LMFDB - Embedded newform 4018.2.a.bt.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4018,2,Mod(1,4018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4018 = 2 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4018.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:	$32.0838915322$
Analytic rank:	$0$
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} - x^{9} - 23x^{8} + 19x^{7} + 181x^{6} - 109x^{5} - 579x^{4} + 231x^{3} + 608x^{2} - 204x - 12 $ x^10 - x^9 - 23x^8 + 19x^7 + 181x^6 - 109x^5 - 579x^4 + 231x^3 + 608x^2 - 204x - 12
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 574)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.0511860$ of defining polynomial
Character	$\chi$	$=$	4018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.0511860 q^{3} +1.00000 q^{4} +0.949433 q^{5} +0.0511860 q^{6} +1.00000 q^{8} -2.99738 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.0511860 q^{3} +1.00000 q^{4} +0.949433 q^{5} +0.0511860 q^{6} +1.00000 q^{8} -2.99738 q^{9} +0.949433 q^{10} +0.0646501 q^{11} +0.0511860 q^{12} +3.36102 q^{13} +0.0485977 q^{15} +1.00000 q^{16} +4.94681 q^{17} -2.99738 q^{18} -0.771511 q^{19} +0.949433 q^{20} +0.0646501 q^{22} +4.13758 q^{23} +0.0511860 q^{24} -4.09858 q^{25} +3.36102 q^{26} -0.306982 q^{27} +8.87614 q^{29} +0.0485977 q^{30} -9.05629 q^{31} +1.00000 q^{32} +0.00330918 q^{33} +4.94681 q^{34} -2.99738 q^{36} +7.65270 q^{37} -0.771511 q^{38} +0.172037 q^{39} +0.949433 q^{40} -1.00000 q^{41} +6.78628 q^{43} +0.0646501 q^{44} -2.84581 q^{45} +4.13758 q^{46} -9.14066 q^{47} +0.0511860 q^{48} -4.09858 q^{50} +0.253208 q^{51} +3.36102 q^{52} +1.26497 q^{53} -0.306982 q^{54} +0.0613809 q^{55} -0.0394906 q^{57} +8.87614 q^{58} -2.61418 q^{59} +0.0485977 q^{60} -3.21938 q^{61} -9.05629 q^{62} +1.00000 q^{64} +3.19106 q^{65} +0.00330918 q^{66} +4.96028 q^{67} +4.94681 q^{68} +0.211786 q^{69} +5.15893 q^{71} -2.99738 q^{72} +14.4640 q^{73} +7.65270 q^{74} -0.209790 q^{75} -0.771511 q^{76} +0.172037 q^{78} +13.8393 q^{79} +0.949433 q^{80} +8.97643 q^{81} -1.00000 q^{82} -12.6235 q^{83} +4.69667 q^{85} +6.78628 q^{86} +0.454334 q^{87} +0.0646501 q^{88} +8.53849 q^{89} -2.84581 q^{90} +4.13758 q^{92} -0.463555 q^{93} -9.14066 q^{94} -0.732498 q^{95} +0.0511860 q^{96} -8.70966 q^{97} -0.193781 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} - q^{3} + 10 q^{4} + 2 q^{5} - q^{6} + 10 q^{8} + 17 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 - q^3 + 10 * q^4 + 2 * q^5 - q^6 + 10 * q^8 + 17 * q^9	$ 10 q + 10 q^{2} - q^{3} + 10 q^{4} + 2 q^{5} - q^{6} + 10 q^{8} + 17 q^{9} + 2 q^{10} + 11 q^{11} - q^{12} - 4 q^{13} + 4 q^{15} + 10 q^{16} - 5 q^{17} + 17 q^{18} + q^{19} + 2 q^{20} + 11 q^{22} + 9 q^{23} - q^{24} + 24 q^{25} - 4 q^{26} - 7 q^{27} + 23 q^{29} + 4 q^{30} + 5 q^{31} + 10 q^{32} + 5 q^{33} - 5 q^{34} + 17 q^{36} + 16 q^{37} + q^{38} - 7 q^{39} + 2 q^{40} - 10 q^{41} + 20 q^{43} + 11 q^{44} + 42 q^{45} + 9 q^{46} + 16 q^{47} - q^{48} + 24 q^{50} + 13 q^{51} - 4 q^{52} + 26 q^{53} - 7 q^{54} - 7 q^{55} + 37 q^{57} + 23 q^{58} + 10 q^{59} + 4 q^{60} + 5 q^{62} + 10 q^{64} + 18 q^{65} + 5 q^{66} + 7 q^{67} - 5 q^{68} - 39 q^{69} + 5 q^{71} + 17 q^{72} + 13 q^{73} + 16 q^{74} - 19 q^{75} + q^{76} - 7 q^{78} - q^{79} + 2 q^{80} + 18 q^{81} - 10 q^{82} - 21 q^{83} + 34 q^{85} + 20 q^{86} - 2 q^{87} + 11 q^{88} - 6 q^{89} + 42 q^{90} + 9 q^{92} - 5 q^{93} + 16 q^{94} + 24 q^{95} - q^{96} - 29 q^{97} + 48 q^{99}+O(q^{100}) $ 10 * q + 10 * q^2 - q^3 + 10 * q^4 + 2 * q^5 - q^6 + 10 * q^8 + 17 * q^9 + 2 * q^10 + 11 * q^11 - q^12 - 4 * q^13 + 4 * q^15 + 10 * q^16 - 5 * q^17 + 17 * q^18 + q^19 + 2 * q^20 + 11 * q^22 + 9 * q^23 - q^24 + 24 * q^25 - 4 * q^26 - 7 * q^27 + 23 * q^29 + 4 * q^30 + 5 * q^31 + 10 * q^32 + 5 * q^33 - 5 * q^34 + 17 * q^36 + 16 * q^37 + q^38 - 7 * q^39 + 2 * q^40 - 10 * q^41 + 20 * q^43 + 11 * q^44 + 42 * q^45 + 9 * q^46 + 16 * q^47 - q^48 + 24 * q^50 + 13 * q^51 - 4 * q^52 + 26 * q^53 - 7 * q^54 - 7 * q^55 + 37 * q^57 + 23 * q^58 + 10 * q^59 + 4 * q^60 + 5 * q^62 + 10 * q^64 + 18 * q^65 + 5 * q^66 + 7 * q^67 - 5 * q^68 - 39 * q^69 + 5 * q^71 + 17 * q^72 + 13 * q^73 + 16 * q^74 - 19 * q^75 + q^76 - 7 * q^78 - q^79 + 2 * q^80 + 18 * q^81 - 10 * q^82 - 21 * q^83 + 34 * q^85 + 20 * q^86 - 2 * q^87 + 11 * q^88 - 6 * q^89 + 42 * q^90 + 9 * q^92 - 5 * q^93 + 16 * q^94 + 24 * q^95 - q^96 - 29 * q^97 + 48 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.0511860	0.0295523	0.0147761	−	0.999891i	$-0.495296\pi$
$3$	0.0511860	0.0295523	0.0147761	+	0.999891i	$0.495296\pi$
$4$	1.00000	0.500000
$5$	0.949433	0.424599	0.212300	−	0.977205i	$-0.431905\pi$
$5$	0.949433	0.424599	0.212300	+	0.977205i	$0.431905\pi$
$6$	0.0511860	0.0208966
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	−2.99738	−0.999127
$10$	0.949433	0.300237
$11$	0.0646501	0.0194927	0.00974636	−	0.999953i	$-0.496898\pi$
$11$	0.0646501	0.0194927	0.00974636	+	0.999953i	$0.496898\pi$
$12$	0.0511860	0.0147761
$13$	3.36102	0.932178	0.466089	−	0.884738i	$-0.345663\pi$
$13$	3.36102	0.932178	0.466089	+	0.884738i	$0.345663\pi$
$14$	0	0
$15$	0.0485977	0.0125479
$16$	1.00000	0.250000
$17$	4.94681	1.19978	0.599889	−	0.800083i	$-0.295211\pi$
$17$	4.94681	1.19978	0.599889	+	0.800083i	$0.295211\pi$
$18$	−2.99738	−0.706489
$19$	−0.771511	−0.176997	−0.0884984	−	0.996076i	$-0.528207\pi$
$19$	−0.771511	−0.176997	−0.0884984	+	0.996076i	$0.528207\pi$
$20$	0.949433	0.212300
$21$	0	0
$22$	0.0646501	0.0137834
$23$	4.13758	0.862745	0.431373	−	0.902174i	$-0.358029\pi$
$23$	4.13758	0.862745	0.431373	+	0.902174i	$0.358029\pi$
$24$	0.0511860	0.0104483
$25$	−4.09858	−0.819715
$26$	3.36102	0.659150
$27$	−0.306982	−0.0590787
$28$	0	0
$29$	8.87614	1.64826	0.824129	−	0.566403i	$-0.191665\pi$
$29$	8.87614	1.64826	0.824129	+	0.566403i	$0.191665\pi$
$30$	0.0485977	0.00887268
$31$	−9.05629	−1.62656	−0.813279	−	0.581874i	$-0.802320\pi$
$31$	−9.05629	−1.62656	−0.813279	+	0.581874i	$0.802320\pi$
$32$	1.00000	0.176777
$33$	0.00330918	0.000576054 0
$34$	4.94681	0.848371
$35$	0	0
$36$	−2.99738	−0.499563
$37$	7.65270	1.25810	0.629048	−	0.777366i	$-0.283445\pi$
$37$	7.65270	1.25810	0.629048	+	0.777366i	$0.283445\pi$
$38$	−0.771511	−0.125156
$39$	0.172037	0.0275480
$40$	0.949433	0.150118
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	6.78628	1.03490	0.517449	−	0.855714i	$-0.326882\pi$
$43$	6.78628	1.03490	0.517449	+	0.855714i	$0.326882\pi$
$44$	0.0646501	0.00974636
$45$	−2.84581	−0.424228
$46$	4.13758	0.610053
$47$	−9.14066	−1.33330	−0.666651	−	0.745370i	$-0.732273\pi$
$47$	−9.14066	−1.33330	−0.666651	+	0.745370i	$0.732273\pi$
$48$	0.0511860	0.00738806
$49$	0	0
$50$	−4.09858	−0.579626
$51$	0.253208	0.0354562
$52$	3.36102	0.466089
$53$	1.26497	0.173757	0.0868787	−	0.996219i	$-0.472311\pi$
$53$	1.26497	0.173757	0.0868787	+	0.996219i	$0.472311\pi$
$54$	−0.306982	−0.0417750
$55$	0.0613809	0.00827660
$56$	0	0
$57$	−0.0394906	−0.00523065
$58$	8.87614	1.16549
$59$	−2.61418	−0.340338	−0.170169	−	0.985415i	$-0.554431\pi$
$59$	−2.61418	−0.340338	−0.170169	+	0.985415i	$0.554431\pi$
$60$	0.0485977	0.00627393
$61$	−3.21938	−0.412200	−0.206100	−	0.978531i	$-0.566077\pi$
$61$	−3.21938	−0.412200	−0.206100	+	0.978531i	$0.566077\pi$
$62$	−9.05629	−1.15015
$63$	0	0
$64$	1.00000	0.125000
$65$	3.19106	0.395802
$66$	0.00330918	0.000407332 0
$67$	4.96028	0.605994	0.302997	−	0.952991i	$-0.402013\pi$
$67$	4.96028	0.605994	0.302997	+	0.952991i	$0.402013\pi$
$68$	4.94681	0.599889
$69$	0.211786	0.0254961
$70$	0	0
$71$	5.15893	0.612253	0.306126	−	0.951991i	$-0.400967\pi$
$71$	5.15893	0.612253	0.306126	+	0.951991i	$0.400967\pi$
$72$	−2.99738	−0.353245
$73$	14.4640	1.69288	0.846441	−	0.532482i	$-0.178741\pi$
$73$	14.4640	1.69288	0.846441	+	0.532482i	$0.178741\pi$
$74$	7.65270	0.889608
$75$	−0.209790	−0.0242244
$76$	−0.771511	−0.0884984
$77$	0	0
$78$	0.172037	0.0194794
$79$	13.8393	1.55705	0.778524	−	0.627615i	$-0.215969\pi$
$79$	13.8393	1.55705	0.778524	+	0.627615i	$0.215969\pi$
$80$	0.949433	0.106150
$81$	8.97643	0.997381
$82$	−1.00000	−0.110432
$83$	−12.6235	−1.38561	−0.692805	−	0.721125i	$-0.743625\pi$
$83$	−12.6235	−1.38561	−0.692805	+	0.721125i	$0.743625\pi$
$84$	0	0
$85$	4.69667	0.509425
$86$	6.78628	0.731784
$87$	0.454334	0.0487097
$88$	0.0646501	0.00689172
$89$	8.53849	0.905078	0.452539	−	0.891745i	$-0.350518\pi$
$89$	8.53849	0.905078	0.452539	+	0.891745i	$0.350518\pi$
$90$	−2.84581	−0.299975
$91$	0	0
$92$	4.13758	0.431373
$93$	−0.463555	−0.0480685
$94$	−9.14066	−0.942787
$95$	−0.732498	−0.0751527
$96$	0.0511860	0.00522415
$97$	−8.70966	−0.884332	−0.442166	−	0.896933i	$-0.645790\pi$
$97$	−8.70966	−0.884332	−0.442166	+	0.896933i	$0.645790\pi$
$98$	0	0
$99$	−0.193781	−0.0194757
$100$	−4.09858	−0.409858
$101$	14.7208	1.46478	0.732389	−	0.680886i	$-0.238405\pi$
$101$	14.7208	1.46478	0.732389	+	0.680886i	$0.238405\pi$
$102$	0.253208	0.0250713
$103$	13.3064	1.31112	0.655561	−	0.755142i	$-0.272432\pi$
$103$	13.3064	1.31112	0.655561	+	0.755142i	$0.272432\pi$
$104$	3.36102	0.329575
$105$	0	0
$106$	1.26497	0.122865
$107$	−16.9192	−1.63564	−0.817818	−	0.575477i	$-0.804816\pi$
$107$	−16.9192	−1.63564	−0.817818	+	0.575477i	$0.804816\pi$
$108$	−0.306982	−0.0295394
$109$	−3.44444	−0.329918	−0.164959	−	0.986300i	$-0.552749\pi$
$109$	−3.44444	−0.329918	−0.164959	+	0.986300i	$0.552749\pi$
$110$	0.0613809	0.00585244
$111$	0.391711	0.0371796
$112$	0	0
$113$	1.61725	0.152138	0.0760690	−	0.997103i	$-0.475763\pi$
$113$	1.61725	0.152138	0.0760690	+	0.997103i	$0.475763\pi$
$114$	−0.0394906	−0.00369863
$115$	3.92835	0.366321
$116$	8.87614	0.824129
$117$	−10.0742	−0.931364
$118$	−2.61418	−0.240655
$119$	0	0
$120$	0.0485977	0.00443634
$121$	−10.9958	−0.999620
$122$	−3.21938	−0.291469
$123$	−0.0511860	−0.00461529
$124$	−9.05629	−0.813279
$125$	−8.63849	−0.772650
$126$	0	0
$127$	19.3445	1.71655	0.858275	−	0.513190i	$-0.171536\pi$
$127$	19.3445	1.71655	0.858275	+	0.513190i	$0.171536\pi$
$128$	1.00000	0.0883883
$129$	0.347363	0.0305836
$130$	3.19106	0.279874
$131$	5.13821	0.448927	0.224464	−	0.974482i	$-0.427937\pi$
$131$	5.13821	0.448927	0.224464	+	0.974482i	$0.427937\pi$
$132$	0.00330918	0.000288027 0
$133$	0	0
$134$	4.96028	0.428503
$135$	−0.291459	−0.0250848
$136$	4.94681	0.424186
$137$	7.23145	0.617825	0.308912	−	0.951091i	$-0.400035\pi$
$137$	7.23145	0.617825	0.308912	+	0.951091i	$0.400035\pi$
$138$	0.211786	0.0180284
$139$	13.7875	1.16944	0.584720	−	0.811236i	$-0.301205\pi$
$139$	13.7875	1.16944	0.584720	+	0.811236i	$0.301205\pi$
$140$	0	0
$141$	−0.467874	−0.0394021
$142$	5.15893	0.432928
$143$	0.217290	0.0181707
$144$	−2.99738	−0.249782
$145$	8.42730	0.699849
$146$	14.4640	1.19705
$147$	0	0
$148$	7.65270	0.629048
$149$	−6.98630	−0.572340	−0.286170	−	0.958179i	$-0.592382\pi$
$149$	−6.98630	−0.572340	−0.286170	+	0.958179i	$0.592382\pi$
$150$	−0.209790	−0.0171293
$151$	14.4872	1.17895	0.589475	−	0.807787i	$-0.299335\pi$
$151$	14.4872	1.17895	0.589475	+	0.807787i	$0.299335\pi$
$152$	−0.771511	−0.0625778
$153$	−14.8275	−1.19873
$154$	0	0
$155$	−8.59834	−0.690635
$156$	0.172037	0.0137740
$157$	14.7236	1.17507	0.587536	−	0.809198i	$-0.300098\pi$
$157$	14.7236	1.17507	0.587536	+	0.809198i	$0.300098\pi$
$158$	13.8393	1.10100
$159$	0.0647490	0.00513493
$160$	0.949433	0.0750592
$161$	0	0
$162$	8.97643	0.705255
$163$	−7.43755	−0.582554	−0.291277	−	0.956639i	$-0.594080\pi$
$163$	−7.43755	−0.582554	−0.291277	+	0.956639i	$0.594080\pi$
$164$	−1.00000	−0.0780869
$165$	0.00314184	0.000244592 0
$166$	−12.6235	−0.979774
$167$	−19.1204	−1.47958	−0.739789	−	0.672838i	$-0.765075\pi$
$167$	−19.1204	−1.47958	−0.739789	+	0.672838i	$0.765075\pi$
$168$	0	0
$169$	−1.70356	−0.131043
$170$	4.69667	0.360218
$171$	2.31251	0.176842
$172$	6.78628	0.517449
$173$	−9.44608	−0.718172	−0.359086	−	0.933304i	$-0.616912\pi$
$173$	−9.44608	−0.718172	−0.359086	+	0.933304i	$0.616912\pi$
$174$	0.454334	0.0344430
$175$	0	0
$176$	0.0646501	0.00487318
$177$	−0.133810	−0.0100577
$178$	8.53849	0.639987
$179$	−9.41954	−0.704049	−0.352025	−	0.935991i	$-0.614507\pi$
$179$	−9.41954	−0.704049	−0.352025	+	0.935991i	$0.614507\pi$
$180$	−2.84581	−0.212114
$181$	11.9245	0.886344	0.443172	−	0.896437i	$-0.353853\pi$
$181$	11.9245	0.886344	0.443172	+	0.896437i	$0.353853\pi$
$182$	0	0
$183$	−0.164787	−0.0121814
$184$	4.13758	0.305026
$185$	7.26572	0.534187
$186$	−0.463555	−0.0339895
$187$	0.319812	0.0233870
$188$	−9.14066	−0.666651
$189$	0	0
$190$	−0.732498	−0.0531410
$191$	14.6842	1.06251	0.531254	−	0.847212i	$-0.321721\pi$
$191$	14.6842	1.06251	0.531254	+	0.847212i	$0.321721\pi$
$192$	0.0511860	0.00369403
$193$	1.33718	0.0962521	0.0481260	−	0.998841i	$-0.484675\pi$
$193$	1.33718	0.0962521	0.0481260	+	0.998841i	$0.484675\pi$
$194$	−8.70966	−0.625317
$195$	0.163338	0.0116969
$196$	0	0
$197$	−17.6251	−1.25574	−0.627868	−	0.778320i	$-0.716072\pi$
$197$	−17.6251	−1.25574	−0.627868	+	0.778320i	$0.716072\pi$
$198$	−0.193781	−0.0137714
$199$	−4.95745	−0.351425	−0.175712	−	0.984442i	$-0.556223\pi$
$199$	−4.95745	−0.351425	−0.175712	+	0.984442i	$0.556223\pi$
$200$	−4.09858	−0.289813
$201$	0.253897	0.0179085
$202$	14.7208	1.03575
$203$	0	0
$204$	0.253208	0.0177281
$205$	−0.949433	−0.0663113
$206$	13.3064	0.927103
$207$	−12.4019	−0.861992
$208$	3.36102	0.233045
$209$	−0.0498782	−0.00345015
$210$	0	0
$211$	0.993023	0.0683625	0.0341813	−	0.999416i	$-0.489118\pi$
$211$	0.993023	0.0683625	0.0341813	+	0.999416i	$0.489118\pi$
$212$	1.26497	0.0868787
$213$	0.264065	0.0180935
$214$	−16.9192	−1.15657
$215$	6.44312	0.439417
$216$	−0.306982	−0.0208875
$217$	0	0
$218$	−3.44444	−0.233287
$219$	0.740354	0.0500285
$220$	0.0613809	0.00413830
$221$	16.6263	1.11841
$222$	0.391711	0.0262899
$223$	−26.4458	−1.77094	−0.885472	−	0.464693i	$-0.846165\pi$
$223$	−26.4458	−1.77094	−0.885472	+	0.464693i	$0.846165\pi$
$224$	0	0
$225$	12.2850	0.819000
$226$	1.61725	0.107578
$227$	−11.3494	−0.753288	−0.376644	−	0.926358i	$-0.622922\pi$
$227$	−11.3494	−0.753288	−0.376644	+	0.926358i	$0.622922\pi$
$228$	−0.0394906	−0.00261533
$229$	−23.8159	−1.57380	−0.786898	−	0.617083i	$-0.788314\pi$
$229$	−23.8159	−1.57380	−0.786898	+	0.617083i	$0.788314\pi$
$230$	3.92835	0.259028
$231$	0	0
$232$	8.87614	0.582747
$233$	17.4015	1.14001	0.570006	−	0.821641i	$-0.306941\pi$
$233$	17.4015	1.14001	0.570006	+	0.821641i	$0.306941\pi$
$234$	−10.0742	−0.658574
$235$	−8.67844	−0.566119
$236$	−2.61418	−0.170169
$237$	0.708381	0.0460143
$238$	0	0
$239$	22.1434	1.43234	0.716168	−	0.697928i	$-0.245894\pi$
$239$	22.1434	1.43234	0.716168	+	0.697928i	$0.245894\pi$
$240$	0.0485977	0.00313697
$241$	1.86267	0.119985	0.0599925	−	0.998199i	$-0.480892\pi$
$241$	1.86267	0.119985	0.0599925	+	0.998199i	$0.480892\pi$
$242$	−10.9958	−0.706838
$243$	1.38041	0.0885536
$244$	−3.21938	−0.206100
$245$	0	0
$246$	−0.0511860	−0.00326350
$247$	−2.59306	−0.164993
$248$	−9.05629	−0.575075
$249$	−0.646147	−0.0409479
$250$	−8.63849	−0.546346
$251$	−9.05891	−0.571793	−0.285897	−	0.958260i	$-0.592291\pi$
$251$	−9.05891	−0.571793	−0.285897	+	0.958260i	$0.592291\pi$
$252$	0	0
$253$	0.267495	0.0168173
$254$	19.3445	1.21378
$255$	0.240404	0.0150547
$256$	1.00000	0.0625000
$257$	2.05292	0.128058	0.0640290	−	0.997948i	$-0.479605\pi$
$257$	2.05292	0.128058	0.0640290	+	0.997948i	$0.479605\pi$
$258$	0.347363	0.0216259
$259$	0	0
$260$	3.19106	0.197901
$261$	−26.6052	−1.64682
$262$	5.13821	0.317439
$263$	−29.7197	−1.83259	−0.916297	−	0.400499i	$-0.868837\pi$
$263$	−29.7197	−1.83259	−0.916297	+	0.400499i	$0.868837\pi$
$264$	0.00330918	0.000203666 0
$265$	1.20101	0.0737773
$266$	0	0
$267$	0.437051	0.0267471
$268$	4.96028	0.302997
$269$	19.4622	1.18663	0.593315	−	0.804971i	$-0.297819\pi$
$269$	19.4622	1.18663	0.593315	+	0.804971i	$0.297819\pi$
$270$	−0.291459	−0.0177376
$271$	1.75254	0.106459	0.0532296	−	0.998582i	$-0.483048\pi$
$271$	1.75254	0.106459	0.0532296	+	0.998582i	$0.483048\pi$
$272$	4.94681	0.299945
$273$	0	0
$274$	7.23145	0.436868
$275$	−0.264973	−0.0159785
$276$	0.211786	0.0127480
$277$	−16.1849	−0.972454	−0.486227	−	0.873832i	$-0.661627\pi$
$277$	−16.1849	−0.972454	−0.486227	+	0.873832i	$0.661627\pi$
$278$	13.7875	0.826918
$279$	27.1451	1.62514
$280$	0	0
$281$	−18.0627	−1.07753	−0.538766	−	0.842455i	$-0.681109\pi$
$281$	−18.0627	−1.07753	−0.538766	+	0.842455i	$0.681109\pi$
$282$	−0.467874	−0.0278615
$283$	−10.0866	−0.599587	−0.299794	−	0.954004i	$-0.596918\pi$
$283$	−10.0866	−0.599587	−0.299794	+	0.954004i	$0.596918\pi$
$284$	5.15893	0.306126
$285$	−0.0374936	−0.00222093
$286$	0.217290	0.0128486
$287$	0	0
$288$	−2.99738	−0.176622
$289$	7.47096	0.439468
$290$	8.42730	0.494868
$291$	−0.445813	−0.0261340
$292$	14.4640	0.846441
$293$	−14.6369	−0.855095	−0.427547	−	0.903993i	$-0.640622\pi$
$293$	−14.6369	−0.855095	−0.427547	+	0.903993i	$0.640622\pi$
$294$	0	0
$295$	−2.48199	−0.144507
$296$	7.65270	0.444804
$297$	−0.0198464	−0.00115161
$298$	−6.98630	−0.404705
$299$	13.9065	0.804232
$300$	−0.209790	−0.0121122
$301$	0	0
$302$	14.4872	0.833644
$303$	0.753501	0.0432875
$304$	−0.771511	−0.0442492
$305$	−3.05659	−0.175020
$306$	−14.8275	−0.847630
$307$	−19.8519	−1.13301	−0.566505	−	0.824058i	$-0.691705\pi$
$307$	−19.8519	−1.13301	−0.566505	+	0.824058i	$0.691705\pi$
$308$	0	0
$309$	0.681103	0.0387466
$310$	−8.59834	−0.488353
$311$	9.15965	0.519396	0.259698	−	0.965690i	$-0.416377\pi$
$311$	9.15965	0.519396	0.259698	+	0.965690i	$0.416377\pi$
$312$	0.172037	0.00973968
$313$	2.99024	0.169018	0.0845091	−	0.996423i	$-0.473068\pi$
$313$	2.99024	0.169018	0.0845091	+	0.996423i	$0.473068\pi$
$314$	14.7236	0.830901
$315$	0	0
$316$	13.8393	0.778524
$317$	17.9992	1.01093	0.505467	−	0.862846i	$-0.331320\pi$
$317$	17.9992	1.01093	0.505467	+	0.862846i	$0.331320\pi$
$318$	0.0647490	0.00363094
$319$	0.573843	0.0321290
$320$	0.949433	0.0530749
$321$	−0.866024	−0.0483367
$322$	0	0
$323$	−3.81652	−0.212357
$324$	8.97643	0.498690
$325$	−13.7754	−0.764121
$326$	−7.43755	−0.411928
$327$	−0.176307	−0.00974982
$328$	−1.00000	−0.0552158
$329$	0	0
$330$	0.00314184	0.000172953 0
$331$	−25.3125	−1.39130	−0.695650	−	0.718381i	$-0.744883\pi$
$331$	−25.3125	−1.39130	−0.695650	+	0.718381i	$0.744883\pi$
$332$	−12.6235	−0.692805
$333$	−22.9380	−1.25700
$334$	−19.1204	−1.04622
$335$	4.70945	0.257305
$336$	0	0
$337$	−2.96293	−0.161401	−0.0807005	−	0.996738i	$-0.525716\pi$
$337$	−2.96293	−0.161401	−0.0807005	+	0.996738i	$0.525716\pi$
$338$	−1.70356	−0.0926616
$339$	0.0827805	0.00449602
$340$	4.69667	0.254712
$341$	−0.585490	−0.0317060
$342$	2.31251	0.125046
$343$	0	0
$344$	6.78628	0.365892
$345$	0.201077	0.0108256
$346$	−9.44608	−0.507824
$347$	24.6149	1.32140	0.660700	−	0.750650i	$-0.270260\pi$
$347$	24.6149	1.32140	0.660700	+	0.750650i	$0.270260\pi$
$348$	0.454334	0.0243549
$349$	−27.5583	−1.47516	−0.737582	−	0.675257i	$-0.764033\pi$
$349$	−27.5583	−1.47516	−0.737582	+	0.675257i	$0.764033\pi$
$350$	0	0
$351$	−1.03177	−0.0550719
$352$	0.0646501	0.00344586
$353$	−11.6635	−0.620786	−0.310393	−	0.950608i	$-0.600461\pi$
$353$	−11.6635	−0.620786	−0.310393	+	0.950608i	$0.600461\pi$
$354$	−0.133810	−0.00711190
$355$	4.89806	0.259962
$356$	8.53849	0.452539
$357$	0	0
$358$	−9.41954	−0.497838
$359$	17.4849	0.922818	0.461409	−	0.887188i	$-0.347344\pi$
$359$	17.4849	0.922818	0.461409	+	0.887188i	$0.347344\pi$
$360$	−2.84581	−0.149987
$361$	−18.4048	−0.968672
$362$	11.9245	0.626740
$363$	−0.562832	−0.0295410
$364$	0	0
$365$	13.7326	0.718797
$366$	−0.164787	−0.00861357
$367$	20.2595	1.05754	0.528769	−	0.848766i	$-0.322654\pi$
$367$	20.2595	1.05754	0.528769	+	0.848766i	$0.322654\pi$
$368$	4.13758	0.215686
$369$	2.99738	0.156037
$370$	7.26572	0.377727
$371$	0	0
$372$	−0.463555	−0.0240342
$373$	−1.82070	−0.0942722	−0.0471361	−	0.998888i	$-0.515009\pi$
$373$	−1.82070	−0.0942722	−0.0471361	+	0.998888i	$0.515009\pi$
$374$	0.319812	0.0165371
$375$	−0.442170	−0.0228335
$376$	−9.14066	−0.471393
$377$	29.8329	1.53647
$378$	0	0
$379$	−17.0815	−0.877418	−0.438709	−	0.898629i	$-0.644564\pi$
$379$	−17.0815	−0.877418	−0.438709	+	0.898629i	$0.644564\pi$
$380$	−0.732498	−0.0375763
$381$	0.990170	0.0507279
$382$	14.6842	0.751307
$383$	0.138065	0.00705478	0.00352739	−	0.999994i	$-0.498877\pi$
$383$	0.138065	0.00705478	0.00352739	+	0.999994i	$0.498877\pi$
$384$	0.0511860	0.00261208
$385$	0	0
$386$	1.33718	0.0680605
$387$	−20.3411	−1.03399
$388$	−8.70966	−0.442166
$389$	37.4848	1.90055	0.950277	−	0.311405i	$-0.100800\pi$
$389$	37.4848	1.90055	0.950277	+	0.311405i	$0.100800\pi$
$390$	0.163338	0.00827092
$391$	20.4678	1.03510
$392$	0	0
$393$	0.263004	0.0132668
$394$	−17.6251	−0.887940
$395$	13.1395	0.661122
$396$	−0.193781	−0.00973785
$397$	−25.9422	−1.30200	−0.651000	−	0.759078i	$-0.725650\pi$
$397$	−25.9422	−1.30200	−0.651000	+	0.759078i	$0.725650\pi$
$398$	−4.95745	−0.248495
$399$	0	0
$400$	−4.09858	−0.204929
$401$	21.4268	1.07000	0.535002	−	0.844851i	$-0.320311\pi$
$401$	21.4268	1.07000	0.535002	+	0.844851i	$0.320311\pi$
$402$	0.253897	0.0126632
$403$	−30.4383	−1.51624
$404$	14.7208	0.732389
$405$	8.52251	0.423487
$406$	0	0
$407$	0.494748	0.0245237
$408$	0.253208	0.0125356
$409$	19.6351	0.970893	0.485446	−	0.874266i	$-0.338657\pi$
$409$	19.6351	0.970893	0.485446	+	0.874266i	$0.338657\pi$
$410$	−0.949433	−0.0468891
$411$	0.370149	0.0182581
$412$	13.3064	0.655561
$413$	0	0
$414$	−12.4019	−0.609520
$415$	−11.9852	−0.588329
$416$	3.36102	0.164787
$417$	0.705726	0.0345596
$418$	−0.0498782	−0.00243962
$419$	9.44883	0.461606	0.230803	−	0.973001i	$-0.425865\pi$
$419$	9.44883	0.461606	0.230803	+	0.973001i	$0.425865\pi$
$420$	0	0
$421$	34.3374	1.67350	0.836752	−	0.547582i	$-0.184452\pi$
$421$	34.3374	1.67350	0.836752	+	0.547582i	$0.184452\pi$
$422$	0.993023	0.0483396
$423$	27.3980	1.33214
$424$	1.26497	0.0614325
$425$	−20.2749	−0.983477
$426$	0.264065	0.0127940
$427$	0	0
$428$	−16.9192	−0.817818
$429$	0.0111222	0.000536985 0
$430$	6.44312	0.310715
$431$	−16.5458	−0.796983	−0.398492	−	0.917172i	$-0.630466\pi$
$431$	−16.5458	−0.796983	−0.398492	+	0.917172i	$0.630466\pi$
$432$	−0.306982	−0.0147697
$433$	−12.3872	−0.595289	−0.297645	−	0.954677i	$-0.596201\pi$
$433$	−12.3872	−0.595289	−0.297645	+	0.954677i	$0.596201\pi$
$434$	0	0
$435$	0.431360	0.0206821
$436$	−3.44444	−0.164959
$437$	−3.19219	−0.152703
$438$	0.740354	0.0353755
$439$	−10.4888	−0.500601	−0.250301	−	0.968168i	$-0.580529\pi$
$439$	−10.4888	−0.500601	−0.250301	+	0.968168i	$0.580529\pi$
$440$	0.0613809	0.00292622
$441$	0	0
$442$	16.6263	0.790834
$443$	17.6179	0.837051	0.418526	−	0.908205i	$-0.362547\pi$
$443$	17.6179	0.837051	0.418526	+	0.908205i	$0.362547\pi$
$444$	0.391711	0.0185898
$445$	8.10672	0.384296
$446$	−26.4458	−1.25225
$447$	−0.357601	−0.0169139
$448$	0	0
$449$	−23.1017	−1.09024	−0.545118	−	0.838359i	$-0.683515\pi$
$449$	−23.1017	−1.09024	−0.545118	+	0.838359i	$0.683515\pi$
$450$	12.2850	0.579120
$451$	−0.0646501	−0.00304425
$452$	1.61725	0.0760690
$453$	0.741541	0.0348406
$454$	−11.3494	−0.532655
$455$	0	0
$456$	−0.0394906	−0.00184932
$457$	6.90710	0.323100	0.161550	−	0.986865i	$-0.448351\pi$
$457$	6.90710	0.323100	0.161550	+	0.986865i	$0.448351\pi$
$458$	−23.8159	−1.11284
$459$	−1.51858	−0.0708814
$460$	3.92835	0.183160
$461$	−19.2649	−0.897257	−0.448629	−	0.893718i	$-0.648087\pi$
$461$	−19.2649	−0.897257	−0.448629	+	0.893718i	$0.648087\pi$
$462$	0	0
$463$	−26.6956	−1.24065	−0.620324	−	0.784345i	$-0.712999\pi$
$463$	−26.6956	−1.24065	−0.620324	+	0.784345i	$0.712999\pi$
$464$	8.87614	0.412064
$465$	−0.440115	−0.0204098
$466$	17.4015	0.806110
$467$	−3.55516	−0.164513	−0.0822567	−	0.996611i	$-0.526213\pi$
$467$	−3.55516	−0.164513	−0.0822567	+	0.996611i	$0.526213\pi$
$468$	−10.0742	−0.465682
$469$	0	0
$470$	−8.67844	−0.400307
$471$	0.753642	0.0347260
$472$	−2.61418	−0.120328
$473$	0.438734	0.0201730
$474$	0.708381	0.0325370
$475$	3.16210	0.145087
$476$	0	0
$477$	−3.79161	−0.173606
$478$	22.1434	1.01281
$479$	−15.5694	−0.711385	−0.355693	−	0.934603i	$-0.615755\pi$
$479$	−15.5694	−0.711385	−0.355693	+	0.934603i	$0.615755\pi$
$480$	0.0485977	0.00221817
$481$	25.7209	1.17277
$482$	1.86267	0.0848422
$483$	0	0
$484$	−10.9958	−0.499810
$485$	−8.26923	−0.375487
$486$	1.38041	0.0626168
$487$	25.3719	1.14971	0.574855	−	0.818255i	$-0.305059\pi$
$487$	25.3719	1.14971	0.574855	+	0.818255i	$0.305059\pi$
$488$	−3.21938	−0.145735
$489$	−0.380699	−0.0172158
$490$	0	0
$491$	−4.90620	−0.221414	−0.110707	−	0.993853i	$-0.535311\pi$
$491$	−4.90620	−0.221414	−0.110707	+	0.993853i	$0.535311\pi$
$492$	−0.0511860	−0.00230764
$493$	43.9086	1.97754
$494$	−2.59306	−0.116667
$495$	−0.183982	−0.00826937
$496$	−9.05629	−0.406639
$497$	0	0
$498$	−0.646147	−0.0289545
$499$	−29.3022	−1.31175	−0.655874	−	0.754870i	$-0.727700\pi$
$499$	−29.3022	−1.31175	−0.655874	+	0.754870i	$0.727700\pi$
$500$	−8.63849	−0.386325
$501$	−0.978696	−0.0437249
$502$	−9.05891	−0.404319
$503$	21.3899	0.953729	0.476864	−	0.878977i	$-0.341773\pi$
$503$	21.3899	0.953729	0.476864	+	0.878977i	$0.341773\pi$
$504$	0	0
$505$	13.9764	0.621944
$506$	0.267495	0.0118916
$507$	−0.0871986	−0.00387263
$508$	19.3445	0.858275
$509$	24.2270	1.07384	0.536922	−	0.843632i	$-0.319587\pi$
$509$	24.2270	1.07384	0.536922	+	0.843632i	$0.319587\pi$
$510$	0.240404	0.0106453
$511$	0	0
$512$	1.00000	0.0441942
$513$	0.236840	0.0104567
$514$	2.05292	0.0905506
$515$	12.6336	0.556701
$516$	0.347363	0.0152918
$517$	−0.590944	−0.0259897
$518$	0	0
$519$	−0.483507	−0.0212236
$520$	3.19106	0.139937
$521$	−5.62189	−0.246300	−0.123150	−	0.992388i	$-0.539300\pi$
$521$	−5.62189	−0.246300	−0.123150	+	0.992388i	$0.539300\pi$
$522$	−26.6052	−1.16448
$523$	3.05241	0.133473	0.0667364	−	0.997771i	$-0.478741\pi$
$523$	3.05241	0.133473	0.0667364	+	0.997771i	$0.478741\pi$
$524$	5.13821	0.224464
$525$	0	0
$526$	−29.7197	−1.29584
$527$	−44.7998	−1.95151
$528$	0.00330918	0.000144014 0
$529$	−5.88043	−0.255671
$530$	1.20101	0.0521684
$531$	7.83570	0.340040
$532$	0	0
$533$	−3.36102	−0.145582
$534$	0.437051	0.0189131
$535$	−16.0636	−0.694490
$536$	4.96028	0.214251
$537$	−0.482148	−0.0208062
$538$	19.4622	0.839074
$539$	0	0
$540$	−0.291459	−0.0125424
$541$	13.0773	0.562236	0.281118	−	0.959673i	$-0.409295\pi$
$541$	13.0773	0.562236	0.281118	+	0.959673i	$0.409295\pi$
$542$	1.75254	0.0752780
$543$	0.610369	0.0261935
$544$	4.94681	0.212093
$545$	−3.27027	−0.140083
$546$	0	0
$547$	−5.59578	−0.239258	−0.119629	−	0.992819i	$-0.538171\pi$
$547$	−5.59578	−0.239258	−0.119629	+	0.992819i	$0.538171\pi$
$548$	7.23145	0.308912
$549$	9.64971	0.411840
$550$	−0.264973	−0.0112985
$551$	−6.84804	−0.291736
$552$	0.211786	0.00901422
$553$	0	0
$554$	−16.1849	−0.687629
$555$	0.371903	0.0157864
$556$	13.7875	0.584720
$557$	44.5637	1.88822	0.944112	−	0.329626i	$-0.106923\pi$
$557$	44.5637	1.88822	0.944112	+	0.329626i	$0.106923\pi$
$558$	27.1451	1.14915
$559$	22.8088	0.964710
$560$	0	0
$561$	0.0163699	0.000691137 0
$562$	−18.0627	−0.761930
$563$	−37.6266	−1.58577	−0.792887	−	0.609369i	$-0.791423\pi$
$563$	−37.6266	−1.58577	−0.792887	+	0.609369i	$0.791423\pi$
$564$	−0.467874	−0.0197010
$565$	1.53547	0.0645977
$566$	−10.0866	−0.423972
$567$	0	0
$568$	5.15893	0.216464
$569$	−26.6046	−1.11532	−0.557661	−	0.830069i	$-0.688301\pi$
$569$	−26.6046	−1.11532	−0.557661	+	0.830069i	$0.688301\pi$
$570$	−0.0374936	−0.00157044
$571$	−39.8686	−1.66845	−0.834224	−	0.551425i	$-0.814084\pi$
$571$	−39.8686	−1.66845	−0.834224	+	0.551425i	$0.814084\pi$
$572$	0.217290	0.00908535
$573$	0.751624	0.0313995
$574$	0	0
$575$	−16.9582	−0.707205
$576$	−2.99738	−0.124891
$577$	−0.852672	−0.0354972	−0.0177486	−	0.999842i	$-0.505650\pi$
$577$	−0.852672	−0.0354972	−0.0177486	+	0.999842i	$0.505650\pi$
$578$	7.47096	0.310751
$579$	0.0684447	0.00284447
$580$	8.42730	0.349924
$581$	0	0
$582$	−0.445813	−0.0184795
$583$	0.0817806	0.00338701
$584$	14.4640	0.598524
$585$	−9.56482	−0.395457
$586$	−14.6369	−0.604643
$587$	0.382455	0.0157856	0.00789281	−	0.999969i	$-0.497488\pi$
$587$	0.382455	0.0157856	0.00789281	+	0.999969i	$0.497488\pi$
$588$	0	0
$589$	6.98703	0.287895
$590$	−2.48199	−0.102182
$591$	−0.902159	−0.0371098
$592$	7.65270	0.314524
$593$	−27.1855	−1.11638	−0.558188	−	0.829714i	$-0.688503\pi$
$593$	−27.1855	−1.11638	−0.558188	+	0.829714i	$0.688503\pi$
$594$	−0.0198464	−0.000814308 0
$595$	0	0
$596$	−6.98630	−0.286170
$597$	−0.253752	−0.0103854
$598$	13.9065	0.568678
$599$	14.1441	0.577912	0.288956	−	0.957342i	$-0.406692\pi$
$599$	14.1441	0.577912	0.288956	+	0.957342i	$0.406692\pi$
$600$	−0.209790	−0.00856463
$601$	−3.69576	−0.150753	−0.0753767	−	0.997155i	$-0.524016\pi$
$601$	−3.69576	−0.150753	−0.0753767	+	0.997155i	$0.524016\pi$
$602$	0	0
$603$	−14.8678	−0.605465
$604$	14.4872	0.589475
$605$	−10.4398	−0.424438
$606$	0.753501	0.0306089
$607$	−14.7009	−0.596692	−0.298346	−	0.954458i	$-0.596435\pi$
$607$	−14.7009	−0.596692	−0.298346	+	0.954458i	$0.596435\pi$
$608$	−0.771511	−0.0312889
$609$	0	0
$610$	−3.05659	−0.123758
$611$	−30.7219	−1.24288
$612$	−14.8275	−0.599365
$613$	−40.1769	−1.62273	−0.811365	−	0.584541i	$-0.801275\pi$
$613$	−40.1769	−1.62273	−0.811365	+	0.584541i	$0.801275\pi$
$614$	−19.8519	−0.801159
$615$	−0.0485977	−0.00195965
$616$	0	0
$617$	5.78459	0.232879	0.116439	−	0.993198i	$-0.462852\pi$
$617$	5.78459	0.232879	0.116439	+	0.993198i	$0.462852\pi$
$618$	0.681103	0.0273980
$619$	−42.1098	−1.69254	−0.846268	−	0.532757i	$-0.821156\pi$
$619$	−42.1098	−1.69254	−0.846268	+	0.532757i	$0.821156\pi$
$620$	−8.59834	−0.345318
$621$	−1.27016	−0.0509699
$622$	9.15965	0.367268
$623$	0	0
$624$	0.172037	0.00688699
$625$	12.2912	0.491649
$626$	2.99024	0.119514
$627$	−0.00255307	−0.000101960 0
$628$	14.7236	0.587536
$629$	37.8565	1.50944
$630$	0	0
$631$	−42.6215	−1.69673	−0.848367	−	0.529408i	$-0.822414\pi$
$631$	−42.6215	−1.69673	−0.848367	+	0.529408i	$0.822414\pi$
$632$	13.8393	0.550500
$633$	0.0508289	0.00202027
$634$	17.9992	0.714838
$635$	18.3663	0.728846
$636$	0.0647490	0.00256746
$637$	0	0
$638$	0.573843	0.0227187
$639$	−15.4633	−0.611718
$640$	0.949433	0.0375296
$641$	−35.5554	−1.40435	−0.702176	−	0.712003i	$-0.747788\pi$
$641$	−35.5554	−1.40435	−0.702176	+	0.712003i	$0.747788\pi$
$642$	−0.866024	−0.0341792
$643$	−13.7599	−0.542639	−0.271320	−	0.962489i	$-0.587460\pi$
$643$	−13.7599	−0.542639	−0.271320	+	0.962489i	$0.587460\pi$
$644$	0	0
$645$	0.329798	0.0129858
$646$	−3.81652	−0.150159
$647$	−9.90899	−0.389563	−0.194781	−	0.980847i	$-0.562400\pi$
$647$	−9.90899	−0.389563	−0.194781	+	0.980847i	$0.562400\pi$
$648$	8.97643	0.352627
$649$	−0.169007	−0.00663411
$650$	−13.7754	−0.540315
$651$	0	0
$652$	−7.43755	−0.291277
$653$	7.84673	0.307066	0.153533	−	0.988143i	$-0.450935\pi$
$653$	7.84673	0.307066	0.153533	+	0.988143i	$0.450935\pi$
$654$	−0.176307	−0.00689417
$655$	4.87838	0.190614
$656$	−1.00000	−0.0390434
$657$	−43.3541	−1.69140
$658$	0	0
$659$	13.6138	0.530319	0.265160	−	0.964205i	$-0.414575\pi$
$659$	13.6138	0.530319	0.265160	+	0.964205i	$0.414575\pi$
$660$	0.00314184	0.000122296 0
$661$	17.6983	0.688385	0.344192	−	0.938899i	$-0.388153\pi$
$661$	17.6983	0.688385	0.344192	+	0.938899i	$0.388153\pi$
$662$	−25.3125	−0.983798
$663$	0.851035	0.0330515
$664$	−12.6235	−0.489887
$665$	0	0
$666$	−22.9380	−0.888831
$667$	36.7257	1.42203
$668$	−19.1204	−0.739789
$669$	−1.35366	−0.0523354
$670$	4.70945	0.181942
$671$	−0.208133	−0.00803490
$672$	0	0
$673$	14.9047	0.574534	0.287267	−	0.957850i	$-0.407253\pi$
$673$	14.9047	0.574534	0.287267	+	0.957850i	$0.407253\pi$
$674$	−2.96293	−0.114128
$675$	1.25819	0.0484277
$676$	−1.70356	−0.0655217
$677$	−6.60121	−0.253705	−0.126853	−	0.991922i	$-0.540488\pi$
$677$	−6.60121	−0.253705	−0.126853	+	0.991922i	$0.540488\pi$
$678$	0.0827805	0.00317917
$679$	0	0
$680$	4.69667	0.180109
$681$	−0.580932	−0.0222614
$682$	−0.585490	−0.0224196
$683$	0.747894	0.0286174	0.0143087	−	0.999898i	$-0.495445\pi$
$683$	0.747894	0.0286174	0.0143087	+	0.999898i	$0.495445\pi$
$684$	2.31251	0.0884211
$685$	6.86578	0.262328
$686$	0	0
$687$	−1.21904	−0.0465092
$688$	6.78628	0.258725
$689$	4.25160	0.161973
$690$	0.201077	0.00765486
$691$	−32.9457	−1.25331	−0.626657	−	0.779295i	$-0.715577\pi$
$691$	−32.9457	−1.25331	−0.626657	+	0.779295i	$0.715577\pi$
$692$	−9.44608	−0.359086
$693$	0	0
$694$	24.6149	0.934370
$695$	13.0903	0.496543
$696$	0.454334	0.0172215
$697$	−4.94681	−0.187374
$698$	−27.5583	−1.04310
$699$	0.890714	0.0336899
$700$	0	0
$701$	38.5645	1.45656	0.728280	−	0.685280i	$-0.240320\pi$
$701$	38.5645	1.45656	0.728280	+	0.685280i	$0.240320\pi$
$702$	−1.03177	−0.0389417
$703$	−5.90414	−0.222679
$704$	0.0646501	0.00243659
$705$	−0.444215	−0.0167301
$706$	−11.6635	−0.438962
$707$	0	0
$708$	−0.133810	−0.00502887
$709$	−16.6379	−0.624848	−0.312424	−	0.949943i	$-0.601141\pi$
$709$	−16.6379	−0.624848	−0.312424	+	0.949943i	$0.601141\pi$
$710$	4.89806	0.183821
$711$	−41.4818	−1.55569
$712$	8.53849	0.319994
$713$	−37.4711	−1.40330
$714$	0	0
$715$	0.206302	0.00771527
$716$	−9.41954	−0.352025
$717$	1.13343	0.0423288
$718$	17.4849	0.652531
$719$	1.03449	0.0385799	0.0192899	−	0.999814i	$-0.493859\pi$
$719$	1.03449	0.0385799	0.0192899	+	0.999814i	$0.493859\pi$
$720$	−2.84581	−0.106057
$721$	0	0
$722$	−18.4048	−0.684955
$723$	0.0953425	0.00354583
$724$	11.9245	0.443172
$725$	−36.3795	−1.35110
$726$	−0.562832	−0.0208887
$727$	0.916202	0.0339801	0.0169900	−	0.999856i	$-0.494592\pi$
$727$	0.916202	0.0339801	0.0169900	+	0.999856i	$0.494592\pi$
$728$	0	0
$729$	−26.8586	−0.994764
$730$	13.7326	0.508266
$731$	33.5705	1.24165
$732$	−0.164787	−0.00609071
$733$	38.1321	1.40844	0.704221	−	0.709981i	$-0.251297\pi$
$733$	38.1321	1.40844	0.704221	+	0.709981i	$0.251297\pi$
$734$	20.2595	0.747793
$735$	0	0
$736$	4.13758	0.152513
$737$	0.320682	0.0118125
$738$	2.99738	0.110335
$739$	38.3324	1.41008	0.705041	−	0.709167i	$-0.250929\pi$
$739$	38.3324	1.41008	0.705041	+	0.709167i	$0.250929\pi$
$740$	7.26572	0.267093
$741$	−0.132728	−0.00487590
$742$	0	0
$743$	−19.6433	−0.720643	−0.360321	−	0.932828i	$-0.617333\pi$
$743$	−19.6433	−0.720643	−0.360321	+	0.932828i	$0.617333\pi$
$744$	−0.463555	−0.0169948
$745$	−6.63302	−0.243015
$746$	−1.82070	−0.0666605
$747$	37.8374	1.38440
$748$	0.319812	0.0116935
$749$	0	0
$750$	−0.442170	−0.0161458
$751$	−29.0811	−1.06118	−0.530592	−	0.847628i	$-0.678030\pi$
$751$	−29.0811	−1.06118	−0.530592	+	0.847628i	$0.678030\pi$
$752$	−9.14066	−0.333325
$753$	−0.463689	−0.0168978
$754$	29.8329	1.08645
$755$	13.7546	0.500581
$756$	0	0
$757$	−0.127399	−0.00463040	−0.00231520	−	0.999997i	$-0.500737\pi$
$757$	−0.127399	−0.00463040	−0.00231520	+	0.999997i	$0.500737\pi$
$758$	−17.0815	−0.620429
$759$	0.0136920	0.000496988 0
$760$	−0.732498	−0.0265705
$761$	−28.1454	−1.02027	−0.510136	−	0.860094i	$-0.670405\pi$
$761$	−28.1454	−1.02027	−0.510136	+	0.860094i	$0.670405\pi$
$762$	0.990170	0.0358701
$763$	0	0
$764$	14.6842	0.531254
$765$	−14.0777	−0.508980
$766$	0.138065	0.00498848
$767$	−8.78631	−0.317255
$768$	0.0511860	0.00184702
$769$	5.39573	0.194575	0.0972875	−	0.995256i	$-0.468983\pi$
$769$	5.39573	0.194575	0.0972875	+	0.995256i	$0.468983\pi$
$770$	0	0
$771$	0.105081	0.00378440
$772$	1.33718	0.0481260
$773$	−29.0398	−1.04449	−0.522244	−	0.852796i	$-0.674905\pi$
$773$	−29.0398	−1.04449	−0.522244	+	0.852796i	$0.674905\pi$
$774$	−20.3411	−0.731145
$775$	37.1179	1.33331
$776$	−8.70966	−0.312658
$777$	0	0
$778$	37.4848	1.34389
$779$	0.771511	0.0276422
$780$	0.163338	0.00584843
$781$	0.333525	0.0119345
$782$	20.4678	0.731928
$783$	−2.72481	−0.0973769
$784$	0	0
$785$	13.9791	0.498934
$786$	0.263004	0.00938105
$787$	−2.71870	−0.0969111	−0.0484556	−	0.998825i	$-0.515430\pi$
$787$	−2.71870	−0.0969111	−0.0484556	+	0.998825i	$0.515430\pi$
$788$	−17.6251	−0.627868
$789$	−1.52123	−0.0541573
$790$	13.1395	0.467484
$791$	0	0
$792$	−0.193781	−0.00688570
$793$	−10.8204	−0.384244
$794$	−25.9422	−0.920653
$795$	0.0614748	0.00218029
$796$	−4.95745	−0.175712
$797$	48.1391	1.70517	0.852587	−	0.522585i	$-0.175032\pi$
$797$	48.1391	1.70517	0.852587	+	0.522585i	$0.175032\pi$
$798$	0	0
$799$	−45.2171	−1.59967
$800$	−4.09858	−0.144907
$801$	−25.5931	−0.904288
$802$	21.4268	0.756607
$803$	0.935098	0.0329989
$804$	0.253897	0.00895425
$805$	0	0
$806$	−30.4383	−1.07215
$807$	0.996191	0.0350676
$808$	14.7208	0.517877
$809$	16.3481	0.574768	0.287384	−	0.957815i	$-0.407214\pi$
$809$	16.3481	0.574768	0.287384	+	0.957815i	$0.407214\pi$
$810$	8.52251	0.299451
$811$	−23.9135	−0.839716	−0.419858	−	0.907590i	$-0.637920\pi$
$811$	−23.9135	−0.839716	−0.419858	+	0.907590i	$0.637920\pi$
$812$	0	0
$813$	0.0897055	0.00314611
$814$	0.494748	0.0173409
$815$	−7.06146	−0.247352
$816$	0.253208	0.00886404
$817$	−5.23569	−0.183174
$818$	19.6351	0.686525
$819$	0	0
$820$	−0.949433	−0.0331556
$821$	−30.1430	−1.05200	−0.526000	−	0.850485i	$-0.676309\pi$
$821$	−30.1430	−1.05200	−0.526000	+	0.850485i	$0.676309\pi$
$822$	0.370149	0.0129104
$823$	−16.7056	−0.582321	−0.291161	−	0.956674i	$-0.594041\pi$
$823$	−16.7056	−0.582321	−0.291161	+	0.956674i	$0.594041\pi$
$824$	13.3064	0.463552
$825$	−0.0135629	−0.000472201 0
$826$	0	0
$827$	−1.96640	−0.0683784	−0.0341892	−	0.999415i	$-0.510885\pi$
$827$	−1.96640	−0.0683784	−0.0341892	+	0.999415i	$0.510885\pi$
$828$	−12.4019	−0.430996
$829$	−0.118913	−0.00413001	−0.00206501	−	0.999998i	$-0.500657\pi$
$829$	−0.118913	−0.00413001	−0.00206501	+	0.999998i	$0.500657\pi$
$830$	−11.9852	−0.416011
$831$	−0.828439	−0.0287382
$832$	3.36102	0.116522
$833$	0	0
$834$	0.705726	0.0244373
$835$	−18.1535	−0.628228
$836$	−0.0498782	−0.00172507
$837$	2.78012	0.0960949
$838$	9.44883	0.326404
$839$	18.0542	0.623302	0.311651	−	0.950197i	$-0.399118\pi$
$839$	18.0542	0.623302	0.311651	+	0.950197i	$0.399118\pi$
$840$	0	0
$841$	49.7858	1.71675
$842$	34.3374	1.18335
$843$	−0.924559	−0.0318435
$844$	0.993023	0.0341813
$845$	−1.61742	−0.0556409
$846$	27.3980	0.941963
$847$	0	0
$848$	1.26497	0.0434394
$849$	−0.516294	−0.0177192
$850$	−20.2749	−0.695423
$851$	31.6637	1.08542
$852$	0.264065	0.00904673
$853$	−8.64226	−0.295905	−0.147953	−	0.988994i	$-0.547268\pi$
$853$	−8.64226	−0.295905	−0.147953	+	0.988994i	$0.547268\pi$
$854$	0	0
$855$	2.19557	0.0750871
$856$	−16.9192	−0.578285
$857$	−52.6725	−1.79926	−0.899629	−	0.436655i	$-0.856163\pi$
$857$	−52.6725	−1.79926	−0.899629	+	0.436655i	$0.856163\pi$
$858$	0.0111222	0.000379706 0
$859$	19.0529	0.650077	0.325038	−	0.945701i	$-0.394623\pi$
$859$	19.0529	0.650077	0.325038	+	0.945701i	$0.394623\pi$
$860$	6.44312	0.219709
$861$	0	0
$862$	−16.5458	−0.563552
$863$	−29.4988	−1.00415	−0.502075	−	0.864824i	$-0.667430\pi$
$863$	−29.4988	−1.00415	−0.502075	+	0.864824i	$0.667430\pi$
$864$	−0.306982	−0.0104437
$865$	−8.96842	−0.304935
$866$	−12.3872	−0.420933
$867$	0.382408	0.0129873
$868$	0	0
$869$	0.894715	0.0303511
$870$	0.431360	0.0146245
$871$	16.6716	0.564895
$872$	−3.44444	−0.116644
$873$	26.1062	0.883559
$874$	−3.19219	−0.107977
$875$	0	0
$876$	0.740354	0.0250143
$877$	−18.5425	−0.626135	−0.313068	−	0.949731i	$-0.601357\pi$
$877$	−18.5425	−0.626135	−0.313068	+	0.949731i	$0.601357\pi$
$878$	−10.4888	−0.353978
$879$	−0.749203	−0.0252700
$880$	0.0613809	0.00206915
$881$	38.6189	1.30110	0.650551	−	0.759462i	$-0.274538\pi$
$881$	38.6189	1.30110	0.650551	+	0.759462i	$0.274538\pi$
$882$	0	0
$883$	−29.7216	−1.00021	−0.500106	−	0.865964i	$-0.666705\pi$
$883$	−29.7216	−1.00021	−0.500106	+	0.865964i	$0.666705\pi$
$884$	16.6263	0.559204
$885$	−0.127043	−0.00427051
$886$	17.6179	0.591885
$887$	−17.8249	−0.598503	−0.299252	−	0.954174i	$-0.596737\pi$
$887$	−17.8249	−0.598503	−0.299252	+	0.954174i	$0.596737\pi$
$888$	0.391711	0.0131450
$889$	0	0
$890$	8.10672	0.271738
$891$	0.580327	0.0194417
$892$	−26.4458	−0.885472
$893$	7.05212	0.235990
$894$	−0.357601	−0.0119600
$895$	−8.94322	−0.298939
$896$	0	0
$897$	0.711817	0.0237669
$898$	−23.1017	−0.770914
$899$	−80.3849	−2.68099
$900$	12.2850	0.409500
$901$	6.25759	0.208470
$902$	−0.0646501	−0.00215261
$903$	0	0
$904$	1.61725	0.0537889
$905$	11.3215	0.376341
$906$	0.741541	0.0246361
$907$	18.4763	0.613494	0.306747	−	0.951791i	$-0.400759\pi$
$907$	18.4763	0.613494	0.306747	+	0.951791i	$0.400759\pi$
$908$	−11.3494	−0.376644
$909$	−44.1239	−1.46350
$910$	0	0
$911$	5.08625	0.168515	0.0842575	−	0.996444i	$-0.473148\pi$
$911$	5.08625	0.168515	0.0842575	+	0.996444i	$0.473148\pi$
$912$	−0.0394906	−0.00130766
$913$	−0.816110	−0.0270093
$914$	6.90710	0.228466
$915$	−0.156454	−0.00517223
$916$	−23.8159	−0.786898
$917$	0	0
$918$	−1.51858	−0.0501207
$919$	32.6727	1.07777	0.538887	−	0.842378i	$-0.318845\pi$
$919$	32.6727	1.07777	0.538887	+	0.842378i	$0.318845\pi$
$920$	3.92835	0.129514
$921$	−1.01614	−0.0334830
$922$	−19.2649	−0.634457
$923$	17.3393	0.570729
$924$	0	0
$925$	−31.3652	−1.03128
$926$	−26.6956	−0.877271
$927$	−39.8844	−1.30998
$928$	8.87614	0.291373
$929$	40.5075	1.32901	0.664504	−	0.747285i	$-0.268643\pi$
$929$	40.5075	1.32901	0.664504	+	0.747285i	$0.268643\pi$
$930$	−0.440115	−0.0144319
$931$	0	0
$932$	17.4015	0.570006
$933$	0.468846	0.0153493
$934$	−3.55516	−0.116329
$935$	0.303640	0.00993008
$936$	−10.0742	−0.329287
$937$	−12.0514	−0.393701	−0.196850	−	0.980434i	$-0.563071\pi$
$937$	−12.0514	−0.393701	−0.196850	+	0.980434i	$0.563071\pi$
$938$	0	0
$939$	0.153058	0.00499487
$940$	−8.67844	−0.283059
$941$	−55.5449	−1.81071	−0.905356	−	0.424653i	$-0.860396\pi$
$941$	−55.5449	−1.81071	−0.905356	+	0.424653i	$0.860396\pi$
$942$	0.753642	0.0245550
$943$	−4.13758	−0.134738
$944$	−2.61418	−0.0850844
$945$	0	0
$946$	0.438734	0.0142645
$947$	−9.34724	−0.303745	−0.151872	−	0.988400i	$-0.548530\pi$
$947$	−9.34724	−0.303745	−0.151872	+	0.988400i	$0.548530\pi$
$948$	0.708381	0.0230072
$949$	48.6137	1.57807
$950$	3.16210	0.102592
$951$	0.921305	0.0298754
$952$	0	0
$953$	−40.2375	−1.30342	−0.651711	−	0.758468i	$-0.725948\pi$
$953$	−40.2375	−1.30342	−0.651711	+	0.758468i	$0.725948\pi$
$954$	−3.79161	−0.122758
$955$	13.9416	0.451140
$956$	22.1434	0.716168
$957$	0.0293727	0.000949486 0
$958$	−15.5694	−0.503025
$959$	0	0
$960$	0.0485977	0.00156848
$961$	51.0164	1.64569
$962$	25.7209	0.829274
$963$	50.7131	1.63421
$964$	1.86267	0.0599925
$965$	1.26956	0.0408686
$966$	0	0
$967$	−26.4351	−0.850096	−0.425048	−	0.905171i	$-0.639743\pi$
$967$	−26.4351	−0.850096	−0.425048	+	0.905171i	$0.639743\pi$
$968$	−10.9958	−0.353419
$969$	−0.195352	−0.00627563
$970$	−8.26923	−0.265509
$971$	−11.2781	−0.361933	−0.180967	−	0.983489i	$-0.557923\pi$
$971$	−11.2781	−0.361933	−0.180967	+	0.983489i	$0.557923\pi$
$972$	1.38041	0.0442768
$973$	0	0
$974$	25.3719	0.812967
$975$	−0.705107	−0.0225815
$976$	−3.21938	−0.103050
$977$	0.873975	0.0279609	0.0139805	−	0.999902i	$-0.495550\pi$
$977$	0.873975	0.0279609	0.0139805	+	0.999902i	$0.495550\pi$
$978$	−0.380699	−0.0121734
$979$	0.552014	0.0176424
$980$	0	0
$981$	10.3243	0.329630
$982$	−4.90620	−0.156563
$983$	21.6430	0.690305	0.345152	−	0.938547i	$-0.387827\pi$
$983$	21.6430	0.690305	0.345152	+	0.938547i	$0.387827\pi$
$984$	−0.0511860	−0.00163175
$985$	−16.7338	−0.533185
$986$	43.9086	1.39833
$987$	0	0
$988$	−2.59306	−0.0824963
$989$	28.0788	0.892853
$990$	−0.183982	−0.00584733
$991$	−53.2708	−1.69220	−0.846102	−	0.533021i	$-0.821056\pi$
$991$	−53.2708	−1.69220	−0.846102	+	0.533021i	$0.821056\pi$
$992$	−9.05629	−0.287537
$993$	−1.29565	−0.0411161
$994$	0	0
$995$	−4.70677	−0.149215
$996$	−0.646147	−0.0204739
$997$	31.7016	1.00400	0.502000	−	0.864868i	$-0.332598\pi$
$997$	31.7016	1.00400	0.502000	+	0.864868i	$0.332598\pi$
$998$	−29.3022	−0.927546
$999$	−2.34924	−0.0743267

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bt.1.6		10
7.2	even	3		574.2.e.h.165.5	✓	20
7.4	even	3		574.2.e.h.247.5	yes	20
7.6	odd	2		4018.2.a.bu.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.e.h.165.5	✓	20	7.2	even	3
574.2.e.h.247.5	yes	20	7.4	even	3
4018.2.a.bt.1.6		10	1.1	even	1	trivial
4018.2.a.bu.1.5		10	7.6	odd	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:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.0511860 q^{3} +1.00000 q^{4} +0.949433 q^{5} +0.0511860 q^{6} +1.00000 q^{8} -2.99738 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.0511860 q^{3} +1.00000 q^{4} +0.949433 q^{5} +0.0511860 q^{6} +1.00000 q^{8} -2.99738 q^{9} +0.949433 q^{10} +0.0646501 q^{11} +0.0511860 q^{12} +3.36102 q^{13} +0.0485977 q^{15} +1.00000 q^{16} +4.94681 q^{17} -2.99738 q^{18} -0.771511 q^{19} +0.949433 q^{20} +0.0646501 q^{22} +4.13758 q^{23} +0.0511860 q^{24} -4.09858 q^{25} +3.36102 q^{26} -0.306982 q^{27} +8.87614 q^{29} +0.0485977 q^{30} -9.05629 q^{31} +1.00000 q^{32} +0.00330918 q^{33} +4.94681 q^{34} -2.99738 q^{36} +7.65270 q^{37} -0.771511 q^{38} +0.172037 q^{39} +0.949433 q^{40} -1.00000 q^{41} +6.78628 q^{43} +0.0646501 q^{44} -2.84581 q^{45} +4.13758 q^{46} -9.14066 q^{47} +0.0511860 q^{48} -4.09858 q^{50} +0.253208 q^{51} +3.36102 q^{52} +1.26497 q^{53} -0.306982 q^{54} +0.0613809 q^{55} -0.0394906 q^{57} +8.87614 q^{58} -2.61418 q^{59} +0.0485977 q^{60} -3.21938 q^{61} -9.05629 q^{62} +1.00000 q^{64} +3.19106 q^{65} +0.00330918 q^{66} +4.96028 q^{67} +4.94681 q^{68} +0.211786 q^{69} +5.15893 q^{71} -2.99738 q^{72} +14.4640 q^{73} +7.65270 q^{74} -0.209790 q^{75} -0.771511 q^{76} +0.172037 q^{78} +13.8393 q^{79} +0.949433 q^{80} +8.97643 q^{81} -1.00000 q^{82} -12.6235 q^{83} +4.69667 q^{85} +6.78628 q^{86} +0.454334 q^{87} +0.0646501 q^{88} +8.53849 q^{89} -2.84581 q^{90} +4.13758 q^{92} -0.463555 q^{93} -9.14066 q^{94} -0.732498 q^{95} +0.0511860 q^{96} -8.70966 q^{97} -0.193781 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} - q^{3} + 10 q^{4} + 2 q^{5} - q^{6} + 10 q^{8} + 17 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 - q^3 + 10 * q^4 + 2 * q^5 - q^6 + 10 * q^8 + 17 * q^9	\( 10 q + 10 q^{2} - q^{3} + 10 q^{4} + 2 q^{5} - q^{6} + 10 q^{8} + 17 q^{9} + 2 q^{10} + 11 q^{11} - q^{12} - 4 q^{13} + 4 q^{15} + 10 q^{16} - 5 q^{17} + 17 q^{18} + q^{19} + 2 q^{20} + 11 q^{22} + 9 q^{23} - q^{24} + 24 q^{25} - 4 q^{26} - 7 q^{27} + 23 q^{29} + 4 q^{30} + 5 q^{31} + 10 q^{32} + 5 q^{33} - 5 q^{34} + 17 q^{36} + 16 q^{37} + q^{38} - 7 q^{39} + 2 q^{40} - 10 q^{41} + 20 q^{43} + 11 q^{44} + 42 q^{45} + 9 q^{46} + 16 q^{47} - q^{48} + 24 q^{50} + 13 q^{51} - 4 q^{52} + 26 q^{53} - 7 q^{54} - 7 q^{55} + 37 q^{57} + 23 q^{58} + 10 q^{59} + 4 q^{60} + 5 q^{62} + 10 q^{64} + 18 q^{65} + 5 q^{66} + 7 q^{67} - 5 q^{68} - 39 q^{69} + 5 q^{71} + 17 q^{72} + 13 q^{73} + 16 q^{74} - 19 q^{75} + q^{76} - 7 q^{78} - q^{79} + 2 q^{80} + 18 q^{81} - 10 q^{82} - 21 q^{83} + 34 q^{85} + 20 q^{86} - 2 q^{87} + 11 q^{88} - 6 q^{89} + 42 q^{90} + 9 q^{92} - 5 q^{93} + 16 q^{94} + 24 q^{95} - q^{96} - 29 q^{97} + 48 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - q^3 + 10 * q^4 + 2 * q^5 - q^6 + 10 * q^8 + 17 * q^9 + 2 * q^10 + 11 * q^11 - q^12 - 4 * q^13 + 4 * q^15 + 10 * q^16 - 5 * q^17 + 17 * q^18 + q^19 + 2 * q^20 + 11 * q^22 + 9 * q^23 - q^24 + 24 * q^25 - 4 * q^26 - 7 * q^27 + 23 * q^29 + 4 * q^30 + 5 * q^31 + 10 * q^32 + 5 * q^33 - 5 * q^34 + 17 * q^36 + 16 * q^37 + q^38 - 7 * q^39 + 2 * q^40 - 10 * q^41 + 20 * q^43 + 11 * q^44 + 42 * q^45 + 9 * q^46 + 16 * q^47 - q^48 + 24 * q^50 + 13 * q^51 - 4 * q^52 + 26 * q^53 - 7 * q^54 - 7 * q^55 + 37 * q^57 + 23 * q^58 + 10 * q^59 + 4 * q^60 + 5 * q^62 + 10 * q^64 + 18 * q^65 + 5 * q^66 + 7 * q^67 - 5 * q^68 - 39 * q^69 + 5 * q^71 + 17 * q^72 + 13 * q^73 + 16 * q^74 - 19 * q^75 + q^76 - 7 * q^78 - q^79 + 2 * q^80 + 18 * q^81 - 10 * q^82 - 21 * q^83 + 34 * q^85 + 20 * q^86 - 2 * q^87 + 11 * q^88 - 6 * q^89 + 42 * q^90 + 9 * q^92 - 5 * q^93 + 16 * q^94 + 24 * q^95 - q^96 - 29 * q^97 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more