LMFDB - Embedded newform 8034.2.a.s.1.8

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:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 15x^{8} + 72x^{7} - 27x^{6} - 115x^{5} + 54x^{4} + 68x^{3} - 15x^{2} - 15x - 2 $ x^10 - 4x^9 - 15x^8 + 72x^7 - 27x^6 - 115x^5 + 54x^4 + 68x^3 - 15x^2 - 15*x - 2
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			1.8
Root			$2.73145$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.66497 q^{5} +1.00000 q^{6} +2.36859 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.66497 q^{5} +1.00000 q^{6} +2.36859 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.66497 q^{10} +2.99046 q^{11} -1.00000 q^{12} -1.00000 q^{13} -2.36859 q^{14} -2.66497 q^{15} +1.00000 q^{16} -5.10004 q^{17} -1.00000 q^{18} -4.97673 q^{19} +2.66497 q^{20} -2.36859 q^{21} -2.99046 q^{22} +8.19215 q^{23} +1.00000 q^{24} +2.10207 q^{25} +1.00000 q^{26} -1.00000 q^{27} +2.36859 q^{28} -8.89325 q^{29} +2.66497 q^{30} +2.96518 q^{31} -1.00000 q^{32} -2.99046 q^{33} +5.10004 q^{34} +6.31222 q^{35} +1.00000 q^{36} -7.50176 q^{37} +4.97673 q^{38} +1.00000 q^{39} -2.66497 q^{40} -5.29737 q^{41} +2.36859 q^{42} +5.03485 q^{43} +2.99046 q^{44} +2.66497 q^{45} -8.19215 q^{46} -6.68426 q^{47} -1.00000 q^{48} -1.38978 q^{49} -2.10207 q^{50} +5.10004 q^{51} -1.00000 q^{52} -9.57222 q^{53} +1.00000 q^{54} +7.96949 q^{55} -2.36859 q^{56} +4.97673 q^{57} +8.89325 q^{58} +4.13496 q^{59} -2.66497 q^{60} -0.907884 q^{61} -2.96518 q^{62} +2.36859 q^{63} +1.00000 q^{64} -2.66497 q^{65} +2.99046 q^{66} -3.14935 q^{67} -5.10004 q^{68} -8.19215 q^{69} -6.31222 q^{70} -9.42543 q^{71} -1.00000 q^{72} +1.53198 q^{73} +7.50176 q^{74} -2.10207 q^{75} -4.97673 q^{76} +7.08317 q^{77} -1.00000 q^{78} -16.6133 q^{79} +2.66497 q^{80} +1.00000 q^{81} +5.29737 q^{82} -10.6717 q^{83} -2.36859 q^{84} -13.5915 q^{85} -5.03485 q^{86} +8.89325 q^{87} -2.99046 q^{88} +14.2388 q^{89} -2.66497 q^{90} -2.36859 q^{91} +8.19215 q^{92} -2.96518 q^{93} +6.68426 q^{94} -13.2629 q^{95} +1.00000 q^{96} -5.63892 q^{97} +1.38978 q^{98} +2.99046 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} + 10 q^{6} - 9 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + 6 * q^5 + 10 * q^6 - 9 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} + 10 q^{6} - 9 q^{7} - 10 q^{8} + 10 q^{9} - 6 q^{10} - q^{11} - 10 q^{12} - 10 q^{13} + 9 q^{14} - 6 q^{15} + 10 q^{16} + 5 q^{17} - 10 q^{18} - 9 q^{19} + 6 q^{20} + 9 q^{21} + q^{22} + q^{23} + 10 q^{24} + 20 q^{25} + 10 q^{26} - 10 q^{27} - 9 q^{28} - 22 q^{29} + 6 q^{30} - 13 q^{31} - 10 q^{32} + q^{33} - 5 q^{34} + 14 q^{35} + 10 q^{36} + 10 q^{37} + 9 q^{38} + 10 q^{39} - 6 q^{40} - 18 q^{41} - 9 q^{42} + 10 q^{43} - q^{44} + 6 q^{45} - q^{46} + 28 q^{47} - 10 q^{48} + 11 q^{49} - 20 q^{50} - 5 q^{51} - 10 q^{52} + 6 q^{53} + 10 q^{54} - 26 q^{55} + 9 q^{56} + 9 q^{57} + 22 q^{58} + 7 q^{59} - 6 q^{60} - 20 q^{61} + 13 q^{62} - 9 q^{63} + 10 q^{64} - 6 q^{65} - q^{66} - 21 q^{67} + 5 q^{68} - q^{69} - 14 q^{70} - 19 q^{71} - 10 q^{72} + 3 q^{73} - 10 q^{74} - 20 q^{75} - 9 q^{76} + 28 q^{77} - 10 q^{78} - 11 q^{79} + 6 q^{80} + 10 q^{81} + 18 q^{82} + 20 q^{83} + 9 q^{84} - q^{85} - 10 q^{86} + 22 q^{87} + q^{88} + 22 q^{89} - 6 q^{90} + 9 q^{91} + q^{92} + 13 q^{93} - 28 q^{94} + 10 q^{96} - 10 q^{97} - 11 q^{98} - q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + 6 * q^5 + 10 * q^6 - 9 * q^7 - 10 * q^8 + 10 * q^9 - 6 * q^10 - q^11 - 10 * q^12 - 10 * q^13 + 9 * q^14 - 6 * q^15 + 10 * q^16 + 5 * q^17 - 10 * q^18 - 9 * q^19 + 6 * q^20 + 9 * q^21 + q^22 + q^23 + 10 * q^24 + 20 * q^25 + 10 * q^26 - 10 * q^27 - 9 * q^28 - 22 * q^29 + 6 * q^30 - 13 * q^31 - 10 * q^32 + q^33 - 5 * q^34 + 14 * q^35 + 10 * q^36 + 10 * q^37 + 9 * q^38 + 10 * q^39 - 6 * q^40 - 18 * q^41 - 9 * q^42 + 10 * q^43 - q^44 + 6 * q^45 - q^46 + 28 * q^47 - 10 * q^48 + 11 * q^49 - 20 * q^50 - 5 * q^51 - 10 * q^52 + 6 * q^53 + 10 * q^54 - 26 * q^55 + 9 * q^56 + 9 * q^57 + 22 * q^58 + 7 * q^59 - 6 * q^60 - 20 * q^61 + 13 * q^62 - 9 * q^63 + 10 * q^64 - 6 * q^65 - q^66 - 21 * q^67 + 5 * q^68 - q^69 - 14 * q^70 - 19 * q^71 - 10 * q^72 + 3 * q^73 - 10 * q^74 - 20 * q^75 - 9 * q^76 + 28 * q^77 - 10 * q^78 - 11 * q^79 + 6 * q^80 + 10 * q^81 + 18 * q^82 + 20 * q^83 + 9 * q^84 - q^85 - 10 * q^86 + 22 * q^87 + q^88 + 22 * q^89 - 6 * q^90 + 9 * q^91 + q^92 + 13 * q^93 - 28 * q^94 + 10 * q^96 - 10 * q^97 - 11 * 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
$5$	2.66497	1.19181	0.595906	−	0.803054i	$-0.296793\pi$
$5$	2.66497	1.19181	0.595906	+	0.803054i	$0.296793\pi$
$6$	1.00000	0.408248
$7$	2.36859	0.895243	0.447621	−	0.894223i	$-0.352271\pi$
$7$	2.36859	0.895243	0.447621	+	0.894223i	$0.352271\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−2.66497	−0.842738
$11$	2.99046	0.901657	0.450829	−	0.892611i	$-0.351129\pi$
$11$	2.99046	0.901657	0.450829	+	0.892611i	$0.351129\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−2.36859	−0.633032
$15$	−2.66497	−0.688093
$16$	1.00000	0.250000
$17$	−5.10004	−1.23694	−0.618471	−	0.785808i	$-0.712247\pi$
$17$	−5.10004	−1.23694	−0.618471	+	0.785808i	$0.712247\pi$
$18$	−1.00000	−0.235702
$19$	−4.97673	−1.14174	−0.570871	−	0.821040i	$-0.693394\pi$
$19$	−4.97673	−1.14174	−0.570871	+	0.821040i	$0.693394\pi$
$20$	2.66497	0.595906
$21$	−2.36859	−0.516869
$22$	−2.99046	−0.637568
$23$	8.19215	1.70818	0.854091	−	0.520124i	$-0.174114\pi$
$23$	8.19215	1.70818	0.854091	+	0.520124i	$0.174114\pi$
$24$	1.00000	0.204124
$25$	2.10207	0.420414
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	2.36859	0.447621
$29$	−8.89325	−1.65143	−0.825717	−	0.564084i	$-0.809229\pi$
$29$	−8.89325	−1.65143	−0.825717	+	0.564084i	$0.809229\pi$
$30$	2.66497	0.486555
$31$	2.96518	0.532563	0.266281	−	0.963895i	$-0.414205\pi$
$31$	2.96518	0.532563	0.266281	+	0.963895i	$0.414205\pi$
$32$	−1.00000	−0.176777
$33$	−2.99046	−0.520572
$34$	5.10004	0.874649
$35$	6.31222	1.06696
$36$	1.00000	0.166667
$37$	−7.50176	−1.23328	−0.616641	−	0.787244i	$-0.711507\pi$
$37$	−7.50176	−1.23328	−0.616641	+	0.787244i	$0.711507\pi$
$38$	4.97673	0.807333
$39$	1.00000	0.160128
$40$	−2.66497	−0.421369
$41$	−5.29737	−0.827310	−0.413655	−	0.910434i	$-0.635748\pi$
$41$	−5.29737	−0.827310	−0.413655	+	0.910434i	$0.635748\pi$
$42$	2.36859	0.365481
$43$	5.03485	0.767808	0.383904	−	0.923373i	$-0.374579\pi$
$43$	5.03485	0.767808	0.383904	+	0.923373i	$0.374579\pi$
$44$	2.99046	0.450829
$45$	2.66497	0.397270
$46$	−8.19215	−1.20787
$47$	−6.68426	−0.975000	−0.487500	−	0.873123i	$-0.662091\pi$
$47$	−6.68426	−0.975000	−0.487500	+	0.873123i	$0.662091\pi$
$48$	−1.00000	−0.144338
$49$	−1.38978	−0.198541
$50$	−2.10207	−0.297278
$51$	5.10004	0.714148
$52$	−1.00000	−0.138675
$53$	−9.57222	−1.31485	−0.657423	−	0.753522i	$-0.728353\pi$
$53$	−9.57222	−1.31485	−0.657423	+	0.753522i	$0.728353\pi$
$54$	1.00000	0.136083
$55$	7.96949	1.07461
$56$	−2.36859	−0.316516
$57$	4.97673	0.659185
$58$	8.89325	1.16774
$59$	4.13496	0.538326	0.269163	−	0.963095i	$-0.413253\pi$
$59$	4.13496	0.538326	0.269163	+	0.963095i	$0.413253\pi$
$60$	−2.66497	−0.344046
$61$	−0.907884	−0.116243	−0.0581213	−	0.998310i	$-0.518511\pi$
$61$	−0.907884	−0.116243	−0.0581213	+	0.998310i	$0.518511\pi$
$62$	−2.96518	−0.376579
$63$	2.36859	0.298414
$64$	1.00000	0.125000
$65$	−2.66497	−0.330549
$66$	2.99046	0.368100
$67$	−3.14935	−0.384755	−0.192377	−	0.981321i	$-0.561620\pi$
$67$	−3.14935	−0.384755	−0.192377	+	0.981321i	$0.561620\pi$
$68$	−5.10004	−0.618471
$69$	−8.19215	−0.986219
$70$	−6.31222	−0.754455
$71$	−9.42543	−1.11859	−0.559296	−	0.828968i	$-0.688929\pi$
$71$	−9.42543	−1.11859	−0.559296	+	0.828968i	$0.688929\pi$
$72$	−1.00000	−0.117851
$73$	1.53198	0.179305	0.0896526	−	0.995973i	$-0.471424\pi$
$73$	1.53198	0.179305	0.0896526	+	0.995973i	$0.471424\pi$
$74$	7.50176	0.872062
$75$	−2.10207	−0.242726
$76$	−4.97673	−0.570871
$77$	7.08317	0.807202
$78$	−1.00000	−0.113228
$79$	−16.6133	−1.86914	−0.934571	−	0.355777i	$-0.884216\pi$
$79$	−16.6133	−1.86914	−0.934571	+	0.355777i	$0.884216\pi$
$80$	2.66497	0.297953
$81$	1.00000	0.111111
$82$	5.29737	0.584997
$83$	−10.6717	−1.17137	−0.585687	−	0.810537i	$-0.699175\pi$
$83$	−10.6717	−1.17137	−0.585687	+	0.810537i	$0.699175\pi$
$84$	−2.36859	−0.258434
$85$	−13.5915	−1.47420
$86$	−5.03485	−0.542922
$87$	8.89325	0.953456
$88$	−2.99046	−0.318784
$89$	14.2388	1.50931	0.754654	−	0.656123i	$-0.227805\pi$
$89$	14.2388	1.50931	0.754654	+	0.656123i	$0.227805\pi$
$90$	−2.66497	−0.280913
$91$	−2.36859	−0.248296
$92$	8.19215	0.854091
$93$	−2.96518	−0.307475
$94$	6.68426	0.689429
$95$	−13.2629	−1.36074
$96$	1.00000	0.102062
$97$	−5.63892	−0.572546	−0.286273	−	0.958148i	$-0.592416\pi$
$97$	−5.63892	−0.572546	−0.286273	+	0.958148i	$0.592416\pi$
$98$	1.38978	0.140389
$99$	2.99046	0.300552
$100$	2.10207	0.210207
$101$	−8.11468	−0.807440	−0.403720	−	0.914882i	$-0.632283\pi$
$101$	−8.11468	−0.807440	−0.403720	+	0.914882i	$0.632283\pi$
$102$	−5.10004	−0.504979
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.00000	0.0980581
$105$	−6.31222	−0.616010
$106$	9.57222	0.929736
$107$	−8.82181	−0.852837	−0.426418	−	0.904526i	$-0.640225\pi$
$107$	−8.82181	−0.852837	−0.426418	+	0.904526i	$0.640225\pi$
$108$	−1.00000	−0.0962250
$109$	−4.89164	−0.468534	−0.234267	−	0.972172i	$-0.575269\pi$
$109$	−4.89164	−0.468534	−0.234267	+	0.972172i	$0.575269\pi$
$110$	−7.96949	−0.759861
$111$	7.50176	0.712036
$112$	2.36859	0.223811
$113$	0.199059	0.0187259	0.00936296	−	0.999956i	$-0.497020\pi$
$113$	0.199059	0.0187259	0.00936296	+	0.999956i	$0.497020\pi$
$114$	−4.97673	−0.466114
$115$	21.8318	2.03583
$116$	−8.89325	−0.825717
$117$	−1.00000	−0.0924500
$118$	−4.13496	−0.380654
$119$	−12.0799	−1.10736
$120$	2.66497	0.243277
$121$	−2.05715	−0.187014
$122$	0.907884	0.0821959
$123$	5.29737	0.477648
$124$	2.96518	0.266281
$125$	−7.72290	−0.690757
$126$	−2.36859	−0.211011
$127$	−14.4539	−1.28258	−0.641290	−	0.767299i	$-0.721600\pi$
$127$	−14.4539	−1.28258	−0.641290	+	0.767299i	$0.721600\pi$
$128$	−1.00000	−0.0883883
$129$	−5.03485	−0.443294
$130$	2.66497	0.233733
$131$	11.1968	0.978269	0.489134	−	0.872208i	$-0.337313\pi$
$131$	11.1968	0.978269	0.489134	+	0.872208i	$0.337313\pi$
$132$	−2.99046	−0.260286
$133$	−11.7878	−1.02214
$134$	3.14935	0.272063
$135$	−2.66497	−0.229364
$136$	5.10004	0.437325
$137$	−1.38948	−0.118711	−0.0593555	−	0.998237i	$-0.518905\pi$
$137$	−1.38948	−0.118711	−0.0593555	+	0.998237i	$0.518905\pi$
$138$	8.19215	0.697362
$139$	−14.7431	−1.25049	−0.625245	−	0.780428i	$-0.715001\pi$
$139$	−14.7431	−1.25049	−0.625245	+	0.780428i	$0.715001\pi$
$140$	6.31222	0.533480
$141$	6.68426	0.562917
$142$	9.42543	0.790964
$143$	−2.99046	−0.250075
$144$	1.00000	0.0833333
$145$	−23.7002	−1.96820
$146$	−1.53198	−0.126788
$147$	1.38978	0.114627
$148$	−7.50176	−0.616641
$149$	−9.30260	−0.762099	−0.381049	−	0.924555i	$-0.624437\pi$
$149$	−9.30260	−0.762099	−0.381049	+	0.924555i	$0.624437\pi$
$150$	2.10207	0.171633
$151$	−19.5117	−1.58784	−0.793919	−	0.608024i	$-0.791963\pi$
$151$	−19.5117	−1.58784	−0.793919	+	0.608024i	$0.791963\pi$
$152$	4.97673	0.403666
$153$	−5.10004	−0.412314
$154$	−7.08317	−0.570778
$155$	7.90213	0.634714
$156$	1.00000	0.0800641
$157$	12.7383	1.01663	0.508314	−	0.861172i	$-0.330269\pi$
$157$	12.7383	1.01663	0.508314	+	0.861172i	$0.330269\pi$
$158$	16.6133	1.32168
$159$	9.57222	0.759126
$160$	−2.66497	−0.210684
$161$	19.4038	1.52924
$162$	−1.00000	−0.0785674
$163$	20.0360	1.56934	0.784671	−	0.619912i	$-0.212832\pi$
$163$	20.0360	1.56934	0.784671	+	0.619912i	$0.212832\pi$
$164$	−5.29737	−0.413655
$165$	−7.96949	−0.620424
$166$	10.6717	0.828287
$167$	−12.2588	−0.948611	−0.474305	−	0.880360i	$-0.657301\pi$
$167$	−12.2588	−0.948611	−0.474305	+	0.880360i	$0.657301\pi$
$168$	2.36859	0.182741
$169$	1.00000	0.0769231
$170$	13.5915	1.04242
$171$	−4.97673	−0.380580
$172$	5.03485	0.383904
$173$	−10.4013	−0.790795	−0.395398	−	0.918510i	$-0.629393\pi$
$173$	−10.4013	−0.790795	−0.395398	+	0.918510i	$0.629393\pi$
$174$	−8.89325	−0.674195
$175$	4.97894	0.376373
$176$	2.99046	0.225414
$177$	−4.13496	−0.310803
$178$	−14.2388	−1.06724
$179$	25.8043	1.92870	0.964352	−	0.264622i	$-0.0852471\pi$
$179$	25.8043	1.92870	0.964352	+	0.264622i	$0.0852471\pi$
$180$	2.66497	0.198635
$181$	−1.38863	−0.103216	−0.0516082	−	0.998667i	$-0.516435\pi$
$181$	−1.38863	−0.103216	−0.0516082	+	0.998667i	$0.516435\pi$
$182$	2.36859	0.175572
$183$	0.907884	0.0671127
$184$	−8.19215	−0.603933
$185$	−19.9920	−1.46984
$186$	2.96518	0.217418
$187$	−15.2515	−1.11530
$188$	−6.68426	−0.487500
$189$	−2.36859	−0.172290
$190$	13.2629	0.962189
$191$	20.9559	1.51632	0.758159	−	0.652070i	$-0.226099\pi$
$191$	20.9559	1.51632	0.758159	+	0.652070i	$0.226099\pi$
$192$	−1.00000	−0.0721688
$193$	14.1557	1.01895	0.509474	−	0.860486i	$-0.329840\pi$
$193$	14.1557	1.01895	0.509474	+	0.860486i	$0.329840\pi$
$194$	5.63892	0.404851
$195$	2.66497	0.190843
$196$	−1.38978	−0.0992703
$197$	3.89385	0.277426	0.138713	−	0.990333i	$-0.455704\pi$
$197$	3.89385	0.277426	0.138713	+	0.990333i	$0.455704\pi$
$198$	−2.99046	−0.212523
$199$	−0.00132986	−9.42710e−5 0	−4.71355e−5	−	1.00000i	$-0.500015\pi$
$199$	−0.00132986	−9.42710e−5 0	−4.71355e−5		1.00000i	$0.500015\pi$
$200$	−2.10207	−0.148639
$201$	3.14935	0.222138
$202$	8.11468	0.570947
$203$	−21.0644	−1.47843
$204$	5.10004	0.357074
$205$	−14.1173	−0.985998
$206$	1.00000	0.0696733
$207$	8.19215	0.569394
$208$	−1.00000	−0.0693375
$209$	−14.8827	−1.02946
$210$	6.31222	0.435585
$211$	−3.76040	−0.258877	−0.129438	−	0.991587i	$-0.541317\pi$
$211$	−3.76040	−0.258877	−0.129438	+	0.991587i	$0.541317\pi$
$212$	−9.57222	−0.657423
$213$	9.42543	0.645820
$214$	8.82181	0.603047
$215$	13.4177	0.915082
$216$	1.00000	0.0680414
$217$	7.02330	0.476773
$218$	4.89164	0.331304
$219$	−1.53198	−0.103522
$220$	7.96949	0.537303
$221$	5.10004	0.343066
$222$	−7.50176	−0.503485
$223$	−20.0488	−1.34257	−0.671285	−	0.741200i	$-0.734257\pi$
$223$	−20.0488	−1.34257	−0.671285	+	0.741200i	$0.734257\pi$
$224$	−2.36859	−0.158258
$225$	2.10207	0.140138
$226$	−0.199059	−0.0132412
$227$	15.7644	1.04632	0.523159	−	0.852235i	$-0.324753\pi$
$227$	15.7644	1.04632	0.523159	+	0.852235i	$0.324753\pi$
$228$	4.97673	0.329592
$229$	23.7161	1.56720	0.783602	−	0.621263i	$-0.213380\pi$
$229$	23.7161	1.56720	0.783602	+	0.621263i	$0.213380\pi$
$230$	−21.8318	−1.43955
$231$	−7.08317	−0.466038
$232$	8.89325	0.583870
$233$	23.6830	1.55153	0.775763	−	0.631024i	$-0.217365\pi$
$233$	23.6830	1.55153	0.775763	+	0.631024i	$0.217365\pi$
$234$	1.00000	0.0653720
$235$	−17.8134	−1.16202
$236$	4.13496	0.269163
$237$	16.6133	1.07915
$238$	12.0799	0.783024
$239$	−12.8452	−0.830884	−0.415442	−	0.909620i	$-0.636373\pi$
$239$	−12.8452	−0.830884	−0.415442	+	0.909620i	$0.636373\pi$
$240$	−2.66497	−0.172023
$241$	−16.9050	−1.08895	−0.544473	−	0.838778i	$-0.683270\pi$
$241$	−16.9050	−1.08895	−0.544473	+	0.838778i	$0.683270\pi$
$242$	2.05715	0.132239
$243$	−1.00000	−0.0641500
$244$	−0.907884	−0.0581213
$245$	−3.70373	−0.236623
$246$	−5.29737	−0.337748
$247$	4.97673	0.316662
$248$	−2.96518	−0.188289
$249$	10.6717	0.676293
$250$	7.72290	0.488439
$251$	26.3714	1.66455	0.832274	−	0.554364i	$-0.187039\pi$
$251$	26.3714	1.66455	0.832274	+	0.554364i	$0.187039\pi$
$252$	2.36859	0.149207
$253$	24.4983	1.54019
$254$	14.4539	0.906921
$255$	13.5915	0.851130
$256$	1.00000	0.0625000
$257$	−12.2911	−0.766700	−0.383350	−	0.923603i	$-0.625230\pi$
$257$	−12.2911	−0.766700	−0.383350	+	0.923603i	$0.625230\pi$
$258$	5.03485	0.313456
$259$	−17.7686	−1.10409
$260$	−2.66497	−0.165274
$261$	−8.89325	−0.550478
$262$	−11.1968	−0.691741
$263$	−3.65412	−0.225323	−0.112661	−	0.993633i	$-0.535938\pi$
$263$	−3.65412	−0.225323	−0.112661	+	0.993633i	$0.535938\pi$
$264$	2.99046	0.184050
$265$	−25.5097	−1.56705
$266$	11.7878	0.722759
$267$	−14.2388	−0.871399
$268$	−3.14935	−0.192377
$269$	8.85845	0.540109	0.270055	−	0.962845i	$-0.412958\pi$
$269$	8.85845	0.540109	0.270055	+	0.962845i	$0.412958\pi$
$270$	2.66497	0.162185
$271$	−17.8907	−1.08679	−0.543393	−	0.839479i	$-0.682860\pi$
$271$	−17.8907	−1.08679	−0.543393	+	0.839479i	$0.682860\pi$
$272$	−5.10004	−0.309235
$273$	2.36859	0.143354
$274$	1.38948	0.0839414
$275$	6.28616	0.379070
$276$	−8.19215	−0.493109
$277$	−19.2663	−1.15760	−0.578799	−	0.815470i	$-0.696478\pi$
$277$	−19.2663	−1.15760	−0.578799	+	0.815470i	$0.696478\pi$
$278$	14.7431	0.884230
$279$	2.96518	0.177521
$280$	−6.31222	−0.377227
$281$	26.0446	1.55369	0.776846	−	0.629691i	$-0.216819\pi$
$281$	26.0446	1.55369	0.776846	+	0.629691i	$0.216819\pi$
$282$	−6.68426	−0.398042
$283$	14.4965	0.861729	0.430864	−	0.902417i	$-0.358209\pi$
$283$	14.4965	0.861729	0.430864	+	0.902417i	$0.358209\pi$
$284$	−9.42543	−0.559296
$285$	13.2629	0.785624
$286$	2.99046	0.176830
$287$	−12.5473	−0.740644
$288$	−1.00000	−0.0589256
$289$	9.01040	0.530023
$290$	23.7002	1.39173
$291$	5.63892	0.330559
$292$	1.53198	0.0896526
$293$	29.9123	1.74750	0.873749	−	0.486377i	$-0.161682\pi$
$293$	29.9123	1.74750	0.873749	+	0.486377i	$0.161682\pi$
$294$	−1.38978	−0.0810539
$295$	11.0196	0.641583
$296$	7.50176	0.436031
$297$	−2.99046	−0.173524
$298$	9.30260	0.538885
$299$	−8.19215	−0.473764
$300$	−2.10207	−0.121363
$301$	11.9255	0.687375
$302$	19.5117	1.12277
$303$	8.11468	0.466176
$304$	−4.97673	−0.285435
$305$	−2.41948	−0.138539
$306$	5.10004	0.291550
$307$	31.7716	1.81330	0.906651	−	0.421881i	$-0.138630\pi$
$307$	31.7716	1.81330	0.906651	+	0.421881i	$0.138630\pi$
$308$	7.08317	0.403601
$309$	1.00000	0.0568880
$310$	−7.90213	−0.448811
$311$	4.13303	0.234363	0.117181	−	0.993111i	$-0.462614\pi$
$311$	4.13303	0.234363	0.117181	+	0.993111i	$0.462614\pi$
$312$	−1.00000	−0.0566139
$313$	22.5791	1.27624	0.638122	−	0.769935i	$-0.279711\pi$
$313$	22.5791	1.27624	0.638122	+	0.769935i	$0.279711\pi$
$314$	−12.7383	−0.718864
$315$	6.31222	0.355653
$316$	−16.6133	−0.934571
$317$	25.2757	1.41962	0.709812	−	0.704391i	$-0.248780\pi$
$317$	25.2757	1.41962	0.709812	+	0.704391i	$0.248780\pi$
$318$	−9.57222	−0.536783
$319$	−26.5949	−1.48903
$320$	2.66497	0.148976
$321$	8.82181	0.492385
$322$	−19.4038	−1.08133
$323$	25.3815	1.41227
$324$	1.00000	0.0555556
$325$	−2.10207	−0.116602
$326$	−20.0360	−1.10969
$327$	4.89164	0.270508
$328$	5.29737	0.292498
$329$	−15.8323	−0.872862
$330$	7.96949	0.438706
$331$	15.2198	0.836558	0.418279	−	0.908319i	$-0.362633\pi$
$331$	15.2198	0.836558	0.418279	+	0.908319i	$0.362633\pi$
$332$	−10.6717	−0.585687
$333$	−7.50176	−0.411094
$334$	12.2588	0.670769
$335$	−8.39293	−0.458555
$336$	−2.36859	−0.129217
$337$	10.7086	0.583336	0.291668	−	0.956520i	$-0.405790\pi$
$337$	10.7086	0.583336	0.291668	+	0.956520i	$0.405790\pi$
$338$	−1.00000	−0.0543928
$339$	−0.199059	−0.0108114
$340$	−13.5915	−0.737100
$341$	8.86726	0.480189
$342$	4.97673	0.269111
$343$	−19.8720	−1.07298
$344$	−5.03485	−0.271461
$345$	−21.8318	−1.17539
$346$	10.4013	0.559177
$347$	−9.32187	−0.500424	−0.250212	−	0.968191i	$-0.580500\pi$
$347$	−9.32187	−0.500424	−0.250212	+	0.968191i	$0.580500\pi$
$348$	8.89325	0.476728
$349$	−7.12865	−0.381588	−0.190794	−	0.981630i	$-0.561106\pi$
$349$	−7.12865	−0.381588	−0.190794	+	0.981630i	$0.561106\pi$
$350$	−4.97894	−0.266136
$351$	1.00000	0.0533761
$352$	−2.99046	−0.159392
$353$	−1.14759	−0.0610801	−0.0305401	−	0.999534i	$-0.509723\pi$
$353$	−1.14759	−0.0610801	−0.0305401	+	0.999534i	$0.509723\pi$
$354$	4.13496	0.219771
$355$	−25.1185	−1.33315
$356$	14.2388	0.754654
$357$	12.0799	0.639336
$358$	−25.8043	−1.36380
$359$	36.2087	1.91102	0.955510	−	0.294959i	$-0.0953060\pi$
$359$	36.2087	1.91102	0.955510	+	0.294959i	$0.0953060\pi$
$360$	−2.66497	−0.140456
$361$	5.76789	0.303573
$362$	1.38863	0.0729850
$363$	2.05715	0.107973
$364$	−2.36859	−0.124148
$365$	4.08269	0.213698
$366$	−0.907884	−0.0474558
$367$	−33.5446	−1.75101	−0.875507	−	0.483206i	$-0.839472\pi$
$367$	−33.5446	−1.75101	−0.875507	+	0.483206i	$0.839472\pi$
$368$	8.19215	0.427045
$369$	−5.29737	−0.275770
$370$	19.9920	1.03933
$371$	−22.6727	−1.17711
$372$	−2.96518	−0.153738
$373$	−15.4244	−0.798647	−0.399323	−	0.916810i	$-0.630755\pi$
$373$	−15.4244	−0.798647	−0.399323	+	0.916810i	$0.630755\pi$
$374$	15.2515	0.788634
$375$	7.72290	0.398809
$376$	6.68426	0.344715
$377$	8.89325	0.458025
$378$	2.36859	0.121827
$379$	−35.1670	−1.80641	−0.903204	−	0.429212i	$-0.858791\pi$
$379$	−35.1670	−1.80641	−0.903204	+	0.429212i	$0.858791\pi$
$380$	−13.2629	−0.680370
$381$	14.4539	0.740498
$382$	−20.9559	−1.07220
$383$	19.8437	1.01397	0.506983	−	0.861956i	$-0.330761\pi$
$383$	19.8437	1.01397	0.506983	+	0.861956i	$0.330761\pi$
$384$	1.00000	0.0510310
$385$	18.8764	0.962033
$386$	−14.1557	−0.720505
$387$	5.03485	0.255936
$388$	−5.63892	−0.286273
$389$	−6.15603	−0.312123	−0.156062	−	0.987747i	$-0.549880\pi$
$389$	−6.15603	−0.312123	−0.156062	+	0.987747i	$0.549880\pi$
$390$	−2.66497	−0.134946
$391$	−41.7803	−2.11292
$392$	1.38978	0.0701947
$393$	−11.1968	−0.564804
$394$	−3.89385	−0.196170
$395$	−44.2739	−2.22766
$396$	2.99046	0.150276
$397$	−10.2420	−0.514030	−0.257015	−	0.966407i	$-0.582739\pi$
$397$	−10.2420	−0.514030	−0.257015	+	0.966407i	$0.582739\pi$
$398$	0.00132986	6.66597e−5 0
$399$	11.7878	0.590130
$400$	2.10207	0.105104
$401$	2.63594	0.131633	0.0658163	−	0.997832i	$-0.479035\pi$
$401$	2.63594	0.131633	0.0658163	+	0.997832i	$0.479035\pi$
$402$	−3.14935	−0.157075
$403$	−2.96518	−0.147706
$404$	−8.11468	−0.403720
$405$	2.66497	0.132423
$406$	21.0644	1.04541
$407$	−22.4337	−1.11200
$408$	−5.10004	−0.252490
$409$	30.9063	1.52822	0.764110	−	0.645087i	$-0.223179\pi$
$409$	30.9063	1.52822	0.764110	+	0.645087i	$0.223179\pi$
$410$	14.1173	0.697206
$411$	1.38948	0.0685379
$412$	−1.00000	−0.0492665
$413$	9.79403	0.481933
$414$	−8.19215	−0.402622
$415$	−28.4398	−1.39606
$416$	1.00000	0.0490290
$417$	14.7431	0.721971
$418$	14.8827	0.727938
$419$	−32.7095	−1.59796	−0.798981	−	0.601357i	$-0.794627\pi$
$419$	−32.7095	−1.59796	−0.798981	+	0.601357i	$0.794627\pi$
$420$	−6.31222	−0.308005
$421$	31.0744	1.51448	0.757238	−	0.653140i	$-0.226548\pi$
$421$	31.0744	1.51448	0.757238	+	0.653140i	$0.226548\pi$
$422$	3.76040	0.183053
$423$	−6.68426	−0.325000
$424$	9.57222	0.464868
$425$	−10.7206	−0.520028
$426$	−9.42543	−0.456663
$427$	−2.15040	−0.104065
$428$	−8.82181	−0.426418
$429$	2.99046	0.144381
$430$	−13.4177	−0.647061
$431$	33.4471	1.61109	0.805544	−	0.592536i	$-0.201873\pi$
$431$	33.4471	1.61109	0.805544	+	0.592536i	$0.201873\pi$
$432$	−1.00000	−0.0481125
$433$	19.6562	0.944619	0.472309	−	0.881433i	$-0.343420\pi$
$433$	19.6562	0.944619	0.472309	+	0.881433i	$0.343420\pi$
$434$	−7.02330	−0.337129
$435$	23.7002	1.13634
$436$	−4.89164	−0.234267
$437$	−40.7701	−1.95030
$438$	1.53198	0.0732010
$439$	−17.4337	−0.832064	−0.416032	−	0.909350i	$-0.636579\pi$
$439$	−17.4337	−0.832064	−0.416032	+	0.909350i	$0.636579\pi$
$440$	−7.96949	−0.379930
$441$	−1.38978	−0.0661802
$442$	−5.10004	−0.242584
$443$	−33.1504	−1.57502	−0.787511	−	0.616301i	$-0.788631\pi$
$443$	−33.1504	−1.57502	−0.787511	+	0.616301i	$0.788631\pi$
$444$	7.50176	0.356018
$445$	37.9459	1.79881
$446$	20.0488	0.949340
$447$	9.30260	0.439998
$448$	2.36859	0.111905
$449$	−17.4809	−0.824974	−0.412487	−	0.910963i	$-0.635340\pi$
$449$	−17.4809	−0.824974	−0.412487	+	0.910963i	$0.635340\pi$
$450$	−2.10207	−0.0990926
$451$	−15.8416	−0.745951
$452$	0.199059	0.00936296
$453$	19.5117	0.916738
$454$	−15.7644	−0.739859
$455$	−6.31222	−0.295922
$456$	−4.97673	−0.233057
$457$	5.47979	0.256334	0.128167	−	0.991753i	$-0.459091\pi$
$457$	5.47979	0.256334	0.128167	+	0.991753i	$0.459091\pi$
$458$	−23.7161	−1.10818
$459$	5.10004	0.238049
$460$	21.8318	1.01791
$461$	14.4209	0.671650	0.335825	−	0.941924i	$-0.390985\pi$
$461$	14.4209	0.671650	0.335825	+	0.941924i	$0.390985\pi$
$462$	7.08317	0.329539
$463$	−14.3003	−0.664593	−0.332296	−	0.943175i	$-0.607823\pi$
$463$	−14.3003	−0.664593	−0.332296	+	0.943175i	$0.607823\pi$
$464$	−8.89325	−0.412859
$465$	−7.90213	−0.366452
$466$	−23.6830	−1.09709
$467$	−20.5623	−0.951510	−0.475755	−	0.879578i	$-0.657825\pi$
$467$	−20.5623	−0.951510	−0.475755	+	0.879578i	$0.657825\pi$
$468$	−1.00000	−0.0462250
$469$	−7.45952	−0.344449
$470$	17.8134	0.821669
$471$	−12.7383	−0.586950
$472$	−4.13496	−0.190327
$473$	15.0565	0.692300
$474$	−16.6133	−0.763074
$475$	−10.4614	−0.480004
$476$	−12.0799	−0.553681
$477$	−9.57222	−0.438282
$478$	12.8452	0.587524
$479$	−38.1472	−1.74299	−0.871494	−	0.490406i	$-0.836848\pi$
$479$	−38.1472	−1.74299	−0.871494	+	0.490406i	$0.836848\pi$
$480$	2.66497	0.121639
$481$	7.50176	0.342051
$482$	16.9050	0.770001
$483$	−19.4038	−0.882905
$484$	−2.05715	−0.0935070
$485$	−15.0276	−0.682366
$486$	1.00000	0.0453609
$487$	2.46128	0.111531	0.0557657	−	0.998444i	$-0.482240\pi$
$487$	2.46128	0.111531	0.0557657	+	0.998444i	$0.482240\pi$
$488$	0.907884	0.0410980
$489$	−20.0360	−0.906060
$490$	3.70373	0.167318
$491$	1.04891	0.0473368	0.0236684	−	0.999720i	$-0.492465\pi$
$491$	1.04891	0.0473368	0.0236684	+	0.999720i	$0.492465\pi$
$492$	5.29737	0.238824
$493$	45.3559	2.04273
$494$	−4.97673	−0.223914
$495$	7.96949	0.358202
$496$	2.96518	0.133141
$497$	−22.3250	−1.00141
$498$	−10.6717	−0.478212
$499$	−12.0797	−0.540761	−0.270380	−	0.962754i	$-0.587149\pi$
$499$	−12.0797	−0.540761	−0.270380	+	0.962754i	$0.587149\pi$
$500$	−7.72290	−0.345378
$501$	12.2588	0.547681
$502$	−26.3714	−1.17701
$503$	5.46186	0.243532	0.121766	−	0.992559i	$-0.461144\pi$
$503$	5.46186	0.243532	0.121766	+	0.992559i	$0.461144\pi$
$504$	−2.36859	−0.105505
$505$	−21.6254	−0.962317
$506$	−24.4983	−1.08908
$507$	−1.00000	−0.0444116
$508$	−14.4539	−0.641290
$509$	19.5818	0.867948	0.433974	−	0.900925i	$-0.357111\pi$
$509$	19.5818	0.867948	0.433974	+	0.900925i	$0.357111\pi$
$510$	−13.5915	−0.601840
$511$	3.62864	0.160522
$512$	−1.00000	−0.0441942
$513$	4.97673	0.219728
$514$	12.2911	0.542139
$515$	−2.66497	−0.117433
$516$	−5.03485	−0.221647
$517$	−19.9890	−0.879116
$518$	17.7686	0.780707
$519$	10.4013	0.456566
$520$	2.66497	0.116867
$521$	−10.9348	−0.479062	−0.239531	−	0.970889i	$-0.576994\pi$
$521$	−10.9348	−0.479062	−0.239531	+	0.970889i	$0.576994\pi$
$522$	8.89325	0.389247
$523$	−7.86901	−0.344088	−0.172044	−	0.985089i	$-0.555037\pi$
$523$	−7.86901	−0.344088	−0.172044	+	0.985089i	$0.555037\pi$
$524$	11.1968	0.489134
$525$	−4.97894	−0.217299
$526$	3.65412	0.159327
$527$	−15.1226	−0.658749
$528$	−2.99046	−0.130143
$529$	44.1113	1.91788
$530$	25.5097	1.10807
$531$	4.13496	0.179442
$532$	−11.7878	−0.511068
$533$	5.29737	0.229455
$534$	14.2388	0.616172
$535$	−23.5099	−1.01642
$536$	3.14935	0.136031
$537$	−25.8043	−1.11354
$538$	−8.85845	−0.381915
$539$	−4.15609	−0.179016
$540$	−2.66497	−0.114682
$541$	−0.912894	−0.0392484	−0.0196242	−	0.999807i	$-0.506247\pi$
$541$	−0.912894	−0.0392484	−0.0196242	+	0.999807i	$0.506247\pi$
$542$	17.8907	0.768473
$543$	1.38863	0.0595920
$544$	5.10004	0.218662
$545$	−13.0361	−0.558404
$546$	−2.36859	−0.101366
$547$	37.8306	1.61752	0.808759	−	0.588140i	$-0.200139\pi$
$547$	37.8306	1.61752	0.808759	+	0.588140i	$0.200139\pi$
$548$	−1.38948	−0.0593555
$549$	−0.907884	−0.0387475
$550$	−6.28616	−0.268043
$551$	44.2593	1.88551
$552$	8.19215	0.348681
$553$	−39.3501	−1.67334
$554$	19.2663	0.818545
$555$	19.9920	0.848612
$556$	−14.7431	−0.625245
$557$	38.7902	1.64359	0.821796	−	0.569781i	$-0.192972\pi$
$557$	38.7902	1.64359	0.821796	+	0.569781i	$0.192972\pi$
$558$	−2.96518	−0.125526
$559$	−5.03485	−0.212952
$560$	6.31222	0.266740
$561$	15.2515	0.643917
$562$	−26.0446	−1.09863
$563$	11.3724	0.479291	0.239646	−	0.970860i	$-0.422969\pi$
$563$	11.3724	0.479291	0.239646	+	0.970860i	$0.422969\pi$
$564$	6.68426	0.281458
$565$	0.530487	0.0223178
$566$	−14.4965	−0.609334
$567$	2.36859	0.0994714
$568$	9.42543	0.395482
$569$	−22.9131	−0.960567	−0.480283	−	0.877113i	$-0.659466\pi$
$569$	−22.9131	−0.960567	−0.480283	+	0.877113i	$0.659466\pi$
$570$	−13.2629	−0.555520
$571$	5.11351	0.213994	0.106997	−	0.994259i	$-0.465876\pi$
$571$	5.11351	0.213994	0.106997	+	0.994259i	$0.465876\pi$
$572$	−2.99046	−0.125037
$573$	−20.9559	−0.875446
$574$	12.5473	0.523714
$575$	17.2205	0.718144
$576$	1.00000	0.0416667
$577$	1.23404	0.0513737	0.0256869	−	0.999670i	$-0.491823\pi$
$577$	1.23404	0.0513737	0.0256869	+	0.999670i	$0.491823\pi$
$578$	−9.01040	−0.374783
$579$	−14.1557	−0.588290
$580$	−23.7002	−0.984099
$581$	−25.2769	−1.04866
$582$	−5.63892	−0.233741
$583$	−28.6253	−1.18554
$584$	−1.53198	−0.0633940
$585$	−2.66497	−0.110183
$586$	−29.9123	−1.23567
$587$	43.7486	1.80570	0.902850	−	0.429956i	$-0.141471\pi$
$587$	43.7486	1.80570	0.902850	+	0.429956i	$0.141471\pi$
$588$	1.38978	0.0573137
$589$	−14.7569	−0.608049
$590$	−11.0196	−0.453668
$591$	−3.89385	−0.160172
$592$	−7.50176	−0.308321
$593$	42.4140	1.74173	0.870867	−	0.491519i	$-0.163558\pi$
$593$	42.4140	1.74173	0.870867	+	0.491519i	$0.163558\pi$
$594$	2.99046	0.122700
$595$	−32.1926	−1.31977
$596$	−9.30260	−0.381049
$597$	0.00132986	5.44274e−5 0
$598$	8.19215	0.335002
$599$	−5.37854	−0.219761	−0.109881	−	0.993945i	$-0.535047\pi$
$599$	−5.37854	−0.219761	−0.109881	+	0.993945i	$0.535047\pi$
$600$	2.10207	0.0858167
$601$	−39.0827	−1.59422	−0.797108	−	0.603836i	$-0.793638\pi$
$601$	−39.0827	−1.59422	−0.797108	+	0.603836i	$0.793638\pi$
$602$	−11.9255	−0.486047
$603$	−3.14935	−0.128252
$604$	−19.5117	−0.793919
$605$	−5.48226	−0.222885
$606$	−8.11468	−0.329636
$607$	−1.75743	−0.0713319	−0.0356660	−	0.999364i	$-0.511355\pi$
$607$	−1.75743	−0.0713319	−0.0356660	+	0.999364i	$0.511355\pi$
$608$	4.97673	0.201833
$609$	21.0644	0.853574
$610$	2.41948	0.0979620
$611$	6.68426	0.270416
$612$	−5.10004	−0.206157
$613$	43.1060	1.74104	0.870518	−	0.492137i	$-0.163784\pi$
$613$	43.1060	1.74104	0.870518	+	0.492137i	$0.163784\pi$
$614$	−31.7716	−1.28220
$615$	14.1173	0.569266
$616$	−7.08317	−0.285389
$617$	−8.90061	−0.358325	−0.179163	−	0.983819i	$-0.557339\pi$
$617$	−8.90061	−0.358325	−0.179163	+	0.983819i	$0.557339\pi$
$618$	−1.00000	−0.0402259
$619$	−18.6732	−0.750539	−0.375269	−	0.926916i	$-0.622450\pi$
$619$	−18.6732	−0.750539	−0.375269	+	0.926916i	$0.622450\pi$
$620$	7.90213	0.317357
$621$	−8.19215	−0.328740
$622$	−4.13303	−0.165719
$623$	33.7258	1.35120
$624$	1.00000	0.0400320
$625$	−31.0917	−1.24367
$626$	−22.5791	−0.902441
$627$	14.8827	0.594359
$628$	12.7383	0.508314
$629$	38.2593	1.52550
$630$	−6.31222	−0.251485
$631$	−25.6853	−1.02252	−0.511258	−	0.859427i	$-0.670820\pi$
$631$	−25.6853	−1.02252	−0.511258	+	0.859427i	$0.670820\pi$
$632$	16.6133	0.660841
$633$	3.76040	0.149463
$634$	−25.2757	−1.00383
$635$	−38.5193	−1.52859
$636$	9.57222	0.379563
$637$	1.38978	0.0550652
$638$	26.5949	1.05290
$639$	−9.42543	−0.372864
$640$	−2.66497	−0.105342
$641$	−38.5952	−1.52442	−0.762210	−	0.647330i	$-0.775886\pi$
$641$	−38.5952	−1.52442	−0.762210	+	0.647330i	$0.775886\pi$
$642$	−8.82181	−0.348169
$643$	9.19011	0.362422	0.181211	−	0.983444i	$-0.441998\pi$
$643$	9.19011	0.362422	0.181211	+	0.983444i	$0.441998\pi$
$644$	19.4038	0.764618
$645$	−13.4177	−0.528323
$646$	−25.3815	−0.998623
$647$	39.2802	1.54426	0.772131	−	0.635463i	$-0.219191\pi$
$647$	39.2802	1.54426	0.772131	+	0.635463i	$0.219191\pi$
$648$	−1.00000	−0.0392837
$649$	12.3654	0.485386
$650$	2.10207	0.0824500
$651$	−7.02330	−0.275265
$652$	20.0360	0.784671
$653$	15.5078	0.606868	0.303434	−	0.952853i	$-0.401867\pi$
$653$	15.5078	0.606868	0.303434	+	0.952853i	$0.401867\pi$
$654$	−4.89164	−0.191278
$655$	29.8391	1.16591
$656$	−5.29737	−0.206828
$657$	1.53198	0.0597684
$658$	15.8323	0.617206
$659$	0.674271	0.0262659	0.0131329	−	0.999914i	$-0.495820\pi$
$659$	0.674271	0.0262659	0.0131329	+	0.999914i	$0.495820\pi$
$660$	−7.96949	−0.310212
$661$	−11.5269	−0.448346	−0.224173	−	0.974549i	$-0.571968\pi$
$661$	−11.5269	−0.448346	−0.224173	+	0.974549i	$0.571968\pi$
$662$	−15.2198	−0.591536
$663$	−5.10004	−0.198069
$664$	10.6717	0.414143
$665$	−31.4143	−1.21819
$666$	7.50176	0.290687
$667$	−72.8548	−2.82095
$668$	−12.2588	−0.474305
$669$	20.0488	0.775133
$670$	8.39293	0.324247
$671$	−2.71499	−0.104811
$672$	2.36859	0.0913703
$673$	−32.8853	−1.26763	−0.633817	−	0.773483i	$-0.718513\pi$
$673$	−32.8853	−1.26763	−0.633817	+	0.773483i	$0.718513\pi$
$674$	−10.7086	−0.412481
$675$	−2.10207	−0.0809088
$676$	1.00000	0.0384615
$677$	−35.9038	−1.37989	−0.689947	−	0.723860i	$-0.742366\pi$
$677$	−35.9038	−1.37989	−0.689947	+	0.723860i	$0.742366\pi$
$678$	0.199059	0.00764483
$679$	−13.3563	−0.512567
$680$	13.5915	0.521209
$681$	−15.7644	−0.604092
$682$	−8.86726	−0.339545
$683$	48.6651	1.86212	0.931058	−	0.364870i	$-0.118887\pi$
$683$	48.6651	1.86212	0.931058	+	0.364870i	$0.118887\pi$
$684$	−4.97673	−0.190290
$685$	−3.70292	−0.141481
$686$	19.8720	0.758715
$687$	−23.7161	−0.904825
$688$	5.03485	0.191952
$689$	9.57222	0.364672
$690$	21.8318	0.831124
$691$	−47.6923	−1.81430	−0.907151	−	0.420805i	$-0.861748\pi$
$691$	−47.6923	−1.81430	−0.907151	+	0.420805i	$0.861748\pi$
$692$	−10.4013	−0.395398
$693$	7.08317	0.269067
$694$	9.32187	0.353853
$695$	−39.2898	−1.49035
$696$	−8.89325	−0.337098
$697$	27.0168	1.02333
$698$	7.12865	0.269823
$699$	−23.6830	−0.895774
$700$	4.97894	0.188186
$701$	−25.7819	−0.973770	−0.486885	−	0.873466i	$-0.661867\pi$
$701$	−25.7819	−0.973770	−0.486885	+	0.873466i	$0.661867\pi$
$702$	−1.00000	−0.0377426
$703$	37.3343	1.40809
$704$	2.99046	0.112707
$705$	17.8134	0.670890
$706$	1.14759	0.0431902
$707$	−19.2203	−0.722855
$708$	−4.13496	−0.155401
$709$	−18.4148	−0.691582	−0.345791	−	0.938311i	$-0.612389\pi$
$709$	−18.4148	−0.691582	−0.345791	+	0.938311i	$0.612389\pi$
$710$	25.1185	0.942680
$711$	−16.6133	−0.623047
$712$	−14.2388	−0.533621
$713$	24.2912	0.909714
$714$	−12.0799	−0.452079
$715$	−7.96949	−0.298042
$716$	25.8043	0.964352
$717$	12.8452	0.479711
$718$	−36.2087	−1.35130
$719$	−12.1404	−0.452761	−0.226380	−	0.974039i	$-0.572689\pi$
$719$	−12.1404	−0.452761	−0.226380	+	0.974039i	$0.572689\pi$
$720$	2.66497	0.0993176
$721$	−2.36859	−0.0882109
$722$	−5.76789	−0.214659
$723$	16.9050	0.628704
$724$	−1.38863	−0.0516082
$725$	−18.6942	−0.694286
$726$	−2.05715	−0.0763482
$727$	12.6521	0.469241	0.234620	−	0.972087i	$-0.424615\pi$
$727$	12.6521	0.469241	0.234620	+	0.972087i	$0.424615\pi$
$728$	2.36859	0.0877858
$729$	1.00000	0.0370370
$730$	−4.08269	−0.151107
$731$	−25.6780	−0.949733
$732$	0.907884	0.0335563
$733$	37.5181	1.38576	0.692882	−	0.721051i	$-0.256341\pi$
$733$	37.5181	1.38576	0.692882	+	0.721051i	$0.256341\pi$
$734$	33.5446	1.23815
$735$	3.70373	0.136614
$736$	−8.19215	−0.301967
$737$	−9.41801	−0.346917
$738$	5.29737	0.194999
$739$	11.4565	0.421434	0.210717	−	0.977547i	$-0.432420\pi$
$739$	11.4565	0.421434	0.210717	+	0.977547i	$0.432420\pi$
$740$	−19.9920	−0.734920
$741$	−4.97673	−0.182825
$742$	22.6727	0.832339
$743$	−36.5129	−1.33953	−0.669765	−	0.742574i	$-0.733605\pi$
$743$	−36.5129	−1.33953	−0.669765	+	0.742574i	$0.733605\pi$
$744$	2.96518	0.108709
$745$	−24.7912	−0.908278
$746$	15.4244	0.564729
$747$	−10.6717	−0.390458
$748$	−15.2515	−0.557649
$749$	−20.8952	−0.763496
$750$	−7.72290	−0.282000
$751$	13.9344	0.508474	0.254237	−	0.967142i	$-0.418176\pi$
$751$	13.9344	0.508474	0.254237	+	0.967142i	$0.418176\pi$
$752$	−6.68426	−0.243750
$753$	−26.3714	−0.961027
$754$	−8.89325	−0.323873
$755$	−51.9980	−1.89240
$756$	−2.36859	−0.0861448
$757$	−2.38247	−0.0865923	−0.0432961	−	0.999062i	$-0.513786\pi$
$757$	−2.38247	−0.0865923	−0.0432961	+	0.999062i	$0.513786\pi$
$758$	35.1670	1.27732
$759$	−24.4983	−0.889231
$760$	13.2629	0.481094
$761$	34.7359	1.25918	0.629588	−	0.776929i	$-0.283224\pi$
$761$	34.7359	1.25918	0.629588	+	0.776929i	$0.283224\pi$
$762$	−14.4539	−0.523611
$763$	−11.5863	−0.419452
$764$	20.9559	0.758159
$765$	−13.5915	−0.491400
$766$	−19.8437	−0.716982
$767$	−4.13496	−0.149305
$768$	−1.00000	−0.0360844
$769$	−37.7064	−1.35973	−0.679863	−	0.733339i	$-0.737961\pi$
$769$	−37.7064	−1.35973	−0.679863	+	0.733339i	$0.737961\pi$
$770$	−18.8764	−0.680260
$771$	12.2911	0.442655
$772$	14.1557	0.509474
$773$	20.7852	0.747590	0.373795	−	0.927511i	$-0.378056\pi$
$773$	20.7852	0.747590	0.373795	+	0.927511i	$0.378056\pi$
$774$	−5.03485	−0.180974
$775$	6.23303	0.223897
$776$	5.63892	0.202425
$777$	17.7686	0.637445
$778$	6.15603	0.220704
$779$	26.3636	0.944574
$780$	2.66497	0.0954213
$781$	−28.1864	−1.00859
$782$	41.7803	1.49406
$783$	8.89325	0.317819
$784$	−1.38978	−0.0496351
$785$	33.9472	1.21163
$786$	11.1968	0.399377
$787$	−11.9047	−0.424356	−0.212178	−	0.977231i	$-0.568056\pi$
$787$	−11.9047	−0.424356	−0.212178	+	0.977231i	$0.568056\pi$
$788$	3.89385	0.138713
$789$	3.65412	0.130090
$790$	44.2739	1.57520
$791$	0.471490	0.0167642
$792$	−2.99046	−0.106261
$793$	0.907884	0.0322399
$794$	10.2420	0.363474
$795$	25.5097	0.904735
$796$	−0.00132986	−4.71355e−5 0
$797$	−13.5767	−0.480913	−0.240456	−	0.970660i	$-0.577297\pi$
$797$	−13.5767	−0.480913	−0.240456	+	0.970660i	$0.577297\pi$
$798$	−11.7878	−0.417285
$799$	34.0900	1.20602
$800$	−2.10207	−0.0743194
$801$	14.2388	0.503103
$802$	−2.63594	−0.0930784
$803$	4.58134	0.161672
$804$	3.14935	0.111069
$805$	51.7107	1.82256
$806$	2.96518	0.104444
$807$	−8.85845	−0.311832
$808$	8.11468	0.285473
$809$	25.5432	0.898052	0.449026	−	0.893519i	$-0.351771\pi$
$809$	25.5432	0.898052	0.449026	+	0.893519i	$0.351771\pi$
$810$	−2.66497	−0.0936375
$811$	7.57835	0.266112	0.133056	−	0.991109i	$-0.457521\pi$
$811$	7.57835	0.266112	0.133056	+	0.991109i	$0.457521\pi$
$812$	−21.0644	−0.739217
$813$	17.8907	0.627456
$814$	22.4337	0.786301
$815$	53.3954	1.87036
$816$	5.10004	0.178537
$817$	−25.0571	−0.876638
$818$	−30.9063	−1.08061
$819$	−2.36859	−0.0827652
$820$	−14.1173	−0.492999
$821$	−52.6488	−1.83745	−0.918727	−	0.394893i	$-0.870782\pi$
$821$	−52.6488	−1.83745	−0.918727	+	0.394893i	$0.870782\pi$
$822$	−1.38948	−0.0484636
$823$	30.3736	1.05876	0.529378	−	0.848386i	$-0.322425\pi$
$823$	30.3736	1.05876	0.529378	+	0.848386i	$0.322425\pi$
$824$	1.00000	0.0348367
$825$	−6.28616	−0.218856
$826$	−9.79403	−0.340778
$827$	19.3903	0.674267	0.337134	−	0.941457i	$-0.390543\pi$
$827$	19.3903	0.674267	0.337134	+	0.941457i	$0.390543\pi$
$828$	8.19215	0.284697
$829$	16.0871	0.558729	0.279365	−	0.960185i	$-0.409876\pi$
$829$	16.0871	0.558729	0.279365	+	0.960185i	$0.409876\pi$
$830$	28.4398	0.987162
$831$	19.2663	0.668339
$832$	−1.00000	−0.0346688
$833$	7.08795	0.245583
$834$	−14.7431	−0.510511
$835$	−32.6692	−1.13057
$836$	−14.8827	−0.514730
$837$	−2.96518	−0.102492
$838$	32.7095	1.12993
$839$	11.8089	0.407689	0.203845	−	0.979003i	$-0.434656\pi$
$839$	11.8089	0.407689	0.203845	+	0.979003i	$0.434656\pi$
$840$	6.31222	0.217792
$841$	50.0898	1.72723
$842$	−31.0744	−1.07090
$843$	−26.0446	−0.897024
$844$	−3.76040	−0.129438
$845$	2.66497	0.0916778
$846$	6.68426	0.229810
$847$	−4.87255	−0.167423
$848$	−9.57222	−0.328711
$849$	−14.4965	−0.497519
$850$	10.7206	0.367715
$851$	−61.4556	−2.10667
$852$	9.42543	0.322910
$853$	−52.8427	−1.80930	−0.904649	−	0.426157i	$-0.859867\pi$
$853$	−52.8427	−1.80930	−0.904649	+	0.426157i	$0.859867\pi$
$854$	2.15040	0.0735853
$855$	−13.2629	−0.453580
$856$	8.82181	0.301523
$857$	3.42181	0.116887	0.0584435	−	0.998291i	$-0.481386\pi$
$857$	3.42181	0.116887	0.0584435	+	0.998291i	$0.481386\pi$
$858$	−2.99046	−0.102093
$859$	24.6277	0.840286	0.420143	−	0.907458i	$-0.361980\pi$
$859$	24.6277	0.840286	0.420143	+	0.907458i	$0.361980\pi$
$860$	13.4177	0.457541
$861$	12.5473	0.427611
$862$	−33.4471	−1.13921
$863$	−29.4581	−1.00277	−0.501383	−	0.865225i	$-0.667175\pi$
$863$	−29.4581	−1.00277	−0.501383	+	0.865225i	$0.667175\pi$
$864$	1.00000	0.0340207
$865$	−27.7191	−0.942479
$866$	−19.6562	−0.667946
$867$	−9.01040	−0.306009
$868$	7.02330	0.238386
$869$	−49.6814	−1.68533
$870$	−23.7002	−0.803513
$871$	3.14935	0.106712
$872$	4.89164	0.165652
$873$	−5.63892	−0.190849
$874$	40.7701	1.37907
$875$	−18.2924	−0.618395
$876$	−1.53198	−0.0517609
$877$	−28.3168	−0.956191	−0.478096	−	0.878308i	$-0.658673\pi$
$877$	−28.3168	−0.956191	−0.478096	+	0.878308i	$0.658673\pi$
$878$	17.4337	0.588358
$879$	−29.9123	−1.00892
$880$	7.96949	0.268651
$881$	−31.1817	−1.05054	−0.525269	−	0.850936i	$-0.676035\pi$
$881$	−31.1817	−1.05054	−0.525269	+	0.850936i	$0.676035\pi$
$882$	1.38978	0.0467965
$883$	8.37798	0.281941	0.140971	−	0.990014i	$-0.454978\pi$
$883$	8.37798	0.281941	0.140971	+	0.990014i	$0.454978\pi$
$884$	5.10004	0.171533
$885$	−11.0196	−0.370418
$886$	33.1504	1.11371
$887$	15.5261	0.521315	0.260657	−	0.965431i	$-0.416061\pi$
$887$	15.5261	0.521315	0.260657	+	0.965431i	$0.416061\pi$
$888$	−7.50176	−0.251743
$889$	−34.2355	−1.14822
$890$	−37.9459	−1.27195
$891$	2.99046	0.100184
$892$	−20.0488	−0.671285
$893$	33.2658	1.11320
$894$	−9.30260	−0.311126
$895$	68.7677	2.29865
$896$	−2.36859	−0.0791290
$897$	8.19215	0.273528
$898$	17.4809	0.583345
$899$	−26.3701	−0.879492
$900$	2.10207	0.0700690
$901$	48.8187	1.62639
$902$	15.8416	0.527467
$903$	−11.9255	−0.396856
$904$	−0.199059	−0.00662062
$905$	−3.70067	−0.123014
$906$	−19.5117	−0.648232
$907$	16.8837	0.560614	0.280307	−	0.959910i	$-0.409564\pi$
$907$	16.8837	0.560614	0.280307	+	0.959910i	$0.409564\pi$
$908$	15.7644	0.523159
$909$	−8.11468	−0.269147
$910$	6.31222	0.209248
$911$	−20.4608	−0.677897	−0.338948	−	0.940805i	$-0.610071\pi$
$911$	−20.4608	−0.677897	−0.338948	+	0.940805i	$0.610071\pi$
$912$	4.97673	0.164796
$913$	−31.9134	−1.05618
$914$	−5.47979	−0.181255
$915$	2.41948	0.0799857
$916$	23.7161	0.783602
$917$	26.5206	0.875788
$918$	−5.10004	−0.168326
$919$	−37.9458	−1.25172	−0.625859	−	0.779936i	$-0.715251\pi$
$919$	−37.9458	−1.25172	−0.625859	+	0.779936i	$0.715251\pi$
$920$	−21.8318	−0.719774
$921$	−31.7716	−1.04691
$922$	−14.4209	−0.474928
$923$	9.42543	0.310242
$924$	−7.08317	−0.233019
$925$	−15.7692	−0.518489
$926$	14.3003	0.469938
$927$	−1.00000	−0.0328443
$928$	8.89325	0.291935
$929$	35.4190	1.16206	0.581029	−	0.813883i	$-0.302650\pi$
$929$	35.4190	1.16206	0.581029	+	0.813883i	$0.302650\pi$
$930$	7.90213	0.259121
$931$	6.91659	0.226682
$932$	23.6830	0.775763
$933$	−4.13303	−0.135309
$934$	20.5623	0.672819
$935$	−40.6447	−1.32922
$936$	1.00000	0.0326860
$937$	1.85281	0.0605286	0.0302643	−	0.999542i	$-0.490365\pi$
$937$	1.85281	0.0605286	0.0302643	+	0.999542i	$0.490365\pi$
$938$	7.45952	0.243562
$939$	−22.5791	−0.736840
$940$	−17.8134	−0.581008
$941$	−22.7289	−0.740943	−0.370471	−	0.928844i	$-0.620804\pi$
$941$	−22.7289	−0.740943	−0.370471	+	0.928844i	$0.620804\pi$
$942$	12.7383	0.415036
$943$	−43.3969	−1.41320
$944$	4.13496	0.134582
$945$	−6.31222	−0.205337
$946$	−15.0565	−0.489530
$947$	−33.6662	−1.09401	−0.547003	−	0.837131i	$-0.684231\pi$
$947$	−33.6662	−1.09401	−0.547003	+	0.837131i	$0.684231\pi$
$948$	16.6133	0.539575
$949$	−1.53198	−0.0497303
$950$	10.4614	0.339414
$951$	−25.2757	−0.819621
$952$	12.0799	0.391512
$953$	−8.12488	−0.263191	−0.131595	−	0.991304i	$-0.542010\pi$
$953$	−8.12488	−0.263191	−0.131595	+	0.991304i	$0.542010\pi$
$954$	9.57222	0.309912
$955$	55.8469	1.80716
$956$	−12.8452	−0.415442
$957$	26.5949	0.859691
$958$	38.1472	1.23248
$959$	−3.29110	−0.106275
$960$	−2.66497	−0.0860116
$961$	−22.2077	−0.716377
$962$	−7.50176	−0.241867
$963$	−8.82181	−0.284279
$964$	−16.9050	−0.544473
$965$	37.7245	1.21439
$966$	19.4038	0.624308
$967$	−59.1015	−1.90058	−0.950288	−	0.311371i	$-0.899212\pi$
$967$	−59.1015	−1.90058	−0.950288	+	0.311371i	$0.899212\pi$
$968$	2.05715	0.0661195
$969$	−25.3815	−0.815373
$970$	15.0276	0.482506
$971$	49.7150	1.59543	0.797715	−	0.603034i	$-0.206042\pi$
$971$	49.7150	1.59543	0.797715	+	0.603034i	$0.206042\pi$
$972$	−1.00000	−0.0320750
$973$	−34.9203	−1.11949
$974$	−2.46128	−0.0788646
$975$	2.10207	0.0673202
$976$	−0.907884	−0.0290607
$977$	−57.6564	−1.84459	−0.922296	−	0.386483i	$-0.873690\pi$
$977$	−57.6564	−1.84459	−0.922296	+	0.386483i	$0.873690\pi$
$978$	20.0360	0.640681
$979$	42.5805	1.36088
$980$	−3.70373	−0.118311
$981$	−4.89164	−0.156178
$982$	−1.04891	−0.0334721
$983$	−21.3741	−0.681728	−0.340864	−	0.940113i	$-0.610720\pi$
$983$	−21.3741	−0.681728	−0.340864	+	0.940113i	$0.610720\pi$
$984$	−5.29737	−0.168874
$985$	10.3770	0.330639
$986$	−45.3559	−1.44443
$987$	15.8323	0.503947
$988$	4.97673	0.158331
$989$	41.2463	1.31156
$990$	−7.96949	−0.253287
$991$	−47.2476	−1.50087	−0.750435	−	0.660945i	$-0.770156\pi$
$991$	−47.2476	−1.50087	−0.750435	+	0.660945i	$0.770156\pi$
$992$	−2.96518	−0.0941447
$993$	−15.2198	−0.482987
$994$	22.3250	0.708105
$995$	−0.00354403	−0.000112353 0
$996$	10.6717	0.338147
$997$	12.5339	0.396953	0.198477	−	0.980106i	$-0.436401\pi$
$997$	12.5339	0.396953	0.198477	+	0.980106i	$0.436401\pi$
$998$	12.0797	0.382376
$999$	7.50176	0.237345

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.s.1.8	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.s.1.8	✓	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.66497 q^{5} +1.00000 q^{6} +2.36859 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.66497 q^{5} +1.00000 q^{6} +2.36859 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.66497 q^{10} +2.99046 q^{11} -1.00000 q^{12} -1.00000 q^{13} -2.36859 q^{14} -2.66497 q^{15} +1.00000 q^{16} -5.10004 q^{17} -1.00000 q^{18} -4.97673 q^{19} +2.66497 q^{20} -2.36859 q^{21} -2.99046 q^{22} +8.19215 q^{23} +1.00000 q^{24} +2.10207 q^{25} +1.00000 q^{26} -1.00000 q^{27} +2.36859 q^{28} -8.89325 q^{29} +2.66497 q^{30} +2.96518 q^{31} -1.00000 q^{32} -2.99046 q^{33} +5.10004 q^{34} +6.31222 q^{35} +1.00000 q^{36} -7.50176 q^{37} +4.97673 q^{38} +1.00000 q^{39} -2.66497 q^{40} -5.29737 q^{41} +2.36859 q^{42} +5.03485 q^{43} +2.99046 q^{44} +2.66497 q^{45} -8.19215 q^{46} -6.68426 q^{47} -1.00000 q^{48} -1.38978 q^{49} -2.10207 q^{50} +5.10004 q^{51} -1.00000 q^{52} -9.57222 q^{53} +1.00000 q^{54} +7.96949 q^{55} -2.36859 q^{56} +4.97673 q^{57} +8.89325 q^{58} +4.13496 q^{59} -2.66497 q^{60} -0.907884 q^{61} -2.96518 q^{62} +2.36859 q^{63} +1.00000 q^{64} -2.66497 q^{65} +2.99046 q^{66} -3.14935 q^{67} -5.10004 q^{68} -8.19215 q^{69} -6.31222 q^{70} -9.42543 q^{71} -1.00000 q^{72} +1.53198 q^{73} +7.50176 q^{74} -2.10207 q^{75} -4.97673 q^{76} +7.08317 q^{77} -1.00000 q^{78} -16.6133 q^{79} +2.66497 q^{80} +1.00000 q^{81} +5.29737 q^{82} -10.6717 q^{83} -2.36859 q^{84} -13.5915 q^{85} -5.03485 q^{86} +8.89325 q^{87} -2.99046 q^{88} +14.2388 q^{89} -2.66497 q^{90} -2.36859 q^{91} +8.19215 q^{92} -2.96518 q^{93} +6.68426 q^{94} -13.2629 q^{95} +1.00000 q^{96} -5.63892 q^{97} +1.38978 q^{98} +2.99046 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} + 10 q^{6} - 9 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + 6 * q^5 + 10 * q^6 - 9 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} + 10 q^{6} - 9 q^{7} - 10 q^{8} + 10 q^{9} - 6 q^{10} - q^{11} - 10 q^{12} - 10 q^{13} + 9 q^{14} - 6 q^{15} + 10 q^{16} + 5 q^{17} - 10 q^{18} - 9 q^{19} + 6 q^{20} + 9 q^{21} + q^{22} + q^{23} + 10 q^{24} + 20 q^{25} + 10 q^{26} - 10 q^{27} - 9 q^{28} - 22 q^{29} + 6 q^{30} - 13 q^{31} - 10 q^{32} + q^{33} - 5 q^{34} + 14 q^{35} + 10 q^{36} + 10 q^{37} + 9 q^{38} + 10 q^{39} - 6 q^{40} - 18 q^{41} - 9 q^{42} + 10 q^{43} - q^{44} + 6 q^{45} - q^{46} + 28 q^{47} - 10 q^{48} + 11 q^{49} - 20 q^{50} - 5 q^{51} - 10 q^{52} + 6 q^{53} + 10 q^{54} - 26 q^{55} + 9 q^{56} + 9 q^{57} + 22 q^{58} + 7 q^{59} - 6 q^{60} - 20 q^{61} + 13 q^{62} - 9 q^{63} + 10 q^{64} - 6 q^{65} - q^{66} - 21 q^{67} + 5 q^{68} - q^{69} - 14 q^{70} - 19 q^{71} - 10 q^{72} + 3 q^{73} - 10 q^{74} - 20 q^{75} - 9 q^{76} + 28 q^{77} - 10 q^{78} - 11 q^{79} + 6 q^{80} + 10 q^{81} + 18 q^{82} + 20 q^{83} + 9 q^{84} - q^{85} - 10 q^{86} + 22 q^{87} + q^{88} + 22 q^{89} - 6 q^{90} + 9 q^{91} + q^{92} + 13 q^{93} - 28 q^{94} + 10 q^{96} - 10 q^{97} - 11 q^{98} - q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + 6 * q^5 + 10 * q^6 - 9 * q^7 - 10 * q^8 + 10 * q^9 - 6 * q^10 - q^11 - 10 * q^12 - 10 * q^13 + 9 * q^14 - 6 * q^15 + 10 * q^16 + 5 * q^17 - 10 * q^18 - 9 * q^19 + 6 * q^20 + 9 * q^21 + q^22 + q^23 + 10 * q^24 + 20 * q^25 + 10 * q^26 - 10 * q^27 - 9 * q^28 - 22 * q^29 + 6 * q^30 - 13 * q^31 - 10 * q^32 + q^33 - 5 * q^34 + 14 * q^35 + 10 * q^36 + 10 * q^37 + 9 * q^38 + 10 * q^39 - 6 * q^40 - 18 * q^41 - 9 * q^42 + 10 * q^43 - q^44 + 6 * q^45 - q^46 + 28 * q^47 - 10 * q^48 + 11 * q^49 - 20 * q^50 - 5 * q^51 - 10 * q^52 + 6 * q^53 + 10 * q^54 - 26 * q^55 + 9 * q^56 + 9 * q^57 + 22 * q^58 + 7 * q^59 - 6 * q^60 - 20 * q^61 + 13 * q^62 - 9 * q^63 + 10 * q^64 - 6 * q^65 - q^66 - 21 * q^67 + 5 * q^68 - q^69 - 14 * q^70 - 19 * q^71 - 10 * q^72 + 3 * q^73 - 10 * q^74 - 20 * q^75 - 9 * q^76 + 28 * q^77 - 10 * q^78 - 11 * q^79 + 6 * q^80 + 10 * q^81 + 18 * q^82 + 20 * q^83 + 9 * q^84 - q^85 - 10 * q^86 + 22 * q^87 + q^88 + 22 * q^89 - 6 * q^90 + 9 * q^91 + q^92 + 13 * q^93 - 28 * q^94 + 10 * q^96 - 10 * q^97 - 11 * q^98 - q^99

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