LMFDB - Embedded newform 8034.2.a.bd.1.9

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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} - 36 x^{14} + 196 x^{13} + 498 x^{12} - 3101 x^{11} - 3150 x^{10} + 25368 x^{9} + \cdots - 66432 $ x^16 - 5x^15 - 36x^14 + 196x^13 + 498x^12 - 3101x^11 - 3150x^10 + 25368x^9 + 6763x^8 - 113788x^7 + 19731x^6 + 270913x^5 - 122680x^4 - 296326x^3 + 185524x^2 + 94528*x - 66432
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$0.808021$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.808021 q^{5} +1.00000 q^{6} +3.24300 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.808021 q^{5} +1.00000 q^{6} +3.24300 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.808021 q^{10} +4.15216 q^{11} +1.00000 q^{12} -1.00000 q^{13} +3.24300 q^{14} +0.808021 q^{15} +1.00000 q^{16} +7.76632 q^{17} +1.00000 q^{18} +8.59590 q^{19} +0.808021 q^{20} +3.24300 q^{21} +4.15216 q^{22} -8.64744 q^{23} +1.00000 q^{24} -4.34710 q^{25} -1.00000 q^{26} +1.00000 q^{27} +3.24300 q^{28} +4.23930 q^{29} +0.808021 q^{30} -6.26307 q^{31} +1.00000 q^{32} +4.15216 q^{33} +7.76632 q^{34} +2.62041 q^{35} +1.00000 q^{36} +5.67059 q^{37} +8.59590 q^{38} -1.00000 q^{39} +0.808021 q^{40} +1.67856 q^{41} +3.24300 q^{42} +0.621687 q^{43} +4.15216 q^{44} +0.808021 q^{45} -8.64744 q^{46} -10.5592 q^{47} +1.00000 q^{48} +3.51704 q^{49} -4.34710 q^{50} +7.76632 q^{51} -1.00000 q^{52} +6.13590 q^{53} +1.00000 q^{54} +3.35504 q^{55} +3.24300 q^{56} +8.59590 q^{57} +4.23930 q^{58} -12.2258 q^{59} +0.808021 q^{60} -10.0049 q^{61} -6.26307 q^{62} +3.24300 q^{63} +1.00000 q^{64} -0.808021 q^{65} +4.15216 q^{66} -11.2176 q^{67} +7.76632 q^{68} -8.64744 q^{69} +2.62041 q^{70} +4.12480 q^{71} +1.00000 q^{72} +13.8673 q^{73} +5.67059 q^{74} -4.34710 q^{75} +8.59590 q^{76} +13.4655 q^{77} -1.00000 q^{78} -14.1068 q^{79} +0.808021 q^{80} +1.00000 q^{81} +1.67856 q^{82} -14.9176 q^{83} +3.24300 q^{84} +6.27535 q^{85} +0.621687 q^{86} +4.23930 q^{87} +4.15216 q^{88} -8.36437 q^{89} +0.808021 q^{90} -3.24300 q^{91} -8.64744 q^{92} -6.26307 q^{93} -10.5592 q^{94} +6.94567 q^{95} +1.00000 q^{96} +3.02487 q^{97} +3.51704 q^{98} +4.15216 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9} + 5 q^{10} + 18 q^{11} + 16 q^{12} - 16 q^{13} + 4 q^{14} + 5 q^{15} + 16 q^{16} + 17 q^{17} + 16 q^{18} + 8 q^{19} + 5 q^{20} + 4 q^{21} + 18 q^{22} + 9 q^{23} + 16 q^{24} + 17 q^{25} - 16 q^{26} + 16 q^{27} + 4 q^{28} + 14 q^{29} + 5 q^{30} + 12 q^{31} + 16 q^{32} + 18 q^{33} + 17 q^{34} + 16 q^{35} + 16 q^{36} + 31 q^{37} + 8 q^{38} - 16 q^{39} + 5 q^{40} + 29 q^{41} + 4 q^{42} + 30 q^{43} + 18 q^{44} + 5 q^{45} + 9 q^{46} - q^{47} + 16 q^{48} + 36 q^{49} + 17 q^{50} + 17 q^{51} - 16 q^{52} + 12 q^{53} + 16 q^{54} + 30 q^{55} + 4 q^{56} + 8 q^{57} + 14 q^{58} + 38 q^{59} + 5 q^{60} + 12 q^{62} + 4 q^{63} + 16 q^{64} - 5 q^{65} + 18 q^{66} + 28 q^{67} + 17 q^{68} + 9 q^{69} + 16 q^{70} + 32 q^{71} + 16 q^{72} + 20 q^{73} + 31 q^{74} + 17 q^{75} + 8 q^{76} + 26 q^{77} - 16 q^{78} + 13 q^{79} + 5 q^{80} + 16 q^{81} + 29 q^{82} + 39 q^{83} + 4 q^{84} + 31 q^{85} + 30 q^{86} + 14 q^{87} + 18 q^{88} + 9 q^{89} + 5 q^{90} - 4 q^{91} + 9 q^{92} + 12 q^{93} - q^{94} - 20 q^{95} + 16 q^{96} + 35 q^{97} + 36 q^{98} + 18 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9 + 5 * q^10 + 18 * q^11 + 16 * q^12 - 16 * q^13 + 4 * q^14 + 5 * q^15 + 16 * q^16 + 17 * q^17 + 16 * q^18 + 8 * q^19 + 5 * q^20 + 4 * q^21 + 18 * q^22 + 9 * q^23 + 16 * q^24 + 17 * q^25 - 16 * q^26 + 16 * q^27 + 4 * q^28 + 14 * q^29 + 5 * q^30 + 12 * q^31 + 16 * q^32 + 18 * q^33 + 17 * q^34 + 16 * q^35 + 16 * q^36 + 31 * q^37 + 8 * q^38 - 16 * q^39 + 5 * q^40 + 29 * q^41 + 4 * q^42 + 30 * q^43 + 18 * q^44 + 5 * q^45 + 9 * q^46 - q^47 + 16 * q^48 + 36 * q^49 + 17 * q^50 + 17 * q^51 - 16 * q^52 + 12 * q^53 + 16 * q^54 + 30 * q^55 + 4 * q^56 + 8 * q^57 + 14 * q^58 + 38 * q^59 + 5 * q^60 + 12 * q^62 + 4 * q^63 + 16 * q^64 - 5 * q^65 + 18 * q^66 + 28 * q^67 + 17 * q^68 + 9 * q^69 + 16 * q^70 + 32 * q^71 + 16 * q^72 + 20 * q^73 + 31 * q^74 + 17 * q^75 + 8 * q^76 + 26 * q^77 - 16 * q^78 + 13 * q^79 + 5 * q^80 + 16 * q^81 + 29 * q^82 + 39 * q^83 + 4 * q^84 + 31 * q^85 + 30 * q^86 + 14 * q^87 + 18 * q^88 + 9 * q^89 + 5 * q^90 - 4 * q^91 + 9 * q^92 + 12 * q^93 - q^94 - 20 * q^95 + 16 * q^96 + 35 * q^97 + 36 * q^98 + 18 * 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
$5$	0.808021	0.361358	0.180679	−	0.983542i	$-0.442170\pi$
$5$	0.808021	0.361358	0.180679	+	0.983542i	$0.442170\pi$
$6$	1.00000	0.408248
$7$	3.24300	1.22574	0.612869	−	0.790184i	$-0.290015\pi$
$7$	3.24300	1.22574	0.612869	+	0.790184i	$0.290015\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.808021	0.255519
$11$	4.15216	1.25192	0.625962	−	0.779853i	$-0.284706\pi$
$11$	4.15216	1.25192	0.625962	+	0.779853i	$0.284706\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	3.24300	0.866728
$15$	0.808021	0.208630
$16$	1.00000	0.250000
$17$	7.76632	1.88361	0.941805	−	0.336159i	$-0.109128\pi$
$17$	7.76632	1.88361	0.941805	+	0.336159i	$0.109128\pi$
$18$	1.00000	0.235702
$19$	8.59590	1.97204	0.986018	−	0.166641i	$-0.0532922\pi$
$19$	8.59590	1.97204	0.986018	+	0.166641i	$0.0532922\pi$
$20$	0.808021	0.180679
$21$	3.24300	0.707680
$22$	4.15216	0.885244
$23$	−8.64744	−1.80312	−0.901558	−	0.432657i	$-0.857576\pi$
$23$	−8.64744	−1.80312	−0.901558	+	0.432657i	$0.857576\pi$
$24$	1.00000	0.204124
$25$	−4.34710	−0.869420
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	3.24300	0.612869
$29$	4.23930	0.787219	0.393610	−	0.919278i	$-0.371226\pi$
$29$	4.23930	0.787219	0.393610	+	0.919278i	$0.371226\pi$
$30$	0.808021	0.147524
$31$	−6.26307	−1.12488	−0.562440	−	0.826838i	$-0.690137\pi$
$31$	−6.26307	−1.12488	−0.562440	+	0.826838i	$0.690137\pi$
$32$	1.00000	0.176777
$33$	4.15216	0.722799
$34$	7.76632	1.33191
$35$	2.62041	0.442930
$36$	1.00000	0.166667
$37$	5.67059	0.932239	0.466120	−	0.884722i	$-0.345652\pi$
$37$	5.67059	0.932239	0.466120	+	0.884722i	$0.345652\pi$
$38$	8.59590	1.39444
$39$	−1.00000	−0.160128
$40$	0.808021	0.127759
$41$	1.67856	0.262146	0.131073	−	0.991373i	$-0.458158\pi$
$41$	1.67856	0.262146	0.131073	+	0.991373i	$0.458158\pi$
$42$	3.24300	0.500406
$43$	0.621687	0.0948064	0.0474032	−	0.998876i	$-0.484905\pi$
$43$	0.621687	0.0948064	0.0474032	+	0.998876i	$0.484905\pi$
$44$	4.15216	0.625962
$45$	0.808021	0.120453
$46$	−8.64744	−1.27500
$47$	−10.5592	−1.54022	−0.770108	−	0.637914i	$-0.779798\pi$
$47$	−10.5592	−1.54022	−0.770108	+	0.637914i	$0.779798\pi$
$48$	1.00000	0.144338
$49$	3.51704	0.502434
$50$	−4.34710	−0.614773
$51$	7.76632	1.08750
$52$	−1.00000	−0.138675
$53$	6.13590	0.842831	0.421415	−	0.906868i	$-0.361533\pi$
$53$	6.13590	0.842831	0.421415	+	0.906868i	$0.361533\pi$
$54$	1.00000	0.136083
$55$	3.35504	0.452393
$56$	3.24300	0.433364
$57$	8.59590	1.13856
$58$	4.23930	0.556648
$59$	−12.2258	−1.59167	−0.795835	−	0.605514i	$-0.792968\pi$
$59$	−12.2258	−1.59167	−0.795835	+	0.605514i	$0.792968\pi$
$60$	0.808021	0.104315
$61$	−10.0049	−1.28100	−0.640498	−	0.767960i	$-0.721272\pi$
$61$	−10.0049	−1.28100	−0.640498	+	0.767960i	$0.721272\pi$
$62$	−6.26307	−0.795411
$63$	3.24300	0.408579
$64$	1.00000	0.125000
$65$	−0.808021	−0.100223
$66$	4.15216	0.511096
$67$	−11.2176	−1.37045	−0.685227	−	0.728330i	$-0.740297\pi$
$67$	−11.2176	−1.37045	−0.685227	+	0.728330i	$0.740297\pi$
$68$	7.76632	0.941805
$69$	−8.64744	−1.04103
$70$	2.62041	0.313199
$71$	4.12480	0.489524	0.244762	−	0.969583i	$-0.421290\pi$
$71$	4.12480	0.489524	0.244762	+	0.969583i	$0.421290\pi$
$72$	1.00000	0.117851
$73$	13.8673	1.62305	0.811525	−	0.584318i	$-0.198638\pi$
$73$	13.8673	1.62305	0.811525	+	0.584318i	$0.198638\pi$
$74$	5.67059	0.659193
$75$	−4.34710	−0.501960
$76$	8.59590	0.986018
$77$	13.4655	1.53453
$78$	−1.00000	−0.113228
$79$	−14.1068	−1.58714	−0.793568	−	0.608482i	$-0.791779\pi$
$79$	−14.1068	−1.58714	−0.793568	+	0.608482i	$0.791779\pi$
$80$	0.808021	0.0903395
$81$	1.00000	0.111111
$82$	1.67856	0.185366
$83$	−14.9176	−1.63742	−0.818709	−	0.574208i	$-0.805310\pi$
$83$	−14.9176	−1.63742	−0.818709	+	0.574208i	$0.805310\pi$
$84$	3.24300	0.353840
$85$	6.27535	0.680658
$86$	0.621687	0.0670383
$87$	4.23930	0.454501
$88$	4.15216	0.442622
$89$	−8.36437	−0.886622	−0.443311	−	0.896368i	$-0.646196\pi$
$89$	−8.36437	−0.886622	−0.443311	+	0.896368i	$0.646196\pi$
$90$	0.808021	0.0851729
$91$	−3.24300	−0.339959
$92$	−8.64744	−0.901558
$93$	−6.26307	−0.649450
$94$	−10.5592	−1.08910
$95$	6.94567	0.712611
$96$	1.00000	0.102062
$97$	3.02487	0.307129	0.153564	−	0.988139i	$-0.450925\pi$
$97$	3.02487	0.307129	0.153564	+	0.988139i	$0.450925\pi$
$98$	3.51704	0.355275
$99$	4.15216	0.417308
$100$	−4.34710	−0.434710
$101$	12.2137	1.21531	0.607653	−	0.794202i	$-0.292111\pi$
$101$	12.2137	1.21531	0.607653	+	0.794202i	$0.292111\pi$
$102$	7.76632	0.768981
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	2.62041	0.255726
$106$	6.13590	0.595971
$107$	0.530297	0.0512657	0.0256328	−	0.999671i	$-0.491840\pi$
$107$	0.530297	0.0512657	0.0256328	+	0.999671i	$0.491840\pi$
$108$	1.00000	0.0962250
$109$	−1.40297	−0.134380	−0.0671902	−	0.997740i	$-0.521403\pi$
$109$	−1.40297	−0.134380	−0.0671902	+	0.997740i	$0.521403\pi$
$110$	3.35504	0.319890
$111$	5.67059	0.538228
$112$	3.24300	0.306435
$113$	−15.9476	−1.50022	−0.750111	−	0.661312i	$-0.770000\pi$
$113$	−15.9476	−1.50022	−0.750111	+	0.661312i	$0.770000\pi$
$114$	8.59590	0.805080
$115$	−6.98732	−0.651571
$116$	4.23930	0.393610
$117$	−1.00000	−0.0924500
$118$	−12.2258	−1.12548
$119$	25.1862	2.30881
$120$	0.808021	0.0737619
$121$	6.24047	0.567316
$122$	−10.0049	−0.905801
$123$	1.67856	0.151350
$124$	−6.26307	−0.562440
$125$	−7.55266	−0.675530
$126$	3.24300	0.288909
$127$	−5.15738	−0.457644	−0.228822	−	0.973468i	$-0.573487\pi$
$127$	−5.15738	−0.457644	−0.228822	+	0.973468i	$0.573487\pi$
$128$	1.00000	0.0883883
$129$	0.621687	0.0547365
$130$	−0.808021	−0.0708681
$131$	0.509744	0.0445366	0.0222683	−	0.999752i	$-0.492911\pi$
$131$	0.509744	0.0445366	0.0222683	+	0.999752i	$0.492911\pi$
$132$	4.15216	0.361400
$133$	27.8765	2.41720
$134$	−11.2176	−0.969057
$135$	0.808021	0.0695434
$136$	7.76632	0.665957
$137$	−8.22378	−0.702605	−0.351302	−	0.936262i	$-0.614261\pi$
$137$	−8.22378	−0.702605	−0.351302	+	0.936262i	$0.614261\pi$
$138$	−8.64744	−0.736119
$139$	−14.5980	−1.23819	−0.619094	−	0.785317i	$-0.712500\pi$
$139$	−14.5980	−1.23819	−0.619094	+	0.785317i	$0.712500\pi$
$140$	2.62041	0.221465
$141$	−10.5592	−0.889244
$142$	4.12480	0.346146
$143$	−4.15216	−0.347221
$144$	1.00000	0.0833333
$145$	3.42545	0.284468
$146$	13.8673	1.14767
$147$	3.51704	0.290081
$148$	5.67059	0.466120
$149$	−3.96159	−0.324546	−0.162273	−	0.986746i	$-0.551883\pi$
$149$	−3.96159	−0.324546	−0.162273	+	0.986746i	$0.551883\pi$
$150$	−4.34710	−0.354939
$151$	−2.69321	−0.219171	−0.109585	−	0.993977i	$-0.534952\pi$
$151$	−2.69321	−0.219171	−0.109585	+	0.993977i	$0.534952\pi$
$152$	8.59590	0.697220
$153$	7.76632	0.627870
$154$	13.4655	1.08508
$155$	−5.06069	−0.406485
$156$	−1.00000	−0.0800641
$157$	−18.1386	−1.44762	−0.723809	−	0.690000i	$-0.757610\pi$
$157$	−18.1386	−1.44762	−0.723809	+	0.690000i	$0.757610\pi$
$158$	−14.1068	−1.12227
$159$	6.13590	0.486609
$160$	0.808021	0.0638797
$161$	−28.0436	−2.21015
$162$	1.00000	0.0785674
$163$	15.9190	1.24687	0.623436	−	0.781874i	$-0.285736\pi$
$163$	15.9190	1.24687	0.623436	+	0.781874i	$0.285736\pi$
$164$	1.67856	0.131073
$165$	3.35504	0.261189
$166$	−14.9176	−1.15783
$167$	21.7955	1.68658	0.843292	−	0.537456i	$-0.180614\pi$
$167$	21.7955	1.68658	0.843292	+	0.537456i	$0.180614\pi$
$168$	3.24300	0.250203
$169$	1.00000	0.0769231
$170$	6.27535	0.481298
$171$	8.59590	0.657345
$172$	0.621687	0.0474032
$173$	−7.22504	−0.549310	−0.274655	−	0.961543i	$-0.588564\pi$
$173$	−7.22504	−0.549310	−0.274655	+	0.961543i	$0.588564\pi$
$174$	4.23930	0.321381
$175$	−14.0976	−1.06568
$176$	4.15216	0.312981
$177$	−12.2258	−0.918951
$178$	−8.36437	−0.626936
$179$	1.51059	0.112907	0.0564534	−	0.998405i	$-0.482021\pi$
$179$	1.51059	0.112907	0.0564534	+	0.998405i	$0.482021\pi$
$180$	0.808021	0.0602263
$181$	4.03456	0.299886	0.149943	−	0.988695i	$-0.452091\pi$
$181$	4.03456	0.299886	0.149943	+	0.988695i	$0.452091\pi$
$182$	−3.24300	−0.240387
$183$	−10.0049	−0.739583
$184$	−8.64744	−0.637498
$185$	4.58196	0.336872
$186$	−6.26307	−0.459230
$187$	32.2471	2.35814
$188$	−10.5592	−0.770108
$189$	3.24300	0.235893
$190$	6.94567	0.503892
$191$	11.5886	0.838518	0.419259	−	0.907867i	$-0.362290\pi$
$191$	11.5886	0.838518	0.419259	+	0.907867i	$0.362290\pi$
$192$	1.00000	0.0721688
$193$	−1.16862	−0.0841194	−0.0420597	−	0.999115i	$-0.513392\pi$
$193$	−1.16862	−0.0841194	−0.0420597	+	0.999115i	$0.513392\pi$
$194$	3.02487	0.217173
$195$	−0.808021	−0.0578636
$196$	3.51704	0.251217
$197$	−22.7068	−1.61780	−0.808898	−	0.587950i	$-0.799935\pi$
$197$	−22.7068	−1.61780	−0.808898	+	0.587950i	$0.799935\pi$
$198$	4.15216	0.295081
$199$	−21.8807	−1.55108	−0.775541	−	0.631297i	$-0.782523\pi$
$199$	−21.8807	−1.55108	−0.775541	+	0.631297i	$0.782523\pi$
$200$	−4.34710	−0.307387
$201$	−11.2176	−0.791232
$202$	12.2137	0.859352
$203$	13.7481	0.964924
$204$	7.76632	0.543751
$205$	1.35631	0.0947287
$206$	1.00000	0.0696733
$207$	−8.64744	−0.601039
$208$	−1.00000	−0.0693375
$209$	35.6916	2.46884
$210$	2.62041	0.180826
$211$	0.590099	0.0406241	0.0203120	−	0.999794i	$-0.493534\pi$
$211$	0.590099	0.0406241	0.0203120	+	0.999794i	$0.493534\pi$
$212$	6.13590	0.421415
$213$	4.12480	0.282627
$214$	0.530297	0.0362503
$215$	0.502336	0.0342591
$216$	1.00000	0.0680414
$217$	−20.3111	−1.37881
$218$	−1.40297	−0.0950213
$219$	13.8673	0.937068
$220$	3.35504	0.226197
$221$	−7.76632	−0.522419
$222$	5.67059	0.380585
$223$	23.7424	1.58991	0.794954	−	0.606670i	$-0.207495\pi$
$223$	23.7424	1.58991	0.794954	+	0.606670i	$0.207495\pi$
$224$	3.24300	0.216682
$225$	−4.34710	−0.289807
$226$	−15.9476	−1.06082
$227$	−2.77610	−0.184256	−0.0921280	−	0.995747i	$-0.529367\pi$
$227$	−2.77610	−0.184256	−0.0921280	+	0.995747i	$0.529367\pi$
$228$	8.59590	0.569278
$229$	−26.2266	−1.73310	−0.866551	−	0.499089i	$-0.833668\pi$
$229$	−26.2266	−1.73310	−0.866551	+	0.499089i	$0.833668\pi$
$230$	−6.98732	−0.460730
$231$	13.4655	0.885962
$232$	4.23930	0.278324
$233$	2.40864	0.157795	0.0788975	−	0.996883i	$-0.474860\pi$
$233$	2.40864	0.157795	0.0788975	+	0.996883i	$0.474860\pi$
$234$	−1.00000	−0.0653720
$235$	−8.53204	−0.556569
$236$	−12.2258	−0.795835
$237$	−14.1068	−0.916333
$238$	25.1862	1.63258
$239$	6.82164	0.441255	0.220628	−	0.975358i	$-0.429189\pi$
$239$	6.82164	0.441255	0.220628	+	0.975358i	$0.429189\pi$
$240$	0.808021	0.0521575
$241$	26.0809	1.68002	0.840011	−	0.542570i	$-0.182549\pi$
$241$	26.0809	1.68002	0.840011	+	0.542570i	$0.182549\pi$
$242$	6.24047	0.401153
$243$	1.00000	0.0641500
$244$	−10.0049	−0.640498
$245$	2.84184	0.181559
$246$	1.67856	0.107021
$247$	−8.59590	−0.546944
$248$	−6.26307	−0.397705
$249$	−14.9176	−0.945364
$250$	−7.55266	−0.477672
$251$	−1.74155	−0.109925	−0.0549627	−	0.998488i	$-0.517504\pi$
$251$	−1.74155	−0.109925	−0.0549627	+	0.998488i	$0.517504\pi$
$252$	3.24300	0.204290
$253$	−35.9056	−2.25737
$254$	−5.15738	−0.323603
$255$	6.27535	0.392978
$256$	1.00000	0.0625000
$257$	12.3840	0.772495	0.386247	−	0.922395i	$-0.373771\pi$
$257$	12.3840	0.772495	0.386247	+	0.922395i	$0.373771\pi$
$258$	0.621687	0.0387046
$259$	18.3897	1.14268
$260$	−0.808021	−0.0501113
$261$	4.23930	0.262406
$262$	0.509744	0.0314921
$263$	14.1956	0.875339	0.437670	−	0.899136i	$-0.355804\pi$
$263$	14.1956	0.875339	0.437670	+	0.899136i	$0.355804\pi$
$264$	4.15216	0.255548
$265$	4.95794	0.304564
$266$	27.8765	1.70922
$267$	−8.36437	−0.511891
$268$	−11.2176	−0.685227
$269$	2.89416	0.176460	0.0882300	−	0.996100i	$-0.471879\pi$
$269$	2.89416	0.176460	0.0882300	+	0.996100i	$0.471879\pi$
$270$	0.808021	0.0491746
$271$	−3.63848	−0.221022	−0.110511	−	0.993875i	$-0.535249\pi$
$271$	−3.63848	−0.221022	−0.110511	+	0.993875i	$0.535249\pi$
$272$	7.76632	0.470903
$273$	−3.24300	−0.196275
$274$	−8.22378	−0.496816
$275$	−18.0499	−1.08845
$276$	−8.64744	−0.520515
$277$	24.7013	1.48416	0.742080	−	0.670312i	$-0.233840\pi$
$277$	24.7013	1.48416	0.742080	+	0.670312i	$0.233840\pi$
$278$	−14.5980	−0.875531
$279$	−6.26307	−0.374960
$280$	2.62041	0.156600
$281$	7.92008	0.472473	0.236236	−	0.971696i	$-0.424086\pi$
$281$	7.92008	0.472473	0.236236	+	0.971696i	$0.424086\pi$
$282$	−10.5592	−0.628790
$283$	21.6308	1.28582	0.642910	−	0.765942i	$-0.277727\pi$
$283$	21.6308	1.28582	0.642910	+	0.765942i	$0.277727\pi$
$284$	4.12480	0.244762
$285$	6.94567	0.411426
$286$	−4.15216	−0.245523
$287$	5.44355	0.321323
$288$	1.00000	0.0589256
$289$	43.3158	2.54799
$290$	3.42545	0.201149
$291$	3.02487	0.177321
$292$	13.8673	0.811525
$293$	10.9756	0.641203	0.320601	−	0.947214i	$-0.396115\pi$
$293$	10.9756	0.641203	0.320601	+	0.947214i	$0.396115\pi$
$294$	3.51704	0.205118
$295$	−9.87874	−0.575163
$296$	5.67059	0.329596
$297$	4.15216	0.240933
$298$	−3.96159	−0.229489
$299$	8.64744	0.500095
$300$	−4.34710	−0.250980
$301$	2.01613	0.116208
$302$	−2.69321	−0.154977
$303$	12.2137	0.701658
$304$	8.59590	0.493009
$305$	−8.08417	−0.462898
$306$	7.76632	0.443971
$307$	−14.0960	−0.804504	−0.402252	−	0.915529i	$-0.631772\pi$
$307$	−14.0960	−0.804504	−0.402252	+	0.915529i	$0.631772\pi$
$308$	13.4655	0.767266
$309$	1.00000	0.0568880
$310$	−5.06069	−0.287428
$311$	−5.20425	−0.295106	−0.147553	−	0.989054i	$-0.547140\pi$
$311$	−5.20425	−0.295106	−0.147553	+	0.989054i	$0.547140\pi$
$312$	−1.00000	−0.0566139
$313$	4.00558	0.226409	0.113204	−	0.993572i	$-0.463889\pi$
$313$	4.00558	0.226409	0.113204	+	0.993572i	$0.463889\pi$
$314$	−18.1386	−1.02362
$315$	2.62041	0.147643
$316$	−14.1068	−0.793568
$317$	−3.26012	−0.183106	−0.0915532	−	0.995800i	$-0.529183\pi$
$317$	−3.26012	−0.183106	−0.0915532	+	0.995800i	$0.529183\pi$
$318$	6.13590	0.344084
$319$	17.6023	0.985539
$320$	0.808021	0.0451698
$321$	0.530297	0.0295983
$322$	−28.0436	−1.56281
$323$	66.7586	3.71455
$324$	1.00000	0.0555556
$325$	4.34710	0.241134
$326$	15.9190	0.881672
$327$	−1.40297	−0.0775846
$328$	1.67856	0.0926828
$329$	−34.2434	−1.88790
$330$	3.35504	0.184689
$331$	−2.80347	−0.154092	−0.0770462	−	0.997028i	$-0.524549\pi$
$331$	−2.80347	−0.154092	−0.0770462	+	0.997028i	$0.524549\pi$
$332$	−14.9176	−0.818709
$333$	5.67059	0.310746
$334$	21.7955	1.19259
$335$	−9.06409	−0.495224
$336$	3.24300	0.176920
$337$	−9.53649	−0.519486	−0.259743	−	0.965678i	$-0.583638\pi$
$337$	−9.53649	−0.519486	−0.259743	+	0.965678i	$0.583638\pi$
$338$	1.00000	0.0543928
$339$	−15.9476	−0.866154
$340$	6.27535	0.340329
$341$	−26.0053	−1.40827
$342$	8.59590	0.464813
$343$	−11.2952	−0.609885
$344$	0.621687	0.0335191
$345$	−6.98732	−0.376185
$346$	−7.22504	−0.388421
$347$	8.47381	0.454898	0.227449	−	0.973790i	$-0.426962\pi$
$347$	8.47381	0.454898	0.227449	+	0.973790i	$0.426962\pi$
$348$	4.23930	0.227251
$349$	−12.1276	−0.649173	−0.324586	−	0.945856i	$-0.605225\pi$
$349$	−12.1276	−0.649173	−0.324586	+	0.945856i	$0.605225\pi$
$350$	−14.0976	−0.753551
$351$	−1.00000	−0.0533761
$352$	4.15216	0.221311
$353$	2.41300	0.128431	0.0642156	−	0.997936i	$-0.479545\pi$
$353$	2.41300	0.128431	0.0642156	+	0.997936i	$0.479545\pi$
$354$	−12.2258	−0.649796
$355$	3.33293	0.176893
$356$	−8.36437	−0.443311
$357$	25.1862	1.33299
$358$	1.51059	0.0798372
$359$	−4.29733	−0.226804	−0.113402	−	0.993549i	$-0.536175\pi$
$359$	−4.29733	−0.226804	−0.113402	+	0.993549i	$0.536175\pi$
$360$	0.808021	0.0425864
$361$	54.8895	2.88892
$362$	4.03456	0.212052
$363$	6.24047	0.327540
$364$	−3.24300	−0.169979
$365$	11.2051	0.586502
$366$	−10.0049	−0.522964
$367$	9.13736	0.476966	0.238483	−	0.971147i	$-0.423350\pi$
$367$	9.13736	0.476966	0.238483	+	0.971147i	$0.423350\pi$
$368$	−8.64744	−0.450779
$369$	1.67856	0.0873821
$370$	4.58196	0.238205
$371$	19.8987	1.03309
$372$	−6.26307	−0.324725
$373$	16.1454	0.835979	0.417990	−	0.908452i	$-0.362735\pi$
$373$	16.1454	0.835979	0.417990	+	0.908452i	$0.362735\pi$
$374$	32.2471	1.66746
$375$	−7.55266	−0.390017
$376$	−10.5592	−0.544548
$377$	−4.23930	−0.218335
$378$	3.24300	0.166802
$379$	−25.5292	−1.31135	−0.655673	−	0.755045i	$-0.727615\pi$
$379$	−25.5292	−1.31135	−0.655673	+	0.755045i	$0.727615\pi$
$380$	6.94567	0.356305
$381$	−5.15738	−0.264221
$382$	11.5886	0.592922
$383$	27.4748	1.40390	0.701948	−	0.712229i	$-0.252314\pi$
$383$	27.4748	1.40390	0.701948	+	0.712229i	$0.252314\pi$
$384$	1.00000	0.0510310
$385$	10.8804	0.554515
$386$	−1.16862	−0.0594814
$387$	0.621687	0.0316021
$388$	3.02487	0.153564
$389$	9.21329	0.467132	0.233566	−	0.972341i	$-0.424960\pi$
$389$	9.21329	0.467132	0.233566	+	0.972341i	$0.424960\pi$
$390$	−0.808021	−0.0409157
$391$	−67.1589	−3.39637
$392$	3.51704	0.177637
$393$	0.509744	0.0257132
$394$	−22.7068	−1.14395
$395$	−11.3986	−0.573524
$396$	4.15216	0.208654
$397$	−1.52055	−0.0763142	−0.0381571	−	0.999272i	$-0.512149\pi$
$397$	−1.52055	−0.0763142	−0.0381571	+	0.999272i	$0.512149\pi$
$398$	−21.8807	−1.09678
$399$	27.8765	1.39557
$400$	−4.34710	−0.217355
$401$	5.91594	0.295428	0.147714	−	0.989030i	$-0.452809\pi$
$401$	5.91594	0.295428	0.147714	+	0.989030i	$0.452809\pi$
$402$	−11.2176	−0.559485
$403$	6.26307	0.311986
$404$	12.2137	0.607653
$405$	0.808021	0.0401509
$406$	13.7481	0.682305
$407$	23.5452	1.16709
$408$	7.76632	0.384490
$409$	−16.6091	−0.821268	−0.410634	−	0.911800i	$-0.634693\pi$
$409$	−16.6091	−0.821268	−0.410634	+	0.911800i	$0.634693\pi$
$410$	1.35631	0.0669833
$411$	−8.22378	−0.405649
$412$	1.00000	0.0492665
$413$	−39.6484	−1.95097
$414$	−8.64744	−0.424999
$415$	−12.0537	−0.591694
$416$	−1.00000	−0.0490290
$417$	−14.5980	−0.714868
$418$	35.6916	1.74573
$419$	1.71675	0.0838686	0.0419343	−	0.999120i	$-0.486648\pi$
$419$	1.71675	0.0838686	0.0419343	+	0.999120i	$0.486648\pi$
$420$	2.62041	0.127863
$421$	−32.9663	−1.60668	−0.803340	−	0.595520i	$-0.796946\pi$
$421$	−32.9663	−1.60668	−0.803340	+	0.595520i	$0.796946\pi$
$422$	0.590099	0.0287256
$423$	−10.5592	−0.513405
$424$	6.13590	0.297986
$425$	−33.7610	−1.63765
$426$	4.12480	0.199847
$427$	−32.4459	−1.57017
$428$	0.530297	0.0256328
$429$	−4.15216	−0.200468
$430$	0.502336	0.0242248
$431$	23.5251	1.13317	0.566583	−	0.824005i	$-0.308265\pi$
$431$	23.5251	1.13317	0.566583	+	0.824005i	$0.308265\pi$
$432$	1.00000	0.0481125
$433$	26.4575	1.27146	0.635732	−	0.771910i	$-0.280698\pi$
$433$	26.4575	1.27146	0.635732	+	0.771910i	$0.280698\pi$
$434$	−20.3111	−0.974965
$435$	3.42545	0.164238
$436$	−1.40297	−0.0671902
$437$	−74.3326	−3.55581
$438$	13.8673	0.662607
$439$	−1.55491	−0.0742118	−0.0371059	−	0.999311i	$-0.511814\pi$
$439$	−1.55491	−0.0742118	−0.0371059	+	0.999311i	$0.511814\pi$
$440$	3.35504	0.159945
$441$	3.51704	0.167478
$442$	−7.76632	−0.369406
$443$	3.72538	0.176998	0.0884990	−	0.996076i	$-0.471793\pi$
$443$	3.72538	0.176998	0.0884990	+	0.996076i	$0.471793\pi$
$444$	5.67059	0.269114
$445$	−6.75859	−0.320388
$446$	23.7424	1.12423
$447$	−3.96159	−0.187377
$448$	3.24300	0.153217
$449$	26.2702	1.23977	0.619884	−	0.784694i	$-0.287180\pi$
$449$	26.2702	1.23977	0.619884	+	0.784694i	$0.287180\pi$
$450$	−4.34710	−0.204924
$451$	6.96964	0.328188
$452$	−15.9476	−0.750111
$453$	−2.69321	−0.126538
$454$	−2.77610	−0.130289
$455$	−2.62041	−0.122847
$456$	8.59590	0.402540
$457$	−17.1670	−0.803037	−0.401518	−	0.915851i	$-0.631517\pi$
$457$	−17.1670	−0.803037	−0.401518	+	0.915851i	$0.631517\pi$
$458$	−26.2266	−1.22549
$459$	7.76632	0.362501
$460$	−6.98732	−0.325785
$461$	−2.59128	−0.120688	−0.0603439	−	0.998178i	$-0.519220\pi$
$461$	−2.59128	−0.120688	−0.0603439	+	0.998178i	$0.519220\pi$
$462$	13.4655	0.626470
$463$	−30.8714	−1.43472	−0.717358	−	0.696705i	$-0.754649\pi$
$463$	−30.8714	−1.43472	−0.717358	+	0.696705i	$0.754649\pi$
$464$	4.23930	0.196805
$465$	−5.06069	−0.234684
$466$	2.40864	0.111578
$467$	19.7850	0.915541	0.457771	−	0.889070i	$-0.348648\pi$
$467$	19.7850	0.915541	0.457771	+	0.889070i	$0.348648\pi$
$468$	−1.00000	−0.0462250
$469$	−36.3788	−1.67982
$470$	−8.53204	−0.393554
$471$	−18.1386	−0.835783
$472$	−12.2258	−0.562740
$473$	2.58135	0.118691
$474$	−14.1068	−0.647945
$475$	−37.3673	−1.71453
$476$	25.1862	1.15441
$477$	6.13590	0.280944
$478$	6.82164	0.312015
$479$	−10.1618	−0.464306	−0.232153	−	0.972679i	$-0.574577\pi$
$479$	−10.1618	−0.464306	−0.232153	+	0.972679i	$0.574577\pi$
$480$	0.808021	0.0368809
$481$	−5.67059	−0.258557
$482$	26.0809	1.18795
$483$	−28.0436	−1.27603
$484$	6.24047	0.283658
$485$	2.44416	0.110983
$486$	1.00000	0.0453609
$487$	−39.4004	−1.78540	−0.892702	−	0.450647i	$-0.851193\pi$
$487$	−39.4004	−1.78540	−0.892702	+	0.450647i	$0.851193\pi$
$488$	−10.0049	−0.452900
$489$	15.9190	0.719882
$490$	2.84184	0.128381
$491$	26.2570	1.18496	0.592480	−	0.805585i	$-0.298149\pi$
$491$	26.2570	1.18496	0.592480	+	0.805585i	$0.298149\pi$
$492$	1.67856	0.0756752
$493$	32.9238	1.48281
$494$	−8.59590	−0.386748
$495$	3.35504	0.150798
$496$	−6.26307	−0.281220
$497$	13.3767	0.600028
$498$	−14.9176	−0.668473
$499$	−6.57128	−0.294171	−0.147086	−	0.989124i	$-0.546989\pi$
$499$	−6.57128	−0.294171	−0.147086	+	0.989124i	$0.546989\pi$
$500$	−7.55266	−0.337765
$501$	21.7955	0.973750
$502$	−1.74155	−0.0777290
$503$	40.4174	1.80212	0.901062	−	0.433690i	$-0.142789\pi$
$503$	40.4174	1.80212	0.901062	+	0.433690i	$0.142789\pi$
$504$	3.24300	0.144455
$505$	9.86891	0.439161
$506$	−35.9056	−1.59620
$507$	1.00000	0.0444116
$508$	−5.15738	−0.228822
$509$	−9.13173	−0.404757	−0.202378	−	0.979307i	$-0.564867\pi$
$509$	−9.13173	−0.404757	−0.202378	+	0.979307i	$0.564867\pi$
$510$	6.27535	0.277877
$511$	44.9718	1.98943
$512$	1.00000	0.0441942
$513$	8.59590	0.379518
$514$	12.3840	0.546236
$515$	0.808021	0.0356057
$516$	0.621687	0.0273683
$517$	−43.8435	−1.92823
$518$	18.3897	0.807997
$519$	−7.22504	−0.317144
$520$	−0.808021	−0.0354341
$521$	13.9197	0.609832	0.304916	−	0.952379i	$-0.401372\pi$
$521$	13.9197	0.609832	0.304916	+	0.952379i	$0.401372\pi$
$522$	4.23930	0.185549
$523$	6.81800	0.298131	0.149065	−	0.988827i	$-0.452374\pi$
$523$	6.81800	0.298131	0.149065	+	0.988827i	$0.452374\pi$
$524$	0.509744	0.0222683
$525$	−14.0976	−0.615272
$526$	14.1956	0.618958
$527$	−48.6410	−2.11884
$528$	4.15216	0.180700
$529$	51.7783	2.25123
$530$	4.95794	0.215359
$531$	−12.2258	−0.530557
$532$	27.8765	1.20860
$533$	−1.67856	−0.0727063
$534$	−8.36437	−0.361962
$535$	0.428491	0.0185253
$536$	−11.2176	−0.484529
$537$	1.51059	0.0651868
$538$	2.89416	0.124776
$539$	14.6033	0.629010
$540$	0.808021	0.0347717
$541$	−36.1087	−1.55243	−0.776216	−	0.630467i	$-0.782863\pi$
$541$	−36.1087	−1.55243	−0.776216	+	0.630467i	$0.782863\pi$
$542$	−3.63848	−0.156286
$543$	4.03456	0.173139
$544$	7.76632	0.332978
$545$	−1.13363	−0.0485595
$546$	−3.24300	−0.138788
$547$	−21.2363	−0.907997	−0.453999	−	0.891002i	$-0.650003\pi$
$547$	−21.2363	−0.907997	−0.453999	+	0.891002i	$0.650003\pi$
$548$	−8.22378	−0.351302
$549$	−10.0049	−0.426999
$550$	−18.0499	−0.769650
$551$	36.4406	1.55242
$552$	−8.64744	−0.368060
$553$	−45.7482	−1.94541
$554$	24.7013	1.04946
$555$	4.58196	0.194493
$556$	−14.5980	−0.619094
$557$	−34.7050	−1.47050	−0.735250	−	0.677796i	$-0.762935\pi$
$557$	−34.7050	−1.47050	−0.735250	+	0.677796i	$0.762935\pi$
$558$	−6.26307	−0.265137
$559$	−0.621687	−0.0262946
$560$	2.62041	0.110733
$561$	32.2471	1.36147
$562$	7.92008	0.334089
$563$	−23.1255	−0.974622	−0.487311	−	0.873228i	$-0.662022\pi$
$563$	−23.1255	−0.974622	−0.487311	+	0.873228i	$0.662022\pi$
$564$	−10.5592	−0.444622
$565$	−12.8860	−0.542117
$566$	21.6308	0.909212
$567$	3.24300	0.136193
$568$	4.12480	0.173073
$569$	31.6380	1.32634	0.663168	−	0.748471i	$-0.269212\pi$
$569$	31.6380	1.32634	0.663168	+	0.748471i	$0.269212\pi$
$570$	6.94567	0.290922
$571$	14.9369	0.625089	0.312544	−	0.949903i	$-0.398819\pi$
$571$	14.9369	0.625089	0.312544	+	0.949903i	$0.398819\pi$
$572$	−4.15216	−0.173611
$573$	11.5886	0.484119
$574$	5.44355	0.227210
$575$	37.5913	1.56767
$576$	1.00000	0.0416667
$577$	25.2735	1.05215	0.526074	−	0.850439i	$-0.323663\pi$
$577$	25.2735	1.05215	0.526074	+	0.850439i	$0.323663\pi$
$578$	43.3158	1.80170
$579$	−1.16862	−0.0485663
$580$	3.42545	0.142234
$581$	−48.3777	−2.00705
$582$	3.02487	0.125385
$583$	25.4773	1.05516
$584$	13.8673	0.573835
$585$	−0.808021	−0.0334076
$586$	10.9756	0.453399
$587$	17.8524	0.736846	0.368423	−	0.929658i	$-0.379898\pi$
$587$	17.8524	0.736846	0.368423	+	0.929658i	$0.379898\pi$
$588$	3.51704	0.145040
$589$	−53.8367	−2.21830
$590$	−9.87874	−0.406701
$591$	−22.7068	−0.934035
$592$	5.67059	0.233060
$593$	44.5806	1.83071	0.915353	−	0.402653i	$-0.131912\pi$
$593$	44.5806	1.83071	0.915353	+	0.402653i	$0.131912\pi$
$594$	4.15216	0.170365
$595$	20.3510	0.834308
$596$	−3.96159	−0.162273
$597$	−21.8807	−0.895517
$598$	8.64744	0.353620
$599$	−5.96523	−0.243733	−0.121866	−	0.992547i	$-0.538888\pi$
$599$	−5.96523	−0.243733	−0.121866	+	0.992547i	$0.538888\pi$
$600$	−4.34710	−0.177470
$601$	26.5651	1.08361	0.541806	−	0.840504i	$-0.317741\pi$
$601$	26.5651	1.08361	0.541806	+	0.840504i	$0.317741\pi$
$602$	2.01613	0.0821714
$603$	−11.2176	−0.456818
$604$	−2.69321	−0.109585
$605$	5.04243	0.205004
$606$	12.2137	0.496147
$607$	−24.3019	−0.986383	−0.493192	−	0.869921i	$-0.664170\pi$
$607$	−24.3019	−0.986383	−0.493192	+	0.869921i	$0.664170\pi$
$608$	8.59590	0.348610
$609$	13.7481	0.557099
$610$	−8.08417	−0.327318
$611$	10.5592	0.427179
$612$	7.76632	0.313935
$613$	−0.617576	−0.0249437	−0.0124718	−	0.999922i	$-0.503970\pi$
$613$	−0.617576	−0.0249437	−0.0124718	+	0.999922i	$0.503970\pi$
$614$	−14.0960	−0.568870
$615$	1.35631	0.0546916
$616$	13.4655	0.542539
$617$	−22.5973	−0.909732	−0.454866	−	0.890560i	$-0.650313\pi$
$617$	−22.5973	−0.909732	−0.454866	+	0.890560i	$0.650313\pi$
$618$	1.00000	0.0402259
$619$	−32.9642	−1.32494	−0.662472	−	0.749086i	$-0.730493\pi$
$619$	−32.9642	−1.32494	−0.662472	+	0.749086i	$0.730493\pi$
$620$	−5.06069	−0.203242
$621$	−8.64744	−0.347010
$622$	−5.20425	−0.208672
$623$	−27.1256	−1.08677
$624$	−1.00000	−0.0400320
$625$	15.6328	0.625312
$626$	4.00558	0.160095
$627$	35.6916	1.42539
$628$	−18.1386	−0.723809
$629$	44.0396	1.75598
$630$	2.62041	0.104400
$631$	35.3071	1.40555	0.702777	−	0.711410i	$-0.251943\pi$
$631$	35.3071	1.40555	0.702777	+	0.711410i	$0.251943\pi$
$632$	−14.1068	−0.561137
$633$	0.590099	0.0234543
$634$	−3.26012	−0.129476
$635$	−4.16728	−0.165373
$636$	6.13590	0.243304
$637$	−3.51704	−0.139350
$638$	17.6023	0.696881
$639$	4.12480	0.163175
$640$	0.808021	0.0319398
$641$	−6.18105	−0.244137	−0.122068	−	0.992522i	$-0.538953\pi$
$641$	−6.18105	−0.244137	−0.122068	+	0.992522i	$0.538953\pi$
$642$	0.530297	0.0209291
$643$	35.9717	1.41859	0.709293	−	0.704914i	$-0.249014\pi$
$643$	35.9717	1.41859	0.709293	+	0.704914i	$0.249014\pi$
$644$	−28.0436	−1.10507
$645$	0.502336	0.0197795
$646$	66.7586	2.62658
$647$	−25.7896	−1.01389	−0.506946	−	0.861978i	$-0.669226\pi$
$647$	−25.7896	−1.01389	−0.506946	+	0.861978i	$0.669226\pi$
$648$	1.00000	0.0392837
$649$	−50.7637	−1.99265
$650$	4.34710	0.170507
$651$	−20.3111	−0.796056
$652$	15.9190	0.623436
$653$	−6.09455	−0.238498	−0.119249	−	0.992864i	$-0.538049\pi$
$653$	−6.09455	−0.238498	−0.119249	+	0.992864i	$0.538049\pi$
$654$	−1.40297	−0.0548606
$655$	0.411884	0.0160936
$656$	1.67856	0.0655366
$657$	13.8673	0.541017
$658$	−34.2434	−1.33495
$659$	8.89271	0.346411	0.173205	−	0.984886i	$-0.444588\pi$
$659$	8.89271	0.346411	0.173205	+	0.984886i	$0.444588\pi$
$660$	3.35504	0.130595
$661$	41.6401	1.61961	0.809806	−	0.586698i	$-0.199573\pi$
$661$	41.6401	1.61961	0.809806	+	0.586698i	$0.199573\pi$
$662$	−2.80347	−0.108960
$663$	−7.76632	−0.301619
$664$	−14.9176	−0.578915
$665$	22.5248	0.873474
$666$	5.67059	0.219731
$667$	−36.6591	−1.41945
$668$	21.7955	0.843292
$669$	23.7424	0.917934
$670$	−9.06409	−0.350177
$671$	−41.5420	−1.60371
$672$	3.24300	0.125101
$673$	−5.75620	−0.221885	−0.110943	−	0.993827i	$-0.535387\pi$
$673$	−5.75620	−0.221885	−0.110943	+	0.993827i	$0.535387\pi$
$674$	−9.53649	−0.367332
$675$	−4.34710	−0.167320
$676$	1.00000	0.0384615
$677$	49.1410	1.88864	0.944321	−	0.329027i	$-0.106721\pi$
$677$	49.1410	1.88864	0.944321	+	0.329027i	$0.106721\pi$
$678$	−15.9476	−0.612463
$679$	9.80964	0.376459
$680$	6.27535	0.240649
$681$	−2.77610	−0.106380
$682$	−26.0053	−0.995794
$683$	−22.0907	−0.845278	−0.422639	−	0.906298i	$-0.638896\pi$
$683$	−22.0907	−0.845278	−0.422639	+	0.906298i	$0.638896\pi$
$684$	8.59590	0.328673
$685$	−6.64498	−0.253892
$686$	−11.2952	−0.431254
$687$	−26.2266	−1.00061
$688$	0.621687	0.0237016
$689$	−6.13590	−0.233759
$690$	−6.98732	−0.266003
$691$	50.7375	1.93015	0.965073	−	0.261980i	$-0.0843756\pi$
$691$	50.7375	1.93015	0.965073	+	0.261980i	$0.0843756\pi$
$692$	−7.22504	−0.274655
$693$	13.4655	0.511511
$694$	8.47381	0.321661
$695$	−11.7955	−0.447429
$696$	4.23930	0.160690
$697$	13.0362	0.493782
$698$	−12.1276	−0.459035
$699$	2.40864	0.0911030
$700$	−14.0976	−0.532841
$701$	29.9644	1.13174	0.565871	−	0.824494i	$-0.308540\pi$
$701$	29.9644	1.13174	0.565871	+	0.824494i	$0.308540\pi$
$702$	−1.00000	−0.0377426
$703$	48.7438	1.83841
$704$	4.15216	0.156491
$705$	−8.53204	−0.321335
$706$	2.41300	0.0908146
$707$	39.6090	1.48965
$708$	−12.2258	−0.459475
$709$	−17.5704	−0.659870	−0.329935	−	0.944004i	$-0.607027\pi$
$709$	−17.5704	−0.659870	−0.329935	+	0.944004i	$0.607027\pi$
$710$	3.33293	0.125083
$711$	−14.1068	−0.529045
$712$	−8.36437	−0.313468
$713$	54.1595	2.02829
$714$	25.1862	0.942569
$715$	−3.35504	−0.125471
$716$	1.51059	0.0564534
$717$	6.82164	0.254759
$718$	−4.29733	−0.160375
$719$	15.9090	0.593304	0.296652	−	0.954986i	$-0.404130\pi$
$719$	15.9090	0.593304	0.296652	+	0.954986i	$0.404130\pi$
$720$	0.808021	0.0301132
$721$	3.24300	0.120776
$722$	54.8895	2.04278
$723$	26.0809	0.969961
$724$	4.03456	0.149943
$725$	−18.4287	−0.684424
$726$	6.24047	0.231606
$727$	−22.5620	−0.836778	−0.418389	−	0.908268i	$-0.637405\pi$
$727$	−22.5620	−0.836778	−0.418389	+	0.908268i	$0.637405\pi$
$728$	−3.24300	−0.120194
$729$	1.00000	0.0370370
$730$	11.2051	0.414720
$731$	4.82822	0.178578
$732$	−10.0049	−0.369792
$733$	−5.95341	−0.219894	−0.109947	−	0.993937i	$-0.535068\pi$
$733$	−5.95341	−0.219894	−0.109947	+	0.993937i	$0.535068\pi$
$734$	9.13736	0.337266
$735$	2.84184	0.104823
$736$	−8.64744	−0.318749
$737$	−46.5775	−1.71570
$738$	1.67856	0.0617885
$739$	32.8439	1.20818	0.604090	−	0.796916i	$-0.293537\pi$
$739$	32.8439	1.20818	0.604090	+	0.796916i	$0.293537\pi$
$740$	4.58196	0.168436
$741$	−8.59590	−0.315778
$742$	19.8987	0.730505
$743$	−24.8183	−0.910493	−0.455247	−	0.890365i	$-0.650449\pi$
$743$	−24.8183	−0.910493	−0.455247	+	0.890365i	$0.650449\pi$
$744$	−6.26307	−0.229615
$745$	−3.20105	−0.117277
$746$	16.1454	0.591127
$747$	−14.9176	−0.545806
$748$	32.2471	1.17907
$749$	1.71975	0.0628383
$750$	−7.55266	−0.275784
$751$	35.1991	1.28443	0.642217	−	0.766523i	$-0.278015\pi$
$751$	35.1991	1.28443	0.642217	+	0.766523i	$0.278015\pi$
$752$	−10.5592	−0.385054
$753$	−1.74155	−0.0634655
$754$	−4.23930	−0.154386
$755$	−2.17617	−0.0791991
$756$	3.24300	0.117947
$757$	−32.5090	−1.18156	−0.590781	−	0.806832i	$-0.701180\pi$
$757$	−32.5090	−1.18156	−0.590781	+	0.806832i	$0.701180\pi$
$758$	−25.5292	−0.927261
$759$	−35.9056	−1.30329
$760$	6.94567	0.251946
$761$	9.02410	0.327123	0.163562	−	0.986533i	$-0.447702\pi$
$761$	9.02410	0.327123	0.163562	+	0.986533i	$0.447702\pi$
$762$	−5.15738	−0.186832
$763$	−4.54984	−0.164715
$764$	11.5886	0.419259
$765$	6.27535	0.226886
$766$	27.4748	0.992704
$767$	12.2258	0.441450
$768$	1.00000	0.0360844
$769$	−22.2013	−0.800598	−0.400299	−	0.916385i	$-0.631094\pi$
$769$	−22.2013	−0.800598	−0.400299	+	0.916385i	$0.631094\pi$
$770$	10.8804	0.392102
$771$	12.3840	0.446000
$772$	−1.16862	−0.0420597
$773$	−7.83404	−0.281771	−0.140885	−	0.990026i	$-0.544995\pi$
$773$	−7.83404	−0.281771	−0.140885	+	0.990026i	$0.544995\pi$
$774$	0.621687	0.0223461
$775$	27.2262	0.977994
$776$	3.02487	0.108586
$777$	18.3897	0.659727
$778$	9.21329	0.330312
$779$	14.4287	0.516962
$780$	−0.808021	−0.0289318
$781$	17.1269	0.612847
$782$	−67.1589	−2.40160
$783$	4.23930	0.151500
$784$	3.51704	0.125609
$785$	−14.6564	−0.523108
$786$	0.509744	0.0181820
$787$	−27.5116	−0.980681	−0.490341	−	0.871531i	$-0.663128\pi$
$787$	−27.5116	−0.980681	−0.490341	+	0.871531i	$0.663128\pi$
$788$	−22.7068	−0.808898
$789$	14.1956	0.505377
$790$	−11.3986	−0.405543
$791$	−51.7180	−1.83888
$792$	4.15216	0.147541
$793$	10.0049	0.355284
$794$	−1.52055	−0.0539623
$795$	4.95794	0.175840
$796$	−21.8807	−0.775541
$797$	32.3472	1.14580	0.572898	−	0.819626i	$-0.305819\pi$
$797$	32.3472	1.14580	0.572898	+	0.819626i	$0.305819\pi$
$798$	27.8765	0.986817
$799$	−82.0060	−2.90117
$800$	−4.34710	−0.153693
$801$	−8.36437	−0.295541
$802$	5.91594	0.208899
$803$	57.5795	2.03194
$804$	−11.2176	−0.395616
$805$	−22.6599	−0.798655
$806$	6.26307	0.220607
$807$	2.89416	0.101879
$808$	12.2137	0.429676
$809$	17.7588	0.624366	0.312183	−	0.950022i	$-0.398940\pi$
$809$	17.7588	0.624366	0.312183	+	0.950022i	$0.398940\pi$
$810$	0.808021	0.0283910
$811$	4.09101	0.143655	0.0718273	−	0.997417i	$-0.477117\pi$
$811$	4.09101	0.143655	0.0718273	+	0.997417i	$0.477117\pi$
$812$	13.7481	0.482462
$813$	−3.63848	−0.127607
$814$	23.5452	0.825259
$815$	12.8629	0.450567
$816$	7.76632	0.271876
$817$	5.34396	0.186962
$818$	−16.6091	−0.580724
$819$	−3.24300	−0.113320
$820$	1.35631	0.0473644
$821$	21.4712	0.749349	0.374674	−	0.927156i	$-0.377755\pi$
$821$	21.4712	0.749349	0.374674	+	0.927156i	$0.377755\pi$
$822$	−8.22378	−0.286837
$823$	24.8955	0.867802	0.433901	−	0.900961i	$-0.357137\pi$
$823$	24.8955	0.867802	0.433901	+	0.900961i	$0.357137\pi$
$824$	1.00000	0.0348367
$825$	−18.0499	−0.628416
$826$	−39.6484	−1.37954
$827$	−6.08948	−0.211752	−0.105876	−	0.994379i	$-0.533765\pi$
$827$	−6.08948	−0.211752	−0.105876	+	0.994379i	$0.533765\pi$
$828$	−8.64744	−0.300519
$829$	4.42657	0.153741	0.0768705	−	0.997041i	$-0.475507\pi$
$829$	4.42657	0.153741	0.0768705	+	0.997041i	$0.475507\pi$
$830$	−12.0537	−0.418391
$831$	24.7013	0.856880
$832$	−1.00000	−0.0346688
$833$	27.3145	0.946390
$834$	−14.5980	−0.505488
$835$	17.6112	0.609461
$836$	35.6916	1.23442
$837$	−6.26307	−0.216483
$838$	1.71675	0.0593040
$839$	21.4548	0.740701	0.370350	−	0.928892i	$-0.379238\pi$
$839$	21.4548	0.740701	0.370350	+	0.928892i	$0.379238\pi$
$840$	2.62041	0.0904128
$841$	−11.0283	−0.380286
$842$	−32.9663	−1.13609
$843$	7.92008	0.272782
$844$	0.590099	0.0203120
$845$	0.808021	0.0277968
$846$	−10.5592	−0.363032
$847$	20.2378	0.695380
$848$	6.13590	0.210708
$849$	21.6308	0.742368
$850$	−33.7610	−1.15799
$851$	−49.0361	−1.68094
$852$	4.12480	0.141313
$853$	−9.35371	−0.320265	−0.160132	−	0.987096i	$-0.551192\pi$
$853$	−9.35371	−0.320265	−0.160132	+	0.987096i	$0.551192\pi$
$854$	−32.4459	−1.11027
$855$	6.94567	0.237537
$856$	0.530297	0.0181252
$857$	16.8397	0.575232	0.287616	−	0.957746i	$-0.407137\pi$
$857$	16.8397	0.575232	0.287616	+	0.957746i	$0.407137\pi$
$858$	−4.15216	−0.141753
$859$	−10.2004	−0.348035	−0.174017	−	0.984743i	$-0.555675\pi$
$859$	−10.2004	−0.348035	−0.174017	+	0.984743i	$0.555675\pi$
$860$	0.502336	0.0171295
$861$	5.44355	0.185516
$862$	23.5251	0.801270
$863$	−40.2954	−1.37167	−0.685836	−	0.727756i	$-0.740563\pi$
$863$	−40.2954	−1.37167	−0.685836	+	0.727756i	$0.740563\pi$
$864$	1.00000	0.0340207
$865$	−5.83798	−0.198497
$866$	26.4575	0.899061
$867$	43.3158	1.47108
$868$	−20.3111	−0.689404
$869$	−58.5736	−1.98697
$870$	3.42545	0.116134
$871$	11.2176	0.380095
$872$	−1.40297	−0.0475107
$873$	3.02487	0.102376
$874$	−74.3326	−2.51434
$875$	−24.4932	−0.828023
$876$	13.8673	0.468534
$877$	−43.1234	−1.45617	−0.728087	−	0.685485i	$-0.759590\pi$
$877$	−43.1234	−1.45617	−0.728087	+	0.685485i	$0.759590\pi$
$878$	−1.55491	−0.0524757
$879$	10.9756	0.370199
$880$	3.35504	0.113098
$881$	−36.4338	−1.22749	−0.613743	−	0.789506i	$-0.710337\pi$
$881$	−36.4338	−1.22749	−0.613743	+	0.789506i	$0.710337\pi$
$882$	3.51704	0.118425
$883$	−42.8201	−1.44101	−0.720506	−	0.693449i	$-0.756090\pi$
$883$	−42.8201	−1.44101	−0.720506	+	0.693449i	$0.756090\pi$
$884$	−7.76632	−0.261210
$885$	−9.87874	−0.332070
$886$	3.72538	0.125156
$887$	−37.5568	−1.26104	−0.630518	−	0.776175i	$-0.717157\pi$
$887$	−37.5568	−1.26104	−0.630518	+	0.776175i	$0.717157\pi$
$888$	5.67059	0.190292
$889$	−16.7254	−0.560952
$890$	−6.75859	−0.226548
$891$	4.15216	0.139103
$892$	23.7424	0.794954
$893$	−90.7657	−3.03736
$894$	−3.96159	−0.132495
$895$	1.22059	0.0407998
$896$	3.24300	0.108341
$897$	8.64744	0.288730
$898$	26.2702	0.876648
$899$	−26.5511	−0.885527
$900$	−4.34710	−0.144903
$901$	47.6534	1.58756
$902$	6.96964	0.232064
$903$	2.01613	0.0670926
$904$	−15.9476	−0.530409
$905$	3.26001	0.108366
$906$	−2.69321	−0.0894761
$907$	−50.1342	−1.66468	−0.832339	−	0.554267i	$-0.812999\pi$
$907$	−50.1342	−1.66468	−0.832339	+	0.554267i	$0.812999\pi$
$908$	−2.77610	−0.0921280
$909$	12.2137	0.405102
$910$	−2.62041	−0.0868658
$911$	−46.5932	−1.54370	−0.771851	−	0.635803i	$-0.780669\pi$
$911$	−46.5932	−1.54370	−0.771851	+	0.635803i	$0.780669\pi$
$912$	8.59590	0.284639
$913$	−61.9403	−2.04993
$914$	−17.1670	−0.567833
$915$	−8.08417	−0.267254
$916$	−26.2266	−0.866551
$917$	1.65310	0.0545902
$918$	7.76632	0.256327
$919$	−14.2416	−0.469786	−0.234893	−	0.972021i	$-0.575474\pi$
$919$	−14.2416	−0.469786	−0.234893	+	0.972021i	$0.575474\pi$
$920$	−6.98732	−0.230365
$921$	−14.0960	−0.464480
$922$	−2.59128	−0.0853391
$923$	−4.12480	−0.135770
$924$	13.4655	0.442981
$925$	−24.6506	−0.810508
$926$	−30.8714	−1.01450
$927$	1.00000	0.0328443
$928$	4.23930	0.139162
$929$	3.79770	0.124599	0.0622993	−	0.998058i	$-0.480157\pi$
$929$	3.79770	0.124599	0.0622993	+	0.998058i	$0.480157\pi$
$930$	−5.06069	−0.165947
$931$	30.2321	0.990818
$932$	2.40864	0.0788975
$933$	−5.20425	−0.170380
$934$	19.7850	0.647386
$935$	26.0563	0.852132
$936$	−1.00000	−0.0326860
$937$	27.3691	0.894111	0.447055	−	0.894506i	$-0.352473\pi$
$937$	27.3691	0.894111	0.447055	+	0.894506i	$0.352473\pi$
$938$	−36.3788	−1.18781
$939$	4.00558	0.130717
$940$	−8.53204	−0.278285
$941$	30.6755	0.999994	0.499997	−	0.866027i	$-0.333334\pi$
$941$	30.6755	0.999994	0.499997	+	0.866027i	$0.333334\pi$
$942$	−18.1386	−0.590988
$943$	−14.5152	−0.472681
$944$	−12.2258	−0.397917
$945$	2.62041	0.0852420
$946$	2.58135	0.0839269
$947$	−10.6801	−0.347056	−0.173528	−	0.984829i	$-0.555517\pi$
$947$	−10.6801	−0.347056	−0.173528	+	0.984829i	$0.555517\pi$
$948$	−14.1068	−0.458166
$949$	−13.8673	−0.450153
$950$	−37.3673	−1.21235
$951$	−3.26012	−0.105716
$952$	25.1862	0.816289
$953$	−35.7031	−1.15654	−0.578268	−	0.815847i	$-0.696271\pi$
$953$	−35.7031	−1.15654	−0.578268	+	0.815847i	$0.696271\pi$
$954$	6.13590	0.198657
$955$	9.36380	0.303005
$956$	6.82164	0.220628
$957$	17.6023	0.569001
$958$	−10.1618	−0.328314
$959$	−26.6697	−0.861209
$960$	0.808021	0.0260788
$961$	8.22603	0.265356
$962$	−5.67059	−0.182827
$963$	0.530297	0.0170886
$964$	26.0809	0.840011
$965$	−0.944272	−0.0303972
$966$	−28.0436	−0.902290
$967$	8.09442	0.260299	0.130149	−	0.991494i	$-0.458454\pi$
$967$	8.09442	0.260299	0.130149	+	0.991494i	$0.458454\pi$
$968$	6.24047	0.200576
$969$	66.7586	2.14459
$970$	2.44416	0.0784771
$971$	−48.2088	−1.54709	−0.773547	−	0.633739i	$-0.781519\pi$
$971$	−48.2088	−1.54709	−0.773547	+	0.633739i	$0.781519\pi$
$972$	1.00000	0.0320750
$973$	−47.3414	−1.51769
$974$	−39.4004	−1.26247
$975$	4.34710	0.139219
$976$	−10.0049	−0.320249
$977$	42.5120	1.36008	0.680040	−	0.733175i	$-0.261963\pi$
$977$	42.5120	1.36008	0.680040	+	0.733175i	$0.261963\pi$
$978$	15.9190	0.509034
$979$	−34.7302	−1.10998
$980$	2.84184	0.0907793
$981$	−1.40297	−0.0447935
$982$	26.2570	0.837894
$983$	−47.8717	−1.52687	−0.763435	−	0.645884i	$-0.776489\pi$
$983$	−47.8717	−1.52687	−0.763435	+	0.645884i	$0.776489\pi$
$984$	1.67856	0.0535104
$985$	−18.3476	−0.584603
$986$	32.9238	1.04851
$987$	−34.2434	−1.08998
$988$	−8.59590	−0.273472
$989$	−5.37601	−0.170947
$990$	3.35504	0.106630
$991$	19.7180	0.626362	0.313181	−	0.949693i	$-0.398605\pi$
$991$	19.7180	0.626362	0.313181	+	0.949693i	$0.398605\pi$
$992$	−6.26307	−0.198853
$993$	−2.80347	−0.0889653
$994$	13.3767	0.424284
$995$	−17.6801	−0.560496
$996$	−14.9176	−0.472682
$997$	−37.0099	−1.17212	−0.586058	−	0.810269i	$-0.699321\pi$
$997$	−37.0099	−1.17212	−0.586058	+	0.810269i	$0.699321\pi$
$998$	−6.57128	−0.208010
$999$	5.67059	0.179409

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.bd.1.9	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.bd.1.9	✓	16	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.808021 q^{5} +1.00000 q^{6} +3.24300 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.808021 q^{5} +1.00000 q^{6} +3.24300 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.808021 q^{10} +4.15216 q^{11} +1.00000 q^{12} -1.00000 q^{13} +3.24300 q^{14} +0.808021 q^{15} +1.00000 q^{16} +7.76632 q^{17} +1.00000 q^{18} +8.59590 q^{19} +0.808021 q^{20} +3.24300 q^{21} +4.15216 q^{22} -8.64744 q^{23} +1.00000 q^{24} -4.34710 q^{25} -1.00000 q^{26} +1.00000 q^{27} +3.24300 q^{28} +4.23930 q^{29} +0.808021 q^{30} -6.26307 q^{31} +1.00000 q^{32} +4.15216 q^{33} +7.76632 q^{34} +2.62041 q^{35} +1.00000 q^{36} +5.67059 q^{37} +8.59590 q^{38} -1.00000 q^{39} +0.808021 q^{40} +1.67856 q^{41} +3.24300 q^{42} +0.621687 q^{43} +4.15216 q^{44} +0.808021 q^{45} -8.64744 q^{46} -10.5592 q^{47} +1.00000 q^{48} +3.51704 q^{49} -4.34710 q^{50} +7.76632 q^{51} -1.00000 q^{52} +6.13590 q^{53} +1.00000 q^{54} +3.35504 q^{55} +3.24300 q^{56} +8.59590 q^{57} +4.23930 q^{58} -12.2258 q^{59} +0.808021 q^{60} -10.0049 q^{61} -6.26307 q^{62} +3.24300 q^{63} +1.00000 q^{64} -0.808021 q^{65} +4.15216 q^{66} -11.2176 q^{67} +7.76632 q^{68} -8.64744 q^{69} +2.62041 q^{70} +4.12480 q^{71} +1.00000 q^{72} +13.8673 q^{73} +5.67059 q^{74} -4.34710 q^{75} +8.59590 q^{76} +13.4655 q^{77} -1.00000 q^{78} -14.1068 q^{79} +0.808021 q^{80} +1.00000 q^{81} +1.67856 q^{82} -14.9176 q^{83} +3.24300 q^{84} +6.27535 q^{85} +0.621687 q^{86} +4.23930 q^{87} +4.15216 q^{88} -8.36437 q^{89} +0.808021 q^{90} -3.24300 q^{91} -8.64744 q^{92} -6.26307 q^{93} -10.5592 q^{94} +6.94567 q^{95} +1.00000 q^{96} +3.02487 q^{97} +3.51704 q^{98} +4.15216 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9} + 5 q^{10} + 18 q^{11} + 16 q^{12} - 16 q^{13} + 4 q^{14} + 5 q^{15} + 16 q^{16} + 17 q^{17} + 16 q^{18} + 8 q^{19} + 5 q^{20} + 4 q^{21} + 18 q^{22} + 9 q^{23} + 16 q^{24} + 17 q^{25} - 16 q^{26} + 16 q^{27} + 4 q^{28} + 14 q^{29} + 5 q^{30} + 12 q^{31} + 16 q^{32} + 18 q^{33} + 17 q^{34} + 16 q^{35} + 16 q^{36} + 31 q^{37} + 8 q^{38} - 16 q^{39} + 5 q^{40} + 29 q^{41} + 4 q^{42} + 30 q^{43} + 18 q^{44} + 5 q^{45} + 9 q^{46} - q^{47} + 16 q^{48} + 36 q^{49} + 17 q^{50} + 17 q^{51} - 16 q^{52} + 12 q^{53} + 16 q^{54} + 30 q^{55} + 4 q^{56} + 8 q^{57} + 14 q^{58} + 38 q^{59} + 5 q^{60} + 12 q^{62} + 4 q^{63} + 16 q^{64} - 5 q^{65} + 18 q^{66} + 28 q^{67} + 17 q^{68} + 9 q^{69} + 16 q^{70} + 32 q^{71} + 16 q^{72} + 20 q^{73} + 31 q^{74} + 17 q^{75} + 8 q^{76} + 26 q^{77} - 16 q^{78} + 13 q^{79} + 5 q^{80} + 16 q^{81} + 29 q^{82} + 39 q^{83} + 4 q^{84} + 31 q^{85} + 30 q^{86} + 14 q^{87} + 18 q^{88} + 9 q^{89} + 5 q^{90} - 4 q^{91} + 9 q^{92} + 12 q^{93} - q^{94} - 20 q^{95} + 16 q^{96} + 35 q^{97} + 36 q^{98} + 18 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9 + 5 * q^10 + 18 * q^11 + 16 * q^12 - 16 * q^13 + 4 * q^14 + 5 * q^15 + 16 * q^16 + 17 * q^17 + 16 * q^18 + 8 * q^19 + 5 * q^20 + 4 * q^21 + 18 * q^22 + 9 * q^23 + 16 * q^24 + 17 * q^25 - 16 * q^26 + 16 * q^27 + 4 * q^28 + 14 * q^29 + 5 * q^30 + 12 * q^31 + 16 * q^32 + 18 * q^33 + 17 * q^34 + 16 * q^35 + 16 * q^36 + 31 * q^37 + 8 * q^38 - 16 * q^39 + 5 * q^40 + 29 * q^41 + 4 * q^42 + 30 * q^43 + 18 * q^44 + 5 * q^45 + 9 * q^46 - q^47 + 16 * q^48 + 36 * q^49 + 17 * q^50 + 17 * q^51 - 16 * q^52 + 12 * q^53 + 16 * q^54 + 30 * q^55 + 4 * q^56 + 8 * q^57 + 14 * q^58 + 38 * q^59 + 5 * q^60 + 12 * q^62 + 4 * q^63 + 16 * q^64 - 5 * q^65 + 18 * q^66 + 28 * q^67 + 17 * q^68 + 9 * q^69 + 16 * q^70 + 32 * q^71 + 16 * q^72 + 20 * q^73 + 31 * q^74 + 17 * q^75 + 8 * q^76 + 26 * q^77 - 16 * q^78 + 13 * q^79 + 5 * q^80 + 16 * q^81 + 29 * q^82 + 39 * q^83 + 4 * q^84 + 31 * q^85 + 30 * q^86 + 14 * q^87 + 18 * q^88 + 9 * q^89 + 5 * q^90 - 4 * q^91 + 9 * q^92 + 12 * q^93 - q^94 - 20 * q^95 + 16 * q^96 + 35 * q^97 + 36 * q^98 + 18 * q^99

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