LMFDB - Embedded newform 8034.2.a.ba.1.4

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			1.4
Root			$2.71343$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.71343 q^{5} +1.00000 q^{6} -2.34175 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.71343 q^{5} +1.00000 q^{6} -2.34175 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.71343 q^{10} +0.805528 q^{11} -1.00000 q^{12} -1.00000 q^{13} +2.34175 q^{14} +2.71343 q^{15} +1.00000 q^{16} -7.05126 q^{17} -1.00000 q^{18} +3.05101 q^{19} -2.71343 q^{20} +2.34175 q^{21} -0.805528 q^{22} -3.54988 q^{23} +1.00000 q^{24} +2.36272 q^{25} +1.00000 q^{26} -1.00000 q^{27} -2.34175 q^{28} -1.98812 q^{29} -2.71343 q^{30} -7.06425 q^{31} -1.00000 q^{32} -0.805528 q^{33} +7.05126 q^{34} +6.35418 q^{35} +1.00000 q^{36} +1.93939 q^{37} -3.05101 q^{38} +1.00000 q^{39} +2.71343 q^{40} -1.08094 q^{41} -2.34175 q^{42} -3.41372 q^{43} +0.805528 q^{44} -2.71343 q^{45} +3.54988 q^{46} -12.0993 q^{47} -1.00000 q^{48} -1.51621 q^{49} -2.36272 q^{50} +7.05126 q^{51} -1.00000 q^{52} +6.23971 q^{53} +1.00000 q^{54} -2.18575 q^{55} +2.34175 q^{56} -3.05101 q^{57} +1.98812 q^{58} +1.79179 q^{59} +2.71343 q^{60} -2.31314 q^{61} +7.06425 q^{62} -2.34175 q^{63} +1.00000 q^{64} +2.71343 q^{65} +0.805528 q^{66} +4.26635 q^{67} -7.05126 q^{68} +3.54988 q^{69} -6.35418 q^{70} -0.749357 q^{71} -1.00000 q^{72} -4.06343 q^{73} -1.93939 q^{74} -2.36272 q^{75} +3.05101 q^{76} -1.88635 q^{77} -1.00000 q^{78} +4.75496 q^{79} -2.71343 q^{80} +1.00000 q^{81} +1.08094 q^{82} -12.8746 q^{83} +2.34175 q^{84} +19.1331 q^{85} +3.41372 q^{86} +1.98812 q^{87} -0.805528 q^{88} -7.49391 q^{89} +2.71343 q^{90} +2.34175 q^{91} -3.54988 q^{92} +7.06425 q^{93} +12.0993 q^{94} -8.27870 q^{95} +1.00000 q^{96} -9.03214 q^{97} +1.51621 q^{98} +0.805528 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−2.71343	−1.21348	−0.606742	−	0.794899i	$-0.707524\pi$
$5$	−2.71343	−1.21348	−0.606742	+	0.794899i	$0.707524\pi$
$6$	1.00000	0.408248
$7$	−2.34175	−0.885098	−0.442549	−	0.896744i	$-0.645926\pi$
$7$	−2.34175	−0.885098	−0.442549	+	0.896744i	$0.645926\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.71343	0.858063
$11$	0.805528	0.242876	0.121438	−	0.992599i	$-0.461249\pi$
$11$	0.805528	0.242876	0.121438	+	0.992599i	$0.461249\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	2.34175	0.625859
$15$	2.71343	0.700606
$16$	1.00000	0.250000
$17$	−7.05126	−1.71018	−0.855091	−	0.518478i	$-0.826499\pi$
$17$	−7.05126	−1.71018	−0.855091	+	0.518478i	$0.826499\pi$
$18$	−1.00000	−0.235702
$19$	3.05101	0.699949	0.349974	−	0.936759i	$-0.386190\pi$
$19$	3.05101	0.699949	0.349974	+	0.936759i	$0.386190\pi$
$20$	−2.71343	−0.606742
$21$	2.34175	0.511012
$22$	−0.805528	−0.171739
$23$	−3.54988	−0.740202	−0.370101	−	0.928992i	$-0.620677\pi$
$23$	−3.54988	−0.740202	−0.370101	+	0.928992i	$0.620677\pi$
$24$	1.00000	0.204124
$25$	2.36272	0.472544
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	−2.34175	−0.442549
$29$	−1.98812	−0.369185	−0.184592	−	0.982815i	$-0.559097\pi$
$29$	−1.98812	−0.369185	−0.184592	+	0.982815i	$0.559097\pi$
$30$	−2.71343	−0.495403
$31$	−7.06425	−1.26878	−0.634389	−	0.773014i	$-0.718748\pi$
$31$	−7.06425	−1.26878	−0.634389	+	0.773014i	$0.718748\pi$
$32$	−1.00000	−0.176777
$33$	−0.805528	−0.140225
$34$	7.05126	1.20928
$35$	6.35418	1.07405
$36$	1.00000	0.166667
$37$	1.93939	0.318834	0.159417	−	0.987211i	$-0.449039\pi$
$37$	1.93939	0.318834	0.159417	+	0.987211i	$0.449039\pi$
$38$	−3.05101	−0.494939
$39$	1.00000	0.160128
$40$	2.71343	0.429032
$41$	−1.08094	−0.168814	−0.0844069	−	0.996431i	$-0.526900\pi$
$41$	−1.08094	−0.168814	−0.0844069	+	0.996431i	$0.526900\pi$
$42$	−2.34175	−0.361340
$43$	−3.41372	−0.520587	−0.260294	−	0.965530i	$-0.583819\pi$
$43$	−3.41372	−0.520587	−0.260294	+	0.965530i	$0.583819\pi$
$44$	0.805528	0.121438
$45$	−2.71343	−0.404495
$46$	3.54988	0.523402
$47$	−12.0993	−1.76486	−0.882432	−	0.470440i	$-0.844095\pi$
$47$	−12.0993	−1.76486	−0.882432	+	0.470440i	$0.844095\pi$
$48$	−1.00000	−0.144338
$49$	−1.51621	−0.216601
$50$	−2.36272	−0.334139
$51$	7.05126	0.987374
$52$	−1.00000	−0.138675
$53$	6.23971	0.857089	0.428545	−	0.903521i	$-0.359026\pi$
$53$	6.23971	0.857089	0.428545	+	0.903521i	$0.359026\pi$
$54$	1.00000	0.136083
$55$	−2.18575	−0.294726
$56$	2.34175	0.312930
$57$	−3.05101	−0.404116
$58$	1.98812	0.261053
$59$	1.79179	0.233271	0.116635	−	0.993175i	$-0.462789\pi$
$59$	1.79179	0.233271	0.116635	+	0.993175i	$0.462789\pi$
$60$	2.71343	0.350303
$61$	−2.31314	−0.296167	−0.148084	−	0.988975i	$-0.547310\pi$
$61$	−2.31314	−0.296167	−0.148084	+	0.988975i	$0.547310\pi$
$62$	7.06425	0.897161
$63$	−2.34175	−0.295033
$64$	1.00000	0.125000
$65$	2.71343	0.336560
$66$	0.805528	0.0991537
$67$	4.26635	0.521218	0.260609	−	0.965444i	$-0.416077\pi$
$67$	4.26635	0.521218	0.260609	+	0.965444i	$0.416077\pi$
$68$	−7.05126	−0.855091
$69$	3.54988	0.427356
$70$	−6.35418	−0.759470
$71$	−0.749357	−0.0889323	−0.0444661	−	0.999011i	$-0.514159\pi$
$71$	−0.749357	−0.0889323	−0.0444661	+	0.999011i	$0.514159\pi$
$72$	−1.00000	−0.117851
$73$	−4.06343	−0.475589	−0.237794	−	0.971316i	$-0.576424\pi$
$73$	−4.06343	−0.475589	−0.237794	+	0.971316i	$0.576424\pi$
$74$	−1.93939	−0.225450
$75$	−2.36272	−0.272824
$76$	3.05101	0.349974
$77$	−1.88635	−0.214969
$78$	−1.00000	−0.113228
$79$	4.75496	0.534974	0.267487	−	0.963561i	$-0.413807\pi$
$79$	4.75496	0.534974	0.267487	+	0.963561i	$0.413807\pi$
$80$	−2.71343	−0.303371
$81$	1.00000	0.111111
$82$	1.08094	0.119369
$83$	−12.8746	−1.41317	−0.706584	−	0.707629i	$-0.749765\pi$
$83$	−12.8746	−1.41317	−0.706584	+	0.707629i	$0.749765\pi$
$84$	2.34175	0.255506
$85$	19.1331	2.07528
$86$	3.41372	0.368111
$87$	1.98812	0.213149
$88$	−0.805528	−0.0858696
$89$	−7.49391	−0.794353	−0.397176	−	0.917742i	$-0.630010\pi$
$89$	−7.49391	−0.794353	−0.397176	+	0.917742i	$0.630010\pi$
$90$	2.71343	0.286021
$91$	2.34175	0.245482
$92$	−3.54988	−0.370101
$93$	7.06425	0.732529
$94$	12.0993	1.24795
$95$	−8.27870	−0.849377
$96$	1.00000	0.102062
$97$	−9.03214	−0.917075	−0.458537	−	0.888675i	$-0.651627\pi$
$97$	−9.03214	−0.917075	−0.458537	+	0.888675i	$0.651627\pi$
$98$	1.51621	0.153160
$99$	0.805528	0.0809587
$100$	2.36272	0.236272
$101$	−8.39612	−0.835445	−0.417723	−	0.908575i	$-0.637172\pi$
$101$	−8.39612	−0.835445	−0.417723	+	0.908575i	$0.637172\pi$
$102$	−7.05126	−0.698179
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	−6.35418	−0.620105
$106$	−6.23971	−0.606054
$107$	−6.34500	−0.613394	−0.306697	−	0.951807i	$-0.599224\pi$
$107$	−6.34500	−0.613394	−0.306697	+	0.951807i	$0.599224\pi$
$108$	−1.00000	−0.0962250
$109$	−3.27488	−0.313676	−0.156838	−	0.987624i	$-0.550130\pi$
$109$	−3.27488	−0.313676	−0.156838	+	0.987624i	$0.550130\pi$
$110$	2.18575	0.208403
$111$	−1.93939	−0.184079
$112$	−2.34175	−0.221275
$113$	−11.0842	−1.04271	−0.521355	−	0.853340i	$-0.674573\pi$
$113$	−11.0842	−1.04271	−0.521355	+	0.853340i	$0.674573\pi$
$114$	3.05101	0.285753
$115$	9.63237	0.898223
$116$	−1.98812	−0.184592
$117$	−1.00000	−0.0924500
$118$	−1.79179	−0.164947
$119$	16.5123	1.51368
$120$	−2.71343	−0.247701
$121$	−10.3511	−0.941011
$122$	2.31314	0.209422
$123$	1.08094	0.0974647
$124$	−7.06425	−0.634389
$125$	7.15608	0.640059
$126$	2.34175	0.208620
$127$	−20.2440	−1.79636	−0.898181	−	0.439627i	$-0.855111\pi$
$127$	−20.2440	−1.79636	−0.898181	+	0.439627i	$0.855111\pi$
$128$	−1.00000	−0.0883883
$129$	3.41372	0.300561
$130$	−2.71343	−0.237984
$131$	−18.2985	−1.59875	−0.799374	−	0.600833i	$-0.794835\pi$
$131$	−18.2985	−1.59875	−0.799374	+	0.600833i	$0.794835\pi$
$132$	−0.805528	−0.0701123
$133$	−7.14469	−0.619524
$134$	−4.26635	−0.368557
$135$	2.71343	0.233535
$136$	7.05126	0.604641
$137$	−9.99842	−0.854222	−0.427111	−	0.904199i	$-0.640469\pi$
$137$	−9.99842	−0.854222	−0.427111	+	0.904199i	$0.640469\pi$
$138$	−3.54988	−0.302186
$139$	8.86959	0.752309	0.376154	−	0.926557i	$-0.377246\pi$
$139$	8.86959	0.752309	0.376154	+	0.926557i	$0.377246\pi$
$140$	6.35418	0.537026
$141$	12.0993	1.01894
$142$	0.749357	0.0628846
$143$	−0.805528	−0.0673617
$144$	1.00000	0.0833333
$145$	5.39464	0.448000
$146$	4.06343	0.336292
$147$	1.51621	0.125055
$148$	1.93939	0.159417
$149$	1.38681	0.113612	0.0568058	−	0.998385i	$-0.481908\pi$
$149$	1.38681	0.113612	0.0568058	+	0.998385i	$0.481908\pi$
$150$	2.36272	0.192915
$151$	14.3074	1.16432	0.582159	−	0.813075i	$-0.302208\pi$
$151$	14.3074	1.16432	0.582159	+	0.813075i	$0.302208\pi$
$152$	−3.05101	−0.247469
$153$	−7.05126	−0.570061
$154$	1.88635	0.152006
$155$	19.1684	1.53964
$156$	1.00000	0.0800641
$157$	−8.73671	−0.697265	−0.348633	−	0.937259i	$-0.613354\pi$
$157$	−8.73671	−0.697265	−0.348633	+	0.937259i	$0.613354\pi$
$158$	−4.75496	−0.378284
$159$	−6.23971	−0.494841
$160$	2.71343	0.214516
$161$	8.31294	0.655151
$162$	−1.00000	−0.0785674
$163$	23.6512	1.85251	0.926253	−	0.376902i	$-0.123011\pi$
$163$	23.6512	1.85251	0.926253	+	0.376902i	$0.123011\pi$
$164$	−1.08094	−0.0844069
$165$	2.18575	0.170160
$166$	12.8746	0.999260
$167$	0.498550	0.0385790	0.0192895	−	0.999814i	$-0.493860\pi$
$167$	0.498550	0.0385790	0.0192895	+	0.999814i	$0.493860\pi$
$168$	−2.34175	−0.180670
$169$	1.00000	0.0769231
$170$	−19.1331	−1.46744
$171$	3.05101	0.233316
$172$	−3.41372	−0.260294
$173$	1.59065	0.120935	0.0604676	−	0.998170i	$-0.480741\pi$
$173$	1.59065	0.120935	0.0604676	+	0.998170i	$0.480741\pi$
$174$	−1.98812	−0.150719
$175$	−5.53290	−0.418248
$176$	0.805528	0.0607190
$177$	−1.79179	−0.134679
$178$	7.49391	0.561692
$179$	−19.1240	−1.42939	−0.714696	−	0.699436i	$-0.753435\pi$
$179$	−19.1240	−1.42939	−0.714696	+	0.699436i	$0.753435\pi$
$180$	−2.71343	−0.202247
$181$	13.3384	0.991436	0.495718	−	0.868483i	$-0.334905\pi$
$181$	13.3384	0.991436	0.495718	+	0.868483i	$0.334905\pi$
$182$	−2.34175	−0.173582
$183$	2.31314	0.170992
$184$	3.54988	0.261701
$185$	−5.26241	−0.386900
$186$	−7.06425	−0.517976
$187$	−5.67999	−0.415362
$188$	−12.0993	−0.882432
$189$	2.34175	0.170337
$190$	8.27870	0.600600
$191$	−20.3164	−1.47004	−0.735022	−	0.678043i	$-0.762828\pi$
$191$	−20.3164	−1.47004	−0.735022	+	0.678043i	$0.762828\pi$
$192$	−1.00000	−0.0721688
$193$	−19.0532	−1.37148	−0.685740	−	0.727847i	$-0.740521\pi$
$193$	−19.0532	−1.37148	−0.685740	+	0.727847i	$0.740521\pi$
$194$	9.03214	0.648470
$195$	−2.71343	−0.194313
$196$	−1.51621	−0.108300
$197$	0.799715	0.0569774	0.0284887	−	0.999594i	$-0.490931\pi$
$197$	0.799715	0.0569774	0.0284887	+	0.999594i	$0.490931\pi$
$198$	−0.805528	−0.0572464
$199$	−11.3388	−0.803786	−0.401893	−	0.915687i	$-0.631648\pi$
$199$	−11.3388	−0.803786	−0.401893	+	0.915687i	$0.631648\pi$
$200$	−2.36272	−0.167070
$201$	−4.26635	−0.300925
$202$	8.39612	0.590749
$203$	4.65568	0.326765
$204$	7.05126	0.493687
$205$	2.93305	0.204853
$206$	−1.00000	−0.0696733
$207$	−3.54988	−0.246734
$208$	−1.00000	−0.0693375
$209$	2.45767	0.170001
$210$	6.35418	0.438480
$211$	−18.5295	−1.27562	−0.637811	−	0.770193i	$-0.720160\pi$
$211$	−18.5295	−1.27562	−0.637811	+	0.770193i	$0.720160\pi$
$212$	6.23971	0.428545
$213$	0.749357	0.0513451
$214$	6.34500	0.433735
$215$	9.26290	0.631724
$216$	1.00000	0.0680414
$217$	16.5427	1.12299
$218$	3.27488	0.221803
$219$	4.06343	0.274581
$220$	−2.18575	−0.147363
$221$	7.05126	0.474319
$222$	1.93939	0.130163
$223$	−21.4736	−1.43798	−0.718988	−	0.695022i	$-0.755395\pi$
$223$	−21.4736	−1.43798	−0.718988	+	0.695022i	$0.755395\pi$
$224$	2.34175	0.156465
$225$	2.36272	0.157515
$226$	11.0842	0.737307
$227$	−5.45603	−0.362129	−0.181065	−	0.983471i	$-0.557954\pi$
$227$	−5.45603	−0.362129	−0.181065	+	0.983471i	$0.557954\pi$
$228$	−3.05101	−0.202058
$229$	2.36284	0.156141	0.0780703	−	0.996948i	$-0.475124\pi$
$229$	2.36284	0.156141	0.0780703	+	0.996948i	$0.475124\pi$
$230$	−9.63237	−0.635140
$231$	1.88635	0.124112
$232$	1.98812	0.130527
$233$	4.80781	0.314970	0.157485	−	0.987521i	$-0.449661\pi$
$233$	4.80781	0.314970	0.157485	+	0.987521i	$0.449661\pi$
$234$	1.00000	0.0653720
$235$	32.8306	2.14163
$236$	1.79179	0.116635
$237$	−4.75496	−0.308868
$238$	−16.5123	−1.07033
$239$	−25.2866	−1.63565	−0.817826	−	0.575465i	$-0.804821\pi$
$239$	−25.2866	−1.63565	−0.817826	+	0.575465i	$0.804821\pi$
$240$	2.71343	0.175151
$241$	3.99306	0.257215	0.128608	−	0.991696i	$-0.458949\pi$
$241$	3.99306	0.257215	0.128608	+	0.991696i	$0.458949\pi$
$242$	10.3511	0.665395
$243$	−1.00000	−0.0641500
$244$	−2.31314	−0.148084
$245$	4.11413	0.262842
$246$	−1.08094	−0.0689180
$247$	−3.05101	−0.194131
$248$	7.06425	0.448580
$249$	12.8746	0.815893
$250$	−7.15608	−0.452590
$251$	−2.60067	−0.164153	−0.0820764	−	0.996626i	$-0.526155\pi$
$251$	−2.60067	−0.164153	−0.0820764	+	0.996626i	$0.526155\pi$
$252$	−2.34175	−0.147516
$253$	−2.85953	−0.179777
$254$	20.2440	1.27022
$255$	−19.1331	−1.19816
$256$	1.00000	0.0625000
$257$	1.93178	0.120501	0.0602506	−	0.998183i	$-0.480810\pi$
$257$	1.93178	0.120501	0.0602506	+	0.998183i	$0.480810\pi$
$258$	−3.41372	−0.212529
$259$	−4.54157	−0.282200
$260$	2.71343	0.168280
$261$	−1.98812	−0.123062
$262$	18.2985	1.13049
$263$	19.7974	1.22076	0.610380	−	0.792109i	$-0.291017\pi$
$263$	19.7974	1.22076	0.610380	+	0.792109i	$0.291017\pi$
$264$	0.805528	0.0495769
$265$	−16.9310	−1.04006
$266$	7.14469	0.438069
$267$	7.49391	0.458620
$268$	4.26635	0.260609
$269$	20.6511	1.25912	0.629560	−	0.776952i	$-0.283235\pi$
$269$	20.6511	1.25912	0.629560	+	0.776952i	$0.283235\pi$
$270$	−2.71343	−0.165134
$271$	3.84564	0.233606	0.116803	−	0.993155i	$-0.462735\pi$
$271$	3.84564	0.233606	0.116803	+	0.993155i	$0.462735\pi$
$272$	−7.05126	−0.427546
$273$	−2.34175	−0.141729
$274$	9.99842	0.604026
$275$	1.90324	0.114770
$276$	3.54988	0.213678
$277$	−0.0114465	−0.000687752 0	−0.000343876	−	1.00000i	$-0.500109\pi$
$277$	−0.0114465	−0.000687752 0	−0.000343876		1.00000i	$0.500109\pi$
$278$	−8.86959	−0.531963
$279$	−7.06425	−0.422926
$280$	−6.35418	−0.379735
$281$	33.0434	1.97120	0.985601	−	0.169089i	$-0.0540824\pi$
$281$	33.0434	1.97120	0.985601	+	0.169089i	$0.0540824\pi$
$282$	−12.0993	−0.720503
$283$	26.6102	1.58181	0.790906	−	0.611938i	$-0.209610\pi$
$283$	26.6102	1.58181	0.790906	+	0.611938i	$0.209610\pi$
$284$	−0.749357	−0.0444661
$285$	8.27870	0.490388
$286$	0.805528	0.0476319
$287$	2.53128	0.149417
$288$	−1.00000	−0.0589256
$289$	32.7203	1.92472
$290$	−5.39464	−0.316784
$291$	9.03214	0.529473
$292$	−4.06343	−0.237794
$293$	−1.54531	−0.0902778	−0.0451389	−	0.998981i	$-0.514373\pi$
$293$	−1.54531	−0.0902778	−0.0451389	+	0.998981i	$0.514373\pi$
$294$	−1.51621	−0.0884270
$295$	−4.86189	−0.283070
$296$	−1.93939	−0.112725
$297$	−0.805528	−0.0467415
$298$	−1.38681	−0.0803356
$299$	3.54988	0.205295
$300$	−2.36272	−0.136412
$301$	7.99407	0.460771
$302$	−14.3074	−0.823297
$303$	8.39612	0.482345
$304$	3.05101	0.174987
$305$	6.27655	0.359394
$306$	7.05126	0.403094
$307$	−12.1150	−0.691442	−0.345721	−	0.938337i	$-0.612366\pi$
$307$	−12.1150	−0.691442	−0.345721	+	0.938337i	$0.612366\pi$
$308$	−1.88635	−0.107485
$309$	−1.00000	−0.0568880
$310$	−19.1684	−1.08869
$311$	23.1713	1.31393	0.656963	−	0.753923i	$-0.271841\pi$
$311$	23.1713	1.31393	0.656963	+	0.753923i	$0.271841\pi$
$312$	−1.00000	−0.0566139
$313$	−24.8428	−1.40420	−0.702098	−	0.712080i	$-0.747753\pi$
$313$	−24.8428	−1.40420	−0.702098	+	0.712080i	$0.747753\pi$
$314$	8.73671	0.493041
$315$	6.35418	0.358018
$316$	4.75496	0.267487
$317$	3.82838	0.215023	0.107512	−	0.994204i	$-0.465712\pi$
$317$	3.82838	0.215023	0.107512	+	0.994204i	$0.465712\pi$
$318$	6.23971	0.349905
$319$	−1.60149	−0.0896661
$320$	−2.71343	−0.151686
$321$	6.34500	0.354143
$322$	−8.31294	−0.463262
$323$	−21.5134	−1.19704
$324$	1.00000	0.0555556
$325$	−2.36272	−0.131060
$326$	−23.6512	−1.30992
$327$	3.27488	0.181101
$328$	1.08094	0.0596847
$329$	28.3335	1.56208
$330$	−2.18575	−0.120321
$331$	−14.1012	−0.775071	−0.387536	−	0.921855i	$-0.626674\pi$
$331$	−14.1012	−0.775071	−0.387536	+	0.921855i	$0.626674\pi$
$332$	−12.8746	−0.706584
$333$	1.93939	0.106278
$334$	−0.498550	−0.0272795
$335$	−11.5765	−0.632489
$336$	2.34175	0.127753
$337$	4.39388	0.239350	0.119675	−	0.992813i	$-0.461815\pi$
$337$	4.39388	0.239350	0.119675	+	0.992813i	$0.461815\pi$
$338$	−1.00000	−0.0543928
$339$	11.0842	0.602009
$340$	19.1331	1.03764
$341$	−5.69046	−0.308155
$342$	−3.05101	−0.164980
$343$	19.9428	1.07681
$344$	3.41372	0.184055
$345$	−9.63237	−0.518589
$346$	−1.59065	−0.0855141
$347$	−22.7230	−1.21984	−0.609918	−	0.792465i	$-0.708797\pi$
$347$	−22.7230	−1.21984	−0.609918	+	0.792465i	$0.708797\pi$
$348$	1.98812	0.106575
$349$	10.5744	0.566033	0.283017	−	0.959115i	$-0.408665\pi$
$349$	10.5744	0.566033	0.283017	+	0.959115i	$0.408665\pi$
$350$	5.53290	0.295746
$351$	1.00000	0.0533761
$352$	−0.805528	−0.0429348
$353$	−22.2749	−1.18557	−0.592787	−	0.805359i	$-0.701972\pi$
$353$	−22.2749	−1.18557	−0.592787	+	0.805359i	$0.701972\pi$
$354$	1.79179	0.0952324
$355$	2.03333	0.107918
$356$	−7.49391	−0.397176
$357$	−16.5123	−0.873923
$358$	19.1240	1.01073
$359$	37.2802	1.96757	0.983786	−	0.179344i	$-0.0573974\pi$
$359$	37.2802	1.96757	0.983786	+	0.179344i	$0.0573974\pi$
$360$	2.71343	0.143011
$361$	−9.69136	−0.510072
$362$	−13.3384	−0.701051
$363$	10.3511	0.543293
$364$	2.34175	0.122741
$365$	11.0259	0.577120
$366$	−2.31314	−0.120910
$367$	31.1367	1.62532	0.812662	−	0.582736i	$-0.198018\pi$
$367$	31.1367	1.62532	0.812662	+	0.582736i	$0.198018\pi$
$368$	−3.54988	−0.185050
$369$	−1.08094	−0.0562713
$370$	5.26241	0.273580
$371$	−14.6118	−0.758608
$372$	7.06425	0.366264
$373$	19.0317	0.985426	0.492713	−	0.870192i	$-0.336005\pi$
$373$	19.0317	0.985426	0.492713	+	0.870192i	$0.336005\pi$
$374$	5.67999	0.293705
$375$	−7.15608	−0.369538
$376$	12.0993	0.623974
$377$	1.98812	0.102393
$378$	−2.34175	−0.120447
$379$	16.7080	0.858235	0.429117	−	0.903249i	$-0.358825\pi$
$379$	16.7080	0.858235	0.429117	+	0.903249i	$0.358825\pi$
$380$	−8.27870	−0.424688
$381$	20.2440	1.03713
$382$	20.3164	1.03948
$383$	20.9445	1.07022	0.535108	−	0.844784i	$-0.320271\pi$
$383$	20.9445	1.07022	0.535108	+	0.844784i	$0.320271\pi$
$384$	1.00000	0.0510310
$385$	5.11848	0.260862
$386$	19.0532	0.969783
$387$	−3.41372	−0.173529
$388$	−9.03214	−0.458537
$389$	−12.5690	−0.637273	−0.318636	−	0.947877i	$-0.603225\pi$
$389$	−12.5690	−0.637273	−0.318636	+	0.947877i	$0.603225\pi$
$390$	2.71343	0.137400
$391$	25.0311	1.26588
$392$	1.51621	0.0765800
$393$	18.2985	0.923038
$394$	−0.799715	−0.0402891
$395$	−12.9023	−0.649183
$396$	0.805528	0.0404793
$397$	−13.8447	−0.694843	−0.347422	−	0.937709i	$-0.612943\pi$
$397$	−13.8447	−0.694843	−0.347422	+	0.937709i	$0.612943\pi$
$398$	11.3388	0.568363
$399$	7.14469	0.357682
$400$	2.36272	0.118136
$401$	2.71854	0.135758	0.0678788	−	0.997694i	$-0.478377\pi$
$401$	2.71854	0.135758	0.0678788	+	0.997694i	$0.478377\pi$
$402$	4.26635	0.212786
$403$	7.06425	0.351895
$404$	−8.39612	−0.417723
$405$	−2.71343	−0.134832
$406$	−4.65568	−0.231058
$407$	1.56224	0.0774371
$408$	−7.05126	−0.349090
$409$	27.6900	1.36918	0.684591	−	0.728927i	$-0.259981\pi$
$409$	27.6900	1.36918	0.684591	+	0.728927i	$0.259981\pi$
$410$	−2.93305	−0.144853
$411$	9.99842	0.493186
$412$	1.00000	0.0492665
$413$	−4.19592	−0.206468
$414$	3.54988	0.174467
$415$	34.9343	1.71486
$416$	1.00000	0.0490290
$417$	−8.86959	−0.434346
$418$	−2.45767	−0.120209
$419$	−3.53590	−0.172740	−0.0863700	−	0.996263i	$-0.527527\pi$
$419$	−3.53590	−0.172740	−0.0863700	+	0.996263i	$0.527527\pi$
$420$	−6.35418	−0.310052
$421$	1.25978	0.0613979	0.0306990	−	0.999529i	$-0.490227\pi$
$421$	1.25978	0.0613979	0.0306990	+	0.999529i	$0.490227\pi$
$422$	18.5295	0.902001
$423$	−12.0993	−0.588288
$424$	−6.23971	−0.303027
$425$	−16.6602	−0.808137
$426$	−0.749357	−0.0363065
$427$	5.41680	0.262137
$428$	−6.34500	−0.306697
$429$	0.805528	0.0388913
$430$	−9.26290	−0.446697
$431$	1.84789	0.0890098	0.0445049	−	0.999009i	$-0.485829\pi$
$431$	1.84789	0.0890098	0.0445049	+	0.999009i	$0.485829\pi$
$432$	−1.00000	−0.0481125
$433$	−13.8258	−0.664427	−0.332213	−	0.943204i	$-0.607795\pi$
$433$	−13.8258	−0.664427	−0.332213	+	0.943204i	$0.607795\pi$
$434$	−16.5427	−0.794076
$435$	−5.39464	−0.258653
$436$	−3.27488	−0.156838
$437$	−10.8307	−0.518103
$438$	−4.06343	−0.194158
$439$	17.6012	0.840059	0.420030	−	0.907510i	$-0.362020\pi$
$439$	17.6012	0.840059	0.420030	+	0.907510i	$0.362020\pi$
$440$	2.18575	0.104201
$441$	−1.51621	−0.0722003
$442$	−7.05126	−0.335394
$443$	−15.0423	−0.714681	−0.357341	−	0.933974i	$-0.616316\pi$
$443$	−15.0423	−0.714681	−0.357341	+	0.933974i	$0.616316\pi$
$444$	−1.93939	−0.0920395
$445$	20.3342	0.963935
$446$	21.4736	1.01680
$447$	−1.38681	−0.0655937
$448$	−2.34175	−0.110637
$449$	11.1989	0.528509	0.264255	−	0.964453i	$-0.414874\pi$
$449$	11.1989	0.528509	0.264255	+	0.964453i	$0.414874\pi$
$450$	−2.36272	−0.111380
$451$	−0.870725	−0.0410008
$452$	−11.0842	−0.521355
$453$	−14.3074	−0.672219
$454$	5.45603	0.256064
$455$	−6.35418	−0.297889
$456$	3.05101	0.142876
$457$	8.67449	0.405775	0.202888	−	0.979202i	$-0.434967\pi$
$457$	8.67449	0.405775	0.202888	+	0.979202i	$0.434967\pi$
$458$	−2.36284	−0.110408
$459$	7.05126	0.329125
$460$	9.63237	0.449111
$461$	10.0534	0.468233	0.234116	−	0.972209i	$-0.424780\pi$
$461$	10.0534	0.468233	0.234116	+	0.972209i	$0.424780\pi$
$462$	−1.88635	−0.0877608
$463$	33.8559	1.57342	0.786708	−	0.617325i	$-0.211784\pi$
$463$	33.8559	1.57342	0.786708	+	0.617325i	$0.211784\pi$
$464$	−1.98812	−0.0922962
$465$	−19.1684	−0.888912
$466$	−4.80781	−0.222717
$467$	−18.4086	−0.851848	−0.425924	−	0.904759i	$-0.640051\pi$
$467$	−18.4086	−0.851848	−0.425924	+	0.904759i	$0.640051\pi$
$468$	−1.00000	−0.0462250
$469$	−9.99073	−0.461329
$470$	−32.8306	−1.51436
$471$	8.73671	0.402566
$472$	−1.79179	−0.0824737
$473$	−2.74985	−0.126438
$474$	4.75496	0.218402
$475$	7.20868	0.330757
$476$	16.5123	0.756840
$477$	6.23971	0.285696
$478$	25.2866	1.15658
$479$	−33.3664	−1.52455	−0.762275	−	0.647254i	$-0.775917\pi$
$479$	−33.3664	−1.52455	−0.762275	+	0.647254i	$0.775917\pi$
$480$	−2.71343	−0.123851
$481$	−1.93939	−0.0884287
$482$	−3.99306	−0.181879
$483$	−8.31294	−0.378252
$484$	−10.3511	−0.470506
$485$	24.5081	1.11286
$486$	1.00000	0.0453609
$487$	16.6033	0.752367	0.376184	−	0.926545i	$-0.377236\pi$
$487$	16.6033	0.752367	0.376184	+	0.926545i	$0.377236\pi$
$488$	2.31314	0.104711
$489$	−23.6512	−1.06955
$490$	−4.11413	−0.185857
$491$	21.0116	0.948242	0.474121	−	0.880460i	$-0.342766\pi$
$491$	21.0116	0.948242	0.474121	+	0.880460i	$0.342766\pi$
$492$	1.08094	0.0487324
$493$	14.0188	0.631374
$494$	3.05101	0.137271
$495$	−2.18575	−0.0982421
$496$	−7.06425	−0.317194
$497$	1.75481	0.0787138
$498$	−12.8746	−0.576923
$499$	9.64276	0.431669	0.215834	−	0.976430i	$-0.430753\pi$
$499$	9.64276	0.431669	0.215834	+	0.976430i	$0.430753\pi$
$500$	7.15608	0.320030
$501$	−0.498550	−0.0222736
$502$	2.60067	0.116074
$503$	−10.0013	−0.445938	−0.222969	−	0.974826i	$-0.571575\pi$
$503$	−10.0013	−0.445938	−0.222969	+	0.974826i	$0.571575\pi$
$504$	2.34175	0.104310
$505$	22.7823	1.01380
$506$	2.85953	0.127122
$507$	−1.00000	−0.0444116
$508$	−20.2440	−0.898181
$509$	11.4095	0.505718	0.252859	−	0.967503i	$-0.418629\pi$
$509$	11.4095	0.505718	0.252859	+	0.967503i	$0.418629\pi$
$510$	19.1331	0.847229
$511$	9.51554	0.420943
$512$	−1.00000	−0.0441942
$513$	−3.05101	−0.134705
$514$	−1.93178	−0.0852072
$515$	−2.71343	−0.119568
$516$	3.41372	0.150281
$517$	−9.74633	−0.428643
$518$	4.54157	0.199545
$519$	−1.59065	−0.0698220
$520$	−2.71343	−0.118992
$521$	−26.1445	−1.14541	−0.572707	−	0.819760i	$-0.694107\pi$
$521$	−26.1445	−1.14541	−0.572707	+	0.819760i	$0.694107\pi$
$522$	1.98812	0.0870177
$523$	−33.5042	−1.46503	−0.732517	−	0.680748i	$-0.761655\pi$
$523$	−33.5042	−1.46503	−0.732517	+	0.680748i	$0.761655\pi$
$524$	−18.2985	−0.799374
$525$	5.53290	0.241476
$526$	−19.7974	−0.863208
$527$	49.8119	2.16984
$528$	−0.805528	−0.0350561
$529$	−10.3983	−0.452102
$530$	16.9310	0.735437
$531$	1.79179	0.0777569
$532$	−7.14469	−0.309762
$533$	1.08094	0.0468205
$534$	−7.49391	−0.324293
$535$	17.2167	0.744344
$536$	−4.26635	−0.184278
$537$	19.1240	0.825260
$538$	−20.6511	−0.890333
$539$	−1.22135	−0.0526072
$540$	2.71343	0.116768
$541$	−35.4070	−1.52226	−0.761132	−	0.648597i	$-0.775356\pi$
$541$	−35.4070	−1.52226	−0.761132	+	0.648597i	$0.775356\pi$
$542$	−3.84564	−0.165184
$543$	−13.3384	−0.572406
$544$	7.05126	0.302320
$545$	8.88616	0.380641
$546$	2.34175	0.100218
$547$	42.6935	1.82544	0.912722	−	0.408582i	$-0.133977\pi$
$547$	42.6935	1.82544	0.912722	+	0.408582i	$0.133977\pi$
$548$	−9.99842	−0.427111
$549$	−2.31314	−0.0987224
$550$	−1.90324	−0.0811544
$551$	−6.06577	−0.258411
$552$	−3.54988	−0.151093
$553$	−11.1349	−0.473505
$554$	0.0114465	0.000486314 0
$555$	5.26241	0.223377
$556$	8.86959	0.376154
$557$	33.9092	1.43678	0.718390	−	0.695640i	$-0.244879\pi$
$557$	33.9092	1.43678	0.718390	+	0.695640i	$0.244879\pi$
$558$	7.06425	0.299054
$559$	3.41372	0.144385
$560$	6.35418	0.268513
$561$	5.67999	0.239809
$562$	−33.0434	−1.39385
$563$	3.43746	0.144872	0.0724359	−	0.997373i	$-0.476923\pi$
$563$	3.43746	0.144872	0.0724359	+	0.997373i	$0.476923\pi$
$564$	12.0993	0.509472
$565$	30.0761	1.26531
$566$	−26.6102	−1.11851
$567$	−2.34175	−0.0983443
$568$	0.749357	0.0314423
$569$	−29.7936	−1.24901	−0.624507	−	0.781019i	$-0.714700\pi$
$569$	−29.7936	−1.24901	−0.624507	+	0.781019i	$0.714700\pi$
$570$	−8.27870	−0.346757
$571$	2.28764	0.0957349	0.0478675	−	0.998854i	$-0.484757\pi$
$571$	2.28764	0.0957349	0.0478675	+	0.998854i	$0.484757\pi$
$572$	−0.805528	−0.0336808
$573$	20.3164	0.848731
$574$	−2.53128	−0.105654
$575$	−8.38738	−0.349778
$576$	1.00000	0.0416667
$577$	−11.9061	−0.495657	−0.247828	−	0.968804i	$-0.579717\pi$
$577$	−11.9061	−0.495657	−0.247828	+	0.968804i	$0.579717\pi$
$578$	−32.7203	−1.36099
$579$	19.0532	0.791824
$580$	5.39464	0.224000
$581$	30.1490	1.25079
$582$	−9.03214	−0.374394
$583$	5.02626	0.208166
$584$	4.06343	0.168146
$585$	2.71343	0.112187
$586$	1.54531	0.0638361
$587$	−29.3687	−1.21218	−0.606088	−	0.795397i	$-0.707262\pi$
$587$	−29.3687	−1.21218	−0.606088	+	0.795397i	$0.707262\pi$
$588$	1.51621	0.0625273
$589$	−21.5531	−0.888079
$590$	4.86189	0.200161
$591$	−0.799715	−0.0328959
$592$	1.93939	0.0797085
$593$	−24.4812	−1.00532	−0.502661	−	0.864484i	$-0.667646\pi$
$593$	−24.4812	−1.00532	−0.502661	+	0.864484i	$0.667646\pi$
$594$	0.805528	0.0330512
$595$	−44.8050	−1.83683
$596$	1.38681	0.0568058
$597$	11.3388	0.464066
$598$	−3.54988	−0.145165
$599$	−21.3771	−0.873445	−0.436722	−	0.899596i	$-0.643861\pi$
$599$	−21.3771	−0.873445	−0.436722	+	0.899596i	$0.643861\pi$
$600$	2.36272	0.0964577
$601$	−10.3517	−0.422253	−0.211127	−	0.977459i	$-0.567713\pi$
$601$	−10.3517	−0.422253	−0.211127	+	0.977459i	$0.567713\pi$
$602$	−7.99407	−0.325814
$603$	4.26635	0.173739
$604$	14.3074	0.582159
$605$	28.0871	1.14190
$606$	−8.39612	−0.341069
$607$	−8.26118	−0.335311	−0.167655	−	0.985846i	$-0.553620\pi$
$607$	−8.26118	−0.335311	−0.167655	+	0.985846i	$0.553620\pi$
$608$	−3.05101	−0.123735
$609$	−4.65568	−0.188658
$610$	−6.27655	−0.254130
$611$	12.0993	0.489485
$612$	−7.05126	−0.285030
$613$	23.6435	0.954951	0.477476	−	0.878645i	$-0.341552\pi$
$613$	23.6435	0.954951	0.477476	+	0.878645i	$0.341552\pi$
$614$	12.1150	0.488923
$615$	−2.93305	−0.118272
$616$	1.88635	0.0760031
$617$	−6.83016	−0.274972	−0.137486	−	0.990504i	$-0.543902\pi$
$617$	−6.83016	−0.274972	−0.137486	+	0.990504i	$0.543902\pi$
$618$	1.00000	0.0402259
$619$	9.60961	0.386243	0.193121	−	0.981175i	$-0.438139\pi$
$619$	9.60961	0.386243	0.193121	+	0.981175i	$0.438139\pi$
$620$	19.1684	0.769821
$621$	3.54988	0.142452
$622$	−23.1713	−0.929086
$623$	17.5489	0.703080
$624$	1.00000	0.0400320
$625$	−31.2312	−1.24925
$626$	24.8428	0.992917
$627$	−2.45767	−0.0981500
$628$	−8.73671	−0.348633
$629$	−13.6752	−0.545264
$630$	−6.35418	−0.253157
$631$	25.4180	1.01188	0.505938	−	0.862570i	$-0.331146\pi$
$631$	25.4180	1.01188	0.505938	+	0.862570i	$0.331146\pi$
$632$	−4.75496	−0.189142
$633$	18.5295	0.736481
$634$	−3.82838	−0.152044
$635$	54.9306	2.17986
$636$	−6.23971	−0.247420
$637$	1.51621	0.0600743
$638$	1.60149	0.0634035
$639$	−0.749357	−0.0296441
$640$	2.71343	0.107258
$641$	−34.7435	−1.37229	−0.686143	−	0.727467i	$-0.740698\pi$
$641$	−34.7435	−1.37229	−0.686143	+	0.727467i	$0.740698\pi$
$642$	−6.34500	−0.250417
$643$	−7.13330	−0.281310	−0.140655	−	0.990059i	$-0.544921\pi$
$643$	−7.13330	−0.281310	−0.140655	+	0.990059i	$0.544921\pi$
$644$	8.31294	0.327576
$645$	−9.26290	−0.364726
$646$	21.5134	0.846435
$647$	−1.15514	−0.0454131	−0.0227066	−	0.999742i	$-0.507228\pi$
$647$	−1.15514	−0.0454131	−0.0227066	+	0.999742i	$0.507228\pi$
$648$	−1.00000	−0.0392837
$649$	1.44334	0.0566559
$650$	2.36272	0.0926736
$651$	−16.5427	−0.648360
$652$	23.6512	0.926253
$653$	6.30977	0.246920	0.123460	−	0.992350i	$-0.460601\pi$
$653$	6.30977	0.246920	0.123460	+	0.992350i	$0.460601\pi$
$654$	−3.27488	−0.128058
$655$	49.6518	1.94006
$656$	−1.08094	−0.0422035
$657$	−4.06343	−0.158530
$658$	−28.3335	−1.10456
$659$	−0.690152	−0.0268845	−0.0134423	−	0.999910i	$-0.504279\pi$
$659$	−0.690152	−0.0268845	−0.0134423	+	0.999910i	$0.504279\pi$
$660$	2.18575	0.0850801
$661$	23.7004	0.921839	0.460919	−	0.887442i	$-0.347520\pi$
$661$	23.7004	0.921839	0.460919	+	0.887442i	$0.347520\pi$
$662$	14.1012	0.548058
$663$	−7.05126	−0.273848
$664$	12.8746	0.499630
$665$	19.3867	0.751782
$666$	−1.93939	−0.0751499
$667$	7.05760	0.273271
$668$	0.498550	0.0192895
$669$	21.4736	0.830216
$670$	11.5765	0.447238
$671$	−1.86330	−0.0719319
$672$	−2.34175	−0.0903350
$673$	0.0367792	0.00141773	0.000708867	−	1.00000i	$-0.499774\pi$
$673$	0.0367792	0.00141773	0.000708867		1.00000i	$0.499774\pi$
$674$	−4.39388	−0.169246
$675$	−2.36272	−0.0909412
$676$	1.00000	0.0384615
$677$	−33.0504	−1.27023	−0.635115	−	0.772417i	$-0.719047\pi$
$677$	−33.0504	−1.27023	−0.635115	+	0.772417i	$0.719047\pi$
$678$	−11.0842	−0.425684
$679$	21.1510	0.811701
$680$	−19.1331	−0.733722
$681$	5.45603	0.209076
$682$	5.69046	0.217899
$683$	35.3472	1.35252	0.676261	−	0.736662i	$-0.263599\pi$
$683$	35.3472	1.35252	0.676261	+	0.736662i	$0.263599\pi$
$684$	3.05101	0.116658
$685$	27.1300	1.03659
$686$	−19.9428	−0.761421
$687$	−2.36284	−0.0901478
$688$	−3.41372	−0.130147
$689$	−6.23971	−0.237714
$690$	9.63237	0.366698
$691$	26.1666	0.995423	0.497711	−	0.867343i	$-0.334174\pi$
$691$	26.1666	0.995423	0.497711	+	0.867343i	$0.334174\pi$
$692$	1.59065	0.0604676
$693$	−1.88635	−0.0716564
$694$	22.7230	0.862554
$695$	−24.0670	−0.912915
$696$	−1.98812	−0.0753596
$697$	7.62196	0.288702
$698$	−10.5744	−0.400246
$699$	−4.80781	−0.181848
$700$	−5.53290	−0.209124
$701$	1.48336	0.0560259	0.0280130	−	0.999608i	$-0.491082\pi$
$701$	1.48336	0.0560259	0.0280130	+	0.999608i	$0.491082\pi$
$702$	−1.00000	−0.0377426
$703$	5.91710	0.223168
$704$	0.805528	0.0303595
$705$	−32.8306	−1.23647
$706$	22.2749	0.838328
$707$	19.6616	0.739451
$708$	−1.79179	−0.0673395
$709$	34.3436	1.28980	0.644901	−	0.764266i	$-0.276899\pi$
$709$	34.3436	1.28980	0.644901	+	0.764266i	$0.276899\pi$
$710$	−2.03333	−0.0763095
$711$	4.75496	0.178325
$712$	7.49391	0.280846
$713$	25.0773	0.939151
$714$	16.5123	0.617957
$715$	2.18575	0.0817423
$716$	−19.1240	−0.714696
$717$	25.2866	0.944344
$718$	−37.2802	−1.39128
$719$	−21.8973	−0.816632	−0.408316	−	0.912841i	$-0.633884\pi$
$719$	−21.8973	−0.816632	−0.408316	+	0.912841i	$0.633884\pi$
$720$	−2.71343	−0.101124
$721$	−2.34175	−0.0872113
$722$	9.69136	0.360675
$723$	−3.99306	−0.148503
$724$	13.3384	0.495718
$725$	−4.69738	−0.174456
$726$	−10.3511	−0.384166
$727$	−11.0035	−0.408096	−0.204048	−	0.978961i	$-0.565410\pi$
$727$	−11.0035	−0.408096	−0.204048	+	0.978961i	$0.565410\pi$
$728$	−2.34175	−0.0867910
$729$	1.00000	0.0370370
$730$	−11.0259	−0.408085
$731$	24.0710	0.890299
$732$	2.31314	0.0854961
$733$	−18.8770	−0.697238	−0.348619	−	0.937265i	$-0.613349\pi$
$733$	−18.8770	−0.697238	−0.348619	+	0.937265i	$0.613349\pi$
$734$	−31.1367	−1.14928
$735$	−4.11413	−0.151752
$736$	3.54988	0.130850
$737$	3.43667	0.126591
$738$	1.08094	0.0397898
$739$	34.2502	1.25991	0.629956	−	0.776631i	$-0.283073\pi$
$739$	34.2502	1.25991	0.629956	+	0.776631i	$0.283073\pi$
$740$	−5.26241	−0.193450
$741$	3.05101	0.112082
$742$	14.6118	0.536417
$743$	−9.59805	−0.352118	−0.176059	−	0.984380i	$-0.556335\pi$
$743$	−9.59805	−0.352118	−0.176059	+	0.984380i	$0.556335\pi$
$744$	−7.06425	−0.258988
$745$	−3.76301	−0.137866
$746$	−19.0317	−0.696802
$747$	−12.8746	−0.471056
$748$	−5.67999	−0.207681
$749$	14.8584	0.542914
$750$	7.15608	0.261303
$751$	31.5449	1.15109	0.575545	−	0.817770i	$-0.304790\pi$
$751$	31.5449	1.15109	0.575545	+	0.817770i	$0.304790\pi$
$752$	−12.0993	−0.441216
$753$	2.60067	0.0947737
$754$	−1.98812	−0.0724031
$755$	−38.8221	−1.41288
$756$	2.34175	0.0851686
$757$	4.66137	0.169420	0.0847101	−	0.996406i	$-0.473004\pi$
$757$	4.66137	0.169420	0.0847101	+	0.996406i	$0.473004\pi$
$758$	−16.7080	−0.606864
$759$	2.85953	0.103794
$760$	8.27870	0.300300
$761$	−21.2740	−0.771181	−0.385590	−	0.922670i	$-0.626002\pi$
$761$	−21.2740	−0.771181	−0.385590	+	0.922670i	$0.626002\pi$
$762$	−20.2440	−0.733361
$763$	7.66894	0.277634
$764$	−20.3164	−0.735022
$765$	19.1331	0.691760
$766$	−20.9445	−0.756757
$767$	−1.79179	−0.0646977
$768$	−1.00000	−0.0360844
$769$	39.3228	1.41802	0.709008	−	0.705201i	$-0.249143\pi$
$769$	39.3228	1.41802	0.709008	+	0.705201i	$0.249143\pi$
$770$	−5.11848	−0.184457
$771$	−1.93178	−0.0695714
$772$	−19.0532	−0.685740
$773$	−9.02272	−0.324525	−0.162262	−	0.986748i	$-0.551879\pi$
$773$	−9.02272	−0.324525	−0.162262	+	0.986748i	$0.551879\pi$
$774$	3.41372	0.122704
$775$	−16.6909	−0.599553
$776$	9.03214	0.324235
$777$	4.54157	0.162928
$778$	12.5690	0.450620
$779$	−3.29794	−0.118161
$780$	−2.71343	−0.0971565
$781$	−0.603628	−0.0215995
$782$	−25.0311	−0.895112
$783$	1.98812	0.0710497
$784$	−1.51621	−0.0541502
$785$	23.7065	0.846120
$786$	−18.2985	−0.652686
$787$	−23.0968	−0.823312	−0.411656	−	0.911339i	$-0.635050\pi$
$787$	−23.0968	−0.823312	−0.411656	+	0.911339i	$0.635050\pi$
$788$	0.799715	0.0284887
$789$	−19.7974	−0.704806
$790$	12.9023	0.459042
$791$	25.9563	0.922900
$792$	−0.805528	−0.0286232
$793$	2.31314	0.0821420
$794$	13.8447	0.491328
$795$	16.9310	0.600482
$796$	−11.3388	−0.401893
$797$	−34.9077	−1.23650	−0.618248	−	0.785983i	$-0.712157\pi$
$797$	−34.9077	−1.23650	−0.618248	+	0.785983i	$0.712157\pi$
$798$	−7.14469	−0.252919
$799$	85.3153	3.01824
$800$	−2.36272	−0.0835348
$801$	−7.49391	−0.264784
$802$	−2.71854	−0.0959951
$803$	−3.27321	−0.115509
$804$	−4.26635	−0.150463
$805$	−22.5566	−0.795016
$806$	−7.06425	−0.248828
$807$	−20.6511	−0.726953
$808$	8.39612	0.295374
$809$	33.8401	1.18975	0.594877	−	0.803817i	$-0.297201\pi$
$809$	33.8401	1.18975	0.594877	+	0.803817i	$0.297201\pi$
$810$	2.71343	0.0953403
$811$	−46.2855	−1.62530	−0.812651	−	0.582751i	$-0.801976\pi$
$811$	−46.2855	−1.62530	−0.812651	+	0.582751i	$0.801976\pi$
$812$	4.65568	0.163382
$813$	−3.84564	−0.134872
$814$	−1.56224	−0.0547563
$815$	−64.1760	−2.24799
$816$	7.05126	0.246844
$817$	−10.4153	−0.364384
$818$	−27.6900	−0.968158
$819$	2.34175	0.0818274
$820$	2.93305	0.102426
$821$	−20.1519	−0.703305	−0.351653	−	0.936131i	$-0.614380\pi$
$821$	−20.1519	−0.703305	−0.351653	+	0.936131i	$0.614380\pi$
$822$	−9.99842	−0.348735
$823$	−20.7515	−0.723353	−0.361676	−	0.932304i	$-0.617795\pi$
$823$	−20.7515	−0.723353	−0.361676	+	0.932304i	$0.617795\pi$
$824$	−1.00000	−0.0348367
$825$	−1.90324	−0.0662623
$826$	4.19592	0.145995
$827$	−3.60766	−0.125451	−0.0627253	−	0.998031i	$-0.519979\pi$
$827$	−3.60766	−0.125451	−0.0627253	+	0.998031i	$0.519979\pi$
$828$	−3.54988	−0.123367
$829$	−13.0412	−0.452941	−0.226471	−	0.974018i	$-0.572719\pi$
$829$	−13.0412	−0.452941	−0.226471	+	0.974018i	$0.572719\pi$
$830$	−34.9343	−1.21259
$831$	0.0114465	0.000397074 0
$832$	−1.00000	−0.0346688
$833$	10.6912	0.370427
$834$	8.86959	0.307129
$835$	−1.35278	−0.0468150
$836$	2.45767	0.0850004
$837$	7.06425	0.244176
$838$	3.53590	0.122146
$839$	16.3968	0.566081	0.283041	−	0.959108i	$-0.408657\pi$
$839$	16.3968	0.566081	0.283041	+	0.959108i	$0.408657\pi$
$840$	6.35418	0.219240
$841$	−25.0474	−0.863702
$842$	−1.25978	−0.0434149
$843$	−33.0434	−1.13807
$844$	−18.5295	−0.637811
$845$	−2.71343	−0.0933450
$846$	12.0993	0.415982
$847$	24.2397	0.832888
$848$	6.23971	0.214272
$849$	−26.6102	−0.913259
$850$	16.6602	0.571439
$851$	−6.88461	−0.236001
$852$	0.749357	0.0256725
$853$	−41.3915	−1.41722	−0.708610	−	0.705601i	$-0.750677\pi$
$853$	−41.3915	−1.41722	−0.708610	+	0.705601i	$0.750677\pi$
$854$	−5.41680	−0.185359
$855$	−8.27870	−0.283126
$856$	6.34500	0.216867
$857$	19.7619	0.675055	0.337527	−	0.941316i	$-0.390409\pi$
$857$	19.7619	0.675055	0.337527	+	0.941316i	$0.390409\pi$
$858$	−0.805528	−0.0275003
$859$	38.9296	1.32826	0.664130	−	0.747617i	$-0.268802\pi$
$859$	38.9296	1.32826	0.664130	+	0.747617i	$0.268802\pi$
$860$	9.26290	0.315862
$861$	−2.53128	−0.0862659
$862$	−1.84789	−0.0629395
$863$	53.6130	1.82501	0.912504	−	0.409067i	$-0.134146\pi$
$863$	53.6130	1.82501	0.912504	+	0.409067i	$0.134146\pi$
$864$	1.00000	0.0340207
$865$	−4.31614	−0.146753
$866$	13.8258	0.469821
$867$	−32.7203	−1.11124
$868$	16.5427	0.561496
$869$	3.83025	0.129932
$870$	5.39464	0.182895
$871$	−4.26635	−0.144560
$872$	3.27488	0.110901
$873$	−9.03214	−0.305692
$874$	10.8307	0.366354
$875$	−16.7578	−0.566515
$876$	4.06343	0.137291
$877$	−40.5319	−1.36867	−0.684333	−	0.729170i	$-0.739906\pi$
$877$	−40.5319	−1.36867	−0.684333	+	0.729170i	$0.739906\pi$
$878$	−17.6012	−0.594011
$879$	1.54531	0.0521219
$880$	−2.18575	−0.0736815
$881$	−25.9077	−0.872854	−0.436427	−	0.899740i	$-0.643756\pi$
$881$	−25.9077	−0.872854	−0.436427	+	0.899740i	$0.643756\pi$
$882$	1.51621	0.0510533
$883$	10.4702	0.352351	0.176175	−	0.984359i	$-0.443627\pi$
$883$	10.4702	0.352351	0.176175	+	0.984359i	$0.443627\pi$
$884$	7.05126	0.237160
$885$	4.86189	0.163431
$886$	15.0423	0.505356
$887$	9.90172	0.332467	0.166234	−	0.986086i	$-0.446839\pi$
$887$	9.90172	0.332467	0.166234	+	0.986086i	$0.446839\pi$
$888$	1.93939	0.0650817
$889$	47.4063	1.58996
$890$	−20.3342	−0.681605
$891$	0.805528	0.0269862
$892$	−21.4736	−0.718988
$893$	−36.9150	−1.23531
$894$	1.38681	0.0463818
$895$	51.8916	1.73454
$896$	2.34175	0.0782324
$897$	−3.54988	−0.118527
$898$	−11.1989	−0.373713
$899$	14.0446	0.468413
$900$	2.36272	0.0787574
$901$	−43.9978	−1.46578
$902$	0.870725	0.0289920
$903$	−7.99407	−0.266026
$904$	11.0842	0.368653
$905$	−36.1929	−1.20309
$906$	14.3074	0.475331
$907$	8.30387	0.275726	0.137863	−	0.990451i	$-0.455977\pi$
$907$	8.30387	0.275726	0.137863	+	0.990451i	$0.455977\pi$
$908$	−5.45603	−0.181065
$909$	−8.39612	−0.278482
$910$	6.35418	0.210639
$911$	3.19275	0.105780	0.0528902	−	0.998600i	$-0.483157\pi$
$911$	3.19275	0.105780	0.0528902	+	0.998600i	$0.483157\pi$
$912$	−3.05101	−0.101029
$913$	−10.3708	−0.343224
$914$	−8.67449	−0.286927
$915$	−6.27655	−0.207496
$916$	2.36284	0.0780703
$917$	42.8505	1.41505
$918$	−7.05126	−0.232726
$919$	−2.87135	−0.0947171	−0.0473586	−	0.998878i	$-0.515080\pi$
$919$	−2.87135	−0.0947171	−0.0473586	+	0.998878i	$0.515080\pi$
$920$	−9.63237	−0.317570
$921$	12.1150	0.399204
$922$	−10.0534	−0.331090
$923$	0.749357	0.0246654
$924$	1.88635	0.0620562
$925$	4.58224	0.150663
$926$	−33.8559	−1.11257
$927$	1.00000	0.0328443
$928$	1.98812	0.0652633
$929$	27.2997	0.895673	0.447836	−	0.894116i	$-0.352195\pi$
$929$	27.2997	0.895673	0.447836	+	0.894116i	$0.352195\pi$
$930$	19.1684	0.628556
$931$	−4.62596	−0.151610
$932$	4.80781	0.157485
$933$	−23.1713	−0.758595
$934$	18.4086	0.602347
$935$	15.4123	0.504036
$936$	1.00000	0.0326860
$937$	−17.2594	−0.563839	−0.281920	−	0.959438i	$-0.590971\pi$
$937$	−17.2594	−0.563839	−0.281920	+	0.959438i	$0.590971\pi$
$938$	9.99073	0.326209
$939$	24.8428	0.810713
$940$	32.8306	1.07082
$941$	11.7910	0.384376	0.192188	−	0.981358i	$-0.438442\pi$
$941$	11.7910	0.384376	0.192188	+	0.981358i	$0.438442\pi$
$942$	−8.73671	−0.284657
$943$	3.83720	0.124956
$944$	1.79179	0.0583177
$945$	−6.35418	−0.206702
$946$	2.74985	0.0894052
$947$	−1.42209	−0.0462116	−0.0231058	−	0.999733i	$-0.507355\pi$
$947$	−1.42209	−0.0462116	−0.0231058	+	0.999733i	$0.507355\pi$
$948$	−4.75496	−0.154434
$949$	4.06343	0.131905
$950$	−7.20868	−0.233880
$951$	−3.82838	−0.124144
$952$	−16.5123	−0.535167
$953$	−5.98592	−0.193903	−0.0969515	−	0.995289i	$-0.530909\pi$
$953$	−5.98592	−0.193903	−0.0969515	+	0.995289i	$0.530909\pi$
$954$	−6.23971	−0.202018
$955$	55.1273	1.78388
$956$	−25.2866	−0.817826
$957$	1.60149	0.0517688
$958$	33.3664	1.07802
$959$	23.4138	0.756071
$960$	2.71343	0.0875757
$961$	18.9037	0.609795
$962$	1.93939	0.0625285
$963$	−6.34500	−0.204465
$964$	3.99306	0.128608
$965$	51.6996	1.66427
$966$	8.31294	0.267464
$967$	42.6878	1.37275	0.686374	−	0.727249i	$-0.259201\pi$
$967$	42.6878	1.37275	0.686374	+	0.727249i	$0.259201\pi$
$968$	10.3511	0.332698
$969$	21.5134	0.691111
$970$	−24.5081	−0.786908
$971$	45.7866	1.46936	0.734682	−	0.678412i	$-0.237332\pi$
$971$	45.7866	1.46936	0.734682	+	0.678412i	$0.237332\pi$
$972$	−1.00000	−0.0320750
$973$	−20.7704	−0.665867
$974$	−16.6033	−0.532004
$975$	2.36272	0.0756676
$976$	−2.31314	−0.0740418
$977$	34.8691	1.11556	0.557781	−	0.829988i	$-0.311653\pi$
$977$	34.8691	1.11556	0.557781	+	0.829988i	$0.311653\pi$
$978$	23.6512	0.756283
$979$	−6.03656	−0.192929
$980$	4.11413	0.131421
$981$	−3.27488	−0.104559
$982$	−21.0116	−0.670508
$983$	−10.3386	−0.329749	−0.164874	−	0.986315i	$-0.552722\pi$
$983$	−10.3386	−0.329749	−0.164874	+	0.986315i	$0.552722\pi$
$984$	−1.08094	−0.0344590
$985$	−2.16997	−0.0691411
$986$	−14.0188	−0.446449
$987$	−28.3335	−0.901866
$988$	−3.05101	−0.0970654
$989$	12.1183	0.385339
$990$	2.18575	0.0694676
$991$	20.6801	0.656926	0.328463	−	0.944517i	$-0.393469\pi$
$991$	20.6801	0.656926	0.328463	+	0.944517i	$0.393469\pi$
$992$	7.06425	0.224290
$993$	14.1012	0.447488
$994$	−1.75481	−0.0556591
$995$	30.7671	0.975382
$996$	12.8746	0.407946
$997$	10.6927	0.338642	0.169321	−	0.985561i	$-0.445843\pi$
$997$	10.6927	0.338642	0.169321	+	0.985561i	$0.445843\pi$
$998$	−9.64276	−0.305236
$999$	−1.93939	−0.0613596

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.ba.1.4	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.ba.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.71343 q^{5} +1.00000 q^{6} -2.34175 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.71343 q^{5} +1.00000 q^{6} -2.34175 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.71343 q^{10} +0.805528 q^{11} -1.00000 q^{12} -1.00000 q^{13} +2.34175 q^{14} +2.71343 q^{15} +1.00000 q^{16} -7.05126 q^{17} -1.00000 q^{18} +3.05101 q^{19} -2.71343 q^{20} +2.34175 q^{21} -0.805528 q^{22} -3.54988 q^{23} +1.00000 q^{24} +2.36272 q^{25} +1.00000 q^{26} -1.00000 q^{27} -2.34175 q^{28} -1.98812 q^{29} -2.71343 q^{30} -7.06425 q^{31} -1.00000 q^{32} -0.805528 q^{33} +7.05126 q^{34} +6.35418 q^{35} +1.00000 q^{36} +1.93939 q^{37} -3.05101 q^{38} +1.00000 q^{39} +2.71343 q^{40} -1.08094 q^{41} -2.34175 q^{42} -3.41372 q^{43} +0.805528 q^{44} -2.71343 q^{45} +3.54988 q^{46} -12.0993 q^{47} -1.00000 q^{48} -1.51621 q^{49} -2.36272 q^{50} +7.05126 q^{51} -1.00000 q^{52} +6.23971 q^{53} +1.00000 q^{54} -2.18575 q^{55} +2.34175 q^{56} -3.05101 q^{57} +1.98812 q^{58} +1.79179 q^{59} +2.71343 q^{60} -2.31314 q^{61} +7.06425 q^{62} -2.34175 q^{63} +1.00000 q^{64} +2.71343 q^{65} +0.805528 q^{66} +4.26635 q^{67} -7.05126 q^{68} +3.54988 q^{69} -6.35418 q^{70} -0.749357 q^{71} -1.00000 q^{72} -4.06343 q^{73} -1.93939 q^{74} -2.36272 q^{75} +3.05101 q^{76} -1.88635 q^{77} -1.00000 q^{78} +4.75496 q^{79} -2.71343 q^{80} +1.00000 q^{81} +1.08094 q^{82} -12.8746 q^{83} +2.34175 q^{84} +19.1331 q^{85} +3.41372 q^{86} +1.98812 q^{87} -0.805528 q^{88} -7.49391 q^{89} +2.71343 q^{90} +2.34175 q^{91} -3.54988 q^{92} +7.06425 q^{93} +12.0993 q^{94} -8.27870 q^{95} +1.00000 q^{96} -9.03214 q^{97} +1.51621 q^{98} +0.805528 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) \) 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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