LMFDB - Embedded newform 4018.2.a.bu.1.4

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			1.4
Root			$-1.56572$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.56572 q^{3} +1.00000 q^{4} -2.99546 q^{5} -1.56572 q^{6} +1.00000 q^{8} -0.548522 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.56572 q^{3} +1.00000 q^{4} -2.99546 q^{5} -1.56572 q^{6} +1.00000 q^{8} -0.548522 q^{9} -2.99546 q^{10} -3.62474 q^{11} -1.56572 q^{12} +2.72846 q^{13} +4.69005 q^{15} +1.00000 q^{16} -4.54398 q^{17} -0.548522 q^{18} -6.43693 q^{19} -2.99546 q^{20} -3.62474 q^{22} +4.22473 q^{23} -1.56572 q^{24} +3.97276 q^{25} +2.72846 q^{26} +5.55599 q^{27} +0.274990 q^{29} +4.69005 q^{30} -6.70397 q^{31} +1.00000 q^{32} +5.67533 q^{33} -4.54398 q^{34} -0.548522 q^{36} +5.22818 q^{37} -6.43693 q^{38} -4.27200 q^{39} -2.99546 q^{40} +1.00000 q^{41} -10.1930 q^{43} -3.62474 q^{44} +1.64307 q^{45} +4.22473 q^{46} -12.1755 q^{47} -1.56572 q^{48} +3.97276 q^{50} +7.11460 q^{51} +2.72846 q^{52} +8.07076 q^{53} +5.55599 q^{54} +10.8578 q^{55} +10.0784 q^{57} +0.274990 q^{58} +8.81022 q^{59} +4.69005 q^{60} -4.33155 q^{61} -6.70397 q^{62} +1.00000 q^{64} -8.17299 q^{65} +5.67533 q^{66} -0.646484 q^{67} -4.54398 q^{68} -6.61474 q^{69} +12.4539 q^{71} -0.548522 q^{72} -4.55192 q^{73} +5.22818 q^{74} -6.22023 q^{75} -6.43693 q^{76} -4.27200 q^{78} +5.56633 q^{79} -2.99546 q^{80} -7.05356 q^{81} +1.00000 q^{82} +6.05680 q^{83} +13.6113 q^{85} -10.1930 q^{86} -0.430558 q^{87} -3.62474 q^{88} +17.9750 q^{89} +1.64307 q^{90} +4.22473 q^{92} +10.4965 q^{93} -12.1755 q^{94} +19.2816 q^{95} -1.56572 q^{96} -6.88541 q^{97} +1.98825 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.56572	−0.903969	−0.451984	−	0.892026i	$-0.649284\pi$
$3$	−1.56572	−0.903969	−0.451984	+	0.892026i	$0.649284\pi$
$4$	1.00000	0.500000
$5$	−2.99546	−1.33961	−0.669804	−	0.742538i	$-0.733622\pi$
$5$	−2.99546	−1.33961	−0.669804	+	0.742538i	$0.733622\pi$
$6$	−1.56572	−0.639202
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	−0.548522	−0.182841
$10$	−2.99546	−0.947247
$11$	−3.62474	−1.09290	−0.546451	−	0.837491i	$-0.684021\pi$
$11$	−3.62474	−1.09290	−0.546451	+	0.837491i	$0.684021\pi$
$12$	−1.56572	−0.451984
$13$	2.72846	0.756739	0.378369	−	0.925655i	$-0.376485\pi$
$13$	2.72846	0.756739	0.378369	+	0.925655i	$0.376485\pi$
$14$	0	0
$15$	4.69005	1.21096
$16$	1.00000	0.250000
$17$	−4.54398	−1.10208	−0.551038	−	0.834480i	$-0.685768\pi$
$17$	−4.54398	−1.10208	−0.551038	+	0.834480i	$0.685768\pi$
$18$	−0.548522	−0.129288
$19$	−6.43693	−1.47673	−0.738367	−	0.674399i	$-0.764403\pi$
$19$	−6.43693	−1.47673	−0.738367	+	0.674399i	$0.764403\pi$
$20$	−2.99546	−0.669804
$21$	0	0
$22$	−3.62474	−0.772798
$23$	4.22473	0.880917	0.440458	−	0.897773i	$-0.354816\pi$
$23$	4.22473	0.880917	0.440458	+	0.897773i	$0.354816\pi$
$24$	−1.56572	−0.319601
$25$	3.97276	0.794552
$26$	2.72846	0.535095
$27$	5.55599	1.06925
$28$	0	0
$29$	0.274990	0.0510644	0.0255322	−	0.999674i	$-0.491872\pi$
$29$	0.274990	0.0510644	0.0255322	+	0.999674i	$0.491872\pi$
$30$	4.69005	0.856281
$31$	−6.70397	−1.20407	−0.602034	−	0.798470i	$-0.705643\pi$
$31$	−6.70397	−1.20407	−0.602034	+	0.798470i	$0.705643\pi$
$32$	1.00000	0.176777
$33$	5.67533	0.987948
$34$	−4.54398	−0.779286
$35$	0	0
$36$	−0.548522	−0.0914203
$37$	5.22818	0.859507	0.429754	−	0.902946i	$-0.358600\pi$
$37$	5.22818	0.859507	0.429754	+	0.902946i	$0.358600\pi$
$38$	−6.43693	−1.04421
$39$	−4.27200	−0.684068
$40$	−2.99546	−0.473623
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−10.1930	−1.55442	−0.777211	−	0.629240i	$-0.783366\pi$
$43$	−10.1930	−1.55442	−0.777211	+	0.629240i	$0.783366\pi$
$44$	−3.62474	−0.546451
$45$	1.64307	0.244935
$46$	4.22473	0.622902
$47$	−12.1755	−1.77598	−0.887991	−	0.459861i	$-0.847899\pi$
$47$	−12.1755	−1.77598	−0.887991	+	0.459861i	$0.847899\pi$
$48$	−1.56572	−0.225992
$49$	0	0
$50$	3.97276	0.561833
$51$	7.11460	0.996243
$52$	2.72846	0.378369
$53$	8.07076	1.10860	0.554302	−	0.832315i	$-0.312985\pi$
$53$	8.07076	1.10860	0.554302	+	0.832315i	$0.312985\pi$
$54$	5.55599	0.756075
$55$	10.8578	1.46406
$56$	0	0
$57$	10.0784	1.33492
$58$	0.274990	0.0361080
$59$	8.81022	1.14699	0.573497	−	0.819208i	$-0.305587\pi$
$59$	8.81022	1.14699	0.573497	+	0.819208i	$0.305587\pi$
$60$	4.69005	0.605482
$61$	−4.33155	−0.554598	−0.277299	−	0.960784i	$-0.589439\pi$
$61$	−4.33155	−0.554598	−0.277299	+	0.960784i	$0.589439\pi$
$62$	−6.70397	−0.851405
$63$	0	0
$64$	1.00000	0.125000
$65$	−8.17299	−1.01373
$66$	5.67533	0.698585
$67$	−0.646484	−0.0789806	−0.0394903	−	0.999220i	$-0.512573\pi$
$67$	−0.646484	−0.0789806	−0.0394903	+	0.999220i	$0.512573\pi$
$68$	−4.54398	−0.551038
$69$	−6.61474	−0.796321
$70$	0	0
$71$	12.4539	1.47801	0.739004	−	0.673701i	$-0.235297\pi$
$71$	12.4539	1.47801	0.739004	+	0.673701i	$0.235297\pi$
$72$	−0.548522	−0.0646439
$73$	−4.55192	−0.532762	−0.266381	−	0.963868i	$-0.585828\pi$
$73$	−4.55192	−0.532762	−0.266381	+	0.963868i	$0.585828\pi$
$74$	5.22818	0.607764
$75$	−6.22023	−0.718250
$76$	−6.43693	−0.738367
$77$	0	0
$78$	−4.27200	−0.483709
$79$	5.56633	0.626262	0.313131	−	0.949710i	$-0.398622\pi$
$79$	5.56633	0.626262	0.313131	+	0.949710i	$0.398622\pi$
$80$	−2.99546	−0.334902
$81$	−7.05356	−0.783729
$82$	1.00000	0.110432
$83$	6.05680	0.664820	0.332410	−	0.943135i	$-0.392138\pi$
$83$	6.05680	0.664820	0.332410	+	0.943135i	$0.392138\pi$
$84$	0	0
$85$	13.6113	1.47635
$86$	−10.1930	−1.09914
$87$	−0.430558	−0.0461606
$88$	−3.62474	−0.386399
$89$	17.9750	1.90534	0.952671	−	0.304003i	$-0.0983233\pi$
$89$	17.9750	1.90534	0.952671	+	0.304003i	$0.0983233\pi$
$90$	1.64307	0.173195
$91$	0	0
$92$	4.22473	0.440458
$93$	10.4965	1.08844
$94$	−12.1755	−1.25581
$95$	19.2816	1.97825
$96$	−1.56572	−0.159801
$97$	−6.88541	−0.699107	−0.349554	−	0.936916i	$-0.613667\pi$
$97$	−6.88541	−0.699107	−0.349554	+	0.936916i	$0.613667\pi$
$98$	0	0
$99$	1.98825	0.199827
$100$	3.97276	0.397276
$101$	7.03832	0.700339	0.350169	−	0.936686i	$-0.386124\pi$
$101$	7.03832	0.700339	0.350169	+	0.936686i	$0.386124\pi$
$102$	7.11460	0.704450
$103$	11.7713	1.15986	0.579929	−	0.814667i	$-0.303080\pi$
$103$	11.7713	1.15986	0.579929	+	0.814667i	$0.303080\pi$
$104$	2.72846	0.267548
$105$	0	0
$106$	8.07076	0.783902
$107$	−2.11976	−0.204925	−0.102462	−	0.994737i	$-0.532672\pi$
$107$	−2.11976	−0.204925	−0.102462	+	0.994737i	$0.532672\pi$
$108$	5.55599	0.534625
$109$	7.26554	0.695912	0.347956	−	0.937511i	$-0.386876\pi$
$109$	7.26554	0.695912	0.347956	+	0.937511i	$0.386876\pi$
$110$	10.8578	1.03525
$111$	−8.18586	−0.776968
$112$	0	0
$113$	−5.55518	−0.522588	−0.261294	−	0.965259i	$-0.584149\pi$
$113$	−5.55518	−0.522588	−0.261294	+	0.965259i	$0.584149\pi$
$114$	10.0784	0.943932
$115$	−12.6550	−1.18008
$116$	0.274990	0.0255322
$117$	−1.49662	−0.138363
$118$	8.81022	0.811047
$119$	0	0
$120$	4.69005	0.428141
$121$	2.13876	0.194433
$122$	−4.33155	−0.392160
$123$	−1.56572	−0.141176
$124$	−6.70397	−0.602034
$125$	3.07705	0.275220
$126$	0	0
$127$	7.30532	0.648242	0.324121	−	0.946016i	$-0.394932\pi$
$127$	7.30532	0.648242	0.324121	+	0.946016i	$0.394932\pi$
$128$	1.00000	0.0883883
$129$	15.9594	1.40515
$130$	−8.17299	−0.716818
$131$	1.37171	0.119847	0.0599235	−	0.998203i	$-0.480914\pi$
$131$	1.37171	0.119847	0.0599235	+	0.998203i	$0.480914\pi$
$132$	5.67533	0.493974
$133$	0	0
$134$	−0.646484	−0.0558477
$135$	−16.6427	−1.43238
$136$	−4.54398	−0.389643
$137$	−15.5253	−1.32642	−0.663208	−	0.748435i	$-0.730806\pi$
$137$	−15.5253	−1.32642	−0.663208	+	0.748435i	$0.730806\pi$
$138$	−6.61474	−0.563084
$139$	6.35673	0.539171	0.269585	−	0.962976i	$-0.413113\pi$
$139$	6.35673	0.539171	0.269585	+	0.962976i	$0.413113\pi$
$140$	0	0
$141$	19.0635	1.60543
$142$	12.4539	1.04511
$143$	−9.88997	−0.827041
$144$	−0.548522	−0.0457102
$145$	−0.823721	−0.0684063
$146$	−4.55192	−0.376720
$147$	0	0
$148$	5.22818	0.429754
$149$	6.61561	0.541972	0.270986	−	0.962583i	$-0.412650\pi$
$149$	6.61561	0.541972	0.270986	+	0.962583i	$0.412650\pi$
$150$	−6.22023	−0.507880
$151$	−23.7848	−1.93558	−0.967788	−	0.251766i	$-0.918989\pi$
$151$	−23.7848	−1.93558	−0.967788	+	0.251766i	$0.918989\pi$
$152$	−6.43693	−0.522104
$153$	2.49247	0.201504
$154$	0	0
$155$	20.0814	1.61298
$156$	−4.27200	−0.342034
$157$	6.39750	0.510576	0.255288	−	0.966865i	$-0.417830\pi$
$157$	6.39750	0.510576	0.255288	+	0.966865i	$0.417830\pi$
$158$	5.56633	0.442834
$159$	−12.6366	−1.00214
$160$	−2.99546	−0.236812
$161$	0	0
$162$	−7.05356	−0.554180
$163$	−24.7124	−1.93562	−0.967811	−	0.251676i	$-0.919018\pi$
$163$	−24.7124	−1.93562	−0.967811	+	0.251676i	$0.919018\pi$
$164$	1.00000	0.0780869
$165$	−17.0002	−1.32346
$166$	6.05680	0.470099
$167$	16.9087	1.30844	0.654219	−	0.756305i	$-0.272997\pi$
$167$	16.9087	1.30844	0.654219	+	0.756305i	$0.272997\pi$
$168$	0	0
$169$	−5.55550	−0.427346
$170$	13.6113	1.04394
$171$	3.53080	0.270007
$172$	−10.1930	−0.777211
$173$	1.26620	0.0962670	0.0481335	−	0.998841i	$-0.484673\pi$
$173$	1.26620	0.0962670	0.0481335	+	0.998841i	$0.484673\pi$
$174$	−0.430558	−0.0326405
$175$	0	0
$176$	−3.62474	−0.273225
$177$	−13.7943	−1.03685
$178$	17.9750	1.34728
$179$	22.0922	1.65125	0.825624	−	0.564220i	$-0.190823\pi$
$179$	22.0922	1.65125	0.825624	+	0.564220i	$0.190823\pi$
$180$	1.64307	0.122467
$181$	15.1230	1.12408	0.562042	−	0.827108i	$-0.310016\pi$
$181$	15.1230	1.12408	0.562042	+	0.827108i	$0.310016\pi$
$182$	0	0
$183$	6.78199	0.501339
$184$	4.22473	0.311451
$185$	−15.6608	−1.15140
$186$	10.4965	0.769643
$187$	16.4708	1.20446
$188$	−12.1755	−0.887991
$189$	0	0
$190$	19.2816	1.39883
$191$	3.71215	0.268602	0.134301	−	0.990941i	$-0.457121\pi$
$191$	3.71215	0.268602	0.134301	+	0.990941i	$0.457121\pi$
$192$	−1.56572	−0.112996
$193$	−3.81922	−0.274914	−0.137457	−	0.990508i	$-0.543893\pi$
$193$	−3.81922	−0.274914	−0.137457	+	0.990508i	$0.543893\pi$
$194$	−6.88541	−0.494343
$195$	12.7966	0.916384
$196$	0	0
$197$	10.5978	0.755063	0.377531	−	0.925997i	$-0.376773\pi$
$197$	10.5978	0.755063	0.377531	+	0.925997i	$0.376773\pi$
$198$	1.98825	0.141299
$199$	17.4439	1.23657	0.618284	−	0.785954i	$-0.287828\pi$
$199$	17.4439	1.23657	0.618284	+	0.785954i	$0.287828\pi$
$200$	3.97276	0.280917
$201$	1.01221	0.0713960
$202$	7.03832	0.495214
$203$	0	0
$204$	7.11460	0.498121
$205$	−2.99546	−0.209212
$206$	11.7713	0.820144
$207$	−2.31736	−0.161067
$208$	2.72846	0.189185
$209$	23.3322	1.61392
$210$	0	0
$211$	1.30659	0.0899491	0.0449745	−	0.998988i	$-0.485679\pi$
$211$	1.30659	0.0899491	0.0449745	+	0.998988i	$0.485679\pi$
$212$	8.07076	0.554302
$213$	−19.4993	−1.33607
$214$	−2.11976	−0.144904
$215$	30.5328	2.08232
$216$	5.55599	0.378037
$217$	0	0
$218$	7.26554	0.492084
$219$	7.12703	0.481600
$220$	10.8578	0.732030
$221$	−12.3981	−0.833984
$222$	−8.18586	−0.549399
$223$	28.4776	1.90700	0.953500	−	0.301394i	$-0.0974519\pi$
$223$	28.4776	1.90700	0.953500	+	0.301394i	$0.0974519\pi$
$224$	0	0
$225$	−2.17915	−0.145276
$226$	−5.55518	−0.369525
$227$	14.7928	0.981831	0.490915	−	0.871207i	$-0.336662\pi$
$227$	14.7928	0.981831	0.490915	+	0.871207i	$0.336662\pi$
$228$	10.0784	0.667461
$229$	11.0825	0.732350	0.366175	−	0.930546i	$-0.380667\pi$
$229$	11.0825	0.732350	0.366175	+	0.930546i	$0.380667\pi$
$230$	−12.6550	−0.834446
$231$	0	0
$232$	0.274990	0.0180540
$233$	−5.84348	−0.382819	−0.191410	−	0.981510i	$-0.561306\pi$
$233$	−5.84348	−0.382819	−0.191410	+	0.981510i	$0.561306\pi$
$234$	−1.49662	−0.0978371
$235$	36.4712	2.37912
$236$	8.81022	0.573497
$237$	−8.71532	−0.566121
$238$	0	0
$239$	−22.2698	−1.44051	−0.720256	−	0.693708i	$-0.755976\pi$
$239$	−22.2698	−1.44051	−0.720256	+	0.693708i	$0.755976\pi$
$240$	4.69005	0.302741
$241$	−21.0481	−1.35583	−0.677913	−	0.735142i	$-0.737116\pi$
$241$	−21.0481	−1.35583	−0.677913	+	0.735142i	$0.737116\pi$
$242$	2.13876	0.137485
$243$	−5.62408	−0.360785
$244$	−4.33155	−0.277299
$245$	0	0
$246$	−1.56572	−0.0998266
$247$	−17.5629	−1.11750
$248$	−6.70397	−0.425702
$249$	−9.48325	−0.600976
$250$	3.07705	0.194610
$251$	12.9484	0.817295	0.408648	−	0.912692i	$-0.366001\pi$
$251$	12.9484	0.817295	0.408648	+	0.912692i	$0.366001\pi$
$252$	0	0
$253$	−15.3136	−0.962755
$254$	7.30532	0.458376
$255$	−21.3115	−1.33458
$256$	1.00000	0.0625000
$257$	19.7245	1.23038	0.615190	−	0.788379i	$-0.289079\pi$
$257$	19.7245	1.23038	0.615190	+	0.788379i	$0.289079\pi$
$258$	15.9594	0.993591
$259$	0	0
$260$	−8.17299	−0.506867
$261$	−0.150838	−0.00933665
$262$	1.37171	0.0847446
$263$	2.66909	0.164583	0.0822915	−	0.996608i	$-0.473776\pi$
$263$	2.66909	0.164583	0.0822915	+	0.996608i	$0.473776\pi$
$264$	5.67533	0.349293
$265$	−24.1756	−1.48510
$266$	0	0
$267$	−28.1438	−1.72237
$268$	−0.646484	−0.0394903
$269$	9.75411	0.594719	0.297359	−	0.954766i	$-0.403894\pi$
$269$	9.75411	0.594719	0.297359	+	0.954766i	$0.403894\pi$
$270$	−16.6427	−1.01284
$271$	−23.0516	−1.40028	−0.700142	−	0.714004i	$-0.746880\pi$
$271$	−23.0516	−1.40028	−0.700142	+	0.714004i	$0.746880\pi$
$272$	−4.54398	−0.275519
$273$	0	0
$274$	−15.5253	−0.937918
$275$	−14.4002	−0.868367
$276$	−6.61474	−0.398161
$277$	20.3599	1.22331	0.611654	−	0.791125i	$-0.290505\pi$
$277$	20.3599	1.22331	0.611654	+	0.791125i	$0.290505\pi$
$278$	6.35673	0.381251
$279$	3.67727	0.220153
$280$	0	0
$281$	13.6975	0.817126	0.408563	−	0.912730i	$-0.366030\pi$
$281$	13.6975	0.817126	0.408563	+	0.912730i	$0.366030\pi$
$282$	19.0635	1.13521
$283$	−23.5866	−1.40208	−0.701038	−	0.713124i	$-0.747280\pi$
$283$	−23.5866	−1.40208	−0.701038	+	0.713124i	$0.747280\pi$
$284$	12.4539	0.739004
$285$	−30.1895	−1.78827
$286$	−9.88997	−0.584806
$287$	0	0
$288$	−0.548522	−0.0323220
$289$	3.64774	0.214573
$290$	−0.823721	−0.0483706
$291$	10.7806	0.631971
$292$	−4.55192	−0.266381
$293$	−16.6067	−0.970173	−0.485087	−	0.874466i	$-0.661212\pi$
$293$	−16.6067	−0.970173	−0.485087	+	0.874466i	$0.661212\pi$
$294$	0	0
$295$	−26.3906	−1.53652
$296$	5.22818	0.303882
$297$	−20.1390	−1.16859
$298$	6.61561	0.383232
$299$	11.5270	0.666624
$300$	−6.22023	−0.359125
$301$	0	0
$302$	−23.7848	−1.36866
$303$	−11.0200	−0.633084
$304$	−6.43693	−0.369183
$305$	12.9750	0.742944
$306$	2.49247	0.142485
$307$	−23.2097	−1.32465	−0.662324	−	0.749218i	$-0.730430\pi$
$307$	−23.2097	−1.32465	−0.662324	+	0.749218i	$0.730430\pi$
$308$	0	0
$309$	−18.4305	−1.04848
$310$	20.0814	1.14055
$311$	16.9486	0.961068	0.480534	−	0.876976i	$-0.340443\pi$
$311$	16.9486	0.961068	0.480534	+	0.876976i	$0.340443\pi$
$312$	−4.27200	−0.241855
$313$	8.55902	0.483785	0.241892	−	0.970303i	$-0.422232\pi$
$313$	8.55902	0.483785	0.241892	+	0.970303i	$0.422232\pi$
$314$	6.39750	0.361032
$315$	0	0
$316$	5.56633	0.313131
$317$	15.2110	0.854336	0.427168	−	0.904172i	$-0.359511\pi$
$317$	15.2110	0.854336	0.427168	+	0.904172i	$0.359511\pi$
$318$	−12.6366	−0.708623
$319$	−0.996769	−0.0558083
$320$	−2.99546	−0.167451
$321$	3.31895	0.185246
$322$	0	0
$323$	29.2493	1.62747
$324$	−7.05356	−0.391864
$325$	10.8395	0.601268
$326$	−24.7124	−1.36869
$327$	−11.3758	−0.629083
$328$	1.00000	0.0552158
$329$	0	0
$330$	−17.0002	−0.935831
$331$	−11.6607	−0.640932	−0.320466	−	0.947260i	$-0.603839\pi$
$331$	−11.6607	−0.640932	−0.320466	+	0.947260i	$0.603839\pi$
$332$	6.05680	0.332410
$333$	−2.86777	−0.157153
$334$	16.9087	0.925205
$335$	1.93652	0.105803
$336$	0	0
$337$	7.30118	0.397721	0.198860	−	0.980028i	$-0.436276\pi$
$337$	7.30118	0.397721	0.198860	+	0.980028i	$0.436276\pi$
$338$	−5.55550	−0.302180
$339$	8.69786	0.472403
$340$	13.6113	0.738176
$341$	24.3002	1.31593
$342$	3.53080	0.190924
$343$	0	0
$344$	−10.1930	−0.549571
$345$	19.8142	1.06676
$346$	1.26620	0.0680711
$347$	−33.7189	−1.81012	−0.905061	−	0.425281i	$-0.860175\pi$
$347$	−33.7189	−1.81012	−0.905061	+	0.425281i	$0.860175\pi$
$348$	−0.430558	−0.0230803
$349$	−8.93064	−0.478046	−0.239023	−	0.971014i	$-0.576827\pi$
$349$	−8.93064	−0.478046	−0.239023	+	0.971014i	$0.576827\pi$
$350$	0	0
$351$	15.1593	0.809144
$352$	−3.62474	−0.193199
$353$	−21.1904	−1.12785	−0.563927	−	0.825825i	$-0.690710\pi$
$353$	−21.1904	−1.12785	−0.563927	+	0.825825i	$0.690710\pi$
$354$	−13.7943	−0.733161
$355$	−37.3051	−1.97995
$356$	17.9750	0.952671
$357$	0	0
$358$	22.0922	1.16761
$359$	−3.40262	−0.179583	−0.0897916	−	0.995961i	$-0.528620\pi$
$359$	−3.40262	−0.179583	−0.0897916	+	0.995961i	$0.528620\pi$
$360$	1.64307	0.0865976
$361$	22.4341	1.18074
$362$	15.1230	0.794848
$363$	−3.34871	−0.175761
$364$	0	0
$365$	13.6351	0.713693
$366$	6.78199	0.354500
$367$	−0.619992	−0.0323633	−0.0161817	−	0.999869i	$-0.505151\pi$
$367$	−0.619992	−0.0323633	−0.0161817	+	0.999869i	$0.505151\pi$
$368$	4.22473	0.220229
$369$	−0.548522	−0.0285549
$370$	−15.6608	−0.814166
$371$	0	0
$372$	10.4965	0.544220
$373$	33.7095	1.74541	0.872706	−	0.488246i	$-0.162363\pi$
$373$	33.7095	1.74541	0.872706	+	0.488246i	$0.162363\pi$
$374$	16.4708	0.851683
$375$	−4.81780	−0.248790
$376$	−12.1755	−0.627905
$377$	0.750300	0.0386424
$378$	0	0
$379$	−4.70303	−0.241578	−0.120789	−	0.992678i	$-0.538542\pi$
$379$	−4.70303	−0.241578	−0.120789	+	0.992678i	$0.538542\pi$
$380$	19.2816	0.989123
$381$	−11.4381	−0.585990
$382$	3.71215	0.189930
$383$	−20.9664	−1.07133	−0.535666	−	0.844430i	$-0.679939\pi$
$383$	−20.9664	−1.07133	−0.535666	+	0.844430i	$0.679939\pi$
$384$	−1.56572	−0.0799003
$385$	0	0
$386$	−3.81922	−0.194393
$387$	5.59110	0.284212
$388$	−6.88541	−0.349554
$389$	34.1692	1.73245	0.866225	−	0.499654i	$-0.166540\pi$
$389$	34.1692	1.73245	0.866225	+	0.499654i	$0.166540\pi$
$390$	12.7966	0.647981
$391$	−19.1971	−0.970838
$392$	0	0
$393$	−2.14772	−0.108338
$394$	10.5978	0.533910
$395$	−16.6737	−0.838946
$396$	1.98825	0.0999134
$397$	16.2303	0.814574	0.407287	−	0.913300i	$-0.366475\pi$
$397$	16.2303	0.814574	0.407287	+	0.913300i	$0.366475\pi$
$398$	17.4439	0.874386
$399$	0	0
$400$	3.97276	0.198638
$401$	5.25347	0.262346	0.131173	−	0.991360i	$-0.458126\pi$
$401$	5.25347	0.262346	0.131173	+	0.991360i	$0.458126\pi$
$402$	1.01221	0.0504846
$403$	−18.2915	−0.911165
$404$	7.03832	0.350169
$405$	21.1286	1.04989
$406$	0	0
$407$	−18.9508	−0.939357
$408$	7.11460	0.352225
$409$	2.34520	0.115962	0.0579812	−	0.998318i	$-0.481534\pi$
$409$	2.34520	0.115962	0.0579812	+	0.998318i	$0.481534\pi$
$410$	−2.99546	−0.147935
$411$	24.3083	1.19904
$412$	11.7713	0.579929
$413$	0	0
$414$	−2.31736	−0.113892
$415$	−18.1429	−0.890599
$416$	2.72846	0.133774
$417$	−9.95286	−0.487393
$418$	23.3322	1.14122
$419$	−24.4607	−1.19498	−0.597492	−	0.801875i	$-0.703836\pi$
$419$	−24.4607	−1.19498	−0.597492	+	0.801875i	$0.703836\pi$
$420$	0	0
$421$	−7.04746	−0.343472	−0.171736	−	0.985143i	$-0.554938\pi$
$421$	−7.04746	−0.343472	−0.171736	+	0.985143i	$0.554938\pi$
$422$	1.30659	0.0636036
$423$	6.67854	0.324722
$424$	8.07076	0.391951
$425$	−18.0521	−0.875657
$426$	−19.4993	−0.944746
$427$	0	0
$428$	−2.11976	−0.102462
$429$	15.4849	0.747619
$430$	30.5328	1.47242
$431$	1.00435	0.0483780	0.0241890	−	0.999707i	$-0.492300\pi$
$431$	1.00435	0.0483780	0.0241890	+	0.999707i	$0.492300\pi$
$432$	5.55599	0.267313
$433$	−16.3166	−0.784126	−0.392063	−	0.919938i	$-0.628239\pi$
$433$	−16.3166	−0.784126	−0.392063	+	0.919938i	$0.628239\pi$
$434$	0	0
$435$	1.28972	0.0618372
$436$	7.26554	0.347956
$437$	−27.1943	−1.30088
$438$	7.12703	0.340543
$439$	−22.6613	−1.08157	−0.540783	−	0.841162i	$-0.681872\pi$
$439$	−22.6613	−1.08157	−0.540783	+	0.841162i	$0.681872\pi$
$440$	10.8578	0.517623
$441$	0	0
$442$	−12.3981	−0.589716
$443$	5.16361	0.245330	0.122665	−	0.992448i	$-0.460856\pi$
$443$	5.16361	0.245330	0.122665	+	0.992448i	$0.460856\pi$
$444$	−8.18586	−0.388484
$445$	−53.8432	−2.55241
$446$	28.4776	1.34845
$447$	−10.3582	−0.489926
$448$	0	0
$449$	−23.2686	−1.09811	−0.549057	−	0.835785i	$-0.685013\pi$
$449$	−23.2686	−1.09811	−0.549057	+	0.835785i	$0.685013\pi$
$450$	−2.17915	−0.102726
$451$	−3.62474	−0.170682
$452$	−5.55518	−0.261294
$453$	37.2403	1.74970
$454$	14.7928	0.694259
$455$	0	0
$456$	10.0784	0.471966
$457$	−11.5931	−0.542304	−0.271152	−	0.962537i	$-0.587405\pi$
$457$	−11.5931	−0.542304	−0.271152	+	0.962537i	$0.587405\pi$
$458$	11.0825	0.517849
$459$	−25.2463	−1.17840
$460$	−12.6550	−0.590042
$461$	−29.4146	−1.36997	−0.684987	−	0.728556i	$-0.740192\pi$
$461$	−29.4146	−1.36997	−0.684987	+	0.728556i	$0.740192\pi$
$462$	0	0
$463$	−14.7200	−0.684097	−0.342048	−	0.939682i	$-0.611121\pi$
$463$	−14.7200	−0.684097	−0.342048	+	0.939682i	$0.611121\pi$
$464$	0.274990	0.0127661
$465$	−31.4419	−1.45808
$466$	−5.84348	−0.270694
$467$	9.02806	0.417769	0.208884	−	0.977940i	$-0.433017\pi$
$467$	9.02806	0.417769	0.208884	+	0.977940i	$0.433017\pi$
$468$	−1.49662	−0.0691813
$469$	0	0
$470$	36.4712	1.68229
$471$	−10.0167	−0.461545
$472$	8.81022	0.405523
$473$	36.9471	1.69883
$474$	−8.71532	−0.400308
$475$	−25.5724	−1.17334
$476$	0	0
$477$	−4.42699	−0.202698
$478$	−22.2698	−1.01860
$479$	25.7075	1.17461	0.587304	−	0.809367i	$-0.300189\pi$
$479$	25.7075	1.17461	0.587304	+	0.809367i	$0.300189\pi$
$480$	4.69005	0.214070
$481$	14.2649	0.650423
$482$	−21.0481	−0.958714
$483$	0	0
$484$	2.13876	0.0972166
$485$	20.6249	0.936530
$486$	−5.62408	−0.255113
$487$	−1.86891	−0.0846885	−0.0423442	−	0.999103i	$-0.513483\pi$
$487$	−1.86891	−0.0846885	−0.0423442	+	0.999103i	$0.513483\pi$
$488$	−4.33155	−0.196080
$489$	38.6927	1.74974
$490$	0	0
$491$	6.24464	0.281817	0.140908	−	0.990023i	$-0.454998\pi$
$491$	6.24464	0.281817	0.140908	+	0.990023i	$0.454998\pi$
$492$	−1.56572	−0.0705881
$493$	−1.24955	−0.0562769
$494$	−17.5629	−0.790193
$495$	−5.95572	−0.267690
$496$	−6.70397	−0.301017
$497$	0	0
$498$	−9.48325	−0.424955
$499$	−6.61934	−0.296322	−0.148161	−	0.988963i	$-0.547335\pi$
$499$	−6.61934	−0.296322	−0.148161	+	0.988963i	$0.547335\pi$
$500$	3.07705	0.137610
$501$	−26.4744	−1.18279
$502$	12.9484	0.577915
$503$	31.7222	1.41442	0.707212	−	0.707002i	$-0.249953\pi$
$503$	31.7222	1.41442	0.707212	+	0.707002i	$0.249953\pi$
$504$	0	0
$505$	−21.0830	−0.938180
$506$	−15.3136	−0.680771
$507$	8.69836	0.386308
$508$	7.30532	0.324121
$509$	−11.8616	−0.525757	−0.262879	−	0.964829i	$-0.584672\pi$
$509$	−11.8616	−0.525757	−0.262879	+	0.964829i	$0.584672\pi$
$510$	−21.3115	−0.943688
$511$	0	0
$512$	1.00000	0.0441942
$513$	−35.7635	−1.57900
$514$	19.7245	0.870010
$515$	−35.2604	−1.55376
$516$	15.9594	0.702575
$517$	44.1331	1.94097
$518$	0	0
$519$	−1.98251	−0.0870224
$520$	−8.17299	−0.358409
$521$	43.3043	1.89720	0.948598	−	0.316483i	$-0.102502\pi$
$521$	43.3043	1.89720	0.948598	+	0.316483i	$0.102502\pi$
$522$	−0.150838	−0.00660201
$523$	−11.8186	−0.516793	−0.258397	−	0.966039i	$-0.583194\pi$
$523$	−11.8186	−0.516793	−0.258397	+	0.966039i	$0.583194\pi$
$524$	1.37171	0.0599235
$525$	0	0
$526$	2.66909	0.116378
$527$	30.4627	1.32698
$528$	5.67533	0.246987
$529$	−5.15166	−0.223985
$530$	−24.1756	−1.05012
$531$	−4.83260	−0.209717
$532$	0	0
$533$	2.72846	0.118183
$534$	−28.1438	−1.21790
$535$	6.34964	0.274519
$536$	−0.646484	−0.0279239
$537$	−34.5902	−1.49268
$538$	9.75411	0.420530
$539$	0	0
$540$	−16.6427	−0.716189
$541$	29.7771	1.28022	0.640109	−	0.768284i	$-0.278889\pi$
$541$	29.7771	1.28022	0.640109	+	0.768284i	$0.278889\pi$
$542$	−23.0516	−0.990150
$543$	−23.6784	−1.01614
$544$	−4.54398	−0.194821
$545$	−21.7636	−0.932250
$546$	0	0
$547$	−17.7804	−0.760236	−0.380118	−	0.924938i	$-0.624117\pi$
$547$	−17.7804	−0.760236	−0.380118	+	0.924938i	$0.624117\pi$
$548$	−15.5253	−0.663208
$549$	2.37595	0.101403
$550$	−14.4002	−0.614028
$551$	−1.77009	−0.0754085
$552$	−6.61474	−0.281542
$553$	0	0
$554$	20.3599	0.865009
$555$	24.5204	1.04083
$556$	6.35673	0.269585
$557$	2.64921	0.112250	0.0561252	−	0.998424i	$-0.482125\pi$
$557$	2.64921	0.112250	0.0561252	+	0.998424i	$0.482125\pi$
$558$	3.67727	0.155671
$559$	−27.8113	−1.17629
$560$	0	0
$561$	−25.7886	−1.08880
$562$	13.6975	0.577795
$563$	27.9479	1.17786	0.588932	−	0.808183i	$-0.299549\pi$
$563$	27.9479	1.17786	0.588932	+	0.808183i	$0.299549\pi$
$564$	19.0635	0.802716
$565$	16.6403	0.700063
$566$	−23.5866	−0.991417
$567$	0	0
$568$	12.4539	0.522554
$569$	−1.21836	−0.0510763	−0.0255382	−	0.999674i	$-0.508130\pi$
$569$	−1.21836	−0.0510763	−0.0255382	+	0.999674i	$0.508130\pi$
$570$	−30.1895	−1.26450
$571$	40.4672	1.69350	0.846750	−	0.531991i	$-0.178556\pi$
$571$	40.4672	1.69350	0.846750	+	0.531991i	$0.178556\pi$
$572$	−9.88997	−0.413520
$573$	−5.81218	−0.242807
$574$	0	0
$575$	16.7838	0.699935
$576$	−0.548522	−0.0228551
$577$	−19.0969	−0.795015	−0.397507	−	0.917599i	$-0.630125\pi$
$577$	−19.0969	−0.795015	−0.397507	+	0.917599i	$0.630125\pi$
$578$	3.64774	0.151726
$579$	5.97983	0.248513
$580$	−0.823721	−0.0342032
$581$	0	0
$582$	10.7806	0.446871
$583$	−29.2544	−1.21160
$584$	−4.55192	−0.188360
$585$	4.48306	0.185352
$586$	−16.6067	−0.686016
$587$	−34.4870	−1.42343	−0.711716	−	0.702467i	$-0.752082\pi$
$587$	−34.4870	−1.42343	−0.711716	+	0.702467i	$0.752082\pi$
$588$	0	0
$589$	43.1530	1.77809
$590$	−26.3906	−1.08649
$591$	−16.5932	−0.682553
$592$	5.22818	0.214877
$593$	0.661903	0.0271811	0.0135906	−	0.999908i	$-0.495674\pi$
$593$	0.661903	0.0271811	0.0135906	+	0.999908i	$0.495674\pi$
$594$	−20.1390	−0.826315
$595$	0	0
$596$	6.61561	0.270986
$597$	−27.3123	−1.11782
$598$	11.5270	0.471374
$599$	−32.2612	−1.31816	−0.659079	−	0.752074i	$-0.729054\pi$
$599$	−32.2612	−1.31816	−0.659079	+	0.752074i	$0.729054\pi$
$600$	−6.22023	−0.253940
$601$	−5.90684	−0.240945	−0.120473	−	0.992717i	$-0.538441\pi$
$601$	−5.90684	−0.240945	−0.120473	+	0.992717i	$0.538441\pi$
$602$	0	0
$603$	0.354611	0.0144409
$604$	−23.7848	−0.967788
$605$	−6.40658	−0.260464
$606$	−11.0200	−0.447658
$607$	−2.15964	−0.0876570	−0.0438285	−	0.999039i	$-0.513956\pi$
$607$	−2.15964	−0.0876570	−0.0438285	+	0.999039i	$0.513956\pi$
$608$	−6.43693	−0.261052
$609$	0	0
$610$	12.9750	0.525341
$611$	−33.2204	−1.34395
$612$	2.49247	0.100752
$613$	43.2488	1.74680	0.873401	−	0.487002i	$-0.161910\pi$
$613$	43.2488	1.74680	0.873401	+	0.487002i	$0.161910\pi$
$614$	−23.2097	−0.936667
$615$	4.69005	0.189121
$616$	0	0
$617$	−0.115993	−0.00466969	−0.00233485	−	0.999997i	$-0.500743\pi$
$617$	−0.115993	−0.00466969	−0.00233485	+	0.999997i	$0.500743\pi$
$618$	−18.4305	−0.741384
$619$	−23.4045	−0.940704	−0.470352	−	0.882479i	$-0.655873\pi$
$619$	−23.4045	−0.940704	−0.470352	+	0.882479i	$0.655873\pi$
$620$	20.0814	0.806490
$621$	23.4726	0.941921
$622$	16.9486	0.679577
$623$	0	0
$624$	−4.27200	−0.171017
$625$	−29.0810	−1.16324
$626$	8.55902	0.342087
$627$	−36.5317	−1.45894
$628$	6.39750	0.255288
$629$	−23.7567	−0.947243
$630$	0	0
$631$	36.6327	1.45833	0.729163	−	0.684340i	$-0.239910\pi$
$631$	36.6327	1.45833	0.729163	+	0.684340i	$0.239910\pi$
$632$	5.56633	0.221417
$633$	−2.04575	−0.0813111
$634$	15.2110	0.604107
$635$	−21.8828	−0.868391
$636$	−12.6366	−0.501072
$637$	0	0
$638$	−0.996769	−0.0394625
$639$	−6.83124	−0.270240
$640$	−2.99546	−0.118406
$641$	−15.4629	−0.610747	−0.305373	−	0.952233i	$-0.598781\pi$
$641$	−15.4629	−0.610747	−0.305373	+	0.952233i	$0.598781\pi$
$642$	3.31895	0.130988
$643$	−18.0335	−0.711171	−0.355586	−	0.934644i	$-0.615719\pi$
$643$	−18.0335	−0.711171	−0.355586	+	0.934644i	$0.615719\pi$
$644$	0	0
$645$	−47.8058	−1.88235
$646$	29.2493	1.15080
$647$	−31.7105	−1.24667	−0.623334	−	0.781956i	$-0.714222\pi$
$647$	−31.7105	−1.24667	−0.623334	+	0.781956i	$0.714222\pi$
$648$	−7.05356	−0.277090
$649$	−31.9348	−1.25355
$650$	10.8395	0.425161
$651$	0	0
$652$	−24.7124	−0.967811
$653$	12.8999	0.504812	0.252406	−	0.967621i	$-0.418778\pi$
$653$	12.8999	0.504812	0.252406	+	0.967621i	$0.418778\pi$
$654$	−11.3758	−0.444829
$655$	−4.10890	−0.160548
$656$	1.00000	0.0390434
$657$	2.49683	0.0974106
$658$	0	0
$659$	−40.3036	−1.57000	−0.785002	−	0.619493i	$-0.787338\pi$
$659$	−40.3036	−1.57000	−0.785002	+	0.619493i	$0.787338\pi$
$660$	−17.0002	−0.661732
$661$	−7.72323	−0.300399	−0.150199	−	0.988656i	$-0.547992\pi$
$661$	−7.72323	−0.300399	−0.150199	+	0.988656i	$0.547992\pi$
$662$	−11.6607	−0.453207
$663$	19.4119	0.753896
$664$	6.05680	0.235049
$665$	0	0
$666$	−2.86777	−0.111124
$667$	1.16176	0.0449835
$668$	16.9087	0.654219
$669$	−44.5879	−1.72387
$670$	1.93652	0.0748141
$671$	15.7007	0.606120
$672$	0	0
$673$	−22.6398	−0.872701	−0.436350	−	0.899777i	$-0.643729\pi$
$673$	−22.6398	−0.872701	−0.436350	+	0.899777i	$0.643729\pi$
$674$	7.30118	0.281231
$675$	22.0726	0.849576
$676$	−5.55550	−0.213673
$677$	8.35274	0.321022	0.160511	−	0.987034i	$-0.448686\pi$
$677$	8.35274	0.321022	0.160511	+	0.987034i	$0.448686\pi$
$678$	8.69786	0.334039
$679$	0	0
$680$	13.6113	0.521969
$681$	−23.1613	−0.887544
$682$	24.3002	0.930501
$683$	7.66259	0.293201	0.146600	−	0.989196i	$-0.453167\pi$
$683$	7.66259	0.293201	0.146600	+	0.989196i	$0.453167\pi$
$684$	3.53080	0.135003
$685$	46.5054	1.77688
$686$	0	0
$687$	−17.3520	−0.662021
$688$	−10.1930	−0.388606
$689$	22.0208	0.838924
$690$	19.8142	0.754313
$691$	25.1561	0.956985	0.478492	−	0.878092i	$-0.341183\pi$
$691$	25.1561	0.956985	0.478492	+	0.878092i	$0.341183\pi$
$692$	1.26620	0.0481335
$693$	0	0
$694$	−33.7189	−1.27995
$695$	−19.0413	−0.722278
$696$	−0.430558	−0.0163202
$697$	−4.54398	−0.172115
$698$	−8.93064	−0.338030
$699$	9.14926	0.346057
$700$	0	0
$701$	11.3299	0.427923	0.213962	−	0.976842i	$-0.431363\pi$
$701$	11.3299	0.427923	0.213962	+	0.976842i	$0.431363\pi$
$702$	15.1593	0.572151
$703$	−33.6534	−1.26926
$704$	−3.62474	−0.136613
$705$	−57.1037	−2.15065
$706$	−21.1904	−0.797513
$707$	0	0
$708$	−13.7943	−0.518423
$709$	−3.83449	−0.144007	−0.0720036	−	0.997404i	$-0.522939\pi$
$709$	−3.83449	−0.144007	−0.0720036	+	0.997404i	$0.522939\pi$
$710$	−37.3051	−1.40004
$711$	−3.05326	−0.114506
$712$	17.9750	0.673640
$713$	−28.3224	−1.06068
$714$	0	0
$715$	29.6250	1.10791
$716$	22.0922	0.825624
$717$	34.8682	1.30218
$718$	−3.40262	−0.126985
$719$	−33.5569	−1.25146	−0.625731	−	0.780039i	$-0.715199\pi$
$719$	−33.5569	−1.25146	−0.625731	+	0.780039i	$0.715199\pi$
$720$	1.64307	0.0612337
$721$	0	0
$722$	22.4341	0.834911
$723$	32.9554	1.22562
$724$	15.1230	0.562042
$725$	1.09247	0.0405733
$726$	−3.34871	−0.124282
$727$	43.0668	1.59726	0.798629	−	0.601824i	$-0.205559\pi$
$727$	43.0668	1.59726	0.798629	+	0.601824i	$0.205559\pi$
$728$	0	0
$729$	29.9664	1.10987
$730$	13.6351	0.504657
$731$	46.3169	1.71309
$732$	6.78199	0.250669
$733$	22.1057	0.816494	0.408247	−	0.912872i	$-0.366140\pi$
$733$	22.1057	0.816494	0.408247	+	0.912872i	$0.366140\pi$
$734$	−0.619992	−0.0228843
$735$	0	0
$736$	4.22473	0.155726
$737$	2.34334	0.0863180
$738$	−0.548522	−0.0201914
$739$	4.39419	0.161643	0.0808215	−	0.996729i	$-0.474246\pi$
$739$	4.39419	0.161643	0.0808215	+	0.996729i	$0.474246\pi$
$740$	−15.6608	−0.575702
$741$	27.4986	1.01019
$742$	0	0
$743$	−1.21436	−0.0445507	−0.0222753	−	0.999752i	$-0.507091\pi$
$743$	−1.21436	−0.0445507	−0.0222753	+	0.999752i	$0.507091\pi$
$744$	10.4965	0.384822
$745$	−19.8168	−0.726030
$746$	33.7095	1.23419
$747$	−3.32229	−0.121556
$748$	16.4708	0.602230
$749$	0	0
$750$	−4.81780	−0.175921
$751$	3.89174	0.142012	0.0710058	−	0.997476i	$-0.477379\pi$
$751$	3.89174	0.142012	0.0710058	+	0.997476i	$0.477379\pi$
$752$	−12.1755	−0.443996
$753$	−20.2735	−0.738809
$754$	0.750300	0.0273243
$755$	71.2462	2.59292
$756$	0	0
$757$	47.4976	1.72633	0.863165	−	0.504922i	$-0.168479\pi$
$757$	47.4976	1.72633	0.863165	+	0.504922i	$0.168479\pi$
$758$	−4.70303	−0.170822
$759$	23.9767	0.870301
$760$	19.2816	0.699416
$761$	−27.6941	−1.00391	−0.501956	−	0.864893i	$-0.667386\pi$
$761$	−27.6941	−1.00391	−0.501956	+	0.864893i	$0.667386\pi$
$762$	−11.4381	−0.414358
$763$	0	0
$764$	3.71215	0.134301
$765$	−7.46609	−0.269937
$766$	−20.9664	−0.757546
$767$	24.0383	0.867974
$768$	−1.56572	−0.0564980
$769$	8.67921	0.312980	0.156490	−	0.987680i	$-0.449982\pi$
$769$	8.67921	0.312980	0.156490	+	0.987680i	$0.449982\pi$
$770$	0	0
$771$	−30.8830	−1.11223
$772$	−3.81922	−0.137457
$773$	8.29054	0.298190	0.149095	−	0.988823i	$-0.452364\pi$
$773$	8.29054	0.298190	0.149095	+	0.988823i	$0.452364\pi$
$774$	5.59110	0.200968
$775$	−26.6333	−0.956695
$776$	−6.88541	−0.247172
$777$	0	0
$778$	34.1692	1.22503
$779$	−6.43693	−0.230627
$780$	12.7966	0.458192
$781$	−45.1422	−1.61532
$782$	−19.1971	−0.686486
$783$	1.52784	0.0546006
$784$	0	0
$785$	−19.1634	−0.683972
$786$	−2.14772	−0.0766065
$787$	41.3158	1.47275	0.736375	−	0.676573i	$-0.236536\pi$
$787$	41.3158	1.47275	0.736375	+	0.676573i	$0.236536\pi$
$788$	10.5978	0.377531
$789$	−4.17905	−0.148778
$790$	−16.6737	−0.593224
$791$	0	0
$792$	1.98825	0.0706494
$793$	−11.8185	−0.419685
$794$	16.2303	0.575991
$795$	37.8522	1.34248
$796$	17.4439	0.618284
$797$	−31.4873	−1.11534	−0.557670	−	0.830063i	$-0.688304\pi$
$797$	−31.4873	−1.11534	−0.557670	+	0.830063i	$0.688304\pi$
$798$	0	0
$799$	55.3253	1.95727
$800$	3.97276	0.140458
$801$	−9.85966	−0.348374
$802$	5.25347	0.185506
$803$	16.4995	0.582256
$804$	1.01221	0.0356980
$805$	0	0
$806$	−18.2915	−0.644291
$807$	−15.2722	−0.537607
$808$	7.03832	0.247607
$809$	29.9089	1.05154	0.525770	−	0.850627i	$-0.323777\pi$
$809$	29.9089	1.05154	0.525770	+	0.850627i	$0.323777\pi$
$810$	21.1286	0.742384
$811$	30.5526	1.07285	0.536423	−	0.843949i	$-0.319775\pi$
$811$	30.5526	1.07285	0.536423	+	0.843949i	$0.319775\pi$
$812$	0	0
$813$	36.0923	1.26581
$814$	−18.9508	−0.664226
$815$	74.0249	2.59298
$816$	7.11460	0.249061
$817$	65.6119	2.29547
$818$	2.34520	0.0819978
$819$	0	0
$820$	−2.99546	−0.104606
$821$	19.6634	0.686259	0.343129	−	0.939288i	$-0.388513\pi$
$821$	19.6634	0.686259	0.343129	+	0.939288i	$0.388513\pi$
$822$	24.3083	0.847849
$823$	−43.2437	−1.50738	−0.753690	−	0.657230i	$-0.771728\pi$
$823$	−43.2437	−1.50738	−0.753690	+	0.657230i	$0.771728\pi$
$824$	11.7713	0.410072
$825$	22.5467	0.784977
$826$	0	0
$827$	12.4127	0.431633	0.215816	−	0.976434i	$-0.430759\pi$
$827$	12.4127	0.431633	0.215816	+	0.976434i	$0.430759\pi$
$828$	−2.31736	−0.0805337
$829$	−30.7887	−1.06934	−0.534669	−	0.845062i	$-0.679564\pi$
$829$	−30.7887	−1.06934	−0.534669	+	0.845062i	$0.679564\pi$
$830$	−18.1429	−0.629748
$831$	−31.8779	−1.10583
$832$	2.72846	0.0945923
$833$	0	0
$834$	−9.95286	−0.344639
$835$	−50.6494	−1.75280
$836$	23.3322	0.806962
$837$	−37.2472	−1.28745
$838$	−24.4607	−0.844981
$839$	−17.7361	−0.612318	−0.306159	−	0.951980i	$-0.599044\pi$
$839$	−17.7361	−0.612318	−0.306159	+	0.951980i	$0.599044\pi$
$840$	0	0
$841$	−28.9244	−0.997392
$842$	−7.04746	−0.242872
$843$	−21.4465	−0.738656
$844$	1.30659	0.0449745
$845$	16.6413	0.572477
$846$	6.67854	0.229613
$847$	0	0
$848$	8.07076	0.277151
$849$	36.9299	1.26743
$850$	−18.0521	−0.619183
$851$	22.0876	0.757155
$852$	−19.4993	−0.668036
$853$	39.5082	1.35273	0.676367	−	0.736565i	$-0.263553\pi$
$853$	39.5082	1.35273	0.676367	+	0.736565i	$0.263553\pi$
$854$	0	0
$855$	−10.5764	−0.361704
$856$	−2.11976	−0.0724518
$857$	38.7776	1.32462	0.662308	−	0.749231i	$-0.269577\pi$
$857$	38.7776	1.32462	0.662308	+	0.749231i	$0.269577\pi$
$858$	15.4849	0.528646
$859$	−46.0658	−1.57175	−0.785873	−	0.618388i	$-0.787786\pi$
$859$	−46.0658	−1.57175	−0.785873	+	0.618388i	$0.787786\pi$
$860$	30.5328	1.04116
$861$	0	0
$862$	1.00435	0.0342084
$863$	38.9203	1.32486	0.662432	−	0.749122i	$-0.269524\pi$
$863$	38.9203	1.32486	0.662432	+	0.749122i	$0.269524\pi$
$864$	5.55599	0.189019
$865$	−3.79283	−0.128960
$866$	−16.3166	−0.554461
$867$	−5.71134	−0.193967
$868$	0	0
$869$	−20.1765	−0.684442
$870$	1.28972	0.0437255
$871$	−1.76391	−0.0597677
$872$	7.26554	0.246042
$873$	3.77680	0.127825
$874$	−27.1943	−0.919861
$875$	0	0
$876$	7.12703	0.240800
$877$	24.8636	0.839584	0.419792	−	0.907620i	$-0.362103\pi$
$877$	24.8636	0.839584	0.419792	+	0.907620i	$0.362103\pi$
$878$	−22.6613	−0.764783
$879$	26.0014	0.877006
$880$	10.8578	0.366015
$881$	−24.2391	−0.816638	−0.408319	−	0.912839i	$-0.633885\pi$
$881$	−24.2391	−0.816638	−0.408319	+	0.912839i	$0.633885\pi$
$882$	0	0
$883$	−47.5430	−1.59995	−0.799974	−	0.600035i	$-0.795153\pi$
$883$	−47.5430	−1.59995	−0.799974	+	0.600035i	$0.795153\pi$
$884$	−12.3981	−0.416992
$885$	41.3203	1.38897
$886$	5.16361	0.173475
$887$	52.5126	1.76320	0.881600	−	0.471996i	$-0.156466\pi$
$887$	52.5126	1.76320	0.881600	+	0.471996i	$0.156466\pi$
$888$	−8.18586	−0.274700
$889$	0	0
$890$	−53.8432	−1.80483
$891$	25.5673	0.856538
$892$	28.4776	0.953500
$893$	78.3730	2.62265
$894$	−10.3582	−0.346430
$895$	−66.1762	−2.21203
$896$	0	0
$897$	−18.0481	−0.602607
$898$	−23.2686	−0.776484
$899$	−1.84352	−0.0614850
$900$	−2.17915	−0.0726382
$901$	−36.6734	−1.22177
$902$	−3.62474	−0.120691
$903$	0	0
$904$	−5.55518	−0.184763
$905$	−45.3003	−1.50583
$906$	37.2403	1.23723
$907$	3.44416	0.114361	0.0571806	−	0.998364i	$-0.481789\pi$
$907$	3.44416	0.114361	0.0571806	+	0.998364i	$0.481789\pi$
$908$	14.7928	0.490915
$909$	−3.86067	−0.128050
$910$	0	0
$911$	−49.6495	−1.64496	−0.822481	−	0.568792i	$-0.807411\pi$
$911$	−49.6495	−1.64496	−0.822481	+	0.568792i	$0.807411\pi$
$912$	10.0784	0.333730
$913$	−21.9543	−0.726583
$914$	−11.5931	−0.383467
$915$	−20.3151	−0.671598
$916$	11.0825	0.366175
$917$	0	0
$918$	−25.2463	−0.833252
$919$	−42.5008	−1.40197	−0.700987	−	0.713174i	$-0.747257\pi$
$919$	−42.5008	−1.40197	−0.700987	+	0.713174i	$0.747257\pi$
$920$	−12.6550	−0.417223
$921$	36.3399	1.19744
$922$	−29.4146	−0.968717
$923$	33.9800	1.11847
$924$	0	0
$925$	20.7703	0.682924
$926$	−14.7200	−0.483729
$927$	−6.45680	−0.212069
$928$	0.274990	0.00902699
$929$	−40.2648	−1.32104	−0.660522	−	0.750807i	$-0.729665\pi$
$929$	−40.2648	−1.32104	−0.660522	+	0.750807i	$0.729665\pi$
$930$	−31.4419	−1.03102
$931$	0	0
$932$	−5.84348	−0.191410
$933$	−26.5368	−0.868775
$934$	9.02806	0.295407
$935$	−49.3374	−1.61351
$936$	−1.49662	−0.0489186
$937$	20.9632	0.684839	0.342419	−	0.939547i	$-0.388754\pi$
$937$	20.9632	0.684839	0.342419	+	0.939547i	$0.388754\pi$
$938$	0	0
$939$	−13.4010	−0.437326
$940$	36.4712	1.18956
$941$	5.85679	0.190926	0.0954629	−	0.995433i	$-0.469567\pi$
$941$	5.85679	0.190926	0.0954629	+	0.995433i	$0.469567\pi$
$942$	−10.0167	−0.326361
$943$	4.22473	0.137576
$944$	8.81022	0.286748
$945$	0	0
$946$	36.9471	1.20125
$947$	51.6992	1.68000	0.840000	−	0.542587i	$-0.182555\pi$
$947$	51.6992	1.68000	0.840000	+	0.542587i	$0.182555\pi$
$948$	−8.71532	−0.283060
$949$	−12.4197	−0.403162
$950$	−25.5724	−0.829678
$951$	−23.8162	−0.772293
$952$	0	0
$953$	−50.8966	−1.64870	−0.824352	−	0.566078i	$-0.808460\pi$
$953$	−50.8966	−1.64870	−0.824352	+	0.566078i	$0.808460\pi$
$954$	−4.42699	−0.143329
$955$	−11.1196	−0.359821
$956$	−22.2698	−0.720256
$957$	1.56066	0.0504490
$958$	25.7075	0.830573
$959$	0	0
$960$	4.69005	0.151371
$961$	13.9432	0.449780
$962$	14.2649	0.459918
$963$	1.16273	0.0374686
$964$	−21.0481	−0.677913
$965$	11.4403	0.368277
$966$	0	0
$967$	42.0360	1.35179	0.675893	−	0.737000i	$-0.263758\pi$
$967$	42.0360	1.35179	0.675893	+	0.737000i	$0.263758\pi$
$968$	2.13876	0.0687425
$969$	−45.7962	−1.47119
$970$	20.6249	0.662227
$971$	−18.2456	−0.585530	−0.292765	−	0.956184i	$-0.594575\pi$
$971$	−18.2456	−0.585530	−0.292765	+	0.956184i	$0.594575\pi$
$972$	−5.62408	−0.180392
$973$	0	0
$974$	−1.86891	−0.0598838
$975$	−16.9717	−0.543528
$976$	−4.33155	−0.138649
$977$	37.3936	1.19633	0.598164	−	0.801374i	$-0.295897\pi$
$977$	37.3936	1.19633	0.598164	+	0.801374i	$0.295897\pi$
$978$	38.6927	1.23725
$979$	−65.1546	−2.08235
$980$	0	0
$981$	−3.98531	−0.127241
$982$	6.24464	0.199275
$983$	14.5423	0.463828	0.231914	−	0.972736i	$-0.425501\pi$
$983$	14.5423	0.463828	0.231914	+	0.972736i	$0.425501\pi$
$984$	−1.56572	−0.0499133
$985$	−31.7453	−1.01149
$986$	−1.24955	−0.0397938
$987$	0	0
$988$	−17.5629	−0.558751
$989$	−43.0628	−1.36932
$990$	−5.95572	−0.189285
$991$	−23.8770	−0.758477	−0.379238	−	0.925299i	$-0.623814\pi$
$991$	−23.8770	−0.758477	−0.379238	+	0.925299i	$0.623814\pi$
$992$	−6.70397	−0.212851
$993$	18.2574	0.579382
$994$	0	0
$995$	−52.2526	−1.65652
$996$	−9.48325	−0.300488
$997$	41.3223	1.30869	0.654345	−	0.756196i	$-0.272944\pi$
$997$	41.3223	1.30869	0.654345	+	0.756196i	$0.272944\pi$
$998$	−6.61934	−0.209532
$999$	29.0477	0.919029

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bu.1.4		10
7.3	odd	6		574.2.e.h.247.4	yes	20
7.5	odd	6		574.2.e.h.165.4	✓	20
7.6	odd	2		4018.2.a.bt.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.e.h.165.4	✓	20	7.5	odd	6
574.2.e.h.247.4	yes	20	7.3	odd	6
4018.2.a.bt.1.7		10	7.6	odd	2
4018.2.a.bu.1.4		10	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:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.56572 q^{3} +1.00000 q^{4} -2.99546 q^{5} -1.56572 q^{6} +1.00000 q^{8} -0.548522 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.56572 q^{3} +1.00000 q^{4} -2.99546 q^{5} -1.56572 q^{6} +1.00000 q^{8} -0.548522 q^{9} -2.99546 q^{10} -3.62474 q^{11} -1.56572 q^{12} +2.72846 q^{13} +4.69005 q^{15} +1.00000 q^{16} -4.54398 q^{17} -0.548522 q^{18} -6.43693 q^{19} -2.99546 q^{20} -3.62474 q^{22} +4.22473 q^{23} -1.56572 q^{24} +3.97276 q^{25} +2.72846 q^{26} +5.55599 q^{27} +0.274990 q^{29} +4.69005 q^{30} -6.70397 q^{31} +1.00000 q^{32} +5.67533 q^{33} -4.54398 q^{34} -0.548522 q^{36} +5.22818 q^{37} -6.43693 q^{38} -4.27200 q^{39} -2.99546 q^{40} +1.00000 q^{41} -10.1930 q^{43} -3.62474 q^{44} +1.64307 q^{45} +4.22473 q^{46} -12.1755 q^{47} -1.56572 q^{48} +3.97276 q^{50} +7.11460 q^{51} +2.72846 q^{52} +8.07076 q^{53} +5.55599 q^{54} +10.8578 q^{55} +10.0784 q^{57} +0.274990 q^{58} +8.81022 q^{59} +4.69005 q^{60} -4.33155 q^{61} -6.70397 q^{62} +1.00000 q^{64} -8.17299 q^{65} +5.67533 q^{66} -0.646484 q^{67} -4.54398 q^{68} -6.61474 q^{69} +12.4539 q^{71} -0.548522 q^{72} -4.55192 q^{73} +5.22818 q^{74} -6.22023 q^{75} -6.43693 q^{76} -4.27200 q^{78} +5.56633 q^{79} -2.99546 q^{80} -7.05356 q^{81} +1.00000 q^{82} +6.05680 q^{83} +13.6113 q^{85} -10.1930 q^{86} -0.430558 q^{87} -3.62474 q^{88} +17.9750 q^{89} +1.64307 q^{90} +4.22473 q^{92} +10.4965 q^{93} -12.1755 q^{94} +19.2816 q^{95} -1.56572 q^{96} -6.88541 q^{97} +1.98825 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + q^{3} + 10 q^{4} - 2 q^{5} + q^{6} + 10 q^{8} + 17 q^{9}+O(q^{10}) \) 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