LMFDB - Embedded newform 241.2.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [241,2,Mod(1,241)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(241, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("241.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	241.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:	$1.92439468871$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 14 x^{10} + 44 x^{9} + 65 x^{8} - 219 x^{7} - 123 x^{6} + 444 x^{5} + 105 x^{4} + \cdots - 1 $ x^12 - 3x^11 - 14x^10 + 44x^9 + 65x^8 - 219x^7 - 123x^6 + 444x^5 + 105x^4 - 328x^3 - 45x^2 + 18*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.342147$ of defining polynomial
Character	$\chi$	$=$	241.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.342147 q^{2} +2.18519 q^{3} -1.88294 q^{4} -0.548903 q^{5} -0.747658 q^{6} +1.82459 q^{7} +1.32853 q^{8} +1.77508 q^{9} +O(q^{10})$	\(q-0.342147 q^{2} +2.18519 q^{3} -1.88294 q^{4} -0.548903 q^{5} -0.747658 q^{6} +1.82459 q^{7} +1.32853 q^{8} +1.77508 q^{9} +0.187805 q^{10} +5.99218 q^{11} -4.11458 q^{12} +3.70515 q^{13} -0.624278 q^{14} -1.19946 q^{15} +3.31132 q^{16} -1.64451 q^{17} -0.607337 q^{18} -3.15821 q^{19} +1.03355 q^{20} +3.98709 q^{21} -2.05021 q^{22} -5.46015 q^{23} +2.90311 q^{24} -4.69871 q^{25} -1.26771 q^{26} -2.67670 q^{27} -3.43559 q^{28} +7.24801 q^{29} +0.410391 q^{30} -9.41700 q^{31} -3.79003 q^{32} +13.0941 q^{33} +0.562662 q^{34} -1.00152 q^{35} -3.34236 q^{36} +1.27680 q^{37} +1.08057 q^{38} +8.09648 q^{39} -0.729236 q^{40} -5.81239 q^{41} -1.36417 q^{42} +7.82887 q^{43} -11.2829 q^{44} -0.974345 q^{45} +1.86817 q^{46} +2.61568 q^{47} +7.23587 q^{48} -3.67086 q^{49} +1.60765 q^{50} -3.59356 q^{51} -6.97656 q^{52} +8.81076 q^{53} +0.915823 q^{54} -3.28912 q^{55} +2.42403 q^{56} -6.90130 q^{57} -2.47989 q^{58} -7.78270 q^{59} +2.25850 q^{60} +1.03194 q^{61} +3.22200 q^{62} +3.23879 q^{63} -5.32589 q^{64} -2.03377 q^{65} -4.48010 q^{66} -8.39801 q^{67} +3.09650 q^{68} -11.9315 q^{69} +0.342668 q^{70} +13.1691 q^{71} +2.35825 q^{72} -13.3963 q^{73} -0.436852 q^{74} -10.2676 q^{75} +5.94670 q^{76} +10.9333 q^{77} -2.77018 q^{78} -10.6362 q^{79} -1.81759 q^{80} -11.1743 q^{81} +1.98869 q^{82} +6.25636 q^{83} -7.50743 q^{84} +0.902673 q^{85} -2.67862 q^{86} +15.8383 q^{87} +7.96082 q^{88} -3.94129 q^{89} +0.333369 q^{90} +6.76039 q^{91} +10.2811 q^{92} -20.5780 q^{93} -0.894948 q^{94} +1.73355 q^{95} -8.28195 q^{96} -2.22451 q^{97} +1.25598 q^{98} +10.6366 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + q^{3} + 13 q^{4} + 6 q^{5} - q^{6} + 3 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + q^3 + 13 * q^4 + 6 * q^5 - q^6 + 3 * q^7 + 9 * q^8 + 15 * q^9	\( 12 q + 3 q^{2} + q^{3} + 13 q^{4} + 6 q^{5} - q^{6} + 3 q^{7} + 9 q^{8} + 15 q^{9} - 7 q^{10} + 22 q^{11} - 7 q^{12} - 5 q^{13} + 6 q^{14} + 13 q^{15} + 15 q^{16} - 4 q^{17} - q^{18} - 6 q^{19} + 10 q^{20} - 14 q^{21} - 12 q^{22} + 32 q^{23} - 15 q^{24} + 4 q^{25} + 8 q^{26} - 5 q^{27} - 11 q^{28} + 6 q^{29} - 19 q^{30} + 8 q^{31} + q^{32} - 24 q^{33} - 19 q^{34} + 15 q^{35} - 8 q^{36} - 8 q^{37} - 10 q^{38} + 31 q^{39} - 52 q^{40} - q^{41} - 49 q^{42} - 2 q^{43} + 42 q^{44} - 15 q^{45} - 25 q^{46} + 34 q^{47} - 49 q^{48} - 9 q^{49} - 27 q^{50} - 3 q^{51} - 41 q^{52} + 5 q^{53} - 40 q^{54} - 3 q^{55} + q^{56} - 22 q^{57} - 33 q^{58} + 26 q^{59} - 57 q^{60} - 26 q^{61} - 17 q^{62} - 4 q^{63} + 13 q^{64} - 25 q^{65} - 2 q^{66} + 6 q^{67} - 35 q^{68} - 2 q^{69} - 4 q^{70} + 94 q^{71} + 17 q^{72} - 22 q^{73} + 26 q^{74} - 20 q^{76} - 7 q^{77} + 54 q^{78} + 9 q^{79} + 19 q^{80} + 4 q^{81} + 15 q^{82} - 8 q^{83} + 2 q^{84} + 4 q^{85} + 9 q^{86} + 4 q^{87} + 6 q^{88} - 3 q^{89} + 11 q^{90} - 20 q^{91} + 36 q^{92} + 12 q^{93} + 48 q^{94} + 33 q^{95} - 23 q^{96} - 29 q^{97} + 28 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + q^3 + 13 * q^4 + 6 * q^5 - q^6 + 3 * q^7 + 9 * q^8 + 15 * q^9 - 7 * q^10 + 22 * q^11 - 7 * q^12 - 5 * q^13 + 6 * q^14 + 13 * q^15 + 15 * q^16 - 4 * q^17 - q^18 - 6 * q^19 + 10 * q^20 - 14 * q^21 - 12 * q^22 + 32 * q^23 - 15 * q^24 + 4 * q^25 + 8 * q^26 - 5 * q^27 - 11 * q^28 + 6 * q^29 - 19 * q^30 + 8 * q^31 + q^32 - 24 * q^33 - 19 * q^34 + 15 * q^35 - 8 * q^36 - 8 * q^37 - 10 * q^38 + 31 * q^39 - 52 * q^40 - q^41 - 49 * q^42 - 2 * q^43 + 42 * q^44 - 15 * q^45 - 25 * q^46 + 34 * q^47 - 49 * q^48 - 9 * q^49 - 27 * q^50 - 3 * q^51 - 41 * q^52 + 5 * q^53 - 40 * q^54 - 3 * q^55 + q^56 - 22 * q^57 - 33 * q^58 + 26 * q^59 - 57 * q^60 - 26 * q^61 - 17 * q^62 - 4 * q^63 + 13 * q^64 - 25 * q^65 - 2 * q^66 + 6 * q^67 - 35 * q^68 - 2 * q^69 - 4 * q^70 + 94 * q^71 + 17 * q^72 - 22 * q^73 + 26 * q^74 - 20 * q^76 - 7 * q^77 + 54 * q^78 + 9 * q^79 + 19 * q^80 + 4 * q^81 + 15 * q^82 - 8 * q^83 + 2 * q^84 + 4 * q^85 + 9 * q^86 + 4 * q^87 + 6 * q^88 - 3 * q^89 + 11 * q^90 - 20 * q^91 + 36 * q^92 + 12 * q^93 + 48 * q^94 + 33 * q^95 - 23 * q^96 - 29 * q^97 + 28 * q^98 + 36 * 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 $

$2$	−0.342147	−0.241934	−0.120967	−	0.992657i	$-0.538600\pi$
$2$	−0.342147	−0.241934	−0.120967	+	0.992657i	$0.538600\pi$
$3$	2.18519	1.26162	0.630811	−	0.775936i	$-0.282722\pi$
$3$	2.18519	1.26162	0.630811	+	0.775936i	$0.282722\pi$
$4$	−1.88294	−0.941468
$5$	−0.548903	−0.245477	−0.122738	−	0.992439i	$-0.539168\pi$
$5$	−0.548903	−0.245477	−0.122738	+	0.992439i	$0.539168\pi$
$6$	−0.747658	−0.305230
$7$	1.82459	0.689631	0.344815	−	0.938671i	$-0.387942\pi$
$7$	1.82459	0.689631	0.344815	+	0.938671i	$0.387942\pi$
$8$	1.32853	0.469708
$9$	1.77508	0.591692
$10$	0.187805	0.0593893
$11$	5.99218	1.80671	0.903355	−	0.428894i	$-0.141096\pi$
$11$	5.99218	1.80671	0.903355	+	0.428894i	$0.141096\pi$
$12$	−4.11458	−1.18778
$13$	3.70515	1.02762	0.513812	−	0.857903i	$-0.328233\pi$
$13$	3.70515	1.02762	0.513812	+	0.857903i	$0.328233\pi$
$14$	−0.624278	−0.166845
$15$	−1.19946	−0.309699
$16$	3.31132	0.827829
$17$	−1.64451	−0.398851	−0.199426	−	0.979913i	$-0.563908\pi$
$17$	−1.64451	−0.398851	−0.199426	+	0.979913i	$0.563908\pi$
$18$	−0.607337	−0.143151
$19$	−3.15821	−0.724543	−0.362271	−	0.932073i	$-0.617999\pi$
$19$	−3.15821	−0.724543	−0.362271	+	0.932073i	$0.617999\pi$
$20$	1.03355	0.231108
$21$	3.98709	0.870054
$22$	−2.05021	−0.437105
$23$	−5.46015	−1.13852	−0.569260	−	0.822158i	$-0.692770\pi$
$23$	−5.46015	−1.13852	−0.569260	+	0.822158i	$0.692770\pi$
$24$	2.90311	0.592594
$25$	−4.69871	−0.939741
$26$	−1.26771	−0.248618
$27$	−2.67670	−0.515130
$28$	−3.43559	−0.649265
$29$	7.24801	1.34592	0.672961	−	0.739678i	$-0.265022\pi$
$29$	7.24801	1.34592	0.672961	+	0.739678i	$0.265022\pi$
$30$	0.410391	0.0749269
$31$	−9.41700	−1.69134	−0.845672	−	0.533703i	$-0.820800\pi$
$31$	−9.41700	−1.69134	−0.845672	+	0.533703i	$0.820800\pi$
$32$	−3.79003	−0.669988
$33$	13.0941	2.27939
$34$	0.562662	0.0964958
$35$	−1.00152	−0.169288
$36$	−3.34236	−0.557059
$37$	1.27680	0.209904	0.104952	−	0.994477i	$-0.466531\pi$
$37$	1.27680	0.209904	0.104952	+	0.994477i	$0.466531\pi$
$38$	1.08057	0.175292
$39$	8.09648	1.29647
$40$	−0.729236	−0.115302
$41$	−5.81239	−0.907743	−0.453872	−	0.891067i	$-0.649958\pi$
$41$	−5.81239	−0.907743	−0.453872	+	0.891067i	$0.649958\pi$
$42$	−1.36417	−0.210496
$43$	7.82887	1.19389	0.596946	−	0.802281i	$-0.296381\pi$
$43$	7.82887	1.19389	0.596946	+	0.802281i	$0.296381\pi$
$44$	−11.2829	−1.70096
$45$	−0.974345	−0.145247
$46$	1.86817	0.275447
$47$	2.61568	0.381537	0.190768	−	0.981635i	$-0.438902\pi$
$47$	2.61568	0.381537	0.190768	+	0.981635i	$0.438902\pi$
$48$	7.23587	1.04441
$49$	−3.67086	−0.524409
$50$	1.60765	0.227356
$51$	−3.59356	−0.503200
$52$	−6.97656	−0.967475
$53$	8.81076	1.21025	0.605126	−	0.796130i	$-0.293123\pi$
$53$	8.81076	1.21025	0.605126	+	0.796130i	$0.293123\pi$
$54$	0.915823	0.124628
$55$	−3.28912	−0.443505
$56$	2.42403	0.323925
$57$	−6.90130	−0.914100
$58$	−2.47989	−0.325625
$59$	−7.78270	−1.01322	−0.506610	−	0.862175i	$-0.669102\pi$
$59$	−7.78270	−1.01322	−0.506610	+	0.862175i	$0.669102\pi$
$60$	2.25850	0.291572
$61$	1.03194	0.132127	0.0660635	−	0.997815i	$-0.478956\pi$
$61$	1.03194	0.132127	0.0660635	+	0.997815i	$0.478956\pi$
$62$	3.22200	0.409194
$63$	3.23879	0.408049
$64$	−5.32589	−0.665736
$65$	−2.03377	−0.252258
$66$	−4.48010	−0.551462
$67$	−8.39801	−1.02598	−0.512990	−	0.858395i	$-0.671462\pi$
$67$	−8.39801	−1.02598	−0.512990	+	0.858395i	$0.671462\pi$
$68$	3.09650	0.375505
$69$	−11.9315	−1.43638
$70$	0.342668	0.0409567
$71$	13.1691	1.56288	0.781440	−	0.623981i	$-0.214486\pi$
$71$	13.1691	1.56288	0.781440	+	0.623981i	$0.214486\pi$
$72$	2.35825	0.277923
$73$	−13.3963	−1.56792	−0.783959	−	0.620813i	$-0.786803\pi$
$73$	−13.3963	−1.56792	−0.783959	+	0.620813i	$0.786803\pi$
$74$	−0.436852	−0.0507830
$75$	−10.2676	−1.18560
$76$	5.94670	0.682133
$77$	10.9333	1.24596
$78$	−2.77018	−0.313662
$79$	−10.6362	−1.19666	−0.598332	−	0.801248i	$-0.704170\pi$
$79$	−10.6362	−1.19666	−0.598332	+	0.801248i	$0.704170\pi$
$80$	−1.81759	−0.203213
$81$	−11.1743	−1.24159
$82$	1.98869	0.219614
$83$	6.25636	0.686725	0.343362	−	0.939203i	$-0.388434\pi$
$83$	6.25636	0.686725	0.343362	+	0.939203i	$0.388434\pi$
$84$	−7.50743	−0.819128
$85$	0.902673	0.0979087
$86$	−2.67862	−0.288844
$87$	15.8383	1.69805
$88$	7.96082	0.848626
$89$	−3.94129	−0.417776	−0.208888	−	0.977940i	$-0.566984\pi$
$89$	−3.94129	−0.417776	−0.208888	+	0.977940i	$0.566984\pi$
$90$	0.333369	0.0351402
$91$	6.76039	0.708681
$92$	10.2811	1.07188
$93$	−20.5780	−2.13384
$94$	−0.894948	−0.0923069
$95$	1.73355	0.177858
$96$	−8.28195	−0.845273
$97$	−2.22451	−0.225865	−0.112933	−	0.993603i	$-0.536024\pi$
$97$	−2.22451	−0.225865	−0.112933	+	0.993603i	$0.536024\pi$
$98$	1.25598	0.126873
$99$	10.6366	1.06902
$100$	8.84736	0.884736
$101$	−4.24027	−0.421923	−0.210962	−	0.977494i	$-0.567659\pi$
$101$	−4.24027	−0.421923	−0.210962	+	0.977494i	$0.567659\pi$
$102$	1.22953	0.121741
$103$	0.164858	0.0162439	0.00812196	−	0.999967i	$-0.497415\pi$
$103$	0.164858	0.0162439	0.00812196	+	0.999967i	$0.497415\pi$
$104$	4.92242	0.482683
$105$	−2.18852	−0.213578
$106$	−3.01458	−0.292801
$107$	9.28536	0.897650	0.448825	−	0.893620i	$-0.351843\pi$
$107$	9.28536	0.897650	0.448825	+	0.893620i	$0.351843\pi$
$108$	5.04005	0.484979
$109$	12.1952	1.16809	0.584044	−	0.811722i	$-0.301470\pi$
$109$	12.1952	1.16809	0.584044	+	0.811722i	$0.301470\pi$
$110$	1.12536	0.107299
$111$	2.79005	0.264820
$112$	6.04180	0.570897
$113$	13.1834	1.24019	0.620093	−	0.784528i	$-0.287095\pi$
$113$	13.1834	1.24019	0.620093	+	0.784528i	$0.287095\pi$
$114$	2.36126	0.221152
$115$	2.99709	0.279480
$116$	−13.6475	−1.26714
$117$	6.57693	0.608037
$118$	2.66283	0.245133
$119$	−3.00055	−0.275060
$120$	−1.59352	−0.145468
$121$	24.9062	2.26420
$122$	−0.353077	−0.0319661
$123$	−12.7012	−1.14523
$124$	17.7316	1.59235
$125$	5.32365	0.476161
$126$	−1.10814	−0.0987212
$127$	−11.7563	−1.04321	−0.521603	−	0.853188i	$-0.674666\pi$
$127$	−11.7563	−1.04321	−0.521603	+	0.853188i	$0.674666\pi$
$128$	9.40229	0.831053
$129$	17.1076	1.50624
$130$	0.695847	0.0610298
$131$	14.0839	1.23051	0.615257	−	0.788326i	$-0.289052\pi$
$131$	14.0839	1.23051	0.615257	+	0.788326i	$0.289052\pi$
$132$	−24.6553	−2.14597
$133$	−5.76244	−0.499667
$134$	2.87335	0.248220
$135$	1.46925	0.126453
$136$	−2.18478	−0.187343
$137$	−12.3993	−1.05935	−0.529673	−	0.848202i	$-0.677685\pi$
$137$	−12.3993	−1.05935	−0.529673	+	0.848202i	$0.677685\pi$
$138$	4.08232	0.347510
$139$	−10.5456	−0.894464	−0.447232	−	0.894418i	$-0.647590\pi$
$139$	−10.5456	−0.894464	−0.447232	+	0.894418i	$0.647590\pi$
$140$	1.88580	0.159380
$141$	5.71578	0.481356
$142$	−4.50575	−0.378114
$143$	22.2019	1.85662
$144$	5.87784	0.489820
$145$	−3.97845	−0.330393
$146$	4.58350	0.379333
$147$	−8.02156	−0.661607
$148$	−2.40412	−0.197618
$149$	−9.30604	−0.762380	−0.381190	−	0.924497i	$-0.624486\pi$
$149$	−9.30604	−0.762380	−0.381190	+	0.924497i	$0.624486\pi$
$150$	3.51302	0.286837
$151$	10.2870	0.837143	0.418572	−	0.908184i	$-0.362531\pi$
$151$	10.2870	0.837143	0.418572	+	0.908184i	$0.362531\pi$
$152$	−4.19579	−0.340323
$153$	−2.91912	−0.235997
$154$	−3.74079	−0.301441
$155$	5.16902	0.415186
$156$	−15.2451	−1.22059
$157$	−4.23848	−0.338268	−0.169134	−	0.985593i	$-0.554097\pi$
$157$	−4.23848	−0.338268	−0.169134	+	0.985593i	$0.554097\pi$
$158$	3.63914	0.289514
$159$	19.2532	1.52688
$160$	2.08036	0.164467
$161$	−9.96254	−0.785159
$162$	3.82326	0.300384
$163$	−6.42582	−0.503309	−0.251655	−	0.967817i	$-0.580975\pi$
$163$	−6.42582	−0.503309	−0.251655	+	0.967817i	$0.580975\pi$
$164$	10.9444	0.854611
$165$	−7.18738	−0.559536
$166$	−2.14060	−0.166142
$167$	3.96260	0.306636	0.153318	−	0.988177i	$-0.451004\pi$
$167$	3.96260	0.306636	0.153318	+	0.988177i	$0.451004\pi$
$168$	5.29698	0.408671
$169$	0.728137	0.0560105
$170$	−0.308847	−0.0236875
$171$	−5.60606	−0.428706
$172$	−14.7413	−1.12401
$173$	−8.45221	−0.642610	−0.321305	−	0.946976i	$-0.604121\pi$
$173$	−8.45221	−0.642610	−0.321305	+	0.946976i	$0.604121\pi$
$174$	−5.41903	−0.410816
$175$	−8.57322	−0.648075
$176$	19.8420	1.49565
$177$	−17.0067	−1.27830
$178$	1.34850	0.101074
$179$	−10.5847	−0.791138	−0.395569	−	0.918436i	$-0.629453\pi$
$179$	−10.5847	−0.791138	−0.395569	+	0.918436i	$0.629453\pi$
$180$	1.83463	0.136745
$181$	−19.4914	−1.44879	−0.724394	−	0.689387i	$-0.757880\pi$
$181$	−19.4914	−1.44879	−0.724394	+	0.689387i	$0.757880\pi$
$182$	−2.31305	−0.171454
$183$	2.25500	0.166694
$184$	−7.25400	−0.534772
$185$	−0.700837	−0.0515265
$186$	7.04070	0.516249
$187$	−9.85417	−0.720608
$188$	−4.92517	−0.359205
$189$	−4.88388	−0.355250
$190$	−0.593128	−0.0430301
$191$	−2.21537	−0.160298	−0.0801491	−	0.996783i	$-0.525540\pi$
$191$	−2.21537	−0.160298	−0.0801491	+	0.996783i	$0.525540\pi$
$192$	−11.6381	−0.839908
$193$	−8.84755	−0.636861	−0.318430	−	0.947946i	$-0.603156\pi$
$193$	−8.84755	−0.636861	−0.318430	+	0.947946i	$0.603156\pi$
$194$	0.761111	0.0546446
$195$	−4.44418	−0.318254
$196$	6.91200	0.493714
$197$	6.19744	0.441549	0.220775	−	0.975325i	$-0.429141\pi$
$197$	6.19744	0.441549	0.220775	+	0.975325i	$0.429141\pi$
$198$	−3.63927	−0.258632
$199$	20.2303	1.43409	0.717043	−	0.697028i	$-0.245495\pi$
$199$	20.2303	1.43409	0.717043	+	0.697028i	$0.245495\pi$
$200$	−6.24239	−0.441404
$201$	−18.3513	−1.29440
$202$	1.45080	0.102078
$203$	13.2247	0.928190
$204$	6.76645	0.473746
$205$	3.19044	0.222830
$206$	−0.0564056	−0.00392996
$207$	−9.69219	−0.673653
$208$	12.2689	0.850697
$209$	−18.9245	−1.30904
$210$	0.748797	0.0516719
$211$	1.96502	0.135278	0.0676388	−	0.997710i	$-0.478453\pi$
$211$	1.96502	0.135278	0.0676388	+	0.997710i	$0.478453\pi$
$212$	−16.5901	−1.13941
$213$	28.7769	1.97176
$214$	−3.17696	−0.217172
$215$	−4.29729	−0.293073
$216$	−3.55608	−0.241961
$217$	−17.1822	−1.16640
$218$	−4.17255	−0.282600
$219$	−29.2735	−1.97812
$220$	6.19321	0.417546
$221$	−6.09314	−0.409869
$222$	−0.954606	−0.0640690
$223$	21.4906	1.43911	0.719557	−	0.694433i	$-0.244345\pi$
$223$	21.4906	1.43911	0.719557	+	0.694433i	$0.244345\pi$
$224$	−6.91525	−0.462045
$225$	−8.34056	−0.556038
$226$	−4.51065	−0.300044
$227$	20.7806	1.37925	0.689627	−	0.724165i	$-0.257774\pi$
$227$	20.7806	1.37925	0.689627	+	0.724165i	$0.257774\pi$
$228$	12.9947	0.860595
$229$	28.4761	1.88176	0.940878	−	0.338746i	$-0.110003\pi$
$229$	28.4761	1.88176	0.940878	+	0.338746i	$0.110003\pi$
$230$	−1.02545	−0.0676159
$231$	23.8914	1.57194
$232$	9.62924	0.632190
$233$	−2.19220	−0.143616	−0.0718079	−	0.997418i	$-0.522877\pi$
$233$	−2.19220	−0.143616	−0.0718079	+	0.997418i	$0.522877\pi$
$234$	−2.25028	−0.147105
$235$	−1.43576	−0.0936584
$236$	14.6543	0.953915
$237$	−23.2421	−1.50974
$238$	1.02663	0.0665465
$239$	25.2449	1.63296	0.816478	−	0.577377i	$-0.195924\pi$
$239$	25.2449	1.63296	0.816478	+	0.577377i	$0.195924\pi$
$240$	−3.97179	−0.256378
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−8.52158	−0.547788
$243$	−16.3880	−1.05129
$244$	−1.94309	−0.124393
$245$	2.01495	0.128730
$246$	4.34568	0.277071
$247$	−11.7016	−0.744557
$248$	−12.5108	−0.794437
$249$	13.6714	0.866388
$250$	−1.82147	−0.115200
$251$	21.2167	1.33919	0.669593	−	0.742728i	$-0.266468\pi$
$251$	21.2167	1.33919	0.669593	+	0.742728i	$0.266468\pi$
$252$	−6.09843	−0.384165
$253$	−32.7182	−2.05698
$254$	4.02240	0.252388
$255$	1.97252	0.123524
$256$	7.43481	0.464676
$257$	19.1130	1.19224	0.596119	−	0.802896i	$-0.296708\pi$
$257$	19.1130	1.19224	0.596119	+	0.802896i	$0.296708\pi$
$258$	−5.85332	−0.364412
$259$	2.32963	0.144756
$260$	3.82945	0.237493
$261$	12.8658	0.796372
$262$	−4.81876	−0.297704
$263$	−12.7792	−0.787999	−0.394000	−	0.919111i	$-0.628909\pi$
$263$	−12.7792	−0.787999	−0.394000	+	0.919111i	$0.628909\pi$
$264$	17.3959	1.07065
$265$	−4.83625	−0.297089
$266$	1.97160	0.120887
$267$	−8.61249	−0.527076
$268$	15.8129	0.965927
$269$	1.65545	0.100934	0.0504672	−	0.998726i	$-0.483929\pi$
$269$	1.65545	0.100934	0.0504672	+	0.998726i	$0.483929\pi$
$270$	−0.502698	−0.0305932
$271$	−17.0226	−1.03405	−0.517023	−	0.855971i	$-0.672960\pi$
$271$	−17.0226	−1.03405	−0.517023	+	0.855971i	$0.672960\pi$
$272$	−5.44548	−0.330181
$273$	14.7728	0.894088
$274$	4.24239	0.256292
$275$	−28.1555	−1.69784
$276$	22.4662	1.35231
$277$	16.8245	1.01089	0.505443	−	0.862860i	$-0.331329\pi$
$277$	16.8245	1.01089	0.505443	+	0.862860i	$0.331329\pi$
$278$	3.60814	0.216402
$279$	−16.7159	−1.00076
$280$	−1.33056	−0.0795161
$281$	−16.1664	−0.964405	−0.482203	−	0.876060i	$-0.660163\pi$
$281$	−16.1664	−0.964405	−0.482203	+	0.876060i	$0.660163\pi$
$282$	−1.95564	−0.116456
$283$	2.53878	0.150915	0.0754573	−	0.997149i	$-0.475958\pi$
$283$	2.53878	0.150915	0.0754573	+	0.997149i	$0.475958\pi$
$284$	−24.7965	−1.47140
$285$	3.78814	0.224390
$286$	−7.59632	−0.449180
$287$	−10.6052	−0.626008
$288$	−6.72759	−0.396427
$289$	−14.2956	−0.840918
$290$	1.36122	0.0799334
$291$	−4.86100	−0.284957
$292$	25.2243	1.47614
$293$	−22.8971	−1.33767	−0.668833	−	0.743413i	$-0.733206\pi$
$293$	−22.8971	−1.33767	−0.668833	+	0.743413i	$0.733206\pi$
$294$	2.74455	0.160065
$295$	4.27194	0.248722
$296$	1.69627	0.0985935
$297$	−16.0392	−0.930691
$298$	3.18403	0.184446
$299$	−20.2307	−1.16997
$300$	19.3332	1.11620
$301$	14.2845	0.823345
$302$	−3.51966	−0.202534
$303$	−9.26583	−0.532308
$304$	−10.4578	−0.599798
$305$	−0.566437	−0.0324341
$306$	0.998769	0.0570958
$307$	−4.71512	−0.269106	−0.134553	−	0.990906i	$-0.542960\pi$
$307$	−4.71512	−0.269106	−0.134553	+	0.990906i	$0.542960\pi$
$308$	−20.5867	−1.17303
$309$	0.360246	0.0204937
$310$	−1.76856	−0.100448
$311$	4.63908	0.263058	0.131529	−	0.991312i	$-0.458011\pi$
$311$	4.63908	0.263058	0.131529	+	0.991312i	$0.458011\pi$
$312$	10.7564	0.608964
$313$	−5.04057	−0.284910	−0.142455	−	0.989801i	$-0.545500\pi$
$313$	−5.04057	−0.284910	−0.142455	+	0.989801i	$0.545500\pi$
$314$	1.45018	0.0818386
$315$	−1.77778	−0.100167
$316$	20.0272	1.12662
$317$	−28.0992	−1.57821	−0.789105	−	0.614259i	$-0.789455\pi$
$317$	−28.0992	−1.57821	−0.789105	+	0.614259i	$0.789455\pi$
$318$	−6.58744	−0.369405
$319$	43.4314	2.43169
$320$	2.92339	0.163423
$321$	20.2903	1.13250
$322$	3.40865	0.189957
$323$	5.19369	0.288985
$324$	21.0405	1.16892
$325$	−17.4094	−0.965700
$326$	2.19858	0.121768
$327$	26.6489	1.47369
$328$	−7.72197	−0.426374
$329$	4.77256	0.263120
$330$	2.45914	0.135371
$331$	29.6777	1.63124	0.815618	−	0.578590i	$-0.196397\pi$
$331$	29.6777	1.63124	0.815618	+	0.578590i	$0.196397\pi$
$332$	−11.7803	−0.646529
$333$	2.26641	0.124199
$334$	−1.35579	−0.0741857
$335$	4.60969	0.251854
$336$	13.2025	0.720256
$337$	−12.2225	−0.665799	−0.332900	−	0.942962i	$-0.608027\pi$
$337$	−12.2225	−0.665799	−0.332900	+	0.942962i	$0.608027\pi$
$338$	−0.249130	−0.0135509
$339$	28.8082	1.56465
$340$	−1.69968	−0.0921779
$341$	−56.4284	−3.05577
$342$	1.91810	0.103719
$343$	−19.4700	−1.05128
$344$	10.4009	0.560780
$345$	6.54923	0.352599
$346$	2.89190	0.155469
$347$	−17.9815	−0.965296	−0.482648	−	0.875814i	$-0.660325\pi$
$347$	−17.9815	−0.965296	−0.482648	+	0.875814i	$0.660325\pi$
$348$	−29.8225	−1.59866
$349$	26.2848	1.40699	0.703496	−	0.710699i	$-0.251621\pi$
$349$	26.2848	1.40699	0.703496	+	0.710699i	$0.251621\pi$
$350$	2.93330	0.156792
$351$	−9.91756	−0.529360
$352$	−22.7105	−1.21047
$353$	−13.7610	−0.732424	−0.366212	−	0.930531i	$-0.619346\pi$
$353$	−13.7610	−0.732424	−0.366212	+	0.930531i	$0.619346\pi$
$354$	5.81879	0.309265
$355$	−7.22853	−0.383651
$356$	7.42120	0.393323
$357$	−6.55679	−0.347022
$358$	3.62152	0.191403
$359$	−1.32555	−0.0699598	−0.0349799	−	0.999388i	$-0.511137\pi$
$359$	−1.32555	−0.0699598	−0.0349799	+	0.999388i	$0.511137\pi$
$360$	−1.29445	−0.0682235
$361$	−9.02572	−0.475038
$362$	6.66894	0.350511
$363$	54.4249	2.85657
$364$	−12.7294	−0.667200
$365$	7.35326	0.384887
$366$	−0.771541	−0.0403291
$367$	6.05979	0.316319	0.158159	−	0.987414i	$-0.449444\pi$
$367$	6.05979	0.316319	0.158159	+	0.987414i	$0.449444\pi$
$368$	−18.0803	−0.942500
$369$	−10.3174	−0.537105
$370$	0.239789	0.0124660
$371$	16.0760	0.834627
$372$	38.7470	2.00894
$373$	20.4445	1.05858	0.529288	−	0.848442i	$-0.322459\pi$
$373$	20.4445	1.05858	0.529288	+	0.848442i	$0.322459\pi$
$374$	3.37157	0.174340
$375$	11.6332	0.600736
$376$	3.47503	0.179211
$377$	26.8550	1.38310
$378$	1.67100	0.0859471
$379$	35.4042	1.81859	0.909296	−	0.416150i	$-0.136621\pi$
$379$	35.4042	1.81859	0.909296	+	0.416150i	$0.136621\pi$
$380$	−3.26416	−0.167448
$381$	−25.6899	−1.31613
$382$	0.757981	0.0387817
$383$	6.79327	0.347120	0.173560	−	0.984823i	$-0.444473\pi$
$383$	6.79327	0.347120	0.173560	+	0.984823i	$0.444473\pi$
$384$	20.5458	1.04848
$385$	−6.00131	−0.305855
$386$	3.02716	0.154079
$387$	13.8969	0.706417
$388$	4.18862	0.212645
$389$	24.6869	1.25168	0.625838	−	0.779953i	$-0.284757\pi$
$389$	24.6869	1.25168	0.625838	+	0.779953i	$0.284757\pi$
$390$	1.52056	0.0769966
$391$	8.97924	0.454100
$392$	−4.87687	−0.246319
$393$	30.7760	1.55245
$394$	−2.12043	−0.106826
$395$	5.83823	0.293753
$396$	−20.0280	−1.00644
$397$	14.3804	0.721730	0.360865	−	0.932618i	$-0.382482\pi$
$397$	14.3804	0.721730	0.360865	+	0.932618i	$0.382482\pi$
$398$	−6.92173	−0.346955
$399$	−12.5921	−0.630391
$400$	−15.5589	−0.777945
$401$	7.62276	0.380663	0.190331	−	0.981720i	$-0.439044\pi$
$401$	7.62276	0.380663	0.190331	+	0.981720i	$0.439044\pi$
$402$	6.27883	0.313160
$403$	−34.8914	−1.73806
$404$	7.98416	0.397227
$405$	6.13362	0.304782
$406$	−4.52478	−0.224561
$407$	7.65079	0.379236
$408$	−4.77417	−0.236357
$409$	5.12423	0.253377	0.126688	−	0.991943i	$-0.459565\pi$
$409$	5.12423	0.253377	0.126688	+	0.991943i	$0.459565\pi$
$410$	−1.09160	−0.0539102
$411$	−27.0949	−1.33649
$412$	−0.310416	−0.0152931
$413$	−14.2002	−0.698748
$414$	3.31615	0.162980
$415$	−3.43413	−0.168575
$416$	−14.0426	−0.688496
$417$	−23.0441	−1.12848
$418$	6.47498	0.316701
$419$	13.3513	0.652254	0.326127	−	0.945326i	$-0.394256\pi$
$419$	13.3513	0.652254	0.326127	+	0.945326i	$0.394256\pi$
$420$	4.12085	0.201077
$421$	27.8059	1.35518	0.677588	−	0.735442i	$-0.263025\pi$
$421$	27.8059	1.35518	0.677588	+	0.735442i	$0.263025\pi$
$422$	−0.672326	−0.0327283
$423$	4.64304	0.225752
$424$	11.7054	0.568465
$425$	7.72705	0.374817
$426$	−9.84594	−0.477038
$427$	1.88288	0.0911188
$428$	−17.4837	−0.845109
$429$	48.5155	2.34235
$430$	1.47030	0.0709044
$431$	18.5717	0.894567	0.447283	−	0.894392i	$-0.352392\pi$
$431$	18.5717	0.894567	0.447283	+	0.894392i	$0.352392\pi$
$432$	−8.86339	−0.426440
$433$	−7.19376	−0.345710	−0.172855	−	0.984947i	$-0.555299\pi$
$433$	−7.19376	−0.345710	−0.172855	+	0.984947i	$0.555299\pi$
$434$	5.87883	0.282193
$435$	−8.69370	−0.416831
$436$	−22.9628	−1.09972
$437$	17.2443	0.824906
$438$	10.0158	0.478575
$439$	−16.2866	−0.777315	−0.388657	−	0.921382i	$-0.627061\pi$
$439$	−16.2866	−0.777315	−0.388657	+	0.921382i	$0.627061\pi$
$440$	−4.36971	−0.208318
$441$	−6.51607	−0.310289
$442$	2.08475	0.0991614
$443$	−37.0915	−1.76227	−0.881135	−	0.472864i	$-0.843220\pi$
$443$	−37.0915	−1.76227	−0.881135	+	0.472864i	$0.843220\pi$
$444$	−5.25348	−0.249319
$445$	2.16338	0.102554
$446$	−7.35293	−0.348171
$447$	−20.3355	−0.961837
$448$	−9.71757	−0.459112
$449$	−17.1059	−0.807275	−0.403638	−	0.914919i	$-0.632254\pi$
$449$	−17.1059	−0.807275	−0.403638	+	0.914919i	$0.632254\pi$
$450$	2.85370	0.134525
$451$	−34.8289	−1.64003
$452$	−24.8234	−1.16760
$453$	22.4791	1.05616
$454$	−7.11001	−0.333689
$455$	−3.71079	−0.173965
$456$	−9.16861	−0.429360
$457$	−9.35857	−0.437776	−0.218888	−	0.975750i	$-0.570243\pi$
$457$	−9.35857	−0.437776	−0.218888	+	0.975750i	$0.570243\pi$
$458$	−9.74302	−0.455262
$459$	4.40184	0.205460
$460$	−5.64333	−0.263122
$461$	−15.8670	−0.738999	−0.369500	−	0.929231i	$-0.620471\pi$
$461$	−15.8670	−0.738999	−0.369500	+	0.929231i	$0.620471\pi$
$462$	−8.17435	−0.380305
$463$	−6.99749	−0.325201	−0.162601	−	0.986692i	$-0.551988\pi$
$463$	−6.99749	−0.325201	−0.162601	+	0.986692i	$0.551988\pi$
$464$	24.0005	1.11419
$465$	11.2953	0.523808
$466$	0.750055	0.0347456
$467$	−24.2782	−1.12346	−0.561729	−	0.827321i	$-0.689864\pi$
$467$	−24.2782	−1.12346	−0.561729	+	0.827321i	$0.689864\pi$
$468$	−12.3839	−0.572447
$469$	−15.3229	−0.707547
$470$	0.491240	0.0226592
$471$	−9.26191	−0.426766
$472$	−10.3396	−0.475918
$473$	46.9120	2.15702
$474$	7.95222	0.365258
$475$	14.8395	0.680882
$476$	5.64984	0.258960
$477$	15.6398	0.716096
$478$	−8.63746	−0.395068
$479$	8.93171	0.408100	0.204050	−	0.978960i	$-0.434589\pi$
$479$	8.93171	0.408100	0.204050	+	0.978960i	$0.434589\pi$
$480$	4.54598	0.207495
$481$	4.73072	0.215702
$482$	−0.342147	−0.0155844
$483$	−21.7701	−0.990574
$484$	−46.8968	−2.13167
$485$	1.22104	0.0554447
$486$	5.60711	0.254344
$487$	34.5963	1.56771	0.783855	−	0.620944i	$-0.213250\pi$
$487$	34.5963	1.56771	0.783855	+	0.620944i	$0.213250\pi$
$488$	1.37097	0.0620611
$489$	−14.0417	−0.634987
$490$	−0.689408	−0.0311443
$491$	34.3798	1.55154	0.775770	−	0.631016i	$-0.217362\pi$
$491$	34.3798	1.55154	0.775770	+	0.631016i	$0.217362\pi$
$492$	23.9156	1.07820
$493$	−11.9194	−0.536823
$494$	4.00368	0.180134
$495$	−5.83845	−0.262419
$496$	−31.1827	−1.40014
$497$	24.0281	1.07781
$498$	−4.67762	−0.209609
$499$	38.3126	1.71511	0.857554	−	0.514394i	$-0.171983\pi$
$499$	38.3126	1.71511	0.857554	+	0.514394i	$0.171983\pi$
$500$	−10.0241	−0.448291
$501$	8.65906	0.386858
$502$	−7.25923	−0.323995
$503$	−12.6073	−0.562132	−0.281066	−	0.959688i	$-0.590688\pi$
$503$	−12.6073	−0.562132	−0.281066	+	0.959688i	$0.590688\pi$
$504$	4.30285	0.191664
$505$	2.32750	0.103572
$506$	11.1944	0.497653
$507$	1.59112	0.0706641
$508$	22.1364	0.982146
$509$	−19.0748	−0.845476	−0.422738	−	0.906252i	$-0.638931\pi$
$509$	−19.0748	−0.845476	−0.422738	+	0.906252i	$0.638931\pi$
$510$	−0.674891	−0.0298847
$511$	−24.4428	−1.08128
$512$	−21.3484	−0.943474
$513$	8.45356	0.373234
$514$	−6.53947	−0.288444
$515$	−0.0904909	−0.00398750
$516$	−32.2125	−1.41808
$517$	15.6737	0.689326
$518$	−0.797076	−0.0350215
$519$	−18.4697	−0.810731
$520$	−2.70193	−0.118487
$521$	11.5960	0.508028	0.254014	−	0.967201i	$-0.418249\pi$
$521$	11.5960	0.508028	0.254014	+	0.967201i	$0.418249\pi$
$522$	−4.40199	−0.192670
$523$	−26.2727	−1.14883	−0.574413	−	0.818566i	$-0.694770\pi$
$523$	−26.2727	−1.14883	−0.574413	+	0.818566i	$0.694770\pi$
$524$	−26.5190	−1.15849
$525$	−18.7342	−0.817626
$526$	4.37236	0.190644
$527$	15.4863	0.674594
$528$	43.3586	1.88694
$529$	6.81324	0.296228
$530$	1.65471	0.0718760
$531$	−13.8149	−0.599515
$532$	10.8503	0.470420
$533$	−21.5358	−0.932819
$534$	2.94674	0.127518
$535$	−5.09676	−0.220352
$536$	−11.1570	−0.481911
$537$	−23.1296	−0.998118
$538$	−0.566406	−0.0244195
$539$	−21.9965	−0.947455
$540$	−2.76649	−0.119051
$541$	−15.1441	−0.651097	−0.325548	−	0.945525i	$-0.605549\pi$
$541$	−15.1441	−0.651097	−0.325548	+	0.945525i	$0.605549\pi$
$542$	5.82421	0.250171
$543$	−42.5926	−1.82782
$544$	6.23272	0.267226
$545$	−6.69397	−0.286738
$546$	−5.05446	−0.216311
$547$	34.7331	1.48508	0.742540	−	0.669802i	$-0.233621\pi$
$547$	34.7331	1.48508	0.742540	+	0.669802i	$0.233621\pi$
$548$	23.3471	0.997339
$549$	1.83178	0.0781785
$550$	9.63331	0.410766
$551$	−22.8907	−0.975178
$552$	−15.8514	−0.674680
$553$	−19.4067	−0.825256
$554$	−5.75645	−0.244568
$555$	−1.53146	−0.0650071
$556$	19.8566	0.842109
$557$	34.1470	1.44685	0.723427	−	0.690401i	$-0.242566\pi$
$557$	34.1470	1.44685	0.723427	+	0.690401i	$0.242566\pi$
$558$	5.71930	0.242117
$559$	29.0071	1.22687
$560$	−3.31636	−0.140142
$561$	−21.5333	−0.909136
$562$	5.53128	0.233323
$563$	−19.2900	−0.812975	−0.406488	−	0.913656i	$-0.633247\pi$
$563$	−19.2900	−0.812975	−0.406488	+	0.913656i	$0.633247\pi$
$564$	−10.7624	−0.453181
$565$	−7.23638	−0.304437
$566$	−0.868635	−0.0365114
$567$	−20.3886	−0.856241
$568$	17.4955	0.734097
$569$	−33.4263	−1.40130	−0.700652	−	0.713503i	$-0.747107\pi$
$569$	−33.4263	−1.40130	−0.700652	+	0.713503i	$0.747107\pi$
$570$	−1.29610	−0.0542877
$571$	3.07936	0.128867	0.0644336	−	0.997922i	$-0.479476\pi$
$571$	3.07936	0.128867	0.0644336	+	0.997922i	$0.479476\pi$
$572$	−41.8048	−1.74795
$573$	−4.84101	−0.202236
$574$	3.62855	0.151453
$575$	25.6556	1.06991
$576$	−9.45386	−0.393911
$577$	−5.95435	−0.247883	−0.123941	−	0.992290i	$-0.539553\pi$
$577$	−5.95435	−0.247883	−0.123941	+	0.992290i	$0.539553\pi$
$578$	4.89120	0.203447
$579$	−19.3336	−0.803478
$580$	7.49117	0.311054
$581$	11.4153	0.473587
$582$	1.66318	0.0689408
$583$	52.7957	2.18657
$584$	−17.7974	−0.736463
$585$	−3.61009	−0.149259
$586$	7.83419	0.323627
$587$	42.0432	1.73531	0.867655	−	0.497167i	$-0.165626\pi$
$587$	42.0432	1.73531	0.867655	+	0.497167i	$0.165626\pi$
$588$	15.1041	0.622881
$589$	29.7409	1.22545
$590$	−1.46163	−0.0601745
$591$	13.5426	0.557068
$592$	4.22788	0.173765
$593$	40.9908	1.68329	0.841645	−	0.540031i	$-0.181587\pi$
$593$	40.9908	1.68329	0.841645	+	0.540031i	$0.181587\pi$
$594$	5.48778	0.225166
$595$	1.64701	0.0675208
$596$	17.5227	0.717757
$597$	44.2071	1.80928
$598$	6.92186	0.283056
$599$	−27.0862	−1.10671	−0.553356	−	0.832945i	$-0.686653\pi$
$599$	−27.0862	−1.10671	−0.553356	+	0.832945i	$0.686653\pi$
$600$	−13.6408	−0.556885
$601$	−3.03033	−0.123610	−0.0618049	−	0.998088i	$-0.519686\pi$
$601$	−3.03033	−0.123610	−0.0618049	+	0.998088i	$0.519686\pi$
$602$	−4.88740	−0.199195
$603$	−14.9071	−0.607064
$604$	−19.3697	−0.788144
$605$	−13.6711	−0.555809
$606$	3.17027	0.128784
$607$	0.560838	0.0227637	0.0113818	−	0.999935i	$-0.496377\pi$
$607$	0.560838	0.0227637	0.0113818	+	0.999935i	$0.496377\pi$
$608$	11.9697	0.485435
$609$	28.8985	1.17103
$610$	0.193805	0.00784693
$611$	9.69150	0.392076
$612$	5.49652	0.222184
$613$	23.7388	0.958801	0.479401	−	0.877596i	$-0.340854\pi$
$613$	23.7388	0.958801	0.479401	+	0.877596i	$0.340854\pi$
$614$	1.61326	0.0651061
$615$	6.97173	0.281127
$616$	14.5252	0.585239
$617$	−10.2411	−0.412290	−0.206145	−	0.978521i	$-0.566092\pi$
$617$	−10.2411	−0.412290	−0.206145	+	0.978521i	$0.566092\pi$
$618$	−0.123257	−0.00495813
$619$	−27.8348	−1.11878	−0.559388	−	0.828906i	$-0.688964\pi$
$619$	−27.8348	−1.11878	−0.559388	+	0.828906i	$0.688964\pi$
$620$	−9.73293	−0.390884
$621$	14.6152	0.586486
$622$	−1.58725	−0.0636428
$623$	−7.19125	−0.288111
$624$	26.8100	1.07326
$625$	20.5714	0.822855
$626$	1.72462	0.0689295
$627$	−41.3538	−1.65151
$628$	7.98079	0.318468
$629$	−2.09970	−0.0837204
$630$	0.608262	0.0242338
$631$	23.0564	0.917861	0.458931	−	0.888472i	$-0.348233\pi$
$631$	23.0564	0.917861	0.458931	+	0.888472i	$0.348233\pi$
$632$	−14.1305	−0.562082
$633$	4.29396	0.170669
$634$	9.61406	0.381823
$635$	6.45309	0.256083
$636$	−36.2526	−1.43751
$637$	−13.6011	−0.538895
$638$	−14.8599	−0.588310
$639$	23.3761	0.924744
$640$	−5.16094	−0.204004
$641$	35.6143	1.40668	0.703340	−	0.710853i	$-0.251691\pi$
$641$	35.6143	1.40668	0.703340	+	0.710853i	$0.251691\pi$
$642$	−6.94227	−0.273990
$643$	−28.2806	−1.11528	−0.557639	−	0.830084i	$-0.688293\pi$
$643$	−28.2806	−1.11528	−0.557639	+	0.830084i	$0.688293\pi$
$644$	18.7588	0.739201
$645$	−9.39042	−0.369747
$646$	−1.77700	−0.0699153
$647$	14.5953	0.573802	0.286901	−	0.957960i	$-0.407375\pi$
$647$	14.5953	0.573802	0.286901	+	0.957960i	$0.407375\pi$
$648$	−14.8455	−0.583186
$649$	−46.6353	−1.83060
$650$	5.95658	0.233636
$651$	−37.5464	−1.47156
$652$	12.0994	0.473850
$653$	−28.0718	−1.09853	−0.549267	−	0.835647i	$-0.685093\pi$
$653$	−28.0718	−1.09853	−0.549267	+	0.835647i	$0.685093\pi$
$654$	−9.11783	−0.356535
$655$	−7.73068	−0.302063
$656$	−19.2467	−0.751457
$657$	−23.7794	−0.927724
$658$	−1.63292	−0.0636577
$659$	−2.33181	−0.0908343	−0.0454172	−	0.998968i	$-0.514462\pi$
$659$	−2.33181	−0.0908343	−0.0454172	+	0.998968i	$0.514462\pi$
$660$	13.5334	0.526786
$661$	−21.3409	−0.830063	−0.415031	−	0.909807i	$-0.636229\pi$
$661$	−21.3409	−0.830063	−0.415031	+	0.909807i	$0.636229\pi$
$662$	−10.1542	−0.394652
$663$	−13.3147	−0.517100
$664$	8.31179	0.322560
$665$	3.16302	0.122657
$666$	−0.775446	−0.0300479
$667$	−39.5752	−1.53236
$668$	−7.46133	−0.288687
$669$	46.9611	1.81562
$670$	−1.57719	−0.0609322
$671$	6.18360	0.238715
$672$	−15.1112	−0.582926
$673$	−25.0948	−0.967333	−0.483667	−	0.875252i	$-0.660695\pi$
$673$	−25.0948	−0.967333	−0.483667	+	0.875252i	$0.660695\pi$
$674$	4.18187	0.161080
$675$	12.5770	0.484089
$676$	−1.37103	−0.0527321
$677$	−7.78669	−0.299267	−0.149633	−	0.988742i	$-0.547809\pi$
$677$	−7.78669	−0.299267	−0.149633	+	0.988742i	$0.547809\pi$
$678$	−9.85664	−0.378542
$679$	−4.05883	−0.155764
$680$	1.19923	0.0459885
$681$	45.4096	1.74010
$682$	19.3068	0.739295
$683$	2.68470	0.102727	0.0513636	−	0.998680i	$-0.483643\pi$
$683$	2.68470	0.102727	0.0513636	+	0.998680i	$0.483643\pi$
$684$	10.5559	0.403613
$685$	6.80602	0.260045
$686$	6.66159	0.254341
$687$	62.2259	2.37407
$688$	25.9239	0.988339
$689$	32.6452	1.24368
$690$	−2.24080	−0.0853057
$691$	−46.3260	−1.76232	−0.881162	−	0.472814i	$-0.843238\pi$
$691$	−46.3260	−1.76232	−0.881162	+	0.472814i	$0.843238\pi$
$692$	15.9150	0.604996
$693$	19.4074	0.737227
$694$	6.15230	0.233538
$695$	5.78849	0.219570
$696$	21.0418	0.797586
$697$	9.55851	0.362054
$698$	−8.99326	−0.340400
$699$	−4.79039	−0.181189
$700$	16.1428	0.610141
$701$	4.33233	0.163630	0.0818150	−	0.996648i	$-0.473928\pi$
$701$	4.33233	0.163630	0.0818150	+	0.996648i	$0.473928\pi$
$702$	3.39326	0.128070
$703$	−4.03239	−0.152084
$704$	−31.9137	−1.20279
$705$	−3.13741	−0.118162
$706$	4.70829	0.177199
$707$	−7.73677	−0.290971
$708$	32.0225	1.20348
$709$	−45.2491	−1.69936	−0.849682	−	0.527295i	$-0.823206\pi$
$709$	−45.2491	−1.69936	−0.849682	+	0.527295i	$0.823206\pi$
$710$	2.47322	0.0928183
$711$	−18.8800	−0.708057
$712$	−5.23614	−0.196233
$713$	51.4182	1.92563
$714$	2.24338	0.0839566
$715$	−12.1867	−0.455757
$716$	19.9303	0.744831
$717$	55.1650	2.06017
$718$	0.453533	0.0169257
$719$	34.3560	1.28126	0.640632	−	0.767848i	$-0.278672\pi$
$719$	34.3560	1.28126	0.640632	+	0.767848i	$0.278672\pi$
$720$	−3.22636	−0.120239
$721$	0.300798	0.0112023
$722$	3.08812	0.114928
$723$	2.18519	0.0812683
$724$	36.7011	1.36399
$725$	−34.0563	−1.26482
$726$	−18.6213	−0.691102
$727$	−29.1579	−1.08141	−0.540703	−	0.841213i	$-0.681842\pi$
$727$	−29.1579	−1.08141	−0.540703	+	0.841213i	$0.681842\pi$
$728$	8.98141	0.332873
$729$	−2.28799	−0.0847405
$730$	−2.51590	−0.0931175
$731$	−12.8746	−0.476185
$732$	−4.24602	−0.156937
$733$	36.8326	1.36044	0.680222	−	0.733007i	$-0.261884\pi$
$733$	36.8326	1.36044	0.680222	+	0.733007i	$0.261884\pi$
$734$	−2.07334	−0.0765283
$735$	4.40305	0.162409
$736$	20.6941	0.762795
$737$	−50.3224	−1.85365
$738$	3.53008	0.129944
$739$	24.4258	0.898517	0.449258	−	0.893402i	$-0.351688\pi$
$739$	24.4258	0.898517	0.449258	+	0.893402i	$0.351688\pi$
$740$	1.31963	0.0485106
$741$	−25.5704	−0.939350
$742$	−5.50037	−0.201925
$743$	−24.4245	−0.896049	−0.448024	−	0.894021i	$-0.647872\pi$
$743$	−24.4245	−0.896049	−0.448024	+	0.894021i	$0.647872\pi$
$744$	−27.3386	−1.00228
$745$	5.10811	0.187147
$746$	−6.99503	−0.256106
$747$	11.1055	0.406330
$748$	18.5548	0.678429
$749$	16.9420	0.619047
$750$	−3.98027	−0.145339
$751$	−30.0598	−1.09690	−0.548449	−	0.836184i	$-0.684781\pi$
$751$	−30.0598	−1.09690	−0.548449	+	0.836184i	$0.684781\pi$
$752$	8.66136	0.315847
$753$	46.3627	1.68955
$754$	−9.18835	−0.334620
$755$	−5.64656	−0.205499
$756$	9.19603	0.334456
$757$	5.79087	0.210473	0.105236	−	0.994447i	$-0.466440\pi$
$757$	5.79087	0.210473	0.105236	+	0.994447i	$0.466440\pi$
$758$	−12.1134	−0.439980
$759$	−71.4956	−2.59513
$760$	2.30308	0.0835415
$761$	2.42691	0.0879754	0.0439877	−	0.999032i	$-0.485994\pi$
$761$	2.42691	0.0879754	0.0439877	+	0.999032i	$0.485994\pi$
$762$	8.78972	0.318418
$763$	22.2512	0.805549
$764$	4.17139	0.150916
$765$	1.60231	0.0579318
$766$	−2.32430	−0.0839803
$767$	−28.8361	−1.04121
$768$	16.2465	0.586246
$769$	22.0750	0.796045	0.398022	−	0.917376i	$-0.369697\pi$
$769$	22.0750	0.796045	0.398022	+	0.917376i	$0.369697\pi$
$770$	2.05333	0.0739968
$771$	41.7657	1.50416
$772$	16.6594	0.599584
$773$	28.7802	1.03515	0.517576	−	0.855637i	$-0.326834\pi$
$773$	28.7802	1.03515	0.517576	+	0.855637i	$0.326834\pi$
$774$	−4.75476	−0.170906
$775$	44.2477	1.58943
$776$	−2.95534	−0.106091
$777$	5.09070	0.182628
$778$	−8.44655	−0.302824
$779$	18.3567	0.657699
$780$	8.36810	0.299626
$781$	78.9113	2.82367
$782$	−3.07222	−0.109862
$783$	−19.4007	−0.693325
$784$	−12.1554	−0.434121
$785$	2.32651	0.0830369
$786$	−10.5299	−0.375590
$787$	−53.4388	−1.90489	−0.952443	−	0.304715i	$-0.901439\pi$
$787$	−53.4388	−1.90489	−0.952443	+	0.304715i	$0.901439\pi$
$788$	−11.6694	−0.415704
$789$	−27.9250	−0.994158
$790$	−1.99753	−0.0710690
$791$	24.0543	0.855271
$792$	14.1311	0.502125
$793$	3.82351	0.135777
$794$	−4.92020	−0.174611
$795$	−10.5682	−0.374814
$796$	−38.0923	−1.35015
$797$	10.4149	0.368914	0.184457	−	0.982841i	$-0.440947\pi$
$797$	10.4149	0.368914	0.184457	+	0.982841i	$0.440947\pi$
$798$	4.30833	0.152513
$799$	−4.30151	−0.152176
$800$	17.8082	0.629616
$801$	−6.99609	−0.247195
$802$	−2.60810	−0.0920954
$803$	−80.2730	−2.83277
$804$	34.5543	1.21864
$805$	5.46847	0.192738
$806$	11.9380	0.420498
$807$	3.61747	0.127341
$808$	−5.63335	−0.198181
$809$	−25.9467	−0.912237	−0.456118	−	0.889919i	$-0.650761\pi$
$809$	−25.9467	−0.912237	−0.456118	+	0.889919i	$0.650761\pi$
$810$	−2.09860	−0.0737373
$811$	−11.1712	−0.392275	−0.196137	−	0.980576i	$-0.562840\pi$
$811$	−11.1712	−0.392275	−0.196137	+	0.980576i	$0.562840\pi$
$812$	−24.9012	−0.873861
$813$	−37.1976	−1.30458
$814$	−2.61769	−0.0917501
$815$	3.52715	0.123551
$816$	−11.8994	−0.416563
$817$	−24.7252	−0.865026
$818$	−1.75324	−0.0613005
$819$	12.0002	0.419321
$820$	−6.00739	−0.209787
$821$	18.3232	0.639484	0.319742	−	0.947505i	$-0.396404\pi$
$821$	18.3232	0.639484	0.319742	+	0.947505i	$0.396404\pi$
$822$	9.27045	0.323344
$823$	21.1230	0.736301	0.368150	−	0.929766i	$-0.379991\pi$
$823$	21.1230	0.736301	0.368150	+	0.929766i	$0.379991\pi$
$824$	0.219019	0.00762989
$825$	−61.5252	−2.14203
$826$	4.85857	0.169051
$827$	47.5383	1.65307	0.826534	−	0.562887i	$-0.190310\pi$
$827$	47.5383	1.65307	0.826534	+	0.562887i	$0.190310\pi$
$828$	18.2498	0.634223
$829$	15.8701	0.551190	0.275595	−	0.961274i	$-0.411125\pi$
$829$	15.8701	0.551190	0.275595	+	0.961274i	$0.411125\pi$
$830$	1.17498	0.0407841
$831$	36.7648	1.27536
$832$	−19.7332	−0.684126
$833$	6.03676	0.209161
$834$	7.88448	0.273017
$835$	−2.17508	−0.0752719
$836$	35.6337	1.23242
$837$	25.2065	0.871262
$838$	−4.56811	−0.157803
$839$	34.3114	1.18456	0.592281	−	0.805732i	$-0.298228\pi$
$839$	34.3114	1.18456	0.592281	+	0.805732i	$0.298228\pi$
$840$	−2.90753	−0.100319
$841$	23.5337	0.811507
$842$	−9.51370	−0.327864
$843$	−35.3267	−1.21672
$844$	−3.70001	−0.127360
$845$	−0.399676	−0.0137493
$846$	−1.58860	−0.0546173
$847$	45.4437	1.56146
$848$	29.1752	1.00188
$849$	5.54772	0.190397
$850$	−2.64379	−0.0906811
$851$	−6.97150	−0.238980
$852$	−54.1851	−1.85635
$853$	−45.8466	−1.56976	−0.784879	−	0.619649i	$-0.787275\pi$
$853$	−45.8466	−1.56976	−0.784879	+	0.619649i	$0.787275\pi$
$854$	−0.644221	−0.0220448
$855$	3.07718	0.105237
$856$	12.3359	0.421633
$857$	21.7254	0.742125	0.371063	−	0.928608i	$-0.378993\pi$
$857$	21.7254	0.742125	0.371063	+	0.928608i	$0.378993\pi$
$858$	−16.5994	−0.566696
$859$	52.5363	1.79252	0.896258	−	0.443534i	$-0.146275\pi$
$859$	52.5363	1.79252	0.896258	+	0.443534i	$0.146275\pi$
$860$	8.09152	0.275919
$861$	−23.1745	−0.789786
$862$	−6.35425	−0.216427
$863$	32.9971	1.12323	0.561617	−	0.827397i	$-0.310179\pi$
$863$	32.9971	1.12323	0.561617	+	0.827397i	$0.310179\pi$
$864$	10.1447	0.345131
$865$	4.63944	0.157746
$866$	2.46132	0.0836392
$867$	−31.2387	−1.06092
$868$	32.3529	1.09813
$869$	−63.7339	−2.16202
$870$	2.97452	0.100846
$871$	−31.1159	−1.05432
$872$	16.2017	0.548660
$873$	−3.94868	−0.133643
$874$	−5.90008	−0.199573
$875$	9.71348	0.328376
$876$	55.1201	1.86234
$877$	−21.4221	−0.723372	−0.361686	−	0.932300i	$-0.617799\pi$
$877$	−21.4221	−0.723372	−0.361686	+	0.932300i	$0.617799\pi$
$878$	5.57239	0.188059
$879$	−50.0347	−1.68763
$880$	−10.8913	−0.367147
$881$	−39.1162	−1.31786	−0.658929	−	0.752205i	$-0.728990\pi$
$881$	−39.1162	−1.31786	−0.658929	+	0.752205i	$0.728990\pi$
$882$	2.22945	0.0750696
$883$	−2.84717	−0.0958150	−0.0479075	−	0.998852i	$-0.515255\pi$
$883$	−2.84717	−0.0958150	−0.0479075	+	0.998852i	$0.515255\pi$
$884$	11.4730	0.385878
$885$	9.33503	0.313794
$886$	12.6907	0.426354
$887$	−46.9262	−1.57563	−0.787814	−	0.615913i	$-0.788787\pi$
$887$	−46.9262	−1.57563	−0.787814	+	0.615913i	$0.788787\pi$
$888$	3.70667	0.124388
$889$	−21.4505	−0.719428
$890$	−0.740196	−0.0248114
$891$	−66.9586	−2.24320
$892$	−40.4653	−1.35488
$893$	−8.26088	−0.276440
$894$	6.95773	0.232701
$895$	5.80997	0.194206
$896$	17.1553	0.573120
$897$	−44.2080	−1.47606
$898$	5.85272	0.195308
$899$	−68.2546	−2.27642
$900$	15.7047	0.523491
$901$	−14.4893	−0.482710
$902$	11.9166	0.396779
$903$	31.2144	1.03875
$904$	17.5145	0.582525
$905$	10.6989	0.355644
$906$	−7.69115	−0.255521
$907$	15.7164	0.521856	0.260928	−	0.965358i	$-0.415972\pi$
$907$	15.7164	0.521856	0.260928	+	0.965358i	$0.415972\pi$
$908$	−39.1285	−1.29852
$909$	−7.52681	−0.249649
$910$	1.26964	0.0420881
$911$	0.0451186	0.00149485	0.000747423	−	1.00000i	$-0.499762\pi$
$911$	0.0451186	0.00149485	0.000747423		1.00000i	$0.499762\pi$
$912$	−22.8524	−0.756718
$913$	37.4892	1.24071
$914$	3.20201	0.105913
$915$	−1.23778	−0.0409196
$916$	−53.6187	−1.77161
$917$	25.6973	0.848601
$918$	−1.50608	−0.0497079
$919$	−7.88987	−0.260263	−0.130131	−	0.991497i	$-0.541540\pi$
$919$	−7.88987	−0.260263	−0.130131	+	0.991497i	$0.541540\pi$
$920$	3.98174	0.131274
$921$	−10.3035	−0.339511
$922$	5.42884	0.178789
$923$	48.7933	1.60605
$924$	−44.9859	−1.47993
$925$	−5.99929	−0.197255
$926$	2.39417	0.0786773
$927$	0.292635	0.00961140
$928$	−27.4702	−0.901752
$929$	25.6276	0.840815	0.420408	−	0.907335i	$-0.361887\pi$
$929$	25.6276	0.840815	0.420408	+	0.907335i	$0.361887\pi$
$930$	−3.86466	−0.126727
$931$	11.5934	0.379957
$932$	4.12777	0.135210
$933$	10.1373	0.331880
$934$	8.30670	0.271803
$935$	5.40898	0.176893
$936$	8.73767	0.285600
$937$	−57.8627	−1.89029	−0.945146	−	0.326649i	$-0.894081\pi$
$937$	−57.8627	−1.89029	−0.945146	+	0.326649i	$0.894081\pi$
$938$	5.24269	0.171180
$939$	−11.0146	−0.359449
$940$	2.70344	0.0881764
$941$	−14.1272	−0.460533	−0.230266	−	0.973128i	$-0.573960\pi$
$941$	−14.1272	−0.460533	−0.230266	+	0.973128i	$0.573960\pi$
$942$	3.16893	0.103249
$943$	31.7365	1.03348
$944$	−25.7710	−0.838774
$945$	2.68077	0.0872056
$946$	−16.0508	−0.521857
$947$	22.5318	0.732185	0.366092	−	0.930578i	$-0.380695\pi$
$947$	22.5318	0.732185	0.366092	+	0.930578i	$0.380695\pi$
$948$	43.7634	1.42137
$949$	−49.6353	−1.61123
$950$	−5.07729	−0.164729
$951$	−61.4023	−1.99110
$952$	−3.98633	−0.129198
$953$	−34.0142	−1.10183	−0.550914	−	0.834562i	$-0.685721\pi$
$953$	−34.0142	−1.10183	−0.550914	+	0.834562i	$0.685721\pi$
$954$	−5.35110	−0.173248
$955$	1.21602	0.0393495
$956$	−47.5345	−1.53737
$957$	94.9061	3.06788
$958$	−3.05596	−0.0987335
$959$	−22.6237	−0.730557
$960$	6.38819	0.206178
$961$	57.6799	1.86064
$962$	−1.61860	−0.0521858
$963$	16.4822	0.531133
$964$	−1.88294	−0.0606453
$965$	4.85644	0.156334
$966$	7.44857	0.239654
$967$	−62.1874	−1.99981	−0.999906	−	0.0137093i	$-0.995636\pi$
$967$	−62.1874	−1.99981	−0.999906	+	0.0137093i	$0.995636\pi$
$968$	33.0888	1.06351
$969$	11.3492	0.364590
$970$	−0.417776	−0.0134140
$971$	18.4346	0.591594	0.295797	−	0.955251i	$-0.404415\pi$
$971$	18.4346	0.591594	0.295797	+	0.955251i	$0.404415\pi$
$972$	30.8576	0.989757
$973$	−19.2414	−0.616850
$974$	−11.8370	−0.379283
$975$	−38.0430	−1.21835
$976$	3.41710	0.109379
$977$	25.2228	0.806949	0.403474	−	0.914991i	$-0.367802\pi$
$977$	25.2228	0.806949	0.403474	+	0.914991i	$0.367802\pi$
$978$	4.80432	0.153625
$979$	−23.6169	−0.754800
$980$	−3.79402	−0.121195
$981$	21.6474	0.691148
$982$	−11.7630	−0.375371
$983$	12.7405	0.406358	0.203179	−	0.979142i	$-0.434873\pi$
$983$	12.7405	0.406358	0.203179	+	0.979142i	$0.434873\pi$
$984$	−16.8740	−0.537923
$985$	−3.40179	−0.108390
$986$	4.07819	0.129876
$987$	10.4290	0.331958
$988$	22.0334	0.700977
$989$	−42.7468	−1.35927
$990$	1.99761	0.0634881
$991$	15.6775	0.498011	0.249005	−	0.968502i	$-0.419896\pi$
$991$	15.6775	0.498011	0.249005	+	0.968502i	$0.419896\pi$
$992$	35.6907	1.13318
$993$	64.8517	2.05801
$994$	−8.22116	−0.260759
$995$	−11.1045	−0.352035
$996$	−25.7423	−0.815676
$997$	28.1048	0.890088	0.445044	−	0.895509i	$-0.353188\pi$
$997$	28.1048	0.890088	0.445044	+	0.895509i	$0.353188\pi$
$998$	−13.1085	−0.414944
$999$	−3.41759	−0.108128

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	241.2.a.b.1.5	✓	12
3.2	odd	2		2169.2.a.h.1.8		12
4.3	odd	2		3856.2.a.n.1.3		12
5.4	even	2		6025.2.a.h.1.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.a.b.1.5	✓	12	1.1	even	1	trivial
2169.2.a.h.1.8		12	3.2	odd	2
3856.2.a.n.1.3		12	4.3	odd	2
6025.2.a.h.1.8		12	5.4	even	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:	\( N \)	\(=\)	\( 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	241.a (trivial)

\(f(q)\)	\(=\)	\(q-0.342147 q^{2} +2.18519 q^{3} -1.88294 q^{4} -0.548903 q^{5} -0.747658 q^{6} +1.82459 q^{7} +1.32853 q^{8} +1.77508 q^{9} +O(q^{10})\)	\(q-0.342147 q^{2} +2.18519 q^{3} -1.88294 q^{4} -0.548903 q^{5} -0.747658 q^{6} +1.82459 q^{7} +1.32853 q^{8} +1.77508 q^{9} +0.187805 q^{10} +5.99218 q^{11} -4.11458 q^{12} +3.70515 q^{13} -0.624278 q^{14} -1.19946 q^{15} +3.31132 q^{16} -1.64451 q^{17} -0.607337 q^{18} -3.15821 q^{19} +1.03355 q^{20} +3.98709 q^{21} -2.05021 q^{22} -5.46015 q^{23} +2.90311 q^{24} -4.69871 q^{25} -1.26771 q^{26} -2.67670 q^{27} -3.43559 q^{28} +7.24801 q^{29} +0.410391 q^{30} -9.41700 q^{31} -3.79003 q^{32} +13.0941 q^{33} +0.562662 q^{34} -1.00152 q^{35} -3.34236 q^{36} +1.27680 q^{37} +1.08057 q^{38} +8.09648 q^{39} -0.729236 q^{40} -5.81239 q^{41} -1.36417 q^{42} +7.82887 q^{43} -11.2829 q^{44} -0.974345 q^{45} +1.86817 q^{46} +2.61568 q^{47} +7.23587 q^{48} -3.67086 q^{49} +1.60765 q^{50} -3.59356 q^{51} -6.97656 q^{52} +8.81076 q^{53} +0.915823 q^{54} -3.28912 q^{55} +2.42403 q^{56} -6.90130 q^{57} -2.47989 q^{58} -7.78270 q^{59} +2.25850 q^{60} +1.03194 q^{61} +3.22200 q^{62} +3.23879 q^{63} -5.32589 q^{64} -2.03377 q^{65} -4.48010 q^{66} -8.39801 q^{67} +3.09650 q^{68} -11.9315 q^{69} +0.342668 q^{70} +13.1691 q^{71} +2.35825 q^{72} -13.3963 q^{73} -0.436852 q^{74} -10.2676 q^{75} +5.94670 q^{76} +10.9333 q^{77} -2.77018 q^{78} -10.6362 q^{79} -1.81759 q^{80} -11.1743 q^{81} +1.98869 q^{82} +6.25636 q^{83} -7.50743 q^{84} +0.902673 q^{85} -2.67862 q^{86} +15.8383 q^{87} +7.96082 q^{88} -3.94129 q^{89} +0.333369 q^{90} +6.76039 q^{91} +10.2811 q^{92} -20.5780 q^{93} -0.894948 q^{94} +1.73355 q^{95} -8.28195 q^{96} -2.22451 q^{97} +1.25598 q^{98} +10.6366 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + q^{3} + 13 q^{4} + 6 q^{5} - q^{6} + 3 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + q^3 + 13 * q^4 + 6 * q^5 - q^6 + 3 * q^7 + 9 * q^8 + 15 * q^9	\( 12 q + 3 q^{2} + q^{3} + 13 q^{4} + 6 q^{5} - q^{6} + 3 q^{7} + 9 q^{8} + 15 q^{9} - 7 q^{10} + 22 q^{11} - 7 q^{12} - 5 q^{13} + 6 q^{14} + 13 q^{15} + 15 q^{16} - 4 q^{17} - q^{18} - 6 q^{19} + 10 q^{20} - 14 q^{21} - 12 q^{22} + 32 q^{23} - 15 q^{24} + 4 q^{25} + 8 q^{26} - 5 q^{27} - 11 q^{28} + 6 q^{29} - 19 q^{30} + 8 q^{31} + q^{32} - 24 q^{33} - 19 q^{34} + 15 q^{35} - 8 q^{36} - 8 q^{37} - 10 q^{38} + 31 q^{39} - 52 q^{40} - q^{41} - 49 q^{42} - 2 q^{43} + 42 q^{44} - 15 q^{45} - 25 q^{46} + 34 q^{47} - 49 q^{48} - 9 q^{49} - 27 q^{50} - 3 q^{51} - 41 q^{52} + 5 q^{53} - 40 q^{54} - 3 q^{55} + q^{56} - 22 q^{57} - 33 q^{58} + 26 q^{59} - 57 q^{60} - 26 q^{61} - 17 q^{62} - 4 q^{63} + 13 q^{64} - 25 q^{65} - 2 q^{66} + 6 q^{67} - 35 q^{68} - 2 q^{69} - 4 q^{70} + 94 q^{71} + 17 q^{72} - 22 q^{73} + 26 q^{74} - 20 q^{76} - 7 q^{77} + 54 q^{78} + 9 q^{79} + 19 q^{80} + 4 q^{81} + 15 q^{82} - 8 q^{83} + 2 q^{84} + 4 q^{85} + 9 q^{86} + 4 q^{87} + 6 q^{88} - 3 q^{89} + 11 q^{90} - 20 q^{91} + 36 q^{92} + 12 q^{93} + 48 q^{94} + 33 q^{95} - 23 q^{96} - 29 q^{97} + 28 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + q^3 + 13 * q^4 + 6 * q^5 - q^6 + 3 * q^7 + 9 * q^8 + 15 * q^9 - 7 * q^10 + 22 * q^11 - 7 * q^12 - 5 * q^13 + 6 * q^14 + 13 * q^15 + 15 * q^16 - 4 * q^17 - q^18 - 6 * q^19 + 10 * q^20 - 14 * q^21 - 12 * q^22 + 32 * q^23 - 15 * q^24 + 4 * q^25 + 8 * q^26 - 5 * q^27 - 11 * q^28 + 6 * q^29 - 19 * q^30 + 8 * q^31 + q^32 - 24 * q^33 - 19 * q^34 + 15 * q^35 - 8 * q^36 - 8 * q^37 - 10 * q^38 + 31 * q^39 - 52 * q^40 - q^41 - 49 * q^42 - 2 * q^43 + 42 * q^44 - 15 * q^45 - 25 * q^46 + 34 * q^47 - 49 * q^48 - 9 * q^49 - 27 * q^50 - 3 * q^51 - 41 * q^52 + 5 * q^53 - 40 * q^54 - 3 * q^55 + q^56 - 22 * q^57 - 33 * q^58 + 26 * q^59 - 57 * q^60 - 26 * q^61 - 17 * q^62 - 4 * q^63 + 13 * q^64 - 25 * q^65 - 2 * q^66 + 6 * q^67 - 35 * q^68 - 2 * q^69 - 4 * q^70 + 94 * q^71 + 17 * q^72 - 22 * q^73 + 26 * q^74 - 20 * q^76 - 7 * q^77 + 54 * q^78 + 9 * q^79 + 19 * q^80 + 4 * q^81 + 15 * q^82 - 8 * q^83 + 2 * q^84 + 4 * q^85 + 9 * q^86 + 4 * q^87 + 6 * q^88 - 3 * q^89 + 11 * q^90 - 20 * q^91 + 36 * q^92 + 12 * q^93 + 48 * q^94 + 33 * q^95 - 23 * q^96 - 29 * q^97 + 28 * q^98 + 36 * q^99

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