LMFDB - Embedded newform 525.2.d.e.274.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(274,525)]

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, 1, 0]))

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

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

chi := DirichletCharacter("525.274");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.d (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.1
Root			$-1.61803i$ of defining polynomial
Character	$\chi$	$=$	525.274
Dual form			525.2.d.e.274.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61803i q^{2} +1.00000i q^{3} -4.85410 q^{4} +2.61803 q^{6} +1.00000i q^{7} +7.47214i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.61803i q^{2} +1.00000i q^{3} -4.85410 q^{4} +2.61803 q^{6} +1.00000i q^{7} +7.47214i q^{8} -1.00000 q^{9} -5.47214 q^{11} -4.85410i q^{12} +0.763932i q^{13} +2.61803 q^{14} +9.85410 q^{16} +7.70820i q^{17} +2.61803i q^{18} +3.23607 q^{19} -1.00000 q^{21} +14.3262i q^{22} +5.00000i q^{23} -7.47214 q^{24} +2.00000 q^{26} -1.00000i q^{27} -4.85410i q^{28} -4.70820 q^{29} +4.47214 q^{31} -10.8541i q^{32} -5.47214i q^{33} +20.1803 q^{34} +4.85410 q^{36} -5.47214i q^{37} -8.47214i q^{38} -0.763932 q^{39} -8.00000 q^{41} +2.61803i q^{42} +8.23607i q^{43} +26.5623 q^{44} +13.0902 q^{46} -7.23607i q^{47} +9.85410i q^{48} -1.00000 q^{49} -7.70820 q^{51} -3.70820i q^{52} +0.472136i q^{53} -2.61803 q^{54} -7.47214 q^{56} +3.23607i q^{57} +12.3262i q^{58} +0.763932 q^{59} -15.4164 q^{61} -11.7082i q^{62} -1.00000i q^{63} -8.70820 q^{64} -14.3262 q^{66} +2.70820i q^{67} -37.4164i q^{68} -5.00000 q^{69} -0.527864 q^{71} -7.47214i q^{72} +1.23607i q^{73} -14.3262 q^{74} -15.7082 q^{76} -5.47214i q^{77} +2.00000i q^{78} -1.76393 q^{79} +1.00000 q^{81} +20.9443i q^{82} +12.4721i q^{83} +4.85410 q^{84} +21.5623 q^{86} -4.70820i q^{87} -40.8885i q^{88} +5.70820 q^{89} -0.763932 q^{91} -24.2705i q^{92} +4.47214i q^{93} -18.9443 q^{94} +10.8541 q^{96} -12.4721i q^{97} +2.61803i q^{98} +5.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{4} + 6 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q - 6 * q^4 + 6 * q^6 - 4 * q^9	$ 4 q - 6 q^{4} + 6 q^{6} - 4 q^{9} - 4 q^{11} + 6 q^{14} + 26 q^{16} + 4 q^{19} - 4 q^{21} - 12 q^{24} + 8 q^{26} + 8 q^{29} + 36 q^{34} + 6 q^{36} - 12 q^{39} - 32 q^{41} + 66 q^{44} + 30 q^{46} - 4 q^{49} - 4 q^{51} - 6 q^{54} - 12 q^{56} + 12 q^{59} - 8 q^{61} - 8 q^{64} - 26 q^{66} - 20 q^{69} - 20 q^{71} - 26 q^{74} - 36 q^{76} - 16 q^{79} + 4 q^{81} + 6 q^{84} + 46 q^{86} - 4 q^{89} - 12 q^{91} - 40 q^{94} + 30 q^{96} + 4 q^{99}+O(q^{100}) $ 4 * q - 6 * q^4 + 6 * q^6 - 4 * q^9 - 4 * q^11 + 6 * q^14 + 26 * q^16 + 4 * q^19 - 4 * q^21 - 12 * q^24 + 8 * q^26 + 8 * q^29 + 36 * q^34 + 6 * q^36 - 12 * q^39 - 32 * q^41 + 66 * q^44 + 30 * q^46 - 4 * q^49 - 4 * q^51 - 6 * q^54 - 12 * q^56 + 12 * q^59 - 8 * q^61 - 8 * q^64 - 26 * q^66 - 20 * q^69 - 20 * q^71 - 26 * q^74 - 36 * q^76 - 16 * q^79 + 4 * q^81 + 6 * q^84 + 46 * q^86 - 4 * q^89 - 12 * q^91 - 40 * q^94 + 30 * q^96 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	− 2.61803i	− 1.85123i	−0.378467	−	0.925615i	$-0.623549\pi$
$2$	− 2.61803i	− 1.85123i	0.378467	−	0.925615i	$-0.376451\pi$
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	−4.85410	−2.42705
$5$	0	0
$5$	0	0
$6$	2.61803	1.06881
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	7.47214i	2.64180i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−5.47214	−1.64991	−0.824956	−	0.565198i	$-0.808800\pi$
$11$	−5.47214	−1.64991	−0.824956	+	0.565198i	$0.808800\pi$
$12$	− 4.85410i	− 1.40126i
$13$	0.763932i	0.211877i	0.994373	+	0.105938i	$0.0337846\pi$
$13$	0.763932i	0.211877i	−0.994373	+	0.105938i	$0.966215\pi$
$14$	2.61803	0.699699
$15$	0	0
$16$	9.85410	2.46353
$17$	7.70820i	1.86951i	0.355288	+	0.934757i	$0.384383\pi$
$17$	7.70820i	1.86951i	−0.355288	+	0.934757i	$0.615617\pi$
$18$	2.61803i	0.617077i
$19$	3.23607	0.742405	0.371202	−	0.928552i	$-0.378946\pi$
$19$	3.23607	0.742405	0.371202	+	0.928552i	$0.378946\pi$
$20$	0	0
$21$	−1.00000	−0.218218
$22$	14.3262i	3.05436i
$23$	5.00000i	1.04257i	0.853382	+	0.521286i	$0.174548\pi$
$23$	5.00000i	1.04257i	−0.853382	+	0.521286i	$0.825452\pi$
$24$	−7.47214	−1.52524
$25$	0	0
$26$	2.00000	0.392232
$27$	− 1.00000i	− 0.192450i
$28$	− 4.85410i	− 0.917339i
$29$	−4.70820	−0.874292	−0.437146	−	0.899391i	$-0.644011\pi$
$29$	−4.70820	−0.874292	−0.437146	+	0.899391i	$0.644011\pi$
$30$	0	0
$31$	4.47214	0.803219	0.401610	−	0.915811i	$-0.368451\pi$
$31$	4.47214	0.803219	0.401610	+	0.915811i	$0.368451\pi$
$32$	− 10.8541i	− 1.91875i
$33$	− 5.47214i	− 0.952577i
$34$	20.1803	3.46090
$35$	0	0
$36$	4.85410	0.809017
$37$	− 5.47214i	− 0.899614i	−0.893126	−	0.449807i	$-0.851493\pi$
$37$	− 5.47214i	− 0.899614i	0.893126	−	0.449807i	$-0.148507\pi$
$38$	− 8.47214i	− 1.37436i
$39$	−0.763932	−0.122327
$40$	0	0
$41$	−8.00000	−1.24939	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	−8.00000	−1.24939	−0.624695	+	0.780869i	$0.714777\pi$
$42$	2.61803i	0.403971i
$43$	8.23607i	1.25599i	0.778218	+	0.627994i	$0.216124\pi$
$43$	8.23607i	1.25599i	−0.778218	+	0.627994i	$0.783876\pi$
$44$	26.5623	4.00442
$45$	0	0
$46$	13.0902	1.93004
$47$	− 7.23607i	− 1.05549i	−0.849403	−	0.527744i	$-0.823038\pi$
$47$	− 7.23607i	− 1.05549i	0.849403	−	0.527744i	$-0.176962\pi$
$48$	9.85410i	1.42232i
$49$	−1.00000	−0.142857
$50$	0	0
$51$	−7.70820	−1.07936
$52$	− 3.70820i	− 0.514235i
$53$	0.472136i	0.0648529i	0.999474	+	0.0324264i	$0.0103235\pi$
$53$	0.472136i	0.0648529i	−0.999474	+	0.0324264i	$0.989677\pi$
$54$	−2.61803	−0.356269
$55$	0	0
$56$	−7.47214	−0.998506
$57$	3.23607i	0.428628i
$58$	12.3262i	1.61851i
$59$	0.763932	0.0994555	0.0497277	−	0.998763i	$-0.484165\pi$
$59$	0.763932	0.0994555	0.0497277	+	0.998763i	$0.484165\pi$
$60$	0	0
$61$	−15.4164	−1.97387	−0.986934	−	0.161123i	$-0.948489\pi$
$61$	−15.4164	−1.97387	−0.986934	+	0.161123i	$0.948489\pi$
$62$	− 11.7082i	− 1.48694i
$63$	− 1.00000i	− 0.125988i
$64$	−8.70820	−1.08853
$65$	0	0
$66$	−14.3262	−1.76344
$67$	2.70820i	0.330860i	0.986222	+	0.165430i	$0.0529012\pi$
$67$	2.70820i	0.330860i	−0.986222	+	0.165430i	$0.947099\pi$
$68$	− 37.4164i	− 4.53741i
$69$	−5.00000	−0.601929
$70$	0	0
$71$	−0.527864	−0.0626459	−0.0313230	−	0.999509i	$-0.509972\pi$
$71$	−0.527864	−0.0626459	−0.0313230	+	0.999509i	$0.509972\pi$
$72$	− 7.47214i	− 0.880600i
$73$	1.23607i	0.144671i	0.997380	+	0.0723354i	$0.0230452\pi$
$73$	1.23607i	0.144671i	−0.997380	+	0.0723354i	$0.976955\pi$
$74$	−14.3262	−1.66539
$75$	0	0
$76$	−15.7082	−1.80185
$77$	− 5.47214i	− 0.623608i
$78$	2.00000i	0.226455i
$79$	−1.76393	−0.198458	−0.0992289	−	0.995065i	$-0.531638\pi$
$79$	−1.76393	−0.198458	−0.0992289	+	0.995065i	$0.531638\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	20.9443i	2.31291i
$83$	12.4721i	1.36899i	0.729015	+	0.684497i	$0.239978\pi$
$83$	12.4721i	1.36899i	−0.729015	+	0.684497i	$0.760022\pi$
$84$	4.85410	0.529626
$85$	0	0
$86$	21.5623	2.32512
$87$	− 4.70820i	− 0.504772i
$88$	− 40.8885i	− 4.35873i
$89$	5.70820	0.605068	0.302534	−	0.953139i	$-0.402167\pi$
$89$	5.70820	0.605068	0.302534	+	0.953139i	$0.402167\pi$
$90$	0	0
$91$	−0.763932	−0.0800818
$92$	− 24.2705i	− 2.53038i
$93$	4.47214i	0.463739i
$94$	−18.9443	−1.95395
$95$	0	0
$96$	10.8541	1.10779
$97$	− 12.4721i	− 1.26635i	−0.774007	−	0.633177i	$-0.781751\pi$
$97$	− 12.4721i	− 1.26635i	0.774007	−	0.633177i	$-0.218249\pi$
$98$	2.61803i	0.264461i
$99$	5.47214	0.549970
$100$	0	0
$101$	−4.29180	−0.427050	−0.213525	−	0.976938i	$-0.568494\pi$
$101$	−4.29180	−0.427050	−0.213525	+	0.976938i	$0.568494\pi$
$102$	20.1803i	1.99815i
$103$	9.70820i	0.956578i	0.878203	+	0.478289i	$0.158743\pi$
$103$	9.70820i	0.956578i	−0.878203	+	0.478289i	$0.841257\pi$
$104$	−5.70820	−0.559735
$105$	0	0
$106$	1.23607	0.120058
$107$	4.94427i	0.477981i	0.971022	+	0.238990i	$0.0768164\pi$
$107$	4.94427i	0.477981i	−0.971022	+	0.238990i	$0.923184\pi$
$108$	4.85410i	0.467086i
$109$	6.41641	0.614580	0.307290	−	0.951616i	$-0.400578\pi$
$109$	6.41641	0.614580	0.307290	+	0.951616i	$0.400578\pi$
$110$	0	0
$111$	5.47214	0.519392
$112$	9.85410i	0.931125i
$113$	− 16.2361i	− 1.52736i	−0.645594	−	0.763680i	$-0.723390\pi$
$113$	− 16.2361i	− 1.52736i	0.645594	−	0.763680i	$-0.276610\pi$
$114$	8.47214	0.793488
$115$	0	0
$116$	22.8541	2.12195
$117$	− 0.763932i	− 0.0706255i
$118$	− 2.00000i	− 0.184115i
$119$	−7.70820	−0.706610
$120$	0	0
$121$	18.9443	1.72221
$122$	40.3607i	3.65408i
$123$	− 8.00000i	− 0.721336i
$124$	−21.7082	−1.94945
$125$	0	0
$126$	−2.61803	−0.233233
$127$	12.2361i	1.08578i	0.839805	+	0.542888i	$0.182669\pi$
$127$	12.2361i	1.08578i	−0.839805	+	0.542888i	$0.817331\pi$
$128$	1.09017i	0.0963583i
$129$	−8.23607	−0.725145
$130$	0	0
$131$	−4.29180	−0.374976	−0.187488	−	0.982267i	$-0.560035\pi$
$131$	−4.29180	−0.374976	−0.187488	+	0.982267i	$0.560035\pi$
$132$	26.5623i	2.31195i
$133$	3.23607i	0.280603i
$134$	7.09017	0.612497
$135$	0	0
$136$	−57.5967	−4.93888
$137$	0.472136i	0.0403373i	0.999797	+	0.0201686i	$0.00642032\pi$
$137$	0.472136i	0.0403373i	−0.999797	+	0.0201686i	$0.993580\pi$
$138$	13.0902i	1.11431i
$139$	−3.70820	−0.314526	−0.157263	−	0.987557i	$-0.550267\pi$
$139$	−3.70820	−0.314526	−0.157263	+	0.987557i	$0.550267\pi$
$140$	0	0
$141$	7.23607	0.609387
$142$	1.38197i	0.115972i
$143$	− 4.18034i	− 0.349578i
$144$	−9.85410	−0.821175
$145$	0	0
$146$	3.23607	0.267819
$147$	− 1.00000i	− 0.0824786i
$148$	26.5623i	2.18341i
$149$	−8.23607	−0.674725	−0.337362	−	0.941375i	$-0.609535\pi$
$149$	−8.23607	−0.674725	−0.337362	+	0.941375i	$0.609535\pi$
$150$	0	0
$151$	1.29180	0.105125	0.0525624	−	0.998618i	$-0.483261\pi$
$151$	1.29180	0.105125	0.0525624	+	0.998618i	$0.483261\pi$
$152$	24.1803i	1.96128i
$153$	− 7.70820i	− 0.623171i
$154$	−14.3262	−1.15444
$155$	0	0
$156$	3.70820	0.296894
$157$	− 16.9443i	− 1.35230i	−0.736764	−	0.676150i	$-0.763647\pi$
$157$	− 16.9443i	− 1.35230i	0.736764	−	0.676150i	$-0.236353\pi$
$158$	4.61803i	0.367391i
$159$	−0.472136	−0.0374428
$160$	0	0
$161$	−5.00000	−0.394055
$162$	− 2.61803i	− 0.205692i
$163$	18.4721i	1.44685i	0.690403	+	0.723425i	$0.257433\pi$
$163$	18.4721i	1.44685i	−0.690403	+	0.723425i	$0.742567\pi$
$164$	38.8328	3.03233
$165$	0	0
$166$	32.6525	2.53432
$167$	6.29180i	0.486874i	0.969917	+	0.243437i	$0.0782749\pi$
$167$	6.29180i	0.486874i	−0.969917	+	0.243437i	$0.921725\pi$
$168$	− 7.47214i	− 0.576488i
$169$	12.4164	0.955108
$170$	0	0
$171$	−3.23607	−0.247468
$172$	− 39.9787i	− 3.04835i
$173$	− 3.81966i	− 0.290403i	−0.989402	−	0.145202i	$-0.953617\pi$
$173$	− 3.81966i	− 0.290403i	0.989402	−	0.145202i	$-0.0463831\pi$
$174$	−12.3262	−0.934450
$175$	0	0
$176$	−53.9230	−4.06460
$177$	0.763932i	0.0574206i
$178$	− 14.9443i	− 1.12012i
$179$	−4.94427	−0.369552	−0.184776	−	0.982781i	$-0.559156\pi$
$179$	−4.94427	−0.369552	−0.184776	+	0.982781i	$0.559156\pi$
$180$	0	0
$181$	4.65248	0.345816	0.172908	−	0.984938i	$-0.444684\pi$
$181$	4.65248	0.345816	0.172908	+	0.984938i	$0.444684\pi$
$182$	2.00000i	0.148250i
$183$	− 15.4164i	− 1.13961i
$184$	−37.3607	−2.75427
$185$	0	0
$186$	11.7082	0.858487
$187$	− 42.1803i	− 3.08453i
$188$	35.1246i	2.56173i
$189$	1.00000	0.0727393
$190$	0	0
$191$	−11.4164	−0.826062	−0.413031	−	0.910717i	$-0.635530\pi$
$191$	−11.4164	−0.826062	−0.413031	+	0.910717i	$0.635530\pi$
$192$	− 8.70820i	− 0.628460i
$193$	0.416408i	0.0299737i	0.999888	+	0.0149868i	$0.00477064\pi$
$193$	0.416408i	0.0299737i	−0.999888	+	0.0149868i	$0.995229\pi$
$194$	−32.6525	−2.34431
$195$	0	0
$196$	4.85410	0.346722
$197$	5.76393i	0.410663i	0.978692	+	0.205332i	$0.0658273\pi$
$197$	5.76393i	0.410663i	−0.978692	+	0.205332i	$0.934173\pi$
$198$	− 14.3262i	− 1.01812i
$199$	16.0000	1.13421	0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000	1.13421	0.567105	+	0.823646i	$0.308063\pi$
$200$	0	0
$201$	−2.70820	−0.191022
$202$	11.2361i	0.790567i
$203$	− 4.70820i	− 0.330451i
$204$	37.4164	2.61967
$205$	0	0
$206$	25.4164	1.77085
$207$	− 5.00000i	− 0.347524i
$208$	7.52786i	0.521963i
$209$	−17.7082	−1.22490
$210$	0	0
$211$	12.9443	0.891120	0.445560	−	0.895252i	$-0.353005\pi$
$211$	12.9443	0.891120	0.445560	+	0.895252i	$0.353005\pi$
$212$	− 2.29180i	− 0.157401i
$213$	− 0.527864i	− 0.0361686i
$214$	12.9443	0.884852
$215$	0	0
$216$	7.47214	0.508414
$217$	4.47214i	0.303588i
$218$	− 16.7984i	− 1.13773i
$219$	−1.23607	−0.0835257
$220$	0	0
$221$	−5.88854	−0.396106
$222$	− 14.3262i	− 0.961514i
$223$	− 1.23607i	− 0.0827732i	−0.999143	−	0.0413866i	$-0.986822\pi$
$223$	− 1.23607i	− 0.0827732i	0.999143	−	0.0413866i	$-0.0131775\pi$
$224$	10.8541	0.725220
$225$	0	0
$226$	−42.5066	−2.82750
$227$	4.76393i	0.316193i	0.987424	+	0.158097i	$0.0505358\pi$
$227$	4.76393i	0.316193i	−0.987424	+	0.158097i	$0.949464\pi$
$228$	− 15.7082i	− 1.04030i
$229$	−22.3607	−1.47764	−0.738818	−	0.673905i	$-0.764616\pi$
$229$	−22.3607	−1.47764	−0.738818	+	0.673905i	$0.764616\pi$
$230$	0	0
$231$	5.47214	0.360040
$232$	− 35.1803i	− 2.30970i
$233$	7.29180i	0.477701i	0.971056	+	0.238851i	$0.0767707\pi$
$233$	7.29180i	0.477701i	−0.971056	+	0.238851i	$0.923229\pi$
$234$	−2.00000	−0.130744
$235$	0	0
$236$	−3.70820	−0.241384
$237$	− 1.76393i	− 0.114580i
$238$	20.1803i	1.30810i
$239$	28.3607	1.83450	0.917250	−	0.398312i	$-0.130404\pi$
$239$	28.3607	1.83450	0.917250	+	0.398312i	$0.130404\pi$
$240$	0	0
$241$	19.2361	1.23910	0.619552	−	0.784956i	$-0.287314\pi$
$241$	19.2361	1.23910	0.619552	+	0.784956i	$0.287314\pi$
$242$	− 49.5967i	− 3.18820i
$243$	1.00000i	0.0641500i
$244$	74.8328	4.79068
$245$	0	0
$246$	−20.9443	−1.33536
$247$	2.47214i	0.157298i
$248$	33.4164i	2.12194i
$249$	−12.4721	−0.790390
$250$	0	0
$251$	2.76393	0.174458	0.0872289	−	0.996188i	$-0.472199\pi$
$251$	2.76393	0.174458	0.0872289	+	0.996188i	$0.472199\pi$
$252$	4.85410i	0.305780i
$253$	− 27.3607i	− 1.72015i
$254$	32.0344	2.01002
$255$	0	0
$256$	−14.5623	−0.910144
$257$	8.47214i	0.528477i	0.964457	+	0.264239i	$0.0851207\pi$
$257$	8.47214i	0.528477i	−0.964457	+	0.264239i	$0.914879\pi$
$258$	21.5623i	1.34241i
$259$	5.47214	0.340022
$260$	0	0
$261$	4.70820	0.291431
$262$	11.2361i	0.694167i
$263$	2.05573i	0.126762i	0.997989	+	0.0633808i	$0.0201883\pi$
$263$	2.05573i	0.126762i	−0.997989	+	0.0633808i	$0.979812\pi$
$264$	40.8885	2.51652
$265$	0	0
$266$	8.47214	0.519460
$267$	5.70820i	0.349336i
$268$	− 13.1459i	− 0.803014i
$269$	28.4721	1.73598	0.867988	−	0.496584i	$-0.165413\pi$
$269$	28.4721	1.73598	0.867988	+	0.496584i	$0.165413\pi$
$270$	0	0
$271$	23.2361	1.41149	0.705745	−	0.708466i	$-0.250612\pi$
$271$	23.2361	1.41149	0.705745	+	0.708466i	$0.250612\pi$
$272$	75.9574i	4.60560i
$273$	− 0.763932i	− 0.0462353i
$274$	1.23607	0.0746736
$275$	0	0
$276$	24.2705	1.46091
$277$	15.8885i	0.954650i	0.878727	+	0.477325i	$0.158394\pi$
$277$	15.8885i	0.954650i	−0.878727	+	0.477325i	$0.841606\pi$
$278$	9.70820i	0.582259i
$279$	−4.47214	−0.267740
$280$	0	0
$281$	13.6525	0.814438	0.407219	−	0.913330i	$-0.366499\pi$
$281$	13.6525	0.814438	0.407219	+	0.913330i	$0.366499\pi$
$282$	− 18.9443i	− 1.12811i
$283$	− 13.4164i	− 0.797523i	−0.917055	−	0.398761i	$-0.869440\pi$
$283$	− 13.4164i	− 0.797523i	0.917055	−	0.398761i	$-0.130560\pi$
$284$	2.56231	0.152045
$285$	0	0
$286$	−10.9443	−0.647148
$287$	− 8.00000i	− 0.472225i
$288$	10.8541i	0.639584i
$289$	−42.4164	−2.49508
$290$	0	0
$291$	12.4721	0.731130
$292$	− 6.00000i	− 0.351123i
$293$	− 26.6525i	− 1.55705i	−0.627611	−	0.778527i	$-0.715967\pi$
$293$	− 26.6525i	− 1.55705i	0.627611	−	0.778527i	$-0.284033\pi$
$294$	−2.61803	−0.152687
$295$	0	0
$296$	40.8885	2.37660
$297$	5.47214i	0.317526i
$298$	21.5623i	1.24907i
$299$	−3.81966	−0.220897
$300$	0	0
$301$	−8.23607	−0.474719
$302$	− 3.38197i	− 0.194610i
$303$	− 4.29180i	− 0.246557i
$304$	31.8885	1.82893
$305$	0	0
$306$	−20.1803	−1.15363
$307$	− 24.6525i	− 1.40699i	−0.710700	−	0.703496i	$-0.751621\pi$
$307$	− 24.6525i	− 1.40699i	0.710700	−	0.703496i	$-0.248379\pi$
$308$	26.5623i	1.51353i
$309$	−9.70820	−0.552280
$310$	0	0
$311$	13.2361	0.750549	0.375274	−	0.926914i	$-0.377549\pi$
$311$	13.2361	0.750549	0.375274	+	0.926914i	$0.377549\pi$
$312$	− 5.70820i	− 0.323163i
$313$	− 5.70820i	− 0.322647i	−0.986902	−	0.161323i	$-0.948424\pi$
$313$	− 5.70820i	− 0.322647i	0.986902	−	0.161323i	$-0.0515762\pi$
$314$	−44.3607	−2.50342
$315$	0	0
$316$	8.56231	0.481667
$317$	− 17.6525i	− 0.991462i	−0.868476	−	0.495731i	$-0.834900\pi$
$317$	− 17.6525i	− 0.991462i	0.868476	−	0.495731i	$-0.165100\pi$
$318$	1.23607i	0.0693153i
$319$	25.7639	1.44250
$320$	0	0
$321$	−4.94427	−0.275962
$322$	13.0902i	0.729487i
$323$	24.9443i	1.38794i
$324$	−4.85410	−0.269672
$325$	0	0
$326$	48.3607	2.67845
$327$	6.41641i	0.354828i
$328$	− 59.7771i	− 3.30064i
$329$	7.23607	0.398937
$330$	0	0
$331$	13.7639	0.756534	0.378267	−	0.925697i	$-0.376520\pi$
$331$	13.7639	0.756534	0.378267	+	0.925697i	$0.376520\pi$
$332$	− 60.5410i	− 3.32262i
$333$	5.47214i	0.299871i
$334$	16.4721	0.901315
$335$	0	0
$336$	−9.85410	−0.537585
$337$	28.4721i	1.55098i	0.631362	+	0.775488i	$0.282496\pi$
$337$	28.4721i	1.55098i	−0.631362	+	0.775488i	$0.717504\pi$
$338$	− 32.5066i	− 1.76812i
$339$	16.2361	0.881822
$340$	0	0
$341$	−24.4721	−1.32524
$342$	8.47214i	0.458121i
$343$	− 1.00000i	− 0.0539949i
$344$	−61.5410	−3.31807
$345$	0	0
$346$	−10.0000	−0.537603
$347$	13.0000i	0.697877i	0.937146	+	0.348938i	$0.113458\pi$
$347$	13.0000i	0.697877i	−0.937146	+	0.348938i	$0.886542\pi$
$348$	22.8541i	1.22511i
$349$	−0.763932	−0.0408923	−0.0204462	−	0.999791i	$-0.506509\pi$
$349$	−0.763932	−0.0408923	−0.0204462	+	0.999791i	$0.506509\pi$
$350$	0	0
$351$	0.763932	0.0407757
$352$	59.3951i	3.16577i
$353$	1.05573i	0.0561907i	0.999605	+	0.0280954i	$0.00894421\pi$
$353$	1.05573i	0.0561907i	−0.999605	+	0.0280954i	$0.991056\pi$
$354$	2.00000	0.106299
$355$	0	0
$356$	−27.7082	−1.46853
$357$	− 7.70820i	− 0.407961i
$358$	12.9443i	0.684126i
$359$	−25.9443	−1.36929	−0.684643	−	0.728878i	$-0.740042\pi$
$359$	−25.9443	−1.36929	−0.684643	+	0.728878i	$0.740042\pi$
$360$	0	0
$361$	−8.52786	−0.448835
$362$	− 12.1803i	− 0.640184i
$363$	18.9443i	0.994316i
$364$	3.70820	0.194363
$365$	0	0
$366$	−40.3607	−2.10969
$367$	8.94427i	0.466887i	0.972370	+	0.233444i	$0.0749994\pi$
$367$	8.94427i	0.466887i	−0.972370	+	0.233444i	$0.925001\pi$
$368$	49.2705i	2.56840i
$369$	8.00000	0.416463
$370$	0	0
$371$	−0.472136	−0.0245121
$372$	− 21.7082i	− 1.12552i
$373$	− 15.0000i	− 0.776671i	−0.921518	−	0.388335i	$-0.873050\pi$
$373$	− 15.0000i	− 0.776671i	0.921518	−	0.388335i	$-0.126950\pi$
$374$	−110.430	−5.71018
$375$	0	0
$376$	54.0689	2.78839
$377$	− 3.59675i	− 0.185242i
$378$	− 2.61803i	− 0.134657i
$379$	−16.5967	−0.852518	−0.426259	−	0.904601i	$-0.640169\pi$
$379$	−16.5967	−0.852518	−0.426259	+	0.904601i	$0.640169\pi$
$380$	0	0
$381$	−12.2361	−0.626873
$382$	29.8885i	1.52923i
$383$	25.1246i	1.28381i	0.766785	+	0.641904i	$0.221855\pi$
$383$	25.1246i	1.28381i	−0.766785	+	0.641904i	$0.778145\pi$
$384$	−1.09017	−0.0556325
$385$	0	0
$386$	1.09017	0.0554882
$387$	− 8.23607i	− 0.418663i
$388$	60.5410i	3.07350i
$389$	1.76393	0.0894349	0.0447175	−	0.999000i	$-0.485761\pi$
$389$	1.76393	0.0894349	0.0447175	+	0.999000i	$0.485761\pi$
$390$	0	0
$391$	−38.5410	−1.94910
$392$	− 7.47214i	− 0.377400i
$393$	− 4.29180i	− 0.216492i
$394$	15.0902	0.760232
$395$	0	0
$396$	−26.5623	−1.33481
$397$	18.0000i	0.903394i	0.892171	+	0.451697i	$0.149181\pi$
$397$	18.0000i	0.903394i	−0.892171	+	0.451697i	$0.850819\pi$
$398$	− 41.8885i	− 2.09968i
$399$	−3.23607	−0.162006
$400$	0	0
$401$	−26.7082	−1.33374	−0.666872	−	0.745172i	$-0.732367\pi$
$401$	−26.7082	−1.33374	−0.666872	+	0.745172i	$0.732367\pi$
$402$	7.09017i	0.353626i
$403$	3.41641i	0.170183i
$404$	20.8328	1.03647
$405$	0	0
$406$	−12.3262	−0.611741
$407$	29.9443i	1.48428i
$408$	− 57.5967i	− 2.85146i
$409$	8.18034	0.404492	0.202246	−	0.979335i	$-0.435176\pi$
$409$	8.18034	0.404492	0.202246	+	0.979335i	$0.435176\pi$
$410$	0	0
$411$	−0.472136	−0.0232887
$412$	− 47.1246i	− 2.32166i
$413$	0.763932i	0.0375906i
$414$	−13.0902	−0.643347
$415$	0	0
$416$	8.29180	0.406539
$417$	− 3.70820i	− 0.181592i
$418$	46.3607i	2.26757i
$419$	−9.05573	−0.442401	−0.221201	−	0.975228i	$-0.570998\pi$
$419$	−9.05573	−0.442401	−0.221201	+	0.975228i	$0.570998\pi$
$420$	0	0
$421$	−0.416408	−0.0202945	−0.0101472	−	0.999949i	$-0.503230\pi$
$421$	−0.416408	−0.0202945	−0.0101472	+	0.999949i	$0.503230\pi$
$422$	− 33.8885i	− 1.64967i
$423$	7.23607i	0.351830i
$424$	−3.52786	−0.171328
$425$	0	0
$426$	−1.38197	−0.0669565
$427$	− 15.4164i	− 0.746052i
$428$	− 24.0000i	− 1.16008i
$429$	4.18034	0.201829
$430$	0	0
$431$	33.8885	1.63235	0.816177	−	0.577802i	$-0.196089\pi$
$431$	33.8885	1.63235	0.816177	+	0.577802i	$0.196089\pi$
$432$	− 9.85410i	− 0.474106i
$433$	37.3050i	1.79276i	0.443285	+	0.896381i	$0.353813\pi$
$433$	37.3050i	1.79276i	−0.443285	+	0.896381i	$0.646187\pi$
$434$	11.7082	0.562012
$435$	0	0
$436$	−31.1459	−1.49162
$437$	16.1803i	0.774011i
$438$	3.23607i	0.154625i
$439$	11.2361	0.536268	0.268134	−	0.963382i	$-0.413593\pi$
$439$	11.2361	0.536268	0.268134	+	0.963382i	$0.413593\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	15.4164i	0.733284i
$443$	12.5836i	0.597865i	0.954274	+	0.298932i	$0.0966305\pi$
$443$	12.5836i	0.597865i	−0.954274	+	0.298932i	$0.903370\pi$
$444$	−26.5623	−1.26059
$445$	0	0
$446$	−3.23607	−0.153232
$447$	− 8.23607i	− 0.389553i
$448$	− 8.70820i	− 0.411424i
$449$	−3.29180	−0.155349	−0.0776747	−	0.996979i	$-0.524750\pi$
$449$	−3.29180	−0.155349	−0.0776747	+	0.996979i	$0.524750\pi$
$450$	0	0
$451$	43.7771	2.06138
$452$	78.8115i	3.70698i
$453$	1.29180i	0.0606939i
$454$	12.4721	0.585346
$455$	0	0
$456$	−24.1803	−1.13235
$457$	29.4721i	1.37865i	0.724453	+	0.689324i	$0.242092\pi$
$457$	29.4721i	1.37865i	−0.724453	+	0.689324i	$0.757908\pi$
$458$	58.5410i	2.73544i
$459$	7.70820	0.359788
$460$	0	0
$461$	10.6525	0.496135	0.248068	−	0.968743i	$-0.420204\pi$
$461$	10.6525	0.496135	0.248068	+	0.968743i	$0.420204\pi$
$462$	− 14.3262i	− 0.666517i
$463$	28.3607i	1.31803i	0.752129	+	0.659016i	$0.229027\pi$
$463$	28.3607i	1.31803i	−0.752129	+	0.659016i	$0.770973\pi$
$464$	−46.3951	−2.15384
$465$	0	0
$466$	19.0902	0.884335
$467$	− 23.8885i	− 1.10543i	−0.833370	−	0.552715i	$-0.813592\pi$
$467$	− 23.8885i	− 1.10543i	0.833370	−	0.552715i	$-0.186408\pi$
$468$	3.70820i	0.171412i
$469$	−2.70820	−0.125053
$470$	0	0
$471$	16.9443	0.780751
$472$	5.70820i	0.262741i
$473$	− 45.0689i	− 2.07227i
$474$	−4.61803	−0.212113
$475$	0	0
$476$	37.4164	1.71498
$477$	− 0.472136i	− 0.0216176i
$478$	− 74.2492i	− 3.39608i
$479$	23.2361	1.06168	0.530842	−	0.847471i	$-0.321876\pi$
$479$	23.2361	1.06168	0.530842	+	0.847471i	$0.321876\pi$
$480$	0	0
$481$	4.18034	0.190607
$482$	− 50.3607i	− 2.29387i
$483$	− 5.00000i	− 0.227508i
$484$	−91.9574	−4.17988
$485$	0	0
$486$	2.61803	0.118756
$487$	6.81966i	0.309028i	0.987991	+	0.154514i	$0.0493812\pi$
$487$	6.81966i	0.309028i	−0.987991	+	0.154514i	$0.950619\pi$
$488$	− 115.193i	− 5.21456i
$489$	−18.4721	−0.835339
$490$	0	0
$491$	−0.527864	−0.0238222	−0.0119111	−	0.999929i	$-0.503792\pi$
$491$	−0.527864	−0.0238222	−0.0119111	+	0.999929i	$0.503792\pi$
$492$	38.8328i	1.75072i
$493$	− 36.2918i	− 1.63450i
$494$	6.47214	0.291195
$495$	0	0
$496$	44.0689	1.97875
$497$	− 0.527864i	− 0.0236779i
$498$	32.6525i	1.46319i
$499$	31.7771	1.42254	0.711269	−	0.702920i	$-0.248121\pi$
$499$	31.7771	1.42254	0.711269	+	0.702920i	$0.248121\pi$
$500$	0	0
$501$	−6.29180	−0.281097
$502$	− 7.23607i	− 0.322962i
$503$	17.4164i	0.776559i	0.921542	+	0.388280i	$0.126931\pi$
$503$	17.4164i	0.776559i	−0.921542	+	0.388280i	$0.873069\pi$
$504$	7.47214	0.332835
$505$	0	0
$506$	−71.6312	−3.18439
$507$	12.4164i	0.551432i
$508$	− 59.3951i	− 2.63523i
$509$	30.6525	1.35865	0.679324	−	0.733839i	$-0.262273\pi$
$509$	30.6525	1.35865	0.679324	+	0.733839i	$0.262273\pi$
$510$	0	0
$511$	−1.23607	−0.0546804
$512$	40.3050i	1.78124i
$513$	− 3.23607i	− 0.142876i
$514$	22.1803	0.978333
$515$	0	0
$516$	39.9787	1.75996
$517$	39.5967i	1.74146i
$518$	− 14.3262i	− 0.629459i
$519$	3.81966	0.167664
$520$	0	0
$521$	−37.7771	−1.65504	−0.827522	−	0.561433i	$-0.810250\pi$
$521$	−37.7771	−1.65504	−0.827522	+	0.561433i	$0.810250\pi$
$522$	− 12.3262i	− 0.539505i
$523$	− 35.7771i	− 1.56442i	−0.623013	−	0.782211i	$-0.714092\pi$
$523$	− 35.7771i	− 1.56442i	0.623013	−	0.782211i	$-0.285908\pi$
$524$	20.8328	0.910086
$525$	0	0
$526$	5.38197	0.234665
$527$	34.4721i	1.50163i
$528$	− 53.9230i	− 2.34670i
$529$	−2.00000	−0.0869565
$530$	0	0
$531$	−0.763932	−0.0331518
$532$	− 15.7082i	− 0.681037i
$533$	− 6.11146i	− 0.264717i
$534$	14.9443	0.646702
$535$	0	0
$536$	−20.2361	−0.874065
$537$	− 4.94427i	− 0.213361i
$538$	− 74.5410i	− 3.21369i
$539$	5.47214	0.235702
$540$	0	0
$541$	−17.9443	−0.771485	−0.385742	−	0.922607i	$-0.626055\pi$
$541$	−17.9443	−0.771485	−0.385742	+	0.922607i	$0.626055\pi$
$542$	− 60.8328i	− 2.61299i
$543$	4.65248i	0.199657i
$544$	83.6656	3.58713
$545$	0	0
$546$	−2.00000	−0.0855921
$547$	35.0689i	1.49944i	0.661757	+	0.749719i	$0.269811\pi$
$547$	35.0689i	1.49944i	−0.661757	+	0.749719i	$0.730189\pi$
$548$	− 2.29180i	− 0.0979007i
$549$	15.4164	0.657956
$550$	0	0
$551$	−15.2361	−0.649078
$552$	− 37.3607i	− 1.59018i
$553$	− 1.76393i	− 0.0750100i
$554$	41.5967	1.76728
$555$	0	0
$556$	18.0000	0.763370
$557$	7.65248i	0.324246i	0.986771	+	0.162123i	$0.0518341\pi$
$557$	7.65248i	0.324246i	−0.986771	+	0.162123i	$0.948166\pi$
$558$	11.7082i	0.495648i
$559$	−6.29180	−0.266115
$560$	0	0
$561$	42.1803	1.78086
$562$	− 35.7426i	− 1.50771i
$563$	35.3050i	1.48793i	0.668221	+	0.743963i	$0.267056\pi$
$563$	35.3050i	1.48793i	−0.668221	+	0.743963i	$0.732944\pi$
$564$	−35.1246	−1.47901
$565$	0	0
$566$	−35.1246	−1.47640
$567$	1.00000i	0.0419961i
$568$	− 3.94427i	− 0.165498i
$569$	12.2361	0.512963	0.256481	−	0.966549i	$-0.417437\pi$
$569$	12.2361	0.512963	0.256481	+	0.966549i	$0.417437\pi$
$570$	0	0
$571$	−40.7082	−1.70359	−0.851793	−	0.523879i	$-0.824484\pi$
$571$	−40.7082	−1.70359	−0.851793	+	0.523879i	$0.824484\pi$
$572$	20.2918i	0.848443i
$573$	− 11.4164i	− 0.476927i
$574$	−20.9443	−0.874197
$575$	0	0
$576$	8.70820	0.362842
$577$	− 11.2361i	− 0.467764i	−0.972265	−	0.233882i	$-0.924857\pi$
$577$	− 11.2361i	− 0.467764i	0.972265	−	0.233882i	$-0.0751429\pi$
$578$	111.048i	4.61897i
$579$	−0.416408	−0.0173053
$580$	0	0
$581$	−12.4721	−0.517431
$582$	− 32.6525i	− 1.35349i
$583$	− 2.58359i	− 0.107001i
$584$	−9.23607	−0.382191
$585$	0	0
$586$	−69.7771	−2.88246
$587$	7.12461i	0.294064i	0.989132	+	0.147032i	$0.0469721\pi$
$587$	7.12461i	0.294064i	−0.989132	+	0.147032i	$0.953028\pi$
$588$	4.85410i	0.200180i
$589$	14.4721	0.596314
$590$	0	0
$591$	−5.76393	−0.237096
$592$	− 53.9230i	− 2.21622i
$593$	25.3050i	1.03915i	0.854425	+	0.519575i	$0.173910\pi$
$593$	25.3050i	1.03915i	−0.854425	+	0.519575i	$0.826090\pi$
$594$	14.3262	0.587813
$595$	0	0
$596$	39.9787	1.63759
$597$	16.0000i	0.654836i
$598$	10.0000i	0.408930i
$599$	45.9443	1.87723	0.938616	−	0.344964i	$-0.112109\pi$
$599$	45.9443	1.87723	0.938616	+	0.344964i	$0.112109\pi$
$600$	0	0
$601$	−28.3607	−1.15686	−0.578428	−	0.815733i	$-0.696334\pi$
$601$	−28.3607	−1.15686	−0.578428	+	0.815733i	$0.696334\pi$
$602$	21.5623i	0.878814i
$603$	− 2.70820i	− 0.110287i
$604$	−6.27051	−0.255143
$605$	0	0
$606$	−11.2361	−0.456434
$607$	− 2.29180i	− 0.0930211i	−0.998918	−	0.0465106i	$-0.985190\pi$
$607$	− 2.29180i	− 0.0930211i	0.998918	−	0.0465106i	$-0.0148101\pi$
$608$	− 35.1246i	− 1.42449i
$609$	4.70820	0.190786
$610$	0	0
$611$	5.52786	0.223633
$612$	37.4164i	1.51247i
$613$	10.0557i	0.406147i	0.979163	+	0.203074i	$0.0650930\pi$
$613$	10.0557i	0.406147i	−0.979163	+	0.203074i	$0.934907\pi$
$614$	−64.5410	−2.60466
$615$	0	0
$616$	40.8885	1.64745
$617$	21.6525i	0.871696i	0.900020	+	0.435848i	$0.143551\pi$
$617$	21.6525i	0.871696i	−0.900020	+	0.435848i	$0.856449\pi$
$618$	25.4164i	1.02240i
$619$	−25.1246	−1.00984	−0.504922	−	0.863165i	$-0.668479\pi$
$619$	−25.1246	−1.00984	−0.504922	+	0.863165i	$0.668479\pi$
$620$	0	0
$621$	5.00000	0.200643
$622$	− 34.6525i	− 1.38944i
$623$	5.70820i	0.228694i
$624$	−7.52786	−0.301356
$625$	0	0
$626$	−14.9443	−0.597293
$627$	− 17.7082i	− 0.707198i
$628$	82.2492i	3.28210i
$629$	42.1803	1.68184
$630$	0	0
$631$	−40.1246	−1.59734	−0.798668	−	0.601772i	$-0.794462\pi$
$631$	−40.1246	−1.59734	−0.798668	+	0.601772i	$0.794462\pi$
$632$	− 13.1803i	− 0.524286i
$633$	12.9443i	0.514489i
$634$	−46.2148	−1.83542
$635$	0	0
$636$	2.29180	0.0908756
$637$	− 0.763932i	− 0.0302681i
$638$	− 67.4508i	− 2.67040i
$639$	0.527864	0.0208820
$640$	0	0
$641$	−15.2918	−0.603990	−0.301995	−	0.953310i	$-0.597653\pi$
$641$	−15.2918	−0.603990	−0.301995	+	0.953310i	$0.597653\pi$
$642$	12.9443i	0.510870i
$643$	− 44.7214i	− 1.76364i	−0.471588	−	0.881819i	$-0.656319\pi$
$643$	− 44.7214i	− 1.76364i	0.471588	−	0.881819i	$-0.343681\pi$
$644$	24.2705	0.956392
$645$	0	0
$646$	65.3050	2.56939
$647$	1.05573i	0.0415050i	0.999785	+	0.0207525i	$0.00660619\pi$
$647$	1.05573i	0.0415050i	−0.999785	+	0.0207525i	$0.993394\pi$
$648$	7.47214i	0.293533i
$649$	−4.18034	−0.164093
$650$	0	0
$651$	−4.47214	−0.175277
$652$	− 89.6656i	− 3.51158i
$653$	25.4164i	0.994621i	0.867573	+	0.497310i	$0.165679\pi$
$653$	25.4164i	0.994621i	−0.867573	+	0.497310i	$0.834321\pi$
$654$	16.7984	0.656868
$655$	0	0
$656$	−78.8328	−3.07790
$657$	− 1.23607i	− 0.0482236i
$658$	− 18.9443i	− 0.738525i
$659$	−40.9443	−1.59496	−0.797481	−	0.603344i	$-0.793835\pi$
$659$	−40.9443	−1.59496	−0.797481	+	0.603344i	$0.793835\pi$
$660$	0	0
$661$	8.18034	0.318178	0.159089	−	0.987264i	$-0.449144\pi$
$661$	8.18034	0.318178	0.159089	+	0.987264i	$0.449144\pi$
$662$	− 36.0344i	− 1.40052i
$663$	− 5.88854i	− 0.228692i
$664$	−93.1935	−3.61661
$665$	0	0
$666$	14.3262	0.555130
$667$	− 23.5410i	− 0.911512i
$668$	− 30.5410i	− 1.18167i
$669$	1.23607	0.0477891
$670$	0	0
$671$	84.3607	3.25671
$672$	10.8541i	0.418706i
$673$	− 6.00000i	− 0.231283i	−0.993291	−	0.115642i	$-0.963108\pi$
$673$	− 6.00000i	− 0.231283i	0.993291	−	0.115642i	$-0.0368924\pi$
$674$	74.5410	2.87121
$675$	0	0
$676$	−60.2705	−2.31810
$677$	− 43.3050i	− 1.66434i	−0.554517	−	0.832172i	$-0.687097\pi$
$677$	− 43.3050i	− 1.66434i	0.554517	−	0.832172i	$-0.312903\pi$
$678$	− 42.5066i	− 1.63246i
$679$	12.4721	0.478637
$680$	0	0
$681$	−4.76393	−0.182554
$682$	64.0689i	2.45332i
$683$	5.11146i	0.195584i	0.995207	+	0.0977922i	$0.0311781\pi$
$683$	5.11146i	0.195584i	−0.995207	+	0.0977922i	$0.968822\pi$
$684$	15.7082	0.600618
$685$	0	0
$686$	−2.61803	−0.0999570
$687$	− 22.3607i	− 0.853113i
$688$	81.1591i	3.09416i
$689$	−0.360680	−0.0137408
$690$	0	0
$691$	−12.3607	−0.470222	−0.235111	−	0.971968i	$-0.575545\pi$
$691$	−12.3607	−0.470222	−0.235111	+	0.971968i	$0.575545\pi$
$692$	18.5410i	0.704824i
$693$	5.47214i	0.207869i
$694$	34.0344	1.29193
$695$	0	0
$696$	35.1803	1.33351
$697$	− 61.6656i	− 2.33575i
$698$	2.00000i	0.0757011i
$699$	−7.29180	−0.275801
$700$	0	0
$701$	33.4164	1.26212	0.631060	−	0.775734i	$-0.282620\pi$
$701$	33.4164	1.26212	0.631060	+	0.775734i	$0.282620\pi$
$702$	− 2.00000i	− 0.0754851i
$703$	− 17.7082i	− 0.667878i
$704$	47.6525	1.79597
$705$	0	0
$706$	2.76393	0.104022
$707$	− 4.29180i	− 0.161410i
$708$	− 3.70820i	− 0.139363i
$709$	−43.8885	−1.64827	−0.824134	−	0.566394i	$-0.808338\pi$
$709$	−43.8885	−1.64827	−0.824134	+	0.566394i	$0.808338\pi$
$710$	0	0
$711$	1.76393	0.0661526
$712$	42.6525i	1.59847i
$713$	22.3607i	0.837414i
$714$	−20.1803	−0.755230
$715$	0	0
$716$	24.0000	0.896922
$717$	28.3607i	1.05915i
$718$	67.9230i	2.53486i
$719$	−42.2492	−1.57563	−0.787815	−	0.615912i	$-0.788788\pi$
$719$	−42.2492	−1.57563	−0.787815	+	0.615912i	$0.788788\pi$
$720$	0	0
$721$	−9.70820	−0.361552
$722$	22.3262i	0.830897i
$723$	19.2361i	0.715397i
$724$	−22.5836	−0.839313
$725$	0	0
$726$	49.5967	1.84071
$727$	18.5410i	0.687648i	0.939034	+	0.343824i	$0.111722\pi$
$727$	18.5410i	0.687648i	−0.939034	+	0.343824i	$0.888278\pi$
$728$	− 5.70820i	− 0.211560i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−63.4853	−2.34809
$732$	74.8328i	2.76590i
$733$	12.0000i	0.443230i	0.975134	+	0.221615i	$0.0711328\pi$
$733$	12.0000i	0.443230i	−0.975134	+	0.221615i	$0.928867\pi$
$734$	23.4164	0.864315
$735$	0	0
$736$	54.2705	2.00044
$737$	− 14.8197i	− 0.545889i
$738$	− 20.9443i	− 0.770969i
$739$	−3.76393	−0.138458	−0.0692292	−	0.997601i	$-0.522054\pi$
$739$	−3.76393	−0.138458	−0.0692292	+	0.997601i	$0.522054\pi$
$740$	0	0
$741$	−2.47214	−0.0908162
$742$	1.23607i	0.0453775i
$743$	− 30.2492i	− 1.10974i	−0.831938	−	0.554868i	$-0.812769\pi$
$743$	− 30.2492i	− 1.10974i	0.831938	−	0.554868i	$-0.187231\pi$
$744$	−33.4164	−1.22510
$745$	0	0
$746$	−39.2705	−1.43780
$747$	− 12.4721i	− 0.456332i
$748$	204.748i	7.48632i
$749$	−4.94427	−0.180660
$750$	0	0
$751$	40.3607	1.47278	0.736391	−	0.676556i	$-0.236528\pi$
$751$	40.3607	1.47278	0.736391	+	0.676556i	$0.236528\pi$
$752$	− 71.3050i	− 2.60022i
$753$	2.76393i	0.100723i
$754$	−9.41641	−0.342925
$755$	0	0
$756$	−4.85410	−0.176542
$757$	13.9443i	0.506813i	0.967360	+	0.253407i	$0.0815510\pi$
$757$	13.9443i	0.506813i	−0.967360	+	0.253407i	$0.918449\pi$
$758$	43.4508i	1.57821i
$759$	27.3607	0.993130
$760$	0	0
$761$	9.30495	0.337304	0.168652	−	0.985676i	$-0.446059\pi$
$761$	9.30495	0.337304	0.168652	+	0.985676i	$0.446059\pi$
$762$	32.0344i	1.16049i
$763$	6.41641i	0.232290i
$764$	55.4164	2.00490
$765$	0	0
$766$	65.7771	2.37662
$767$	0.583592i	0.0210723i
$768$	− 14.5623i	− 0.525472i
$769$	−35.4164	−1.27715	−0.638574	−	0.769560i	$-0.720475\pi$
$769$	−35.4164	−1.27715	−0.638574	+	0.769560i	$0.720475\pi$
$770$	0	0
$771$	−8.47214	−0.305117
$772$	− 2.02129i	− 0.0727477i
$773$	− 34.9443i	− 1.25686i	−0.777867	−	0.628429i	$-0.783698\pi$
$773$	− 34.9443i	− 1.25686i	0.777867	−	0.628429i	$-0.216302\pi$
$774$	−21.5623	−0.775041
$775$	0	0
$776$	93.1935	3.34545
$777$	5.47214i	0.196312i
$778$	− 4.61803i	− 0.165565i
$779$	−25.8885	−0.927553
$780$	0	0
$781$	2.88854	0.103360
$782$	100.902i	3.60824i
$783$	4.70820i	0.168257i
$784$	−9.85410	−0.351932
$785$	0	0
$786$	−11.2361	−0.400777
$787$	− 38.7639i	− 1.38178i	−0.722958	−	0.690892i	$-0.757218\pi$
$787$	− 38.7639i	− 1.38178i	0.722958	−	0.690892i	$-0.242782\pi$
$788$	− 27.9787i	− 0.996700i
$789$	−2.05573	−0.0731859
$790$	0	0
$791$	16.2361	0.577288
$792$	40.8885i	1.45291i
$793$	− 11.7771i	− 0.418217i
$794$	47.1246	1.67239
$795$	0	0
$796$	−77.6656	−2.75279
$797$	40.0689i	1.41931i	0.704548	+	0.709656i	$0.251150\pi$
$797$	40.0689i	1.41931i	−0.704548	+	0.709656i	$0.748850\pi$
$798$	8.47214i	0.299910i
$799$	55.7771	1.97325
$800$	0	0
$801$	−5.70820	−0.201689
$802$	69.9230i	2.46907i
$803$	− 6.76393i	− 0.238694i
$804$	13.1459	0.463620
$805$	0	0
$806$	8.94427	0.315049
$807$	28.4721i	1.00227i
$808$	− 32.0689i	− 1.12818i
$809$	6.81966	0.239766	0.119883	−	0.992788i	$-0.461748\pi$
$809$	6.81966	0.239766	0.119883	+	0.992788i	$0.461748\pi$
$810$	0	0
$811$	−6.00000	−0.210688	−0.105344	−	0.994436i	$-0.533594\pi$
$811$	−6.00000	−0.210688	−0.105344	+	0.994436i	$0.533594\pi$
$812$	22.8541i	0.802022i
$813$	23.2361i	0.814924i
$814$	78.3951	2.74775
$815$	0	0
$816$	−75.9574	−2.65904
$817$	26.6525i	0.932452i
$818$	− 21.4164i	− 0.748807i
$819$	0.763932	0.0266939
$820$	0	0
$821$	−10.9443	−0.381958	−0.190979	−	0.981594i	$-0.561166\pi$
$821$	−10.9443	−0.381958	−0.190979	+	0.981594i	$0.561166\pi$
$822$	1.23607i	0.0431128i
$823$	− 44.0132i	− 1.53420i	−0.641526	−	0.767101i	$-0.721698\pi$
$823$	− 44.0132i	− 1.53420i	0.641526	−	0.767101i	$-0.278302\pi$
$824$	−72.5410	−2.52709
$825$	0	0
$826$	2.00000	0.0695889
$827$	− 31.9443i	− 1.11081i	−0.831580	−	0.555406i	$-0.812563\pi$
$827$	− 31.9443i	− 1.11081i	0.831580	−	0.555406i	$-0.187437\pi$
$828$	24.2705i	0.843459i
$829$	−26.7639	−0.929550	−0.464775	−	0.885429i	$-0.653865\pi$
$829$	−26.7639	−0.929550	−0.464775	+	0.885429i	$0.653865\pi$
$830$	0	0
$831$	−15.8885	−0.551167
$832$	− 6.65248i	− 0.230633i
$833$	− 7.70820i	− 0.267073i
$834$	−9.70820	−0.336168
$835$	0	0
$836$	85.9574	2.97290
$837$	− 4.47214i	− 0.154580i
$838$	23.7082i	0.818986i
$839$	−27.1246	−0.936446	−0.468223	−	0.883610i	$-0.655106\pi$
$839$	−27.1246	−0.936446	−0.468223	+	0.883610i	$0.655106\pi$
$840$	0	0
$841$	−6.83282	−0.235614
$842$	1.09017i	0.0375697i
$843$	13.6525i	0.470216i
$844$	−62.8328	−2.16279
$845$	0	0
$846$	18.9443	0.651317
$847$	18.9443i	0.650933i
$848$	4.65248i	0.159767i
$849$	13.4164	0.460450
$850$	0	0
$851$	27.3607	0.937912
$852$	2.56231i	0.0877832i
$853$	52.3607i	1.79280i	0.443251	+	0.896398i	$0.353825\pi$
$853$	52.3607i	1.79280i	−0.443251	+	0.896398i	$0.646175\pi$
$854$	−40.3607	−1.38111
$855$	0	0
$856$	−36.9443	−1.26273
$857$	− 39.4164i	− 1.34644i	−0.739443	−	0.673219i	$-0.764911\pi$
$857$	− 39.4164i	− 1.34644i	0.739443	−	0.673219i	$-0.235089\pi$
$858$	− 10.9443i	− 0.373631i
$859$	0.472136	0.0161091	0.00805454	−	0.999968i	$-0.497436\pi$
$859$	0.472136	0.0161091	0.00805454	+	0.999968i	$0.497436\pi$
$860$	0	0
$861$	8.00000	0.272639
$862$	− 88.7214i	− 3.02186i
$863$	2.05573i	0.0699778i	0.999388	+	0.0349889i	$0.0111396\pi$
$863$	2.05573i	0.0699778i	−0.999388	+	0.0349889i	$0.988860\pi$
$864$	−10.8541	−0.369264
$865$	0	0
$866$	97.6656	3.31881
$867$	− 42.4164i	− 1.44054i
$868$	− 21.7082i	− 0.736824i
$869$	9.65248	0.327438
$870$	0	0
$871$	−2.06888	−0.0701015
$872$	47.9443i	1.62360i
$873$	12.4721i	0.422118i
$874$	42.3607	1.43287
$875$	0	0
$876$	6.00000	0.202721
$877$	− 6.00000i	− 0.202606i	−0.994856	−	0.101303i	$-0.967699\pi$
$877$	− 6.00000i	− 0.202606i	0.994856	−	0.101303i	$-0.0323011\pi$
$878$	− 29.4164i	− 0.992756i
$879$	26.6525	0.898966
$880$	0	0
$881$	−38.3607	−1.29240	−0.646202	−	0.763166i	$-0.723644\pi$
$881$	−38.3607	−1.29240	−0.646202	+	0.763166i	$0.723644\pi$
$882$	− 2.61803i	− 0.0881538i
$883$	34.2361i	1.15214i	0.817402	+	0.576068i	$0.195414\pi$
$883$	34.2361i	1.15214i	−0.817402	+	0.576068i	$0.804586\pi$
$884$	28.5836	0.961370
$885$	0	0
$886$	32.9443	1.10678
$887$	15.4164i	0.517632i	0.965927	+	0.258816i	$0.0833324\pi$
$887$	15.4164i	0.517632i	−0.965927	+	0.258816i	$0.916668\pi$
$888$	40.8885i	1.37213i
$889$	−12.2361	−0.410385
$890$	0	0
$891$	−5.47214	−0.183323
$892$	6.00000i	0.200895i
$893$	− 23.4164i	− 0.783600i
$894$	−21.5623	−0.721151
$895$	0	0
$896$	−1.09017	−0.0364200
$897$	− 3.81966i	− 0.127535i
$898$	8.61803i	0.287588i
$899$	−21.0557	−0.702248
$900$	0	0
$901$	−3.63932	−0.121243
$902$	− 114.610i	− 3.81609i
$903$	− 8.23607i	− 0.274079i
$904$	121.318	4.03498
$905$	0	0
$906$	3.38197	0.112358
$907$	16.3607i	0.543247i	0.962404	+	0.271624i	$0.0875606\pi$
$907$	16.3607i	0.543247i	−0.962404	+	0.271624i	$0.912439\pi$
$908$	− 23.1246i	− 0.767417i
$909$	4.29180	0.142350
$910$	0	0
$911$	7.58359	0.251256	0.125628	−	0.992077i	$-0.459905\pi$
$911$	7.58359	0.251256	0.125628	+	0.992077i	$0.459905\pi$
$912$	31.8885i	1.05594i
$913$	− 68.2492i	− 2.25872i
$914$	77.1591	2.55219
$915$	0	0
$916$	108.541	3.58630
$917$	− 4.29180i	− 0.141728i
$918$	− 20.1803i	− 0.666050i
$919$	−36.0132	−1.18796	−0.593982	−	0.804478i	$-0.702445\pi$
$919$	−36.0132	−1.18796	−0.593982	+	0.804478i	$0.702445\pi$
$920$	0	0
$921$	24.6525	0.812327
$922$	− 27.8885i	− 0.918460i
$923$	− 0.403252i	− 0.0132732i
$924$	−26.5623	−0.873836
$925$	0	0
$926$	74.2492	2.43998
$927$	− 9.70820i	− 0.318859i
$928$	51.1033i	1.67755i
$929$	30.1803	0.990185	0.495092	−	0.868840i	$-0.335134\pi$
$929$	30.1803	0.990185	0.495092	+	0.868840i	$0.335134\pi$
$930$	0	0
$931$	−3.23607	−0.106058
$932$	− 35.3951i	− 1.15941i
$933$	13.2361i	0.433329i
$934$	−62.5410	−2.04640
$935$	0	0
$936$	5.70820	0.186578
$937$	− 4.36068i	− 0.142457i	−0.997460	−	0.0712286i	$-0.977308\pi$
$937$	− 4.36068i	− 0.142457i	0.997460	−	0.0712286i	$-0.0226920\pi$
$938$	7.09017i	0.231502i
$939$	5.70820	0.186280
$940$	0	0
$941$	44.8328	1.46151	0.730754	−	0.682641i	$-0.239169\pi$
$941$	44.8328	1.46151	0.730754	+	0.682641i	$0.239169\pi$
$942$	− 44.3607i	− 1.44535i
$943$	− 40.0000i	− 1.30258i
$944$	7.52786	0.245011
$945$	0	0
$946$	−117.992	−3.83625
$947$	− 32.9443i	− 1.07054i	−0.844679	−	0.535272i	$-0.820209\pi$
$947$	− 32.9443i	− 1.07054i	0.844679	−	0.535272i	$-0.179791\pi$
$948$	8.56231i	0.278091i
$949$	−0.944272	−0.0306524
$950$	0	0
$951$	17.6525	0.572421
$952$	− 57.5967i	− 1.86672i
$953$	16.1246i	0.522327i	0.965295	+	0.261164i	$0.0841062\pi$
$953$	16.1246i	0.522327i	−0.965295	+	0.261164i	$0.915894\pi$
$954$	−1.23607	−0.0400192
$955$	0	0
$956$	−137.666	−4.45242
$957$	25.7639i	0.832830i
$958$	− 60.8328i	− 1.96542i
$959$	−0.472136	−0.0152461
$960$	0	0
$961$	−11.0000	−0.354839
$962$	− 10.9443i	− 0.352857i
$963$	− 4.94427i	− 0.159327i
$964$	−93.3738	−3.00737
$965$	0	0
$966$	−13.0902	−0.421169
$967$	2.11146i	0.0678999i	0.999424	+	0.0339499i	$0.0108087\pi$
$967$	2.11146i	0.0678999i	−0.999424	+	0.0339499i	$0.989191\pi$
$968$	141.554i	4.54972i
$969$	−24.9443	−0.801325
$970$	0	0
$971$	11.5967	0.372157	0.186079	−	0.982535i	$-0.440422\pi$
$971$	11.5967	0.372157	0.186079	+	0.982535i	$0.440422\pi$
$972$	− 4.85410i	− 0.155695i
$973$	− 3.70820i	− 0.118880i
$974$	17.8541	0.572082
$975$	0	0
$976$	−151.915	−4.86268
$977$	− 3.29180i	− 0.105314i	−0.998613	−	0.0526569i	$-0.983231\pi$
$977$	− 3.29180i	− 0.105314i	0.998613	−	0.0526569i	$-0.0167690\pi$
$978$	48.3607i	1.54640i
$979$	−31.2361	−0.998309
$980$	0	0
$981$	−6.41641	−0.204860
$982$	1.38197i	0.0441003i
$983$	− 2.58359i	− 0.0824038i	−0.999151	−	0.0412019i	$-0.986881\pi$
$983$	− 2.58359i	− 0.0824038i	0.999151	−	0.0412019i	$-0.0131187\pi$
$984$	59.7771	1.90562
$985$	0	0
$986$	−95.0132	−3.02584
$987$	7.23607i	0.230327i
$988$	− 12.0000i	− 0.381771i
$989$	−41.1803	−1.30946
$990$	0	0
$991$	8.59675	0.273085	0.136542	−	0.990634i	$-0.456401\pi$
$991$	8.59675	0.273085	0.136542	+	0.990634i	$0.456401\pi$
$992$	− 48.5410i	− 1.54118i
$993$	13.7639i	0.436785i
$994$	−1.38197	−0.0438333
$995$	0	0
$996$	60.5410	1.91832
$997$	− 52.5410i	− 1.66399i	−0.554783	−	0.831995i	$-0.687199\pi$
$997$	− 52.5410i	− 1.66399i	0.554783	−	0.831995i	$-0.312801\pi$
$998$	− 83.1935i	− 2.63344i
$999$	−5.47214	−0.173131

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.d.e.274.1		4
3.2	odd	2		1575.2.d.f.1324.4		4
5.2	odd	4		525.2.a.i.1.2	yes	2
5.3	odd	4		525.2.a.e.1.1	✓	2
5.4	even	2	inner	525.2.d.e.274.4		4
15.2	even	4		1575.2.a.l.1.1		2
15.8	even	4		1575.2.a.v.1.2		2
15.14	odd	2		1575.2.d.f.1324.1		4
20.3	even	4		8400.2.a.da.1.2		2
20.7	even	4		8400.2.a.cy.1.2		2
35.13	even	4		3675.2.a.r.1.1		2
35.27	even	4		3675.2.a.bh.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.a.e.1.1	✓	2	5.3	odd	4
525.2.a.i.1.2	yes	2	5.2	odd	4
525.2.d.e.274.1		4	1.1	even	1	trivial
525.2.d.e.274.4		4	5.4	even	2	inner
1575.2.a.l.1.1		2	15.2	even	4
1575.2.a.v.1.2		2	15.8	even	4
1575.2.d.f.1324.1		4	15.14	odd	2
1575.2.d.f.1324.4		4	3.2	odd	2
3675.2.a.r.1.1		2	35.13	even	4
3675.2.a.bh.1.2		2	35.27	even	4
8400.2.a.cy.1.2		2	20.7	even	4
8400.2.a.da.1.2		2	20.3	even	4

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.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.61803i q^{2} +1.00000i q^{3} -4.85410 q^{4} +2.61803 q^{6} +1.00000i q^{7} +7.47214i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.61803i q^{2} +1.00000i q^{3} -4.85410 q^{4} +2.61803 q^{6} +1.00000i q^{7} +7.47214i q^{8} -1.00000 q^{9} -5.47214 q^{11} -4.85410i q^{12} +0.763932i q^{13} +2.61803 q^{14} +9.85410 q^{16} +7.70820i q^{17} +2.61803i q^{18} +3.23607 q^{19} -1.00000 q^{21} +14.3262i q^{22} +5.00000i q^{23} -7.47214 q^{24} +2.00000 q^{26} -1.00000i q^{27} -4.85410i q^{28} -4.70820 q^{29} +4.47214 q^{31} -10.8541i q^{32} -5.47214i q^{33} +20.1803 q^{34} +4.85410 q^{36} -5.47214i q^{37} -8.47214i q^{38} -0.763932 q^{39} -8.00000 q^{41} +2.61803i q^{42} +8.23607i q^{43} +26.5623 q^{44} +13.0902 q^{46} -7.23607i q^{47} +9.85410i q^{48} -1.00000 q^{49} -7.70820 q^{51} -3.70820i q^{52} +0.472136i q^{53} -2.61803 q^{54} -7.47214 q^{56} +3.23607i q^{57} +12.3262i q^{58} +0.763932 q^{59} -15.4164 q^{61} -11.7082i q^{62} -1.00000i q^{63} -8.70820 q^{64} -14.3262 q^{66} +2.70820i q^{67} -37.4164i q^{68} -5.00000 q^{69} -0.527864 q^{71} -7.47214i q^{72} +1.23607i q^{73} -14.3262 q^{74} -15.7082 q^{76} -5.47214i q^{77} +2.00000i q^{78} -1.76393 q^{79} +1.00000 q^{81} +20.9443i q^{82} +12.4721i q^{83} +4.85410 q^{84} +21.5623 q^{86} -4.70820i q^{87} -40.8885i q^{88} +5.70820 q^{89} -0.763932 q^{91} -24.2705i q^{92} +4.47214i q^{93} -18.9443 q^{94} +10.8541 q^{96} -12.4721i q^{97} +2.61803i q^{98} +5.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{4} + 6 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 6 * q^4 + 6 * q^6 - 4 * q^9	\( 4 q - 6 q^{4} + 6 q^{6} - 4 q^{9} - 4 q^{11} + 6 q^{14} + 26 q^{16} + 4 q^{19} - 4 q^{21} - 12 q^{24} + 8 q^{26} + 8 q^{29} + 36 q^{34} + 6 q^{36} - 12 q^{39} - 32 q^{41} + 66 q^{44} + 30 q^{46} - 4 q^{49} - 4 q^{51} - 6 q^{54} - 12 q^{56} + 12 q^{59} - 8 q^{61} - 8 q^{64} - 26 q^{66} - 20 q^{69} - 20 q^{71} - 26 q^{74} - 36 q^{76} - 16 q^{79} + 4 q^{81} + 6 q^{84} + 46 q^{86} - 4 q^{89} - 12 q^{91} - 40 q^{94} + 30 q^{96} + 4 q^{99}+O(q^{100}) \) 4 * q - 6 * q^4 + 6 * q^6 - 4 * q^9 - 4 * q^11 + 6 * q^14 + 26 * q^16 + 4 * q^19 - 4 * q^21 - 12 * q^24 + 8 * q^26 + 8 * q^29 + 36 * q^34 + 6 * q^36 - 12 * q^39 - 32 * q^41 + 66 * q^44 + 30 * q^46 - 4 * q^49 - 4 * q^51 - 6 * q^54 - 12 * q^56 + 12 * q^59 - 8 * q^61 - 8 * q^64 - 26 * q^66 - 20 * q^69 - 20 * q^71 - 26 * q^74 - 36 * q^76 - 16 * q^79 + 4 * q^81 + 6 * q^84 + 46 * q^86 - 4 * q^89 - 12 * q^91 - 40 * q^94 + 30 * q^96 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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