LMFDB - Embedded newform 4026.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.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:	$32.1477718538$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
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			1.1
Root			$2.56155$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.56155 q^{5} -1.00000 q^{6} +3.12311 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.56155 q^{5} -1.00000 q^{6} +3.12311 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.56155 q^{10} +1.00000 q^{11} -1.00000 q^{12} +0.438447 q^{13} +3.12311 q^{14} +3.56155 q^{15} +1.00000 q^{16} +5.12311 q^{17} +1.00000 q^{18} -4.00000 q^{19} -3.56155 q^{20} -3.12311 q^{21} +1.00000 q^{22} -1.00000 q^{24} +7.68466 q^{25} +0.438447 q^{26} -1.00000 q^{27} +3.12311 q^{28} +0.438447 q^{29} +3.56155 q^{30} -4.68466 q^{31} +1.00000 q^{32} -1.00000 q^{33} +5.12311 q^{34} -11.1231 q^{35} +1.00000 q^{36} -6.00000 q^{37} -4.00000 q^{38} -0.438447 q^{39} -3.56155 q^{40} +11.5616 q^{41} -3.12311 q^{42} -6.24621 q^{43} +1.00000 q^{44} -3.56155 q^{45} +10.2462 q^{47} -1.00000 q^{48} +2.75379 q^{49} +7.68466 q^{50} -5.12311 q^{51} +0.438447 q^{52} -5.12311 q^{53} -1.00000 q^{54} -3.56155 q^{55} +3.12311 q^{56} +4.00000 q^{57} +0.438447 q^{58} +1.56155 q^{59} +3.56155 q^{60} +1.00000 q^{61} -4.68466 q^{62} +3.12311 q^{63} +1.00000 q^{64} -1.56155 q^{65} -1.00000 q^{66} +4.00000 q^{67} +5.12311 q^{68} -11.1231 q^{70} +3.12311 q^{71} +1.00000 q^{72} +5.12311 q^{73} -6.00000 q^{74} -7.68466 q^{75} -4.00000 q^{76} +3.12311 q^{77} -0.438447 q^{78} -3.56155 q^{80} +1.00000 q^{81} +11.5616 q^{82} -6.24621 q^{83} -3.12311 q^{84} -18.2462 q^{85} -6.24621 q^{86} -0.438447 q^{87} +1.00000 q^{88} +13.8078 q^{89} -3.56155 q^{90} +1.36932 q^{91} +4.68466 q^{93} +10.2462 q^{94} +14.2462 q^{95} -1.00000 q^{96} -6.68466 q^{97} +2.75379 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 3 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 3 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 3 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} - 3 q^{10} + 2 q^{11} - 2 q^{12} + 5 q^{13} - 2 q^{14} + 3 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} - 8 q^{19} - 3 q^{20} + 2 q^{21} + 2 q^{22} - 2 q^{24} + 3 q^{25} + 5 q^{26} - 2 q^{27} - 2 q^{28} + 5 q^{29} + 3 q^{30} + 3 q^{31} + 2 q^{32} - 2 q^{33} + 2 q^{34} - 14 q^{35} + 2 q^{36} - 12 q^{37} - 8 q^{38} - 5 q^{39} - 3 q^{40} + 19 q^{41} + 2 q^{42} + 4 q^{43} + 2 q^{44} - 3 q^{45} + 4 q^{47} - 2 q^{48} + 22 q^{49} + 3 q^{50} - 2 q^{51} + 5 q^{52} - 2 q^{53} - 2 q^{54} - 3 q^{55} - 2 q^{56} + 8 q^{57} + 5 q^{58} - q^{59} + 3 q^{60} + 2 q^{61} + 3 q^{62} - 2 q^{63} + 2 q^{64} + q^{65} - 2 q^{66} + 8 q^{67} + 2 q^{68} - 14 q^{70} - 2 q^{71} + 2 q^{72} + 2 q^{73} - 12 q^{74} - 3 q^{75} - 8 q^{76} - 2 q^{77} - 5 q^{78} - 3 q^{80} + 2 q^{81} + 19 q^{82} + 4 q^{83} + 2 q^{84} - 20 q^{85} + 4 q^{86} - 5 q^{87} + 2 q^{88} + 7 q^{89} - 3 q^{90} - 22 q^{91} - 3 q^{93} + 4 q^{94} + 12 q^{95} - 2 q^{96} - q^{97} + 22 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 3 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9 - 3 * q^10 + 2 * q^11 - 2 * q^12 + 5 * q^13 - 2 * q^14 + 3 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^18 - 8 * q^19 - 3 * q^20 + 2 * q^21 + 2 * q^22 - 2 * q^24 + 3 * q^25 + 5 * q^26 - 2 * q^27 - 2 * q^28 + 5 * q^29 + 3 * q^30 + 3 * q^31 + 2 * q^32 - 2 * q^33 + 2 * q^34 - 14 * q^35 + 2 * q^36 - 12 * q^37 - 8 * q^38 - 5 * q^39 - 3 * q^40 + 19 * q^41 + 2 * q^42 + 4 * q^43 + 2 * q^44 - 3 * q^45 + 4 * q^47 - 2 * q^48 + 22 * q^49 + 3 * q^50 - 2 * q^51 + 5 * q^52 - 2 * q^53 - 2 * q^54 - 3 * q^55 - 2 * q^56 + 8 * q^57 + 5 * q^58 - q^59 + 3 * q^60 + 2 * q^61 + 3 * q^62 - 2 * q^63 + 2 * q^64 + q^65 - 2 * q^66 + 8 * q^67 + 2 * q^68 - 14 * q^70 - 2 * q^71 + 2 * q^72 + 2 * q^73 - 12 * q^74 - 3 * q^75 - 8 * q^76 - 2 * q^77 - 5 * q^78 - 3 * q^80 + 2 * q^81 + 19 * q^82 + 4 * q^83 + 2 * q^84 - 20 * q^85 + 4 * q^86 - 5 * q^87 + 2 * q^88 + 7 * q^89 - 3 * q^90 - 22 * q^91 - 3 * q^93 + 4 * q^94 + 12 * q^95 - 2 * q^96 - q^97 + 22 * q^98 + 2 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−3.56155	−1.59277	−0.796387	−	0.604787i	$-0.793258\pi$
$5$	−3.56155	−1.59277	−0.796387	+	0.604787i	$0.793258\pi$
$6$	−1.00000	−0.408248
$7$	3.12311	1.18042	0.590211	−	0.807249i	$-0.299044\pi$
$7$	3.12311	1.18042	0.590211	+	0.807249i	$0.299044\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.56155	−1.12626
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	0.438447	0.121603	0.0608017	−	0.998150i	$-0.480634\pi$
$13$	0.438447	0.121603	0.0608017	+	0.998150i	$0.480634\pi$
$14$	3.12311	0.834685
$15$	3.56155	0.919589
$16$	1.00000	0.250000
$17$	5.12311	1.24254	0.621268	−	0.783598i	$-0.286618\pi$
$17$	5.12311	1.24254	0.621268	+	0.783598i	$0.286618\pi$
$18$	1.00000	0.235702
$19$	−4.00000	−0.917663	−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000	−0.917663	−0.458831	+	0.888523i	$0.651732\pi$
$20$	−3.56155	−0.796387
$21$	−3.12311	−0.681518
$22$	1.00000	0.213201
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	−1.00000	−0.204124
$25$	7.68466	1.53693
$26$	0.438447	0.0859866
$27$	−1.00000	−0.192450
$28$	3.12311	0.590211
$29$	0.438447	0.0814176	0.0407088	−	0.999171i	$-0.487038\pi$
$29$	0.438447	0.0814176	0.0407088	+	0.999171i	$0.487038\pi$
$30$	3.56155	0.650248
$31$	−4.68466	−0.841389	−0.420695	−	0.907202i	$-0.638214\pi$
$31$	−4.68466	−0.841389	−0.420695	+	0.907202i	$0.638214\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	5.12311	0.878605
$35$	−11.1231	−1.88015
$36$	1.00000	0.166667
$37$	−6.00000	−0.986394	−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000	−0.986394	−0.493197	+	0.869918i	$0.664172\pi$
$38$	−4.00000	−0.648886
$39$	−0.438447	−0.0702077
$40$	−3.56155	−0.563131
$41$	11.5616	1.80561	0.902806	−	0.430049i	$-0.141504\pi$
$41$	11.5616	1.80561	0.902806	+	0.430049i	$0.141504\pi$
$42$	−3.12311	−0.481906
$43$	−6.24621	−0.952538	−0.476269	−	0.879300i	$-0.658011\pi$
$43$	−6.24621	−0.952538	−0.476269	+	0.879300i	$0.658011\pi$
$44$	1.00000	0.150756
$45$	−3.56155	−0.530925
$46$	0	0
$47$	10.2462	1.49456	0.747282	−	0.664507i	$-0.231359\pi$
$47$	10.2462	1.49456	0.747282	+	0.664507i	$0.231359\pi$
$48$	−1.00000	−0.144338
$49$	2.75379	0.393398
$50$	7.68466	1.08677
$51$	−5.12311	−0.717378
$52$	0.438447	0.0608017
$53$	−5.12311	−0.703713	−0.351856	−	0.936054i	$-0.614449\pi$
$53$	−5.12311	−0.703713	−0.351856	+	0.936054i	$0.614449\pi$
$54$	−1.00000	−0.136083
$55$	−3.56155	−0.480240
$56$	3.12311	0.417343
$57$	4.00000	0.529813
$58$	0.438447	0.0575709
$59$	1.56155	0.203297	0.101648	−	0.994820i	$-0.467588\pi$
$59$	1.56155	0.203297	0.101648	+	0.994820i	$0.467588\pi$
$60$	3.56155	0.459794
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−4.68466	−0.594952
$63$	3.12311	0.393474
$64$	1.00000	0.125000
$65$	−1.56155	−0.193687
$66$	−1.00000	−0.123091
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	5.12311	0.621268
$69$	0	0
$70$	−11.1231	−1.32947
$71$	3.12311	0.370644	0.185322	−	0.982678i	$-0.440667\pi$
$71$	3.12311	0.370644	0.185322	+	0.982678i	$0.440667\pi$
$72$	1.00000	0.117851
$73$	5.12311	0.599614	0.299807	−	0.954000i	$-0.403078\pi$
$73$	5.12311	0.599614	0.299807	+	0.954000i	$0.403078\pi$
$74$	−6.00000	−0.697486
$75$	−7.68466	−0.887348
$76$	−4.00000	−0.458831
$77$	3.12311	0.355911
$78$	−0.438447	−0.0496444
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	−3.56155	−0.398194
$81$	1.00000	0.111111
$82$	11.5616	1.27676
$83$	−6.24621	−0.685611	−0.342805	−	0.939406i	$-0.611377\pi$
$83$	−6.24621	−0.685611	−0.342805	+	0.939406i	$0.611377\pi$
$84$	−3.12311	−0.340759
$85$	−18.2462	−1.97908
$86$	−6.24621	−0.673546
$87$	−0.438447	−0.0470065
$88$	1.00000	0.106600
$89$	13.8078	1.46362	0.731810	−	0.681509i	$-0.238676\pi$
$89$	13.8078	1.46362	0.731810	+	0.681509i	$0.238676\pi$
$90$	−3.56155	−0.375421
$91$	1.36932	0.143543
$92$	0	0
$93$	4.68466	0.485776
$94$	10.2462	1.05682
$95$	14.2462	1.46163
$96$	−1.00000	−0.102062
$97$	−6.68466	−0.678724	−0.339362	−	0.940656i	$-0.610211\pi$
$97$	−6.68466	−0.678724	−0.339362	+	0.940656i	$0.610211\pi$
$98$	2.75379	0.278175
$99$	1.00000	0.100504
$100$	7.68466	0.768466
$101$	8.43845	0.839657	0.419828	−	0.907603i	$-0.362090\pi$
$101$	8.43845	0.839657	0.419828	+	0.907603i	$0.362090\pi$
$102$	−5.12311	−0.507263
$103$	16.0000	1.57653	0.788263	−	0.615338i	$-0.210980\pi$
$103$	16.0000	1.57653	0.788263	+	0.615338i	$0.210980\pi$
$104$	0.438447	0.0429933
$105$	11.1231	1.08550
$106$	−5.12311	−0.497600
$107$	5.56155	0.537656	0.268828	−	0.963188i	$-0.413364\pi$
$107$	5.56155	0.537656	0.268828	+	0.963188i	$0.413364\pi$
$108$	−1.00000	−0.0962250
$109$	5.31534	0.509117	0.254559	−	0.967057i	$-0.418070\pi$
$109$	5.31534	0.509117	0.254559	+	0.967057i	$0.418070\pi$
$110$	−3.56155	−0.339581
$111$	6.00000	0.569495
$112$	3.12311	0.295106
$113$	3.75379	0.353127	0.176563	−	0.984289i	$-0.443502\pi$
$113$	3.75379	0.353127	0.176563	+	0.984289i	$0.443502\pi$
$114$	4.00000	0.374634
$115$	0	0
$116$	0.438447	0.0407088
$117$	0.438447	0.0405345
$118$	1.56155	0.143753
$119$	16.0000	1.46672
$120$	3.56155	0.325124
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	−11.5616	−1.04247
$124$	−4.68466	−0.420695
$125$	−9.56155	−0.855211
$126$	3.12311	0.278228
$127$	20.4924	1.81841	0.909204	−	0.416350i	$-0.136691\pi$
$127$	20.4924	1.81841	0.909204	+	0.416350i	$0.136691\pi$
$128$	1.00000	0.0883883
$129$	6.24621	0.549948
$130$	−1.56155	−0.136957
$131$	11.8078	1.03165	0.515825	−	0.856694i	$-0.327486\pi$
$131$	11.8078	1.03165	0.515825	+	0.856694i	$0.327486\pi$
$132$	−1.00000	−0.0870388
$133$	−12.4924	−1.08323
$134$	4.00000	0.345547
$135$	3.56155	0.306530
$136$	5.12311	0.439303
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	0	0
$139$	−3.80776	−0.322970	−0.161485	−	0.986875i	$-0.551628\pi$
$139$	−3.80776	−0.322970	−0.161485	+	0.986875i	$0.551628\pi$
$140$	−11.1231	−0.940074
$141$	−10.2462	−0.862887
$142$	3.12311	0.262085
$143$	0.438447	0.0366648
$144$	1.00000	0.0833333
$145$	−1.56155	−0.129680
$146$	5.12311	0.423991
$147$	−2.75379	−0.227129
$148$	−6.00000	−0.493197
$149$	2.87689	0.235684	0.117842	−	0.993032i	$-0.462402\pi$
$149$	2.87689	0.235684	0.117842	+	0.993032i	$0.462402\pi$
$150$	−7.68466	−0.627450
$151$	−16.0000	−1.30206	−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000	−1.30206	−0.651031	+	0.759051i	$0.725663\pi$
$152$	−4.00000	−0.324443
$153$	5.12311	0.414179
$154$	3.12311	0.251667
$155$	16.6847	1.34014
$156$	−0.438447	−0.0351039
$157$	18.6847	1.49120	0.745599	−	0.666395i	$-0.232163\pi$
$157$	18.6847	1.49120	0.745599	+	0.666395i	$0.232163\pi$
$158$	0	0
$159$	5.12311	0.406289
$160$	−3.56155	−0.281565
$161$	0	0
$162$	1.00000	0.0785674
$163$	−12.6847	−0.993539	−0.496770	−	0.867882i	$-0.665481\pi$
$163$	−12.6847	−0.993539	−0.496770	+	0.867882i	$0.665481\pi$
$164$	11.5616	0.902806
$165$	3.56155	0.277267
$166$	−6.24621	−0.484800
$167$	14.2462	1.10240	0.551202	−	0.834372i	$-0.314169\pi$
$167$	14.2462	1.10240	0.551202	+	0.834372i	$0.314169\pi$
$168$	−3.12311	−0.240953
$169$	−12.8078	−0.985213
$170$	−18.2462	−1.39942
$171$	−4.00000	−0.305888
$172$	−6.24621	−0.476269
$173$	22.6847	1.72468	0.862341	−	0.506327i	$-0.168997\pi$
$173$	22.6847	1.72468	0.862341	+	0.506327i	$0.168997\pi$
$174$	−0.438447	−0.0332386
$175$	24.0000	1.81423
$176$	1.00000	0.0753778
$177$	−1.56155	−0.117373
$178$	13.8078	1.03494
$179$	−7.12311	−0.532406	−0.266203	−	0.963917i	$-0.585769\pi$
$179$	−7.12311	−0.532406	−0.266203	+	0.963917i	$0.585769\pi$
$180$	−3.56155	−0.265462
$181$	−1.80776	−0.134370	−0.0671850	−	0.997741i	$-0.521402\pi$
$181$	−1.80776	−0.134370	−0.0671850	+	0.997741i	$0.521402\pi$
$182$	1.36932	0.101501
$183$	−1.00000	−0.0739221
$184$	0	0
$185$	21.3693	1.57110
$186$	4.68466	0.343496
$187$	5.12311	0.374639
$188$	10.2462	0.747282
$189$	−3.12311	−0.227173
$190$	14.2462	1.03353
$191$	4.87689	0.352880	0.176440	−	0.984311i	$-0.443542\pi$
$191$	4.87689	0.352880	0.176440	+	0.984311i	$0.443542\pi$
$192$	−1.00000	−0.0721688
$193$	−13.8078	−0.993905	−0.496952	−	0.867778i	$-0.665548\pi$
$193$	−13.8078	−0.993905	−0.496952	+	0.867778i	$0.665548\pi$
$194$	−6.68466	−0.479931
$195$	1.56155	0.111825
$196$	2.75379	0.196699
$197$	4.24621	0.302530	0.151265	−	0.988493i	$-0.451665\pi$
$197$	4.24621	0.302530	0.151265	+	0.988493i	$0.451665\pi$
$198$	1.00000	0.0710669
$199$	17.3693	1.23128	0.615639	−	0.788028i	$-0.288898\pi$
$199$	17.3693	1.23128	0.615639	+	0.788028i	$0.288898\pi$
$200$	7.68466	0.543387
$201$	−4.00000	−0.282138
$202$	8.43845	0.593727
$203$	1.36932	0.0961072
$204$	−5.12311	−0.358689
$205$	−41.1771	−2.87593
$206$	16.0000	1.11477
$207$	0	0
$208$	0.438447	0.0304008
$209$	−4.00000	−0.276686
$210$	11.1231	0.767567
$211$	13.5616	0.933616	0.466808	−	0.884359i	$-0.345404\pi$
$211$	13.5616	0.933616	0.466808	+	0.884359i	$0.345404\pi$
$212$	−5.12311	−0.351856
$213$	−3.12311	−0.213992
$214$	5.56155	0.380180
$215$	22.2462	1.51718
$216$	−1.00000	−0.0680414
$217$	−14.6307	−0.993195
$218$	5.31534	0.360000
$219$	−5.12311	−0.346187
$220$	−3.56155	−0.240120
$221$	2.24621	0.151097
$222$	6.00000	0.402694
$223$	4.00000	0.267860	0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000	0.267860	0.133930	+	0.990991i	$0.457240\pi$
$224$	3.12311	0.208671
$225$	7.68466	0.512311
$226$	3.75379	0.249698
$227$	2.24621	0.149086	0.0745431	−	0.997218i	$-0.476250\pi$
$227$	2.24621	0.149086	0.0745431	+	0.997218i	$0.476250\pi$
$228$	4.00000	0.264906
$229$	2.87689	0.190111	0.0950553	−	0.995472i	$-0.469697\pi$
$229$	2.87689	0.190111	0.0950553	+	0.995472i	$0.469697\pi$
$230$	0	0
$231$	−3.12311	−0.205485
$232$	0.438447	0.0287855
$233$	27.3693	1.79302	0.896512	−	0.443020i	$-0.146093\pi$
$233$	27.3693	1.79302	0.896512	+	0.443020i	$0.146093\pi$
$234$	0.438447	0.0286622
$235$	−36.4924	−2.38050
$236$	1.56155	0.101648
$237$	0	0
$238$	16.0000	1.03713
$239$	−9.75379	−0.630920	−0.315460	−	0.948939i	$-0.602159\pi$
$239$	−9.75379	−0.630920	−0.315460	+	0.948939i	$0.602159\pi$
$240$	3.56155	0.229897
$241$	−15.3693	−0.990025	−0.495012	−	0.868886i	$-0.664836\pi$
$241$	−15.3693	−0.990025	−0.495012	+	0.868886i	$0.664836\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	1.00000	0.0640184
$245$	−9.80776	−0.626595
$246$	−11.5616	−0.737138
$247$	−1.75379	−0.111591
$248$	−4.68466	−0.297476
$249$	6.24621	0.395838
$250$	−9.56155	−0.604726
$251$	25.5616	1.61343	0.806715	−	0.590940i	$-0.201243\pi$
$251$	25.5616	1.61343	0.806715	+	0.590940i	$0.201243\pi$
$252$	3.12311	0.196737
$253$	0	0
$254$	20.4924	1.28581
$255$	18.2462	1.14262
$256$	1.00000	0.0625000
$257$	−26.4924	−1.65255	−0.826276	−	0.563266i	$-0.809545\pi$
$257$	−26.4924	−1.65255	−0.826276	+	0.563266i	$0.809545\pi$
$258$	6.24621	0.388872
$259$	−18.7386	−1.16436
$260$	−1.56155	−0.0968434
$261$	0.438447	0.0271392
$262$	11.8078	0.729486
$263$	−4.87689	−0.300722	−0.150361	−	0.988631i	$-0.548044\pi$
$263$	−4.87689	−0.300722	−0.150361	+	0.988631i	$0.548044\pi$
$264$	−1.00000	−0.0615457
$265$	18.2462	1.12086
$266$	−12.4924	−0.765960
$267$	−13.8078	−0.845021
$268$	4.00000	0.244339
$269$	−8.05398	−0.491060	−0.245530	−	0.969389i	$-0.578962\pi$
$269$	−8.05398	−0.491060	−0.245530	+	0.969389i	$0.578962\pi$
$270$	3.56155	0.216749
$271$	6.24621	0.379430	0.189715	−	0.981839i	$-0.439244\pi$
$271$	6.24621	0.379430	0.189715	+	0.981839i	$0.439244\pi$
$272$	5.12311	0.310634
$273$	−1.36932	−0.0828748
$274$	−6.00000	−0.362473
$275$	7.68466	0.463402
$276$	0	0
$277$	−2.00000	−0.120168	−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000	−0.120168	−0.0600842	+	0.998193i	$0.519137\pi$
$278$	−3.80776	−0.228375
$279$	−4.68466	−0.280463
$280$	−11.1231	−0.664733
$281$	−15.3693	−0.916857	−0.458428	−	0.888731i	$-0.651587\pi$
$281$	−15.3693	−0.916857	−0.458428	+	0.888731i	$0.651587\pi$
$282$	−10.2462	−0.610153
$283$	−12.0000	−0.713326	−0.356663	−	0.934233i	$-0.616086\pi$
$283$	−12.0000	−0.713326	−0.356663	+	0.934233i	$0.616086\pi$
$284$	3.12311	0.185322
$285$	−14.2462	−0.843873
$286$	0.438447	0.0259259
$287$	36.1080	2.13138
$288$	1.00000	0.0589256
$289$	9.24621	0.543895
$290$	−1.56155	−0.0916975
$291$	6.68466	0.391862
$292$	5.12311	0.299807
$293$	33.1231	1.93507	0.967536	−	0.252732i	$-0.0813292\pi$
$293$	33.1231	1.93507	0.967536	+	0.252732i	$0.0813292\pi$
$294$	−2.75379	−0.160604
$295$	−5.56155	−0.323806
$296$	−6.00000	−0.348743
$297$	−1.00000	−0.0580259
$298$	2.87689	0.166654
$299$	0	0
$300$	−7.68466	−0.443674
$301$	−19.5076	−1.12440
$302$	−16.0000	−0.920697
$303$	−8.43845	−0.484776
$304$	−4.00000	−0.229416
$305$	−3.56155	−0.203934
$306$	5.12311	0.292868
$307$	13.1771	0.752056	0.376028	−	0.926608i	$-0.377290\pi$
$307$	13.1771	0.752056	0.376028	+	0.926608i	$0.377290\pi$
$308$	3.12311	0.177955
$309$	−16.0000	−0.910208
$310$	16.6847	0.947625
$311$	−14.2462	−0.807829	−0.403914	−	0.914797i	$-0.632351\pi$
$311$	−14.2462	−0.807829	−0.403914	+	0.914797i	$0.632351\pi$
$312$	−0.438447	−0.0248222
$313$	−9.12311	−0.515668	−0.257834	−	0.966189i	$-0.583009\pi$
$313$	−9.12311	−0.515668	−0.257834	+	0.966189i	$0.583009\pi$
$314$	18.6847	1.05444
$315$	−11.1231	−0.626716
$316$	0	0
$317$	10.6847	0.600110	0.300055	−	0.953922i	$-0.402995\pi$
$317$	10.6847	0.600110	0.300055	+	0.953922i	$0.402995\pi$
$318$	5.12311	0.287289
$319$	0.438447	0.0245483
$320$	−3.56155	−0.199097
$321$	−5.56155	−0.310416
$322$	0	0
$323$	−20.4924	−1.14023
$324$	1.00000	0.0555556
$325$	3.36932	0.186896
$326$	−12.6847	−0.702538
$327$	−5.31534	−0.293939
$328$	11.5616	0.638380
$329$	32.0000	1.76422
$330$	3.56155	0.196057
$331$	5.75379	0.316257	0.158128	−	0.987419i	$-0.449454\pi$
$331$	5.75379	0.316257	0.158128	+	0.987419i	$0.449454\pi$
$332$	−6.24621	−0.342805
$333$	−6.00000	−0.328798
$334$	14.2462	0.779518
$335$	−14.2462	−0.778354
$336$	−3.12311	−0.170379
$337$	30.6847	1.67150	0.835750	−	0.549110i	$-0.185033\pi$
$337$	30.6847	1.67150	0.835750	+	0.549110i	$0.185033\pi$
$338$	−12.8078	−0.696651
$339$	−3.75379	−0.203878
$340$	−18.2462	−0.989540
$341$	−4.68466	−0.253688
$342$	−4.00000	−0.216295
$343$	−13.2614	−0.716046
$344$	−6.24621	−0.336773
$345$	0	0
$346$	22.6847	1.21953
$347$	−7.31534	−0.392708	−0.196354	−	0.980533i	$-0.562910\pi$
$347$	−7.31534	−0.392708	−0.196354	+	0.980533i	$0.562910\pi$
$348$	−0.438447	−0.0235032
$349$	−27.3693	−1.46505	−0.732523	−	0.680742i	$-0.761657\pi$
$349$	−27.3693	−1.46505	−0.732523	+	0.680742i	$0.761657\pi$
$350$	24.0000	1.28285
$351$	−0.438447	−0.0234026
$352$	1.00000	0.0533002
$353$	−30.0000	−1.59674	−0.798369	−	0.602168i	$-0.794304\pi$
$353$	−30.0000	−1.59674	−0.798369	+	0.602168i	$0.794304\pi$
$354$	−1.56155	−0.0829956
$355$	−11.1231	−0.590353
$356$	13.8078	0.731810
$357$	−16.0000	−0.846810
$358$	−7.12311	−0.376468
$359$	3.80776	0.200966	0.100483	−	0.994939i	$-0.467961\pi$
$359$	3.80776	0.200966	0.100483	+	0.994939i	$0.467961\pi$
$360$	−3.56155	−0.187710
$361$	−3.00000	−0.157895
$362$	−1.80776	−0.0950140
$363$	−1.00000	−0.0524864
$364$	1.36932	0.0717717
$365$	−18.2462	−0.955050
$366$	−1.00000	−0.0522708
$367$	9.36932	0.489074	0.244537	−	0.969640i	$-0.421364\pi$
$367$	9.36932	0.489074	0.244537	+	0.969640i	$0.421364\pi$
$368$	0	0
$369$	11.5616	0.601870
$370$	21.3693	1.11094
$371$	−16.0000	−0.830679
$372$	4.68466	0.242888
$373$	27.8617	1.44263	0.721313	−	0.692609i	$-0.243539\pi$
$373$	27.8617	1.44263	0.721313	+	0.692609i	$0.243539\pi$
$374$	5.12311	0.264909
$375$	9.56155	0.493756
$376$	10.2462	0.528408
$377$	0.192236	0.00990065
$378$	−3.12311	−0.160635
$379$	31.8078	1.63386	0.816928	−	0.576740i	$-0.195676\pi$
$379$	31.8078	1.63386	0.816928	+	0.576740i	$0.195676\pi$
$380$	14.2462	0.730815
$381$	−20.4924	−1.04986
$382$	4.87689	0.249524
$383$	−23.6155	−1.20670	−0.603349	−	0.797478i	$-0.706167\pi$
$383$	−23.6155	−1.20670	−0.603349	+	0.797478i	$0.706167\pi$
$384$	−1.00000	−0.0510310
$385$	−11.1231	−0.566886
$386$	−13.8078	−0.702797
$387$	−6.24621	−0.317513
$388$	−6.68466	−0.339362
$389$	−31.8617	−1.61545	−0.807727	−	0.589556i	$-0.799303\pi$
$389$	−31.8617	−1.61545	−0.807727	+	0.589556i	$0.799303\pi$
$390$	1.56155	0.0790723
$391$	0	0
$392$	2.75379	0.139087
$393$	−11.8078	−0.595623
$394$	4.24621	0.213921
$395$	0	0
$396$	1.00000	0.0502519
$397$	21.8078	1.09450	0.547250	−	0.836969i	$-0.315675\pi$
$397$	21.8078	1.09450	0.547250	+	0.836969i	$0.315675\pi$
$398$	17.3693	0.870645
$399$	12.4924	0.625403
$400$	7.68466	0.384233
$401$	−8.05398	−0.402196	−0.201098	−	0.979571i	$-0.564451\pi$
$401$	−8.05398	−0.402196	−0.201098	+	0.979571i	$0.564451\pi$
$402$	−4.00000	−0.199502
$403$	−2.05398	−0.102316
$404$	8.43845	0.419828
$405$	−3.56155	−0.176975
$406$	1.36932	0.0679581
$407$	−6.00000	−0.297409
$408$	−5.12311	−0.253632
$409$	19.1771	0.948246	0.474123	−	0.880459i	$-0.342765\pi$
$409$	19.1771	0.948246	0.474123	+	0.880459i	$0.342765\pi$
$410$	−41.1771	−2.03359
$411$	6.00000	0.295958
$412$	16.0000	0.788263
$413$	4.87689	0.239976
$414$	0	0
$415$	22.2462	1.09202
$416$	0.438447	0.0214966
$417$	3.80776	0.186467
$418$	−4.00000	−0.195646
$419$	12.0000	0.586238	0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000	0.586238	0.293119	+	0.956076i	$0.405307\pi$
$420$	11.1231	0.542752
$421$	10.6847	0.520738	0.260369	−	0.965509i	$-0.416156\pi$
$421$	10.6847	0.520738	0.260369	+	0.965509i	$0.416156\pi$
$422$	13.5616	0.660166
$423$	10.2462	0.498188
$424$	−5.12311	−0.248800
$425$	39.3693	1.90969
$426$	−3.12311	−0.151315
$427$	3.12311	0.151138
$428$	5.56155	0.268828
$429$	−0.438447	−0.0211684
$430$	22.2462	1.07281
$431$	−35.1231	−1.69182	−0.845910	−	0.533325i	$-0.820942\pi$
$431$	−35.1231	−1.69182	−0.845910	+	0.533325i	$0.820942\pi$
$432$	−1.00000	−0.0481125
$433$	−18.8769	−0.907166	−0.453583	−	0.891214i	$-0.649854\pi$
$433$	−18.8769	−0.907166	−0.453583	+	0.891214i	$0.649854\pi$
$434$	−14.6307	−0.702295
$435$	1.56155	0.0748707
$436$	5.31534	0.254559
$437$	0	0
$438$	−5.12311	−0.244791
$439$	24.3002	1.15978	0.579892	−	0.814693i	$-0.303095\pi$
$439$	24.3002	1.15978	0.579892	+	0.814693i	$0.303095\pi$
$440$	−3.56155	−0.169790
$441$	2.75379	0.131133
$442$	2.24621	0.106841
$443$	−0.876894	−0.0416625	−0.0208313	−	0.999783i	$-0.506631\pi$
$443$	−0.876894	−0.0416625	−0.0208313	+	0.999783i	$0.506631\pi$
$444$	6.00000	0.284747
$445$	−49.1771	−2.33122
$446$	4.00000	0.189405
$447$	−2.87689	−0.136072
$448$	3.12311	0.147553
$449$	−39.3693	−1.85795	−0.928976	−	0.370139i	$-0.879310\pi$
$449$	−39.3693	−1.85795	−0.928976	+	0.370139i	$0.879310\pi$
$450$	7.68466	0.362258
$451$	11.5616	0.544412
$452$	3.75379	0.176563
$453$	16.0000	0.751746
$454$	2.24621	0.105420
$455$	−4.87689	−0.228632
$456$	4.00000	0.187317
$457$	24.7386	1.15722	0.578612	−	0.815603i	$-0.303594\pi$
$457$	24.7386	1.15722	0.578612	+	0.815603i	$0.303594\pi$
$458$	2.87689	0.134428
$459$	−5.12311	−0.239126
$460$	0	0
$461$	34.4924	1.60647	0.803236	−	0.595661i	$-0.203110\pi$
$461$	34.4924	1.60647	0.803236	+	0.595661i	$0.203110\pi$
$462$	−3.12311	−0.145300
$463$	−25.3693	−1.17901	−0.589506	−	0.807764i	$-0.700678\pi$
$463$	−25.3693	−1.17901	−0.589506	+	0.807764i	$0.700678\pi$
$464$	0.438447	0.0203544
$465$	−16.6847	−0.773733
$466$	27.3693	1.26786
$467$	19.3153	0.893807	0.446904	−	0.894582i	$-0.352527\pi$
$467$	19.3153	0.893807	0.446904	+	0.894582i	$0.352527\pi$
$468$	0.438447	0.0202672
$469$	12.4924	0.576846
$470$	−36.4924	−1.68327
$471$	−18.6847	−0.860944
$472$	1.56155	0.0718763
$473$	−6.24621	−0.287201
$474$	0	0
$475$	−30.7386	−1.41039
$476$	16.0000	0.733359
$477$	−5.12311	−0.234571
$478$	−9.75379	−0.446128
$479$	−14.2462	−0.650926	−0.325463	−	0.945555i	$-0.605520\pi$
$479$	−14.2462	−0.650926	−0.325463	+	0.945555i	$0.605520\pi$
$480$	3.56155	0.162562
$481$	−2.63068	−0.119949
$482$	−15.3693	−0.700053
$483$	0	0
$484$	1.00000	0.0454545
$485$	23.8078	1.08105
$486$	−1.00000	−0.0453609
$487$	−18.7386	−0.849129	−0.424564	−	0.905398i	$-0.639573\pi$
$487$	−18.7386	−0.849129	−0.424564	+	0.905398i	$0.639573\pi$
$488$	1.00000	0.0452679
$489$	12.6847	0.573620
$490$	−9.80776	−0.443070
$491$	−18.7386	−0.845663	−0.422831	−	0.906208i	$-0.638964\pi$
$491$	−18.7386	−0.845663	−0.422831	+	0.906208i	$0.638964\pi$
$492$	−11.5616	−0.521235
$493$	2.24621	0.101164
$494$	−1.75379	−0.0789067
$495$	−3.56155	−0.160080
$496$	−4.68466	−0.210347
$497$	9.75379	0.437517
$498$	6.24621	0.279899
$499$	−27.6155	−1.23624	−0.618120	−	0.786083i	$-0.712106\pi$
$499$	−27.6155	−1.23624	−0.618120	+	0.786083i	$0.712106\pi$
$500$	−9.56155	−0.427606
$501$	−14.2462	−0.636474
$502$	25.5616	1.14087
$503$	4.87689	0.217450	0.108725	−	0.994072i	$-0.465323\pi$
$503$	4.87689	0.217450	0.108725	+	0.994072i	$0.465323\pi$
$504$	3.12311	0.139114
$505$	−30.0540	−1.33738
$506$	0	0
$507$	12.8078	0.568813
$508$	20.4924	0.909204
$509$	−29.1231	−1.29086	−0.645429	−	0.763820i	$-0.723322\pi$
$509$	−29.1231	−1.29086	−0.645429	+	0.763820i	$0.723322\pi$
$510$	18.2462	0.807956
$511$	16.0000	0.707798
$512$	1.00000	0.0441942
$513$	4.00000	0.176604
$514$	−26.4924	−1.16853
$515$	−56.9848	−2.51105
$516$	6.24621	0.274974
$517$	10.2462	0.450628
$518$	−18.7386	−0.823328
$519$	−22.6847	−0.995746
$520$	−1.56155	−0.0684786
$521$	−30.9848	−1.35747	−0.678735	−	0.734383i	$-0.737472\pi$
$521$	−30.9848	−1.35747	−0.678735	+	0.734383i	$0.737472\pi$
$522$	0.438447	0.0191903
$523$	−32.6847	−1.42920	−0.714600	−	0.699533i	$-0.753391\pi$
$523$	−32.6847	−1.42920	−0.714600	+	0.699533i	$0.753391\pi$
$524$	11.8078	0.515825
$525$	−24.0000	−1.04745
$526$	−4.87689	−0.212643
$527$	−24.0000	−1.04546
$528$	−1.00000	−0.0435194
$529$	−23.0000	−1.00000
$530$	18.2462	0.792565
$531$	1.56155	0.0677656
$532$	−12.4924	−0.541615
$533$	5.06913	0.219568
$534$	−13.8078	−0.597520
$535$	−19.8078	−0.856364
$536$	4.00000	0.172774
$537$	7.12311	0.307385
$538$	−8.05398	−0.347232
$539$	2.75379	0.118614
$540$	3.56155	0.153265
$541$	−3.36932	−0.144858	−0.0724291	−	0.997374i	$-0.523075\pi$
$541$	−3.36932	−0.144858	−0.0724291	+	0.997374i	$0.523075\pi$
$542$	6.24621	0.268298
$543$	1.80776	0.0775786
$544$	5.12311	0.219651
$545$	−18.9309	−0.810909
$546$	−1.36932	−0.0586014
$547$	−16.6847	−0.713384	−0.356692	−	0.934222i	$-0.616096\pi$
$547$	−16.6847	−0.713384	−0.356692	+	0.934222i	$0.616096\pi$
$548$	−6.00000	−0.256307
$549$	1.00000	0.0426790
$550$	7.68466	0.327675
$551$	−1.75379	−0.0747139
$552$	0	0
$553$	0	0
$554$	−2.00000	−0.0849719
$555$	−21.3693	−0.907077
$556$	−3.80776	−0.161485
$557$	19.1771	0.812559	0.406279	−	0.913749i	$-0.366826\pi$
$557$	19.1771	0.812559	0.406279	+	0.913749i	$0.366826\pi$
$558$	−4.68466	−0.198317
$559$	−2.73863	−0.115832
$560$	−11.1231	−0.470037
$561$	−5.12311	−0.216298
$562$	−15.3693	−0.648316
$563$	−24.0000	−1.01148	−0.505740	−	0.862686i	$-0.668780\pi$
$563$	−24.0000	−1.01148	−0.505740	+	0.862686i	$0.668780\pi$
$564$	−10.2462	−0.431443
$565$	−13.3693	−0.562451
$566$	−12.0000	−0.504398
$567$	3.12311	0.131158
$568$	3.12311	0.131043
$569$	27.1771	1.13932	0.569661	−	0.821880i	$-0.307074\pi$
$569$	27.1771	1.13932	0.569661	+	0.821880i	$0.307074\pi$
$570$	−14.2462	−0.596708
$571$	−4.00000	−0.167395	−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000	−0.167395	−0.0836974	+	0.996491i	$0.526673\pi$
$572$	0.438447	0.0183324
$573$	−4.87689	−0.203735
$574$	36.1080	1.50712
$575$	0	0
$576$	1.00000	0.0416667
$577$	11.3693	0.473311	0.236655	−	0.971594i	$-0.423949\pi$
$577$	11.3693	0.473311	0.236655	+	0.971594i	$0.423949\pi$
$578$	9.24621	0.384592
$579$	13.8078	0.573831
$580$	−1.56155	−0.0648400
$581$	−19.5076	−0.809311
$582$	6.68466	0.277088
$583$	−5.12311	−0.212177
$584$	5.12311	0.211996
$585$	−1.56155	−0.0645623
$586$	33.1231	1.36830
$587$	−39.8078	−1.64304	−0.821521	−	0.570178i	$-0.806874\pi$
$587$	−39.8078	−1.64304	−0.821521	+	0.570178i	$0.806874\pi$
$588$	−2.75379	−0.113564
$589$	18.7386	0.772112
$590$	−5.56155	−0.228966
$591$	−4.24621	−0.174666
$592$	−6.00000	−0.246598
$593$	13.5076	0.554690	0.277345	−	0.960770i	$-0.410546\pi$
$593$	13.5076	0.554690	0.277345	+	0.960770i	$0.410546\pi$
$594$	−1.00000	−0.0410305
$595$	−56.9848	−2.33615
$596$	2.87689	0.117842
$597$	−17.3693	−0.710879
$598$	0	0
$599$	−18.7386	−0.765640	−0.382820	−	0.923823i	$-0.625047\pi$
$599$	−18.7386	−0.765640	−0.382820	+	0.923823i	$0.625047\pi$
$600$	−7.68466	−0.313725
$601$	−30.0000	−1.22373	−0.611863	−	0.790964i	$-0.709580\pi$
$601$	−30.0000	−1.22373	−0.611863	+	0.790964i	$0.709580\pi$
$602$	−19.5076	−0.795070
$603$	4.00000	0.162893
$604$	−16.0000	−0.651031
$605$	−3.56155	−0.144798
$606$	−8.43845	−0.342788
$607$	2.05398	0.0833683	0.0416841	−	0.999131i	$-0.486728\pi$
$607$	2.05398	0.0833683	0.0416841	+	0.999131i	$0.486728\pi$
$608$	−4.00000	−0.162221
$609$	−1.36932	−0.0554875
$610$	−3.56155	−0.144203
$611$	4.49242	0.181744
$612$	5.12311	0.207089
$613$	19.5616	0.790084	0.395042	−	0.918663i	$-0.370730\pi$
$613$	19.5616	0.790084	0.395042	+	0.918663i	$0.370730\pi$
$614$	13.1771	0.531784
$615$	41.1771	1.66042
$616$	3.12311	0.125834
$617$	34.6847	1.39635	0.698176	−	0.715926i	$-0.253995\pi$
$617$	34.6847	1.39635	0.698176	+	0.715926i	$0.253995\pi$
$618$	−16.0000	−0.643614
$619$	−22.0540	−0.886424	−0.443212	−	0.896417i	$-0.646161\pi$
$619$	−22.0540	−0.886424	−0.443212	+	0.896417i	$0.646161\pi$
$620$	16.6847	0.670072
$621$	0	0
$622$	−14.2462	−0.571221
$623$	43.1231	1.72769
$624$	−0.438447	−0.0175519
$625$	−4.36932	−0.174773
$626$	−9.12311	−0.364633
$627$	4.00000	0.159745
$628$	18.6847	0.745599
$629$	−30.7386	−1.22563
$630$	−11.1231	−0.443155
$631$	−10.2462	−0.407895	−0.203948	−	0.978982i	$-0.565377\pi$
$631$	−10.2462	−0.407895	−0.203948	+	0.978982i	$0.565377\pi$
$632$	0	0
$633$	−13.5616	−0.539023
$634$	10.6847	0.424342
$635$	−72.9848	−2.89632
$636$	5.12311	0.203144
$637$	1.20739	0.0478386
$638$	0.438447	0.0173583
$639$	3.12311	0.123548
$640$	−3.56155	−0.140783
$641$	36.7386	1.45109	0.725544	−	0.688175i	$-0.241588\pi$
$641$	36.7386	1.45109	0.725544	+	0.688175i	$0.241588\pi$
$642$	−5.56155	−0.219497
$643$	2.63068	0.103744	0.0518720	−	0.998654i	$-0.483481\pi$
$643$	2.63068	0.103744	0.0518720	+	0.998654i	$0.483481\pi$
$644$	0	0
$645$	−22.2462	−0.875944
$646$	−20.4924	−0.806264
$647$	−37.8617	−1.48850	−0.744249	−	0.667902i	$-0.767193\pi$
$647$	−37.8617	−1.48850	−0.744249	+	0.667902i	$0.767193\pi$
$648$	1.00000	0.0392837
$649$	1.56155	0.0612963
$650$	3.36932	0.132155
$651$	14.6307	0.573422
$652$	−12.6847	−0.496770
$653$	15.3693	0.601448	0.300724	−	0.953711i	$-0.402772\pi$
$653$	15.3693	0.601448	0.300724	+	0.953711i	$0.402772\pi$
$654$	−5.31534	−0.207846
$655$	−42.0540	−1.64318
$656$	11.5616	0.451403
$657$	5.12311	0.199871
$658$	32.0000	1.24749
$659$	43.8078	1.70651	0.853254	−	0.521495i	$-0.174626\pi$
$659$	43.8078	1.70651	0.853254	+	0.521495i	$0.174626\pi$
$660$	3.56155	0.138633
$661$	−2.19224	−0.0852681	−0.0426340	−	0.999091i	$-0.513575\pi$
$661$	−2.19224	−0.0852681	−0.0426340	+	0.999091i	$0.513575\pi$
$662$	5.75379	0.223627
$663$	−2.24621	−0.0872356
$664$	−6.24621	−0.242400
$665$	44.4924	1.72534
$666$	−6.00000	−0.232495
$667$	0	0
$668$	14.2462	0.551202
$669$	−4.00000	−0.154649
$670$	−14.2462	−0.550379
$671$	1.00000	0.0386046
$672$	−3.12311	−0.120476
$673$	4.93087	0.190071	0.0950355	−	0.995474i	$-0.469704\pi$
$673$	4.93087	0.190071	0.0950355	+	0.995474i	$0.469704\pi$
$674$	30.6847	1.18193
$675$	−7.68466	−0.295783
$676$	−12.8078	−0.492606
$677$	−6.49242	−0.249524	−0.124762	−	0.992187i	$-0.539817\pi$
$677$	−6.49242	−0.249524	−0.124762	+	0.992187i	$0.539817\pi$
$678$	−3.75379	−0.144163
$679$	−20.8769	−0.801182
$680$	−18.2462	−0.699710
$681$	−2.24621	−0.0860750
$682$	−4.68466	−0.179385
$683$	16.8769	0.645776	0.322888	−	0.946437i	$-0.395346\pi$
$683$	16.8769	0.645776	0.322888	+	0.946437i	$0.395346\pi$
$684$	−4.00000	−0.152944
$685$	21.3693	0.816480
$686$	−13.2614	−0.506321
$687$	−2.87689	−0.109760
$688$	−6.24621	−0.238135
$689$	−2.24621	−0.0855738
$690$	0	0
$691$	22.4384	0.853599	0.426799	−	0.904346i	$-0.359641\pi$
$691$	22.4384	0.853599	0.426799	+	0.904346i	$0.359641\pi$
$692$	22.6847	0.862341
$693$	3.12311	0.118637
$694$	−7.31534	−0.277687
$695$	13.5616	0.514419
$696$	−0.438447	−0.0166193
$697$	59.2311	2.24354
$698$	−27.3693	−1.03594
$699$	−27.3693	−1.03520
$700$	24.0000	0.907115
$701$	28.9309	1.09270	0.546352	−	0.837556i	$-0.316016\pi$
$701$	28.9309	1.09270	0.546352	+	0.837556i	$0.316016\pi$
$702$	−0.438447	−0.0165481
$703$	24.0000	0.905177
$704$	1.00000	0.0376889
$705$	36.4924	1.37438
$706$	−30.0000	−1.12906
$707$	26.3542	0.991150
$708$	−1.56155	−0.0586867
$709$	−11.5616	−0.434203	−0.217102	−	0.976149i	$-0.569660\pi$
$709$	−11.5616	−0.434203	−0.217102	+	0.976149i	$0.569660\pi$
$710$	−11.1231	−0.417443
$711$	0	0
$712$	13.8078	0.517468
$713$	0	0
$714$	−16.0000	−0.598785
$715$	−1.56155	−0.0583988
$716$	−7.12311	−0.266203
$717$	9.75379	0.364262
$718$	3.80776	0.142104
$719$	21.7538	0.811279	0.405640	−	0.914033i	$-0.367049\pi$
$719$	21.7538	0.811279	0.405640	+	0.914033i	$0.367049\pi$
$720$	−3.56155	−0.132731
$721$	49.9697	1.86097
$722$	−3.00000	−0.111648
$723$	15.3693	0.571591
$724$	−1.80776	−0.0671850
$725$	3.36932	0.125133
$726$	−1.00000	−0.0371135
$727$	32.0000	1.18681	0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000	1.18681	0.593407	+	0.804902i	$0.297782\pi$
$728$	1.36932	0.0507503
$729$	1.00000	0.0370370
$730$	−18.2462	−0.675323
$731$	−32.0000	−1.18356
$732$	−1.00000	−0.0369611
$733$	32.7386	1.20923	0.604615	−	0.796518i	$-0.293327\pi$
$733$	32.7386	1.20923	0.604615	+	0.796518i	$0.293327\pi$
$734$	9.36932	0.345828
$735$	9.80776	0.361765
$736$	0	0
$737$	4.00000	0.147342
$738$	11.5616	0.425587
$739$	27.4233	1.00878	0.504391	−	0.863475i	$-0.331717\pi$
$739$	27.4233	1.00878	0.504391	+	0.863475i	$0.331717\pi$
$740$	21.3693	0.785552
$741$	1.75379	0.0644270
$742$	−16.0000	−0.587378
$743$	−18.4384	−0.676441	−0.338221	−	0.941067i	$-0.609825\pi$
$743$	−18.4384	−0.676441	−0.338221	+	0.941067i	$0.609825\pi$
$744$	4.68466	0.171748
$745$	−10.2462	−0.375392
$746$	27.8617	1.02009
$747$	−6.24621	−0.228537
$748$	5.12311	0.187319
$749$	17.3693	0.634661
$750$	9.56155	0.349139
$751$	−15.6155	−0.569819	−0.284909	−	0.958554i	$-0.591964\pi$
$751$	−15.6155	−0.569819	−0.284909	+	0.958554i	$0.591964\pi$
$752$	10.2462	0.373641
$753$	−25.5616	−0.931515
$754$	0.192236	0.00700082
$755$	56.9848	2.07389
$756$	−3.12311	−0.113586
$757$	−8.63068	−0.313688	−0.156844	−	0.987623i	$-0.550132\pi$
$757$	−8.63068	−0.313688	−0.156844	+	0.987623i	$0.550132\pi$
$758$	31.8078	1.15531
$759$	0	0
$760$	14.2462	0.516764
$761$	−39.3693	−1.42714	−0.713568	−	0.700586i	$-0.752922\pi$
$761$	−39.3693	−1.42714	−0.713568	+	0.700586i	$0.752922\pi$
$762$	−20.4924	−0.742362
$763$	16.6004	0.600974
$764$	4.87689	0.176440
$765$	−18.2462	−0.659693
$766$	−23.6155	−0.853264
$767$	0.684658	0.0247216
$768$	−1.00000	−0.0360844
$769$	30.3002	1.09265	0.546326	−	0.837572i	$-0.316026\pi$
$769$	30.3002	1.09265	0.546326	+	0.837572i	$0.316026\pi$
$770$	−11.1231	−0.400849
$771$	26.4924	0.954101
$772$	−13.8078	−0.496952
$773$	−28.9309	−1.04057	−0.520286	−	0.853992i	$-0.674174\pi$
$773$	−28.9309	−1.04057	−0.520286	+	0.853992i	$0.674174\pi$
$774$	−6.24621	−0.224515
$775$	−36.0000	−1.29316
$776$	−6.68466	−0.239965
$777$	18.7386	0.672245
$778$	−31.8617	−1.14230
$779$	−46.2462	−1.65694
$780$	1.56155	0.0559126
$781$	3.12311	0.111754
$782$	0	0
$783$	−0.438447	−0.0156688
$784$	2.75379	0.0983496
$785$	−66.5464	−2.37514
$786$	−11.8078	−0.421169
$787$	−3.80776	−0.135732	−0.0678661	−	0.997694i	$-0.521619\pi$
$787$	−3.80776	−0.135732	−0.0678661	+	0.997694i	$0.521619\pi$
$788$	4.24621	0.151265
$789$	4.87689	0.173622
$790$	0	0
$791$	11.7235	0.416839
$792$	1.00000	0.0355335
$793$	0.438447	0.0155697
$794$	21.8078	0.773929
$795$	−18.2462	−0.647126
$796$	17.3693	0.615639
$797$	18.0000	0.637593	0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000	0.637593	0.318796	+	0.947823i	$0.396721\pi$
$798$	12.4924	0.442227
$799$	52.4924	1.85705
$800$	7.68466	0.271694
$801$	13.8078	0.487873
$802$	−8.05398	−0.284396
$803$	5.12311	0.180790
$804$	−4.00000	−0.141069
$805$	0	0
$806$	−2.05398	−0.0723482
$807$	8.05398	0.283513
$808$	8.43845	0.296864
$809$	17.4233	0.612570	0.306285	−	0.951940i	$-0.400914\pi$
$809$	17.4233	0.612570	0.306285	+	0.951940i	$0.400914\pi$
$810$	−3.56155	−0.125140
$811$	50.7386	1.78167	0.890837	−	0.454323i	$-0.150119\pi$
$811$	50.7386	1.78167	0.890837	+	0.454323i	$0.150119\pi$
$812$	1.36932	0.0480536
$813$	−6.24621	−0.219064
$814$	−6.00000	−0.210300
$815$	45.1771	1.58248
$816$	−5.12311	−0.179345
$817$	24.9848	0.874109
$818$	19.1771	0.670511
$819$	1.36932	0.0478478
$820$	−41.1771	−1.43797
$821$	24.7386	0.863384	0.431692	−	0.902021i	$-0.357917\pi$
$821$	24.7386	0.863384	0.431692	+	0.902021i	$0.357917\pi$
$822$	6.00000	0.209274
$823$	−31.8078	−1.10875	−0.554374	−	0.832267i	$-0.687042\pi$
$823$	−31.8078	−1.10875	−0.554374	+	0.832267i	$0.687042\pi$
$824$	16.0000	0.557386
$825$	−7.68466	−0.267545
$826$	4.87689	0.169689
$827$	9.75379	0.339172	0.169586	−	0.985515i	$-0.445757\pi$
$827$	9.75379	0.339172	0.169586	+	0.985515i	$0.445757\pi$
$828$	0	0
$829$	15.3693	0.533798	0.266899	−	0.963724i	$-0.414001\pi$
$829$	15.3693	0.533798	0.266899	+	0.963724i	$0.414001\pi$
$830$	22.2462	0.772177
$831$	2.00000	0.0693792
$832$	0.438447	0.0152004
$833$	14.1080	0.488812
$834$	3.80776	0.131852
$835$	−50.7386	−1.75588
$836$	−4.00000	−0.138343
$837$	4.68466	0.161925
$838$	12.0000	0.414533
$839$	−31.8078	−1.09813	−0.549063	−	0.835781i	$-0.685015\pi$
$839$	−31.8078	−1.09813	−0.549063	+	0.835781i	$0.685015\pi$
$840$	11.1231	0.383784
$841$	−28.8078	−0.993371
$842$	10.6847	0.368218
$843$	15.3693	0.529347
$844$	13.5616	0.466808
$845$	45.6155	1.56922
$846$	10.2462	0.352272
$847$	3.12311	0.107311
$848$	−5.12311	−0.175928
$849$	12.0000	0.411839
$850$	39.3693	1.35036
$851$	0	0
$852$	−3.12311	−0.106996
$853$	25.8078	0.883641	0.441821	−	0.897103i	$-0.354333\pi$
$853$	25.8078	0.883641	0.441821	+	0.897103i	$0.354333\pi$
$854$	3.12311	0.106870
$855$	14.2462	0.487210
$856$	5.56155	0.190090
$857$	−20.0540	−0.685031	−0.342515	−	0.939512i	$-0.611279\pi$
$857$	−20.0540	−0.685031	−0.342515	+	0.939512i	$0.611279\pi$
$858$	−0.438447	−0.0149683
$859$	38.0540	1.29838	0.649192	−	0.760624i	$-0.275107\pi$
$859$	38.0540	1.29838	0.649192	+	0.760624i	$0.275107\pi$
$860$	22.2462	0.758590
$861$	−36.1080	−1.23056
$862$	−35.1231	−1.19630
$863$	−43.3153	−1.47447	−0.737236	−	0.675636i	$-0.763869\pi$
$863$	−43.3153	−1.47447	−0.737236	+	0.675636i	$0.763869\pi$
$864$	−1.00000	−0.0340207
$865$	−80.7926	−2.74703
$866$	−18.8769	−0.641463
$867$	−9.24621	−0.314018
$868$	−14.6307	−0.496598
$869$	0	0
$870$	1.56155	0.0529416
$871$	1.75379	0.0594249
$872$	5.31534	0.180000
$873$	−6.68466	−0.226241
$874$	0	0
$875$	−29.8617	−1.00951
$876$	−5.12311	−0.173094
$877$	−8.63068	−0.291437	−0.145719	−	0.989326i	$-0.546549\pi$
$877$	−8.63068	−0.291437	−0.145719	+	0.989326i	$0.546549\pi$
$878$	24.3002	0.820092
$879$	−33.1231	−1.11721
$880$	−3.56155	−0.120060
$881$	8.63068	0.290775	0.145388	−	0.989375i	$-0.453557\pi$
$881$	8.63068	0.290775	0.145388	+	0.989375i	$0.453557\pi$
$882$	2.75379	0.0927249
$883$	−29.7538	−1.00129	−0.500647	−	0.865651i	$-0.666905\pi$
$883$	−29.7538	−1.00129	−0.500647	+	0.865651i	$0.666905\pi$
$884$	2.24621	0.0755483
$885$	5.56155	0.186950
$886$	−0.876894	−0.0294598
$887$	24.9848	0.838909	0.419454	−	0.907776i	$-0.362221\pi$
$887$	24.9848	0.838909	0.419454	+	0.907776i	$0.362221\pi$
$888$	6.00000	0.201347
$889$	64.0000	2.14649
$890$	−49.1771	−1.64842
$891$	1.00000	0.0335013
$892$	4.00000	0.133930
$893$	−40.9848	−1.37151
$894$	−2.87689	−0.0962177
$895$	25.3693	0.848003
$896$	3.12311	0.104336
$897$	0	0
$898$	−39.3693	−1.31377
$899$	−2.05398	−0.0685039
$900$	7.68466	0.256155
$901$	−26.2462	−0.874388
$902$	11.5616	0.384958
$903$	19.5076	0.649172
$904$	3.75379	0.124849
$905$	6.43845	0.214021
$906$	16.0000	0.531564
$907$	−22.7386	−0.755024	−0.377512	−	0.926005i	$-0.623220\pi$
$907$	−22.7386	−0.755024	−0.377512	+	0.926005i	$0.623220\pi$
$908$	2.24621	0.0745431
$909$	8.43845	0.279886
$910$	−4.87689	−0.161667
$911$	−4.68466	−0.155210	−0.0776048	−	0.996984i	$-0.524727\pi$
$911$	−4.68466	−0.155210	−0.0776048	+	0.996984i	$0.524727\pi$
$912$	4.00000	0.132453
$913$	−6.24621	−0.206719
$914$	24.7386	0.818281
$915$	3.56155	0.117741
$916$	2.87689	0.0950553
$917$	36.8769	1.21778
$918$	−5.12311	−0.169088
$919$	−9.06913	−0.299163	−0.149582	−	0.988749i	$-0.547793\pi$
$919$	−9.06913	−0.299163	−0.149582	+	0.988749i	$0.547793\pi$
$920$	0	0
$921$	−13.1771	−0.434200
$922$	34.4924	1.13595
$923$	1.36932	0.0450716
$924$	−3.12311	−0.102743
$925$	−46.1080	−1.51602
$926$	−25.3693	−0.833687
$927$	16.0000	0.525509
$928$	0.438447	0.0143927
$929$	22.1080	0.725338	0.362669	−	0.931918i	$-0.381866\pi$
$929$	22.1080	0.725338	0.362669	+	0.931918i	$0.381866\pi$
$930$	−16.6847	−0.547112
$931$	−11.0152	−0.361007
$932$	27.3693	0.896512
$933$	14.2462	0.466400
$934$	19.3153	0.632017
$935$	−18.2462	−0.596715
$936$	0.438447	0.0143311
$937$	10.0000	0.326686	0.163343	−	0.986569i	$-0.447772\pi$
$937$	10.0000	0.326686	0.163343	+	0.986569i	$0.447772\pi$
$938$	12.4924	0.407892
$939$	9.12311	0.297721
$940$	−36.4924	−1.19025
$941$	22.6847	0.739499	0.369749	−	0.929132i	$-0.379444\pi$
$941$	22.6847	0.739499	0.369749	+	0.929132i	$0.379444\pi$
$942$	−18.6847	−0.608779
$943$	0	0
$944$	1.56155	0.0508242
$945$	11.1231	0.361835
$946$	−6.24621	−0.203082
$947$	−51.2311	−1.66479	−0.832393	−	0.554186i	$-0.813030\pi$
$947$	−51.2311	−1.66479	−0.832393	+	0.554186i	$0.813030\pi$
$948$	0	0
$949$	2.24621	0.0729151
$950$	−30.7386	−0.997293
$951$	−10.6847	−0.346474
$952$	16.0000	0.518563
$953$	11.7538	0.380743	0.190371	−	0.981712i	$-0.439031\pi$
$953$	11.7538	0.380743	0.190371	+	0.981712i	$0.439031\pi$
$954$	−5.12311	−0.165867
$955$	−17.3693	−0.562058
$956$	−9.75379	−0.315460
$957$	−0.438447	−0.0141730
$958$	−14.2462	−0.460274
$959$	−18.7386	−0.605102
$960$	3.56155	0.114949
$961$	−9.05398	−0.292064
$962$	−2.63068	−0.0848166
$963$	5.56155	0.179219
$964$	−15.3693	−0.495012
$965$	49.1771	1.58307
$966$	0	0
$967$	−21.9460	−0.705737	−0.352868	−	0.935673i	$-0.614794\pi$
$967$	−21.9460	−0.705737	−0.352868	+	0.935673i	$0.614794\pi$
$968$	1.00000	0.0321412
$969$	20.4924	0.658311
$970$	23.8078	0.764421
$971$	−36.0000	−1.15529	−0.577647	−	0.816286i	$-0.696029\pi$
$971$	−36.0000	−1.15529	−0.577647	+	0.816286i	$0.696029\pi$
$972$	−1.00000	−0.0320750
$973$	−11.8920	−0.381242
$974$	−18.7386	−0.600425
$975$	−3.36932	−0.107904
$976$	1.00000	0.0320092
$977$	44.3542	1.41902	0.709508	−	0.704698i	$-0.248917\pi$
$977$	44.3542	1.41902	0.709508	+	0.704698i	$0.248917\pi$
$978$	12.6847	0.405611
$979$	13.8078	0.441298
$980$	−9.80776	−0.313298
$981$	5.31534	0.169706
$982$	−18.7386	−0.597974
$983$	−28.8769	−0.921030	−0.460515	−	0.887652i	$-0.652335\pi$
$983$	−28.8769	−0.921030	−0.460515	+	0.887652i	$0.652335\pi$
$984$	−11.5616	−0.368569
$985$	−15.1231	−0.481862
$986$	2.24621	0.0715339
$987$	−32.0000	−1.01857
$988$	−1.75379	−0.0557955
$989$	0	0
$990$	−3.56155	−0.113194
$991$	−20.1080	−0.638750	−0.319375	−	0.947628i	$-0.603473\pi$
$991$	−20.1080	−0.638750	−0.319375	+	0.947628i	$0.603473\pi$
$992$	−4.68466	−0.148738
$993$	−5.75379	−0.182591
$994$	9.75379	0.309371
$995$	−61.8617	−1.96115
$996$	6.24621	0.197919
$997$	−15.8617	−0.502346	−0.251173	−	0.967942i	$-0.580816\pi$
$997$	−15.8617	−0.502346	−0.251173	+	0.967942i	$0.580816\pi$
$998$	−27.6155	−0.874154
$999$	6.00000	0.189832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.l.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.l.1.1	✓	2	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:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.56155 q^{5} -1.00000 q^{6} +3.12311 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.56155 q^{5} -1.00000 q^{6} +3.12311 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.56155 q^{10} +1.00000 q^{11} -1.00000 q^{12} +0.438447 q^{13} +3.12311 q^{14} +3.56155 q^{15} +1.00000 q^{16} +5.12311 q^{17} +1.00000 q^{18} -4.00000 q^{19} -3.56155 q^{20} -3.12311 q^{21} +1.00000 q^{22} -1.00000 q^{24} +7.68466 q^{25} +0.438447 q^{26} -1.00000 q^{27} +3.12311 q^{28} +0.438447 q^{29} +3.56155 q^{30} -4.68466 q^{31} +1.00000 q^{32} -1.00000 q^{33} +5.12311 q^{34} -11.1231 q^{35} +1.00000 q^{36} -6.00000 q^{37} -4.00000 q^{38} -0.438447 q^{39} -3.56155 q^{40} +11.5616 q^{41} -3.12311 q^{42} -6.24621 q^{43} +1.00000 q^{44} -3.56155 q^{45} +10.2462 q^{47} -1.00000 q^{48} +2.75379 q^{49} +7.68466 q^{50} -5.12311 q^{51} +0.438447 q^{52} -5.12311 q^{53} -1.00000 q^{54} -3.56155 q^{55} +3.12311 q^{56} +4.00000 q^{57} +0.438447 q^{58} +1.56155 q^{59} +3.56155 q^{60} +1.00000 q^{61} -4.68466 q^{62} +3.12311 q^{63} +1.00000 q^{64} -1.56155 q^{65} -1.00000 q^{66} +4.00000 q^{67} +5.12311 q^{68} -11.1231 q^{70} +3.12311 q^{71} +1.00000 q^{72} +5.12311 q^{73} -6.00000 q^{74} -7.68466 q^{75} -4.00000 q^{76} +3.12311 q^{77} -0.438447 q^{78} -3.56155 q^{80} +1.00000 q^{81} +11.5616 q^{82} -6.24621 q^{83} -3.12311 q^{84} -18.2462 q^{85} -6.24621 q^{86} -0.438447 q^{87} +1.00000 q^{88} +13.8078 q^{89} -3.56155 q^{90} +1.36932 q^{91} +4.68466 q^{93} +10.2462 q^{94} +14.2462 q^{95} -1.00000 q^{96} -6.68466 q^{97} +2.75379 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 3 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 3 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 3 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} - 3 q^{10} + 2 q^{11} - 2 q^{12} + 5 q^{13} - 2 q^{14} + 3 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} - 8 q^{19} - 3 q^{20} + 2 q^{21} + 2 q^{22} - 2 q^{24} + 3 q^{25} + 5 q^{26} - 2 q^{27} - 2 q^{28} + 5 q^{29} + 3 q^{30} + 3 q^{31} + 2 q^{32} - 2 q^{33} + 2 q^{34} - 14 q^{35} + 2 q^{36} - 12 q^{37} - 8 q^{38} - 5 q^{39} - 3 q^{40} + 19 q^{41} + 2 q^{42} + 4 q^{43} + 2 q^{44} - 3 q^{45} + 4 q^{47} - 2 q^{48} + 22 q^{49} + 3 q^{50} - 2 q^{51} + 5 q^{52} - 2 q^{53} - 2 q^{54} - 3 q^{55} - 2 q^{56} + 8 q^{57} + 5 q^{58} - q^{59} + 3 q^{60} + 2 q^{61} + 3 q^{62} - 2 q^{63} + 2 q^{64} + q^{65} - 2 q^{66} + 8 q^{67} + 2 q^{68} - 14 q^{70} - 2 q^{71} + 2 q^{72} + 2 q^{73} - 12 q^{74} - 3 q^{75} - 8 q^{76} - 2 q^{77} - 5 q^{78} - 3 q^{80} + 2 q^{81} + 19 q^{82} + 4 q^{83} + 2 q^{84} - 20 q^{85} + 4 q^{86} - 5 q^{87} + 2 q^{88} + 7 q^{89} - 3 q^{90} - 22 q^{91} - 3 q^{93} + 4 q^{94} + 12 q^{95} - 2 q^{96} - q^{97} + 22 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 3 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9 - 3 * q^10 + 2 * q^11 - 2 * q^12 + 5 * q^13 - 2 * q^14 + 3 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^18 - 8 * q^19 - 3 * q^20 + 2 * q^21 + 2 * q^22 - 2 * q^24 + 3 * q^25 + 5 * q^26 - 2 * q^27 - 2 * q^28 + 5 * q^29 + 3 * q^30 + 3 * q^31 + 2 * q^32 - 2 * q^33 + 2 * q^34 - 14 * q^35 + 2 * q^36 - 12 * q^37 - 8 * q^38 - 5 * q^39 - 3 * q^40 + 19 * q^41 + 2 * q^42 + 4 * q^43 + 2 * q^44 - 3 * q^45 + 4 * q^47 - 2 * q^48 + 22 * q^49 + 3 * q^50 - 2 * q^51 + 5 * q^52 - 2 * q^53 - 2 * q^54 - 3 * q^55 - 2 * q^56 + 8 * q^57 + 5 * q^58 - q^59 + 3 * q^60 + 2 * q^61 + 3 * q^62 - 2 * q^63 + 2 * q^64 + q^65 - 2 * q^66 + 8 * q^67 + 2 * q^68 - 14 * q^70 - 2 * q^71 + 2 * q^72 + 2 * q^73 - 12 * q^74 - 3 * q^75 - 8 * q^76 - 2 * q^77 - 5 * q^78 - 3 * q^80 + 2 * q^81 + 19 * q^82 + 4 * q^83 + 2 * q^84 - 20 * q^85 + 4 * q^86 - 5 * q^87 + 2 * q^88 + 7 * q^89 - 3 * q^90 - 22 * q^91 - 3 * q^93 + 4 * q^94 + 12 * q^95 - 2 * q^96 - q^97 + 22 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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