LMFDB - Embedded newform 3525.2.a.bb.1.4

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:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 9x^{5} + 6x^{4} + 20x^{3} - 9x^{2} - 12x + 3 $ x^7 - x^6 - 9x^5 + 6x^4 + 20x^3 - 9x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.231416$ 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)

$f(q)$	$=$	$q+0.231416 q^{2} -1.00000 q^{3} -1.94645 q^{4} -0.231416 q^{6} +4.71752 q^{7} -0.913273 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.231416 q^{2} -1.00000 q^{3} -1.94645 q^{4} -0.231416 q^{6} +4.71752 q^{7} -0.913273 q^{8} +1.00000 q^{9} -3.55959 q^{11} +1.94645 q^{12} -3.00919 q^{13} +1.09171 q^{14} +3.68155 q^{16} -6.94165 q^{17} +0.231416 q^{18} +4.84716 q^{19} -4.71752 q^{21} -0.823748 q^{22} +3.68923 q^{23} +0.913273 q^{24} -0.696376 q^{26} -1.00000 q^{27} -9.18239 q^{28} +5.90847 q^{29} -3.00627 q^{31} +2.67852 q^{32} +3.55959 q^{33} -1.60641 q^{34} -1.94645 q^{36} +9.98763 q^{37} +1.12171 q^{38} +3.00919 q^{39} -5.71179 q^{41} -1.09171 q^{42} +0.0371443 q^{43} +6.92855 q^{44} +0.853749 q^{46} -1.00000 q^{47} -3.68155 q^{48} +15.2550 q^{49} +6.94165 q^{51} +5.85722 q^{52} -11.2541 q^{53} -0.231416 q^{54} -4.30838 q^{56} -4.84716 q^{57} +1.36732 q^{58} -4.96189 q^{59} -1.18776 q^{61} -0.695700 q^{62} +4.71752 q^{63} -6.74324 q^{64} +0.823748 q^{66} -2.47408 q^{67} +13.5115 q^{68} -3.68923 q^{69} -4.82785 q^{71} -0.913273 q^{72} +14.3020 q^{73} +2.31130 q^{74} -9.43473 q^{76} -16.7924 q^{77} +0.696376 q^{78} -4.90598 q^{79} +1.00000 q^{81} -1.32180 q^{82} +3.27023 q^{83} +9.18239 q^{84} +0.00859581 q^{86} -5.90847 q^{87} +3.25088 q^{88} -8.89855 q^{89} -14.1959 q^{91} -7.18089 q^{92} +3.00627 q^{93} -0.231416 q^{94} -2.67852 q^{96} +19.2977 q^{97} +3.53025 q^{98} -3.55959 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + q^{2} - 7 q^{3} + 5 q^{4} - q^{6} + 11 q^{7} + 6 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + q^2 - 7 * q^3 + 5 * q^4 - q^6 + 11 * q^7 + 6 * q^8 + 7 * q^9	$ 7 q + q^{2} - 7 q^{3} + 5 q^{4} - q^{6} + 11 q^{7} + 6 q^{8} + 7 q^{9} - 8 q^{11} - 5 q^{12} + 5 q^{13} - 3 q^{14} + 9 q^{16} + 10 q^{17} + q^{18} + 7 q^{19} - 11 q^{21} + 20 q^{22} + 4 q^{23} - 6 q^{24} - 7 q^{27} + 2 q^{28} - 11 q^{29} + 3 q^{31} + 28 q^{32} + 8 q^{33} + 8 q^{34} + 5 q^{36} + 11 q^{37} - 2 q^{38} - 5 q^{39} - 20 q^{41} + 3 q^{42} + 18 q^{43} + q^{44} - 19 q^{46} - 7 q^{47} - 9 q^{48} + 14 q^{49} - 10 q^{51} + 29 q^{52} + 12 q^{53} - q^{54} - 47 q^{56} - 7 q^{57} - 19 q^{58} + 18 q^{59} - 4 q^{61} + 12 q^{62} + 11 q^{63} + 42 q^{64} - 20 q^{66} + 22 q^{67} + 44 q^{68} - 4 q^{69} - 14 q^{71} + 6 q^{72} + 30 q^{73} + 31 q^{74} - 2 q^{76} - 8 q^{77} - q^{79} + 7 q^{81} + 29 q^{82} + 54 q^{83} - 2 q^{84} - 29 q^{86} + 11 q^{87} - 22 q^{88} - 14 q^{89} + 20 q^{91} - 5 q^{92} - 3 q^{93} - q^{94} - 28 q^{96} + 24 q^{97} - 26 q^{98} - 8 q^{99}+O(q^{100}) $ 7 * q + q^2 - 7 * q^3 + 5 * q^4 - q^6 + 11 * q^7 + 6 * q^8 + 7 * q^9 - 8 * q^11 - 5 * q^12 + 5 * q^13 - 3 * q^14 + 9 * q^16 + 10 * q^17 + q^18 + 7 * q^19 - 11 * q^21 + 20 * q^22 + 4 * q^23 - 6 * q^24 - 7 * q^27 + 2 * q^28 - 11 * q^29 + 3 * q^31 + 28 * q^32 + 8 * q^33 + 8 * q^34 + 5 * q^36 + 11 * q^37 - 2 * q^38 - 5 * q^39 - 20 * q^41 + 3 * q^42 + 18 * q^43 + q^44 - 19 * q^46 - 7 * q^47 - 9 * q^48 + 14 * q^49 - 10 * q^51 + 29 * q^52 + 12 * q^53 - q^54 - 47 * q^56 - 7 * q^57 - 19 * q^58 + 18 * q^59 - 4 * q^61 + 12 * q^62 + 11 * q^63 + 42 * q^64 - 20 * q^66 + 22 * q^67 + 44 * q^68 - 4 * q^69 - 14 * q^71 + 6 * q^72 + 30 * q^73 + 31 * q^74 - 2 * q^76 - 8 * q^77 - q^79 + 7 * q^81 + 29 * q^82 + 54 * q^83 - 2 * q^84 - 29 * q^86 + 11 * q^87 - 22 * q^88 - 14 * q^89 + 20 * q^91 - 5 * q^92 - 3 * q^93 - q^94 - 28 * q^96 + 24 * q^97 - 26 * q^98 - 8 * 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 $

$2$	0.231416	0.163636	0.0818181	−	0.996647i	$-0.473927\pi$
$2$	0.231416	0.163636	0.0818181	+	0.996647i	$0.473927\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.94645	−0.973223
$5$	0	0
$5$	0	0
$6$	−0.231416	−0.0944754
$7$	4.71752	1.78305	0.891527	−	0.452968i	$-0.149635\pi$
$7$	4.71752	1.78305	0.891527	+	0.452968i	$0.149635\pi$
$8$	−0.913273	−0.322891
$9$	1.00000	0.333333
$10$	0	0
$11$	−3.55959	−1.07326	−0.536629	−	0.843819i	$-0.680302\pi$
$11$	−3.55959	−1.07326	−0.536629	+	0.843819i	$0.680302\pi$
$12$	1.94645	0.561891
$13$	−3.00919	−0.834599	−0.417299	−	0.908769i	$-0.637023\pi$
$13$	−3.00919	−0.834599	−0.417299	+	0.908769i	$0.637023\pi$
$14$	1.09171	0.291772
$15$	0	0
$16$	3.68155	0.920387
$17$	−6.94165	−1.68360	−0.841799	−	0.539792i	$-0.818503\pi$
$17$	−6.94165	−1.68360	−0.841799	+	0.539792i	$0.818503\pi$
$18$	0.231416	0.0545454
$19$	4.84716	1.11201	0.556007	−	0.831177i	$-0.312333\pi$
$19$	4.84716	1.11201	0.556007	+	0.831177i	$0.312333\pi$
$20$	0	0
$21$	−4.71752	−1.02945
$22$	−0.823748	−0.175624
$23$	3.68923	0.769258	0.384629	−	0.923071i	$-0.374329\pi$
$23$	3.68923	0.769258	0.384629	+	0.923071i	$0.374329\pi$
$24$	0.913273	0.186421
$25$	0	0
$26$	−0.696376	−0.136571
$27$	−1.00000	−0.192450
$28$	−9.18239	−1.73531
$29$	5.90847	1.09718	0.548588	−	0.836093i	$-0.315166\pi$
$29$	5.90847	1.09718	0.548588	+	0.836093i	$0.315166\pi$
$30$	0	0
$31$	−3.00627	−0.539941	−0.269971	−	0.962869i	$-0.587014\pi$
$31$	−3.00627	−0.539941	−0.269971	+	0.962869i	$0.587014\pi$
$32$	2.67852	0.473499
$33$	3.55959	0.619645
$34$	−1.60641	−0.275497
$35$	0	0
$36$	−1.94645	−0.324408
$37$	9.98763	1.64196	0.820978	−	0.570960i	$-0.193429\pi$
$37$	9.98763	1.64196	0.820978	+	0.570960i	$0.193429\pi$
$38$	1.12171	0.181966
$39$	3.00919	0.481856
$40$	0	0
$41$	−5.71179	−0.892032	−0.446016	−	0.895025i	$-0.647158\pi$
$41$	−5.71179	−0.892032	−0.446016	+	0.895025i	$0.647158\pi$
$42$	−1.09171	−0.168455
$43$	0.0371443	0.00566446	0.00283223	−	0.999996i	$-0.499098\pi$
$43$	0.0371443	0.00566446	0.00283223	+	0.999996i	$0.499098\pi$
$44$	6.92855	1.04452
$45$	0	0
$46$	0.853749	0.125878
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	−3.68155	−0.531385
$49$	15.2550	2.17928
$50$	0	0
$51$	6.94165	0.972025
$52$	5.85722	0.812251
$53$	−11.2541	−1.54587	−0.772937	−	0.634483i	$-0.781213\pi$
$53$	−11.2541	−1.54587	−0.772937	+	0.634483i	$0.781213\pi$
$54$	−0.231416	−0.0314918
$55$	0	0
$56$	−4.30838	−0.575732
$57$	−4.84716	−0.642022
$58$	1.36732	0.179538
$59$	−4.96189	−0.645983	−0.322991	−	0.946402i	$-0.604688\pi$
$59$	−4.96189	−0.645983	−0.322991	+	0.946402i	$0.604688\pi$
$60$	0	0
$61$	−1.18776	−0.152077	−0.0760387	−	0.997105i	$-0.524227\pi$
$61$	−1.18776	−0.152077	−0.0760387	+	0.997105i	$0.524227\pi$
$62$	−0.695700	−0.0883540
$63$	4.71752	0.594351
$64$	−6.74324	−0.842905
$65$	0	0
$66$	0.823748	0.101396
$67$	−2.47408	−0.302257	−0.151129	−	0.988514i	$-0.548291\pi$
$67$	−2.47408	−0.302257	−0.151129	+	0.988514i	$0.548291\pi$
$68$	13.5115	1.63852
$69$	−3.68923	−0.444131
$70$	0	0
$71$	−4.82785	−0.572961	−0.286480	−	0.958086i	$-0.592485\pi$
$71$	−4.82785	−0.572961	−0.286480	+	0.958086i	$0.592485\pi$
$72$	−0.913273	−0.107630
$73$	14.3020	1.67392	0.836959	−	0.547266i	$-0.184331\pi$
$73$	14.3020	1.67392	0.836959	+	0.547266i	$0.184331\pi$
$74$	2.31130	0.268683
$75$	0	0
$76$	−9.43473	−1.08224
$77$	−16.7924	−1.91368
$78$	0.696376	0.0788490
$79$	−4.90598	−0.551966	−0.275983	−	0.961163i	$-0.589003\pi$
$79$	−4.90598	−0.551966	−0.275983	+	0.961163i	$0.589003\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−1.32180	−0.145969
$83$	3.27023	0.358955	0.179477	−	0.983762i	$-0.442559\pi$
$83$	3.27023	0.358955	0.179477	+	0.983762i	$0.442559\pi$
$84$	9.18239	1.00188
$85$	0	0
$86$	0.00859581	0.000926910 0
$87$	−5.90847	−0.633455
$88$	3.25088	0.346545
$89$	−8.89855	−0.943245	−0.471622	−	0.881801i	$-0.656331\pi$
$89$	−8.89855	−0.943245	−0.471622	+	0.881801i	$0.656331\pi$
$90$	0	0
$91$	−14.1959	−1.48813
$92$	−7.18089	−0.748660
$93$	3.00627	0.311735
$94$	−0.231416	−0.0238688
$95$	0	0
$96$	−2.67852	−0.273375
$97$	19.2977	1.95939	0.979694	−	0.200500i	$-0.0642568\pi$
$97$	19.2977	1.95939	0.979694	+	0.200500i	$0.0642568\pi$
$98$	3.53025	0.356609
$99$	−3.55959	−0.357752
$100$	0	0
$101$	9.41725	0.937052	0.468526	−	0.883450i	$-0.344785\pi$
$101$	9.41725	0.937052	0.468526	+	0.883450i	$0.344785\pi$
$102$	1.60641	0.159058
$103$	8.33932	0.821697	0.410849	−	0.911704i	$-0.365232\pi$
$103$	8.33932	0.821697	0.410849	+	0.911704i	$0.365232\pi$
$104$	2.74821	0.269484
$105$	0	0
$106$	−2.60439	−0.252961
$107$	16.2212	1.56816	0.784081	−	0.620659i	$-0.213135\pi$
$107$	16.2212	1.56816	0.784081	+	0.620659i	$0.213135\pi$
$108$	1.94645	0.187297
$109$	4.38534	0.420039	0.210019	−	0.977697i	$-0.432647\pi$
$109$	4.38534	0.420039	0.210019	+	0.977697i	$0.432647\pi$
$110$	0	0
$111$	−9.98763	−0.947983
$112$	17.3678	1.64110
$113$	17.3100	1.62839	0.814196	−	0.580590i	$-0.197178\pi$
$113$	17.3100	1.62839	0.814196	+	0.580590i	$0.197178\pi$
$114$	−1.12171	−0.105058
$115$	0	0
$116$	−11.5005	−1.06780
$117$	−3.00919	−0.278200
$118$	−1.14826	−0.105706
$119$	−32.7473	−3.00194
$120$	0	0
$121$	1.67069	0.151881
$122$	−0.274868	−0.0248854
$123$	5.71179	0.515015
$124$	5.85154	0.525484
$125$	0	0
$126$	1.09171	0.0972574
$127$	−18.8097	−1.66909	−0.834543	−	0.550942i	$-0.814269\pi$
$127$	−18.8097	−1.66909	−0.834543	+	0.550942i	$0.814269\pi$
$128$	−6.91753	−0.611429
$129$	−0.0371443	−0.00327037
$130$	0	0
$131$	7.64573	0.668010	0.334005	−	0.942571i	$-0.391600\pi$
$131$	7.64573	0.668010	0.334005	+	0.942571i	$0.391600\pi$
$132$	−6.92855	−0.603053
$133$	22.8666	1.98278
$134$	−0.572544	−0.0494602
$135$	0	0
$136$	6.33962	0.543618
$137$	14.4352	1.23328	0.616639	−	0.787246i	$-0.288494\pi$
$137$	14.4352	1.23328	0.616639	+	0.787246i	$0.288494\pi$
$138$	−0.853749	−0.0726760
$139$	0.662540	0.0561959	0.0280980	−	0.999605i	$-0.491055\pi$
$139$	0.662540	0.0561959	0.0280980	+	0.999605i	$0.491055\pi$
$140$	0	0
$141$	1.00000	0.0842152
$142$	−1.11724	−0.0937571
$143$	10.7115	0.895739
$144$	3.68155	0.306796
$145$	0	0
$146$	3.30971	0.273913
$147$	−15.2550	−1.25821
$148$	−19.4404	−1.59799
$149$	22.3680	1.83246	0.916231	−	0.400651i	$-0.131216\pi$
$149$	22.3680	1.83246	0.916231	+	0.400651i	$0.131216\pi$
$150$	0	0
$151$	−10.3742	−0.844240	−0.422120	−	0.906540i	$-0.638714\pi$
$151$	−10.3742	−0.844240	−0.422120	+	0.906540i	$0.638714\pi$
$152$	−4.42678	−0.359059
$153$	−6.94165	−0.561199
$154$	−3.88605	−0.313147
$155$	0	0
$156$	−5.85722	−0.468953
$157$	16.7206	1.33445	0.667224	−	0.744857i	$-0.267482\pi$
$157$	16.7206	1.33445	0.667224	+	0.744857i	$0.267482\pi$
$158$	−1.13532	−0.0903215
$159$	11.2541	0.892510
$160$	0	0
$161$	17.4040	1.37163
$162$	0.231416	0.0181818
$163$	−2.51612	−0.197078	−0.0985389	−	0.995133i	$-0.531417\pi$
$163$	−2.51612	−0.197078	−0.0985389	+	0.995133i	$0.531417\pi$
$164$	11.1177	0.868146
$165$	0	0
$166$	0.756786	0.0587379
$167$	9.42178	0.729079	0.364540	−	0.931188i	$-0.381226\pi$
$167$	9.42178	0.729079	0.364540	+	0.931188i	$0.381226\pi$
$168$	4.30838	0.332399
$169$	−3.94479	−0.303445
$170$	0	0
$171$	4.84716	0.370671
$172$	−0.0722994	−0.00551278
$173$	−4.18540	−0.318210	−0.159105	−	0.987262i	$-0.550861\pi$
$173$	−4.18540	−0.318210	−0.159105	+	0.987262i	$0.550861\pi$
$174$	−1.36732	−0.103656
$175$	0	0
$176$	−13.1048	−0.987812
$177$	4.96189	0.372958
$178$	−2.05927	−0.154349
$179$	16.6680	1.24583	0.622913	−	0.782291i	$-0.285949\pi$
$179$	16.6680	1.24583	0.622913	+	0.782291i	$0.285949\pi$
$180$	0	0
$181$	6.57438	0.488670	0.244335	−	0.969691i	$-0.421430\pi$
$181$	6.57438	0.488670	0.244335	+	0.969691i	$0.421430\pi$
$182$	−3.28516	−0.243513
$183$	1.18776	0.0878020
$184$	−3.36928	−0.248386
$185$	0	0
$186$	0.695700	0.0510112
$187$	24.7094	1.80693
$188$	1.94645	0.141959
$189$	−4.71752	−0.343149
$190$	0	0
$191$	1.50553	0.108936	0.0544682	−	0.998516i	$-0.482654\pi$
$191$	1.50553	0.108936	0.0544682	+	0.998516i	$0.482654\pi$
$192$	6.74324	0.486651
$193$	−21.6047	−1.55514	−0.777572	−	0.628794i	$-0.783549\pi$
$193$	−21.6047	−1.55514	−0.777572	+	0.628794i	$0.783549\pi$
$194$	4.46581	0.320627
$195$	0	0
$196$	−29.6930	−2.12093
$197$	0.883760	0.0629653	0.0314826	−	0.999504i	$-0.489977\pi$
$197$	0.883760	0.0629653	0.0314826	+	0.999504i	$0.489977\pi$
$198$	−0.823748	−0.0585412
$199$	0.854677	0.0605864	0.0302932	−	0.999541i	$-0.490356\pi$
$199$	0.854677	0.0605864	0.0302932	+	0.999541i	$0.490356\pi$
$200$	0	0
$201$	2.47408	0.174508
$202$	2.17931	0.153336
$203$	27.8733	1.95632
$204$	−13.5115	−0.945997
$205$	0	0
$206$	1.92986	0.134459
$207$	3.68923	0.256419
$208$	−11.0785	−0.768153
$209$	−17.2539	−1.19348
$210$	0	0
$211$	−2.19748	−0.151281	−0.0756404	−	0.997135i	$-0.524100\pi$
$211$	−2.19748	−0.151281	−0.0756404	+	0.997135i	$0.524100\pi$
$212$	21.9056	1.50448
$213$	4.82785	0.330799
$214$	3.75385	0.256608
$215$	0	0
$216$	0.913273	0.0621403
$217$	−14.1821	−0.962745
$218$	1.01484	0.0687336
$219$	−14.3020	−0.966437
$220$	0	0
$221$	20.8887	1.40513
$222$	−2.31130	−0.155124
$223$	22.4599	1.50403	0.752013	−	0.659149i	$-0.229083\pi$
$223$	22.4599	1.50403	0.752013	+	0.659149i	$0.229083\pi$
$224$	12.6359	0.844275
$225$	0	0
$226$	4.00583	0.266464
$227$	14.2680	0.947002	0.473501	−	0.880793i	$-0.342990\pi$
$227$	14.2680	0.947002	0.473501	+	0.880793i	$0.342990\pi$
$228$	9.43473	0.624831
$229$	17.4827	1.15529	0.577645	−	0.816288i	$-0.303972\pi$
$229$	17.4827	1.15529	0.577645	+	0.816288i	$0.303972\pi$
$230$	0	0
$231$	16.7924	1.10486
$232$	−5.39605	−0.354268
$233$	−10.0126	−0.655944	−0.327972	−	0.944687i	$-0.606365\pi$
$233$	−10.0126	−0.655944	−0.327972	+	0.944687i	$0.606365\pi$
$234$	−0.696376	−0.0455235
$235$	0	0
$236$	9.65805	0.628685
$237$	4.90598	0.318678
$238$	−7.57828	−0.491227
$239$	0.192613	0.0124591	0.00622956	−	0.999981i	$-0.498017\pi$
$239$	0.192613	0.0124591	0.00622956	+	0.999981i	$0.498017\pi$
$240$	0	0
$241$	11.0948	0.714676	0.357338	−	0.933975i	$-0.383684\pi$
$241$	11.0948	0.714676	0.357338	+	0.933975i	$0.383684\pi$
$242$	0.386626	0.0248532
$243$	−1.00000	−0.0641500
$244$	2.31192	0.148005
$245$	0	0
$246$	1.32180	0.0842751
$247$	−14.5860	−0.928086
$248$	2.74554	0.174342
$249$	−3.27023	−0.207243
$250$	0	0
$251$	−2.26226	−0.142793	−0.0713963	−	0.997448i	$-0.522746\pi$
$251$	−2.26226	−0.142793	−0.0713963	+	0.997448i	$0.522746\pi$
$252$	−9.18239	−0.578437
$253$	−13.1322	−0.825612
$254$	−4.35286	−0.273123
$255$	0	0
$256$	11.8856	0.742853
$257$	26.1201	1.62933	0.814663	−	0.579935i	$-0.196922\pi$
$257$	26.1201	1.62933	0.814663	+	0.579935i	$0.196922\pi$
$258$	−0.00859581	−0.000535152 0
$259$	47.1168	2.92770
$260$	0	0
$261$	5.90847	0.365725
$262$	1.76935	0.109311
$263$	26.1478	1.61234	0.806172	−	0.591681i	$-0.201536\pi$
$263$	26.1478	1.61234	0.806172	+	0.591681i	$0.201536\pi$
$264$	−3.25088	−0.200078
$265$	0	0
$266$	5.29170	0.324455
$267$	8.89855	0.544583
$268$	4.81567	0.294164
$269$	−7.55179	−0.460441	−0.230220	−	0.973139i	$-0.573945\pi$
$269$	−7.55179	−0.460441	−0.230220	+	0.973139i	$0.573945\pi$
$270$	0	0
$271$	30.1728	1.83287	0.916433	−	0.400189i	$-0.131055\pi$
$271$	30.1728	1.83287	0.916433	+	0.400189i	$0.131055\pi$
$272$	−25.5560	−1.54956
$273$	14.1959	0.859175
$274$	3.34053	0.201809
$275$	0	0
$276$	7.18089	0.432239
$277$	−5.06076	−0.304072	−0.152036	−	0.988375i	$-0.548583\pi$
$277$	−5.06076	−0.304072	−0.152036	+	0.988375i	$0.548583\pi$
$278$	0.153323	0.00919569
$279$	−3.00627	−0.179980
$280$	0	0
$281$	−32.8656	−1.96060	−0.980300	−	0.197516i	$-0.936713\pi$
$281$	−32.8656	−1.96060	−0.980300	+	0.197516i	$0.936713\pi$
$282$	0.231416	0.0137807
$283$	19.9203	1.18414	0.592069	−	0.805887i	$-0.298311\pi$
$283$	19.9203	1.18414	0.592069	+	0.805887i	$0.298311\pi$
$284$	9.39715	0.557619
$285$	0	0
$286$	2.47881	0.146575
$287$	−26.9455	−1.59054
$288$	2.67852	0.157833
$289$	31.1865	1.83450
$290$	0	0
$291$	−19.2977	−1.13125
$292$	−27.8380	−1.62910
$293$	−16.5313	−0.965768	−0.482884	−	0.875684i	$-0.660411\pi$
$293$	−16.5313	−0.965768	−0.482884	+	0.875684i	$0.660411\pi$
$294$	−3.53025	−0.205888
$295$	0	0
$296$	−9.12143	−0.530172
$297$	3.55959	0.206548
$298$	5.17633	0.299857
$299$	−11.1016	−0.642022
$300$	0	0
$301$	0.175229	0.0101000
$302$	−2.40076	−0.138148
$303$	−9.41725	−0.541007
$304$	17.8450	1.02348
$305$	0	0
$306$	−1.60641	−0.0918325
$307$	25.0064	1.42719	0.713596	−	0.700558i	$-0.247065\pi$
$307$	25.0064	1.42719	0.713596	+	0.700558i	$0.247065\pi$
$308$	32.6856	1.86243
$309$	−8.33932	−0.474407
$310$	0	0
$311$	−8.10281	−0.459468	−0.229734	−	0.973253i	$-0.573786\pi$
$311$	−8.10281	−0.459468	−0.229734	+	0.973253i	$0.573786\pi$
$312$	−2.74821	−0.155587
$313$	−27.1854	−1.53661	−0.768304	−	0.640085i	$-0.778899\pi$
$313$	−27.1854	−1.53661	−0.768304	+	0.640085i	$0.778899\pi$
$314$	3.86942	0.218364
$315$	0	0
$316$	9.54922	0.537186
$317$	18.9285	1.06313	0.531564	−	0.847018i	$-0.321604\pi$
$317$	18.9285	1.06313	0.531564	+	0.847018i	$0.321604\pi$
$318$	2.60439	0.146047
$319$	−21.0318	−1.17755
$320$	0	0
$321$	−16.2212	−0.905378
$322$	4.02758	0.224448
$323$	−33.6473	−1.87218
$324$	−1.94645	−0.108136
$325$	0	0
$326$	−0.582272	−0.0322491
$327$	−4.38534	−0.242510
$328$	5.21643	0.288029
$329$	−4.71752	−0.260085
$330$	0	0
$331$	−21.3379	−1.17284	−0.586418	−	0.810008i	$-0.699462\pi$
$331$	−21.3379	−1.17284	−0.586418	+	0.810008i	$0.699462\pi$
$332$	−6.36533	−0.349343
$333$	9.98763	0.547318
$334$	2.18036	0.119304
$335$	0	0
$336$	−17.3678	−0.947489
$337$	18.5779	1.01200	0.506002	−	0.862532i	$-0.331123\pi$
$337$	18.5779	1.01200	0.506002	+	0.862532i	$0.331123\pi$
$338$	−0.912889	−0.0496546
$339$	−17.3100	−0.940152
$340$	0	0
$341$	10.7011	0.579496
$342$	1.12171	0.0606553
$343$	38.9430	2.10272
$344$	−0.0339229	−0.00182900
$345$	0	0
$346$	−0.968571	−0.0520707
$347$	6.68047	0.358626	0.179313	−	0.983792i	$-0.442612\pi$
$347$	6.68047	0.358626	0.179313	+	0.983792i	$0.442612\pi$
$348$	11.5005	0.616493
$349$	17.0571	0.913043	0.456522	−	0.889712i	$-0.349095\pi$
$349$	17.0571	0.913043	0.456522	+	0.889712i	$0.349095\pi$
$350$	0	0
$351$	3.00919	0.160619
$352$	−9.53442	−0.508186
$353$	3.02056	0.160768	0.0803841	−	0.996764i	$-0.474385\pi$
$353$	3.02056	0.160768	0.0803841	+	0.996764i	$0.474385\pi$
$354$	1.14826	0.0610295
$355$	0	0
$356$	17.3206	0.917988
$357$	32.7473	1.73317
$358$	3.85726	0.203862
$359$	−11.9555	−0.630988	−0.315494	−	0.948928i	$-0.602170\pi$
$359$	−11.9555	−0.630988	−0.315494	+	0.948928i	$0.602170\pi$
$360$	0	0
$361$	4.49494	0.236576
$362$	1.52142	0.0799641
$363$	−1.67069	−0.0876885
$364$	27.6315	1.44829
$365$	0	0
$366$	0.274868	0.0143676
$367$	1.47952	0.0772305	0.0386153	−	0.999254i	$-0.487705\pi$
$367$	1.47952	0.0772305	0.0386153	+	0.999254i	$0.487705\pi$
$368$	13.5821	0.708015
$369$	−5.71179	−0.297344
$370$	0	0
$371$	−53.0915	−2.75638
$372$	−5.85154	−0.303388
$373$	−6.38430	−0.330566	−0.165283	−	0.986246i	$-0.552854\pi$
$373$	−6.38430	−0.330566	−0.165283	+	0.986246i	$0.552854\pi$
$374$	5.71817	0.295680
$375$	0	0
$376$	0.913273	0.0470984
$377$	−17.7797	−0.915702
$378$	−1.09171	−0.0561516
$379$	−7.36640	−0.378387	−0.189193	−	0.981940i	$-0.560587\pi$
$379$	−7.36640	−0.378387	−0.189193	+	0.981940i	$0.560587\pi$
$380$	0	0
$381$	18.8097	0.963648
$382$	0.348405	0.0178259
$383$	22.6499	1.15736	0.578678	−	0.815556i	$-0.303569\pi$
$383$	22.6499	1.15736	0.578678	+	0.815556i	$0.303569\pi$
$384$	6.91753	0.353009
$385$	0	0
$386$	−4.99970	−0.254478
$387$	0.0371443	0.00188815
$388$	−37.5620	−1.90692
$389$	−8.21881	−0.416710	−0.208355	−	0.978053i	$-0.566811\pi$
$389$	−8.21881	−0.416710	−0.208355	+	0.978053i	$0.566811\pi$
$390$	0	0
$391$	−25.6094	−1.29512
$392$	−13.9319	−0.703670
$393$	−7.64573	−0.385676
$394$	0.204517	0.0103034
$395$	0	0
$396$	6.92855	0.348173
$397$	−10.8945	−0.546779	−0.273390	−	0.961903i	$-0.588145\pi$
$397$	−10.8945	−0.546779	−0.273390	+	0.961903i	$0.588145\pi$
$398$	0.197786	0.00991413
$399$	−22.8666	−1.14476
$400$	0	0
$401$	−2.30978	−0.115345	−0.0576725	−	0.998336i	$-0.518368\pi$
$401$	−2.30978	−0.115345	−0.0576725	+	0.998336i	$0.518368\pi$
$402$	0.572544	0.0285559
$403$	9.04642	0.450634
$404$	−18.3302	−0.911960
$405$	0	0
$406$	6.45035	0.320125
$407$	−35.5519	−1.76224
$408$	−6.33962	−0.313858
$409$	−2.30838	−0.114142	−0.0570709	−	0.998370i	$-0.518176\pi$
$409$	−2.30838	−0.114142	−0.0570709	+	0.998370i	$0.518176\pi$
$410$	0	0
$411$	−14.4352	−0.712034
$412$	−16.2320	−0.799695
$413$	−23.4078	−1.15182
$414$	0.853749	0.0419595
$415$	0	0
$416$	−8.06016	−0.395182
$417$	−0.662540	−0.0324447
$418$	−3.99284	−0.195296
$419$	−11.6943	−0.571302	−0.285651	−	0.958334i	$-0.592210\pi$
$419$	−11.6943	−0.571302	−0.285651	+	0.958334i	$0.592210\pi$
$420$	0	0
$421$	20.8453	1.01594	0.507969	−	0.861376i	$-0.330397\pi$
$421$	20.8453	1.01594	0.507969	+	0.861376i	$0.330397\pi$
$422$	−0.508533	−0.0247550
$423$	−1.00000	−0.0486217
$424$	10.2781	0.499148
$425$	0	0
$426$	1.11724	0.0541307
$427$	−5.60329	−0.271162
$428$	−31.5737	−1.52617
$429$	−10.7115	−0.517155
$430$	0	0
$431$	−14.0326	−0.675927	−0.337963	−	0.941159i	$-0.609738\pi$
$431$	−14.0326	−0.675927	−0.337963	+	0.941159i	$0.609738\pi$
$432$	−3.68155	−0.177128
$433$	−29.5741	−1.42124	−0.710621	−	0.703575i	$-0.751586\pi$
$433$	−29.5741	−1.42124	−0.710621	+	0.703575i	$0.751586\pi$
$434$	−3.28198	−0.157540
$435$	0	0
$436$	−8.53582	−0.408792
$437$	17.8823	0.855426
$438$	−3.30971	−0.158144
$439$	31.7478	1.51524	0.757620	−	0.652695i	$-0.226362\pi$
$439$	31.7478	1.51524	0.757620	+	0.652695i	$0.226362\pi$
$440$	0	0
$441$	15.2550	0.726427
$442$	4.83400	0.229930
$443$	35.1951	1.67217	0.836084	−	0.548601i	$-0.184840\pi$
$443$	35.1951	1.67217	0.836084	+	0.548601i	$0.184840\pi$
$444$	19.4404	0.922599
$445$	0	0
$446$	5.19759	0.246113
$447$	−22.3680	−1.05797
$448$	−31.8114	−1.50295
$449$	−29.9858	−1.41512	−0.707559	−	0.706654i	$-0.750204\pi$
$449$	−29.9858	−1.41512	−0.707559	+	0.706654i	$0.750204\pi$
$450$	0	0
$451$	20.3317	0.957380
$452$	−33.6931	−1.58479
$453$	10.3742	0.487422
$454$	3.30186	0.154964
$455$	0	0
$456$	4.42678	0.207303
$457$	−12.2154	−0.571414	−0.285707	−	0.958317i	$-0.592228\pi$
$457$	−12.2154	−0.571414	−0.285707	+	0.958317i	$0.592228\pi$
$458$	4.04579	0.189047
$459$	6.94165	0.324008
$460$	0	0
$461$	5.75492	0.268033	0.134017	−	0.990979i	$-0.457212\pi$
$461$	5.75492	0.268033	0.134017	+	0.990979i	$0.457212\pi$
$462$	3.88605	0.180795
$463$	−24.2552	−1.12724	−0.563618	−	0.826035i	$-0.690591\pi$
$463$	−24.2552	−1.12724	−0.563618	+	0.826035i	$0.690591\pi$
$464$	21.7523	1.00983
$465$	0	0
$466$	−2.31707	−0.107336
$467$	−3.47869	−0.160974	−0.0804872	−	0.996756i	$-0.525648\pi$
$467$	−3.47869	−0.160974	−0.0804872	+	0.996756i	$0.525648\pi$
$468$	5.85722	0.270750
$469$	−11.6715	−0.538941
$470$	0	0
$471$	−16.7206	−0.770444
$472$	4.53156	0.208582
$473$	−0.132219	−0.00607942
$474$	1.13532	0.0521472
$475$	0	0
$476$	63.7410	2.92156
$477$	−11.2541	−0.515291
$478$	0.0445739	0.00203876
$479$	−26.8517	−1.22688	−0.613442	−	0.789740i	$-0.710215\pi$
$479$	−26.8517	−1.22688	−0.613442	+	0.789740i	$0.710215\pi$
$480$	0	0
$481$	−30.0546	−1.37037
$482$	2.56751	0.116947
$483$	−17.4040	−0.791910
$484$	−3.25191	−0.147814
$485$	0	0
$486$	−0.231416	−0.0104973
$487$	6.82903	0.309453	0.154726	−	0.987957i	$-0.450550\pi$
$487$	6.82903	0.309453	0.154726	+	0.987957i	$0.450550\pi$
$488$	1.08475	0.0491044
$489$	2.51612	0.113783
$490$	0	0
$491$	−19.4377	−0.877209	−0.438605	−	0.898680i	$-0.644527\pi$
$491$	−19.4377	−0.877209	−0.438605	+	0.898680i	$0.644527\pi$
$492$	−11.1177	−0.501225
$493$	−41.0146	−1.84720
$494$	−3.37544	−0.151868
$495$	0	0
$496$	−11.0677	−0.496955
$497$	−22.7755	−1.02162
$498$	−0.756786	−0.0339124
$499$	−31.2036	−1.39687	−0.698433	−	0.715676i	$-0.746119\pi$
$499$	−31.2036	−1.39687	−0.698433	+	0.715676i	$0.746119\pi$
$500$	0	0
$501$	−9.42178	−0.420934
$502$	−0.523525	−0.0233660
$503$	−12.4371	−0.554542	−0.277271	−	0.960792i	$-0.589430\pi$
$503$	−12.4371	−0.554542	−0.277271	+	0.960792i	$0.589430\pi$
$504$	−4.30838	−0.191911
$505$	0	0
$506$	−3.03900	−0.135100
$507$	3.94479	0.175194
$508$	36.6120	1.62439
$509$	43.9904	1.94984	0.974921	−	0.222552i	$-0.0714387\pi$
$509$	43.9904	1.94984	0.974921	+	0.222552i	$0.0714387\pi$
$510$	0	0
$511$	67.4697	2.98469
$512$	16.5856	0.732987
$513$	−4.84716	−0.214007
$514$	6.04462	0.266617
$515$	0	0
$516$	0.0722994	0.00318280
$517$	3.55959	0.156551
$518$	10.9036	0.479077
$519$	4.18540	0.183719
$520$	0	0
$521$	−9.93667	−0.435333	−0.217667	−	0.976023i	$-0.569845\pi$
$521$	−9.93667	−0.435333	−0.217667	+	0.976023i	$0.569845\pi$
$522$	1.36732	0.0598459
$523$	−29.4124	−1.28611	−0.643056	−	0.765819i	$-0.722334\pi$
$523$	−29.4124	−1.28611	−0.643056	+	0.765819i	$0.722334\pi$
$524$	−14.8820	−0.650123
$525$	0	0
$526$	6.05104	0.263838
$527$	20.8684	0.909044
$528$	13.1048	0.570313
$529$	−9.38956	−0.408242
$530$	0	0
$531$	−4.96189	−0.215328
$532$	−44.5085	−1.92969
$533$	17.1879	0.744489
$534$	2.05927	0.0891134
$535$	0	0
$536$	2.25951	0.0975961
$537$	−16.6680	−0.719279
$538$	−1.74761	−0.0753447
$539$	−54.3015	−2.33893
$540$	0	0
$541$	−15.2798	−0.656930	−0.328465	−	0.944516i	$-0.606531\pi$
$541$	−15.2798	−0.656930	−0.328465	+	0.944516i	$0.606531\pi$
$542$	6.98248	0.299923
$543$	−6.57438	−0.282134
$544$	−18.5933	−0.797182
$545$	0	0
$546$	3.28516	0.140592
$547$	−2.81229	−0.120245	−0.0601225	−	0.998191i	$-0.519149\pi$
$547$	−2.81229	−0.120245	−0.0601225	+	0.998191i	$0.519149\pi$
$548$	−28.0973	−1.20026
$549$	−1.18776	−0.0506925
$550$	0	0
$551$	28.6393	1.22008
$552$	3.36928	0.143406
$553$	−23.1440	−0.984185
$554$	−1.17114	−0.0497571
$555$	0	0
$556$	−1.28960	−0.0546912
$557$	−9.38771	−0.397770	−0.198885	−	0.980023i	$-0.563732\pi$
$557$	−9.38771	−0.397770	−0.198885	+	0.980023i	$0.563732\pi$
$558$	−0.695700	−0.0294513
$559$	−0.111774	−0.00472755
$560$	0	0
$561$	−24.7094	−1.04323
$562$	−7.60565	−0.320825
$563$	1.14641	0.0483153	0.0241576	−	0.999708i	$-0.492310\pi$
$563$	1.14641	0.0483153	0.0241576	+	0.999708i	$0.492310\pi$
$564$	−1.94645	−0.0819602
$565$	0	0
$566$	4.60988	0.193768
$567$	4.71752	0.198117
$568$	4.40915	0.185004
$569$	−18.3152	−0.767815	−0.383908	−	0.923372i	$-0.625422\pi$
$569$	−18.3152	−0.767815	−0.383908	+	0.923372i	$0.625422\pi$
$570$	0	0
$571$	21.8996	0.916471	0.458236	−	0.888831i	$-0.348482\pi$
$571$	21.8996	0.916471	0.458236	+	0.888831i	$0.348482\pi$
$572$	−20.8493	−0.871754
$573$	−1.50553	−0.0628945
$574$	−6.23563	−0.260270
$575$	0	0
$576$	−6.74324	−0.280968
$577$	15.5004	0.645288	0.322644	−	0.946520i	$-0.395428\pi$
$577$	15.5004	0.645288	0.322644	+	0.946520i	$0.395428\pi$
$578$	7.21707	0.300190
$579$	21.6047	0.897863
$580$	0	0
$581$	15.4274	0.640035
$582$	−4.46581	−0.185114
$583$	40.0601	1.65912
$584$	−13.0616	−0.540492
$585$	0	0
$586$	−3.82561	−0.158035
$587$	28.8260	1.18978	0.594889	−	0.803808i	$-0.297196\pi$
$587$	28.8260	1.18978	0.594889	+	0.803808i	$0.297196\pi$
$588$	29.6930	1.22452
$589$	−14.5719	−0.600423
$590$	0	0
$591$	−0.883760	−0.0363530
$592$	36.7699	1.51123
$593$	−6.39418	−0.262577	−0.131289	−	0.991344i	$-0.541911\pi$
$593$	−6.39418	−0.262577	−0.131289	+	0.991344i	$0.541911\pi$
$594$	0.823748	0.0337988
$595$	0	0
$596$	−43.5382	−1.78339
$597$	−0.854677	−0.0349796
$598$	−2.56909	−0.105058
$599$	2.86729	0.117154	0.0585771	−	0.998283i	$-0.481344\pi$
$599$	2.86729	0.117154	0.0585771	+	0.998283i	$0.481344\pi$
$600$	0	0
$601$	−11.6084	−0.473517	−0.236758	−	0.971569i	$-0.576085\pi$
$601$	−11.6084	−0.473517	−0.236758	+	0.971569i	$0.576085\pi$
$602$	0.0405509	0.00165273
$603$	−2.47408	−0.100752
$604$	20.1928	0.821634
$605$	0	0
$606$	−2.17931	−0.0885283
$607$	−6.03085	−0.244785	−0.122392	−	0.992482i	$-0.539057\pi$
$607$	−6.03085	−0.244785	−0.122392	+	0.992482i	$0.539057\pi$
$608$	12.9832	0.526538
$609$	−27.8733	−1.12948
$610$	0	0
$611$	3.00919	0.121739
$612$	13.5115	0.546172
$613$	34.4167	1.39008	0.695038	−	0.718973i	$-0.255388\pi$
$613$	34.4167	1.39008	0.695038	+	0.718973i	$0.255388\pi$
$614$	5.78690	0.233540
$615$	0	0
$616$	15.3361	0.617908
$617$	13.7464	0.553408	0.276704	−	0.960955i	$-0.410758\pi$
$617$	13.7464	0.553408	0.276704	+	0.960955i	$0.410758\pi$
$618$	−1.92986	−0.0776302
$619$	−25.2696	−1.01567	−0.507835	−	0.861455i	$-0.669554\pi$
$619$	−25.2696	−1.01567	−0.507835	+	0.861455i	$0.669554\pi$
$620$	0	0
$621$	−3.68923	−0.148044
$622$	−1.87512	−0.0751856
$623$	−41.9791	−1.68186
$624$	11.0785	0.443494
$625$	0	0
$626$	−6.29114	−0.251445
$627$	17.2539	0.689055
$628$	−32.5457	−1.29872
$629$	−69.3306	−2.76439
$630$	0	0
$631$	0.132626	0.00527977	0.00263989	−	0.999997i	$-0.499160\pi$
$631$	0.132626	0.00527977	0.00263989	+	0.999997i	$0.499160\pi$
$632$	4.48050	0.178225
$633$	2.19748	0.0873420
$634$	4.38036	0.173966
$635$	0	0
$636$	−21.9056	−0.868612
$637$	−45.9051	−1.81883
$638$	−4.86710	−0.192690
$639$	−4.82785	−0.190987
$640$	0	0
$641$	−44.3210	−1.75057	−0.875287	−	0.483604i	$-0.839327\pi$
$641$	−44.3210	−1.75057	−0.875287	+	0.483604i	$0.839327\pi$
$642$	−3.75385	−0.148153
$643$	1.23540	0.0487193	0.0243596	−	0.999703i	$-0.492245\pi$
$643$	1.23540	0.0487193	0.0243596	+	0.999703i	$0.492245\pi$
$644$	−33.8760	−1.33490
$645$	0	0
$646$	−7.78653	−0.306357
$647$	−14.9531	−0.587868	−0.293934	−	0.955826i	$-0.594965\pi$
$647$	−14.9531	−0.587868	−0.293934	+	0.955826i	$0.594965\pi$
$648$	−0.913273	−0.0358767
$649$	17.6623	0.693305
$650$	0	0
$651$	14.1821	0.555841
$652$	4.89749	0.191801
$653$	9.00758	0.352494	0.176247	−	0.984346i	$-0.443604\pi$
$653$	9.00758	0.352494	0.176247	+	0.984346i	$0.443604\pi$
$654$	−1.01484	−0.0396833
$655$	0	0
$656$	−21.0282	−0.821015
$657$	14.3020	0.557972
$658$	−1.09171	−0.0425593
$659$	0.998263	0.0388868	0.0194434	−	0.999811i	$-0.493811\pi$
$659$	0.998263	0.0388868	0.0194434	+	0.999811i	$0.493811\pi$
$660$	0	0
$661$	−14.9246	−0.580499	−0.290250	−	0.956951i	$-0.593738\pi$
$661$	−14.9246	−0.580499	−0.290250	+	0.956951i	$0.593738\pi$
$662$	−4.93794	−0.191918
$663$	−20.8887	−0.811251
$664$	−2.98661	−0.115903
$665$	0	0
$666$	2.31130	0.0895611
$667$	21.7977	0.844012
$668$	−18.3390	−0.709557
$669$	−22.4599	−0.868349
$670$	0	0
$671$	4.22795	0.163218
$672$	−12.6359	−0.487442
$673$	1.36337	0.0525540	0.0262770	−	0.999655i	$-0.491635\pi$
$673$	1.36337	0.0525540	0.0262770	+	0.999655i	$0.491635\pi$
$674$	4.29924	0.165600
$675$	0	0
$676$	7.67832	0.295320
$677$	−28.2037	−1.08396	−0.541978	−	0.840392i	$-0.682325\pi$
$677$	−28.2037	−1.08396	−0.541978	+	0.840392i	$0.682325\pi$
$678$	−4.00583	−0.153843
$679$	91.0374	3.49369
$680$	0	0
$681$	−14.2680	−0.546752
$682$	2.47641	0.0948265
$683$	−36.0392	−1.37900	−0.689501	−	0.724285i	$-0.742170\pi$
$683$	−36.0392	−1.37900	−0.689501	+	0.724285i	$0.742170\pi$
$684$	−9.43473	−0.360746
$685$	0	0
$686$	9.01205	0.344081
$687$	−17.4827	−0.667007
$688$	0.136749	0.00521349
$689$	33.8658	1.29018
$690$	0	0
$691$	50.6321	1.92613	0.963067	−	0.269261i	$-0.0867793\pi$
$691$	50.6321	1.92613	0.963067	+	0.269261i	$0.0867793\pi$
$692$	8.14666	0.309690
$693$	−16.7924	−0.637892
$694$	1.54597	0.0586842
$695$	0	0
$696$	5.39605	0.204537
$697$	39.6493	1.50182
$698$	3.94728	0.149407
$699$	10.0126	0.378710
$700$	0	0
$701$	45.4876	1.71804	0.859022	−	0.511939i	$-0.171073\pi$
$701$	45.4876	1.71804	0.859022	+	0.511939i	$0.171073\pi$
$702$	0.696376	0.0262830
$703$	48.4116	1.82588
$704$	24.0032	0.904654
$705$	0	0
$706$	0.699007	0.0263075
$707$	44.4260	1.67081
$708$	−9.65805	−0.362972
$709$	−9.16598	−0.344236	−0.172118	−	0.985076i	$-0.555061\pi$
$709$	−9.16598	−0.344236	−0.172118	+	0.985076i	$0.555061\pi$
$710$	0	0
$711$	−4.90598	−0.183989
$712$	8.12681	0.304565
$713$	−11.0908	−0.415354
$714$	7.57828	0.283610
$715$	0	0
$716$	−32.4434	−1.21247
$717$	−0.192613	−0.00719328
$718$	−2.76670	−0.103252
$719$	47.9624	1.78870	0.894348	−	0.447372i	$-0.147640\pi$
$719$	47.9624	1.78870	0.894348	+	0.447372i	$0.147640\pi$
$720$	0	0
$721$	39.3409	1.46513
$722$	1.04020	0.0387124
$723$	−11.0948	−0.412618
$724$	−12.7967	−0.475585
$725$	0	0
$726$	−0.386626	−0.0143490
$727$	45.9128	1.70281	0.851406	−	0.524507i	$-0.175750\pi$
$727$	45.9128	1.70281	0.851406	+	0.524507i	$0.175750\pi$
$728$	12.9647	0.480505
$729$	1.00000	0.0370370
$730$	0	0
$731$	−0.257843	−0.00953666
$732$	−2.31192	−0.0854509
$733$	−38.0105	−1.40395	−0.701976	−	0.712201i	$-0.747699\pi$
$733$	−38.0105	−1.40395	−0.701976	+	0.712201i	$0.747699\pi$
$734$	0.342386	0.0126377
$735$	0	0
$736$	9.88167	0.364243
$737$	8.80672	0.324400
$738$	−1.32180	−0.0486562
$739$	−53.2205	−1.95775	−0.978874	−	0.204462i	$-0.934455\pi$
$739$	−53.2205	−1.95775	−0.978874	+	0.204462i	$0.934455\pi$
$740$	0	0
$741$	14.5860	0.535830
$742$	−12.2863	−0.451043
$743$	38.7613	1.42201	0.711006	−	0.703186i	$-0.248240\pi$
$743$	38.7613	1.42201	0.711006	+	0.703186i	$0.248240\pi$
$744$	−2.74554	−0.100656
$745$	0	0
$746$	−1.47743	−0.0540926
$747$	3.27023	0.119652
$748$	−48.0956	−1.75855
$749$	76.5237	2.79612
$750$	0	0
$751$	3.10748	0.113393	0.0566967	−	0.998391i	$-0.481943\pi$
$751$	3.10748	0.113393	0.0566967	+	0.998391i	$0.481943\pi$
$752$	−3.68155	−0.134252
$753$	2.26226	0.0824414
$754$	−4.11452	−0.149842
$755$	0	0
$756$	9.18239	0.333960
$757$	−7.86102	−0.285714	−0.142857	−	0.989743i	$-0.545629\pi$
$757$	−7.86102	−0.285714	−0.142857	+	0.989743i	$0.545629\pi$
$758$	−1.70471	−0.0619178
$759$	13.1322	0.476667
$760$	0	0
$761$	−24.4843	−0.887556	−0.443778	−	0.896137i	$-0.646362\pi$
$761$	−24.4843	−0.887556	−0.443778	+	0.896137i	$0.646362\pi$
$762$	4.35286	0.157688
$763$	20.6879	0.748952
$764$	−2.93044	−0.106019
$765$	0	0
$766$	5.24156	0.189385
$767$	14.9312	0.539136
$768$	−11.8856	−0.428886
$769$	13.4674	0.485645	0.242823	−	0.970071i	$-0.421927\pi$
$769$	13.4674	0.485645	0.242823	+	0.970071i	$0.421927\pi$
$770$	0	0
$771$	−26.1201	−0.940691
$772$	42.0525	1.51350
$773$	12.9199	0.464695	0.232348	−	0.972633i	$-0.425359\pi$
$773$	12.9199	0.464695	0.232348	+	0.972633i	$0.425359\pi$
$774$	0.00859581	0.000308970 0
$775$	0	0
$776$	−17.6241	−0.632668
$777$	−47.1168	−1.69031
$778$	−1.90197	−0.0681889
$779$	−27.6860	−0.991953
$780$	0	0
$781$	17.1852	0.614934
$782$	−5.92643	−0.211929
$783$	−5.90847	−0.211152
$784$	56.1619	2.00578
$785$	0	0
$786$	−1.76935	−0.0631105
$787$	34.1958	1.21895	0.609475	−	0.792805i	$-0.291380\pi$
$787$	34.1958	1.21895	0.609475	+	0.792805i	$0.291380\pi$
$788$	−1.72019	−0.0612793
$789$	−26.1478	−0.930887
$790$	0	0
$791$	81.6604	2.90351
$792$	3.25088	0.115515
$793$	3.57420	0.126924
$794$	−2.52117	−0.0894729
$795$	0	0
$796$	−1.66358	−0.0589641
$797$	−2.88148	−0.102067	−0.0510337	−	0.998697i	$-0.516252\pi$
$797$	−2.88148	−0.102067	−0.0510337	+	0.998697i	$0.516252\pi$
$798$	−5.29170	−0.187324
$799$	6.94165	0.245578
$800$	0	0
$801$	−8.89855	−0.314415
$802$	−0.534521	−0.0188746
$803$	−50.9091	−1.79654
$804$	−4.81567	−0.169836
$805$	0	0
$806$	2.09349	0.0737401
$807$	7.55179	0.265836
$808$	−8.60052	−0.302565
$809$	−30.1940	−1.06157	−0.530783	−	0.847508i	$-0.678102\pi$
$809$	−30.1940	−1.06157	−0.530783	+	0.847508i	$0.678102\pi$
$810$	0	0
$811$	38.0825	1.33726	0.668628	−	0.743597i	$-0.266882\pi$
$811$	38.0825	1.33726	0.668628	+	0.743597i	$0.266882\pi$
$812$	−54.2539	−1.90394
$813$	−30.1728	−1.05821
$814$	−8.22729	−0.288366
$815$	0	0
$816$	25.5560	0.894639
$817$	0.180044	0.00629896
$818$	−0.534196	−0.0186777
$819$	−14.1959	−0.496045
$820$	0	0
$821$	−15.8285	−0.552418	−0.276209	−	0.961098i	$-0.589078\pi$
$821$	−15.8285	−0.552418	−0.276209	+	0.961098i	$0.589078\pi$
$822$	−3.34053	−0.116515
$823$	36.6577	1.27781	0.638904	−	0.769287i	$-0.279388\pi$
$823$	36.6577	1.27781	0.638904	+	0.769287i	$0.279388\pi$
$824$	−7.61607	−0.265318
$825$	0	0
$826$	−5.41695	−0.188480
$827$	−37.0595	−1.28868	−0.644342	−	0.764738i	$-0.722869\pi$
$827$	−37.0595	−1.28868	−0.644342	+	0.764738i	$0.722869\pi$
$828$	−7.18089	−0.249553
$829$	−2.58132	−0.0896529	−0.0448264	−	0.998995i	$-0.514273\pi$
$829$	−2.58132	−0.0896529	−0.0448264	+	0.998995i	$0.514273\pi$
$830$	0	0
$831$	5.06076	0.175556
$832$	20.2917	0.703487
$833$	−105.895	−3.66903
$834$	−0.153323	−0.00530913
$835$	0	0
$836$	33.5838	1.16152
$837$	3.00627	0.103912
$838$	−2.70625	−0.0934857
$839$	4.61370	0.159283	0.0796413	−	0.996824i	$-0.474623\pi$
$839$	4.61370	0.159283	0.0796413	+	0.996824i	$0.474623\pi$
$840$	0	0
$841$	5.91007	0.203796
$842$	4.82394	0.166244
$843$	32.8656	1.13195
$844$	4.27728	0.147230
$845$	0	0
$846$	−0.231416	−0.00795626
$847$	7.88151	0.270812
$848$	−41.4326	−1.42280
$849$	−19.9203	−0.683663
$850$	0	0
$851$	36.8467	1.26309
$852$	−9.39715	−0.321941
$853$	−28.0982	−0.962064	−0.481032	−	0.876703i	$-0.659738\pi$
$853$	−28.0982	−0.962064	−0.481032	+	0.876703i	$0.659738\pi$
$854$	−1.29669	−0.0443720
$855$	0	0
$856$	−14.8144	−0.506345
$857$	26.6018	0.908699	0.454350	−	0.890823i	$-0.349872\pi$
$857$	26.6018	0.908699	0.454350	+	0.890823i	$0.349872\pi$
$858$	−2.47881	−0.0846253
$859$	29.6635	1.01211	0.506053	−	0.862503i	$-0.331104\pi$
$859$	29.6635	1.01211	0.506053	+	0.862503i	$0.331104\pi$
$860$	0	0
$861$	26.9455	0.918300
$862$	−3.24738	−0.110606
$863$	−44.8435	−1.52649	−0.763246	−	0.646108i	$-0.776395\pi$
$863$	−44.8435	−1.52649	−0.763246	+	0.646108i	$0.776395\pi$
$864$	−2.67852	−0.0911250
$865$	0	0
$866$	−6.84394	−0.232567
$867$	−31.1865	−1.05915
$868$	27.6047	0.936966
$869$	17.4633	0.592401
$870$	0	0
$871$	7.44498	0.252264
$872$	−4.00501	−0.135627
$873$	19.2977	0.653129
$874$	4.13826	0.139979
$875$	0	0
$876$	27.8380	0.940559
$877$	40.3330	1.36195	0.680974	−	0.732308i	$-0.261557\pi$
$877$	40.3330	1.36195	0.680974	+	0.732308i	$0.261557\pi$
$878$	7.34697	0.247948
$879$	16.5313	0.557586
$880$	0	0
$881$	20.1831	0.679985	0.339992	−	0.940428i	$-0.389575\pi$
$881$	20.1831	0.679985	0.339992	+	0.940428i	$0.389575\pi$
$882$	3.53025	0.118870
$883$	−38.1729	−1.28462	−0.642311	−	0.766445i	$-0.722024\pi$
$883$	−38.1729	−1.28462	−0.642311	+	0.766445i	$0.722024\pi$
$884$	−40.6588	−1.36750
$885$	0	0
$886$	8.14472	0.273627
$887$	4.96236	0.166620	0.0833099	−	0.996524i	$-0.473451\pi$
$887$	4.96236	0.166620	0.0833099	+	0.996524i	$0.473451\pi$
$888$	9.12143	0.306095
$889$	−88.7349	−2.97607
$890$	0	0
$891$	−3.55959	−0.119251
$892$	−43.7170	−1.46375
$893$	−4.84716	−0.162204
$894$	−5.17633	−0.173123
$895$	0	0
$896$	−32.6336	−1.09021
$897$	11.1016	0.370671
$898$	−6.93921	−0.231564
$899$	−17.7625	−0.592411
$900$	0	0
$901$	78.1222	2.60263
$902$	4.70508	0.156662
$903$	−0.175229	−0.00583125
$904$	−15.8088	−0.525793
$905$	0	0
$906$	2.40076	0.0797599
$907$	19.3509	0.642537	0.321269	−	0.946988i	$-0.395891\pi$
$907$	19.3509	0.642537	0.321269	+	0.946988i	$0.395891\pi$
$908$	−27.7720	−0.921645
$909$	9.41725	0.312351
$910$	0	0
$911$	−42.0073	−1.39176	−0.695881	−	0.718157i	$-0.744986\pi$
$911$	−42.0073	−1.39176	−0.695881	+	0.718157i	$0.744986\pi$
$912$	−17.8450	−0.590908
$913$	−11.6407	−0.385251
$914$	−2.82685	−0.0935040
$915$	0	0
$916$	−34.0292	−1.12436
$917$	36.0688	1.19110
$918$	1.60641	0.0530195
$919$	−13.4696	−0.444320	−0.222160	−	0.975010i	$-0.571311\pi$
$919$	−13.4696	−0.444320	−0.222160	+	0.975010i	$0.571311\pi$
$920$	0	0
$921$	−25.0064	−0.823989
$922$	1.33178	0.0438600
$923$	14.5279	0.478192
$924$	−32.6856	−1.07528
$925$	0	0
$926$	−5.61306	−0.184457
$927$	8.33932	0.273899
$928$	15.8259	0.519512
$929$	−17.8611	−0.586005	−0.293003	−	0.956112i	$-0.594654\pi$
$929$	−17.8611	−0.586005	−0.293003	+	0.956112i	$0.594654\pi$
$930$	0	0
$931$	73.9433	2.42339
$932$	19.4889	0.638380
$933$	8.10281	0.265274
$934$	−0.805025	−0.0263412
$935$	0	0
$936$	2.74821	0.0898280
$937$	41.7550	1.36408	0.682038	−	0.731317i	$-0.261094\pi$
$937$	41.7550	1.36408	0.682038	+	0.731317i	$0.261094\pi$
$938$	−2.70098	−0.0881903
$939$	27.1854	0.887161
$940$	0	0
$941$	−15.3534	−0.500507	−0.250254	−	0.968180i	$-0.580514\pi$
$941$	−15.3534	−0.500507	−0.250254	+	0.968180i	$0.580514\pi$
$942$	−3.86942	−0.126073
$943$	−21.0721	−0.686203
$944$	−18.2674	−0.594554
$945$	0	0
$946$	−0.0305976	−0.000994813 0
$947$	−10.6920	−0.347444	−0.173722	−	0.984795i	$-0.555579\pi$
$947$	−10.6920	−0.347444	−0.173722	+	0.984795i	$0.555579\pi$
$948$	−9.54922	−0.310144
$949$	−43.0373	−1.39705
$950$	0	0
$951$	−18.9285	−0.613798
$952$	29.9073	0.969300
$953$	50.4837	1.63533	0.817664	−	0.575696i	$-0.195269\pi$
$953$	50.4837	1.63533	0.817664	+	0.575696i	$0.195269\pi$
$954$	−2.60439	−0.0843203
$955$	0	0
$956$	−0.374912	−0.0121255
$957$	21.0318	0.679860
$958$	−6.21392	−0.200763
$959$	68.0981	2.19900
$960$	0	0
$961$	−21.9624	−0.708463
$962$	−6.95514	−0.224243
$963$	16.2212	0.522720
$964$	−21.5953	−0.695539
$965$	0	0
$966$	−4.02758	−0.129585
$967$	−23.0933	−0.742629	−0.371315	−	0.928507i	$-0.621093\pi$
$967$	−23.0933	−0.742629	−0.371315	+	0.928507i	$0.621093\pi$
$968$	−1.52580	−0.0490410
$969$	33.6473	1.08091
$970$	0	0
$971$	−32.8172	−1.05315	−0.526576	−	0.850128i	$-0.676525\pi$
$971$	−32.8172	−1.05315	−0.526576	+	0.850128i	$0.676525\pi$
$972$	1.94645	0.0624323
$973$	3.12555	0.100200
$974$	1.58035	0.0506377
$975$	0	0
$976$	−4.37280	−0.139970
$977$	−52.1471	−1.66833	−0.834166	−	0.551513i	$-0.814051\pi$
$977$	−52.1471	−1.66833	−0.834166	+	0.551513i	$0.814051\pi$
$978$	0.582272	0.0186190
$979$	31.6752	1.01234
$980$	0	0
$981$	4.38534	0.140013
$982$	−4.49819	−0.143543
$983$	−34.8188	−1.11055	−0.555273	−	0.831668i	$-0.687386\pi$
$983$	−34.8188	−1.11055	−0.555273	+	0.831668i	$0.687386\pi$
$984$	−5.21643	−0.166294
$985$	0	0
$986$	−9.49144	−0.302269
$987$	4.71752	0.150160
$988$	28.3909	0.903234
$989$	0.137034	0.00435743
$990$	0	0
$991$	−12.1182	−0.384949	−0.192474	−	0.981302i	$-0.561651\pi$
$991$	−12.1182	−0.384949	−0.192474	+	0.981302i	$0.561651\pi$
$992$	−8.05233	−0.255662
$993$	21.3379	0.677138
$994$	−5.27062	−0.167174
$995$	0	0
$996$	6.36533	0.201693
$997$	−37.5575	−1.18946	−0.594729	−	0.803926i	$-0.702741\pi$
$997$	−37.5575	−1.18946	−0.594729	+	0.803926i	$0.702741\pi$
$998$	−7.22103	−0.228578
$999$	−9.98763	−0.315994

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.bb.1.4	yes	7
5.4	even	2		3525.2.a.y.1.4	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.2.a.y.1.4	✓	7	5.4	even	2
3525.2.a.bb.1.4	yes	7	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+0.231416 q^{2} -1.00000 q^{3} -1.94645 q^{4} -0.231416 q^{6} +4.71752 q^{7} -0.913273 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.231416 q^{2} -1.00000 q^{3} -1.94645 q^{4} -0.231416 q^{6} +4.71752 q^{7} -0.913273 q^{8} +1.00000 q^{9} -3.55959 q^{11} +1.94645 q^{12} -3.00919 q^{13} +1.09171 q^{14} +3.68155 q^{16} -6.94165 q^{17} +0.231416 q^{18} +4.84716 q^{19} -4.71752 q^{21} -0.823748 q^{22} +3.68923 q^{23} +0.913273 q^{24} -0.696376 q^{26} -1.00000 q^{27} -9.18239 q^{28} +5.90847 q^{29} -3.00627 q^{31} +2.67852 q^{32} +3.55959 q^{33} -1.60641 q^{34} -1.94645 q^{36} +9.98763 q^{37} +1.12171 q^{38} +3.00919 q^{39} -5.71179 q^{41} -1.09171 q^{42} +0.0371443 q^{43} +6.92855 q^{44} +0.853749 q^{46} -1.00000 q^{47} -3.68155 q^{48} +15.2550 q^{49} +6.94165 q^{51} +5.85722 q^{52} -11.2541 q^{53} -0.231416 q^{54} -4.30838 q^{56} -4.84716 q^{57} +1.36732 q^{58} -4.96189 q^{59} -1.18776 q^{61} -0.695700 q^{62} +4.71752 q^{63} -6.74324 q^{64} +0.823748 q^{66} -2.47408 q^{67} +13.5115 q^{68} -3.68923 q^{69} -4.82785 q^{71} -0.913273 q^{72} +14.3020 q^{73} +2.31130 q^{74} -9.43473 q^{76} -16.7924 q^{77} +0.696376 q^{78} -4.90598 q^{79} +1.00000 q^{81} -1.32180 q^{82} +3.27023 q^{83} +9.18239 q^{84} +0.00859581 q^{86} -5.90847 q^{87} +3.25088 q^{88} -8.89855 q^{89} -14.1959 q^{91} -7.18089 q^{92} +3.00627 q^{93} -0.231416 q^{94} -2.67852 q^{96} +19.2977 q^{97} +3.53025 q^{98} -3.55959 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + q^{2} - 7 q^{3} + 5 q^{4} - q^{6} + 11 q^{7} + 6 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + q^2 - 7 * q^3 + 5 * q^4 - q^6 + 11 * q^7 + 6 * q^8 + 7 * q^9	\( 7 q + q^{2} - 7 q^{3} + 5 q^{4} - q^{6} + 11 q^{7} + 6 q^{8} + 7 q^{9} - 8 q^{11} - 5 q^{12} + 5 q^{13} - 3 q^{14} + 9 q^{16} + 10 q^{17} + q^{18} + 7 q^{19} - 11 q^{21} + 20 q^{22} + 4 q^{23} - 6 q^{24} - 7 q^{27} + 2 q^{28} - 11 q^{29} + 3 q^{31} + 28 q^{32} + 8 q^{33} + 8 q^{34} + 5 q^{36} + 11 q^{37} - 2 q^{38} - 5 q^{39} - 20 q^{41} + 3 q^{42} + 18 q^{43} + q^{44} - 19 q^{46} - 7 q^{47} - 9 q^{48} + 14 q^{49} - 10 q^{51} + 29 q^{52} + 12 q^{53} - q^{54} - 47 q^{56} - 7 q^{57} - 19 q^{58} + 18 q^{59} - 4 q^{61} + 12 q^{62} + 11 q^{63} + 42 q^{64} - 20 q^{66} + 22 q^{67} + 44 q^{68} - 4 q^{69} - 14 q^{71} + 6 q^{72} + 30 q^{73} + 31 q^{74} - 2 q^{76} - 8 q^{77} - q^{79} + 7 q^{81} + 29 q^{82} + 54 q^{83} - 2 q^{84} - 29 q^{86} + 11 q^{87} - 22 q^{88} - 14 q^{89} + 20 q^{91} - 5 q^{92} - 3 q^{93} - q^{94} - 28 q^{96} + 24 q^{97} - 26 q^{98} - 8 q^{99}+O(q^{100}) \) 7 * q + q^2 - 7 * q^3 + 5 * q^4 - q^6 + 11 * q^7 + 6 * q^8 + 7 * q^9 - 8 * q^11 - 5 * q^12 + 5 * q^13 - 3 * q^14 + 9 * q^16 + 10 * q^17 + q^18 + 7 * q^19 - 11 * q^21 + 20 * q^22 + 4 * q^23 - 6 * q^24 - 7 * q^27 + 2 * q^28 - 11 * q^29 + 3 * q^31 + 28 * q^32 + 8 * q^33 + 8 * q^34 + 5 * q^36 + 11 * q^37 - 2 * q^38 - 5 * q^39 - 20 * q^41 + 3 * q^42 + 18 * q^43 + q^44 - 19 * q^46 - 7 * q^47 - 9 * q^48 + 14 * q^49 - 10 * q^51 + 29 * q^52 + 12 * q^53 - q^54 - 47 * q^56 - 7 * q^57 - 19 * q^58 + 18 * q^59 - 4 * q^61 + 12 * q^62 + 11 * q^63 + 42 * q^64 - 20 * q^66 + 22 * q^67 + 44 * q^68 - 4 * q^69 - 14 * q^71 + 6 * q^72 + 30 * q^73 + 31 * q^74 - 2 * q^76 - 8 * q^77 - q^79 + 7 * q^81 + 29 * q^82 + 54 * q^83 - 2 * q^84 - 29 * q^86 + 11 * q^87 - 22 * q^88 - 14 * q^89 + 20 * q^91 - 5 * q^92 - 3 * q^93 - q^94 - 28 * q^96 + 24 * q^97 - 26 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more