LMFDB - Embedded newform 4235.2.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4235,2,Mod(1,4235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, 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("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.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:	$33.8166452560$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 385)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23607 q^{2} +0.618034 q^{3} +3.00000 q^{4} -1.00000 q^{5} -1.38197 q^{6} -1.00000 q^{7} -2.23607 q^{8} -2.61803 q^{9} +O(q^{10})$	\(q-2.23607 q^{2} +0.618034 q^{3} +3.00000 q^{4} -1.00000 q^{5} -1.38197 q^{6} -1.00000 q^{7} -2.23607 q^{8} -2.61803 q^{9} +2.23607 q^{10} +1.85410 q^{12} +4.61803 q^{13} +2.23607 q^{14} -0.618034 q^{15} -1.00000 q^{16} +5.61803 q^{17} +5.85410 q^{18} -3.23607 q^{19} -3.00000 q^{20} -0.618034 q^{21} -4.47214 q^{23} -1.38197 q^{24} +1.00000 q^{25} -10.3262 q^{26} -3.47214 q^{27} -3.00000 q^{28} +0.854102 q^{29} +1.38197 q^{30} +3.23607 q^{31} +6.70820 q^{32} -12.5623 q^{34} +1.00000 q^{35} -7.85410 q^{36} -7.23607 q^{37} +7.23607 q^{38} +2.85410 q^{39} +2.23607 q^{40} +2.47214 q^{41} +1.38197 q^{42} -5.23607 q^{43} +2.61803 q^{45} +10.0000 q^{46} -1.14590 q^{47} -0.618034 q^{48} +1.00000 q^{49} -2.23607 q^{50} +3.47214 q^{51} +13.8541 q^{52} -1.52786 q^{53} +7.76393 q^{54} +2.23607 q^{56} -2.00000 q^{57} -1.90983 q^{58} -9.23607 q^{59} -1.85410 q^{60} -4.76393 q^{61} -7.23607 q^{62} +2.61803 q^{63} -13.0000 q^{64} -4.61803 q^{65} +8.18034 q^{67} +16.8541 q^{68} -2.76393 q^{69} -2.23607 q^{70} +16.3262 q^{71} +5.85410 q^{72} +6.38197 q^{73} +16.1803 q^{74} +0.618034 q^{75} -9.70820 q^{76} -6.38197 q^{78} +10.7984 q^{79} +1.00000 q^{80} +5.70820 q^{81} -5.52786 q^{82} +9.56231 q^{83} -1.85410 q^{84} -5.61803 q^{85} +11.7082 q^{86} +0.527864 q^{87} +12.7639 q^{89} -5.85410 q^{90} -4.61803 q^{91} -13.4164 q^{92} +2.00000 q^{93} +2.56231 q^{94} +3.23607 q^{95} +4.14590 q^{96} -15.3262 q^{97} -2.23607 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} + 6 q^{4} - 2 q^{5} - 5 q^{6} - 2 q^{7} - 3 q^{9}+O(q^{10}) $ 2 * q - q^3 + 6 * q^4 - 2 * q^5 - 5 * q^6 - 2 * q^7 - 3 * q^9	$ 2 q - q^{3} + 6 q^{4} - 2 q^{5} - 5 q^{6} - 2 q^{7} - 3 q^{9} - 3 q^{12} + 7 q^{13} + q^{15} - 2 q^{16} + 9 q^{17} + 5 q^{18} - 2 q^{19} - 6 q^{20} + q^{21} - 5 q^{24} + 2 q^{25} - 5 q^{26} + 2 q^{27} - 6 q^{28} - 5 q^{29} + 5 q^{30} + 2 q^{31} - 5 q^{34} + 2 q^{35} - 9 q^{36} - 10 q^{37} + 10 q^{38} - q^{39} - 4 q^{41} + 5 q^{42} - 6 q^{43} + 3 q^{45} + 20 q^{46} - 9 q^{47} + q^{48} + 2 q^{49} - 2 q^{51} + 21 q^{52} - 12 q^{53} + 20 q^{54} - 4 q^{57} - 15 q^{58} - 14 q^{59} + 3 q^{60} - 14 q^{61} - 10 q^{62} + 3 q^{63} - 26 q^{64} - 7 q^{65} - 6 q^{67} + 27 q^{68} - 10 q^{69} + 17 q^{71} + 5 q^{72} + 15 q^{73} + 10 q^{74} - q^{75} - 6 q^{76} - 15 q^{78} - 3 q^{79} + 2 q^{80} - 2 q^{81} - 20 q^{82} - q^{83} + 3 q^{84} - 9 q^{85} + 10 q^{86} + 10 q^{87} + 30 q^{89} - 5 q^{90} - 7 q^{91} + 4 q^{93} - 15 q^{94} + 2 q^{95} + 15 q^{96} - 15 q^{97}+O(q^{100}) $ 2 * q - q^3 + 6 * q^4 - 2 * q^5 - 5 * q^6 - 2 * q^7 - 3 * q^9 - 3 * q^12 + 7 * q^13 + q^15 - 2 * q^16 + 9 * q^17 + 5 * q^18 - 2 * q^19 - 6 * q^20 + q^21 - 5 * q^24 + 2 * q^25 - 5 * q^26 + 2 * q^27 - 6 * q^28 - 5 * q^29 + 5 * q^30 + 2 * q^31 - 5 * q^34 + 2 * q^35 - 9 * q^36 - 10 * q^37 + 10 * q^38 - q^39 - 4 * q^41 + 5 * q^42 - 6 * q^43 + 3 * q^45 + 20 * q^46 - 9 * q^47 + q^48 + 2 * q^49 - 2 * q^51 + 21 * q^52 - 12 * q^53 + 20 * q^54 - 4 * q^57 - 15 * q^58 - 14 * q^59 + 3 * q^60 - 14 * q^61 - 10 * q^62 + 3 * q^63 - 26 * q^64 - 7 * q^65 - 6 * q^67 + 27 * q^68 - 10 * q^69 + 17 * q^71 + 5 * q^72 + 15 * q^73 + 10 * q^74 - q^75 - 6 * q^76 - 15 * q^78 - 3 * q^79 + 2 * q^80 - 2 * q^81 - 20 * q^82 - q^83 + 3 * q^84 - 9 * q^85 + 10 * q^86 + 10 * q^87 + 30 * q^89 - 5 * q^90 - 7 * q^91 + 4 * q^93 - 15 * q^94 + 2 * q^95 + 15 * q^96 - 15 * q^97

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 $

$2$	−2.23607	−1.58114	−0.790569	−	0.612372i	$-0.790215\pi$
$2$	−2.23607	−1.58114	−0.790569	+	0.612372i	$0.790215\pi$
$3$	0.618034	0.356822	0.178411	−	0.983956i	$-0.442904\pi$
$3$	0.618034	0.356822	0.178411	+	0.983956i	$0.442904\pi$
$4$	3.00000	1.50000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.38197	−0.564185
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.23607	−0.790569
$9$	−2.61803	−0.872678
$10$	2.23607	0.707107
$11$	0	0
$11$	0	0
$12$	1.85410	0.535233
$13$	4.61803	1.28081	0.640406	−	0.768036i	$-0.278766\pi$
$13$	4.61803	1.28081	0.640406	+	0.768036i	$0.278766\pi$
$14$	2.23607	0.597614
$15$	−0.618034	−0.159576
$16$	−1.00000	−0.250000
$17$	5.61803	1.36257	0.681287	−	0.732017i	$-0.261421\pi$
$17$	5.61803	1.36257	0.681287	+	0.732017i	$0.261421\pi$
$18$	5.85410	1.37983
$19$	−3.23607	−0.742405	−0.371202	−	0.928552i	$-0.621054\pi$
$19$	−3.23607	−0.742405	−0.371202	+	0.928552i	$0.621054\pi$
$20$	−3.00000	−0.670820
$21$	−0.618034	−0.134866
$22$	0	0
$23$	−4.47214	−0.932505	−0.466252	−	0.884652i	$-0.654396\pi$
$23$	−4.47214	−0.932505	−0.466252	+	0.884652i	$0.654396\pi$
$24$	−1.38197	−0.282093
$25$	1.00000	0.200000
$26$	−10.3262	−2.02514
$27$	−3.47214	−0.668213
$28$	−3.00000	−0.566947
$29$	0.854102	0.158603	0.0793014	−	0.996851i	$-0.474731\pi$
$29$	0.854102	0.158603	0.0793014	+	0.996851i	$0.474731\pi$
$30$	1.38197	0.252311
$31$	3.23607	0.581215	0.290607	−	0.956842i	$-0.406143\pi$
$31$	3.23607	0.581215	0.290607	+	0.956842i	$0.406143\pi$
$32$	6.70820	1.18585
$33$	0	0
$34$	−12.5623	−2.15442
$35$	1.00000	0.169031
$36$	−7.85410	−1.30902
$37$	−7.23607	−1.18960	−0.594801	−	0.803873i	$-0.702769\pi$
$37$	−7.23607	−1.18960	−0.594801	+	0.803873i	$0.702769\pi$
$38$	7.23607	1.17385
$39$	2.85410	0.457022
$40$	2.23607	0.353553
$41$	2.47214	0.386083	0.193041	−	0.981191i	$-0.438165\pi$
$41$	2.47214	0.386083	0.193041	+	0.981191i	$0.438165\pi$
$42$	1.38197	0.213242
$43$	−5.23607	−0.798493	−0.399246	−	0.916844i	$-0.630728\pi$
$43$	−5.23607	−0.798493	−0.399246	+	0.916844i	$0.630728\pi$
$44$	0	0
$45$	2.61803	0.390273
$46$	10.0000	1.47442
$47$	−1.14590	−0.167146	−0.0835732	−	0.996502i	$-0.526633\pi$
$47$	−1.14590	−0.167146	−0.0835732	+	0.996502i	$0.526633\pi$
$48$	−0.618034	−0.0892055
$49$	1.00000	0.142857
$50$	−2.23607	−0.316228
$51$	3.47214	0.486196
$52$	13.8541	1.92122
$53$	−1.52786	−0.209868	−0.104934	−	0.994479i	$-0.533463\pi$
$53$	−1.52786	−0.209868	−0.104934	+	0.994479i	$0.533463\pi$
$54$	7.76393	1.05654
$55$	0	0
$56$	2.23607	0.298807
$57$	−2.00000	−0.264906
$58$	−1.90983	−0.250773
$59$	−9.23607	−1.20243	−0.601217	−	0.799086i	$-0.705317\pi$
$59$	−9.23607	−1.20243	−0.601217	+	0.799086i	$0.705317\pi$
$60$	−1.85410	−0.239364
$61$	−4.76393	−0.609959	−0.304979	−	0.952359i	$-0.598650\pi$
$61$	−4.76393	−0.609959	−0.304979	+	0.952359i	$0.598650\pi$
$62$	−7.23607	−0.918982
$63$	2.61803	0.329841
$64$	−13.0000	−1.62500
$65$	−4.61803	−0.572797
$66$	0	0
$67$	8.18034	0.999388	0.499694	−	0.866202i	$-0.333446\pi$
$67$	8.18034	0.999388	0.499694	+	0.866202i	$0.333446\pi$
$68$	16.8541	2.04386
$69$	−2.76393	−0.332738
$70$	−2.23607	−0.267261
$71$	16.3262	1.93757	0.968784	−	0.247906i	$-0.0797425\pi$
$71$	16.3262	1.93757	0.968784	+	0.247906i	$0.0797425\pi$
$72$	5.85410	0.689913
$73$	6.38197	0.746953	0.373476	−	0.927640i	$-0.378166\pi$
$73$	6.38197	0.746953	0.373476	+	0.927640i	$0.378166\pi$
$74$	16.1803	1.88093
$75$	0.618034	0.0713644
$76$	−9.70820	−1.11361
$77$	0	0
$78$	−6.38197	−0.722615
$79$	10.7984	1.21491	0.607456	−	0.794353i	$-0.292190\pi$
$79$	10.7984	1.21491	0.607456	+	0.794353i	$0.292190\pi$
$80$	1.00000	0.111803
$81$	5.70820	0.634245
$82$	−5.52786	−0.610450
$83$	9.56231	1.04960	0.524800	−	0.851226i	$-0.324140\pi$
$83$	9.56231	1.04960	0.524800	+	0.851226i	$0.324140\pi$
$84$	−1.85410	−0.202299
$85$	−5.61803	−0.609361
$86$	11.7082	1.26253
$87$	0.527864	0.0565930
$88$	0	0
$89$	12.7639	1.35297	0.676487	−	0.736455i	$-0.263501\pi$
$89$	12.7639	1.35297	0.676487	+	0.736455i	$0.263501\pi$
$90$	−5.85410	−0.617077
$91$	−4.61803	−0.484102
$92$	−13.4164	−1.39876
$93$	2.00000	0.207390
$94$	2.56231	0.264282
$95$	3.23607	0.332014
$96$	4.14590	0.423139
$97$	−15.3262	−1.55614	−0.778072	−	0.628175i	$-0.783802\pi$
$97$	−15.3262	−1.55614	−0.778072	+	0.628175i	$0.783802\pi$
$98$	−2.23607	−0.225877
$99$	0	0
$100$	3.00000	0.300000
$101$	−13.7082	−1.36402	−0.682009	−	0.731344i	$-0.738893\pi$
$101$	−13.7082	−1.36402	−0.682009	+	0.731344i	$0.738893\pi$
$102$	−7.76393	−0.768744
$103$	−17.3262	−1.70720	−0.853602	−	0.520925i	$-0.825587\pi$
$103$	−17.3262	−1.70720	−0.853602	+	0.520925i	$0.825587\pi$
$104$	−10.3262	−1.01257
$105$	0.618034	0.0603139
$106$	3.41641	0.331831
$107$	−7.23607	−0.699537	−0.349769	−	0.936836i	$-0.613740\pi$
$107$	−7.23607	−0.699537	−0.349769	+	0.936836i	$0.613740\pi$
$108$	−10.4164	−1.00232
$109$	−11.5279	−1.10417	−0.552085	−	0.833788i	$-0.686167\pi$
$109$	−11.5279	−1.10417	−0.552085	+	0.833788i	$0.686167\pi$
$110$	0	0
$111$	−4.47214	−0.424476
$112$	1.00000	0.0944911
$113$	10.4721	0.985136	0.492568	−	0.870274i	$-0.336058\pi$
$113$	10.4721	0.985136	0.492568	+	0.870274i	$0.336058\pi$
$114$	4.47214	0.418854
$115$	4.47214	0.417029
$116$	2.56231	0.237904
$117$	−12.0902	−1.11774
$118$	20.6525	1.90121
$119$	−5.61803	−0.515004
$120$	1.38197	0.126156
$121$	0	0
$122$	10.6525	0.964430
$123$	1.52786	0.137763
$124$	9.70820	0.871822
$125$	−1.00000	−0.0894427
$126$	−5.85410	−0.521525
$127$	9.23607	0.819569	0.409784	−	0.912182i	$-0.365604\pi$
$127$	9.23607	0.819569	0.409784	+	0.912182i	$0.365604\pi$
$128$	15.6525	1.38350
$129$	−3.23607	−0.284920
$130$	10.3262	0.905671
$131$	8.00000	0.698963	0.349482	−	0.936943i	$-0.386358\pi$
$131$	8.00000	0.698963	0.349482	+	0.936943i	$0.386358\pi$
$132$	0	0
$133$	3.23607	0.280603
$134$	−18.2918	−1.58017
$135$	3.47214	0.298834
$136$	−12.5623	−1.07721
$137$	−11.4164	−0.975370	−0.487685	−	0.873020i	$-0.662158\pi$
$137$	−11.4164	−0.975370	−0.487685	+	0.873020i	$0.662158\pi$
$138$	6.18034	0.526105
$139$	5.52786	0.468867	0.234434	−	0.972132i	$-0.424676\pi$
$139$	5.52786	0.468867	0.234434	+	0.972132i	$0.424676\pi$
$140$	3.00000	0.253546
$141$	−0.708204	−0.0596415
$142$	−36.5066	−3.06356
$143$	0	0
$144$	2.61803	0.218169
$145$	−0.854102	−0.0709293
$146$	−14.2705	−1.18104
$147$	0.618034	0.0509746
$148$	−21.7082	−1.78440
$149$	−17.8541	−1.46267	−0.731333	−	0.682021i	$-0.761101\pi$
$149$	−17.8541	−1.46267	−0.731333	+	0.682021i	$0.761101\pi$
$150$	−1.38197	−0.112837
$151$	−0.381966	−0.0310840	−0.0155420	−	0.999879i	$-0.504947\pi$
$151$	−0.381966	−0.0310840	−0.0155420	+	0.999879i	$0.504947\pi$
$152$	7.23607	0.586923
$153$	−14.7082	−1.18909
$154$	0	0
$155$	−3.23607	−0.259927
$156$	8.56231	0.685533
$157$	−16.0902	−1.28414	−0.642068	−	0.766648i	$-0.721923\pi$
$157$	−16.0902	−1.28414	−0.642068	+	0.766648i	$0.721923\pi$
$158$	−24.1459	−1.92094
$159$	−0.944272	−0.0748856
$160$	−6.70820	−0.530330
$161$	4.47214	0.352454
$162$	−12.7639	−1.00283
$163$	−22.1803	−1.73730	−0.868649	−	0.495428i	$-0.835011\pi$
$163$	−22.1803	−1.73730	−0.868649	+	0.495428i	$0.835011\pi$
$164$	7.41641	0.579124
$165$	0	0
$166$	−21.3820	−1.65956
$167$	−12.0000	−0.928588	−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000	−0.928588	−0.464294	+	0.885681i	$0.653692\pi$
$168$	1.38197	0.106621
$169$	8.32624	0.640480
$170$	12.5623	0.963485
$171$	8.47214	0.647880
$172$	−15.7082	−1.19774
$173$	−1.56231	−0.118780	−0.0593900	−	0.998235i	$-0.518916\pi$
$173$	−1.56231	−0.118780	−0.0593900	+	0.998235i	$0.518916\pi$
$174$	−1.18034	−0.0894813
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	−5.70820	−0.429055
$178$	−28.5410	−2.13924
$179$	19.6180	1.46632	0.733160	−	0.680056i	$-0.238044\pi$
$179$	19.6180	1.46632	0.733160	+	0.680056i	$0.238044\pi$
$180$	7.85410	0.585410
$181$	5.52786	0.410883	0.205441	−	0.978669i	$-0.434137\pi$
$181$	5.52786	0.410883	0.205441	+	0.978669i	$0.434137\pi$
$182$	10.3262	0.765432
$183$	−2.94427	−0.217647
$184$	10.0000	0.737210
$185$	7.23607	0.532006
$186$	−4.47214	−0.327913
$187$	0	0
$188$	−3.43769	−0.250720
$189$	3.47214	0.252561
$190$	−7.23607	−0.524960
$191$	23.0902	1.67075	0.835373	−	0.549683i	$-0.185252\pi$
$191$	23.0902	1.67075	0.835373	+	0.549683i	$0.185252\pi$
$192$	−8.03444	−0.579836
$193$	4.00000	0.287926	0.143963	−	0.989583i	$-0.454015\pi$
$193$	4.00000	0.287926	0.143963	+	0.989583i	$0.454015\pi$
$194$	34.2705	2.46048
$195$	−2.85410	−0.204386
$196$	3.00000	0.214286
$197$	−12.0000	−0.854965	−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000	−0.854965	−0.427482	+	0.904024i	$0.640599\pi$
$198$	0	0
$199$	−18.0000	−1.27599	−0.637993	−	0.770042i	$-0.720235\pi$
$199$	−18.0000	−1.27599	−0.637993	+	0.770042i	$0.720235\pi$
$200$	−2.23607	−0.158114
$201$	5.05573	0.356604
$202$	30.6525	2.15670
$203$	−0.854102	−0.0599462
$204$	10.4164	0.729294
$205$	−2.47214	−0.172661
$206$	38.7426	2.69933
$207$	11.7082	0.813776
$208$	−4.61803	−0.320203
$209$	0	0
$210$	−1.38197	−0.0953647
$211$	7.67376	0.528284	0.264142	−	0.964484i	$-0.414911\pi$
$211$	7.67376	0.528284	0.264142	+	0.964484i	$0.414911\pi$
$212$	−4.58359	−0.314802
$213$	10.0902	0.691367
$214$	16.1803	1.10607
$215$	5.23607	0.357097
$216$	7.76393	0.528269
$217$	−3.23607	−0.219679
$218$	25.7771	1.74584
$219$	3.94427	0.266529
$220$	0	0
$221$	25.9443	1.74520
$222$	10.0000	0.671156
$223$	1.52786	0.102313	0.0511567	−	0.998691i	$-0.483709\pi$
$223$	1.52786	0.102313	0.0511567	+	0.998691i	$0.483709\pi$
$224$	−6.70820	−0.448211
$225$	−2.61803	−0.174536
$226$	−23.4164	−1.55764
$227$	−10.7984	−0.716713	−0.358357	−	0.933585i	$-0.616663\pi$
$227$	−10.7984	−0.716713	−0.358357	+	0.933585i	$0.616663\pi$
$228$	−6.00000	−0.397360
$229$	−24.7639	−1.63645	−0.818223	−	0.574900i	$-0.805041\pi$
$229$	−24.7639	−1.63645	−0.818223	+	0.574900i	$0.805041\pi$
$230$	−10.0000	−0.659380
$231$	0	0
$232$	−1.90983	−0.125386
$233$	6.65248	0.435818	0.217909	−	0.975969i	$-0.430076\pi$
$233$	6.65248	0.435818	0.217909	+	0.975969i	$0.430076\pi$
$234$	27.0344	1.76730
$235$	1.14590	0.0747501
$236$	−27.7082	−1.80365
$237$	6.67376	0.433507
$238$	12.5623	0.814293
$239$	24.9787	1.61574	0.807869	−	0.589362i	$-0.200621\pi$
$239$	24.9787	1.61574	0.807869	+	0.589362i	$0.200621\pi$
$240$	0.618034	0.0398939
$241$	−17.1246	−1.10309	−0.551547	−	0.834144i	$-0.685962\pi$
$241$	−17.1246	−1.10309	−0.551547	+	0.834144i	$0.685962\pi$
$242$	0	0
$243$	13.9443	0.894525
$244$	−14.2918	−0.914938
$245$	−1.00000	−0.0638877
$246$	−3.41641	−0.217822
$247$	−14.9443	−0.950881
$248$	−7.23607	−0.459491
$249$	5.90983	0.374520
$250$	2.23607	0.141421
$251$	−7.70820	−0.486538	−0.243269	−	0.969959i	$-0.578220\pi$
$251$	−7.70820	−0.486538	−0.243269	+	0.969959i	$0.578220\pi$
$252$	7.85410	0.494762
$253$	0	0
$254$	−20.6525	−1.29585
$255$	−3.47214	−0.217434
$256$	−9.00000	−0.562500
$257$	−2.38197	−0.148583	−0.0742915	−	0.997237i	$-0.523670\pi$
$257$	−2.38197	−0.148583	−0.0742915	+	0.997237i	$0.523670\pi$
$258$	7.23607	0.450498
$259$	7.23607	0.449627
$260$	−13.8541	−0.859195
$261$	−2.23607	−0.138409
$262$	−17.8885	−1.10516
$263$	14.1803	0.874397	0.437199	−	0.899365i	$-0.355971\pi$
$263$	14.1803	0.874397	0.437199	+	0.899365i	$0.355971\pi$
$264$	0	0
$265$	1.52786	0.0938559
$266$	−7.23607	−0.443672
$267$	7.88854	0.482771
$268$	24.5410	1.49908
$269$	−18.6525	−1.13726	−0.568631	−	0.822593i	$-0.692527\pi$
$269$	−18.6525	−1.13726	−0.568631	+	0.822593i	$0.692527\pi$
$270$	−7.76393	−0.472498
$271$	23.2361	1.41149	0.705745	−	0.708466i	$-0.250612\pi$
$271$	23.2361	1.41149	0.705745	+	0.708466i	$0.250612\pi$
$272$	−5.61803	−0.340643
$273$	−2.85410	−0.172738
$274$	25.5279	1.54219
$275$	0	0
$276$	−8.29180	−0.499107
$277$	−9.41641	−0.565777	−0.282889	−	0.959153i	$-0.591293\pi$
$277$	−9.41641	−0.565777	−0.282889	+	0.959153i	$0.591293\pi$
$278$	−12.3607	−0.741344
$279$	−8.47214	−0.507214
$280$	−2.23607	−0.133631
$281$	−8.47214	−0.505405	−0.252703	−	0.967544i	$-0.581319\pi$
$281$	−8.47214	−0.505405	−0.252703	+	0.967544i	$0.581319\pi$
$282$	1.58359	0.0943015
$283$	−7.43769	−0.442125	−0.221063	−	0.975260i	$-0.570952\pi$
$283$	−7.43769	−0.442125	−0.221063	+	0.975260i	$0.570952\pi$
$284$	48.9787	2.90635
$285$	2.00000	0.118470
$286$	0	0
$287$	−2.47214	−0.145926
$288$	−17.5623	−1.03487
$289$	14.5623	0.856606
$290$	1.90983	0.112149
$291$	−9.47214	−0.555266
$292$	19.1459	1.12043
$293$	−9.41641	−0.550112	−0.275056	−	0.961428i	$-0.588696\pi$
$293$	−9.41641	−0.550112	−0.275056	+	0.961428i	$0.588696\pi$
$294$	−1.38197	−0.0805979
$295$	9.23607	0.537745
$296$	16.1803	0.940463
$297$	0	0
$298$	39.9230	2.31268
$299$	−20.6525	−1.19436
$300$	1.85410	0.107047
$301$	5.23607	0.301802
$302$	0.854102	0.0491480
$303$	−8.47214	−0.486711
$304$	3.23607	0.185601
$305$	4.76393	0.272782
$306$	32.8885	1.88011
$307$	−20.5623	−1.17355	−0.586776	−	0.809749i	$-0.699603\pi$
$307$	−20.5623	−1.17355	−0.586776	+	0.809749i	$0.699603\pi$
$308$	0	0
$309$	−10.7082	−0.609168
$310$	7.23607	0.410981
$311$	13.1246	0.744228	0.372114	−	0.928187i	$-0.378633\pi$
$311$	13.1246	0.744228	0.372114	+	0.928187i	$0.378633\pi$
$312$	−6.38197	−0.361308
$313$	−18.0000	−1.01742	−0.508710	−	0.860938i	$-0.669877\pi$
$313$	−18.0000	−1.01742	−0.508710	+	0.860938i	$0.669877\pi$
$314$	35.9787	2.03040
$315$	−2.61803	−0.147510
$316$	32.3951	1.82237
$317$	−21.5279	−1.20913	−0.604563	−	0.796558i	$-0.706652\pi$
$317$	−21.5279	−1.20913	−0.604563	+	0.796558i	$0.706652\pi$
$318$	2.11146	0.118405
$319$	0	0
$320$	13.0000	0.726722
$321$	−4.47214	−0.249610
$322$	−10.0000	−0.557278
$323$	−18.1803	−1.01158
$324$	17.1246	0.951367
$325$	4.61803	0.256162
$326$	49.5967	2.74691
$327$	−7.12461	−0.393992
$328$	−5.52786	−0.305225
$329$	1.14590	0.0631754
$330$	0	0
$331$	−18.5066	−1.01721	−0.508607	−	0.860999i	$-0.669839\pi$
$331$	−18.5066	−1.01721	−0.508607	+	0.860999i	$0.669839\pi$
$332$	28.6869	1.57440
$333$	18.9443	1.03814
$334$	26.8328	1.46823
$335$	−8.18034	−0.446940
$336$	0.618034	0.0337165
$337$	−31.4164	−1.71136	−0.855680	−	0.517505i	$-0.826861\pi$
$337$	−31.4164	−1.71136	−0.855680	+	0.517505i	$0.826861\pi$
$338$	−18.6180	−1.01269
$339$	6.47214	0.351518
$340$	−16.8541	−0.914042
$341$	0	0
$342$	−18.9443	−1.02439
$343$	−1.00000	−0.0539949
$344$	11.7082	0.631264
$345$	2.76393	0.148805
$346$	3.49342	0.187808
$347$	−1.52786	−0.0820200	−0.0410100	−	0.999159i	$-0.513058\pi$
$347$	−1.52786	−0.0820200	−0.0410100	+	0.999159i	$0.513058\pi$
$348$	1.58359	0.0848894
$349$	3.88854	0.208149	0.104074	−	0.994570i	$-0.466812\pi$
$349$	3.88854	0.208149	0.104074	+	0.994570i	$0.466812\pi$
$350$	2.23607	0.119523
$351$	−16.0344	−0.855855
$352$	0	0
$353$	−13.5623	−0.721849	−0.360924	−	0.932595i	$-0.617539\pi$
$353$	−13.5623	−0.721849	−0.360924	+	0.932595i	$0.617539\pi$
$354$	12.7639	0.678395
$355$	−16.3262	−0.866507
$356$	38.2918	2.02946
$357$	−3.47214	−0.183765
$358$	−43.8673	−2.31846
$359$	−12.9787	−0.684990	−0.342495	−	0.939520i	$-0.611272\pi$
$359$	−12.9787	−0.684990	−0.342495	+	0.939520i	$0.611272\pi$
$360$	−5.85410	−0.308538
$361$	−8.52786	−0.448835
$362$	−12.3607	−0.649663
$363$	0	0
$364$	−13.8541	−0.726152
$365$	−6.38197	−0.334047
$366$	6.58359	0.344130
$367$	−31.4508	−1.64172	−0.820860	−	0.571129i	$-0.806506\pi$
$367$	−31.4508	−1.64172	−0.820860	+	0.571129i	$0.806506\pi$
$368$	4.47214	0.233126
$369$	−6.47214	−0.336926
$370$	−16.1803	−0.841176
$371$	1.52786	0.0793227
$372$	6.00000	0.311086
$373$	11.1246	0.576011	0.288005	−	0.957629i	$-0.407008\pi$
$373$	11.1246	0.576011	0.288005	+	0.957629i	$0.407008\pi$
$374$	0	0
$375$	−0.618034	−0.0319151
$376$	2.56231	0.132141
$377$	3.94427	0.203140
$378$	−7.76393	−0.399334
$379$	24.7426	1.27094	0.635472	−	0.772124i	$-0.280805\pi$
$379$	24.7426	1.27094	0.635472	+	0.772124i	$0.280805\pi$
$380$	9.70820	0.498020
$381$	5.70820	0.292440
$382$	−51.6312	−2.64168
$383$	26.7984	1.36933	0.684666	−	0.728857i	$-0.259948\pi$
$383$	26.7984	1.36933	0.684666	+	0.728857i	$0.259948\pi$
$384$	9.67376	0.493662
$385$	0	0
$386$	−8.94427	−0.455251
$387$	13.7082	0.696827
$388$	−45.9787	−2.33422
$389$	−33.5623	−1.70168	−0.850838	−	0.525428i	$-0.823905\pi$
$389$	−33.5623	−1.70168	−0.850838	+	0.525428i	$0.823905\pi$
$390$	6.38197	0.323163
$391$	−25.1246	−1.27061
$392$	−2.23607	−0.112938
$393$	4.94427	0.249406
$394$	26.8328	1.35182
$395$	−10.7984	−0.543325
$396$	0	0
$397$	35.1591	1.76458	0.882291	−	0.470704i	$-0.156000\pi$
$397$	35.1591	1.76458	0.882291	+	0.470704i	$0.156000\pi$
$398$	40.2492	2.01751
$399$	2.00000	0.100125
$400$	−1.00000	−0.0500000
$401$	15.5066	0.774362	0.387181	−	0.922004i	$-0.373449\pi$
$401$	15.5066	0.774362	0.387181	+	0.922004i	$0.373449\pi$
$402$	−11.3050	−0.563840
$403$	14.9443	0.744427
$404$	−41.1246	−2.04603
$405$	−5.70820	−0.283643
$406$	1.90983	0.0947833
$407$	0	0
$408$	−7.76393	−0.384372
$409$	−3.23607	−0.160013	−0.0800066	−	0.996794i	$-0.525494\pi$
$409$	−3.23607	−0.160013	−0.0800066	+	0.996794i	$0.525494\pi$
$410$	5.52786	0.273002
$411$	−7.05573	−0.348033
$412$	−51.9787	−2.56081
$413$	9.23607	0.454477
$414$	−26.1803	−1.28669
$415$	−9.56231	−0.469395
$416$	30.9787	1.51886
$417$	3.41641	0.167302
$418$	0	0
$419$	−35.3050	−1.72476	−0.862380	−	0.506262i	$-0.831027\pi$
$419$	−35.3050	−1.72476	−0.862380	+	0.506262i	$0.831027\pi$
$420$	1.85410	0.0904709
$421$	−34.5066	−1.68175	−0.840874	−	0.541231i	$-0.817958\pi$
$421$	−34.5066	−1.68175	−0.840874	+	0.541231i	$0.817958\pi$
$422$	−17.1591	−0.835290
$423$	3.00000	0.145865
$424$	3.41641	0.165915
$425$	5.61803	0.272515
$426$	−22.5623	−1.09315
$427$	4.76393	0.230543
$428$	−21.7082	−1.04931
$429$	0	0
$430$	−11.7082	−0.564620
$431$	−5.32624	−0.256556	−0.128278	−	0.991738i	$-0.540945\pi$
$431$	−5.32624	−0.256556	−0.128278	+	0.991738i	$0.540945\pi$
$432$	3.47214	0.167053
$433$	12.0344	0.578338	0.289169	−	0.957278i	$-0.406621\pi$
$433$	12.0344	0.578338	0.289169	+	0.957278i	$0.406621\pi$
$434$	7.23607	0.347342
$435$	−0.527864	−0.0253091
$436$	−34.5836	−1.65625
$437$	14.4721	0.692296
$438$	−8.81966	−0.421420
$439$	4.29180	0.204836	0.102418	−	0.994741i	$-0.467342\pi$
$439$	4.29180	0.204836	0.102418	+	0.994741i	$0.467342\pi$
$440$	0	0
$441$	−2.61803	−0.124668
$442$	−58.0132	−2.75940
$443$	−3.34752	−0.159046	−0.0795228	−	0.996833i	$-0.525340\pi$
$443$	−3.34752	−0.159046	−0.0795228	+	0.996833i	$0.525340\pi$
$444$	−13.4164	−0.636715
$445$	−12.7639	−0.605068
$446$	−3.41641	−0.161772
$447$	−11.0344	−0.521911
$448$	13.0000	0.614192
$449$	−9.27051	−0.437502	−0.218751	−	0.975781i	$-0.570198\pi$
$449$	−9.27051	−0.437502	−0.218751	+	0.975781i	$0.570198\pi$
$450$	5.85410	0.275965
$451$	0	0
$452$	31.4164	1.47770
$453$	−0.236068	−0.0110914
$454$	24.1459	1.13322
$455$	4.61803	0.216497
$456$	4.47214	0.209427
$457$	−37.7771	−1.76714	−0.883569	−	0.468301i	$-0.844866\pi$
$457$	−37.7771	−1.76714	−0.883569	+	0.468301i	$0.844866\pi$
$458$	55.3738	2.58745
$459$	−19.5066	−0.910489
$460$	13.4164	0.625543
$461$	16.2918	0.758785	0.379392	−	0.925236i	$-0.376133\pi$
$461$	16.2918	0.758785	0.379392	+	0.925236i	$0.376133\pi$
$462$	0	0
$463$	−17.1246	−0.795848	−0.397924	−	0.917418i	$-0.630269\pi$
$463$	−17.1246	−0.795848	−0.397924	+	0.917418i	$0.630269\pi$
$464$	−0.854102	−0.0396507
$465$	−2.00000	−0.0927478
$466$	−14.8754	−0.689089
$467$	−32.3262	−1.49588	−0.747940	−	0.663766i	$-0.768957\pi$
$467$	−32.3262	−1.49588	−0.747940	+	0.663766i	$0.768957\pi$
$468$	−36.2705	−1.67660
$469$	−8.18034	−0.377733
$470$	−2.56231	−0.118190
$471$	−9.94427	−0.458208
$472$	20.6525	0.950607
$473$	0	0
$474$	−14.9230	−0.685435
$475$	−3.23607	−0.148481
$476$	−16.8541	−0.772506
$477$	4.00000	0.183147
$478$	−55.8541	−2.55471
$479$	22.6525	1.03502	0.517509	−	0.855678i	$-0.326859\pi$
$479$	22.6525	1.03502	0.517509	+	0.855678i	$0.326859\pi$
$480$	−4.14590	−0.189233
$481$	−33.4164	−1.52366
$482$	38.2918	1.74414
$483$	2.76393	0.125763
$484$	0	0
$485$	15.3262	0.695929
$486$	−31.1803	−1.41437
$487$	−1.81966	−0.0824567	−0.0412283	−	0.999150i	$-0.513127\pi$
$487$	−1.81966	−0.0824567	−0.0412283	+	0.999150i	$0.513127\pi$
$488$	10.6525	0.482215
$489$	−13.7082	−0.619906
$490$	2.23607	0.101015
$491$	2.11146	0.0952887	0.0476443	−	0.998864i	$-0.484829\pi$
$491$	2.11146	0.0952887	0.0476443	+	0.998864i	$0.484829\pi$
$492$	4.58359	0.206644
$493$	4.79837	0.216108
$494$	33.4164	1.50348
$495$	0	0
$496$	−3.23607	−0.145304
$497$	−16.3262	−0.732332
$498$	−13.2148	−0.592169
$499$	−23.0344	−1.03116	−0.515582	−	0.856840i	$-0.672424\pi$
$499$	−23.0344	−1.03116	−0.515582	+	0.856840i	$0.672424\pi$
$500$	−3.00000	−0.134164
$501$	−7.41641	−0.331341
$502$	17.2361	0.769283
$503$	3.09017	0.137784	0.0688919	−	0.997624i	$-0.478054\pi$
$503$	3.09017	0.137784	0.0688919	+	0.997624i	$0.478054\pi$
$504$	−5.85410	−0.260762
$505$	13.7082	0.610007
$506$	0	0
$507$	5.14590	0.228537
$508$	27.7082	1.22935
$509$	26.3607	1.16842	0.584208	−	0.811604i	$-0.301405\pi$
$509$	26.3607	1.16842	0.584208	+	0.811604i	$0.301405\pi$
$510$	7.76393	0.343793
$511$	−6.38197	−0.282322
$512$	−11.1803	−0.494106
$513$	11.2361	0.496085
$514$	5.32624	0.234930
$515$	17.3262	0.763485
$516$	−9.70820	−0.427380
$517$	0	0
$518$	−16.1803	−0.710923
$519$	−0.965558	−0.0423833
$520$	10.3262	0.452835
$521$	−14.1803	−0.621252	−0.310626	−	0.950532i	$-0.600539\pi$
$521$	−14.1803	−0.621252	−0.310626	+	0.950532i	$0.600539\pi$
$522$	5.00000	0.218844
$523$	1.14590	0.0501066	0.0250533	−	0.999686i	$-0.492024\pi$
$523$	1.14590	0.0501066	0.0250533	+	0.999686i	$0.492024\pi$
$524$	24.0000	1.04844
$525$	−0.618034	−0.0269732
$526$	−31.7082	−1.38254
$527$	18.1803	0.791948
$528$	0	0
$529$	−3.00000	−0.130435
$530$	−3.41641	−0.148399
$531$	24.1803	1.04934
$532$	9.70820	0.420904
$533$	11.4164	0.494500
$534$	−17.6393	−0.763328
$535$	7.23607	0.312842
$536$	−18.2918	−0.790085
$537$	12.1246	0.523216
$538$	41.7082	1.79817
$539$	0	0
$540$	10.4164	0.448251
$541$	6.14590	0.264233	0.132116	−	0.991234i	$-0.457823\pi$
$541$	6.14590	0.264233	0.132116	+	0.991234i	$0.457823\pi$
$542$	−51.9574	−2.23176
$543$	3.41641	0.146612
$544$	37.6869	1.61581
$545$	11.5279	0.493799
$546$	6.38197	0.273123
$547$	−18.0689	−0.772570	−0.386285	−	0.922380i	$-0.626242\pi$
$547$	−18.0689	−0.772570	−0.386285	+	0.922380i	$0.626242\pi$
$548$	−34.2492	−1.46305
$549$	12.4721	0.532298
$550$	0	0
$551$	−2.76393	−0.117747
$552$	6.18034	0.263053
$553$	−10.7984	−0.459194
$554$	21.0557	0.894572
$555$	4.47214	0.189832
$556$	16.5836	0.703301
$557$	−17.7082	−0.750321	−0.375160	−	0.926960i	$-0.622412\pi$
$557$	−17.7082	−0.750321	−0.375160	+	0.926960i	$0.622412\pi$
$558$	18.9443	0.801975
$559$	−24.1803	−1.02272
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	18.9443	0.799116
$563$	−23.6180	−0.995381	−0.497691	−	0.867355i	$-0.665819\pi$
$563$	−23.6180	−0.995381	−0.497691	+	0.867355i	$0.665819\pi$
$564$	−2.12461	−0.0894623
$565$	−10.4721	−0.440566
$566$	16.6312	0.699061
$567$	−5.70820	−0.239722
$568$	−36.5066	−1.53178
$569$	−37.7984	−1.58459	−0.792295	−	0.610138i	$-0.791114\pi$
$569$	−37.7984	−1.58459	−0.792295	+	0.610138i	$0.791114\pi$
$570$	−4.47214	−0.187317
$571$	−35.9787	−1.50566	−0.752831	−	0.658214i	$-0.771312\pi$
$571$	−35.9787	−1.50566	−0.752831	+	0.658214i	$0.771312\pi$
$572$	0	0
$573$	14.2705	0.596159
$574$	5.52786	0.230729
$575$	−4.47214	−0.186501
$576$	34.0344	1.41810
$577$	33.2148	1.38275	0.691375	−	0.722496i	$-0.257005\pi$
$577$	33.2148	1.38275	0.691375	+	0.722496i	$0.257005\pi$
$578$	−32.5623	−1.35441
$579$	2.47214	0.102738
$580$	−2.56231	−0.106394
$581$	−9.56231	−0.396711
$582$	21.1803	0.877953
$583$	0	0
$584$	−14.2705	−0.590518
$585$	12.0902	0.499867
$586$	21.0557	0.869804
$587$	6.72949	0.277756	0.138878	−	0.990310i	$-0.455650\pi$
$587$	6.72949	0.277756	0.138878	+	0.990310i	$0.455650\pi$
$588$	1.85410	0.0764619
$589$	−10.4721	−0.431497
$590$	−20.6525	−0.850249
$591$	−7.41641	−0.305070
$592$	7.23607	0.297401
$593$	9.79837	0.402371	0.201185	−	0.979553i	$-0.435521\pi$
$593$	9.79837	0.402371	0.201185	+	0.979553i	$0.435521\pi$
$594$	0	0
$595$	5.61803	0.230317
$596$	−53.5623	−2.19400
$597$	−11.1246	−0.455300
$598$	46.1803	1.88845
$599$	26.2705	1.07338	0.536692	−	0.843778i	$-0.319674\pi$
$599$	26.2705	1.07338	0.536692	+	0.843778i	$0.319674\pi$
$600$	−1.38197	−0.0564185
$601$	−15.4164	−0.628848	−0.314424	−	0.949283i	$-0.601811\pi$
$601$	−15.4164	−0.628848	−0.314424	+	0.949283i	$0.601811\pi$
$602$	−11.7082	−0.477191
$603$	−21.4164	−0.872144
$604$	−1.14590	−0.0466259
$605$	0	0
$606$	18.9443	0.769558
$607$	−1.90983	−0.0775176	−0.0387588	−	0.999249i	$-0.512340\pi$
$607$	−1.90983	−0.0775176	−0.0387588	+	0.999249i	$0.512340\pi$
$608$	−21.7082	−0.880384
$609$	−0.527864	−0.0213901
$610$	−10.6525	−0.431306
$611$	−5.29180	−0.214083
$612$	−44.1246	−1.78363
$613$	−40.8328	−1.64922	−0.824611	−	0.565700i	$-0.808606\pi$
$613$	−40.8328	−1.64922	−0.824611	+	0.565700i	$0.808606\pi$
$614$	45.9787	1.85555
$615$	−1.52786	−0.0616094
$616$	0	0
$617$	−2.76393	−0.111272	−0.0556359	−	0.998451i	$-0.517719\pi$
$617$	−2.76393	−0.111272	−0.0556359	+	0.998451i	$0.517719\pi$
$618$	23.9443	0.963180
$619$	−22.4721	−0.903231	−0.451616	−	0.892213i	$-0.649152\pi$
$619$	−22.4721	−0.903231	−0.451616	+	0.892213i	$0.649152\pi$
$620$	−9.70820	−0.389891
$621$	15.5279	0.623112
$622$	−29.3475	−1.17673
$623$	−12.7639	−0.511376
$624$	−2.85410	−0.114256
$625$	1.00000	0.0400000
$626$	40.2492	1.60868
$627$	0	0
$628$	−48.2705	−1.92620
$629$	−40.6525	−1.62092
$630$	5.85410	0.233233
$631$	−9.50658	−0.378451	−0.189225	−	0.981934i	$-0.560598\pi$
$631$	−9.50658	−0.378451	−0.189225	+	0.981934i	$0.560598\pi$
$632$	−24.1459	−0.960472
$633$	4.74265	0.188503
$634$	48.1378	1.91179
$635$	−9.23607	−0.366522
$636$	−2.83282	−0.112328
$637$	4.61803	0.182973
$638$	0	0
$639$	−42.7426	−1.69087
$640$	−15.6525	−0.618718
$641$	20.9787	0.828609	0.414305	−	0.910138i	$-0.364025\pi$
$641$	20.9787	0.828609	0.414305	+	0.910138i	$0.364025\pi$
$642$	10.0000	0.394669
$643$	10.7984	0.425846	0.212923	−	0.977069i	$-0.431702\pi$
$643$	10.7984	0.425846	0.212923	+	0.977069i	$0.431702\pi$
$644$	13.4164	0.528681
$645$	3.23607	0.127420
$646$	40.6525	1.59945
$647$	−46.8541	−1.84202	−0.921012	−	0.389533i	$-0.872636\pi$
$647$	−46.8541	−1.84202	−0.921012	+	0.389533i	$0.872636\pi$
$648$	−12.7639	−0.501415
$649$	0	0
$650$	−10.3262	−0.405028
$651$	−2.00000	−0.0783862
$652$	−66.5410	−2.60595
$653$	−38.1803	−1.49411	−0.747056	−	0.664761i	$-0.768533\pi$
$653$	−38.1803	−1.49411	−0.747056	+	0.664761i	$0.768533\pi$
$654$	15.9311	0.622956
$655$	−8.00000	−0.312586
$656$	−2.47214	−0.0965207
$657$	−16.7082	−0.651849
$658$	−2.56231	−0.0998891
$659$	−4.03444	−0.157160	−0.0785798	−	0.996908i	$-0.525039\pi$
$659$	−4.03444	−0.157160	−0.0785798	+	0.996908i	$0.525039\pi$
$660$	0	0
$661$	−6.58359	−0.256072	−0.128036	−	0.991770i	$-0.540867\pi$
$661$	−6.58359	−0.256072	−0.128036	+	0.991770i	$0.540867\pi$
$662$	41.3820	1.60836
$663$	16.0344	0.622726
$664$	−21.3820	−0.829781
$665$	−3.23607	−0.125489
$666$	−42.3607	−1.64144
$667$	−3.81966	−0.147898
$668$	−36.0000	−1.39288
$669$	0.944272	0.0365077
$670$	18.2918	0.706674
$671$	0	0
$672$	−4.14590	−0.159931
$673$	21.8885	0.843741	0.421871	−	0.906656i	$-0.361374\pi$
$673$	21.8885	0.843741	0.421871	+	0.906656i	$0.361374\pi$
$674$	70.2492	2.70590
$675$	−3.47214	−0.133643
$676$	24.9787	0.960720
$677$	48.8541	1.87762	0.938808	−	0.344441i	$-0.111932\pi$
$677$	48.8541	1.87762	0.938808	+	0.344441i	$0.111932\pi$
$678$	−14.4721	−0.555799
$679$	15.3262	0.588167
$680$	12.5623	0.481742
$681$	−6.67376	−0.255739
$682$	0	0
$683$	34.7639	1.33020	0.665102	−	0.746752i	$-0.268388\pi$
$683$	34.7639	1.33020	0.665102	+	0.746752i	$0.268388\pi$
$684$	25.4164	0.971821
$685$	11.4164	0.436199
$686$	2.23607	0.0853735
$687$	−15.3050	−0.583920
$688$	5.23607	0.199623
$689$	−7.05573	−0.268802
$690$	−6.18034	−0.235282
$691$	−26.8328	−1.02077	−0.510384	−	0.859946i	$-0.670497\pi$
$691$	−26.8328	−1.02077	−0.510384	+	0.859946i	$0.670497\pi$
$692$	−4.68692	−0.178170
$693$	0	0
$694$	3.41641	0.129685
$695$	−5.52786	−0.209684
$696$	−1.18034	−0.0447407
$697$	13.8885	0.526066
$698$	−8.69505	−0.329112
$699$	4.11146	0.155510
$700$	−3.00000	−0.113389
$701$	−51.3050	−1.93776	−0.968881	−	0.247528i	$-0.920382\pi$
$701$	−51.3050	−1.93776	−0.968881	+	0.247528i	$0.920382\pi$
$702$	35.8541	1.35323
$703$	23.4164	0.883167
$704$	0	0
$705$	0.708204	0.0266725
$706$	30.3262	1.14134
$707$	13.7082	0.515550
$708$	−17.1246	−0.643582
$709$	0.257354	0.00966514	0.00483257	−	0.999988i	$-0.498462\pi$
$709$	0.257354	0.00966514	0.00483257	+	0.999988i	$0.498462\pi$
$710$	36.5066	1.37007
$711$	−28.2705	−1.06023
$712$	−28.5410	−1.06962
$713$	−14.4721	−0.541986
$714$	7.76393	0.290558
$715$	0	0
$716$	58.8541	2.19948
$717$	15.4377	0.576531
$718$	29.0213	1.08306
$719$	21.8885	0.816305	0.408152	−	0.912914i	$-0.366173\pi$
$719$	21.8885	0.816305	0.408152	+	0.912914i	$0.366173\pi$
$720$	−2.61803	−0.0975684
$721$	17.3262	0.645263
$722$	19.0689	0.709670
$723$	−10.5836	−0.393608
$724$	16.5836	0.616324
$725$	0.854102	0.0317206
$726$	0	0
$727$	−41.5623	−1.54146	−0.770730	−	0.637162i	$-0.780108\pi$
$727$	−41.5623	−1.54146	−0.770730	+	0.637162i	$0.780108\pi$
$728$	10.3262	0.382716
$729$	−8.50658	−0.315058
$730$	14.2705	0.528175
$731$	−29.4164	−1.08801
$732$	−8.83282	−0.326470
$733$	34.8673	1.28785	0.643926	−	0.765088i	$-0.277305\pi$
$733$	34.8673	1.28785	0.643926	+	0.765088i	$0.277305\pi$
$734$	70.3262	2.59579
$735$	−0.618034	−0.0227965
$736$	−30.0000	−1.10581
$737$	0	0
$738$	14.4721	0.532727
$739$	12.0000	0.441427	0.220714	−	0.975339i	$-0.429161\pi$
$739$	12.0000	0.441427	0.220714	+	0.975339i	$0.429161\pi$
$740$	21.7082	0.798009
$741$	−9.23607	−0.339295
$742$	−3.41641	−0.125420
$743$	5.34752	0.196182	0.0980908	−	0.995177i	$-0.468726\pi$
$743$	5.34752	0.196182	0.0980908	+	0.995177i	$0.468726\pi$
$744$	−4.47214	−0.163956
$745$	17.8541	0.654124
$746$	−24.8754	−0.910753
$747$	−25.0344	−0.915962
$748$	0	0
$749$	7.23607	0.264400
$750$	1.38197	0.0504623
$751$	37.3262	1.36205	0.681027	−	0.732258i	$-0.261534\pi$
$751$	37.3262	1.36205	0.681027	+	0.732258i	$0.261534\pi$
$752$	1.14590	0.0417866
$753$	−4.76393	−0.173607
$754$	−8.81966	−0.321193
$755$	0.381966	0.0139012
$756$	10.4164	0.378841
$757$	4.18034	0.151937	0.0759685	−	0.997110i	$-0.475795\pi$
$757$	4.18034	0.151937	0.0759685	+	0.997110i	$0.475795\pi$
$758$	−55.3262	−2.00954
$759$	0	0
$760$	−7.23607	−0.262480
$761$	48.8328	1.77019	0.885094	−	0.465412i	$-0.154094\pi$
$761$	48.8328	1.77019	0.885094	+	0.465412i	$0.154094\pi$
$762$	−12.7639	−0.462388
$763$	11.5279	0.417337
$764$	69.2705	2.50612
$765$	14.7082	0.531776
$766$	−59.9230	−2.16511
$767$	−42.6525	−1.54009
$768$	−5.56231	−0.200712
$769$	11.7082	0.422209	0.211104	−	0.977464i	$-0.432294\pi$
$769$	11.7082	0.422209	0.211104	+	0.977464i	$0.432294\pi$
$770$	0	0
$771$	−1.47214	−0.0530177
$772$	12.0000	0.431889
$773$	−27.3820	−0.984861	−0.492430	−	0.870352i	$-0.663891\pi$
$773$	−27.3820	−0.984861	−0.492430	+	0.870352i	$0.663891\pi$
$774$	−30.6525	−1.10178
$775$	3.23607	0.116243
$776$	34.2705	1.23024
$777$	4.47214	0.160437
$778$	75.0476	2.69059
$779$	−8.00000	−0.286630
$780$	−8.56231	−0.306580
$781$	0	0
$782$	56.1803	2.00900
$783$	−2.96556	−0.105980
$784$	−1.00000	−0.0357143
$785$	16.0902	0.574283
$786$	−11.0557	−0.394345
$787$	40.0344	1.42707	0.713537	−	0.700618i	$-0.247092\pi$
$787$	40.0344	1.42707	0.713537	+	0.700618i	$0.247092\pi$
$788$	−36.0000	−1.28245
$789$	8.76393	0.312004
$790$	24.1459	0.859072
$791$	−10.4721	−0.372346
$792$	0	0
$793$	−22.0000	−0.781243
$794$	−78.6180	−2.79005
$795$	0.944272	0.0334899
$796$	−54.0000	−1.91398
$797$	44.1033	1.56222	0.781110	−	0.624393i	$-0.214654\pi$
$797$	44.1033	1.56222	0.781110	+	0.624393i	$0.214654\pi$
$798$	−4.47214	−0.158312
$799$	−6.43769	−0.227749
$800$	6.70820	0.237171
$801$	−33.4164	−1.18071
$802$	−34.6738	−1.22437
$803$	0	0
$804$	15.1672	0.534905
$805$	−4.47214	−0.157622
$806$	−33.4164	−1.17704
$807$	−11.5279	−0.405800
$808$	30.6525	1.07835
$809$	−3.09017	−0.108645	−0.0543223	−	0.998523i	$-0.517300\pi$
$809$	−3.09017	−0.108645	−0.0543223	+	0.998523i	$0.517300\pi$
$810$	12.7639	0.448479
$811$	31.4164	1.10318	0.551590	−	0.834116i	$-0.314021\pi$
$811$	31.4164	1.10318	0.551590	+	0.834116i	$0.314021\pi$
$812$	−2.56231	−0.0899193
$813$	14.3607	0.503651
$814$	0	0
$815$	22.1803	0.776943
$816$	−3.47214	−0.121549
$817$	16.9443	0.592805
$818$	7.23607	0.253003
$819$	12.0902	0.422465
$820$	−7.41641	−0.258992
$821$	12.6738	0.442317	0.221159	−	0.975238i	$-0.429016\pi$
$821$	12.6738	0.442317	0.221159	+	0.975238i	$0.429016\pi$
$822$	15.7771	0.550289
$823$	−20.0000	−0.697156	−0.348578	−	0.937280i	$-0.613335\pi$
$823$	−20.0000	−0.697156	−0.348578	+	0.937280i	$0.613335\pi$
$824$	38.7426	1.34966
$825$	0	0
$826$	−20.6525	−0.718592
$827$	−37.8885	−1.31751	−0.658757	−	0.752356i	$-0.728917\pi$
$827$	−37.8885	−1.31751	−0.658757	+	0.752356i	$0.728917\pi$
$828$	35.1246	1.22066
$829$	33.8885	1.17700	0.588499	−	0.808498i	$-0.299719\pi$
$829$	33.8885	1.17700	0.588499	+	0.808498i	$0.299719\pi$
$830$	21.3820	0.742179
$831$	−5.81966	−0.201882
$832$	−60.0344	−2.08132
$833$	5.61803	0.194653
$834$	−7.63932	−0.264528
$835$	12.0000	0.415277
$836$	0	0
$837$	−11.2361	−0.388375
$838$	78.9443	2.72708
$839$	7.63932	0.263739	0.131869	−	0.991267i	$-0.457902\pi$
$839$	7.63932	0.263739	0.131869	+	0.991267i	$0.457902\pi$
$840$	−1.38197	−0.0476824
$841$	−28.2705	−0.974845
$842$	77.1591	2.65908
$843$	−5.23607	−0.180340
$844$	23.0213	0.792425
$845$	−8.32624	−0.286431
$846$	−6.70820	−0.230633
$847$	0	0
$848$	1.52786	0.0524671
$849$	−4.59675	−0.157760
$850$	−12.5623	−0.430884
$851$	32.3607	1.10931
$852$	30.2705	1.03705
$853$	18.4377	0.631295	0.315647	−	0.948877i	$-0.397778\pi$
$853$	18.4377	0.631295	0.315647	+	0.948877i	$0.397778\pi$
$854$	−10.6525	−0.364520
$855$	−8.47214	−0.289741
$856$	16.1803	0.553033
$857$	−57.1935	−1.95369	−0.976846	−	0.213942i	$-0.931370\pi$
$857$	−57.1935	−1.95369	−0.976846	+	0.213942i	$0.931370\pi$
$858$	0	0
$859$	−11.0557	−0.377217	−0.188608	−	0.982052i	$-0.560398\pi$
$859$	−11.0557	−0.377217	−0.188608	+	0.982052i	$0.560398\pi$
$860$	15.7082	0.535645
$861$	−1.52786	−0.0520695
$862$	11.9098	0.405650
$863$	3.05573	0.104018	0.0520091	−	0.998647i	$-0.483438\pi$
$863$	3.05573	0.104018	0.0520091	+	0.998647i	$0.483438\pi$
$864$	−23.2918	−0.792403
$865$	1.56231	0.0531200
$866$	−26.9098	−0.914433
$867$	9.00000	0.305656
$868$	−9.70820	−0.329518
$869$	0	0
$870$	1.18034	0.0400173
$871$	37.7771	1.28003
$872$	25.7771	0.872922
$873$	40.1246	1.35801
$874$	−32.3607	−1.09462
$875$	1.00000	0.0338062
$876$	11.8328	0.399794
$877$	55.0132	1.85766	0.928831	−	0.370503i	$-0.120815\pi$
$877$	55.0132	1.85766	0.928831	+	0.370503i	$0.120815\pi$
$878$	−9.59675	−0.323875
$879$	−5.81966	−0.196292
$880$	0	0
$881$	−5.23607	−0.176408	−0.0882038	−	0.996102i	$-0.528113\pi$
$881$	−5.23607	−0.176408	−0.0882038	+	0.996102i	$0.528113\pi$
$882$	5.85410	0.197118
$883$	−10.1803	−0.342596	−0.171298	−	0.985219i	$-0.554796\pi$
$883$	−10.1803	−0.342596	−0.171298	+	0.985219i	$0.554796\pi$
$884$	77.8328	2.61780
$885$	5.70820	0.191879
$886$	7.48529	0.251473
$887$	−21.1459	−0.710010	−0.355005	−	0.934864i	$-0.615521\pi$
$887$	−21.1459	−0.710010	−0.355005	+	0.934864i	$0.615521\pi$
$888$	10.0000	0.335578
$889$	−9.23607	−0.309768
$890$	28.5410	0.956697
$891$	0	0
$892$	4.58359	0.153470
$893$	3.70820	0.124090
$894$	24.6738	0.825214
$895$	−19.6180	−0.655759
$896$	−15.6525	−0.522913
$897$	−12.7639	−0.426175
$898$	20.7295	0.691752
$899$	2.76393	0.0921823
$900$	−7.85410	−0.261803
$901$	−8.58359	−0.285961
$902$	0	0
$903$	3.23607	0.107690
$904$	−23.4164	−0.778818
$905$	−5.52786	−0.183752
$906$	0.527864	0.0175371
$907$	27.8885	0.926024	0.463012	−	0.886352i	$-0.346769\pi$
$907$	27.8885	0.926024	0.463012	+	0.886352i	$0.346769\pi$
$908$	−32.3951	−1.07507
$909$	35.8885	1.19035
$910$	−10.3262	−0.342311
$911$	−1.50658	−0.0499151	−0.0249576	−	0.999689i	$-0.507945\pi$
$911$	−1.50658	−0.0499151	−0.0249576	+	0.999689i	$0.507945\pi$
$912$	2.00000	0.0662266
$913$	0	0
$914$	84.4721	2.79409
$915$	2.94427	0.0973346
$916$	−74.2918	−2.45467
$917$	−8.00000	−0.264183
$918$	43.6180	1.43961
$919$	2.27051	0.0748972	0.0374486	−	0.999299i	$-0.488077\pi$
$919$	2.27051	0.0748972	0.0374486	+	0.999299i	$0.488077\pi$
$920$	−10.0000	−0.329690
$921$	−12.7082	−0.418750
$922$	−36.4296	−1.19974
$923$	75.3951	2.48166
$924$	0	0
$925$	−7.23607	−0.237920
$926$	38.2918	1.25835
$927$	45.3607	1.48984
$928$	5.72949	0.188080
$929$	−17.8885	−0.586904	−0.293452	−	0.955974i	$-0.594804\pi$
$929$	−17.8885	−0.586904	−0.293452	+	0.955974i	$0.594804\pi$
$930$	4.47214	0.146647
$931$	−3.23607	−0.106058
$932$	19.9574	0.653727
$933$	8.11146	0.265557
$934$	72.2837	2.36519
$935$	0	0
$936$	27.0344	0.883648
$937$	0.549150	0.0179400	0.00896998	−	0.999960i	$-0.497145\pi$
$937$	0.549150	0.0179400	0.00896998	+	0.999960i	$0.497145\pi$
$938$	18.2918	0.597248
$939$	−11.1246	−0.363038
$940$	3.43769	0.112125
$941$	−30.5410	−0.995609	−0.497804	−	0.867289i	$-0.665860\pi$
$941$	−30.5410	−0.995609	−0.497804	+	0.867289i	$0.665860\pi$
$942$	22.2361	0.724490
$943$	−11.0557	−0.360024
$944$	9.23607	0.300608
$945$	−3.47214	−0.112949
$946$	0	0
$947$	34.0689	1.10709	0.553545	−	0.832819i	$-0.313275\pi$
$947$	34.0689	1.10709	0.553545	+	0.832819i	$0.313275\pi$
$948$	20.0213	0.650261
$949$	29.4721	0.956706
$950$	7.23607	0.234769
$951$	−13.3050	−0.431443
$952$	12.5623	0.407147
$953$	42.9443	1.39110	0.695551	−	0.718477i	$-0.255160\pi$
$953$	42.9443	1.39110	0.695551	+	0.718477i	$0.255160\pi$
$954$	−8.94427	−0.289581
$955$	−23.0902	−0.747180
$956$	74.9361	2.42361
$957$	0	0
$958$	−50.6525	−1.63651
$959$	11.4164	0.368655
$960$	8.03444	0.259310
$961$	−20.5279	−0.662189
$962$	74.7214	2.40911
$963$	18.9443	0.610471
$964$	−51.3738	−1.65464
$965$	−4.00000	−0.128765
$966$	−6.18034	−0.198849
$967$	−16.7639	−0.539092	−0.269546	−	0.962988i	$-0.586874\pi$
$967$	−16.7639	−0.539092	−0.269546	+	0.962988i	$0.586874\pi$
$968$	0	0
$969$	−11.2361	−0.360955
$970$	−34.2705	−1.10036
$971$	−2.58359	−0.0829114	−0.0414557	−	0.999140i	$-0.513200\pi$
$971$	−2.58359	−0.0829114	−0.0414557	+	0.999140i	$0.513200\pi$
$972$	41.8328	1.34179
$973$	−5.52786	−0.177215
$974$	4.06888	0.130375
$975$	2.85410	0.0914044
$976$	4.76393	0.152490
$977$	41.2361	1.31926	0.659629	−	0.751591i	$-0.270713\pi$
$977$	41.2361	1.31926	0.659629	+	0.751591i	$0.270713\pi$
$978$	30.6525	0.980158
$979$	0	0
$980$	−3.00000	−0.0958315
$981$	30.1803	0.963584
$982$	−4.72136	−0.150665
$983$	−27.9787	−0.892382	−0.446191	−	0.894938i	$-0.647220\pi$
$983$	−27.9787	−0.892382	−0.446191	+	0.894938i	$0.647220\pi$
$984$	−3.41641	−0.108911
$985$	12.0000	0.382352
$986$	−10.7295	−0.341697
$987$	0.708204	0.0225424
$988$	−44.8328	−1.42632
$989$	23.4164	0.744598
$990$	0	0
$991$	13.8541	0.440090	0.220045	−	0.975490i	$-0.429380\pi$
$991$	13.8541	0.440090	0.220045	+	0.975490i	$0.429380\pi$
$992$	21.7082	0.689236
$993$	−11.4377	−0.362964
$994$	36.5066	1.15792
$995$	18.0000	0.570638
$996$	17.7295	0.561780
$997$	−25.2148	−0.798560	−0.399280	−	0.916829i	$-0.630740\pi$
$997$	−25.2148	−0.798560	−0.399280	+	0.916829i	$0.630740\pi$
$998$	51.5066	1.63041
$999$	25.1246	0.794908

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.j.1.1		2
11.5	even	5		385.2.n.b.36.1	✓	4
11.9	even	5		385.2.n.b.246.1	yes	4
11.10	odd	2		4235.2.a.k.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.b.36.1	✓	4	11.5	even	5
385.2.n.b.246.1	yes	4	11.9	even	5
4235.2.a.j.1.1		2	1.1	even	1	trivial
4235.2.a.k.1.2		2	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q-2.23607 q^{2} +0.618034 q^{3} +3.00000 q^{4} -1.00000 q^{5} -1.38197 q^{6} -1.00000 q^{7} -2.23607 q^{8} -2.61803 q^{9} +O(q^{10})\)	\(q-2.23607 q^{2} +0.618034 q^{3} +3.00000 q^{4} -1.00000 q^{5} -1.38197 q^{6} -1.00000 q^{7} -2.23607 q^{8} -2.61803 q^{9} +2.23607 q^{10} +1.85410 q^{12} +4.61803 q^{13} +2.23607 q^{14} -0.618034 q^{15} -1.00000 q^{16} +5.61803 q^{17} +5.85410 q^{18} -3.23607 q^{19} -3.00000 q^{20} -0.618034 q^{21} -4.47214 q^{23} -1.38197 q^{24} +1.00000 q^{25} -10.3262 q^{26} -3.47214 q^{27} -3.00000 q^{28} +0.854102 q^{29} +1.38197 q^{30} +3.23607 q^{31} +6.70820 q^{32} -12.5623 q^{34} +1.00000 q^{35} -7.85410 q^{36} -7.23607 q^{37} +7.23607 q^{38} +2.85410 q^{39} +2.23607 q^{40} +2.47214 q^{41} +1.38197 q^{42} -5.23607 q^{43} +2.61803 q^{45} +10.0000 q^{46} -1.14590 q^{47} -0.618034 q^{48} +1.00000 q^{49} -2.23607 q^{50} +3.47214 q^{51} +13.8541 q^{52} -1.52786 q^{53} +7.76393 q^{54} +2.23607 q^{56} -2.00000 q^{57} -1.90983 q^{58} -9.23607 q^{59} -1.85410 q^{60} -4.76393 q^{61} -7.23607 q^{62} +2.61803 q^{63} -13.0000 q^{64} -4.61803 q^{65} +8.18034 q^{67} +16.8541 q^{68} -2.76393 q^{69} -2.23607 q^{70} +16.3262 q^{71} +5.85410 q^{72} +6.38197 q^{73} +16.1803 q^{74} +0.618034 q^{75} -9.70820 q^{76} -6.38197 q^{78} +10.7984 q^{79} +1.00000 q^{80} +5.70820 q^{81} -5.52786 q^{82} +9.56231 q^{83} -1.85410 q^{84} -5.61803 q^{85} +11.7082 q^{86} +0.527864 q^{87} +12.7639 q^{89} -5.85410 q^{90} -4.61803 q^{91} -13.4164 q^{92} +2.00000 q^{93} +2.56231 q^{94} +3.23607 q^{95} +4.14590 q^{96} -15.3262 q^{97} -2.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} + 6 q^{4} - 2 q^{5} - 5 q^{6} - 2 q^{7} - 3 q^{9}+O(q^{10}) \) 2 * q - q^3 + 6 * q^4 - 2 * q^5 - 5 * q^6 - 2 * q^7 - 3 * q^9	\( 2 q - q^{3} + 6 q^{4} - 2 q^{5} - 5 q^{6} - 2 q^{7} - 3 q^{9} - 3 q^{12} + 7 q^{13} + q^{15} - 2 q^{16} + 9 q^{17} + 5 q^{18} - 2 q^{19} - 6 q^{20} + q^{21} - 5 q^{24} + 2 q^{25} - 5 q^{26} + 2 q^{27} - 6 q^{28} - 5 q^{29} + 5 q^{30} + 2 q^{31} - 5 q^{34} + 2 q^{35} - 9 q^{36} - 10 q^{37} + 10 q^{38} - q^{39} - 4 q^{41} + 5 q^{42} - 6 q^{43} + 3 q^{45} + 20 q^{46} - 9 q^{47} + q^{48} + 2 q^{49} - 2 q^{51} + 21 q^{52} - 12 q^{53} + 20 q^{54} - 4 q^{57} - 15 q^{58} - 14 q^{59} + 3 q^{60} - 14 q^{61} - 10 q^{62} + 3 q^{63} - 26 q^{64} - 7 q^{65} - 6 q^{67} + 27 q^{68} - 10 q^{69} + 17 q^{71} + 5 q^{72} + 15 q^{73} + 10 q^{74} - q^{75} - 6 q^{76} - 15 q^{78} - 3 q^{79} + 2 q^{80} - 2 q^{81} - 20 q^{82} - q^{83} + 3 q^{84} - 9 q^{85} + 10 q^{86} + 10 q^{87} + 30 q^{89} - 5 q^{90} - 7 q^{91} + 4 q^{93} - 15 q^{94} + 2 q^{95} + 15 q^{96} - 15 q^{97}+O(q^{100}) \) 2 * q - q^3 + 6 * q^4 - 2 * q^5 - 5 * q^6 - 2 * q^7 - 3 * q^9 - 3 * q^12 + 7 * q^13 + q^15 - 2 * q^16 + 9 * q^17 + 5 * q^18 - 2 * q^19 - 6 * q^20 + q^21 - 5 * q^24 + 2 * q^25 - 5 * q^26 + 2 * q^27 - 6 * q^28 - 5 * q^29 + 5 * q^30 + 2 * q^31 - 5 * q^34 + 2 * q^35 - 9 * q^36 - 10 * q^37 + 10 * q^38 - q^39 - 4 * q^41 + 5 * q^42 - 6 * q^43 + 3 * q^45 + 20 * q^46 - 9 * q^47 + q^48 + 2 * q^49 - 2 * q^51 + 21 * q^52 - 12 * q^53 + 20 * q^54 - 4 * q^57 - 15 * q^58 - 14 * q^59 + 3 * q^60 - 14 * q^61 - 10 * q^62 + 3 * q^63 - 26 * q^64 - 7 * q^65 - 6 * q^67 + 27 * q^68 - 10 * q^69 + 17 * q^71 + 5 * q^72 + 15 * q^73 + 10 * q^74 - q^75 - 6 * q^76 - 15 * q^78 - 3 * q^79 + 2 * q^80 - 2 * q^81 - 20 * q^82 - q^83 + 3 * q^84 - 9 * q^85 + 10 * q^86 + 10 * q^87 + 30 * q^89 - 5 * q^90 - 7 * q^91 + 4 * q^93 - 15 * q^94 + 2 * q^95 + 15 * q^96 - 15 * q^97

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