LMFDB - Embedded newform 8034.2.a.ba.1.5

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:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 44 x^{12} + 36 x^{11} + 722 x^{10} - 451 x^{9} - 5438 x^{8} + 2268 x^{7} + 18441 x^{6} + \cdots - 1492 $ x^14 - x^13 - 44x^12 + 36x^11 + 722x^10 - 451x^9 - 5438x^8 + 2268x^7 + 18441x^6 - 4126x^5 - 22759x^4 + 2997x^3 + 10504x^2 - 506x - 1492
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.924862$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.924862 q^{5} +1.00000 q^{6} -4.24556 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.924862 q^{5} +1.00000 q^{6} -4.24556 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.924862 q^{10} +2.47789 q^{11} -1.00000 q^{12} -1.00000 q^{13} +4.24556 q^{14} +0.924862 q^{15} +1.00000 q^{16} +0.549056 q^{17} -1.00000 q^{18} -4.66906 q^{19} -0.924862 q^{20} +4.24556 q^{21} -2.47789 q^{22} -2.37974 q^{23} +1.00000 q^{24} -4.14463 q^{25} +1.00000 q^{26} -1.00000 q^{27} -4.24556 q^{28} +7.33896 q^{29} -0.924862 q^{30} +8.34581 q^{31} -1.00000 q^{32} -2.47789 q^{33} -0.549056 q^{34} +3.92656 q^{35} +1.00000 q^{36} -9.19443 q^{37} +4.66906 q^{38} +1.00000 q^{39} +0.924862 q^{40} -0.968492 q^{41} -4.24556 q^{42} -11.3612 q^{43} +2.47789 q^{44} -0.924862 q^{45} +2.37974 q^{46} +2.40638 q^{47} -1.00000 q^{48} +11.0248 q^{49} +4.14463 q^{50} -0.549056 q^{51} -1.00000 q^{52} -10.3792 q^{53} +1.00000 q^{54} -2.29171 q^{55} +4.24556 q^{56} +4.66906 q^{57} -7.33896 q^{58} +3.20528 q^{59} +0.924862 q^{60} -6.92554 q^{61} -8.34581 q^{62} -4.24556 q^{63} +1.00000 q^{64} +0.924862 q^{65} +2.47789 q^{66} -2.85465 q^{67} +0.549056 q^{68} +2.37974 q^{69} -3.92656 q^{70} -7.09939 q^{71} -1.00000 q^{72} +7.73116 q^{73} +9.19443 q^{74} +4.14463 q^{75} -4.66906 q^{76} -10.5200 q^{77} -1.00000 q^{78} +11.8927 q^{79} -0.924862 q^{80} +1.00000 q^{81} +0.968492 q^{82} +7.46254 q^{83} +4.24556 q^{84} -0.507801 q^{85} +11.3612 q^{86} -7.33896 q^{87} -2.47789 q^{88} -0.591240 q^{89} +0.924862 q^{90} +4.24556 q^{91} -2.37974 q^{92} -8.34581 q^{93} -2.40638 q^{94} +4.31824 q^{95} +1.00000 q^{96} -7.00078 q^{97} -11.0248 q^{98} +2.47789 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9} + q^{10} - q^{11} - 14 q^{12} - 14 q^{13} - 5 q^{14} + q^{15} + 14 q^{16} - 12 q^{17} - 14 q^{18} + 10 q^{19} - q^{20} - 5 q^{21} + q^{22} - q^{23} + 14 q^{24} + 19 q^{25} + 14 q^{26} - 14 q^{27} + 5 q^{28} + 6 q^{29} - q^{30} + 20 q^{31} - 14 q^{32} + q^{33} + 12 q^{34} - 16 q^{35} + 14 q^{36} - 3 q^{37} - 10 q^{38} + 14 q^{39} + q^{40} + q^{41} + 5 q^{42} + 6 q^{43} - q^{44} - q^{45} + q^{46} - 13 q^{47} - 14 q^{48} + 9 q^{49} - 19 q^{50} + 12 q^{51} - 14 q^{52} - 27 q^{53} + 14 q^{54} + 10 q^{55} - 5 q^{56} - 10 q^{57} - 6 q^{58} - 6 q^{59} + q^{60} - 4 q^{61} - 20 q^{62} + 5 q^{63} + 14 q^{64} + q^{65} - q^{66} + 13 q^{67} - 12 q^{68} + q^{69} + 16 q^{70} + 18 q^{71} - 14 q^{72} + 11 q^{73} + 3 q^{74} - 19 q^{75} + 10 q^{76} - 15 q^{77} - 14 q^{78} + 33 q^{79} - q^{80} + 14 q^{81} - q^{82} - 25 q^{83} - 5 q^{84} + 25 q^{85} - 6 q^{86} - 6 q^{87} + q^{88} + 3 q^{89} + q^{90} - 5 q^{91} - q^{92} - 20 q^{93} + 13 q^{94} + 30 q^{95} + 14 q^{96} + 11 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9 + q^10 - q^11 - 14 * q^12 - 14 * q^13 - 5 * q^14 + q^15 + 14 * q^16 - 12 * q^17 - 14 * q^18 + 10 * q^19 - q^20 - 5 * q^21 + q^22 - q^23 + 14 * q^24 + 19 * q^25 + 14 * q^26 - 14 * q^27 + 5 * q^28 + 6 * q^29 - q^30 + 20 * q^31 - 14 * q^32 + q^33 + 12 * q^34 - 16 * q^35 + 14 * q^36 - 3 * q^37 - 10 * q^38 + 14 * q^39 + q^40 + q^41 + 5 * q^42 + 6 * q^43 - q^44 - q^45 + q^46 - 13 * q^47 - 14 * q^48 + 9 * q^49 - 19 * q^50 + 12 * q^51 - 14 * q^52 - 27 * q^53 + 14 * q^54 + 10 * q^55 - 5 * q^56 - 10 * q^57 - 6 * q^58 - 6 * q^59 + q^60 - 4 * q^61 - 20 * q^62 + 5 * q^63 + 14 * q^64 + q^65 - q^66 + 13 * q^67 - 12 * q^68 + q^69 + 16 * q^70 + 18 * q^71 - 14 * q^72 + 11 * q^73 + 3 * q^74 - 19 * q^75 + 10 * q^76 - 15 * q^77 - 14 * q^78 + 33 * q^79 - q^80 + 14 * q^81 - q^82 - 25 * q^83 - 5 * q^84 + 25 * q^85 - 6 * q^86 - 6 * q^87 + q^88 + 3 * q^89 + q^90 - 5 * q^91 - q^92 - 20 * q^93 + 13 * q^94 + 30 * q^95 + 14 * q^96 + 11 * q^97 - 9 * q^98 - 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
$5$	−0.924862	−0.413611	−0.206805	−	0.978382i	$-0.566307\pi$
$5$	−0.924862	−0.413611	−0.206805	+	0.978382i	$0.566307\pi$
$6$	1.00000	0.408248
$7$	−4.24556	−1.60467	−0.802335	−	0.596874i	$-0.796409\pi$
$7$	−4.24556	−1.60467	−0.802335	+	0.596874i	$0.796409\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.924862	0.292467
$11$	2.47789	0.747113	0.373556	−	0.927608i	$-0.378138\pi$
$11$	2.47789	0.747113	0.373556	+	0.927608i	$0.378138\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	4.24556	1.13467
$15$	0.924862	0.238798
$16$	1.00000	0.250000
$17$	0.549056	0.133166	0.0665828	−	0.997781i	$-0.478790\pi$
$17$	0.549056	0.133166	0.0665828	+	0.997781i	$0.478790\pi$
$18$	−1.00000	−0.235702
$19$	−4.66906	−1.07116	−0.535578	−	0.844486i	$-0.679906\pi$
$19$	−4.66906	−1.07116	−0.535578	+	0.844486i	$0.679906\pi$
$20$	−0.924862	−0.206805
$21$	4.24556	0.926457
$22$	−2.47789	−0.528288
$23$	−2.37974	−0.496210	−0.248105	−	0.968733i	$-0.579808\pi$
$23$	−2.37974	−0.496210	−0.248105	+	0.968733i	$0.579808\pi$
$24$	1.00000	0.204124
$25$	−4.14463	−0.828926
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	−4.24556	−0.802335
$29$	7.33896	1.36281	0.681406	−	0.731906i	$-0.261369\pi$
$29$	7.33896	1.36281	0.681406	+	0.731906i	$0.261369\pi$
$30$	−0.924862	−0.168856
$31$	8.34581	1.49895	0.749476	−	0.662032i	$-0.230306\pi$
$31$	8.34581	1.49895	0.749476	+	0.662032i	$0.230306\pi$
$32$	−1.00000	−0.176777
$33$	−2.47789	−0.431346
$34$	−0.549056	−0.0941623
$35$	3.92656	0.663709
$36$	1.00000	0.166667
$37$	−9.19443	−1.51155	−0.755777	−	0.654829i	$-0.772741\pi$
$37$	−9.19443	−1.51155	−0.755777	+	0.654829i	$0.772741\pi$
$38$	4.66906	0.757422
$39$	1.00000	0.160128
$40$	0.924862	0.146234
$41$	−0.968492	−0.151253	−0.0756265	−	0.997136i	$-0.524096\pi$
$41$	−0.968492	−0.151253	−0.0756265	+	0.997136i	$0.524096\pi$
$42$	−4.24556	−0.655104
$43$	−11.3612	−1.73257	−0.866284	−	0.499553i	$-0.833498\pi$
$43$	−11.3612	−1.73257	−0.866284	+	0.499553i	$0.833498\pi$
$44$	2.47789	0.373556
$45$	−0.924862	−0.137870
$46$	2.37974	0.350874
$47$	2.40638	0.351007	0.175503	−	0.984479i	$-0.443845\pi$
$47$	2.40638	0.351007	0.175503	+	0.984479i	$0.443845\pi$
$48$	−1.00000	−0.144338
$49$	11.0248	1.57497
$50$	4.14463	0.586139
$51$	−0.549056	−0.0768832
$52$	−1.00000	−0.138675
$53$	−10.3792	−1.42570	−0.712850	−	0.701317i	$-0.752596\pi$
$53$	−10.3792	−1.42570	−0.712850	+	0.701317i	$0.752596\pi$
$54$	1.00000	0.136083
$55$	−2.29171	−0.309014
$56$	4.24556	0.567337
$57$	4.66906	0.618433
$58$	−7.33896	−0.963653
$59$	3.20528	0.417293	0.208646	−	0.977991i	$-0.433094\pi$
$59$	3.20528	0.417293	0.208646	+	0.977991i	$0.433094\pi$
$60$	0.924862	0.119399
$61$	−6.92554	−0.886725	−0.443363	−	0.896342i	$-0.646215\pi$
$61$	−6.92554	−0.886725	−0.443363	+	0.896342i	$0.646215\pi$
$62$	−8.34581	−1.05992
$63$	−4.24556	−0.534890
$64$	1.00000	0.125000
$65$	0.924862	0.114715
$66$	2.47789	0.305007
$67$	−2.85465	−0.348751	−0.174376	−	0.984679i	$-0.555791\pi$
$67$	−2.85465	−0.348751	−0.174376	+	0.984679i	$0.555791\pi$
$68$	0.549056	0.0665828
$69$	2.37974	0.286487
$70$	−3.92656	−0.469313
$71$	−7.09939	−0.842543	−0.421271	−	0.906935i	$-0.638416\pi$
$71$	−7.09939	−0.842543	−0.421271	+	0.906935i	$0.638416\pi$
$72$	−1.00000	−0.117851
$73$	7.73116	0.904863	0.452432	−	0.891799i	$-0.350557\pi$
$73$	7.73116	0.904863	0.452432	+	0.891799i	$0.350557\pi$
$74$	9.19443	1.06883
$75$	4.14463	0.478581
$76$	−4.66906	−0.535578
$77$	−10.5200	−1.19887
$78$	−1.00000	−0.113228
$79$	11.8927	1.33804	0.669018	−	0.743246i	$-0.266715\pi$
$79$	11.8927	1.33804	0.669018	+	0.743246i	$0.266715\pi$
$80$	−0.924862	−0.103403
$81$	1.00000	0.111111
$82$	0.968492	0.106952
$83$	7.46254	0.819120	0.409560	−	0.912283i	$-0.365682\pi$
$83$	7.46254	0.819120	0.409560	+	0.912283i	$0.365682\pi$
$84$	4.24556	0.463228
$85$	−0.507801	−0.0550788
$86$	11.3612	1.22511
$87$	−7.33896	−0.786819
$88$	−2.47789	−0.264144
$89$	−0.591240	−0.0626713	−0.0313357	−	0.999509i	$-0.509976\pi$
$89$	−0.591240	−0.0626713	−0.0313357	+	0.999509i	$0.509976\pi$
$90$	0.924862	0.0974890
$91$	4.24556	0.445056
$92$	−2.37974	−0.248105
$93$	−8.34581	−0.865420
$94$	−2.40638	−0.248199
$95$	4.31824	0.443042
$96$	1.00000	0.102062
$97$	−7.00078	−0.710821	−0.355411	−	0.934710i	$-0.615659\pi$
$97$	−7.00078	−0.710821	−0.355411	+	0.934710i	$0.615659\pi$
$98$	−11.0248	−1.11367
$99$	2.47789	0.249038
$100$	−4.14463	−0.414463
$101$	−16.7023	−1.66194	−0.830971	−	0.556316i	$-0.812215\pi$
$101$	−16.7023	−1.66194	−0.830971	+	0.556316i	$0.812215\pi$
$102$	0.549056	0.0543646
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	−3.92656	−0.383193
$106$	10.3792	1.00812
$107$	−15.5404	−1.50234	−0.751172	−	0.660107i	$-0.770511\pi$
$107$	−15.5404	−1.50234	−0.751172	+	0.660107i	$0.770511\pi$
$108$	−1.00000	−0.0962250
$109$	−2.53988	−0.243277	−0.121638	−	0.992574i	$-0.538815\pi$
$109$	−2.53988	−0.243277	−0.121638	+	0.992574i	$0.538815\pi$
$110$	2.29171	0.218506
$111$	9.19443	0.872697
$112$	−4.24556	−0.401168
$113$	−0.761050	−0.0715936	−0.0357968	−	0.999359i	$-0.511397\pi$
$113$	−0.761050	−0.0715936	−0.0357968	+	0.999359i	$0.511397\pi$
$114$	−4.66906	−0.437298
$115$	2.20093	0.205238
$116$	7.33896	0.681406
$117$	−1.00000	−0.0924500
$118$	−3.20528	−0.295070
$119$	−2.33105	−0.213687
$120$	−0.924862	−0.0844280
$121$	−4.86005	−0.441823
$122$	6.92554	0.627009
$123$	0.968492	0.0873260
$124$	8.34581	0.749476
$125$	8.45752	0.756464
$126$	4.24556	0.378224
$127$	7.62232	0.676372	0.338186	−	0.941079i	$-0.390187\pi$
$127$	7.62232	0.676372	0.338186	+	0.941079i	$0.390187\pi$
$128$	−1.00000	−0.0883883
$129$	11.3612	1.00030
$130$	−0.924862	−0.0811158
$131$	−17.1454	−1.49800	−0.749002	−	0.662567i	$-0.769467\pi$
$131$	−17.1454	−1.49800	−0.749002	+	0.662567i	$0.769467\pi$
$132$	−2.47789	−0.215673
$133$	19.8228	1.71885
$134$	2.85465	0.246604
$135$	0.924862	0.0795994
$136$	−0.549056	−0.0470812
$137$	−2.30953	−0.197316	−0.0986581	−	0.995121i	$-0.531455\pi$
$137$	−2.30953	−0.197316	−0.0986581	+	0.995121i	$0.531455\pi$
$138$	−2.37974	−0.202577
$139$	−5.43429	−0.460931	−0.230465	−	0.973081i	$-0.574025\pi$
$139$	−5.43429	−0.460931	−0.230465	+	0.973081i	$0.574025\pi$
$140$	3.92656	0.331855
$141$	−2.40638	−0.202654
$142$	7.09939	0.595768
$143$	−2.47789	−0.207212
$144$	1.00000	0.0833333
$145$	−6.78753	−0.563674
$146$	−7.73116	−0.639835
$147$	−11.0248	−0.909308
$148$	−9.19443	−0.755777
$149$	−18.1116	−1.48376	−0.741879	−	0.670533i	$-0.766065\pi$
$149$	−18.1116	−1.48376	−0.741879	+	0.670533i	$0.766065\pi$
$150$	−4.14463	−0.338408
$151$	18.4752	1.50349	0.751745	−	0.659454i	$-0.229213\pi$
$151$	18.4752	1.50349	0.751745	+	0.659454i	$0.229213\pi$
$152$	4.66906	0.378711
$153$	0.549056	0.0443885
$154$	10.5200	0.847729
$155$	−7.71872	−0.619983
$156$	1.00000	0.0800641
$157$	−2.42290	−0.193368	−0.0966840	−	0.995315i	$-0.530824\pi$
$157$	−2.42290	−0.193368	−0.0966840	+	0.995315i	$0.530824\pi$
$158$	−11.8927	−0.946135
$159$	10.3792	0.823128
$160$	0.924862	0.0731168
$161$	10.1033	0.796254
$162$	−1.00000	−0.0785674
$163$	−0.347587	−0.0272251	−0.0136126	−	0.999907i	$-0.504333\pi$
$163$	−0.347587	−0.0272251	−0.0136126	+	0.999907i	$0.504333\pi$
$164$	−0.968492	−0.0756265
$165$	2.29171	0.178409
$166$	−7.46254	−0.579206
$167$	−2.09894	−0.162421	−0.0812106	−	0.996697i	$-0.525879\pi$
$167$	−2.09894	−0.162421	−0.0812106	+	0.996697i	$0.525879\pi$
$168$	−4.24556	−0.327552
$169$	1.00000	0.0769231
$170$	0.507801	0.0389466
$171$	−4.66906	−0.357052
$172$	−11.3612	−0.866284
$173$	−6.76812	−0.514570	−0.257285	−	0.966336i	$-0.582828\pi$
$173$	−6.76812	−0.514570	−0.257285	+	0.966336i	$0.582828\pi$
$174$	7.33896	0.556365
$175$	17.5963	1.33015
$176$	2.47789	0.186778
$177$	−3.20528	−0.240924
$178$	0.591240	0.0443153
$179$	18.8614	1.40976	0.704882	−	0.709325i	$-0.251000\pi$
$179$	18.8614	1.40976	0.704882	+	0.709325i	$0.251000\pi$
$180$	−0.924862	−0.0689351
$181$	−21.5859	−1.60447	−0.802234	−	0.597010i	$-0.796355\pi$
$181$	−21.5859	−1.60447	−0.802234	+	0.597010i	$0.796355\pi$
$182$	−4.24556	−0.314702
$183$	6.92554	0.511951
$184$	2.37974	0.175437
$185$	8.50358	0.625195
$186$	8.34581	0.611945
$187$	1.36050	0.0994897
$188$	2.40638	0.175503
$189$	4.24556	0.308819
$190$	−4.31824	−0.313278
$191$	5.01170	0.362634	0.181317	−	0.983425i	$-0.441964\pi$
$191$	5.01170	0.362634	0.181317	+	0.983425i	$0.441964\pi$
$192$	−1.00000	−0.0721688
$193$	8.23014	0.592418	0.296209	−	0.955123i	$-0.404277\pi$
$193$	8.23014	0.592418	0.296209	+	0.955123i	$0.404277\pi$
$194$	7.00078	0.502626
$195$	−0.924862	−0.0662307
$196$	11.0248	0.787484
$197$	−0.479465	−0.0341605	−0.0170802	−	0.999854i	$-0.505437\pi$
$197$	−0.479465	−0.0341605	−0.0170802	+	0.999854i	$0.505437\pi$
$198$	−2.47789	−0.176096
$199$	−12.7103	−0.901007	−0.450504	−	0.892775i	$-0.648756\pi$
$199$	−12.7103	−0.901007	−0.450504	+	0.892775i	$0.648756\pi$
$200$	4.14463	0.293070
$201$	2.85465	0.201352
$202$	16.7023	1.17517
$203$	−31.1580	−2.18686
$204$	−0.549056	−0.0384416
$205$	0.895721	0.0625599
$206$	−1.00000	−0.0696733
$207$	−2.37974	−0.165403
$208$	−1.00000	−0.0693375
$209$	−11.5694	−0.800275
$210$	3.92656	0.270958
$211$	10.6225	0.731286	0.365643	−	0.930755i	$-0.380849\pi$
$211$	10.6225	0.731286	0.365643	+	0.930755i	$0.380849\pi$
$212$	−10.3792	−0.712850
$213$	7.09939	0.486442
$214$	15.5404	1.06232
$215$	10.5075	0.716609
$216$	1.00000	0.0680414
$217$	−35.4326	−2.40532
$218$	2.53988	0.172023
$219$	−7.73116	−0.522423
$220$	−2.29171	−0.154507
$221$	−0.549056	−0.0369335
$222$	−9.19443	−0.617090
$223$	19.4059	1.29951	0.649756	−	0.760143i	$-0.274871\pi$
$223$	19.4059	1.29951	0.649756	+	0.760143i	$0.274871\pi$
$224$	4.24556	0.283668
$225$	−4.14463	−0.276309
$226$	0.761050	0.0506243
$227$	−7.36686	−0.488956	−0.244478	−	0.969655i	$-0.578617\pi$
$227$	−7.36686	−0.488956	−0.244478	+	0.969655i	$0.578617\pi$
$228$	4.66906	0.309216
$229$	2.87706	0.190122	0.0950608	−	0.995471i	$-0.469695\pi$
$229$	2.87706	0.190122	0.0950608	+	0.995471i	$0.469695\pi$
$230$	−2.20093	−0.145125
$231$	10.5200	0.692168
$232$	−7.33896	−0.481827
$233$	21.3454	1.39838	0.699190	−	0.714936i	$-0.253544\pi$
$233$	21.3454	1.39838	0.699190	+	0.714936i	$0.253544\pi$
$234$	1.00000	0.0653720
$235$	−2.22557	−0.145180
$236$	3.20528	0.208646
$237$	−11.8927	−0.772516
$238$	2.33105	0.151100
$239$	−4.40691	−0.285059	−0.142530	−	0.989791i	$-0.545524\pi$
$239$	−4.40691	−0.285059	−0.142530	+	0.989791i	$0.545524\pi$
$240$	0.924862	0.0596996
$241$	3.62912	0.233772	0.116886	−	0.993145i	$-0.462709\pi$
$241$	3.62912	0.233772	0.116886	+	0.993145i	$0.462709\pi$
$242$	4.86005	0.312416
$243$	−1.00000	−0.0641500
$244$	−6.92554	−0.443363
$245$	−10.1964	−0.651424
$246$	−0.968492	−0.0617488
$247$	4.66906	0.297085
$248$	−8.34581	−0.529960
$249$	−7.46254	−0.472919
$250$	−8.45752	−0.534901
$251$	15.8324	0.999332	0.499666	−	0.866218i	$-0.333456\pi$
$251$	15.8324	0.999332	0.499666	+	0.866218i	$0.333456\pi$
$252$	−4.24556	−0.267445
$253$	−5.89674	−0.370725
$254$	−7.62232	−0.478267
$255$	0.507801	0.0317997
$256$	1.00000	0.0625000
$257$	−27.4973	−1.71523	−0.857617	−	0.514289i	$-0.828056\pi$
$257$	−27.4973	−1.71523	−0.857617	+	0.514289i	$0.828056\pi$
$258$	−11.3612	−0.707318
$259$	39.0355	2.42555
$260$	0.924862	0.0573575
$261$	7.33896	0.454270
$262$	17.1454	1.05925
$263$	−16.7345	−1.03190	−0.515948	−	0.856620i	$-0.672560\pi$
$263$	−16.7345	−1.03190	−0.515948	+	0.856620i	$0.672560\pi$
$264$	2.47789	0.152504
$265$	9.59937	0.589685
$266$	−19.8228	−1.21541
$267$	0.591240	0.0361833
$268$	−2.85465	−0.174376
$269$	10.8418	0.661035	0.330517	−	0.943800i	$-0.392777\pi$
$269$	10.8418	0.661035	0.330517	+	0.943800i	$0.392777\pi$
$270$	−0.924862	−0.0562853
$271$	17.9774	1.09205	0.546026	−	0.837769i	$-0.316140\pi$
$271$	17.9774	1.09205	0.546026	+	0.837769i	$0.316140\pi$
$272$	0.549056	0.0332914
$273$	−4.24556	−0.256953
$274$	2.30953	0.139524
$275$	−10.2699	−0.619301
$276$	2.37974	0.143244
$277$	25.6652	1.54207	0.771036	−	0.636792i	$-0.219739\pi$
$277$	25.6652	1.54207	0.771036	+	0.636792i	$0.219739\pi$
$278$	5.43429	0.325927
$279$	8.34581	0.499651
$280$	−3.92656	−0.234657
$281$	23.1458	1.38076	0.690380	−	0.723447i	$-0.257443\pi$
$281$	23.1458	1.38076	0.690380	+	0.723447i	$0.257443\pi$
$282$	2.40638	0.143298
$283$	−16.1782	−0.961694	−0.480847	−	0.876805i	$-0.659671\pi$
$283$	−16.1782	−0.961694	−0.480847	+	0.876805i	$0.659671\pi$
$284$	−7.09939	−0.421271
$285$	−4.31824	−0.255790
$286$	2.47789	0.146521
$287$	4.11179	0.242711
$288$	−1.00000	−0.0589256
$289$	−16.6985	−0.982267
$290$	6.78753	0.398577
$291$	7.00078	0.410393
$292$	7.73116	0.452432
$293$	25.8709	1.51139	0.755696	−	0.654923i	$-0.227299\pi$
$293$	25.8709	1.51139	0.755696	+	0.654923i	$0.227299\pi$
$294$	11.0248	0.642978
$295$	−2.96445	−0.172597
$296$	9.19443	0.534415
$297$	−2.47789	−0.143782
$298$	18.1116	1.04918
$299$	2.37974	0.137624
$300$	4.14463	0.239290
$301$	48.2347	2.78020
$302$	−18.4752	−1.06313
$303$	16.7023	0.959523
$304$	−4.66906	−0.267789
$305$	6.40517	0.366759
$306$	−0.549056	−0.0313874
$307$	3.15586	0.180114	0.0900572	−	0.995937i	$-0.471295\pi$
$307$	3.15586	0.180114	0.0900572	+	0.995937i	$0.471295\pi$
$308$	−10.5200	−0.599435
$309$	−1.00000	−0.0568880
$310$	7.71872	0.438394
$311$	6.63267	0.376104	0.188052	−	0.982159i	$-0.439783\pi$
$311$	6.63267	0.376104	0.188052	+	0.982159i	$0.439783\pi$
$312$	−1.00000	−0.0566139
$313$	−8.29547	−0.468888	−0.234444	−	0.972130i	$-0.575327\pi$
$313$	−8.29547	−0.468888	−0.234444	+	0.972130i	$0.575327\pi$
$314$	2.42290	0.136732
$315$	3.92656	0.221236
$316$	11.8927	0.669018
$317$	1.19753	0.0672602	0.0336301	−	0.999434i	$-0.489293\pi$
$317$	1.19753	0.0672602	0.0336301	+	0.999434i	$0.489293\pi$
$318$	−10.3792	−0.582039
$319$	18.1852	1.01817
$320$	−0.924862	−0.0517014
$321$	15.5404	0.867378
$322$	−10.1033	−0.563037
$323$	−2.56358	−0.142641
$324$	1.00000	0.0555556
$325$	4.14463	0.229903
$326$	0.347587	0.0192511
$327$	2.53988	0.140456
$328$	0.968492	0.0534760
$329$	−10.2164	−0.563250
$330$	−2.29171	−0.126154
$331$	15.5698	0.855791	0.427896	−	0.903828i	$-0.359255\pi$
$331$	15.5698	0.855791	0.427896	+	0.903828i	$0.359255\pi$
$332$	7.46254	0.409560
$333$	−9.19443	−0.503852
$334$	2.09894	0.114849
$335$	2.64016	0.144247
$336$	4.24556	0.231614
$337$	−12.9559	−0.705752	−0.352876	−	0.935670i	$-0.614796\pi$
$337$	−12.9559	−0.705752	−0.352876	+	0.935670i	$0.614796\pi$
$338$	−1.00000	−0.0543928
$339$	0.761050	0.0413346
$340$	−0.507801	−0.0275394
$341$	20.6800	1.11989
$342$	4.66906	0.252474
$343$	−17.0874	−0.922633
$344$	11.3612	0.612555
$345$	−2.20093	−0.118494
$346$	6.76812	0.363856
$347$	30.5303	1.63895	0.819476	−	0.573113i	$-0.194264\pi$
$347$	30.5303	1.63895	0.819476	+	0.573113i	$0.194264\pi$
$348$	−7.33896	−0.393410
$349$	5.81081	0.311046	0.155523	−	0.987832i	$-0.450294\pi$
$349$	5.81081	0.311046	0.155523	+	0.987832i	$0.450294\pi$
$350$	−17.5963	−0.940560
$351$	1.00000	0.0533761
$352$	−2.47789	−0.132072
$353$	−21.3783	−1.13785	−0.568926	−	0.822389i	$-0.692641\pi$
$353$	−21.3783	−1.13785	−0.568926	+	0.822389i	$0.692641\pi$
$354$	3.20528	0.170359
$355$	6.56596	0.348485
$356$	−0.591240	−0.0313357
$357$	2.33105	0.123372
$358$	−18.8614	−0.996854
$359$	6.87350	0.362769	0.181385	−	0.983412i	$-0.441942\pi$
$359$	6.87350	0.362769	0.181385	+	0.983412i	$0.441942\pi$
$360$	0.924862	0.0487445
$361$	2.80016	0.147377
$362$	21.5859	1.13453
$363$	4.86005	0.255087
$364$	4.24556	0.222528
$365$	−7.15025	−0.374261
$366$	−6.92554	−0.362004
$367$	23.9000	1.24757	0.623786	−	0.781595i	$-0.285594\pi$
$367$	23.9000	1.24757	0.623786	+	0.781595i	$0.285594\pi$
$368$	−2.37974	−0.124053
$369$	−0.968492	−0.0504177
$370$	−8.50358	−0.442080
$371$	44.0657	2.28778
$372$	−8.34581	−0.432710
$373$	−19.9817	−1.03461	−0.517307	−	0.855800i	$-0.673066\pi$
$373$	−19.9817	−1.03461	−0.517307	+	0.855800i	$0.673066\pi$
$374$	−1.36050	−0.0703499
$375$	−8.45752	−0.436745
$376$	−2.40638	−0.124100
$377$	−7.33896	−0.377976
$378$	−4.24556	−0.218368
$379$	−9.19649	−0.472392	−0.236196	−	0.971705i	$-0.575901\pi$
$379$	−9.19649	−0.472392	−0.236196	+	0.971705i	$0.575901\pi$
$380$	4.31824	0.221521
$381$	−7.62232	−0.390503
$382$	−5.01170	−0.256421
$383$	−20.1021	−1.02717	−0.513586	−	0.858038i	$-0.671683\pi$
$383$	−20.1021	−1.02717	−0.513586	+	0.858038i	$0.671683\pi$
$384$	1.00000	0.0510310
$385$	9.72958	0.495865
$386$	−8.23014	−0.418903
$387$	−11.3612	−0.577522
$388$	−7.00078	−0.355411
$389$	21.9274	1.11176	0.555882	−	0.831261i	$-0.312381\pi$
$389$	21.9274	1.11176	0.555882	+	0.831261i	$0.312381\pi$
$390$	0.924862	0.0468322
$391$	−1.30661	−0.0660782
$392$	−11.0248	−0.556835
$393$	17.1454	0.864874
$394$	0.479465	0.0241551
$395$	−10.9991	−0.553426
$396$	2.47789	0.124519
$397$	28.3446	1.42258	0.711288	−	0.702900i	$-0.248112\pi$
$397$	28.3446	1.42258	0.711288	+	0.702900i	$0.248112\pi$
$398$	12.7103	0.637108
$399$	−19.8228	−0.992381
$400$	−4.14463	−0.207232
$401$	−21.8488	−1.09108	−0.545539	−	0.838086i	$-0.683675\pi$
$401$	−21.8488	−1.09108	−0.545539	+	0.838086i	$0.683675\pi$
$402$	−2.85465	−0.142377
$403$	−8.34581	−0.415734
$404$	−16.7023	−0.830971
$405$	−0.924862	−0.0459568
$406$	31.1580	1.54635
$407$	−22.7828	−1.12930
$408$	0.549056	0.0271823
$409$	2.98848	0.147771	0.0738854	−	0.997267i	$-0.476460\pi$
$409$	2.98848	0.147771	0.0738854	+	0.997267i	$0.476460\pi$
$410$	−0.895721	−0.0442365
$411$	2.30953	0.113921
$412$	1.00000	0.0492665
$413$	−13.6082	−0.669617
$414$	2.37974	0.116958
$415$	−6.90182	−0.338797
$416$	1.00000	0.0490290
$417$	5.43429	0.266118
$418$	11.5694	0.565880
$419$	7.64382	0.373425	0.186713	−	0.982415i	$-0.440217\pi$
$419$	7.64382	0.373425	0.186713	+	0.982415i	$0.440217\pi$
$420$	−3.92656	−0.191596
$421$	6.62472	0.322869	0.161435	−	0.986883i	$-0.448388\pi$
$421$	6.62472	0.322869	0.161435	+	0.986883i	$0.448388\pi$
$422$	−10.6225	−0.517097
$423$	2.40638	0.117002
$424$	10.3792	0.504061
$425$	−2.27563	−0.110384
$426$	−7.09939	−0.343967
$427$	29.4028	1.42290
$428$	−15.5404	−0.751172
$429$	2.47789	0.119634
$430$	−10.5075	−0.506719
$431$	−23.7953	−1.14618	−0.573089	−	0.819493i	$-0.694255\pi$
$431$	−23.7953	−1.14618	−0.573089	+	0.819493i	$0.694255\pi$
$432$	−1.00000	−0.0481125
$433$	9.20725	0.442472	0.221236	−	0.975220i	$-0.428991\pi$
$433$	9.20725	0.442472	0.221236	+	0.975220i	$0.428991\pi$
$434$	35.4326	1.70082
$435$	6.78753	0.325437
$436$	−2.53988	−0.121638
$437$	11.1112	0.531519
$438$	7.73116	0.369409
$439$	−1.68419	−0.0803819	−0.0401910	−	0.999192i	$-0.512797\pi$
$439$	−1.68419	−0.0803819	−0.0401910	+	0.999192i	$0.512797\pi$
$440$	2.29171	0.109253
$441$	11.0248	0.524989
$442$	0.549056	0.0261159
$443$	−4.58842	−0.218003	−0.109001	−	0.994042i	$-0.534765\pi$
$443$	−4.58842	−0.218003	−0.109001	+	0.994042i	$0.534765\pi$
$444$	9.19443	0.436348
$445$	0.546816	0.0259215
$446$	−19.4059	−0.918894
$447$	18.1116	0.856648
$448$	−4.24556	−0.200584
$449$	5.14126	0.242631	0.121316	−	0.992614i	$-0.461289\pi$
$449$	5.14126	0.242631	0.121316	+	0.992614i	$0.461289\pi$
$450$	4.14463	0.195380
$451$	−2.39982	−0.113003
$452$	−0.761050	−0.0357968
$453$	−18.4752	−0.868040
$454$	7.36686	0.345744
$455$	−3.92656	−0.184080
$456$	−4.66906	−0.218649
$457$	20.4298	0.955665	0.477833	−	0.878451i	$-0.341423\pi$
$457$	20.4298	0.955665	0.477833	+	0.878451i	$0.341423\pi$
$458$	−2.87706	−0.134436
$459$	−0.549056	−0.0256277
$460$	2.20093	0.102619
$461$	−6.15593	−0.286710	−0.143355	−	0.989671i	$-0.545789\pi$
$461$	−6.15593	−0.286710	−0.143355	+	0.989671i	$0.545789\pi$
$462$	−10.5200	−0.489436
$463$	15.7448	0.731722	0.365861	−	0.930670i	$-0.380775\pi$
$463$	15.7448	0.731722	0.365861	+	0.930670i	$0.380775\pi$
$464$	7.33896	0.340703
$465$	7.71872	0.357947
$466$	−21.3454	−0.988804
$467$	32.0932	1.48510	0.742549	−	0.669791i	$-0.233617\pi$
$467$	32.0932	1.48510	0.742549	+	0.669791i	$0.233617\pi$
$468$	−1.00000	−0.0462250
$469$	12.1196	0.559631
$470$	2.22557	0.102658
$471$	2.42290	0.111641
$472$	−3.20528	−0.147535
$473$	−28.1518	−1.29442
$474$	11.8927	0.546251
$475$	19.3515	0.887910
$476$	−2.33105	−0.106843
$477$	−10.3792	−0.475233
$478$	4.40691	0.201567
$479$	41.1788	1.88151	0.940753	−	0.339093i	$-0.110120\pi$
$479$	41.1788	1.88151	0.940753	+	0.339093i	$0.110120\pi$
$480$	−0.924862	−0.0422140
$481$	9.19443	0.419230
$482$	−3.62912	−0.165302
$483$	−10.1033	−0.459718
$484$	−4.86005	−0.220911
$485$	6.47475	0.294003
$486$	1.00000	0.0453609
$487$	5.83363	0.264347	0.132174	−	0.991227i	$-0.457804\pi$
$487$	5.83363	0.264347	0.132174	+	0.991227i	$0.457804\pi$
$488$	6.92554	0.313505
$489$	0.347587	0.0157184
$490$	10.1964	0.460626
$491$	8.06550	0.363991	0.181995	−	0.983299i	$-0.441744\pi$
$491$	8.06550	0.363991	0.181995	+	0.983299i	$0.441744\pi$
$492$	0.968492	0.0436630
$493$	4.02950	0.181480
$494$	−4.66906	−0.210071
$495$	−2.29171	−0.103005
$496$	8.34581	0.374738
$497$	30.1409	1.35200
$498$	7.46254	0.334404
$499$	−1.14142	−0.0510970	−0.0255485	−	0.999674i	$-0.508133\pi$
$499$	−1.14142	−0.0510970	−0.0255485	+	0.999674i	$0.508133\pi$
$500$	8.45752	0.378232
$501$	2.09894	0.0937739
$502$	−15.8324	−0.706635
$503$	−31.0106	−1.38270	−0.691348	−	0.722522i	$-0.742983\pi$
$503$	−31.0106	−1.38270	−0.691348	+	0.722522i	$0.742983\pi$
$504$	4.24556	0.189112
$505$	15.4473	0.687397
$506$	5.89674	0.262142
$507$	−1.00000	−0.0444116
$508$	7.62232	0.338186
$509$	−8.44767	−0.374436	−0.187218	−	0.982318i	$-0.559947\pi$
$509$	−8.44767	−0.374436	−0.187218	+	0.982318i	$0.559947\pi$
$510$	−0.507801	−0.0224858
$511$	−32.8231	−1.45201
$512$	−1.00000	−0.0441942
$513$	4.66906	0.206144
$514$	27.4973	1.21285
$515$	−0.924862	−0.0407543
$516$	11.3612	0.500149
$517$	5.96275	0.262241
$518$	−39.0355	−1.71512
$519$	6.76812	0.297087
$520$	−0.924862	−0.0405579
$521$	−12.4275	−0.544459	−0.272230	−	0.962232i	$-0.587761\pi$
$521$	−12.4275	−0.544459	−0.272230	+	0.962232i	$0.587761\pi$
$522$	−7.33896	−0.321218
$523$	19.8778	0.869195	0.434597	−	0.900625i	$-0.356891\pi$
$523$	19.8778	0.869195	0.434597	+	0.900625i	$0.356891\pi$
$524$	−17.1454	−0.749002
$525$	−17.5963	−0.767964
$526$	16.7345	0.729660
$527$	4.58232	0.199609
$528$	−2.47789	−0.107836
$529$	−17.3368	−0.753775
$530$	−9.59937	−0.416970
$531$	3.20528	0.139098
$532$	19.8228	0.859427
$533$	0.968492	0.0419500
$534$	−0.591240	−0.0255855
$535$	14.3727	0.621386
$536$	2.85465	0.123302
$537$	−18.8614	−0.813928
$538$	−10.8418	−0.467422
$539$	27.3182	1.17668
$540$	0.924862	0.0397997
$541$	−22.9394	−0.986243	−0.493122	−	0.869960i	$-0.664144\pi$
$541$	−22.9394	−0.986243	−0.493122	+	0.869960i	$0.664144\pi$
$542$	−17.9774	−0.772197
$543$	21.5859	0.926340
$544$	−0.549056	−0.0235406
$545$	2.34904	0.100622
$546$	4.24556	0.181693
$547$	−29.0471	−1.24196	−0.620981	−	0.783825i	$-0.713266\pi$
$547$	−29.0471	−1.24196	−0.620981	+	0.783825i	$0.713266\pi$
$548$	−2.30953	−0.0986581
$549$	−6.92554	−0.295575
$550$	10.2699	0.437912
$551$	−34.2661	−1.45978
$552$	−2.37974	−0.101289
$553$	−50.4913	−2.14711
$554$	−25.6652	−1.09041
$555$	−8.50358	−0.360957
$556$	−5.43429	−0.230465
$557$	−1.52392	−0.0645706	−0.0322853	−	0.999479i	$-0.510279\pi$
$557$	−1.52392	−0.0645706	−0.0322853	+	0.999479i	$0.510279\pi$
$558$	−8.34581	−0.353306
$559$	11.3612	0.480528
$560$	3.92656	0.165927
$561$	−1.36050	−0.0574404
$562$	−23.1458	−0.976345
$563$	−28.0389	−1.18170	−0.590850	−	0.806781i	$-0.701207\pi$
$563$	−28.0389	−1.18170	−0.590850	+	0.806781i	$0.701207\pi$
$564$	−2.40638	−0.101327
$565$	0.703866	0.0296119
$566$	16.1782	0.680020
$567$	−4.24556	−0.178297
$568$	7.09939	0.297884
$569$	−32.8020	−1.37513	−0.687566	−	0.726122i	$-0.741321\pi$
$569$	−32.8020	−1.37513	−0.687566	+	0.726122i	$0.741321\pi$
$570$	4.31824	0.180871
$571$	42.3562	1.77255	0.886277	−	0.463156i	$-0.153283\pi$
$571$	42.3562	1.77255	0.886277	+	0.463156i	$0.153283\pi$
$572$	−2.47789	−0.103606
$573$	−5.01170	−0.209367
$574$	−4.11179	−0.171623
$575$	9.86315	0.411322
$576$	1.00000	0.0416667
$577$	30.3341	1.26283	0.631413	−	0.775447i	$-0.282475\pi$
$577$	30.3341	1.26283	0.631413	+	0.775447i	$0.282475\pi$
$578$	16.6985	0.694568
$579$	−8.23014	−0.342033
$580$	−6.78753	−0.281837
$581$	−31.6827	−1.31442
$582$	−7.00078	−0.290191
$583$	−25.7187	−1.06516
$584$	−7.73116	−0.319918
$585$	0.924862	0.0382383
$586$	−25.8709	−1.06872
$587$	12.0373	0.496834	0.248417	−	0.968653i	$-0.420090\pi$
$587$	12.0373	0.496834	0.248417	+	0.968653i	$0.420090\pi$
$588$	−11.0248	−0.454654
$589$	−38.9671	−1.60561
$590$	2.96445	0.122044
$591$	0.479465	0.0197226
$592$	−9.19443	−0.377889
$593$	13.7264	0.563676	0.281838	−	0.959462i	$-0.409056\pi$
$593$	13.7264	0.563676	0.281838	+	0.959462i	$0.409056\pi$
$594$	2.47789	0.101669
$595$	2.15590	0.0883833
$596$	−18.1116	−0.741879
$597$	12.7103	0.520197
$598$	−2.37974	−0.0973149
$599$	−7.25685	−0.296507	−0.148253	−	0.988949i	$-0.547365\pi$
$599$	−7.25685	−0.296507	−0.148253	+	0.988949i	$0.547365\pi$
$600$	−4.14463	−0.169204
$601$	23.7190	0.967517	0.483758	−	0.875202i	$-0.339271\pi$
$601$	23.7190	0.967517	0.483758	+	0.875202i	$0.339271\pi$
$602$	−48.2347	−1.96590
$603$	−2.85465	−0.116250
$604$	18.4752	0.751745
$605$	4.49488	0.182743
$606$	−16.7023	−0.678485
$607$	24.7564	1.00483	0.502416	−	0.864626i	$-0.332445\pi$
$607$	24.7564	1.00483	0.502416	+	0.864626i	$0.332445\pi$
$608$	4.66906	0.189356
$609$	31.1580	1.26259
$610$	−6.40517	−0.259338
$611$	−2.40638	−0.0973517
$612$	0.549056	0.0221943
$613$	37.8561	1.52899	0.764496	−	0.644629i	$-0.222988\pi$
$613$	37.8561	1.52899	0.764496	+	0.644629i	$0.222988\pi$
$614$	−3.15586	−0.127360
$615$	−0.895721	−0.0361190
$616$	10.5200	0.423864
$617$	6.05777	0.243877	0.121938	−	0.992538i	$-0.461089\pi$
$617$	6.05777	0.243877	0.121938	+	0.992538i	$0.461089\pi$
$618$	1.00000	0.0402259
$619$	−30.3573	−1.22016	−0.610081	−	0.792339i	$-0.708863\pi$
$619$	−30.3573	−1.22016	−0.610081	+	0.792339i	$0.708863\pi$
$620$	−7.71872	−0.309991
$621$	2.37974	0.0954958
$622$	−6.63267	−0.265946
$623$	2.51015	0.100567
$624$	1.00000	0.0400320
$625$	12.9011	0.516044
$626$	8.29547	0.331554
$627$	11.5694	0.462039
$628$	−2.42290	−0.0966840
$629$	−5.04826	−0.201287
$630$	−3.92656	−0.156438
$631$	−0.227520	−0.00905741	−0.00452871	−	0.999990i	$-0.501442\pi$
$631$	−0.227520	−0.00905741	−0.00452871	+	0.999990i	$0.501442\pi$
$632$	−11.8927	−0.473067
$633$	−10.6225	−0.422208
$634$	−1.19753	−0.0475601
$635$	−7.04960	−0.279755
$636$	10.3792	0.411564
$637$	−11.0248	−0.436817
$638$	−18.1852	−0.719957
$639$	−7.09939	−0.280848
$640$	0.924862	0.0365584
$641$	−32.0388	−1.26546	−0.632728	−	0.774374i	$-0.718065\pi$
$641$	−32.0388	−1.26546	−0.632728	+	0.774374i	$0.718065\pi$
$642$	−15.5404	−0.613329
$643$	10.9375	0.431334	0.215667	−	0.976467i	$-0.430807\pi$
$643$	10.9375	0.431334	0.215667	+	0.976467i	$0.430807\pi$
$644$	10.1033	0.398127
$645$	−10.5075	−0.413734
$646$	2.56358	0.100863
$647$	0.956751	0.0376137	0.0188069	−	0.999823i	$-0.494013\pi$
$647$	0.956751	0.0376137	0.0188069	+	0.999823i	$0.494013\pi$
$648$	−1.00000	−0.0392837
$649$	7.94235	0.311764
$650$	−4.14463	−0.162566
$651$	35.4326	1.38871
$652$	−0.347587	−0.0136126
$653$	40.7145	1.59328	0.796641	−	0.604453i	$-0.206608\pi$
$653$	40.7145	1.59328	0.796641	+	0.604453i	$0.206608\pi$
$654$	−2.53988	−0.0993173
$655$	15.8572	0.619591
$656$	−0.968492	−0.0378133
$657$	7.73116	0.301621
$658$	10.2164	0.398278
$659$	1.62392	0.0632589	0.0316295	−	0.999500i	$-0.489930\pi$
$659$	1.62392	0.0632589	0.0316295	+	0.999500i	$0.489930\pi$
$660$	2.29171	0.0892046
$661$	−28.9108	−1.12450	−0.562251	−	0.826967i	$-0.690064\pi$
$661$	−28.9108	−1.12450	−0.562251	+	0.826967i	$0.690064\pi$
$662$	−15.5698	−0.605136
$663$	0.549056	0.0213236
$664$	−7.46254	−0.289603
$665$	−18.3333	−0.710937
$666$	9.19443	0.356277
$667$	−17.4648	−0.676241
$668$	−2.09894	−0.0812106
$669$	−19.4059	−0.750274
$670$	−2.64016	−0.101998
$671$	−17.1608	−0.662483
$672$	−4.24556	−0.163776
$673$	28.5791	1.10164	0.550821	−	0.834624i	$-0.314315\pi$
$673$	28.5791	1.10164	0.550821	+	0.834624i	$0.314315\pi$
$674$	12.9559	0.499042
$675$	4.14463	0.159527
$676$	1.00000	0.0384615
$677$	−7.90647	−0.303870	−0.151935	−	0.988390i	$-0.548550\pi$
$677$	−7.90647	−0.303870	−0.151935	+	0.988390i	$0.548550\pi$
$678$	−0.761050	−0.0292279
$679$	29.7222	1.14063
$680$	0.507801	0.0194733
$681$	7.36686	0.282299
$682$	−20.6800	−0.791879
$683$	29.6214	1.13343	0.566716	−	0.823913i	$-0.308214\pi$
$683$	29.6214	1.13343	0.566716	+	0.823913i	$0.308214\pi$
$684$	−4.66906	−0.178526
$685$	2.13599	0.0816121
$686$	17.0874	0.652400
$687$	−2.87706	−0.109767
$688$	−11.3612	−0.433142
$689$	10.3792	0.395418
$690$	2.20093	0.0837881
$691$	−7.71057	−0.293324	−0.146662	−	0.989187i	$-0.546853\pi$
$691$	−7.71057	−0.293324	−0.146662	+	0.989187i	$0.546853\pi$
$692$	−6.76812	−0.257285
$693$	−10.5200	−0.399623
$694$	−30.5303	−1.15891
$695$	5.02597	0.190646
$696$	7.33896	0.278183
$697$	−0.531756	−0.0201417
$698$	−5.81081	−0.219942
$699$	−21.3454	−0.807355
$700$	17.5963	0.665077
$701$	25.3023	0.955654	0.477827	−	0.878454i	$-0.341425\pi$
$701$	25.3023	0.955654	0.477827	+	0.878454i	$0.341425\pi$
$702$	−1.00000	−0.0377426
$703$	42.9294	1.61911
$704$	2.47789	0.0933891
$705$	2.22557	0.0838198
$706$	21.3783	0.804582
$707$	70.9107	2.66687
$708$	−3.20528	−0.120462
$709$	−13.7359	−0.515861	−0.257930	−	0.966164i	$-0.583041\pi$
$709$	−13.7359	−0.515861	−0.257930	+	0.966164i	$0.583041\pi$
$710$	−6.56596	−0.246416
$711$	11.8927	0.446012
$712$	0.591240	0.0221577
$713$	−19.8609	−0.743796
$714$	−2.33105	−0.0872373
$715$	2.29171	0.0857050
$716$	18.8614	0.704882
$717$	4.40691	0.164579
$718$	−6.87350	−0.256517
$719$	−8.94794	−0.333702	−0.166851	−	0.985982i	$-0.553360\pi$
$719$	−8.94794	−0.333702	−0.166851	+	0.985982i	$0.553360\pi$
$720$	−0.924862	−0.0344676
$721$	−4.24556	−0.158113
$722$	−2.80016	−0.104211
$723$	−3.62912	−0.134968
$724$	−21.5859	−0.802234
$725$	−30.4173	−1.12967
$726$	−4.86005	−0.180373
$727$	40.1106	1.48762	0.743809	−	0.668392i	$-0.233017\pi$
$727$	40.1106	1.48762	0.743809	+	0.668392i	$0.233017\pi$
$728$	−4.24556	−0.157351
$729$	1.00000	0.0370370
$730$	7.15025	0.264643
$731$	−6.23794	−0.230718
$732$	6.92554	0.255975
$733$	30.3820	1.12219	0.561093	−	0.827753i	$-0.310381\pi$
$733$	30.3820	1.12219	0.561093	+	0.827753i	$0.310381\pi$
$734$	−23.9000	−0.882166
$735$	10.1964	0.376100
$736$	2.37974	0.0877185
$737$	−7.07352	−0.260557
$738$	0.968492	0.0356507
$739$	48.9164	1.79942	0.899710	−	0.436489i	$-0.143778\pi$
$739$	48.9164	1.79942	0.899710	+	0.436489i	$0.143778\pi$
$740$	8.50358	0.312598
$741$	−4.66906	−0.171522
$742$	−44.0657	−1.61770
$743$	6.61259	0.242592	0.121296	−	0.992616i	$-0.461295\pi$
$743$	6.61259	0.242592	0.121296	+	0.992616i	$0.461295\pi$
$744$	8.34581	0.305972
$745$	16.7507	0.613699
$746$	19.9817	0.731583
$747$	7.46254	0.273040
$748$	1.36050	0.0497449
$749$	65.9775	2.41077
$750$	8.45752	0.308825
$751$	32.7253	1.19416	0.597081	−	0.802181i	$-0.296327\pi$
$751$	32.7253	1.19416	0.597081	+	0.802181i	$0.296327\pi$
$752$	2.40638	0.0877517
$753$	−15.8324	−0.576965
$754$	7.33896	0.267269
$755$	−17.0870	−0.621860
$756$	4.24556	0.154409
$757$	−30.9809	−1.12602	−0.563010	−	0.826450i	$-0.690357\pi$
$757$	−30.9809	−1.12602	−0.563010	+	0.826450i	$0.690357\pi$
$758$	9.19649	0.334032
$759$	5.89674	0.214038
$760$	−4.31824	−0.156639
$761$	0.601756	0.0218136	0.0109068	−	0.999941i	$-0.496528\pi$
$761$	0.601756	0.0218136	0.0109068	+	0.999941i	$0.496528\pi$
$762$	7.62232	0.276128
$763$	10.7832	0.390379
$764$	5.01170	0.181317
$765$	−0.507801	−0.0183596
$766$	20.1021	0.726320
$767$	−3.20528	−0.115736
$768$	−1.00000	−0.0360844
$769$	25.4331	0.917142	0.458571	−	0.888658i	$-0.348361\pi$
$769$	25.4331	0.917142	0.458571	+	0.888658i	$0.348361\pi$
$770$	−9.72958	−0.350630
$771$	27.4973	0.990291
$772$	8.23014	0.296209
$773$	2.97235	0.106908	0.0534540	−	0.998570i	$-0.482977\pi$
$773$	2.97235	0.106908	0.0534540	+	0.998570i	$0.482977\pi$
$774$	11.3612	0.408370
$775$	−34.5903	−1.24252
$776$	7.00078	0.251313
$777$	−39.0355	−1.40039
$778$	−21.9274	−0.786136
$779$	4.52195	0.162016
$780$	−0.924862	−0.0331154
$781$	−17.5915	−0.629474
$782$	1.30661	0.0467243
$783$	−7.33896	−0.262273
$784$	11.0248	0.393742
$785$	2.24084	0.0799791
$786$	−17.1454	−0.611558
$787$	49.4887	1.76408	0.882041	−	0.471173i	$-0.156169\pi$
$787$	49.4887	1.76408	0.882041	+	0.471173i	$0.156169\pi$
$788$	−0.479465	−0.0170802
$789$	16.7345	0.595765
$790$	10.9991	0.391332
$791$	3.23108	0.114884
$792$	−2.47789	−0.0880481
$793$	6.92554	0.245933
$794$	−28.3446	−1.00591
$795$	−9.59937	−0.340455
$796$	−12.7103	−0.450504
$797$	24.3948	0.864107	0.432054	−	0.901848i	$-0.357789\pi$
$797$	24.3948	0.864107	0.432054	+	0.901848i	$0.357789\pi$
$798$	19.8228	0.701719
$799$	1.32124	0.0467420
$800$	4.14463	0.146535
$801$	−0.591240	−0.0208904
$802$	21.8488	0.771508
$803$	19.1570	0.676035
$804$	2.85465	0.100676
$805$	−9.34419	−0.329339
$806$	8.34581	0.293969
$807$	−10.8418	−0.381649
$808$	16.7023	0.587585
$809$	−16.6019	−0.583692	−0.291846	−	0.956465i	$-0.594270\pi$
$809$	−16.6019	−0.583692	−0.291846	+	0.956465i	$0.594270\pi$
$810$	0.924862	0.0324963
$811$	−28.0278	−0.984189	−0.492094	−	0.870542i	$-0.663769\pi$
$811$	−28.0278	−0.984189	−0.492094	+	0.870542i	$0.663769\pi$
$812$	−31.1580	−1.09343
$813$	−17.9774	−0.630496
$814$	22.7828	0.798537
$815$	0.321470	0.0112606
$816$	−0.549056	−0.0192208
$817$	53.0462	1.85585
$818$	−2.98848	−0.104490
$819$	4.24556	0.148352
$820$	0.895721	0.0312799
$821$	−8.96226	−0.312785	−0.156393	−	0.987695i	$-0.549987\pi$
$821$	−8.96226	−0.312785	−0.156393	+	0.987695i	$0.549987\pi$
$822$	−2.30953	−0.0805540
$823$	29.9469	1.04388	0.521942	−	0.852981i	$-0.325208\pi$
$823$	29.9469	1.04388	0.521942	+	0.852981i	$0.325208\pi$
$824$	−1.00000	−0.0348367
$825$	10.2699	0.357554
$826$	13.6082	0.473491
$827$	−26.2269	−0.911999	−0.455999	−	0.889980i	$-0.650718\pi$
$827$	−26.2269	−0.911999	−0.455999	+	0.889980i	$0.650718\pi$
$828$	−2.37974	−0.0827017
$829$	−36.2795	−1.26004	−0.630020	−	0.776579i	$-0.716953\pi$
$829$	−36.2795	−1.26004	−0.630020	+	0.776579i	$0.716953\pi$
$830$	6.90182	0.239566
$831$	−25.6652	−0.890315
$832$	−1.00000	−0.0346688
$833$	6.05322	0.209732
$834$	−5.43429	−0.188174
$835$	1.94123	0.0671791
$836$	−11.5694	−0.400137
$837$	−8.34581	−0.288473
$838$	−7.64382	−0.264051
$839$	43.7783	1.51139	0.755697	−	0.654921i	$-0.227298\pi$
$839$	43.7783	1.51139	0.755697	+	0.654921i	$0.227298\pi$
$840$	3.92656	0.135479
$841$	24.8604	0.857255
$842$	−6.62472	−0.228303
$843$	−23.1458	−0.797182
$844$	10.6225	0.365643
$845$	−0.924862	−0.0318162
$846$	−2.40638	−0.0827331
$847$	20.6336	0.708980
$848$	−10.3792	−0.356425
$849$	16.1782	0.555234
$850$	2.27563	0.0780536
$851$	21.8804	0.750049
$852$	7.09939	0.243221
$853$	24.6685	0.844632	0.422316	−	0.906449i	$-0.361217\pi$
$853$	24.6685	0.844632	0.422316	+	0.906449i	$0.361217\pi$
$854$	−29.4028	−1.00614
$855$	4.31824	0.147681
$856$	15.5404	0.531159
$857$	35.4427	1.21070	0.605350	−	0.795959i	$-0.293033\pi$
$857$	35.4427	1.21070	0.605350	+	0.795959i	$0.293033\pi$
$858$	−2.47789	−0.0845938
$859$	−5.55366	−0.189488	−0.0947442	−	0.995502i	$-0.530203\pi$
$859$	−5.55366	−0.189488	−0.0947442	+	0.995502i	$0.530203\pi$
$860$	10.5075	0.358304
$861$	−4.11179	−0.140129
$862$	23.7953	0.810470
$863$	−45.0178	−1.53242	−0.766211	−	0.642589i	$-0.777860\pi$
$863$	−45.0178	−1.53242	−0.766211	+	0.642589i	$0.777860\pi$
$864$	1.00000	0.0340207
$865$	6.25957	0.212832
$866$	−9.20725	−0.312875
$867$	16.6985	0.567112
$868$	−35.4326	−1.20266
$869$	29.4689	0.999664
$870$	−6.78753	−0.230119
$871$	2.85465	0.0967262
$872$	2.53988	0.0860113
$873$	−7.00078	−0.236940
$874$	−11.1112	−0.375841
$875$	−35.9069	−1.21387
$876$	−7.73116	−0.261212
$877$	22.3613	0.755089	0.377545	−	0.925991i	$-0.376769\pi$
$877$	22.3613	0.755089	0.377545	+	0.925991i	$0.376769\pi$
$878$	1.68419	0.0568386
$879$	−25.8709	−0.872602
$880$	−2.29171	−0.0772535
$881$	16.0301	0.540067	0.270033	−	0.962851i	$-0.412965\pi$
$881$	16.0301	0.540067	0.270033	+	0.962851i	$0.412965\pi$
$882$	−11.0248	−0.371223
$883$	−11.1985	−0.376859	−0.188429	−	0.982087i	$-0.560340\pi$
$883$	−11.1985	−0.376859	−0.188429	+	0.982087i	$0.560340\pi$
$884$	−0.549056	−0.0184668
$885$	2.96445	0.0996488
$886$	4.58842	0.154151
$887$	34.0707	1.14398	0.571992	−	0.820259i	$-0.306171\pi$
$887$	34.0707	1.14398	0.571992	+	0.820259i	$0.306171\pi$
$888$	−9.19443	−0.308545
$889$	−32.3610	−1.08535
$890$	−0.546816	−0.0183293
$891$	2.47789	0.0830125
$892$	19.4059	0.649756
$893$	−11.2355	−0.375983
$894$	−18.1116	−0.605742
$895$	−17.4442	−0.583094
$896$	4.24556	0.141834
$897$	−2.37974	−0.0794573
$898$	−5.14126	−0.171566
$899$	61.2496	2.04279
$900$	−4.14463	−0.138154
$901$	−5.69879	−0.189854
$902$	2.39982	0.0799052
$903$	−48.2347	−1.60515
$904$	0.761050	0.0253121
$905$	19.9640	0.663625
$906$	18.4752	0.613797
$907$	10.0554	0.333885	0.166943	−	0.985967i	$-0.446610\pi$
$907$	10.0554	0.333885	0.166943	+	0.985967i	$0.446610\pi$
$908$	−7.36686	−0.244478
$909$	−16.7023	−0.553981
$910$	3.92656	0.130164
$911$	9.21796	0.305405	0.152702	−	0.988272i	$-0.451202\pi$
$911$	9.21796	0.305405	0.152702	+	0.988272i	$0.451202\pi$
$912$	4.66906	0.154608
$913$	18.4914	0.611975
$914$	−20.4298	−0.675758
$915$	−6.40517	−0.211748
$916$	2.87706	0.0950608
$917$	72.7920	2.40380
$918$	0.549056	0.0181215
$919$	51.7380	1.70668	0.853339	−	0.521356i	$-0.174574\pi$
$919$	51.7380	1.70668	0.853339	+	0.521356i	$0.174574\pi$
$920$	−2.20093	−0.0725626
$921$	−3.15586	−0.103989
$922$	6.15593	0.202735
$923$	7.09939	0.233679
$924$	10.5200	0.346084
$925$	38.1075	1.25297
$926$	−15.7448	−0.517406
$927$	1.00000	0.0328443
$928$	−7.33896	−0.240913
$929$	15.4283	0.506185	0.253092	−	0.967442i	$-0.418552\pi$
$929$	15.4283	0.506185	0.253092	+	0.967442i	$0.418552\pi$
$930$	−7.71872	−0.253107
$931$	−51.4754	−1.68704
$932$	21.3454	0.699190
$933$	−6.63267	−0.217144
$934$	−32.0932	−1.05012
$935$	−1.25828	−0.0411500
$936$	1.00000	0.0326860
$937$	−24.8677	−0.812392	−0.406196	−	0.913786i	$-0.633145\pi$
$937$	−24.8677	−0.812392	−0.406196	+	0.913786i	$0.633145\pi$
$938$	−12.1196	−0.395719
$939$	8.29547	0.270713
$940$	−2.22557	−0.0725901
$941$	20.6871	0.674379	0.337189	−	0.941437i	$-0.390524\pi$
$941$	20.6871	0.674379	0.337189	+	0.941437i	$0.390524\pi$
$942$	−2.42290	−0.0789422
$943$	2.30476	0.0750533
$944$	3.20528	0.104323
$945$	−3.92656	−0.127731
$946$	28.1518	0.915295
$947$	−56.3540	−1.83126	−0.915629	−	0.402024i	$-0.868307\pi$
$947$	−56.3540	−1.83126	−0.915629	+	0.402024i	$0.868307\pi$
$948$	−11.8927	−0.386258
$949$	−7.73116	−0.250964
$950$	−19.3515	−0.627847
$951$	−1.19753	−0.0388327
$952$	2.33105	0.0755498
$953$	16.3780	0.530537	0.265268	−	0.964175i	$-0.414539\pi$
$953$	16.3780	0.530537	0.265268	+	0.964175i	$0.414539\pi$
$954$	10.3792	0.336041
$955$	−4.63513	−0.149989
$956$	−4.40691	−0.142530
$957$	−18.1852	−0.587843
$958$	−41.1788	−1.33043
$959$	9.80523	0.316627
$960$	0.924862	0.0298498
$961$	38.6526	1.24686
$962$	−9.19443	−0.296440
$963$	−15.5404	−0.500781
$964$	3.62912	0.116886
$965$	−7.61174	−0.245031
$966$	10.1033	0.325069
$967$	−6.28152	−0.202000	−0.101000	−	0.994886i	$-0.532204\pi$
$967$	−6.28152	−0.202000	−0.101000	+	0.994886i	$0.532204\pi$
$968$	4.86005	0.156208
$969$	2.56358	0.0823540
$970$	−6.47475	−0.207892
$971$	−16.8905	−0.542042	−0.271021	−	0.962573i	$-0.587361\pi$
$971$	−16.8905	−0.542042	−0.271021	+	0.962573i	$0.587361\pi$
$972$	−1.00000	−0.0320750
$973$	23.0716	0.739642
$974$	−5.83363	−0.186922
$975$	−4.14463	−0.132734
$976$	−6.92554	−0.221681
$977$	52.3227	1.67395	0.836976	−	0.547240i	$-0.184321\pi$
$977$	52.3227	1.67395	0.836976	+	0.547240i	$0.184321\pi$
$978$	−0.347587	−0.0111146
$979$	−1.46503	−0.0468226
$980$	−10.1964	−0.325712
$981$	−2.53988	−0.0810922
$982$	−8.06550	−0.257380
$983$	−13.1119	−0.418205	−0.209102	−	0.977894i	$-0.567054\pi$
$983$	−13.1119	−0.418205	−0.209102	+	0.977894i	$0.567054\pi$
$984$	−0.968492	−0.0308744
$985$	0.443439	0.0141291
$986$	−4.02950	−0.128325
$987$	10.2164	0.325193
$988$	4.66906	0.148543
$989$	27.0367	0.859718
$990$	2.29171	0.0728353
$991$	23.5113	0.746861	0.373430	−	0.927658i	$-0.378181\pi$
$991$	23.5113	0.746861	0.373430	+	0.927658i	$0.378181\pi$
$992$	−8.34581	−0.264980
$993$	−15.5698	−0.494091
$994$	−30.1409	−0.956011
$995$	11.7552	0.372666
$996$	−7.46254	−0.236460
$997$	−23.0393	−0.729662	−0.364831	−	0.931074i	$-0.618873\pi$
$997$	−23.0393	−0.729662	−0.364831	+	0.931074i	$0.618873\pi$
$998$	1.14142	0.0361311
$999$	9.19443	0.290899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.ba.1.5	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.ba.1.5	✓	14	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.924862 q^{5} +1.00000 q^{6} -4.24556 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.924862 q^{5} +1.00000 q^{6} -4.24556 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.924862 q^{10} +2.47789 q^{11} -1.00000 q^{12} -1.00000 q^{13} +4.24556 q^{14} +0.924862 q^{15} +1.00000 q^{16} +0.549056 q^{17} -1.00000 q^{18} -4.66906 q^{19} -0.924862 q^{20} +4.24556 q^{21} -2.47789 q^{22} -2.37974 q^{23} +1.00000 q^{24} -4.14463 q^{25} +1.00000 q^{26} -1.00000 q^{27} -4.24556 q^{28} +7.33896 q^{29} -0.924862 q^{30} +8.34581 q^{31} -1.00000 q^{32} -2.47789 q^{33} -0.549056 q^{34} +3.92656 q^{35} +1.00000 q^{36} -9.19443 q^{37} +4.66906 q^{38} +1.00000 q^{39} +0.924862 q^{40} -0.968492 q^{41} -4.24556 q^{42} -11.3612 q^{43} +2.47789 q^{44} -0.924862 q^{45} +2.37974 q^{46} +2.40638 q^{47} -1.00000 q^{48} +11.0248 q^{49} +4.14463 q^{50} -0.549056 q^{51} -1.00000 q^{52} -10.3792 q^{53} +1.00000 q^{54} -2.29171 q^{55} +4.24556 q^{56} +4.66906 q^{57} -7.33896 q^{58} +3.20528 q^{59} +0.924862 q^{60} -6.92554 q^{61} -8.34581 q^{62} -4.24556 q^{63} +1.00000 q^{64} +0.924862 q^{65} +2.47789 q^{66} -2.85465 q^{67} +0.549056 q^{68} +2.37974 q^{69} -3.92656 q^{70} -7.09939 q^{71} -1.00000 q^{72} +7.73116 q^{73} +9.19443 q^{74} +4.14463 q^{75} -4.66906 q^{76} -10.5200 q^{77} -1.00000 q^{78} +11.8927 q^{79} -0.924862 q^{80} +1.00000 q^{81} +0.968492 q^{82} +7.46254 q^{83} +4.24556 q^{84} -0.507801 q^{85} +11.3612 q^{86} -7.33896 q^{87} -2.47789 q^{88} -0.591240 q^{89} +0.924862 q^{90} +4.24556 q^{91} -2.37974 q^{92} -8.34581 q^{93} -2.40638 q^{94} +4.31824 q^{95} +1.00000 q^{96} -7.00078 q^{97} -11.0248 q^{98} +2.47789 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9} + q^{10} - q^{11} - 14 q^{12} - 14 q^{13} - 5 q^{14} + q^{15} + 14 q^{16} - 12 q^{17} - 14 q^{18} + 10 q^{19} - q^{20} - 5 q^{21} + q^{22} - q^{23} + 14 q^{24} + 19 q^{25} + 14 q^{26} - 14 q^{27} + 5 q^{28} + 6 q^{29} - q^{30} + 20 q^{31} - 14 q^{32} + q^{33} + 12 q^{34} - 16 q^{35} + 14 q^{36} - 3 q^{37} - 10 q^{38} + 14 q^{39} + q^{40} + q^{41} + 5 q^{42} + 6 q^{43} - q^{44} - q^{45} + q^{46} - 13 q^{47} - 14 q^{48} + 9 q^{49} - 19 q^{50} + 12 q^{51} - 14 q^{52} - 27 q^{53} + 14 q^{54} + 10 q^{55} - 5 q^{56} - 10 q^{57} - 6 q^{58} - 6 q^{59} + q^{60} - 4 q^{61} - 20 q^{62} + 5 q^{63} + 14 q^{64} + q^{65} - q^{66} + 13 q^{67} - 12 q^{68} + q^{69} + 16 q^{70} + 18 q^{71} - 14 q^{72} + 11 q^{73} + 3 q^{74} - 19 q^{75} + 10 q^{76} - 15 q^{77} - 14 q^{78} + 33 q^{79} - q^{80} + 14 q^{81} - q^{82} - 25 q^{83} - 5 q^{84} + 25 q^{85} - 6 q^{86} - 6 q^{87} + q^{88} + 3 q^{89} + q^{90} - 5 q^{91} - q^{92} - 20 q^{93} + 13 q^{94} + 30 q^{95} + 14 q^{96} + 11 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9 + q^10 - q^11 - 14 * q^12 - 14 * q^13 - 5 * q^14 + q^15 + 14 * q^16 - 12 * q^17 - 14 * q^18 + 10 * q^19 - q^20 - 5 * q^21 + q^22 - q^23 + 14 * q^24 + 19 * q^25 + 14 * q^26 - 14 * q^27 + 5 * q^28 + 6 * q^29 - q^30 + 20 * q^31 - 14 * q^32 + q^33 + 12 * q^34 - 16 * q^35 + 14 * q^36 - 3 * q^37 - 10 * q^38 + 14 * q^39 + q^40 + q^41 + 5 * q^42 + 6 * q^43 - q^44 - q^45 + q^46 - 13 * q^47 - 14 * q^48 + 9 * q^49 - 19 * q^50 + 12 * q^51 - 14 * q^52 - 27 * q^53 + 14 * q^54 + 10 * q^55 - 5 * q^56 - 10 * q^57 - 6 * q^58 - 6 * q^59 + q^60 - 4 * q^61 - 20 * q^62 + 5 * q^63 + 14 * q^64 + q^65 - q^66 + 13 * q^67 - 12 * q^68 + q^69 + 16 * q^70 + 18 * q^71 - 14 * q^72 + 11 * q^73 + 3 * q^74 - 19 * q^75 + 10 * q^76 - 15 * q^77 - 14 * q^78 + 33 * q^79 - q^80 + 14 * q^81 - q^82 - 25 * q^83 - 5 * q^84 + 25 * q^85 - 6 * q^86 - 6 * q^87 + q^88 + 3 * q^89 + q^90 - 5 * q^91 - q^92 - 20 * q^93 + 13 * q^94 + 30 * q^95 + 14 * q^96 + 11 * q^97 - 9 * q^98 - q^99

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