LMFDB - Embedded newform 1441.2.a.c.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,2,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1441.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1441.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$11.5064429313$
Analytic rank:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.363851 q^{2} -2.50967 q^{3} -1.86761 q^{4} -1.53260 q^{5} +0.913144 q^{6} -1.87155 q^{7} +1.40723 q^{8} +3.29843 q^{9} +O(q^{10})$	\(q-0.363851 q^{2} -2.50967 q^{3} -1.86761 q^{4} -1.53260 q^{5} +0.913144 q^{6} -1.87155 q^{7} +1.40723 q^{8} +3.29843 q^{9} +0.557639 q^{10} +1.00000 q^{11} +4.68709 q^{12} +0.782509 q^{13} +0.680966 q^{14} +3.84632 q^{15} +3.22320 q^{16} -1.92175 q^{17} -1.20014 q^{18} -0.355415 q^{19} +2.86231 q^{20} +4.69698 q^{21} -0.363851 q^{22} +4.07369 q^{23} -3.53169 q^{24} -2.65113 q^{25} -0.284716 q^{26} -0.748957 q^{27} +3.49534 q^{28} +3.98152 q^{29} -1.39949 q^{30} +8.49526 q^{31} -3.98723 q^{32} -2.50967 q^{33} +0.699230 q^{34} +2.86835 q^{35} -6.16019 q^{36} +9.50219 q^{37} +0.129318 q^{38} -1.96384 q^{39} -2.15673 q^{40} -1.85752 q^{41} -1.70900 q^{42} -10.2252 q^{43} -1.86761 q^{44} -5.05518 q^{45} -1.48222 q^{46} +8.35242 q^{47} -8.08916 q^{48} -3.49728 q^{49} +0.964615 q^{50} +4.82295 q^{51} -1.46142 q^{52} +4.19124 q^{53} +0.272509 q^{54} -1.53260 q^{55} -2.63371 q^{56} +0.891973 q^{57} -1.44868 q^{58} -12.4807 q^{59} -7.18344 q^{60} -10.3966 q^{61} -3.09101 q^{62} -6.17319 q^{63} -4.99565 q^{64} -1.19928 q^{65} +0.913144 q^{66} +8.93269 q^{67} +3.58908 q^{68} -10.2236 q^{69} -1.04365 q^{70} -15.4054 q^{71} +4.64166 q^{72} +0.658197 q^{73} -3.45738 q^{74} +6.65345 q^{75} +0.663777 q^{76} -1.87155 q^{77} +0.714544 q^{78} -17.3125 q^{79} -4.93989 q^{80} -8.01565 q^{81} +0.675861 q^{82} -3.79108 q^{83} -8.77214 q^{84} +2.94528 q^{85} +3.72045 q^{86} -9.99229 q^{87} +1.40723 q^{88} +12.5900 q^{89} +1.83933 q^{90} -1.46451 q^{91} -7.60808 q^{92} -21.3203 q^{93} -3.03903 q^{94} +0.544710 q^{95} +10.0066 q^{96} +8.38475 q^{97} +1.27249 q^{98} +3.29843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9}+O(q^{10}) $ 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9} - 2 q^{10} + 23 q^{11} + 8 q^{12} - 24 q^{13} - 13 q^{14} - 27 q^{15} + 7 q^{16} - 7 q^{17} - 14 q^{18} - 18 q^{19} - 4 q^{20} - 29 q^{21} - 7 q^{22} - 26 q^{23} - 4 q^{24} + 18 q^{25} + 8 q^{26} - 3 q^{27} - 11 q^{28} - 45 q^{29} + 19 q^{30} - 23 q^{31} - 34 q^{32} - 3 q^{33} - 2 q^{34} - 18 q^{35} - 6 q^{36} - 2 q^{37} - 8 q^{38} - 40 q^{39} - 24 q^{40} - 23 q^{41} + 59 q^{42} - 14 q^{43} + 15 q^{44} - 18 q^{45} - 12 q^{46} - 55 q^{47} + 10 q^{48} + 11 q^{49} - 41 q^{50} - 21 q^{51} - 37 q^{52} - 10 q^{53} - 68 q^{54} - 9 q^{55} + 2 q^{56} - 18 q^{57} + 27 q^{58} - 75 q^{59} - 63 q^{60} - 55 q^{61} + 14 q^{62} - 16 q^{63} + 19 q^{64} - 25 q^{65} - 11 q^{66} + 17 q^{67} + 41 q^{68} - 22 q^{69} + 27 q^{70} - 105 q^{71} - 11 q^{72} - 3 q^{73} - 39 q^{74} + 25 q^{75} - 30 q^{76} - 12 q^{77} + 25 q^{78} - 48 q^{79} - 37 q^{80} + 3 q^{81} + 36 q^{82} + 4 q^{83} - 111 q^{84} - 30 q^{85} + 22 q^{86} + 5 q^{87} - 21 q^{88} - 39 q^{89} + 100 q^{90} - 22 q^{91} - 30 q^{92} - 5 q^{93} + 11 q^{94} - 88 q^{95} + 13 q^{96} + 24 q^{97} - 91 q^{98} + 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9 - 2 * q^10 + 23 * q^11 + 8 * q^12 - 24 * q^13 - 13 * q^14 - 27 * q^15 + 7 * q^16 - 7 * q^17 - 14 * q^18 - 18 * q^19 - 4 * q^20 - 29 * q^21 - 7 * q^22 - 26 * q^23 - 4 * q^24 + 18 * q^25 + 8 * q^26 - 3 * q^27 - 11 * q^28 - 45 * q^29 + 19 * q^30 - 23 * q^31 - 34 * q^32 - 3 * q^33 - 2 * q^34 - 18 * q^35 - 6 * q^36 - 2 * q^37 - 8 * q^38 - 40 * q^39 - 24 * q^40 - 23 * q^41 + 59 * q^42 - 14 * q^43 + 15 * q^44 - 18 * q^45 - 12 * q^46 - 55 * q^47 + 10 * q^48 + 11 * q^49 - 41 * q^50 - 21 * q^51 - 37 * q^52 - 10 * q^53 - 68 * q^54 - 9 * q^55 + 2 * q^56 - 18 * q^57 + 27 * q^58 - 75 * q^59 - 63 * q^60 - 55 * q^61 + 14 * q^62 - 16 * q^63 + 19 * q^64 - 25 * q^65 - 11 * q^66 + 17 * q^67 + 41 * q^68 - 22 * q^69 + 27 * q^70 - 105 * q^71 - 11 * q^72 - 3 * q^73 - 39 * q^74 + 25 * q^75 - 30 * q^76 - 12 * q^77 + 25 * q^78 - 48 * q^79 - 37 * q^80 + 3 * q^81 + 36 * q^82 + 4 * q^83 - 111 * q^84 - 30 * q^85 + 22 * q^86 + 5 * q^87 - 21 * q^88 - 39 * q^89 + 100 * q^90 - 22 * q^91 - 30 * q^92 - 5 * q^93 + 11 * q^94 - 88 * q^95 + 13 * q^96 + 24 * q^97 - 91 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.363851	−0.257281	−0.128641	−	0.991691i	$-0.541061\pi$
$2$	−0.363851	−0.257281	−0.128641	+	0.991691i	$0.541061\pi$
$3$	−2.50967	−1.44896	−0.724478	−	0.689297i	$-0.757919\pi$
$3$	−2.50967	−1.44896	−0.724478	+	0.689297i	$0.757919\pi$
$4$	−1.86761	−0.933806
$5$	−1.53260	−0.685401	−0.342700	−	0.939445i	$-0.611342\pi$
$5$	−1.53260	−0.685401	−0.342700	+	0.939445i	$0.611342\pi$
$6$	0.913144	0.372790
$7$	−1.87155	−0.707381	−0.353691	−	0.935363i	$-0.615073\pi$
$7$	−1.87155	−0.707381	−0.353691	+	0.935363i	$0.615073\pi$
$8$	1.40723	0.497532
$9$	3.29843	1.09948
$10$	0.557639	0.176341
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	4.68709	1.35305
$13$	0.782509	0.217029	0.108514	−	0.994095i	$-0.465391\pi$
$13$	0.782509	0.217029	0.108514	+	0.994095i	$0.465391\pi$
$14$	0.680966	0.181996
$15$	3.84632	0.993117
$16$	3.22320	0.805801
$17$	−1.92175	−0.466092	−0.233046	−	0.972466i	$-0.574869\pi$
$17$	−1.92175	−0.466092	−0.233046	+	0.972466i	$0.574869\pi$
$18$	−1.20014	−0.282875
$19$	−0.355415	−0.0815377	−0.0407689	−	0.999169i	$-0.512981\pi$
$19$	−0.355415	−0.0815377	−0.0407689	+	0.999169i	$0.512981\pi$
$20$	2.86231	0.640032
$21$	4.69698	1.02496
$22$	−0.363851	−0.0775732
$23$	4.07369	0.849424	0.424712	−	0.905329i	$-0.360375\pi$
$23$	4.07369	0.849424	0.424712	+	0.905329i	$0.360375\pi$
$24$	−3.53169	−0.720903
$25$	−2.65113	−0.530226
$26$	−0.284716	−0.0558375
$27$	−0.748957	−0.144137
$28$	3.49534	0.660557
$29$	3.98152	0.739350	0.369675	−	0.929161i	$-0.379469\pi$
$29$	3.98152	0.739350	0.369675	+	0.929161i	$0.379469\pi$
$30$	−1.39949	−0.255510
$31$	8.49526	1.52579	0.762897	−	0.646520i	$-0.223776\pi$
$31$	8.49526	1.52579	0.762897	+	0.646520i	$0.223776\pi$
$32$	−3.98723	−0.704850
$33$	−2.50967	−0.436877
$34$	0.699230	0.119917
$35$	2.86835	0.484840
$36$	−6.16019	−1.02670
$37$	9.50219	1.56215	0.781075	−	0.624437i	$-0.214671\pi$
$37$	9.50219	1.56215	0.781075	+	0.624437i	$0.214671\pi$
$38$	0.129318	0.0209781
$39$	−1.96384	−0.314466
$40$	−2.15673	−0.341009
$41$	−1.85752	−0.290096	−0.145048	−	0.989425i	$-0.546334\pi$
$41$	−1.85752	−0.290096	−0.145048	+	0.989425i	$0.546334\pi$
$42$	−1.70900	−0.263704
$43$	−10.2252	−1.55933	−0.779666	−	0.626196i	$-0.784611\pi$
$43$	−10.2252	−1.55933	−0.779666	+	0.626196i	$0.784611\pi$
$44$	−1.86761	−0.281553
$45$	−5.05518	−0.753582
$46$	−1.48222	−0.218541
$47$	8.35242	1.21833	0.609163	−	0.793045i	$-0.291506\pi$
$47$	8.35242	1.21833	0.609163	+	0.793045i	$0.291506\pi$
$48$	−8.08916	−1.16757
$49$	−3.49728	−0.499612
$50$	0.964615	0.136417
$51$	4.82295	0.675348
$52$	−1.46142	−0.202663
$53$	4.19124	0.575712	0.287856	−	0.957674i	$-0.407058\pi$
$53$	4.19124	0.575712	0.287856	+	0.957674i	$0.407058\pi$
$54$	0.272509	0.0370837
$55$	−1.53260	−0.206656
$56$	−2.63371	−0.351945
$57$	0.891973	0.118145
$58$	−1.44868	−0.190221
$59$	−12.4807	−1.62484	−0.812422	−	0.583070i	$-0.801851\pi$
$59$	−12.4807	−1.62484	−0.812422	+	0.583070i	$0.801851\pi$
$60$	−7.18344	−0.927378
$61$	−10.3966	−1.33115	−0.665575	−	0.746331i	$-0.731814\pi$
$61$	−10.3966	−1.33115	−0.665575	+	0.746331i	$0.731814\pi$
$62$	−3.09101	−0.392558
$63$	−6.17319	−0.777749
$64$	−4.99565	−0.624456
$65$	−1.19928	−0.148752
$66$	0.913144	0.112400
$67$	8.93269	1.09130	0.545651	−	0.838013i	$-0.316283\pi$
$67$	8.93269	1.09130	0.545651	+	0.838013i	$0.316283\pi$
$68$	3.58908	0.435240
$69$	−10.2236	−1.23078
$70$	−1.04365	−0.124740
$71$	−15.4054	−1.82829	−0.914144	−	0.405390i	$-0.867136\pi$
$71$	−15.4054	−1.82829	−0.914144	+	0.405390i	$0.867136\pi$
$72$	4.64166	0.547025
$73$	0.658197	0.0770361	0.0385181	−	0.999258i	$-0.487736\pi$
$73$	0.658197	0.0770361	0.0385181	+	0.999258i	$0.487736\pi$
$74$	−3.45738	−0.401912
$75$	6.65345	0.768274
$76$	0.663777	0.0761405
$77$	−1.87155	−0.213283
$78$	0.714544	0.0809061
$79$	−17.3125	−1.94780	−0.973902	−	0.226970i	$-0.927118\pi$
$79$	−17.3125	−1.94780	−0.973902	+	0.226970i	$0.927118\pi$
$80$	−4.93989	−0.552296
$81$	−8.01565	−0.890628
$82$	0.675861	0.0746364
$83$	−3.79108	−0.416125	−0.208063	−	0.978116i	$-0.566716\pi$
$83$	−3.79108	−0.416125	−0.208063	+	0.978116i	$0.566716\pi$
$84$	−8.77214	−0.957119
$85$	2.94528	0.319460
$86$	3.72045	0.401187
$87$	−9.99229	−1.07129
$88$	1.40723	0.150012
$89$	12.5900	1.33454	0.667269	−	0.744817i	$-0.267463\pi$
$89$	12.5900	1.33454	0.667269	+	0.744817i	$0.267463\pi$
$90$	1.83933	0.193883
$91$	−1.46451	−0.153522
$92$	−7.60808	−0.793197
$93$	−21.3203	−2.21081
$94$	−3.03903	−0.313452
$95$	0.544710	0.0558861
$96$	10.0066	1.02130
$97$	8.38475	0.851342	0.425671	−	0.904878i	$-0.360038\pi$
$97$	8.38475	0.851342	0.425671	+	0.904878i	$0.360038\pi$
$98$	1.27249	0.128541
$99$	3.29843	0.331505
$100$	4.95128	0.495128
$101$	15.9746	1.58954	0.794768	−	0.606914i	$-0.207593\pi$
$101$	15.9746	1.58954	0.794768	+	0.606914i	$0.207593\pi$
$102$	−1.75483	−0.173754
$103$	15.3652	1.51398	0.756990	−	0.653427i	$-0.226669\pi$
$103$	15.3652	1.51398	0.756990	+	0.653427i	$0.226669\pi$
$104$	1.10117	0.107979
$105$	−7.19860	−0.702512
$106$	−1.52499	−0.148120
$107$	−15.1130	−1.46102	−0.730512	−	0.682899i	$-0.760719\pi$
$107$	−15.1130	−1.46102	−0.730512	+	0.682899i	$0.760719\pi$
$108$	1.39876	0.134596
$109$	8.33058	0.797925	0.398962	−	0.916967i	$-0.369370\pi$
$109$	8.33058	0.797925	0.398962	+	0.916967i	$0.369370\pi$
$110$	0.557639	0.0531688
$111$	−23.8473	−2.26349
$112$	−6.03240	−0.570008
$113$	−11.0169	−1.03638	−0.518192	−	0.855264i	$-0.673395\pi$
$113$	−11.0169	−1.03638	−0.518192	+	0.855264i	$0.673395\pi$
$114$	−0.324545	−0.0303964
$115$	−6.24336	−0.582196
$116$	−7.43594	−0.690409
$117$	2.58105	0.238618
$118$	4.54110	0.418042
$119$	3.59666	0.329705
$120$	5.41268	0.494108
$121$	1.00000	0.0909091
$122$	3.78282	0.342480
$123$	4.66177	0.420337
$124$	−15.8659	−1.42480
$125$	11.7261	1.04882
$126$	2.24612	0.200100
$127$	−4.38013	−0.388673	−0.194337	−	0.980935i	$-0.562255\pi$
$127$	−4.38013	−0.388673	−0.194337	+	0.980935i	$0.562255\pi$
$128$	9.79213	0.865511
$129$	25.6619	2.25940
$130$	0.436357	0.0382711
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	4.68709	0.407958
$133$	0.665178	0.0576783
$134$	−3.25017	−0.280772
$135$	1.14785	0.0987916
$136$	−2.70435	−0.231896
$137$	−3.47159	−0.296598	−0.148299	−	0.988943i	$-0.547380\pi$
$137$	−3.47159	−0.296598	−0.148299	+	0.988943i	$0.547380\pi$
$138$	3.71987	0.316656
$139$	−21.3011	−1.80674	−0.903368	−	0.428865i	$-0.858914\pi$
$139$	−21.3011	−1.80674	−0.903368	+	0.428865i	$0.858914\pi$
$140$	−5.35697	−0.452746
$141$	−20.9618	−1.76530
$142$	5.60528	0.470384
$143$	0.782509	0.0654367
$144$	10.6315	0.885959
$145$	−6.10209	−0.506751
$146$	−0.239486	−0.0198200
$147$	8.77702	0.723916
$148$	−17.7464	−1.45875
$149$	16.6835	1.36676	0.683382	−	0.730061i	$-0.260508\pi$
$149$	16.6835	1.36676	0.683382	+	0.730061i	$0.260508\pi$
$150$	−2.42086	−0.197663
$151$	1.10342	0.0897946	0.0448973	−	0.998992i	$-0.485704\pi$
$151$	1.10342	0.0897946	0.0448973	+	0.998992i	$0.485704\pi$
$152$	−0.500152	−0.0405677
$153$	−6.33875	−0.512458
$154$	0.680966	0.0548738
$155$	−13.0199	−1.04578
$156$	3.66769	0.293650
$157$	9.34268	0.745627	0.372814	−	0.927906i	$-0.378393\pi$
$157$	9.34268	0.745627	0.372814	+	0.927906i	$0.378393\pi$
$158$	6.29915	0.501134
$159$	−10.5186	−0.834181
$160$	6.11084	0.483105
$161$	−7.62414	−0.600866
$162$	2.91650	0.229142
$163$	2.54821	0.199592	0.0997958	−	0.995008i	$-0.468181\pi$
$163$	2.54821	0.199592	0.0997958	+	0.995008i	$0.468181\pi$
$164$	3.46913	0.270894
$165$	3.84632	0.299436
$166$	1.37939	0.107061
$167$	19.0994	1.47796	0.738980	−	0.673728i	$-0.235308\pi$
$167$	19.0994	1.47796	0.738980	+	0.673728i	$0.235308\pi$
$168$	6.60975	0.509953
$169$	−12.3877	−0.952898
$170$	−1.07164	−0.0821911
$171$	−1.17231	−0.0896488
$172$	19.0967	1.45611
$173$	5.92928	0.450795	0.225398	−	0.974267i	$-0.427632\pi$
$173$	5.92928	0.450795	0.225398	+	0.974267i	$0.427632\pi$
$174$	3.63570	0.275622
$175$	4.96173	0.375071
$176$	3.22320	0.242958
$177$	31.3223	2.35433
$178$	−4.58089	−0.343352
$179$	−8.47592	−0.633520	−0.316760	−	0.948506i	$-0.602595\pi$
$179$	−8.47592	−0.633520	−0.316760	+	0.948506i	$0.602595\pi$
$180$	9.44112	0.703700
$181$	12.8675	0.956436	0.478218	−	0.878241i	$-0.341283\pi$
$181$	12.8675	0.956436	0.478218	+	0.878241i	$0.341283\pi$
$182$	0.532862	0.0394984
$183$	26.0920	1.92878
$184$	5.73264	0.422616
$185$	−14.5631	−1.07070
$186$	7.75740	0.568800
$187$	−1.92175	−0.140532
$188$	−15.5991	−1.13768
$189$	1.40171	0.101960
$190$	−0.198193	−0.0143784
$191$	−23.9381	−1.73210	−0.866049	−	0.499959i	$-0.833348\pi$
$191$	−23.9381	−1.73210	−0.866049	+	0.499959i	$0.833348\pi$
$192$	12.5374	0.904810
$193$	7.45287	0.536470	0.268235	−	0.963354i	$-0.413560\pi$
$193$	7.45287	0.536470	0.268235	+	0.963354i	$0.413560\pi$
$194$	−3.05080	−0.219034
$195$	3.00978	0.215535
$196$	6.53157	0.466541
$197$	−18.5075	−1.31861	−0.659303	−	0.751877i	$-0.729149\pi$
$197$	−18.5075	−1.31861	−0.659303	+	0.751877i	$0.729149\pi$
$198$	−1.20014	−0.0852899
$199$	−18.1803	−1.28877	−0.644383	−	0.764703i	$-0.722886\pi$
$199$	−18.1803	−1.28877	−0.644383	+	0.764703i	$0.722886\pi$
$200$	−3.73076	−0.263804
$201$	−22.4181	−1.58125
$202$	−5.81238	−0.408958
$203$	−7.45163	−0.523002
$204$	−9.00740	−0.630644
$205$	2.84685	0.198832
$206$	−5.59065	−0.389519
$207$	13.4368	0.933921
$208$	2.52218	0.174882
$209$	−0.355415	−0.0245846
$210$	2.61922	0.180743
$211$	−5.03567	−0.346670	−0.173335	−	0.984863i	$-0.555454\pi$
$211$	−5.03567	−0.346670	−0.173335	+	0.984863i	$0.555454\pi$
$212$	−7.82762	−0.537603
$213$	38.6625	2.64911
$214$	5.49886	0.375894
$215$	15.6712	1.06877
$216$	−1.05396	−0.0717128
$217$	−15.8993	−1.07932
$218$	−3.03109	−0.205291
$219$	−1.65186	−0.111622
$220$	2.86231	0.192977
$221$	−1.50379	−0.101156
$222$	8.67687	0.582354
$223$	3.64555	0.244124	0.122062	−	0.992522i	$-0.461049\pi$
$223$	3.64555	0.244124	0.122062	+	0.992522i	$0.461049\pi$
$224$	7.46232	0.498597
$225$	−8.74456	−0.582970
$226$	4.00851	0.266642
$227$	−14.2350	−0.944807	−0.472404	−	0.881382i	$-0.656614\pi$
$227$	−14.2350	−0.944807	−0.472404	+	0.881382i	$0.656614\pi$
$228$	−1.66586	−0.110324
$229$	9.88332	0.653108	0.326554	−	0.945179i	$-0.394112\pi$
$229$	9.88332	0.653108	0.326554	+	0.945179i	$0.394112\pi$
$230$	2.27165	0.149788
$231$	4.69698	0.309038
$232$	5.60293	0.367850
$233$	−27.6009	−1.80820	−0.904099	−	0.427324i	$-0.859456\pi$
$233$	−27.6009	−1.80820	−0.904099	+	0.427324i	$0.859456\pi$
$234$	−0.939117	−0.0613920
$235$	−12.8009	−0.835042
$236$	23.3090	1.51729
$237$	43.4485	2.82228
$238$	−1.30865	−0.0848269
$239$	4.56700	0.295415	0.147707	−	0.989031i	$-0.452811\pi$
$239$	4.56700	0.295415	0.147707	+	0.989031i	$0.452811\pi$
$240$	12.3975	0.800254
$241$	14.1495	0.911452	0.455726	−	0.890120i	$-0.349380\pi$
$241$	14.1495	0.911452	0.455726	+	0.890120i	$0.349380\pi$
$242$	−0.363851	−0.0233892
$243$	22.3635	1.43462
$244$	19.4168	1.24304
$245$	5.35995	0.342435
$246$	−1.69619	−0.108145
$247$	−0.278115	−0.0176960
$248$	11.9548	0.759132
$249$	9.51435	0.602948
$250$	−4.26657	−0.269841
$251$	−1.70978	−0.107920	−0.0539601	−	0.998543i	$-0.517184\pi$
$251$	−1.70978	−0.107920	−0.0539601	+	0.998543i	$0.517184\pi$
$252$	11.5291	0.726267
$253$	4.07369	0.256111
$254$	1.59371	0.0999984
$255$	−7.39167	−0.462884
$256$	6.42842	0.401776
$257$	−9.71521	−0.606018	−0.303009	−	0.952988i	$-0.597991\pi$
$257$	−9.71521	−0.606018	−0.303009	+	0.952988i	$0.597991\pi$
$258$	−9.33710	−0.581302
$259$	−17.7839	−1.10504
$260$	2.23978	0.138905
$261$	13.1328	0.812897
$262$	−0.363851	−0.0224788
$263$	−17.3525	−1.07000	−0.535000	−	0.844852i	$-0.679688\pi$
$263$	−17.3525	−1.07000	−0.535000	+	0.844852i	$0.679688\pi$
$264$	−3.53169	−0.217360
$265$	−6.42351	−0.394593
$266$	−0.242026	−0.0148395
$267$	−31.5967	−1.93369
$268$	−16.6828	−1.01906
$269$	−13.1505	−0.801797	−0.400899	−	0.916122i	$-0.631302\pi$
$269$	−13.1505	−0.801797	−0.400899	+	0.916122i	$0.631302\pi$
$270$	−0.417648	−0.0254172
$271$	3.20456	0.194663	0.0973315	−	0.995252i	$-0.468969\pi$
$271$	3.20456	0.194663	0.0973315	+	0.995252i	$0.468969\pi$
$272$	−6.19418	−0.375578
$273$	3.67543	0.222447
$274$	1.26314	0.0763091
$275$	−2.65113	−0.159869
$276$	19.0938	1.14931
$277$	27.0625	1.62603	0.813014	−	0.582244i	$-0.197825\pi$
$277$	27.0625	1.62603	0.813014	+	0.582244i	$0.197825\pi$
$278$	7.75043	0.464840
$279$	28.0210	1.67757
$280$	4.03644	0.241223
$281$	28.1938	1.68190	0.840950	−	0.541113i	$-0.181997\pi$
$281$	28.1938	1.68190	0.840950	+	0.541113i	$0.181997\pi$
$282$	7.62696	0.454179
$283$	24.4551	1.45370	0.726852	−	0.686794i	$-0.240982\pi$
$283$	24.4551	1.45370	0.726852	+	0.686794i	$0.240982\pi$
$284$	28.7714	1.70727
$285$	−1.36704	−0.0809765
$286$	−0.284716	−0.0168356
$287$	3.47646	0.205209
$288$	−13.1516	−0.774966
$289$	−13.3069	−0.782758
$290$	2.22025	0.130378
$291$	−21.0429	−1.23356
$292$	−1.22926	−0.0719368
$293$	−27.9425	−1.63242	−0.816210	−	0.577755i	$-0.803929\pi$
$293$	−27.9425	−1.63242	−0.816210	+	0.577755i	$0.803929\pi$
$294$	−3.19353	−0.186250
$295$	19.1279	1.11367
$296$	13.3718	0.777221
$297$	−0.748957	−0.0434589
$298$	−6.07030	−0.351643
$299$	3.18770	0.184350
$300$	−12.4261	−0.717419
$301$	19.1371	1.10304
$302$	−0.401478	−0.0231025
$303$	−40.0910	−2.30317
$304$	−1.14557	−0.0657032
$305$	15.9339	0.912371
$306$	2.30636	0.131846
$307$	−30.9660	−1.76732	−0.883662	−	0.468126i	$-0.844929\pi$
$307$	−30.9660	−1.76732	−0.883662	+	0.468126i	$0.844929\pi$
$308$	3.49534	0.199165
$309$	−38.5616	−2.19369
$310$	4.73729	0.269060
$311$	−33.6435	−1.90775	−0.953875	−	0.300205i	$-0.902945\pi$
$311$	−33.6435	−1.90775	−0.953875	+	0.300205i	$0.902945\pi$
$312$	−2.76358	−0.156457
$313$	−17.0906	−0.966016	−0.483008	−	0.875616i	$-0.660456\pi$
$313$	−17.0906	−0.966016	−0.483008	+	0.875616i	$0.660456\pi$
$314$	−3.39934	−0.191836
$315$	9.46105	0.533070
$316$	32.3330	1.81887
$317$	10.9120	0.612880	0.306440	−	0.951890i	$-0.400862\pi$
$317$	10.9120	0.612880	0.306440	+	0.951890i	$0.400862\pi$
$318$	3.82721	0.214619
$319$	3.98152	0.222922
$320$	7.65634	0.428003
$321$	37.9285	2.11696
$322$	2.77405	0.154592
$323$	0.683018	0.0380041
$324$	14.9701	0.831674
$325$	−2.07453	−0.115074
$326$	−0.927170	−0.0513512
$327$	−20.9070	−1.15616
$328$	−2.61397	−0.144332
$329$	−15.6320	−0.861820
$330$	−1.39949	−0.0770393
$331$	24.7256	1.35904	0.679521	−	0.733656i	$-0.262188\pi$
$331$	24.7256	1.35904	0.679521	+	0.733656i	$0.262188\pi$
$332$	7.08027	0.388580
$333$	31.3423	1.71755
$334$	−6.94935	−0.380251
$335$	−13.6903	−0.747979
$336$	15.1393	0.825917
$337$	−12.1853	−0.663773	−0.331887	−	0.943319i	$-0.607685\pi$
$337$	−12.1853	−0.663773	−0.331887	+	0.943319i	$0.607685\pi$
$338$	4.50727	0.245163
$339$	27.6488	1.50168
$340$	−5.50064	−0.298314
$341$	8.49526	0.460044
$342$	0.426546	0.0230650
$343$	19.6462	1.06080
$344$	−14.3893	−0.775818
$345$	15.6687	0.843577
$346$	−2.15737	−0.115981
$347$	0.343303	0.0184295	0.00921474	−	0.999958i	$-0.497067\pi$
$347$	0.343303	0.0184295	0.00921474	+	0.999958i	$0.497067\pi$
$348$	18.6617	1.00037
$349$	−14.7494	−0.789517	−0.394759	−	0.918785i	$-0.629172\pi$
$349$	−14.7494	−0.789517	−0.394759	+	0.918785i	$0.629172\pi$
$350$	−1.80533	−0.0964989
$351$	−0.586066	−0.0312819
$352$	−3.98723	−0.212520
$353$	−5.16774	−0.275051	−0.137525	−	0.990498i	$-0.543915\pi$
$353$	−5.16774	−0.275051	−0.137525	+	0.990498i	$0.543915\pi$
$354$	−11.3966	−0.605725
$355$	23.6104	1.25311
$356$	−23.5133	−1.24620
$357$	−9.02641	−0.477728
$358$	3.08397	0.162993
$359$	−21.2957	−1.12394	−0.561972	−	0.827156i	$-0.689957\pi$
$359$	−21.2957	−1.12394	−0.561972	+	0.827156i	$0.689957\pi$
$360$	−7.11382	−0.374931
$361$	−18.8737	−0.993352
$362$	−4.68186	−0.246073
$363$	−2.50967	−0.131723
$364$	2.73513	0.143360
$365$	−1.00875	−0.0528006
$366$	−9.49361	−0.496239
$367$	−1.45877	−0.0761472	−0.0380736	−	0.999275i	$-0.512122\pi$
$367$	−1.45877	−0.0761472	−0.0380736	+	0.999275i	$0.512122\pi$
$368$	13.1303	0.684466
$369$	−6.12691	−0.318954
$370$	5.29879	0.275471
$371$	−7.84414	−0.407248
$372$	39.8180	2.06447
$373$	5.61678	0.290826	0.145413	−	0.989371i	$-0.453549\pi$
$373$	5.61678	0.290826	0.145413	+	0.989371i	$0.453549\pi$
$374$	0.699230	0.0361563
$375$	−29.4287	−1.51969
$376$	11.7538	0.606156
$377$	3.11557	0.160460
$378$	−0.510015	−0.0262323
$379$	−12.5510	−0.644700	−0.322350	−	0.946621i	$-0.604473\pi$
$379$	−12.5510	−0.644700	−0.322350	+	0.946621i	$0.604473\pi$
$380$	−1.01731	−0.0521867
$381$	10.9927	0.563171
$382$	8.70988	0.445636
$383$	10.8252	0.553143	0.276572	−	0.960993i	$-0.410802\pi$
$383$	10.8252	0.553143	0.276572	+	0.960993i	$0.410802\pi$
$384$	−24.5750	−1.25409
$385$	2.86835	0.146185
$386$	−2.71173	−0.138024
$387$	−33.7272	−1.71445
$388$	−15.6595	−0.794989
$389$	−21.9830	−1.11458	−0.557291	−	0.830317i	$-0.688159\pi$
$389$	−21.9830	−1.11458	−0.557291	+	0.830317i	$0.688159\pi$
$390$	−1.09511	−0.0554531
$391$	−7.82861	−0.395910
$392$	−4.92150	−0.248573
$393$	−2.50967	−0.126596
$394$	6.73398	0.339253
$395$	26.5331	1.33503
$396$	−6.16019	−0.309561
$397$	−26.2828	−1.31909	−0.659547	−	0.751663i	$-0.729252\pi$
$397$	−26.2828	−1.31909	−0.659547	+	0.751663i	$0.729252\pi$
$398$	6.61491	0.331576
$399$	−1.66938	−0.0835733
$400$	−8.54512	−0.427256
$401$	7.47677	0.373372	0.186686	−	0.982420i	$-0.440225\pi$
$401$	7.47677	0.373372	0.186686	+	0.982420i	$0.440225\pi$
$402$	8.15683	0.406826
$403$	6.64762	0.331141
$404$	−29.8344	−1.48432
$405$	12.2848	0.610437
$406$	2.71128	0.134559
$407$	9.50219	0.471006
$408$	6.78702	0.336007
$409$	31.2104	1.54325	0.771627	−	0.636075i	$-0.219443\pi$
$409$	31.2104	1.54325	0.771627	+	0.636075i	$0.219443\pi$
$410$	−1.03583	−0.0511559
$411$	8.71254	0.429758
$412$	−28.6963	−1.41376
$413$	23.3582	1.14938
$414$	−4.88899	−0.240281
$415$	5.81022	0.285213
$416$	−3.12004	−0.152973
$417$	53.4587	2.61788
$418$	0.129318	0.00632515
$419$	−20.5930	−1.00603	−0.503016	−	0.864277i	$-0.667776\pi$
$419$	−20.5930	−1.00603	−0.503016	+	0.864277i	$0.667776\pi$
$420$	13.4442	0.656010
$421$	31.6967	1.54480	0.772401	−	0.635135i	$-0.219056\pi$
$421$	31.6967	1.54480	0.772401	+	0.635135i	$0.219056\pi$
$422$	1.83223	0.0891918
$423$	27.5499	1.33952
$424$	5.89806	0.286435
$425$	5.09480	0.247134
$426$	−14.0674	−0.681567
$427$	19.4578	0.941630
$428$	28.2251	1.36431
$429$	−1.96384	−0.0948149
$430$	−5.70198	−0.274974
$431$	−18.1224	−0.872923	−0.436461	−	0.899723i	$-0.643768\pi$
$431$	−18.1224	−0.872923	−0.436461	+	0.899723i	$0.643768\pi$
$432$	−2.41404	−0.116146
$433$	−36.2976	−1.74435	−0.872176	−	0.489192i	$-0.837292\pi$
$433$	−36.2976	−1.74435	−0.872176	+	0.489192i	$0.837292\pi$
$434$	5.78499	0.277688
$435$	15.3142	0.734260
$436$	−15.5583	−0.745107
$437$	−1.44785	−0.0692601
$438$	0.601029	0.0287183
$439$	−11.2670	−0.537746	−0.268873	−	0.963176i	$-0.586651\pi$
$439$	−11.2670	−0.537746	−0.268873	+	0.963176i	$0.586651\pi$
$440$	−2.15673	−0.102818
$441$	−11.5355	−0.549312
$442$	0.547153	0.0260254
$443$	−4.12917	−0.196183	−0.0980914	−	0.995177i	$-0.531274\pi$
$443$	−4.12917	−0.196183	−0.0980914	+	0.995177i	$0.531274\pi$
$444$	44.5376	2.11366
$445$	−19.2955	−0.914694
$446$	−1.32644	−0.0628085
$447$	−41.8700	−1.98038
$448$	9.34962	0.441728
$449$	−17.5329	−0.827427	−0.413713	−	0.910407i	$-0.635768\pi$
$449$	−17.5329	−0.827427	−0.413713	+	0.910407i	$0.635768\pi$
$450$	3.18171	0.149987
$451$	−1.85752	−0.0874674
$452$	20.5753	0.967782
$453$	−2.76920	−0.130109
$454$	5.17940	0.243081
$455$	2.24451	0.105224
$456$	1.25521	0.0587808
$457$	−13.5356	−0.633168	−0.316584	−	0.948565i	$-0.602536\pi$
$457$	−13.5356	−0.633168	−0.316584	+	0.948565i	$0.602536\pi$
$458$	−3.59605	−0.168033
$459$	1.43931	0.0671811
$460$	11.6602	0.543658
$461$	−12.2772	−0.571807	−0.285904	−	0.958258i	$-0.592294\pi$
$461$	−12.2772	−0.571807	−0.285904	+	0.958258i	$0.592294\pi$
$462$	−1.70900	−0.0795098
$463$	−18.0224	−0.837574	−0.418787	−	0.908085i	$-0.637545\pi$
$463$	−18.0224	−0.837574	−0.418787	+	0.908085i	$0.637545\pi$
$464$	12.8332	0.595768
$465$	32.6755	1.51529
$466$	10.0426	0.465215
$467$	10.7293	0.496491	0.248246	−	0.968697i	$-0.420146\pi$
$467$	10.7293	0.496491	0.248246	+	0.968697i	$0.420146\pi$
$468$	−4.82040	−0.222823
$469$	−16.7180	−0.771966
$470$	4.65763	0.214841
$471$	−23.4470	−1.08038
$472$	−17.5632	−0.808412
$473$	−10.2252	−0.470156
$474$	−15.8088	−0.726121
$475$	0.942250	0.0432334
$476$	−6.71716	−0.307881
$477$	13.8245	0.632981
$478$	−1.66171	−0.0760048
$479$	−37.1072	−1.69547	−0.847736	−	0.530419i	$-0.822035\pi$
$479$	−37.1072	−1.69547	−0.847736	+	0.530419i	$0.822035\pi$
$480$	−15.3362	−0.699998
$481$	7.43555	0.339032
$482$	−5.14832	−0.234500
$483$	19.1341	0.870629
$484$	−1.86761	−0.0848915
$485$	−12.8505	−0.583511
$486$	−8.13697	−0.369101
$487$	29.4136	1.33286	0.666428	−	0.745570i	$-0.267822\pi$
$487$	29.4136	1.33286	0.666428	+	0.745570i	$0.267822\pi$
$488$	−14.6305	−0.662290
$489$	−6.39517	−0.289200
$490$	−1.95022	−0.0881020
$491$	−10.2167	−0.461074	−0.230537	−	0.973064i	$-0.574048\pi$
$491$	−10.2167	−0.461074	−0.230537	+	0.973064i	$0.574048\pi$
$492$	−8.70637	−0.392514
$493$	−7.65148	−0.344605
$494$	0.101192	0.00455286
$495$	−5.05518	−0.227214
$496$	27.3819	1.22949
$497$	28.8321	1.29330
$498$	−3.46180	−0.155127
$499$	35.6446	1.59567	0.797836	−	0.602875i	$-0.205978\pi$
$499$	35.6446	1.59567	0.797836	+	0.602875i	$0.205978\pi$
$500$	−21.8999	−0.979393
$501$	−47.9332	−2.14150
$502$	0.622104	0.0277659
$503$	−22.7552	−1.01461	−0.507303	−	0.861768i	$-0.669357\pi$
$503$	−22.7552	−1.01461	−0.507303	+	0.861768i	$0.669357\pi$
$504$	−8.68712	−0.386955
$505$	−24.4828	−1.08947
$506$	−1.48222	−0.0658926
$507$	31.0890	1.38071
$508$	8.18038	0.362946
$509$	21.1543	0.937650	0.468825	−	0.883291i	$-0.344678\pi$
$509$	21.1543	0.937650	0.468825	+	0.883291i	$0.344678\pi$
$510$	2.68946	0.119091
$511$	−1.23185	−0.0544939
$512$	−21.9233	−0.968880
$513$	0.266191	0.0117526
$514$	3.53489	0.155917
$515$	−23.5488	−1.03768
$516$	−47.9265	−2.10985
$517$	8.35242	0.367339
$518$	6.47067	0.284305
$519$	−14.8805	−0.653183
$520$	−1.68766	−0.0740088
$521$	23.2593	1.01901	0.509503	−	0.860469i	$-0.329829\pi$
$521$	23.2593	1.01901	0.509503	+	0.860469i	$0.329829\pi$
$522$	−4.77836	−0.209143
$523$	36.7511	1.60701	0.803506	−	0.595297i	$-0.202965\pi$
$523$	36.7511	1.60701	0.803506	+	0.595297i	$0.202965\pi$
$524$	−1.86761	−0.0815870
$525$	−12.4523	−0.543462
$526$	6.31371	0.275291
$527$	−16.3258	−0.711161
$528$	−8.08916	−0.352036
$529$	−6.40502	−0.278479
$530$	2.33720	0.101522
$531$	−41.1666	−1.78648
$532$	−1.24230	−0.0538603
$533$	−1.45353	−0.0629593
$534$	11.4965	0.497502
$535$	23.1622	1.00139
$536$	12.5704	0.542958
$537$	21.2717	0.917943
$538$	4.78480	0.206288
$539$	−3.49728	−0.150639
$540$	−2.14375	−0.0922522
$541$	−9.88409	−0.424950	−0.212475	−	0.977166i	$-0.568152\pi$
$541$	−9.88409	−0.424950	−0.212475	+	0.977166i	$0.568152\pi$
$542$	−1.16598	−0.0500831
$543$	−32.2932	−1.38583
$544$	7.66246	0.328525
$545$	−12.7675	−0.546899
$546$	−1.33731	−0.0572315
$547$	5.63135	0.240779	0.120390	−	0.992727i	$-0.461586\pi$
$547$	5.63135	0.240779	0.120390	+	0.992727i	$0.461586\pi$
$548$	6.48359	0.276965
$549$	−34.2925	−1.46357
$550$	0.964615	0.0411313
$551$	−1.41509	−0.0602849
$552$	−14.3870	−0.612352
$553$	32.4012	1.37784
$554$	−9.84671	−0.418347
$555$	36.5485	1.55140
$556$	39.7822	1.68714
$557$	−17.9579	−0.760899	−0.380449	−	0.924802i	$-0.624231\pi$
$557$	−17.9579	−0.760899	−0.380449	+	0.924802i	$0.624231\pi$
$558$	−10.1955	−0.431609
$559$	−8.00132	−0.338420
$560$	9.24527	0.390684
$561$	4.82295	0.203625
$562$	−10.2583	−0.432721
$563$	−8.98283	−0.378581	−0.189291	−	0.981921i	$-0.560619\pi$
$563$	−8.98283	−0.378581	−0.189291	+	0.981921i	$0.560619\pi$
$564$	39.1485	1.64845
$565$	16.8846	0.710339
$566$	−8.89801	−0.374011
$567$	15.0017	0.630013
$568$	−21.6790	−0.909632
$569$	−37.8361	−1.58617	−0.793087	−	0.609108i	$-0.791527\pi$
$569$	−37.8361	−1.58617	−0.793087	+	0.609108i	$0.791527\pi$
$570$	0.497399	0.0208337
$571$	−31.2031	−1.30581	−0.652904	−	0.757441i	$-0.726449\pi$
$571$	−31.2031	−1.30581	−0.652904	+	0.757441i	$0.726449\pi$
$572$	−1.46142	−0.0611052
$573$	60.0766	2.50973
$574$	−1.26491	−0.0527964
$575$	−10.7999	−0.450386
$576$	−16.4778	−0.686574
$577$	29.1271	1.21258	0.606288	−	0.795245i	$-0.292658\pi$
$577$	29.1271	1.21258	0.606288	+	0.795245i	$0.292658\pi$
$578$	4.84172	0.201389
$579$	−18.7042	−0.777321
$580$	11.3963	0.473207
$581$	7.09521	0.294359
$582$	7.65648	0.317371
$583$	4.19124	0.173584
$584$	0.926237	0.0383280
$585$	−3.95573	−0.163549
$586$	10.1669	0.419991
$587$	12.3156	0.508318	0.254159	−	0.967162i	$-0.418201\pi$
$587$	12.3156	0.508318	0.254159	+	0.967162i	$0.418201\pi$
$588$	−16.3921	−0.675998
$589$	−3.01934	−0.124410
$590$	−6.95970	−0.286526
$591$	46.4477	1.91060
$592$	30.6275	1.25878
$593$	−22.4097	−0.920257	−0.460128	−	0.887852i	$-0.652197\pi$
$593$	−22.4097	−0.920257	−0.460128	+	0.887852i	$0.652197\pi$
$594$	0.272509	0.0111812
$595$	−5.51225	−0.225980
$596$	−31.1583	−1.27629
$597$	45.6265	1.86737
$598$	−1.15985	−0.0474297
$599$	−27.9746	−1.14301	−0.571506	−	0.820598i	$-0.693641\pi$
$599$	−27.9746	−1.14301	−0.571506	+	0.820598i	$0.693641\pi$
$600$	9.36296	0.382241
$601$	23.2738	0.949360	0.474680	−	0.880159i	$-0.342564\pi$
$601$	23.2738	0.949360	0.474680	+	0.880159i	$0.342564\pi$
$602$	−6.96303	−0.283792
$603$	29.4638	1.19986
$604$	−2.06075	−0.0838508
$605$	−1.53260	−0.0623092
$606$	14.5871	0.592562
$607$	34.7558	1.41069	0.705347	−	0.708863i	$-0.250791\pi$
$607$	34.7558	1.41069	0.705347	+	0.708863i	$0.250791\pi$
$608$	1.41712	0.0574719
$609$	18.7011	0.757807
$610$	−5.79755	−0.234736
$611$	6.53584	0.264412
$612$	11.8383	0.478536
$613$	−35.5972	−1.43776	−0.718879	−	0.695135i	$-0.755345\pi$
$613$	−35.5972	−1.43776	−0.718879	+	0.695135i	$0.755345\pi$
$614$	11.2670	0.454699
$615$	−7.14464	−0.288100
$616$	−2.63371	−0.106115
$617$	19.4506	0.783052	0.391526	−	0.920167i	$-0.371947\pi$
$617$	19.4506	0.783052	0.391526	+	0.920167i	$0.371947\pi$
$618$	14.0307	0.564396
$619$	−10.2657	−0.412614	−0.206307	−	0.978487i	$-0.566145\pi$
$619$	−10.2657	−0.412614	−0.206307	+	0.978487i	$0.566145\pi$
$620$	24.3161	0.976556
$621$	−3.05102	−0.122433
$622$	12.2412	0.490828
$623$	−23.5629	−0.944027
$624$	−6.32984	−0.253397
$625$	−4.71588	−0.188635
$626$	6.21841	0.248538
$627$	0.891973	0.0356220
$628$	−17.4485	−0.696272
$629$	−18.2608	−0.728107
$630$	−3.44241	−0.137149
$631$	13.8473	0.551253	0.275627	−	0.961265i	$-0.411115\pi$
$631$	13.8473	0.551253	0.275627	+	0.961265i	$0.411115\pi$
$632$	−24.3627	−0.969095
$633$	12.6379	0.502310
$634$	−3.97035	−0.157683
$635$	6.71299	0.266397
$636$	19.6447	0.778964
$637$	−2.73666	−0.108430
$638$	−1.44868	−0.0573537
$639$	−50.8137	−2.01016
$640$	−15.0075	−0.593222
$641$	−11.3503	−0.448309	−0.224154	−	0.974554i	$-0.571962\pi$
$641$	−11.3503	−0.448309	−0.224154	+	0.974554i	$0.571962\pi$
$642$	−13.8003	−0.544655
$643$	18.6224	0.734397	0.367198	−	0.930143i	$-0.380317\pi$
$643$	18.6224	0.734397	0.367198	+	0.930143i	$0.380317\pi$
$644$	14.2389	0.561093
$645$	−39.3295	−1.54860
$646$	−0.248517	−0.00977775
$647$	1.18317	0.0465150	0.0232575	−	0.999730i	$-0.492596\pi$
$647$	1.18317	0.0465150	0.0232575	+	0.999730i	$0.492596\pi$
$648$	−11.2799	−0.443116
$649$	−12.4807	−0.489909
$650$	0.754820	0.0296065
$651$	39.9021	1.56388
$652$	−4.75908	−0.186380
$653$	17.3383	0.678501	0.339251	−	0.940696i	$-0.389827\pi$
$653$	17.3383	0.678501	0.339251	+	0.940696i	$0.389827\pi$
$654$	7.60702	0.297458
$655$	−1.53260	−0.0598838
$656$	−5.98717	−0.233760
$657$	2.17102	0.0846994
$658$	5.68772	0.221730
$659$	−21.1959	−0.825674	−0.412837	−	0.910805i	$-0.635462\pi$
$659$	−21.1959	−0.825674	−0.412837	+	0.910805i	$0.635462\pi$
$660$	−7.18344	−0.279615
$661$	−5.64511	−0.219569	−0.109785	−	0.993955i	$-0.535016\pi$
$661$	−5.64511	−0.219569	−0.109785	+	0.993955i	$0.535016\pi$
$662$	−8.99643	−0.349656
$663$	3.77400	0.146570
$664$	−5.33494	−0.207036
$665$	−1.01945	−0.0395327
$666$	−11.4039	−0.441893
$667$	16.2195	0.628021
$668$	−35.6704	−1.38013
$669$	−9.14911	−0.353725
$670$	4.98121	0.192441
$671$	−10.3966	−0.401357
$672$	−18.7279	−0.722446
$673$	−9.99613	−0.385323	−0.192661	−	0.981265i	$-0.561712\pi$
$673$	−9.99613	−0.385323	−0.192661	+	0.981265i	$0.561712\pi$
$674$	4.43362	0.170776
$675$	1.98558	0.0764251
$676$	23.1354	0.889823
$677$	24.4214	0.938591	0.469295	−	0.883041i	$-0.344508\pi$
$677$	24.4214	0.938591	0.469295	+	0.883041i	$0.344508\pi$
$678$	−10.0600	−0.386353
$679$	−15.6925	−0.602223
$680$	4.14469	0.158942
$681$	35.7250	1.36899
$682$	−3.09101	−0.118361
$683$	11.7807	0.450777	0.225389	−	0.974269i	$-0.427635\pi$
$683$	11.7807	0.450777	0.225389	+	0.974269i	$0.427635\pi$
$684$	2.18942	0.0837146
$685$	5.32057	0.203289
$686$	−7.14830	−0.272923
$687$	−24.8038	−0.946325
$688$	−32.9579	−1.25651
$689$	3.27969	0.124946
$690$	−5.70108	−0.217037
$691$	−10.9258	−0.415637	−0.207818	−	0.978167i	$-0.566636\pi$
$691$	−10.9258	−0.415637	−0.207818	+	0.978167i	$0.566636\pi$
$692$	−11.0736	−0.420955
$693$	−6.17319	−0.234500
$694$	−0.124911	−0.00474156
$695$	32.6462	1.23834
$696$	−14.0615	−0.532999
$697$	3.56969	0.135212
$698$	5.36658	0.203128
$699$	69.2692	2.62000
$700$	−9.26659	−0.350244
$701$	−22.1788	−0.837682	−0.418841	−	0.908060i	$-0.637564\pi$
$701$	−22.1788	−0.837682	−0.418841	+	0.908060i	$0.637564\pi$
$702$	0.213240	0.00804824
$703$	−3.37722	−0.127374
$704$	−4.99565	−0.188281
$705$	32.1261	1.20994
$706$	1.88029	0.0707655
$707$	−29.8974	−1.12441
$708$	−58.4979	−2.19849
$709$	5.39772	0.202715	0.101358	−	0.994850i	$-0.467681\pi$
$709$	5.39772	0.202715	0.101358	+	0.994850i	$0.467681\pi$
$710$	−8.59066	−0.322402
$711$	−57.1039	−2.14156
$712$	17.7171	0.663976
$713$	34.6071	1.29605
$714$	3.28427	0.122911
$715$	−1.19928	−0.0448504
$716$	15.8297	0.591585
$717$	−11.4617	−0.428044
$718$	7.74846	0.289170
$719$	−25.7068	−0.958703	−0.479351	−	0.877623i	$-0.659128\pi$
$719$	−25.7068	−0.958703	−0.479351	+	0.877623i	$0.659128\pi$
$720$	−16.2939	−0.607237
$721$	−28.7568	−1.07096
$722$	6.86720	0.255571
$723$	−35.5106	−1.32065
$724$	−24.0316	−0.893126
$725$	−10.5555	−0.392022
$726$	0.913144	0.0338900
$727$	33.4254	1.23968	0.619840	−	0.784728i	$-0.287198\pi$
$727$	33.4254	1.23968	0.619840	+	0.784728i	$0.287198\pi$
$728$	−2.06091	−0.0763822
$729$	−32.0780	−1.18807
$730$	0.367036	0.0135846
$731$	19.6503	0.726792
$732$	−48.7298	−1.80111
$733$	−21.3551	−0.788767	−0.394383	−	0.918946i	$-0.629042\pi$
$733$	−21.3551	−0.788767	−0.394383	+	0.918946i	$0.629042\pi$
$734$	0.530775	0.0195912
$735$	−13.4517	−0.496173
$736$	−16.2428	−0.598716
$737$	8.93269	0.329040
$738$	2.22928	0.0820609
$739$	11.5411	0.424545	0.212272	−	0.977211i	$-0.431914\pi$
$739$	11.5411	0.424545	0.212272	+	0.977211i	$0.431914\pi$
$740$	27.1982	0.999826
$741$	0.697977	0.0256408
$742$	2.85410	0.104777
$743$	−8.28620	−0.303991	−0.151996	−	0.988381i	$-0.548570\pi$
$743$	−8.28620	−0.303991	−0.151996	+	0.988381i	$0.548570\pi$
$744$	−30.0026	−1.09995
$745$	−25.5692	−0.936782
$746$	−2.04367	−0.0748241
$747$	−12.5046	−0.457520
$748$	3.58908	0.131230
$749$	28.2847	1.03350
$750$	10.7077	0.390988
$751$	17.7489	0.647668	0.323834	−	0.946114i	$-0.395028\pi$
$751$	17.7489	0.647668	0.323834	+	0.946114i	$0.395028\pi$
$752$	26.9215	0.981727
$753$	4.29097	0.156372
$754$	−1.13360	−0.0412834
$755$	−1.69110	−0.0615453
$756$	−2.61786	−0.0952106
$757$	−2.34071	−0.0850747	−0.0425373	−	0.999095i	$-0.513544\pi$
$757$	−2.34071	−0.0850747	−0.0425373	+	0.999095i	$0.513544\pi$
$758$	4.56668	0.165869
$759$	−10.2236	−0.371094
$760$	0.766534	0.0278051
$761$	−23.4953	−0.851703	−0.425851	−	0.904793i	$-0.640025\pi$
$761$	−23.4953	−0.851703	−0.425851	+	0.904793i	$0.640025\pi$
$762$	−3.99969	−0.144893
$763$	−15.5911	−0.564437
$764$	44.7070	1.61744
$765$	9.71479	0.351239
$766$	−3.93877	−0.142313
$767$	−9.76623	−0.352638
$768$	−16.1332	−0.582156
$769$	−16.5158	−0.595576	−0.297788	−	0.954632i	$-0.596249\pi$
$769$	−16.5158	−0.595576	−0.297788	+	0.954632i	$0.596249\pi$
$770$	−1.04365	−0.0376106
$771$	24.3819	0.878094
$772$	−13.9191	−0.500959
$773$	−9.56272	−0.343947	−0.171974	−	0.985102i	$-0.555014\pi$
$773$	−9.56272	−0.343947	−0.171974	+	0.985102i	$0.555014\pi$
$774$	12.2717	0.441095
$775$	−22.5220	−0.809015
$776$	11.7993	0.423570
$777$	44.6316	1.60115
$778$	7.99853	0.286761
$779$	0.660191	0.0236538
$780$	−5.62111	−0.201268
$781$	−15.4054	−0.551250
$782$	2.84845	0.101860
$783$	−2.98199	−0.106568
$784$	−11.2725	−0.402588
$785$	−14.3186	−0.511054
$786$	0.913144	0.0325708
$787$	1.80643	0.0643921	0.0321961	−	0.999482i	$-0.489750\pi$
$787$	1.80643	0.0643921	0.0321961	+	0.999482i	$0.489750\pi$
$788$	34.5649	1.23132
$789$	43.5489	1.55038
$790$	−9.65410	−0.343477
$791$	20.6188	0.733119
$792$	4.64166	0.164934
$793$	−8.13544	−0.288898
$794$	9.56300	0.339378
$795$	16.1209	0.571749
$796$	33.9537	1.20346
$797$	−0.652561	−0.0231149	−0.0115575	−	0.999933i	$-0.503679\pi$
$797$	−0.652561	−0.0231149	−0.0115575	+	0.999933i	$0.503679\pi$
$798$	0.607404	0.0215019
$799$	−16.0512	−0.567852
$800$	10.5707	0.373729
$801$	41.5273	1.46729
$802$	−2.72043	−0.0960617
$803$	0.658197	0.0232273
$804$	41.8683	1.47658
$805$	11.6848	0.411834
$806$	−2.41874	−0.0851965
$807$	33.0033	1.16177
$808$	22.4800	0.790845
$809$	4.06978	0.143086	0.0715430	−	0.997438i	$-0.477208\pi$
$809$	4.06978	0.143086	0.0715430	+	0.997438i	$0.477208\pi$
$810$	−4.46984	−0.157054
$811$	15.7512	0.553099	0.276550	−	0.961000i	$-0.410809\pi$
$811$	15.7512	0.553099	0.276550	+	0.961000i	$0.410809\pi$
$812$	13.9168	0.488382
$813$	−8.04237	−0.282058
$814$	−3.45738	−0.121181
$815$	−3.90540	−0.136800
$816$	15.5453	0.544196
$817$	3.63419	0.127144
$818$	−11.3559	−0.397051
$819$	−4.83058	−0.168794
$820$	−5.31681	−0.185671
$821$	−35.4434	−1.23698	−0.618491	−	0.785792i	$-0.712256\pi$
$821$	−35.4434	−1.23698	−0.618491	+	0.785792i	$0.712256\pi$
$822$	−3.17006	−0.110569
$823$	−54.0323	−1.88345	−0.941724	−	0.336386i	$-0.890795\pi$
$823$	−54.0323	−1.88345	−0.941724	+	0.336386i	$0.890795\pi$
$824$	21.6225	0.753254
$825$	6.65345	0.231643
$826$	−8.49891	−0.295715
$827$	51.1220	1.77769	0.888843	−	0.458211i	$-0.151510\pi$
$827$	51.1220	1.77769	0.888843	+	0.458211i	$0.151510\pi$
$828$	−25.0947	−0.872102
$829$	−11.6076	−0.403149	−0.201575	−	0.979473i	$-0.564606\pi$
$829$	−11.6076	−0.403149	−0.201575	+	0.979473i	$0.564606\pi$
$830$	−2.11405	−0.0733799
$831$	−67.9179	−2.35604
$832$	−3.90914	−0.135525
$833$	6.72090	0.232865
$834$	−19.4510	−0.673533
$835$	−29.2719	−1.01299
$836$	0.663777	0.0229572
$837$	−6.36259	−0.219923
$838$	7.49277	0.258833
$839$	−28.7093	−0.991157	−0.495578	−	0.868563i	$-0.665044\pi$
$839$	−28.7093	−0.991157	−0.495578	+	0.868563i	$0.665044\pi$
$840$	−10.1301	−0.349522
$841$	−13.1475	−0.453362
$842$	−11.5329	−0.397449
$843$	−70.7570	−2.43700
$844$	9.40469	0.323723
$845$	18.9854	0.653118
$846$	−10.0240	−0.344634
$847$	−1.87155	−0.0643074
$848$	13.5092	0.463909
$849$	−61.3742	−2.10636
$850$	−1.85375	−0.0635830
$851$	38.7090	1.32693
$852$	−72.2066	−2.47376
$853$	4.52684	0.154996	0.0774980	−	0.996993i	$-0.475307\pi$
$853$	4.52684	0.154996	0.0774980	+	0.996993i	$0.475307\pi$
$854$	−7.07974	−0.242264
$855$	1.79669	0.0614454
$856$	−21.2675	−0.726907
$857$	−10.2114	−0.348816	−0.174408	−	0.984673i	$-0.555801\pi$
$857$	−10.2114	−0.348816	−0.174408	+	0.984673i	$0.555801\pi$
$858$	0.714544	0.0243941
$859$	−3.81095	−0.130028	−0.0650140	−	0.997884i	$-0.520709\pi$
$859$	−3.81095	−0.130028	−0.0650140	+	0.997884i	$0.520709\pi$
$860$	−29.2677	−0.998022
$861$	−8.72475	−0.297339
$862$	6.59383	0.224587
$863$	−19.3497	−0.658673	−0.329337	−	0.944213i	$-0.606825\pi$
$863$	−19.3497	−0.658673	−0.329337	+	0.944213i	$0.606825\pi$
$864$	2.98627	0.101595
$865$	−9.08724	−0.308975
$866$	13.2069	0.448789
$867$	33.3958	1.13418
$868$	29.6938	1.00787
$869$	−17.3125	−0.587285
$870$	−5.57209	−0.188911
$871$	6.98991	0.236844
$872$	11.7231	0.396993
$873$	27.6565	0.936030
$874$	0.526802	0.0178193
$875$	−21.9461	−0.741914
$876$	3.08503	0.104233
$877$	35.0197	1.18253	0.591265	−	0.806477i	$-0.298629\pi$
$877$	35.0197	1.18253	0.591265	+	0.806477i	$0.298629\pi$
$878$	4.09952	0.138352
$879$	70.1265	2.36531
$880$	−4.93989	−0.166524
$881$	−25.6143	−0.862968	−0.431484	−	0.902121i	$-0.642010\pi$
$881$	−25.6143	−0.862968	−0.431484	+	0.902121i	$0.642010\pi$
$882$	4.19722	0.141328
$883$	31.6179	1.06403	0.532013	−	0.846736i	$-0.321436\pi$
$883$	31.6179	1.06403	0.532013	+	0.846736i	$0.321436\pi$
$884$	2.80849	0.0944597
$885$	−48.0047	−1.61366
$886$	1.50240	0.0504742
$887$	−31.0113	−1.04126	−0.520628	−	0.853783i	$-0.674302\pi$
$887$	−31.0113	−1.04126	−0.520628	+	0.853783i	$0.674302\pi$
$888$	−33.5588	−1.12616
$889$	8.19764	0.274940
$890$	7.02068	0.235334
$891$	−8.01565	−0.268534
$892$	−6.80847	−0.227964
$893$	−2.96857	−0.0993395
$894$	15.2344	0.509516
$895$	12.9902	0.434215
$896$	−18.3265	−0.612246
$897$	−8.00007	−0.267115
$898$	6.37934	0.212881
$899$	33.8240	1.12809
$900$	16.3314	0.544381
$901$	−8.05452	−0.268335
$902$	0.675861	0.0225037
$903$	−48.0276	−1.59826
$904$	−15.5034	−0.515635
$905$	−19.7208	−0.655542
$906$	1.00758	0.0334745
$907$	9.97488	0.331210	0.165605	−	0.986192i	$-0.447042\pi$
$907$	9.97488	0.331210	0.165605	+	0.986192i	$0.447042\pi$
$908$	26.5854	0.882267
$909$	52.6912	1.74766
$910$	−0.816666	−0.0270722
$911$	−29.9893	−0.993590	−0.496795	−	0.867868i	$-0.665490\pi$
$911$	−29.9893	−0.993590	−0.496795	+	0.867868i	$0.665490\pi$
$912$	2.87501	0.0952011
$913$	−3.79108	−0.125466
$914$	4.92493	0.162902
$915$	−39.9887	−1.32199
$916$	−18.4582	−0.609876
$917$	−1.87155	−0.0618042
$918$	−0.523693	−0.0172845
$919$	−49.6871	−1.63903	−0.819513	−	0.573061i	$-0.805756\pi$
$919$	−49.6871	−1.63903	−0.819513	+	0.573061i	$0.805756\pi$
$920$	−8.78586	−0.289661
$921$	77.7144	2.56077
$922$	4.46708	0.147115
$923$	−12.0549	−0.396791
$924$	−8.77214	−0.288582
$925$	−25.1915	−0.828292
$926$	6.55748	0.215492
$927$	50.6811	1.66458
$928$	−15.8752	−0.521130
$929$	5.60220	0.183802	0.0919012	−	0.995768i	$-0.470706\pi$
$929$	5.60220	0.183802	0.0919012	+	0.995768i	$0.470706\pi$
$930$	−11.8890	−0.389856
$931$	1.24299	0.0407372
$932$	51.5478	1.68851
$933$	84.4340	2.76425
$934$	−3.90385	−0.127738
$935$	2.94528	0.0963209
$936$	3.63214	0.118720
$937$	−3.12200	−0.101991	−0.0509956	−	0.998699i	$-0.516239\pi$
$937$	−3.12200	−0.101991	−0.0509956	+	0.998699i	$0.516239\pi$
$938$	6.08286	0.198612
$939$	42.8916	1.39971
$940$	23.9072	0.779767
$941$	−9.37070	−0.305476	−0.152738	−	0.988267i	$-0.548809\pi$
$941$	−9.37070	−0.305476	−0.152738	+	0.988267i	$0.548809\pi$
$942$	8.53122	0.277962
$943$	−7.56698	−0.246415
$944$	−40.2277	−1.30930
$945$	−2.14827	−0.0698833
$946$	3.72045	0.120962
$947$	3.12977	0.101704	0.0508520	−	0.998706i	$-0.483806\pi$
$947$	3.12977	0.101704	0.0508520	+	0.998706i	$0.483806\pi$
$948$	−81.1450	−2.63547
$949$	0.515045	0.0167191
$950$	−0.342838	−0.0111231
$951$	−27.3855	−0.888037
$952$	5.06134	0.164039
$953$	38.2071	1.23765	0.618825	−	0.785529i	$-0.287609\pi$
$953$	38.2071	1.23765	0.618825	+	0.785529i	$0.287609\pi$
$954$	−5.03006	−0.162854
$955$	36.6876	1.18718
$956$	−8.52940	−0.275860
$957$	−9.99229	−0.323005
$958$	13.5015	0.436213
$959$	6.49727	0.209808
$960$	−19.2149	−0.620157
$961$	41.1694	1.32805
$962$	−2.70543	−0.0872266
$963$	−49.8490	−1.60636
$964$	−26.4259	−0.851119
$965$	−11.4223	−0.367697
$966$	−6.96194	−0.223997
$967$	−39.2503	−1.26220	−0.631102	−	0.775700i	$-0.717397\pi$
$967$	−39.2503	−1.26220	−0.631102	+	0.775700i	$0.717397\pi$
$968$	1.40723	0.0452302
$969$	−1.71415	−0.0550663
$970$	4.67566	0.150126
$971$	14.2680	0.457883	0.228941	−	0.973440i	$-0.426474\pi$
$971$	14.2680	0.457883	0.228941	+	0.973440i	$0.426474\pi$
$972$	−41.7663	−1.33966
$973$	39.8662	1.27805
$974$	−10.7021	−0.342919
$975$	5.20638	0.166738
$976$	−33.5104	−1.07264
$977$	4.00882	0.128254	0.0641268	−	0.997942i	$-0.479574\pi$
$977$	4.00882	0.128254	0.0641268	+	0.997942i	$0.479574\pi$
$978$	2.32689	0.0744057
$979$	12.5900	0.402379
$980$	−10.0103	−0.319768
$981$	27.4778	0.877300
$982$	3.71736	0.118626
$983$	−26.0950	−0.832302	−0.416151	−	0.909296i	$-0.636621\pi$
$983$	−26.0950	−0.832302	−0.416151	+	0.909296i	$0.636621\pi$
$984$	6.56019	0.209131
$985$	28.3647	0.903774
$986$	2.78400	0.0886605
$987$	39.2311	1.24874
$988$	0.519412	0.0165247
$989$	−41.6544	−1.32453
$990$	1.83933	0.0584578
$991$	12.6063	0.400453	0.200226	−	0.979750i	$-0.435832\pi$
$991$	12.6063	0.400453	0.200226	+	0.979750i	$0.435832\pi$
$992$	−33.8726	−1.07546
$993$	−62.0530	−1.96919
$994$	−10.4906	−0.332741
$995$	27.8632	0.883322
$996$	−17.7691	−0.563036
$997$	45.3031	1.43476	0.717382	−	0.696680i	$-0.245340\pi$
$997$	45.3031	1.43476	0.717382	+	0.696680i	$0.245340\pi$
$998$	−12.9693	−0.410536
$999$	−7.11674	−0.225164

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.c.1.11	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.c.1.11	✓	23	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-0.363851 q^{2} -2.50967 q^{3} -1.86761 q^{4} -1.53260 q^{5} +0.913144 q^{6} -1.87155 q^{7} +1.40723 q^{8} +3.29843 q^{9} +O(q^{10})\)	\(q-0.363851 q^{2} -2.50967 q^{3} -1.86761 q^{4} -1.53260 q^{5} +0.913144 q^{6} -1.87155 q^{7} +1.40723 q^{8} +3.29843 q^{9} +0.557639 q^{10} +1.00000 q^{11} +4.68709 q^{12} +0.782509 q^{13} +0.680966 q^{14} +3.84632 q^{15} +3.22320 q^{16} -1.92175 q^{17} -1.20014 q^{18} -0.355415 q^{19} +2.86231 q^{20} +4.69698 q^{21} -0.363851 q^{22} +4.07369 q^{23} -3.53169 q^{24} -2.65113 q^{25} -0.284716 q^{26} -0.748957 q^{27} +3.49534 q^{28} +3.98152 q^{29} -1.39949 q^{30} +8.49526 q^{31} -3.98723 q^{32} -2.50967 q^{33} +0.699230 q^{34} +2.86835 q^{35} -6.16019 q^{36} +9.50219 q^{37} +0.129318 q^{38} -1.96384 q^{39} -2.15673 q^{40} -1.85752 q^{41} -1.70900 q^{42} -10.2252 q^{43} -1.86761 q^{44} -5.05518 q^{45} -1.48222 q^{46} +8.35242 q^{47} -8.08916 q^{48} -3.49728 q^{49} +0.964615 q^{50} +4.82295 q^{51} -1.46142 q^{52} +4.19124 q^{53} +0.272509 q^{54} -1.53260 q^{55} -2.63371 q^{56} +0.891973 q^{57} -1.44868 q^{58} -12.4807 q^{59} -7.18344 q^{60} -10.3966 q^{61} -3.09101 q^{62} -6.17319 q^{63} -4.99565 q^{64} -1.19928 q^{65} +0.913144 q^{66} +8.93269 q^{67} +3.58908 q^{68} -10.2236 q^{69} -1.04365 q^{70} -15.4054 q^{71} +4.64166 q^{72} +0.658197 q^{73} -3.45738 q^{74} +6.65345 q^{75} +0.663777 q^{76} -1.87155 q^{77} +0.714544 q^{78} -17.3125 q^{79} -4.93989 q^{80} -8.01565 q^{81} +0.675861 q^{82} -3.79108 q^{83} -8.77214 q^{84} +2.94528 q^{85} +3.72045 q^{86} -9.99229 q^{87} +1.40723 q^{88} +12.5900 q^{89} +1.83933 q^{90} -1.46451 q^{91} -7.60808 q^{92} -21.3203 q^{93} -3.03903 q^{94} +0.544710 q^{95} +10.0066 q^{96} +8.38475 q^{97} +1.27249 q^{98} +3.29843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9}+O(q^{10}) \) 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9} - 2 q^{10} + 23 q^{11} + 8 q^{12} - 24 q^{13} - 13 q^{14} - 27 q^{15} + 7 q^{16} - 7 q^{17} - 14 q^{18} - 18 q^{19} - 4 q^{20} - 29 q^{21} - 7 q^{22} - 26 q^{23} - 4 q^{24} + 18 q^{25} + 8 q^{26} - 3 q^{27} - 11 q^{28} - 45 q^{29} + 19 q^{30} - 23 q^{31} - 34 q^{32} - 3 q^{33} - 2 q^{34} - 18 q^{35} - 6 q^{36} - 2 q^{37} - 8 q^{38} - 40 q^{39} - 24 q^{40} - 23 q^{41} + 59 q^{42} - 14 q^{43} + 15 q^{44} - 18 q^{45} - 12 q^{46} - 55 q^{47} + 10 q^{48} + 11 q^{49} - 41 q^{50} - 21 q^{51} - 37 q^{52} - 10 q^{53} - 68 q^{54} - 9 q^{55} + 2 q^{56} - 18 q^{57} + 27 q^{58} - 75 q^{59} - 63 q^{60} - 55 q^{61} + 14 q^{62} - 16 q^{63} + 19 q^{64} - 25 q^{65} - 11 q^{66} + 17 q^{67} + 41 q^{68} - 22 q^{69} + 27 q^{70} - 105 q^{71} - 11 q^{72} - 3 q^{73} - 39 q^{74} + 25 q^{75} - 30 q^{76} - 12 q^{77} + 25 q^{78} - 48 q^{79} - 37 q^{80} + 3 q^{81} + 36 q^{82} + 4 q^{83} - 111 q^{84} - 30 q^{85} + 22 q^{86} + 5 q^{87} - 21 q^{88} - 39 q^{89} + 100 q^{90} - 22 q^{91} - 30 q^{92} - 5 q^{93} + 11 q^{94} - 88 q^{95} + 13 q^{96} + 24 q^{97} - 91 q^{98} + 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9 - 2 * q^10 + 23 * q^11 + 8 * q^12 - 24 * q^13 - 13 * q^14 - 27 * q^15 + 7 * q^16 - 7 * q^17 - 14 * q^18 - 18 * q^19 - 4 * q^20 - 29 * q^21 - 7 * q^22 - 26 * q^23 - 4 * q^24 + 18 * q^25 + 8 * q^26 - 3 * q^27 - 11 * q^28 - 45 * q^29 + 19 * q^30 - 23 * q^31 - 34 * q^32 - 3 * q^33 - 2 * q^34 - 18 * q^35 - 6 * q^36 - 2 * q^37 - 8 * q^38 - 40 * q^39 - 24 * q^40 - 23 * q^41 + 59 * q^42 - 14 * q^43 + 15 * q^44 - 18 * q^45 - 12 * q^46 - 55 * q^47 + 10 * q^48 + 11 * q^49 - 41 * q^50 - 21 * q^51 - 37 * q^52 - 10 * q^53 - 68 * q^54 - 9 * q^55 + 2 * q^56 - 18 * q^57 + 27 * q^58 - 75 * q^59 - 63 * q^60 - 55 * q^61 + 14 * q^62 - 16 * q^63 + 19 * q^64 - 25 * q^65 - 11 * q^66 + 17 * q^67 + 41 * q^68 - 22 * q^69 + 27 * q^70 - 105 * q^71 - 11 * q^72 - 3 * q^73 - 39 * q^74 + 25 * q^75 - 30 * q^76 - 12 * q^77 + 25 * q^78 - 48 * q^79 - 37 * q^80 + 3 * q^81 + 36 * q^82 + 4 * q^83 - 111 * q^84 - 30 * q^85 + 22 * q^86 + 5 * q^87 - 21 * q^88 - 39 * q^89 + 100 * q^90 - 22 * q^91 - 30 * q^92 - 5 * q^93 + 11 * q^94 - 88 * q^95 + 13 * q^96 + 24 * q^97 - 91 * q^98 + 12 * q^99

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