LMFDB - Embedded newform 525.2.a.j.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(1,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 105)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.48119$ of defining polynomial
Character	$\chi$	$=$	525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.193937 q^{2} +1.00000 q^{3} -1.96239 q^{4} -0.193937 q^{6} +1.00000 q^{7} +0.768452 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.193937 q^{2} +1.00000 q^{3} -1.96239 q^{4} -0.193937 q^{6} +1.00000 q^{7} +0.768452 q^{8} +1.00000 q^{9} +2.00000 q^{11} -1.96239 q^{12} -1.35026 q^{13} -0.193937 q^{14} +3.77575 q^{16} +3.35026 q^{17} -0.193937 q^{18} +5.35026 q^{19} +1.00000 q^{21} -0.387873 q^{22} -4.96239 q^{23} +0.768452 q^{24} +0.261865 q^{26} +1.00000 q^{27} -1.96239 q^{28} +7.92478 q^{29} +4.57452 q^{31} -2.26916 q^{32} +2.00000 q^{33} -0.649738 q^{34} -1.96239 q^{36} +0.775746 q^{37} -1.03761 q^{38} -1.35026 q^{39} +3.73813 q^{41} -0.193937 q^{42} +12.6253 q^{43} -3.92478 q^{44} +0.962389 q^{46} -9.92478 q^{47} +3.77575 q^{48} +1.00000 q^{49} +3.35026 q^{51} +2.64974 q^{52} -8.57452 q^{53} -0.193937 q^{54} +0.768452 q^{56} +5.35026 q^{57} -1.53690 q^{58} -8.62530 q^{59} -8.70052 q^{61} -0.887166 q^{62} +1.00000 q^{63} -7.11142 q^{64} -0.387873 q^{66} -9.92478 q^{67} -6.57452 q^{68} -4.96239 q^{69} +2.00000 q^{71} +0.768452 q^{72} +9.35026 q^{73} -0.150446 q^{74} -10.4993 q^{76} +2.00000 q^{77} +0.261865 q^{78} +10.7005 q^{79} +1.00000 q^{81} -0.724961 q^{82} -3.22425 q^{83} -1.96239 q^{84} -2.44851 q^{86} +7.92478 q^{87} +1.53690 q^{88} +1.03761 q^{89} -1.35026 q^{91} +9.73813 q^{92} +4.57452 q^{93} +1.92478 q^{94} -2.26916 q^{96} +18.4993 q^{97} -0.193937 q^{98} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} + 3 q^{3} + 5 q^{4} - q^{6} + 3 q^{7} - 9 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - q^2 + 3 * q^3 + 5 * q^4 - q^6 + 3 * q^7 - 9 * q^8 + 3 * q^9	$ 3 q - q^{2} + 3 q^{3} + 5 q^{4} - q^{6} + 3 q^{7} - 9 q^{8} + 3 q^{9} + 6 q^{11} + 5 q^{12} + 6 q^{13} - q^{14} + 13 q^{16} - q^{18} + 6 q^{19} + 3 q^{21} - 2 q^{22} - 4 q^{23} - 9 q^{24} + 10 q^{26} + 3 q^{27} + 5 q^{28} + 2 q^{29} + 2 q^{31} - 29 q^{32} + 6 q^{33} - 12 q^{34} + 5 q^{36} + 4 q^{37} - 14 q^{38} + 6 q^{39} + 2 q^{41} - q^{42} - 4 q^{43} + 10 q^{44} - 8 q^{46} - 8 q^{47} + 13 q^{48} + 3 q^{49} + 18 q^{52} - 14 q^{53} - q^{54} - 9 q^{56} + 6 q^{57} + 18 q^{58} + 16 q^{59} - 6 q^{61} + 30 q^{62} + 3 q^{63} + 13 q^{64} - 2 q^{66} - 8 q^{67} - 8 q^{68} - 4 q^{69} + 6 q^{71} - 9 q^{72} + 18 q^{73} - 44 q^{74} + 2 q^{76} + 6 q^{77} + 10 q^{78} + 12 q^{79} + 3 q^{81} - 34 q^{82} - 8 q^{83} + 5 q^{84} - 4 q^{86} + 2 q^{87} - 18 q^{88} + 14 q^{89} + 6 q^{91} + 20 q^{92} + 2 q^{93} - 16 q^{94} - 29 q^{96} + 22 q^{97} - q^{98} + 6 q^{99}+O(q^{100}) $ 3 * q - q^2 + 3 * q^3 + 5 * q^4 - q^6 + 3 * q^7 - 9 * q^8 + 3 * q^9 + 6 * q^11 + 5 * q^12 + 6 * q^13 - q^14 + 13 * q^16 - q^18 + 6 * q^19 + 3 * q^21 - 2 * q^22 - 4 * q^23 - 9 * q^24 + 10 * q^26 + 3 * q^27 + 5 * q^28 + 2 * q^29 + 2 * q^31 - 29 * q^32 + 6 * q^33 - 12 * q^34 + 5 * q^36 + 4 * q^37 - 14 * q^38 + 6 * q^39 + 2 * q^41 - q^42 - 4 * q^43 + 10 * q^44 - 8 * q^46 - 8 * q^47 + 13 * q^48 + 3 * q^49 + 18 * q^52 - 14 * q^53 - q^54 - 9 * q^56 + 6 * q^57 + 18 * q^58 + 16 * q^59 - 6 * q^61 + 30 * q^62 + 3 * q^63 + 13 * q^64 - 2 * q^66 - 8 * q^67 - 8 * q^68 - 4 * q^69 + 6 * q^71 - 9 * q^72 + 18 * q^73 - 44 * q^74 + 2 * q^76 + 6 * q^77 + 10 * q^78 + 12 * q^79 + 3 * q^81 - 34 * q^82 - 8 * q^83 + 5 * q^84 - 4 * q^86 + 2 * q^87 - 18 * q^88 + 14 * q^89 + 6 * q^91 + 20 * q^92 + 2 * q^93 - 16 * q^94 - 29 * q^96 + 22 * q^97 - q^98 + 6 * 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 $

$2$	−0.193937	−0.137134	−0.0685669	−	0.997647i	$-0.521843\pi$
$2$	−0.193937	−0.137134	−0.0685669	+	0.997647i	$0.521843\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.96239	−0.981194
$5$	0	0
$5$	0	0
$6$	−0.193937	−0.0791743
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.768452	0.271689
$9$	1.00000	0.333333
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	−1.96239	−0.566493
$13$	−1.35026	−0.374495	−0.187248	−	0.982313i	$-0.559957\pi$
$13$	−1.35026	−0.374495	−0.187248	+	0.982313i	$0.559957\pi$
$14$	−0.193937	−0.0518317
$15$	0	0
$16$	3.77575	0.943937
$17$	3.35026	0.812558	0.406279	−	0.913749i	$-0.366826\pi$
$17$	3.35026	0.812558	0.406279	+	0.913749i	$0.366826\pi$
$18$	−0.193937	−0.0457113
$19$	5.35026	1.22743	0.613717	−	0.789526i	$-0.289674\pi$
$19$	5.35026	1.22743	0.613717	+	0.789526i	$0.289674\pi$
$20$	0	0
$21$	1.00000	0.218218
$22$	−0.387873	−0.0826948
$23$	−4.96239	−1.03473	−0.517365	−	0.855765i	$-0.673087\pi$
$23$	−4.96239	−1.03473	−0.517365	+	0.855765i	$0.673087\pi$
$24$	0.768452	0.156860
$25$	0	0
$26$	0.261865	0.0513560
$27$	1.00000	0.192450
$28$	−1.96239	−0.370857
$29$	7.92478	1.47159	0.735797	−	0.677202i	$-0.236808\pi$
$29$	7.92478	1.47159	0.735797	+	0.677202i	$0.236808\pi$
$30$	0	0
$31$	4.57452	0.821607	0.410804	−	0.911724i	$-0.365248\pi$
$31$	4.57452	0.821607	0.410804	+	0.911724i	$0.365248\pi$
$32$	−2.26916	−0.401134
$33$	2.00000	0.348155
$34$	−0.649738	−0.111429
$35$	0	0
$36$	−1.96239	−0.327065
$37$	0.775746	0.127532	0.0637660	−	0.997965i	$-0.479689\pi$
$37$	0.775746	0.127532	0.0637660	+	0.997965i	$0.479689\pi$
$38$	−1.03761	−0.168323
$39$	−1.35026	−0.216215
$40$	0	0
$41$	3.73813	0.583799	0.291899	−	0.956449i	$-0.405713\pi$
$41$	3.73813	0.583799	0.291899	+	0.956449i	$0.405713\pi$
$42$	−0.193937	−0.0299251
$43$	12.6253	1.92534	0.962670	−	0.270677i	$-0.0872476\pi$
$43$	12.6253	1.92534	0.962670	+	0.270677i	$0.0872476\pi$
$44$	−3.92478	−0.591682
$45$	0	0
$46$	0.962389	0.141896
$47$	−9.92478	−1.44768	−0.723839	−	0.689969i	$-0.757624\pi$
$47$	−9.92478	−1.44768	−0.723839	+	0.689969i	$0.757624\pi$
$48$	3.77575	0.544982
$49$	1.00000	0.142857
$50$	0	0
$51$	3.35026	0.469130
$52$	2.64974	0.367453
$53$	−8.57452	−1.17780	−0.588900	−	0.808206i	$-0.700439\pi$
$53$	−8.57452	−1.17780	−0.588900	+	0.808206i	$0.700439\pi$
$54$	−0.193937	−0.0263914
$55$	0	0
$56$	0.768452	0.102689
$57$	5.35026	0.708659
$58$	−1.53690	−0.201805
$59$	−8.62530	−1.12292	−0.561459	−	0.827504i	$-0.689760\pi$
$59$	−8.62530	−1.12292	−0.561459	+	0.827504i	$0.689760\pi$
$60$	0	0
$61$	−8.70052	−1.11399	−0.556994	−	0.830517i	$-0.688045\pi$
$61$	−8.70052	−1.11399	−0.556994	+	0.830517i	$0.688045\pi$
$62$	−0.887166	−0.112670
$63$	1.00000	0.125988
$64$	−7.11142	−0.888927
$65$	0	0
$66$	−0.387873	−0.0477439
$67$	−9.92478	−1.21250	−0.606252	−	0.795272i	$-0.707328\pi$
$67$	−9.92478	−1.21250	−0.606252	+	0.795272i	$0.707328\pi$
$68$	−6.57452	−0.797277
$69$	−4.96239	−0.597401
$70$	0	0
$71$	2.00000	0.237356	0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000	0.237356	0.118678	+	0.992933i	$0.462134\pi$
$72$	0.768452	0.0905629
$73$	9.35026	1.09437	0.547183	−	0.837013i	$-0.315700\pi$
$73$	9.35026	1.09437	0.547183	+	0.837013i	$0.315700\pi$
$74$	−0.150446	−0.0174889
$75$	0	0
$76$	−10.4993	−1.20435
$77$	2.00000	0.227921
$78$	0.261865	0.0296504
$79$	10.7005	1.20390	0.601951	−	0.798533i	$-0.294390\pi$
$79$	10.7005	1.20390	0.601951	+	0.798533i	$0.294390\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−0.724961	−0.0800586
$83$	−3.22425	−0.353908	−0.176954	−	0.984219i	$-0.556624\pi$
$83$	−3.22425	−0.353908	−0.176954	+	0.984219i	$0.556624\pi$
$84$	−1.96239	−0.214114
$85$	0	0
$86$	−2.44851	−0.264029
$87$	7.92478	0.849625
$88$	1.53690	0.163835
$89$	1.03761	0.109987	0.0549933	−	0.998487i	$-0.482486\pi$
$89$	1.03761	0.109987	0.0549933	+	0.998487i	$0.482486\pi$
$90$	0	0
$91$	−1.35026	−0.141546
$92$	9.73813	1.01527
$93$	4.57452	0.474355
$94$	1.92478	0.198526
$95$	0	0
$96$	−2.26916	−0.231595
$97$	18.4993	1.87832	0.939159	−	0.343482i	$-0.111606\pi$
$97$	18.4993	1.87832	0.939159	+	0.343482i	$0.111606\pi$
$98$	−0.193937	−0.0195906
$99$	2.00000	0.201008
$100$	0	0
$101$	−17.6629	−1.75753	−0.878763	−	0.477259i	$-0.841630\pi$
$101$	−17.6629	−1.75753	−0.878763	+	0.477259i	$0.841630\pi$
$102$	−0.649738	−0.0643337
$103$	−6.70052	−0.660222	−0.330111	−	0.943942i	$-0.607086\pi$
$103$	−6.70052	−0.660222	−0.330111	+	0.943942i	$0.607086\pi$
$104$	−1.03761	−0.101746
$105$	0	0
$106$	1.66291	0.161516
$107$	−13.7381	−1.32812	−0.664058	−	0.747681i	$-0.731167\pi$
$107$	−13.7381	−1.32812	−0.664058	+	0.747681i	$0.731167\pi$
$108$	−1.96239	−0.188831
$109$	−2.77575	−0.265868	−0.132934	−	0.991125i	$-0.542440\pi$
$109$	−2.77575	−0.265868	−0.132934	+	0.991125i	$0.542440\pi$
$110$	0	0
$111$	0.775746	0.0736306
$112$	3.77575	0.356774
$113$	−12.0508	−1.13364	−0.566821	−	0.823841i	$-0.691827\pi$
$113$	−12.0508	−1.13364	−0.566821	+	0.823841i	$0.691827\pi$
$114$	−1.03761	−0.0971812
$115$	0	0
$116$	−15.5515	−1.44392
$117$	−1.35026	−0.124832
$118$	1.67276	0.153990
$119$	3.35026	0.307118
$120$	0	0
$121$	−7.00000	−0.636364
$122$	1.68735	0.152765
$123$	3.73813	0.337056
$124$	−8.97698	−0.806156
$125$	0	0
$126$	−0.193937	−0.0172772
$127$	−2.70052	−0.239633	−0.119816	−	0.992796i	$-0.538231\pi$
$127$	−2.70052	−0.239633	−0.119816	+	0.992796i	$0.538231\pi$
$128$	5.91748	0.523037
$129$	12.6253	1.11160
$130$	0	0
$131$	20.6253	1.80204	0.901020	−	0.433777i	$-0.142819\pi$
$131$	20.6253	1.80204	0.901020	+	0.433777i	$0.142819\pi$
$132$	−3.92478	−0.341608
$133$	5.35026	0.463927
$134$	1.92478	0.166275
$135$	0	0
$136$	2.57452	0.220763
$137$	−22.4993	−1.92224	−0.961122	−	0.276124i	$-0.910950\pi$
$137$	−22.4993	−1.92224	−0.961122	+	0.276124i	$0.910950\pi$
$138$	0.962389	0.0819240
$139$	−3.27504	−0.277785	−0.138893	−	0.990307i	$-0.544354\pi$
$139$	−3.27504	−0.277785	−0.138893	+	0.990307i	$0.544354\pi$
$140$	0	0
$141$	−9.92478	−0.835817
$142$	−0.387873	−0.0325496
$143$	−2.70052	−0.225829
$144$	3.77575	0.314646
$145$	0	0
$146$	−1.81336	−0.150075
$147$	1.00000	0.0824786
$148$	−1.52232	−0.125134
$149$	−4.44851	−0.364436	−0.182218	−	0.983258i	$-0.558328\pi$
$149$	−4.44851	−0.364436	−0.182218	+	0.983258i	$0.558328\pi$
$150$	0	0
$151$	1.29948	0.105750	0.0528749	−	0.998601i	$-0.483162\pi$
$151$	1.29948	0.105750	0.0528749	+	0.998601i	$0.483162\pi$
$152$	4.11142	0.333480
$153$	3.35026	0.270853
$154$	−0.387873	−0.0312557
$155$	0	0
$156$	2.64974	0.212149
$157$	2.64974	0.211472	0.105736	−	0.994394i	$-0.466280\pi$
$157$	2.64974	0.211472	0.105736	+	0.994394i	$0.466280\pi$
$158$	−2.07522	−0.165096
$159$	−8.57452	−0.680003
$160$	0	0
$161$	−4.96239	−0.391091
$162$	−0.193937	−0.0152371
$163$	−5.29948	−0.415087	−0.207544	−	0.978226i	$-0.566547\pi$
$163$	−5.29948	−0.415087	−0.207544	+	0.978226i	$0.566547\pi$
$164$	−7.33567	−0.572820
$165$	0	0
$166$	0.625301	0.0485327
$167$	14.5501	1.12592	0.562959	−	0.826485i	$-0.309663\pi$
$167$	14.5501	1.12592	0.562959	+	0.826485i	$0.309663\pi$
$168$	0.768452	0.0592874
$169$	−11.1768	−0.859753
$170$	0	0
$171$	5.35026	0.409145
$172$	−24.7757	−1.88913
$173$	4.49929	0.342075	0.171037	−	0.985265i	$-0.445288\pi$
$173$	4.49929	0.342075	0.171037	+	0.985265i	$0.445288\pi$
$174$	−1.53690	−0.116512
$175$	0	0
$176$	7.55149	0.569215
$177$	−8.62530	−0.648317
$178$	−0.201231	−0.0150829
$179$	10.0000	0.747435	0.373718	−	0.927543i	$-0.378083\pi$
$179$	10.0000	0.747435	0.373718	+	0.927543i	$0.378083\pi$
$180$	0	0
$181$	10.6253	0.789772	0.394886	−	0.918730i	$-0.370784\pi$
$181$	10.6253	0.789772	0.394886	+	0.918730i	$0.370784\pi$
$182$	0.261865	0.0194107
$183$	−8.70052	−0.643161
$184$	−3.81336	−0.281124
$185$	0	0
$186$	−0.887166	−0.0650502
$187$	6.70052	0.489991
$188$	19.4763	1.42045
$189$	1.00000	0.0727393
$190$	0	0
$191$	−13.8496	−1.00212	−0.501059	−	0.865413i	$-0.667056\pi$
$191$	−13.8496	−1.00212	−0.501059	+	0.865413i	$0.667056\pi$
$192$	−7.11142	−0.513222
$193$	−15.3258	−1.10318	−0.551588	−	0.834116i	$-0.685978\pi$
$193$	−15.3258	−1.10318	−0.551588	+	0.834116i	$0.685978\pi$
$194$	−3.58769	−0.257581
$195$	0	0
$196$	−1.96239	−0.140171
$197$	0.574515	0.0409325	0.0204663	−	0.999791i	$-0.493485\pi$
$197$	0.574515	0.0409325	0.0204663	+	0.999791i	$0.493485\pi$
$198$	−0.387873	−0.0275649
$199$	−0.201231	−0.0142649	−0.00713244	−	0.999975i	$-0.502270\pi$
$199$	−0.201231	−0.0142649	−0.00713244	+	0.999975i	$0.502270\pi$
$200$	0	0
$201$	−9.92478	−0.700040
$202$	3.42548	0.241016
$203$	7.92478	0.556210
$204$	−6.57452	−0.460308
$205$	0	0
$206$	1.29948	0.0905388
$207$	−4.96239	−0.344910
$208$	−5.09825	−0.353500
$209$	10.7005	0.740171
$210$	0	0
$211$	6.44851	0.443934	0.221967	−	0.975054i	$-0.428752\pi$
$211$	6.44851	0.443934	0.221967	+	0.975054i	$0.428752\pi$
$212$	16.8265	1.15565
$213$	2.00000	0.137038
$214$	2.66433	0.182130
$215$	0	0
$216$	0.768452	0.0522865
$217$	4.57452	0.310538
$218$	0.538319	0.0364595
$219$	9.35026	0.631832
$220$	0	0
$221$	−4.52373	−0.304299
$222$	−0.150446	−0.0100972
$223$	−1.55149	−0.103896	−0.0519478	−	0.998650i	$-0.516543\pi$
$223$	−1.55149	−0.103896	−0.0519478	+	0.998650i	$0.516543\pi$
$224$	−2.26916	−0.151615
$225$	0	0
$226$	2.33709	0.155461
$227$	13.1490	0.872732	0.436366	−	0.899769i	$-0.356265\pi$
$227$	13.1490	0.872732	0.436366	+	0.899769i	$0.356265\pi$
$228$	−10.4993	−0.695333
$229$	2.77575	0.183426	0.0917132	−	0.995785i	$-0.470766\pi$
$229$	2.77575	0.183426	0.0917132	+	0.995785i	$0.470766\pi$
$230$	0	0
$231$	2.00000	0.131590
$232$	6.08981	0.399816
$233$	0.0507852	0.00332705	0.00166353	−	0.999999i	$-0.499470\pi$
$233$	0.0507852	0.00332705	0.00166353	+	0.999999i	$0.499470\pi$
$234$	0.261865	0.0171187
$235$	0	0
$236$	16.9262	1.10180
$237$	10.7005	0.695074
$238$	−0.649738	−0.0421163
$239$	5.84955	0.378376	0.189188	−	0.981941i	$-0.439414\pi$
$239$	5.84955	0.378376	0.189188	+	0.981941i	$0.439414\pi$
$240$	0	0
$241$	−0.0752228	−0.00484553	−0.00242276	−	0.999997i	$-0.500771\pi$
$241$	−0.0752228	−0.00484553	−0.00242276	+	0.999997i	$0.500771\pi$
$242$	1.35756	0.0872670
$243$	1.00000	0.0641500
$244$	17.0738	1.09304
$245$	0	0
$246$	−0.724961	−0.0462218
$247$	−7.22425	−0.459668
$248$	3.51530	0.223222
$249$	−3.22425	−0.204329
$250$	0	0
$251$	19.2243	1.21342	0.606712	−	0.794922i	$-0.292488\pi$
$251$	19.2243	1.21342	0.606712	+	0.794922i	$0.292488\pi$
$252$	−1.96239	−0.123619
$253$	−9.92478	−0.623965
$254$	0.523730	0.0328618
$255$	0	0
$256$	13.0752	0.817201
$257$	−7.35026	−0.458497	−0.229248	−	0.973368i	$-0.573627\pi$
$257$	−7.35026	−0.458497	−0.229248	+	0.973368i	$0.573627\pi$
$258$	−2.44851	−0.152437
$259$	0.775746	0.0482025
$260$	0	0
$261$	7.92478	0.490531
$262$	−4.00000	−0.247121
$263$	12.9624	0.799295	0.399648	−	0.916669i	$-0.369133\pi$
$263$	12.9624	0.799295	0.399648	+	0.916669i	$0.369133\pi$
$264$	1.53690	0.0945899
$265$	0	0
$266$	−1.03761	−0.0636200
$267$	1.03761	0.0635008
$268$	19.4763	1.18970
$269$	4.11142	0.250678	0.125339	−	0.992114i	$-0.459998\pi$
$269$	4.11142	0.250678	0.125339	+	0.992114i	$0.459998\pi$
$270$	0	0
$271$	−16.4241	−0.997691	−0.498846	−	0.866691i	$-0.666243\pi$
$271$	−16.4241	−0.997691	−0.498846	+	0.866691i	$0.666243\pi$
$272$	12.6497	0.767003
$273$	−1.35026	−0.0817216
$274$	4.36344	0.263605
$275$	0	0
$276$	9.73813	0.586167
$277$	11.0738	0.665361	0.332680	−	0.943040i	$-0.392047\pi$
$277$	11.0738	0.665361	0.332680	+	0.943040i	$0.392047\pi$
$278$	0.635150	0.0380938
$279$	4.57452	0.273869
$280$	0	0
$281$	14.3733	0.857438	0.428719	−	0.903438i	$-0.358965\pi$
$281$	14.3733	0.857438	0.428719	+	0.903438i	$0.358965\pi$
$282$	1.92478	0.114619
$283$	−1.14903	−0.0683028	−0.0341514	−	0.999417i	$-0.510873\pi$
$283$	−1.14903	−0.0683028	−0.0341514	+	0.999417i	$0.510873\pi$
$284$	−3.92478	−0.232893
$285$	0	0
$286$	0.523730	0.0309688
$287$	3.73813	0.220655
$288$	−2.26916	−0.133711
$289$	−5.77575	−0.339750
$290$	0	0
$291$	18.4993	1.08445
$292$	−18.3488	−1.07379
$293$	−0.649738	−0.0379581	−0.0189791	−	0.999820i	$-0.506042\pi$
$293$	−0.649738	−0.0379581	−0.0189791	+	0.999820i	$0.506042\pi$
$294$	−0.193937	−0.0113106
$295$	0	0
$296$	0.596124	0.0346490
$297$	2.00000	0.116052
$298$	0.862728	0.0499765
$299$	6.70052	0.387501
$300$	0	0
$301$	12.6253	0.727710
$302$	−0.252016	−0.0145019
$303$	−17.6629	−1.01471
$304$	20.2012	1.15862
$305$	0	0
$306$	−0.649738	−0.0371431
$307$	−24.1016	−1.37555	−0.687775	−	0.725924i	$-0.741412\pi$
$307$	−24.1016	−1.37555	−0.687775	+	0.725924i	$0.741412\pi$
$308$	−3.92478	−0.223635
$309$	−6.70052	−0.381179
$310$	0	0
$311$	8.25202	0.467929	0.233964	−	0.972245i	$-0.424830\pi$
$311$	8.25202	0.467929	0.233964	+	0.972245i	$0.424830\pi$
$312$	−1.03761	−0.0587432
$313$	14.9018	0.842297	0.421148	−	0.906992i	$-0.361627\pi$
$313$	14.9018	0.842297	0.421148	+	0.906992i	$0.361627\pi$
$314$	−0.513881	−0.0290000
$315$	0	0
$316$	−20.9986	−1.18126
$317$	−10.1260	−0.568733	−0.284367	−	0.958716i	$-0.591783\pi$
$317$	−10.1260	−0.568733	−0.284367	+	0.958716i	$0.591783\pi$
$318$	1.66291	0.0932515
$319$	15.8496	0.887405
$320$	0	0
$321$	−13.7381	−0.766788
$322$	0.962389	0.0536318
$323$	17.9248	0.997361
$324$	−1.96239	−0.109022
$325$	0	0
$326$	1.02776	0.0569225
$327$	−2.77575	−0.153499
$328$	2.87258	0.158612
$329$	−9.92478	−0.547171
$330$	0	0
$331$	27.8496	1.53075	0.765375	−	0.643585i	$-0.222554\pi$
$331$	27.8496	1.53075	0.765375	+	0.643585i	$0.222554\pi$
$332$	6.32724	0.347252
$333$	0.775746	0.0425106
$334$	−2.82179	−0.154402
$335$	0	0
$336$	3.77575	0.205984
$337$	3.84955	0.209699	0.104849	−	0.994488i	$-0.466564\pi$
$337$	3.84955	0.209699	0.104849	+	0.994488i	$0.466564\pi$
$338$	2.16759	0.117901
$339$	−12.0508	−0.654509
$340$	0	0
$341$	9.14903	0.495448
$342$	−1.03761	−0.0561076
$343$	1.00000	0.0539949
$344$	9.70194	0.523093
$345$	0	0
$346$	−0.872577	−0.0469101
$347$	−9.58769	−0.514694	−0.257347	−	0.966319i	$-0.582848\pi$
$347$	−9.58769	−0.514694	−0.257347	+	0.966319i	$0.582848\pi$
$348$	−15.5515	−0.833648
$349$	−15.1490	−0.810909	−0.405455	−	0.914115i	$-0.632887\pi$
$349$	−15.1490	−0.810909	−0.405455	+	0.914115i	$0.632887\pi$
$350$	0	0
$351$	−1.35026	−0.0720716
$352$	−4.53832	−0.241893
$353$	20.3488	1.08306	0.541530	−	0.840681i	$-0.317845\pi$
$353$	20.3488	1.08306	0.541530	+	0.840681i	$0.317845\pi$
$354$	1.67276	0.0889063
$355$	0	0
$356$	−2.03620	−0.107918
$357$	3.35026	0.177315
$358$	−1.93937	−0.102499
$359$	−31.4010	−1.65728	−0.828642	−	0.559779i	$-0.810886\pi$
$359$	−31.4010	−1.65728	−0.828642	+	0.559779i	$0.810886\pi$
$360$	0	0
$361$	9.62530	0.506595
$362$	−2.06063	−0.108305
$363$	−7.00000	−0.367405
$364$	2.64974	0.138884
$365$	0	0
$366$	1.68735	0.0881992
$367$	29.4010	1.53472	0.767361	−	0.641215i	$-0.221569\pi$
$367$	29.4010	1.53472	0.767361	+	0.641215i	$0.221569\pi$
$368$	−18.7367	−0.976719
$369$	3.73813	0.194600
$370$	0	0
$371$	−8.57452	−0.445167
$372$	−8.97698	−0.465435
$373$	−16.0000	−0.828449	−0.414224	−	0.910175i	$-0.635947\pi$
$373$	−16.0000	−0.828449	−0.414224	+	0.910175i	$0.635947\pi$
$374$	−1.29948	−0.0671943
$375$	0	0
$376$	−7.62672	−0.393318
$377$	−10.7005	−0.551105
$378$	−0.193937	−0.00997502
$379$	10.7005	0.549649	0.274824	−	0.961494i	$-0.411380\pi$
$379$	10.7005	0.549649	0.274824	+	0.961494i	$0.411380\pi$
$380$	0	0
$381$	−2.70052	−0.138352
$382$	2.68594	0.137424
$383$	16.7757	0.857201	0.428600	−	0.903494i	$-0.359007\pi$
$383$	16.7757	0.857201	0.428600	+	0.903494i	$0.359007\pi$
$384$	5.91748	0.301975
$385$	0	0
$386$	2.97224	0.151283
$387$	12.6253	0.641780
$388$	−36.3028	−1.84300
$389$	−29.3258	−1.48688	−0.743439	−	0.668804i	$-0.766807\pi$
$389$	−29.3258	−1.48688	−0.743439	+	0.668804i	$0.766807\pi$
$390$	0	0
$391$	−16.6253	−0.840778
$392$	0.768452	0.0388127
$393$	20.6253	1.04041
$394$	−0.111420	−0.00561324
$395$	0	0
$396$	−3.92478	−0.197227
$397$	−18.3488	−0.920902	−0.460451	−	0.887685i	$-0.652312\pi$
$397$	−18.3488	−0.920902	−0.460451	+	0.887685i	$0.652312\pi$
$398$	0.0390260	0.00195620
$399$	5.35026	0.267848
$400$	0	0
$401$	−37.3258	−1.86396	−0.931981	−	0.362506i	$-0.881921\pi$
$401$	−37.3258	−1.86396	−0.931981	+	0.362506i	$0.881921\pi$
$402$	1.92478	0.0959992
$403$	−6.17679	−0.307688
$404$	34.6615	1.72447
$405$	0	0
$406$	−1.53690	−0.0762753
$407$	1.55149	0.0769046
$408$	2.57452	0.127458
$409$	−22.3733	−1.10629	−0.553144	−	0.833086i	$-0.686572\pi$
$409$	−22.3733	−1.10629	−0.553144	+	0.833086i	$0.686572\pi$
$410$	0	0
$411$	−22.4993	−1.10981
$412$	13.1490	0.647806
$413$	−8.62530	−0.424423
$414$	0.962389	0.0472988
$415$	0	0
$416$	3.06396	0.150223
$417$	−3.27504	−0.160379
$418$	−2.07522	−0.101502
$419$	23.4763	1.14689	0.573445	−	0.819244i	$-0.305606\pi$
$419$	23.4763	1.14689	0.573445	+	0.819244i	$0.305606\pi$
$420$	0	0
$421$	−25.2243	−1.22935	−0.614677	−	0.788779i	$-0.710714\pi$
$421$	−25.2243	−1.22935	−0.614677	+	0.788779i	$0.710714\pi$
$422$	−1.25060	−0.0608783
$423$	−9.92478	−0.482559
$424$	−6.58910	−0.319995
$425$	0	0
$426$	−0.387873	−0.0187925
$427$	−8.70052	−0.421048
$428$	26.9596	1.30314
$429$	−2.70052	−0.130383
$430$	0	0
$431$	−19.4010	−0.934516	−0.467258	−	0.884121i	$-0.654758\pi$
$431$	−19.4010	−0.934516	−0.467258	+	0.884121i	$0.654758\pi$
$432$	3.77575	0.181661
$433$	−6.49929	−0.312336	−0.156168	−	0.987731i	$-0.549914\pi$
$433$	−6.49929	−0.312336	−0.156168	+	0.987731i	$0.549914\pi$
$434$	−0.887166	−0.0425853
$435$	0	0
$436$	5.44709	0.260868
$437$	−26.5501	−1.27006
$438$	−1.81336	−0.0866456
$439$	−14.6497	−0.699194	−0.349597	−	0.936900i	$-0.613681\pi$
$439$	−14.6497	−0.699194	−0.349597	+	0.936900i	$0.613681\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	0.877317	0.0417297
$443$	−19.1392	−0.909330	−0.454665	−	0.890663i	$-0.650241\pi$
$443$	−19.1392	−0.909330	−0.454665	+	0.890663i	$0.650241\pi$
$444$	−1.52232	−0.0722459
$445$	0	0
$446$	0.300891	0.0142476
$447$	−4.44851	−0.210407
$448$	−7.11142	−0.335983
$449$	−32.8021	−1.54803	−0.774013	−	0.633169i	$-0.781754\pi$
$449$	−32.8021	−1.54803	−0.774013	+	0.633169i	$0.781754\pi$
$450$	0	0
$451$	7.47627	0.352044
$452$	23.6483	1.11232
$453$	1.29948	0.0610547
$454$	−2.55008	−0.119681
$455$	0	0
$456$	4.11142	0.192535
$457$	18.7005	0.874774	0.437387	−	0.899273i	$-0.355904\pi$
$457$	18.7005	0.874774	0.437387	+	0.899273i	$0.355904\pi$
$458$	−0.538319	−0.0251540
$459$	3.35026	0.156377
$460$	0	0
$461$	−6.96239	−0.324271	−0.162135	−	0.986769i	$-0.551838\pi$
$461$	−6.96239	−0.324271	−0.162135	+	0.986769i	$0.551838\pi$
$462$	−0.387873	−0.0180455
$463$	−5.29948	−0.246288	−0.123144	−	0.992389i	$-0.539298\pi$
$463$	−5.29948	−0.246288	−0.123144	+	0.992389i	$0.539298\pi$
$464$	29.9219	1.38909
$465$	0	0
$466$	−0.00984911	−0.000456251 0
$467$	13.1490	0.608465	0.304232	−	0.952598i	$-0.401600\pi$
$467$	13.1490	0.608465	0.304232	+	0.952598i	$0.401600\pi$
$468$	2.64974	0.122484
$469$	−9.92478	−0.458284
$470$	0	0
$471$	2.64974	0.122093
$472$	−6.62813	−0.305084
$473$	25.2506	1.16102
$474$	−2.07522	−0.0953181
$475$	0	0
$476$	−6.57452	−0.301342
$477$	−8.57452	−0.392600
$478$	−1.13444	−0.0518882
$479$	5.14903	0.235265	0.117633	−	0.993057i	$-0.462469\pi$
$479$	5.14903	0.235265	0.117633	+	0.993057i	$0.462469\pi$
$480$	0	0
$481$	−1.04746	−0.0477601
$482$	0.0145884	0.000664486 0
$483$	−4.96239	−0.225797
$484$	13.7367	0.624396
$485$	0	0
$486$	−0.193937	−0.00879714
$487$	22.1768	1.00493	0.502463	−	0.864599i	$-0.332427\pi$
$487$	22.1768	1.00493	0.502463	+	0.864599i	$0.332427\pi$
$488$	−6.68594	−0.302658
$489$	−5.29948	−0.239651
$490$	0	0
$491$	2.00000	0.0902587	0.0451294	−	0.998981i	$-0.485630\pi$
$491$	2.00000	0.0902587	0.0451294	+	0.998981i	$0.485630\pi$
$492$	−7.33567	−0.330718
$493$	26.5501	1.19576
$494$	1.40105	0.0630361
$495$	0	0
$496$	17.2722	0.775545
$497$	2.00000	0.0897123
$498$	0.625301	0.0280204
$499$	−6.55008	−0.293222	−0.146611	−	0.989194i	$-0.546837\pi$
$499$	−6.55008	−0.293222	−0.146611	+	0.989194i	$0.546837\pi$
$500$	0	0
$501$	14.5501	0.650050
$502$	−3.72829	−0.166402
$503$	−8.77575	−0.391291	−0.195646	−	0.980675i	$-0.562680\pi$
$503$	−8.77575	−0.391291	−0.195646	+	0.980675i	$0.562680\pi$
$504$	0.768452	0.0342296
$505$	0	0
$506$	1.92478	0.0855668
$507$	−11.1768	−0.496379
$508$	5.29948	0.235126
$509$	13.1392	0.582384	0.291192	−	0.956665i	$-0.405948\pi$
$509$	13.1392	0.582384	0.291192	+	0.956665i	$0.405948\pi$
$510$	0	0
$511$	9.35026	0.413631
$512$	−14.3707	−0.635103
$513$	5.35026	0.236220
$514$	1.42548	0.0628754
$515$	0	0
$516$	−24.7757	−1.09069
$517$	−19.8496	−0.872982
$518$	−0.150446	−0.00661020
$519$	4.49929	0.197497
$520$	0	0
$521$	−37.6629	−1.65004	−0.825021	−	0.565102i	$-0.808837\pi$
$521$	−37.6629	−1.65004	−0.825021	+	0.565102i	$0.808837\pi$
$522$	−1.53690	−0.0672685
$523$	4.00000	0.174908	0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000	0.174908	0.0874539	+	0.996169i	$0.472127\pi$
$524$	−40.4749	−1.76815
$525$	0	0
$526$	−2.51388	−0.109610
$527$	15.3258	0.667603
$528$	7.55149	0.328637
$529$	1.62530	0.0706652
$530$	0	0
$531$	−8.62530	−0.374306
$532$	−10.4993	−0.455202
$533$	−5.04746	−0.218630
$534$	−0.201231	−0.00870811
$535$	0	0
$536$	−7.62672	−0.329424
$537$	10.0000	0.431532
$538$	−0.797355	−0.0343764
$539$	2.00000	0.0861461
$540$	0	0
$541$	−22.4749	−0.966269	−0.483135	−	0.875546i	$-0.660502\pi$
$541$	−22.4749	−0.966269	−0.483135	+	0.875546i	$0.660502\pi$
$542$	3.18523	0.136817
$543$	10.6253	0.455975
$544$	−7.60228	−0.325945
$545$	0	0
$546$	0.261865	0.0112068
$547$	25.9248	1.10846	0.554232	−	0.832362i	$-0.313012\pi$
$547$	25.9248	1.10846	0.554232	+	0.832362i	$0.313012\pi$
$548$	44.1524	1.88610
$549$	−8.70052	−0.371329
$550$	0	0
$551$	42.3996	1.80629
$552$	−3.81336	−0.162307
$553$	10.7005	0.455033
$554$	−2.14762	−0.0912435
$555$	0	0
$556$	6.42690	0.272561
$557$	28.5256	1.20867	0.604335	−	0.796730i	$-0.293439\pi$
$557$	28.5256	1.20867	0.604335	+	0.796730i	$0.293439\pi$
$558$	−0.887166	−0.0375567
$559$	−17.0475	−0.721031
$560$	0	0
$561$	6.70052	0.282896
$562$	−2.78751	−0.117584
$563$	11.6267	0.490008	0.245004	−	0.969522i	$-0.421211\pi$
$563$	11.6267	0.490008	0.245004	+	0.969522i	$0.421211\pi$
$564$	19.4763	0.820099
$565$	0	0
$566$	0.222839	0.00936663
$567$	1.00000	0.0419961
$568$	1.53690	0.0644871
$569$	9.32582	0.390959	0.195479	−	0.980708i	$-0.437374\pi$
$569$	9.32582	0.390959	0.195479	+	0.980708i	$0.437374\pi$
$570$	0	0
$571$	−19.6991	−0.824382	−0.412191	−	0.911097i	$-0.635236\pi$
$571$	−19.6991	−0.824382	−0.412191	+	0.911097i	$0.635236\pi$
$572$	5.29948	0.221582
$573$	−13.8496	−0.578573
$574$	−0.724961	−0.0302593
$575$	0	0
$576$	−7.11142	−0.296309
$577$	−32.7974	−1.36537	−0.682686	−	0.730712i	$-0.739188\pi$
$577$	−32.7974	−1.36537	−0.682686	+	0.730712i	$0.739188\pi$
$578$	1.12013	0.0465912
$579$	−15.3258	−0.636920
$580$	0	0
$581$	−3.22425	−0.133765
$582$	−3.58769	−0.148715
$583$	−17.1490	−0.710240
$584$	7.18523	0.297327
$585$	0	0
$586$	0.126008	0.00520534
$587$	−18.8218	−0.776859	−0.388429	−	0.921479i	$-0.626982\pi$
$587$	−18.8218	−0.776859	−0.388429	+	0.921479i	$0.626982\pi$
$588$	−1.96239	−0.0809275
$589$	24.4749	1.00847
$590$	0	0
$591$	0.574515	0.0236324
$592$	2.92902	0.120382
$593$	−33.7499	−1.38594	−0.692971	−	0.720965i	$-0.743699\pi$
$593$	−33.7499	−1.38594	−0.692971	+	0.720965i	$0.743699\pi$
$594$	−0.387873	−0.0159146
$595$	0	0
$596$	8.72970	0.357582
$597$	−0.201231	−0.00823583
$598$	−1.29948	−0.0531395
$599$	−20.2981	−0.829356	−0.414678	−	0.909968i	$-0.636106\pi$
$599$	−20.2981	−0.829356	−0.414678	+	0.909968i	$0.636106\pi$
$600$	0	0
$601$	−13.8496	−0.564935	−0.282468	−	0.959277i	$-0.591153\pi$
$601$	−13.8496	−0.564935	−0.282468	+	0.959277i	$0.591153\pi$
$602$	−2.44851	−0.0997937
$603$	−9.92478	−0.404168
$604$	−2.55008	−0.103761
$605$	0	0
$606$	3.42548	0.139151
$607$	25.2506	1.02489	0.512445	−	0.858720i	$-0.328740\pi$
$607$	25.2506	1.02489	0.512445	+	0.858720i	$0.328740\pi$
$608$	−12.1406	−0.492366
$609$	7.92478	0.321128
$610$	0	0
$611$	13.4010	0.542148
$612$	−6.57452	−0.265759
$613$	9.14903	0.369526	0.184763	−	0.982783i	$-0.440848\pi$
$613$	9.14903	0.369526	0.184763	+	0.982783i	$0.440848\pi$
$614$	4.67418	0.188634
$615$	0	0
$616$	1.53690	0.0619236
$617$	−15.9492	−0.642091	−0.321046	−	0.947064i	$-0.604034\pi$
$617$	−15.9492	−0.642091	−0.321046	+	0.947064i	$0.604034\pi$
$618$	1.29948	0.0522726
$619$	11.1735	0.449100	0.224550	−	0.974463i	$-0.427909\pi$
$619$	11.1735	0.449100	0.224550	+	0.974463i	$0.427909\pi$
$620$	0	0
$621$	−4.96239	−0.199134
$622$	−1.60037	−0.0641689
$623$	1.03761	0.0415710
$624$	−5.09825	−0.204093
$625$	0	0
$626$	−2.89000	−0.115507
$627$	10.7005	0.427338
$628$	−5.19982	−0.207495
$629$	2.59895	0.103627
$630$	0	0
$631$	−14.5501	−0.579229	−0.289615	−	0.957143i	$-0.593527\pi$
$631$	−14.5501	−0.579229	−0.289615	+	0.957143i	$0.593527\pi$
$632$	8.22284	0.327087
$633$	6.44851	0.256305
$634$	1.96380	0.0779926
$635$	0	0
$636$	16.8265	0.667215
$637$	−1.35026	−0.0534993
$638$	−3.07381	−0.121693
$639$	2.00000	0.0791188
$640$	0	0
$641$	−38.7269	−1.52962	−0.764810	−	0.644256i	$-0.777167\pi$
$641$	−38.7269	−1.52962	−0.764810	+	0.644256i	$0.777167\pi$
$642$	2.66433	0.105153
$643$	11.9511	0.471306	0.235653	−	0.971837i	$-0.424277\pi$
$643$	11.9511	0.471306	0.235653	+	0.971837i	$0.424277\pi$
$644$	9.73813	0.383736
$645$	0	0
$646$	−3.47627	−0.136772
$647$	14.5501	0.572023	0.286011	−	0.958226i	$-0.407671\pi$
$647$	14.5501	0.572023	0.286011	+	0.958226i	$0.407671\pi$
$648$	0.768452	0.0301876
$649$	−17.2506	−0.677145
$650$	0	0
$651$	4.57452	0.179289
$652$	10.3996	0.407281
$653$	−49.9756	−1.95569	−0.977847	−	0.209319i	$-0.932875\pi$
$653$	−49.9756	−1.95569	−0.977847	+	0.209319i	$0.932875\pi$
$654$	0.538319	0.0210499
$655$	0	0
$656$	14.1142	0.551069
$657$	9.35026	0.364788
$658$	1.92478	0.0750356
$659$	−16.9525	−0.660377	−0.330189	−	0.943915i	$-0.607112\pi$
$659$	−16.9525	−0.660377	−0.330189	+	0.943915i	$0.607112\pi$
$660$	0	0
$661$	−15.6531	−0.608834	−0.304417	−	0.952539i	$-0.598462\pi$
$661$	−15.6531	−0.608834	−0.304417	+	0.952539i	$0.598462\pi$
$662$	−5.40105	−0.209918
$663$	−4.52373	−0.175687
$664$	−2.47768	−0.0961528
$665$	0	0
$666$	−0.150446	−0.00582965
$667$	−39.3258	−1.52270
$668$	−28.5529	−1.10475
$669$	−1.55149	−0.0599842
$670$	0	0
$671$	−17.4010	−0.671760
$672$	−2.26916	−0.0875347
$673$	−26.0263	−1.00324	−0.501621	−	0.865088i	$-0.667263\pi$
$673$	−26.0263	−1.00324	−0.501621	+	0.865088i	$0.667263\pi$
$674$	−0.746569	−0.0287568
$675$	0	0
$676$	21.9332	0.843585
$677$	35.4518	1.36252	0.681262	−	0.732039i	$-0.261431\pi$
$677$	35.4518	1.36252	0.681262	+	0.732039i	$0.261431\pi$
$678$	2.33709	0.0897553
$679$	18.4993	0.709938
$680$	0	0
$681$	13.1490	0.503872
$682$	−1.77433	−0.0679427
$683$	23.6629	0.905436	0.452718	−	0.891654i	$-0.350454\pi$
$683$	23.6629	0.905436	0.452718	+	0.891654i	$0.350454\pi$
$684$	−10.4993	−0.401450
$685$	0	0
$686$	−0.193937	−0.00740453
$687$	2.77575	0.105901
$688$	47.6699	1.81740
$689$	11.5778	0.441081
$690$	0	0
$691$	−0.574515	−0.0218556	−0.0109278	−	0.999940i	$-0.503478\pi$
$691$	−0.574515	−0.0218556	−0.0109278	+	0.999940i	$0.503478\pi$
$692$	−8.82936	−0.335642
$693$	2.00000	0.0759737
$694$	1.85940	0.0705820
$695$	0	0
$696$	6.08981	0.230834
$697$	12.5237	0.474370
$698$	2.93795	0.111203
$699$	0.0507852	0.00192087
$700$	0	0
$701$	42.7269	1.61377	0.806886	−	0.590707i	$-0.201151\pi$
$701$	42.7269	1.61377	0.806886	+	0.590707i	$0.201151\pi$
$702$	0.261865	0.00988346
$703$	4.15045	0.156537
$704$	−14.2228	−0.536043
$705$	0	0
$706$	−3.94639	−0.148524
$707$	−17.6629	−0.664282
$708$	16.9262	0.636125
$709$	27.2506	1.02342	0.511709	−	0.859159i	$-0.329013\pi$
$709$	27.2506	1.02342	0.511709	+	0.859159i	$0.329013\pi$
$710$	0	0
$711$	10.7005	0.401301
$712$	0.797355	0.0298821
$713$	−22.7005	−0.850141
$714$	−0.649738	−0.0243158
$715$	0	0
$716$	−19.6239	−0.733379
$717$	5.84955	0.218456
$718$	6.08981	0.227270
$719$	−10.7005	−0.399062	−0.199531	−	0.979891i	$-0.563942\pi$
$719$	−10.7005	−0.399062	−0.199531	+	0.979891i	$0.563942\pi$
$720$	0	0
$721$	−6.70052	−0.249541
$722$	−1.86670	−0.0694713
$723$	−0.0752228	−0.00279757
$724$	−20.8510	−0.774920
$725$	0	0
$726$	1.35756	0.0503836
$727$	−39.9511	−1.48171	−0.740853	−	0.671668i	$-0.765578\pi$
$727$	−39.9511	−1.48171	−0.740853	+	0.671668i	$0.765578\pi$
$728$	−1.03761	−0.0384564
$729$	1.00000	0.0370370
$730$	0	0
$731$	42.2981	1.56445
$732$	17.0738	0.631066
$733$	30.3488	1.12096	0.560480	−	0.828168i	$-0.310617\pi$
$733$	30.3488	1.12096	0.560480	+	0.828168i	$0.310617\pi$
$734$	−5.70194	−0.210462
$735$	0	0
$736$	11.2605	0.415066
$737$	−19.8496	−0.731168
$738$	−0.724961	−0.0266862
$739$	37.2506	1.37029	0.685143	−	0.728409i	$-0.259740\pi$
$739$	37.2506	1.37029	0.685143	+	0.728409i	$0.259740\pi$
$740$	0	0
$741$	−7.22425	−0.265390
$742$	1.66291	0.0610474
$743$	−26.3634	−0.967181	−0.483590	−	0.875294i	$-0.660668\pi$
$743$	−26.3634	−0.967181	−0.483590	+	0.875294i	$0.660668\pi$
$744$	3.51530	0.128877
$745$	0	0
$746$	3.10299	0.113608
$747$	−3.22425	−0.117969
$748$	−13.1490	−0.480776
$749$	−13.7381	−0.501981
$750$	0	0
$751$	50.6516	1.84830	0.924152	−	0.382024i	$-0.124773\pi$
$751$	50.6516	1.84830	0.924152	+	0.382024i	$0.124773\pi$
$752$	−37.4734	−1.36652
$753$	19.2243	0.700571
$754$	2.07522	0.0755752
$755$	0	0
$756$	−1.96239	−0.0713714
$757$	−38.9525	−1.41575	−0.707877	−	0.706336i	$-0.750347\pi$
$757$	−38.9525	−1.41575	−0.707877	+	0.706336i	$0.750347\pi$
$758$	−2.07522	−0.0753755
$759$	−9.92478	−0.360247
$760$	0	0
$761$	48.2130	1.74772	0.873860	−	0.486178i	$-0.161609\pi$
$761$	48.2130	1.74772	0.873860	+	0.486178i	$0.161609\pi$
$762$	0.523730	0.0189727
$763$	−2.77575	−0.100489
$764$	27.1782	0.983273
$765$	0	0
$766$	−3.25343	−0.117551
$767$	11.6464	0.420528
$768$	13.0752	0.471811
$769$	4.44851	0.160417	0.0802086	−	0.996778i	$-0.474441\pi$
$769$	4.44851	0.160417	0.0802086	+	0.996778i	$0.474441\pi$
$770$	0	0
$771$	−7.35026	−0.264713
$772$	30.0752	1.08243
$773$	−39.3014	−1.41357	−0.706786	−	0.707427i	$-0.749856\pi$
$773$	−39.3014	−1.41357	−0.706786	+	0.707427i	$0.749856\pi$
$774$	−2.44851	−0.0880098
$775$	0	0
$776$	14.2158	0.510318
$777$	0.775746	0.0278297
$778$	5.68735	0.203901
$779$	20.0000	0.716574
$780$	0	0
$781$	4.00000	0.143131
$782$	3.22425	0.115299
$783$	7.92478	0.283208
$784$	3.77575	0.134848
$785$	0	0
$786$	−4.00000	−0.142675
$787$	−0.897015	−0.0319751	−0.0159876	−	0.999872i	$-0.505089\pi$
$787$	−0.897015	−0.0319751	−0.0159876	+	0.999872i	$0.505089\pi$
$788$	−1.12742	−0.0401628
$789$	12.9624	0.461473
$790$	0	0
$791$	−12.0508	−0.428477
$792$	1.53690	0.0546115
$793$	11.7480	0.417183
$794$	3.55851	0.126287
$795$	0	0
$796$	0.394893	0.0139966
$797$	−3.19982	−0.113343	−0.0566717	−	0.998393i	$-0.518049\pi$
$797$	−3.19982	−0.113343	−0.0566717	+	0.998393i	$0.518049\pi$
$798$	−1.03761	−0.0367310
$799$	−33.2506	−1.17632
$800$	0	0
$801$	1.03761	0.0366622
$802$	7.23884	0.255612
$803$	18.7005	0.659927
$804$	19.4763	0.686875
$805$	0	0
$806$	1.19791	0.0421944
$807$	4.11142	0.144729
$808$	−13.5731	−0.477500
$809$	4.44851	0.156401	0.0782006	−	0.996938i	$-0.475083\pi$
$809$	4.44851	0.156401	0.0782006	+	0.996938i	$0.475083\pi$
$810$	0	0
$811$	37.6747	1.32294	0.661468	−	0.749973i	$-0.269934\pi$
$811$	37.6747	1.32294	0.661468	+	0.749973i	$0.269934\pi$
$812$	−15.5515	−0.545750
$813$	−16.4241	−0.576017
$814$	−0.300891	−0.0105462
$815$	0	0
$816$	12.6497	0.442829
$817$	67.5487	2.36323
$818$	4.33900	0.151710
$819$	−1.35026	−0.0471820
$820$	0	0
$821$	−0.749399	−0.0261542	−0.0130771	−	0.999914i	$-0.504163\pi$
$821$	−0.749399	−0.0261542	−0.0130771	+	0.999914i	$0.504163\pi$
$822$	4.36344	0.152192
$823$	26.3996	0.920233	0.460117	−	0.887858i	$-0.347808\pi$
$823$	26.3996	0.920233	0.460117	+	0.887858i	$0.347808\pi$
$824$	−5.14903	−0.179375
$825$	0	0
$826$	1.67276	0.0582028
$827$	−5.43724	−0.189071	−0.0945357	−	0.995521i	$-0.530137\pi$
$827$	−5.43724	−0.189071	−0.0945357	+	0.995521i	$0.530137\pi$
$828$	9.73813	0.338424
$829$	22.7757	0.791034	0.395517	−	0.918459i	$-0.370565\pi$
$829$	22.7757	0.791034	0.395517	+	0.918459i	$0.370565\pi$
$830$	0	0
$831$	11.0738	0.384146
$832$	9.60228	0.332899
$833$	3.35026	0.116080
$834$	0.635150	0.0219934
$835$	0	0
$836$	−20.9986	−0.726251
$837$	4.57452	0.158118
$838$	−4.55291	−0.157278
$839$	15.8496	0.547187	0.273594	−	0.961845i	$-0.411788\pi$
$839$	15.8496	0.547187	0.273594	+	0.961845i	$0.411788\pi$
$840$	0	0
$841$	33.8021	1.16559
$842$	4.89191	0.168586
$843$	14.3733	0.495042
$844$	−12.6545	−0.435585
$845$	0	0
$846$	1.92478	0.0661752
$847$	−7.00000	−0.240523
$848$	−32.3752	−1.11177
$849$	−1.14903	−0.0394346
$850$	0	0
$851$	−3.84955	−0.131961
$852$	−3.92478	−0.134461
$853$	21.0494	0.720717	0.360358	−	0.932814i	$-0.382654\pi$
$853$	21.0494	0.720717	0.360358	+	0.932814i	$0.382654\pi$
$854$	1.68735	0.0577399
$855$	0	0
$856$	−10.5571	−0.360834
$857$	−50.1524	−1.71317	−0.856586	−	0.516004i	$-0.827419\pi$
$857$	−50.1524	−1.71317	−0.856586	+	0.516004i	$0.827419\pi$
$858$	0.523730	0.0178799
$859$	−5.35026	−0.182549	−0.0912743	−	0.995826i	$-0.529094\pi$
$859$	−5.35026	−0.182549	−0.0912743	+	0.995826i	$0.529094\pi$
$860$	0	0
$861$	3.73813	0.127395
$862$	3.76257	0.128154
$863$	33.6893	1.14680	0.573398	−	0.819277i	$-0.305625\pi$
$863$	33.6893	1.14680	0.573398	+	0.819277i	$0.305625\pi$
$864$	−2.26916	−0.0771984
$865$	0	0
$866$	1.26045	0.0428319
$867$	−5.77575	−0.196155
$868$	−8.97698	−0.304698
$869$	21.4010	0.725981
$870$	0	0
$871$	13.4010	0.454077
$872$	−2.13303	−0.0722334
$873$	18.4993	0.626106
$874$	5.14903	0.174169
$875$	0	0
$876$	−18.3488	−0.619950
$877$	21.5026	0.726092	0.363046	−	0.931771i	$-0.381737\pi$
$877$	21.5026	0.726092	0.363046	+	0.931771i	$0.381737\pi$
$878$	2.84112	0.0958832
$879$	−0.649738	−0.0219151
$880$	0	0
$881$	32.3634	1.09035	0.545176	−	0.838322i	$-0.316463\pi$
$881$	32.3634	1.09035	0.545176	+	0.838322i	$0.316463\pi$
$882$	−0.193937	−0.00653018
$883$	2.59895	0.0874617	0.0437309	−	0.999043i	$-0.486076\pi$
$883$	2.59895	0.0874617	0.0437309	+	0.999043i	$0.486076\pi$
$884$	8.87732	0.298576
$885$	0	0
$886$	3.71179	0.124700
$887$	−38.2784	−1.28526	−0.642631	−	0.766176i	$-0.722157\pi$
$887$	−38.2784	−1.28526	−0.642631	+	0.766176i	$0.722157\pi$
$888$	0.596124	0.0200046
$889$	−2.70052	−0.0905727
$890$	0	0
$891$	2.00000	0.0670025
$892$	3.04463	0.101942
$893$	−53.1002	−1.77693
$894$	0.862728	0.0288539
$895$	0	0
$896$	5.91748	0.197689
$897$	6.70052	0.223724
$898$	6.36153	0.212287
$899$	36.2520	1.20907
$900$	0	0
$901$	−28.7269	−0.957031
$902$	−1.44992	−0.0482771
$903$	12.6253	0.420144
$904$	−9.26045	−0.307998
$905$	0	0
$906$	−0.252016	−0.00837267
$907$	49.9972	1.66013	0.830064	−	0.557668i	$-0.188304\pi$
$907$	49.9972	1.66013	0.830064	+	0.557668i	$0.188304\pi$
$908$	−25.8035	−0.856320
$909$	−17.6629	−0.585842
$910$	0	0
$911$	−24.9525	−0.826715	−0.413357	−	0.910569i	$-0.635644\pi$
$911$	−24.9525	−0.826715	−0.413357	+	0.910569i	$0.635644\pi$
$912$	20.2012	0.668930
$913$	−6.44851	−0.213414
$914$	−3.62672	−0.119961
$915$	0	0
$916$	−5.44709	−0.179977
$917$	20.6253	0.681107
$918$	−0.649738	−0.0214446
$919$	−11.6991	−0.385918	−0.192959	−	0.981207i	$-0.561808\pi$
$919$	−11.6991	−0.385918	−0.192959	+	0.981207i	$0.561808\pi$
$920$	0	0
$921$	−24.1016	−0.794174
$922$	1.35026	0.0444685
$923$	−2.70052	−0.0888888
$924$	−3.92478	−0.129116
$925$	0	0
$926$	1.02776	0.0337744
$927$	−6.70052	−0.220074
$928$	−17.9826	−0.590307
$929$	23.7090	0.777866	0.388933	−	0.921266i	$-0.372844\pi$
$929$	23.7090	0.777866	0.388933	+	0.921266i	$0.372844\pi$
$930$	0	0
$931$	5.35026	0.175348
$932$	−0.0996603	−0.00326448
$933$	8.25202	0.270159
$934$	−2.55008	−0.0834411
$935$	0	0
$936$	−1.03761	−0.0339154
$937$	19.9003	0.650116	0.325058	−	0.945694i	$-0.394616\pi$
$937$	19.9003	0.650116	0.325058	+	0.945694i	$0.394616\pi$
$938$	1.92478	0.0628462
$939$	14.9018	0.486300
$940$	0	0
$941$	−6.28821	−0.204990	−0.102495	−	0.994734i	$-0.532683\pi$
$941$	−6.28821	−0.204990	−0.102495	+	0.994734i	$0.532683\pi$
$942$	−0.513881	−0.0167432
$943$	−18.5501	−0.604074
$944$	−32.5669	−1.05996
$945$	0	0
$946$	−4.89701	−0.159216
$947$	40.0362	1.30100	0.650501	−	0.759506i	$-0.274559\pi$
$947$	40.0362	1.30100	0.650501	+	0.759506i	$0.274559\pi$
$948$	−20.9986	−0.682002
$949$	−12.6253	−0.409835
$950$	0	0
$951$	−10.1260	−0.328358
$952$	2.57452	0.0834405
$953$	−40.9478	−1.32643	−0.663215	−	0.748429i	$-0.730808\pi$
$953$	−40.9478	−1.32643	−0.663215	+	0.748429i	$0.730808\pi$
$954$	1.66291	0.0538388
$955$	0	0
$956$	−11.4791	−0.371261
$957$	15.8496	0.512343
$958$	−0.998585	−0.0322628
$959$	−22.4993	−0.726540
$960$	0	0
$961$	−10.0738	−0.324962
$962$	0.203141	0.00654953
$963$	−13.7381	−0.442705
$964$	0.147616	0.00475440
$965$	0	0
$966$	0.962389	0.0309643
$967$	−38.2784	−1.23095	−0.615475	−	0.788157i	$-0.711036\pi$
$967$	−38.2784	−1.23095	−0.615475	+	0.788157i	$0.711036\pi$
$968$	−5.37916	−0.172893
$969$	17.9248	0.575827
$970$	0	0
$971$	−28.7269	−0.921889	−0.460945	−	0.887429i	$-0.652489\pi$
$971$	−28.7269	−0.921889	−0.460945	+	0.887429i	$0.652489\pi$
$972$	−1.96239	−0.0629436
$973$	−3.27504	−0.104993
$974$	−4.30089	−0.137809
$975$	0	0
$976$	−32.8510	−1.05153
$977$	41.3014	1.32135	0.660674	−	0.750673i	$-0.270270\pi$
$977$	41.3014	1.32135	0.660674	+	0.750673i	$0.270270\pi$
$978$	1.02776	0.0328642
$979$	2.07522	0.0663244
$980$	0	0
$981$	−2.77575	−0.0886228
$982$	−0.387873	−0.0123775
$983$	24.0000	0.765481	0.382741	−	0.923856i	$-0.374980\pi$
$983$	24.0000	0.765481	0.382741	+	0.923856i	$0.374980\pi$
$984$	2.87258	0.0915744
$985$	0	0
$986$	−5.14903	−0.163979
$987$	−9.92478	−0.315909
$988$	14.1768	0.451024
$989$	−62.6516	−1.99221
$990$	0	0
$991$	25.1002	0.797333	0.398666	−	0.917096i	$-0.369473\pi$
$991$	25.1002	0.797333	0.398666	+	0.917096i	$0.369473\pi$
$992$	−10.3803	−0.329575
$993$	27.8496	0.883779
$994$	−0.387873	−0.0123026
$995$	0	0
$996$	6.32724	0.200486
$997$	−32.7974	−1.03870	−0.519351	−	0.854561i	$-0.673826\pi$
$997$	−32.7974	−1.03870	−0.519351	+	0.854561i	$0.673826\pi$
$998$	1.27030	0.0402106
$999$	0.775746	0.0245435

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.a.j.1.2		3
3.2	odd	2		1575.2.a.x.1.2		3
4.3	odd	2		8400.2.a.dg.1.1		3
5.2	odd	4		105.2.d.b.64.3	✓	6
5.3	odd	4		105.2.d.b.64.4	yes	6
5.4	even	2		525.2.a.k.1.2		3
7.6	odd	2		3675.2.a.bi.1.2		3
15.2	even	4		315.2.d.e.64.4		6
15.8	even	4		315.2.d.e.64.3		6
15.14	odd	2		1575.2.a.w.1.2		3
20.3	even	4		1680.2.t.k.1009.1		6
20.7	even	4		1680.2.t.k.1009.4		6
20.19	odd	2		8400.2.a.dj.1.3		3
35.2	odd	12		735.2.q.e.214.3		12
35.3	even	12		735.2.q.f.79.3		12
35.12	even	12		735.2.q.f.214.3		12
35.13	even	4		735.2.d.b.589.4		6
35.17	even	12		735.2.q.f.79.4		12
35.18	odd	12		735.2.q.e.79.3		12
35.23	odd	12		735.2.q.e.214.4		12
35.27	even	4		735.2.d.b.589.3		6
35.32	odd	12		735.2.q.e.79.4		12
35.33	even	12		735.2.q.f.214.4		12
35.34	odd	2		3675.2.a.bj.1.2		3
60.23	odd	4		5040.2.t.v.1009.5		6
60.47	odd	4		5040.2.t.v.1009.6		6
105.62	odd	4		2205.2.d.l.1324.4		6
105.83	odd	4		2205.2.d.l.1324.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.d.b.64.3	✓	6	5.2	odd	4
105.2.d.b.64.4	yes	6	5.3	odd	4
315.2.d.e.64.3		6	15.8	even	4
315.2.d.e.64.4		6	15.2	even	4
525.2.a.j.1.2		3	1.1	even	1	trivial
525.2.a.k.1.2		3	5.4	even	2
735.2.d.b.589.3		6	35.27	even	4
735.2.d.b.589.4		6	35.13	even	4
735.2.q.e.79.3		12	35.18	odd	12
735.2.q.e.79.4		12	35.32	odd	12
735.2.q.e.214.3		12	35.2	odd	12
735.2.q.e.214.4		12	35.23	odd	12
735.2.q.f.79.3		12	35.3	even	12
735.2.q.f.79.4		12	35.17	even	12
735.2.q.f.214.3		12	35.12	even	12
735.2.q.f.214.4		12	35.33	even	12
1575.2.a.w.1.2		3	15.14	odd	2
1575.2.a.x.1.2		3	3.2	odd	2
1680.2.t.k.1009.1		6	20.3	even	4
1680.2.t.k.1009.4		6	20.7	even	4
2205.2.d.l.1324.3		6	105.83	odd	4
2205.2.d.l.1324.4		6	105.62	odd	4
3675.2.a.bi.1.2		3	7.6	odd	2
3675.2.a.bj.1.2		3	35.34	odd	2
5040.2.t.v.1009.5		6	60.23	odd	4
5040.2.t.v.1009.6		6	60.47	odd	4
8400.2.a.dg.1.1		3	4.3	odd	2
8400.2.a.dj.1.3		3	20.19	odd	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.a (trivial)

\(f(q)\)	\(=\)	\(q-0.193937 q^{2} +1.00000 q^{3} -1.96239 q^{4} -0.193937 q^{6} +1.00000 q^{7} +0.768452 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.193937 q^{2} +1.00000 q^{3} -1.96239 q^{4} -0.193937 q^{6} +1.00000 q^{7} +0.768452 q^{8} +1.00000 q^{9} +2.00000 q^{11} -1.96239 q^{12} -1.35026 q^{13} -0.193937 q^{14} +3.77575 q^{16} +3.35026 q^{17} -0.193937 q^{18} +5.35026 q^{19} +1.00000 q^{21} -0.387873 q^{22} -4.96239 q^{23} +0.768452 q^{24} +0.261865 q^{26} +1.00000 q^{27} -1.96239 q^{28} +7.92478 q^{29} +4.57452 q^{31} -2.26916 q^{32} +2.00000 q^{33} -0.649738 q^{34} -1.96239 q^{36} +0.775746 q^{37} -1.03761 q^{38} -1.35026 q^{39} +3.73813 q^{41} -0.193937 q^{42} +12.6253 q^{43} -3.92478 q^{44} +0.962389 q^{46} -9.92478 q^{47} +3.77575 q^{48} +1.00000 q^{49} +3.35026 q^{51} +2.64974 q^{52} -8.57452 q^{53} -0.193937 q^{54} +0.768452 q^{56} +5.35026 q^{57} -1.53690 q^{58} -8.62530 q^{59} -8.70052 q^{61} -0.887166 q^{62} +1.00000 q^{63} -7.11142 q^{64} -0.387873 q^{66} -9.92478 q^{67} -6.57452 q^{68} -4.96239 q^{69} +2.00000 q^{71} +0.768452 q^{72} +9.35026 q^{73} -0.150446 q^{74} -10.4993 q^{76} +2.00000 q^{77} +0.261865 q^{78} +10.7005 q^{79} +1.00000 q^{81} -0.724961 q^{82} -3.22425 q^{83} -1.96239 q^{84} -2.44851 q^{86} +7.92478 q^{87} +1.53690 q^{88} +1.03761 q^{89} -1.35026 q^{91} +9.73813 q^{92} +4.57452 q^{93} +1.92478 q^{94} -2.26916 q^{96} +18.4993 q^{97} -0.193937 q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} + 3 q^{3} + 5 q^{4} - q^{6} + 3 q^{7} - 9 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - q^2 + 3 * q^3 + 5 * q^4 - q^6 + 3 * q^7 - 9 * q^8 + 3 * q^9	\( 3 q - q^{2} + 3 q^{3} + 5 q^{4} - q^{6} + 3 q^{7} - 9 q^{8} + 3 q^{9} + 6 q^{11} + 5 q^{12} + 6 q^{13} - q^{14} + 13 q^{16} - q^{18} + 6 q^{19} + 3 q^{21} - 2 q^{22} - 4 q^{23} - 9 q^{24} + 10 q^{26} + 3 q^{27} + 5 q^{28} + 2 q^{29} + 2 q^{31} - 29 q^{32} + 6 q^{33} - 12 q^{34} + 5 q^{36} + 4 q^{37} - 14 q^{38} + 6 q^{39} + 2 q^{41} - q^{42} - 4 q^{43} + 10 q^{44} - 8 q^{46} - 8 q^{47} + 13 q^{48} + 3 q^{49} + 18 q^{52} - 14 q^{53} - q^{54} - 9 q^{56} + 6 q^{57} + 18 q^{58} + 16 q^{59} - 6 q^{61} + 30 q^{62} + 3 q^{63} + 13 q^{64} - 2 q^{66} - 8 q^{67} - 8 q^{68} - 4 q^{69} + 6 q^{71} - 9 q^{72} + 18 q^{73} - 44 q^{74} + 2 q^{76} + 6 q^{77} + 10 q^{78} + 12 q^{79} + 3 q^{81} - 34 q^{82} - 8 q^{83} + 5 q^{84} - 4 q^{86} + 2 q^{87} - 18 q^{88} + 14 q^{89} + 6 q^{91} + 20 q^{92} + 2 q^{93} - 16 q^{94} - 29 q^{96} + 22 q^{97} - q^{98} + 6 q^{99}+O(q^{100}) \) 3 * q - q^2 + 3 * q^3 + 5 * q^4 - q^6 + 3 * q^7 - 9 * q^8 + 3 * q^9 + 6 * q^11 + 5 * q^12 + 6 * q^13 - q^14 + 13 * q^16 - q^18 + 6 * q^19 + 3 * q^21 - 2 * q^22 - 4 * q^23 - 9 * q^24 + 10 * q^26 + 3 * q^27 + 5 * q^28 + 2 * q^29 + 2 * q^31 - 29 * q^32 + 6 * q^33 - 12 * q^34 + 5 * q^36 + 4 * q^37 - 14 * q^38 + 6 * q^39 + 2 * q^41 - q^42 - 4 * q^43 + 10 * q^44 - 8 * q^46 - 8 * q^47 + 13 * q^48 + 3 * q^49 + 18 * q^52 - 14 * q^53 - q^54 - 9 * q^56 + 6 * q^57 + 18 * q^58 + 16 * q^59 - 6 * q^61 + 30 * q^62 + 3 * q^63 + 13 * q^64 - 2 * q^66 - 8 * q^67 - 8 * q^68 - 4 * q^69 + 6 * q^71 - 9 * q^72 + 18 * q^73 - 44 * q^74 + 2 * q^76 + 6 * q^77 + 10 * q^78 + 12 * q^79 + 3 * q^81 - 34 * q^82 - 8 * q^83 + 5 * q^84 - 4 * q^86 + 2 * q^87 - 18 * q^88 + 14 * q^89 + 6 * q^91 + 20 * q^92 + 2 * q^93 - 16 * q^94 - 29 * q^96 + 22 * q^97 - q^98 + 6 * q^99

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