LMFDB - Embedded newform 4026.2.a.v.1.3

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:	$5$
Coefficient field:	5.5.11492689.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 9x^{3} + 13x^{2} + 18x - 8 $ x^5 - 2x^4 - 9x^3 + 13x^2 + 18x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.371979$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.37198 q^{5} -1.00000 q^{6} +4.23361 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.37198 q^{5} -1.00000 q^{6} +4.23361 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.37198 q^{10} +1.00000 q^{11} -1.00000 q^{12} -5.14772 q^{13} +4.23361 q^{14} -1.37198 q^{15} +1.00000 q^{16} -4.20093 q^{17} +1.00000 q^{18} +7.86163 q^{19} +1.37198 q^{20} -4.23361 q^{21} +1.00000 q^{22} +4.25414 q^{23} -1.00000 q^{24} -3.11767 q^{25} -5.14772 q^{26} -1.00000 q^{27} +4.23361 q^{28} +1.03268 q^{29} -1.37198 q^{30} +4.77574 q^{31} +1.00000 q^{32} -1.00000 q^{33} -4.20093 q^{34} +5.80842 q^{35} +1.00000 q^{36} -1.57555 q^{37} +7.86163 q^{38} +5.14772 q^{39} +1.37198 q^{40} +10.4973 q^{41} -4.23361 q^{42} -1.91411 q^{43} +1.00000 q^{44} +1.37198 q^{45} +4.25414 q^{46} +5.37108 q^{47} -1.00000 q^{48} +10.9235 q^{49} -3.11767 q^{50} +4.20093 q^{51} -5.14772 q^{52} -6.73278 q^{53} -1.00000 q^{54} +1.37198 q^{55} +4.23361 q^{56} -7.86163 q^{57} +1.03268 q^{58} +6.26365 q^{59} -1.37198 q^{60} +1.00000 q^{61} +4.77574 q^{62} +4.23361 q^{63} +1.00000 q^{64} -7.06256 q^{65} -1.00000 q^{66} -1.68123 q^{67} -4.20093 q^{68} -4.25414 q^{69} +5.80842 q^{70} +6.54477 q^{71} +1.00000 q^{72} -10.8805 q^{73} -1.57555 q^{74} +3.11767 q^{75} +7.86163 q^{76} +4.23361 q^{77} +5.14772 q^{78} +3.88142 q^{79} +1.37198 q^{80} +1.00000 q^{81} +10.4973 q^{82} -11.0919 q^{83} -4.23361 q^{84} -5.76358 q^{85} -1.91411 q^{86} -1.03268 q^{87} +1.00000 q^{88} -6.47674 q^{89} +1.37198 q^{90} -21.7934 q^{91} +4.25414 q^{92} -4.77574 q^{93} +5.37108 q^{94} +10.7860 q^{95} -1.00000 q^{96} +3.40393 q^{97} +10.9235 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 7 q^{5} - 5 q^{6} + 5 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + 7 * q^5 - 5 * q^6 + 5 * q^8 + 5 * q^9	$ 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 7 q^{5} - 5 q^{6} + 5 q^{8} + 5 q^{9} + 7 q^{10} + 5 q^{11} - 5 q^{12} - 2 q^{13} - 7 q^{15} + 5 q^{16} + 2 q^{17} + 5 q^{18} + 18 q^{19} + 7 q^{20} + 5 q^{22} - q^{23} - 5 q^{24} + 6 q^{25} - 2 q^{26} - 5 q^{27} + 7 q^{29} - 7 q^{30} + 5 q^{32} - 5 q^{33} + 2 q^{34} + 7 q^{35} + 5 q^{36} + 11 q^{37} + 18 q^{38} + 2 q^{39} + 7 q^{40} + 8 q^{41} - 7 q^{43} + 5 q^{44} + 7 q^{45} - q^{46} + q^{47} - 5 q^{48} + 7 q^{49} + 6 q^{50} - 2 q^{51} - 2 q^{52} + 10 q^{53} - 5 q^{54} + 7 q^{55} - 18 q^{57} + 7 q^{58} + 8 q^{59} - 7 q^{60} + 5 q^{61} + 5 q^{64} + 9 q^{65} - 5 q^{66} - 9 q^{67} + 2 q^{68} + q^{69} + 7 q^{70} + 34 q^{71} + 5 q^{72} + 13 q^{73} + 11 q^{74} - 6 q^{75} + 18 q^{76} + 2 q^{78} + 15 q^{79} + 7 q^{80} + 5 q^{81} + 8 q^{82} - 27 q^{83} - 2 q^{85} - 7 q^{86} - 7 q^{87} + 5 q^{88} + 11 q^{89} + 7 q^{90} + q^{91} - q^{92} + q^{94} + 11 q^{95} - 5 q^{96} + 37 q^{97} + 7 q^{98} + 5 q^{99}+O(q^{100}) $ 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + 7 * q^5 - 5 * q^6 + 5 * q^8 + 5 * q^9 + 7 * q^10 + 5 * q^11 - 5 * q^12 - 2 * q^13 - 7 * q^15 + 5 * q^16 + 2 * q^17 + 5 * q^18 + 18 * q^19 + 7 * q^20 + 5 * q^22 - q^23 - 5 * q^24 + 6 * q^25 - 2 * q^26 - 5 * q^27 + 7 * q^29 - 7 * q^30 + 5 * q^32 - 5 * q^33 + 2 * q^34 + 7 * q^35 + 5 * q^36 + 11 * q^37 + 18 * q^38 + 2 * q^39 + 7 * q^40 + 8 * q^41 - 7 * q^43 + 5 * q^44 + 7 * q^45 - q^46 + q^47 - 5 * q^48 + 7 * q^49 + 6 * q^50 - 2 * q^51 - 2 * q^52 + 10 * q^53 - 5 * q^54 + 7 * q^55 - 18 * q^57 + 7 * q^58 + 8 * q^59 - 7 * q^60 + 5 * q^61 + 5 * q^64 + 9 * q^65 - 5 * q^66 - 9 * q^67 + 2 * q^68 + q^69 + 7 * q^70 + 34 * q^71 + 5 * q^72 + 13 * q^73 + 11 * q^74 - 6 * q^75 + 18 * q^76 + 2 * q^78 + 15 * q^79 + 7 * q^80 + 5 * q^81 + 8 * q^82 - 27 * q^83 - 2 * q^85 - 7 * q^86 - 7 * q^87 + 5 * q^88 + 11 * q^89 + 7 * q^90 + q^91 - q^92 + q^94 + 11 * q^95 - 5 * q^96 + 37 * q^97 + 7 * q^98 + 5 * 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
$5$	1.37198	0.613567	0.306784	−	0.951779i	$-0.400747\pi$
$5$	1.37198	0.613567	0.306784	+	0.951779i	$0.400747\pi$
$6$	−1.00000	−0.408248
$7$	4.23361	1.60015	0.800077	−	0.599897i	$-0.204792\pi$
$7$	4.23361	1.60015	0.800077	+	0.599897i	$0.204792\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.37198	0.433858
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	−5.14772	−1.42772	−0.713860	−	0.700288i	$-0.753055\pi$
$13$	−5.14772	−1.42772	−0.713860	+	0.700288i	$0.753055\pi$
$14$	4.23361	1.13148
$15$	−1.37198	−0.354243
$16$	1.00000	0.250000
$17$	−4.20093	−1.01887	−0.509437	−	0.860508i	$-0.670146\pi$
$17$	−4.20093	−1.01887	−0.509437	+	0.860508i	$0.670146\pi$
$18$	1.00000	0.235702
$19$	7.86163	1.80358	0.901791	−	0.432172i	$-0.142253\pi$
$19$	7.86163	1.80358	0.901791	+	0.432172i	$0.142253\pi$
$20$	1.37198	0.306784
$21$	−4.23361	−0.923850
$22$	1.00000	0.213201
$23$	4.25414	0.887049	0.443524	−	0.896262i	$-0.353728\pi$
$23$	4.25414	0.887049	0.443524	+	0.896262i	$0.353728\pi$
$24$	−1.00000	−0.204124
$25$	−3.11767	−0.623535
$26$	−5.14772	−1.00955
$27$	−1.00000	−0.192450
$28$	4.23361	0.800077
$29$	1.03268	0.191764	0.0958822	−	0.995393i	$-0.469433\pi$
$29$	1.03268	0.191764	0.0958822	+	0.995393i	$0.469433\pi$
$30$	−1.37198	−0.250488
$31$	4.77574	0.857748	0.428874	−	0.903364i	$-0.358910\pi$
$31$	4.77574	0.857748	0.428874	+	0.903364i	$0.358910\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	−4.20093	−0.720453
$35$	5.80842	0.981803
$36$	1.00000	0.166667
$37$	−1.57555	−0.259018	−0.129509	−	0.991578i	$-0.541340\pi$
$37$	−1.57555	−0.259018	−0.129509	+	0.991578i	$0.541340\pi$
$38$	7.86163	1.27533
$39$	5.14772	0.824295
$40$	1.37198	0.216929
$41$	10.4973	1.63940	0.819699	−	0.572795i	$-0.194141\pi$
$41$	10.4973	1.63940	0.819699	+	0.572795i	$0.194141\pi$
$42$	−4.23361	−0.653260
$43$	−1.91411	−0.291899	−0.145949	−	0.989292i	$-0.546624\pi$
$43$	−1.91411	−0.291899	−0.145949	+	0.989292i	$0.546624\pi$
$44$	1.00000	0.150756
$45$	1.37198	0.204522
$46$	4.25414	0.627238
$47$	5.37108	0.783452	0.391726	−	0.920082i	$-0.371878\pi$
$47$	5.37108	0.783452	0.391726	+	0.920082i	$0.371878\pi$
$48$	−1.00000	−0.144338
$49$	10.9235	1.56049
$50$	−3.11767	−0.440906
$51$	4.20093	0.588247
$52$	−5.14772	−0.713860
$53$	−6.73278	−0.924819	−0.462409	−	0.886667i	$-0.653015\pi$
$53$	−6.73278	−0.924819	−0.462409	+	0.886667i	$0.653015\pi$
$54$	−1.00000	−0.136083
$55$	1.37198	0.184998
$56$	4.23361	0.565740
$57$	−7.86163	−1.04130
$58$	1.03268	0.135598
$59$	6.26365	0.815458	0.407729	−	0.913103i	$-0.366321\pi$
$59$	6.26365	0.815458	0.407729	+	0.913103i	$0.366321\pi$
$60$	−1.37198	−0.177122
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	4.77574	0.606520
$63$	4.23361	0.533385
$64$	1.00000	0.125000
$65$	−7.06256	−0.876003
$66$	−1.00000	−0.123091
$67$	−1.68123	−0.205395	−0.102697	−	0.994713i	$-0.532747\pi$
$67$	−1.68123	−0.205395	−0.102697	+	0.994713i	$0.532747\pi$
$68$	−4.20093	−0.509437
$69$	−4.25414	−0.512138
$70$	5.80842	0.694239
$71$	6.54477	0.776721	0.388361	−	0.921507i	$-0.373042\pi$
$71$	6.54477	0.776721	0.388361	+	0.921507i	$0.373042\pi$
$72$	1.00000	0.117851
$73$	−10.8805	−1.27347	−0.636733	−	0.771084i	$-0.719715\pi$
$73$	−10.8805	−1.27347	−0.636733	+	0.771084i	$0.719715\pi$
$74$	−1.57555	−0.183153
$75$	3.11767	0.359998
$76$	7.86163	0.901791
$77$	4.23361	0.482465
$78$	5.14772	0.582864
$79$	3.88142	0.436694	0.218347	−	0.975871i	$-0.429933\pi$
$79$	3.88142	0.436694	0.218347	+	0.975871i	$0.429933\pi$
$80$	1.37198	0.153392
$81$	1.00000	0.111111
$82$	10.4973	1.15923
$83$	−11.0919	−1.21749	−0.608745	−	0.793366i	$-0.708327\pi$
$83$	−11.0919	−1.21749	−0.608745	+	0.793366i	$0.708327\pi$
$84$	−4.23361	−0.461925
$85$	−5.76358	−0.625148
$86$	−1.91411	−0.206404
$87$	−1.03268	−0.110715
$88$	1.00000	0.106600
$89$	−6.47674	−0.686533	−0.343266	−	0.939238i	$-0.611533\pi$
$89$	−6.47674	−0.686533	−0.343266	+	0.939238i	$0.611533\pi$
$90$	1.37198	0.144619
$91$	−21.7934	−2.28457
$92$	4.25414	0.443524
$93$	−4.77574	−0.495221
$94$	5.37108	0.553984
$95$	10.7860	1.10662
$96$	−1.00000	−0.102062
$97$	3.40393	0.345617	0.172808	−	0.984955i	$-0.444716\pi$
$97$	3.40393	0.345617	0.172808	+	0.984955i	$0.444716\pi$
$98$	10.9235	1.10344
$99$	1.00000	0.100504
$100$	−3.11767	−0.311767
$101$	4.23552	0.421450	0.210725	−	0.977545i	$-0.432418\pi$
$101$	4.23552	0.421450	0.210725	+	0.977545i	$0.432418\pi$
$102$	4.20093	0.415954
$103$	−9.15036	−0.901612	−0.450806	−	0.892622i	$-0.648863\pi$
$103$	−9.15036	−0.901612	−0.450806	+	0.892622i	$0.648863\pi$
$104$	−5.14772	−0.504775
$105$	−5.80842	−0.566844
$106$	−6.73278	−0.653946
$107$	2.92700	0.282964	0.141482	−	0.989941i	$-0.454813\pi$
$107$	2.92700	0.282964	0.141482	+	0.989941i	$0.454813\pi$
$108$	−1.00000	−0.0962250
$109$	−12.3589	−1.18377	−0.591884	−	0.806023i	$-0.701616\pi$
$109$	−12.3589	−1.18377	−0.591884	+	0.806023i	$0.701616\pi$
$110$	1.37198	0.130813
$111$	1.57555	0.149544
$112$	4.23361	0.400039
$113$	11.7531	1.10564	0.552821	−	0.833300i	$-0.313551\pi$
$113$	11.7531	1.10564	0.552821	+	0.833300i	$0.313551\pi$
$114$	−7.86163	−0.736309
$115$	5.83658	0.544264
$116$	1.03268	0.0958822
$117$	−5.14772	−0.475907
$118$	6.26365	0.576616
$119$	−17.7851	−1.63036
$120$	−1.37198	−0.125244
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	−10.4973	−0.946506
$124$	4.77574	0.428874
$125$	−11.1373	−0.996148
$126$	4.23361	0.377160
$127$	3.52234	0.312557	0.156278	−	0.987713i	$-0.450050\pi$
$127$	3.52234	0.312557	0.156278	+	0.987713i	$0.450050\pi$
$128$	1.00000	0.0883883
$129$	1.91411	0.168528
$130$	−7.06256	−0.619427
$131$	12.4775	1.09016	0.545082	−	0.838383i	$-0.316499\pi$
$131$	12.4775	1.09016	0.545082	+	0.838383i	$0.316499\pi$
$132$	−1.00000	−0.0870388
$133$	33.2831	2.88601
$134$	−1.68123	−0.145236
$135$	−1.37198	−0.118081
$136$	−4.20093	−0.360227
$137$	9.74306	0.832405	0.416203	−	0.909272i	$-0.363361\pi$
$137$	9.74306	0.832405	0.416203	+	0.909272i	$0.363361\pi$
$138$	−4.25414	−0.362136
$139$	8.79627	0.746090	0.373045	−	0.927813i	$-0.378314\pi$
$139$	8.79627	0.746090	0.373045	+	0.927813i	$0.378314\pi$
$140$	5.80842	0.490901
$141$	−5.37108	−0.452326
$142$	6.54477	0.549225
$143$	−5.14772	−0.430474
$144$	1.00000	0.0833333
$145$	1.41682	0.117660
$146$	−10.8805	−0.900477
$147$	−10.9235	−0.900952
$148$	−1.57555	−0.129509
$149$	−3.91484	−0.320716	−0.160358	−	0.987059i	$-0.551265\pi$
$149$	−3.91484	−0.320716	−0.160358	+	0.987059i	$0.551265\pi$
$150$	3.11767	0.254557
$151$	16.4019	1.33476	0.667382	−	0.744716i	$-0.267415\pi$
$151$	16.4019	1.33476	0.667382	+	0.744716i	$0.267415\pi$
$152$	7.86163	0.637663
$153$	−4.20093	−0.339625
$154$	4.23361	0.341154
$155$	6.55221	0.526286
$156$	5.14772	0.412147
$157$	−7.43454	−0.593341	−0.296670	−	0.954980i	$-0.595876\pi$
$157$	−7.43454	−0.593341	−0.296670	+	0.954980i	$0.595876\pi$
$158$	3.88142	0.308790
$159$	6.73278	0.533944
$160$	1.37198	0.108464
$161$	18.0104	1.41941
$162$	1.00000	0.0785674
$163$	−14.4138	−1.12898	−0.564490	−	0.825440i	$-0.690927\pi$
$163$	−14.4138	−1.12898	−0.564490	+	0.825440i	$0.690927\pi$
$164$	10.4973	0.819699
$165$	−1.37198	−0.106808
$166$	−11.0919	−0.860896
$167$	5.98882	0.463429	0.231715	−	0.972784i	$-0.425566\pi$
$167$	5.98882	0.463429	0.231715	+	0.972784i	$0.425566\pi$
$168$	−4.23361	−0.326630
$169$	13.4990	1.03838
$170$	−5.76358	−0.442047
$171$	7.86163	0.601194
$172$	−1.91411	−0.145949
$173$	−11.4999	−0.874322	−0.437161	−	0.899383i	$-0.644016\pi$
$173$	−11.4999	−0.874322	−0.437161	+	0.899383i	$0.644016\pi$
$174$	−1.03268	−0.0782875
$175$	−13.1990	−0.997752
$176$	1.00000	0.0753778
$177$	−6.26365	−0.470805
$178$	−6.47674	−0.485452
$179$	−5.42328	−0.405355	−0.202678	−	0.979246i	$-0.564964\pi$
$179$	−5.42328	−0.405355	−0.202678	+	0.979246i	$0.564964\pi$
$180$	1.37198	0.102261
$181$	3.53259	0.262575	0.131288	−	0.991344i	$-0.458089\pi$
$181$	3.53259	0.262575	0.131288	+	0.991344i	$0.458089\pi$
$182$	−21.7934	−1.61544
$183$	−1.00000	−0.0739221
$184$	4.25414	0.313619
$185$	−2.16161	−0.158925
$186$	−4.77574	−0.350174
$187$	−4.20093	−0.307202
$188$	5.37108	0.391726
$189$	−4.23361	−0.307950
$190$	10.7860	0.782498
$191$	9.00669	0.651701	0.325850	−	0.945421i	$-0.394349\pi$
$191$	9.00669	0.651701	0.325850	+	0.945421i	$0.394349\pi$
$192$	−1.00000	−0.0721688
$193$	−12.8358	−0.923943	−0.461972	−	0.886895i	$-0.652858\pi$
$193$	−12.8358	−0.923943	−0.461972	+	0.886895i	$0.652858\pi$
$194$	3.40393	0.244388
$195$	7.06256	0.505760
$196$	10.9235	0.780247
$197$	−1.65616	−0.117996	−0.0589982	−	0.998258i	$-0.518791\pi$
$197$	−1.65616	−0.117996	−0.0589982	+	0.998258i	$0.518791\pi$
$198$	1.00000	0.0710669
$199$	2.28609	0.162056	0.0810282	−	0.996712i	$-0.474180\pi$
$199$	2.28609	0.162056	0.0810282	+	0.996712i	$0.474180\pi$
$200$	−3.11767	−0.220453
$201$	1.68123	0.118585
$202$	4.23552	0.298010
$203$	4.37198	0.306853
$204$	4.20093	0.294124
$205$	14.4020	1.00588
$206$	−9.15036	−0.637536
$207$	4.25414	0.295683
$208$	−5.14772	−0.356930
$209$	7.86163	0.543800
$210$	−5.80842	−0.400819
$211$	9.11501	0.627503	0.313752	−	0.949505i	$-0.398414\pi$
$211$	9.11501	0.627503	0.313752	+	0.949505i	$0.398414\pi$
$212$	−6.73278	−0.462409
$213$	−6.54477	−0.448440
$214$	2.92700	0.200085
$215$	−2.62611	−0.179100
$216$	−1.00000	−0.0680414
$217$	20.2186	1.37253
$218$	−12.3589	−0.837050
$219$	10.8805	0.735236
$220$	1.37198	0.0924988
$221$	21.6252	1.45467
$222$	1.57555	0.105744
$223$	−22.5214	−1.50815	−0.754073	−	0.656791i	$-0.771913\pi$
$223$	−22.5214	−1.50815	−0.754073	+	0.656791i	$0.771913\pi$
$224$	4.23361	0.282870
$225$	−3.11767	−0.207845
$226$	11.7531	0.781807
$227$	−7.33837	−0.487065	−0.243532	−	0.969893i	$-0.578306\pi$
$227$	−7.33837	−0.487065	−0.243532	+	0.969893i	$0.578306\pi$
$228$	−7.86163	−0.520649
$229$	−8.62429	−0.569909	−0.284955	−	0.958541i	$-0.591979\pi$
$229$	−8.62429	−0.569909	−0.284955	+	0.958541i	$0.591979\pi$
$230$	5.83658	0.384853
$231$	−4.23361	−0.278551
$232$	1.03268	0.0677990
$233$	−25.8674	−1.69463	−0.847315	−	0.531090i	$-0.821783\pi$
$233$	−25.8674	−1.69463	−0.847315	+	0.531090i	$0.821783\pi$
$234$	−5.14772	−0.336517
$235$	7.36900	0.480701
$236$	6.26365	0.407729
$237$	−3.88142	−0.252126
$238$	−17.7851	−1.15284
$239$	−9.94325	−0.643175	−0.321588	−	0.946880i	$-0.604216\pi$
$239$	−9.94325	−0.643175	−0.321588	+	0.946880i	$0.604216\pi$
$240$	−1.37198	−0.0885608
$241$	19.1681	1.23472	0.617362	−	0.786679i	$-0.288201\pi$
$241$	19.1681	1.23472	0.617362	+	0.786679i	$0.288201\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	1.00000	0.0640184
$245$	14.9868	0.957468
$246$	−10.4973	−0.669281
$247$	−40.4695	−2.57501
$248$	4.77574	0.303260
$249$	11.0919	0.702919
$250$	−11.1373	−0.704383
$251$	24.0272	1.51658	0.758292	−	0.651915i	$-0.226034\pi$
$251$	24.0272	1.51658	0.758292	+	0.651915i	$0.226034\pi$
$252$	4.23361	0.266692
$253$	4.25414	0.267455
$254$	3.52234	0.221011
$255$	5.76358	0.360930
$256$	1.00000	0.0625000
$257$	16.6553	1.03893	0.519463	−	0.854493i	$-0.326132\pi$
$257$	16.6553	1.03893	0.519463	+	0.854493i	$0.326132\pi$
$258$	1.91411	0.119167
$259$	−6.67025	−0.414469
$260$	−7.06256	−0.438001
$261$	1.03268	0.0639215
$262$	12.4775	0.770862
$263$	29.6338	1.82730	0.913649	−	0.406503i	$-0.133252\pi$
$263$	29.6338	1.82730	0.913649	+	0.406503i	$0.133252\pi$
$264$	−1.00000	−0.0615457
$265$	−9.23723	−0.567439
$266$	33.2831	2.04072
$267$	6.47674	0.396370
$268$	−1.68123	−0.102697
$269$	29.3663	1.79050	0.895249	−	0.445567i	$-0.146998\pi$
$269$	29.3663	1.79050	0.895249	+	0.445567i	$0.146998\pi$
$270$	−1.37198	−0.0834960
$271$	−9.74553	−0.591999	−0.295999	−	0.955188i	$-0.595653\pi$
$271$	−9.74553	−0.591999	−0.295999	+	0.955188i	$0.595653\pi$
$272$	−4.20093	−0.254719
$273$	21.7934	1.31900
$274$	9.74306	0.588600
$275$	−3.11767	−0.188003
$276$	−4.25414	−0.256069
$277$	6.47938	0.389308	0.194654	−	0.980872i	$-0.437642\pi$
$277$	6.47938	0.389308	0.194654	+	0.980872i	$0.437642\pi$
$278$	8.79627	0.527565
$279$	4.77574	0.285916
$280$	5.80842	0.347120
$281$	−7.33837	−0.437770	−0.218885	−	0.975751i	$-0.570242\pi$
$281$	−7.33837	−0.437770	−0.218885	+	0.975751i	$0.570242\pi$
$282$	−5.37108	−0.319843
$283$	8.15533	0.484784	0.242392	−	0.970178i	$-0.422068\pi$
$283$	8.15533	0.484784	0.242392	+	0.970178i	$0.422068\pi$
$284$	6.54477	0.388361
$285$	−10.7860	−0.638907
$286$	−5.14772	−0.304391
$287$	44.4413	2.62329
$288$	1.00000	0.0589256
$289$	0.647790	0.0381053
$290$	1.41682	0.0831985
$291$	−3.40393	−0.199542
$292$	−10.8805	−0.636733
$293$	−13.0151	−0.760348	−0.380174	−	0.924915i	$-0.624136\pi$
$293$	−13.0151	−0.760348	−0.380174	+	0.924915i	$0.624136\pi$
$294$	−10.9235	−0.637069
$295$	8.59360	0.500339
$296$	−1.57555	−0.0915767
$297$	−1.00000	−0.0580259
$298$	−3.91484	−0.226781
$299$	−21.8991	−1.26646
$300$	3.11767	0.179999
$301$	−8.10359	−0.467083
$302$	16.4019	0.943821
$303$	−4.23552	−0.243324
$304$	7.86163	0.450896
$305$	1.37198	0.0785593
$306$	−4.20093	−0.240151
$307$	−11.2833	−0.643971	−0.321985	−	0.946745i	$-0.604350\pi$
$307$	−11.2833	−0.643971	−0.321985	+	0.946745i	$0.604350\pi$
$308$	4.23361	0.241232
$309$	9.15036	0.520546
$310$	6.55221	0.372141
$311$	19.9457	1.13102	0.565508	−	0.824743i	$-0.308680\pi$
$311$	19.9457	1.13102	0.565508	+	0.824743i	$0.308680\pi$
$312$	5.14772	0.291432
$313$	−16.9421	−0.957623	−0.478811	−	0.877918i	$-0.658932\pi$
$313$	−16.9421	−0.957623	−0.478811	+	0.877918i	$0.658932\pi$
$314$	−7.43454	−0.419555
$315$	5.80842	0.327268
$316$	3.88142	0.218347
$317$	20.4517	1.14868	0.574340	−	0.818617i	$-0.305259\pi$
$317$	20.4517	1.14868	0.574340	+	0.818617i	$0.305259\pi$
$318$	6.73278	0.377556
$319$	1.03268	0.0578192
$320$	1.37198	0.0766959
$321$	−2.92700	−0.163369
$322$	18.0104	1.00368
$323$	−33.0261	−1.83762
$324$	1.00000	0.0555556
$325$	16.0489	0.890233
$326$	−14.4138	−0.798309
$327$	12.3589	0.683449
$328$	10.4973	0.579614
$329$	22.7391	1.25364
$330$	−1.37198	−0.0755249
$331$	−0.249332	−0.0137045	−0.00685227	−	0.999977i	$-0.502181\pi$
$331$	−0.249332	−0.0137045	−0.00685227	+	0.999977i	$0.502181\pi$
$332$	−11.0919	−0.608745
$333$	−1.57555	−0.0863394
$334$	5.98882	0.327694
$335$	−2.30661	−0.126024
$336$	−4.23361	−0.230962
$337$	−17.9449	−0.977520	−0.488760	−	0.872418i	$-0.662551\pi$
$337$	−17.9449	−0.977520	−0.488760	+	0.872418i	$0.662551\pi$
$338$	13.4990	0.734249
$339$	−11.7531	−0.638343
$340$	−5.76358	−0.312574
$341$	4.77574	0.258621
$342$	7.86163	0.425108
$343$	16.6104	0.896877
$344$	−1.91411	−0.103202
$345$	−5.83658	−0.314231
$346$	−11.4999	−0.618239
$347$	−14.2654	−0.765805	−0.382903	−	0.923789i	$-0.625076\pi$
$347$	−14.2654	−0.765805	−0.382903	+	0.923789i	$0.625076\pi$
$348$	−1.03268	−0.0553576
$349$	29.6224	1.58565	0.792825	−	0.609449i	$-0.208609\pi$
$349$	29.6224	1.58565	0.792825	+	0.609449i	$0.208609\pi$
$350$	−13.1990	−0.705517
$351$	5.14772	0.274765
$352$	1.00000	0.0533002
$353$	−9.04774	−0.481563	−0.240781	−	0.970579i	$-0.577404\pi$
$353$	−9.04774	−0.481563	−0.240781	+	0.970579i	$0.577404\pi$
$354$	−6.26365	−0.332909
$355$	8.97928	0.476571
$356$	−6.47674	−0.343266
$357$	17.7851	0.941287
$358$	−5.42328	−0.286629
$359$	3.67859	0.194149	0.0970743	−	0.995277i	$-0.469052\pi$
$359$	3.67859	0.194149	0.0970743	+	0.995277i	$0.469052\pi$
$360$	1.37198	0.0723096
$361$	42.8053	2.25291
$362$	3.53259	0.185669
$363$	−1.00000	−0.0524864
$364$	−21.7934	−1.14229
$365$	−14.9278	−0.781357
$366$	−1.00000	−0.0522708
$367$	−23.6967	−1.23696	−0.618480	−	0.785801i	$-0.712251\pi$
$367$	−23.6967	−1.23696	−0.618480	+	0.785801i	$0.712251\pi$
$368$	4.25414	0.221762
$369$	10.4973	0.546466
$370$	−2.16161	−0.112377
$371$	−28.5040	−1.47985
$372$	−4.77574	−0.247611
$373$	18.1335	0.938916	0.469458	−	0.882955i	$-0.344449\pi$
$373$	18.1335	0.938916	0.469458	+	0.882955i	$0.344449\pi$
$374$	−4.20093	−0.217225
$375$	11.1373	0.575126
$376$	5.37108	0.276992
$377$	−5.31596	−0.273786
$378$	−4.23361	−0.217753
$379$	−33.4264	−1.71700	−0.858500	−	0.512813i	$-0.828603\pi$
$379$	−33.4264	−1.71700	−0.858500	+	0.512813i	$0.828603\pi$
$380$	10.7860	0.553310
$381$	−3.52234	−0.180455
$382$	9.00669	0.460822
$383$	−6.52807	−0.333569	−0.166784	−	0.985993i	$-0.553338\pi$
$383$	−6.52807	−0.333569	−0.166784	+	0.985993i	$0.553338\pi$
$384$	−1.00000	−0.0510310
$385$	5.80842	0.296025
$386$	−12.8358	−0.653326
$387$	−1.91411	−0.0972996
$388$	3.40393	0.172808
$389$	−23.6749	−1.20036	−0.600181	−	0.799864i	$-0.704905\pi$
$389$	−23.6749	−1.20036	−0.600181	+	0.799864i	$0.704905\pi$
$390$	7.06256	0.357627
$391$	−17.8713	−0.903791
$392$	10.9235	0.551718
$393$	−12.4775	−0.629406
$394$	−1.65616	−0.0834361
$395$	5.32523	0.267941
$396$	1.00000	0.0502519
$397$	30.8692	1.54928	0.774639	−	0.632403i	$-0.217931\pi$
$397$	30.8692	1.54928	0.774639	+	0.632403i	$0.217931\pi$
$398$	2.28609	0.114591
$399$	−33.2831	−1.66624
$400$	−3.11767	−0.155884
$401$	−21.8082	−1.08905	−0.544526	−	0.838744i	$-0.683290\pi$
$401$	−21.8082	−1.08905	−0.544526	+	0.838744i	$0.683290\pi$
$402$	1.68123	0.0838522
$403$	−24.5842	−1.22462
$404$	4.23552	0.210725
$405$	1.37198	0.0681742
$406$	4.37198	0.216978
$407$	−1.57555	−0.0780969
$408$	4.20093	0.207977
$409$	−2.97037	−0.146875	−0.0734377	−	0.997300i	$-0.523397\pi$
$409$	−2.97037	−0.146875	−0.0734377	+	0.997300i	$0.523397\pi$
$410$	14.4020	0.711265
$411$	−9.74306	−0.480590
$412$	−9.15036	−0.450806
$413$	26.5179	1.30486
$414$	4.25414	0.209079
$415$	−15.2178	−0.747013
$416$	−5.14772	−0.252388
$417$	−8.79627	−0.430755
$418$	7.86163	0.384525
$419$	7.03252	0.343561	0.171780	−	0.985135i	$-0.445048\pi$
$419$	7.03252	0.343561	0.171780	+	0.985135i	$0.445048\pi$
$420$	−5.80842	−0.283422
$421$	21.0069	1.02381	0.511906	−	0.859041i	$-0.328939\pi$
$421$	21.0069	1.02381	0.511906	+	0.859041i	$0.328939\pi$
$422$	9.11501	0.443712
$423$	5.37108	0.261151
$424$	−6.73278	−0.326973
$425$	13.0971	0.635304
$426$	−6.54477	−0.317095
$427$	4.23361	0.204879
$428$	2.92700	0.141482
$429$	5.14772	0.248534
$430$	−2.62611	−0.126643
$431$	−35.1204	−1.69169	−0.845845	−	0.533428i	$-0.820903\pi$
$431$	−35.1204	−1.69169	−0.845845	+	0.533428i	$0.820903\pi$
$432$	−1.00000	−0.0481125
$433$	31.6740	1.52216	0.761079	−	0.648660i	$-0.224670\pi$
$433$	31.6740	1.52216	0.761079	+	0.648660i	$0.224670\pi$
$434$	20.2186	0.970525
$435$	−1.41682	−0.0679313
$436$	−12.3589	−0.591884
$437$	33.4445	1.59987
$438$	10.8805	0.519890
$439$	−40.4881	−1.93239	−0.966195	−	0.257811i	$-0.916999\pi$
$439$	−40.4881	−1.93239	−0.966195	+	0.257811i	$0.916999\pi$
$440$	1.37198	0.0654065
$441$	10.9235	0.520165
$442$	21.6252	1.02861
$443$	−15.1838	−0.721403	−0.360701	−	0.932681i	$-0.617463\pi$
$443$	−15.1838	−0.721403	−0.360701	+	0.932681i	$0.617463\pi$
$444$	1.57555	0.0747721
$445$	−8.88595	−0.421234
$446$	−22.5214	−1.06642
$447$	3.91484	0.185166
$448$	4.23361	0.200019
$449$	−23.4850	−1.10833	−0.554163	−	0.832408i	$-0.686962\pi$
$449$	−23.4850	−1.10833	−0.554163	+	0.832408i	$0.686962\pi$
$450$	−3.11767	−0.146969
$451$	10.4973	0.494297
$452$	11.7531	0.552821
$453$	−16.4019	−0.770626
$454$	−7.33837	−0.344407
$455$	−29.9001	−1.40174
$456$	−7.86163	−0.368155
$457$	−38.8252	−1.81617	−0.908084	−	0.418788i	$-0.862455\pi$
$457$	−38.8252	−1.81617	−0.908084	+	0.418788i	$0.862455\pi$
$458$	−8.62429	−0.402987
$459$	4.20093	0.196082
$460$	5.83658	0.272132
$461$	−36.0486	−1.67895	−0.839474	−	0.543399i	$-0.817137\pi$
$461$	−36.0486	−1.67895	−0.839474	+	0.543399i	$0.817137\pi$
$462$	−4.23361	−0.196965
$463$	−12.2291	−0.568333	−0.284166	−	0.958775i	$-0.591717\pi$
$463$	−12.2291	−0.568333	−0.284166	+	0.958775i	$0.591717\pi$
$464$	1.03268	0.0479411
$465$	−6.55221	−0.303852
$466$	−25.8674	−1.19828
$467$	−1.45481	−0.0673204	−0.0336602	−	0.999433i	$-0.510716\pi$
$467$	−1.45481	−0.0673204	−0.0336602	+	0.999433i	$0.510716\pi$
$468$	−5.14772	−0.237953
$469$	−7.11767	−0.328664
$470$	7.36900	0.339907
$471$	7.43454	0.342565
$472$	6.26365	0.288308
$473$	−1.91411	−0.0880108
$474$	−3.88142	−0.178280
$475$	−24.5100	−1.12460
$476$	−17.7851	−0.815178
$477$	−6.73278	−0.308273
$478$	−9.94325	−0.454794
$479$	26.4079	1.20661	0.603304	−	0.797511i	$-0.293850\pi$
$479$	26.4079	1.20661	0.603304	+	0.797511i	$0.293850\pi$
$480$	−1.37198	−0.0626220
$481$	8.11046	0.369805
$482$	19.1681	0.873082
$483$	−18.0104	−0.819500
$484$	1.00000	0.0454545
$485$	4.67012	0.212059
$486$	−1.00000	−0.0453609
$487$	37.6487	1.70603	0.853013	−	0.521890i	$-0.174773\pi$
$487$	37.6487	1.70603	0.853013	+	0.521890i	$0.174773\pi$
$488$	1.00000	0.0452679
$489$	14.4138	0.651817
$490$	14.9868	0.677032
$491$	11.3718	0.513202	0.256601	−	0.966517i	$-0.417397\pi$
$491$	11.3718	0.513202	0.256601	+	0.966517i	$0.417397\pi$
$492$	−10.4973	−0.473253
$493$	−4.33823	−0.195384
$494$	−40.4695	−1.82081
$495$	1.37198	0.0616659
$496$	4.77574	0.214437
$497$	27.7080	1.24287
$498$	11.0919	0.497039
$499$	−33.6794	−1.50770	−0.753849	−	0.657048i	$-0.771805\pi$
$499$	−33.6794	−1.50770	−0.753849	+	0.657048i	$0.771805\pi$
$500$	−11.1373	−0.498074
$501$	−5.98882	−0.267561
$502$	24.0272	1.07239
$503$	−39.3821	−1.75596	−0.877981	−	0.478695i	$-0.841110\pi$
$503$	−39.3821	−1.75596	−0.877981	+	0.478695i	$0.841110\pi$
$504$	4.23361	0.188580
$505$	5.81104	0.258588
$506$	4.25414	0.189119
$507$	−13.4990	−0.599512
$508$	3.52234	0.156278
$509$	−29.0915	−1.28946	−0.644729	−	0.764411i	$-0.723030\pi$
$509$	−29.0915	−1.28946	−0.644729	+	0.764411i	$0.723030\pi$
$510$	5.76358	0.255216
$511$	−46.0638	−2.03774
$512$	1.00000	0.0441942
$513$	−7.86163	−0.347100
$514$	16.6553	0.734632
$515$	−12.5541	−0.553200
$516$	1.91411	0.0842639
$517$	5.37108	0.236220
$518$	−6.67025	−0.293074
$519$	11.4999	0.504790
$520$	−7.06256	−0.309714
$521$	−6.42443	−0.281459	−0.140730	−	0.990048i	$-0.544945\pi$
$521$	−6.42443	−0.281459	−0.140730	+	0.990048i	$0.544945\pi$
$522$	1.03268	0.0451993
$523$	−0.372879	−0.0163049	−0.00815244	−	0.999967i	$-0.502595\pi$
$523$	−0.372879	−0.0163049	−0.00815244	+	0.999967i	$0.502595\pi$
$524$	12.4775	0.545082
$525$	13.1990	0.576052
$526$	29.6338	1.29210
$527$	−20.0625	−0.873938
$528$	−1.00000	−0.0435194
$529$	−4.90232	−0.213145
$530$	−9.23723	−0.401240
$531$	6.26365	0.271819
$532$	33.2831	1.44300
$533$	−54.0370	−2.34060
$534$	6.47674	0.280276
$535$	4.01578	0.173617
$536$	−1.68123	−0.0726181
$537$	5.42328	0.234032
$538$	29.3663	1.26607
$539$	10.9235	0.470507
$540$	−1.37198	−0.0590406
$541$	−43.5028	−1.87033	−0.935165	−	0.354212i	$-0.884749\pi$
$541$	−43.5028	−1.87033	−0.935165	+	0.354212i	$0.884749\pi$
$542$	−9.74553	−0.418606
$543$	−3.53259	−0.151598
$544$	−4.20093	−0.180113
$545$	−16.9561	−0.726321
$546$	21.7934	0.932673
$547$	−29.0600	−1.24252	−0.621258	−	0.783606i	$-0.713378\pi$
$547$	−29.0600	−1.24252	−0.621258	+	0.783606i	$0.713378\pi$
$548$	9.74306	0.416203
$549$	1.00000	0.0426790
$550$	−3.11767	−0.132938
$551$	8.11858	0.345863
$552$	−4.25414	−0.181068
$553$	16.4324	0.698778
$554$	6.47938	0.275282
$555$	2.16161	0.0917554
$556$	8.79627	0.373045
$557$	21.4786	0.910079	0.455040	−	0.890471i	$-0.349625\pi$
$557$	21.4786	0.910079	0.455040	+	0.890471i	$0.349625\pi$
$558$	4.77574	0.202173
$559$	9.85329	0.416750
$560$	5.80842	0.245451
$561$	4.20093	0.177363
$562$	−7.33837	−0.309550
$563$	43.0178	1.81298	0.906491	−	0.422225i	$-0.138751\pi$
$563$	43.0178	1.81298	0.906491	+	0.422225i	$0.138751\pi$
$564$	−5.37108	−0.226163
$565$	16.1251	0.678386
$566$	8.15533	0.342794
$567$	4.23361	0.177795
$568$	6.54477	0.274612
$569$	24.3835	1.02221	0.511105	−	0.859519i	$-0.329236\pi$
$569$	24.3835	1.02221	0.511105	+	0.859519i	$0.329236\pi$
$570$	−10.7860	−0.451775
$571$	−3.33329	−0.139494	−0.0697470	−	0.997565i	$-0.522219\pi$
$571$	−3.33329	−0.139494	−0.0697470	+	0.997565i	$0.522219\pi$
$572$	−5.14772	−0.215237
$573$	−9.00669	−0.376260
$574$	44.4413	1.85495
$575$	−13.2630	−0.553106
$576$	1.00000	0.0416667
$577$	−24.7809	−1.03164	−0.515820	−	0.856697i	$-0.672513\pi$
$577$	−24.7809	−1.03164	−0.515820	+	0.856697i	$0.672513\pi$
$578$	0.647790	0.0269445
$579$	12.8358	0.533439
$580$	1.41682	0.0588302
$581$	−46.9587	−1.94817
$582$	−3.40393	−0.141097
$583$	−6.73278	−0.278843
$584$	−10.8805	−0.450238
$585$	−7.06256	−0.292001
$586$	−13.0151	−0.537647
$587$	−11.4748	−0.473617	−0.236809	−	0.971556i	$-0.576101\pi$
$587$	−11.4748	−0.473617	−0.236809	+	0.971556i	$0.576101\pi$
$588$	−10.9235	−0.450476
$589$	37.5451	1.54702
$590$	8.59360	0.353793
$591$	1.65616	0.0681253
$592$	−1.57555	−0.0647545
$593$	25.2079	1.03516	0.517582	−	0.855634i	$-0.326832\pi$
$593$	25.2079	1.03516	0.517582	+	0.855634i	$0.326832\pi$
$594$	−1.00000	−0.0410305
$595$	−24.4008	−1.00033
$596$	−3.91484	−0.160358
$597$	−2.28609	−0.0935633
$598$	−21.8991	−0.895521
$599$	−45.5692	−1.86191	−0.930953	−	0.365139i	$-0.881021\pi$
$599$	−45.5692	−1.86191	−0.930953	+	0.365139i	$0.881021\pi$
$600$	3.11767	0.127279
$601$	−32.5731	−1.32869	−0.664343	−	0.747428i	$-0.731289\pi$
$601$	−32.5731	−1.32869	−0.664343	+	0.747428i	$0.731289\pi$
$602$	−8.10359	−0.330278
$603$	−1.68123	−0.0684650
$604$	16.4019	0.667382
$605$	1.37198	0.0557789
$606$	−4.23552	−0.172056
$607$	19.1588	0.777632	0.388816	−	0.921315i	$-0.372884\pi$
$607$	19.1588	0.777632	0.388816	+	0.921315i	$0.372884\pi$
$608$	7.86163	0.318831
$609$	−4.37198	−0.177162
$610$	1.37198	0.0555498
$611$	−27.6488	−1.11855
$612$	−4.20093	−0.169812
$613$	−0.530307	−0.0214189	−0.0107094	−	0.999943i	$-0.503409\pi$
$613$	−0.530307	−0.0214189	−0.0107094	+	0.999943i	$0.503409\pi$
$614$	−11.2833	−0.455356
$615$	−14.4020	−0.580746
$616$	4.23361	0.170577
$617$	41.3131	1.66320	0.831602	−	0.555373i	$-0.187424\pi$
$617$	41.3131	1.66320	0.831602	+	0.555373i	$0.187424\pi$
$618$	9.15036	0.368081
$619$	−15.9072	−0.639363	−0.319682	−	0.947525i	$-0.603576\pi$
$619$	−15.9072	−0.639363	−0.319682	+	0.947525i	$0.603576\pi$
$620$	6.55221	0.263143
$621$	−4.25414	−0.170713
$622$	19.9457	0.799750
$623$	−27.4200	−1.09856
$624$	5.14772	0.206074
$625$	0.308270	0.0123308
$626$	−16.9421	−0.677142
$627$	−7.86163	−0.313963
$628$	−7.43454	−0.296670
$629$	6.61875	0.263907
$630$	5.80842	0.231413
$631$	−6.87371	−0.273638	−0.136819	−	0.990596i	$-0.543688\pi$
$631$	−6.87371	−0.273638	−0.136819	+	0.990596i	$0.543688\pi$
$632$	3.88142	0.154395
$633$	−9.11501	−0.362289
$634$	20.4517	0.812239
$635$	4.83257	0.191775
$636$	6.73278	0.266972
$637$	−56.2309	−2.22795
$638$	1.03268	0.0408843
$639$	6.54477	0.258907
$640$	1.37198	0.0542322
$641$	−2.09145	−0.0826074	−0.0413037	−	0.999147i	$-0.513151\pi$
$641$	−2.09145	−0.0826074	−0.0413037	+	0.999147i	$0.513151\pi$
$642$	−2.92700	−0.115519
$643$	−30.6330	−1.20805	−0.604024	−	0.796966i	$-0.706437\pi$
$643$	−30.6330	−1.20805	−0.604024	+	0.796966i	$0.706437\pi$
$644$	18.0104	0.709707
$645$	2.62611	0.103403
$646$	−33.0261	−1.29940
$647$	43.8932	1.72562	0.862810	−	0.505528i	$-0.168702\pi$
$647$	43.8932	1.72562	0.862810	+	0.505528i	$0.168702\pi$
$648$	1.00000	0.0392837
$649$	6.26365	0.245870
$650$	16.0489	0.629490
$651$	−20.2186	−0.792430
$652$	−14.4138	−0.564490
$653$	−31.4024	−1.22887	−0.614436	−	0.788967i	$-0.710616\pi$
$653$	−31.4024	−1.22887	−0.614436	+	0.788967i	$0.710616\pi$
$654$	12.3589	0.483271
$655$	17.1189	0.668889
$656$	10.4973	0.409849
$657$	−10.8805	−0.424489
$658$	22.7391	0.886461
$659$	14.5332	0.566131	0.283066	−	0.959101i	$-0.408649\pi$
$659$	14.5332	0.566131	0.283066	+	0.959101i	$0.408649\pi$
$660$	−1.37198	−0.0534042
$661$	−35.9503	−1.39831	−0.699153	−	0.714972i	$-0.746439\pi$
$661$	−35.9503	−1.39831	−0.699153	+	0.714972i	$0.746439\pi$
$662$	−0.249332	−0.00969058
$663$	−21.6252	−0.839853
$664$	−11.0919	−0.430448
$665$	45.6637	1.77076
$666$	−1.57555	−0.0610512
$667$	4.39318	0.170104
$668$	5.98882	0.231715
$669$	22.5214	0.870728
$670$	−2.30661	−0.0891122
$671$	1.00000	0.0386046
$672$	−4.23361	−0.163315
$673$	29.3361	1.13082	0.565412	−	0.824808i	$-0.308717\pi$
$673$	29.3361	1.13082	0.565412	+	0.824808i	$0.308717\pi$
$674$	−17.9449	−0.691211
$675$	3.11767	0.119999
$676$	13.4990	0.519192
$677$	7.20277	0.276825	0.138412	−	0.990375i	$-0.455800\pi$
$677$	7.20277	0.276825	0.138412	+	0.990375i	$0.455800\pi$
$678$	−11.7531	−0.451377
$679$	14.4109	0.553040
$680$	−5.76358	−0.221023
$681$	7.33837	0.281207
$682$	4.77574	0.182873
$683$	−7.64473	−0.292518	−0.146259	−	0.989246i	$-0.546723\pi$
$683$	−7.64473	−0.292518	−0.146259	+	0.989246i	$0.546723\pi$
$684$	7.86163	0.300597
$685$	13.3673	0.510737
$686$	16.6104	0.634188
$687$	8.62429	0.329037
$688$	−1.91411	−0.0729747
$689$	34.6585	1.32038
$690$	−5.83658	−0.222195
$691$	11.4529	0.435687	0.217844	−	0.975984i	$-0.430098\pi$
$691$	11.4529	0.435687	0.217844	+	0.975984i	$0.430098\pi$
$692$	−11.4999	−0.437161
$693$	4.23361	0.160822
$694$	−14.2654	−0.541506
$695$	12.0683	0.457776
$696$	−1.03268	−0.0391438
$697$	−44.0982	−1.67034
$698$	29.6224	1.12122
$699$	25.8674	0.978396
$700$	−13.1990	−0.498876
$701$	−21.3565	−0.806625	−0.403312	−	0.915062i	$-0.632141\pi$
$701$	−21.3565	−0.806625	−0.403312	+	0.915062i	$0.632141\pi$
$702$	5.14772	0.194288
$703$	−12.3864	−0.467160
$704$	1.00000	0.0376889
$705$	−7.36900	−0.277533
$706$	−9.04774	−0.340516
$707$	17.9315	0.674385
$708$	−6.26365	−0.235403
$709$	2.01084	0.0755188	0.0377594	−	0.999287i	$-0.487978\pi$
$709$	2.01084	0.0755188	0.0377594	+	0.999287i	$0.487978\pi$
$710$	8.97928	0.336986
$711$	3.88142	0.145565
$712$	−6.47674	−0.242726
$713$	20.3166	0.760864
$714$	17.7851	0.665590
$715$	−7.06256	−0.264125
$716$	−5.42328	−0.202678
$717$	9.94325	0.371337
$718$	3.67859	0.137284
$719$	−9.07537	−0.338454	−0.169227	−	0.985577i	$-0.554127\pi$
$719$	−9.07537	−0.338454	−0.169227	+	0.985577i	$0.554127\pi$
$720$	1.37198	0.0511306
$721$	−38.7391	−1.44272
$722$	42.8053	1.59305
$723$	−19.1681	−0.712868
$724$	3.53259	0.131288
$725$	−3.21957	−0.119572
$726$	−1.00000	−0.0371135
$727$	23.1483	0.858523	0.429262	−	0.903180i	$-0.358774\pi$
$727$	23.1483	0.858523	0.429262	+	0.903180i	$0.358774\pi$
$728$	−21.7934	−0.807718
$729$	1.00000	0.0370370
$730$	−14.9278	−0.552503
$731$	8.04103	0.297408
$732$	−1.00000	−0.0369611
$733$	−33.7428	−1.24632	−0.623159	−	0.782095i	$-0.714151\pi$
$733$	−33.7428	−1.24632	−0.623159	+	0.782095i	$0.714151\pi$
$734$	−23.6967	−0.874662
$735$	−14.9868	−0.552795
$736$	4.25414	0.156810
$737$	−1.68123	−0.0619289
$738$	10.4973	0.386410
$739$	25.4950	0.937850	0.468925	−	0.883238i	$-0.344642\pi$
$739$	25.4950	0.937850	0.468925	+	0.883238i	$0.344642\pi$
$740$	−2.16161	−0.0794625
$741$	40.4695	1.48668
$742$	−28.5040	−1.04641
$743$	−3.04377	−0.111665	−0.0558326	−	0.998440i	$-0.517781\pi$
$743$	−3.04377	−0.111665	−0.0558326	+	0.998440i	$0.517781\pi$
$744$	−4.77574	−0.175087
$745$	−5.37108	−0.196781
$746$	18.1335	0.663914
$747$	−11.0919	−0.405830
$748$	−4.20093	−0.153601
$749$	12.3918	0.452785
$750$	11.1373	0.406676
$751$	−43.5026	−1.58743	−0.793716	−	0.608289i	$-0.791856\pi$
$751$	−43.5026	−1.58743	−0.793716	+	0.608289i	$0.791856\pi$
$752$	5.37108	0.195863
$753$	−24.0272	−0.875600
$754$	−5.31596	−0.193596
$755$	22.5030	0.818968
$756$	−4.23361	−0.153975
$757$	−23.3141	−0.847364	−0.423682	−	0.905811i	$-0.639263\pi$
$757$	−23.3141	−0.847364	−0.423682	+	0.905811i	$0.639263\pi$
$758$	−33.4264	−1.21410
$759$	−4.25414	−0.154415
$760$	10.7860	0.391249
$761$	8.15963	0.295786	0.147893	−	0.989003i	$-0.452751\pi$
$761$	8.15963	0.295786	0.147893	+	0.989003i	$0.452751\pi$
$762$	−3.52234	−0.127601
$763$	−52.3228	−1.89421
$764$	9.00669	0.325850
$765$	−5.76358	−0.208383
$766$	−6.52807	−0.235869
$767$	−32.2435	−1.16425
$768$	−1.00000	−0.0360844
$769$	4.88931	0.176313	0.0881565	−	0.996107i	$-0.471902\pi$
$769$	4.88931	0.176313	0.0881565	+	0.996107i	$0.471902\pi$
$770$	5.80842	0.209321
$771$	−16.6553	−0.599824
$772$	−12.8358	−0.461972
$773$	21.5452	0.774926	0.387463	−	0.921885i	$-0.373352\pi$
$773$	21.5452	0.774926	0.387463	+	0.921885i	$0.373352\pi$
$774$	−1.91411	−0.0688012
$775$	−14.8892	−0.534836
$776$	3.40393	0.122194
$777$	6.67025	0.239294
$778$	−23.6749	−0.848785
$779$	82.5256	2.95679
$780$	7.06256	0.252880
$781$	6.54477	0.234190
$782$	−17.8713	−0.639077
$783$	−1.03268	−0.0369051
$784$	10.9235	0.390123
$785$	−10.2000	−0.364055
$786$	−12.4775	−0.445058
$787$	26.6115	0.948599	0.474300	−	0.880364i	$-0.342701\pi$
$787$	26.6115	0.948599	0.474300	+	0.880364i	$0.342701\pi$
$788$	−1.65616	−0.0589982
$789$	−29.6338	−1.05499
$790$	5.32523	0.189463
$791$	49.7582	1.76920
$792$	1.00000	0.0355335
$793$	−5.14772	−0.182801
$794$	30.8692	1.09551
$795$	9.23723	0.327611
$796$	2.28609	0.0810282
$797$	−29.1014	−1.03082	−0.515412	−	0.856943i	$-0.672361\pi$
$797$	−29.1014	−1.03082	−0.515412	+	0.856943i	$0.672361\pi$
$798$	−33.2831	−1.17821
$799$	−22.5635	−0.798240
$800$	−3.11767	−0.110226
$801$	−6.47674	−0.228844
$802$	−21.8082	−0.770075
$803$	−10.8805	−0.383965
$804$	1.68123	0.0592924
$805$	24.7098	0.870907
$806$	−24.5842	−0.865940
$807$	−29.3663	−1.03374
$808$	4.23552	0.149005
$809$	−20.9192	−0.735482	−0.367741	−	0.929928i	$-0.619869\pi$
$809$	−20.9192	−0.735482	−0.367741	+	0.929928i	$0.619869\pi$
$810$	1.37198	0.0482064
$811$	−18.9063	−0.663891	−0.331946	−	0.943299i	$-0.607705\pi$
$811$	−18.9063	−0.663891	−0.331946	+	0.943299i	$0.607705\pi$
$812$	4.37198	0.153426
$813$	9.74553	0.341791
$814$	−1.57555	−0.0552228
$815$	−19.7755	−0.692705
$816$	4.20093	0.147062
$817$	−15.0480	−0.526463
$818$	−2.97037	−0.103857
$819$	−21.7934	−0.761524
$820$	14.4020	0.502940
$821$	−19.4854	−0.680044	−0.340022	−	0.940418i	$-0.610434\pi$
$821$	−19.4854	−0.680044	−0.340022	+	0.940418i	$0.610434\pi$
$822$	−9.74306	−0.339828
$823$	54.3327	1.89392	0.946959	−	0.321355i	$-0.104138\pi$
$823$	54.3327	1.89392	0.946959	+	0.321355i	$0.104138\pi$
$824$	−9.15036	−0.318768
$825$	3.11767	0.108544
$826$	26.5179	0.922675
$827$	8.14663	0.283286	0.141643	−	0.989918i	$-0.454762\pi$
$827$	8.14663	0.283286	0.141643	+	0.989918i	$0.454762\pi$
$828$	4.25414	0.147841
$829$	17.5434	0.609306	0.304653	−	0.952463i	$-0.401459\pi$
$829$	17.5434	0.609306	0.304653	+	0.952463i	$0.401459\pi$
$830$	−15.2178	−0.528218
$831$	−6.47938	−0.224767
$832$	−5.14772	−0.178465
$833$	−45.8887	−1.58995
$834$	−8.79627	−0.304590
$835$	8.21654	0.284345
$836$	7.86163	0.271900
$837$	−4.77574	−0.165074
$838$	7.03252	0.242934
$839$	5.30881	0.183281	0.0916403	−	0.995792i	$-0.470789\pi$
$839$	5.30881	0.183281	0.0916403	+	0.995792i	$0.470789\pi$
$840$	−5.80842	−0.200410
$841$	−27.9336	−0.963226
$842$	21.0069	0.723945
$843$	7.33837	0.252747
$844$	9.11501	0.313752
$845$	18.5203	0.637119
$846$	5.37108	0.184661
$847$	4.23361	0.145469
$848$	−6.73278	−0.231205
$849$	−8.15533	−0.279890
$850$	13.0971	0.449228
$851$	−6.70259	−0.229762
$852$	−6.54477	−0.224220
$853$	−35.9407	−1.23059	−0.615294	−	0.788298i	$-0.710963\pi$
$853$	−35.9407	−1.23059	−0.615294	+	0.788298i	$0.710963\pi$
$854$	4.23361	0.144871
$855$	10.7860	0.368873
$856$	2.92700	0.100043
$857$	8.76815	0.299514	0.149757	−	0.988723i	$-0.452151\pi$
$857$	8.76815	0.299514	0.149757	+	0.988723i	$0.452151\pi$
$858$	5.14772	0.175740
$859$	−25.7471	−0.878481	−0.439241	−	0.898370i	$-0.644752\pi$
$859$	−25.7471	−0.878481	−0.439241	+	0.898370i	$0.644752\pi$
$860$	−2.62611	−0.0895498
$861$	−44.4413	−1.51456
$862$	−35.1204	−1.19621
$863$	−42.8809	−1.45968	−0.729841	−	0.683617i	$-0.760406\pi$
$863$	−42.8809	−1.45968	−0.729841	+	0.683617i	$0.760406\pi$
$864$	−1.00000	−0.0340207
$865$	−15.7776	−0.536455
$866$	31.6740	1.07633
$867$	−0.647790	−0.0220001
$868$	20.2186	0.686265
$869$	3.88142	0.131668
$870$	−1.41682	−0.0480347
$871$	8.65450	0.293247
$872$	−12.3589	−0.418525
$873$	3.40393	0.115206
$874$	33.4445	1.13128
$875$	−47.1509	−1.59399
$876$	10.8805	0.367618
$877$	−36.5467	−1.23410	−0.617048	−	0.786926i	$-0.711672\pi$
$877$	−36.5467	−1.23410	−0.617048	+	0.786926i	$0.711672\pi$
$878$	−40.4881	−1.36641
$879$	13.0151	0.438987
$880$	1.37198	0.0462494
$881$	24.7370	0.833411	0.416706	−	0.909041i	$-0.363185\pi$
$881$	24.7370	0.833411	0.416706	+	0.909041i	$0.363185\pi$
$882$	10.9235	0.367812
$883$	20.5683	0.692178	0.346089	−	0.938202i	$-0.387510\pi$
$883$	20.5683	0.692178	0.346089	+	0.938202i	$0.387510\pi$
$884$	21.6252	0.727334
$885$	−8.59360	−0.288871
$886$	−15.1838	−0.510109
$887$	44.6124	1.49794	0.748969	−	0.662606i	$-0.230549\pi$
$887$	44.6124	1.49794	0.748969	+	0.662606i	$0.230549\pi$
$888$	1.57555	0.0528718
$889$	14.9122	0.500139
$890$	−8.88595	−0.297858
$891$	1.00000	0.0335013
$892$	−22.5214	−0.754073
$893$	42.2254	1.41302
$894$	3.91484	0.130932
$895$	−7.44063	−0.248713
$896$	4.23361	0.141435
$897$	21.8991	0.731190
$898$	−23.4850	−0.783705
$899$	4.93183	0.164486
$900$	−3.11767	−0.103922
$901$	28.2839	0.942274
$902$	10.4973	0.349521
$903$	8.10359	0.269670
$904$	11.7531	0.390904
$905$	4.84663	0.161108
$906$	−16.4019	−0.544915
$907$	−27.3611	−0.908511	−0.454256	−	0.890871i	$-0.650095\pi$
$907$	−27.3611	−0.908511	−0.454256	+	0.890871i	$0.650095\pi$
$908$	−7.33837	−0.243532
$909$	4.23552	0.140483
$910$	−29.9001	−0.991179
$911$	14.4816	0.479796	0.239898	−	0.970798i	$-0.422886\pi$
$911$	14.4816	0.479796	0.239898	+	0.970798i	$0.422886\pi$
$912$	−7.86163	−0.260325
$913$	−11.0919	−0.367087
$914$	−38.8252	−1.28422
$915$	−1.37198	−0.0453562
$916$	−8.62429	−0.284955
$917$	52.8249	1.74443
$918$	4.20093	0.138651
$919$	−41.8457	−1.38036	−0.690182	−	0.723636i	$-0.742469\pi$
$919$	−41.8457	−1.38036	−0.690182	+	0.723636i	$0.742469\pi$
$920$	5.83658	0.192426
$921$	11.2833	0.371797
$922$	−36.0486	−1.18720
$923$	−33.6906	−1.10894
$924$	−4.23361	−0.139276
$925$	4.91204	0.161507
$926$	−12.2291	−0.401872
$927$	−9.15036	−0.300537
$928$	1.03268	0.0338995
$929$	16.9390	0.555751	0.277875	−	0.960617i	$-0.410370\pi$
$929$	16.9390	0.555751	0.277875	+	0.960617i	$0.410370\pi$
$930$	−6.55221	−0.214856
$931$	85.8762	2.81448
$932$	−25.8674	−0.847315
$933$	−19.9457	−0.652993
$934$	−1.45481	−0.0476027
$935$	−5.76358	−0.188489
$936$	−5.14772	−0.168258
$937$	17.7190	0.578854	0.289427	−	0.957200i	$-0.406535\pi$
$937$	17.7190	0.578854	0.289427	+	0.957200i	$0.406535\pi$
$938$	−7.11767	−0.232400
$939$	16.9421	0.552884
$940$	7.36900	0.240350
$941$	4.85660	0.158321	0.0791603	−	0.996862i	$-0.474776\pi$
$941$	4.85660	0.158321	0.0791603	+	0.996862i	$0.474776\pi$
$942$	7.43454	0.242230
$943$	44.6568	1.45423
$944$	6.26365	0.203865
$945$	−5.80842	−0.188948
$946$	−1.91411	−0.0622330
$947$	12.6664	0.411602	0.205801	−	0.978594i	$-0.434020\pi$
$947$	12.6664	0.411602	0.205801	+	0.978594i	$0.434020\pi$
$948$	−3.88142	−0.126063
$949$	56.0097	1.81815
$950$	−24.5100	−0.795210
$951$	−20.4517	−0.663191
$952$	−17.7851	−0.576418
$953$	55.7933	1.80732	0.903662	−	0.428247i	$-0.140869\pi$
$953$	55.7933	1.80732	0.903662	+	0.428247i	$0.140869\pi$
$954$	−6.73278	−0.217982
$955$	12.3570	0.399863
$956$	−9.94325	−0.321588
$957$	−1.03268	−0.0333819
$958$	26.4079	0.853201
$959$	41.2483	1.33198
$960$	−1.37198	−0.0442804
$961$	−8.19231	−0.264268
$962$	8.11046	0.261492
$963$	2.92700	0.0943212
$964$	19.1681	0.617362
$965$	−17.6105	−0.566901
$966$	−18.0104	−0.579474
$967$	−40.8421	−1.31339	−0.656696	−	0.754155i	$-0.728047\pi$
$967$	−40.8421	−1.31339	−0.656696	+	0.754155i	$0.728047\pi$
$968$	1.00000	0.0321412
$969$	33.0261	1.06095
$970$	4.67012	0.149948
$971$	39.3208	1.26187	0.630933	−	0.775837i	$-0.282672\pi$
$971$	39.3208	1.26187	0.630933	+	0.775837i	$0.282672\pi$
$972$	−1.00000	−0.0320750
$973$	37.2400	1.19386
$974$	37.6487	1.20634
$975$	−16.0489	−0.513977
$976$	1.00000	0.0320092
$977$	25.3021	0.809485	0.404742	−	0.914431i	$-0.367361\pi$
$977$	25.3021	0.809485	0.404742	+	0.914431i	$0.367361\pi$
$978$	14.4138	0.460904
$979$	−6.47674	−0.206997
$980$	14.9868	0.478734
$981$	−12.3589	−0.394589
$982$	11.3718	0.362888
$983$	2.24936	0.0717433	0.0358717	−	0.999356i	$-0.488579\pi$
$983$	2.24936	0.0717433	0.0358717	+	0.999356i	$0.488579\pi$
$984$	−10.4973	−0.334641
$985$	−2.27221	−0.0723988
$986$	−4.33823	−0.138157
$987$	−22.7391	−0.723792
$988$	−40.4695	−1.28751
$989$	−8.14288	−0.258928
$990$	1.37198	0.0436043
$991$	−19.4311	−0.617249	−0.308625	−	0.951184i	$-0.599869\pi$
$991$	−19.4311	−0.617249	−0.308625	+	0.951184i	$0.599869\pi$
$992$	4.77574	0.151630
$993$	0.249332	0.00791232
$994$	27.7080	0.878844
$995$	3.13646	0.0994325
$996$	11.0919	0.351459
$997$	35.5169	1.12483	0.562416	−	0.826854i	$-0.309872\pi$
$997$	35.5169	1.12483	0.562416	+	0.826854i	$0.309872\pi$
$998$	−33.6794	−1.06610
$999$	1.57555	0.0498481

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.v.1.3	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.v.1.3	✓	5	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.37198 q^{5} -1.00000 q^{6} +4.23361 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.37198 q^{5} -1.00000 q^{6} +4.23361 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.37198 q^{10} +1.00000 q^{11} -1.00000 q^{12} -5.14772 q^{13} +4.23361 q^{14} -1.37198 q^{15} +1.00000 q^{16} -4.20093 q^{17} +1.00000 q^{18} +7.86163 q^{19} +1.37198 q^{20} -4.23361 q^{21} +1.00000 q^{22} +4.25414 q^{23} -1.00000 q^{24} -3.11767 q^{25} -5.14772 q^{26} -1.00000 q^{27} +4.23361 q^{28} +1.03268 q^{29} -1.37198 q^{30} +4.77574 q^{31} +1.00000 q^{32} -1.00000 q^{33} -4.20093 q^{34} +5.80842 q^{35} +1.00000 q^{36} -1.57555 q^{37} +7.86163 q^{38} +5.14772 q^{39} +1.37198 q^{40} +10.4973 q^{41} -4.23361 q^{42} -1.91411 q^{43} +1.00000 q^{44} +1.37198 q^{45} +4.25414 q^{46} +5.37108 q^{47} -1.00000 q^{48} +10.9235 q^{49} -3.11767 q^{50} +4.20093 q^{51} -5.14772 q^{52} -6.73278 q^{53} -1.00000 q^{54} +1.37198 q^{55} +4.23361 q^{56} -7.86163 q^{57} +1.03268 q^{58} +6.26365 q^{59} -1.37198 q^{60} +1.00000 q^{61} +4.77574 q^{62} +4.23361 q^{63} +1.00000 q^{64} -7.06256 q^{65} -1.00000 q^{66} -1.68123 q^{67} -4.20093 q^{68} -4.25414 q^{69} +5.80842 q^{70} +6.54477 q^{71} +1.00000 q^{72} -10.8805 q^{73} -1.57555 q^{74} +3.11767 q^{75} +7.86163 q^{76} +4.23361 q^{77} +5.14772 q^{78} +3.88142 q^{79} +1.37198 q^{80} +1.00000 q^{81} +10.4973 q^{82} -11.0919 q^{83} -4.23361 q^{84} -5.76358 q^{85} -1.91411 q^{86} -1.03268 q^{87} +1.00000 q^{88} -6.47674 q^{89} +1.37198 q^{90} -21.7934 q^{91} +4.25414 q^{92} -4.77574 q^{93} +5.37108 q^{94} +10.7860 q^{95} -1.00000 q^{96} +3.40393 q^{97} +10.9235 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 7 q^{5} - 5 q^{6} + 5 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + 7 * q^5 - 5 * q^6 + 5 * q^8 + 5 * q^9	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 7 q^{5} - 5 q^{6} + 5 q^{8} + 5 q^{9} + 7 q^{10} + 5 q^{11} - 5 q^{12} - 2 q^{13} - 7 q^{15} + 5 q^{16} + 2 q^{17} + 5 q^{18} + 18 q^{19} + 7 q^{20} + 5 q^{22} - q^{23} - 5 q^{24} + 6 q^{25} - 2 q^{26} - 5 q^{27} + 7 q^{29} - 7 q^{30} + 5 q^{32} - 5 q^{33} + 2 q^{34} + 7 q^{35} + 5 q^{36} + 11 q^{37} + 18 q^{38} + 2 q^{39} + 7 q^{40} + 8 q^{41} - 7 q^{43} + 5 q^{44} + 7 q^{45} - q^{46} + q^{47} - 5 q^{48} + 7 q^{49} + 6 q^{50} - 2 q^{51} - 2 q^{52} + 10 q^{53} - 5 q^{54} + 7 q^{55} - 18 q^{57} + 7 q^{58} + 8 q^{59} - 7 q^{60} + 5 q^{61} + 5 q^{64} + 9 q^{65} - 5 q^{66} - 9 q^{67} + 2 q^{68} + q^{69} + 7 q^{70} + 34 q^{71} + 5 q^{72} + 13 q^{73} + 11 q^{74} - 6 q^{75} + 18 q^{76} + 2 q^{78} + 15 q^{79} + 7 q^{80} + 5 q^{81} + 8 q^{82} - 27 q^{83} - 2 q^{85} - 7 q^{86} - 7 q^{87} + 5 q^{88} + 11 q^{89} + 7 q^{90} + q^{91} - q^{92} + q^{94} + 11 q^{95} - 5 q^{96} + 37 q^{97} + 7 q^{98} + 5 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + 7 * q^5 - 5 * q^6 + 5 * q^8 + 5 * q^9 + 7 * q^10 + 5 * q^11 - 5 * q^12 - 2 * q^13 - 7 * q^15 + 5 * q^16 + 2 * q^17 + 5 * q^18 + 18 * q^19 + 7 * q^20 + 5 * q^22 - q^23 - 5 * q^24 + 6 * q^25 - 2 * q^26 - 5 * q^27 + 7 * q^29 - 7 * q^30 + 5 * q^32 - 5 * q^33 + 2 * q^34 + 7 * q^35 + 5 * q^36 + 11 * q^37 + 18 * q^38 + 2 * q^39 + 7 * q^40 + 8 * q^41 - 7 * q^43 + 5 * q^44 + 7 * q^45 - q^46 + q^47 - 5 * q^48 + 7 * q^49 + 6 * q^50 - 2 * q^51 - 2 * q^52 + 10 * q^53 - 5 * q^54 + 7 * q^55 - 18 * q^57 + 7 * q^58 + 8 * q^59 - 7 * q^60 + 5 * q^61 + 5 * q^64 + 9 * q^65 - 5 * q^66 - 9 * q^67 + 2 * q^68 + q^69 + 7 * q^70 + 34 * q^71 + 5 * q^72 + 13 * q^73 + 11 * q^74 - 6 * q^75 + 18 * q^76 + 2 * q^78 + 15 * q^79 + 7 * q^80 + 5 * q^81 + 8 * q^82 - 27 * q^83 - 2 * q^85 - 7 * q^86 - 7 * q^87 + 5 * q^88 + 11 * q^89 + 7 * q^90 + q^91 - q^92 + q^94 + 11 * q^95 - 5 * q^96 + 37 * q^97 + 7 * q^98 + 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more