LMFDB - Embedded newform 503.2.a.f.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [503,2,Mod(1,503)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(503, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("503.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 503 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	503.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:	$4.01647522167$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	503.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.425199 q^{2} -1.16576 q^{3} -1.81921 q^{4} -3.04539 q^{5} +0.495677 q^{6} +0.946556 q^{7} +1.62392 q^{8} -1.64102 q^{9} +O(q^{10})$	\(q-0.425199 q^{2} -1.16576 q^{3} -1.81921 q^{4} -3.04539 q^{5} +0.495677 q^{6} +0.946556 q^{7} +1.62392 q^{8} -1.64102 q^{9} +1.29490 q^{10} -5.26958 q^{11} +2.12075 q^{12} +4.98081 q^{13} -0.402474 q^{14} +3.55018 q^{15} +2.94792 q^{16} -4.70676 q^{17} +0.697757 q^{18} +6.27914 q^{19} +5.54020 q^{20} -1.10345 q^{21} +2.24062 q^{22} -4.26619 q^{23} -1.89309 q^{24} +4.27442 q^{25} -2.11783 q^{26} +5.41029 q^{27} -1.72198 q^{28} +9.05010 q^{29} -1.50953 q^{30} +6.05473 q^{31} -4.50130 q^{32} +6.14304 q^{33} +2.00131 q^{34} -2.88264 q^{35} +2.98534 q^{36} +0.0493818 q^{37} -2.66988 q^{38} -5.80641 q^{39} -4.94548 q^{40} +4.78649 q^{41} +0.469187 q^{42} -8.15210 q^{43} +9.58645 q^{44} +4.99754 q^{45} +1.81398 q^{46} +12.9257 q^{47} -3.43656 q^{48} -6.10403 q^{49} -1.81748 q^{50} +5.48693 q^{51} -9.06112 q^{52} +3.38346 q^{53} -2.30045 q^{54} +16.0479 q^{55} +1.53713 q^{56} -7.31994 q^{57} -3.84809 q^{58} -6.40570 q^{59} -6.45851 q^{60} -13.0919 q^{61} -2.57446 q^{62} -1.55331 q^{63} -3.98190 q^{64} -15.1685 q^{65} -2.61201 q^{66} -6.83640 q^{67} +8.56257 q^{68} +4.97334 q^{69} +1.22569 q^{70} +0.707071 q^{71} -2.66488 q^{72} +9.30909 q^{73} -0.0209971 q^{74} -4.98293 q^{75} -11.4230 q^{76} -4.98795 q^{77} +2.46888 q^{78} +12.8093 q^{79} -8.97759 q^{80} -1.38402 q^{81} -2.03521 q^{82} -6.10655 q^{83} +2.00741 q^{84} +14.3339 q^{85} +3.46626 q^{86} -10.5502 q^{87} -8.55738 q^{88} +7.70505 q^{89} -2.12495 q^{90} +4.71462 q^{91} +7.76108 q^{92} -7.05833 q^{93} -5.49597 q^{94} -19.1225 q^{95} +5.24741 q^{96} +7.42978 q^{97} +2.59543 q^{98} +8.64746 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9}+O(q^{10}) $ 26 * q + 4 * q^2 + 4 * q^3 + 36 * q^4 + 9 * q^5 - 4 * q^6 + 11 * q^7 + 18 * q^8 + 42 * q^9	\( 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9} + 4 q^{10} - 17 q^{11} + 19 q^{12} + 14 q^{13} + q^{14} + 18 q^{15} + 48 q^{16} + 17 q^{17} - 10 q^{18} - 22 q^{19} - 19 q^{20} - 16 q^{21} + 38 q^{22} + 27 q^{23} - 9 q^{24} + 93 q^{25} + q^{26} + 31 q^{27} - 9 q^{28} + 13 q^{29} - 28 q^{30} + 26 q^{31} + 5 q^{32} + 6 q^{33} - 32 q^{34} - 22 q^{35} + 52 q^{36} + 55 q^{37} - 24 q^{38} - 15 q^{39} - 7 q^{40} + 24 q^{41} - 50 q^{42} + 20 q^{43} - 27 q^{44} - 8 q^{45} + 6 q^{46} - 25 q^{47} + 29 q^{48} + 65 q^{49} - 16 q^{50} + 7 q^{51} + 32 q^{52} + 30 q^{53} - 82 q^{54} + 25 q^{55} + 3 q^{56} + 9 q^{57} + 58 q^{58} - 26 q^{59} - 68 q^{60} + 15 q^{61} - 12 q^{62} - 19 q^{63} + 44 q^{64} + 20 q^{65} - 55 q^{66} - 20 q^{67} - 4 q^{68} - 27 q^{69} + 2 q^{70} - 35 q^{71} - 26 q^{72} + 38 q^{73} - 59 q^{74} + 2 q^{75} - 42 q^{76} - 6 q^{77} - 47 q^{78} + 21 q^{79} - 100 q^{80} + 70 q^{81} - 59 q^{82} - 48 q^{83} - 116 q^{84} + 6 q^{85} - 7 q^{86} - 9 q^{87} + 106 q^{88} - 5 q^{89} - 118 q^{90} - 24 q^{91} + 26 q^{92} - 8 q^{93} - 22 q^{94} + 43 q^{95} - 100 q^{96} + 142 q^{97} - 38 q^{98} - 50 q^{99}+O(q^{100}) \) 26 * q + 4 * q^2 + 4 * q^3 + 36 * q^4 + 9 * q^5 - 4 * q^6 + 11 * q^7 + 18 * q^8 + 42 * q^9 + 4 * q^10 - 17 * q^11 + 19 * q^12 + 14 * q^13 + q^14 + 18 * q^15 + 48 * q^16 + 17 * q^17 - 10 * q^18 - 22 * q^19 - 19 * q^20 - 16 * q^21 + 38 * q^22 + 27 * q^23 - 9 * q^24 + 93 * q^25 + q^26 + 31 * q^27 - 9 * q^28 + 13 * q^29 - 28 * q^30 + 26 * q^31 + 5 * q^32 + 6 * q^33 - 32 * q^34 - 22 * q^35 + 52 * q^36 + 55 * q^37 - 24 * q^38 - 15 * q^39 - 7 * q^40 + 24 * q^41 - 50 * q^42 + 20 * q^43 - 27 * q^44 - 8 * q^45 + 6 * q^46 - 25 * q^47 + 29 * q^48 + 65 * q^49 - 16 * q^50 + 7 * q^51 + 32 * q^52 + 30 * q^53 - 82 * q^54 + 25 * q^55 + 3 * q^56 + 9 * q^57 + 58 * q^58 - 26 * q^59 - 68 * q^60 + 15 * q^61 - 12 * q^62 - 19 * q^63 + 44 * q^64 + 20 * q^65 - 55 * q^66 - 20 * q^67 - 4 * q^68 - 27 * q^69 + 2 * q^70 - 35 * q^71 - 26 * q^72 + 38 * q^73 - 59 * q^74 + 2 * q^75 - 42 * q^76 - 6 * q^77 - 47 * q^78 + 21 * q^79 - 100 * q^80 + 70 * q^81 - 59 * q^82 - 48 * q^83 - 116 * q^84 + 6 * q^85 - 7 * q^86 - 9 * q^87 + 106 * q^88 - 5 * q^89 - 118 * q^90 - 24 * q^91 + 26 * q^92 - 8 * q^93 - 22 * q^94 + 43 * q^95 - 100 * q^96 + 142 * q^97 - 38 * q^98 - 50 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.425199	−0.300661	−0.150330	−	0.988636i	$-0.548034\pi$
$2$	−0.425199	−0.300661	−0.150330	+	0.988636i	$0.548034\pi$
$3$	−1.16576	−0.673049	−0.336524	−	0.941675i	$-0.609251\pi$
$3$	−1.16576	−0.673049	−0.336524	+	0.941675i	$0.609251\pi$
$4$	−1.81921	−0.909603
$5$	−3.04539	−1.36194	−0.680971	−	0.732311i	$-0.738442\pi$
$5$	−3.04539	−1.36194	−0.680971	+	0.732311i	$0.738442\pi$
$6$	0.495677	0.202359
$7$	0.946556	0.357765	0.178882	−	0.983870i	$-0.442752\pi$
$7$	0.946556	0.357765	0.178882	+	0.983870i	$0.442752\pi$
$8$	1.62392	0.574143
$9$	−1.64102	−0.547005
$10$	1.29490	0.409482
$11$	−5.26958	−1.58884	−0.794419	−	0.607371i	$-0.792224\pi$
$11$	−5.26958	−1.58884	−0.794419	+	0.607371i	$0.792224\pi$
$12$	2.12075	0.612207
$13$	4.98081	1.38143	0.690714	−	0.723128i	$-0.257296\pi$
$13$	4.98081	1.38143	0.690714	+	0.723128i	$0.257296\pi$
$14$	−0.402474	−0.107566
$15$	3.55018	0.916653
$16$	2.94792	0.736981
$17$	−4.70676	−1.14156	−0.570779	−	0.821104i	$-0.693359\pi$
$17$	−4.70676	−1.14156	−0.570779	+	0.821104i	$0.693359\pi$
$18$	0.697757	0.164463
$19$	6.27914	1.44053	0.720267	−	0.693697i	$-0.244019\pi$
$19$	6.27914	1.44053	0.720267	+	0.693697i	$0.244019\pi$
$20$	5.54020	1.23883
$21$	−1.10345	−0.240793
$22$	2.24062	0.477701
$23$	−4.26619	−0.889563	−0.444781	−	0.895639i	$-0.646719\pi$
$23$	−4.26619	−0.889563	−0.444781	+	0.895639i	$0.646719\pi$
$24$	−1.89309	−0.386426
$25$	4.27442	0.854884
$26$	−2.11783	−0.415341
$27$	5.41029	1.04121
$28$	−1.72198	−0.325424
$29$	9.05010	1.68056	0.840281	−	0.542152i	$-0.182390\pi$
$29$	9.05010	1.68056	0.840281	+	0.542152i	$0.182390\pi$
$30$	−1.50953	−0.275602
$31$	6.05473	1.08746	0.543731	−	0.839260i	$-0.317011\pi$
$31$	6.05473	1.08746	0.543731	+	0.839260i	$0.317011\pi$
$32$	−4.50130	−0.795724
$33$	6.14304	1.06937
$34$	2.00131	0.343222
$35$	−2.88264	−0.487254
$36$	2.98534	0.497557
$37$	0.0493818	0.00811831	0.00405916	−	0.999992i	$-0.498708\pi$
$37$	0.0493818	0.00811831	0.00405916	+	0.999992i	$0.498708\pi$
$38$	−2.66988	−0.433112
$39$	−5.80641	−0.929769
$40$	−4.94548	−0.781949
$41$	4.78649	0.747523	0.373762	−	0.927525i	$-0.378068\pi$
$41$	4.78649	0.747523	0.373762	+	0.927525i	$0.378068\pi$
$42$	0.469187	0.0723971
$43$	−8.15210	−1.24318	−0.621592	−	0.783341i	$-0.713514\pi$
$43$	−8.15210	−1.24318	−0.621592	+	0.783341i	$0.713514\pi$
$44$	9.58645	1.44521
$45$	4.99754	0.744989
$46$	1.81398	0.267457
$47$	12.9257	1.88540	0.942701	−	0.333639i	$-0.108277\pi$
$47$	12.9257	1.88540	0.942701	+	0.333639i	$0.108277\pi$
$48$	−3.43656	−0.496024
$49$	−6.10403	−0.872004
$50$	−1.81748	−0.257030
$51$	5.48693	0.768324
$52$	−9.06112	−1.25655
$53$	3.38346	0.464754	0.232377	−	0.972626i	$-0.425350\pi$
$53$	3.38346	0.464754	0.232377	+	0.972626i	$0.425350\pi$
$54$	−2.30045	−0.313051
$55$	16.0479	2.16390
$56$	1.53713	0.205408
$57$	−7.31994	−0.969550
$58$	−3.84809	−0.505279
$59$	−6.40570	−0.833951	−0.416975	−	0.908918i	$-0.636910\pi$
$59$	−6.40570	−0.833951	−0.416975	+	0.908918i	$0.636910\pi$
$60$	−6.45851	−0.833791
$61$	−13.0919	−1.67625	−0.838126	−	0.545477i	$-0.816349\pi$
$61$	−13.0919	−1.67625	−0.838126	+	0.545477i	$0.816349\pi$
$62$	−2.57446	−0.326957
$63$	−1.55331	−0.195699
$64$	−3.98190	−0.497738
$65$	−15.1685	−1.88142
$66$	−2.61201	−0.321516
$67$	−6.83640	−0.835200	−0.417600	−	0.908631i	$-0.637129\pi$
$67$	−6.83640	−0.835200	−0.417600	+	0.908631i	$0.637129\pi$
$68$	8.56257	1.03836
$69$	4.97334	0.598719
$70$	1.22569	0.146498
$71$	0.707071	0.0839139	0.0419570	−	0.999119i	$-0.486641\pi$
$71$	0.707071	0.0839139	0.0419570	+	0.999119i	$0.486641\pi$
$72$	−2.66488	−0.314059
$73$	9.30909	1.08955	0.544773	−	0.838583i	$-0.316616\pi$
$73$	9.30909	1.08955	0.544773	+	0.838583i	$0.316616\pi$
$74$	−0.0209971	−0.00244086
$75$	−4.98293	−0.575379
$76$	−11.4230	−1.31031
$77$	−4.98795	−0.568430
$78$	2.46888	0.279545
$79$	12.8093	1.44116	0.720581	−	0.693370i	$-0.243875\pi$
$79$	12.8093	1.44116	0.720581	+	0.693370i	$0.243875\pi$
$80$	−8.97759	−1.00372
$81$	−1.38402	−0.153780
$82$	−2.03521	−0.224751
$83$	−6.10655	−0.670281	−0.335140	−	0.942168i	$-0.608784\pi$
$83$	−6.10655	−0.670281	−0.335140	+	0.942168i	$0.608784\pi$
$84$	2.00741	0.219026
$85$	14.3339	1.55473
$86$	3.46626	0.373777
$87$	−10.5502	−1.13110
$88$	−8.55738	−0.912220
$89$	7.70505	0.816733	0.408367	−	0.912818i	$-0.366099\pi$
$89$	7.70505	0.816733	0.408367	+	0.912818i	$0.366099\pi$
$90$	−2.12495	−0.223989
$91$	4.71462	0.494226
$92$	7.76108	0.809149
$93$	−7.05833	−0.731915
$94$	−5.49597	−0.566866
$95$	−19.1225	−1.96192
$96$	5.24741	0.535561
$97$	7.42978	0.754380	0.377190	−	0.926136i	$-0.376890\pi$
$97$	7.42978	0.754380	0.377190	+	0.926136i	$0.376890\pi$
$98$	2.59543	0.262178
$99$	8.64746	0.869102
$100$	−7.77605	−0.777605
$101$	−2.44307	−0.243095	−0.121547	−	0.992586i	$-0.538786\pi$
$101$	−2.44307	−0.243095	−0.121547	+	0.992586i	$0.538786\pi$
$102$	−2.33304	−0.231005
$103$	−0.861446	−0.0848808	−0.0424404	−	0.999099i	$-0.513513\pi$
$103$	−0.861446	−0.0848808	−0.0424404	+	0.999099i	$0.513513\pi$
$104$	8.08845	0.793137
$105$	3.36045	0.327946
$106$	−1.43864	−0.139733
$107$	9.51324	0.919680	0.459840	−	0.888002i	$-0.347907\pi$
$107$	9.51324	0.919680	0.459840	+	0.888002i	$0.347907\pi$
$108$	−9.84243	−0.947088
$109$	10.5857	1.01393	0.506964	−	0.861967i	$-0.330768\pi$
$109$	10.5857	1.01393	0.506964	+	0.861967i	$0.330768\pi$
$110$	−6.82356	−0.650601
$111$	−0.0575671	−0.00546402
$112$	2.79038	0.263666
$113$	−3.44339	−0.323927	−0.161964	−	0.986797i	$-0.551783\pi$
$113$	−3.44339	−0.323927	−0.161964	+	0.986797i	$0.551783\pi$
$114$	3.11243	0.291506
$115$	12.9922	1.21153
$116$	−16.4640	−1.52864
$117$	−8.17359	−0.755648
$118$	2.72369	0.250736
$119$	−4.45522	−0.408409
$120$	5.76522	0.526290
$121$	16.7684	1.52440
$122$	5.56668	0.503983
$123$	−5.57987	−0.503120
$124$	−11.0148	−0.989158
$125$	2.20967	0.197639
$126$	0.660467	0.0588391
$127$	5.32565	0.472575	0.236288	−	0.971683i	$-0.424069\pi$
$127$	5.32565	0.472575	0.236288	+	0.971683i	$0.424069\pi$
$128$	10.6957	0.945374
$129$	9.50335	0.836723
$130$	6.44964	0.565671
$131$	−6.30936	−0.551252	−0.275626	−	0.961265i	$-0.588885\pi$
$131$	−6.30936	−0.551252	−0.275626	+	0.961265i	$0.588885\pi$
$132$	−11.1754	−0.972698
$133$	5.94356	0.515372
$134$	2.90683	0.251112
$135$	−16.4765	−1.41807
$136$	−7.64341	−0.655417
$137$	−0.728302	−0.0622231	−0.0311115	−	0.999516i	$-0.509905\pi$
$137$	−0.728302	−0.0622231	−0.0311115	+	0.999516i	$0.509905\pi$
$138$	−2.11466	−0.180011
$139$	−12.8073	−1.08630	−0.543152	−	0.839634i	$-0.682769\pi$
$139$	−12.8073	−1.08630	−0.543152	+	0.839634i	$0.682769\pi$
$140$	5.24411	0.443208
$141$	−15.0682	−1.26897
$142$	−0.300646	−0.0252296
$143$	−26.2468	−2.19487
$144$	−4.83759	−0.403132
$145$	−27.5611	−2.28883
$146$	−3.95821	−0.327584
$147$	7.11580	0.586902
$148$	−0.0898356	−0.00738444
$149$	21.2953	1.74458	0.872290	−	0.488989i	$-0.162634\pi$
$149$	21.2953	1.74458	0.872290	+	0.488989i	$0.162634\pi$
$150$	2.11873	0.172994
$151$	−18.5640	−1.51071	−0.755357	−	0.655314i	$-0.772536\pi$
$151$	−18.5640	−1.51071	−0.755357	+	0.655314i	$0.772536\pi$
$152$	10.1968	0.827072
$153$	7.72387	0.624438
$154$	2.12087	0.170905
$155$	−18.4390	−1.48106
$156$	10.5630	0.845721
$157$	7.38222	0.589166	0.294583	−	0.955626i	$-0.404819\pi$
$157$	7.38222	0.589166	0.294583	+	0.955626i	$0.404819\pi$
$158$	−5.44651	−0.433301
$159$	−3.94429	−0.312802
$160$	13.7082	1.08373
$161$	−4.03819	−0.318254
$162$	0.588485	0.0462357
$163$	−8.57330	−0.671513	−0.335757	−	0.941949i	$-0.608992\pi$
$163$	−8.57330	−0.671513	−0.335757	+	0.941949i	$0.608992\pi$
$164$	−8.70760	−0.679950
$165$	−18.7080	−1.45641
$166$	2.59650	0.201527
$167$	24.6909	1.91064	0.955318	−	0.295581i	$-0.0955132\pi$
$167$	24.6909	1.91064	0.955318	+	0.295581i	$0.0955132\pi$
$168$	−1.79192	−0.138250
$169$	11.8085	0.908345
$170$	−6.09477	−0.467448
$171$	−10.3042	−0.787979
$172$	14.8303	1.13080
$173$	−5.69821	−0.433227	−0.216613	−	0.976257i	$-0.569501\pi$
$173$	−5.69821	−0.433227	−0.216613	+	0.976257i	$0.569501\pi$
$174$	4.48593	0.340077
$175$	4.04598	0.305847
$176$	−15.5343	−1.17094
$177$	7.46747	0.561290
$178$	−3.27617	−0.245560
$179$	6.64416	0.496608	0.248304	−	0.968682i	$-0.420127\pi$
$179$	6.64416	0.496608	0.248304	+	0.968682i	$0.420127\pi$
$180$	−9.09155	−0.677644
$181$	−1.23739	−0.0919746	−0.0459873	−	0.998942i	$-0.514643\pi$
$181$	−1.23739	−0.0919746	−0.0459873	+	0.998942i	$0.514643\pi$
$182$	−2.00465	−0.148594
$183$	15.2620	1.12820
$184$	−6.92796	−0.510736
$185$	−0.150387	−0.0110567
$186$	3.00119	0.220058
$187$	24.8026	1.81375
$188$	−23.5144	−1.71497
$189$	5.12114	0.372508
$190$	8.13084	0.589873
$191$	−1.78498	−0.129157	−0.0645783	−	0.997913i	$-0.520570\pi$
$191$	−1.78498	−0.129157	−0.0645783	+	0.997913i	$0.520570\pi$
$192$	4.64192	0.335002
$193$	21.4873	1.54669	0.773345	−	0.633986i	$-0.218582\pi$
$193$	21.4873	1.54669	0.773345	+	0.633986i	$0.218582\pi$
$194$	−3.15913	−0.226812
$195$	17.6828	1.26629
$196$	11.1045	0.793178
$197$	18.4500	1.31451	0.657253	−	0.753670i	$-0.271718\pi$
$197$	18.4500	1.31451	0.657253	+	0.753670i	$0.271718\pi$
$198$	−3.67689	−0.261305
$199$	23.5776	1.67137	0.835686	−	0.549207i	$-0.185070\pi$
$199$	23.5776	1.67137	0.835686	+	0.549207i	$0.185070\pi$
$200$	6.94132	0.490826
$201$	7.96957	0.562130
$202$	1.03879	0.0730891
$203$	8.56643	0.601245
$204$	−9.98186	−0.698870
$205$	−14.5767	−1.01808
$206$	0.366286	0.0255203
$207$	7.00089	0.486595
$208$	14.6830	1.01809
$209$	−33.0884	−2.28877
$210$	−1.42886	−0.0986006
$211$	−8.98431	−0.618505	−0.309253	−	0.950980i	$-0.600079\pi$
$211$	−8.98431	−0.618505	−0.309253	+	0.950980i	$0.600079\pi$
$212$	−6.15521	−0.422742
$213$	−0.824272	−0.0564782
$214$	−4.04502	−0.276512
$215$	24.8263	1.69314
$216$	8.78588	0.597803
$217$	5.73114	0.389055
$218$	−4.50104	−0.304849
$219$	−10.8521	−0.733318
$220$	−29.1945	−1.96829
$221$	−23.4435	−1.57698
$222$	0.0244774	0.00164282
$223$	3.57817	0.239612	0.119806	−	0.992797i	$-0.461773\pi$
$223$	3.57817	0.239612	0.119806	+	0.992797i	$0.461773\pi$
$224$	−4.26073	−0.284682
$225$	−7.01439	−0.467626
$226$	1.46413	0.0973922
$227$	14.3381	0.951651	0.475826	−	0.879540i	$-0.342149\pi$
$227$	14.3381	0.951651	0.475826	+	0.879540i	$0.342149\pi$
$228$	13.3165	0.881905
$229$	−18.6635	−1.23332	−0.616660	−	0.787229i	$-0.711515\pi$
$229$	−18.6635	−1.23332	−0.616660	+	0.787229i	$0.711515\pi$
$230$	−5.52428	−0.364260
$231$	5.81473	0.382581
$232$	14.6966	0.964882
$233$	12.7731	0.836792	0.418396	−	0.908265i	$-0.362592\pi$
$233$	12.7731	0.836792	0.418396	+	0.908265i	$0.362592\pi$
$234$	3.47540	0.227194
$235$	−39.3637	−2.56781
$236$	11.6533	0.758564
$237$	−14.9325	−0.969973
$238$	1.89435	0.122793
$239$	−9.81773	−0.635056	−0.317528	−	0.948249i	$-0.602853\pi$
$239$	−9.81773	−0.635056	−0.317528	+	0.948249i	$0.602853\pi$
$240$	10.4657	0.675556
$241$	27.0449	1.74212	0.871059	−	0.491178i	$-0.163434\pi$
$241$	27.0449	1.74212	0.871059	+	0.491178i	$0.163434\pi$
$242$	−7.12992	−0.458329
$243$	−14.6174	−0.937708
$244$	23.8169	1.52472
$245$	18.5892	1.18762
$246$	2.37255	0.151268
$247$	31.2752	1.98999
$248$	9.83240	0.624358
$249$	7.11874	0.451132
$250$	−0.939551	−0.0594224
$251$	−21.9017	−1.38242	−0.691211	−	0.722653i	$-0.742922\pi$
$251$	−21.9017	−1.38242	−0.691211	+	0.722653i	$0.742922\pi$
$252$	2.82580	0.178008
$253$	22.4810	1.41337
$254$	−2.26446	−0.142085
$255$	−16.7099	−1.04641
$256$	3.41601	0.213501
$257$	1.42333	0.0887852	0.0443926	−	0.999014i	$-0.485865\pi$
$257$	1.42333	0.0887852	0.0443926	+	0.999014i	$0.485865\pi$
$258$	−4.04081	−0.251570
$259$	0.0467426	0.00290445
$260$	27.5947	1.71135
$261$	−14.8514	−0.919276
$262$	2.68273	0.165740
$263$	21.4215	1.32091	0.660453	−	0.750867i	$-0.270364\pi$
$263$	21.4215	1.32091	0.660453	+	0.750867i	$0.270364\pi$
$264$	9.97581	0.613968
$265$	−10.3040	−0.632968
$266$	−2.52719	−0.154952
$267$	−8.98220	−0.549701
$268$	12.4368	0.759700
$269$	28.3745	1.73002	0.865011	−	0.501753i	$-0.167311\pi$
$269$	28.3745	1.73002	0.865011	+	0.501753i	$0.167311\pi$
$270$	7.00576	0.426357
$271$	−11.9277	−0.724557	−0.362278	−	0.932070i	$-0.618001\pi$
$271$	−11.9277	−0.724557	−0.362278	+	0.932070i	$0.618001\pi$
$272$	−13.8752	−0.841306
$273$	−5.49609	−0.332639
$274$	0.309673	0.0187080
$275$	−22.5244	−1.35827
$276$	−9.04752	−0.544597
$277$	4.48698	0.269597	0.134798	−	0.990873i	$-0.456961\pi$
$277$	4.48698	0.269597	0.134798	+	0.990873i	$0.456961\pi$
$278$	5.44566	0.326609
$279$	−9.93590	−0.594847
$280$	−4.68117	−0.279754
$281$	14.2557	0.850424	0.425212	−	0.905094i	$-0.360200\pi$
$281$	14.2557	0.850424	0.425212	+	0.905094i	$0.360200\pi$
$282$	6.40696	0.381529
$283$	−4.40751	−0.261999	−0.131000	−	0.991382i	$-0.541819\pi$
$283$	−4.40751	−0.261999	−0.131000	+	0.991382i	$0.541819\pi$
$284$	−1.28631	−0.0763284
$285$	22.2921	1.32047
$286$	11.1601	0.659910
$287$	4.53068	0.267438
$288$	7.38669	0.435265
$289$	5.15361	0.303153
$290$	11.7189	0.688160
$291$	−8.66130	−0.507735
$292$	−16.9352	−0.991055
$293$	−24.6104	−1.43776	−0.718879	−	0.695136i	$-0.755344\pi$
$293$	−24.6104	−1.43776	−0.718879	+	0.695136i	$0.755344\pi$
$294$	−3.02563	−0.176458
$295$	19.5079	1.13579
$296$	0.0801921	0.00466107
$297$	−28.5099	−1.65431
$298$	−9.05474	−0.524527
$299$	−21.2491	−1.22887
$300$	9.06497	0.523366
$301$	−7.71642	−0.444767
$302$	7.89337	0.454212
$303$	2.84802	0.163615
$304$	18.5104	1.06165
$305$	39.8701	2.28296
$306$	−3.28418	−0.187744
$307$	−20.7200	−1.18255	−0.591275	−	0.806470i	$-0.701375\pi$
$307$	−20.7200	−1.18255	−0.591275	+	0.806470i	$0.701375\pi$
$308$	9.07411	0.517046
$309$	1.00424	0.0571290
$310$	7.84025	0.445296
$311$	−19.1818	−1.08770	−0.543849	−	0.839183i	$-0.683033\pi$
$311$	−19.1818	−1.08770	−0.543849	+	0.839183i	$0.683033\pi$
$312$	−9.42915	−0.533820
$313$	17.8254	1.00755	0.503775	−	0.863835i	$-0.331944\pi$
$313$	17.8254	1.00755	0.503775	+	0.863835i	$0.331944\pi$
$314$	−3.13891	−0.177139
$315$	4.73045	0.266531
$316$	−23.3028	−1.31089
$317$	17.9832	1.01004	0.505020	−	0.863108i	$-0.331485\pi$
$317$	17.9832	1.01004	0.505020	+	0.863108i	$0.331485\pi$
$318$	1.67711	0.0940474
$319$	−47.6902	−2.67014
$320$	12.1265	0.677890
$321$	−11.0901	−0.618990
$322$	1.71703	0.0956865
$323$	−29.5544	−1.64445
$324$	2.51782	0.139879
$325$	21.2901	1.18096
$326$	3.64536	0.201898
$327$	−12.3404	−0.682424
$328$	7.77288	0.429185
$329$	12.2349	0.674530
$330$	7.95460	0.437886
$331$	−14.0001	−0.769516	−0.384758	−	0.923018i	$-0.625715\pi$
$331$	−14.0001	−0.769516	−0.384758	+	0.923018i	$0.625715\pi$
$332$	11.1091	0.609690
$333$	−0.0810363	−0.00444076
$334$	−10.4985	−0.574453
$335$	20.8195	1.13749
$336$	−3.25289	−0.177460
$337$	7.61057	0.414574	0.207287	−	0.978280i	$-0.433537\pi$
$337$	7.61057	0.414574	0.207287	+	0.978280i	$0.433537\pi$
$338$	−5.02095	−0.273104
$339$	4.01415	0.218019
$340$	−26.0764	−1.41419
$341$	−31.9059	−1.72780
$342$	4.38132	0.236914
$343$	−12.4037	−0.669737
$344$	−13.2384	−0.713765
$345$	−15.1458	−0.815420
$346$	2.42287	0.130254
$347$	9.89632	0.531262	0.265631	−	0.964075i	$-0.414420\pi$
$347$	9.89632	0.531262	0.265631	+	0.964075i	$0.414420\pi$
$348$	19.1930	1.02885
$349$	26.2356	1.40436	0.702179	−	0.712001i	$-0.252211\pi$
$349$	26.2356	1.40436	0.702179	+	0.712001i	$0.252211\pi$
$350$	−1.72035	−0.0919563
$351$	26.9476	1.43836
$352$	23.7199	1.26428
$353$	13.4861	0.717791	0.358896	−	0.933378i	$-0.383153\pi$
$353$	13.4861	0.717791	0.358896	+	0.933378i	$0.383153\pi$
$354$	−3.17516	−0.168758
$355$	−2.15331	−0.114286
$356$	−14.0171	−0.742903
$357$	5.19369	0.274879
$358$	−2.82509	−0.149311
$359$	20.7781	1.09663	0.548314	−	0.836272i	$-0.315270\pi$
$359$	20.7781	1.09663	0.548314	+	0.836272i	$0.315270\pi$
$360$	8.11561	0.427730
$361$	20.4276	1.07514
$362$	0.526137	0.0276532
$363$	−19.5479	−1.02600
$364$	−8.57686	−0.449550
$365$	−28.3498	−1.48390
$366$	−6.48938	−0.339205
$367$	−10.0667	−0.525477	−0.262738	−	0.964867i	$-0.584626\pi$
$367$	−10.0667	−0.525477	−0.262738	+	0.964867i	$0.584626\pi$
$368$	−12.5764	−0.655591
$369$	−7.85470	−0.408899
$370$	0.0639443	0.00332431
$371$	3.20264	0.166273
$372$	12.8406	0.665752
$373$	14.8220	0.767455	0.383727	−	0.923446i	$-0.374640\pi$
$373$	14.8220	0.767455	0.383727	+	0.923446i	$0.374640\pi$
$374$	−10.5461	−0.545323
$375$	−2.57594	−0.133021
$376$	20.9903	1.08249
$377$	45.0768	2.32158
$378$	−2.17750	−0.111999
$379$	−31.3165	−1.60862	−0.804310	−	0.594209i	$-0.797465\pi$
$379$	−31.3165	−1.60862	−0.804310	+	0.594209i	$0.797465\pi$
$380$	34.7877	1.78457
$381$	−6.20841	−0.318066
$382$	0.758970	0.0388323
$383$	−22.7814	−1.16407	−0.582037	−	0.813162i	$-0.697744\pi$
$383$	−22.7814	−1.16407	−0.582037	+	0.813162i	$0.697744\pi$
$384$	−12.4686	−0.636283
$385$	15.1903	0.774168
$386$	−9.13637	−0.465029
$387$	13.3777	0.680028
$388$	−13.5163	−0.686186
$389$	−12.6937	−0.643596	−0.321798	−	0.946808i	$-0.604287\pi$
$389$	−12.6937	−0.643596	−0.321798	+	0.946808i	$0.604287\pi$
$390$	−7.51870	−0.380724
$391$	20.0800	1.01549
$392$	−9.91247	−0.500655
$393$	7.35517	0.371019
$394$	−7.84490	−0.395221
$395$	−39.0095	−1.96278
$396$	−15.7315	−0.790538
$397$	−14.5079	−0.728131	−0.364065	−	0.931373i	$-0.618612\pi$
$397$	−14.5079	−0.728131	−0.364065	+	0.931373i	$0.618612\pi$
$398$	−10.0252	−0.502516
$399$	−6.92873	−0.346871
$400$	12.6007	0.630033
$401$	−30.1900	−1.50762	−0.753808	−	0.657095i	$-0.771785\pi$
$401$	−30.1900	−1.50762	−0.753808	+	0.657095i	$0.771785\pi$
$402$	−3.38865	−0.169011
$403$	30.1575	1.50225
$404$	4.44445	0.221120
$405$	4.21490	0.209440
$406$	−3.64243	−0.180771
$407$	−0.260221	−0.0128987
$408$	8.91034	0.441128
$409$	13.4655	0.665824	0.332912	−	0.942958i	$-0.391969\pi$
$409$	13.4655	0.665824	0.332912	+	0.942958i	$0.391969\pi$
$410$	6.19801	0.306098
$411$	0.849022	0.0418792
$412$	1.56715	0.0772079
$413$	−6.06335	−0.298358
$414$	−2.97677	−0.146300
$415$	18.5968	0.912883
$416$	−22.4201	−1.09924
$417$	14.9302	0.731136
$418$	14.0691	0.688144
$419$	11.3193	0.552983	0.276491	−	0.961016i	$-0.410828\pi$
$419$	11.3193	0.552983	0.276491	+	0.961016i	$0.410828\pi$
$420$	−6.11335	−0.298301
$421$	−1.51985	−0.0740728	−0.0370364	−	0.999314i	$-0.511792\pi$
$421$	−1.51985	−0.0740728	−0.0370364	+	0.999314i	$0.511792\pi$
$422$	3.82012	0.185960
$423$	−21.2112	−1.03132
$424$	5.49447	0.266835
$425$	−20.1187	−0.975899
$426$	0.350479	0.0169808
$427$	−12.3923	−0.599704
$428$	−17.3066	−0.836544
$429$	30.5973	1.47725
$430$	−10.5561	−0.509062
$431$	−8.01315	−0.385980	−0.192990	−	0.981201i	$-0.561818\pi$
$431$	−8.01315	−0.385980	−0.192990	+	0.981201i	$0.561818\pi$
$432$	15.9491	0.767352
$433$	−0.923286	−0.0443703	−0.0221852	−	0.999754i	$-0.507062\pi$
$433$	−0.923286	−0.0443703	−0.0221852	+	0.999754i	$0.507062\pi$
$434$	−2.43687	−0.116974
$435$	32.1295	1.54049
$436$	−19.2576	−0.922273
$437$	−26.7880	−1.28144
$438$	4.61431	0.220480
$439$	−16.5904	−0.791819	−0.395909	−	0.918290i	$-0.629571\pi$
$439$	−16.5904	−0.791819	−0.395909	+	0.918290i	$0.629571\pi$
$440$	26.0606	1.24239
$441$	10.0168	0.476991
$442$	9.96814	0.474136
$443$	14.0669	0.668338	0.334169	−	0.942513i	$-0.391544\pi$
$443$	14.0669	0.668338	0.334169	+	0.942513i	$0.391544\pi$
$444$	0.104726	0.00497009
$445$	−23.4649	−1.11234
$446$	−1.52143	−0.0720420
$447$	−24.8251	−1.17419
$448$	−3.76909	−0.178073
$449$	7.99294	0.377210	0.188605	−	0.982053i	$-0.439603\pi$
$449$	7.99294	0.377210	0.188605	+	0.982053i	$0.439603\pi$
$450$	2.98251	0.140597
$451$	−25.2228	−1.18769
$452$	6.26424	0.294645
$453$	21.6410	1.01678
$454$	−6.09653	−0.286124
$455$	−14.3579	−0.673107
$456$	−11.8870	−0.556660
$457$	8.58940	0.401795	0.200898	−	0.979612i	$-0.435614\pi$
$457$	8.58940	0.401795	0.200898	+	0.979612i	$0.435614\pi$
$458$	7.93570	0.370811
$459$	−25.4649	−1.18860
$460$	−23.6356	−1.10201
$461$	−26.6903	−1.24309	−0.621547	−	0.783377i	$-0.713495\pi$
$461$	−26.6903	−1.24309	−0.621547	+	0.783377i	$0.713495\pi$
$462$	−2.47242	−0.115027
$463$	−32.9401	−1.53085	−0.765427	−	0.643522i	$-0.777472\pi$
$463$	−32.9401	−1.53085	−0.765427	+	0.643522i	$0.777472\pi$
$464$	26.6790	1.23854
$465$	21.4954	0.996825
$466$	−5.43110	−0.251591
$467$	−23.4770	−1.08638	−0.543192	−	0.839608i	$-0.682784\pi$
$467$	−23.4770	−1.08638	−0.543192	+	0.839608i	$0.682784\pi$
$468$	14.8694	0.687340
$469$	−6.47104	−0.298805
$470$	16.7374	0.772039
$471$	−8.60586	−0.396537
$472$	−10.4023	−0.478807
$473$	42.9581	1.97522
$474$	6.34930	0.291633
$475$	26.8397	1.23149
$476$	8.10496	0.371490
$477$	−5.55231	−0.254223
$478$	4.17449	0.190937
$479$	11.0771	0.506128	0.253064	−	0.967450i	$-0.418562\pi$
$479$	11.0771	0.506128	0.253064	+	0.967450i	$0.418562\pi$
$480$	−15.9804	−0.729403
$481$	0.245961	0.0112149
$482$	−11.4995	−0.523787
$483$	4.70754	0.214201
$484$	−30.5053	−1.38660
$485$	−22.6266	−1.02742
$486$	6.21531	0.281932
$487$	14.3579	0.650620	0.325310	−	0.945607i	$-0.394531\pi$
$487$	14.3579	0.650620	0.325310	+	0.945607i	$0.394531\pi$
$488$	−21.2603	−0.962408
$489$	9.99437	0.451961
$490$	−7.90409	−0.357070
$491$	24.8206	1.12014	0.560068	−	0.828447i	$-0.310775\pi$
$491$	24.8206	1.12014	0.560068	+	0.828447i	$0.310775\pi$
$492$	10.1509	0.457639
$493$	−42.5967	−1.91846
$494$	−13.2982	−0.598313
$495$	−26.3349	−1.18367
$496$	17.8489	0.801438
$497$	0.669283	0.0300214
$498$	−3.02688	−0.135638
$499$	8.94277	0.400333	0.200167	−	0.979762i	$-0.435852\pi$
$499$	8.94277	0.400333	0.200167	+	0.979762i	$0.435852\pi$
$500$	−4.01985	−0.179773
$501$	−28.7835	−1.28595
$502$	9.31256	0.415640
$503$	1.00000	0.0445878
$503$	1.00000	0.0445878
$504$	−2.52246	−0.112359
$505$	7.44011	0.331081
$506$	−9.55890	−0.424945
$507$	−13.7658	−0.611360
$508$	−9.68846	−0.429856
$509$	−29.0226	−1.28641	−0.643203	−	0.765696i	$-0.722395\pi$
$509$	−29.0226	−1.28641	−0.643203	+	0.765696i	$0.722395\pi$
$510$	7.10501	0.314615
$511$	8.81158	0.389801
$512$	−22.8439	−1.00957
$513$	33.9719	1.49990
$514$	−0.605200	−0.0266942
$515$	2.62344	0.115603
$516$	−17.2886	−0.761086
$517$	−68.1128	−2.99560
$518$	−0.0198749	−0.000873253 0
$519$	6.64272	0.291583
$520$	−24.6325	−1.08021
$521$	−12.7528	−0.558710	−0.279355	−	0.960188i	$-0.590121\pi$
$521$	−12.7528	−0.558710	−0.279355	+	0.960188i	$0.590121\pi$
$522$	6.31477	0.276390
$523$	33.4251	1.46158	0.730789	−	0.682603i	$-0.239152\pi$
$523$	33.4251	1.46158	0.730789	+	0.682603i	$0.239152\pi$
$524$	11.4780	0.501420
$525$	−4.71662	−0.205850
$526$	−9.10840	−0.397145
$527$	−28.4982	−1.24140
$528$	18.1092	0.788102
$529$	−4.79960	−0.208678
$530$	4.38123	0.190309
$531$	10.5118	0.456175
$532$	−10.8126	−0.468784
$533$	23.8406	1.03265
$534$	3.81922	0.165274
$535$	−28.9716	−1.25255
$536$	−11.1018	−0.479524
$537$	−7.74546	−0.334241
$538$	−12.0648	−0.520150
$539$	32.1657	1.38547
$540$	29.9741	1.28988
$541$	40.1089	1.72442	0.862208	−	0.506554i	$-0.169081\pi$
$541$	40.1089	1.72442	0.862208	+	0.506554i	$0.169081\pi$
$542$	5.07164	0.217846
$543$	1.44250	0.0619034
$544$	21.1865	0.908365
$545$	−32.2377	−1.38091
$546$	2.33693	0.100011
$547$	−10.6304	−0.454525	−0.227262	−	0.973834i	$-0.572978\pi$
$547$	−10.6304	−0.454525	−0.227262	+	0.973834i	$0.572978\pi$
$548$	1.32493	0.0565983
$549$	21.4841	0.916918
$550$	9.57734	0.408379
$551$	56.8268	2.42090
$552$	8.07631	0.343750
$553$	12.1248	0.515597
$554$	−1.90786	−0.0810571
$555$	0.175314	0.00744168
$556$	23.2992	0.988106
$557$	−1.94138	−0.0822588	−0.0411294	−	0.999154i	$-0.513096\pi$
$557$	−1.94138	−0.0822588	−0.0411294	+	0.999154i	$0.513096\pi$
$558$	4.22473	0.178847
$559$	−40.6041	−1.71737
$560$	−8.49779	−0.359097
$561$	−28.9138	−1.22074
$562$	−6.06151	−0.255689
$563$	−9.66422	−0.407298	−0.203649	−	0.979044i	$-0.565280\pi$
$563$	−9.66422	−0.407298	−0.203649	+	0.979044i	$0.565280\pi$
$564$	27.4121	1.15426
$565$	10.4865	0.441170
$566$	1.87407	0.0787729
$567$	−1.31006	−0.0550172
$568$	1.14823	0.0481786
$569$	−3.24217	−0.135919	−0.0679595	−	0.997688i	$-0.521649\pi$
$569$	−3.24217	−0.135919	−0.0679595	+	0.997688i	$0.521649\pi$
$570$	−9.47857	−0.397013
$571$	−20.2048	−0.845546	−0.422773	−	0.906236i	$-0.638943\pi$
$571$	−20.2048	−0.845546	−0.422773	+	0.906236i	$0.638943\pi$
$572$	47.7483	1.99646
$573$	2.08085	0.0869287
$574$	−1.92644	−0.0804080
$575$	−18.2355	−0.760473
$576$	6.53436	0.272265
$577$	18.9102	0.787241	0.393621	−	0.919273i	$-0.371222\pi$
$577$	18.9102	0.787241	0.393621	+	0.919273i	$0.371222\pi$
$578$	−2.19131	−0.0911464
$579$	−25.0489	−1.04100
$580$	50.1393	2.08192
$581$	−5.78019	−0.239803
$582$	3.68277	0.152656
$583$	−17.8294	−0.738419
$584$	15.1172	0.625556
$585$	24.8918	1.02915
$586$	10.4643	0.432277
$587$	−0.0156371	−0.000645414 0	−0.000322707	−	1.00000i	$-0.500103\pi$
$587$	−0.0156371	−0.000645414 0	−0.000322707		1.00000i	$0.500103\pi$
$588$	−12.9451	−0.533848
$589$	38.0185	1.56652
$590$	−8.29472	−0.341488
$591$	−21.5082	−0.884727
$592$	0.145574	0.00598304
$593$	−24.0728	−0.988551	−0.494275	−	0.869305i	$-0.664567\pi$
$593$	−24.0728	−0.988551	−0.494275	+	0.869305i	$0.664567\pi$
$594$	12.1224	0.497387
$595$	13.5679	0.556229
$596$	−38.7406	−1.58688
$597$	−27.4857	−1.12492
$598$	9.03509	0.369472
$599$	14.1490	0.578112	0.289056	−	0.957312i	$-0.406659\pi$
$599$	14.1490	0.578112	0.289056	+	0.957312i	$0.406659\pi$
$600$	−8.09188	−0.330350
$601$	14.9260	0.608845	0.304422	−	0.952537i	$-0.401537\pi$
$601$	14.9260	0.608845	0.304422	+	0.952537i	$0.401537\pi$
$602$	3.28101	0.133724
$603$	11.2186	0.456858
$604$	33.7717	1.37415
$605$	−51.0665	−2.07615
$606$	−1.21098	−0.0491925
$607$	−13.3949	−0.543681	−0.271840	−	0.962342i	$-0.587632\pi$
$607$	−13.3949	−0.543681	−0.271840	+	0.962342i	$0.587632\pi$
$608$	−28.2643	−1.14627
$609$	−9.98636	−0.404668
$610$	−16.9527	−0.686396
$611$	64.3803	2.60455
$612$	−14.0513	−0.567990
$613$	20.2642	0.818463	0.409232	−	0.912431i	$-0.365797\pi$
$613$	20.2642	0.818463	0.409232	+	0.912431i	$0.365797\pi$
$614$	8.81010	0.355547
$615$	16.9929	0.685220
$616$	−8.10004	−0.326360
$617$	−25.2260	−1.01556	−0.507781	−	0.861486i	$-0.669534\pi$
$617$	−25.2260	−1.01556	−0.507781	+	0.861486i	$0.669534\pi$
$618$	−0.426999	−0.0171764
$619$	−14.4142	−0.579354	−0.289677	−	0.957124i	$-0.593548\pi$
$619$	−14.4142	−0.579354	−0.289677	+	0.957124i	$0.593548\pi$
$620$	33.5444	1.34718
$621$	−23.0813	−0.926222
$622$	8.15605	0.327028
$623$	7.29326	0.292198
$624$	−17.1168	−0.685222
$625$	−28.1014	−1.12406
$626$	−7.57933	−0.302931
$627$	38.5730	1.54046
$628$	−13.4298	−0.535907
$629$	−0.232428	−0.00926752
$630$	−2.01138	−0.0801353
$631$	1.30592	0.0519877	0.0259938	−	0.999662i	$-0.491725\pi$
$631$	1.30592	0.0519877	0.0259938	+	0.999662i	$0.491725\pi$
$632$	20.8014	0.827433
$633$	10.4735	0.416284
$634$	−7.64645	−0.303679
$635$	−16.2187	−0.643620
$636$	7.17547	0.284526
$637$	−30.4030	−1.20461
$638$	20.2778	0.802806
$639$	−1.16031	−0.0459013
$640$	−32.5726	−1.28754
$641$	20.5617	0.812139	0.406070	−	0.913842i	$-0.366899\pi$
$641$	20.5617	0.812139	0.406070	+	0.913842i	$0.366899\pi$
$642$	4.71550	0.186106
$643$	27.9532	1.10237	0.551183	−	0.834385i	$-0.314177\pi$
$643$	27.9532	1.10237	0.551183	+	0.834385i	$0.314177\pi$
$644$	7.34630	0.289485
$645$	−28.9414	−1.13957
$646$	12.5665	0.494422
$647$	−20.3933	−0.801743	−0.400872	−	0.916134i	$-0.631293\pi$
$647$	−20.3933	−0.801743	−0.400872	+	0.916134i	$0.631293\pi$
$648$	−2.24755	−0.0882919
$649$	33.7553	1.32501
$650$	−9.05251	−0.355069
$651$	−6.68111	−0.261853
$652$	15.5966	0.610810
$653$	−19.0975	−0.747341	−0.373671	−	0.927561i	$-0.621901\pi$
$653$	−19.0975	−0.747341	−0.373671	+	0.927561i	$0.621901\pi$
$654$	5.24711	0.205178
$655$	19.2145	0.750772
$656$	14.1102	0.550910
$657$	−15.2764	−0.595988
$658$	−5.20225	−0.202805
$659$	−45.5316	−1.77366	−0.886829	−	0.462098i	$-0.847097\pi$
$659$	−45.5316	−1.77366	−0.886829	+	0.462098i	$0.847097\pi$
$660$	34.0336	1.32476
$661$	−34.7182	−1.35038	−0.675191	−	0.737643i	$-0.735939\pi$
$661$	−34.7182	−1.35038	−0.675191	+	0.737643i	$0.735939\pi$
$662$	5.95283	0.231363
$663$	27.3294	1.06138
$664$	−9.91656	−0.384837
$665$	−18.1005	−0.701906
$666$	0.0344565	0.00133516
$667$	−38.6095	−1.49496
$668$	−44.9177	−1.73792
$669$	−4.17127	−0.161271
$670$	−8.85244	−0.342000
$671$	68.9890	2.66329
$672$	4.96697	0.191605
$673$	43.3056	1.66931	0.834653	−	0.550775i	$-0.185668\pi$
$673$	43.3056	1.66931	0.834653	+	0.550775i	$0.185668\pi$
$674$	−3.23600	−0.124646
$675$	23.1258	0.890114
$676$	−21.4821	−0.826233
$677$	32.8850	1.26387	0.631936	−	0.775020i	$-0.282260\pi$
$677$	32.8850	1.26387	0.631936	+	0.775020i	$0.282260\pi$
$678$	−1.70681	−0.0655497
$679$	7.03270	0.269890
$680$	23.2772	0.892640
$681$	−16.7147	−0.640508
$682$	13.5663	0.519482
$683$	23.0225	0.880932	0.440466	−	0.897769i	$-0.354813\pi$
$683$	23.0225	0.880932	0.440466	+	0.897769i	$0.354813\pi$
$684$	18.7454	0.716748
$685$	2.21797	0.0847442
$686$	5.27404	0.201364
$687$	21.7571	0.830085
$688$	−24.0318	−0.916202
$689$	16.8524	0.642025
$690$	6.43996	0.245165
$691$	21.7543	0.827571	0.413785	−	0.910374i	$-0.364206\pi$
$691$	21.7543	0.827571	0.413785	+	0.910374i	$0.364206\pi$
$692$	10.3662	0.394064
$693$	8.18531	0.310934
$694$	−4.20790	−0.159730
$695$	39.0034	1.47948
$696$	−17.1327	−0.649413
$697$	−22.5288	−0.853341
$698$	−11.1553	−0.422235
$699$	−14.8903	−0.563202
$700$	−7.36047	−0.278200
$701$	30.6194	1.15648	0.578240	−	0.815867i	$-0.303740\pi$
$701$	30.6194	1.15648	0.578240	+	0.815867i	$0.303740\pi$
$702$	−11.4581	−0.432458
$703$	0.310075	0.0116947
$704$	20.9829	0.790824
$705$	45.8885	1.72826
$706$	−5.73426	−0.215812
$707$	−2.31251	−0.0869707
$708$	−13.5849	−0.510551
$709$	−38.1556	−1.43296	−0.716482	−	0.697605i	$-0.754249\pi$
$709$	−38.1556	−1.43296	−0.716482	+	0.697605i	$0.754249\pi$
$710$	0.915585	0.0343613
$711$	−21.0203	−0.788323
$712$	12.5124	0.468922
$713$	−25.8306	−0.967365
$714$	−2.20835	−0.0826454
$715$	79.9317	2.98928
$716$	−12.0871	−0.451716
$717$	11.4451	0.427424
$718$	−8.83484	−0.329713
$719$	−12.4956	−0.466006	−0.233003	−	0.972476i	$-0.574855\pi$
$719$	−12.4956	−0.466006	−0.233003	+	0.972476i	$0.574855\pi$
$720$	14.7324	0.549042
$721$	−0.815407	−0.0303674
$722$	−8.68579	−0.323251
$723$	−31.5278	−1.17253
$724$	2.25107	0.0836604
$725$	38.6839	1.43669
$726$	8.31174	0.308478
$727$	35.5447	1.31828	0.659140	−	0.752020i	$-0.270920\pi$
$727$	35.5447	1.31828	0.659140	+	0.752020i	$0.270920\pi$
$728$	7.65617	0.283757
$729$	21.1924	0.784904
$730$	12.0543	0.446150
$731$	38.3700	1.41917
$732$	−27.7647	−1.02621
$733$	−35.0084	−1.29306	−0.646531	−	0.762887i	$-0.723781\pi$
$733$	−35.0084	−1.29306	−0.646531	+	0.762887i	$0.723781\pi$
$734$	4.28034	0.157990
$735$	−21.6704	−0.799326
$736$	19.2034	0.707846
$737$	36.0250	1.32700
$738$	3.33981	0.122940
$739$	50.7286	1.86608	0.933041	−	0.359770i	$-0.117145\pi$
$739$	50.7286	1.86608	0.933041	+	0.359770i	$0.117145\pi$
$740$	0.273585	0.0100572
$741$	−36.4592	−1.33936
$742$	−1.36176	−0.0499917
$743$	28.4073	1.04216	0.521082	−	0.853507i	$-0.325529\pi$
$743$	28.4073	1.04216	0.521082	+	0.853507i	$0.325529\pi$
$744$	−11.4622	−0.420224
$745$	−64.8526	−2.37602
$746$	−6.30230	−0.230744
$747$	10.0209	0.366647
$748$	−45.1211	−1.64979
$749$	9.00482	0.329029
$750$	1.09529	0.0399942
$751$	−22.4979	−0.820960	−0.410480	−	0.911870i	$-0.634639\pi$
$751$	−22.4979	−0.820960	−0.410480	+	0.911870i	$0.634639\pi$
$752$	38.1039	1.38950
$753$	25.5320	0.930437
$754$	−19.1666	−0.698007
$755$	56.5346	2.05750
$756$	−9.31641	−0.338835
$757$	−9.04087	−0.328596	−0.164298	−	0.986411i	$-0.552536\pi$
$757$	−9.04087	−0.328596	−0.164298	+	0.986411i	$0.552536\pi$
$758$	13.3157	0.483649
$759$	−26.2074	−0.951268
$760$	−31.0534	−1.12642
$761$	−13.3889	−0.485347	−0.242674	−	0.970108i	$-0.578024\pi$
$761$	−13.3889	−0.485347	−0.242674	+	0.970108i	$0.578024\pi$
$762$	2.63981	0.0956301
$763$	10.0200	0.362748
$764$	3.24724	0.117481
$765$	−23.5222	−0.850448
$766$	9.68662	0.349992
$767$	−31.9056	−1.15204
$768$	−3.98223	−0.143696
$769$	24.1417	0.870572	0.435286	−	0.900292i	$-0.356647\pi$
$769$	24.1417	0.870572	0.435286	+	0.900292i	$0.356647\pi$
$770$	−6.45888	−0.232762
$771$	−1.65926	−0.0597568
$772$	−39.0898	−1.40687
$773$	0.580377	0.0208747	0.0104374	−	0.999946i	$-0.496678\pi$
$773$	0.580377	0.0208747	0.0104374	+	0.999946i	$0.496678\pi$
$774$	−5.68819	−0.204458
$775$	25.8805	0.929654
$776$	12.0654	0.433122
$777$	−0.0544905	−0.00195483
$778$	5.39734	0.193504
$779$	30.0550	1.07683
$780$	−32.1686	−1.15182
$781$	−3.72597	−0.133326
$782$	−8.53797	−0.305317
$783$	48.9636	1.74982
$784$	−17.9942	−0.642651
$785$	−22.4818	−0.802409
$786$	−3.12741	−0.111551
$787$	41.3871	1.47529	0.737645	−	0.675189i	$-0.235938\pi$
$787$	41.3871	1.47529	0.737645	+	0.675189i	$0.235938\pi$
$788$	−33.5643	−1.19568
$789$	−24.9722	−0.889035
$790$	16.5868	0.590131
$791$	−3.25937	−0.115890
$792$	14.0428	0.498989
$793$	−65.2085	−2.31562
$794$	6.16874	0.218920
$795$	12.0119	0.426018
$796$	−42.8925	−1.52029
$797$	53.2368	1.88575	0.942873	−	0.333154i	$-0.108113\pi$
$797$	53.2368	1.88575	0.942873	+	0.333154i	$0.108113\pi$
$798$	2.94609	0.104290
$799$	−60.8380	−2.15229
$800$	−19.2404	−0.680252
$801$	−12.6441	−0.446757
$802$	12.8367	0.453281
$803$	−49.0550	−1.73111
$804$	−14.4983	−0.511315
$805$	12.2979	0.433443
$806$	−12.8229	−0.451668
$807$	−33.0777	−1.16439
$808$	−3.96736	−0.139571
$809$	−24.9831	−0.878358	−0.439179	−	0.898400i	$-0.644731\pi$
$809$	−24.9831	−0.878358	−0.439179	+	0.898400i	$0.644731\pi$
$810$	−1.79217	−0.0629704
$811$	9.60801	0.337383	0.168691	−	0.985669i	$-0.446046\pi$
$811$	9.60801	0.337383	0.168691	+	0.985669i	$0.446046\pi$
$812$	−15.5841	−0.546895
$813$	13.9048	0.487662
$814$	0.110646	0.00387813
$815$	26.1091	0.914561
$816$	16.1751	0.566240
$817$	−51.1882	−1.79085
$818$	−5.72549	−0.200187
$819$	−7.73676	−0.270344
$820$	26.5181	0.926052
$821$	30.3206	1.05820	0.529098	−	0.848561i	$-0.322531\pi$
$821$	30.3206	1.05820	0.529098	+	0.848561i	$0.322531\pi$
$822$	−0.361003	−0.0125914
$823$	19.7390	0.688060	0.344030	−	0.938959i	$-0.388208\pi$
$823$	19.7390	0.688060	0.344030	+	0.938959i	$0.388208\pi$
$824$	−1.39892	−0.0487337
$825$	26.2579	0.914183
$826$	2.57813	0.0897046
$827$	23.3164	0.810792	0.405396	−	0.914141i	$-0.367134\pi$
$827$	23.3164	0.810792	0.405396	+	0.914141i	$0.367134\pi$
$828$	−12.7361	−0.442609
$829$	−6.98350	−0.242547	−0.121274	−	0.992619i	$-0.538698\pi$
$829$	−6.98350	−0.242547	−0.121274	+	0.992619i	$0.538698\pi$
$830$	−7.90735	−0.274468
$831$	−5.23072	−0.181452
$832$	−19.8331	−0.687589
$833$	28.7302	0.995443
$834$	−6.34831	−0.219824
$835$	−75.1934	−2.60217
$836$	60.1946	2.08188
$837$	32.7578	1.13228
$838$	−4.81294	−0.166260
$839$	26.3200	0.908666	0.454333	−	0.890832i	$-0.349878\pi$
$839$	26.3200	0.908666	0.454333	+	0.890832i	$0.349878\pi$
$840$	5.45710	0.188288
$841$	52.9043	1.82429
$842$	0.646237	0.0222708
$843$	−16.6187	−0.572377
$844$	16.3443	0.562594
$845$	−35.9615	−1.23711
$846$	9.01898	0.310079
$847$	15.8723	0.545378
$848$	9.97418	0.342515
$849$	5.13808	0.176338
$850$	8.55444	0.293415
$851$	−0.210672	−0.00722175
$852$	1.49952	0.0513727
$853$	3.58233	0.122657	0.0613283	−	0.998118i	$-0.480466\pi$
$853$	3.58233	0.122657	0.0613283	+	0.998118i	$0.480466\pi$
$854$	5.26917	0.180307
$855$	31.3802	1.07318
$856$	15.4488	0.528028
$857$	−4.74136	−0.161962	−0.0809810	−	0.996716i	$-0.525805\pi$
$857$	−4.74136	−0.161962	−0.0809810	+	0.996716i	$0.525805\pi$
$858$	−13.0099	−0.444152
$859$	19.9131	0.679425	0.339713	−	0.940529i	$-0.389670\pi$
$859$	19.9131	0.679425	0.339713	+	0.940529i	$0.389670\pi$
$860$	−45.1642	−1.54009
$861$	−5.28166	−0.179999
$862$	3.40718	0.116049
$863$	26.7053	0.909059	0.454529	−	0.890732i	$-0.349807\pi$
$863$	26.7053	0.909059	0.454529	+	0.890732i	$0.349807\pi$
$864$	−24.3533	−0.828516
$865$	17.3533	0.590030
$866$	0.392580	0.0133404
$867$	−6.00784	−0.204037
$868$	−10.4261	−0.353886
$869$	−67.4998	−2.28977
$870$	−13.6614	−0.463166
$871$	−34.0508	−1.15377
$872$	17.1904	0.582140
$873$	−12.1924	−0.412650
$874$	11.3902	0.385280
$875$	2.09158	0.0707084
$876$	19.7422	0.667029
$877$	51.9905	1.75559	0.877796	−	0.479034i	$-0.159013\pi$
$877$	51.9905	1.75559	0.877796	+	0.479034i	$0.159013\pi$
$878$	7.05423	0.238069
$879$	28.6897	0.967681
$880$	47.3081	1.59476
$881$	22.5537	0.759855	0.379927	−	0.925016i	$-0.375949\pi$
$881$	22.5537	0.759855	0.379927	+	0.925016i	$0.375949\pi$
$882$	−4.25913	−0.143412
$883$	−19.0973	−0.642674	−0.321337	−	0.946965i	$-0.604132\pi$
$883$	−19.0973	−0.642674	−0.321337	+	0.946965i	$0.604132\pi$
$884$	42.6485	1.43443
$885$	−22.7414	−0.764444
$886$	−5.98122	−0.200943
$887$	−21.4067	−0.718768	−0.359384	−	0.933190i	$-0.617013\pi$
$887$	−21.4067	−0.718768	−0.359384	+	0.933190i	$0.617013\pi$
$888$	−0.0934844	−0.00313713
$889$	5.04103	0.169071
$890$	9.97724	0.334438
$891$	7.29322	0.244332
$892$	−6.50943	−0.217952
$893$	81.1620	2.71598
$894$	10.5556	0.353032
$895$	−20.2341	−0.676351
$896$	10.1241	0.338222
$897$	24.7712	0.827088
$898$	−3.39859	−0.113412
$899$	54.7959	1.82755
$900$	12.7606	0.425354
$901$	−15.9251	−0.530543
$902$	10.7247	0.357093
$903$	8.99546	0.299350
$904$	−5.59180	−0.185980
$905$	3.76834	0.125264
$906$	−9.20174	−0.305707
$907$	6.26775	0.208117	0.104059	−	0.994571i	$-0.466817\pi$
$907$	6.26775	0.208117	0.104059	+	0.994571i	$0.466817\pi$
$908$	−26.0839	−0.865625
$909$	4.00912	0.132974
$910$	6.10495	0.202377
$911$	−8.04040	−0.266390	−0.133195	−	0.991090i	$-0.542524\pi$
$911$	−8.04040	−0.266390	−0.133195	+	0.991090i	$0.542524\pi$
$912$	−21.5786	−0.714539
$913$	32.1789	1.06497
$914$	−3.65220	−0.120804
$915$	−46.4788	−1.53654
$916$	33.9528	1.12183
$917$	−5.97217	−0.197218
$918$	10.8277	0.357366
$919$	−30.5624	−1.00816	−0.504080	−	0.863657i	$-0.668168\pi$
$919$	−30.5624	−1.00816	−0.504080	+	0.863657i	$0.668168\pi$
$920$	21.0984	0.695593
$921$	24.1544	0.795914
$922$	11.3487	0.373750
$923$	3.52179	0.115921
$924$	−10.5782	−0.347997
$925$	0.211078	0.00694022
$926$	14.0061	0.460268
$927$	1.41365	0.0464302
$928$	−40.7372	−1.33726
$929$	−14.6661	−0.481180	−0.240590	−	0.970627i	$-0.577341\pi$
$929$	−14.6661	−0.481180	−0.240590	+	0.970627i	$0.577341\pi$
$930$	−9.13981	−0.299706
$931$	−38.3281	−1.25615
$932$	−23.2369	−0.761149
$933$	22.3612	0.732074
$934$	9.98237	0.326633
$935$	−75.5338	−2.47022
$936$	−13.2733	−0.433850
$937$	39.3587	1.28579	0.642897	−	0.765953i	$-0.277732\pi$
$937$	39.3587	1.28579	0.642897	+	0.765953i	$0.277732\pi$
$938$	2.75148	0.0898389
$939$	−20.7800	−0.678131
$940$	71.6107	2.33568
$941$	−35.4002	−1.15401	−0.577006	−	0.816740i	$-0.695779\pi$
$941$	−35.4002	−1.15401	−0.577006	+	0.816740i	$0.695779\pi$
$942$	3.65920	0.119223
$943$	−20.4201	−0.664969
$944$	−18.8835	−0.614606
$945$	−15.5959	−0.507334
$946$	−18.2657	−0.593870
$947$	37.1198	1.20623	0.603116	−	0.797654i	$-0.293926\pi$
$947$	37.1198	1.20623	0.603116	+	0.797654i	$0.293926\pi$
$948$	27.1654	0.882291
$949$	46.3668	1.50513
$950$	−11.4122	−0.370261
$951$	−20.9641	−0.679806
$952$	−7.23492	−0.234485
$953$	17.0538	0.552425	0.276213	−	0.961097i	$-0.410921\pi$
$953$	17.0538	0.552425	0.276213	+	0.961097i	$0.410921\pi$
$954$	2.36083	0.0764349
$955$	5.43596	0.175904
$956$	17.8605	0.577649
$957$	55.5951	1.79713
$958$	−4.70999	−0.152173
$959$	−0.689379	−0.0222612
$960$	−14.1365	−0.456253
$961$	5.65976	0.182573
$962$	−0.104582	−0.00337187
$963$	−15.6114	−0.503070
$964$	−49.2003	−1.58464
$965$	−65.4373	−2.10650
$966$	−2.00164	−0.0644017
$967$	−28.0236	−0.901178	−0.450589	−	0.892732i	$-0.648786\pi$
$967$	−28.0236	−0.901178	−0.450589	+	0.892732i	$0.648786\pi$
$968$	27.2306	0.875226
$969$	34.4532	1.10680
$970$	9.62080	0.308905
$971$	−24.9706	−0.801345	−0.400672	−	0.916221i	$-0.631223\pi$
$971$	−24.9706	−0.801345	−0.400672	+	0.916221i	$0.631223\pi$
$972$	26.5921	0.852942
$973$	−12.1229	−0.388641
$974$	−6.10497	−0.195616
$975$	−24.8190	−0.794845
$976$	−38.5940	−1.23537
$977$	−43.3293	−1.38623	−0.693114	−	0.720828i	$-0.743762\pi$
$977$	−43.3293	−1.38623	−0.693114	+	0.720828i	$0.743762\pi$
$978$	−4.24959	−0.135887
$979$	−40.6023	−1.29766
$980$	−33.8175	−1.08026
$981$	−17.3713	−0.554624
$982$	−10.5537	−0.336781
$983$	1.82326	0.0581530	0.0290765	−	0.999577i	$-0.490743\pi$
$983$	1.82326	0.0581530	0.0290765	+	0.999577i	$0.490743\pi$
$984$	−9.06127	−0.288863
$985$	−56.1874	−1.79028
$986$	18.1120	0.576805
$987$	−14.2629	−0.453992
$988$	−56.8961	−1.81010
$989$	34.7784	1.10589
$990$	11.1976	0.355882
$991$	4.34705	0.138089	0.0690443	−	0.997614i	$-0.478005\pi$
$991$	4.34705	0.138089	0.0690443	+	0.997614i	$0.478005\pi$
$992$	−27.2541	−0.865319
$993$	16.3207	0.517922
$994$	−0.284578	−0.00902627
$995$	−71.8031	−2.27631
$996$	−12.9505	−0.410351
$997$	−7.66217	−0.242663	−0.121332	−	0.992612i	$-0.538716\pi$
$997$	−7.66217	−0.242663	−0.121332	+	0.992612i	$0.538716\pi$
$998$	−3.80245	−0.120365
$999$	0.267170	0.00845287

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	503.2.a.f.1.11	✓	26
3.2	odd	2		4527.2.a.o.1.16		26
4.3	odd	2		8048.2.a.u.1.19		26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
503.2.a.f.1.11	✓	26	1.1	even	1	trivial
4527.2.a.o.1.16		26	3.2	odd	2
8048.2.a.u.1.19		26	4.3	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:	\( N \)	\(=\)	\( 503 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	503.a (trivial)

\(f(q)\)	\(=\)	\(q-0.425199 q^{2} -1.16576 q^{3} -1.81921 q^{4} -3.04539 q^{5} +0.495677 q^{6} +0.946556 q^{7} +1.62392 q^{8} -1.64102 q^{9} +O(q^{10})\)	\(q-0.425199 q^{2} -1.16576 q^{3} -1.81921 q^{4} -3.04539 q^{5} +0.495677 q^{6} +0.946556 q^{7} +1.62392 q^{8} -1.64102 q^{9} +1.29490 q^{10} -5.26958 q^{11} +2.12075 q^{12} +4.98081 q^{13} -0.402474 q^{14} +3.55018 q^{15} +2.94792 q^{16} -4.70676 q^{17} +0.697757 q^{18} +6.27914 q^{19} +5.54020 q^{20} -1.10345 q^{21} +2.24062 q^{22} -4.26619 q^{23} -1.89309 q^{24} +4.27442 q^{25} -2.11783 q^{26} +5.41029 q^{27} -1.72198 q^{28} +9.05010 q^{29} -1.50953 q^{30} +6.05473 q^{31} -4.50130 q^{32} +6.14304 q^{33} +2.00131 q^{34} -2.88264 q^{35} +2.98534 q^{36} +0.0493818 q^{37} -2.66988 q^{38} -5.80641 q^{39} -4.94548 q^{40} +4.78649 q^{41} +0.469187 q^{42} -8.15210 q^{43} +9.58645 q^{44} +4.99754 q^{45} +1.81398 q^{46} +12.9257 q^{47} -3.43656 q^{48} -6.10403 q^{49} -1.81748 q^{50} +5.48693 q^{51} -9.06112 q^{52} +3.38346 q^{53} -2.30045 q^{54} +16.0479 q^{55} +1.53713 q^{56} -7.31994 q^{57} -3.84809 q^{58} -6.40570 q^{59} -6.45851 q^{60} -13.0919 q^{61} -2.57446 q^{62} -1.55331 q^{63} -3.98190 q^{64} -15.1685 q^{65} -2.61201 q^{66} -6.83640 q^{67} +8.56257 q^{68} +4.97334 q^{69} +1.22569 q^{70} +0.707071 q^{71} -2.66488 q^{72} +9.30909 q^{73} -0.0209971 q^{74} -4.98293 q^{75} -11.4230 q^{76} -4.98795 q^{77} +2.46888 q^{78} +12.8093 q^{79} -8.97759 q^{80} -1.38402 q^{81} -2.03521 q^{82} -6.10655 q^{83} +2.00741 q^{84} +14.3339 q^{85} +3.46626 q^{86} -10.5502 q^{87} -8.55738 q^{88} +7.70505 q^{89} -2.12495 q^{90} +4.71462 q^{91} +7.76108 q^{92} -7.05833 q^{93} -5.49597 q^{94} -19.1225 q^{95} +5.24741 q^{96} +7.42978 q^{97} +2.59543 q^{98} +8.64746 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9}+O(q^{10}) \) 26 * q + 4 * q^2 + 4 * q^3 + 36 * q^4 + 9 * q^5 - 4 * q^6 + 11 * q^7 + 18 * q^8 + 42 * q^9	\( 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9} + 4 q^{10} - 17 q^{11} + 19 q^{12} + 14 q^{13} + q^{14} + 18 q^{15} + 48 q^{16} + 17 q^{17} - 10 q^{18} - 22 q^{19} - 19 q^{20} - 16 q^{21} + 38 q^{22} + 27 q^{23} - 9 q^{24} + 93 q^{25} + q^{26} + 31 q^{27} - 9 q^{28} + 13 q^{29} - 28 q^{30} + 26 q^{31} + 5 q^{32} + 6 q^{33} - 32 q^{34} - 22 q^{35} + 52 q^{36} + 55 q^{37} - 24 q^{38} - 15 q^{39} - 7 q^{40} + 24 q^{41} - 50 q^{42} + 20 q^{43} - 27 q^{44} - 8 q^{45} + 6 q^{46} - 25 q^{47} + 29 q^{48} + 65 q^{49} - 16 q^{50} + 7 q^{51} + 32 q^{52} + 30 q^{53} - 82 q^{54} + 25 q^{55} + 3 q^{56} + 9 q^{57} + 58 q^{58} - 26 q^{59} - 68 q^{60} + 15 q^{61} - 12 q^{62} - 19 q^{63} + 44 q^{64} + 20 q^{65} - 55 q^{66} - 20 q^{67} - 4 q^{68} - 27 q^{69} + 2 q^{70} - 35 q^{71} - 26 q^{72} + 38 q^{73} - 59 q^{74} + 2 q^{75} - 42 q^{76} - 6 q^{77} - 47 q^{78} + 21 q^{79} - 100 q^{80} + 70 q^{81} - 59 q^{82} - 48 q^{83} - 116 q^{84} + 6 q^{85} - 7 q^{86} - 9 q^{87} + 106 q^{88} - 5 q^{89} - 118 q^{90} - 24 q^{91} + 26 q^{92} - 8 q^{93} - 22 q^{94} + 43 q^{95} - 100 q^{96} + 142 q^{97} - 38 q^{98} - 50 q^{99}+O(q^{100}) \) 26 * q + 4 * q^2 + 4 * q^3 + 36 * q^4 + 9 * q^5 - 4 * q^6 + 11 * q^7 + 18 * q^8 + 42 * q^9 + 4 * q^10 - 17 * q^11 + 19 * q^12 + 14 * q^13 + q^14 + 18 * q^15 + 48 * q^16 + 17 * q^17 - 10 * q^18 - 22 * q^19 - 19 * q^20 - 16 * q^21 + 38 * q^22 + 27 * q^23 - 9 * q^24 + 93 * q^25 + q^26 + 31 * q^27 - 9 * q^28 + 13 * q^29 - 28 * q^30 + 26 * q^31 + 5 * q^32 + 6 * q^33 - 32 * q^34 - 22 * q^35 + 52 * q^36 + 55 * q^37 - 24 * q^38 - 15 * q^39 - 7 * q^40 + 24 * q^41 - 50 * q^42 + 20 * q^43 - 27 * q^44 - 8 * q^45 + 6 * q^46 - 25 * q^47 + 29 * q^48 + 65 * q^49 - 16 * q^50 + 7 * q^51 + 32 * q^52 + 30 * q^53 - 82 * q^54 + 25 * q^55 + 3 * q^56 + 9 * q^57 + 58 * q^58 - 26 * q^59 - 68 * q^60 + 15 * q^61 - 12 * q^62 - 19 * q^63 + 44 * q^64 + 20 * q^65 - 55 * q^66 - 20 * q^67 - 4 * q^68 - 27 * q^69 + 2 * q^70 - 35 * q^71 - 26 * q^72 + 38 * q^73 - 59 * q^74 + 2 * q^75 - 42 * q^76 - 6 * q^77 - 47 * q^78 + 21 * q^79 - 100 * q^80 + 70 * q^81 - 59 * q^82 - 48 * q^83 - 116 * q^84 + 6 * q^85 - 7 * q^86 - 9 * q^87 + 106 * q^88 - 5 * q^89 - 118 * q^90 - 24 * q^91 + 26 * q^92 - 8 * q^93 - 22 * q^94 + 43 * q^95 - 100 * q^96 + 142 * q^97 - 38 * q^98 - 50 * q^99

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