LMFDB - Embedded newform 3525.2.a.bf.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$28.1472667125$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 9x^{8} + 29x^{7} + 25x^{6} - 91x^{5} - 21x^{4} + 101x^{3} + 6x^{2} - 30x - 4 $ x^10 - 3x^9 - 9x^8 + 29x^7 + 25x^6 - 91x^5 - 21x^4 + 101x^3 + 6x^2 - 30*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 705)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.138546$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.138546 q^{2} +1.00000 q^{3} -1.98081 q^{4} +0.138546 q^{6} -3.39422 q^{7} -0.551524 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.138546 q^{2} +1.00000 q^{3} -1.98081 q^{4} +0.138546 q^{6} -3.39422 q^{7} -0.551524 q^{8} +1.00000 q^{9} -1.27610 q^{11} -1.98081 q^{12} +6.80735 q^{13} -0.470255 q^{14} +3.88520 q^{16} -2.22084 q^{17} +0.138546 q^{18} +2.16976 q^{19} -3.39422 q^{21} -0.176798 q^{22} -2.74977 q^{23} -0.551524 q^{24} +0.943129 q^{26} +1.00000 q^{27} +6.72329 q^{28} -7.04400 q^{29} +2.01078 q^{31} +1.64132 q^{32} -1.27610 q^{33} -0.307688 q^{34} -1.98081 q^{36} +7.28467 q^{37} +0.300610 q^{38} +6.80735 q^{39} -3.25761 q^{41} -0.470255 q^{42} -3.97212 q^{43} +2.52770 q^{44} -0.380969 q^{46} -1.00000 q^{47} +3.88520 q^{48} +4.52073 q^{49} -2.22084 q^{51} -13.4840 q^{52} -6.84455 q^{53} +0.138546 q^{54} +1.87199 q^{56} +2.16976 q^{57} -0.975916 q^{58} -0.794495 q^{59} -5.78822 q^{61} +0.278585 q^{62} -3.39422 q^{63} -7.54300 q^{64} -0.176798 q^{66} -9.51996 q^{67} +4.39905 q^{68} -2.74977 q^{69} +13.4096 q^{71} -0.551524 q^{72} -3.68282 q^{73} +1.00926 q^{74} -4.29786 q^{76} +4.33136 q^{77} +0.943129 q^{78} +2.26082 q^{79} +1.00000 q^{81} -0.451328 q^{82} +2.78900 q^{83} +6.72329 q^{84} -0.550320 q^{86} -7.04400 q^{87} +0.703798 q^{88} +0.120483 q^{89} -23.1056 q^{91} +5.44676 q^{92} +2.01078 q^{93} -0.138546 q^{94} +1.64132 q^{96} +10.6935 q^{97} +0.626328 q^{98} -1.27610 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{2} + 10 q^{3} + 7 q^{4} - 3 q^{6} - 9 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 3 * q^2 + 10 * q^3 + 7 * q^4 - 3 * q^6 - 9 * q^8 + 10 * q^9	$ 10 q - 3 q^{2} + 10 q^{3} + 7 q^{4} - 3 q^{6} - 9 q^{8} + 10 q^{9} - 16 q^{11} + 7 q^{12} - q^{13} - 12 q^{14} - 3 q^{16} - 14 q^{17} - 3 q^{18} - 26 q^{19} - 7 q^{23} - 9 q^{24} - 10 q^{26} + 10 q^{27} + 24 q^{28} - 14 q^{29} - 22 q^{31} - 11 q^{32} - 16 q^{33} - 12 q^{34} + 7 q^{36} - 2 q^{37} + 2 q^{38} - q^{39} - 22 q^{41} - 12 q^{42} + 11 q^{43} - 36 q^{44} - 14 q^{46} - 10 q^{47} - 3 q^{48} + 2 q^{49} - 14 q^{51} - 14 q^{52} - 22 q^{53} - 3 q^{54} - 48 q^{56} - 26 q^{57} + 20 q^{58} - 37 q^{59} - 25 q^{61} + 2 q^{62} - 7 q^{64} + 4 q^{67} - 8 q^{68} - 7 q^{69} - 27 q^{71} - 9 q^{72} - q^{73} + 4 q^{74} - 42 q^{76} - 34 q^{77} - 10 q^{78} + 5 q^{79} + 10 q^{81} + 32 q^{82} - 2 q^{83} + 24 q^{84} - 6 q^{86} - 14 q^{87} + 58 q^{88} + 9 q^{89} - 64 q^{91} - 34 q^{92} - 22 q^{93} + 3 q^{94} - 11 q^{96} + 40 q^{97} - 29 q^{98} - 16 q^{99}+O(q^{100}) $ 10 * q - 3 * q^2 + 10 * q^3 + 7 * q^4 - 3 * q^6 - 9 * q^8 + 10 * q^9 - 16 * q^11 + 7 * q^12 - q^13 - 12 * q^14 - 3 * q^16 - 14 * q^17 - 3 * q^18 - 26 * q^19 - 7 * q^23 - 9 * q^24 - 10 * q^26 + 10 * q^27 + 24 * q^28 - 14 * q^29 - 22 * q^31 - 11 * q^32 - 16 * q^33 - 12 * q^34 + 7 * q^36 - 2 * q^37 + 2 * q^38 - q^39 - 22 * q^41 - 12 * q^42 + 11 * q^43 - 36 * q^44 - 14 * q^46 - 10 * q^47 - 3 * q^48 + 2 * q^49 - 14 * q^51 - 14 * q^52 - 22 * q^53 - 3 * q^54 - 48 * q^56 - 26 * q^57 + 20 * q^58 - 37 * q^59 - 25 * q^61 + 2 * q^62 - 7 * q^64 + 4 * q^67 - 8 * q^68 - 7 * q^69 - 27 * q^71 - 9 * q^72 - q^73 + 4 * q^74 - 42 * q^76 - 34 * q^77 - 10 * q^78 + 5 * q^79 + 10 * q^81 + 32 * q^82 - 2 * q^83 + 24 * q^84 - 6 * q^86 - 14 * q^87 + 58 * q^88 + 9 * q^89 - 64 * q^91 - 34 * q^92 - 22 * q^93 + 3 * q^94 - 11 * q^96 + 40 * q^97 - 29 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.138546	0.0979666	0.0489833	−	0.998800i	$-0.484402\pi$
$2$	0.138546	0.0979666	0.0489833	+	0.998800i	$0.484402\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.98081	−0.990403
$5$	0	0
$5$	0	0
$6$	0.138546	0.0565611
$7$	−3.39422	−1.28289	−0.641447	−	0.767167i	$-0.721666\pi$
$7$	−3.39422	−1.28289	−0.641447	+	0.767167i	$0.721666\pi$
$8$	−0.551524	−0.194993
$9$	1.00000	0.333333
$10$	0	0
$11$	−1.27610	−0.384758	−0.192379	−	0.981321i	$-0.561620\pi$
$11$	−1.27610	−0.384758	−0.192379	+	0.981321i	$0.561620\pi$
$12$	−1.98081	−0.571809
$13$	6.80735	1.88802	0.944010	−	0.329918i	$-0.107021\pi$
$13$	6.80735	1.88802	0.944010	+	0.329918i	$0.107021\pi$
$14$	−0.470255	−0.125681
$15$	0	0
$16$	3.88520	0.971300
$17$	−2.22084	−0.538632	−0.269316	−	0.963052i	$-0.586798\pi$
$17$	−2.22084	−0.538632	−0.269316	+	0.963052i	$0.586798\pi$
$18$	0.138546	0.0326555
$19$	2.16976	0.497776	0.248888	−	0.968532i	$-0.419935\pi$
$19$	2.16976	0.497776	0.248888	+	0.968532i	$0.419935\pi$
$20$	0	0
$21$	−3.39422	−0.740680
$22$	−0.176798	−0.0376934
$23$	−2.74977	−0.573367	−0.286684	−	0.958025i	$-0.592553\pi$
$23$	−2.74977	−0.573367	−0.286684	+	0.958025i	$0.592553\pi$
$24$	−0.551524	−0.112579
$25$	0	0
$26$	0.943129	0.184963
$27$	1.00000	0.192450
$28$	6.72329	1.27058
$29$	−7.04400	−1.30804	−0.654019	−	0.756478i	$-0.726918\pi$
$29$	−7.04400	−1.30804	−0.654019	+	0.756478i	$0.726918\pi$
$30$	0	0
$31$	2.01078	0.361146	0.180573	−	0.983562i	$-0.442205\pi$
$31$	2.01078	0.361146	0.180573	+	0.983562i	$0.442205\pi$
$32$	1.64132	0.290148
$33$	−1.27610	−0.222140
$34$	−0.307688	−0.0527680
$35$	0	0
$36$	−1.98081	−0.330134
$37$	7.28467	1.19759	0.598796	−	0.800901i	$-0.295646\pi$
$37$	7.28467	1.19759	0.598796	+	0.800901i	$0.295646\pi$
$38$	0.300610	0.0487655
$39$	6.80735	1.09005
$40$	0	0
$41$	−3.25761	−0.508754	−0.254377	−	0.967105i	$-0.581870\pi$
$41$	−3.25761	−0.508754	−0.254377	+	0.967105i	$0.581870\pi$
$42$	−0.470255	−0.0725619
$43$	−3.97212	−0.605743	−0.302871	−	0.953031i	$-0.597945\pi$
$43$	−3.97212	−0.605743	−0.302871	+	0.953031i	$0.597945\pi$
$44$	2.52770	0.381065
$45$	0	0
$46$	−0.380969	−0.0561708
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	3.88520	0.560780
$49$	4.52073	0.645819
$50$	0	0
$51$	−2.22084	−0.310979
$52$	−13.4840	−1.86990
$53$	−6.84455	−0.940172	−0.470086	−	0.882621i	$-0.655777\pi$
$53$	−6.84455	−0.940172	−0.470086	+	0.882621i	$0.655777\pi$
$54$	0.138546	0.0188537
$55$	0	0
$56$	1.87199	0.250156
$57$	2.16976	0.287391
$58$	−0.975916	−0.128144
$59$	−0.794495	−0.103434	−0.0517172	−	0.998662i	$-0.516469\pi$
$59$	−0.794495	−0.103434	−0.0517172	+	0.998662i	$0.516469\pi$
$60$	0	0
$61$	−5.78822	−0.741106	−0.370553	−	0.928811i	$-0.620832\pi$
$61$	−5.78822	−0.741106	−0.370553	+	0.928811i	$0.620832\pi$
$62$	0.278585	0.0353803
$63$	−3.39422	−0.427632
$64$	−7.54300	−0.942875
$65$	0	0
$66$	−0.176798	−0.0217623
$67$	−9.51996	−1.16305	−0.581524	−	0.813529i	$-0.697543\pi$
$67$	−9.51996	−1.16305	−0.581524	+	0.813529i	$0.697543\pi$
$68$	4.39905	0.533463
$69$	−2.74977	−0.331034
$70$	0	0
$71$	13.4096	1.59143	0.795715	−	0.605672i	$-0.207096\pi$
$71$	13.4096	1.59143	0.795715	+	0.605672i	$0.207096\pi$
$72$	−0.551524	−0.0649977
$73$	−3.68282	−0.431041	−0.215521	−	0.976499i	$-0.569145\pi$
$73$	−3.68282	−0.431041	−0.215521	+	0.976499i	$0.569145\pi$
$74$	1.00926	0.117324
$75$	0	0
$76$	−4.29786	−0.492999
$77$	4.33136	0.493604
$78$	0.943129	0.106788
$79$	2.26082	0.254363	0.127181	−	0.991879i	$-0.459407\pi$
$79$	2.26082	0.254363	0.127181	+	0.991879i	$0.459407\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−0.451328	−0.0498409
$83$	2.78900	0.306133	0.153066	−	0.988216i	$-0.451085\pi$
$83$	2.78900	0.306133	0.153066	+	0.988216i	$0.451085\pi$
$84$	6.72329	0.733571
$85$	0	0
$86$	−0.550320	−0.0593426
$87$	−7.04400	−0.755196
$88$	0.703798	0.0750251
$89$	0.120483	0.0127712	0.00638558	−	0.999980i	$-0.497967\pi$
$89$	0.120483	0.0127712	0.00638558	+	0.999980i	$0.497967\pi$
$90$	0	0
$91$	−23.1056	−2.42213
$92$	5.44676	0.567864
$93$	2.01078	0.208508
$94$	−0.138546	−0.0142899
$95$	0	0
$96$	1.64132	0.167517
$97$	10.6935	1.08576	0.542881	−	0.839810i	$-0.317333\pi$
$97$	10.6935	1.08576	0.542881	+	0.839810i	$0.317333\pi$
$98$	0.626328	0.0632687
$99$	−1.27610	−0.128253
$100$	0	0
$101$	−17.9942	−1.79049	−0.895244	−	0.445577i	$-0.852999\pi$
$101$	−17.9942	−1.79049	−0.895244	+	0.445577i	$0.852999\pi$
$102$	−0.307688	−0.0304656
$103$	1.79613	0.176978	0.0884889	−	0.996077i	$-0.471796\pi$
$103$	1.79613	0.176978	0.0884889	+	0.996077i	$0.471796\pi$
$104$	−3.75441	−0.368151
$105$	0	0
$106$	−0.948284	−0.0921055
$107$	0.172495	0.0166757	0.00833787	−	0.999965i	$-0.497346\pi$
$107$	0.172495	0.0166757	0.00833787	+	0.999965i	$0.497346\pi$
$108$	−1.98081	−0.190603
$109$	−13.3600	−1.27965	−0.639826	−	0.768520i	$-0.720993\pi$
$109$	−13.3600	−1.27965	−0.639826	+	0.768520i	$0.720993\pi$
$110$	0	0
$111$	7.28467	0.691431
$112$	−13.1872	−1.24608
$113$	−17.4806	−1.64443	−0.822216	−	0.569175i	$-0.807263\pi$
$113$	−17.4806	−1.64443	−0.822216	+	0.569175i	$0.807263\pi$
$114$	0.300610	0.0281548
$115$	0	0
$116$	13.9528	1.29548
$117$	6.80735	0.629340
$118$	−0.110074	−0.0101331
$119$	7.53801	0.691008
$120$	0	0
$121$	−9.37158	−0.851961
$122$	−0.801933	−0.0726036
$123$	−3.25761	−0.293729
$124$	−3.98296	−0.357680
$125$	0	0
$126$	−0.470255	−0.0418936
$127$	−10.9561	−0.972198	−0.486099	−	0.873904i	$-0.661580\pi$
$127$	−10.9561	−0.972198	−0.486099	+	0.873904i	$0.661580\pi$
$128$	−4.32770	−0.382518
$129$	−3.97212	−0.349726
$130$	0	0
$131$	−22.4698	−1.96319	−0.981597	−	0.190965i	$-0.938838\pi$
$131$	−22.4698	−1.96319	−0.981597	+	0.190965i	$0.938838\pi$
$132$	2.52770	0.220008
$133$	−7.36463	−0.638595
$134$	−1.31895	−0.113940
$135$	0	0
$136$	1.22484	0.105030
$137$	10.2364	0.874554	0.437277	−	0.899327i	$-0.355943\pi$
$137$	10.2364	0.874554	0.437277	+	0.899327i	$0.355943\pi$
$138$	−0.380969	−0.0324303
$139$	−14.1537	−1.20050	−0.600250	−	0.799813i	$-0.704932\pi$
$139$	−14.1537	−1.20050	−0.600250	+	0.799813i	$0.704932\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	1.85785	0.155907
$143$	−8.68684	−0.726430
$144$	3.88520	0.323767
$145$	0	0
$146$	−0.510238	−0.0422276
$147$	4.52073	0.372864
$148$	−14.4295	−1.18610
$149$	−19.0861	−1.56359	−0.781795	−	0.623535i	$-0.785696\pi$
$149$	−19.0861	−1.56359	−0.781795	+	0.623535i	$0.785696\pi$
$150$	0	0
$151$	−21.9633	−1.78735	−0.893674	−	0.448717i	$-0.851881\pi$
$151$	−21.9633	−1.78735	−0.893674	+	0.448717i	$0.851881\pi$
$152$	−1.19667	−0.0970629
$153$	−2.22084	−0.179544
$154$	0.600091	0.0483567
$155$	0	0
$156$	−13.4840	−1.07959
$157$	10.4105	0.830846	0.415423	−	0.909628i	$-0.363634\pi$
$157$	10.4105	0.830846	0.415423	+	0.909628i	$0.363634\pi$
$158$	0.313228	0.0249190
$159$	−6.84455	−0.542808
$160$	0	0
$161$	9.33333	0.735570
$162$	0.138546	0.0108852
$163$	5.60941	0.439363	0.219681	−	0.975572i	$-0.429498\pi$
$163$	5.60941	0.439363	0.219681	+	0.975572i	$0.429498\pi$
$164$	6.45269	0.503871
$165$	0	0
$166$	0.386405	0.0299908
$167$	−8.36242	−0.647104	−0.323552	−	0.946210i	$-0.604877\pi$
$167$	−8.36242	−0.647104	−0.323552	+	0.946210i	$0.604877\pi$
$168$	1.87199	0.144427
$169$	33.3400	2.56462
$170$	0	0
$171$	2.16976	0.165925
$172$	7.86800	0.599929
$173$	−20.9614	−1.59367	−0.796834	−	0.604199i	$-0.793493\pi$
$173$	−20.9614	−1.59367	−0.796834	+	0.604199i	$0.793493\pi$
$174$	−0.975916	−0.0739840
$175$	0	0
$176$	−4.95789	−0.373715
$177$	−0.794495	−0.0597179
$178$	0.0166924	0.00125115
$179$	11.3133	0.845598	0.422799	−	0.906224i	$-0.361048\pi$
$179$	11.3133	0.845598	0.422799	+	0.906224i	$0.361048\pi$
$180$	0	0
$181$	22.4271	1.66700	0.833498	−	0.552522i	$-0.186335\pi$
$181$	22.4271	1.66700	0.833498	+	0.552522i	$0.186335\pi$
$182$	−3.20119	−0.237288
$183$	−5.78822	−0.427878
$184$	1.51656	0.111803
$185$	0	0
$186$	0.278585	0.0204268
$187$	2.83400	0.207243
$188$	1.98081	0.144465
$189$	−3.39422	−0.246893
$190$	0	0
$191$	−10.1248	−0.732607	−0.366303	−	0.930496i	$-0.619377\pi$
$191$	−10.1248	−0.732607	−0.366303	+	0.930496i	$0.619377\pi$
$192$	−7.54300	−0.544369
$193$	1.88964	0.136019	0.0680095	−	0.997685i	$-0.478335\pi$
$193$	1.88964	0.136019	0.0680095	+	0.997685i	$0.478335\pi$
$194$	1.48154	0.106368
$195$	0	0
$196$	−8.95469	−0.639621
$197$	17.5796	1.25250	0.626249	−	0.779623i	$-0.284589\pi$
$197$	17.5796	1.25250	0.626249	+	0.779623i	$0.284589\pi$
$198$	−0.176798	−0.0125645
$199$	−12.6482	−0.896605	−0.448303	−	0.893882i	$-0.647971\pi$
$199$	−12.6482	−0.896605	−0.448303	+	0.893882i	$0.647971\pi$
$200$	0	0
$201$	−9.51996	−0.671486
$202$	−2.49302	−0.175408
$203$	23.9089	1.67807
$204$	4.39905	0.307995
$205$	0	0
$206$	0.248846	0.0173379
$207$	−2.74977	−0.191122
$208$	26.4479	1.83383
$209$	−2.76882	−0.191523
$210$	0	0
$211$	−25.2419	−1.73772	−0.868862	−	0.495055i	$-0.835148\pi$
$211$	−25.2419	−1.73772	−0.868862	+	0.495055i	$0.835148\pi$
$212$	13.5577	0.931148
$213$	13.4096	0.918812
$214$	0.0238985	0.00163367
$215$	0	0
$216$	−0.551524	−0.0375264
$217$	−6.82502	−0.463313
$218$	−1.85096	−0.125363
$219$	−3.68282	−0.248862
$220$	0	0
$221$	−15.1180	−1.01695
$222$	1.00926	0.0677371
$223$	12.9533	0.867415	0.433708	−	0.901054i	$-0.357205\pi$
$223$	12.9533	0.867415	0.433708	+	0.901054i	$0.357205\pi$
$224$	−5.57102	−0.372229
$225$	0	0
$226$	−2.42186	−0.161100
$227$	−15.3479	−1.01868	−0.509340	−	0.860566i	$-0.670110\pi$
$227$	−15.3479	−1.01868	−0.509340	+	0.860566i	$0.670110\pi$
$228$	−4.29786	−0.284633
$229$	−15.9788	−1.05591	−0.527954	−	0.849273i	$-0.677041\pi$
$229$	−15.9788	−1.05591	−0.527954	+	0.849273i	$0.677041\pi$
$230$	0	0
$231$	4.33136	0.284982
$232$	3.88493	0.255058
$233$	23.8907	1.56513	0.782567	−	0.622567i	$-0.213910\pi$
$233$	23.8907	1.56513	0.782567	+	0.622567i	$0.213910\pi$
$234$	0.943129	0.0616543
$235$	0	0
$236$	1.57374	0.102442
$237$	2.26082	0.146856
$238$	1.04436	0.0676958
$239$	−4.31375	−0.279033	−0.139517	−	0.990220i	$-0.544555\pi$
$239$	−4.31375	−0.279033	−0.139517	+	0.990220i	$0.544555\pi$
$240$	0	0
$241$	−9.79805	−0.631148	−0.315574	−	0.948901i	$-0.602197\pi$
$241$	−9.79805	−0.631148	−0.315574	+	0.948901i	$0.602197\pi$
$242$	−1.29839	−0.0834638
$243$	1.00000	0.0641500
$244$	11.4653	0.733993
$245$	0	0
$246$	−0.451328	−0.0287756
$247$	14.7703	0.939811
$248$	−1.10899	−0.0704210
$249$	2.78900	0.176746
$250$	0	0
$251$	11.7481	0.741534	0.370767	−	0.928726i	$-0.379095\pi$
$251$	11.7481	0.741534	0.370767	+	0.928726i	$0.379095\pi$
$252$	6.72329	0.423527
$253$	3.50898	0.220607
$254$	−1.51792	−0.0952429
$255$	0	0
$256$	14.4864	0.905401
$257$	30.2719	1.88831	0.944153	−	0.329506i	$-0.106882\pi$
$257$	30.2719	1.88831	0.944153	+	0.329506i	$0.106882\pi$
$258$	−0.550320	−0.0342615
$259$	−24.7258	−1.53639
$260$	0	0
$261$	−7.04400	−0.436013
$262$	−3.11309	−0.192327
$263$	−12.4160	−0.765604	−0.382802	−	0.923830i	$-0.625041\pi$
$263$	−12.4160	−0.765604	−0.382802	+	0.923830i	$0.625041\pi$
$264$	0.703798	0.0433158
$265$	0	0
$266$	−1.02034	−0.0625610
$267$	0.120483	0.00737343
$268$	18.8572	1.15189
$269$	−0.633678	−0.0386360	−0.0193180	−	0.999813i	$-0.506149\pi$
$269$	−0.633678	−0.0386360	−0.0193180	+	0.999813i	$0.506149\pi$
$270$	0	0
$271$	11.0636	0.672067	0.336034	−	0.941850i	$-0.390914\pi$
$271$	11.0636	0.672067	0.336034	+	0.941850i	$0.390914\pi$
$272$	−8.62840	−0.523173
$273$	−23.1056	−1.39842
$274$	1.41821	0.0856772
$275$	0	0
$276$	5.44676	0.327857
$277$	6.59406	0.396199	0.198099	−	0.980182i	$-0.436523\pi$
$277$	6.59406	0.396199	0.198099	+	0.980182i	$0.436523\pi$
$278$	−1.96093	−0.117609
$279$	2.01078	0.120382
$280$	0	0
$281$	4.22131	0.251822	0.125911	−	0.992042i	$-0.459815\pi$
$281$	4.22131	0.251822	0.125911	+	0.992042i	$0.459815\pi$
$282$	−0.138546	−0.00825028
$283$	10.9411	0.650378	0.325189	−	0.945649i	$-0.394572\pi$
$283$	10.9411	0.650378	0.325189	+	0.945649i	$0.394572\pi$
$284$	−26.5618	−1.57616
$285$	0	0
$286$	−1.20352	−0.0711659
$287$	11.0571	0.652677
$288$	1.64132	0.0967160
$289$	−12.0679	−0.709875
$290$	0	0
$291$	10.6935	0.626865
$292$	7.29494	0.426904
$293$	20.4785	1.19637	0.598184	−	0.801359i	$-0.295889\pi$
$293$	20.4785	1.19637	0.598184	+	0.801359i	$0.295889\pi$
$294$	0.626328	0.0365282
$295$	0	0
$296$	−4.01767	−0.233522
$297$	−1.27610	−0.0740467
$298$	−2.64429	−0.153180
$299$	−18.7187	−1.08253
$300$	0	0
$301$	13.4823	0.777104
$302$	−3.04292	−0.175100
$303$	−17.9942	−1.03374
$304$	8.42993	0.483490
$305$	0	0
$306$	−0.307688	−0.0175893
$307$	31.9856	1.82551	0.912756	−	0.408505i	$-0.133950\pi$
$307$	31.9856	1.82551	0.912756	+	0.408505i	$0.133950\pi$
$308$	−8.57957	−0.488866
$309$	1.79613	0.102178
$310$	0	0
$311$	−19.5542	−1.10882	−0.554409	−	0.832244i	$-0.687056\pi$
$311$	−19.5542	−1.10882	−0.554409	+	0.832244i	$0.687056\pi$
$312$	−3.75441	−0.212552
$313$	15.1931	0.858766	0.429383	−	0.903123i	$-0.358731\pi$
$313$	15.1931	0.858766	0.429383	+	0.903123i	$0.358731\pi$
$314$	1.44233	0.0813952
$315$	0	0
$316$	−4.47825	−0.251921
$317$	−26.3996	−1.48275	−0.741375	−	0.671091i	$-0.765826\pi$
$317$	−26.3996	−1.48275	−0.741375	+	0.671091i	$0.765826\pi$
$318$	−0.948284	−0.0531771
$319$	8.98883	0.503278
$320$	0	0
$321$	0.172495	0.00962774
$322$	1.29309	0.0720613
$323$	−4.81868	−0.268118
$324$	−1.98081	−0.110045
$325$	0	0
$326$	0.777160	0.0430429
$327$	−13.3600	−0.738807
$328$	1.79665	0.0992034
$329$	3.39422	0.187129
$330$	0	0
$331$	7.75385	0.426190	0.213095	−	0.977031i	$-0.431646\pi$
$331$	7.75385	0.426190	0.213095	+	0.977031i	$0.431646\pi$
$332$	−5.52447	−0.303195
$333$	7.28467	0.399198
$334$	−1.15858	−0.0633946
$335$	0	0
$336$	−13.1872	−0.719422
$337$	16.5309	0.900495	0.450247	−	0.892904i	$-0.351336\pi$
$337$	16.5309	0.900495	0.450247	+	0.892904i	$0.351336\pi$
$338$	4.61912	0.251247
$339$	−17.4806	−0.949414
$340$	0	0
$341$	−2.56595	−0.138954
$342$	0.300610	0.0162552
$343$	8.41518	0.454377
$344$	2.19072	0.118116
$345$	0	0
$346$	−2.90412	−0.156126
$347$	−5.89088	−0.316239	−0.158120	−	0.987420i	$-0.550543\pi$
$347$	−5.89088	−0.316239	−0.158120	+	0.987420i	$0.550543\pi$
$348$	13.9528	0.747948
$349$	15.5504	0.832393	0.416197	−	0.909275i	$-0.363363\pi$
$349$	15.5504	0.832393	0.416197	+	0.909275i	$0.363363\pi$
$350$	0	0
$351$	6.80735	0.363349
$352$	−2.09449	−0.111637
$353$	2.28406	0.121568	0.0607841	−	0.998151i	$-0.480640\pi$
$353$	2.28406	0.121568	0.0607841	+	0.998151i	$0.480640\pi$
$354$	−0.110074	−0.00585036
$355$	0	0
$356$	−0.238653	−0.0126486
$357$	7.53801	0.398954
$358$	1.56741	0.0828404
$359$	−16.9622	−0.895233	−0.447617	−	0.894226i	$-0.647727\pi$
$359$	−16.9622	−0.895233	−0.447617	+	0.894226i	$0.647727\pi$
$360$	0	0
$361$	−14.2922	−0.752219
$362$	3.10718	0.163310
$363$	−9.37158	−0.491880
$364$	45.7678	2.39888
$365$	0	0
$366$	−0.801933	−0.0419177
$367$	−29.7456	−1.55271	−0.776354	−	0.630297i	$-0.782933\pi$
$367$	−29.7456	−1.55271	−0.776354	+	0.630297i	$0.782933\pi$
$368$	−10.6834	−0.556911
$369$	−3.25761	−0.169585
$370$	0	0
$371$	23.2319	1.20614
$372$	−3.98296	−0.206507
$373$	14.1285	0.731546	0.365773	−	0.930704i	$-0.380805\pi$
$373$	14.1285	0.731546	0.365773	+	0.930704i	$0.380805\pi$
$374$	0.392639	0.0203029
$375$	0	0
$376$	0.551524	0.0284427
$377$	−47.9510	−2.46960
$378$	−0.470255	−0.0241873
$379$	−11.5694	−0.594281	−0.297141	−	0.954834i	$-0.596033\pi$
$379$	−11.5694	−0.594281	−0.297141	+	0.954834i	$0.596033\pi$
$380$	0	0
$381$	−10.9561	−0.561299
$382$	−1.40275	−0.0717710
$383$	−5.10445	−0.260825	−0.130412	−	0.991460i	$-0.541630\pi$
$383$	−5.10445	−0.260825	−0.130412	+	0.991460i	$0.541630\pi$
$384$	−4.32770	−0.220847
$385$	0	0
$386$	0.261801	0.0133253
$387$	−3.97212	−0.201914
$388$	−21.1818	−1.07534
$389$	31.4474	1.59445	0.797223	−	0.603685i	$-0.206301\pi$
$389$	31.4474	1.59445	0.797223	+	0.603685i	$0.206301\pi$
$390$	0	0
$391$	6.10680	0.308834
$392$	−2.49329	−0.125930
$393$	−22.4698	−1.13345
$394$	2.43558	0.122703
$395$	0	0
$396$	2.52770	0.127022
$397$	1.12039	0.0562306	0.0281153	−	0.999605i	$-0.491049\pi$
$397$	1.12039	0.0562306	0.0281153	+	0.999605i	$0.491049\pi$
$398$	−1.75235	−0.0878374
$399$	−7.36463	−0.368693
$400$	0	0
$401$	0.0480193	0.00239797	0.00119899	−	0.999999i	$-0.499618\pi$
$401$	0.0480193	0.00239797	0.00119899	+	0.999999i	$0.499618\pi$
$402$	−1.31895	−0.0657832
$403$	13.6881	0.681851
$404$	35.6430	1.77330
$405$	0	0
$406$	3.31247	0.164395
$407$	−9.29595	−0.460783
$408$	1.22484	0.0606388
$409$	12.0556	0.596111	0.298056	−	0.954548i	$-0.403662\pi$
$409$	12.0556	0.596111	0.298056	+	0.954548i	$0.403662\pi$
$410$	0	0
$411$	10.2364	0.504924
$412$	−3.55778	−0.175279
$413$	2.69669	0.132695
$414$	−0.380969	−0.0187236
$415$	0	0
$416$	11.1731	0.547805
$417$	−14.1537	−0.693109
$418$	−0.383608	−0.0187629
$419$	−0.586311	−0.0286432	−0.0143216	−	0.999897i	$-0.504559\pi$
$419$	−0.586311	−0.0286432	−0.0143216	+	0.999897i	$0.504559\pi$
$420$	0	0
$421$	23.4173	1.14129	0.570646	−	0.821196i	$-0.306693\pi$
$421$	23.4173	1.14129	0.570646	+	0.821196i	$0.306693\pi$
$422$	−3.49716	−0.170239
$423$	−1.00000	−0.0486217
$424$	3.77493	0.183327
$425$	0	0
$426$	1.85785	0.0900129
$427$	19.6465	0.950761
$428$	−0.341679	−0.0165157
$429$	−8.68684	−0.419405
$430$	0	0
$431$	−20.0579	−0.966154	−0.483077	−	0.875578i	$-0.660481\pi$
$431$	−20.0579	−0.966154	−0.483077	+	0.875578i	$0.660481\pi$
$432$	3.88520	0.186927
$433$	28.8533	1.38660	0.693301	−	0.720649i	$-0.256156\pi$
$433$	28.8533	1.38660	0.693301	+	0.720649i	$0.256156\pi$
$434$	−0.945578	−0.0453892
$435$	0	0
$436$	26.4635	1.26737
$437$	−5.96634	−0.285409
$438$	−0.510238	−0.0243801
$439$	−9.61973	−0.459125	−0.229562	−	0.973294i	$-0.573729\pi$
$439$	−9.61973	−0.459125	−0.229562	+	0.973294i	$0.573729\pi$
$440$	0	0
$441$	4.52073	0.215273
$442$	−2.09454	−0.0996270
$443$	−19.8199	−0.941671	−0.470836	−	0.882221i	$-0.656047\pi$
$443$	−19.8199	−0.941671	−0.470836	+	0.882221i	$0.656047\pi$
$444$	−14.4295	−0.684795
$445$	0	0
$446$	1.79462	0.0849777
$447$	−19.0861	−0.902739
$448$	25.6026	1.20961
$449$	4.42469	0.208814	0.104407	−	0.994535i	$-0.466706\pi$
$449$	4.42469	0.208814	0.104407	+	0.994535i	$0.466706\pi$
$450$	0	0
$451$	4.15703	0.195747
$452$	34.6256	1.62865
$453$	−21.9633	−1.03193
$454$	−2.12639	−0.0997966
$455$	0	0
$456$	−1.19667	−0.0560393
$457$	−16.6281	−0.777828	−0.388914	−	0.921274i	$-0.627150\pi$
$457$	−16.6281	−0.777828	−0.388914	+	0.921274i	$0.627150\pi$
$458$	−2.21379	−0.103444
$459$	−2.22084	−0.103660
$460$	0	0
$461$	7.07727	0.329621	0.164811	−	0.986325i	$-0.447299\pi$
$461$	7.07727	0.329621	0.164811	+	0.986325i	$0.447299\pi$
$462$	0.600091	0.0279188
$463$	−40.5694	−1.88542	−0.942710	−	0.333612i	$-0.891732\pi$
$463$	−40.5694	−1.88542	−0.942710	+	0.333612i	$0.891732\pi$
$464$	−27.3673	−1.27050
$465$	0	0
$466$	3.30996	0.153331
$467$	−29.5132	−1.36571	−0.682854	−	0.730555i	$-0.739261\pi$
$467$	−29.5132	−1.36571	−0.682854	+	0.730555i	$0.739261\pi$
$468$	−13.4840	−0.623300
$469$	32.3128	1.49207
$470$	0	0
$471$	10.4105	0.479689
$472$	0.438182	0.0201690
$473$	5.06881	0.233064
$474$	0.313228	0.0143870
$475$	0	0
$476$	−14.9313	−0.684377
$477$	−6.84455	−0.313391
$478$	−0.597652	−0.0273359
$479$	19.2630	0.880150	0.440075	−	0.897961i	$-0.354952\pi$
$479$	19.2630	0.880150	0.440075	+	0.897961i	$0.354952\pi$
$480$	0	0
$481$	49.5893	2.26108
$482$	−1.35748	−0.0618314
$483$	9.33333	0.424681
$484$	18.5633	0.843785
$485$	0	0
$486$	0.138546	0.00628456
$487$	9.31092	0.421918	0.210959	−	0.977495i	$-0.432341\pi$
$487$	9.31092	0.421918	0.210959	+	0.977495i	$0.432341\pi$
$488$	3.19234	0.144510
$489$	5.60941	0.253666
$490$	0	0
$491$	−12.4983	−0.564039	−0.282019	−	0.959409i	$-0.591004\pi$
$491$	−12.4983	−0.564039	−0.282019	+	0.959409i	$0.591004\pi$
$492$	6.45269	0.290910
$493$	15.6436	0.704551
$494$	2.04636	0.0920701
$495$	0	0
$496$	7.81227	0.350781
$497$	−45.5152	−2.04164
$498$	0.386405	0.0173152
$499$	−40.3997	−1.80854	−0.904271	−	0.426960i	$-0.859585\pi$
$499$	−40.3997	−1.80854	−0.904271	+	0.426960i	$0.859585\pi$
$500$	0	0
$501$	−8.36242	−0.373605
$502$	1.62765	0.0726456
$503$	3.68747	0.164416	0.0822080	−	0.996615i	$-0.473803\pi$
$503$	3.68747	0.164416	0.0822080	+	0.996615i	$0.473803\pi$
$504$	1.87199	0.0833852
$505$	0	0
$506$	0.486154	0.0216122
$507$	33.3400	1.48068
$508$	21.7019	0.962867
$509$	42.4461	1.88139	0.940694	−	0.339255i	$-0.110175\pi$
$509$	42.4461	1.88139	0.940694	+	0.339255i	$0.110175\pi$
$510$	0	0
$511$	12.5003	0.552980
$512$	10.6624	0.471217
$513$	2.16976	0.0957971
$514$	4.19404	0.184991
$515$	0	0
$516$	7.86800	0.346369
$517$	1.27610	0.0561227
$518$	−3.42565	−0.150515
$519$	−20.9614	−0.920104
$520$	0	0
$521$	−6.88875	−0.301801	−0.150901	−	0.988549i	$-0.548217\pi$
$521$	−6.88875	−0.301801	−0.150901	+	0.988549i	$0.548217\pi$
$522$	−0.975916	−0.0427147
$523$	−14.2137	−0.621521	−0.310761	−	0.950488i	$-0.600584\pi$
$523$	−14.2137	−0.621521	−0.310761	+	0.950488i	$0.600584\pi$
$524$	44.5082	1.94435
$525$	0	0
$526$	−1.72018	−0.0750036
$527$	−4.46561	−0.194525
$528$	−4.95789	−0.215765
$529$	−15.4388	−0.671250
$530$	0	0
$531$	−0.794495	−0.0344781
$532$	14.5879	0.632466
$533$	−22.1757	−0.960536
$534$	0.0166924	0.000722350 0
$535$	0	0
$536$	5.25048	0.226786
$537$	11.3133	0.488206
$538$	−0.0877934	−0.00378504
$539$	−5.76890	−0.248484
$540$	0	0
$541$	24.8134	1.06681	0.533405	−	0.845860i	$-0.320912\pi$
$541$	24.8134	1.06681	0.533405	+	0.845860i	$0.320912\pi$
$542$	1.53282	0.0658401
$543$	22.4271	0.962441
$544$	−3.64512	−0.156283
$545$	0	0
$546$	−3.20119	−0.136998
$547$	1.68677	0.0721211	0.0360606	−	0.999350i	$-0.488519\pi$
$547$	1.68677	0.0721211	0.0360606	+	0.999350i	$0.488519\pi$
$548$	−20.2763	−0.866161
$549$	−5.78822	−0.247035
$550$	0	0
$551$	−15.2838	−0.651110
$552$	1.51656	0.0645493
$553$	−7.67374	−0.326320
$554$	0.913580	0.0388143
$555$	0	0
$556$	28.0357	1.18898
$557$	10.5190	0.445702	0.222851	−	0.974852i	$-0.428464\pi$
$557$	10.5190	0.445702	0.222851	+	0.974852i	$0.428464\pi$
$558$	0.278585	0.0117934
$559$	−27.0396	−1.14365
$560$	0	0
$561$	2.83400	0.119652
$562$	0.584845	0.0246702
$563$	11.1707	0.470789	0.235395	−	0.971900i	$-0.424362\pi$
$563$	11.1707	0.470789	0.235395	+	0.971900i	$0.424362\pi$
$564$	1.98081	0.0834069
$565$	0	0
$566$	1.51584	0.0637154
$567$	−3.39422	−0.142544
$568$	−7.39572	−0.310318
$569$	−5.71846	−0.239730	−0.119865	−	0.992790i	$-0.538246\pi$
$569$	−5.71846	−0.239730	−0.119865	+	0.992790i	$0.538246\pi$
$570$	0	0
$571$	−19.5685	−0.818917	−0.409458	−	0.912329i	$-0.634282\pi$
$571$	−19.5685	−0.818917	−0.409458	+	0.912329i	$0.634282\pi$
$572$	17.2069	0.719458
$573$	−10.1248	−0.422971
$574$	1.53191	0.0639406
$575$	0	0
$576$	−7.54300	−0.314292
$577$	27.7135	1.15373	0.576865	−	0.816840i	$-0.304276\pi$
$577$	27.7135	1.15373	0.576865	+	0.816840i	$0.304276\pi$
$578$	−1.67195	−0.0695441
$579$	1.88964	0.0785306
$580$	0	0
$581$	−9.46650	−0.392736
$582$	1.48154	0.0614118
$583$	8.73432	0.361738
$584$	2.03116	0.0840500
$585$	0	0
$586$	2.83721	0.117204
$587$	−32.8229	−1.35475	−0.677373	−	0.735640i	$-0.736881\pi$
$587$	−32.8229	−1.35475	−0.677373	+	0.735640i	$0.736881\pi$
$588$	−8.95469	−0.369285
$589$	4.36290	0.179770
$590$	0	0
$591$	17.5796	0.723130
$592$	28.3024	1.16322
$593$	0.177398	0.00728486	0.00364243	−	0.999993i	$-0.498841\pi$
$593$	0.177398	0.00728486	0.00364243	+	0.999993i	$0.498841\pi$
$594$	−0.176798	−0.00725410
$595$	0	0
$596$	37.8058	1.54858
$597$	−12.6482	−0.517655
$598$	−2.59339	−0.106052
$599$	32.1150	1.31218	0.656091	−	0.754682i	$-0.272209\pi$
$599$	32.1150	1.31218	0.656091	+	0.754682i	$0.272209\pi$
$600$	0	0
$601$	−28.0856	−1.14564	−0.572818	−	0.819683i	$-0.694150\pi$
$601$	−28.0856	−1.14564	−0.572818	+	0.819683i	$0.694150\pi$
$602$	1.86791	0.0761303
$603$	−9.51996	−0.387683
$604$	43.5050	1.77019
$605$	0	0
$606$	−2.49302	−0.101272
$607$	8.07438	0.327729	0.163864	−	0.986483i	$-0.447604\pi$
$607$	8.07438	0.327729	0.163864	+	0.986483i	$0.447604\pi$
$608$	3.56128	0.144429
$609$	23.9089	0.968837
$610$	0	0
$611$	−6.80735	−0.275396
$612$	4.39905	0.177821
$613$	3.21312	0.129777	0.0648883	−	0.997893i	$-0.479331\pi$
$613$	3.21312	0.129777	0.0648883	+	0.997893i	$0.479331\pi$
$614$	4.43146	0.178839
$615$	0	0
$616$	−2.38884	−0.0962493
$617$	−45.0988	−1.81561	−0.907805	−	0.419393i	$-0.862243\pi$
$617$	−45.0988	−1.81561	−0.907805	+	0.419393i	$0.862243\pi$
$618$	0.248846	0.0100101
$619$	−19.3902	−0.779358	−0.389679	−	0.920951i	$-0.627414\pi$
$619$	−19.3902	−0.779358	−0.389679	+	0.920951i	$0.627414\pi$
$620$	0	0
$621$	−2.74977	−0.110345
$622$	−2.70915	−0.108627
$623$	−0.408945	−0.0163840
$624$	26.4479	1.05876
$625$	0	0
$626$	2.10494	0.0841304
$627$	−2.76882	−0.110576
$628$	−20.6211	−0.822872
$629$	−16.1781	−0.645062
$630$	0	0
$631$	−19.1415	−0.762012	−0.381006	−	0.924573i	$-0.624422\pi$
$631$	−19.1415	−0.762012	−0.381006	+	0.924573i	$0.624422\pi$
$632$	−1.24690	−0.0495989
$633$	−25.2419	−1.00327
$634$	−3.65755	−0.145260
$635$	0	0
$636$	13.5577	0.537599
$637$	30.7742	1.21932
$638$	1.24536	0.0493044
$639$	13.4096	0.530476
$640$	0	0
$641$	−6.19630	−0.244739	−0.122370	−	0.992485i	$-0.539049\pi$
$641$	−6.19630	−0.244739	−0.122370	+	0.992485i	$0.539049\pi$
$642$	0.0238985	0.000943197 0
$643$	23.1524	0.913043	0.456522	−	0.889712i	$-0.349095\pi$
$643$	23.1524	0.913043	0.456522	+	0.889712i	$0.349095\pi$
$644$	−18.4875	−0.728510
$645$	0	0
$646$	−0.667607	−0.0262666
$647$	−18.6508	−0.733239	−0.366620	−	0.930371i	$-0.619485\pi$
$647$	−18.6508	−0.733239	−0.366620	+	0.930371i	$0.619485\pi$
$648$	−0.551524	−0.0216659
$649$	1.01385	0.0397972
$650$	0	0
$651$	−6.82502	−0.267494
$652$	−11.1111	−0.435146
$653$	31.1736	1.21992	0.609958	−	0.792434i	$-0.291186\pi$
$653$	31.1736	1.21992	0.609958	+	0.792434i	$0.291186\pi$
$654$	−1.85096	−0.0723784
$655$	0	0
$656$	−12.6565	−0.494152
$657$	−3.68282	−0.143680
$658$	0.470255	0.0183324
$659$	−0.0948194	−0.00369364	−0.00184682	−	0.999998i	$-0.500588\pi$
$659$	−0.0948194	−0.00369364	−0.00184682	+	0.999998i	$0.500588\pi$
$660$	0	0
$661$	1.79777	0.0699253	0.0349626	−	0.999389i	$-0.488869\pi$
$661$	1.79777	0.0699253	0.0349626	+	0.999389i	$0.488869\pi$
$662$	1.07426	0.0417524
$663$	−15.1180	−0.587135
$664$	−1.53820	−0.0596938
$665$	0	0
$666$	1.00926	0.0391080
$667$	19.3694	0.749986
$668$	16.5643	0.640893
$669$	12.9533	0.500802
$670$	0	0
$671$	7.38633	0.285146
$672$	−5.57102	−0.214907
$673$	−6.17864	−0.238169	−0.119085	−	0.992884i	$-0.537996\pi$
$673$	−6.17864	−0.238169	−0.119085	+	0.992884i	$0.537996\pi$
$674$	2.29028	0.0882185
$675$	0	0
$676$	−66.0401	−2.54000
$677$	2.46766	0.0948399	0.0474200	−	0.998875i	$-0.484900\pi$
$677$	2.46766	0.0948399	0.0474200	+	0.998875i	$0.484900\pi$
$678$	−2.42186	−0.0930109
$679$	−36.2961	−1.39292
$680$	0	0
$681$	−15.3479	−0.588135
$682$	−0.355501	−0.0136128
$683$	−33.0927	−1.26626	−0.633129	−	0.774047i	$-0.718230\pi$
$683$	−33.0927	−1.26626	−0.633129	+	0.774047i	$0.718230\pi$
$684$	−4.29786	−0.164333
$685$	0	0
$686$	1.16589	0.0445138
$687$	−15.9788	−0.609629
$688$	−15.4325	−0.588358
$689$	−46.5933	−1.77506
$690$	0	0
$691$	12.7402	0.484659	0.242329	−	0.970194i	$-0.422089\pi$
$691$	12.7402	0.484659	0.242329	+	0.970194i	$0.422089\pi$
$692$	41.5205	1.57837
$693$	4.33136	0.164535
$694$	−0.816157	−0.0309809
$695$	0	0
$696$	3.88493	0.147258
$697$	7.23463	0.274031
$698$	2.15444	0.0815467
$699$	23.8907	0.903630
$700$	0	0
$701$	32.6094	1.23164	0.615820	−	0.787887i	$-0.288825\pi$
$701$	32.6094	1.23164	0.615820	+	0.787887i	$0.288825\pi$
$702$	0.943129	0.0355961
$703$	15.8060	0.596133
$704$	9.62560	0.362778
$705$	0	0
$706$	0.316447	0.0119096
$707$	61.0762	2.29701
$708$	1.57374	0.0591447
$709$	26.5764	0.998097	0.499048	−	0.866574i	$-0.333683\pi$
$709$	26.5764	0.998097	0.499048	+	0.866574i	$0.333683\pi$
$710$	0	0
$711$	2.26082	0.0847875
$712$	−0.0664491	−0.00249029
$713$	−5.52918	−0.207069
$714$	1.04436	0.0390842
$715$	0	0
$716$	−22.4095	−0.837482
$717$	−4.31375	−0.161100
$718$	−2.35005	−0.0877030
$719$	50.5537	1.88533	0.942667	−	0.333735i	$-0.108309\pi$
$719$	50.5537	1.88533	0.942667	+	0.333735i	$0.108309\pi$
$720$	0	0
$721$	−6.09646	−0.227044
$722$	−1.98012	−0.0736923
$723$	−9.79805	−0.364393
$724$	−44.4238	−1.65100
$725$	0	0
$726$	−1.29839	−0.0481878
$727$	−18.2950	−0.678525	−0.339262	−	0.940692i	$-0.610177\pi$
$727$	−18.2950	−0.678525	−0.339262	+	0.940692i	$0.610177\pi$
$728$	12.7433	0.472298
$729$	1.00000	0.0370370
$730$	0	0
$731$	8.82143	0.326273
$732$	11.4653	0.423771
$733$	12.7481	0.470862	0.235431	−	0.971891i	$-0.424350\pi$
$733$	12.7481	0.470862	0.235431	+	0.971891i	$0.424350\pi$
$734$	−4.12113	−0.152114
$735$	0	0
$736$	−4.51327	−0.166361
$737$	12.1484	0.447492
$738$	−0.451328	−0.0166136
$739$	3.58371	0.131829	0.0659144	−	0.997825i	$-0.479004\pi$
$739$	3.58371	0.131829	0.0659144	+	0.997825i	$0.479004\pi$
$740$	0	0
$741$	14.7703	0.542600
$742$	3.21868	0.118162
$743$	−16.7058	−0.612875	−0.306437	−	0.951891i	$-0.599137\pi$
$743$	−16.7058	−0.612875	−0.306437	+	0.951891i	$0.599137\pi$
$744$	−1.10899	−0.0406576
$745$	0	0
$746$	1.95744	0.0716671
$747$	2.78900	0.102044
$748$	−5.61361	−0.205254
$749$	−0.585487	−0.0213932
$750$	0	0
$751$	29.1683	1.06437	0.532183	−	0.846629i	$-0.321372\pi$
$751$	29.1683	1.06437	0.532183	+	0.846629i	$0.321372\pi$
$752$	−3.88520	−0.141679
$753$	11.7481	0.428125
$754$	−6.64340	−0.241938
$755$	0	0
$756$	6.72329	0.244524
$757$	−33.8356	−1.22978	−0.614888	−	0.788615i	$-0.710799\pi$
$757$	−33.8356	−1.22978	−0.614888	+	0.788615i	$0.710799\pi$
$758$	−1.60289	−0.0582197
$759$	3.50898	0.127368
$760$	0	0
$761$	45.9926	1.66723	0.833615	−	0.552345i	$-0.186267\pi$
$761$	45.9926	1.66723	0.833615	+	0.552345i	$0.186267\pi$
$762$	−1.51792	−0.0549885
$763$	45.3466	1.64166
$764$	20.0553	0.725575
$765$	0	0
$766$	−0.707199	−0.0255521
$767$	−5.40840	−0.195286
$768$	14.4864	0.522733
$769$	−50.8875	−1.83505	−0.917525	−	0.397679i	$-0.869816\pi$
$769$	−50.8875	−1.83505	−0.917525	+	0.397679i	$0.869816\pi$
$770$	0	0
$771$	30.2719	1.09021
$772$	−3.74300	−0.134714
$773$	−24.7134	−0.888879	−0.444439	−	0.895809i	$-0.646597\pi$
$773$	−24.7134	−0.888879	−0.444439	+	0.895809i	$0.646597\pi$
$774$	−0.550320	−0.0197809
$775$	0	0
$776$	−5.89773	−0.211716
$777$	−24.7258	−0.887033
$778$	4.35690	0.156203
$779$	−7.06822	−0.253245
$780$	0	0
$781$	−17.1120	−0.612315
$782$	0.846071	0.0302554
$783$	−7.04400	−0.251732
$784$	17.5639	0.627284
$785$	0	0
$786$	−3.11309	−0.111040
$787$	46.3655	1.65275	0.826375	−	0.563120i	$-0.190399\pi$
$787$	46.3655	1.65275	0.826375	+	0.563120i	$0.190399\pi$
$788$	−34.8218	−1.24048
$789$	−12.4160	−0.442021
$790$	0	0
$791$	59.3329	2.10963
$792$	0.703798	0.0250084
$793$	−39.4024	−1.39922
$794$	0.155225	0.00550873
$795$	0	0
$796$	25.0536	0.888000
$797$	30.5370	1.08168	0.540838	−	0.841126i	$-0.318107\pi$
$797$	30.5370	1.08168	0.540838	+	0.841126i	$0.318107\pi$
$798$	−1.02034	−0.0361196
$799$	2.22084	0.0785676
$800$	0	0
$801$	0.120483	0.00425705
$802$	0.00665287	0.000234921 0
$803$	4.69963	0.165846
$804$	18.8572	0.665041
$805$	0	0
$806$	1.89642	0.0667987
$807$	−0.633678	−0.0223065
$808$	9.92421	0.349133
$809$	−30.3221	−1.06607	−0.533033	−	0.846094i	$-0.678948\pi$
$809$	−30.3221	−1.06607	−0.533033	+	0.846094i	$0.678948\pi$
$810$	0	0
$811$	−20.6246	−0.724227	−0.362113	−	0.932134i	$-0.617945\pi$
$811$	−20.6246	−0.724227	−0.362113	+	0.932134i	$0.617945\pi$
$812$	−47.3588	−1.66197
$813$	11.0636	0.388018
$814$	−1.28791	−0.0451414
$815$	0	0
$816$	−8.62840	−0.302054
$817$	−8.61853	−0.301524
$818$	1.67025	0.0583990
$819$	−23.1056	−0.807377
$820$	0	0
$821$	−1.67441	−0.0584373	−0.0292186	−	0.999573i	$-0.509302\pi$
$821$	−1.67441	−0.0584373	−0.0292186	+	0.999573i	$0.509302\pi$
$822$	1.41821	0.0494657
$823$	−4.96411	−0.173038	−0.0865189	−	0.996250i	$-0.527574\pi$
$823$	−4.96411	−0.173038	−0.0865189	+	0.996250i	$0.527574\pi$
$824$	−0.990607	−0.0345094
$825$	0	0
$826$	0.373615	0.0129997
$827$	1.70895	0.0594261	0.0297131	−	0.999558i	$-0.490541\pi$
$827$	1.70895	0.0594261	0.0297131	+	0.999558i	$0.490541\pi$
$828$	5.44676	0.189288
$829$	9.34891	0.324701	0.162350	−	0.986733i	$-0.448092\pi$
$829$	9.34891	0.324701	0.162350	+	0.986733i	$0.448092\pi$
$830$	0	0
$831$	6.59406	0.228746
$832$	−51.3478	−1.78017
$833$	−10.0398	−0.347859
$834$	−1.96093	−0.0679015
$835$	0	0
$836$	5.48449	0.189685
$837$	2.01078	0.0695027
$838$	−0.0812309	−0.00280607
$839$	−4.13826	−0.142869	−0.0714344	−	0.997445i	$-0.522758\pi$
$839$	−4.13826	−0.142869	−0.0714344	+	0.997445i	$0.522758\pi$
$840$	0	0
$841$	20.6179	0.710963
$842$	3.24437	0.111808
$843$	4.22131	0.145390
$844$	49.9993	1.72105
$845$	0	0
$846$	−0.138546	−0.00476330
$847$	31.8092	1.09298
$848$	−26.5925	−0.913189
$849$	10.9411	0.375496
$850$	0	0
$851$	−20.0312	−0.686660
$852$	−26.5618	−0.909994
$853$	44.6214	1.52781	0.763903	−	0.645331i	$-0.223280\pi$
$853$	44.6214	1.52781	0.763903	+	0.645331i	$0.223280\pi$
$854$	2.72194	0.0931428
$855$	0	0
$856$	−0.0951352	−0.00325165
$857$	7.70080	0.263054	0.131527	−	0.991313i	$-0.458012\pi$
$857$	7.70080	0.263054	0.131527	+	0.991313i	$0.458012\pi$
$858$	−1.20352	−0.0410877
$859$	−27.8046	−0.948680	−0.474340	−	0.880342i	$-0.657313\pi$
$859$	−27.8046	−0.948680	−0.474340	+	0.880342i	$0.657313\pi$
$860$	0	0
$861$	11.0571	0.376823
$862$	−2.77893	−0.0946509
$863$	−4.85689	−0.165330	−0.0826652	−	0.996577i	$-0.526343\pi$
$863$	−4.85689	−0.165330	−0.0826652	+	0.996577i	$0.526343\pi$
$864$	1.64132	0.0558390
$865$	0	0
$866$	3.99750	0.135841
$867$	−12.0679	−0.409847
$868$	13.5190	0.458866
$869$	−2.88503	−0.0978680
$870$	0	0
$871$	−64.8057	−2.19586
$872$	7.36833	0.249523
$873$	10.6935	0.361921
$874$	−0.826610	−0.0279605
$875$	0	0
$876$	7.29494	0.246473
$877$	19.2791	0.651010	0.325505	−	0.945540i	$-0.394466\pi$
$877$	19.2791	0.651010	0.325505	+	0.945540i	$0.394466\pi$
$878$	−1.33277	−0.0449789
$879$	20.4785	0.690723
$880$	0	0
$881$	38.3911	1.29343	0.646714	−	0.762733i	$-0.276143\pi$
$881$	38.3911	1.29343	0.646714	+	0.762733i	$0.276143\pi$
$882$	0.626328	0.0210896
$883$	20.3454	0.684676	0.342338	−	0.939577i	$-0.388781\pi$
$883$	20.3454	0.684676	0.342338	+	0.939577i	$0.388781\pi$
$884$	29.9458	1.00719
$885$	0	0
$886$	−2.74596	−0.0922523
$887$	7.24185	0.243157	0.121579	−	0.992582i	$-0.461204\pi$
$887$	7.24185	0.243157	0.121579	+	0.992582i	$0.461204\pi$
$888$	−4.01767	−0.134824
$889$	37.1875	1.24723
$890$	0	0
$891$	−1.27610	−0.0427509
$892$	−25.6579	−0.859090
$893$	−2.16976	−0.0726081
$894$	−2.64429	−0.0884383
$895$	0	0
$896$	14.6892	0.490731
$897$	−18.7187	−0.624998
$898$	0.613022	0.0204568
$899$	−14.1639	−0.472393
$900$	0	0
$901$	15.2006	0.506407
$902$	0.575939	0.0191767
$903$	13.4823	0.448661
$904$	9.64094	0.320653
$905$	0	0
$906$	−3.04292	−0.101094
$907$	−42.5925	−1.41426	−0.707131	−	0.707083i	$-0.750011\pi$
$907$	−42.5925	−1.41426	−0.707131	+	0.707083i	$0.750011\pi$
$908$	30.4013	1.00890
$909$	−17.9942	−0.596829
$910$	0	0
$911$	−7.48037	−0.247836	−0.123918	−	0.992292i	$-0.539546\pi$
$911$	−7.48037	−0.247836	−0.123918	+	0.992292i	$0.539546\pi$
$912$	8.42993	0.279143
$913$	−3.55904	−0.117787
$914$	−2.30375	−0.0762011
$915$	0	0
$916$	31.6509	1.04577
$917$	76.2674	2.51857
$918$	−0.307688	−0.0101552
$919$	10.3381	0.341024	0.170512	−	0.985356i	$-0.445458\pi$
$919$	10.3381	0.341024	0.170512	+	0.985356i	$0.445458\pi$
$920$	0	0
$921$	31.9856	1.05396
$922$	0.980526	0.0322919
$923$	91.2840	3.00465
$924$	−8.57957	−0.282247
$925$	0	0
$926$	−5.62072	−0.184708
$927$	1.79613	0.0589926
$928$	−11.5615	−0.379525
$929$	−45.3398	−1.48755	−0.743775	−	0.668430i	$-0.766966\pi$
$929$	−45.3398	−1.48755	−0.743775	+	0.668430i	$0.766966\pi$
$930$	0	0
$931$	9.80889	0.321473
$932$	−47.3229	−1.55011
$933$	−19.5542	−0.640176
$934$	−4.08893	−0.133794
$935$	0	0
$936$	−3.75441	−0.122717
$937$	−38.4906	−1.25743	−0.628717	−	0.777634i	$-0.716420\pi$
$937$	−38.4906	−1.25743	−0.628717	+	0.777634i	$0.716420\pi$
$938$	4.47681	0.146173
$939$	15.1931	0.495809
$940$	0	0
$941$	11.4224	0.372359	0.186180	−	0.982516i	$-0.440389\pi$
$941$	11.4224	0.372359	0.186180	+	0.982516i	$0.440389\pi$
$942$	1.44233	0.0469935
$943$	8.95769	0.291703
$944$	−3.08677	−0.100466
$945$	0	0
$946$	0.702262	0.0228325
$947$	−37.6988	−1.22505	−0.612524	−	0.790452i	$-0.709846\pi$
$947$	−37.6988	−1.22505	−0.612524	+	0.790452i	$0.709846\pi$
$948$	−4.47825	−0.145447
$949$	−25.0702	−0.813814
$950$	0	0
$951$	−26.3996	−0.856066
$952$	−4.15739	−0.134742
$953$	−49.0239	−1.58804	−0.794020	−	0.607891i	$-0.792016\pi$
$953$	−49.0239	−1.58804	−0.794020	+	0.607891i	$0.792016\pi$
$954$	−0.948284	−0.0307018
$955$	0	0
$956$	8.54470	0.276355
$957$	8.98883	0.290568
$958$	2.66881	0.0862253
$959$	−34.7446	−1.12196
$960$	0	0
$961$	−26.9568	−0.869573
$962$	6.87039	0.221510
$963$	0.172495	0.00555858
$964$	19.4080	0.625090
$965$	0	0
$966$	1.29309	0.0416046
$967$	58.9994	1.89729	0.948647	−	0.316338i	$-0.102453\pi$
$967$	58.9994	1.89729	0.948647	+	0.316338i	$0.102453\pi$
$968$	5.16865	0.166127
$969$	−4.81868	−0.154798
$970$	0	0
$971$	53.0079	1.70111	0.850553	−	0.525889i	$-0.176267\pi$
$971$	53.0079	1.70111	0.850553	+	0.525889i	$0.176267\pi$
$972$	−1.98081	−0.0635344
$973$	48.0407	1.54011
$974$	1.28999	0.0413339
$975$	0	0
$976$	−22.4884	−0.719836
$977$	−37.3085	−1.19361	−0.596803	−	0.802388i	$-0.703563\pi$
$977$	−37.3085	−1.19361	−0.596803	+	0.802388i	$0.703563\pi$
$978$	0.777160	0.0248508
$979$	−0.153748	−0.00491380
$980$	0	0
$981$	−13.3600	−0.426550
$982$	−1.73158	−0.0552570
$983$	−15.4430	−0.492554	−0.246277	−	0.969199i	$-0.579207\pi$
$983$	−15.4430	−0.492554	−0.246277	+	0.969199i	$0.579207\pi$
$984$	1.79665	0.0572751
$985$	0	0
$986$	2.16735	0.0690225
$987$	3.39422	0.108039
$988$	−29.2571	−0.930791
$989$	10.9224	0.347313
$990$	0	0
$991$	−29.2293	−0.928499	−0.464250	−	0.885704i	$-0.653676\pi$
$991$	−29.2293	−0.928499	−0.464250	+	0.885704i	$0.653676\pi$
$992$	3.30034	0.104786
$993$	7.75385	0.246061
$994$	−6.30594	−0.200012
$995$	0	0
$996$	−5.52447	−0.175050
$997$	−32.9469	−1.04344	−0.521719	−	0.853118i	$-0.674709\pi$
$997$	−32.9469	−1.04344	−0.521719	+	0.853118i	$0.674709\pi$
$998$	−5.59721	−0.177177
$999$	7.28467	0.230477

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.bf.1.6		10
5.2	odd	4		705.2.c.b.424.11	yes	20
5.3	odd	4		705.2.c.b.424.10	✓	20
5.4	even	2		3525.2.a.bg.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.2.c.b.424.10	✓	20	5.3	odd	4
705.2.c.b.424.11	yes	20	5.2	odd	4
3525.2.a.bf.1.6		10	1.1	even	1	trivial
3525.2.a.bg.1.5		10	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q+0.138546 q^{2} +1.00000 q^{3} -1.98081 q^{4} +0.138546 q^{6} -3.39422 q^{7} -0.551524 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.138546 q^{2} +1.00000 q^{3} -1.98081 q^{4} +0.138546 q^{6} -3.39422 q^{7} -0.551524 q^{8} +1.00000 q^{9} -1.27610 q^{11} -1.98081 q^{12} +6.80735 q^{13} -0.470255 q^{14} +3.88520 q^{16} -2.22084 q^{17} +0.138546 q^{18} +2.16976 q^{19} -3.39422 q^{21} -0.176798 q^{22} -2.74977 q^{23} -0.551524 q^{24} +0.943129 q^{26} +1.00000 q^{27} +6.72329 q^{28} -7.04400 q^{29} +2.01078 q^{31} +1.64132 q^{32} -1.27610 q^{33} -0.307688 q^{34} -1.98081 q^{36} +7.28467 q^{37} +0.300610 q^{38} +6.80735 q^{39} -3.25761 q^{41} -0.470255 q^{42} -3.97212 q^{43} +2.52770 q^{44} -0.380969 q^{46} -1.00000 q^{47} +3.88520 q^{48} +4.52073 q^{49} -2.22084 q^{51} -13.4840 q^{52} -6.84455 q^{53} +0.138546 q^{54} +1.87199 q^{56} +2.16976 q^{57} -0.975916 q^{58} -0.794495 q^{59} -5.78822 q^{61} +0.278585 q^{62} -3.39422 q^{63} -7.54300 q^{64} -0.176798 q^{66} -9.51996 q^{67} +4.39905 q^{68} -2.74977 q^{69} +13.4096 q^{71} -0.551524 q^{72} -3.68282 q^{73} +1.00926 q^{74} -4.29786 q^{76} +4.33136 q^{77} +0.943129 q^{78} +2.26082 q^{79} +1.00000 q^{81} -0.451328 q^{82} +2.78900 q^{83} +6.72329 q^{84} -0.550320 q^{86} -7.04400 q^{87} +0.703798 q^{88} +0.120483 q^{89} -23.1056 q^{91} +5.44676 q^{92} +2.01078 q^{93} -0.138546 q^{94} +1.64132 q^{96} +10.6935 q^{97} +0.626328 q^{98} -1.27610 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{2} + 10 q^{3} + 7 q^{4} - 3 q^{6} - 9 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 3 * q^2 + 10 * q^3 + 7 * q^4 - 3 * q^6 - 9 * q^8 + 10 * q^9	\( 10 q - 3 q^{2} + 10 q^{3} + 7 q^{4} - 3 q^{6} - 9 q^{8} + 10 q^{9} - 16 q^{11} + 7 q^{12} - q^{13} - 12 q^{14} - 3 q^{16} - 14 q^{17} - 3 q^{18} - 26 q^{19} - 7 q^{23} - 9 q^{24} - 10 q^{26} + 10 q^{27} + 24 q^{28} - 14 q^{29} - 22 q^{31} - 11 q^{32} - 16 q^{33} - 12 q^{34} + 7 q^{36} - 2 q^{37} + 2 q^{38} - q^{39} - 22 q^{41} - 12 q^{42} + 11 q^{43} - 36 q^{44} - 14 q^{46} - 10 q^{47} - 3 q^{48} + 2 q^{49} - 14 q^{51} - 14 q^{52} - 22 q^{53} - 3 q^{54} - 48 q^{56} - 26 q^{57} + 20 q^{58} - 37 q^{59} - 25 q^{61} + 2 q^{62} - 7 q^{64} + 4 q^{67} - 8 q^{68} - 7 q^{69} - 27 q^{71} - 9 q^{72} - q^{73} + 4 q^{74} - 42 q^{76} - 34 q^{77} - 10 q^{78} + 5 q^{79} + 10 q^{81} + 32 q^{82} - 2 q^{83} + 24 q^{84} - 6 q^{86} - 14 q^{87} + 58 q^{88} + 9 q^{89} - 64 q^{91} - 34 q^{92} - 22 q^{93} + 3 q^{94} - 11 q^{96} + 40 q^{97} - 29 q^{98} - 16 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 + 10 * q^3 + 7 * q^4 - 3 * q^6 - 9 * q^8 + 10 * q^9 - 16 * q^11 + 7 * q^12 - q^13 - 12 * q^14 - 3 * q^16 - 14 * q^17 - 3 * q^18 - 26 * q^19 - 7 * q^23 - 9 * q^24 - 10 * q^26 + 10 * q^27 + 24 * q^28 - 14 * q^29 - 22 * q^31 - 11 * q^32 - 16 * q^33 - 12 * q^34 + 7 * q^36 - 2 * q^37 + 2 * q^38 - q^39 - 22 * q^41 - 12 * q^42 + 11 * q^43 - 36 * q^44 - 14 * q^46 - 10 * q^47 - 3 * q^48 + 2 * q^49 - 14 * q^51 - 14 * q^52 - 22 * q^53 - 3 * q^54 - 48 * q^56 - 26 * q^57 + 20 * q^58 - 37 * q^59 - 25 * q^61 + 2 * q^62 - 7 * q^64 + 4 * q^67 - 8 * q^68 - 7 * q^69 - 27 * q^71 - 9 * q^72 - q^73 + 4 * q^74 - 42 * q^76 - 34 * q^77 - 10 * q^78 + 5 * q^79 + 10 * q^81 + 32 * q^82 - 2 * q^83 + 24 * q^84 - 6 * q^86 - 14 * q^87 + 58 * q^88 + 9 * q^89 - 64 * q^91 - 34 * q^92 - 22 * q^93 + 3 * q^94 - 11 * q^96 + 40 * q^97 - 29 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more