LMFDB - Embedded newform 1502.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1502,2,Mod(1,1502)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1502, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1502.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1502 = 2 \cdot 751 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1502.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:	$11.9935303836$
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} - 25 x^{14} + 59 x^{13} + 273 x^{12} - 443 x^{11} - 1620 x^{10} + 1595 x^{9} + \cdots + 864 $ x^16 - 3x^15 - 25x^14 + 59x^13 + 273x^12 - 443x^11 - 1620x^10 + 1595x^9 + 5490x^8 - 2787x^7 - 10540x^6 + 1919x^5 + 10822x^4 + 132x^3 - 5202x^2 - 408*x + 864
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.78209$ of defining polynomial
Character	$\chi$	$=$	1502.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.78209 q^{3} +1.00000 q^{4} -0.612854 q^{5} -2.78209 q^{6} +3.29799 q^{7} +1.00000 q^{8} +4.74004 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.78209 q^{3} +1.00000 q^{4} -0.612854 q^{5} -2.78209 q^{6} +3.29799 q^{7} +1.00000 q^{8} +4.74004 q^{9} -0.612854 q^{10} +0.414098 q^{11} -2.78209 q^{12} +3.22547 q^{13} +3.29799 q^{14} +1.70502 q^{15} +1.00000 q^{16} -3.44237 q^{17} +4.74004 q^{18} +0.166655 q^{19} -0.612854 q^{20} -9.17531 q^{21} +0.414098 q^{22} -5.28363 q^{23} -2.78209 q^{24} -4.62441 q^{25} +3.22547 q^{26} -4.84095 q^{27} +3.29799 q^{28} -0.393601 q^{29} +1.70502 q^{30} +7.14330 q^{31} +1.00000 q^{32} -1.15206 q^{33} -3.44237 q^{34} -2.02119 q^{35} +4.74004 q^{36} +7.24429 q^{37} +0.166655 q^{38} -8.97356 q^{39} -0.612854 q^{40} +1.89387 q^{41} -9.17531 q^{42} +3.22093 q^{43} +0.414098 q^{44} -2.90495 q^{45} -5.28363 q^{46} +11.1036 q^{47} -2.78209 q^{48} +3.87674 q^{49} -4.62441 q^{50} +9.57699 q^{51} +3.22547 q^{52} -0.396855 q^{53} -4.84095 q^{54} -0.253781 q^{55} +3.29799 q^{56} -0.463649 q^{57} -0.393601 q^{58} +10.5344 q^{59} +1.70502 q^{60} +4.54193 q^{61} +7.14330 q^{62} +15.6326 q^{63} +1.00000 q^{64} -1.97674 q^{65} -1.15206 q^{66} +6.02048 q^{67} -3.44237 q^{68} +14.6996 q^{69} -2.02119 q^{70} -11.9882 q^{71} +4.74004 q^{72} +15.7021 q^{73} +7.24429 q^{74} +12.8655 q^{75} +0.166655 q^{76} +1.36569 q^{77} -8.97356 q^{78} +6.42408 q^{79} -0.612854 q^{80} -0.752148 q^{81} +1.89387 q^{82} +1.14168 q^{83} -9.17531 q^{84} +2.10967 q^{85} +3.22093 q^{86} +1.09504 q^{87} +0.414098 q^{88} -12.0973 q^{89} -2.90495 q^{90} +10.6376 q^{91} -5.28363 q^{92} -19.8733 q^{93} +11.1036 q^{94} -0.102135 q^{95} -2.78209 q^{96} -6.57059 q^{97} +3.87674 q^{98} +1.96284 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 13 q^{3} + 16 q^{4} + 4 q^{5} + 13 q^{6} + 7 q^{7} + 16 q^{8} + 21 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 + 13 * q^3 + 16 * q^4 + 4 * q^5 + 13 * q^6 + 7 * q^7 + 16 * q^8 + 21 * q^9	\( 16 q + 16 q^{2} + 13 q^{3} + 16 q^{4} + 4 q^{5} + 13 q^{6} + 7 q^{7} + 16 q^{8} + 21 q^{9} + 4 q^{10} + 4 q^{11} + 13 q^{12} + 17 q^{13} + 7 q^{14} + 8 q^{15} + 16 q^{16} - q^{17} + 21 q^{18} + 23 q^{19} + 4 q^{20} + 9 q^{21} + 4 q^{22} + 15 q^{23} + 13 q^{24} + 24 q^{25} + 17 q^{26} + 31 q^{27} + 7 q^{28} + 4 q^{29} + 8 q^{30} + 42 q^{31} + 16 q^{32} + 3 q^{33} - q^{34} - 13 q^{35} + 21 q^{36} + 31 q^{37} + 23 q^{38} - 2 q^{39} + 4 q^{40} - 9 q^{41} + 9 q^{42} + 13 q^{43} + 4 q^{44} - 2 q^{45} + 15 q^{46} + 18 q^{47} + 13 q^{48} - 9 q^{49} + 24 q^{50} - 2 q^{51} + 17 q^{52} - 14 q^{53} + 31 q^{54} - 2 q^{55} + 7 q^{56} - 18 q^{57} + 4 q^{58} + 4 q^{59} + 8 q^{60} + q^{61} + 42 q^{62} + 17 q^{63} + 16 q^{64} - 32 q^{65} + 3 q^{66} + 5 q^{67} - q^{68} + 6 q^{69} - 13 q^{70} + 9 q^{71} + 21 q^{72} + 28 q^{73} + 31 q^{74} + 16 q^{75} + 23 q^{76} - 30 q^{77} - 2 q^{78} + 10 q^{79} + 4 q^{80} + 12 q^{81} - 9 q^{82} + 3 q^{83} + 9 q^{84} - 7 q^{85} + 13 q^{86} - 22 q^{87} + 4 q^{88} - 17 q^{89} - 2 q^{90} + 12 q^{91} + 15 q^{92} - q^{93} + 18 q^{94} - 4 q^{95} + 13 q^{96} - 17 q^{97} - 9 q^{98} - 10 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 13 * q^3 + 16 * q^4 + 4 * q^5 + 13 * q^6 + 7 * q^7 + 16 * q^8 + 21 * q^9 + 4 * q^10 + 4 * q^11 + 13 * q^12 + 17 * q^13 + 7 * q^14 + 8 * q^15 + 16 * q^16 - q^17 + 21 * q^18 + 23 * q^19 + 4 * q^20 + 9 * q^21 + 4 * q^22 + 15 * q^23 + 13 * q^24 + 24 * q^25 + 17 * q^26 + 31 * q^27 + 7 * q^28 + 4 * q^29 + 8 * q^30 + 42 * q^31 + 16 * q^32 + 3 * q^33 - q^34 - 13 * q^35 + 21 * q^36 + 31 * q^37 + 23 * q^38 - 2 * q^39 + 4 * q^40 - 9 * q^41 + 9 * q^42 + 13 * q^43 + 4 * q^44 - 2 * q^45 + 15 * q^46 + 18 * q^47 + 13 * q^48 - 9 * q^49 + 24 * q^50 - 2 * q^51 + 17 * q^52 - 14 * q^53 + 31 * q^54 - 2 * q^55 + 7 * q^56 - 18 * q^57 + 4 * q^58 + 4 * q^59 + 8 * q^60 + q^61 + 42 * q^62 + 17 * q^63 + 16 * q^64 - 32 * q^65 + 3 * q^66 + 5 * q^67 - q^68 + 6 * q^69 - 13 * q^70 + 9 * q^71 + 21 * q^72 + 28 * q^73 + 31 * q^74 + 16 * q^75 + 23 * q^76 - 30 * q^77 - 2 * q^78 + 10 * q^79 + 4 * q^80 + 12 * q^81 - 9 * q^82 + 3 * q^83 + 9 * q^84 - 7 * q^85 + 13 * q^86 - 22 * q^87 + 4 * q^88 - 17 * q^89 - 2 * q^90 + 12 * q^91 + 15 * q^92 - q^93 + 18 * q^94 - 4 * q^95 + 13 * q^96 - 17 * q^97 - 9 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.78209	−1.60624	−0.803121	−	0.595816i	$-0.796829\pi$
$3$	−2.78209	−1.60624	−0.803121	+	0.595816i	$0.796829\pi$
$4$	1.00000	0.500000
$5$	−0.612854	−0.274077	−0.137038	−	0.990566i	$-0.543758\pi$
$5$	−0.612854	−0.274077	−0.137038	+	0.990566i	$0.543758\pi$
$6$	−2.78209	−1.13578
$7$	3.29799	1.24652	0.623262	−	0.782013i	$-0.285807\pi$
$7$	3.29799	1.24652	0.623262	+	0.782013i	$0.285807\pi$
$8$	1.00000	0.353553
$9$	4.74004	1.58001
$10$	−0.612854	−0.193801
$11$	0.414098	0.124855	0.0624276	−	0.998049i	$-0.480116\pi$
$11$	0.414098	0.124855	0.0624276	+	0.998049i	$0.480116\pi$
$12$	−2.78209	−0.803121
$13$	3.22547	0.894584	0.447292	−	0.894388i	$-0.352388\pi$
$13$	3.22547	0.894584	0.447292	+	0.894388i	$0.352388\pi$
$14$	3.29799	0.881425
$15$	1.70502	0.440233
$16$	1.00000	0.250000
$17$	−3.44237	−0.834897	−0.417449	−	0.908701i	$-0.637076\pi$
$17$	−3.44237	−0.834897	−0.417449	+	0.908701i	$0.637076\pi$
$18$	4.74004	1.11724
$19$	0.166655	0.0382332	0.0191166	−	0.999817i	$-0.493915\pi$
$19$	0.166655	0.0382332	0.0191166	+	0.999817i	$0.493915\pi$
$20$	−0.612854	−0.137038
$21$	−9.17531	−2.00222
$22$	0.414098	0.0882859
$23$	−5.28363	−1.10171	−0.550857	−	0.834600i	$-0.685699\pi$
$23$	−5.28363	−1.10171	−0.550857	+	0.834600i	$0.685699\pi$
$24$	−2.78209	−0.567892
$25$	−4.62441	−0.924882
$26$	3.22547	0.632567
$27$	−4.84095	−0.931641
$28$	3.29799	0.623262
$29$	−0.393601	−0.0730900	−0.0365450	−	0.999332i	$-0.511635\pi$
$29$	−0.393601	−0.0730900	−0.0365450	+	0.999332i	$0.511635\pi$
$30$	1.70502	0.311292
$31$	7.14330	1.28297	0.641487	−	0.767134i	$-0.278318\pi$
$31$	7.14330	1.28297	0.641487	+	0.767134i	$0.278318\pi$
$32$	1.00000	0.176777
$33$	−1.15206	−0.200548
$34$	−3.44237	−0.590362
$35$	−2.02119	−0.341643
$36$	4.74004	0.790006
$37$	7.24429	1.19095	0.595477	−	0.803372i	$-0.296963\pi$
$37$	7.24429	1.19095	0.595477	+	0.803372i	$0.296963\pi$
$38$	0.166655	0.0270350
$39$	−8.97356	−1.43692
$40$	−0.612854	−0.0969007
$41$	1.89387	0.295772	0.147886	−	0.989004i	$-0.452753\pi$
$41$	1.89387	0.295772	0.147886	+	0.989004i	$0.452753\pi$
$42$	−9.17531	−1.41578
$43$	3.22093	0.491187	0.245594	−	0.969373i	$-0.421017\pi$
$43$	3.22093	0.491187	0.245594	+	0.969373i	$0.421017\pi$
$44$	0.414098	0.0624276
$45$	−2.90495	−0.433045
$46$	−5.28363	−0.779029
$47$	11.1036	1.61963	0.809817	−	0.586683i	$-0.199567\pi$
$47$	11.1036	1.61963	0.809817	+	0.586683i	$0.199567\pi$
$48$	−2.78209	−0.401560
$49$	3.87674	0.553820
$50$	−4.62441	−0.653990
$51$	9.57699	1.34105
$52$	3.22547	0.447292
$53$	−0.396855	−0.0545123	−0.0272561	−	0.999628i	$-0.508677\pi$
$53$	−0.396855	−0.0545123	−0.0272561	+	0.999628i	$0.508677\pi$
$54$	−4.84095	−0.658770
$55$	−0.253781	−0.0342199
$56$	3.29799	0.440712
$57$	−0.463649	−0.0614118
$58$	−0.393601	−0.0516824
$59$	10.5344	1.37146	0.685732	−	0.727854i	$-0.259482\pi$
$59$	10.5344	1.37146	0.685732	+	0.727854i	$0.259482\pi$
$60$	1.70502	0.220117
$61$	4.54193	0.581534	0.290767	−	0.956794i	$-0.406089\pi$
$61$	4.54193	0.581534	0.290767	+	0.956794i	$0.406089\pi$
$62$	7.14330	0.907200
$63$	15.6326	1.96952
$64$	1.00000	0.125000
$65$	−1.97674	−0.245185
$66$	−1.15206	−0.141809
$67$	6.02048	0.735519	0.367760	−	0.929921i	$-0.380125\pi$
$67$	6.02048	0.735519	0.367760	+	0.929921i	$0.380125\pi$
$68$	−3.44237	−0.417449
$69$	14.6996	1.76962
$70$	−2.02119	−0.241578
$71$	−11.9882	−1.42274	−0.711370	−	0.702818i	$-0.751925\pi$
$71$	−11.9882	−1.42274	−0.711370	+	0.702818i	$0.751925\pi$
$72$	4.74004	0.558619
$73$	15.7021	1.83779	0.918896	−	0.394501i	$-0.129083\pi$
$73$	15.7021	1.83779	0.918896	+	0.394501i	$0.129083\pi$
$74$	7.24429	0.842132
$75$	12.8655	1.48558
$76$	0.166655	0.0191166
$77$	1.36569	0.155635
$78$	−8.97356	−1.01606
$79$	6.42408	0.722765	0.361383	−	0.932418i	$-0.382305\pi$
$79$	6.42408	0.722765	0.361383	+	0.932418i	$0.382305\pi$
$80$	−0.612854	−0.0685191
$81$	−0.752148	−0.0835720
$82$	1.89387	0.209143
$83$	1.14168	0.125316	0.0626581	−	0.998035i	$-0.480042\pi$
$83$	1.14168	0.125316	0.0626581	+	0.998035i	$0.480042\pi$
$84$	−9.17531	−1.00111
$85$	2.10967	0.228826
$86$	3.22093	0.347322
$87$	1.09504	0.117400
$88$	0.414098	0.0441429
$89$	−12.0973	−1.28231	−0.641155	−	0.767411i	$-0.721544\pi$
$89$	−12.0973	−1.28231	−0.641155	+	0.767411i	$0.721544\pi$
$90$	−2.90495	−0.306209
$91$	10.6376	1.11512
$92$	−5.28363	−0.550857
$93$	−19.8733	−2.06077
$94$	11.1036	1.14525
$95$	−0.102135	−0.0104788
$96$	−2.78209	−0.283946
$97$	−6.57059	−0.667143	−0.333571	−	0.942725i	$-0.608254\pi$
$97$	−6.57059	−0.667143	−0.333571	+	0.942725i	$0.608254\pi$
$98$	3.87674	0.391610
$99$	1.96284	0.197273
$100$	−4.62441	−0.462441
$101$	11.0831	1.10281	0.551405	−	0.834238i	$-0.314092\pi$
$101$	11.0831	1.10281	0.551405	+	0.834238i	$0.314092\pi$
$102$	9.57699	0.948263
$103$	−6.31463	−0.622199	−0.311100	−	0.950377i	$-0.600697\pi$
$103$	−6.31463	−0.622199	−0.311100	+	0.950377i	$0.600697\pi$
$104$	3.22547	0.316283
$105$	5.62313	0.548761
$106$	−0.396855	−0.0385460
$107$	11.7239	1.13339	0.566696	−	0.823927i	$-0.308221\pi$
$107$	11.7239	1.13339	0.566696	+	0.823927i	$0.308221\pi$
$108$	−4.84095	−0.465821
$109$	−5.06152	−0.484806	−0.242403	−	0.970176i	$-0.577936\pi$
$109$	−5.06152	−0.484806	−0.242403	+	0.970176i	$0.577936\pi$
$110$	−0.253781	−0.0241971
$111$	−20.1543	−1.91296
$112$	3.29799	0.311631
$113$	−10.4755	−0.985448	−0.492724	−	0.870186i	$-0.663999\pi$
$113$	−10.4755	−0.985448	−0.492724	+	0.870186i	$0.663999\pi$
$114$	−0.463649	−0.0434247
$115$	3.23810	0.301954
$116$	−0.393601	−0.0365450
$117$	15.2889	1.41346
$118$	10.5344	0.969771
$119$	−11.3529	−1.04072
$120$	1.70502	0.155646
$121$	−10.8285	−0.984411
$122$	4.54193	0.411207
$123$	−5.26891	−0.475082
$124$	7.14330	0.641487
$125$	5.89836	0.527565
$126$	15.6326	1.39266
$127$	−0.309924	−0.0275013	−0.0137507	−	0.999905i	$-0.504377\pi$
$127$	−0.309924	−0.0275013	−0.0137507	+	0.999905i	$0.504377\pi$
$128$	1.00000	0.0883883
$129$	−8.96093	−0.788966
$130$	−1.97674	−0.173372
$131$	1.20789	0.105534	0.0527668	−	0.998607i	$-0.483196\pi$
$131$	1.20789	0.105534	0.0527668	+	0.998607i	$0.483196\pi$
$132$	−1.15206	−0.100274
$133$	0.549626	0.0476586
$134$	6.02048	0.520091
$135$	2.96679	0.255341
$136$	−3.44237	−0.295181
$137$	5.30816	0.453507	0.226753	−	0.973952i	$-0.427189\pi$
$137$	5.30816	0.453507	0.226753	+	0.973952i	$0.427189\pi$
$138$	14.6996	1.25131
$139$	18.5451	1.57297	0.786487	−	0.617607i	$-0.211898\pi$
$139$	18.5451	1.57297	0.786487	+	0.617607i	$0.211898\pi$
$140$	−2.02119	−0.170821
$141$	−30.8914	−2.60152
$142$	−11.9882	−1.00603
$143$	1.33566	0.111693
$144$	4.74004	0.395003
$145$	0.241220	0.0200322
$146$	15.7021	1.29951
$147$	−10.7854	−0.889568
$148$	7.24429	0.595477
$149$	12.8374	1.05168	0.525840	−	0.850583i	$-0.323751\pi$
$149$	12.8374	1.05168	0.525840	+	0.850583i	$0.323751\pi$
$150$	12.8655	1.05047
$151$	4.25111	0.345951	0.172975	−	0.984926i	$-0.444662\pi$
$151$	4.25111	0.345951	0.172975	+	0.984926i	$0.444662\pi$
$152$	0.166655	0.0135175
$153$	−16.3170	−1.31915
$154$	1.36569	0.110050
$155$	−4.37780	−0.351633
$156$	−8.97356	−0.718460
$157$	−7.46821	−0.596028	−0.298014	−	0.954562i	$-0.596324\pi$
$157$	−7.46821	−0.596028	−0.298014	+	0.954562i	$0.596324\pi$
$158$	6.42408	0.511072
$159$	1.10409	0.0875599
$160$	−0.612854	−0.0484503
$161$	−17.4254	−1.37331
$162$	−0.752148	−0.0590943
$163$	13.2451	1.03744	0.518719	−	0.854945i	$-0.326409\pi$
$163$	13.2451	1.03744	0.518719	+	0.854945i	$0.326409\pi$
$164$	1.89387	0.147886
$165$	0.706043	0.0549654
$166$	1.14168	0.0886119
$167$	16.0158	1.23934	0.619671	−	0.784862i	$-0.287266\pi$
$167$	16.0158	1.23934	0.619671	+	0.784862i	$0.287266\pi$
$168$	−9.17531	−0.707891
$169$	−2.59634	−0.199719
$170$	2.10967	0.161804
$171$	0.789950	0.0604090
$172$	3.22093	0.245594
$173$	−16.0238	−1.21827	−0.609133	−	0.793068i	$-0.708483\pi$
$173$	−16.0238	−1.21827	−0.609133	+	0.793068i	$0.708483\pi$
$174$	1.09504	0.0830144
$175$	−15.2513	−1.15289
$176$	0.414098	0.0312138
$177$	−29.3077	−2.20290
$178$	−12.0973	−0.906730
$179$	1.03217	0.0771481	0.0385741	−	0.999256i	$-0.487718\pi$
$179$	1.03217	0.0771481	0.0385741	+	0.999256i	$0.487718\pi$
$180$	−2.90495	−0.216522
$181$	−14.6601	−1.08968	−0.544840	−	0.838540i	$-0.683410\pi$
$181$	−14.6601	−1.08968	−0.544840	+	0.838540i	$0.683410\pi$
$182$	10.6376	0.788509
$183$	−12.6361	−0.934085
$184$	−5.28363	−0.389515
$185$	−4.43969	−0.326413
$186$	−19.8733	−1.45718
$187$	−1.42548	−0.104241
$188$	11.1036	0.809817
$189$	−15.9654	−1.16131
$190$	−0.102135	−0.00740965
$191$	−13.9781	−1.01142	−0.505709	−	0.862704i	$-0.668769\pi$
$191$	−13.9781	−1.01142	−0.505709	+	0.862704i	$0.668769\pi$
$192$	−2.78209	−0.200780
$193$	11.7177	0.843456	0.421728	−	0.906722i	$-0.361424\pi$
$193$	11.7177	0.843456	0.421728	+	0.906722i	$0.361424\pi$
$194$	−6.57059	−0.471741
$195$	5.49948	0.393826
$196$	3.87674	0.276910
$197$	−16.5733	−1.18080	−0.590399	−	0.807112i	$-0.701030\pi$
$197$	−16.5733	−1.18080	−0.590399	+	0.807112i	$0.701030\pi$
$198$	1.96284	0.139493
$199$	12.0501	0.854211	0.427105	−	0.904202i	$-0.359533\pi$
$199$	12.0501	0.854211	0.427105	+	0.904202i	$0.359533\pi$
$200$	−4.62441	−0.326995
$201$	−16.7495	−1.18142
$202$	11.0831	0.779804
$203$	−1.29809	−0.0911083
$204$	9.57699	0.670524
$205$	−1.16066	−0.0810642
$206$	−6.31463	−0.439961
$207$	−25.0446	−1.74072
$208$	3.22547	0.223646
$209$	0.0690113	0.00477361
$210$	5.62313	0.388033
$211$	−5.65510	−0.389313	−0.194657	−	0.980871i	$-0.562359\pi$
$211$	−5.65510	−0.389313	−0.194657	+	0.980871i	$0.562359\pi$
$212$	−0.396855	−0.0272561
$213$	33.3523	2.28526
$214$	11.7239	0.801430
$215$	−1.97396	−0.134623
$216$	−4.84095	−0.329385
$217$	23.5585	1.59926
$218$	−5.06152	−0.342809
$219$	−43.6847	−2.95194
$220$	−0.253781	−0.0171099
$221$	−11.1033	−0.746886
$222$	−20.1543	−1.35267
$223$	−12.4178	−0.831556	−0.415778	−	0.909466i	$-0.636491\pi$
$223$	−12.4178	−0.831556	−0.415778	+	0.909466i	$0.636491\pi$
$224$	3.29799	0.220356
$225$	−21.9199	−1.46133
$226$	−10.4755	−0.696817
$227$	20.7506	1.37726	0.688632	−	0.725111i	$-0.258211\pi$
$227$	20.7506	1.37726	0.688632	+	0.725111i	$0.258211\pi$
$228$	−0.463649	−0.0307059
$229$	17.9757	1.18787	0.593933	−	0.804515i	$-0.297575\pi$
$229$	17.9757	1.18787	0.593933	+	0.804515i	$0.297575\pi$
$230$	3.23810	0.213514
$231$	−3.79947	−0.249987
$232$	−0.393601	−0.0258412
$233$	10.0134	0.656001	0.328001	−	0.944677i	$-0.393625\pi$
$233$	10.0134	0.656001	0.328001	+	0.944677i	$0.393625\pi$
$234$	15.2889	0.999464
$235$	−6.80491	−0.443903
$236$	10.5344	0.685732
$237$	−17.8724	−1.16094
$238$	−11.3529	−0.735899
$239$	11.4347	0.739647	0.369824	−	0.929102i	$-0.379418\pi$
$239$	11.4347	0.739647	0.369824	+	0.929102i	$0.379418\pi$
$240$	1.70502	0.110058
$241$	6.85263	0.441417	0.220708	−	0.975340i	$-0.429163\pi$
$241$	6.85263	0.441417	0.220708	+	0.975340i	$0.429163\pi$
$242$	−10.8285	−0.696084
$243$	16.6154	1.06588
$244$	4.54193	0.290767
$245$	−2.37587	−0.151789
$246$	−5.26891	−0.335934
$247$	0.537540	0.0342028
$248$	7.14330	0.453600
$249$	−3.17627	−0.201288
$250$	5.89836	0.373045
$251$	−14.6262	−0.923199	−0.461599	−	0.887088i	$-0.652724\pi$
$251$	−14.6262	−0.923199	−0.461599	+	0.887088i	$0.652724\pi$
$252$	15.6326	0.984761
$253$	−2.18794	−0.137555
$254$	−0.309924	−0.0194464
$255$	−5.86930	−0.367550
$256$	1.00000	0.0625000
$257$	2.76455	0.172448	0.0862239	−	0.996276i	$-0.472520\pi$
$257$	2.76455	0.172448	0.0862239	+	0.996276i	$0.472520\pi$
$258$	−8.96093	−0.557883
$259$	23.8916	1.48455
$260$	−1.97674	−0.122592
$261$	−1.86569	−0.115483
$262$	1.20789	0.0746235
$263$	−2.14048	−0.131988	−0.0659938	−	0.997820i	$-0.521022\pi$
$263$	−2.14048	−0.131988	−0.0659938	+	0.997820i	$0.521022\pi$
$264$	−1.15206	−0.0709043
$265$	0.243214	0.0149405
$266$	0.549626	0.0336997
$267$	33.6558	2.05970
$268$	6.02048	0.367760
$269$	−12.9858	−0.791756	−0.395878	−	0.918303i	$-0.629560\pi$
$269$	−12.9858	−0.791756	−0.395878	+	0.918303i	$0.629560\pi$
$270$	2.96679	0.180553
$271$	8.20419	0.498369	0.249185	−	0.968456i	$-0.419837\pi$
$271$	8.20419	0.498369	0.249185	+	0.968456i	$0.419837\pi$
$272$	−3.44237	−0.208724
$273$	−29.5947	−1.79115
$274$	5.30816	0.320678
$275$	−1.91496	−0.115476
$276$	14.6996	0.884810
$277$	−12.8250	−0.770579	−0.385290	−	0.922796i	$-0.625898\pi$
$277$	−12.8250	−0.770579	−0.385290	+	0.922796i	$0.625898\pi$
$278$	18.5451	1.11226
$279$	33.8595	2.02712
$280$	−2.02119	−0.120789
$281$	−29.7621	−1.77546	−0.887730	−	0.460364i	$-0.847719\pi$
$281$	−29.7621	−1.77546	−0.887730	+	0.460364i	$0.847719\pi$
$282$	−30.8914	−1.83955
$283$	−14.0896	−0.837538	−0.418769	−	0.908093i	$-0.637538\pi$
$283$	−14.0896	−0.837538	−0.418769	+	0.908093i	$0.637538\pi$
$284$	−11.9882	−0.711370
$285$	0.284149	0.0168315
$286$	1.33566	0.0789792
$287$	6.24595	0.368687
$288$	4.74004	0.279309
$289$	−5.15009	−0.302946
$290$	0.241220	0.0141649
$291$	18.2800	1.07159
$292$	15.7021	0.918896
$293$	−6.18012	−0.361047	−0.180523	−	0.983571i	$-0.557779\pi$
$293$	−6.18012	−0.361047	−0.180523	+	0.983571i	$0.557779\pi$
$294$	−10.7854	−0.629020
$295$	−6.45605	−0.375886
$296$	7.24429	0.421066
$297$	−2.00463	−0.116320
$298$	12.8374	0.743651
$299$	−17.0422	−0.985576
$300$	12.8655	0.742792
$301$	10.6226	0.612276
$302$	4.25111	0.244624
$303$	−30.8342	−1.77138
$304$	0.166655	0.00955831
$305$	−2.78354	−0.159385
$306$	−16.3170	−0.932779
$307$	−22.8344	−1.30323	−0.651614	−	0.758550i	$-0.725908\pi$
$307$	−22.8344	−1.30323	−0.651614	+	0.758550i	$0.725908\pi$
$308$	1.36569	0.0778174
$309$	17.5679	0.999403
$310$	−4.37780	−0.248642
$311$	−12.7029	−0.720314	−0.360157	−	0.932892i	$-0.617277\pi$
$311$	−12.7029	−0.720314	−0.360157	+	0.932892i	$0.617277\pi$
$312$	−8.97356	−0.508028
$313$	15.4492	0.873242	0.436621	−	0.899646i	$-0.356175\pi$
$313$	15.4492	0.873242	0.436621	+	0.899646i	$0.356175\pi$
$314$	−7.46821	−0.421455
$315$	−9.58050	−0.539800
$316$	6.42408	0.361383
$317$	13.9162	0.781610	0.390805	−	0.920474i	$-0.372197\pi$
$317$	13.9162	0.781610	0.390805	+	0.920474i	$0.372197\pi$
$318$	1.10409	0.0619142
$319$	−0.162989	−0.00912566
$320$	−0.612854	−0.0342596
$321$	−32.6170	−1.82050
$322$	−17.4254	−0.971078
$323$	−0.573687	−0.0319208
$324$	−0.752148	−0.0417860
$325$	−14.9159	−0.827385
$326$	13.2451	0.733580
$327$	14.0816	0.778715
$328$	1.89387	0.104571
$329$	36.6197	2.01891
$330$	0.706043	0.0388664
$331$	−24.6209	−1.35329	−0.676644	−	0.736310i	$-0.736566\pi$
$331$	−24.6209	−1.35329	−0.676644	+	0.736310i	$0.736566\pi$
$332$	1.14168	0.0626581
$333$	34.3382	1.88172
$334$	16.0158	0.876346
$335$	−3.68968	−0.201589
$336$	−9.17531	−0.500554
$337$	−19.7118	−1.07377	−0.536886	−	0.843655i	$-0.680400\pi$
$337$	−19.7118	−1.07377	−0.536886	+	0.843655i	$0.680400\pi$
$338$	−2.59634	−0.141222
$339$	29.1437	1.58287
$340$	2.10967	0.114413
$341$	2.95802	0.160186
$342$	0.789950	0.0427156
$343$	−10.3005	−0.556174
$344$	3.22093	0.173661
$345$	−9.00868	−0.485011
$346$	−16.0238	−0.861445
$347$	−5.40205	−0.289997	−0.144998	−	0.989432i	$-0.546318\pi$
$347$	−5.40205	−0.289997	−0.144998	+	0.989432i	$0.546318\pi$
$348$	1.09504	0.0587001
$349$	15.0883	0.807660	0.403830	−	0.914834i	$-0.367679\pi$
$349$	15.0883	0.807660	0.403830	+	0.914834i	$0.367679\pi$
$350$	−15.2513	−0.815214
$351$	−15.6143	−0.833432
$352$	0.414098	0.0220715
$353$	6.98075	0.371548	0.185774	−	0.982593i	$-0.440521\pi$
$353$	6.98075	0.371548	0.185774	+	0.982593i	$0.440521\pi$
$354$	−29.3077	−1.55769
$355$	7.34703	0.389940
$356$	−12.0973	−0.641155
$357$	31.5848	1.67165
$358$	1.03217	0.0545520
$359$	−32.0681	−1.69249	−0.846245	−	0.532794i	$-0.821142\pi$
$359$	−32.0681	−1.69249	−0.846245	+	0.532794i	$0.821142\pi$
$360$	−2.90495	−0.153104
$361$	−18.9722	−0.998538
$362$	−14.6601	−0.770520
$363$	30.1260	1.58120
$364$	10.6376	0.557560
$365$	−9.62309	−0.503695
$366$	−12.6361	−0.660498
$367$	10.0093	0.522483	0.261241	−	0.965274i	$-0.415868\pi$
$367$	10.0093	0.522483	0.261241	+	0.965274i	$0.415868\pi$
$368$	−5.28363	−0.275428
$369$	8.97700	0.467324
$370$	−4.43969	−0.230809
$371$	−1.30882	−0.0679508
$372$	−19.8733	−1.03038
$373$	−21.7939	−1.12845	−0.564223	−	0.825622i	$-0.690824\pi$
$373$	−21.7939	−1.12845	−0.564223	+	0.825622i	$0.690824\pi$
$374$	−1.42548	−0.0737097
$375$	−16.4098	−0.847397
$376$	11.1036	0.572627
$377$	−1.26955	−0.0653851
$378$	−15.9654	−0.821172
$379$	−4.27455	−0.219569	−0.109784	−	0.993955i	$-0.535016\pi$
$379$	−4.27455	−0.219569	−0.109784	+	0.993955i	$0.535016\pi$
$380$	−0.102135	−0.00523941
$381$	0.862238	0.0441738
$382$	−13.9781	−0.715180
$383$	−5.60475	−0.286390	−0.143195	−	0.989695i	$-0.545738\pi$
$383$	−5.60475	−0.286390	−0.143195	+	0.989695i	$0.545738\pi$
$384$	−2.78209	−0.141973
$385$	−0.836968	−0.0426558
$386$	11.7177	0.596414
$387$	15.2673	0.776082
$388$	−6.57059	−0.333571
$389$	−6.79131	−0.344333	−0.172166	−	0.985068i	$-0.555077\pi$
$389$	−6.79131	−0.344333	−0.172166	+	0.985068i	$0.555077\pi$
$390$	5.49948	0.278477
$391$	18.1882	0.919818
$392$	3.87674	0.195805
$393$	−3.36045	−0.169512
$394$	−16.5733	−0.834950
$395$	−3.93702	−0.198093
$396$	1.96284	0.0986363
$397$	3.70503	0.185950	0.0929751	−	0.995668i	$-0.470362\pi$
$397$	3.70503	0.185950	0.0929751	+	0.995668i	$0.470362\pi$
$398$	12.0501	0.604018
$399$	−1.52911	−0.0765512
$400$	−4.62441	−0.231221
$401$	20.1144	1.00447	0.502234	−	0.864732i	$-0.332512\pi$
$401$	20.1144	1.00447	0.502234	+	0.864732i	$0.332512\pi$
$402$	−16.7495	−0.835391
$403$	23.0405	1.14773
$404$	11.0831	0.551405
$405$	0.460957	0.0229051
$406$	−1.29809	−0.0644233
$407$	2.99984	0.148697
$408$	9.57699	0.474132
$409$	−26.8755	−1.32891	−0.664454	−	0.747330i	$-0.731336\pi$
$409$	−26.8755	−1.32891	−0.664454	+	0.747330i	$0.731336\pi$
$410$	−1.16066	−0.0573211
$411$	−14.7678	−0.728441
$412$	−6.31463	−0.311100
$413$	34.7424	1.70956
$414$	−25.0446	−1.23088
$415$	−0.699686	−0.0343462
$416$	3.22547	0.158142
$417$	−51.5942	−2.52658
$418$	0.0690113	0.00337545
$419$	0.173061	0.00845459	0.00422729	−	0.999991i	$-0.498654\pi$
$419$	0.173061	0.00845459	0.00422729	+	0.999991i	$0.498654\pi$
$420$	5.62313	0.274380
$421$	−28.8001	−1.40363	−0.701815	−	0.712360i	$-0.747627\pi$
$421$	−28.8001	−1.40363	−0.701815	+	0.712360i	$0.747627\pi$
$422$	−5.65510	−0.275286
$423$	52.6317	2.55904
$424$	−0.396855	−0.0192730
$425$	15.9189	0.772182
$426$	33.3523	1.61593
$427$	14.9792	0.724896
$428$	11.7239	0.566696
$429$	−3.71593	−0.179407
$430$	−1.97396	−0.0951928
$431$	8.61224	0.414837	0.207419	−	0.978252i	$-0.433494\pi$
$431$	8.61224	0.414837	0.207419	+	0.978252i	$0.433494\pi$
$432$	−4.84095	−0.232910
$433$	12.4701	0.599276	0.299638	−	0.954053i	$-0.403134\pi$
$433$	12.4701	0.599276	0.299638	+	0.954053i	$0.403134\pi$
$434$	23.5585	1.13085
$435$	−0.671097	−0.0321766
$436$	−5.06152	−0.242403
$437$	−0.880543	−0.0421221
$438$	−43.6847	−2.08733
$439$	12.3583	0.589831	0.294916	−	0.955523i	$-0.404708\pi$
$439$	12.3583	0.589831	0.294916	+	0.955523i	$0.404708\pi$
$440$	−0.253781	−0.0120985
$441$	18.3759	0.875042
$442$	−11.1033	−0.528128
$443$	32.1862	1.52921	0.764606	−	0.644498i	$-0.222934\pi$
$443$	32.1862	1.52921	0.764606	+	0.644498i	$0.222934\pi$
$444$	−20.1543	−0.956480
$445$	7.41387	0.351451
$446$	−12.4178	−0.587999
$447$	−35.7148	−1.68925
$448$	3.29799	0.155815
$449$	9.11977	0.430389	0.215194	−	0.976571i	$-0.430961\pi$
$449$	9.11977	0.430389	0.215194	+	0.976571i	$0.430961\pi$
$450$	−21.9199	−1.03331
$451$	0.784246	0.0369287
$452$	−10.4755	−0.492724
$453$	−11.8270	−0.555681
$454$	20.7506	0.973873
$455$	−6.51927	−0.305628
$456$	−0.463649	−0.0217123
$457$	−0.742522	−0.0347337	−0.0173669	−	0.999849i	$-0.505528\pi$
$457$	−0.742522	−0.0347337	−0.0173669	+	0.999849i	$0.505528\pi$
$458$	17.9757	0.839948
$459$	16.6643	0.777825
$460$	3.23810	0.150977
$461$	−21.5528	−1.00381	−0.501906	−	0.864922i	$-0.667368\pi$
$461$	−21.5528	−1.00381	−0.501906	+	0.864922i	$0.667368\pi$
$462$	−3.79947	−0.176768
$463$	5.93483	0.275815	0.137907	−	0.990445i	$-0.455962\pi$
$463$	5.93483	0.275815	0.137907	+	0.990445i	$0.455962\pi$
$464$	−0.393601	−0.0182725
$465$	12.1794	0.564808
$466$	10.0134	0.463863
$467$	−0.480753	−0.0222466	−0.0111233	−	0.999938i	$-0.503541\pi$
$467$	−0.480753	−0.0222466	−0.0111233	+	0.999938i	$0.503541\pi$
$468$	15.2889	0.706728
$469$	19.8555	0.916842
$470$	−6.80491	−0.313887
$471$	20.7772	0.957365
$472$	10.5344	0.484886
$473$	1.33378	0.0613273
$474$	−17.8724	−0.820906
$475$	−0.770680	−0.0353612
$476$	−11.3529	−0.520359
$477$	−1.88111	−0.0861301
$478$	11.4347	0.523010
$479$	−21.0738	−0.962887	−0.481443	−	0.876477i	$-0.659887\pi$
$479$	−21.0738	−0.962887	−0.481443	+	0.876477i	$0.659887\pi$
$480$	1.70502	0.0778230
$481$	23.3662	1.06541
$482$	6.85263	0.312129
$483$	48.4790	2.20587
$484$	−10.8285	−0.492206
$485$	4.02681	0.182848
$486$	16.6154	0.753690
$487$	6.54032	0.296370	0.148185	−	0.988960i	$-0.452657\pi$
$487$	6.54032	0.296370	0.148185	+	0.988960i	$0.452657\pi$
$488$	4.54193	0.205603
$489$	−36.8492	−1.66638
$490$	−2.37587	−0.107331
$491$	40.0997	1.80967	0.904836	−	0.425760i	$-0.139993\pi$
$491$	40.0997	1.80967	0.904836	+	0.425760i	$0.139993\pi$
$492$	−5.26891	−0.237541
$493$	1.35492	0.0610226
$494$	0.537540	0.0241851
$495$	−1.20293	−0.0540678
$496$	7.14330	0.320743
$497$	−39.5370	−1.77348
$498$	−3.17627	−0.142332
$499$	−8.82193	−0.394924	−0.197462	−	0.980311i	$-0.563270\pi$
$499$	−8.82193	−0.394924	−0.197462	+	0.980311i	$0.563270\pi$
$500$	5.89836	0.263783
$501$	−44.5575	−1.99068
$502$	−14.6262	−0.652800
$503$	−37.8313	−1.68681	−0.843407	−	0.537276i	$-0.819453\pi$
$503$	−37.8313	−1.68681	−0.843407	+	0.537276i	$0.819453\pi$
$504$	15.6326	0.696331
$505$	−6.79232	−0.302254
$506$	−2.18794	−0.0972658
$507$	7.22327	0.320796
$508$	−0.309924	−0.0137507
$509$	−11.9463	−0.529512	−0.264756	−	0.964315i	$-0.585291\pi$
$509$	−11.9463	−0.529512	−0.264756	+	0.964315i	$0.585291\pi$
$510$	−5.86930	−0.259897
$511$	51.7853	2.29085
$512$	1.00000	0.0441942
$513$	−0.806767	−0.0356196
$514$	2.76455	0.121939
$515$	3.86995	0.170530
$516$	−8.96093	−0.394483
$517$	4.59799	0.202219
$518$	23.8916	1.04974
$519$	44.5797	1.95683
$520$	−1.97674	−0.0866859
$521$	−23.7067	−1.03861	−0.519304	−	0.854590i	$-0.673809\pi$
$521$	−23.7067	−1.03861	−0.519304	+	0.854590i	$0.673809\pi$
$522$	−1.86569	−0.0816589
$523$	28.6603	1.25323	0.626614	−	0.779330i	$-0.284440\pi$
$523$	28.6603	1.25323	0.626614	+	0.779330i	$0.284440\pi$
$524$	1.20789	0.0527668
$525$	42.4304	1.85181
$526$	−2.14048	−0.0933294
$527$	−24.5899	−1.07115
$528$	−1.15206	−0.0501369
$529$	4.91679	0.213774
$530$	0.243214	0.0105646
$531$	49.9335	2.16693
$532$	0.549626	0.0238293
$533$	6.10861	0.264593
$534$	33.6558	1.45643
$535$	−7.18504	−0.310636
$536$	6.02048	0.260045
$537$	−2.87160	−0.123919
$538$	−12.9858	−0.559856
$539$	1.60535	0.0691472
$540$	2.96679	0.127670
$541$	9.65944	0.415292	0.207646	−	0.978204i	$-0.433420\pi$
$541$	9.65944	0.415292	0.207646	+	0.978204i	$0.433420\pi$
$542$	8.20419	0.352400
$543$	40.7859	1.75029
$544$	−3.44237	−0.147590
$545$	3.10197	0.132874
$546$	−29.5947	−1.26654
$547$	30.4079	1.30015	0.650074	−	0.759871i	$-0.274738\pi$
$547$	30.4079	1.30015	0.650074	+	0.759871i	$0.274738\pi$
$548$	5.30816	0.226753
$549$	21.5289	0.918832
$550$	−1.91496	−0.0816540
$551$	−0.0655956	−0.00279446
$552$	14.6996	0.625655
$553$	21.1865	0.900944
$554$	−12.8250	−0.544882
$555$	12.3516	0.524298
$556$	18.5451	0.786487
$557$	−12.1594	−0.515209	−0.257604	−	0.966250i	$-0.582933\pi$
$557$	−12.1594	−0.515209	−0.257604	+	0.966250i	$0.582933\pi$
$558$	33.8595	1.43339
$559$	10.3890	0.439409
$560$	−2.02119	−0.0854107
$561$	3.96581	0.167437
$562$	−29.7621	−1.25544
$563$	43.2848	1.82424	0.912119	−	0.409925i	$-0.134445\pi$
$563$	43.2848	1.82424	0.912119	+	0.409925i	$0.134445\pi$
$564$	−30.8914	−1.30076
$565$	6.41993	0.270088
$566$	−14.0896	−0.592229
$567$	−2.48058	−0.104174
$568$	−11.9882	−0.503015
$569$	29.5017	1.23678	0.618388	−	0.785873i	$-0.287786\pi$
$569$	29.5017	1.23678	0.618388	+	0.785873i	$0.287786\pi$
$570$	0.284149	0.0119017
$571$	−8.54565	−0.357624	−0.178812	−	0.983883i	$-0.557225\pi$
$571$	−8.54565	−0.357624	−0.178812	+	0.983883i	$0.557225\pi$
$572$	1.33566	0.0558467
$573$	38.8883	1.62458
$574$	6.24595	0.260701
$575$	24.4337	1.01896
$576$	4.74004	0.197502
$577$	−38.0276	−1.58311	−0.791554	−	0.611099i	$-0.790728\pi$
$577$	−38.0276	−1.58311	−0.791554	+	0.611099i	$0.790728\pi$
$578$	−5.15009	−0.214215
$579$	−32.5996	−1.35479
$580$	0.241220	0.0100161
$581$	3.76526	0.156210
$582$	18.2800	0.757730
$583$	−0.164337	−0.00680613
$584$	15.7021	0.649757
$585$	−9.36983	−0.387395
$586$	−6.18012	−0.255298
$587$	−21.6517	−0.893662	−0.446831	−	0.894618i	$-0.647447\pi$
$587$	−21.6517	−0.893662	−0.446831	+	0.894618i	$0.647447\pi$
$588$	−10.7854	−0.444784
$589$	1.19046	0.0490522
$590$	−6.45605	−0.265792
$591$	46.1084	1.89665
$592$	7.24429	0.297739
$593$	28.4475	1.16820	0.584100	−	0.811681i	$-0.301447\pi$
$593$	28.4475	1.16820	0.584100	+	0.811681i	$0.301447\pi$
$594$	−2.00463	−0.0822508
$595$	6.95767	0.285237
$596$	12.8374	0.525840
$597$	−33.5246	−1.37207
$598$	−17.0422	−0.696908
$599$	−34.3761	−1.40457	−0.702284	−	0.711897i	$-0.747836\pi$
$599$	−34.3761	−1.40457	−0.702284	+	0.711897i	$0.747836\pi$
$600$	12.8655	0.525233
$601$	−36.3499	−1.48274	−0.741371	−	0.671096i	$-0.765824\pi$
$601$	−36.3499	−1.48274	−0.741371	+	0.671096i	$0.765824\pi$
$602$	10.6226	0.432945
$603$	28.5373	1.16213
$604$	4.25111	0.172975
$605$	6.63630	0.269804
$606$	−30.8342	−1.25255
$607$	−13.6255	−0.553043	−0.276521	−	0.961008i	$-0.589182\pi$
$607$	−13.6255	−0.553043	−0.276521	+	0.961008i	$0.589182\pi$
$608$	0.166655	0.00675874
$609$	3.61142	0.146342
$610$	−2.78354	−0.112702
$611$	35.8145	1.44890
$612$	−16.3170	−0.659574
$613$	7.85015	0.317065	0.158532	−	0.987354i	$-0.449324\pi$
$613$	7.85015	0.317065	0.158532	+	0.987354i	$0.449324\pi$
$614$	−22.8344	−0.921522
$615$	3.22907	0.130209
$616$	1.36569	0.0550252
$617$	−29.2870	−1.17905	−0.589525	−	0.807750i	$-0.700685\pi$
$617$	−29.2870	−1.17905	−0.589525	+	0.807750i	$0.700685\pi$
$618$	17.5679	0.706685
$619$	−25.0492	−1.00681	−0.503405	−	0.864050i	$-0.667920\pi$
$619$	−25.0492	−1.00681	−0.503405	+	0.864050i	$0.667920\pi$
$620$	−4.37780	−0.175817
$621$	25.5778	1.02640
$622$	−12.7029	−0.509339
$623$	−39.8967	−1.59843
$624$	−8.97356	−0.359230
$625$	19.5072	0.780289
$626$	15.4492	0.617475
$627$	−0.191996	−0.00766758
$628$	−7.46821	−0.298014
$629$	−24.9375	−0.994325
$630$	−9.58050	−0.381696
$631$	−35.0554	−1.39553	−0.697767	−	0.716325i	$-0.745823\pi$
$631$	−35.0554	−1.39553	−0.697767	+	0.716325i	$0.745823\pi$
$632$	6.42408	0.255536
$633$	15.7330	0.625331
$634$	13.9162	0.552681
$635$	0.189938	0.00753747
$636$	1.10409	0.0437799
$637$	12.5043	0.495438
$638$	−0.162989	−0.00645281
$639$	−56.8246	−2.24795
$640$	−0.612854	−0.0242252
$641$	19.6499	0.776124	0.388062	−	0.921633i	$-0.373145\pi$
$641$	19.6499	0.776124	0.388062	+	0.921633i	$0.373145\pi$
$642$	−32.6170	−1.28729
$643$	−43.5467	−1.71731	−0.858657	−	0.512551i	$-0.828700\pi$
$643$	−43.5467	−1.71731	−0.858657	+	0.512551i	$0.828700\pi$
$644$	−17.4254	−0.686656
$645$	5.49174	0.216237
$646$	−0.573687	−0.0225714
$647$	37.8865	1.48947	0.744736	−	0.667359i	$-0.232575\pi$
$647$	37.8865	1.48947	0.744736	+	0.667359i	$0.232575\pi$
$648$	−0.752148	−0.0295472
$649$	4.36227	0.171234
$650$	−14.9159	−0.585050
$651$	−65.5420	−2.56879
$652$	13.2451	0.518719
$653$	−30.1177	−1.17860	−0.589298	−	0.807916i	$-0.700595\pi$
$653$	−30.1177	−1.17860	−0.589298	+	0.807916i	$0.700595\pi$
$654$	14.0816	0.550635
$655$	−0.740258	−0.0289243
$656$	1.89387	0.0739431
$657$	74.4285	2.90373
$658$	36.6197	1.42758
$659$	−33.1990	−1.29325	−0.646626	−	0.762808i	$-0.723820\pi$
$659$	−33.1990	−1.29325	−0.646626	+	0.762808i	$0.723820\pi$
$660$	0.706043	0.0274827
$661$	15.8359	0.615944	0.307972	−	0.951395i	$-0.400350\pi$
$661$	15.8359	0.615944	0.307972	+	0.951395i	$0.400350\pi$
$662$	−24.6209	−0.956919
$663$	30.8903	1.19968
$664$	1.14168	0.0443060
$665$	−0.336840	−0.0130621
$666$	34.3382	1.33058
$667$	2.07965	0.0805242
$668$	16.0158	0.619671
$669$	34.5474	1.33568
$670$	−3.68968	−0.142545
$671$	1.88080	0.0726076
$672$	−9.17531	−0.353945
$673$	26.0897	1.00568	0.502842	−	0.864378i	$-0.332288\pi$
$673$	26.0897	1.00568	0.502842	+	0.864378i	$0.332288\pi$
$674$	−19.7118	−0.759272
$675$	22.3865	0.861658
$676$	−2.59634	−0.0998593
$677$	−2.49496	−0.0958891	−0.0479445	−	0.998850i	$-0.515267\pi$
$677$	−2.49496	−0.0958891	−0.0479445	+	0.998850i	$0.515267\pi$
$678$	29.1437	1.11926
$679$	−21.6698	−0.831609
$680$	2.10967	0.0809021
$681$	−57.7301	−2.21222
$682$	2.95802	0.113269
$683$	26.1952	1.00233	0.501166	−	0.865351i	$-0.332905\pi$
$683$	26.1952	1.00233	0.501166	+	0.865351i	$0.332905\pi$
$684$	0.789950	0.0302045
$685$	−3.25313	−0.124296
$686$	−10.3005	−0.393274
$687$	−50.0100	−1.90800
$688$	3.22093	0.122797
$689$	−1.28004	−0.0487658
$690$	−9.00868	−0.342955
$691$	2.83663	0.107911	0.0539553	−	0.998543i	$-0.482817\pi$
$691$	2.83663	0.107911	0.0539553	+	0.998543i	$0.482817\pi$
$692$	−16.0238	−0.609133
$693$	6.47342	0.245905
$694$	−5.40205	−0.205059
$695$	−11.3654	−0.431115
$696$	1.09504	0.0415072
$697$	−6.51939	−0.246939
$698$	15.0883	0.571102
$699$	−27.8583	−1.05370
$700$	−15.2513	−0.576443
$701$	−43.2358	−1.63300	−0.816498	−	0.577349i	$-0.804087\pi$
$701$	−43.2358	−1.63300	−0.816498	+	0.577349i	$0.804087\pi$
$702$	−15.6143	−0.589325
$703$	1.20730	0.0455340
$704$	0.414098	0.0156069
$705$	18.9319	0.713016
$706$	6.98075	0.262724
$707$	36.5519	1.37468
$708$	−29.3077	−1.10145
$709$	−11.0965	−0.416738	−0.208369	−	0.978050i	$-0.566816\pi$
$709$	−11.0965	−0.416738	−0.208369	+	0.978050i	$0.566816\pi$
$710$	7.34703	0.275729
$711$	30.4504	1.14198
$712$	−12.0973	−0.453365
$713$	−37.7426	−1.41347
$714$	31.5848	1.18203
$715$	−0.818564	−0.0306126
$716$	1.03217	0.0385741
$717$	−31.8123	−1.18805
$718$	−32.0681	−1.19677
$719$	−2.62836	−0.0980214	−0.0490107	−	0.998798i	$-0.515607\pi$
$719$	−2.62836	−0.0980214	−0.0490107	+	0.998798i	$0.515607\pi$
$720$	−2.90495	−0.108261
$721$	−20.8256	−0.775586
$722$	−18.9722	−0.706073
$723$	−19.0647	−0.709022
$724$	−14.6601	−0.544840
$725$	1.82017	0.0675996
$726$	30.1260	1.11808
$727$	−19.1134	−0.708877	−0.354438	−	0.935079i	$-0.615328\pi$
$727$	−19.1134	−0.708877	−0.354438	+	0.935079i	$0.615328\pi$
$728$	10.6376	0.394254
$729$	−43.9691	−1.62849
$730$	−9.62309	−0.356166
$731$	−11.0876	−0.410091
$732$	−12.6361	−0.467043
$733$	−5.54694	−0.204881	−0.102440	−	0.994739i	$-0.532665\pi$
$733$	−5.54694	−0.204881	−0.102440	+	0.994739i	$0.532665\pi$
$734$	10.0093	0.369451
$735$	6.60990	0.243810
$736$	−5.28363	−0.194757
$737$	2.49307	0.0918333
$738$	8.97700	0.330448
$739$	−11.5570	−0.425130	−0.212565	−	0.977147i	$-0.568182\pi$
$739$	−11.5570	−0.425130	−0.212565	+	0.977147i	$0.568182\pi$
$740$	−4.43969	−0.163206
$741$	−1.49549	−0.0549380
$742$	−1.30882	−0.0480485
$743$	9.91661	0.363805	0.181903	−	0.983317i	$-0.441774\pi$
$743$	9.91661	0.363805	0.181903	+	0.983317i	$0.441774\pi$
$744$	−19.8733	−0.728591
$745$	−7.86745	−0.288241
$746$	−21.7939	−0.797932
$747$	5.41163	0.198001
$748$	−1.42548	−0.0521206
$749$	38.6653	1.41280
$750$	−16.4098	−0.599200
$751$	−1.00000	−0.0364905
$751$	−1.00000	−0.0364905
$752$	11.1036	0.404908
$753$	40.6915	1.48288
$754$	−1.26955	−0.0462343
$755$	−2.60531	−0.0948170
$756$	−15.9654	−0.580656
$757$	52.6772	1.91458	0.957292	−	0.289121i	$-0.0933631\pi$
$757$	52.6772	1.91458	0.957292	+	0.289121i	$0.0933631\pi$
$758$	−4.27455	−0.155259
$759$	6.08705	0.220946
$760$	−0.102135	−0.00370483
$761$	21.1023	0.764958	0.382479	−	0.923964i	$-0.375070\pi$
$761$	21.1023	0.764958	0.382479	+	0.923964i	$0.375070\pi$
$762$	0.862238	0.0312356
$763$	−16.6928	−0.604321
$764$	−13.9781	−0.505709
$765$	9.99992	0.361548
$766$	−5.60475	−0.202508
$767$	33.9784	1.22689
$768$	−2.78209	−0.100390
$769$	21.7346	0.783770	0.391885	−	0.920014i	$-0.371823\pi$
$769$	21.7346	0.783770	0.391885	+	0.920014i	$0.371823\pi$
$770$	−0.836968	−0.0301622
$771$	−7.69123	−0.276993
$772$	11.7177	0.421728
$773$	14.1373	0.508482	0.254241	−	0.967141i	$-0.418174\pi$
$773$	14.1373	0.508482	0.254241	+	0.967141i	$0.418174\pi$
$774$	15.2673	0.548773
$775$	−33.0335	−1.18660
$776$	−6.57059	−0.235871
$777$	−66.4686	−2.38455
$778$	−6.79131	−0.243480
$779$	0.315622	0.0113083
$780$	5.49948	0.196913
$781$	−4.96429	−0.177636
$782$	18.1882	0.650410
$783$	1.90540	0.0680936
$784$	3.87674	0.138455
$785$	4.57692	0.163357
$786$	−3.36045	−0.119863
$787$	42.4314	1.51252	0.756259	−	0.654273i	$-0.227025\pi$
$787$	42.4314	1.51252	0.756259	+	0.654273i	$0.227025\pi$
$788$	−16.5733	−0.590399
$789$	5.95501	0.212004
$790$	−3.93702	−0.140073
$791$	−34.5480	−1.22838
$792$	1.96284	0.0697464
$793$	14.6499	0.520232
$794$	3.70503	0.131487
$795$	−0.676644	−0.0239981
$796$	12.0501	0.427105
$797$	−23.5403	−0.833840	−0.416920	−	0.908943i	$-0.636890\pi$
$797$	−23.5403	−0.833840	−0.416920	+	0.908943i	$0.636890\pi$
$798$	−1.52911	−0.0541299
$799$	−38.2229	−1.35223
$800$	−4.62441	−0.163498
$801$	−57.3416	−2.02607
$802$	20.1144	0.710265
$803$	6.50220	0.229458
$804$	−16.7495	−0.590711
$805$	10.6792	0.376393
$806$	23.0405	0.811567
$807$	36.1276	1.27175
$808$	11.0831	0.389902
$809$	30.6174	1.07645	0.538226	−	0.842801i	$-0.319095\pi$
$809$	30.6174	1.07645	0.538226	+	0.842801i	$0.319095\pi$
$810$	0.460957	0.0161964
$811$	1.70210	0.0597688	0.0298844	−	0.999553i	$-0.490486\pi$
$811$	1.70210	0.0597688	0.0298844	+	0.999553i	$0.490486\pi$
$812$	−1.29809	−0.0455542
$813$	−22.8248	−0.800501
$814$	2.99984	0.105144
$815$	−8.11733	−0.284338
$816$	9.57699	0.335262
$817$	0.536783	0.0187797
$818$	−26.8755	−0.939679
$819$	50.4225	1.76190
$820$	−1.16066	−0.0405321
$821$	−10.1938	−0.355766	−0.177883	−	0.984052i	$-0.556925\pi$
$821$	−10.1938	−0.355766	−0.177883	+	0.984052i	$0.556925\pi$
$822$	−14.7678	−0.515086
$823$	−25.6296	−0.893393	−0.446696	−	0.894686i	$-0.647400\pi$
$823$	−25.6296	−0.893393	−0.446696	+	0.894686i	$0.647400\pi$
$824$	−6.31463	−0.219981
$825$	5.32759	0.185483
$826$	34.7424	1.20884
$827$	4.16951	0.144988	0.0724940	−	0.997369i	$-0.476904\pi$
$827$	4.16951	0.144988	0.0724940	+	0.997369i	$0.476904\pi$
$828$	−25.0446	−0.870361
$829$	47.7577	1.65869	0.829347	−	0.558734i	$-0.188713\pi$
$829$	47.7577	1.65869	0.829347	+	0.558734i	$0.188713\pi$
$830$	−0.699686	−0.0242865
$831$	35.6803	1.23774
$832$	3.22547	0.111823
$833$	−13.3452	−0.462383
$834$	−51.5942	−1.78656
$835$	−9.81535	−0.339674
$836$	0.0690113	0.00238681
$837$	−34.5803	−1.19527
$838$	0.173061	0.00597829
$839$	5.37010	0.185396	0.0926982	−	0.995694i	$-0.470451\pi$
$839$	5.37010	0.185396	0.0926982	+	0.995694i	$0.470451\pi$
$840$	5.62313	0.194016
$841$	−28.8451	−0.994658
$842$	−28.8001	−0.992516
$843$	82.8010	2.85182
$844$	−5.65510	−0.194657
$845$	1.59118	0.0547382
$846$	52.6317	1.80952
$847$	−35.7124	−1.22709
$848$	−0.396855	−0.0136281
$849$	39.1985	1.34529
$850$	15.9189	0.546015
$851$	−38.2762	−1.31209
$852$	33.3523	1.14263
$853$	−39.2446	−1.34371	−0.671855	−	0.740683i	$-0.734502\pi$
$853$	−39.2446	−1.34371	−0.671855	+	0.740683i	$0.734502\pi$
$854$	14.9792	0.512579
$855$	−0.484124	−0.0165567
$856$	11.7239	0.400715
$857$	−13.2255	−0.451775	−0.225888	−	0.974153i	$-0.572528\pi$
$857$	−13.2255	−0.451775	−0.225888	+	0.974153i	$0.572528\pi$
$858$	−3.71593	−0.126860
$859$	−1.79288	−0.0611722	−0.0305861	−	0.999532i	$-0.509737\pi$
$859$	−1.79288	−0.0611722	−0.0305861	+	0.999532i	$0.509737\pi$
$860$	−1.97396	−0.0673115
$861$	−17.3768	−0.592200
$862$	8.61224	0.293334
$863$	4.98749	0.169776	0.0848880	−	0.996390i	$-0.472947\pi$
$863$	4.98749	0.169776	0.0848880	+	0.996390i	$0.472947\pi$
$864$	−4.84095	−0.164692
$865$	9.82025	0.333898
$866$	12.4701	0.423752
$867$	14.3280	0.486605
$868$	23.5585	0.799628
$869$	2.66020	0.0902409
$870$	−0.671097	−0.0227523
$871$	19.4189	0.657984
$872$	−5.06152	−0.171405
$873$	−31.1449	−1.05409
$874$	−0.880543	−0.0297848
$875$	19.4527	0.657622
$876$	−43.6847	−1.47597
$877$	48.0442	1.62234	0.811169	−	0.584811i	$-0.198831\pi$
$877$	48.0442	1.62234	0.811169	+	0.584811i	$0.198831\pi$
$878$	12.3583	0.417074
$879$	17.1937	0.579928
$880$	−0.253781	−0.00855497
$881$	18.7197	0.630682	0.315341	−	0.948978i	$-0.397881\pi$
$881$	18.7197	0.630682	0.315341	+	0.948978i	$0.397881\pi$
$882$	18.3759	0.618748
$883$	−48.1285	−1.61965	−0.809826	−	0.586670i	$-0.800439\pi$
$883$	−48.1285	−1.61965	−0.809826	+	0.586670i	$0.800439\pi$
$884$	−11.1033	−0.373443
$885$	17.9613	0.603764
$886$	32.1862	1.08132
$887$	−15.0778	−0.506264	−0.253132	−	0.967432i	$-0.581461\pi$
$887$	−15.0778	−0.506264	−0.253132	+	0.967432i	$0.581461\pi$
$888$	−20.1543	−0.676334
$889$	−1.02213	−0.0342810
$890$	7.41387	0.248513
$891$	−0.311463	−0.0104344
$892$	−12.4178	−0.415778
$893$	1.85048	0.0619238
$894$	−35.7148	−1.19448
$895$	−0.632570	−0.0211445
$896$	3.29799	0.110178
$897$	47.4130	1.58307
$898$	9.11977	0.304331
$899$	−2.81161	−0.0937725
$900$	−21.9199	−0.730663
$901$	1.36612	0.0455121
$902$	0.784246	0.0261125
$903$	−29.5531	−0.983464
$904$	−10.4755	−0.348409
$905$	8.98453	0.298656
$906$	−11.8270	−0.392926
$907$	57.7472	1.91747	0.958733	−	0.284309i	$-0.0917640\pi$
$907$	57.7472	1.91747	0.958733	+	0.284309i	$0.0917640\pi$
$908$	20.7506	0.688632
$909$	52.5343	1.74245
$910$	−6.51927	−0.216112
$911$	−53.2164	−1.76314	−0.881570	−	0.472054i	$-0.843513\pi$
$911$	−53.2164	−1.76314	−0.881570	+	0.472054i	$0.843513\pi$
$912$	−0.463649	−0.0153529
$913$	0.472769	0.0156464
$914$	−0.742522	−0.0245605
$915$	7.74406	0.256011
$916$	17.9757	0.593933
$917$	3.98360	0.131550
$918$	16.6643	0.550005
$919$	23.8123	0.785496	0.392748	−	0.919646i	$-0.371524\pi$
$919$	23.8123	0.785496	0.392748	+	0.919646i	$0.371524\pi$
$920$	3.23810	0.106757
$921$	63.5274	2.09330
$922$	−21.5528	−0.709803
$923$	−38.6677	−1.27276
$924$	−3.79947	−0.124994
$925$	−33.5006	−1.10149
$926$	5.93483	0.195031
$927$	−29.9316	−0.983083
$928$	−0.393601	−0.0129206
$929$	−57.9873	−1.90250	−0.951251	−	0.308418i	$-0.900200\pi$
$929$	−57.9873	−1.90250	−0.951251	+	0.308418i	$0.900200\pi$
$930$	12.1794	0.399379
$931$	0.646077	0.0211743
$932$	10.0134	0.328001
$933$	35.3406	1.15700
$934$	−0.480753	−0.0157307
$935$	0.873609	0.0285701
$936$	15.2889	0.499732
$937$	−23.9004	−0.780792	−0.390396	−	0.920647i	$-0.627662\pi$
$937$	−23.9004	−0.780792	−0.390396	+	0.920647i	$0.627662\pi$
$938$	19.8555	0.648305
$939$	−42.9812	−1.40264
$940$	−6.80491	−0.221952
$941$	3.45662	0.112682	0.0563412	−	0.998412i	$-0.482057\pi$
$941$	3.45662	0.112682	0.0563412	+	0.998412i	$0.482057\pi$
$942$	20.7772	0.676959
$943$	−10.0065	−0.325856
$944$	10.5344	0.342866
$945$	9.78446	0.318288
$946$	1.33378	0.0433649
$947$	11.8878	0.386302	0.193151	−	0.981169i	$-0.438129\pi$
$947$	11.8878	0.386302	0.193151	+	0.981169i	$0.438129\pi$
$948$	−17.8724	−0.580468
$949$	50.6466	1.64406
$950$	−0.770680	−0.0250042
$951$	−38.7161	−1.25545
$952$	−11.3529	−0.367950
$953$	−0.543540	−0.0176070	−0.00880350	−	0.999961i	$-0.502802\pi$
$953$	−0.543540	−0.0176070	−0.00880350	+	0.999961i	$0.502802\pi$
$954$	−1.88111	−0.0609032
$955$	8.56651	0.277206
$956$	11.4347	0.369824
$957$	0.453452	0.0146580
$958$	−21.0738	−0.680864
$959$	17.5063	0.565307
$960$	1.70502	0.0550292
$961$	20.0267	0.646022
$962$	23.3662	0.753358
$963$	55.5718	1.79078
$964$	6.85263	0.220708
$965$	−7.18122	−0.231172
$966$	48.4790	1.55979
$967$	−14.5216	−0.466982	−0.233491	−	0.972359i	$-0.575015\pi$
$967$	−14.5216	−0.466982	−0.233491	+	0.972359i	$0.575015\pi$
$968$	−10.8285	−0.348042
$969$	1.59605	0.0512725
$970$	4.02681	0.129293
$971$	−20.9213	−0.671396	−0.335698	−	0.941970i	$-0.608972\pi$
$971$	−20.9213	−0.671396	−0.335698	+	0.941970i	$0.608972\pi$
$972$	16.6154	0.532939
$973$	61.1615	1.96075
$974$	6.54032	0.209565
$975$	41.4974	1.32898
$976$	4.54193	0.145384
$977$	−28.2545	−0.903941	−0.451970	−	0.892033i	$-0.649279\pi$
$977$	−28.2545	−0.903941	−0.451970	+	0.892033i	$0.649279\pi$
$978$	−36.8492	−1.17831
$979$	−5.00946	−0.160103
$980$	−2.37587	−0.0758945
$981$	−23.9918	−0.765999
$982$	40.0997	1.27963
$983$	−12.0043	−0.382876	−0.191438	−	0.981505i	$-0.561315\pi$
$983$	−12.0043	−0.382876	−0.191438	+	0.981505i	$0.561315\pi$
$984$	−5.26891	−0.167967
$985$	10.1570	0.323629
$986$	1.35492	0.0431495
$987$	−101.879	−3.24286
$988$	0.537540	0.0171014
$989$	−17.0182	−0.541148
$990$	−1.20293	−0.0382317
$991$	3.56572	0.113269	0.0566345	−	0.998395i	$-0.481963\pi$
$991$	3.56572	0.113269	0.0566345	+	0.998395i	$0.481963\pi$
$992$	7.14330	0.226800
$993$	68.4977	2.17371
$994$	−39.5370	−1.25404
$995$	−7.38497	−0.234119
$996$	−3.17627	−0.100644
$997$	−44.6589	−1.41436	−0.707181	−	0.707032i	$-0.750034\pi$
$997$	−44.6589	−1.41436	−0.707181	+	0.707032i	$0.750034\pi$
$998$	−8.82193	−0.279253
$999$	−35.0692	−1.10954

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1502.2.a.g.1.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1502.2.a.g.1.1	✓	16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1502 = 2 \cdot 751 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1502.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.78209 q^{3} +1.00000 q^{4} -0.612854 q^{5} -2.78209 q^{6} +3.29799 q^{7} +1.00000 q^{8} +4.74004 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.78209 q^{3} +1.00000 q^{4} -0.612854 q^{5} -2.78209 q^{6} +3.29799 q^{7} +1.00000 q^{8} +4.74004 q^{9} -0.612854 q^{10} +0.414098 q^{11} -2.78209 q^{12} +3.22547 q^{13} +3.29799 q^{14} +1.70502 q^{15} +1.00000 q^{16} -3.44237 q^{17} +4.74004 q^{18} +0.166655 q^{19} -0.612854 q^{20} -9.17531 q^{21} +0.414098 q^{22} -5.28363 q^{23} -2.78209 q^{24} -4.62441 q^{25} +3.22547 q^{26} -4.84095 q^{27} +3.29799 q^{28} -0.393601 q^{29} +1.70502 q^{30} +7.14330 q^{31} +1.00000 q^{32} -1.15206 q^{33} -3.44237 q^{34} -2.02119 q^{35} +4.74004 q^{36} +7.24429 q^{37} +0.166655 q^{38} -8.97356 q^{39} -0.612854 q^{40} +1.89387 q^{41} -9.17531 q^{42} +3.22093 q^{43} +0.414098 q^{44} -2.90495 q^{45} -5.28363 q^{46} +11.1036 q^{47} -2.78209 q^{48} +3.87674 q^{49} -4.62441 q^{50} +9.57699 q^{51} +3.22547 q^{52} -0.396855 q^{53} -4.84095 q^{54} -0.253781 q^{55} +3.29799 q^{56} -0.463649 q^{57} -0.393601 q^{58} +10.5344 q^{59} +1.70502 q^{60} +4.54193 q^{61} +7.14330 q^{62} +15.6326 q^{63} +1.00000 q^{64} -1.97674 q^{65} -1.15206 q^{66} +6.02048 q^{67} -3.44237 q^{68} +14.6996 q^{69} -2.02119 q^{70} -11.9882 q^{71} +4.74004 q^{72} +15.7021 q^{73} +7.24429 q^{74} +12.8655 q^{75} +0.166655 q^{76} +1.36569 q^{77} -8.97356 q^{78} +6.42408 q^{79} -0.612854 q^{80} -0.752148 q^{81} +1.89387 q^{82} +1.14168 q^{83} -9.17531 q^{84} +2.10967 q^{85} +3.22093 q^{86} +1.09504 q^{87} +0.414098 q^{88} -12.0973 q^{89} -2.90495 q^{90} +10.6376 q^{91} -5.28363 q^{92} -19.8733 q^{93} +11.1036 q^{94} -0.102135 q^{95} -2.78209 q^{96} -6.57059 q^{97} +3.87674 q^{98} +1.96284 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 13 q^{3} + 16 q^{4} + 4 q^{5} + 13 q^{6} + 7 q^{7} + 16 q^{8} + 21 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 + 13 * q^3 + 16 * q^4 + 4 * q^5 + 13 * q^6 + 7 * q^7 + 16 * q^8 + 21 * q^9	\( 16 q + 16 q^{2} + 13 q^{3} + 16 q^{4} + 4 q^{5} + 13 q^{6} + 7 q^{7} + 16 q^{8} + 21 q^{9} + 4 q^{10} + 4 q^{11} + 13 q^{12} + 17 q^{13} + 7 q^{14} + 8 q^{15} + 16 q^{16} - q^{17} + 21 q^{18} + 23 q^{19} + 4 q^{20} + 9 q^{21} + 4 q^{22} + 15 q^{23} + 13 q^{24} + 24 q^{25} + 17 q^{26} + 31 q^{27} + 7 q^{28} + 4 q^{29} + 8 q^{30} + 42 q^{31} + 16 q^{32} + 3 q^{33} - q^{34} - 13 q^{35} + 21 q^{36} + 31 q^{37} + 23 q^{38} - 2 q^{39} + 4 q^{40} - 9 q^{41} + 9 q^{42} + 13 q^{43} + 4 q^{44} - 2 q^{45} + 15 q^{46} + 18 q^{47} + 13 q^{48} - 9 q^{49} + 24 q^{50} - 2 q^{51} + 17 q^{52} - 14 q^{53} + 31 q^{54} - 2 q^{55} + 7 q^{56} - 18 q^{57} + 4 q^{58} + 4 q^{59} + 8 q^{60} + q^{61} + 42 q^{62} + 17 q^{63} + 16 q^{64} - 32 q^{65} + 3 q^{66} + 5 q^{67} - q^{68} + 6 q^{69} - 13 q^{70} + 9 q^{71} + 21 q^{72} + 28 q^{73} + 31 q^{74} + 16 q^{75} + 23 q^{76} - 30 q^{77} - 2 q^{78} + 10 q^{79} + 4 q^{80} + 12 q^{81} - 9 q^{82} + 3 q^{83} + 9 q^{84} - 7 q^{85} + 13 q^{86} - 22 q^{87} + 4 q^{88} - 17 q^{89} - 2 q^{90} + 12 q^{91} + 15 q^{92} - q^{93} + 18 q^{94} - 4 q^{95} + 13 q^{96} - 17 q^{97} - 9 q^{98} - 10 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 13 * q^3 + 16 * q^4 + 4 * q^5 + 13 * q^6 + 7 * q^7 + 16 * q^8 + 21 * q^9 + 4 * q^10 + 4 * q^11 + 13 * q^12 + 17 * q^13 + 7 * q^14 + 8 * q^15 + 16 * q^16 - q^17 + 21 * q^18 + 23 * q^19 + 4 * q^20 + 9 * q^21 + 4 * q^22 + 15 * q^23 + 13 * q^24 + 24 * q^25 + 17 * q^26 + 31 * q^27 + 7 * q^28 + 4 * q^29 + 8 * q^30 + 42 * q^31 + 16 * q^32 + 3 * q^33 - q^34 - 13 * q^35 + 21 * q^36 + 31 * q^37 + 23 * q^38 - 2 * q^39 + 4 * q^40 - 9 * q^41 + 9 * q^42 + 13 * q^43 + 4 * q^44 - 2 * q^45 + 15 * q^46 + 18 * q^47 + 13 * q^48 - 9 * q^49 + 24 * q^50 - 2 * q^51 + 17 * q^52 - 14 * q^53 + 31 * q^54 - 2 * q^55 + 7 * q^56 - 18 * q^57 + 4 * q^58 + 4 * q^59 + 8 * q^60 + q^61 + 42 * q^62 + 17 * q^63 + 16 * q^64 - 32 * q^65 + 3 * q^66 + 5 * q^67 - q^68 + 6 * q^69 - 13 * q^70 + 9 * q^71 + 21 * q^72 + 28 * q^73 + 31 * q^74 + 16 * q^75 + 23 * q^76 - 30 * q^77 - 2 * q^78 + 10 * q^79 + 4 * q^80 + 12 * q^81 - 9 * q^82 + 3 * q^83 + 9 * q^84 - 7 * q^85 + 13 * q^86 - 22 * q^87 + 4 * q^88 - 17 * q^89 - 2 * q^90 + 12 * q^91 + 15 * q^92 - q^93 + 18 * q^94 - 4 * q^95 + 13 * q^96 - 17 * q^97 - 9 * q^98 - 10 * q^99

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