LMFDB - Embedded newform 8470.2.a.cw.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8470,2,Mod(1,8470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8470, 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("8470.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8470.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:	$67.6332905120$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.19898000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 10x^{4} + 7x^{3} + 24x^{2} - 15x - 5 $ x^6 - x^5 - 10x^4 + 7x^3 + 24x^2 - 15x - 5
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 770)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.68692$ of defining polynomial
Character	$\chi$	$=$	8470.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.68692 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.68692 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.154300 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.68692 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.68692 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.154300 q^{9} -1.00000 q^{10} -1.68692 q^{12} +0.0425741 q^{13} -1.00000 q^{14} -1.68692 q^{15} +1.00000 q^{16} -4.72038 q^{17} +0.154300 q^{18} -1.71340 q^{19} +1.00000 q^{20} -1.68692 q^{21} -6.95966 q^{23} +1.68692 q^{24} +1.00000 q^{25} -0.0425741 q^{26} +5.32105 q^{27} +1.00000 q^{28} -1.34277 q^{29} +1.68692 q^{30} +6.01245 q^{31} -1.00000 q^{32} +4.72038 q^{34} +1.00000 q^{35} -0.154300 q^{36} +8.48459 q^{37} +1.71340 q^{38} -0.0718191 q^{39} -1.00000 q^{40} +3.91371 q^{41} +1.68692 q^{42} +6.42455 q^{43} -0.154300 q^{45} +6.95966 q^{46} +4.59129 q^{47} -1.68692 q^{48} +1.00000 q^{49} -1.00000 q^{50} +7.96291 q^{51} +0.0425741 q^{52} -14.1024 q^{53} -5.32105 q^{54} -1.00000 q^{56} +2.89036 q^{57} +1.34277 q^{58} -10.2177 q^{59} -1.68692 q^{60} +13.8661 q^{61} -6.01245 q^{62} -0.154300 q^{63} +1.00000 q^{64} +0.0425741 q^{65} +6.39600 q^{67} -4.72038 q^{68} +11.7404 q^{69} -1.00000 q^{70} +11.3041 q^{71} +0.154300 q^{72} -1.98728 q^{73} -8.48459 q^{74} -1.68692 q^{75} -1.71340 q^{76} +0.0718191 q^{78} -8.87065 q^{79} +1.00000 q^{80} -8.51329 q^{81} -3.91371 q^{82} -10.0807 q^{83} -1.68692 q^{84} -4.72038 q^{85} -6.42455 q^{86} +2.26515 q^{87} +2.93362 q^{89} +0.154300 q^{90} +0.0425741 q^{91} -6.95966 q^{92} -10.1425 q^{93} -4.59129 q^{94} -1.71340 q^{95} +1.68692 q^{96} -17.4812 q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - q^{3} + 6 q^{4} + 6 q^{5} + q^{6} + 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - q^3 + 6 * q^4 + 6 * q^5 + q^6 + 6 * q^7 - 6 * q^8 + 3 * q^9	$ 6 q - 6 q^{2} - q^{3} + 6 q^{4} + 6 q^{5} + q^{6} + 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} - q^{12} - 9 q^{13} - 6 q^{14} - q^{15} + 6 q^{16} - 9 q^{17} - 3 q^{18} - 12 q^{19} + 6 q^{20} - q^{21} + 4 q^{23} + q^{24} + 6 q^{25} + 9 q^{26} - 4 q^{27} + 6 q^{28} - 15 q^{29} + q^{30} + 8 q^{31} - 6 q^{32} + 9 q^{34} + 6 q^{35} + 3 q^{36} - 4 q^{37} + 12 q^{38} + 19 q^{39} - 6 q^{40} - 4 q^{41} + q^{42} - 30 q^{43} + 3 q^{45} - 4 q^{46} - 7 q^{47} - q^{48} + 6 q^{49} - 6 q^{50} - 16 q^{51} - 9 q^{52} - 6 q^{53} + 4 q^{54} - 6 q^{56} + 14 q^{57} + 15 q^{58} + 4 q^{59} - q^{60} + 14 q^{61} - 8 q^{62} + 3 q^{63} + 6 q^{64} - 9 q^{65} + 18 q^{67} - 9 q^{68} - 10 q^{69} - 6 q^{70} + 23 q^{71} - 3 q^{72} - 23 q^{73} + 4 q^{74} - q^{75} - 12 q^{76} - 19 q^{78} - 21 q^{79} + 6 q^{80} - 18 q^{81} + 4 q^{82} - 25 q^{83} - q^{84} - 9 q^{85} + 30 q^{86} - 14 q^{87} - 18 q^{89} - 3 q^{90} - 9 q^{91} + 4 q^{92} - 24 q^{93} + 7 q^{94} - 12 q^{95} + q^{96} + 7 q^{97} - 6 q^{98}+O(q^{100}) $ 6 * q - 6 * q^2 - q^3 + 6 * q^4 + 6 * q^5 + q^6 + 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 - q^12 - 9 * q^13 - 6 * q^14 - q^15 + 6 * q^16 - 9 * q^17 - 3 * q^18 - 12 * q^19 + 6 * q^20 - q^21 + 4 * q^23 + q^24 + 6 * q^25 + 9 * q^26 - 4 * q^27 + 6 * q^28 - 15 * q^29 + q^30 + 8 * q^31 - 6 * q^32 + 9 * q^34 + 6 * q^35 + 3 * q^36 - 4 * q^37 + 12 * q^38 + 19 * q^39 - 6 * q^40 - 4 * q^41 + q^42 - 30 * q^43 + 3 * q^45 - 4 * q^46 - 7 * q^47 - q^48 + 6 * q^49 - 6 * q^50 - 16 * q^51 - 9 * q^52 - 6 * q^53 + 4 * q^54 - 6 * q^56 + 14 * q^57 + 15 * q^58 + 4 * q^59 - q^60 + 14 * q^61 - 8 * q^62 + 3 * q^63 + 6 * q^64 - 9 * q^65 + 18 * q^67 - 9 * q^68 - 10 * q^69 - 6 * q^70 + 23 * q^71 - 3 * q^72 - 23 * q^73 + 4 * q^74 - q^75 - 12 * q^76 - 19 * q^78 - 21 * q^79 + 6 * q^80 - 18 * q^81 + 4 * q^82 - 25 * q^83 - q^84 - 9 * q^85 + 30 * q^86 - 14 * q^87 - 18 * q^89 - 3 * q^90 - 9 * q^91 + 4 * q^92 - 24 * q^93 + 7 * q^94 - 12 * q^95 + q^96 + 7 * q^97 - 6 * q^98

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
$3$	−1.68692	−0.973944	−0.486972	−	0.873418i	$-0.661899\pi$
$3$	−1.68692	−0.973944	−0.486972	+	0.873418i	$0.661899\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.68692	0.688682
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−0.154300	−0.0514332
$10$	−1.00000	−0.316228
$11$	0	0
$11$	0	0
$12$	−1.68692	−0.486972
$13$	0.0425741	0.0118079	0.00590397	−	0.999983i	$-0.498121\pi$
$13$	0.0425741	0.0118079	0.00590397	+	0.999983i	$0.498121\pi$
$14$	−1.00000	−0.267261
$15$	−1.68692	−0.435561
$16$	1.00000	0.250000
$17$	−4.72038	−1.14486	−0.572430	−	0.819953i	$-0.693999\pi$
$17$	−4.72038	−1.14486	−0.572430	+	0.819953i	$0.693999\pi$
$18$	0.154300	0.0363688
$19$	−1.71340	−0.393080	−0.196540	−	0.980496i	$-0.562971\pi$
$19$	−1.71340	−0.393080	−0.196540	+	0.980496i	$0.562971\pi$
$20$	1.00000	0.223607
$21$	−1.68692	−0.368116
$22$	0	0
$23$	−6.95966	−1.45119	−0.725595	−	0.688122i	$-0.758435\pi$
$23$	−6.95966	−1.45119	−0.725595	+	0.688122i	$0.758435\pi$
$24$	1.68692	0.344341
$25$	1.00000	0.200000
$26$	−0.0425741	−0.00834947
$27$	5.32105	1.02404
$28$	1.00000	0.188982
$29$	−1.34277	−0.249346	−0.124673	−	0.992198i	$-0.539788\pi$
$29$	−1.34277	−0.249346	−0.124673	+	0.992198i	$0.539788\pi$
$30$	1.68692	0.307988
$31$	6.01245	1.07987	0.539934	−	0.841707i	$-0.318449\pi$
$31$	6.01245	1.07987	0.539934	+	0.841707i	$0.318449\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	4.72038	0.809539
$35$	1.00000	0.169031
$36$	−0.154300	−0.0257166
$37$	8.48459	1.39486	0.697429	−	0.716654i	$-0.254327\pi$
$37$	8.48459	1.39486	0.697429	+	0.716654i	$0.254327\pi$
$38$	1.71340	0.277950
$39$	−0.0718191	−0.0115003
$40$	−1.00000	−0.158114
$41$	3.91371	0.611219	0.305609	−	0.952157i	$-0.401140\pi$
$41$	3.91371	0.611219	0.305609	+	0.952157i	$0.401140\pi$
$42$	1.68692	0.260297
$43$	6.42455	0.979735	0.489867	−	0.871797i	$-0.337045\pi$
$43$	6.42455	0.979735	0.489867	+	0.871797i	$0.337045\pi$
$44$	0	0
$45$	−0.154300	−0.0230016
$46$	6.95966	1.02615
$47$	4.59129	0.669709	0.334854	−	0.942270i	$-0.391313\pi$
$47$	4.59129	0.669709	0.334854	+	0.942270i	$0.391313\pi$
$48$	−1.68692	−0.243486
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	7.96291	1.11503
$52$	0.0425741	0.00590397
$53$	−14.1024	−1.93711	−0.968554	−	0.248804i	$-0.919963\pi$
$53$	−14.1024	−1.93711	−0.968554	+	0.248804i	$0.919963\pi$
$54$	−5.32105	−0.724104
$55$	0	0
$56$	−1.00000	−0.133631
$57$	2.89036	0.382838
$58$	1.34277	0.176315
$59$	−10.2177	−1.33023	−0.665117	−	0.746739i	$-0.731619\pi$
$59$	−10.2177	−1.33023	−0.665117	+	0.746739i	$0.731619\pi$
$60$	−1.68692	−0.217780
$61$	13.8661	1.77538	0.887688	−	0.460446i	$-0.152310\pi$
$61$	13.8661	1.77538	0.887688	+	0.460446i	$0.152310\pi$
$62$	−6.01245	−0.763582
$63$	−0.154300	−0.0194399
$64$	1.00000	0.125000
$65$	0.0425741	0.00528067
$66$	0	0
$67$	6.39600	0.781396	0.390698	−	0.920519i	$-0.372234\pi$
$67$	6.39600	0.781396	0.390698	+	0.920519i	$0.372234\pi$
$68$	−4.72038	−0.572430
$69$	11.7404	1.41338
$70$	−1.00000	−0.119523
$71$	11.3041	1.34155	0.670774	−	0.741662i	$-0.265962\pi$
$71$	11.3041	1.34155	0.670774	+	0.741662i	$0.265962\pi$
$72$	0.154300	0.0181844
$73$	−1.98728	−0.232594	−0.116297	−	0.993214i	$-0.537102\pi$
$73$	−1.98728	−0.232594	−0.116297	+	0.993214i	$0.537102\pi$
$74$	−8.48459	−0.986313
$75$	−1.68692	−0.194789
$76$	−1.71340	−0.196540
$77$	0	0
$78$	0.0718191	0.00813192
$79$	−8.87065	−0.998026	−0.499013	−	0.866595i	$-0.666304\pi$
$79$	−8.87065	−0.998026	−0.499013	+	0.866595i	$0.666304\pi$
$80$	1.00000	0.111803
$81$	−8.51329	−0.945921
$82$	−3.91371	−0.432197
$83$	−10.0807	−1.10650	−0.553249	−	0.833016i	$-0.686612\pi$
$83$	−10.0807	−1.10650	−0.553249	+	0.833016i	$0.686612\pi$
$84$	−1.68692	−0.184058
$85$	−4.72038	−0.511997
$86$	−6.42455	−0.692777
$87$	2.26515	0.242849
$88$	0	0
$89$	2.93362	0.310963	0.155481	−	0.987839i	$-0.450307\pi$
$89$	2.93362	0.310963	0.155481	+	0.987839i	$0.450307\pi$
$90$	0.154300	0.0162646
$91$	0.0425741	0.00446298
$92$	−6.95966	−0.725595
$93$	−10.1425	−1.05173
$94$	−4.59129	−0.473556
$95$	−1.71340	−0.175791
$96$	1.68692	0.172171
$97$	−17.4812	−1.77495	−0.887474	−	0.460857i	$-0.847542\pi$
$97$	−17.4812	−1.77495	−0.887474	+	0.460857i	$0.847542\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	−5.70914	−0.568081	−0.284040	−	0.958812i	$-0.591675\pi$
$101$	−5.70914	−0.568081	−0.284040	+	0.958812i	$0.591675\pi$
$102$	−7.96291	−0.788445
$103$	13.4052	1.32085	0.660425	−	0.750892i	$-0.270376\pi$
$103$	13.4052	1.32085	0.660425	+	0.750892i	$0.270376\pi$
$104$	−0.0425741	−0.00417474
$105$	−1.68692	−0.164627
$106$	14.1024	1.36974
$107$	−15.9669	−1.54358	−0.771790	−	0.635878i	$-0.780638\pi$
$107$	−15.9669	−1.54358	−0.771790	+	0.635878i	$0.780638\pi$
$108$	5.32105	0.512019
$109$	15.9501	1.52774	0.763871	−	0.645369i	$-0.223297\pi$
$109$	15.9501	1.52774	0.763871	+	0.645369i	$0.223297\pi$
$110$	0	0
$111$	−14.3128	−1.35851
$112$	1.00000	0.0944911
$113$	8.65087	0.813805	0.406903	−	0.913472i	$-0.366609\pi$
$113$	8.65087	0.813805	0.406903	+	0.913472i	$0.366609\pi$
$114$	−2.89036	−0.270707
$115$	−6.95966	−0.648992
$116$	−1.34277	−0.124673
$117$	−0.00656917	−0.000607320 0
$118$	10.2177	0.940618
$119$	−4.72038	−0.432717
$120$	1.68692	0.153994
$121$	0	0
$122$	−13.8661	−1.25538
$123$	−6.60212	−0.595293
$124$	6.01245	0.539934
$125$	1.00000	0.0894427
$126$	0.154300	0.0137461
$127$	−1.82824	−0.162230	−0.0811149	−	0.996705i	$-0.525848\pi$
$127$	−1.82824	−0.162230	−0.0811149	+	0.996705i	$0.525848\pi$
$128$	−1.00000	−0.0883883
$129$	−10.8377	−0.954207
$130$	−0.0425741	−0.00373400
$131$	−1.61678	−0.141259	−0.0706294	−	0.997503i	$-0.522501\pi$
$131$	−1.61678	−0.141259	−0.0706294	+	0.997503i	$0.522501\pi$
$132$	0	0
$133$	−1.71340	−0.148570
$134$	−6.39600	−0.552530
$135$	5.32105	0.457963
$136$	4.72038	0.404769
$137$	10.2667	0.877144	0.438572	−	0.898696i	$-0.355484\pi$
$137$	10.2667	0.877144	0.438572	+	0.898696i	$0.355484\pi$
$138$	−11.7404	−0.999409
$139$	−1.94758	−0.165191	−0.0825957	−	0.996583i	$-0.526321\pi$
$139$	−1.94758	−0.165191	−0.0825957	+	0.996583i	$0.526321\pi$
$140$	1.00000	0.0845154
$141$	−7.74515	−0.652259
$142$	−11.3041	−0.948617
$143$	0	0
$144$	−0.154300	−0.0128583
$145$	−1.34277	−0.111511
$146$	1.98728	0.164469
$147$	−1.68692	−0.139135
$148$	8.48459	0.697429
$149$	−6.46920	−0.529978	−0.264989	−	0.964251i	$-0.585368\pi$
$149$	−6.46920	−0.529978	−0.264989	+	0.964251i	$0.585368\pi$
$150$	1.68692	0.137736
$151$	−23.6110	−1.92143	−0.960717	−	0.277531i	$-0.910484\pi$
$151$	−23.6110	−1.92143	−0.960717	+	0.277531i	$0.910484\pi$
$152$	1.71340	0.138975
$153$	0.728353	0.0588839
$154$	0	0
$155$	6.01245	0.482932
$156$	−0.0718191	−0.00575013
$157$	11.4891	0.916932	0.458466	−	0.888712i	$-0.348399\pi$
$157$	11.4891	0.916932	0.458466	+	0.888712i	$0.348399\pi$
$158$	8.87065	0.705711
$159$	23.7896	1.88663
$160$	−1.00000	−0.0790569
$161$	−6.95966	−0.548498
$162$	8.51329	0.668867
$163$	−14.1296	−1.10672	−0.553359	−	0.832943i	$-0.686654\pi$
$163$	−14.1296	−1.10672	−0.553359	+	0.832943i	$0.686654\pi$
$164$	3.91371	0.305609
$165$	0	0
$166$	10.0807	0.782412
$167$	−15.6015	−1.20728	−0.603641	−	0.797256i	$-0.706284\pi$
$167$	−15.6015	−1.20728	−0.603641	+	0.797256i	$0.706284\pi$
$168$	1.68692	0.130149
$169$	−12.9982	−0.999861
$170$	4.72038	0.362037
$171$	0.264377	0.0202174
$172$	6.42455	0.489867
$173$	6.21176	0.472271	0.236136	−	0.971720i	$-0.424119\pi$
$173$	6.21176	0.472271	0.236136	+	0.971720i	$0.424119\pi$
$174$	−2.26515	−0.171721
$175$	1.00000	0.0755929
$176$	0	0
$177$	17.2365	1.29557
$178$	−2.93362	−0.219884
$179$	15.9071	1.18895	0.594475	−	0.804114i	$-0.297360\pi$
$179$	15.9071	1.18895	0.594475	+	0.804114i	$0.297360\pi$
$180$	−0.154300	−0.0115008
$181$	−6.59938	−0.490528	−0.245264	−	0.969456i	$-0.578875\pi$
$181$	−6.59938	−0.490528	−0.245264	+	0.969456i	$0.578875\pi$
$182$	−0.0425741	−0.00315580
$183$	−23.3911	−1.72912
$184$	6.95966	0.513073
$185$	8.48459	0.623799
$186$	10.1425	0.743686
$187$	0	0
$188$	4.59129	0.334854
$189$	5.32105	0.387050
$190$	1.71340	0.124303
$191$	17.1690	1.24231	0.621153	−	0.783689i	$-0.286664\pi$
$191$	17.1690	1.24231	0.621153	+	0.783689i	$0.286664\pi$
$192$	−1.68692	−0.121743
$193$	−10.2185	−0.735541	−0.367771	−	0.929917i	$-0.619879\pi$
$193$	−10.2185	−0.735541	−0.367771	+	0.929917i	$0.619879\pi$
$194$	17.4812	1.25508
$195$	−0.0718191	−0.00514308
$196$	1.00000	0.0714286
$197$	−7.33268	−0.522432	−0.261216	−	0.965280i	$-0.584124\pi$
$197$	−7.33268	−0.522432	−0.261216	+	0.965280i	$0.584124\pi$
$198$	0	0
$199$	−8.90352	−0.631154	−0.315577	−	0.948900i	$-0.602198\pi$
$199$	−8.90352	−0.631154	−0.315577	+	0.948900i	$0.602198\pi$
$200$	−1.00000	−0.0707107
$201$	−10.7895	−0.761036
$202$	5.70914	0.401694
$203$	−1.34277	−0.0942441
$204$	7.96291	0.557515
$205$	3.91371	0.273345
$206$	−13.4052	−0.933982
$207$	1.07387	0.0746394
$208$	0.0425741	0.00295198
$209$	0	0
$210$	1.68692	0.116409
$211$	4.54767	0.313075	0.156537	−	0.987672i	$-0.449967\pi$
$211$	4.54767	0.313075	0.156537	+	0.987672i	$0.449967\pi$
$212$	−14.1024	−0.968554
$213$	−19.0691	−1.30659
$214$	15.9669	1.09148
$215$	6.42455	0.438151
$216$	−5.32105	−0.362052
$217$	6.01245	0.408152
$218$	−15.9501	−1.08028
$219$	3.35239	0.226533
$220$	0	0
$221$	−0.200966	−0.0135184
$222$	14.3128	0.960614
$223$	18.0702	1.21007	0.605034	−	0.796200i	$-0.293160\pi$
$223$	18.0702	1.21007	0.605034	+	0.796200i	$0.293160\pi$
$224$	−1.00000	−0.0668153
$225$	−0.154300	−0.0102866
$226$	−8.65087	−0.575447
$227$	0.970501	0.0644144	0.0322072	−	0.999481i	$-0.489746\pi$
$227$	0.970501	0.0644144	0.0322072	+	0.999481i	$0.489746\pi$
$228$	2.89036	0.191419
$229$	−2.46292	−0.162755	−0.0813773	−	0.996683i	$-0.525932\pi$
$229$	−2.46292	−0.162755	−0.0813773	+	0.996683i	$0.525932\pi$
$230$	6.95966	0.458907
$231$	0	0
$232$	1.34277	0.0881573
$233$	−6.65041	−0.435683	−0.217841	−	0.975984i	$-0.569902\pi$
$233$	−6.65041	−0.435683	−0.217841	+	0.975984i	$0.569902\pi$
$234$	0.00656917	0.000429440 0
$235$	4.59129	0.299503
$236$	−10.2177	−0.665117
$237$	14.9641	0.972021
$238$	4.72038	0.305977
$239$	21.0529	1.36180	0.680900	−	0.732377i	$-0.261589\pi$
$239$	21.0529	1.36180	0.680900	+	0.732377i	$0.261589\pi$
$240$	−1.68692	−0.108890
$241$	−7.93244	−0.510973	−0.255487	−	0.966813i	$-0.582236\pi$
$241$	−7.93244	−0.510973	−0.255487	+	0.966813i	$0.582236\pi$
$242$	0	0
$243$	−1.60191	−0.102763
$244$	13.8661	0.887688
$245$	1.00000	0.0638877
$246$	6.60212	0.420936
$247$	−0.0729463	−0.00464146
$248$	−6.01245	−0.381791
$249$	17.0053	1.07767
$250$	−1.00000	−0.0632456
$251$	18.9431	1.19568	0.597839	−	0.801617i	$-0.296026\pi$
$251$	18.9431	1.19568	0.597839	+	0.801617i	$0.296026\pi$
$252$	−0.154300	−0.00971997
$253$	0	0
$254$	1.82824	0.114714
$255$	7.96291	0.498657
$256$	1.00000	0.0625000
$257$	−26.8598	−1.67547	−0.837736	−	0.546076i	$-0.816121\pi$
$257$	−26.8598	−1.67547	−0.837736	+	0.546076i	$0.816121\pi$
$258$	10.8377	0.674726
$259$	8.48459	0.527207
$260$	0.0425741	0.00264033
$261$	0.207189	0.0128247
$262$	1.61678	0.0998850
$263$	−13.3750	−0.824740	−0.412370	−	0.911017i	$-0.635299\pi$
$263$	−13.3750	−0.824740	−0.412370	+	0.911017i	$0.635299\pi$
$264$	0	0
$265$	−14.1024	−0.866301
$266$	1.71340	0.105055
$267$	−4.94878	−0.302860
$268$	6.39600	0.390698
$269$	−4.05979	−0.247530	−0.123765	−	0.992312i	$-0.539497\pi$
$269$	−4.05979	−0.247530	−0.123765	+	0.992312i	$0.539497\pi$
$270$	−5.32105	−0.323829
$271$	23.0226	1.39852	0.699261	−	0.714866i	$-0.253512\pi$
$271$	23.0226	1.39852	0.699261	+	0.714866i	$0.253512\pi$
$272$	−4.72038	−0.286215
$273$	−0.0718191	−0.00434669
$274$	−10.2667	−0.620235
$275$	0	0
$276$	11.7404	0.706689
$277$	−22.2862	−1.33905	−0.669524	−	0.742790i	$-0.733502\pi$
$277$	−22.2862	−1.33905	−0.669524	+	0.742790i	$0.733502\pi$
$278$	1.94758	0.116808
$279$	−0.927720	−0.0555411
$280$	−1.00000	−0.0597614
$281$	−2.24959	−0.134199	−0.0670996	−	0.997746i	$-0.521375\pi$
$281$	−2.24959	−0.134199	−0.0670996	+	0.997746i	$0.521375\pi$
$282$	7.74515	0.461217
$283$	−3.71034	−0.220557	−0.110279	−	0.993901i	$-0.535174\pi$
$283$	−3.71034	−0.220557	−0.110279	+	0.993901i	$0.535174\pi$
$284$	11.3041	0.670774
$285$	2.89036	0.171210
$286$	0	0
$287$	3.91371	0.231019
$288$	0.154300	0.00909220
$289$	5.28199	0.310705
$290$	1.34277	0.0788503
$291$	29.4894	1.72870
$292$	−1.98728	−0.116297
$293$	1.85170	0.108177	0.0540886	−	0.998536i	$-0.482775\pi$
$293$	1.85170	0.108177	0.0540886	+	0.998536i	$0.482775\pi$
$294$	1.68692	0.0983832
$295$	−10.2177	−0.594899
$296$	−8.48459	−0.493157
$297$	0	0
$298$	6.46920	0.374751
$299$	−0.296302	−0.0171356
$300$	−1.68692	−0.0973944
$301$	6.42455	0.370305
$302$	23.6110	1.35866
$303$	9.63087	0.553279
$304$	−1.71340	−0.0982700
$305$	13.8661	0.793972
$306$	−0.728353	−0.0416372
$307$	−6.66980	−0.380666	−0.190333	−	0.981720i	$-0.560957\pi$
$307$	−6.66980	−0.380666	−0.190333	+	0.981720i	$0.560957\pi$
$308$	0	0
$309$	−22.6134	−1.28643
$310$	−6.01245	−0.341484
$311$	15.0969	0.856067	0.428034	−	0.903763i	$-0.359207\pi$
$311$	15.0969	0.856067	0.428034	+	0.903763i	$0.359207\pi$
$312$	0.0718191	0.00406596
$313$	7.33744	0.414736	0.207368	−	0.978263i	$-0.433510\pi$
$313$	7.33744	0.414736	0.207368	+	0.978263i	$0.433510\pi$
$314$	−11.4891	−0.648369
$315$	−0.154300	−0.00869380
$316$	−8.87065	−0.499013
$317$	22.4900	1.26316	0.631581	−	0.775310i	$-0.282406\pi$
$317$	22.4900	1.26316	0.631581	+	0.775310i	$0.282406\pi$
$318$	−23.7896	−1.33405
$319$	0	0
$320$	1.00000	0.0559017
$321$	26.9349	1.50336
$322$	6.95966	0.387847
$323$	8.08788	0.450022
$324$	−8.51329	−0.472961
$325$	0.0425741	0.00236159
$326$	14.1296	0.782568
$327$	−26.9065	−1.48793
$328$	−3.91371	−0.216099
$329$	4.59129	0.253126
$330$	0	0
$331$	10.3154	0.566987	0.283494	−	0.958974i	$-0.408507\pi$
$331$	10.3154	0.566987	0.283494	+	0.958974i	$0.408507\pi$
$332$	−10.0807	−0.553249
$333$	−1.30917	−0.0717420
$334$	15.6015	0.853677
$335$	6.39600	0.349451
$336$	−1.68692	−0.0920291
$337$	−27.2073	−1.48208	−0.741038	−	0.671463i	$-0.765666\pi$
$337$	−27.2073	−1.48208	−0.741038	+	0.671463i	$0.765666\pi$
$338$	12.9982	0.707008
$339$	−14.5933	−0.792600
$340$	−4.72038	−0.255999
$341$	0	0
$342$	−0.264377	−0.0142958
$343$	1.00000	0.0539949
$344$	−6.42455	−0.346389
$345$	11.7404	0.632082
$346$	−6.21176	−0.333946
$347$	−6.65299	−0.357151	−0.178576	−	0.983926i	$-0.557149\pi$
$347$	−6.65299	−0.357151	−0.178576	+	0.983926i	$0.557149\pi$
$348$	2.26515	0.121425
$349$	−25.4581	−1.36274	−0.681371	−	0.731938i	$-0.738616\pi$
$349$	−25.4581	−1.36274	−0.681371	+	0.731938i	$0.738616\pi$
$350$	−1.00000	−0.0534522
$351$	0.226539	0.0120918
$352$	0	0
$353$	−29.0584	−1.54662	−0.773311	−	0.634026i	$-0.781401\pi$
$353$	−29.0584	−1.54662	−0.773311	+	0.634026i	$0.781401\pi$
$354$	−17.2365	−0.916109
$355$	11.3041	0.599958
$356$	2.93362	0.155481
$357$	7.96291	0.421442
$358$	−15.9071	−0.840715
$359$	−28.3224	−1.49480	−0.747400	−	0.664375i	$-0.768698\pi$
$359$	−28.3224	−1.49480	−0.747400	+	0.664375i	$0.768698\pi$
$360$	0.154300	0.00813231
$361$	−16.0643	−0.845488
$362$	6.59938	0.346856
$363$	0	0
$364$	0.0425741	0.00223149
$365$	−1.98728	−0.104019
$366$	23.3911	1.22267
$367$	−27.5184	−1.43645	−0.718224	−	0.695812i	$-0.755044\pi$
$367$	−27.5184	−1.43645	−0.718224	+	0.695812i	$0.755044\pi$
$368$	−6.95966	−0.362798
$369$	−0.603884	−0.0314370
$370$	−8.48459	−0.441093
$371$	−14.1024	−0.732158
$372$	−10.1425	−0.525866
$373$	−22.9306	−1.18730	−0.593650	−	0.804724i	$-0.702313\pi$
$373$	−22.9306	−1.18730	−0.593650	+	0.804724i	$0.702313\pi$
$374$	0	0
$375$	−1.68692	−0.0871122
$376$	−4.59129	−0.236778
$377$	−0.0571673	−0.00294427
$378$	−5.32105	−0.273685
$379$	15.4140	0.791764	0.395882	−	0.918301i	$-0.370439\pi$
$379$	15.4140	0.791764	0.395882	+	0.918301i	$0.370439\pi$
$380$	−1.71340	−0.0878954
$381$	3.08409	0.158003
$382$	−17.1690	−0.878443
$383$	−30.8927	−1.57854	−0.789270	−	0.614046i	$-0.789541\pi$
$383$	−30.8927	−1.57854	−0.789270	+	0.614046i	$0.789541\pi$
$384$	1.68692	0.0860853
$385$	0	0
$386$	10.2185	0.520106
$387$	−0.991306	−0.0503909
$388$	−17.4812	−0.887474
$389$	0.452651	0.0229503	0.0114752	−	0.999934i	$-0.496347\pi$
$389$	0.452651	0.0229503	0.0114752	+	0.999934i	$0.496347\pi$
$390$	0.0718191	0.00363670
$391$	32.8523	1.66141
$392$	−1.00000	−0.0505076
$393$	2.72738	0.137578
$394$	7.33268	0.369415
$395$	−8.87065	−0.446331
$396$	0	0
$397$	24.1263	1.21086	0.605431	−	0.795897i	$-0.293001\pi$
$397$	24.1263	1.21086	0.605431	+	0.795897i	$0.293001\pi$
$398$	8.90352	0.446293
$399$	2.89036	0.144699
$400$	1.00000	0.0500000
$401$	−11.2261	−0.560603	−0.280301	−	0.959912i	$-0.590434\pi$
$401$	−11.2261	−0.560603	−0.280301	+	0.959912i	$0.590434\pi$
$402$	10.7895	0.538134
$403$	0.255975	0.0127510
$404$	−5.70914	−0.284040
$405$	−8.51329	−0.423029
$406$	1.34277	0.0666406
$407$	0	0
$408$	−7.96291	−0.394223
$409$	−30.4772	−1.50700	−0.753500	−	0.657448i	$-0.771636\pi$
$409$	−30.4772	−1.50700	−0.753500	+	0.657448i	$0.771636\pi$
$410$	−3.91371	−0.193284
$411$	−17.3191	−0.854289
$412$	13.4052	0.660425
$413$	−10.2177	−0.502782
$414$	−1.07387	−0.0527780
$415$	−10.0807	−0.494841
$416$	−0.0425741	−0.00208737
$417$	3.28541	0.160887
$418$	0	0
$419$	11.8710	0.579937	0.289968	−	0.957036i	$-0.406355\pi$
$419$	11.8710	0.579937	0.289968	+	0.957036i	$0.406355\pi$
$420$	−1.68692	−0.0823133
$421$	23.7676	1.15836	0.579181	−	0.815199i	$-0.303373\pi$
$421$	23.7676	1.15836	0.579181	+	0.815199i	$0.303373\pi$
$422$	−4.54767	−0.221377
$423$	−0.708435	−0.0344453
$424$	14.1024	0.684871
$425$	−4.72038	−0.228972
$426$	19.0691	0.923900
$427$	13.8661	0.671029
$428$	−15.9669	−0.771790
$429$	0	0
$430$	−6.42455	−0.309819
$431$	27.1939	1.30989	0.654943	−	0.755678i	$-0.272693\pi$
$431$	27.1939	1.30989	0.654943	+	0.755678i	$0.272693\pi$
$432$	5.32105	0.256009
$433$	−2.21065	−0.106237	−0.0531185	−	0.998588i	$-0.516916\pi$
$433$	−2.21065	−0.106237	−0.0531185	+	0.998588i	$0.516916\pi$
$434$	−6.01245	−0.288607
$435$	2.26515	0.108606
$436$	15.9501	0.763871
$437$	11.9247	0.570434
$438$	−3.35239	−0.160183
$439$	−6.47985	−0.309267	−0.154633	−	0.987972i	$-0.549420\pi$
$439$	−6.47985	−0.309267	−0.154633	+	0.987972i	$0.549420\pi$
$440$	0	0
$441$	−0.154300	−0.00734760
$442$	0.200966	0.00955898
$443$	17.0792	0.811456	0.405728	−	0.913994i	$-0.367018\pi$
$443$	17.0792	0.811456	0.405728	+	0.913994i	$0.367018\pi$
$444$	−14.3128	−0.679257
$445$	2.93362	0.139067
$446$	−18.0702	−0.855647
$447$	10.9130	0.516169
$448$	1.00000	0.0472456
$449$	13.1328	0.619774	0.309887	−	0.950773i	$-0.399709\pi$
$449$	13.1328	0.619774	0.309887	+	0.950773i	$0.399709\pi$
$450$	0.154300	0.00727376
$451$	0	0
$452$	8.65087	0.406903
$453$	39.8298	1.87137
$454$	−0.970501	−0.0455479
$455$	0.0425741	0.00199591
$456$	−2.89036	−0.135354
$457$	15.4508	0.722758	0.361379	−	0.932419i	$-0.382306\pi$
$457$	15.4508	0.722758	0.361379	+	0.932419i	$0.382306\pi$
$458$	2.46292	0.115085
$459$	−25.1174	−1.17238
$460$	−6.95966	−0.324496
$461$	−33.8352	−1.57586	−0.787932	−	0.615763i	$-0.788848\pi$
$461$	−33.8352	−1.57586	−0.787932	+	0.615763i	$0.788848\pi$
$462$	0	0
$463$	31.7915	1.47748	0.738738	−	0.673993i	$-0.235422\pi$
$463$	31.7915	1.47748	0.738738	+	0.673993i	$0.235422\pi$
$464$	−1.34277	−0.0623366
$465$	−10.1425	−0.470349
$466$	6.65041	0.308074
$467$	−17.0295	−0.788032	−0.394016	−	0.919104i	$-0.628915\pi$
$467$	−17.0295	−0.788032	−0.394016	+	0.919104i	$0.628915\pi$
$468$	−0.00656917	−0.000303660 0
$469$	6.39600	0.295340
$470$	−4.59129	−0.211781
$471$	−19.3812	−0.893040
$472$	10.2177	0.470309
$473$	0	0
$474$	−14.9641	−0.687323
$475$	−1.71340	−0.0786160
$476$	−4.72038	−0.216358
$477$	2.17599	0.0996317
$478$	−21.0529	−0.962938
$479$	29.9718	1.36945	0.684724	−	0.728802i	$-0.259923\pi$
$479$	29.9718	1.36945	0.684724	+	0.728802i	$0.259923\pi$
$480$	1.68692	0.0769970
$481$	0.361224	0.0164704
$482$	7.93244	0.361313
$483$	11.7404	0.534207
$484$	0	0
$485$	−17.4812	−0.793781
$486$	1.60191	0.0726641
$487$	0.733047	0.0332175	0.0166088	−	0.999862i	$-0.494713\pi$
$487$	0.733047	0.0332175	0.0166088	+	0.999862i	$0.494713\pi$
$488$	−13.8661	−0.627690
$489$	23.8356	1.07788
$490$	−1.00000	−0.0451754
$491$	10.1494	0.458035	0.229018	−	0.973422i	$-0.426449\pi$
$491$	10.1494	0.458035	0.229018	+	0.973422i	$0.426449\pi$
$492$	−6.60212	−0.297646
$493$	6.33839	0.285467
$494$	0.0729463	0.00328201
$495$	0	0
$496$	6.01245	0.269967
$497$	11.3041	0.507057
$498$	−17.0053	−0.762025
$499$	−11.1673	−0.499919	−0.249959	−	0.968256i	$-0.580417\pi$
$499$	−11.1673	−0.499919	−0.249959	+	0.968256i	$0.580417\pi$
$500$	1.00000	0.0447214
$501$	26.3185	1.17582
$502$	−18.9431	−0.845471
$503$	−7.46249	−0.332736	−0.166368	−	0.986064i	$-0.553204\pi$
$503$	−7.46249	−0.332736	−0.166368	+	0.986064i	$0.553204\pi$
$504$	0.154300	0.00687305
$505$	−5.70914	−0.254053
$506$	0	0
$507$	21.9269	0.973808
$508$	−1.82824	−0.0811149
$509$	−30.8240	−1.36625	−0.683125	−	0.730302i	$-0.739380\pi$
$509$	−30.8240	−1.36625	−0.683125	+	0.730302i	$0.739380\pi$
$510$	−7.96291	−0.352603
$511$	−1.98728	−0.0879122
$512$	−1.00000	−0.0441942
$513$	−9.11707	−0.402529
$514$	26.8598	1.18474
$515$	13.4052	0.590702
$516$	−10.8377	−0.477103
$517$	0	0
$518$	−8.48459	−0.372791
$519$	−10.4787	−0.459966
$520$	−0.0425741	−0.00186700
$521$	−14.5848	−0.638970	−0.319485	−	0.947591i	$-0.603510\pi$
$521$	−14.5848	−0.638970	−0.319485	+	0.947591i	$0.603510\pi$
$522$	−0.207189	−0.00906843
$523$	−9.58569	−0.419153	−0.209576	−	0.977792i	$-0.567208\pi$
$523$	−9.58569	−0.419153	−0.209576	+	0.977792i	$0.567208\pi$
$524$	−1.61678	−0.0706294
$525$	−1.68692	−0.0736232
$526$	13.3750	0.583179
$527$	−28.3811	−1.23630
$528$	0	0
$529$	25.4369	1.10595
$530$	14.1024	0.612567
$531$	1.57659	0.0684183
$532$	−1.71340	−0.0742852
$533$	0.166623	0.00721723
$534$	4.94878	0.214155
$535$	−15.9669	−0.690310
$536$	−6.39600	−0.276265
$537$	−26.8340	−1.15797
$538$	4.05979	0.175030
$539$	0	0
$540$	5.32105	0.228982
$541$	1.71177	0.0735948	0.0367974	−	0.999323i	$-0.488284\pi$
$541$	1.71177	0.0735948	0.0367974	+	0.999323i	$0.488284\pi$
$542$	−23.0226	−0.988905
$543$	11.1326	0.477747
$544$	4.72038	0.202385
$545$	15.9501	0.683227
$546$	0.0718191	0.00307358
$547$	17.4770	0.747262	0.373631	−	0.927577i	$-0.378113\pi$
$547$	17.4770	0.747262	0.373631	+	0.927577i	$0.378113\pi$
$548$	10.2667	0.438572
$549$	−2.13954	−0.0913133
$550$	0	0
$551$	2.30070	0.0980131
$552$	−11.7404	−0.499705
$553$	−8.87065	−0.377218
$554$	22.2862	0.946850
$555$	−14.3128	−0.607546
$556$	−1.94758	−0.0825957
$557$	−25.6895	−1.08850	−0.544250	−	0.838923i	$-0.683186\pi$
$557$	−25.6895	−1.08850	−0.544250	+	0.838923i	$0.683186\pi$
$558$	0.927720	0.0392735
$559$	0.273520	0.0115686
$560$	1.00000	0.0422577
$561$	0	0
$562$	2.24959	0.0948932
$563$	−19.3434	−0.815225	−0.407613	−	0.913155i	$-0.633639\pi$
$563$	−19.3434	−0.815225	−0.407613	+	0.913155i	$0.633639\pi$
$564$	−7.74515	−0.326129
$565$	8.65087	0.363945
$566$	3.71034	0.155957
$567$	−8.51329	−0.357525
$568$	−11.3041	−0.474309
$569$	1.51921	0.0636886	0.0318443	−	0.999493i	$-0.489862\pi$
$569$	1.51921	0.0636886	0.0318443	+	0.999493i	$0.489862\pi$
$570$	−2.89036	−0.121064
$571$	4.97687	0.208276	0.104138	−	0.994563i	$-0.466792\pi$
$571$	4.97687	0.208276	0.104138	+	0.994563i	$0.466792\pi$
$572$	0	0
$573$	−28.9628	−1.20994
$574$	−3.91371	−0.163355
$575$	−6.95966	−0.290238
$576$	−0.154300	−0.00642915
$577$	−31.6102	−1.31595	−0.657976	−	0.753039i	$-0.728587\pi$
$577$	−31.6102	−1.31595	−0.657976	+	0.753039i	$0.728587\pi$
$578$	−5.28199	−0.219702
$579$	17.2377	0.716376
$580$	−1.34277	−0.0557556
$581$	−10.0807	−0.418217
$582$	−29.4894	−1.22238
$583$	0	0
$584$	1.98728	0.0822343
$585$	−0.00656917	−0.000271602 0
$586$	−1.85170	−0.0764928
$587$	7.11885	0.293826	0.146913	−	0.989149i	$-0.453066\pi$
$587$	7.11885	0.293826	0.146913	+	0.989149i	$0.453066\pi$
$588$	−1.68692	−0.0695674
$589$	−10.3017	−0.424475
$590$	10.2177	0.420657
$591$	12.3697	0.508820
$592$	8.48459	0.348714
$593$	−18.4209	−0.756456	−0.378228	−	0.925713i	$-0.623466\pi$
$593$	−18.4209	−0.756456	−0.378228	+	0.925713i	$0.623466\pi$
$594$	0	0
$595$	−4.72038	−0.193517
$596$	−6.46920	−0.264989
$597$	15.0195	0.614709
$598$	0.296302	0.0121167
$599$	−1.22319	−0.0499783	−0.0249892	−	0.999688i	$-0.507955\pi$
$599$	−1.22319	−0.0499783	−0.0249892	+	0.999688i	$0.507955\pi$
$600$	1.68692	0.0688682
$601$	−20.6888	−0.843916	−0.421958	−	0.906615i	$-0.638657\pi$
$601$	−20.6888	−0.843916	−0.421958	+	0.906615i	$0.638657\pi$
$602$	−6.42455	−0.261845
$603$	−0.986901	−0.0401897
$604$	−23.6110	−0.960717
$605$	0	0
$606$	−9.63087	−0.391227
$607$	−10.3033	−0.418199	−0.209100	−	0.977894i	$-0.567053\pi$
$607$	−10.3033	−0.418199	−0.209100	+	0.977894i	$0.567053\pi$
$608$	1.71340	0.0694874
$609$	2.26515	0.0917885
$610$	−13.8661	−0.561423
$611$	0.195470	0.00790788
$612$	0.728353	0.0294419
$613$	−42.7503	−1.72667	−0.863333	−	0.504634i	$-0.831627\pi$
$613$	−42.7503	−1.72667	−0.863333	+	0.504634i	$0.831627\pi$
$614$	6.66980	0.269171
$615$	−6.60212	−0.266223
$616$	0	0
$617$	10.3582	0.417004	0.208502	−	0.978022i	$-0.433141\pi$
$617$	10.3582	0.417004	0.208502	+	0.978022i	$0.433141\pi$
$618$	22.6134	0.909646
$619$	14.2901	0.574368	0.287184	−	0.957875i	$-0.407281\pi$
$619$	14.2901	0.574368	0.287184	+	0.957875i	$0.407281\pi$
$620$	6.01245	0.241466
$621$	−37.0327	−1.48607
$622$	−15.0969	−0.605331
$623$	2.93362	0.117533
$624$	−0.0718191	−0.00287507
$625$	1.00000	0.0400000
$626$	−7.33744	−0.293263
$627$	0	0
$628$	11.4891	0.458466
$629$	−40.0505	−1.59692
$630$	0.154300	0.00614745
$631$	−11.6481	−0.463703	−0.231851	−	0.972751i	$-0.574478\pi$
$631$	−11.6481	−0.463703	−0.231851	+	0.972751i	$0.574478\pi$
$632$	8.87065	0.352855
$633$	−7.67156	−0.304917
$634$	−22.4900	−0.893190
$635$	−1.82824	−0.0725514
$636$	23.7896	0.943317
$637$	0.0425741	0.00168685
$638$	0	0
$639$	−1.74422	−0.0690001
$640$	−1.00000	−0.0395285
$641$	18.0247	0.711931	0.355965	−	0.934499i	$-0.384152\pi$
$641$	18.0247	0.711931	0.355965	+	0.934499i	$0.384152\pi$
$642$	−26.9349	−1.06304
$643$	−10.6620	−0.420469	−0.210235	−	0.977651i	$-0.567423\pi$
$643$	−10.6620	−0.420469	−0.210235	+	0.977651i	$0.567423\pi$
$644$	−6.95966	−0.274249
$645$	−10.8377	−0.426734
$646$	−8.08788	−0.318214
$647$	−21.7314	−0.854348	−0.427174	−	0.904170i	$-0.640491\pi$
$647$	−21.7314	−0.854348	−0.427174	+	0.904170i	$0.640491\pi$
$648$	8.51329	0.334434
$649$	0	0
$650$	−0.0425741	−0.00166989
$651$	−10.1425	−0.397517
$652$	−14.1296	−0.553359
$653$	1.06200	0.0415592	0.0207796	−	0.999784i	$-0.493385\pi$
$653$	1.06200	0.0415592	0.0207796	+	0.999784i	$0.493385\pi$
$654$	26.9065	1.05213
$655$	−1.61678	−0.0631728
$656$	3.91371	0.152805
$657$	0.306637	0.0119630
$658$	−4.59129	−0.178987
$659$	33.2641	1.29578	0.647892	−	0.761732i	$-0.275651\pi$
$659$	33.2641	1.29578	0.647892	+	0.761732i	$0.275651\pi$
$660$	0	0
$661$	−8.99126	−0.349719	−0.174860	−	0.984593i	$-0.555947\pi$
$661$	−8.99126	−0.349719	−0.174860	+	0.984593i	$0.555947\pi$
$662$	−10.3154	−0.400920
$663$	0.339014	0.0131662
$664$	10.0807	0.391206
$665$	−1.71340	−0.0664427
$666$	1.30917	0.0507293
$667$	9.34524	0.361849
$668$	−15.6015	−0.603641
$669$	−30.4829	−1.17854
$670$	−6.39600	−0.247099
$671$	0	0
$672$	1.68692	0.0650744
$673$	−9.38976	−0.361949	−0.180974	−	0.983488i	$-0.557925\pi$
$673$	−9.38976	−0.361949	−0.180974	+	0.983488i	$0.557925\pi$
$674$	27.2073	1.04799
$675$	5.32105	0.204807
$676$	−12.9982	−0.499930
$677$	37.7060	1.44916	0.724579	−	0.689191i	$-0.242034\pi$
$677$	37.7060	1.44916	0.724579	+	0.689191i	$0.242034\pi$
$678$	14.5933	0.560453
$679$	−17.4812	−0.670868
$680$	4.72038	0.181018
$681$	−1.63716	−0.0627360
$682$	0	0
$683$	11.5317	0.441248	0.220624	−	0.975359i	$-0.429191\pi$
$683$	11.5317	0.441248	0.220624	+	0.975359i	$0.429191\pi$
$684$	0.264377	0.0101087
$685$	10.2667	0.392271
$686$	−1.00000	−0.0381802
$687$	4.15476	0.158514
$688$	6.42455	0.244934
$689$	−0.600395	−0.0228732
$690$	−11.7404	−0.446949
$691$	−12.7280	−0.484196	−0.242098	−	0.970252i	$-0.577835\pi$
$691$	−12.7280	−0.484196	−0.242098	+	0.970252i	$0.577835\pi$
$692$	6.21176	0.236136
$693$	0	0
$694$	6.65299	0.252544
$695$	−1.94758	−0.0738758
$696$	−2.26515	−0.0858603
$697$	−18.4742	−0.699760
$698$	25.4581	0.963604
$699$	11.2187	0.424331
$700$	1.00000	0.0377964
$701$	11.1988	0.422972	0.211486	−	0.977381i	$-0.432170\pi$
$701$	11.1988	0.422972	0.211486	+	0.977381i	$0.432170\pi$
$702$	−0.226539	−0.00855017
$703$	−14.5375	−0.548291
$704$	0	0
$705$	−7.74515	−0.291699
$706$	29.0584	1.09363
$707$	−5.70914	−0.214714
$708$	17.2365	0.647787
$709$	−28.4744	−1.06938	−0.534688	−	0.845049i	$-0.679571\pi$
$709$	−28.4744	−1.06938	−0.534688	+	0.845049i	$0.679571\pi$
$710$	−11.3041	−0.424234
$711$	1.36874	0.0513317
$712$	−2.93362	−0.109942
$713$	−41.8447	−1.56709
$714$	−7.96291	−0.298004
$715$	0	0
$716$	15.9071	0.594475
$717$	−35.5146	−1.32632
$718$	28.3224	1.05698
$719$	−44.5968	−1.66318	−0.831589	−	0.555391i	$-0.812569\pi$
$719$	−44.5968	−1.66318	−0.831589	+	0.555391i	$0.812569\pi$
$720$	−0.154300	−0.00575041
$721$	13.4052	0.499234
$722$	16.0643	0.597850
$723$	13.3814	0.497659
$724$	−6.59938	−0.245264
$725$	−1.34277	−0.0498693
$726$	0	0
$727$	50.4565	1.87133	0.935664	−	0.352892i	$-0.114802\pi$
$727$	50.4565	1.87133	0.935664	+	0.352892i	$0.114802\pi$
$728$	−0.0425741	−0.00157790
$729$	28.2422	1.04601
$730$	1.98728	0.0735526
$731$	−30.3263	−1.12166
$732$	−23.3911	−0.864558
$733$	38.0995	1.40724	0.703618	−	0.710578i	$-0.251566\pi$
$733$	38.0995	1.40724	0.703618	+	0.710578i	$0.251566\pi$
$734$	27.5184	1.01572
$735$	−1.68692	−0.0622230
$736$	6.95966	0.256537
$737$	0	0
$738$	0.603884	0.0222293
$739$	0.758286	0.0278940	0.0139470	−	0.999903i	$-0.495560\pi$
$739$	0.758286	0.0278940	0.0139470	+	0.999903i	$0.495560\pi$
$740$	8.48459	0.311900
$741$	0.123055	0.00452053
$742$	14.1024	0.517714
$743$	−34.7125	−1.27348	−0.636739	−	0.771079i	$-0.719717\pi$
$743$	−34.7125	−1.27348	−0.636739	+	0.771079i	$0.719717\pi$
$744$	10.1425	0.371843
$745$	−6.46920	−0.237013
$746$	22.9306	0.839547
$747$	1.55544	0.0569107
$748$	0	0
$749$	−15.9669	−0.583418
$750$	1.68692	0.0615976
$751$	−46.0088	−1.67889	−0.839443	−	0.543448i	$-0.817119\pi$
$751$	−46.0088	−1.67889	−0.839443	+	0.543448i	$0.817119\pi$
$752$	4.59129	0.167427
$753$	−31.9555	−1.16452
$754$	0.0571673	0.00208191
$755$	−23.6110	−0.859291
$756$	5.32105	0.193525
$757$	−23.1505	−0.841420	−0.420710	−	0.907195i	$-0.638219\pi$
$757$	−23.1505	−0.841420	−0.420710	+	0.907195i	$0.638219\pi$
$758$	−15.4140	−0.559862
$759$	0	0
$760$	1.71340	0.0621514
$761$	7.19624	0.260864	0.130432	−	0.991457i	$-0.458364\pi$
$761$	7.19624	0.260864	0.130432	+	0.991457i	$0.458364\pi$
$762$	−3.08409	−0.111725
$763$	15.9501	0.577432
$764$	17.1690	0.621153
$765$	0.728353	0.0263337
$766$	30.8927	1.11620
$767$	−0.435011	−0.0157073
$768$	−1.68692	−0.0608715
$769$	8.64296	0.311673	0.155837	−	0.987783i	$-0.450193\pi$
$769$	8.64296	0.311673	0.155837	+	0.987783i	$0.450193\pi$
$770$	0	0
$771$	45.3104	1.63181
$772$	−10.2185	−0.367771
$773$	−39.4190	−1.41780	−0.708901	−	0.705308i	$-0.750809\pi$
$773$	−39.4190	−1.41780	−0.708901	+	0.705308i	$0.750809\pi$
$774$	0.991306	0.0356318
$775$	6.01245	0.215974
$776$	17.4812	0.627539
$777$	−14.3128	−0.513470
$778$	−0.452651	−0.0162283
$779$	−6.70574	−0.240258
$780$	−0.0718191	−0.00257154
$781$	0	0
$782$	−32.8523	−1.17479
$783$	−7.14496	−0.255340
$784$	1.00000	0.0357143
$785$	11.4891	0.410064
$786$	−2.72738	−0.0972824
$787$	−44.2814	−1.57846	−0.789230	−	0.614098i	$-0.789520\pi$
$787$	−44.2814	−1.57846	−0.789230	+	0.614098i	$0.789520\pi$
$788$	−7.33268	−0.261216
$789$	22.5626	0.803250
$790$	8.87065	0.315603
$791$	8.65087	0.307589
$792$	0	0
$793$	0.590338	0.0209635
$794$	−24.1263	−0.856209
$795$	23.7896	0.843729
$796$	−8.90352	−0.315577
$797$	−20.9781	−0.743081	−0.371540	−	0.928417i	$-0.621170\pi$
$797$	−20.9781	−0.743081	−0.371540	+	0.928417i	$0.621170\pi$
$798$	−2.89036	−0.102318
$799$	−21.6726	−0.766723
$800$	−1.00000	−0.0353553
$801$	−0.452656	−0.0159938
$802$	11.2261	0.396406
$803$	0	0
$804$	−10.7895	−0.380518
$805$	−6.95966	−0.245296
$806$	−0.255975	−0.00901633
$807$	6.84854	0.241080
$808$	5.70914	0.200847
$809$	−24.2672	−0.853190	−0.426595	−	0.904443i	$-0.640287\pi$
$809$	−24.2672	−0.853190	−0.426595	+	0.904443i	$0.640287\pi$
$810$	8.51329	0.299127
$811$	−37.0315	−1.30035	−0.650175	−	0.759784i	$-0.725305\pi$
$811$	−37.0315	−1.30035	−0.650175	+	0.759784i	$0.725305\pi$
$812$	−1.34277	−0.0471221
$813$	−38.8373	−1.36208
$814$	0	0
$815$	−14.1296	−0.494940
$816$	7.96291	0.278757
$817$	−11.0078	−0.385114
$818$	30.4772	1.06561
$819$	−0.00656917	−0.000229546 0
$820$	3.91371	0.136673
$821$	22.0348	0.769019	0.384509	−	0.923121i	$-0.374371\pi$
$821$	22.0348	0.769019	0.384509	+	0.923121i	$0.374371\pi$
$822$	17.3191	0.604074
$823$	25.6954	0.895684	0.447842	−	0.894113i	$-0.352193\pi$
$823$	25.6954	0.895684	0.447842	+	0.894113i	$0.352193\pi$
$824$	−13.4052	−0.466991
$825$	0	0
$826$	10.2177	0.355520
$827$	−16.8897	−0.587313	−0.293657	−	0.955911i	$-0.594872\pi$
$827$	−16.8897	−0.587313	−0.293657	+	0.955911i	$0.594872\pi$
$828$	1.07387	0.0373197
$829$	−20.4637	−0.710732	−0.355366	−	0.934727i	$-0.615644\pi$
$829$	−20.4637	−0.710732	−0.355366	+	0.934727i	$0.615644\pi$
$830$	10.0807	0.349905
$831$	37.5951	1.30416
$832$	0.0425741	0.00147599
$833$	−4.72038	−0.163551
$834$	−3.28541	−0.113764
$835$	−15.6015	−0.539913
$836$	0	0
$837$	31.9926	1.10583
$838$	−11.8710	−0.410077
$839$	34.0393	1.17517	0.587584	−	0.809163i	$-0.300079\pi$
$839$	34.0393	1.17517	0.587584	+	0.809163i	$0.300079\pi$
$840$	1.68692	0.0582043
$841$	−27.1970	−0.937826
$842$	−23.7676	−0.819085
$843$	3.79488	0.130703
$844$	4.54767	0.156537
$845$	−12.9982	−0.447151
$846$	0.708435	0.0243565
$847$	0	0
$848$	−14.1024	−0.484277
$849$	6.25906	0.214810
$850$	4.72038	0.161908
$851$	−59.0499	−2.02420
$852$	−19.0691	−0.653296
$853$	−20.6791	−0.708040	−0.354020	−	0.935238i	$-0.615186\pi$
$853$	−20.6791	−0.708040	−0.354020	+	0.935238i	$0.615186\pi$
$854$	−13.8661	−0.474489
$855$	0.264377	0.00904149
$856$	15.9669	0.545738
$857$	−44.5639	−1.52227	−0.761136	−	0.648592i	$-0.775358\pi$
$857$	−44.5639	−1.52227	−0.761136	+	0.648592i	$0.775358\pi$
$858$	0	0
$859$	0.992443	0.0338617	0.0169309	−	0.999857i	$-0.494610\pi$
$859$	0.992443	0.0338617	0.0169309	+	0.999857i	$0.494610\pi$
$860$	6.42455	0.219075
$861$	−6.60212	−0.225000
$862$	−27.1939	−0.926229
$863$	34.0157	1.15791	0.578954	−	0.815360i	$-0.303461\pi$
$863$	34.0157	1.15791	0.578954	+	0.815360i	$0.303461\pi$
$864$	−5.32105	−0.181026
$865$	6.21176	0.211206
$866$	2.21065	0.0751209
$867$	−8.91030	−0.302610
$868$	6.01245	0.204076
$869$	0	0
$870$	−2.26515	−0.0767957
$871$	0.272304	0.00922667
$872$	−15.9501	−0.540138
$873$	2.69735	0.0912914
$874$	−11.9247	−0.403358
$875$	1.00000	0.0338062
$876$	3.35239	0.113267
$877$	37.7370	1.27429	0.637144	−	0.770745i	$-0.280116\pi$
$877$	37.7370	1.27429	0.637144	+	0.770745i	$0.280116\pi$
$878$	6.47985	0.218685
$879$	−3.12366	−0.105359
$880$	0	0
$881$	12.1850	0.410522	0.205261	−	0.978707i	$-0.434196\pi$
$881$	12.1850	0.410522	0.205261	+	0.978707i	$0.434196\pi$
$882$	0.154300	0.00519554
$883$	−23.9895	−0.807311	−0.403656	−	0.914911i	$-0.632261\pi$
$883$	−23.9895	−0.807311	−0.403656	+	0.914911i	$0.632261\pi$
$884$	−0.200966	−0.00675922
$885$	17.2365	0.579398
$886$	−17.0792	−0.573786
$887$	−42.9265	−1.44133	−0.720666	−	0.693282i	$-0.756164\pi$
$887$	−42.9265	−1.44133	−0.720666	+	0.693282i	$0.756164\pi$
$888$	14.3128	0.480307
$889$	−1.82824	−0.0613171
$890$	−2.93362	−0.0983351
$891$	0	0
$892$	18.0702	0.605034
$893$	−7.86670	−0.263249
$894$	−10.9130	−0.364986
$895$	15.9071	0.531715
$896$	−1.00000	−0.0334077
$897$	0.499837	0.0166891
$898$	−13.1328	−0.438246
$899$	−8.07335	−0.269261
$900$	−0.154300	−0.00514332
$901$	66.5685	2.21772
$902$	0	0
$903$	−10.8377	−0.360656
$904$	−8.65087	−0.287724
$905$	−6.59938	−0.219371
$906$	−39.8298	−1.32326
$907$	17.8773	0.593606	0.296803	−	0.954939i	$-0.404079\pi$
$907$	17.8773	0.593606	0.296803	+	0.954939i	$0.404079\pi$
$908$	0.970501	0.0322072
$909$	0.880919	0.0292182
$910$	−0.0425741	−0.00141132
$911$	−26.8557	−0.889769	−0.444885	−	0.895588i	$-0.646755\pi$
$911$	−26.8557	−0.889769	−0.444885	+	0.895588i	$0.646755\pi$
$912$	2.89036	0.0957095
$913$	0	0
$914$	−15.4508	−0.511067
$915$	−23.3911	−0.773284
$916$	−2.46292	−0.0813773
$917$	−1.61678	−0.0533908
$918$	25.1174	0.828997
$919$	16.2819	0.537091	0.268546	−	0.963267i	$-0.413457\pi$
$919$	16.2819	0.537091	0.268546	+	0.963267i	$0.413457\pi$
$920$	6.95966	0.229453
$921$	11.2514	0.370747
$922$	33.8352	1.11430
$923$	0.481261	0.0158409
$924$	0	0
$925$	8.48459	0.278972
$926$	−31.7915	−1.04473
$927$	−2.06841	−0.0679356
$928$	1.34277	0.0440786
$929$	−36.6780	−1.20337	−0.601684	−	0.798734i	$-0.705503\pi$
$929$	−36.6780	−1.20337	−0.601684	+	0.798734i	$0.705503\pi$
$930$	10.1425	0.332587
$931$	−1.71340	−0.0561543
$932$	−6.65041	−0.217841
$933$	−25.4673	−0.833761
$934$	17.0295	0.557223
$935$	0	0
$936$	0.00656917	0.000214720 0
$937$	−29.0963	−0.950536	−0.475268	−	0.879841i	$-0.657649\pi$
$937$	−29.0963	−0.950536	−0.475268	+	0.879841i	$0.657649\pi$
$938$	−6.39600	−0.208837
$939$	−12.3777	−0.403930
$940$	4.59129	0.149751
$941$	−5.63123	−0.183573	−0.0917865	−	0.995779i	$-0.529258\pi$
$941$	−5.63123	−0.183573	−0.0917865	+	0.995779i	$0.529258\pi$
$942$	19.3812	0.631475
$943$	−27.2381	−0.886995
$944$	−10.2177	−0.332559
$945$	5.32105	0.173094
$946$	0	0
$947$	−25.4396	−0.826677	−0.413338	−	0.910577i	$-0.635637\pi$
$947$	−25.4396	−0.826677	−0.413338	+	0.910577i	$0.635637\pi$
$948$	14.9641	0.486011
$949$	−0.0846068	−0.00274645
$950$	1.71340	0.0555899
$951$	−37.9388	−1.23025
$952$	4.72038	0.152988
$953$	−36.6858	−1.18837	−0.594184	−	0.804329i	$-0.702525\pi$
$953$	−36.6858	−1.18837	−0.594184	+	0.804329i	$0.702525\pi$
$954$	−2.17599	−0.0704503
$955$	17.1690	0.555576
$956$	21.0529	0.680900
$957$	0	0
$958$	−29.9718	−0.968346
$959$	10.2667	0.331529
$960$	−1.68692	−0.0544451
$961$	5.14959	0.166116
$962$	−0.361224	−0.0116463
$963$	2.46369	0.0793913
$964$	−7.93244	−0.255487
$965$	−10.2185	−0.328944
$966$	−11.7404	−0.377741
$967$	23.5537	0.757438	0.378719	−	0.925512i	$-0.376365\pi$
$967$	23.5537	0.757438	0.378719	+	0.925512i	$0.376365\pi$
$968$	0	0
$969$	−13.6436	−0.438296
$970$	17.4812	0.561288
$971$	7.95989	0.255445	0.127722	−	0.991810i	$-0.459233\pi$
$971$	7.95989	0.255445	0.127722	+	0.991810i	$0.459233\pi$
$972$	−1.60191	−0.0513813
$973$	−1.94758	−0.0624365
$974$	−0.733047	−0.0234884
$975$	−0.0718191	−0.00230005
$976$	13.8661	0.443844
$977$	16.8029	0.537574	0.268787	−	0.963200i	$-0.413377\pi$
$977$	16.8029	0.537574	0.268787	+	0.963200i	$0.413377\pi$
$978$	−23.8356	−0.762178
$979$	0	0
$980$	1.00000	0.0319438
$981$	−2.46109	−0.0785767
$982$	−10.1494	−0.323880
$983$	−6.64006	−0.211785	−0.105893	−	0.994378i	$-0.533770\pi$
$983$	−6.64006	−0.211785	−0.105893	+	0.994378i	$0.533770\pi$
$984$	6.60212	0.210468
$985$	−7.33268	−0.233639
$986$	−6.33839	−0.201856
$987$	−7.74515	−0.246531
$988$	−0.0729463	−0.00232073
$989$	−44.7127	−1.42178
$990$	0	0
$991$	−49.2695	−1.56510	−0.782548	−	0.622590i	$-0.786080\pi$
$991$	−49.2695	−1.56510	−0.782548	+	0.622590i	$0.786080\pi$
$992$	−6.01245	−0.190896
$993$	−17.4013	−0.552214
$994$	−11.3041	−0.358544
$995$	−8.90352	−0.282261
$996$	17.0053	0.538833
$997$	32.5523	1.03094	0.515471	−	0.856907i	$-0.327617\pi$
$997$	32.5523	1.03094	0.515471	+	0.856907i	$0.327617\pi$
$998$	11.1673	0.353496
$999$	45.1469	1.42839

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.cw.1.2		6
11.5	even	5		770.2.n.j.421.1	✓	12
11.9	even	5		770.2.n.j.631.1	yes	12
11.10	odd	2		8470.2.a.dc.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.j.421.1	✓	12	11.5	even	5
770.2.n.j.631.1	yes	12	11.9	even	5
8470.2.a.cw.1.2		6	1.1	even	1	trivial
8470.2.a.dc.1.2		6	11.10	odd	2

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:	\( N \)	\(=\)	\( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8470.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.68692 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.68692 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.154300 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.68692 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.68692 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.154300 q^{9} -1.00000 q^{10} -1.68692 q^{12} +0.0425741 q^{13} -1.00000 q^{14} -1.68692 q^{15} +1.00000 q^{16} -4.72038 q^{17} +0.154300 q^{18} -1.71340 q^{19} +1.00000 q^{20} -1.68692 q^{21} -6.95966 q^{23} +1.68692 q^{24} +1.00000 q^{25} -0.0425741 q^{26} +5.32105 q^{27} +1.00000 q^{28} -1.34277 q^{29} +1.68692 q^{30} +6.01245 q^{31} -1.00000 q^{32} +4.72038 q^{34} +1.00000 q^{35} -0.154300 q^{36} +8.48459 q^{37} +1.71340 q^{38} -0.0718191 q^{39} -1.00000 q^{40} +3.91371 q^{41} +1.68692 q^{42} +6.42455 q^{43} -0.154300 q^{45} +6.95966 q^{46} +4.59129 q^{47} -1.68692 q^{48} +1.00000 q^{49} -1.00000 q^{50} +7.96291 q^{51} +0.0425741 q^{52} -14.1024 q^{53} -5.32105 q^{54} -1.00000 q^{56} +2.89036 q^{57} +1.34277 q^{58} -10.2177 q^{59} -1.68692 q^{60} +13.8661 q^{61} -6.01245 q^{62} -0.154300 q^{63} +1.00000 q^{64} +0.0425741 q^{65} +6.39600 q^{67} -4.72038 q^{68} +11.7404 q^{69} -1.00000 q^{70} +11.3041 q^{71} +0.154300 q^{72} -1.98728 q^{73} -8.48459 q^{74} -1.68692 q^{75} -1.71340 q^{76} +0.0718191 q^{78} -8.87065 q^{79} +1.00000 q^{80} -8.51329 q^{81} -3.91371 q^{82} -10.0807 q^{83} -1.68692 q^{84} -4.72038 q^{85} -6.42455 q^{86} +2.26515 q^{87} +2.93362 q^{89} +0.154300 q^{90} +0.0425741 q^{91} -6.95966 q^{92} -10.1425 q^{93} -4.59129 q^{94} -1.71340 q^{95} +1.68692 q^{96} -17.4812 q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - q^{3} + 6 q^{4} + 6 q^{5} + q^{6} + 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - q^3 + 6 * q^4 + 6 * q^5 + q^6 + 6 * q^7 - 6 * q^8 + 3 * q^9	\( 6 q - 6 q^{2} - q^{3} + 6 q^{4} + 6 q^{5} + q^{6} + 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} - q^{12} - 9 q^{13} - 6 q^{14} - q^{15} + 6 q^{16} - 9 q^{17} - 3 q^{18} - 12 q^{19} + 6 q^{20} - q^{21} + 4 q^{23} + q^{24} + 6 q^{25} + 9 q^{26} - 4 q^{27} + 6 q^{28} - 15 q^{29} + q^{30} + 8 q^{31} - 6 q^{32} + 9 q^{34} + 6 q^{35} + 3 q^{36} - 4 q^{37} + 12 q^{38} + 19 q^{39} - 6 q^{40} - 4 q^{41} + q^{42} - 30 q^{43} + 3 q^{45} - 4 q^{46} - 7 q^{47} - q^{48} + 6 q^{49} - 6 q^{50} - 16 q^{51} - 9 q^{52} - 6 q^{53} + 4 q^{54} - 6 q^{56} + 14 q^{57} + 15 q^{58} + 4 q^{59} - q^{60} + 14 q^{61} - 8 q^{62} + 3 q^{63} + 6 q^{64} - 9 q^{65} + 18 q^{67} - 9 q^{68} - 10 q^{69} - 6 q^{70} + 23 q^{71} - 3 q^{72} - 23 q^{73} + 4 q^{74} - q^{75} - 12 q^{76} - 19 q^{78} - 21 q^{79} + 6 q^{80} - 18 q^{81} + 4 q^{82} - 25 q^{83} - q^{84} - 9 q^{85} + 30 q^{86} - 14 q^{87} - 18 q^{89} - 3 q^{90} - 9 q^{91} + 4 q^{92} - 24 q^{93} + 7 q^{94} - 12 q^{95} + q^{96} + 7 q^{97} - 6 q^{98}+O(q^{100}) \) 6 * q - 6 * q^2 - q^3 + 6 * q^4 + 6 * q^5 + q^6 + 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 - q^12 - 9 * q^13 - 6 * q^14 - q^15 + 6 * q^16 - 9 * q^17 - 3 * q^18 - 12 * q^19 + 6 * q^20 - q^21 + 4 * q^23 + q^24 + 6 * q^25 + 9 * q^26 - 4 * q^27 + 6 * q^28 - 15 * q^29 + q^30 + 8 * q^31 - 6 * q^32 + 9 * q^34 + 6 * q^35 + 3 * q^36 - 4 * q^37 + 12 * q^38 + 19 * q^39 - 6 * q^40 - 4 * q^41 + q^42 - 30 * q^43 + 3 * q^45 - 4 * q^46 - 7 * q^47 - q^48 + 6 * q^49 - 6 * q^50 - 16 * q^51 - 9 * q^52 - 6 * q^53 + 4 * q^54 - 6 * q^56 + 14 * q^57 + 15 * q^58 + 4 * q^59 - q^60 + 14 * q^61 - 8 * q^62 + 3 * q^63 + 6 * q^64 - 9 * q^65 + 18 * q^67 - 9 * q^68 - 10 * q^69 - 6 * q^70 + 23 * q^71 - 3 * q^72 - 23 * q^73 + 4 * q^74 - q^75 - 12 * q^76 - 19 * q^78 - 21 * q^79 + 6 * q^80 - 18 * q^81 + 4 * q^82 - 25 * q^83 - q^84 - 9 * q^85 + 30 * q^86 - 14 * q^87 - 18 * q^89 - 3 * q^90 - 9 * q^91 + 4 * q^92 - 24 * q^93 + 7 * q^94 - 12 * q^95 + q^96 + 7 * q^97 - 6 * q^98

Introduction

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