LMFDB - Embedded newform 525.4.d.b.274.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,4,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, 4, names="a")

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

chi := DirichletCharacter("525.274");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
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:	$30.9760027530$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	525.274
Dual form			525.4.d.b.274.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000i q^{2} -3.00000i q^{3} -8.00000 q^{4} -12.0000 q^{6} +7.00000i q^{7} -9.00000 q^{9} +O(q^{10})$	\(q-4.00000i q^{2} -3.00000i q^{3} -8.00000 q^{4} -12.0000 q^{6} +7.00000i q^{7} -9.00000 q^{9} +62.0000 q^{11} +24.0000i q^{12} -62.0000i q^{13} +28.0000 q^{14} -64.0000 q^{16} -84.0000i q^{17} +36.0000i q^{18} -100.000 q^{19} +21.0000 q^{21} -248.000i q^{22} -42.0000i q^{23} -248.000 q^{26} +27.0000i q^{27} -56.0000i q^{28} +10.0000 q^{29} -48.0000 q^{31} +256.000i q^{32} -186.000i q^{33} -336.000 q^{34} +72.0000 q^{36} +246.000i q^{37} +400.000i q^{38} -186.000 q^{39} -248.000 q^{41} -84.0000i q^{42} +68.0000i q^{43} -496.000 q^{44} -168.000 q^{46} -324.000i q^{47} +192.000i q^{48} -49.0000 q^{49} -252.000 q^{51} +496.000i q^{52} +258.000i q^{53} +108.000 q^{54} +300.000i q^{57} -40.0000i q^{58} -120.000 q^{59} +622.000 q^{61} +192.000i q^{62} -63.0000i q^{63} +512.000 q^{64} -744.000 q^{66} -904.000i q^{67} +672.000i q^{68} -126.000 q^{69} -678.000 q^{71} -642.000i q^{73} +984.000 q^{74} +800.000 q^{76} +434.000i q^{77} +744.000i q^{78} -740.000 q^{79} +81.0000 q^{81} +992.000i q^{82} +468.000i q^{83} -168.000 q^{84} +272.000 q^{86} -30.0000i q^{87} -200.000 q^{89} +434.000 q^{91} +336.000i q^{92} +144.000i q^{93} -1296.00 q^{94} +768.000 q^{96} +1266.00i q^{97} +196.000i q^{98} -558.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 16 q^{4} - 24 q^{6} - 18 q^{9}+O(q^{10}) $ 2 * q - 16 * q^4 - 24 * q^6 - 18 * q^9	$ 2 q - 16 q^{4} - 24 q^{6} - 18 q^{9} + 124 q^{11} + 56 q^{14} - 128 q^{16} - 200 q^{19} + 42 q^{21} - 496 q^{26} + 20 q^{29} - 96 q^{31} - 672 q^{34} + 144 q^{36} - 372 q^{39} - 496 q^{41} - 992 q^{44} - 336 q^{46} - 98 q^{49} - 504 q^{51} + 216 q^{54} - 240 q^{59} + 1244 q^{61} + 1024 q^{64} - 1488 q^{66} - 252 q^{69} - 1356 q^{71} + 1968 q^{74} + 1600 q^{76} - 1480 q^{79} + 162 q^{81} - 336 q^{84} + 544 q^{86} - 400 q^{89} + 868 q^{91} - 2592 q^{94} + 1536 q^{96} - 1116 q^{99}+O(q^{100}) $ 2 * q - 16 * q^4 - 24 * q^6 - 18 * q^9 + 124 * q^11 + 56 * q^14 - 128 * q^16 - 200 * q^19 + 42 * q^21 - 496 * q^26 + 20 * q^29 - 96 * q^31 - 672 * q^34 + 144 * q^36 - 372 * q^39 - 496 * q^41 - 992 * q^44 - 336 * q^46 - 98 * q^49 - 504 * q^51 + 216 * q^54 - 240 * q^59 + 1244 * q^61 + 1024 * q^64 - 1488 * q^66 - 252 * q^69 - 1356 * q^71 + 1968 * q^74 + 1600 * q^76 - 1480 * q^79 + 162 * q^81 - 336 * q^84 + 544 * q^86 - 400 * q^89 + 868 * q^91 - 2592 * q^94 + 1536 * q^96 - 1116 * 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 $

$2$	− 4.00000i	− 1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$2$	− 4.00000i	− 1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$3$	− 3.00000i	− 0.577350i
$3$	− 3.00000i	− 0.577350i
$4$	−8.00000	−1.00000
$5$	0	0
$5$	0	0
$6$	−12.0000	−0.816497
$7$	7.00000i	0.377964i
$7$	7.00000i	0.377964i
$8$	0	0
$9$	−9.00000	−0.333333
$10$	0	0
$11$	62.0000	1.69943	0.849714	−	0.527244i	$-0.176775\pi$
$11$	62.0000	1.69943	0.849714	+	0.527244i	$0.176775\pi$
$12$	24.0000i	0.577350i
$13$	− 62.0000i	− 1.32275i	−0.750057	−	0.661373i	$-0.769974\pi$
$13$	− 62.0000i	− 1.32275i	0.750057	−	0.661373i	$-0.230026\pi$
$14$	28.0000	0.534522
$15$	0	0
$16$	−64.0000	−1.00000
$17$	− 84.0000i	− 1.19841i	−0.800595	−	0.599206i	$-0.795483\pi$
$17$	− 84.0000i	− 1.19841i	0.800595	−	0.599206i	$-0.204517\pi$
$18$	36.0000i	0.471405i
$19$	−100.000	−1.20745	−0.603726	−	0.797192i	$-0.706318\pi$
$19$	−100.000	−1.20745	−0.603726	+	0.797192i	$0.706318\pi$
$20$	0	0
$21$	21.0000	0.218218
$22$	− 248.000i	− 2.40335i
$23$	− 42.0000i	− 0.380765i	−0.981710	−	0.190383i	$-0.939027\pi$
$23$	− 42.0000i	− 0.380765i	0.981710	−	0.190383i	$-0.0609729\pi$
$24$	0	0
$25$	0	0
$26$	−248.000	−1.87065
$27$	27.0000i	0.192450i
$28$	− 56.0000i	− 0.377964i
$29$	10.0000	0.0640329	0.0320164	−	0.999487i	$-0.489807\pi$
$29$	10.0000	0.0640329	0.0320164	+	0.999487i	$0.489807\pi$
$30$	0	0
$31$	−48.0000	−0.278099	−0.139049	−	0.990285i	$-0.544405\pi$
$31$	−48.0000	−0.278099	−0.139049	+	0.990285i	$0.544405\pi$
$32$	256.000i	1.41421i
$33$	− 186.000i	− 0.981165i
$34$	−336.000	−1.69481
$35$	0	0
$36$	72.0000	0.333333
$37$	246.000i	1.09303i	0.837449	+	0.546516i	$0.184046\pi$
$37$	246.000i	1.09303i	−0.837449	+	0.546516i	$0.815954\pi$
$38$	400.000i	1.70759i
$39$	−186.000	−0.763688
$40$	0	0
$41$	−248.000	−0.944661	−0.472330	−	0.881422i	$-0.656587\pi$
$41$	−248.000	−0.944661	−0.472330	+	0.881422i	$0.656587\pi$
$42$	− 84.0000i	− 0.308607i
$43$	68.0000i	0.241161i	0.992704	+	0.120580i	$0.0384755\pi$
$43$	68.0000i	0.241161i	−0.992704	+	0.120580i	$0.961524\pi$
$44$	−496.000	−1.69943
$45$	0	0
$46$	−168.000	−0.538484
$47$	− 324.000i	− 1.00554i	−0.864421	−	0.502769i	$-0.832315\pi$
$47$	− 324.000i	− 1.00554i	0.864421	−	0.502769i	$-0.167685\pi$
$48$	192.000i	0.577350i
$49$	−49.0000	−0.142857
$50$	0	0
$51$	−252.000	−0.691903
$52$	496.000i	1.32275i
$53$	258.000i	0.668661i	0.942456	+	0.334330i	$0.108510\pi$
$53$	258.000i	0.668661i	−0.942456	+	0.334330i	$0.891490\pi$
$54$	108.000	0.272166
$55$	0	0
$56$	0	0
$57$	300.000i	0.697122i
$58$	− 40.0000i	− 0.0905562i
$59$	−120.000	−0.264791	−0.132396	−	0.991197i	$-0.542267\pi$
$59$	−120.000	−0.264791	−0.132396	+	0.991197i	$0.542267\pi$
$60$	0	0
$61$	622.000	1.30556	0.652778	−	0.757549i	$-0.273603\pi$
$61$	622.000	1.30556	0.652778	+	0.757549i	$0.273603\pi$
$62$	192.000i	0.393291i
$63$	− 63.0000i	− 0.125988i
$64$	512.000	1.00000
$65$	0	0
$66$	−744.000	−1.38758
$67$	− 904.000i	− 1.64838i	−0.566316	−	0.824188i	$-0.691632\pi$
$67$	− 904.000i	− 1.64838i	0.566316	−	0.824188i	$-0.308368\pi$
$68$	672.000i	1.19841i
$69$	−126.000	−0.219835
$70$	0	0
$71$	−678.000	−1.13329	−0.566646	−	0.823961i	$-0.691759\pi$
$71$	−678.000	−1.13329	−0.566646	+	0.823961i	$0.691759\pi$
$72$	0	0
$73$	− 642.000i	− 1.02932i	−0.857394	−	0.514660i	$-0.827918\pi$
$73$	− 642.000i	− 1.02932i	0.857394	−	0.514660i	$-0.172082\pi$
$74$	984.000	1.54578
$75$	0	0
$76$	800.000	1.20745
$77$	434.000i	0.642323i
$78$	744.000i	1.08002i
$79$	−740.000	−1.05388	−0.526940	−	0.849903i	$-0.676661\pi$
$79$	−740.000	−1.05388	−0.526940	+	0.849903i	$0.676661\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	992.000i	1.33595i
$83$	468.000i	0.618912i	0.950914	+	0.309456i	$0.100147\pi$
$83$	468.000i	0.618912i	−0.950914	+	0.309456i	$0.899853\pi$
$84$	−168.000	−0.218218
$85$	0	0
$86$	272.000	0.341052
$87$	− 30.0000i	− 0.0369694i
$88$	0	0
$89$	−200.000	−0.238202	−0.119101	−	0.992882i	$-0.538001\pi$
$89$	−200.000	−0.238202	−0.119101	+	0.992882i	$0.538001\pi$
$90$	0	0
$91$	434.000	0.499951
$92$	336.000i	0.380765i
$93$	144.000i	0.160560i
$94$	−1296.00	−1.42204
$95$	0	0
$96$	768.000	0.816497
$97$	1266.00i	1.32518i	0.748981	+	0.662592i	$0.230544\pi$
$97$	1266.00i	1.32518i	−0.748981	+	0.662592i	$0.769456\pi$
$98$	196.000i	0.202031i
$99$	−558.000	−0.566476
$100$	0	0
$101$	232.000	0.228563	0.114281	−	0.993448i	$-0.463543\pi$
$101$	232.000	0.228563	0.114281	+	0.993448i	$0.463543\pi$
$102$	1008.00i	0.978499i
$103$	− 1792.00i	− 1.71428i	−0.515082	−	0.857141i	$-0.672239\pi$
$103$	− 1792.00i	− 1.71428i	0.515082	−	0.857141i	$-0.327761\pi$
$104$	0	0
$105$	0	0
$106$	1032.00	0.945629
$107$	1906.00i	1.72206i	0.508558	+	0.861028i	$0.330179\pi$
$107$	1906.00i	1.72206i	−0.508558	+	0.861028i	$0.669821\pi$
$108$	− 216.000i	− 0.192450i
$109$	90.0000	0.0790866	0.0395433	−	0.999218i	$-0.487410\pi$
$109$	90.0000	0.0790866	0.0395433	+	0.999218i	$0.487410\pi$
$110$	0	0
$111$	738.000	0.631062
$112$	− 448.000i	− 0.377964i
$113$	458.000i	0.381283i	0.981660	+	0.190642i	$0.0610569\pi$
$113$	458.000i	0.381283i	−0.981660	+	0.190642i	$0.938943\pi$
$114$	1200.00	0.985880
$115$	0	0
$116$	−80.0000	−0.0640329
$117$	558.000i	0.440916i
$118$	480.000i	0.374471i
$119$	588.000	0.452957
$120$	0	0
$121$	2513.00	1.88805
$122$	− 2488.00i	− 1.84634i
$123$	744.000i	0.545400i
$124$	384.000	0.278099
$125$	0	0
$126$	−252.000	−0.178174
$127$	− 804.000i	− 0.561760i	−0.959743	−	0.280880i	$-0.909374\pi$
$127$	− 804.000i	− 0.561760i	0.959743	−	0.280880i	$-0.0906262\pi$
$128$	0	0
$129$	204.000	0.139234
$130$	0	0
$131$	812.000	0.541563	0.270782	−	0.962641i	$-0.412718\pi$
$131$	812.000	0.541563	0.270782	+	0.962641i	$0.412718\pi$
$132$	1488.00i	0.981165i
$133$	− 700.000i	− 0.456374i
$134$	−3616.00	−2.33116
$135$	0	0
$136$	0	0
$137$	− 414.000i	− 0.258178i	−0.991633	−	0.129089i	$-0.958795\pi$
$137$	− 414.000i	− 0.258178i	0.991633	−	0.129089i	$-0.0412053\pi$
$138$	504.000i	0.310894i
$139$	1620.00	0.988537	0.494268	−	0.869309i	$-0.335436\pi$
$139$	1620.00	0.988537	0.494268	+	0.869309i	$0.335436\pi$
$140$	0	0
$141$	−972.000	−0.580547
$142$	2712.00i	1.60272i
$143$	− 3844.00i	− 2.24791i
$144$	576.000	0.333333
$145$	0	0
$146$	−2568.00	−1.45568
$147$	147.000i	0.0824786i
$148$	− 1968.00i	− 1.09303i
$149$	−2370.00	−1.30307	−0.651537	−	0.758617i	$-0.725875\pi$
$149$	−2370.00	−1.30307	−0.651537	+	0.758617i	$0.725875\pi$
$150$	0	0
$151$	−568.000	−0.306114	−0.153057	−	0.988217i	$-0.548912\pi$
$151$	−568.000	−0.306114	−0.153057	+	0.988217i	$0.548912\pi$
$152$	0	0
$153$	756.000i	0.399470i
$154$	1736.00	0.908382
$155$	0	0
$156$	1488.00	0.763688
$157$	266.000i	0.135217i	0.997712	+	0.0676086i	$0.0215369\pi$
$157$	266.000i	0.135217i	−0.997712	+	0.0676086i	$0.978463\pi$
$158$	2960.00i	1.49041i
$159$	774.000	0.386052
$160$	0	0
$161$	294.000	0.143916
$162$	− 324.000i	− 0.157135i
$163$	− 272.000i	− 0.130704i	−0.997862	−	0.0653518i	$-0.979183\pi$
$163$	− 272.000i	− 0.130704i	0.997862	−	0.0653518i	$-0.0208170\pi$
$164$	1984.00	0.944661
$165$	0	0
$166$	1872.00	0.875273
$167$	1876.00i	0.869277i	0.900605	+	0.434638i	$0.143124\pi$
$167$	1876.00i	0.869277i	−0.900605	+	0.434638i	$0.856876\pi$
$168$	0	0
$169$	−1647.00	−0.749659
$170$	0	0
$171$	900.000	0.402484
$172$	− 544.000i	− 0.241161i
$173$	− 152.000i	− 0.0667997i	−0.999442	−	0.0333998i	$-0.989367\pi$
$173$	− 152.000i	− 0.0667997i	0.999442	−	0.0333998i	$-0.0106335\pi$
$174$	−120.000	−0.0522826
$175$	0	0
$176$	−3968.00	−1.69943
$177$	360.000i	0.152877i
$178$	800.000i	0.336868i
$179$	−610.000	−0.254713	−0.127356	−	0.991857i	$-0.540649\pi$
$179$	−610.000	−0.254713	−0.127356	+	0.991857i	$0.540649\pi$
$180$	0	0
$181$	1042.00	0.427907	0.213954	−	0.976844i	$-0.431366\pi$
$181$	1042.00	0.427907	0.213954	+	0.976844i	$0.431366\pi$
$182$	− 1736.00i	− 0.707038i
$183$	− 1866.00i	− 0.753763i
$184$	0	0
$185$	0	0
$186$	576.000	0.227067
$187$	− 5208.00i	− 2.03661i
$188$	2592.00i	1.00554i
$189$	−189.000	−0.0727393
$190$	0	0
$191$	−2038.00	−0.772065	−0.386033	−	0.922485i	$-0.626155\pi$
$191$	−2038.00	−0.772065	−0.386033	+	0.922485i	$0.626155\pi$
$192$	− 1536.00i	− 0.577350i
$193$	− 2602.00i	− 0.970446i	−0.874390	−	0.485223i	$-0.838738\pi$
$193$	− 2602.00i	− 0.970446i	0.874390	−	0.485223i	$-0.161262\pi$
$194$	5064.00	1.87409
$195$	0	0
$196$	392.000	0.142857
$197$	− 2354.00i	− 0.851348i	−0.904877	−	0.425674i	$-0.860037\pi$
$197$	− 2354.00i	− 0.851348i	0.904877	−	0.425674i	$-0.139963\pi$
$198$	2232.00i	0.801118i
$199$	−1680.00	−0.598452	−0.299226	−	0.954182i	$-0.596729\pi$
$199$	−1680.00	−0.598452	−0.299226	+	0.954182i	$0.596729\pi$
$200$	0	0
$201$	−2712.00	−0.951690
$202$	− 928.000i	− 0.323237i
$203$	70.0000i	0.0242022i
$204$	2016.00	0.691903
$205$	0	0
$206$	−7168.00	−2.42436
$207$	378.000i	0.126922i
$208$	3968.00i	1.32275i
$209$	−6200.00	−2.05198
$210$	0	0
$211$	−668.000	−0.217948	−0.108974	−	0.994045i	$-0.534757\pi$
$211$	−668.000	−0.217948	−0.108974	+	0.994045i	$0.534757\pi$
$212$	− 2064.00i	− 0.668661i
$213$	2034.00i	0.654307i
$214$	7624.00	2.43535
$215$	0	0
$216$	0	0
$217$	− 336.000i	− 0.105111i
$218$	− 360.000i	− 0.111845i
$219$	−1926.00	−0.594279
$220$	0	0
$221$	−5208.00	−1.58519
$222$	− 2952.00i	− 0.892456i
$223$	− 1832.00i	− 0.550134i	−0.961425	−	0.275067i	$-0.911300\pi$
$223$	− 1832.00i	− 0.550134i	0.961425	−	0.275067i	$-0.0887000\pi$
$224$	−1792.00	−0.534522
$225$	0	0
$226$	1832.00	0.539216
$227$	− 4944.00i	− 1.44557i	−0.691072	−	0.722786i	$-0.742861\pi$
$227$	− 4944.00i	− 1.44557i	0.691072	−	0.722786i	$-0.257139\pi$
$228$	− 2400.00i	− 0.697122i
$229$	5470.00	1.57846	0.789231	−	0.614096i	$-0.210479\pi$
$229$	5470.00	1.57846	0.789231	+	0.614096i	$0.210479\pi$
$230$	0	0
$231$	1302.00	0.370846
$232$	0	0
$233$	− 2802.00i	− 0.787833i	−0.919146	−	0.393917i	$-0.871120\pi$
$233$	− 2802.00i	− 0.787833i	0.919146	−	0.393917i	$-0.128880\pi$
$234$	2232.00	0.623549
$235$	0	0
$236$	960.000	0.264791
$237$	2220.00i	0.608458i
$238$	− 2352.00i	− 0.640578i
$239$	1170.00	0.316657	0.158328	−	0.987386i	$-0.449390\pi$
$239$	1170.00	0.316657	0.158328	+	0.987386i	$0.449390\pi$
$240$	0	0
$241$	−2338.00	−0.624912	−0.312456	−	0.949932i	$-0.601152\pi$
$241$	−2338.00	−0.624912	−0.312456	+	0.949932i	$0.601152\pi$
$242$	− 10052.0i	− 2.67011i
$243$	− 243.000i	− 0.0641500i
$244$	−4976.00	−1.30556
$245$	0	0
$246$	2976.00	0.771312
$247$	6200.00i	1.59715i
$248$	0	0
$249$	1404.00	0.357329
$250$	0	0
$251$	2792.00	0.702109	0.351055	−	0.936355i	$-0.385823\pi$
$251$	2792.00	0.702109	0.351055	+	0.936355i	$0.385823\pi$
$252$	504.000i	0.125988i
$253$	− 2604.00i	− 0.647083i
$254$	−3216.00	−0.794448
$255$	0	0
$256$	4096.00	1.00000
$257$	− 7024.00i	− 1.70484i	−0.522854	−	0.852422i	$-0.675133\pi$
$257$	− 7024.00i	− 1.70484i	0.522854	−	0.852422i	$-0.324867\pi$
$258$	− 816.000i	− 0.196907i
$259$	−1722.00	−0.413127
$260$	0	0
$261$	−90.0000	−0.0213443
$262$	− 3248.00i	− 0.765886i
$263$	2438.00i	0.571610i	0.958288	+	0.285805i	$0.0922610\pi$
$263$	2438.00i	0.571610i	−0.958288	+	0.285805i	$0.907739\pi$
$264$	0	0
$265$	0	0
$266$	−2800.00	−0.645410
$267$	600.000i	0.137526i
$268$	7232.00i	1.64838i
$269$	6780.00	1.53674	0.768372	−	0.640004i	$-0.221067\pi$
$269$	6780.00	1.53674	0.768372	+	0.640004i	$0.221067\pi$
$270$	0	0
$271$	−1928.00	−0.432168	−0.216084	−	0.976375i	$-0.569329\pi$
$271$	−1928.00	−0.432168	−0.216084	+	0.976375i	$0.569329\pi$
$272$	5376.00i	1.19841i
$273$	− 1302.00i	− 0.288647i
$274$	−1656.00	−0.365119
$275$	0	0
$276$	1008.00	0.219835
$277$	− 5554.00i	− 1.20472i	−0.798224	−	0.602360i	$-0.794227\pi$
$277$	− 5554.00i	− 1.20472i	0.798224	−	0.602360i	$-0.205773\pi$
$278$	− 6480.00i	− 1.39800i
$279$	432.000	0.0926995
$280$	0	0
$281$	1942.00	0.412278	0.206139	−	0.978523i	$-0.433910\pi$
$281$	1942.00	0.412278	0.206139	+	0.978523i	$0.433910\pi$
$282$	3888.00i	0.821018i
$283$	4828.00i	1.01412i	0.861912	+	0.507058i	$0.169267\pi$
$283$	4828.00i	1.01412i	−0.861912	+	0.507058i	$0.830733\pi$
$284$	5424.00	1.13329
$285$	0	0
$286$	−15376.0	−3.17903
$287$	− 1736.00i	− 0.357048i
$288$	− 2304.00i	− 0.471405i
$289$	−2143.00	−0.436190
$290$	0	0
$291$	3798.00	0.765095
$292$	5136.00i	1.02932i
$293$	− 6152.00i	− 1.22663i	−0.789837	−	0.613317i	$-0.789835\pi$
$293$	− 6152.00i	− 1.22663i	0.789837	−	0.613317i	$-0.210165\pi$
$294$	588.000	0.116642
$295$	0	0
$296$	0	0
$297$	1674.00i	0.327055i
$298$	9480.00i	1.84282i
$299$	−2604.00	−0.503656
$300$	0	0
$301$	−476.000	−0.0911501
$302$	2272.00i	0.432910i
$303$	− 696.000i	− 0.131961i
$304$	6400.00	1.20745
$305$	0	0
$306$	3024.00	0.564937
$307$	− 5884.00i	− 1.09387i	−0.837176	−	0.546934i	$-0.815795\pi$
$307$	− 5884.00i	− 1.09387i	0.837176	−	0.546934i	$-0.184205\pi$
$308$	− 3472.00i	− 0.642323i
$309$	−5376.00	−0.989741
$310$	0	0
$311$	9132.00	1.66504	0.832521	−	0.553993i	$-0.186897\pi$
$311$	9132.00	1.66504	0.832521	+	0.553993i	$0.186897\pi$
$312$	0	0
$313$	− 9382.00i	− 1.69426i	−0.531389	−	0.847128i	$-0.678330\pi$
$313$	− 9382.00i	− 1.69426i	0.531389	−	0.847128i	$-0.321670\pi$
$314$	1064.00	0.191226
$315$	0	0
$316$	5920.00	1.05388
$317$	− 3114.00i	− 0.551734i	−0.961196	−	0.275867i	$-0.911035\pi$
$317$	− 3114.00i	− 0.551734i	0.961196	−	0.275867i	$-0.0889649\pi$
$318$	− 3096.00i	− 0.545959i
$319$	620.000	0.108819
$320$	0	0
$321$	5718.00	0.994229
$322$	− 1176.00i	− 0.203528i
$323$	8400.00i	1.44702i
$324$	−648.000	−0.111111
$325$	0	0
$326$	−1088.00	−0.184843
$327$	− 270.000i	− 0.0456607i
$328$	0	0
$329$	2268.00	0.380057
$330$	0	0
$331$	1532.00	0.254400	0.127200	−	0.991877i	$-0.459401\pi$
$331$	1532.00	0.254400	0.127200	+	0.991877i	$0.459401\pi$
$332$	− 3744.00i	− 0.618912i
$333$	− 2214.00i	− 0.364344i
$334$	7504.00	1.22934
$335$	0	0
$336$	−1344.00	−0.218218
$337$	4166.00i	0.673402i	0.941612	+	0.336701i	$0.109311\pi$
$337$	4166.00i	0.673402i	−0.941612	+	0.336701i	$0.890689\pi$
$338$	6588.00i	1.06018i
$339$	1374.00	0.220134
$340$	0	0
$341$	−2976.00	−0.472608
$342$	− 3600.00i	− 0.569198i
$343$	− 343.000i	− 0.0539949i
$344$	0	0
$345$	0	0
$346$	−608.000	−0.0944690
$347$	11366.0i	1.75838i	0.476469	+	0.879191i	$0.341917\pi$
$347$	11366.0i	1.75838i	−0.476469	+	0.879191i	$0.658083\pi$
$348$	240.000i	0.0369694i
$349$	−9310.00	−1.42795	−0.713973	−	0.700174i	$-0.753106\pi$
$349$	−9310.00	−1.42795	−0.713973	+	0.700174i	$0.753106\pi$
$350$	0	0
$351$	1674.00	0.254563
$352$	15872.0i	2.40335i
$353$	− 8572.00i	− 1.29247i	−0.763139	−	0.646234i	$-0.776343\pi$
$353$	− 8572.00i	− 1.29247i	0.763139	−	0.646234i	$-0.223657\pi$
$354$	1440.00	0.216201
$355$	0	0
$356$	1600.00	0.238202
$357$	− 1764.00i	− 0.261515i
$358$	2440.00i	0.360218i
$359$	4790.00	0.704196	0.352098	−	0.935963i	$-0.385468\pi$
$359$	4790.00	0.704196	0.352098	+	0.935963i	$0.385468\pi$
$360$	0	0
$361$	3141.00	0.457938
$362$	− 4168.00i	− 0.605153i
$363$	− 7539.00i	− 1.09007i
$364$	−3472.00	−0.499951
$365$	0	0
$366$	−7464.00	−1.06598
$367$	− 5424.00i	− 0.771473i	−0.922609	−	0.385736i	$-0.873947\pi$
$367$	− 5424.00i	− 0.771473i	0.922609	−	0.385736i	$-0.126053\pi$
$368$	2688.00i	0.380765i
$369$	2232.00	0.314887
$370$	0	0
$371$	−1806.00	−0.252730
$372$	− 1152.00i	− 0.160560i
$373$	1838.00i	0.255142i	0.991829	+	0.127571i	$0.0407181\pi$
$373$	1838.00i	0.255142i	−0.991829	+	0.127571i	$0.959282\pi$
$374$	−20832.0	−2.88021
$375$	0	0
$376$	0	0
$377$	− 620.000i	− 0.0846993i
$378$	756.000i	0.102869i
$379$	4260.00	0.577365	0.288683	−	0.957425i	$-0.406783\pi$
$379$	4260.00	0.577365	0.288683	+	0.957425i	$0.406783\pi$
$380$	0	0
$381$	−2412.00	−0.324332
$382$	8152.00i	1.09187i
$383$	9048.00i	1.20713i	0.797313	+	0.603566i	$0.206254\pi$
$383$	9048.00i	1.20713i	−0.797313	+	0.603566i	$0.793746\pi$
$384$	0	0
$385$	0	0
$386$	−10408.0	−1.37242
$387$	− 612.000i	− 0.0803868i
$388$	− 10128.0i	− 1.32518i
$389$	11490.0	1.49760	0.748800	−	0.662796i	$-0.230631\pi$
$389$	11490.0	1.49760	0.748800	+	0.662796i	$0.230631\pi$
$390$	0	0
$391$	−3528.00	−0.456314
$392$	0	0
$393$	− 2436.00i	− 0.312672i
$394$	−9416.00	−1.20399
$395$	0	0
$396$	4464.00	0.566476
$397$	1866.00i	0.235899i	0.993020	+	0.117949i	$0.0376321\pi$
$397$	1866.00i	0.235899i	−0.993020	+	0.117949i	$0.962368\pi$
$398$	6720.00i	0.846340i
$399$	−2100.00	−0.263487
$400$	0	0
$401$	13662.0	1.70137	0.850683	−	0.525679i	$-0.176189\pi$
$401$	13662.0	1.70137	0.850683	+	0.525679i	$0.176189\pi$
$402$	10848.0i	1.34589i
$403$	2976.00i	0.367854i
$404$	−1856.00	−0.228563
$405$	0	0
$406$	280.000	0.0342270
$407$	15252.0i	1.85753i
$408$	0	0
$409$	13210.0	1.59705	0.798524	−	0.601963i	$-0.205615\pi$
$409$	13210.0	1.59705	0.798524	+	0.601963i	$0.205615\pi$
$410$	0	0
$411$	−1242.00	−0.149059
$412$	14336.0i	1.71428i
$413$	− 840.000i	− 0.100082i
$414$	1512.00	0.179495
$415$	0	0
$416$	15872.0	1.87065
$417$	− 4860.00i	− 0.570732i
$418$	24800.0i	2.90193i
$419$	−6960.00	−0.811499	−0.405750	−	0.913984i	$-0.632990\pi$
$419$	−6960.00	−0.811499	−0.405750	+	0.913984i	$0.632990\pi$
$420$	0	0
$421$	8162.00	0.944873	0.472437	−	0.881365i	$-0.343375\pi$
$421$	8162.00	0.944873	0.472437	+	0.881365i	$0.343375\pi$
$422$	2672.00i	0.308225i
$423$	2916.00i	0.335179i
$424$	0	0
$425$	0	0
$426$	8136.00	0.925330
$427$	4354.00i	0.493454i
$428$	− 15248.0i	− 1.72206i
$429$	−11532.0	−1.29783
$430$	0	0
$431$	16602.0	1.85543	0.927715	−	0.373290i	$-0.121770\pi$
$431$	16602.0	1.85543	0.927715	+	0.373290i	$0.121770\pi$
$432$	− 1728.00i	− 0.192450i
$433$	7738.00i	0.858810i	0.903112	+	0.429405i	$0.141277\pi$
$433$	7738.00i	0.858810i	−0.903112	+	0.429405i	$0.858723\pi$
$434$	−1344.00	−0.148650
$435$	0	0
$436$	−720.000	−0.0790866
$437$	4200.00i	0.459756i
$438$	7704.00i	0.840437i
$439$	840.000	0.0913235	0.0456617	−	0.998957i	$-0.485460\pi$
$439$	840.000	0.0913235	0.0456617	+	0.998957i	$0.485460\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	20832.0i	2.24180i
$443$	6618.00i	0.709776i	0.934909	+	0.354888i	$0.115481\pi$
$443$	6618.00i	0.709776i	−0.934909	+	0.354888i	$0.884519\pi$
$444$	−5904.00	−0.631062
$445$	0	0
$446$	−7328.00	−0.778006
$447$	7110.00i	0.752330i
$448$	3584.00i	0.377964i
$449$	−3090.00	−0.324780	−0.162390	−	0.986727i	$-0.551920\pi$
$449$	−3090.00	−0.324780	−0.162390	+	0.986727i	$0.551920\pi$
$450$	0	0
$451$	−15376.0	−1.60538
$452$	− 3664.00i	− 0.381283i
$453$	1704.00i	0.176735i
$454$	−19776.0	−2.04435
$455$	0	0
$456$	0	0
$457$	− 5914.00i	− 0.605351i	−0.953094	−	0.302675i	$-0.902120\pi$
$457$	− 5914.00i	− 0.605351i	0.953094	−	0.302675i	$-0.0978798\pi$
$458$	− 21880.0i	− 2.23228i
$459$	2268.00	0.230634
$460$	0	0
$461$	−15968.0	−1.61324	−0.806620	−	0.591070i	$-0.798706\pi$
$461$	−15968.0	−1.61324	−0.806620	+	0.591070i	$0.798706\pi$
$462$	− 5208.00i	− 0.524455i
$463$	− 1172.00i	− 0.117640i	−0.998269	−	0.0588202i	$-0.981266\pi$
$463$	− 1172.00i	− 0.117640i	0.998269	−	0.0588202i	$-0.0187338\pi$
$464$	−640.000	−0.0640329
$465$	0	0
$466$	−11208.0	−1.11416
$467$	− 5304.00i	− 0.525567i	−0.964855	−	0.262784i	$-0.915359\pi$
$467$	− 5304.00i	− 0.525567i	0.964855	−	0.262784i	$-0.0846405\pi$
$468$	− 4464.00i	− 0.440916i
$469$	6328.00	0.623027
$470$	0	0
$471$	798.000	0.0780677
$472$	0	0
$473$	4216.00i	0.409835i
$474$	8880.00	0.860489
$475$	0	0
$476$	−4704.00	−0.452957
$477$	− 2322.00i	− 0.222887i
$478$	− 4680.00i	− 0.447821i
$479$	−5740.00	−0.547531	−0.273765	−	0.961796i	$-0.588269\pi$
$479$	−5740.00	−0.547531	−0.273765	+	0.961796i	$0.588269\pi$
$480$	0	0
$481$	15252.0	1.44580
$482$	9352.00i	0.883759i
$483$	− 882.000i	− 0.0830898i
$484$	−20104.0	−1.88805
$485$	0	0
$486$	−972.000	−0.0907218
$487$	− 8944.00i	− 0.832220i	−0.909314	−	0.416110i	$-0.863393\pi$
$487$	− 8944.00i	− 0.832220i	0.909314	−	0.416110i	$-0.136607\pi$
$488$	0	0
$489$	−816.000	−0.0754617
$490$	0	0
$491$	−5558.00	−0.510853	−0.255427	−	0.966828i	$-0.582216\pi$
$491$	−5558.00	−0.510853	−0.255427	+	0.966828i	$0.582216\pi$
$492$	− 5952.00i	− 0.545400i
$493$	− 840.000i	− 0.0767377i
$494$	24800.0	2.25871
$495$	0	0
$496$	3072.00	0.278099
$497$	− 4746.00i	− 0.428344i
$498$	− 5616.00i	− 0.505339i
$499$	19820.0	1.77809	0.889043	−	0.457823i	$-0.151371\pi$
$499$	19820.0	1.77809	0.889043	+	0.457823i	$0.151371\pi$
$500$	0	0
$501$	5628.00	0.501877
$502$	− 11168.0i	− 0.992933i
$503$	1848.00i	0.163814i	0.996640	+	0.0819068i	$0.0261010\pi$
$503$	1848.00i	0.163814i	−0.996640	+	0.0819068i	$0.973899\pi$
$504$	0	0
$505$	0	0
$506$	−10416.0	−0.915114
$507$	4941.00i	0.432816i
$508$	6432.00i	0.561760i
$509$	−340.000	−0.0296075	−0.0148038	−	0.999890i	$-0.504712\pi$
$509$	−340.000	−0.0296075	−0.0148038	+	0.999890i	$0.504712\pi$
$510$	0	0
$511$	4494.00	0.389047
$512$	− 16384.0i	− 1.41421i
$513$	− 2700.00i	− 0.232374i
$514$	−28096.0	−2.41101
$515$	0	0
$516$	−1632.00	−0.139234
$517$	− 20088.0i	− 1.70884i
$518$	6888.00i	0.584250i
$519$	−456.000	−0.0385668
$520$	0	0
$521$	10212.0	0.858725	0.429363	−	0.903132i	$-0.358738\pi$
$521$	10212.0	0.858725	0.429363	+	0.903132i	$0.358738\pi$
$522$	360.000i	0.0301854i
$523$	− 9332.00i	− 0.780229i	−0.920766	−	0.390115i	$-0.872435\pi$
$523$	− 9332.00i	− 0.780229i	0.920766	−	0.390115i	$-0.127565\pi$
$524$	−6496.00	−0.541563
$525$	0	0
$526$	9752.00	0.808379
$527$	4032.00i	0.333276i
$528$	11904.0i	0.981165i
$529$	10403.0	0.855018
$530$	0	0
$531$	1080.00	0.0882637
$532$	5600.00i	0.456374i
$533$	15376.0i	1.24955i
$534$	2400.00	0.194491
$535$	0	0
$536$	0	0
$537$	1830.00i	0.147058i
$538$	− 27120.0i	− 2.17328i
$539$	−3038.00	−0.242775
$540$	0	0
$541$	−8998.00	−0.715073	−0.357536	−	0.933899i	$-0.616383\pi$
$541$	−8998.00	−0.715073	−0.357536	+	0.933899i	$0.616383\pi$
$542$	7712.00i	0.611179i
$543$	− 3126.00i	− 0.247052i
$544$	21504.0	1.69481
$545$	0	0
$546$	−5208.00	−0.408208
$547$	3416.00i	0.267016i	0.991048	+	0.133508i	$0.0426241\pi$
$547$	3416.00i	0.267016i	−0.991048	+	0.133508i	$0.957376\pi$
$548$	3312.00i	0.258178i
$549$	−5598.00	−0.435185
$550$	0	0
$551$	−1000.00	−0.0773166
$552$	0	0
$553$	− 5180.00i	− 0.398329i
$554$	−22216.0	−1.70373
$555$	0	0
$556$	−12960.0	−0.988537
$557$	526.000i	0.0400132i	0.999800	+	0.0200066i	$0.00636872\pi$
$557$	526.000i	0.0400132i	−0.999800	+	0.0200066i	$0.993631\pi$
$558$	− 1728.00i	− 0.131097i
$559$	4216.00	0.318994
$560$	0	0
$561$	−15624.0	−1.17584
$562$	− 7768.00i	− 0.583049i
$563$	− 6712.00i	− 0.502446i	−0.967929	−	0.251223i	$-0.919167\pi$
$563$	− 6712.00i	− 0.502446i	0.967929	−	0.251223i	$-0.0808327\pi$
$564$	7776.00	0.580547
$565$	0	0
$566$	19312.0	1.43418
$567$	567.000i	0.0419961i
$568$	0	0
$569$	−4190.00	−0.308706	−0.154353	−	0.988016i	$-0.549329\pi$
$569$	−4190.00	−0.308706	−0.154353	+	0.988016i	$0.549329\pi$
$570$	0	0
$571$	3032.00	0.222216	0.111108	−	0.993808i	$-0.464560\pi$
$571$	3032.00	0.222216	0.111108	+	0.993808i	$0.464560\pi$
$572$	30752.0i	2.24791i
$573$	6114.00i	0.445752i
$574$	−6944.00	−0.504942
$575$	0	0
$576$	−4608.00	−0.333333
$577$	− 5434.00i	− 0.392063i	−0.980598	−	0.196032i	$-0.937195\pi$
$577$	− 5434.00i	− 0.392063i	0.980598	−	0.196032i	$-0.0628055\pi$
$578$	8572.00i	0.616865i
$579$	−7806.00	−0.560287
$580$	0	0
$581$	−3276.00	−0.233927
$582$	− 15192.0i	− 1.08201i
$583$	15996.0i	1.13634i
$584$	0	0
$585$	0	0
$586$	−24608.0	−1.73472
$587$	− 464.000i	− 0.0326258i	−0.999867	−	0.0163129i	$-0.994807\pi$
$587$	− 464.000i	− 0.0326258i	0.999867	−	0.0163129i	$-0.00519278\pi$
$588$	− 1176.00i	− 0.0824786i
$589$	4800.00	0.335790
$590$	0	0
$591$	−7062.00	−0.491526
$592$	− 15744.0i	− 1.09303i
$593$	11748.0i	0.813546i	0.913529	+	0.406773i	$0.133346\pi$
$593$	11748.0i	0.813546i	−0.913529	+	0.406773i	$0.866654\pi$
$594$	6696.00	0.462526
$595$	0	0
$596$	18960.0	1.30307
$597$	5040.00i	0.345517i
$598$	10416.0i	0.712277i
$599$	−7650.00	−0.521821	−0.260910	−	0.965363i	$-0.584023\pi$
$599$	−7650.00	−0.521821	−0.260910	+	0.965363i	$0.584023\pi$
$600$	0	0
$601$	−22878.0	−1.55277	−0.776384	−	0.630261i	$-0.782948\pi$
$601$	−22878.0	−1.55277	−0.776384	+	0.630261i	$0.782948\pi$
$602$	1904.00i	0.128906i
$603$	8136.00i	0.549459i
$604$	4544.00	0.306114
$605$	0	0
$606$	−2784.00	−0.186621
$607$	− 704.000i	− 0.0470749i	−0.999723	−	0.0235375i	$-0.992507\pi$
$607$	− 704.000i	− 0.0470749i	0.999723	−	0.0235375i	$-0.00749290\pi$
$608$	− 25600.0i	− 1.70759i
$609$	210.000	0.0139731
$610$	0	0
$611$	−20088.0	−1.33007
$612$	− 6048.00i	− 0.399470i
$613$	24958.0i	1.64444i	0.569167	+	0.822222i	$0.307266\pi$
$613$	24958.0i	1.64444i	−0.569167	+	0.822222i	$0.692734\pi$
$614$	−23536.0	−1.54696
$615$	0	0
$616$	0	0
$617$	8826.00i	0.575886i	0.957648	+	0.287943i	$0.0929713\pi$
$617$	8826.00i	0.575886i	−0.957648	+	0.287943i	$0.907029\pi$
$618$	21504.0i	1.39971i
$619$	−21220.0	−1.37787	−0.688937	−	0.724821i	$-0.741922\pi$
$619$	−21220.0	−1.37787	−0.688937	+	0.724821i	$0.741922\pi$
$620$	0	0
$621$	1134.00	0.0732783
$622$	− 36528.0i	− 2.35473i
$623$	− 1400.00i	− 0.0900318i
$624$	11904.0	0.763688
$625$	0	0
$626$	−37528.0	−2.39604
$627$	18600.0i	1.18471i
$628$	− 2128.00i	− 0.135217i
$629$	20664.0	1.30990
$630$	0	0
$631$	−3268.00	−0.206176	−0.103088	−	0.994672i	$-0.532872\pi$
$631$	−3268.00	−0.206176	−0.103088	+	0.994672i	$0.532872\pi$
$632$	0	0
$633$	2004.00i	0.125832i
$634$	−12456.0	−0.780270
$635$	0	0
$636$	−6192.00	−0.386052
$637$	3038.00i	0.188964i
$638$	− 2480.00i	− 0.153894i
$639$	6102.00	0.377764
$640$	0	0
$641$	13062.0	0.804864	0.402432	−	0.915450i	$-0.368165\pi$
$641$	13062.0	0.804864	0.402432	+	0.915450i	$0.368165\pi$
$642$	− 22872.0i	− 1.40605i
$643$	− 28012.0i	− 1.71802i	−0.511961	−	0.859009i	$-0.671081\pi$
$643$	− 28012.0i	− 1.71802i	0.511961	−	0.859009i	$-0.328919\pi$
$644$	−2352.00	−0.143916
$645$	0	0
$646$	33600.0	2.04640
$647$	− 3844.00i	− 0.233575i	−0.993157	−	0.116788i	$-0.962740\pi$
$647$	− 3844.00i	− 0.233575i	0.993157	−	0.116788i	$-0.0372597\pi$
$648$	0	0
$649$	−7440.00	−0.449993
$650$	0	0
$651$	−1008.00	−0.0606861
$652$	2176.00i	0.130704i
$653$	− 28482.0i	− 1.70687i	−0.521198	−	0.853436i	$-0.674515\pi$
$653$	− 28482.0i	− 1.70687i	0.521198	−	0.853436i	$-0.325485\pi$
$654$	−1080.00	−0.0645739
$655$	0	0
$656$	15872.0	0.944661
$657$	5778.00i	0.343107i
$658$	− 9072.00i	− 0.537482i
$659$	9330.00	0.551510	0.275755	−	0.961228i	$-0.411072\pi$
$659$	9330.00	0.551510	0.275755	+	0.961228i	$0.411072\pi$
$660$	0	0
$661$	8782.00	0.516763	0.258381	−	0.966043i	$-0.416811\pi$
$661$	8782.00	0.516763	0.258381	+	0.966043i	$0.416811\pi$
$662$	− 6128.00i	− 0.359776i
$663$	15624.0i	0.915212i
$664$	0	0
$665$	0	0
$666$	−8856.00	−0.515260
$667$	− 420.000i	− 0.0243815i
$668$	− 15008.0i	− 0.869277i
$669$	−5496.00	−0.317620
$670$	0	0
$671$	38564.0	2.21870
$672$	5376.00i	0.308607i
$673$	− 10562.0i	− 0.604956i	−0.953156	−	0.302478i	$-0.902186\pi$
$673$	− 10562.0i	− 0.604956i	0.953156	−	0.302478i	$-0.0978138\pi$
$674$	16664.0	0.952334
$675$	0	0
$676$	13176.0	0.749659
$677$	26016.0i	1.47692i	0.674296	+	0.738461i	$0.264447\pi$
$677$	26016.0i	1.47692i	−0.674296	+	0.738461i	$0.735553\pi$
$678$	− 5496.00i	− 0.311317i
$679$	−8862.00	−0.500872
$680$	0	0
$681$	−14832.0	−0.834601
$682$	11904.0i	0.668369i
$683$	8898.00i	0.498496i	0.968440	+	0.249248i	$0.0801834\pi$
$683$	8898.00i	0.498496i	−0.968440	+	0.249248i	$0.919817\pi$
$684$	−7200.00	−0.402484
$685$	0	0
$686$	−1372.00	−0.0763604
$687$	− 16410.0i	− 0.911325i
$688$	− 4352.00i	− 0.241161i
$689$	15996.0	0.884469
$690$	0	0
$691$	30572.0	1.68309	0.841544	−	0.540189i	$-0.181647\pi$
$691$	30572.0	1.68309	0.841544	+	0.540189i	$0.181647\pi$
$692$	1216.00i	0.0667997i
$693$	− 3906.00i	− 0.214108i
$694$	45464.0	2.48673
$695$	0	0
$696$	0	0
$697$	20832.0i	1.13209i
$698$	37240.0i	2.01942i
$699$	−8406.00	−0.454856
$700$	0	0
$701$	−30618.0	−1.64968	−0.824840	−	0.565366i	$-0.808735\pi$
$701$	−30618.0	−1.64968	−0.824840	+	0.565366i	$0.808735\pi$
$702$	− 6696.00i	− 0.360006i
$703$	− 24600.0i	− 1.31978i
$704$	31744.0	1.69943
$705$	0	0
$706$	−34288.0	−1.82783
$707$	1624.00i	0.0863887i
$708$	− 2880.00i	− 0.152877i
$709$	8130.00	0.430647	0.215323	−	0.976543i	$-0.430919\pi$
$709$	8130.00	0.430647	0.215323	+	0.976543i	$0.430919\pi$
$710$	0	0
$711$	6660.00	0.351293
$712$	0	0
$713$	2016.00i	0.105890i
$714$	−7056.00	−0.369838
$715$	0	0
$716$	4880.00	0.254713
$717$	− 3510.00i	− 0.182822i
$718$	− 19160.0i	− 0.995884i
$719$	27840.0	1.44403	0.722014	−	0.691878i	$-0.243216\pi$
$719$	27840.0	1.44403	0.722014	+	0.691878i	$0.243216\pi$
$720$	0	0
$721$	12544.0	0.647938
$722$	− 12564.0i	− 0.647623i
$723$	7014.00i	0.360793i
$724$	−8336.00	−0.427907
$725$	0	0
$726$	−30156.0	−1.54159
$727$	− 14624.0i	− 0.746044i	−0.927822	−	0.373022i	$-0.878322\pi$
$727$	− 14624.0i	− 0.746044i	0.927822	−	0.373022i	$-0.121678\pi$
$728$	0	0
$729$	−729.000	−0.0370370
$730$	0	0
$731$	5712.00	0.289010
$732$	14928.0i	0.753763i
$733$	− 20862.0i	− 1.05124i	−0.850721	−	0.525618i	$-0.823834\pi$
$733$	− 20862.0i	− 1.05124i	0.850721	−	0.525618i	$-0.176166\pi$
$734$	−21696.0	−1.09103
$735$	0	0
$736$	10752.0	0.538484
$737$	− 56048.0i	− 2.80130i
$738$	− 8928.00i	− 0.445317i
$739$	13920.0	0.692903	0.346452	−	0.938068i	$-0.387386\pi$
$739$	13920.0	0.692903	0.346452	+	0.938068i	$0.387386\pi$
$740$	0	0
$741$	18600.0	0.922116
$742$	7224.00i	0.357414i
$743$	25578.0i	1.26294i	0.775400	+	0.631471i	$0.217548\pi$
$743$	25578.0i	1.26294i	−0.775400	+	0.631471i	$0.782452\pi$
$744$	0	0
$745$	0	0
$746$	7352.00	0.360826
$747$	− 4212.00i	− 0.206304i
$748$	41664.0i	2.03661i
$749$	−13342.0	−0.650876
$750$	0	0
$751$	33472.0	1.62638	0.813189	−	0.581999i	$-0.197729\pi$
$751$	33472.0	1.62638	0.813189	+	0.581999i	$0.197729\pi$
$752$	20736.0i	1.00554i
$753$	− 8376.00i	− 0.405363i
$754$	−2480.00	−0.119783
$755$	0	0
$756$	1512.00	0.0727393
$757$	− 25934.0i	− 1.24516i	−0.782556	−	0.622581i	$-0.786084\pi$
$757$	− 25934.0i	− 1.24516i	0.782556	−	0.622581i	$-0.213916\pi$
$758$	− 17040.0i	− 0.816518i
$759$	−7812.00	−0.373594
$760$	0	0
$761$	26952.0	1.28385	0.641925	−	0.766768i	$-0.278136\pi$
$761$	26952.0	1.28385	0.641925	+	0.766768i	$0.278136\pi$
$762$	9648.00i	0.458675i
$763$	630.000i	0.0298919i
$764$	16304.0	0.772065
$765$	0	0
$766$	36192.0	1.70714
$767$	7440.00i	0.350251i
$768$	− 12288.0i	− 0.577350i
$769$	−23450.0	−1.09965	−0.549824	−	0.835281i	$-0.685305\pi$
$769$	−23450.0	−1.09965	−0.549824	+	0.835281i	$0.685305\pi$
$770$	0	0
$771$	−21072.0	−0.984293
$772$	20816.0i	0.970446i
$773$	39568.0i	1.84109i	0.390637	+	0.920545i	$0.372255\pi$
$773$	39568.0i	1.84109i	−0.390637	+	0.920545i	$0.627745\pi$
$774$	−2448.00	−0.113684
$775$	0	0
$776$	0	0
$777$	5166.00i	0.238519i
$778$	− 45960.0i	− 2.11793i
$779$	24800.0	1.14063
$780$	0	0
$781$	−42036.0	−1.92595
$782$	14112.0i	0.645325i
$783$	270.000i	0.0123231i
$784$	3136.00	0.142857
$785$	0	0
$786$	−9744.00	−0.442184
$787$	12356.0i	0.559649i	0.960051	+	0.279825i	$0.0902763\pi$
$787$	12356.0i	0.559649i	−0.960051	+	0.279825i	$0.909724\pi$
$788$	18832.0i	0.851348i
$789$	7314.00	0.330019
$790$	0	0
$791$	−3206.00	−0.144112
$792$	0	0
$793$	− 38564.0i	− 1.72692i
$794$	7464.00	0.333611
$795$	0	0
$796$	13440.0	0.598452
$797$	21736.0i	0.966033i	0.875611	+	0.483017i	$0.160459\pi$
$797$	21736.0i	0.966033i	−0.875611	+	0.483017i	$0.839541\pi$
$798$	8400.00i	0.372628i
$799$	−27216.0	−1.20505
$800$	0	0
$801$	1800.00	0.0794006
$802$	− 54648.0i	− 2.40609i
$803$	− 39804.0i	− 1.74926i
$804$	21696.0	0.951690
$805$	0	0
$806$	11904.0	0.520224
$807$	− 20340.0i	− 0.887239i
$808$	0	0
$809$	38310.0	1.66490	0.832452	−	0.554097i	$-0.186936\pi$
$809$	38310.0	1.66490	0.832452	+	0.554097i	$0.186936\pi$
$810$	0	0
$811$	2132.00	0.0923115	0.0461558	−	0.998934i	$-0.485303\pi$
$811$	2132.00	0.0923115	0.0461558	+	0.998934i	$0.485303\pi$
$812$	− 560.000i	− 0.0242022i
$813$	5784.00i	0.249513i
$814$	61008.0	2.62694
$815$	0	0
$816$	16128.0	0.691903
$817$	− 6800.00i	− 0.291190i
$818$	− 52840.0i	− 2.25857i
$819$	−3906.00	−0.166650
$820$	0	0
$821$	5002.00	0.212632	0.106316	−	0.994332i	$-0.466094\pi$
$821$	5002.00	0.212632	0.106316	+	0.994332i	$0.466094\pi$
$822$	4968.00i	0.210802i
$823$	− 3612.00i	− 0.152985i	−0.997070	−	0.0764923i	$-0.975628\pi$
$823$	− 3612.00i	− 0.152985i	0.997070	−	0.0764923i	$-0.0243721\pi$
$824$	0	0
$825$	0	0
$826$	−3360.00	−0.141537
$827$	27666.0i	1.16329i	0.813443	+	0.581645i	$0.197591\pi$
$827$	27666.0i	1.16329i	−0.813443	+	0.581645i	$0.802409\pi$
$828$	− 3024.00i	− 0.126922i
$829$	−12890.0	−0.540034	−0.270017	−	0.962856i	$-0.587029\pi$
$829$	−12890.0	−0.540034	−0.270017	+	0.962856i	$0.587029\pi$
$830$	0	0
$831$	−16662.0	−0.695546
$832$	− 31744.0i	− 1.32275i
$833$	4116.00i	0.171202i
$834$	−19440.0	−0.807137
$835$	0	0
$836$	49600.0	2.05198
$837$	− 1296.00i	− 0.0535201i
$838$	27840.0i	1.14763i
$839$	9340.00	0.384330	0.192165	−	0.981363i	$-0.438449\pi$
$839$	9340.00	0.384330	0.192165	+	0.981363i	$0.438449\pi$
$840$	0	0
$841$	−24289.0	−0.995900
$842$	− 32648.0i	− 1.33625i
$843$	− 5826.00i	− 0.238029i
$844$	5344.00	0.217948
$845$	0	0
$846$	11664.0	0.474015
$847$	17591.0i	0.713617i
$848$	− 16512.0i	− 0.668661i
$849$	14484.0	0.585500
$850$	0	0
$851$	10332.0	0.416188
$852$	− 16272.0i	− 0.654307i
$853$	− 33082.0i	− 1.32791i	−0.747773	−	0.663954i	$-0.768877\pi$
$853$	− 33082.0i	− 1.32791i	0.747773	−	0.663954i	$-0.231123\pi$
$854$	17416.0	0.697849
$855$	0	0
$856$	0	0
$857$	− 7544.00i	− 0.300698i	−0.988633	−	0.150349i	$-0.951960\pi$
$857$	− 7544.00i	− 0.300698i	0.988633	−	0.150349i	$-0.0480397\pi$
$858$	46128.0i	1.83541i
$859$	−8180.00	−0.324910	−0.162455	−	0.986716i	$-0.551941\pi$
$859$	−8180.00	−0.324910	−0.162455	+	0.986716i	$0.551941\pi$
$860$	0	0
$861$	−5208.00	−0.206142
$862$	− 66408.0i	− 2.62397i
$863$	10518.0i	0.414875i	0.978248	+	0.207437i	$0.0665123\pi$
$863$	10518.0i	0.414875i	−0.978248	+	0.207437i	$0.933488\pi$
$864$	−6912.00	−0.272166
$865$	0	0
$866$	30952.0	1.21454
$867$	6429.00i	0.251834i
$868$	2688.00i	0.105111i
$869$	−45880.0	−1.79099
$870$	0	0
$871$	−56048.0	−2.18038
$872$	0	0
$873$	− 11394.0i	− 0.441728i
$874$	16800.0	0.650193
$875$	0	0
$876$	15408.0	0.594279
$877$	− 14134.0i	− 0.544209i	−0.962268	−	0.272104i	$-0.912280\pi$
$877$	− 14134.0i	− 0.544209i	0.962268	−	0.272104i	$-0.0877196\pi$
$878$	− 3360.00i	− 0.129151i
$879$	−18456.0	−0.708197
$880$	0	0
$881$	6492.00	0.248265	0.124132	−	0.992266i	$-0.460385\pi$
$881$	6492.00	0.248265	0.124132	+	0.992266i	$0.460385\pi$
$882$	− 1764.00i	− 0.0673435i
$883$	38228.0i	1.45694i	0.685080	+	0.728468i	$0.259767\pi$
$883$	38228.0i	1.45694i	−0.685080	+	0.728468i	$0.740233\pi$
$884$	41664.0	1.58519
$885$	0	0
$886$	26472.0	1.00377
$887$	43076.0i	1.63061i	0.579032	+	0.815305i	$0.303431\pi$
$887$	43076.0i	1.63061i	−0.579032	+	0.815305i	$0.696569\pi$
$888$	0	0
$889$	5628.00	0.212325
$890$	0	0
$891$	5022.00	0.188825
$892$	14656.0i	0.550134i
$893$	32400.0i	1.21414i
$894$	28440.0	1.06396
$895$	0	0
$896$	0	0
$897$	7812.00i	0.290786i
$898$	12360.0i	0.459308i
$899$	−480.000	−0.0178074
$900$	0	0
$901$	21672.0	0.801331
$902$	61504.0i	2.27035i
$903$	1428.00i	0.0526255i
$904$	0	0
$905$	0	0
$906$	6816.00	0.249941
$907$	32236.0i	1.18013i	0.807355	+	0.590065i	$0.200898\pi$
$907$	32236.0i	1.18013i	−0.807355	+	0.590065i	$0.799102\pi$
$908$	39552.0i	1.44557i
$909$	−2088.00	−0.0761877
$910$	0	0
$911$	−46518.0	−1.69178	−0.845889	−	0.533359i	$-0.820930\pi$
$911$	−46518.0	−1.69178	−0.845889	+	0.533359i	$0.820930\pi$
$912$	− 19200.0i	− 0.697122i
$913$	29016.0i	1.05180i
$914$	−23656.0	−0.856095
$915$	0	0
$916$	−43760.0	−1.57846
$917$	5684.00i	0.204692i
$918$	− 9072.00i	− 0.326166i
$919$	−17840.0	−0.640356	−0.320178	−	0.947357i	$-0.603743\pi$
$919$	−17840.0	−0.640356	−0.320178	+	0.947357i	$0.603743\pi$
$920$	0	0
$921$	−17652.0	−0.631545
$922$	63872.0i	2.28147i
$923$	42036.0i	1.49906i
$924$	−10416.0	−0.370846
$925$	0	0
$926$	−4688.00	−0.166369
$927$	16128.0i	0.571427i
$928$	2560.00i	0.0905562i
$929$	−7000.00	−0.247215	−0.123607	−	0.992331i	$-0.539446\pi$
$929$	−7000.00	−0.247215	−0.123607	+	0.992331i	$0.539446\pi$
$930$	0	0
$931$	4900.00	0.172493
$932$	22416.0i	0.787833i
$933$	− 27396.0i	− 0.961313i
$934$	−21216.0	−0.743264
$935$	0	0
$936$	0	0
$937$	− 36114.0i	− 1.25912i	−0.776953	−	0.629559i	$-0.783236\pi$
$937$	− 36114.0i	− 1.25912i	0.776953	−	0.629559i	$-0.216764\pi$
$938$	− 25312.0i	− 0.881094i
$939$	−28146.0	−0.978179
$940$	0	0
$941$	−4748.00	−0.164485	−0.0822425	−	0.996612i	$-0.526208\pi$
$941$	−4748.00	−0.164485	−0.0822425	+	0.996612i	$0.526208\pi$
$942$	− 3192.00i	− 0.110404i
$943$	10416.0i	0.359694i
$944$	7680.00	0.264791
$945$	0	0
$946$	16864.0	0.579594
$947$	− 42694.0i	− 1.46501i	−0.680759	−	0.732507i	$-0.738350\pi$
$947$	− 42694.0i	− 1.46501i	0.680759	−	0.732507i	$-0.261650\pi$
$948$	− 17760.0i	− 0.608458i
$949$	−39804.0	−1.36153
$950$	0	0
$951$	−9342.00	−0.318544
$952$	0	0
$953$	− 16742.0i	− 0.569073i	−0.958665	−	0.284537i	$-0.908160\pi$
$953$	− 16742.0i	− 0.569073i	0.958665	−	0.284537i	$-0.0918397\pi$
$954$	−9288.00	−0.315210
$955$	0	0
$956$	−9360.00	−0.316657
$957$	− 1860.00i	− 0.0628268i
$958$	22960.0i	0.774326i
$959$	2898.00	0.0975822
$960$	0	0
$961$	−27487.0	−0.922661
$962$	− 61008.0i	− 2.04467i
$963$	− 17154.0i	− 0.574019i
$964$	18704.0	0.624912
$965$	0	0
$966$	−3528.00	−0.117507
$967$	9956.00i	0.331089i	0.986202	+	0.165545i	$0.0529382\pi$
$967$	9956.00i	0.331089i	−0.986202	+	0.165545i	$0.947062\pi$
$968$	0	0
$969$	25200.0	0.835439
$970$	0	0
$971$	−26388.0	−0.872123	−0.436061	−	0.899917i	$-0.643627\pi$
$971$	−26388.0	−0.872123	−0.436061	+	0.899917i	$0.643627\pi$
$972$	1944.00i	0.0641500i
$973$	11340.0i	0.373632i
$974$	−35776.0	−1.17694
$975$	0	0
$976$	−39808.0	−1.30556
$977$	786.000i	0.0257383i	0.999917	+	0.0128692i	$0.00409650\pi$
$977$	786.000i	0.0257383i	−0.999917	+	0.0128692i	$0.995904\pi$
$978$	3264.00i	0.106719i
$979$	−12400.0	−0.404807
$980$	0	0
$981$	−810.000	−0.0263622
$982$	22232.0i	0.722456i
$983$	51888.0i	1.68359i	0.539796	+	0.841796i	$0.318501\pi$
$983$	51888.0i	1.68359i	−0.539796	+	0.841796i	$0.681499\pi$
$984$	0	0
$985$	0	0
$986$	−3360.00	−0.108524
$987$	− 6804.00i	− 0.219426i
$988$	− 49600.0i	− 1.59715i
$989$	2856.00	0.0918256
$990$	0	0
$991$	−51928.0	−1.66453	−0.832264	−	0.554379i	$-0.812956\pi$
$991$	−51928.0	−1.66453	−0.832264	+	0.554379i	$0.812956\pi$
$992$	− 12288.0i	− 0.393291i
$993$	− 4596.00i	− 0.146878i
$994$	−18984.0	−0.605771
$995$	0	0
$996$	−11232.0	−0.357329
$997$	386.000i	0.0122615i	0.999981	+	0.00613076i	$0.00195149\pi$
$997$	386.000i	0.0122615i	−0.999981	+	0.00613076i	$0.998049\pi$
$998$	− 79280.0i	− 2.51459i
$999$	−6642.00	−0.210354

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.d.b.274.1		2
5.2	odd	4		21.4.a.b.1.1	✓	1
5.3	odd	4		525.4.a.b.1.1		1
5.4	even	2	inner	525.4.d.b.274.2		2
15.2	even	4		63.4.a.a.1.1		1
15.8	even	4		1575.4.a.k.1.1		1
20.7	even	4		336.4.a.h.1.1		1
35.2	odd	12		147.4.e.c.67.1		2
35.12	even	12		147.4.e.b.67.1		2
35.17	even	12		147.4.e.b.79.1		2
35.27	even	4		147.4.a.g.1.1		1
35.32	odd	12		147.4.e.c.79.1		2
40.27	even	4		1344.4.a.i.1.1		1
40.37	odd	4		1344.4.a.w.1.1		1
60.47	odd	4		1008.4.a.m.1.1		1
105.2	even	12		441.4.e.m.361.1		2
105.17	odd	12		441.4.e.n.226.1		2
105.32	even	12		441.4.e.m.226.1		2
105.47	odd	12		441.4.e.n.361.1		2
105.62	odd	4		441.4.a.b.1.1		1
140.27	odd	4		2352.4.a.l.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.a.b.1.1	✓	1	5.2	odd	4
63.4.a.a.1.1		1	15.2	even	4
147.4.a.g.1.1		1	35.27	even	4
147.4.e.b.67.1		2	35.12	even	12
147.4.e.b.79.1		2	35.17	even	12
147.4.e.c.67.1		2	35.2	odd	12
147.4.e.c.79.1		2	35.32	odd	12
336.4.a.h.1.1		1	20.7	even	4
441.4.a.b.1.1		1	105.62	odd	4
441.4.e.m.226.1		2	105.32	even	12
441.4.e.m.361.1		2	105.2	even	12
441.4.e.n.226.1		2	105.17	odd	12
441.4.e.n.361.1		2	105.47	odd	12
525.4.a.b.1.1		1	5.3	odd	4
525.4.d.b.274.1		2	1.1	even	1	trivial
525.4.d.b.274.2		2	5.4	even	2	inner
1008.4.a.m.1.1		1	60.47	odd	4
1344.4.a.i.1.1		1	40.27	even	4
1344.4.a.w.1.1		1	40.37	odd	4
1575.4.a.k.1.1		1	15.8	even	4
2352.4.a.l.1.1		1	140.27	odd	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	525.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-4.00000i q^{2} -3.00000i q^{3} -8.00000 q^{4} -12.0000 q^{6} +7.00000i q^{7} -9.00000 q^{9} +O(q^{10})\)	\(q-4.00000i q^{2} -3.00000i q^{3} -8.00000 q^{4} -12.0000 q^{6} +7.00000i q^{7} -9.00000 q^{9} +62.0000 q^{11} +24.0000i q^{12} -62.0000i q^{13} +28.0000 q^{14} -64.0000 q^{16} -84.0000i q^{17} +36.0000i q^{18} -100.000 q^{19} +21.0000 q^{21} -248.000i q^{22} -42.0000i q^{23} -248.000 q^{26} +27.0000i q^{27} -56.0000i q^{28} +10.0000 q^{29} -48.0000 q^{31} +256.000i q^{32} -186.000i q^{33} -336.000 q^{34} +72.0000 q^{36} +246.000i q^{37} +400.000i q^{38} -186.000 q^{39} -248.000 q^{41} -84.0000i q^{42} +68.0000i q^{43} -496.000 q^{44} -168.000 q^{46} -324.000i q^{47} +192.000i q^{48} -49.0000 q^{49} -252.000 q^{51} +496.000i q^{52} +258.000i q^{53} +108.000 q^{54} +300.000i q^{57} -40.0000i q^{58} -120.000 q^{59} +622.000 q^{61} +192.000i q^{62} -63.0000i q^{63} +512.000 q^{64} -744.000 q^{66} -904.000i q^{67} +672.000i q^{68} -126.000 q^{69} -678.000 q^{71} -642.000i q^{73} +984.000 q^{74} +800.000 q^{76} +434.000i q^{77} +744.000i q^{78} -740.000 q^{79} +81.0000 q^{81} +992.000i q^{82} +468.000i q^{83} -168.000 q^{84} +272.000 q^{86} -30.0000i q^{87} -200.000 q^{89} +434.000 q^{91} +336.000i q^{92} +144.000i q^{93} -1296.00 q^{94} +768.000 q^{96} +1266.00i q^{97} +196.000i q^{98} -558.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 16 q^{4} - 24 q^{6} - 18 q^{9}+O(q^{10}) \) 2 * q - 16 * q^4 - 24 * q^6 - 18 * q^9	\( 2 q - 16 q^{4} - 24 q^{6} - 18 q^{9} + 124 q^{11} + 56 q^{14} - 128 q^{16} - 200 q^{19} + 42 q^{21} - 496 q^{26} + 20 q^{29} - 96 q^{31} - 672 q^{34} + 144 q^{36} - 372 q^{39} - 496 q^{41} - 992 q^{44} - 336 q^{46} - 98 q^{49} - 504 q^{51} + 216 q^{54} - 240 q^{59} + 1244 q^{61} + 1024 q^{64} - 1488 q^{66} - 252 q^{69} - 1356 q^{71} + 1968 q^{74} + 1600 q^{76} - 1480 q^{79} + 162 q^{81} - 336 q^{84} + 544 q^{86} - 400 q^{89} + 868 q^{91} - 2592 q^{94} + 1536 q^{96} - 1116 q^{99}+O(q^{100}) \) 2 * q - 16 * q^4 - 24 * q^6 - 18 * q^9 + 124 * q^11 + 56 * q^14 - 128 * q^16 - 200 * q^19 + 42 * q^21 - 496 * q^26 + 20 * q^29 - 96 * q^31 - 672 * q^34 + 144 * q^36 - 372 * q^39 - 496 * q^41 - 992 * q^44 - 336 * q^46 - 98 * q^49 - 504 * q^51 + 216 * q^54 - 240 * q^59 + 1244 * q^61 + 1024 * q^64 - 1488 * q^66 - 252 * q^69 - 1356 * q^71 + 1968 * q^74 + 1600 * q^76 - 1480 * q^79 + 162 * q^81 - 336 * q^84 + 544 * q^86 - 400 * q^89 + 868 * q^91 - 2592 * q^94 + 1536 * q^96 - 1116 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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