LMFDB - Embedded newform 1250.2.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1250,2,Mod(1,1250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1250, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1250.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1250 = 2 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1250.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:	$9.98130025266$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	1250.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +0.618034 q^{7} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +0.618034 q^{7} -1.00000 q^{8} -2.00000 q^{9} -3.00000 q^{11} +1.00000 q^{12} -3.47214 q^{13} -0.618034 q^{14} +1.00000 q^{16} +7.85410 q^{17} +2.00000 q^{18} -2.76393 q^{19} +0.618034 q^{21} +3.00000 q^{22} -4.85410 q^{23} -1.00000 q^{24} +3.47214 q^{26} -5.00000 q^{27} +0.618034 q^{28} -6.70820 q^{29} -10.2361 q^{31} -1.00000 q^{32} -3.00000 q^{33} -7.85410 q^{34} -2.00000 q^{36} +5.09017 q^{37} +2.76393 q^{38} -3.47214 q^{39} +3.70820 q^{41} -0.618034 q^{42} -0.909830 q^{43} -3.00000 q^{44} +4.85410 q^{46} -3.00000 q^{47} +1.00000 q^{48} -6.61803 q^{49} +7.85410 q^{51} -3.47214 q^{52} -0.708204 q^{53} +5.00000 q^{54} -0.618034 q^{56} -2.76393 q^{57} +6.70820 q^{58} +6.70820 q^{59} -10.2361 q^{61} +10.2361 q^{62} -1.23607 q^{63} +1.00000 q^{64} +3.00000 q^{66} +11.4721 q^{67} +7.85410 q^{68} -4.85410 q^{69} +14.5623 q^{71} +2.00000 q^{72} -1.23607 q^{73} -5.09017 q^{74} -2.76393 q^{76} -1.85410 q^{77} +3.47214 q^{78} -13.9443 q^{79} +1.00000 q^{81} -3.70820 q^{82} +1.85410 q^{83} +0.618034 q^{84} +0.909830 q^{86} -6.70820 q^{87} +3.00000 q^{88} -13.4164 q^{89} -2.14590 q^{91} -4.85410 q^{92} -10.2361 q^{93} +3.00000 q^{94} -1.00000 q^{96} -10.2361 q^{97} +6.61803 q^{98} +6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} - q^{7} - 2 q^{8} - 4 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 - q^7 - 2 * q^8 - 4 * q^9	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} - q^{7} - 2 q^{8} - 4 q^{9} - 6 q^{11} + 2 q^{12} + 2 q^{13} + q^{14} + 2 q^{16} + 9 q^{17} + 4 q^{18} - 10 q^{19} - q^{21} + 6 q^{22} - 3 q^{23} - 2 q^{24} - 2 q^{26} - 10 q^{27} - q^{28} - 16 q^{31} - 2 q^{32} - 6 q^{33} - 9 q^{34} - 4 q^{36} - q^{37} + 10 q^{38} + 2 q^{39} - 6 q^{41} + q^{42} - 13 q^{43} - 6 q^{44} + 3 q^{46} - 6 q^{47} + 2 q^{48} - 11 q^{49} + 9 q^{51} + 2 q^{52} + 12 q^{53} + 10 q^{54} + q^{56} - 10 q^{57} - 16 q^{61} + 16 q^{62} + 2 q^{63} + 2 q^{64} + 6 q^{66} + 14 q^{67} + 9 q^{68} - 3 q^{69} + 9 q^{71} + 4 q^{72} + 2 q^{73} + q^{74} - 10 q^{76} + 3 q^{77} - 2 q^{78} - 10 q^{79} + 2 q^{81} + 6 q^{82} - 3 q^{83} - q^{84} + 13 q^{86} + 6 q^{88} - 11 q^{91} - 3 q^{92} - 16 q^{93} + 6 q^{94} - 2 q^{96} - 16 q^{97} + 11 q^{98} + 12 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 - q^7 - 2 * q^8 - 4 * q^9 - 6 * q^11 + 2 * q^12 + 2 * q^13 + q^14 + 2 * q^16 + 9 * q^17 + 4 * q^18 - 10 * q^19 - q^21 + 6 * q^22 - 3 * q^23 - 2 * q^24 - 2 * q^26 - 10 * q^27 - q^28 - 16 * q^31 - 2 * q^32 - 6 * q^33 - 9 * q^34 - 4 * q^36 - q^37 + 10 * q^38 + 2 * q^39 - 6 * q^41 + q^42 - 13 * q^43 - 6 * q^44 + 3 * q^46 - 6 * q^47 + 2 * q^48 - 11 * q^49 + 9 * q^51 + 2 * q^52 + 12 * q^53 + 10 * q^54 + q^56 - 10 * q^57 - 16 * q^61 + 16 * q^62 + 2 * q^63 + 2 * q^64 + 6 * q^66 + 14 * q^67 + 9 * q^68 - 3 * q^69 + 9 * q^71 + 4 * q^72 + 2 * q^73 + q^74 - 10 * q^76 + 3 * q^77 - 2 * q^78 - 10 * q^79 + 2 * q^81 + 6 * q^82 - 3 * q^83 - q^84 + 13 * q^86 + 6 * q^88 - 11 * q^91 - 3 * q^92 - 16 * q^93 + 6 * q^94 - 2 * q^96 - 16 * q^97 + 11 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350	0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	0.618034	0.233595	0.116797	−	0.993156i	$-0.462737\pi$
$7$	0.618034	0.233595	0.116797	+	0.993156i	$0.462737\pi$
$8$	−1.00000	−0.353553
$9$	−2.00000	−0.666667
$10$	0	0
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	1.00000	0.288675
$13$	−3.47214	−0.962997	−0.481499	−	0.876447i	$-0.659907\pi$
$13$	−3.47214	−0.962997	−0.481499	+	0.876447i	$0.659907\pi$
$14$	−0.618034	−0.165177
$15$	0	0
$16$	1.00000	0.250000
$17$	7.85410	1.90490	0.952450	−	0.304696i	$-0.0985548\pi$
$17$	7.85410	1.90490	0.952450	+	0.304696i	$0.0985548\pi$
$18$	2.00000	0.471405
$19$	−2.76393	−0.634089	−0.317045	−	0.948411i	$-0.602691\pi$
$19$	−2.76393	−0.634089	−0.317045	+	0.948411i	$0.602691\pi$
$20$	0	0
$21$	0.618034	0.134866
$22$	3.00000	0.639602
$23$	−4.85410	−1.01215	−0.506075	−	0.862489i	$-0.668904\pi$
$23$	−4.85410	−1.01215	−0.506075	+	0.862489i	$0.668904\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	3.47214	0.680942
$27$	−5.00000	−0.962250
$28$	0.618034	0.116797
$29$	−6.70820	−1.24568	−0.622841	−	0.782348i	$-0.714022\pi$
$29$	−6.70820	−1.24568	−0.622841	+	0.782348i	$0.714022\pi$
$30$	0	0
$31$	−10.2361	−1.83845	−0.919226	−	0.393730i	$-0.871184\pi$
$31$	−10.2361	−1.83845	−0.919226	+	0.393730i	$0.871184\pi$
$32$	−1.00000	−0.176777
$33$	−3.00000	−0.522233
$34$	−7.85410	−1.34697
$35$	0	0
$36$	−2.00000	−0.333333
$37$	5.09017	0.836819	0.418409	−	0.908259i	$-0.362588\pi$
$37$	5.09017	0.836819	0.418409	+	0.908259i	$0.362588\pi$
$38$	2.76393	0.448369
$39$	−3.47214	−0.555987
$40$	0	0
$41$	3.70820	0.579124	0.289562	−	0.957159i	$-0.406490\pi$
$41$	3.70820	0.579124	0.289562	+	0.957159i	$0.406490\pi$
$42$	−0.618034	−0.0953647
$43$	−0.909830	−0.138748	−0.0693739	−	0.997591i	$-0.522100\pi$
$43$	−0.909830	−0.138748	−0.0693739	+	0.997591i	$0.522100\pi$
$44$	−3.00000	−0.452267
$45$	0	0
$46$	4.85410	0.715698
$47$	−3.00000	−0.437595	−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000	−0.437595	−0.218797	+	0.975770i	$0.570213\pi$
$48$	1.00000	0.144338
$49$	−6.61803	−0.945433
$50$	0	0
$51$	7.85410	1.09979
$52$	−3.47214	−0.481499
$53$	−0.708204	−0.0972793	−0.0486396	−	0.998816i	$-0.515489\pi$
$53$	−0.708204	−0.0972793	−0.0486396	+	0.998816i	$0.515489\pi$
$54$	5.00000	0.680414
$55$	0	0
$56$	−0.618034	−0.0825883
$57$	−2.76393	−0.366092
$58$	6.70820	0.880830
$59$	6.70820	0.873334	0.436667	−	0.899623i	$-0.356159\pi$
$59$	6.70820	0.873334	0.436667	+	0.899623i	$0.356159\pi$
$60$	0	0
$61$	−10.2361	−1.31059	−0.655297	−	0.755371i	$-0.727457\pi$
$61$	−10.2361	−1.31059	−0.655297	+	0.755371i	$0.727457\pi$
$62$	10.2361	1.29998
$63$	−1.23607	−0.155730
$64$	1.00000	0.125000
$65$	0	0
$66$	3.00000	0.369274
$67$	11.4721	1.40154	0.700772	−	0.713385i	$-0.252839\pi$
$67$	11.4721	1.40154	0.700772	+	0.713385i	$0.252839\pi$
$68$	7.85410	0.952450
$69$	−4.85410	−0.584365
$70$	0	0
$71$	14.5623	1.72823	0.864114	−	0.503296i	$-0.167880\pi$
$71$	14.5623	1.72823	0.864114	+	0.503296i	$0.167880\pi$
$72$	2.00000	0.235702
$73$	−1.23607	−0.144671	−0.0723354	−	0.997380i	$-0.523045\pi$
$73$	−1.23607	−0.144671	−0.0723354	+	0.997380i	$0.523045\pi$
$74$	−5.09017	−0.591720
$75$	0	0
$76$	−2.76393	−0.317045
$77$	−1.85410	−0.211295
$78$	3.47214	0.393142
$79$	−13.9443	−1.56885	−0.784427	−	0.620222i	$-0.787043\pi$
$79$	−13.9443	−1.56885	−0.784427	+	0.620222i	$0.787043\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−3.70820	−0.409503
$83$	1.85410	0.203514	0.101757	−	0.994809i	$-0.467554\pi$
$83$	1.85410	0.203514	0.101757	+	0.994809i	$0.467554\pi$
$84$	0.618034	0.0674330
$85$	0	0
$86$	0.909830	0.0981095
$87$	−6.70820	−0.719195
$88$	3.00000	0.319801
$89$	−13.4164	−1.42214	−0.711068	−	0.703123i	$-0.751788\pi$
$89$	−13.4164	−1.42214	−0.711068	+	0.703123i	$0.751788\pi$
$90$	0	0
$91$	−2.14590	−0.224951
$92$	−4.85410	−0.506075
$93$	−10.2361	−1.06143
$94$	3.00000	0.309426
$95$	0	0
$96$	−1.00000	−0.102062
$97$	−10.2361	−1.03932	−0.519658	−	0.854375i	$-0.673940\pi$
$97$	−10.2361	−1.03932	−0.519658	+	0.854375i	$0.673940\pi$
$98$	6.61803	0.668522
$99$	6.00000	0.603023
$100$	0	0
$101$	−3.00000	−0.298511	−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000	−0.298511	−0.149256	+	0.988799i	$0.547688\pi$
$102$	−7.85410	−0.777672
$103$	−3.47214	−0.342120	−0.171060	−	0.985261i	$-0.554719\pi$
$103$	−3.47214	−0.342120	−0.171060	+	0.985261i	$0.554719\pi$
$104$	3.47214	0.340471
$105$	0	0
$106$	0.708204	0.0687868
$107$	−16.4164	−1.58703	−0.793517	−	0.608548i	$-0.791752\pi$
$107$	−16.4164	−1.58703	−0.793517	+	0.608548i	$0.791752\pi$
$108$	−5.00000	−0.481125
$109$	3.94427	0.377793	0.188896	−	0.981997i	$-0.439509\pi$
$109$	3.94427	0.377793	0.188896	+	0.981997i	$0.439509\pi$
$110$	0	0
$111$	5.09017	0.483138
$112$	0.618034	0.0583987
$113$	8.56231	0.805474	0.402737	−	0.915316i	$-0.368059\pi$
$113$	8.56231	0.805474	0.402737	+	0.915316i	$0.368059\pi$
$114$	2.76393	0.258866
$115$	0	0
$116$	−6.70820	−0.622841
$117$	6.94427	0.641998
$118$	−6.70820	−0.617540
$119$	4.85410	0.444975
$120$	0	0
$121$	−2.00000	−0.181818
$122$	10.2361	0.926730
$123$	3.70820	0.334357
$124$	−10.2361	−0.919226
$125$	0	0
$126$	1.23607	0.110118
$127$	0.618034	0.0548416	0.0274208	−	0.999624i	$-0.491271\pi$
$127$	0.618034	0.0548416	0.0274208	+	0.999624i	$0.491271\pi$
$128$	−1.00000	−0.0883883
$129$	−0.909830	−0.0801061
$130$	0	0
$131$	5.29180	0.462346	0.231173	−	0.972913i	$-0.425744\pi$
$131$	5.29180	0.462346	0.231173	+	0.972913i	$0.425744\pi$
$132$	−3.00000	−0.261116
$133$	−1.70820	−0.148120
$134$	−11.4721	−0.991042
$135$	0	0
$136$	−7.85410	−0.673484
$137$	3.70820	0.316813	0.158407	−	0.987374i	$-0.449364\pi$
$137$	3.70820	0.316813	0.158407	+	0.987374i	$0.449364\pi$
$138$	4.85410	0.413209
$139$	6.18034	0.524210	0.262105	−	0.965039i	$-0.415583\pi$
$139$	6.18034	0.524210	0.262105	+	0.965039i	$0.415583\pi$
$140$	0	0
$141$	−3.00000	−0.252646
$142$	−14.5623	−1.22204
$143$	10.4164	0.871064
$144$	−2.00000	−0.166667
$145$	0	0
$146$	1.23607	0.102298
$147$	−6.61803	−0.545846
$148$	5.09017	0.418409
$149$	17.5623	1.43876	0.719380	−	0.694617i	$-0.244426\pi$
$149$	17.5623	1.43876	0.719380	+	0.694617i	$0.244426\pi$
$150$	0	0
$151$	−19.5066	−1.58742	−0.793711	−	0.608295i	$-0.791854\pi$
$151$	−19.5066	−1.58742	−0.793711	+	0.608295i	$0.791854\pi$
$152$	2.76393	0.224184
$153$	−15.7082	−1.26993
$154$	1.85410	0.149408
$155$	0	0
$156$	−3.47214	−0.277993
$157$	19.5623	1.56124	0.780621	−	0.625005i	$-0.214903\pi$
$157$	19.5623	1.56124	0.780621	+	0.625005i	$0.214903\pi$
$158$	13.9443	1.10935
$159$	−0.708204	−0.0561642
$160$	0	0
$161$	−3.00000	−0.236433
$162$	−1.00000	−0.0785674
$163$	−21.5623	−1.68889	−0.844445	−	0.535642i	$-0.820070\pi$
$163$	−21.5623	−1.68889	−0.844445	+	0.535642i	$0.820070\pi$
$164$	3.70820	0.289562
$165$	0	0
$166$	−1.85410	−0.143906
$167$	−11.2918	−0.873785	−0.436893	−	0.899514i	$-0.643921\pi$
$167$	−11.2918	−0.873785	−0.436893	+	0.899514i	$0.643921\pi$
$168$	−0.618034	−0.0476824
$169$	−0.944272	−0.0726363
$170$	0	0
$171$	5.52786	0.422726
$172$	−0.909830	−0.0693739
$173$	12.7082	0.966187	0.483093	−	0.875569i	$-0.339513\pi$
$173$	12.7082	0.966187	0.483093	+	0.875569i	$0.339513\pi$
$174$	6.70820	0.508548
$175$	0	0
$176$	−3.00000	−0.226134
$177$	6.70820	0.504219
$178$	13.4164	1.00560
$179$	10.8541	0.811274	0.405637	−	0.914034i	$-0.367050\pi$
$179$	10.8541	0.811274	0.405637	+	0.914034i	$0.367050\pi$
$180$	0	0
$181$	11.7984	0.876966	0.438483	−	0.898739i	$-0.355516\pi$
$181$	11.7984	0.876966	0.438483	+	0.898739i	$0.355516\pi$
$182$	2.14590	0.159065
$183$	−10.2361	−0.756672
$184$	4.85410	0.357849
$185$	0	0
$186$	10.2361	0.750545
$187$	−23.5623	−1.72305
$188$	−3.00000	−0.218797
$189$	−3.09017	−0.224777
$190$	0	0
$191$	−5.56231	−0.402474	−0.201237	−	0.979543i	$-0.564496\pi$
$191$	−5.56231	−0.402474	−0.201237	+	0.979543i	$0.564496\pi$
$192$	1.00000	0.0721688
$193$	−24.1246	−1.73653	−0.868264	−	0.496103i	$-0.834764\pi$
$193$	−24.1246	−1.73653	−0.868264	+	0.496103i	$0.834764\pi$
$194$	10.2361	0.734907
$195$	0	0
$196$	−6.61803	−0.472717
$197$	−1.41641	−0.100915	−0.0504574	−	0.998726i	$-0.516068\pi$
$197$	−1.41641	−0.100915	−0.0504574	+	0.998726i	$0.516068\pi$
$198$	−6.00000	−0.426401
$199$	−3.09017	−0.219056	−0.109528	−	0.993984i	$-0.534934\pi$
$199$	−3.09017	−0.219056	−0.109528	+	0.993984i	$0.534934\pi$
$200$	0	0
$201$	11.4721	0.809182
$202$	3.00000	0.211079
$203$	−4.14590	−0.290985
$204$	7.85410	0.549897
$205$	0	0
$206$	3.47214	0.241915
$207$	9.70820	0.674767
$208$	−3.47214	−0.240749
$209$	8.29180	0.573556
$210$	0	0
$211$	20.0902	1.38306	0.691532	−	0.722346i	$-0.256936\pi$
$211$	20.0902	1.38306	0.691532	+	0.722346i	$0.256936\pi$
$212$	−0.708204	−0.0486396
$213$	14.5623	0.997793
$214$	16.4164	1.12220
$215$	0	0
$216$	5.00000	0.340207
$217$	−6.32624	−0.429453
$218$	−3.94427	−0.267140
$219$	−1.23607	−0.0835257
$220$	0	0
$221$	−27.2705	−1.83441
$222$	−5.09017	−0.341630
$223$	−21.0344	−1.40857	−0.704285	−	0.709917i	$-0.748732\pi$
$223$	−21.0344	−1.40857	−0.704285	+	0.709917i	$0.748732\pi$
$224$	−0.618034	−0.0412941
$225$	0	0
$226$	−8.56231	−0.569556
$227$	14.5623	0.966534	0.483267	−	0.875473i	$-0.339450\pi$
$227$	14.5623	0.966534	0.483267	+	0.875473i	$0.339450\pi$
$228$	−2.76393	−0.183046
$229$	−0.201626	−0.0133238	−0.00666191	−	0.999978i	$-0.502121\pi$
$229$	−0.201626	−0.0133238	−0.00666191	+	0.999978i	$0.502121\pi$
$230$	0	0
$231$	−1.85410	−0.121991
$232$	6.70820	0.440415
$233$	−14.1246	−0.925334	−0.462667	−	0.886532i	$-0.653107\pi$
$233$	−14.1246	−0.925334	−0.462667	+	0.886532i	$0.653107\pi$
$234$	−6.94427	−0.453961
$235$	0	0
$236$	6.70820	0.436667
$237$	−13.9443	−0.905778
$238$	−4.85410	−0.314645
$239$	−8.29180	−0.536352	−0.268176	−	0.963370i	$-0.586421\pi$
$239$	−8.29180	−0.536352	−0.268176	+	0.963370i	$0.586421\pi$
$240$	0	0
$241$	9.23607	0.594947	0.297474	−	0.954730i	$-0.403856\pi$
$241$	9.23607	0.594947	0.297474	+	0.954730i	$0.403856\pi$
$242$	2.00000	0.128565
$243$	16.0000	1.02640
$244$	−10.2361	−0.655297
$245$	0	0
$246$	−3.70820	−0.236426
$247$	9.59675	0.610626
$248$	10.2361	0.649991
$249$	1.85410	0.117499
$250$	0	0
$251$	−3.00000	−0.189358	−0.0946792	−	0.995508i	$-0.530183\pi$
$251$	−3.00000	−0.189358	−0.0946792	+	0.995508i	$0.530183\pi$
$252$	−1.23607	−0.0778650
$253$	14.5623	0.915524
$254$	−0.618034	−0.0387789
$255$	0	0
$256$	1.00000	0.0625000
$257$	10.4164	0.649758	0.324879	−	0.945756i	$-0.394676\pi$
$257$	10.4164	0.649758	0.324879	+	0.945756i	$0.394676\pi$
$258$	0.909830	0.0566435
$259$	3.14590	0.195477
$260$	0	0
$261$	13.4164	0.830455
$262$	−5.29180	−0.326928
$263$	−6.43769	−0.396965	−0.198483	−	0.980104i	$-0.563601\pi$
$263$	−6.43769	−0.396965	−0.198483	+	0.980104i	$0.563601\pi$
$264$	3.00000	0.184637
$265$	0	0
$266$	1.70820	0.104737
$267$	−13.4164	−0.821071
$268$	11.4721	0.700772
$269$	10.8541	0.661786	0.330893	−	0.943668i	$-0.392650\pi$
$269$	10.8541	0.661786	0.330893	+	0.943668i	$0.392650\pi$
$270$	0	0
$271$	−15.0344	−0.913277	−0.456639	−	0.889652i	$-0.650947\pi$
$271$	−15.0344	−0.913277	−0.456639	+	0.889652i	$0.650947\pi$
$272$	7.85410	0.476225
$273$	−2.14590	−0.129876
$274$	−3.70820	−0.224021
$275$	0	0
$276$	−4.85410	−0.292183
$277$	11.4721	0.689294	0.344647	−	0.938732i	$-0.387999\pi$
$277$	11.4721	0.689294	0.344647	+	0.938732i	$0.387999\pi$
$278$	−6.18034	−0.370672
$279$	20.4721	1.22563
$280$	0	0
$281$	27.0000	1.61068	0.805342	−	0.592810i	$-0.201981\pi$
$281$	27.0000	1.61068	0.805342	+	0.592810i	$0.201981\pi$
$282$	3.00000	0.178647
$283$	28.5623	1.69785	0.848926	−	0.528511i	$-0.177249\pi$
$283$	28.5623	1.69785	0.848926	+	0.528511i	$0.177249\pi$
$284$	14.5623	0.864114
$285$	0	0
$286$	−10.4164	−0.615935
$287$	2.29180	0.135280
$288$	2.00000	0.117851
$289$	44.6869	2.62864
$290$	0	0
$291$	−10.2361	−0.600049
$292$	−1.23607	−0.0723354
$293$	16.8541	0.984627	0.492314	−	0.870418i	$-0.336151\pi$
$293$	16.8541	0.984627	0.492314	+	0.870418i	$0.336151\pi$
$294$	6.61803	0.385972
$295$	0	0
$296$	−5.09017	−0.295860
$297$	15.0000	0.870388
$298$	−17.5623	−1.01736
$299$	16.8541	0.974698
$300$	0	0
$301$	−0.562306	−0.0324108
$302$	19.5066	1.12248
$303$	−3.00000	−0.172345
$304$	−2.76393	−0.158522
$305$	0	0
$306$	15.7082	0.897978
$307$	−1.61803	−0.0923461	−0.0461730	−	0.998933i	$-0.514703\pi$
$307$	−1.61803	−0.0923461	−0.0461730	+	0.998933i	$0.514703\pi$
$308$	−1.85410	−0.105647
$309$	−3.47214	−0.197523
$310$	0	0
$311$	16.1459	0.915550	0.457775	−	0.889068i	$-0.348647\pi$
$311$	16.1459	0.915550	0.457775	+	0.889068i	$0.348647\pi$
$312$	3.47214	0.196571
$313$	9.61803	0.543643	0.271822	−	0.962348i	$-0.412374\pi$
$313$	9.61803	0.543643	0.271822	+	0.962348i	$0.412374\pi$
$314$	−19.5623	−1.10396
$315$	0	0
$316$	−13.9443	−0.784427
$317$	−5.56231	−0.312410	−0.156205	−	0.987725i	$-0.549926\pi$
$317$	−5.56231	−0.312410	−0.156205	+	0.987725i	$0.549926\pi$
$318$	0.708204	0.0397141
$319$	20.1246	1.12676
$320$	0	0
$321$	−16.4164	−0.916275
$322$	3.00000	0.167183
$323$	−21.7082	−1.20788
$324$	1.00000	0.0555556
$325$	0	0
$326$	21.5623	1.19423
$327$	3.94427	0.218119
$328$	−3.70820	−0.204751
$329$	−1.85410	−0.102220
$330$	0	0
$331$	−23.3262	−1.28213	−0.641063	−	0.767488i	$-0.721506\pi$
$331$	−23.3262	−1.28213	−0.641063	+	0.767488i	$0.721506\pi$
$332$	1.85410	0.101757
$333$	−10.1803	−0.557879
$334$	11.2918	0.617860
$335$	0	0
$336$	0.618034	0.0337165
$337$	20.7426	1.12992	0.564962	−	0.825117i	$-0.308891\pi$
$337$	20.7426	1.12992	0.564962	+	0.825117i	$0.308891\pi$
$338$	0.944272	0.0513616
$339$	8.56231	0.465041
$340$	0	0
$341$	30.7082	1.66294
$342$	−5.52786	−0.298913
$343$	−8.41641	−0.454443
$344$	0.909830	0.0490547
$345$	0	0
$346$	−12.7082	−0.683197
$347$	−23.1246	−1.24139	−0.620697	−	0.784050i	$-0.713150\pi$
$347$	−23.1246	−1.24139	−0.620697	+	0.784050i	$0.713150\pi$
$348$	−6.70820	−0.359597
$349$	−11.0557	−0.591800	−0.295900	−	0.955219i	$-0.595619\pi$
$349$	−11.0557	−0.591800	−0.295900	+	0.955219i	$0.595619\pi$
$350$	0	0
$351$	17.3607	0.926645
$352$	3.00000	0.159901
$353$	10.1459	0.540012	0.270006	−	0.962859i	$-0.412974\pi$
$353$	10.1459	0.540012	0.270006	+	0.962859i	$0.412974\pi$
$354$	−6.70820	−0.356537
$355$	0	0
$356$	−13.4164	−0.711068
$357$	4.85410	0.256906
$358$	−10.8541	−0.573657
$359$	19.1459	1.01048	0.505241	−	0.862978i	$-0.331404\pi$
$359$	19.1459	1.01048	0.505241	+	0.862978i	$0.331404\pi$
$360$	0	0
$361$	−11.3607	−0.597931
$362$	−11.7984	−0.620109
$363$	−2.00000	−0.104973
$364$	−2.14590	−0.112476
$365$	0	0
$366$	10.2361	0.535048
$367$	−10.8885	−0.568377	−0.284189	−	0.958768i	$-0.591724\pi$
$367$	−10.8885	−0.568377	−0.284189	+	0.958768i	$0.591724\pi$
$368$	−4.85410	−0.253038
$369$	−7.41641	−0.386083
$370$	0	0
$371$	−0.437694	−0.0227239
$372$	−10.2361	−0.530715
$373$	28.5623	1.47890	0.739450	−	0.673211i	$-0.235086\pi$
$373$	28.5623	1.47890	0.739450	+	0.673211i	$0.235086\pi$
$374$	23.5623	1.21838
$375$	0	0
$376$	3.00000	0.154713
$377$	23.2918	1.19959
$378$	3.09017	0.158941
$379$	−3.09017	−0.158731	−0.0793657	−	0.996846i	$-0.525289\pi$
$379$	−3.09017	−0.158731	−0.0793657	+	0.996846i	$0.525289\pi$
$380$	0	0
$381$	0.618034	0.0316628
$382$	5.56231	0.284592
$383$	1.85410	0.0947402	0.0473701	−	0.998877i	$-0.484916\pi$
$383$	1.85410	0.0947402	0.0473701	+	0.998877i	$0.484916\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	24.1246	1.22791
$387$	1.81966	0.0924985
$388$	−10.2361	−0.519658
$389$	−24.2705	−1.23056	−0.615282	−	0.788307i	$-0.710958\pi$
$389$	−24.2705	−1.23056	−0.615282	+	0.788307i	$0.710958\pi$
$390$	0	0
$391$	−38.1246	−1.92804
$392$	6.61803	0.334261
$393$	5.29180	0.266936
$394$	1.41641	0.0713576
$395$	0	0
$396$	6.00000	0.301511
$397$	30.9443	1.55305	0.776524	−	0.630087i	$-0.216981\pi$
$397$	30.9443	1.55305	0.776524	+	0.630087i	$0.216981\pi$
$398$	3.09017	0.154896
$399$	−1.70820	−0.0855172
$400$	0	0
$401$	−13.8541	−0.691841	−0.345920	−	0.938264i	$-0.612433\pi$
$401$	−13.8541	−0.691841	−0.345920	+	0.938264i	$0.612433\pi$
$402$	−11.4721	−0.572178
$403$	35.5410	1.77042
$404$	−3.00000	−0.149256
$405$	0	0
$406$	4.14590	0.205757
$407$	−15.2705	−0.756931
$408$	−7.85410	−0.388836
$409$	6.18034	0.305598	0.152799	−	0.988257i	$-0.451171\pi$
$409$	6.18034	0.305598	0.152799	+	0.988257i	$0.451171\pi$
$410$	0	0
$411$	3.70820	0.182912
$412$	−3.47214	−0.171060
$413$	4.14590	0.204006
$414$	−9.70820	−0.477132
$415$	0	0
$416$	3.47214	0.170235
$417$	6.18034	0.302653
$418$	−8.29180	−0.405565
$419$	−15.0000	−0.732798	−0.366399	−	0.930458i	$-0.619409\pi$
$419$	−15.0000	−0.732798	−0.366399	+	0.930458i	$0.619409\pi$
$420$	0	0
$421$	−11.8197	−0.576055	−0.288027	−	0.957622i	$-0.592999\pi$
$421$	−11.8197	−0.576055	−0.288027	+	0.957622i	$0.592999\pi$
$422$	−20.0902	−0.977974
$423$	6.00000	0.291730
$424$	0.708204	0.0343934
$425$	0	0
$426$	−14.5623	−0.705546
$427$	−6.32624	−0.306148
$428$	−16.4164	−0.793517
$429$	10.4164	0.502909
$430$	0	0
$431$	10.4164	0.501741	0.250870	−	0.968021i	$-0.419283\pi$
$431$	10.4164	0.501741	0.250870	+	0.968021i	$0.419283\pi$
$432$	−5.00000	−0.240563
$433$	29.7426	1.42934	0.714670	−	0.699462i	$-0.246577\pi$
$433$	29.7426	1.42934	0.714670	+	0.699462i	$0.246577\pi$
$434$	6.32624	0.303669
$435$	0	0
$436$	3.94427	0.188896
$437$	13.4164	0.641794
$438$	1.23607	0.0590616
$439$	8.09017	0.386123	0.193061	−	0.981187i	$-0.438158\pi$
$439$	8.09017	0.386123	0.193061	+	0.981187i	$0.438158\pi$
$440$	0	0
$441$	13.2361	0.630289
$442$	27.2705	1.29713
$443$	39.5410	1.87865	0.939325	−	0.343028i	$-0.111452\pi$
$443$	39.5410	1.87865	0.939325	+	0.343028i	$0.111452\pi$
$444$	5.09017	0.241569
$445$	0	0
$446$	21.0344	0.996010
$447$	17.5623	0.830669
$448$	0.618034	0.0291994
$449$	−24.2705	−1.14540	−0.572698	−	0.819766i	$-0.694103\pi$
$449$	−24.2705	−1.14540	−0.572698	+	0.819766i	$0.694103\pi$
$450$	0	0
$451$	−11.1246	−0.523838
$452$	8.56231	0.402737
$453$	−19.5066	−0.916499
$454$	−14.5623	−0.683443
$455$	0	0
$456$	2.76393	0.129433
$457$	2.52786	0.118248	0.0591242	−	0.998251i	$-0.481169\pi$
$457$	2.52786	0.118248	0.0591242	+	0.998251i	$0.481169\pi$
$458$	0.201626	0.00942137
$459$	−39.2705	−1.83299
$460$	0	0
$461$	−27.2705	−1.27011	−0.635057	−	0.772465i	$-0.719023\pi$
$461$	−27.2705	−1.27011	−0.635057	+	0.772465i	$0.719023\pi$
$462$	1.85410	0.0862606
$463$	−22.6180	−1.05115	−0.525575	−	0.850748i	$-0.676150\pi$
$463$	−22.6180	−1.05115	−0.525575	+	0.850748i	$0.676150\pi$
$464$	−6.70820	−0.311421
$465$	0	0
$466$	14.1246	0.654310
$467$	−31.4164	−1.45378	−0.726889	−	0.686755i	$-0.759035\pi$
$467$	−31.4164	−1.45378	−0.726889	+	0.686755i	$0.759035\pi$
$468$	6.94427	0.320999
$469$	7.09017	0.327394
$470$	0	0
$471$	19.5623	0.901383
$472$	−6.70820	−0.308770
$473$	2.72949	0.125502
$474$	13.9443	0.640482
$475$	0	0
$476$	4.85410	0.222487
$477$	1.41641	0.0648529
$478$	8.29180	0.379258
$479$	4.14590	0.189431	0.0947155	−	0.995504i	$-0.469806\pi$
$479$	4.14590	0.189431	0.0947155	+	0.995504i	$0.469806\pi$
$480$	0	0
$481$	−17.6738	−0.805854
$482$	−9.23607	−0.420691
$483$	−3.00000	−0.136505
$484$	−2.00000	−0.0909091
$485$	0	0
$486$	−16.0000	−0.725775
$487$	2.00000	0.0906287	0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000	0.0906287	0.0453143	+	0.998973i	$0.485571\pi$
$488$	10.2361	0.463365
$489$	−21.5623	−0.975081
$490$	0	0
$491$	3.70820	0.167349	0.0836745	−	0.996493i	$-0.473334\pi$
$491$	3.70820	0.167349	0.0836745	+	0.996493i	$0.473334\pi$
$492$	3.70820	0.167179
$493$	−52.6869	−2.37290
$494$	−9.59675	−0.431778
$495$	0	0
$496$	−10.2361	−0.459613
$497$	9.00000	0.403705
$498$	−1.85410	−0.0830843
$499$	−27.5623	−1.23386	−0.616929	−	0.787019i	$-0.711623\pi$
$499$	−27.5623	−1.23386	−0.616929	+	0.787019i	$0.711623\pi$
$500$	0	0
$501$	−11.2918	−0.504480
$502$	3.00000	0.133897
$503$	15.2705	0.680878	0.340439	−	0.940267i	$-0.389424\pi$
$503$	15.2705	0.680878	0.340439	+	0.940267i	$0.389424\pi$
$504$	1.23607	0.0550588
$505$	0	0
$506$	−14.5623	−0.647373
$507$	−0.944272	−0.0419366
$508$	0.618034	0.0274208
$509$	−32.5623	−1.44330	−0.721649	−	0.692259i	$-0.756616\pi$
$509$	−32.5623	−1.44330	−0.721649	+	0.692259i	$0.756616\pi$
$510$	0	0
$511$	−0.763932	−0.0337944
$512$	−1.00000	−0.0441942
$513$	13.8197	0.610153
$514$	−10.4164	−0.459448
$515$	0	0
$516$	−0.909830	−0.0400530
$517$	9.00000	0.395820
$518$	−3.14590	−0.138223
$519$	12.7082	0.557828
$520$	0	0
$521$	27.0000	1.18289	0.591446	−	0.806345i	$-0.298557\pi$
$521$	27.0000	1.18289	0.591446	+	0.806345i	$0.298557\pi$
$522$	−13.4164	−0.587220
$523$	28.1591	1.23131	0.615655	−	0.788016i	$-0.288892\pi$
$523$	28.1591	1.23131	0.615655	+	0.788016i	$0.288892\pi$
$524$	5.29180	0.231173
$525$	0	0
$526$	6.43769	0.280697
$527$	−80.3951	−3.50207
$528$	−3.00000	−0.130558
$529$	0.562306	0.0244481
$530$	0	0
$531$	−13.4164	−0.582223
$532$	−1.70820	−0.0740600
$533$	−12.8754	−0.557695
$534$	13.4164	0.580585
$535$	0	0
$536$	−11.4721	−0.495521
$537$	10.8541	0.468389
$538$	−10.8541	−0.467954
$539$	19.8541	0.855177
$540$	0	0
$541$	−18.1246	−0.779238	−0.389619	−	0.920976i	$-0.627393\pi$
$541$	−18.1246	−0.779238	−0.389619	+	0.920976i	$0.627393\pi$
$542$	15.0344	0.645785
$543$	11.7984	0.506317
$544$	−7.85410	−0.336742
$545$	0	0
$546$	2.14590	0.0918360
$547$	−35.7639	−1.52916	−0.764578	−	0.644532i	$-0.777052\pi$
$547$	−35.7639	−1.52916	−0.764578	+	0.644532i	$0.777052\pi$
$548$	3.70820	0.158407
$549$	20.4721	0.873729
$550$	0	0
$551$	18.5410	0.789874
$552$	4.85410	0.206604
$553$	−8.61803	−0.366476
$554$	−11.4721	−0.487404
$555$	0	0
$556$	6.18034	0.262105
$557$	−24.7082	−1.04692	−0.523460	−	0.852050i	$-0.675359\pi$
$557$	−24.7082	−1.04692	−0.523460	+	0.852050i	$0.675359\pi$
$558$	−20.4721	−0.866655
$559$	3.15905	0.133614
$560$	0	0
$561$	−23.5623	−0.994801
$562$	−27.0000	−1.13893
$563$	36.0000	1.51722	0.758610	−	0.651546i	$-0.225879\pi$
$563$	36.0000	1.51722	0.758610	+	0.651546i	$0.225879\pi$
$564$	−3.00000	−0.126323
$565$	0	0
$566$	−28.5623	−1.20056
$567$	0.618034	0.0259550
$568$	−14.5623	−0.611021
$569$	0	0		−	1.00000i	$-0.5\pi$
$569$	0	0			1.00000i	$0.5\pi$
$570$	0	0
$571$	20.7426	0.868053	0.434026	−	0.900900i	$-0.357092\pi$
$571$	20.7426	0.868053	0.434026	+	0.900900i	$0.357092\pi$
$572$	10.4164	0.435532
$573$	−5.56231	−0.232369
$574$	−2.29180	−0.0956577
$575$	0	0
$576$	−2.00000	−0.0833333
$577$	−35.1591	−1.46369	−0.731845	−	0.681471i	$-0.761341\pi$
$577$	−35.1591	−1.46369	−0.731845	+	0.681471i	$0.761341\pi$
$578$	−44.6869	−1.85873
$579$	−24.1246	−1.00258
$580$	0	0
$581$	1.14590	0.0475399
$582$	10.2361	0.424299
$583$	2.12461	0.0879924
$584$	1.23607	0.0511489
$585$	0	0
$586$	−16.8541	−0.696237
$587$	13.5836	0.560655	0.280327	−	0.959904i	$-0.409557\pi$
$587$	13.5836	0.560655	0.280327	+	0.959904i	$0.409557\pi$
$588$	−6.61803	−0.272923
$589$	28.2918	1.16574
$590$	0	0
$591$	−1.41641	−0.0582632
$592$	5.09017	0.209205
$593$	−15.7082	−0.645059	−0.322529	−	0.946559i	$-0.604533\pi$
$593$	−15.7082	−0.645059	−0.322529	+	0.946559i	$0.604533\pi$
$594$	−15.0000	−0.615457
$595$	0	0
$596$	17.5623	0.719380
$597$	−3.09017	−0.126472
$598$	−16.8541	−0.689215
$599$	−12.4377	−0.508190	−0.254095	−	0.967179i	$-0.581778\pi$
$599$	−12.4377	−0.508190	−0.254095	+	0.967179i	$0.581778\pi$
$600$	0	0
$601$	4.56231	0.186100	0.0930502	−	0.995661i	$-0.470338\pi$
$601$	4.56231	0.186100	0.0930502	+	0.995661i	$0.470338\pi$
$602$	0.562306	0.0229179
$603$	−22.9443	−0.934363
$604$	−19.5066	−0.793711
$605$	0	0
$606$	3.00000	0.121867
$607$	−19.5066	−0.791748	−0.395874	−	0.918305i	$-0.629558\pi$
$607$	−19.5066	−0.791748	−0.395874	+	0.918305i	$0.629558\pi$
$608$	2.76393	0.112092
$609$	−4.14590	−0.168000
$610$	0	0
$611$	10.4164	0.421403
$612$	−15.7082	−0.634967
$613$	0.347524	0.0140364	0.00701818	−	0.999975i	$-0.497766\pi$
$613$	0.347524	0.0140364	0.00701818	+	0.999975i	$0.497766\pi$
$614$	1.61803	0.0652985
$615$	0	0
$616$	1.85410	0.0747039
$617$	21.2705	0.856318	0.428159	−	0.903703i	$-0.359162\pi$
$617$	21.2705	0.856318	0.428159	+	0.903703i	$0.359162\pi$
$618$	3.47214	0.139670
$619$	−37.8885	−1.52287	−0.761435	−	0.648242i	$-0.775505\pi$
$619$	−37.8885	−1.52287	−0.761435	+	0.648242i	$0.775505\pi$
$620$	0	0
$621$	24.2705	0.973942
$622$	−16.1459	−0.647392
$623$	−8.29180	−0.332204
$624$	−3.47214	−0.138997
$625$	0	0
$626$	−9.61803	−0.384414
$627$	8.29180	0.331142
$628$	19.5623	0.780621
$629$	39.9787	1.59406
$630$	0	0
$631$	−7.34752	−0.292500	−0.146250	−	0.989248i	$-0.546720\pi$
$631$	−7.34752	−0.292500	−0.146250	+	0.989248i	$0.546720\pi$
$632$	13.9443	0.554673
$633$	20.0902	0.798513
$634$	5.56231	0.220907
$635$	0	0
$636$	−0.708204	−0.0280821
$637$	22.9787	0.910450
$638$	−20.1246	−0.796741
$639$	−29.1246	−1.15215
$640$	0	0
$641$	30.5410	1.20630	0.603149	−	0.797629i	$-0.293912\pi$
$641$	30.5410	1.20630	0.603149	+	0.797629i	$0.293912\pi$
$642$	16.4164	0.647904
$643$	−1.23607	−0.0487458	−0.0243729	−	0.999703i	$-0.507759\pi$
$643$	−1.23607	−0.0487458	−0.0243729	+	0.999703i	$0.507759\pi$
$644$	−3.00000	−0.118217
$645$	0	0
$646$	21.7082	0.854098
$647$	22.8541	0.898487	0.449244	−	0.893409i	$-0.351693\pi$
$647$	22.8541	0.898487	0.449244	+	0.893409i	$0.351693\pi$
$648$	−1.00000	−0.0392837
$649$	−20.1246	−0.789960
$650$	0	0
$651$	−6.32624	−0.247945
$652$	−21.5623	−0.844445
$653$	13.6869	0.535610	0.267805	−	0.963473i	$-0.413702\pi$
$653$	13.6869	0.535610	0.267805	+	0.963473i	$0.413702\pi$
$654$	−3.94427	−0.154233
$655$	0	0
$656$	3.70820	0.144781
$657$	2.47214	0.0964472
$658$	1.85410	0.0722804
$659$	−48.5410	−1.89089	−0.945445	−	0.325782i	$-0.894372\pi$
$659$	−48.5410	−1.89089	−0.945445	+	0.325782i	$0.894372\pi$
$660$	0	0
$661$	−41.2148	−1.60307	−0.801535	−	0.597948i	$-0.795983\pi$
$661$	−41.2148	−1.60307	−0.801535	+	0.597948i	$0.795983\pi$
$662$	23.3262	0.906600
$663$	−27.2705	−1.05910
$664$	−1.85410	−0.0719531
$665$	0	0
$666$	10.1803	0.394480
$667$	32.5623	1.26082
$668$	−11.2918	−0.436893
$669$	−21.0344	−0.813239
$670$	0	0
$671$	30.7082	1.18548
$672$	−0.618034	−0.0238412
$673$	13.5623	0.522788	0.261394	−	0.965232i	$-0.415818\pi$
$673$	13.5623	0.522788	0.261394	+	0.965232i	$0.415818\pi$
$674$	−20.7426	−0.798977
$675$	0	0
$676$	−0.944272	−0.0363182
$677$	−5.56231	−0.213777	−0.106888	−	0.994271i	$-0.534089\pi$
$677$	−5.56231	−0.213777	−0.106888	+	0.994271i	$0.534089\pi$
$678$	−8.56231	−0.328833
$679$	−6.32624	−0.242779
$680$	0	0
$681$	14.5623	0.558029
$682$	−30.7082	−1.17588
$683$	4.41641	0.168989	0.0844946	−	0.996424i	$-0.473072\pi$
$683$	4.41641	0.168989	0.0844946	+	0.996424i	$0.473072\pi$
$684$	5.52786	0.211363
$685$	0	0
$686$	8.41641	0.321340
$687$	−0.201626	−0.00769252
$688$	−0.909830	−0.0346869
$689$	2.45898	0.0936797
$690$	0	0
$691$	−21.0902	−0.802308	−0.401154	−	0.916011i	$-0.631391\pi$
$691$	−21.0902	−0.802308	−0.401154	+	0.916011i	$0.631391\pi$
$692$	12.7082	0.483093
$693$	3.70820	0.140863
$694$	23.1246	0.877798
$695$	0	0
$696$	6.70820	0.254274
$697$	29.1246	1.10317
$698$	11.0557	0.418465
$699$	−14.1246	−0.534242
$700$	0	0
$701$	18.7082	0.706599	0.353300	−	0.935510i	$-0.385060\pi$
$701$	18.7082	0.706599	0.353300	+	0.935510i	$0.385060\pi$
$702$	−17.3607	−0.655237
$703$	−14.0689	−0.530618
$704$	−3.00000	−0.113067
$705$	0	0
$706$	−10.1459	−0.381846
$707$	−1.85410	−0.0697307
$708$	6.70820	0.252110
$709$	−10.0000	−0.375558	−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000	−0.375558	−0.187779	+	0.982211i	$0.560129\pi$
$710$	0	0
$711$	27.8885	1.04590
$712$	13.4164	0.502801
$713$	49.6869	1.86079
$714$	−4.85410	−0.181660
$715$	0	0
$716$	10.8541	0.405637
$717$	−8.29180	−0.309663
$718$	−19.1459	−0.714519
$719$	−21.7082	−0.809579	−0.404790	−	0.914410i	$-0.632655\pi$
$719$	−21.7082	−0.809579	−0.404790	+	0.914410i	$0.632655\pi$
$720$	0	0
$721$	−2.14590	−0.0799174
$722$	11.3607	0.422801
$723$	9.23607	0.343493
$724$	11.7984	0.438483
$725$	0	0
$726$	2.00000	0.0742270
$727$	−33.5279	−1.24348	−0.621740	−	0.783224i	$-0.713574\pi$
$727$	−33.5279	−1.24348	−0.621740	+	0.783224i	$0.713574\pi$
$728$	2.14590	0.0795323
$729$	13.0000	0.481481
$730$	0	0
$731$	−7.14590	−0.264301
$732$	−10.2361	−0.378336
$733$	−24.1246	−0.891063	−0.445531	−	0.895266i	$-0.646985\pi$
$733$	−24.1246	−0.891063	−0.445531	+	0.895266i	$0.646985\pi$
$734$	10.8885	0.401903
$735$	0	0
$736$	4.85410	0.178925
$737$	−34.4164	−1.26774
$738$	7.41641	0.273002
$739$	3.94427	0.145092	0.0725462	−	0.997365i	$-0.476888\pi$
$739$	3.94427	0.145092	0.0725462	+	0.997365i	$0.476888\pi$
$740$	0	0
$741$	9.59675	0.352545
$742$	0.437694	0.0160683
$743$	6.00000	0.220119	0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000	0.220119	0.110059	+	0.993925i	$0.464896\pi$
$744$	10.2361	0.375272
$745$	0	0
$746$	−28.5623	−1.04574
$747$	−3.70820	−0.135676
$748$	−23.5623	−0.861523
$749$	−10.1459	−0.370723
$750$	0	0
$751$	7.65248	0.279243	0.139621	−	0.990205i	$-0.455411\pi$
$751$	7.65248	0.279243	0.139621	+	0.990205i	$0.455411\pi$
$752$	−3.00000	−0.109399
$753$	−3.00000	−0.109326
$754$	−23.2918	−0.848237
$755$	0	0
$756$	−3.09017	−0.112388
$757$	−21.0902	−0.766535	−0.383268	−	0.923637i	$-0.625201\pi$
$757$	−21.0902	−0.766535	−0.383268	+	0.923637i	$0.625201\pi$
$758$	3.09017	0.112240
$759$	14.5623	0.528578
$760$	0	0
$761$	−15.4377	−0.559616	−0.279808	−	0.960056i	$-0.590271\pi$
$761$	−15.4377	−0.559616	−0.279808	+	0.960056i	$0.590271\pi$
$762$	−0.618034	−0.0223890
$763$	2.43769	0.0882505
$764$	−5.56231	−0.201237
$765$	0	0
$766$	−1.85410	−0.0669914
$767$	−23.2918	−0.841018
$768$	1.00000	0.0360844
$769$	6.18034	0.222869	0.111434	−	0.993772i	$-0.464456\pi$
$769$	6.18034	0.222869	0.111434	+	0.993772i	$0.464456\pi$
$770$	0	0
$771$	10.4164	0.375138
$772$	−24.1246	−0.868264
$773$	19.4164	0.698360	0.349180	−	0.937056i	$-0.386460\pi$
$773$	19.4164	0.698360	0.349180	+	0.937056i	$0.386460\pi$
$774$	−1.81966	−0.0654063
$775$	0	0
$776$	10.2361	0.367453
$777$	3.14590	0.112858
$778$	24.2705	0.870140
$779$	−10.2492	−0.367217
$780$	0	0
$781$	−43.6869	−1.56324
$782$	38.1246	1.36333
$783$	33.5410	1.19866
$784$	−6.61803	−0.236358
$785$	0	0
$786$	−5.29180	−0.188752
$787$	11.8754	0.423312	0.211656	−	0.977344i	$-0.432114\pi$
$787$	11.8754	0.423312	0.211656	+	0.977344i	$0.432114\pi$
$788$	−1.41641	−0.0504574
$789$	−6.43769	−0.229188
$790$	0	0
$791$	5.29180	0.188155
$792$	−6.00000	−0.213201
$793$	35.5410	1.26210
$794$	−30.9443	−1.09817
$795$	0	0
$796$	−3.09017	−0.109528
$797$	−29.8328	−1.05673	−0.528366	−	0.849017i	$-0.677195\pi$
$797$	−29.8328	−1.05673	−0.528366	+	0.849017i	$0.677195\pi$
$798$	1.70820	0.0604698
$799$	−23.5623	−0.833574
$800$	0	0
$801$	26.8328	0.948091
$802$	13.8541	0.489205
$803$	3.70820	0.130860
$804$	11.4721	0.404591
$805$	0	0
$806$	−35.5410	−1.25188
$807$	10.8541	0.382082
$808$	3.00000	0.105540
$809$	4.14590	0.145762	0.0728810	−	0.997341i	$-0.476781\pi$
$809$	4.14590	0.145762	0.0728810	+	0.997341i	$0.476781\pi$
$810$	0	0
$811$	−18.1246	−0.636441	−0.318221	−	0.948017i	$-0.603085\pi$
$811$	−18.1246	−0.636441	−0.318221	+	0.948017i	$0.603085\pi$
$812$	−4.14590	−0.145492
$813$	−15.0344	−0.527281
$814$	15.2705	0.535231
$815$	0	0
$816$	7.85410	0.274949
$817$	2.51471	0.0879785
$818$	−6.18034	−0.216091
$819$	4.29180	0.149967
$820$	0	0
$821$	14.5623	0.508228	0.254114	−	0.967174i	$-0.418216\pi$
$821$	14.5623	0.508228	0.254114	+	0.967174i	$0.418216\pi$
$822$	−3.70820	−0.129338
$823$	−50.4296	−1.75786	−0.878932	−	0.476947i	$-0.841743\pi$
$823$	−50.4296	−1.75786	−0.878932	+	0.476947i	$0.841743\pi$
$824$	3.47214	0.120958
$825$	0	0
$826$	−4.14590	−0.144254
$827$	18.7082	0.650548	0.325274	−	0.945620i	$-0.394543\pi$
$827$	18.7082	0.650548	0.325274	+	0.945620i	$0.394543\pi$
$828$	9.70820	0.337383
$829$	−35.3262	−1.22693	−0.613465	−	0.789722i	$-0.710225\pi$
$829$	−35.3262	−1.22693	−0.613465	+	0.789722i	$0.710225\pi$
$830$	0	0
$831$	11.4721	0.397964
$832$	−3.47214	−0.120375
$833$	−51.9787	−1.80096
$834$	−6.18034	−0.214008
$835$	0	0
$836$	8.29180	0.286778
$837$	51.1803	1.76905
$838$	15.0000	0.518166
$839$	−51.7082	−1.78517	−0.892583	−	0.450884i	$-0.851109\pi$
$839$	−51.7082	−1.78517	−0.892583	+	0.450884i	$0.851109\pi$
$840$	0	0
$841$	16.0000	0.551724
$842$	11.8197	0.407332
$843$	27.0000	0.929929
$844$	20.0902	0.691532
$845$	0	0
$846$	−6.00000	−0.206284
$847$	−1.23607	−0.0424718
$848$	−0.708204	−0.0243198
$849$	28.5623	0.980256
$850$	0	0
$851$	−24.7082	−0.846986
$852$	14.5623	0.498896
$853$	11.2016	0.383536	0.191768	−	0.981440i	$-0.438578\pi$
$853$	11.2016	0.383536	0.191768	+	0.981440i	$0.438578\pi$
$854$	6.32624	0.216479
$855$	0	0
$856$	16.4164	0.561101
$857$	18.7082	0.639060	0.319530	−	0.947576i	$-0.396475\pi$
$857$	18.7082	0.639060	0.319530	+	0.947576i	$0.396475\pi$
$858$	−10.4164	−0.355610
$859$	17.0344	0.581208	0.290604	−	0.956843i	$-0.406144\pi$
$859$	17.0344	0.581208	0.290604	+	0.956843i	$0.406144\pi$
$860$	0	0
$861$	2.29180	0.0781042
$862$	−10.4164	−0.354784
$863$	−39.0000	−1.32758	−0.663788	−	0.747921i	$-0.731052\pi$
$863$	−39.0000	−1.32758	−0.663788	+	0.747921i	$0.731052\pi$
$864$	5.00000	0.170103
$865$	0	0
$866$	−29.7426	−1.01070
$867$	44.6869	1.51765
$868$	−6.32624	−0.214727
$869$	41.8328	1.41908
$870$	0	0
$871$	−39.8328	−1.34968
$872$	−3.94427	−0.133570
$873$	20.4721	0.692877
$874$	−13.4164	−0.453817
$875$	0	0
$876$	−1.23607	−0.0417629
$877$	39.6869	1.34013	0.670066	−	0.742302i	$-0.266266\pi$
$877$	39.6869	1.34013	0.670066	+	0.742302i	$0.266266\pi$
$878$	−8.09017	−0.273030
$879$	16.8541	0.568475
$880$	0	0
$881$	−3.00000	−0.101073	−0.0505363	−	0.998722i	$-0.516093\pi$
$881$	−3.00000	−0.101073	−0.0505363	+	0.998722i	$0.516093\pi$
$882$	−13.2361	−0.445682
$883$	26.5279	0.892734	0.446367	−	0.894850i	$-0.352718\pi$
$883$	26.5279	0.892734	0.446367	+	0.894850i	$0.352718\pi$
$884$	−27.2705	−0.917207
$885$	0	0
$886$	−39.5410	−1.32841
$887$	15.5410	0.521816	0.260908	−	0.965364i	$-0.415978\pi$
$887$	15.5410	0.521816	0.260908	+	0.965364i	$0.415978\pi$
$888$	−5.09017	−0.170815
$889$	0.381966	0.0128107
$890$	0	0
$891$	−3.00000	−0.100504
$892$	−21.0344	−0.704285
$893$	8.29180	0.277474
$894$	−17.5623	−0.587371
$895$	0	0
$896$	−0.618034	−0.0206471
$897$	16.8541	0.562742
$898$	24.2705	0.809917
$899$	68.6656	2.29013
$900$	0	0
$901$	−5.56231	−0.185307
$902$	11.1246	0.370409
$903$	−0.562306	−0.0187124
$904$	−8.56231	−0.284778
$905$	0	0
$906$	19.5066	0.648063
$907$	−4.18034	−0.138806	−0.0694030	−	0.997589i	$-0.522109\pi$
$907$	−4.18034	−0.138806	−0.0694030	+	0.997589i	$0.522109\pi$
$908$	14.5623	0.483267
$909$	6.00000	0.199007
$910$	0	0
$911$	−20.5623	−0.681260	−0.340630	−	0.940198i	$-0.610640\pi$
$911$	−20.5623	−0.681260	−0.340630	+	0.940198i	$0.610640\pi$
$912$	−2.76393	−0.0915229
$913$	−5.56231	−0.184085
$914$	−2.52786	−0.0836143
$915$	0	0
$916$	−0.201626	−0.00666191
$917$	3.27051	0.108002
$918$	39.2705	1.29612
$919$	38.7426	1.27800	0.639001	−	0.769206i	$-0.279348\pi$
$919$	38.7426	1.27800	0.639001	+	0.769206i	$0.279348\pi$
$920$	0	0
$921$	−1.61803	−0.0533160
$922$	27.2705	0.898106
$923$	−50.5623	−1.66428
$924$	−1.85410	−0.0609955
$925$	0	0
$926$	22.6180	0.743275
$927$	6.94427	0.228080
$928$	6.70820	0.220208
$929$	−19.1459	−0.628157	−0.314078	−	0.949397i	$-0.601695\pi$
$929$	−19.1459	−0.628157	−0.314078	+	0.949397i	$0.601695\pi$
$930$	0	0
$931$	18.2918	0.599489
$932$	−14.1246	−0.462667
$933$	16.1459	0.528593
$934$	31.4164	1.02798
$935$	0	0
$936$	−6.94427	−0.226981
$937$	−8.32624	−0.272006	−0.136003	−	0.990708i	$-0.543426\pi$
$937$	−8.32624	−0.272006	−0.136003	+	0.990708i	$0.543426\pi$
$938$	−7.09017	−0.231502
$939$	9.61803	0.313873
$940$	0	0
$941$	20.2918	0.661494	0.330747	−	0.943720i	$-0.392699\pi$
$941$	20.2918	0.661494	0.330747	+	0.943720i	$0.392699\pi$
$942$	−19.5623	−0.637374
$943$	−18.0000	−0.586161
$944$	6.70820	0.218333
$945$	0	0
$946$	−2.72949	−0.0887434
$947$	1.14590	0.0372367	0.0186183	−	0.999827i	$-0.494073\pi$
$947$	1.14590	0.0372367	0.0186183	+	0.999827i	$0.494073\pi$
$948$	−13.9443	−0.452889
$949$	4.29180	0.139318
$950$	0	0
$951$	−5.56231	−0.180370
$952$	−4.85410	−0.157322
$953$	3.43769	0.111358	0.0556789	−	0.998449i	$-0.482268\pi$
$953$	3.43769	0.111358	0.0556789	+	0.998449i	$0.482268\pi$
$954$	−1.41641	−0.0458579
$955$	0	0
$956$	−8.29180	−0.268176
$957$	20.1246	0.650536
$958$	−4.14590	−0.133948
$959$	2.29180	0.0740060
$960$	0	0
$961$	73.7771	2.37991
$962$	17.6738	0.569825
$963$	32.8328	1.05802
$964$	9.23607	0.297474
$965$	0	0
$966$	3.00000	0.0965234
$967$	−52.0689	−1.67442	−0.837211	−	0.546880i	$-0.815816\pi$
$967$	−52.0689	−1.67442	−0.837211	+	0.546880i	$0.815816\pi$
$968$	2.00000	0.0642824
$969$	−21.7082	−0.697368
$970$	0	0
$971$	−43.8541	−1.40735	−0.703673	−	0.710524i	$-0.748458\pi$
$971$	−43.8541	−1.40735	−0.703673	+	0.710524i	$0.748458\pi$
$972$	16.0000	0.513200
$973$	3.81966	0.122453
$974$	−2.00000	−0.0640841
$975$	0	0
$976$	−10.2361	−0.327649
$977$	−15.4377	−0.493896	−0.246948	−	0.969029i	$-0.579428\pi$
$977$	−15.4377	−0.493896	−0.246948	+	0.969029i	$0.579428\pi$
$978$	21.5623	0.689487
$979$	40.2492	1.28637
$980$	0	0
$981$	−7.88854	−0.251862
$982$	−3.70820	−0.118334
$983$	−51.8115	−1.65253	−0.826266	−	0.563281i	$-0.809539\pi$
$983$	−51.8115	−1.65253	−0.826266	+	0.563281i	$0.809539\pi$
$984$	−3.70820	−0.118213
$985$	0	0
$986$	52.6869	1.67789
$987$	−1.85410	−0.0590167
$988$	9.59675	0.305313
$989$	4.41641	0.140434
$990$	0	0
$991$	5.09017	0.161695	0.0808473	−	0.996727i	$-0.474237\pi$
$991$	5.09017	0.161695	0.0808473	+	0.996727i	$0.474237\pi$
$992$	10.2361	0.324995
$993$	−23.3262	−0.740236
$994$	−9.00000	−0.285463
$995$	0	0
$996$	1.85410	0.0587495
$997$	22.6525	0.717411	0.358706	−	0.933451i	$-0.383218\pi$
$997$	22.6525	0.717411	0.358706	+	0.933451i	$0.383218\pi$
$998$	27.5623	0.872470
$999$	−25.4508	−0.805229

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1250.2.a.b.1.2	✓	2
4.3	odd	2		10000.2.a.d.1.1		2
5.2	odd	4		1250.2.b.a.1249.2		4
5.3	odd	4		1250.2.b.a.1249.3		4
5.4	even	2		1250.2.a.c.1.1	yes	2
20.19	odd	2		10000.2.a.k.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1250.2.a.b.1.2	✓	2	1.1	even	1	trivial
1250.2.a.c.1.1	yes	2	5.4	even	2
1250.2.b.a.1249.2		4	5.2	odd	4
1250.2.b.a.1249.3		4	5.3	odd	4
10000.2.a.d.1.1		2	4.3	odd	2
10000.2.a.k.1.2		2	20.19	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:	\( N \)	\(=\)	\( 1250 = 2 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1250.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +0.618034 q^{7} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +0.618034 q^{7} -1.00000 q^{8} -2.00000 q^{9} -3.00000 q^{11} +1.00000 q^{12} -3.47214 q^{13} -0.618034 q^{14} +1.00000 q^{16} +7.85410 q^{17} +2.00000 q^{18} -2.76393 q^{19} +0.618034 q^{21} +3.00000 q^{22} -4.85410 q^{23} -1.00000 q^{24} +3.47214 q^{26} -5.00000 q^{27} +0.618034 q^{28} -6.70820 q^{29} -10.2361 q^{31} -1.00000 q^{32} -3.00000 q^{33} -7.85410 q^{34} -2.00000 q^{36} +5.09017 q^{37} +2.76393 q^{38} -3.47214 q^{39} +3.70820 q^{41} -0.618034 q^{42} -0.909830 q^{43} -3.00000 q^{44} +4.85410 q^{46} -3.00000 q^{47} +1.00000 q^{48} -6.61803 q^{49} +7.85410 q^{51} -3.47214 q^{52} -0.708204 q^{53} +5.00000 q^{54} -0.618034 q^{56} -2.76393 q^{57} +6.70820 q^{58} +6.70820 q^{59} -10.2361 q^{61} +10.2361 q^{62} -1.23607 q^{63} +1.00000 q^{64} +3.00000 q^{66} +11.4721 q^{67} +7.85410 q^{68} -4.85410 q^{69} +14.5623 q^{71} +2.00000 q^{72} -1.23607 q^{73} -5.09017 q^{74} -2.76393 q^{76} -1.85410 q^{77} +3.47214 q^{78} -13.9443 q^{79} +1.00000 q^{81} -3.70820 q^{82} +1.85410 q^{83} +0.618034 q^{84} +0.909830 q^{86} -6.70820 q^{87} +3.00000 q^{88} -13.4164 q^{89} -2.14590 q^{91} -4.85410 q^{92} -10.2361 q^{93} +3.00000 q^{94} -1.00000 q^{96} -10.2361 q^{97} +6.61803 q^{98} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} - q^{7} - 2 q^{8} - 4 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 - q^7 - 2 * q^8 - 4 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} - q^{7} - 2 q^{8} - 4 q^{9} - 6 q^{11} + 2 q^{12} + 2 q^{13} + q^{14} + 2 q^{16} + 9 q^{17} + 4 q^{18} - 10 q^{19} - q^{21} + 6 q^{22} - 3 q^{23} - 2 q^{24} - 2 q^{26} - 10 q^{27} - q^{28} - 16 q^{31} - 2 q^{32} - 6 q^{33} - 9 q^{34} - 4 q^{36} - q^{37} + 10 q^{38} + 2 q^{39} - 6 q^{41} + q^{42} - 13 q^{43} - 6 q^{44} + 3 q^{46} - 6 q^{47} + 2 q^{48} - 11 q^{49} + 9 q^{51} + 2 q^{52} + 12 q^{53} + 10 q^{54} + q^{56} - 10 q^{57} - 16 q^{61} + 16 q^{62} + 2 q^{63} + 2 q^{64} + 6 q^{66} + 14 q^{67} + 9 q^{68} - 3 q^{69} + 9 q^{71} + 4 q^{72} + 2 q^{73} + q^{74} - 10 q^{76} + 3 q^{77} - 2 q^{78} - 10 q^{79} + 2 q^{81} + 6 q^{82} - 3 q^{83} - q^{84} + 13 q^{86} + 6 q^{88} - 11 q^{91} - 3 q^{92} - 16 q^{93} + 6 q^{94} - 2 q^{96} - 16 q^{97} + 11 q^{98} + 12 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 - q^7 - 2 * q^8 - 4 * q^9 - 6 * q^11 + 2 * q^12 + 2 * q^13 + q^14 + 2 * q^16 + 9 * q^17 + 4 * q^18 - 10 * q^19 - q^21 + 6 * q^22 - 3 * q^23 - 2 * q^24 - 2 * q^26 - 10 * q^27 - q^28 - 16 * q^31 - 2 * q^32 - 6 * q^33 - 9 * q^34 - 4 * q^36 - q^37 + 10 * q^38 + 2 * q^39 - 6 * q^41 + q^42 - 13 * q^43 - 6 * q^44 + 3 * q^46 - 6 * q^47 + 2 * q^48 - 11 * q^49 + 9 * q^51 + 2 * q^52 + 12 * q^53 + 10 * q^54 + q^56 - 10 * q^57 - 16 * q^61 + 16 * q^62 + 2 * q^63 + 2 * q^64 + 6 * q^66 + 14 * q^67 + 9 * q^68 - 3 * q^69 + 9 * q^71 + 4 * q^72 + 2 * q^73 + q^74 - 10 * q^76 + 3 * q^77 - 2 * q^78 - 10 * q^79 + 2 * q^81 + 6 * q^82 - 3 * q^83 - q^84 + 13 * q^86 + 6 * q^88 - 11 * q^91 - 3 * q^92 - 16 * q^93 + 6 * q^94 - 2 * q^96 - 16 * q^97 + 11 * q^98 + 12 * q^99

Introduction

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