LMFDB - Embedded newform 671.2.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(1,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, 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("671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.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:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 5 x^{18} - 18 x^{17} + 122 x^{16} + 78 x^{15} - 1177 x^{14} + 387 x^{13} + 5755 x^{12} + \cdots - 43 $ x^19 - 5x^18 - 18x^17 + 122x^16 + 78x^15 - 1177x^14 + 387x^13 + 5755x^12 - 4673x^11 - 15053x^10 + 16875x^9 + 20141x^8 - 28019x^7 - 11589x^6 + 21077x^5 + 1674x^4 - 6404x^3 + 241x^2 + 643x - 43
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.82302$ of defining polynomial
Character	$\chi$	$=$	671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.82302 q^{2} +3.09920 q^{3} +1.32341 q^{4} -3.15385 q^{5} -5.64991 q^{6} -0.287436 q^{7} +1.23344 q^{8} +6.60505 q^{9} +O(q^{10})$	\(q-1.82302 q^{2} +3.09920 q^{3} +1.32341 q^{4} -3.15385 q^{5} -5.64991 q^{6} -0.287436 q^{7} +1.23344 q^{8} +6.60505 q^{9} +5.74953 q^{10} +1.00000 q^{11} +4.10152 q^{12} +0.910644 q^{13} +0.524002 q^{14} -9.77441 q^{15} -4.89541 q^{16} +0.621790 q^{17} -12.0412 q^{18} +6.81024 q^{19} -4.17384 q^{20} -0.890822 q^{21} -1.82302 q^{22} -7.16003 q^{23} +3.82267 q^{24} +4.94675 q^{25} -1.66012 q^{26} +11.1728 q^{27} -0.380396 q^{28} +7.26934 q^{29} +17.8190 q^{30} +5.73531 q^{31} +6.45756 q^{32} +3.09920 q^{33} -1.13354 q^{34} +0.906529 q^{35} +8.74120 q^{36} +9.51534 q^{37} -12.4152 q^{38} +2.82227 q^{39} -3.89007 q^{40} +6.96842 q^{41} +1.62399 q^{42} +1.62703 q^{43} +1.32341 q^{44} -20.8313 q^{45} +13.0529 q^{46} -11.4314 q^{47} -15.1718 q^{48} -6.91738 q^{49} -9.01804 q^{50} +1.92705 q^{51} +1.20516 q^{52} +2.14938 q^{53} -20.3682 q^{54} -3.15385 q^{55} -0.354534 q^{56} +21.1063 q^{57} -13.2522 q^{58} +4.08607 q^{59} -12.9356 q^{60} -1.00000 q^{61} -10.4556 q^{62} -1.89853 q^{63} -1.98147 q^{64} -2.87203 q^{65} -5.64991 q^{66} +11.2048 q^{67} +0.822884 q^{68} -22.1904 q^{69} -1.65262 q^{70} +4.90057 q^{71} +8.14691 q^{72} +9.71284 q^{73} -17.3467 q^{74} +15.3310 q^{75} +9.01275 q^{76} -0.287436 q^{77} -5.14506 q^{78} -4.88947 q^{79} +15.4394 q^{80} +14.8115 q^{81} -12.7036 q^{82} -8.93050 q^{83} -1.17892 q^{84} -1.96103 q^{85} -2.96610 q^{86} +22.5292 q^{87} +1.23344 q^{88} -13.4860 q^{89} +37.9760 q^{90} -0.261752 q^{91} -9.47567 q^{92} +17.7749 q^{93} +20.8398 q^{94} -21.4785 q^{95} +20.0133 q^{96} +3.68860 q^{97} +12.6105 q^{98} +6.60505 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9}+O(q^{10}) $ 19 * q + 5 * q^2 + 23 * q^4 + q^6 + 9 * q^7 + 9 * q^8 + 29 * q^9	\( 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9} + 7 q^{10} + 19 q^{11} - 4 q^{12} + 8 q^{13} - 11 q^{14} - 5 q^{15} + 31 q^{16} + 9 q^{17} + 10 q^{18} + 17 q^{19} - 6 q^{20} + 18 q^{21} + 5 q^{22} - 10 q^{23} + 26 q^{24} + 45 q^{25} + 5 q^{26} - 33 q^{27} + 36 q^{28} + 27 q^{29} - 30 q^{30} + 7 q^{31} + 8 q^{32} - 5 q^{34} + 17 q^{35} + 38 q^{36} + 20 q^{37} - 37 q^{38} + 24 q^{39} + 10 q^{40} + 19 q^{41} + 21 q^{42} + 20 q^{43} + 23 q^{44} - 32 q^{45} + 41 q^{46} - 19 q^{47} + 5 q^{48} + 42 q^{49} + 36 q^{50} + 47 q^{51} - 28 q^{52} + 3 q^{53} - 33 q^{54} - 44 q^{56} + 11 q^{57} + 23 q^{58} - 28 q^{59} - 96 q^{60} - 19 q^{61} - 11 q^{62} - 32 q^{63} + 47 q^{64} + 25 q^{65} + q^{66} + 3 q^{67} + 38 q^{68} + 3 q^{70} - 19 q^{71} + 34 q^{72} + 20 q^{73} - 22 q^{74} - 50 q^{75} - 25 q^{76} + 9 q^{77} - 94 q^{78} + 69 q^{79} - 36 q^{80} + 47 q^{81} - 61 q^{82} + q^{83} - 28 q^{84} + 24 q^{85} - 27 q^{86} - 58 q^{87} + 9 q^{88} + 36 q^{90} + 24 q^{91} - 67 q^{92} - 14 q^{93} + 64 q^{94} - 3 q^{95} - 26 q^{96} + 21 q^{97} - 87 q^{98} + 29 q^{99}+O(q^{100}) \) 19 * q + 5 * q^2 + 23 * q^4 + q^6 + 9 * q^7 + 9 * q^8 + 29 * q^9 + 7 * q^10 + 19 * q^11 - 4 * q^12 + 8 * q^13 - 11 * q^14 - 5 * q^15 + 31 * q^16 + 9 * q^17 + 10 * q^18 + 17 * q^19 - 6 * q^20 + 18 * q^21 + 5 * q^22 - 10 * q^23 + 26 * q^24 + 45 * q^25 + 5 * q^26 - 33 * q^27 + 36 * q^28 + 27 * q^29 - 30 * q^30 + 7 * q^31 + 8 * q^32 - 5 * q^34 + 17 * q^35 + 38 * q^36 + 20 * q^37 - 37 * q^38 + 24 * q^39 + 10 * q^40 + 19 * q^41 + 21 * q^42 + 20 * q^43 + 23 * q^44 - 32 * q^45 + 41 * q^46 - 19 * q^47 + 5 * q^48 + 42 * q^49 + 36 * q^50 + 47 * q^51 - 28 * q^52 + 3 * q^53 - 33 * q^54 - 44 * q^56 + 11 * q^57 + 23 * q^58 - 28 * q^59 - 96 * q^60 - 19 * q^61 - 11 * q^62 - 32 * q^63 + 47 * q^64 + 25 * q^65 + q^66 + 3 * q^67 + 38 * q^68 + 3 * q^70 - 19 * q^71 + 34 * q^72 + 20 * q^73 - 22 * q^74 - 50 * q^75 - 25 * q^76 + 9 * q^77 - 94 * q^78 + 69 * q^79 - 36 * q^80 + 47 * q^81 - 61 * q^82 + q^83 - 28 * q^84 + 24 * q^85 - 27 * q^86 - 58 * q^87 + 9 * q^88 + 36 * q^90 + 24 * q^91 - 67 * q^92 - 14 * q^93 + 64 * q^94 - 3 * q^95 - 26 * q^96 + 21 * q^97 - 87 * q^98 + 29 * 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 $

$2$	−1.82302	−1.28907	−0.644536	−	0.764574i	$-0.722949\pi$
$2$	−1.82302	−1.28907	−0.644536	+	0.764574i	$0.722949\pi$
$3$	3.09920	1.78932	0.894662	−	0.446743i	$-0.147416\pi$
$3$	3.09920	1.78932	0.894662	+	0.446743i	$0.147416\pi$
$4$	1.32341	0.661705
$5$	−3.15385	−1.41044	−0.705222	−	0.708987i	$-0.749152\pi$
$5$	−3.15385	−1.41044	−0.705222	+	0.708987i	$0.749152\pi$
$6$	−5.64991	−2.30657
$7$	−0.287436	−0.108641	−0.0543203	−	0.998524i	$-0.517299\pi$
$7$	−0.287436	−0.108641	−0.0543203	+	0.998524i	$0.517299\pi$
$8$	1.23344	0.436086
$9$	6.60505	2.20168
$10$	5.74953	1.81816
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	4.10152	1.18401
$13$	0.910644	0.252567	0.126284	−	0.991994i	$-0.459695\pi$
$13$	0.910644	0.252567	0.126284	+	0.991994i	$0.459695\pi$
$14$	0.524002	0.140045
$15$	−9.77441	−2.52374
$16$	−4.89541	−1.22385
$17$	0.621790	0.150806	0.0754031	−	0.997153i	$-0.475976\pi$
$17$	0.621790	0.150806	0.0754031	+	0.997153i	$0.475976\pi$
$18$	−12.0412	−2.83813
$19$	6.81024	1.56238	0.781188	−	0.624295i	$-0.214614\pi$
$19$	6.81024	1.56238	0.781188	+	0.624295i	$0.214614\pi$
$20$	−4.17384	−0.933298
$21$	−0.890822	−0.194393
$22$	−1.82302	−0.388670
$23$	−7.16003	−1.49297	−0.746485	−	0.665402i	$-0.768260\pi$
$23$	−7.16003	−1.49297	−0.746485	+	0.665402i	$0.768260\pi$
$24$	3.82267	0.780299
$25$	4.94675	0.989350
$26$	−1.66012	−0.325577
$27$	11.1728	2.15020
$28$	−0.380396	−0.0718881
$29$	7.26934	1.34988	0.674942	−	0.737871i	$-0.264169\pi$
$29$	7.26934	1.34988	0.674942	+	0.737871i	$0.264169\pi$
$30$	17.8190	3.25328
$31$	5.73531	1.03009	0.515046	−	0.857162i	$-0.327775\pi$
$31$	5.73531	1.03009	0.515046	+	0.857162i	$0.327775\pi$
$32$	6.45756	1.14155
$33$	3.09920	0.539502
$34$	−1.13354	−0.194400
$35$	0.906529	0.153231
$36$	8.74120	1.45687
$37$	9.51534	1.56431	0.782156	−	0.623082i	$-0.214120\pi$
$37$	9.51534	1.56431	0.782156	+	0.623082i	$0.214120\pi$
$38$	−12.4152	−2.01402
$39$	2.82227	0.451925
$40$	−3.89007	−0.615074
$41$	6.96842	1.08828	0.544142	−	0.838993i	$-0.316855\pi$
$41$	6.96842	1.08828	0.544142	+	0.838993i	$0.316855\pi$
$42$	1.62399	0.250587
$43$	1.62703	0.248119	0.124060	−	0.992275i	$-0.460409\pi$
$43$	1.62703	0.248119	0.124060	+	0.992275i	$0.460409\pi$
$44$	1.32341	0.199512
$45$	−20.8313	−3.10535
$46$	13.0529	1.92455
$47$	−11.4314	−1.66745	−0.833724	−	0.552181i	$-0.813796\pi$
$47$	−11.4314	−1.66745	−0.833724	+	0.552181i	$0.813796\pi$
$48$	−15.1718	−2.18987
$49$	−6.91738	−0.988197
$50$	−9.01804	−1.27534
$51$	1.92705	0.269841
$52$	1.20516	0.167125
$53$	2.14938	0.295240	0.147620	−	0.989044i	$-0.452839\pi$
$53$	2.14938	0.295240	0.147620	+	0.989044i	$0.452839\pi$
$54$	−20.3682	−2.77176
$55$	−3.15385	−0.425265
$56$	−0.354534	−0.0473766
$57$	21.1063	2.79560
$58$	−13.2522	−1.74010
$59$	4.08607	0.531961	0.265981	−	0.963978i	$-0.414304\pi$
$59$	4.08607	0.531961	0.265981	+	0.963978i	$0.414304\pi$
$60$	−12.9356	−1.66997
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−10.4556	−1.32786
$63$	−1.89853	−0.239192
$64$	−1.98147	−0.247683
$65$	−2.87203	−0.356232
$66$	−5.64991	−0.695456
$67$	11.2048	1.36888	0.684442	−	0.729067i	$-0.260046\pi$
$67$	11.2048	1.36888	0.684442	+	0.729067i	$0.260046\pi$
$68$	0.822884	0.0997893
$69$	−22.1904	−2.67141
$70$	−1.65262	−0.197526
$71$	4.90057	0.581591	0.290795	−	0.956785i	$-0.406080\pi$
$71$	4.90057	0.581591	0.290795	+	0.956785i	$0.406080\pi$
$72$	8.14691	0.960123
$73$	9.71284	1.13680	0.568401	−	0.822752i	$-0.307562\pi$
$73$	9.71284	1.13680	0.568401	+	0.822752i	$0.307562\pi$
$74$	−17.3467	−2.01651
$75$	15.3310	1.77027
$76$	9.01275	1.03383
$77$	−0.287436	−0.0327564
$78$	−5.14506	−0.582563
$79$	−4.88947	−0.550109	−0.275054	−	0.961429i	$-0.588696\pi$
$79$	−4.88947	−0.550109	−0.275054	+	0.961429i	$0.588696\pi$
$80$	15.4394	1.72617
$81$	14.8115	1.64573
$82$	−12.7036	−1.40288
$83$	−8.93050	−0.980250	−0.490125	−	0.871652i	$-0.663049\pi$
$83$	−8.93050	−0.980250	−0.490125	+	0.871652i	$0.663049\pi$
$84$	−1.17892	−0.128631
$85$	−1.96103	−0.212704
$86$	−2.96610	−0.319843
$87$	22.5292	2.41538
$88$	1.23344	0.131485
$89$	−13.4860	−1.42952	−0.714758	−	0.699372i	$-0.753463\pi$
$89$	−13.4860	−1.42952	−0.714758	+	0.699372i	$0.753463\pi$
$90$	37.9760	4.00302
$91$	−0.261752	−0.0274390
$92$	−9.47567	−0.987906
$93$	17.7749	1.84317
$94$	20.8398	2.14946
$95$	−21.4785	−2.20364
$96$	20.0133	2.04260
$97$	3.68860	0.374520	0.187260	−	0.982310i	$-0.440039\pi$
$97$	3.68860	0.374520	0.187260	+	0.982310i	$0.440039\pi$
$98$	12.6105	1.27386
$99$	6.60505	0.663832
$100$	6.54658	0.654658
$101$	−10.0944	−1.00443	−0.502217	−	0.864742i	$-0.667482\pi$
$101$	−10.0944	−1.00443	−0.502217	+	0.864742i	$0.667482\pi$
$102$	−3.51306	−0.347845
$103$	−10.5365	−1.03819	−0.519097	−	0.854715i	$-0.673732\pi$
$103$	−10.5365	−1.03819	−0.519097	+	0.854715i	$0.673732\pi$
$104$	1.12322	0.110141
$105$	2.80952	0.274181
$106$	−3.91836	−0.380585
$107$	16.3056	1.57632	0.788160	−	0.615470i	$-0.211034\pi$
$107$	16.3056	1.57632	0.788160	+	0.615470i	$0.211034\pi$
$108$	14.7862	1.42280
$109$	5.49319	0.526152	0.263076	−	0.964775i	$-0.415263\pi$
$109$	5.49319	0.526152	0.263076	+	0.964775i	$0.415263\pi$
$110$	5.74953	0.548197
$111$	29.4900	2.79906
$112$	1.40712	0.132960
$113$	−11.7663	−1.10688	−0.553442	−	0.832887i	$-0.686686\pi$
$113$	−11.7663	−1.10688	−0.553442	+	0.832887i	$0.686686\pi$
$114$	−38.4773	−3.60373
$115$	22.5816	2.10575
$116$	9.62033	0.893225
$117$	6.01485	0.556073
$118$	−7.44900	−0.685736
$119$	−0.178725	−0.0163837
$120$	−12.0561	−1.10057
$121$	1.00000	0.0909091
$122$	1.82302	0.165049
$123$	21.5965	1.94729
$124$	7.59017	0.681618
$125$	0.167943	0.0150213
$126$	3.46106	0.308336
$127$	−17.6684	−1.56781	−0.783907	−	0.620878i	$-0.786776\pi$
$127$	−17.6684	−1.56781	−0.783907	+	0.620878i	$0.786776\pi$
$128$	−9.30286	−0.822265
$129$	5.04248	0.443966
$130$	5.23578	0.459208
$131$	−6.52874	−0.570419	−0.285209	−	0.958465i	$-0.592063\pi$
$131$	−6.52874	−0.570419	−0.285209	+	0.958465i	$0.592063\pi$
$132$	4.10152	0.356991
$133$	−1.95751	−0.169738
$134$	−20.4266	−1.76459
$135$	−35.2372	−3.03274
$136$	0.766939	0.0657645
$137$	−14.2878	−1.22069	−0.610345	−	0.792136i	$-0.708969\pi$
$137$	−14.2878	−1.22069	−0.610345	+	0.792136i	$0.708969\pi$
$138$	40.4536	3.44364
$139$	−0.596965	−0.0506339	−0.0253169	−	0.999679i	$-0.508059\pi$
$139$	−0.596965	−0.0506339	−0.0253169	+	0.999679i	$0.508059\pi$
$140$	1.19971	0.101394
$141$	−35.4284	−2.98361
$142$	−8.93385	−0.749712
$143$	0.910644	0.0761519
$144$	−32.3344	−2.69453
$145$	−22.9264	−1.90393
$146$	−17.7067	−1.46542
$147$	−21.4384	−1.76821
$148$	12.5927	1.03511
$149$	15.4628	1.26676	0.633382	−	0.773839i	$-0.281666\pi$
$149$	15.4628	1.26676	0.633382	+	0.773839i	$0.281666\pi$
$150$	−27.9487	−2.28200
$151$	7.37707	0.600338	0.300169	−	0.953886i	$-0.402957\pi$
$151$	7.37707	0.600338	0.300169	+	0.953886i	$0.402957\pi$
$152$	8.40001	0.681330
$153$	4.10695	0.332028
$154$	0.524002	0.0422253
$155$	−18.0883	−1.45289
$156$	3.73502	0.299041
$157$	7.79705	0.622272	0.311136	−	0.950365i	$-0.399291\pi$
$157$	7.79705	0.622272	0.311136	+	0.950365i	$0.399291\pi$
$158$	8.91362	0.709129
$159$	6.66135	0.528280
$160$	−20.3662	−1.61009
$161$	2.05805	0.162197
$162$	−27.0018	−2.12146
$163$	−0.591572	−0.0463355	−0.0231677	−	0.999732i	$-0.507375\pi$
$163$	−0.591572	−0.0463355	−0.0231677	+	0.999732i	$0.507375\pi$
$164$	9.22208	0.720123
$165$	−9.77441	−0.760937
$166$	16.2805	1.26361
$167$	3.67811	0.284621	0.142310	−	0.989822i	$-0.454547\pi$
$167$	3.67811	0.284621	0.142310	+	0.989822i	$0.454547\pi$
$168$	−1.09877	−0.0847721
$169$	−12.1707	−0.936210
$170$	3.57500	0.274190
$171$	44.9820	3.43986
$172$	2.15322	0.164182
$173$	−12.9607	−0.985383	−0.492692	−	0.870204i	$-0.663987\pi$
$173$	−12.9607	−0.985383	−0.492692	+	0.870204i	$0.663987\pi$
$174$	−41.0712	−3.11360
$175$	−1.42187	−0.107484
$176$	−4.89541	−0.369005
$177$	12.6636	0.951851
$178$	24.5853	1.84275
$179$	−10.0940	−0.754458	−0.377229	−	0.926120i	$-0.623123\pi$
$179$	−10.0940	−0.754458	−0.377229	+	0.926120i	$0.623123\pi$
$180$	−27.5684	−2.05483
$181$	−16.4988	−1.22635	−0.613174	−	0.789948i	$-0.710108\pi$
$181$	−16.4988	−1.22635	−0.613174	+	0.789948i	$0.710108\pi$
$182$	0.477179	0.0353709
$183$	−3.09920	−0.229100
$184$	−8.83145	−0.651063
$185$	−30.0099	−2.20637
$186$	−32.4040	−2.37598
$187$	0.621790	0.0454698
$188$	−15.1285	−1.10336
$189$	−3.21146	−0.233599
$190$	39.1557	2.84065
$191$	7.51056	0.543445	0.271722	−	0.962376i	$-0.412407\pi$
$191$	7.51056	0.543445	0.271722	+	0.962376i	$0.412407\pi$
$192$	−6.14096	−0.443186
$193$	−20.3457	−1.46451	−0.732257	−	0.681029i	$-0.761533\pi$
$193$	−20.3457	−1.46451	−0.732257	+	0.681029i	$0.761533\pi$
$194$	−6.72439	−0.482783
$195$	−8.90101	−0.637414
$196$	−9.15454	−0.653896
$197$	−10.2107	−0.727481	−0.363741	−	0.931500i	$-0.618501\pi$
$197$	−10.2107	−0.727481	−0.363741	+	0.931500i	$0.618501\pi$
$198$	−12.0412	−0.855728
$199$	9.42808	0.668339	0.334169	−	0.942513i	$-0.391544\pi$
$199$	9.42808	0.668339	0.334169	+	0.942513i	$0.391544\pi$
$200$	6.10150	0.431441
$201$	34.7259	2.44938
$202$	18.4024	1.29479
$203$	−2.08947	−0.146652
$204$	2.55028	0.178555
$205$	−21.9773	−1.53496
$206$	19.2083	1.33831
$207$	−47.2924	−3.28705
$208$	−4.45797	−0.309105
$209$	6.81024	0.471074
$210$	−5.12181	−0.353438
$211$	−12.0384	−0.828761	−0.414380	−	0.910104i	$-0.636002\pi$
$211$	−12.0384	−0.828761	−0.414380	+	0.910104i	$0.636002\pi$
$212$	2.84451	0.195362
$213$	15.1879	1.04065
$214$	−29.7254	−2.03199
$215$	−5.13139	−0.349958
$216$	13.7809	0.937673
$217$	−1.64853	−0.111910
$218$	−10.0142	−0.678248
$219$	30.1020	2.03411
$220$	−4.17384	−0.281400
$221$	0.566229	0.0380887
$222$	−53.7609	−3.60819
$223$	16.0854	1.07715	0.538577	−	0.842576i	$-0.318962\pi$
$223$	16.0854	1.07715	0.538577	+	0.842576i	$0.318962\pi$
$224$	−1.85613	−0.124018
$225$	32.6735	2.17824
$226$	21.4503	1.42685
$227$	8.88217	0.589530	0.294765	−	0.955570i	$-0.404759\pi$
$227$	8.88217	0.589530	0.294765	+	0.955570i	$0.404759\pi$
$228$	27.9323	1.84986
$229$	−11.2325	−0.742264	−0.371132	−	0.928580i	$-0.621030\pi$
$229$	−11.2325	−0.742264	−0.371132	+	0.928580i	$0.621030\pi$
$230$	−41.1668	−2.71446
$231$	−0.890822	−0.0586118
$232$	8.96628	0.588665
$233$	15.7110	1.02926	0.514631	−	0.857412i	$-0.327929\pi$
$233$	15.7110	1.02926	0.514631	+	0.857412i	$0.327929\pi$
$234$	−10.9652	−0.716818
$235$	36.0530	2.35184
$236$	5.40755	0.352002
$237$	−15.1535	−0.984323
$238$	0.325819	0.0211197
$239$	6.28509	0.406549	0.203274	−	0.979122i	$-0.434842\pi$
$239$	6.28509	0.406549	0.203274	+	0.979122i	$0.434842\pi$
$240$	47.8497	3.08868
$241$	3.70185	0.238457	0.119229	−	0.992867i	$-0.461958\pi$
$241$	3.70185	0.238457	0.119229	+	0.992867i	$0.461958\pi$
$242$	−1.82302	−0.117188
$243$	12.3856	0.794537
$244$	−1.32341	−0.0847227
$245$	21.8164	1.39380
$246$	−39.3710	−2.51020
$247$	6.20171	0.394605
$248$	7.07414	0.449209
$249$	−27.6774	−1.75399
$250$	−0.306165	−0.0193636
$251$	7.05635	0.445393	0.222696	−	0.974888i	$-0.428514\pi$
$251$	7.05635	0.445393	0.222696	+	0.974888i	$0.428514\pi$
$252$	−2.51253	−0.158275
$253$	−7.16003	−0.450147
$254$	32.2098	2.02102
$255$	−6.07763	−0.380596
$256$	20.9223	1.30764
$257$	−4.59045	−0.286345	−0.143172	−	0.989698i	$-0.545730\pi$
$257$	−4.59045	−0.286345	−0.143172	+	0.989698i	$0.545730\pi$
$258$	−9.19255	−0.572303
$259$	−2.73505	−0.169948
$260$	−3.80088	−0.235720
$261$	48.0144	2.97202
$262$	11.9020	0.735310
$263$	0.961078	0.0592626	0.0296313	−	0.999561i	$-0.490567\pi$
$263$	0.961078	0.0592626	0.0296313	+	0.999561i	$0.490567\pi$
$264$	3.82267	0.235269
$265$	−6.77881	−0.416419
$266$	3.56858	0.218804
$267$	−41.7959	−2.55787
$268$	14.8286	0.905799
$269$	13.6257	0.830773	0.415386	−	0.909645i	$-0.363646\pi$
$269$	13.6257	0.830773	0.415386	+	0.909645i	$0.363646\pi$
$270$	64.2382	3.90942
$271$	−29.0169	−1.76265	−0.881327	−	0.472507i	$-0.843349\pi$
$271$	−29.0169	−1.76265	−0.881327	+	0.472507i	$0.843349\pi$
$272$	−3.04391	−0.184564
$273$	−0.811222	−0.0490974
$274$	26.0470	1.57356
$275$	4.94675	0.298300
$276$	−29.3670	−1.76769
$277$	−16.5957	−0.997137	−0.498569	−	0.866850i	$-0.666141\pi$
$277$	−16.5957	−0.997137	−0.498569	+	0.866850i	$0.666141\pi$
$278$	1.08828	0.0652707
$279$	37.8820	2.26794
$280$	1.11815	0.0668220
$281$	7.06643	0.421548	0.210774	−	0.977535i	$-0.432402\pi$
$281$	7.06643	0.421548	0.210774	+	0.977535i	$0.432402\pi$
$282$	64.5867	3.84608
$283$	−14.4028	−0.856160	−0.428080	−	0.903741i	$-0.640810\pi$
$283$	−14.4028	−0.856160	−0.428080	+	0.903741i	$0.640810\pi$
$284$	6.48547	0.384842
$285$	−66.5661	−3.94303
$286$	−1.66012	−0.0981652
$287$	−2.00297	−0.118232
$288$	42.6525	2.51332
$289$	−16.6134	−0.977257
$290$	41.7953	2.45431
$291$	11.4317	0.670138
$292$	12.8541	0.752228
$293$	−28.4883	−1.66431	−0.832153	−	0.554547i	$-0.812892\pi$
$293$	−28.4883	−1.66431	−0.832153	+	0.554547i	$0.812892\pi$
$294$	39.0826	2.27934
$295$	−12.8868	−0.750301
$296$	11.7366	0.682175
$297$	11.1728	0.648310
$298$	−28.1891	−1.63295
$299$	−6.52024	−0.377075
$300$	20.2892	1.17140
$301$	−0.467666	−0.0269558
$302$	−13.4486	−0.773878
$303$	−31.2847	−1.79726
$304$	−33.3389	−1.91212
$305$	3.15385	0.180589
$306$	−7.48707	−0.428007
$307$	10.5356	0.601297	0.300649	−	0.953735i	$-0.402797\pi$
$307$	10.5356	0.601297	0.300649	+	0.953735i	$0.402797\pi$
$308$	−0.380396	−0.0216751
$309$	−32.6548	−1.85767
$310$	32.9754	1.87287
$311$	16.5963	0.941087	0.470544	−	0.882377i	$-0.344058\pi$
$311$	16.5963	0.941087	0.470544	+	0.882377i	$0.344058\pi$
$312$	3.48109	0.197078
$313$	9.85264	0.556904	0.278452	−	0.960450i	$-0.410179\pi$
$313$	9.85264	0.556904	0.278452	+	0.960450i	$0.410179\pi$
$314$	−14.2142	−0.802153
$315$	5.98767	0.337367
$316$	−6.47078	−0.364010
$317$	−29.8035	−1.67393	−0.836964	−	0.547257i	$-0.815672\pi$
$317$	−29.8035	−1.67393	−0.836964	+	0.547257i	$0.815672\pi$
$318$	−12.1438	−0.680990
$319$	7.26934	0.407005
$320$	6.24924	0.349343
$321$	50.5343	2.82055
$322$	−3.75187	−0.209084
$323$	4.23454	0.235616
$324$	19.6017	1.08899
$325$	4.50473	0.249877
$326$	1.07845	0.0597297
$327$	17.0245	0.941457
$328$	8.59510	0.474585
$329$	3.28581	0.181153
$330$	17.8190	0.980902
$331$	−33.2914	−1.82986	−0.914931	−	0.403611i	$-0.867755\pi$
$331$	−33.2914	−1.82986	−0.914931	+	0.403611i	$0.867755\pi$
$332$	−11.8187	−0.648637
$333$	62.8493	3.44412
$334$	−6.70528	−0.366897
$335$	−35.3382	−1.93073
$336$	4.36093	0.237908
$337$	17.5453	0.955753	0.477876	−	0.878427i	$-0.341407\pi$
$337$	17.5453	0.955753	0.477876	+	0.878427i	$0.341407\pi$
$338$	22.1875	1.20684
$339$	−36.4663	−1.98058
$340$	−2.59525	−0.140747
$341$	5.73531	0.310585
$342$	−82.0032	−4.43422
$343$	4.00035	0.215999
$344$	2.00683	0.108201
$345$	69.9851	3.76787
$346$	23.6276	1.27023
$347$	19.7792	1.06180	0.530902	−	0.847433i	$-0.321853\pi$
$347$	19.7792	1.06180	0.530902	+	0.847433i	$0.321853\pi$
$348$	29.8153	1.59827
$349$	−19.0217	−1.01821	−0.509103	−	0.860705i	$-0.670023\pi$
$349$	−19.0217	−1.01821	−0.509103	+	0.860705i	$0.670023\pi$
$350$	2.59211	0.138554
$351$	10.1744	0.543070
$352$	6.45756	0.344189
$353$	−28.2882	−1.50563	−0.752814	−	0.658233i	$-0.771304\pi$
$353$	−28.2882	−1.50563	−0.752814	+	0.658233i	$0.771304\pi$
$354$	−23.0860	−1.22700
$355$	−15.4557	−0.820301
$356$	−17.8476	−0.945918
$357$	−0.553904	−0.0293157
$358$	18.4015	0.972551
$359$	−19.0153	−1.00359	−0.501796	−	0.864986i	$-0.667327\pi$
$359$	−19.0153	−1.00359	−0.501796	+	0.864986i	$0.667327\pi$
$360$	−25.6941	−1.35420
$361$	27.3794	1.44102
$362$	30.0777	1.58085
$363$	3.09920	0.162666
$364$	−0.346405	−0.0181566
$365$	−30.6328	−1.60339
$366$	5.64991	0.295326
$367$	1.78686	0.0932731	0.0466365	−	0.998912i	$-0.485150\pi$
$367$	1.78686	0.0932731	0.0466365	+	0.998912i	$0.485150\pi$
$368$	35.0513	1.82717
$369$	46.0267	2.39606
$370$	54.7088	2.84417
$371$	−0.617808	−0.0320750
$372$	23.5235	1.21964
$373$	19.1615	0.992146	0.496073	−	0.868281i	$-0.334775\pi$
$373$	19.1615	0.992146	0.496073	+	0.868281i	$0.334775\pi$
$374$	−1.13354	−0.0586138
$375$	0.520491	0.0268780
$376$	−14.1000	−0.727151
$377$	6.61979	0.340936
$378$	5.85456	0.301126
$379$	−22.8534	−1.17390	−0.586949	−	0.809624i	$-0.699671\pi$
$379$	−22.8534	−1.17390	−0.586949	+	0.809624i	$0.699671\pi$
$380$	−28.4248	−1.45816
$381$	−54.7578	−2.80533
$382$	−13.6919	−0.700539
$383$	7.28326	0.372157	0.186079	−	0.982535i	$-0.440422\pi$
$383$	7.28326	0.372157	0.186079	+	0.982535i	$0.440422\pi$
$384$	−28.8314	−1.47130
$385$	0.906529	0.0462010
$386$	37.0906	1.88786
$387$	10.7466	0.546280
$388$	4.88153	0.247822
$389$	20.4440	1.03655	0.518276	−	0.855214i	$-0.326574\pi$
$389$	20.4440	1.03655	0.518276	+	0.855214i	$0.326574\pi$
$390$	16.2267	0.821673
$391$	−4.45204	−0.225149
$392$	−8.53215	−0.430939
$393$	−20.2339	−1.02066
$394$	18.6143	0.937775
$395$	15.4206	0.775897
$396$	8.74120	0.439262
$397$	15.9369	0.799852	0.399926	−	0.916547i	$-0.369036\pi$
$397$	15.9369	0.799852	0.399926	+	0.916547i	$0.369036\pi$
$398$	−17.1876	−0.861537
$399$	−6.06671	−0.303716
$400$	−24.2163	−1.21082
$401$	37.1941	1.85738	0.928692	−	0.370852i	$-0.120934\pi$
$401$	37.1941	1.85738	0.928692	+	0.370852i	$0.120934\pi$
$402$	−63.3062	−3.15743
$403$	5.22283	0.260168
$404$	−13.3591	−0.664640
$405$	−46.7133	−2.32120
$406$	3.80915	0.189045
$407$	9.51534	0.471658
$408$	2.37690	0.117674
$409$	33.4964	1.65629	0.828145	−	0.560513i	$-0.189396\pi$
$409$	33.4964	1.65629	0.828145	+	0.560513i	$0.189396\pi$
$410$	40.0651	1.97868
$411$	−44.2808	−2.18421
$412$	−13.9441	−0.686978
$413$	−1.17448	−0.0577926
$414$	86.2151	4.23724
$415$	28.1654	1.38259
$416$	5.88054	0.288317
$417$	−1.85011	−0.0906005
$418$	−12.4152	−0.607249
$419$	−10.6606	−0.520803	−0.260402	−	0.965500i	$-0.583855\pi$
$419$	−10.6606	−0.520803	−0.260402	+	0.965500i	$0.583855\pi$
$420$	3.71814	0.181427
$421$	34.4306	1.67804	0.839021	−	0.544098i	$-0.183128\pi$
$421$	34.4306	1.67804	0.839021	+	0.544098i	$0.183128\pi$
$422$	21.9464	1.06833
$423$	−75.5053	−3.67119
$424$	2.65112	0.128750
$425$	3.07584	0.149200
$426$	−27.6878	−1.34148
$427$	0.287436	0.0139100
$428$	21.5790	1.04306
$429$	2.82227	0.136260
$430$	9.35464	0.451121
$431$	−10.8437	−0.522324	−0.261162	−	0.965295i	$-0.584106\pi$
$431$	−10.8437	−0.522324	−0.261162	+	0.965295i	$0.584106\pi$
$432$	−54.6953	−2.63153
$433$	−1.14549	−0.0550485	−0.0275243	−	0.999621i	$-0.508762\pi$
$433$	−1.14549	−0.0550485	−0.0275243	+	0.999621i	$0.508762\pi$
$434$	3.00532	0.144260
$435$	−71.0535	−3.40676
$436$	7.26975	0.348158
$437$	−48.7616	−2.33258
$438$	−54.8767	−2.62211
$439$	30.5933	1.46014	0.730069	−	0.683373i	$-0.239488\pi$
$439$	30.5933	1.46014	0.730069	+	0.683373i	$0.239488\pi$
$440$	−3.89007	−0.185452
$441$	−45.6896	−2.17570
$442$	−1.03225	−0.0490991
$443$	−9.53948	−0.453234	−0.226617	−	0.973984i	$-0.572767\pi$
$443$	−9.53948	−0.453234	−0.226617	+	0.973984i	$0.572767\pi$
$444$	39.0273	1.85216
$445$	42.5329	2.01625
$446$	−29.3240	−1.38853
$447$	47.9224	2.26665
$448$	0.569545	0.0269085
$449$	16.6546	0.785979	0.392990	−	0.919543i	$-0.371441\pi$
$449$	16.6546	0.785979	0.392990	+	0.919543i	$0.371441\pi$
$450$	−59.5646	−2.80790
$451$	6.96842	0.328130
$452$	−15.5717	−0.732432
$453$	22.8630	1.07420
$454$	−16.1924	−0.759947
$455$	0.825525	0.0387012
$456$	26.0333	1.21912
$457$	6.60614	0.309022	0.154511	−	0.987991i	$-0.450620\pi$
$457$	6.60614	0.309022	0.154511	+	0.987991i	$0.450620\pi$
$458$	20.4771	0.956832
$459$	6.94712	0.324264
$460$	29.8848	1.39339
$461$	9.91877	0.461963	0.230982	−	0.972958i	$-0.425806\pi$
$461$	9.91877	0.461963	0.230982	+	0.972958i	$0.425806\pi$
$462$	1.62399	0.0755548
$463$	−19.7305	−0.916953	−0.458477	−	0.888707i	$-0.651605\pi$
$463$	−19.7305	−0.916953	−0.458477	+	0.888707i	$0.651605\pi$
$464$	−35.5864	−1.65206
$465$	−56.0593	−2.59969
$466$	−28.6415	−1.32679
$467$	24.2804	1.12356	0.561782	−	0.827285i	$-0.310116\pi$
$467$	24.2804	1.12356	0.561782	+	0.827285i	$0.310116\pi$
$468$	7.96012	0.367957
$469$	−3.22066	−0.148716
$470$	−65.7255	−3.03169
$471$	24.1646	1.11345
$472$	5.03991	0.231981
$473$	1.62703	0.0748107
$474$	27.6251	1.26886
$475$	33.6886	1.54574
$476$	−0.236526	−0.0108412
$477$	14.1967	0.650024
$478$	−11.4579	−0.524070
$479$	3.15535	0.144172	0.0720859	−	0.997398i	$-0.477034\pi$
$479$	3.15535	0.144172	0.0720859	+	0.997398i	$0.477034\pi$
$480$	−63.1188	−2.88097
$481$	8.66509	0.395094
$482$	−6.74856	−0.307388
$483$	6.37831	0.290223
$484$	1.32341	0.0601550
$485$	−11.6333	−0.528239
$486$	−22.5792	−1.02421
$487$	−37.8261	−1.71406	−0.857031	−	0.515265i	$-0.827694\pi$
$487$	−37.8261	−1.71406	−0.857031	+	0.515265i	$0.827694\pi$
$488$	−1.23344	−0.0558351
$489$	−1.83340	−0.0829092
$490$	−39.7717	−1.79670
$491$	32.9576	1.48736	0.743678	−	0.668538i	$-0.233080\pi$
$491$	32.9576	1.48736	0.743678	+	0.668538i	$0.233080\pi$
$492$	28.5811	1.28853
$493$	4.52001	0.203571
$494$	−11.3059	−0.508674
$495$	−20.8313	−0.936298
$496$	−28.0767	−1.26068
$497$	−1.40860	−0.0631844
$498$	50.4566	2.26101
$499$	−16.4934	−0.738345	−0.369173	−	0.929361i	$-0.620359\pi$
$499$	−16.4934	−0.738345	−0.369173	+	0.929361i	$0.620359\pi$
$500$	0.222258	0.00993969
$501$	11.3992	0.509279
$502$	−12.8639	−0.574143
$503$	27.8051	1.23977	0.619883	−	0.784694i	$-0.287180\pi$
$503$	27.8051	1.23977	0.619883	+	0.784694i	$0.287180\pi$
$504$	−2.34172	−0.104308
$505$	31.8363	1.41670
$506$	13.0529	0.580272
$507$	−37.7195	−1.67518
$508$	−23.3825	−1.03743
$509$	22.1434	0.981487	0.490744	−	0.871304i	$-0.336725\pi$
$509$	22.1434	0.981487	0.490744	+	0.871304i	$0.336725\pi$
$510$	11.0797	0.490615
$511$	−2.79182	−0.123503
$512$	−19.5360	−0.863378
$513$	76.0893	3.35943
$514$	8.36850	0.369119
$515$	33.2306	1.46431
$516$	6.67327	0.293774
$517$	−11.4314	−0.502755
$518$	4.98606	0.219075
$519$	−40.1678	−1.76317
$520$	−3.54247	−0.155348
$521$	5.33123	0.233565	0.116783	−	0.993157i	$-0.462742\pi$
$521$	5.33123	0.233565	0.116783	+	0.993157i	$0.462742\pi$
$522$	−87.5313	−3.83114
$523$	14.4681	0.632645	0.316322	−	0.948652i	$-0.397552\pi$
$523$	14.4681	0.632645	0.316322	+	0.948652i	$0.397552\pi$
$524$	−8.64020	−0.377449
$525$	−4.40667	−0.192323
$526$	−1.75207	−0.0763938
$527$	3.56616	0.155344
$528$	−15.1718	−0.660270
$529$	28.2661	1.22896
$530$	12.3579	0.536794
$531$	26.9887	1.17121
$532$	−2.59059	−0.112316
$533$	6.34575	0.274865
$534$	76.1949	3.29728
$535$	−51.4253	−2.22331
$536$	13.8204	0.596951
$537$	−31.2832	−1.34997
$538$	−24.8399	−1.07093
$539$	−6.91738	−0.297953
$540$	−46.6333	−2.00678
$541$	18.4464	0.793073	0.396536	−	0.918019i	$-0.370212\pi$
$541$	18.4464	0.793073	0.396536	+	0.918019i	$0.370212\pi$
$542$	52.8985	2.27219
$543$	−51.1332	−2.19434
$544$	4.01525	0.172152
$545$	−17.3247	−0.742108
$546$	1.47888	0.0632900
$547$	−36.5079	−1.56097	−0.780483	−	0.625177i	$-0.785027\pi$
$547$	−36.5079	−1.56097	−0.780483	+	0.625177i	$0.785027\pi$
$548$	−18.9086	−0.807737
$549$	−6.60505	−0.281897
$550$	−9.01804	−0.384530
$551$	49.5060	2.10903
$552$	−27.3704	−1.16496
$553$	1.40541	0.0597641
$554$	30.2543	1.28538
$555$	−93.0068	−3.94792
$556$	−0.790030	−0.0335047
$557$	15.5872	0.660449	0.330225	−	0.943902i	$-0.392876\pi$
$557$	15.5872	0.660449	0.330225	+	0.943902i	$0.392876\pi$
$558$	−69.0598	−2.92353
$559$	1.48164	0.0626667
$560$	−4.43783	−0.187532
$561$	1.92705	0.0813602
$562$	−12.8823	−0.543406
$563$	−30.8511	−1.30022	−0.650110	−	0.759840i	$-0.725277\pi$
$563$	−30.8511	−1.30022	−0.650110	+	0.759840i	$0.725277\pi$
$564$	−46.8863	−1.97427
$565$	37.1093	1.56120
$566$	26.2567	1.10365
$567$	−4.25737	−0.178793
$568$	6.04455	0.253624
$569$	40.2875	1.68894	0.844469	−	0.535604i	$-0.179916\pi$
$569$	40.2875	1.68894	0.844469	+	0.535604i	$0.179916\pi$
$570$	121.351	5.08285
$571$	−34.7792	−1.45546	−0.727732	−	0.685861i	$-0.759426\pi$
$571$	−34.7792	−1.45546	−0.727732	+	0.685861i	$0.759426\pi$
$572$	1.20516	0.0503901
$573$	23.2767	0.972400
$574$	3.65146	0.152409
$575$	−35.4189	−1.47707
$576$	−13.0877	−0.545320
$577$	−3.33773	−0.138951	−0.0694757	−	0.997584i	$-0.522133\pi$
$577$	−3.33773	−0.138951	−0.0694757	+	0.997584i	$0.522133\pi$
$578$	30.2866	1.25975
$579$	−63.0553	−2.62049
$580$	−30.3410	−1.25984
$581$	2.56695	0.106495
$582$	−20.8403	−0.863856
$583$	2.14938	0.0890181
$584$	11.9802	0.495743
$585$	−18.9699	−0.784309
$586$	51.9348	2.14541
$587$	−27.5509	−1.13715	−0.568575	−	0.822632i	$-0.692505\pi$
$587$	−27.5509	−1.13715	−0.568575	+	0.822632i	$0.692505\pi$
$588$	−28.3718	−1.17003
$589$	39.0589	1.60939
$590$	23.4930	0.967192
$591$	−31.6450	−1.30170
$592$	−46.5815	−1.91449
$593$	0.856831	0.0351858	0.0175929	−	0.999845i	$-0.494400\pi$
$593$	0.856831	0.0351858	0.0175929	+	0.999845i	$0.494400\pi$
$594$	−20.3682	−0.835718
$595$	0.563671	0.0231082
$596$	20.4637	0.838225
$597$	29.2195	1.19588
$598$	11.8865	0.486077
$599$	−18.1092	−0.739920	−0.369960	−	0.929048i	$-0.620629\pi$
$599$	−18.1092	−0.739920	−0.369960	+	0.929048i	$0.620629\pi$
$600$	18.9098	0.771989
$601$	18.2819	0.745736	0.372868	−	0.927884i	$-0.378375\pi$
$601$	18.2819	0.745736	0.372868	+	0.927884i	$0.378375\pi$
$602$	0.852565	0.0347479
$603$	74.0083	3.01385
$604$	9.76290	0.397247
$605$	−3.15385	−0.128222
$606$	57.0327	2.31680
$607$	6.78910	0.275561	0.137781	−	0.990463i	$-0.456003\pi$
$607$	6.78910	0.275561	0.137781	+	0.990463i	$0.456003\pi$
$608$	43.9776	1.78353
$609$	−6.47569	−0.262408
$610$	−5.74953	−0.232792
$611$	−10.4100	−0.421143
$612$	5.43519	0.219704
$613$	−25.5339	−1.03131	−0.515653	−	0.856797i	$-0.672451\pi$
$613$	−25.5339	−1.03131	−0.515653	+	0.856797i	$0.672451\pi$
$614$	−19.2066	−0.775115
$615$	−68.1121	−2.74655
$616$	−0.354534	−0.0142846
$617$	0.104760	0.00421748	0.00210874	−	0.999998i	$-0.499329\pi$
$617$	0.104760	0.00421748	0.00210874	+	0.999998i	$0.499329\pi$
$618$	59.5304	2.39466
$619$	26.2158	1.05370	0.526852	−	0.849957i	$-0.323372\pi$
$619$	26.2158	1.05370	0.526852	+	0.849957i	$0.323372\pi$
$620$	−23.9382	−0.961383
$621$	−79.9974	−3.21019
$622$	−30.2553	−1.21313
$623$	3.87637	0.155303
$624$	−13.8162	−0.553089
$625$	−25.2634	−1.01054
$626$	−17.9616	−0.717889
$627$	21.1063	0.842905
$628$	10.3187	0.411761
$629$	5.91655	0.235908
$630$	−10.9157	−0.434890
$631$	20.1814	0.803408	0.401704	−	0.915769i	$-0.368418\pi$
$631$	20.1814	0.803408	0.401704	+	0.915769i	$0.368418\pi$
$632$	−6.03086	−0.239895
$633$	−37.3096	−1.48292
$634$	54.3324	2.15781
$635$	55.7233	2.21131
$636$	8.81571	0.349566
$637$	−6.29927	−0.249586
$638$	−13.2522	−0.524659
$639$	32.3685	1.28048
$640$	29.3398	1.15976
$641$	3.60690	0.142464	0.0712319	−	0.997460i	$-0.477307\pi$
$641$	3.60690	0.142464	0.0712319	+	0.997460i	$0.477307\pi$
$642$	−92.1251	−3.63589
$643$	−33.7876	−1.33245	−0.666226	−	0.745750i	$-0.732091\pi$
$643$	−33.7876	−1.33245	−0.666226	+	0.745750i	$0.732091\pi$
$644$	2.72365	0.107327
$645$	−15.9032	−0.626188
$646$	−7.71966	−0.303726
$647$	−0.768454	−0.0302110	−0.0151055	−	0.999886i	$-0.504808\pi$
$647$	−0.768454	−0.0302110	−0.0151055	+	0.999886i	$0.504808\pi$
$648$	18.2691	0.717678
$649$	4.08607	0.160392
$650$	−8.21222	−0.322110
$651$	−5.10914	−0.200243
$652$	−0.782893	−0.0306604
$653$	−36.4030	−1.42456	−0.712280	−	0.701896i	$-0.752337\pi$
$653$	−36.4030	−1.42456	−0.712280	+	0.701896i	$0.752337\pi$
$654$	−31.0360	−1.21361
$655$	20.5906	0.804543
$656$	−34.1132	−1.33190
$657$	64.1538	2.50288
$658$	−5.99010	−0.233519
$659$	−13.4552	−0.524142	−0.262071	−	0.965049i	$-0.584405\pi$
$659$	−13.4552	−0.524142	−0.262071	+	0.965049i	$0.584405\pi$
$660$	−12.9356	−0.503516
$661$	−28.1101	−1.09335	−0.546677	−	0.837343i	$-0.684108\pi$
$661$	−28.1101	−1.09335	−0.546677	+	0.837343i	$0.684108\pi$
$662$	60.6910	2.35882
$663$	1.75486	0.0681531
$664$	−11.0152	−0.427473
$665$	6.17368	0.239405
$666$	−114.576	−4.43972
$667$	−52.0487	−2.01534
$668$	4.86766	0.188335
$669$	49.8517	1.92738
$670$	64.4224	2.48885
$671$	−1.00000	−0.0386046
$672$	−5.75254	−0.221909
$673$	−33.4248	−1.28843	−0.644216	−	0.764844i	$-0.722816\pi$
$673$	−33.4248	−1.28843	−0.644216	+	0.764844i	$0.722816\pi$
$674$	−31.9855	−1.23203
$675$	55.2689	2.12730
$676$	−16.1069	−0.619495
$677$	−33.9964	−1.30659	−0.653294	−	0.757104i	$-0.726613\pi$
$677$	−33.9964	−1.30659	−0.653294	+	0.757104i	$0.726613\pi$
$678$	66.4789	2.55311
$679$	−1.06023	−0.0406881
$680$	−2.41881	−0.0927570
$681$	27.5276	1.05486
$682$	−10.4556	−0.400366
$683$	14.0398	0.537218	0.268609	−	0.963249i	$-0.413436\pi$
$683$	14.0398	0.537218	0.268609	+	0.963249i	$0.413436\pi$
$684$	59.5297	2.27617
$685$	45.0615	1.72171
$686$	−7.29274	−0.278438
$687$	−34.8118	−1.32815
$688$	−7.96495	−0.303661
$689$	1.95732	0.0745679
$690$	−127.584	−4.85705
$691$	−8.49435	−0.323140	−0.161570	−	0.986861i	$-0.551656\pi$
$691$	−8.49435	−0.323140	−0.161570	+	0.986861i	$0.551656\pi$
$692$	−17.1523	−0.652033
$693$	−1.89853	−0.0721191
$694$	−36.0580	−1.36874
$695$	1.88274	0.0714162
$696$	27.7883	1.05331
$697$	4.33289	0.164120
$698$	34.6769	1.31254
$699$	48.6916	1.84168
$700$	−1.88172	−0.0711224
$701$	42.8308	1.61770	0.808849	−	0.588016i	$-0.200091\pi$
$701$	42.8308	1.61770	0.808849	+	0.588016i	$0.200091\pi$
$702$	−18.5482	−0.700057
$703$	64.8018	2.44405
$704$	−1.98147	−0.0746793
$705$	111.736	4.20821
$706$	51.5700	1.94086
$707$	2.90150	0.109122
$708$	16.7591	0.629845
$709$	43.5929	1.63716	0.818582	−	0.574389i	$-0.194760\pi$
$709$	43.5929	1.63716	0.818582	+	0.574389i	$0.194760\pi$
$710$	28.1760	1.05743
$711$	−32.2952	−1.21116
$712$	−16.6342	−0.623392
$713$	−41.0650	−1.53790
$714$	1.00978	0.0377901
$715$	−2.87203	−0.107408
$716$	−13.3585	−0.499229
$717$	19.4788	0.727448
$718$	34.6654	1.29370
$719$	29.8724	1.11405	0.557026	−	0.830495i	$-0.311942\pi$
$719$	29.8724	1.11405	0.557026	+	0.830495i	$0.311942\pi$
$720$	101.978	3.80049
$721$	3.02857	0.112790
$722$	−49.9133	−1.85758
$723$	11.4728	0.426677
$724$	−21.8347	−0.811482
$725$	35.9596	1.33551
$726$	−5.64991	−0.209688
$727$	9.05098	0.335682	0.167841	−	0.985814i	$-0.446320\pi$
$727$	9.05098	0.335682	0.167841	+	0.985814i	$0.446320\pi$
$728$	−0.322854	−0.0119658
$729$	−6.04913	−0.224042
$730$	55.8443	2.06689
$731$	1.01167	0.0374179
$732$	−4.10152	−0.151596
$733$	34.7099	1.28204	0.641019	−	0.767525i	$-0.278512\pi$
$733$	34.7099	1.28204	0.641019	+	0.767525i	$0.278512\pi$
$734$	−3.25748	−0.120236
$735$	67.6133	2.49395
$736$	−46.2363	−1.70429
$737$	11.2048	0.412734
$738$	−83.9078	−3.08869
$739$	−5.55188	−0.204229	−0.102115	−	0.994773i	$-0.532561\pi$
$739$	−5.55188	−0.204229	−0.102115	+	0.994773i	$0.532561\pi$
$740$	−39.7155	−1.45997
$741$	19.2203	0.706077
$742$	1.12628	0.0413470
$743$	−2.08882	−0.0766315	−0.0383158	−	0.999266i	$-0.512199\pi$
$743$	−2.08882	−0.0766315	−0.0383158	+	0.999266i	$0.512199\pi$
$744$	21.9242	0.803780
$745$	−48.7674	−1.78670
$746$	−34.9319	−1.27895
$747$	−58.9864	−2.15820
$748$	0.822884	0.0300876
$749$	−4.68681	−0.171252
$750$	−0.948866	−0.0346477
$751$	10.8303	0.395203	0.197601	−	0.980282i	$-0.436685\pi$
$751$	10.8303	0.395203	0.197601	+	0.980282i	$0.436685\pi$
$752$	55.9616	2.04071
$753$	21.8691	0.796953
$754$	−12.0680	−0.439491
$755$	−23.2662	−0.846742
$756$	−4.25008	−0.154574
$757$	−23.2966	−0.846730	−0.423365	−	0.905959i	$-0.639151\pi$
$757$	−23.2966	−0.846730	−0.423365	+	0.905959i	$0.639151\pi$
$758$	41.6622	1.51324
$759$	−22.1904	−0.805460
$760$	−26.4923	−0.960978
$761$	−53.5346	−1.94063	−0.970314	−	0.241849i	$-0.922246\pi$
$761$	−53.5346	−1.94063	−0.970314	+	0.241849i	$0.922246\pi$
$762$	99.8248	3.61627
$763$	−1.57894	−0.0571615
$764$	9.93956	0.359601
$765$	−12.9527	−0.468306
$766$	−13.2775	−0.479737
$767$	3.72096	0.134356
$768$	64.8423	2.33979
$769$	26.4098	0.952363	0.476182	−	0.879347i	$-0.342020\pi$
$769$	26.4098	0.952363	0.476182	+	0.879347i	$0.342020\pi$
$770$	−1.65262	−0.0595564
$771$	−14.2267	−0.512363
$772$	−26.9257	−0.969076
$773$	23.6677	0.851269	0.425635	−	0.904895i	$-0.360051\pi$
$773$	23.6677	0.851269	0.425635	+	0.904895i	$0.360051\pi$
$774$	−19.5913	−0.704193
$775$	28.3711	1.01912
$776$	4.54965	0.163323
$777$	−8.47648	−0.304092
$778$	−37.2698	−1.33619
$779$	47.4566	1.70031
$780$	−11.7797	−0.421781
$781$	4.90057	0.175356
$782$	8.11616	0.290233
$783$	81.2188	2.90252
$784$	33.8634	1.20941
$785$	−24.5907	−0.877679
$786$	36.8868	1.31571
$787$	−45.9007	−1.63618	−0.818092	−	0.575088i	$-0.804968\pi$
$787$	−45.9007	−1.63618	−0.818092	+	0.575088i	$0.804968\pi$
$788$	−13.5129	−0.481378
$789$	2.97858	0.106040
$790$	−28.1122	−1.00019
$791$	3.38207	0.120253
$792$	8.14691	0.289488
$793$	−0.910644	−0.0323379
$794$	−29.0534	−1.03107
$795$	−21.0089	−0.745108
$796$	12.4772	0.442243
$797$	−32.7460	−1.15992	−0.579962	−	0.814644i	$-0.696933\pi$
$797$	−32.7460	−1.15992	−0.579962	+	0.814644i	$0.696933\pi$
$798$	11.0598	0.391511
$799$	−7.10796	−0.251462
$800$	31.9439	1.12939
$801$	−89.0759	−3.14734
$802$	−67.8057	−2.39430
$803$	9.71284	0.342759
$804$	45.9567	1.62077
$805$	−6.49078	−0.228770
$806$	−9.52133	−0.335375
$807$	42.2287	1.48652
$808$	−12.4509	−0.438020
$809$	−48.2215	−1.69538	−0.847688	−	0.530495i	$-0.822006\pi$
$809$	−48.2215	−1.69538	−0.847688	+	0.530495i	$0.822006\pi$
$810$	85.1594	2.99220
$811$	−28.8635	−1.01353	−0.506767	−	0.862083i	$-0.669160\pi$
$811$	−28.8635	−1.01353	−0.506767	+	0.862083i	$0.669160\pi$
$812$	−2.76523	−0.0970405
$813$	−89.9293	−3.15396
$814$	−17.3467	−0.608001
$815$	1.86573	0.0653536
$816$	−9.43370	−0.330246
$817$	11.0804	0.387655
$818$	−61.0647	−2.13508
$819$	−1.72888	−0.0604121
$820$	−29.0850	−1.01569
$821$	50.5520	1.76428	0.882139	−	0.470989i	$-0.156103\pi$
$821$	50.5520	1.76428	0.882139	+	0.470989i	$0.156103\pi$
$822$	80.7249	2.81560
$823$	−29.2399	−1.01924	−0.509619	−	0.860400i	$-0.670214\pi$
$823$	−29.2399	−1.01924	−0.509619	+	0.860400i	$0.670214\pi$
$824$	−12.9961	−0.452742
$825$	15.3310	0.533756
$826$	2.14111	0.0744988
$827$	17.1084	0.594918	0.297459	−	0.954735i	$-0.403861\pi$
$827$	17.1084	0.594918	0.297459	+	0.954735i	$0.403861\pi$
$828$	−62.5872	−2.17506
$829$	−35.4183	−1.23013	−0.615064	−	0.788477i	$-0.710870\pi$
$829$	−35.4183	−1.23013	−0.615064	+	0.788477i	$0.710870\pi$
$830$	−51.3462	−1.78225
$831$	−51.4333	−1.78420
$832$	−1.80441	−0.0625567
$833$	−4.30116	−0.149026
$834$	3.37280	0.116791
$835$	−11.6002	−0.401442
$836$	9.01275	0.311712
$837$	64.0793	2.21491
$838$	19.4345	0.671353
$839$	−32.8599	−1.13445	−0.567224	−	0.823564i	$-0.691983\pi$
$839$	−32.8599	−1.13445	−0.567224	+	0.823564i	$0.691983\pi$
$840$	3.46536	0.119566
$841$	23.8434	0.822185
$842$	−62.7677	−2.16312
$843$	21.9003	0.754286
$844$	−15.9318	−0.548396
$845$	38.3846	1.32047
$846$	137.648	4.73243
$847$	−0.287436	−0.00987641
$848$	−10.5221	−0.361329
$849$	−44.6373	−1.53195
$850$	−5.60733	−0.192330
$851$	−68.1302	−2.33547
$852$	20.0998	0.688607
$853$	1.85750	0.0635996	0.0317998	−	0.999494i	$-0.489876\pi$
$853$	1.85750	0.0635996	0.0317998	+	0.999494i	$0.489876\pi$
$854$	−0.524002	−0.0179310
$855$	−141.866	−4.85173
$856$	20.1119	0.687411
$857$	43.9149	1.50010	0.750052	−	0.661379i	$-0.230029\pi$
$857$	43.9149	1.50010	0.750052	+	0.661379i	$0.230029\pi$
$858$	−5.14506	−0.175649
$859$	14.8800	0.507698	0.253849	−	0.967244i	$-0.418303\pi$
$859$	14.8800	0.507698	0.253849	+	0.967244i	$0.418303\pi$
$860$	−6.79094	−0.231569
$861$	−6.20762	−0.211555
$862$	19.7684	0.673313
$863$	−44.5369	−1.51605	−0.758027	−	0.652224i	$-0.773836\pi$
$863$	−44.5369	−1.51605	−0.758027	+	0.652224i	$0.773836\pi$
$864$	72.1489	2.45455
$865$	40.8760	1.38983
$866$	2.08825	0.0709615
$867$	−51.4882	−1.74863
$868$	−2.18169	−0.0740513
$869$	−4.88947	−0.165864
$870$	129.532	4.39155
$871$	10.2036	0.345735
$872$	6.77550	0.229447
$873$	24.3634	0.824575
$874$	88.8934	3.00686
$875$	−0.0482730	−0.00163192
$876$	39.8374	1.34598
$877$	−20.2794	−0.684787	−0.342393	−	0.939557i	$-0.611238\pi$
$877$	−20.2794	−0.684787	−0.342393	+	0.939557i	$0.611238\pi$
$878$	−55.7723	−1.88222
$879$	−88.2910	−2.97798
$880$	15.4394	0.520461
$881$	−40.5359	−1.36569	−0.682844	−	0.730564i	$-0.739257\pi$
$881$	−40.5359	−1.36569	−0.682844	+	0.730564i	$0.739257\pi$
$882$	83.2932	2.80463
$883$	8.55778	0.287992	0.143996	−	0.989578i	$-0.454005\pi$
$883$	8.55778	0.287992	0.143996	+	0.989578i	$0.454005\pi$
$884$	0.749354	0.0252035
$885$	−39.9389	−1.34253
$886$	17.3907	0.584251
$887$	10.5486	0.354188	0.177094	−	0.984194i	$-0.443330\pi$
$887$	10.5486	0.354188	0.177094	+	0.984194i	$0.443330\pi$
$888$	36.3740	1.22063
$889$	5.07852	0.170328
$890$	−77.5384	−2.59909
$891$	14.8115	0.496205
$892$	21.2875	0.712759
$893$	−77.8509	−2.60518
$894$	−87.3636	−2.92188
$895$	31.8348	1.06412
$896$	2.67398	0.0893313
$897$	−20.2075	−0.674710
$898$	−30.3617	−1.01318
$899$	41.6920	1.39050
$900$	43.2405	1.44135
$901$	1.33646	0.0445240
$902$	−12.7036	−0.422983
$903$	−1.44939	−0.0482327
$904$	−14.5130	−0.482697
$905$	52.0348	1.72970
$906$	−41.6798	−1.38472
$907$	3.88830	0.129109	0.0645544	−	0.997914i	$-0.479437\pi$
$907$	3.88830	0.129109	0.0645544	+	0.997914i	$0.479437\pi$
$908$	11.7548	0.390095
$909$	−66.6743	−2.21145
$910$	−1.50495	−0.0498886
$911$	36.2379	1.20061	0.600307	−	0.799769i	$-0.295045\pi$
$911$	36.2379	1.20061	0.600307	+	0.799769i	$0.295045\pi$
$912$	−103.324	−3.42140
$913$	−8.93050	−0.295556
$914$	−12.0431	−0.398352
$915$	9.77441	0.323132
$916$	−14.8652	−0.491160
$917$	1.87659	0.0619706
$918$	−12.6648	−0.417999
$919$	−43.8784	−1.44741	−0.723707	−	0.690107i	$-0.757563\pi$
$919$	−43.8784	−1.44741	−0.723707	+	0.690107i	$0.757563\pi$
$920$	27.8530	0.918287
$921$	32.6519	1.07592
$922$	−18.0821	−0.595503
$923$	4.46268	0.146891
$924$	−1.17892	−0.0387837
$925$	47.0700	1.54765
$926$	35.9691	1.18202
$927$	−69.5942	−2.28577
$928$	46.9422	1.54095
$929$	29.9320	0.982036	0.491018	−	0.871149i	$-0.336625\pi$
$929$	29.9320	0.982036	0.491018	+	0.871149i	$0.336625\pi$
$930$	102.197	3.35118
$931$	−47.1090	−1.54394
$932$	20.7921	0.681068
$933$	51.4351	1.68391
$934$	−44.2638	−1.44836
$935$	−1.96103	−0.0641326
$936$	7.41894	0.242496
$937$	−0.358168	−0.0117008	−0.00585041	−	0.999983i	$-0.501862\pi$
$937$	−0.358168	−0.0117008	−0.00585041	+	0.999983i	$0.501862\pi$
$938$	5.87134	0.191706
$939$	30.5353	0.996482
$940$	47.7130	1.55623
$941$	−46.6762	−1.52160	−0.760801	−	0.648985i	$-0.775194\pi$
$941$	−46.6762	−1.52160	−0.760801	+	0.648985i	$0.775194\pi$
$942$	−44.0526	−1.43531
$943$	−49.8941	−1.62478
$944$	−20.0030	−0.651041
$945$	10.1284	0.329478
$946$	−2.96610	−0.0964364
$947$	26.4645	0.859981	0.429990	−	0.902833i	$-0.358517\pi$
$947$	26.4645	0.859981	0.429990	+	0.902833i	$0.358517\pi$
$948$	−20.0543	−0.651332
$949$	8.84494	0.287119
$950$	−61.4150	−1.99257
$951$	−92.3669	−2.99520
$952$	−0.220446	−0.00714469
$953$	−41.6677	−1.34975	−0.674874	−	0.737933i	$-0.735802\pi$
$953$	−41.6677	−1.34975	−0.674874	+	0.737933i	$0.735802\pi$
$954$	−25.8810	−0.837928
$955$	−23.6872	−0.766498
$956$	8.31776	0.269016
$957$	22.5292	0.728264
$958$	−5.75228	−0.185848
$959$	4.10683	0.132616
$960$	19.3677	0.625088
$961$	1.89379	0.0610901
$962$	−15.7967	−0.509305
$963$	107.699	3.47056
$964$	4.89907	0.157788
$965$	64.1671	2.06561
$966$	−11.6278	−0.374119
$967$	−26.2577	−0.844390	−0.422195	−	0.906505i	$-0.638740\pi$
$967$	−26.2577	−0.844390	−0.422195	+	0.906505i	$0.638740\pi$
$968$	1.23344	0.0396442
$969$	13.1237	0.421594
$970$	21.2077	0.680938
$971$	−35.2185	−1.13021	−0.565107	−	0.825017i	$-0.691165\pi$
$971$	−35.2185	−1.13021	−0.565107	+	0.825017i	$0.691165\pi$
$972$	16.3912	0.525749
$973$	0.171589	0.00550090
$974$	68.9577	2.20955
$975$	13.9611	0.447112
$976$	4.89541	0.156698
$977$	61.8806	1.97974	0.989868	−	0.141987i	$-0.0453493\pi$
$977$	61.8806	1.97974	0.989868	+	0.141987i	$0.0453493\pi$
$978$	3.34233	0.106876
$979$	−13.4860	−0.431015
$980$	28.8720	0.922282
$981$	36.2828	1.15842
$982$	−60.0825	−1.91731
$983$	28.0245	0.893842	0.446921	−	0.894573i	$-0.352521\pi$
$983$	28.0245	0.893842	0.446921	+	0.894573i	$0.352521\pi$
$984$	26.6380	0.849187
$985$	32.2029	1.02607
$986$	−8.24007	−0.262417
$987$	10.1834	0.324141
$988$	8.20741	0.261112
$989$	−11.6496	−0.370434
$990$	37.9760	1.20696
$991$	2.64549	0.0840367	0.0420184	−	0.999117i	$-0.486621\pi$
$991$	2.64549	0.0840367	0.0420184	+	0.999117i	$0.486621\pi$
$992$	37.0361	1.17590
$993$	−103.177	−3.27422
$994$	2.56791	0.0814492
$995$	−29.7347	−0.942654
$996$	−36.6286	−1.16062
$997$	57.5224	1.82175	0.910876	−	0.412680i	$-0.135407\pi$
$997$	57.5224	1.82175	0.910876	+	0.412680i	$0.135407\pi$
$998$	30.0678	0.951780
$999$	106.313	3.36359

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.c.1.4	✓	19
3.2	odd	2		6039.2.a.k.1.16		19
11.10	odd	2		7381.2.a.i.1.16		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.c.1.4	✓	19	1.1	even	1	trivial
6039.2.a.k.1.16		19	3.2	odd	2
7381.2.a.i.1.16		19	11.10	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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.a (trivial)

\(f(q)\)	\(=\)	\(q-1.82302 q^{2} +3.09920 q^{3} +1.32341 q^{4} -3.15385 q^{5} -5.64991 q^{6} -0.287436 q^{7} +1.23344 q^{8} +6.60505 q^{9} +O(q^{10})\)	\(q-1.82302 q^{2} +3.09920 q^{3} +1.32341 q^{4} -3.15385 q^{5} -5.64991 q^{6} -0.287436 q^{7} +1.23344 q^{8} +6.60505 q^{9} +5.74953 q^{10} +1.00000 q^{11} +4.10152 q^{12} +0.910644 q^{13} +0.524002 q^{14} -9.77441 q^{15} -4.89541 q^{16} +0.621790 q^{17} -12.0412 q^{18} +6.81024 q^{19} -4.17384 q^{20} -0.890822 q^{21} -1.82302 q^{22} -7.16003 q^{23} +3.82267 q^{24} +4.94675 q^{25} -1.66012 q^{26} +11.1728 q^{27} -0.380396 q^{28} +7.26934 q^{29} +17.8190 q^{30} +5.73531 q^{31} +6.45756 q^{32} +3.09920 q^{33} -1.13354 q^{34} +0.906529 q^{35} +8.74120 q^{36} +9.51534 q^{37} -12.4152 q^{38} +2.82227 q^{39} -3.89007 q^{40} +6.96842 q^{41} +1.62399 q^{42} +1.62703 q^{43} +1.32341 q^{44} -20.8313 q^{45} +13.0529 q^{46} -11.4314 q^{47} -15.1718 q^{48} -6.91738 q^{49} -9.01804 q^{50} +1.92705 q^{51} +1.20516 q^{52} +2.14938 q^{53} -20.3682 q^{54} -3.15385 q^{55} -0.354534 q^{56} +21.1063 q^{57} -13.2522 q^{58} +4.08607 q^{59} -12.9356 q^{60} -1.00000 q^{61} -10.4556 q^{62} -1.89853 q^{63} -1.98147 q^{64} -2.87203 q^{65} -5.64991 q^{66} +11.2048 q^{67} +0.822884 q^{68} -22.1904 q^{69} -1.65262 q^{70} +4.90057 q^{71} +8.14691 q^{72} +9.71284 q^{73} -17.3467 q^{74} +15.3310 q^{75} +9.01275 q^{76} -0.287436 q^{77} -5.14506 q^{78} -4.88947 q^{79} +15.4394 q^{80} +14.8115 q^{81} -12.7036 q^{82} -8.93050 q^{83} -1.17892 q^{84} -1.96103 q^{85} -2.96610 q^{86} +22.5292 q^{87} +1.23344 q^{88} -13.4860 q^{89} +37.9760 q^{90} -0.261752 q^{91} -9.47567 q^{92} +17.7749 q^{93} +20.8398 q^{94} -21.4785 q^{95} +20.0133 q^{96} +3.68860 q^{97} +12.6105 q^{98} +6.60505 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9}+O(q^{10}) \) 19 * q + 5 * q^2 + 23 * q^4 + q^6 + 9 * q^7 + 9 * q^8 + 29 * q^9	\( 19 q + 5 q^{2} + 23 q^{4} + q^{6} + 9 q^{7} + 9 q^{8} + 29 q^{9} + 7 q^{10} + 19 q^{11} - 4 q^{12} + 8 q^{13} - 11 q^{14} - 5 q^{15} + 31 q^{16} + 9 q^{17} + 10 q^{18} + 17 q^{19} - 6 q^{20} + 18 q^{21} + 5 q^{22} - 10 q^{23} + 26 q^{24} + 45 q^{25} + 5 q^{26} - 33 q^{27} + 36 q^{28} + 27 q^{29} - 30 q^{30} + 7 q^{31} + 8 q^{32} - 5 q^{34} + 17 q^{35} + 38 q^{36} + 20 q^{37} - 37 q^{38} + 24 q^{39} + 10 q^{40} + 19 q^{41} + 21 q^{42} + 20 q^{43} + 23 q^{44} - 32 q^{45} + 41 q^{46} - 19 q^{47} + 5 q^{48} + 42 q^{49} + 36 q^{50} + 47 q^{51} - 28 q^{52} + 3 q^{53} - 33 q^{54} - 44 q^{56} + 11 q^{57} + 23 q^{58} - 28 q^{59} - 96 q^{60} - 19 q^{61} - 11 q^{62} - 32 q^{63} + 47 q^{64} + 25 q^{65} + q^{66} + 3 q^{67} + 38 q^{68} + 3 q^{70} - 19 q^{71} + 34 q^{72} + 20 q^{73} - 22 q^{74} - 50 q^{75} - 25 q^{76} + 9 q^{77} - 94 q^{78} + 69 q^{79} - 36 q^{80} + 47 q^{81} - 61 q^{82} + q^{83} - 28 q^{84} + 24 q^{85} - 27 q^{86} - 58 q^{87} + 9 q^{88} + 36 q^{90} + 24 q^{91} - 67 q^{92} - 14 q^{93} + 64 q^{94} - 3 q^{95} - 26 q^{96} + 21 q^{97} - 87 q^{98} + 29 q^{99}+O(q^{100}) \) 19 * q + 5 * q^2 + 23 * q^4 + q^6 + 9 * q^7 + 9 * q^8 + 29 * q^9 + 7 * q^10 + 19 * q^11 - 4 * q^12 + 8 * q^13 - 11 * q^14 - 5 * q^15 + 31 * q^16 + 9 * q^17 + 10 * q^18 + 17 * q^19 - 6 * q^20 + 18 * q^21 + 5 * q^22 - 10 * q^23 + 26 * q^24 + 45 * q^25 + 5 * q^26 - 33 * q^27 + 36 * q^28 + 27 * q^29 - 30 * q^30 + 7 * q^31 + 8 * q^32 - 5 * q^34 + 17 * q^35 + 38 * q^36 + 20 * q^37 - 37 * q^38 + 24 * q^39 + 10 * q^40 + 19 * q^41 + 21 * q^42 + 20 * q^43 + 23 * q^44 - 32 * q^45 + 41 * q^46 - 19 * q^47 + 5 * q^48 + 42 * q^49 + 36 * q^50 + 47 * q^51 - 28 * q^52 + 3 * q^53 - 33 * q^54 - 44 * q^56 + 11 * q^57 + 23 * q^58 - 28 * q^59 - 96 * q^60 - 19 * q^61 - 11 * q^62 - 32 * q^63 + 47 * q^64 + 25 * q^65 + q^66 + 3 * q^67 + 38 * q^68 + 3 * q^70 - 19 * q^71 + 34 * q^72 + 20 * q^73 - 22 * q^74 - 50 * q^75 - 25 * q^76 + 9 * q^77 - 94 * q^78 + 69 * q^79 - 36 * q^80 + 47 * q^81 - 61 * q^82 + q^83 - 28 * q^84 + 24 * q^85 - 27 * q^86 - 58 * q^87 + 9 * q^88 + 36 * q^90 + 24 * q^91 - 67 * q^92 - 14 * q^93 + 64 * q^94 - 3 * q^95 - 26 * q^96 + 21 * q^97 - 87 * q^98 + 29 * q^99

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