LMFDB - Embedded newform 8034.2.a.x.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - x^{12} - 40 x^{11} + 34 x^{10} + 604 x^{9} - 381 x^{8} - 4352 x^{7} + 1474 x^{6} + 15809 x^{5} + \cdots + 8832 $ x^13 - x^12 - 40x^11 + 34x^10 + 604x^9 - 381x^8 - 4352x^7 + 1474x^6 + 15809x^5 - 368x^4 - 27369x^3 - 7621x^2 + 17300*x + 8832
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-3.54523$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.54523 q^{5} -1.00000 q^{6} +0.166701 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.54523 q^{5} -1.00000 q^{6} +0.166701 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.54523 q^{10} +4.41321 q^{11} +1.00000 q^{12} +1.00000 q^{13} -0.166701 q^{14} -3.54523 q^{15} +1.00000 q^{16} +5.92847 q^{17} -1.00000 q^{18} +5.45439 q^{19} -3.54523 q^{20} +0.166701 q^{21} -4.41321 q^{22} +6.44327 q^{23} -1.00000 q^{24} +7.56864 q^{25} -1.00000 q^{26} +1.00000 q^{27} +0.166701 q^{28} +0.584971 q^{29} +3.54523 q^{30} -4.19458 q^{31} -1.00000 q^{32} +4.41321 q^{33} -5.92847 q^{34} -0.590994 q^{35} +1.00000 q^{36} +8.59476 q^{37} -5.45439 q^{38} +1.00000 q^{39} +3.54523 q^{40} -7.73673 q^{41} -0.166701 q^{42} -7.36207 q^{43} +4.41321 q^{44} -3.54523 q^{45} -6.44327 q^{46} +12.7766 q^{47} +1.00000 q^{48} -6.97221 q^{49} -7.56864 q^{50} +5.92847 q^{51} +1.00000 q^{52} +1.83140 q^{53} -1.00000 q^{54} -15.6458 q^{55} -0.166701 q^{56} +5.45439 q^{57} -0.584971 q^{58} +15.1468 q^{59} -3.54523 q^{60} +10.5545 q^{61} +4.19458 q^{62} +0.166701 q^{63} +1.00000 q^{64} -3.54523 q^{65} -4.41321 q^{66} -14.3239 q^{67} +5.92847 q^{68} +6.44327 q^{69} +0.590994 q^{70} +1.93330 q^{71} -1.00000 q^{72} -13.3410 q^{73} -8.59476 q^{74} +7.56864 q^{75} +5.45439 q^{76} +0.735688 q^{77} -1.00000 q^{78} -5.41863 q^{79} -3.54523 q^{80} +1.00000 q^{81} +7.73673 q^{82} +0.0310976 q^{83} +0.166701 q^{84} -21.0178 q^{85} +7.36207 q^{86} +0.584971 q^{87} -4.41321 q^{88} -1.88292 q^{89} +3.54523 q^{90} +0.166701 q^{91} +6.44327 q^{92} -4.19458 q^{93} -12.7766 q^{94} -19.3371 q^{95} -1.00000 q^{96} +1.26550 q^{97} +6.97221 q^{98} +4.41321 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} + q^{5} - 13 q^{6} - q^{7} - 13 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 + q^5 - 13 * q^6 - q^7 - 13 * q^8 + 13 * q^9	\( 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} + q^{5} - 13 q^{6} - q^{7} - 13 q^{8} + 13 q^{9} - q^{10} + 6 q^{11} + 13 q^{12} + 13 q^{13} + q^{14} + q^{15} + 13 q^{16} + 18 q^{17} - 13 q^{18} - q^{19} + q^{20} - q^{21} - 6 q^{22} + 20 q^{23} - 13 q^{24} + 16 q^{25} - 13 q^{26} + 13 q^{27} - q^{28} + 25 q^{29} - q^{30} - 5 q^{31} - 13 q^{32} + 6 q^{33} - 18 q^{34} + 26 q^{35} + 13 q^{36} - 6 q^{37} + q^{38} + 13 q^{39} - q^{40} + 13 q^{41} + q^{42} - 2 q^{43} + 6 q^{44} + q^{45} - 20 q^{46} + 5 q^{47} + 13 q^{48} - 16 q^{50} + 18 q^{51} + 13 q^{52} + 21 q^{53} - 13 q^{54} + 2 q^{55} + q^{56} - q^{57} - 25 q^{58} + 22 q^{59} + q^{60} + 2 q^{61} + 5 q^{62} - q^{63} + 13 q^{64} + q^{65} - 6 q^{66} - q^{67} + 18 q^{68} + 20 q^{69} - 26 q^{70} + 32 q^{71} - 13 q^{72} - 13 q^{73} + 6 q^{74} + 16 q^{75} - q^{76} + 33 q^{77} - 13 q^{78} - 7 q^{79} + q^{80} + 13 q^{81} - 13 q^{82} + 17 q^{83} - q^{84} - 25 q^{85} + 2 q^{86} + 25 q^{87} - 6 q^{88} - 12 q^{89} - q^{90} - q^{91} + 20 q^{92} - 5 q^{93} - 5 q^{94} + 36 q^{95} - 13 q^{96} - 42 q^{97} + 6 q^{99}+O(q^{100}) \) 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 + q^5 - 13 * q^6 - q^7 - 13 * q^8 + 13 * q^9 - q^10 + 6 * q^11 + 13 * q^12 + 13 * q^13 + q^14 + q^15 + 13 * q^16 + 18 * q^17 - 13 * q^18 - q^19 + q^20 - q^21 - 6 * q^22 + 20 * q^23 - 13 * q^24 + 16 * q^25 - 13 * q^26 + 13 * q^27 - q^28 + 25 * q^29 - q^30 - 5 * q^31 - 13 * q^32 + 6 * q^33 - 18 * q^34 + 26 * q^35 + 13 * q^36 - 6 * q^37 + q^38 + 13 * q^39 - q^40 + 13 * q^41 + q^42 - 2 * q^43 + 6 * q^44 + q^45 - 20 * q^46 + 5 * q^47 + 13 * q^48 - 16 * q^50 + 18 * q^51 + 13 * q^52 + 21 * q^53 - 13 * q^54 + 2 * q^55 + q^56 - q^57 - 25 * q^58 + 22 * q^59 + q^60 + 2 * q^61 + 5 * q^62 - q^63 + 13 * q^64 + q^65 - 6 * q^66 - q^67 + 18 * q^68 + 20 * q^69 - 26 * q^70 + 32 * q^71 - 13 * q^72 - 13 * q^73 + 6 * q^74 + 16 * q^75 - q^76 + 33 * q^77 - 13 * q^78 - 7 * q^79 + q^80 + 13 * q^81 - 13 * q^82 + 17 * q^83 - q^84 - 25 * q^85 + 2 * q^86 + 25 * q^87 - 6 * q^88 - 12 * q^89 - q^90 - q^91 + 20 * q^92 - 5 * q^93 - 5 * q^94 + 36 * q^95 - 13 * q^96 - 42 * q^97 + 6 * 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
$5$	−3.54523	−1.58547	−0.792737	−	0.609564i	$-0.791345\pi$
$5$	−3.54523	−1.58547	−0.792737	+	0.609564i	$0.791345\pi$
$6$	−1.00000	−0.408248
$7$	0.166701	0.0630071	0.0315036	−	0.999504i	$-0.489970\pi$
$7$	0.166701	0.0630071	0.0315036	+	0.999504i	$0.489970\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.54523	1.12110
$11$	4.41321	1.33063	0.665317	−	0.746561i	$-0.268297\pi$
$11$	4.41321	1.33063	0.665317	+	0.746561i	$0.268297\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−0.166701	−0.0445528
$15$	−3.54523	−0.915374
$16$	1.00000	0.250000
$17$	5.92847	1.43786	0.718932	−	0.695080i	$-0.244631\pi$
$17$	5.92847	1.43786	0.718932	+	0.695080i	$0.244631\pi$
$18$	−1.00000	−0.235702
$19$	5.45439	1.25132	0.625662	−	0.780094i	$-0.284829\pi$
$19$	5.45439	1.25132	0.625662	+	0.780094i	$0.284829\pi$
$20$	−3.54523	−0.792737
$21$	0.166701	0.0363772
$22$	−4.41321	−0.940900
$23$	6.44327	1.34352	0.671758	−	0.740771i	$-0.265540\pi$
$23$	6.44327	1.34352	0.671758	+	0.740771i	$0.265540\pi$
$24$	−1.00000	−0.204124
$25$	7.56864	1.51373
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	0.166701	0.0315036
$29$	0.584971	0.108626	0.0543132	−	0.998524i	$-0.482703\pi$
$29$	0.584971	0.108626	0.0543132	+	0.998524i	$0.482703\pi$
$30$	3.54523	0.647267
$31$	−4.19458	−0.753369	−0.376684	−	0.926342i	$-0.622936\pi$
$31$	−4.19458	−0.753369	−0.376684	+	0.926342i	$0.622936\pi$
$32$	−1.00000	−0.176777
$33$	4.41321	0.768242
$34$	−5.92847	−1.01672
$35$	−0.590994	−0.0998962
$36$	1.00000	0.166667
$37$	8.59476	1.41297	0.706485	−	0.707728i	$-0.250280\pi$
$37$	8.59476	1.41297	0.706485	+	0.707728i	$0.250280\pi$
$38$	−5.45439	−0.884819
$39$	1.00000	0.160128
$40$	3.54523	0.560550
$41$	−7.73673	−1.20827	−0.604137	−	0.796880i	$-0.706482\pi$
$41$	−7.73673	−1.20827	−0.604137	+	0.796880i	$0.706482\pi$
$42$	−0.166701	−0.0257226
$43$	−7.36207	−1.12270	−0.561352	−	0.827577i	$-0.689719\pi$
$43$	−7.36207	−1.12270	−0.561352	+	0.827577i	$0.689719\pi$
$44$	4.41321	0.665317
$45$	−3.54523	−0.528491
$46$	−6.44327	−0.950009
$47$	12.7766	1.86366	0.931829	−	0.362899i	$-0.118213\pi$
$47$	12.7766	1.86366	0.931829	+	0.362899i	$0.118213\pi$
$48$	1.00000	0.144338
$49$	−6.97221	−0.996030
$50$	−7.56864	−1.07037
$51$	5.92847	0.830151
$52$	1.00000	0.138675
$53$	1.83140	0.251563	0.125781	−	0.992058i	$-0.459856\pi$
$53$	1.83140	0.251563	0.125781	+	0.992058i	$0.459856\pi$
$54$	−1.00000	−0.136083
$55$	−15.6458	−2.10969
$56$	−0.166701	−0.0222764
$57$	5.45439	0.722452
$58$	−0.584971	−0.0768105
$59$	15.1468	1.97194	0.985972	−	0.166911i	$-0.0533793\pi$
$59$	15.1468	1.97194	0.985972	+	0.166911i	$0.0533793\pi$
$60$	−3.54523	−0.457687
$61$	10.5545	1.35137	0.675684	−	0.737192i	$-0.263848\pi$
$61$	10.5545	1.35137	0.675684	+	0.737192i	$0.263848\pi$
$62$	4.19458	0.532712
$63$	0.166701	0.0210024
$64$	1.00000	0.125000
$65$	−3.54523	−0.439731
$66$	−4.41321	−0.543229
$67$	−14.3239	−1.74994	−0.874970	−	0.484178i	$-0.839119\pi$
$67$	−14.3239	−1.74994	−0.874970	+	0.484178i	$0.839119\pi$
$68$	5.92847	0.718932
$69$	6.44327	0.775679
$70$	0.590994	0.0706373
$71$	1.93330	0.229440	0.114720	−	0.993398i	$-0.463403\pi$
$71$	1.93330	0.229440	0.114720	+	0.993398i	$0.463403\pi$
$72$	−1.00000	−0.117851
$73$	−13.3410	−1.56145	−0.780724	−	0.624876i	$-0.785149\pi$
$73$	−13.3410	−1.56145	−0.780724	+	0.624876i	$0.785149\pi$
$74$	−8.59476	−0.999121
$75$	7.56864	0.873952
$76$	5.45439	0.625662
$77$	0.735688	0.0838394
$78$	−1.00000	−0.113228
$79$	−5.41863	−0.609644	−0.304822	−	0.952409i	$-0.598597\pi$
$79$	−5.41863	−0.609644	−0.304822	+	0.952409i	$0.598597\pi$
$80$	−3.54523	−0.396369
$81$	1.00000	0.111111
$82$	7.73673	0.854379
$83$	0.0310976	0.00341341	0.00170670	−	0.999999i	$-0.499457\pi$
$83$	0.0310976	0.00341341	0.00170670	+	0.999999i	$0.499457\pi$
$84$	0.166701	0.0181886
$85$	−21.0178	−2.27970
$86$	7.36207	0.793872
$87$	0.584971	0.0627155
$88$	−4.41321	−0.470450
$89$	−1.88292	−0.199589	−0.0997947	−	0.995008i	$-0.531819\pi$
$89$	−1.88292	−0.199589	−0.0997947	+	0.995008i	$0.531819\pi$
$90$	3.54523	0.373700
$91$	0.166701	0.0174750
$92$	6.44327	0.671758
$93$	−4.19458	−0.434958
$94$	−12.7766	−1.31780
$95$	−19.3371	−1.98394
$96$	−1.00000	−0.102062
$97$	1.26550	0.128493	0.0642463	−	0.997934i	$-0.479536\pi$
$97$	1.26550	0.128493	0.0642463	+	0.997934i	$0.479536\pi$
$98$	6.97221	0.704300
$99$	4.41321	0.443544
$100$	7.56864	0.756864
$101$	11.4085	1.13519	0.567596	−	0.823307i	$-0.307874\pi$
$101$	11.4085	1.13519	0.567596	+	0.823307i	$0.307874\pi$
$102$	−5.92847	−0.587006
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	−0.590994	−0.0576751
$106$	−1.83140	−0.177882
$107$	−7.43278	−0.718554	−0.359277	−	0.933231i	$-0.616977\pi$
$107$	−7.43278	−0.718554	−0.359277	+	0.933231i	$0.616977\pi$
$108$	1.00000	0.0962250
$109$	−6.41750	−0.614685	−0.307343	−	0.951599i	$-0.599440\pi$
$109$	−6.41750	−0.614685	−0.307343	+	0.951599i	$0.599440\pi$
$110$	15.6458	1.49177
$111$	8.59476	0.815779
$112$	0.166701	0.0157518
$113$	0.936328	0.0880823	0.0440412	−	0.999030i	$-0.485977\pi$
$113$	0.936328	0.0880823	0.0440412	+	0.999030i	$0.485977\pi$
$114$	−5.45439	−0.510851
$115$	−22.8429	−2.13011
$116$	0.584971	0.0543132
$117$	1.00000	0.0924500
$118$	−15.1468	−1.39437
$119$	0.988283	0.0905957
$120$	3.54523	0.323634
$121$	8.47644	0.770585
$122$	−10.5545	−0.955561
$123$	−7.73673	−0.697598
$124$	−4.19458	−0.376684
$125$	−9.10643	−0.814504
$126$	−0.166701	−0.0148509
$127$	20.8839	1.85315	0.926575	−	0.376111i	$-0.122739\pi$
$127$	20.8839	1.85315	0.926575	+	0.376111i	$0.122739\pi$
$128$	−1.00000	−0.0883883
$129$	−7.36207	−0.648194
$130$	3.54523	0.310937
$131$	0.957541	0.0836607	0.0418304	−	0.999125i	$-0.486681\pi$
$131$	0.957541	0.0836607	0.0418304	+	0.999125i	$0.486681\pi$
$132$	4.41321	0.384121
$133$	0.909254	0.0788423
$134$	14.3239	1.23739
$135$	−3.54523	−0.305125
$136$	−5.92847	−0.508362
$137$	−13.0164	−1.11207	−0.556035	−	0.831159i	$-0.687678\pi$
$137$	−13.0164	−1.11207	−0.556035	+	0.831159i	$0.687678\pi$
$138$	−6.44327	−0.548488
$139$	−1.41313	−0.119860	−0.0599301	−	0.998203i	$-0.519088\pi$
$139$	−1.41313	−0.119860	−0.0599301	+	0.998203i	$0.519088\pi$
$140$	−0.590994	−0.0499481
$141$	12.7766	1.07598
$142$	−1.93330	−0.162239
$143$	4.41321	0.369051
$144$	1.00000	0.0833333
$145$	−2.07386	−0.172224
$146$	13.3410	1.10411
$147$	−6.97221	−0.575058
$148$	8.59476	0.706485
$149$	−7.00440	−0.573823	−0.286912	−	0.957957i	$-0.592629\pi$
$149$	−7.00440	−0.573823	−0.286912	+	0.957957i	$0.592629\pi$
$150$	−7.56864	−0.617977
$151$	17.6617	1.43729	0.718643	−	0.695379i	$-0.244764\pi$
$151$	17.6617	1.43729	0.718643	+	0.695379i	$0.244764\pi$
$152$	−5.45439	−0.442410
$153$	5.92847	0.479288
$154$	−0.735688	−0.0592834
$155$	14.8707	1.19445
$156$	1.00000	0.0800641
$157$	−12.5859	−1.00446	−0.502231	−	0.864734i	$-0.667487\pi$
$157$	−12.5859	−1.00446	−0.502231	+	0.864734i	$0.667487\pi$
$158$	5.41863	0.431083
$159$	1.83140	0.145240
$160$	3.54523	0.280275
$161$	1.07410	0.0846511
$162$	−1.00000	−0.0785674
$163$	−22.7916	−1.78518	−0.892589	−	0.450872i	$-0.851113\pi$
$163$	−22.7916	−1.78518	−0.892589	+	0.450872i	$0.851113\pi$
$164$	−7.73673	−0.604137
$165$	−15.6458	−1.21803
$166$	−0.0310976	−0.00241364
$167$	−3.49484	−0.270439	−0.135220	−	0.990816i	$-0.543174\pi$
$167$	−3.49484	−0.270439	−0.135220	+	0.990816i	$0.543174\pi$
$168$	−0.166701	−0.0128613
$169$	1.00000	0.0769231
$170$	21.0178	1.61199
$171$	5.45439	0.417108
$172$	−7.36207	−0.561352
$173$	13.3786	1.01716	0.508578	−	0.861016i	$-0.330171\pi$
$173$	13.3786	1.01716	0.508578	+	0.861016i	$0.330171\pi$
$174$	−0.584971	−0.0443465
$175$	1.26170	0.0953757
$176$	4.41321	0.332658
$177$	15.1468	1.13850
$178$	1.88292	0.141131
$179$	1.33946	0.100116	0.0500580	−	0.998746i	$-0.484059\pi$
$179$	1.33946	0.100116	0.0500580	+	0.998746i	$0.484059\pi$
$180$	−3.54523	−0.264246
$181$	−5.60284	−0.416456	−0.208228	−	0.978080i	$-0.566770\pi$
$181$	−5.60284	−0.416456	−0.208228	+	0.978080i	$0.566770\pi$
$182$	−0.166701	−0.0123567
$183$	10.5545	0.780212
$184$	−6.44327	−0.475005
$185$	−30.4704	−2.24023
$186$	4.19458	0.307562
$187$	26.1636	1.91327
$188$	12.7766	0.931829
$189$	0.166701	0.0121257
$190$	19.3371	1.40286
$191$	8.01970	0.580285	0.290143	−	0.956983i	$-0.406297\pi$
$191$	8.01970	0.580285	0.290143	+	0.956983i	$0.406297\pi$
$192$	1.00000	0.0721688
$193$	16.5029	1.18790	0.593952	−	0.804501i	$-0.297567\pi$
$193$	16.5029	1.18790	0.593952	+	0.804501i	$0.297567\pi$
$194$	−1.26550	−0.0908579
$195$	−3.54523	−0.253879
$196$	−6.97221	−0.498015
$197$	−21.0006	−1.49623	−0.748114	−	0.663570i	$-0.769040\pi$
$197$	−21.0006	−1.49623	−0.748114	+	0.663570i	$0.769040\pi$
$198$	−4.41321	−0.313633
$199$	−22.0758	−1.56491	−0.782455	−	0.622707i	$-0.786033\pi$
$199$	−22.0758	−1.56491	−0.782455	+	0.622707i	$0.786033\pi$
$200$	−7.56864	−0.535184
$201$	−14.3239	−1.01033
$202$	−11.4085	−0.802702
$203$	0.0975154	0.00684424
$204$	5.92847	0.415076
$205$	27.4285	1.91569
$206$	−1.00000	−0.0696733
$207$	6.44327	0.447839
$208$	1.00000	0.0693375
$209$	24.0714	1.66505
$210$	0.590994	0.0407825
$211$	17.8887	1.23151	0.615755	−	0.787937i	$-0.288851\pi$
$211$	17.8887	1.23151	0.615755	+	0.787937i	$0.288851\pi$
$212$	1.83140	0.125781
$213$	1.93330	0.132467
$214$	7.43278	0.508095
$215$	26.1002	1.78002
$216$	−1.00000	−0.0680414
$217$	−0.699242	−0.0474676
$218$	6.41750	0.434648
$219$	−13.3410	−0.901502
$220$	−15.6458	−1.05484
$221$	5.92847	0.398792
$222$	−8.59476	−0.576843
$223$	−16.1109	−1.07887	−0.539433	−	0.842029i	$-0.681361\pi$
$223$	−16.1109	−1.07887	−0.539433	+	0.842029i	$0.681361\pi$
$224$	−0.166701	−0.0111382
$225$	7.56864	0.504576
$226$	−0.936328	−0.0622836
$227$	−14.0683	−0.933749	−0.466874	−	0.884324i	$-0.654620\pi$
$227$	−14.0683	−0.933749	−0.466874	+	0.884324i	$0.654620\pi$
$228$	5.45439	0.361226
$229$	9.68824	0.640217	0.320109	−	0.947381i	$-0.396281\pi$
$229$	9.68824	0.640217	0.320109	+	0.947381i	$0.396281\pi$
$230$	22.8429	1.50621
$231$	0.735688	0.0484047
$232$	−0.584971	−0.0384052
$233$	15.9605	1.04561	0.522804	−	0.852453i	$-0.324886\pi$
$233$	15.9605	1.04561	0.522804	+	0.852453i	$0.324886\pi$
$234$	−1.00000	−0.0653720
$235$	−45.2959	−2.95478
$236$	15.1468	0.985972
$237$	−5.41863	−0.351978
$238$	−0.988283	−0.0640608
$239$	−22.7497	−1.47156	−0.735779	−	0.677222i	$-0.763184\pi$
$239$	−22.7497	−1.47156	−0.735779	+	0.677222i	$0.763184\pi$
$240$	−3.54523	−0.228844
$241$	−4.90865	−0.316194	−0.158097	−	0.987424i	$-0.550536\pi$
$241$	−4.90865	−0.316194	−0.158097	+	0.987424i	$0.550536\pi$
$242$	−8.47644	−0.544886
$243$	1.00000	0.0641500
$244$	10.5545	0.675684
$245$	24.7181	1.57918
$246$	7.73673	0.493276
$247$	5.45439	0.347055
$248$	4.19458	0.266356
$249$	0.0310976	0.00197073
$250$	9.10643	0.575941
$251$	−18.4284	−1.16319	−0.581594	−	0.813479i	$-0.697571\pi$
$251$	−18.4284	−1.16319	−0.581594	+	0.813479i	$0.697571\pi$
$252$	0.166701	0.0105012
$253$	28.4355	1.78773
$254$	−20.8839	−1.31037
$255$	−21.0178	−1.31618
$256$	1.00000	0.0625000
$257$	29.7453	1.85546	0.927730	−	0.373253i	$-0.121758\pi$
$257$	29.7453	1.85546	0.927730	+	0.373253i	$0.121758\pi$
$258$	7.36207	0.458342
$259$	1.43276	0.0890272
$260$	−3.54523	−0.219866
$261$	0.584971	0.0362088
$262$	−0.957541	−0.0591571
$263$	20.2991	1.25170	0.625849	−	0.779944i	$-0.284752\pi$
$263$	20.2991	1.25170	0.625849	+	0.779944i	$0.284752\pi$
$264$	−4.41321	−0.271614
$265$	−6.49274	−0.398846
$266$	−0.909254	−0.0557499
$267$	−1.88292	−0.115233
$268$	−14.3239	−0.874970
$269$	6.33144	0.386035	0.193017	−	0.981195i	$-0.438173\pi$
$269$	6.33144	0.386035	0.193017	+	0.981195i	$0.438173\pi$
$270$	3.54523	0.215756
$271$	−29.3163	−1.78084	−0.890418	−	0.455143i	$-0.849588\pi$
$271$	−29.3163	−1.78084	−0.890418	+	0.455143i	$0.849588\pi$
$272$	5.92847	0.359466
$273$	0.166701	0.0100892
$274$	13.0164	0.786352
$275$	33.4020	2.01422
$276$	6.44327	0.387840
$277$	27.2323	1.63623	0.818114	−	0.575056i	$-0.195020\pi$
$277$	27.2323	1.63623	0.818114	+	0.575056i	$0.195020\pi$
$278$	1.41313	0.0847540
$279$	−4.19458	−0.251123
$280$	0.590994	0.0353186
$281$	−22.5088	−1.34276	−0.671382	−	0.741111i	$-0.734299\pi$
$281$	−22.5088	−1.34276	−0.671382	+	0.741111i	$0.734299\pi$
$282$	−12.7766	−0.760835
$283$	14.8017	0.879872	0.439936	−	0.898029i	$-0.355001\pi$
$283$	14.8017	0.879872	0.439936	+	0.898029i	$0.355001\pi$
$284$	1.93330	0.114720
$285$	−19.3371	−1.14543
$286$	−4.41321	−0.260959
$287$	−1.28972	−0.0761299
$288$	−1.00000	−0.0589256
$289$	18.1467	1.06745
$290$	2.07386	0.121781
$291$	1.26550	0.0741852
$292$	−13.3410	−0.780724
$293$	2.36229	0.138007	0.0690033	−	0.997616i	$-0.478018\pi$
$293$	2.36229	0.138007	0.0690033	+	0.997616i	$0.478018\pi$
$294$	6.97221	0.406628
$295$	−53.6988	−3.12647
$296$	−8.59476	−0.499560
$297$	4.41321	0.256081
$298$	7.00440	0.405754
$299$	6.44327	0.372624
$300$	7.56864	0.436976
$301$	−1.22727	−0.0707384
$302$	−17.6617	−1.01631
$303$	11.4085	0.655403
$304$	5.45439	0.312831
$305$	−37.4182	−2.14256
$306$	−5.92847	−0.338908
$307$	33.3405	1.90284	0.951422	−	0.307889i	$-0.0996224\pi$
$307$	33.3405	1.90284	0.951422	+	0.307889i	$0.0996224\pi$
$308$	0.735688	0.0419197
$309$	1.00000	0.0568880
$310$	−14.8707	−0.844602
$311$	26.8070	1.52008	0.760042	−	0.649874i	$-0.225178\pi$
$311$	26.8070	1.52008	0.760042	+	0.649874i	$0.225178\pi$
$312$	−1.00000	−0.0566139
$313$	10.1194	0.571985	0.285993	−	0.958232i	$-0.407677\pi$
$313$	10.1194	0.571985	0.285993	+	0.958232i	$0.407677\pi$
$314$	12.5859	0.710261
$315$	−0.590994	−0.0332987
$316$	−5.41863	−0.304822
$317$	12.7234	0.714615	0.357307	−	0.933987i	$-0.383695\pi$
$317$	12.7234	0.714615	0.357307	+	0.933987i	$0.383695\pi$
$318$	−1.83140	−0.102700
$319$	2.58160	0.144542
$320$	−3.54523	−0.198184
$321$	−7.43278	−0.414858
$322$	−1.07410	−0.0598574
$323$	32.3362	1.79923
$324$	1.00000	0.0555556
$325$	7.56864	0.419833
$326$	22.7916	1.26231
$327$	−6.41750	−0.354889
$328$	7.73673	0.427190
$329$	2.12987	0.117424
$330$	15.6458	0.861275
$331$	−18.0998	−0.994854	−0.497427	−	0.867506i	$-0.665722\pi$
$331$	−18.0998	−0.994854	−0.497427	+	0.867506i	$0.665722\pi$
$332$	0.0310976	0.00170670
$333$	8.59476	0.470990
$334$	3.49484	0.191229
$335$	50.7814	2.77448
$336$	0.166701	0.00909430
$337$	−13.9374	−0.759216	−0.379608	−	0.925147i	$-0.623941\pi$
$337$	−13.9374	−0.759216	−0.379608	+	0.925147i	$0.623941\pi$
$338$	−1.00000	−0.0543928
$339$	0.936328	0.0508544
$340$	−21.0178	−1.13985
$341$	−18.5116	−1.00246
$342$	−5.45439	−0.294940
$343$	−2.32918	−0.125764
$344$	7.36207	0.396936
$345$	−22.8429	−1.22982
$346$	−13.3786	−0.719238
$347$	−2.89499	−0.155411	−0.0777056	−	0.996976i	$-0.524759\pi$
$347$	−2.89499	−0.155411	−0.0777056	+	0.996976i	$0.524759\pi$
$348$	0.584971	0.0313577
$349$	3.83614	0.205344	0.102672	−	0.994715i	$-0.467261\pi$
$349$	3.83614	0.205344	0.102672	+	0.994715i	$0.467261\pi$
$350$	−1.26170	−0.0674408
$351$	1.00000	0.0533761
$352$	−4.41321	−0.235225
$353$	14.3426	0.763378	0.381689	−	0.924291i	$-0.375343\pi$
$353$	14.3426	0.763378	0.381689	+	0.924291i	$0.375343\pi$
$354$	−15.1468	−0.805043
$355$	−6.85399	−0.363772
$356$	−1.88292	−0.0997947
$357$	0.988283	0.0523055
$358$	−1.33946	−0.0707926
$359$	29.9911	1.58287	0.791434	−	0.611255i	$-0.209335\pi$
$359$	29.9911	1.58287	0.791434	+	0.611255i	$0.209335\pi$
$360$	3.54523	0.186850
$361$	10.7504	0.565810
$362$	5.60284	0.294479
$363$	8.47644	0.444898
$364$	0.166701	0.00873752
$365$	47.2969	2.47563
$366$	−10.5545	−0.551694
$367$	−2.25358	−0.117636	−0.0588180	−	0.998269i	$-0.518733\pi$
$367$	−2.25358	−0.117636	−0.0588180	+	0.998269i	$0.518733\pi$
$368$	6.44327	0.335879
$369$	−7.73673	−0.402758
$370$	30.4704	1.58408
$371$	0.305297	0.0158502
$372$	−4.19458	−0.217479
$373$	26.3702	1.36540	0.682700	−	0.730699i	$-0.260806\pi$
$373$	26.3702	1.36540	0.682700	+	0.730699i	$0.260806\pi$
$374$	−26.1636	−1.35289
$375$	−9.10643	−0.470254
$376$	−12.7766	−0.658902
$377$	0.584971	0.0301275
$378$	−0.166701	−0.00857419
$379$	7.86050	0.403767	0.201883	−	0.979410i	$-0.435294\pi$
$379$	7.86050	0.403767	0.201883	+	0.979410i	$0.435294\pi$
$380$	−19.3371	−0.991971
$381$	20.8839	1.06992
$382$	−8.01970	−0.410324
$383$	4.79907	0.245221	0.122611	−	0.992455i	$-0.460873\pi$
$383$	4.79907	0.245221	0.122611	+	0.992455i	$0.460873\pi$
$384$	−1.00000	−0.0510310
$385$	−2.60818	−0.132925
$386$	−16.5029	−0.839975
$387$	−7.36207	−0.374235
$388$	1.26550	0.0642463
$389$	−6.03796	−0.306137	−0.153068	−	0.988216i	$-0.548915\pi$
$389$	−6.03796	−0.306137	−0.153068	+	0.988216i	$0.548915\pi$
$390$	3.54523	0.179520
$391$	38.1987	1.93179
$392$	6.97221	0.352150
$393$	0.957541	0.0483015
$394$	21.0006	1.05799
$395$	19.2103	0.966574
$396$	4.41321	0.221772
$397$	8.58208	0.430722	0.215361	−	0.976534i	$-0.430907\pi$
$397$	8.58208	0.430722	0.215361	+	0.976534i	$0.430907\pi$
$398$	22.0758	1.10656
$399$	0.909254	0.0455196
$400$	7.56864	0.378432
$401$	−8.93961	−0.446423	−0.223211	−	0.974770i	$-0.571654\pi$
$401$	−8.93961	−0.446423	−0.223211	+	0.974770i	$0.571654\pi$
$402$	14.3239	0.714410
$403$	−4.19458	−0.208947
$404$	11.4085	0.567596
$405$	−3.54523	−0.176164
$406$	−0.0975154	−0.00483961
$407$	37.9305	1.88015
$408$	−5.92847	−0.293503
$409$	−12.8873	−0.637237	−0.318619	−	0.947883i	$-0.603219\pi$
$409$	−12.8873	−0.637237	−0.318619	+	0.947883i	$0.603219\pi$
$410$	−27.4285	−1.35460
$411$	−13.0164	−0.642054
$412$	1.00000	0.0492665
$413$	2.52499	0.124247
$414$	−6.44327	−0.316670
$415$	−0.110248	−0.00541187
$416$	−1.00000	−0.0490290
$417$	−1.41313	−0.0692013
$418$	−24.0714	−1.17737
$419$	37.2192	1.81828	0.909138	−	0.416495i	$-0.136742\pi$
$419$	37.2192	1.81828	0.909138	+	0.416495i	$0.136742\pi$
$420$	−0.590994	−0.0288376
$421$	19.7551	0.962803	0.481402	−	0.876500i	$-0.340128\pi$
$421$	19.7551	0.962803	0.481402	+	0.876500i	$0.340128\pi$
$422$	−17.8887	−0.870810
$423$	12.7766	0.621219
$424$	−1.83140	−0.0889408
$425$	44.8705	2.17654
$426$	−1.93330	−0.0936687
$427$	1.75945	0.0851458
$428$	−7.43278	−0.359277
$429$	4.41321	0.213072
$430$	−26.1002	−1.25866
$431$	−9.88375	−0.476084	−0.238042	−	0.971255i	$-0.576506\pi$
$431$	−9.88375	−0.476084	−0.238042	+	0.971255i	$0.576506\pi$
$432$	1.00000	0.0481125
$433$	−6.36387	−0.305828	−0.152914	−	0.988239i	$-0.548866\pi$
$433$	−6.36387	−0.305828	−0.152914	+	0.988239i	$0.548866\pi$
$434$	0.699242	0.0335647
$435$	−2.07386	−0.0994338
$436$	−6.41750	−0.307343
$437$	35.1441	1.68117
$438$	13.3410	0.637458
$439$	19.3688	0.924421	0.462210	−	0.886770i	$-0.347057\pi$
$439$	19.3688	0.924421	0.462210	+	0.886770i	$0.347057\pi$
$440$	15.6458	0.745886
$441$	−6.97221	−0.332010
$442$	−5.92847	−0.281988
$443$	7.47721	0.355253	0.177626	−	0.984098i	$-0.443158\pi$
$443$	7.47721	0.355253	0.177626	+	0.984098i	$0.443158\pi$
$444$	8.59476	0.407889
$445$	6.67539	0.316444
$446$	16.1109	0.762873
$447$	−7.00440	−0.331297
$448$	0.166701	0.00787589
$449$	15.5110	0.732010	0.366005	−	0.930613i	$-0.380725\pi$
$449$	15.5110	0.732010	0.366005	+	0.930613i	$0.380725\pi$
$450$	−7.56864	−0.356789
$451$	−34.1438	−1.60777
$452$	0.936328	0.0440412
$453$	17.6617	0.829817
$454$	14.0683	0.660260
$455$	−0.590994	−0.0277062
$456$	−5.45439	−0.255425
$457$	−15.0435	−0.703707	−0.351853	−	0.936055i	$-0.614448\pi$
$457$	−15.0435	−0.703707	−0.351853	+	0.936055i	$0.614448\pi$
$458$	−9.68824	−0.452702
$459$	5.92847	0.276717
$460$	−22.8429	−1.06505
$461$	−3.44551	−0.160473	−0.0802367	−	0.996776i	$-0.525568\pi$
$461$	−3.44551	−0.160473	−0.0802367	+	0.996776i	$0.525568\pi$
$462$	−0.735688	−0.0342273
$463$	−7.48545	−0.347878	−0.173939	−	0.984756i	$-0.555650\pi$
$463$	−7.48545	−0.347878	−0.173939	+	0.984756i	$0.555650\pi$
$464$	0.584971	0.0271566
$465$	14.8707	0.689614
$466$	−15.9605	−0.739357
$467$	−12.9657	−0.599982	−0.299991	−	0.953942i	$-0.596984\pi$
$467$	−12.9657	−0.599982	−0.299991	+	0.953942i	$0.596984\pi$
$468$	1.00000	0.0462250
$469$	−2.38781	−0.110259
$470$	45.2959	2.08935
$471$	−12.5859	−0.579926
$472$	−15.1468	−0.697187
$473$	−32.4904	−1.49391
$474$	5.41863	0.248886
$475$	41.2824	1.89416
$476$	0.988283	0.0452979
$477$	1.83140	0.0838542
$478$	22.7497	1.04055
$479$	−6.53720	−0.298692	−0.149346	−	0.988785i	$-0.547717\pi$
$479$	−6.53720	−0.298692	−0.149346	+	0.988785i	$0.547717\pi$
$480$	3.54523	0.161817
$481$	8.59476	0.391887
$482$	4.90865	0.223583
$483$	1.07410	0.0488733
$484$	8.47644	0.385293
$485$	−4.48650	−0.203722
$486$	−1.00000	−0.0453609
$487$	−20.2434	−0.917314	−0.458657	−	0.888613i	$-0.651669\pi$
$487$	−20.2434	−0.917314	−0.458657	+	0.888613i	$0.651669\pi$
$488$	−10.5545	−0.477781
$489$	−22.7916	−1.03067
$490$	−24.7181	−1.11665
$491$	7.77786	0.351010	0.175505	−	0.984479i	$-0.443844\pi$
$491$	7.77786	0.351010	0.175505	+	0.984479i	$0.443844\pi$
$492$	−7.73673	−0.348799
$493$	3.46798	0.156190
$494$	−5.45439	−0.245405
$495$	−15.6458	−0.703228
$496$	−4.19458	−0.188342
$497$	0.322283	0.0144564
$498$	−0.0310976	−0.00139352
$499$	8.02423	0.359214	0.179607	−	0.983738i	$-0.442517\pi$
$499$	8.02423	0.359214	0.179607	+	0.983738i	$0.442517\pi$
$500$	−9.10643	−0.407252
$501$	−3.49484	−0.156138
$502$	18.4284	0.822498
$503$	−22.2740	−0.993147	−0.496574	−	0.867995i	$-0.665409\pi$
$503$	−22.2740	−0.993147	−0.496574	+	0.867995i	$0.665409\pi$
$504$	−0.166701	−0.00742546
$505$	−40.4459	−1.79982
$506$	−28.4355	−1.26411
$507$	1.00000	0.0444116
$508$	20.8839	0.926575
$509$	−26.1289	−1.15814	−0.579072	−	0.815276i	$-0.696585\pi$
$509$	−26.1289	−1.15814	−0.579072	+	0.815276i	$0.696585\pi$
$510$	21.0178	0.930682
$511$	−2.22396	−0.0983823
$512$	−1.00000	−0.0441942
$513$	5.45439	0.240817
$514$	−29.7453	−1.31201
$515$	−3.54523	−0.156221
$516$	−7.36207	−0.324097
$517$	56.3858	2.47984
$518$	−1.43276	−0.0629518
$519$	13.3786	0.587256
$520$	3.54523	0.155469
$521$	38.1165	1.66991	0.834957	−	0.550315i	$-0.185493\pi$
$521$	38.1165	1.66991	0.834957	+	0.550315i	$0.185493\pi$
$522$	−0.584971	−0.0256035
$523$	−40.0912	−1.75307	−0.876534	−	0.481341i	$-0.840150\pi$
$523$	−40.0912	−1.75307	−0.876534	+	0.481341i	$0.840150\pi$
$524$	0.957541	0.0418304
$525$	1.26170	0.0550652
$526$	−20.2991	−0.885085
$527$	−24.8674	−1.08324
$528$	4.41321	0.192060
$529$	18.5158	0.805034
$530$	6.49274	0.282027
$531$	15.1468	0.657315
$532$	0.909254	0.0394212
$533$	−7.73673	−0.335115
$534$	1.88292	0.0814820
$535$	26.3509	1.13925
$536$	14.3239	0.618697
$537$	1.33946	0.0578020
$538$	−6.33144	−0.272968
$539$	−30.7698	−1.32535
$540$	−3.54523	−0.152562
$541$	14.7556	0.634395	0.317197	−	0.948360i	$-0.397258\pi$
$541$	14.7556	0.634395	0.317197	+	0.948360i	$0.397258\pi$
$542$	29.3163	1.25924
$543$	−5.60284	−0.240441
$544$	−5.92847	−0.254181
$545$	22.7515	0.974567
$546$	−0.166701	−0.00713415
$547$	−10.2583	−0.438613	−0.219307	−	0.975656i	$-0.570380\pi$
$547$	−10.2583	−0.438613	−0.219307	+	0.975656i	$0.570380\pi$
$548$	−13.0164	−0.556035
$549$	10.5545	0.450456
$550$	−33.4020	−1.42427
$551$	3.19066	0.135927
$552$	−6.44327	−0.274244
$553$	−0.903293	−0.0384119
$554$	−27.2323	−1.15699
$555$	−30.4704	−1.29340
$556$	−1.41313	−0.0599301
$557$	31.5065	1.33497	0.667486	−	0.744622i	$-0.267370\pi$
$557$	31.5065	1.33497	0.667486	+	0.744622i	$0.267370\pi$
$558$	4.19458	0.177571
$559$	−7.36207	−0.311382
$560$	−0.590994	−0.0249741
$561$	26.1636	1.10463
$562$	22.5088	0.949478
$563$	−14.2498	−0.600556	−0.300278	−	0.953852i	$-0.597079\pi$
$563$	−14.2498	−0.600556	−0.300278	+	0.953852i	$0.597079\pi$
$564$	12.7766	0.537991
$565$	−3.31950	−0.139652
$566$	−14.8017	−0.622163
$567$	0.166701	0.00700079
$568$	−1.93330	−0.0811194
$569$	−6.96402	−0.291947	−0.145973	−	0.989289i	$-0.546631\pi$
$569$	−6.96402	−0.291947	−0.145973	+	0.989289i	$0.546631\pi$
$570$	19.3371	0.809941
$571$	−12.5116	−0.523592	−0.261796	−	0.965123i	$-0.584315\pi$
$571$	−12.5116	−0.523592	−0.261796	+	0.965123i	$0.584315\pi$
$572$	4.41321	0.184526
$573$	8.01970	0.335028
$574$	1.28972	0.0538320
$575$	48.7669	2.03372
$576$	1.00000	0.0416667
$577$	−0.602483	−0.0250817	−0.0125408	−	0.999921i	$-0.503992\pi$
$577$	−0.602483	−0.0250817	−0.0125408	+	0.999921i	$0.503992\pi$
$578$	−18.1467	−0.754804
$579$	16.5029	0.685836
$580$	−2.07386	−0.0861122
$581$	0.00518401	0.000215069 0
$582$	−1.26550	−0.0524569
$583$	8.08237	0.334738
$584$	13.3410	0.552055
$585$	−3.54523	−0.146577
$586$	−2.36229	−0.0975854
$587$	−32.4538	−1.33951	−0.669755	−	0.742582i	$-0.733601\pi$
$587$	−32.4538	−1.33951	−0.669755	+	0.742582i	$0.733601\pi$
$588$	−6.97221	−0.287529
$589$	−22.8789	−0.942708
$590$	53.6988	2.21075
$591$	−21.0006	−0.863848
$592$	8.59476	0.353243
$593$	−0.494938	−0.0203247	−0.0101623	−	0.999948i	$-0.503235\pi$
$593$	−0.494938	−0.0203247	−0.0101623	+	0.999948i	$0.503235\pi$
$594$	−4.41321	−0.181076
$595$	−3.50369	−0.143637
$596$	−7.00440	−0.286912
$597$	−22.0758	−0.903502
$598$	−6.44327	−0.263485
$599$	−28.8497	−1.17876	−0.589382	−	0.807854i	$-0.700629\pi$
$599$	−28.8497	−1.17876	−0.589382	+	0.807854i	$0.700629\pi$
$600$	−7.56864	−0.308989
$601$	45.1024	1.83977	0.919883	−	0.392192i	$-0.128283\pi$
$601$	45.1024	1.83977	0.919883	+	0.392192i	$0.128283\pi$
$602$	1.22727	0.0500196
$603$	−14.3239	−0.583313
$604$	17.6617	0.718643
$605$	−30.0509	−1.22174
$606$	−11.4085	−0.463440
$607$	−34.7633	−1.41100	−0.705500	−	0.708710i	$-0.749277\pi$
$607$	−34.7633	−1.41100	−0.705500	+	0.708710i	$0.749277\pi$
$608$	−5.45439	−0.221205
$609$	0.0975154	0.00395152
$610$	37.4182	1.51502
$611$	12.7766	0.516885
$612$	5.92847	0.239644
$613$	−14.6854	−0.593137	−0.296569	−	0.955012i	$-0.595842\pi$
$613$	−14.6854	−0.593137	−0.296569	+	0.955012i	$0.595842\pi$
$614$	−33.3405	−1.34551
$615$	27.4285	1.10602
$616$	−0.735688	−0.0296417
$617$	24.2856	0.977702	0.488851	−	0.872367i	$-0.337416\pi$
$617$	24.2856	0.977702	0.488851	+	0.872367i	$0.337416\pi$
$618$	−1.00000	−0.0402259
$619$	−23.9388	−0.962183	−0.481092	−	0.876670i	$-0.659760\pi$
$619$	−23.9388	−0.962183	−0.481092	+	0.876670i	$0.659760\pi$
$620$	14.8707	0.597223
$621$	6.44327	0.258560
$622$	−26.8070	−1.07486
$623$	−0.313886	−0.0125756
$624$	1.00000	0.0400320
$625$	−5.55884	−0.222354
$626$	−10.1194	−0.404454
$627$	24.0714	0.961319
$628$	−12.5859	−0.502231
$629$	50.9538	2.03166
$630$	0.590994	0.0235458
$631$	21.3458	0.849763	0.424881	−	0.905249i	$-0.360316\pi$
$631$	21.3458	0.849763	0.424881	+	0.905249i	$0.360316\pi$
$632$	5.41863	0.215542
$633$	17.8887	0.711013
$634$	−12.7234	−0.505309
$635$	−74.0383	−2.93812
$636$	1.83140	0.0726199
$637$	−6.97221	−0.276249
$638$	−2.58160	−0.102207
$639$	1.93330	0.0764801
$640$	3.54523	0.140137
$641$	−9.82132	−0.387919	−0.193959	−	0.981010i	$-0.562133\pi$
$641$	−9.82132	−0.387919	−0.193959	+	0.981010i	$0.562133\pi$
$642$	7.43278	0.293349
$643$	−35.6944	−1.40765	−0.703825	−	0.710373i	$-0.748526\pi$
$643$	−35.6944	−1.40765	−0.703825	+	0.710373i	$0.748526\pi$
$644$	1.07410	0.0423255
$645$	26.1002	1.02769
$646$	−32.3362	−1.27225
$647$	−23.9578	−0.941877	−0.470938	−	0.882166i	$-0.656085\pi$
$647$	−23.9578	−0.941877	−0.470938	+	0.882166i	$0.656085\pi$
$648$	−1.00000	−0.0392837
$649$	66.8460	2.62393
$650$	−7.56864	−0.296867
$651$	−0.699242	−0.0274054
$652$	−22.7916	−0.892589
$653$	−23.3322	−0.913058	−0.456529	−	0.889708i	$-0.650908\pi$
$653$	−23.3322	−0.913058	−0.456529	+	0.889708i	$0.650908\pi$
$654$	6.41750	0.250944
$655$	−3.39470	−0.132642
$656$	−7.73673	−0.302069
$657$	−13.3410	−0.520482
$658$	−2.12987	−0.0830311
$659$	−18.8562	−0.734533	−0.367267	−	0.930116i	$-0.619706\pi$
$659$	−18.8562	−0.734533	−0.367267	+	0.930116i	$0.619706\pi$
$660$	−15.6458	−0.609014
$661$	−8.21926	−0.319692	−0.159846	−	0.987142i	$-0.551100\pi$
$661$	−8.21926	−0.319692	−0.159846	+	0.987142i	$0.551100\pi$
$662$	18.0998	0.703468
$663$	5.92847	0.230243
$664$	−0.0310976	−0.00120682
$665$	−3.22351	−0.125002
$666$	−8.59476	−0.333040
$667$	3.76913	0.145941
$668$	−3.49484	−0.135220
$669$	−16.1109	−0.622883
$670$	−50.7814	−1.96186
$671$	46.5793	1.79817
$672$	−0.166701	−0.00643064
$673$	7.82248	0.301534	0.150767	−	0.988569i	$-0.451826\pi$
$673$	7.82248	0.301534	0.150767	+	0.988569i	$0.451826\pi$
$674$	13.9374	0.536847
$675$	7.56864	0.291317
$676$	1.00000	0.0384615
$677$	0.944147	0.0362865	0.0181433	−	0.999835i	$-0.494225\pi$
$677$	0.944147	0.0362865	0.0181433	+	0.999835i	$0.494225\pi$
$678$	−0.936328	−0.0359595
$679$	0.210961	0.00809595
$680$	21.0178	0.805995
$681$	−14.0683	−0.539100
$682$	18.5116	0.708845
$683$	−13.5829	−0.519736	−0.259868	−	0.965644i	$-0.583679\pi$
$683$	−13.5829	−0.519736	−0.259868	+	0.965644i	$0.583679\pi$
$684$	5.45439	0.208554
$685$	46.1462	1.76316
$686$	2.32918	0.0889287
$687$	9.68824	0.369630
$688$	−7.36207	−0.280676
$689$	1.83140	0.0697709
$690$	22.8429	0.869614
$691$	6.10311	0.232173	0.116087	−	0.993239i	$-0.462965\pi$
$691$	6.10311	0.232173	0.116087	+	0.993239i	$0.462965\pi$
$692$	13.3786	0.508578
$693$	0.735688	0.0279465
$694$	2.89499	0.109892
$695$	5.00987	0.190035
$696$	−0.584971	−0.0221733
$697$	−45.8670	−1.73733
$698$	−3.83614	−0.145200
$699$	15.9605	0.603683
$700$	1.26170	0.0476879
$701$	9.00589	0.340148	0.170074	−	0.985431i	$-0.445599\pi$
$701$	9.00589	0.340148	0.170074	+	0.985431i	$0.445599\pi$
$702$	−1.00000	−0.0377426
$703$	46.8792	1.76808
$704$	4.41321	0.166329
$705$	−45.2959	−1.70594
$706$	−14.3426	−0.539789
$707$	1.90182	0.0715252
$708$	15.1468	0.569251
$709$	−17.0731	−0.641193	−0.320597	−	0.947216i	$-0.603883\pi$
$709$	−17.0731	−0.641193	−0.320597	+	0.947216i	$0.603883\pi$
$710$	6.85399	0.257226
$711$	−5.41863	−0.203215
$712$	1.88292	0.0705655
$713$	−27.0268	−1.01216
$714$	−0.988283	−0.0369855
$715$	−15.6458	−0.585121
$716$	1.33946	0.0500580
$717$	−22.7497	−0.849604
$718$	−29.9911	−1.11926
$719$	−50.5592	−1.88554	−0.942771	−	0.333441i	$-0.891790\pi$
$719$	−50.5592	−1.88554	−0.942771	+	0.333441i	$0.891790\pi$
$720$	−3.54523	−0.132123
$721$	0.166701	0.00620828
$722$	−10.7504	−0.400088
$723$	−4.90865	−0.182555
$724$	−5.60284	−0.208228
$725$	4.42744	0.164431
$726$	−8.47644	−0.314590
$727$	24.0375	0.891500	0.445750	−	0.895157i	$-0.352937\pi$
$727$	24.0375	0.891500	0.445750	+	0.895157i	$0.352937\pi$
$728$	−0.166701	−0.00617836
$729$	1.00000	0.0370370
$730$	−47.2969	−1.75054
$731$	−43.6458	−1.61430
$732$	10.5545	0.390106
$733$	−7.01068	−0.258945	−0.129473	−	0.991583i	$-0.541328\pi$
$733$	−7.01068	−0.258945	−0.129473	+	0.991583i	$0.541328\pi$
$734$	2.25358	0.0831812
$735$	24.7181	0.911740
$736$	−6.44327	−0.237502
$737$	−63.2143	−2.32853
$738$	7.73673	0.284793
$739$	37.0958	1.36459	0.682296	−	0.731076i	$-0.260982\pi$
$739$	37.0958	1.36459	0.682296	+	0.731076i	$0.260982\pi$
$740$	−30.4704	−1.12011
$741$	5.45439	0.200372
$742$	−0.305297	−0.0112078
$743$	−12.5006	−0.458604	−0.229302	−	0.973355i	$-0.573644\pi$
$743$	−12.5006	−0.458604	−0.229302	+	0.973355i	$0.573644\pi$
$744$	4.19458	0.153781
$745$	24.8322	0.909782
$746$	−26.3702	−0.965483
$747$	0.0310976	0.00113780
$748$	26.1636	0.956635
$749$	−1.23905	−0.0452741
$750$	9.10643	0.332520
$751$	39.4781	1.44058	0.720288	−	0.693675i	$-0.244009\pi$
$751$	39.4781	1.44058	0.720288	+	0.693675i	$0.244009\pi$
$752$	12.7766	0.465914
$753$	−18.4284	−0.671567
$754$	−0.584971	−0.0213034
$755$	−62.6146	−2.27878
$756$	0.166701	0.00606287
$757$	−7.13120	−0.259188	−0.129594	−	0.991567i	$-0.541367\pi$
$757$	−7.13120	−0.259188	−0.129594	+	0.991567i	$0.541367\pi$
$758$	−7.86050	−0.285506
$759$	28.4355	1.03214
$760$	19.3371	0.701429
$761$	−31.6705	−1.14805	−0.574026	−	0.818837i	$-0.694619\pi$
$761$	−31.6705	−1.14805	−0.574026	+	0.818837i	$0.694619\pi$
$762$	−20.8839	−0.756545
$763$	−1.06981	−0.0387295
$764$	8.01970	0.290143
$765$	−21.0178	−0.759899
$766$	−4.79907	−0.173397
$767$	15.1468	0.546919
$768$	1.00000	0.0360844
$769$	23.1490	0.834775	0.417387	−	0.908729i	$-0.362946\pi$
$769$	23.1490	0.834775	0.417387	+	0.908729i	$0.362946\pi$
$770$	2.60818	0.0939923
$771$	29.7453	1.07125
$772$	16.5029	0.593952
$773$	34.1894	1.22971	0.614853	−	0.788642i	$-0.289215\pi$
$773$	34.1894	1.22971	0.614853	+	0.788642i	$0.289215\pi$
$774$	7.36207	0.264624
$775$	−31.7473	−1.14040
$776$	−1.26550	−0.0454290
$777$	1.43276	0.0513999
$778$	6.03796	0.216471
$779$	−42.1992	−1.51194
$780$	−3.54523	−0.126940
$781$	8.53206	0.305301
$782$	−38.1987	−1.36598
$783$	0.584971	0.0209052
$784$	−6.97221	−0.249008
$785$	44.6198	1.59255
$786$	−0.957541	−0.0341543
$787$	−2.16408	−0.0771411	−0.0385705	−	0.999256i	$-0.512280\pi$
$787$	−2.16408	−0.0771411	−0.0385705	+	0.999256i	$0.512280\pi$
$788$	−21.0006	−0.748114
$789$	20.2991	0.722669
$790$	−19.2103	−0.683471
$791$	0.156087	0.00554982
$792$	−4.41321	−0.156817
$793$	10.5545	0.374802
$794$	−8.58208	−0.304567
$795$	−6.49274	−0.230274
$796$	−22.0758	−0.782455
$797$	9.88873	0.350277	0.175138	−	0.984544i	$-0.443963\pi$
$797$	9.88873	0.350277	0.175138	+	0.984544i	$0.443963\pi$
$798$	−0.909254	−0.0321872
$799$	75.7456	2.67969
$800$	−7.56864	−0.267592
$801$	−1.88292	−0.0665298
$802$	8.93961	0.315668
$803$	−58.8767	−2.07771
$804$	−14.3239	−0.505164
$805$	−3.80794	−0.134212
$806$	4.19458	0.147748
$807$	6.33144	0.222877
$808$	−11.4085	−0.401351
$809$	−26.1335	−0.918805	−0.459402	−	0.888228i	$-0.651936\pi$
$809$	−26.1335	−0.918805	−0.459402	+	0.888228i	$0.651936\pi$
$810$	3.54523	0.124567
$811$	12.2978	0.431834	0.215917	−	0.976412i	$-0.430726\pi$
$811$	12.2978	0.431834	0.215917	+	0.976412i	$0.430726\pi$
$812$	0.0975154	0.00342212
$813$	−29.3163	−1.02817
$814$	−37.9305	−1.32946
$815$	80.8015	2.83035
$816$	5.92847	0.207538
$817$	−40.1556	−1.40487
$818$	12.8873	0.450595
$819$	0.166701	0.00582501
$820$	27.4285	0.957844
$821$	51.1200	1.78410	0.892051	−	0.451935i	$-0.149266\pi$
$821$	51.1200	1.78410	0.892051	+	0.451935i	$0.149266\pi$
$822$	13.0164	0.454000
$823$	30.7770	1.07282	0.536409	−	0.843958i	$-0.319781\pi$
$823$	30.7770	1.07282	0.536409	+	0.843958i	$0.319781\pi$
$824$	−1.00000	−0.0348367
$825$	33.4020	1.16291
$826$	−2.52499	−0.0878556
$827$	31.3675	1.09075	0.545377	−	0.838191i	$-0.316386\pi$
$827$	31.3675	1.09075	0.545377	+	0.838191i	$0.316386\pi$
$828$	6.44327	0.223919
$829$	−11.7624	−0.408524	−0.204262	−	0.978916i	$-0.565479\pi$
$829$	−11.7624	−0.408524	−0.204262	+	0.978916i	$0.565479\pi$
$830$	0.110248	0.00382677
$831$	27.2323	0.944677
$832$	1.00000	0.0346688
$833$	−41.3345	−1.43216
$834$	1.41313	0.0489327
$835$	12.3900	0.428774
$836$	24.0714	0.832526
$837$	−4.19458	−0.144986
$838$	−37.2192	−1.28572
$839$	49.1695	1.69752	0.848760	−	0.528778i	$-0.177350\pi$
$839$	49.1695	1.69752	0.848760	+	0.528778i	$0.177350\pi$
$840$	0.590994	0.0203912
$841$	−28.6578	−0.988200
$842$	−19.7551	−0.680805
$843$	−22.5088	−0.775245
$844$	17.8887	0.615755
$845$	−3.54523	−0.121960
$846$	−12.7766	−0.439268
$847$	1.41303	0.0485524
$848$	1.83140	0.0628906
$849$	14.8017	0.507994
$850$	−44.8705	−1.53904
$851$	55.3784	1.89835
$852$	1.93330	0.0662337
$853$	−52.5264	−1.79847	−0.899235	−	0.437466i	$-0.855876\pi$
$853$	−52.5264	−1.79847	−0.899235	+	0.437466i	$0.855876\pi$
$854$	−1.75945	−0.0602072
$855$	−19.3371	−0.661314
$856$	7.43278	0.254047
$857$	29.6276	1.01206	0.506030	−	0.862516i	$-0.331112\pi$
$857$	29.6276	1.01206	0.506030	+	0.862516i	$0.331112\pi$
$858$	−4.41321	−0.150665
$859$	12.5133	0.426948	0.213474	−	0.976949i	$-0.431522\pi$
$859$	12.5133	0.426948	0.213474	+	0.976949i	$0.431522\pi$
$860$	26.1002	0.890010
$861$	−1.28972	−0.0439536
$862$	9.88375	0.336642
$863$	−14.7839	−0.503251	−0.251626	−	0.967825i	$-0.580965\pi$
$863$	−14.7839	−0.503251	−0.251626	+	0.967825i	$0.580965\pi$
$864$	−1.00000	−0.0340207
$865$	−47.4302	−1.61268
$866$	6.36387	0.216253
$867$	18.1467	0.616295
$868$	−0.699242	−0.0237338
$869$	−23.9136	−0.811212
$870$	2.07386	0.0703103
$871$	−14.3239	−0.485346
$872$	6.41750	0.217324
$873$	1.26550	0.0428308
$874$	−35.1441	−1.18877
$875$	−1.51805	−0.0513196
$876$	−13.3410	−0.450751
$877$	−23.8254	−0.804528	−0.402264	−	0.915524i	$-0.631777\pi$
$877$	−23.8254	−0.804528	−0.402264	+	0.915524i	$0.631777\pi$
$878$	−19.3688	−0.653664
$879$	2.36229	0.0796781
$880$	−15.6458	−0.527421
$881$	−44.5646	−1.50142	−0.750709	−	0.660633i	$-0.770288\pi$
$881$	−44.5646	−1.50142	−0.750709	+	0.660633i	$0.770288\pi$
$882$	6.97221	0.234767
$883$	−27.3495	−0.920383	−0.460192	−	0.887820i	$-0.652219\pi$
$883$	−27.3495	−0.920383	−0.460192	+	0.887820i	$0.652219\pi$
$884$	5.92847	0.199396
$885$	−53.6988	−1.80507
$886$	−7.47721	−0.251202
$887$	−21.7534	−0.730406	−0.365203	−	0.930928i	$-0.619000\pi$
$887$	−21.7534	−0.730406	−0.365203	+	0.930928i	$0.619000\pi$
$888$	−8.59476	−0.288421
$889$	3.48138	0.116762
$890$	−6.67539	−0.223760
$891$	4.41321	0.147848
$892$	−16.1109	−0.539433
$893$	69.6885	2.33204
$894$	7.00440	0.234262
$895$	−4.74869	−0.158731
$896$	−0.166701	−0.00556910
$897$	6.44327	0.215135
$898$	−15.5110	−0.517609
$899$	−2.45371	−0.0818357
$900$	7.56864	0.252288
$901$	10.8574	0.361713
$902$	34.1438	1.13687
$903$	−1.22727	−0.0408408
$904$	−0.936328	−0.0311418
$905$	19.8633	0.660280
$906$	−17.6617	−0.586769
$907$	−37.6797	−1.25113	−0.625567	−	0.780170i	$-0.715132\pi$
$907$	−37.6797	−1.25113	−0.625567	+	0.780170i	$0.715132\pi$
$908$	−14.0683	−0.466874
$909$	11.4085	0.378397
$910$	0.590994	0.0195913
$911$	3.70168	0.122642	0.0613211	−	0.998118i	$-0.480469\pi$
$911$	3.70168	0.122642	0.0613211	+	0.998118i	$0.480469\pi$
$912$	5.45439	0.180613
$913$	0.137240	0.00454199
$914$	15.0435	0.497596
$915$	−37.4182	−1.23701
$916$	9.68824	0.320109
$917$	0.159623	0.00527122
$918$	−5.92847	−0.195669
$919$	14.3948	0.474840	0.237420	−	0.971407i	$-0.423698\pi$
$919$	14.3948	0.474840	0.237420	+	0.971407i	$0.423698\pi$
$920$	22.8429	0.753107
$921$	33.3405	1.09861
$922$	3.44551	0.113472
$923$	1.93330	0.0636353
$924$	0.735688	0.0242024
$925$	65.0507	2.13885
$926$	7.48545	0.245987
$927$	1.00000	0.0328443
$928$	−0.584971	−0.0192026
$929$	54.2687	1.78050	0.890248	−	0.455475i	$-0.150531\pi$
$929$	54.2687	1.78050	0.890248	+	0.455475i	$0.150531\pi$
$930$	−14.8707	−0.487631
$931$	−38.0292	−1.24636
$932$	15.9605	0.522804
$933$	26.8070	0.877621
$934$	12.9657	0.424251
$935$	−92.7559	−3.03344
$936$	−1.00000	−0.0326860
$937$	46.9426	1.53355	0.766774	−	0.641917i	$-0.221861\pi$
$937$	46.9426	1.53355	0.766774	+	0.641917i	$0.221861\pi$
$938$	2.38781	0.0779647
$939$	10.1194	0.330236
$940$	−45.2959	−1.47739
$941$	−50.9187	−1.65990	−0.829952	−	0.557835i	$-0.811632\pi$
$941$	−50.9187	−1.65990	−0.829952	+	0.557835i	$0.811632\pi$
$942$	12.5859	0.410070
$943$	−49.8499	−1.62334
$944$	15.1468	0.492986
$945$	−0.590994	−0.0192250
$946$	32.4904	1.05635
$947$	25.2555	0.820694	0.410347	−	0.911929i	$-0.365408\pi$
$947$	25.2555	0.820694	0.410347	+	0.911929i	$0.365408\pi$
$948$	−5.41863	−0.175989
$949$	−13.3410	−0.433068
$950$	−41.2824	−1.33938
$951$	12.7234	0.412583
$952$	−0.988283	−0.0320304
$953$	−13.8384	−0.448268	−0.224134	−	0.974558i	$-0.571955\pi$
$953$	−13.8384	−0.448268	−0.224134	+	0.974558i	$0.571955\pi$
$954$	−1.83140	−0.0592939
$955$	−28.4317	−0.920027
$956$	−22.7497	−0.735779
$957$	2.58160	0.0834513
$958$	6.53720	0.211207
$959$	−2.16986	−0.0700683
$960$	−3.54523	−0.114422
$961$	−13.4055	−0.432435
$962$	−8.59476	−0.277106
$963$	−7.43278	−0.239518
$964$	−4.90865	−0.158097
$965$	−58.5065	−1.88339
$966$	−1.07410	−0.0345587
$967$	−4.71481	−0.151618	−0.0758090	−	0.997122i	$-0.524154\pi$
$967$	−4.71481	−0.151618	−0.0758090	+	0.997122i	$0.524154\pi$
$968$	−8.47644	−0.272443
$969$	32.3362	1.03879
$970$	4.48650	0.144053
$971$	5.24617	0.168358	0.0841788	−	0.996451i	$-0.473173\pi$
$971$	5.24617	0.168358	0.0841788	+	0.996451i	$0.473173\pi$
$972$	1.00000	0.0320750
$973$	−0.235571	−0.00755205
$974$	20.2434	0.648639
$975$	7.56864	0.242391
$976$	10.5545	0.337842
$977$	38.5977	1.23485	0.617425	−	0.786630i	$-0.288176\pi$
$977$	38.5977	1.23485	0.617425	+	0.786630i	$0.288176\pi$
$978$	22.7916	0.728795
$979$	−8.30974	−0.265580
$980$	24.7181	0.789590
$981$	−6.41750	−0.204895
$982$	−7.77786	−0.248201
$983$	54.0601	1.72425	0.862124	−	0.506697i	$-0.169134\pi$
$983$	54.0601	1.72425	0.862124	+	0.506697i	$0.169134\pi$
$984$	7.73673	0.246638
$985$	74.4518	2.37223
$986$	−3.46798	−0.110443
$987$	2.12987	0.0677946
$988$	5.45439	0.173527
$989$	−47.4358	−1.50837
$990$	15.6458	0.497258
$991$	54.8753	1.74317	0.871586	−	0.490242i	$-0.163092\pi$
$991$	54.8753	1.74317	0.871586	+	0.490242i	$0.163092\pi$
$992$	4.19458	0.133178
$993$	−18.0998	−0.574379
$994$	−0.322283	−0.0102222
$995$	78.2637	2.48113
$996$	0.0310976	0.000985365 0
$997$	−32.5661	−1.03138	−0.515690	−	0.856775i	$-0.672464\pi$
$997$	−32.5661	−1.03138	−0.515690	+	0.856775i	$0.672464\pi$
$998$	−8.02423	−0.254003
$999$	8.59476	0.271926

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.x.1.2	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.x.1.2	✓	13	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.54523 q^{5} -1.00000 q^{6} +0.166701 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.54523 q^{5} -1.00000 q^{6} +0.166701 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.54523 q^{10} +4.41321 q^{11} +1.00000 q^{12} +1.00000 q^{13} -0.166701 q^{14} -3.54523 q^{15} +1.00000 q^{16} +5.92847 q^{17} -1.00000 q^{18} +5.45439 q^{19} -3.54523 q^{20} +0.166701 q^{21} -4.41321 q^{22} +6.44327 q^{23} -1.00000 q^{24} +7.56864 q^{25} -1.00000 q^{26} +1.00000 q^{27} +0.166701 q^{28} +0.584971 q^{29} +3.54523 q^{30} -4.19458 q^{31} -1.00000 q^{32} +4.41321 q^{33} -5.92847 q^{34} -0.590994 q^{35} +1.00000 q^{36} +8.59476 q^{37} -5.45439 q^{38} +1.00000 q^{39} +3.54523 q^{40} -7.73673 q^{41} -0.166701 q^{42} -7.36207 q^{43} +4.41321 q^{44} -3.54523 q^{45} -6.44327 q^{46} +12.7766 q^{47} +1.00000 q^{48} -6.97221 q^{49} -7.56864 q^{50} +5.92847 q^{51} +1.00000 q^{52} +1.83140 q^{53} -1.00000 q^{54} -15.6458 q^{55} -0.166701 q^{56} +5.45439 q^{57} -0.584971 q^{58} +15.1468 q^{59} -3.54523 q^{60} +10.5545 q^{61} +4.19458 q^{62} +0.166701 q^{63} +1.00000 q^{64} -3.54523 q^{65} -4.41321 q^{66} -14.3239 q^{67} +5.92847 q^{68} +6.44327 q^{69} +0.590994 q^{70} +1.93330 q^{71} -1.00000 q^{72} -13.3410 q^{73} -8.59476 q^{74} +7.56864 q^{75} +5.45439 q^{76} +0.735688 q^{77} -1.00000 q^{78} -5.41863 q^{79} -3.54523 q^{80} +1.00000 q^{81} +7.73673 q^{82} +0.0310976 q^{83} +0.166701 q^{84} -21.0178 q^{85} +7.36207 q^{86} +0.584971 q^{87} -4.41321 q^{88} -1.88292 q^{89} +3.54523 q^{90} +0.166701 q^{91} +6.44327 q^{92} -4.19458 q^{93} -12.7766 q^{94} -19.3371 q^{95} -1.00000 q^{96} +1.26550 q^{97} +6.97221 q^{98} +4.41321 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} + q^{5} - 13 q^{6} - q^{7} - 13 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 + q^5 - 13 * q^6 - q^7 - 13 * q^8 + 13 * q^9	\( 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} + q^{5} - 13 q^{6} - q^{7} - 13 q^{8} + 13 q^{9} - q^{10} + 6 q^{11} + 13 q^{12} + 13 q^{13} + q^{14} + q^{15} + 13 q^{16} + 18 q^{17} - 13 q^{18} - q^{19} + q^{20} - q^{21} - 6 q^{22} + 20 q^{23} - 13 q^{24} + 16 q^{25} - 13 q^{26} + 13 q^{27} - q^{28} + 25 q^{29} - q^{30} - 5 q^{31} - 13 q^{32} + 6 q^{33} - 18 q^{34} + 26 q^{35} + 13 q^{36} - 6 q^{37} + q^{38} + 13 q^{39} - q^{40} + 13 q^{41} + q^{42} - 2 q^{43} + 6 q^{44} + q^{45} - 20 q^{46} + 5 q^{47} + 13 q^{48} - 16 q^{50} + 18 q^{51} + 13 q^{52} + 21 q^{53} - 13 q^{54} + 2 q^{55} + q^{56} - q^{57} - 25 q^{58} + 22 q^{59} + q^{60} + 2 q^{61} + 5 q^{62} - q^{63} + 13 q^{64} + q^{65} - 6 q^{66} - q^{67} + 18 q^{68} + 20 q^{69} - 26 q^{70} + 32 q^{71} - 13 q^{72} - 13 q^{73} + 6 q^{74} + 16 q^{75} - q^{76} + 33 q^{77} - 13 q^{78} - 7 q^{79} + q^{80} + 13 q^{81} - 13 q^{82} + 17 q^{83} - q^{84} - 25 q^{85} + 2 q^{86} + 25 q^{87} - 6 q^{88} - 12 q^{89} - q^{90} - q^{91} + 20 q^{92} - 5 q^{93} - 5 q^{94} + 36 q^{95} - 13 q^{96} - 42 q^{97} + 6 q^{99}+O(q^{100}) \) 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 + q^5 - 13 * q^6 - q^7 - 13 * q^8 + 13 * q^9 - q^10 + 6 * q^11 + 13 * q^12 + 13 * q^13 + q^14 + q^15 + 13 * q^16 + 18 * q^17 - 13 * q^18 - q^19 + q^20 - q^21 - 6 * q^22 + 20 * q^23 - 13 * q^24 + 16 * q^25 - 13 * q^26 + 13 * q^27 - q^28 + 25 * q^29 - q^30 - 5 * q^31 - 13 * q^32 + 6 * q^33 - 18 * q^34 + 26 * q^35 + 13 * q^36 - 6 * q^37 + q^38 + 13 * q^39 - q^40 + 13 * q^41 + q^42 - 2 * q^43 + 6 * q^44 + q^45 - 20 * q^46 + 5 * q^47 + 13 * q^48 - 16 * q^50 + 18 * q^51 + 13 * q^52 + 21 * q^53 - 13 * q^54 + 2 * q^55 + q^56 - q^57 - 25 * q^58 + 22 * q^59 + q^60 + 2 * q^61 + 5 * q^62 - q^63 + 13 * q^64 + q^65 - 6 * q^66 - q^67 + 18 * q^68 + 20 * q^69 - 26 * q^70 + 32 * q^71 - 13 * q^72 - 13 * q^73 + 6 * q^74 + 16 * q^75 - q^76 + 33 * q^77 - 13 * q^78 - 7 * q^79 + q^80 + 13 * q^81 - 13 * q^82 + 17 * q^83 - q^84 - 25 * q^85 + 2 * q^86 + 25 * q^87 - 6 * q^88 - 12 * q^89 - q^90 - q^91 + 20 * q^92 - 5 * q^93 - 5 * q^94 + 36 * q^95 - 13 * q^96 - 42 * q^97 + 6 * q^99

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