LMFDB - Embedded newform 6025.2.a.l.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, 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("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.14940 q^{2} +0.361587 q^{3} -0.678878 q^{4} -0.415609 q^{6} -3.63700 q^{7} +3.07910 q^{8} -2.86925 q^{9} +O(q^{10})$	\(q-1.14940 q^{2} +0.361587 q^{3} -0.678878 q^{4} -0.415609 q^{6} -3.63700 q^{7} +3.07910 q^{8} -2.86925 q^{9} -3.31008 q^{11} -0.245473 q^{12} +3.42302 q^{13} +4.18037 q^{14} -2.18137 q^{16} -0.605765 q^{17} +3.29792 q^{18} -1.21792 q^{19} -1.31509 q^{21} +3.80461 q^{22} +6.22482 q^{23} +1.11336 q^{24} -3.93442 q^{26} -2.12225 q^{27} +2.46908 q^{28} +3.29498 q^{29} +0.187069 q^{31} -3.65094 q^{32} -1.19688 q^{33} +0.696266 q^{34} +1.94787 q^{36} -0.174751 q^{37} +1.39988 q^{38} +1.23772 q^{39} +9.28617 q^{41} +1.51157 q^{42} -5.81664 q^{43} +2.24714 q^{44} -7.15482 q^{46} -3.12220 q^{47} -0.788755 q^{48} +6.22774 q^{49} -0.219037 q^{51} -2.32381 q^{52} +2.23321 q^{53} +2.43931 q^{54} -11.1987 q^{56} -0.440386 q^{57} -3.78725 q^{58} +6.04532 q^{59} +2.39259 q^{61} -0.215017 q^{62} +10.4355 q^{63} +8.55913 q^{64} +1.37570 q^{66} +5.48219 q^{67} +0.411240 q^{68} +2.25082 q^{69} +6.38307 q^{71} -8.83473 q^{72} -0.625385 q^{73} +0.200859 q^{74} +0.826821 q^{76} +12.0388 q^{77} -1.42264 q^{78} +6.61180 q^{79} +7.84039 q^{81} -10.6735 q^{82} -13.1244 q^{83} +0.892786 q^{84} +6.68566 q^{86} +1.19142 q^{87} -10.1921 q^{88} -1.26185 q^{89} -12.4495 q^{91} -4.22589 q^{92} +0.0676417 q^{93} +3.58866 q^{94} -1.32013 q^{96} +0.489708 q^{97} -7.15817 q^{98} +9.49746 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9}+O(q^{10}) $ 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9	$ 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9} + q^{11} - 14 q^{12} - 9 q^{13} - q^{14} + 43 q^{16} - 12 q^{17} - 42 q^{18} + 2 q^{21} - 5 q^{22} - 77 q^{23} - 2 q^{24} + 2 q^{26} - 38 q^{27} - 42 q^{28} + 2 q^{29} + q^{31} - 72 q^{32} - 20 q^{33} + 5 q^{34} + 32 q^{36} - 28 q^{37} - 23 q^{38} - 2 q^{39} - 2 q^{41} - 37 q^{42} - 31 q^{43} + 3 q^{44} + 14 q^{46} - 96 q^{47} - 13 q^{48} + 40 q^{49} - 10 q^{51} - 42 q^{52} - 54 q^{53} + 4 q^{54} - 15 q^{56} - 37 q^{57} - 27 q^{58} + q^{59} + 5 q^{61} - 39 q^{62} - 70 q^{63} + 65 q^{64} - 52 q^{66} - 34 q^{67} - 52 q^{68} + 21 q^{69} - 9 q^{71} - 70 q^{72} - 25 q^{73} + 22 q^{74} - 47 q^{76} - 54 q^{77} - 58 q^{78} + 13 q^{79} + 12 q^{81} + 5 q^{82} - 63 q^{83} + 95 q^{84} - 18 q^{86} - 47 q^{87} - 13 q^{88} + 19 q^{89} - 31 q^{91} - 137 q^{92} - 52 q^{93} + 120 q^{94} - 49 q^{96} - 36 q^{97} - 64 q^{98} + 16 q^{99}+O(q^{100}) $ 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9 + q^11 - 14 * q^12 - 9 * q^13 - q^14 + 43 * q^16 - 12 * q^17 - 42 * q^18 + 2 * q^21 - 5 * q^22 - 77 * q^23 - 2 * q^24 + 2 * q^26 - 38 * q^27 - 42 * q^28 + 2 * q^29 + q^31 - 72 * q^32 - 20 * q^33 + 5 * q^34 + 32 * q^36 - 28 * q^37 - 23 * q^38 - 2 * q^39 - 2 * q^41 - 37 * q^42 - 31 * q^43 + 3 * q^44 + 14 * q^46 - 96 * q^47 - 13 * q^48 + 40 * q^49 - 10 * q^51 - 42 * q^52 - 54 * q^53 + 4 * q^54 - 15 * q^56 - 37 * q^57 - 27 * q^58 + q^59 + 5 * q^61 - 39 * q^62 - 70 * q^63 + 65 * q^64 - 52 * q^66 - 34 * q^67 - 52 * q^68 + 21 * q^69 - 9 * q^71 - 70 * q^72 - 25 * q^73 + 22 * q^74 - 47 * q^76 - 54 * q^77 - 58 * q^78 + 13 * q^79 + 12 * q^81 + 5 * q^82 - 63 * q^83 + 95 * q^84 - 18 * q^86 - 47 * q^87 - 13 * q^88 + 19 * q^89 - 31 * q^91 - 137 * q^92 - 52 * q^93 + 120 * q^94 - 49 * q^96 - 36 * q^97 - 64 * q^98 + 16 * 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 $

$2$	−1.14940	−0.812749	−0.406375	−	0.913707i	$-0.633207\pi$
$2$	−1.14940	−0.812749	−0.406375	+	0.913707i	$0.633207\pi$
$3$	0.361587	0.208762	0.104381	−	0.994537i	$-0.466714\pi$
$3$	0.361587	0.208762	0.104381	+	0.994537i	$0.466714\pi$
$4$	−0.678878	−0.339439
$5$	0	0
$5$	0	0
$6$	−0.415609	−0.169672
$7$	−3.63700	−1.37466	−0.687328	−	0.726347i	$-0.741216\pi$
$7$	−3.63700	−1.37466	−0.687328	+	0.726347i	$0.741216\pi$
$8$	3.07910	1.08863
$9$	−2.86925	−0.956418
$10$	0	0
$11$	−3.31008	−0.998027	−0.499013	−	0.866594i	$-0.666304\pi$
$11$	−3.31008	−0.998027	−0.499013	+	0.866594i	$0.666304\pi$
$12$	−0.245473	−0.0708621
$13$	3.42302	0.949375	0.474687	−	0.880155i	$-0.342561\pi$
$13$	3.42302	0.949375	0.474687	+	0.880155i	$0.342561\pi$
$14$	4.18037	1.11725
$15$	0	0
$16$	−2.18137	−0.545342
$17$	−0.605765	−0.146919	−0.0734597	−	0.997298i	$-0.523404\pi$
$17$	−0.605765	−0.146919	−0.0734597	+	0.997298i	$0.523404\pi$
$18$	3.29792	0.777328
$19$	−1.21792	−0.279411	−0.139705	−	0.990193i	$-0.544616\pi$
$19$	−1.21792	−0.279411	−0.139705	+	0.990193i	$0.544616\pi$
$20$	0	0
$21$	−1.31509	−0.286976
$22$	3.80461	0.811146
$23$	6.22482	1.29797	0.648983	−	0.760803i	$-0.275195\pi$
$23$	6.22482	1.29797	0.648983	+	0.760803i	$0.275195\pi$
$24$	1.11336	0.227265
$25$	0	0
$26$	−3.93442	−0.771603
$27$	−2.12225	−0.408427
$28$	2.46908	0.466611
$29$	3.29498	0.611863	0.305931	−	0.952054i	$-0.401032\pi$
$29$	3.29498	0.611863	0.305931	+	0.952054i	$0.401032\pi$
$30$	0	0
$31$	0.187069	0.0335986	0.0167993	−	0.999859i	$-0.494652\pi$
$31$	0.187069	0.0335986	0.0167993	+	0.999859i	$0.494652\pi$
$32$	−3.65094	−0.645401
$33$	−1.19688	−0.208351
$34$	0.696266	0.119409
$35$	0	0
$36$	1.94787	0.324645
$37$	−0.174751	−0.0287289	−0.0143645	−	0.999897i	$-0.504573\pi$
$37$	−0.174751	−0.0287289	−0.0143645	+	0.999897i	$0.504573\pi$
$38$	1.39988	0.227091
$39$	1.23772	0.198194
$40$	0	0
$41$	9.28617	1.45026	0.725128	−	0.688614i	$-0.241780\pi$
$41$	9.28617	1.45026	0.725128	+	0.688614i	$0.241780\pi$
$42$	1.51157	0.233240
$43$	−5.81664	−0.887030	−0.443515	−	0.896267i	$-0.646269\pi$
$43$	−5.81664	−0.887030	−0.443515	+	0.896267i	$0.646269\pi$
$44$	2.24714	0.338769
$45$	0	0
$46$	−7.15482	−1.05492
$47$	−3.12220	−0.455420	−0.227710	−	0.973729i	$-0.573124\pi$
$47$	−3.12220	−0.455420	−0.227710	+	0.973729i	$0.573124\pi$
$48$	−0.788755	−0.113847
$49$	6.22774	0.889677
$50$	0	0
$51$	−0.219037	−0.0306713
$52$	−2.32381	−0.322255
$53$	2.23321	0.306755	0.153378	−	0.988168i	$-0.450985\pi$
$53$	2.23321	0.306755	0.153378	+	0.988168i	$0.450985\pi$
$54$	2.43931	0.331948
$55$	0	0
$56$	−11.1987	−1.49649
$57$	−0.440386	−0.0583305
$58$	−3.78725	−0.497291
$59$	6.04532	0.787034	0.393517	−	0.919317i	$-0.371258\pi$
$59$	6.04532	0.787034	0.393517	+	0.919317i	$0.371258\pi$
$60$	0	0
$61$	2.39259	0.306340	0.153170	−	0.988200i	$-0.451052\pi$
$61$	2.39259	0.306340	0.153170	+	0.988200i	$0.451052\pi$
$62$	−0.215017	−0.0273072
$63$	10.4355	1.31475
$64$	8.55913	1.06989
$65$	0	0
$66$	1.37570	0.169337
$67$	5.48219	0.669756	0.334878	−	0.942261i	$-0.391305\pi$
$67$	5.48219	0.669756	0.334878	+	0.942261i	$0.391305\pi$
$68$	0.411240	0.0498702
$69$	2.25082	0.270966
$70$	0	0
$71$	6.38307	0.757531	0.378765	−	0.925493i	$-0.376349\pi$
$71$	6.38307	0.757531	0.378765	+	0.925493i	$0.376349\pi$
$72$	−8.83473	−1.04118
$73$	−0.625385	−0.0731957	−0.0365979	−	0.999330i	$-0.511652\pi$
$73$	−0.625385	−0.0731957	−0.0365979	+	0.999330i	$0.511652\pi$
$74$	0.200859	0.0233494
$75$	0	0
$76$	0.826821	0.0948429
$77$	12.0388	1.37194
$78$	−1.42264	−0.161082
$79$	6.61180	0.743886	0.371943	−	0.928256i	$-0.378692\pi$
$79$	6.61180	0.743886	0.371943	+	0.928256i	$0.378692\pi$
$80$	0	0
$81$	7.84039	0.871154
$82$	−10.6735	−1.17869
$83$	−13.1244	−1.44059	−0.720297	−	0.693666i	$-0.755994\pi$
$83$	−13.1244	−1.44059	−0.720297	+	0.693666i	$0.755994\pi$
$84$	0.892786	0.0974109
$85$	0	0
$86$	6.68566	0.720933
$87$	1.19142	0.127734
$88$	−10.1921	−1.08648
$89$	−1.26185	−0.133756	−0.0668779	−	0.997761i	$-0.521304\pi$
$89$	−1.26185	−0.133756	−0.0668779	+	0.997761i	$0.521304\pi$
$90$	0	0
$91$	−12.4495	−1.30506
$92$	−4.22589	−0.440580
$93$	0.0676417	0.00701412
$94$	3.58866	0.370143
$95$	0	0
$96$	−1.32013	−0.134736
$97$	0.489708	0.0497223	0.0248612	−	0.999691i	$-0.492086\pi$
$97$	0.489708	0.0497223	0.0248612	+	0.999691i	$0.492086\pi$
$98$	−7.15817	−0.723085
$99$	9.49746	0.954531
$100$	0	0
$101$	−2.80782	−0.279388	−0.139694	−	0.990195i	$-0.544612\pi$
$101$	−2.80782	−0.279388	−0.139694	+	0.990195i	$0.544612\pi$
$102$	0.251761	0.0249281
$103$	−13.1100	−1.29177	−0.645884	−	0.763436i	$-0.723511\pi$
$103$	−13.1100	−1.29177	−0.645884	+	0.763436i	$0.723511\pi$
$104$	10.5398	1.03352
$105$	0	0
$106$	−2.56686	−0.249315
$107$	−3.36714	−0.325514	−0.162757	−	0.986666i	$-0.552039\pi$
$107$	−3.36714	−0.325514	−0.162757	+	0.986666i	$0.552039\pi$
$108$	1.44075	0.138636
$109$	7.11162	0.681170	0.340585	−	0.940214i	$-0.389375\pi$
$109$	7.11162	0.681170	0.340585	+	0.940214i	$0.389375\pi$
$110$	0	0
$111$	−0.0631879	−0.00599753
$112$	7.93363	0.749658
$113$	11.2316	1.05658	0.528291	−	0.849064i	$-0.322833\pi$
$113$	11.2316	1.05658	0.528291	+	0.849064i	$0.322833\pi$
$114$	0.506180	0.0474081
$115$	0	0
$116$	−2.23689	−0.207690
$117$	−9.82151	−0.907999
$118$	−6.94850	−0.639661
$119$	2.20316	0.201964
$120$	0	0
$121$	−0.0433654	−0.00394231
$122$	−2.75005	−0.248978
$123$	3.35776	0.302759
$124$	−0.126997	−0.0114047
$125$	0	0
$126$	−11.9945	−1.06856
$127$	19.1172	1.69638	0.848189	−	0.529693i	$-0.177693\pi$
$127$	19.1172	1.69638	0.848189	+	0.529693i	$0.177693\pi$
$128$	−2.53600	−0.224152
$129$	−2.10322	−0.185179
$130$	0	0
$131$	9.46608	0.827055	0.413528	−	0.910492i	$-0.364296\pi$
$131$	9.46608	0.827055	0.413528	+	0.910492i	$0.364296\pi$
$132$	0.812537	0.0707223
$133$	4.42959	0.384094
$134$	−6.30123	−0.544344
$135$	0	0
$136$	−1.86521	−0.159941
$137$	−16.7033	−1.42706	−0.713528	−	0.700626i	$-0.752904\pi$
$137$	−16.7033	−1.42706	−0.713528	+	0.700626i	$0.752904\pi$
$138$	−2.58709	−0.220228
$139$	−8.45064	−0.716774	−0.358387	−	0.933573i	$-0.616673\pi$
$139$	−8.45064	−0.716774	−0.358387	+	0.933573i	$0.616673\pi$
$140$	0	0
$141$	−1.12895	−0.0950747
$142$	−7.33670	−0.615682
$143$	−11.3305	−0.947501
$144$	6.25891	0.521576
$145$	0	0
$146$	0.718818	0.0594898
$147$	2.25187	0.185731
$148$	0.118635	0.00975172
$149$	−8.57298	−0.702326	−0.351163	−	0.936314i	$-0.614214\pi$
$149$	−8.57298	−0.702326	−0.351163	+	0.936314i	$0.614214\pi$
$150$	0	0
$151$	−17.1314	−1.39413	−0.697066	−	0.717007i	$-0.745511\pi$
$151$	−17.1314	−1.39413	−0.697066	+	0.717007i	$0.745511\pi$
$152$	−3.75012	−0.304175
$153$	1.73809	0.140516
$154$	−13.8374	−1.11505
$155$	0	0
$156$	−0.840260	−0.0672747
$157$	−14.1271	−1.12746	−0.563732	−	0.825958i	$-0.690635\pi$
$157$	−14.1271	−1.12746	−0.563732	+	0.825958i	$0.690635\pi$
$158$	−7.59961	−0.604592
$159$	0.807501	0.0640390
$160$	0	0
$161$	−22.6397	−1.78425
$162$	−9.01175	−0.708030
$163$	−9.98079	−0.781756	−0.390878	−	0.920443i	$-0.627829\pi$
$163$	−9.98079	−0.781756	−0.390878	+	0.920443i	$0.627829\pi$
$164$	−6.30418	−0.492273
$165$	0	0
$166$	15.0852	1.17084
$167$	−1.72404	−0.133410	−0.0667050	−	0.997773i	$-0.521249\pi$
$167$	−1.72404	−0.133410	−0.0667050	+	0.997773i	$0.521249\pi$
$168$	−4.04930	−0.312411
$169$	−1.28294	−0.0986879
$170$	0	0
$171$	3.49453	0.267234
$172$	3.94879	0.301092
$173$	17.0426	1.29572	0.647862	−	0.761758i	$-0.275663\pi$
$173$	17.0426	1.29572	0.647862	+	0.761758i	$0.275663\pi$
$174$	−1.36942	−0.103816
$175$	0	0
$176$	7.22051	0.544266
$177$	2.18591	0.164303
$178$	1.45037	0.108710
$179$	−13.9513	−1.04277	−0.521384	−	0.853322i	$-0.674584\pi$
$179$	−13.9513	−1.04277	−0.521384	+	0.853322i	$0.674584\pi$
$180$	0	0
$181$	13.1649	0.978536	0.489268	−	0.872133i	$-0.337264\pi$
$181$	13.1649	0.978536	0.489268	+	0.872133i	$0.337264\pi$
$182$	14.3095	1.06069
$183$	0.865131	0.0639523
$184$	19.1669	1.41300
$185$	0	0
$186$	−0.0777474	−0.00570072
$187$	2.00513	0.146630
$188$	2.11959	0.154587
$189$	7.71861	0.561446
$190$	0	0
$191$	22.1886	1.60551	0.802756	−	0.596308i	$-0.203366\pi$
$191$	22.1886	1.60551	0.802756	+	0.596308i	$0.203366\pi$
$192$	3.09487	0.223353
$193$	−5.06056	−0.364267	−0.182134	−	0.983274i	$-0.558300\pi$
$193$	−5.06056	−0.364267	−0.182134	+	0.983274i	$0.558300\pi$
$194$	−0.562871	−0.0404118
$195$	0	0
$196$	−4.22787	−0.301991
$197$	3.62547	0.258304	0.129152	−	0.991625i	$-0.458775\pi$
$197$	3.62547	0.258304	0.129152	+	0.991625i	$0.458775\pi$
$198$	−10.9164	−0.775794
$199$	−0.289466	−0.0205197	−0.0102599	−	0.999947i	$-0.503266\pi$
$199$	−0.289466	−0.0205197	−0.0102599	+	0.999947i	$0.503266\pi$
$200$	0	0
$201$	1.98229	0.139820
$202$	3.22731	0.227073
$203$	−11.9838	−0.841100
$204$	0.148699	0.0104110
$205$	0	0
$206$	15.0687	1.04988
$207$	−17.8606	−1.24140
$208$	−7.46687	−0.517734
$209$	4.03143	0.278860
$210$	0	0
$211$	−17.8956	−1.23198	−0.615992	−	0.787752i	$-0.711245\pi$
$211$	−17.8956	−1.23198	−0.615992	+	0.787752i	$0.711245\pi$
$212$	−1.51608	−0.104125
$213$	2.30803	0.158144
$214$	3.87019	0.264561
$215$	0	0
$216$	−6.53462	−0.444625
$217$	−0.680369	−0.0461864
$218$	−8.17410	−0.553620
$219$	−0.226131	−0.0152805
$220$	0	0
$221$	−2.07354	−0.139482
$222$	0.0726282	0.00487448
$223$	−24.3454	−1.63029	−0.815145	−	0.579257i	$-0.803343\pi$
$223$	−24.3454	−1.63029	−0.815145	+	0.579257i	$0.803343\pi$
$224$	13.2785	0.887204
$225$	0	0
$226$	−12.9096	−0.858735
$227$	−7.75396	−0.514648	−0.257324	−	0.966325i	$-0.582841\pi$
$227$	−7.75396	−0.514648	−0.257324	+	0.966325i	$0.582841\pi$
$228$	0.298968	0.0197996
$229$	24.1455	1.59558	0.797790	−	0.602935i	$-0.206002\pi$
$229$	24.1455	1.59558	0.797790	+	0.602935i	$0.206002\pi$
$230$	0	0
$231$	4.35306	0.286410
$232$	10.1456	0.666091
$233$	−9.06363	−0.593778	−0.296889	−	0.954912i	$-0.595949\pi$
$233$	−9.06363	−0.593778	−0.296889	+	0.954912i	$0.595949\pi$
$234$	11.2889	0.737976
$235$	0	0
$236$	−4.10403	−0.267150
$237$	2.39074	0.155295
$238$	−2.53232	−0.164146
$239$	−13.0403	−0.843504	−0.421752	−	0.906711i	$-0.638585\pi$
$239$	−13.0403	−0.843504	−0.421752	+	0.906711i	$0.638585\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	0.0498442	0.00320411
$243$	9.20172	0.590291
$244$	−1.62428	−0.103984
$245$	0	0
$246$	−3.85941	−0.246067
$247$	−4.16898	−0.265266
$248$	0.576005	0.0365763
$249$	−4.74563	−0.300742
$250$	0	0
$251$	−8.42229	−0.531610	−0.265805	−	0.964027i	$-0.585638\pi$
$251$	−8.42229	−0.531610	−0.265805	+	0.964027i	$0.585638\pi$
$252$	−7.08441	−0.446276
$253$	−20.6047	−1.29540
$254$	−21.9733	−1.37873
$255$	0	0
$256$	−14.2034	−0.887712
$257$	−2.04403	−0.127503	−0.0637517	−	0.997966i	$-0.520307\pi$
$257$	−2.04403	−0.127503	−0.0637517	+	0.997966i	$0.520307\pi$
$258$	2.41745	0.150504
$259$	0.635570	0.0394924
$260$	0	0
$261$	−9.45414	−0.585197
$262$	−10.8803	−0.672189
$263$	−26.0710	−1.60761	−0.803805	−	0.594893i	$-0.797194\pi$
$263$	−26.0710	−1.60761	−0.803805	+	0.594893i	$0.797194\pi$
$264$	−3.68533	−0.226816
$265$	0	0
$266$	−5.09137	−0.312172
$267$	−0.456269	−0.0279232
$268$	−3.72174	−0.227341
$269$	8.87038	0.540837	0.270418	−	0.962743i	$-0.412838\pi$
$269$	8.87038	0.540837	0.270418	+	0.962743i	$0.412838\pi$
$270$	0	0
$271$	0.842226	0.0511616	0.0255808	−	0.999673i	$-0.491856\pi$
$271$	0.842226	0.0511616	0.0255808	+	0.999673i	$0.491856\pi$
$272$	1.32140	0.0801214
$273$	−4.50158	−0.272448
$274$	19.1988	1.15984
$275$	0	0
$276$	−1.52803	−0.0919765
$277$	−13.3430	−0.801704	−0.400852	−	0.916143i	$-0.631286\pi$
$277$	−13.3430	−0.801704	−0.400852	+	0.916143i	$0.631286\pi$
$278$	9.71317	0.582557
$279$	−0.536748	−0.0321343
$280$	0	0
$281$	11.8691	0.708054	0.354027	−	0.935235i	$-0.384812\pi$
$281$	11.8691	0.708054	0.354027	+	0.935235i	$0.384812\pi$
$282$	1.29762	0.0772719
$283$	25.4643	1.51369	0.756847	−	0.653592i	$-0.226739\pi$
$283$	25.4643	1.51369	0.756847	+	0.653592i	$0.226739\pi$
$284$	−4.33332	−0.257135
$285$	0	0
$286$	13.0233	0.770081
$287$	−33.7738	−1.99360
$288$	10.4755	0.617273
$289$	−16.6330	−0.978415
$290$	0	0
$291$	0.177072	0.0103802
$292$	0.424560	0.0248455
$293$	31.0311	1.81285	0.906427	−	0.422362i	$-0.138799\pi$
$293$	31.0311	1.81285	0.906427	+	0.422362i	$0.138799\pi$
$294$	−2.58830	−0.150953
$295$	0	0
$296$	−0.538078	−0.0312751
$297$	7.02481	0.407621
$298$	9.85379	0.570815
$299$	21.3077	1.23226
$300$	0	0
$301$	21.1551	1.21936
$302$	19.6908	1.13308
$303$	−1.01527	−0.0583258
$304$	2.65674	0.152375
$305$	0	0
$306$	−1.99777	−0.114205
$307$	−3.24000	−0.184916	−0.0924582	−	0.995717i	$-0.529472\pi$
$307$	−3.24000	−0.184916	−0.0924582	+	0.995717i	$0.529472\pi$
$308$	−8.17284	−0.465691
$309$	−4.74041	−0.269673
$310$	0	0
$311$	4.66898	0.264754	0.132377	−	0.991199i	$-0.457739\pi$
$311$	4.66898	0.264754	0.132377	+	0.991199i	$0.457739\pi$
$312$	3.81107	0.215759
$313$	−27.9019	−1.57711	−0.788554	−	0.614965i	$-0.789170\pi$
$313$	−27.9019	−1.57711	−0.788554	+	0.614965i	$0.789170\pi$
$314$	16.2377	0.916345
$315$	0	0
$316$	−4.48860	−0.252504
$317$	−23.5760	−1.32416	−0.662080	−	0.749434i	$-0.730326\pi$
$317$	−23.5760	−1.32416	−0.662080	+	0.749434i	$0.730326\pi$
$318$	−0.928142	−0.0520476
$319$	−10.9067	−0.610655
$320$	0	0
$321$	−1.21751	−0.0679550
$322$	26.0220	1.45015
$323$	0.737775	0.0410509
$324$	−5.32266	−0.295704
$325$	0	0
$326$	11.4719	0.635371
$327$	2.57147	0.142203
$328$	28.5931	1.57879
$329$	11.3554	0.626046
$330$	0	0
$331$	−11.0029	−0.604773	−0.302387	−	0.953185i	$-0.597783\pi$
$331$	−11.0029	−0.604773	−0.302387	+	0.953185i	$0.597783\pi$
$332$	8.90988	0.488993
$333$	0.501406	0.0274769
$334$	1.98161	0.108429
$335$	0	0
$336$	2.86870	0.156500
$337$	−6.84048	−0.372625	−0.186312	−	0.982491i	$-0.559654\pi$
$337$	−6.84048	−0.372625	−0.186312	+	0.982491i	$0.559654\pi$
$338$	1.47462	0.0802085
$339$	4.06121	0.220574
$340$	0	0
$341$	−0.619213	−0.0335323
$342$	−4.01662	−0.217194
$343$	2.80870	0.151656
$344$	−17.9101	−0.965645
$345$	0	0
$346$	−19.5888	−1.05310
$347$	7.59996	0.407987	0.203994	−	0.978972i	$-0.434608\pi$
$347$	7.59996	0.407987	0.203994	+	0.978972i	$0.434608\pi$
$348$	−0.808830	−0.0433579
$349$	10.5572	0.565112	0.282556	−	0.959251i	$-0.408818\pi$
$349$	10.5572	0.565112	0.282556	+	0.959251i	$0.408818\pi$
$350$	0	0
$351$	−7.26449	−0.387750
$352$	12.0849	0.644128
$353$	−31.2951	−1.66567	−0.832834	−	0.553523i	$-0.813283\pi$
$353$	−31.2951	−1.66567	−0.832834	+	0.553523i	$0.813283\pi$
$354$	−2.51249	−0.133537
$355$	0	0
$356$	0.856641	0.0454019
$357$	0.796636	0.0421624
$358$	16.0356	0.847509
$359$	12.2270	0.645319	0.322659	−	0.946515i	$-0.395423\pi$
$359$	12.2270	0.645319	0.322659	+	0.946515i	$0.395423\pi$
$360$	0	0
$361$	−17.5167	−0.921930
$362$	−15.1317	−0.795305
$363$	−0.0156804	−0.000823006 0
$364$	8.45169	0.442989
$365$	0	0
$366$	−0.994382	−0.0519772
$367$	−4.97683	−0.259788	−0.129894	−	0.991528i	$-0.541464\pi$
$367$	−4.97683	−0.259788	−0.129894	+	0.991528i	$0.541464\pi$
$368$	−13.5786	−0.707835
$369$	−26.6444	−1.38705
$370$	0	0
$371$	−8.12219	−0.421683
$372$	−0.0459204	−0.00238086
$373$	14.0011	0.724951	0.362476	−	0.931993i	$-0.381932\pi$
$373$	14.0011	0.724951	0.362476	+	0.931993i	$0.381932\pi$
$374$	−2.30470	−0.119173
$375$	0	0
$376$	−9.61359	−0.495783
$377$	11.2788	0.580887
$378$	−8.87177	−0.456315
$379$	15.1424	0.777812	0.388906	−	0.921277i	$-0.372853\pi$
$379$	15.1424	0.777812	0.388906	+	0.921277i	$0.372853\pi$
$380$	0	0
$381$	6.91254	0.354140
$382$	−25.5036	−1.30488
$383$	15.3097	0.782291	0.391145	−	0.920329i	$-0.372079\pi$
$383$	15.3097	0.782291	0.391145	+	0.920329i	$0.372079\pi$
$384$	−0.916984	−0.0467946
$385$	0	0
$386$	5.81661	0.296058
$387$	16.6894	0.848372
$388$	−0.332452	−0.0168777
$389$	35.9486	1.82267	0.911334	−	0.411667i	$-0.135053\pi$
$389$	35.9486	1.82267	0.911334	+	0.411667i	$0.135053\pi$
$390$	0	0
$391$	−3.77078	−0.190696
$392$	19.1759	0.968528
$393$	3.42281	0.172658
$394$	−4.16711	−0.209936
$395$	0	0
$396$	−6.44762	−0.324005
$397$	−12.6507	−0.634919	−0.317460	−	0.948272i	$-0.602830\pi$
$397$	−12.6507	−0.634919	−0.317460	+	0.948272i	$0.602830\pi$
$398$	0.332713	0.0166774
$399$	1.60168	0.0801844
$400$	0	0
$401$	17.7283	0.885308	0.442654	−	0.896692i	$-0.354037\pi$
$401$	17.7283	0.885308	0.442654	+	0.896692i	$0.354037\pi$
$402$	−2.27845	−0.113639
$403$	0.640340	0.0318976
$404$	1.90616	0.0948352
$405$	0	0
$406$	13.7742	0.683604
$407$	0.578441	0.0286723
$408$	−0.674437	−0.0333896
$409$	−27.5554	−1.36253	−0.681264	−	0.732038i	$-0.738569\pi$
$409$	−27.5554	−1.36253	−0.681264	+	0.732038i	$0.738569\pi$
$410$	0	0
$411$	−6.03969	−0.297916
$412$	8.90009	0.438476
$413$	−21.9868	−1.08190
$414$	20.5290	1.00894
$415$	0	0
$416$	−12.4972	−0.612727
$417$	−3.05564	−0.149635
$418$	−4.63373	−0.226643
$419$	6.46452	0.315813	0.157906	−	0.987454i	$-0.449526\pi$
$419$	6.46452	0.315813	0.157906	+	0.987454i	$0.449526\pi$
$420$	0	0
$421$	−24.5361	−1.19582	−0.597909	−	0.801564i	$-0.704002\pi$
$421$	−24.5361	−1.19582	−0.597909	+	0.801564i	$0.704002\pi$
$422$	20.5692	1.00129
$423$	8.95840	0.435572
$424$	6.87630	0.333942
$425$	0	0
$426$	−2.65286	−0.128531
$427$	−8.70185	−0.421112
$428$	2.28587	0.110492
$429$	−4.09695	−0.197803
$430$	0	0
$431$	−12.1862	−0.586986	−0.293493	−	0.955961i	$-0.594818\pi$
$431$	−12.1862	−0.586986	−0.293493	+	0.955961i	$0.594818\pi$
$432$	4.62941	0.222732
$433$	1.90864	0.0917233	0.0458616	−	0.998948i	$-0.485397\pi$
$433$	1.90864	0.0917233	0.0458616	+	0.998948i	$0.485397\pi$
$434$	0.782017	0.0375380
$435$	0	0
$436$	−4.82792	−0.231215
$437$	−7.58136	−0.362666
$438$	0.259915	0.0124192
$439$	15.4413	0.736973	0.368486	−	0.929633i	$-0.379876\pi$
$439$	15.4413	0.736973	0.368486	+	0.929633i	$0.379876\pi$
$440$	0	0
$441$	−17.8690	−0.850904
$442$	2.38333	0.113364
$443$	−35.2713	−1.67579	−0.837894	−	0.545833i	$-0.816213\pi$
$443$	−35.2713	−1.67579	−0.837894	+	0.545833i	$0.816213\pi$
$444$	0.0428968	0.00203579
$445$	0	0
$446$	27.9827	1.32502
$447$	−3.09988	−0.146619
$448$	−31.1295	−1.47073
$449$	−7.11761	−0.335901	−0.167950	−	0.985795i	$-0.553715\pi$
$449$	−7.11761	−0.335901	−0.167950	+	0.985795i	$0.553715\pi$
$450$	0	0
$451$	−30.7380	−1.44740
$452$	−7.62489	−0.358645
$453$	−6.19448	−0.291042
$454$	8.91241	0.418280
$455$	0	0
$456$	−1.35599	−0.0635002
$457$	−2.85579	−0.133588	−0.0667941	−	0.997767i	$-0.521277\pi$
$457$	−2.85579	−0.133588	−0.0667941	+	0.997767i	$0.521277\pi$
$458$	−27.7529	−1.29681
$459$	1.28558	0.0600058
$460$	0	0
$461$	−16.6995	−0.777772	−0.388886	−	0.921286i	$-0.627140\pi$
$461$	−16.6995	−0.777772	−0.388886	+	0.921286i	$0.627140\pi$
$462$	−5.00341	−0.232780
$463$	10.8186	0.502784	0.251392	−	0.967885i	$-0.419112\pi$
$463$	10.8186	0.502784	0.251392	+	0.967885i	$0.419112\pi$
$464$	−7.18757	−0.333675
$465$	0	0
$466$	10.4177	0.482593
$467$	−16.8745	−0.780859	−0.390430	−	0.920633i	$-0.627674\pi$
$467$	−16.8745	−0.780859	−0.390430	+	0.920633i	$0.627674\pi$
$468$	6.66761	0.308210
$469$	−19.9387	−0.920684
$470$	0	0
$471$	−5.10817	−0.235372
$472$	18.6142	0.856787
$473$	19.2536	0.885280
$474$	−2.74792	−0.126216
$475$	0	0
$476$	−1.49568	−0.0685543
$477$	−6.40766	−0.293386
$478$	14.9885	0.685557
$479$	−3.17196	−0.144931	−0.0724653	−	0.997371i	$-0.523087\pi$
$479$	−3.17196	−0.144931	−0.0724653	+	0.997371i	$0.523087\pi$
$480$	0	0
$481$	−0.598177	−0.0272745
$482$	1.14940	0.0523538
$483$	−8.18621	−0.372485
$484$	0.0294398	0.00133817
$485$	0	0
$486$	−10.5765	−0.479758
$487$	6.17755	0.279931	0.139966	−	0.990156i	$-0.455301\pi$
$487$	6.17755	0.279931	0.139966	+	0.990156i	$0.455301\pi$
$488$	7.36704	0.333490
$489$	−3.60893	−0.163201
$490$	0	0
$491$	−24.4496	−1.10340	−0.551698	−	0.834044i	$-0.686020\pi$
$491$	−24.4496	−1.10340	−0.551698	+	0.834044i	$0.686020\pi$
$492$	−2.27951	−0.102768
$493$	−1.99598	−0.0898946
$494$	4.79183	0.215594
$495$	0	0
$496$	−0.408066	−0.0183227
$497$	−23.2152	−1.04134
$498$	5.45463	0.244428
$499$	−2.03667	−0.0911737	−0.0455869	−	0.998960i	$-0.514516\pi$
$499$	−2.03667	−0.0911737	−0.0455869	+	0.998960i	$0.514516\pi$
$500$	0	0
$501$	−0.623390	−0.0278510
$502$	9.68059	0.432066
$503$	−36.6362	−1.63353	−0.816764	−	0.576971i	$-0.804234\pi$
$503$	−36.6362	−1.63353	−0.816764	+	0.576971i	$0.804234\pi$
$504$	32.1319	1.43127
$505$	0	0
$506$	23.6830	1.05284
$507$	−0.463896	−0.0206023
$508$	−12.9782	−0.575817
$509$	15.6418	0.693309	0.346655	−	0.937993i	$-0.387318\pi$
$509$	15.6418	0.693309	0.346655	+	0.937993i	$0.387318\pi$
$510$	0	0
$511$	2.27452	0.100619
$512$	21.3974	0.945640
$513$	2.58474	0.114119
$514$	2.34941	0.103628
$515$	0	0
$516$	1.42783	0.0628568
$517$	10.3347	0.454522
$518$	−0.730525	−0.0320974
$519$	6.16238	0.270498
$520$	0	0
$521$	31.0010	1.35818	0.679088	−	0.734056i	$-0.262375\pi$
$521$	31.0010	1.35818	0.679088	+	0.734056i	$0.262375\pi$
$522$	10.8666	0.475618
$523$	13.3801	0.585073	0.292537	−	0.956254i	$-0.405501\pi$
$523$	13.3801	0.585073	0.292537	+	0.956254i	$0.405501\pi$
$524$	−6.42631	−0.280735
$525$	0	0
$526$	29.9661	1.30658
$527$	−0.113320	−0.00493628
$528$	2.61084	0.113622
$529$	15.7484	0.684713
$530$	0	0
$531$	−17.3456	−0.752734
$532$	−3.00715	−0.130376
$533$	31.7867	1.37684
$534$	0.524435	0.0226945
$535$	0	0
$536$	16.8802	0.729115
$537$	−5.04461	−0.217691
$538$	−10.1956	−0.439565
$539$	−20.6143	−0.887922
$540$	0	0
$541$	9.42663	0.405282	0.202641	−	0.979253i	$-0.435047\pi$
$541$	9.42663	0.405282	0.202641	+	0.979253i	$0.435047\pi$
$542$	−0.968055	−0.0415815
$543$	4.76025	0.204282
$544$	2.21161	0.0948220
$545$	0	0
$546$	5.17412	0.221432
$547$	36.1196	1.54436	0.772181	−	0.635402i	$-0.219166\pi$
$547$	36.1196	1.54436	0.772181	+	0.635402i	$0.219166\pi$
$548$	11.3395	0.484398
$549$	−6.86496	−0.292989
$550$	0	0
$551$	−4.01304	−0.170961
$552$	6.93050	0.294982
$553$	−24.0471	−1.02259
$554$	15.3365	0.651584
$555$	0	0
$556$	5.73695	0.243301
$557$	−44.4300	−1.88256	−0.941281	−	0.337625i	$-0.890376\pi$
$557$	−44.4300	−1.88256	−0.941281	+	0.337625i	$0.890376\pi$
$558$	0.616939	0.0261171
$559$	−19.9105	−0.842124
$560$	0	0
$561$	0.725029	0.0306108
$562$	−13.6424	−0.575470
$563$	−35.7024	−1.50468	−0.752338	−	0.658778i	$-0.771074\pi$
$563$	−35.7024	−1.50468	−0.752338	+	0.658778i	$0.771074\pi$
$564$	0.766418	0.0322720
$565$	0	0
$566$	−29.2687	−1.23025
$567$	−28.5155	−1.19754
$568$	19.6541	0.824669
$569$	−25.6913	−1.07704	−0.538518	−	0.842614i	$-0.681016\pi$
$569$	−25.6913	−1.07704	−0.538518	+	0.842614i	$0.681016\pi$
$570$	0	0
$571$	7.37401	0.308593	0.154296	−	0.988025i	$-0.450689\pi$
$571$	7.37401	0.308593	0.154296	+	0.988025i	$0.450689\pi$
$572$	7.69200	0.321619
$573$	8.02312	0.335171
$574$	38.8196	1.62030
$575$	0	0
$576$	−24.5583	−1.02326
$577$	5.58190	0.232377	0.116189	−	0.993227i	$-0.462932\pi$
$577$	5.58190	0.232377	0.116189	+	0.993227i	$0.462932\pi$
$578$	19.1180	0.795206
$579$	−1.82983	−0.0760453
$580$	0	0
$581$	47.7335	1.98032
$582$	−0.203527	−0.00843646
$583$	−7.39211	−0.306150
$584$	−1.92562	−0.0796829
$585$	0	0
$586$	−35.6671	−1.47340
$587$	−10.0599	−0.415217	−0.207608	−	0.978212i	$-0.566568\pi$
$587$	−10.0599	−0.415217	−0.207608	+	0.978212i	$0.566568\pi$
$588$	−1.52875	−0.0630444
$589$	−0.227836	−0.00938781
$590$	0	0
$591$	1.31092	0.0539241
$592$	0.381197	0.0156671
$593$	−21.7142	−0.891694	−0.445847	−	0.895109i	$-0.647097\pi$
$593$	−21.7142	−0.891694	−0.445847	+	0.895109i	$0.647097\pi$
$594$	−8.07432	−0.331293
$595$	0	0
$596$	5.82000	0.238397
$597$	−0.104667	−0.00428375
$598$	−24.4911	−1.00151
$599$	−40.5561	−1.65708	−0.828538	−	0.559933i	$-0.810827\pi$
$599$	−40.5561	−1.65708	−0.828538	+	0.559933i	$0.810827\pi$
$600$	0	0
$601$	32.4901	1.32530	0.662650	−	0.748929i	$-0.269432\pi$
$601$	32.4901	1.32530	0.662650	+	0.748929i	$0.269432\pi$
$602$	−24.3157	−0.991034
$603$	−15.7298	−0.640567
$604$	11.6301	0.473222
$605$	0	0
$606$	1.16695	0.0474042
$607$	−17.7595	−0.720836	−0.360418	−	0.932791i	$-0.617366\pi$
$607$	−17.7595	−0.720836	−0.360418	+	0.932791i	$0.617366\pi$
$608$	4.44657	0.180332
$609$	−4.33320	−0.175590
$610$	0	0
$611$	−10.6874	−0.432365
$612$	−1.17995	−0.0476967
$613$	−11.4399	−0.462055	−0.231027	−	0.972947i	$-0.574209\pi$
$613$	−11.4399	−0.462055	−0.231027	+	0.972947i	$0.574209\pi$
$614$	3.72406	0.150291
$615$	0	0
$616$	37.0686	1.49354
$617$	−3.85094	−0.155033	−0.0775164	−	0.996991i	$-0.524699\pi$
$617$	−3.85094	−0.155033	−0.0775164	+	0.996991i	$0.524699\pi$
$618$	5.44863	0.219176
$619$	−38.1133	−1.53190	−0.765951	−	0.642899i	$-0.777732\pi$
$619$	−38.1133	−1.53190	−0.765951	+	0.642899i	$0.777732\pi$
$620$	0	0
$621$	−13.2106	−0.530124
$622$	−5.36653	−0.215178
$623$	4.58934	0.183868
$624$	−2.69992	−0.108083
$625$	0	0
$626$	32.0705	1.28179
$627$	1.45771	0.0582154
$628$	9.59056	0.382705
$629$	0.105858	0.00422084
$630$	0	0
$631$	17.4812	0.695916	0.347958	−	0.937510i	$-0.386875\pi$
$631$	17.4812	0.695916	0.347958	+	0.937510i	$0.386875\pi$
$632$	20.3584	0.809814
$633$	−6.47082	−0.257192
$634$	27.0983	1.07621
$635$	0	0
$636$	−0.548194	−0.0217373
$637$	21.3177	0.844637
$638$	12.5361	0.496310
$639$	−18.3146	−0.724516
$640$	0	0
$641$	20.7032	0.817728	0.408864	−	0.912595i	$-0.365925\pi$
$641$	20.7032	0.817728	0.408864	+	0.912595i	$0.365925\pi$
$642$	1.39941	0.0552304
$643$	−30.8231	−1.21555	−0.607773	−	0.794111i	$-0.707937\pi$
$643$	−30.8231	−1.21555	−0.607773	+	0.794111i	$0.707937\pi$
$644$	15.3696	0.605645
$645$	0	0
$646$	−0.848000	−0.0333641
$647$	16.3330	0.642115	0.321058	−	0.947060i	$-0.395962\pi$
$647$	16.3330	0.642115	0.321058	+	0.947060i	$0.395962\pi$
$648$	24.1414	0.948363
$649$	−20.0105	−0.785481
$650$	0	0
$651$	−0.246013	−0.00964200
$652$	6.77573	0.265358
$653$	24.9915	0.977992	0.488996	−	0.872286i	$-0.337363\pi$
$653$	24.9915	0.977992	0.488996	+	0.872286i	$0.337363\pi$
$654$	−2.95565	−0.115575
$655$	0	0
$656$	−20.2566	−0.790887
$657$	1.79439	0.0700057
$658$	−13.0520	−0.508818
$659$	6.70558	0.261212	0.130606	−	0.991434i	$-0.458308\pi$
$659$	6.70558	0.261212	0.130606	+	0.991434i	$0.458308\pi$
$660$	0	0
$661$	−6.84172	−0.266112	−0.133056	−	0.991109i	$-0.542479\pi$
$661$	−6.84172	−0.266112	−0.133056	+	0.991109i	$0.542479\pi$
$662$	12.6467	0.491529
$663$	−0.749767	−0.0291185
$664$	−40.4115	−1.56827
$665$	0	0
$666$	−0.576317	−0.0223318
$667$	20.5107	0.794176
$668$	1.17041	0.0452845
$669$	−8.80299	−0.340343
$670$	0	0
$671$	−7.91967	−0.305736
$672$	4.80132	0.185215
$673$	21.1590	0.815620	0.407810	−	0.913067i	$-0.366293\pi$
$673$	21.1590	0.815620	0.407810	+	0.913067i	$0.366293\pi$
$674$	7.86246	0.302851
$675$	0	0
$676$	0.870961	0.0334985
$677$	−44.9217	−1.72648	−0.863240	−	0.504793i	$-0.831569\pi$
$677$	−44.9217	−1.72648	−0.863240	+	0.504793i	$0.831569\pi$
$678$	−4.66795	−0.179272
$679$	−1.78107	−0.0683511
$680$	0	0
$681$	−2.80373	−0.107439
$682$	0.711724	0.0272533
$683$	−2.48221	−0.0949792	−0.0474896	−	0.998872i	$-0.515122\pi$
$683$	−2.48221	−0.0949792	−0.0474896	+	0.998872i	$0.515122\pi$
$684$	−2.37236	−0.0907095
$685$	0	0
$686$	−3.22832	−0.123258
$687$	8.73071	0.333097
$688$	12.6883	0.483735
$689$	7.64433	0.291226
$690$	0	0
$691$	−17.1466	−0.652289	−0.326144	−	0.945320i	$-0.605750\pi$
$691$	−17.1466	−0.652289	−0.326144	+	0.945320i	$0.605750\pi$
$692$	−11.5698	−0.439819
$693$	−34.5422	−1.31215
$694$	−8.73540	−0.331591
$695$	0	0
$696$	3.66852	0.139055
$697$	−5.62524	−0.213071
$698$	−12.1344	−0.459294
$699$	−3.27729	−0.123959
$700$	0	0
$701$	−37.4818	−1.41567	−0.707835	−	0.706378i	$-0.750328\pi$
$701$	−37.4818	−1.41567	−0.707835	+	0.706378i	$0.750328\pi$
$702$	8.34981	0.315143
$703$	0.212834	0.00802718
$704$	−28.3314	−1.06778
$705$	0	0
$706$	35.9706	1.35377
$707$	10.2120	0.384063
$708$	−1.48397	−0.0557709
$709$	−39.0821	−1.46776	−0.733880	−	0.679279i	$-0.762293\pi$
$709$	−39.0821	−1.46776	−0.733880	+	0.679279i	$0.762293\pi$
$710$	0	0
$711$	−18.9709	−0.711466
$712$	−3.88537	−0.145610
$713$	1.16447	0.0436098
$714$	−0.915654	−0.0342675
$715$	0	0
$716$	9.47122	0.353956
$717$	−4.71519	−0.176092
$718$	−14.0538	−0.524482
$719$	1.23516	0.0460638	0.0230319	−	0.999735i	$-0.492668\pi$
$719$	1.23516	0.0460638	0.0230319	+	0.999735i	$0.492668\pi$
$720$	0	0
$721$	47.6811	1.77574
$722$	20.1337	0.749297
$723$	−0.361587	−0.0134476
$724$	−8.93733	−0.332153
$725$	0	0
$726$	0.0180230	0.000668897 0
$727$	−20.6303	−0.765136	−0.382568	−	0.923927i	$-0.624960\pi$
$727$	−20.6303	−0.765136	−0.382568	+	0.923927i	$0.624960\pi$
$728$	−38.3333	−1.42073
$729$	−20.1939	−0.747924
$730$	0	0
$731$	3.52352	0.130322
$732$	−0.587318	−0.0217079
$733$	6.08021	0.224578	0.112289	−	0.993676i	$-0.464182\pi$
$733$	6.08021	0.224578	0.112289	+	0.993676i	$0.464182\pi$
$734$	5.72037	0.211143
$735$	0	0
$736$	−22.7265	−0.837708
$737$	−18.1465	−0.668435
$738$	30.6251	1.12733
$739$	−25.4962	−0.937891	−0.468946	−	0.883227i	$-0.655366\pi$
$739$	−25.4962	−0.937891	−0.468946	+	0.883227i	$0.655366\pi$
$740$	0	0
$741$	−1.50745	−0.0553775
$742$	9.33565	0.342722
$743$	11.9936	0.440004	0.220002	−	0.975499i	$-0.429394\pi$
$743$	11.9936	0.440004	0.220002	+	0.975499i	$0.429394\pi$
$744$	0.208276	0.00763576
$745$	0	0
$746$	−16.0929	−0.589204
$747$	37.6573	1.37781
$748$	−1.36124	−0.0497718
$749$	12.2463	0.447469
$750$	0	0
$751$	41.0878	1.49932	0.749658	−	0.661825i	$-0.230218\pi$
$751$	41.0878	1.49932	0.749658	+	0.661825i	$0.230218\pi$
$752$	6.81068	0.248360
$753$	−3.04539	−0.110980
$754$	−12.9638	−0.472115
$755$	0	0
$756$	−5.23999	−0.190577
$757$	25.6422	0.931982	0.465991	−	0.884789i	$-0.345698\pi$
$757$	25.6422	0.931982	0.465991	+	0.884789i	$0.345698\pi$
$758$	−17.4047	−0.632166
$759$	−7.45038	−0.270432
$760$	0	0
$761$	−6.85649	−0.248548	−0.124274	−	0.992248i	$-0.539660\pi$
$761$	−6.85649	−0.248548	−0.124274	+	0.992248i	$0.539660\pi$
$762$	−7.94528	−0.287827
$763$	−25.8649	−0.936374
$764$	−15.0634	−0.544973
$765$	0	0
$766$	−17.5970	−0.635806
$767$	20.6933	0.747190
$768$	−5.13576	−0.185321
$769$	54.2872	1.95765	0.978823	−	0.204707i	$-0.0656240\pi$
$769$	54.2872	1.95765	0.978823	+	0.204707i	$0.0656240\pi$
$770$	0	0
$771$	−0.739097	−0.0266179
$772$	3.43550	0.123646
$773$	44.2104	1.59014	0.795068	−	0.606520i	$-0.207435\pi$
$773$	44.2104	1.59014	0.795068	+	0.606520i	$0.207435\pi$
$774$	−19.1829	−0.689513
$775$	0	0
$776$	1.50786	0.0541291
$777$	0.229814	0.00824453
$778$	−41.3194	−1.48137
$779$	−11.3099	−0.405218
$780$	0	0
$781$	−21.1285	−0.756036
$782$	4.33413	0.154988
$783$	−6.99276	−0.249901
$784$	−13.5850	−0.485179
$785$	0	0
$786$	−3.93418	−0.140328
$787$	11.0923	0.395398	0.197699	−	0.980263i	$-0.436653\pi$
$787$	11.0923	0.395398	0.197699	+	0.980263i	$0.436653\pi$
$788$	−2.46125	−0.0876783
$789$	−9.42696	−0.335608
$790$	0	0
$791$	−40.8493	−1.45243
$792$	29.2437	1.03913
$793$	8.18989	0.290831
$794$	14.5407	0.516030
$795$	0	0
$796$	0.196512	0.00696519
$797$	4.22546	0.149673	0.0748367	−	0.997196i	$-0.476156\pi$
$797$	4.22546	0.149673	0.0748367	+	0.997196i	$0.476156\pi$
$798$	−1.84097	−0.0651698
$799$	1.89132	0.0669101
$800$	0	0
$801$	3.62057	0.127926
$802$	−20.3769	−0.719533
$803$	2.07007	0.0730513
$804$	−1.34573	−0.0474603
$805$	0	0
$806$	−0.736008	−0.0259248
$807$	3.20742	0.112906
$808$	−8.64556	−0.304150
$809$	−23.3178	−0.819812	−0.409906	−	0.912128i	$-0.634438\pi$
$809$	−23.3178	−0.819812	−0.409906	+	0.912128i	$0.634438\pi$
$810$	0	0
$811$	−13.6244	−0.478417	−0.239208	−	0.970968i	$-0.576888\pi$
$811$	−13.6244	−0.478417	−0.239208	+	0.970968i	$0.576888\pi$
$812$	8.13556	0.285502
$813$	0.304538	0.0106806
$814$	−0.664861	−0.0233034
$815$	0	0
$816$	0.477800	0.0167263
$817$	7.08423	0.247846
$818$	31.6722	1.10739
$819$	35.7208	1.24819
$820$	0	0
$821$	12.7743	0.445825	0.222912	−	0.974838i	$-0.428444\pi$
$821$	12.7743	0.445825	0.222912	+	0.974838i	$0.428444\pi$
$822$	6.94202	0.242131
$823$	−6.14329	−0.214142	−0.107071	−	0.994251i	$-0.534147\pi$
$823$	−6.14329	−0.214142	−0.107071	+	0.994251i	$0.534147\pi$
$824$	−40.3671	−1.40625
$825$	0	0
$826$	25.2717	0.879314
$827$	−21.6909	−0.754267	−0.377133	−	0.926159i	$-0.623090\pi$
$827$	−21.6909	−0.754267	−0.377133	+	0.926159i	$0.623090\pi$
$828$	12.1252	0.421378
$829$	−12.2263	−0.424638	−0.212319	−	0.977200i	$-0.568102\pi$
$829$	−12.2263	−0.424638	−0.212319	+	0.977200i	$0.568102\pi$
$830$	0	0
$831$	−4.82466	−0.167366
$832$	29.2981	1.01573
$833$	−3.77255	−0.130711
$834$	3.51216	0.121616
$835$	0	0
$836$	−2.73685	−0.0946558
$837$	−0.397006	−0.0137225
$838$	−7.43033	−0.256677
$839$	−24.4507	−0.844130	−0.422065	−	0.906566i	$-0.638695\pi$
$839$	−24.4507	−0.844130	−0.422065	+	0.906566i	$0.638695\pi$
$840$	0	0
$841$	−18.1431	−0.625624
$842$	28.2019	0.971900
$843$	4.29173	0.147815
$844$	12.1489	0.418183
$845$	0	0
$846$	−10.2968	−0.354011
$847$	0.157720	0.00541931
$848$	−4.87146	−0.167287
$849$	9.20755	0.316002
$850$	0	0
$851$	−1.08780	−0.0372892
$852$	−1.56687	−0.0536802
$853$	29.8098	1.02067	0.510334	−	0.859976i	$-0.329522\pi$
$853$	29.8098	1.02067	0.510334	+	0.859976i	$0.329522\pi$
$854$	10.0019	0.342258
$855$	0	0
$856$	−10.3678	−0.354363
$857$	18.6128	0.635801	0.317900	−	0.948124i	$-0.397022\pi$
$857$	18.6128	0.635801	0.317900	+	0.948124i	$0.397022\pi$
$858$	4.70904	0.160764
$859$	−49.9154	−1.70309	−0.851546	−	0.524281i	$-0.824334\pi$
$859$	−49.9154	−1.70309	−0.851546	+	0.524281i	$0.824334\pi$
$860$	0	0
$861$	−12.2122	−0.416189
$862$	14.0068	0.477073
$863$	28.4944	0.969960	0.484980	−	0.874525i	$-0.338827\pi$
$863$	28.4944	0.969960	0.484980	+	0.874525i	$0.338827\pi$
$864$	7.74820	0.263599
$865$	0	0
$866$	−2.19379	−0.0745480
$867$	−6.01430	−0.204256
$868$	0.461887	0.0156775
$869$	−21.8856	−0.742418
$870$	0	0
$871$	18.7656	0.635849
$872$	21.8974	0.741540
$873$	−1.40510	−0.0475553
$874$	8.71402	0.294756
$875$	0	0
$876$	0.153515	0.00518680
$877$	37.6957	1.27289	0.636447	−	0.771320i	$-0.280403\pi$
$877$	37.6957	1.27289	0.636447	+	0.771320i	$0.280403\pi$
$878$	−17.7482	−0.598974
$879$	11.2204	0.378456
$880$	0	0
$881$	43.3287	1.45978	0.729891	−	0.683563i	$-0.239571\pi$
$881$	43.3287	1.45978	0.729891	+	0.683563i	$0.239571\pi$
$882$	20.5386	0.691571
$883$	−16.8177	−0.565960	−0.282980	−	0.959126i	$-0.591323\pi$
$883$	−16.8177	−0.565960	−0.282980	+	0.959126i	$0.591323\pi$
$884$	1.40768	0.0473455
$885$	0	0
$886$	40.5408	1.36200
$887$	−42.9652	−1.44263	−0.721316	−	0.692607i	$-0.756462\pi$
$887$	−42.9652	−1.44263	−0.721316	+	0.692607i	$0.756462\pi$
$888$	−0.194562	−0.00652907
$889$	−69.5292	−2.33194
$890$	0	0
$891$	−25.9523	−0.869435
$892$	16.5276	0.553384
$893$	3.80261	0.127249
$894$	3.56300	0.119165
$895$	0	0
$896$	9.22341	0.308132
$897$	7.70458	0.257249
$898$	8.18098	0.273003
$899$	0.616388	0.0205577
$900$	0	0
$901$	−1.35280	−0.0450683
$902$	35.3303	1.17637
$903$	7.64942	0.254557
$904$	34.5833	1.15022
$905$	0	0
$906$	7.11994	0.236544
$907$	3.48910	0.115854	0.0579268	−	0.998321i	$-0.481551\pi$
$907$	3.48910	0.115854	0.0579268	+	0.998321i	$0.481551\pi$
$908$	5.26399	0.174692
$909$	8.05634	0.267212
$910$	0	0
$911$	2.19869	0.0728459	0.0364230	−	0.999336i	$-0.488404\pi$
$911$	2.19869	0.0728459	0.0364230	+	0.999336i	$0.488404\pi$
$912$	0.960644	0.0318101
$913$	43.4429	1.43775
$914$	3.28245	0.108574
$915$	0	0
$916$	−16.3918	−0.541602
$917$	−34.4281	−1.13692
$918$	−1.47765	−0.0487697
$919$	−5.02474	−0.165751	−0.0828754	−	0.996560i	$-0.526410\pi$
$919$	−5.02474	−0.165751	−0.0828754	+	0.996560i	$0.526410\pi$
$920$	0	0
$921$	−1.17154	−0.0386036
$922$	19.1944	0.632134
$923$	21.8494	0.719180
$924$	−2.95519	−0.0972187
$925$	0	0
$926$	−12.4349	−0.408637
$927$	37.6160	1.23547
$928$	−12.0298	−0.394897
$929$	20.3424	0.667413	0.333706	−	0.942677i	$-0.391701\pi$
$929$	20.3424	0.667413	0.333706	+	0.942677i	$0.391701\pi$
$930$	0	0
$931$	−7.58492	−0.248586
$932$	6.15309	0.201551
$933$	1.68824	0.0552707
$934$	19.3956	0.634643
$935$	0	0
$936$	−30.2415	−0.988473
$937$	−32.8768	−1.07404	−0.537018	−	0.843571i	$-0.680449\pi$
$937$	−32.8768	−1.07404	−0.537018	+	0.843571i	$0.680449\pi$
$938$	22.9176	0.748285
$939$	−10.0890	−0.329241
$940$	0	0
$941$	−23.1409	−0.754373	−0.377186	−	0.926137i	$-0.623108\pi$
$941$	−23.1409	−0.754373	−0.377186	+	0.926137i	$0.623108\pi$
$942$	5.87134	0.191298
$943$	57.8048	1.88238
$944$	−13.1871	−0.429203
$945$	0	0
$946$	−22.1301	−0.719510
$947$	−16.0089	−0.520219	−0.260110	−	0.965579i	$-0.583759\pi$
$947$	−16.0089	−0.520219	−0.260110	+	0.965579i	$0.583759\pi$
$948$	−1.62302	−0.0527133
$949$	−2.14070	−0.0694902
$950$	0	0
$951$	−8.52477	−0.276435
$952$	6.78377	0.219863
$953$	−1.56075	−0.0505577	−0.0252789	−	0.999680i	$-0.508047\pi$
$953$	−1.56075	−0.0505577	−0.0252789	+	0.999680i	$0.508047\pi$
$954$	7.36497	0.238450
$955$	0	0
$956$	8.85274	0.286318
$957$	−3.94371	−0.127482
$958$	3.64585	0.117792
$959$	60.7497	1.96171
$960$	0	0
$961$	−30.9650	−0.998871
$962$	0.687545	0.0221674
$963$	9.66118	0.311327
$964$	0.678878	0.0218652
$965$	0	0
$966$	9.40923	0.302737
$967$	−18.4147	−0.592175	−0.296088	−	0.955161i	$-0.595682\pi$
$967$	−18.4147	−0.592175	−0.296088	+	0.955161i	$0.595682\pi$
$968$	−0.133526	−0.00429170
$969$	0.266770	0.00856989
$970$	0	0
$971$	−0.699689	−0.0224541	−0.0112271	−	0.999937i	$-0.503574\pi$
$971$	−0.699689	−0.0224541	−0.0112271	+	0.999937i	$0.503574\pi$
$972$	−6.24685	−0.200368
$973$	30.7349	0.985317
$974$	−7.10048	−0.227514
$975$	0	0
$976$	−5.21913	−0.167060
$977$	13.0194	0.416527	0.208263	−	0.978073i	$-0.433219\pi$
$977$	13.0194	0.416527	0.208263	+	0.978073i	$0.433219\pi$
$978$	4.14810	0.132642
$979$	4.17682	0.133492
$980$	0	0
$981$	−20.4050	−0.651483
$982$	28.1024	0.896785
$983$	−36.2357	−1.15574	−0.577870	−	0.816129i	$-0.696116\pi$
$983$	−36.2357	−1.15574	−0.577870	+	0.816129i	$0.696116\pi$
$984$	10.3389	0.329592
$985$	0	0
$986$	2.29418	0.0730617
$987$	4.10598	0.130695
$988$	2.83023	0.0900415
$989$	−36.2076	−1.15133
$990$	0	0
$991$	−6.84413	−0.217411	−0.108705	−	0.994074i	$-0.534671\pi$
$991$	−6.84413	−0.217411	−0.108705	+	0.994074i	$0.534671\pi$
$992$	−0.682977	−0.0216845
$993$	−3.97850	−0.126254
$994$	26.6836	0.846351
$995$	0	0
$996$	3.22170	0.102083
$997$	−2.65302	−0.0840221	−0.0420110	−	0.999117i	$-0.513376\pi$
$997$	−2.65302	−0.0840221	−0.0420110	+	0.999117i	$0.513376\pi$
$998$	2.34095	0.0741014
$999$	0.370866	0.0117337

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.l.1.17	✓	40
5.4	even	2		6025.2.a.o.1.24	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6025.2.a.l.1.17	✓	40	1.1	even	1	trivial
6025.2.a.o.1.24	yes	40	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:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-1.14940 q^{2} +0.361587 q^{3} -0.678878 q^{4} -0.415609 q^{6} -3.63700 q^{7} +3.07910 q^{8} -2.86925 q^{9} +O(q^{10})\)	\(q-1.14940 q^{2} +0.361587 q^{3} -0.678878 q^{4} -0.415609 q^{6} -3.63700 q^{7} +3.07910 q^{8} -2.86925 q^{9} -3.31008 q^{11} -0.245473 q^{12} +3.42302 q^{13} +4.18037 q^{14} -2.18137 q^{16} -0.605765 q^{17} +3.29792 q^{18} -1.21792 q^{19} -1.31509 q^{21} +3.80461 q^{22} +6.22482 q^{23} +1.11336 q^{24} -3.93442 q^{26} -2.12225 q^{27} +2.46908 q^{28} +3.29498 q^{29} +0.187069 q^{31} -3.65094 q^{32} -1.19688 q^{33} +0.696266 q^{34} +1.94787 q^{36} -0.174751 q^{37} +1.39988 q^{38} +1.23772 q^{39} +9.28617 q^{41} +1.51157 q^{42} -5.81664 q^{43} +2.24714 q^{44} -7.15482 q^{46} -3.12220 q^{47} -0.788755 q^{48} +6.22774 q^{49} -0.219037 q^{51} -2.32381 q^{52} +2.23321 q^{53} +2.43931 q^{54} -11.1987 q^{56} -0.440386 q^{57} -3.78725 q^{58} +6.04532 q^{59} +2.39259 q^{61} -0.215017 q^{62} +10.4355 q^{63} +8.55913 q^{64} +1.37570 q^{66} +5.48219 q^{67} +0.411240 q^{68} +2.25082 q^{69} +6.38307 q^{71} -8.83473 q^{72} -0.625385 q^{73} +0.200859 q^{74} +0.826821 q^{76} +12.0388 q^{77} -1.42264 q^{78} +6.61180 q^{79} +7.84039 q^{81} -10.6735 q^{82} -13.1244 q^{83} +0.892786 q^{84} +6.68566 q^{86} +1.19142 q^{87} -10.1921 q^{88} -1.26185 q^{89} -12.4495 q^{91} -4.22589 q^{92} +0.0676417 q^{93} +3.58866 q^{94} -1.32013 q^{96} +0.489708 q^{97} -7.15817 q^{98} +9.49746 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9}+O(q^{10}) \) 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9	\( 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9} + q^{11} - 14 q^{12} - 9 q^{13} - q^{14} + 43 q^{16} - 12 q^{17} - 42 q^{18} + 2 q^{21} - 5 q^{22} - 77 q^{23} - 2 q^{24} + 2 q^{26} - 38 q^{27} - 42 q^{28} + 2 q^{29} + q^{31} - 72 q^{32} - 20 q^{33} + 5 q^{34} + 32 q^{36} - 28 q^{37} - 23 q^{38} - 2 q^{39} - 2 q^{41} - 37 q^{42} - 31 q^{43} + 3 q^{44} + 14 q^{46} - 96 q^{47} - 13 q^{48} + 40 q^{49} - 10 q^{51} - 42 q^{52} - 54 q^{53} + 4 q^{54} - 15 q^{56} - 37 q^{57} - 27 q^{58} + q^{59} + 5 q^{61} - 39 q^{62} - 70 q^{63} + 65 q^{64} - 52 q^{66} - 34 q^{67} - 52 q^{68} + 21 q^{69} - 9 q^{71} - 70 q^{72} - 25 q^{73} + 22 q^{74} - 47 q^{76} - 54 q^{77} - 58 q^{78} + 13 q^{79} + 12 q^{81} + 5 q^{82} - 63 q^{83} + 95 q^{84} - 18 q^{86} - 47 q^{87} - 13 q^{88} + 19 q^{89} - 31 q^{91} - 137 q^{92} - 52 q^{93} + 120 q^{94} - 49 q^{96} - 36 q^{97} - 64 q^{98} + 16 q^{99}+O(q^{100}) \) 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9 + q^11 - 14 * q^12 - 9 * q^13 - q^14 + 43 * q^16 - 12 * q^17 - 42 * q^18 + 2 * q^21 - 5 * q^22 - 77 * q^23 - 2 * q^24 + 2 * q^26 - 38 * q^27 - 42 * q^28 + 2 * q^29 + q^31 - 72 * q^32 - 20 * q^33 + 5 * q^34 + 32 * q^36 - 28 * q^37 - 23 * q^38 - 2 * q^39 - 2 * q^41 - 37 * q^42 - 31 * q^43 + 3 * q^44 + 14 * q^46 - 96 * q^47 - 13 * q^48 + 40 * q^49 - 10 * q^51 - 42 * q^52 - 54 * q^53 + 4 * q^54 - 15 * q^56 - 37 * q^57 - 27 * q^58 + q^59 + 5 * q^61 - 39 * q^62 - 70 * q^63 + 65 * q^64 - 52 * q^66 - 34 * q^67 - 52 * q^68 + 21 * q^69 - 9 * q^71 - 70 * q^72 - 25 * q^73 + 22 * q^74 - 47 * q^76 - 54 * q^77 - 58 * q^78 + 13 * q^79 + 12 * q^81 + 5 * q^82 - 63 * q^83 + 95 * q^84 - 18 * q^86 - 47 * q^87 - 13 * q^88 + 19 * q^89 - 31 * q^91 - 137 * q^92 - 52 * q^93 + 120 * q^94 - 49 * q^96 - 36 * q^97 - 64 * q^98 + 16 * q^99

Introduction

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