LMFDB - Embedded newform 4375.2.a.g.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4375,2,Mod(1,4375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4375, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4375.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4375 = 5^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4375.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:	$34.9345508843$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 18 x^{12} + 34 x^{11} + 127 x^{10} - 226 x^{9} - 441 x^{8} + 745 x^{7} + 761 x^{6} + \cdots - 1 $ x^14 - 2x^13 - 18x^12 + 34x^11 + 127x^10 - 226x^9 - 441x^8 + 745x^7 + 761x^6 - 1249x^5 - 546x^4 + 926x^3 + 52x^2 - 154*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 175)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-1.59048$ of defining polynomial
Character	$\chi$	$=$	4375.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.59048 q^{2} -0.991912 q^{3} +0.529618 q^{4} -1.57761 q^{6} -1.00000 q^{7} -2.33861 q^{8} -2.01611 q^{9} +O(q^{10})$	\(q+1.59048 q^{2} -0.991912 q^{3} +0.529618 q^{4} -1.57761 q^{6} -1.00000 q^{7} -2.33861 q^{8} -2.01611 q^{9} +1.36842 q^{11} -0.525335 q^{12} +6.17505 q^{13} -1.59048 q^{14} -4.77874 q^{16} +4.19129 q^{17} -3.20658 q^{18} -4.06393 q^{19} +0.991912 q^{21} +2.17643 q^{22} +2.92951 q^{23} +2.31969 q^{24} +9.82128 q^{26} +4.97554 q^{27} -0.529618 q^{28} -6.28689 q^{29} +1.91200 q^{31} -2.92326 q^{32} -1.35735 q^{33} +6.66615 q^{34} -1.06777 q^{36} -11.6020 q^{37} -6.46359 q^{38} -6.12511 q^{39} -3.27696 q^{41} +1.57761 q^{42} +5.62950 q^{43} +0.724738 q^{44} +4.65932 q^{46} -10.4189 q^{47} +4.74009 q^{48} +1.00000 q^{49} -4.15739 q^{51} +3.27042 q^{52} -4.71551 q^{53} +7.91348 q^{54} +2.33861 q^{56} +4.03106 q^{57} -9.99916 q^{58} -0.586172 q^{59} +12.1062 q^{61} +3.04100 q^{62} +2.01611 q^{63} +4.90810 q^{64} -2.15883 q^{66} -8.03234 q^{67} +2.21978 q^{68} -2.90582 q^{69} +9.27682 q^{71} +4.71489 q^{72} -2.65930 q^{73} -18.4527 q^{74} -2.15233 q^{76} -1.36842 q^{77} -9.74184 q^{78} +1.45661 q^{79} +1.11303 q^{81} -5.21192 q^{82} -14.7230 q^{83} +0.525335 q^{84} +8.95360 q^{86} +6.23604 q^{87} -3.20019 q^{88} -6.64967 q^{89} -6.17505 q^{91} +1.55152 q^{92} -1.89654 q^{93} -16.5710 q^{94} +2.89962 q^{96} -3.06640 q^{97} +1.59048 q^{98} -2.75888 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} - 3 q^{3} + 12 q^{4} + 15 q^{6} - 14 q^{7} - 6 q^{8} + 15 q^{9}+O(q^{10}) $ 14 * q - 2 * q^2 - 3 * q^3 + 12 * q^4 + 15 * q^6 - 14 * q^7 - 6 * q^8 + 15 * q^9	$ 14 q - 2 q^{2} - 3 q^{3} + 12 q^{4} + 15 q^{6} - 14 q^{7} - 6 q^{8} + 15 q^{9} + 6 q^{11} - 14 q^{12} + q^{13} + 2 q^{14} - 12 q^{16} - 23 q^{17} - 31 q^{18} - 4 q^{19} + 3 q^{21} - 19 q^{22} - 22 q^{23} + 19 q^{24} - 4 q^{26} - 3 q^{27} - 12 q^{28} + 14 q^{29} - 8 q^{31} - 24 q^{32} - 9 q^{33} + 35 q^{34} + 27 q^{36} - 15 q^{37} - 5 q^{38} - 38 q^{39} - 15 q^{41} - 15 q^{42} - 9 q^{43} - 55 q^{44} - 2 q^{46} - 38 q^{47} - 28 q^{48} + 14 q^{49} + q^{51} + 18 q^{52} - 27 q^{53} + 28 q^{54} + 6 q^{56} - 31 q^{57} - 29 q^{58} + 3 q^{59} - 9 q^{61} - 11 q^{62} - 15 q^{63} - 10 q^{64} - 87 q^{66} + 3 q^{67} - 57 q^{68} + 3 q^{69} + 31 q^{71} - 25 q^{72} - 41 q^{73} + 35 q^{74} - 3 q^{76} - 6 q^{77} - 13 q^{78} + 59 q^{79} - 50 q^{81} - 13 q^{82} + 8 q^{83} + 14 q^{84} + 25 q^{86} - 40 q^{87} + 26 q^{88} - 31 q^{89} - q^{91} + 5 q^{92} - 48 q^{93} - 29 q^{94} + 21 q^{96} - 34 q^{97} - 2 q^{98} + 31 q^{99}+O(q^{100}) $ 14 * q - 2 * q^2 - 3 * q^3 + 12 * q^4 + 15 * q^6 - 14 * q^7 - 6 * q^8 + 15 * q^9 + 6 * q^11 - 14 * q^12 + q^13 + 2 * q^14 - 12 * q^16 - 23 * q^17 - 31 * q^18 - 4 * q^19 + 3 * q^21 - 19 * q^22 - 22 * q^23 + 19 * q^24 - 4 * q^26 - 3 * q^27 - 12 * q^28 + 14 * q^29 - 8 * q^31 - 24 * q^32 - 9 * q^33 + 35 * q^34 + 27 * q^36 - 15 * q^37 - 5 * q^38 - 38 * q^39 - 15 * q^41 - 15 * q^42 - 9 * q^43 - 55 * q^44 - 2 * q^46 - 38 * q^47 - 28 * q^48 + 14 * q^49 + q^51 + 18 * q^52 - 27 * q^53 + 28 * q^54 + 6 * q^56 - 31 * q^57 - 29 * q^58 + 3 * q^59 - 9 * q^61 - 11 * q^62 - 15 * q^63 - 10 * q^64 - 87 * q^66 + 3 * q^67 - 57 * q^68 + 3 * q^69 + 31 * q^71 - 25 * q^72 - 41 * q^73 + 35 * q^74 - 3 * q^76 - 6 * q^77 - 13 * q^78 + 59 * q^79 - 50 * q^81 - 13 * q^82 + 8 * q^83 + 14 * q^84 + 25 * q^86 - 40 * q^87 + 26 * q^88 - 31 * q^89 - q^91 + 5 * q^92 - 48 * q^93 - 29 * q^94 + 21 * q^96 - 34 * q^97 - 2 * q^98 + 31 * 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 $

$2$	1.59048	1.12464	0.562319	−	0.826921i	$-0.309909\pi$
$2$	1.59048	1.12464	0.562319	+	0.826921i	$0.309909\pi$
$3$	−0.991912	−0.572681	−0.286340	−	0.958128i	$-0.592439\pi$
$3$	−0.991912	−0.572681	−0.286340	+	0.958128i	$0.592439\pi$
$4$	0.529618	0.264809
$5$	0	0
$5$	0	0
$6$	−1.57761	−0.644058
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.33861	−0.826823
$9$	−2.01611	−0.672037
$10$	0	0
$11$	1.36842	0.412593	0.206296	−	0.978490i	$-0.433859\pi$
$11$	1.36842	0.412593	0.206296	+	0.978490i	$0.433859\pi$
$12$	−0.525335	−0.151651
$13$	6.17505	1.71265	0.856325	−	0.516437i	$-0.172742\pi$
$13$	6.17505	1.71265	0.856325	+	0.516437i	$0.172742\pi$
$14$	−1.59048	−0.425073
$15$	0	0
$16$	−4.77874	−1.19469
$17$	4.19129	1.01654	0.508268	−	0.861199i	$-0.330286\pi$
$17$	4.19129	1.01654	0.508268	+	0.861199i	$0.330286\pi$
$18$	−3.20658	−0.755798
$19$	−4.06393	−0.932329	−0.466165	−	0.884698i	$-0.654365\pi$
$19$	−4.06393	−0.932329	−0.466165	+	0.884698i	$0.654365\pi$
$20$	0	0
$21$	0.991912	0.216453
$22$	2.17643	0.464017
$23$	2.92951	0.610845	0.305423	−	0.952217i	$-0.401202\pi$
$23$	2.92951	0.610845	0.305423	+	0.952217i	$0.401202\pi$
$24$	2.31969	0.473506
$25$	0	0
$26$	9.82128	1.92611
$27$	4.97554	0.957543
$28$	−0.529618	−0.100088
$29$	−6.28689	−1.16745	−0.583723	−	0.811953i	$-0.698405\pi$
$29$	−6.28689	−1.16745	−0.583723	+	0.811953i	$0.698405\pi$
$30$	0	0
$31$	1.91200	0.343406	0.171703	−	0.985149i	$-0.445073\pi$
$31$	1.91200	0.343406	0.171703	+	0.985149i	$0.445073\pi$
$32$	−2.92326	−0.516765
$33$	−1.35735	−0.236284
$34$	6.66615	1.14324
$35$	0	0
$36$	−1.06777	−0.177962
$37$	−11.6020	−1.90736	−0.953679	−	0.300825i	$-0.902738\pi$
$37$	−11.6020	−1.90736	−0.953679	+	0.300825i	$0.902738\pi$
$38$	−6.46359	−1.04853
$39$	−6.12511	−0.980802
$40$	0	0
$41$	−3.27696	−0.511774	−0.255887	−	0.966707i	$-0.582368\pi$
$41$	−3.27696	−0.511774	−0.255887	+	0.966707i	$0.582368\pi$
$42$	1.57761	0.243431
$43$	5.62950	0.858491	0.429246	−	0.903188i	$-0.358779\pi$
$43$	5.62950	0.858491	0.429246	+	0.903188i	$0.358779\pi$
$44$	0.724738	0.109258
$45$	0	0
$46$	4.65932	0.686979
$47$	−10.4189	−1.51975	−0.759874	−	0.650070i	$-0.774739\pi$
$47$	−10.4189	−1.51975	−0.759874	+	0.650070i	$0.774739\pi$
$48$	4.74009	0.684173
$49$	1.00000	0.142857
$50$	0	0
$51$	−4.15739	−0.582151
$52$	3.27042	0.453526
$53$	−4.71551	−0.647725	−0.323863	−	0.946104i	$-0.604982\pi$
$53$	−4.71551	−0.647725	−0.323863	+	0.946104i	$0.604982\pi$
$54$	7.91348	1.07689
$55$	0	0
$56$	2.33861	0.312510
$57$	4.03106	0.533927
$58$	−9.99916	−1.31295
$59$	−0.586172	−0.0763131	−0.0381565	−	0.999272i	$-0.512149\pi$
$59$	−0.586172	−0.0763131	−0.0381565	+	0.999272i	$0.512149\pi$
$60$	0	0
$61$	12.1062	1.55004	0.775021	−	0.631936i	$-0.217739\pi$
$61$	12.1062	1.55004	0.775021	+	0.631936i	$0.217739\pi$
$62$	3.04100	0.386207
$63$	2.01611	0.254006
$64$	4.90810	0.613512
$65$	0	0
$66$	−2.15883	−0.265734
$67$	−8.03234	−0.981306	−0.490653	−	0.871355i	$-0.663242\pi$
$67$	−8.03234	−0.981306	−0.490653	+	0.871355i	$0.663242\pi$
$68$	2.21978	0.269188
$69$	−2.90582	−0.349819
$70$	0	0
$71$	9.27682	1.10096	0.550478	−	0.834850i	$-0.314445\pi$
$71$	9.27682	1.10096	0.550478	+	0.834850i	$0.314445\pi$
$72$	4.71489	0.555656
$73$	−2.65930	−0.311247	−0.155624	−	0.987816i	$-0.549739\pi$
$73$	−2.65930	−0.311247	−0.155624	+	0.987816i	$0.549739\pi$
$74$	−18.4527	−2.14509
$75$	0	0
$76$	−2.15233	−0.246889
$77$	−1.36842	−0.155945
$78$	−9.74184	−1.10305
$79$	1.45661	0.163881	0.0819407	−	0.996637i	$-0.473888\pi$
$79$	1.45661	0.163881	0.0819407	+	0.996637i	$0.473888\pi$
$80$	0	0
$81$	1.11303	0.123670
$82$	−5.21192	−0.575561
$83$	−14.7230	−1.61605	−0.808027	−	0.589145i	$-0.799465\pi$
$83$	−14.7230	−1.61605	−0.808027	+	0.589145i	$0.799465\pi$
$84$	0.525335	0.0573187
$85$	0	0
$86$	8.95360	0.965491
$87$	6.23604	0.668574
$88$	−3.20019	−0.341141
$89$	−6.64967	−0.704863	−0.352432	−	0.935838i	$-0.614645\pi$
$89$	−6.64967	−0.704863	−0.352432	+	0.935838i	$0.614645\pi$
$90$	0	0
$91$	−6.17505	−0.647321
$92$	1.55152	0.161757
$93$	−1.89654	−0.196662
$94$	−16.5710	−1.70917
$95$	0	0
$96$	2.89962	0.295941
$97$	−3.06640	−0.311346	−0.155673	−	0.987809i	$-0.549755\pi$
$97$	−3.06640	−0.311346	−0.155673	+	0.987809i	$0.549755\pi$
$98$	1.59048	0.160662
$99$	−2.75888	−0.277277
$100$	0	0
$101$	−8.13698	−0.809660	−0.404830	−	0.914392i	$-0.632669\pi$
$101$	−8.13698	−0.809660	−0.404830	+	0.914392i	$0.632669\pi$
$102$	−6.61223	−0.654709
$103$	−14.9986	−1.47785	−0.738927	−	0.673785i	$-0.764667\pi$
$103$	−14.9986	−1.47785	−0.738927	+	0.673785i	$0.764667\pi$
$104$	−14.4410	−1.41606
$105$	0	0
$106$	−7.49992	−0.728456
$107$	−0.599745	−0.0579795	−0.0289898	−	0.999580i	$-0.509229\pi$
$107$	−0.599745	−0.0579795	−0.0289898	+	0.999580i	$0.509229\pi$
$108$	2.63514	0.253566
$109$	−9.07924	−0.869633	−0.434817	−	0.900519i	$-0.643187\pi$
$109$	−9.07924	−0.869633	−0.434817	+	0.900519i	$0.643187\pi$
$110$	0	0
$111$	11.5082	1.09231
$112$	4.77874	0.451549
$113$	−16.9460	−1.59414	−0.797071	−	0.603885i	$-0.793619\pi$
$113$	−16.9460	−1.59414	−0.797071	+	0.603885i	$0.793619\pi$
$114$	6.41131	0.600474
$115$	0	0
$116$	−3.32965	−0.309150
$117$	−12.4496	−1.15096
$118$	−0.932293	−0.0858245
$119$	−4.19129	−0.384215
$120$	0	0
$121$	−9.12744	−0.829767
$122$	19.2547	1.74323
$123$	3.25045	0.293083
$124$	1.01263	0.0909371
$125$	0	0
$126$	3.20658	0.285665
$127$	−18.9867	−1.68480	−0.842399	−	0.538854i	$-0.818857\pi$
$127$	−18.9867	−1.68480	−0.842399	+	0.538854i	$0.818857\pi$
$128$	13.6527	1.20674
$129$	−5.58397	−0.491641
$130$	0	0
$131$	−2.86215	−0.250068	−0.125034	−	0.992152i	$-0.539904\pi$
$131$	−2.86215	−0.250068	−0.125034	+	0.992152i	$0.539904\pi$
$132$	−0.718876	−0.0625701
$133$	4.06393	0.352387
$134$	−12.7753	−1.10361
$135$	0	0
$136$	−9.80178	−0.840496
$137$	−6.92579	−0.591711	−0.295855	−	0.955233i	$-0.595605\pi$
$137$	−6.92579	−0.591711	−0.295855	+	0.955233i	$0.595605\pi$
$138$	−4.62164	−0.393420
$139$	−10.5992	−0.899015	−0.449508	−	0.893276i	$-0.648401\pi$
$139$	−10.5992	−0.899015	−0.449508	+	0.893276i	$0.648401\pi$
$140$	0	0
$141$	10.3346	0.870330
$142$	14.7546	1.23818
$143$	8.45003	0.706627
$144$	9.63447	0.802873
$145$	0	0
$146$	−4.22955	−0.350040
$147$	−0.991912	−0.0818115
$148$	−6.14464	−0.505086
$149$	−2.42821	−0.198927	−0.0994634	−	0.995041i	$-0.531713\pi$
$149$	−2.42821	−0.198927	−0.0994634	+	0.995041i	$0.531713\pi$
$150$	0	0
$151$	−1.10475	−0.0899031	−0.0449516	−	0.998989i	$-0.514313\pi$
$151$	−1.10475	−0.0899031	−0.0449516	+	0.998989i	$0.514313\pi$
$152$	9.50394	0.770871
$153$	−8.45010	−0.683150
$154$	−2.17643	−0.175382
$155$	0	0
$156$	−3.24397	−0.259725
$157$	5.81742	0.464281	0.232140	−	0.972682i	$-0.425427\pi$
$157$	5.81742	0.464281	0.232140	+	0.972682i	$0.425427\pi$
$158$	2.31670	0.184307
$159$	4.67737	0.370940
$160$	0	0
$161$	−2.92951	−0.230878
$162$	1.77025	0.139084
$163$	3.75451	0.294076	0.147038	−	0.989131i	$-0.453026\pi$
$163$	3.75451	0.294076	0.147038	+	0.989131i	$0.453026\pi$
$164$	−1.73554	−0.135523
$165$	0	0
$166$	−23.4165	−1.81748
$167$	9.23599	0.714703	0.357351	−	0.933970i	$-0.383680\pi$
$167$	9.23599	0.714703	0.357351	+	0.933970i	$0.383680\pi$
$168$	−2.31969	−0.178968
$169$	25.1312	1.93317
$170$	0	0
$171$	8.19333	0.626560
$172$	2.98149	0.227336
$173$	−7.41184	−0.563512	−0.281756	−	0.959486i	$-0.590917\pi$
$173$	−7.41184	−0.563512	−0.281756	+	0.959486i	$0.590917\pi$
$174$	9.91828	0.751903
$175$	0	0
$176$	−6.53930	−0.492918
$177$	0.581431	0.0437030
$178$	−10.5761	−0.792715
$179$	9.04791	0.676272	0.338136	−	0.941097i	$-0.390204\pi$
$179$	9.04791	0.676272	0.338136	+	0.941097i	$0.390204\pi$
$180$	0	0
$181$	−6.27181	−0.466180	−0.233090	−	0.972455i	$-0.574884\pi$
$181$	−6.27181	−0.466180	−0.233090	+	0.972455i	$0.574884\pi$
$182$	−9.82128	−0.728001
$183$	−12.0083	−0.887679
$184$	−6.85098	−0.505061
$185$	0	0
$186$	−3.01640	−0.221173
$187$	5.73542	0.419416
$188$	−5.51803	−0.402443
$189$	−4.97554	−0.361917
$190$	0	0
$191$	18.1493	1.31324	0.656620	−	0.754221i	$-0.271985\pi$
$191$	18.1493	1.31324	0.656620	+	0.754221i	$0.271985\pi$
$192$	−4.86840	−0.351347
$193$	18.7214	1.34760	0.673798	−	0.738916i	$-0.264662\pi$
$193$	18.7214	1.34760	0.673798	+	0.738916i	$0.264662\pi$
$194$	−4.87705	−0.350152
$195$	0	0
$196$	0.529618	0.0378299
$197$	4.76068	0.339184	0.169592	−	0.985514i	$-0.445755\pi$
$197$	4.76068	0.339184	0.169592	+	0.985514i	$0.445755\pi$
$198$	−4.38793	−0.311837
$199$	−1.01540	−0.0719796	−0.0359898	−	0.999352i	$-0.511458\pi$
$199$	−1.01540	−0.0719796	−0.0359898	+	0.999352i	$0.511458\pi$
$200$	0	0
$201$	7.96737	0.561975
$202$	−12.9417	−0.910574
$203$	6.28689	0.441253
$204$	−2.20183	−0.154159
$205$	0	0
$206$	−23.8549	−1.66205
$207$	−5.90622	−0.410510
$208$	−29.5090	−2.04608
$209$	−5.56114	−0.384672
$210$	0	0
$211$	19.3866	1.33463	0.667314	−	0.744776i	$-0.267444\pi$
$211$	19.3866	1.33463	0.667314	+	0.744776i	$0.267444\pi$
$212$	−2.49742	−0.171524
$213$	−9.20179	−0.630496
$214$	−0.953880	−0.0652059
$215$	0	0
$216$	−11.6358	−0.791719
$217$	−1.91200	−0.129795
$218$	−14.4403	−0.978022
$219$	2.63779	0.178245
$220$	0	0
$221$	25.8814	1.74097
$222$	18.3035	1.22845
$223$	−20.5432	−1.37568	−0.687838	−	0.725865i	$-0.741440\pi$
$223$	−20.5432	−1.37568	−0.687838	+	0.725865i	$0.741440\pi$
$224$	2.92326	0.195319
$225$	0	0
$226$	−26.9522	−1.79283
$227$	18.8817	1.25322	0.626611	−	0.779332i	$-0.284441\pi$
$227$	18.8817	1.25322	0.626611	+	0.779332i	$0.284441\pi$
$228$	2.13492	0.141389
$229$	6.80288	0.449547	0.224774	−	0.974411i	$-0.427836\pi$
$229$	6.80288	0.449547	0.224774	+	0.974411i	$0.427836\pi$
$230$	0	0
$231$	1.35735	0.0893069
$232$	14.7026	0.965271
$233$	−7.36861	−0.482734	−0.241367	−	0.970434i	$-0.577596\pi$
$233$	−7.36861	−0.482734	−0.241367	+	0.970434i	$0.577596\pi$
$234$	−19.8008	−1.29442
$235$	0	0
$236$	−0.310447	−0.0202084
$237$	−1.44483	−0.0938517
$238$	−6.66615	−0.432102
$239$	14.1027	0.912225	0.456112	−	0.889922i	$-0.349242\pi$
$239$	14.1027	0.912225	0.456112	+	0.889922i	$0.349242\pi$
$240$	0	0
$241$	−28.8681	−1.85956	−0.929780	−	0.368115i	$-0.880003\pi$
$241$	−28.8681	−1.85956	−0.929780	+	0.368115i	$0.880003\pi$
$242$	−14.5170	−0.933187
$243$	−16.0307	−1.02837
$244$	6.41167	0.410465
$245$	0	0
$246$	5.16977	0.329612
$247$	−25.0950	−1.59675
$248$	−4.47143	−0.283936
$249$	14.6039	0.925483
$250$	0	0
$251$	7.01314	0.442666	0.221333	−	0.975198i	$-0.428959\pi$
$251$	7.01314	0.442666	0.221333	+	0.975198i	$0.428959\pi$
$252$	1.06777	0.0672631
$253$	4.00879	0.252030
$254$	−30.1979	−1.89479
$255$	0	0
$256$	11.8982	0.743637
$257$	−2.89490	−0.180579	−0.0902895	−	0.995916i	$-0.528779\pi$
$257$	−2.89490	−0.180579	−0.0902895	+	0.995916i	$0.528779\pi$
$258$	−8.88118	−0.552918
$259$	11.6020	0.720914
$260$	0	0
$261$	12.6751	0.784567
$262$	−4.55219	−0.281235
$263$	−6.58356	−0.405960	−0.202980	−	0.979183i	$-0.565063\pi$
$263$	−6.58356	−0.405960	−0.202980	+	0.979183i	$0.565063\pi$
$264$	3.17430	0.195365
$265$	0	0
$266$	6.46359	0.396308
$267$	6.59588	0.403662
$268$	−4.25407	−0.259859
$269$	−1.78629	−0.108912	−0.0544559	−	0.998516i	$-0.517342\pi$
$269$	−1.78629	−0.108912	−0.0544559	+	0.998516i	$0.517342\pi$
$270$	0	0
$271$	−8.29723	−0.504021	−0.252010	−	0.967725i	$-0.581092\pi$
$271$	−8.29723	−0.504021	−0.252010	+	0.967725i	$0.581092\pi$
$272$	−20.0291	−1.21444
$273$	6.12511	0.370708
$274$	−11.0153	−0.665460
$275$	0	0
$276$	−1.53897	−0.0926353
$277$	14.5690	0.875366	0.437683	−	0.899129i	$-0.355799\pi$
$277$	14.5690	0.875366	0.437683	+	0.899129i	$0.355799\pi$
$278$	−16.8578	−1.01107
$279$	−3.85481	−0.230781
$280$	0	0
$281$	−21.8681	−1.30454	−0.652271	−	0.757986i	$-0.726183\pi$
$281$	−21.8681	−1.30454	−0.652271	+	0.757986i	$0.726183\pi$
$282$	16.4370	0.978806
$283$	16.5219	0.982124	0.491062	−	0.871125i	$-0.336609\pi$
$283$	16.5219	0.982124	0.491062	+	0.871125i	$0.336609\pi$
$284$	4.91318	0.291543
$285$	0	0
$286$	13.4396	0.794699
$287$	3.27696	0.193433
$288$	5.89362	0.347285
$289$	0.566892	0.0333466
$290$	0	0
$291$	3.04160	0.178302
$292$	−1.40841	−0.0824211
$293$	−12.0870	−0.706131	−0.353065	−	0.935599i	$-0.614861\pi$
$293$	−12.0870	−0.706131	−0.353065	+	0.935599i	$0.614861\pi$
$294$	−1.57761	−0.0920083
$295$	0	0
$296$	27.1326	1.57705
$297$	6.80860	0.395075
$298$	−3.86201	−0.223720
$299$	18.0899	1.04616
$300$	0	0
$301$	−5.62950	−0.324479
$302$	−1.75708	−0.101108
$303$	8.07117	0.463677
$304$	19.4205	1.11384
$305$	0	0
$306$	−13.4397	−0.768296
$307$	18.2333	1.04063	0.520316	−	0.853974i	$-0.325814\pi$
$307$	18.2333	1.04063	0.520316	+	0.853974i	$0.325814\pi$
$308$	−0.724738	−0.0412958
$309$	14.8773	0.846339
$310$	0	0
$311$	−8.60245	−0.487800	−0.243900	−	0.969800i	$-0.578427\pi$
$311$	−8.60245	−0.487800	−0.243900	+	0.969800i	$0.578427\pi$
$312$	14.3242	0.810950
$313$	−17.7696	−1.00440	−0.502198	−	0.864753i	$-0.667475\pi$
$313$	−17.7696	−1.00440	−0.502198	+	0.864753i	$0.667475\pi$
$314$	9.25248	0.522147
$315$	0	0
$316$	0.771447	0.0433973
$317$	−11.8454	−0.665306	−0.332653	−	0.943049i	$-0.607944\pi$
$317$	−11.8454	−0.665306	−0.332653	+	0.943049i	$0.607944\pi$
$318$	7.43926	0.417173
$319$	−8.60307	−0.481680
$320$	0	0
$321$	0.594894	0.0332037
$322$	−4.65932	−0.259654
$323$	−17.0331	−0.947747
$324$	0.589483	0.0327490
$325$	0	0
$326$	5.97146	0.330729
$327$	9.00581	0.498022
$328$	7.66352	0.423147
$329$	10.4189	0.574411
$330$	0	0
$331$	15.2372	0.837514	0.418757	−	0.908098i	$-0.362466\pi$
$331$	15.2372	0.837514	0.418757	+	0.908098i	$0.362466\pi$
$332$	−7.79755	−0.427946
$333$	23.3909	1.28182
$334$	14.6896	0.803781
$335$	0	0
$336$	−4.74009	−0.258593
$337$	30.6342	1.66875	0.834375	−	0.551197i	$-0.185829\pi$
$337$	30.6342	1.66875	0.834375	+	0.551197i	$0.185829\pi$
$338$	39.9707	2.17412
$339$	16.8089	0.912935
$340$	0	0
$341$	2.61641	0.141687
$342$	13.0313	0.704652
$343$	−1.00000	−0.0539949
$344$	−13.1652	−0.709820
$345$	0	0
$346$	−11.7884	−0.633747
$347$	−28.4671	−1.52819	−0.764097	−	0.645101i	$-0.776815\pi$
$347$	−28.4671	−1.52819	−0.764097	+	0.645101i	$0.776815\pi$
$348$	3.30272	0.177045
$349$	−18.5302	−0.991901	−0.495951	−	0.868351i	$-0.665180\pi$
$349$	−18.5302	−0.991901	−0.495951	+	0.868351i	$0.665180\pi$
$350$	0	0
$351$	30.7242	1.63994
$352$	−4.00024	−0.213213
$353$	−1.46617	−0.0780362	−0.0390181	−	0.999239i	$-0.512423\pi$
$353$	−1.46617	−0.0780362	−0.0390181	+	0.999239i	$0.512423\pi$
$354$	0.924753	0.0491501
$355$	0	0
$356$	−3.52179	−0.186654
$357$	4.15739	0.220032
$358$	14.3905	0.760561
$359$	7.70077	0.406431	0.203216	−	0.979134i	$-0.434861\pi$
$359$	7.70077	0.406431	0.203216	+	0.979134i	$0.434861\pi$
$360$	0	0
$361$	−2.48447	−0.130762
$362$	−9.97518	−0.524284
$363$	9.05362	0.475192
$364$	−3.27042	−0.171417
$365$	0	0
$366$	−19.0989	−0.998317
$367$	−21.4056	−1.11736	−0.558682	−	0.829382i	$-0.688693\pi$
$367$	−21.4056	−1.11736	−0.558682	+	0.829382i	$0.688693\pi$
$368$	−13.9994	−0.729768
$369$	6.60670	0.343931
$370$	0	0
$371$	4.71551	0.244817
$372$	−1.00444	−0.0520779
$373$	−0.462879	−0.0239670	−0.0119835	−	0.999928i	$-0.503815\pi$
$373$	−0.462879	−0.0239670	−0.0119835	+	0.999928i	$0.503815\pi$
$374$	9.12206	0.471690
$375$	0	0
$376$	24.3657	1.25656
$377$	−38.8218	−1.99943
$378$	−7.91348	−0.407026
$379$	27.2959	1.40209	0.701047	−	0.713115i	$-0.252716\pi$
$379$	27.2959	1.40209	0.701047	+	0.713115i	$0.252716\pi$
$380$	0	0
$381$	18.8331	0.964851
$382$	28.8661	1.47692
$383$	29.9453	1.53013	0.765067	−	0.643951i	$-0.222706\pi$
$383$	29.9453	1.53013	0.765067	+	0.643951i	$0.222706\pi$
$384$	−13.5423	−0.691079
$385$	0	0
$386$	29.7760	1.51556
$387$	−11.3497	−0.576938
$388$	−1.62402	−0.0824474
$389$	0.256431	0.0130016	0.00650079	−	0.999979i	$-0.497931\pi$
$389$	0.256431	0.0130016	0.00650079	+	0.999979i	$0.497931\pi$
$390$	0	0
$391$	12.2784	0.620946
$392$	−2.33861	−0.118118
$393$	2.83901	0.143209
$394$	7.57175	0.381459
$395$	0	0
$396$	−1.46115	−0.0734256
$397$	−2.83558	−0.142314	−0.0711569	−	0.997465i	$-0.522669\pi$
$397$	−2.83558	−0.142314	−0.0711569	+	0.997465i	$0.522669\pi$
$398$	−1.61497	−0.0809510
$399$	−4.03106	−0.201805
$400$	0	0
$401$	−17.2543	−0.861641	−0.430820	−	0.902438i	$-0.641776\pi$
$401$	−17.2543	−0.861641	−0.430820	+	0.902438i	$0.641776\pi$
$402$	12.6719	0.632018
$403$	11.8067	0.588134
$404$	−4.30950	−0.214405
$405$	0	0
$406$	9.99916	0.496250
$407$	−15.8764	−0.786962
$408$	9.72251	0.481336
$409$	17.3841	0.859588	0.429794	−	0.902927i	$-0.358586\pi$
$409$	17.3841	0.859588	0.429794	+	0.902927i	$0.358586\pi$
$410$	0	0
$411$	6.86978	0.338861
$412$	−7.94353	−0.391349
$413$	0.586172	0.0288436
$414$	−9.39370	−0.461675
$415$	0	0
$416$	−18.0513	−0.885037
$417$	10.5135	0.514849
$418$	−8.84487	−0.432617
$419$	5.07799	0.248076	0.124038	−	0.992277i	$-0.460416\pi$
$419$	5.07799	0.248076	0.124038	+	0.992277i	$0.460416\pi$
$420$	0	0
$421$	−30.1686	−1.47033	−0.735163	−	0.677891i	$-0.762894\pi$
$421$	−30.1686	−1.47033	−0.735163	+	0.677891i	$0.762894\pi$
$422$	30.8339	1.50097
$423$	21.0056	1.02133
$424$	11.0277	0.535554
$425$	0	0
$426$	−14.6352	−0.709080
$427$	−12.1062	−0.585860
$428$	−0.317636	−0.0153535
$429$	−8.38169	−0.404672
$430$	0	0
$431$	38.0494	1.83277	0.916387	−	0.400293i	$-0.131092\pi$
$431$	38.0494	1.83277	0.916387	+	0.400293i	$0.131092\pi$
$432$	−23.7768	−1.14396
$433$	14.3015	0.687285	0.343643	−	0.939100i	$-0.388339\pi$
$433$	14.3015	0.687285	0.343643	+	0.939100i	$0.388339\pi$
$434$	−3.04100	−0.145973
$435$	0	0
$436$	−4.80853	−0.230287
$437$	−11.9053	−0.569509
$438$	4.19534	0.200461
$439$	−23.8018	−1.13600	−0.568000	−	0.823028i	$-0.692283\pi$
$439$	−23.8018	−1.13600	−0.568000	+	0.823028i	$0.692283\pi$
$440$	0	0
$441$	−2.01611	−0.0960053
$442$	41.1638	1.95796
$443$	−34.0901	−1.61967	−0.809835	−	0.586658i	$-0.800443\pi$
$443$	−34.0901	−1.61967	−0.809835	+	0.586658i	$0.800443\pi$
$444$	6.09494	0.289253
$445$	0	0
$446$	−32.6735	−1.54714
$447$	2.40857	0.113922
$448$	−4.90810	−0.231886
$449$	−10.0195	−0.472848	−0.236424	−	0.971650i	$-0.575975\pi$
$449$	−10.0195	−0.472848	−0.236424	+	0.971650i	$0.575975\pi$
$450$	0	0
$451$	−4.48424	−0.211154
$452$	−8.97490	−0.422144
$453$	1.09581	0.0514858
$454$	30.0309	1.40942
$455$	0	0
$456$	−9.42707	−0.441463
$457$	16.1014	0.753193	0.376597	−	0.926377i	$-0.377094\pi$
$457$	16.1014	0.753193	0.376597	+	0.926377i	$0.377094\pi$
$458$	10.8198	0.505578
$459$	20.8539	0.973378
$460$	0	0
$461$	−9.10748	−0.424178	−0.212089	−	0.977250i	$-0.568027\pi$
$461$	−9.10748	−0.424178	−0.212089	+	0.977250i	$0.568027\pi$
$462$	2.15883	0.100438
$463$	13.3768	0.621672	0.310836	−	0.950464i	$-0.399391\pi$
$463$	13.3768	0.621672	0.310836	+	0.950464i	$0.399391\pi$
$464$	30.0434	1.39473
$465$	0	0
$466$	−11.7196	−0.542900
$467$	−3.16578	−0.146495	−0.0732474	−	0.997314i	$-0.523336\pi$
$467$	−3.16578	−0.146495	−0.0732474	+	0.997314i	$0.523336\pi$
$468$	−6.59353	−0.304786
$469$	8.03234	0.370899
$470$	0	0
$471$	−5.77037	−0.265885
$472$	1.37083	0.0630974
$473$	7.70350	0.354207
$474$	−2.29797	−0.105549
$475$	0	0
$476$	−2.21978	−0.101744
$477$	9.50699	0.435295
$478$	22.4299	1.02592
$479$	32.0208	1.46307	0.731533	−	0.681806i	$-0.238805\pi$
$479$	32.0208	1.46307	0.731533	+	0.681806i	$0.238805\pi$
$480$	0	0
$481$	−71.6430	−3.26664
$482$	−45.9141	−2.09133
$483$	2.90582	0.132219
$484$	−4.83406	−0.219730
$485$	0	0
$486$	−25.4964	−1.15654
$487$	31.8524	1.44337	0.721684	−	0.692223i	$-0.243368\pi$
$487$	31.8524	1.44337	0.721684	+	0.692223i	$0.243368\pi$
$488$	−28.3117	−1.28161
$489$	−3.72414	−0.168412
$490$	0	0
$491$	−41.3163	−1.86458	−0.932290	−	0.361713i	$-0.882192\pi$
$491$	−41.3163	−1.86458	−0.932290	+	0.361713i	$0.882192\pi$
$492$	1.72150	0.0776112
$493$	−26.3502	−1.18675
$494$	−39.9130	−1.79577
$495$	0	0
$496$	−9.13697	−0.410262
$497$	−9.27682	−0.416122
$498$	23.2271	1.04083
$499$	−4.16196	−0.186315	−0.0931576	−	0.995651i	$-0.529696\pi$
$499$	−4.16196	−0.186315	−0.0931576	+	0.995651i	$0.529696\pi$
$500$	0	0
$501$	−9.16129	−0.409296
$502$	11.1542	0.497838
$503$	−22.3085	−0.994685	−0.497342	−	0.867554i	$-0.665691\pi$
$503$	−22.3085	−0.994685	−0.497342	+	0.867554i	$0.665691\pi$
$504$	−4.71489	−0.210018
$505$	0	0
$506$	6.37588	0.283443
$507$	−24.9280	−1.10709
$508$	−10.0557	−0.446150
$509$	14.6711	0.650284	0.325142	−	0.945665i	$-0.394588\pi$
$509$	14.6711	0.650284	0.325142	+	0.945665i	$0.394588\pi$
$510$	0	0
$511$	2.65930	0.117640
$512$	−8.38170	−0.370422
$513$	−20.2202	−0.892746
$514$	−4.60427	−0.203086
$515$	0	0
$516$	−2.95737	−0.130191
$517$	−14.2573	−0.627037
$518$	18.4527	0.810767
$519$	7.35190	0.322712
$520$	0	0
$521$	12.4587	0.545824	0.272912	−	0.962039i	$-0.412013\pi$
$521$	12.4587	0.545824	0.272912	+	0.962039i	$0.412013\pi$
$522$	20.1594	0.882353
$523$	−28.7239	−1.25601	−0.628005	−	0.778209i	$-0.716128\pi$
$523$	−28.7239	−1.25601	−0.628005	+	0.778209i	$0.716128\pi$
$524$	−1.51585	−0.0662202
$525$	0	0
$526$	−10.4710	−0.456557
$527$	8.01376	0.349085
$528$	6.48641	0.282285
$529$	−14.4180	−0.626868
$530$	0	0
$531$	1.18179	0.0512852
$532$	2.15233	0.0933154
$533$	−20.2354	−0.876491
$534$	10.4906	0.453973
$535$	0	0
$536$	18.7845	0.811367
$537$	−8.97473	−0.387288
$538$	−2.84105	−0.122486
$539$	1.36842	0.0589418
$540$	0	0
$541$	10.1059	0.434486	0.217243	−	0.976118i	$-0.430294\pi$
$541$	10.1059	0.434486	0.217243	+	0.976118i	$0.430294\pi$
$542$	−13.1966	−0.566841
$543$	6.22109	0.266972
$544$	−12.2522	−0.525310
$545$	0	0
$546$	9.74184	0.416912
$547$	−36.6923	−1.56885	−0.784425	−	0.620223i	$-0.787042\pi$
$547$	−36.6923	−1.56885	−0.784425	+	0.620223i	$0.787042\pi$
$548$	−3.66803	−0.156690
$549$	−24.4075	−1.04168
$550$	0	0
$551$	25.5495	1.08844
$552$	6.79557	0.289239
$553$	−1.45661	−0.0619413
$554$	23.1717	0.984470
$555$	0	0
$556$	−5.61355	−0.238068
$557$	−4.45573	−0.188795	−0.0943976	−	0.995535i	$-0.530093\pi$
$557$	−4.45573	−0.188795	−0.0943976	+	0.995535i	$0.530093\pi$
$558$	−6.13099	−0.259545
$559$	34.7625	1.47030
$560$	0	0
$561$	−5.68903	−0.240191
$562$	−34.7807	−1.46714
$563$	41.6365	1.75477	0.877384	−	0.479789i	$-0.159287\pi$
$563$	41.6365	1.75477	0.877384	+	0.479789i	$0.159287\pi$
$564$	5.47340	0.230472
$565$	0	0
$566$	26.2777	1.10453
$567$	−1.11303	−0.0467430
$568$	−21.6949	−0.910296
$569$	27.8378	1.16702	0.583510	−	0.812106i	$-0.301679\pi$
$569$	27.8378	1.16702	0.583510	+	0.812106i	$0.301679\pi$
$570$	0	0
$571$	19.0783	0.798402	0.399201	−	0.916863i	$-0.369288\pi$
$571$	19.0783	0.798402	0.399201	+	0.916863i	$0.369288\pi$
$572$	4.47529	0.187121
$573$	−18.0026	−0.752067
$574$	5.21192	0.217541
$575$	0	0
$576$	−9.89527	−0.412303
$577$	−0.407281	−0.0169553	−0.00847767	−	0.999964i	$-0.502699\pi$
$577$	−0.407281	−0.0169553	−0.00847767	+	0.999964i	$0.502699\pi$
$578$	0.901629	0.0375028
$579$	−18.5700	−0.771742
$580$	0	0
$581$	14.7230	0.610811
$582$	4.83760	0.200525
$583$	−6.45278	−0.267247
$584$	6.21905	0.257346
$585$	0	0
$586$	−19.2241	−0.794141
$587$	−19.0480	−0.786195	−0.393097	−	0.919497i	$-0.628596\pi$
$587$	−19.0480	−0.786195	−0.393097	+	0.919497i	$0.628596\pi$
$588$	−0.525335	−0.0216644
$589$	−7.77025	−0.320168
$590$	0	0
$591$	−4.72217	−0.194244
$592$	55.4430	2.27869
$593$	−17.2428	−0.708076	−0.354038	−	0.935231i	$-0.615192\pi$
$593$	−17.2428	−0.708076	−0.354038	+	0.935231i	$0.615192\pi$
$594$	10.8289	0.444316
$595$	0	0
$596$	−1.28602	−0.0526776
$597$	1.00719	0.0412213
$598$	28.7715	1.17656
$599$	26.4257	1.07972	0.539862	−	0.841753i	$-0.318476\pi$
$599$	26.4257	1.07972	0.539862	+	0.841753i	$0.318476\pi$
$600$	0	0
$601$	16.3134	0.665437	0.332718	−	0.943026i	$-0.392034\pi$
$601$	16.3134	0.665437	0.332718	+	0.943026i	$0.392034\pi$
$602$	−8.95360	−0.364921
$603$	16.1941	0.659474
$604$	−0.585095	−0.0238072
$605$	0	0
$606$	12.8370	0.521468
$607$	16.3699	0.664432	0.332216	−	0.943203i	$-0.392204\pi$
$607$	16.3699	0.664432	0.332216	+	0.943203i	$0.392204\pi$
$608$	11.8799	0.481795
$609$	−6.23604	−0.252697
$610$	0	0
$611$	−64.3370	−2.60280
$612$	−4.47533	−0.180904
$613$	44.3989	1.79325	0.896626	−	0.442788i	$-0.146011\pi$
$613$	44.3989	1.79325	0.896626	+	0.442788i	$0.146011\pi$
$614$	28.9997	1.17033
$615$	0	0
$616$	3.20019	0.128939
$617$	−1.85627	−0.0747308	−0.0373654	−	0.999302i	$-0.511897\pi$
$617$	−1.85627	−0.0747308	−0.0373654	+	0.999302i	$0.511897\pi$
$618$	23.6620	0.951824
$619$	26.5450	1.06693	0.533467	−	0.845821i	$-0.320889\pi$
$619$	26.5450	1.06693	0.533467	+	0.845821i	$0.320889\pi$
$620$	0	0
$621$	14.5759	0.584911
$622$	−13.6820	−0.548598
$623$	6.64967	0.266413
$624$	29.2703	1.17175
$625$	0	0
$626$	−28.2621	−1.12958
$627$	5.51616	0.220294
$628$	3.08101	0.122946
$629$	−48.6274	−1.93890
$630$	0	0
$631$	45.9782	1.83036	0.915181	−	0.403042i	$-0.132047\pi$
$631$	45.9782	1.83036	0.915181	+	0.403042i	$0.132047\pi$
$632$	−3.40644	−0.135501
$633$	−19.2298	−0.764316
$634$	−18.8399	−0.748228
$635$	0	0
$636$	2.47722	0.0982283
$637$	6.17505	0.244664
$638$	−13.6830	−0.541715
$639$	−18.7031	−0.739883
$640$	0	0
$641$	41.0391	1.62095	0.810474	−	0.585775i	$-0.199210\pi$
$641$	41.0391	1.62095	0.810474	+	0.585775i	$0.199210\pi$
$642$	0.946166	0.0373422
$643$	8.92058	0.351793	0.175897	−	0.984409i	$-0.443718\pi$
$643$	8.92058	0.351793	0.175897	+	0.984409i	$0.443718\pi$
$644$	−1.55152	−0.0611386
$645$	0	0
$646$	−27.0908	−1.06587
$647$	4.99172	0.196245	0.0981224	−	0.995174i	$-0.468716\pi$
$647$	4.99172	0.196245	0.0981224	+	0.995174i	$0.468716\pi$
$648$	−2.60295	−0.102253
$649$	−0.802126	−0.0314862
$650$	0	0
$651$	1.89654	0.0743312
$652$	1.98846	0.0778740
$653$	−11.6727	−0.456787	−0.228393	−	0.973569i	$-0.573347\pi$
$653$	−11.6727	−0.456787	−0.228393	+	0.973569i	$0.573347\pi$
$654$	14.3235	0.560094
$655$	0	0
$656$	15.6597	0.611409
$657$	5.36144	0.209170
$658$	16.5710	0.646004
$659$	−48.1143	−1.87427	−0.937134	−	0.348971i	$-0.886531\pi$
$659$	−48.1143	−1.87427	−0.937134	+	0.348971i	$0.886531\pi$
$660$	0	0
$661$	−21.3214	−0.829307	−0.414653	−	0.909979i	$-0.636097\pi$
$661$	−21.3214	−0.829307	−0.414653	+	0.909979i	$0.636097\pi$
$662$	24.2345	0.941899
$663$	−25.6721	−0.997021
$664$	34.4312	1.33619
$665$	0	0
$666$	37.2027	1.44158
$667$	−18.4175	−0.713129
$668$	4.89155	0.189260
$669$	20.3771	0.787823
$670$	0	0
$671$	16.5663	0.639536
$672$	−2.89962	−0.111855
$673$	−30.3571	−1.17018	−0.585090	−	0.810968i	$-0.698941\pi$
$673$	−30.3571	−1.17018	−0.585090	+	0.810968i	$0.698941\pi$
$674$	48.7230	1.87674
$675$	0	0
$676$	13.3100	0.511922
$677$	−42.1907	−1.62152	−0.810761	−	0.585378i	$-0.800946\pi$
$677$	−42.1907	−1.62152	−0.810761	+	0.585378i	$0.800946\pi$
$678$	26.7342	1.02672
$679$	3.06640	0.117678
$680$	0	0
$681$	−18.7290	−0.717696
$682$	4.16135	0.159346
$683$	26.1761	1.00160	0.500800	−	0.865563i	$-0.333039\pi$
$683$	26.1761	1.00160	0.500800	+	0.865563i	$0.333039\pi$
$684$	4.33934	0.165919
$685$	0	0
$686$	−1.59048	−0.0607247
$687$	−6.74786	−0.257447
$688$	−26.9019	−1.02563
$689$	−29.1185	−1.10933
$690$	0	0
$691$	5.85427	0.222707	0.111354	−	0.993781i	$-0.464481\pi$
$691$	5.85427	0.222707	0.111354	+	0.993781i	$0.464481\pi$
$692$	−3.92545	−0.149223
$693$	2.75888	0.104801
$694$	−45.2763	−1.71866
$695$	0	0
$696$	−14.5837	−0.552792
$697$	−13.7347	−0.520237
$698$	−29.4719	−1.11553
$699$	7.30901	0.276452
$700$	0	0
$701$	50.9656	1.92494	0.962471	−	0.271384i	$-0.0874812\pi$
$701$	50.9656	1.92494	0.962471	+	0.271384i	$0.0874812\pi$
$702$	48.8662	1.84433
$703$	47.1497	1.77829
$704$	6.71632	0.253131
$705$	0	0
$706$	−2.33190	−0.0877624
$707$	8.13698	0.306023
$708$	0.307937	0.0115730
$709$	0.907977	0.0340998	0.0170499	−	0.999855i	$-0.494573\pi$
$709$	0.907977	0.0340998	0.0170499	+	0.999855i	$0.494573\pi$
$710$	0	0
$711$	−2.93669	−0.110134
$712$	15.5510	0.582797
$713$	5.60123	0.209768
$714$	6.61223	0.247457
$715$	0	0
$716$	4.79194	0.179083
$717$	−13.9886	−0.522413
$718$	12.2479	0.457088
$719$	10.2864	0.383616	0.191808	−	0.981432i	$-0.438565\pi$
$719$	10.2864	0.383616	0.191808	+	0.981432i	$0.438565\pi$
$720$	0	0
$721$	14.9986	0.558576
$722$	−3.95150	−0.147060
$723$	28.6347	1.06493
$724$	−3.32167	−0.123449
$725$	0	0
$726$	14.3996	0.534418
$727$	2.49869	0.0926714	0.0463357	−	0.998926i	$-0.485246\pi$
$727$	2.49869	0.0926714	0.0463357	+	0.998926i	$0.485246\pi$
$728$	14.4410	0.535220
$729$	12.5619	0.465255
$730$	0	0
$731$	23.5949	0.872688
$732$	−6.35981	−0.235065
$733$	−6.82202	−0.251977	−0.125988	−	0.992032i	$-0.540210\pi$
$733$	−6.82202	−0.251977	−0.125988	+	0.992032i	$0.540210\pi$
$734$	−34.0452	−1.25663
$735$	0	0
$736$	−8.56373	−0.315663
$737$	−10.9916	−0.404880
$738$	10.5078	0.386798
$739$	−6.99076	−0.257159	−0.128580	−	0.991699i	$-0.541042\pi$
$739$	−6.99076	−0.257159	−0.128580	+	0.991699i	$0.541042\pi$
$740$	0	0
$741$	24.8920	0.914430
$742$	7.49992	0.275331
$743$	−37.7430	−1.38466	−0.692328	−	0.721583i	$-0.743415\pi$
$743$	−37.7430	−1.38466	−0.692328	+	0.721583i	$0.743415\pi$
$744$	4.43526	0.162605
$745$	0	0
$746$	−0.736199	−0.0269542
$747$	29.6831	1.08605
$748$	3.03758	0.111065
$749$	0.599745	0.0219142
$750$	0	0
$751$	−42.0524	−1.53451	−0.767256	−	0.641341i	$-0.778378\pi$
$751$	−42.0524	−1.53451	−0.767256	+	0.641341i	$0.778378\pi$
$752$	49.7891	1.81562
$753$	−6.95642	−0.253506
$754$	−61.7453	−2.24863
$755$	0	0
$756$	−2.63514	−0.0958390
$757$	6.02693	0.219052	0.109526	−	0.993984i	$-0.465067\pi$
$757$	6.02693	0.219052	0.109526	+	0.993984i	$0.465067\pi$
$758$	43.4135	1.57685
$759$	−3.97636	−0.144333
$760$	0	0
$761$	31.6680	1.14796	0.573982	−	0.818868i	$-0.305398\pi$
$761$	31.6680	1.14796	0.573982	+	0.818868i	$0.305398\pi$
$762$	29.9537	1.08511
$763$	9.07924	0.328690
$764$	9.61223	0.347758
$765$	0	0
$766$	47.6273	1.72085
$767$	−3.61964	−0.130698
$768$	−11.8020	−0.425866
$769$	−18.0739	−0.651762	−0.325881	−	0.945411i	$-0.605661\pi$
$769$	−18.0739	−0.651762	−0.325881	+	0.945411i	$0.605661\pi$
$770$	0	0
$771$	2.87149	0.103414
$772$	9.91520	0.356856
$773$	−33.1832	−1.19352	−0.596758	−	0.802421i	$-0.703545\pi$
$773$	−33.1832	−1.19352	−0.596758	+	0.802421i	$0.703545\pi$
$774$	−18.0514	−0.648846
$775$	0	0
$776$	7.17112	0.257428
$777$	−11.5082	−0.412853
$778$	0.407848	0.0146221
$779$	13.3173	0.477142
$780$	0	0
$781$	12.6945	0.454246
$782$	19.5285	0.698340
$783$	−31.2807	−1.11788
$784$	−4.77874	−0.170669
$785$	0	0
$786$	4.51537	0.161058
$787$	−35.6375	−1.27034	−0.635169	−	0.772373i	$-0.719070\pi$
$787$	−35.6375	−1.27034	−0.635169	+	0.772373i	$0.719070\pi$
$788$	2.52134	0.0898191
$789$	6.53031	0.232485
$790$	0	0
$791$	16.9460	0.602529
$792$	6.45193	0.229259
$793$	74.7564	2.65468
$794$	−4.50993	−0.160052
$795$	0	0
$796$	−0.537773	−0.0190609
$797$	42.3704	1.50084	0.750418	−	0.660963i	$-0.229852\pi$
$797$	42.3704	1.50084	0.750418	+	0.660963i	$0.229852\pi$
$798$	−6.41131	−0.226958
$799$	−43.6685	−1.54488
$800$	0	0
$801$	13.4065	0.473694
$802$	−27.4426	−0.969033
$803$	−3.63902	−0.128418
$804$	4.21967	0.148816
$805$	0	0
$806$	18.7783	0.661438
$807$	1.77184	0.0623716
$808$	19.0292	0.669446
$809$	21.2408	0.746785	0.373393	−	0.927673i	$-0.378194\pi$
$809$	21.2408	0.746785	0.373393	+	0.927673i	$0.378194\pi$
$810$	0	0
$811$	39.0038	1.36961	0.684805	−	0.728726i	$-0.259887\pi$
$811$	39.0038	1.36961	0.684805	+	0.728726i	$0.259887\pi$
$812$	3.32965	0.116848
$813$	8.23012	0.288643
$814$	−25.2510	−0.885047
$815$	0	0
$816$	19.8671	0.695487
$817$	−22.8779	−0.800397
$818$	27.6490	0.966725
$819$	12.4496	0.435024
$820$	0	0
$821$	−3.21682	−0.112268	−0.0561339	−	0.998423i	$-0.517877\pi$
$821$	−3.21682	−0.112268	−0.0561339	+	0.998423i	$0.517877\pi$
$822$	10.9262	0.381096
$823$	48.2862	1.68315	0.841576	−	0.540138i	$-0.181628\pi$
$823$	48.2862	1.68315	0.841576	+	0.540138i	$0.181628\pi$
$824$	35.0758	1.22192
$825$	0	0
$826$	0.932293	0.0324386
$827$	3.08477	0.107268	0.0536341	−	0.998561i	$-0.482920\pi$
$827$	3.08477	0.107268	0.0536341	+	0.998561i	$0.482920\pi$
$828$	−3.12804	−0.108707
$829$	−52.2250	−1.81385	−0.906924	−	0.421295i	$-0.861576\pi$
$829$	−52.2250	−1.81385	−0.906924	+	0.421295i	$0.861576\pi$
$830$	0	0
$831$	−14.4512	−0.501305
$832$	30.3078	1.05073
$833$	4.19129	0.145220
$834$	16.7215	0.579018
$835$	0	0
$836$	−2.94528	−0.101865
$837$	9.51325	0.328826
$838$	8.07642	0.278995
$839$	−23.7660	−0.820495	−0.410247	−	0.911974i	$-0.634558\pi$
$839$	−23.7660	−0.820495	−0.410247	+	0.911974i	$0.634558\pi$
$840$	0	0
$841$	10.5250	0.362930
$842$	−47.9824	−1.65358
$843$	21.6912	0.747086
$844$	10.2675	0.353422
$845$	0	0
$846$	33.4089	1.14862
$847$	9.12744	0.313623
$848$	22.5342	0.773828
$849$	−16.3883	−0.562443
$850$	0	0
$851$	−33.9882	−1.16510
$852$	−4.87344	−0.166961
$853$	−10.5653	−0.361748	−0.180874	−	0.983506i	$-0.557893\pi$
$853$	−10.5653	−0.361748	−0.180874	+	0.983506i	$0.557893\pi$
$854$	−19.2547	−0.658881
$855$	0	0
$856$	1.40257	0.0479388
$857$	−9.90009	−0.338181	−0.169090	−	0.985601i	$-0.554083\pi$
$857$	−9.90009	−0.338181	−0.169090	+	0.985601i	$0.554083\pi$
$858$	−13.3309	−0.455109
$859$	−35.7600	−1.22012	−0.610058	−	0.792357i	$-0.708854\pi$
$859$	−35.7600	−1.22012	−0.610058	+	0.792357i	$0.708854\pi$
$860$	0	0
$861$	−3.25045	−0.110775
$862$	60.5167	2.06121
$863$	33.2798	1.13286	0.566428	−	0.824111i	$-0.308325\pi$
$863$	33.2798	1.13286	0.566428	+	0.824111i	$0.308325\pi$
$864$	−14.5448	−0.494825
$865$	0	0
$866$	22.7462	0.772947
$867$	−0.562307	−0.0190970
$868$	−1.01263	−0.0343710
$869$	1.99325	0.0676163
$870$	0	0
$871$	−49.6001	−1.68063
$872$	21.2328	0.719033
$873$	6.18221	0.209236
$874$	−18.9351	−0.640491
$875$	0	0
$876$	1.39702	0.0472010
$877$	−35.1878	−1.18821	−0.594103	−	0.804389i	$-0.702493\pi$
$877$	−35.1878	−1.18821	−0.594103	+	0.804389i	$0.702493\pi$
$878$	−37.8563	−1.27759
$879$	11.9893	0.404387
$880$	0	0
$881$	1.72086	0.0579774	0.0289887	−	0.999580i	$-0.490771\pi$
$881$	1.72086	0.0579774	0.0289887	+	0.999580i	$0.490771\pi$
$882$	−3.20658	−0.107971
$883$	−9.29164	−0.312689	−0.156344	−	0.987703i	$-0.549971\pi$
$883$	−9.29164	−0.312689	−0.156344	+	0.987703i	$0.549971\pi$
$884$	13.7073	0.461025
$885$	0	0
$886$	−54.2196	−1.82154
$887$	−51.0116	−1.71280	−0.856401	−	0.516311i	$-0.827305\pi$
$887$	−51.0116	−1.71280	−0.856401	+	0.516311i	$0.827305\pi$
$888$	−26.9131	−0.903145
$889$	18.9867	0.636794
$890$	0	0
$891$	1.52309	0.0510255
$892$	−10.8801	−0.364291
$893$	42.3416	1.41691
$894$	3.83078	0.128120
$895$	0	0
$896$	−13.6527	−0.456106
$897$	−17.9436	−0.599118
$898$	−15.9357	−0.531782
$899$	−12.0206	−0.400908
$900$	0	0
$901$	−19.7641	−0.658437
$902$	−7.13207	−0.237472
$903$	5.58397	0.185823
$904$	39.6300	1.31807
$905$	0	0
$906$	1.74287	0.0579028
$907$	−24.3602	−0.808868	−0.404434	−	0.914567i	$-0.632532\pi$
$907$	−24.3602	−0.808868	−0.404434	+	0.914567i	$0.632532\pi$
$908$	10.0001	0.331865
$909$	16.4051	0.544121
$910$	0	0
$911$	18.3145	0.606787	0.303394	−	0.952865i	$-0.401880\pi$
$911$	18.3145	0.606787	0.303394	+	0.952865i	$0.401880\pi$
$912$	−19.2634	−0.637875
$913$	−20.1471	−0.666772
$914$	25.6090	0.847069
$915$	0	0
$916$	3.60293	0.119044
$917$	2.86215	0.0945167
$918$	33.1677	1.09470
$919$	4.11743	0.135821	0.0679107	−	0.997691i	$-0.478367\pi$
$919$	4.11743	0.135821	0.0679107	+	0.997691i	$0.478367\pi$
$920$	0	0
$921$	−18.0859	−0.595950
$922$	−14.4852	−0.477046
$923$	57.2848	1.88555
$924$	0.718876	0.0236493
$925$	0	0
$926$	21.2755	0.699155
$927$	30.2388	0.993172
$928$	18.3782	0.603295
$929$	29.9390	0.982267	0.491133	−	0.871084i	$-0.336583\pi$
$929$	29.9390	0.982267	0.491133	+	0.871084i	$0.336583\pi$
$930$	0	0
$931$	−4.06393	−0.133190
$932$	−3.90255	−0.127832
$933$	8.53287	0.279354
$934$	−5.03510	−0.164754
$935$	0	0
$936$	29.1147	0.951644
$937$	44.4937	1.45355	0.726774	−	0.686877i	$-0.241019\pi$
$937$	44.4937	1.45355	0.726774	+	0.686877i	$0.241019\pi$
$938$	12.7753	0.417127
$939$	17.6259	0.575198
$940$	0	0
$941$	−35.9941	−1.17337	−0.586687	−	0.809814i	$-0.699568\pi$
$941$	−35.9941	−1.17337	−0.586687	+	0.809814i	$0.699568\pi$
$942$	−9.17764	−0.299024
$943$	−9.59987	−0.312615
$944$	2.80116	0.0911701
$945$	0	0
$946$	12.2522	0.398355
$947$	29.3672	0.954306	0.477153	−	0.878820i	$-0.341669\pi$
$947$	29.3672	0.954306	0.477153	+	0.878820i	$0.341669\pi$
$948$	−0.765208	−0.0248528
$949$	−16.4213	−0.533058
$950$	0	0
$951$	11.7496	0.381008
$952$	9.80178	0.317678
$953$	−5.25228	−0.170138	−0.0850690	−	0.996375i	$-0.527111\pi$
$953$	−5.25228	−0.170138	−0.0850690	+	0.996375i	$0.527111\pi$
$954$	15.1207	0.489549
$955$	0	0
$956$	7.46902	0.241565
$957$	8.53349	0.275849
$958$	50.9283	1.64542
$959$	6.92579	0.223646
$960$	0	0
$961$	−27.3442	−0.882072
$962$	−113.947	−3.67378
$963$	1.20915	0.0389644
$964$	−15.2891	−0.492429
$965$	0	0
$966$	4.62164	0.148699
$967$	−33.8833	−1.08961	−0.544807	−	0.838561i	$-0.683397\pi$
$967$	−33.8833	−1.08961	−0.544807	+	0.838561i	$0.683397\pi$
$968$	21.3455	0.686071
$969$	16.8953	0.542756
$970$	0	0
$971$	−55.3844	−1.77737	−0.888685	−	0.458518i	$-0.848380\pi$
$971$	−55.3844	−1.77737	−0.888685	+	0.458518i	$0.848380\pi$
$972$	−8.49013	−0.272321
$973$	10.5992	0.339796
$974$	50.6604	1.62327
$975$	0	0
$976$	−57.8524	−1.85181
$977$	−38.5924	−1.23468	−0.617340	−	0.786697i	$-0.711790\pi$
$977$	−38.5924	−1.23468	−0.617340	+	0.786697i	$0.711790\pi$
$978$	−5.92317	−0.189402
$979$	−9.09950	−0.290821
$980$	0	0
$981$	18.3047	0.584426
$982$	−65.7127	−2.09698
$983$	−8.75242	−0.279159	−0.139579	−	0.990211i	$-0.544575\pi$
$983$	−8.75242	−0.279159	−0.139579	+	0.990211i	$0.544575\pi$
$984$	−7.60153	−0.242328
$985$	0	0
$986$	−41.9093	−1.33467
$987$	−10.3346	−0.328954
$988$	−13.2908	−0.422835
$989$	16.4917	0.524405
$990$	0	0
$991$	−0.444851	−0.0141311	−0.00706557	−	0.999975i	$-0.502249\pi$
$991$	−0.444851	−0.0141311	−0.00706557	+	0.999975i	$0.502249\pi$
$992$	−5.58929	−0.177460
$993$	−15.1140	−0.479628
$994$	−14.7546	−0.467987
$995$	0	0
$996$	7.73448	0.245076
$997$	45.3092	1.43496	0.717479	−	0.696580i	$-0.245296\pi$
$997$	45.3092	1.43496	0.717479	+	0.696580i	$0.245296\pi$
$998$	−6.61951	−0.209537
$999$	−57.7263	−1.82638

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4375.2.a.g.1.10		14
5.4	even	2		4375.2.a.h.1.5		14
25.3	odd	20		875.2.n.b.799.4		56
25.4	even	10		875.2.h.b.701.6		28
25.6	even	5		175.2.h.b.36.2	✓	28
25.8	odd	20		875.2.n.b.449.11		56
25.17	odd	20		875.2.n.b.449.4		56
25.19	even	10		875.2.h.b.176.6		28
25.21	even	5		175.2.h.b.141.2	yes	28
25.22	odd	20		875.2.n.b.799.11		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.h.b.36.2	✓	28	25.6	even	5
175.2.h.b.141.2	yes	28	25.21	even	5
875.2.h.b.176.6		28	25.19	even	10
875.2.h.b.701.6		28	25.4	even	10
875.2.n.b.449.4		56	25.17	odd	20
875.2.n.b.449.11		56	25.8	odd	20
875.2.n.b.799.4		56	25.3	odd	20
875.2.n.b.799.11		56	25.22	odd	20
4375.2.a.g.1.10		14	1.1	even	1	trivial
4375.2.a.h.1.5		14	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:	\( N \)	\(=\)	\( 4375 = 5^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4375.a (trivial)

\(f(q)\)	\(=\)	\(q+1.59048 q^{2} -0.991912 q^{3} +0.529618 q^{4} -1.57761 q^{6} -1.00000 q^{7} -2.33861 q^{8} -2.01611 q^{9} +O(q^{10})\)	\(q+1.59048 q^{2} -0.991912 q^{3} +0.529618 q^{4} -1.57761 q^{6} -1.00000 q^{7} -2.33861 q^{8} -2.01611 q^{9} +1.36842 q^{11} -0.525335 q^{12} +6.17505 q^{13} -1.59048 q^{14} -4.77874 q^{16} +4.19129 q^{17} -3.20658 q^{18} -4.06393 q^{19} +0.991912 q^{21} +2.17643 q^{22} +2.92951 q^{23} +2.31969 q^{24} +9.82128 q^{26} +4.97554 q^{27} -0.529618 q^{28} -6.28689 q^{29} +1.91200 q^{31} -2.92326 q^{32} -1.35735 q^{33} +6.66615 q^{34} -1.06777 q^{36} -11.6020 q^{37} -6.46359 q^{38} -6.12511 q^{39} -3.27696 q^{41} +1.57761 q^{42} +5.62950 q^{43} +0.724738 q^{44} +4.65932 q^{46} -10.4189 q^{47} +4.74009 q^{48} +1.00000 q^{49} -4.15739 q^{51} +3.27042 q^{52} -4.71551 q^{53} +7.91348 q^{54} +2.33861 q^{56} +4.03106 q^{57} -9.99916 q^{58} -0.586172 q^{59} +12.1062 q^{61} +3.04100 q^{62} +2.01611 q^{63} +4.90810 q^{64} -2.15883 q^{66} -8.03234 q^{67} +2.21978 q^{68} -2.90582 q^{69} +9.27682 q^{71} +4.71489 q^{72} -2.65930 q^{73} -18.4527 q^{74} -2.15233 q^{76} -1.36842 q^{77} -9.74184 q^{78} +1.45661 q^{79} +1.11303 q^{81} -5.21192 q^{82} -14.7230 q^{83} +0.525335 q^{84} +8.95360 q^{86} +6.23604 q^{87} -3.20019 q^{88} -6.64967 q^{89} -6.17505 q^{91} +1.55152 q^{92} -1.89654 q^{93} -16.5710 q^{94} +2.89962 q^{96} -3.06640 q^{97} +1.59048 q^{98} -2.75888 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} - 3 q^{3} + 12 q^{4} + 15 q^{6} - 14 q^{7} - 6 q^{8} + 15 q^{9}+O(q^{10}) \) 14 * q - 2 * q^2 - 3 * q^3 + 12 * q^4 + 15 * q^6 - 14 * q^7 - 6 * q^8 + 15 * q^9	\( 14 q - 2 q^{2} - 3 q^{3} + 12 q^{4} + 15 q^{6} - 14 q^{7} - 6 q^{8} + 15 q^{9} + 6 q^{11} - 14 q^{12} + q^{13} + 2 q^{14} - 12 q^{16} - 23 q^{17} - 31 q^{18} - 4 q^{19} + 3 q^{21} - 19 q^{22} - 22 q^{23} + 19 q^{24} - 4 q^{26} - 3 q^{27} - 12 q^{28} + 14 q^{29} - 8 q^{31} - 24 q^{32} - 9 q^{33} + 35 q^{34} + 27 q^{36} - 15 q^{37} - 5 q^{38} - 38 q^{39} - 15 q^{41} - 15 q^{42} - 9 q^{43} - 55 q^{44} - 2 q^{46} - 38 q^{47} - 28 q^{48} + 14 q^{49} + q^{51} + 18 q^{52} - 27 q^{53} + 28 q^{54} + 6 q^{56} - 31 q^{57} - 29 q^{58} + 3 q^{59} - 9 q^{61} - 11 q^{62} - 15 q^{63} - 10 q^{64} - 87 q^{66} + 3 q^{67} - 57 q^{68} + 3 q^{69} + 31 q^{71} - 25 q^{72} - 41 q^{73} + 35 q^{74} - 3 q^{76} - 6 q^{77} - 13 q^{78} + 59 q^{79} - 50 q^{81} - 13 q^{82} + 8 q^{83} + 14 q^{84} + 25 q^{86} - 40 q^{87} + 26 q^{88} - 31 q^{89} - q^{91} + 5 q^{92} - 48 q^{93} - 29 q^{94} + 21 q^{96} - 34 q^{97} - 2 q^{98} + 31 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 - 3 * q^3 + 12 * q^4 + 15 * q^6 - 14 * q^7 - 6 * q^8 + 15 * q^9 + 6 * q^11 - 14 * q^12 + q^13 + 2 * q^14 - 12 * q^16 - 23 * q^17 - 31 * q^18 - 4 * q^19 + 3 * q^21 - 19 * q^22 - 22 * q^23 + 19 * q^24 - 4 * q^26 - 3 * q^27 - 12 * q^28 + 14 * q^29 - 8 * q^31 - 24 * q^32 - 9 * q^33 + 35 * q^34 + 27 * q^36 - 15 * q^37 - 5 * q^38 - 38 * q^39 - 15 * q^41 - 15 * q^42 - 9 * q^43 - 55 * q^44 - 2 * q^46 - 38 * q^47 - 28 * q^48 + 14 * q^49 + q^51 + 18 * q^52 - 27 * q^53 + 28 * q^54 + 6 * q^56 - 31 * q^57 - 29 * q^58 + 3 * q^59 - 9 * q^61 - 11 * q^62 - 15 * q^63 - 10 * q^64 - 87 * q^66 + 3 * q^67 - 57 * q^68 + 3 * q^69 + 31 * q^71 - 25 * q^72 - 41 * q^73 + 35 * q^74 - 3 * q^76 - 6 * q^77 - 13 * q^78 + 59 * q^79 - 50 * q^81 - 13 * q^82 + 8 * q^83 + 14 * q^84 + 25 * q^86 - 40 * q^87 + 26 * q^88 - 31 * q^89 - q^91 + 5 * q^92 - 48 * q^93 - 29 * q^94 + 21 * q^96 - 34 * q^97 - 2 * q^98 + 31 * q^99

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