LMFDB - Embedded newform 6025.2.a.l.1.12

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			1.12
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)

$f(q)$	$=$	$q-1.59175 q^{2} +0.0342835 q^{3} +0.533671 q^{4} -0.0545707 q^{6} -1.01795 q^{7} +2.33403 q^{8} -2.99882 q^{9} +O(q^{10})$	\(q-1.59175 q^{2} +0.0342835 q^{3} +0.533671 q^{4} -0.0545707 q^{6} -1.01795 q^{7} +2.33403 q^{8} -2.99882 q^{9} +5.74092 q^{11} +0.0182961 q^{12} +4.77625 q^{13} +1.62032 q^{14} -4.78254 q^{16} -2.20671 q^{17} +4.77338 q^{18} +7.81958 q^{19} -0.0348989 q^{21} -9.13812 q^{22} -3.98508 q^{23} +0.0800186 q^{24} -7.60260 q^{26} -0.205661 q^{27} -0.543251 q^{28} +0.409391 q^{29} -9.04105 q^{31} +2.94455 q^{32} +0.196819 q^{33} +3.51253 q^{34} -1.60039 q^{36} -7.42508 q^{37} -12.4468 q^{38} +0.163746 q^{39} -12.1893 q^{41} +0.0555503 q^{42} -0.457663 q^{43} +3.06377 q^{44} +6.34326 q^{46} -6.21788 q^{47} -0.163962 q^{48} -5.96378 q^{49} -0.0756537 q^{51} +2.54895 q^{52} -2.25459 q^{53} +0.327360 q^{54} -2.37593 q^{56} +0.268082 q^{57} -0.651649 q^{58} +8.50068 q^{59} +2.47487 q^{61} +14.3911 q^{62} +3.05266 q^{63} +4.87809 q^{64} -0.313286 q^{66} +3.16911 q^{67} -1.17766 q^{68} -0.136622 q^{69} +1.46327 q^{71} -6.99935 q^{72} -10.8698 q^{73} +11.8189 q^{74} +4.17308 q^{76} -5.84398 q^{77} -0.260644 q^{78} +16.2231 q^{79} +8.98942 q^{81} +19.4024 q^{82} -2.52675 q^{83} -0.0186245 q^{84} +0.728485 q^{86} +0.0140353 q^{87} +13.3995 q^{88} -11.5557 q^{89} -4.86199 q^{91} -2.12672 q^{92} -0.309959 q^{93} +9.89732 q^{94} +0.100949 q^{96} -13.1176 q^{97} +9.49285 q^{98} -17.2160 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.59175	−1.12554	−0.562769	−	0.826614i	$-0.690264\pi$
$2$	−1.59175	−1.12554	−0.562769	+	0.826614i	$0.690264\pi$
$3$	0.0342835	0.0197936	0.00989678	−	0.999951i	$-0.496850\pi$
$3$	0.0342835	0.0197936	0.00989678	+	0.999951i	$0.496850\pi$
$4$	0.533671	0.266836
$5$	0	0
$5$	0	0
$6$	−0.0545707	−0.0222784
$7$	−1.01795	−0.384749	−0.192375	−	0.981322i	$-0.561619\pi$
$7$	−1.01795	−0.384749	−0.192375	+	0.981322i	$0.561619\pi$
$8$	2.33403	0.825204
$9$	−2.99882	−0.999608
$10$	0	0
$11$	5.74092	1.73095	0.865477	−	0.500949i	$-0.167016\pi$
$11$	5.74092	1.73095	0.865477	+	0.500949i	$0.167016\pi$
$12$	0.0182961	0.00528163
$13$	4.77625	1.32469	0.662347	−	0.749197i	$-0.269561\pi$
$13$	4.77625	1.32469	0.662347	+	0.749197i	$0.269561\pi$
$14$	1.62032	0.433050
$15$	0	0
$16$	−4.78254	−1.19563
$17$	−2.20671	−0.535206	−0.267603	−	0.963529i	$-0.586232\pi$
$17$	−2.20671	−0.535206	−0.267603	+	0.963529i	$0.586232\pi$
$18$	4.77338	1.12510
$19$	7.81958	1.79393	0.896967	−	0.442097i	$-0.145765\pi$
$19$	7.81958	1.79393	0.896967	+	0.442097i	$0.145765\pi$
$20$	0	0
$21$	−0.0348989	−0.00761556
$22$	−9.13812	−1.94825
$23$	−3.98508	−0.830947	−0.415474	−	0.909605i	$-0.636384\pi$
$23$	−3.98508	−0.830947	−0.415474	+	0.909605i	$0.636384\pi$
$24$	0.0800186	0.0163337
$25$	0	0
$26$	−7.60260	−1.49099
$27$	−0.205661	−0.0395794
$28$	−0.543251	−0.102665
$29$	0.409391	0.0760220	0.0380110	−	0.999277i	$-0.487898\pi$
$29$	0.409391	0.0760220	0.0380110	+	0.999277i	$0.487898\pi$
$30$	0	0
$31$	−9.04105	−1.62382	−0.811911	−	0.583782i	$-0.801572\pi$
$31$	−9.04105	−1.62382	−0.811911	+	0.583782i	$0.801572\pi$
$32$	2.94455	0.520528
$33$	0.196819	0.0342617
$34$	3.51253	0.602395
$35$	0	0
$36$	−1.60039	−0.266731
$37$	−7.42508	−1.22067	−0.610337	−	0.792142i	$-0.708966\pi$
$37$	−7.42508	−1.22067	−0.610337	+	0.792142i	$0.708966\pi$
$38$	−12.4468	−2.01914
$39$	0.163746	0.0262204
$40$	0	0
$41$	−12.1893	−1.90365	−0.951827	−	0.306635i	$-0.900797\pi$
$41$	−12.1893	−1.90365	−0.951827	+	0.306635i	$0.900797\pi$
$42$	0.0555503	0.00857160
$43$	−0.457663	−0.0697929	−0.0348965	−	0.999391i	$-0.511110\pi$
$43$	−0.457663	−0.0697929	−0.0348965	+	0.999391i	$0.511110\pi$
$44$	3.06377	0.461880
$45$	0	0
$46$	6.34326	0.935263
$47$	−6.21788	−0.906971	−0.453486	−	0.891264i	$-0.649820\pi$
$47$	−6.21788	−0.906971	−0.453486	+	0.891264i	$0.649820\pi$
$48$	−0.163962	−0.0236659
$49$	−5.96378	−0.851968
$50$	0	0
$51$	−0.0756537	−0.0105936
$52$	2.54895	0.353476
$53$	−2.25459	−0.309692	−0.154846	−	0.987939i	$-0.549488\pi$
$53$	−2.25459	−0.309692	−0.154846	+	0.987939i	$0.549488\pi$
$54$	0.327360	0.0445481
$55$	0	0
$56$	−2.37593	−0.317497
$57$	0.268082	0.0355084
$58$	−0.651649	−0.0855656
$59$	8.50068	1.10669	0.553347	−	0.832951i	$-0.313350\pi$
$59$	8.50068	1.10669	0.553347	+	0.832951i	$0.313350\pi$
$60$	0	0
$61$	2.47487	0.316874	0.158437	−	0.987369i	$-0.449355\pi$
$61$	2.47487	0.316874	0.158437	+	0.987369i	$0.449355\pi$
$62$	14.3911	1.82767
$63$	3.05266	0.384599
$64$	4.87809	0.609761
$65$	0	0
$66$	−0.313286	−0.0385629
$67$	3.16911	0.387169	0.193584	−	0.981084i	$-0.437989\pi$
$67$	3.16911	0.387169	0.193584	+	0.981084i	$0.437989\pi$
$68$	−1.17766	−0.142812
$69$	−0.136622	−0.0164474
$70$	0	0
$71$	1.46327	0.173658	0.0868288	−	0.996223i	$-0.472327\pi$
$71$	1.46327	0.173658	0.0868288	+	0.996223i	$0.472327\pi$
$72$	−6.99935	−0.824881
$73$	−10.8698	−1.27222	−0.636109	−	0.771599i	$-0.719457\pi$
$73$	−10.8698	−1.27222	−0.636109	+	0.771599i	$0.719457\pi$
$74$	11.8189	1.37392
$75$	0	0
$76$	4.17308	0.478686
$77$	−5.84398	−0.665983
$78$	−0.260644	−0.0295121
$79$	16.2231	1.82524	0.912621	−	0.408806i	$-0.134055\pi$
$79$	16.2231	1.82524	0.912621	+	0.408806i	$0.134055\pi$
$80$	0	0
$81$	8.98942	0.998825
$82$	19.4024	2.14264
$83$	−2.52675	−0.277347	−0.138674	−	0.990338i	$-0.544284\pi$
$83$	−2.52675	−0.277347	−0.138674	+	0.990338i	$0.544284\pi$
$84$	−0.0186245	−0.00203210
$85$	0	0
$86$	0.728485	0.0785546
$87$	0.0140353	0.00150475
$88$	13.3995	1.42839
$89$	−11.5557	−1.22491	−0.612453	−	0.790507i	$-0.709817\pi$
$89$	−11.5557	−1.22491	−0.612453	+	0.790507i	$0.709817\pi$
$90$	0	0
$91$	−4.86199	−0.509675
$92$	−2.12672	−0.221726
$93$	−0.309959	−0.0321412
$94$	9.89732	1.02083
$95$	0	0
$96$	0.100949	0.0103031
$97$	−13.1176	−1.33189	−0.665945	−	0.746001i	$-0.731972\pi$
$97$	−13.1176	−1.33189	−0.665945	+	0.746001i	$0.731972\pi$
$98$	9.49285	0.958922
$99$	−17.2160	−1.73028
$100$	0	0
$101$	18.7144	1.86216	0.931078	−	0.364821i	$-0.118870\pi$
$101$	18.7144	1.86216	0.931078	+	0.364821i	$0.118870\pi$
$102$	0.120422	0.0119235
$103$	16.5410	1.62983	0.814915	−	0.579581i	$-0.196784\pi$
$103$	16.5410	1.62983	0.814915	+	0.579581i	$0.196784\pi$
$104$	11.1479	1.09314
$105$	0	0
$106$	3.58875	0.348570
$107$	9.75782	0.943324	0.471662	−	0.881779i	$-0.343654\pi$
$107$	9.75782	0.943324	0.471662	+	0.881779i	$0.343654\pi$
$108$	−0.109755	−0.0105612
$109$	2.29356	0.219683	0.109841	−	0.993949i	$-0.464966\pi$
$109$	2.29356	0.219683	0.109841	+	0.993949i	$0.464966\pi$
$110$	0	0
$111$	−0.254557	−0.0241615
$112$	4.86839	0.460020
$113$	−10.0532	−0.945727	−0.472864	−	0.881136i	$-0.656780\pi$
$113$	−10.0532	−0.945727	−0.472864	+	0.881136i	$0.656780\pi$
$114$	−0.426720	−0.0399660
$115$	0	0
$116$	0.218480	0.0202854
$117$	−14.3231	−1.32417
$118$	−13.5310	−1.24563
$119$	2.24632	0.205920
$120$	0	0
$121$	21.9582	1.99620
$122$	−3.93937	−0.356654
$123$	−0.417893	−0.0376801
$124$	−4.82495	−0.433293
$125$	0	0
$126$	−4.85907	−0.432880
$127$	−17.5071	−1.55350	−0.776750	−	0.629809i	$-0.783133\pi$
$127$	−17.5071	−1.55350	−0.776750	+	0.629809i	$0.783133\pi$
$128$	−13.6538	−1.20684
$129$	−0.0156903	−0.00138145
$130$	0	0
$131$	9.80696	0.856838	0.428419	−	0.903580i	$-0.359071\pi$
$131$	9.80696	0.856838	0.428419	+	0.903580i	$0.359071\pi$
$132$	0.105037	0.00914226
$133$	−7.95995	−0.690215
$134$	−5.04444	−0.435773
$135$	0	0
$136$	−5.15053	−0.441654
$137$	−1.80059	−0.153835	−0.0769175	−	0.997037i	$-0.524508\pi$
$137$	−1.80059	−0.153835	−0.0769175	+	0.997037i	$0.524508\pi$
$138$	0.217469	0.0185122
$139$	−4.92304	−0.417566	−0.208783	−	0.977962i	$-0.566950\pi$
$139$	−4.92304	−0.417566	−0.208783	+	0.977962i	$0.566950\pi$
$140$	0	0
$141$	−0.213171	−0.0179522
$142$	−2.32915	−0.195458
$143$	27.4201	2.29298
$144$	14.3420	1.19517
$145$	0	0
$146$	17.3021	1.43193
$147$	−0.204459	−0.0168635
$148$	−3.96255	−0.325720
$149$	7.29802	0.597877	0.298938	−	0.954272i	$-0.403367\pi$
$149$	7.29802	0.597877	0.298938	+	0.954272i	$0.403367\pi$
$150$	0	0
$151$	−6.96990	−0.567202	−0.283601	−	0.958942i	$-0.591529\pi$
$151$	−6.96990	−0.567202	−0.283601	+	0.958942i	$0.591529\pi$
$152$	18.2511	1.48036
$153$	6.61754	0.534996
$154$	9.30216	0.749589
$155$	0	0
$156$	0.0873868	0.00699654
$157$	−21.5262	−1.71798	−0.858991	−	0.511991i	$-0.828908\pi$
$157$	−21.5262	−1.71798	−0.858991	+	0.511991i	$0.828908\pi$
$158$	−25.8232	−2.05438
$159$	−0.0772953	−0.00612992
$160$	0	0
$161$	4.05662	0.319706
$162$	−14.3089	−1.12422
$163$	3.55531	0.278473	0.139237	−	0.990259i	$-0.455535\pi$
$163$	3.55531	0.278473	0.139237	+	0.990259i	$0.455535\pi$
$164$	−6.50510	−0.507963
$165$	0	0
$166$	4.02196	0.312165
$167$	−11.9448	−0.924317	−0.462158	−	0.886797i	$-0.652925\pi$
$167$	−11.9448	−0.924317	−0.462158	+	0.886797i	$0.652925\pi$
$168$	−0.0814551	−0.00628439
$169$	9.81257	0.754813
$170$	0	0
$171$	−23.4495	−1.79323
$172$	−0.244241	−0.0186232
$173$	−4.86182	−0.369637	−0.184819	−	0.982773i	$-0.559170\pi$
$173$	−4.86182	−0.369637	−0.184819	+	0.982773i	$0.559170\pi$
$174$	−0.0223408	−0.00169365
$175$	0	0
$176$	−27.4562	−2.06959
$177$	0.291433	0.0219054
$178$	18.3939	1.37868
$179$	1.77821	0.132910	0.0664548	−	0.997789i	$-0.478831\pi$
$179$	1.77821	0.132910	0.0664548	+	0.997789i	$0.478831\pi$
$180$	0	0
$181$	9.10703	0.676921	0.338460	−	0.940981i	$-0.390094\pi$
$181$	9.10703	0.676921	0.338460	+	0.940981i	$0.390094\pi$
$182$	7.73908	0.573659
$183$	0.0848470	0.00627207
$184$	−9.30131	−0.685701
$185$	0	0
$186$	0.493377	0.0361762
$187$	−12.6686	−0.926417
$188$	−3.31831	−0.242012
$189$	0.209352	0.0152281
$190$	0	0
$191$	5.97595	0.432405	0.216202	−	0.976349i	$-0.430633\pi$
$191$	5.97595	0.432405	0.216202	+	0.976349i	$0.430633\pi$
$192$	0.167238	0.0120693
$193$	−20.2480	−1.45749	−0.728743	−	0.684788i	$-0.759895\pi$
$193$	−20.2480	−1.45749	−0.728743	+	0.684788i	$0.759895\pi$
$194$	20.8800	1.49909
$195$	0	0
$196$	−3.18270	−0.227335
$197$	−5.59926	−0.398931	−0.199465	−	0.979905i	$-0.563921\pi$
$197$	−5.59926	−0.398931	−0.199465	+	0.979905i	$0.563921\pi$
$198$	27.4036	1.94749
$199$	−11.8854	−0.842532	−0.421266	−	0.906937i	$-0.638414\pi$
$199$	−11.8854	−0.842532	−0.421266	+	0.906937i	$0.638414\pi$
$200$	0	0
$201$	0.108648	0.00766345
$202$	−29.7887	−2.09593
$203$	−0.416740	−0.0292494
$204$	−0.0403742	−0.00282676
$205$	0	0
$206$	−26.3291	−1.83444
$207$	11.9506	0.830622
$208$	−22.8426	−1.58385
$209$	44.8916	3.10522
$210$	0	0
$211$	4.99471	0.343850	0.171925	−	0.985110i	$-0.445001\pi$
$211$	4.99471	0.343850	0.171925	+	0.985110i	$0.445001\pi$
$212$	−1.20321	−0.0826369
$213$	0.0501658	0.00343730
$214$	−15.5320	−1.06175
$215$	0	0
$216$	−0.480018	−0.0326611
$217$	9.20335	0.624764
$218$	−3.65077	−0.247261
$219$	−0.372656	−0.0251817
$220$	0	0
$221$	−10.5398	−0.708984
$222$	0.405192	0.0271947
$223$	9.69650	0.649325	0.324663	−	0.945830i	$-0.394749\pi$
$223$	9.69650	0.649325	0.324663	+	0.945830i	$0.394749\pi$
$224$	−2.99741	−0.200273
$225$	0	0
$226$	16.0022	1.06445
$227$	−13.8085	−0.916504	−0.458252	−	0.888822i	$-0.651524\pi$
$227$	−13.8085	−0.916504	−0.458252	+	0.888822i	$0.651524\pi$
$228$	0.143068	0.00947490
$229$	−8.18876	−0.541128	−0.270564	−	0.962702i	$-0.587210\pi$
$229$	−8.18876	−0.541128	−0.270564	+	0.962702i	$0.587210\pi$
$230$	0	0
$231$	−0.200352	−0.0131822
$232$	0.955531	0.0627337
$233$	−16.0598	−1.05211	−0.526055	−	0.850450i	$-0.676329\pi$
$233$	−16.0598	−1.05211	−0.526055	+	0.850450i	$0.676329\pi$
$234$	22.7989	1.49041
$235$	0	0
$236$	4.53657	0.295306
$237$	0.556184	0.0361281
$238$	−3.57559	−0.231771
$239$	−21.1719	−1.36950	−0.684749	−	0.728779i	$-0.740088\pi$
$239$	−21.1719	−1.36950	−0.684749	+	0.728779i	$0.740088\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	−34.9520	−2.24680
$243$	0.925170	0.0593497
$244$	1.32076	0.0845533
$245$	0	0
$246$	0.665181	0.0424104
$247$	37.3483	2.37641
$248$	−21.1021	−1.33998
$249$	−0.0866259	−0.00548969
$250$	0	0
$251$	−11.5406	−0.728436	−0.364218	−	0.931314i	$-0.618664\pi$
$251$	−11.5406	−0.728436	−0.364218	+	0.931314i	$0.618664\pi$
$252$	1.62912	0.102625
$253$	−22.8781	−1.43833
$254$	27.8669	1.74852
$255$	0	0
$256$	11.9773	0.748580
$257$	31.1018	1.94008	0.970039	−	0.242948i	$-0.0781145\pi$
$257$	31.1018	1.94008	0.970039	+	0.242948i	$0.0781145\pi$
$258$	0.0249750	0.00155488
$259$	7.55836	0.469654
$260$	0	0
$261$	−1.22769	−0.0759922
$262$	−15.6102	−0.964404
$263$	−3.93805	−0.242831	−0.121415	−	0.992602i	$-0.538743\pi$
$263$	−3.93805	−0.242831	−0.121415	+	0.992602i	$0.538743\pi$
$264$	0.459381	0.0282729
$265$	0	0
$266$	12.6703	0.776863
$267$	−0.396171	−0.0242453
$268$	1.69126	0.103310
$269$	−29.5233	−1.80007	−0.900034	−	0.435821i	$-0.856458\pi$
$269$	−29.5233	−1.80007	−0.900034	+	0.435821i	$0.856458\pi$
$270$	0	0
$271$	−2.87037	−0.174362	−0.0871812	−	0.996192i	$-0.527786\pi$
$271$	−2.87037	−0.174362	−0.0871812	+	0.996192i	$0.527786\pi$
$272$	10.5537	0.639911
$273$	−0.166686	−0.0100883
$274$	2.86610	0.173147
$275$	0	0
$276$	−0.0729115	−0.00438876
$277$	−14.7589	−0.886777	−0.443389	−	0.896330i	$-0.646224\pi$
$277$	−14.7589	−0.886777	−0.443389	+	0.896330i	$0.646224\pi$
$278$	7.83625	0.469987
$279$	27.1125	1.62319
$280$	0	0
$281$	−24.6731	−1.47187	−0.735937	−	0.677050i	$-0.763258\pi$
$281$	−24.6731	−1.47187	−0.735937	+	0.677050i	$0.763258\pi$
$282$	0.339315	0.0202059
$283$	−9.54548	−0.567420	−0.283710	−	0.958910i	$-0.591565\pi$
$283$	−9.54548	−0.567420	−0.283710	+	0.958910i	$0.591565\pi$
$284$	0.780903	0.0463381
$285$	0	0
$286$	−43.6460	−2.58084
$287$	12.4081	0.732430
$288$	−8.83019	−0.520324
$289$	−12.1304	−0.713555
$290$	0	0
$291$	−0.449717	−0.0263629
$292$	−5.80092	−0.339473
$293$	21.8810	1.27830	0.639151	−	0.769082i	$-0.279286\pi$
$293$	21.8810	1.27830	0.639151	+	0.769082i	$0.279286\pi$
$294$	0.325448	0.0189805
$295$	0	0
$296$	−17.3304	−1.00731
$297$	−1.18068	−0.0685101
$298$	−11.6166	−0.672933
$299$	−19.0338	−1.10075
$300$	0	0
$301$	0.465878	0.0268528
$302$	11.0943	0.638408
$303$	0.641596	0.0368587
$304$	−37.3974	−2.14489
$305$	0	0
$306$	−10.5335	−0.602159
$307$	−1.80394	−0.102957	−0.0514783	−	0.998674i	$-0.516393\pi$
$307$	−1.80394	−0.102957	−0.0514783	+	0.998674i	$0.516393\pi$
$308$	−3.11876	−0.177708
$309$	0.567082	0.0322601
$310$	0	0
$311$	−26.7668	−1.51781	−0.758904	−	0.651203i	$-0.774265\pi$
$311$	−26.7668	−1.51781	−0.758904	+	0.651203i	$0.774265\pi$
$312$	0.382189	0.0216372
$313$	10.1814	0.575488	0.287744	−	0.957707i	$-0.407095\pi$
$313$	10.1814	0.575488	0.287744	+	0.957707i	$0.407095\pi$
$314$	34.2644	1.93365
$315$	0	0
$316$	8.65781	0.487040
$317$	7.59564	0.426614	0.213307	−	0.976985i	$-0.431577\pi$
$317$	7.59564	0.426614	0.213307	+	0.976985i	$0.431577\pi$
$318$	0.123035	0.00689945
$319$	2.35028	0.131591
$320$	0	0
$321$	0.334532	0.0186718
$322$	−6.45713	−0.359842
$323$	−17.2555	−0.960124
$324$	4.79740	0.266522
$325$	0	0
$326$	−5.65917	−0.313432
$327$	0.0786310	0.00434831
$328$	−28.4503	−1.57090
$329$	6.32950	0.348957
$330$	0	0
$331$	−13.5457	−0.744540	−0.372270	−	0.928125i	$-0.621420\pi$
$331$	−13.5457	−0.744540	−0.372270	+	0.928125i	$0.621420\pi$
$332$	−1.34846	−0.0740061
$333$	22.2665	1.22020
$334$	19.0132	1.04035
$335$	0	0
$336$	0.166905	0.00910543
$337$	18.7266	1.02010	0.510051	−	0.860144i	$-0.329626\pi$
$337$	18.7266	1.02010	0.510051	+	0.860144i	$0.329626\pi$
$338$	−15.6192	−0.849571
$339$	−0.344659	−0.0187193
$340$	0	0
$341$	−51.9040	−2.81076
$342$	37.3258	2.01835
$343$	13.1965	0.712543
$344$	−1.06820	−0.0575934
$345$	0	0
$346$	7.73880	0.416041
$347$	−24.5071	−1.31561	−0.657805	−	0.753189i	$-0.728515\pi$
$347$	−24.5071	−1.31561	−0.657805	+	0.753189i	$0.728515\pi$
$348$	0.00749026	0.000401520 0
$349$	28.7644	1.53972	0.769860	−	0.638213i	$-0.220326\pi$
$349$	28.7644	1.53972	0.769860	+	0.638213i	$0.220326\pi$
$350$	0	0
$351$	−0.982286	−0.0524306
$352$	16.9044	0.901009
$353$	−3.86101	−0.205501	−0.102750	−	0.994707i	$-0.532764\pi$
$353$	−3.86101	−0.205501	−0.102750	+	0.994707i	$0.532764\pi$
$354$	−0.463888	−0.0246554
$355$	0	0
$356$	−6.16697	−0.326849
$357$	0.0770118	0.00407589
$358$	−2.83046	−0.149595
$359$	−9.19684	−0.485391	−0.242695	−	0.970103i	$-0.578032\pi$
$359$	−9.19684	−0.485391	−0.242695	+	0.970103i	$0.578032\pi$
$360$	0	0
$361$	42.1458	2.21820
$362$	−14.4961	−0.761900
$363$	0.752803	0.0395119
$364$	−2.59470	−0.135999
$365$	0	0
$366$	−0.135055	−0.00705945
$367$	25.7878	1.34611	0.673057	−	0.739590i	$-0.264981\pi$
$367$	25.7878	1.34611	0.673057	+	0.739590i	$0.264981\pi$
$368$	19.0588	0.993509
$369$	36.5537	1.90291
$370$	0	0
$371$	2.29507	0.119154
$372$	−0.165416	−0.00857642
$373$	−24.5838	−1.27290	−0.636450	−	0.771318i	$-0.719598\pi$
$373$	−24.5838	−1.27290	−0.636450	+	0.771318i	$0.719598\pi$
$374$	20.1652	1.04272
$375$	0	0
$376$	−14.5127	−0.748437
$377$	1.95535	0.100706
$378$	−0.333237	−0.0171399
$379$	13.3858	0.687584	0.343792	−	0.939046i	$-0.388288\pi$
$379$	13.3858	0.687584	0.343792	+	0.939046i	$0.388288\pi$
$380$	0	0
$381$	−0.600202	−0.0307493
$382$	−9.51223	−0.486688
$383$	5.75124	0.293875	0.146937	−	0.989146i	$-0.453058\pi$
$383$	5.75124	0.293875	0.146937	+	0.989146i	$0.453058\pi$
$384$	−0.468100	−0.0238876
$385$	0	0
$386$	32.2298	1.64046
$387$	1.37245	0.0697656
$388$	−7.00049	−0.355396
$389$	−11.5104	−0.583598	−0.291799	−	0.956480i	$-0.594254\pi$
$389$	−11.5104	−0.583598	−0.291799	+	0.956480i	$0.594254\pi$
$390$	0	0
$391$	8.79393	0.444728
$392$	−13.9196	−0.703048
$393$	0.336217	0.0169599
$394$	8.91262	0.449012
$395$	0	0
$396$	−9.18770	−0.461699
$397$	11.7261	0.588518	0.294259	−	0.955726i	$-0.404927\pi$
$397$	11.7261	0.588518	0.294259	+	0.955726i	$0.404927\pi$
$398$	18.9186	0.948301
$399$	−0.272895	−0.0136618
$400$	0	0
$401$	−0.795398	−0.0397203	−0.0198602	−	0.999803i	$-0.506322\pi$
$401$	−0.795398	−0.0397203	−0.0198602	+	0.999803i	$0.506322\pi$
$402$	−0.172941	−0.00862550
$403$	−43.1823	−2.15107
$404$	9.98735	0.496889
$405$	0	0
$406$	0.663346	0.0329213
$407$	−42.6268	−2.11293
$408$	−0.176578	−0.00874191
$409$	2.98099	0.147401	0.0737004	−	0.997280i	$-0.476519\pi$
$409$	2.98099	0.147401	0.0737004	+	0.997280i	$0.476519\pi$
$410$	0	0
$411$	−0.0617306	−0.00304494
$412$	8.82744	0.434897
$413$	−8.65328	−0.425800
$414$	−19.0223	−0.934896
$415$	0	0
$416$	14.0639	0.689540
$417$	−0.168779	−0.00826513
$418$	−71.4562	−3.49504
$419$	24.7131	1.20731	0.603656	−	0.797245i	$-0.293710\pi$
$419$	24.7131	1.20731	0.603656	+	0.797245i	$0.293710\pi$
$420$	0	0
$421$	18.7598	0.914298	0.457149	−	0.889390i	$-0.348871\pi$
$421$	18.7598	0.914298	0.457149	+	0.889390i	$0.348871\pi$
$422$	−7.95033	−0.387016
$423$	18.6463	0.906616
$424$	−5.26229	−0.255559
$425$	0	0
$426$	−0.0798515	−0.00386882
$427$	−2.51929	−0.121917
$428$	5.20747	0.251713
$429$	0.940056	0.0453863
$430$	0	0
$431$	−1.10510	−0.0532307	−0.0266154	−	0.999646i	$-0.508473\pi$
$431$	−1.10510	−0.0532307	−0.0266154	+	0.999646i	$0.508473\pi$
$432$	0.983579	0.0473225
$433$	32.9637	1.58413	0.792066	−	0.610435i	$-0.209005\pi$
$433$	32.9637	1.58413	0.792066	+	0.610435i	$0.209005\pi$
$434$	−14.6494	−0.703196
$435$	0	0
$436$	1.22400	0.0586192
$437$	−31.1617	−1.49067
$438$	0.593175	0.0283430
$439$	3.06090	0.146089	0.0730444	−	0.997329i	$-0.476729\pi$
$439$	3.06090	0.146089	0.0730444	+	0.997329i	$0.476729\pi$
$440$	0	0
$441$	17.8843	0.851634
$442$	16.7767	0.797988
$443$	25.7992	1.22576	0.612879	−	0.790177i	$-0.290011\pi$
$443$	25.7992	1.22576	0.612879	+	0.790177i	$0.290011\pi$
$444$	−0.135850	−0.00644715
$445$	0	0
$446$	−15.4344	−0.730840
$447$	0.250201	0.0118341
$448$	−4.96565	−0.234605
$449$	−33.3883	−1.57569	−0.787846	−	0.615872i	$-0.788804\pi$
$449$	−33.3883	−1.57569	−0.787846	+	0.615872i	$0.788804\pi$
$450$	0	0
$451$	−69.9780	−3.29514
$452$	−5.36511	−0.252354
$453$	−0.238952	−0.0112270
$454$	21.9797	1.03156
$455$	0	0
$456$	0.625712	0.0293017
$457$	−1.59727	−0.0747172	−0.0373586	−	0.999302i	$-0.511894\pi$
$457$	−1.59727	−0.0747172	−0.0373586	+	0.999302i	$0.511894\pi$
$458$	13.0345	0.609060
$459$	0.453833	0.0211831
$460$	0	0
$461$	12.6226	0.587892	0.293946	−	0.955822i	$-0.405031\pi$
$461$	12.6226	0.587892	0.293946	+	0.955822i	$0.405031\pi$
$462$	0.318910	0.0148370
$463$	5.97980	0.277905	0.138953	−	0.990299i	$-0.455626\pi$
$463$	5.97980	0.277905	0.138953	+	0.990299i	$0.455626\pi$
$464$	−1.95793	−0.0908945
$465$	0	0
$466$	25.5632	1.18419
$467$	10.4848	0.485180	0.242590	−	0.970129i	$-0.422003\pi$
$467$	10.4848	0.485180	0.242590	+	0.970129i	$0.422003\pi$
$468$	−7.64385	−0.353337
$469$	−3.22600	−0.148963
$470$	0	0
$471$	−0.737994	−0.0340050
$472$	19.8408	0.913249
$473$	−2.62741	−0.120808
$474$	−0.885307	−0.0406635
$475$	0	0
$476$	1.19880	0.0549468
$477$	6.76113	0.309571
$478$	33.7004	1.54142
$479$	2.88134	0.131652	0.0658258	−	0.997831i	$-0.479032\pi$
$479$	2.88134	0.131652	0.0658258	+	0.997831i	$0.479032\pi$
$480$	0	0
$481$	−35.4640	−1.61702
$482$	1.59175	0.0725023
$483$	0.139075	0.00632813
$484$	11.7185	0.532657
$485$	0	0
$486$	−1.47264	−0.0668003
$487$	−18.2911	−0.828850	−0.414425	−	0.910083i	$-0.636017\pi$
$487$	−18.2911	−0.828850	−0.414425	+	0.910083i	$0.636017\pi$
$488$	5.77641	0.261486
$489$	0.121888	0.00551198
$490$	0	0
$491$	20.0482	0.904762	0.452381	−	0.891825i	$-0.350575\pi$
$491$	20.0482	0.904762	0.452381	+	0.891825i	$0.350575\pi$
$492$	−0.223017	−0.0100544
$493$	−0.903407	−0.0406874
$494$	−59.4491	−2.67474
$495$	0	0
$496$	43.2392	1.94150
$497$	−1.48953	−0.0668147
$498$	0.137887	0.00617885
$499$	5.02273	0.224848	0.112424	−	0.993660i	$-0.464138\pi$
$499$	5.02273	0.224848	0.112424	+	0.993660i	$0.464138\pi$
$500$	0	0
$501$	−0.409509	−0.0182955
$502$	18.3698	0.819882
$503$	12.6546	0.564242	0.282121	−	0.959379i	$-0.408962\pi$
$503$	12.6546	0.564242	0.282121	+	0.959379i	$0.408962\pi$
$504$	7.12499	0.317372
$505$	0	0
$506$	36.4162	1.61890
$507$	0.336409	0.0149405
$508$	−9.34301	−0.414529
$509$	−7.20912	−0.319539	−0.159769	−	0.987154i	$-0.551075\pi$
$509$	−7.20912	−0.319539	−0.159769	+	0.987154i	$0.551075\pi$
$510$	0	0
$511$	11.0650	0.489485
$512$	8.24276	0.364282
$513$	−1.60818	−0.0710028
$514$	−49.5064	−2.18363
$515$	0	0
$516$	−0.00837344	−0.000368620 0
$517$	−35.6964	−1.56993
$518$	−12.0310	−0.528613
$519$	−0.166680	−0.00731644
$520$	0	0
$521$	2.53657	0.111129	0.0555647	−	0.998455i	$-0.482304\pi$
$521$	2.53657	0.111129	0.0555647	+	0.998455i	$0.482304\pi$
$522$	1.95418	0.0855321
$523$	−4.55695	−0.199262	−0.0996308	−	0.995024i	$-0.531766\pi$
$523$	−4.55695	−0.199262	−0.0996308	+	0.995024i	$0.531766\pi$
$524$	5.23369	0.228635
$525$	0	0
$526$	6.26840	0.273315
$527$	19.9510	0.869079
$528$	−0.941293	−0.0409645
$529$	−7.11911	−0.309526
$530$	0	0
$531$	−25.4921	−1.10626
$532$	−4.24800	−0.184174
$533$	−58.2193	−2.52176
$534$	0.630606	0.0272890
$535$	0	0
$536$	7.39680	0.319493
$537$	0.0609631	0.00263075
$538$	46.9937	2.02604
$539$	−34.2376	−1.47472
$540$	0	0
$541$	−32.9491	−1.41659	−0.708296	−	0.705915i	$-0.750536\pi$
$541$	−32.9491	−1.41659	−0.708296	+	0.705915i	$0.750536\pi$
$542$	4.56891	0.196252
$543$	0.312221	0.0133987
$544$	−6.49777	−0.278589
$545$	0	0
$546$	0.265322	0.0113548
$547$	5.31970	0.227454	0.113727	−	0.993512i	$-0.463721\pi$
$547$	5.31970	0.227454	0.113727	+	0.993512i	$0.463721\pi$
$548$	−0.960925	−0.0410487
$549$	−7.42169	−0.316750
$550$	0	0
$551$	3.20127	0.136378
$552$	−0.318881	−0.0135725
$553$	−16.5143	−0.702261
$554$	23.4925	0.998101
$555$	0	0
$556$	−2.62728	−0.111422
$557$	−34.5349	−1.46329	−0.731644	−	0.681687i	$-0.761247\pi$
$557$	−34.5349	−1.46329	−0.731644	+	0.681687i	$0.761247\pi$
$558$	−43.1564	−1.82696
$559$	−2.18591	−0.0924542
$560$	0	0
$561$	−0.434322	−0.0183371
$562$	39.2734	1.65665
$563$	−3.85041	−0.162275	−0.0811377	−	0.996703i	$-0.525855\pi$
$563$	−3.85041	−0.162275	−0.0811377	+	0.996703i	$0.525855\pi$
$564$	−0.113763	−0.00479029
$565$	0	0
$566$	15.1940	0.638653
$567$	−9.15079	−0.384297
$568$	3.41531	0.143303
$569$	−42.1707	−1.76789	−0.883943	−	0.467595i	$-0.845121\pi$
$569$	−42.1707	−1.76789	−0.883943	+	0.467595i	$0.845121\pi$
$570$	0	0
$571$	23.9479	1.00219	0.501094	−	0.865393i	$-0.332931\pi$
$571$	23.9479	1.00219	0.501094	+	0.865393i	$0.332931\pi$
$572$	14.6333	0.611850
$573$	0.204876	0.00855883
$574$	−19.7507	−0.824378
$575$	0	0
$576$	−14.6285	−0.609522
$577$	−32.2352	−1.34197	−0.670984	−	0.741472i	$-0.734128\pi$
$577$	−32.2352	−1.34197	−0.670984	+	0.741472i	$0.734128\pi$
$578$	19.3086	0.803133
$579$	−0.694173	−0.0288488
$580$	0	0
$581$	2.57211	0.106709
$582$	0.715837	0.0296724
$583$	−12.9434	−0.536063
$584$	−25.3705	−1.04984
$585$	0	0
$586$	−34.8291	−1.43878
$587$	−18.8703	−0.778863	−0.389431	−	0.921056i	$-0.627328\pi$
$587$	−18.8703	−0.778863	−0.389431	+	0.921056i	$0.627328\pi$
$588$	−0.109114	−0.00449978
$589$	−70.6972	−2.91303
$590$	0	0
$591$	−0.191962	−0.00789626
$592$	35.5107	1.45948
$593$	36.3745	1.49372	0.746860	−	0.664981i	$-0.231560\pi$
$593$	36.3745	1.49372	0.746860	+	0.664981i	$0.231560\pi$
$594$	1.87935	0.0771107
$595$	0	0
$596$	3.89474	0.159535
$597$	−0.407472	−0.0166767
$598$	30.2970	1.23894
$599$	9.75093	0.398412	0.199206	−	0.979958i	$-0.436164\pi$
$599$	9.75093	0.398412	0.199206	+	0.979958i	$0.436164\pi$
$600$	0	0
$601$	−9.19087	−0.374903	−0.187452	−	0.982274i	$-0.560023\pi$
$601$	−9.19087	−0.374903	−0.187452	+	0.982274i	$0.560023\pi$
$602$	−0.741562	−0.0302238
$603$	−9.50361	−0.387017
$604$	−3.71964	−0.151350
$605$	0	0
$606$	−1.02126	−0.0414859
$607$	−6.58402	−0.267237	−0.133618	−	0.991033i	$-0.542660\pi$
$607$	−6.58402	−0.267237	−0.133618	+	0.991033i	$0.542660\pi$
$608$	23.0251	0.933792
$609$	−0.0142873	−0.000578950 0
$610$	0	0
$611$	−29.6982	−1.20146
$612$	3.53159	0.142756
$613$	−37.4431	−1.51231	−0.756156	−	0.654392i	$-0.772925\pi$
$613$	−37.4431	−1.51231	−0.756156	+	0.654392i	$0.772925\pi$
$614$	2.87143	0.115881
$615$	0	0
$616$	−13.6400	−0.549572
$617$	−34.9827	−1.40835	−0.704175	−	0.710026i	$-0.748683\pi$
$617$	−34.9827	−1.40835	−0.704175	+	0.710026i	$0.748683\pi$
$618$	−0.902653	−0.0363100
$619$	5.12303	0.205912	0.102956	−	0.994686i	$-0.467170\pi$
$619$	5.12303	0.205912	0.102956	+	0.994686i	$0.467170\pi$
$620$	0	0
$621$	0.819574	0.0328884
$622$	42.6061	1.70835
$623$	11.7632	0.471282
$624$	−0.783124	−0.0313500
$625$	0	0
$626$	−16.2063	−0.647734
$627$	1.53904	0.0614633
$628$	−11.4879	−0.458419
$629$	16.3850	0.653312
$630$	0	0
$631$	−6.57742	−0.261843	−0.130922	−	0.991393i	$-0.541794\pi$
$631$	−6.57742	−0.261843	−0.130922	+	0.991393i	$0.541794\pi$
$632$	37.8652	1.50620
$633$	0.171236	0.00680601
$634$	−12.0904	−0.480170
$635$	0	0
$636$	−0.0412503	−0.00163568
$637$	−28.4845	−1.12860
$638$	−3.74106	−0.148110
$639$	−4.38808	−0.173590
$640$	0	0
$641$	−8.14309	−0.321633	−0.160816	−	0.986984i	$-0.551413\pi$
$641$	−8.14309	−0.321633	−0.160816	+	0.986984i	$0.551413\pi$
$642$	−0.532492	−0.0210158
$643$	−9.93346	−0.391737	−0.195869	−	0.980630i	$-0.562753\pi$
$643$	−9.93346	−0.391737	−0.195869	+	0.980630i	$0.562753\pi$
$644$	2.16490	0.0853091
$645$	0	0
$646$	27.4665	1.08066
$647$	−33.9129	−1.33325	−0.666627	−	0.745391i	$-0.732263\pi$
$647$	−33.9129	−1.33325	−0.666627	+	0.745391i	$0.732263\pi$
$648$	20.9816	0.824234
$649$	48.8018	1.91564
$650$	0	0
$651$	0.315523	0.0123663
$652$	1.89737	0.0743066
$653$	6.12347	0.239630	0.119815	−	0.992796i	$-0.461770\pi$
$653$	6.12347	0.239630	0.119815	+	0.992796i	$0.461770\pi$
$654$	−0.125161	−0.00489418
$655$	0	0
$656$	58.2960	2.27607
$657$	32.5967	1.27172
$658$	−10.0750	−0.392764
$659$	−18.4602	−0.719106	−0.359553	−	0.933125i	$-0.617071\pi$
$659$	−18.4602	−0.719106	−0.359553	+	0.933125i	$0.617071\pi$
$660$	0	0
$661$	18.1393	0.705536	0.352768	−	0.935711i	$-0.385240\pi$
$661$	18.1393	0.705536	0.352768	+	0.935711i	$0.385240\pi$
$662$	21.5614	0.838008
$663$	−0.361341	−0.0140333
$664$	−5.89752	−0.228868
$665$	0	0
$666$	−35.4427	−1.37338
$667$	−1.63146	−0.0631703
$668$	−6.37460	−0.246641
$669$	0.332429	0.0128525
$670$	0	0
$671$	14.2080	0.548494
$672$	−0.102761	−0.00396411
$673$	39.1328	1.50846	0.754229	−	0.656611i	$-0.228011\pi$
$673$	39.1328	1.50846	0.754229	+	0.656611i	$0.228011\pi$
$674$	−29.8081	−1.14816
$675$	0	0
$676$	5.23669	0.201411
$677$	−11.9755	−0.460256	−0.230128	−	0.973160i	$-0.573915\pi$
$677$	−11.9755	−0.460256	−0.230128	+	0.973160i	$0.573915\pi$
$678$	0.548612	0.0210693
$679$	13.3531	0.512444
$680$	0	0
$681$	−0.473404	−0.0181409
$682$	82.6182	3.16362
$683$	19.4941	0.745923	0.372961	−	0.927847i	$-0.378342\pi$
$683$	19.4941	0.745923	0.372961	+	0.927847i	$0.378342\pi$
$684$	−12.5143	−0.478498
$685$	0	0
$686$	−21.0055	−0.801995
$687$	−0.280739	−0.0107109
$688$	2.18879	0.0834468
$689$	−10.7685	−0.410247
$690$	0	0
$691$	20.0515	0.762795	0.381397	−	0.924411i	$-0.375443\pi$
$691$	20.0515	0.762795	0.381397	+	0.924411i	$0.375443\pi$
$692$	−2.59461	−0.0986324
$693$	17.5251	0.665722
$694$	39.0092	1.48077
$695$	0	0
$696$	0.0327589	0.00124172
$697$	26.8983	1.01885
$698$	−45.7857	−1.73301
$699$	−0.550585	−0.0208250
$700$	0	0
$701$	15.4415	0.583217	0.291609	−	0.956538i	$-0.405810\pi$
$701$	15.4415	0.583217	0.291609	+	0.956538i	$0.405810\pi$
$702$	1.56356	0.0590126
$703$	−58.0610	−2.18981
$704$	28.0047	1.05547
$705$	0	0
$706$	6.14576	0.231299
$707$	−19.0504	−0.716463
$708$	0.155529	0.00584515
$709$	7.99965	0.300433	0.150216	−	0.988653i	$-0.452003\pi$
$709$	7.99965	0.300433	0.150216	+	0.988653i	$0.452003\pi$
$710$	0	0
$711$	−48.6503	−1.82453
$712$	−26.9715	−1.01080
$713$	36.0294	1.34931
$714$	−0.122584	−0.00458757
$715$	0	0
$716$	0.948979	0.0354650
$717$	−0.725847	−0.0271072
$718$	14.6391	0.546326
$719$	−32.7769	−1.22237	−0.611187	−	0.791487i	$-0.709307\pi$
$719$	−32.7769	−1.22237	−0.611187	+	0.791487i	$0.709307\pi$
$720$	0	0
$721$	−16.8379	−0.627076
$722$	−67.0856	−2.49667
$723$	−0.0342835	−0.00127502
$724$	4.86016	0.180627
$725$	0	0
$726$	−1.19828	−0.0444722
$727$	42.1467	1.56313	0.781567	−	0.623821i	$-0.214420\pi$
$727$	42.1467	1.56313	0.781567	+	0.623821i	$0.214420\pi$
$728$	−11.3480	−0.420586
$729$	−26.9366	−0.997650
$730$	0	0
$731$	1.00993	0.0373536
$732$	0.0452804	0.00167361
$733$	−47.9618	−1.77151	−0.885755	−	0.464153i	$-0.846359\pi$
$733$	−47.9618	−1.77151	−0.885755	+	0.464153i	$0.846359\pi$
$734$	−41.0478	−1.51510
$735$	0	0
$736$	−11.7343	−0.432531
$737$	18.1936	0.670171
$738$	−58.1844	−2.14180
$739$	−20.8420	−0.766686	−0.383343	−	0.923606i	$-0.625227\pi$
$739$	−20.8420	−0.766686	−0.383343	+	0.923606i	$0.625227\pi$
$740$	0	0
$741$	1.28043	0.0470377
$742$	−3.65317	−0.134112
$743$	7.06747	0.259280	0.129640	−	0.991561i	$-0.458618\pi$
$743$	7.06747	0.259280	0.129640	+	0.991561i	$0.458618\pi$
$744$	−0.723453	−0.0265231
$745$	0	0
$746$	39.1312	1.43270
$747$	7.57729	0.277239
$748$	−6.76084	−0.247201
$749$	−9.93298	−0.362943
$750$	0	0
$751$	8.09920	0.295544	0.147772	−	0.989021i	$-0.452790\pi$
$751$	8.09920	0.295544	0.147772	+	0.989021i	$0.452790\pi$
$752$	29.7373	1.08441
$753$	−0.395652	−0.0144183
$754$	−3.11244	−0.113348
$755$	0	0
$756$	0.111725	0.00406341
$757$	−3.77993	−0.137384	−0.0686919	−	0.997638i	$-0.521883\pi$
$757$	−3.77993	−0.137384	−0.0686919	+	0.997638i	$0.521883\pi$
$758$	−21.3069	−0.773902
$759$	−0.784339	−0.0284697
$760$	0	0
$761$	−21.6997	−0.786614	−0.393307	−	0.919407i	$-0.628669\pi$
$761$	−21.6997	−0.786614	−0.393307	+	0.919407i	$0.628669\pi$
$762$	0.955373	0.0346095
$763$	−2.33473	−0.0845228
$764$	3.18920	0.115381
$765$	0	0
$766$	−9.15455	−0.330767
$767$	40.6014	1.46603
$768$	0.410622	0.0148171
$769$	12.8260	0.462519	0.231260	−	0.972892i	$-0.425715\pi$
$769$	12.8260	0.462519	0.231260	+	0.972892i	$0.425715\pi$
$770$	0	0
$771$	1.06628	0.0384011
$772$	−10.8058	−0.388909
$773$	−32.0226	−1.15177	−0.575887	−	0.817529i	$-0.695343\pi$
$773$	−32.0226	−1.15177	−0.575887	+	0.817529i	$0.695343\pi$
$774$	−2.18460	−0.0785238
$775$	0	0
$776$	−30.6169	−1.09908
$777$	0.259127	0.00929613
$778$	18.3216	0.656862
$779$	−95.3155	−3.41503
$780$	0	0
$781$	8.40049	0.300593
$782$	−13.9977	−0.500558
$783$	−0.0841956	−0.00300890
$784$	28.5220	1.01864
$785$	0	0
$786$	−0.535173	−0.0190890
$787$	30.4017	1.08370	0.541851	−	0.840474i	$-0.317724\pi$
$787$	30.4017	1.08370	0.541851	+	0.840474i	$0.317724\pi$
$788$	−2.98816	−0.106449
$789$	−0.135010	−0.00480648
$790$	0	0
$791$	10.2337	0.363868
$792$	−40.1827	−1.42783
$793$	11.8206	0.419761
$794$	−18.6651	−0.662399
$795$	0	0
$796$	−6.34288	−0.224817
$797$	−6.52493	−0.231125	−0.115562	−	0.993300i	$-0.536867\pi$
$797$	−6.52493	−0.231125	−0.115562	+	0.993300i	$0.536867\pi$
$798$	0.434380	0.0153769
$799$	13.7211	0.485417
$800$	0	0
$801$	34.6537	1.22443
$802$	1.26608	0.0447067
$803$	−62.4029	−2.20215
$804$	0.0579824	0.00204488
$805$	0	0
$806$	68.7355	2.42111
$807$	−1.01216	−0.0356298
$808$	43.6800	1.53666
$809$	39.8132	1.39976	0.699878	−	0.714262i	$-0.253238\pi$
$809$	39.8132	1.39976	0.699878	+	0.714262i	$0.253238\pi$
$810$	0	0
$811$	2.57329	0.0903604	0.0451802	−	0.998979i	$-0.485614\pi$
$811$	2.57329	0.0903604	0.0451802	+	0.998979i	$0.485614\pi$
$812$	−0.222402	−0.00780479
$813$	−0.0984062	−0.00345126
$814$	67.8512	2.37818
$815$	0	0
$816$	0.361817	0.0126661
$817$	−3.57873	−0.125204
$818$	−4.74500	−0.165905
$819$	14.5803	0.509475
$820$	0	0
$821$	1.14063	0.0398081	0.0199041	−	0.999802i	$-0.493664\pi$
$821$	1.14063	0.0398081	0.0199041	+	0.999802i	$0.493664\pi$
$822$	0.0982597	0.00342720
$823$	17.9025	0.624041	0.312020	−	0.950075i	$-0.398994\pi$
$823$	17.9025	0.624041	0.312020	+	0.950075i	$0.398994\pi$
$824$	38.6071	1.34494
$825$	0	0
$826$	13.7739	0.479254
$827$	−19.4059	−0.674809	−0.337405	−	0.941360i	$-0.609549\pi$
$827$	−19.4059	−0.674809	−0.337405	+	0.941360i	$0.609549\pi$
$828$	6.37768	0.221640
$829$	−23.7397	−0.824512	−0.412256	−	0.911068i	$-0.635259\pi$
$829$	−23.7397	−0.824512	−0.412256	+	0.911068i	$0.635259\pi$
$830$	0	0
$831$	−0.505987	−0.0175525
$832$	23.2990	0.807746
$833$	13.1603	0.455978
$834$	0.268654	0.00930272
$835$	0	0
$836$	23.9574	0.828583
$837$	1.85939	0.0642698
$838$	−39.3370	−1.35888
$839$	4.72509	0.163128	0.0815642	−	0.996668i	$-0.474008\pi$
$839$	4.72509	0.163128	0.0815642	+	0.996668i	$0.474008\pi$
$840$	0	0
$841$	−28.8324	−0.994221
$842$	−29.8610	−1.02908
$843$	−0.845879	−0.0291336
$844$	2.66553	0.0917514
$845$	0	0
$846$	−29.6803	−1.02043
$847$	−22.3524	−0.768037
$848$	10.7827	0.370279
$849$	−0.327252	−0.0112313
$850$	0	0
$851$	29.5895	1.01432
$852$	0.0267721	0.000917196 0
$853$	−58.2448	−1.99426	−0.997132	−	0.0756804i	$-0.975887\pi$
$853$	−58.2448	−1.99426	−0.997132	+	0.0756804i	$0.975887\pi$
$854$	4.01009	0.137222
$855$	0	0
$856$	22.7750	0.778435
$857$	−55.0013	−1.87881	−0.939404	−	0.342812i	$-0.888621\pi$
$857$	−55.0013	−1.87881	−0.939404	+	0.342812i	$0.888621\pi$
$858$	−1.49633	−0.0510840
$859$	48.6222	1.65897	0.829483	−	0.558532i	$-0.188635\pi$
$859$	48.6222	1.65897	0.829483	+	0.558532i	$0.188635\pi$
$860$	0	0
$861$	0.425394	0.0144974
$862$	1.75904	0.0599132
$863$	−57.3980	−1.95385	−0.976926	−	0.213579i	$-0.931488\pi$
$863$	−57.3980	−1.95385	−0.976926	+	0.213579i	$0.931488\pi$
$864$	−0.605577	−0.0206022
$865$	0	0
$866$	−52.4699	−1.78300
$867$	−0.415873	−0.0141238
$868$	4.91156	0.166709
$869$	93.1356	3.15941
$870$	0	0
$871$	15.1365	0.512880
$872$	5.35323	0.181283
$873$	39.3374	1.33137
$874$	49.6016	1.67780
$875$	0	0
$876$	−0.198876	−0.00671939
$877$	25.2704	0.853320	0.426660	−	0.904412i	$-0.359690\pi$
$877$	25.2704	0.853320	0.426660	+	0.904412i	$0.359690\pi$
$878$	−4.87219	−0.164428
$879$	0.750156	0.0253021
$880$	0	0
$881$	−34.5670	−1.16459	−0.582297	−	0.812976i	$-0.697846\pi$
$881$	−34.5670	−1.16459	−0.582297	+	0.812976i	$0.697846\pi$
$882$	−28.4674	−0.958547
$883$	38.6836	1.30181	0.650904	−	0.759160i	$-0.274390\pi$
$883$	38.6836	1.30181	0.650904	+	0.759160i	$0.274390\pi$
$884$	−5.62479	−0.189182
$885$	0	0
$886$	−41.0659	−1.37964
$887$	−26.4989	−0.889746	−0.444873	−	0.895594i	$-0.646751\pi$
$887$	−26.4989	−0.889746	−0.444873	+	0.895594i	$0.646751\pi$
$888$	−0.594145	−0.0199382
$889$	17.8213	0.597708
$890$	0	0
$891$	51.6076	1.72892
$892$	5.17474	0.173263
$893$	−48.6212	−1.62705
$894$	−0.398258	−0.0133198
$895$	0	0
$896$	13.8989	0.464330
$897$	−0.652543	−0.0217878
$898$	53.1459	1.77350
$899$	−3.70133	−0.123446
$900$	0	0
$901$	4.97524	0.165749
$902$	111.388	3.70880
$903$	0.0159719	0.000531512 0
$904$	−23.4645	−0.780418
$905$	0	0
$906$	0.380353	0.0126364
$907$	47.6929	1.58362	0.791809	−	0.610769i	$-0.209140\pi$
$907$	47.6929	1.58362	0.791809	+	0.610769i	$0.209140\pi$
$908$	−7.36921	−0.244556
$909$	−56.1213	−1.86143
$910$	0	0
$911$	−45.1515	−1.49594	−0.747969	−	0.663734i	$-0.768971\pi$
$911$	−45.1515	−1.49594	−0.747969	+	0.663734i	$0.768971\pi$
$912$	−1.28211	−0.0424550
$913$	−14.5059	−0.480075
$914$	2.54246	0.0840971
$915$	0	0
$916$	−4.37010	−0.144392
$917$	−9.98300	−0.329668
$918$	−0.722389	−0.0238424
$919$	−30.2152	−0.996706	−0.498353	−	0.866974i	$-0.666062\pi$
$919$	−30.2152	−0.996706	−0.498353	+	0.866974i	$0.666062\pi$
$920$	0	0
$921$	−0.0618455	−0.00203788
$922$	−20.0920	−0.661695
$923$	6.98892	0.230043
$924$	−0.106922	−0.00351748
$925$	0	0
$926$	−9.51836	−0.312793
$927$	−49.6035	−1.62919
$928$	1.20547	0.0395715
$929$	−49.6981	−1.63054	−0.815270	−	0.579081i	$-0.803412\pi$
$929$	−49.6981	−1.63054	−0.815270	+	0.579081i	$0.803412\pi$
$930$	0	0
$931$	−46.6342	−1.52837
$932$	−8.57064	−0.280741
$933$	−0.917659	−0.0300428
$934$	−16.6892	−0.546088
$935$	0	0
$936$	−33.4306	−1.09271
$937$	−0.189215	−0.00618140	−0.00309070	−	0.999995i	$-0.500984\pi$
$937$	−0.189215	−0.00618140	−0.00309070	+	0.999995i	$0.500984\pi$
$938$	5.13499	0.167663
$939$	0.349055	0.0113910
$940$	0	0
$941$	14.7887	0.482098	0.241049	−	0.970513i	$-0.422508\pi$
$941$	14.7887	0.482098	0.241049	+	0.970513i	$0.422508\pi$
$942$	1.17470	0.0382739
$943$	48.5755	1.58184
$944$	−40.6548	−1.32320
$945$	0	0
$946$	4.18218	0.135974
$947$	6.06365	0.197042	0.0985211	−	0.995135i	$-0.468589\pi$
$947$	6.06365	0.197042	0.0985211	+	0.995135i	$0.468589\pi$
$948$	0.296820	0.00964026
$949$	−51.9171	−1.68530
$950$	0	0
$951$	0.260405	0.00844421
$952$	5.24299	0.169926
$953$	48.1276	1.55900	0.779502	−	0.626400i	$-0.215472\pi$
$953$	48.1276	1.55900	0.779502	+	0.626400i	$0.215472\pi$
$954$	−10.7620	−0.348434
$955$	0	0
$956$	−11.2988	−0.365431
$957$	0.0805758	0.00260465
$958$	−4.58637	−0.148179
$959$	1.83292	0.0591879
$960$	0	0
$961$	50.7407	1.63680
$962$	56.4499	1.82002
$963$	−29.2620	−0.942955
$964$	−0.533671	−0.0171884
$965$	0	0
$966$	−0.221373	−0.00712255
$967$	25.6884	0.826083	0.413042	−	0.910712i	$-0.364466\pi$
$967$	25.6884	0.826083	0.413042	+	0.910712i	$0.364466\pi$
$968$	51.2511	1.64727
$969$	−0.591580	−0.0190043
$970$	0	0
$971$	31.8393	1.02177	0.510886	−	0.859649i	$-0.329318\pi$
$971$	31.8393	1.02177	0.510886	+	0.859649i	$0.329318\pi$
$972$	0.493737	0.0158366
$973$	5.01141	0.160658
$974$	29.1149	0.932903
$975$	0	0
$976$	−11.8361	−0.378866
$977$	−16.9361	−0.541834	−0.270917	−	0.962603i	$-0.587327\pi$
$977$	−16.9361	−0.541834	−0.270917	+	0.962603i	$0.587327\pi$
$978$	−0.194016	−0.00620394
$979$	−66.3407	−2.12026
$980$	0	0
$981$	−6.87797	−0.219597
$982$	−31.9117	−1.01834
$983$	12.8294	0.409194	0.204597	−	0.978846i	$-0.434412\pi$
$983$	12.8294	0.409194	0.204597	+	0.978846i	$0.434412\pi$
$984$	−0.975374	−0.0310938
$985$	0	0
$986$	1.43800	0.0457952
$987$	0.216997	0.00690710
$988$	19.9317	0.634112
$989$	1.82382	0.0579942
$990$	0	0
$991$	−1.11578	−0.0354438	−0.0177219	−	0.999843i	$-0.505641\pi$
$991$	−1.11578	−0.0354438	−0.0177219	+	0.999843i	$0.505641\pi$
$992$	−26.6218	−0.845244
$993$	−0.464394	−0.0147371
$994$	2.37097	0.0752024
$995$	0	0
$996$	−0.0462297	−0.00146485
$997$	18.4505	0.584334	0.292167	−	0.956367i	$-0.405624\pi$
$997$	18.4505	0.584334	0.292167	+	0.956367i	$0.405624\pi$
$998$	−7.99494	−0.253075
$999$	1.52704	0.0483136

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.l.1.12	✓	40
5.4	even	2		6025.2.a.o.1.29	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6025.2.a.l.1.12	✓	40	1.1	even	1	trivial
6025.2.a.o.1.29	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)

\(f(q)\)	\(=\)	\(q-1.59175 q^{2} +0.0342835 q^{3} +0.533671 q^{4} -0.0545707 q^{6} -1.01795 q^{7} +2.33403 q^{8} -2.99882 q^{9} +O(q^{10})\)	\(q-1.59175 q^{2} +0.0342835 q^{3} +0.533671 q^{4} -0.0545707 q^{6} -1.01795 q^{7} +2.33403 q^{8} -2.99882 q^{9} +5.74092 q^{11} +0.0182961 q^{12} +4.77625 q^{13} +1.62032 q^{14} -4.78254 q^{16} -2.20671 q^{17} +4.77338 q^{18} +7.81958 q^{19} -0.0348989 q^{21} -9.13812 q^{22} -3.98508 q^{23} +0.0800186 q^{24} -7.60260 q^{26} -0.205661 q^{27} -0.543251 q^{28} +0.409391 q^{29} -9.04105 q^{31} +2.94455 q^{32} +0.196819 q^{33} +3.51253 q^{34} -1.60039 q^{36} -7.42508 q^{37} -12.4468 q^{38} +0.163746 q^{39} -12.1893 q^{41} +0.0555503 q^{42} -0.457663 q^{43} +3.06377 q^{44} +6.34326 q^{46} -6.21788 q^{47} -0.163962 q^{48} -5.96378 q^{49} -0.0756537 q^{51} +2.54895 q^{52} -2.25459 q^{53} +0.327360 q^{54} -2.37593 q^{56} +0.268082 q^{57} -0.651649 q^{58} +8.50068 q^{59} +2.47487 q^{61} +14.3911 q^{62} +3.05266 q^{63} +4.87809 q^{64} -0.313286 q^{66} +3.16911 q^{67} -1.17766 q^{68} -0.136622 q^{69} +1.46327 q^{71} -6.99935 q^{72} -10.8698 q^{73} +11.8189 q^{74} +4.17308 q^{76} -5.84398 q^{77} -0.260644 q^{78} +16.2231 q^{79} +8.98942 q^{81} +19.4024 q^{82} -2.52675 q^{83} -0.0186245 q^{84} +0.728485 q^{86} +0.0140353 q^{87} +13.3995 q^{88} -11.5557 q^{89} -4.86199 q^{91} -2.12672 q^{92} -0.309959 q^{93} +9.89732 q^{94} +0.100949 q^{96} -13.1176 q^{97} +9.49285 q^{98} -17.2160 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9}+O(q^{10}) \) 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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