LMFDB - Embedded newform 4334.2.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 5 x^{16} - 19 x^{15} + 121 x^{14} + 112 x^{13} - 1172 x^{12} - 25 x^{11} + 5845 x^{10} + \cdots + 16 $ x^17 - 5x^16 - 19x^15 + 121x^14 + 112x^13 - 1172x^12 - 25x^11 + 5845x^10 - 2233x^9 - 16035x^8 + 9174x^7 + 23882x^6 - 15232x^5 - 17609x^4 + 10764x^3 + 4764x^2 - 2368x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.86328$ of defining polynomial
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.86328 q^{3} +1.00000 q^{4} -0.189598 q^{5} +1.86328 q^{6} -4.05138 q^{7} -1.00000 q^{8} +0.471817 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.86328 q^{3} +1.00000 q^{4} -0.189598 q^{5} +1.86328 q^{6} -4.05138 q^{7} -1.00000 q^{8} +0.471817 q^{9} +0.189598 q^{10} -1.00000 q^{11} -1.86328 q^{12} +2.20380 q^{13} +4.05138 q^{14} +0.353274 q^{15} +1.00000 q^{16} -2.49348 q^{17} -0.471817 q^{18} +3.29586 q^{19} -0.189598 q^{20} +7.54887 q^{21} +1.00000 q^{22} +2.66988 q^{23} +1.86328 q^{24} -4.96405 q^{25} -2.20380 q^{26} +4.71072 q^{27} -4.05138 q^{28} -6.69910 q^{29} -0.353274 q^{30} +0.251246 q^{31} -1.00000 q^{32} +1.86328 q^{33} +2.49348 q^{34} +0.768134 q^{35} +0.471817 q^{36} +7.30039 q^{37} -3.29586 q^{38} -4.10631 q^{39} +0.189598 q^{40} +3.69313 q^{41} -7.54887 q^{42} -2.58037 q^{43} -1.00000 q^{44} -0.0894557 q^{45} -2.66988 q^{46} +11.2360 q^{47} -1.86328 q^{48} +9.41371 q^{49} +4.96405 q^{50} +4.64606 q^{51} +2.20380 q^{52} +6.06005 q^{53} -4.71072 q^{54} +0.189598 q^{55} +4.05138 q^{56} -6.14111 q^{57} +6.69910 q^{58} +3.76286 q^{59} +0.353274 q^{60} -15.4913 q^{61} -0.251246 q^{62} -1.91151 q^{63} +1.00000 q^{64} -0.417837 q^{65} -1.86328 q^{66} +4.97217 q^{67} -2.49348 q^{68} -4.97473 q^{69} -0.768134 q^{70} +5.09766 q^{71} -0.471817 q^{72} +7.97292 q^{73} -7.30039 q^{74} +9.24943 q^{75} +3.29586 q^{76} +4.05138 q^{77} +4.10631 q^{78} -1.72364 q^{79} -0.189598 q^{80} -10.1928 q^{81} -3.69313 q^{82} +2.47784 q^{83} +7.54887 q^{84} +0.472759 q^{85} +2.58037 q^{86} +12.4823 q^{87} +1.00000 q^{88} +3.84485 q^{89} +0.0894557 q^{90} -8.92845 q^{91} +2.66988 q^{92} -0.468142 q^{93} -11.2360 q^{94} -0.624888 q^{95} +1.86328 q^{96} -5.55984 q^{97} -9.41371 q^{98} -0.471817 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9}+O(q^{10}) $ 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9	\( 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9} - 6 q^{10} - 17 q^{11} + 5 q^{12} - 16 q^{13} + 9 q^{14} + 17 q^{16} - 8 q^{17} - 12 q^{18} - 23 q^{19} + 6 q^{20} - 15 q^{21} + 17 q^{22} + 12 q^{23} - 5 q^{24} + 11 q^{25} + 16 q^{26} + 17 q^{27} - 9 q^{28} - 8 q^{31} - 17 q^{32} - 5 q^{33} + 8 q^{34} + 6 q^{35} + 12 q^{36} - 7 q^{37} + 23 q^{38} - 9 q^{39} - 6 q^{40} - 27 q^{41} + 15 q^{42} - 13 q^{43} - 17 q^{44} - 11 q^{45} - 12 q^{46} + 23 q^{47} + 5 q^{48} - 8 q^{49} - 11 q^{50} - 40 q^{51} - 16 q^{52} + 14 q^{53} - 17 q^{54} - 6 q^{55} + 9 q^{56} - 18 q^{57} + 2 q^{59} - 49 q^{61} + 8 q^{62} - 42 q^{63} + 17 q^{64} - 57 q^{65} + 5 q^{66} - 5 q^{67} - 8 q^{68} - 9 q^{69} - 6 q^{70} - 5 q^{71} - 12 q^{72} - 54 q^{73} + 7 q^{74} + 7 q^{75} - 23 q^{76} + 9 q^{77} + 9 q^{78} - 11 q^{79} + 6 q^{80} - 35 q^{81} + 27 q^{82} - 8 q^{83} - 15 q^{84} - 65 q^{85} + 13 q^{86} - 20 q^{87} + 17 q^{88} - 9 q^{89} + 11 q^{90} - 9 q^{91} + 12 q^{92} - 50 q^{93} - 23 q^{94} - 27 q^{95} - 5 q^{96} - 42 q^{97} + 8 q^{98} - 12 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9 - 6 * q^10 - 17 * q^11 + 5 * q^12 - 16 * q^13 + 9 * q^14 + 17 * q^16 - 8 * q^17 - 12 * q^18 - 23 * q^19 + 6 * q^20 - 15 * q^21 + 17 * q^22 + 12 * q^23 - 5 * q^24 + 11 * q^25 + 16 * q^26 + 17 * q^27 - 9 * q^28 - 8 * q^31 - 17 * q^32 - 5 * q^33 + 8 * q^34 + 6 * q^35 + 12 * q^36 - 7 * q^37 + 23 * q^38 - 9 * q^39 - 6 * q^40 - 27 * q^41 + 15 * q^42 - 13 * q^43 - 17 * q^44 - 11 * q^45 - 12 * q^46 + 23 * q^47 + 5 * q^48 - 8 * q^49 - 11 * q^50 - 40 * q^51 - 16 * q^52 + 14 * q^53 - 17 * q^54 - 6 * q^55 + 9 * q^56 - 18 * q^57 + 2 * q^59 - 49 * q^61 + 8 * q^62 - 42 * q^63 + 17 * q^64 - 57 * q^65 + 5 * q^66 - 5 * q^67 - 8 * q^68 - 9 * q^69 - 6 * q^70 - 5 * q^71 - 12 * q^72 - 54 * q^73 + 7 * q^74 + 7 * q^75 - 23 * q^76 + 9 * q^77 + 9 * q^78 - 11 * q^79 + 6 * q^80 - 35 * q^81 + 27 * q^82 - 8 * q^83 - 15 * q^84 - 65 * q^85 + 13 * q^86 - 20 * q^87 + 17 * q^88 - 9 * q^89 + 11 * q^90 - 9 * q^91 + 12 * q^92 - 50 * q^93 - 23 * q^94 - 27 * q^95 - 5 * q^96 - 42 * q^97 + 8 * q^98 - 12 * 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
$3$	−1.86328	−1.07577	−0.537883	−	0.843020i	$-0.680776\pi$
$3$	−1.86328	−1.07577	−0.537883	+	0.843020i	$0.680776\pi$
$4$	1.00000	0.500000
$5$	−0.189598	−0.0847908	−0.0423954	−	0.999101i	$-0.513499\pi$
$5$	−0.189598	−0.0847908	−0.0423954	+	0.999101i	$0.513499\pi$
$6$	1.86328	0.760681
$7$	−4.05138	−1.53128	−0.765640	−	0.643270i	$-0.777577\pi$
$7$	−4.05138	−1.53128	−0.765640	+	0.643270i	$0.777577\pi$
$8$	−1.00000	−0.353553
$9$	0.471817	0.157272
$10$	0.189598	0.0599562
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.86328	−0.537883
$13$	2.20380	0.611225	0.305613	−	0.952156i	$-0.401139\pi$
$13$	2.20380	0.611225	0.305613	+	0.952156i	$0.401139\pi$
$14$	4.05138	1.08278
$15$	0.353274	0.0912151
$16$	1.00000	0.250000
$17$	−2.49348	−0.604758	−0.302379	−	0.953188i	$-0.597781\pi$
$17$	−2.49348	−0.604758	−0.302379	+	0.953188i	$0.597781\pi$
$18$	−0.471817	−0.111208
$19$	3.29586	0.756121	0.378061	−	0.925781i	$-0.376591\pi$
$19$	3.29586	0.756121	0.378061	+	0.925781i	$0.376591\pi$
$20$	−0.189598	−0.0423954
$21$	7.54887	1.64730
$22$	1.00000	0.213201
$23$	2.66988	0.556708	0.278354	−	0.960479i	$-0.410211\pi$
$23$	2.66988	0.556708	0.278354	+	0.960479i	$0.410211\pi$
$24$	1.86328	0.380341
$25$	−4.96405	−0.992811
$26$	−2.20380	−0.432201
$27$	4.71072	0.906578
$28$	−4.05138	−0.765640
$29$	−6.69910	−1.24399	−0.621996	−	0.783021i	$-0.713678\pi$
$29$	−6.69910	−1.24399	−0.621996	+	0.783021i	$0.713678\pi$
$30$	−0.353274	−0.0644988
$31$	0.251246	0.0451251	0.0225626	−	0.999745i	$-0.492818\pi$
$31$	0.251246	0.0451251	0.0225626	+	0.999745i	$0.492818\pi$
$32$	−1.00000	−0.176777
$33$	1.86328	0.324356
$34$	2.49348	0.427629
$35$	0.768134	0.129838
$36$	0.471817	0.0786362
$37$	7.30039	1.20018	0.600088	−	0.799934i	$-0.295132\pi$
$37$	7.30039	1.20018	0.600088	+	0.799934i	$0.295132\pi$
$38$	−3.29586	−0.534658
$39$	−4.10631	−0.657535
$40$	0.189598	0.0299781
$41$	3.69313	0.576769	0.288385	−	0.957515i	$-0.406882\pi$
$41$	3.69313	0.576769	0.288385	+	0.957515i	$0.406882\pi$
$42$	−7.54887	−1.16482
$43$	−2.58037	−0.393503	−0.196751	−	0.980453i	$-0.563039\pi$
$43$	−2.58037	−0.393503	−0.196751	+	0.980453i	$0.563039\pi$
$44$	−1.00000	−0.150756
$45$	−0.0894557	−0.0133353
$46$	−2.66988	−0.393652
$47$	11.2360	1.63894	0.819471	−	0.573121i	$-0.194268\pi$
$47$	11.2360	1.63894	0.819471	+	0.573121i	$0.194268\pi$
$48$	−1.86328	−0.268941
$49$	9.41371	1.34482
$50$	4.96405	0.702023
$51$	4.64606	0.650578
$52$	2.20380	0.305613
$53$	6.06005	0.832412	0.416206	−	0.909270i	$-0.363360\pi$
$53$	6.06005	0.832412	0.416206	+	0.909270i	$0.363360\pi$
$54$	−4.71072	−0.641047
$55$	0.189598	0.0255654
$56$	4.05138	0.541389
$57$	−6.14111	−0.813410
$58$	6.69910	0.879635
$59$	3.76286	0.489882	0.244941	−	0.969538i	$-0.421231\pi$
$59$	3.76286	0.489882	0.244941	+	0.969538i	$0.421231\pi$
$60$	0.353274	0.0456075
$61$	−15.4913	−1.98346	−0.991728	−	0.128355i	$-0.959030\pi$
$61$	−15.4913	−1.98346	−0.991728	+	0.128355i	$0.959030\pi$
$62$	−0.251246	−0.0319083
$63$	−1.91151	−0.240828
$64$	1.00000	0.125000
$65$	−0.417837	−0.0518263
$66$	−1.86328	−0.229354
$67$	4.97217	0.607448	0.303724	−	0.952760i	$-0.401770\pi$
$67$	4.97217	0.607448	0.303724	+	0.952760i	$0.401770\pi$
$68$	−2.49348	−0.302379
$69$	−4.97473	−0.598887
$70$	−0.768134	−0.0918096
$71$	5.09766	0.604981	0.302490	−	0.953152i	$-0.402182\pi$
$71$	5.09766	0.604981	0.302490	+	0.953152i	$0.402182\pi$
$72$	−0.471817	−0.0556042
$73$	7.97292	0.933159	0.466580	−	0.884479i	$-0.345486\pi$
$73$	7.97292	0.933159	0.466580	+	0.884479i	$0.345486\pi$
$74$	−7.30039	−0.848653
$75$	9.24943	1.06803
$76$	3.29586	0.378061
$77$	4.05138	0.461698
$78$	4.10631	0.464948
$79$	−1.72364	−0.193924	−0.0969620	−	0.995288i	$-0.530913\pi$
$79$	−1.72364	−0.193924	−0.0969620	+	0.995288i	$0.530913\pi$
$80$	−0.189598	−0.0211977
$81$	−10.1928	−1.13254
$82$	−3.69313	−0.407837
$83$	2.47784	0.271979	0.135989	−	0.990710i	$-0.456579\pi$
$83$	2.47784	0.271979	0.135989	+	0.990710i	$0.456579\pi$
$84$	7.54887	0.823649
$85$	0.472759	0.0512780
$86$	2.58037	0.278248
$87$	12.4823	1.33824
$88$	1.00000	0.106600
$89$	3.84485	0.407554	0.203777	−	0.979017i	$-0.434678\pi$
$89$	3.84485	0.407554	0.203777	+	0.979017i	$0.434678\pi$
$90$	0.0894557	0.00942945
$91$	−8.92845	−0.935956
$92$	2.66988	0.278354
$93$	−0.468142	−0.0485441
$94$	−11.2360	−1.15891
$95$	−0.624888	−0.0641121
$96$	1.86328	0.190170
$97$	−5.55984	−0.564516	−0.282258	−	0.959339i	$-0.591083\pi$
$97$	−5.55984	−0.564516	−0.282258	+	0.959339i	$0.591083\pi$
$98$	−9.41371	−0.950929
$99$	−0.471817	−0.0474194
$100$	−4.96405	−0.496405
$101$	1.38237	0.137551	0.0687757	−	0.997632i	$-0.478091\pi$
$101$	1.38237	0.137551	0.0687757	+	0.997632i	$0.478091\pi$
$102$	−4.64606	−0.460028
$103$	−9.63972	−0.949829	−0.474915	−	0.880032i	$-0.657521\pi$
$103$	−9.63972	−0.949829	−0.474915	+	0.880032i	$0.657521\pi$
$104$	−2.20380	−0.216101
$105$	−1.43125	−0.139676
$106$	−6.06005	−0.588604
$107$	−9.47253	−0.915744	−0.457872	−	0.889018i	$-0.651388\pi$
$107$	−9.47253	−0.915744	−0.457872	+	0.889018i	$0.651388\pi$
$108$	4.71072	0.453289
$109$	2.29392	0.219717	0.109859	−	0.993947i	$-0.464960\pi$
$109$	2.29392	0.219717	0.109859	+	0.993947i	$0.464960\pi$
$110$	−0.189598	−0.0180775
$111$	−13.6027	−1.29111
$112$	−4.05138	−0.382820
$113$	−9.81420	−0.923242	−0.461621	−	0.887077i	$-0.652732\pi$
$113$	−9.81420	−0.923242	−0.461621	+	0.887077i	$0.652732\pi$
$114$	6.14111	0.575167
$115$	−0.506203	−0.0472037
$116$	−6.69910	−0.621996
$117$	1.03979	0.0961289
$118$	−3.76286	−0.346399
$119$	10.1021	0.926054
$120$	−0.353274	−0.0322494
$121$	1.00000	0.0909091
$122$	15.4913	1.40252
$123$	−6.88133	−0.620469
$124$	0.251246	0.0225626
$125$	1.88916	0.168972
$126$	1.91151	0.170291
$127$	10.9255	0.969483	0.484741	−	0.874658i	$-0.338914\pi$
$127$	10.9255	0.969483	0.484741	+	0.874658i	$0.338914\pi$
$128$	−1.00000	−0.0883883
$129$	4.80796	0.423317
$130$	0.417837	0.0366467
$131$	18.2410	1.59372	0.796861	−	0.604163i	$-0.206493\pi$
$131$	18.2410	1.59372	0.796861	+	0.604163i	$0.206493\pi$
$132$	1.86328	0.162178
$133$	−13.3528	−1.15783
$134$	−4.97217	−0.429530
$135$	−0.893142	−0.0768695
$136$	2.49348	0.213814
$137$	4.27108	0.364903	0.182452	−	0.983215i	$-0.441597\pi$
$137$	4.27108	0.364903	0.182452	+	0.983215i	$0.441597\pi$
$138$	4.97473	0.423477
$139$	−14.9447	−1.26759	−0.633797	−	0.773499i	$-0.718505\pi$
$139$	−14.9447	−1.26759	−0.633797	+	0.773499i	$0.718505\pi$
$140$	0.768134	0.0649192
$141$	−20.9359	−1.76312
$142$	−5.09766	−0.427786
$143$	−2.20380	−0.184291
$144$	0.471817	0.0393181
$145$	1.27014	0.105479
$146$	−7.97292	−0.659843
$147$	−17.5404	−1.44671
$148$	7.30039	0.600088
$149$	−10.0987	−0.827314	−0.413657	−	0.910433i	$-0.635749\pi$
$149$	−10.0987	−0.827314	−0.413657	+	0.910433i	$0.635749\pi$
$150$	−9.24943	−0.755213
$151$	9.07689	0.738667	0.369333	−	0.929297i	$-0.379586\pi$
$151$	9.07689	0.738667	0.369333	+	0.929297i	$0.379586\pi$
$152$	−3.29586	−0.267329
$153$	−1.17647	−0.0951119
$154$	−4.05138	−0.326470
$155$	−0.0476358	−0.00382620
$156$	−4.10631	−0.328768
$157$	−15.1043	−1.20545	−0.602725	−	0.797949i	$-0.705919\pi$
$157$	−15.1043	−1.20545	−0.602725	+	0.797949i	$0.705919\pi$
$158$	1.72364	0.137125
$159$	−11.2916	−0.895480
$160$	0.189598	0.0149890
$161$	−10.8167	−0.852475
$162$	10.1928	0.800825
$163$	23.7800	1.86259	0.931295	−	0.364265i	$-0.118680\pi$
$163$	23.7800	1.86259	0.931295	+	0.364265i	$0.118680\pi$
$164$	3.69313	0.288385
$165$	−0.353274	−0.0275024
$166$	−2.47784	−0.192318
$167$	1.59992	0.123806	0.0619029	−	0.998082i	$-0.480283\pi$
$167$	1.59992	0.123806	0.0619029	+	0.998082i	$0.480283\pi$
$168$	−7.54887	−0.582408
$169$	−8.14325	−0.626404
$170$	−0.472759	−0.0362590
$171$	1.55504	0.118917
$172$	−2.58037	−0.196751
$173$	13.1641	1.00085	0.500425	−	0.865780i	$-0.333177\pi$
$173$	13.1641	1.00085	0.500425	+	0.865780i	$0.333177\pi$
$174$	−12.4823	−0.946281
$175$	20.1113	1.52027
$176$	−1.00000	−0.0753778
$177$	−7.01126	−0.526999
$178$	−3.84485	−0.288184
$179$	−25.0496	−1.87229	−0.936147	−	0.351609i	$-0.885635\pi$
$179$	−25.0496	−1.87229	−0.936147	+	0.351609i	$0.885635\pi$
$180$	−0.0894557	−0.00666763
$181$	−9.50781	−0.706710	−0.353355	−	0.935489i	$-0.614959\pi$
$181$	−9.50781	−0.706710	−0.353355	+	0.935489i	$0.614959\pi$
$182$	8.92845	0.661821
$183$	28.8646	2.13374
$184$	−2.66988	−0.196826
$185$	−1.38414	−0.101764
$186$	0.468142	0.0343258
$187$	2.49348	0.182342
$188$	11.2360	0.819471
$189$	−19.0849	−1.38822
$190$	0.624888	0.0453341
$191$	−10.6295	−0.769125	−0.384563	−	0.923099i	$-0.625648\pi$
$191$	−10.6295	−0.769125	−0.384563	+	0.923099i	$0.625648\pi$
$192$	−1.86328	−0.134471
$193$	13.0807	0.941572	0.470786	−	0.882247i	$-0.343970\pi$
$193$	13.0807	0.941572	0.470786	+	0.882247i	$0.343970\pi$
$194$	5.55984	0.399173
$195$	0.778547	0.0557529
$196$	9.41371	0.672408
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	0.471817	0.0335306
$199$	24.8010	1.75809	0.879047	−	0.476736i	$-0.158180\pi$
$199$	24.8010	1.75809	0.879047	+	0.476736i	$0.158180\pi$
$200$	4.96405	0.351012
$201$	−9.26456	−0.653472
$202$	−1.38237	−0.0972635
$203$	27.1406	1.90490
$204$	4.64606	0.325289
$205$	−0.700209	−0.0489047
$206$	9.63972	0.671631
$207$	1.25969	0.0875548
$208$	2.20380	0.152806
$209$	−3.29586	−0.227979
$210$	1.43125	0.0987657
$211$	−3.23335	−0.222593	−0.111296	−	0.993787i	$-0.535500\pi$
$211$	−3.23335	−0.222593	−0.111296	+	0.993787i	$0.535500\pi$
$212$	6.06005	0.416206
$213$	−9.49837	−0.650818
$214$	9.47253	0.647529
$215$	0.489233	0.0333654
$216$	−4.71072	−0.320524
$217$	−1.01789	−0.0690992
$218$	−2.29392	−0.155364
$219$	−14.8558	−1.00386
$220$	0.189598	0.0127827
$221$	−5.49515	−0.369643
$222$	13.6027	0.912952
$223$	−4.94625	−0.331226	−0.165613	−	0.986191i	$-0.552960\pi$
$223$	−4.94625	−0.331226	−0.165613	+	0.986191i	$0.552960\pi$
$224$	4.05138	0.270694
$225$	−2.34213	−0.156142
$226$	9.81420	0.652831
$227$	21.7249	1.44193	0.720965	−	0.692972i	$-0.243699\pi$
$227$	21.7249	1.44193	0.720965	+	0.692972i	$0.243699\pi$
$228$	−6.14111	−0.406705
$229$	24.7312	1.63428	0.817141	−	0.576438i	$-0.195558\pi$
$229$	24.7312	1.63428	0.817141	+	0.576438i	$0.195558\pi$
$230$	0.506203	0.0333781
$231$	−7.54887	−0.496679
$232$	6.69910	0.439817
$233$	−16.0625	−1.05229	−0.526145	−	0.850395i	$-0.676363\pi$
$233$	−16.0625	−1.05229	−0.526145	+	0.850395i	$0.676363\pi$
$234$	−1.03979	−0.0679734
$235$	−2.13033	−0.138967
$236$	3.76286	0.244941
$237$	3.21162	0.208617
$238$	−10.1021	−0.654819
$239$	−11.7001	−0.756814	−0.378407	−	0.925639i	$-0.623528\pi$
$239$	−11.7001	−0.756814	−0.378407	+	0.925639i	$0.623528\pi$
$240$	0.353274	0.0228038
$241$	−2.09930	−0.135228	−0.0676138	−	0.997712i	$-0.521539\pi$
$241$	−2.09930	−0.135228	−0.0676138	+	0.997712i	$0.521539\pi$
$242$	−1.00000	−0.0642824
$243$	4.85998	0.311768
$244$	−15.4913	−0.991728
$245$	−1.78482	−0.114028
$246$	6.88133	0.438738
$247$	7.26342	0.462160
$248$	−0.251246	−0.0159541
$249$	−4.61692	−0.292585
$250$	−1.88916	−0.119481
$251$	−13.2545	−0.836619	−0.418310	−	0.908305i	$-0.637377\pi$
$251$	−13.2545	−0.836619	−0.418310	+	0.908305i	$0.637377\pi$
$252$	−1.91151	−0.120414
$253$	−2.66988	−0.167854
$254$	−10.9255	−0.685528
$255$	−0.880884	−0.0551631
$256$	1.00000	0.0625000
$257$	−14.2453	−0.888598	−0.444299	−	0.895879i	$-0.646547\pi$
$257$	−14.2453	−0.888598	−0.444299	+	0.895879i	$0.646547\pi$
$258$	−4.80796	−0.299330
$259$	−29.5767	−1.83781
$260$	−0.417837	−0.0259131
$261$	−3.16075	−0.195646
$262$	−18.2410	−1.12693
$263$	−11.0526	−0.681535	−0.340767	−	0.940148i	$-0.610687\pi$
$263$	−11.0526	−0.681535	−0.340767	+	0.940148i	$0.610687\pi$
$264$	−1.86328	−0.114677
$265$	−1.14897	−0.0705809
$266$	13.3528	0.818711
$267$	−7.16404	−0.438432
$268$	4.97217	0.303724
$269$	−19.5796	−1.19379	−0.596896	−	0.802319i	$-0.703599\pi$
$269$	−19.5796	−1.19379	−0.596896	+	0.802319i	$0.703599\pi$
$270$	0.893142	0.0543549
$271$	−28.7244	−1.74488	−0.872441	−	0.488720i	$-0.837464\pi$
$271$	−28.7244	−1.74488	−0.872441	+	0.488720i	$0.837464\pi$
$272$	−2.49348	−0.151190
$273$	16.6362	1.00687
$274$	−4.27108	−0.258025
$275$	4.96405	0.299344
$276$	−4.97473	−0.299444
$277$	−22.4956	−1.35163	−0.675814	−	0.737072i	$-0.736208\pi$
$277$	−22.4956	−1.35163	−0.675814	+	0.737072i	$0.736208\pi$
$278$	14.9447	0.896324
$279$	0.118542	0.00709694
$280$	−0.768134	−0.0459048
$281$	21.4788	1.28132	0.640658	−	0.767826i	$-0.278662\pi$
$281$	21.4788	1.28132	0.640658	+	0.767826i	$0.278662\pi$
$282$	20.9359	1.24671
$283$	−5.99852	−0.356575	−0.178287	−	0.983978i	$-0.557056\pi$
$283$	−5.99852	−0.356575	−0.178287	+	0.983978i	$0.557056\pi$
$284$	5.09766	0.302490
$285$	1.16434	0.0689697
$286$	2.20380	0.130314
$287$	−14.9623	−0.883195
$288$	−0.471817	−0.0278021
$289$	−10.7825	−0.634267
$290$	−1.27014	−0.0745849
$291$	10.3595	0.607287
$292$	7.97292	0.466580
$293$	−24.2273	−1.41537	−0.707686	−	0.706527i	$-0.750261\pi$
$293$	−24.2273	−1.41537	−0.707686	+	0.706527i	$0.750261\pi$
$294$	17.5404	1.02298
$295$	−0.713430	−0.0415375
$296$	−7.30039	−0.424327
$297$	−4.71072	−0.273343
$298$	10.0987	0.584999
$299$	5.88388	0.340274
$300$	9.24943	0.534016
$301$	10.4541	0.602563
$302$	−9.07689	−0.522316
$303$	−2.57575	−0.147973
$304$	3.29586	0.189030
$305$	2.93712	0.168179
$306$	1.17647	0.0672542
$307$	−12.1578	−0.693882	−0.346941	−	0.937887i	$-0.612780\pi$
$307$	−12.1578	−0.693882	−0.346941	+	0.937887i	$0.612780\pi$
$308$	4.05138	0.230849
$309$	17.9615	1.02179
$310$	0.0476358	0.00270553
$311$	28.7599	1.63083	0.815413	−	0.578880i	$-0.196510\pi$
$311$	28.7599	1.63083	0.815413	+	0.578880i	$0.196510\pi$
$312$	4.10631	0.232474
$313$	23.5816	1.33291	0.666455	−	0.745545i	$-0.267811\pi$
$313$	23.5816	1.33291	0.666455	+	0.745545i	$0.267811\pi$
$314$	15.1043	0.852383
$315$	0.362419	0.0204200
$316$	−1.72364	−0.0969620
$317$	−15.5011	−0.870626	−0.435313	−	0.900279i	$-0.643362\pi$
$317$	−15.5011	−0.870626	−0.435313	+	0.900279i	$0.643362\pi$
$318$	11.2916	0.633200
$319$	6.69910	0.375078
$320$	−0.189598	−0.0105989
$321$	17.6500	0.985126
$322$	10.8167	0.602791
$323$	−8.21816	−0.457271
$324$	−10.1928	−0.566269
$325$	−10.9398	−0.606831
$326$	−23.7800	−1.31705
$327$	−4.27421	−0.236364
$328$	−3.69313	−0.203919
$329$	−45.5214	−2.50968
$330$	0.353274	0.0194471
$331$	−27.5209	−1.51269	−0.756343	−	0.654176i	$-0.773016\pi$
$331$	−27.5209	−1.51269	−0.756343	+	0.654176i	$0.773016\pi$
$332$	2.47784	0.135989
$333$	3.44445	0.188755
$334$	−1.59992	−0.0875439
$335$	−0.942714	−0.0515060
$336$	7.54887	0.411825
$337$	−31.6235	−1.72264	−0.861320	−	0.508063i	$-0.830362\pi$
$337$	−31.6235	−1.72264	−0.861320	+	0.508063i	$0.830362\pi$
$338$	8.14325	0.442934
$339$	18.2866	0.993193
$340$	0.472759	0.0256390
$341$	−0.251246	−0.0136057
$342$	−1.55504	−0.0840871
$343$	−9.77888	−0.528010
$344$	2.58037	0.139124
$345$	0.943199	0.0507801
$346$	−13.1641	−0.707708
$347$	28.7317	1.54240	0.771199	−	0.636594i	$-0.219657\pi$
$347$	28.7317	1.54240	0.771199	+	0.636594i	$0.219657\pi$
$348$	12.4823	0.669122
$349$	−34.5087	−1.84721	−0.923604	−	0.383348i	$-0.874771\pi$
$349$	−34.5087	−1.84721	−0.923604	+	0.383348i	$0.874771\pi$
$350$	−20.1113	−1.07499
$351$	10.3815	0.554123
$352$	1.00000	0.0533002
$353$	17.0096	0.905330	0.452665	−	0.891681i	$-0.350473\pi$
$353$	17.0096	0.905330	0.452665	+	0.891681i	$0.350473\pi$
$354$	7.01126	0.372644
$355$	−0.966506	−0.0512968
$356$	3.84485	0.203777
$357$	−18.8230	−0.996217
$358$	25.0496	1.32391
$359$	−5.62114	−0.296672	−0.148336	−	0.988937i	$-0.547392\pi$
$359$	−5.62114	−0.296672	−0.148336	+	0.988937i	$0.547392\pi$
$360$	0.0894557	0.00471473
$361$	−8.13733	−0.428281
$362$	9.50781	0.499719
$363$	−1.86328	−0.0977969
$364$	−8.92845	−0.467978
$365$	−1.51165	−0.0791233
$366$	−28.8646	−1.50878
$367$	2.69714	0.140789	0.0703947	−	0.997519i	$-0.477574\pi$
$367$	2.69714	0.140789	0.0703947	+	0.997519i	$0.477574\pi$
$368$	2.66988	0.139177
$369$	1.74248	0.0907099
$370$	1.38414	0.0719580
$371$	−24.5516	−1.27465
$372$	−0.468142	−0.0242720
$373$	17.2531	0.893330	0.446665	−	0.894701i	$-0.352612\pi$
$373$	17.2531	0.893330	0.446665	+	0.894701i	$0.352612\pi$
$374$	−2.49348	−0.128935
$375$	−3.52005	−0.181774
$376$	−11.2360	−0.579453
$377$	−14.7635	−0.760359
$378$	19.0849	0.981622
$379$	−14.1127	−0.724919	−0.362460	−	0.932000i	$-0.618063\pi$
$379$	−14.1127	−0.724919	−0.362460	+	0.932000i	$0.618063\pi$
$380$	−0.624888	−0.0320561
$381$	−20.3573	−1.04294
$382$	10.6295	0.543854
$383$	28.1303	1.43739	0.718695	−	0.695326i	$-0.244740\pi$
$383$	28.1303	1.43739	0.718695	+	0.695326i	$0.244740\pi$
$384$	1.86328	0.0950852
$385$	−0.768134	−0.0391478
$386$	−13.0807	−0.665792
$387$	−1.21746	−0.0618872
$388$	−5.55984	−0.282258
$389$	−28.9466	−1.46765	−0.733825	−	0.679339i	$-0.762267\pi$
$389$	−28.9466	−1.46765	−0.733825	+	0.679339i	$0.762267\pi$
$390$	−0.778547	−0.0394233
$391$	−6.65729	−0.336674
$392$	−9.41371	−0.475464
$393$	−33.9881	−1.71447
$394$	1.00000	0.0503793
$395$	0.326798	0.0164430
$396$	−0.471817	−0.0237097
$397$	−7.10651	−0.356665	−0.178333	−	0.983970i	$-0.557070\pi$
$397$	−7.10651	−0.356665	−0.178333	+	0.983970i	$0.557070\pi$
$398$	−24.8010	−1.24316
$399$	24.8800	1.24556
$400$	−4.96405	−0.248203
$401$	−14.3530	−0.716754	−0.358377	−	0.933577i	$-0.616670\pi$
$401$	−14.3530	−0.716754	−0.358377	+	0.933577i	$0.616670\pi$
$402$	9.26456	0.462074
$403$	0.553697	0.0275816
$404$	1.38237	0.0687757
$405$	1.93254	0.0960288
$406$	−27.1406	−1.34697
$407$	−7.30039	−0.361867
$408$	−4.64606	−0.230014
$409$	2.06233	0.101976	0.0509879	−	0.998699i	$-0.483763\pi$
$409$	2.06233	0.101976	0.0509879	+	0.998699i	$0.483763\pi$
$410$	0.700209	0.0345809
$411$	−7.95822	−0.392550
$412$	−9.63972	−0.474915
$413$	−15.2448	−0.750146
$414$	−1.25969	−0.0619106
$415$	−0.469794	−0.0230613
$416$	−2.20380	−0.108050
$417$	27.8462	1.36363
$418$	3.29586	0.161206
$419$	29.2093	1.42697	0.713483	−	0.700672i	$-0.247116\pi$
$419$	29.2093	1.42697	0.713483	+	0.700672i	$0.247116\pi$
$420$	−1.43125	−0.0698379
$421$	3.30991	0.161315	0.0806576	−	0.996742i	$-0.474298\pi$
$421$	3.30991	0.161315	0.0806576	+	0.996742i	$0.474298\pi$
$422$	3.23335	0.157397
$423$	5.30135	0.257760
$424$	−6.06005	−0.294302
$425$	12.3778	0.600410
$426$	9.49837	0.460198
$427$	62.7612	3.03723
$428$	−9.47253	−0.457872
$429$	4.10631	0.198254
$430$	−0.489233	−0.0235929
$431$	30.7807	1.48265	0.741326	−	0.671145i	$-0.234197\pi$
$431$	30.7807	1.48265	0.741326	+	0.671145i	$0.234197\pi$
$432$	4.71072	0.226644
$433$	−20.4291	−0.981762	−0.490881	−	0.871227i	$-0.663325\pi$
$433$	−20.4291	−0.981762	−0.490881	+	0.871227i	$0.663325\pi$
$434$	1.01789	0.0488605
$435$	−2.36662	−0.113471
$436$	2.29392	0.109859
$437$	8.79953	0.420939
$438$	14.8558	0.709837
$439$	−26.7485	−1.27664	−0.638319	−	0.769772i	$-0.720370\pi$
$439$	−26.7485	−1.27664	−0.638319	+	0.769772i	$0.720370\pi$
$440$	−0.189598	−0.00903873
$441$	4.44155	0.211503
$442$	5.49515	0.261377
$443$	−14.7319	−0.699934	−0.349967	−	0.936762i	$-0.613807\pi$
$443$	−14.7319	−0.699934	−0.349967	+	0.936762i	$0.613807\pi$
$444$	−13.6027	−0.645555
$445$	−0.728977	−0.0345568
$446$	4.94625	0.234212
$447$	18.8166	0.889996
$448$	−4.05138	−0.191410
$449$	−20.1503	−0.950950	−0.475475	−	0.879729i	$-0.657724\pi$
$449$	−20.1503	−0.950950	−0.475475	+	0.879729i	$0.657724\pi$
$450$	2.34213	0.110409
$451$	−3.69313	−0.173902
$452$	−9.81420	−0.461621
$453$	−16.9128	−0.794632
$454$	−21.7249	−1.01960
$455$	1.69282	0.0793605
$456$	6.14111	0.287584
$457$	−7.51796	−0.351675	−0.175838	−	0.984419i	$-0.556263\pi$
$457$	−7.51796	−0.351675	−0.175838	+	0.984419i	$0.556263\pi$
$458$	−24.7312	−1.15561
$459$	−11.7461	−0.548260
$460$	−0.506203	−0.0236019
$461$	−2.16884	−0.101013	−0.0505064	−	0.998724i	$-0.516084\pi$
$461$	−2.16884	−0.101013	−0.0505064	+	0.998724i	$0.516084\pi$
$462$	7.54887	0.351205
$463$	−31.2881	−1.45408	−0.727041	−	0.686594i	$-0.759105\pi$
$463$	−31.2881	−1.45408	−0.727041	+	0.686594i	$0.759105\pi$
$464$	−6.69910	−0.310998
$465$	0.0887588	0.00411609
$466$	16.0625	0.744081
$467$	3.67702	0.170152	0.0850760	−	0.996374i	$-0.472887\pi$
$467$	3.67702	0.170152	0.0850760	+	0.996374i	$0.472887\pi$
$468$	1.03979	0.0480644
$469$	−20.1442	−0.930172
$470$	2.13033	0.0982646
$471$	28.1435	1.29678
$472$	−3.76286	−0.173199
$473$	2.58037	0.118646
$474$	−3.21162	−0.147514
$475$	−16.3608	−0.750685
$476$	10.1021	0.463027
$477$	2.85924	0.130915
$478$	11.7001	0.535148
$479$	−35.3131	−1.61350	−0.806749	−	0.590895i	$-0.798775\pi$
$479$	−35.3131	−1.61350	−0.806749	+	0.590895i	$0.798775\pi$
$480$	−0.353274	−0.0161247
$481$	16.0886	0.733578
$482$	2.09930	0.0956204
$483$	20.1546	0.917064
$484$	1.00000	0.0454545
$485$	1.05413	0.0478658
$486$	−4.85998	−0.220453
$487$	5.83825	0.264556	0.132278	−	0.991213i	$-0.457771\pi$
$487$	5.83825	0.264556	0.132278	+	0.991213i	$0.457771\pi$
$488$	15.4913	0.701258
$489$	−44.3088	−2.00371
$490$	1.78482	0.0806300
$491$	13.7630	0.621114	0.310557	−	0.950555i	$-0.399484\pi$
$491$	13.7630	0.621114	0.310557	+	0.950555i	$0.399484\pi$
$492$	−6.88133	−0.310234
$493$	16.7041	0.752314
$494$	−7.26342	−0.326797
$495$	0.0894557	0.00402073
$496$	0.251246	0.0112813
$497$	−20.6526	−0.926394
$498$	4.61692	0.206889
$499$	31.3474	1.40330	0.701651	−	0.712520i	$-0.252446\pi$
$499$	31.3474	1.40330	0.701651	+	0.712520i	$0.252446\pi$
$500$	1.88916	0.0844860
$501$	−2.98111	−0.133186
$502$	13.2545	0.591579
$503$	19.7787	0.881887	0.440943	−	0.897535i	$-0.354644\pi$
$503$	19.7787	0.881887	0.440943	+	0.897535i	$0.354644\pi$
$504$	1.91151	0.0851456
$505$	−0.262096	−0.0116631
$506$	2.66988	0.118691
$507$	15.1732	0.673864
$508$	10.9255	0.484741
$509$	−9.83436	−0.435901	−0.217950	−	0.975960i	$-0.569937\pi$
$509$	−9.83436	−0.435901	−0.217950	+	0.975960i	$0.569937\pi$
$510$	0.880884	0.0390062
$511$	−32.3013	−1.42893
$512$	−1.00000	−0.0441942
$513$	15.5258	0.685483
$514$	14.2453	0.628333
$515$	1.82767	0.0805368
$516$	4.80796	0.211658
$517$	−11.2360	−0.494159
$518$	29.5767	1.29952
$519$	−24.5285	−1.07668
$520$	0.417837	0.0183234
$521$	−4.10766	−0.179960	−0.0899798	−	0.995944i	$-0.528680\pi$
$521$	−4.10766	−0.179960	−0.0899798	+	0.995944i	$0.528680\pi$
$522$	3.16075	0.138342
$523$	−33.4763	−1.46381	−0.731907	−	0.681404i	$-0.761370\pi$
$523$	−33.4763	−1.46381	−0.731907	+	0.681404i	$0.761370\pi$
$524$	18.2410	0.796861
$525$	−37.4730	−1.63545
$526$	11.0526	0.481918
$527$	−0.626478	−0.0272898
$528$	1.86328	0.0810889
$529$	−15.8718	−0.690076
$530$	1.14897	0.0499082
$531$	1.77538	0.0770450
$532$	−13.3528	−0.578916
$533$	8.13892	0.352536
$534$	7.16404	0.310018
$535$	1.79597	0.0776467
$536$	−4.97217	−0.214765
$537$	46.6744	2.01415
$538$	19.5796	0.844138
$539$	−9.41371	−0.405477
$540$	−0.893142	−0.0384347
$541$	0.0925166	0.00397760	0.00198880	−	0.999998i	$-0.499367\pi$
$541$	0.0925166	0.00397760	0.00198880	+	0.999998i	$0.499367\pi$
$542$	28.7244	1.23382
$543$	17.7157	0.760254
$544$	2.49348	0.106907
$545$	−0.434922	−0.0186300
$546$	−16.6362	−0.711965
$547$	6.97043	0.298034	0.149017	−	0.988835i	$-0.452389\pi$
$547$	6.97043	0.298034	0.149017	+	0.988835i	$0.452389\pi$
$548$	4.27108	0.182452
$549$	−7.30906	−0.311943
$550$	−4.96405	−0.211668
$551$	−22.0793	−0.940608
$552$	4.97473	0.211739
$553$	6.98311	0.296952
$554$	22.4956	0.955746
$555$	2.57904	0.109474
$556$	−14.9447	−0.633797
$557$	−0.0975893	−0.00413499	−0.00206750	−	0.999998i	$-0.500658\pi$
$557$	−0.0975893	−0.00413499	−0.00206750	+	0.999998i	$0.500658\pi$
$558$	−0.118542	−0.00501830
$559$	−5.68663	−0.240519
$560$	0.768134	0.0324596
$561$	−4.64606	−0.196157
$562$	−21.4788	−0.906028
$563$	24.1401	1.01739	0.508693	−	0.860948i	$-0.330129\pi$
$563$	24.1401	1.01739	0.508693	+	0.860948i	$0.330129\pi$
$564$	−20.9359	−0.881559
$565$	1.86075	0.0782825
$566$	5.99852	0.252137
$567$	41.2951	1.73423
$568$	−5.09766	−0.213893
$569$	−42.9061	−1.79872	−0.899359	−	0.437210i	$-0.855967\pi$
$569$	−42.9061	−1.79872	−0.899359	+	0.437210i	$0.855967\pi$
$570$	−1.16434	−0.0487689
$571$	−32.3172	−1.35243	−0.676216	−	0.736704i	$-0.736381\pi$
$571$	−32.3172	−1.35243	−0.676216	+	0.736704i	$0.736381\pi$
$572$	−2.20380	−0.0921457
$573$	19.8058	0.827399
$574$	14.9623	0.624513
$575$	−13.2534	−0.552705
$576$	0.471817	0.0196591
$577$	32.3669	1.34745	0.673726	−	0.738981i	$-0.264693\pi$
$577$	32.3669	1.34745	0.673726	+	0.738981i	$0.264693\pi$
$578$	10.7825	0.448495
$579$	−24.3731	−1.01291
$580$	1.27014	0.0527395
$581$	−10.0387	−0.416475
$582$	−10.3595	−0.429417
$583$	−6.06005	−0.250982
$584$	−7.97292	−0.329922
$585$	−0.197143	−0.00815085
$586$	24.2273	1.00082
$587$	−3.23856	−0.133670	−0.0668348	−	0.997764i	$-0.521290\pi$
$587$	−3.23856	−0.133670	−0.0668348	+	0.997764i	$0.521290\pi$
$588$	−17.5404	−0.723354
$589$	0.828071	0.0341201
$590$	0.713430	0.0293714
$591$	1.86328	0.0766452
$592$	7.30039	0.300044
$593$	−1.12101	−0.0460344	−0.0230172	−	0.999735i	$-0.507327\pi$
$593$	−1.12101	−0.0460344	−0.0230172	+	0.999735i	$0.507327\pi$
$594$	4.71072	0.193283
$595$	−1.91533	−0.0785209
$596$	−10.0987	−0.413657
$597$	−46.2112	−1.89130
$598$	−5.88388	−0.240610
$599$	17.6882	0.722722	0.361361	−	0.932426i	$-0.382312\pi$
$599$	17.6882	0.722722	0.361361	+	0.932426i	$0.382312\pi$
$600$	−9.24943	−0.377606
$601$	−47.7487	−1.94771	−0.973855	−	0.227171i	$-0.927052\pi$
$601$	−47.7487	−1.94771	−0.973855	+	0.227171i	$0.927052\pi$
$602$	−10.4541	−0.426076
$603$	2.34596	0.0955348
$604$	9.07689	0.369333
$605$	−0.189598	−0.00770826
$606$	2.57575	0.104633
$607$	−45.1070	−1.83084	−0.915418	−	0.402506i	$-0.868139\pi$
$607$	−45.1070	−1.83084	−0.915418	+	0.402506i	$0.868139\pi$
$608$	−3.29586	−0.133665
$609$	−50.5706	−2.04922
$610$	−2.93712	−0.118920
$611$	24.7620	1.00176
$612$	−1.17647	−0.0475559
$613$	−1.70347	−0.0688025	−0.0344013	−	0.999408i	$-0.510952\pi$
$613$	−1.70347	−0.0688025	−0.0344013	+	0.999408i	$0.510952\pi$
$614$	12.1578	0.490649
$615$	1.30469	0.0526100
$616$	−4.05138	−0.163235
$617$	25.9582	1.04504	0.522520	−	0.852627i	$-0.324992\pi$
$617$	25.9582	1.04504	0.522520	+	0.852627i	$0.324992\pi$
$618$	−17.9615	−0.722518
$619$	−18.5991	−0.747561	−0.373780	−	0.927517i	$-0.621939\pi$
$619$	−18.5991	−0.747561	−0.373780	+	0.927517i	$0.621939\pi$
$620$	−0.0476358	−0.00191310
$621$	12.5770	0.504699
$622$	−28.7599	−1.15317
$623$	−15.5770	−0.624078
$624$	−4.10631	−0.164384
$625$	24.4621	0.978483
$626$	−23.5816	−0.942510
$627$	6.14111	0.245252
$628$	−15.1043	−0.602725
$629$	−18.2034	−0.725817
$630$	−0.362419	−0.0144391
$631$	−30.2879	−1.20574	−0.602871	−	0.797838i	$-0.705977\pi$
$631$	−30.2879	−1.20574	−0.602871	+	0.797838i	$0.705977\pi$
$632$	1.72364	0.0685625
$633$	6.02463	0.239458
$634$	15.5011	0.615626
$635$	−2.07146	−0.0822032
$636$	−11.2916	−0.447740
$637$	20.7460	0.821985
$638$	−6.69910	−0.265220
$639$	2.40516	0.0951468
$640$	0.189598	0.00749452
$641$	19.9735	0.788906	0.394453	−	0.918916i	$-0.370934\pi$
$641$	19.9735	0.788906	0.394453	+	0.918916i	$0.370934\pi$
$642$	−17.6500	−0.696589
$643$	8.64037	0.340743	0.170371	−	0.985380i	$-0.445503\pi$
$643$	8.64037	0.340743	0.170371	+	0.985380i	$0.445503\pi$
$644$	−10.8167	−0.426238
$645$	−0.911579	−0.0358934
$646$	8.21816	0.323339
$647$	20.5089	0.806286	0.403143	−	0.915137i	$-0.367918\pi$
$647$	20.5089	0.806286	0.403143	+	0.915137i	$0.367918\pi$
$648$	10.1928	0.400413
$649$	−3.76286	−0.147705
$650$	10.9398	0.429094
$651$	1.89662	0.0743345
$652$	23.7800	0.931295
$653$	34.0963	1.33429	0.667146	−	0.744927i	$-0.267516\pi$
$653$	34.0963	1.33429	0.667146	+	0.744927i	$0.267516\pi$
$654$	4.27421	0.167135
$655$	−3.45845	−0.135133
$656$	3.69313	0.144192
$657$	3.76176	0.146760
$658$	45.5214	1.77461
$659$	−8.48274	−0.330441	−0.165220	−	0.986257i	$-0.552834\pi$
$659$	−8.48274	−0.330441	−0.165220	+	0.986257i	$0.552834\pi$
$660$	−0.353274	−0.0137512
$661$	−20.8092	−0.809385	−0.404692	−	0.914453i	$-0.632621\pi$
$661$	−20.8092	−0.809385	−0.404692	+	0.914453i	$0.632621\pi$
$662$	27.5209	1.06963
$663$	10.2390	0.397650
$664$	−2.47784	−0.0961590
$665$	2.53166	0.0981736
$666$	−3.44445	−0.133470
$667$	−17.8858	−0.692540
$668$	1.59992	0.0619029
$669$	9.21626	0.356321
$670$	0.942714	0.0364202
$671$	15.4913	0.598035
$672$	−7.54887	−0.291204
$673$	29.3146	1.13000	0.564998	−	0.825092i	$-0.308877\pi$
$673$	29.3146	1.13000	0.564998	+	0.825092i	$0.308877\pi$
$674$	31.6235	1.21809
$675$	−23.3842	−0.900060
$676$	−8.14325	−0.313202
$677$	38.7083	1.48768	0.743841	−	0.668356i	$-0.233002\pi$
$677$	38.7083	1.48768	0.743841	+	0.668356i	$0.233002\pi$
$678$	−18.2866	−0.702293
$679$	22.5250	0.864432
$680$	−0.472759	−0.0181295
$681$	−40.4795	−1.55118
$682$	0.251246	0.00962071
$683$	−27.0588	−1.03537	−0.517687	−	0.855570i	$-0.673207\pi$
$683$	−27.0588	−1.03537	−0.517687	+	0.855570i	$0.673207\pi$
$684$	1.55504	0.0594585
$685$	−0.809788	−0.0309404
$686$	9.77888	0.373359
$687$	−46.0811	−1.75810
$688$	−2.58037	−0.0983757
$689$	13.3552	0.508791
$690$	−0.943199	−0.0359070
$691$	44.4848	1.69228	0.846141	−	0.532958i	$-0.178920\pi$
$691$	44.4848	1.69228	0.846141	+	0.532958i	$0.178920\pi$
$692$	13.1641	0.500425
$693$	1.91151	0.0726124
$694$	−28.7317	−1.09064
$695$	2.83349	0.107480
$696$	−12.4823	−0.473141
$697$	−9.20874	−0.348806
$698$	34.5087	1.30617
$699$	29.9290	1.13202
$700$	20.1113	0.760135
$701$	31.0518	1.17281	0.586406	−	0.810017i	$-0.300542\pi$
$701$	31.0518	1.17281	0.586406	+	0.810017i	$0.300542\pi$
$702$	−10.3815	−0.391824
$703$	24.0610	0.907479
$704$	−1.00000	−0.0376889
$705$	3.96940	0.149496
$706$	−17.0096	−0.640165
$707$	−5.60053	−0.210630
$708$	−7.01126	−0.263499
$709$	−27.6107	−1.03694	−0.518470	−	0.855096i	$-0.673498\pi$
$709$	−27.6107	−1.03694	−0.518470	+	0.855096i	$0.673498\pi$
$710$	0.966506	0.0362723
$711$	−0.813241	−0.0304989
$712$	−3.84485	−0.144092
$713$	0.670796	0.0251215
$714$	18.8230	0.704432
$715$	0.417837	0.0156262
$716$	−25.0496	−0.936147
$717$	21.8005	0.814155
$718$	5.62114	0.209779
$719$	41.4362	1.54531	0.772654	−	0.634827i	$-0.218929\pi$
$719$	41.4362	1.54531	0.772654	+	0.634827i	$0.218929\pi$
$720$	−0.0894557	−0.00333382
$721$	39.0542	1.45445
$722$	8.13733	0.302840
$723$	3.91158	0.145473
$724$	−9.50781	−0.353355
$725$	33.2547	1.23505
$726$	1.86328	0.0691529
$727$	4.35074	0.161360	0.0806800	−	0.996740i	$-0.474291\pi$
$727$	4.35074	0.161360	0.0806800	+	0.996740i	$0.474291\pi$
$728$	8.92845	0.330911
$729$	21.5230	0.797148
$730$	1.51165	0.0559486
$731$	6.43411	0.237974
$732$	28.8646	1.06687
$733$	−22.9079	−0.846123	−0.423061	−	0.906101i	$-0.639045\pi$
$733$	−22.9079	−0.846123	−0.423061	+	0.906101i	$0.639045\pi$
$734$	−2.69714	−0.0995532
$735$	3.32562	0.122668
$736$	−2.66988	−0.0984130
$737$	−4.97217	−0.183152
$738$	−1.74248	−0.0641416
$739$	−3.01670	−0.110971	−0.0554855	−	0.998459i	$-0.517671\pi$
$739$	−3.01670	−0.110971	−0.0554855	+	0.998459i	$0.517671\pi$
$740$	−1.38414	−0.0508820
$741$	−13.5338	−0.497176
$742$	24.5516	0.901317
$743$	14.6510	0.537494	0.268747	−	0.963211i	$-0.413390\pi$
$743$	14.6510	0.537494	0.268747	+	0.963211i	$0.413390\pi$
$744$	0.468142	0.0171629
$745$	1.91469	0.0701486
$746$	−17.2531	−0.631680
$747$	1.16909	0.0427748
$748$	2.49348	0.0911708
$749$	38.3769	1.40226
$750$	3.52005	0.128534
$751$	4.72999	0.172600	0.0862999	−	0.996269i	$-0.472496\pi$
$751$	4.72999	0.172600	0.0862999	+	0.996269i	$0.472496\pi$
$752$	11.2360	0.409735
$753$	24.6969	0.900006
$754$	14.7635	0.537655
$755$	−1.72096	−0.0626321
$756$	−19.0849	−0.694112
$757$	26.6014	0.966846	0.483423	−	0.875387i	$-0.339393\pi$
$757$	26.6014	0.966846	0.483423	+	0.875387i	$0.339393\pi$
$758$	14.1127	0.512595
$759$	4.97473	0.180571
$760$	0.624888	0.0226671
$761$	11.2566	0.408050	0.204025	−	0.978966i	$-0.434598\pi$
$761$	11.2566	0.408050	0.204025	+	0.978966i	$0.434598\pi$
$762$	20.3573	0.737468
$763$	−9.29353	−0.336449
$764$	−10.6295	−0.384563
$765$	0.223056	0.00806461
$766$	−28.1303	−1.01639
$767$	8.29259	0.299428
$768$	−1.86328	−0.0672354
$769$	47.0567	1.69691	0.848454	−	0.529270i	$-0.177534\pi$
$769$	47.0567	1.69691	0.848454	+	0.529270i	$0.177534\pi$
$770$	0.768134	0.0276816
$771$	26.5430	0.955923
$772$	13.0807	0.470786
$773$	23.1081	0.831139	0.415569	−	0.909561i	$-0.363582\pi$
$773$	23.1081	0.831139	0.415569	+	0.909561i	$0.363582\pi$
$774$	1.21746	0.0437608
$775$	−1.24720	−0.0448007
$776$	5.55984	0.199587
$777$	55.1097	1.97705
$778$	28.9466	1.03778
$779$	12.1720	0.436107
$780$	0.778547	0.0278765
$781$	−5.09766	−0.182409
$782$	6.65729	0.238064
$783$	−31.5575	−1.12777
$784$	9.41371	0.336204
$785$	2.86374	0.102211
$786$	33.9881	1.21231
$787$	−26.6361	−0.949476	−0.474738	−	0.880127i	$-0.657457\pi$
$787$	−26.6361	−0.949476	−0.474738	+	0.880127i	$0.657457\pi$
$788$	−1.00000	−0.0356235
$789$	20.5942	0.733172
$790$	−0.326798	−0.0116269
$791$	39.7611	1.41374
$792$	0.471817	0.0167653
$793$	−34.1398	−1.21234
$794$	7.10651	0.252200
$795$	2.14086	0.0759285
$796$	24.8010	0.879047
$797$	6.31772	0.223785	0.111892	−	0.993720i	$-0.464309\pi$
$797$	6.31772	0.223785	0.111892	+	0.993720i	$0.464309\pi$
$798$	−24.8800	−0.880742
$799$	−28.0168	−0.991163
$800$	4.96405	0.175506
$801$	1.81407	0.0640970
$802$	14.3530	0.506822
$803$	−7.97292	−0.281358
$804$	−9.26456	−0.326736
$805$	2.05082	0.0722821
$806$	−0.553697	−0.0195031
$807$	36.4824	1.28424
$808$	−1.38237	−0.0486318
$809$	34.0637	1.19762	0.598808	−	0.800893i	$-0.295641\pi$
$809$	34.0637	1.19762	0.598808	+	0.800893i	$0.295641\pi$
$810$	−1.93254	−0.0679026
$811$	54.3798	1.90953	0.954767	−	0.297356i	$-0.0961048\pi$
$811$	54.3798	1.90953	0.954767	+	0.297356i	$0.0961048\pi$
$812$	27.1406	0.952449
$813$	53.5216	1.87708
$814$	7.30039	0.255879
$815$	−4.50863	−0.157931
$816$	4.64606	0.162645
$817$	−8.50453	−0.297536
$818$	−2.06233	−0.0721077
$819$	−4.21260	−0.147200
$820$	−0.700209	−0.0244524
$821$	−34.4244	−1.20142	−0.600710	−	0.799467i	$-0.705115\pi$
$821$	−34.4244	−1.20142	−0.600710	+	0.799467i	$0.705115\pi$
$822$	7.95822	0.277575
$823$	−10.7702	−0.375425	−0.187713	−	0.982224i	$-0.560107\pi$
$823$	−10.7702	−0.375425	−0.187713	+	0.982224i	$0.560107\pi$
$824$	9.63972	0.335815
$825$	−9.24943	−0.322024
$826$	15.2448	0.530434
$827$	−4.58262	−0.159353	−0.0796767	−	0.996821i	$-0.525389\pi$
$827$	−4.58262	−0.159353	−0.0796767	+	0.996821i	$0.525389\pi$
$828$	1.25969	0.0437774
$829$	−32.0745	−1.11399	−0.556996	−	0.830515i	$-0.688046\pi$
$829$	−32.0745	−1.11399	−0.556996	+	0.830515i	$0.688046\pi$
$830$	0.469794	0.0163068
$831$	41.9156	1.45404
$832$	2.20380	0.0764031
$833$	−23.4729	−0.813289
$834$	−27.8462	−0.964235
$835$	−0.303342	−0.0104976
$836$	−3.29586	−0.113990
$837$	1.18355	0.0409094
$838$	−29.2093	−1.00902
$839$	−22.3993	−0.773309	−0.386654	−	0.922225i	$-0.626369\pi$
$839$	−22.3993	−0.773309	−0.386654	+	0.922225i	$0.626369\pi$
$840$	1.43125	0.0493828
$841$	15.8779	0.547515
$842$	−3.30991	−0.114067
$843$	−40.0210	−1.37840
$844$	−3.23335	−0.111296
$845$	1.54394	0.0531133
$846$	−5.30135	−0.182264
$847$	−4.05138	−0.139207
$848$	6.06005	0.208103
$849$	11.1769	0.383591
$850$	−12.3778	−0.424554
$851$	19.4911	0.668148
$852$	−9.49837	−0.325409
$853$	32.4507	1.11109	0.555545	−	0.831486i	$-0.312509\pi$
$853$	32.4507	1.11109	0.555545	+	0.831486i	$0.312509\pi$
$854$	−62.7612	−2.14764
$855$	−0.294833	−0.0100831
$856$	9.47253	0.323764
$857$	27.8891	0.952674	0.476337	−	0.879263i	$-0.341964\pi$
$857$	27.8891	0.952674	0.476337	+	0.879263i	$0.341964\pi$
$858$	−4.10631	−0.140187
$859$	−51.7638	−1.76616	−0.883079	−	0.469225i	$-0.844533\pi$
$859$	−51.7638	−1.76616	−0.883079	+	0.469225i	$0.844533\pi$
$860$	0.489233	0.0166827
$861$	27.8789	0.950111
$862$	−30.7807	−1.04839
$863$	15.8882	0.540840	0.270420	−	0.962742i	$-0.412837\pi$
$863$	15.8882	0.540840	0.270420	+	0.962742i	$0.412837\pi$
$864$	−4.71072	−0.160262
$865$	−2.49589	−0.0848628
$866$	20.4291	0.694210
$867$	20.0909	0.682323
$868$	−1.01789	−0.0345496
$869$	1.72364	0.0584703
$870$	2.36662	0.0802360
$871$	10.9577	0.371287
$872$	−2.29392	−0.0776818
$873$	−2.62323	−0.0887828
$874$	−8.79953	−0.297649
$875$	−7.65373	−0.258743
$876$	−14.8558	−0.501930
$877$	13.7055	0.462801	0.231401	−	0.972859i	$-0.425669\pi$
$877$	13.7055	0.462801	0.231401	+	0.972859i	$0.425669\pi$
$878$	26.7485	0.902720
$879$	45.1422	1.52261
$880$	0.189598	0.00639135
$881$	27.5119	0.926900	0.463450	−	0.886123i	$-0.346611\pi$
$881$	27.5119	0.926900	0.463450	+	0.886123i	$0.346611\pi$
$882$	−4.44155	−0.149555
$883$	8.68818	0.292380	0.146190	−	0.989256i	$-0.453299\pi$
$883$	8.68818	0.292380	0.146190	+	0.989256i	$0.453299\pi$
$884$	−5.49515	−0.184822
$885$	1.32932	0.0446846
$886$	14.7319	0.494928
$887$	−41.9916	−1.40994	−0.704971	−	0.709237i	$-0.749040\pi$
$887$	−41.9916	−1.40994	−0.704971	+	0.709237i	$0.749040\pi$
$888$	13.6027	0.456476
$889$	−44.2635	−1.48455
$890$	0.728977	0.0244353
$891$	10.1928	0.341473
$892$	−4.94625	−0.165613
$893$	37.0323	1.23924
$894$	−18.8166	−0.629323
$895$	4.74935	0.158753
$896$	4.05138	0.135347
$897$	−10.9633	−0.366055
$898$	20.1503	0.672423
$899$	−1.68312	−0.0561353
$900$	−2.34213	−0.0780709
$901$	−15.1106	−0.503408
$902$	3.69313	0.122968
$903$	−19.4789	−0.648216
$904$	9.81420	0.326415
$905$	1.80266	0.0599225
$906$	16.9128	0.561890
$907$	−52.1493	−1.73159	−0.865794	−	0.500400i	$-0.833186\pi$
$907$	−52.1493	−1.73159	−0.865794	+	0.500400i	$0.833186\pi$
$908$	21.7249	0.720965
$909$	0.652229	0.0216331
$910$	−1.69282	−0.0561163
$911$	10.6774	0.353757	0.176878	−	0.984233i	$-0.443400\pi$
$911$	10.6774	0.353757	0.176878	+	0.984233i	$0.443400\pi$
$912$	−6.14111	−0.203352
$913$	−2.47784	−0.0820047
$914$	7.51796	0.248672
$915$	−5.47268	−0.180921
$916$	24.7312	0.817141
$917$	−73.9012	−2.44043
$918$	11.7461	0.387679
$919$	−3.53488	−0.116605	−0.0583024	−	0.998299i	$-0.518569\pi$
$919$	−3.53488	−0.116605	−0.0583024	+	0.998299i	$0.518569\pi$
$920$	0.506203	0.0166890
$921$	22.6534	0.746455
$922$	2.16884	0.0714268
$923$	11.2342	0.369779
$924$	−7.54887	−0.248340
$925$	−36.2395	−1.19155
$926$	31.2881	1.02819
$927$	−4.54819	−0.149382
$928$	6.69910	0.219909
$929$	17.6184	0.578042	0.289021	−	0.957323i	$-0.406670\pi$
$929$	17.6184	0.578042	0.289021	+	0.957323i	$0.406670\pi$
$930$	−0.0887588	−0.00291052
$931$	31.0262	1.01684
$932$	−16.0625	−0.526145
$933$	−53.5878	−1.75439
$934$	−3.67702	−0.120316
$935$	−0.472759	−0.0154609
$936$	−1.03979	−0.0339867
$937$	−38.4254	−1.25530	−0.627651	−	0.778495i	$-0.715983\pi$
$937$	−38.4254	−1.25530	−0.627651	+	0.778495i	$0.715983\pi$
$938$	20.1442	0.657731
$939$	−43.9391	−1.43390
$940$	−2.13033	−0.0694836
$941$	22.9518	0.748207	0.374103	−	0.927387i	$-0.377951\pi$
$941$	22.9518	0.748207	0.374103	+	0.927387i	$0.377951\pi$
$942$	−28.1435	−0.916964
$943$	9.86019	0.321092
$944$	3.76286	0.122471
$945$	3.61846	0.117709
$946$	−2.58037	−0.0838951
$947$	18.0791	0.587491	0.293746	−	0.955884i	$-0.405098\pi$
$947$	18.0791	0.587491	0.293746	+	0.955884i	$0.405098\pi$
$948$	3.21162	0.104308
$949$	17.5707	0.570370
$950$	16.3608	0.530815
$951$	28.8828	0.936590
$952$	−10.1021	−0.327410
$953$	−33.1792	−1.07478	−0.537390	−	0.843334i	$-0.680590\pi$
$953$	−33.1792	−1.07478	−0.537390	+	0.843334i	$0.680590\pi$
$954$	−2.85924	−0.0925712
$955$	2.01534	0.0652147
$956$	−11.7001	−0.378407
$957$	−12.4823	−0.403496
$958$	35.3131	1.14091
$959$	−17.3038	−0.558768
$960$	0.353274	0.0114019
$961$	−30.9369	−0.997964
$962$	−16.0886	−0.518718
$963$	−4.46930	−0.144021
$964$	−2.09930	−0.0676138
$965$	−2.48008	−0.0798366
$966$	−20.1546	−0.648462
$967$	−44.4044	−1.42795	−0.713975	−	0.700171i	$-0.753107\pi$
$967$	−44.4044	−1.42795	−0.713975	+	0.700171i	$0.753107\pi$
$968$	−1.00000	−0.0321412
$969$	15.3127	0.491916
$970$	−1.05413	−0.0338462
$971$	−16.6321	−0.533749	−0.266875	−	0.963731i	$-0.585991\pi$
$971$	−16.6321	−0.533749	−0.266875	+	0.963731i	$0.585991\pi$
$972$	4.85998	0.155884
$973$	60.5468	1.94104
$974$	−5.83825	−0.187070
$975$	20.3839	0.652808
$976$	−15.4913	−0.495864
$977$	−0.980561	−0.0313709	−0.0156855	−	0.999877i	$-0.504993\pi$
$977$	−0.980561	−0.0313709	−0.0156855	+	0.999877i	$0.504993\pi$
$978$	44.3088	1.41684
$979$	−3.84485	−0.122882
$980$	−1.78482	−0.0570140
$981$	1.08231	0.0345555
$982$	−13.7630	−0.439194
$983$	7.57108	0.241480	0.120740	−	0.992684i	$-0.461473\pi$
$983$	7.57108	0.241480	0.120740	+	0.992684i	$0.461473\pi$
$984$	6.88133	0.219369
$985$	0.189598	0.00604110
$986$	−16.7041	−0.531967
$987$	84.8192	2.69982
$988$	7.26342	0.231080
$989$	−6.88927	−0.219066
$990$	−0.0894557	−0.00284309
$991$	15.7407	0.500021	0.250011	−	0.968243i	$-0.419566\pi$
$991$	15.7407	0.500021	0.250011	+	0.968243i	$0.419566\pi$
$992$	−0.251246	−0.00797707
$993$	51.2792	1.62730
$994$	20.6526	0.655060
$995$	−4.70221	−0.149070
$996$	−4.61692	−0.146293
$997$	−24.8947	−0.788423	−0.394211	−	0.919020i	$-0.628982\pi$
$997$	−24.8947	−0.788423	−0.394211	+	0.919020i	$0.628982\pi$
$998$	−31.3474	−0.992285
$999$	34.3901	1.08805

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.c.1.4	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.c.1.4	✓	17	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.86328 q^{3} +1.00000 q^{4} -0.189598 q^{5} +1.86328 q^{6} -4.05138 q^{7} -1.00000 q^{8} +0.471817 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.86328 q^{3} +1.00000 q^{4} -0.189598 q^{5} +1.86328 q^{6} -4.05138 q^{7} -1.00000 q^{8} +0.471817 q^{9} +0.189598 q^{10} -1.00000 q^{11} -1.86328 q^{12} +2.20380 q^{13} +4.05138 q^{14} +0.353274 q^{15} +1.00000 q^{16} -2.49348 q^{17} -0.471817 q^{18} +3.29586 q^{19} -0.189598 q^{20} +7.54887 q^{21} +1.00000 q^{22} +2.66988 q^{23} +1.86328 q^{24} -4.96405 q^{25} -2.20380 q^{26} +4.71072 q^{27} -4.05138 q^{28} -6.69910 q^{29} -0.353274 q^{30} +0.251246 q^{31} -1.00000 q^{32} +1.86328 q^{33} +2.49348 q^{34} +0.768134 q^{35} +0.471817 q^{36} +7.30039 q^{37} -3.29586 q^{38} -4.10631 q^{39} +0.189598 q^{40} +3.69313 q^{41} -7.54887 q^{42} -2.58037 q^{43} -1.00000 q^{44} -0.0894557 q^{45} -2.66988 q^{46} +11.2360 q^{47} -1.86328 q^{48} +9.41371 q^{49} +4.96405 q^{50} +4.64606 q^{51} +2.20380 q^{52} +6.06005 q^{53} -4.71072 q^{54} +0.189598 q^{55} +4.05138 q^{56} -6.14111 q^{57} +6.69910 q^{58} +3.76286 q^{59} +0.353274 q^{60} -15.4913 q^{61} -0.251246 q^{62} -1.91151 q^{63} +1.00000 q^{64} -0.417837 q^{65} -1.86328 q^{66} +4.97217 q^{67} -2.49348 q^{68} -4.97473 q^{69} -0.768134 q^{70} +5.09766 q^{71} -0.471817 q^{72} +7.97292 q^{73} -7.30039 q^{74} +9.24943 q^{75} +3.29586 q^{76} +4.05138 q^{77} +4.10631 q^{78} -1.72364 q^{79} -0.189598 q^{80} -10.1928 q^{81} -3.69313 q^{82} +2.47784 q^{83} +7.54887 q^{84} +0.472759 q^{85} +2.58037 q^{86} +12.4823 q^{87} +1.00000 q^{88} +3.84485 q^{89} +0.0894557 q^{90} -8.92845 q^{91} +2.66988 q^{92} -0.468142 q^{93} -11.2360 q^{94} -0.624888 q^{95} +1.86328 q^{96} -5.55984 q^{97} -9.41371 q^{98} -0.471817 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9}+O(q^{10}) \) 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9	\( 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9} - 6 q^{10} - 17 q^{11} + 5 q^{12} - 16 q^{13} + 9 q^{14} + 17 q^{16} - 8 q^{17} - 12 q^{18} - 23 q^{19} + 6 q^{20} - 15 q^{21} + 17 q^{22} + 12 q^{23} - 5 q^{24} + 11 q^{25} + 16 q^{26} + 17 q^{27} - 9 q^{28} - 8 q^{31} - 17 q^{32} - 5 q^{33} + 8 q^{34} + 6 q^{35} + 12 q^{36} - 7 q^{37} + 23 q^{38} - 9 q^{39} - 6 q^{40} - 27 q^{41} + 15 q^{42} - 13 q^{43} - 17 q^{44} - 11 q^{45} - 12 q^{46} + 23 q^{47} + 5 q^{48} - 8 q^{49} - 11 q^{50} - 40 q^{51} - 16 q^{52} + 14 q^{53} - 17 q^{54} - 6 q^{55} + 9 q^{56} - 18 q^{57} + 2 q^{59} - 49 q^{61} + 8 q^{62} - 42 q^{63} + 17 q^{64} - 57 q^{65} + 5 q^{66} - 5 q^{67} - 8 q^{68} - 9 q^{69} - 6 q^{70} - 5 q^{71} - 12 q^{72} - 54 q^{73} + 7 q^{74} + 7 q^{75} - 23 q^{76} + 9 q^{77} + 9 q^{78} - 11 q^{79} + 6 q^{80} - 35 q^{81} + 27 q^{82} - 8 q^{83} - 15 q^{84} - 65 q^{85} + 13 q^{86} - 20 q^{87} + 17 q^{88} - 9 q^{89} + 11 q^{90} - 9 q^{91} + 12 q^{92} - 50 q^{93} - 23 q^{94} - 27 q^{95} - 5 q^{96} - 42 q^{97} + 8 q^{98} - 12 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9 - 6 * q^10 - 17 * q^11 + 5 * q^12 - 16 * q^13 + 9 * q^14 + 17 * q^16 - 8 * q^17 - 12 * q^18 - 23 * q^19 + 6 * q^20 - 15 * q^21 + 17 * q^22 + 12 * q^23 - 5 * q^24 + 11 * q^25 + 16 * q^26 + 17 * q^27 - 9 * q^28 - 8 * q^31 - 17 * q^32 - 5 * q^33 + 8 * q^34 + 6 * q^35 + 12 * q^36 - 7 * q^37 + 23 * q^38 - 9 * q^39 - 6 * q^40 - 27 * q^41 + 15 * q^42 - 13 * q^43 - 17 * q^44 - 11 * q^45 - 12 * q^46 + 23 * q^47 + 5 * q^48 - 8 * q^49 - 11 * q^50 - 40 * q^51 - 16 * q^52 + 14 * q^53 - 17 * q^54 - 6 * q^55 + 9 * q^56 - 18 * q^57 + 2 * q^59 - 49 * q^61 + 8 * q^62 - 42 * q^63 + 17 * q^64 - 57 * q^65 + 5 * q^66 - 5 * q^67 - 8 * q^68 - 9 * q^69 - 6 * q^70 - 5 * q^71 - 12 * q^72 - 54 * q^73 + 7 * q^74 + 7 * q^75 - 23 * q^76 + 9 * q^77 + 9 * q^78 - 11 * q^79 + 6 * q^80 - 35 * q^81 + 27 * q^82 - 8 * q^83 - 15 * q^84 - 65 * q^85 + 13 * q^86 - 20 * q^87 + 17 * q^88 - 9 * q^89 + 11 * q^90 - 9 * q^91 + 12 * q^92 - 50 * q^93 - 23 * q^94 - 27 * q^95 - 5 * q^96 - 42 * q^97 + 8 * q^98 - 12 * q^99

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