LMFDB - Embedded newform 3525.2.a.x.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,2,Mod(1,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, 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("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.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:	$28.1472667125$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 5x^{5} + 18x^{4} - 15x^{2} + 1 $ x^7 - 3x^6 - 5x^5 + 18x^4 - 15x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.833881$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.833881 q^{2} -1.00000 q^{3} -1.30464 q^{4} -0.833881 q^{6} -1.65674 q^{7} -2.75568 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.833881 q^{2} -1.00000 q^{3} -1.30464 q^{4} -0.833881 q^{6} -1.65674 q^{7} -2.75568 q^{8} +1.00000 q^{9} +5.28334 q^{11} +1.30464 q^{12} -0.534400 q^{13} -1.38152 q^{14} +0.311378 q^{16} -7.84567 q^{17} +0.833881 q^{18} +3.07897 q^{19} +1.65674 q^{21} +4.40568 q^{22} +5.72676 q^{23} +2.75568 q^{24} -0.445626 q^{26} -1.00000 q^{27} +2.16145 q^{28} -2.72688 q^{29} +6.36496 q^{31} +5.77101 q^{32} -5.28334 q^{33} -6.54236 q^{34} -1.30464 q^{36} -10.5696 q^{37} +2.56749 q^{38} +0.534400 q^{39} +1.07525 q^{41} +1.38152 q^{42} -0.928668 q^{43} -6.89287 q^{44} +4.77543 q^{46} +1.00000 q^{47} -0.311378 q^{48} -4.25523 q^{49} +7.84567 q^{51} +0.697201 q^{52} +7.37405 q^{53} -0.833881 q^{54} +4.56543 q^{56} -3.07897 q^{57} -2.27389 q^{58} +5.63027 q^{59} -1.87327 q^{61} +5.30762 q^{62} -1.65674 q^{63} +4.18958 q^{64} -4.40568 q^{66} +4.20514 q^{67} +10.2358 q^{68} -5.72676 q^{69} -16.4655 q^{71} -2.75568 q^{72} +7.74882 q^{73} -8.81379 q^{74} -4.01695 q^{76} -8.75310 q^{77} +0.445626 q^{78} -7.48755 q^{79} +1.00000 q^{81} +0.896633 q^{82} -17.1007 q^{83} -2.16145 q^{84} -0.774399 q^{86} +2.72688 q^{87} -14.5592 q^{88} -1.59310 q^{89} +0.885359 q^{91} -7.47137 q^{92} -6.36496 q^{93} +0.833881 q^{94} -5.77101 q^{96} -5.08324 q^{97} -3.54835 q^{98} +5.28334 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 3 q^{2} - 7 q^{3} + 5 q^{4} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 3 * q^2 - 7 * q^3 + 5 * q^4 + 3 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9	$ 7 q - 3 q^{2} - 7 q^{3} + 5 q^{4} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9} + 4 q^{11} - 5 q^{12} - 5 q^{13} + 5 q^{14} + 9 q^{16} - 10 q^{17} - 3 q^{18} + q^{19} + 5 q^{21} - 10 q^{22} - 10 q^{23} + 6 q^{24} + 12 q^{26} - 7 q^{27} - 2 q^{28} + 9 q^{29} + 3 q^{31} - 4 q^{33} - 20 q^{34} + 5 q^{36} - 9 q^{37} + 2 q^{38} + 5 q^{39} + 20 q^{41} - 5 q^{42} - 16 q^{43} - 5 q^{44} - q^{46} + 7 q^{47} - 9 q^{48} - 10 q^{49} + 10 q^{51} - 21 q^{52} + 3 q^{54} + 21 q^{56} - q^{57} - 19 q^{58} + 18 q^{59} + 2 q^{62} - 5 q^{63} - 30 q^{64} + 10 q^{66} - 8 q^{67} - 20 q^{68} + 10 q^{69} + 14 q^{71} - 6 q^{72} - 4 q^{73} - 17 q^{74} + 12 q^{76} - 2 q^{77} - 12 q^{78} - 21 q^{79} + 7 q^{81} + 7 q^{82} - 22 q^{83} + 2 q^{84} + 35 q^{86} - 9 q^{87} - 14 q^{88} + 2 q^{89} - 2 q^{91} - 5 q^{92} - 3 q^{93} - 3 q^{94} - 12 q^{97} - 30 q^{98} + 4 q^{99}+O(q^{100}) $ 7 * q - 3 * q^2 - 7 * q^3 + 5 * q^4 + 3 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9 + 4 * q^11 - 5 * q^12 - 5 * q^13 + 5 * q^14 + 9 * q^16 - 10 * q^17 - 3 * q^18 + q^19 + 5 * q^21 - 10 * q^22 - 10 * q^23 + 6 * q^24 + 12 * q^26 - 7 * q^27 - 2 * q^28 + 9 * q^29 + 3 * q^31 - 4 * q^33 - 20 * q^34 + 5 * q^36 - 9 * q^37 + 2 * q^38 + 5 * q^39 + 20 * q^41 - 5 * q^42 - 16 * q^43 - 5 * q^44 - q^46 + 7 * q^47 - 9 * q^48 - 10 * q^49 + 10 * q^51 - 21 * q^52 + 3 * q^54 + 21 * q^56 - q^57 - 19 * q^58 + 18 * q^59 + 2 * q^62 - 5 * q^63 - 30 * q^64 + 10 * q^66 - 8 * q^67 - 20 * q^68 + 10 * q^69 + 14 * q^71 - 6 * q^72 - 4 * q^73 - 17 * q^74 + 12 * q^76 - 2 * q^77 - 12 * q^78 - 21 * q^79 + 7 * q^81 + 7 * q^82 - 22 * q^83 + 2 * q^84 + 35 * q^86 - 9 * q^87 - 14 * q^88 + 2 * q^89 - 2 * q^91 - 5 * q^92 - 3 * q^93 - 3 * q^94 - 12 * q^97 - 30 * q^98 + 4 * 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 $

$2$	0.833881	0.589643	0.294821	−	0.955552i	$-0.404740\pi$
$2$	0.833881	0.589643	0.294821	+	0.955552i	$0.404740\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.30464	−0.652321
$5$	0	0
$5$	0	0
$6$	−0.833881	−0.340430
$7$	−1.65674	−0.626187	−0.313093	−	0.949722i	$-0.601365\pi$
$7$	−1.65674	−0.626187	−0.313093	+	0.949722i	$0.601365\pi$
$8$	−2.75568	−0.974279
$9$	1.00000	0.333333
$10$	0	0
$11$	5.28334	1.59299	0.796494	−	0.604647i	$-0.206686\pi$
$11$	5.28334	1.59299	0.796494	+	0.604647i	$0.206686\pi$
$12$	1.30464	0.376618
$13$	−0.534400	−0.148216	−0.0741079	−	0.997250i	$-0.523611\pi$
$13$	−0.534400	−0.148216	−0.0741079	+	0.997250i	$0.523611\pi$
$14$	−1.38152	−0.369227
$15$	0	0
$16$	0.311378	0.0778446
$17$	−7.84567	−1.90286	−0.951428	−	0.307873i	$-0.900383\pi$
$17$	−7.84567	−1.90286	−0.951428	+	0.307873i	$0.900383\pi$
$18$	0.833881	0.196548
$19$	3.07897	0.706364	0.353182	−	0.935555i	$-0.385100\pi$
$19$	3.07897	0.706364	0.353182	+	0.935555i	$0.385100\pi$
$20$	0	0
$21$	1.65674	0.361529
$22$	4.40568	0.939294
$23$	5.72676	1.19411	0.597056	−	0.802200i	$-0.296337\pi$
$23$	5.72676	1.19411	0.597056	+	0.802200i	$0.296337\pi$
$24$	2.75568	0.562500
$25$	0	0
$26$	−0.445626	−0.0873944
$27$	−1.00000	−0.192450
$28$	2.16145	0.408475
$29$	−2.72688	−0.506368	−0.253184	−	0.967418i	$-0.581478\pi$
$29$	−2.72688	−0.506368	−0.253184	+	0.967418i	$0.581478\pi$
$30$	0	0
$31$	6.36496	1.14318	0.571591	−	0.820539i	$-0.306327\pi$
$31$	6.36496	1.14318	0.571591	+	0.820539i	$0.306327\pi$
$32$	5.77101	1.02018
$33$	−5.28334	−0.919712
$34$	−6.54236	−1.12200
$35$	0	0
$36$	−1.30464	−0.217440
$37$	−10.5696	−1.73763	−0.868816	−	0.495135i	$-0.835118\pi$
$37$	−10.5696	−1.73763	−0.868816	+	0.495135i	$0.835118\pi$
$38$	2.56749	0.416502
$39$	0.534400	0.0855724
$40$	0	0
$41$	1.07525	0.167926	0.0839632	−	0.996469i	$-0.473242\pi$
$41$	1.07525	0.167926	0.0839632	+	0.996469i	$0.473242\pi$
$42$	1.38152	0.213173
$43$	−0.928668	−0.141621	−0.0708103	−	0.997490i	$-0.522558\pi$
$43$	−0.928668	−0.141621	−0.0708103	+	0.997490i	$0.522558\pi$
$44$	−6.89287	−1.03914
$45$	0	0
$46$	4.77543	0.704099
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	−0.311378	−0.0449436
$49$	−4.25523	−0.607890
$50$	0	0
$51$	7.84567	1.09861
$52$	0.697201	0.0966843
$53$	7.37405	1.01290	0.506452	−	0.862268i	$-0.330957\pi$
$53$	7.37405	1.01290	0.506452	+	0.862268i	$0.330957\pi$
$54$	−0.833881	−0.113477
$55$	0	0
$56$	4.56543	0.610081
$57$	−3.07897	−0.407819
$58$	−2.27389	−0.298576
$59$	5.63027	0.732999	0.366500	−	0.930418i	$-0.380556\pi$
$59$	5.63027	0.732999	0.366500	+	0.930418i	$0.380556\pi$
$60$	0	0
$61$	−1.87327	−0.239847	−0.119924	−	0.992783i	$-0.538265\pi$
$61$	−1.87327	−0.239847	−0.119924	+	0.992783i	$0.538265\pi$
$62$	5.30762	0.674069
$63$	−1.65674	−0.208729
$64$	4.18958	0.523697
$65$	0	0
$66$	−4.40568	−0.542301
$67$	4.20514	0.513740	0.256870	−	0.966446i	$-0.417309\pi$
$67$	4.20514	0.513740	0.256870	+	0.966446i	$0.417309\pi$
$68$	10.2358	1.24127
$69$	−5.72676	−0.689420
$70$	0	0
$71$	−16.4655	−1.95409	−0.977045	−	0.213034i	$-0.931666\pi$
$71$	−16.4655	−1.95409	−0.977045	+	0.213034i	$0.931666\pi$
$72$	−2.75568	−0.324760
$73$	7.74882	0.906931	0.453465	−	0.891274i	$-0.350188\pi$
$73$	7.74882	0.906931	0.453465	+	0.891274i	$0.350188\pi$
$74$	−8.81379	−1.02458
$75$	0	0
$76$	−4.01695	−0.460776
$77$	−8.75310	−0.997508
$78$	0.445626	0.0504572
$79$	−7.48755	−0.842415	−0.421207	−	0.906964i	$-0.638394\pi$
$79$	−7.48755	−0.842415	−0.421207	+	0.906964i	$0.638394\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0.896633	0.0990166
$83$	−17.1007	−1.87704	−0.938522	−	0.345220i	$-0.887804\pi$
$83$	−17.1007	−1.87704	−0.938522	+	0.345220i	$0.887804\pi$
$84$	−2.16145	−0.235833
$85$	0	0
$86$	−0.774399	−0.0835056
$87$	2.72688	0.292352
$88$	−14.5592	−1.55201
$89$	−1.59310	−0.168868	−0.0844340	−	0.996429i	$-0.526908\pi$
$89$	−1.59310	−0.168868	−0.0844340	+	0.996429i	$0.526908\pi$
$90$	0	0
$91$	0.885359	0.0928108
$92$	−7.47137	−0.778944
$93$	−6.36496	−0.660016
$94$	0.833881	0.0860082
$95$	0	0
$96$	−5.77101	−0.589001
$97$	−5.08324	−0.516125	−0.258063	−	0.966128i	$-0.583084\pi$
$97$	−5.08324	−0.516125	−0.258063	+	0.966128i	$0.583084\pi$
$98$	−3.54835	−0.358438
$99$	5.28334	0.530996
$100$	0	0
$101$	−8.02270	−0.798288	−0.399144	−	0.916888i	$-0.630693\pi$
$101$	−8.02270	−0.798288	−0.399144	+	0.916888i	$0.630693\pi$
$102$	6.54236	0.647790
$103$	6.93676	0.683499	0.341750	−	0.939791i	$-0.388981\pi$
$103$	6.93676	0.683499	0.341750	+	0.939791i	$0.388981\pi$
$104$	1.47263	0.144404
$105$	0	0
$106$	6.14908	0.597252
$107$	−9.20543	−0.889923	−0.444961	−	0.895550i	$-0.646783\pi$
$107$	−9.20543	−0.889923	−0.444961	+	0.895550i	$0.646783\pi$
$108$	1.30464	0.125539
$109$	−18.8372	−1.80428	−0.902140	−	0.431443i	$-0.858005\pi$
$109$	−18.8372	−1.80428	−0.902140	+	0.431443i	$0.858005\pi$
$110$	0	0
$111$	10.5696	1.00322
$112$	−0.515872	−0.0487453
$113$	−16.7570	−1.57636	−0.788181	−	0.615443i	$-0.788977\pi$
$113$	−16.7570	−1.57636	−0.788181	+	0.615443i	$0.788977\pi$
$114$	−2.56749	−0.240468
$115$	0	0
$116$	3.55760	0.330315
$117$	−0.534400	−0.0494053
$118$	4.69498	0.432208
$119$	12.9982	1.19154
$120$	0	0
$121$	16.9137	1.53761
$122$	−1.56208	−0.141424
$123$	−1.07525	−0.0969523
$124$	−8.30400	−0.745722
$125$	0	0
$126$	−1.38152	−0.123076
$127$	2.78769	0.247368	0.123684	−	0.992322i	$-0.460529\pi$
$127$	2.78769	0.247368	0.123684	+	0.992322i	$0.460529\pi$
$128$	−8.04841	−0.711386
$129$	0.928668	0.0817647
$130$	0	0
$131$	−8.42981	−0.736516	−0.368258	−	0.929724i	$-0.620046\pi$
$131$	−8.42981	−0.736516	−0.368258	+	0.929724i	$0.620046\pi$
$132$	6.89287	0.599948
$133$	−5.10103	−0.442316
$134$	3.50659	0.302923
$135$	0	0
$136$	21.6202	1.85391
$137$	2.91888	0.249377	0.124688	−	0.992196i	$-0.460207\pi$
$137$	2.91888	0.249377	0.124688	+	0.992196i	$0.460207\pi$
$138$	−4.77543	−0.406512
$139$	−11.1117	−0.942480	−0.471240	−	0.882005i	$-0.656193\pi$
$139$	−11.1117	−0.942480	−0.471240	+	0.882005i	$0.656193\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	−13.7302	−1.15221
$143$	−2.82342	−0.236106
$144$	0.311378	0.0259482
$145$	0	0
$146$	6.46159	0.534765
$147$	4.25523	0.350965
$148$	13.7896	1.13349
$149$	3.09207	0.253312	0.126656	−	0.991947i	$-0.459576\pi$
$149$	3.09207	0.253312	0.126656	+	0.991947i	$0.459576\pi$
$150$	0	0
$151$	4.70115	0.382574	0.191287	−	0.981534i	$-0.438734\pi$
$151$	4.70115	0.382574	0.191287	+	0.981534i	$0.438734\pi$
$152$	−8.48465	−0.688196
$153$	−7.84567	−0.634285
$154$	−7.29904	−0.588173
$155$	0	0
$156$	−0.697201	−0.0558207
$157$	11.7108	0.934621	0.467311	−	0.884093i	$-0.345223\pi$
$157$	11.7108	0.934621	0.467311	+	0.884093i	$0.345223\pi$
$158$	−6.24372	−0.496724
$159$	−7.37405	−0.584800
$160$	0	0
$161$	−9.48772	−0.747737
$162$	0.833881	0.0655159
$163$	13.8108	1.08175	0.540873	−	0.841104i	$-0.318094\pi$
$163$	13.8108	1.08175	0.540873	+	0.841104i	$0.318094\pi$
$164$	−1.40282	−0.109542
$165$	0	0
$166$	−14.2599	−1.10679
$167$	−16.5240	−1.27866	−0.639331	−	0.768932i	$-0.720789\pi$
$167$	−16.5240	−1.27866	−0.639331	+	0.768932i	$0.720789\pi$
$168$	−4.56543	−0.352230
$169$	−12.7144	−0.978032
$170$	0	0
$171$	3.07897	0.235455
$172$	1.21158	0.0923822
$173$	−25.4724	−1.93663	−0.968317	−	0.249726i	$-0.919659\pi$
$173$	−25.4724	−1.93663	−0.968317	+	0.249726i	$0.919659\pi$
$174$	2.27389	0.172383
$175$	0	0
$176$	1.64512	0.124006
$177$	−5.63027	−0.423197
$178$	−1.32845	−0.0995718
$179$	5.15357	0.385196	0.192598	−	0.981278i	$-0.438309\pi$
$179$	5.15357	0.385196	0.192598	+	0.981278i	$0.438309\pi$
$180$	0	0
$181$	7.11727	0.529023	0.264511	−	0.964383i	$-0.414789\pi$
$181$	7.11727	0.529023	0.264511	+	0.964383i	$0.414789\pi$
$182$	0.738284	0.0547252
$183$	1.87327	0.138476
$184$	−15.7811	−1.16340
$185$	0	0
$186$	−5.30762	−0.389174
$187$	−41.4514	−3.03122
$188$	−1.30464	−0.0951509
$189$	1.65674	0.120510
$190$	0	0
$191$	19.9135	1.44089	0.720447	−	0.693510i	$-0.243937\pi$
$191$	19.9135	1.44089	0.720447	+	0.693510i	$0.243937\pi$
$192$	−4.18958	−0.302357
$193$	−25.3674	−1.82599	−0.912993	−	0.407975i	$-0.866235\pi$
$193$	−25.3674	−1.82599	−0.912993	+	0.407975i	$0.866235\pi$
$194$	−4.23882	−0.304329
$195$	0	0
$196$	5.55155	0.396540
$197$	0.852809	0.0607602	0.0303801	−	0.999538i	$-0.490328\pi$
$197$	0.852809	0.0607602	0.0303801	+	0.999538i	$0.490328\pi$
$198$	4.40568	0.313098
$199$	0.508406	0.0360399	0.0180200	−	0.999838i	$-0.494264\pi$
$199$	0.508406	0.0360399	0.0180200	+	0.999838i	$0.494264\pi$
$200$	0	0
$201$	−4.20514	−0.296608
$202$	−6.68998	−0.470705
$203$	4.51771	0.317081
$204$	−10.2358	−0.716649
$205$	0	0
$206$	5.78443	0.403020
$207$	5.72676	0.398037
$208$	−0.166401	−0.0115378
$209$	16.2672	1.12523
$210$	0	0
$211$	−9.10854	−0.627058	−0.313529	−	0.949579i	$-0.601511\pi$
$211$	−9.10854	−0.627058	−0.313529	+	0.949579i	$0.601511\pi$
$212$	−9.62051	−0.660739
$213$	16.4655	1.12819
$214$	−7.67623	−0.524736
$215$	0	0
$216$	2.75568	0.187500
$217$	−10.5451	−0.715845
$218$	−15.7080	−1.06388
$219$	−7.74882	−0.523617
$220$	0	0
$221$	4.19272	0.282033
$222$	8.81379	0.591543
$223$	−16.0845	−1.07710	−0.538548	−	0.842595i	$-0.681027\pi$
$223$	−16.0845	−1.07710	−0.538548	+	0.842595i	$0.681027\pi$
$224$	−9.56103	−0.638823
$225$	0	0
$226$	−13.9733	−0.929491
$227$	10.6764	0.708618	0.354309	−	0.935128i	$-0.384716\pi$
$227$	10.6764	0.708618	0.354309	+	0.935128i	$0.384716\pi$
$228$	4.01695	0.266029
$229$	−3.70165	−0.244612	−0.122306	−	0.992492i	$-0.539029\pi$
$229$	−3.70165	−0.244612	−0.122306	+	0.992492i	$0.539029\pi$
$230$	0	0
$231$	8.75310	0.575912
$232$	7.51439	0.493344
$233$	−18.3829	−1.20430	−0.602152	−	0.798382i	$-0.705690\pi$
$233$	−18.3829	−1.20430	−0.602152	+	0.798382i	$0.705690\pi$
$234$	−0.445626	−0.0291315
$235$	0	0
$236$	−7.34549	−0.478151
$237$	7.48755	0.486368
$238$	10.8390	0.702585
$239$	16.8431	1.08949	0.544745	−	0.838602i	$-0.316627\pi$
$239$	16.8431	1.08949	0.544745	+	0.838602i	$0.316627\pi$
$240$	0	0
$241$	−20.9368	−1.34866	−0.674330	−	0.738430i	$-0.735567\pi$
$241$	−20.9368	−1.34866	−0.674330	+	0.738430i	$0.735567\pi$
$242$	14.1040	0.906640
$243$	−1.00000	−0.0641500
$244$	2.44395	0.156458
$245$	0	0
$246$	−0.896633	−0.0571673
$247$	−1.64540	−0.104694
$248$	−17.5398	−1.11378
$249$	17.1007	1.08371
$250$	0	0
$251$	−4.62601	−0.291991	−0.145996	−	0.989285i	$-0.546639\pi$
$251$	−4.62601	−0.291991	−0.145996	+	0.989285i	$0.546639\pi$
$252$	2.16145	0.136158
$253$	30.2564	1.90220
$254$	2.32460	0.145859
$255$	0	0
$256$	−15.0906	−0.943161
$257$	12.1390	0.757210	0.378605	−	0.925558i	$-0.376404\pi$
$257$	12.1390	0.757210	0.378605	+	0.925558i	$0.376404\pi$
$258$	0.774399	0.0482120
$259$	17.5110	1.08808
$260$	0	0
$261$	−2.72688	−0.168789
$262$	−7.02945	−0.434281
$263$	−16.2707	−1.00330	−0.501649	−	0.865071i	$-0.667273\pi$
$263$	−16.2707	−1.00330	−0.501649	+	0.865071i	$0.667273\pi$
$264$	14.5592	0.896056
$265$	0	0
$266$	−4.25365	−0.260808
$267$	1.59310	0.0974960
$268$	−5.48621	−0.335123
$269$	−12.4654	−0.760026	−0.380013	−	0.924981i	$-0.624080\pi$
$269$	−12.4654	−0.760026	−0.380013	+	0.924981i	$0.624080\pi$
$270$	0	0
$271$	−15.0332	−0.913200	−0.456600	−	0.889672i	$-0.650933\pi$
$271$	−15.0332	−0.913200	−0.456600	+	0.889672i	$0.650933\pi$
$272$	−2.44297	−0.148127
$273$	−0.885359	−0.0535843
$274$	2.43400	0.147043
$275$	0	0
$276$	7.47137	0.449724
$277$	−2.53021	−0.152026	−0.0760128	−	0.997107i	$-0.524219\pi$
$277$	−2.53021	−0.152026	−0.0760128	+	0.997107i	$0.524219\pi$
$278$	−9.26581	−0.555727
$279$	6.36496	0.381060
$280$	0	0
$281$	19.0472	1.13626	0.568131	−	0.822938i	$-0.307667\pi$
$281$	19.0472	1.13626	0.568131	+	0.822938i	$0.307667\pi$
$282$	−0.833881	−0.0496569
$283$	−6.83464	−0.406277	−0.203139	−	0.979150i	$-0.565114\pi$
$283$	−6.83464	−0.406277	−0.203139	+	0.979150i	$0.565114\pi$
$284$	21.4815	1.27469
$285$	0	0
$286$	−2.35439	−0.139218
$287$	−1.78141	−0.105153
$288$	5.77101	0.340060
$289$	44.5546	2.62086
$290$	0	0
$291$	5.08324	0.297985
$292$	−10.1094	−0.591610
$293$	32.0909	1.87477	0.937386	−	0.348292i	$-0.113238\pi$
$293$	32.0909	1.87477	0.937386	+	0.348292i	$0.113238\pi$
$294$	3.54835	0.206944
$295$	0	0
$296$	29.1264	1.69294
$297$	−5.28334	−0.306571
$298$	2.57842	0.149364
$299$	−3.06038	−0.176986
$300$	0	0
$301$	1.53856	0.0886810
$302$	3.92020	0.225582
$303$	8.02270	0.460892
$304$	0.958725	0.0549866
$305$	0	0
$306$	−6.54236	−0.374002
$307$	16.0132	0.913923	0.456962	−	0.889486i	$-0.348938\pi$
$307$	16.0132	0.913923	0.456962	+	0.889486i	$0.348938\pi$
$308$	11.4197	0.650696
$309$	−6.93676	−0.394619
$310$	0	0
$311$	−15.3760	−0.871895	−0.435947	−	0.899972i	$-0.643587\pi$
$311$	−15.3760	−0.871895	−0.435947	+	0.899972i	$0.643587\pi$
$312$	−1.47263	−0.0833714
$313$	−34.1592	−1.93079	−0.965395	−	0.260792i	$-0.916016\pi$
$313$	−34.1592	−1.93079	−0.965395	+	0.260792i	$0.916016\pi$
$314$	9.76539	0.551093
$315$	0	0
$316$	9.76857	0.549525
$317$	14.6078	0.820454	0.410227	−	0.911984i	$-0.365450\pi$
$317$	14.6078	0.820454	0.410227	+	0.911984i	$0.365450\pi$
$318$	−6.14908	−0.344823
$319$	−14.4070	−0.806638
$320$	0	0
$321$	9.20543	0.513797
$322$	−7.91163	−0.440898
$323$	−24.1566	−1.34411
$324$	−1.30464	−0.0724802
$325$	0	0
$326$	11.5166	0.637844
$327$	18.8372	1.04170
$328$	−2.96305	−0.163607
$329$	−1.65674	−0.0913388
$330$	0	0
$331$	15.4721	0.850425	0.425212	−	0.905094i	$-0.360199\pi$
$331$	15.4721	0.850425	0.425212	+	0.905094i	$0.360199\pi$
$332$	22.3103	1.22444
$333$	−10.5696	−0.579211
$334$	−13.7790	−0.753954
$335$	0	0
$336$	0.515872	0.0281431
$337$	−5.77644	−0.314663	−0.157331	−	0.987546i	$-0.550289\pi$
$337$	−5.77644	−0.314663	−0.157331	+	0.987546i	$0.550289\pi$
$338$	−10.6023	−0.576690
$339$	16.7570	0.910113
$340$	0	0
$341$	33.6283	1.82107
$342$	2.56749	0.138834
$343$	18.6469	1.00684
$344$	2.55911	0.137978
$345$	0	0
$346$	−21.2410	−1.14192
$347$	17.5622	0.942786	0.471393	−	0.881923i	$-0.343751\pi$
$347$	17.5622	0.942786	0.471393	+	0.881923i	$0.343751\pi$
$348$	−3.55760	−0.190707
$349$	13.3989	0.717227	0.358614	−	0.933486i	$-0.383250\pi$
$349$	13.3989	0.717227	0.358614	+	0.933486i	$0.383250\pi$
$350$	0	0
$351$	0.534400	0.0285241
$352$	30.4902	1.62513
$353$	30.0046	1.59698	0.798492	−	0.602005i	$-0.205631\pi$
$353$	30.0046	1.59698	0.798492	+	0.602005i	$0.205631\pi$
$354$	−4.69498	−0.249535
$355$	0	0
$356$	2.07842	0.110156
$357$	−12.9982	−0.687938
$358$	4.29746	0.227128
$359$	−20.5380	−1.08395	−0.541977	−	0.840393i	$-0.682324\pi$
$359$	−20.5380	−1.08395	−0.541977	+	0.840393i	$0.682324\pi$
$360$	0	0
$361$	−9.51995	−0.501050
$362$	5.93496	0.311934
$363$	−16.9137	−0.887739
$364$	−1.15508	−0.0605425
$365$	0	0
$366$	1.56208	0.0816514
$367$	17.1959	0.897616	0.448808	−	0.893628i	$-0.351849\pi$
$367$	17.1959	0.897616	0.448808	+	0.893628i	$0.351849\pi$
$368$	1.78319	0.0929551
$369$	1.07525	0.0559755
$370$	0	0
$371$	−12.2169	−0.634267
$372$	8.30400	0.430543
$373$	22.3010	1.15470	0.577351	−	0.816496i	$-0.304086\pi$
$373$	22.3010	1.15470	0.577351	+	0.816496i	$0.304086\pi$
$374$	−34.5655	−1.78734
$375$	0	0
$376$	−2.75568	−0.142113
$377$	1.45724	0.0750518
$378$	1.38152	0.0710577
$379$	−19.3940	−0.996205	−0.498102	−	0.867118i	$-0.665970\pi$
$379$	−19.3940	−0.996205	−0.498102	+	0.867118i	$0.665970\pi$
$380$	0	0
$381$	−2.78769	−0.142818
$382$	16.6055	0.849612
$383$	6.06948	0.310136	0.155068	−	0.987904i	$-0.450440\pi$
$383$	6.06948	0.310136	0.155068	+	0.987904i	$0.450440\pi$
$384$	8.04841	0.410719
$385$	0	0
$386$	−21.1534	−1.07668
$387$	−0.928668	−0.0472069
$388$	6.63182	0.336679
$389$	32.2912	1.63723	0.818614	−	0.574344i	$-0.194743\pi$
$389$	32.2912	1.63723	0.818614	+	0.574344i	$0.194743\pi$
$390$	0	0
$391$	−44.9303	−2.27222
$392$	11.7260	0.592255
$393$	8.42981	0.425228
$394$	0.711141	0.0358268
$395$	0	0
$396$	−6.89287	−0.346380
$397$	−9.39648	−0.471596	−0.235798	−	0.971802i	$-0.575770\pi$
$397$	−9.39648	−0.471596	−0.235798	+	0.971802i	$0.575770\pi$
$398$	0.423950	0.0212507
$399$	5.10103	0.255371
$400$	0	0
$401$	18.6711	0.932391	0.466195	−	0.884682i	$-0.345624\pi$
$401$	18.6711	0.932391	0.466195	+	0.884682i	$0.345624\pi$
$402$	−3.50659	−0.174893
$403$	−3.40143	−0.169438
$404$	10.4668	0.520741
$405$	0	0
$406$	3.76723	0.186965
$407$	−55.8428	−2.76803
$408$	−21.6202	−1.07036
$409$	−38.2064	−1.88918	−0.944592	−	0.328248i	$-0.893542\pi$
$409$	−38.2064	−1.88918	−0.944592	+	0.328248i	$0.893542\pi$
$410$	0	0
$411$	−2.91888	−0.143978
$412$	−9.04999	−0.445861
$413$	−9.32787	−0.458994
$414$	4.77543	0.234700
$415$	0	0
$416$	−3.08402	−0.151207
$417$	11.1117	0.544141
$418$	13.5649	0.663483
$419$	−0.589408	−0.0287944	−0.0143972	−	0.999896i	$-0.504583\pi$
$419$	−0.589408	−0.0287944	−0.0143972	+	0.999896i	$0.504583\pi$
$420$	0	0
$421$	31.1920	1.52021	0.760103	−	0.649802i	$-0.225148\pi$
$421$	31.1920	1.52021	0.760103	+	0.649802i	$0.225148\pi$
$422$	−7.59544	−0.369740
$423$	1.00000	0.0486217
$424$	−20.3205	−0.986852
$425$	0	0
$426$	13.7302	0.665232
$427$	3.10351	0.150189
$428$	12.0098	0.580516
$429$	2.82342	0.136316
$430$	0	0
$431$	3.21665	0.154940	0.0774702	−	0.996995i	$-0.475316\pi$
$431$	3.21665	0.154940	0.0774702	+	0.996995i	$0.475316\pi$
$432$	−0.311378	−0.0149812
$433$	5.62749	0.270440	0.135220	−	0.990816i	$-0.456826\pi$
$433$	5.62749	0.270440	0.135220	+	0.990816i	$0.456826\pi$
$434$	−8.79332	−0.422093
$435$	0	0
$436$	24.5759	1.17697
$437$	17.6325	0.843477
$438$	−6.46159	−0.308747
$439$	−14.5012	−0.692102	−0.346051	−	0.938216i	$-0.612478\pi$
$439$	−14.5012	−0.692102	−0.346051	+	0.938216i	$0.612478\pi$
$440$	0	0
$441$	−4.25523	−0.202630
$442$	3.49623	0.166299
$443$	9.63503	0.457774	0.228887	−	0.973453i	$-0.426491\pi$
$443$	9.63503	0.457774	0.228887	+	0.973453i	$0.426491\pi$
$444$	−13.7896	−0.654423
$445$	0	0
$446$	−13.4125	−0.635102
$447$	−3.09207	−0.146250
$448$	−6.94102	−0.327932
$449$	34.1109	1.60979	0.804897	−	0.593414i	$-0.202220\pi$
$449$	34.1109	1.60979	0.804897	+	0.593414i	$0.202220\pi$
$450$	0	0
$451$	5.68093	0.267505
$452$	21.8618	1.02829
$453$	−4.70115	−0.220879
$454$	8.90285	0.417831
$455$	0	0
$456$	8.48465	0.397330
$457$	−21.3092	−0.996801	−0.498401	−	0.866947i	$-0.666079\pi$
$457$	−21.3092	−0.996801	−0.498401	+	0.866947i	$0.666079\pi$
$458$	−3.08674	−0.144234
$459$	7.84567	0.366205
$460$	0	0
$461$	−39.3250	−1.83155	−0.915775	−	0.401692i	$-0.868422\pi$
$461$	−39.3250	−1.83155	−0.915775	+	0.401692i	$0.868422\pi$
$462$	7.29904	0.339582
$463$	−35.1576	−1.63391	−0.816956	−	0.576700i	$-0.804340\pi$
$463$	−35.1576	−1.63391	−0.816956	+	0.576700i	$0.804340\pi$
$464$	−0.849091	−0.0394180
$465$	0	0
$466$	−15.3291	−0.710109
$467$	−17.9177	−0.829133	−0.414566	−	0.910019i	$-0.636067\pi$
$467$	−17.9177	−0.829133	−0.414566	+	0.910019i	$0.636067\pi$
$468$	0.697201	0.0322281
$469$	−6.96680	−0.321697
$470$	0	0
$471$	−11.7108	−0.539604
$472$	−15.5152	−0.714146
$473$	−4.90647	−0.225600
$474$	6.24372	0.286784
$475$	0	0
$476$	−16.9580	−0.777269
$477$	7.37405	0.337635
$478$	14.0451	0.642409
$479$	−18.5240	−0.846385	−0.423193	−	0.906040i	$-0.639091\pi$
$479$	−18.5240	−0.846385	−0.423193	+	0.906040i	$0.639091\pi$
$480$	0	0
$481$	5.64839	0.257544
$482$	−17.4588	−0.795227
$483$	9.48772	0.431706
$484$	−22.0663	−1.00302
$485$	0	0
$486$	−0.833881	−0.0378256
$487$	26.3605	1.19451	0.597253	−	0.802053i	$-0.296259\pi$
$487$	26.3605	1.19451	0.597253	+	0.802053i	$0.296259\pi$
$488$	5.16213	0.233678
$489$	−13.8108	−0.624546
$490$	0	0
$491$	−1.07208	−0.0483822	−0.0241911	−	0.999707i	$-0.507701\pi$
$491$	−1.07208	−0.0483822	−0.0241911	+	0.999707i	$0.507701\pi$
$492$	1.40282	0.0632441
$493$	21.3942	0.963545
$494$	−1.37207	−0.0617322
$495$	0	0
$496$	1.98191	0.0889905
$497$	27.2789	1.22363
$498$	14.2599	0.639003
$499$	−3.23167	−0.144670	−0.0723348	−	0.997380i	$-0.523045\pi$
$499$	−3.23167	−0.144670	−0.0723348	+	0.997380i	$0.523045\pi$
$500$	0	0
$501$	16.5240	0.738236
$502$	−3.85754	−0.172170
$503$	−16.3623	−0.729559	−0.364779	−	0.931094i	$-0.618856\pi$
$503$	−16.3623	−0.729559	−0.364779	+	0.931094i	$0.618856\pi$
$504$	4.56543	0.203360
$505$	0	0
$506$	25.2302	1.12162
$507$	12.7144	0.564667
$508$	−3.63694	−0.161363
$509$	−4.75432	−0.210731	−0.105366	−	0.994434i	$-0.533601\pi$
$509$	−4.75432	−0.210731	−0.105366	+	0.994434i	$0.533601\pi$
$510$	0	0
$511$	−12.8377	−0.567908
$512$	3.51309	0.155258
$513$	−3.07897	−0.135940
$514$	10.1225	0.446483
$515$	0	0
$516$	−1.21158	−0.0533369
$517$	5.28334	0.232361
$518$	14.6021	0.641580
$519$	25.4724	1.11812
$520$	0	0
$521$	6.68226	0.292755	0.146378	−	0.989229i	$-0.453239\pi$
$521$	6.68226	0.292755	0.146378	+	0.989229i	$0.453239\pi$
$522$	−2.27389	−0.0995254
$523$	−5.93088	−0.259339	−0.129670	−	0.991557i	$-0.541392\pi$
$523$	−5.93088	−0.259339	−0.129670	+	0.991557i	$0.541392\pi$
$524$	10.9979	0.480445
$525$	0	0
$526$	−13.5679	−0.591587
$527$	−49.9374	−2.17531
$528$	−1.64512	−0.0715946
$529$	9.79574	0.425902
$530$	0	0
$531$	5.63027	0.244333
$532$	6.65503	0.288532
$533$	−0.574615	−0.0248893
$534$	1.32845	0.0574878
$535$	0	0
$536$	−11.5880	−0.500526
$537$	−5.15357	−0.222393
$538$	−10.3946	−0.448144
$539$	−22.4818	−0.968361
$540$	0	0
$541$	3.82011	0.164239	0.0821196	−	0.996622i	$-0.473831\pi$
$541$	3.82011	0.164239	0.0821196	+	0.996622i	$0.473831\pi$
$542$	−12.5359	−0.538462
$543$	−7.11727	−0.305431
$544$	−45.2774	−1.94125
$545$	0	0
$546$	−0.738284	−0.0315956
$547$	0.569076	0.0243319	0.0121660	−	0.999926i	$-0.496127\pi$
$547$	0.569076	0.0243319	0.0121660	+	0.999926i	$0.496127\pi$
$548$	−3.80810	−0.162674
$549$	−1.87327	−0.0799492
$550$	0	0
$551$	−8.39597	−0.357680
$552$	15.7811	0.671688
$553$	12.4049	0.527509
$554$	−2.10989	−0.0896408
$555$	0	0
$556$	14.4968	0.614800
$557$	−29.3735	−1.24460	−0.622298	−	0.782781i	$-0.713801\pi$
$557$	−29.3735	−1.24460	−0.622298	+	0.782781i	$0.713801\pi$
$558$	5.30762	0.224690
$559$	0.496280	0.0209904
$560$	0	0
$561$	41.4514	1.75008
$562$	15.8831	0.669989
$563$	−17.8943	−0.754155	−0.377078	−	0.926182i	$-0.623071\pi$
$563$	−17.8943	−0.754155	−0.377078	+	0.926182i	$0.623071\pi$
$564$	1.30464	0.0549354
$565$	0	0
$566$	−5.69928	−0.239559
$567$	−1.65674	−0.0695763
$568$	45.3735	1.90383
$569$	45.4441	1.90512	0.952559	−	0.304355i	$-0.0984409\pi$
$569$	45.4441	1.90512	0.952559	+	0.304355i	$0.0984409\pi$
$570$	0	0
$571$	36.1094	1.51113	0.755565	−	0.655074i	$-0.227363\pi$
$571$	36.1094	1.51113	0.755565	+	0.655074i	$0.227363\pi$
$572$	3.68355	0.154017
$573$	−19.9135	−0.831900
$574$	−1.48548	−0.0620029
$575$	0	0
$576$	4.18958	0.174566
$577$	−39.8548	−1.65918	−0.829589	−	0.558374i	$-0.811425\pi$
$577$	−39.8548	−1.65918	−0.829589	+	0.558374i	$0.811425\pi$
$578$	37.1532	1.54537
$579$	25.3674	1.05423
$580$	0	0
$581$	28.3313	1.17538
$582$	4.23882	0.175705
$583$	38.9596	1.61354
$584$	−21.3533	−0.883604
$585$	0	0
$586$	26.7600	1.10545
$587$	−23.1249	−0.954465	−0.477233	−	0.878777i	$-0.658360\pi$
$587$	−23.1249	−0.954465	−0.477233	+	0.878777i	$0.658360\pi$
$588$	−5.55155	−0.228942
$589$	19.5975	0.807502
$590$	0	0
$591$	−0.852809	−0.0350799
$592$	−3.29115	−0.135265
$593$	12.5263	0.514395	0.257197	−	0.966359i	$-0.417201\pi$
$593$	12.5263	0.514395	0.257197	+	0.966359i	$0.417201\pi$
$594$	−4.40568	−0.180767
$595$	0	0
$596$	−4.03405	−0.165241
$597$	−0.508406	−0.0208077
$598$	−2.55199	−0.104359
$599$	5.20577	0.212702	0.106351	−	0.994329i	$-0.466083\pi$
$599$	5.20577	0.212702	0.106351	+	0.994329i	$0.466083\pi$
$600$	0	0
$601$	−44.1658	−1.80156	−0.900779	−	0.434277i	$-0.857004\pi$
$601$	−44.1658	−1.80156	−0.900779	+	0.434277i	$0.857004\pi$
$602$	1.28297	0.0522901
$603$	4.20514	0.171247
$604$	−6.13332	−0.249561
$605$	0	0
$606$	6.68998	0.271762
$607$	27.2664	1.10671	0.553354	−	0.832946i	$-0.313348\pi$
$607$	27.2664	1.10671	0.553354	+	0.832946i	$0.313348\pi$
$608$	17.7688	0.720618
$609$	−4.51771	−0.183067
$610$	0	0
$611$	−0.534400	−0.0216195
$612$	10.2358	0.413758
$613$	2.69854	0.108993	0.0544966	−	0.998514i	$-0.482645\pi$
$613$	2.69854	0.108993	0.0544966	+	0.998514i	$0.482645\pi$
$614$	13.3531	0.538888
$615$	0	0
$616$	24.1207	0.971852
$617$	24.4235	0.983254	0.491627	−	0.870806i	$-0.336402\pi$
$617$	24.4235	0.983254	0.491627	+	0.870806i	$0.336402\pi$
$618$	−5.78443	−0.232684
$619$	19.8493	0.797811	0.398906	−	0.916992i	$-0.369390\pi$
$619$	19.8493	0.797811	0.398906	+	0.916992i	$0.369390\pi$
$620$	0	0
$621$	−5.72676	−0.229807
$622$	−12.8218	−0.514106
$623$	2.63934	0.105743
$624$	0.166401	0.00666135
$625$	0	0
$626$	−28.4847	−1.13848
$627$	−16.2672	−0.649651
$628$	−15.2784	−0.609674
$629$	82.9256	3.30646
$630$	0	0
$631$	−36.9133	−1.46949	−0.734747	−	0.678342i	$-0.762699\pi$
$631$	−36.9133	−1.46949	−0.734747	+	0.678342i	$0.762699\pi$
$632$	20.6333	0.820747
$633$	9.10854	0.362032
$634$	12.1811	0.483775
$635$	0	0
$636$	9.62051	0.381478
$637$	2.27399	0.0900989
$638$	−12.0137	−0.475628
$639$	−16.4655	−0.651363
$640$	0	0
$641$	15.9871	0.631451	0.315725	−	0.948851i	$-0.397752\pi$
$641$	15.9871	0.631451	0.315725	+	0.948851i	$0.397752\pi$
$642$	7.67623	0.302957
$643$	−22.7865	−0.898613	−0.449307	−	0.893378i	$-0.648329\pi$
$643$	−22.7865	−0.898613	−0.449307	+	0.893378i	$0.648329\pi$
$644$	12.3781	0.487765
$645$	0	0
$646$	−20.1437	−0.792544
$647$	10.3411	0.406552	0.203276	−	0.979121i	$-0.434841\pi$
$647$	10.3411	0.406552	0.203276	+	0.979121i	$0.434841\pi$
$648$	−2.75568	−0.108253
$649$	29.7467	1.16766
$650$	0	0
$651$	10.5451	0.413293
$652$	−18.0182	−0.705646
$653$	−2.43816	−0.0954127	−0.0477063	−	0.998861i	$-0.515191\pi$
$653$	−2.43816	−0.0954127	−0.0477063	+	0.998861i	$0.515191\pi$
$654$	15.7080	0.614232
$655$	0	0
$656$	0.334811	0.0130722
$657$	7.74882	0.302310
$658$	−1.38152	−0.0538572
$659$	5.01124	0.195210	0.0976050	−	0.995225i	$-0.468882\pi$
$659$	5.01124	0.195210	0.0976050	+	0.995225i	$0.468882\pi$
$660$	0	0
$661$	−26.5054	−1.03094	−0.515470	−	0.856908i	$-0.672383\pi$
$661$	−26.5054	−1.03094	−0.515470	+	0.856908i	$0.672383\pi$
$662$	12.9019	0.501447
$663$	−4.19272	−0.162832
$664$	47.1240	1.82877
$665$	0	0
$666$	−8.81379	−0.341527
$667$	−15.6162	−0.604660
$668$	21.5579	0.834099
$669$	16.0845	0.621861
$670$	0	0
$671$	−9.89712	−0.382074
$672$	9.56103	0.368825
$673$	20.6329	0.795339	0.397670	−	0.917529i	$-0.369819\pi$
$673$	20.6329	0.795339	0.397670	+	0.917529i	$0.369819\pi$
$674$	−4.81687	−0.185539
$675$	0	0
$676$	16.5878	0.637991
$677$	18.4732	0.709981	0.354991	−	0.934870i	$-0.384484\pi$
$677$	18.4732	0.709981	0.354991	+	0.934870i	$0.384484\pi$
$678$	13.9733	0.536642
$679$	8.42159	0.323191
$680$	0	0
$681$	−10.6764	−0.409121
$682$	28.0420	1.07378
$683$	42.5576	1.62842	0.814211	−	0.580568i	$-0.197170\pi$
$683$	42.5576	1.62842	0.814211	+	0.580568i	$0.197170\pi$
$684$	−4.01695	−0.153592
$685$	0	0
$686$	15.5493	0.593676
$687$	3.70165	0.141227
$688$	−0.289167	−0.0110244
$689$	−3.94069	−0.150128
$690$	0	0
$691$	−41.2336	−1.56860	−0.784300	−	0.620382i	$-0.786978\pi$
$691$	−41.2336	−1.56860	−0.784300	+	0.620382i	$0.786978\pi$
$692$	33.2324	1.26331
$693$	−8.75310	−0.332503
$694$	14.6447	0.555907
$695$	0	0
$696$	−7.51439	−0.284832
$697$	−8.43609	−0.319540
$698$	11.1731	0.422908
$699$	18.3829	0.695305
$700$	0	0
$701$	9.18501	0.346913	0.173457	−	0.984842i	$-0.444506\pi$
$701$	9.18501	0.346913	0.173457	+	0.984842i	$0.444506\pi$
$702$	0.445626	0.0168191
$703$	−32.5435	−1.22740
$704$	22.1350	0.834243
$705$	0	0
$706$	25.0203	0.941650
$707$	13.2915	0.499878
$708$	7.34549	0.276061
$709$	−35.1053	−1.31841	−0.659203	−	0.751965i	$-0.729106\pi$
$709$	−35.1053	−1.31841	−0.659203	+	0.751965i	$0.729106\pi$
$710$	0	0
$711$	−7.48755	−0.280805
$712$	4.39006	0.164525
$713$	36.4506	1.36509
$714$	−10.8390	−0.405638
$715$	0	0
$716$	−6.72357	−0.251272
$717$	−16.8431	−0.629017
$718$	−17.1263	−0.639146
$719$	16.2130	0.604643	0.302321	−	0.953206i	$-0.402238\pi$
$719$	16.2130	0.604643	0.302321	+	0.953206i	$0.402238\pi$
$720$	0	0
$721$	−11.4924	−0.427998
$722$	−7.93851	−0.295441
$723$	20.9368	0.778649
$724$	−9.28550	−0.345093
$725$	0	0
$726$	−14.1040	−0.523449
$727$	3.88686	0.144156	0.0720779	−	0.997399i	$-0.477037\pi$
$727$	3.88686	0.144156	0.0720779	+	0.997399i	$0.477037\pi$
$728$	−2.43976	−0.0904236
$729$	1.00000	0.0370370
$730$	0	0
$731$	7.28603	0.269484
$732$	−2.44395	−0.0903309
$733$	29.6387	1.09473	0.547365	−	0.836894i	$-0.315631\pi$
$733$	29.6387	1.09473	0.547365	+	0.836894i	$0.315631\pi$
$734$	14.3393	0.529273
$735$	0	0
$736$	33.0492	1.21821
$737$	22.2172	0.818381
$738$	0.896633	0.0330055
$739$	−30.5549	−1.12398	−0.561991	−	0.827144i	$-0.689964\pi$
$739$	−30.5549	−1.12398	−0.561991	+	0.827144i	$0.689964\pi$
$740$	0	0
$741$	1.64540	0.0604453
$742$	−10.1874	−0.373991
$743$	12.4756	0.457686	0.228843	−	0.973463i	$-0.426506\pi$
$743$	12.4756	0.457686	0.228843	+	0.973463i	$0.426506\pi$
$744$	17.5398	0.643040
$745$	0	0
$746$	18.5964	0.680862
$747$	−17.1007	−0.625681
$748$	54.0792	1.97733
$749$	15.2510	0.557258
$750$	0	0
$751$	−30.9199	−1.12828	−0.564141	−	0.825679i	$-0.690793\pi$
$751$	−30.9199	−1.12828	−0.564141	+	0.825679i	$0.690793\pi$
$752$	0.311378	0.0113548
$753$	4.62601	0.168581
$754$	1.21517	0.0442537
$755$	0	0
$756$	−2.16145	−0.0786111
$757$	−32.9810	−1.19871	−0.599357	−	0.800482i	$-0.704577\pi$
$757$	−32.9810	−1.19871	−0.599357	+	0.800482i	$0.704577\pi$
$758$	−16.1723	−0.587405
$759$	−30.2564	−1.09824
$760$	0	0
$761$	−46.8022	−1.69658	−0.848290	−	0.529533i	$-0.822367\pi$
$761$	−46.8022	−1.69658	−0.848290	+	0.529533i	$0.822367\pi$
$762$	−2.32460	−0.0842115
$763$	31.2083	1.12982
$764$	−25.9801	−0.939925
$765$	0	0
$766$	5.06122	0.182869
$767$	−3.00882	−0.108642
$768$	15.0906	0.544534
$769$	−25.0182	−0.902181	−0.451091	−	0.892478i	$-0.648965\pi$
$769$	−25.0182	−0.902181	−0.451091	+	0.892478i	$0.648965\pi$
$770$	0	0
$771$	−12.1390	−0.437175
$772$	33.0954	1.19113
$773$	−23.4683	−0.844095	−0.422047	−	0.906574i	$-0.638688\pi$
$773$	−23.4683	−0.844095	−0.422047	+	0.906574i	$0.638688\pi$
$774$	−0.774399	−0.0278352
$775$	0	0
$776$	14.0078	0.502850
$777$	−17.5110	−0.628205
$778$	26.9270	0.965379
$779$	3.31067	0.118617
$780$	0	0
$781$	−86.9926	−3.11284
$782$	−37.4665	−1.33980
$783$	2.72688	0.0974506
$784$	−1.32499	−0.0473210
$785$	0	0
$786$	7.02945	0.250732
$787$	−10.3777	−0.369926	−0.184963	−	0.982745i	$-0.559217\pi$
$787$	−10.3777	−0.369926	−0.184963	+	0.982745i	$0.559217\pi$
$788$	−1.11261	−0.0396352
$789$	16.2707	0.579254
$790$	0	0
$791$	27.7618	0.987098
$792$	−14.5592	−0.517338
$793$	1.00107	0.0355492
$794$	−7.83554	−0.278073
$795$	0	0
$796$	−0.663288	−0.0235096
$797$	−39.5305	−1.40024	−0.700122	−	0.714024i	$-0.746871\pi$
$797$	−39.5305	−1.40024	−0.700122	+	0.714024i	$0.746871\pi$
$798$	4.25365	0.150578
$799$	−7.84567	−0.277560
$800$	0	0
$801$	−1.59310	−0.0562893
$802$	15.5695	0.549778
$803$	40.9397	1.44473
$804$	5.48621	0.193484
$805$	0	0
$806$	−2.83639	−0.0999076
$807$	12.4654	0.438801
$808$	22.1080	0.777756
$809$	−27.3835	−0.962753	−0.481377	−	0.876514i	$-0.659863\pi$
$809$	−27.3835	−0.962753	−0.481377	+	0.876514i	$0.659863\pi$
$810$	0	0
$811$	28.5383	1.00212	0.501058	−	0.865414i	$-0.332944\pi$
$811$	28.5383	1.00212	0.501058	+	0.865414i	$0.332944\pi$
$812$	−5.89400	−0.206839
$813$	15.0332	0.527236
$814$	−46.5663	−1.63215
$815$	0	0
$816$	2.44297	0.0855212
$817$	−2.85934	−0.100036
$818$	−31.8596	−1.11394
$819$	0.885359	0.0309369
$820$	0	0
$821$	48.2822	1.68506	0.842531	−	0.538649i	$-0.181065\pi$
$821$	48.2822	1.68506	0.842531	+	0.538649i	$0.181065\pi$
$822$	−2.43400	−0.0848955
$823$	−39.6296	−1.38140	−0.690700	−	0.723141i	$-0.742698\pi$
$823$	−39.6296	−1.38140	−0.690700	+	0.723141i	$0.742698\pi$
$824$	−19.1155	−0.665919
$825$	0	0
$826$	−7.77833	−0.270643
$827$	1.37220	0.0477161	0.0238581	−	0.999715i	$-0.492405\pi$
$827$	1.37220	0.0477161	0.0238581	+	0.999715i	$0.492405\pi$
$828$	−7.47137	−0.259648
$829$	0.718240	0.0249455	0.0124728	−	0.999922i	$-0.496030\pi$
$829$	0.718240	0.0249455	0.0124728	+	0.999922i	$0.496030\pi$
$830$	0	0
$831$	2.53021	0.0877721
$832$	−2.23891	−0.0776202
$833$	33.3851	1.15673
$834$	9.26581	0.320849
$835$	0	0
$836$	−21.2229	−0.734011
$837$	−6.36496	−0.220005
$838$	−0.491496	−0.0169784
$839$	38.5944	1.33243	0.666213	−	0.745761i	$-0.267914\pi$
$839$	38.5944	1.33243	0.666213	+	0.745761i	$0.267914\pi$
$840$	0	0
$841$	−21.5641	−0.743591
$842$	26.0104	0.896379
$843$	−19.0472	−0.656021
$844$	11.8834	0.409043
$845$	0	0
$846$	0.833881	0.0286694
$847$	−28.0215	−0.962831
$848$	2.29612	0.0788491
$849$	6.83464	0.234564
$850$	0	0
$851$	−60.5295	−2.07493
$852$	−21.4815	−0.735945
$853$	27.2305	0.932354	0.466177	−	0.884691i	$-0.345631\pi$
$853$	27.2305	0.932354	0.466177	+	0.884691i	$0.345631\pi$
$854$	2.58796	0.0885581
$855$	0	0
$856$	25.3672	0.867033
$857$	15.1510	0.517549	0.258775	−	0.965938i	$-0.416681\pi$
$857$	15.1510	0.517549	0.258775	+	0.965938i	$0.416681\pi$
$858$	2.35439	0.0803776
$859$	−31.9698	−1.09080	−0.545398	−	0.838178i	$-0.683621\pi$
$859$	−31.9698	−1.09080	−0.545398	+	0.838178i	$0.683621\pi$
$860$	0	0
$861$	1.78141	0.0607103
$862$	2.68230	0.0913595
$863$	5.51462	0.187720	0.0938600	−	0.995585i	$-0.470079\pi$
$863$	5.51462	0.187720	0.0938600	+	0.995585i	$0.470079\pi$
$864$	−5.77101	−0.196334
$865$	0	0
$866$	4.69266	0.159463
$867$	−44.5546	−1.51315
$868$	13.7575	0.466961
$869$	−39.5593	−1.34196
$870$	0	0
$871$	−2.24722	−0.0761443
$872$	51.9094	1.75787
$873$	−5.08324	−0.172042
$874$	14.7034	0.497350
$875$	0	0
$876$	10.1094	0.341566
$877$	22.5508	0.761485	0.380743	−	0.924681i	$-0.375668\pi$
$877$	22.5508	0.761485	0.380743	+	0.924681i	$0.375668\pi$
$878$	−12.0922	−0.408093
$879$	−32.0909	−1.08240
$880$	0	0
$881$	−33.6648	−1.13419	−0.567097	−	0.823651i	$-0.691934\pi$
$881$	−33.6648	−1.13419	−0.567097	+	0.823651i	$0.691934\pi$
$882$	−3.54835	−0.119479
$883$	45.0424	1.51580	0.757898	−	0.652373i	$-0.226226\pi$
$883$	45.0424	1.51580	0.757898	+	0.652373i	$0.226226\pi$
$884$	−5.47001	−0.183976
$885$	0	0
$886$	8.03447	0.269923
$887$	−10.3467	−0.347408	−0.173704	−	0.984798i	$-0.555574\pi$
$887$	−10.3467	−0.347408	−0.173704	+	0.984798i	$0.555574\pi$
$888$	−29.1264	−0.977419
$889$	−4.61847	−0.154898
$890$	0	0
$891$	5.28334	0.176999
$892$	20.9845	0.702612
$893$	3.07897	0.103034
$894$	−2.57842	−0.0862352
$895$	0	0
$896$	13.3341	0.445460
$897$	3.06038	0.102183
$898$	28.4444	0.949204
$899$	−17.3565	−0.578871
$900$	0	0
$901$	−57.8544	−1.92741
$902$	4.73722	0.157732
$903$	−1.53856	−0.0512000
$904$	46.1768	1.53582
$905$	0	0
$906$	−3.92020	−0.130240
$907$	−37.3067	−1.23875	−0.619375	−	0.785096i	$-0.712614\pi$
$907$	−37.3067	−1.23875	−0.619375	+	0.785096i	$0.712614\pi$
$908$	−13.9289	−0.462247
$909$	−8.02270	−0.266096
$910$	0	0
$911$	3.38318	0.112090	0.0560448	−	0.998428i	$-0.482151\pi$
$911$	3.38318	0.112090	0.0560448	+	0.998428i	$0.482151\pi$
$912$	−0.958725	−0.0317465
$913$	−90.3488	−2.99011
$914$	−17.7693	−0.587757
$915$	0	0
$916$	4.82934	0.159566
$917$	13.9660	0.461197
$918$	6.54236	0.215930
$919$	−31.2966	−1.03238	−0.516190	−	0.856474i	$-0.672650\pi$
$919$	−31.2966	−1.03238	−0.516190	+	0.856474i	$0.672650\pi$
$920$	0	0
$921$	−16.0132	−0.527654
$922$	−32.7924	−1.07996
$923$	8.79913	0.289627
$924$	−11.4197	−0.375679
$925$	0	0
$926$	−29.3172	−0.963425
$927$	6.93676	0.227833
$928$	−15.7368	−0.516587
$929$	51.3320	1.68415	0.842073	−	0.539363i	$-0.181335\pi$
$929$	51.3320	1.68415	0.842073	+	0.539363i	$0.181335\pi$
$930$	0	0
$931$	−13.1017	−0.429391
$932$	23.9831	0.785593
$933$	15.3760	0.503389
$934$	−14.9412	−0.488892
$935$	0	0
$936$	1.47263	0.0481345
$937$	14.2961	0.467033	0.233516	−	0.972353i	$-0.424977\pi$
$937$	14.2961	0.467033	0.233516	+	0.972353i	$0.424977\pi$
$938$	−5.80948	−0.189686
$939$	34.1592	1.11474
$940$	0	0
$941$	−2.87655	−0.0937730	−0.0468865	−	0.998900i	$-0.514930\pi$
$941$	−2.87655	−0.0937730	−0.0468865	+	0.998900i	$0.514930\pi$
$942$	−9.76539	−0.318174
$943$	6.15772	0.200523
$944$	1.75315	0.0570600
$945$	0	0
$946$	−4.09141	−0.133023
$947$	−15.2869	−0.496756	−0.248378	−	0.968663i	$-0.579897\pi$
$947$	−15.2869	−0.496756	−0.248378	+	0.968663i	$0.579897\pi$
$948$	−9.76857	−0.317268
$949$	−4.14097	−0.134421
$950$	0	0
$951$	−14.6078	−0.473689
$952$	−35.8189	−1.16090
$953$	5.23474	0.169570	0.0847849	−	0.996399i	$-0.472980\pi$
$953$	5.23474	0.169570	0.0847849	+	0.996399i	$0.472980\pi$
$954$	6.14908	0.199084
$955$	0	0
$956$	−21.9742	−0.710697
$957$	14.4070	0.465713
$958$	−15.4468	−0.499065
$959$	−4.83581	−0.156157
$960$	0	0
$961$	9.51276	0.306863
$962$	4.71008	0.151859
$963$	−9.20543	−0.296641
$964$	27.3151	0.879760
$965$	0	0
$966$	7.91163	0.254552
$967$	32.6978	1.05149	0.525745	−	0.850642i	$-0.323787\pi$
$967$	32.6978	1.05149	0.525745	+	0.850642i	$0.323787\pi$
$968$	−46.6087	−1.49806
$969$	24.1566	0.776021
$970$	0	0
$971$	−26.9098	−0.863577	−0.431788	−	0.901975i	$-0.642117\pi$
$971$	−26.9098	−0.863577	−0.431788	+	0.901975i	$0.642117\pi$
$972$	1.30464	0.0418464
$973$	18.4091	0.590169
$974$	21.9815	0.704332
$975$	0	0
$976$	−0.583296	−0.0186708
$977$	6.23178	0.199372	0.0996861	−	0.995019i	$-0.468216\pi$
$977$	6.23178	0.199372	0.0996861	+	0.995019i	$0.468216\pi$
$978$	−11.5166	−0.368259
$979$	−8.41688	−0.269005
$980$	0	0
$981$	−18.8372	−0.601427
$982$	−0.893986	−0.0285282
$983$	4.04712	0.129083	0.0645415	−	0.997915i	$-0.479442\pi$
$983$	4.04712	0.129083	0.0645415	+	0.997915i	$0.479442\pi$
$984$	2.96305	0.0944587
$985$	0	0
$986$	17.8402	0.568148
$987$	1.65674	0.0527345
$988$	2.14666	0.0682943
$989$	−5.31826	−0.169111
$990$	0	0
$991$	24.1662	0.767664	0.383832	−	0.923403i	$-0.374604\pi$
$991$	24.1662	0.767664	0.383832	+	0.923403i	$0.374604\pi$
$992$	36.7323	1.16625
$993$	−15.4721	−0.490993
$994$	22.7473	0.721502
$995$	0	0
$996$	−22.3103	−0.706928
$997$	16.4213	0.520067	0.260033	−	0.965600i	$-0.416266\pi$
$997$	16.4213	0.520067	0.260033	+	0.965600i	$0.416266\pi$
$998$	−2.69483	−0.0853034
$999$	10.5696	0.334407

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.x.1.6	✓	7
5.4	even	2		3525.2.a.bc.1.2	yes	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.2.a.x.1.6	✓	7	1.1	even	1	trivial
3525.2.a.bc.1.2	yes	7	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:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q+0.833881 q^{2} -1.00000 q^{3} -1.30464 q^{4} -0.833881 q^{6} -1.65674 q^{7} -2.75568 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.833881 q^{2} -1.00000 q^{3} -1.30464 q^{4} -0.833881 q^{6} -1.65674 q^{7} -2.75568 q^{8} +1.00000 q^{9} +5.28334 q^{11} +1.30464 q^{12} -0.534400 q^{13} -1.38152 q^{14} +0.311378 q^{16} -7.84567 q^{17} +0.833881 q^{18} +3.07897 q^{19} +1.65674 q^{21} +4.40568 q^{22} +5.72676 q^{23} +2.75568 q^{24} -0.445626 q^{26} -1.00000 q^{27} +2.16145 q^{28} -2.72688 q^{29} +6.36496 q^{31} +5.77101 q^{32} -5.28334 q^{33} -6.54236 q^{34} -1.30464 q^{36} -10.5696 q^{37} +2.56749 q^{38} +0.534400 q^{39} +1.07525 q^{41} +1.38152 q^{42} -0.928668 q^{43} -6.89287 q^{44} +4.77543 q^{46} +1.00000 q^{47} -0.311378 q^{48} -4.25523 q^{49} +7.84567 q^{51} +0.697201 q^{52} +7.37405 q^{53} -0.833881 q^{54} +4.56543 q^{56} -3.07897 q^{57} -2.27389 q^{58} +5.63027 q^{59} -1.87327 q^{61} +5.30762 q^{62} -1.65674 q^{63} +4.18958 q^{64} -4.40568 q^{66} +4.20514 q^{67} +10.2358 q^{68} -5.72676 q^{69} -16.4655 q^{71} -2.75568 q^{72} +7.74882 q^{73} -8.81379 q^{74} -4.01695 q^{76} -8.75310 q^{77} +0.445626 q^{78} -7.48755 q^{79} +1.00000 q^{81} +0.896633 q^{82} -17.1007 q^{83} -2.16145 q^{84} -0.774399 q^{86} +2.72688 q^{87} -14.5592 q^{88} -1.59310 q^{89} +0.885359 q^{91} -7.47137 q^{92} -6.36496 q^{93} +0.833881 q^{94} -5.77101 q^{96} -5.08324 q^{97} -3.54835 q^{98} +5.28334 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 3 q^{2} - 7 q^{3} + 5 q^{4} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 3 * q^2 - 7 * q^3 + 5 * q^4 + 3 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9	\( 7 q - 3 q^{2} - 7 q^{3} + 5 q^{4} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9} + 4 q^{11} - 5 q^{12} - 5 q^{13} + 5 q^{14} + 9 q^{16} - 10 q^{17} - 3 q^{18} + q^{19} + 5 q^{21} - 10 q^{22} - 10 q^{23} + 6 q^{24} + 12 q^{26} - 7 q^{27} - 2 q^{28} + 9 q^{29} + 3 q^{31} - 4 q^{33} - 20 q^{34} + 5 q^{36} - 9 q^{37} + 2 q^{38} + 5 q^{39} + 20 q^{41} - 5 q^{42} - 16 q^{43} - 5 q^{44} - q^{46} + 7 q^{47} - 9 q^{48} - 10 q^{49} + 10 q^{51} - 21 q^{52} + 3 q^{54} + 21 q^{56} - q^{57} - 19 q^{58} + 18 q^{59} + 2 q^{62} - 5 q^{63} - 30 q^{64} + 10 q^{66} - 8 q^{67} - 20 q^{68} + 10 q^{69} + 14 q^{71} - 6 q^{72} - 4 q^{73} - 17 q^{74} + 12 q^{76} - 2 q^{77} - 12 q^{78} - 21 q^{79} + 7 q^{81} + 7 q^{82} - 22 q^{83} + 2 q^{84} + 35 q^{86} - 9 q^{87} - 14 q^{88} + 2 q^{89} - 2 q^{91} - 5 q^{92} - 3 q^{93} - 3 q^{94} - 12 q^{97} - 30 q^{98} + 4 q^{99}+O(q^{100}) \) 7 * q - 3 * q^2 - 7 * q^3 + 5 * q^4 + 3 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9 + 4 * q^11 - 5 * q^12 - 5 * q^13 + 5 * q^14 + 9 * q^16 - 10 * q^17 - 3 * q^18 + q^19 + 5 * q^21 - 10 * q^22 - 10 * q^23 + 6 * q^24 + 12 * q^26 - 7 * q^27 - 2 * q^28 + 9 * q^29 + 3 * q^31 - 4 * q^33 - 20 * q^34 + 5 * q^36 - 9 * q^37 + 2 * q^38 + 5 * q^39 + 20 * q^41 - 5 * q^42 - 16 * q^43 - 5 * q^44 - q^46 + 7 * q^47 - 9 * q^48 - 10 * q^49 + 10 * q^51 - 21 * q^52 + 3 * q^54 + 21 * q^56 - q^57 - 19 * q^58 + 18 * q^59 + 2 * q^62 - 5 * q^63 - 30 * q^64 + 10 * q^66 - 8 * q^67 - 20 * q^68 + 10 * q^69 + 14 * q^71 - 6 * q^72 - 4 * q^73 - 17 * q^74 + 12 * q^76 - 2 * q^77 - 12 * q^78 - 21 * q^79 + 7 * q^81 + 7 * q^82 - 22 * q^83 + 2 * q^84 + 35 * q^86 - 9 * q^87 - 14 * q^88 + 2 * q^89 - 2 * q^91 - 5 * q^92 - 3 * q^93 - 3 * q^94 - 12 * q^97 - 30 * q^98 + 4 * q^99

Introduction

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