LMFDB - Embedded newform 1045.2.a.e.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.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:	$8.34436701122$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.36497.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 3x^{3} + 5x^{2} + x - 1 $ x^5 - 2x^4 - 3x^3 + 5*x^2 + x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.410375$ of defining polynomial
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.02642 q^{2} -0.589625 q^{3} +2.10637 q^{4} -1.00000 q^{5} -1.19483 q^{6} -0.911544 q^{7} +0.215549 q^{8} -2.65234 q^{9} +O(q^{10})$	\(q+2.02642 q^{2} -0.589625 q^{3} +2.10637 q^{4} -1.00000 q^{5} -1.19483 q^{6} -0.911544 q^{7} +0.215549 q^{8} -2.65234 q^{9} -2.02642 q^{10} +1.00000 q^{11} -1.24197 q^{12} -6.64953 q^{13} -1.84717 q^{14} +0.589625 q^{15} -3.77595 q^{16} -5.09764 q^{17} -5.37476 q^{18} +1.00000 q^{19} -2.10637 q^{20} +0.537469 q^{21} +2.02642 q^{22} +7.09147 q^{23} -0.127093 q^{24} +1.00000 q^{25} -13.4747 q^{26} +3.33276 q^{27} -1.92005 q^{28} -0.220789 q^{29} +1.19483 q^{30} -5.38841 q^{31} -8.08274 q^{32} -0.589625 q^{33} -10.3300 q^{34} +0.911544 q^{35} -5.58681 q^{36} +9.78398 q^{37} +2.02642 q^{38} +3.92073 q^{39} -0.215549 q^{40} -6.38092 q^{41} +1.08914 q^{42} +0.507468 q^{43} +2.10637 q^{44} +2.65234 q^{45} +14.3703 q^{46} +7.55593 q^{47} +2.22639 q^{48} -6.16909 q^{49} +2.02642 q^{50} +3.00569 q^{51} -14.0064 q^{52} -1.04480 q^{53} +6.75357 q^{54} -1.00000 q^{55} -0.196483 q^{56} -0.589625 q^{57} -0.447410 q^{58} +6.15281 q^{59} +1.24197 q^{60} -13.4133 q^{61} -10.9192 q^{62} +2.41773 q^{63} -8.82713 q^{64} +6.64953 q^{65} -1.19483 q^{66} +5.35877 q^{67} -10.7375 q^{68} -4.18131 q^{69} +1.84717 q^{70} -11.8408 q^{71} -0.571711 q^{72} -7.42820 q^{73} +19.8264 q^{74} -0.589625 q^{75} +2.10637 q^{76} -0.911544 q^{77} +7.94503 q^{78} -3.78628 q^{79} +3.77595 q^{80} +5.99195 q^{81} -12.9304 q^{82} -15.7392 q^{83} +1.13211 q^{84} +5.09764 q^{85} +1.02834 q^{86} +0.130182 q^{87} +0.215549 q^{88} +12.2736 q^{89} +5.37476 q^{90} +6.06134 q^{91} +14.9373 q^{92} +3.17714 q^{93} +15.3115 q^{94} -1.00000 q^{95} +4.76578 q^{96} +7.72309 q^{97} -12.5012 q^{98} -2.65234 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - q^{2} - 3 q^{3} + q^{4} - 5 q^{5} - 4 q^{6} + 3 q^{7} + 3 q^{8} - 4 q^{9}+O(q^{10}) $ 5 * q - q^2 - 3 * q^3 + q^4 - 5 * q^5 - 4 * q^6 + 3 * q^7 + 3 * q^8 - 4 * q^9	\( 5 q - q^{2} - 3 q^{3} + q^{4} - 5 q^{5} - 4 q^{6} + 3 q^{7} + 3 q^{8} - 4 q^{9} + q^{10} + 5 q^{11} + 3 q^{12} - 3 q^{13} + 2 q^{14} + 3 q^{15} - 11 q^{16} - 11 q^{17} + 3 q^{18} + 5 q^{19} - q^{20} - 3 q^{21} - q^{22} + 5 q^{24} + 5 q^{25} - 8 q^{26} - 8 q^{28} - 15 q^{29} + 4 q^{30} - 9 q^{31} - 3 q^{33} - 14 q^{34} - 3 q^{35} - 7 q^{36} + 11 q^{37} - q^{38} - 10 q^{39} - 3 q^{40} - 23 q^{41} - 15 q^{42} + 9 q^{43} + q^{44} + 4 q^{45} + 8 q^{46} - 6 q^{47} + 4 q^{48} - 12 q^{49} - q^{50} - 27 q^{52} - 13 q^{53} + 9 q^{54} - 5 q^{55} - 12 q^{56} - 3 q^{57} + 17 q^{58} - 21 q^{59} - 3 q^{60} - 31 q^{61} - 18 q^{62} + 10 q^{63} - q^{64} + 3 q^{65} - 4 q^{66} + 5 q^{68} - 2 q^{70} - 28 q^{71} - 20 q^{72} - 14 q^{73} + 21 q^{74} - 3 q^{75} + q^{76} + 3 q^{77} + 13 q^{78} + 3 q^{79} + 11 q^{80} - 3 q^{81} - 18 q^{82} - 33 q^{83} + 13 q^{84} + 11 q^{85} - 20 q^{86} + 22 q^{87} + 3 q^{88} - 10 q^{89} - 3 q^{90} + 14 q^{91} + 21 q^{92} + 30 q^{93} + 14 q^{94} - 5 q^{95} - 3 q^{96} - 10 q^{97} + 8 q^{98} - 4 q^{99}+O(q^{100}) \) 5 * q - q^2 - 3 * q^3 + q^4 - 5 * q^5 - 4 * q^6 + 3 * q^7 + 3 * q^8 - 4 * q^9 + q^10 + 5 * q^11 + 3 * q^12 - 3 * q^13 + 2 * q^14 + 3 * q^15 - 11 * q^16 - 11 * q^17 + 3 * q^18 + 5 * q^19 - q^20 - 3 * q^21 - q^22 + 5 * q^24 + 5 * q^25 - 8 * q^26 - 8 * q^28 - 15 * q^29 + 4 * q^30 - 9 * q^31 - 3 * q^33 - 14 * q^34 - 3 * q^35 - 7 * q^36 + 11 * q^37 - q^38 - 10 * q^39 - 3 * q^40 - 23 * q^41 - 15 * q^42 + 9 * q^43 + q^44 + 4 * q^45 + 8 * q^46 - 6 * q^47 + 4 * q^48 - 12 * q^49 - q^50 - 27 * q^52 - 13 * q^53 + 9 * q^54 - 5 * q^55 - 12 * q^56 - 3 * q^57 + 17 * q^58 - 21 * q^59 - 3 * q^60 - 31 * q^61 - 18 * q^62 + 10 * q^63 - q^64 + 3 * q^65 - 4 * q^66 + 5 * q^68 - 2 * q^70 - 28 * q^71 - 20 * q^72 - 14 * q^73 + 21 * q^74 - 3 * q^75 + q^76 + 3 * q^77 + 13 * q^78 + 3 * q^79 + 11 * q^80 - 3 * q^81 - 18 * q^82 - 33 * q^83 + 13 * q^84 + 11 * q^85 - 20 * q^86 + 22 * q^87 + 3 * q^88 - 10 * q^89 - 3 * q^90 + 14 * q^91 + 21 * q^92 + 30 * q^93 + 14 * q^94 - 5 * q^95 - 3 * q^96 - 10 * q^97 + 8 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.02642	1.43289	0.716447	−	0.697642i	$-0.245767\pi$
$2$	2.02642	1.43289	0.716447	+	0.697642i	$0.245767\pi$
$3$	−0.589625	−0.340420	−0.170210	−	0.985408i	$-0.554445\pi$
$3$	−0.589625	−0.340420	−0.170210	+	0.985408i	$0.554445\pi$
$4$	2.10637	1.05318
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.19483	−0.487786
$7$	−0.911544	−0.344531	−0.172266	−	0.985051i	$-0.555109\pi$
$7$	−0.911544	−0.344531	−0.172266	+	0.985051i	$0.555109\pi$
$8$	0.215549	0.0762082
$9$	−2.65234	−0.884114
$10$	−2.02642	−0.640810
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.24197	−0.358525
$13$	−6.64953	−1.84425	−0.922124	−	0.386894i	$-0.873548\pi$
$13$	−6.64953	−1.84425	−0.922124	+	0.386894i	$0.873548\pi$
$14$	−1.84717	−0.493677
$15$	0.589625	0.152240
$16$	−3.77595	−0.943987
$17$	−5.09764	−1.23636	−0.618180	−	0.786037i	$-0.712130\pi$
$17$	−5.09764	−1.23636	−0.618180	+	0.786037i	$0.712130\pi$
$18$	−5.37476	−1.26684
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−2.10637	−0.470999
$21$	0.537469	0.117285
$22$	2.02642	0.432034
$23$	7.09147	1.47867	0.739337	−	0.673335i	$-0.235139\pi$
$23$	7.09147	1.47867	0.739337	+	0.673335i	$0.235139\pi$
$24$	−0.127093	−0.0259428
$25$	1.00000	0.200000
$26$	−13.4747	−2.64261
$27$	3.33276	0.641390
$28$	−1.92005	−0.362855
$29$	−0.220789	−0.0409994	−0.0204997	−	0.999790i	$-0.506526\pi$
$29$	−0.220789	−0.0409994	−0.0204997	+	0.999790i	$0.506526\pi$
$30$	1.19483	0.218144
$31$	−5.38841	−0.967786	−0.483893	−	0.875127i	$-0.660778\pi$
$31$	−5.38841	−0.967786	−0.483893	+	0.875127i	$0.660778\pi$
$32$	−8.08274	−1.42884
$33$	−0.589625	−0.102640
$34$	−10.3300	−1.77157
$35$	0.911544	0.154079
$36$	−5.58681	−0.931136
$37$	9.78398	1.60848	0.804238	−	0.594307i	$-0.202574\pi$
$37$	9.78398	1.60848	0.804238	+	0.594307i	$0.202574\pi$
$38$	2.02642	0.328728
$39$	3.92073	0.627819
$40$	−0.215549	−0.0340814
$41$	−6.38092	−0.996533	−0.498266	−	0.867024i	$-0.666030\pi$
$41$	−6.38092	−0.996533	−0.498266	+	0.867024i	$0.666030\pi$
$42$	1.08914	0.168057
$43$	0.507468	0.0773882	0.0386941	−	0.999251i	$-0.487680\pi$
$43$	0.507468	0.0773882	0.0386941	+	0.999251i	$0.487680\pi$
$44$	2.10637	0.317547
$45$	2.65234	0.395388
$46$	14.3703	2.11878
$47$	7.55593	1.10215	0.551073	−	0.834457i	$-0.314219\pi$
$47$	7.55593	1.10215	0.551073	+	0.834457i	$0.314219\pi$
$48$	2.22639	0.321352
$49$	−6.16909	−0.881298
$50$	2.02642	0.286579
$51$	3.00569	0.420881
$52$	−14.0064	−1.94233
$53$	−1.04480	−0.143515	−0.0717575	−	0.997422i	$-0.522861\pi$
$53$	−1.04480	−0.143515	−0.0717575	+	0.997422i	$0.522861\pi$
$54$	6.75357	0.919044
$55$	−1.00000	−0.134840
$56$	−0.196483	−0.0262561
$57$	−0.589625	−0.0780977
$58$	−0.447410	−0.0587478
$59$	6.15281	0.801028	0.400514	−	0.916291i	$-0.368832\pi$
$59$	6.15281	0.801028	0.400514	+	0.916291i	$0.368832\pi$
$60$	1.24197	0.160337
$61$	−13.4133	−1.71739	−0.858696	−	0.512485i	$-0.828725\pi$
$61$	−13.4133	−1.71739	−0.858696	+	0.512485i	$0.828725\pi$
$62$	−10.9192	−1.38674
$63$	2.41773	0.304605
$64$	−8.82713	−1.10339
$65$	6.64953	0.824773
$66$	−1.19483	−0.147073
$67$	5.35877	0.654678	0.327339	−	0.944907i	$-0.393848\pi$
$67$	5.35877	0.654678	0.327339	+	0.944907i	$0.393848\pi$
$68$	−10.7375	−1.30212
$69$	−4.18131	−0.503370
$70$	1.84717	0.220779
$71$	−11.8408	−1.40524	−0.702621	−	0.711564i	$-0.747987\pi$
$71$	−11.8408	−1.40524	−0.702621	+	0.711564i	$0.747987\pi$
$72$	−0.571711	−0.0673768
$73$	−7.42820	−0.869405	−0.434702	−	0.900574i	$-0.643146\pi$
$73$	−7.42820	−0.869405	−0.434702	+	0.900574i	$0.643146\pi$
$74$	19.8264	2.30478
$75$	−0.589625	−0.0680840
$76$	2.10637	0.241617
$77$	−0.911544	−0.103880
$78$	7.94503	0.899598
$79$	−3.78628	−0.425990	−0.212995	−	0.977053i	$-0.568322\pi$
$79$	−3.78628	−0.425990	−0.212995	+	0.977053i	$0.568322\pi$
$80$	3.77595	0.422164
$81$	5.99195	0.665772
$82$	−12.9304	−1.42793
$83$	−15.7392	−1.72760	−0.863799	−	0.503836i	$-0.831922\pi$
$83$	−15.7392	−1.72760	−0.863799	+	0.503836i	$0.831922\pi$
$84$	1.13211	0.123523
$85$	5.09764	0.552917
$86$	1.02834	0.110889
$87$	0.130182	0.0139570
$88$	0.215549	0.0229777
$89$	12.2736	1.30100	0.650500	−	0.759506i	$-0.274559\pi$
$89$	12.2736	1.30100	0.650500	+	0.759506i	$0.274559\pi$
$90$	5.37476	0.566549
$91$	6.06134	0.635401
$92$	14.9373	1.55732
$93$	3.17714	0.329454
$94$	15.3115	1.57926
$95$	−1.00000	−0.102598
$96$	4.76578	0.486406
$97$	7.72309	0.784161	0.392081	−	0.919931i	$-0.371755\pi$
$97$	7.72309	0.784161	0.392081	+	0.919931i	$0.371755\pi$
$98$	−12.5012	−1.26281
$99$	−2.65234	−0.266570
$100$	2.10637	0.210637
$101$	13.0880	1.30230	0.651151	−	0.758949i	$-0.274287\pi$
$101$	13.0880	1.30230	0.651151	+	0.758949i	$0.274287\pi$
$102$	6.09079	0.603078
$103$	3.21344	0.316629	0.158315	−	0.987389i	$-0.449394\pi$
$103$	3.21344	0.316629	0.158315	+	0.987389i	$0.449394\pi$
$104$	−1.43330	−0.140547
$105$	−0.537469	−0.0524516
$106$	−2.11721	−0.205642
$107$	8.21812	0.794475	0.397238	−	0.917716i	$-0.369969\pi$
$107$	8.21812	0.794475	0.397238	+	0.917716i	$0.369969\pi$
$108$	7.02003	0.675502
$109$	−14.6989	−1.40790	−0.703949	−	0.710251i	$-0.748581\pi$
$109$	−14.6989	−1.40790	−0.703949	+	0.710251i	$0.748581\pi$
$110$	−2.02642	−0.193211
$111$	−5.76887	−0.547557
$112$	3.44194	0.325233
$113$	−14.4682	−1.36105	−0.680525	−	0.732725i	$-0.738248\pi$
$113$	−14.4682	−1.36105	−0.680525	+	0.732725i	$0.738248\pi$
$114$	−1.19483	−0.111906
$115$	−7.09147	−0.661283
$116$	−0.465062	−0.0431800
$117$	17.6368	1.63053
$118$	12.4682	1.14779
$119$	4.64672	0.425964
$120$	0.127093	0.0116020
$121$	1.00000	0.0909091
$122$	−27.1809	−2.46084
$123$	3.76235	0.339240
$124$	−11.3500	−1.01926
$125$	−1.00000	−0.0894427
$126$	4.89932	0.436467
$127$	6.54316	0.580612	0.290306	−	0.956934i	$-0.406243\pi$
$127$	6.54316	0.580612	0.290306	+	0.956934i	$0.406243\pi$
$128$	−1.72196	−0.152201
$129$	−0.299216	−0.0263445
$130$	13.4747	1.18181
$131$	−10.5700	−0.923505	−0.461752	−	0.887009i	$-0.652779\pi$
$131$	−10.5700	−0.923505	−0.461752	+	0.887009i	$0.652779\pi$
$132$	−1.24197	−0.108099
$133$	−0.911544	−0.0790409
$134$	10.8591	0.938083
$135$	−3.33276	−0.286838
$136$	−1.09879	−0.0942208
$137$	3.95543	0.337935	0.168967	−	0.985622i	$-0.445957\pi$
$137$	3.95543	0.337935	0.168967	+	0.985622i	$0.445957\pi$
$138$	−8.47308	−0.721276
$139$	12.1712	1.03235	0.516173	−	0.856484i	$-0.327356\pi$
$139$	12.1712	1.03235	0.516173	+	0.856484i	$0.327356\pi$
$140$	1.92005	0.162274
$141$	−4.45516	−0.375192
$142$	−23.9944	−2.01356
$143$	−6.64953	−0.556062
$144$	10.0151	0.834592
$145$	0.220789	0.0183355
$146$	−15.0526	−1.24576
$147$	3.63745	0.300011
$148$	20.6087	1.69402
$149$	−9.92478	−0.813070	−0.406535	−	0.913635i	$-0.633263\pi$
$149$	−9.92478	−0.813070	−0.406535	+	0.913635i	$0.633263\pi$
$150$	−1.19483	−0.0975571
$151$	−5.10852	−0.415725	−0.207863	−	0.978158i	$-0.566651\pi$
$151$	−5.10852	−0.415725	−0.207863	+	0.978158i	$0.566651\pi$
$152$	0.215549	0.0174834
$153$	13.5207	1.09308
$154$	−1.84717	−0.148849
$155$	5.38841	0.432807
$156$	8.25850	0.661209
$157$	−6.52997	−0.521148	−0.260574	−	0.965454i	$-0.583912\pi$
$157$	−6.52997	−0.521148	−0.260574	+	0.965454i	$0.583912\pi$
$158$	−7.67259	−0.610399
$159$	0.616043	0.0488554
$160$	8.08274	0.638997
$161$	−6.46419	−0.509449
$162$	12.1422	0.953981
$163$	11.7577	0.920937	0.460468	−	0.887676i	$-0.347681\pi$
$163$	11.7577	0.920937	0.460468	+	0.887676i	$0.347681\pi$
$164$	−13.4406	−1.04953
$165$	0.589625	0.0459022
$166$	−31.8941	−2.47547
$167$	12.9652	1.00327	0.501637	−	0.865078i	$-0.332731\pi$
$167$	12.9652	1.00327	0.501637	+	0.865078i	$0.332731\pi$
$168$	0.115851	0.00893811
$169$	31.2163	2.40125
$170$	10.3300	0.792271
$171$	−2.65234	−0.202830
$172$	1.06892	0.0815041
$173$	8.58374	0.652609	0.326305	−	0.945265i	$-0.394196\pi$
$173$	8.58374	0.652609	0.326305	+	0.945265i	$0.394196\pi$
$174$	0.263804	0.0199989
$175$	−0.911544	−0.0689062
$176$	−3.77595	−0.284623
$177$	−3.62785	−0.272686
$178$	24.8715	1.86419
$179$	−6.16633	−0.460893	−0.230447	−	0.973085i	$-0.574019\pi$
$179$	−6.16633	−0.460893	−0.230447	+	0.973085i	$0.574019\pi$
$180$	5.58681	0.416417
$181$	−5.19132	−0.385868	−0.192934	−	0.981212i	$-0.561800\pi$
$181$	−5.19132	−0.385868	−0.192934	+	0.981212i	$0.561800\pi$
$182$	12.2828	0.910462
$183$	7.90879	0.584634
$184$	1.52856	0.112687
$185$	−9.78398	−0.719332
$186$	6.43821	0.472072
$187$	−5.09764	−0.372776
$188$	15.9156	1.16076
$189$	−3.03796	−0.220979
$190$	−2.02642	−0.147012
$191$	−19.9214	−1.44146	−0.720732	−	0.693213i	$-0.756194\pi$
$191$	−19.9214	−1.44146	−0.720732	+	0.693213i	$0.756194\pi$
$192$	5.20469	0.375616
$193$	−10.1064	−0.727471	−0.363736	−	0.931502i	$-0.618499\pi$
$193$	−10.1064	−0.727471	−0.363736	+	0.931502i	$0.618499\pi$
$194$	15.6502	1.12362
$195$	−3.92073	−0.280769
$196$	−12.9944	−0.928170
$197$	−16.5644	−1.18017	−0.590083	−	0.807343i	$-0.700905\pi$
$197$	−16.5644	−1.18017	−0.590083	+	0.807343i	$0.700905\pi$
$198$	−5.37476	−0.381967
$199$	−7.53251	−0.533965	−0.266983	−	0.963701i	$-0.586027\pi$
$199$	−7.53251	−0.533965	−0.266983	+	0.963701i	$0.586027\pi$
$200$	0.215549	0.0152416
$201$	−3.15966	−0.222865
$202$	26.5217	1.86606
$203$	0.201258	0.0141256
$204$	6.33110	0.443266
$205$	6.38092	0.445663
$206$	6.51177	0.453696
$207$	−18.8090	−1.30732
$208$	25.1083	1.74095
$209$	1.00000	0.0691714
$210$	−1.08914	−0.0751575
$211$	1.85075	0.127411	0.0637055	−	0.997969i	$-0.479708\pi$
$211$	1.85075	0.127411	0.0637055	+	0.997969i	$0.479708\pi$
$212$	−2.20074	−0.151148
$213$	6.98161	0.478372
$214$	16.6533	1.13840
$215$	−0.507468	−0.0346091
$216$	0.718375	0.0488792
$217$	4.91177	0.333433
$218$	−29.7861	−2.01737
$219$	4.37985	0.295963
$220$	−2.10637	−0.142011
$221$	33.8969	2.28015
$222$	−11.6901	−0.784591
$223$	−0.852917	−0.0571156	−0.0285578	−	0.999592i	$-0.509091\pi$
$223$	−0.852917	−0.0571156	−0.0285578	+	0.999592i	$0.509091\pi$
$224$	7.36778	0.492280
$225$	−2.65234	−0.176823
$226$	−29.3185	−1.95024
$227$	−21.8530	−1.45043	−0.725217	−	0.688520i	$-0.758261\pi$
$227$	−21.8530	−1.45043	−0.725217	+	0.688520i	$0.758261\pi$
$228$	−1.24197	−0.0822513
$229$	6.44409	0.425837	0.212919	−	0.977070i	$-0.431703\pi$
$229$	6.44409	0.425837	0.212919	+	0.977070i	$0.431703\pi$
$230$	−14.3703	−0.947549
$231$	0.537469	0.0353628
$232$	−0.0475909	−0.00312449
$233$	7.38073	0.483528	0.241764	−	0.970335i	$-0.422274\pi$
$233$	7.38073	0.483528	0.241764	+	0.970335i	$0.422274\pi$
$234$	35.7396	2.33637
$235$	−7.55593	−0.492895
$236$	12.9601	0.843631
$237$	2.23249	0.145016
$238$	9.41620	0.610362
$239$	−1.35211	−0.0874605	−0.0437302	−	0.999043i	$-0.513924\pi$
$239$	−1.35211	−0.0874605	−0.0437302	+	0.999043i	$0.513924\pi$
$240$	−2.22639	−0.143713
$241$	−8.81218	−0.567643	−0.283821	−	0.958877i	$-0.591602\pi$
$241$	−8.81218	−0.567643	−0.283821	+	0.958877i	$0.591602\pi$
$242$	2.02642	0.130263
$243$	−13.5313	−0.868032
$244$	−28.2533	−1.80873
$245$	6.16909	0.394129
$246$	7.62409	0.486094
$247$	−6.64953	−0.423100
$248$	−1.16147	−0.0737533
$249$	9.28020	0.588109
$250$	−2.02642	−0.128162
$251$	−26.5602	−1.67646	−0.838231	−	0.545315i	$-0.816410\pi$
$251$	−26.5602	−1.67646	−0.838231	+	0.545315i	$0.816410\pi$
$252$	5.09263	0.320805
$253$	7.09147	0.445837
$254$	13.2592	0.831955
$255$	−3.00569	−0.188224
$256$	14.1648	0.885303
$257$	−19.5099	−1.21699	−0.608496	−	0.793557i	$-0.708227\pi$
$257$	−19.5099	−1.21699	−0.608496	+	0.793557i	$0.708227\pi$
$258$	−0.606337	−0.0377489
$259$	−8.91852	−0.554170
$260$	14.0064	0.868638
$261$	0.585607	0.0362482
$262$	−21.4192	−1.32328
$263$	−1.57813	−0.0973114	−0.0486557	−	0.998816i	$-0.515494\pi$
$263$	−1.57813	−0.0973114	−0.0486557	+	0.998816i	$0.515494\pi$
$264$	−0.127093	−0.00782205
$265$	1.04480	0.0641818
$266$	−1.84717	−0.113257
$267$	−7.23682	−0.442886
$268$	11.2875	0.689497
$269$	−4.31184	−0.262898	−0.131449	−	0.991323i	$-0.541963\pi$
$269$	−4.31184	−0.262898	−0.131449	+	0.991323i	$0.541963\pi$
$270$	−6.75357	−0.411009
$271$	15.8088	0.960315	0.480157	−	0.877182i	$-0.340580\pi$
$271$	15.8088	0.960315	0.480157	+	0.877182i	$0.340580\pi$
$272$	19.2484	1.16711
$273$	−3.57392	−0.216303
$274$	8.01535	0.484225
$275$	1.00000	0.0603023
$276$	−8.80738	−0.530142
$277$	18.4501	1.10856	0.554279	−	0.832331i	$-0.312994\pi$
$277$	18.4501	1.10856	0.554279	+	0.832331i	$0.312994\pi$
$278$	24.6639	1.47924
$279$	14.2919	0.855634
$280$	0.196483	0.0117421
$281$	30.5225	1.82082	0.910408	−	0.413711i	$-0.135767\pi$
$281$	30.5225	1.82082	0.910408	+	0.413711i	$0.135767\pi$
$282$	−9.02802	−0.537611
$283$	1.16221	0.0690862	0.0345431	−	0.999403i	$-0.489002\pi$
$283$	1.16221	0.0690862	0.0345431	+	0.999403i	$0.489002\pi$
$284$	−24.9411	−1.47998
$285$	0.589625	0.0349263
$286$	−13.4747	−0.796778
$287$	5.81649	0.343337
$288$	21.4382	1.26326
$289$	8.98594	0.528585
$290$	0.447410	0.0262728
$291$	−4.55373	−0.266944
$292$	−15.6465	−0.915644
$293$	20.9503	1.22393	0.611965	−	0.790885i	$-0.290379\pi$
$293$	20.9503	1.22393	0.611965	+	0.790885i	$0.290379\pi$
$294$	7.37099	0.429885
$295$	−6.15281	−0.358231
$296$	2.10893	0.122579
$297$	3.33276	0.193386
$298$	−20.1118	−1.16504
$299$	−47.1550	−2.72704
$300$	−1.24197	−0.0717050
$301$	−0.462580	−0.0266627
$302$	−10.3520	−0.595690
$303$	−7.71699	−0.443329
$304$	−3.77595	−0.216565
$305$	13.4133	0.768041
$306$	27.3986	1.56627
$307$	−21.2726	−1.21409	−0.607047	−	0.794666i	$-0.707646\pi$
$307$	−21.2726	−1.21409	−0.607047	+	0.794666i	$0.707646\pi$
$308$	−1.92005	−0.109405
$309$	−1.89472	−0.107787
$310$	10.9192	0.620167
$311$	−22.9147	−1.29937	−0.649687	−	0.760202i	$-0.725100\pi$
$311$	−22.9147	−1.29937	−0.649687	+	0.760202i	$0.725100\pi$
$312$	0.845111	0.0478450
$313$	12.7352	0.719837	0.359919	−	0.932984i	$-0.382804\pi$
$313$	12.7352	0.719837	0.359919	+	0.932984i	$0.382804\pi$
$314$	−13.2324	−0.746750
$315$	−2.41773	−0.136223
$316$	−7.97531	−0.448646
$317$	1.65384	0.0928887	0.0464444	−	0.998921i	$-0.485211\pi$
$317$	1.65384	0.0928887	0.0464444	+	0.998921i	$0.485211\pi$
$318$	1.24836	0.0700045
$319$	−0.220789	−0.0123618
$320$	8.82713	0.493451
$321$	−4.84560	−0.270455
$322$	−13.0991	−0.729987
$323$	−5.09764	−0.283640
$324$	12.6213	0.701181
$325$	−6.64953	−0.368850
$326$	23.8261	1.31960
$327$	8.66682	0.479276
$328$	−1.37540	−0.0759440
$329$	−6.88756	−0.379724
$330$	1.19483	0.0657730
$331$	−21.8765	−1.20244	−0.601220	−	0.799083i	$-0.705319\pi$
$331$	−21.8765	−1.20244	−0.601220	+	0.799083i	$0.705319\pi$
$332$	−33.1525	−1.81948
$333$	−25.9505	−1.42208
$334$	26.2728	1.43758
$335$	−5.35877	−0.292781
$336$	−2.02945	−0.110716
$337$	−8.53060	−0.464692	−0.232346	−	0.972633i	$-0.574640\pi$
$337$	−8.53060	−0.464692	−0.232346	+	0.972633i	$0.574640\pi$
$338$	63.2572	3.44074
$339$	8.53078	0.463328
$340$	10.7375	0.582324
$341$	−5.38841	−0.291799
$342$	−5.37476	−0.290633
$343$	12.0042	0.648166
$344$	0.109385	0.00589762
$345$	4.18131	0.225114
$346$	17.3942	0.935120
$347$	−17.3674	−0.932332	−0.466166	−	0.884697i	$-0.654365\pi$
$347$	−17.3674	−0.932332	−0.466166	+	0.884697i	$0.654365\pi$
$348$	0.274212	0.0146993
$349$	−33.8851	−1.81383	−0.906913	−	0.421318i	$-0.861568\pi$
$349$	−33.8851	−1.81383	−0.906913	+	0.421318i	$0.861568\pi$
$350$	−1.84717	−0.0987353
$351$	−22.1613	−1.18288
$352$	−8.08274	−0.430812
$353$	−15.0158	−0.799212	−0.399606	−	0.916687i	$-0.630853\pi$
$353$	−15.0158	−0.799212	−0.399606	+	0.916687i	$0.630853\pi$
$354$	−7.35154	−0.390730
$355$	11.8408	0.628443
$356$	25.8528	1.37019
$357$	−2.73982	−0.145007
$358$	−12.4956	−0.660411
$359$	−14.2723	−0.753265	−0.376633	−	0.926363i	$-0.622918\pi$
$359$	−14.2723	−0.753265	−0.376633	+	0.926363i	$0.622918\pi$
$360$	0.571711	0.0301318
$361$	1.00000	0.0526316
$362$	−10.5198	−0.552907
$363$	−0.589625	−0.0309473
$364$	12.7674	0.669195
$365$	7.42820	0.388810
$366$	16.0265	0.837719
$367$	13.4440	0.701771	0.350885	−	0.936418i	$-0.385881\pi$
$367$	13.4440	0.701771	0.350885	+	0.936418i	$0.385881\pi$
$368$	−26.7770	−1.39585
$369$	16.9244	0.881049
$370$	−19.8264	−1.03073
$371$	0.952385	0.0494454
$372$	6.69223	0.346976
$373$	−23.0986	−1.19600	−0.598000	−	0.801496i	$-0.704038\pi$
$373$	−23.0986	−1.19600	−0.598000	+	0.801496i	$0.704038\pi$
$374$	−10.3300	−0.534149
$375$	0.589625	0.0304481
$376$	1.62868	0.0839926
$377$	1.46814	0.0756131
$378$	−6.15617	−0.316639
$379$	10.3481	0.531548	0.265774	−	0.964035i	$-0.414373\pi$
$379$	10.3481	0.531548	0.265774	+	0.964035i	$0.414373\pi$
$380$	−2.10637	−0.108054
$381$	−3.85801	−0.197652
$382$	−40.3692	−2.06547
$383$	−7.16326	−0.366026	−0.183013	−	0.983111i	$-0.558585\pi$
$383$	−7.16326	−0.366026	−0.183013	+	0.983111i	$0.558585\pi$
$384$	1.01531	0.0518122
$385$	0.911544	0.0464566
$386$	−20.4797	−1.04239
$387$	−1.34598	−0.0684200
$388$	16.2677	0.825867
$389$	10.9989	0.557667	0.278834	−	0.960339i	$-0.410052\pi$
$389$	10.9989	0.557667	0.278834	+	0.960339i	$0.410052\pi$
$390$	−7.94503	−0.402312
$391$	−36.1498	−1.82817
$392$	−1.32974	−0.0671622
$393$	6.23233	0.314379
$394$	−33.5664	−1.69105
$395$	3.78628	0.190509
$396$	−5.58681	−0.280748
$397$	27.0281	1.35650	0.678251	−	0.734830i	$-0.262738\pi$
$397$	27.0281	1.35650	0.678251	+	0.734830i	$0.262738\pi$
$398$	−15.2640	−0.765116
$399$	0.537469	0.0269071
$400$	−3.77595	−0.188797
$401$	23.6700	1.18202	0.591011	−	0.806663i	$-0.298729\pi$
$401$	23.6700	1.18202	0.591011	+	0.806663i	$0.298729\pi$
$402$	−6.40279	−0.319342
$403$	35.8304	1.78484
$404$	27.5681	1.37156
$405$	−5.99195	−0.297742
$406$	0.407834	0.0202404
$407$	9.78398	0.484974
$408$	0.647876	0.0320746
$409$	−19.5785	−0.968094	−0.484047	−	0.875042i	$-0.660834\pi$
$409$	−19.5785	−0.968094	−0.484047	+	0.875042i	$0.660834\pi$
$410$	12.9304	0.638588
$411$	−2.33222	−0.115040
$412$	6.76869	0.333469
$413$	−5.60856	−0.275979
$414$	−38.1149	−1.87325
$415$	15.7392	0.772606
$416$	53.7465	2.63514
$417$	−7.17643	−0.351431
$418$	2.02642	0.0991153
$419$	−23.0199	−1.12460	−0.562298	−	0.826934i	$-0.690083\pi$
$419$	−23.0199	−1.12460	−0.562298	+	0.826934i	$0.690083\pi$
$420$	−1.13211	−0.0552412
$421$	−11.2565	−0.548610	−0.274305	−	0.961643i	$-0.588448\pi$
$421$	−11.2565	−0.548610	−0.274305	+	0.961643i	$0.588448\pi$
$422$	3.75039	0.182566
$423$	−20.0409	−0.974423
$424$	−0.225207	−0.0109370
$425$	−5.09764	−0.247272
$426$	14.1477	0.685457
$427$	12.2268	0.591695
$428$	17.3104	0.836729
$429$	3.92073	0.189295
$430$	−1.02834	−0.0495911
$431$	26.3343	1.26848	0.634240	−	0.773136i	$-0.281313\pi$
$431$	26.3343	1.26848	0.634240	+	0.773136i	$0.281313\pi$
$432$	−12.5843	−0.605464
$433$	−7.29725	−0.350683	−0.175342	−	0.984508i	$-0.556103\pi$
$433$	−7.29725	−0.350683	−0.175342	+	0.984508i	$0.556103\pi$
$434$	9.95330	0.477773
$435$	−0.130182	−0.00624177
$436$	−30.9613	−1.48278
$437$	7.09147	0.339231
$438$	8.87540	0.424083
$439$	37.4748	1.78858	0.894288	−	0.447492i	$-0.147683\pi$
$439$	37.4748	1.78858	0.894288	+	0.447492i	$0.147683\pi$
$440$	−0.215549	−0.0102759
$441$	16.3625	0.779168
$442$	68.6893	3.26722
$443$	24.8647	1.18136	0.590679	−	0.806907i	$-0.298860\pi$
$443$	24.8647	1.18136	0.590679	+	0.806907i	$0.298860\pi$
$444$	−12.1514	−0.576679
$445$	−12.2736	−0.581825
$446$	−1.72837	−0.0818406
$447$	5.85190	0.276785
$448$	8.04631	0.380152
$449$	−20.2656	−0.956395	−0.478197	−	0.878252i	$-0.658710\pi$
$449$	−20.2656	−0.956395	−0.478197	+	0.878252i	$0.658710\pi$
$450$	−5.37476	−0.253368
$451$	−6.38092	−0.300466
$452$	−30.4753	−1.43344
$453$	3.01211	0.141521
$454$	−44.2833	−2.07832
$455$	−6.06134	−0.284160
$456$	−0.127093	−0.00595169
$457$	10.8878	0.509308	0.254654	−	0.967032i	$-0.418038\pi$
$457$	10.8878	0.509308	0.254654	+	0.967032i	$0.418038\pi$
$458$	13.0584	0.610180
$459$	−16.9892	−0.792989
$460$	−14.9373	−0.696454
$461$	21.3828	0.995895	0.497948	−	0.867207i	$-0.334087\pi$
$461$	21.3828	0.995895	0.497948	+	0.867207i	$0.334087\pi$
$462$	1.08914	0.0506712
$463$	0.736180	0.0342132	0.0171066	−	0.999854i	$-0.494555\pi$
$463$	0.736180	0.0342132	0.0171066	+	0.999854i	$0.494555\pi$
$464$	0.833686	0.0387029
$465$	−3.17714	−0.147336
$466$	14.9564	0.692844
$467$	−33.8245	−1.56521	−0.782606	−	0.622517i	$-0.786110\pi$
$467$	−33.8245	−1.56521	−0.782606	+	0.622517i	$0.786110\pi$
$468$	37.1497	1.71725
$469$	−4.88475	−0.225557
$470$	−15.3115	−0.706266
$471$	3.85023	0.177409
$472$	1.32624	0.0610449
$473$	0.507468	0.0233334
$474$	4.52395	0.207792
$475$	1.00000	0.0458831
$476$	9.78772	0.448619
$477$	2.77118	0.126884
$478$	−2.73993	−0.125322
$479$	13.4855	0.616169	0.308084	−	0.951359i	$-0.400312\pi$
$479$	13.4855	0.616169	0.308084	+	0.951359i	$0.400312\pi$
$480$	−4.76578	−0.217527
$481$	−65.0589	−2.96643
$482$	−17.8572	−0.813372
$483$	3.81144	0.173427
$484$	2.10637	0.0957441
$485$	−7.72309	−0.350688
$486$	−27.4200	−1.24380
$487$	38.6776	1.75265	0.876325	−	0.481720i	$-0.159988\pi$
$487$	38.6776	1.75265	0.876325	+	0.481720i	$0.159988\pi$
$488$	−2.89122	−0.130879
$489$	−6.93265	−0.313505
$490$	12.5012	0.564744
$491$	40.9225	1.84680	0.923402	−	0.383834i	$-0.125396\pi$
$491$	40.9225	1.84680	0.923402	+	0.383834i	$0.125396\pi$
$492$	7.92490	0.357282
$493$	1.12550	0.0506900
$494$	−13.4747	−0.606257
$495$	2.65234	0.119214
$496$	20.3463	0.913577
$497$	10.7934	0.484150
$498$	18.8056	0.842698
$499$	−33.5397	−1.50144	−0.750722	−	0.660618i	$-0.770294\pi$
$499$	−33.5397	−1.50144	−0.750722	+	0.660618i	$0.770294\pi$
$500$	−2.10637	−0.0941997
$501$	−7.64457	−0.341534
$502$	−53.8220	−2.40219
$503$	−21.2872	−0.949151	−0.474575	−	0.880215i	$-0.657398\pi$
$503$	−21.2872	−0.949151	−0.474575	+	0.880215i	$0.657398\pi$
$504$	0.521140	0.0232134
$505$	−13.0880	−0.582407
$506$	14.3703	0.638837
$507$	−18.4059	−0.817434
$508$	13.7823	0.611492
$509$	−32.5262	−1.44170	−0.720850	−	0.693091i	$-0.756248\pi$
$509$	−32.5262	−1.44170	−0.720850	+	0.693091i	$0.756248\pi$
$510$	−6.09079	−0.269705
$511$	6.77113	0.299537
$512$	32.1478	1.42075
$513$	3.33276	0.147145
$514$	−39.5351	−1.74382
$515$	−3.21344	−0.141601
$516$	−0.630259	−0.0277456
$517$	7.55593	0.332309
$518$	−18.0727	−0.794067
$519$	−5.06118	−0.222161
$520$	1.43330	0.0628545
$521$	−38.4564	−1.68481	−0.842404	−	0.538847i	$-0.818860\pi$
$521$	−38.4564	−1.68481	−0.842404	+	0.538847i	$0.818860\pi$
$522$	1.18668	0.0519398
$523$	−28.9345	−1.26522	−0.632608	−	0.774472i	$-0.718016\pi$
$523$	−28.9345	−1.26522	−0.632608	+	0.774472i	$0.718016\pi$
$524$	−22.2643	−0.972621
$525$	0.537469	0.0234571
$526$	−3.19794	−0.139437
$527$	27.4682	1.19653
$528$	2.22639	0.0968912
$529$	27.2890	1.18648
$530$	2.11721	0.0919658
$531$	−16.3194	−0.708200
$532$	−1.92005	−0.0832446
$533$	42.4302	1.83785
$534$	−14.6648	−0.634609
$535$	−8.21812	−0.355300
$536$	1.15508	0.0498918
$537$	3.63582	0.156897
$538$	−8.73760	−0.376704
$539$	−6.16909	−0.265721
$540$	−7.02003	−0.302094
$541$	4.18991	0.180138	0.0900691	−	0.995936i	$-0.471291\pi$
$541$	4.18991	0.180138	0.0900691	+	0.995936i	$0.471291\pi$
$542$	32.0352	1.37603
$543$	3.06093	0.131357
$544$	41.2029	1.76656
$545$	14.6989	0.629631
$546$	−7.24225	−0.309940
$547$	39.8603	1.70430	0.852152	−	0.523294i	$-0.175297\pi$
$547$	39.8603	1.70430	0.852152	+	0.523294i	$0.175297\pi$
$548$	8.33159	0.355908
$549$	35.5766	1.51837
$550$	2.02642	0.0864068
$551$	−0.220789	−0.00940591
$552$	−0.901279	−0.0383610
$553$	3.45136	0.146767
$554$	37.3876	1.58844
$555$	5.76887	0.244875
$556$	25.6370	1.08725
$557$	24.7975	1.05070	0.525352	−	0.850885i	$-0.323934\pi$
$557$	24.7975	1.05070	0.525352	+	0.850885i	$0.323934\pi$
$558$	28.9614	1.22603
$559$	−3.37443	−0.142723
$560$	−3.44194	−0.145449
$561$	3.00569	0.126901
$562$	61.8512	2.60904
$563$	14.9700	0.630911	0.315455	−	0.948940i	$-0.397843\pi$
$563$	14.9700	0.630911	0.315455	+	0.948940i	$0.397843\pi$
$564$	−9.38422	−0.395147
$565$	14.4682	0.608680
$566$	2.35512	0.0989932
$567$	−5.46193	−0.229379
$568$	−2.55227	−0.107091
$569$	19.1532	0.802944	0.401472	−	0.915871i	$-0.368499\pi$
$569$	19.1532	0.802944	0.401472	+	0.915871i	$0.368499\pi$
$570$	1.19483	0.0500458
$571$	−13.1882	−0.551908	−0.275954	−	0.961171i	$-0.588994\pi$
$571$	−13.1882	−0.551908	−0.275954	+	0.961171i	$0.588994\pi$
$572$	−14.0064	−0.585636
$573$	11.7462	0.490703
$574$	11.7866	0.491965
$575$	7.09147	0.295735
$576$	23.4126	0.975523
$577$	39.6231	1.64953	0.824766	−	0.565474i	$-0.191307\pi$
$577$	39.6231	1.64953	0.824766	+	0.565474i	$0.191307\pi$
$578$	18.2093	0.757406
$579$	5.95895	0.247646
$580$	0.465062	0.0193107
$581$	14.3469	0.595212
$582$	−9.22775	−0.382503
$583$	−1.04480	−0.0432714
$584$	−1.60114	−0.0662558
$585$	−17.6368	−0.729194
$586$	42.4541	1.75376
$587$	−35.9963	−1.48572	−0.742862	−	0.669444i	$-0.766532\pi$
$587$	−35.9963	−1.48572	−0.742862	+	0.669444i	$0.766532\pi$
$588$	7.66181	0.315968
$589$	−5.38841	−0.222025
$590$	−12.4682	−0.513306
$591$	9.76679	0.401752
$592$	−36.9438	−1.51838
$593$	−18.4885	−0.759230	−0.379615	−	0.925145i	$-0.623943\pi$
$593$	−18.4885	−0.759230	−0.379615	+	0.925145i	$0.623943\pi$
$594$	6.75357	0.277102
$595$	−4.64672	−0.190497
$596$	−20.9053	−0.856313
$597$	4.44135	0.181772
$598$	−95.5557	−3.90756
$599$	12.9755	0.530163	0.265081	−	0.964226i	$-0.414601\pi$
$599$	12.9755	0.530163	0.265081	+	0.964226i	$0.414601\pi$
$600$	−0.127093	−0.00518856
$601$	9.73651	0.397160	0.198580	−	0.980085i	$-0.436367\pi$
$601$	9.73651	0.397160	0.198580	+	0.980085i	$0.436367\pi$
$602$	−0.937380	−0.0382048
$603$	−14.2133	−0.578810
$604$	−10.7604	−0.437836
$605$	−1.00000	−0.0406558
$606$	−15.6378	−0.635244
$607$	37.0798	1.50502	0.752512	−	0.658578i	$-0.228842\pi$
$607$	37.0798	1.50502	0.752512	+	0.658578i	$0.228842\pi$
$608$	−8.08274	−0.327799
$609$	−0.118667	−0.00480863
$610$	27.1809	1.10052
$611$	−50.2434	−2.03263
$612$	28.4796	1.15122
$613$	−5.21244	−0.210528	−0.105264	−	0.994444i	$-0.533569\pi$
$613$	−5.21244	−0.210528	−0.105264	+	0.994444i	$0.533569\pi$
$614$	−43.1072	−1.73967
$615$	−3.76235	−0.151713
$616$	−0.196483	−0.00791652
$617$	−35.8080	−1.44157	−0.720787	−	0.693157i	$-0.756219\pi$
$617$	−35.8080	−1.44157	−0.720787	+	0.693157i	$0.756219\pi$
$618$	−3.83950	−0.154447
$619$	−22.1314	−0.889537	−0.444769	−	0.895646i	$-0.646714\pi$
$619$	−22.1314	−0.889537	−0.444769	+	0.895646i	$0.646714\pi$
$620$	11.3500	0.455826
$621$	23.6342	0.948407
$622$	−46.4348	−1.86186
$623$	−11.1879	−0.448235
$624$	−14.8045	−0.592653
$625$	1.00000	0.0400000
$626$	25.8069	1.03145
$627$	−0.589625	−0.0235473
$628$	−13.7545	−0.548865
$629$	−49.8752	−1.98865
$630$	−4.89932	−0.195194
$631$	−20.2054	−0.804365	−0.402183	−	0.915559i	$-0.631748\pi$
$631$	−20.2054	−0.804365	−0.402183	+	0.915559i	$0.631748\pi$
$632$	−0.816131	−0.0324640
$633$	−1.09125	−0.0433732
$634$	3.35136	0.133100
$635$	−6.54316	−0.259658
$636$	1.29761	0.0514537
$637$	41.0216	1.62533
$638$	−0.447410	−0.0177131
$639$	31.4058	1.24239
$640$	1.72196	0.0680663
$641$	13.7753	0.544091	0.272045	−	0.962284i	$-0.412300\pi$
$641$	13.7753	0.544091	0.272045	+	0.962284i	$0.412300\pi$
$642$	−9.81922	−0.387534
$643$	30.6180	1.20745	0.603727	−	0.797191i	$-0.293682\pi$
$643$	30.6180	1.20745	0.603727	+	0.797191i	$0.293682\pi$
$644$	−13.6160	−0.536544
$645$	0.299216	0.0117816
$646$	−10.3300	−0.406426
$647$	22.3937	0.880387	0.440194	−	0.897903i	$-0.354910\pi$
$647$	22.3937	0.880387	0.440194	+	0.897903i	$0.354910\pi$
$648$	1.29156	0.0507373
$649$	6.15281	0.241519
$650$	−13.4747	−0.528522
$651$	−2.89610	−0.113507
$652$	24.7661	0.969917
$653$	−33.6543	−1.31699	−0.658497	−	0.752583i	$-0.728808\pi$
$653$	−33.6543	−1.31699	−0.658497	+	0.752583i	$0.728808\pi$
$654$	17.5626	0.686752
$655$	10.5700	0.413004
$656$	24.0940	0.940713
$657$	19.7021	0.768653
$658$	−13.9571	−0.544104
$659$	−25.3912	−0.989101	−0.494551	−	0.869149i	$-0.664667\pi$
$659$	−25.3912	−0.989101	−0.494551	+	0.869149i	$0.664667\pi$
$660$	1.24197	0.0483435
$661$	−25.2638	−0.982649	−0.491324	−	0.870977i	$-0.663487\pi$
$661$	−25.2638	−0.982649	−0.491324	+	0.870977i	$0.663487\pi$
$662$	−44.3309	−1.72297
$663$	−19.9865	−0.776210
$664$	−3.39257	−0.131657
$665$	0.911544	0.0353482
$666$	−52.5865	−2.03768
$667$	−1.56572	−0.0606248
$668$	27.3094	1.05663
$669$	0.502901	0.0194433
$670$	−10.8591	−0.419524
$671$	−13.4133	−0.517813
$672$	−4.34422	−0.167582
$673$	−1.16960	−0.0450850	−0.0225425	−	0.999746i	$-0.507176\pi$
$673$	−1.16960	−0.0450850	−0.0225425	+	0.999746i	$0.507176\pi$
$674$	−17.2866	−0.665854
$675$	3.33276	0.128278
$676$	65.7530	2.52896
$677$	−19.2131	−0.738421	−0.369210	−	0.929346i	$-0.620372\pi$
$677$	−19.2131	−0.738421	−0.369210	+	0.929346i	$0.620372\pi$
$678$	17.2869	0.663900
$679$	−7.03994	−0.270168
$680$	1.09879	0.0421368
$681$	12.8851	0.493757
$682$	−10.9192	−0.418116
$683$	23.4580	0.897594	0.448797	−	0.893634i	$-0.351853\pi$
$683$	23.4580	0.897594	0.448797	+	0.893634i	$0.351853\pi$
$684$	−5.58681	−0.213617
$685$	−3.95543	−0.151129
$686$	24.3255	0.928753
$687$	−3.79959	−0.144964
$688$	−1.91617	−0.0730534
$689$	6.94746	0.264677
$690$	8.47308	0.322564
$691$	14.8315	0.564215	0.282108	−	0.959383i	$-0.408966\pi$
$691$	14.8315	0.564215	0.282108	+	0.959383i	$0.408966\pi$
$692$	18.0805	0.687318
$693$	2.41773	0.0918418
$694$	−35.1936	−1.33593
$695$	−12.1712	−0.461679
$696$	0.0280607	0.00106364
$697$	32.5277	1.23207
$698$	−68.6653	−2.59902
$699$	−4.35186	−0.164602
$700$	−1.92005	−0.0725710
$701$	−25.1611	−0.950321	−0.475161	−	0.879899i	$-0.657610\pi$
$701$	−25.1611	−0.950321	−0.475161	+	0.879899i	$0.657610\pi$
$702$	−44.9081	−1.69495
$703$	9.78398	0.369010
$704$	−8.82713	−0.332685
$705$	4.45516	0.167791
$706$	−30.4283	−1.14519
$707$	−11.9303	−0.448683
$708$	−7.64159	−0.287189
$709$	18.5123	0.695245	0.347622	−	0.937635i	$-0.386989\pi$
$709$	18.5123	0.695245	0.347622	+	0.937635i	$0.386989\pi$
$710$	23.9944	0.900492
$711$	10.0425	0.376624
$712$	2.64557	0.0991469
$713$	−38.2117	−1.43104
$714$	−5.55202	−0.207779
$715$	6.64953	0.248678
$716$	−12.9886	−0.485406
$717$	0.797235	0.0297733
$718$	−28.9217	−1.07935
$719$	−17.3073	−0.645454	−0.322727	−	0.946492i	$-0.604599\pi$
$719$	−17.3073	−0.645454	−0.322727	+	0.946492i	$0.604599\pi$
$720$	−10.0151	−0.373241
$721$	−2.92919	−0.109089
$722$	2.02642	0.0754155
$723$	5.19588	0.193237
$724$	−10.9348	−0.406390
$725$	−0.220789	−0.00819988
$726$	−1.19483	−0.0443441
$727$	−15.1803	−0.563006	−0.281503	−	0.959560i	$-0.590833\pi$
$727$	−15.1803	−0.563006	−0.281503	+	0.959560i	$0.590833\pi$
$728$	1.30652	0.0484228
$729$	−9.99747	−0.370277
$730$	15.0526	0.557123
$731$	−2.58689	−0.0956797
$732$	16.6588	0.615728
$733$	22.8904	0.845476	0.422738	−	0.906252i	$-0.361069\pi$
$733$	22.8904	0.845476	0.422738	+	0.906252i	$0.361069\pi$
$734$	27.2432	1.00556
$735$	−3.63745	−0.134169
$736$	−57.3186	−2.11279
$737$	5.35877	0.197393
$738$	34.2959	1.26245
$739$	−36.2088	−1.33196	−0.665982	−	0.745968i	$-0.731987\pi$
$739$	−36.2088	−1.33196	−0.665982	+	0.745968i	$0.731987\pi$
$740$	−20.6087	−0.757590
$741$	3.92073	0.144032
$742$	1.92993	0.0708500
$743$	−27.1410	−0.995708	−0.497854	−	0.867261i	$-0.665878\pi$
$743$	−27.1410	−0.995708	−0.497854	+	0.867261i	$0.665878\pi$
$744$	0.684830	0.0251071
$745$	9.92478	0.363616
$746$	−46.8074	−1.71374
$747$	41.7457	1.52739
$748$	−10.7375	−0.392602
$749$	−7.49117	−0.273722
$750$	1.19483	0.0436289
$751$	17.1725	0.626634	0.313317	−	0.949649i	$-0.398560\pi$
$751$	17.1725	0.626634	0.313317	+	0.949649i	$0.398560\pi$
$752$	−28.5308	−1.04041
$753$	15.6605	0.570701
$754$	2.97507	0.108346
$755$	5.10852	0.185918
$756$	−6.39906	−0.232732
$757$	−29.9521	−1.08863	−0.544315	−	0.838881i	$-0.683210\pi$
$757$	−29.9521	−1.08863	−0.544315	+	0.838881i	$0.683210\pi$
$758$	20.9696	0.761652
$759$	−4.18131	−0.151772
$760$	−0.215549	−0.00781880
$761$	−22.5916	−0.818944	−0.409472	−	0.912323i	$-0.634287\pi$
$761$	−22.5916	−0.818944	−0.409472	+	0.912323i	$0.634287\pi$
$762$	−7.81794	−0.283214
$763$	13.3987	0.485064
$764$	−41.9619	−1.51813
$765$	−13.5207	−0.488842
$766$	−14.5158	−0.524476
$767$	−40.9133	−1.47729
$768$	−8.35194	−0.301375
$769$	4.05504	0.146228	0.0731142	−	0.997324i	$-0.476706\pi$
$769$	4.05504	0.146228	0.0731142	+	0.997324i	$0.476706\pi$
$770$	1.84717	0.0665673
$771$	11.5035	0.414288
$772$	−21.2877	−0.766162
$773$	30.9717	1.11398	0.556988	−	0.830520i	$-0.311957\pi$
$773$	30.9717	1.11398	0.556988	+	0.830520i	$0.311957\pi$
$774$	−2.72752	−0.0980386
$775$	−5.38841	−0.193557
$776$	1.66471	0.0597596
$777$	5.25858	0.188651
$778$	22.2884	0.799078
$779$	−6.38092	−0.228620
$780$	−8.25850	−0.295702
$781$	−11.8408	−0.423696
$782$	−73.2546	−2.61958
$783$	−0.735835	−0.0262966
$784$	23.2941	0.831934
$785$	6.52997	0.233065
$786$	12.6293	0.450472
$787$	−34.3399	−1.22409	−0.612043	−	0.790824i	$-0.709652\pi$
$787$	−34.3399	−1.22409	−0.612043	+	0.790824i	$0.709652\pi$
$788$	−34.8908	−1.24293
$789$	0.930502	0.0331267
$790$	7.67259	0.272979
$791$	13.1884	0.468924
$792$	−0.571711	−0.0203149
$793$	89.1919	3.16730
$794$	54.7703	1.94372
$795$	−0.616043	−0.0218488
$796$	−15.8662	−0.562364
$797$	42.9203	1.52032	0.760158	−	0.649739i	$-0.225122\pi$
$797$	42.9203	1.52032	0.760158	+	0.649739i	$0.225122\pi$
$798$	1.08914	0.0385550
$799$	−38.5174	−1.36265
$800$	−8.08274	−0.285768
$801$	−32.5538	−1.15023
$802$	47.9653	1.69371
$803$	−7.42820	−0.262135
$804$	−6.65541	−0.234718
$805$	6.46419	0.227833
$806$	72.6073	2.55748
$807$	2.54237	0.0894956
$808$	2.82110	0.0992461
$809$	−33.0173	−1.16083	−0.580413	−	0.814322i	$-0.697109\pi$
$809$	−33.0173	−1.16083	−0.580413	+	0.814322i	$0.697109\pi$
$810$	−12.1422	−0.426633
$811$	46.0997	1.61878	0.809390	−	0.587271i	$-0.199798\pi$
$811$	46.0997	1.61878	0.809390	+	0.587271i	$0.199798\pi$
$812$	0.423925	0.0148768
$813$	−9.32125	−0.326910
$814$	19.8264	0.694916
$815$	−11.7577	−0.411856
$816$	−11.3493	−0.397306
$817$	0.507468	0.0177541
$818$	−39.6742	−1.38718
$819$	−16.0768	−0.561767
$820$	13.4406	0.469365
$821$	−18.9482	−0.661297	−0.330648	−	0.943754i	$-0.607267\pi$
$821$	−18.9482	−0.661297	−0.330648	+	0.943754i	$0.607267\pi$
$822$	−4.72605	−0.164840
$823$	18.3333	0.639058	0.319529	−	0.947576i	$-0.396475\pi$
$823$	18.3333	0.639058	0.319529	+	0.947576i	$0.396475\pi$
$824$	0.692655	0.0241298
$825$	−0.589625	−0.0205281
$826$	−11.3653	−0.395449
$827$	6.62592	0.230406	0.115203	−	0.993342i	$-0.463248\pi$
$827$	6.62592	0.230406	0.115203	+	0.993342i	$0.463248\pi$
$828$	−39.6187	−1.37685
$829$	12.5013	0.434186	0.217093	−	0.976151i	$-0.430342\pi$
$829$	12.5013	0.434186	0.217093	+	0.976151i	$0.430342\pi$
$830$	31.8941	1.10706
$831$	−10.8786	−0.377375
$832$	58.6963	2.03493
$833$	31.4478	1.08960
$834$	−14.5424	−0.503564
$835$	−12.9652	−0.448678
$836$	2.10637	0.0728503
$837$	−17.9583	−0.620729
$838$	−46.6480	−1.61143
$839$	30.9956	1.07009	0.535043	−	0.844825i	$-0.320295\pi$
$839$	30.9956	1.07009	0.535043	+	0.844825i	$0.320295\pi$
$840$	−0.115851	−0.00399724
$841$	−28.9513	−0.998319
$842$	−22.8104	−0.786099
$843$	−17.9968	−0.619842
$844$	3.89837	0.134187
$845$	−31.2163	−1.07387
$846$	−40.6113	−1.39624
$847$	−0.911544	−0.0313210
$848$	3.94513	0.135476
$849$	−0.685268	−0.0235183
$850$	−10.3300	−0.354314
$851$	69.3828	2.37841
$852$	14.7059	0.503814
$853$	39.3169	1.34619	0.673093	−	0.739558i	$-0.264966\pi$
$853$	39.3169	1.34619	0.673093	+	0.739558i	$0.264966\pi$
$854$	24.7766	0.847836
$855$	2.65234	0.0907082
$856$	1.77141	0.0605456
$857$	−2.57194	−0.0878559	−0.0439279	−	0.999035i	$-0.513987\pi$
$857$	−2.57194	−0.0878559	−0.0439279	+	0.999035i	$0.513987\pi$
$858$	7.94503	0.271239
$859$	44.0100	1.50160	0.750800	−	0.660529i	$-0.229668\pi$
$859$	44.0100	1.50160	0.750800	+	0.660529i	$0.229668\pi$
$860$	−1.06892	−0.0364497
$861$	−3.42955	−0.116879
$862$	53.3644	1.81760
$863$	33.4811	1.13971	0.569856	−	0.821745i	$-0.306999\pi$
$863$	33.4811	1.13971	0.569856	+	0.821745i	$0.306999\pi$
$864$	−26.9378	−0.916444
$865$	−8.58374	−0.291856
$866$	−14.7873	−0.502492
$867$	−5.29833	−0.179941
$868$	10.3460	0.351166
$869$	−3.78628	−0.128441
$870$	−0.263804	−0.00894379
$871$	−35.6333	−1.20739
$872$	−3.16834	−0.107293
$873$	−20.4843	−0.693288
$874$	14.3703	0.486082
$875$	0.911544	0.0308158
$876$	9.22558	0.311703
$877$	−21.8506	−0.737842	−0.368921	−	0.929461i	$-0.620273\pi$
$877$	−21.8506	−0.737842	−0.368921	+	0.929461i	$0.620273\pi$
$878$	75.9397	2.56284
$879$	−12.3528	−0.416650
$880$	3.77595	0.127287
$881$	51.8042	1.74533	0.872663	−	0.488322i	$-0.162391\pi$
$881$	51.8042	1.74533	0.872663	+	0.488322i	$0.162391\pi$
$882$	33.1573	1.11647
$883$	−12.4503	−0.418985	−0.209493	−	0.977810i	$-0.567181\pi$
$883$	−12.4503	−0.418985	−0.209493	+	0.977810i	$0.567181\pi$
$884$	71.3995	2.40142
$885$	3.62785	0.121949
$886$	50.3863	1.69276
$887$	−36.8879	−1.23857	−0.619287	−	0.785165i	$-0.712578\pi$
$887$	−36.8879	−1.23857	−0.619287	+	0.785165i	$0.712578\pi$
$888$	−1.24348	−0.0417284
$889$	−5.96438	−0.200039
$890$	−24.8715	−0.833693
$891$	5.99195	0.200738
$892$	−1.79656	−0.0601533
$893$	7.55593	0.252850
$894$	11.8584	0.396604
$895$	6.16633	0.206118
$896$	1.56964	0.0524380
$897$	27.8037	0.928340
$898$	−41.0667	−1.37041
$899$	1.18970	0.0396787
$900$	−5.58681	−0.186227
$901$	5.32604	0.177436
$902$	−12.9304	−0.430536
$903$	0.272748	0.00907650
$904$	−3.11860	−0.103723
$905$	5.19132	0.172565
$906$	6.10379	0.202785
$907$	11.4311	0.379564	0.189782	−	0.981826i	$-0.439222\pi$
$907$	11.4311	0.379564	0.189782	+	0.981826i	$0.439222\pi$
$908$	−46.0305	−1.52758
$909$	−34.7138	−1.15138
$910$	−12.2828	−0.407171
$911$	12.3404	0.408856	0.204428	−	0.978882i	$-0.434467\pi$
$911$	12.3404	0.408856	0.204428	+	0.978882i	$0.434467\pi$
$912$	2.22639	0.0737232
$913$	−15.7392	−0.520891
$914$	22.0632	0.729784
$915$	−7.90879	−0.261456
$916$	13.5736	0.448486
$917$	9.63501	0.318176
$918$	−34.4273	−1.13627
$919$	16.6373	0.548814	0.274407	−	0.961614i	$-0.411518\pi$
$919$	16.6373	0.548814	0.274407	+	0.961614i	$0.411518\pi$
$920$	−1.52856	−0.0503952
$921$	12.5429	0.413301
$922$	43.3304	1.42701
$923$	78.7356	2.59161
$924$	1.13211	0.0372436
$925$	9.78398	0.321695
$926$	1.49181	0.0490238
$927$	−8.52314	−0.279937
$928$	1.78458	0.0585816
$929$	−54.7650	−1.79678	−0.898390	−	0.439198i	$-0.855263\pi$
$929$	−54.7650	−1.79678	−0.898390	+	0.439198i	$0.855263\pi$
$930$	−6.43821	−0.211117
$931$	−6.16909	−0.202184
$932$	15.5465	0.509244
$933$	13.5111	0.442333
$934$	−68.5426	−2.24278
$935$	5.09764	0.166711
$936$	3.80161	0.124260
$937$	37.8727	1.23725	0.618623	−	0.785688i	$-0.287691\pi$
$937$	37.8727	1.23725	0.618623	+	0.785688i	$0.287691\pi$
$938$	−9.89855	−0.323199
$939$	−7.50900	−0.245047
$940$	−15.9156	−0.519109
$941$	31.7522	1.03509	0.517546	−	0.855655i	$-0.326845\pi$
$941$	31.7522	1.03509	0.517546	+	0.855655i	$0.326845\pi$
$942$	7.80217	0.254209
$943$	−45.2501	−1.47355
$944$	−23.2327	−0.756160
$945$	3.03796	0.0988248
$946$	1.02834	0.0334343
$947$	22.0953	0.718001	0.359001	−	0.933337i	$-0.383118\pi$
$947$	22.0953	0.718001	0.359001	+	0.933337i	$0.383118\pi$
$948$	4.70244	0.152728
$949$	49.3940	1.60340
$950$	2.02642	0.0657457
$951$	−0.975143	−0.0316212
$952$	1.00160	0.0324620
$953$	−38.1668	−1.23634	−0.618172	−	0.786043i	$-0.712127\pi$
$953$	−38.1668	−1.23634	−0.618172	+	0.786043i	$0.712127\pi$
$954$	5.61557	0.181811
$955$	19.9214	0.644643
$956$	−2.84804	−0.0921121
$957$	0.130182	0.00420820
$958$	27.3273	0.882905
$959$	−3.60554	−0.116429
$960$	−5.20469	−0.167981
$961$	−1.96508	−0.0633896
$962$	−131.836	−4.25058
$963$	−21.7973	−0.702407
$964$	−18.5617	−0.597833
$965$	10.1064	0.325335
$966$	7.72358	0.248502
$967$	−45.4834	−1.46265	−0.731323	−	0.682031i	$-0.761097\pi$
$967$	−45.4834	−1.46265	−0.731323	+	0.682031i	$0.761097\pi$
$968$	0.215549	0.00692802
$969$	3.00569	0.0965568
$970$	−15.6502	−0.502498
$971$	−39.3248	−1.26199	−0.630996	−	0.775786i	$-0.717354\pi$
$971$	−39.3248	−1.26199	−0.630996	+	0.775786i	$0.717354\pi$
$972$	−28.5019	−0.914198
$973$	−11.0946	−0.355675
$974$	78.3770	2.51136
$975$	3.92073	0.125564
$976$	50.6477	1.62119
$977$	40.8332	1.30637	0.653185	−	0.757199i	$-0.273433\pi$
$977$	40.8332	1.30637	0.653185	+	0.757199i	$0.273433\pi$
$978$	−14.0484	−0.449220
$979$	12.2736	0.392266
$980$	12.9944	0.415090
$981$	38.9865	1.24474
$982$	82.9260	2.64627
$983$	−36.7311	−1.17154	−0.585770	−	0.810477i	$-0.699208\pi$
$983$	−36.7311	−1.17154	−0.585770	+	0.810477i	$0.699208\pi$
$984$	0.810972	0.0258529
$985$	16.5644	0.527786
$986$	2.28074	0.0726334
$987$	4.06108	0.129265
$988$	−14.0064	−0.445602
$989$	3.59870	0.114432
$990$	5.37476	0.170821
$991$	17.7013	0.562302	0.281151	−	0.959664i	$-0.409284\pi$
$991$	17.7013	0.562302	0.281151	+	0.959664i	$0.409284\pi$
$992$	43.5531	1.38281
$993$	12.8989	0.409335
$994$	21.8719	0.693735
$995$	7.53251	0.238797
$996$	19.5475	0.619387
$997$	61.9413	1.96170	0.980850	−	0.194767i	$-0.0623950\pi$
$997$	61.9413	1.96170	0.980850	+	0.194767i	$0.0623950\pi$
$998$	−67.9655	−2.15141
$999$	32.6077	1.03166

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.a.e.1.5	✓	5
3.2	odd	2		9405.2.a.u.1.1		5
5.4	even	2		5225.2.a.i.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.a.e.1.5	✓	5	1.1	even	1	trivial
5225.2.a.i.1.1		5	5.4	even	2
9405.2.a.u.1.1		5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q+2.02642 q^{2} -0.589625 q^{3} +2.10637 q^{4} -1.00000 q^{5} -1.19483 q^{6} -0.911544 q^{7} +0.215549 q^{8} -2.65234 q^{9} +O(q^{10})\)	\(q+2.02642 q^{2} -0.589625 q^{3} +2.10637 q^{4} -1.00000 q^{5} -1.19483 q^{6} -0.911544 q^{7} +0.215549 q^{8} -2.65234 q^{9} -2.02642 q^{10} +1.00000 q^{11} -1.24197 q^{12} -6.64953 q^{13} -1.84717 q^{14} +0.589625 q^{15} -3.77595 q^{16} -5.09764 q^{17} -5.37476 q^{18} +1.00000 q^{19} -2.10637 q^{20} +0.537469 q^{21} +2.02642 q^{22} +7.09147 q^{23} -0.127093 q^{24} +1.00000 q^{25} -13.4747 q^{26} +3.33276 q^{27} -1.92005 q^{28} -0.220789 q^{29} +1.19483 q^{30} -5.38841 q^{31} -8.08274 q^{32} -0.589625 q^{33} -10.3300 q^{34} +0.911544 q^{35} -5.58681 q^{36} +9.78398 q^{37} +2.02642 q^{38} +3.92073 q^{39} -0.215549 q^{40} -6.38092 q^{41} +1.08914 q^{42} +0.507468 q^{43} +2.10637 q^{44} +2.65234 q^{45} +14.3703 q^{46} +7.55593 q^{47} +2.22639 q^{48} -6.16909 q^{49} +2.02642 q^{50} +3.00569 q^{51} -14.0064 q^{52} -1.04480 q^{53} +6.75357 q^{54} -1.00000 q^{55} -0.196483 q^{56} -0.589625 q^{57} -0.447410 q^{58} +6.15281 q^{59} +1.24197 q^{60} -13.4133 q^{61} -10.9192 q^{62} +2.41773 q^{63} -8.82713 q^{64} +6.64953 q^{65} -1.19483 q^{66} +5.35877 q^{67} -10.7375 q^{68} -4.18131 q^{69} +1.84717 q^{70} -11.8408 q^{71} -0.571711 q^{72} -7.42820 q^{73} +19.8264 q^{74} -0.589625 q^{75} +2.10637 q^{76} -0.911544 q^{77} +7.94503 q^{78} -3.78628 q^{79} +3.77595 q^{80} +5.99195 q^{81} -12.9304 q^{82} -15.7392 q^{83} +1.13211 q^{84} +5.09764 q^{85} +1.02834 q^{86} +0.130182 q^{87} +0.215549 q^{88} +12.2736 q^{89} +5.37476 q^{90} +6.06134 q^{91} +14.9373 q^{92} +3.17714 q^{93} +15.3115 q^{94} -1.00000 q^{95} +4.76578 q^{96} +7.72309 q^{97} -12.5012 q^{98} -2.65234 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - q^{2} - 3 q^{3} + q^{4} - 5 q^{5} - 4 q^{6} + 3 q^{7} + 3 q^{8} - 4 q^{9}+O(q^{10}) \) 5 * q - q^2 - 3 * q^3 + q^4 - 5 * q^5 - 4 * q^6 + 3 * q^7 + 3 * q^8 - 4 * q^9	\( 5 q - q^{2} - 3 q^{3} + q^{4} - 5 q^{5} - 4 q^{6} + 3 q^{7} + 3 q^{8} - 4 q^{9} + q^{10} + 5 q^{11} + 3 q^{12} - 3 q^{13} + 2 q^{14} + 3 q^{15} - 11 q^{16} - 11 q^{17} + 3 q^{18} + 5 q^{19} - q^{20} - 3 q^{21} - q^{22} + 5 q^{24} + 5 q^{25} - 8 q^{26} - 8 q^{28} - 15 q^{29} + 4 q^{30} - 9 q^{31} - 3 q^{33} - 14 q^{34} - 3 q^{35} - 7 q^{36} + 11 q^{37} - q^{38} - 10 q^{39} - 3 q^{40} - 23 q^{41} - 15 q^{42} + 9 q^{43} + q^{44} + 4 q^{45} + 8 q^{46} - 6 q^{47} + 4 q^{48} - 12 q^{49} - q^{50} - 27 q^{52} - 13 q^{53} + 9 q^{54} - 5 q^{55} - 12 q^{56} - 3 q^{57} + 17 q^{58} - 21 q^{59} - 3 q^{60} - 31 q^{61} - 18 q^{62} + 10 q^{63} - q^{64} + 3 q^{65} - 4 q^{66} + 5 q^{68} - 2 q^{70} - 28 q^{71} - 20 q^{72} - 14 q^{73} + 21 q^{74} - 3 q^{75} + q^{76} + 3 q^{77} + 13 q^{78} + 3 q^{79} + 11 q^{80} - 3 q^{81} - 18 q^{82} - 33 q^{83} + 13 q^{84} + 11 q^{85} - 20 q^{86} + 22 q^{87} + 3 q^{88} - 10 q^{89} - 3 q^{90} + 14 q^{91} + 21 q^{92} + 30 q^{93} + 14 q^{94} - 5 q^{95} - 3 q^{96} - 10 q^{97} + 8 q^{98} - 4 q^{99}+O(q^{100}) \) 5 * q - q^2 - 3 * q^3 + q^4 - 5 * q^5 - 4 * q^6 + 3 * q^7 + 3 * q^8 - 4 * q^9 + q^10 + 5 * q^11 + 3 * q^12 - 3 * q^13 + 2 * q^14 + 3 * q^15 - 11 * q^16 - 11 * q^17 + 3 * q^18 + 5 * q^19 - q^20 - 3 * q^21 - q^22 + 5 * q^24 + 5 * q^25 - 8 * q^26 - 8 * q^28 - 15 * q^29 + 4 * q^30 - 9 * q^31 - 3 * q^33 - 14 * q^34 - 3 * q^35 - 7 * q^36 + 11 * q^37 - q^38 - 10 * q^39 - 3 * q^40 - 23 * q^41 - 15 * q^42 + 9 * q^43 + q^44 + 4 * q^45 + 8 * q^46 - 6 * q^47 + 4 * q^48 - 12 * q^49 - q^50 - 27 * q^52 - 13 * q^53 + 9 * q^54 - 5 * q^55 - 12 * q^56 - 3 * q^57 + 17 * q^58 - 21 * q^59 - 3 * q^60 - 31 * q^61 - 18 * q^62 + 10 * q^63 - q^64 + 3 * q^65 - 4 * q^66 + 5 * q^68 - 2 * q^70 - 28 * q^71 - 20 * q^72 - 14 * q^73 + 21 * q^74 - 3 * q^75 + q^76 + 3 * q^77 + 13 * q^78 + 3 * q^79 + 11 * q^80 - 3 * q^81 - 18 * q^82 - 33 * q^83 + 13 * q^84 + 11 * q^85 - 20 * q^86 + 22 * q^87 + 3 * q^88 - 10 * q^89 - 3 * q^90 + 14 * q^91 + 21 * q^92 + 30 * q^93 + 14 * q^94 - 5 * q^95 - 3 * q^96 - 10 * q^97 + 8 * q^98 - 4 * q^99

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