LMFDB - Embedded newform 5915.2.a.bp.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5915,2,Mod(1,5915)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5915, 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("5915.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5915 = 5 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5915.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:	$47.2315127956$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	5915.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.136571 q^{2} +0.775570 q^{3} -1.98135 q^{4} +1.00000 q^{5} -0.105921 q^{6} +1.00000 q^{7} +0.543737 q^{8} -2.39849 q^{9} +O(q^{10})$	\(q-0.136571 q^{2} +0.775570 q^{3} -1.98135 q^{4} +1.00000 q^{5} -0.105921 q^{6} +1.00000 q^{7} +0.543737 q^{8} -2.39849 q^{9} -0.136571 q^{10} +1.73348 q^{11} -1.53668 q^{12} -0.136571 q^{14} +0.775570 q^{15} +3.88844 q^{16} +3.06812 q^{17} +0.327565 q^{18} -4.13370 q^{19} -1.98135 q^{20} +0.775570 q^{21} -0.236743 q^{22} +1.13720 q^{23} +0.421707 q^{24} +1.00000 q^{25} -4.18691 q^{27} -1.98135 q^{28} +4.65564 q^{29} -0.105921 q^{30} -2.36450 q^{31} -1.61852 q^{32} +1.34443 q^{33} -0.419017 q^{34} +1.00000 q^{35} +4.75225 q^{36} +4.43585 q^{37} +0.564544 q^{38} +0.543737 q^{40} -1.92216 q^{41} -0.105921 q^{42} +3.97379 q^{43} -3.43462 q^{44} -2.39849 q^{45} -0.155309 q^{46} +0.686497 q^{47} +3.01576 q^{48} +1.00000 q^{49} -0.136571 q^{50} +2.37954 q^{51} -7.61674 q^{53} +0.571811 q^{54} +1.73348 q^{55} +0.543737 q^{56} -3.20598 q^{57} -0.635826 q^{58} -1.83421 q^{59} -1.53668 q^{60} +7.98708 q^{61} +0.322922 q^{62} -2.39849 q^{63} -7.55583 q^{64} -0.183611 q^{66} -4.47247 q^{67} -6.07902 q^{68} +0.881978 q^{69} -0.136571 q^{70} -2.36722 q^{71} -1.30415 q^{72} +15.0951 q^{73} -0.605810 q^{74} +0.775570 q^{75} +8.19030 q^{76} +1.73348 q^{77} -11.9181 q^{79} +3.88844 q^{80} +3.94823 q^{81} +0.262511 q^{82} +8.44680 q^{83} -1.53668 q^{84} +3.06812 q^{85} -0.542705 q^{86} +3.61077 q^{87} +0.942556 q^{88} +11.6275 q^{89} +0.327565 q^{90} -2.25319 q^{92} -1.83383 q^{93} -0.0937557 q^{94} -4.13370 q^{95} -1.25528 q^{96} -1.50221 q^{97} -0.136571 q^{98} -4.15773 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 4 q^{2} + 5 q^{3} + 20 q^{4} + 21 q^{5} + 4 q^{6} + 21 q^{7} + 9 q^{8} + 28 q^{9}+O(q^{10}) $ 21 * q + 4 * q^2 + 5 * q^3 + 20 * q^4 + 21 * q^5 + 4 * q^6 + 21 * q^7 + 9 * q^8 + 28 * q^9	\( 21 q + 4 q^{2} + 5 q^{3} + 20 q^{4} + 21 q^{5} + 4 q^{6} + 21 q^{7} + 9 q^{8} + 28 q^{9} + 4 q^{10} + 2 q^{11} + 23 q^{12} + 4 q^{14} + 5 q^{15} + 18 q^{16} - 6 q^{17} + 32 q^{18} + 8 q^{19} + 20 q^{20} + 5 q^{21} - 17 q^{22} - 14 q^{23} + 27 q^{24} + 21 q^{25} + 11 q^{27} + 20 q^{28} + 20 q^{29} + 4 q^{30} + 22 q^{31} + 22 q^{32} + 33 q^{33} + 22 q^{34} + 21 q^{35} - 8 q^{36} + 48 q^{37} + 42 q^{38} + 9 q^{40} - 5 q^{41} + 4 q^{42} - 27 q^{43} - 4 q^{44} + 28 q^{45} + 9 q^{46} + 27 q^{48} + 21 q^{49} + 4 q^{50} - 4 q^{51} - 28 q^{53} + 27 q^{54} + 2 q^{55} + 9 q^{56} + 56 q^{57} + 44 q^{58} + 7 q^{59} + 23 q^{60} + 25 q^{61} - 17 q^{62} + 28 q^{63} + 47 q^{64} - 30 q^{66} + 40 q^{67} - 19 q^{68} + 13 q^{69} + 4 q^{70} + 15 q^{71} + 42 q^{72} + 16 q^{73} + 37 q^{74} + 5 q^{75} + 58 q^{76} + 2 q^{77} - 10 q^{79} + 18 q^{80} + 25 q^{81} + 14 q^{82} - 11 q^{83} + 23 q^{84} - 6 q^{85} + 35 q^{86} + 65 q^{87} - 74 q^{88} + 24 q^{89} + 32 q^{90} - 89 q^{92} + 82 q^{93} + 21 q^{94} + 8 q^{95} - 22 q^{96} + 57 q^{97} + 4 q^{98} + 6 q^{99}+O(q^{100}) \) 21 * q + 4 * q^2 + 5 * q^3 + 20 * q^4 + 21 * q^5 + 4 * q^6 + 21 * q^7 + 9 * q^8 + 28 * q^9 + 4 * q^10 + 2 * q^11 + 23 * q^12 + 4 * q^14 + 5 * q^15 + 18 * q^16 - 6 * q^17 + 32 * q^18 + 8 * q^19 + 20 * q^20 + 5 * q^21 - 17 * q^22 - 14 * q^23 + 27 * q^24 + 21 * q^25 + 11 * q^27 + 20 * q^28 + 20 * q^29 + 4 * q^30 + 22 * q^31 + 22 * q^32 + 33 * q^33 + 22 * q^34 + 21 * q^35 - 8 * q^36 + 48 * q^37 + 42 * q^38 + 9 * q^40 - 5 * q^41 + 4 * q^42 - 27 * q^43 - 4 * q^44 + 28 * q^45 + 9 * q^46 + 27 * q^48 + 21 * q^49 + 4 * q^50 - 4 * q^51 - 28 * q^53 + 27 * q^54 + 2 * q^55 + 9 * q^56 + 56 * q^57 + 44 * q^58 + 7 * q^59 + 23 * q^60 + 25 * q^61 - 17 * q^62 + 28 * q^63 + 47 * q^64 - 30 * q^66 + 40 * q^67 - 19 * q^68 + 13 * q^69 + 4 * q^70 + 15 * q^71 + 42 * q^72 + 16 * q^73 + 37 * q^74 + 5 * q^75 + 58 * q^76 + 2 * q^77 - 10 * q^79 + 18 * q^80 + 25 * q^81 + 14 * q^82 - 11 * q^83 + 23 * q^84 - 6 * q^85 + 35 * q^86 + 65 * q^87 - 74 * q^88 + 24 * q^89 + 32 * q^90 - 89 * q^92 + 82 * q^93 + 21 * q^94 + 8 * q^95 - 22 * q^96 + 57 * q^97 + 4 * q^98 + 6 * 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 $

$2$	−0.136571	−0.0965704	−0.0482852	−	0.998834i	$-0.515376\pi$
$2$	−0.136571	−0.0965704	−0.0482852	+	0.998834i	$0.515376\pi$
$3$	0.775570	0.447776	0.223888	−	0.974615i	$-0.428125\pi$
$3$	0.775570	0.447776	0.223888	+	0.974615i	$0.428125\pi$
$4$	−1.98135	−0.990674
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.105921	−0.0432419
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.543737	0.192240
$9$	−2.39849	−0.799497
$10$	−0.136571	−0.0431876
$11$	1.73348	0.522663	0.261331	−	0.965249i	$-0.415838\pi$
$11$	1.73348	0.522663	0.261331	+	0.965249i	$0.415838\pi$
$12$	−1.53668	−0.443600
$13$	0	0
$13$	0	0
$14$	−0.136571	−0.0365002
$15$	0.775570	0.200251
$16$	3.88844	0.972109
$17$	3.06812	0.744129	0.372065	−	0.928207i	$-0.378650\pi$
$17$	3.06812	0.744129	0.372065	+	0.928207i	$0.378650\pi$
$18$	0.327565	0.0772077
$19$	−4.13370	−0.948336	−0.474168	−	0.880434i	$-0.657251\pi$
$19$	−4.13370	−0.948336	−0.474168	+	0.880434i	$0.657251\pi$
$20$	−1.98135	−0.443043
$21$	0.775570	0.169243
$22$	−0.236743	−0.0504738
$23$	1.13720	0.237122	0.118561	−	0.992947i	$-0.462172\pi$
$23$	1.13720	0.237122	0.118561	+	0.992947i	$0.462172\pi$
$24$	0.421707	0.0860805
$25$	1.00000	0.200000
$26$	0	0
$27$	−4.18691	−0.805771
$28$	−1.98135	−0.374440
$29$	4.65564	0.864530	0.432265	−	0.901747i	$-0.357715\pi$
$29$	4.65564	0.864530	0.432265	+	0.901747i	$0.357715\pi$
$30$	−0.105921	−0.0193384
$31$	−2.36450	−0.424676	−0.212338	−	0.977196i	$-0.568108\pi$
$31$	−2.36450	−0.424676	−0.212338	+	0.977196i	$0.568108\pi$
$32$	−1.61852	−0.286117
$33$	1.34443	0.234036
$34$	−0.419017	−0.0718608
$35$	1.00000	0.169031
$36$	4.75225	0.792041
$37$	4.43585	0.729250	0.364625	−	0.931154i	$-0.381197\pi$
$37$	4.43585	0.729250	0.364625	+	0.931154i	$0.381197\pi$
$38$	0.564544	0.0915812
$39$	0	0
$40$	0.543737	0.0859724
$41$	−1.92216	−0.300190	−0.150095	−	0.988672i	$-0.547958\pi$
$41$	−1.92216	−0.300190	−0.150095	+	0.988672i	$0.547958\pi$
$42$	−0.105921	−0.0163439
$43$	3.97379	0.605997	0.302999	−	0.952991i	$-0.402012\pi$
$43$	3.97379	0.605997	0.302999	+	0.952991i	$0.402012\pi$
$44$	−3.43462	−0.517789
$45$	−2.39849	−0.357546
$46$	−0.155309	−0.0228990
$47$	0.686497	0.100136	0.0500679	−	0.998746i	$-0.484056\pi$
$47$	0.686497	0.100136	0.0500679	+	0.998746i	$0.484056\pi$
$48$	3.01576	0.435287
$49$	1.00000	0.142857
$50$	−0.136571	−0.0193141
$51$	2.37954	0.333203
$52$	0	0
$53$	−7.61674	−1.04624	−0.523120	−	0.852259i	$-0.675232\pi$
$53$	−7.61674	−1.04624	−0.523120	+	0.852259i	$0.675232\pi$
$54$	0.571811	0.0778137
$55$	1.73348	0.233742
$56$	0.543737	0.0726600
$57$	−3.20598	−0.424642
$58$	−0.635826	−0.0834880
$59$	−1.83421	−0.238794	−0.119397	−	0.992847i	$-0.538096\pi$
$59$	−1.83421	−0.238794	−0.119397	+	0.992847i	$0.538096\pi$
$60$	−1.53668	−0.198384
$61$	7.98708	1.02264	0.511321	−	0.859390i	$-0.329156\pi$
$61$	7.98708	1.02264	0.511321	+	0.859390i	$0.329156\pi$
$62$	0.322922	0.0410112
$63$	−2.39849	−0.302181
$64$	−7.55583	−0.944479
$65$	0	0
$66$	−0.183611	−0.0226009
$67$	−4.47247	−0.546399	−0.273200	−	0.961957i	$-0.588082\pi$
$67$	−4.47247	−0.546399	−0.273200	+	0.961957i	$0.588082\pi$
$68$	−6.07902	−0.737189
$69$	0.881978	0.106178
$70$	−0.136571	−0.0163234
$71$	−2.36722	−0.280937	−0.140469	−	0.990085i	$-0.544861\pi$
$71$	−2.36722	−0.280937	−0.140469	+	0.990085i	$0.544861\pi$
$72$	−1.30415	−0.153695
$73$	15.0951	1.76675	0.883373	−	0.468670i	$-0.155267\pi$
$73$	15.0951	1.76675	0.883373	+	0.468670i	$0.155267\pi$
$74$	−0.605810	−0.0704240
$75$	0.775570	0.0895552
$76$	8.19030	0.939492
$77$	1.73348	0.197548
$78$	0	0
$79$	−11.9181	−1.34089	−0.670446	−	0.741958i	$-0.733897\pi$
$79$	−11.9181	−1.34089	−0.670446	+	0.741958i	$0.733897\pi$
$80$	3.88844	0.434741
$81$	3.94823	0.438692
$82$	0.262511	0.0289895
$83$	8.44680	0.927156	0.463578	−	0.886056i	$-0.346565\pi$
$83$	8.44680	0.927156	0.463578	+	0.886056i	$0.346565\pi$
$84$	−1.53668	−0.167665
$85$	3.06812	0.332785
$86$	−0.542705	−0.0585214
$87$	3.61077	0.387116
$88$	0.942556	0.100477
$89$	11.6275	1.23252	0.616259	−	0.787544i	$-0.288648\pi$
$89$	11.6275	1.23252	0.616259	+	0.787544i	$0.288648\pi$
$90$	0.327565	0.0345284
$91$	0	0
$92$	−2.25319	−0.234911
$93$	−1.83383	−0.190160
$94$	−0.0937557	−0.00967016
$95$	−4.13370	−0.424109
$96$	−1.25528	−0.128116
$97$	−1.50221	−0.152526	−0.0762629	−	0.997088i	$-0.524299\pi$
$97$	−1.50221	−0.152526	−0.0762629	+	0.997088i	$0.524299\pi$
$98$	−0.136571	−0.0137958
$99$	−4.15773	−0.417867
$100$	−1.98135	−0.198135
$101$	6.46766	0.643556	0.321778	−	0.946815i	$-0.395719\pi$
$101$	6.46766	0.643556	0.321778	+	0.946815i	$0.395719\pi$
$102$	−0.324977	−0.0321775
$103$	−0.287300	−0.0283085	−0.0141543	−	0.999900i	$-0.504506\pi$
$103$	−0.287300	−0.0283085	−0.0141543	+	0.999900i	$0.504506\pi$
$104$	0	0
$105$	0.775570	0.0756879
$106$	1.04023	0.101036
$107$	3.74431	0.361977	0.180988	−	0.983485i	$-0.442070\pi$
$107$	3.74431	0.361977	0.180988	+	0.983485i	$0.442070\pi$
$108$	8.29573	0.798257
$109$	−4.93840	−0.473013	−0.236507	−	0.971630i	$-0.576003\pi$
$109$	−4.93840	−0.473013	−0.236507	+	0.971630i	$0.576003\pi$
$110$	−0.236743	−0.0225726
$111$	3.44032	0.326540
$112$	3.88844	0.367423
$113$	9.77852	0.919885	0.459943	−	0.887949i	$-0.347870\pi$
$113$	9.77852	0.919885	0.459943	+	0.887949i	$0.347870\pi$
$114$	0.437844	0.0410078
$115$	1.13720	0.106044
$116$	−9.22444	−0.856467
$117$	0	0
$118$	0.250501	0.0230604
$119$	3.06812	0.281254
$120$	0.421707	0.0384964
$121$	−7.99506	−0.726824
$122$	−1.09081	−0.0987569
$123$	−1.49077	−0.134418
$124$	4.68489	0.420716
$125$	1.00000	0.0894427
$126$	0.327565	0.0291818
$127$	3.35964	0.298120	0.149060	−	0.988828i	$-0.452375\pi$
$127$	3.35964	0.298120	0.149060	+	0.988828i	$0.452375\pi$
$128$	4.26896	0.377326
$129$	3.08195	0.271351
$130$	0	0
$131$	−5.28820	−0.462032	−0.231016	−	0.972950i	$-0.574205\pi$
$131$	−5.28820	−0.462032	−0.231016	+	0.972950i	$0.574205\pi$
$132$	−2.66379	−0.231853
$133$	−4.13370	−0.358437
$134$	0.610811	0.0527660
$135$	−4.18691	−0.360352
$136$	1.66825	0.143052
$137$	3.48871	0.298061	0.149031	−	0.988833i	$-0.452385\pi$
$137$	3.48871	0.298061	0.149031	+	0.988833i	$0.452385\pi$
$138$	−0.120453	−0.0102536
$139$	−19.4299	−1.64803	−0.824013	−	0.566571i	$-0.808270\pi$
$139$	−19.4299	−1.64803	−0.824013	+	0.566571i	$0.808270\pi$
$140$	−1.98135	−0.167454
$141$	0.532426	0.0448384
$142$	0.323294	0.0271302
$143$	0	0
$144$	−9.32638	−0.777198
$145$	4.65564	0.386629
$146$	−2.06155	−0.170615
$147$	0.775570	0.0639680
$148$	−8.78897	−0.722449
$149$	9.13859	0.748663	0.374331	−	0.927295i	$-0.377872\pi$
$149$	9.13859	0.748663	0.374331	+	0.927295i	$0.377872\pi$
$150$	−0.105921	−0.00864838
$151$	17.0427	1.38691	0.693457	−	0.720498i	$-0.256087\pi$
$151$	17.0427	1.38691	0.693457	+	0.720498i	$0.256087\pi$
$152$	−2.24765	−0.182308
$153$	−7.35886	−0.594929
$154$	−0.236743	−0.0190773
$155$	−2.36450	−0.189921
$156$	0	0
$157$	−7.50219	−0.598740	−0.299370	−	0.954137i	$-0.596776\pi$
$157$	−7.50219	−0.598740	−0.299370	+	0.954137i	$0.596776\pi$
$158$	1.62767	0.129491
$159$	−5.90732	−0.468481
$160$	−1.61852	−0.127956
$161$	1.13720	0.0896238
$162$	−0.539214	−0.0423647
$163$	15.1477	1.18646	0.593231	−	0.805032i	$-0.297852\pi$
$163$	15.1477	1.18646	0.593231	+	0.805032i	$0.297852\pi$
$164$	3.80846	0.297391
$165$	1.34443	0.104664
$166$	−1.15359	−0.0895359
$167$	23.3877	1.80979	0.904897	−	0.425630i	$-0.139947\pi$
$167$	23.3877	1.80979	0.904897	+	0.425630i	$0.139947\pi$
$168$	0.421707	0.0325354
$169$	0	0
$170$	−0.419017	−0.0321371
$171$	9.91464	0.758192
$172$	−7.87346	−0.600346
$173$	13.1058	0.996418	0.498209	−	0.867057i	$-0.333991\pi$
$173$	13.1058	0.996418	0.498209	+	0.867057i	$0.333991\pi$
$174$	−0.493128	−0.0373839
$175$	1.00000	0.0755929
$176$	6.74052	0.508086
$177$	−1.42256	−0.106926
$178$	−1.58799	−0.119025
$179$	−13.4321	−1.00396	−0.501980	−	0.864879i	$-0.667395\pi$
$179$	−13.4321	−1.00396	−0.501980	+	0.864879i	$0.667395\pi$
$180$	4.75225	0.354211
$181$	13.1135	0.974721	0.487360	−	0.873201i	$-0.337960\pi$
$181$	13.1135	0.974721	0.487360	+	0.873201i	$0.337960\pi$
$182$	0	0
$183$	6.19455	0.457914
$184$	0.618338	0.0455844
$185$	4.43585	0.326130
$186$	0.250449	0.0183638
$187$	5.31852	0.388929
$188$	−1.36019	−0.0992020
$189$	−4.18691	−0.304553
$190$	0.564544	0.0409564
$191$	4.34955	0.314722	0.157361	−	0.987541i	$-0.449701\pi$
$191$	4.34955	0.314722	0.157361	+	0.987541i	$0.449701\pi$
$192$	−5.86008	−0.422915
$193$	−12.6870	−0.913230	−0.456615	−	0.889664i	$-0.650938\pi$
$193$	−12.6870	−0.913230	−0.456615	+	0.889664i	$0.650938\pi$
$194$	0.205158	0.0147295
$195$	0	0
$196$	−1.98135	−0.141525
$197$	19.9430	1.42088	0.710439	−	0.703759i	$-0.248497\pi$
$197$	19.9430	1.42088	0.710439	+	0.703759i	$0.248497\pi$
$198$	0.567826	0.0403536
$199$	−10.4397	−0.740049	−0.370024	−	0.929022i	$-0.620651\pi$
$199$	−10.4397	−0.740049	−0.370024	+	0.929022i	$0.620651\pi$
$200$	0.543737	0.0384480
$201$	−3.46872	−0.244664
$202$	−0.883296	−0.0621485
$203$	4.65564	0.326762
$204$	−4.71471	−0.330096
$205$	−1.92216	−0.134249
$206$	0.0392370	0.00273377
$207$	−2.72756	−0.189579
$208$	0	0
$209$	−7.16567	−0.495660
$210$	−0.105921	−0.00730921
$211$	26.9314	1.85403	0.927015	−	0.375023i	$-0.122365\pi$
$211$	26.9314	1.85403	0.927015	+	0.375023i	$0.122365\pi$
$212$	15.0914	1.03648
$213$	−1.83594	−0.125797
$214$	−0.511366	−0.0349562
$215$	3.97379	0.271010
$216$	−2.27658	−0.154902
$217$	−2.36450	−0.160513
$218$	0.674444	0.0456791
$219$	11.7073	0.791106
$220$	−3.43462	−0.231562
$221$	0	0
$222$	−0.469848	−0.0315341
$223$	10.0768	0.674790	0.337395	−	0.941363i	$-0.390454\pi$
$223$	10.0768	0.674790	0.337395	+	0.941363i	$0.390454\pi$
$224$	−1.61852	−0.108142
$225$	−2.39849	−0.159899
$226$	−1.33546	−0.0888337
$227$	−8.34841	−0.554103	−0.277052	−	0.960855i	$-0.589357\pi$
$227$	−8.34841	−0.554103	−0.277052	+	0.960855i	$0.589357\pi$
$228$	6.35216	0.420682
$229$	11.4627	0.757480	0.378740	−	0.925503i	$-0.376358\pi$
$229$	11.4627	0.757480	0.378740	+	0.925503i	$0.376358\pi$
$230$	−0.155309	−0.0102407
$231$	1.34443	0.0884572
$232$	2.53144	0.166197
$233$	16.6287	1.08938	0.544692	−	0.838636i	$-0.316647\pi$
$233$	16.6287	1.08938	0.544692	+	0.838636i	$0.316647\pi$
$234$	0	0
$235$	0.686497	0.0447821
$236$	3.63421	0.236567
$237$	−9.24333	−0.600419
$238$	−0.419017	−0.0271608
$239$	−12.7548	−0.825038	−0.412519	−	0.910949i	$-0.635351\pi$
$239$	−12.7548	−0.825038	−0.412519	+	0.910949i	$0.635351\pi$
$240$	3.01576	0.194666
$241$	8.77234	0.565076	0.282538	−	0.959256i	$-0.408824\pi$
$241$	8.77234	0.565076	0.282538	+	0.959256i	$0.408824\pi$
$242$	1.09189	0.0701896
$243$	15.6229	1.00221
$244$	−15.8252	−1.01310
$245$	1.00000	0.0638877
$246$	0.203596	0.0129808
$247$	0	0
$248$	−1.28567	−0.0816398
$249$	6.55109	0.415158
$250$	−0.136571	−0.00863752
$251$	11.6438	0.734948	0.367474	−	0.930034i	$-0.380223\pi$
$251$	11.6438	0.734948	0.367474	+	0.930034i	$0.380223\pi$
$252$	4.75225	0.299363
$253$	1.97131	0.123935
$254$	−0.458830	−0.0287896
$255$	2.37954	0.149013
$256$	14.5286	0.908040
$257$	−20.4034	−1.27273	−0.636366	−	0.771387i	$-0.719563\pi$
$257$	−20.4034	−1.27273	−0.636366	+	0.771387i	$0.719563\pi$
$258$	−0.420906	−0.0262045
$259$	4.43585	0.275631
$260$	0	0
$261$	−11.1665	−0.691189
$262$	0.722216	0.0446187
$263$	21.5798	1.33067	0.665335	−	0.746545i	$-0.268289\pi$
$263$	21.5798	1.33067	0.665335	+	0.746545i	$0.268289\pi$
$264$	0.731019	0.0449911
$265$	−7.61674	−0.467893
$266$	0.564544	0.0346144
$267$	9.01798	0.551891
$268$	8.86152	0.541304
$269$	−0.495702	−0.0302235	−0.0151117	−	0.999886i	$-0.504810\pi$
$269$	−0.495702	−0.0302235	−0.0151117	+	0.999886i	$0.504810\pi$
$270$	0.571811	0.0347993
$271$	−16.7786	−1.01923	−0.509615	−	0.860403i	$-0.670212\pi$
$271$	−16.7786	−1.01923	−0.509615	+	0.860403i	$0.670212\pi$
$272$	11.9302	0.723375
$273$	0	0
$274$	−0.476458	−0.0287839
$275$	1.73348	0.104533
$276$	−1.74750	−0.105187
$277$	−9.37837	−0.563491	−0.281746	−	0.959489i	$-0.590913\pi$
$277$	−9.37837	−0.563491	−0.281746	+	0.959489i	$0.590913\pi$
$278$	2.65357	0.159151
$279$	5.67122	0.339527
$280$	0.543737	0.0324945
$281$	18.2448	1.08839	0.544197	−	0.838958i	$-0.316834\pi$
$281$	18.2448	1.08839	0.544197	+	0.838958i	$0.316834\pi$
$282$	−0.0727141	−0.00433006
$283$	−8.93336	−0.531033	−0.265516	−	0.964106i	$-0.585542\pi$
$283$	−8.93336	−0.531033	−0.265516	+	0.964106i	$0.585542\pi$
$284$	4.69028	0.278317
$285$	−3.20598	−0.189906
$286$	0	0
$287$	−1.92216	−0.113461
$288$	3.88201	0.228750
$289$	−7.58662	−0.446272
$290$	−0.635826	−0.0373370
$291$	−1.16507	−0.0682974
$292$	−29.9086	−1.75027
$293$	−14.2760	−0.834012	−0.417006	−	0.908904i	$-0.636921\pi$
$293$	−14.2760	−0.834012	−0.417006	+	0.908904i	$0.636921\pi$
$294$	−0.105921	−0.00617741
$295$	−1.83421	−0.106792
$296$	2.41194	0.140191
$297$	−7.25791	−0.421147
$298$	−1.24807	−0.0722987
$299$	0	0
$300$	−1.53668	−0.0887200
$301$	3.97379	0.229045
$302$	−2.32754	−0.133935
$303$	5.01613	0.288169
$304$	−16.0736	−0.921886
$305$	7.98708	0.457339
$306$	1.00501	0.0574525
$307$	−0.990805	−0.0565482	−0.0282741	−	0.999600i	$-0.509001\pi$
$307$	−0.990805	−0.0565482	−0.0282741	+	0.999600i	$0.509001\pi$
$308$	−3.43462	−0.195706
$309$	−0.222822	−0.0126759
$310$	0.322922	0.0183407
$311$	−16.8148	−0.953481	−0.476741	−	0.879044i	$-0.658182\pi$
$311$	−16.8148	−0.953481	−0.476741	+	0.879044i	$0.658182\pi$
$312$	0	0
$313$	−17.0858	−0.965749	−0.482874	−	0.875690i	$-0.660407\pi$
$313$	−17.0858	−0.965749	−0.482874	+	0.875690i	$0.660407\pi$
$314$	1.02458	0.0578206
$315$	−2.39849	−0.135140
$316$	23.6139	1.32839
$317$	32.9200	1.84897	0.924486	−	0.381216i	$-0.124495\pi$
$317$	32.9200	1.84897	0.924486	+	0.381216i	$0.124495\pi$
$318$	0.806769	0.0452414
$319$	8.07044	0.451858
$320$	−7.55583	−0.422384
$321$	2.90398	0.162084
$322$	−0.155309	−0.00865501
$323$	−12.6827	−0.705684
$324$	−7.82282	−0.434601
$325$	0	0
$326$	−2.06875	−0.114577
$327$	−3.83008	−0.211804
$328$	−1.04515	−0.0577087
$329$	0.686497	0.0378478
$330$	−0.183611	−0.0101074
$331$	0.624627	0.0343326	0.0171663	−	0.999853i	$-0.494536\pi$
$331$	0.624627	0.0343326	0.0171663	+	0.999853i	$0.494536\pi$
$332$	−16.7360	−0.918510
$333$	−10.6394	−0.583033
$334$	−3.19409	−0.174773
$335$	−4.47247	−0.244357
$336$	3.01576	0.164523
$337$	21.7313	1.18378	0.591889	−	0.806020i	$-0.298383\pi$
$337$	21.7313	1.18378	0.591889	+	0.806020i	$0.298383\pi$
$338$	0	0
$339$	7.58393	0.411902
$340$	−6.07902	−0.329681
$341$	−4.09880	−0.221962
$342$	−1.35405	−0.0732189
$343$	1.00000	0.0539949
$344$	2.16070	0.116497
$345$	0.881978	0.0474841
$346$	−1.78988	−0.0962245
$347$	25.7179	1.38061	0.690304	−	0.723520i	$-0.257477\pi$
$347$	25.7179	1.38061	0.690304	+	0.723520i	$0.257477\pi$
$348$	−7.15420	−0.383505
$349$	16.8880	0.903993	0.451996	−	0.892020i	$-0.350712\pi$
$349$	16.8880	0.903993	0.451996	+	0.892020i	$0.350712\pi$
$350$	−0.136571	−0.00730004
$351$	0	0
$352$	−2.80567	−0.149543
$353$	24.0742	1.28134	0.640670	−	0.767816i	$-0.278657\pi$
$353$	24.0742	1.28134	0.640670	+	0.767816i	$0.278657\pi$
$354$	0.194281	0.0103259
$355$	−2.36722	−0.125639
$356$	−23.0382	−1.22102
$357$	2.37954	0.125939
$358$	1.83444	0.0969529
$359$	−14.0573	−0.741917	−0.370959	−	0.928649i	$-0.620971\pi$
$359$	−14.0573	−0.741917	−0.370959	+	0.928649i	$0.620971\pi$
$360$	−1.30415	−0.0687347
$361$	−1.91251	−0.100659
$362$	−1.79093	−0.0941292
$363$	−6.20073	−0.325454
$364$	0	0
$365$	15.0951	0.790113
$366$	−0.845996	−0.0442209
$367$	26.4942	1.38298	0.691492	−	0.722384i	$-0.256954\pi$
$367$	26.4942	1.38298	0.691492	+	0.722384i	$0.256954\pi$
$368$	4.42193	0.230509
$369$	4.61027	0.240001
$370$	−0.605810	−0.0314946
$371$	−7.61674	−0.395441
$372$	3.63346	0.188386
$373$	9.25169	0.479034	0.239517	−	0.970892i	$-0.423011\pi$
$373$	9.25169	0.479034	0.239517	+	0.970892i	$0.423011\pi$
$374$	−0.726356	−0.0375590
$375$	0.775570	0.0400503
$376$	0.373274	0.0192501
$377$	0	0
$378$	0.571811	0.0294108
$379$	12.4715	0.640617	0.320309	−	0.947313i	$-0.396213\pi$
$379$	12.4715	0.640617	0.320309	+	0.947313i	$0.396213\pi$
$380$	8.19030	0.420154
$381$	2.60564	0.133491
$382$	−0.594023	−0.0303928
$383$	4.81155	0.245859	0.122929	−	0.992415i	$-0.460771\pi$
$383$	4.81155	0.245859	0.122929	+	0.992415i	$0.460771\pi$
$384$	3.31088	0.168957
$385$	1.73348	0.0883462
$386$	1.73268	0.0881910
$387$	−9.53109	−0.484493
$388$	2.97639	0.151103
$389$	−5.74437	−0.291251	−0.145626	−	0.989340i	$-0.546519\pi$
$389$	−5.74437	−0.291251	−0.145626	+	0.989340i	$0.546519\pi$
$390$	0	0
$391$	3.48906	0.176450
$392$	0.543737	0.0274629
$393$	−4.10137	−0.206887
$394$	−2.72363	−0.137215
$395$	−11.9181	−0.599665
$396$	8.23791	0.413970
$397$	13.3265	0.668839	0.334419	−	0.942424i	$-0.391460\pi$
$397$	13.3265	0.668839	0.334419	+	0.942424i	$0.391460\pi$
$398$	1.42576	0.0714668
$399$	−3.20598	−0.160500
$400$	3.88844	0.194422
$401$	−29.1070	−1.45353	−0.726766	−	0.686885i	$-0.758978\pi$
$401$	−29.1070	−1.45353	−0.726766	+	0.686885i	$0.758978\pi$
$402$	0.473727	0.0236273
$403$	0	0
$404$	−12.8147	−0.637555
$405$	3.94823	0.196189
$406$	−0.635826	−0.0315555
$407$	7.68945	0.381152
$408$	1.29385	0.0640550
$409$	27.0716	1.33860	0.669301	−	0.742991i	$-0.266593\pi$
$409$	27.0716	1.33860	0.669301	+	0.742991i	$0.266593\pi$
$410$	0.262511	0.0129645
$411$	2.70574	0.133465
$412$	0.569242	0.0280445
$413$	−1.83421	−0.0902557
$414$	0.372506	0.0183077
$415$	8.44680	0.414637
$416$	0	0
$417$	−15.0693	−0.737946
$418$	0.978625	0.0478661
$419$	15.2858	0.746758	0.373379	−	0.927679i	$-0.378199\pi$
$419$	15.2858	0.746758	0.373379	+	0.927679i	$0.378199\pi$
$420$	−1.53668	−0.0749821
$421$	−36.9385	−1.80027	−0.900137	−	0.435607i	$-0.856534\pi$
$421$	−36.9385	−1.80027	−0.900137	+	0.435607i	$0.856534\pi$
$422$	−3.67805	−0.179045
$423$	−1.64656	−0.0800583
$424$	−4.14151	−0.201129
$425$	3.06812	0.148826
$426$	0.250737	0.0121483
$427$	7.98708	0.386522
$428$	−7.41879	−0.358601
$429$	0	0
$430$	−0.542705	−0.0261716
$431$	32.1989	1.55097	0.775484	−	0.631368i	$-0.217506\pi$
$431$	32.1989	1.55097	0.775484	+	0.631368i	$0.217506\pi$
$432$	−16.2805	−0.783298
$433$	13.4960	0.648577	0.324289	−	0.945958i	$-0.394875\pi$
$433$	13.4960	0.648577	0.324289	+	0.945958i	$0.394875\pi$
$434$	0.322922	0.0155008
$435$	3.61077	0.173123
$436$	9.78470	0.468602
$437$	−4.70084	−0.224872
$438$	−1.59888	−0.0763975
$439$	−29.5545	−1.41056	−0.705280	−	0.708929i	$-0.749179\pi$
$439$	−29.5545	−1.41056	−0.705280	+	0.708929i	$0.749179\pi$
$440$	0.942556	0.0449346
$441$	−2.39849	−0.114214
$442$	0	0
$443$	−33.3324	−1.58367	−0.791836	−	0.610733i	$-0.790875\pi$
$443$	−33.3324	−1.58367	−0.791836	+	0.610733i	$0.790875\pi$
$444$	−6.81647	−0.323495
$445$	11.6275	0.551198
$446$	−1.37620	−0.0651648
$447$	7.08762	0.335233
$448$	−7.55583	−0.356979
$449$	−20.8165	−0.982389	−0.491195	−	0.871050i	$-0.663440\pi$
$449$	−20.8165	−0.982389	−0.491195	+	0.871050i	$0.663440\pi$
$450$	0.327565	0.0154415
$451$	−3.33201	−0.156898
$452$	−19.3746	−0.911307
$453$	13.2178	0.621026
$454$	1.14015	0.0535100
$455$	0	0
$456$	−1.74321	−0.0816333
$457$	14.2927	0.668584	0.334292	−	0.942470i	$-0.391503\pi$
$457$	14.2927	0.668584	0.334292	+	0.942470i	$0.391503\pi$
$458$	−1.56548	−0.0731501
$459$	−12.8460	−0.599598
$460$	−2.25319	−0.105055
$461$	15.5397	0.723755	0.361877	−	0.932226i	$-0.382136\pi$
$461$	15.5397	0.723755	0.361877	+	0.932226i	$0.382136\pi$
$462$	−0.183611	−0.00854235
$463$	3.83602	0.178275	0.0891374	−	0.996019i	$-0.471589\pi$
$463$	3.83602	0.178275	0.0891374	+	0.996019i	$0.471589\pi$
$464$	18.1031	0.840418
$465$	−1.83383	−0.0850420
$466$	−2.27100	−0.105202
$467$	15.2896	0.707518	0.353759	−	0.935337i	$-0.384903\pi$
$467$	15.2896	0.707518	0.353759	+	0.935337i	$0.384903\pi$
$468$	0	0
$469$	−4.47247	−0.206519
$470$	−0.0937557	−0.00432463
$471$	−5.81848	−0.268101
$472$	−0.997330	−0.0459058
$473$	6.88847	0.316732
$474$	1.26237	0.0579827
$475$	−4.13370	−0.189667
$476$	−6.07902	−0.278631
$477$	18.2687	0.836465
$478$	1.74194	0.0796743
$479$	34.4350	1.57338	0.786688	−	0.617351i	$-0.211794\pi$
$479$	34.4350	1.57338	0.786688	+	0.617351i	$0.211794\pi$
$480$	−1.25528	−0.0572954
$481$	0	0
$482$	−1.19805	−0.0545696
$483$	0.881978	0.0401314
$484$	15.8410	0.720045
$485$	−1.50221	−0.0682116
$486$	−2.13363	−0.0967835
$487$	−6.07653	−0.275354	−0.137677	−	0.990477i	$-0.543964\pi$
$487$	−6.07653	−0.275354	−0.137677	+	0.990477i	$0.543964\pi$
$488$	4.34288	0.196593
$489$	11.7481	0.531269
$490$	−0.136571	−0.00616966
$491$	17.7006	0.798816	0.399408	−	0.916773i	$-0.369216\pi$
$491$	17.7006	0.798816	0.399408	+	0.916773i	$0.369216\pi$
$492$	2.95373	0.133164
$493$	14.2841	0.643322
$494$	0	0
$495$	−4.15773	−0.186876
$496$	−9.19420	−0.412832
$497$	−2.36722	−0.106184
$498$	−0.894690	−0.0400920
$499$	28.0709	1.25662	0.628312	−	0.777961i	$-0.283746\pi$
$499$	28.0709	1.25662	0.628312	+	0.777961i	$0.283746\pi$
$500$	−1.98135	−0.0886086
$501$	18.1388	0.810382
$502$	−1.59020	−0.0709742
$503$	−26.5311	−1.18297	−0.591483	−	0.806318i	$-0.701457\pi$
$503$	−26.5311	−1.18297	−0.591483	+	0.806318i	$0.701457\pi$
$504$	−1.30415	−0.0580914
$505$	6.46766	0.287807
$506$	−0.269224	−0.0119685
$507$	0	0
$508$	−6.65662	−0.295340
$509$	−39.2868	−1.74136	−0.870678	−	0.491854i	$-0.836319\pi$
$509$	−39.2868	−1.74136	−0.870678	+	0.491854i	$0.836319\pi$
$510$	−0.324977	−0.0143902
$511$	15.0951	0.667768
$512$	−10.5221	−0.465016
$513$	17.3074	0.764142
$514$	2.78652	0.122908
$515$	−0.287300	−0.0126600
$516$	−6.10642	−0.268820
$517$	1.19003	0.0523373
$518$	−0.605810	−0.0266178
$519$	10.1645	0.446172
$520$	0	0
$521$	39.8512	1.74591	0.872956	−	0.487799i	$-0.162200\pi$
$521$	39.8512	1.74591	0.872956	+	0.487799i	$0.162200\pi$
$522$	1.52502	0.0667484
$523$	−4.18433	−0.182968	−0.0914840	−	0.995807i	$-0.529161\pi$
$523$	−4.18433	−0.182968	−0.0914840	+	0.995807i	$0.529161\pi$
$524$	10.4778	0.457724
$525$	0.775570	0.0338487
$526$	−2.94718	−0.128503
$527$	−7.25457	−0.316014
$528$	5.22774	0.227508
$529$	−21.7068	−0.943773
$530$	1.04023	0.0451846
$531$	4.39934	0.190915
$532$	8.19030	0.355095
$533$	0	0
$534$	−1.23160	−0.0532964
$535$	3.74431	0.161881
$536$	−2.43185	−0.105040
$537$	−10.4175	−0.449549
$538$	0.0676986	0.00291869
$539$	1.73348	0.0746661
$540$	8.29573	0.356991
$541$	15.9967	0.687752	0.343876	−	0.939015i	$-0.388260\pi$
$541$	15.9967	0.687752	0.343876	+	0.939015i	$0.388260\pi$
$542$	2.29148	0.0984274
$543$	10.1705	0.436456
$544$	−4.96583	−0.212908
$545$	−4.93840	−0.211538
$546$	0	0
$547$	6.52716	0.279081	0.139541	−	0.990216i	$-0.455437\pi$
$547$	6.52716	0.279081	0.139541	+	0.990216i	$0.455437\pi$
$548$	−6.91236	−0.295281
$549$	−19.1569	−0.817598
$550$	−0.236743	−0.0100948
$551$	−19.2450	−0.819865
$552$	0.479564	0.0204116
$553$	−11.9181	−0.506810
$554$	1.28081	0.0544166
$555$	3.44032	0.146033
$556$	38.4975	1.63266
$557$	22.4597	0.951648	0.475824	−	0.879540i	$-0.342150\pi$
$557$	22.4597	0.951648	0.475824	+	0.879540i	$0.342150\pi$
$558$	−0.774526	−0.0327883
$559$	0	0
$560$	3.88844	0.164316
$561$	4.12489	0.174153
$562$	−2.49171	−0.105107
$563$	−5.85615	−0.246807	−0.123404	−	0.992357i	$-0.539381\pi$
$563$	−5.85615	−0.246807	−0.123404	+	0.992357i	$0.539381\pi$
$564$	−1.05492	−0.0444202
$565$	9.77852	0.411385
$566$	1.22004	0.0512821
$567$	3.94823	0.165810
$568$	−1.28715	−0.0540074
$569$	−5.97327	−0.250413	−0.125206	−	0.992131i	$-0.539959\pi$
$569$	−5.97327	−0.250413	−0.125206	+	0.992131i	$0.539959\pi$
$570$	0.437844	0.0183393
$571$	−46.3450	−1.93948	−0.969739	−	0.244144i	$-0.921493\pi$
$571$	−46.3450	−1.93948	−0.969739	+	0.244144i	$0.921493\pi$
$572$	0	0
$573$	3.37338	0.140925
$574$	0.262511	0.0109570
$575$	1.13720	0.0474245
$576$	18.1226	0.755108
$577$	19.0878	0.794636	0.397318	−	0.917681i	$-0.369941\pi$
$577$	19.0878	0.794636	0.397318	+	0.917681i	$0.369941\pi$
$578$	1.03611	0.0430967
$579$	−9.83966	−0.408922
$580$	−9.22444	−0.383024
$581$	8.44680	0.350432
$582$	0.159114	0.00659551
$583$	−13.2034	−0.546831
$584$	8.20777	0.339640
$585$	0	0
$586$	1.94969	0.0805409
$587$	14.1426	0.583726	0.291863	−	0.956460i	$-0.405725\pi$
$587$	14.1426	0.583726	0.291863	+	0.956460i	$0.405725\pi$
$588$	−1.53668	−0.0633714
$589$	9.77412	0.402736
$590$	0.250501	0.0103129
$591$	15.4672	0.636235
$592$	17.2485	0.708911
$593$	−19.4754	−0.799759	−0.399880	−	0.916568i	$-0.630948\pi$
$593$	−19.4754	−0.799759	−0.399880	+	0.916568i	$0.630948\pi$
$594$	0.991221	0.0406703
$595$	3.06812	0.125781
$596$	−18.1067	−0.741681
$597$	−8.09670	−0.331376
$598$	0	0
$599$	−13.6852	−0.559162	−0.279581	−	0.960122i	$-0.590196\pi$
$599$	−13.6852	−0.559162	−0.279581	+	0.960122i	$0.590196\pi$
$600$	0.421707	0.0172161
$601$	25.4860	1.03960	0.519798	−	0.854289i	$-0.326007\pi$
$601$	25.4860	1.03960	0.519798	+	0.854289i	$0.326007\pi$
$602$	−0.542705	−0.0221190
$603$	10.7272	0.436844
$604$	−33.7675	−1.37398
$605$	−7.99506	−0.325045
$606$	−0.685058	−0.0278286
$607$	−39.2425	−1.59280	−0.796402	−	0.604767i	$-0.793266\pi$
$607$	−39.2425	−1.59280	−0.796402	+	0.604767i	$0.793266\pi$
$608$	6.69049	0.271335
$609$	3.61077	0.146316
$610$	−1.09081	−0.0441654
$611$	0	0
$612$	14.5805	0.589381
$613$	−36.4785	−1.47335	−0.736677	−	0.676245i	$-0.763606\pi$
$613$	−36.4785	−1.47335	−0.736677	+	0.676245i	$0.763606\pi$
$614$	0.135315	0.00546088
$615$	−1.49077	−0.0601136
$616$	0.942556	0.0379767
$617$	9.11032	0.366768	0.183384	−	0.983041i	$-0.441295\pi$
$617$	9.11032	0.366768	0.183384	+	0.983041i	$0.441295\pi$
$618$	0.0304310	0.00122412
$619$	21.8716	0.879092	0.439546	−	0.898220i	$-0.355139\pi$
$619$	21.8716	0.879092	0.439546	+	0.898220i	$0.355139\pi$
$620$	4.68489	0.188150
$621$	−4.76135	−0.191066
$622$	2.29642	0.0920781
$623$	11.6275	0.465848
$624$	0	0
$625$	1.00000	0.0400000
$626$	2.33343	0.0932627
$627$	−5.55749	−0.221945
$628$	14.8644	0.593156
$629$	13.6097	0.542656
$630$	0.327565	0.0130505
$631$	22.1580	0.882096	0.441048	−	0.897483i	$-0.354607\pi$
$631$	22.1580	0.882096	0.441048	+	0.897483i	$0.354607\pi$
$632$	−6.48032	−0.257773
$633$	20.8872	0.830190
$634$	−4.49592	−0.178556
$635$	3.35964	0.133323
$636$	11.7045	0.464112
$637$	0	0
$638$	−1.10219	−0.0436361
$639$	5.67775	0.224608
$640$	4.26896	0.168745
$641$	−48.2156	−1.90440	−0.952201	−	0.305474i	$-0.901185\pi$
$641$	−48.2156	−1.90440	−0.952201	+	0.305474i	$0.901185\pi$
$642$	−0.396600	−0.0156526
$643$	−17.5997	−0.694063	−0.347031	−	0.937853i	$-0.612810\pi$
$643$	−17.5997	−0.694063	−0.347031	+	0.937853i	$0.612810\pi$
$644$	−2.25319	−0.0887880
$645$	3.08195	0.121352
$646$	1.73209	0.0681482
$647$	5.30558	0.208584	0.104292	−	0.994547i	$-0.466742\pi$
$647$	5.30558	0.208584	0.104292	+	0.994547i	$0.466742\pi$
$648$	2.14680	0.0843343
$649$	−3.17956	−0.124809
$650$	0	0
$651$	−1.83383	−0.0718736
$652$	−30.0130	−1.17540
$653$	−40.8748	−1.59956	−0.799778	−	0.600296i	$-0.795050\pi$
$653$	−40.8748	−1.59956	−0.799778	+	0.600296i	$0.795050\pi$
$654$	0.523079	0.0204540
$655$	−5.28820	−0.206627
$656$	−7.47419	−0.291818
$657$	−36.2054	−1.41251
$658$	−0.0937557	−0.00365498
$659$	25.1380	0.979237	0.489618	−	0.871937i	$-0.337136\pi$
$659$	25.1380	0.979237	0.489618	+	0.871937i	$0.337136\pi$
$660$	−2.66379	−0.103688
$661$	2.45980	0.0956751	0.0478376	−	0.998855i	$-0.484767\pi$
$661$	2.45980	0.0956751	0.0478376	+	0.998855i	$0.484767\pi$
$662$	−0.0853060	−0.00331551
$663$	0	0
$664$	4.59284	0.178237
$665$	−4.13370	−0.160298
$666$	1.45303	0.0563037
$667$	5.29438	0.204999
$668$	−46.3392	−1.79292
$669$	7.81524	0.302155
$670$	0.610811	0.0235977
$671$	13.8454	0.534497
$672$	−1.25528	−0.0484234
$673$	35.5215	1.36926	0.684628	−	0.728893i	$-0.259965\pi$
$673$	35.5215	1.36926	0.684628	+	0.728893i	$0.259965\pi$
$674$	−2.96786	−0.114318
$675$	−4.18691	−0.161154
$676$	0	0
$677$	−44.7051	−1.71815	−0.859077	−	0.511846i	$-0.828962\pi$
$677$	−44.7051	−1.71815	−0.859077	+	0.511846i	$0.828962\pi$
$678$	−1.03575	−0.0397776
$679$	−1.50221	−0.0576494
$680$	1.66825	0.0639746
$681$	−6.47478	−0.248114
$682$	0.559778	0.0214350
$683$	24.8734	0.951754	0.475877	−	0.879512i	$-0.342131\pi$
$683$	24.8734	0.951754	0.475877	+	0.879512i	$0.342131\pi$
$684$	−19.6444	−0.751121
$685$	3.48871	0.133297
$686$	−0.136571	−0.00521431
$687$	8.89017	0.339181
$688$	15.4518	0.589095
$689$	0	0
$690$	−0.120453	−0.00458556
$691$	−19.7472	−0.751219	−0.375609	−	0.926778i	$-0.622567\pi$
$691$	−19.7472	−0.751219	−0.375609	+	0.926778i	$0.622567\pi$
$692$	−25.9672	−0.987126
$693$	−4.15773	−0.157939
$694$	−3.51232	−0.133326
$695$	−19.4299	−0.737020
$696$	1.96331	0.0744192
$697$	−5.89741	−0.223380
$698$	−2.30641	−0.0872990
$699$	12.8967	0.487800
$700$	−1.98135	−0.0748879
$701$	−1.00373	−0.0379103	−0.0189552	−	0.999820i	$-0.506034\pi$
$701$	−1.00373	−0.0379103	−0.0189552	+	0.999820i	$0.506034\pi$
$702$	0	0
$703$	−18.3365	−0.691574
$704$	−13.0979	−0.493644
$705$	0.532426	0.0200523
$706$	−3.28784	−0.123740
$707$	6.46766	0.243241
$708$	2.81859	0.105929
$709$	−9.02435	−0.338916	−0.169458	−	0.985537i	$-0.554202\pi$
$709$	−9.02435	−0.338916	−0.169458	+	0.985537i	$0.554202\pi$
$710$	0.323294	0.0121330
$711$	28.5855	1.07204
$712$	6.32233	0.236939
$713$	−2.68890	−0.100700
$714$	−0.324977	−0.0121620
$715$	0	0
$716$	26.6136	0.994598
$717$	−9.89223	−0.369432
$718$	1.91983	0.0716473
$719$	3.55805	0.132693	0.0663465	−	0.997797i	$-0.478866\pi$
$719$	3.55805	0.132693	0.0663465	+	0.997797i	$0.478866\pi$
$720$	−9.32638	−0.347574
$721$	−0.287300	−0.0106996
$722$	0.261194	0.00972065
$723$	6.80357	0.253027
$724$	−25.9825	−0.965630
$725$	4.65564	0.172906
$726$	0.846841	0.0314292
$727$	35.8263	1.32873	0.664363	−	0.747410i	$-0.268703\pi$
$727$	35.8263	1.32873	0.664363	+	0.747410i	$0.268703\pi$
$728$	0	0
$729$	0.271940	0.0100719
$730$	−2.06155	−0.0763016
$731$	12.1921	0.450940
$732$	−12.2736	−0.453644
$733$	39.9969	1.47732	0.738661	−	0.674078i	$-0.235459\pi$
$733$	39.9969	1.47732	0.738661	+	0.674078i	$0.235459\pi$
$734$	−3.61834	−0.133555
$735$	0.775570	0.0286073
$736$	−1.84058	−0.0678448
$737$	−7.75292	−0.285583
$738$	−0.629631	−0.0231770
$739$	−13.8809	−0.510617	−0.255309	−	0.966860i	$-0.582177\pi$
$739$	−13.8809	−0.510617	−0.255309	+	0.966860i	$0.582177\pi$
$740$	−8.78897	−0.323089
$741$	0	0
$742$	1.04023	0.0381879
$743$	10.7900	0.395845	0.197923	−	0.980218i	$-0.436581\pi$
$743$	10.7900	0.395845	0.197923	+	0.980218i	$0.436581\pi$
$744$	−0.997124	−0.0365563
$745$	9.13859	0.334812
$746$	−1.26351	−0.0462605
$747$	−20.2596	−0.741259
$748$	−10.5378	−0.385302
$749$	3.74431	0.136814
$750$	−0.105921	−0.00386767
$751$	14.1658	0.516919	0.258460	−	0.966022i	$-0.416785\pi$
$751$	14.1658	0.516919	0.258460	+	0.966022i	$0.416785\pi$
$752$	2.66940	0.0973430
$753$	9.03056	0.329092
$754$	0	0
$755$	17.0427	0.620246
$756$	8.29573	0.301713
$757$	−19.4552	−0.707111	−0.353555	−	0.935414i	$-0.615027\pi$
$757$	−19.4552	−0.707111	−0.353555	+	0.935414i	$0.615027\pi$
$758$	−1.70325	−0.0618647
$759$	1.52889	0.0554951
$760$	−2.24765	−0.0815308
$761$	5.92542	0.214796	0.107398	−	0.994216i	$-0.465748\pi$
$761$	5.92542	0.214796	0.107398	+	0.994216i	$0.465748\pi$
$762$	−0.355855	−0.0128913
$763$	−4.93840	−0.178782
$764$	−8.61797	−0.311787
$765$	−7.35886	−0.266060
$766$	−0.657119	−0.0237427
$767$	0	0
$768$	11.2680	0.406599
$769$	−0.885546	−0.0319336	−0.0159668	−	0.999873i	$-0.505083\pi$
$769$	−0.885546	−0.0319336	−0.0159668	+	0.999873i	$0.505083\pi$
$770$	−0.236743	−0.00853162
$771$	−15.8243	−0.569899
$772$	25.1374	0.904714
$773$	−17.2743	−0.621315	−0.310657	−	0.950522i	$-0.600549\pi$
$773$	−17.2743	−0.621315	−0.310657	+	0.950522i	$0.600549\pi$
$774$	1.30167	0.0467877
$775$	−2.36450	−0.0849352
$776$	−0.816806	−0.0293216
$777$	3.44032	0.123421
$778$	0.784515	0.0281262
$779$	7.94562	0.284681
$780$	0	0
$781$	−4.10352	−0.146835
$782$	−0.476506	−0.0170398
$783$	−19.4927	−0.696613
$784$	3.88844	0.138873
$785$	−7.50219	−0.267765
$786$	0.560130	0.0199792
$787$	−50.6428	−1.80522	−0.902610	−	0.430459i	$-0.858352\pi$
$787$	−50.6428	−1.80522	−0.902610	+	0.430459i	$0.858352\pi$
$788$	−39.5140	−1.40763
$789$	16.7367	0.595842
$790$	1.62767	0.0579099
$791$	9.77852	0.347684
$792$	−2.26071	−0.0803309
$793$	0	0
$794$	−1.82002	−0.0645900
$795$	−5.90732	−0.209511
$796$	20.6846	0.733147
$797$	−15.7538	−0.558028	−0.279014	−	0.960287i	$-0.590008\pi$
$797$	−15.7538	−0.558028	−0.279014	+	0.960287i	$0.590008\pi$
$798$	0.437844	0.0154995
$799$	2.10626	0.0745140
$800$	−1.61852	−0.0572234
$801$	−27.8886	−0.985394
$802$	3.97517	0.140368
$803$	26.1670	0.923413
$804$	6.87273	0.242383
$805$	1.13720	0.0400810
$806$	0	0
$807$	−0.384452	−0.0135333
$808$	3.51671	0.123717
$809$	21.4937	0.755679	0.377840	−	0.925871i	$-0.376667\pi$
$809$	21.4937	0.755679	0.377840	+	0.925871i	$0.376667\pi$
$810$	−0.539214	−0.0189461
$811$	−26.2295	−0.921043	−0.460521	−	0.887649i	$-0.652338\pi$
$811$	−26.2295	−0.921043	−0.460521	+	0.887649i	$0.652338\pi$
$812$	−9.22444	−0.323714
$813$	−13.0130	−0.456386
$814$	−1.05016	−0.0368080
$815$	15.1477	0.530602
$816$	9.25271	0.323910
$817$	−16.4265	−0.574689
$818$	−3.69720	−0.129269
$819$	0	0
$820$	3.80846	0.132997
$821$	11.4566	0.399840	0.199920	−	0.979812i	$-0.435932\pi$
$821$	11.4566	0.399840	0.199920	+	0.979812i	$0.435932\pi$
$822$	−0.369527	−0.0128887
$823$	−54.1107	−1.88618	−0.943090	−	0.332537i	$-0.892095\pi$
$823$	−54.1107	−1.88618	−0.943090	+	0.332537i	$0.892095\pi$
$824$	−0.156216	−0.00544204
$825$	1.34443	0.0468072
$826$	0.250501	0.00871603
$827$	15.0268	0.522534	0.261267	−	0.965267i	$-0.415860\pi$
$827$	15.0268	0.522534	0.261267	+	0.965267i	$0.415860\pi$
$828$	5.40425	0.187811
$829$	31.6993	1.10096	0.550482	−	0.834847i	$-0.314444\pi$
$829$	31.6993	1.10096	0.550482	+	0.834847i	$0.314444\pi$
$830$	−1.15359	−0.0400417
$831$	−7.27358	−0.252318
$832$	0	0
$833$	3.06812	0.106304
$834$	2.05803	0.0712638
$835$	23.3877	0.809365
$836$	14.1977	0.491038
$837$	9.89993	0.342192
$838$	−2.08759	−0.0721147
$839$	−54.8784	−1.89461	−0.947306	−	0.320331i	$-0.896206\pi$
$839$	−54.8784	−1.89461	−0.947306	+	0.320331i	$0.896206\pi$
$840$	0.421707	0.0145503
$841$	−7.32506	−0.252588
$842$	5.04474	0.173853
$843$	14.1501	0.487356
$844$	−53.3604	−1.83674
$845$	0	0
$846$	0.224872	0.00773126
$847$	−7.99506	−0.274713
$848$	−29.6172	−1.01706
$849$	−6.92845	−0.237784
$850$	−0.419017	−0.0143722
$851$	5.04445	0.172921
$852$	3.63765	0.124624
$853$	6.50913	0.222868	0.111434	−	0.993772i	$-0.464456\pi$
$853$	6.50913	0.222868	0.111434	+	0.993772i	$0.464456\pi$
$854$	−1.09081	−0.0373266
$855$	9.91464	0.339074
$856$	2.03592	0.0695865
$857$	30.2446	1.03314	0.516568	−	0.856246i	$-0.327210\pi$
$857$	30.2446	1.03314	0.516568	+	0.856246i	$0.327210\pi$
$858$	0	0
$859$	−6.33055	−0.215995	−0.107998	−	0.994151i	$-0.534444\pi$
$859$	−6.33055	−0.215995	−0.107998	+	0.994151i	$0.534444\pi$
$860$	−7.87346	−0.268483
$861$	−1.49077	−0.0508052
$862$	−4.39744	−0.149778
$863$	−14.8043	−0.503943	−0.251971	−	0.967735i	$-0.581079\pi$
$863$	−14.8043	−0.503943	−0.251971	+	0.967735i	$0.581079\pi$
$864$	6.77661	0.230545
$865$	13.1058	0.445612
$866$	−1.84317	−0.0626334
$867$	−5.88396	−0.199830
$868$	4.68489	0.159016
$869$	−20.6598	−0.700835
$870$	−0.493128	−0.0167186
$871$	0	0
$872$	−2.68520	−0.0909322
$873$	3.60303	0.121944
$874$	0.641999	0.0217159
$875$	1.00000	0.0338062
$876$	−23.1963	−0.783729
$877$	−34.6830	−1.17116	−0.585580	−	0.810614i	$-0.699133\pi$
$877$	−34.6830	−1.17116	−0.585580	+	0.810614i	$0.699133\pi$
$878$	4.03630	0.136218
$879$	−11.0720	−0.373451
$880$	6.74052	0.227223
$881$	5.04828	0.170081	0.0850405	−	0.996377i	$-0.472898\pi$
$881$	5.04828	0.170081	0.0850405	+	0.996377i	$0.472898\pi$
$882$	0.327565	0.0110297
$883$	−22.3759	−0.753009	−0.376505	−	0.926415i	$-0.622874\pi$
$883$	−22.3759	−0.753009	−0.376505	+	0.926415i	$0.622874\pi$
$884$	0	0
$885$	−1.42256	−0.0478189
$886$	4.55225	0.152936
$887$	0.351445	0.0118004	0.00590018	−	0.999983i	$-0.498122\pi$
$887$	0.351445	0.0118004	0.00590018	+	0.999983i	$0.498122\pi$
$888$	1.87063	0.0627742
$889$	3.35964	0.112679
$890$	−1.58799	−0.0532295
$891$	6.84416	0.229288
$892$	−19.9656	−0.668497
$893$	−2.83777	−0.0949624
$894$	−0.967965	−0.0323736
$895$	−13.4321	−0.448985
$896$	4.26896	0.142616
$897$	0	0
$898$	2.84293	0.0948697
$899$	−11.0082	−0.367145
$900$	4.75225	0.158408
$901$	−23.3691	−0.778537
$902$	0.455057	0.0151517
$903$	3.08195	0.102561
$904$	5.31695	0.176839
$905$	13.1135	0.435908
$906$	−1.80517	−0.0599728
$907$	−45.4303	−1.50849	−0.754245	−	0.656593i	$-0.771997\pi$
$907$	−45.4303	−1.50849	−0.754245	+	0.656593i	$0.771997\pi$
$908$	16.5411	0.548936
$909$	−15.5126	−0.514521
$910$	0	0
$911$	39.8982	1.32189	0.660944	−	0.750435i	$-0.270156\pi$
$911$	39.8982	1.32189	0.660944	+	0.750435i	$0.270156\pi$
$912$	−12.4662	−0.412798
$913$	14.6423	0.484590
$914$	−1.95197	−0.0645654
$915$	6.19455	0.204785
$916$	−22.7117	−0.750416
$917$	−5.28820	−0.174632
$918$	1.75439	0.0579034
$919$	−21.5269	−0.710108	−0.355054	−	0.934846i	$-0.615538\pi$
$919$	−21.5269	−0.710108	−0.355054	+	0.934846i	$0.615538\pi$
$920$	0.618338	0.0203860
$921$	−0.768439	−0.0253209
$922$	−2.12227	−0.0698933
$923$	0	0
$924$	−2.66379	−0.0876323
$925$	4.43585	0.145850
$926$	−0.523890	−0.0172161
$927$	0.689087	0.0226326
$928$	−7.53526	−0.247357
$929$	13.8905	0.455733	0.227866	−	0.973692i	$-0.426825\pi$
$929$	13.8905	0.455733	0.227866	+	0.973692i	$0.426825\pi$
$930$	0.250449	0.00821254
$931$	−4.13370	−0.135477
$932$	−32.9473	−1.07922
$933$	−13.0411	−0.426946
$934$	−2.08812	−0.0683253
$935$	5.31852	0.173934
$936$	0	0
$937$	−7.14874	−0.233539	−0.116770	−	0.993159i	$-0.537254\pi$
$937$	−7.14874	−0.233539	−0.116770	+	0.993159i	$0.537254\pi$
$938$	0.610811	0.0199437
$939$	−13.2513	−0.432439
$940$	−1.36019	−0.0443645
$941$	−1.48540	−0.0484227	−0.0242114	−	0.999707i	$-0.507707\pi$
$941$	−1.48540	−0.0484227	−0.0242114	+	0.999707i	$0.507707\pi$
$942$	0.794636	0.0258906
$943$	−2.18587	−0.0711819
$944$	−7.13222	−0.232134
$945$	−4.18691	−0.136200
$946$	−0.940766	−0.0305870
$947$	7.72633	0.251072	0.125536	−	0.992089i	$-0.459935\pi$
$947$	7.72633	0.251072	0.125536	+	0.992089i	$0.459935\pi$
$948$	18.3143	0.594820
$949$	0	0
$950$	0.564544	0.0183162
$951$	25.5318	0.827925
$952$	1.66825	0.0540684
$953$	9.43975	0.305783	0.152892	−	0.988243i	$-0.451141\pi$
$953$	9.43975	0.305783	0.152892	+	0.988243i	$0.451141\pi$
$954$	−2.49497	−0.0807778
$955$	4.34955	0.140748
$956$	25.2717	0.817344
$957$	6.25919	0.202331
$958$	−4.70283	−0.151941
$959$	3.48871	0.112656
$960$	−5.86008	−0.189133
$961$	−25.4092	−0.819650
$962$	0	0
$963$	−8.98070	−0.289399
$964$	−17.3811	−0.559806
$965$	−12.6870	−0.408409
$966$	−0.120453	−0.00387550
$967$	38.2850	1.23116	0.615581	−	0.788074i	$-0.288921\pi$
$967$	38.2850	1.23116	0.615581	+	0.788074i	$0.288921\pi$
$968$	−4.34721	−0.139725
$969$	−9.83633	−0.315988
$970$	0.205158	0.00658723
$971$	−1.65230	−0.0530250	−0.0265125	−	0.999648i	$-0.508440\pi$
$971$	−1.65230	−0.0530250	−0.0265125	+	0.999648i	$0.508440\pi$
$972$	−30.9543	−0.992860
$973$	−19.4299	−0.622895
$974$	0.829879	0.0265910
$975$	0	0
$976$	31.0573	0.994119
$977$	−48.2062	−1.54225	−0.771127	−	0.636681i	$-0.780307\pi$
$977$	−48.2062	−1.54225	−0.771127	+	0.636681i	$0.780307\pi$
$978$	−1.60446	−0.0513049
$979$	20.1561	0.644191
$980$	−1.98135	−0.0632919
$981$	11.8447	0.378173
$982$	−2.41739	−0.0771420
$983$	25.4821	0.812753	0.406377	−	0.913706i	$-0.366792\pi$
$983$	25.4821	0.812753	0.406377	+	0.913706i	$0.366792\pi$
$984$	−0.810586	−0.0258406
$985$	19.9430	0.635436
$986$	−1.95079	−0.0621258
$987$	0.532426	0.0169473
$988$	0	0
$989$	4.51899	0.143695
$990$	0.567826	0.0180467
$991$	44.6135	1.41719	0.708597	−	0.705613i	$-0.249328\pi$
$991$	44.6135	1.41719	0.708597	+	0.705613i	$0.249328\pi$
$992$	3.82699	0.121507
$993$	0.484442	0.0153733
$994$	0.323294	0.0102543
$995$	−10.4397	−0.330960
$996$	−12.9800	−0.411286
$997$	−54.9545	−1.74043	−0.870213	−	0.492676i	$-0.836019\pi$
$997$	−54.9545	−1.74043	−0.870213	+	0.492676i	$0.836019\pi$
$998$	−3.83367	−0.121353
$999$	−18.5725	−0.587608

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5915.2.a.bp.1.10	yes	21
13.12	even	2		5915.2.a.bo.1.12	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5915.2.a.bo.1.12	✓	21	13.12	even	2
5915.2.a.bp.1.10	yes	21	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:	\( N \)	\(=\)	\( 5915 = 5 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5915.a (trivial)

\(f(q)\)	\(=\)	\(q-0.136571 q^{2} +0.775570 q^{3} -1.98135 q^{4} +1.00000 q^{5} -0.105921 q^{6} +1.00000 q^{7} +0.543737 q^{8} -2.39849 q^{9} +O(q^{10})\)	\(q-0.136571 q^{2} +0.775570 q^{3} -1.98135 q^{4} +1.00000 q^{5} -0.105921 q^{6} +1.00000 q^{7} +0.543737 q^{8} -2.39849 q^{9} -0.136571 q^{10} +1.73348 q^{11} -1.53668 q^{12} -0.136571 q^{14} +0.775570 q^{15} +3.88844 q^{16} +3.06812 q^{17} +0.327565 q^{18} -4.13370 q^{19} -1.98135 q^{20} +0.775570 q^{21} -0.236743 q^{22} +1.13720 q^{23} +0.421707 q^{24} +1.00000 q^{25} -4.18691 q^{27} -1.98135 q^{28} +4.65564 q^{29} -0.105921 q^{30} -2.36450 q^{31} -1.61852 q^{32} +1.34443 q^{33} -0.419017 q^{34} +1.00000 q^{35} +4.75225 q^{36} +4.43585 q^{37} +0.564544 q^{38} +0.543737 q^{40} -1.92216 q^{41} -0.105921 q^{42} +3.97379 q^{43} -3.43462 q^{44} -2.39849 q^{45} -0.155309 q^{46} +0.686497 q^{47} +3.01576 q^{48} +1.00000 q^{49} -0.136571 q^{50} +2.37954 q^{51} -7.61674 q^{53} +0.571811 q^{54} +1.73348 q^{55} +0.543737 q^{56} -3.20598 q^{57} -0.635826 q^{58} -1.83421 q^{59} -1.53668 q^{60} +7.98708 q^{61} +0.322922 q^{62} -2.39849 q^{63} -7.55583 q^{64} -0.183611 q^{66} -4.47247 q^{67} -6.07902 q^{68} +0.881978 q^{69} -0.136571 q^{70} -2.36722 q^{71} -1.30415 q^{72} +15.0951 q^{73} -0.605810 q^{74} +0.775570 q^{75} +8.19030 q^{76} +1.73348 q^{77} -11.9181 q^{79} +3.88844 q^{80} +3.94823 q^{81} +0.262511 q^{82} +8.44680 q^{83} -1.53668 q^{84} +3.06812 q^{85} -0.542705 q^{86} +3.61077 q^{87} +0.942556 q^{88} +11.6275 q^{89} +0.327565 q^{90} -2.25319 q^{92} -1.83383 q^{93} -0.0937557 q^{94} -4.13370 q^{95} -1.25528 q^{96} -1.50221 q^{97} -0.136571 q^{98} -4.15773 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 4 q^{2} + 5 q^{3} + 20 q^{4} + 21 q^{5} + 4 q^{6} + 21 q^{7} + 9 q^{8} + 28 q^{9}+O(q^{10}) \) 21 * q + 4 * q^2 + 5 * q^3 + 20 * q^4 + 21 * q^5 + 4 * q^6 + 21 * q^7 + 9 * q^8 + 28 * q^9	\( 21 q + 4 q^{2} + 5 q^{3} + 20 q^{4} + 21 q^{5} + 4 q^{6} + 21 q^{7} + 9 q^{8} + 28 q^{9} + 4 q^{10} + 2 q^{11} + 23 q^{12} + 4 q^{14} + 5 q^{15} + 18 q^{16} - 6 q^{17} + 32 q^{18} + 8 q^{19} + 20 q^{20} + 5 q^{21} - 17 q^{22} - 14 q^{23} + 27 q^{24} + 21 q^{25} + 11 q^{27} + 20 q^{28} + 20 q^{29} + 4 q^{30} + 22 q^{31} + 22 q^{32} + 33 q^{33} + 22 q^{34} + 21 q^{35} - 8 q^{36} + 48 q^{37} + 42 q^{38} + 9 q^{40} - 5 q^{41} + 4 q^{42} - 27 q^{43} - 4 q^{44} + 28 q^{45} + 9 q^{46} + 27 q^{48} + 21 q^{49} + 4 q^{50} - 4 q^{51} - 28 q^{53} + 27 q^{54} + 2 q^{55} + 9 q^{56} + 56 q^{57} + 44 q^{58} + 7 q^{59} + 23 q^{60} + 25 q^{61} - 17 q^{62} + 28 q^{63} + 47 q^{64} - 30 q^{66} + 40 q^{67} - 19 q^{68} + 13 q^{69} + 4 q^{70} + 15 q^{71} + 42 q^{72} + 16 q^{73} + 37 q^{74} + 5 q^{75} + 58 q^{76} + 2 q^{77} - 10 q^{79} + 18 q^{80} + 25 q^{81} + 14 q^{82} - 11 q^{83} + 23 q^{84} - 6 q^{85} + 35 q^{86} + 65 q^{87} - 74 q^{88} + 24 q^{89} + 32 q^{90} - 89 q^{92} + 82 q^{93} + 21 q^{94} + 8 q^{95} - 22 q^{96} + 57 q^{97} + 4 q^{98} + 6 q^{99}+O(q^{100}) \) 21 * q + 4 * q^2 + 5 * q^3 + 20 * q^4 + 21 * q^5 + 4 * q^6 + 21 * q^7 + 9 * q^8 + 28 * q^9 + 4 * q^10 + 2 * q^11 + 23 * q^12 + 4 * q^14 + 5 * q^15 + 18 * q^16 - 6 * q^17 + 32 * q^18 + 8 * q^19 + 20 * q^20 + 5 * q^21 - 17 * q^22 - 14 * q^23 + 27 * q^24 + 21 * q^25 + 11 * q^27 + 20 * q^28 + 20 * q^29 + 4 * q^30 + 22 * q^31 + 22 * q^32 + 33 * q^33 + 22 * q^34 + 21 * q^35 - 8 * q^36 + 48 * q^37 + 42 * q^38 + 9 * q^40 - 5 * q^41 + 4 * q^42 - 27 * q^43 - 4 * q^44 + 28 * q^45 + 9 * q^46 + 27 * q^48 + 21 * q^49 + 4 * q^50 - 4 * q^51 - 28 * q^53 + 27 * q^54 + 2 * q^55 + 9 * q^56 + 56 * q^57 + 44 * q^58 + 7 * q^59 + 23 * q^60 + 25 * q^61 - 17 * q^62 + 28 * q^63 + 47 * q^64 - 30 * q^66 + 40 * q^67 - 19 * q^68 + 13 * q^69 + 4 * q^70 + 15 * q^71 + 42 * q^72 + 16 * q^73 + 37 * q^74 + 5 * q^75 + 58 * q^76 + 2 * q^77 - 10 * q^79 + 18 * q^80 + 25 * q^81 + 14 * q^82 - 11 * q^83 + 23 * q^84 - 6 * q^85 + 35 * q^86 + 65 * q^87 - 74 * q^88 + 24 * q^89 + 32 * q^90 - 89 * q^92 + 82 * q^93 + 21 * q^94 + 8 * q^95 - 22 * q^96 + 57 * q^97 + 4 * q^98 + 6 * q^99

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