LMFDB - Embedded newform 1502.2.a.e.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1502,2,Mod(1,1502)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1502, 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("1502.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1502 = 2 \cdot 751 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1502.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:	$11.9935303836$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 4x^{10} - 9x^{9} + 58x^{8} - 40x^{7} - 146x^{6} + 237x^{5} - 47x^{4} - 89x^{3} + 39x^{2} - 1 $ x^11 - 4x^10 - 9x^9 + 58x^8 - 40x^7 - 146x^6 + 237x^5 - 47x^4 - 89x^3 + 39*x^2 - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$0.235096$ of defining polynomial
Character	$\chi$	$=$	1502.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.13096 q^{3} +1.00000 q^{4} +0.446946 q^{5} -2.13096 q^{6} -1.57697 q^{7} -1.00000 q^{8} +1.54099 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.13096 q^{3} +1.00000 q^{4} +0.446946 q^{5} -2.13096 q^{6} -1.57697 q^{7} -1.00000 q^{8} +1.54099 q^{9} -0.446946 q^{10} -4.27746 q^{11} +2.13096 q^{12} -6.29600 q^{13} +1.57697 q^{14} +0.952423 q^{15} +1.00000 q^{16} +0.352429 q^{17} -1.54099 q^{18} +6.75221 q^{19} +0.446946 q^{20} -3.36045 q^{21} +4.27746 q^{22} -1.57083 q^{23} -2.13096 q^{24} -4.80024 q^{25} +6.29600 q^{26} -3.10910 q^{27} -1.57697 q^{28} -1.26190 q^{29} -0.952423 q^{30} -5.51866 q^{31} -1.00000 q^{32} -9.11510 q^{33} -0.352429 q^{34} -0.704818 q^{35} +1.54099 q^{36} +4.73360 q^{37} -6.75221 q^{38} -13.4165 q^{39} -0.446946 q^{40} +3.24629 q^{41} +3.36045 q^{42} -11.8877 q^{43} -4.27746 q^{44} +0.688738 q^{45} +1.57083 q^{46} +2.12532 q^{47} +2.13096 q^{48} -4.51318 q^{49} +4.80024 q^{50} +0.751012 q^{51} -6.29600 q^{52} +2.42024 q^{53} +3.10910 q^{54} -1.91179 q^{55} +1.57697 q^{56} +14.3887 q^{57} +1.26190 q^{58} -12.1640 q^{59} +0.952423 q^{60} -2.74416 q^{61} +5.51866 q^{62} -2.43009 q^{63} +1.00000 q^{64} -2.81397 q^{65} +9.11510 q^{66} +4.64394 q^{67} +0.352429 q^{68} -3.34737 q^{69} +0.704818 q^{70} +9.09940 q^{71} -1.54099 q^{72} -4.43298 q^{73} -4.73360 q^{74} -10.2291 q^{75} +6.75221 q^{76} +6.74541 q^{77} +13.4165 q^{78} +16.7417 q^{79} +0.446946 q^{80} -11.2483 q^{81} -3.24629 q^{82} -4.87014 q^{83} -3.36045 q^{84} +0.157517 q^{85} +11.8877 q^{86} -2.68905 q^{87} +4.27746 q^{88} -1.72711 q^{89} -0.688738 q^{90} +9.92859 q^{91} -1.57083 q^{92} -11.7600 q^{93} -2.12532 q^{94} +3.01787 q^{95} -2.13096 q^{96} -18.6547 q^{97} +4.51318 q^{98} -6.59151 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9	\( 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9} - q^{10} + 4 q^{11} - 4 q^{12} - 19 q^{13} + 6 q^{14} + q^{15} + 11 q^{16} - 8 q^{17} - 3 q^{18} - 9 q^{19} + q^{20} - 6 q^{21} - 4 q^{22} + 2 q^{23} + 4 q^{24} - 2 q^{25} + 19 q^{26} - 16 q^{27} - 6 q^{28} + 13 q^{29} - q^{30} - 19 q^{31} - 11 q^{32} - 37 q^{33} + 8 q^{34} + 3 q^{35} + 3 q^{36} - 29 q^{37} + 9 q^{38} + 8 q^{39} - q^{40} - 23 q^{41} + 6 q^{42} - 13 q^{43} + 4 q^{44} - 6 q^{45} - 2 q^{46} - 16 q^{47} - 4 q^{48} - 5 q^{49} + 2 q^{50} + 33 q^{51} - 19 q^{52} - 25 q^{53} + 16 q^{54} - 14 q^{55} + 6 q^{56} + 4 q^{57} - 13 q^{58} + 6 q^{59} + q^{60} + 10 q^{61} + 19 q^{62} - 7 q^{63} + 11 q^{64} - 19 q^{65} + 37 q^{66} - 16 q^{67} - 8 q^{68} - 25 q^{69} - 3 q^{70} + 8 q^{71} - 3 q^{72} - 56 q^{73} + 29 q^{74} - 50 q^{75} - 9 q^{76} - 7 q^{77} - 8 q^{78} + 2 q^{79} + q^{80} - 5 q^{81} + 23 q^{82} + 21 q^{83} - 6 q^{84} - 55 q^{85} + 13 q^{86} - 11 q^{87} - 4 q^{88} - 24 q^{89} + 6 q^{90} - 43 q^{91} + 2 q^{92} + 10 q^{93} + 16 q^{94} + 25 q^{95} + 4 q^{96} - 84 q^{97} + 5 q^{98} + 14 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9 - q^10 + 4 * q^11 - 4 * q^12 - 19 * q^13 + 6 * q^14 + q^15 + 11 * q^16 - 8 * q^17 - 3 * q^18 - 9 * q^19 + q^20 - 6 * q^21 - 4 * q^22 + 2 * q^23 + 4 * q^24 - 2 * q^25 + 19 * q^26 - 16 * q^27 - 6 * q^28 + 13 * q^29 - q^30 - 19 * q^31 - 11 * q^32 - 37 * q^33 + 8 * q^34 + 3 * q^35 + 3 * q^36 - 29 * q^37 + 9 * q^38 + 8 * q^39 - q^40 - 23 * q^41 + 6 * q^42 - 13 * q^43 + 4 * q^44 - 6 * q^45 - 2 * q^46 - 16 * q^47 - 4 * q^48 - 5 * q^49 + 2 * q^50 + 33 * q^51 - 19 * q^52 - 25 * q^53 + 16 * q^54 - 14 * q^55 + 6 * q^56 + 4 * q^57 - 13 * q^58 + 6 * q^59 + q^60 + 10 * q^61 + 19 * q^62 - 7 * q^63 + 11 * q^64 - 19 * q^65 + 37 * q^66 - 16 * q^67 - 8 * q^68 - 25 * q^69 - 3 * q^70 + 8 * q^71 - 3 * q^72 - 56 * q^73 + 29 * q^74 - 50 * q^75 - 9 * q^76 - 7 * q^77 - 8 * q^78 + 2 * q^79 + q^80 - 5 * q^81 + 23 * q^82 + 21 * q^83 - 6 * q^84 - 55 * q^85 + 13 * q^86 - 11 * q^87 - 4 * q^88 - 24 * q^89 + 6 * q^90 - 43 * q^91 + 2 * q^92 + 10 * q^93 + 16 * q^94 + 25 * q^95 + 4 * q^96 - 84 * q^97 + 5 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.13096	1.23031	0.615155	−	0.788406i	$-0.289093\pi$
$3$	2.13096	1.23031	0.615155	+	0.788406i	$0.289093\pi$
$4$	1.00000	0.500000
$5$	0.446946	0.199880	0.0999401	−	0.994993i	$-0.468135\pi$
$5$	0.446946	0.199880	0.0999401	+	0.994993i	$0.468135\pi$
$6$	−2.13096	−0.869960
$7$	−1.57697	−0.596037	−0.298019	−	0.954560i	$-0.596326\pi$
$7$	−1.57697	−0.596037	−0.298019	+	0.954560i	$0.596326\pi$
$8$	−1.00000	−0.353553
$9$	1.54099	0.513662
$10$	−0.446946	−0.141337
$11$	−4.27746	−1.28970	−0.644852	−	0.764308i	$-0.723081\pi$
$11$	−4.27746	−1.28970	−0.644852	+	0.764308i	$0.723081\pi$
$12$	2.13096	0.615155
$13$	−6.29600	−1.74620	−0.873099	−	0.487543i	$-0.837893\pi$
$13$	−6.29600	−1.74620	−0.873099	+	0.487543i	$0.837893\pi$
$14$	1.57697	0.421462
$15$	0.952423	0.245915
$16$	1.00000	0.250000
$17$	0.352429	0.0854766	0.0427383	−	0.999086i	$-0.486392\pi$
$17$	0.352429	0.0854766	0.0427383	+	0.999086i	$0.486392\pi$
$18$	−1.54099	−0.363214
$19$	6.75221	1.54906	0.774532	−	0.632535i	$-0.217986\pi$
$19$	6.75221	1.54906	0.774532	+	0.632535i	$0.217986\pi$
$20$	0.446946	0.0999401
$21$	−3.36045	−0.733311
$22$	4.27746	0.911958
$23$	−1.57083	−0.327540	−0.163770	−	0.986499i	$-0.552365\pi$
$23$	−1.57083	−0.327540	−0.163770	+	0.986499i	$0.552365\pi$
$24$	−2.13096	−0.434980
$25$	−4.80024	−0.960048
$26$	6.29600	1.23475
$27$	−3.10910	−0.598346
$28$	−1.57697	−0.298019
$29$	−1.26190	−0.234328	−0.117164	−	0.993113i	$-0.537380\pi$
$29$	−1.26190	−0.234328	−0.117164	+	0.993113i	$0.537380\pi$
$30$	−0.952423	−0.173888
$31$	−5.51866	−0.991181	−0.495591	−	0.868556i	$-0.665048\pi$
$31$	−5.51866	−0.991181	−0.495591	+	0.868556i	$0.665048\pi$
$32$	−1.00000	−0.176777
$33$	−9.11510	−1.58673
$34$	−0.352429	−0.0604411
$35$	−0.704818	−0.119136
$36$	1.54099	0.256831
$37$	4.73360	0.778199	0.389100	−	0.921196i	$-0.372786\pi$
$37$	4.73360	0.778199	0.389100	+	0.921196i	$0.372786\pi$
$38$	−6.75221	−1.09535
$39$	−13.4165	−2.14836
$40$	−0.446946	−0.0706683
$41$	3.24629	0.506985	0.253493	−	0.967337i	$-0.418421\pi$
$41$	3.24629	0.506985	0.253493	+	0.967337i	$0.418421\pi$
$42$	3.36045	0.518529
$43$	−11.8877	−1.81286	−0.906432	−	0.422351i	$-0.861205\pi$
$43$	−11.8877	−1.81286	−0.906432	+	0.422351i	$0.861205\pi$
$44$	−4.27746	−0.644852
$45$	0.688738	0.102671
$46$	1.57083	0.231606
$47$	2.12532	0.310010	0.155005	−	0.987914i	$-0.450461\pi$
$47$	2.12532	0.310010	0.155005	+	0.987914i	$0.450461\pi$
$48$	2.13096	0.307577
$49$	−4.51318	−0.644740
$50$	4.80024	0.678856
$51$	0.751012	0.105163
$52$	−6.29600	−0.873099
$53$	2.42024	0.332445	0.166223	−	0.986088i	$-0.446843\pi$
$53$	2.42024	0.332445	0.166223	+	0.986088i	$0.446843\pi$
$54$	3.10910	0.423094
$55$	−1.91179	−0.257786
$56$	1.57697	0.210731
$57$	14.3887	1.90583
$58$	1.26190	0.165695
$59$	−12.1640	−1.58361	−0.791806	−	0.610773i	$-0.790859\pi$
$59$	−12.1640	−1.58361	−0.791806	+	0.610773i	$0.790859\pi$
$60$	0.952423	0.122957
$61$	−2.74416	−0.351353	−0.175677	−	0.984448i	$-0.556211\pi$
$61$	−2.74416	−0.351353	−0.175677	+	0.984448i	$0.556211\pi$
$62$	5.51866	0.700871
$63$	−2.43009	−0.306162
$64$	1.00000	0.125000
$65$	−2.81397	−0.349030
$66$	9.11510	1.12199
$67$	4.64394	0.567347	0.283674	−	0.958921i	$-0.408447\pi$
$67$	4.64394	0.567347	0.283674	+	0.958921i	$0.408447\pi$
$68$	0.352429	0.0427383
$69$	−3.34737	−0.402976
$70$	0.704818	0.0842419
$71$	9.09940	1.07990	0.539950	−	0.841697i	$-0.318443\pi$
$71$	9.09940	1.07990	0.539950	+	0.841697i	$0.318443\pi$
$72$	−1.54099	−0.181607
$73$	−4.43298	−0.518841	−0.259420	−	0.965764i	$-0.583532\pi$
$73$	−4.43298	−0.518841	−0.259420	+	0.965764i	$0.583532\pi$
$74$	−4.73360	−0.550270
$75$	−10.2291	−1.18116
$76$	6.75221	0.774532
$77$	6.74541	0.768711
$78$	13.4165	1.51912
$79$	16.7417	1.88359	0.941796	−	0.336184i	$-0.109136\pi$
$79$	16.7417	1.88359	0.941796	+	0.336184i	$0.109136\pi$
$80$	0.446946	0.0499701
$81$	−11.2483	−1.24981
$82$	−3.24629	−0.358493
$83$	−4.87014	−0.534567	−0.267284	−	0.963618i	$-0.586126\pi$
$83$	−4.87014	−0.534567	−0.267284	+	0.963618i	$0.586126\pi$
$84$	−3.36045	−0.366655
$85$	0.157517	0.0170851
$86$	11.8877	1.28189
$87$	−2.68905	−0.288297
$88$	4.27746	0.455979
$89$	−1.72711	−0.183073	−0.0915364	−	0.995802i	$-0.529178\pi$
$89$	−1.72711	−0.183073	−0.0915364	+	0.995802i	$0.529178\pi$
$90$	−0.688738	−0.0725993
$91$	9.92859	1.04080
$92$	−1.57083	−0.163770
$93$	−11.7600	−1.21946
$94$	−2.12532	−0.219210
$95$	3.01787	0.309627
$96$	−2.13096	−0.217490
$97$	−18.6547	−1.89410	−0.947050	−	0.321086i	$-0.895952\pi$
$97$	−18.6547	−1.89410	−0.947050	+	0.321086i	$0.895952\pi$
$98$	4.51318	0.455900
$99$	−6.59151	−0.662472
$100$	−4.80024	−0.480024
$101$	15.0433	1.49686	0.748430	−	0.663213i	$-0.230808\pi$
$101$	15.0433	1.49686	0.748430	+	0.663213i	$0.230808\pi$
$102$	−0.751012	−0.0743613
$103$	−8.17753	−0.805756	−0.402878	−	0.915254i	$-0.631990\pi$
$103$	−8.17753	−0.805756	−0.402878	+	0.915254i	$0.631990\pi$
$104$	6.29600	0.617374
$105$	−1.50194	−0.146574
$106$	−2.42024	−0.235074
$107$	−1.14722	−0.110906	−0.0554528	−	0.998461i	$-0.517660\pi$
$107$	−1.14722	−0.110906	−0.0554528	+	0.998461i	$0.517660\pi$
$108$	−3.10910	−0.299173
$109$	5.85038	0.560365	0.280183	−	0.959947i	$-0.409605\pi$
$109$	5.85038	0.560365	0.280183	+	0.959947i	$0.409605\pi$
$110$	1.91179	0.182282
$111$	10.0871	0.957426
$112$	−1.57697	−0.149009
$113$	18.9283	1.78062	0.890312	−	0.455350i	$-0.150486\pi$
$113$	18.9283	1.78062	0.890312	+	0.455350i	$0.150486\pi$
$114$	−14.3887	−1.34762
$115$	−0.702074	−0.0654688
$116$	−1.26190	−0.117164
$117$	−9.70206	−0.896956
$118$	12.1640	1.11978
$119$	−0.555769	−0.0509473
$120$	−0.952423	−0.0869439
$121$	7.29668	0.663335
$122$	2.74416	0.248444
$123$	6.91771	0.623749
$124$	−5.51866	−0.495591
$125$	−4.38018	−0.391775
$126$	2.43009	0.216489
$127$	6.74130	0.598194	0.299097	−	0.954223i	$-0.403315\pi$
$127$	6.74130	0.598194	0.299097	+	0.954223i	$0.403315\pi$
$128$	−1.00000	−0.0883883
$129$	−25.3323	−2.23039
$130$	2.81397	0.246802
$131$	2.38584	0.208452	0.104226	−	0.994554i	$-0.466763\pi$
$131$	2.38584	0.208452	0.104226	+	0.994554i	$0.466763\pi$
$132$	−9.11510	−0.793367
$133$	−10.6480	−0.923300
$134$	−4.64394	−0.401175
$135$	−1.38960	−0.119598
$136$	−0.352429	−0.0302205
$137$	−23.2043	−1.98248	−0.991240	−	0.132071i	$-0.957837\pi$
$137$	−23.2043	−1.98248	−0.991240	+	0.132071i	$0.957837\pi$
$138$	3.34737	0.284947
$139$	17.1889	1.45794	0.728971	−	0.684544i	$-0.239999\pi$
$139$	17.1889	1.45794	0.728971	+	0.684544i	$0.239999\pi$
$140$	−0.704818	−0.0595680
$141$	4.52898	0.381409
$142$	−9.09940	−0.763605
$143$	26.9309	2.25208
$144$	1.54099	0.128416
$145$	−0.564000	−0.0468376
$146$	4.43298	0.366876
$147$	−9.61740	−0.793229
$148$	4.73360	0.389100
$149$	6.50903	0.533240	0.266620	−	0.963802i	$-0.414093\pi$
$149$	6.50903	0.533240	0.266620	+	0.963802i	$0.414093\pi$
$150$	10.2291	0.835204
$151$	−8.56864	−0.697306	−0.348653	−	0.937252i	$-0.613361\pi$
$151$	−8.56864	−0.697306	−0.348653	+	0.937252i	$0.613361\pi$
$152$	−6.75221	−0.547677
$153$	0.543089	0.0439061
$154$	−6.74541	−0.543561
$155$	−2.46654	−0.198118
$156$	−13.4165	−1.07418
$157$	−4.27687	−0.341331	−0.170666	−	0.985329i	$-0.554592\pi$
$157$	−4.27687	−0.341331	−0.170666	+	0.985329i	$0.554592\pi$
$158$	−16.7417	−1.33190
$159$	5.15743	0.409011
$160$	−0.446946	−0.0353342
$161$	2.47714	0.195226
$162$	11.2483	0.883751
$163$	−3.92648	−0.307545	−0.153773	−	0.988106i	$-0.549142\pi$
$163$	−3.92648	−0.307545	−0.153773	+	0.988106i	$0.549142\pi$
$164$	3.24629	0.253493
$165$	−4.07395	−0.317157
$166$	4.87014	0.377996
$167$	20.8732	1.61521	0.807607	−	0.589721i	$-0.200762\pi$
$167$	20.8732	1.61521	0.807607	+	0.589721i	$0.200762\pi$
$168$	3.36045	0.259264
$169$	26.6397	2.04921
$170$	−0.157517	−0.0120810
$171$	10.4051	0.795696
$172$	−11.8877	−0.906432
$173$	17.7545	1.34985	0.674923	−	0.737888i	$-0.264177\pi$
$173$	17.7545	1.34985	0.674923	+	0.737888i	$0.264177\pi$
$174$	2.68905	0.203857
$175$	7.56982	0.572224
$176$	−4.27746	−0.322426
$177$	−25.9209	−1.94833
$178$	1.72711	0.129452
$179$	−23.0560	−1.72329	−0.861644	−	0.507514i	$-0.830565\pi$
$179$	−23.0560	−1.72329	−0.861644	+	0.507514i	$0.830565\pi$
$180$	0.688738	0.0513355
$181$	−13.7769	−1.02403	−0.512013	−	0.858978i	$-0.671100\pi$
$181$	−13.7769	−1.02403	−0.512013	+	0.858978i	$0.671100\pi$
$182$	−9.92859	−0.735956
$183$	−5.84769	−0.432274
$184$	1.57083	0.115803
$185$	2.11566	0.155547
$186$	11.7600	0.862289
$187$	−1.50750	−0.110239
$188$	2.12532	0.155005
$189$	4.90294	0.356637
$190$	−3.01787	−0.218939
$191$	−11.1882	−0.809551	−0.404775	−	0.914416i	$-0.632650\pi$
$191$	−11.1882	−0.809551	−0.404775	+	0.914416i	$0.632650\pi$
$192$	2.13096	0.153789
$193$	−14.3647	−1.03399	−0.516997	−	0.855987i	$-0.672950\pi$
$193$	−14.3647	−1.03399	−0.516997	+	0.855987i	$0.672950\pi$
$194$	18.6547	1.33933
$195$	−5.99646	−0.429415
$196$	−4.51318	−0.322370
$197$	−6.05793	−0.431610	−0.215805	−	0.976437i	$-0.569238\pi$
$197$	−6.05793	−0.431610	−0.215805	+	0.976437i	$0.569238\pi$
$198$	6.59151	0.468439
$199$	−2.96102	−0.209901	−0.104950	−	0.994477i	$-0.533468\pi$
$199$	−2.96102	−0.209901	−0.104950	+	0.994477i	$0.533468\pi$
$200$	4.80024	0.339428
$201$	9.89604	0.698013
$202$	−15.0433	−1.05844
$203$	1.98997	0.139669
$204$	0.751012	0.0525814
$205$	1.45092	0.101336
$206$	8.17753	0.569755
$207$	−2.42062	−0.168245
$208$	−6.29600	−0.436549
$209$	−28.8823	−1.99783
$210$	1.50194	0.103644
$211$	15.3294	1.05532	0.527661	−	0.849455i	$-0.323069\pi$
$211$	15.3294	1.05532	0.527661	+	0.849455i	$0.323069\pi$
$212$	2.42024	0.166223
$213$	19.3905	1.32861
$214$	1.14722	0.0784220
$215$	−5.31318	−0.362356
$216$	3.10910	0.211547
$217$	8.70275	0.590781
$218$	−5.85038	−0.396238
$219$	−9.44650	−0.638335
$220$	−1.91179	−0.128893
$221$	−2.21890	−0.149259
$222$	−10.0871	−0.677003
$223$	−15.5092	−1.03857	−0.519286	−	0.854601i	$-0.673802\pi$
$223$	−15.5092	−1.03857	−0.519286	+	0.854601i	$0.673802\pi$
$224$	1.57697	0.105366
$225$	−7.39711	−0.493141
$226$	−18.9283	−1.25909
$227$	−10.2245	−0.678625	−0.339313	−	0.940674i	$-0.610194\pi$
$227$	−10.2245	−0.678625	−0.339313	+	0.940674i	$0.610194\pi$
$228$	14.3887	0.952914
$229$	−9.72540	−0.642672	−0.321336	−	0.946965i	$-0.604132\pi$
$229$	−9.72540	−0.642672	−0.321336	+	0.946965i	$0.604132\pi$
$230$	0.702074	0.0462934
$231$	14.3742	0.945753
$232$	1.26190	0.0828476
$233$	4.74422	0.310804	0.155402	−	0.987851i	$-0.450333\pi$
$233$	4.74422	0.310804	0.155402	+	0.987851i	$0.450333\pi$
$234$	9.70206	0.634244
$235$	0.949905	0.0619649
$236$	−12.1640	−0.791806
$237$	35.6760	2.31740
$238$	0.555769	0.0360251
$239$	−12.0095	−0.776830	−0.388415	−	0.921485i	$-0.626977\pi$
$239$	−12.0095	−0.776830	−0.388415	+	0.921485i	$0.626977\pi$
$240$	0.952423	0.0614787
$241$	−7.44020	−0.479265	−0.239633	−	0.970864i	$-0.577027\pi$
$241$	−7.44020	−0.479265	−0.239633	+	0.970864i	$0.577027\pi$
$242$	−7.29668	−0.469049
$243$	−14.6424	−0.939312
$244$	−2.74416	−0.175677
$245$	−2.01715	−0.128871
$246$	−6.91771	−0.441057
$247$	−42.5119	−2.70497
$248$	5.51866	0.350436
$249$	−10.3781	−0.657683
$250$	4.38018	0.277027
$251$	−0.116541	−0.00735600	−0.00367800	−	0.999993i	$-0.501171\pi$
$251$	−0.116541	−0.00735600	−0.00367800	+	0.999993i	$0.501171\pi$
$252$	−2.43009	−0.153081
$253$	6.71915	0.422429
$254$	−6.74130	−0.422987
$255$	0.335662	0.0210199
$256$	1.00000	0.0625000
$257$	3.34490	0.208649	0.104325	−	0.994543i	$-0.466732\pi$
$257$	3.34490	0.208649	0.104325	+	0.994543i	$0.466732\pi$
$258$	25.3323	1.57712
$259$	−7.46473	−0.463836
$260$	−2.81397	−0.174515
$261$	−1.94457	−0.120366
$262$	−2.38584	−0.147398
$263$	11.5307	0.711015	0.355508	−	0.934673i	$-0.384308\pi$
$263$	11.5307	0.711015	0.355508	+	0.934673i	$0.384308\pi$
$264$	9.11510	0.560995
$265$	1.08171	0.0664492
$266$	10.6480	0.652871
$267$	−3.68039	−0.225236
$268$	4.64394	0.283674
$269$	26.1663	1.59539	0.797694	−	0.603062i	$-0.206053\pi$
$269$	26.1663	1.59539	0.797694	+	0.603062i	$0.206053\pi$
$270$	1.38960	0.0845682
$271$	−10.7493	−0.652973	−0.326487	−	0.945202i	$-0.605865\pi$
$271$	−10.7493	−0.652973	−0.326487	+	0.945202i	$0.605865\pi$
$272$	0.352429	0.0213692
$273$	21.1574	1.28051
$274$	23.2043	1.40183
$275$	20.5328	1.23818
$276$	−3.34737	−0.201488
$277$	−24.9605	−1.49973	−0.749864	−	0.661592i	$-0.769881\pi$
$277$	−24.9605	−1.49973	−0.749864	+	0.661592i	$0.769881\pi$
$278$	−17.1889	−1.03092
$279$	−8.50419	−0.509133
$280$	0.704818	0.0421210
$281$	28.7551	1.71539	0.857694	−	0.514161i	$-0.171897\pi$
$281$	28.7551	1.71539	0.857694	+	0.514161i	$0.171897\pi$
$282$	−4.52898	−0.269697
$283$	−19.3613	−1.15091	−0.575456	−	0.817833i	$-0.695175\pi$
$283$	−19.3613	−1.15091	−0.575456	+	0.817833i	$0.695175\pi$
$284$	9.09940	0.539950
$285$	6.43096	0.380937
$286$	−26.9309	−1.59246
$287$	−5.11929	−0.302182
$288$	−1.54099	−0.0908035
$289$	−16.8758	−0.992694
$290$	0.564000	0.0331192
$291$	−39.7525	−2.33033
$292$	−4.43298	−0.259420
$293$	−11.8692	−0.693406	−0.346703	−	0.937975i	$-0.612699\pi$
$293$	−11.8692	−0.693406	−0.346703	+	0.937975i	$0.612699\pi$
$294$	9.61740	0.560898
$295$	−5.43663	−0.316533
$296$	−4.73360	−0.275135
$297$	13.2990	0.771689
$298$	−6.50903	−0.377058
$299$	9.88993	0.571949
$300$	−10.2291	−0.590578
$301$	18.7466	1.08053
$302$	8.56864	0.493070
$303$	32.0566	1.84160
$304$	6.75221	0.387266
$305$	−1.22649	−0.0702286
$306$	−0.543089	−0.0310463
$307$	29.4375	1.68009	0.840043	−	0.542519i	$-0.182529\pi$
$307$	29.4375	1.68009	0.840043	+	0.542519i	$0.182529\pi$
$308$	6.74541	0.384356
$309$	−17.4260	−0.991329
$310$	2.46654	0.140090
$311$	18.8312	1.06782	0.533911	−	0.845541i	$-0.320722\pi$
$311$	18.8312	1.06782	0.533911	+	0.845541i	$0.320722\pi$
$312$	13.4165	0.759561
$313$	1.96564	0.111104	0.0555522	−	0.998456i	$-0.482308\pi$
$313$	1.96564	0.111104	0.0555522	+	0.998456i	$0.482308\pi$
$314$	4.27687	0.241358
$315$	−1.08612	−0.0611957
$316$	16.7417	0.941796
$317$	23.9998	1.34796	0.673982	−	0.738748i	$-0.264583\pi$
$317$	23.9998	1.34796	0.673982	+	0.738748i	$0.264583\pi$
$318$	−5.15743	−0.289214
$319$	5.39772	0.302214
$320$	0.446946	0.0249850
$321$	−2.44467	−0.136448
$322$	−2.47714	−0.138046
$323$	2.37968	0.132409
$324$	−11.2483	−0.624907
$325$	30.2223	1.67643
$326$	3.92648	0.217467
$327$	12.4669	0.689423
$328$	−3.24629	−0.179246
$329$	−3.35157	−0.184778
$330$	4.07395	0.224264
$331$	−13.2454	−0.728033	−0.364017	−	0.931392i	$-0.618595\pi$
$331$	−13.2454	−0.728033	−0.364017	+	0.931392i	$0.618595\pi$
$332$	−4.87014	−0.267284
$333$	7.29442	0.399732
$334$	−20.8732	−1.14213
$335$	2.07559	0.113401
$336$	−3.36045	−0.183328
$337$	−22.3702	−1.21858	−0.609291	−	0.792946i	$-0.708546\pi$
$337$	−22.3702	−1.21858	−0.609291	+	0.792946i	$0.708546\pi$
$338$	−26.6397	−1.44901
$339$	40.3354	2.19072
$340$	0.157517	0.00854254
$341$	23.6059	1.27833
$342$	−10.4051	−0.562642
$343$	18.1559	0.980326
$344$	11.8877	0.640944
$345$	−1.49609	−0.0805469
$346$	−17.7545	−0.954485
$347$	31.1726	1.67343	0.836717	−	0.547636i	$-0.184472\pi$
$347$	31.1726	1.67343	0.836717	+	0.547636i	$0.184472\pi$
$348$	−2.68905	−0.144148
$349$	−27.8798	−1.49237	−0.746185	−	0.665738i	$-0.768117\pi$
$349$	−27.8798	−1.49237	−0.746185	+	0.665738i	$0.768117\pi$
$350$	−7.56982	−0.404624
$351$	19.5749	1.04483
$352$	4.27746	0.227990
$353$	17.7439	0.944414	0.472207	−	0.881488i	$-0.343458\pi$
$353$	17.7439	0.944414	0.472207	+	0.881488i	$0.343458\pi$
$354$	25.9209	1.37768
$355$	4.06694	0.215851
$356$	−1.72711	−0.0915364
$357$	−1.18432	−0.0626809
$358$	23.0560	1.21855
$359$	−9.16291	−0.483600	−0.241800	−	0.970326i	$-0.577738\pi$
$359$	−9.16291	−0.483600	−0.241800	+	0.970326i	$0.577738\pi$
$360$	−0.688738	−0.0362997
$361$	26.5924	1.39960
$362$	13.7769	0.724095
$363$	15.5489	0.816107
$364$	9.92859	0.520399
$365$	−1.98130	−0.103706
$366$	5.84769	0.305664
$367$	0.603125	0.0314828	0.0157414	−	0.999876i	$-0.494989\pi$
$367$	0.603125	0.0314828	0.0157414	+	0.999876i	$0.494989\pi$
$368$	−1.57083	−0.0818850
$369$	5.00249	0.260419
$370$	−2.11566	−0.109988
$371$	−3.81663	−0.198150
$372$	−11.7600	−0.609730
$373$	23.8740	1.23615	0.618074	−	0.786120i	$-0.287913\pi$
$373$	23.8740	1.23615	0.618074	+	0.786120i	$0.287913\pi$
$374$	1.50750	0.0779511
$375$	−9.33398	−0.482004
$376$	−2.12532	−0.109605
$377$	7.94491	0.409184
$378$	−4.90294	−0.252180
$379$	33.0901	1.69972	0.849861	−	0.527006i	$-0.176686\pi$
$379$	33.0901	1.69972	0.849861	+	0.527006i	$0.176686\pi$
$380$	3.01787	0.154814
$381$	14.3654	0.735964
$382$	11.1882	0.572439
$383$	14.6723	0.749720	0.374860	−	0.927081i	$-0.377691\pi$
$383$	14.6723	0.749720	0.374860	+	0.927081i	$0.377691\pi$
$384$	−2.13096	−0.108745
$385$	3.01483	0.153650
$386$	14.3647	0.731144
$387$	−18.3189	−0.931200
$388$	−18.6547	−0.947050
$389$	−17.4471	−0.884605	−0.442302	−	0.896866i	$-0.645838\pi$
$389$	−17.4471	−0.884605	−0.442302	+	0.896866i	$0.645838\pi$
$390$	5.99646	0.303643
$391$	−0.553605	−0.0279970
$392$	4.51318	0.227950
$393$	5.08414	0.256461
$394$	6.05793	0.305194
$395$	7.48265	0.376493
$396$	−6.59151	−0.331236
$397$	25.1799	1.26374	0.631870	−	0.775074i	$-0.282288\pi$
$397$	25.1799	1.26374	0.631870	+	0.775074i	$0.282288\pi$
$398$	2.96102	0.148422
$399$	−22.6905	−1.13594
$400$	−4.80024	−0.240012
$401$	−18.8737	−0.942508	−0.471254	−	0.881998i	$-0.656198\pi$
$401$	−18.8737	−0.942508	−0.471254	+	0.881998i	$0.656198\pi$
$402$	−9.89604	−0.493570
$403$	34.7455	1.73080
$404$	15.0433	0.748430
$405$	−5.02739	−0.249813
$406$	−1.98997	−0.0987606
$407$	−20.2478	−1.00365
$408$	−0.751012	−0.0371806
$409$	−24.5345	−1.21315	−0.606577	−	0.795024i	$-0.707458\pi$
$409$	−24.5345	−1.21315	−0.606577	+	0.795024i	$0.707458\pi$
$410$	−1.45092	−0.0716556
$411$	−49.4475	−2.43907
$412$	−8.17753	−0.402878
$413$	19.1821	0.943892
$414$	2.42062	0.118967
$415$	−2.17669	−0.106849
$416$	6.29600	0.308687
$417$	36.6288	1.79372
$418$	28.8823	1.41268
$419$	11.1079	0.542655	0.271328	−	0.962487i	$-0.412537\pi$
$419$	11.1079	0.542655	0.271328	+	0.962487i	$0.412537\pi$
$420$	−1.50194	−0.0732871
$421$	−12.7728	−0.622510	−0.311255	−	0.950326i	$-0.600749\pi$
$421$	−12.7728	−0.622510	−0.311255	+	0.950326i	$0.600749\pi$
$422$	−15.3294	−0.746225
$423$	3.27510	0.159241
$424$	−2.42024	−0.117537
$425$	−1.69174	−0.0820616
$426$	−19.3905	−0.939471
$427$	4.32745	0.209420
$428$	−1.14722	−0.0554528
$429$	57.3887	2.77075
$430$	5.31318	0.256224
$431$	−5.21419	−0.251159	−0.125579	−	0.992084i	$-0.540079\pi$
$431$	−5.21419	−0.251159	−0.125579	+	0.992084i	$0.540079\pi$
$432$	−3.10910	−0.149586
$433$	−30.2875	−1.45552	−0.727762	−	0.685830i	$-0.759439\pi$
$433$	−30.2875	−1.45552	−0.727762	+	0.685830i	$0.759439\pi$
$434$	−8.70275	−0.417745
$435$	−1.20186	−0.0576248
$436$	5.85038	0.280183
$437$	−10.6066	−0.507380
$438$	9.44650	0.451371
$439$	29.6583	1.41551	0.707756	−	0.706457i	$-0.249707\pi$
$439$	29.6583	1.41551	0.707756	+	0.706457i	$0.249707\pi$
$440$	1.91179	0.0911412
$441$	−6.95475	−0.331178
$442$	2.21890	0.105542
$443$	11.9654	0.568496	0.284248	−	0.958751i	$-0.408256\pi$
$443$	11.9654	0.568496	0.284248	+	0.958751i	$0.408256\pi$
$444$	10.0871	0.478713
$445$	−0.771922	−0.0365926
$446$	15.5092	0.734381
$447$	13.8705	0.656051
$448$	−1.57697	−0.0745047
$449$	20.0475	0.946101	0.473050	−	0.881035i	$-0.343153\pi$
$449$	20.0475	0.946101	0.473050	+	0.881035i	$0.343153\pi$
$450$	7.39711	0.348703
$451$	−13.8859	−0.653861
$452$	18.9283	0.890312
$453$	−18.2594	−0.857902
$454$	10.2245	0.479861
$455$	4.43754	0.208035
$456$	−14.3887	−0.673812
$457$	−23.0129	−1.07650	−0.538249	−	0.842786i	$-0.680914\pi$
$457$	−23.0129	−1.07650	−0.538249	+	0.842786i	$0.680914\pi$
$458$	9.72540	0.454438
$459$	−1.09574	−0.0511446
$460$	−0.702074	−0.0327344
$461$	−24.4882	−1.14053	−0.570266	−	0.821460i	$-0.693160\pi$
$461$	−24.4882	−1.14053	−0.570266	+	0.821460i	$0.693160\pi$
$462$	−14.3742	−0.668748
$463$	−21.9883	−1.02188	−0.510942	−	0.859615i	$-0.670703\pi$
$463$	−21.9883	−1.02188	−0.510942	+	0.859615i	$0.670703\pi$
$464$	−1.26190	−0.0585821
$465$	−5.25610	−0.243746
$466$	−4.74422	−0.219772
$467$	−6.54614	−0.302919	−0.151460	−	0.988463i	$-0.548397\pi$
$467$	−6.54614	−0.302919	−0.151460	+	0.988463i	$0.548397\pi$
$468$	−9.70206	−0.448478
$469$	−7.32333	−0.338160
$470$	−0.949905	−0.0438158
$471$	−9.11383	−0.419943
$472$	12.1640	0.559891
$473$	50.8494	2.33806
$474$	−35.6760	−1.63865
$475$	−32.4122	−1.48718
$476$	−0.555769	−0.0254736
$477$	3.72955	0.170765
$478$	12.0095	0.549302
$479$	13.8307	0.631942	0.315971	−	0.948769i	$-0.397670\pi$
$479$	13.8307	0.631942	0.315971	+	0.948769i	$0.397670\pi$
$480$	−0.952423	−0.0434720
$481$	−29.8028	−1.35889
$482$	7.44020	0.338892
$483$	5.27869	0.240189
$484$	7.29668	0.331667
$485$	−8.33765	−0.378593
$486$	14.6424	0.664194
$487$	−21.9250	−0.993515	−0.496757	−	0.867889i	$-0.665476\pi$
$487$	−21.9250	−0.993515	−0.496757	+	0.867889i	$0.665476\pi$
$488$	2.74416	0.124222
$489$	−8.36716	−0.378376
$490$	2.01715	0.0911253
$491$	−8.19196	−0.369698	−0.184849	−	0.982767i	$-0.559180\pi$
$491$	−8.19196	−0.369698	−0.184849	+	0.982767i	$0.559180\pi$
$492$	6.91771	0.311874
$493$	−0.444729	−0.0200296
$494$	42.5119	1.91270
$495$	−2.94605	−0.132415
$496$	−5.51866	−0.247795
$497$	−14.3495	−0.643661
$498$	10.3781	0.465052
$499$	14.4234	0.645678	0.322839	−	0.946454i	$-0.395363\pi$
$499$	14.4234	0.645678	0.322839	+	0.946454i	$0.395363\pi$
$500$	−4.38018	−0.195887
$501$	44.4799	1.98721
$502$	0.116541	0.00520148
$503$	−1.64672	−0.0734238	−0.0367119	−	0.999326i	$-0.511688\pi$
$503$	−1.64672	−0.0734238	−0.0367119	+	0.999326i	$0.511688\pi$
$504$	2.43009	0.108245
$505$	6.72352	0.299193
$506$	−6.71915	−0.298703
$507$	56.7681	2.52116
$508$	6.74130	0.299097
$509$	−26.3528	−1.16807	−0.584033	−	0.811730i	$-0.698526\pi$
$509$	−26.3528	−1.16807	−0.584033	+	0.811730i	$0.698526\pi$
$510$	−0.335662	−0.0148633
$511$	6.99066	0.309249
$512$	−1.00000	−0.0441942
$513$	−20.9933	−0.926876
$514$	−3.34490	−0.147537
$515$	−3.65491	−0.161055
$516$	−25.3323	−1.11519
$517$	−9.09099	−0.399821
$518$	7.46473	0.327981
$519$	37.8340	1.66073
$520$	2.81397	0.123401
$521$	−10.8550	−0.475564	−0.237782	−	0.971319i	$-0.576420\pi$
$521$	−10.8550	−0.475564	−0.237782	+	0.971319i	$0.576420\pi$
$522$	1.94457	0.0851114
$523$	14.7136	0.643382	0.321691	−	0.946845i	$-0.395749\pi$
$523$	14.7136	0.643382	0.321691	+	0.946845i	$0.395749\pi$
$524$	2.38584	0.104226
$525$	16.1310	0.704013
$526$	−11.5307	−0.502764
$527$	−1.94494	−0.0847228
$528$	−9.11510	−0.396684
$529$	−20.5325	−0.892718
$530$	−1.08171	−0.0469867
$531$	−18.7445	−0.813442
$532$	−10.6480	−0.461650
$533$	−20.4387	−0.885296
$534$	3.68039	0.159266
$535$	−0.512743	−0.0221678
$536$	−4.64394	−0.200588
$537$	−49.1314	−2.12018
$538$	−26.1663	−1.12811
$539$	19.3049	0.831523
$540$	−1.38960	−0.0597988
$541$	−16.9216	−0.727516	−0.363758	−	0.931494i	$-0.618506\pi$
$541$	−16.9216	−0.727516	−0.363758	+	0.931494i	$0.618506\pi$
$542$	10.7493	0.461722
$543$	−29.3579	−1.25987
$544$	−0.352429	−0.0151103
$545$	2.61480	0.112006
$546$	−21.1574	−0.905454
$547$	9.57099	0.409226	0.204613	−	0.978843i	$-0.434406\pi$
$547$	9.57099	0.409226	0.204613	+	0.978843i	$0.434406\pi$
$548$	−23.2043	−0.991240
$549$	−4.22871	−0.180477
$550$	−20.5328	−0.875523
$551$	−8.52060	−0.362990
$552$	3.34737	0.142473
$553$	−26.4012	−1.12269
$554$	24.9605	1.06047
$555$	4.50839	0.191371
$556$	17.1889	0.728971
$557$	−35.4109	−1.50041	−0.750204	−	0.661207i	$-0.770045\pi$
$557$	−35.4109	−1.50041	−0.750204	+	0.661207i	$0.770045\pi$
$558$	8.50419	0.360011
$559$	74.8453	3.16562
$560$	−0.704818	−0.0297840
$561$	−3.21243	−0.135629
$562$	−28.7551	−1.21296
$563$	6.09525	0.256884	0.128442	−	0.991717i	$-0.459002\pi$
$563$	6.09525	0.256884	0.128442	+	0.991717i	$0.459002\pi$
$564$	4.52898	0.190704
$565$	8.45992	0.355912
$566$	19.3613	0.813817
$567$	17.7382	0.744935
$568$	−9.09940	−0.381802
$569$	23.0449	0.966092	0.483046	−	0.875595i	$-0.339530\pi$
$569$	23.0449	0.966092	0.483046	+	0.875595i	$0.339530\pi$
$570$	−6.43096	−0.269363
$571$	−28.0696	−1.17468	−0.587338	−	0.809342i	$-0.699824\pi$
$571$	−28.0696	−1.17468	−0.587338	+	0.809342i	$0.699824\pi$
$572$	26.9309	1.12604
$573$	−23.8416	−0.995999
$574$	5.11929	0.213675
$575$	7.54034	0.314454
$576$	1.54099	0.0642078
$577$	−8.18562	−0.340772	−0.170386	−	0.985377i	$-0.554501\pi$
$577$	−8.18562	−0.340772	−0.170386	+	0.985377i	$0.554501\pi$
$578$	16.8758	0.701940
$579$	−30.6106	−1.27213
$580$	−0.564000	−0.0234188
$581$	7.68005	0.318622
$582$	39.7525	1.64779
$583$	−10.3525	−0.428756
$584$	4.43298	0.183438
$585$	−4.33630	−0.179284
$586$	11.8692	0.490312
$587$	−34.7485	−1.43423	−0.717113	−	0.696957i	$-0.754537\pi$
$587$	−34.7485	−1.43423	−0.717113	+	0.696957i	$0.754537\pi$
$588$	−9.61740	−0.396615
$589$	−37.2632	−1.53540
$590$	5.43663	0.223822
$591$	−12.9092	−0.531014
$592$	4.73360	0.194550
$593$	3.01839	0.123951	0.0619753	−	0.998078i	$-0.480260\pi$
$593$	3.01839	0.123951	0.0619753	+	0.998078i	$0.480260\pi$
$594$	−13.2990	−0.545666
$595$	−0.248399	−0.0101833
$596$	6.50903	0.266620
$597$	−6.30981	−0.258243
$598$	−9.88993	−0.404429
$599$	47.6361	1.94636	0.973180	−	0.230046i	$-0.0738875\pi$
$599$	47.6361	1.94636	0.973180	+	0.230046i	$0.0738875\pi$
$600$	10.2291	0.417602
$601$	−19.7778	−0.806754	−0.403377	−	0.915034i	$-0.632164\pi$
$601$	−19.7778	−0.806754	−0.403377	+	0.915034i	$0.632164\pi$
$602$	−18.7466	−0.764054
$603$	7.15625	0.291425
$604$	−8.56864	−0.348653
$605$	3.26122	0.132588
$606$	−32.0566	−1.30221
$607$	28.0024	1.13658	0.568291	−	0.822828i	$-0.307605\pi$
$607$	28.0024	1.13658	0.568291	+	0.822828i	$0.307605\pi$
$608$	−6.75221	−0.273838
$609$	4.24054	0.171836
$610$	1.22649	0.0496591
$611$	−13.3811	−0.541339
$612$	0.543089	0.0219531
$613$	−26.8100	−1.08284	−0.541422	−	0.840751i	$-0.682114\pi$
$613$	−26.8100	−1.08284	−0.541422	+	0.840751i	$0.682114\pi$
$614$	−29.4375	−1.18800
$615$	3.09184	0.124675
$616$	−6.74541	−0.271781
$617$	−31.4721	−1.26702	−0.633510	−	0.773735i	$-0.718386\pi$
$617$	−31.4721	−1.26702	−0.633510	+	0.773735i	$0.718386\pi$
$618$	17.4260	0.700976
$619$	−6.20171	−0.249268	−0.124634	−	0.992203i	$-0.539776\pi$
$619$	−6.20171	−0.249268	−0.124634	+	0.992203i	$0.539776\pi$
$620$	−2.46654	−0.0990588
$621$	4.88385	0.195982
$622$	−18.8312	−0.755064
$623$	2.72359	0.109118
$624$	−13.4165	−0.537091
$625$	22.0435	0.881740
$626$	−1.96564	−0.0785626
$627$	−61.5471	−2.45795
$628$	−4.27687	−0.170666
$629$	1.66826	0.0665178
$630$	1.08612	0.0432719
$631$	40.5668	1.61494	0.807469	−	0.589911i	$-0.200837\pi$
$631$	40.5668	1.61494	0.807469	+	0.589911i	$0.200837\pi$
$632$	−16.7417	−0.665951
$633$	32.6664	1.29837
$634$	−23.9998	−0.953154
$635$	3.01300	0.119567
$636$	5.15743	0.204505
$637$	28.4150	1.12584
$638$	−5.39772	−0.213698
$639$	14.0221	0.554704
$640$	−0.446946	−0.0176671
$641$	30.8918	1.22015	0.610077	−	0.792342i	$-0.291139\pi$
$641$	30.8918	1.22015	0.610077	+	0.792342i	$0.291139\pi$
$642$	2.44467	0.0964834
$643$	29.5453	1.16515	0.582577	−	0.812775i	$-0.302044\pi$
$643$	29.5453	1.16515	0.582577	+	0.812775i	$0.302044\pi$
$644$	2.47714	0.0976130
$645$	−11.3222	−0.445810
$646$	−2.37968	−0.0936271
$647$	−11.6546	−0.458190	−0.229095	−	0.973404i	$-0.573577\pi$
$647$	−11.6546	−0.458190	−0.229095	+	0.973404i	$0.573577\pi$
$648$	11.2483	0.441876
$649$	52.0309	2.04239
$650$	−30.2223	−1.18542
$651$	18.5452	0.726844
$652$	−3.92648	−0.153773
$653$	−9.81146	−0.383952	−0.191976	−	0.981400i	$-0.561490\pi$
$653$	−9.81146	−0.383952	−0.191976	+	0.981400i	$0.561490\pi$
$654$	−12.4669	−0.487495
$655$	1.06634	0.0416655
$656$	3.24629	0.126746
$657$	−6.83116	−0.266509
$658$	3.35157	0.130658
$659$	−22.7973	−0.888057	−0.444029	−	0.896013i	$-0.646451\pi$
$659$	−22.7973	−0.888057	−0.444029	+	0.896013i	$0.646451\pi$
$660$	−4.07395	−0.158578
$661$	0.461515	0.0179509	0.00897543	−	0.999960i	$-0.497143\pi$
$661$	0.461515	0.0179509	0.00897543	+	0.999960i	$0.497143\pi$
$662$	13.2454	0.514797
$663$	−4.72838	−0.183635
$664$	4.87014	0.188998
$665$	−4.75908	−0.184549
$666$	−7.29442	−0.282653
$667$	1.98222	0.0767519
$668$	20.8732	0.807607
$669$	−33.0494	−1.27776
$670$	−2.07559	−0.0801869
$671$	11.7380	0.453142
$672$	3.36045	0.129632
$673$	12.7026	0.489648	0.244824	−	0.969568i	$-0.421270\pi$
$673$	12.7026	0.489648	0.244824	+	0.969568i	$0.421270\pi$
$674$	22.3702	0.861668
$675$	14.9244	0.574441
$676$	26.6397	1.02460
$677$	−16.1623	−0.621167	−0.310583	−	0.950546i	$-0.600524\pi$
$677$	−16.1623	−0.621167	−0.310583	+	0.950546i	$0.600524\pi$
$678$	−40.3354	−1.54907
$679$	29.4179	1.12895
$680$	−0.157517	−0.00604049
$681$	−21.7880	−0.834919
$682$	−23.6059	−0.903916
$683$	−21.7063	−0.830568	−0.415284	−	0.909692i	$-0.636318\pi$
$683$	−21.7063	−0.830568	−0.415284	+	0.909692i	$0.636318\pi$
$684$	10.4051	0.397848
$685$	−10.3711	−0.396259
$686$	−18.1559	−0.693195
$687$	−20.7244	−0.790686
$688$	−11.8877	−0.453216
$689$	−15.2378	−0.580515
$690$	1.49609	0.0569552
$691$	33.1721	1.26193	0.630963	−	0.775813i	$-0.282660\pi$
$691$	33.1721	1.26193	0.630963	+	0.775813i	$0.282660\pi$
$692$	17.7545	0.674923
$693$	10.3946	0.394858
$694$	−31.1726	−1.18330
$695$	7.68250	0.291414
$696$	2.68905	0.101928
$697$	1.14409	0.0433354
$698$	27.8798	1.05527
$699$	10.1097	0.382385
$700$	7.56982	0.286112
$701$	28.2320	1.06631	0.533155	−	0.846018i	$-0.321006\pi$
$701$	28.2320	1.06631	0.533155	+	0.846018i	$0.321006\pi$
$702$	−19.5749	−0.738806
$703$	31.9623	1.20548
$704$	−4.27746	−0.161213
$705$	2.02421	0.0762361
$706$	−17.7439	−0.667801
$707$	−23.7227	−0.892185
$708$	−25.9209	−0.974167
$709$	20.0914	0.754547	0.377274	−	0.926102i	$-0.376862\pi$
$709$	20.0914	0.754547	0.377274	+	0.926102i	$0.376862\pi$
$710$	−4.06694	−0.152630
$711$	25.7988	0.967531
$712$	1.72711	0.0647260
$713$	8.66886	0.324652
$714$	1.18432	0.0443221
$715$	12.0367	0.450146
$716$	−23.0560	−0.861644
$717$	−25.5917	−0.955741
$718$	9.16291	0.341957
$719$	−4.37756	−0.163255	−0.0816277	−	0.996663i	$-0.526012\pi$
$719$	−4.37756	−0.163255	−0.0816277	+	0.996663i	$0.526012\pi$
$720$	0.688738	0.0256677
$721$	12.8957	0.480260
$722$	−26.5924	−0.989665
$723$	−15.8548	−0.589645
$724$	−13.7769	−0.512013
$725$	6.05741	0.224967
$726$	−15.5489	−0.577075
$727$	−44.9317	−1.66642	−0.833211	−	0.552955i	$-0.813500\pi$
$727$	−44.9317	−1.66642	−0.833211	+	0.552955i	$0.813500\pi$
$728$	−9.92859	−0.367978
$729$	2.54256	0.0941687
$730$	1.98130	0.0733312
$731$	−4.18959	−0.154958
$732$	−5.84769	−0.216137
$733$	−8.67495	−0.320417	−0.160208	−	0.987083i	$-0.551217\pi$
$733$	−8.67495	−0.320417	−0.160208	+	0.987083i	$0.551217\pi$
$734$	−0.603125	−0.0222617
$735$	−4.29845	−0.158551
$736$	1.57083	0.0579014
$737$	−19.8643	−0.731710
$738$	−5.00249	−0.184144
$739$	−42.9779	−1.58097	−0.790484	−	0.612483i	$-0.790171\pi$
$739$	−42.9779	−1.58097	−0.790484	+	0.612483i	$0.790171\pi$
$740$	2.11566	0.0777733
$741$	−90.5912	−3.32795
$742$	3.81663	0.140113
$743$	−26.4004	−0.968538	−0.484269	−	0.874919i	$-0.660914\pi$
$743$	−26.4004	−0.968538	−0.484269	+	0.874919i	$0.660914\pi$
$744$	11.7600	0.431144
$745$	2.90918	0.106584
$746$	−23.8740	−0.874089
$747$	−7.50482	−0.274587
$748$	−1.50750	−0.0551197
$749$	1.80912	0.0661038
$750$	9.33398	0.340829
$751$	−1.00000	−0.0364905
$751$	−1.00000	−0.0364905
$752$	2.12532	0.0775026
$753$	−0.248344	−0.00905016
$754$	−7.94491	−0.289337
$755$	−3.82972	−0.139378
$756$	4.90294	0.178318
$757$	−29.4587	−1.07069	−0.535347	−	0.844632i	$-0.679819\pi$
$757$	−29.4587	−1.07069	−0.535347	+	0.844632i	$0.679819\pi$
$758$	−33.0901	−1.20189
$759$	14.3182	0.519719
$760$	−3.01787	−0.109470
$761$	−23.1581	−0.839482	−0.419741	−	0.907644i	$-0.637879\pi$
$761$	−23.1581	−0.839482	−0.419741	+	0.907644i	$0.637879\pi$
$762$	−14.3654	−0.520405
$763$	−9.22586	−0.333998
$764$	−11.1882	−0.404775
$765$	0.242731	0.00877597
$766$	−14.6723	−0.530132
$767$	76.5843	2.76530
$768$	2.13096	0.0768944
$769$	−1.23760	−0.0446292	−0.0223146	−	0.999751i	$-0.507104\pi$
$769$	−1.23760	−0.0446292	−0.0223146	+	0.999751i	$0.507104\pi$
$770$	−3.01483	−0.108647
$771$	7.12785	0.256703
$772$	−14.3647	−0.516997
$773$	−3.92686	−0.141239	−0.0706197	−	0.997503i	$-0.522498\pi$
$773$	−3.92686	−0.141239	−0.0706197	+	0.997503i	$0.522498\pi$
$774$	18.3189	0.658458
$775$	26.4909	0.951582
$776$	18.6547	0.669666
$777$	−15.9070	−0.570662
$778$	17.4471	0.625510
$779$	21.9196	0.785352
$780$	−5.99646	−0.214708
$781$	−38.9224	−1.39275
$782$	0.553605	0.0197969
$783$	3.92336	0.140209
$784$	−4.51318	−0.161185
$785$	−1.91153	−0.0682253
$786$	−5.08414	−0.181345
$787$	−44.4952	−1.58608	−0.793041	−	0.609168i	$-0.791504\pi$
$787$	−44.4952	−1.58608	−0.793041	+	0.609168i	$0.791504\pi$
$788$	−6.05793	−0.215805
$789$	24.5715	0.874769
$790$	−7.48265	−0.266221
$791$	−29.8493	−1.06132
$792$	6.59151	0.234219
$793$	17.2772	0.613533
$794$	−25.1799	−0.893600
$795$	2.30509	0.0817531
$796$	−2.96102	−0.104950
$797$	−25.9650	−0.919728	−0.459864	−	0.887989i	$-0.652102\pi$
$797$	−25.9650	−0.919728	−0.459864	+	0.887989i	$0.652102\pi$
$798$	22.6905	0.803234
$799$	0.749026	0.0264986
$800$	4.80024	0.169714
$801$	−2.66145	−0.0940376
$802$	18.8737	0.666454
$803$	18.9619	0.669151
$804$	9.89604	0.349006
$805$	1.10715	0.0390218
$806$	−34.7455	−1.22386
$807$	55.7594	1.96282
$808$	−15.0433	−0.529220
$809$	5.95929	0.209517	0.104759	−	0.994498i	$-0.466593\pi$
$809$	5.95929	0.209517	0.104759	+	0.994498i	$0.466593\pi$
$810$	5.02739	0.176644
$811$	4.82767	0.169523	0.0847613	−	0.996401i	$-0.472987\pi$
$811$	4.82767	0.169523	0.0847613	+	0.996401i	$0.472987\pi$
$812$	1.98997	0.0698343
$813$	−22.9063	−0.803360
$814$	20.2478	0.709685
$815$	−1.75492	−0.0614722
$816$	0.751012	0.0262907
$817$	−80.2686	−2.80824
$818$	24.5345	0.857830
$819$	15.2998	0.534619
$820$	1.45092	0.0506682
$821$	13.4405	0.469076	0.234538	−	0.972107i	$-0.424642\pi$
$821$	13.4405	0.469076	0.234538	+	0.972107i	$0.424642\pi$
$822$	49.4475	1.72468
$823$	−24.4155	−0.851072	−0.425536	−	0.904941i	$-0.639915\pi$
$823$	−24.4155	−0.851072	−0.425536	+	0.904941i	$0.639915\pi$
$824$	8.17753	0.284878
$825$	43.7547	1.52334
$826$	−19.1821	−0.667432
$827$	−15.9805	−0.555697	−0.277849	−	0.960625i	$-0.589621\pi$
$827$	−15.9805	−0.555697	−0.277849	+	0.960625i	$0.589621\pi$
$828$	−2.42062	−0.0841225
$829$	−32.6664	−1.13455	−0.567276	−	0.823528i	$-0.692003\pi$
$829$	−32.6664	−1.13455	−0.567276	+	0.823528i	$0.692003\pi$
$830$	2.17669	0.0755539
$831$	−53.1897	−1.84513
$832$	−6.29600	−0.218275
$833$	−1.59057	−0.0551102
$834$	−36.6288	−1.26835
$835$	9.32917	0.322849
$836$	−28.8823	−0.998916
$837$	17.1581	0.593069
$838$	−11.1079	−0.383715
$839$	48.5703	1.67683	0.838416	−	0.545031i	$-0.183482\pi$
$839$	48.5703	1.67683	0.838416	+	0.545031i	$0.183482\pi$
$840$	1.50194	0.0518218
$841$	−27.4076	−0.945090
$842$	12.7728	0.440181
$843$	61.2760	2.11046
$844$	15.3294	0.527661
$845$	11.9065	0.409596
$846$	−3.27510	−0.112600
$847$	−11.5066	−0.395372
$848$	2.42024	0.0831113
$849$	−41.2582	−1.41598
$850$	1.69174	0.0580263
$851$	−7.43567	−0.254891
$852$	19.3905	0.664306
$853$	39.5608	1.35454	0.677269	−	0.735736i	$-0.263163\pi$
$853$	39.5608	1.35454	0.677269	+	0.735736i	$0.263163\pi$
$854$	−4.32745	−0.148082
$855$	4.65050	0.159044
$856$	1.14722	0.0392110
$857$	29.3106	1.00123	0.500615	−	0.865670i	$-0.333107\pi$
$857$	29.3106	1.00123	0.500615	+	0.865670i	$0.333107\pi$
$858$	−57.3887	−1.95922
$859$	58.0412	1.98034	0.990171	−	0.139864i	$-0.0446664\pi$
$859$	58.0412	1.98034	0.990171	+	0.139864i	$0.0446664\pi$
$860$	−5.31318	−0.181178
$861$	−10.9090	−0.371778
$862$	5.21419	0.177596
$863$	−45.5105	−1.54920	−0.774598	−	0.632453i	$-0.782048\pi$
$863$	−45.5105	−1.54920	−0.774598	+	0.632453i	$0.782048\pi$
$864$	3.10910	0.105774
$865$	7.93528	0.269807
$866$	30.2875	1.02921
$867$	−35.9616	−1.22132
$868$	8.70275	0.295391
$869$	−71.6122	−2.42928
$870$	1.20186	0.0407469
$871$	−29.2382	−0.990700
$872$	−5.85038	−0.198119
$873$	−28.7467	−0.972928
$874$	10.6066	0.358772
$875$	6.90739	0.233512
$876$	−9.44650	−0.319168
$877$	−20.9775	−0.708361	−0.354180	−	0.935177i	$-0.615240\pi$
$877$	−20.9775	−0.708361	−0.354180	+	0.935177i	$0.615240\pi$
$878$	−29.6583	−1.00092
$879$	−25.2928	−0.853104
$880$	−1.91179	−0.0644465
$881$	−2.68725	−0.0905358	−0.0452679	−	0.998975i	$-0.514414\pi$
$881$	−2.68725	−0.0905358	−0.0452679	+	0.998975i	$0.514414\pi$
$882$	6.95475	0.234179
$883$	31.9730	1.07598	0.537988	−	0.842952i	$-0.319185\pi$
$883$	31.9730	1.07598	0.537988	+	0.842952i	$0.319185\pi$
$884$	−2.21890	−0.0746295
$885$	−11.5852	−0.389433
$886$	−11.9654	−0.401987
$887$	3.23107	0.108489	0.0542444	−	0.998528i	$-0.482725\pi$
$887$	3.23107	0.108489	0.0542444	+	0.998528i	$0.482725\pi$
$888$	−10.0871	−0.338501
$889$	−10.6308	−0.356546
$890$	0.771922	0.0258749
$891$	48.1143	1.61189
$892$	−15.5092	−0.519286
$893$	14.3506	0.480226
$894$	−13.8705	−0.463898
$895$	−10.3048	−0.344451
$896$	1.57697	0.0526828
$897$	21.0750	0.703675
$898$	−20.0475	−0.668994
$899$	6.96399	0.232262
$900$	−7.39711	−0.246570
$901$	0.852962	0.0284163
$902$	13.8859	0.462349
$903$	39.9482	1.32939
$904$	−18.9283	−0.629546
$905$	−6.15751	−0.204682
$906$	18.2594	0.606629
$907$	−27.0284	−0.897465	−0.448732	−	0.893666i	$-0.648124\pi$
$907$	−27.0284	−0.897465	−0.448732	+	0.893666i	$0.648124\pi$
$908$	−10.2245	−0.339313
$909$	23.1815	0.768881
$910$	−4.43754	−0.147103
$911$	−26.3973	−0.874581	−0.437290	−	0.899320i	$-0.644062\pi$
$911$	−26.3973	−0.874581	−0.437290	+	0.899320i	$0.644062\pi$
$912$	14.3887	0.476457
$913$	20.8318	0.689433
$914$	23.0129	0.761199
$915$	−2.61360	−0.0864030
$916$	−9.72540	−0.321336
$917$	−3.76240	−0.124245
$918$	1.09574	0.0361647
$919$	49.8135	1.64319	0.821597	−	0.570068i	$-0.193083\pi$
$919$	49.8135	1.64319	0.821597	+	0.570068i	$0.193083\pi$
$920$	0.702074	0.0231467
$921$	62.7301	2.06703
$922$	24.4882	0.806477
$923$	−57.2899	−1.88572
$924$	14.3742	0.472877
$925$	−22.7224	−0.747109
$926$	21.9883	0.722581
$927$	−12.6015	−0.413886
$928$	1.26190	0.0414238
$929$	−46.7833	−1.53491	−0.767456	−	0.641102i	$-0.778478\pi$
$929$	−46.7833	−1.53491	−0.767456	+	0.641102i	$0.778478\pi$
$930$	5.25610	0.172354
$931$	−30.4739	−0.998742
$932$	4.74422	0.155402
$933$	40.1286	1.31375
$934$	6.54614	0.214196
$935$	−0.673772	−0.0220347
$936$	9.70206	0.317122
$937$	32.0184	1.04600	0.522998	−	0.852334i	$-0.324814\pi$
$937$	32.0184	1.04600	0.522998	+	0.852334i	$0.324814\pi$
$938$	7.32333	0.239115
$939$	4.18869	0.136693
$940$	0.949905	0.0309825
$941$	−41.4125	−1.35001	−0.675005	−	0.737813i	$-0.735859\pi$
$941$	−41.4125	−1.35001	−0.675005	+	0.737813i	$0.735859\pi$
$942$	9.11383	0.296945
$943$	−5.09936	−0.166058
$944$	−12.1640	−0.395903
$945$	2.19135	0.0712846
$946$	−50.8494	−1.65326
$947$	−38.9587	−1.26599	−0.632995	−	0.774156i	$-0.718174\pi$
$947$	−38.9587	−1.26599	−0.632995	+	0.774156i	$0.718174\pi$
$948$	35.6760	1.15870
$949$	27.9101	0.905999
$950$	32.4122	1.05159
$951$	51.1426	1.65841
$952$	0.555769	0.0180126
$953$	−23.1673	−0.750461	−0.375230	−	0.926932i	$-0.622436\pi$
$953$	−23.1673	−0.750461	−0.375230	+	0.926932i	$0.622436\pi$
$954$	−3.72955	−0.120749
$955$	−5.00053	−0.161813
$956$	−12.0095	−0.388415
$957$	11.5023	0.371817
$958$	−13.8307	−0.446850
$959$	36.5925	1.18163
$960$	0.952423	0.0307393
$961$	−0.544347	−0.0175596
$962$	29.8028	0.960880
$963$	−1.76784	−0.0569680
$964$	−7.44020	−0.239633
$965$	−6.42024	−0.206675
$966$	−5.27869	−0.169839
$967$	−28.6311	−0.920713	−0.460356	−	0.887734i	$-0.652278\pi$
$967$	−28.6311	−0.920713	−0.460356	+	0.887734i	$0.652278\pi$
$968$	−7.29668	−0.234524
$969$	5.07099	0.162904
$970$	8.33765	0.267706
$971$	5.24134	0.168203	0.0841013	−	0.996457i	$-0.473198\pi$
$971$	5.24134	0.168203	0.0841013	+	0.996457i	$0.473198\pi$
$972$	−14.6424	−0.469656
$973$	−27.1063	−0.868988
$974$	21.9250	0.702521
$975$	64.4026	2.06253
$976$	−2.74416	−0.0878384
$977$	26.0686	0.834009	0.417005	−	0.908904i	$-0.363080\pi$
$977$	26.0686	0.834009	0.417005	+	0.908904i	$0.363080\pi$
$978$	8.36716	0.267552
$979$	7.38763	0.236110
$980$	−2.01715	−0.0644353
$981$	9.01537	0.287838
$982$	8.19196	0.261416
$983$	55.1435	1.75881	0.879403	−	0.476078i	$-0.157942\pi$
$983$	55.1435	1.75881	0.879403	+	0.476078i	$0.157942\pi$
$984$	−6.91771	−0.220529
$985$	−2.70757	−0.0862703
$986$	0.444729	0.0141631
$987$	−7.14205	−0.227334
$988$	−42.5119	−1.35249
$989$	18.6736	0.593786
$990$	2.94605	0.0936316
$991$	33.7668	1.07264	0.536319	−	0.844016i	$-0.319815\pi$
$991$	33.7668	1.07264	0.536319	+	0.844016i	$0.319815\pi$
$992$	5.51866	0.175218
$993$	−28.2254	−0.895707
$994$	14.3495	0.455137
$995$	−1.32341	−0.0419550
$996$	−10.3781	−0.328842
$997$	−31.9946	−1.01328	−0.506639	−	0.862158i	$-0.669112\pi$
$997$	−31.9946	−1.01328	−0.506639	+	0.862158i	$0.669112\pi$
$998$	−14.4234	−0.456563
$999$	−14.7172	−0.465632

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1502.2.a.e.1.10	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1502.2.a.e.1.10	✓	11	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:	\( N \)	\(=\)	\( 1502 = 2 \cdot 751 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1502.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.13096 q^{3} +1.00000 q^{4} +0.446946 q^{5} -2.13096 q^{6} -1.57697 q^{7} -1.00000 q^{8} +1.54099 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.13096 q^{3} +1.00000 q^{4} +0.446946 q^{5} -2.13096 q^{6} -1.57697 q^{7} -1.00000 q^{8} +1.54099 q^{9} -0.446946 q^{10} -4.27746 q^{11} +2.13096 q^{12} -6.29600 q^{13} +1.57697 q^{14} +0.952423 q^{15} +1.00000 q^{16} +0.352429 q^{17} -1.54099 q^{18} +6.75221 q^{19} +0.446946 q^{20} -3.36045 q^{21} +4.27746 q^{22} -1.57083 q^{23} -2.13096 q^{24} -4.80024 q^{25} +6.29600 q^{26} -3.10910 q^{27} -1.57697 q^{28} -1.26190 q^{29} -0.952423 q^{30} -5.51866 q^{31} -1.00000 q^{32} -9.11510 q^{33} -0.352429 q^{34} -0.704818 q^{35} +1.54099 q^{36} +4.73360 q^{37} -6.75221 q^{38} -13.4165 q^{39} -0.446946 q^{40} +3.24629 q^{41} +3.36045 q^{42} -11.8877 q^{43} -4.27746 q^{44} +0.688738 q^{45} +1.57083 q^{46} +2.12532 q^{47} +2.13096 q^{48} -4.51318 q^{49} +4.80024 q^{50} +0.751012 q^{51} -6.29600 q^{52} +2.42024 q^{53} +3.10910 q^{54} -1.91179 q^{55} +1.57697 q^{56} +14.3887 q^{57} +1.26190 q^{58} -12.1640 q^{59} +0.952423 q^{60} -2.74416 q^{61} +5.51866 q^{62} -2.43009 q^{63} +1.00000 q^{64} -2.81397 q^{65} +9.11510 q^{66} +4.64394 q^{67} +0.352429 q^{68} -3.34737 q^{69} +0.704818 q^{70} +9.09940 q^{71} -1.54099 q^{72} -4.43298 q^{73} -4.73360 q^{74} -10.2291 q^{75} +6.75221 q^{76} +6.74541 q^{77} +13.4165 q^{78} +16.7417 q^{79} +0.446946 q^{80} -11.2483 q^{81} -3.24629 q^{82} -4.87014 q^{83} -3.36045 q^{84} +0.157517 q^{85} +11.8877 q^{86} -2.68905 q^{87} +4.27746 q^{88} -1.72711 q^{89} -0.688738 q^{90} +9.92859 q^{91} -1.57083 q^{92} -11.7600 q^{93} -2.12532 q^{94} +3.01787 q^{95} -2.13096 q^{96} -18.6547 q^{97} +4.51318 q^{98} -6.59151 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9	\( 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9} - q^{10} + 4 q^{11} - 4 q^{12} - 19 q^{13} + 6 q^{14} + q^{15} + 11 q^{16} - 8 q^{17} - 3 q^{18} - 9 q^{19} + q^{20} - 6 q^{21} - 4 q^{22} + 2 q^{23} + 4 q^{24} - 2 q^{25} + 19 q^{26} - 16 q^{27} - 6 q^{28} + 13 q^{29} - q^{30} - 19 q^{31} - 11 q^{32} - 37 q^{33} + 8 q^{34} + 3 q^{35} + 3 q^{36} - 29 q^{37} + 9 q^{38} + 8 q^{39} - q^{40} - 23 q^{41} + 6 q^{42} - 13 q^{43} + 4 q^{44} - 6 q^{45} - 2 q^{46} - 16 q^{47} - 4 q^{48} - 5 q^{49} + 2 q^{50} + 33 q^{51} - 19 q^{52} - 25 q^{53} + 16 q^{54} - 14 q^{55} + 6 q^{56} + 4 q^{57} - 13 q^{58} + 6 q^{59} + q^{60} + 10 q^{61} + 19 q^{62} - 7 q^{63} + 11 q^{64} - 19 q^{65} + 37 q^{66} - 16 q^{67} - 8 q^{68} - 25 q^{69} - 3 q^{70} + 8 q^{71} - 3 q^{72} - 56 q^{73} + 29 q^{74} - 50 q^{75} - 9 q^{76} - 7 q^{77} - 8 q^{78} + 2 q^{79} + q^{80} - 5 q^{81} + 23 q^{82} + 21 q^{83} - 6 q^{84} - 55 q^{85} + 13 q^{86} - 11 q^{87} - 4 q^{88} - 24 q^{89} + 6 q^{90} - 43 q^{91} + 2 q^{92} + 10 q^{93} + 16 q^{94} + 25 q^{95} + 4 q^{96} - 84 q^{97} + 5 q^{98} + 14 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9 - q^10 + 4 * q^11 - 4 * q^12 - 19 * q^13 + 6 * q^14 + q^15 + 11 * q^16 - 8 * q^17 - 3 * q^18 - 9 * q^19 + q^20 - 6 * q^21 - 4 * q^22 + 2 * q^23 + 4 * q^24 - 2 * q^25 + 19 * q^26 - 16 * q^27 - 6 * q^28 + 13 * q^29 - q^30 - 19 * q^31 - 11 * q^32 - 37 * q^33 + 8 * q^34 + 3 * q^35 + 3 * q^36 - 29 * q^37 + 9 * q^38 + 8 * q^39 - q^40 - 23 * q^41 + 6 * q^42 - 13 * q^43 + 4 * q^44 - 6 * q^45 - 2 * q^46 - 16 * q^47 - 4 * q^48 - 5 * q^49 + 2 * q^50 + 33 * q^51 - 19 * q^52 - 25 * q^53 + 16 * q^54 - 14 * q^55 + 6 * q^56 + 4 * q^57 - 13 * q^58 + 6 * q^59 + q^60 + 10 * q^61 + 19 * q^62 - 7 * q^63 + 11 * q^64 - 19 * q^65 + 37 * q^66 - 16 * q^67 - 8 * q^68 - 25 * q^69 - 3 * q^70 + 8 * q^71 - 3 * q^72 - 56 * q^73 + 29 * q^74 - 50 * q^75 - 9 * q^76 - 7 * q^77 - 8 * q^78 + 2 * q^79 + q^80 - 5 * q^81 + 23 * q^82 + 21 * q^83 - 6 * q^84 - 55 * q^85 + 13 * q^86 - 11 * q^87 - 4 * q^88 - 24 * q^89 + 6 * q^90 - 43 * q^91 + 2 * q^92 + 10 * q^93 + 16 * q^94 + 25 * q^95 + 4 * q^96 - 84 * q^97 + 5 * q^98 + 14 * q^99

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