LMFDB - Embedded newform 3525.2.a.bd.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,2,Mod(1,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, 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("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.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:	$28.1472667125$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 7x^{6} + 24x^{5} + 8x^{4} - 47x^{3} + 8x^{2} + 13x + 2 $ x^8 - 3x^7 - 7x^6 + 24x^5 + 8x^4 - 47x^3 + 8x^2 + 13*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.19791$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.19791 q^{2} +1.00000 q^{3} +2.83083 q^{4} -2.19791 q^{6} +1.05086 q^{7} -1.82609 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.19791 q^{2} +1.00000 q^{3} +2.83083 q^{4} -2.19791 q^{6} +1.05086 q^{7} -1.82609 q^{8} +1.00000 q^{9} -3.22580 q^{11} +2.83083 q^{12} +2.58899 q^{13} -2.30971 q^{14} -1.64807 q^{16} -7.50374 q^{17} -2.19791 q^{18} +1.70135 q^{19} +1.05086 q^{21} +7.09002 q^{22} -2.21428 q^{23} -1.82609 q^{24} -5.69038 q^{26} +1.00000 q^{27} +2.97481 q^{28} +6.74234 q^{29} +10.8019 q^{31} +7.27449 q^{32} -3.22580 q^{33} +16.4926 q^{34} +2.83083 q^{36} -11.7806 q^{37} -3.73942 q^{38} +2.58899 q^{39} -5.81601 q^{41} -2.30971 q^{42} -3.39497 q^{43} -9.13167 q^{44} +4.86680 q^{46} -1.00000 q^{47} -1.64807 q^{48} -5.89569 q^{49} -7.50374 q^{51} +7.32898 q^{52} -11.1690 q^{53} -2.19791 q^{54} -1.91897 q^{56} +1.70135 q^{57} -14.8191 q^{58} +12.3261 q^{59} -6.55166 q^{61} -23.7417 q^{62} +1.05086 q^{63} -12.6926 q^{64} +7.09002 q^{66} +0.750116 q^{67} -21.2418 q^{68} -2.21428 q^{69} +2.09231 q^{71} -1.82609 q^{72} +4.80219 q^{73} +25.8928 q^{74} +4.81623 q^{76} -3.38987 q^{77} -5.69038 q^{78} +6.59991 q^{79} +1.00000 q^{81} +12.7831 q^{82} -15.6214 q^{83} +2.97481 q^{84} +7.46185 q^{86} +6.74234 q^{87} +5.89058 q^{88} -15.4144 q^{89} +2.72067 q^{91} -6.26825 q^{92} +10.8019 q^{93} +2.19791 q^{94} +7.27449 q^{96} +11.6829 q^{97} +12.9582 q^{98} -3.22580 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{2} + 8 q^{3} + 7 q^{4} - 3 q^{6} - 8 q^{7} - 6 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 3 * q^2 + 8 * q^3 + 7 * q^4 - 3 * q^6 - 8 * q^7 - 6 * q^8 + 8 * q^9	$ 8 q - 3 q^{2} + 8 q^{3} + 7 q^{4} - 3 q^{6} - 8 q^{7} - 6 q^{8} + 8 q^{9} - 8 q^{11} + 7 q^{12} - 10 q^{13} + q^{14} + 5 q^{16} - 6 q^{17} - 3 q^{18} - 2 q^{19} - 8 q^{21} - 10 q^{23} - 6 q^{24} - 14 q^{26} + 8 q^{27} - 44 q^{28} - 13 q^{29} - 10 q^{32} - 8 q^{33} + 28 q^{34} + 7 q^{36} - 3 q^{37} - 36 q^{38} - 10 q^{39} - 16 q^{41} + q^{42} - 25 q^{43} - 17 q^{44} - 5 q^{46} - 8 q^{47} + 5 q^{48} + 16 q^{49} - 6 q^{51} + 17 q^{52} - 4 q^{53} - 3 q^{54} + 37 q^{56} - 2 q^{57} - 15 q^{58} - 8 q^{59} + 15 q^{61} - 6 q^{62} - 8 q^{63} - 14 q^{64} - 27 q^{67} - 14 q^{68} - 10 q^{69} + 14 q^{71} - 6 q^{72} - 28 q^{73} - 21 q^{74} + 6 q^{76} - 4 q^{77} - 14 q^{78} + 7 q^{79} + 8 q^{81} + 53 q^{82} - 60 q^{83} - 44 q^{84} - 3 q^{86} - 13 q^{87} - 54 q^{88} - 34 q^{89} + 23 q^{91} + 43 q^{92} + 3 q^{94} - 10 q^{96} - 7 q^{97} - 40 q^{98} - 8 q^{99}+O(q^{100}) $ 8 * q - 3 * q^2 + 8 * q^3 + 7 * q^4 - 3 * q^6 - 8 * q^7 - 6 * q^8 + 8 * q^9 - 8 * q^11 + 7 * q^12 - 10 * q^13 + q^14 + 5 * q^16 - 6 * q^17 - 3 * q^18 - 2 * q^19 - 8 * q^21 - 10 * q^23 - 6 * q^24 - 14 * q^26 + 8 * q^27 - 44 * q^28 - 13 * q^29 - 10 * q^32 - 8 * q^33 + 28 * q^34 + 7 * q^36 - 3 * q^37 - 36 * q^38 - 10 * q^39 - 16 * q^41 + q^42 - 25 * q^43 - 17 * q^44 - 5 * q^46 - 8 * q^47 + 5 * q^48 + 16 * q^49 - 6 * q^51 + 17 * q^52 - 4 * q^53 - 3 * q^54 + 37 * q^56 - 2 * q^57 - 15 * q^58 - 8 * q^59 + 15 * q^61 - 6 * q^62 - 8 * q^63 - 14 * q^64 - 27 * q^67 - 14 * q^68 - 10 * q^69 + 14 * q^71 - 6 * q^72 - 28 * q^73 - 21 * q^74 + 6 * q^76 - 4 * q^77 - 14 * q^78 + 7 * q^79 + 8 * q^81 + 53 * q^82 - 60 * q^83 - 44 * q^84 - 3 * q^86 - 13 * q^87 - 54 * q^88 - 34 * q^89 + 23 * q^91 + 43 * q^92 + 3 * q^94 - 10 * q^96 - 7 * q^97 - 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.19791	−1.55416	−0.777080	−	0.629402i	$-0.783300\pi$
$2$	−2.19791	−1.55416	−0.777080	+	0.629402i	$0.783300\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.83083	1.41541
$5$	0	0
$5$	0	0
$6$	−2.19791	−0.897295
$7$	1.05086	0.397189	0.198595	−	0.980082i	$-0.436362\pi$
$7$	1.05086	0.397189	0.198595	+	0.980082i	$0.436362\pi$
$8$	−1.82609	−0.645619
$9$	1.00000	0.333333
$10$	0	0
$11$	−3.22580	−0.972614	−0.486307	−	0.873788i	$-0.661656\pi$
$11$	−3.22580	−0.972614	−0.486307	+	0.873788i	$0.661656\pi$
$12$	2.83083	0.817189
$13$	2.58899	0.718056	0.359028	−	0.933327i	$-0.383108\pi$
$13$	2.58899	0.718056	0.359028	+	0.933327i	$0.383108\pi$
$14$	−2.30971	−0.617295
$15$	0	0
$16$	−1.64807	−0.412018
$17$	−7.50374	−1.81992	−0.909962	−	0.414691i	$-0.863890\pi$
$17$	−7.50374	−1.81992	−0.909962	+	0.414691i	$0.863890\pi$
$18$	−2.19791	−0.518053
$19$	1.70135	0.390316	0.195158	−	0.980772i	$-0.437478\pi$
$19$	1.70135	0.390316	0.195158	+	0.980772i	$0.437478\pi$
$20$	0	0
$21$	1.05086	0.229317
$22$	7.09002	1.51160
$23$	−2.21428	−0.461710	−0.230855	−	0.972988i	$-0.574152\pi$
$23$	−2.21428	−0.461710	−0.230855	+	0.972988i	$0.574152\pi$
$24$	−1.82609	−0.372748
$25$	0	0
$26$	−5.69038	−1.11597
$27$	1.00000	0.192450
$28$	2.97481	0.562187
$29$	6.74234	1.25202	0.626010	−	0.779815i	$-0.284687\pi$
$29$	6.74234	1.25202	0.626010	+	0.779815i	$0.284687\pi$
$30$	0	0
$31$	10.8019	1.94008	0.970041	−	0.242942i	$-0.0781123\pi$
$31$	10.8019	1.94008	0.970041	+	0.242942i	$0.0781123\pi$
$32$	7.27449	1.28596
$33$	−3.22580	−0.561539
$34$	16.4926	2.82845
$35$	0	0
$36$	2.83083	0.471804
$37$	−11.7806	−1.93672	−0.968361	−	0.249552i	$-0.919717\pi$
$37$	−11.7806	−1.93672	−0.968361	+	0.249552i	$0.919717\pi$
$38$	−3.73942	−0.606614
$39$	2.58899	0.414570
$40$	0	0
$41$	−5.81601	−0.908308	−0.454154	−	0.890923i	$-0.650058\pi$
$41$	−5.81601	−0.908308	−0.454154	+	0.890923i	$0.650058\pi$
$42$	−2.30971	−0.356396
$43$	−3.39497	−0.517728	−0.258864	−	0.965914i	$-0.583348\pi$
$43$	−3.39497	−0.517728	−0.258864	+	0.965914i	$0.583348\pi$
$44$	−9.13167	−1.37665
$45$	0	0
$46$	4.86680	0.717571
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	−1.64807	−0.237879
$49$	−5.89569	−0.842241
$50$	0	0
$51$	−7.50374	−1.05073
$52$	7.32898	1.01635
$53$	−11.1690	−1.53418	−0.767090	−	0.641539i	$-0.778296\pi$
$53$	−11.1690	−1.53418	−0.767090	+	0.641539i	$0.778296\pi$
$54$	−2.19791	−0.299098
$55$	0	0
$56$	−1.91897	−0.256433
$57$	1.70135	0.225349
$58$	−14.8191	−1.94584
$59$	12.3261	1.60472	0.802361	−	0.596839i	$-0.203577\pi$
$59$	12.3261	1.60472	0.802361	+	0.596839i	$0.203577\pi$
$60$	0	0
$61$	−6.55166	−0.838854	−0.419427	−	0.907789i	$-0.637769\pi$
$61$	−6.55166	−0.838854	−0.419427	+	0.907789i	$0.637769\pi$
$62$	−23.7417	−3.01520
$63$	1.05086	0.132396
$64$	−12.6926	−1.58657
$65$	0	0
$66$	7.09002	0.872722
$67$	0.750116	0.0916412	0.0458206	−	0.998950i	$-0.485410\pi$
$67$	0.750116	0.0916412	0.0458206	+	0.998950i	$0.485410\pi$
$68$	−21.2418	−2.57595
$69$	−2.21428	−0.266568
$70$	0	0
$71$	2.09231	0.248311	0.124156	−	0.992263i	$-0.460378\pi$
$71$	2.09231	0.248311	0.124156	+	0.992263i	$0.460378\pi$
$72$	−1.82609	−0.215206
$73$	4.80219	0.562054	0.281027	−	0.959700i	$-0.409325\pi$
$73$	4.80219	0.562054	0.281027	+	0.959700i	$0.409325\pi$
$74$	25.8928	3.00998
$75$	0	0
$76$	4.81623	0.552459
$77$	−3.38987	−0.386312
$78$	−5.69038	−0.644308
$79$	6.59991	0.742548	0.371274	−	0.928523i	$-0.378921\pi$
$79$	6.59991	0.742548	0.371274	+	0.928523i	$0.378921\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	12.7831	1.41166
$83$	−15.6214	−1.71467	−0.857334	−	0.514761i	$-0.827881\pi$
$83$	−15.6214	−1.71467	−0.857334	+	0.514761i	$0.827881\pi$
$84$	2.97481	0.324579
$85$	0	0
$86$	7.46185	0.804632
$87$	6.74234	0.722854
$88$	5.89058	0.627938
$89$	−15.4144	−1.63392	−0.816960	−	0.576694i	$-0.804343\pi$
$89$	−15.4144	−1.63392	−0.816960	+	0.576694i	$0.804343\pi$
$90$	0	0
$91$	2.72067	0.285204
$92$	−6.26825	−0.653510
$93$	10.8019	1.12011
$94$	2.19791	0.226698
$95$	0	0
$96$	7.27449	0.742450
$97$	11.6829	1.18622	0.593109	−	0.805122i	$-0.297900\pi$
$97$	11.6829	1.18622	0.593109	+	0.805122i	$0.297900\pi$
$98$	12.9582	1.30898
$99$	−3.22580	−0.324205
$100$	0	0
$101$	−3.43631	−0.341925	−0.170963	−	0.985278i	$-0.554688\pi$
$101$	−3.43631	−0.341925	−0.170963	+	0.985278i	$0.554688\pi$
$102$	16.4926	1.63301
$103$	−12.4894	−1.23061	−0.615307	−	0.788288i	$-0.710968\pi$
$103$	−12.4894	−1.23061	−0.615307	+	0.788288i	$0.710968\pi$
$104$	−4.72772	−0.463591
$105$	0	0
$106$	24.5485	2.38436
$107$	20.2622	1.95882	0.979410	−	0.201879i	$-0.0647048\pi$
$107$	20.2622	1.95882	0.979410	+	0.201879i	$0.0647048\pi$
$108$	2.83083	0.272396
$109$	−12.9693	−1.24224	−0.621118	−	0.783717i	$-0.713321\pi$
$109$	−12.9693	−1.24224	−0.621118	+	0.783717i	$0.713321\pi$
$110$	0	0
$111$	−11.7806	−1.11817
$112$	−1.73190	−0.163649
$113$	−14.6725	−1.38027	−0.690136	−	0.723680i	$-0.742449\pi$
$113$	−14.6725	−1.38027	−0.690136	+	0.723680i	$0.742449\pi$
$114$	−3.73942	−0.350229
$115$	0	0
$116$	19.0864	1.77213
$117$	2.58899	0.239352
$118$	−27.0917	−2.49400
$119$	−7.88541	−0.722854
$120$	0	0
$121$	−0.594237	−0.0540216
$122$	14.4000	1.30371
$123$	−5.81601	−0.524412
$124$	30.5784	2.74602
$125$	0	0
$126$	−2.30971	−0.205765
$127$	−14.6756	−1.30225	−0.651123	−	0.758972i	$-0.725702\pi$
$127$	−14.6756	−1.30225	−0.651123	+	0.758972i	$0.725702\pi$
$128$	13.3482	1.17982
$129$	−3.39497	−0.298910
$130$	0	0
$131$	−15.1152	−1.32062	−0.660309	−	0.750994i	$-0.729575\pi$
$131$	−15.1152	−1.32062	−0.660309	+	0.750994i	$0.729575\pi$
$132$	−9.13167	−0.794810
$133$	1.78789	0.155029
$134$	−1.64869	−0.142425
$135$	0	0
$136$	13.7025	1.17498
$137$	17.6256	1.50585	0.752927	−	0.658104i	$-0.228641\pi$
$137$	17.6256	1.50585	0.752927	+	0.658104i	$0.228641\pi$
$138$	4.86680	0.414290
$139$	9.44352	0.800989	0.400495	−	0.916299i	$-0.368838\pi$
$139$	9.44352	0.800989	0.400495	+	0.916299i	$0.368838\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	−4.59871	−0.385916
$143$	−8.35155	−0.698392
$144$	−1.64807	−0.137339
$145$	0	0
$146$	−10.5548	−0.873521
$147$	−5.89569	−0.486268
$148$	−33.3489	−2.74126
$149$	5.63097	0.461307	0.230653	−	0.973036i	$-0.425914\pi$
$149$	5.63097	0.461307	0.230653	+	0.973036i	$0.425914\pi$
$150$	0	0
$151$	13.8349	1.12587	0.562933	−	0.826503i	$-0.309673\pi$
$151$	13.8349	1.12587	0.562933	+	0.826503i	$0.309673\pi$
$152$	−3.10681	−0.251996
$153$	−7.50374	−0.606641
$154$	7.45065	0.600390
$155$	0	0
$156$	7.32898	0.586788
$157$	−4.25611	−0.339675	−0.169837	−	0.985472i	$-0.554324\pi$
$157$	−4.25611	−0.339675	−0.169837	+	0.985472i	$0.554324\pi$
$158$	−14.5060	−1.15404
$159$	−11.1690	−0.885760
$160$	0	0
$161$	−2.32691	−0.183386
$162$	−2.19791	−0.172684
$163$	7.80011	0.610952	0.305476	−	0.952200i	$-0.401184\pi$
$163$	7.80011	0.610952	0.305476	+	0.952200i	$0.401184\pi$
$164$	−16.4641	−1.28563
$165$	0	0
$166$	34.3344	2.66487
$167$	−11.0275	−0.853336	−0.426668	−	0.904408i	$-0.640313\pi$
$167$	−11.0275	−0.853336	−0.426668	+	0.904408i	$0.640313\pi$
$168$	−1.91897	−0.148052
$169$	−6.29713	−0.484395
$170$	0	0
$171$	1.70135	0.130105
$172$	−9.61057	−0.732799
$173$	3.88852	0.295639	0.147819	−	0.989014i	$-0.452775\pi$
$173$	3.88852	0.295639	0.147819	+	0.989014i	$0.452775\pi$
$174$	−14.8191	−1.12343
$175$	0	0
$176$	5.31635	0.400735
$177$	12.3261	0.926487
$178$	33.8795	2.53937
$179$	0.395968	0.0295961	0.0147980	−	0.999891i	$-0.495289\pi$
$179$	0.395968	0.0295961	0.0147980	+	0.999891i	$0.495289\pi$
$180$	0	0
$181$	−13.9286	−1.03530	−0.517651	−	0.855592i	$-0.673194\pi$
$181$	−13.9286	−1.03530	−0.517651	+	0.855592i	$0.673194\pi$
$182$	−5.97981	−0.443253
$183$	−6.55166	−0.484312
$184$	4.04347	0.298089
$185$	0	0
$186$	−23.7417	−1.74083
$187$	24.2055	1.77008
$188$	−2.83083	−0.206459
$189$	1.05086	0.0764391
$190$	0	0
$191$	−7.94141	−0.574620	−0.287310	−	0.957838i	$-0.592761\pi$
$191$	−7.94141	−0.574620	−0.287310	+	0.957838i	$0.592761\pi$
$192$	−12.6926	−0.916007
$193$	12.8812	0.927211	0.463606	−	0.886042i	$-0.346555\pi$
$193$	12.8812	0.927211	0.463606	+	0.886042i	$0.346555\pi$
$194$	−25.6780	−1.84357
$195$	0	0
$196$	−16.6897	−1.19212
$197$	−8.58344	−0.611545	−0.305772	−	0.952105i	$-0.598915\pi$
$197$	−8.58344	−0.611545	−0.305772	+	0.952105i	$0.598915\pi$
$198$	7.09002	0.503866
$199$	11.9505	0.847149	0.423574	−	0.905861i	$-0.360775\pi$
$199$	11.9505	0.847149	0.423574	+	0.905861i	$0.360775\pi$
$200$	0	0
$201$	0.750116	0.0529091
$202$	7.55271	0.531407
$203$	7.08528	0.497289
$204$	−21.2418	−1.48722
$205$	0	0
$206$	27.4506	1.91257
$207$	−2.21428	−0.153903
$208$	−4.26684	−0.295852
$209$	−5.48821	−0.379627
$210$	0	0
$211$	5.97104	0.411063	0.205532	−	0.978650i	$-0.434108\pi$
$211$	5.97104	0.411063	0.205532	+	0.978650i	$0.434108\pi$
$212$	−31.6175	−2.17150
$213$	2.09231	0.143363
$214$	−44.5346	−3.04432
$215$	0	0
$216$	−1.82609	−0.124249
$217$	11.3513	0.770579
$218$	28.5055	1.93063
$219$	4.80219	0.324502
$220$	0	0
$221$	−19.4271	−1.30681
$222$	25.8928	1.73781
$223$	−12.1892	−0.816247	−0.408124	−	0.912927i	$-0.633817\pi$
$223$	−12.1892	−0.816247	−0.408124	+	0.912927i	$0.633817\pi$
$224$	7.64450	0.510770
$225$	0	0
$226$	32.2489	2.14516
$227$	−25.3158	−1.68027	−0.840136	−	0.542376i	$-0.817525\pi$
$227$	−25.3158	−1.68027	−0.840136	+	0.542376i	$0.817525\pi$
$228$	4.81623	0.318962
$229$	13.1238	0.867247	0.433623	−	0.901094i	$-0.357235\pi$
$229$	13.1238	0.867247	0.433623	+	0.901094i	$0.357235\pi$
$230$	0	0
$231$	−3.38987	−0.223037
$232$	−12.3121	−0.808328
$233$	20.8072	1.36313	0.681563	−	0.731759i	$-0.261300\pi$
$233$	20.8072	1.36313	0.681563	+	0.731759i	$0.261300\pi$
$234$	−5.69038	−0.371992
$235$	0	0
$236$	34.8931	2.27135
$237$	6.59991	0.428710
$238$	17.3314	1.12343
$239$	0.988409	0.0639349	0.0319674	−	0.999489i	$-0.489823\pi$
$239$	0.988409	0.0639349	0.0319674	+	0.999489i	$0.489823\pi$
$240$	0	0
$241$	16.0839	1.03606	0.518028	−	0.855364i	$-0.326666\pi$
$241$	16.0839	1.03606	0.518028	+	0.855364i	$0.326666\pi$
$242$	1.30608	0.0839582
$243$	1.00000	0.0641500
$244$	−18.5466	−1.18732
$245$	0	0
$246$	12.7831	0.815020
$247$	4.40478	0.280269
$248$	−19.7252	−1.25255
$249$	−15.6214	−0.989964
$250$	0	0
$251$	−10.5672	−0.666997	−0.333498	−	0.942751i	$-0.608229\pi$
$251$	−10.5672	−0.666997	−0.333498	+	0.942751i	$0.608229\pi$
$252$	2.97481	0.187396
$253$	7.14282	0.449066
$254$	32.2556	2.02390
$255$	0	0
$256$	−3.95304	−0.247065
$257$	−23.9740	−1.49546	−0.747728	−	0.664005i	$-0.768855\pi$
$257$	−23.9740	−1.49546	−0.747728	+	0.664005i	$0.768855\pi$
$258$	7.46185	0.464555
$259$	−12.3798	−0.769245
$260$	0	0
$261$	6.74234	0.417340
$262$	33.2218	2.05245
$263$	−2.96013	−0.182530	−0.0912649	−	0.995827i	$-0.529091\pi$
$263$	−2.96013	−0.182530	−0.0912649	+	0.995827i	$0.529091\pi$
$264$	5.89058	0.362540
$265$	0	0
$266$	−3.92962	−0.240941
$267$	−15.4144	−0.943345
$268$	2.12345	0.129710
$269$	30.7826	1.87685	0.938423	−	0.345489i	$-0.112287\pi$
$269$	30.7826	1.87685	0.938423	+	0.345489i	$0.112287\pi$
$270$	0	0
$271$	−11.6106	−0.705296	−0.352648	−	0.935756i	$-0.614719\pi$
$271$	−11.6106	−0.705296	−0.352648	+	0.935756i	$0.614719\pi$
$272$	12.3667	0.749842
$273$	2.72067	0.164663
$274$	−38.7395	−2.34034
$275$	0	0
$276$	−6.26825	−0.377304
$277$	−0.511633	−0.0307410	−0.0153705	−	0.999882i	$-0.504893\pi$
$277$	−0.511633	−0.0307410	−0.0153705	+	0.999882i	$0.504893\pi$
$278$	−20.7561	−1.24487
$279$	10.8019	0.646694
$280$	0	0
$281$	−25.0058	−1.49172	−0.745862	−	0.666101i	$-0.767962\pi$
$281$	−25.0058	−1.49172	−0.745862	+	0.666101i	$0.767962\pi$
$282$	2.19791	0.130884
$283$	−31.8811	−1.89513	−0.947567	−	0.319556i	$-0.896466\pi$
$283$	−31.8811	−1.89513	−0.947567	+	0.319556i	$0.896466\pi$
$284$	5.92296	0.351463
$285$	0	0
$286$	18.3560	1.08541
$287$	−6.11183	−0.360770
$288$	7.27449	0.428654
$289$	39.3061	2.31212
$290$	0	0
$291$	11.6829	0.684863
$292$	13.5942	0.795538
$293$	11.7501	0.686447	0.343223	−	0.939254i	$-0.388481\pi$
$293$	11.7501	0.686447	0.343223	+	0.939254i	$0.388481\pi$
$294$	12.9582	0.755738
$295$	0	0
$296$	21.5124	1.25039
$297$	−3.22580	−0.187180
$298$	−12.3764	−0.716944
$299$	−5.73275	−0.331534
$300$	0	0
$301$	−3.56765	−0.205636
$302$	−30.4078	−1.74978
$303$	−3.43631	−0.197411
$304$	−2.80395	−0.160817
$305$	0	0
$306$	16.4926	0.942818
$307$	−14.3166	−0.817092	−0.408546	−	0.912738i	$-0.633964\pi$
$307$	−14.3166	−0.817092	−0.408546	+	0.912738i	$0.633964\pi$
$308$	−9.59614	−0.546791
$309$	−12.4894	−0.710495
$310$	0	0
$311$	−15.9784	−0.906050	−0.453025	−	0.891498i	$-0.649655\pi$
$311$	−15.9784	−0.906050	−0.453025	+	0.891498i	$0.649655\pi$
$312$	−4.72772	−0.267654
$313$	17.1969	0.972025	0.486013	−	0.873952i	$-0.338451\pi$
$313$	17.1969	0.972025	0.486013	+	0.873952i	$0.338451\pi$
$314$	9.35458	0.527909
$315$	0	0
$316$	18.6832	1.05101
$317$	−24.6354	−1.38366	−0.691830	−	0.722061i	$-0.743195\pi$
$317$	−24.6354	−1.38366	−0.691830	+	0.722061i	$0.743195\pi$
$318$	24.5485	1.37661
$319$	−21.7494	−1.21773
$320$	0	0
$321$	20.2622	1.13093
$322$	5.11435	0.285011
$323$	−12.7665	−0.710346
$324$	2.83083	0.157268
$325$	0	0
$326$	−17.1440	−0.949517
$327$	−12.9693	−0.717205
$328$	10.6205	0.586421
$329$	−1.05086	−0.0579360
$330$	0	0
$331$	−7.11931	−0.391313	−0.195656	−	0.980673i	$-0.562684\pi$
$331$	−7.11931	−0.391313	−0.195656	+	0.980673i	$0.562684\pi$
$332$	−44.2214	−2.42696
$333$	−11.7806	−0.645574
$334$	24.2376	1.32622
$335$	0	0
$336$	−1.73190	−0.0944828
$337$	−7.95185	−0.433165	−0.216582	−	0.976264i	$-0.569491\pi$
$337$	−7.95185	−0.433165	−0.216582	+	0.976264i	$0.569491\pi$
$338$	13.8406	0.752827
$339$	−14.6725	−0.796900
$340$	0	0
$341$	−34.8448	−1.88695
$342$	−3.73942	−0.202205
$343$	−13.5516	−0.731718
$344$	6.19951	0.334255
$345$	0	0
$346$	−8.54664	−0.459470
$347$	−1.56985	−0.0842738	−0.0421369	−	0.999112i	$-0.513417\pi$
$347$	−1.56985	−0.0842738	−0.0421369	+	0.999112i	$0.513417\pi$
$348$	19.0864	1.02314
$349$	−20.9148	−1.11954	−0.559771	−	0.828647i	$-0.689111\pi$
$349$	−20.9148	−1.11954	−0.559771	+	0.828647i	$0.689111\pi$
$350$	0	0
$351$	2.58899	0.138190
$352$	−23.4660	−1.25074
$353$	11.0677	0.589075	0.294537	−	0.955640i	$-0.404834\pi$
$353$	11.0677	0.589075	0.294537	+	0.955640i	$0.404834\pi$
$354$	−27.0917	−1.43991
$355$	0	0
$356$	−43.6354	−2.31267
$357$	−7.88541	−0.417340
$358$	−0.870304	−0.0459970
$359$	−21.3955	−1.12921	−0.564607	−	0.825360i	$-0.690972\pi$
$359$	−21.3955	−1.12921	−0.564607	+	0.825360i	$0.690972\pi$
$360$	0	0
$361$	−16.1054	−0.847653
$362$	30.6138	1.60903
$363$	−0.594237	−0.0311894
$364$	7.70176	0.403682
$365$	0	0
$366$	14.4000	0.752699
$367$	22.9905	1.20009	0.600046	−	0.799965i	$-0.295149\pi$
$367$	22.9905	1.20009	0.600046	+	0.799965i	$0.295149\pi$
$368$	3.64930	0.190233
$369$	−5.81601	−0.302769
$370$	0	0
$371$	−11.7371	−0.609360
$372$	30.5784	1.58541
$373$	−30.8418	−1.59693	−0.798464	−	0.602042i	$-0.794354\pi$
$373$	−30.8418	−1.59693	−0.798464	+	0.602042i	$0.794354\pi$
$374$	−53.2017	−2.75099
$375$	0	0
$376$	1.82609	0.0941732
$377$	17.4558	0.899021
$378$	−2.30971	−0.118799
$379$	−18.6754	−0.959290	−0.479645	−	0.877463i	$-0.659235\pi$
$379$	−18.6754	−0.959290	−0.479645	+	0.877463i	$0.659235\pi$
$380$	0	0
$381$	−14.6756	−0.751852
$382$	17.4545	0.893052
$383$	−11.9269	−0.609438	−0.304719	−	0.952442i	$-0.598562\pi$
$383$	−11.9269	−0.609438	−0.304719	+	0.952442i	$0.598562\pi$
$384$	13.3482	0.681172
$385$	0	0
$386$	−28.3118	−1.44104
$387$	−3.39497	−0.172576
$388$	33.0722	1.67899
$389$	3.23480	0.164011	0.0820054	−	0.996632i	$-0.473868\pi$
$389$	3.23480	0.164011	0.0820054	+	0.996632i	$0.473868\pi$
$390$	0	0
$391$	16.6154	0.840277
$392$	10.7660	0.543767
$393$	−15.1152	−0.762459
$394$	18.8657	0.950438
$395$	0	0
$396$	−9.13167	−0.458884
$397$	−0.211311	−0.0106054	−0.00530270	−	0.999986i	$-0.501688\pi$
$397$	−0.211311	−0.0106054	−0.00530270	+	0.999986i	$0.501688\pi$
$398$	−26.2662	−1.31661
$399$	1.78789	0.0895063
$400$	0	0
$401$	28.7778	1.43710	0.718548	−	0.695478i	$-0.244807\pi$
$401$	28.7778	1.43710	0.718548	+	0.695478i	$0.244807\pi$
$402$	−1.64869	−0.0822292
$403$	27.9661	1.39309
$404$	−9.72759	−0.483966
$405$	0	0
$406$	−15.5728	−0.772866
$407$	38.0019	1.88368
$408$	13.7025	0.678374
$409$	3.37349	0.166808	0.0834042	−	0.996516i	$-0.473421\pi$
$409$	3.37349	0.166808	0.0834042	+	0.996516i	$0.473421\pi$
$410$	0	0
$411$	17.6256	0.869406
$412$	−35.3552	−1.74183
$413$	12.9531	0.637378
$414$	4.86680	0.239190
$415$	0	0
$416$	18.8336	0.923393
$417$	9.44352	0.462451
$418$	12.0626	0.590002
$419$	8.59815	0.420047	0.210024	−	0.977696i	$-0.432646\pi$
$419$	8.59815	0.420047	0.210024	+	0.977696i	$0.432646\pi$
$420$	0	0
$421$	−33.4340	−1.62947	−0.814737	−	0.579831i	$-0.803118\pi$
$421$	−33.4340	−1.62947	−0.814737	+	0.579831i	$0.803118\pi$
$422$	−13.1238	−0.638858
$423$	−1.00000	−0.0486217
$424$	20.3956	0.990496
$425$	0	0
$426$	−4.59871	−0.222808
$427$	−6.88490	−0.333183
$428$	57.3588	2.77254
$429$	−8.35155	−0.403217
$430$	0	0
$431$	−20.7133	−0.997726	−0.498863	−	0.866681i	$-0.666249\pi$
$431$	−20.7133	−0.997726	−0.498863	+	0.866681i	$0.666249\pi$
$432$	−1.64807	−0.0792929
$433$	25.6067	1.23058	0.615291	−	0.788300i	$-0.289039\pi$
$433$	25.6067	1.23058	0.615291	+	0.788300i	$0.289039\pi$
$434$	−24.9493	−1.19760
$435$	0	0
$436$	−36.7139	−1.75828
$437$	−3.76727	−0.180213
$438$	−10.5548	−0.504328
$439$	−2.07924	−0.0992367	−0.0496183	−	0.998768i	$-0.515800\pi$
$439$	−2.07924	−0.0992367	−0.0496183	+	0.998768i	$0.515800\pi$
$440$	0	0
$441$	−5.89569	−0.280747
$442$	42.6991	2.03099
$443$	21.9500	1.04287	0.521437	−	0.853290i	$-0.325396\pi$
$443$	21.9500	1.04287	0.521437	+	0.853290i	$0.325396\pi$
$444$	−33.3489	−1.58267
$445$	0	0
$446$	26.7907	1.26858
$447$	5.63097	0.266336
$448$	−13.3382	−0.630169
$449$	2.61869	0.123583	0.0617917	−	0.998089i	$-0.480319\pi$
$449$	2.61869	0.123583	0.0617917	+	0.998089i	$0.480319\pi$
$450$	0	0
$451$	18.7613	0.883433
$452$	−41.5353	−1.95365
$453$	13.8349	0.650019
$454$	55.6421	2.61141
$455$	0	0
$456$	−3.10681	−0.145490
$457$	−31.5801	−1.47726	−0.738628	−	0.674113i	$-0.764526\pi$
$457$	−31.5801	−1.47726	−0.738628	+	0.674113i	$0.764526\pi$
$458$	−28.8450	−1.34784
$459$	−7.50374	−0.350245
$460$	0	0
$461$	0.891136	0.0415043	0.0207522	−	0.999785i	$-0.493394\pi$
$461$	0.891136	0.0415043	0.0207522	+	0.999785i	$0.493394\pi$
$462$	7.45065	0.346635
$463$	−15.1369	−0.703470	−0.351735	−	0.936100i	$-0.614408\pi$
$463$	−15.1369	−0.703470	−0.351735	+	0.936100i	$0.614408\pi$
$464$	−11.1119	−0.515855
$465$	0	0
$466$	−45.7325	−2.11852
$467$	−2.92279	−0.135251	−0.0676253	−	0.997711i	$-0.521542\pi$
$467$	−2.92279	−0.135251	−0.0676253	+	0.997711i	$0.521542\pi$
$468$	7.32898	0.338782
$469$	0.788269	0.0363989
$470$	0	0
$471$	−4.25611	−0.196111
$472$	−22.5085	−1.03604
$473$	10.9515	0.503550
$474$	−14.5060	−0.666284
$475$	0	0
$476$	−22.3222	−1.02314
$477$	−11.1690	−0.511394
$478$	−2.17244	−0.0993650
$479$	−13.3779	−0.611252	−0.305626	−	0.952152i	$-0.598866\pi$
$479$	−13.3779	−0.611252	−0.305626	+	0.952152i	$0.598866\pi$
$480$	0	0
$481$	−30.4999	−1.39068
$482$	−35.3511	−1.61020
$483$	−2.32691	−0.105878
$484$	−1.68218	−0.0764629
$485$	0	0
$486$	−2.19791	−0.0996994
$487$	−36.9084	−1.67248	−0.836239	−	0.548365i	$-0.815251\pi$
$487$	−36.9084	−1.67248	−0.836239	+	0.548365i	$0.815251\pi$
$488$	11.9639	0.541580
$489$	7.80011	0.352733
$490$	0	0
$491$	6.79535	0.306670	0.153335	−	0.988174i	$-0.450999\pi$
$491$	6.79535	0.306670	0.153335	+	0.988174i	$0.450999\pi$
$492$	−16.4641	−0.742259
$493$	−50.5927	−2.27858
$494$	−9.68132	−0.435583
$495$	0	0
$496$	−17.8023	−0.799349
$497$	2.19873	0.0986265
$498$	34.3344	1.53856
$499$	−5.04952	−0.226047	−0.113024	−	0.993592i	$-0.536054\pi$
$499$	−5.04952	−0.226047	−0.113024	+	0.993592i	$0.536054\pi$
$500$	0	0
$501$	−11.0275	−0.492674
$502$	23.2258	1.03662
$503$	18.6865	0.833191	0.416595	−	0.909092i	$-0.363223\pi$
$503$	18.6865	0.833191	0.416595	+	0.909092i	$0.363223\pi$
$504$	−1.91897	−0.0854776
$505$	0	0
$506$	−15.6993	−0.697920
$507$	−6.29713	−0.279666
$508$	−41.5440	−1.84322
$509$	26.5029	1.17472	0.587360	−	0.809326i	$-0.300167\pi$
$509$	26.5029	1.17472	0.587360	+	0.809326i	$0.300167\pi$
$510$	0	0
$511$	5.04644	0.223242
$512$	−18.0079	−0.795846
$513$	1.70135	0.0751164
$514$	52.6928	2.32418
$515$	0	0
$516$	−9.61057	−0.423082
$517$	3.22580	0.141870
$518$	27.2098	1.19553
$519$	3.88852	0.170687
$520$	0	0
$521$	−14.1654	−0.620600	−0.310300	−	0.950639i	$-0.600429\pi$
$521$	−14.1654	−0.620600	−0.310300	+	0.950639i	$0.600429\pi$
$522$	−14.8191	−0.648613
$523$	14.9461	0.653549	0.326775	−	0.945102i	$-0.394038\pi$
$523$	14.9461	0.653549	0.326775	+	0.945102i	$0.394038\pi$
$524$	−42.7884	−1.86922
$525$	0	0
$526$	6.50612	0.283680
$527$	−81.0548	−3.53080
$528$	5.31635	0.231364
$529$	−18.0970	−0.786824
$530$	0	0
$531$	12.3261	0.534907
$532$	5.06120	0.219431
$533$	−15.0576	−0.652216
$534$	33.8795	1.46611
$535$	0	0
$536$	−1.36978	−0.0591653
$537$	0.395968	0.0170873
$538$	−67.6574	−2.91692
$539$	19.0183	0.819175
$540$	0	0
$541$	8.91744	0.383391	0.191695	−	0.981454i	$-0.438601\pi$
$541$	8.91744	0.383391	0.191695	+	0.981454i	$0.438601\pi$
$542$	25.5192	1.09614
$543$	−13.9286	−0.597732
$544$	−54.5859	−2.34035
$545$	0	0
$546$	−5.97981	−0.255912
$547$	−8.89021	−0.380118	−0.190059	−	0.981773i	$-0.560868\pi$
$547$	−8.89021	−0.380118	−0.190059	+	0.981773i	$0.560868\pi$
$548$	49.8950	2.13141
$549$	−6.55166	−0.279618
$550$	0	0
$551$	11.4711	0.488684
$552$	4.04347	0.172102
$553$	6.93560	0.294932
$554$	1.12452	0.0477765
$555$	0	0
$556$	26.7330	1.13373
$557$	35.1323	1.48860	0.744301	−	0.667844i	$-0.232783\pi$
$557$	35.1323	1.48860	0.744301	+	0.667844i	$0.232783\pi$
$558$	−23.7417	−1.00507
$559$	−8.78954	−0.371758
$560$	0	0
$561$	24.2055	1.02196
$562$	54.9607	2.31838
$563$	29.2562	1.23300	0.616502	−	0.787354i	$-0.288549\pi$
$563$	29.2562	1.23300	0.616502	+	0.787354i	$0.288549\pi$
$564$	−2.83083	−0.119199
$565$	0	0
$566$	70.0719	2.94534
$567$	1.05086	0.0441321
$568$	−3.82074	−0.160315
$569$	−9.51183	−0.398756	−0.199378	−	0.979923i	$-0.563892\pi$
$569$	−9.51183	−0.398756	−0.199378	+	0.979923i	$0.563892\pi$
$570$	0	0
$571$	1.71387	0.0717231	0.0358615	−	0.999357i	$-0.488582\pi$
$571$	1.71387	0.0717231	0.0358615	+	0.999357i	$0.488582\pi$
$572$	−23.6418	−0.988513
$573$	−7.94141	−0.331757
$574$	13.4333	0.560694
$575$	0	0
$576$	−12.6926	−0.528857
$577$	22.3271	0.929491	0.464746	−	0.885444i	$-0.346146\pi$
$577$	22.3271	0.929491	0.464746	+	0.885444i	$0.346146\pi$
$578$	−86.3915	−3.59341
$579$	12.8812	0.535326
$580$	0	0
$581$	−16.4159	−0.681047
$582$	−25.6780	−1.06439
$583$	36.0289	1.49217
$584$	−8.76921	−0.362873
$585$	0	0
$586$	−25.8257	−1.06685
$587$	15.3439	0.633311	0.316655	−	0.948541i	$-0.397440\pi$
$587$	15.3439	0.633311	0.316655	+	0.948541i	$0.397440\pi$
$588$	−16.6897	−0.688270
$589$	18.3778	0.757246
$590$	0	0
$591$	−8.58344	−0.353075
$592$	19.4153	0.797965
$593$	−25.0738	−1.02966	−0.514830	−	0.857293i	$-0.672145\pi$
$593$	−25.0738	−1.02966	−0.514830	+	0.857293i	$0.672145\pi$
$594$	7.09002	0.290907
$595$	0	0
$596$	15.9403	0.652940
$597$	11.9505	0.489102
$598$	12.6001	0.515256
$599$	−45.9704	−1.87830	−0.939150	−	0.343506i	$-0.888385\pi$
$599$	−45.9704	−1.87830	−0.939150	+	0.343506i	$0.888385\pi$
$600$	0	0
$601$	−20.2362	−0.825453	−0.412727	−	0.910855i	$-0.635423\pi$
$601$	−20.2362	−0.825453	−0.412727	+	0.910855i	$0.635423\pi$
$602$	7.84139	0.319591
$603$	0.750116	0.0305471
$604$	39.1641	1.59357
$605$	0	0
$606$	7.55271	0.306808
$607$	2.94855	0.119678	0.0598389	−	0.998208i	$-0.480941\pi$
$607$	2.94855	0.119678	0.0598389	+	0.998208i	$0.480941\pi$
$608$	12.3765	0.501932
$609$	7.08528	0.287110
$610$	0	0
$611$	−2.58899	−0.104739
$612$	−21.2418	−0.858649
$613$	21.0447	0.849987	0.424993	−	0.905196i	$-0.360276\pi$
$613$	21.0447	0.849987	0.424993	+	0.905196i	$0.360276\pi$
$614$	31.4667	1.26989
$615$	0	0
$616$	6.19020	0.249410
$617$	16.6437	0.670051	0.335026	−	0.942209i	$-0.391255\pi$
$617$	16.6437	0.670051	0.335026	+	0.942209i	$0.391255\pi$
$618$	27.4506	1.10422
$619$	38.9234	1.56446	0.782232	−	0.622987i	$-0.214081\pi$
$619$	38.9234	1.56446	0.782232	+	0.622987i	$0.214081\pi$
$620$	0	0
$621$	−2.21428	−0.0888561
$622$	35.1191	1.40815
$623$	−16.1984	−0.648975
$624$	−4.26684	−0.170810
$625$	0	0
$626$	−37.7973	−1.51068
$627$	−5.48821	−0.219178
$628$	−12.0483	−0.480780
$629$	88.3987	3.52469
$630$	0	0
$631$	−19.6963	−0.784097	−0.392049	−	0.919945i	$-0.628233\pi$
$631$	−19.6963	−0.784097	−0.392049	+	0.919945i	$0.628233\pi$
$632$	−12.0520	−0.479403
$633$	5.97104	0.237328
$634$	54.1464	2.15043
$635$	0	0
$636$	−31.6175	−1.25372
$637$	−15.2639	−0.604776
$638$	47.8033	1.89255
$639$	2.09231	0.0827704
$640$	0	0
$641$	−6.39022	−0.252399	−0.126199	−	0.992005i	$-0.540278\pi$
$641$	−6.39022	−0.252399	−0.126199	+	0.992005i	$0.540278\pi$
$642$	−44.5346	−1.75764
$643$	−39.9323	−1.57477	−0.787387	−	0.616459i	$-0.788567\pi$
$643$	−39.9323	−1.57477	−0.787387	+	0.616459i	$0.788567\pi$
$644$	−6.58708	−0.259567
$645$	0	0
$646$	28.0596	1.10399
$647$	28.4879	1.11998	0.559988	−	0.828501i	$-0.310806\pi$
$647$	28.4879	1.11998	0.559988	+	0.828501i	$0.310806\pi$
$648$	−1.82609	−0.0717355
$649$	−39.7615	−1.56078
$650$	0	0
$651$	11.3513	0.444894
$652$	22.0808	0.864750
$653$	38.6045	1.51071	0.755355	−	0.655316i	$-0.227465\pi$
$653$	38.6045	1.51071	0.755355	+	0.655316i	$0.227465\pi$
$654$	28.5055	1.11465
$655$	0	0
$656$	9.58520	0.374239
$657$	4.80219	0.187351
$658$	2.30971	0.0900418
$659$	−18.9279	−0.737324	−0.368662	−	0.929563i	$-0.620184\pi$
$659$	−18.9279	−0.737324	−0.368662	+	0.929563i	$0.620184\pi$
$660$	0	0
$661$	−0.518381	−0.0201627	−0.0100813	−	0.999949i	$-0.503209\pi$
$661$	−0.518381	−0.0201627	−0.0100813	+	0.999949i	$0.503209\pi$
$662$	15.6476	0.608162
$663$	−19.4271	−0.754486
$664$	28.5260	1.10702
$665$	0	0
$666$	25.8928	1.00333
$667$	−14.9294	−0.578070
$668$	−31.2170	−1.20782
$669$	−12.1892	−0.471260
$670$	0	0
$671$	21.1343	0.815881
$672$	7.64450	0.294893
$673$	−17.7260	−0.683288	−0.341644	−	0.939829i	$-0.610984\pi$
$673$	−17.7260	−0.683288	−0.341644	+	0.939829i	$0.610984\pi$
$674$	17.4775	0.673207
$675$	0	0
$676$	−17.8261	−0.685619
$677$	3.62115	0.139172	0.0695861	−	0.997576i	$-0.477832\pi$
$677$	3.62115	0.139172	0.0695861	+	0.997576i	$0.477832\pi$
$678$	32.2489	1.23851
$679$	12.2771	0.471153
$680$	0	0
$681$	−25.3158	−0.970105
$682$	76.5859	2.93262
$683$	−1.75071	−0.0669889	−0.0334944	−	0.999439i	$-0.510664\pi$
$683$	−1.75071	−0.0669889	−0.0334944	+	0.999439i	$0.510664\pi$
$684$	4.81623	0.184153
$685$	0	0
$686$	29.7853	1.13721
$687$	13.1238	0.500705
$688$	5.59516	0.213313
$689$	−28.9164	−1.10163
$690$	0	0
$691$	11.3812	0.432963	0.216481	−	0.976287i	$-0.430542\pi$
$691$	11.3812	0.432963	0.216481	+	0.976287i	$0.430542\pi$
$692$	11.0077	0.418451
$693$	−3.38987	−0.128771
$694$	3.45039	0.130975
$695$	0	0
$696$	−12.3121	−0.466689
$697$	43.6418	1.65305
$698$	45.9689	1.73995
$699$	20.8072	0.787001
$700$	0	0
$701$	14.5746	0.550476	0.275238	−	0.961376i	$-0.411243\pi$
$701$	14.5746	0.550476	0.275238	+	0.961376i	$0.411243\pi$
$702$	−5.69038	−0.214769
$703$	−20.0430	−0.755935
$704$	40.9437	1.54312
$705$	0	0
$706$	−24.3259	−0.915516
$707$	−3.61109	−0.135809
$708$	34.8931	1.31136
$709$	−18.7870	−0.705561	−0.352780	−	0.935706i	$-0.614764\pi$
$709$	−18.7870	−0.705561	−0.352780	+	0.935706i	$0.614764\pi$
$710$	0	0
$711$	6.59991	0.247516
$712$	28.1480	1.05489
$713$	−23.9185	−0.895755
$714$	17.3314	0.648613
$715$	0	0
$716$	1.12092	0.0418907
$717$	0.988409	0.0369128
$718$	47.0256	1.75498
$719$	−9.79963	−0.365465	−0.182732	−	0.983163i	$-0.558494\pi$
$719$	−9.79963	−0.365465	−0.182732	+	0.983163i	$0.558494\pi$
$720$	0	0
$721$	−13.1246	−0.488786
$722$	35.3983	1.31739
$723$	16.0839	0.598167
$724$	−39.4294	−1.46538
$725$	0	0
$726$	1.30608	0.0484733
$727$	−25.5912	−0.949126	−0.474563	−	0.880221i	$-0.657394\pi$
$727$	−25.5912	−0.949126	−0.474563	+	0.880221i	$0.657394\pi$
$728$	−4.96819	−0.184133
$729$	1.00000	0.0370370
$730$	0	0
$731$	25.4750	0.942226
$732$	−18.5466	−0.685502
$733$	−42.3314	−1.56354	−0.781772	−	0.623564i	$-0.785684\pi$
$733$	−42.3314	−1.56354	−0.781772	+	0.623564i	$0.785684\pi$
$734$	−50.5311	−1.86514
$735$	0	0
$736$	−16.1078	−0.593741
$737$	−2.41972	−0.0891316
$738$	12.7831	0.470552
$739$	−1.65177	−0.0607612	−0.0303806	−	0.999538i	$-0.509672\pi$
$739$	−1.65177	−0.0607612	−0.0303806	+	0.999538i	$0.509672\pi$
$740$	0	0
$741$	4.40478	0.161814
$742$	25.7971	0.947043
$743$	30.1467	1.10597	0.552987	−	0.833190i	$-0.313488\pi$
$743$	30.1467	1.10597	0.552987	+	0.833190i	$0.313488\pi$
$744$	−19.7252	−0.723162
$745$	0	0
$746$	67.7877	2.48188
$747$	−15.6214	−0.571556
$748$	68.5217	2.50540
$749$	21.2928	0.778022
$750$	0	0
$751$	−4.44762	−0.162296	−0.0811479	−	0.996702i	$-0.525859\pi$
$751$	−4.44762	−0.162296	−0.0811479	+	0.996702i	$0.525859\pi$
$752$	1.64807	0.0600990
$753$	−10.5672	−0.385091
$754$	−38.3664	−1.39722
$755$	0	0
$756$	2.97481	0.108193
$757$	41.9419	1.52441	0.762203	−	0.647338i	$-0.224118\pi$
$757$	41.9419	1.52441	0.762203	+	0.647338i	$0.224118\pi$
$758$	41.0469	1.49089
$759$	7.14282	0.259268
$760$	0	0
$761$	−27.1036	−0.982504	−0.491252	−	0.871018i	$-0.663461\pi$
$761$	−27.1036	−0.982504	−0.491252	+	0.871018i	$0.663461\pi$
$762$	32.2556	1.16850
$763$	−13.6290	−0.493402
$764$	−22.4808	−0.813325
$765$	0	0
$766$	26.2144	0.947163
$767$	31.9122	1.15228
$768$	−3.95304	−0.142643
$769$	32.8683	1.18526	0.592631	−	0.805474i	$-0.298089\pi$
$769$	32.8683	1.18526	0.592631	+	0.805474i	$0.298089\pi$
$770$	0	0
$771$	−23.9740	−0.863402
$772$	36.4645	1.31239
$773$	−21.9310	−0.788804	−0.394402	−	0.918938i	$-0.629048\pi$
$773$	−21.9310	−0.788804	−0.394402	+	0.918938i	$0.629048\pi$
$774$	7.46185	0.268211
$775$	0	0
$776$	−21.3340	−0.765845
$777$	−12.3798	−0.444124
$778$	−7.10981	−0.254899
$779$	−9.89506	−0.354527
$780$	0	0
$781$	−6.74936	−0.241511
$782$	−36.5192	−1.30592
$783$	6.74234	0.240951
$784$	9.71652	0.347018
$785$	0	0
$786$	33.2218	1.18498
$787$	−53.6288	−1.91166	−0.955830	−	0.293920i	$-0.905040\pi$
$787$	−53.6288	−1.91166	−0.955830	+	0.293920i	$0.905040\pi$
$788$	−24.2982	−0.865588
$789$	−2.96013	−0.105384
$790$	0	0
$791$	−15.4188	−0.548229
$792$	5.89058	0.209313
$793$	−16.9622	−0.602344
$794$	0.464444	0.0164825
$795$	0	0
$796$	33.8298	1.19907
$797$	4.21744	0.149389	0.0746946	−	0.997206i	$-0.476202\pi$
$797$	4.21744	0.149389	0.0746946	+	0.997206i	$0.476202\pi$
$798$	−3.92962	−0.139107
$799$	7.50374	0.265463
$800$	0	0
$801$	−15.4144	−0.544640
$802$	−63.2512	−2.23348
$803$	−15.4909	−0.546661
$804$	2.12345	0.0748883
$805$	0	0
$806$	−61.4670	−2.16508
$807$	30.7826	1.08360
$808$	6.27500	0.220754
$809$	−9.77548	−0.343688	−0.171844	−	0.985124i	$-0.554972\pi$
$809$	−9.77548	−0.343688	−0.171844	+	0.985124i	$0.554972\pi$
$810$	0	0
$811$	13.9279	0.489075	0.244538	−	0.969640i	$-0.421364\pi$
$811$	13.9279	0.489075	0.244538	+	0.969640i	$0.421364\pi$
$812$	20.0572	0.703869
$813$	−11.6106	−0.407203
$814$	−83.5249	−2.92755
$815$	0	0
$816$	12.3667	0.432921
$817$	−5.77603	−0.202078
$818$	−7.41465	−0.259247
$819$	2.72067	0.0950681
$820$	0	0
$821$	0.631310	0.0220329	0.0110164	−	0.999939i	$-0.496493\pi$
$821$	0.631310	0.0220329	0.0110164	+	0.999939i	$0.496493\pi$
$822$	−38.7395	−1.35120
$823$	26.9584	0.939711	0.469855	−	0.882743i	$-0.344306\pi$
$823$	26.9584	0.939711	0.469855	+	0.882743i	$0.344306\pi$
$824$	22.8067	0.794508
$825$	0	0
$826$	−28.4697	−0.990588
$827$	19.3808	0.673937	0.336968	−	0.941516i	$-0.390598\pi$
$827$	19.3808	0.673937	0.336968	+	0.941516i	$0.390598\pi$
$828$	−6.26825	−0.217837
$829$	44.6224	1.54980	0.774900	−	0.632083i	$-0.217800\pi$
$829$	44.6224	1.54980	0.774900	+	0.632083i	$0.217800\pi$
$830$	0	0
$831$	−0.511633	−0.0177483
$832$	−32.8609	−1.13925
$833$	44.2397	1.53281
$834$	−20.7561	−0.718723
$835$	0	0
$836$	−15.5362	−0.537330
$837$	10.8019	0.373369
$838$	−18.8980	−0.652820
$839$	25.8332	0.891860	0.445930	−	0.895068i	$-0.352873\pi$
$839$	25.8332	0.891860	0.445930	+	0.895068i	$0.352873\pi$
$840$	0	0
$841$	16.4591	0.567555
$842$	73.4851	2.53246
$843$	−25.0058	−0.861247
$844$	16.9030	0.581825
$845$	0	0
$846$	2.19791	0.0755658
$847$	−0.624462	−0.0214568
$848$	18.4073	0.632110
$849$	−31.8811	−1.09416
$850$	0	0
$851$	26.0856	0.894204
$852$	5.92296	0.202917
$853$	−1.16342	−0.0398346	−0.0199173	−	0.999802i	$-0.506340\pi$
$853$	−1.16342	−0.0398346	−0.0199173	+	0.999802i	$0.506340\pi$
$854$	15.1324	0.517820
$855$	0	0
$856$	−37.0005	−1.26465
$857$	−26.9612	−0.920976	−0.460488	−	0.887666i	$-0.652326\pi$
$857$	−26.9612	−0.920976	−0.460488	+	0.887666i	$0.652326\pi$
$858$	18.3560	0.626663
$859$	−16.1012	−0.549367	−0.274683	−	0.961535i	$-0.588573\pi$
$859$	−16.1012	−0.549367	−0.274683	+	0.961535i	$0.588573\pi$
$860$	0	0
$861$	−6.11183	−0.208291
$862$	45.5261	1.55063
$863$	9.69771	0.330114	0.165057	−	0.986284i	$-0.447219\pi$
$863$	9.69771	0.330114	0.165057	+	0.986284i	$0.447219\pi$
$864$	7.27449	0.247483
$865$	0	0
$866$	−56.2814	−1.91252
$867$	39.3061	1.33491
$868$	32.1337	1.09069
$869$	−21.2900	−0.722212
$870$	0	0
$871$	1.94204	0.0658036
$872$	23.6831	0.802011
$873$	11.6829	0.395406
$874$	8.28013	0.280080
$875$	0	0
$876$	13.5942	0.459304
$877$	−2.85277	−0.0963312	−0.0481656	−	0.998839i	$-0.515338\pi$
$877$	−2.85277	−0.0963312	−0.0481656	+	0.998839i	$0.515338\pi$
$878$	4.56999	0.154230
$879$	11.7501	0.396320
$880$	0	0
$881$	31.9431	1.07619	0.538095	−	0.842884i	$-0.319144\pi$
$881$	31.9431	1.07619	0.538095	+	0.842884i	$0.319144\pi$
$882$	12.9582	0.436326
$883$	−21.5997	−0.726886	−0.363443	−	0.931616i	$-0.618399\pi$
$883$	−21.5997	−0.726886	−0.363443	+	0.931616i	$0.618399\pi$
$884$	−54.9948	−1.84967
$885$	0	0
$886$	−48.2442	−1.62079
$887$	32.1151	1.07832	0.539160	−	0.842203i	$-0.318742\pi$
$887$	32.1151	1.07832	0.539160	+	0.842203i	$0.318742\pi$
$888$	21.5124	0.721910
$889$	−15.4220	−0.517238
$890$	0	0
$891$	−3.22580	−0.108068
$892$	−34.5054	−1.15533
$893$	−1.70135	−0.0569335
$894$	−12.3764	−0.413928
$895$	0	0
$896$	14.0271	0.468613
$897$	−5.73275	−0.191411
$898$	−5.75565	−0.192068
$899$	72.8302	2.42902
$900$	0	0
$901$	83.8093	2.79209
$902$	−41.2356	−1.37300
$903$	−3.56765	−0.118724
$904$	26.7932	0.891129
$905$	0	0
$906$	−30.4078	−1.01023
$907$	23.2655	0.772519	0.386259	−	0.922390i	$-0.373767\pi$
$907$	23.2655	0.772519	0.386259	+	0.922390i	$0.373767\pi$
$908$	−71.6648	−2.37828
$909$	−3.43631	−0.113975
$910$	0	0
$911$	−27.7030	−0.917841	−0.458920	−	0.888477i	$-0.651764\pi$
$911$	−27.7030	−0.917841	−0.458920	+	0.888477i	$0.651764\pi$
$912$	−2.80395	−0.0928480
$913$	50.3913	1.66771
$914$	69.4104	2.29589
$915$	0	0
$916$	37.1513	1.22751
$917$	−15.8840	−0.524535
$918$	16.4926	0.544336
$919$	−3.21697	−0.106118	−0.0530590	−	0.998591i	$-0.516897\pi$
$919$	−3.21697	−0.106118	−0.0530590	+	0.998591i	$0.516897\pi$
$920$	0	0
$921$	−14.3166	−0.471748
$922$	−1.95864	−0.0645044
$923$	5.41696	0.178302
$924$	−9.59614	−0.315690
$925$	0	0
$926$	33.2695	1.09330
$927$	−12.4894	−0.410205
$928$	49.0471	1.61005
$929$	−5.48067	−0.179815	−0.0899075	−	0.995950i	$-0.528657\pi$
$929$	−5.48067	−0.179815	−0.0899075	+	0.995950i	$0.528657\pi$
$930$	0	0
$931$	−10.0306	−0.328740
$932$	58.9016	1.92939
$933$	−15.9784	−0.523108
$934$	6.42404	0.210201
$935$	0	0
$936$	−4.72772	−0.154530
$937$	3.03424	0.0991242	0.0495621	−	0.998771i	$-0.484217\pi$
$937$	3.03424	0.0991242	0.0495621	+	0.998771i	$0.484217\pi$
$938$	−1.73255	−0.0565697
$939$	17.1969	0.561199
$940$	0	0
$941$	−47.1897	−1.53834	−0.769170	−	0.639045i	$-0.779330\pi$
$941$	−47.1897	−1.53834	−0.769170	+	0.639045i	$0.779330\pi$
$942$	9.35458	0.304789
$943$	12.8783	0.419375
$944$	−20.3143	−0.661175
$945$	0	0
$946$	−24.0704	−0.782597
$947$	38.9579	1.26596	0.632982	−	0.774167i	$-0.281831\pi$
$947$	38.9579	1.26596	0.632982	+	0.774167i	$0.281831\pi$
$948$	18.6832	0.606802
$949$	12.4328	0.403586
$950$	0	0
$951$	−24.6354	−0.798856
$952$	14.3994	0.466688
$953$	21.3170	0.690524	0.345262	−	0.938506i	$-0.387790\pi$
$953$	21.3170	0.690524	0.345262	+	0.938506i	$0.387790\pi$
$954$	24.5485	0.794788
$955$	0	0
$956$	2.79801	0.0904943
$957$	−21.7494	−0.703058
$958$	29.4035	0.949983
$959$	18.5221	0.598109
$960$	0	0
$961$	85.6814	2.76392
$962$	67.0362	2.16133
$963$	20.2622	0.652940
$964$	45.5308	1.46645
$965$	0	0
$966$	5.11435	0.164551
$967$	−48.1797	−1.54935	−0.774677	−	0.632358i	$-0.782087\pi$
$967$	−48.1797	−1.54935	−0.774677	+	0.632358i	$0.782087\pi$
$968$	1.08513	0.0348774
$969$	−12.7665	−0.410119
$970$	0	0
$971$	29.4387	0.944732	0.472366	−	0.881402i	$-0.343400\pi$
$971$	29.4387	0.944732	0.472366	+	0.881402i	$0.343400\pi$
$972$	2.83083	0.0907988
$973$	9.92385	0.318144
$974$	81.1215	2.59930
$975$	0	0
$976$	10.7976	0.345623
$977$	44.7657	1.43218	0.716091	−	0.698007i	$-0.245930\pi$
$977$	44.7657	1.43218	0.716091	+	0.698007i	$0.245930\pi$
$978$	−17.1440	−0.548204
$979$	49.7236	1.58917
$980$	0	0
$981$	−12.9693	−0.414079
$982$	−14.9356	−0.476614
$983$	41.8646	1.33527	0.667637	−	0.744487i	$-0.267306\pi$
$983$	41.8646	1.33527	0.667637	+	0.744487i	$0.267306\pi$
$984$	10.6205	0.338570
$985$	0	0
$986$	111.199	3.54128
$987$	−1.05086	−0.0334494
$988$	12.4692	0.396697
$989$	7.51742	0.239040
$990$	0	0
$991$	−28.5991	−0.908480	−0.454240	−	0.890879i	$-0.650089\pi$
$991$	−28.5991	−0.908480	−0.454240	+	0.890879i	$0.650089\pi$
$992$	78.5785	2.49487
$993$	−7.11931	−0.225924
$994$	−4.83262	−0.153281
$995$	0	0
$996$	−44.2214	−1.40121
$997$	24.6378	0.780287	0.390144	−	0.920754i	$-0.372425\pi$
$997$	24.6378	0.780287	0.390144	+	0.920754i	$0.372425\pi$
$998$	11.0984	0.351314
$999$	−11.7806	−0.372722

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.bd.1.2	✓	8
5.4	even	2		3525.2.a.be.1.7	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.2.a.bd.1.2	✓	8	1.1	even	1	trivial
3525.2.a.be.1.7	yes	8	5.4	even	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:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q-2.19791 q^{2} +1.00000 q^{3} +2.83083 q^{4} -2.19791 q^{6} +1.05086 q^{7} -1.82609 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.19791 q^{2} +1.00000 q^{3} +2.83083 q^{4} -2.19791 q^{6} +1.05086 q^{7} -1.82609 q^{8} +1.00000 q^{9} -3.22580 q^{11} +2.83083 q^{12} +2.58899 q^{13} -2.30971 q^{14} -1.64807 q^{16} -7.50374 q^{17} -2.19791 q^{18} +1.70135 q^{19} +1.05086 q^{21} +7.09002 q^{22} -2.21428 q^{23} -1.82609 q^{24} -5.69038 q^{26} +1.00000 q^{27} +2.97481 q^{28} +6.74234 q^{29} +10.8019 q^{31} +7.27449 q^{32} -3.22580 q^{33} +16.4926 q^{34} +2.83083 q^{36} -11.7806 q^{37} -3.73942 q^{38} +2.58899 q^{39} -5.81601 q^{41} -2.30971 q^{42} -3.39497 q^{43} -9.13167 q^{44} +4.86680 q^{46} -1.00000 q^{47} -1.64807 q^{48} -5.89569 q^{49} -7.50374 q^{51} +7.32898 q^{52} -11.1690 q^{53} -2.19791 q^{54} -1.91897 q^{56} +1.70135 q^{57} -14.8191 q^{58} +12.3261 q^{59} -6.55166 q^{61} -23.7417 q^{62} +1.05086 q^{63} -12.6926 q^{64} +7.09002 q^{66} +0.750116 q^{67} -21.2418 q^{68} -2.21428 q^{69} +2.09231 q^{71} -1.82609 q^{72} +4.80219 q^{73} +25.8928 q^{74} +4.81623 q^{76} -3.38987 q^{77} -5.69038 q^{78} +6.59991 q^{79} +1.00000 q^{81} +12.7831 q^{82} -15.6214 q^{83} +2.97481 q^{84} +7.46185 q^{86} +6.74234 q^{87} +5.89058 q^{88} -15.4144 q^{89} +2.72067 q^{91} -6.26825 q^{92} +10.8019 q^{93} +2.19791 q^{94} +7.27449 q^{96} +11.6829 q^{97} +12.9582 q^{98} -3.22580 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{2} + 8 q^{3} + 7 q^{4} - 3 q^{6} - 8 q^{7} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 3 * q^2 + 8 * q^3 + 7 * q^4 - 3 * q^6 - 8 * q^7 - 6 * q^8 + 8 * q^9	\( 8 q - 3 q^{2} + 8 q^{3} + 7 q^{4} - 3 q^{6} - 8 q^{7} - 6 q^{8} + 8 q^{9} - 8 q^{11} + 7 q^{12} - 10 q^{13} + q^{14} + 5 q^{16} - 6 q^{17} - 3 q^{18} - 2 q^{19} - 8 q^{21} - 10 q^{23} - 6 q^{24} - 14 q^{26} + 8 q^{27} - 44 q^{28} - 13 q^{29} - 10 q^{32} - 8 q^{33} + 28 q^{34} + 7 q^{36} - 3 q^{37} - 36 q^{38} - 10 q^{39} - 16 q^{41} + q^{42} - 25 q^{43} - 17 q^{44} - 5 q^{46} - 8 q^{47} + 5 q^{48} + 16 q^{49} - 6 q^{51} + 17 q^{52} - 4 q^{53} - 3 q^{54} + 37 q^{56} - 2 q^{57} - 15 q^{58} - 8 q^{59} + 15 q^{61} - 6 q^{62} - 8 q^{63} - 14 q^{64} - 27 q^{67} - 14 q^{68} - 10 q^{69} + 14 q^{71} - 6 q^{72} - 28 q^{73} - 21 q^{74} + 6 q^{76} - 4 q^{77} - 14 q^{78} + 7 q^{79} + 8 q^{81} + 53 q^{82} - 60 q^{83} - 44 q^{84} - 3 q^{86} - 13 q^{87} - 54 q^{88} - 34 q^{89} + 23 q^{91} + 43 q^{92} + 3 q^{94} - 10 q^{96} - 7 q^{97} - 40 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 3 * q^2 + 8 * q^3 + 7 * q^4 - 3 * q^6 - 8 * q^7 - 6 * q^8 + 8 * q^9 - 8 * q^11 + 7 * q^12 - 10 * q^13 + q^14 + 5 * q^16 - 6 * q^17 - 3 * q^18 - 2 * q^19 - 8 * q^21 - 10 * q^23 - 6 * q^24 - 14 * q^26 + 8 * q^27 - 44 * q^28 - 13 * q^29 - 10 * q^32 - 8 * q^33 + 28 * q^34 + 7 * q^36 - 3 * q^37 - 36 * q^38 - 10 * q^39 - 16 * q^41 + q^42 - 25 * q^43 - 17 * q^44 - 5 * q^46 - 8 * q^47 + 5 * q^48 + 16 * q^49 - 6 * q^51 + 17 * q^52 - 4 * q^53 - 3 * q^54 + 37 * q^56 - 2 * q^57 - 15 * q^58 - 8 * q^59 + 15 * q^61 - 6 * q^62 - 8 * q^63 - 14 * q^64 - 27 * q^67 - 14 * q^68 - 10 * q^69 + 14 * q^71 - 6 * q^72 - 28 * q^73 - 21 * q^74 + 6 * q^76 - 4 * q^77 - 14 * q^78 + 7 * q^79 + 8 * q^81 + 53 * q^82 - 60 * q^83 - 44 * q^84 - 3 * q^86 - 13 * q^87 - 54 * q^88 - 34 * q^89 + 23 * q^91 + 43 * q^92 + 3 * q^94 - 10 * q^96 - 7 * q^97 - 40 * q^98 - 8 * q^99

Introduction

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