LMFDB - Embedded newform 4025.2.a.bc.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, 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("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.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:	$32.1397868136$
Analytic rank:	$0$
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} - 3 x^{13} - 18 x^{12} + 58 x^{11} + 111 x^{10} - 414 x^{9} - 244 x^{8} + 1330 x^{7} - 27 x^{6} + \cdots - 9 $ x^14 - 3x^13 - 18x^12 + 58x^11 + 111x^10 - 414x^9 - 244x^8 + 1330x^7 - 27x^6 - 1853x^5 + 539x^4 + 891x^3 - 218x^2 - 133*x - 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$1.31920$ of defining polynomial
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.31920 q^{2} +2.92477 q^{3} -0.259709 q^{4} +3.85835 q^{6} +1.00000 q^{7} -2.98101 q^{8} +5.55425 q^{9} +O(q^{10})$	\(q+1.31920 q^{2} +2.92477 q^{3} -0.259709 q^{4} +3.85835 q^{6} +1.00000 q^{7} -2.98101 q^{8} +5.55425 q^{9} +0.868311 q^{11} -0.759589 q^{12} +6.38750 q^{13} +1.31920 q^{14} -3.41313 q^{16} -1.51452 q^{17} +7.32717 q^{18} +6.70540 q^{19} +2.92477 q^{21} +1.14548 q^{22} +1.00000 q^{23} -8.71876 q^{24} +8.42639 q^{26} +7.47058 q^{27} -0.259709 q^{28} -6.03716 q^{29} -8.00792 q^{31} +1.45941 q^{32} +2.53961 q^{33} -1.99796 q^{34} -1.44249 q^{36} -0.642278 q^{37} +8.84576 q^{38} +18.6819 q^{39} +2.73351 q^{41} +3.85835 q^{42} -2.06872 q^{43} -0.225509 q^{44} +1.31920 q^{46} +6.47726 q^{47} -9.98261 q^{48} +1.00000 q^{49} -4.42963 q^{51} -1.65889 q^{52} -0.149052 q^{53} +9.85520 q^{54} -2.98101 q^{56} +19.6117 q^{57} -7.96423 q^{58} +7.34394 q^{59} +2.26843 q^{61} -10.5641 q^{62} +5.55425 q^{63} +8.75152 q^{64} +3.35025 q^{66} -15.1477 q^{67} +0.393336 q^{68} +2.92477 q^{69} -10.8820 q^{71} -16.5573 q^{72} +2.05467 q^{73} -0.847294 q^{74} -1.74145 q^{76} +0.868311 q^{77} +24.6452 q^{78} +13.1616 q^{79} +5.18695 q^{81} +3.60605 q^{82} +7.99279 q^{83} -0.759589 q^{84} -2.72906 q^{86} -17.6573 q^{87} -2.58844 q^{88} +8.46919 q^{89} +6.38750 q^{91} -0.259709 q^{92} -23.4213 q^{93} +8.54481 q^{94} +4.26844 q^{96} -6.18936 q^{97} +1.31920 q^{98} +4.82282 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 3 q^{2} + 4 q^{3} + 17 q^{4} - 4 q^{6} + 14 q^{7} + 3 q^{8} + 18 q^{9}+O(q^{10}) $ 14 * q + 3 * q^2 + 4 * q^3 + 17 * q^4 - 4 * q^6 + 14 * q^7 + 3 * q^8 + 18 * q^9	$ 14 q + 3 q^{2} + 4 q^{3} + 17 q^{4} - 4 q^{6} + 14 q^{7} + 3 q^{8} + 18 q^{9} + 5 q^{11} + 17 q^{12} + 11 q^{13} + 3 q^{14} + 23 q^{16} + 3 q^{17} + 15 q^{18} - 2 q^{19} + 4 q^{21} + 23 q^{22} + 14 q^{23} - 12 q^{24} - 9 q^{26} + 25 q^{27} + 17 q^{28} + 7 q^{29} - 3 q^{31} + 24 q^{32} + 6 q^{33} - 14 q^{34} + 13 q^{36} + 22 q^{37} + 20 q^{38} - 10 q^{39} - 17 q^{41} - 4 q^{42} + 18 q^{43} + 28 q^{44} + 3 q^{46} + 30 q^{47} + 8 q^{48} + 14 q^{49} + 4 q^{51} + 8 q^{52} + 11 q^{53} + 20 q^{54} + 3 q^{56} + 18 q^{57} + 38 q^{58} - 22 q^{59} - 8 q^{61} - 22 q^{62} + 18 q^{63} + 29 q^{64} - 9 q^{66} + 39 q^{67} + q^{68} + 4 q^{69} - 5 q^{71} - 24 q^{72} + 18 q^{73} + 35 q^{74} - 41 q^{76} + 5 q^{77} - 22 q^{78} + 10 q^{79} + 2 q^{81} - 8 q^{82} + 24 q^{83} + 17 q^{84} - 26 q^{86} + 5 q^{87} + 58 q^{88} + 25 q^{89} + 11 q^{91} + 17 q^{92} + 47 q^{93} - 2 q^{94} - 117 q^{96} + 43 q^{97} + 3 q^{98} + 55 q^{99}+O(q^{100}) $ 14 * q + 3 * q^2 + 4 * q^3 + 17 * q^4 - 4 * q^6 + 14 * q^7 + 3 * q^8 + 18 * q^9 + 5 * q^11 + 17 * q^12 + 11 * q^13 + 3 * q^14 + 23 * q^16 + 3 * q^17 + 15 * q^18 - 2 * q^19 + 4 * q^21 + 23 * q^22 + 14 * q^23 - 12 * q^24 - 9 * q^26 + 25 * q^27 + 17 * q^28 + 7 * q^29 - 3 * q^31 + 24 * q^32 + 6 * q^33 - 14 * q^34 + 13 * q^36 + 22 * q^37 + 20 * q^38 - 10 * q^39 - 17 * q^41 - 4 * q^42 + 18 * q^43 + 28 * q^44 + 3 * q^46 + 30 * q^47 + 8 * q^48 + 14 * q^49 + 4 * q^51 + 8 * q^52 + 11 * q^53 + 20 * q^54 + 3 * q^56 + 18 * q^57 + 38 * q^58 - 22 * q^59 - 8 * q^61 - 22 * q^62 + 18 * q^63 + 29 * q^64 - 9 * q^66 + 39 * q^67 + q^68 + 4 * q^69 - 5 * q^71 - 24 * q^72 + 18 * q^73 + 35 * q^74 - 41 * q^76 + 5 * q^77 - 22 * q^78 + 10 * q^79 + 2 * q^81 - 8 * q^82 + 24 * q^83 + 17 * q^84 - 26 * q^86 + 5 * q^87 + 58 * q^88 + 25 * q^89 + 11 * q^91 + 17 * q^92 + 47 * q^93 - 2 * q^94 - 117 * q^96 + 43 * q^97 + 3 * q^98 + 55 * 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 $

$2$	1.31920	0.932816	0.466408	−	0.884570i	$-0.345548\pi$
$2$	1.31920	0.932816	0.466408	+	0.884570i	$0.345548\pi$
$3$	2.92477	1.68861	0.844307	−	0.535860i	$-0.180012\pi$
$3$	2.92477	1.68861	0.844307	+	0.535860i	$0.180012\pi$
$4$	−0.259709	−0.129855
$5$	0	0
$5$	0	0
$6$	3.85835	1.57517
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.98101	−1.05395
$9$	5.55425	1.85142
$10$	0	0
$11$	0.868311	0.261806	0.130903	−	0.991395i	$-0.458212\pi$
$11$	0.868311	0.261806	0.130903	+	0.991395i	$0.458212\pi$
$12$	−0.759589	−0.219275
$13$	6.38750	1.77157	0.885787	−	0.464092i	$-0.153619\pi$
$13$	6.38750	1.77157	0.885787	+	0.464092i	$0.153619\pi$
$14$	1.31920	0.352571
$15$	0	0
$16$	−3.41313	−0.853283
$17$	−1.51452	−0.367326	−0.183663	−	0.982989i	$-0.558795\pi$
$17$	−1.51452	−0.367326	−0.183663	+	0.982989i	$0.558795\pi$
$18$	7.32717	1.72703
$19$	6.70540	1.53832	0.769162	−	0.639054i	$-0.220674\pi$
$19$	6.70540	1.53832	0.769162	+	0.639054i	$0.220674\pi$
$20$	0	0
$21$	2.92477	0.638236
$22$	1.14548	0.244216
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−8.71876	−1.77971
$25$	0	0
$26$	8.42639	1.65255
$27$	7.47058	1.43771
$28$	−0.259709	−0.0490805
$29$	−6.03716	−1.12107	−0.560537	−	0.828130i	$-0.689405\pi$
$29$	−6.03716	−1.12107	−0.560537	+	0.828130i	$0.689405\pi$
$30$	0	0
$31$	−8.00792	−1.43826	−0.719132	−	0.694873i	$-0.755461\pi$
$31$	−8.00792	−1.43826	−0.719132	+	0.694873i	$0.755461\pi$
$32$	1.45941	0.257990
$33$	2.53961	0.442089
$34$	−1.99796	−0.342647
$35$	0	0
$36$	−1.44249	−0.240415
$37$	−0.642278	−0.105590	−0.0527949	−	0.998605i	$-0.516813\pi$
$37$	−0.642278	−0.105590	−0.0527949	+	0.998605i	$0.516813\pi$
$38$	8.84576	1.43497
$39$	18.6819	2.99150
$40$	0	0
$41$	2.73351	0.426903	0.213451	−	0.976954i	$-0.431530\pi$
$41$	2.73351	0.426903	0.213451	+	0.976954i	$0.431530\pi$
$42$	3.85835	0.595357
$43$	−2.06872	−0.315477	−0.157738	−	0.987481i	$-0.550420\pi$
$43$	−2.06872	−0.315477	−0.157738	+	0.987481i	$0.550420\pi$
$44$	−0.225509	−0.0339967
$45$	0	0
$46$	1.31920	0.194506
$47$	6.47726	0.944806	0.472403	−	0.881383i	$-0.343387\pi$
$47$	6.47726	0.944806	0.472403	+	0.881383i	$0.343387\pi$
$48$	−9.98261	−1.44087
$49$	1.00000	0.142857
$50$	0	0
$51$	−4.42963	−0.620272
$52$	−1.65889	−0.230047
$53$	−0.149052	−0.0204739	−0.0102369	−	0.999948i	$-0.503259\pi$
$53$	−0.149052	−0.0204739	−0.0102369	+	0.999948i	$0.503259\pi$
$54$	9.85520	1.34112
$55$	0	0
$56$	−2.98101	−0.398354
$57$	19.6117	2.59763
$58$	−7.96423	−1.04575
$59$	7.34394	0.956100	0.478050	−	0.878333i	$-0.341344\pi$
$59$	7.34394	0.956100	0.478050	+	0.878333i	$0.341344\pi$
$60$	0	0
$61$	2.26843	0.290442	0.145221	−	0.989399i	$-0.453611\pi$
$61$	2.26843	0.290442	0.145221	+	0.989399i	$0.453611\pi$
$62$	−10.5641	−1.34164
$63$	5.55425	0.699770
$64$	8.75152	1.09394
$65$	0	0
$66$	3.35025	0.412387
$67$	−15.1477	−1.85059	−0.925295	−	0.379249i	$-0.876182\pi$
$67$	−15.1477	−1.85059	−0.925295	+	0.379249i	$0.876182\pi$
$68$	0.393336	0.0476990
$69$	2.92477	0.352100
$70$	0	0
$71$	−10.8820	−1.29145	−0.645727	−	0.763568i	$-0.723446\pi$
$71$	−10.8820	−1.29145	−0.645727	+	0.763568i	$0.723446\pi$
$72$	−16.5573	−1.95129
$73$	2.05467	0.240481	0.120241	−	0.992745i	$-0.461633\pi$
$73$	2.05467	0.240481	0.120241	+	0.992745i	$0.461633\pi$
$74$	−0.847294	−0.0984959
$75$	0	0
$76$	−1.74145	−0.199759
$77$	0.868311	0.0989532
$78$	24.6452	2.79052
$79$	13.1616	1.48080	0.740399	−	0.672168i	$-0.234637\pi$
$79$	13.1616	1.48080	0.740399	+	0.672168i	$0.234637\pi$
$80$	0	0
$81$	5.18695	0.576328
$82$	3.60605	0.398221
$83$	7.99279	0.877323	0.438661	−	0.898652i	$-0.355453\pi$
$83$	7.99279	0.877323	0.438661	+	0.898652i	$0.355453\pi$
$84$	−0.759589	−0.0828780
$85$	0	0
$86$	−2.72906	−0.294282
$87$	−17.6573	−1.89306
$88$	−2.58844	−0.275929
$89$	8.46919	0.897732	0.448866	−	0.893599i	$-0.351828\pi$
$89$	8.46919	0.897732	0.448866	+	0.893599i	$0.351828\pi$
$90$	0	0
$91$	6.38750	0.669592
$92$	−0.259709	−0.0270766
$93$	−23.4213	−2.42867
$94$	8.54481	0.881330
$95$	0	0
$96$	4.26844	0.435646
$97$	−6.18936	−0.628435	−0.314217	−	0.949351i	$-0.601742\pi$
$97$	−6.18936	−0.628435	−0.314217	+	0.949351i	$0.601742\pi$
$98$	1.31920	0.133259
$99$	4.82282	0.484711
$100$	0	0
$101$	9.31297	0.926675	0.463338	−	0.886182i	$-0.346652\pi$
$101$	9.31297	0.926675	0.463338	+	0.886182i	$0.346652\pi$
$102$	−5.84357	−0.578599
$103$	4.05608	0.399658	0.199829	−	0.979831i	$-0.435961\pi$
$103$	4.05608	0.399658	0.199829	+	0.979831i	$0.435961\pi$
$104$	−19.0412	−1.86714
$105$	0	0
$106$	−0.196629	−0.0190983
$107$	6.80490	0.657855	0.328927	−	0.944355i	$-0.393313\pi$
$107$	6.80490	0.657855	0.328927	+	0.944355i	$0.393313\pi$
$108$	−1.94018	−0.186694
$109$	8.75082	0.838177	0.419088	−	0.907945i	$-0.362350\pi$
$109$	8.75082	0.838177	0.419088	+	0.907945i	$0.362350\pi$
$110$	0	0
$111$	−1.87851	−0.178301
$112$	−3.41313	−0.322511
$113$	−13.1530	−1.23733	−0.618666	−	0.785654i	$-0.712327\pi$
$113$	−13.1530	−1.23733	−0.618666	+	0.785654i	$0.712327\pi$
$114$	25.8718	2.42311
$115$	0	0
$116$	1.56791	0.145577
$117$	35.4778	3.27992
$118$	9.68813	0.891865
$119$	−1.51452	−0.138836
$120$	0	0
$121$	−10.2460	−0.931458
$122$	2.99251	0.270929
$123$	7.99488	0.720874
$124$	2.07973	0.186765
$125$	0	0
$126$	7.32717	0.652756
$127$	4.89344	0.434223	0.217111	−	0.976147i	$-0.430337\pi$
$127$	4.89344	0.434223	0.217111	+	0.976147i	$0.430337\pi$
$128$	8.62619	0.762455
$129$	−6.05052	−0.532719
$130$	0	0
$131$	1.81951	0.158971	0.0794855	−	0.996836i	$-0.474672\pi$
$131$	1.81951	0.158971	0.0794855	+	0.996836i	$0.474672\pi$
$132$	−0.659560	−0.0574073
$133$	6.70540	0.581432
$134$	−19.9829	−1.72626
$135$	0	0
$136$	4.51481	0.387142
$137$	−17.7257	−1.51441	−0.757203	−	0.653180i	$-0.773435\pi$
$137$	−17.7257	−1.51441	−0.757203	+	0.653180i	$0.773435\pi$
$138$	3.85835	0.328445
$139$	−7.05663	−0.598535	−0.299268	−	0.954169i	$-0.596742\pi$
$139$	−7.05663	−0.598535	−0.299268	+	0.954169i	$0.596742\pi$
$140$	0	0
$141$	18.9445	1.59541
$142$	−14.3555	−1.20469
$143$	5.54634	0.463808
$144$	−18.9574	−1.57978
$145$	0	0
$146$	2.71053	0.224325
$147$	2.92477	0.241231
$148$	0.166806	0.0137113
$149$	11.7254	0.960578	0.480289	−	0.877110i	$-0.340532\pi$
$149$	11.7254	0.960578	0.480289	+	0.877110i	$0.340532\pi$
$150$	0	0
$151$	15.5657	1.26671	0.633357	−	0.773859i	$-0.281676\pi$
$151$	15.5657	1.26671	0.633357	+	0.773859i	$0.281676\pi$
$152$	−19.9889	−1.62131
$153$	−8.41204	−0.680073
$154$	1.14548	0.0923051
$155$	0	0
$156$	−4.85188	−0.388461
$157$	13.2451	1.05708	0.528539	−	0.848909i	$-0.322740\pi$
$157$	13.2451	1.05708	0.528539	+	0.848909i	$0.322740\pi$
$158$	17.3628	1.38131
$159$	−0.435942	−0.0345724
$160$	0	0
$161$	1.00000	0.0788110
$162$	6.84263	0.537608
$163$	−14.0268	−1.09867	−0.549334	−	0.835603i	$-0.685118\pi$
$163$	−14.0268	−1.09867	−0.549334	+	0.835603i	$0.685118\pi$
$164$	−0.709918	−0.0554353
$165$	0	0
$166$	10.5441	0.818380
$167$	−16.0378	−1.24104	−0.620521	−	0.784190i	$-0.713079\pi$
$167$	−16.0378	−1.24104	−0.620521	+	0.784190i	$0.713079\pi$
$168$	−8.71876	−0.672667
$169$	27.8002	2.13847
$170$	0	0
$171$	37.2435	2.84808
$172$	0.537266	0.0409662
$173$	9.87355	0.750672	0.375336	−	0.926889i	$-0.377527\pi$
$173$	9.87355	0.750672	0.375336	+	0.926889i	$0.377527\pi$
$174$	−23.2935	−1.76588
$175$	0	0
$176$	−2.96366	−0.223394
$177$	21.4793	1.61448
$178$	11.1726	0.837419
$179$	−18.6861	−1.39666	−0.698331	−	0.715775i	$-0.746073\pi$
$179$	−18.6861	−1.39666	−0.698331	+	0.715775i	$0.746073\pi$
$180$	0	0
$181$	7.69198	0.571741	0.285870	−	0.958268i	$-0.407717\pi$
$181$	7.69198	0.571741	0.285870	+	0.958268i	$0.407717\pi$
$182$	8.42639	0.624606
$183$	6.63462	0.490445
$184$	−2.98101	−0.219763
$185$	0	0
$186$	−30.8974	−2.26551
$187$	−1.31508	−0.0961680
$188$	−1.68221	−0.122688
$189$	7.47058	0.543405
$190$	0	0
$191$	−22.4874	−1.62713	−0.813567	−	0.581471i	$-0.802477\pi$
$191$	−22.4874	−1.62713	−0.813567	+	0.581471i	$0.802477\pi$
$192$	25.5962	1.84724
$193$	−11.1608	−0.803372	−0.401686	−	0.915778i	$-0.631576\pi$
$193$	−11.1608	−0.803372	−0.401686	+	0.915778i	$0.631576\pi$
$194$	−8.16501	−0.586214
$195$	0	0
$196$	−0.259709	−0.0185507
$197$	−22.2357	−1.58423	−0.792115	−	0.610371i	$-0.791020\pi$
$197$	−22.2357	−1.58423	−0.792115	+	0.610371i	$0.791020\pi$
$198$	6.36226	0.452146
$199$	−2.09717	−0.148665	−0.0743323	−	0.997234i	$-0.523683\pi$
$199$	−2.09717	−0.148665	−0.0743323	+	0.997234i	$0.523683\pi$
$200$	0	0
$201$	−44.3035	−3.12493
$202$	12.2857	0.864417
$203$	−6.03716	−0.423726
$204$	1.15042	0.0805452
$205$	0	0
$206$	5.35079	0.372807
$207$	5.55425	0.386047
$208$	−21.8014	−1.51165
$209$	5.82237	0.402742
$210$	0	0
$211$	−19.3289	−1.33066	−0.665330	−	0.746549i	$-0.731709\pi$
$211$	−19.3289	−1.33066	−0.665330	+	0.746549i	$0.731709\pi$
$212$	0.0387102	0.00265863
$213$	−31.8273	−2.18077
$214$	8.97703	0.613657
$215$	0	0
$216$	−22.2699	−1.51527
$217$	−8.00792	−0.543613
$218$	11.5441	0.781864
$219$	6.00944	0.406080
$220$	0	0
$221$	−9.67402	−0.650745
$222$	−2.47814	−0.166322
$223$	9.13897	0.611991	0.305995	−	0.952033i	$-0.401011\pi$
$223$	9.13897	0.611991	0.305995	+	0.952033i	$0.401011\pi$
$224$	1.45941	0.0975112
$225$	0	0
$226$	−17.3515	−1.15420
$227$	10.6284	0.705434	0.352717	−	0.935730i	$-0.385258\pi$
$227$	10.6284	0.705434	0.352717	+	0.935730i	$0.385258\pi$
$228$	−5.09335	−0.337315
$229$	−18.6150	−1.23011	−0.615057	−	0.788482i	$-0.710867\pi$
$229$	−18.6150	−1.23011	−0.615057	+	0.788482i	$0.710867\pi$
$230$	0	0
$231$	2.53961	0.167094
$232$	17.9968	1.18155
$233$	6.02705	0.394845	0.197423	−	0.980318i	$-0.436743\pi$
$233$	6.02705	0.394845	0.197423	+	0.980318i	$0.436743\pi$
$234$	46.8023	3.05956
$235$	0	0
$236$	−1.90729	−0.124154
$237$	38.4947	2.50050
$238$	−1.99796	−0.129509
$239$	2.13377	0.138022	0.0690110	−	0.997616i	$-0.478016\pi$
$239$	2.13377	0.138022	0.0690110	+	0.997616i	$0.478016\pi$
$240$	0	0
$241$	1.80263	0.116117	0.0580587	−	0.998313i	$-0.481509\pi$
$241$	1.80263	0.116117	0.0580587	+	0.998313i	$0.481509\pi$
$242$	−13.5166	−0.868879
$243$	−7.24114	−0.464519
$244$	−0.589132	−0.0377153
$245$	0	0
$246$	10.5468	0.672442
$247$	42.8307	2.72525
$248$	23.8717	1.51585
$249$	23.3770	1.48146
$250$	0	0
$251$	−27.8767	−1.75956	−0.879781	−	0.475380i	$-0.842311\pi$
$251$	−27.8767	−1.75956	−0.879781	+	0.475380i	$0.842311\pi$
$252$	−1.44249	−0.0908684
$253$	0.868311	0.0545902
$254$	6.45543	0.405050
$255$	0	0
$256$	−6.12337	−0.382711
$257$	−10.7703	−0.671830	−0.335915	−	0.941892i	$-0.609046\pi$
$257$	−10.7703	−0.671830	−0.335915	+	0.941892i	$0.609046\pi$
$258$	−7.98185	−0.496928
$259$	−0.642278	−0.0399092
$260$	0	0
$261$	−33.5319	−2.07557
$262$	2.40029	0.148291
$263$	−25.4961	−1.57215	−0.786077	−	0.618128i	$-0.787891\pi$
$263$	−25.4961	−1.57215	−0.786077	+	0.618128i	$0.787891\pi$
$264$	−7.57059	−0.465938
$265$	0	0
$266$	8.84576	0.542369
$267$	24.7704	1.51592
$268$	3.93401	0.240308
$269$	−0.290767	−0.0177284	−0.00886420	−	0.999961i	$-0.502822\pi$
$269$	−0.290767	−0.0177284	−0.00886420	+	0.999961i	$0.502822\pi$
$270$	0	0
$271$	−6.68541	−0.406109	−0.203055	−	0.979167i	$-0.565087\pi$
$271$	−6.68541	−0.406109	−0.203055	+	0.979167i	$0.565087\pi$
$272$	5.16927	0.313433
$273$	18.6819	1.13068
$274$	−23.3837	−1.41266
$275$	0	0
$276$	−0.759589	−0.0457219
$277$	−22.1955	−1.33360	−0.666800	−	0.745237i	$-0.732336\pi$
$277$	−22.1955	−1.33360	−0.666800	+	0.745237i	$0.732336\pi$
$278$	−9.30911	−0.558323
$279$	−44.4780	−2.66283
$280$	0	0
$281$	−24.4533	−1.45876	−0.729381	−	0.684107i	$-0.760192\pi$
$281$	−24.4533	−1.45876	−0.729381	+	0.684107i	$0.760192\pi$
$282$	24.9916	1.48823
$283$	27.9586	1.66197	0.830983	−	0.556298i	$-0.187779\pi$
$283$	27.9586	1.66197	0.830983	+	0.556298i	$0.187779\pi$
$284$	2.82616	0.167701
$285$	0	0
$286$	7.31673	0.432647
$287$	2.73351	0.161354
$288$	8.10595	0.477648
$289$	−14.7062	−0.865072
$290$	0	0
$291$	−18.1024	−1.06118
$292$	−0.533618	−0.0312277
$293$	8.50236	0.496713	0.248357	−	0.968669i	$-0.420110\pi$
$293$	8.50236	0.496713	0.248357	+	0.968669i	$0.420110\pi$
$294$	3.85835	0.225024
$295$	0	0
$296$	1.91464	0.111286
$297$	6.48679	0.376402
$298$	15.4681	0.896042
$299$	6.38750	0.369399
$300$	0	0
$301$	−2.06872	−0.119239
$302$	20.5342	1.18161
$303$	27.2383	1.56480
$304$	−22.8864	−1.31263
$305$	0	0
$306$	−11.0972	−0.634383
$307$	24.0852	1.37462	0.687309	−	0.726365i	$-0.258792\pi$
$307$	24.0852	1.37462	0.687309	+	0.726365i	$0.258792\pi$
$308$	−0.225509	−0.0128495
$309$	11.8631	0.674868
$310$	0	0
$311$	−15.7156	−0.891150	−0.445575	−	0.895245i	$-0.647001\pi$
$311$	−15.7156	−0.891150	−0.445575	+	0.895245i	$0.647001\pi$
$312$	−55.6910	−3.15288
$313$	12.7181	0.718871	0.359436	−	0.933170i	$-0.382969\pi$
$313$	12.7181	0.718871	0.359436	+	0.933170i	$0.382969\pi$
$314$	17.4730	0.986059
$315$	0	0
$316$	−3.41820	−0.192289
$317$	−22.2744	−1.25106	−0.625529	−	0.780201i	$-0.715117\pi$
$317$	−22.2744	−1.25106	−0.625529	+	0.780201i	$0.715117\pi$
$318$	−0.575095	−0.0322497
$319$	−5.24214	−0.293503
$320$	0	0
$321$	19.9027	1.11086
$322$	1.31920	0.0735162
$323$	−10.1555	−0.565066
$324$	−1.34710	−0.0748389
$325$	0	0
$326$	−18.5042	−1.02485
$327$	25.5941	1.41536
$328$	−8.14862	−0.449932
$329$	6.47726	0.357103
$330$	0	0
$331$	−0.897778	−0.0493463	−0.0246732	−	0.999696i	$-0.507855\pi$
$331$	−0.897778	−0.0493463	−0.0246732	+	0.999696i	$0.507855\pi$
$332$	−2.07580	−0.113925
$333$	−3.56737	−0.195491
$334$	−21.1571	−1.15766
$335$	0	0
$336$	−9.98261	−0.544596
$337$	30.4611	1.65932	0.829662	−	0.558266i	$-0.188533\pi$
$337$	30.4611	1.65932	0.829662	+	0.558266i	$0.188533\pi$
$338$	36.6740	1.99480
$339$	−38.4695	−2.08938
$340$	0	0
$341$	−6.95336	−0.376546
$342$	49.1316	2.65673
$343$	1.00000	0.0539949
$344$	6.16688	0.332496
$345$	0	0
$346$	13.0252	0.700238
$347$	−19.8987	−1.06822	−0.534109	−	0.845415i	$-0.679353\pi$
$347$	−19.8987	−1.06822	−0.534109	+	0.845415i	$0.679353\pi$
$348$	4.58576	0.245823
$349$	−33.7467	−1.80642	−0.903211	−	0.429198i	$-0.858796\pi$
$349$	−33.7467	−1.80642	−0.903211	+	0.429198i	$0.858796\pi$
$350$	0	0
$351$	47.7184	2.54702
$352$	1.26723	0.0675433
$353$	−16.0139	−0.852335	−0.426168	−	0.904644i	$-0.640137\pi$
$353$	−16.0139	−0.852335	−0.426168	+	0.904644i	$0.640137\pi$
$354$	28.3355	1.50602
$355$	0	0
$356$	−2.19953	−0.116575
$357$	−4.42963	−0.234441
$358$	−24.6507	−1.30283
$359$	−24.8046	−1.30914	−0.654569	−	0.756002i	$-0.727150\pi$
$359$	−24.8046	−1.30914	−0.654569	+	0.756002i	$0.727150\pi$
$360$	0	0
$361$	25.9623	1.36644
$362$	10.1473	0.533329
$363$	−29.9672	−1.57287
$364$	−1.65889	−0.0869497
$365$	0	0
$366$	8.75240	0.457495
$367$	7.66912	0.400325	0.200162	−	0.979763i	$-0.435853\pi$
$367$	7.66912	0.400325	0.200162	+	0.979763i	$0.435853\pi$
$368$	−3.41313	−0.177922
$369$	15.1826	0.790375
$370$	0	0
$371$	−0.149052	−0.00773839
$372$	6.08273	0.315375
$373$	−16.1482	−0.836124	−0.418062	−	0.908418i	$-0.637291\pi$
$373$	−16.1482	−0.836124	−0.418062	+	0.908418i	$0.637291\pi$
$374$	−1.73485	−0.0897070
$375$	0	0
$376$	−19.3088	−0.995775
$377$	−38.5624	−1.98606
$378$	9.85520	0.506897
$379$	28.2469	1.45095	0.725474	−	0.688250i	$-0.241621\pi$
$379$	28.2469	1.45095	0.725474	+	0.688250i	$0.241621\pi$
$380$	0	0
$381$	14.3122	0.733235
$382$	−29.6654	−1.51782
$383$	21.3320	1.09001	0.545006	−	0.838432i	$-0.316527\pi$
$383$	21.3320	1.09001	0.545006	+	0.838432i	$0.316527\pi$
$384$	25.2296	1.28749
$385$	0	0
$386$	−14.7233	−0.749398
$387$	−11.4902	−0.584079
$388$	1.60744	0.0816052
$389$	33.1646	1.68151	0.840757	−	0.541413i	$-0.182110\pi$
$389$	33.1646	1.68151	0.840757	+	0.541413i	$0.182110\pi$
$390$	0	0
$391$	−1.51452	−0.0765927
$392$	−2.98101	−0.150564
$393$	5.32163	0.268441
$394$	−29.3334	−1.47780
$395$	0	0
$396$	−1.25253	−0.0629421
$397$	−25.2573	−1.26763	−0.633813	−	0.773486i	$-0.718511\pi$
$397$	−25.2573	−1.26763	−0.633813	+	0.773486i	$0.718511\pi$
$398$	−2.76659	−0.138677
$399$	19.6117	0.981813
$400$	0	0
$401$	4.85880	0.242637	0.121319	−	0.992614i	$-0.461288\pi$
$401$	4.85880	0.242637	0.121319	+	0.992614i	$0.461288\pi$
$402$	−58.4453	−2.91498
$403$	−51.1506	−2.54799
$404$	−2.41867	−0.120333
$405$	0	0
$406$	−7.96423	−0.395258
$407$	−0.557697	−0.0276440
$408$	13.2048	0.653733
$409$	−27.0926	−1.33964	−0.669820	−	0.742523i	$-0.733629\pi$
$409$	−27.0926	−1.33964	−0.669820	+	0.742523i	$0.733629\pi$
$410$	0	0
$411$	−51.8434	−2.55725
$412$	−1.05340	−0.0518974
$413$	7.34394	0.361372
$414$	7.32717	0.360111
$415$	0	0
$416$	9.32201	0.457049
$417$	−20.6390	−1.01069
$418$	7.68087	0.375684
$419$	−23.6925	−1.15745	−0.578727	−	0.815522i	$-0.696450\pi$
$419$	−23.6925	−1.15745	−0.578727	+	0.815522i	$0.696450\pi$
$420$	0	0
$421$	−26.4688	−1.29001	−0.645005	−	0.764179i	$-0.723145\pi$
$421$	−26.4688	−1.29001	−0.645005	+	0.764179i	$0.723145\pi$
$422$	−25.4988	−1.24126
$423$	35.9763	1.74923
$424$	0.444325	0.0215783
$425$	0	0
$426$	−41.9866	−2.03426
$427$	2.26843	0.109777
$428$	−1.76730	−0.0854255
$429$	16.2217	0.783192
$430$	0	0
$431$	−6.80682	−0.327873	−0.163937	−	0.986471i	$-0.552419\pi$
$431$	−6.80682	−0.327873	−0.163937	+	0.986471i	$0.552419\pi$
$432$	−25.4981	−1.22678
$433$	−19.2022	−0.922799	−0.461399	−	0.887192i	$-0.652653\pi$
$433$	−19.2022	−0.922799	−0.461399	+	0.887192i	$0.652653\pi$
$434$	−10.5641	−0.507091
$435$	0	0
$436$	−2.27267	−0.108841
$437$	6.70540	0.320763
$438$	7.92766	0.378798
$439$	18.8757	0.900890	0.450445	−	0.892804i	$-0.351265\pi$
$439$	18.8757	0.900890	0.450445	+	0.892804i	$0.351265\pi$
$440$	0	0
$441$	5.55425	0.264488
$442$	−12.7620	−0.607025
$443$	−26.1317	−1.24155	−0.620777	−	0.783987i	$-0.713183\pi$
$443$	−26.1317	−1.24155	−0.620777	+	0.783987i	$0.713183\pi$
$444$	0.487868	0.0231532
$445$	0	0
$446$	12.0561	0.570875
$447$	34.2939	1.62205
$448$	8.75152	0.413471
$449$	−16.6696	−0.786686	−0.393343	−	0.919392i	$-0.628681\pi$
$449$	−16.6696	−0.786686	−0.393343	+	0.919392i	$0.628681\pi$
$450$	0	0
$451$	2.37354	0.111765
$452$	3.41597	0.160674
$453$	45.5259	2.13899
$454$	14.0210	0.658040
$455$	0	0
$456$	−58.4627	−2.73777
$457$	−0.813011	−0.0380311	−0.0190155	−	0.999819i	$-0.506053\pi$
$457$	−0.813011	−0.0380311	−0.0190155	+	0.999819i	$0.506053\pi$
$458$	−24.5569	−1.14747
$459$	−11.3144	−0.528110
$460$	0	0
$461$	31.2050	1.45336	0.726682	−	0.686974i	$-0.241061\pi$
$461$	31.2050	1.45336	0.726682	+	0.686974i	$0.241061\pi$
$462$	3.35025	0.155868
$463$	8.66426	0.402663	0.201331	−	0.979523i	$-0.435473\pi$
$463$	8.66426	0.402663	0.201331	+	0.979523i	$0.435473\pi$
$464$	20.6056	0.956593
$465$	0	0
$466$	7.95089	0.368318
$467$	1.58947	0.0735520	0.0367760	−	0.999324i	$-0.488291\pi$
$467$	1.58947	0.0735520	0.0367760	+	0.999324i	$0.488291\pi$
$468$	−9.21391	−0.425913
$469$	−15.1477	−0.699457
$470$	0	0
$471$	38.7389	1.78500
$472$	−21.8924	−1.00768
$473$	−1.79629	−0.0825936
$474$	50.7822	2.33250
$475$	0	0
$476$	0.393336	0.0180285
$477$	−0.827872	−0.0379056
$478$	2.81487	0.128749
$479$	−2.92907	−0.133833	−0.0669163	−	0.997759i	$-0.521316\pi$
$479$	−2.92907	−0.133833	−0.0669163	+	0.997759i	$0.521316\pi$
$480$	0	0
$481$	−4.10255	−0.187060
$482$	2.37803	0.108316
$483$	2.92477	0.133081
$484$	2.66099	0.120954
$485$	0	0
$486$	−9.55252	−0.433311
$487$	3.65957	0.165831	0.0829154	−	0.996557i	$-0.473577\pi$
$487$	3.65957	0.165831	0.0829154	+	0.996557i	$0.473577\pi$
$488$	−6.76221	−0.306111
$489$	−41.0252	−1.85523
$490$	0	0
$491$	30.2239	1.36399	0.681993	−	0.731359i	$-0.261114\pi$
$491$	30.2239	1.36399	0.681993	+	0.731359i	$0.261114\pi$
$492$	−2.07634	−0.0936089
$493$	9.14343	0.411799
$494$	56.5023	2.54216
$495$	0	0
$496$	27.3321	1.22725
$497$	−10.8820	−0.488124
$498$	30.8390	1.38193
$499$	−36.2393	−1.62229	−0.811147	−	0.584842i	$-0.801156\pi$
$499$	−36.2393	−1.62229	−0.811147	+	0.584842i	$0.801156\pi$
$500$	0	0
$501$	−46.9068	−2.09564
$502$	−36.7750	−1.64135
$503$	20.6137	0.919119	0.459559	−	0.888147i	$-0.348007\pi$
$503$	20.6137	0.919119	0.459559	+	0.888147i	$0.348007\pi$
$504$	−16.5573	−0.737520
$505$	0	0
$506$	1.14548	0.0509226
$507$	81.3089	3.61106
$508$	−1.27087	−0.0563859
$509$	7.86152	0.348456	0.174228	−	0.984705i	$-0.444257\pi$
$509$	7.86152	0.348456	0.174228	+	0.984705i	$0.444257\pi$
$510$	0	0
$511$	2.05467	0.0908935
$512$	−25.3303	−1.11945
$513$	50.0932	2.21167
$514$	−14.2081	−0.626694
$515$	0	0
$516$	1.57138	0.0691760
$517$	5.62428	0.247355
$518$	−0.847294	−0.0372280
$519$	28.8778	1.26759
$520$	0	0
$521$	38.4336	1.68380	0.841902	−	0.539630i	$-0.181436\pi$
$521$	38.4336	1.68380	0.841902	+	0.539630i	$0.181436\pi$
$522$	−44.2353	−1.93613
$523$	−25.6662	−1.12230	−0.561152	−	0.827713i	$-0.689642\pi$
$523$	−25.6662	−1.12230	−0.561152	+	0.827713i	$0.689642\pi$
$524$	−0.472543	−0.0206431
$525$	0	0
$526$	−33.6344	−1.46653
$527$	12.1282	0.528312
$528$	−8.66801	−0.377227
$529$	1.00000	0.0434783
$530$	0	0
$531$	40.7901	1.77014
$532$	−1.74145	−0.0755016
$533$	17.4603	0.756289
$534$	32.6771	1.41408
$535$	0	0
$536$	45.1555	1.95042
$537$	−54.6523	−2.35842
$538$	−0.383581	−0.0165373
$539$	0.868311	0.0374008
$540$	0	0
$541$	20.5155	0.882030	0.441015	−	0.897500i	$-0.354619\pi$
$541$	20.5155	0.882030	0.441015	+	0.897500i	$0.354619\pi$
$542$	−8.81939	−0.378825
$543$	22.4972	0.965449
$544$	−2.21032	−0.0947666
$545$	0	0
$546$	24.6452	1.05472
$547$	33.6480	1.43868	0.719342	−	0.694656i	$-0.244443\pi$
$547$	33.6480	1.43868	0.719342	+	0.694656i	$0.244443\pi$
$548$	4.60352	0.196653
$549$	12.5994	0.537730
$550$	0	0
$551$	−40.4816	−1.72457
$552$	−8.71876	−0.371095
$553$	13.1616	0.559689
$554$	−29.2803	−1.24400
$555$	0	0
$556$	1.83267	0.0777226
$557$	17.8611	0.756801	0.378400	−	0.925642i	$-0.376474\pi$
$557$	17.8611	0.756801	0.378400	+	0.925642i	$0.376474\pi$
$558$	−58.6754	−2.48393
$559$	−13.2140	−0.558891
$560$	0	0
$561$	−3.84629	−0.162391
$562$	−32.2588	−1.36076
$563$	29.7505	1.25383	0.626917	−	0.779086i	$-0.284316\pi$
$563$	29.7505	1.25383	0.626917	+	0.779086i	$0.284316\pi$
$564$	−4.92006	−0.207172
$565$	0	0
$566$	36.8830	1.55031
$567$	5.18695	0.217831
$568$	32.4393	1.36112
$569$	−41.6993	−1.74812	−0.874062	−	0.485814i	$-0.838523\pi$
$569$	−41.6993	−1.74812	−0.874062	+	0.485814i	$0.838523\pi$
$570$	0	0
$571$	27.1132	1.13465	0.567327	−	0.823493i	$-0.307978\pi$
$571$	27.1132	1.13465	0.567327	+	0.823493i	$0.307978\pi$
$572$	−1.44044	−0.0602277
$573$	−65.7705	−2.74760
$574$	3.60605	0.150514
$575$	0	0
$576$	48.6082	2.02534
$577$	6.01146	0.250260	0.125130	−	0.992140i	$-0.460065\pi$
$577$	6.01146	0.250260	0.125130	+	0.992140i	$0.460065\pi$
$578$	−19.4005	−0.806953
$579$	−32.6427	−1.35658
$580$	0	0
$581$	7.99279	0.331597
$582$	−23.8807	−0.989889
$583$	−0.129423	−0.00536017
$584$	−6.12501	−0.253455
$585$	0	0
$586$	11.2163	0.463342
$587$	−28.4080	−1.17252	−0.586261	−	0.810122i	$-0.699401\pi$
$587$	−28.4080	−1.17252	−0.586261	+	0.810122i	$0.699401\pi$
$588$	−0.759589	−0.0313249
$589$	−53.6963	−2.21252
$590$	0	0
$591$	−65.0343	−2.67515
$592$	2.19218	0.0900981
$593$	−1.03848	−0.0426454	−0.0213227	−	0.999773i	$-0.506788\pi$
$593$	−1.03848	−0.0426454	−0.0213227	+	0.999773i	$0.506788\pi$
$594$	8.55738	0.351113
$595$	0	0
$596$	−3.04518	−0.124736
$597$	−6.13373	−0.251037
$598$	8.42639	0.344581
$599$	−26.1530	−1.06858	−0.534292	−	0.845300i	$-0.679422\pi$
$599$	−26.1530	−1.06858	−0.534292	+	0.845300i	$0.679422\pi$
$600$	0	0
$601$	−34.0822	−1.39024	−0.695122	−	0.718892i	$-0.744649\pi$
$601$	−34.0822	−1.39024	−0.695122	+	0.718892i	$0.744649\pi$
$602$	−2.72906	−0.111228
$603$	−84.1343	−3.42621
$604$	−4.04255	−0.164489
$605$	0	0
$606$	35.9327	1.45967
$607$	43.4665	1.76425	0.882125	−	0.471016i	$-0.156113\pi$
$607$	43.4665	1.76425	0.882125	+	0.471016i	$0.156113\pi$
$608$	9.78595	0.396873
$609$	−17.6573	−0.715509
$610$	0	0
$611$	41.3735	1.67379
$612$	2.18469	0.0883108
$613$	24.1027	0.973498	0.486749	−	0.873542i	$-0.338183\pi$
$613$	24.1027	0.973498	0.486749	+	0.873542i	$0.338183\pi$
$614$	31.7733	1.28226
$615$	0	0
$616$	−2.58844	−0.104291
$617$	2.76763	0.111421	0.0557103	−	0.998447i	$-0.482258\pi$
$617$	2.76763	0.111421	0.0557103	+	0.998447i	$0.482258\pi$
$618$	15.6498	0.629527
$619$	22.0412	0.885913	0.442956	−	0.896543i	$-0.353930\pi$
$619$	22.0412	0.885913	0.442956	+	0.896543i	$0.353930\pi$
$620$	0	0
$621$	7.47058	0.299784
$622$	−20.7320	−0.831279
$623$	8.46919	0.339311
$624$	−63.7639	−2.55260
$625$	0	0
$626$	16.7778	0.670574
$627$	17.0291	0.680075
$628$	−3.43989	−0.137267
$629$	0.972746	0.0387859
$630$	0	0
$631$	24.9191	0.992014	0.496007	−	0.868318i	$-0.334799\pi$
$631$	24.9191	0.992014	0.496007	+	0.868318i	$0.334799\pi$
$632$	−39.2349	−1.56068
$633$	−56.5326	−2.24697
$634$	−29.3845	−1.16701
$635$	0	0
$636$	0.113218	0.00448939
$637$	6.38750	0.253082
$638$	−6.91543	−0.273784
$639$	−60.4413	−2.39102
$640$	0	0
$641$	−9.33424	−0.368680	−0.184340	−	0.982863i	$-0.559015\pi$
$641$	−9.33424	−0.368680	−0.184340	+	0.982863i	$0.559015\pi$
$642$	26.2557	1.03623
$643$	43.2724	1.70650	0.853248	−	0.521506i	$-0.174629\pi$
$643$	43.2724	1.70650	0.853248	+	0.521506i	$0.174629\pi$
$644$	−0.259709	−0.0102340
$645$	0	0
$646$	−13.3971	−0.527103
$647$	−0.808444	−0.0317832	−0.0158916	−	0.999874i	$-0.505059\pi$
$647$	−0.808444	−0.0317832	−0.0158916	+	0.999874i	$0.505059\pi$
$648$	−15.4624	−0.607419
$649$	6.37683	0.250312
$650$	0	0
$651$	−23.4213	−0.917952
$652$	3.64291	0.142667
$653$	2.29590	0.0898454	0.0449227	−	0.998990i	$-0.485696\pi$
$653$	2.29590	0.0898454	0.0449227	+	0.998990i	$0.485696\pi$
$654$	33.7637	1.32027
$655$	0	0
$656$	−9.32983	−0.364269
$657$	11.4122	0.445231
$658$	8.54481	0.333111
$659$	−24.6811	−0.961439	−0.480719	−	0.876874i	$-0.659624\pi$
$659$	−24.6811	−0.961439	−0.480719	+	0.876874i	$0.659624\pi$
$660$	0	0
$661$	0.918584	0.0357288	0.0178644	−	0.999840i	$-0.494313\pi$
$661$	0.918584	0.0357288	0.0178644	+	0.999840i	$0.494313\pi$
$662$	−1.18435	−0.0460310
$663$	−28.2942	−1.09886
$664$	−23.8266	−0.924651
$665$	0	0
$666$	−4.70608	−0.182357
$667$	−6.03716	−0.233760
$668$	4.16517	0.161155
$669$	26.7293	1.03342
$670$	0	0
$671$	1.96970	0.0760395
$672$	4.26844	0.164659
$673$	35.1370	1.35443	0.677217	−	0.735784i	$-0.263186\pi$
$673$	35.1370	1.35443	0.677217	+	0.735784i	$0.263186\pi$
$674$	40.1844	1.54784
$675$	0	0
$676$	−7.21996	−0.277691
$677$	1.59262	0.0612092	0.0306046	−	0.999532i	$-0.490257\pi$
$677$	1.59262	0.0612092	0.0306046	+	0.999532i	$0.490257\pi$
$678$	−50.7490	−1.94900
$679$	−6.18936	−0.237526
$680$	0	0
$681$	31.0857	1.19121
$682$	−9.17288	−0.351248
$683$	6.66803	0.255145	0.127573	−	0.991829i	$-0.459281\pi$
$683$	6.66803	0.255145	0.127573	+	0.991829i	$0.459281\pi$
$684$	−9.67248	−0.369836
$685$	0	0
$686$	1.31920	0.0503673
$687$	−54.4445	−2.07719
$688$	7.06082	0.269191
$689$	−0.952069	−0.0362709
$690$	0	0
$691$	47.3256	1.80035	0.900175	−	0.435528i	$-0.143438\pi$
$691$	47.3256	1.80035	0.900175	+	0.435528i	$0.143438\pi$
$692$	−2.56425	−0.0974783
$693$	4.82282	0.183204
$694$	−26.2504	−0.996451
$695$	0	0
$696$	52.6366	1.99518
$697$	−4.13997	−0.156812
$698$	−44.5187	−1.68506
$699$	17.6277	0.666741
$700$	0	0
$701$	44.8261	1.69306	0.846530	−	0.532341i	$-0.178688\pi$
$701$	44.8261	1.69306	0.846530	+	0.532341i	$0.178688\pi$
$702$	62.9501	2.37590
$703$	−4.30673	−0.162431
$704$	7.59904	0.286400
$705$	0	0
$706$	−21.1256	−0.795072
$707$	9.31297	0.350250
$708$	−5.57838	−0.209648
$709$	23.8243	0.894742	0.447371	−	0.894349i	$-0.352360\pi$
$709$	23.8243	0.894742	0.447371	+	0.894349i	$0.352360\pi$
$710$	0	0
$711$	73.1029	2.74157
$712$	−25.2467	−0.946162
$713$	−8.00792	−0.299899
$714$	−5.84357	−0.218690
$715$	0	0
$716$	4.85295	0.181363
$717$	6.24077	0.233066
$718$	−32.7223	−1.22119
$719$	45.6319	1.70178	0.850890	−	0.525343i	$-0.176063\pi$
$719$	45.6319	1.70178	0.850890	+	0.525343i	$0.176063\pi$
$720$	0	0
$721$	4.05608	0.151056
$722$	34.2495	1.27464
$723$	5.27226	0.196078
$724$	−1.99768	−0.0742432
$725$	0	0
$726$	−39.5328	−1.46720
$727$	−9.19379	−0.340979	−0.170489	−	0.985360i	$-0.554535\pi$
$727$	−9.19379	−0.340979	−0.170489	+	0.985360i	$0.554535\pi$
$728$	−19.0412	−0.705714
$729$	−36.7395	−1.36072
$730$	0	0
$731$	3.13313	0.115883
$732$	−1.72307	−0.0636866
$733$	14.4617	0.534154	0.267077	−	0.963675i	$-0.413942\pi$
$733$	14.4617	0.534154	0.267077	+	0.963675i	$0.413942\pi$
$734$	10.1171	0.373429
$735$	0	0
$736$	1.45941	0.0537947
$737$	−13.1529	−0.484495
$738$	20.0289	0.737274
$739$	−18.6183	−0.684887	−0.342443	−	0.939538i	$-0.611254\pi$
$739$	−18.6183	−0.684887	−0.342443	+	0.939538i	$0.611254\pi$
$740$	0	0
$741$	125.270	4.60190
$742$	−0.196629	−0.00721849
$743$	13.5139	0.495778	0.247889	−	0.968788i	$-0.420263\pi$
$743$	13.5139	0.495778	0.247889	+	0.968788i	$0.420263\pi$
$744$	69.8191	2.55969
$745$	0	0
$746$	−21.3028	−0.779950
$747$	44.3940	1.62429
$748$	0.341538	0.0124879
$749$	6.80490	0.248646
$750$	0	0
$751$	−45.6930	−1.66736	−0.833681	−	0.552247i	$-0.813771\pi$
$751$	−45.6930	−1.66736	−0.833681	+	0.552247i	$0.813771\pi$
$752$	−22.1078	−0.806187
$753$	−81.5328	−2.97122
$754$	−50.8715	−1.85263
$755$	0	0
$756$	−1.94018	−0.0705637
$757$	26.9591	0.979846	0.489923	−	0.871766i	$-0.337025\pi$
$757$	26.9591	0.979846	0.489923	+	0.871766i	$0.337025\pi$
$758$	37.2634	1.35347
$759$	2.53961	0.0921818
$760$	0	0
$761$	−45.2806	−1.64142	−0.820709	−	0.571346i	$-0.806421\pi$
$761$	−45.2806	−1.64142	−0.820709	+	0.571346i	$0.806421\pi$
$762$	18.8806	0.683973
$763$	8.75082	0.316801
$764$	5.84020	0.211291
$765$	0	0
$766$	28.1411	1.01678
$767$	46.9094	1.69380
$768$	−17.9094	−0.646251
$769$	43.3929	1.56479	0.782393	−	0.622785i	$-0.213999\pi$
$769$	43.3929	1.56479	0.782393	+	0.622785i	$0.213999\pi$
$770$	0	0
$771$	−31.5005	−1.13446
$772$	2.89856	0.104322
$773$	−12.0192	−0.432300	−0.216150	−	0.976360i	$-0.569350\pi$
$773$	−12.0192	−0.432300	−0.216150	+	0.976360i	$0.569350\pi$
$774$	−15.1579	−0.544838
$775$	0	0
$776$	18.4506	0.662336
$777$	−1.87851	−0.0673913
$778$	43.7508	1.56854
$779$	18.3293	0.656714
$780$	0	0
$781$	−9.44895	−0.338110
$782$	−1.99796	−0.0714469
$783$	−45.1011	−1.61178
$784$	−3.41313	−0.121898
$785$	0	0
$786$	7.02030	0.250406
$787$	−23.5521	−0.839542	−0.419771	−	0.907630i	$-0.637890\pi$
$787$	−23.5521	−0.839542	−0.419771	+	0.907630i	$0.637890\pi$
$788$	5.77483	0.205720
$789$	−74.5700	−2.65476
$790$	0	0
$791$	−13.1530	−0.467668
$792$	−14.3769	−0.510860
$793$	14.4896	0.514540
$794$	−33.3194	−1.18246
$795$	0	0
$796$	0.544655	0.0193048
$797$	15.0266	0.532269	0.266134	−	0.963936i	$-0.414253\pi$
$797$	15.0266	0.532269	0.266134	+	0.963936i	$0.414253\pi$
$798$	25.8718	0.915851
$799$	−9.80997	−0.347052
$800$	0	0
$801$	47.0400	1.66208
$802$	6.40974	0.226336
$803$	1.78410	0.0629594
$804$	11.5060	0.405787
$805$	0	0
$806$	−67.4779	−2.37681
$807$	−0.850426	−0.0299364
$808$	−27.7621	−0.976666
$809$	−0.100900	−0.00354745	−0.00177373	−	0.999998i	$-0.500565\pi$
$809$	−0.100900	−0.00354745	−0.00177373	+	0.999998i	$0.500565\pi$
$810$	0	0
$811$	26.4645	0.929295	0.464647	−	0.885496i	$-0.346181\pi$
$811$	26.4645	0.929295	0.464647	+	0.885496i	$0.346181\pi$
$812$	1.56791	0.0550228
$813$	−19.5532	−0.685762
$814$	−0.735715	−0.0257868
$815$	0	0
$816$	15.1189	0.529267
$817$	−13.8716	−0.485306
$818$	−35.7405	−1.24964
$819$	35.4778	1.23969
$820$	0	0
$821$	30.1197	1.05118	0.525592	−	0.850737i	$-0.323844\pi$
$821$	30.1197	1.05118	0.525592	+	0.850737i	$0.323844\pi$
$822$	−68.3918	−2.38544
$823$	17.4202	0.607231	0.303616	−	0.952795i	$-0.401806\pi$
$823$	17.4202	0.607231	0.303616	+	0.952795i	$0.401806\pi$
$824$	−12.0912	−0.421218
$825$	0	0
$826$	9.68813	0.337093
$827$	−37.7595	−1.31303	−0.656513	−	0.754315i	$-0.727969\pi$
$827$	−37.7595	−1.31303	−0.656513	+	0.754315i	$0.727969\pi$
$828$	−1.44249	−0.0501300
$829$	0.696165	0.0241788	0.0120894	−	0.999927i	$-0.496152\pi$
$829$	0.696165	0.0241788	0.0120894	+	0.999927i	$0.496152\pi$
$830$	0	0
$831$	−64.9167	−2.25193
$832$	55.9004	1.93800
$833$	−1.51452	−0.0524751
$834$	−27.2270	−0.942792
$835$	0	0
$836$	−1.51212	−0.0522979
$837$	−59.8238	−2.06781
$838$	−31.2551	−1.07969
$839$	−50.4825	−1.74285	−0.871424	−	0.490530i	$-0.836803\pi$
$839$	−50.4825	−1.74285	−0.871424	+	0.490530i	$0.836803\pi$
$840$	0	0
$841$	7.44735	0.256805
$842$	−34.9176	−1.20334
$843$	−71.5202	−2.46329
$844$	5.01991	0.172792
$845$	0	0
$846$	47.4600	1.63171
$847$	−10.2460	−0.352058
$848$	0.508734	0.0174700
$849$	81.7723	2.80642
$850$	0	0
$851$	−0.642278	−0.0220170
$852$	8.26584	0.283183
$853$	29.4981	1.01000	0.504998	−	0.863120i	$-0.331493\pi$
$853$	29.4981	1.01000	0.504998	+	0.863120i	$0.331493\pi$
$854$	2.99251	0.102402
$855$	0	0
$856$	−20.2855	−0.693343
$857$	18.7919	0.641921	0.320960	−	0.947093i	$-0.395994\pi$
$857$	18.7919	0.641921	0.320960	+	0.947093i	$0.395994\pi$
$858$	21.3997	0.730574
$859$	−4.97637	−0.169792	−0.0848958	−	0.996390i	$-0.527056\pi$
$859$	−4.97637	−0.169792	−0.0848958	+	0.996390i	$0.527056\pi$
$860$	0	0
$861$	7.99488	0.272465
$862$	−8.97957	−0.305845
$863$	49.6259	1.68929	0.844643	−	0.535331i	$-0.179813\pi$
$863$	49.6259	1.68929	0.844643	+	0.535331i	$0.179813\pi$
$864$	10.9027	0.370917
$865$	0	0
$866$	−25.3316	−0.860801
$867$	−43.0122	−1.46077
$868$	2.07973	0.0705907
$869$	11.4284	0.387681
$870$	0	0
$871$	−96.7561	−3.27846
$872$	−26.0863	−0.883393
$873$	−34.3773	−1.16349
$874$	8.84576	0.299212
$875$	0	0
$876$	−1.56071	−0.0527315
$877$	−0.793789	−0.0268043	−0.0134022	−	0.999910i	$-0.504266\pi$
$877$	−0.793789	−0.0268043	−0.0134022	+	0.999910i	$0.504266\pi$
$878$	24.9009	0.840365
$879$	24.8674	0.838757
$880$	0	0
$881$	56.2971	1.89670	0.948349	−	0.317227i	$-0.102752\pi$
$881$	56.2971	1.89670	0.948349	+	0.317227i	$0.102752\pi$
$882$	7.32717	0.246719
$883$	15.9848	0.537930	0.268965	−	0.963150i	$-0.413318\pi$
$883$	15.9848	0.537930	0.268965	+	0.963150i	$0.413318\pi$
$884$	2.51243	0.0845023
$885$	0	0
$886$	−34.4730	−1.15814
$887$	−35.0663	−1.17741	−0.588705	−	0.808348i	$-0.700362\pi$
$887$	−35.0663	−1.17741	−0.588705	+	0.808348i	$0.700362\pi$
$888$	5.59987	0.187919
$889$	4.89344	0.164121
$890$	0	0
$891$	4.50389	0.150886
$892$	−2.37348	−0.0794699
$893$	43.4326	1.45342
$894$	45.2405	1.51307
$895$	0	0
$896$	8.62619	0.288181
$897$	18.6819	0.623772
$898$	−21.9905	−0.733833
$899$	48.3451	1.61240
$900$	0	0
$901$	0.225743	0.00752058
$902$	3.13117	0.104257
$903$	−6.05052	−0.201349
$904$	39.2093	1.30408
$905$	0	0
$906$	60.0578	1.99529
$907$	25.1166	0.833983	0.416991	−	0.908910i	$-0.363084\pi$
$907$	25.1166	0.833983	0.416991	+	0.908910i	$0.363084\pi$
$908$	−2.76030	−0.0916039
$909$	51.7266	1.71566
$910$	0	0
$911$	13.4685	0.446231	0.223115	−	0.974792i	$-0.428377\pi$
$911$	13.4685	0.446231	0.223115	+	0.974792i	$0.428377\pi$
$912$	−66.9374	−2.21652
$913$	6.94023	0.229688
$914$	−1.07252	−0.0354760
$915$	0	0
$916$	4.83449	0.159736
$917$	1.81951	0.0600854
$918$	−14.9259	−0.492629
$919$	−36.6860	−1.21016	−0.605080	−	0.796165i	$-0.706859\pi$
$919$	−36.6860	−1.21016	−0.605080	+	0.796165i	$0.706859\pi$
$920$	0	0
$921$	70.4437	2.32120
$922$	41.1657	1.35572
$923$	−69.5087	−2.28791
$924$	−0.659560	−0.0216979
$925$	0	0
$926$	11.4299	0.375610
$927$	22.5285	0.739933
$928$	−8.81072	−0.289226
$929$	−4.37991	−0.143700	−0.0718500	−	0.997415i	$-0.522890\pi$
$929$	−4.37991	−0.143700	−0.0718500	+	0.997415i	$0.522890\pi$
$930$	0	0
$931$	6.70540	0.219760
$932$	−1.56528	−0.0512725
$933$	−45.9645	−1.50481
$934$	2.09683	0.0686104
$935$	0	0
$936$	−105.760	−3.45686
$937$	−25.7783	−0.842140	−0.421070	−	0.907028i	$-0.638345\pi$
$937$	−25.7783	−0.842140	−0.421070	+	0.907028i	$0.638345\pi$
$938$	−19.9829	−0.652464
$939$	37.1975	1.21390
$940$	0	0
$941$	−11.8254	−0.385496	−0.192748	−	0.981248i	$-0.561740\pi$
$941$	−11.8254	−0.385496	−0.192748	+	0.981248i	$0.561740\pi$
$942$	51.1044	1.66507
$943$	2.73351	0.0890153
$944$	−25.0658	−0.815824
$945$	0	0
$946$	−2.36967	−0.0770446
$947$	−10.3688	−0.336942	−0.168471	−	0.985707i	$-0.553883\pi$
$947$	−10.3688	−0.336942	−0.168471	+	0.985707i	$0.553883\pi$
$948$	−9.99743	−0.324701
$949$	13.1242	0.426031
$950$	0	0
$951$	−65.1475	−2.11255
$952$	4.51481	0.146326
$953$	50.9028	1.64890	0.824451	−	0.565933i	$-0.191484\pi$
$953$	50.9028	1.64890	0.824451	+	0.565933i	$0.191484\pi$
$954$	−1.09213	−0.0353590
$955$	0	0
$956$	−0.554160	−0.0179228
$957$	−15.3320	−0.495614
$958$	−3.86403	−0.124841
$959$	−17.7257	−0.572391
$960$	0	0
$961$	33.1268	1.06861
$962$	−5.41209	−0.174493
$963$	37.7961	1.21796
$964$	−0.468159	−0.0150784
$965$	0	0
$966$	3.85835	0.124140
$967$	26.2198	0.843172	0.421586	−	0.906789i	$-0.361474\pi$
$967$	26.2198	0.843172	0.421586	+	0.906789i	$0.361474\pi$
$968$	30.5435	0.981707
$969$	−29.7024	−0.954178
$970$	0	0
$971$	1.27436	0.0408962	0.0204481	−	0.999791i	$-0.493491\pi$
$971$	1.27436	0.0408962	0.0204481	+	0.999791i	$0.493491\pi$
$972$	1.88059	0.0603200
$973$	−7.05663	−0.226225
$974$	4.82770	0.154690
$975$	0	0
$976$	−7.74245	−0.247830
$977$	45.4142	1.45293	0.726465	−	0.687203i	$-0.241162\pi$
$977$	45.4142	1.45293	0.726465	+	0.687203i	$0.241162\pi$
$978$	−54.1205	−1.73058
$979$	7.35389	0.235031
$980$	0	0
$981$	48.6043	1.55181
$982$	39.8714	1.27235
$983$	−13.8715	−0.442432	−0.221216	−	0.975225i	$-0.571003\pi$
$983$	−13.8715	−0.442432	−0.221216	+	0.975225i	$0.571003\pi$
$984$	−23.8328	−0.759762
$985$	0	0
$986$	12.0620	0.384133
$987$	18.9445	0.603009
$988$	−11.1235	−0.353887
$989$	−2.06872	−0.0657815
$990$	0	0
$991$	−20.7205	−0.658208	−0.329104	−	0.944294i	$-0.606747\pi$
$991$	−20.7205	−0.658208	−0.329104	+	0.944294i	$0.606747\pi$
$992$	−11.6869	−0.371059
$993$	−2.62579	−0.0833269
$994$	−14.3555	−0.455330
$995$	0	0
$996$	−6.07124	−0.192375
$997$	20.9813	0.664485	0.332242	−	0.943194i	$-0.392195\pi$
$997$	20.9813	0.664485	0.332242	+	0.943194i	$0.392195\pi$
$998$	−47.8069	−1.51330
$999$	−4.79819	−0.151808

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.bc.1.10	yes	14
5.4	even	2		4025.2.a.z.1.5	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4025.2.a.z.1.5	✓	14	5.4	even	2
4025.2.a.bc.1.10	yes	14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q+1.31920 q^{2} +2.92477 q^{3} -0.259709 q^{4} +3.85835 q^{6} +1.00000 q^{7} -2.98101 q^{8} +5.55425 q^{9} +O(q^{10})\)	\(q+1.31920 q^{2} +2.92477 q^{3} -0.259709 q^{4} +3.85835 q^{6} +1.00000 q^{7} -2.98101 q^{8} +5.55425 q^{9} +0.868311 q^{11} -0.759589 q^{12} +6.38750 q^{13} +1.31920 q^{14} -3.41313 q^{16} -1.51452 q^{17} +7.32717 q^{18} +6.70540 q^{19} +2.92477 q^{21} +1.14548 q^{22} +1.00000 q^{23} -8.71876 q^{24} +8.42639 q^{26} +7.47058 q^{27} -0.259709 q^{28} -6.03716 q^{29} -8.00792 q^{31} +1.45941 q^{32} +2.53961 q^{33} -1.99796 q^{34} -1.44249 q^{36} -0.642278 q^{37} +8.84576 q^{38} +18.6819 q^{39} +2.73351 q^{41} +3.85835 q^{42} -2.06872 q^{43} -0.225509 q^{44} +1.31920 q^{46} +6.47726 q^{47} -9.98261 q^{48} +1.00000 q^{49} -4.42963 q^{51} -1.65889 q^{52} -0.149052 q^{53} +9.85520 q^{54} -2.98101 q^{56} +19.6117 q^{57} -7.96423 q^{58} +7.34394 q^{59} +2.26843 q^{61} -10.5641 q^{62} +5.55425 q^{63} +8.75152 q^{64} +3.35025 q^{66} -15.1477 q^{67} +0.393336 q^{68} +2.92477 q^{69} -10.8820 q^{71} -16.5573 q^{72} +2.05467 q^{73} -0.847294 q^{74} -1.74145 q^{76} +0.868311 q^{77} +24.6452 q^{78} +13.1616 q^{79} +5.18695 q^{81} +3.60605 q^{82} +7.99279 q^{83} -0.759589 q^{84} -2.72906 q^{86} -17.6573 q^{87} -2.58844 q^{88} +8.46919 q^{89} +6.38750 q^{91} -0.259709 q^{92} -23.4213 q^{93} +8.54481 q^{94} +4.26844 q^{96} -6.18936 q^{97} +1.31920 q^{98} +4.82282 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 3 q^{2} + 4 q^{3} + 17 q^{4} - 4 q^{6} + 14 q^{7} + 3 q^{8} + 18 q^{9}+O(q^{10}) \) 14 * q + 3 * q^2 + 4 * q^3 + 17 * q^4 - 4 * q^6 + 14 * q^7 + 3 * q^8 + 18 * q^9	\( 14 q + 3 q^{2} + 4 q^{3} + 17 q^{4} - 4 q^{6} + 14 q^{7} + 3 q^{8} + 18 q^{9} + 5 q^{11} + 17 q^{12} + 11 q^{13} + 3 q^{14} + 23 q^{16} + 3 q^{17} + 15 q^{18} - 2 q^{19} + 4 q^{21} + 23 q^{22} + 14 q^{23} - 12 q^{24} - 9 q^{26} + 25 q^{27} + 17 q^{28} + 7 q^{29} - 3 q^{31} + 24 q^{32} + 6 q^{33} - 14 q^{34} + 13 q^{36} + 22 q^{37} + 20 q^{38} - 10 q^{39} - 17 q^{41} - 4 q^{42} + 18 q^{43} + 28 q^{44} + 3 q^{46} + 30 q^{47} + 8 q^{48} + 14 q^{49} + 4 q^{51} + 8 q^{52} + 11 q^{53} + 20 q^{54} + 3 q^{56} + 18 q^{57} + 38 q^{58} - 22 q^{59} - 8 q^{61} - 22 q^{62} + 18 q^{63} + 29 q^{64} - 9 q^{66} + 39 q^{67} + q^{68} + 4 q^{69} - 5 q^{71} - 24 q^{72} + 18 q^{73} + 35 q^{74} - 41 q^{76} + 5 q^{77} - 22 q^{78} + 10 q^{79} + 2 q^{81} - 8 q^{82} + 24 q^{83} + 17 q^{84} - 26 q^{86} + 5 q^{87} + 58 q^{88} + 25 q^{89} + 11 q^{91} + 17 q^{92} + 47 q^{93} - 2 q^{94} - 117 q^{96} + 43 q^{97} + 3 q^{98} + 55 q^{99}+O(q^{100}) \) 14 * q + 3 * q^2 + 4 * q^3 + 17 * q^4 - 4 * q^6 + 14 * q^7 + 3 * q^8 + 18 * q^9 + 5 * q^11 + 17 * q^12 + 11 * q^13 + 3 * q^14 + 23 * q^16 + 3 * q^17 + 15 * q^18 - 2 * q^19 + 4 * q^21 + 23 * q^22 + 14 * q^23 - 12 * q^24 - 9 * q^26 + 25 * q^27 + 17 * q^28 + 7 * q^29 - 3 * q^31 + 24 * q^32 + 6 * q^33 - 14 * q^34 + 13 * q^36 + 22 * q^37 + 20 * q^38 - 10 * q^39 - 17 * q^41 - 4 * q^42 + 18 * q^43 + 28 * q^44 + 3 * q^46 + 30 * q^47 + 8 * q^48 + 14 * q^49 + 4 * q^51 + 8 * q^52 + 11 * q^53 + 20 * q^54 + 3 * q^56 + 18 * q^57 + 38 * q^58 - 22 * q^59 - 8 * q^61 - 22 * q^62 + 18 * q^63 + 29 * q^64 - 9 * q^66 + 39 * q^67 + q^68 + 4 * q^69 - 5 * q^71 - 24 * q^72 + 18 * q^73 + 35 * q^74 - 41 * q^76 + 5 * q^77 - 22 * q^78 + 10 * q^79 + 2 * q^81 - 8 * q^82 + 24 * q^83 + 17 * q^84 - 26 * q^86 + 5 * q^87 + 58 * q^88 + 25 * q^89 + 11 * q^91 + 17 * q^92 + 47 * q^93 - 2 * q^94 - 117 * q^96 + 43 * q^97 + 3 * q^98 + 55 * q^99

Introduction

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