LMFDB - Embedded newform 8022.2.a.r.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8022,2,Mod(1,8022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8022, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8022 = 2 \cdot 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8022.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:	$64.0559925015$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 19x^{8} + 28x^{7} + 114x^{6} - 110x^{5} - 282x^{4} + 149x^{3} + 285x^{2} - 49x - 79 $ x^10 - 2x^9 - 19x^8 + 28x^7 + 114x^6 - 110x^5 - 282x^4 + 149x^3 + 285x^2 - 49*x - 79
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-1.38859$ of defining polynomial
Character	$\chi$	$=$	8022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.38859 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.38859 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.38859 q^{10} +2.28784 q^{11} -1.00000 q^{12} +3.54302 q^{13} +1.00000 q^{14} -2.38859 q^{15} +1.00000 q^{16} -0.267087 q^{17} +1.00000 q^{18} -1.76669 q^{19} +2.38859 q^{20} -1.00000 q^{21} +2.28784 q^{22} -8.05531 q^{23} -1.00000 q^{24} +0.705377 q^{25} +3.54302 q^{26} -1.00000 q^{27} +1.00000 q^{28} +1.85105 q^{29} -2.38859 q^{30} +3.42028 q^{31} +1.00000 q^{32} -2.28784 q^{33} -0.267087 q^{34} +2.38859 q^{35} +1.00000 q^{36} +3.21741 q^{37} -1.76669 q^{38} -3.54302 q^{39} +2.38859 q^{40} -3.32364 q^{41} -1.00000 q^{42} +6.22819 q^{43} +2.28784 q^{44} +2.38859 q^{45} -8.05531 q^{46} +8.03043 q^{47} -1.00000 q^{48} +1.00000 q^{49} +0.705377 q^{50} +0.267087 q^{51} +3.54302 q^{52} +6.63303 q^{53} -1.00000 q^{54} +5.46473 q^{55} +1.00000 q^{56} +1.76669 q^{57} +1.85105 q^{58} +10.2900 q^{59} -2.38859 q^{60} -2.94671 q^{61} +3.42028 q^{62} +1.00000 q^{63} +1.00000 q^{64} +8.46283 q^{65} -2.28784 q^{66} -0.0848121 q^{67} -0.267087 q^{68} +8.05531 q^{69} +2.38859 q^{70} +15.0933 q^{71} +1.00000 q^{72} -5.97084 q^{73} +3.21741 q^{74} -0.705377 q^{75} -1.76669 q^{76} +2.28784 q^{77} -3.54302 q^{78} +4.20389 q^{79} +2.38859 q^{80} +1.00000 q^{81} -3.32364 q^{82} +2.14083 q^{83} -1.00000 q^{84} -0.637962 q^{85} +6.22819 q^{86} -1.85105 q^{87} +2.28784 q^{88} -7.58807 q^{89} +2.38859 q^{90} +3.54302 q^{91} -8.05531 q^{92} -3.42028 q^{93} +8.03043 q^{94} -4.21991 q^{95} -1.00000 q^{96} -7.25221 q^{97} +1.00000 q^{98} +2.28784 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 8 q^{5} - 10 q^{6} + 10 q^{7} + 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 8 * q^5 - 10 * q^6 + 10 * q^7 + 10 * q^8 + 10 * q^9	\( 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 8 q^{5} - 10 q^{6} + 10 q^{7} + 10 q^{8} + 10 q^{9} + 8 q^{10} + 4 q^{11} - 10 q^{12} + 6 q^{13} + 10 q^{14} - 8 q^{15} + 10 q^{16} + 5 q^{17} + 10 q^{18} + 15 q^{19} + 8 q^{20} - 10 q^{21} + 4 q^{22} + 12 q^{23} - 10 q^{24} - 2 q^{25} + 6 q^{26} - 10 q^{27} + 10 q^{28} + 7 q^{29} - 8 q^{30} + 28 q^{31} + 10 q^{32} - 4 q^{33} + 5 q^{34} + 8 q^{35} + 10 q^{36} - 3 q^{37} + 15 q^{38} - 6 q^{39} + 8 q^{40} + 24 q^{41} - 10 q^{42} + 4 q^{43} + 4 q^{44} + 8 q^{45} + 12 q^{46} + 16 q^{47} - 10 q^{48} + 10 q^{49} - 2 q^{50} - 5 q^{51} + 6 q^{52} + 5 q^{53} - 10 q^{54} - q^{55} + 10 q^{56} - 15 q^{57} + 7 q^{58} + 17 q^{59} - 8 q^{60} + 15 q^{61} + 28 q^{62} + 10 q^{63} + 10 q^{64} + 14 q^{65} - 4 q^{66} + 6 q^{67} + 5 q^{68} - 12 q^{69} + 8 q^{70} + 5 q^{71} + 10 q^{72} + 16 q^{73} - 3 q^{74} + 2 q^{75} + 15 q^{76} + 4 q^{77} - 6 q^{78} - 5 q^{79} + 8 q^{80} + 10 q^{81} + 24 q^{82} + 24 q^{83} - 10 q^{84} - 19 q^{85} + 4 q^{86} - 7 q^{87} + 4 q^{88} + 17 q^{89} + 8 q^{90} + 6 q^{91} + 12 q^{92} - 28 q^{93} + 16 q^{94} + 15 q^{95} - 10 q^{96} + 20 q^{97} + 10 q^{98} + 4 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 8 * q^5 - 10 * q^6 + 10 * q^7 + 10 * q^8 + 10 * q^9 + 8 * q^10 + 4 * q^11 - 10 * q^12 + 6 * q^13 + 10 * q^14 - 8 * q^15 + 10 * q^16 + 5 * q^17 + 10 * q^18 + 15 * q^19 + 8 * q^20 - 10 * q^21 + 4 * q^22 + 12 * q^23 - 10 * q^24 - 2 * q^25 + 6 * q^26 - 10 * q^27 + 10 * q^28 + 7 * q^29 - 8 * q^30 + 28 * q^31 + 10 * q^32 - 4 * q^33 + 5 * q^34 + 8 * q^35 + 10 * q^36 - 3 * q^37 + 15 * q^38 - 6 * q^39 + 8 * q^40 + 24 * q^41 - 10 * q^42 + 4 * q^43 + 4 * q^44 + 8 * q^45 + 12 * q^46 + 16 * q^47 - 10 * q^48 + 10 * q^49 - 2 * q^50 - 5 * q^51 + 6 * q^52 + 5 * q^53 - 10 * q^54 - q^55 + 10 * q^56 - 15 * q^57 + 7 * q^58 + 17 * q^59 - 8 * q^60 + 15 * q^61 + 28 * q^62 + 10 * q^63 + 10 * q^64 + 14 * q^65 - 4 * q^66 + 6 * q^67 + 5 * q^68 - 12 * q^69 + 8 * q^70 + 5 * q^71 + 10 * q^72 + 16 * q^73 - 3 * q^74 + 2 * q^75 + 15 * q^76 + 4 * q^77 - 6 * q^78 - 5 * q^79 + 8 * q^80 + 10 * q^81 + 24 * q^82 + 24 * q^83 - 10 * q^84 - 19 * q^85 + 4 * q^86 - 7 * q^87 + 4 * q^88 + 17 * q^89 + 8 * q^90 + 6 * q^91 + 12 * q^92 - 28 * q^93 + 16 * q^94 + 15 * q^95 - 10 * q^96 + 20 * q^97 + 10 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	2.38859	1.06821	0.534106	−	0.845418i	$-0.320648\pi$
$5$	2.38859	1.06821	0.534106	+	0.845418i	$0.320648\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.38859	0.755339
$11$	2.28784	0.689811	0.344905	−	0.938637i	$-0.387911\pi$
$11$	2.28784	0.689811	0.344905	+	0.938637i	$0.387911\pi$
$12$	−1.00000	−0.288675
$13$	3.54302	0.982656	0.491328	−	0.870974i	$-0.336512\pi$
$13$	3.54302	0.982656	0.491328	+	0.870974i	$0.336512\pi$
$14$	1.00000	0.267261
$15$	−2.38859	−0.616732
$16$	1.00000	0.250000
$17$	−0.267087	−0.0647780	−0.0323890	−	0.999475i	$-0.510312\pi$
$17$	−0.267087	−0.0647780	−0.0323890	+	0.999475i	$0.510312\pi$
$18$	1.00000	0.235702
$19$	−1.76669	−0.405307	−0.202654	−	0.979250i	$-0.564957\pi$
$19$	−1.76669	−0.405307	−0.202654	+	0.979250i	$0.564957\pi$
$20$	2.38859	0.534106
$21$	−1.00000	−0.218218
$22$	2.28784	0.487770
$23$	−8.05531	−1.67965	−0.839824	−	0.542859i	$-0.817342\pi$
$23$	−8.05531	−1.67965	−0.839824	+	0.542859i	$0.817342\pi$
$24$	−1.00000	−0.204124
$25$	0.705377	0.141075
$26$	3.54302	0.694843
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	1.85105	0.343732	0.171866	−	0.985120i	$-0.445020\pi$
$29$	1.85105	0.343732	0.171866	+	0.985120i	$0.445020\pi$
$30$	−2.38859	−0.436095
$31$	3.42028	0.614300	0.307150	−	0.951661i	$-0.400625\pi$
$31$	3.42028	0.614300	0.307150	+	0.951661i	$0.400625\pi$
$32$	1.00000	0.176777
$33$	−2.28784	−0.398262
$34$	−0.267087	−0.0458050
$35$	2.38859	0.403746
$36$	1.00000	0.166667
$37$	3.21741	0.528939	0.264469	−	0.964394i	$-0.414803\pi$
$37$	3.21741	0.528939	0.264469	+	0.964394i	$0.414803\pi$
$38$	−1.76669	−0.286596
$39$	−3.54302	−0.567337
$40$	2.38859	0.377670
$41$	−3.32364	−0.519065	−0.259532	−	0.965734i	$-0.583568\pi$
$41$	−3.32364	−0.519065	−0.259532	+	0.965734i	$0.583568\pi$
$42$	−1.00000	−0.154303
$43$	6.22819	0.949790	0.474895	−	0.880043i	$-0.342486\pi$
$43$	6.22819	0.949790	0.474895	+	0.880043i	$0.342486\pi$
$44$	2.28784	0.344905
$45$	2.38859	0.356070
$46$	−8.05531	−1.18769
$47$	8.03043	1.17136	0.585680	−	0.810543i	$-0.300828\pi$
$47$	8.03043	1.17136	0.585680	+	0.810543i	$0.300828\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	0.705377	0.0997553
$51$	0.267087	0.0373996
$52$	3.54302	0.491328
$53$	6.63303	0.911116	0.455558	−	0.890206i	$-0.349440\pi$
$53$	6.63303	0.911116	0.455558	+	0.890206i	$0.349440\pi$
$54$	−1.00000	−0.136083
$55$	5.46473	0.736863
$56$	1.00000	0.133631
$57$	1.76669	0.234004
$58$	1.85105	0.243055
$59$	10.2900	1.33964	0.669820	−	0.742523i	$-0.266371\pi$
$59$	10.2900	1.33964	0.669820	+	0.742523i	$0.266371\pi$
$60$	−2.38859	−0.308366
$61$	−2.94671	−0.377288	−0.188644	−	0.982046i	$-0.560409\pi$
$61$	−2.94671	−0.377288	−0.188644	+	0.982046i	$0.560409\pi$
$62$	3.42028	0.434376
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	8.46283	1.04968
$66$	−2.28784	−0.281614
$67$	−0.0848121	−0.0103615	−0.00518073	−	0.999987i	$-0.501649\pi$
$67$	−0.0848121	−0.0103615	−0.00518073	+	0.999987i	$0.501649\pi$
$68$	−0.267087	−0.0323890
$69$	8.05531	0.969745
$70$	2.38859	0.285491
$71$	15.0933	1.79124	0.895622	−	0.444816i	$-0.146731\pi$
$71$	15.0933	1.79124	0.895622	+	0.444816i	$0.146731\pi$
$72$	1.00000	0.117851
$73$	−5.97084	−0.698834	−0.349417	−	0.936967i	$-0.613620\pi$
$73$	−5.97084	−0.698834	−0.349417	+	0.936967i	$0.613620\pi$
$74$	3.21741	0.374016
$75$	−0.705377	−0.0814499
$76$	−1.76669	−0.202654
$77$	2.28784	0.260724
$78$	−3.54302	−0.401168
$79$	4.20389	0.472975	0.236487	−	0.971635i	$-0.424004\pi$
$79$	4.20389	0.472975	0.236487	+	0.971635i	$0.424004\pi$
$80$	2.38859	0.267053
$81$	1.00000	0.111111
$82$	−3.32364	−0.367034
$83$	2.14083	0.234986	0.117493	−	0.993074i	$-0.462514\pi$
$83$	2.14083	0.234986	0.117493	+	0.993074i	$0.462514\pi$
$84$	−1.00000	−0.109109
$85$	−0.637962	−0.0691966
$86$	6.22819	0.671603
$87$	−1.85105	−0.198454
$88$	2.28784	0.243885
$89$	−7.58807	−0.804334	−0.402167	−	0.915566i	$-0.631743\pi$
$89$	−7.58807	−0.804334	−0.402167	+	0.915566i	$0.631743\pi$
$90$	2.38859	0.251780
$91$	3.54302	0.371409
$92$	−8.05531	−0.839824
$93$	−3.42028	−0.354667
$94$	8.03043	0.828276
$95$	−4.21991	−0.432954
$96$	−1.00000	−0.102062
$97$	−7.25221	−0.736350	−0.368175	−	0.929756i	$-0.620017\pi$
$97$	−7.25221	−0.736350	−0.368175	+	0.929756i	$0.620017\pi$
$98$	1.00000	0.101015
$99$	2.28784	0.229937
$100$	0.705377	0.0705377
$101$	7.83271	0.779383	0.389692	−	0.920945i	$-0.372582\pi$
$101$	7.83271	0.779383	0.389692	+	0.920945i	$0.372582\pi$
$102$	0.267087	0.0264455
$103$	0.560769	0.0552543	0.0276271	−	0.999618i	$-0.491205\pi$
$103$	0.560769	0.0552543	0.0276271	+	0.999618i	$0.491205\pi$
$104$	3.54302	0.347422
$105$	−2.38859	−0.233103
$106$	6.63303	0.644257
$107$	12.5139	1.20976	0.604881	−	0.796316i	$-0.293221\pi$
$107$	12.5139	1.20976	0.604881	+	0.796316i	$0.293221\pi$
$108$	−1.00000	−0.0962250
$109$	−8.43485	−0.807913	−0.403956	−	0.914778i	$-0.632365\pi$
$109$	−8.43485	−0.807913	−0.403956	+	0.914778i	$0.632365\pi$
$110$	5.46473	0.521041
$111$	−3.21741	−0.305383
$112$	1.00000	0.0944911
$113$	−5.61728	−0.528429	−0.264215	−	0.964464i	$-0.585113\pi$
$113$	−5.61728	−0.528429	−0.264215	+	0.964464i	$0.585113\pi$
$114$	1.76669	0.165466
$115$	−19.2409	−1.79422
$116$	1.85105	0.171866
$117$	3.54302	0.327552
$118$	10.2900	0.947269
$119$	−0.267087	−0.0244838
$120$	−2.38859	−0.218048
$121$	−5.76577	−0.524161
$122$	−2.94671	−0.266783
$123$	3.32364	0.299682
$124$	3.42028	0.307150
$125$	−10.2581	−0.917513
$126$	1.00000	0.0890871
$127$	−14.7772	−1.31127	−0.655634	−	0.755079i	$-0.727598\pi$
$127$	−14.7772	−1.31127	−0.655634	+	0.755079i	$0.727598\pi$
$128$	1.00000	0.0883883
$129$	−6.22819	−0.548361
$130$	8.46283	0.742239
$131$	−14.2790	−1.24756	−0.623779	−	0.781601i	$-0.714403\pi$
$131$	−14.2790	−1.24756	−0.623779	+	0.781601i	$0.714403\pi$
$132$	−2.28784	−0.199131
$133$	−1.76669	−0.153192
$134$	−0.0848121	−0.00732665
$135$	−2.38859	−0.205577
$136$	−0.267087	−0.0229025
$137$	−13.0155	−1.11199	−0.555993	−	0.831187i	$-0.687662\pi$
$137$	−13.0155	−1.11199	−0.555993	+	0.831187i	$0.687662\pi$
$138$	8.05531	0.685713
$139$	17.2513	1.46324	0.731620	−	0.681713i	$-0.238765\pi$
$139$	17.2513	1.46324	0.731620	+	0.681713i	$0.238765\pi$
$140$	2.38859	0.201873
$141$	−8.03043	−0.676284
$142$	15.0933	1.26660
$143$	8.10587	0.677847
$144$	1.00000	0.0833333
$145$	4.42141	0.367178
$146$	−5.97084	−0.494150
$147$	−1.00000	−0.0824786
$148$	3.21741	0.264469
$149$	−7.77496	−0.636950	−0.318475	−	0.947931i	$-0.603171\pi$
$149$	−7.77496	−0.636950	−0.318475	+	0.947931i	$0.603171\pi$
$150$	−0.705377	−0.0575938
$151$	5.59000	0.454908	0.227454	−	0.973789i	$-0.426960\pi$
$151$	5.59000	0.454908	0.227454	+	0.973789i	$0.426960\pi$
$152$	−1.76669	−0.143298
$153$	−0.267087	−0.0215927
$154$	2.28784	0.184360
$155$	8.16966	0.656203
$156$	−3.54302	−0.283668
$157$	−0.231671	−0.0184894	−0.00924470	−	0.999957i	$-0.502943\pi$
$157$	−0.231671	−0.0184894	−0.00924470	+	0.999957i	$0.502943\pi$
$158$	4.20389	0.334444
$159$	−6.63303	−0.526033
$160$	2.38859	0.188835
$161$	−8.05531	−0.634847
$162$	1.00000	0.0785674
$163$	18.8979	1.48019	0.740097	−	0.672500i	$-0.234779\pi$
$163$	18.8979	1.48019	0.740097	+	0.672500i	$0.234779\pi$
$164$	−3.32364	−0.259532
$165$	−5.46473	−0.425428
$166$	2.14083	0.166161
$167$	9.74424	0.754032	0.377016	−	0.926207i	$-0.376950\pi$
$167$	9.74424	0.754032	0.377016	+	0.926207i	$0.376950\pi$
$168$	−1.00000	−0.0771517
$169$	−0.447021	−0.0343862
$170$	−0.637962	−0.0489294
$171$	−1.76669	−0.135102
$172$	6.22819	0.474895
$173$	−14.2746	−1.08528	−0.542640	−	0.839965i	$-0.682575\pi$
$173$	−14.2746	−1.08528	−0.542640	+	0.839965i	$0.682575\pi$
$174$	−1.85105	−0.140328
$175$	0.705377	0.0533215
$176$	2.28784	0.172453
$177$	−10.2900	−0.773442
$178$	−7.58807	−0.568750
$179$	−8.05485	−0.602048	−0.301024	−	0.953617i	$-0.597328\pi$
$179$	−8.05485	−0.602048	−0.301024	+	0.953617i	$0.597328\pi$
$180$	2.38859	0.178035
$181$	8.99087	0.668286	0.334143	−	0.942522i	$-0.391553\pi$
$181$	8.99087	0.668286	0.334143	+	0.942522i	$0.391553\pi$
$182$	3.54302	0.262626
$183$	2.94671	0.217827
$184$	−8.05531	−0.593845
$185$	7.68508	0.565018
$186$	−3.42028	−0.250787
$187$	−0.611053	−0.0446846
$188$	8.03043	0.585680
$189$	−1.00000	−0.0727393
$190$	−4.21991	−0.306145
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	−1.00000	−0.0721688
$193$	11.2197	0.807613	0.403806	−	0.914844i	$-0.367687\pi$
$193$	11.2197	0.807613	0.403806	+	0.914844i	$0.367687\pi$
$194$	−7.25221	−0.520678
$195$	−8.46283	−0.606036
$196$	1.00000	0.0714286
$197$	2.37012	0.168864	0.0844320	−	0.996429i	$-0.473092\pi$
$197$	2.37012	0.168864	0.0844320	+	0.996429i	$0.473092\pi$
$198$	2.28784	0.162590
$199$	2.94766	0.208954	0.104477	−	0.994527i	$-0.466683\pi$
$199$	2.94766	0.208954	0.104477	+	0.994527i	$0.466683\pi$
$200$	0.705377	0.0498777
$201$	0.0848121	0.00598219
$202$	7.83271	0.551107
$203$	1.85105	0.129918
$204$	0.267087	0.0186998
$205$	−7.93882	−0.554471
$206$	0.560769	0.0390707
$207$	−8.05531	−0.559883
$208$	3.54302	0.245664
$209$	−4.04192	−0.279585
$210$	−2.38859	−0.164829
$211$	−20.5064	−1.41172	−0.705860	−	0.708351i	$-0.749439\pi$
$211$	−20.5064	−1.41172	−0.705860	+	0.708351i	$0.749439\pi$
$212$	6.63303	0.455558
$213$	−15.0933	−1.03418
$214$	12.5139	0.855431
$215$	14.8766	1.01458
$216$	−1.00000	−0.0680414
$217$	3.42028	0.232184
$218$	−8.43485	−0.571280
$219$	5.97084	0.403472
$220$	5.46473	0.368432
$221$	−0.946293	−0.0636546
$222$	−3.21741	−0.215938
$223$	10.0996	0.676319	0.338159	−	0.941089i	$-0.390196\pi$
$223$	10.0996	0.676319	0.338159	+	0.941089i	$0.390196\pi$
$224$	1.00000	0.0668153
$225$	0.705377	0.0470251
$226$	−5.61728	−0.373656
$227$	14.9692	0.993538	0.496769	−	0.867883i	$-0.334520\pi$
$227$	14.9692	0.993538	0.496769	+	0.867883i	$0.334520\pi$
$228$	1.76669	0.117002
$229$	22.5899	1.49278	0.746392	−	0.665507i	$-0.231784\pi$
$229$	22.5899	1.49278	0.746392	+	0.665507i	$0.231784\pi$
$230$	−19.2409	−1.26870
$231$	−2.28784	−0.150529
$232$	1.85105	0.121528
$233$	22.2019	1.45450	0.727249	−	0.686374i	$-0.240799\pi$
$233$	22.2019	1.45450	0.727249	+	0.686374i	$0.240799\pi$
$234$	3.54302	0.231614
$235$	19.1814	1.25126
$236$	10.2900	0.669820
$237$	−4.20389	−0.273072
$238$	−0.267087	−0.0173127
$239$	−7.43307	−0.480805	−0.240403	−	0.970673i	$-0.577279\pi$
$239$	−7.43307	−0.480805	−0.240403	+	0.970673i	$0.577279\pi$
$240$	−2.38859	−0.154183
$241$	−19.0471	−1.22693	−0.613465	−	0.789722i	$-0.710225\pi$
$241$	−19.0471	−1.22693	−0.613465	+	0.789722i	$0.710225\pi$
$242$	−5.76577	−0.370638
$243$	−1.00000	−0.0641500
$244$	−2.94671	−0.188644
$245$	2.38859	0.152602
$246$	3.32364	0.211907
$247$	−6.25943	−0.398278
$248$	3.42028	0.217188
$249$	−2.14083	−0.135670
$250$	−10.2581	−0.648780
$251$	1.23953	0.0782382	0.0391191	−	0.999235i	$-0.487545\pi$
$251$	1.23953	0.0782382	0.0391191	+	0.999235i	$0.487545\pi$
$252$	1.00000	0.0629941
$253$	−18.4293	−1.15864
$254$	−14.7772	−0.927206
$255$	0.637962	0.0399507
$256$	1.00000	0.0625000
$257$	−7.36599	−0.459478	−0.229739	−	0.973252i	$-0.573787\pi$
$257$	−7.36599	−0.459478	−0.229739	+	0.973252i	$0.573787\pi$
$258$	−6.22819	−0.387750
$259$	3.21741	0.199920
$260$	8.46283	0.524842
$261$	1.85105	0.114577
$262$	−14.2790	−0.882157
$263$	−5.00353	−0.308531	−0.154265	−	0.988029i	$-0.549301\pi$
$263$	−5.00353	−0.308531	−0.154265	+	0.988029i	$0.549301\pi$
$264$	−2.28784	−0.140807
$265$	15.8436	0.973265
$266$	−1.76669	−0.108323
$267$	7.58807	0.464383
$268$	−0.0848121	−0.00518073
$269$	9.68302	0.590384	0.295192	−	0.955438i	$-0.404616\pi$
$269$	9.68302	0.590384	0.295192	+	0.955438i	$0.404616\pi$
$270$	−2.38859	−0.145365
$271$	17.8811	1.08620	0.543100	−	0.839668i	$-0.317250\pi$
$271$	17.8811	1.08620	0.543100	+	0.839668i	$0.317250\pi$
$272$	−0.267087	−0.0161945
$273$	−3.54302	−0.214433
$274$	−13.0155	−0.786293
$275$	1.61379	0.0973153
$276$	8.05531	0.484873
$277$	7.16722	0.430637	0.215318	−	0.976544i	$-0.430921\pi$
$277$	7.16722	0.430637	0.215318	+	0.976544i	$0.430921\pi$
$278$	17.2513	1.03467
$279$	3.42028	0.204767
$280$	2.38859	0.142746
$281$	−11.9650	−0.713771	−0.356885	−	0.934148i	$-0.616161\pi$
$281$	−11.9650	−0.713771	−0.356885	+	0.934148i	$0.616161\pi$
$282$	−8.03043	−0.478205
$283$	18.8476	1.12037	0.560187	−	0.828366i	$-0.310729\pi$
$283$	18.8476	1.12037	0.560187	+	0.828366i	$0.310729\pi$
$284$	15.0933	0.895622
$285$	4.21991	0.249966
$286$	8.10587	0.479310
$287$	−3.32364	−0.196188
$288$	1.00000	0.0589256
$289$	−16.9287	−0.995804
$290$	4.42141	0.259634
$291$	7.25221	0.425132
$292$	−5.97084	−0.349417
$293$	26.5397	1.55046	0.775232	−	0.631677i	$-0.217633\pi$
$293$	26.5397	1.55046	0.775232	+	0.631677i	$0.217633\pi$
$294$	−1.00000	−0.0583212
$295$	24.5786	1.43102
$296$	3.21741	0.187008
$297$	−2.28784	−0.132754
$298$	−7.77496	−0.450391
$299$	−28.5401	−1.65052
$300$	−0.705377	−0.0407249
$301$	6.22819	0.358987
$302$	5.59000	0.321669
$303$	−7.83271	−0.449977
$304$	−1.76669	−0.101327
$305$	−7.03850	−0.403023
$306$	−0.267087	−0.0152683
$307$	0.947457	0.0540742	0.0270371	−	0.999634i	$-0.491393\pi$
$307$	0.947457	0.0540742	0.0270371	+	0.999634i	$0.491393\pi$
$308$	2.28784	0.130362
$309$	−0.560769	−0.0319011
$310$	8.16966	0.464005
$311$	−15.6088	−0.885093	−0.442546	−	0.896746i	$-0.645925\pi$
$311$	−15.6088	−0.885093	−0.442546	+	0.896746i	$0.645925\pi$
$312$	−3.54302	−0.200584
$313$	−17.3696	−0.981787	−0.490894	−	0.871219i	$-0.663330\pi$
$313$	−17.3696	−0.981787	−0.490894	+	0.871219i	$0.663330\pi$
$314$	−0.231671	−0.0130740
$315$	2.38859	0.134582
$316$	4.20389	0.236487
$317$	−14.3301	−0.804860	−0.402430	−	0.915451i	$-0.631834\pi$
$317$	−14.3301	−0.804860	−0.402430	+	0.915451i	$0.631834\pi$
$318$	−6.63303	−0.371962
$319$	4.23492	0.237110
$320$	2.38859	0.133526
$321$	−12.5139	−0.698456
$322$	−8.05531	−0.448905
$323$	0.471860	0.0262550
$324$	1.00000	0.0555556
$325$	2.49916	0.138629
$326$	18.8979	1.04666
$327$	8.43485	0.466449
$328$	−3.32364	−0.183517
$329$	8.03043	0.442732
$330$	−5.46473	−0.300823
$331$	−7.12276	−0.391502	−0.195751	−	0.980654i	$-0.562714\pi$
$331$	−7.12276	−0.391502	−0.195751	+	0.980654i	$0.562714\pi$
$332$	2.14083	0.117493
$333$	3.21741	0.176313
$334$	9.74424	0.533181
$335$	−0.202582	−0.0110682
$336$	−1.00000	−0.0545545
$337$	−27.7585	−1.51210	−0.756050	−	0.654514i	$-0.772873\pi$
$337$	−27.7585	−1.51210	−0.756050	+	0.654514i	$0.772873\pi$
$338$	−0.447021	−0.0243147
$339$	5.61728	0.305089
$340$	−0.637962	−0.0345983
$341$	7.82506	0.423751
$342$	−1.76669	−0.0955319
$343$	1.00000	0.0539949
$344$	6.22819	0.335801
$345$	19.2409	1.03589
$346$	−14.2746	−0.767409
$347$	2.81815	0.151286	0.0756432	−	0.997135i	$-0.475899\pi$
$347$	2.81815	0.151286	0.0756432	+	0.997135i	$0.475899\pi$
$348$	−1.85105	−0.0992269
$349$	8.44696	0.452155	0.226078	−	0.974109i	$-0.427410\pi$
$349$	8.44696	0.452155	0.226078	+	0.974109i	$0.427410\pi$
$350$	0.705377	0.0377040
$351$	−3.54302	−0.189112
$352$	2.28784	0.121942
$353$	22.2010	1.18164	0.590821	−	0.806803i	$-0.298804\pi$
$353$	22.2010	1.18164	0.590821	+	0.806803i	$0.298804\pi$
$354$	−10.2900	−0.546906
$355$	36.0517	1.91343
$356$	−7.58807	−0.402167
$357$	0.267087	0.0141357
$358$	−8.05485	−0.425712
$359$	13.1864	0.695953	0.347976	−	0.937503i	$-0.386869\pi$
$359$	13.1864	0.695953	0.347976	+	0.937503i	$0.386869\pi$
$360$	2.38859	0.125890
$361$	−15.8788	−0.835726
$362$	8.99087	0.472549
$363$	5.76577	0.302625
$364$	3.54302	0.185705
$365$	−14.2619	−0.746502
$366$	2.94671	0.154027
$367$	5.13790	0.268196	0.134098	−	0.990968i	$-0.457186\pi$
$367$	5.13790	0.268196	0.134098	+	0.990968i	$0.457186\pi$
$368$	−8.05531	−0.419912
$369$	−3.32364	−0.173022
$370$	7.68508	0.399528
$371$	6.63303	0.344370
$372$	−3.42028	−0.177333
$373$	25.6767	1.32949	0.664745	−	0.747070i	$-0.268540\pi$
$373$	25.6767	1.32949	0.664745	+	0.747070i	$0.268540\pi$
$374$	−0.611053	−0.0315968
$375$	10.2581	0.529726
$376$	8.03043	0.414138
$377$	6.55831	0.337770
$378$	−1.00000	−0.0514344
$379$	13.5588	0.696469	0.348235	−	0.937407i	$-0.386781\pi$
$379$	13.5588	0.696469	0.348235	+	0.937407i	$0.386781\pi$
$380$	−4.21991	−0.216477
$381$	14.7772	0.757061
$382$	1.00000	0.0511645
$383$	−2.61689	−0.133717	−0.0668583	−	0.997762i	$-0.521298\pi$
$383$	−2.61689	−0.133717	−0.0668583	+	0.997762i	$0.521298\pi$
$384$	−1.00000	−0.0510310
$385$	5.46473	0.278508
$386$	11.2197	0.571068
$387$	6.22819	0.316597
$388$	−7.25221	−0.368175
$389$	20.4220	1.03543	0.517717	−	0.855552i	$-0.326782\pi$
$389$	20.4220	1.03543	0.517717	+	0.855552i	$0.326782\pi$
$390$	−8.46283	−0.428532
$391$	2.15147	0.108804
$392$	1.00000	0.0505076
$393$	14.2790	0.720278
$394$	2.37012	0.119405
$395$	10.0414	0.505237
$396$	2.28784	0.114968
$397$	25.4577	1.27769	0.638843	−	0.769337i	$-0.279413\pi$
$397$	25.4577	1.27769	0.638843	+	0.769337i	$0.279413\pi$
$398$	2.94766	0.147753
$399$	1.76669	0.0884453
$400$	0.705377	0.0352688
$401$	−25.6696	−1.28188	−0.640938	−	0.767592i	$-0.721455\pi$
$401$	−25.6696	−1.28188	−0.640938	+	0.767592i	$0.721455\pi$
$402$	0.0848121	0.00423005
$403$	12.1181	0.603646
$404$	7.83271	0.389692
$405$	2.38859	0.118690
$406$	1.85105	0.0918662
$407$	7.36093	0.364868
$408$	0.267087	0.0132228
$409$	16.1625	0.799183	0.399592	−	0.916693i	$-0.369152\pi$
$409$	16.1625	0.799183	0.399592	+	0.916693i	$0.369152\pi$
$410$	−7.93882	−0.392070
$411$	13.0155	0.642006
$412$	0.560769	0.0276271
$413$	10.2900	0.506336
$414$	−8.05531	−0.395897
$415$	5.11357	0.251015
$416$	3.54302	0.173711
$417$	−17.2513	−0.844802
$418$	−4.04192	−0.197697
$419$	1.93730	0.0946431	0.0473216	−	0.998880i	$-0.484931\pi$
$419$	1.93730	0.0946431	0.0473216	+	0.998880i	$0.484931\pi$
$420$	−2.38859	−0.116551
$421$	−5.79158	−0.282264	−0.141132	−	0.989991i	$-0.545074\pi$
$421$	−5.79158	−0.282264	−0.141132	+	0.989991i	$0.545074\pi$
$422$	−20.5064	−0.998237
$423$	8.03043	0.390453
$424$	6.63303	0.322128
$425$	−0.188397	−0.00913859
$426$	−15.0933	−0.731272
$427$	−2.94671	−0.142601
$428$	12.5139	0.604881
$429$	−8.10587	−0.391355
$430$	14.8766	0.717414
$431$	2.06031	0.0992415	0.0496208	−	0.998768i	$-0.484199\pi$
$431$	2.06031	0.0992415	0.0496208	+	0.998768i	$0.484199\pi$
$432$	−1.00000	−0.0481125
$433$	−39.6438	−1.90516	−0.952579	−	0.304291i	$-0.901580\pi$
$433$	−39.6438	−1.90516	−0.952579	+	0.304291i	$0.901580\pi$
$434$	3.42028	0.164179
$435$	−4.42141	−0.211990
$436$	−8.43485	−0.403956
$437$	14.2313	0.680774
$438$	5.97084	0.285298
$439$	−26.6078	−1.26992	−0.634959	−	0.772546i	$-0.718983\pi$
$439$	−26.6078	−1.26992	−0.634959	+	0.772546i	$0.718983\pi$
$440$	5.46473	0.260521
$441$	1.00000	0.0476190
$442$	−0.946293	−0.0450106
$443$	−7.30527	−0.347084	−0.173542	−	0.984826i	$-0.555521\pi$
$443$	−7.30527	−0.347084	−0.173542	+	0.984826i	$0.555521\pi$
$444$	−3.21741	−0.152691
$445$	−18.1248	−0.859199
$446$	10.0996	0.478229
$447$	7.77496	0.367743
$448$	1.00000	0.0472456
$449$	−17.1305	−0.808439	−0.404219	−	0.914662i	$-0.632457\pi$
$449$	−17.1305	−0.808439	−0.404219	+	0.914662i	$0.632457\pi$
$450$	0.705377	0.0332518
$451$	−7.60396	−0.358057
$452$	−5.61728	−0.264215
$453$	−5.59000	−0.262641
$454$	14.9692	0.702537
$455$	8.46283	0.396744
$456$	1.76669	0.0827330
$457$	−9.82835	−0.459751	−0.229875	−	0.973220i	$-0.573832\pi$
$457$	−9.82835	−0.459751	−0.229875	+	0.973220i	$0.573832\pi$
$458$	22.5899	1.05556
$459$	0.267087	0.0124665
$460$	−19.2409	−0.897110
$461$	25.4306	1.18442	0.592209	−	0.805784i	$-0.298256\pi$
$461$	25.4306	1.18442	0.592209	+	0.805784i	$0.298256\pi$
$462$	−2.28784	−0.106440
$463$	−37.7941	−1.75644	−0.878219	−	0.478258i	$-0.841268\pi$
$463$	−37.7941	−1.75644	−0.878219	+	0.478258i	$0.841268\pi$
$464$	1.85105	0.0859330
$465$	−8.16966	−0.378859
$466$	22.2019	1.02848
$467$	−0.604844	−0.0279889	−0.0139944	−	0.999902i	$-0.504455\pi$
$467$	−0.604844	−0.0279889	−0.0139944	+	0.999902i	$0.504455\pi$
$468$	3.54302	0.163776
$469$	−0.0848121	−0.00391626
$470$	19.1814	0.884774
$471$	0.231671	0.0106749
$472$	10.2900	0.473634
$473$	14.2491	0.655175
$474$	−4.20389	−0.193091
$475$	−1.24618	−0.0571789
$476$	−0.267087	−0.0122419
$477$	6.63303	0.303705
$478$	−7.43307	−0.339981
$479$	−4.30124	−0.196529	−0.0982643	−	0.995160i	$-0.531329\pi$
$479$	−4.30124	−0.196529	−0.0982643	+	0.995160i	$0.531329\pi$
$480$	−2.38859	−0.109024
$481$	11.3993	0.519765
$482$	−19.0471	−0.867571
$483$	8.05531	0.366529
$484$	−5.76577	−0.262081
$485$	−17.3226	−0.786577
$486$	−1.00000	−0.0453609
$487$	−9.42295	−0.426995	−0.213497	−	0.976944i	$-0.568485\pi$
$487$	−9.42295	−0.426995	−0.213497	+	0.976944i	$0.568485\pi$
$488$	−2.94671	−0.133391
$489$	−18.8979	−0.854591
$490$	2.38859	0.107906
$491$	33.3982	1.50724	0.753620	−	0.657310i	$-0.228306\pi$
$491$	33.3982	1.50724	0.753620	+	0.657310i	$0.228306\pi$
$492$	3.32364	0.149841
$493$	−0.494392	−0.0222663
$494$	−6.25943	−0.281625
$495$	5.46473	0.245621
$496$	3.42028	0.153575
$497$	15.0933	0.677027
$498$	−2.14083	−0.0959328
$499$	3.38855	0.151692	0.0758461	−	0.997120i	$-0.475834\pi$
$499$	3.38855	0.151692	0.0758461	+	0.997120i	$0.475834\pi$
$500$	−10.2581	−0.458756
$501$	−9.74424	−0.435341
$502$	1.23953	0.0553228
$503$	8.74567	0.389950	0.194975	−	0.980808i	$-0.437537\pi$
$503$	8.74567	0.389950	0.194975	+	0.980808i	$0.437537\pi$
$504$	1.00000	0.0445435
$505$	18.7091	0.832546
$506$	−18.4293	−0.819282
$507$	0.447021	0.0198529
$508$	−14.7772	−0.655634
$509$	−15.7222	−0.696875	−0.348438	−	0.937332i	$-0.613288\pi$
$509$	−15.7222	−0.696875	−0.348438	+	0.937332i	$0.613288\pi$
$510$	0.637962	0.0282494
$511$	−5.97084	−0.264134
$512$	1.00000	0.0441942
$513$	1.76669	0.0780014
$514$	−7.36599	−0.324900
$515$	1.33945	0.0590232
$516$	−6.22819	−0.274181
$517$	18.3724	0.808016
$518$	3.21741	0.141365
$519$	14.2746	0.626587
$520$	8.46283	0.371120
$521$	0.958730	0.0420027	0.0210014	−	0.999779i	$-0.493315\pi$
$521$	0.958730	0.0420027	0.0210014	+	0.999779i	$0.493315\pi$
$522$	1.85105	0.0810184
$523$	−12.8260	−0.560842	−0.280421	−	0.959877i	$-0.590474\pi$
$523$	−12.8260	−0.560842	−0.280421	+	0.959877i	$0.590474\pi$
$524$	−14.2790	−0.623779
$525$	−0.705377	−0.0307852
$526$	−5.00353	−0.218164
$527$	−0.913511	−0.0397932
$528$	−2.28784	−0.0995656
$529$	41.8880	1.82122
$530$	15.8436	0.688202
$531$	10.2900	0.446547
$532$	−1.76669	−0.0765959
$533$	−11.7757	−0.510063
$534$	7.58807	0.328368
$535$	29.8905	1.29228
$536$	−0.0848121	−0.00366333
$537$	8.05485	0.347593
$538$	9.68302	0.417465
$539$	2.28784	0.0985444
$540$	−2.38859	−0.102789
$541$	−11.0949	−0.477007	−0.238504	−	0.971142i	$-0.576657\pi$
$541$	−11.0949	−0.477007	−0.238504	+	0.971142i	$0.576657\pi$
$542$	17.8811	0.768059
$543$	−8.99087	−0.385835
$544$	−0.267087	−0.0114512
$545$	−20.1474	−0.863021
$546$	−3.54302	−0.151627
$547$	−33.3571	−1.42625	−0.713123	−	0.701039i	$-0.752720\pi$
$547$	−33.3571	−1.42625	−0.713123	+	0.701039i	$0.752720\pi$
$548$	−13.0155	−0.555993
$549$	−2.94671	−0.125763
$550$	1.61379	0.0688123
$551$	−3.27024	−0.139317
$552$	8.05531	0.342857
$553$	4.20389	0.178768
$554$	7.16722	0.304506
$555$	−7.68508	−0.326214
$556$	17.2513	0.731620
$557$	−35.7186	−1.51344	−0.756722	−	0.653736i	$-0.773201\pi$
$557$	−35.7186	−1.51344	−0.756722	+	0.653736i	$0.773201\pi$
$558$	3.42028	0.144792
$559$	22.0666	0.933317
$560$	2.38859	0.100936
$561$	0.611053	0.0257987
$562$	−11.9650	−0.504712
$563$	−1.58191	−0.0666694	−0.0333347	−	0.999444i	$-0.510613\pi$
$563$	−1.58191	−0.0666694	−0.0333347	+	0.999444i	$0.510613\pi$
$564$	−8.03043	−0.338142
$565$	−13.4174	−0.564474
$566$	18.8476	0.792224
$567$	1.00000	0.0419961
$568$	15.0933	0.633300
$569$	−24.6008	−1.03132	−0.515659	−	0.856794i	$-0.672453\pi$
$569$	−24.6008	−1.03132	−0.515659	+	0.856794i	$0.672453\pi$
$570$	4.21991	0.176753
$571$	−22.0116	−0.921159	−0.460579	−	0.887619i	$-0.652358\pi$
$571$	−22.0116	−0.921159	−0.460579	+	0.887619i	$0.652358\pi$
$572$	8.10587	0.338923
$573$	−1.00000	−0.0417756
$574$	−3.32364	−0.138726
$575$	−5.68203	−0.236957
$576$	1.00000	0.0416667
$577$	17.7500	0.738941	0.369470	−	0.929243i	$-0.379539\pi$
$577$	17.7500	0.738941	0.369470	+	0.929243i	$0.379539\pi$
$578$	−16.9287	−0.704140
$579$	−11.2197	−0.466275
$580$	4.42141	0.183589
$581$	2.14083	0.0888165
$582$	7.25221	0.300614
$583$	15.1753	0.628498
$584$	−5.97084	−0.247075
$585$	8.46283	0.349895
$586$	26.5397	1.09634
$587$	−15.9192	−0.657056	−0.328528	−	0.944494i	$-0.606553\pi$
$587$	−15.9192	−0.657056	−0.328528	+	0.944494i	$0.606553\pi$
$588$	−1.00000	−0.0412393
$589$	−6.04259	−0.248980
$590$	24.5786	1.01188
$591$	−2.37012	−0.0974937
$592$	3.21741	0.132235
$593$	6.52954	0.268136	0.134068	−	0.990972i	$-0.457196\pi$
$593$	6.52954	0.268136	0.134068	+	0.990972i	$0.457196\pi$
$594$	−2.28784	−0.0938713
$595$	−0.637962	−0.0261539
$596$	−7.77496	−0.318475
$597$	−2.94766	−0.120640
$598$	−28.5401	−1.16709
$599$	15.5187	0.634078	0.317039	−	0.948413i	$-0.397311\pi$
$599$	15.5187	0.634078	0.317039	+	0.948413i	$0.397311\pi$
$600$	−0.705377	−0.0287969
$601$	7.75012	0.316134	0.158067	−	0.987428i	$-0.449474\pi$
$601$	7.75012	0.316134	0.158067	+	0.987428i	$0.449474\pi$
$602$	6.22819	0.253842
$603$	−0.0848121	−0.00345382
$604$	5.59000	0.227454
$605$	−13.7721	−0.559915
$606$	−7.83271	−0.318182
$607$	−47.0948	−1.91152	−0.955760	−	0.294146i	$-0.904965\pi$
$607$	−47.0948	−1.91152	−0.955760	+	0.294146i	$0.904965\pi$
$608$	−1.76669	−0.0716489
$609$	−1.85105	−0.0750085
$610$	−7.03850	−0.284980
$611$	28.4520	1.15104
$612$	−0.267087	−0.0107963
$613$	26.1821	1.05749	0.528743	−	0.848782i	$-0.322664\pi$
$613$	26.1821	1.05749	0.528743	+	0.848782i	$0.322664\pi$
$614$	0.947457	0.0382362
$615$	7.93882	0.320124
$616$	2.28784	0.0921798
$617$	18.8780	0.759999	0.379999	−	0.924987i	$-0.375924\pi$
$617$	18.8780	0.759999	0.379999	+	0.924987i	$0.375924\pi$
$618$	−0.560769	−0.0225575
$619$	38.7846	1.55888	0.779442	−	0.626475i	$-0.215503\pi$
$619$	38.7846	1.55888	0.779442	+	0.626475i	$0.215503\pi$
$620$	8.16966	0.328101
$621$	8.05531	0.323248
$622$	−15.6088	−0.625855
$623$	−7.58807	−0.304010
$624$	−3.54302	−0.141834
$625$	−28.0293	−1.12117
$626$	−17.3696	−0.694229
$627$	4.04192	0.161419
$628$	−0.231671	−0.00924470
$629$	−0.859327	−0.0342636
$630$	2.38859	0.0951638
$631$	−35.6293	−1.41838	−0.709190	−	0.705018i	$-0.750939\pi$
$631$	−35.6293	−1.41838	−0.709190	+	0.705018i	$0.750939\pi$
$632$	4.20389	0.167222
$633$	20.5064	0.815057
$634$	−14.3301	−0.569122
$635$	−35.2968	−1.40071
$636$	−6.63303	−0.263017
$637$	3.54302	0.140379
$638$	4.23492	0.167662
$639$	15.0933	0.597081
$640$	2.38859	0.0944174
$641$	26.0916	1.03056	0.515278	−	0.857023i	$-0.327689\pi$
$641$	26.0916	1.03056	0.515278	+	0.857023i	$0.327689\pi$
$642$	−12.5139	−0.493883
$643$	−6.98058	−0.275287	−0.137644	−	0.990482i	$-0.543953\pi$
$643$	−6.98058	−0.275287	−0.137644	+	0.990482i	$0.543953\pi$
$644$	−8.05531	−0.317424
$645$	−14.8766	−0.585766
$646$	0.471860	0.0185651
$647$	17.3372	0.681595	0.340798	−	0.940137i	$-0.389303\pi$
$647$	17.3372	0.681595	0.340798	+	0.940137i	$0.389303\pi$
$648$	1.00000	0.0392837
$649$	23.5418	0.924098
$650$	2.49916	0.0980252
$651$	−3.42028	−0.134051
$652$	18.8979	0.740097
$653$	19.6008	0.767040	0.383520	−	0.923533i	$-0.374712\pi$
$653$	19.6008	0.767040	0.383520	+	0.923533i	$0.374712\pi$
$654$	8.43485	0.329829
$655$	−34.1066	−1.33266
$656$	−3.32364	−0.129766
$657$	−5.97084	−0.232945
$658$	8.03043	0.313059
$659$	1.58008	0.0615511	0.0307756	−	0.999526i	$-0.490202\pi$
$659$	1.58008	0.0615511	0.0307756	+	0.999526i	$0.490202\pi$
$660$	−5.46473	−0.212714
$661$	38.1585	1.48419	0.742096	−	0.670293i	$-0.233832\pi$
$661$	38.1585	1.48419	0.742096	+	0.670293i	$0.233832\pi$
$662$	−7.12276	−0.276834
$663$	0.946293	0.0367510
$664$	2.14083	0.0830803
$665$	−4.21991	−0.163641
$666$	3.21741	0.124672
$667$	−14.9108	−0.577349
$668$	9.74424	0.377016
$669$	−10.0996	−0.390473
$670$	−0.202582	−0.00782641
$671$	−6.74162	−0.260257
$672$	−1.00000	−0.0385758
$673$	15.5368	0.598901	0.299450	−	0.954112i	$-0.403197\pi$
$673$	15.5368	0.598901	0.299450	+	0.954112i	$0.403197\pi$
$674$	−27.7585	−1.06922
$675$	−0.705377	−0.0271500
$676$	−0.447021	−0.0171931
$677$	−35.1826	−1.35218	−0.676089	−	0.736820i	$-0.736326\pi$
$677$	−35.1826	−1.35218	−0.676089	+	0.736820i	$0.736326\pi$
$678$	5.61728	0.215730
$679$	−7.25221	−0.278314
$680$	−0.637962	−0.0244647
$681$	−14.9692	−0.573619
$682$	7.82506	0.299637
$683$	−25.0959	−0.960269	−0.480134	−	0.877195i	$-0.659412\pi$
$683$	−25.0959	−0.960269	−0.480134	+	0.877195i	$0.659412\pi$
$684$	−1.76669	−0.0675512
$685$	−31.0887	−1.18784
$686$	1.00000	0.0381802
$687$	−22.5899	−0.861859
$688$	6.22819	0.237447
$689$	23.5009	0.895314
$690$	19.2409	0.732487
$691$	−4.06565	−0.154665	−0.0773324	−	0.997005i	$-0.524640\pi$
$691$	−4.06565	−0.154665	−0.0773324	+	0.997005i	$0.524640\pi$
$692$	−14.2746	−0.542640
$693$	2.28784	0.0869080
$694$	2.81815	0.106976
$695$	41.2064	1.56305
$696$	−1.85105	−0.0701640
$697$	0.887699	0.0336240
$698$	8.44696	0.319722
$699$	−22.2019	−0.839754
$700$	0.705377	0.0266607
$701$	−46.8968	−1.77127	−0.885635	−	0.464382i	$-0.846276\pi$
$701$	−46.8968	−1.77127	−0.885635	+	0.464382i	$0.846276\pi$
$702$	−3.54302	−0.133723
$703$	−5.68418	−0.214383
$704$	2.28784	0.0862263
$705$	−19.1814	−0.722415
$706$	22.2010	0.835547
$707$	7.83271	0.294579
$708$	−10.2900	−0.386721
$709$	−24.7812	−0.930678	−0.465339	−	0.885133i	$-0.654068\pi$
$709$	−24.7812	−0.930678	−0.465339	+	0.885133i	$0.654068\pi$
$710$	36.0517	1.35300
$711$	4.20389	0.157658
$712$	−7.58807	−0.284375
$713$	−27.5514	−1.03181
$714$	0.267087	0.00999547
$715$	19.3616	0.724084
$716$	−8.05485	−0.301024
$717$	7.43307	0.277593
$718$	13.1864	0.492113
$719$	−27.0935	−1.01042	−0.505208	−	0.862998i	$-0.668584\pi$
$719$	−27.0935	−1.01042	−0.505208	+	0.862998i	$0.668584\pi$
$720$	2.38859	0.0890176
$721$	0.560769	0.0208841
$722$	−15.8788	−0.590948
$723$	19.0471	0.708369
$724$	8.99087	0.334143
$725$	1.30569	0.0484921
$726$	5.76577	0.213988
$727$	−7.18753	−0.266571	−0.133285	−	0.991078i	$-0.542553\pi$
$727$	−7.18753	−0.266571	−0.133285	+	0.991078i	$0.542553\pi$
$728$	3.54302	0.131313
$729$	1.00000	0.0370370
$730$	−14.2619	−0.527857
$731$	−1.66347	−0.0615255
$732$	2.94671	0.108914
$733$	−23.9581	−0.884912	−0.442456	−	0.896790i	$-0.645893\pi$
$733$	−23.9581	−0.884912	−0.442456	+	0.896790i	$0.645893\pi$
$734$	5.13790	0.189644
$735$	−2.38859	−0.0881046
$736$	−8.05531	−0.296923
$737$	−0.194037	−0.00714744
$738$	−3.32364	−0.122345
$739$	19.5132	0.717804	0.358902	−	0.933375i	$-0.383151\pi$
$739$	19.5132	0.717804	0.358902	+	0.933375i	$0.383151\pi$
$740$	7.68508	0.282509
$741$	6.25943	0.229946
$742$	6.63303	0.243506
$743$	−44.6537	−1.63819	−0.819093	−	0.573660i	$-0.805523\pi$
$743$	−44.6537	−1.63819	−0.819093	+	0.573660i	$0.805523\pi$
$744$	−3.42028	−0.125394
$745$	−18.5712	−0.680397
$746$	25.6767	0.940092
$747$	2.14083	0.0783288
$748$	−0.611053	−0.0223423
$749$	12.5139	0.457247
$750$	10.2581	0.374573
$751$	34.1862	1.24747	0.623735	−	0.781636i	$-0.285614\pi$
$751$	34.1862	1.24747	0.623735	+	0.781636i	$0.285614\pi$
$752$	8.03043	0.292840
$753$	−1.23953	−0.0451709
$754$	6.55831	0.238840
$755$	13.3522	0.485938
$756$	−1.00000	−0.0363696
$757$	−29.5895	−1.07545	−0.537724	−	0.843121i	$-0.680716\pi$
$757$	−29.5895	−1.07545	−0.537724	+	0.843121i	$0.680716\pi$
$758$	13.5588	0.492478
$759$	18.4293	0.668941
$760$	−4.21991	−0.153072
$761$	13.9332	0.505077	0.252538	−	0.967587i	$-0.418735\pi$
$761$	13.9332	0.505077	0.252538	+	0.967587i	$0.418735\pi$
$762$	14.7772	0.535323
$763$	−8.43485	−0.305362
$764$	1.00000	0.0361787
$765$	−0.637962	−0.0230655
$766$	−2.61689	−0.0945519
$767$	36.4576	1.31641
$768$	−1.00000	−0.0360844
$769$	−23.7191	−0.855334	−0.427667	−	0.903936i	$-0.640664\pi$
$769$	−23.7191	−0.855334	−0.427667	+	0.903936i	$0.640664\pi$
$770$	5.46473	0.196935
$771$	7.36599	0.265280
$772$	11.2197	0.403806
$773$	48.3947	1.74064	0.870319	−	0.492489i	$-0.163913\pi$
$773$	48.3947	1.74064	0.870319	+	0.492489i	$0.163913\pi$
$774$	6.22819	0.223868
$775$	2.41259	0.0866627
$776$	−7.25221	−0.260339
$777$	−3.21741	−0.115424
$778$	20.4220	0.732163
$779$	5.87185	0.210381
$780$	−8.46283	−0.303018
$781$	34.5311	1.23562
$782$	2.15147	0.0769363
$783$	−1.85105	−0.0661512
$784$	1.00000	0.0357143
$785$	−0.553369	−0.0197506
$786$	14.2790	0.509313
$787$	11.6692	0.415962	0.207981	−	0.978133i	$-0.433311\pi$
$787$	11.6692	0.415962	0.207981	+	0.978133i	$0.433311\pi$
$788$	2.37012	0.0844320
$789$	5.00353	0.178130
$790$	10.0414	0.357257
$791$	−5.61728	−0.199727
$792$	2.28784	0.0812950
$793$	−10.4403	−0.370744
$794$	25.4577	0.903461
$795$	−15.8436	−0.561915
$796$	2.94766	0.104477
$797$	45.0337	1.59518	0.797588	−	0.603202i	$-0.206109\pi$
$797$	45.0337	1.59518	0.797588	+	0.603202i	$0.206109\pi$
$798$	1.76669	0.0625403
$799$	−2.14482	−0.0758784
$800$	0.705377	0.0249388
$801$	−7.58807	−0.268111
$802$	−25.6696	−0.906424
$803$	−13.6603	−0.482063
$804$	0.0848121	0.00299109
$805$	−19.2409	−0.678151
$806$	12.1181	0.426842
$807$	−9.68302	−0.340859
$808$	7.83271	0.275554
$809$	39.7783	1.39853	0.699265	−	0.714862i	$-0.253511\pi$
$809$	39.7783	1.39853	0.699265	+	0.714862i	$0.253511\pi$
$810$	2.38859	0.0839266
$811$	−33.1271	−1.16325	−0.581625	−	0.813457i	$-0.697583\pi$
$811$	−33.1271	−1.16325	−0.581625	+	0.813457i	$0.697583\pi$
$812$	1.85105	0.0649592
$813$	−17.8811	−0.627118
$814$	7.36093	0.258000
$815$	45.1393	1.58116
$816$	0.267087	0.00934991
$817$	−11.0033	−0.384957
$818$	16.1625	0.565108
$819$	3.54302	0.123803
$820$	−7.93882	−0.277236
$821$	−41.2146	−1.43840	−0.719200	−	0.694803i	$-0.755492\pi$
$821$	−41.2146	−1.43840	−0.719200	+	0.694803i	$0.755492\pi$
$822$	13.0155	0.453967
$823$	−28.6943	−1.00022	−0.500110	−	0.865962i	$-0.666707\pi$
$823$	−28.6943	−1.00022	−0.500110	+	0.865962i	$0.666707\pi$
$824$	0.560769	0.0195353
$825$	−1.61379	−0.0561850
$826$	10.2900	0.358034
$827$	22.5889	0.785494	0.392747	−	0.919647i	$-0.371525\pi$
$827$	22.5889	0.785494	0.392747	+	0.919647i	$0.371525\pi$
$828$	−8.05531	−0.279941
$829$	−10.8185	−0.375741	−0.187870	−	0.982194i	$-0.560158\pi$
$829$	−10.8185	−0.375741	−0.187870	+	0.982194i	$0.560158\pi$
$830$	5.11357	0.177495
$831$	−7.16722	−0.248628
$832$	3.54302	0.122832
$833$	−0.267087	−0.00925401
$834$	−17.2513	−0.597365
$835$	23.2750	0.805465
$836$	−4.04192	−0.139793
$837$	−3.42028	−0.118222
$838$	1.93730	0.0669228
$839$	−29.0507	−1.00294	−0.501472	−	0.865174i	$-0.667208\pi$
$839$	−29.0507	−1.00294	−0.501472	+	0.865174i	$0.667208\pi$
$840$	−2.38859	−0.0824143
$841$	−25.5736	−0.881848
$842$	−5.79158	−0.199591
$843$	11.9650	0.412096
$844$	−20.5064	−0.705860
$845$	−1.06775	−0.0367318
$846$	8.03043	0.276092
$847$	−5.76577	−0.198114
$848$	6.63303	0.227779
$849$	−18.8476	−0.646848
$850$	−0.188397	−0.00646196
$851$	−25.9172	−0.888431
$852$	−15.0933	−0.517088
$853$	−34.7896	−1.19117	−0.595587	−	0.803291i	$-0.703081\pi$
$853$	−34.7896	−1.19117	−0.595587	+	0.803291i	$0.703081\pi$
$854$	−2.94671	−0.100834
$855$	−4.21991	−0.144318
$856$	12.5139	0.427715
$857$	36.9914	1.26360	0.631800	−	0.775131i	$-0.282316\pi$
$857$	36.9914	1.26360	0.631800	+	0.775131i	$0.282316\pi$
$858$	−8.10587	−0.276730
$859$	−31.2722	−1.06699	−0.533497	−	0.845802i	$-0.679122\pi$
$859$	−31.2722	−1.06699	−0.533497	+	0.845802i	$0.679122\pi$
$860$	14.8766	0.507288
$861$	3.32364	0.113269
$862$	2.06031	0.0701744
$863$	0.355670	0.0121071	0.00605357	−	0.999982i	$-0.498073\pi$
$863$	0.355670	0.0121071	0.00605357	+	0.999982i	$0.498073\pi$
$864$	−1.00000	−0.0340207
$865$	−34.0963	−1.15931
$866$	−39.6438	−1.34715
$867$	16.9287	0.574928
$868$	3.42028	0.116092
$869$	9.61785	0.326263
$870$	−4.42141	−0.149900
$871$	−0.300491	−0.0101817
$872$	−8.43485	−0.285640
$873$	−7.25221	−0.245450
$874$	14.2313	0.481380
$875$	−10.2581	−0.346787
$876$	5.97084	0.201736
$877$	3.81017	0.128660	0.0643302	−	0.997929i	$-0.479509\pi$
$877$	3.81017	0.128660	0.0643302	+	0.997929i	$0.479509\pi$
$878$	−26.6078	−0.897968
$879$	−26.5397	−0.895160
$880$	5.46473	0.184216
$881$	35.2455	1.18745	0.593726	−	0.804667i	$-0.297656\pi$
$881$	35.2455	1.18745	0.593726	+	0.804667i	$0.297656\pi$
$882$	1.00000	0.0336718
$883$	−8.39813	−0.282619	−0.141310	−	0.989965i	$-0.545131\pi$
$883$	−8.39813	−0.282619	−0.141310	+	0.989965i	$0.545131\pi$
$884$	−0.946293	−0.0318273
$885$	−24.5786	−0.826199
$886$	−7.30527	−0.245425
$887$	53.6027	1.79980	0.899902	−	0.436093i	$-0.143638\pi$
$887$	53.6027	1.79980	0.899902	+	0.436093i	$0.143638\pi$
$888$	−3.21741	−0.107969
$889$	−14.7772	−0.495613
$890$	−18.1248	−0.607545
$891$	2.28784	0.0766456
$892$	10.0996	0.338159
$893$	−14.1873	−0.474760
$894$	7.77496	0.260034
$895$	−19.2398	−0.643115
$896$	1.00000	0.0334077
$897$	28.5401	0.952927
$898$	−17.1305	−0.571653
$899$	6.33112	0.211155
$900$	0.705377	0.0235126
$901$	−1.77159	−0.0590203
$902$	−7.60396	−0.253184
$903$	−6.22819	−0.207261
$904$	−5.61728	−0.186828
$905$	21.4755	0.713870
$906$	−5.59000	−0.185715
$907$	19.0693	0.633187	0.316593	−	0.948561i	$-0.397461\pi$
$907$	19.0693	0.633187	0.316593	+	0.948561i	$0.397461\pi$
$908$	14.9692	0.496769
$909$	7.83271	0.259794
$910$	8.46283	0.280540
$911$	11.4645	0.379835	0.189917	−	0.981800i	$-0.439178\pi$
$911$	11.4645	0.379835	0.189917	+	0.981800i	$0.439178\pi$
$912$	1.76669	0.0585011
$913$	4.89788	0.162096
$914$	−9.82835	−0.325093
$915$	7.03850	0.232686
$916$	22.5899	0.746392
$917$	−14.2790	−0.471532
$918$	0.267087	0.00881518
$919$	−25.4539	−0.839647	−0.419824	−	0.907606i	$-0.637908\pi$
$919$	−25.4539	−0.839647	−0.419824	+	0.907606i	$0.637908\pi$
$920$	−19.2409	−0.634352
$921$	−0.947457	−0.0312198
$922$	25.4306	0.837511
$923$	53.4758	1.76018
$924$	−2.28784	−0.0752645
$925$	2.26949	0.0746202
$926$	−37.7941	−1.24199
$927$	0.560769	0.0184181
$928$	1.85105	0.0607638
$929$	−46.3774	−1.52159	−0.760797	−	0.648990i	$-0.775192\pi$
$929$	−46.3774	−1.52159	−0.760797	+	0.648990i	$0.775192\pi$
$930$	−8.16966	−0.267894
$931$	−1.76669	−0.0579010
$932$	22.2019	0.727249
$933$	15.6088	0.511009
$934$	−0.604844	−0.0197911
$935$	−1.45956	−0.0477326
$936$	3.54302	0.115807
$937$	−6.92232	−0.226142	−0.113071	−	0.993587i	$-0.536069\pi$
$937$	−6.92232	−0.226142	−0.113071	+	0.993587i	$0.536069\pi$
$938$	−0.0848121	−0.00276921
$939$	17.3696	0.566835
$940$	19.1814	0.625629
$941$	−37.4456	−1.22069	−0.610345	−	0.792135i	$-0.708969\pi$
$941$	−37.4456	−1.22069	−0.610345	+	0.792135i	$0.708969\pi$
$942$	0.231671	0.00754826
$943$	26.7729	0.871847
$944$	10.2900	0.334910
$945$	−2.38859	−0.0777009
$946$	14.2491	0.463279
$947$	15.9250	0.517492	0.258746	−	0.965945i	$-0.416691\pi$
$947$	15.9250	0.517492	0.258746	+	0.965945i	$0.416691\pi$
$948$	−4.20389	−0.136536
$949$	−21.1548	−0.686713
$950$	−1.24618	−0.0404316
$951$	14.3301	0.464686
$952$	−0.267087	−0.00865633
$953$	19.3278	0.626090	0.313045	−	0.949738i	$-0.398651\pi$
$953$	19.3278	0.626090	0.313045	+	0.949738i	$0.398651\pi$
$954$	6.63303	0.214752
$955$	2.38859	0.0772931
$956$	−7.43307	−0.240403
$957$	−4.23492	−0.136895
$958$	−4.30124	−0.138967
$959$	−13.0155	−0.420291
$960$	−2.38859	−0.0770915
$961$	−19.3017	−0.622635
$962$	11.3993	0.367529
$963$	12.5139	0.403254
$964$	−19.0471	−0.613465
$965$	26.7993	0.862701
$966$	8.05531	0.259175
$967$	−8.10559	−0.260658	−0.130329	−	0.991471i	$-0.541603\pi$
$967$	−8.10559	−0.260658	−0.130329	+	0.991471i	$0.541603\pi$
$968$	−5.76577	−0.185319
$969$	−0.471860	−0.0151583
$970$	−17.3226	−0.556194
$971$	−13.9972	−0.449193	−0.224596	−	0.974452i	$-0.572106\pi$
$971$	−13.9972	−0.449193	−0.224596	+	0.974452i	$0.572106\pi$
$972$	−1.00000	−0.0320750
$973$	17.2513	0.553053
$974$	−9.42295	−0.301931
$975$	−2.49916	−0.0800373
$976$	−2.94671	−0.0943220
$977$	−45.4778	−1.45496	−0.727481	−	0.686128i	$-0.759309\pi$
$977$	−45.4778	−1.45496	−0.727481	+	0.686128i	$0.759309\pi$
$978$	−18.8979	−0.604287
$979$	−17.3603	−0.554838
$980$	2.38859	0.0763008
$981$	−8.43485	−0.269304
$982$	33.3982	1.06578
$983$	−6.88249	−0.219517	−0.109759	−	0.993958i	$-0.535008\pi$
$983$	−6.88249	−0.219517	−0.109759	+	0.993958i	$0.535008\pi$
$984$	3.32364	0.105954
$985$	5.66125	0.180383
$986$	−0.494392	−0.0157446
$987$	−8.03043	−0.255612
$988$	−6.25943	−0.199139
$989$	−50.1700	−1.59531
$990$	5.46473	0.173680
$991$	−15.4761	−0.491614	−0.245807	−	0.969319i	$-0.579053\pi$
$991$	−15.4761	−0.491614	−0.245807	+	0.969319i	$0.579053\pi$
$992$	3.42028	0.108594
$993$	7.12276	0.226034
$994$	15.0933	0.478730
$995$	7.04075	0.223207
$996$	−2.14083	−0.0678348
$997$	42.5933	1.34894	0.674472	−	0.738301i	$-0.264371\pi$
$997$	42.5933	1.34894	0.674472	+	0.738301i	$0.264371\pi$
$998$	3.38855	0.107263
$999$	−3.21741	−0.101794

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8022.2.a.r.1.8	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8022.2.a.r.1.8	✓	10	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:	\( N \)	\(=\)	\( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.38859 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.38859 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.38859 q^{10} +2.28784 q^{11} -1.00000 q^{12} +3.54302 q^{13} +1.00000 q^{14} -2.38859 q^{15} +1.00000 q^{16} -0.267087 q^{17} +1.00000 q^{18} -1.76669 q^{19} +2.38859 q^{20} -1.00000 q^{21} +2.28784 q^{22} -8.05531 q^{23} -1.00000 q^{24} +0.705377 q^{25} +3.54302 q^{26} -1.00000 q^{27} +1.00000 q^{28} +1.85105 q^{29} -2.38859 q^{30} +3.42028 q^{31} +1.00000 q^{32} -2.28784 q^{33} -0.267087 q^{34} +2.38859 q^{35} +1.00000 q^{36} +3.21741 q^{37} -1.76669 q^{38} -3.54302 q^{39} +2.38859 q^{40} -3.32364 q^{41} -1.00000 q^{42} +6.22819 q^{43} +2.28784 q^{44} +2.38859 q^{45} -8.05531 q^{46} +8.03043 q^{47} -1.00000 q^{48} +1.00000 q^{49} +0.705377 q^{50} +0.267087 q^{51} +3.54302 q^{52} +6.63303 q^{53} -1.00000 q^{54} +5.46473 q^{55} +1.00000 q^{56} +1.76669 q^{57} +1.85105 q^{58} +10.2900 q^{59} -2.38859 q^{60} -2.94671 q^{61} +3.42028 q^{62} +1.00000 q^{63} +1.00000 q^{64} +8.46283 q^{65} -2.28784 q^{66} -0.0848121 q^{67} -0.267087 q^{68} +8.05531 q^{69} +2.38859 q^{70} +15.0933 q^{71} +1.00000 q^{72} -5.97084 q^{73} +3.21741 q^{74} -0.705377 q^{75} -1.76669 q^{76} +2.28784 q^{77} -3.54302 q^{78} +4.20389 q^{79} +2.38859 q^{80} +1.00000 q^{81} -3.32364 q^{82} +2.14083 q^{83} -1.00000 q^{84} -0.637962 q^{85} +6.22819 q^{86} -1.85105 q^{87} +2.28784 q^{88} -7.58807 q^{89} +2.38859 q^{90} +3.54302 q^{91} -8.05531 q^{92} -3.42028 q^{93} +8.03043 q^{94} -4.21991 q^{95} -1.00000 q^{96} -7.25221 q^{97} +1.00000 q^{98} +2.28784 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 8 q^{5} - 10 q^{6} + 10 q^{7} + 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 8 * q^5 - 10 * q^6 + 10 * q^7 + 10 * q^8 + 10 * q^9	\( 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 8 q^{5} - 10 q^{6} + 10 q^{7} + 10 q^{8} + 10 q^{9} + 8 q^{10} + 4 q^{11} - 10 q^{12} + 6 q^{13} + 10 q^{14} - 8 q^{15} + 10 q^{16} + 5 q^{17} + 10 q^{18} + 15 q^{19} + 8 q^{20} - 10 q^{21} + 4 q^{22} + 12 q^{23} - 10 q^{24} - 2 q^{25} + 6 q^{26} - 10 q^{27} + 10 q^{28} + 7 q^{29} - 8 q^{30} + 28 q^{31} + 10 q^{32} - 4 q^{33} + 5 q^{34} + 8 q^{35} + 10 q^{36} - 3 q^{37} + 15 q^{38} - 6 q^{39} + 8 q^{40} + 24 q^{41} - 10 q^{42} + 4 q^{43} + 4 q^{44} + 8 q^{45} + 12 q^{46} + 16 q^{47} - 10 q^{48} + 10 q^{49} - 2 q^{50} - 5 q^{51} + 6 q^{52} + 5 q^{53} - 10 q^{54} - q^{55} + 10 q^{56} - 15 q^{57} + 7 q^{58} + 17 q^{59} - 8 q^{60} + 15 q^{61} + 28 q^{62} + 10 q^{63} + 10 q^{64} + 14 q^{65} - 4 q^{66} + 6 q^{67} + 5 q^{68} - 12 q^{69} + 8 q^{70} + 5 q^{71} + 10 q^{72} + 16 q^{73} - 3 q^{74} + 2 q^{75} + 15 q^{76} + 4 q^{77} - 6 q^{78} - 5 q^{79} + 8 q^{80} + 10 q^{81} + 24 q^{82} + 24 q^{83} - 10 q^{84} - 19 q^{85} + 4 q^{86} - 7 q^{87} + 4 q^{88} + 17 q^{89} + 8 q^{90} + 6 q^{91} + 12 q^{92} - 28 q^{93} + 16 q^{94} + 15 q^{95} - 10 q^{96} + 20 q^{97} + 10 q^{98} + 4 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 8 * q^5 - 10 * q^6 + 10 * q^7 + 10 * q^8 + 10 * q^9 + 8 * q^10 + 4 * q^11 - 10 * q^12 + 6 * q^13 + 10 * q^14 - 8 * q^15 + 10 * q^16 + 5 * q^17 + 10 * q^18 + 15 * q^19 + 8 * q^20 - 10 * q^21 + 4 * q^22 + 12 * q^23 - 10 * q^24 - 2 * q^25 + 6 * q^26 - 10 * q^27 + 10 * q^28 + 7 * q^29 - 8 * q^30 + 28 * q^31 + 10 * q^32 - 4 * q^33 + 5 * q^34 + 8 * q^35 + 10 * q^36 - 3 * q^37 + 15 * q^38 - 6 * q^39 + 8 * q^40 + 24 * q^41 - 10 * q^42 + 4 * q^43 + 4 * q^44 + 8 * q^45 + 12 * q^46 + 16 * q^47 - 10 * q^48 + 10 * q^49 - 2 * q^50 - 5 * q^51 + 6 * q^52 + 5 * q^53 - 10 * q^54 - q^55 + 10 * q^56 - 15 * q^57 + 7 * q^58 + 17 * q^59 - 8 * q^60 + 15 * q^61 + 28 * q^62 + 10 * q^63 + 10 * q^64 + 14 * q^65 - 4 * q^66 + 6 * q^67 + 5 * q^68 - 12 * q^69 + 8 * q^70 + 5 * q^71 + 10 * q^72 + 16 * q^73 - 3 * q^74 + 2 * q^75 + 15 * q^76 + 4 * q^77 - 6 * q^78 - 5 * q^79 + 8 * q^80 + 10 * q^81 + 24 * q^82 + 24 * q^83 - 10 * q^84 - 19 * q^85 + 4 * q^86 - 7 * q^87 + 4 * q^88 + 17 * q^89 + 8 * q^90 + 6 * q^91 + 12 * q^92 - 28 * q^93 + 16 * q^94 + 15 * q^95 - 10 * q^96 + 20 * q^97 + 10 * q^98 + 4 * q^99

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