	−2.77451	−0.115605
$577$	−38.4296	−1.59985	−0.799923	−	0.600103i	$-0.795126\pi$
$577$	−38.4296	−1.59985	−0.799923	+	0.600103i	$0.795126\pi$
$578$	35.0743	1.45890
$579$	−11.1106	−0.461739
$580$	−15.7793	−0.655199
$581$	−38.9322	−1.61518
$582$	4.21414	0.174682
$583$	−19.4098	−0.803873
$584$	−2.70600	−0.111975
$585$	15.5476	0.642814
$586$	−24.5624	−1.01466
$587$	−25.2949	−1.04403	−0.522015	−	0.852936i	$-0.674820\pi$
$587$	−25.2949	−1.04403	−0.522015	+	0.852936i	$0.674820\pi$
$588$	−6.88950	−0.284118
$589$	−0.266541	−0.0109826
$590$	5.01718	0.206554
$591$	−2.47800	−0.101931
$592$	−10.8238	−0.444856
$593$	43.1622	1.77246	0.886229	−	0.463248i	$-0.153316\pi$
$593$	43.1622	1.77246	0.886229	+	0.463248i	$0.153316\pi$
$594$	−15.4230	−0.632812
$595$	61.6041	2.52552
$596$	13.8500	0.567316
$597$	−5.52438	−0.226098
$598$	25.0543	1.02455
$599$	39.9447	1.63210	0.816049	−	0.577983i	$-0.196160\pi$
$599$	39.9447	1.63210	0.816049	+	0.577983i	$0.196160\pi$
$600$	0.765315	0.0312438
$601$	−24.2840	−0.990567	−0.495284	−	0.868731i	$-0.664936\pi$
$601$	−24.2840	−0.990567	−0.495284	+	0.868731i	$0.664936\pi$
$602$	−47.1310	−1.92091
$603$	−19.7929	−0.806028
$604$	−14.4959	−0.589830
$605$	37.9848	1.54430
$606$	−0.225548	−0.00916225
$607$	−33.4236	−1.35662	−0.678311	−	0.734775i	$-0.737288\pi$
$607$	−33.4236	−1.35662	−0.678311	+	0.734775i	$0.737288\pi$
$608$	−1.00000	−0.0405554
$609$	18.8783	0.764989
$610$	7.14139	0.289146
$611$	23.9879	0.970445
$612$	−20.0215	−0.809323
$613$	23.7626	0.959763	0.479881	−	0.877333i	$-0.340680\pi$
$613$	23.7626	0.959763	0.479881	+	0.877333i	$0.340680\pi$
$614$	−28.5751	−1.15320
$615$	3.10446	0.125184
$616$	−26.0851	−1.05100
$617$	29.9434	1.20548	0.602738	−	0.797939i	$-0.294077\pi$
$617$	29.9434	1.20548	0.602738	+	0.797939i	$0.294077\pi$
$618$	5.95682	0.239619
$619$	7.47178	0.300316	0.150158	−	0.988662i	$-0.452022\pi$
$619$	7.47178	0.300316	0.150158	+	0.988662i	$0.452022\pi$
$620$	0.490634	0.0197043
$621$	−22.5672	−0.905590
$622$	−22.8418	−0.915872
$623$	−23.2870	−0.932976
$624$	1.44560	0.0578705
$625$	−14.3442	−0.573768
$626$	−21.7080	−0.867628
$627$	−2.67087	−0.106664
$628$	−16.0173	−0.639160
$629$	−78.1074	−3.11434
$630$	−23.6856	−0.943657
$631$	−47.6424	−1.89661	−0.948307	−	0.317355i	$-0.897205\pi$
$631$	−47.6424	−1.89661	−0.948307	+	0.317355i	$0.897205\pi$
$632$	4.17114	0.165919
$633$	−0.474859	−0.0188740
$634$	−13.6236	−0.541064
$635$	−28.8517	−1.14494
$636$	−1.63870	−0.0649785
$637$	−44.1680	−1.75000
$638$	48.2149	1.90885
$639$	−25.7689	−1.01940
$640$	1.84074	0.0727617
$641$	24.8509	0.981552	0.490776	−	0.871286i	$-0.336713\pi$
$641$	24.8509	0.981552	0.490776	+	0.871286i	$0.336713\pi$
$642$	−6.56612	−0.259144
$643$	5.42529	0.213952	0.106976	−	0.994262i	$-0.465883\pi$
$643$	5.42529	0.213952	0.106976	+	0.994262i	$0.465883\pi$
$644$	−38.1683	−1.50404
$645$	8.88299	0.349767
$646$	−7.21625	−0.283920
$647$	−2.23441	−0.0878436	−0.0439218	−	0.999035i	$-0.513985\pi$
$647$	−2.23441	−0.0878436	−0.0439218	+	0.999035i	$0.513985\pi$
$648$	7.02143	0.275828
$649$	−15.3304	−0.601773
$650$	4.90636	0.192443
$651$	−0.586995	−0.0230062
$652$	13.1324	0.514305
$653$	−24.2927	−0.950648	−0.475324	−	0.879811i	$-0.657669\pi$
$653$	−24.2927	−0.950648	−0.475324	+	0.879811i	$0.657669\pi$
$654$	8.01901	0.313568
$655$	9.18771	0.358994
$656$	−3.55163	−0.138668
$657$	7.50782	0.292908
$658$	−36.5437	−1.42462
$659$	−14.6766	−0.571721	−0.285860	−	0.958271i	$-0.592279\pi$
$659$	−14.6766	−0.571721	−0.285860	+	0.958271i	$0.592279\pi$
$660$	4.91638	0.191370
$661$	−29.9889	−1.16643	−0.583216	−	0.812317i	$-0.698206\pi$
$661$	−29.9889	−1.16643	−0.583216	+	0.812317i	$0.698206\pi$
$662$	−12.3996	−0.481925
$663$	10.4318	0.405139
$664$	−8.39468	−0.325777
$665$	−8.53686	−0.331045
$666$	30.0308	1.16367
$667$	70.5491	2.73167
$668$	18.8778	0.730405
$669$	−9.65502	−0.373285
$670$	13.1315	0.507316
$671$	−21.8211	−0.842395
$672$	−2.20227	−0.0849543
$673$	−35.4257	−1.36556	−0.682781	−	0.730623i	$-0.739230\pi$
$673$	−35.4257	−1.36556	−0.682781	+	0.730623i	$0.739230\pi$
$674$	−19.9941	−0.770145
$675$	−4.41932	−0.170100
$676$	−3.73237	−0.143553
$677$	−19.6061	−0.753525	−0.376762	−	0.926310i	$-0.622963\pi$
$677$	−19.6061	−0.753525	−0.376762	+	0.926310i	$0.622963\pi$
$678$	6.20388	0.238259
$679$	−41.1575	−1.57948
$680$	13.2833	0.509390
$681$	−3.71670	−0.142424
$682$	−1.49918	−0.0574064
$683$	18.1328	0.693831	0.346916	−	0.937896i	$-0.387229\pi$
$683$	18.1328	0.693831	0.346916	+	0.937896i	$0.387229\pi$
$684$	2.77451	0.106086
$685$	5.25090	0.200626
$686$	34.8225	1.32953
$687$	−4.10224	−0.156510
$688$	−10.1625	−0.387442
$689$	−10.5055	−0.400229
$690$	7.19375	0.273861
$691$	−25.6480	−0.975695	−0.487848	−	0.872929i	$-0.662218\pi$
$691$	−25.6480	−0.975695	−0.487848	+	0.872929i	$0.662218\pi$
$692$	13.7005	0.520814
$693$	72.3734	2.74924
$694$	10.2909	0.390639
$695$	14.8166	0.562024
$696$	4.07060	0.154296
$697$	−25.6295	−0.970785
$698$	−1.73012	−0.0654859
$699$	2.92705	0.110711
$700$	−7.47447	−0.282509
$701$	−37.0144	−1.39802	−0.699008	−	0.715114i	$-0.746375\pi$
$701$	−37.0144	−1.39802	−0.699008	+	0.715114i	$0.746375\pi$
$702$	−8.34765	−0.315062
$703$	10.8238	0.408228
$704$	−5.62455	−0.211983
$705$	6.88756	0.259400
$706$	−25.7575	−0.969397
$707$	2.20282	0.0828455
$708$	−1.29429	−0.0486424
$709$	1.32858	0.0498960	0.0249480	−	0.999689i	$-0.492058\pi$
$709$	1.32858	0.0498960	0.0249480	+	0.999689i	$0.492058\pi$
$710$	17.0963	0.641614
$711$	−11.5729	−0.434016
$712$	−5.02122	−0.188178
$713$	−2.19362	−0.0821519
$714$	−15.8921	−0.594747
$715$	31.5185	1.17872
$716$	−13.0348	−0.487133
$717$	−5.93704	−0.221723
$718$	28.6419	1.06891
$719$	31.5874	1.17801	0.589005	−	0.808129i	$-0.299520\pi$
$719$	31.5874	1.17801	0.589005	+	0.808129i	$0.299520\pi$
$720$	−5.10716	−0.190332
$721$	−58.1775	−2.16664
$722$	1.00000	0.0372161
$723$	−5.70625	−0.212218
$724$	22.4363	0.833839
$725$	13.8156	0.513098
$726$	−9.79899	−0.363675
$727$	21.1585	0.784726	0.392363	−	0.919811i	$-0.371658\pi$
$727$	21.1585	0.784726	0.392363	+	0.919811i	$0.371658\pi$
$728$	−14.1185	−0.523268
$729$	−15.5747	−0.576841
$730$	−4.98105	−0.184357
$731$	−73.3352	−2.71240
$732$	−1.84227	−0.0680924
$733$	−20.6318	−0.762054	−0.381027	−	0.924564i	$-0.624430\pi$
$733$	−20.6318	−0.762054	−0.381027	+	0.924564i	$0.624430\pi$
$734$	−8.44469	−0.311699
$735$	−12.6818	−0.467775
$736$	−8.22996	−0.303360
$737$	−40.1246	−1.47801
$738$	9.85404	0.362732
$739$	30.2824	1.11396	0.556978	−	0.830527i	$-0.311961\pi$
$739$	30.2824	1.11396	0.556978	+	0.830527i	$0.311961\pi$
$740$	−19.9239	−0.732416
$741$	−1.44560	−0.0531056
$742$	16.0044	0.587539
$743$	−0.862457	−0.0316405	−0.0158202	−	0.999875i	$-0.505036\pi$
$743$	−0.862457	−0.0316405	−0.0158202	+	0.999875i	$0.505036\pi$
$744$	−0.126570	−0.00464027
$745$	25.4942	0.934035
$746$	−14.7138	−0.538709
$747$	23.2911	0.852177
$748$	−40.5882	−1.48405
$749$	64.1283	2.34320
$750$	5.77921	0.211027
$751$	−34.3214	−1.25240	−0.626202	−	0.779661i	$-0.715392\pi$
$751$	−34.3214	−1.25240	−0.626202	+	0.779661i	$0.715392\pi$
$752$	−7.87966	−0.287341
$753$	9.76657	0.355914
$754$	26.0963	0.950370
$755$	−26.6832	−0.971102
$756$	12.7170	0.462513
$757$	−42.9952	−1.56269	−0.781343	−	0.624102i	$-0.785465\pi$
$757$	−42.9952	−1.56269	−0.781343	+	0.624102i	$0.785465\pi$
$758$	−3.36003	−0.122042
$759$	−21.9811	−0.797865
$760$	−1.84074	−0.0667707
$761$	17.8778	0.648069	0.324034	−	0.946045i	$-0.394961\pi$
$761$	17.8778	0.648069	0.324034	+	0.946045i	$0.394961\pi$
$762$	7.44292	0.269628
$763$	−78.3179	−2.83530
$764$	27.2025	0.984151
$765$	−36.8545	−1.33248
$766$	−11.7152	−0.423289
$767$	−8.29758	−0.299608
$768$	−0.474859	−0.0171350
$769$	41.7488	1.50550	0.752750	−	0.658306i	$-0.228727\pi$
$769$	41.7488	1.50550	0.752750	+	0.658306i	$0.228727\pi$
$770$	−48.0160	−1.73038
$771$	−7.88437	−0.283949
$772$	23.3976	0.842098
$773$	5.55965	0.199967	0.0999834	−	0.994989i	$-0.468121\pi$
$773$	5.55965	0.199967	0.0999834	+	0.994989i	$0.468121\pi$
$774$	28.1960	1.01348
$775$	−0.429576	−0.0154308
$776$	−8.87450	−0.318576
$777$	23.8369	0.855145
$778$	23.3322	0.836500
$779$	3.55163	0.127250
$780$	2.66098	0.0952785
$781$	−52.2394	−1.86927
$782$	−59.3894	−2.12376
$783$	−23.5057	−0.840026
$784$	14.5085	0.518161
$785$	−29.4837	−1.05232
$786$	−2.37017	−0.0845411
$787$	20.8160	0.742009	0.371005	−	0.928631i	$-0.379013\pi$
$787$	20.8160	0.742009	0.371005	+	0.928631i	$0.379013\pi$
$788$	5.21838	0.185897
$789$	3.91929	0.139530
$790$	7.67799	0.273171
$791$	−60.5904	−2.15435
$792$	15.6054	0.554513
$793$	−11.8107	−0.419409
$794$	−23.9570	−0.850204
$795$	−3.01642	−0.106981
$796$	11.6337	0.412346
$797$	−48.3470	−1.71254	−0.856270	−	0.516528i	$-0.827224\pi$
$797$	−48.3470	−1.71254	−0.856270	+	0.516528i	$0.827224\pi$
$798$	2.20227	0.0779594
$799$	−56.8616	−2.01162
$800$	−1.61167	−0.0569810
$801$	13.9314	0.492242
$802$	7.99248	0.282224
$803$	15.2200	0.537103
$804$	−3.38756	−0.119470
$805$	−70.2580	−2.47627
$806$	−0.811426	−0.0285813
$807$	−4.85607	−0.170942
$808$	0.474978	0.0167097
$809$	3.85453	0.135518	0.0677591	−	0.997702i	$-0.478415\pi$
$809$	3.85453	0.135518	0.0677591	+	0.997702i	$0.478415\pi$
$810$	12.9246	0.454125
$811$	−23.0017	−0.807700	−0.403850	−	0.914825i	$-0.632328\pi$
$811$	−23.0017	−0.807700	−0.403850	+	0.914825i	$0.632328\pi$
$812$	−39.7557	−1.39515
$813$	5.17169	0.181379
$814$	60.8791	2.13381
$815$	24.1734	0.846758
$816$	−3.42670	−0.119959
$817$	10.1625	0.355541
$818$	−22.2432	−0.777716
$819$	39.1720	1.36878
$820$	−6.53764	−0.228304
$821$	−27.0814	−0.945146	−0.472573	−	0.881291i	$-0.656675\pi$
$821$	−27.0814	−0.945146	−0.472573	+	0.881291i	$0.656675\pi$
$822$	−1.35458	−0.0472465
$823$	−8.58561	−0.299276	−0.149638	−	0.988741i	$-0.547811\pi$
$823$	−8.58561	−0.299276	−0.149638	+	0.988741i	$0.547811\pi$
$824$	−12.5444	−0.437005
$825$	−4.30455	−0.149865
$826$	12.6407	0.439827
$827$	−40.4593	−1.40691	−0.703453	−	0.710741i	$-0.748360\pi$
$827$	−40.4593	−1.40691	−0.703453	+	0.710741i	$0.748360\pi$
$828$	22.8341	0.793540
$829$	−39.3146	−1.36545	−0.682726	−	0.730675i	$-0.739206\pi$
$829$	−39.3146	−1.36545	−0.682726	+	0.730675i	$0.739206\pi$
$830$	−15.4524	−0.536362
$831$	−9.01798	−0.312830
$832$	−3.04428	−0.105541
$833$	104.697	3.62754
$834$	−3.82225	−0.132354
$835$	34.7492	1.20255
$836$	5.62455	0.194529
$837$	0.730877	0.0252628
$838$	0.431663	0.0149115
$839$	13.6739	0.472076	0.236038	−	0.971744i	$-0.424151\pi$
$839$	13.6739	0.472076	0.236038	+	0.971744i	$0.424151\pi$
$840$	−4.05381	−0.139870
$841$	44.4831	1.53390
$842$	−14.1620	−0.488056
$843$	−1.14829	−0.0395491
$844$	1.00000	0.0344214
$845$	−6.87032	−0.236346
$846$	21.8622	0.751637
$847$	95.7022	3.28837
$848$	3.45091	0.118505
$849$	−4.54915	−0.156126
$850$	−11.6302	−0.398912
$851$	89.0795	3.05361
$852$	−4.41037	−0.151097
$853$	30.6981	1.05108	0.525542	−	0.850768i	$-0.323863\pi$
$853$	30.6981	1.05108	0.525542	+	0.850768i	$0.323863\pi$
$854$	17.9926	0.615695
$855$	5.10716	0.174661
$856$	13.8275	0.472615
$857$	12.9256	0.441529	0.220765	−	0.975327i	$-0.429145\pi$
$857$	12.9256	0.441529	0.220765	+	0.975327i	$0.429145\pi$
$858$	−8.13087	−0.277583
$859$	47.5545	1.62254	0.811269	−	0.584673i	$-0.198777\pi$
$859$	47.5545	1.62254	0.811269	+	0.584673i	$0.198777\pi$
$860$	−18.7066	−0.637889
$861$	7.82164	0.266561
$862$	−0.833087	−0.0283751
$863$	13.5352	0.460745	0.230373	−	0.973102i	$-0.426005\pi$
$863$	13.5352	0.460745	0.230373	+	0.973102i	$0.426005\pi$
$864$	2.74208	0.0932874
$865$	25.2190	0.857473
$866$	3.06801	0.104255
$867$	−16.6553	−0.565645
$868$	1.23615	0.0419575
$869$	−23.4608	−0.795852
$870$	7.49293	0.254034
$871$	−21.7174	−0.735865
$872$	−16.8871	−0.571870
$873$	24.6224	0.833342
$874$	8.22996	0.278382
$875$	−56.4429	−1.90812
$876$	1.28497	0.0434150
$877$	23.6892	0.799927	0.399964	−	0.916531i	$-0.369023\pi$
$877$	23.6892	0.799927	0.399964	+	0.916531i	$0.369023\pi$
$878$	5.17116	0.174518
$879$	11.6637	0.393406
$880$	−10.3533	−0.349011
$881$	−18.1368	−0.611046	−0.305523	−	0.952185i	$-0.598831\pi$
$881$	−18.1368	−0.611046	−0.305523	+	0.952185i	$0.598831\pi$
$882$	−40.2540	−1.35542
$883$	−23.6002	−0.794210	−0.397105	−	0.917773i	$-0.629985\pi$
$883$	−23.6002	−0.794210	−0.397105	+	0.917773i	$0.629985\pi$
$884$	−21.9683	−0.738873
$885$	−2.38245	−0.0800853
$886$	14.0193	0.470987
$887$	−12.4182	−0.416962	−0.208481	−	0.978026i	$-0.566852\pi$
$887$	−12.4182	−0.416962	−0.208481	+	0.978026i	$0.566852\pi$
$888$	5.13979	0.172480
$889$	−72.6915	−2.43799
$890$	−9.24277	−0.309818
$891$	−39.4924	−1.32304
$892$	20.3324	0.680779
$893$	7.87966	0.263683
$894$	−6.57678	−0.219960
$895$	−23.9937	−0.802021
$896$	4.63773	0.154936
$897$	−11.8973	−0.397238
$898$	−20.7436	−0.692224
$899$	−2.28485	−0.0762042
$900$	4.47158	0.149053
$901$	24.9026	0.829627
$902$	19.9763	0.665139
$903$	22.3806	0.744779
$904$	−13.0647	−0.434525
$905$	41.2995	1.37284
$906$	6.88351	0.228689
$907$	11.7595	0.390466	0.195233	−	0.980757i	$-0.437454\pi$
$907$	11.7595	0.390466	0.195233	+	0.980757i	$0.437454\pi$
$908$	7.82695	0.259746
$909$	−1.31783	−0.0437097
$910$	−25.9886	−0.861513
$911$	−6.54557	−0.216864	−0.108432	−	0.994104i	$-0.534583\pi$
$911$	−6.54557	−0.216864	−0.108432	+	0.994104i	$0.534583\pi$
$912$	0.474859	0.0157242
$913$	47.2163	1.56263
$914$	11.4729	0.379489
$915$	−3.39115	−0.112108
$916$	8.63885	0.285436
$917$	23.1483	0.764425
$918$	19.7875	0.653086
$919$	35.1864	1.16069	0.580346	−	0.814370i	$-0.302917\pi$
$919$	35.1864	1.16069	0.580346	+	0.814370i	$0.302917\pi$
$920$	−15.1492	−0.499455
$921$	13.5691	0.447118
$922$	−0.0925437	−0.00304777
$923$	−28.2745	−0.930666
$924$	12.3868	0.407495
$925$	17.4444	0.573568
$926$	24.2909	0.798249
$927$	34.8046	1.14313
$928$	−8.57223	−0.281397
$929$	−32.8913	−1.07913	−0.539565	−	0.841944i	$-0.681411\pi$
$929$	−32.8913	−1.07913	−0.539565	+	0.841944i	$0.681411\pi$
$930$	−0.232982	−0.00763978
$931$	−14.5085	−0.475498
$932$	−6.16404	−0.201910
$933$	10.8466	0.355103
$934$	−5.00099	−0.163638
$935$	−74.7124	−2.44336
$936$	8.44638	0.276079
$937$	−16.5121	−0.539426	−0.269713	−	0.962941i	$-0.586929\pi$
$937$	−16.5121	−0.539426	−0.269713	+	0.962941i	$0.586929\pi$
$938$	33.0847	1.08026
$939$	10.3083	0.336397
$940$	−14.5044	−0.473082
$941$	−4.17470	−0.136091	−0.0680457	−	0.997682i	$-0.521676\pi$
$941$	−4.17470	−0.136091	−0.0680457	+	0.997682i	$0.521676\pi$
$942$	7.60596	0.247816
$943$	29.2298	0.951853
$944$	2.72563	0.0887117
$945$	23.4087	0.761487
$946$	57.1596	1.85842
$947$	46.7850	1.52031	0.760153	−	0.649744i	$-0.225124\pi$
$947$	46.7850	1.52031	0.760153	+	0.649744i	$0.225124\pi$
$948$	−1.98070	−0.0643302
$949$	8.23781	0.267411
$950$	1.61167	0.0522894
$951$	6.46931	0.209782
$952$	33.4670	1.08467
$953$	29.8352	0.966456	0.483228	−	0.875494i	$-0.339464\pi$
$953$	29.8352	0.966456	0.483228	+	0.875494i	$0.339464\pi$
$954$	−9.57458	−0.309989
$955$	50.0727	1.62032
$956$	12.5027	0.404368
$957$	−22.8953	−0.740100
$958$	−13.9462	−0.450582
$959$	13.2296	0.427205
$960$	−0.874093	−0.0282112
$961$	−30.9290	−0.997708
$962$	32.9507	1.06237
$963$	−38.3646	−1.23628
$964$	12.0167	0.387032
$965$	43.0689	1.38644
$966$	18.1246	0.583148
$967$	50.9657	1.63895	0.819474	−	0.573117i	$-0.194266\pi$
$967$	50.9657	1.63895	0.819474	+	0.573117i	$0.194266\pi$
$968$	20.6356	0.663252
$969$	3.42670	0.110082
$970$	−16.3357	−0.524507
$971$	−8.00908	−0.257024	−0.128512	−	0.991708i	$-0.541020\pi$
$971$	−8.00908	−0.257024	−0.128512	+	0.991708i	$0.541020\pi$
$972$	−11.5604	−0.370801
$973$	37.3301	1.19675
$974$	−11.7107	−0.375235
$975$	−2.32983	−0.0746143
$976$	3.87962	0.124184
$977$	46.9517	1.50212	0.751059	−	0.660235i	$-0.229543\pi$
$977$	46.9517	1.50212	0.751059	+	0.660235i	$0.229543\pi$
$978$	−6.23605	−0.199407
$979$	28.2421	0.902621
$980$	26.7064	0.853106
$981$	46.8535	1.49592
$982$	−36.8859	−1.17708
$983$	12.7853	0.407787	0.203894	−	0.978993i	$-0.434640\pi$
$983$	12.7853	0.407787	0.203894	+	0.978993i	$0.434640\pi$
$984$	1.68653	0.0537645
$985$	9.60569	0.306063
$986$	−61.8594	−1.97000
$987$	17.3531	0.552356
$988$	3.04428	0.0968514
$989$	83.6371	2.65950
$990$	28.7255	0.912955
$991$	3.15000	0.100063	0.0500316	−	0.998748i	$-0.484068\pi$
$991$	3.15000	0.100063	0.0500316	+	0.998748i	$0.484068\pi$
$992$	0.266541	0.00846270
$993$	5.88807	0.186852
$994$	43.0740	1.36622
$995$	21.4147	0.678891
$996$	3.98629	0.126310
$997$	−19.4561	−0.616182	−0.308091	−	0.951357i	$-0.599690\pi$
$997$	−19.4561	−0.616182	−0.308091	+	0.951357i	$0.599690\pi$
$998$	−36.5176	−1.15595
$999$	−29.6797	−0.939026

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.e.1.15	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.e.1.15	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.474859 q^{3} +1.00000 q^{4} +1.84074 q^{5} -0.474859 q^{6} +4.63773 q^{7} +1.00000 q^{8} -2.77451 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.474859 q^{3} +1.00000 q^{4} +1.84074 q^{5} -0.474859 q^{6} +4.63773 q^{7} +1.00000 q^{8} -2.77451 q^{9} +1.84074 q^{10} -5.62455 q^{11} -0.474859 q^{12} -3.04428 q^{13} +4.63773 q^{14} -0.874093 q^{15} +1.00000 q^{16} +7.21625 q^{17} -2.77451 q^{18} -1.00000 q^{19} +1.84074 q^{20} -2.20227 q^{21} -5.62455 q^{22} -8.22996 q^{23} -0.474859 q^{24} -1.61167 q^{25} -3.04428 q^{26} +2.74208 q^{27} +4.63773 q^{28} -8.57223 q^{29} -0.874093 q^{30} +0.266541 q^{31} +1.00000 q^{32} +2.67087 q^{33} +7.21625 q^{34} +8.53686 q^{35} -2.77451 q^{36} -10.8238 q^{37} -1.00000 q^{38} +1.44560 q^{39} +1.84074 q^{40} -3.55163 q^{41} -2.20227 q^{42} -10.1625 q^{43} -5.62455 q^{44} -5.10716 q^{45} -8.22996 q^{46} -7.87966 q^{47} -0.474859 q^{48} +14.5085 q^{49} -1.61167 q^{50} -3.42670 q^{51} -3.04428 q^{52} +3.45091 q^{53} +2.74208 q^{54} -10.3533 q^{55} +4.63773 q^{56} +0.474859 q^{57} -8.57223 q^{58} +2.72563 q^{59} -0.874093 q^{60} +3.87962 q^{61} +0.266541 q^{62} -12.8674 q^{63} +1.00000 q^{64} -5.60373 q^{65} +2.67087 q^{66} +7.13383 q^{67} +7.21625 q^{68} +3.90807 q^{69} +8.53686 q^{70} +9.28774 q^{71} -2.77451 q^{72} -2.70600 q^{73} -10.8238 q^{74} +0.765315 q^{75} -1.00000 q^{76} -26.0851 q^{77} +1.44560 q^{78} +4.17114 q^{79} +1.84074 q^{80} +7.02143 q^{81} -3.55163 q^{82} -8.39468 q^{83} -2.20227 q^{84} +13.2833 q^{85} -10.1625 q^{86} +4.07060 q^{87} -5.62455 q^{88} -5.02122 q^{89} -5.10716 q^{90} -14.1185 q^{91} -8.22996 q^{92} -0.126570 q^{93} -7.87966 q^{94} -1.84074 q^{95} -0.474859 q^{96} -8.87450 q^{97} +14.5085 q^{98} +15.6054 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9}+O(q^{10}) \) 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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