LMFDB - Embedded newform 5415.2.a.s.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5415,2,Mod(1,5415)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5415, 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("5415.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5415 = 3 \cdot 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5415.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:	$43.2389926945$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{7}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 7 $ x^2 - 7
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 285)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.64575$ of defining polynomial
Character	$\chi$	$=$	5415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.64575 q^{2} +1.00000 q^{3} +5.00000 q^{4} +1.00000 q^{5} +2.64575 q^{6} +1.64575 q^{7} +7.93725 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.64575 q^{2} +1.00000 q^{3} +5.00000 q^{4} +1.00000 q^{5} +2.64575 q^{6} +1.64575 q^{7} +7.93725 q^{8} +1.00000 q^{9} +2.64575 q^{10} +0.354249 q^{11} +5.00000 q^{12} +0.354249 q^{13} +4.35425 q^{14} +1.00000 q^{15} +11.0000 q^{16} -4.00000 q^{17} +2.64575 q^{18} +5.00000 q^{20} +1.64575 q^{21} +0.937254 q^{22} +9.29150 q^{23} +7.93725 q^{24} +1.00000 q^{25} +0.937254 q^{26} +1.00000 q^{27} +8.22876 q^{28} -8.93725 q^{29} +2.64575 q^{30} -6.00000 q^{31} +13.2288 q^{32} +0.354249 q^{33} -10.5830 q^{34} +1.64575 q^{35} +5.00000 q^{36} -3.64575 q^{37} +0.354249 q^{39} +7.93725 q^{40} +9.64575 q^{41} +4.35425 q^{42} +5.64575 q^{43} +1.77124 q^{44} +1.00000 q^{45} +24.5830 q^{46} -1.29150 q^{47} +11.0000 q^{48} -4.29150 q^{49} +2.64575 q^{50} -4.00000 q^{51} +1.77124 q^{52} -11.2915 q^{53} +2.64575 q^{54} +0.354249 q^{55} +13.0627 q^{56} -23.6458 q^{58} -11.2915 q^{59} +5.00000 q^{60} -11.2915 q^{61} -15.8745 q^{62} +1.64575 q^{63} +13.0000 q^{64} +0.354249 q^{65} +0.937254 q^{66} +6.58301 q^{67} -20.0000 q^{68} +9.29150 q^{69} +4.35425 q^{70} -7.29150 q^{71} +7.93725 q^{72} +10.0000 q^{73} -9.64575 q^{74} +1.00000 q^{75} +0.583005 q^{77} +0.937254 q^{78} -6.58301 q^{79} +11.0000 q^{80} +1.00000 q^{81} +25.5203 q^{82} +6.00000 q^{83} +8.22876 q^{84} -4.00000 q^{85} +14.9373 q^{86} -8.93725 q^{87} +2.81176 q^{88} +16.9373 q^{89} +2.64575 q^{90} +0.583005 q^{91} +46.4575 q^{92} -6.00000 q^{93} -3.41699 q^{94} +13.2288 q^{96} +2.93725 q^{97} -11.3542 q^{98} +0.354249 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} + 10 q^{4} + 2 q^{5} - 2 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^3 + 10 * q^4 + 2 * q^5 - 2 * q^7 + 2 * q^9	$ 2 q + 2 q^{3} + 10 q^{4} + 2 q^{5} - 2 q^{7} + 2 q^{9} + 6 q^{11} + 10 q^{12} + 6 q^{13} + 14 q^{14} + 2 q^{15} + 22 q^{16} - 8 q^{17} + 10 q^{20} - 2 q^{21} - 14 q^{22} + 8 q^{23} + 2 q^{25} - 14 q^{26} + 2 q^{27} - 10 q^{28} - 2 q^{29} - 12 q^{31} + 6 q^{33} - 2 q^{35} + 10 q^{36} - 2 q^{37} + 6 q^{39} + 14 q^{41} + 14 q^{42} + 6 q^{43} + 30 q^{44} + 2 q^{45} + 28 q^{46} + 8 q^{47} + 22 q^{48} + 2 q^{49} - 8 q^{51} + 30 q^{52} - 12 q^{53} + 6 q^{55} + 42 q^{56} - 42 q^{58} - 12 q^{59} + 10 q^{60} - 12 q^{61} - 2 q^{63} + 26 q^{64} + 6 q^{65} - 14 q^{66} - 8 q^{67} - 40 q^{68} + 8 q^{69} + 14 q^{70} - 4 q^{71} + 20 q^{73} - 14 q^{74} + 2 q^{75} - 20 q^{77} - 14 q^{78} + 8 q^{79} + 22 q^{80} + 2 q^{81} + 14 q^{82} + 12 q^{83} - 10 q^{84} - 8 q^{85} + 14 q^{86} - 2 q^{87} - 42 q^{88} + 18 q^{89} - 20 q^{91} + 40 q^{92} - 12 q^{93} - 28 q^{94} - 10 q^{97} - 28 q^{98} + 6 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 + 10 * q^4 + 2 * q^5 - 2 * q^7 + 2 * q^9 + 6 * q^11 + 10 * q^12 + 6 * q^13 + 14 * q^14 + 2 * q^15 + 22 * q^16 - 8 * q^17 + 10 * q^20 - 2 * q^21 - 14 * q^22 + 8 * q^23 + 2 * q^25 - 14 * q^26 + 2 * q^27 - 10 * q^28 - 2 * q^29 - 12 * q^31 + 6 * q^33 - 2 * q^35 + 10 * q^36 - 2 * q^37 + 6 * q^39 + 14 * q^41 + 14 * q^42 + 6 * q^43 + 30 * q^44 + 2 * q^45 + 28 * q^46 + 8 * q^47 + 22 * q^48 + 2 * q^49 - 8 * q^51 + 30 * q^52 - 12 * q^53 + 6 * q^55 + 42 * q^56 - 42 * q^58 - 12 * q^59 + 10 * q^60 - 12 * q^61 - 2 * q^63 + 26 * q^64 + 6 * q^65 - 14 * q^66 - 8 * q^67 - 40 * q^68 + 8 * q^69 + 14 * q^70 - 4 * q^71 + 20 * q^73 - 14 * q^74 + 2 * q^75 - 20 * q^77 - 14 * q^78 + 8 * q^79 + 22 * q^80 + 2 * q^81 + 14 * q^82 + 12 * q^83 - 10 * q^84 - 8 * q^85 + 14 * q^86 - 2 * q^87 - 42 * q^88 + 18 * q^89 - 20 * q^91 + 40 * q^92 - 12 * q^93 - 28 * q^94 - 10 * q^97 - 28 * 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 $

$2$	2.64575	1.87083	0.935414	−	0.353553i	$-0.115027\pi$
$2$	2.64575	1.87083	0.935414	+	0.353553i	$0.115027\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.00000	2.50000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.64575	1.08012
$7$	1.64575	0.622036	0.311018	−	0.950404i	$-0.399330\pi$
$7$	1.64575	0.622036	0.311018	+	0.950404i	$0.399330\pi$
$8$	7.93725	2.80624
$9$	1.00000	0.333333
$10$	2.64575	0.836660
$11$	0.354249	0.106810	0.0534050	−	0.998573i	$-0.482993\pi$
$11$	0.354249	0.106810	0.0534050	+	0.998573i	$0.482993\pi$
$12$	5.00000	1.44338
$13$	0.354249	0.0982509	0.0491255	−	0.998793i	$-0.484357\pi$
$13$	0.354249	0.0982509	0.0491255	+	0.998793i	$0.484357\pi$
$14$	4.35425	1.16372
$15$	1.00000	0.258199
$16$	11.0000	2.75000
$17$	−4.00000	−0.970143	−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000	−0.970143	−0.485071	+	0.874475i	$0.661206\pi$
$18$	2.64575	0.623610
$19$	0	0
$19$	0	0
$20$	5.00000	1.11803
$21$	1.64575	0.359132
$22$	0.937254	0.199823
$23$	9.29150	1.93741	0.968706	−	0.248211i	$-0.0798425\pi$
$23$	9.29150	1.93741	0.968706	+	0.248211i	$0.0798425\pi$
$24$	7.93725	1.62019
$25$	1.00000	0.200000
$26$	0.937254	0.183811
$27$	1.00000	0.192450
$28$	8.22876	1.55509
$29$	−8.93725	−1.65961	−0.829803	−	0.558056i	$-0.811547\pi$
$29$	−8.93725	−1.65961	−0.829803	+	0.558056i	$0.811547\pi$
$30$	2.64575	0.483046
$31$	−6.00000	−1.07763	−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000	−1.07763	−0.538816	+	0.842424i	$0.681128\pi$
$32$	13.2288	2.33854
$33$	0.354249	0.0616668
$34$	−10.5830	−1.81497
$35$	1.64575	0.278183
$36$	5.00000	0.833333
$37$	−3.64575	−0.599358	−0.299679	−	0.954040i	$-0.596880\pi$
$37$	−3.64575	−0.599358	−0.299679	+	0.954040i	$0.596880\pi$
$38$	0	0
$39$	0.354249	0.0567252
$40$	7.93725	1.25499
$41$	9.64575	1.50641	0.753207	−	0.657784i	$-0.228506\pi$
$41$	9.64575	1.50641	0.753207	+	0.657784i	$0.228506\pi$
$42$	4.35425	0.671875
$43$	5.64575	0.860969	0.430485	−	0.902598i	$-0.358343\pi$
$43$	5.64575	0.860969	0.430485	+	0.902598i	$0.358343\pi$
$44$	1.77124	0.267025
$45$	1.00000	0.149071
$46$	24.5830	3.62457
$47$	−1.29150	−0.188385	−0.0941925	−	0.995554i	$-0.530027\pi$
$47$	−1.29150	−0.188385	−0.0941925	+	0.995554i	$0.530027\pi$
$48$	11.0000	1.58771
$49$	−4.29150	−0.613072
$50$	2.64575	0.374166
$51$	−4.00000	−0.560112
$52$	1.77124	0.245627
$53$	−11.2915	−1.55101	−0.775504	−	0.631343i	$-0.782504\pi$
$53$	−11.2915	−1.55101	−0.775504	+	0.631343i	$0.782504\pi$
$54$	2.64575	0.360041
$55$	0.354249	0.0477669
$56$	13.0627	1.74558
$57$	0	0
$58$	−23.6458	−3.10484
$59$	−11.2915	−1.47003	−0.735014	−	0.678052i	$-0.762825\pi$
$59$	−11.2915	−1.47003	−0.735014	+	0.678052i	$0.762825\pi$
$60$	5.00000	0.645497
$61$	−11.2915	−1.44573	−0.722864	−	0.690990i	$-0.757175\pi$
$61$	−11.2915	−1.44573	−0.722864	+	0.690990i	$0.757175\pi$
$62$	−15.8745	−2.01606
$63$	1.64575	0.207345
$64$	13.0000	1.62500
$65$	0.354249	0.0439391
$66$	0.937254	0.115368
$67$	6.58301	0.804242	0.402121	−	0.915587i	$-0.368273\pi$
$67$	6.58301	0.804242	0.402121	+	0.915587i	$0.368273\pi$
$68$	−20.0000	−2.42536
$69$	9.29150	1.11857
$70$	4.35425	0.520432
$71$	−7.29150	−0.865342	−0.432671	−	0.901552i	$-0.642429\pi$
$71$	−7.29150	−0.865342	−0.432671	+	0.901552i	$0.642429\pi$
$72$	7.93725	0.935414
$73$	10.0000	1.17041	0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000	1.17041	0.585206	+	0.810885i	$0.301014\pi$
$74$	−9.64575	−1.12130
$75$	1.00000	0.115470
$76$	0	0
$77$	0.583005	0.0664396
$78$	0.937254	0.106123
$79$	−6.58301	−0.740646	−0.370323	−	0.928903i	$-0.620753\pi$
$79$	−6.58301	−0.740646	−0.370323	+	0.928903i	$0.620753\pi$
$80$	11.0000	1.22984
$81$	1.00000	0.111111
$82$	25.5203	2.81824
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	8.22876	0.897831
$85$	−4.00000	−0.433861
$86$	14.9373	1.61073
$87$	−8.93725	−0.958174
$88$	2.81176	0.299735
$89$	16.9373	1.79535	0.897673	−	0.440663i	$-0.145257\pi$
$89$	16.9373	1.79535	0.897673	+	0.440663i	$0.145257\pi$
$90$	2.64575	0.278887
$91$	0.583005	0.0611156
$92$	46.4575	4.84353
$93$	−6.00000	−0.622171
$94$	−3.41699	−0.352436
$95$	0	0
$96$	13.2288	1.35015
$97$	2.93725	0.298233	0.149116	−	0.988820i	$-0.452357\pi$
$97$	2.93725	0.298233	0.149116	+	0.988820i	$0.452357\pi$
$98$	−11.3542	−1.14695
$99$	0.354249	0.0356033
$100$	5.00000	0.500000
$101$	9.29150	0.924539	0.462270	−	0.886739i	$-0.347035\pi$
$101$	9.29150	0.924539	0.462270	+	0.886739i	$0.347035\pi$
$102$	−10.5830	−1.04787
$103$	10.5830	1.04277	0.521387	−	0.853320i	$-0.325415\pi$
$103$	10.5830	1.04277	0.521387	+	0.853320i	$0.325415\pi$
$104$	2.81176	0.275716
$105$	1.64575	0.160609
$106$	−29.8745	−2.90167
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	5.00000	0.481125
$109$	−5.29150	−0.506834	−0.253417	−	0.967357i	$-0.581554\pi$
$109$	−5.29150	−0.506834	−0.253417	+	0.967357i	$0.581554\pi$
$110$	0.937254	0.0893637
$111$	−3.64575	−0.346039
$112$	18.1033	1.71060
$113$	4.00000	0.376288	0.188144	−	0.982141i	$-0.439753\pi$
$113$	4.00000	0.376288	0.188144	+	0.982141i	$0.439753\pi$
$114$	0	0
$115$	9.29150	0.866437
$116$	−44.6863	−4.14902
$117$	0.354249	0.0327503
$118$	−29.8745	−2.75017
$119$	−6.58301	−0.603463
$120$	7.93725	0.724569
$121$	−10.8745	−0.988592
$122$	−29.8745	−2.70471
$123$	9.64575	0.869728
$124$	−30.0000	−2.69408
$125$	1.00000	0.0894427
$126$	4.35425	0.387907
$127$	−4.00000	−0.354943	−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000	−0.354943	−0.177471	+	0.984126i	$0.556792\pi$
$128$	7.93725	0.701561
$129$	5.64575	0.497081
$130$	0.937254	0.0822026
$131$	−14.2288	−1.24317	−0.621586	−	0.783346i	$-0.713511\pi$
$131$	−14.2288	−1.24317	−0.621586	+	0.783346i	$0.713511\pi$
$132$	1.77124	0.154167
$133$	0	0
$134$	17.4170	1.50460
$135$	1.00000	0.0860663
$136$	−31.7490	−2.72246
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	24.5830	2.09264
$139$	17.8745	1.51610	0.758048	−	0.652199i	$-0.226153\pi$
$139$	17.8745	1.51610	0.758048	+	0.652199i	$0.226153\pi$
$140$	8.22876	0.695457
$141$	−1.29150	−0.108764
$142$	−19.2915	−1.61891
$143$	0.125492	0.0104942
$144$	11.0000	0.916667
$145$	−8.93725	−0.742199
$146$	26.4575	2.18964
$147$	−4.29150	−0.353957
$148$	−18.2288	−1.49839
$149$	−20.5830	−1.68623	−0.843113	−	0.537737i	$-0.819279\pi$
$149$	−20.5830	−1.68623	−0.843113	+	0.537737i	$0.819279\pi$
$150$	2.64575	0.216025
$151$	8.58301	0.698475	0.349238	−	0.937034i	$-0.386441\pi$
$151$	8.58301	0.698475	0.349238	+	0.937034i	$0.386441\pi$
$152$	0	0
$153$	−4.00000	−0.323381
$154$	1.54249	0.124297
$155$	−6.00000	−0.481932
$156$	1.77124	0.141813
$157$	−13.2915	−1.06078	−0.530389	−	0.847755i	$-0.677954\pi$
$157$	−13.2915	−1.06078	−0.530389	+	0.847755i	$0.677954\pi$
$158$	−17.4170	−1.38562
$159$	−11.2915	−0.895474
$160$	13.2288	1.04583
$161$	15.2915	1.20514
$162$	2.64575	0.207870
$163$	−2.35425	−0.184399	−0.0921995	−	0.995741i	$-0.529390\pi$
$163$	−2.35425	−0.184399	−0.0921995	+	0.995741i	$0.529390\pi$
$164$	48.2288	3.76603
$165$	0.354249	0.0275782
$166$	15.8745	1.23210
$167$	21.2915	1.64759	0.823793	−	0.566891i	$-0.191854\pi$
$167$	21.2915	1.64759	0.823793	+	0.566891i	$0.191854\pi$
$168$	13.0627	1.00781
$169$	−12.8745	−0.990347
$170$	−10.5830	−0.811679
$171$	0	0
$172$	28.2288	2.15242
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	−23.6458	−1.79258
$175$	1.64575	0.124407
$176$	3.89674	0.293727
$177$	−11.2915	−0.848721
$178$	44.8118	3.35878
$179$	7.29150	0.544992	0.272496	−	0.962157i	$-0.412151\pi$
$179$	7.29150	0.544992	0.272496	+	0.962157i	$0.412151\pi$
$180$	5.00000	0.372678
$181$	−17.2915	−1.28527	−0.642634	−	0.766174i	$-0.722158\pi$
$181$	−17.2915	−1.28527	−0.642634	+	0.766174i	$0.722158\pi$
$182$	1.54249	0.114337
$183$	−11.2915	−0.834692
$184$	73.7490	5.43685
$185$	−3.64575	−0.268041
$186$	−15.8745	−1.16398
$187$	−1.41699	−0.103621
$188$	−6.45751	−0.470963
$189$	1.64575	0.119711
$190$	0	0
$191$	6.22876	0.450697	0.225349	−	0.974278i	$-0.427648\pi$
$191$	6.22876	0.450697	0.225349	+	0.974278i	$0.427648\pi$
$192$	13.0000	0.938194
$193$	11.6458	0.838280	0.419140	−	0.907922i	$-0.362332\pi$
$193$	11.6458	0.838280	0.419140	+	0.907922i	$0.362332\pi$
$194$	7.77124	0.557943
$195$	0.354249	0.0253683
$196$	−21.4575	−1.53268
$197$	−25.1660	−1.79300	−0.896502	−	0.443040i	$-0.853900\pi$
$197$	−25.1660	−1.79300	−0.896502	+	0.443040i	$0.853900\pi$
$198$	0.937254	0.0666077
$199$	7.29150	0.516881	0.258440	−	0.966027i	$-0.416791\pi$
$199$	7.29150	0.516881	0.258440	+	0.966027i	$0.416791\pi$
$200$	7.93725	0.561249
$201$	6.58301	0.464329
$202$	24.5830	1.72965
$203$	−14.7085	−1.03233
$204$	−20.0000	−1.40028
$205$	9.64575	0.673688
$206$	28.0000	1.95085
$207$	9.29150	0.645804
$208$	3.89674	0.270190
$209$	0	0
$210$	4.35425	0.300472
$211$	−2.58301	−0.177821	−0.0889107	−	0.996040i	$-0.528339\pi$
$211$	−2.58301	−0.177821	−0.0889107	+	0.996040i	$0.528339\pi$
$212$	−56.4575	−3.87752
$213$	−7.29150	−0.499606
$214$	0	0
$215$	5.64575	0.385037
$216$	7.93725	0.540062
$217$	−9.87451	−0.670325
$218$	−14.0000	−0.948200
$219$	10.0000	0.675737
$220$	1.77124	0.119417
$221$	−1.41699	−0.0953174
$222$	−9.64575	−0.647380
$223$	−2.58301	−0.172971	−0.0864854	−	0.996253i	$-0.527564\pi$
$223$	−2.58301	−0.172971	−0.0864854	+	0.996253i	$0.527564\pi$
$224$	21.7712	1.45465
$225$	1.00000	0.0666667
$226$	10.5830	0.703971
$227$	10.7085	0.710748	0.355374	−	0.934724i	$-0.384354\pi$
$227$	10.7085	0.710748	0.355374	+	0.934724i	$0.384354\pi$
$228$	0	0
$229$	8.70850	0.575474	0.287737	−	0.957710i	$-0.407097\pi$
$229$	8.70850	0.575474	0.287737	+	0.957710i	$0.407097\pi$
$230$	24.5830	1.62096
$231$	0.583005	0.0383589
$232$	−70.9373	−4.65726
$233$	−18.0000	−1.17922	−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000	−1.17922	−0.589610	+	0.807688i	$0.700718\pi$
$234$	0.937254	0.0612702
$235$	−1.29150	−0.0842483
$236$	−56.4575	−3.67507
$237$	−6.58301	−0.427612
$238$	−17.4170	−1.12898
$239$	15.6458	1.01204	0.506020	−	0.862522i	$-0.331116\pi$
$239$	15.6458	1.01204	0.506020	+	0.862522i	$0.331116\pi$
$240$	11.0000	0.710047
$241$	−16.5830	−1.06821	−0.534103	−	0.845420i	$-0.679350\pi$
$241$	−16.5830	−1.06821	−0.534103	+	0.845420i	$0.679350\pi$
$242$	−28.7712	−1.84949
$243$	1.00000	0.0641500
$244$	−56.4575	−3.61432
$245$	−4.29150	−0.274174
$246$	25.5203	1.62711
$247$	0	0
$248$	−47.6235	−3.02410
$249$	6.00000	0.380235
$250$	2.64575	0.167332
$251$	−16.3542	−1.03227	−0.516136	−	0.856507i	$-0.672630\pi$
$251$	−16.3542	−1.03227	−0.516136	+	0.856507i	$0.672630\pi$
$252$	8.22876	0.518363
$253$	3.29150	0.206935
$254$	−10.5830	−0.664037
$255$	−4.00000	−0.250490
$256$	−5.00000	−0.312500
$257$	5.41699	0.337903	0.168951	−	0.985624i	$-0.445962\pi$
$257$	5.41699	0.337903	0.168951	+	0.985624i	$0.445962\pi$
$258$	14.9373	0.929953
$259$	−6.00000	−0.372822
$260$	1.77124	0.109848
$261$	−8.93725	−0.553202
$262$	−37.6458	−2.32576
$263$	4.58301	0.282600	0.141300	−	0.989967i	$-0.454872\pi$
$263$	4.58301	0.282600	0.141300	+	0.989967i	$0.454872\pi$
$264$	2.81176	0.173052
$265$	−11.2915	−0.693631
$266$	0	0
$267$	16.9373	1.03654
$268$	32.9150	2.01061
$269$	−4.22876	−0.257832	−0.128916	−	0.991656i	$-0.541150\pi$
$269$	−4.22876	−0.257832	−0.128916	+	0.991656i	$0.541150\pi$
$270$	2.64575	0.161015
$271$	−4.70850	−0.286021	−0.143010	−	0.989721i	$-0.545678\pi$
$271$	−4.70850	−0.286021	−0.143010	+	0.989721i	$0.545678\pi$
$272$	−44.0000	−2.66789
$273$	0.583005	0.0352851
$274$	15.8745	0.959014
$275$	0.354249	0.0213620
$276$	46.4575	2.79641
$277$	0.583005	0.0350294	0.0175147	−	0.999847i	$-0.494425\pi$
$277$	0.583005	0.0350294	0.0175147	+	0.999847i	$0.494425\pi$
$278$	47.2915	2.83636
$279$	−6.00000	−0.359211
$280$	13.0627	0.780648
$281$	32.2288	1.92261	0.961303	−	0.275493i	$-0.0888409\pi$
$281$	32.2288	1.92261	0.961303	+	0.275493i	$0.0888409\pi$
$282$	−3.41699	−0.203479
$283$	−11.5203	−0.684808	−0.342404	−	0.939553i	$-0.611241\pi$
$283$	−11.5203	−0.684808	−0.342404	+	0.939553i	$0.611241\pi$
$284$	−36.4575	−2.16336
$285$	0	0
$286$	0.332021	0.0196328
$287$	15.8745	0.937043
$288$	13.2288	0.779512
$289$	−1.00000	−0.0588235
$290$	−23.6458	−1.38853
$291$	2.93725	0.172185
$292$	50.0000	2.92603
$293$	−5.41699	−0.316464	−0.158232	−	0.987402i	$-0.550579\pi$
$293$	−5.41699	−0.316464	−0.158232	+	0.987402i	$0.550579\pi$
$294$	−11.3542	−0.662193
$295$	−11.2915	−0.657417
$296$	−28.9373	−1.68194
$297$	0.354249	0.0205556
$298$	−54.4575	−3.15464
$299$	3.29150	0.190353
$300$	5.00000	0.288675
$301$	9.29150	0.535553
$302$	22.7085	1.30673
$303$	9.29150	0.533783
$304$	0	0
$305$	−11.2915	−0.646550
$306$	−10.5830	−0.604990
$307$	24.4575	1.39586	0.697932	−	0.716164i	$-0.254104\pi$
$307$	24.4575	1.39586	0.697932	+	0.716164i	$0.254104\pi$
$308$	2.91503	0.166099
$309$	10.5830	0.602046
$310$	−15.8745	−0.901611
$311$	22.9373	1.30065	0.650326	−	0.759655i	$-0.274632\pi$
$311$	22.9373	1.30065	0.650326	+	0.759655i	$0.274632\pi$
$312$	2.81176	0.159185
$313$	17.2915	0.977374	0.488687	−	0.872459i	$-0.337476\pi$
$313$	17.2915	0.977374	0.488687	+	0.872459i	$0.337476\pi$
$314$	−35.1660	−1.98453
$315$	1.64575	0.0927276
$316$	−32.9150	−1.85161
$317$	−20.4575	−1.14901	−0.574504	−	0.818502i	$-0.694805\pi$
$317$	−20.4575	−1.14901	−0.574504	+	0.818502i	$0.694805\pi$
$318$	−29.8745	−1.67528
$319$	−3.16601	−0.177263
$320$	13.0000	0.726722
$321$	0	0
$322$	40.4575	2.25461
$323$	0	0
$324$	5.00000	0.277778
$325$	0.354249	0.0196502
$326$	−6.22876	−0.344979
$327$	−5.29150	−0.292621
$328$	76.5608	4.22736
$329$	−2.12549	−0.117182
$330$	0.937254	0.0515941
$331$	−11.4170	−0.627535	−0.313767	−	0.949500i	$-0.601591\pi$
$331$	−11.4170	−0.627535	−0.313767	+	0.949500i	$0.601591\pi$
$332$	30.0000	1.64646
$333$	−3.64575	−0.199786
$334$	56.3320	3.08235
$335$	6.58301	0.359668
$336$	18.1033	0.987614
$337$	−14.9373	−0.813684	−0.406842	−	0.913499i	$-0.633370\pi$
$337$	−14.9373	−0.813684	−0.406842	+	0.913499i	$0.633370\pi$
$338$	−34.0627	−1.85277
$339$	4.00000	0.217250
$340$	−20.0000	−1.08465
$341$	−2.12549	−0.115102
$342$	0	0
$343$	−18.5830	−1.00339
$344$	44.8118	2.41609
$345$	9.29150	0.500238
$346$	0	0
$347$	26.0000	1.39575	0.697877	−	0.716218i	$-0.254128\pi$
$347$	26.0000	1.39575	0.697877	+	0.716218i	$0.254128\pi$
$348$	−44.6863	−2.39544
$349$	23.1660	1.24005	0.620024	−	0.784583i	$-0.287123\pi$
$349$	23.1660	1.24005	0.620024	+	0.784583i	$0.287123\pi$
$350$	4.35425	0.232744
$351$	0.354249	0.0189084
$352$	4.68627	0.249779
$353$	0.583005	0.0310302	0.0155151	−	0.999880i	$-0.495061\pi$
$353$	0.583005	0.0310302	0.0155151	+	0.999880i	$0.495061\pi$
$354$	−29.8745	−1.58781
$355$	−7.29150	−0.386993
$356$	84.6863	4.48836
$357$	−6.58301	−0.348410
$358$	19.2915	1.01959
$359$	−36.1033	−1.90546	−0.952729	−	0.303822i	$-0.901737\pi$
$359$	−36.1033	−1.90546	−0.952729	+	0.303822i	$0.901737\pi$
$360$	7.93725	0.418330
$361$	0	0
$362$	−45.7490	−2.40451
$363$	−10.8745	−0.570764
$364$	2.91503	0.152789
$365$	10.0000	0.523424
$366$	−29.8745	−1.56157
$367$	1.64575	0.0859075	0.0429538	−	0.999077i	$-0.486323\pi$
$367$	1.64575	0.0859075	0.0429538	+	0.999077i	$0.486323\pi$
$368$	102.207	5.32788
$369$	9.64575	0.502138
$370$	−9.64575	−0.501459
$371$	−18.5830	−0.964782
$372$	−30.0000	−1.55543
$373$	−5.06275	−0.262139	−0.131070	−	0.991373i	$-0.541841\pi$
$373$	−5.06275	−0.262139	−0.131070	+	0.991373i	$0.541841\pi$
$374$	−3.74902	−0.193857
$375$	1.00000	0.0516398
$376$	−10.2510	−0.528654
$377$	−3.16601	−0.163058
$378$	4.35425	0.223958
$379$	−10.0000	−0.513665	−0.256833	−	0.966456i	$-0.582679\pi$
$379$	−10.0000	−0.513665	−0.256833	+	0.966456i	$0.582679\pi$
$380$	0	0
$381$	−4.00000	−0.204926
$382$	16.4797	0.843177
$383$	18.5830	0.949547	0.474774	−	0.880108i	$-0.342530\pi$
$383$	18.5830	0.949547	0.474774	+	0.880108i	$0.342530\pi$
$384$	7.93725	0.405046
$385$	0.583005	0.0297127
$386$	30.8118	1.56828
$387$	5.64575	0.286990
$388$	14.6863	0.745582
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	0.937254	0.0474597
$391$	−37.1660	−1.87957
$392$	−34.0627	−1.72043
$393$	−14.2288	−0.717746
$394$	−66.5830	−3.35440
$395$	−6.58301	−0.331227
$396$	1.77124	0.0890083
$397$	−2.00000	−0.100377	−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000	−0.100377	−0.0501886	+	0.998740i	$0.515982\pi$
$398$	19.2915	0.966996
$399$	0	0
$400$	11.0000	0.550000
$401$	4.93725	0.246555	0.123277	−	0.992372i	$-0.460660\pi$
$401$	4.93725	0.246555	0.123277	+	0.992372i	$0.460660\pi$
$402$	17.4170	0.868681
$403$	−2.12549	−0.105878
$404$	46.4575	2.31135
$405$	1.00000	0.0496904
$406$	−38.9150	−1.93132
$407$	−1.29150	−0.0640174
$408$	−31.7490	−1.57181
$409$	6.70850	0.331714	0.165857	−	0.986150i	$-0.446961\pi$
$409$	6.70850	0.331714	0.165857	+	0.986150i	$0.446961\pi$
$410$	25.5203	1.26036
$411$	6.00000	0.295958
$412$	52.9150	2.60694
$413$	−18.5830	−0.914410
$414$	24.5830	1.20819
$415$	6.00000	0.294528
$416$	4.68627	0.229763
$417$	17.8745	0.875318
$418$	0	0
$419$	38.9373	1.90221	0.951105	−	0.308869i	$-0.0999504\pi$
$419$	38.9373	1.90221	0.951105	+	0.308869i	$0.0999504\pi$
$420$	8.22876	0.401522
$421$	−28.5830	−1.39305	−0.696525	−	0.717532i	$-0.745272\pi$
$421$	−28.5830	−1.39305	−0.696525	+	0.717532i	$0.745272\pi$
$422$	−6.83399	−0.332673
$423$	−1.29150	−0.0627950
$424$	−89.6235	−4.35250
$425$	−4.00000	−0.194029
$426$	−19.2915	−0.934676
$427$	−18.5830	−0.899295
$428$	0	0
$429$	0.125492	0.00605882
$430$	14.9373	0.720338
$431$	−3.29150	−0.158546	−0.0792731	−	0.996853i	$-0.525260\pi$
$431$	−3.29150	−0.158546	−0.0792731	+	0.996853i	$0.525260\pi$
$432$	11.0000	0.529238
$433$	27.6458	1.32857	0.664285	−	0.747479i	$-0.268736\pi$
$433$	27.6458	1.32857	0.664285	+	0.747479i	$0.268736\pi$
$434$	−26.1255	−1.25406
$435$	−8.93725	−0.428509
$436$	−26.4575	−1.26709
$437$	0	0
$438$	26.4575	1.26419
$439$	1.41699	0.0676295	0.0338147	−	0.999428i	$-0.489234\pi$
$439$	1.41699	0.0676295	0.0338147	+	0.999428i	$0.489234\pi$
$440$	2.81176	0.134045
$441$	−4.29150	−0.204357
$442$	−3.74902	−0.178322
$443$	26.7085	1.26896	0.634480	−	0.772940i	$-0.281214\pi$
$443$	26.7085	1.26896	0.634480	+	0.772940i	$0.281214\pi$
$444$	−18.2288	−0.865099
$445$	16.9373	0.802903
$446$	−6.83399	−0.323599
$447$	−20.5830	−0.973543
$448$	21.3948	1.01081
$449$	36.2288	1.70974	0.854870	−	0.518842i	$-0.173637\pi$
$449$	36.2288	1.70974	0.854870	+	0.518842i	$0.173637\pi$
$450$	2.64575	0.124722
$451$	3.41699	0.160900
$452$	20.0000	0.940721
$453$	8.58301	0.403265
$454$	28.3320	1.32969
$455$	0.583005	0.0273317
$456$	0	0
$457$	0.125492	0.00587027	0.00293514	−	0.999996i	$-0.499066\pi$
$457$	0.125492	0.00587027	0.00293514	+	0.999996i	$0.499066\pi$
$458$	23.0405	1.07661
$459$	−4.00000	−0.186704
$460$	46.4575	2.16609
$461$	−37.7490	−1.75815	−0.879073	−	0.476686i	$-0.841838\pi$
$461$	−37.7490	−1.75815	−0.879073	+	0.476686i	$0.841838\pi$
$462$	1.54249	0.0717630
$463$	−35.5203	−1.65077	−0.825383	−	0.564573i	$-0.809041\pi$
$463$	−35.5203	−1.65077	−0.825383	+	0.564573i	$0.809041\pi$
$464$	−98.3098	−4.56392
$465$	−6.00000	−0.278243
$466$	−47.6235	−2.20612
$467$	19.8745	0.919683	0.459841	−	0.888001i	$-0.347906\pi$
$467$	19.8745	0.919683	0.459841	+	0.888001i	$0.347906\pi$
$468$	1.77124	0.0818758
$469$	10.8340	0.500267
$470$	−3.41699	−0.157614
$471$	−13.2915	−0.612440
$472$	−89.6235	−4.12526
$473$	2.00000	0.0919601
$474$	−17.4170	−0.799989
$475$	0	0
$476$	−32.9150	−1.50866
$477$	−11.2915	−0.517002
$478$	41.3948	1.89335
$479$	4.35425	0.198951	0.0994754	−	0.995040i	$-0.468284\pi$
$479$	4.35425	0.198951	0.0994754	+	0.995040i	$0.468284\pi$
$480$	13.2288	0.603807
$481$	−1.29150	−0.0588875
$482$	−43.8745	−1.99843
$483$	15.2915	0.695787
$484$	−54.3725	−2.47148
$485$	2.93725	0.133374
$486$	2.64575	0.120014
$487$	−17.8745	−0.809971	−0.404986	−	0.914323i	$-0.632723\pi$
$487$	−17.8745	−0.809971	−0.404986	+	0.914323i	$0.632723\pi$
$488$	−89.6235	−4.05707
$489$	−2.35425	−0.106463
$490$	−11.3542	−0.512933
$491$	−5.77124	−0.260453	−0.130226	−	0.991484i	$-0.541570\pi$
$491$	−5.77124	−0.260453	−0.130226	+	0.991484i	$0.541570\pi$
$492$	48.2288	2.17432
$493$	35.7490	1.61005
$494$	0	0
$495$	0.354249	0.0159223
$496$	−66.0000	−2.96349
$497$	−12.0000	−0.538274
$498$	15.8745	0.711354
$499$	−31.0405	−1.38956	−0.694782	−	0.719220i	$-0.744499\pi$
$499$	−31.0405	−1.38956	−0.694782	+	0.719220i	$0.744499\pi$
$500$	5.00000	0.223607
$501$	21.2915	0.951234
$502$	−43.2693	−1.93120
$503$	−2.00000	−0.0891756	−0.0445878	−	0.999005i	$-0.514197\pi$
$503$	−2.00000	−0.0891756	−0.0445878	+	0.999005i	$0.514197\pi$
$504$	13.0627	0.581861
$505$	9.29150	0.413466
$506$	8.70850	0.387140
$507$	−12.8745	−0.571777
$508$	−20.0000	−0.887357
$509$	34.1033	1.51160	0.755800	−	0.654802i	$-0.227248\pi$
$509$	34.1033	1.51160	0.755800	+	0.654802i	$0.227248\pi$
$510$	−10.5830	−0.468623
$511$	16.4575	0.728038
$512$	−29.1033	−1.28619
$513$	0	0
$514$	14.3320	0.632158
$515$	10.5830	0.466343
$516$	28.2288	1.24270
$517$	−0.457513	−0.0201214
$518$	−15.8745	−0.697486
$519$	0	0
$520$	2.81176	0.123304
$521$	−22.1033	−0.968362	−0.484181	−	0.874968i	$-0.660882\pi$
$521$	−22.1033	−0.968362	−0.484181	+	0.874968i	$0.660882\pi$
$522$	−23.6458	−1.03495
$523$	23.2915	1.01847	0.509233	−	0.860629i	$-0.329929\pi$
$523$	23.2915	1.01847	0.509233	+	0.860629i	$0.329929\pi$
$524$	−71.1438	−3.10793
$525$	1.64575	0.0718265
$526$	12.1255	0.528697
$527$	24.0000	1.04546
$528$	3.89674	0.169584
$529$	63.3320	2.75357
$530$	−29.8745	−1.29767
$531$	−11.2915	−0.490009
$532$	0	0
$533$	3.41699	0.148006
$534$	44.8118	1.93919
$535$	0	0
$536$	52.2510	2.25690
$537$	7.29150	0.314652
$538$	−11.1882	−0.482359
$539$	−1.52026	−0.0654822
$540$	5.00000	0.215166
$541$	30.0000	1.28980	0.644900	−	0.764267i	$-0.276899\pi$
$541$	30.0000	1.28980	0.644900	+	0.764267i	$0.276899\pi$
$542$	−12.4575	−0.535096
$543$	−17.2915	−0.742049
$544$	−52.9150	−2.26871
$545$	−5.29150	−0.226663
$546$	1.54249	0.0660123
$547$	−1.87451	−0.0801482	−0.0400741	−	0.999197i	$-0.512759\pi$
$547$	−1.87451	−0.0801482	−0.0400741	+	0.999197i	$0.512759\pi$
$548$	30.0000	1.28154
$549$	−11.2915	−0.481910
$550$	0.937254	0.0399646
$551$	0	0
$552$	73.7490	3.13897
$553$	−10.8340	−0.460708
$554$	1.54249	0.0655340
$555$	−3.64575	−0.154754
$556$	89.3725	3.79024
$557$	−11.4170	−0.483754	−0.241877	−	0.970307i	$-0.577763\pi$
$557$	−11.4170	−0.483754	−0.241877	+	0.970307i	$0.577763\pi$
$558$	−15.8745	−0.672022
$559$	2.00000	0.0845910
$560$	18.1033	0.765003
$561$	−1.41699	−0.0598256
$562$	85.2693	3.59687
$563$	−8.12549	−0.342449	−0.171224	−	0.985232i	$-0.554772\pi$
$563$	−8.12549	−0.342449	−0.171224	+	0.985232i	$0.554772\pi$
$564$	−6.45751	−0.271910
$565$	4.00000	0.168281
$566$	−30.4797	−1.28116
$567$	1.64575	0.0691151
$568$	−57.8745	−2.42836
$569$	7.06275	0.296086	0.148043	−	0.988981i	$-0.452703\pi$
$569$	7.06275	0.296086	0.148043	+	0.988981i	$0.452703\pi$
$570$	0	0
$571$	16.7085	0.699229	0.349614	−	0.936894i	$-0.386313\pi$
$571$	16.7085	0.699229	0.349614	+	0.936894i	$0.386313\pi$
$572$	0.627461	0.0262354
$573$	6.22876	0.260210
$574$	42.0000	1.75305
$575$	9.29150	0.387482
$576$	13.0000	0.541667
$577$	−13.2915	−0.553332	−0.276666	−	0.960966i	$-0.589230\pi$
$577$	−13.2915	−0.553332	−0.276666	+	0.960966i	$0.589230\pi$
$578$	−2.64575	−0.110049
$579$	11.6458	0.483981
$580$	−44.6863	−1.85550
$581$	9.87451	0.409664
$582$	7.77124	0.322128
$583$	−4.00000	−0.165663
$584$	79.3725	3.28446
$585$	0.354249	0.0146464
$586$	−14.3320	−0.592050
$587$	−33.2915	−1.37409	−0.687044	−	0.726616i	$-0.741092\pi$
$587$	−33.2915	−1.37409	−0.687044	+	0.726616i	$0.741092\pi$
$588$	−21.4575	−0.884893
$589$	0	0
$590$	−29.8745	−1.22991
$591$	−25.1660	−1.03519
$592$	−40.1033	−1.64823
$593$	3.41699	0.140319	0.0701596	−	0.997536i	$-0.477649\pi$
$593$	3.41699	0.140319	0.0701596	+	0.997536i	$0.477649\pi$
$594$	0.937254	0.0384560
$595$	−6.58301	−0.269877
$596$	−102.915	−4.21556
$597$	7.29150	0.298421
$598$	8.70850	0.356117
$599$	−9.41699	−0.384768	−0.192384	−	0.981320i	$-0.561622\pi$
$599$	−9.41699	−0.384768	−0.192384	+	0.981320i	$0.561622\pi$
$600$	7.93725	0.324037
$601$	−22.7085	−0.926299	−0.463149	−	0.886280i	$-0.653281\pi$
$601$	−22.7085	−0.926299	−0.463149	+	0.886280i	$0.653281\pi$
$602$	24.5830	1.00193
$603$	6.58301	0.268081
$604$	42.9150	1.74619
$605$	−10.8745	−0.442112
$606$	24.5830	0.998616
$607$	43.0405	1.74696	0.873480	−	0.486859i	$-0.161858\pi$
$607$	43.0405	1.74696	0.873480	+	0.486859i	$0.161858\pi$
$608$	0	0
$609$	−14.7085	−0.596018
$610$	−29.8745	−1.20958
$611$	−0.457513	−0.0185090
$612$	−20.0000	−0.808452
$613$	−30.4575	−1.23017	−0.615084	−	0.788462i	$-0.710878\pi$
$613$	−30.4575	−1.23017	−0.615084	+	0.788462i	$0.710878\pi$
$614$	64.7085	2.61142
$615$	9.64575	0.388954
$616$	4.62746	0.186446
$617$	12.0000	0.483102	0.241551	−	0.970388i	$-0.422344\pi$
$617$	12.0000	0.483102	0.241551	+	0.970388i	$0.422344\pi$
$618$	28.0000	1.12633
$619$	23.2915	0.936165	0.468082	−	0.883685i	$-0.344945\pi$
$619$	23.2915	0.936165	0.468082	+	0.883685i	$0.344945\pi$
$620$	−30.0000	−1.20483
$621$	9.29150	0.372855
$622$	60.6863	2.43330
$623$	27.8745	1.11677
$624$	3.89674	0.155994
$625$	1.00000	0.0400000
$626$	45.7490	1.82850
$627$	0	0
$628$	−66.4575	−2.65194
$629$	14.5830	0.581462
$630$	4.35425	0.173477
$631$	−14.5830	−0.580540	−0.290270	−	0.956945i	$-0.593745\pi$
$631$	−14.5830	−0.580540	−0.290270	+	0.956945i	$0.593745\pi$
$632$	−52.2510	−2.07843
$633$	−2.58301	−0.102665
$634$	−54.1255	−2.14960
$635$	−4.00000	−0.158735
$636$	−56.4575	−2.23869
$637$	−1.52026	−0.0602349
$638$	−8.37648	−0.331628
$639$	−7.29150	−0.288447
$640$	7.93725	0.313748
$641$	16.9373	0.668981	0.334491	−	0.942399i	$-0.391436\pi$
$641$	16.9373	0.668981	0.334491	+	0.942399i	$0.391436\pi$
$642$	0	0
$643$	−13.6458	−0.538136	−0.269068	−	0.963121i	$-0.586716\pi$
$643$	−13.6458	−0.538136	−0.269068	+	0.963121i	$0.586716\pi$
$644$	76.4575	3.01285
$645$	5.64575	0.222301
$646$	0	0
$647$	−3.41699	−0.134336	−0.0671680	−	0.997742i	$-0.521396\pi$
$647$	−3.41699	−0.134336	−0.0671680	+	0.997742i	$0.521396\pi$
$648$	7.93725	0.311805
$649$	−4.00000	−0.157014
$650$	0.937254	0.0367621
$651$	−9.87451	−0.387012
$652$	−11.7712	−0.460997
$653$	9.41699	0.368515	0.184258	−	0.982878i	$-0.441012\pi$
$653$	9.41699	0.368515	0.184258	+	0.982878i	$0.441012\pi$
$654$	−14.0000	−0.547443
$655$	−14.2288	−0.555964
$656$	106.103	4.14264
$657$	10.0000	0.390137
$658$	−5.62352	−0.219228
$659$	−25.4170	−0.990106	−0.495053	−	0.868863i	$-0.664851\pi$
$659$	−25.4170	−0.990106	−0.495053	+	0.868863i	$0.664851\pi$
$660$	1.77124	0.0689456
$661$	−1.29150	−0.0502336	−0.0251168	−	0.999685i	$-0.507996\pi$
$661$	−1.29150	−0.0502336	−0.0251168	+	0.999685i	$0.507996\pi$
$662$	−30.2065	−1.17401
$663$	−1.41699	−0.0550315
$664$	47.6235	1.84815
$665$	0	0
$666$	−9.64575	−0.373765
$667$	−83.0405	−3.21534
$668$	106.458	4.11896
$669$	−2.58301	−0.0998648
$670$	17.4170	0.672877
$671$	−4.00000	−0.154418
$672$	21.7712	0.839844
$673$	13.0627	0.503532	0.251766	−	0.967788i	$-0.418989\pi$
$673$	13.0627	0.503532	0.251766	+	0.967788i	$0.418989\pi$
$674$	−39.5203	−1.52226
$675$	1.00000	0.0384900
$676$	−64.3725	−2.47587
$677$	−40.4575	−1.55491	−0.777454	−	0.628939i	$-0.783489\pi$
$677$	−40.4575	−1.55491	−0.777454	+	0.628939i	$0.783489\pi$
$678$	10.5830	0.406438
$679$	4.83399	0.185511
$680$	−31.7490	−1.21752
$681$	10.7085	0.410351
$682$	−5.62352	−0.215336
$683$	−19.7490	−0.755675	−0.377838	−	0.925872i	$-0.623332\pi$
$683$	−19.7490	−0.755675	−0.377838	+	0.925872i	$0.623332\pi$
$684$	0	0
$685$	6.00000	0.229248
$686$	−49.1660	−1.87717
$687$	8.70850	0.332250
$688$	62.1033	2.36766
$689$	−4.00000	−0.152388
$690$	24.5830	0.935859
$691$	−43.0405	−1.63734	−0.818669	−	0.574265i	$-0.805288\pi$
$691$	−43.0405	−1.63734	−0.818669	+	0.574265i	$0.805288\pi$
$692$	0	0
$693$	0.583005	0.0221465
$694$	68.7895	2.61122
$695$	17.8745	0.678019
$696$	−70.9373	−2.68887
$697$	−38.5830	−1.46144
$698$	61.2915	2.31992
$699$	−18.0000	−0.680823
$700$	8.22876	0.311018
$701$	16.5830	0.626331	0.313166	−	0.949698i	$-0.398610\pi$
$701$	16.5830	0.626331	0.313166	+	0.949698i	$0.398610\pi$
$702$	0.937254	0.0353744
$703$	0	0
$704$	4.60523	0.173566
$705$	−1.29150	−0.0486408
$706$	1.54249	0.0580523
$707$	15.2915	0.575096
$708$	−56.4575	−2.12180
$709$	−4.70850	−0.176831	−0.0884157	−	0.996084i	$-0.528180\pi$
$709$	−4.70850	−0.176831	−0.0884157	+	0.996084i	$0.528180\pi$
$710$	−19.2915	−0.723997
$711$	−6.58301	−0.246882
$712$	134.435	5.03818
$713$	−55.7490	−2.08782
$714$	−17.4170	−0.651815
$715$	0.125492	0.00469314
$716$	36.4575	1.36248
$717$	15.6458	0.584301
$718$	−95.5203	−3.56478
$719$	32.8118	1.22367	0.611836	−	0.790985i	$-0.290431\pi$
$719$	32.8118	1.22367	0.611836	+	0.790985i	$0.290431\pi$
$720$	11.0000	0.409946
$721$	17.4170	0.648643
$722$	0	0
$723$	−16.5830	−0.616729
$724$	−86.4575	−3.21317
$725$	−8.93725	−0.331921
$726$	−28.7712	−1.06780
$727$	14.1033	0.523061	0.261531	−	0.965195i	$-0.415773\pi$
$727$	14.1033	0.523061	0.261531	+	0.965195i	$0.415773\pi$
$728$	4.62746	0.171505
$729$	1.00000	0.0370370
$730$	26.4575	0.979236
$731$	−22.5830	−0.835263
$732$	−56.4575	−2.08673
$733$	7.41699	0.273953	0.136976	−	0.990574i	$-0.456262\pi$
$733$	7.41699	0.273953	0.136976	+	0.990574i	$0.456262\pi$
$734$	4.35425	0.160718
$735$	−4.29150	−0.158294
$736$	122.915	4.53071
$737$	2.33202	0.0859011
$738$	25.5203	0.939414
$739$	−20.0000	−0.735712	−0.367856	−	0.929883i	$-0.619908\pi$
$739$	−20.0000	−0.735712	−0.367856	+	0.929883i	$0.619908\pi$
$740$	−18.2288	−0.670102
$741$	0	0
$742$	−49.1660	−1.80494
$743$	10.5830	0.388253	0.194126	−	0.980977i	$-0.437813\pi$
$743$	10.5830	0.388253	0.194126	+	0.980977i	$0.437813\pi$
$744$	−47.6235	−1.74596
$745$	−20.5830	−0.754103
$746$	−13.3948	−0.490417
$747$	6.00000	0.219529
$748$	−7.08497	−0.259052
$749$	0	0
$750$	2.64575	0.0966092
$751$	44.5830	1.62686	0.813428	−	0.581665i	$-0.197599\pi$
$751$	44.5830	1.62686	0.813428	+	0.581665i	$0.197599\pi$
$752$	−14.2065	−0.518059
$753$	−16.3542	−0.595982
$754$	−8.37648	−0.305053
$755$	8.58301	0.312368
$756$	8.22876	0.299277
$757$	−23.8745	−0.867734	−0.433867	−	0.900977i	$-0.642851\pi$
$757$	−23.8745	−0.867734	−0.433867	+	0.900977i	$0.642851\pi$
$758$	−26.4575	−0.960980
$759$	3.29150	0.119474
$760$	0	0
$761$	25.7490	0.933401	0.466701	−	0.884415i	$-0.345443\pi$
$761$	25.7490	0.933401	0.466701	+	0.884415i	$0.345443\pi$
$762$	−10.5830	−0.383382
$763$	−8.70850	−0.315269
$764$	31.1438	1.12674
$765$	−4.00000	−0.144620
$766$	49.1660	1.77644
$767$	−4.00000	−0.144432
$768$	−5.00000	−0.180422
$769$	−17.7490	−0.640046	−0.320023	−	0.947410i	$-0.603691\pi$
$769$	−17.7490	−0.640046	−0.320023	+	0.947410i	$0.603691\pi$
$770$	1.54249	0.0555874
$771$	5.41699	0.195088
$772$	58.2288	2.09570
$773$	8.70850	0.313223	0.156611	−	0.987660i	$-0.449943\pi$
$773$	8.70850	0.313223	0.156611	+	0.987660i	$0.449943\pi$
$774$	14.9373	0.536909
$775$	−6.00000	−0.215526
$776$	23.3137	0.836914
$777$	−6.00000	−0.215249
$778$	−15.8745	−0.569129
$779$	0	0
$780$	1.77124	0.0634207
$781$	−2.58301	−0.0924272
$782$	−98.3320	−3.51635
$783$	−8.93725	−0.319391
$784$	−47.2065	−1.68595
$785$	−13.2915	−0.474394
$786$	−37.6458	−1.34278
$787$	−37.8745	−1.35008	−0.675040	−	0.737781i	$-0.735874\pi$
$787$	−37.8745	−1.35008	−0.675040	+	0.737781i	$0.735874\pi$
$788$	−125.830	−4.48251
$789$	4.58301	0.163159
$790$	−17.4170	−0.619669
$791$	6.58301	0.234065
$792$	2.81176	0.0999116
$793$	−4.00000	−0.142044
$794$	−5.29150	−0.187788
$795$	−11.2915	−0.400468
$796$	36.4575	1.29220
$797$	−40.0000	−1.41687	−0.708436	−	0.705775i	$-0.750599\pi$
$797$	−40.0000	−1.41687	−0.708436	+	0.705775i	$0.750599\pi$
$798$	0	0
$799$	5.16601	0.182760
$800$	13.2288	0.467707
$801$	16.9373	0.598448
$802$	13.0627	0.461262
$803$	3.54249	0.125012
$804$	32.9150	1.16082
$805$	15.2915	0.538955
$806$	−5.62352	−0.198080
$807$	−4.22876	−0.148859
$808$	73.7490	2.59448
$809$	−19.4170	−0.682665	−0.341333	−	0.939943i	$-0.610878\pi$
$809$	−19.4170	−0.682665	−0.341333	+	0.939943i	$0.610878\pi$
$810$	2.64575	0.0929622
$811$	−38.3320	−1.34602	−0.673010	−	0.739634i	$-0.734999\pi$
$811$	−38.3320	−1.34602	−0.673010	+	0.739634i	$0.734999\pi$
$812$	−73.5425	−2.58084
$813$	−4.70850	−0.165134
$814$	−3.41699	−0.119766
$815$	−2.35425	−0.0824657
$816$	−44.0000	−1.54031
$817$	0	0
$818$	17.7490	0.620580
$819$	0.583005	0.0203719
$820$	48.2288	1.68422
$821$	47.6235	1.66207	0.831036	−	0.556218i	$-0.187748\pi$
$821$	47.6235	1.66207	0.831036	+	0.556218i	$0.187748\pi$
$822$	15.8745	0.553687
$823$	4.22876	0.147405	0.0737026	−	0.997280i	$-0.476518\pi$
$823$	4.22876	0.147405	0.0737026	+	0.997280i	$0.476518\pi$
$824$	84.0000	2.92628
$825$	0.354249	0.0123334
$826$	−49.1660	−1.71070
$827$	−30.4575	−1.05911	−0.529556	−	0.848275i	$-0.677641\pi$
$827$	−30.4575	−1.05911	−0.529556	+	0.848275i	$0.677641\pi$
$828$	46.4575	1.61451
$829$	−2.70850	−0.0940700	−0.0470350	−	0.998893i	$-0.514977\pi$
$829$	−2.70850	−0.0940700	−0.0470350	+	0.998893i	$0.514977\pi$
$830$	15.8745	0.551012
$831$	0.583005	0.0202242
$832$	4.60523	0.159658
$833$	17.1660	0.594767
$834$	47.2915	1.63757
$835$	21.2915	0.736823
$836$	0	0
$837$	−6.00000	−0.207390
$838$	103.018	3.55871
$839$	12.4575	0.430081	0.215041	−	0.976605i	$-0.431012\pi$
$839$	12.4575	0.430081	0.215041	+	0.976605i	$0.431012\pi$
$840$	13.0627	0.450708
$841$	50.8745	1.75429
$842$	−75.6235	−2.60616
$843$	32.2288	1.11002
$844$	−12.9150	−0.444554
$845$	−12.8745	−0.442897
$846$	−3.41699	−0.117479
$847$	−17.8967	−0.614939
$848$	−124.207	−4.26527
$849$	−11.5203	−0.395374
$850$	−10.5830	−0.362994
$851$	−33.8745	−1.16120
$852$	−36.4575	−1.24901
$853$	14.7085	0.503609	0.251805	−	0.967778i	$-0.418976\pi$
$853$	14.7085	0.503609	0.251805	+	0.967778i	$0.418976\pi$
$854$	−49.1660	−1.68243
$855$	0	0
$856$	0	0
$857$	−31.0405	−1.06032	−0.530162	−	0.847896i	$-0.677869\pi$
$857$	−31.0405	−1.06032	−0.530162	+	0.847896i	$0.677869\pi$
$858$	0.332021	0.0113350
$859$	−34.3320	−1.17139	−0.585697	−	0.810530i	$-0.699179\pi$
$859$	−34.3320	−1.17139	−0.585697	+	0.810530i	$0.699179\pi$
$860$	28.2288	0.962593
$861$	15.8745	0.541002
$862$	−8.70850	−0.296613
$863$	20.0000	0.680808	0.340404	−	0.940279i	$-0.389436\pi$
$863$	20.0000	0.680808	0.340404	+	0.940279i	$0.389436\pi$
$864$	13.2288	0.450051
$865$	0	0
$866$	73.1438	2.48553
$867$	−1.00000	−0.0339618
$868$	−49.3725	−1.67581
$869$	−2.33202	−0.0791084
$870$	−23.6458	−0.801666
$871$	2.33202	0.0790175
$872$	−42.0000	−1.42230
$873$	2.93725	0.0994110
$874$	0	0
$875$	1.64575	0.0556365
$876$	50.0000	1.68934
$877$	25.0627	0.846309	0.423154	−	0.906058i	$-0.360923\pi$
$877$	25.0627	0.846309	0.423154	+	0.906058i	$0.360923\pi$
$878$	3.74902	0.126523
$879$	−5.41699	−0.182711
$880$	3.89674	0.131359
$881$	−0.125492	−0.00422794	−0.00211397	−	0.999998i	$-0.500673\pi$
$881$	−0.125492	−0.00422794	−0.00211397	+	0.999998i	$0.500673\pi$
$882$	−11.3542	−0.382317
$883$	10.8118	0.363845	0.181922	−	0.983313i	$-0.441768\pi$
$883$	10.8118	0.363845	0.181922	+	0.983313i	$0.441768\pi$
$884$	−7.08497	−0.238293
$885$	−11.2915	−0.379560
$886$	70.6640	2.37400
$887$	24.0000	0.805841	0.402921	−	0.915235i	$-0.367995\pi$
$887$	24.0000	0.805841	0.402921	+	0.915235i	$0.367995\pi$
$888$	−28.9373	−0.971071
$889$	−6.58301	−0.220787
$890$	44.8118	1.50209
$891$	0.354249	0.0118678
$892$	−12.9150	−0.432427
$893$	0	0
$894$	−54.4575	−1.82133
$895$	7.29150	0.243728
$896$	13.0627	0.436396
$897$	3.29150	0.109900
$898$	95.8523	3.19863
$899$	53.6235	1.78844
$900$	5.00000	0.166667
$901$	45.1660	1.50470
$902$	9.04052	0.301016
$903$	9.29150	0.309202
$904$	31.7490	1.05596
$905$	−17.2915	−0.574789
$906$	22.7085	0.754439
$907$	47.0405	1.56195	0.780977	−	0.624559i	$-0.214721\pi$
$907$	47.0405	1.56195	0.780977	+	0.624559i	$0.214721\pi$
$908$	53.5425	1.77687
$909$	9.29150	0.308180
$910$	1.54249	0.0511329
$911$	−26.5830	−0.880734	−0.440367	−	0.897818i	$-0.645152\pi$
$911$	−26.5830	−0.880734	−0.440367	+	0.897818i	$0.645152\pi$
$912$	0	0
$913$	2.12549	0.0703435
$914$	0.332021	0.0109823
$915$	−11.2915	−0.373286
$916$	43.5425	1.43868
$917$	−23.4170	−0.773297
$918$	−10.5830	−0.349291
$919$	14.8340	0.489328	0.244664	−	0.969608i	$-0.421322\pi$
$919$	14.8340	0.489328	0.244664	+	0.969608i	$0.421322\pi$
$920$	73.7490	2.43143
$921$	24.4575	0.805902
$922$	−99.8745	−3.28919
$923$	−2.58301	−0.0850207
$924$	2.91503	0.0958973
$925$	−3.64575	−0.119872
$926$	−93.9778	−3.08830
$927$	10.5830	0.347591
$928$	−118.229	−3.88105
$929$	−11.8745	−0.389590	−0.194795	−	0.980844i	$-0.562404\pi$
$929$	−11.8745	−0.389590	−0.194795	+	0.980844i	$0.562404\pi$
$930$	−15.8745	−0.520546
$931$	0	0
$932$	−90.0000	−2.94805
$933$	22.9373	0.750932
$934$	52.5830	1.72057
$935$	−1.41699	−0.0463407
$936$	2.81176	0.0919053
$937$	20.1255	0.657471	0.328736	−	0.944422i	$-0.393378\pi$
$937$	20.1255	0.657471	0.328736	+	0.944422i	$0.393378\pi$
$938$	28.6640	0.935914
$939$	17.2915	0.564287
$940$	−6.45751	−0.210621
$941$	11.7712	0.383732	0.191866	−	0.981421i	$-0.438546\pi$
$941$	11.7712	0.383732	0.191866	+	0.981421i	$0.438546\pi$
$942$	−35.1660	−1.14577
$943$	89.6235	2.91854
$944$	−124.207	−4.04258
$945$	1.64575	0.0535363
$946$	5.29150	0.172042
$947$	11.4170	0.371002	0.185501	−	0.982644i	$-0.440609\pi$
$947$	11.4170	0.371002	0.185501	+	0.982644i	$0.440609\pi$
$948$	−32.9150	−1.06903
$949$	3.54249	0.114994
$950$	0	0
$951$	−20.4575	−0.663380
$952$	−52.2510	−1.69346
$953$	10.5830	0.342817	0.171409	−	0.985200i	$-0.445168\pi$
$953$	10.5830	0.342817	0.171409	+	0.985200i	$0.445168\pi$
$954$	−29.8745	−0.967223
$955$	6.22876	0.201558
$956$	78.2288	2.53010
$957$	−3.16601	−0.102343
$958$	11.5203	0.372203
$959$	9.87451	0.318864
$960$	13.0000	0.419573
$961$	5.00000	0.161290
$962$	−3.41699	−0.110168
$963$	0	0
$964$	−82.9150	−2.67051
$965$	11.6458	0.374890
$966$	40.4575	1.30170
$967$	−41.6458	−1.33924	−0.669619	−	0.742705i	$-0.733542\pi$
$967$	−41.6458	−1.33924	−0.669619	+	0.742705i	$0.733542\pi$
$968$	−86.3137	−2.77423
$969$	0	0
$970$	7.77124	0.249520
$971$	0	0		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	5.00000	0.160375
$973$	29.4170	0.943066
$974$	−47.2915	−1.51532
$975$	0.354249	0.0113450
$976$	−124.207	−3.97575
$977$	51.0405	1.63293	0.816465	−	0.577394i	$-0.195930\pi$
$977$	51.0405	1.63293	0.816465	+	0.577394i	$0.195930\pi$
$978$	−6.22876	−0.199174
$979$	6.00000	0.191761
$980$	−21.4575	−0.685435
$981$	−5.29150	−0.168945
$982$	−15.2693	−0.487262
$983$	−34.4575	−1.09902	−0.549512	−	0.835486i	$-0.685186\pi$
$983$	−34.4575	−1.09902	−0.549512	+	0.835486i	$0.685186\pi$
$984$	76.5608	2.44067
$985$	−25.1660	−0.801856
$986$	94.5830	3.01214
$987$	−2.12549	−0.0676552
$988$	0	0
$989$	52.4575	1.66805
$990$	0.937254	0.0297879
$991$	35.7490	1.13560	0.567802	−	0.823165i	$-0.307794\pi$
$991$	35.7490	1.13560	0.567802	+	0.823165i	$0.307794\pi$
$992$	−79.3725	−2.52008
$993$	−11.4170	−0.362307
$994$	−31.7490	−1.00702
$995$	7.29150	0.231156
$996$	30.0000	0.950586
$997$	26.7085	0.845867	0.422933	−	0.906161i	$-0.361000\pi$
$997$	26.7085	0.845867	0.422933	+	0.906161i	$0.361000\pi$
$998$	−82.1255	−2.59964
$999$	−3.64575	−0.115346

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5415.2.a.s.1.2		2
19.18	odd	2		285.2.a.d.1.1	✓	2
57.56	even	2		855.2.a.g.1.2		2
76.75	even	2		4560.2.a.bo.1.1		2
95.18	even	4		1425.2.c.i.799.3		4
95.37	even	4		1425.2.c.i.799.2		4
95.94	odd	2		1425.2.a.p.1.2		2
285.284	even	2		4275.2.a.u.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.a.d.1.1	✓	2	19.18	odd	2
855.2.a.g.1.2		2	57.56	even	2
1425.2.a.p.1.2		2	95.94	odd	2
1425.2.c.i.799.2		4	95.37	even	4
1425.2.c.i.799.3		4	95.18	even	4
4275.2.a.u.1.1		2	285.284	even	2
4560.2.a.bo.1.1		2	76.75	even	2
5415.2.a.s.1.2		2	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:	\( N \)	\(=\)	\( 5415 = 3 \cdot 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5415.a (trivial)

\(f(q)\)	\(=\)	\(q+2.64575 q^{2} +1.00000 q^{3} +5.00000 q^{4} +1.00000 q^{5} +2.64575 q^{6} +1.64575 q^{7} +7.93725 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.64575 q^{2} +1.00000 q^{3} +5.00000 q^{4} +1.00000 q^{5} +2.64575 q^{6} +1.64575 q^{7} +7.93725 q^{8} +1.00000 q^{9} +2.64575 q^{10} +0.354249 q^{11} +5.00000 q^{12} +0.354249 q^{13} +4.35425 q^{14} +1.00000 q^{15} +11.0000 q^{16} -4.00000 q^{17} +2.64575 q^{18} +5.00000 q^{20} +1.64575 q^{21} +0.937254 q^{22} +9.29150 q^{23} +7.93725 q^{24} +1.00000 q^{25} +0.937254 q^{26} +1.00000 q^{27} +8.22876 q^{28} -8.93725 q^{29} +2.64575 q^{30} -6.00000 q^{31} +13.2288 q^{32} +0.354249 q^{33} -10.5830 q^{34} +1.64575 q^{35} +5.00000 q^{36} -3.64575 q^{37} +0.354249 q^{39} +7.93725 q^{40} +9.64575 q^{41} +4.35425 q^{42} +5.64575 q^{43} +1.77124 q^{44} +1.00000 q^{45} +24.5830 q^{46} -1.29150 q^{47} +11.0000 q^{48} -4.29150 q^{49} +2.64575 q^{50} -4.00000 q^{51} +1.77124 q^{52} -11.2915 q^{53} +2.64575 q^{54} +0.354249 q^{55} +13.0627 q^{56} -23.6458 q^{58} -11.2915 q^{59} +5.00000 q^{60} -11.2915 q^{61} -15.8745 q^{62} +1.64575 q^{63} +13.0000 q^{64} +0.354249 q^{65} +0.937254 q^{66} +6.58301 q^{67} -20.0000 q^{68} +9.29150 q^{69} +4.35425 q^{70} -7.29150 q^{71} +7.93725 q^{72} +10.0000 q^{73} -9.64575 q^{74} +1.00000 q^{75} +0.583005 q^{77} +0.937254 q^{78} -6.58301 q^{79} +11.0000 q^{80} +1.00000 q^{81} +25.5203 q^{82} +6.00000 q^{83} +8.22876 q^{84} -4.00000 q^{85} +14.9373 q^{86} -8.93725 q^{87} +2.81176 q^{88} +16.9373 q^{89} +2.64575 q^{90} +0.583005 q^{91} +46.4575 q^{92} -6.00000 q^{93} -3.41699 q^{94} +13.2288 q^{96} +2.93725 q^{97} -11.3542 q^{98} +0.354249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} + 10 q^{4} + 2 q^{5} - 2 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^3 + 10 * q^4 + 2 * q^5 - 2 * q^7 + 2 * q^9	\( 2 q + 2 q^{3} + 10 q^{4} + 2 q^{5} - 2 q^{7} + 2 q^{9} + 6 q^{11} + 10 q^{12} + 6 q^{13} + 14 q^{14} + 2 q^{15} + 22 q^{16} - 8 q^{17} + 10 q^{20} - 2 q^{21} - 14 q^{22} + 8 q^{23} + 2 q^{25} - 14 q^{26} + 2 q^{27} - 10 q^{28} - 2 q^{29} - 12 q^{31} + 6 q^{33} - 2 q^{35} + 10 q^{36} - 2 q^{37} + 6 q^{39} + 14 q^{41} + 14 q^{42} + 6 q^{43} + 30 q^{44} + 2 q^{45} + 28 q^{46} + 8 q^{47} + 22 q^{48} + 2 q^{49} - 8 q^{51} + 30 q^{52} - 12 q^{53} + 6 q^{55} + 42 q^{56} - 42 q^{58} - 12 q^{59} + 10 q^{60} - 12 q^{61} - 2 q^{63} + 26 q^{64} + 6 q^{65} - 14 q^{66} - 8 q^{67} - 40 q^{68} + 8 q^{69} + 14 q^{70} - 4 q^{71} + 20 q^{73} - 14 q^{74} + 2 q^{75} - 20 q^{77} - 14 q^{78} + 8 q^{79} + 22 q^{80} + 2 q^{81} + 14 q^{82} + 12 q^{83} - 10 q^{84} - 8 q^{85} + 14 q^{86} - 2 q^{87} - 42 q^{88} + 18 q^{89} - 20 q^{91} + 40 q^{92} - 12 q^{93} - 28 q^{94} - 10 q^{97} - 28 q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 + 10 * q^4 + 2 * q^5 - 2 * q^7 + 2 * q^9 + 6 * q^11 + 10 * q^12 + 6 * q^13 + 14 * q^14 + 2 * q^15 + 22 * q^16 - 8 * q^17 + 10 * q^20 - 2 * q^21 - 14 * q^22 + 8 * q^23 + 2 * q^25 - 14 * q^26 + 2 * q^27 - 10 * q^28 - 2 * q^29 - 12 * q^31 + 6 * q^33 - 2 * q^35 + 10 * q^36 - 2 * q^37 + 6 * q^39 + 14 * q^41 + 14 * q^42 + 6 * q^43 + 30 * q^44 + 2 * q^45 + 28 * q^46 + 8 * q^47 + 22 * q^48 + 2 * q^49 - 8 * q^51 + 30 * q^52 - 12 * q^53 + 6 * q^55 + 42 * q^56 - 42 * q^58 - 12 * q^59 + 10 * q^60 - 12 * q^61 - 2 * q^63 + 26 * q^64 + 6 * q^65 - 14 * q^66 - 8 * q^67 - 40 * q^68 + 8 * q^69 + 14 * q^70 - 4 * q^71 + 20 * q^73 - 14 * q^74 + 2 * q^75 - 20 * q^77 - 14 * q^78 + 8 * q^79 + 22 * q^80 + 2 * q^81 + 14 * q^82 + 12 * q^83 - 10 * q^84 - 8 * q^85 + 14 * q^86 - 2 * q^87 - 42 * q^88 + 18 * q^89 - 20 * q^91 + 40 * q^92 - 12 * q^93 - 28 * q^94 - 10 * q^97 - 28 * q^98 + 6 * q^99

Introduction

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