LMFDB - Embedded newform 4018.2.a.bq.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:	$6$
Coefficient field:	6.6.5163008.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 5x^{2} - 6x + 1 $ x^6 - 2x^5 - 5x^4 + 8x^3 + 5x^2 - 6*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.545336$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.93139 q^{3} +1.00000 q^{4} +1.16627 q^{5} +1.93139 q^{6} +1.00000 q^{8} +0.730254 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.93139 q^{3} +1.00000 q^{4} +1.16627 q^{5} +1.93139 q^{6} +1.00000 q^{8} +0.730254 q^{9} +1.16627 q^{10} +1.40723 q^{11} +1.93139 q^{12} +4.56450 q^{13} +2.25252 q^{15} +1.00000 q^{16} -4.59999 q^{17} +0.730254 q^{18} +1.15929 q^{19} +1.16627 q^{20} +1.40723 q^{22} +6.00670 q^{23} +1.93139 q^{24} -3.63982 q^{25} +4.56450 q^{26} -4.38376 q^{27} +4.33393 q^{29} +2.25252 q^{30} +7.01025 q^{31} +1.00000 q^{32} +2.71791 q^{33} -4.59999 q^{34} +0.730254 q^{36} +3.76336 q^{37} +1.15929 q^{38} +8.81582 q^{39} +1.16627 q^{40} -1.00000 q^{41} -6.83593 q^{43} +1.40723 q^{44} +0.851672 q^{45} +6.00670 q^{46} -7.27779 q^{47} +1.93139 q^{48} -3.63982 q^{50} -8.88435 q^{51} +4.56450 q^{52} -0.473172 q^{53} -4.38376 q^{54} +1.64121 q^{55} +2.23903 q^{57} +4.33393 q^{58} +13.9769 q^{59} +2.25252 q^{60} +7.11656 q^{61} +7.01025 q^{62} +1.00000 q^{64} +5.32344 q^{65} +2.71791 q^{66} -14.5186 q^{67} -4.59999 q^{68} +11.6013 q^{69} -4.30523 q^{71} +0.730254 q^{72} +3.31718 q^{73} +3.76336 q^{74} -7.02989 q^{75} +1.15929 q^{76} +8.81582 q^{78} +10.7168 q^{79} +1.16627 q^{80} -10.6575 q^{81} -1.00000 q^{82} +5.29004 q^{83} -5.36482 q^{85} -6.83593 q^{86} +8.37050 q^{87} +1.40723 q^{88} -7.62205 q^{89} +0.851672 q^{90} +6.00670 q^{92} +13.5395 q^{93} -7.27779 q^{94} +1.35204 q^{95} +1.93139 q^{96} -9.35599 q^{97} +1.02764 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 4 q^{3} + 6 q^{4} + 12 q^{5} + 4 q^{6} + 6 q^{8} + 18 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 4 * q^3 + 6 * q^4 + 12 * q^5 + 4 * q^6 + 6 * q^8 + 18 * q^9	$ 6 q + 6 q^{2} + 4 q^{3} + 6 q^{4} + 12 q^{5} + 4 q^{6} + 6 q^{8} + 18 q^{9} + 12 q^{10} + 4 q^{12} + 8 q^{13} - 4 q^{15} + 6 q^{16} + 16 q^{17} + 18 q^{18} + 12 q^{19} + 12 q^{20} + 12 q^{23} + 4 q^{24} + 14 q^{25} + 8 q^{26} + 28 q^{27} - 4 q^{30} - 4 q^{31} + 6 q^{32} - 20 q^{33} + 16 q^{34} + 18 q^{36} - 24 q^{37} + 12 q^{38} + 4 q^{39} + 12 q^{40} - 6 q^{41} + 4 q^{43} + 28 q^{45} + 12 q^{46} - 16 q^{47} + 4 q^{48} + 14 q^{50} - 16 q^{51} + 8 q^{52} - 16 q^{53} + 28 q^{54} - 12 q^{55} - 28 q^{57} + 16 q^{59} - 4 q^{60} + 32 q^{61} - 4 q^{62} + 6 q^{64} - 4 q^{65} - 20 q^{66} - 20 q^{67} + 16 q^{68} + 56 q^{69} + 12 q^{71} + 18 q^{72} + 16 q^{73} - 24 q^{74} - 4 q^{75} + 12 q^{76} + 4 q^{78} + 12 q^{80} + 42 q^{81} - 6 q^{82} + 32 q^{83} + 48 q^{85} + 4 q^{86} + 20 q^{87} + 8 q^{89} + 28 q^{90} + 12 q^{92} - 12 q^{93} - 16 q^{94} + 28 q^{95} + 4 q^{96} + 8 q^{97} - 76 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 4 * q^3 + 6 * q^4 + 12 * q^5 + 4 * q^6 + 6 * q^8 + 18 * q^9 + 12 * q^10 + 4 * q^12 + 8 * q^13 - 4 * q^15 + 6 * q^16 + 16 * q^17 + 18 * q^18 + 12 * q^19 + 12 * q^20 + 12 * q^23 + 4 * q^24 + 14 * q^25 + 8 * q^26 + 28 * q^27 - 4 * q^30 - 4 * q^31 + 6 * q^32 - 20 * q^33 + 16 * q^34 + 18 * q^36 - 24 * q^37 + 12 * q^38 + 4 * q^39 + 12 * q^40 - 6 * q^41 + 4 * q^43 + 28 * q^45 + 12 * q^46 - 16 * q^47 + 4 * q^48 + 14 * q^50 - 16 * q^51 + 8 * q^52 - 16 * q^53 + 28 * q^54 - 12 * q^55 - 28 * q^57 + 16 * q^59 - 4 * q^60 + 32 * q^61 - 4 * q^62 + 6 * q^64 - 4 * q^65 - 20 * q^66 - 20 * q^67 + 16 * q^68 + 56 * q^69 + 12 * q^71 + 18 * q^72 + 16 * q^73 - 24 * q^74 - 4 * q^75 + 12 * q^76 + 4 * q^78 + 12 * q^80 + 42 * q^81 - 6 * q^82 + 32 * q^83 + 48 * q^85 + 4 * q^86 + 20 * q^87 + 8 * q^89 + 28 * q^90 + 12 * q^92 - 12 * q^93 - 16 * q^94 + 28 * q^95 + 4 * q^96 + 8 * q^97 - 76 * 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
$3$	1.93139	1.11509	0.557543	−	0.830148i	$-0.311744\pi$
$3$	1.93139	1.11509	0.557543	+	0.830148i	$0.311744\pi$
$4$	1.00000	0.500000
$5$	1.16627	0.521571	0.260786	−	0.965397i	$-0.416018\pi$
$5$	1.16627	0.521571	0.260786	+	0.965397i	$0.416018\pi$
$6$	1.93139	0.788485
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	0.730254	0.243418
$10$	1.16627	0.368807
$11$	1.40723	0.424296	0.212148	−	0.977238i	$-0.431954\pi$
$11$	1.40723	0.424296	0.212148	+	0.977238i	$0.431954\pi$
$12$	1.93139	0.557543
$13$	4.56450	1.26597	0.632983	−	0.774166i	$-0.281830\pi$
$13$	4.56450	1.26597	0.632983	+	0.774166i	$0.281830\pi$
$14$	0	0
$15$	2.25252	0.581597
$16$	1.00000	0.250000
$17$	−4.59999	−1.11566	−0.557830	−	0.829955i	$-0.688366\pi$
$17$	−4.59999	−1.11566	−0.557830	+	0.829955i	$0.688366\pi$
$18$	0.730254	0.172122
$19$	1.15929	0.265958	0.132979	−	0.991119i	$-0.457546\pi$
$19$	1.15929	0.265958	0.132979	+	0.991119i	$0.457546\pi$
$20$	1.16627	0.260786
$21$	0	0
$22$	1.40723	0.300023
$23$	6.00670	1.25248	0.626242	−	0.779629i	$-0.284592\pi$
$23$	6.00670	1.25248	0.626242	+	0.779629i	$0.284592\pi$
$24$	1.93139	0.394243
$25$	−3.63982	−0.727963
$26$	4.56450	0.895173
$27$	−4.38376	−0.843654
$28$	0	0
$29$	4.33393	0.804791	0.402396	−	0.915466i	$-0.368178\pi$
$29$	4.33393	0.804791	0.402396	+	0.915466i	$0.368178\pi$
$30$	2.25252	0.411251
$31$	7.01025	1.25908	0.629539	−	0.776969i	$-0.283244\pi$
$31$	7.01025	1.25908	0.629539	+	0.776969i	$0.283244\pi$
$32$	1.00000	0.176777
$33$	2.71791	0.473127
$34$	−4.59999	−0.788891
$35$	0	0
$36$	0.730254	0.121709
$37$	3.76336	0.618693	0.309347	−	0.950949i	$-0.399890\pi$
$37$	3.76336	0.618693	0.309347	+	0.950949i	$0.399890\pi$
$38$	1.15929	0.188061
$39$	8.81582	1.41166
$40$	1.16627	0.184403
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−6.83593	−1.04247	−0.521235	−	0.853413i	$-0.674528\pi$
$43$	−6.83593	−1.04247	−0.521235	+	0.853413i	$0.674528\pi$
$44$	1.40723	0.212148
$45$	0.851672	0.126960
$46$	6.00670	0.885640
$47$	−7.27779	−1.06157	−0.530787	−	0.847505i	$-0.678104\pi$
$47$	−7.27779	−1.06157	−0.530787	+	0.847505i	$0.678104\pi$
$48$	1.93139	0.278772
$49$	0	0
$50$	−3.63982	−0.514748
$51$	−8.88435	−1.24406
$52$	4.56450	0.632983
$53$	−0.473172	−0.0649952	−0.0324976	−	0.999472i	$-0.510346\pi$
$53$	−0.473172	−0.0649952	−0.0324976	+	0.999472i	$0.510346\pi$
$54$	−4.38376	−0.596554
$55$	1.64121	0.221301
$56$	0	0
$57$	2.23903	0.296567
$58$	4.33393	0.569073
$59$	13.9769	1.81963	0.909816	−	0.415011i	$-0.136222\pi$
$59$	13.9769	1.81963	0.909816	+	0.415011i	$0.136222\pi$
$60$	2.25252	0.290799
$61$	7.11656	0.911183	0.455591	−	0.890189i	$-0.349428\pi$
$61$	7.11656	0.911183	0.455591	+	0.890189i	$0.349428\pi$
$62$	7.01025	0.890303
$63$	0	0
$64$	1.00000	0.125000
$65$	5.32344	0.660291
$66$	2.71791	0.334551
$67$	−14.5186	−1.77373	−0.886865	−	0.462029i	$-0.847122\pi$
$67$	−14.5186	−1.77373	−0.886865	+	0.462029i	$0.847122\pi$
$68$	−4.59999	−0.557830
$69$	11.6013	1.39663
$70$	0	0
$71$	−4.30523	−0.510937	−0.255468	−	0.966817i	$-0.582230\pi$
$71$	−4.30523	−0.510937	−0.255468	+	0.966817i	$0.582230\pi$
$72$	0.730254	0.0860612
$73$	3.31718	0.388246	0.194123	−	0.980977i	$-0.437814\pi$
$73$	3.31718	0.388246	0.194123	+	0.980977i	$0.437814\pi$
$74$	3.76336	0.437482
$75$	−7.02989	−0.811742
$76$	1.15929	0.132979
$77$	0	0
$78$	8.81582	0.998195
$79$	10.7168	1.20574	0.602868	−	0.797841i	$-0.294025\pi$
$79$	10.7168	1.20574	0.602868	+	0.797841i	$0.294025\pi$
$80$	1.16627	0.130393
$81$	−10.6575	−1.18417
$82$	−1.00000	−0.110432
$83$	5.29004	0.580658	0.290329	−	0.956927i	$-0.406235\pi$
$83$	5.29004	0.580658	0.290329	+	0.956927i	$0.406235\pi$
$84$	0	0
$85$	−5.36482	−0.581897
$86$	−6.83593	−0.737137
$87$	8.37050	0.897412
$88$	1.40723	0.150011
$89$	−7.62205	−0.807935	−0.403968	−	0.914773i	$-0.632369\pi$
$89$	−7.62205	−0.807935	−0.403968	+	0.914773i	$0.632369\pi$
$90$	0.851672	0.0897741
$91$	0	0
$92$	6.00670	0.626242
$93$	13.5395	1.40398
$94$	−7.27779	−0.750646
$95$	1.35204	0.138716
$96$	1.93139	0.197121
$97$	−9.35599	−0.949957	−0.474979	−	0.879997i	$-0.657544\pi$
$97$	−9.35599	−0.949957	−0.474979	+	0.879997i	$0.657544\pi$
$98$	0	0
$99$	1.02764	0.103281
$100$	−3.63982	−0.363982
$101$	−0.277380	−0.0276004	−0.0138002	−	0.999905i	$-0.504393\pi$
$101$	−0.277380	−0.0276004	−0.0138002	+	0.999905i	$0.504393\pi$
$102$	−8.88435	−0.879682
$103$	12.6605	1.24747	0.623737	−	0.781634i	$-0.285614\pi$
$103$	12.6605	1.24747	0.623737	+	0.781634i	$0.285614\pi$
$104$	4.56450	0.447586
$105$	0	0
$106$	−0.473172	−0.0459585
$107$	8.07041	0.780196	0.390098	−	0.920773i	$-0.372441\pi$
$107$	8.07041	0.780196	0.390098	+	0.920773i	$0.372441\pi$
$108$	−4.38376	−0.421827
$109$	−8.64760	−0.828290	−0.414145	−	0.910211i	$-0.635919\pi$
$109$	−8.64760	−0.828290	−0.414145	+	0.910211i	$0.635919\pi$
$110$	1.64121	0.156483
$111$	7.26851	0.689897
$112$	0	0
$113$	−0.0434830	−0.00409053	−0.00204527	−	0.999998i	$-0.500651\pi$
$113$	−0.0434830	−0.00409053	−0.00204527	+	0.999998i	$0.500651\pi$
$114$	2.23903	0.209704
$115$	7.00543	0.653260
$116$	4.33393	0.402396
$117$	3.33325	0.308159
$118$	13.9769	1.28667
$119$	0	0
$120$	2.25252	0.205626
$121$	−9.01970	−0.819973
$122$	7.11656	0.644303
$123$	−1.93139	−0.174147
$124$	7.01025	0.629539
$125$	−10.0763	−0.901256
$126$	0	0
$127$	−4.68518	−0.415742	−0.207871	−	0.978156i	$-0.566653\pi$
$127$	−4.68518	−0.415742	−0.207871	+	0.978156i	$0.566653\pi$
$128$	1.00000	0.0883883
$129$	−13.2028	−1.16244
$130$	5.32344	0.466896
$131$	−3.81355	−0.333191	−0.166596	−	0.986025i	$-0.553277\pi$
$131$	−3.81355	−0.333191	−0.166596	+	0.986025i	$0.553277\pi$
$132$	2.71791	0.236563
$133$	0	0
$134$	−14.5186	−1.25422
$135$	−5.11264	−0.440026
$136$	−4.59999	−0.394446
$137$	−6.33068	−0.540866	−0.270433	−	0.962739i	$-0.587167\pi$
$137$	−6.33068	−0.540866	−0.270433	+	0.962739i	$0.587167\pi$
$138$	11.6013	0.987565
$139$	−10.5379	−0.893814	−0.446907	−	0.894580i	$-0.647475\pi$
$139$	−10.5379	−0.893814	−0.446907	+	0.894580i	$0.647475\pi$
$140$	0	0
$141$	−14.0562	−1.18375
$142$	−4.30523	−0.361287
$143$	6.42331	0.537144
$144$	0.730254	0.0608545
$145$	5.05453	0.419756
$146$	3.31718	0.274532
$147$	0	0
$148$	3.76336	0.309347
$149$	−17.1423	−1.40435	−0.702174	−	0.712005i	$-0.747787\pi$
$149$	−17.1423	−1.40435	−0.702174	+	0.712005i	$0.747787\pi$
$150$	−7.02989	−0.573988
$151$	−19.1613	−1.55932	−0.779661	−	0.626201i	$-0.784609\pi$
$151$	−19.1613	−1.55932	−0.779661	+	0.626201i	$0.784609\pi$
$152$	1.15929	0.0940305
$153$	−3.35916	−0.271572
$154$	0	0
$155$	8.17584	0.656699
$156$	8.81582	0.705830
$157$	15.3965	1.22877	0.614385	−	0.789006i	$-0.289404\pi$
$157$	15.3965	1.22877	0.614385	+	0.789006i	$0.289404\pi$
$158$	10.7168	0.852584
$159$	−0.913878	−0.0724752
$160$	1.16627	0.0922017
$161$	0	0
$162$	−10.6575	−0.837332
$163$	12.1228	0.949527	0.474764	−	0.880113i	$-0.342534\pi$
$163$	12.1228	0.949527	0.474764	+	0.880113i	$0.342534\pi$
$164$	−1.00000	−0.0780869
$165$	3.16981	0.246769
$166$	5.29004	0.410587
$167$	13.4301	1.03925	0.519626	−	0.854394i	$-0.326071\pi$
$167$	13.4301	1.03925	0.519626	+	0.854394i	$0.326071\pi$
$168$	0	0
$169$	7.83469	0.602668
$170$	−5.36482	−0.411463
$171$	0.846573	0.0647391
$172$	−6.83593	−0.521235
$173$	18.5097	1.40727	0.703633	−	0.710564i	$-0.251560\pi$
$173$	18.5097	1.40727	0.703633	+	0.710564i	$0.251560\pi$
$174$	8.37050	0.634566
$175$	0	0
$176$	1.40723	0.106074
$177$	26.9947	2.02905
$178$	−7.62205	−0.571297
$179$	−3.52711	−0.263629	−0.131814	−	0.991274i	$-0.542080\pi$
$179$	−3.52711	−0.263629	−0.131814	+	0.991274i	$0.542080\pi$
$180$	0.851672	0.0634799
$181$	18.3176	1.36154	0.680769	−	0.732498i	$-0.261646\pi$
$181$	18.3176	1.36154	0.680769	+	0.732498i	$0.261646\pi$
$182$	0	0
$183$	13.7448	1.01605
$184$	6.00670	0.442820
$185$	4.38909	0.322693
$186$	13.5395	0.992765
$187$	−6.47324	−0.473370
$188$	−7.27779	−0.530787
$189$	0	0
$190$	1.35204	0.0980872
$191$	11.8343	0.856302	0.428151	−	0.903707i	$-0.359165\pi$
$191$	11.8343	0.856302	0.428151	+	0.903707i	$0.359165\pi$
$192$	1.93139	0.139386
$193$	−19.7095	−1.41872	−0.709359	−	0.704847i	$-0.751016\pi$
$193$	−19.7095	−1.41872	−0.709359	+	0.704847i	$0.751016\pi$
$194$	−9.35599	−0.671721
$195$	10.2816	0.736282
$196$	0	0
$197$	1.90183	0.135500	0.0677500	−	0.997702i	$-0.478418\pi$
$197$	1.90183	0.135500	0.0677500	+	0.997702i	$0.478418\pi$
$198$	1.02764	0.0730309
$199$	−2.54087	−0.180117	−0.0900587	−	0.995936i	$-0.528705\pi$
$199$	−2.54087	−0.180117	−0.0900587	+	0.995936i	$0.528705\pi$
$200$	−3.63982	−0.257374
$201$	−28.0410	−1.97786
$202$	−0.277380	−0.0195164
$203$	0	0
$204$	−8.88435	−0.622029
$205$	−1.16627	−0.0814558
$206$	12.6605	0.882098
$207$	4.38642	0.304877
$208$	4.56450	0.316491
$209$	1.63138	0.112845
$210$	0	0
$211$	−24.8972	−1.71399	−0.856996	−	0.515323i	$-0.827672\pi$
$211$	−24.8972	−1.71399	−0.856996	+	0.515323i	$0.827672\pi$
$212$	−0.473172	−0.0324976
$213$	−8.31507	−0.569739
$214$	8.07041	0.551682
$215$	−7.97253	−0.543722
$216$	−4.38376	−0.298277
$217$	0	0
$218$	−8.64760	−0.585689
$219$	6.40676	0.432928
$220$	1.64121	0.110650
$221$	−20.9967	−1.41239
$222$	7.26851	0.487831
$223$	−4.27435	−0.286232	−0.143116	−	0.989706i	$-0.545712\pi$
$223$	−4.27435	−0.286232	−0.143116	+	0.989706i	$0.545712\pi$
$224$	0	0
$225$	−2.65799	−0.177199
$226$	−0.0434830	−0.00289244
$227$	−0.927418	−0.0615549	−0.0307775	−	0.999526i	$-0.509798\pi$
$227$	−0.927418	−0.0615549	−0.0307775	+	0.999526i	$0.509798\pi$
$228$	2.23903	0.148283
$229$	6.52448	0.431149	0.215575	−	0.976487i	$-0.430838\pi$
$229$	6.52448	0.431149	0.215575	+	0.976487i	$0.430838\pi$
$230$	7.00543	0.461924
$231$	0	0
$232$	4.33393	0.284537
$233$	5.02732	0.329351	0.164675	−	0.986348i	$-0.447342\pi$
$233$	5.02732	0.329351	0.164675	+	0.986348i	$0.447342\pi$
$234$	3.33325	0.217901
$235$	−8.48786	−0.553687
$236$	13.9769	0.909816
$237$	20.6983	1.34450
$238$	0	0
$239$	2.05210	0.132739	0.0663696	−	0.997795i	$-0.478858\pi$
$239$	2.05210	0.132739	0.0663696	+	0.997795i	$0.478858\pi$
$240$	2.25252	0.145399
$241$	−6.99530	−0.450607	−0.225303	−	0.974289i	$-0.572337\pi$
$241$	−6.99530	−0.450607	−0.225303	+	0.974289i	$0.572337\pi$
$242$	−9.01970	−0.579808
$243$	−7.43246	−0.476793
$244$	7.11656	0.455591
$245$	0	0
$246$	−1.93139	−0.123141
$247$	5.29156	0.336694
$248$	7.01025	0.445151
$249$	10.2171	0.647484
$250$	−10.0763	−0.637284
$251$	−26.0905	−1.64681	−0.823407	−	0.567451i	$-0.807930\pi$
$251$	−26.0905	−1.64681	−0.823407	+	0.567451i	$0.807930\pi$
$252$	0	0
$253$	8.45281	0.531424
$254$	−4.68518	−0.293974
$255$	−10.3615	−0.648865
$256$	1.00000	0.0625000
$257$	21.7190	1.35479	0.677397	−	0.735618i	$-0.263108\pi$
$257$	21.7190	1.35479	0.677397	+	0.735618i	$0.263108\pi$
$258$	−13.2028	−0.821972
$259$	0	0
$260$	5.32344	0.330146
$261$	3.16487	0.195901
$262$	−3.81355	−0.235602
$263$	−15.2717	−0.941692	−0.470846	−	0.882215i	$-0.656051\pi$
$263$	−15.2717	−0.941692	−0.470846	+	0.882215i	$0.656051\pi$
$264$	2.71791	0.167276
$265$	−0.551846	−0.0338996
$266$	0	0
$267$	−14.7211	−0.900918
$268$	−14.5186	−0.886865
$269$	−12.2651	−0.747814	−0.373907	−	0.927466i	$-0.621982\pi$
$269$	−12.2651	−0.747814	−0.373907	+	0.927466i	$0.621982\pi$
$270$	−5.11264	−0.311145
$271$	1.07282	0.0651695	0.0325847	−	0.999469i	$-0.489626\pi$
$271$	1.07282	0.0651695	0.0325847	+	0.999469i	$0.489626\pi$
$272$	−4.59999	−0.278915
$273$	0	0
$274$	−6.33068	−0.382450
$275$	−5.12206	−0.308872
$276$	11.6013	0.698314
$277$	1.99642	0.119953	0.0599766	−	0.998200i	$-0.480897\pi$
$277$	1.99642	0.119953	0.0599766	+	0.998200i	$0.480897\pi$
$278$	−10.5379	−0.632022
$279$	5.11926	0.306482
$280$	0	0
$281$	−6.08738	−0.363143	−0.181571	−	0.983378i	$-0.558118\pi$
$281$	−6.08738	−0.363143	−0.181571	+	0.983378i	$0.558118\pi$
$282$	−14.0562	−0.837036
$283$	−26.8076	−1.59355	−0.796773	−	0.604278i	$-0.793462\pi$
$283$	−26.8076	−1.59355	−0.796773	+	0.604278i	$0.793462\pi$
$284$	−4.30523	−0.255468
$285$	2.61131	0.154681
$286$	6.42331	0.379818
$287$	0	0
$288$	0.730254	0.0430306
$289$	4.15989	0.244699
$290$	5.05453	0.296812
$291$	−18.0700	−1.05928
$292$	3.31718	0.194123
$293$	26.8926	1.57108	0.785541	−	0.618810i	$-0.212385\pi$
$293$	26.8926	1.57108	0.785541	+	0.618810i	$0.212385\pi$
$294$	0	0
$295$	16.3008	0.949068
$296$	3.76336	0.218741
$297$	−6.16896	−0.357959
$298$	−17.1423	−0.993024
$299$	27.4176	1.58560
$300$	−7.02989	−0.405871
$301$	0	0
$302$	−19.1613	−1.10261
$303$	−0.535728	−0.0307768
$304$	1.15929	0.0664896
$305$	8.29983	0.475247
$306$	−3.35916	−0.192030
$307$	−0.427636	−0.0244065	−0.0122032	−	0.999926i	$-0.503885\pi$
$307$	−0.427636	−0.0244065	−0.0122032	+	0.999926i	$0.503885\pi$
$308$	0	0
$309$	24.4523	1.39104
$310$	8.17584	0.464356
$311$	−24.3618	−1.38143	−0.690714	−	0.723128i	$-0.742704\pi$
$311$	−24.3618	−1.38143	−0.690714	+	0.723128i	$0.742704\pi$
$312$	8.81582	0.499097
$313$	4.50817	0.254817	0.127408	−	0.991850i	$-0.459334\pi$
$313$	4.50817	0.254817	0.127408	+	0.991850i	$0.459334\pi$
$314$	15.3965	0.868872
$315$	0	0
$316$	10.7168	0.602868
$317$	−26.6907	−1.49910	−0.749551	−	0.661947i	$-0.769730\pi$
$317$	−26.6907	−1.49910	−0.749551	+	0.661947i	$0.769730\pi$
$318$	−0.913878	−0.0512477
$319$	6.09885	0.341470
$320$	1.16627	0.0651964
$321$	15.5871	0.869986
$322$	0	0
$323$	−5.33270	−0.296719
$324$	−10.6575	−0.592083
$325$	−16.6140	−0.921576
$326$	12.1228	0.671417
$327$	−16.7019	−0.923615
$328$	−1.00000	−0.0552158
$329$	0	0
$330$	3.16981	0.174492
$331$	−6.58196	−0.361777	−0.180889	−	0.983504i	$-0.557897\pi$
$331$	−6.58196	−0.361777	−0.180889	+	0.983504i	$0.557897\pi$
$332$	5.29004	0.290329
$333$	2.74821	0.150601
$334$	13.4301	0.734862
$335$	−16.9326	−0.925127
$336$	0	0
$337$	−34.7174	−1.89118	−0.945589	−	0.325365i	$-0.894513\pi$
$337$	−34.7174	−1.89118	−0.945589	+	0.325365i	$0.894513\pi$
$338$	7.83469	0.426151
$339$	−0.0839824	−0.00456130
$340$	−5.36482	−0.290948
$341$	9.86504	0.534222
$342$	0.846573	0.0457774
$343$	0	0
$344$	−6.83593	−0.368569
$345$	13.5302	0.728441
$346$	18.5097	0.995087
$347$	−6.72261	−0.360889	−0.180444	−	0.983585i	$-0.557754\pi$
$347$	−6.72261	−0.360889	−0.180444	+	0.983585i	$0.557754\pi$
$348$	8.37050	0.448706
$349$	12.3104	0.658962	0.329481	−	0.944162i	$-0.393126\pi$
$349$	12.3104	0.658962	0.329481	+	0.944162i	$0.393126\pi$
$350$	0	0
$351$	−20.0097	−1.06804
$352$	1.40723	0.0750056
$353$	−6.86653	−0.365469	−0.182734	−	0.983162i	$-0.558495\pi$
$353$	−6.86653	−0.365469	−0.182734	+	0.983162i	$0.558495\pi$
$354$	26.9947	1.43475
$355$	−5.02106	−0.266490
$356$	−7.62205	−0.403968
$357$	0	0
$358$	−3.52711	−0.186414
$359$	18.5058	0.976700	0.488350	−	0.872648i	$-0.337599\pi$
$359$	18.5058	0.976700	0.488350	+	0.872648i	$0.337599\pi$
$360$	0.851672	0.0448871
$361$	−17.6561	−0.929266
$362$	18.3176	0.962753
$363$	−17.4205	−0.914341
$364$	0	0
$365$	3.86872	0.202498
$366$	13.7448	0.718454
$367$	−22.0014	−1.14846	−0.574231	−	0.818694i	$-0.694699\pi$
$367$	−22.0014	−1.14846	−0.574231	+	0.818694i	$0.694699\pi$
$368$	6.00670	0.313121
$369$	−0.730254	−0.0380155
$370$	4.38909	0.228178
$371$	0	0
$372$	13.5395	0.701991
$373$	14.7364	0.763020	0.381510	−	0.924365i	$-0.375404\pi$
$373$	14.7364	0.763020	0.381510	+	0.924365i	$0.375404\pi$
$374$	−6.47324	−0.334723
$375$	−19.4613	−1.00498
$376$	−7.27779	−0.375323
$377$	19.7823	1.01884
$378$	0	0
$379$	5.19292	0.266743	0.133371	−	0.991066i	$-0.457420\pi$
$379$	5.19292	0.266743	0.133371	+	0.991066i	$0.457420\pi$
$380$	1.35204	0.0693581
$381$	−9.04889	−0.463589
$382$	11.8343	0.605497
$383$	6.10124	0.311759	0.155879	−	0.987776i	$-0.450179\pi$
$383$	6.10124	0.311759	0.155879	+	0.987776i	$0.450179\pi$
$384$	1.93139	0.0985607
$385$	0	0
$386$	−19.7095	−1.00319
$387$	−4.99196	−0.253756
$388$	−9.35599	−0.474979
$389$	−14.2578	−0.722900	−0.361450	−	0.932392i	$-0.617718\pi$
$389$	−14.2578	−0.722900	−0.361450	+	0.932392i	$0.617718\pi$
$390$	10.2816	0.520630
$391$	−27.6307	−1.39735
$392$	0	0
$393$	−7.36544	−0.371537
$394$	1.90183	0.0958130
$395$	12.4987	0.628877
$396$	1.02764	0.0516406
$397$	−16.0149	−0.803767	−0.401883	−	0.915691i	$-0.631644\pi$
$397$	−16.0149	−0.803767	−0.401883	+	0.915691i	$0.631644\pi$
$398$	−2.54087	−0.127362
$399$	0	0
$400$	−3.63982	−0.181991
$401$	−6.10942	−0.305090	−0.152545	−	0.988297i	$-0.548747\pi$
$401$	−6.10942	−0.305090	−0.152545	+	0.988297i	$0.548747\pi$
$402$	−28.0410	−1.39856
$403$	31.9983	1.59395
$404$	−0.277380	−0.0138002
$405$	−12.4295	−0.617627
$406$	0	0
$407$	5.29592	0.262509
$408$	−8.88435	−0.439841
$409$	−35.7868	−1.76954	−0.884772	−	0.466023i	$-0.845686\pi$
$409$	−35.7868	−1.76954	−0.884772	+	0.466023i	$0.845686\pi$
$410$	−1.16627	−0.0575979
$411$	−12.2270	−0.603113
$412$	12.6605	0.623737
$413$	0	0
$414$	4.38642	0.215581
$415$	6.16961	0.302854
$416$	4.56450	0.223793
$417$	−20.3528	−0.996680
$418$	1.63138	0.0797935
$419$	7.20652	0.352062	0.176031	−	0.984385i	$-0.443674\pi$
$419$	7.20652	0.352062	0.176031	+	0.984385i	$0.443674\pi$
$420$	0	0
$421$	−18.1810	−0.886087	−0.443044	−	0.896500i	$-0.646101\pi$
$421$	−18.1810	−0.886087	−0.443044	+	0.896500i	$0.646101\pi$
$422$	−24.8972	−1.21198
$423$	−5.31463	−0.258406
$424$	−0.473172	−0.0229793
$425$	16.7431	0.812160
$426$	−8.31507	−0.402866
$427$	0	0
$428$	8.07041	0.390098
$429$	12.4059	0.598962
$430$	−7.97253	−0.384470
$431$	29.6276	1.42711	0.713555	−	0.700599i	$-0.247084\pi$
$431$	29.6276	1.42711	0.713555	+	0.700599i	$0.247084\pi$
$432$	−4.38376	−0.210914
$433$	22.7951	1.09546	0.547732	−	0.836654i	$-0.315491\pi$
$433$	22.7951	1.09546	0.547732	+	0.836654i	$0.315491\pi$
$434$	0	0
$435$	9.76226	0.468064
$436$	−8.64760	−0.414145
$437$	6.96348	0.333109
$438$	6.40676	0.306127
$439$	24.9786	1.19217	0.596083	−	0.802923i	$-0.296723\pi$
$439$	24.9786	1.19217	0.596083	+	0.802923i	$0.296723\pi$
$440$	1.64121	0.0782416
$441$	0	0
$442$	−20.9967	−0.998709
$443$	−28.2630	−1.34281	−0.671407	−	0.741089i	$-0.734310\pi$
$443$	−28.2630	−1.34281	−0.671407	+	0.741089i	$0.734310\pi$
$444$	7.26851	0.344948
$445$	−8.88936	−0.421396
$446$	−4.27435	−0.202396
$447$	−33.1083	−1.56597
$448$	0	0
$449$	23.6608	1.11662	0.558311	−	0.829632i	$-0.311450\pi$
$449$	23.6608	1.11662	0.558311	+	0.829632i	$0.311450\pi$
$450$	−2.65799	−0.125299
$451$	−1.40723	−0.0662639
$452$	−0.0434830	−0.00204527
$453$	−37.0078	−1.73878
$454$	−0.927418	−0.0435259
$455$	0	0
$456$	2.23903	0.104852
$457$	35.3465	1.65344	0.826720	−	0.562614i	$-0.190204\pi$
$457$	35.3465	1.65344	0.826720	+	0.562614i	$0.190204\pi$
$458$	6.52448	0.304869
$459$	20.1652	0.941232
$460$	7.00543	0.326630
$461$	−24.9703	−1.16298	−0.581492	−	0.813552i	$-0.697531\pi$
$461$	−24.9703	−1.16298	−0.581492	+	0.813552i	$0.697531\pi$
$462$	0	0
$463$	14.3430	0.666576	0.333288	−	0.942825i	$-0.391842\pi$
$463$	14.3430	0.666576	0.333288	+	0.942825i	$0.391842\pi$
$464$	4.33393	0.201198
$465$	15.7907	0.732276
$466$	5.02732	0.232886
$467$	−14.0060	−0.648121	−0.324060	−	0.946036i	$-0.605048\pi$
$467$	−14.0060	−0.648121	−0.324060	+	0.946036i	$0.605048\pi$
$468$	3.33325	0.154079
$469$	0	0
$470$	−8.48786	−0.391516
$471$	29.7365	1.37019
$472$	13.9769	0.643337
$473$	−9.61973	−0.442316
$474$	20.6983	0.950704
$475$	−4.21959	−0.193608
$476$	0	0
$477$	−0.345536	−0.0158210
$478$	2.05210	0.0938608
$479$	−7.86343	−0.359289	−0.179645	−	0.983732i	$-0.557495\pi$
$479$	−7.86343	−0.359289	−0.179645	+	0.983732i	$0.557495\pi$
$480$	2.25252	0.102813
$481$	17.1779	0.783244
$482$	−6.99530	−0.318627
$483$	0	0
$484$	−9.01970	−0.409986
$485$	−10.9116	−0.495470
$486$	−7.43246	−0.337143
$487$	31.7965	1.44084	0.720418	−	0.693540i	$-0.243950\pi$
$487$	31.7965	1.44084	0.720418	+	0.693540i	$0.243950\pi$
$488$	7.11656	0.322152
$489$	23.4137	1.05881
$490$	0	0
$491$	36.5057	1.64748	0.823740	−	0.566967i	$-0.191883\pi$
$491$	36.5057	1.64748	0.823740	+	0.566967i	$0.191883\pi$
$492$	−1.93139	−0.0870736
$493$	−19.9360	−0.897874
$494$	5.29156	0.238079
$495$	1.19850	0.0538685
$496$	7.01025	0.314770
$497$	0	0
$498$	10.2171	0.457840
$499$	−0.0567669	−0.00254124	−0.00127062	−	0.999999i	$-0.500404\pi$
$499$	−0.0567669	−0.00254124	−0.00127062	+	0.999999i	$0.500404\pi$
$500$	−10.0763	−0.450628
$501$	25.9387	1.15886
$502$	−26.0905	−1.16447
$503$	19.2916	0.860168	0.430084	−	0.902789i	$-0.358484\pi$
$503$	19.2916	0.860168	0.430084	+	0.902789i	$0.358484\pi$
$504$	0	0
$505$	−0.323500	−0.0143956
$506$	8.45281	0.375773
$507$	15.1318	0.672027
$508$	−4.68518	−0.207871
$509$	−27.3333	−1.21153	−0.605764	−	0.795644i	$-0.707132\pi$
$509$	−27.3333	−1.21153	−0.605764	+	0.795644i	$0.707132\pi$
$510$	−10.3615	−0.458817
$511$	0	0
$512$	1.00000	0.0441942
$513$	−5.08203	−0.224377
$514$	21.7190	0.957983
$515$	14.7655	0.650647
$516$	−13.2028	−0.581222
$517$	−10.2415	−0.450422
$518$	0	0
$519$	35.7494	1.56922
$520$	5.32344	0.233448
$521$	18.5181	0.811294	0.405647	−	0.914030i	$-0.367046\pi$
$521$	18.5181	0.811294	0.405647	+	0.914030i	$0.367046\pi$
$522$	3.16487	0.138523
$523$	3.55882	0.155616	0.0778081	−	0.996968i	$-0.475208\pi$
$523$	3.55882	0.155616	0.0778081	+	0.996968i	$0.475208\pi$
$524$	−3.81355	−0.166596
$525$	0	0
$526$	−15.2717	−0.665877
$527$	−32.2471	−1.40470
$528$	2.71791	0.118282
$529$	13.0805	0.568715
$530$	−0.551846	−0.0239707
$531$	10.2067	0.442931
$532$	0	0
$533$	−4.56450	−0.197711
$534$	−14.7211	−0.637045
$535$	9.41227	0.406928
$536$	−14.5186	−0.627108
$537$	−6.81222	−0.293969
$538$	−12.2651	−0.528784
$539$	0	0
$540$	−5.11264	−0.220013
$541$	9.85921	0.423880	0.211940	−	0.977283i	$-0.432022\pi$
$541$	9.85921	0.423880	0.211940	+	0.977283i	$0.432022\pi$
$542$	1.07282	0.0460818
$543$	35.3784	1.51823
$544$	−4.59999	−0.197223
$545$	−10.0854	−0.432012
$546$	0	0
$547$	−3.09103	−0.132163	−0.0660815	−	0.997814i	$-0.521050\pi$
$547$	−3.09103	−0.132163	−0.0660815	+	0.997814i	$0.521050\pi$
$548$	−6.33068	−0.270433
$549$	5.19690	0.221798
$550$	−5.12206	−0.218405
$551$	5.02427	0.214041
$552$	11.6013	0.493782
$553$	0	0
$554$	1.99642	0.0848197
$555$	8.47704	0.359830
$556$	−10.5379	−0.446907
$557$	8.92466	0.378150	0.189075	−	0.981963i	$-0.439451\pi$
$557$	8.92466	0.378150	0.189075	+	0.981963i	$0.439451\pi$
$558$	5.11926	0.216716
$559$	−31.2026	−1.31973
$560$	0	0
$561$	−12.5023	−0.527849
$562$	−6.08738	−0.256781
$563$	−5.12807	−0.216122	−0.108061	−	0.994144i	$-0.534464\pi$
$563$	−5.12807	−0.216122	−0.108061	+	0.994144i	$0.534464\pi$
$564$	−14.0562	−0.591874
$565$	−0.0507128	−0.00213350
$566$	−26.8076	−1.12681
$567$	0	0
$568$	−4.30523	−0.180643
$569$	−3.86301	−0.161946	−0.0809729	−	0.996716i	$-0.525803\pi$
$569$	−3.86301	−0.161946	−0.0809729	+	0.996716i	$0.525803\pi$
$570$	2.61131	0.109376
$571$	−5.18754	−0.217092	−0.108546	−	0.994091i	$-0.534619\pi$
$571$	−5.18754	−0.217092	−0.108546	+	0.994091i	$0.534619\pi$
$572$	6.42331	0.268572
$573$	22.8567	0.954851
$574$	0	0
$575$	−21.8633	−0.911762
$576$	0.730254	0.0304272
$577$	33.2824	1.38556	0.692782	−	0.721148i	$-0.256385\pi$
$577$	33.2824	1.38556	0.692782	+	0.721148i	$0.256385\pi$
$578$	4.15989	0.173029
$579$	−38.0666	−1.58199
$580$	5.05453	0.209878
$581$	0	0
$582$	−18.0700	−0.749027
$583$	−0.665862	−0.0275772
$584$	3.31718	0.137266
$585$	3.88746	0.160727
$586$	26.8926	1.11092
$587$	−4.24519	−0.175218	−0.0876089	−	0.996155i	$-0.527923\pi$
$587$	−4.24519	−0.175218	−0.0876089	+	0.996155i	$0.527923\pi$
$588$	0	0
$589$	8.12689	0.334863
$590$	16.3008	0.671093
$591$	3.67318	0.151094
$592$	3.76336	0.154673
$593$	4.68438	0.192364	0.0961822	−	0.995364i	$-0.469337\pi$
$593$	4.68438	0.192364	0.0961822	+	0.995364i	$0.469337\pi$
$594$	−6.16896	−0.253115
$595$	0	0
$596$	−17.1423	−0.702174
$597$	−4.90740	−0.200846
$598$	27.4176	1.12119
$599$	−7.48952	−0.306014	−0.153007	−	0.988225i	$-0.548896\pi$
$599$	−7.48952	−0.306014	−0.153007	+	0.988225i	$0.548896\pi$
$600$	−7.02989	−0.286994
$601$	−14.8374	−0.605232	−0.302616	−	0.953113i	$-0.597860\pi$
$601$	−14.8374	−0.605232	−0.302616	+	0.953113i	$0.597860\pi$
$602$	0	0
$603$	−10.6023	−0.431758
$604$	−19.1613	−0.779661
$605$	−10.5194	−0.427674
$606$	−0.535728	−0.0217625
$607$	−44.1403	−1.79160	−0.895799	−	0.444459i	$-0.853396\pi$
$607$	−44.1403	−1.79160	−0.895799	+	0.444459i	$0.853396\pi$
$608$	1.15929	0.0470153
$609$	0	0
$610$	8.29983	0.336050
$611$	−33.2195	−1.34392
$612$	−3.35916	−0.135786
$613$	24.9022	1.00579	0.502896	−	0.864347i	$-0.332268\pi$
$613$	24.9022	1.00579	0.502896	+	0.864347i	$0.332268\pi$
$614$	−0.427636	−0.0172580
$615$	−2.25252	−0.0908302
$616$	0	0
$617$	−22.2308	−0.894978	−0.447489	−	0.894290i	$-0.647682\pi$
$617$	−22.2308	−0.894978	−0.447489	+	0.894290i	$0.647682\pi$
$618$	24.4523	0.983615
$619$	19.6916	0.791470	0.395735	−	0.918365i	$-0.370490\pi$
$619$	19.6916	0.791470	0.395735	+	0.918365i	$0.370490\pi$
$620$	8.17584	0.328350
$621$	−26.3319	−1.05666
$622$	−24.3618	−0.976817
$623$	0	0
$624$	8.81582	0.352915
$625$	6.44735	0.257894
$626$	4.50817	0.180183
$627$	3.15083	0.125832
$628$	15.3965	0.614385
$629$	−17.3114	−0.690252
$630$	0	0
$631$	31.6059	1.25821	0.629105	−	0.777320i	$-0.283421\pi$
$631$	31.6059	1.25821	0.629105	+	0.777320i	$0.283421\pi$
$632$	10.7168	0.426292
$633$	−48.0861	−1.91125
$634$	−26.6907	−1.06002
$635$	−5.46418	−0.216839
$636$	−0.913878	−0.0362376
$637$	0	0
$638$	6.09885	0.241456
$639$	−3.14391	−0.124371
$640$	1.16627	0.0461008
$641$	48.7238	1.92448	0.962238	−	0.272211i	$-0.0877549\pi$
$641$	48.7238	1.92448	0.962238	+	0.272211i	$0.0877549\pi$
$642$	15.5871	0.615173
$643$	−37.9836	−1.49793	−0.748963	−	0.662612i	$-0.769448\pi$
$643$	−37.9836	−1.49793	−0.748963	+	0.662612i	$0.769448\pi$
$644$	0	0
$645$	−15.3980	−0.606297
$646$	−5.33270	−0.209812
$647$	34.5284	1.35745	0.678726	−	0.734391i	$-0.262532\pi$
$647$	34.5284	1.35745	0.678726	+	0.734391i	$0.262532\pi$
$648$	−10.6575	−0.418666
$649$	19.6687	0.772063
$650$	−16.6140	−0.651653
$651$	0	0
$652$	12.1228	0.474764
$653$	−26.9958	−1.05643	−0.528215	−	0.849111i	$-0.677138\pi$
$653$	−26.9958	−1.05643	−0.528215	+	0.849111i	$0.677138\pi$
$654$	−16.7019	−0.653094
$655$	−4.44762	−0.173783
$656$	−1.00000	−0.0390434
$657$	2.42238	0.0945061
$658$	0	0
$659$	−2.55300	−0.0994507	−0.0497254	−	0.998763i	$-0.515835\pi$
$659$	−2.55300	−0.0994507	−0.0497254	+	0.998763i	$0.515835\pi$
$660$	3.16981	0.123385
$661$	5.77171	0.224494	0.112247	−	0.993680i	$-0.464195\pi$
$661$	5.77171	0.224494	0.112247	+	0.993680i	$0.464195\pi$
$662$	−6.58196	−0.255815
$663$	−40.5527	−1.57493
$664$	5.29004	0.205294
$665$	0	0
$666$	2.74821	0.106491
$667$	26.0326	1.00799
$668$	13.4301	0.519626
$669$	−8.25542	−0.319173
$670$	−16.9326	−0.654163
$671$	10.0146	0.386611
$672$	0	0
$673$	−4.39347	−0.169356	−0.0846778	−	0.996408i	$-0.526986\pi$
$673$	−4.39347	−0.169356	−0.0846778	+	0.996408i	$0.526986\pi$
$674$	−34.7174	−1.33726
$675$	15.9561	0.614150
$676$	7.83469	0.301334
$677$	−5.05938	−0.194448	−0.0972239	−	0.995263i	$-0.530996\pi$
$677$	−5.05938	−0.194448	−0.0972239	+	0.995263i	$0.530996\pi$
$678$	−0.0839824	−0.00322532
$679$	0	0
$680$	−5.36482	−0.205732
$681$	−1.79120	−0.0686391
$682$	9.86504	0.377752
$683$	−29.2454	−1.11904	−0.559522	−	0.828815i	$-0.689015\pi$
$683$	−29.2454	−1.11904	−0.559522	+	0.828815i	$0.689015\pi$
$684$	0.846573	0.0323695
$685$	−7.38327	−0.282100
$686$	0	0
$687$	12.6013	0.480769
$688$	−6.83593	−0.260617
$689$	−2.15979	−0.0822816
$690$	13.5302	0.515086
$691$	−20.8231	−0.792149	−0.396075	−	0.918218i	$-0.629628\pi$
$691$	−20.8231	−0.792149	−0.396075	+	0.918218i	$0.629628\pi$
$692$	18.5097	0.703633
$693$	0	0
$694$	−6.72261	−0.255187
$695$	−12.2900	−0.466188
$696$	8.37050	0.317283
$697$	4.59999	0.174237
$698$	12.3104	0.465956
$699$	9.70969	0.367254
$700$	0	0
$701$	−31.6975	−1.19720	−0.598599	−	0.801049i	$-0.704276\pi$
$701$	−31.6975	−1.19720	−0.598599	+	0.801049i	$0.704276\pi$
$702$	−20.0097	−0.755216
$703$	4.36282	0.164547
$704$	1.40723	0.0530370
$705$	−16.3933	−0.617409
$706$	−6.86653	−0.258425
$707$	0	0
$708$	26.9947	1.01452
$709$	30.5460	1.14718	0.573590	−	0.819143i	$-0.305550\pi$
$709$	30.5460	1.14718	0.573590	+	0.819143i	$0.305550\pi$
$710$	−5.02106	−0.188437
$711$	7.82599	0.293498
$712$	−7.62205	−0.285648
$713$	42.1085	1.57697
$714$	0	0
$715$	7.49130	0.280159
$716$	−3.52711	−0.131814
$717$	3.96339	0.148016
$718$	18.5058	0.690631
$719$	−30.8037	−1.14879	−0.574393	−	0.818580i	$-0.694762\pi$
$719$	−30.8037	−1.14879	−0.574393	+	0.818580i	$0.694762\pi$
$720$	0.851672	0.0317400
$721$	0	0
$722$	−17.6561	−0.657090
$723$	−13.5106	−0.502466
$724$	18.3176	0.680769
$725$	−15.7747	−0.585859
$726$	−17.4205	−0.646537
$727$	24.1332	0.895052	0.447526	−	0.894271i	$-0.352305\pi$
$727$	24.1332	0.895052	0.447526	+	0.894271i	$0.352305\pi$
$728$	0	0
$729$	17.6175	0.652501
$730$	3.86872	0.143188
$731$	31.4452	1.16304
$732$	13.7448	0.508024
$733$	13.7607	0.508262	0.254131	−	0.967170i	$-0.418211\pi$
$733$	13.7607	0.508262	0.254131	+	0.967170i	$0.418211\pi$
$734$	−22.0014	−0.812085
$735$	0	0
$736$	6.00670	0.221410
$737$	−20.4310	−0.752587
$738$	−0.730254	−0.0268810
$739$	−47.3159	−1.74054	−0.870272	−	0.492572i	$-0.836057\pi$
$739$	−47.3159	−1.74054	−0.870272	+	0.492572i	$0.836057\pi$
$740$	4.38909	0.161346
$741$	10.2201	0.375443
$742$	0	0
$743$	−35.0764	−1.28683	−0.643415	−	0.765518i	$-0.722483\pi$
$743$	−35.0764	−1.28683	−0.643415	+	0.765518i	$0.722483\pi$
$744$	13.5395	0.496382
$745$	−19.9925	−0.732468
$746$	14.7364	0.539536
$747$	3.86307	0.141343
$748$	−6.47324	−0.236685
$749$	0	0
$750$	−19.4613	−0.710627
$751$	−4.92833	−0.179837	−0.0899187	−	0.995949i	$-0.528661\pi$
$751$	−4.92833	−0.179837	−0.0899187	+	0.995949i	$0.528661\pi$
$752$	−7.27779	−0.265394
$753$	−50.3907	−1.83634
$754$	19.7823	0.720427
$755$	−22.3472	−0.813298
$756$	0	0
$757$	−27.3582	−0.994350	−0.497175	−	0.867650i	$-0.665629\pi$
$757$	−27.3582	−0.994350	−0.497175	+	0.867650i	$0.665629\pi$
$758$	5.19292	0.188616
$759$	16.3256	0.592583
$760$	1.35204	0.0490436
$761$	49.2091	1.78383	0.891914	−	0.452205i	$-0.149363\pi$
$761$	49.2091	1.78383	0.891914	+	0.452205i	$0.149363\pi$
$762$	−9.04889	−0.327807
$763$	0	0
$764$	11.8343	0.428151
$765$	−3.91768	−0.141644
$766$	6.10124	0.220447
$767$	63.7974	2.30359
$768$	1.93139	0.0696929
$769$	−15.4411	−0.556822	−0.278411	−	0.960462i	$-0.589808\pi$
$769$	−15.4411	−0.556822	−0.278411	+	0.960462i	$0.589808\pi$
$770$	0	0
$771$	41.9478	1.51071
$772$	−19.7095	−0.709359
$773$	−6.76947	−0.243481	−0.121740	−	0.992562i	$-0.538848\pi$
$773$	−6.76947	−0.243481	−0.121740	+	0.992562i	$0.538848\pi$
$774$	−4.99196	−0.179432
$775$	−25.5160	−0.916563
$776$	−9.35599	−0.335861
$777$	0	0
$778$	−14.2578	−0.511167
$779$	−1.15929	−0.0415357
$780$	10.2816	0.368141
$781$	−6.05845	−0.216789
$782$	−27.6307	−0.988074
$783$	−18.9989	−0.678966
$784$	0	0
$785$	17.9564	0.640892
$786$	−7.36544	−0.262716
$787$	−14.8705	−0.530078	−0.265039	−	0.964238i	$-0.585385\pi$
$787$	−14.8705	−0.530078	−0.265039	+	0.964238i	$0.585385\pi$
$788$	1.90183	0.0677500
$789$	−29.4955	−1.05007
$790$	12.4987	0.444683
$791$	0	0
$792$	1.02764	0.0365154
$793$	32.4836	1.15353
$794$	−16.0149	−0.568349
$795$	−1.06583	−0.0378010
$796$	−2.54087	−0.0900587
$797$	10.3824	0.367763	0.183881	−	0.982948i	$-0.441134\pi$
$797$	10.3824	0.367763	0.183881	+	0.982948i	$0.441134\pi$
$798$	0	0
$799$	33.4777	1.18436
$800$	−3.63982	−0.128687
$801$	−5.56603	−0.196666
$802$	−6.10942	−0.215731
$803$	4.66804	0.164731
$804$	−28.0410	−0.988931
$805$	0	0
$806$	31.9983	1.12709
$807$	−23.6886	−0.833877
$808$	−0.277380	−0.00975820
$809$	−14.8770	−0.523047	−0.261524	−	0.965197i	$-0.584225\pi$
$809$	−14.8770	−0.523047	−0.261524	+	0.965197i	$0.584225\pi$
$810$	−12.4295	−0.436728
$811$	6.62584	0.232665	0.116332	−	0.993210i	$-0.462886\pi$
$811$	6.62584	0.232665	0.116332	+	0.993210i	$0.462886\pi$
$812$	0	0
$813$	2.07204	0.0726696
$814$	5.29592	0.185622
$815$	14.1384	0.495246
$816$	−8.88435	−0.311015
$817$	−7.92480	−0.277254
$818$	−35.7868	−1.25126
$819$	0	0
$820$	−1.16627	−0.0407279
$821$	−10.0369	−0.350290	−0.175145	−	0.984543i	$-0.556039\pi$
$821$	−10.0369	−0.350290	−0.175145	+	0.984543i	$0.556039\pi$
$822$	−12.2270	−0.426465
$823$	−53.8035	−1.87547	−0.937736	−	0.347349i	$-0.887082\pi$
$823$	−53.8035	−1.87547	−0.937736	+	0.347349i	$0.887082\pi$
$824$	12.6605	0.441049
$825$	−9.89268	−0.344419
$826$	0	0
$827$	26.9690	0.937804	0.468902	−	0.883250i	$-0.344650\pi$
$827$	26.9690	0.937804	0.468902	+	0.883250i	$0.344650\pi$
$828$	4.38642	0.152438
$829$	33.8035	1.17404	0.587022	−	0.809571i	$-0.300300\pi$
$829$	33.8035	1.17404	0.587022	+	0.809571i	$0.300300\pi$
$830$	6.16961	0.214150
$831$	3.85586	0.133758
$832$	4.56450	0.158246
$833$	0	0
$834$	−20.3528	−0.704759
$835$	15.6631	0.542044
$836$	1.63138	0.0564226
$837$	−30.7312	−1.06223
$838$	7.20652	0.248945
$839$	−25.3940	−0.876697	−0.438348	−	0.898805i	$-0.644436\pi$
$839$	−25.3940	−0.876697	−0.438348	+	0.898805i	$0.644436\pi$
$840$	0	0
$841$	−10.2170	−0.352311
$842$	−18.1810	−0.626558
$843$	−11.7571	−0.404936
$844$	−24.8972	−0.856996
$845$	9.13735	0.314334
$846$	−5.31463	−0.182721
$847$	0	0
$848$	−0.473172	−0.0162488
$849$	−51.7758	−1.77694
$850$	16.7431	0.574284
$851$	22.6054	0.774903
$852$	−8.31507	−0.284869
$853$	1.82752	0.0625732	0.0312866	−	0.999510i	$-0.490040\pi$
$853$	1.82752	0.0625732	0.0312866	+	0.999510i	$0.490040\pi$
$854$	0	0
$855$	0.987332	0.0337660
$856$	8.07041	0.275841
$857$	−35.2017	−1.20247	−0.601234	−	0.799073i	$-0.705324\pi$
$857$	−35.2017	−1.20247	−0.601234	+	0.799073i	$0.705324\pi$
$858$	12.4059	0.423530
$859$	−5.79707	−0.197794	−0.0988968	−	0.995098i	$-0.531531\pi$
$859$	−5.79707	−0.197794	−0.0988968	+	0.995098i	$0.531531\pi$
$860$	−7.97253	−0.271861
$861$	0	0
$862$	29.6276	1.00912
$863$	46.8718	1.59553	0.797766	−	0.602967i	$-0.206015\pi$
$863$	46.8718	1.59553	0.797766	+	0.602967i	$0.206015\pi$
$864$	−4.38376	−0.149138
$865$	21.5873	0.733989
$866$	22.7951	0.774610
$867$	8.03435	0.272861
$868$	0	0
$869$	15.0810	0.511589
$870$	9.76226	0.330972
$871$	−66.2702	−2.24548
$872$	−8.64760	−0.292845
$873$	−6.83225	−0.231237
$874$	6.96348	0.235543
$875$	0	0
$876$	6.40676	0.216464
$877$	23.2099	0.783742	0.391871	−	0.920020i	$-0.371828\pi$
$877$	23.2099	0.783742	0.391871	+	0.920020i	$0.371828\pi$
$878$	24.9786	0.842988
$879$	51.9400	1.75189
$880$	1.64121	0.0553252
$881$	−36.4204	−1.22703	−0.613517	−	0.789681i	$-0.710246\pi$
$881$	−36.4204	−1.22703	−0.613517	+	0.789681i	$0.710246\pi$
$882$	0	0
$883$	55.3401	1.86234	0.931171	−	0.364584i	$-0.118789\pi$
$883$	55.3401	1.86234	0.931171	+	0.364584i	$0.118789\pi$
$884$	−20.9967	−0.706194
$885$	31.4831	1.05829
$886$	−28.2630	−0.949513
$887$	−22.1780	−0.744664	−0.372332	−	0.928100i	$-0.621442\pi$
$887$	−22.1780	−0.744664	−0.372332	+	0.928100i	$0.621442\pi$
$888$	7.26851	0.243915
$889$	0	0
$890$	−8.88936	−0.297972
$891$	−14.9975	−0.502437
$892$	−4.27435	−0.143116
$893$	−8.43704	−0.282335
$894$	−33.1083	−1.10731
$895$	−4.11356	−0.137501
$896$	0	0
$897$	52.9540	1.76808
$898$	23.6608	0.789571
$899$	30.3820	1.01330
$900$	−2.65799	−0.0885997
$901$	2.17659	0.0725126
$902$	−1.40723	−0.0468557
$903$	0	0
$904$	−0.0434830	−0.00144622
$905$	21.3633	0.710140
$906$	−37.0078	−1.22950
$907$	−35.2268	−1.16969	−0.584843	−	0.811147i	$-0.698844\pi$
$907$	−35.2268	−1.16969	−0.584843	+	0.811147i	$0.698844\pi$
$908$	−0.927418	−0.0307775
$909$	−0.202558	−0.00671842
$910$	0	0
$911$	6.05904	0.200745	0.100373	−	0.994950i	$-0.467997\pi$
$911$	6.05904	0.200745	0.100373	+	0.994950i	$0.467997\pi$
$912$	2.23903	0.0741417
$913$	7.44431	0.246371
$914$	35.3465	1.16916
$915$	16.0302	0.529941
$916$	6.52448	0.215575
$917$	0	0
$918$	20.1652	0.665552
$919$	40.4801	1.33531	0.667657	−	0.744469i	$-0.267297\pi$
$919$	40.4801	1.33531	0.667657	+	0.744469i	$0.267297\pi$
$920$	7.00543	0.230962
$921$	−0.825931	−0.0272154
$922$	−24.9703	−0.822354
$923$	−19.6512	−0.646828
$924$	0	0
$925$	−13.6980	−0.450386
$926$	14.3430	0.471340
$927$	9.24537	0.303658
$928$	4.33393	0.142268
$929$	50.4129	1.65399	0.826997	−	0.562206i	$-0.190047\pi$
$929$	50.4129	1.65399	0.826997	+	0.562206i	$0.190047\pi$
$930$	15.7907	0.517798
$931$	0	0
$932$	5.02732	0.164675
$933$	−47.0520	−1.54041
$934$	−14.0060	−0.458290
$935$	−7.54954	−0.246896
$936$	3.33325	0.108951
$937$	54.2827	1.77334	0.886669	−	0.462404i	$-0.153013\pi$
$937$	54.2827	1.77334	0.886669	+	0.462404i	$0.153013\pi$
$938$	0	0
$939$	8.70702	0.284143
$940$	−8.48786	−0.276843
$941$	13.6603	0.445312	0.222656	−	0.974897i	$-0.428527\pi$
$941$	13.6603	0.445312	0.222656	+	0.974897i	$0.428527\pi$
$942$	29.7365	0.968868
$943$	−6.00670	−0.195605
$944$	13.9769	0.454908
$945$	0	0
$946$	−9.61973	−0.312764
$947$	−50.3446	−1.63598	−0.817989	−	0.575233i	$-0.804911\pi$
$947$	−50.3446	−1.63598	−0.817989	+	0.575233i	$0.804911\pi$
$948$	20.6983	0.672250
$949$	15.1413	0.491507
$950$	−4.21959	−0.136902
$951$	−51.5501	−1.67163
$952$	0	0
$953$	25.4657	0.824915	0.412458	−	0.910977i	$-0.364670\pi$
$953$	25.4657	0.824915	0.412458	+	0.910977i	$0.364670\pi$
$954$	−0.345536	−0.0111871
$955$	13.8020	0.446623
$956$	2.05210	0.0663696
$957$	11.7792	0.380768
$958$	−7.86343	−0.254056
$959$	0	0
$960$	2.25252	0.0726996
$961$	18.1436	0.585278
$962$	17.1779	0.553837
$963$	5.89345	0.189914
$964$	−6.99530	−0.225303
$965$	−22.9865	−0.739963
$966$	0	0
$967$	−15.5963	−0.501544	−0.250772	−	0.968046i	$-0.580684\pi$
$967$	−15.5963	−0.501544	−0.250772	+	0.968046i	$0.580684\pi$
$968$	−9.01970	−0.289904
$969$	−10.2995	−0.330868
$970$	−10.9116	−0.350350
$971$	36.2847	1.16443	0.582216	−	0.813034i	$-0.302186\pi$
$971$	36.2847	1.16443	0.582216	+	0.813034i	$0.302186\pi$
$972$	−7.43246	−0.238396
$973$	0	0
$974$	31.7965	1.01882
$975$	−32.0880	−1.02764
$976$	7.11656	0.227796
$977$	44.0069	1.40791	0.703953	−	0.710247i	$-0.251417\pi$
$977$	44.0069	1.40791	0.703953	+	0.710247i	$0.251417\pi$
$978$	23.4137	0.748688
$979$	−10.7260	−0.342804
$980$	0	0
$981$	−6.31494	−0.201621
$982$	36.5057	1.16494
$983$	43.5975	1.39054	0.695272	−	0.718746i	$-0.255284\pi$
$983$	43.5975	1.39054	0.695272	+	0.718746i	$0.255284\pi$
$984$	−1.93139	−0.0615704
$985$	2.21805	0.0706729
$986$	−19.9360	−0.634893
$987$	0	0
$988$	5.29156	0.168347
$989$	−41.0614	−1.30568
$990$	1.19850	0.0380908
$991$	24.3775	0.774377	0.387189	−	0.922001i	$-0.373446\pi$
$991$	24.3775	0.774377	0.387189	+	0.922001i	$0.373446\pi$
$992$	7.01025	0.222576
$993$	−12.7123	−0.403413
$994$	0	0
$995$	−2.96334	−0.0939441
$996$	10.2171	0.323742
$997$	51.0409	1.61648	0.808241	−	0.588852i	$-0.200420\pi$
$997$	51.0409	1.61648	0.808241	+	0.588852i	$0.200420\pi$
$998$	−0.0567669	−0.00179693
$999$	−16.4977	−0.521963

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bq.1.4	yes	6
7.6	odd	2		4018.2.a.bp.1.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4018.2.a.bp.1.3	✓	6	7.6	odd	2
4018.2.a.bq.1.4	yes	6	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.93139 q^{3} +1.00000 q^{4} +1.16627 q^{5} +1.93139 q^{6} +1.00000 q^{8} +0.730254 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.93139 q^{3} +1.00000 q^{4} +1.16627 q^{5} +1.93139 q^{6} +1.00000 q^{8} +0.730254 q^{9} +1.16627 q^{10} +1.40723 q^{11} +1.93139 q^{12} +4.56450 q^{13} +2.25252 q^{15} +1.00000 q^{16} -4.59999 q^{17} +0.730254 q^{18} +1.15929 q^{19} +1.16627 q^{20} +1.40723 q^{22} +6.00670 q^{23} +1.93139 q^{24} -3.63982 q^{25} +4.56450 q^{26} -4.38376 q^{27} +4.33393 q^{29} +2.25252 q^{30} +7.01025 q^{31} +1.00000 q^{32} +2.71791 q^{33} -4.59999 q^{34} +0.730254 q^{36} +3.76336 q^{37} +1.15929 q^{38} +8.81582 q^{39} +1.16627 q^{40} -1.00000 q^{41} -6.83593 q^{43} +1.40723 q^{44} +0.851672 q^{45} +6.00670 q^{46} -7.27779 q^{47} +1.93139 q^{48} -3.63982 q^{50} -8.88435 q^{51} +4.56450 q^{52} -0.473172 q^{53} -4.38376 q^{54} +1.64121 q^{55} +2.23903 q^{57} +4.33393 q^{58} +13.9769 q^{59} +2.25252 q^{60} +7.11656 q^{61} +7.01025 q^{62} +1.00000 q^{64} +5.32344 q^{65} +2.71791 q^{66} -14.5186 q^{67} -4.59999 q^{68} +11.6013 q^{69} -4.30523 q^{71} +0.730254 q^{72} +3.31718 q^{73} +3.76336 q^{74} -7.02989 q^{75} +1.15929 q^{76} +8.81582 q^{78} +10.7168 q^{79} +1.16627 q^{80} -10.6575 q^{81} -1.00000 q^{82} +5.29004 q^{83} -5.36482 q^{85} -6.83593 q^{86} +8.37050 q^{87} +1.40723 q^{88} -7.62205 q^{89} +0.851672 q^{90} +6.00670 q^{92} +13.5395 q^{93} -7.27779 q^{94} +1.35204 q^{95} +1.93139 q^{96} -9.35599 q^{97} +1.02764 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 4 q^{3} + 6 q^{4} + 12 q^{5} + 4 q^{6} + 6 q^{8} + 18 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 4 * q^3 + 6 * q^4 + 12 * q^5 + 4 * q^6 + 6 * q^8 + 18 * q^9	\( 6 q + 6 q^{2} + 4 q^{3} + 6 q^{4} + 12 q^{5} + 4 q^{6} + 6 q^{8} + 18 q^{9} + 12 q^{10} + 4 q^{12} + 8 q^{13} - 4 q^{15} + 6 q^{16} + 16 q^{17} + 18 q^{18} + 12 q^{19} + 12 q^{20} + 12 q^{23} + 4 q^{24} + 14 q^{25} + 8 q^{26} + 28 q^{27} - 4 q^{30} - 4 q^{31} + 6 q^{32} - 20 q^{33} + 16 q^{34} + 18 q^{36} - 24 q^{37} + 12 q^{38} + 4 q^{39} + 12 q^{40} - 6 q^{41} + 4 q^{43} + 28 q^{45} + 12 q^{46} - 16 q^{47} + 4 q^{48} + 14 q^{50} - 16 q^{51} + 8 q^{52} - 16 q^{53} + 28 q^{54} - 12 q^{55} - 28 q^{57} + 16 q^{59} - 4 q^{60} + 32 q^{61} - 4 q^{62} + 6 q^{64} - 4 q^{65} - 20 q^{66} - 20 q^{67} + 16 q^{68} + 56 q^{69} + 12 q^{71} + 18 q^{72} + 16 q^{73} - 24 q^{74} - 4 q^{75} + 12 q^{76} + 4 q^{78} + 12 q^{80} + 42 q^{81} - 6 q^{82} + 32 q^{83} + 48 q^{85} + 4 q^{86} + 20 q^{87} + 8 q^{89} + 28 q^{90} + 12 q^{92} - 12 q^{93} - 16 q^{94} + 28 q^{95} + 4 q^{96} + 8 q^{97} - 76 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 4 * q^3 + 6 * q^4 + 12 * q^5 + 4 * q^6 + 6 * q^8 + 18 * q^9 + 12 * q^10 + 4 * q^12 + 8 * q^13 - 4 * q^15 + 6 * q^16 + 16 * q^17 + 18 * q^18 + 12 * q^19 + 12 * q^20 + 12 * q^23 + 4 * q^24 + 14 * q^25 + 8 * q^26 + 28 * q^27 - 4 * q^30 - 4 * q^31 + 6 * q^32 - 20 * q^33 + 16 * q^34 + 18 * q^36 - 24 * q^37 + 12 * q^38 + 4 * q^39 + 12 * q^40 - 6 * q^41 + 4 * q^43 + 28 * q^45 + 12 * q^46 - 16 * q^47 + 4 * q^48 + 14 * q^50 - 16 * q^51 + 8 * q^52 - 16 * q^53 + 28 * q^54 - 12 * q^55 - 28 * q^57 + 16 * q^59 - 4 * q^60 + 32 * q^61 - 4 * q^62 + 6 * q^64 - 4 * q^65 - 20 * q^66 - 20 * q^67 + 16 * q^68 + 56 * q^69 + 12 * q^71 + 18 * q^72 + 16 * q^73 - 24 * q^74 - 4 * q^75 + 12 * q^76 + 4 * q^78 + 12 * q^80 + 42 * q^81 - 6 * q^82 + 32 * q^83 + 48 * q^85 + 4 * q^86 + 20 * q^87 + 8 * q^89 + 28 * q^90 + 12 * q^92 - 12 * q^93 - 16 * q^94 + 28 * q^95 + 4 * q^96 + 8 * q^97 - 76 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more