LMFDB - Embedded newform 8027.2.a.d.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.34025 q^{2} -2.24282 q^{3} +3.47677 q^{4} +1.33607 q^{5} +5.24876 q^{6} +2.78387 q^{7} -3.45602 q^{8} +2.03023 q^{9} +O(q^{10})$	\(q-2.34025 q^{2} -2.24282 q^{3} +3.47677 q^{4} +1.33607 q^{5} +5.24876 q^{6} +2.78387 q^{7} -3.45602 q^{8} +2.03023 q^{9} -3.12673 q^{10} +0.858461 q^{11} -7.79777 q^{12} +3.66044 q^{13} -6.51496 q^{14} -2.99656 q^{15} +1.13440 q^{16} -4.11321 q^{17} -4.75126 q^{18} -3.04542 q^{19} +4.64520 q^{20} -6.24373 q^{21} -2.00901 q^{22} -1.00000 q^{23} +7.75122 q^{24} -3.21492 q^{25} -8.56634 q^{26} +2.17501 q^{27} +9.67890 q^{28} +3.41063 q^{29} +7.01270 q^{30} -1.03006 q^{31} +4.25725 q^{32} -1.92537 q^{33} +9.62595 q^{34} +3.71945 q^{35} +7.05866 q^{36} +7.12937 q^{37} +7.12704 q^{38} -8.20970 q^{39} -4.61747 q^{40} +0.294300 q^{41} +14.6119 q^{42} +2.50063 q^{43} +2.98467 q^{44} +2.71253 q^{45} +2.34025 q^{46} -5.77354 q^{47} -2.54425 q^{48} +0.749960 q^{49} +7.52372 q^{50} +9.22519 q^{51} +12.7265 q^{52} +2.90591 q^{53} -5.09007 q^{54} +1.14696 q^{55} -9.62112 q^{56} +6.83032 q^{57} -7.98172 q^{58} +5.65368 q^{59} -10.4184 q^{60} -5.06958 q^{61} +2.41059 q^{62} +5.65192 q^{63} -12.2318 q^{64} +4.89059 q^{65} +4.50585 q^{66} -15.7184 q^{67} -14.3007 q^{68} +2.24282 q^{69} -8.70444 q^{70} +10.7206 q^{71} -7.01652 q^{72} -10.8731 q^{73} -16.6845 q^{74} +7.21048 q^{75} -10.5882 q^{76} +2.38985 q^{77} +19.2127 q^{78} -4.71554 q^{79} +1.51563 q^{80} -10.9689 q^{81} -0.688736 q^{82} +16.7557 q^{83} -21.7080 q^{84} -5.49554 q^{85} -5.85211 q^{86} -7.64941 q^{87} -2.96685 q^{88} +3.64585 q^{89} -6.34800 q^{90} +10.1902 q^{91} -3.47677 q^{92} +2.31023 q^{93} +13.5115 q^{94} -4.06889 q^{95} -9.54825 q^{96} -9.33280 q^{97} -1.75509 q^{98} +1.74288 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9}+O(q^{10}) $ 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9} - 30 q^{10} - 20 q^{11} - 32 q^{12} - 73 q^{13} - 18 q^{14} - 43 q^{15} + 99 q^{16} - 32 q^{17} - 50 q^{18} - 32 q^{19} - 67 q^{20} - 36 q^{21} - 78 q^{22} - 149 q^{23} - 27 q^{24} + 75 q^{25} + 7 q^{26} - 23 q^{27} - 90 q^{28} - 20 q^{29} - 12 q^{30} - 34 q^{31} - 35 q^{32} - 63 q^{33} - 43 q^{34} + 24 q^{35} + 98 q^{36} - 228 q^{37} - 25 q^{38} - 19 q^{39} - 79 q^{40} - 4 q^{41} - 88 q^{42} - 70 q^{43} - 80 q^{44} - 153 q^{45} + 5 q^{46} - 3 q^{47} - 95 q^{48} + 86 q^{49} - 5 q^{50} - 57 q^{51} - 146 q^{52} - 110 q^{53} - 18 q^{54} - 33 q^{55} - 75 q^{56} - 132 q^{57} - 92 q^{58} + 41 q^{59} - 107 q^{60} - 82 q^{61} - 34 q^{62} - 99 q^{63} + 35 q^{64} - 47 q^{65} - 58 q^{66} - 162 q^{67} - 80 q^{68} + 5 q^{69} - 88 q^{70} - q^{71} - 117 q^{72} - 124 q^{73} - 51 q^{74} - q^{75} - 74 q^{76} - 56 q^{77} - 95 q^{78} - 89 q^{79} - 90 q^{80} + 93 q^{81} - 91 q^{82} - 64 q^{83} - 93 q^{84} - 155 q^{85} - 21 q^{86} - 49 q^{87} - 263 q^{88} - 60 q^{89} - 122 q^{90} - 130 q^{91} - 135 q^{92} - 179 q^{93} - 21 q^{94} + 30 q^{95} - 17 q^{96} - 199 q^{97} - 72 q^{98} - 91 q^{99}+O(q^{100}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9 - 30 * q^10 - 20 * q^11 - 32 * q^12 - 73 * q^13 - 18 * q^14 - 43 * q^15 + 99 * q^16 - 32 * q^17 - 50 * q^18 - 32 * q^19 - 67 * q^20 - 36 * q^21 - 78 * q^22 - 149 * q^23 - 27 * q^24 + 75 * q^25 + 7 * q^26 - 23 * q^27 - 90 * q^28 - 20 * q^29 - 12 * q^30 - 34 * q^31 - 35 * q^32 - 63 * q^33 - 43 * q^34 + 24 * q^35 + 98 * q^36 - 228 * q^37 - 25 * q^38 - 19 * q^39 - 79 * q^40 - 4 * q^41 - 88 * q^42 - 70 * q^43 - 80 * q^44 - 153 * q^45 + 5 * q^46 - 3 * q^47 - 95 * q^48 + 86 * q^49 - 5 * q^50 - 57 * q^51 - 146 * q^52 - 110 * q^53 - 18 * q^54 - 33 * q^55 - 75 * q^56 - 132 * q^57 - 92 * q^58 + 41 * q^59 - 107 * q^60 - 82 * q^61 - 34 * q^62 - 99 * q^63 + 35 * q^64 - 47 * q^65 - 58 * q^66 - 162 * q^67 - 80 * q^68 + 5 * q^69 - 88 * q^70 - q^71 - 117 * q^72 - 124 * q^73 - 51 * q^74 - q^75 - 74 * q^76 - 56 * q^77 - 95 * q^78 - 89 * q^79 - 90 * q^80 + 93 * q^81 - 91 * q^82 - 64 * q^83 - 93 * q^84 - 155 * q^85 - 21 * q^86 - 49 * q^87 - 263 * q^88 - 60 * q^89 - 122 * q^90 - 130 * q^91 - 135 * q^92 - 179 * q^93 - 21 * q^94 + 30 * q^95 - 17 * q^96 - 199 * q^97 - 72 * q^98 - 91 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.34025	−1.65481	−0.827403	−	0.561608i	$-0.810183\pi$
$2$	−2.34025	−1.65481	−0.827403	+	0.561608i	$0.810183\pi$
$3$	−2.24282	−1.29489	−0.647446	−	0.762111i	$-0.724163\pi$
$3$	−2.24282	−1.29489	−0.647446	+	0.762111i	$0.724163\pi$
$4$	3.47677	1.73839
$5$	1.33607	0.597508	0.298754	−	0.954330i	$-0.403429\pi$
$5$	1.33607	0.597508	0.298754	+	0.954330i	$0.403429\pi$
$6$	5.24876	2.14280
$7$	2.78387	1.05221	0.526103	−	0.850421i	$-0.323653\pi$
$7$	2.78387	1.05221	0.526103	+	0.850421i	$0.323653\pi$
$8$	−3.45602	−1.22189
$9$	2.03023	0.676745
$10$	−3.12673	−0.988760
$11$	0.858461	0.258836	0.129418	−	0.991590i	$-0.458689\pi$
$11$	0.858461	0.258836	0.129418	+	0.991590i	$0.458689\pi$
$12$	−7.79777	−2.25102
$13$	3.66044	1.01522	0.507611	−	0.861586i	$-0.330529\pi$
$13$	3.66044	1.01522	0.507611	+	0.861586i	$0.330529\pi$
$14$	−6.51496	−1.74120
$15$	−2.99656	−0.773708
$16$	1.13440	0.283600
$17$	−4.11321	−0.997601	−0.498800	−	0.866717i	$-0.666226\pi$
$17$	−4.11321	−0.997601	−0.498800	+	0.866717i	$0.666226\pi$
$18$	−4.75126	−1.11988
$19$	−3.04542	−0.698667	−0.349333	−	0.936999i	$-0.613592\pi$
$19$	−3.04542	−0.698667	−0.349333	+	0.936999i	$0.613592\pi$
$20$	4.64520	1.03870
$21$	−6.24373	−1.36249
$22$	−2.00901	−0.428323
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	7.75122	1.58221
$25$	−3.21492	−0.642984
$26$	−8.56634	−1.68000
$27$	2.17501	0.418581
$28$	9.67890	1.82914
$29$	3.41063	0.633337	0.316669	−	0.948536i	$-0.397436\pi$
$29$	3.41063	0.633337	0.316669	+	0.948536i	$0.397436\pi$
$30$	7.01270	1.28034
$31$	−1.03006	−0.185004	−0.0925020	−	0.995713i	$-0.529486\pi$
$31$	−1.03006	−0.185004	−0.0925020	+	0.995713i	$0.529486\pi$
$32$	4.25725	0.752583
$33$	−1.92537	−0.335164
$34$	9.62595	1.65084
$35$	3.71945	0.628701
$36$	7.05866	1.17644
$37$	7.12937	1.17206	0.586031	−	0.810289i	$-0.300690\pi$
$37$	7.12937	1.17206	0.586031	+	0.810289i	$0.300690\pi$
$38$	7.12704	1.15616
$39$	−8.20970	−1.31460
$40$	−4.61747	−0.730087
$41$	0.294300	0.0459620	0.0229810	−	0.999736i	$-0.492684\pi$
$41$	0.294300	0.0459620	0.0229810	+	0.999736i	$0.492684\pi$
$42$	14.6119	2.25466
$43$	2.50063	0.381343	0.190672	−	0.981654i	$-0.438933\pi$
$43$	2.50063	0.381343	0.190672	+	0.981654i	$0.438933\pi$
$44$	2.98467	0.449956
$45$	2.71253	0.404360
$46$	2.34025	0.345051
$47$	−5.77354	−0.842158	−0.421079	−	0.907024i	$-0.638348\pi$
$47$	−5.77354	−0.842158	−0.421079	+	0.907024i	$0.638348\pi$
$48$	−2.54425	−0.367231
$49$	0.749960	0.107137
$50$	7.52372	1.06401
$51$	9.22519	1.29179
$52$	12.7265	1.76485
$53$	2.90591	0.399157	0.199579	−	0.979882i	$-0.436043\pi$
$53$	2.90591	0.399157	0.199579	+	0.979882i	$0.436043\pi$
$54$	−5.09007	−0.692670
$55$	1.14696	0.154656
$56$	−9.62112	−1.28568
$57$	6.83032	0.904698
$58$	−7.98172	−1.04805
$59$	5.65368	0.736046	0.368023	−	0.929817i	$-0.380035\pi$
$59$	5.65368	0.736046	0.368023	+	0.929817i	$0.380035\pi$
$60$	−10.4184	−1.34500
$61$	−5.06958	−0.649094	−0.324547	−	0.945870i	$-0.605212\pi$
$61$	−5.06958	−0.649094	−0.324547	+	0.945870i	$0.605212\pi$
$62$	2.41059	0.306146
$63$	5.65192	0.712075
$64$	−12.2318	−1.52898
$65$	4.89059	0.606604
$66$	4.50585	0.554632
$67$	−15.7184	−1.92031	−0.960156	−	0.279465i	$-0.909843\pi$
$67$	−15.7184	−1.92031	−0.960156	+	0.279465i	$0.909843\pi$
$68$	−14.3007	−1.73422
$69$	2.24282	0.270004
$70$	−8.70444	−1.04038
$71$	10.7206	1.27230	0.636152	−	0.771564i	$-0.280525\pi$
$71$	10.7206	1.27230	0.636152	+	0.771564i	$0.280525\pi$
$72$	−7.01652	−0.826905
$73$	−10.8731	−1.27260	−0.636298	−	0.771443i	$-0.719535\pi$
$73$	−10.8731	−1.27260	−0.636298	+	0.771443i	$0.719535\pi$
$74$	−16.6845	−1.93954
$75$	7.21048	0.832595
$76$	−10.5882	−1.21455
$77$	2.38985	0.272348
$78$	19.2127	2.17541
$79$	−4.71554	−0.530540	−0.265270	−	0.964174i	$-0.585461\pi$
$79$	−4.71554	−0.530540	−0.265270	+	0.964174i	$0.585461\pi$
$80$	1.51563	0.169453
$81$	−10.9689	−1.21876
$82$	−0.688736	−0.0760582
$83$	16.7557	1.83918	0.919591	−	0.392877i	$-0.128520\pi$
$83$	16.7557	1.83918	0.919591	+	0.392877i	$0.128520\pi$
$84$	−21.7080	−2.36854
$85$	−5.49554	−0.596074
$86$	−5.85211	−0.631049
$87$	−7.64941	−0.820103
$88$	−2.96685	−0.316268
$89$	3.64585	0.386459	0.193229	−	0.981154i	$-0.438104\pi$
$89$	3.64585	0.386459	0.193229	+	0.981154i	$0.438104\pi$
$90$	−6.34800	−0.669138
$91$	10.1902	1.06822
$92$	−3.47677	−0.362479
$93$	2.31023	0.239560
$94$	13.5115	1.39361
$95$	−4.06889	−0.417459
$96$	−9.54825	−0.974514
$97$	−9.33280	−0.947603	−0.473801	−	0.880632i	$-0.657119\pi$
$97$	−9.33280	−0.947603	−0.473801	+	0.880632i	$0.657119\pi$
$98$	−1.75509	−0.177291
$99$	1.74288	0.175166
$100$	−11.1775	−1.11775
$101$	−8.37531	−0.833374	−0.416687	−	0.909050i	$-0.636809\pi$
$101$	−8.37531	−0.833374	−0.416687	+	0.909050i	$0.636809\pi$
$102$	−21.5893	−2.13766
$103$	−2.43393	−0.239823	−0.119911	−	0.992785i	$-0.538261\pi$
$103$	−2.43393	−0.239823	−0.119911	+	0.992785i	$0.538261\pi$
$104$	−12.6505	−1.24049
$105$	−8.34204	−0.814100
$106$	−6.80055	−0.660528
$107$	0.254205	0.0245749	0.0122874	−	0.999925i	$-0.496089\pi$
$107$	0.254205	0.0245749	0.0122874	+	0.999925i	$0.496089\pi$
$108$	7.56201	0.727655
$109$	0.515116	0.0493392	0.0246696	−	0.999696i	$-0.492147\pi$
$109$	0.515116	0.0493392	0.0246696	+	0.999696i	$0.492147\pi$
$110$	−2.68418	−0.255926
$111$	−15.9899	−1.51769
$112$	3.15802	0.298405
$113$	−13.3240	−1.25342	−0.626708	−	0.779254i	$-0.715598\pi$
$113$	−13.3240	−1.25342	−0.626708	+	0.779254i	$0.715598\pi$
$114$	−15.9847	−1.49710
$115$	−1.33607	−0.124589
$116$	11.8580	1.10098
$117$	7.43154	0.687046
$118$	−13.2310	−1.21801
$119$	−11.4507	−1.04968
$120$	10.3562	0.945383
$121$	−10.2630	−0.933004
$122$	11.8641	1.07412
$123$	−0.660062	−0.0595158
$124$	−3.58128	−0.321608
$125$	−10.9757	−0.981696
$126$	−13.2269	−1.17835
$127$	−17.0132	−1.50968	−0.754840	−	0.655909i	$-0.772286\pi$
$127$	−17.0132	−1.50968	−0.754840	+	0.655909i	$0.772286\pi$
$128$	20.1111	1.77758
$129$	−5.60847	−0.493798
$130$	−11.4452	−1.00381
$131$	9.12255	0.797041	0.398520	−	0.917159i	$-0.369524\pi$
$131$	9.12255	0.797041	0.398520	+	0.917159i	$0.369524\pi$
$132$	−6.69408	−0.582645
$133$	−8.47806	−0.735141
$134$	36.7851	3.17774
$135$	2.90596	0.250105
$136$	14.2153	1.21895
$137$	4.87280	0.416311	0.208156	−	0.978096i	$-0.433254\pi$
$137$	4.87280	0.416311	0.208156	+	0.978096i	$0.433254\pi$
$138$	−5.24876	−0.446804
$139$	−6.59639	−0.559499	−0.279749	−	0.960073i	$-0.590251\pi$
$139$	−6.59639	−0.559499	−0.279749	+	0.960073i	$0.590251\pi$
$140$	12.9317	1.09293
$141$	12.9490	1.09050
$142$	−25.0889	−2.10542
$143$	3.14234	0.262776
$144$	2.30309	0.191925
$145$	4.55683	0.378424
$146$	25.4457	2.10590
$147$	−1.68202	−0.138731
$148$	24.7872	2.03749
$149$	8.30875	0.680679	0.340340	−	0.940303i	$-0.389458\pi$
$149$	8.30875	0.680679	0.340340	+	0.940303i	$0.389458\pi$
$150$	−16.8743	−1.37778
$151$	−8.74765	−0.711874	−0.355937	−	0.934510i	$-0.615838\pi$
$151$	−8.74765	−0.711874	−0.355937	+	0.934510i	$0.615838\pi$
$152$	10.5250	0.853691
$153$	−8.35079	−0.675121
$154$	−5.59284	−0.450684
$155$	−1.37623	−0.110541
$156$	−28.5432	−2.28529
$157$	18.4921	1.47583	0.737915	−	0.674894i	$-0.235811\pi$
$157$	18.4921	1.47583	0.737915	+	0.674894i	$0.235811\pi$
$158$	11.0355	0.877941
$159$	−6.51742	−0.516865
$160$	5.68798	0.449675
$161$	−2.78387	−0.219400
$162$	25.6699	2.01681
$163$	−6.52364	−0.510971	−0.255485	−	0.966813i	$-0.582235\pi$
$163$	−6.52364	−0.510971	−0.255485	+	0.966813i	$0.582235\pi$
$164$	1.02321	0.0798996
$165$	−2.57243	−0.200263
$166$	−39.2126	−3.04349
$167$	−15.0704	−1.16619	−0.583093	−	0.812406i	$-0.698158\pi$
$167$	−15.0704	−1.16619	−0.583093	+	0.812406i	$0.698158\pi$
$168$	21.5784	1.66481
$169$	0.398800	0.0306769
$170$	12.8609	0.986388
$171$	−6.18291	−0.472819
$172$	8.69413	0.662922
$173$	−5.98989	−0.455403	−0.227702	−	0.973731i	$-0.573121\pi$
$173$	−5.98989	−0.455403	−0.227702	+	0.973731i	$0.573121\pi$
$174$	17.9015	1.35711
$175$	−8.94994	−0.676552
$176$	0.973837	0.0734057
$177$	−12.6802	−0.953100
$178$	−8.53219	−0.639515
$179$	−26.5815	−1.98679	−0.993397	−	0.114724i	$-0.963402\pi$
$179$	−26.5815	−1.98679	−0.993397	+	0.114724i	$0.963402\pi$
$180$	9.43085	0.702934
$181$	−2.30086	−0.171021	−0.0855107	−	0.996337i	$-0.527252\pi$
$181$	−2.30086	−0.171021	−0.0855107	+	0.996337i	$0.527252\pi$
$182$	−23.8476	−1.76770
$183$	11.3702	0.840506
$184$	3.45602	0.254781
$185$	9.52533	0.700316
$186$	−5.40653	−0.396426
$187$	−3.53103	−0.258215
$188$	−20.0733	−1.46399
$189$	6.05495	0.440433
$190$	9.52221	0.690814
$191$	10.4142	0.753547	0.376773	−	0.926305i	$-0.377034\pi$
$191$	10.4142	0.753547	0.376773	+	0.926305i	$0.377034\pi$
$192$	27.4338	1.97986
$193$	23.2886	1.67635	0.838176	−	0.545400i	$-0.183622\pi$
$193$	23.2886	1.67635	0.838176	+	0.545400i	$0.183622\pi$
$194$	21.8411	1.56810
$195$	−10.9687	−0.785486
$196$	2.60744	0.186246
$197$	6.92089	0.493093	0.246547	−	0.969131i	$-0.420704\pi$
$197$	6.92089	0.493093	0.246547	+	0.969131i	$0.420704\pi$
$198$	−4.07877	−0.289865
$199$	0.372821	0.0264286	0.0132143	−	0.999913i	$-0.495794\pi$
$199$	0.372821	0.0264286	0.0132143	+	0.999913i	$0.495794\pi$
$200$	11.1108	0.785654
$201$	35.2536	2.48660
$202$	19.6003	1.37907
$203$	9.49476	0.666401
$204$	32.0739	2.24562
$205$	0.393205	0.0274626
$206$	5.69601	0.396860
$207$	−2.03023	−0.141111
$208$	4.15240	0.287917
$209$	−2.61437	−0.180840
$210$	19.5225	1.34718
$211$	21.0086	1.44629	0.723146	−	0.690695i	$-0.242695\pi$
$211$	21.0086	1.44629	0.723146	+	0.690695i	$0.242695\pi$
$212$	10.1032	0.693889
$213$	−24.0444	−1.64749
$214$	−0.594902	−0.0406667
$215$	3.34102	0.227856
$216$	−7.51687	−0.511458
$217$	−2.86755	−0.194662
$218$	−1.20550	−0.0816469
$219$	24.3863	1.64787
$220$	3.98773	0.268852
$221$	−15.0562	−1.01279
$222$	37.4203	2.51149
$223$	−14.5375	−0.973502	−0.486751	−	0.873541i	$-0.661818\pi$
$223$	−14.5375	−0.973502	−0.486751	+	0.873541i	$0.661818\pi$
$224$	11.8517	0.791873
$225$	−6.52704	−0.435136
$226$	31.1815	2.07416
$227$	−15.4521	−1.02559	−0.512796	−	0.858510i	$-0.671390\pi$
$227$	−15.4521	−1.02559	−0.512796	+	0.858510i	$0.671390\pi$
$228$	23.7475	1.57271
$229$	6.46276	0.427071	0.213536	−	0.976935i	$-0.431502\pi$
$229$	6.46276	0.427071	0.213536	+	0.976935i	$0.431502\pi$
$230$	3.12673	0.206171
$231$	−5.35999	−0.352662
$232$	−11.7872	−0.773866
$233$	−23.9743	−1.57061	−0.785304	−	0.619111i	$-0.787493\pi$
$233$	−23.9743	−1.57061	−0.785304	+	0.619111i	$0.787493\pi$
$234$	−17.3917	−1.13693
$235$	−7.71385	−0.503196
$236$	19.6566	1.27953
$237$	10.5761	0.686992
$238$	26.7974	1.73702
$239$	−0.216107	−0.0139788	−0.00698939	−	0.999976i	$-0.502225\pi$
$239$	−0.216107	−0.0139788	−0.00698939	+	0.999976i	$0.502225\pi$
$240$	−3.39929	−0.219423
$241$	−20.7875	−1.33904	−0.669520	−	0.742794i	$-0.733500\pi$
$241$	−20.7875	−1.33904	−0.669520	+	0.742794i	$0.733500\pi$
$242$	24.0181	1.54394
$243$	18.0761	1.15958
$244$	−17.6258	−1.12838
$245$	1.00200	0.0640153
$246$	1.54471	0.0984871
$247$	−11.1476	−0.709302
$248$	3.55990	0.226054
$249$	−37.5801	−2.38154
$250$	25.6859	1.62452
$251$	20.6500	1.30342	0.651708	−	0.758470i	$-0.274053\pi$
$251$	20.6500	1.30342	0.651708	+	0.758470i	$0.274053\pi$
$252$	19.6504	1.23786
$253$	−0.858461	−0.0539710
$254$	39.8152	2.49823
$255$	12.3255	0.771852
$256$	−22.6012	−1.41258
$257$	15.7149	0.980269	0.490135	−	0.871647i	$-0.336948\pi$
$257$	15.7149	0.980269	0.490135	+	0.871647i	$0.336948\pi$
$258$	13.1252	0.817140
$259$	19.8473	1.23325
$260$	17.0035	1.05451
$261$	6.92437	0.428608
$262$	−21.3491	−1.31895
$263$	−10.7241	−0.661275	−0.330638	−	0.943758i	$-0.607264\pi$
$263$	−10.7241	−0.661275	−0.330638	+	0.943758i	$0.607264\pi$
$264$	6.65411	0.409532
$265$	3.88249	0.238499
$266$	19.8408	1.21652
$267$	−8.17697	−0.500422
$268$	−54.6494	−3.33824
$269$	7.29145	0.444568	0.222284	−	0.974982i	$-0.428649\pi$
$269$	7.29145	0.444568	0.222284	+	0.974982i	$0.428649\pi$
$270$	−6.80068	−0.413876
$271$	10.1474	0.616410	0.308205	−	0.951320i	$-0.400272\pi$
$271$	10.1474	0.616410	0.308205	+	0.951320i	$0.400272\pi$
$272$	−4.66602	−0.282919
$273$	−22.8548	−1.38323
$274$	−11.4036	−0.688915
$275$	−2.75988	−0.166427
$276$	7.79777	0.469370
$277$	−16.1774	−0.972008	−0.486004	−	0.873957i	$-0.661546\pi$
$277$	−16.1774	−0.972008	−0.486004	+	0.873957i	$0.661546\pi$
$278$	15.4372	0.925862
$279$	−2.09126	−0.125200
$280$	−12.8545	−0.768201
$281$	13.7179	0.818341	0.409170	−	0.912458i	$-0.365818\pi$
$281$	13.7179	0.818341	0.409170	+	0.912458i	$0.365818\pi$
$282$	−30.3039	−1.80457
$283$	−10.4679	−0.622254	−0.311127	−	0.950368i	$-0.600706\pi$
$283$	−10.4679	−0.622254	−0.311127	+	0.950368i	$0.600706\pi$
$284$	37.2731	2.21175
$285$	9.12577	0.540564
$286$	−7.35386	−0.434843
$287$	0.819295	0.0483614
$288$	8.64322	0.509307
$289$	−0.0814702	−0.00479236
$290$	−10.6641	−0.626219
$291$	20.9318	1.22704
$292$	−37.8032	−2.21226
$293$	11.0279	0.644256	0.322128	−	0.946696i	$-0.395602\pi$
$293$	11.0279	0.644256	0.322128	+	0.946696i	$0.395602\pi$
$294$	3.93636	0.229573
$295$	7.55370	0.439794
$296$	−24.6392	−1.43213
$297$	1.86716	0.108344
$298$	−19.4446	−1.12639
$299$	−3.66044	−0.211689
$300$	25.0692	1.44737
$301$	6.96145	0.401251
$302$	20.4717	1.17801
$303$	18.7843	1.07913
$304$	−3.45472	−0.198142
$305$	−6.77331	−0.387839
$306$	19.5429	1.11720
$307$	4.15157	0.236942	0.118471	−	0.992957i	$-0.462201\pi$
$307$	4.15157	0.236942	0.118471	+	0.992957i	$0.462201\pi$
$308$	8.30895	0.473446
$309$	5.45887	0.310544
$310$	3.22072	0.182925
$311$	−33.5918	−1.90482	−0.952409	−	0.304823i	$-0.901403\pi$
$311$	−33.5918	−1.90482	−0.952409	+	0.304823i	$0.901403\pi$
$312$	28.3728	1.60630
$313$	−15.8271	−0.894599	−0.447300	−	0.894384i	$-0.647614\pi$
$313$	−15.8271	−0.894599	−0.447300	+	0.894384i	$0.647614\pi$
$314$	−43.2761	−2.44221
$315$	7.55135	0.425470
$316$	−16.3949	−0.922283
$317$	−17.2764	−0.970337	−0.485168	−	0.874421i	$-0.661242\pi$
$317$	−17.2764	−0.970337	−0.485168	+	0.874421i	$0.661242\pi$
$318$	15.2524	0.855312
$319$	2.92789	0.163930
$320$	−16.3426	−0.913578
$321$	−0.570135	−0.0318218
$322$	6.51496	0.363065
$323$	12.5265	0.696990
$324$	−38.1362	−2.11868
$325$	−11.7680	−0.652772
$326$	15.2670	0.845558
$327$	−1.15531	−0.0638889
$328$	−1.01711	−0.0561603
$329$	−16.0728	−0.886123
$330$	6.02012	0.331397
$331$	31.6306	1.73857	0.869287	−	0.494308i	$-0.164579\pi$
$331$	31.6306	1.73857	0.869287	+	0.494308i	$0.164579\pi$
$332$	58.2559	3.19721
$333$	14.4743	0.793186
$334$	35.2686	1.92981
$335$	−21.0009	−1.14740
$336$	−7.08287	−0.386402
$337$	22.6197	1.23217	0.616086	−	0.787679i	$-0.288717\pi$
$337$	22.6197	1.23217	0.616086	+	0.787679i	$0.288717\pi$
$338$	−0.933291	−0.0507644
$339$	29.8833	1.62304
$340$	−19.1067	−1.03621
$341$	−0.884265	−0.0478856
$342$	14.4696	0.782424
$343$	−17.3993	−0.939476
$344$	−8.64223	−0.465958
$345$	2.99656	0.161329
$346$	14.0179	0.753604
$347$	−35.4047	−1.90062	−0.950311	−	0.311301i	$-0.899235\pi$
$347$	−35.4047	−1.90062	−0.950311	+	0.311301i	$0.899235\pi$
$348$	−26.5953	−1.42566
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	20.9451	1.11956
$351$	7.96148	0.424953
$352$	3.65469	0.194795
$353$	7.79535	0.414905	0.207452	−	0.978245i	$-0.433483\pi$
$353$	7.79535	0.414905	0.207452	+	0.978245i	$0.433483\pi$
$354$	29.6748	1.57720
$355$	14.3235	0.760211
$356$	12.6758	0.671815
$357$	25.6818	1.35922
$358$	62.2074	3.28776
$359$	19.7165	1.04059	0.520297	−	0.853985i	$-0.325821\pi$
$359$	19.7165	1.04059	0.520297	+	0.853985i	$0.325821\pi$
$360$	−9.37455	−0.494082
$361$	−9.72544	−0.511865
$362$	5.38458	0.283007
$363$	23.0181	1.20814
$364$	35.4290	1.85698
$365$	−14.5272	−0.760387
$366$	−26.6090	−1.39088
$367$	30.6411	1.59945	0.799726	−	0.600365i	$-0.204978\pi$
$367$	30.6411	1.59945	0.799726	+	0.600365i	$0.204978\pi$
$368$	−1.13440	−0.0591346
$369$	0.597498	0.0311045
$370$	−22.2917	−1.15889
$371$	8.08968	0.419995
$372$	8.03216	0.416448
$373$	−31.9557	−1.65460	−0.827302	−	0.561758i	$-0.810125\pi$
$373$	−31.9557	−1.65460	−0.827302	+	0.561758i	$0.810125\pi$
$374$	8.26350	0.427295
$375$	24.6165	1.27119
$376$	19.9535	1.02902
$377$	12.4844	0.642978
$378$	−14.1701	−0.728832
$379$	35.6396	1.83069	0.915343	−	0.402676i	$-0.131920\pi$
$379$	35.6396	1.83069	0.915343	+	0.402676i	$0.131920\pi$
$380$	−14.1466	−0.725705
$381$	38.1576	1.95487
$382$	−24.3719	−1.24697
$383$	16.5186	0.844059	0.422030	−	0.906582i	$-0.361318\pi$
$383$	16.5186	0.844059	0.422030	+	0.906582i	$0.361318\pi$
$384$	−45.1054	−2.30178
$385$	3.19300	0.162730
$386$	−54.5012	−2.77404
$387$	5.07687	0.258072
$388$	−32.4480	−1.64730
$389$	17.6225	0.893496	0.446748	−	0.894660i	$-0.352582\pi$
$389$	17.6225	0.893496	0.446748	+	0.894660i	$0.352582\pi$
$390$	25.6695	1.29983
$391$	4.11321	0.208014
$392$	−2.59187	−0.130909
$393$	−20.4602	−1.03208
$394$	−16.1966	−0.815974
$395$	−6.30029	−0.317002
$396$	6.05958	0.304505
$397$	−28.9441	−1.45266	−0.726331	−	0.687345i	$-0.758776\pi$
$397$	−28.9441	−1.45266	−0.726331	+	0.687345i	$0.758776\pi$
$398$	−0.872495	−0.0437342
$399$	19.0147	0.951928
$400$	−3.64700	−0.182350
$401$	−19.8534	−0.991431	−0.495715	−	0.868485i	$-0.665094\pi$
$401$	−19.8534	−0.991431	−0.495715	+	0.868485i	$0.665094\pi$
$402$	−82.5022	−4.11484
$403$	−3.77046	−0.187820
$404$	−29.1190	−1.44873
$405$	−14.6551	−0.728220
$406$	−22.2201	−1.10277
$407$	6.12028	0.303371
$408$	−31.8824	−1.57841
$409$	−35.6467	−1.76262	−0.881308	−	0.472543i	$-0.843336\pi$
$409$	−35.6467	−1.76262	−0.881308	+	0.472543i	$0.843336\pi$
$410$	−0.920198	−0.0454454
$411$	−10.9288	−0.539078
$412$	−8.46223	−0.416904
$413$	15.7391	0.774472
$414$	4.75126	0.233511
$415$	22.3868	1.09893
$416$	15.5834	0.764040
$417$	14.7945	0.724490
$418$	6.11828	0.299255
$419$	20.9633	1.02412	0.512062	−	0.858948i	$-0.328882\pi$
$419$	20.9633	1.02412	0.512062	+	0.858948i	$0.328882\pi$
$420$	−29.0034	−1.41522
$421$	35.3622	1.72345	0.861724	−	0.507378i	$-0.169385\pi$
$421$	35.3622	1.72345	0.861724	+	0.507378i	$0.169385\pi$
$422$	−49.1654	−2.39333
$423$	−11.7216	−0.569926
$424$	−10.0429	−0.487724
$425$	13.2237	0.641442
$426$	56.2699	2.72629
$427$	−14.1131	−0.682980
$428$	0.883811	0.0427206
$429$	−7.04770	−0.340266
$430$	−7.81882	−0.377057
$431$	26.4010	1.27169	0.635846	−	0.771816i	$-0.280651\pi$
$431$	26.4010	1.27169	0.635846	+	0.771816i	$0.280651\pi$
$432$	2.46733	0.118709
$433$	−13.5400	−0.650692	−0.325346	−	0.945595i	$-0.605481\pi$
$433$	−13.5400	−0.650692	−0.325346	+	0.945595i	$0.605481\pi$
$434$	6.71079	0.322128
$435$	−10.2201	−0.490018
$436$	1.79094	0.0857706
$437$	3.04542	0.145682
$438$	−57.0701	−2.72691
$439$	28.4356	1.35716	0.678579	−	0.734527i	$-0.262596\pi$
$439$	28.4356	1.35716	0.678579	+	0.734527i	$0.262596\pi$
$440$	−3.96392	−0.188972
$441$	1.52259	0.0725045
$442$	35.2352	1.67597
$443$	−28.3399	−1.34647	−0.673235	−	0.739428i	$-0.735096\pi$
$443$	−28.3399	−1.34647	−0.673235	+	0.739428i	$0.735096\pi$
$444$	−55.5932	−2.63834
$445$	4.87110	0.230912
$446$	34.0214	1.61096
$447$	−18.6350	−0.881406
$448$	−34.0519	−1.60880
$449$	−28.4766	−1.34390	−0.671948	−	0.740598i	$-0.734542\pi$
$449$	−28.4766	−1.34390	−0.671948	+	0.740598i	$0.734542\pi$
$450$	15.2749	0.720066
$451$	0.252645	0.0118966
$452$	−46.3245	−2.17892
$453$	19.6194	0.921800
$454$	36.1618	1.69716
$455$	13.6148	0.638272
$456$	−23.6057	−1.10544
$457$	6.32134	0.295700	0.147850	−	0.989010i	$-0.452765\pi$
$457$	6.32134	0.295700	0.147850	+	0.989010i	$0.452765\pi$
$458$	−15.1245	−0.706720
$459$	−8.94628	−0.417576
$460$	−4.64520	−0.216584
$461$	−12.2019	−0.568297	−0.284149	−	0.958780i	$-0.591711\pi$
$461$	−12.2019	−0.568297	−0.284149	+	0.958780i	$0.591711\pi$
$462$	12.5437	0.583587
$463$	−7.95317	−0.369615	−0.184808	−	0.982775i	$-0.559166\pi$
$463$	−7.95317	−0.369615	−0.184808	+	0.982775i	$0.559166\pi$
$464$	3.86901	0.179614
$465$	3.08663	0.143139
$466$	56.1058	2.59905
$467$	10.0790	0.466399	0.233199	−	0.972429i	$-0.425081\pi$
$467$	10.0790	0.466399	0.233199	+	0.972429i	$0.425081\pi$
$468$	25.8378	1.19435
$469$	−43.7581	−2.02056
$470$	18.0523	0.832692
$471$	−41.4744	−1.91104
$472$	−19.5392	−0.899365
$473$	2.14670	0.0987052
$474$	−24.7507	−1.13684
$475$	9.79078	0.449232
$476$	−39.8114	−1.82475
$477$	5.89967	0.270127
$478$	0.505744	0.0231322
$479$	14.5333	0.664042	0.332021	−	0.943272i	$-0.392269\pi$
$479$	14.5333	0.664042	0.332021	+	0.943272i	$0.392269\pi$
$480$	−12.7571	−0.582280
$481$	26.0966	1.18990
$482$	48.6479	2.21585
$483$	6.24373	0.284099
$484$	−35.6823	−1.62192
$485$	−12.4693	−0.566200
$486$	−42.3026	−1.91889
$487$	−2.85121	−0.129201	−0.0646003	−	0.997911i	$-0.520577\pi$
$487$	−2.85121	−0.129201	−0.0646003	+	0.997911i	$0.520577\pi$
$488$	17.5206	0.793119
$489$	14.6313	0.661652
$490$	−2.34493	−0.105933
$491$	43.8970	1.98105	0.990523	−	0.137350i	$-0.0438585\pi$
$491$	43.8970	1.98105	0.990523	+	0.137350i	$0.0438585\pi$
$492$	−2.29488	−0.103461
$493$	−14.0286	−0.631818
$494$	26.0881	1.17376
$495$	2.32860	0.104663
$496$	−1.16850	−0.0524671
$497$	29.8449	1.33872
$498$	87.9468	3.94099
$499$	28.6260	1.28148	0.640739	−	0.767759i	$-0.278628\pi$
$499$	28.6260	1.28148	0.640739	+	0.767759i	$0.278628\pi$
$500$	−38.1600	−1.70657
$501$	33.8003	1.51008
$502$	−48.3261	−2.15690
$503$	3.35619	0.149645	0.0748227	−	0.997197i	$-0.476161\pi$
$503$	3.35619	0.149645	0.0748227	+	0.997197i	$0.476161\pi$
$504$	−19.5331	−0.870074
$505$	−11.1900	−0.497948
$506$	2.00901	0.0893115
$507$	−0.894436	−0.0397233
$508$	−59.1511	−2.62441
$509$	−31.4461	−1.39383	−0.696913	−	0.717156i	$-0.745444\pi$
$509$	−31.4461	−1.39383	−0.696913	+	0.717156i	$0.745444\pi$
$510$	−28.8447	−1.27727
$511$	−30.2693	−1.33903
$512$	12.6704	0.559959
$513$	−6.62381	−0.292448
$514$	−36.7768	−1.62216
$515$	−3.25190	−0.143296
$516$	−19.4994	−0.858412
$517$	−4.95636	−0.217980
$518$	−46.4476	−2.04079
$519$	13.4342	0.589698
$520$	−16.9020	−0.741200
$521$	−31.5731	−1.38324	−0.691622	−	0.722260i	$-0.743103\pi$
$521$	−31.5731	−1.38324	−0.691622	+	0.722260i	$0.743103\pi$
$522$	−16.2048	−0.709263
$523$	30.2080	1.32090	0.660452	−	0.750868i	$-0.270365\pi$
$523$	30.2080	1.32090	0.660452	+	0.750868i	$0.270365\pi$
$524$	31.7170	1.38556
$525$	20.0731	0.876061
$526$	25.0970	1.09428
$527$	4.23685	0.184560
$528$	−2.18414	−0.0950524
$529$	1.00000	0.0434783
$530$	−9.08600	−0.394671
$531$	11.4783	0.498115
$532$	−29.4763	−1.27796
$533$	1.07727	0.0466616
$534$	19.1362	0.828102
$535$	0.339635	0.0146837
$536$	54.3231	2.34640
$537$	59.6175	2.57268
$538$	−17.0638	−0.735674
$539$	0.643811	0.0277309
$540$	10.1034	0.434780
$541$	−20.9248	−0.899627	−0.449814	−	0.893122i	$-0.648510\pi$
$541$	−20.9248	−0.899627	−0.449814	+	0.893122i	$0.648510\pi$
$542$	−23.7474	−1.02004
$543$	5.16041	0.221454
$544$	−17.5110	−0.750778
$545$	0.688231	0.0294806
$546$	53.4859	2.28898
$547$	−39.2109	−1.67654	−0.838269	−	0.545257i	$-0.816432\pi$
$547$	−39.2109	−1.67654	−0.838269	+	0.545257i	$0.816432\pi$
$548$	16.9416	0.723709
$549$	−10.2924	−0.439271
$550$	6.45882	0.275405
$551$	−10.3868	−0.442492
$552$	−7.75122	−0.329914
$553$	−13.1275	−0.558237
$554$	37.8593	1.60849
$555$	−21.3636	−0.906833
$556$	−22.9341	−0.972624
$557$	−6.00435	−0.254413	−0.127206	−	0.991876i	$-0.540601\pi$
$557$	−6.00435	−0.254413	−0.127206	+	0.991876i	$0.540601\pi$
$558$	4.89407	0.207183
$559$	9.15341	0.387148
$560$	4.21934	0.178300
$561$	7.91946	0.334360
$562$	−32.1033	−1.35420
$563$	28.1325	1.18564	0.592822	−	0.805334i	$-0.298014\pi$
$563$	28.1325	1.18564	0.592822	+	0.805334i	$0.298014\pi$
$564$	45.0207	1.89571
$565$	−17.8018	−0.748926
$566$	24.4976	1.02971
$567$	−30.5359	−1.28239
$568$	−37.0506	−1.55461
$569$	17.8635	0.748879	0.374439	−	0.927251i	$-0.377835\pi$
$569$	17.8635	0.748879	0.374439	+	0.927251i	$0.377835\pi$
$570$	−21.3566	−0.894529
$571$	−45.2299	−1.89281	−0.946407	−	0.322977i	$-0.895316\pi$
$571$	−45.2299	−1.89281	−0.946407	+	0.322977i	$0.895316\pi$
$572$	10.9252	0.456806
$573$	−23.3572	−0.975761
$574$	−1.91735	−0.0800288
$575$	3.21492	0.134071
$576$	−24.8335	−1.03473
$577$	−23.8155	−0.991451	−0.495725	−	0.868479i	$-0.665098\pi$
$577$	−23.8155	−0.991451	−0.495725	+	0.868479i	$0.665098\pi$
$578$	0.190661	0.00793044
$579$	−52.2322	−2.17069
$580$	15.8431	0.657847
$581$	46.6459	1.93520
$582$	−48.9856	−2.03052
$583$	2.49461	0.103316
$584$	37.5775	1.55497
$585$	9.92905	0.410516
$586$	−25.8080	−1.06612
$587$	−24.6838	−1.01881	−0.509404	−	0.860527i	$-0.670134\pi$
$587$	−24.6838	−1.01881	−0.509404	+	0.860527i	$0.670134\pi$
$588$	−5.84801	−0.241168
$589$	3.13696	0.129256
$590$	−17.6776	−0.727773
$591$	−15.5223	−0.638502
$592$	8.08755	0.332396
$593$	26.4490	1.08613	0.543065	−	0.839690i	$-0.317264\pi$
$593$	26.4490	1.08613	0.543065	+	0.839690i	$0.317264\pi$
$594$	−4.36962	−0.179288
$595$	−15.2989	−0.627193
$596$	28.8876	1.18328
$597$	−0.836171	−0.0342222
$598$	8.56634	0.350304
$599$	30.3589	1.24043	0.620215	−	0.784432i	$-0.287045\pi$
$599$	30.3589	1.24043	0.620215	+	0.784432i	$0.287045\pi$
$600$	−24.9195	−1.01734
$601$	20.8311	0.849717	0.424859	−	0.905260i	$-0.360324\pi$
$601$	20.8311	0.849717	0.424859	+	0.905260i	$0.360324\pi$
$602$	−16.2915	−0.663994
$603$	−31.9121	−1.29956
$604$	−30.4136	−1.23751
$605$	−13.7121	−0.557477
$606$	−43.9599	−1.78575
$607$	−18.4556	−0.749089	−0.374545	−	0.927209i	$-0.622201\pi$
$607$	−18.4556	−0.749089	−0.374545	+	0.927209i	$0.622201\pi$
$608$	−12.9651	−0.525805
$609$	−21.2950	−0.862918
$610$	15.8512	0.641798
$611$	−21.1337	−0.854977
$612$	−29.0338	−1.17362
$613$	17.8228	0.719855	0.359928	−	0.932980i	$-0.382801\pi$
$613$	17.8228	0.719855	0.359928	+	0.932980i	$0.382801\pi$
$614$	−9.71570	−0.392094
$615$	−0.881888	−0.0355611
$616$	−8.25935	−0.332779
$617$	48.0342	1.93378	0.966891	−	0.255188i	$-0.0821374\pi$
$617$	48.0342	1.93378	0.966891	+	0.255188i	$0.0821374\pi$
$618$	−12.7751	−0.513891
$619$	16.4849	0.662585	0.331292	−	0.943528i	$-0.392515\pi$
$619$	16.4849	0.662585	0.331292	+	0.943528i	$0.392515\pi$
$620$	−4.78483	−0.192164
$621$	−2.17501	−0.0872801
$622$	78.6133	3.15211
$623$	10.1496	0.406634
$624$	−9.31307	−0.372821
$625$	1.41032	0.0564130
$626$	37.0393	1.48039
$627$	5.86356	0.234168
$628$	64.2928	2.56556
$629$	−29.3246	−1.16925
$630$	−17.6720	−0.704071
$631$	5.54287	0.220658	0.110329	−	0.993895i	$-0.464810\pi$
$631$	5.54287	0.220658	0.110329	+	0.993895i	$0.464810\pi$
$632$	16.2970	0.648259
$633$	−47.1185	−1.87279
$634$	40.4310	1.60572
$635$	−22.7308	−0.902046
$636$	−22.6596	−0.898511
$637$	2.74518	0.108768
$638$	−6.85199	−0.271273
$639$	21.7654	0.861024
$640$	26.8697	1.06212
$641$	−13.1114	−0.517871	−0.258935	−	0.965895i	$-0.583372\pi$
$641$	−13.1114	−0.517871	−0.258935	+	0.965895i	$0.583372\pi$
$642$	1.33426	0.0526590
$643$	−21.0229	−0.829062	−0.414531	−	0.910035i	$-0.636054\pi$
$643$	−21.0229	−0.829062	−0.414531	+	0.910035i	$0.636054\pi$
$644$	−9.67890	−0.381402
$645$	−7.49330	−0.295048
$646$	−29.3150	−1.15338
$647$	−12.3184	−0.484287	−0.242144	−	0.970240i	$-0.577850\pi$
$647$	−12.3184	−0.484287	−0.242144	+	0.970240i	$0.577850\pi$
$648$	37.9085	1.48919
$649$	4.85346	0.190515
$650$	27.5401	1.08021
$651$	6.43140	0.252067
$652$	−22.6812	−0.888265
$653$	11.2025	0.438388	0.219194	−	0.975681i	$-0.429657\pi$
$653$	11.2025	0.438388	0.219194	+	0.975681i	$0.429657\pi$
$654$	2.70372	0.105724
$655$	12.1884	0.476238
$656$	0.333854	0.0130348
$657$	−22.0749	−0.861223
$658$	37.6144	1.46636
$659$	1.66769	0.0649641	0.0324821	−	0.999472i	$-0.489659\pi$
$659$	1.66769	0.0649641	0.0324821	+	0.999472i	$0.489659\pi$
$660$	−8.94374	−0.348135
$661$	−9.55196	−0.371528	−0.185764	−	0.982594i	$-0.559476\pi$
$661$	−9.55196	−0.371528	−0.185764	+	0.982594i	$0.559476\pi$
$662$	−74.0235	−2.87700
$663$	33.7682	1.31145
$664$	−57.9081	−2.24727
$665$	−11.3273	−0.439253
$666$	−33.8735	−1.31257
$667$	−3.41063	−0.132060
$668$	−52.3965	−2.02728
$669$	32.6049	1.26058
$670$	49.1474	1.89873
$671$	−4.35204	−0.168009
$672$	−26.5811	−1.02539
$673$	−36.3784	−1.40228	−0.701142	−	0.713022i	$-0.747326\pi$
$673$	−36.3784	−1.40228	−0.701142	+	0.713022i	$0.747326\pi$
$674$	−52.9357	−2.03901
$675$	−6.99248	−0.269141
$676$	1.38654	0.0533283
$677$	−21.3826	−0.821798	−0.410899	−	0.911681i	$-0.634785\pi$
$677$	−21.3826	−0.821798	−0.410899	+	0.911681i	$0.634785\pi$
$678$	−69.9344	−2.68581
$679$	−25.9814	−0.997073
$680$	18.9927	0.728335
$681$	34.6563	1.32803
$682$	2.06940	0.0792414
$683$	2.45590	0.0939723	0.0469862	−	0.998896i	$-0.485038\pi$
$683$	2.45590	0.0939723	0.0469862	+	0.998896i	$0.485038\pi$
$684$	−21.4966	−0.821942
$685$	6.51039	0.248749
$686$	40.7188	1.55465
$687$	−14.4948	−0.553011
$688$	2.83672	0.108149
$689$	10.6369	0.405233
$690$	−7.01270	−0.266969
$691$	45.0642	1.71432	0.857161	−	0.515049i	$-0.172226\pi$
$691$	45.0642	1.71432	0.857161	+	0.515049i	$0.172226\pi$
$692$	−20.8255	−0.791667
$693$	4.85195	0.184310
$694$	82.8558	3.14516
$695$	−8.81323	−0.334305
$696$	26.4365	1.00207
$697$	−1.21052	−0.0458517
$698$	2.34025	0.0885798
$699$	53.7699	2.03377
$700$	−31.1169	−1.17611
$701$	−41.5147	−1.56799	−0.783995	−	0.620767i	$-0.786821\pi$
$701$	−41.5147	−1.56799	−0.783995	+	0.620767i	$0.786821\pi$
$702$	−18.6319	−0.703214
$703$	−21.7119	−0.818880
$704$	−10.5006	−0.395754
$705$	17.3008	0.651584
$706$	−18.2431	−0.686587
$707$	−23.3158	−0.876881
$708$	−44.0861	−1.65686
$709$	−13.7134	−0.515016	−0.257508	−	0.966276i	$-0.582901\pi$
$709$	−13.7134	−0.515016	−0.257508	+	0.966276i	$0.582901\pi$
$710$	−33.5205	−1.25800
$711$	−9.57365	−0.359040
$712$	−12.6001	−0.472209
$713$	1.03006	0.0385760
$714$	−60.1018	−2.24925
$715$	4.19838	0.157011
$716$	−92.4178	−3.45382
$717$	0.484688	0.0181010
$718$	−46.1414	−1.72198
$719$	8.22533	0.306753	0.153376	−	0.988168i	$-0.450985\pi$
$719$	8.22533	0.306753	0.153376	+	0.988168i	$0.450985\pi$
$720$	3.07709	0.114676
$721$	−6.77576	−0.252343
$722$	22.7600	0.847038
$723$	46.6226	1.73391
$724$	−7.99956	−0.297301
$725$	−10.9649	−0.407226
$726$	−53.8682	−1.99924
$727$	−5.02948	−0.186533	−0.0932666	−	0.995641i	$-0.529731\pi$
$727$	−5.02948	−0.186533	−0.0932666	+	0.995641i	$0.529731\pi$
$728$	−35.2175	−1.30525
$729$	−7.63488	−0.282774
$730$	33.9972	1.25829
$731$	−10.2856	−0.380428
$732$	39.5314	1.46112
$733$	−23.4918	−0.867688	−0.433844	−	0.900988i	$-0.642843\pi$
$733$	−23.4918	−0.867688	−0.433844	+	0.900988i	$0.642843\pi$
$734$	−71.7078	−2.64678
$735$	−2.24730	−0.0828929
$736$	−4.25725	−0.156924
$737$	−13.4937	−0.497045
$738$	−1.39830	−0.0514720
$739$	−29.2382	−1.07554	−0.537772	−	0.843091i	$-0.680734\pi$
$739$	−29.2382	−1.07554	−0.537772	+	0.843091i	$0.680734\pi$
$740$	33.1174	1.21742
$741$	25.0019	0.918469
$742$	−18.9319	−0.695011
$743$	−15.9287	−0.584367	−0.292183	−	0.956362i	$-0.594382\pi$
$743$	−15.9287	−0.584367	−0.292183	+	0.956362i	$0.594382\pi$
$744$	−7.98421	−0.292715
$745$	11.1011	0.406711
$746$	74.7843	2.73805
$747$	34.0181	1.24466
$748$	−12.2766	−0.448877
$749$	0.707674	0.0258578
$750$	−57.6088	−2.10357
$751$	−19.7505	−0.720706	−0.360353	−	0.932816i	$-0.617344\pi$
$751$	−19.7505	−0.720706	−0.360353	+	0.932816i	$0.617344\pi$
$752$	−6.54950	−0.238836
$753$	−46.3142	−1.68778
$754$	−29.2166	−1.06401
$755$	−11.6875	−0.425350
$756$	21.0517	0.765643
$757$	−18.0138	−0.654724	−0.327362	−	0.944899i	$-0.606160\pi$
$757$	−18.0138	−0.654724	−0.327362	+	0.944899i	$0.606160\pi$
$758$	−83.4057	−3.02943
$759$	1.92537	0.0698865
$760$	14.0621	0.510087
$761$	1.93426	0.0701170	0.0350585	−	0.999385i	$-0.488838\pi$
$761$	1.93426	0.0701170	0.0350585	+	0.999385i	$0.488838\pi$
$762$	−89.2983	−3.23494
$763$	1.43402	0.0519150
$764$	36.2079	1.30995
$765$	−11.1572	−0.403390
$766$	−38.6576	−1.39675
$767$	20.6949	0.747251
$768$	50.6905	1.82913
$769$	−42.8995	−1.54700	−0.773499	−	0.633798i	$-0.781495\pi$
$769$	−42.8995	−1.54700	−0.773499	+	0.633798i	$0.781495\pi$
$770$	−7.47242	−0.269287
$771$	−35.2457	−1.26934
$772$	80.9693	2.91415
$773$	42.1532	1.51615	0.758073	−	0.652169i	$-0.226141\pi$
$773$	42.1532	1.51615	0.758073	+	0.652169i	$0.226141\pi$
$774$	−11.8812	−0.427059
$775$	3.31156	0.118955
$776$	32.2543	1.15786
$777$	−44.5138	−1.59692
$778$	−41.2410	−1.47856
$779$	−0.896267	−0.0321121
$780$	−38.1357	−1.36548
$781$	9.20323	0.329317
$782$	−9.62595	−0.344223
$783$	7.41814	0.265103
$784$	0.850754	0.0303841
$785$	24.7067	0.881820
$786$	47.8820	1.70790
$787$	3.58557	0.127812	0.0639059	−	0.997956i	$-0.479644\pi$
$787$	3.58557	0.127812	0.0639059	+	0.997956i	$0.479644\pi$
$788$	24.0624	0.857186
$789$	24.0522	0.856280
$790$	14.7442	0.524577
$791$	−37.0923	−1.31885
$792$	−6.02341	−0.214032
$793$	−18.5569	−0.658975
$794$	67.7364	2.40387
$795$	−8.70772	−0.308831
$796$	1.29621	0.0459431
$797$	−33.8658	−1.19959	−0.599795	−	0.800154i	$-0.704751\pi$
$797$	−33.8658	−1.19959	−0.599795	+	0.800154i	$0.704751\pi$
$798$	−44.4993	−1.57526
$799$	23.7478	0.840137
$800$	−13.6867	−0.483899
$801$	7.40192	0.261534
$802$	46.4619	1.64063
$803$	−9.33410	−0.329393
$804$	122.569	4.32266
$805$	−3.71945	−0.131093
$806$	8.82383	0.310806
$807$	−16.3534	−0.575667
$808$	28.9452	1.01829
$809$	−24.4534	−0.859734	−0.429867	−	0.902892i	$-0.641440\pi$
$809$	−24.4534	−0.859734	−0.429867	+	0.902892i	$0.641440\pi$
$810$	34.2967	1.20506
$811$	−42.1659	−1.48065	−0.740323	−	0.672252i	$-0.765327\pi$
$811$	−42.1659	−1.48065	−0.740323	+	0.672252i	$0.765327\pi$
$812$	33.0111	1.15846
$813$	−22.7588	−0.798185
$814$	−14.3230	−0.502021
$815$	−8.71603	−0.305309
$816$	10.4650	0.366350
$817$	−7.61547	−0.266432
$818$	83.4222	2.91679
$819$	20.6885	0.722914
$820$	1.36708	0.0477407
$821$	25.0191	0.873172	0.436586	−	0.899662i	$-0.356187\pi$
$821$	25.0191	0.873172	0.436586	+	0.899662i	$0.356187\pi$
$822$	25.5761	0.892070
$823$	−6.91692	−0.241109	−0.120554	−	0.992707i	$-0.538467\pi$
$823$	−6.91692	−0.241109	−0.120554	+	0.992707i	$0.538467\pi$
$824$	8.41171	0.293036
$825$	6.18992	0.215505
$826$	−36.8335	−1.28160
$827$	−46.2230	−1.60733	−0.803666	−	0.595080i	$-0.797120\pi$
$827$	−46.2230	−1.60733	−0.803666	+	0.595080i	$0.797120\pi$
$828$	−7.05866	−0.245305
$829$	44.7716	1.55498	0.777492	−	0.628893i	$-0.216492\pi$
$829$	44.7716	1.55498	0.777492	+	0.628893i	$0.216492\pi$
$830$	−52.3908	−1.81851
$831$	36.2831	1.25865
$832$	−44.7739	−1.55225
$833$	−3.08475	−0.106880
$834$	−34.6228	−1.19889
$835$	−20.1351	−0.696805
$836$	−9.08957	−0.314369
$837$	−2.24039	−0.0774391
$838$	−49.0594	−1.69473
$839$	−57.3260	−1.97911	−0.989557	−	0.144143i	$-0.953958\pi$
$839$	−57.3260	−1.97911	−0.989557	+	0.144143i	$0.953958\pi$
$840$	28.8302	0.994738
$841$	−17.3676	−0.598884
$842$	−82.7564	−2.85197
$843$	−30.7667	−1.05966
$844$	73.0422	2.51421
$845$	0.532824	0.0183297
$846$	27.4316	0.943117
$847$	−28.5710	−0.981712
$848$	3.29646	0.113201
$849$	23.4777	0.805751
$850$	−30.9467	−1.06146
$851$	−7.12937	−0.244392
$852$	−83.5969	−2.86398
$853$	27.0170	0.925045	0.462523	−	0.886607i	$-0.346944\pi$
$853$	27.0170	0.925045	0.462523	+	0.886607i	$0.346944\pi$
$854$	33.0282	1.13020
$855$	−8.26079	−0.282513
$856$	−0.878535	−0.0300277
$857$	12.1981	0.416681	0.208340	−	0.978056i	$-0.433194\pi$
$857$	12.1981	0.416681	0.208340	+	0.978056i	$0.433194\pi$
$858$	16.4934	0.563075
$859$	−1.85742	−0.0633743	−0.0316872	−	0.999498i	$-0.510088\pi$
$859$	−1.85742	−0.0633743	−0.0316872	+	0.999498i	$0.510088\pi$
$860$	11.6160	0.396101
$861$	−1.83753	−0.0626228
$862$	−61.7850	−2.10441
$863$	−50.1604	−1.70748	−0.853740	−	0.520700i	$-0.825671\pi$
$863$	−50.1604	−1.70748	−0.853740	+	0.520700i	$0.825671\pi$
$864$	9.25957	0.315017
$865$	−8.00291	−0.272107
$866$	31.6871	1.07677
$867$	0.182723	0.00620559
$868$	−9.96983	−0.338398
$869$	−4.04811	−0.137323
$870$	23.9177	0.810886
$871$	−57.5363	−1.94954
$872$	−1.78025	−0.0602869
$873$	−18.9478	−0.641285
$874$	−7.12704	−0.241076
$875$	−30.5550	−1.03295
$876$	84.7857	2.86464
$877$	32.8065	1.10780	0.553898	−	0.832584i	$-0.313140\pi$
$877$	32.8065	1.10780	0.553898	+	0.832584i	$0.313140\pi$
$878$	−66.5465	−2.24584
$879$	−24.7335	−0.834242
$880$	1.30111	0.0438605
$881$	−24.0442	−0.810068	−0.405034	−	0.914302i	$-0.632740\pi$
$881$	−24.0442	−0.810068	−0.405034	+	0.914302i	$0.632740\pi$
$882$	−3.56325	−0.119981
$883$	−3.89573	−0.131102	−0.0655509	−	0.997849i	$-0.520880\pi$
$883$	−3.89573	−0.131102	−0.0655509	+	0.997849i	$0.520880\pi$
$884$	−52.3468	−1.76061
$885$	−16.9416	−0.569485
$886$	66.3225	2.22815
$887$	−9.36309	−0.314382	−0.157191	−	0.987568i	$-0.550244\pi$
$887$	−9.36309	−0.314382	−0.157191	+	0.987568i	$0.550244\pi$
$888$	55.2613	1.85445
$889$	−47.3627	−1.58849
$890$	−11.3996	−0.382115
$891$	−9.41633	−0.315459
$892$	−50.5435	−1.69232
$893$	17.5828	0.588387
$894$	43.6106	1.45856
$895$	−35.5147	−1.18713
$896$	55.9867	1.87038
$897$	8.20970	0.274114
$898$	66.6425	2.22389
$899$	−3.51314	−0.117170
$900$	−22.6930	−0.756435
$901$	−11.9526	−0.398199
$902$	−0.591253	−0.0196866
$903$	−15.6133	−0.519577
$904$	46.0479	1.53153
$905$	−3.07410	−0.102187
$906$	−45.9143	−1.52540
$907$	−12.0248	−0.399278	−0.199639	−	0.979870i	$-0.563977\pi$
$907$	−12.0248	−0.399278	−0.199639	+	0.979870i	$0.563977\pi$
$908$	−53.7234	−1.78287
$909$	−17.0038	−0.563982
$910$	−31.8620	−1.05622
$911$	−8.10637	−0.268576	−0.134288	−	0.990942i	$-0.542875\pi$
$911$	−8.10637	−0.268576	−0.134288	+	0.990942i	$0.542875\pi$
$912$	7.74830	0.256572
$913$	14.3841	0.476046
$914$	−14.7935	−0.489326
$915$	15.1913	0.502209
$916$	22.4695	0.742414
$917$	25.3960	0.838651
$918$	20.9365	0.691008
$919$	27.8089	0.917332	0.458666	−	0.888609i	$-0.348327\pi$
$919$	27.8089	0.917332	0.458666	+	0.888609i	$0.348327\pi$
$920$	4.61747	0.152234
$921$	−9.31121	−0.306815
$922$	28.5554	0.940422
$923$	39.2421	1.29167
$924$	−18.6355	−0.613062
$925$	−22.9204	−0.753617
$926$	18.6124	0.611642
$927$	−4.94145	−0.162299
$928$	14.5199	0.476639
$929$	50.2725	1.64939	0.824693	−	0.565581i	$-0.191348\pi$
$929$	50.2725	1.64939	0.824693	+	0.565581i	$0.191348\pi$
$930$	−7.22349	−0.236868
$931$	−2.28394	−0.0748531
$932$	−83.3531	−2.73032
$933$	75.3404	2.46653
$934$	−23.5873	−0.771799
$935$	−4.71770	−0.154285
$936$	−25.6835	−0.839493
$937$	25.9389	0.847388	0.423694	−	0.905805i	$-0.360733\pi$
$937$	25.9389	0.847388	0.423694	+	0.905805i	$0.360733\pi$
$938$	102.405	3.34364
$939$	35.4973	1.15841
$940$	−26.8193	−0.874749
$941$	4.75699	0.155074	0.0775368	−	0.996989i	$-0.475294\pi$
$941$	4.75699	0.155074	0.0775368	+	0.996989i	$0.475294\pi$
$942$	97.0605	3.16240
$943$	−0.294300	−0.00958373
$944$	6.41353	0.208743
$945$	8.08983	0.263162
$946$	−5.02381	−0.163338
$947$	55.7179	1.81059	0.905294	−	0.424786i	$-0.139651\pi$
$947$	55.7179	1.81059	0.905294	+	0.424786i	$0.139651\pi$
$948$	36.7707	1.19426
$949$	−39.8002	−1.29197
$950$	−22.9129	−0.743392
$951$	38.7477	1.25648
$952$	39.5737	1.28259
$953$	−28.8963	−0.936045	−0.468022	−	0.883717i	$-0.655033\pi$
$953$	−28.8963	−0.936045	−0.468022	+	0.883717i	$0.655033\pi$
$954$	−13.8067	−0.447009
$955$	13.9141	0.450250
$956$	−0.751354	−0.0243005
$957$	−6.56672	−0.212272
$958$	−34.0115	−1.09886
$959$	13.5653	0.438045
$960$	36.6534	1.18298
$961$	−29.9390	−0.965774
$962$	−61.0726	−1.96906
$963$	0.516095	0.0166309
$964$	−72.2734	−2.32777
$965$	31.1152	1.00163
$966$	−14.6119	−0.470130
$967$	16.0001	0.514528	0.257264	−	0.966341i	$-0.417179\pi$
$967$	16.0001	0.514528	0.257264	+	0.966341i	$0.417179\pi$
$968$	35.4692	1.14002
$969$	−28.0946	−0.902527
$970$	29.1812	0.936952
$971$	−18.5652	−0.595785	−0.297892	−	0.954599i	$-0.596284\pi$
$971$	−18.5652	−0.595785	−0.297892	+	0.954599i	$0.596284\pi$
$972$	62.8465	2.01580
$973$	−18.3635	−0.588708
$974$	6.67255	0.213802
$975$	26.3935	0.845269
$976$	−5.75093	−0.184083
$977$	−35.1415	−1.12428	−0.562138	−	0.827044i	$-0.690021\pi$
$977$	−35.1415	−1.12428	−0.562138	+	0.827044i	$0.690021\pi$
$978$	−34.2410	−1.09491
$979$	3.12981	0.100029
$980$	3.48372	0.111283
$981$	1.04581	0.0333900
$982$	−102.730	−3.27825
$983$	14.3051	0.456262	0.228131	−	0.973630i	$-0.426739\pi$
$983$	14.3051	0.456262	0.228131	+	0.973630i	$0.426739\pi$
$984$	2.28118	0.0727215
$985$	9.24678	0.294627
$986$	32.8305	1.04554
$987$	36.0484	1.14743
$988$	−38.7575	−1.23304
$989$	−2.50063	−0.0795155
$990$	−5.44951	−0.173197
$991$	28.7360	0.912828	0.456414	−	0.889767i	$-0.349134\pi$
$991$	28.7360	0.912828	0.456414	+	0.889767i	$0.349134\pi$
$992$	−4.38522	−0.139231
$993$	−70.9416	−2.25126
$994$	−69.8444	−2.21533
$995$	0.498115	0.0157913
$996$	−130.657	−4.14004
$997$	−10.2287	−0.323945	−0.161973	−	0.986795i	$-0.551786\pi$
$997$	−10.2287	−0.323945	−0.161973	+	0.986795i	$0.551786\pi$
$998$	−66.9921	−2.12060
$999$	15.5064	0.490602

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.d.1.14	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.d.1.14	✓	149	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.34025 q^{2} -2.24282 q^{3} +3.47677 q^{4} +1.33607 q^{5} +5.24876 q^{6} +2.78387 q^{7} -3.45602 q^{8} +2.03023 q^{9} +O(q^{10})\)	\(q-2.34025 q^{2} -2.24282 q^{3} +3.47677 q^{4} +1.33607 q^{5} +5.24876 q^{6} +2.78387 q^{7} -3.45602 q^{8} +2.03023 q^{9} -3.12673 q^{10} +0.858461 q^{11} -7.79777 q^{12} +3.66044 q^{13} -6.51496 q^{14} -2.99656 q^{15} +1.13440 q^{16} -4.11321 q^{17} -4.75126 q^{18} -3.04542 q^{19} +4.64520 q^{20} -6.24373 q^{21} -2.00901 q^{22} -1.00000 q^{23} +7.75122 q^{24} -3.21492 q^{25} -8.56634 q^{26} +2.17501 q^{27} +9.67890 q^{28} +3.41063 q^{29} +7.01270 q^{30} -1.03006 q^{31} +4.25725 q^{32} -1.92537 q^{33} +9.62595 q^{34} +3.71945 q^{35} +7.05866 q^{36} +7.12937 q^{37} +7.12704 q^{38} -8.20970 q^{39} -4.61747 q^{40} +0.294300 q^{41} +14.6119 q^{42} +2.50063 q^{43} +2.98467 q^{44} +2.71253 q^{45} +2.34025 q^{46} -5.77354 q^{47} -2.54425 q^{48} +0.749960 q^{49} +7.52372 q^{50} +9.22519 q^{51} +12.7265 q^{52} +2.90591 q^{53} -5.09007 q^{54} +1.14696 q^{55} -9.62112 q^{56} +6.83032 q^{57} -7.98172 q^{58} +5.65368 q^{59} -10.4184 q^{60} -5.06958 q^{61} +2.41059 q^{62} +5.65192 q^{63} -12.2318 q^{64} +4.89059 q^{65} +4.50585 q^{66} -15.7184 q^{67} -14.3007 q^{68} +2.24282 q^{69} -8.70444 q^{70} +10.7206 q^{71} -7.01652 q^{72} -10.8731 q^{73} -16.6845 q^{74} +7.21048 q^{75} -10.5882 q^{76} +2.38985 q^{77} +19.2127 q^{78} -4.71554 q^{79} +1.51563 q^{80} -10.9689 q^{81} -0.688736 q^{82} +16.7557 q^{83} -21.7080 q^{84} -5.49554 q^{85} -5.85211 q^{86} -7.64941 q^{87} -2.96685 q^{88} +3.64585 q^{89} -6.34800 q^{90} +10.1902 q^{91} -3.47677 q^{92} +2.31023 q^{93} +13.5115 q^{94} -4.06889 q^{95} -9.54825 q^{96} -9.33280 q^{97} -1.75509 q^{98} +1.74288 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9}+O(q^{10}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9} - 30 q^{10} - 20 q^{11} - 32 q^{12} - 73 q^{13} - 18 q^{14} - 43 q^{15} + 99 q^{16} - 32 q^{17} - 50 q^{18} - 32 q^{19} - 67 q^{20} - 36 q^{21} - 78 q^{22} - 149 q^{23} - 27 q^{24} + 75 q^{25} + 7 q^{26} - 23 q^{27} - 90 q^{28} - 20 q^{29} - 12 q^{30} - 34 q^{31} - 35 q^{32} - 63 q^{33} - 43 q^{34} + 24 q^{35} + 98 q^{36} - 228 q^{37} - 25 q^{38} - 19 q^{39} - 79 q^{40} - 4 q^{41} - 88 q^{42} - 70 q^{43} - 80 q^{44} - 153 q^{45} + 5 q^{46} - 3 q^{47} - 95 q^{48} + 86 q^{49} - 5 q^{50} - 57 q^{51} - 146 q^{52} - 110 q^{53} - 18 q^{54} - 33 q^{55} - 75 q^{56} - 132 q^{57} - 92 q^{58} + 41 q^{59} - 107 q^{60} - 82 q^{61} - 34 q^{62} - 99 q^{63} + 35 q^{64} - 47 q^{65} - 58 q^{66} - 162 q^{67} - 80 q^{68} + 5 q^{69} - 88 q^{70} - q^{71} - 117 q^{72} - 124 q^{73} - 51 q^{74} - q^{75} - 74 q^{76} - 56 q^{77} - 95 q^{78} - 89 q^{79} - 90 q^{80} + 93 q^{81} - 91 q^{82} - 64 q^{83} - 93 q^{84} - 155 q^{85} - 21 q^{86} - 49 q^{87} - 263 q^{88} - 60 q^{89} - 122 q^{90} - 130 q^{91} - 135 q^{92} - 179 q^{93} - 21 q^{94} + 30 q^{95} - 17 q^{96} - 199 q^{97} - 72 q^{98} - 91 q^{99}+O(q^{100}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9 - 30 * q^10 - 20 * q^11 - 32 * q^12 - 73 * q^13 - 18 * q^14 - 43 * q^15 + 99 * q^16 - 32 * q^17 - 50 * q^18 - 32 * q^19 - 67 * q^20 - 36 * q^21 - 78 * q^22 - 149 * q^23 - 27 * q^24 + 75 * q^25 + 7 * q^26 - 23 * q^27 - 90 * q^28 - 20 * q^29 - 12 * q^30 - 34 * q^31 - 35 * q^32 - 63 * q^33 - 43 * q^34 + 24 * q^35 + 98 * q^36 - 228 * q^37 - 25 * q^38 - 19 * q^39 - 79 * q^40 - 4 * q^41 - 88 * q^42 - 70 * q^43 - 80 * q^44 - 153 * q^45 + 5 * q^46 - 3 * q^47 - 95 * q^48 + 86 * q^49 - 5 * q^50 - 57 * q^51 - 146 * q^52 - 110 * q^53 - 18 * q^54 - 33 * q^55 - 75 * q^56 - 132 * q^57 - 92 * q^58 + 41 * q^59 - 107 * q^60 - 82 * q^61 - 34 * q^62 - 99 * q^63 + 35 * q^64 - 47 * q^65 - 58 * q^66 - 162 * q^67 - 80 * q^68 + 5 * q^69 - 88 * q^70 - q^71 - 117 * q^72 - 124 * q^73 - 51 * q^74 - q^75 - 74 * q^76 - 56 * q^77 - 95 * q^78 - 89 * q^79 - 90 * q^80 + 93 * q^81 - 91 * q^82 - 64 * q^83 - 93 * q^84 - 155 * q^85 - 21 * q^86 - 49 * q^87 - 263 * q^88 - 60 * q^89 - 122 * q^90 - 130 * q^91 - 135 * q^92 - 179 * q^93 - 21 * q^94 + 30 * q^95 - 17 * q^96 - 199 * q^97 - 72 * q^98 - 91 * q^99

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