LMFDB - Embedded newform 667.2.a.d.1.13

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			1.13
Root			$2.13862$ 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)

$f(q)$	$=$	$q+2.13862 q^{2} +3.19578 q^{3} +2.57368 q^{4} -0.343330 q^{5} +6.83454 q^{6} -2.49131 q^{7} +1.22687 q^{8} +7.21299 q^{9} +O(q^{10})$	\(q+2.13862 q^{2} +3.19578 q^{3} +2.57368 q^{4} -0.343330 q^{5} +6.83454 q^{6} -2.49131 q^{7} +1.22687 q^{8} +7.21299 q^{9} -0.734251 q^{10} +0.158588 q^{11} +8.22489 q^{12} -0.313547 q^{13} -5.32794 q^{14} -1.09721 q^{15} -2.52354 q^{16} -4.67587 q^{17} +15.4258 q^{18} -4.91384 q^{19} -0.883620 q^{20} -7.96165 q^{21} +0.339159 q^{22} +1.00000 q^{23} +3.92081 q^{24} -4.88212 q^{25} -0.670557 q^{26} +13.4638 q^{27} -6.41181 q^{28} -1.00000 q^{29} -2.34650 q^{30} +8.73283 q^{31} -7.85063 q^{32} +0.506812 q^{33} -9.99988 q^{34} +0.855340 q^{35} +18.5639 q^{36} +7.70294 q^{37} -10.5088 q^{38} -1.00203 q^{39} -0.421222 q^{40} +7.50928 q^{41} -17.0269 q^{42} +4.03395 q^{43} +0.408154 q^{44} -2.47644 q^{45} +2.13862 q^{46} +3.87949 q^{47} -8.06468 q^{48} -0.793397 q^{49} -10.4410 q^{50} -14.9430 q^{51} -0.806969 q^{52} +5.89609 q^{53} +28.7938 q^{54} -0.0544481 q^{55} -3.05651 q^{56} -15.7035 q^{57} -2.13862 q^{58} -7.19090 q^{59} -2.82385 q^{60} +10.4921 q^{61} +18.6762 q^{62} -17.9698 q^{63} -11.7424 q^{64} +0.107650 q^{65} +1.08388 q^{66} -5.79686 q^{67} -12.0342 q^{68} +3.19578 q^{69} +1.82924 q^{70} -0.837052 q^{71} +8.84941 q^{72} -13.4130 q^{73} +16.4736 q^{74} -15.6022 q^{75} -12.6466 q^{76} -0.395091 q^{77} -2.14295 q^{78} +6.13553 q^{79} +0.866409 q^{80} +21.3882 q^{81} +16.0595 q^{82} -10.3618 q^{83} -20.4907 q^{84} +1.60537 q^{85} +8.62706 q^{86} -3.19578 q^{87} +0.194567 q^{88} +3.81659 q^{89} -5.29614 q^{90} +0.781142 q^{91} +2.57368 q^{92} +27.9082 q^{93} +8.29673 q^{94} +1.68707 q^{95} -25.0889 q^{96} +15.2047 q^{97} -1.69677 q^{98} +1.14389 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.13862	1.51223	0.756115	−	0.654439i	$-0.227095\pi$
$2$	2.13862	1.51223	0.756115	+	0.654439i	$0.227095\pi$
$3$	3.19578	1.84508	0.922541	−	0.385899i	$-0.126109\pi$
$3$	3.19578	1.84508	0.922541	+	0.385899i	$0.126109\pi$
$4$	2.57368	1.28684
$5$	−0.343330	−0.153542	−0.0767709	−	0.997049i	$-0.524461\pi$
$5$	−0.343330	−0.153542	−0.0767709	+	0.997049i	$0.524461\pi$
$6$	6.83454	2.79019
$7$	−2.49131	−0.941625	−0.470812	−	0.882233i	$-0.656039\pi$
$7$	−2.49131	−0.941625	−0.470812	+	0.882233i	$0.656039\pi$
$8$	1.22687	0.433765
$9$	7.21299	2.40433
$10$	−0.734251	−0.232191
$11$	0.158588	0.0478161	0.0239080	−	0.999714i	$-0.492389\pi$
$11$	0.158588	0.0478161	0.0239080	+	0.999714i	$0.492389\pi$
$12$	8.22489	2.37432
$13$	−0.313547	−0.0869624	−0.0434812	−	0.999054i	$-0.513845\pi$
$13$	−0.313547	−0.0869624	−0.0434812	+	0.999054i	$0.513845\pi$
$14$	−5.32794	−1.42395
$15$	−1.09721	−0.283297
$16$	−2.52354	−0.630886
$17$	−4.67587	−1.13406	−0.567032	−	0.823696i	$-0.691908\pi$
$17$	−4.67587	−1.13406	−0.567032	+	0.823696i	$0.691908\pi$
$18$	15.4258	3.63590
$19$	−4.91384	−1.12731	−0.563656	−	0.826010i	$-0.690606\pi$
$19$	−4.91384	−1.12731	−0.563656	+	0.826010i	$0.690606\pi$
$20$	−0.883620	−0.197584
$21$	−7.96165	−1.73738
$22$	0.339159	0.0723089
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	3.92081	0.800332
$25$	−4.88212	−0.976425
$26$	−0.670557	−0.131507
$27$	13.4638	2.59110
$28$	−6.41181	−1.21172
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−2.34650	−0.428411
$31$	8.73283	1.56846	0.784232	−	0.620468i	$-0.213057\pi$
$31$	8.73283	1.56846	0.784232	+	0.620468i	$0.213057\pi$
$32$	−7.85063	−1.38781
$33$	0.506812	0.0882246
$34$	−9.99988	−1.71497
$35$	0.855340	0.144579
$36$	18.5639	3.09398
$37$	7.70294	1.26636	0.633178	−	0.774006i	$-0.281750\pi$
$37$	7.70294	1.26636	0.633178	+	0.774006i	$0.281750\pi$
$38$	−10.5088	−1.70475
$39$	−1.00203	−0.160453
$40$	−0.421222	−0.0666011
$41$	7.50928	1.17275	0.586376	−	0.810039i	$-0.300554\pi$
$41$	7.50928	1.17275	0.586376	+	0.810039i	$0.300554\pi$
$42$	−17.0269	−2.62731
$43$	4.03395	0.615171	0.307585	−	0.951520i	$-0.400479\pi$
$43$	4.03395	0.615171	0.307585	+	0.951520i	$0.400479\pi$
$44$	0.408154	0.0615316
$45$	−2.47644	−0.369165
$46$	2.13862	0.315322
$47$	3.87949	0.565882	0.282941	−	0.959137i	$-0.408690\pi$
$47$	3.87949	0.565882	0.282941	+	0.959137i	$0.408690\pi$
$48$	−8.06468	−1.16404
$49$	−0.793397	−0.113342
$50$	−10.4410	−1.47658
$51$	−14.9430	−2.09244
$52$	−0.806969	−0.111907
$53$	5.89609	0.809890	0.404945	−	0.914341i	$-0.367291\pi$
$53$	5.89609	0.809890	0.404945	+	0.914341i	$0.367291\pi$
$54$	28.7938	3.91834
$55$	−0.0544481	−0.00734177
$56$	−3.05651	−0.408444
$57$	−15.7035	−2.07998
$58$	−2.13862	−0.280814
$59$	−7.19090	−0.936175	−0.468088	−	0.883682i	$-0.655057\pi$
$59$	−7.19090	−0.936175	−0.468088	+	0.883682i	$0.655057\pi$
$60$	−2.82385	−0.364558
$61$	10.4921	1.34337	0.671686	−	0.740836i	$-0.265571\pi$
$61$	10.4921	1.34337	0.671686	+	0.740836i	$0.265571\pi$
$62$	18.6762	2.37188
$63$	−17.9698	−2.26398
$64$	−11.7424	−1.46780
$65$	0.107650	0.0133524
$66$	1.08388	0.133416
$67$	−5.79686	−0.708199	−0.354100	−	0.935208i	$-0.615213\pi$
$67$	−5.79686	−0.708199	−0.354100	+	0.935208i	$0.615213\pi$
$68$	−12.0342	−1.45936
$69$	3.19578	0.384726
$70$	1.82924	0.218636
$71$	−0.837052	−0.0993398	−0.0496699	−	0.998766i	$-0.515817\pi$
$71$	−0.837052	−0.0993398	−0.0496699	+	0.998766i	$0.515817\pi$
$72$	8.84941	1.04291
$73$	−13.4130	−1.56987	−0.784936	−	0.619576i	$-0.787304\pi$
$73$	−13.4130	−1.56987	−0.784936	+	0.619576i	$0.787304\pi$
$74$	16.4736	1.91502
$75$	−15.6022	−1.80158
$76$	−12.6466	−1.45067
$77$	−0.395091	−0.0450248
$78$	−2.14295	−0.242641
$79$	6.13553	0.690301	0.345151	−	0.938547i	$-0.387828\pi$
$79$	6.13553	0.690301	0.345151	+	0.938547i	$0.387828\pi$
$80$	0.866409	0.0968674
$81$	21.3882	2.37647
$82$	16.0595	1.77347
$83$	−10.3618	−1.13735	−0.568677	−	0.822561i	$-0.692545\pi$
$83$	−10.3618	−1.13735	−0.568677	+	0.822561i	$0.692545\pi$
$84$	−20.4907	−2.23572
$85$	1.60537	0.174126
$86$	8.62706	0.930280
$87$	−3.19578	−0.342623
$88$	0.194567	0.0207409
$89$	3.81659	0.404557	0.202279	−	0.979328i	$-0.435165\pi$
$89$	3.81659	0.404557	0.202279	+	0.979328i	$0.435165\pi$
$90$	−5.29614	−0.558262
$91$	0.781142	0.0818860
$92$	2.57368	0.268324
$93$	27.9082	2.89394
$94$	8.29673	0.855743
$95$	1.68707	0.173090
$96$	−25.0889	−2.56062
$97$	15.2047	1.54380	0.771902	−	0.635741i	$-0.219306\pi$
$97$	15.2047	1.54380	0.771902	+	0.635741i	$0.219306\pi$
$98$	−1.69677	−0.171400
$99$	1.14389	0.114966
$100$	−12.5650	−1.25650
$101$	−1.28519	−0.127882	−0.0639408	−	0.997954i	$-0.520367\pi$
$101$	−1.28519	−0.127882	−0.0639408	+	0.997954i	$0.520367\pi$
$102$	−31.9574	−3.16425
$103$	−0.696939	−0.0686714	−0.0343357	−	0.999410i	$-0.510932\pi$
$103$	−0.696939	−0.0686714	−0.0343357	+	0.999410i	$0.510932\pi$
$104$	−0.384683	−0.0377212
$105$	2.73348	0.266760
$106$	12.6095	1.22474
$107$	1.07960	0.104369	0.0521846	−	0.998637i	$-0.483382\pi$
$107$	1.07960	0.104369	0.0521846	+	0.998637i	$0.483382\pi$
$108$	34.6514	3.33433
$109$	−14.2835	−1.36811	−0.684054	−	0.729431i	$-0.739785\pi$
$109$	−14.2835	−1.36811	−0.684054	+	0.729431i	$0.739785\pi$
$110$	−0.116443	−0.0111024
$111$	24.6169	2.33653
$112$	6.28692	0.594058
$113$	−7.25184	−0.682196	−0.341098	−	0.940028i	$-0.610799\pi$
$113$	−7.25184	−0.682196	−0.341098	+	0.940028i	$0.610799\pi$
$114$	−33.5838	−3.14541
$115$	−0.343330	−0.0320157
$116$	−2.57368	−0.238960
$117$	−2.26161	−0.209086
$118$	−15.3786	−1.41571
$119$	11.6490	1.06786
$120$	−1.34613	−0.122884
$121$	−10.9748	−0.997714
$122$	22.4385	2.03149
$123$	23.9980	2.16382
$124$	22.4755	2.01836
$125$	3.39283	0.303464
$126$	−38.4304	−3.42365
$127$	−15.9435	−1.41475	−0.707377	−	0.706837i	$-0.750122\pi$
$127$	−15.9435	−1.41475	−0.707377	+	0.706837i	$0.750122\pi$
$128$	−9.41121	−0.831841
$129$	12.8916	1.13504
$130$	0.230222	0.0201918
$131$	0.774574	0.0676748	0.0338374	−	0.999427i	$-0.489227\pi$
$131$	0.774574	0.0676748	0.0338374	+	0.999427i	$0.489227\pi$
$132$	1.30437	0.113531
$133$	12.2419	1.06150
$134$	−12.3973	−1.07096
$135$	−4.62251	−0.397843
$136$	−5.73669	−0.491917
$137$	4.83204	0.412829	0.206415	−	0.978465i	$-0.433820\pi$
$137$	4.83204	0.412829	0.206415	+	0.978465i	$0.433820\pi$
$138$	6.83454	0.581794
$139$	9.99495	0.847761	0.423880	−	0.905718i	$-0.360668\pi$
$139$	9.99495	0.847761	0.423880	+	0.905718i	$0.360668\pi$
$140$	2.20137	0.186050
$141$	12.3980	1.04410
$142$	−1.79013	−0.150225
$143$	−0.0497249	−0.00415820
$144$	−18.2023	−1.51686
$145$	0.343330	0.0285120
$146$	−28.6852	−2.37401
$147$	−2.53552	−0.209126
$148$	19.8249	1.62960
$149$	−16.7051	−1.36854	−0.684269	−	0.729230i	$-0.739879\pi$
$149$	−16.7051	−1.36854	−0.684269	+	0.729230i	$0.739879\pi$
$150$	−33.3671	−2.72441
$151$	4.53234	0.368837	0.184418	−	0.982848i	$-0.440960\pi$
$151$	4.53234	0.368837	0.184418	+	0.982848i	$0.440960\pi$
$152$	−6.02865	−0.488988
$153$	−33.7270	−2.72666
$154$	−0.844948	−0.0680879
$155$	−2.99824	−0.240825
$156$	−2.57889	−0.206477
$157$	19.0521	1.52052	0.760260	−	0.649619i	$-0.225072\pi$
$157$	19.0521	1.52052	0.760260	+	0.649619i	$0.225072\pi$
$158$	13.1215	1.04389
$159$	18.8426	1.49431
$160$	2.69536	0.213087
$161$	−2.49131	−0.196342
$162$	45.7411	3.59376
$163$	0.657843	0.0515263	0.0257631	−	0.999668i	$-0.491798\pi$
$163$	0.657843	0.0515263	0.0257631	+	0.999668i	$0.491798\pi$
$164$	19.3264	1.50914
$165$	−0.174004	−0.0135462
$166$	−22.1599	−1.71994
$167$	10.5082	0.813149	0.406575	−	0.913618i	$-0.366723\pi$
$167$	10.5082	0.813149	0.406575	+	0.913618i	$0.366723\pi$
$168$	−9.76793	−0.753612
$169$	−12.9017	−0.992438
$170$	3.43326	0.263319
$171$	−35.4434	−2.71043
$172$	10.3821	0.791625
$173$	16.1298	1.22633	0.613164	−	0.789955i	$-0.289896\pi$
$173$	16.1298	1.22633	0.613164	+	0.789955i	$0.289896\pi$
$174$	−6.83454	−0.518125
$175$	12.1629	0.919426
$176$	−0.400204	−0.0301665
$177$	−22.9805	−1.72732
$178$	8.16221	0.611783
$179$	4.86868	0.363903	0.181951	−	0.983308i	$-0.441759\pi$
$179$	4.86868	0.363903	0.181951	+	0.983308i	$0.441759\pi$
$180$	−6.37354	−0.475056
$181$	−2.00349	−0.148918	−0.0744592	−	0.997224i	$-0.523723\pi$
$181$	−2.00349	−0.148918	−0.0744592	+	0.997224i	$0.523723\pi$
$182$	1.67056	0.123830
$183$	33.5303	2.47863
$184$	1.22687	0.0904462
$185$	−2.64465	−0.194439
$186$	59.6849	4.37631
$187$	−0.741537	−0.0542265
$188$	9.98454	0.728198
$189$	−33.5423	−2.43985
$190$	3.60799	0.261751
$191$	14.9101	1.07886	0.539429	−	0.842031i	$-0.318640\pi$
$191$	14.9101	1.07886	0.539429	+	0.842031i	$0.318640\pi$
$192$	−37.5261	−2.70821
$193$	−3.17142	−0.228283	−0.114142	−	0.993464i	$-0.536412\pi$
$193$	−3.17142	−0.228283	−0.114142	+	0.993464i	$0.536412\pi$
$194$	32.5170	2.33459
$195$	0.344026	0.0246362
$196$	−2.04195	−0.145853
$197$	20.3560	1.45030	0.725151	−	0.688590i	$-0.241770\pi$
$197$	20.3560	1.45030	0.725151	+	0.688590i	$0.241770\pi$
$198$	2.44635	0.173854
$199$	−15.6500	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$199$	−15.6500	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$200$	−5.98974	−0.423539
$201$	−18.5255	−1.30669
$202$	−2.74854	−0.193386
$203$	2.49131	0.174855
$204$	−38.4585	−2.69263
$205$	−2.57816	−0.180067
$206$	−1.49048	−0.103847
$207$	7.21299	0.501337
$208$	0.791251	0.0548634
$209$	−0.779276	−0.0539036
$210$	5.84585	0.403402
$211$	17.4505	1.20134	0.600670	−	0.799497i	$-0.294901\pi$
$211$	17.4505	1.20134	0.600670	+	0.799497i	$0.294901\pi$
$212$	15.1746	1.04220
$213$	−2.67503	−0.183290
$214$	2.30886	0.157830
$215$	−1.38497	−0.0944545
$216$	16.5183	1.12393
$217$	−21.7562	−1.47690
$218$	−30.5468	−2.06889
$219$	−42.8649	−2.89654
$220$	−0.140132	−0.00944767
$221$	1.46611	0.0986210
$222$	52.6461	3.53337
$223$	−13.4605	−0.901379	−0.450690	−	0.892681i	$-0.648822\pi$
$223$	−13.4605	−0.901379	−0.450690	+	0.892681i	$0.648822\pi$
$224$	19.5583	1.30680
$225$	−35.2147	−2.34765
$226$	−15.5089	−1.03164
$227$	−28.0083	−1.85898	−0.929488	−	0.368853i	$-0.879751\pi$
$227$	−28.0083	−1.85898	−0.929488	+	0.368853i	$0.879751\pi$
$228$	−40.4158	−2.67660
$229$	−15.2203	−1.00578	−0.502892	−	0.864349i	$-0.667731\pi$
$229$	−15.2203	−1.00578	−0.502892	+	0.864349i	$0.667731\pi$
$230$	−0.734251	−0.0484151
$231$	−1.26262	−0.0830745
$232$	−1.22687	−0.0805481
$233$	22.7178	1.48829	0.744147	−	0.668016i	$-0.232856\pi$
$233$	22.7178	1.48829	0.744147	+	0.668016i	$0.232856\pi$
$234$	−4.83672	−0.316186
$235$	−1.33195	−0.0868865
$236$	−18.5070	−1.20471
$237$	19.6078	1.27366
$238$	24.9128	1.61485
$239$	−24.6833	−1.59663	−0.798315	−	0.602240i	$-0.794275\pi$
$239$	−24.6833	−1.59663	−0.798315	+	0.602240i	$0.794275\pi$
$240$	2.76885	0.178728
$241$	−13.6625	−0.880081	−0.440040	−	0.897978i	$-0.645036\pi$
$241$	−13.6625	−0.880081	−0.440040	+	0.897978i	$0.645036\pi$
$242$	−23.4710	−1.50877
$243$	27.9606	1.79368
$244$	27.0032	1.72870
$245$	0.272397	0.0174028
$246$	51.3224	3.27220
$247$	1.54072	0.0980337
$248$	10.7141	0.680344
$249$	−33.1140	−2.09851
$250$	7.25596	0.458907
$251$	8.55413	0.539932	0.269966	−	0.962870i	$-0.412988\pi$
$251$	8.55413	0.539932	0.269966	+	0.962870i	$0.412988\pi$
$252$	−46.2483	−2.91337
$253$	0.158588	0.00997034
$254$	−34.0969	−2.13943
$255$	5.13039	0.321278
$256$	3.35785	0.209865
$257$	11.8392	0.738509	0.369255	−	0.929328i	$-0.379613\pi$
$257$	11.8392	0.738509	0.369255	+	0.929328i	$0.379613\pi$
$258$	27.5701	1.71644
$259$	−19.1904	−1.19243
$260$	0.277057	0.0171823
$261$	−7.21299	−0.446473
$262$	1.65652	0.102340
$263$	21.8415	1.34681	0.673403	−	0.739276i	$-0.264832\pi$
$263$	21.8415	1.34681	0.673403	+	0.739276i	$0.264832\pi$
$264$	0.621793	0.0382687
$265$	−2.02431	−0.124352
$266$	26.1807	1.60524
$267$	12.1970	0.746442
$268$	−14.9192	−0.911337
$269$	−28.5894	−1.74313	−0.871564	−	0.490282i	$-0.836894\pi$
$269$	−28.5894	−1.74313	−0.871564	+	0.490282i	$0.836894\pi$
$270$	−9.88578	−0.601629
$271$	21.7801	1.32305	0.661525	−	0.749923i	$-0.269910\pi$
$271$	21.7801	1.32305	0.661525	+	0.749923i	$0.269910\pi$
$272$	11.7998	0.715465
$273$	2.49636	0.151086
$274$	10.3339	0.624293
$275$	−0.774247	−0.0466888
$276$	8.22489	0.495080
$277$	9.32234	0.560125	0.280063	−	0.959982i	$-0.409645\pi$
$277$	9.32234	0.560125	0.280063	+	0.959982i	$0.409645\pi$
$278$	21.3754	1.28201
$279$	62.9898	3.77110
$280$	1.04939	0.0627132
$281$	−8.41066	−0.501738	−0.250869	−	0.968021i	$-0.580716\pi$
$281$	−8.41066	−0.501738	−0.250869	+	0.968021i	$0.580716\pi$
$282$	26.5145	1.57892
$283$	14.7994	0.879734	0.439867	−	0.898063i	$-0.355026\pi$
$283$	14.7994	0.879734	0.439867	+	0.898063i	$0.355026\pi$
$284$	−2.15430	−0.127834
$285$	5.39149	0.319365
$286$	−0.106342	−0.00628816
$287$	−18.7079	−1.10429
$288$	−56.6265	−3.33675
$289$	4.86373	0.286102
$290$	0.734251	0.0431167
$291$	48.5908	2.84845
$292$	−34.5207	−2.02017
$293$	−10.9419	−0.639230	−0.319615	−	0.947547i	$-0.603554\pi$
$293$	−10.9419	−0.639230	−0.319615	+	0.947547i	$0.603554\pi$
$294$	−5.42250	−0.316247
$295$	2.46885	0.143742
$296$	9.45053	0.549301
$297$	2.13519	0.123896
$298$	−35.7259	−2.06954
$299$	−0.313547	−0.0181329
$300$	−40.1549	−2.31835
$301$	−10.0498	−0.579260
$302$	9.69294	0.557766
$303$	−4.10719	−0.235952
$304$	12.4003	0.711205
$305$	−3.60224	−0.206264
$306$	−72.1290	−4.12334
$307$	−4.26400	−0.243359	−0.121680	−	0.992569i	$-0.538828\pi$
$307$	−4.26400	−0.243359	−0.121680	+	0.992569i	$0.538828\pi$
$308$	−1.01684	−0.0579397
$309$	−2.22726	−0.126704
$310$	−6.41209	−0.364182
$311$	−10.4457	−0.592324	−0.296162	−	0.955138i	$-0.595707\pi$
$311$	−10.4457	−0.592324	−0.296162	+	0.955138i	$0.595707\pi$
$312$	−1.22936	−0.0695988
$313$	33.4362	1.88992	0.944962	−	0.327180i	$-0.106098\pi$
$313$	33.4362	1.88992	0.944962	+	0.327180i	$0.106098\pi$
$314$	40.7450	2.29937
$315$	6.16956	0.347615
$316$	15.7909	0.888306
$317$	18.9342	1.06345	0.531726	−	0.846917i	$-0.321544\pi$
$317$	18.9342	1.06345	0.531726	+	0.846917i	$0.321544\pi$
$318$	40.2970	2.25975
$319$	−0.158588	−0.00887923
$320$	4.03152	0.225369
$321$	3.45017	0.192570
$322$	−5.32794	−0.296915
$323$	22.9765	1.27844
$324$	55.0463	3.05813
$325$	1.53078	0.0849122
$326$	1.40687	0.0779195
$327$	−45.6468	−2.52427
$328$	9.21292	0.508698
$329$	−9.66499	−0.532848
$330$	−0.372127	−0.0204849
$331$	−28.4961	−1.56629	−0.783143	−	0.621842i	$-0.786385\pi$
$331$	−28.4961	−1.56629	−0.783143	+	0.621842i	$0.786385\pi$
$332$	−26.6679	−1.46359
$333$	55.5612	3.04474
$334$	22.4730	1.22967
$335$	1.99024	0.108738
$336$	20.0916	1.09609
$337$	−20.4501	−1.11399	−0.556994	−	0.830517i	$-0.688045\pi$
$337$	−20.4501	−1.11399	−0.556994	+	0.830517i	$0.688045\pi$
$338$	−27.5917	−1.50079
$339$	−23.1753	−1.25871
$340$	4.13169	0.224072
$341$	1.38492	0.0749978
$342$	−75.7999	−4.09879
$343$	19.4157	1.04835
$344$	4.94913	0.266839
$345$	−1.09721	−0.0590716
$346$	34.4955	1.85449
$347$	−23.1503	−1.24277	−0.621387	−	0.783504i	$-0.713430\pi$
$347$	−23.1503	−1.24277	−0.621387	+	0.783504i	$0.713430\pi$
$348$	−8.22489	−0.440901
$349$	4.68704	0.250892	0.125446	−	0.992100i	$-0.459964\pi$
$349$	4.68704	0.250892	0.125446	+	0.992100i	$0.459964\pi$
$350$	26.0117	1.39038
$351$	−4.22153	−0.225328
$352$	−1.24502	−0.0663596
$353$	13.2422	0.704809	0.352404	−	0.935848i	$-0.385364\pi$
$353$	13.2422	0.704809	0.352404	+	0.935848i	$0.385364\pi$
$354$	−49.1465	−2.61210
$355$	0.287385	0.0152528
$356$	9.82266	0.520600
$357$	37.2276	1.97030
$358$	10.4122	0.550304
$359$	−7.78491	−0.410872	−0.205436	−	0.978671i	$-0.565861\pi$
$359$	−7.78491	−0.410872	−0.205436	+	0.978671i	$0.565861\pi$
$360$	−3.03827	−0.160131
$361$	5.14581	0.270832
$362$	−4.28470	−0.225199
$363$	−35.0732	−1.84086
$364$	2.01041	0.105374
$365$	4.60509	0.241041
$366$	71.7084	3.74826
$367$	−7.69335	−0.401590	−0.200795	−	0.979633i	$-0.564352\pi$
$367$	−7.69335	−0.401590	−0.200795	+	0.979633i	$0.564352\pi$
$368$	−2.52354	−0.131549
$369$	54.1643	2.81968
$370$	−5.65589	−0.294036
$371$	−14.6890	−0.762613
$372$	71.8266	3.72404
$373$	−10.7967	−0.559032	−0.279516	−	0.960141i	$-0.590174\pi$
$373$	−10.7967	−0.559032	−0.279516	+	0.960141i	$0.590174\pi$
$374$	−1.58586	−0.0820030
$375$	10.8427	0.559916
$376$	4.75964	0.245459
$377$	0.313547	0.0161485
$378$	−71.7342	−3.68961
$379$	21.1883	1.08837	0.544184	−	0.838966i	$-0.316839\pi$
$379$	21.1883	1.08837	0.544184	+	0.838966i	$0.316839\pi$
$380$	4.34197	0.222738
$381$	−50.9517	−2.61034
$382$	31.8870	1.63148
$383$	−24.7991	−1.26717	−0.633587	−	0.773671i	$-0.718418\pi$
$383$	−24.7991	−1.26717	−0.633587	+	0.773671i	$0.718418\pi$
$384$	−30.0761	−1.53482
$385$	0.135647	0.00691320
$386$	−6.78244	−0.345217
$387$	29.0968	1.47907
$388$	39.1320	1.98663
$389$	32.3160	1.63849	0.819243	−	0.573447i	$-0.194394\pi$
$389$	32.3160	1.63849	0.819243	+	0.573447i	$0.194394\pi$
$390$	0.735740	0.0372556
$391$	−4.67587	−0.236469
$392$	−0.973397	−0.0491640
$393$	2.47536	0.124866
$394$	43.5336	2.19319
$395$	−2.10651	−0.105990
$396$	2.94401	0.147942
$397$	−23.1437	−1.16155	−0.580774	−	0.814065i	$-0.697250\pi$
$397$	−23.1437	−1.16155	−0.580774	+	0.814065i	$0.697250\pi$
$398$	−33.4694	−1.67767
$399$	39.1223	1.95856
$400$	12.3203	0.616013
$401$	30.6044	1.52831	0.764156	−	0.645031i	$-0.223156\pi$
$401$	30.6044	1.52831	0.764156	+	0.645031i	$0.223156\pi$
$402$	−39.6188	−1.97601
$403$	−2.73816	−0.136397
$404$	−3.30767	−0.164563
$405$	−7.34322	−0.364887
$406$	5.32794	0.264421
$407$	1.22159	0.0605522
$408$	−18.3332	−0.907628
$409$	29.2880	1.44820	0.724100	−	0.689695i	$-0.242255\pi$
$409$	29.2880	1.44820	0.724100	+	0.689695i	$0.242255\pi$
$410$	−5.51369	−0.272302
$411$	15.4421	0.761704
$412$	−1.79369	−0.0883690
$413$	17.9147	0.881526
$414$	15.4258	0.758137
$415$	3.55751	0.174632
$416$	2.46155	0.120687
$417$	31.9416	1.56419
$418$	−1.66657	−0.0815147
$419$	−0.0155271	−0.000758550 0	−0.000379275	−	1.00000i	$-0.500121\pi$
$419$	−0.0155271	−0.000758550 0	−0.000379275		1.00000i	$0.500121\pi$
$420$	7.03508	0.343277
$421$	−6.96739	−0.339570	−0.169785	−	0.985481i	$-0.554307\pi$
$421$	−6.96739	−0.339570	−0.169785	+	0.985481i	$0.554307\pi$
$422$	37.3198	1.81670
$423$	27.9827	1.36057
$424$	7.23375	0.351302
$425$	22.8282	1.10733
$426$	−5.72086	−0.277177
$427$	−26.1389	−1.26495
$428$	2.77855	0.134306
$429$	−0.158910	−0.00767222
$430$	−2.96193	−0.142837
$431$	−13.7066	−0.660222	−0.330111	−	0.943942i	$-0.607086\pi$
$431$	−13.7066	−0.660222	−0.330111	+	0.943942i	$0.607086\pi$
$432$	−33.9764	−1.63469
$433$	−38.4571	−1.84813	−0.924065	−	0.382235i	$-0.875155\pi$
$433$	−38.4571	−1.84813	−0.924065	+	0.382235i	$0.875155\pi$
$434$	−46.5281	−2.23342
$435$	1.09721	0.0526070
$436$	−36.7610	−1.76053
$437$	−4.91384	−0.235061
$438$	−91.6716	−4.38024
$439$	−12.7407	−0.608082	−0.304041	−	0.952659i	$-0.598336\pi$
$439$	−12.7407	−0.608082	−0.304041	+	0.952659i	$0.598336\pi$
$440$	−0.0668008	−0.00318460
$441$	−5.72276	−0.272512
$442$	3.13544	0.149138
$443$	−11.6666	−0.554296	−0.277148	−	0.960827i	$-0.589389\pi$
$443$	−11.6666	−0.554296	−0.277148	+	0.960827i	$0.589389\pi$
$444$	63.3559	3.00674
$445$	−1.31035	−0.0621165
$446$	−28.7868	−1.36309
$447$	−53.3859	−2.52507
$448$	29.2539	1.38212
$449$	25.7849	1.21686	0.608432	−	0.793606i	$-0.291799\pi$
$449$	25.7849	1.21686	0.608432	+	0.793606i	$0.291799\pi$
$450$	−75.3107	−3.55018
$451$	1.19088	0.0560764
$452$	−18.6639	−0.877876
$453$	14.4844	0.680534
$454$	−59.8990	−2.81120
$455$	−0.268190	−0.0125729
$456$	−19.2662	−0.902223
$457$	−34.4433	−1.61119	−0.805594	−	0.592468i	$-0.798154\pi$
$457$	−34.4433	−1.61119	−0.805594	+	0.592468i	$0.798154\pi$
$458$	−32.5503	−1.52098
$459$	−62.9548	−2.93848
$460$	−0.883620	−0.0411990
$461$	−14.4672	−0.673805	−0.336902	−	0.941540i	$-0.609379\pi$
$461$	−14.4672	−0.673805	−0.336902	+	0.941540i	$0.609379\pi$
$462$	−2.70027	−0.125628
$463$	−8.72685	−0.405571	−0.202786	−	0.979223i	$-0.564999\pi$
$463$	−8.72685	−0.405571	−0.202786	+	0.979223i	$0.564999\pi$
$464$	2.52354	0.117153
$465$	−9.58172	−0.444342
$466$	48.5847	2.25064
$467$	14.1065	0.652773	0.326386	−	0.945236i	$-0.394169\pi$
$467$	14.1065	0.652773	0.326386	+	0.945236i	$0.394169\pi$
$468$	−5.82066	−0.269060
$469$	14.4417	0.666858
$470$	−2.84852	−0.131392
$471$	60.8861	2.80548
$472$	−8.82231	−0.406080
$473$	0.639735	0.0294151
$474$	41.9335	1.92607
$475$	23.9900	1.10074
$476$	29.9808	1.37417
$477$	42.5284	1.94724
$478$	−52.7881	−2.41447
$479$	0.449722	0.0205483	0.0102742	−	0.999947i	$-0.496730\pi$
$479$	0.449722	0.0205483	0.0102742	+	0.999947i	$0.496730\pi$
$480$	8.61377	0.393163
$481$	−2.41524	−0.110125
$482$	−29.2189	−1.33088
$483$	−7.96165	−0.362268
$484$	−28.2457	−1.28390
$485$	−5.22023	−0.237039
$486$	59.7971	2.71245
$487$	17.8669	0.809627	0.404813	−	0.914399i	$-0.367337\pi$
$487$	17.8669	0.809627	0.404813	+	0.914399i	$0.367337\pi$
$488$	12.8724	0.582707
$489$	2.10232	0.0950702
$490$	0.582553	0.0263170
$491$	−0.575247	−0.0259605	−0.0129803	−	0.999916i	$-0.504132\pi$
$491$	−0.575247	−0.0259605	−0.0129803	+	0.999916i	$0.504132\pi$
$492$	61.7630	2.78449
$493$	4.67587	0.210590
$494$	3.29501	0.148250
$495$	−0.392733	−0.0176520
$496$	−22.0377	−0.989522
$497$	2.08535	0.0935408
$498$	−70.8180	−3.17343
$499$	−10.9754	−0.491327	−0.245663	−	0.969355i	$-0.579006\pi$
$499$	−10.9754	−0.491327	−0.245663	+	0.969355i	$0.579006\pi$
$500$	8.73205	0.390509
$501$	33.5819	1.50033
$502$	18.2940	0.816501
$503$	40.4773	1.80479	0.902396	−	0.430907i	$-0.141806\pi$
$503$	40.4773	1.80479	0.902396	+	0.430907i	$0.141806\pi$
$504$	−22.0466	−0.982033
$505$	0.441246	0.0196352
$506$	0.339159	0.0150774
$507$	−41.2309	−1.83113
$508$	−41.0333	−1.82056
$509$	24.3146	1.07772	0.538862	−	0.842394i	$-0.318854\pi$
$509$	24.3146	1.07772	0.538862	+	0.842394i	$0.318854\pi$
$510$	10.9719	0.485845
$511$	33.4159	1.47823
$512$	26.0036	1.14921
$513$	−66.1587	−2.92098
$514$	25.3195	1.11680
$515$	0.239280	0.0105439
$516$	33.1788	1.46061
$517$	0.615240	0.0270582
$518$	−41.0409	−1.80323
$519$	51.5473	2.26268
$520$	0.132073	0.00579179
$521$	40.6841	1.78240	0.891202	−	0.453607i	$-0.149863\pi$
$521$	40.6841	1.78240	0.891202	+	0.453607i	$0.149863\pi$
$522$	−15.4258	−0.675169
$523$	−22.5315	−0.985233	−0.492616	−	0.870247i	$-0.663959\pi$
$523$	−22.5315	−0.985233	−0.492616	+	0.870247i	$0.663959\pi$
$524$	1.99350	0.0870865
$525$	38.8698	1.69642
$526$	46.7106	2.03668
$527$	−40.8336	−1.77874
$528$	−1.27896	−0.0556597
$529$	1.00000	0.0434783
$530$	−4.32921	−0.188049
$531$	−51.8679	−2.25087
$532$	31.5066	1.36598
$533$	−2.35451	−0.101985
$534$	26.0846	1.12879
$535$	−0.370661	−0.0160251
$536$	−7.11200	−0.307192
$537$	15.5592	0.671430
$538$	−61.1418	−2.63601
$539$	−0.125823	−0.00541959
$540$	−11.8969	−0.511959
$541$	−43.3803	−1.86506	−0.932532	−	0.361088i	$-0.882406\pi$
$541$	−43.3803	−1.86506	−0.932532	+	0.361088i	$0.882406\pi$
$542$	46.5794	2.00075
$543$	−6.40271	−0.274767
$544$	36.7085	1.57387
$545$	4.90394	0.210062
$546$	5.33875	0.228477
$547$	−33.1997	−1.41952	−0.709758	−	0.704446i	$-0.751196\pi$
$547$	−33.1997	−1.41952	−0.709758	+	0.704446i	$0.751196\pi$
$548$	12.4361	0.531244
$549$	75.6791	3.22991
$550$	−1.65582	−0.0706042
$551$	4.91384	0.209337
$552$	3.92081	0.166881
$553$	−15.2855	−0.650005
$554$	19.9369	0.847038
$555$	−8.45172	−0.358755
$556$	25.7238	1.09093
$557$	−4.50127	−0.190725	−0.0953625	−	0.995443i	$-0.530401\pi$
$557$	−4.50127	−0.190725	−0.0953625	+	0.995443i	$0.530401\pi$
$558$	134.711	5.70277
$559$	−1.26483	−0.0534967
$560$	−2.15849	−0.0912128
$561$	−2.36979	−0.100052
$562$	−17.9872	−0.758743
$563$	46.9636	1.97928	0.989641	−	0.143568i	$-0.0458575\pi$
$563$	46.9636	1.97928	0.989641	+	0.143568i	$0.0458575\pi$
$564$	31.9084	1.34358
$565$	2.48978	0.104746
$566$	31.6502	1.33036
$567$	−53.2846	−2.23774
$568$	−1.02696	−0.0430901
$569$	−0.207925	−0.00871668	−0.00435834	−	0.999991i	$-0.501387\pi$
$569$	−0.207925	−0.00871668	−0.00435834	+	0.999991i	$0.501387\pi$
$570$	11.5303	0.482952
$571$	−11.0902	−0.464111	−0.232055	−	0.972703i	$-0.574545\pi$
$571$	−11.0902	−0.464111	−0.232055	+	0.972703i	$0.574545\pi$
$572$	−0.127976	−0.00535093
$573$	47.6494	1.99058
$574$	−40.0090	−1.66994
$575$	−4.88212	−0.203599
$576$	−84.6978	−3.52907
$577$	33.8313	1.40841	0.704207	−	0.709994i	$-0.251303\pi$
$577$	33.8313	1.40841	0.704207	+	0.709994i	$0.251303\pi$
$578$	10.4017	0.432652
$579$	−10.1351	−0.421202
$580$	0.883620	0.0366903
$581$	25.8144	1.07096
$582$	103.917	4.30750
$583$	0.935049	0.0387258
$584$	−16.4560	−0.680956
$585$	0.776480	0.0321035
$586$	−23.4004	−0.966663
$587$	10.3629	0.427723	0.213862	−	0.976864i	$-0.431396\pi$
$587$	10.3629	0.427723	0.213862	+	0.976864i	$0.431396\pi$
$588$	−6.52561	−0.269111
$589$	−42.9117	−1.76815
$590$	5.27993	0.217371
$591$	65.0531	2.67593
$592$	−19.4387	−0.798926
$593$	13.5687	0.557200	0.278600	−	0.960407i	$-0.410130\pi$
$593$	13.5687	0.557200	0.278600	+	0.960407i	$0.410130\pi$
$594$	4.56635	0.187360
$595$	−3.99946	−0.163962
$596$	−42.9936	−1.76109
$597$	−50.0139	−2.04693
$598$	−0.670557	−0.0274211
$599$	−27.9553	−1.14222	−0.571110	−	0.820873i	$-0.693487\pi$
$599$	−27.9553	−1.14222	−0.571110	+	0.820873i	$0.693487\pi$
$600$	−19.1419	−0.781464
$601$	−33.7230	−1.37559	−0.687796	−	0.725904i	$-0.741422\pi$
$601$	−33.7230	−1.37559	−0.687796	+	0.725904i	$0.741422\pi$
$602$	−21.4926	−0.875974
$603$	−41.8127	−1.70274
$604$	11.6648	0.474633
$605$	3.76800	0.153191
$606$	−8.78371	−0.356814
$607$	−46.2277	−1.87633	−0.938163	−	0.346194i	$-0.887474\pi$
$607$	−46.2277	−1.87633	−0.938163	+	0.346194i	$0.887474\pi$
$608$	38.5768	1.56449
$609$	7.96165	0.322623
$610$	−7.70381	−0.311918
$611$	−1.21640	−0.0492104
$612$	−86.8023	−3.50877
$613$	5.12758	0.207101	0.103550	−	0.994624i	$-0.466980\pi$
$613$	5.12758	0.207101	0.103550	+	0.994624i	$0.466980\pi$
$614$	−9.11905	−0.368015
$615$	−8.23922	−0.332238
$616$	−0.484726	−0.0195302
$617$	−12.8558	−0.517553	−0.258777	−	0.965937i	$-0.583319\pi$
$617$	−12.8558	−0.517553	−0.258777	+	0.965937i	$0.583319\pi$
$618$	−4.76325	−0.191606
$619$	−4.23277	−0.170129	−0.0850647	−	0.996375i	$-0.527110\pi$
$619$	−4.23277	−0.170129	−0.0850647	+	0.996375i	$0.527110\pi$
$620$	−7.71651	−0.309903
$621$	13.4638	0.540282
$622$	−22.3394	−0.895729
$623$	−9.50828	−0.380941
$624$	2.52866	0.101227
$625$	23.2458	0.929830
$626$	71.5071	2.85800
$627$	−2.49039	−0.0994567
$628$	49.0338	1.95666
$629$	−36.0179	−1.43613
$630$	13.1943	0.525674
$631$	−41.8169	−1.66470	−0.832351	−	0.554248i	$-0.813006\pi$
$631$	−41.8169	−1.66470	−0.832351	+	0.554248i	$0.813006\pi$
$632$	7.52751	0.299428
$633$	55.7678	2.21657
$634$	40.4930	1.60818
$635$	5.47387	0.217224
$636$	48.4947	1.92294
$637$	0.248768	0.00985653
$638$	−0.339159	−0.0134274
$639$	−6.03764	−0.238845
$640$	3.23115	0.127722
$641$	−32.2839	−1.27514	−0.637569	−	0.770393i	$-0.720060\pi$
$641$	−32.2839	−1.27514	−0.637569	+	0.770393i	$0.720060\pi$
$642$	7.37859	0.291210
$643$	−39.3651	−1.55241	−0.776203	−	0.630483i	$-0.782857\pi$
$643$	−39.3651	−1.55241	−0.776203	+	0.630483i	$0.782857\pi$
$644$	−6.41181	−0.252661
$645$	−4.42607	−0.174276
$646$	49.1378	1.93330
$647$	−22.0399	−0.866479	−0.433239	−	0.901279i	$-0.642630\pi$
$647$	−22.0399	−0.866479	−0.433239	+	0.901279i	$0.642630\pi$
$648$	26.2406	1.03083
$649$	−1.14039	−0.0447642
$650$	3.27374	0.128407
$651$	−69.5278	−2.72501
$652$	1.69308	0.0663059
$653$	−5.30012	−0.207410	−0.103705	−	0.994608i	$-0.533070\pi$
$653$	−5.30012	−0.207410	−0.103705	+	0.994608i	$0.533070\pi$
$654$	−97.6209	−3.81728
$655$	−0.265934	−0.0103909
$656$	−18.9500	−0.739873
$657$	−96.7478	−3.77449
$658$	−20.6697	−0.805789
$659$	0.638640	0.0248779	0.0124389	−	0.999923i	$-0.496040\pi$
$659$	0.638640	0.0248779	0.0124389	+	0.999923i	$0.496040\pi$
$660$	−0.447829	−0.0174317
$661$	22.0446	0.857434	0.428717	−	0.903439i	$-0.358966\pi$
$661$	22.0446	0.857434	0.428717	+	0.903439i	$0.358966\pi$
$662$	−60.9421	−2.36858
$663$	4.68535	0.181964
$664$	−12.7126	−0.493344
$665$	−4.20300	−0.162985
$666$	118.824	4.60434
$667$	−1.00000	−0.0387202
$668$	27.0447	1.04639
$669$	−43.0166	−1.66312
$670$	4.25635	0.164437
$671$	1.66392	0.0642348
$672$	62.5040	2.41115
$673$	−0.261282	−0.0100717	−0.00503584	−	0.999987i	$-0.501603\pi$
$673$	−0.261282	−0.0100717	−0.00503584	+	0.999987i	$0.501603\pi$
$674$	−43.7349	−1.68460
$675$	−65.7318	−2.53002
$676$	−33.2048	−1.27711
$677$	28.9774	1.11369	0.556846	−	0.830616i	$-0.312011\pi$
$677$	28.9774	1.11369	0.556846	+	0.830616i	$0.312011\pi$
$678$	−49.5630	−1.90345
$679$	−37.8796	−1.45368
$680$	1.96958	0.0755299
$681$	−89.5082	−3.42996
$682$	2.96182	0.113414
$683$	17.6353	0.674797	0.337399	−	0.941362i	$-0.390453\pi$
$683$	17.6353	0.674797	0.337399	+	0.941362i	$0.390453\pi$
$684$	−91.2199	−3.48788
$685$	−1.65899	−0.0633866
$686$	41.5228	1.58535
$687$	−48.6406	−1.85575
$688$	−10.1798	−0.388103
$689$	−1.84870	−0.0704300
$690$	−2.34650	−0.0893298
$691$	−23.7385	−0.903053	−0.451527	−	0.892258i	$-0.649120\pi$
$691$	−23.7385	−0.903053	−0.451527	+	0.892258i	$0.649120\pi$
$692$	41.5130	1.57809
$693$	−2.84979	−0.108254
$694$	−49.5096	−1.87936
$695$	−3.43157	−0.130167
$696$	−3.92081	−0.148618
$697$	−35.1124	−1.32998
$698$	10.0238	0.379406
$699$	72.6010	2.74602
$700$	31.3033	1.18315
$701$	−19.1584	−0.723603	−0.361802	−	0.932255i	$-0.617838\pi$
$701$	−19.1584	−0.723603	−0.361802	+	0.932255i	$0.617838\pi$
$702$	−9.02822	−0.340748
$703$	−37.8510	−1.42758
$704$	−1.86220	−0.0701845
$705$	−4.25660	−0.160313
$706$	28.3199	1.06583
$707$	3.20181	0.120417
$708$	−59.1444	−2.22278
$709$	−24.5942	−0.923654	−0.461827	−	0.886970i	$-0.652806\pi$
$709$	−24.5942	−0.923654	−0.461827	+	0.886970i	$0.652806\pi$
$710$	0.614606	0.0230658
$711$	44.2555	1.65971
$712$	4.68246	0.175483
$713$	8.73283	0.327047
$714$	79.6156	2.97954
$715$	0.0170720	0.000638458 0
$716$	12.5304	0.468284
$717$	−78.8823	−2.94592
$718$	−16.6489	−0.621333
$719$	−51.5016	−1.92068	−0.960342	−	0.278825i	$-0.910055\pi$
$719$	−51.5016	−1.92068	−0.960342	+	0.278825i	$0.910055\pi$
$720$	6.24939	0.232901
$721$	1.73629	0.0646627
$722$	11.0049	0.409560
$723$	−43.6624	−1.62382
$724$	−5.15634	−0.191634
$725$	4.88212	0.181318
$726$	−75.0080	−2.78381
$727$	41.4085	1.53575	0.767877	−	0.640597i	$-0.221313\pi$
$727$	41.4085	1.53575	0.767877	+	0.640597i	$0.221313\pi$
$728$	0.958362	0.0355192
$729$	25.1913	0.933013
$730$	9.84851	0.364510
$731$	−18.8622	−0.697643
$732$	86.2961	3.18960
$733$	27.7842	1.02623	0.513116	−	0.858319i	$-0.328491\pi$
$733$	27.7842	1.02623	0.513116	+	0.858319i	$0.328491\pi$
$734$	−16.4531	−0.607296
$735$	0.870520	0.0321096
$736$	−7.85063	−0.289378
$737$	−0.919313	−0.0338633
$738$	115.837	4.26400
$739$	−7.26062	−0.267086	−0.133543	−	0.991043i	$-0.542635\pi$
$739$	−7.26062	−0.267086	−0.133543	+	0.991043i	$0.542635\pi$
$740$	−6.80648	−0.250211
$741$	4.92380	0.180880
$742$	−31.4140	−1.15325
$743$	39.0845	1.43387	0.716936	−	0.697139i	$-0.245544\pi$
$743$	39.0845	1.43387	0.716936	+	0.697139i	$0.245544\pi$
$744$	34.2398	1.25529
$745$	5.73538	0.210128
$746$	−23.0900	−0.845384
$747$	−74.7394	−2.73457
$748$	−1.90847	−0.0697808
$749$	−2.68962	−0.0982767
$750$	23.1884	0.846722
$751$	−5.12605	−0.187052	−0.0935261	−	0.995617i	$-0.529814\pi$
$751$	−5.12605	−0.187052	−0.0935261	+	0.995617i	$0.529814\pi$
$752$	−9.79006	−0.357007
$753$	27.3371	0.996218
$754$	0.670557	0.0244203
$755$	−1.55609	−0.0566319
$756$	−86.3271	−3.13969
$757$	−31.1220	−1.13115	−0.565574	−	0.824697i	$-0.691345\pi$
$757$	−31.1220	−1.13115	−0.565574	+	0.824697i	$0.691345\pi$
$758$	45.3136	1.64586
$759$	0.506812	0.0183961
$760$	2.06982	0.0750802
$761$	11.1825	0.405366	0.202683	−	0.979244i	$-0.435034\pi$
$761$	11.1825	0.405366	0.202683	+	0.979244i	$0.435034\pi$
$762$	−108.966	−3.94743
$763$	35.5845	1.28824
$764$	38.3738	1.38832
$765$	11.5795	0.418657
$766$	−53.0357	−1.91626
$767$	2.25469	0.0814120
$768$	10.7309	0.387219
$769$	36.8803	1.32994	0.664970	−	0.746870i	$-0.268444\pi$
$769$	36.8803	1.32994	0.664970	+	0.746870i	$0.268444\pi$
$770$	0.290096	0.0104543
$771$	37.8355	1.36261
$772$	−8.16220	−0.293764
$773$	52.2607	1.87969	0.939843	−	0.341605i	$-0.110971\pi$
$773$	52.2607	1.87969	0.939843	+	0.341605i	$0.110971\pi$
$774$	62.2268	2.23670
$775$	−42.6348	−1.53149
$776$	18.6542	0.669648
$777$	−61.3282	−2.20014
$778$	69.1115	2.47777
$779$	−36.8994	−1.32206
$780$	0.885412	0.0317028
$781$	−0.132746	−0.00475004
$782$	−9.99988	−0.357595
$783$	−13.4638	−0.481156
$784$	2.00217	0.0715062
$785$	−6.54114	−0.233463
$786$	5.29385	0.188825
$787$	−26.7116	−0.952167	−0.476083	−	0.879400i	$-0.657944\pi$
$787$	−26.7116	−0.952167	−0.476083	+	0.879400i	$0.657944\pi$
$788$	52.3897	1.86630
$789$	69.8006	2.48497
$790$	−4.50502	−0.160281
$791$	18.0666	0.642373
$792$	1.40341	0.0498680
$793$	−3.28976	−0.116823
$794$	−49.4954	−1.75653
$795$	−6.46923	−0.229440
$796$	−40.2781	−1.42762
$797$	27.4579	0.972610	0.486305	−	0.873789i	$-0.338344\pi$
$797$	27.4579	0.972610	0.486305	+	0.873789i	$0.338344\pi$
$798$	83.6675	2.96180
$799$	−18.1400	−0.641746
$800$	38.3278	1.35509
$801$	27.5290	0.972689
$802$	65.4511	2.31116
$803$	−2.12714	−0.0750652
$804$	−47.6785	−1.68149
$805$	0.855340	0.0301468
$806$	−5.85586	−0.206264
$807$	−91.3654	−3.21621
$808$	−1.57677	−0.0554705
$809$	20.1703	0.709149	0.354575	−	0.935028i	$-0.384626\pi$
$809$	20.1703	0.709149	0.354575	+	0.935028i	$0.384626\pi$
$810$	−15.7043	−0.551793
$811$	39.3120	1.38043	0.690216	−	0.723604i	$-0.257516\pi$
$811$	39.3120	1.38043	0.690216	+	0.723604i	$0.257516\pi$
$812$	6.41181	0.225011
$813$	69.6045	2.44114
$814$	2.61252	0.0915688
$815$	−0.225857	−0.00791144
$816$	37.7094	1.32009
$817$	−19.8222	−0.693489
$818$	62.6358	2.19001
$819$	5.63437	0.196881
$820$	−6.63535	−0.231716
$821$	−31.6601	−1.10494	−0.552472	−	0.833531i	$-0.686315\pi$
$821$	−31.6601	−1.10494	−0.552472	+	0.833531i	$0.686315\pi$
$822$	33.0248	1.15187
$823$	−9.48598	−0.330661	−0.165330	−	0.986238i	$-0.552869\pi$
$823$	−9.48598	−0.330661	−0.165330	+	0.986238i	$0.552869\pi$
$824$	−0.855055	−0.0297872
$825$	−2.47432	−0.0861447
$826$	38.3127	1.33307
$827$	−16.0595	−0.558444	−0.279222	−	0.960227i	$-0.590076\pi$
$827$	−16.0595	−0.558444	−0.279222	+	0.960227i	$0.590076\pi$
$828$	18.5639	0.645140
$829$	39.9655	1.38806	0.694030	−	0.719946i	$-0.255834\pi$
$829$	39.9655	1.38806	0.694030	+	0.719946i	$0.255834\pi$
$830$	7.60815	0.264083
$831$	29.7921	1.03348
$832$	3.68180	0.127643
$833$	3.70982	0.128538
$834$	68.3109	2.36541
$835$	−3.60778	−0.124852
$836$	−2.00560	−0.0693653
$837$	117.577	4.06405
$838$	−0.0332065	−0.00114710
$839$	3.17049	0.109457	0.0547287	−	0.998501i	$-0.482571\pi$
$839$	3.17049	0.109457	0.0547287	+	0.998501i	$0.482571\pi$
$840$	3.35363	0.115711
$841$	1.00000	0.0344828
$842$	−14.9006	−0.513507
$843$	−26.8786	−0.925747
$844$	44.9118	1.54593
$845$	4.42954	0.152381
$846$	59.8442	2.05749
$847$	27.3417	0.939472
$848$	−14.8790	−0.510948
$849$	47.2956	1.62318
$850$	48.8207	1.67454
$851$	7.70294	0.264054
$852$	−6.88466	−0.235865
$853$	−32.5145	−1.11328	−0.556638	−	0.830755i	$-0.687909\pi$
$853$	−32.5145	−1.11328	−0.556638	+	0.830755i	$0.687909\pi$
$854$	−55.9011	−1.91290
$855$	12.1688	0.416164
$856$	1.32454	0.0452717
$857$	24.1199	0.823918	0.411959	−	0.911202i	$-0.364845\pi$
$857$	24.1199	0.823918	0.411959	+	0.911202i	$0.364845\pi$
$858$	−0.339846	−0.0116022
$859$	−46.6111	−1.59035	−0.795174	−	0.606381i	$-0.792621\pi$
$859$	−46.6111	−1.59035	−0.795174	+	0.606381i	$0.792621\pi$
$860$	−3.56448	−0.121548
$861$	−59.7863	−2.03751
$862$	−29.3131	−0.998407
$863$	−18.7605	−0.638614	−0.319307	−	0.947651i	$-0.603450\pi$
$863$	−18.7605	−0.638614	−0.319307	+	0.947651i	$0.603450\pi$
$864$	−105.699	−3.59596
$865$	−5.53786	−0.188293
$866$	−82.2450	−2.79480
$867$	15.5434	0.527882
$868$	−55.9933	−1.90054
$869$	0.973022	0.0330075
$870$	2.34650	0.0795539
$871$	1.81759	0.0615867
$872$	−17.5240	−0.593437
$873$	109.671	3.71181
$874$	−10.5088	−0.355466
$875$	−8.45258	−0.285749
$876$	−110.320	−3.72738
$877$	3.96746	0.133972	0.0669858	−	0.997754i	$-0.478662\pi$
$877$	3.96746	0.133972	0.0669858	+	0.997754i	$0.478662\pi$
$878$	−27.2475	−0.919559
$879$	−34.9677	−1.17943
$880$	0.137402	0.00463182
$881$	43.8307	1.47669	0.738346	−	0.674422i	$-0.235607\pi$
$881$	43.8307	1.47669	0.738346	+	0.674422i	$0.235607\pi$
$882$	−12.2388	−0.412101
$883$	−40.1624	−1.35157	−0.675786	−	0.737098i	$-0.736196\pi$
$883$	−40.1624	−1.35157	−0.675786	+	0.737098i	$0.736196\pi$
$884$	3.77328	0.126909
$885$	7.88990	0.265216
$886$	−24.9504	−0.838223
$887$	44.7250	1.50172	0.750860	−	0.660462i	$-0.229639\pi$
$887$	44.7250	1.50172	0.750860	+	0.660462i	$0.229639\pi$
$888$	30.2018	1.01351
$889$	39.7200	1.33217
$890$	−2.80233	−0.0939344
$891$	3.39191	0.113633
$892$	−34.6429	−1.15993
$893$	−19.0632	−0.637925
$894$	−114.172	−3.81848
$895$	−1.67157	−0.0558743
$896$	23.4462	0.783282
$897$	−1.00203	−0.0334567
$898$	55.1440	1.84018
$899$	−8.73283	−0.291256
$900$	−90.6312	−3.02104
$901$	−27.5693	−0.918468
$902$	2.54684	0.0848004
$903$	−32.1169	−1.06878
$904$	−8.89708	−0.295913
$905$	0.687859	0.0228652
$906$	30.9765	1.02912
$907$	1.46051	0.0484955	0.0242477	−	0.999706i	$-0.492281\pi$
$907$	1.46051	0.0484955	0.0242477	+	0.999706i	$0.492281\pi$
$908$	−72.0843	−2.39220
$909$	−9.27009	−0.307469
$910$	−0.573555	−0.0190131
$911$	3.68832	0.122199	0.0610997	−	0.998132i	$-0.480539\pi$
$911$	3.68832	0.122199	0.0610997	+	0.998132i	$0.480539\pi$
$912$	39.6285	1.31223
$913$	−1.64326	−0.0543838
$914$	−73.6609	−2.43649
$915$	−11.5120	−0.380574
$916$	−39.1720	−1.29428
$917$	−1.92970	−0.0637243
$918$	−134.636	−4.44365
$919$	37.3186	1.23103	0.615514	−	0.788126i	$-0.288948\pi$
$919$	37.3186	1.23103	0.615514	+	0.788126i	$0.288948\pi$
$920$	−0.421222	−0.0138873
$921$	−13.6268	−0.449018
$922$	−30.9398	−1.01895
$923$	0.262455	0.00863883
$924$	−3.24958	−0.106903
$925$	−37.6067	−1.23650
$926$	−18.6634	−0.613317
$927$	−5.02701	−0.165109
$928$	7.85063	0.257710
$929$	30.7613	1.00925	0.504623	−	0.863340i	$-0.331631\pi$
$929$	30.7613	1.00925	0.504623	+	0.863340i	$0.331631\pi$
$930$	−20.4916	−0.671946
$931$	3.89863	0.127772
$932$	58.4683	1.91519
$933$	−33.3823	−1.09289
$934$	30.1685	0.987142
$935$	0.254592	0.00832604
$936$	−2.77471	−0.0906942
$937$	3.14121	0.102619	0.0513095	−	0.998683i	$-0.483661\pi$
$937$	3.14121	0.102619	0.0513095	+	0.998683i	$0.483661\pi$
$938$	30.8853	1.00844
$939$	106.855	3.48707
$940$	−3.42799	−0.111809
$941$	31.4897	1.02654	0.513268	−	0.858229i	$-0.328435\pi$
$941$	31.4897	1.02654	0.513268	+	0.858229i	$0.328435\pi$
$942$	130.212	4.24254
$943$	7.50928	0.244536
$944$	18.1466	0.590620
$945$	11.5161	0.374619
$946$	1.36815	0.0444823
$947$	−29.8197	−0.969010	−0.484505	−	0.874789i	$-0.661000\pi$
$947$	−29.8197	−0.969010	−0.484505	+	0.874789i	$0.661000\pi$
$948$	50.4641	1.63900
$949$	4.20561	0.136520
$950$	51.3053	1.66456
$951$	60.5095	1.96216
$952$	14.2918	0.463202
$953$	49.6273	1.60759	0.803793	−	0.594910i	$-0.202812\pi$
$953$	49.6273	1.60759	0.803793	+	0.594910i	$0.202812\pi$
$954$	90.9519	2.94468
$955$	−5.11909	−0.165650
$956$	−63.5268	−2.05460
$957$	−0.506812	−0.0163829
$958$	0.961782	0.0310738
$959$	−12.0381	−0.388730
$960$	12.8838	0.415824
$961$	45.2624	1.46008
$962$	−5.16526	−0.166535
$963$	7.78717	0.250938
$964$	−35.1629	−1.13252
$965$	1.08884	0.0350511
$966$	−17.0269	−0.547832
$967$	19.1279	0.615111	0.307555	−	0.951530i	$-0.400489\pi$
$967$	19.1279	0.615111	0.307555	+	0.951530i	$0.400489\pi$
$968$	−13.4647	−0.432773
$969$	73.4276	2.35883
$970$	−11.1641	−0.358457
$971$	−3.01449	−0.0967394	−0.0483697	−	0.998830i	$-0.515403\pi$
$971$	−3.01449	−0.0967394	−0.0483697	+	0.998830i	$0.515403\pi$
$972$	71.9616	2.30817
$973$	−24.9005	−0.798273
$974$	38.2104	1.22434
$975$	4.89202	0.156670
$976$	−26.4772	−0.847514
$977$	−17.9958	−0.575736	−0.287868	−	0.957670i	$-0.592947\pi$
$977$	−17.9958	−0.575736	−0.287868	+	0.957670i	$0.592947\pi$
$978$	4.49605	0.143768
$979$	0.605265	0.0193444
$980$	0.701062	0.0223946
$981$	−103.026	−3.28938
$982$	−1.23023	−0.0392583
$983$	36.1164	1.15193	0.575967	−	0.817473i	$-0.304625\pi$
$983$	36.1164	1.15193	0.575967	+	0.817473i	$0.304625\pi$
$984$	29.4424	0.938590
$985$	−6.98882	−0.222682
$986$	9.99988	0.318461
$987$	−30.8871	−0.983149
$988$	3.96532	0.126154
$989$	4.03395	0.128272
$990$	−0.839905	−0.0266939
$991$	57.0453	1.81210	0.906052	−	0.423165i	$-0.139081\pi$
$991$	57.0453	1.81210	0.906052	+	0.423165i	$0.139081\pi$
$992$	−68.5583	−2.17673
$993$	−91.0670	−2.88993
$994$	4.45977	0.141455
$995$	5.37312	0.170339
$996$	−85.2246	−2.70044
$997$	27.0324	0.856124	0.428062	−	0.903749i	$-0.359196\pi$
$997$	27.0324	0.856124	0.428062	+	0.903749i	$0.359196\pi$
$998$	−23.4722	−0.742999
$999$	103.711	3.28126

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.d.1.13	✓	16
3.2	odd	2		6003.2.a.q.1.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.d.1.13	✓	16	1.1	even	1	trivial
6003.2.a.q.1.4		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)

\(f(q)\)	\(=\)	\(q+2.13862 q^{2} +3.19578 q^{3} +2.57368 q^{4} -0.343330 q^{5} +6.83454 q^{6} -2.49131 q^{7} +1.22687 q^{8} +7.21299 q^{9} +O(q^{10})\)	\(q+2.13862 q^{2} +3.19578 q^{3} +2.57368 q^{4} -0.343330 q^{5} +6.83454 q^{6} -2.49131 q^{7} +1.22687 q^{8} +7.21299 q^{9} -0.734251 q^{10} +0.158588 q^{11} +8.22489 q^{12} -0.313547 q^{13} -5.32794 q^{14} -1.09721 q^{15} -2.52354 q^{16} -4.67587 q^{17} +15.4258 q^{18} -4.91384 q^{19} -0.883620 q^{20} -7.96165 q^{21} +0.339159 q^{22} +1.00000 q^{23} +3.92081 q^{24} -4.88212 q^{25} -0.670557 q^{26} +13.4638 q^{27} -6.41181 q^{28} -1.00000 q^{29} -2.34650 q^{30} +8.73283 q^{31} -7.85063 q^{32} +0.506812 q^{33} -9.99988 q^{34} +0.855340 q^{35} +18.5639 q^{36} +7.70294 q^{37} -10.5088 q^{38} -1.00203 q^{39} -0.421222 q^{40} +7.50928 q^{41} -17.0269 q^{42} +4.03395 q^{43} +0.408154 q^{44} -2.47644 q^{45} +2.13862 q^{46} +3.87949 q^{47} -8.06468 q^{48} -0.793397 q^{49} -10.4410 q^{50} -14.9430 q^{51} -0.806969 q^{52} +5.89609 q^{53} +28.7938 q^{54} -0.0544481 q^{55} -3.05651 q^{56} -15.7035 q^{57} -2.13862 q^{58} -7.19090 q^{59} -2.82385 q^{60} +10.4921 q^{61} +18.6762 q^{62} -17.9698 q^{63} -11.7424 q^{64} +0.107650 q^{65} +1.08388 q^{66} -5.79686 q^{67} -12.0342 q^{68} +3.19578 q^{69} +1.82924 q^{70} -0.837052 q^{71} +8.84941 q^{72} -13.4130 q^{73} +16.4736 q^{74} -15.6022 q^{75} -12.6466 q^{76} -0.395091 q^{77} -2.14295 q^{78} +6.13553 q^{79} +0.866409 q^{80} +21.3882 q^{81} +16.0595 q^{82} -10.3618 q^{83} -20.4907 q^{84} +1.60537 q^{85} +8.62706 q^{86} -3.19578 q^{87} +0.194567 q^{88} +3.81659 q^{89} -5.29614 q^{90} +0.781142 q^{91} +2.57368 q^{92} +27.9082 q^{93} +8.29673 q^{94} +1.68707 q^{95} -25.0889 q^{96} +15.2047 q^{97} -1.69677 q^{98} +1.14389 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9}+O(q^{10}) \) 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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