LMFDB - Embedded newform 667.2.a.d.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,2,Mod(1,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, 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("667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	667.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:	$5.32602181482$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} - 22 x^{14} + 68 x^{13} + 187 x^{12} - 597 x^{11} - 795 x^{10} + 2592 x^{9} + \cdots + 64 $ x^16 - 3x^15 - 22x^14 + 68x^13 + 187x^12 - 597x^11 - 795x^10 + 2592x^9 + 1860x^8 - 5877x^7 - 2496x^6 + 6612x^5 + 1842x^4 - 3011x^3 - 505x^2 + 336*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$0.745705$ of defining polynomial
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.745705 q^{2} +2.46941 q^{3} -1.44392 q^{4} -2.81935 q^{5} +1.84145 q^{6} +3.27962 q^{7} -2.56815 q^{8} +3.09797 q^{9} +O(q^{10})$	\(q+0.745705 q^{2} +2.46941 q^{3} -1.44392 q^{4} -2.81935 q^{5} +1.84145 q^{6} +3.27962 q^{7} -2.56815 q^{8} +3.09797 q^{9} -2.10240 q^{10} +4.74029 q^{11} -3.56563 q^{12} +5.26065 q^{13} +2.44563 q^{14} -6.96212 q^{15} +0.972761 q^{16} +3.78228 q^{17} +2.31017 q^{18} -5.67624 q^{19} +4.07092 q^{20} +8.09872 q^{21} +3.53486 q^{22} +1.00000 q^{23} -6.34181 q^{24} +2.94872 q^{25} +3.92289 q^{26} +0.241917 q^{27} -4.73553 q^{28} -1.00000 q^{29} -5.19169 q^{30} +3.34398 q^{31} +5.86170 q^{32} +11.7057 q^{33} +2.82046 q^{34} -9.24640 q^{35} -4.47322 q^{36} -7.39041 q^{37} -4.23281 q^{38} +12.9907 q^{39} +7.24052 q^{40} +2.57493 q^{41} +6.03926 q^{42} -2.01679 q^{43} -6.84462 q^{44} -8.73424 q^{45} +0.745705 q^{46} +1.24351 q^{47} +2.40214 q^{48} +3.75593 q^{49} +2.19888 q^{50} +9.33997 q^{51} -7.59597 q^{52} +12.2633 q^{53} +0.180399 q^{54} -13.3645 q^{55} -8.42257 q^{56} -14.0170 q^{57} -0.745705 q^{58} -0.582654 q^{59} +10.0528 q^{60} -12.5729 q^{61} +2.49362 q^{62} +10.1602 q^{63} +2.42558 q^{64} -14.8316 q^{65} +8.72901 q^{66} -6.34363 q^{67} -5.46132 q^{68} +2.46941 q^{69} -6.89509 q^{70} -1.00328 q^{71} -7.95605 q^{72} -15.9306 q^{73} -5.51107 q^{74} +7.28160 q^{75} +8.19606 q^{76} +15.5464 q^{77} +9.68722 q^{78} -14.7676 q^{79} -2.74255 q^{80} -8.69651 q^{81} +1.92014 q^{82} +13.9060 q^{83} -11.6939 q^{84} -10.6636 q^{85} -1.50393 q^{86} -2.46941 q^{87} -12.1738 q^{88} -11.3752 q^{89} -6.51317 q^{90} +17.2529 q^{91} -1.44392 q^{92} +8.25764 q^{93} +0.927294 q^{94} +16.0033 q^{95} +14.4749 q^{96} -12.8661 q^{97} +2.80082 q^{98} +14.6853 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9}+O(q^{10}) $ 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9} - 14 q^{10} + 4 q^{11} + 3 q^{12} + 15 q^{13} + 8 q^{14} + 8 q^{15} + 23 q^{16} + 20 q^{17} + 2 q^{18} - 4 q^{19} + 25 q^{20} + 5 q^{21} + 13 q^{22} + 16 q^{23} - 24 q^{24} + 30 q^{25} + 25 q^{26} + 8 q^{27} - 13 q^{28} - 16 q^{29} - 45 q^{30} - 19 q^{32} + q^{33} - 23 q^{34} + 5 q^{35} + 37 q^{36} + 5 q^{37} + 38 q^{38} - 10 q^{39} - 20 q^{40} + 7 q^{41} + 14 q^{42} - 17 q^{43} - 21 q^{44} + 48 q^{45} + 3 q^{46} + 29 q^{47} + 35 q^{48} + 31 q^{49} - 44 q^{50} - 14 q^{51} + 20 q^{52} + 63 q^{53} - 13 q^{54} + q^{55} - 19 q^{56} - 22 q^{57} - 3 q^{58} + 11 q^{59} - 3 q^{60} + 33 q^{62} - 33 q^{63} + 29 q^{64} + 53 q^{65} - 43 q^{66} - 13 q^{67} + 63 q^{68} + 5 q^{69} - 46 q^{70} - 23 q^{71} + 46 q^{72} - 38 q^{73} - 47 q^{74} + 37 q^{75} - 56 q^{76} + 97 q^{77} - 24 q^{78} - 27 q^{79} + 8 q^{80} + 40 q^{81} + 9 q^{82} + 36 q^{83} + 22 q^{84} + 6 q^{85} - 11 q^{86} - 5 q^{87} - 24 q^{88} - 16 q^{89} - 95 q^{90} - 47 q^{91} + 21 q^{92} + 62 q^{93} + 37 q^{94} - 12 q^{95} - 74 q^{96} - 30 q^{97} - 27 q^{98} - 42 q^{99}+O(q^{100}) \) 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9 - 14 * q^10 + 4 * q^11 + 3 * q^12 + 15 * q^13 + 8 * q^14 + 8 * q^15 + 23 * q^16 + 20 * q^17 + 2 * q^18 - 4 * q^19 + 25 * q^20 + 5 * q^21 + 13 * q^22 + 16 * q^23 - 24 * q^24 + 30 * q^25 + 25 * q^26 + 8 * q^27 - 13 * q^28 - 16 * q^29 - 45 * q^30 - 19 * q^32 + q^33 - 23 * q^34 + 5 * q^35 + 37 * q^36 + 5 * q^37 + 38 * q^38 - 10 * q^39 - 20 * q^40 + 7 * q^41 + 14 * q^42 - 17 * q^43 - 21 * q^44 + 48 * q^45 + 3 * q^46 + 29 * q^47 + 35 * q^48 + 31 * q^49 - 44 * q^50 - 14 * q^51 + 20 * q^52 + 63 * q^53 - 13 * q^54 + q^55 - 19 * q^56 - 22 * q^57 - 3 * q^58 + 11 * q^59 - 3 * q^60 + 33 * q^62 - 33 * q^63 + 29 * q^64 + 53 * q^65 - 43 * q^66 - 13 * q^67 + 63 * q^68 + 5 * q^69 - 46 * q^70 - 23 * q^71 + 46 * q^72 - 38 * q^73 - 47 * q^74 + 37 * q^75 - 56 * q^76 + 97 * q^77 - 24 * q^78 - 27 * q^79 + 8 * q^80 + 40 * q^81 + 9 * q^82 + 36 * q^83 + 22 * q^84 + 6 * q^85 - 11 * q^86 - 5 * q^87 - 24 * q^88 - 16 * q^89 - 95 * q^90 - 47 * q^91 + 21 * q^92 + 62 * q^93 + 37 * q^94 - 12 * q^95 - 74 * q^96 - 30 * q^97 - 27 * q^98 - 42 * 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 $

$2$	0.745705	0.527293	0.263647	−	0.964619i	$-0.415075\pi$
$2$	0.745705	0.527293	0.263647	+	0.964619i	$0.415075\pi$
$3$	2.46941	1.42571	0.712856	−	0.701310i	$-0.247401\pi$
$3$	2.46941	1.42571	0.712856	+	0.701310i	$0.247401\pi$
$4$	−1.44392	−0.721962
$5$	−2.81935	−1.26085	−0.630425	−	0.776250i	$-0.717120\pi$
$5$	−2.81935	−1.26085	−0.630425	+	0.776250i	$0.717120\pi$
$6$	1.84145	0.751769
$7$	3.27962	1.23958	0.619791	−	0.784767i	$-0.287217\pi$
$7$	3.27962	1.23958	0.619791	+	0.784767i	$0.287217\pi$
$8$	−2.56815	−0.907979
$9$	3.09797	1.03266
$10$	−2.10240	−0.664838
$11$	4.74029	1.42925	0.714626	−	0.699507i	$-0.246597\pi$
$11$	4.74029	1.42925	0.714626	+	0.699507i	$0.246597\pi$
$12$	−3.56563	−1.02931
$13$	5.26065	1.45904	0.729521	−	0.683959i	$-0.239743\pi$
$13$	5.26065	1.45904	0.729521	+	0.683959i	$0.239743\pi$
$14$	2.44563	0.653623
$15$	−6.96212	−1.79761
$16$	0.972761	0.243190
$17$	3.78228	0.917337	0.458668	−	0.888608i	$-0.348327\pi$
$17$	3.78228	0.917337	0.458668	+	0.888608i	$0.348327\pi$
$18$	2.31017	0.544512
$19$	−5.67624	−1.30222	−0.651110	−	0.758983i	$-0.725696\pi$
$19$	−5.67624	−1.30222	−0.651110	+	0.758983i	$0.725696\pi$
$20$	4.07092	0.910286
$21$	8.09872	1.76729
$22$	3.53486	0.753635
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−6.34181	−1.29452
$25$	2.94872	0.589745
$26$	3.92289	0.769343
$27$	0.241917	0.0465569
$28$	−4.73553	−0.894930
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−5.19169	−0.947868
$31$	3.34398	0.600597	0.300298	−	0.953845i	$-0.402914\pi$
$31$	3.34398	0.600597	0.300298	+	0.953845i	$0.402914\pi$
$32$	5.86170	1.03621
$33$	11.7057	2.03770
$34$	2.82046	0.483705
$35$	−9.24640	−1.56293
$36$	−4.47322	−0.745537
$37$	−7.39041	−1.21498	−0.607488	−	0.794329i	$-0.707823\pi$
$37$	−7.39041	−1.21498	−0.607488	+	0.794329i	$0.707823\pi$
$38$	−4.23281	−0.686652
$39$	12.9907	2.08017
$40$	7.24052	1.14483
$41$	2.57493	0.402137	0.201068	−	0.979577i	$-0.435559\pi$
$41$	2.57493	0.402137	0.201068	+	0.979577i	$0.435559\pi$
$42$	6.03926	0.931878
$43$	−2.01679	−0.307557	−0.153778	−	0.988105i	$-0.549144\pi$
$43$	−2.01679	−0.307557	−0.153778	+	0.988105i	$0.549144\pi$
$44$	−6.84462	−1.03187
$45$	−8.73424	−1.30202
$46$	0.745705	0.109948
$47$	1.24351	0.181385	0.0906925	−	0.995879i	$-0.471092\pi$
$47$	1.24351	0.181385	0.0906925	+	0.995879i	$0.471092\pi$
$48$	2.40214	0.346719
$49$	3.75593	0.536562
$50$	2.19888	0.310969
$51$	9.33997	1.30786
$52$	−7.59597	−1.05337
$53$	12.2633	1.68449	0.842247	−	0.539092i	$-0.181233\pi$
$53$	12.2633	1.68449	0.842247	+	0.539092i	$0.181233\pi$
$54$	0.180399	0.0245491
$55$	−13.3645	−1.80207
$56$	−8.42257	−1.12551
$57$	−14.0170	−1.85659
$58$	−0.745705	−0.0979159
$59$	−0.582654	−0.0758551	−0.0379276	−	0.999280i	$-0.512076\pi$
$59$	−0.582654	−0.0758551	−0.0379276	+	0.999280i	$0.512076\pi$
$60$	10.0528	1.29781
$61$	−12.5729	−1.60980	−0.804900	−	0.593410i	$-0.797781\pi$
$61$	−12.5729	−1.60980	−0.804900	+	0.593410i	$0.797781\pi$
$62$	2.49362	0.316691
$63$	10.1602	1.28006
$64$	2.42558	0.303197
$65$	−14.8316	−1.83963
$66$	8.72901	1.07447
$67$	−6.34363	−0.774998	−0.387499	−	0.921870i	$-0.626661\pi$
$67$	−6.34363	−0.774998	−0.387499	+	0.921870i	$0.626661\pi$
$68$	−5.46132	−0.662282
$69$	2.46941	0.297282
$70$	−6.89509	−0.824121
$71$	−1.00328	−0.119067	−0.0595335	−	0.998226i	$-0.518961\pi$
$71$	−1.00328	−0.119067	−0.0595335	+	0.998226i	$0.518961\pi$
$72$	−7.95605	−0.937629
$73$	−15.9306	−1.86454	−0.932270	−	0.361764i	$-0.882175\pi$
$73$	−15.9306	−1.86454	−0.932270	+	0.361764i	$0.882175\pi$
$74$	−5.51107	−0.640649
$75$	7.28160	0.840807
$76$	8.19606	0.940153
$77$	15.5464	1.77167
$78$	9.68722	1.09686
$79$	−14.7676	−1.66149	−0.830743	−	0.556656i	$-0.812084\pi$
$79$	−14.7676	−1.66149	−0.830743	+	0.556656i	$0.812084\pi$
$80$	−2.74255	−0.306627
$81$	−8.69651	−0.966278
$82$	1.92014	0.212044
$83$	13.9060	1.52638	0.763189	−	0.646176i	$-0.223633\pi$
$83$	13.9060	1.52638	0.763189	+	0.646176i	$0.223633\pi$
$84$	−11.6939	−1.27591
$85$	−10.6636	−1.15662
$86$	−1.50393	−0.162173
$87$	−2.46941	−0.264748
$88$	−12.1738	−1.29773
$89$	−11.3752	−1.20577	−0.602883	−	0.797830i	$-0.705981\pi$
$89$	−11.3752	−1.20577	−0.602883	+	0.797830i	$0.705981\pi$
$90$	−6.51317	−0.686549
$91$	17.2529	1.80860
$92$	−1.44392	−0.150539
$93$	8.25764	0.856278
$94$	0.927294	0.0956431
$95$	16.0033	1.64190
$96$	14.4749	1.47734
$97$	−12.8661	−1.30635	−0.653176	−	0.757206i	$-0.726564\pi$
$97$	−12.8661	−1.30635	−0.653176	+	0.757206i	$0.726564\pi$
$98$	2.80082	0.282926
$99$	14.6853	1.47592
$100$	−4.25773	−0.425773
$101$	12.1573	1.20969	0.604847	−	0.796342i	$-0.293234\pi$
$101$	12.1573	1.20969	0.604847	+	0.796342i	$0.293234\pi$
$102$	6.96487	0.689625
$103$	4.81864	0.474795	0.237397	−	0.971413i	$-0.423706\pi$
$103$	4.81864	0.474795	0.237397	+	0.971413i	$0.423706\pi$
$104$	−13.5101	−1.32478
$105$	−22.8331	−2.22828
$106$	9.14481	0.888222
$107$	−5.97132	−0.577269	−0.288635	−	0.957439i	$-0.593201\pi$
$107$	−5.97132	−0.577269	−0.288635	+	0.957439i	$0.593201\pi$
$108$	−0.349309	−0.0336123
$109$	7.82520	0.749518	0.374759	−	0.927122i	$-0.377725\pi$
$109$	7.82520	0.749518	0.374759	+	0.927122i	$0.377725\pi$
$110$	−9.96601	−0.950222
$111$	−18.2499	−1.73221
$112$	3.19029	0.301454
$113$	−14.3887	−1.35358	−0.676789	−	0.736177i	$-0.736629\pi$
$113$	−14.3887	−1.35358	−0.676789	+	0.736177i	$0.736629\pi$
$114$	−10.4525	−0.978968
$115$	−2.81935	−0.262906
$116$	1.44392	0.134065
$117$	16.2973	1.50669
$118$	−0.434488	−0.0399979
$119$	12.4044	1.13711
$120$	17.8798	1.63219
$121$	11.4704	1.04276
$122$	−9.37571	−0.848837
$123$	6.35855	0.573331
$124$	−4.82845	−0.433608
$125$	5.78326	0.517270
$126$	7.57649	0.674967
$127$	19.2021	1.70391	0.851954	−	0.523617i	$-0.175418\pi$
$127$	19.2021	1.70391	0.851954	+	0.523617i	$0.175418\pi$
$128$	−9.91463	−0.876338
$129$	−4.98026	−0.438488
$130$	−11.0600	−0.970027
$131$	−6.22530	−0.543907	−0.271954	−	0.962310i	$-0.587670\pi$
$131$	−6.22530	−0.543907	−0.271954	+	0.962310i	$0.587670\pi$
$132$	−16.9021	−1.47114
$133$	−18.6159	−1.61421
$134$	−4.73048	−0.408651
$135$	−0.682048	−0.0587013
$136$	−9.71346	−0.832922
$137$	−6.97582	−0.595984	−0.297992	−	0.954568i	$-0.596317\pi$
$137$	−6.97582	−0.595984	−0.297992	+	0.954568i	$0.596317\pi$
$138$	1.84145	0.156755
$139$	14.6331	1.24116	0.620580	−	0.784143i	$-0.286897\pi$
$139$	14.6331	1.24116	0.620580	+	0.784143i	$0.286897\pi$
$140$	13.3511	1.12837
$141$	3.07074	0.258603
$142$	−0.748148	−0.0627832
$143$	24.9370	2.08534
$144$	3.01358	0.251132
$145$	2.81935	0.234134
$146$	−11.8796	−0.983159
$147$	9.27493	0.764983
$148$	10.6712	0.877166
$149$	3.56243	0.291845	0.145923	−	0.989296i	$-0.453385\pi$
$149$	3.56243	0.291845	0.145923	+	0.989296i	$0.453385\pi$
$150$	5.42993	0.443352
$151$	9.71624	0.790696	0.395348	−	0.918531i	$-0.370624\pi$
$151$	9.71624	0.790696	0.395348	+	0.918531i	$0.370624\pi$
$152$	14.5775	1.18239
$153$	11.7174	0.947292
$154$	11.5930	0.934192
$155$	−9.42785	−0.757263
$156$	−18.7575	−1.50181
$157$	17.6117	1.40557	0.702785	−	0.711403i	$-0.251940\pi$
$157$	17.6117	1.40557	0.702785	+	0.711403i	$0.251940\pi$
$158$	−11.0123	−0.876090
$159$	30.2831	2.40160
$160$	−16.5262	−1.30651
$161$	3.27962	0.258471
$162$	−6.48503	−0.509512
$163$	0.409752	0.0320942	0.0160471	−	0.999871i	$-0.494892\pi$
$163$	0.409752	0.0320942	0.0160471	+	0.999871i	$0.494892\pi$
$164$	−3.71800	−0.290327
$165$	−33.0025	−2.56924
$166$	10.3697	0.804849
$167$	−8.82190	−0.682659	−0.341329	−	0.939944i	$-0.610877\pi$
$167$	−8.82190	−0.682659	−0.341329	+	0.939944i	$0.610877\pi$
$168$	−20.7988	−1.60466
$169$	14.6744	1.12880
$170$	−7.95187	−0.609880
$171$	−17.5848	−1.34474
$172$	2.91208	0.222044
$173$	6.02690	0.458216	0.229108	−	0.973401i	$-0.426419\pi$
$173$	6.02690	0.458216	0.229108	+	0.973401i	$0.426419\pi$
$174$	−1.84145	−0.139600
$175$	9.67071	0.731037
$176$	4.61118	0.347580
$177$	−1.43881	−0.108148
$178$	−8.48253	−0.635792
$179$	15.3815	1.14967	0.574834	−	0.818270i	$-0.305067\pi$
$179$	15.3815	1.14967	0.574834	+	0.818270i	$0.305067\pi$
$180$	12.6116	0.940012
$181$	−16.2761	−1.20979	−0.604897	−	0.796304i	$-0.706786\pi$
$181$	−16.2761	−1.20979	−0.604897	+	0.796304i	$0.706786\pi$
$182$	12.8656	0.953663
$183$	−31.0477	−2.29511
$184$	−2.56815	−0.189327
$185$	20.8361	1.53190
$186$	6.15777	0.451510
$187$	17.9291	1.31111
$188$	−1.79554	−0.130953
$189$	0.793396	0.0577111
$190$	11.9338	0.865766
$191$	−19.7942	−1.43226	−0.716129	−	0.697968i	$-0.754088\pi$
$191$	−19.7942	−1.43226	−0.716129	+	0.697968i	$0.754088\pi$
$192$	5.98974	0.432272
$193$	−13.3338	−0.959787	−0.479893	−	0.877327i	$-0.659325\pi$
$193$	−13.3338	−0.959787	−0.479893	+	0.877327i	$0.659325\pi$
$194$	−9.59430	−0.688831
$195$	−36.6252	−2.62279
$196$	−5.42328	−0.387377
$197$	−15.0077	−1.06926	−0.534628	−	0.845088i	$-0.679548\pi$
$197$	−15.0077	−1.06926	−0.534628	+	0.845088i	$0.679548\pi$
$198$	10.9509	0.778245
$199$	−14.7649	−1.04666	−0.523329	−	0.852130i	$-0.675310\pi$
$199$	−14.7649	−1.04666	−0.523329	+	0.852130i	$0.675310\pi$
$200$	−7.57277	−0.535476
$201$	−15.6650	−1.10492
$202$	9.06575	0.637864
$203$	−3.27962	−0.230184
$204$	−13.4862	−0.944223
$205$	−7.25963	−0.507034
$206$	3.59329	0.250356
$207$	3.09797	0.215323
$208$	5.11736	0.354825
$209$	−26.9071	−1.86120
$210$	−17.0268	−1.17496
$211$	1.23566	0.0850661	0.0425331	−	0.999095i	$-0.486457\pi$
$211$	1.23566	0.0850661	0.0425331	+	0.999095i	$0.486457\pi$
$212$	−17.7073	−1.21614
$213$	−2.47750	−0.169755
$214$	−4.45285	−0.304390
$215$	5.68602	0.387783
$216$	−0.621279	−0.0422727
$217$	10.9670	0.744488
$218$	5.83529	0.395216
$219$	−39.3392	−2.65830
$220$	19.2974	1.30103
$221$	19.8972	1.33843
$222$	−13.6091	−0.913381
$223$	8.41801	0.563712	0.281856	−	0.959457i	$-0.409050\pi$
$223$	8.41801	0.563712	0.281856	+	0.959457i	$0.409050\pi$
$224$	19.2242	1.28447
$225$	9.13505	0.609003
$226$	−10.7298	−0.713733
$227$	−4.12583	−0.273841	−0.136920	−	0.990582i	$-0.543720\pi$
$227$	−4.12583	−0.273841	−0.136920	+	0.990582i	$0.543720\pi$
$228$	20.2394	1.34039
$229$	−24.7522	−1.63567	−0.817836	−	0.575452i	$-0.804826\pi$
$229$	−24.7522	−1.63567	−0.817836	+	0.575452i	$0.804826\pi$
$230$	−2.10240	−0.138628
$231$	38.3903	2.52590
$232$	2.56815	0.168607
$233$	1.60657	0.105250	0.0526249	−	0.998614i	$-0.483241\pi$
$233$	1.60657	0.105250	0.0526249	+	0.998614i	$0.483241\pi$
$234$	12.1530	0.794466
$235$	−3.50589	−0.228699
$236$	0.841308	0.0547645
$237$	−36.4672	−2.36880
$238$	9.25006	0.599592
$239$	8.40977	0.543983	0.271991	−	0.962300i	$-0.412318\pi$
$239$	8.40977	0.543983	0.271991	+	0.962300i	$0.412318\pi$
$240$	−6.77248	−0.437162
$241$	9.41350	0.606377	0.303188	−	0.952931i	$-0.401949\pi$
$241$	9.41350	0.606377	0.303188	+	0.952931i	$0.401949\pi$
$242$	8.55353	0.549842
$243$	−22.2010	−1.42419
$244$	18.1544	1.16221
$245$	−10.5893	−0.676525
$246$	4.74161	0.302314
$247$	−29.8607	−1.89999
$248$	−8.58785	−0.545329
$249$	34.3395	2.17617
$250$	4.31261	0.272753
$251$	4.29577	0.271147	0.135573	−	0.990767i	$-0.456712\pi$
$251$	4.29577	0.271147	0.135573	+	0.990767i	$0.456712\pi$
$252$	−14.6705	−0.924154
$253$	4.74029	0.298020
$254$	14.3191	0.898459
$255$	−26.3326	−1.64901
$256$	−12.2445	−0.765284
$257$	2.32487	0.145021	0.0725106	−	0.997368i	$-0.476899\pi$
$257$	2.32487	0.145021	0.0725106	+	0.997368i	$0.476899\pi$
$258$	−3.71381	−0.231212
$259$	−24.2378	−1.50606
$260$	21.4157	1.32814
$261$	−3.09797	−0.191759
$262$	−4.64224	−0.286799
$263$	−23.0125	−1.41901	−0.709507	−	0.704698i	$-0.751082\pi$
$263$	−23.0125	−1.41901	−0.709507	+	0.704698i	$0.751082\pi$
$264$	−30.0620	−1.85019
$265$	−34.5745	−2.12389
$266$	−13.8820	−0.851161
$267$	−28.0899	−1.71907
$268$	9.15972	0.559519
$269$	21.0938	1.28611	0.643055	−	0.765820i	$-0.277666\pi$
$269$	21.0938	1.28611	0.643055	+	0.765820i	$0.277666\pi$
$270$	−0.508607	−0.0309528
$271$	30.5448	1.85547	0.927733	−	0.373245i	$-0.121755\pi$
$271$	30.5448	1.85547	0.927733	+	0.373245i	$0.121755\pi$
$272$	3.67925	0.223087
$273$	42.6045	2.57854
$274$	−5.20190	−0.314259
$275$	13.9778	0.842894
$276$	−3.56563	−0.214626
$277$	12.8468	0.771889	0.385944	−	0.922522i	$-0.373876\pi$
$277$	12.8468	0.771889	0.385944	+	0.922522i	$0.373876\pi$
$278$	10.9120	0.654456
$279$	10.3595	0.620209
$280$	23.7462	1.41911
$281$	27.5782	1.64518	0.822590	−	0.568635i	$-0.192528\pi$
$281$	27.5782	1.64518	0.822590	+	0.568635i	$0.192528\pi$
$282$	2.28987	0.136359
$283$	−8.83683	−0.525295	−0.262647	−	0.964892i	$-0.584596\pi$
$283$	−8.83683	−0.525295	−0.262647	+	0.964892i	$0.584596\pi$
$284$	1.44865	0.0859618
$285$	39.5187	2.34088
$286$	18.5957	1.09959
$287$	8.44481	0.498481
$288$	18.1593	1.07005
$289$	−2.69439	−0.158494
$290$	2.10240	0.123457
$291$	−31.7716	−1.86248
$292$	23.0026	1.34613
$293$	9.10701	0.532037	0.266019	−	0.963968i	$-0.414292\pi$
$293$	9.10701	0.532037	0.266019	+	0.963968i	$0.414292\pi$
$294$	6.91636	0.403371
$295$	1.64271	0.0956420
$296$	18.9797	1.10317
$297$	1.14676	0.0665416
$298$	2.65652	0.153888
$299$	5.26065	0.304231
$300$	−10.5141	−0.607030
$301$	−6.61430	−0.381242
$302$	7.24545	0.416929
$303$	30.0213	1.72468
$304$	−5.52163	−0.316687
$305$	35.4475	2.02972
$306$	8.73770	0.499501
$307$	−7.67967	−0.438302	−0.219151	−	0.975691i	$-0.570329\pi$
$307$	−7.67967	−0.438302	−0.219151	+	0.975691i	$0.570329\pi$
$308$	−22.4478	−1.27908
$309$	11.8992	0.676921
$310$	−7.03040	−0.399300
$311$	−0.298680	−0.0169366	−0.00846828	−	0.999964i	$-0.502696\pi$
$311$	−0.298680	−0.0169366	−0.00846828	+	0.999964i	$0.502696\pi$
$312$	−33.3620	−1.88875
$313$	−6.69575	−0.378466	−0.189233	−	0.981932i	$-0.560600\pi$
$313$	−6.69575	−0.378466	−0.189233	+	0.981932i	$0.560600\pi$
$314$	13.1332	0.741147
$315$	−28.6450	−1.61397
$316$	21.3233	1.19953
$317$	−10.8920	−0.611757	−0.305879	−	0.952070i	$-0.598950\pi$
$317$	−10.8920	−0.611757	−0.305879	+	0.952070i	$0.598950\pi$
$318$	22.5822	1.26635
$319$	−4.74029	−0.265406
$320$	−6.83855	−0.382286
$321$	−14.7456	−0.823020
$322$	2.44563	0.136290
$323$	−21.4691	−1.19457
$324$	12.5571	0.697616
$325$	15.5122	0.860462
$326$	0.305554	0.0169231
$327$	19.3236	1.06860
$328$	−6.61282	−0.365132
$329$	4.07825	0.224841
$330$	−24.6101	−1.35474
$331$	34.7209	1.90843	0.954215	−	0.299121i	$-0.0966933\pi$
$331$	34.7209	1.90843	0.954215	+	0.299121i	$0.0966933\pi$
$332$	−20.0791	−1.10199
$333$	−22.8952	−1.25465
$334$	−6.57854	−0.359961
$335$	17.8849	0.977157
$336$	7.87813	0.429787
$337$	26.1652	1.42531	0.712655	−	0.701515i	$-0.247493\pi$
$337$	26.1652	1.42531	0.712655	+	0.701515i	$0.247493\pi$
$338$	10.9428	0.595209
$339$	−35.5316	−1.92981
$340$	15.3974	0.835039
$341$	15.8514	0.858404
$342$	−13.1131	−0.709075
$343$	−10.6393	−0.574469
$344$	5.17941	0.279255
$345$	−6.96212	−0.374828
$346$	4.49429	0.241615
$347$	−28.4182	−1.52557	−0.762785	−	0.646652i	$-0.776168\pi$
$347$	−28.4182	−1.52557	−0.762785	+	0.646652i	$0.776168\pi$
$348$	3.56563	0.191138
$349$	14.0179	0.750359	0.375180	−	0.926952i	$-0.377581\pi$
$349$	14.0179	0.750359	0.375180	+	0.926952i	$0.377581\pi$
$350$	7.21150	0.385471
$351$	1.27264	0.0679284
$352$	27.7862	1.48101
$353$	−22.0953	−1.17601	−0.588007	−	0.808856i	$-0.700087\pi$
$353$	−22.0953	−1.17601	−0.588007	+	0.808856i	$0.700087\pi$
$354$	−1.07293	−0.0570255
$355$	2.82858	0.150126
$356$	16.4249	0.870517
$357$	30.6316	1.62120
$358$	11.4701	0.606212
$359$	15.7837	0.833030	0.416515	−	0.909129i	$-0.363251\pi$
$359$	15.7837	0.833030	0.416515	+	0.909129i	$0.363251\pi$
$360$	22.4309	1.18221
$361$	13.2197	0.695776
$362$	−12.1372	−0.637917
$363$	28.3250	1.48668
$364$	−24.9119	−1.30574
$365$	44.9140	2.35091
$366$	−23.1524	−1.21020
$367$	3.85433	0.201194	0.100597	−	0.994927i	$-0.467925\pi$
$367$	3.85433	0.201194	0.100597	+	0.994927i	$0.467925\pi$
$368$	0.972761	0.0507087
$369$	7.97705	0.415269
$370$	15.5376	0.807763
$371$	40.2190	2.08807
$372$	−11.9234	−0.618200
$373$	−21.1675	−1.09601	−0.548007	−	0.836474i	$-0.684613\pi$
$373$	−21.1675	−1.09601	−0.548007	+	0.836474i	$0.684613\pi$
$374$	13.3698	0.691337
$375$	14.2812	0.737479
$376$	−3.19353	−0.164694
$377$	−5.26065	−0.270937
$378$	0.591640	0.0304307
$379$	−17.0072	−0.873602	−0.436801	−	0.899558i	$-0.643889\pi$
$379$	−17.0072	−0.873602	−0.436801	+	0.899558i	$0.643889\pi$
$380$	−23.1076	−1.18539
$381$	47.4177	2.42928
$382$	−14.7606	−0.755220
$383$	5.72087	0.292323	0.146161	−	0.989261i	$-0.453308\pi$
$383$	5.72087	0.292323	0.146161	+	0.989261i	$0.453308\pi$
$384$	−24.4832	−1.24941
$385$	−43.8307	−2.23382
$386$	−9.94308	−0.506089
$387$	−6.24793	−0.317600
$388$	18.5776	0.943136
$389$	13.7727	0.698304	0.349152	−	0.937066i	$-0.386470\pi$
$389$	13.7727	0.698304	0.349152	+	0.937066i	$0.386470\pi$
$390$	−27.3116	−1.38298
$391$	3.78228	0.191278
$392$	−9.64581	−0.487187
$393$	−15.3728	−0.775455
$394$	−11.1913	−0.563811
$395$	41.6350	2.09489
$396$	−21.2044	−1.06556
$397$	−19.0097	−0.954071	−0.477035	−	0.878884i	$-0.658289\pi$
$397$	−19.0097	−0.954071	−0.477035	+	0.878884i	$0.658289\pi$
$398$	−11.0103	−0.551896
$399$	−45.9703	−2.30140
$400$	2.86841	0.143420
$401$	19.5467	0.976116	0.488058	−	0.872811i	$-0.337706\pi$
$401$	19.5467	0.976116	0.488058	+	0.872811i	$0.337706\pi$
$402$	−11.6815	−0.582619
$403$	17.5915	0.876295
$404$	−17.5542	−0.873353
$405$	24.5185	1.21833
$406$	−2.44563	−0.121375
$407$	−35.0327	−1.73651
$408$	−23.9865	−1.18751
$409$	5.43515	0.268751	0.134375	−	0.990931i	$-0.457097\pi$
$409$	5.43515	0.268751	0.134375	+	0.990931i	$0.457097\pi$
$410$	−5.41354	−0.267356
$411$	−17.2261	−0.849702
$412$	−6.95775	−0.342784
$413$	−1.91089	−0.0940286
$414$	2.31017	0.113539
$415$	−39.2057	−1.92453
$416$	30.8363	1.51188
$417$	36.1350	1.76954
$418$	−20.0647	−0.981399
$419$	0.635042	0.0310238	0.0155119	−	0.999880i	$-0.495062\pi$
$419$	0.635042	0.0310238	0.0155119	+	0.999880i	$0.495062\pi$
$420$	32.9693	1.60874
$421$	−38.7954	−1.89077	−0.945385	−	0.325956i	$-0.894314\pi$
$421$	−38.7954	−1.89077	−0.945385	+	0.325956i	$0.894314\pi$
$422$	0.921436	0.0448548
$423$	3.85236	0.187308
$424$	−31.4940	−1.52948
$425$	11.1529	0.540995
$426$	−1.84748	−0.0895108
$427$	−41.2345	−1.99548
$428$	8.62213	0.416766
$429$	61.5796	2.97309
$430$	4.24010	0.204476
$431$	−19.2802	−0.928695	−0.464348	−	0.885653i	$-0.653711\pi$
$431$	−19.2802	−0.928695	−0.464348	+	0.885653i	$0.653711\pi$
$432$	0.235327	0.0113222
$433$	−17.9157	−0.860975	−0.430488	−	0.902596i	$-0.641658\pi$
$433$	−17.9157	−0.860975	−0.430488	+	0.902596i	$0.641658\pi$
$434$	8.17815	0.392564
$435$	6.96212	0.333808
$436$	−11.2990	−0.541123
$437$	−5.67624	−0.271532
$438$	−29.3355	−1.40170
$439$	8.35812	0.398911	0.199456	−	0.979907i	$-0.436083\pi$
$439$	8.35812	0.398911	0.199456	+	0.979907i	$0.436083\pi$
$440$	34.3222	1.63625
$441$	11.6358	0.554084
$442$	14.8375	0.705746
$443$	−16.2571	−0.772399	−0.386200	−	0.922415i	$-0.626212\pi$
$443$	−16.2571	−0.772399	−0.386200	+	0.922415i	$0.626212\pi$
$444$	26.3515	1.25059
$445$	32.0706	1.52029
$446$	6.27736	0.297242
$447$	8.79708	0.416087
$448$	7.95498	0.375838
$449$	−27.3794	−1.29211	−0.646057	−	0.763289i	$-0.723583\pi$
$449$	−27.3794	−1.29211	−0.646057	+	0.763289i	$0.723583\pi$
$450$	6.81205	0.321123
$451$	12.2059	0.574755
$452$	20.7762	0.977232
$453$	23.9933	1.12731
$454$	−3.07665	−0.144394
$455$	−48.6421	−2.28038
$456$	35.9977	1.68575
$457$	−15.4647	−0.723406	−0.361703	−	0.932293i	$-0.617805\pi$
$457$	−15.4647	−0.723406	−0.361703	+	0.932293i	$0.617805\pi$
$458$	−18.4578	−0.862479
$459$	0.914996	0.0427083
$460$	4.07092	0.189808
$461$	18.3026	0.852435	0.426218	−	0.904621i	$-0.359846\pi$
$461$	18.3026	0.852435	0.426218	+	0.904621i	$0.359846\pi$
$462$	28.6279	1.33189
$463$	5.81224	0.270118	0.135059	−	0.990838i	$-0.456878\pi$
$463$	5.81224	0.270118	0.135059	+	0.990838i	$0.456878\pi$
$464$	−0.972761	−0.0451593
$465$	−23.2812	−1.07964
$466$	1.19803	0.0554975
$467$	−25.4048	−1.17559	−0.587797	−	0.809008i	$-0.700005\pi$
$467$	−25.4048	−1.17559	−0.587797	+	0.809008i	$0.700005\pi$
$468$	−23.5321	−1.08777
$469$	−20.8047	−0.960673
$470$	−2.61436	−0.120592
$471$	43.4905	2.00394
$472$	1.49634	0.0688749
$473$	−9.56016	−0.439576
$474$	−27.1938	−1.24905
$475$	−16.7377	−0.767977
$476$	−17.9111	−0.820952
$477$	37.9913	1.73950
$478$	6.27121	0.286838
$479$	−7.68321	−0.351055	−0.175527	−	0.984475i	$-0.556163\pi$
$479$	−7.68321	−0.351055	−0.175527	+	0.984475i	$0.556163\pi$
$480$	−40.8098	−1.86270
$481$	−38.8784	−1.77270
$482$	7.01970	0.319739
$483$	8.09872	0.368505
$484$	−16.5624	−0.752835
$485$	36.2740	1.64712
$486$	−16.5554	−0.750967
$487$	−14.8557	−0.673174	−0.336587	−	0.941652i	$-0.609273\pi$
$487$	−14.8557	−0.673174	−0.336587	+	0.941652i	$0.609273\pi$
$488$	32.2892	1.46166
$489$	1.01184	0.0457572
$490$	−7.89649	−0.356727
$491$	15.8512	0.715353	0.357676	−	0.933846i	$-0.383569\pi$
$491$	15.8512	0.715353	0.357676	+	0.933846i	$0.383569\pi$
$492$	−9.18126	−0.413923
$493$	−3.78228	−0.170345
$494$	−22.2673	−1.00185
$495$	−41.4029	−1.86092
$496$	3.25289	0.146059
$497$	−3.29037	−0.147593
$498$	25.6071	1.14748
$499$	15.1100	0.676416	0.338208	−	0.941071i	$-0.390179\pi$
$499$	15.1100	0.676416	0.338208	+	0.941071i	$0.390179\pi$
$500$	−8.35058	−0.373449
$501$	−21.7848	−0.973275
$502$	3.20338	0.142974
$503$	27.5406	1.22798	0.613988	−	0.789315i	$-0.289564\pi$
$503$	27.5406	1.22798	0.613988	+	0.789315i	$0.289564\pi$
$504$	−26.0928	−1.16227
$505$	−34.2756	−1.52524
$506$	3.53486	0.157144
$507$	36.2371	1.60935
$508$	−27.7263	−1.23016
$509$	−13.8531	−0.614026	−0.307013	−	0.951705i	$-0.599329\pi$
$509$	−13.8531	−0.614026	−0.307013	+	0.951705i	$0.599329\pi$
$510$	−19.6364	−0.869514
$511$	−52.2465	−2.31125
$512$	10.6984	0.472808
$513$	−1.37318	−0.0606273
$514$	1.73366	0.0764687
$515$	−13.5854	−0.598646
$516$	7.19112	0.316571
$517$	5.89461	0.259245
$518$	−18.0742	−0.794136
$519$	14.8829	0.653285
$520$	38.0898	1.67035
$521$	12.3185	0.539682	0.269841	−	0.962905i	$-0.413029\pi$
$521$	12.3185	0.539682	0.269841	+	0.962905i	$0.413029\pi$
$522$	−2.31017	−0.101113
$523$	17.6875	0.773422	0.386711	−	0.922201i	$-0.373611\pi$
$523$	17.6875	0.773422	0.386711	+	0.922201i	$0.373611\pi$
$524$	8.98886	0.392680
$525$	23.8809	1.04225
$526$	−17.1606	−0.748237
$527$	12.6479	0.550949
$528$	11.3869	0.495550
$529$	1.00000	0.0434783
$530$	−25.7824	−1.11992
$531$	−1.80504	−0.0783322
$532$	26.8800	1.16540
$533$	13.5458	0.586734
$534$	−20.9468	−0.906457
$535$	16.8352	0.727851
$536$	16.2914	0.703682
$537$	37.9832	1.63909
$538$	15.7298	0.678158
$539$	17.8042	0.766883
$540$	0.984824	0.0423801
$541$	27.3029	1.17384	0.586922	−	0.809643i	$-0.300340\pi$
$541$	27.3029	1.17384	0.586922	+	0.809643i	$0.300340\pi$
$542$	22.7774	0.978375
$543$	−40.1923	−1.72482
$544$	22.1706	0.950555
$545$	−22.0620	−0.945031
$546$	31.7704	1.35965
$547$	0.929830	0.0397567	0.0198783	−	0.999802i	$-0.493672\pi$
$547$	0.929830	0.0397567	0.0198783	+	0.999802i	$0.493672\pi$
$548$	10.0725	0.430278
$549$	−38.9505	−1.66237
$550$	10.4233	0.444453
$551$	5.67624	0.241816
$552$	−6.34181	−0.269925
$553$	−48.4322	−2.05955
$554$	9.57992	0.407012
$555$	51.4529	2.18405
$556$	−21.1290	−0.896070
$557$	35.6377	1.51002	0.755010	−	0.655713i	$-0.227632\pi$
$557$	35.6377	1.51002	0.755010	+	0.655713i	$0.227632\pi$
$558$	7.72516	0.327032
$559$	−10.6096	−0.448738
$560$	−8.99454	−0.380089
$561$	44.2742	1.86926
$562$	20.5652	0.867493
$563$	−11.9646	−0.504249	−0.252124	−	0.967695i	$-0.581129\pi$
$563$	−11.9646	−0.504249	−0.252124	+	0.967695i	$0.581129\pi$
$564$	−4.43391	−0.186701
$565$	40.5669	1.70666
$566$	−6.58967	−0.276985
$567$	−28.5213	−1.19778
$568$	2.57657	0.108110
$569$	9.64998	0.404548	0.202274	−	0.979329i	$-0.435167\pi$
$569$	9.64998	0.404548	0.202274	+	0.979329i	$0.435167\pi$
$570$	29.4693	1.23433
$571$	16.2945	0.681906	0.340953	−	0.940080i	$-0.389250\pi$
$571$	16.2945	0.681906	0.340953	+	0.940080i	$0.389250\pi$
$572$	−36.0071	−1.50553
$573$	−48.8799	−2.04199
$574$	6.29734	0.262846
$575$	2.94872	0.122970
$576$	7.51436	0.313098
$577$	−2.04221	−0.0850184	−0.0425092	−	0.999096i	$-0.513535\pi$
$577$	−2.04221	−0.0850184	−0.0425092	+	0.999096i	$0.513535\pi$
$578$	−2.00922	−0.0835727
$579$	−32.9265	−1.36838
$580$	−4.07092	−0.169036
$581$	45.6063	1.89207
$582$	−23.6922	−0.982075
$583$	58.1316	2.40757
$584$	40.9123	1.69296
$585$	−45.9478	−1.89971
$586$	6.79115	0.280540
$587$	5.51573	0.227659	0.113829	−	0.993500i	$-0.463688\pi$
$587$	5.51573	0.227659	0.113829	+	0.993500i	$0.463688\pi$
$588$	−13.3923	−0.552289
$589$	−18.9812	−0.782109
$590$	1.22497	0.0504314
$591$	−37.0601	−1.52445
$592$	−7.18911	−0.295470
$593$	−32.7365	−1.34433	−0.672163	−	0.740403i	$-0.734635\pi$
$593$	−32.7365	−1.34433	−0.672163	+	0.740403i	$0.734635\pi$
$594$	0.855143	0.0350869
$595$	−34.9724	−1.43373
$596$	−5.14387	−0.210701
$597$	−36.4606	−1.49223
$598$	3.92289	0.160419
$599$	12.0571	0.492641	0.246321	−	0.969188i	$-0.420778\pi$
$599$	12.0571	0.492641	0.246321	+	0.969188i	$0.420778\pi$
$600$	−18.7003	−0.763435
$601$	1.42188	0.0579996	0.0289998	−	0.999579i	$-0.490768\pi$
$601$	1.42188	0.0579996	0.0289998	+	0.999579i	$0.490768\pi$
$602$	−4.93232	−0.201026
$603$	−19.6524	−0.800306
$604$	−14.0295	−0.570852
$605$	−32.3390	−1.31477
$606$	22.3870	0.909410
$607$	−11.5014	−0.466829	−0.233415	−	0.972377i	$-0.574990\pi$
$607$	−11.5014	−0.466829	−0.233415	+	0.972377i	$0.574990\pi$
$608$	−33.2724	−1.34938
$609$	−8.09872	−0.328177
$610$	26.4334	1.07026
$611$	6.54168	0.264648
$612$	−16.9190	−0.683909
$613$	6.72128	0.271470	0.135735	−	0.990745i	$-0.456660\pi$
$613$	6.72128	0.271470	0.135735	+	0.990745i	$0.456660\pi$
$614$	−5.72677	−0.231114
$615$	−17.9270	−0.722885
$616$	−39.9255	−1.60864
$617$	3.79947	0.152961	0.0764805	−	0.997071i	$-0.475632\pi$
$617$	3.79947	0.152961	0.0764805	+	0.997071i	$0.475632\pi$
$618$	8.87329	0.356936
$619$	−25.5907	−1.02858	−0.514288	−	0.857618i	$-0.671944\pi$
$619$	−25.5907	−1.02858	−0.514288	+	0.857618i	$0.671944\pi$
$620$	13.6131	0.546715
$621$	0.241917	0.00970779
$622$	−0.222727	−0.00893054
$623$	−37.3063	−1.49464
$624$	12.6368	0.505878
$625$	−31.0486	−1.24195
$626$	−4.99306	−0.199563
$627$	−66.4445	−2.65354
$628$	−25.4300	−1.01477
$629$	−27.9526	−1.11454
$630$	−21.3608	−0.851033
$631$	29.8982	1.19023	0.595113	−	0.803642i	$-0.297107\pi$
$631$	29.8982	1.19023	0.595113	+	0.803642i	$0.297107\pi$
$632$	37.9255	1.50859
$633$	3.05134	0.121280
$634$	−8.12225	−0.322576
$635$	−54.1373	−2.14837
$636$	−43.7264	−1.73387
$637$	19.7587	0.782866
$638$	−3.53486	−0.139947
$639$	−3.10811	−0.122955
$640$	27.9528	1.10493
$641$	−19.3111	−0.762743	−0.381371	−	0.924422i	$-0.624548\pi$
$641$	−19.3111	−0.762743	−0.381371	+	0.924422i	$0.624548\pi$
$642$	−10.9959	−0.433973
$643$	24.2854	0.957721	0.478861	−	0.877891i	$-0.341050\pi$
$643$	24.2854	0.957721	0.478861	+	0.877891i	$0.341050\pi$
$644$	−4.73553	−0.186606
$645$	14.0411	0.552868
$646$	−16.0096	−0.629891
$647$	14.0122	0.550876	0.275438	−	0.961319i	$-0.411177\pi$
$647$	14.0122	0.550876	0.275438	+	0.961319i	$0.411177\pi$
$648$	22.3340	0.877361
$649$	−2.76195	−0.108416
$650$	11.5675	0.453716
$651$	27.0820	1.06143
$652$	−0.591650	−0.0231708
$653$	10.7049	0.418915	0.209458	−	0.977818i	$-0.432830\pi$
$653$	10.7049	0.418915	0.209458	+	0.977818i	$0.432830\pi$
$654$	14.4097	0.563464
$655$	17.5513	0.685786
$656$	2.50479	0.0977958
$657$	−49.3526	−1.92543
$658$	3.04118	0.118557
$659$	43.1485	1.68083	0.840413	−	0.541947i	$-0.182313\pi$
$659$	43.1485	1.68083	0.840413	+	0.541947i	$0.182313\pi$
$660$	47.6530	1.85489
$661$	1.22019	0.0474599	0.0237299	−	0.999718i	$-0.492446\pi$
$661$	1.22019	0.0474599	0.0237299	+	0.999718i	$0.492446\pi$
$662$	25.8915	1.00630
$663$	49.1343	1.90822
$664$	−35.7126	−1.38592
$665$	52.4848	2.03527
$666$	−17.0731	−0.661569
$667$	−1.00000	−0.0387202
$668$	12.7381	0.492854
$669$	20.7875	0.803691
$670$	13.3369	0.515248
$671$	−59.5994	−2.30081
$672$	47.4723	1.83128
$673$	0.712833	0.0274777	0.0137388	−	0.999906i	$-0.495627\pi$
$673$	0.712833	0.0274777	0.0137388	+	0.999906i	$0.495627\pi$
$674$	19.5115	0.751556
$675$	0.713346	0.0274567
$676$	−21.1887	−0.814951
$677$	29.3600	1.12840	0.564198	−	0.825640i	$-0.309185\pi$
$677$	29.3600	1.12840	0.564198	+	0.825640i	$0.309185\pi$
$678$	−26.4961	−1.01758
$679$	−42.1959	−1.61933
$680$	27.3856	1.05019
$681$	−10.1883	−0.390418
$682$	11.8205	0.452631
$683$	27.5282	1.05334	0.526668	−	0.850071i	$-0.323441\pi$
$683$	27.5282	1.05334	0.526668	+	0.850071i	$0.323441\pi$
$684$	25.3911	0.970854
$685$	19.6673	0.751447
$686$	−7.93379	−0.302914
$687$	−61.1232	−2.33200
$688$	−1.96185	−0.0747949
$689$	64.5129	2.45775
$690$	−5.19169	−0.197644
$691$	−40.1502	−1.52739	−0.763694	−	0.645579i	$-0.776616\pi$
$691$	−40.1502	−1.52739	−0.763694	+	0.645579i	$0.776616\pi$
$692$	−8.70238	−0.330815
$693$	48.1622	1.82953
$694$	−21.1916	−0.804423
$695$	−41.2557	−1.56492
$696$	6.34181	0.240386
$697$	9.73910	0.368895
$698$	10.4532	0.395660
$699$	3.96727	0.150056
$700$	−13.9638	−0.527781
$701$	−44.3429	−1.67481	−0.837404	−	0.546585i	$-0.815927\pi$
$701$	−44.3429	−1.67481	−0.837404	+	0.546585i	$0.815927\pi$
$702$	0.949014	0.0358182
$703$	41.9498	1.58217
$704$	11.4980	0.433345
$705$	−8.65748	−0.326059
$706$	−16.4766	−0.620104
$707$	39.8713	1.49951
$708$	2.07753	0.0780784
$709$	−4.68949	−0.176118	−0.0880588	−	0.996115i	$-0.528066\pi$
$709$	−4.68949	−0.176118	−0.0880588	+	0.996115i	$0.528066\pi$
$710$	2.10929	0.0791603
$711$	−45.7495	−1.71574
$712$	29.2132	1.09481
$713$	3.34398	0.125233
$714$	22.8422	0.854846
$715$	−70.3061	−2.62930
$716$	−22.2097	−0.830016
$717$	20.7671	0.775563
$718$	11.7700	0.439251
$719$	34.3501	1.28104	0.640521	−	0.767940i	$-0.278718\pi$
$719$	34.3501	1.28104	0.640521	+	0.767940i	$0.278718\pi$
$720$	−8.49634	−0.316640
$721$	15.8033	0.588547
$722$	9.85804	0.366878
$723$	23.2458	0.864519
$724$	23.5015	0.873425
$725$	−2.94872	−0.109513
$726$	21.1221	0.783916
$727$	19.5770	0.726072	0.363036	−	0.931775i	$-0.381740\pi$
$727$	19.5770	0.726072	0.363036	+	0.931775i	$0.381740\pi$
$728$	−44.3082	−1.64217
$729$	−28.7336	−1.06421
$730$	33.4926	1.23962
$731$	−7.62804	−0.282133
$732$	44.8305	1.65698
$733$	23.0325	0.850727	0.425363	−	0.905023i	$-0.360146\pi$
$733$	23.0325	0.850727	0.425363	+	0.905023i	$0.360146\pi$
$734$	2.87420	0.106088
$735$	−26.1493	−0.964530
$736$	5.86170	0.216065
$737$	−30.0707	−1.10767
$738$	5.94853	0.218968
$739$	−20.3767	−0.749569	−0.374784	−	0.927112i	$-0.622283\pi$
$739$	−20.3767	−0.749569	−0.374784	+	0.927112i	$0.622283\pi$
$740$	−30.0858	−1.10598
$741$	−73.7382	−2.70884
$742$	29.9915	1.10102
$743$	−18.2969	−0.671249	−0.335625	−	0.941996i	$-0.608947\pi$
$743$	−18.2969	−0.671249	−0.335625	+	0.941996i	$0.608947\pi$
$744$	−21.2069	−0.777482
$745$	−10.0437	−0.367973
$746$	−15.7848	−0.577921
$747$	43.0802	1.57622
$748$	−25.8882	−0.946568
$749$	−19.5837	−0.715573
$750$	10.6496	0.388868
$751$	32.5971	1.18948	0.594742	−	0.803917i	$-0.297254\pi$
$751$	32.5971	1.18948	0.594742	+	0.803917i	$0.297254\pi$
$752$	1.20964	0.0441111
$753$	10.6080	0.386577
$754$	−3.92289	−0.142863
$755$	−27.3935	−0.996950
$756$	−1.14560	−0.0416652
$757$	46.8094	1.70132	0.850659	−	0.525718i	$-0.176203\pi$
$757$	46.8094	1.70132	0.850659	+	0.525718i	$0.176203\pi$
$758$	−12.6824	−0.460645
$759$	11.7057	0.424890
$760$	−41.0989	−1.49082
$761$	45.5881	1.65257	0.826283	−	0.563254i	$-0.190451\pi$
$761$	45.5881	1.65257	0.826283	+	0.563254i	$0.190451\pi$
$762$	35.3596	1.28094
$763$	25.6637	0.929089
$764$	28.5813	1.03403
$765$	−33.0353	−1.19439
$766$	4.26609	0.154140
$767$	−3.06514	−0.110676
$768$	−30.2368	−1.09108
$769$	−45.0615	−1.62496	−0.812479	−	0.582990i	$-0.801883\pi$
$769$	−45.0615	−1.62496	−0.812479	+	0.582990i	$0.801883\pi$
$770$	−32.6848	−1.17788
$771$	5.74104	0.206758
$772$	19.2530	0.692929
$773$	27.4818	0.988451	0.494225	−	0.869334i	$-0.335452\pi$
$773$	27.4818	0.988451	0.494225	+	0.869334i	$0.335452\pi$
$774$	−4.65912	−0.167469
$775$	9.86048	0.354199
$776$	33.0420	1.18614
$777$	−59.8529	−2.14721
$778$	10.2704	0.368211
$779$	−14.6159	−0.523670
$780$	52.8840	1.89355
$781$	−4.75582	−0.170177
$782$	2.82046	0.100860
$783$	−0.241917	−0.00864540
$784$	3.65363	0.130487
$785$	−49.6536	−1.77221
$786$	−11.4636	−0.408892
$787$	−30.4090	−1.08396	−0.541981	−	0.840391i	$-0.682326\pi$
$787$	−30.4090	−1.08396	−0.541981	+	0.840391i	$0.682326\pi$
$788$	21.6700	0.771961
$789$	−56.8273	−2.02311
$790$	31.0475	1.10462
$791$	−47.1896	−1.67787
$792$	−37.7140	−1.34011
$793$	−66.1418	−2.34876
$794$	−14.1757	−0.503075
$795$	−85.3785	−3.02806
$796$	21.3194	0.755648
$797$	37.4295	1.32582	0.662911	−	0.748698i	$-0.269321\pi$
$797$	37.4295	1.32582	0.662911	+	0.748698i	$0.269321\pi$
$798$	−34.2803	−1.21351
$799$	4.70331	0.166391
$800$	17.2845	0.611101
$801$	−35.2399	−1.24514
$802$	14.5761	0.514699
$803$	−75.5159	−2.66490
$804$	22.6191	0.797713
$805$	−9.24640	−0.325893
$806$	13.1181	0.462065
$807$	52.0891	1.83362
$808$	−31.2217	−1.09838
$809$	−0.0861528	−0.00302897	−0.00151449	−	0.999999i	$-0.500482\pi$
$809$	−0.0861528	−0.00302897	−0.00151449	+	0.999999i	$0.500482\pi$
$810$	18.2836	0.642419
$811$	−11.0489	−0.387979	−0.193990	−	0.981004i	$-0.562143\pi$
$811$	−11.0489	−0.387979	−0.193990	+	0.981004i	$0.562143\pi$
$812$	4.73553	0.166184
$813$	75.4276	2.64536
$814$	−26.1241	−0.915649
$815$	−1.15523	−0.0404661
$816$	9.08557	0.318058
$817$	11.4478	0.400507
$818$	4.05302	0.141711
$819$	53.4490	1.86766
$820$	10.4823	0.366059
$821$	−53.1206	−1.85392	−0.926960	−	0.375160i	$-0.877588\pi$
$821$	−53.1206	−1.85392	−0.926960	+	0.375160i	$0.877588\pi$
$822$	−12.8456	−0.448042
$823$	−4.06031	−0.141534	−0.0707668	−	0.997493i	$-0.522545\pi$
$823$	−4.06031	−0.141534	−0.0707668	+	0.997493i	$0.522545\pi$
$824$	−12.3750	−0.431104
$825$	34.5169	1.20172
$826$	−1.42496	−0.0495807
$827$	0.603295	0.0209786	0.0104893	−	0.999945i	$-0.496661\pi$
$827$	0.603295	0.0209786	0.0104893	+	0.999945i	$0.496661\pi$
$828$	−4.47322	−0.155455
$829$	27.3478	0.949828	0.474914	−	0.880032i	$-0.342479\pi$
$829$	27.3478	0.949828	0.474914	+	0.880032i	$0.342479\pi$
$830$	−29.2359	−1.01479
$831$	31.7239	1.10049
$832$	12.7601	0.442377
$833$	14.2060	0.492208
$834$	26.9461	0.933065
$835$	24.8720	0.860731
$836$	38.8517	1.34372
$837$	0.808965	0.0279619
$838$	0.473554	0.0163587
$839$	−45.0600	−1.55565	−0.777823	−	0.628484i	$-0.783676\pi$
$839$	−45.0600	−1.55565	−0.777823	+	0.628484i	$0.783676\pi$
$840$	58.6389	2.02324
$841$	1.00000	0.0344828
$842$	−28.9299	−0.996991
$843$	68.1019	2.34555
$844$	−1.78419	−0.0614145
$845$	−41.3723	−1.42325
$846$	2.87272	0.0987663
$847$	37.6186	1.29259
$848$	11.9293	0.409653
$849$	−21.8217	−0.748919
$850$	8.31677	0.285263
$851$	−7.39041	−0.253340
$852$	3.57731	0.122557
$853$	16.1362	0.552492	0.276246	−	0.961087i	$-0.410909\pi$
$853$	16.1362	0.552492	0.276246	+	0.961087i	$0.410909\pi$
$854$	−30.7488	−1.05220
$855$	49.5777	1.69552
$856$	15.3353	0.524149
$857$	−6.87649	−0.234896	−0.117448	−	0.993079i	$-0.537471\pi$
$857$	−6.87649	−0.234896	−0.117448	+	0.993079i	$0.537471\pi$
$858$	45.9203	1.56769
$859$	8.84475	0.301779	0.150890	−	0.988551i	$-0.451786\pi$
$859$	8.84475	0.301779	0.150890	+	0.988551i	$0.451786\pi$
$860$	−8.21018	−0.279965
$861$	20.8537	0.710691
$862$	−14.3774	−0.489695
$863$	−29.2923	−0.997122	−0.498561	−	0.866855i	$-0.666138\pi$
$863$	−29.2923	−0.997122	−0.498561	+	0.866855i	$0.666138\pi$
$864$	1.41804	0.0482428
$865$	−16.9919	−0.577743
$866$	−13.3599	−0.453987
$867$	−6.65355	−0.225966
$868$	−15.8355	−0.537492
$869$	−70.0028	−2.37468
$870$	5.19169	0.176015
$871$	−33.3716	−1.13075
$872$	−20.0963	−0.680547
$873$	−39.8587	−1.34901
$874$	−4.23281	−0.143177
$875$	18.9669	0.641199
$876$	56.8028	1.91919
$877$	20.5455	0.693774	0.346887	−	0.937907i	$-0.387239\pi$
$877$	20.5455	0.693774	0.346887	+	0.937907i	$0.387239\pi$
$878$	6.23269	0.210343
$879$	22.4889	0.758532
$880$	−13.0005	−0.438247
$881$	−0.803678	−0.0270766	−0.0135383	−	0.999908i	$-0.504310\pi$
$881$	−0.803678	−0.0270766	−0.0135383	+	0.999908i	$0.504310\pi$
$882$	8.67685	0.292165
$883$	−39.2541	−1.32101	−0.660503	−	0.750823i	$-0.729657\pi$
$883$	−39.2541	−1.32101	−0.660503	+	0.750823i	$0.729657\pi$
$884$	−28.7301	−0.966296
$885$	4.05651	0.136358
$886$	−12.1230	−0.407281
$887$	24.3250	0.816755	0.408378	−	0.912813i	$-0.366095\pi$
$887$	24.3250	0.816755	0.408378	+	0.912813i	$0.366095\pi$
$888$	46.8686	1.57281
$889$	62.9755	2.11213
$890$	23.9152	0.801639
$891$	−41.2240	−1.38106
$892$	−12.1550	−0.406978
$893$	−7.05848	−0.236203
$894$	6.56003	0.219400
$895$	−43.3658	−1.44956
$896$	−32.5163	−1.08629
$897$	12.9907	0.433746
$898$	−20.4170	−0.681323
$899$	−3.34398	−0.111528
$900$	−13.1903	−0.439677
$901$	46.3832	1.54525
$902$	9.10203	0.303064
$903$	−16.3334	−0.543541
$904$	36.9525	1.22902
$905$	45.8881	1.52537
$906$	17.8920	0.594421
$907$	3.04078	0.100967	0.0504837	−	0.998725i	$-0.483924\pi$
$907$	3.04078	0.100967	0.0504837	+	0.998725i	$0.483924\pi$
$908$	5.95738	0.197703
$909$	37.6628	1.24920
$910$	−36.2727	−1.20243
$911$	−40.5839	−1.34460	−0.672302	−	0.740277i	$-0.734694\pi$
$911$	−40.5839	−1.34460	−0.672302	+	0.740277i	$0.734694\pi$
$912$	−13.6351	−0.451505
$913$	65.9183	2.18158
$914$	−11.5321	−0.381447
$915$	87.5343	2.89379
$916$	35.7403	1.18089
$917$	−20.4167	−0.674217
$918$	0.682317	0.0225198
$919$	16.8456	0.555684	0.277842	−	0.960627i	$-0.410381\pi$
$919$	16.8456	0.555684	0.277842	+	0.960627i	$0.410381\pi$
$920$	7.24052	0.238713
$921$	−18.9642	−0.624893
$922$	13.6483	0.449483
$923$	−5.27788	−0.173724
$924$	−55.4327	−1.82360
$925$	−21.7923	−0.716526
$926$	4.33422	0.142431
$927$	14.9280	0.490299
$928$	−5.86170	−0.192420
$929$	−12.9053	−0.423408	−0.211704	−	0.977334i	$-0.567901\pi$
$929$	−12.9053	−0.423408	−0.211704	+	0.977334i	$0.567901\pi$
$930$	−17.3609	−0.569286
$931$	−21.3196	−0.698722
$932$	−2.31976	−0.0759863
$933$	−0.737561	−0.0241467
$934$	−18.9445	−0.619883
$935$	−50.5484	−1.65311
$936$	−41.8540	−1.36804
$937$	31.3663	1.02469	0.512346	−	0.858779i	$-0.328777\pi$
$937$	31.3663	1.02469	0.512346	+	0.858779i	$0.328777\pi$
$938$	−15.5142	−0.506556
$939$	−16.5345	−0.539584
$940$	5.06224	0.165112
$941$	1.74601	0.0569182	0.0284591	−	0.999595i	$-0.490940\pi$
$941$	1.74601	0.0569182	0.0284591	+	0.999595i	$0.490940\pi$
$942$	32.4311	1.05666
$943$	2.57493	0.0838513
$944$	−0.566784	−0.0184472
$945$	−2.23686	−0.0727651
$946$	−7.12906	−0.231786
$947$	−28.0994	−0.913108	−0.456554	−	0.889696i	$-0.650917\pi$
$947$	−28.0994	−0.913108	−0.456554	+	0.889696i	$0.650917\pi$
$948$	52.6559	1.71018
$949$	−83.8054	−2.72044
$950$	−12.4814	−0.404949
$951$	−26.8968	−0.872190
$952$	−31.8565	−1.03248
$953$	20.9344	0.678133	0.339066	−	0.940762i	$-0.389889\pi$
$953$	20.9344	0.678133	0.339066	+	0.940762i	$0.389889\pi$
$954$	28.3303	0.917227
$955$	55.8067	1.80586
$956$	−12.1431	−0.392735
$957$	−11.7057	−0.378392
$958$	−5.72941	−0.185109
$959$	−22.8781	−0.738771
$960$	−16.8872	−0.545030
$961$	−19.8178	−0.639284
$962$	−28.9918	−0.934733
$963$	−18.4989	−0.596120
$964$	−13.5924	−0.437781
$965$	37.5926	1.21015
$966$	6.03926	0.194310
$967$	−58.5319	−1.88226	−0.941130	−	0.338045i	$-0.890234\pi$
$967$	−58.5319	−1.88226	−0.941130	+	0.338045i	$0.890234\pi$
$968$	−29.4577	−0.946806
$969$	−53.0160	−1.70312
$970$	27.0497	0.868513
$971$	18.2934	0.587064	0.293532	−	0.955949i	$-0.405169\pi$
$971$	18.2934	0.587064	0.293532	+	0.955949i	$0.405169\pi$
$972$	32.0565	1.02821
$973$	47.9910	1.53852
$974$	−11.0779	−0.354960
$975$	38.3059	1.22677
$976$	−12.2305	−0.391488
$977$	19.6460	0.628530	0.314265	−	0.949335i	$-0.398242\pi$
$977$	19.6460	0.628530	0.314265	+	0.949335i	$0.398242\pi$
$978$	0.754537	0.0241274
$979$	−53.9216	−1.72334
$980$	15.2901	0.488425
$981$	24.2422	0.773994
$982$	11.8203	0.377201
$983$	5.00069	0.159497	0.0797486	−	0.996815i	$-0.474588\pi$
$983$	5.00069	0.159497	0.0797486	+	0.996815i	$0.474588\pi$
$984$	−16.3297	−0.520573
$985$	42.3120	1.34817
$986$	−2.82046	−0.0898219
$987$	10.0709	0.320559
$988$	43.1166	1.37172
$989$	−2.01679	−0.0641300
$990$	−30.8744	−0.981251
$991$	−30.0105	−0.953314	−0.476657	−	0.879089i	$-0.658152\pi$
$991$	−30.0105	−0.953314	−0.476657	+	0.879089i	$0.658152\pi$
$992$	19.6014	0.622345
$993$	85.7399	2.72087
$994$	−2.45365	−0.0778249
$995$	41.6275	1.31968
$996$	−49.5835	−1.57111
$997$	−11.1032	−0.351641	−0.175820	−	0.984422i	$-0.556258\pi$
$997$	−11.1032	−0.351641	−0.175820	+	0.984422i	$0.556258\pi$
$998$	11.2676	0.356670
$999$	−1.78786	−0.0565655

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.d.1.10	✓	16
3.2	odd	2		6003.2.a.q.1.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.d.1.10	✓	16	1.1	even	1	trivial
6003.2.a.q.1.7		16	3.2	odd	2

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:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q+0.745705 q^{2} +2.46941 q^{3} -1.44392 q^{4} -2.81935 q^{5} +1.84145 q^{6} +3.27962 q^{7} -2.56815 q^{8} +3.09797 q^{9} +O(q^{10})\)	\(q+0.745705 q^{2} +2.46941 q^{3} -1.44392 q^{4} -2.81935 q^{5} +1.84145 q^{6} +3.27962 q^{7} -2.56815 q^{8} +3.09797 q^{9} -2.10240 q^{10} +4.74029 q^{11} -3.56563 q^{12} +5.26065 q^{13} +2.44563 q^{14} -6.96212 q^{15} +0.972761 q^{16} +3.78228 q^{17} +2.31017 q^{18} -5.67624 q^{19} +4.07092 q^{20} +8.09872 q^{21} +3.53486 q^{22} +1.00000 q^{23} -6.34181 q^{24} +2.94872 q^{25} +3.92289 q^{26} +0.241917 q^{27} -4.73553 q^{28} -1.00000 q^{29} -5.19169 q^{30} +3.34398 q^{31} +5.86170 q^{32} +11.7057 q^{33} +2.82046 q^{34} -9.24640 q^{35} -4.47322 q^{36} -7.39041 q^{37} -4.23281 q^{38} +12.9907 q^{39} +7.24052 q^{40} +2.57493 q^{41} +6.03926 q^{42} -2.01679 q^{43} -6.84462 q^{44} -8.73424 q^{45} +0.745705 q^{46} +1.24351 q^{47} +2.40214 q^{48} +3.75593 q^{49} +2.19888 q^{50} +9.33997 q^{51} -7.59597 q^{52} +12.2633 q^{53} +0.180399 q^{54} -13.3645 q^{55} -8.42257 q^{56} -14.0170 q^{57} -0.745705 q^{58} -0.582654 q^{59} +10.0528 q^{60} -12.5729 q^{61} +2.49362 q^{62} +10.1602 q^{63} +2.42558 q^{64} -14.8316 q^{65} +8.72901 q^{66} -6.34363 q^{67} -5.46132 q^{68} +2.46941 q^{69} -6.89509 q^{70} -1.00328 q^{71} -7.95605 q^{72} -15.9306 q^{73} -5.51107 q^{74} +7.28160 q^{75} +8.19606 q^{76} +15.5464 q^{77} +9.68722 q^{78} -14.7676 q^{79} -2.74255 q^{80} -8.69651 q^{81} +1.92014 q^{82} +13.9060 q^{83} -11.6939 q^{84} -10.6636 q^{85} -1.50393 q^{86} -2.46941 q^{87} -12.1738 q^{88} -11.3752 q^{89} -6.51317 q^{90} +17.2529 q^{91} -1.44392 q^{92} +8.25764 q^{93} +0.927294 q^{94} +16.0033 q^{95} +14.4749 q^{96} -12.8661 q^{97} +2.80082 q^{98} +14.6853 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9}+O(q^{10}) \) 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9} - 14 q^{10} + 4 q^{11} + 3 q^{12} + 15 q^{13} + 8 q^{14} + 8 q^{15} + 23 q^{16} + 20 q^{17} + 2 q^{18} - 4 q^{19} + 25 q^{20} + 5 q^{21} + 13 q^{22} + 16 q^{23} - 24 q^{24} + 30 q^{25} + 25 q^{26} + 8 q^{27} - 13 q^{28} - 16 q^{29} - 45 q^{30} - 19 q^{32} + q^{33} - 23 q^{34} + 5 q^{35} + 37 q^{36} + 5 q^{37} + 38 q^{38} - 10 q^{39} - 20 q^{40} + 7 q^{41} + 14 q^{42} - 17 q^{43} - 21 q^{44} + 48 q^{45} + 3 q^{46} + 29 q^{47} + 35 q^{48} + 31 q^{49} - 44 q^{50} - 14 q^{51} + 20 q^{52} + 63 q^{53} - 13 q^{54} + q^{55} - 19 q^{56} - 22 q^{57} - 3 q^{58} + 11 q^{59} - 3 q^{60} + 33 q^{62} - 33 q^{63} + 29 q^{64} + 53 q^{65} - 43 q^{66} - 13 q^{67} + 63 q^{68} + 5 q^{69} - 46 q^{70} - 23 q^{71} + 46 q^{72} - 38 q^{73} - 47 q^{74} + 37 q^{75} - 56 q^{76} + 97 q^{77} - 24 q^{78} - 27 q^{79} + 8 q^{80} + 40 q^{81} + 9 q^{82} + 36 q^{83} + 22 q^{84} + 6 q^{85} - 11 q^{86} - 5 q^{87} - 24 q^{88} - 16 q^{89} - 95 q^{90} - 47 q^{91} + 21 q^{92} + 62 q^{93} + 37 q^{94} - 12 q^{95} - 74 q^{96} - 30 q^{97} - 27 q^{98} - 42 q^{99}+O(q^{100}) \) 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9 - 14 * q^10 + 4 * q^11 + 3 * q^12 + 15 * q^13 + 8 * q^14 + 8 * q^15 + 23 * q^16 + 20 * q^17 + 2 * q^18 - 4 * q^19 + 25 * q^20 + 5 * q^21 + 13 * q^22 + 16 * q^23 - 24 * q^24 + 30 * q^25 + 25 * q^26 + 8 * q^27 - 13 * q^28 - 16 * q^29 - 45 * q^30 - 19 * q^32 + q^33 - 23 * q^34 + 5 * q^35 + 37 * q^36 + 5 * q^37 + 38 * q^38 - 10 * q^39 - 20 * q^40 + 7 * q^41 + 14 * q^42 - 17 * q^43 - 21 * q^44 + 48 * q^45 + 3 * q^46 + 29 * q^47 + 35 * q^48 + 31 * q^49 - 44 * q^50 - 14 * q^51 + 20 * q^52 + 63 * q^53 - 13 * q^54 + q^55 - 19 * q^56 - 22 * q^57 - 3 * q^58 + 11 * q^59 - 3 * q^60 + 33 * q^62 - 33 * q^63 + 29 * q^64 + 53 * q^65 - 43 * q^66 - 13 * q^67 + 63 * q^68 + 5 * q^69 - 46 * q^70 - 23 * q^71 + 46 * q^72 - 38 * q^73 - 47 * q^74 + 37 * q^75 - 56 * q^76 + 97 * q^77 - 24 * q^78 - 27 * q^79 + 8 * q^80 + 40 * q^81 + 9 * q^82 + 36 * q^83 + 22 * q^84 + 6 * q^85 - 11 * q^86 - 5 * q^87 - 24 * q^88 - 16 * q^89 - 95 * q^90 - 47 * q^91 + 21 * q^92 + 62 * q^93 + 37 * q^94 - 12 * q^95 - 74 * q^96 - 30 * q^97 - 27 * q^98 - 42 * q^99

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