LMFDB - Embedded newform 6018.2.a.x.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, 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("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 34x^{8} + 30x^{7} + 341x^{6} - 276x^{5} - 1032x^{4} + 1176x^{3} + 416x^{2} - 896x + 272 $ x^10 - x^9 - 34x^8 + 30x^7 + 341x^6 - 276x^5 - 1032x^4 + 1176x^3 + 416x^2 - 896x + 272
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$4.32662$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.32662 q^{5} +1.00000 q^{6} +3.19198 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.32662 q^{5} +1.00000 q^{6} +3.19198 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.32662 q^{10} +4.37913 q^{11} -1.00000 q^{12} +0.617899 q^{13} -3.19198 q^{14} -4.32662 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +1.19313 q^{19} +4.32662 q^{20} -3.19198 q^{21} -4.37913 q^{22} +4.91809 q^{23} +1.00000 q^{24} +13.7196 q^{25} -0.617899 q^{26} -1.00000 q^{27} +3.19198 q^{28} +5.98405 q^{29} +4.32662 q^{30} -1.28083 q^{31} -1.00000 q^{32} -4.37913 q^{33} -1.00000 q^{34} +13.8105 q^{35} +1.00000 q^{36} -6.55705 q^{37} -1.19313 q^{38} -0.617899 q^{39} -4.32662 q^{40} -7.41643 q^{41} +3.19198 q^{42} -4.76541 q^{43} +4.37913 q^{44} +4.32662 q^{45} -4.91809 q^{46} +2.37675 q^{47} -1.00000 q^{48} +3.18871 q^{49} -13.7196 q^{50} -1.00000 q^{51} +0.617899 q^{52} -3.41324 q^{53} +1.00000 q^{54} +18.9468 q^{55} -3.19198 q^{56} -1.19313 q^{57} -5.98405 q^{58} -1.00000 q^{59} -4.32662 q^{60} -6.96926 q^{61} +1.28083 q^{62} +3.19198 q^{63} +1.00000 q^{64} +2.67341 q^{65} +4.37913 q^{66} +8.70140 q^{67} +1.00000 q^{68} -4.91809 q^{69} -13.8105 q^{70} -0.350208 q^{71} -1.00000 q^{72} +13.6469 q^{73} +6.55705 q^{74} -13.7196 q^{75} +1.19313 q^{76} +13.9781 q^{77} +0.617899 q^{78} +0.864276 q^{79} +4.32662 q^{80} +1.00000 q^{81} +7.41643 q^{82} -2.76138 q^{83} -3.19198 q^{84} +4.32662 q^{85} +4.76541 q^{86} -5.98405 q^{87} -4.37913 q^{88} +3.17514 q^{89} -4.32662 q^{90} +1.97232 q^{91} +4.91809 q^{92} +1.28083 q^{93} -2.37675 q^{94} +5.16223 q^{95} +1.00000 q^{96} +18.0287 q^{97} -3.18871 q^{98} +4.37913 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + q^{5} + 10 q^{6} + 10 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + q^5 + 10 * q^6 + 10 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + q^{5} + 10 q^{6} + 10 q^{7} - 10 q^{8} + 10 q^{9} - q^{10} + 2 q^{11} - 10 q^{12} - 10 q^{14} - q^{15} + 10 q^{16} + 10 q^{17} - 10 q^{18} + 15 q^{19} + q^{20} - 10 q^{21} - 2 q^{22} + 19 q^{23} + 10 q^{24} + 19 q^{25} - 10 q^{27} + 10 q^{28} - q^{29} + q^{30} + 15 q^{31} - 10 q^{32} - 2 q^{33} - 10 q^{34} - 14 q^{35} + 10 q^{36} + q^{37} - 15 q^{38} - q^{40} - 5 q^{41} + 10 q^{42} + 26 q^{43} + 2 q^{44} + q^{45} - 19 q^{46} + 14 q^{47} - 10 q^{48} + 20 q^{49} - 19 q^{50} - 10 q^{51} - 2 q^{53} + 10 q^{54} + 4 q^{55} - 10 q^{56} - 15 q^{57} + q^{58} - 10 q^{59} - q^{60} + 4 q^{61} - 15 q^{62} + 10 q^{63} + 10 q^{64} - 20 q^{65} + 2 q^{66} + 15 q^{67} + 10 q^{68} - 19 q^{69} + 14 q^{70} + 14 q^{71} - 10 q^{72} + 43 q^{73} - q^{74} - 19 q^{75} + 15 q^{76} + 20 q^{77} + q^{80} + 10 q^{81} + 5 q^{82} - 4 q^{83} - 10 q^{84} + q^{85} - 26 q^{86} + q^{87} - 2 q^{88} - 22 q^{89} - q^{90} - q^{91} + 19 q^{92} - 15 q^{93} - 14 q^{94} - 37 q^{95} + 10 q^{96} + 37 q^{97} - 20 q^{98} + 2 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + q^5 + 10 * q^6 + 10 * q^7 - 10 * q^8 + 10 * q^9 - q^10 + 2 * q^11 - 10 * q^12 - 10 * q^14 - q^15 + 10 * q^16 + 10 * q^17 - 10 * q^18 + 15 * q^19 + q^20 - 10 * q^21 - 2 * q^22 + 19 * q^23 + 10 * q^24 + 19 * q^25 - 10 * q^27 + 10 * q^28 - q^29 + q^30 + 15 * q^31 - 10 * q^32 - 2 * q^33 - 10 * q^34 - 14 * q^35 + 10 * q^36 + q^37 - 15 * q^38 - q^40 - 5 * q^41 + 10 * q^42 + 26 * q^43 + 2 * q^44 + q^45 - 19 * q^46 + 14 * q^47 - 10 * q^48 + 20 * q^49 - 19 * q^50 - 10 * q^51 - 2 * q^53 + 10 * q^54 + 4 * q^55 - 10 * q^56 - 15 * q^57 + q^58 - 10 * q^59 - q^60 + 4 * q^61 - 15 * q^62 + 10 * q^63 + 10 * q^64 - 20 * q^65 + 2 * q^66 + 15 * q^67 + 10 * q^68 - 19 * q^69 + 14 * q^70 + 14 * q^71 - 10 * q^72 + 43 * q^73 - q^74 - 19 * q^75 + 15 * q^76 + 20 * q^77 + q^80 + 10 * q^81 + 5 * q^82 - 4 * q^83 - 10 * q^84 + q^85 - 26 * q^86 + q^87 - 2 * q^88 - 22 * q^89 - q^90 - q^91 + 19 * q^92 - 15 * q^93 - 14 * q^94 - 37 * q^95 + 10 * q^96 + 37 * q^97 - 20 * 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
$5$	4.32662	1.93492	0.967461	−	0.253019i	$-0.0814234\pi$
$5$	4.32662	1.93492	0.967461	+	0.253019i	$0.0814234\pi$
$6$	1.00000	0.408248
$7$	3.19198	1.20645	0.603227	−	0.797570i	$-0.293881\pi$
$7$	3.19198	1.20645	0.603227	+	0.797570i	$0.293881\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−4.32662	−1.36820
$11$	4.37913	1.32036	0.660179	−	0.751108i	$-0.270480\pi$
$11$	4.37913	1.32036	0.660179	+	0.751108i	$0.270480\pi$
$12$	−1.00000	−0.288675
$13$	0.617899	0.171374	0.0856872	−	0.996322i	$-0.472691\pi$
$13$	0.617899	0.171374	0.0856872	+	0.996322i	$0.472691\pi$
$14$	−3.19198	−0.853091
$15$	−4.32662	−1.11713
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	1.19313	0.273723	0.136862	−	0.990590i	$-0.456298\pi$
$19$	1.19313	0.273723	0.136862	+	0.990590i	$0.456298\pi$
$20$	4.32662	0.967461
$21$	−3.19198	−0.696546
$22$	−4.37913	−0.933634
$23$	4.91809	1.02549	0.512747	−	0.858540i	$-0.328628\pi$
$23$	4.91809	1.02549	0.512747	+	0.858540i	$0.328628\pi$
$24$	1.00000	0.204124
$25$	13.7196	2.74393
$26$	−0.617899	−0.121180
$27$	−1.00000	−0.192450
$28$	3.19198	0.603227
$29$	5.98405	1.11121	0.555606	−	0.831446i	$-0.312486\pi$
$29$	5.98405	1.11121	0.555606	+	0.831446i	$0.312486\pi$
$30$	4.32662	0.789929
$31$	−1.28083	−0.230044	−0.115022	−	0.993363i	$-0.536694\pi$
$31$	−1.28083	−0.230044	−0.115022	+	0.993363i	$0.536694\pi$
$32$	−1.00000	−0.176777
$33$	−4.37913	−0.762309
$34$	−1.00000	−0.171499
$35$	13.8105	2.33439
$36$	1.00000	0.166667
$37$	−6.55705	−1.07797	−0.538986	−	0.842314i	$-0.681193\pi$
$37$	−6.55705	−1.07797	−0.538986	+	0.842314i	$0.681193\pi$
$38$	−1.19313	−0.193551
$39$	−0.617899	−0.0989431
$40$	−4.32662	−0.684099
$41$	−7.41643	−1.15825	−0.579126	−	0.815238i	$-0.696606\pi$
$41$	−7.41643	−1.15825	−0.579126	+	0.815238i	$0.696606\pi$
$42$	3.19198	0.492533
$43$	−4.76541	−0.726719	−0.363359	−	0.931649i	$-0.618370\pi$
$43$	−4.76541	−0.726719	−0.363359	+	0.931649i	$0.618370\pi$
$44$	4.37913	0.660179
$45$	4.32662	0.644974
$46$	−4.91809	−0.725133
$47$	2.37675	0.346684	0.173342	−	0.984862i	$-0.444543\pi$
$47$	2.37675	0.346684	0.173342	+	0.984862i	$0.444543\pi$
$48$	−1.00000	−0.144338
$49$	3.18871	0.455530
$50$	−13.7196	−1.94025
$51$	−1.00000	−0.140028
$52$	0.617899	0.0856872
$53$	−3.41324	−0.468845	−0.234422	−	0.972135i	$-0.575320\pi$
$53$	−3.41324	−0.468845	−0.234422	+	0.972135i	$0.575320\pi$
$54$	1.00000	0.136083
$55$	18.9468	2.55479
$56$	−3.19198	−0.426546
$57$	−1.19313	−0.158034
$58$	−5.98405	−0.785745
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−4.32662	−0.558564
$61$	−6.96926	−0.892323	−0.446161	−	0.894953i	$-0.647209\pi$
$61$	−6.96926	−0.892323	−0.446161	+	0.894953i	$0.647209\pi$
$62$	1.28083	0.162666
$63$	3.19198	0.402151
$64$	1.00000	0.125000
$65$	2.67341	0.331596
$66$	4.37913	0.539034
$67$	8.70140	1.06305	0.531523	−	0.847044i	$-0.321620\pi$
$67$	8.70140	1.06305	0.531523	+	0.847044i	$0.321620\pi$
$68$	1.00000	0.121268
$69$	−4.91809	−0.592069
$70$	−13.8105	−1.65067
$71$	−0.350208	−0.0415621	−0.0207811	−	0.999784i	$-0.506615\pi$
$71$	−0.350208	−0.0415621	−0.0207811	+	0.999784i	$0.506615\pi$
$72$	−1.00000	−0.117851
$73$	13.6469	1.59724	0.798622	−	0.601832i	$-0.205562\pi$
$73$	13.6469	1.59724	0.798622	+	0.601832i	$0.205562\pi$
$74$	6.55705	0.762242
$75$	−13.7196	−1.58421
$76$	1.19313	0.136862
$77$	13.9781	1.59295
$78$	0.617899	0.0699633
$79$	0.864276	0.0972386	0.0486193	−	0.998817i	$-0.484518\pi$
$79$	0.864276	0.0972386	0.0486193	+	0.998817i	$0.484518\pi$
$80$	4.32662	0.483731
$81$	1.00000	0.111111
$82$	7.41643	0.819008
$83$	−2.76138	−0.303100	−0.151550	−	0.988450i	$-0.548427\pi$
$83$	−2.76138	−0.303100	−0.151550	+	0.988450i	$0.548427\pi$
$84$	−3.19198	−0.348273
$85$	4.32662	0.469288
$86$	4.76541	0.513868
$87$	−5.98405	−0.641558
$88$	−4.37913	−0.466817
$89$	3.17514	0.336564	0.168282	−	0.985739i	$-0.446178\pi$
$89$	3.17514	0.336564	0.168282	+	0.985739i	$0.446178\pi$
$90$	−4.32662	−0.456066
$91$	1.97232	0.206755
$92$	4.91809	0.512747
$93$	1.28083	0.132816
$94$	−2.37675	−0.245143
$95$	5.16223	0.529633
$96$	1.00000	0.102062
$97$	18.0287	1.83053	0.915267	−	0.402848i	$-0.131980\pi$
$97$	18.0287	1.83053	0.915267	+	0.402848i	$0.131980\pi$
$98$	−3.18871	−0.322108
$99$	4.37913	0.440119
$100$	13.7196	1.37196
$101$	19.7913	1.96931	0.984653	−	0.174525i	$-0.0558390\pi$
$101$	19.7913	1.96931	0.984653	+	0.174525i	$0.0558390\pi$
$102$	1.00000	0.0990148
$103$	−14.7534	−1.45370	−0.726848	−	0.686798i	$-0.759016\pi$
$103$	−14.7534	−1.45370	−0.726848	+	0.686798i	$0.759016\pi$
$104$	−0.617899	−0.0605900
$105$	−13.8105	−1.34776
$106$	3.41324	0.331523
$107$	−7.76140	−0.750323	−0.375162	−	0.926959i	$-0.622413\pi$
$107$	−7.76140	−0.750323	−0.375162	+	0.926959i	$0.622413\pi$
$108$	−1.00000	−0.0962250
$109$	−12.3899	−1.18674	−0.593368	−	0.804931i	$-0.702202\pi$
$109$	−12.3899	−1.18674	−0.593368	+	0.804931i	$0.702202\pi$
$110$	−18.9468	−1.80651
$111$	6.55705	0.622368
$112$	3.19198	0.301613
$113$	−16.0162	−1.50667	−0.753337	−	0.657635i	$-0.771557\pi$
$113$	−16.0162	−1.50667	−0.753337	+	0.657635i	$0.771557\pi$
$114$	1.19313	0.111747
$115$	21.2787	1.98425
$116$	5.98405	0.555606
$117$	0.617899	0.0571248
$118$	1.00000	0.0920575
$119$	3.19198	0.292608
$120$	4.32662	0.394964
$121$	8.17679	0.743344
$122$	6.96926	0.630967
$123$	7.41643	0.668717
$124$	−1.28083	−0.115022
$125$	37.7265	3.37436
$126$	−3.19198	−0.284364
$127$	11.2941	1.00219	0.501094	−	0.865393i	$-0.332931\pi$
$127$	11.2941	1.00219	0.501094	+	0.865393i	$0.332931\pi$
$128$	−1.00000	−0.0883883
$129$	4.76541	0.419571
$130$	−2.67341	−0.234474
$131$	−4.23282	−0.369823	−0.184911	−	0.982755i	$-0.559200\pi$
$131$	−4.23282	−0.369823	−0.184911	+	0.982755i	$0.559200\pi$
$132$	−4.37913	−0.381154
$133$	3.80845	0.330234
$134$	−8.70140	−0.751687
$135$	−4.32662	−0.372376
$136$	−1.00000	−0.0857493
$137$	−11.4184	−0.975540	−0.487770	−	0.872972i	$-0.662190\pi$
$137$	−11.4184	−0.975540	−0.487770	+	0.872972i	$0.662190\pi$
$138$	4.91809	0.418656
$139$	−15.1732	−1.28698	−0.643488	−	0.765456i	$-0.722514\pi$
$139$	−15.1732	−1.28698	−0.643488	+	0.765456i	$0.722514\pi$
$140$	13.8105	1.16720
$141$	−2.37675	−0.200158
$142$	0.350208	0.0293888
$143$	2.70586	0.226276
$144$	1.00000	0.0833333
$145$	25.8907	2.15011
$146$	−13.6469	−1.12942
$147$	−3.18871	−0.263000
$148$	−6.55705	−0.538986
$149$	−18.8265	−1.54232	−0.771162	−	0.636639i	$-0.780324\pi$
$149$	−18.8265	−1.54232	−0.771162	+	0.636639i	$0.780324\pi$
$150$	13.7196	1.12020
$151$	−3.94214	−0.320806	−0.160403	−	0.987052i	$-0.551279\pi$
$151$	−3.94214	−0.320806	−0.160403	+	0.987052i	$0.551279\pi$
$152$	−1.19313	−0.0967757
$153$	1.00000	0.0808452
$154$	−13.9781	−1.12639
$155$	−5.54168	−0.445118
$156$	−0.617899	−0.0494715
$157$	−10.1290	−0.808386	−0.404193	−	0.914674i	$-0.632448\pi$
$157$	−10.1290	−0.808386	−0.404193	+	0.914674i	$0.632448\pi$
$158$	−0.864276	−0.0687581
$159$	3.41324	0.270688
$160$	−4.32662	−0.342049
$161$	15.6984	1.23721
$162$	−1.00000	−0.0785674
$163$	−0.0612211	−0.00479521	−0.00239760	−	0.999997i	$-0.500763\pi$
$163$	−0.0612211	−0.00479521	−0.00239760	+	0.999997i	$0.500763\pi$
$164$	−7.41643	−0.579126
$165$	−18.9468	−1.47501
$166$	2.76138	0.214324
$167$	3.25340	0.251755	0.125878	−	0.992046i	$-0.459825\pi$
$167$	3.25340	0.251755	0.125878	+	0.992046i	$0.459825\pi$
$168$	3.19198	0.246266
$169$	−12.6182	−0.970631
$170$	−4.32662	−0.331837
$171$	1.19313	0.0912410
$172$	−4.76541	−0.363359
$173$	−19.4197	−1.47645	−0.738225	−	0.674555i	$-0.764336\pi$
$173$	−19.4197	−1.47645	−0.738225	+	0.674555i	$0.764336\pi$
$174$	5.98405	0.453650
$175$	43.7927	3.31042
$176$	4.37913	0.330089
$177$	1.00000	0.0751646
$178$	−3.17514	−0.237986
$179$	−18.0755	−1.35102	−0.675512	−	0.737349i	$-0.736077\pi$
$179$	−18.0755	−1.35102	−0.675512	+	0.737349i	$0.736077\pi$
$180$	4.32662	0.322487
$181$	−21.0070	−1.56144	−0.780719	−	0.624882i	$-0.785147\pi$
$181$	−21.0070	−1.56144	−0.780719	+	0.624882i	$0.785147\pi$
$182$	−1.97232	−0.146198
$183$	6.96926	0.515183
$184$	−4.91809	−0.362567
$185$	−28.3699	−2.08579
$186$	−1.28083	−0.0939152
$187$	4.37913	0.320234
$188$	2.37675	0.173342
$189$	−3.19198	−0.232182
$190$	−5.16223	−0.374507
$191$	−9.63944	−0.697485	−0.348743	−	0.937219i	$-0.613391\pi$
$191$	−9.63944	−0.697485	−0.348743	+	0.937219i	$0.613391\pi$
$192$	−1.00000	−0.0721688
$193$	−10.0196	−0.721228	−0.360614	−	0.932715i	$-0.617433\pi$
$193$	−10.0196	−0.721228	−0.360614	+	0.932715i	$0.617433\pi$
$194$	−18.0287	−1.29438
$195$	−2.67341	−0.191447
$196$	3.18871	0.227765
$197$	0.291283	0.0207530	0.0103765	−	0.999946i	$-0.496697\pi$
$197$	0.291283	0.0207530	0.0103765	+	0.999946i	$0.496697\pi$
$198$	−4.37913	−0.311211
$199$	−2.43632	−0.172706	−0.0863531	−	0.996265i	$-0.527521\pi$
$199$	−2.43632	−0.172706	−0.0863531	+	0.996265i	$0.527521\pi$
$200$	−13.7196	−0.970124
$201$	−8.70140	−0.613750
$202$	−19.7913	−1.39251
$203$	19.1010	1.34062
$204$	−1.00000	−0.0700140
$205$	−32.0881	−2.24113
$206$	14.7534	1.02792
$207$	4.91809	0.341831
$208$	0.617899	0.0428436
$209$	5.22488	0.361412
$210$	13.8105	0.953013
$211$	−3.68851	−0.253928	−0.126964	−	0.991907i	$-0.540523\pi$
$211$	−3.68851	−0.253928	−0.126964	+	0.991907i	$0.540523\pi$
$212$	−3.41324	−0.234422
$213$	0.350208	0.0239959
$214$	7.76140	0.530559
$215$	−20.6181	−1.40614
$216$	1.00000	0.0680414
$217$	−4.08839	−0.277538
$218$	12.3899	0.839149
$219$	−13.6469	−0.922170
$220$	18.9468	1.27740
$221$	0.617899	0.0415644
$222$	−6.55705	−0.440081
$223$	14.5579	0.974869	0.487435	−	0.873160i	$-0.337933\pi$
$223$	14.5579	0.974869	0.487435	+	0.873160i	$0.337933\pi$
$224$	−3.19198	−0.213273
$225$	13.7196	0.914642
$226$	16.0162	1.06538
$227$	−6.60366	−0.438301	−0.219150	−	0.975691i	$-0.570328\pi$
$227$	−6.60366	−0.438301	−0.219150	+	0.975691i	$0.570328\pi$
$228$	−1.19313	−0.0790171
$229$	−8.17999	−0.540549	−0.270275	−	0.962783i	$-0.587114\pi$
$229$	−8.17999	−0.540549	−0.270275	+	0.962783i	$0.587114\pi$
$230$	−21.2787	−1.40308
$231$	−13.9781	−0.919690
$232$	−5.98405	−0.392872
$233$	−3.53879	−0.231834	−0.115917	−	0.993259i	$-0.536981\pi$
$233$	−3.53879	−0.231834	−0.115917	+	0.993259i	$0.536981\pi$
$234$	−0.617899	−0.0403933
$235$	10.2833	0.670807
$236$	−1.00000	−0.0650945
$237$	−0.864276	−0.0561407
$238$	−3.19198	−0.206905
$239$	−7.17196	−0.463915	−0.231958	−	0.972726i	$-0.574513\pi$
$239$	−7.17196	−0.463915	−0.231958	+	0.972726i	$0.574513\pi$
$240$	−4.32662	−0.279282
$241$	2.08869	0.134545	0.0672723	−	0.997735i	$-0.478570\pi$
$241$	2.08869	0.134545	0.0672723	+	0.997735i	$0.478570\pi$
$242$	−8.17679	−0.525624
$243$	−1.00000	−0.0641500
$244$	−6.96926	−0.446161
$245$	13.7963	0.881416
$246$	−7.41643	−0.472854
$247$	0.737235	0.0469091
$248$	1.28083	0.0813330
$249$	2.76138	0.174995
$250$	−37.7265	−2.38603
$251$	6.72064	0.424203	0.212101	−	0.977248i	$-0.431969\pi$
$251$	6.72064	0.424203	0.212101	+	0.977248i	$0.431969\pi$
$252$	3.19198	0.201076
$253$	21.5370	1.35402
$254$	−11.2941	−0.708654
$255$	−4.32662	−0.270943
$256$	1.00000	0.0625000
$257$	−20.2137	−1.26090	−0.630448	−	0.776232i	$-0.717129\pi$
$257$	−20.2137	−1.26090	−0.630448	+	0.776232i	$0.717129\pi$
$258$	−4.76541	−0.296682
$259$	−20.9300	−1.30052
$260$	2.67341	0.165798
$261$	5.98405	0.370404
$262$	4.23282	0.261504
$263$	9.19721	0.567125	0.283562	−	0.958954i	$-0.408484\pi$
$263$	9.19721	0.567125	0.283562	+	0.958954i	$0.408484\pi$
$264$	4.37913	0.269517
$265$	−14.7678	−0.907179
$266$	−3.80845	−0.233511
$267$	−3.17514	−0.194315
$268$	8.70140	0.531523
$269$	11.8658	0.723470	0.361735	−	0.932281i	$-0.382185\pi$
$269$	11.8658	0.723470	0.361735	+	0.932281i	$0.382185\pi$
$270$	4.32662	0.263310
$271$	17.5808	1.06796	0.533979	−	0.845498i	$-0.320696\pi$
$271$	17.5808	1.06796	0.533979	+	0.845498i	$0.320696\pi$
$272$	1.00000	0.0606339
$273$	−1.97232	−0.119370
$274$	11.4184	0.689811
$275$	60.0801	3.62296
$276$	−4.91809	−0.296034
$277$	−16.9756	−1.01996	−0.509981	−	0.860186i	$-0.670348\pi$
$277$	−16.9756	−1.01996	−0.509981	+	0.860186i	$0.670348\pi$
$278$	15.1732	0.910030
$279$	−1.28083	−0.0766815
$280$	−13.8105	−0.825333
$281$	−28.4817	−1.69907	−0.849537	−	0.527529i	$-0.823119\pi$
$281$	−28.4817	−1.69907	−0.849537	+	0.527529i	$0.823119\pi$
$282$	2.37675	0.141533
$283$	30.3511	1.80419	0.902094	−	0.431540i	$-0.142030\pi$
$283$	30.3511	1.80419	0.902094	+	0.431540i	$0.142030\pi$
$284$	−0.350208	−0.0207811
$285$	−5.16223	−0.305784
$286$	−2.70586	−0.160001
$287$	−23.6731	−1.39738
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−25.8907	−1.52036
$291$	−18.0287	−1.05686
$292$	13.6469	0.798622
$293$	9.13661	0.533766	0.266883	−	0.963729i	$-0.414006\pi$
$293$	9.13661	0.533766	0.266883	+	0.963729i	$0.414006\pi$
$294$	3.18871	0.185969
$295$	−4.32662	−0.251905
$296$	6.55705	0.381121
$297$	−4.37913	−0.254103
$298$	18.8265	1.09059
$299$	3.03889	0.175743
$300$	−13.7196	−0.792103
$301$	−15.2111	−0.876752
$302$	3.94214	0.226844
$303$	−19.7913	−1.13698
$304$	1.19313	0.0684308
$305$	−30.1533	−1.72658
$306$	−1.00000	−0.0571662
$307$	2.67041	0.152408	0.0762041	−	0.997092i	$-0.475720\pi$
$307$	2.67041	0.152408	0.0762041	+	0.997092i	$0.475720\pi$
$308$	13.9781	0.796475
$309$	14.7534	0.839292
$310$	5.54168	0.314746
$311$	−0.740803	−0.0420071	−0.0210035	−	0.999779i	$-0.506686\pi$
$311$	−0.740803	−0.0420071	−0.0210035	+	0.999779i	$0.506686\pi$
$312$	0.617899	0.0349817
$313$	−10.1107	−0.571493	−0.285746	−	0.958305i	$-0.592242\pi$
$313$	−10.1107	−0.571493	−0.285746	+	0.958305i	$0.592242\pi$
$314$	10.1290	0.571615
$315$	13.8105	0.778131
$316$	0.864276	0.0486193
$317$	−1.33871	−0.0751896	−0.0375948	−	0.999293i	$-0.511970\pi$
$317$	−1.33871	−0.0751896	−0.0375948	+	0.999293i	$0.511970\pi$
$318$	−3.41324	−0.191405
$319$	26.2050	1.46720
$320$	4.32662	0.241865
$321$	7.76140	0.433199
$322$	−15.6984	−0.874839
$323$	1.19313	0.0663876
$324$	1.00000	0.0555556
$325$	8.47735	0.470239
$326$	0.0612211	0.00339072
$327$	12.3899	0.685163
$328$	7.41643	0.409504
$329$	7.58652	0.418258
$330$	18.9468	1.04299
$331$	31.7598	1.74568	0.872839	−	0.488008i	$-0.162276\pi$
$331$	31.7598	1.74568	0.872839	+	0.488008i	$0.162276\pi$
$332$	−2.76138	−0.151550
$333$	−6.55705	−0.359324
$334$	−3.25340	−0.178018
$335$	37.6477	2.05691
$336$	−3.19198	−0.174137
$337$	−2.28323	−0.124376	−0.0621878	−	0.998064i	$-0.519808\pi$
$337$	−2.28323	−0.124376	−0.0621878	+	0.998064i	$0.519808\pi$
$338$	12.6182	0.686340
$339$	16.0162	0.869878
$340$	4.32662	0.234644
$341$	−5.60894	−0.303741
$342$	−1.19313	−0.0645172
$343$	−12.1655	−0.656878
$344$	4.76541	0.256934
$345$	−21.2787	−1.14561
$346$	19.4197	1.04401
$347$	28.7100	1.54124	0.770618	−	0.637298i	$-0.219948\pi$
$347$	28.7100	1.54124	0.770618	+	0.637298i	$0.219948\pi$
$348$	−5.98405	−0.320779
$349$	−12.4901	−0.668580	−0.334290	−	0.942470i	$-0.608497\pi$
$349$	−12.4901	−0.668580	−0.334290	+	0.942470i	$0.608497\pi$
$350$	−43.7927	−2.34082
$351$	−0.617899	−0.0329810
$352$	−4.37913	−0.233408
$353$	−15.6142	−0.831060	−0.415530	−	0.909580i	$-0.636404\pi$
$353$	−15.6142	−0.831060	−0.415530	+	0.909580i	$0.636404\pi$
$354$	−1.00000	−0.0531494
$355$	−1.51522	−0.0804195
$356$	3.17514	0.168282
$357$	−3.19198	−0.168937
$358$	18.0755	0.955318
$359$	31.5744	1.66643	0.833216	−	0.552947i	$-0.186497\pi$
$359$	31.5744	1.66643	0.833216	+	0.552947i	$0.186497\pi$
$360$	−4.32662	−0.228033
$361$	−17.5764	−0.925076
$362$	21.0070	1.10410
$363$	−8.17679	−0.429170
$364$	1.97232	0.103378
$365$	59.0448	3.09055
$366$	−6.96926	−0.364289
$367$	−4.35349	−0.227250	−0.113625	−	0.993524i	$-0.536246\pi$
$367$	−4.35349	−0.227250	−0.113625	+	0.993524i	$0.536246\pi$
$368$	4.91809	0.256373
$369$	−7.41643	−0.386084
$370$	28.3699	1.47488
$371$	−10.8950	−0.565640
$372$	1.28083	0.0664081
$373$	31.6739	1.64001	0.820006	−	0.572354i	$-0.193970\pi$
$373$	31.6739	1.64001	0.820006	+	0.572354i	$0.193970\pi$
$374$	−4.37913	−0.226439
$375$	−37.7265	−1.94819
$376$	−2.37675	−0.122571
$377$	3.69754	0.190433
$378$	3.19198	0.164178
$379$	17.3317	0.890268	0.445134	−	0.895464i	$-0.353156\pi$
$379$	17.3317	0.890268	0.445134	+	0.895464i	$0.353156\pi$
$380$	5.16223	0.264817
$381$	−11.2941	−0.578614
$382$	9.63944	0.493197
$383$	−25.3044	−1.29299	−0.646496	−	0.762917i	$-0.723766\pi$
$383$	−25.3044	−1.29299	−0.646496	+	0.762917i	$0.723766\pi$
$384$	1.00000	0.0510310
$385$	60.4778	3.08224
$386$	10.0196	0.509985
$387$	−4.76541	−0.242240
$388$	18.0287	0.915267
$389$	−12.0321	−0.610050	−0.305025	−	0.952344i	$-0.598665\pi$
$389$	−12.0321	−0.610050	−0.305025	+	0.952344i	$0.598665\pi$
$390$	2.67341	0.135374
$391$	4.91809	0.248719
$392$	−3.18871	−0.161054
$393$	4.23282	0.213517
$394$	−0.291283	−0.0146746
$395$	3.73939	0.188149
$396$	4.37913	0.220060
$397$	15.8676	0.796371	0.398185	−	0.917305i	$-0.369640\pi$
$397$	15.8676	0.796371	0.398185	+	0.917305i	$0.369640\pi$
$398$	2.43632	0.122122
$399$	−3.80845	−0.190661
$400$	13.7196	0.685982
$401$	−22.1948	−1.10836	−0.554179	−	0.832398i	$-0.686968\pi$
$401$	−22.1948	−1.10836	−0.554179	+	0.832398i	$0.686968\pi$
$402$	8.70140	0.433987
$403$	−0.791426	−0.0394237
$404$	19.7913	0.984653
$405$	4.32662	0.214991
$406$	−19.1010	−0.947965
$407$	−28.7142	−1.42331
$408$	1.00000	0.0495074
$409$	−13.5784	−0.671409	−0.335705	−	0.941967i	$-0.608974\pi$
$409$	−13.5784	−0.671409	−0.335705	+	0.941967i	$0.608974\pi$
$410$	32.0881	1.58472
$411$	11.4184	0.563228
$412$	−14.7534	−0.726848
$413$	−3.19198	−0.157067
$414$	−4.91809	−0.241711
$415$	−11.9474	−0.586476
$416$	−0.617899	−0.0302950
$417$	15.1732	0.743036
$418$	−5.22488	−0.255557
$419$	−34.2624	−1.67383	−0.836913	−	0.547336i	$-0.815642\pi$
$419$	−34.2624	−1.67383	−0.836913	+	0.547336i	$0.815642\pi$
$420$	−13.8105	−0.673882
$421$	17.5231	0.854021	0.427011	−	0.904247i	$-0.359567\pi$
$421$	17.5231	0.854021	0.427011	+	0.904247i	$0.359567\pi$
$422$	3.68851	0.179554
$423$	2.37675	0.115561
$424$	3.41324	0.165762
$425$	13.7196	0.665500
$426$	−0.350208	−0.0169677
$427$	−22.2457	−1.07655
$428$	−7.76140	−0.375162
$429$	−2.70586	−0.130640
$430$	20.6181	0.994295
$431$	−3.66671	−0.176619	−0.0883096	−	0.996093i	$-0.528146\pi$
$431$	−3.66671	−0.176619	−0.0883096	+	0.996093i	$0.528146\pi$
$432$	−1.00000	−0.0481125
$433$	−9.73834	−0.467995	−0.233997	−	0.972237i	$-0.575181\pi$
$433$	−9.73834	−0.467995	−0.233997	+	0.972237i	$0.575181\pi$
$434$	4.08839	0.196249
$435$	−25.8907	−1.24137
$436$	−12.3899	−0.593368
$437$	5.86793	0.280701
$438$	13.6469	0.652072
$439$	22.8631	1.09120	0.545599	−	0.838046i	$-0.316302\pi$
$439$	22.8631	1.09120	0.545599	+	0.838046i	$0.316302\pi$
$440$	−18.9468	−0.903255
$441$	3.18871	0.151843
$442$	−0.617899	−0.0293905
$443$	−35.3056	−1.67742	−0.838709	−	0.544580i	$-0.816689\pi$
$443$	−35.3056	−1.67742	−0.838709	+	0.544580i	$0.816689\pi$
$444$	6.55705	0.311184
$445$	13.7376	0.651225
$446$	−14.5579	−0.689337
$447$	18.8265	0.890461
$448$	3.19198	0.150807
$449$	15.2933	0.721736	0.360868	−	0.932617i	$-0.382480\pi$
$449$	15.2933	0.721736	0.360868	+	0.932617i	$0.382480\pi$
$450$	−13.7196	−0.646750
$451$	−32.4775	−1.52931
$452$	−16.0162	−0.753337
$453$	3.94214	0.185218
$454$	6.60366	0.309925
$455$	8.53348	0.400056
$456$	1.19313	0.0558735
$457$	15.5096	0.725508	0.362754	−	0.931885i	$-0.381836\pi$
$457$	15.5096	0.725508	0.362754	+	0.931885i	$0.381836\pi$
$458$	8.17999	0.382226
$459$	−1.00000	−0.0466760
$460$	21.2787	0.992125
$461$	−31.7948	−1.48083	−0.740416	−	0.672149i	$-0.765372\pi$
$461$	−31.7948	−1.48083	−0.740416	+	0.672149i	$0.765372\pi$
$462$	13.9781	0.650319
$463$	9.39201	0.436484	0.218242	−	0.975895i	$-0.429968\pi$
$463$	9.39201	0.436484	0.218242	+	0.975895i	$0.429968\pi$
$464$	5.98405	0.277803
$465$	5.54168	0.256989
$466$	3.53879	0.163931
$467$	−33.2389	−1.53811	−0.769056	−	0.639182i	$-0.779273\pi$
$467$	−33.2389	−1.53811	−0.769056	+	0.639182i	$0.779273\pi$
$468$	0.617899	0.0285624
$469$	27.7747	1.28252
$470$	−10.2833	−0.474332
$471$	10.1290	0.466722
$472$	1.00000	0.0460287
$473$	−20.8684	−0.959529
$474$	0.864276	0.0396975
$475$	16.3693	0.751076
$476$	3.19198	0.146304
$477$	−3.41324	−0.156282
$478$	7.17196	0.328038
$479$	−8.56446	−0.391320	−0.195660	−	0.980672i	$-0.562685\pi$
$479$	−8.56446	−0.391320	−0.195660	+	0.980672i	$0.562685\pi$
$480$	4.32662	0.197482
$481$	−4.05160	−0.184737
$482$	−2.08869	−0.0951373
$483$	−15.6984	−0.714303
$484$	8.17679	0.371672
$485$	78.0032	3.54194
$486$	1.00000	0.0453609
$487$	14.8687	0.673763	0.336882	−	0.941547i	$-0.390628\pi$
$487$	14.8687	0.673763	0.336882	+	0.941547i	$0.390628\pi$
$488$	6.96926	0.315484
$489$	0.0612211	0.00276851
$490$	−13.7963	−0.623255
$491$	22.1702	1.00053	0.500264	−	0.865873i	$-0.333236\pi$
$491$	22.1702	1.00053	0.500264	+	0.865873i	$0.333236\pi$
$492$	7.41643	0.334359
$493$	5.98405	0.269508
$494$	−0.737235	−0.0331698
$495$	18.9468	0.851597
$496$	−1.28083	−0.0575111
$497$	−1.11786	−0.0501427
$498$	−2.76138	−0.123740
$499$	21.1461	0.946628	0.473314	−	0.880894i	$-0.343058\pi$
$499$	21.1461	0.946628	0.473314	+	0.880894i	$0.343058\pi$
$500$	37.7265	1.68718
$501$	−3.25340	−0.145351
$502$	−6.72064	−0.299957
$503$	7.01582	0.312820	0.156410	−	0.987692i	$-0.450008\pi$
$503$	7.01582	0.312820	0.156410	+	0.987692i	$0.450008\pi$
$504$	−3.19198	−0.142182
$505$	85.6293	3.81045
$506$	−21.5370	−0.957435
$507$	12.6182	0.560394
$508$	11.2941	0.501094
$509$	−39.5844	−1.75455	−0.877275	−	0.479989i	$-0.840641\pi$
$509$	−39.5844	−1.75455	−0.877275	+	0.479989i	$0.840641\pi$
$510$	4.32662	0.191586
$511$	43.5605	1.92700
$512$	−1.00000	−0.0441942
$513$	−1.19313	−0.0526780
$514$	20.2137	0.891587
$515$	−63.8324	−2.81279
$516$	4.76541	0.209786
$517$	10.4081	0.457747
$518$	20.9300	0.919609
$519$	19.4197	0.852429
$520$	−2.67341	−0.117237
$521$	9.45619	0.414283	0.207142	−	0.978311i	$-0.433584\pi$
$521$	9.45619	0.414283	0.207142	+	0.978311i	$0.433584\pi$
$522$	−5.98405	−0.261915
$523$	23.0271	1.00690	0.503452	−	0.864023i	$-0.332063\pi$
$523$	23.0271	1.00690	0.503452	+	0.864023i	$0.332063\pi$
$524$	−4.23282	−0.184911
$525$	−43.7927	−1.91127
$526$	−9.19721	−0.401018
$527$	−1.28083	−0.0557940
$528$	−4.37913	−0.190577
$529$	1.18763	0.0516360
$530$	14.7678	0.641472
$531$	−1.00000	−0.0433963
$532$	3.80845	0.165117
$533$	−4.58261	−0.198495
$534$	3.17514	0.137402
$535$	−33.5806	−1.45182
$536$	−8.70140	−0.375843
$537$	18.0755	0.780014
$538$	−11.8658	−0.511570
$539$	13.9638	0.601463
$540$	−4.32662	−0.186188
$541$	−31.0061	−1.33306	−0.666529	−	0.745479i	$-0.732221\pi$
$541$	−31.0061	−1.33306	−0.666529	+	0.745479i	$0.732221\pi$
$542$	−17.5808	−0.755160
$543$	21.0070	0.901497
$544$	−1.00000	−0.0428746
$545$	−53.6063	−2.29624
$546$	1.97232	0.0844075
$547$	36.8136	1.57404	0.787019	−	0.616929i	$-0.211623\pi$
$547$	36.8136	1.57404	0.787019	+	0.616929i	$0.211623\pi$
$548$	−11.4184	−0.487770
$549$	−6.96926	−0.297441
$550$	−60.0801	−2.56182
$551$	7.13976	0.304164
$552$	4.91809	0.209328
$553$	2.75875	0.117314
$554$	16.9756	0.721222
$555$	28.3699	1.20423
$556$	−15.1732	−0.643488
$557$	17.0980	0.724464	0.362232	−	0.932088i	$-0.382015\pi$
$557$	17.0980	0.724464	0.362232	+	0.932088i	$0.382015\pi$
$558$	1.28083	0.0542220
$559$	−2.94455	−0.124541
$560$	13.8105	0.583599
$561$	−4.37913	−0.184887
$562$	28.4817	1.20143
$563$	9.09554	0.383331	0.191666	−	0.981460i	$-0.438611\pi$
$563$	9.09554	0.383331	0.191666	+	0.981460i	$0.438611\pi$
$564$	−2.37675	−0.100079
$565$	−69.2958	−2.91530
$566$	−30.3511	−1.27575
$567$	3.19198	0.134050
$568$	0.350208	0.0146944
$569$	−42.1737	−1.76801	−0.884006	−	0.467475i	$-0.845164\pi$
$569$	−42.1737	−1.76801	−0.884006	+	0.467475i	$0.845164\pi$
$570$	5.16223	0.216222
$571$	−26.3348	−1.10208	−0.551039	−	0.834479i	$-0.685769\pi$
$571$	−26.3348	−1.10208	−0.551039	+	0.834479i	$0.685769\pi$
$572$	2.70586	0.113138
$573$	9.63944	0.402693
$574$	23.6731	0.988095
$575$	67.4744	2.81388
$576$	1.00000	0.0416667
$577$	31.4503	1.30929	0.654646	−	0.755936i	$-0.272818\pi$
$577$	31.4503	1.30929	0.654646	+	0.755936i	$0.272818\pi$
$578$	−1.00000	−0.0415945
$579$	10.0196	0.416401
$580$	25.8907	1.07505
$581$	−8.81425	−0.365677
$582$	18.0287	0.747312
$583$	−14.9470	−0.619043
$584$	−13.6469	−0.564711
$585$	2.67341	0.110532
$586$	−9.13661	−0.377430
$587$	−37.8147	−1.56078	−0.780391	−	0.625292i	$-0.784980\pi$
$587$	−37.8147	−1.56078	−0.780391	+	0.625292i	$0.784980\pi$
$588$	−3.18871	−0.131500
$589$	−1.52820	−0.0629685
$590$	4.32662	0.178124
$591$	−0.291283	−0.0119818
$592$	−6.55705	−0.269493
$593$	−36.2756	−1.48966	−0.744830	−	0.667254i	$-0.767470\pi$
$593$	−36.2756	−1.48966	−0.744830	+	0.667254i	$0.767470\pi$
$594$	4.37913	0.179678
$595$	13.8105	0.566174
$596$	−18.8265	−0.771162
$597$	2.43632	0.0997120
$598$	−3.03889	−0.124269
$599$	13.7975	0.563750	0.281875	−	0.959451i	$-0.409044\pi$
$599$	13.7975	0.563750	0.281875	+	0.959451i	$0.409044\pi$
$600$	13.7196	0.560102
$601$	34.4268	1.40430	0.702150	−	0.712029i	$-0.252224\pi$
$601$	34.4268	1.40430	0.702150	+	0.712029i	$0.252224\pi$
$602$	15.2111	0.619958
$603$	8.70140	0.354349
$604$	−3.94214	−0.160403
$605$	35.3778	1.43831
$606$	19.7913	0.803966
$607$	18.6331	0.756296	0.378148	−	0.925745i	$-0.376561\pi$
$607$	18.6331	0.756296	0.378148	+	0.925745i	$0.376561\pi$
$608$	−1.19313	−0.0483879
$609$	−19.1010	−0.774010
$610$	30.1533	1.22087
$611$	1.46859	0.0594128
$612$	1.00000	0.0404226
$613$	−15.9362	−0.643656	−0.321828	−	0.946798i	$-0.604297\pi$
$613$	−15.9362	−0.643656	−0.321828	+	0.946798i	$0.604297\pi$
$614$	−2.67041	−0.107769
$615$	32.0881	1.29392
$616$	−13.9781	−0.563193
$617$	36.3574	1.46370	0.731848	−	0.681468i	$-0.238658\pi$
$617$	36.3574	1.46370	0.731848	+	0.681468i	$0.238658\pi$
$618$	−14.7534	−0.593469
$619$	6.15705	0.247473	0.123736	−	0.992315i	$-0.460512\pi$
$619$	6.15705	0.247473	0.123736	+	0.992315i	$0.460512\pi$
$620$	−5.54168	−0.222559
$621$	−4.91809	−0.197356
$622$	0.740803	0.0297035
$623$	10.1350	0.406048
$624$	−0.617899	−0.0247358
$625$	94.6301	3.78521
$626$	10.1107	0.404107
$627$	−5.22488	−0.208662
$628$	−10.1290	−0.404193
$629$	−6.55705	−0.261447
$630$	−13.8105	−0.550222
$631$	−16.0823	−0.640226	−0.320113	−	0.947379i	$-0.603721\pi$
$631$	−16.0823	−0.640226	−0.320113	+	0.947379i	$0.603721\pi$
$632$	−0.864276	−0.0343790
$633$	3.68851	0.146605
$634$	1.33871	0.0531671
$635$	48.8652	1.93916
$636$	3.41324	0.135344
$637$	1.97030	0.0780662
$638$	−26.2050	−1.03746
$639$	−0.350208	−0.0138540
$640$	−4.32662	−0.171025
$641$	35.2698	1.39307	0.696536	−	0.717522i	$-0.254724\pi$
$641$	35.2698	1.39307	0.696536	+	0.717522i	$0.254724\pi$
$642$	−7.76140	−0.306318
$643$	−5.30157	−0.209074	−0.104537	−	0.994521i	$-0.533336\pi$
$643$	−5.30157	−0.209074	−0.104537	+	0.994521i	$0.533336\pi$
$644$	15.6984	0.618605
$645$	20.6181	0.811838
$646$	−1.19313	−0.0469431
$647$	36.0537	1.41742	0.708709	−	0.705501i	$-0.249278\pi$
$647$	36.0537	1.41742	0.708709	+	0.705501i	$0.249278\pi$
$648$	−1.00000	−0.0392837
$649$	−4.37913	−0.171896
$650$	−8.47735	−0.332509
$651$	4.08839	0.160237
$652$	−0.0612211	−0.00239760
$653$	23.4849	0.919035	0.459517	−	0.888169i	$-0.348022\pi$
$653$	23.4849	0.919035	0.459517	+	0.888169i	$0.348022\pi$
$654$	−12.3899	−0.484483
$655$	−18.3138	−0.715579
$656$	−7.41643	−0.289563
$657$	13.6469	0.532415
$658$	−7.58652	−0.295753
$659$	−7.93231	−0.308999	−0.154500	−	0.987993i	$-0.549377\pi$
$659$	−7.93231	−0.308999	−0.154500	+	0.987993i	$0.549377\pi$
$660$	−18.9468	−0.737504
$661$	5.02211	0.195337	0.0976687	−	0.995219i	$-0.468861\pi$
$661$	5.02211	0.195337	0.0976687	+	0.995219i	$0.468861\pi$
$662$	−31.7598	−1.23438
$663$	−0.617899	−0.0239972
$664$	2.76138	0.107162
$665$	16.4777	0.638978
$666$	6.55705	0.254081
$667$	29.4301	1.13954
$668$	3.25340	0.125878
$669$	−14.5579	−0.562841
$670$	−37.6477	−1.45446
$671$	−30.5193	−1.17819
$672$	3.19198	0.123133
$673$	−9.26686	−0.357211	−0.178606	−	0.983921i	$-0.557159\pi$
$673$	−9.26686	−0.357211	−0.178606	+	0.983921i	$0.557159\pi$
$674$	2.28323	0.0879468
$675$	−13.7196	−0.528069
$676$	−12.6182	−0.485315
$677$	−15.2966	−0.587895	−0.293948	−	0.955822i	$-0.594969\pi$
$677$	−15.2966	−0.587895	−0.293948	+	0.955822i	$0.594969\pi$
$678$	−16.0162	−0.615097
$679$	57.5471	2.20845
$680$	−4.32662	−0.165918
$681$	6.60366	0.253053
$682$	5.60894	0.214777
$683$	41.5082	1.58827	0.794133	−	0.607744i	$-0.207925\pi$
$683$	41.5082	1.58827	0.794133	+	0.607744i	$0.207925\pi$
$684$	1.19313	0.0456205
$685$	−49.4031	−1.88760
$686$	12.1655	0.464483
$687$	8.17999	0.312086
$688$	−4.76541	−0.181680
$689$	−2.10904	−0.0803480
$690$	21.2787	0.810067
$691$	−1.36716	−0.0520094	−0.0260047	−	0.999662i	$-0.508278\pi$
$691$	−1.36716	−0.0520094	−0.0260047	+	0.999662i	$0.508278\pi$
$692$	−19.4197	−0.738225
$693$	13.9781	0.530983
$694$	−28.7100	−1.08982
$695$	−65.6488	−2.49020
$696$	5.98405	0.226825
$697$	−7.41643	−0.280917
$698$	12.4901	0.472758
$699$	3.53879	0.133849
$700$	43.7927	1.65521
$701$	17.7597	0.670774	0.335387	−	0.942080i	$-0.391133\pi$
$701$	17.7597	0.670774	0.335387	+	0.942080i	$0.391133\pi$
$702$	0.617899	0.0233211
$703$	−7.82343	−0.295066
$704$	4.37913	0.165045
$705$	−10.2833	−0.387291
$706$	15.6142	0.587648
$707$	63.1733	2.37588
$708$	1.00000	0.0375823
$709$	38.3945	1.44193	0.720967	−	0.692969i	$-0.243698\pi$
$709$	38.3945	1.44193	0.720967	+	0.692969i	$0.243698\pi$
$710$	1.51522	0.0568651
$711$	0.864276	0.0324129
$712$	−3.17514	−0.118993
$713$	−6.29925	−0.235909
$714$	3.19198	0.119457
$715$	11.7072	0.437826
$716$	−18.0755	−0.675512
$717$	7.17196	0.267842
$718$	−31.5744	−1.17835
$719$	50.7730	1.89351	0.946757	−	0.321949i	$-0.104338\pi$
$719$	50.7730	1.89351	0.946757	+	0.321949i	$0.104338\pi$
$720$	4.32662	0.161244
$721$	−47.0925	−1.75382
$722$	17.5764	0.654127
$723$	−2.08869	−0.0776793
$724$	−21.0070	−0.780719
$725$	82.0990	3.04908
$726$	8.17679	0.303469
$727$	25.7890	0.956462	0.478231	−	0.878234i	$-0.341278\pi$
$727$	25.7890	0.956462	0.478231	+	0.878234i	$0.341278\pi$
$728$	−1.97232	−0.0730990
$729$	1.00000	0.0370370
$730$	−59.0448	−2.18535
$731$	−4.76541	−0.176255
$732$	6.96926	0.257591
$733$	40.6356	1.50091	0.750455	−	0.660922i	$-0.229835\pi$
$733$	40.6356	1.50091	0.750455	+	0.660922i	$0.229835\pi$
$734$	4.35349	0.160690
$735$	−13.7963	−0.508886
$736$	−4.91809	−0.181283
$737$	38.1046	1.40360
$738$	7.41643	0.273003
$739$	−19.7906	−0.728010	−0.364005	−	0.931397i	$-0.618591\pi$
$739$	−19.7906	−0.728010	−0.364005	+	0.931397i	$0.618591\pi$
$740$	−28.3699	−1.04290
$741$	−0.737235	−0.0270830
$742$	10.8950	0.399968
$743$	−10.2540	−0.376182	−0.188091	−	0.982152i	$-0.560230\pi$
$743$	−10.2540	−0.376182	−0.188091	+	0.982152i	$0.560230\pi$
$744$	−1.28083	−0.0469576
$745$	−81.4549	−2.98428
$746$	−31.6739	−1.15966
$747$	−2.76138	−0.101033
$748$	4.37913	0.160117
$749$	−24.7742	−0.905230
$750$	37.7265	1.37758
$751$	0.892066	0.0325519	0.0162760	−	0.999868i	$-0.494819\pi$
$751$	0.892066	0.0325519	0.0162760	+	0.999868i	$0.494819\pi$
$752$	2.37675	0.0866710
$753$	−6.72064	−0.244914
$754$	−3.69754	−0.134657
$755$	−17.0561	−0.620736
$756$	−3.19198	−0.116091
$757$	−15.2054	−0.552651	−0.276326	−	0.961064i	$-0.589117\pi$
$757$	−15.2054	−0.552651	−0.276326	+	0.961064i	$0.589117\pi$
$758$	−17.3317	−0.629515
$759$	−21.5370	−0.781742
$760$	−5.16223	−0.187254
$761$	26.6084	0.964552	0.482276	−	0.876019i	$-0.339810\pi$
$761$	26.6084	0.964552	0.482276	+	0.876019i	$0.339810\pi$
$762$	11.2941	0.409142
$763$	−39.5482	−1.43174
$764$	−9.63944	−0.348743
$765$	4.32662	0.156429
$766$	25.3044	0.914284
$767$	−0.617899	−0.0223110
$768$	−1.00000	−0.0360844
$769$	44.0793	1.58954	0.794770	−	0.606911i	$-0.207591\pi$
$769$	44.0793	1.58954	0.794770	+	0.606911i	$0.207591\pi$
$770$	−60.4778	−2.17947
$771$	20.2137	0.727978
$772$	−10.0196	−0.360614
$773$	−22.8046	−0.820224	−0.410112	−	0.912035i	$-0.634510\pi$
$773$	−22.8046	−0.820224	−0.410112	+	0.912035i	$0.634510\pi$
$774$	4.76541	0.171289
$775$	−17.5726	−0.631225
$776$	−18.0287	−0.647192
$777$	20.9300	0.750858
$778$	12.0321	0.431370
$779$	−8.84878	−0.317040
$780$	−2.67341	−0.0957236
$781$	−1.53361	−0.0548768
$782$	−4.91809	−0.175871
$783$	−5.98405	−0.213853
$784$	3.18871	0.113883
$785$	−43.8245	−1.56416
$786$	−4.23282	−0.150980
$787$	−17.8529	−0.636386	−0.318193	−	0.948026i	$-0.603076\pi$
$787$	−17.8529	−0.636386	−0.318193	+	0.948026i	$0.603076\pi$
$788$	0.291283	0.0103765
$789$	−9.19721	−0.327430
$790$	−3.73939	−0.133042
$791$	−51.1232	−1.81773
$792$	−4.37913	−0.155606
$793$	−4.30630	−0.152921
$794$	−15.8676	−0.563119
$795$	14.7678	0.523760
$796$	−2.43632	−0.0863531
$797$	−8.80144	−0.311763	−0.155882	−	0.987776i	$-0.549822\pi$
$797$	−8.80144	−0.311763	−0.155882	+	0.987776i	$0.549822\pi$
$798$	3.80845	0.134818
$799$	2.37675	0.0840833
$800$	−13.7196	−0.485062
$801$	3.17514	0.112188
$802$	22.1948	0.783727
$803$	59.7614	2.10893
$804$	−8.70140	−0.306875
$805$	67.9211	2.39391
$806$	0.791426	0.0278768
$807$	−11.8658	−0.417695
$808$	−19.7913	−0.696255
$809$	6.98945	0.245736	0.122868	−	0.992423i	$-0.460791\pi$
$809$	6.98945	0.245736	0.122868	+	0.992423i	$0.460791\pi$
$810$	−4.32662	−0.152022
$811$	19.5394	0.686122	0.343061	−	0.939313i	$-0.388536\pi$
$811$	19.5394	0.686122	0.343061	+	0.939313i	$0.388536\pi$
$812$	19.1010	0.670312
$813$	−17.5808	−0.616586
$814$	28.7142	1.00643
$815$	−0.264880	−0.00927836
$816$	−1.00000	−0.0350070
$817$	−5.68577	−0.198920
$818$	13.5784	0.474758
$819$	1.97232	0.0689184
$820$	−32.0881	−1.12056
$821$	−36.4375	−1.27168	−0.635838	−	0.771822i	$-0.719346\pi$
$821$	−36.4375	−1.27168	−0.635838	+	0.771822i	$0.719346\pi$
$822$	−11.4184	−0.398263
$823$	3.12999	0.109105	0.0545523	−	0.998511i	$-0.482627\pi$
$823$	3.12999	0.109105	0.0545523	+	0.998511i	$0.482627\pi$
$824$	14.7534	0.513959
$825$	−60.0801	−2.09172
$826$	3.19198	0.111063
$827$	23.6879	0.823709	0.411855	−	0.911250i	$-0.364881\pi$
$827$	23.6879	0.823709	0.411855	+	0.911250i	$0.364881\pi$
$828$	4.91809	0.170916
$829$	−1.10012	−0.0382088	−0.0191044	−	0.999817i	$-0.506081\pi$
$829$	−1.10012	−0.0382088	−0.0191044	+	0.999817i	$0.506081\pi$
$830$	11.9474	0.414701
$831$	16.9756	0.588875
$832$	0.617899	0.0214218
$833$	3.18871	0.110482
$834$	−15.1732	−0.525406
$835$	14.0762	0.487127
$836$	5.22488	0.180706
$837$	1.28083	0.0442721
$838$	34.2624	1.18357
$839$	38.4022	1.32579	0.662896	−	0.748712i	$-0.269327\pi$
$839$	38.4022	1.32579	0.662896	+	0.748712i	$0.269327\pi$
$840$	13.8105	0.476506
$841$	6.80891	0.234790
$842$	−17.5231	−0.603884
$843$	28.4817	0.980961
$844$	−3.68851	−0.126964
$845$	−54.5941	−1.87810
$846$	−2.37675	−0.0817142
$847$	26.1001	0.896810
$848$	−3.41324	−0.117211
$849$	−30.3511	−1.04165
$850$	−13.7196	−0.470579
$851$	−32.2482	−1.10545
$852$	0.350208	0.0119979
$853$	13.1507	0.450271	0.225135	−	0.974327i	$-0.427718\pi$
$853$	13.1507	0.450271	0.225135	+	0.974327i	$0.427718\pi$
$854$	22.2457	0.761233
$855$	5.16223	0.176544
$856$	7.76140	0.265279
$857$	−18.3474	−0.626736	−0.313368	−	0.949632i	$-0.601457\pi$
$857$	−18.3474	−0.626736	−0.313368	+	0.949632i	$0.601457\pi$
$858$	2.70586	0.0923766
$859$	−25.9481	−0.885336	−0.442668	−	0.896686i	$-0.645968\pi$
$859$	−25.9481	−0.885336	−0.442668	+	0.896686i	$0.645968\pi$
$860$	−20.6181	−0.703072
$861$	23.6731	0.806776
$862$	3.66671	0.124889
$863$	−18.0230	−0.613509	−0.306754	−	0.951789i	$-0.599243\pi$
$863$	−18.0230	−0.613509	−0.306754	+	0.951789i	$0.599243\pi$
$864$	1.00000	0.0340207
$865$	−84.0215	−2.85682
$866$	9.73834	0.330922
$867$	−1.00000	−0.0339618
$868$	−4.08839	−0.138769
$869$	3.78478	0.128390
$870$	25.8907	0.877778
$871$	5.37659	0.182179
$872$	12.3899	0.419575
$873$	18.0287	0.610178
$874$	−5.86793	−0.198486
$875$	120.422	4.07101
$876$	−13.6469	−0.461085
$877$	37.6032	1.26977	0.634886	−	0.772606i	$-0.281047\pi$
$877$	37.6032	1.26977	0.634886	+	0.772606i	$0.281047\pi$
$878$	−22.8631	−0.771593
$879$	−9.13661	−0.308170
$880$	18.9468	0.638698
$881$	−46.1018	−1.55321	−0.776604	−	0.629989i	$-0.783059\pi$
$881$	−46.1018	−1.55321	−0.776604	+	0.629989i	$0.783059\pi$
$882$	−3.18871	−0.107369
$883$	19.7441	0.664441	0.332220	−	0.943202i	$-0.392202\pi$
$883$	19.7441	0.664441	0.332220	+	0.943202i	$0.392202\pi$
$884$	0.617899	0.0207822
$885$	4.32662	0.145438
$886$	35.3056	1.18611
$887$	−0.458878	−0.0154076	−0.00770381	−	0.999970i	$-0.502452\pi$
$887$	−0.458878	−0.0154076	−0.00770381	+	0.999970i	$0.502452\pi$
$888$	−6.55705	−0.220040
$889$	36.0505	1.20909
$890$	−13.7376	−0.460485
$891$	4.37913	0.146706
$892$	14.5579	0.487435
$893$	2.83577	0.0948955
$894$	−18.8265	−0.629651
$895$	−78.2056	−2.61413
$896$	−3.19198	−0.106636
$897$	−3.03889	−0.101465
$898$	−15.2933	−0.510344
$899$	−7.66458	−0.255628
$900$	13.7196	0.457321
$901$	−3.41324	−0.113712
$902$	32.4775	1.08138
$903$	15.2111	0.506193
$904$	16.0162	0.532690
$905$	−90.8893	−3.02126
$906$	−3.94214	−0.130969
$907$	−10.4024	−0.345407	−0.172703	−	0.984974i	$-0.555250\pi$
$907$	−10.4024	−0.345407	−0.172703	+	0.984974i	$0.555250\pi$
$908$	−6.60366	−0.219150
$909$	19.7913	0.656435
$910$	−8.53348	−0.282882
$911$	−7.33256	−0.242939	−0.121469	−	0.992595i	$-0.538761\pi$
$911$	−7.33256	−0.242939	−0.121469	+	0.992595i	$0.538761\pi$
$912$	−1.19313	−0.0395085
$913$	−12.0924	−0.400201
$914$	−15.5096	−0.513012
$915$	30.1533	0.996839
$916$	−8.17999	−0.270275
$917$	−13.5110	−0.446174
$918$	1.00000	0.0330049
$919$	21.1787	0.698620	0.349310	−	0.937007i	$-0.386416\pi$
$919$	21.1787	0.698620	0.349310	+	0.937007i	$0.386416\pi$
$920$	−21.2787	−0.701538
$921$	−2.67041	−0.0879929
$922$	31.7948	1.04711
$923$	−0.216394	−0.00712268
$924$	−13.9781	−0.459845
$925$	−89.9603	−2.95788
$926$	−9.39201	−0.308641
$927$	−14.7534	−0.484565
$928$	−5.98405	−0.196436
$929$	13.4105	0.439985	0.219992	−	0.975502i	$-0.429397\pi$
$929$	13.4105	0.439985	0.219992	+	0.975502i	$0.429397\pi$
$930$	−5.54168	−0.181719
$931$	3.80455	0.124689
$932$	−3.53879	−0.115917
$933$	0.740803	0.0242528
$934$	33.2389	1.08761
$935$	18.9468	0.619628
$936$	−0.617899	−0.0201967
$937$	−2.88197	−0.0941497	−0.0470749	−	0.998891i	$-0.514990\pi$
$937$	−2.88197	−0.0941497	−0.0470749	+	0.998891i	$0.514990\pi$
$938$	−27.7747	−0.906875
$939$	10.1107	0.329952
$940$	10.2833	0.335404
$941$	12.6195	0.411385	0.205693	−	0.978617i	$-0.434055\pi$
$941$	12.6195	0.411385	0.205693	+	0.978617i	$0.434055\pi$
$942$	−10.1290	−0.330022
$943$	−36.4747	−1.18778
$944$	−1.00000	−0.0325472
$945$	−13.8105	−0.449254
$946$	20.8684	0.678489
$947$	28.3273	0.920515	0.460257	−	0.887786i	$-0.347757\pi$
$947$	28.3273	0.920515	0.460257	+	0.887786i	$0.347757\pi$
$948$	−0.864276	−0.0280704
$949$	8.43239	0.273727
$950$	−16.3693	−0.531091
$951$	1.33871	0.0434107
$952$	−3.19198	−0.103453
$953$	54.1260	1.75331	0.876657	−	0.481116i	$-0.159768\pi$
$953$	54.1260	1.75331	0.876657	+	0.481116i	$0.159768\pi$
$954$	3.41324	0.110508
$955$	−41.7062	−1.34958
$956$	−7.17196	−0.231958
$957$	−26.2050	−0.847086
$958$	8.56446	0.276705
$959$	−36.4473	−1.17694
$960$	−4.32662	−0.139641
$961$	−29.3595	−0.947080
$962$	4.05160	0.130629
$963$	−7.76140	−0.250108
$964$	2.08869	0.0672723
$965$	−43.3511	−1.39552
$966$	15.6984	0.505089
$967$	6.80929	0.218972	0.109486	−	0.993988i	$-0.465080\pi$
$967$	6.80929	0.218972	0.109486	+	0.993988i	$0.465080\pi$
$968$	−8.17679	−0.262812
$969$	−1.19313	−0.0383289
$970$	−78.0032	−2.50453
$971$	25.5956	0.821403	0.410702	−	0.911770i	$-0.365284\pi$
$971$	25.5956	0.821403	0.410702	+	0.911770i	$0.365284\pi$
$972$	−1.00000	−0.0320750
$973$	−48.4326	−1.55268
$974$	−14.8687	−0.476422
$975$	−8.47735	−0.271492
$976$	−6.96926	−0.223081
$977$	−25.7486	−0.823772	−0.411886	−	0.911235i	$-0.635130\pi$
$977$	−25.7486	−0.823772	−0.411886	+	0.911235i	$0.635130\pi$
$978$	−0.0612211	−0.00195764
$979$	13.9043	0.444384
$980$	13.7963	0.440708
$981$	−12.3899	−0.395579
$982$	−22.1702	−0.707481
$983$	57.4432	1.83215	0.916076	−	0.401004i	$-0.131339\pi$
$983$	57.4432	1.83215	0.916076	+	0.401004i	$0.131339\pi$
$984$	−7.41643	−0.236427
$985$	1.26027	0.0401555
$986$	−5.98405	−0.190571
$987$	−7.58652	−0.241482
$988$	0.737235	0.0234546
$989$	−23.4367	−0.745245
$990$	−18.9468	−0.602170
$991$	−18.1899	−0.577822	−0.288911	−	0.957356i	$-0.593293\pi$
$991$	−18.1899	−0.577822	−0.288911	+	0.957356i	$0.593293\pi$
$992$	1.28083	0.0406665
$993$	−31.7598	−1.00787
$994$	1.11786	0.0354563
$995$	−10.5410	−0.334173
$996$	2.76138	0.0874976
$997$	37.5714	1.18990	0.594950	−	0.803763i	$-0.297172\pi$
$997$	37.5714	1.18990	0.594950	+	0.803763i	$0.297172\pi$
$998$	−21.1461	−0.669367
$999$	6.55705	0.207456

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.x.1.10	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.x.1.10	✓	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.32662 q^{5} +1.00000 q^{6} +3.19198 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.32662 q^{5} +1.00000 q^{6} +3.19198 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.32662 q^{10} +4.37913 q^{11} -1.00000 q^{12} +0.617899 q^{13} -3.19198 q^{14} -4.32662 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +1.19313 q^{19} +4.32662 q^{20} -3.19198 q^{21} -4.37913 q^{22} +4.91809 q^{23} +1.00000 q^{24} +13.7196 q^{25} -0.617899 q^{26} -1.00000 q^{27} +3.19198 q^{28} +5.98405 q^{29} +4.32662 q^{30} -1.28083 q^{31} -1.00000 q^{32} -4.37913 q^{33} -1.00000 q^{34} +13.8105 q^{35} +1.00000 q^{36} -6.55705 q^{37} -1.19313 q^{38} -0.617899 q^{39} -4.32662 q^{40} -7.41643 q^{41} +3.19198 q^{42} -4.76541 q^{43} +4.37913 q^{44} +4.32662 q^{45} -4.91809 q^{46} +2.37675 q^{47} -1.00000 q^{48} +3.18871 q^{49} -13.7196 q^{50} -1.00000 q^{51} +0.617899 q^{52} -3.41324 q^{53} +1.00000 q^{54} +18.9468 q^{55} -3.19198 q^{56} -1.19313 q^{57} -5.98405 q^{58} -1.00000 q^{59} -4.32662 q^{60} -6.96926 q^{61} +1.28083 q^{62} +3.19198 q^{63} +1.00000 q^{64} +2.67341 q^{65} +4.37913 q^{66} +8.70140 q^{67} +1.00000 q^{68} -4.91809 q^{69} -13.8105 q^{70} -0.350208 q^{71} -1.00000 q^{72} +13.6469 q^{73} +6.55705 q^{74} -13.7196 q^{75} +1.19313 q^{76} +13.9781 q^{77} +0.617899 q^{78} +0.864276 q^{79} +4.32662 q^{80} +1.00000 q^{81} +7.41643 q^{82} -2.76138 q^{83} -3.19198 q^{84} +4.32662 q^{85} +4.76541 q^{86} -5.98405 q^{87} -4.37913 q^{88} +3.17514 q^{89} -4.32662 q^{90} +1.97232 q^{91} +4.91809 q^{92} +1.28083 q^{93} -2.37675 q^{94} +5.16223 q^{95} +1.00000 q^{96} +18.0287 q^{97} -3.18871 q^{98} +4.37913 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + q^{5} + 10 q^{6} + 10 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + q^5 + 10 * q^6 + 10 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + q^{5} + 10 q^{6} + 10 q^{7} - 10 q^{8} + 10 q^{9} - q^{10} + 2 q^{11} - 10 q^{12} - 10 q^{14} - q^{15} + 10 q^{16} + 10 q^{17} - 10 q^{18} + 15 q^{19} + q^{20} - 10 q^{21} - 2 q^{22} + 19 q^{23} + 10 q^{24} + 19 q^{25} - 10 q^{27} + 10 q^{28} - q^{29} + q^{30} + 15 q^{31} - 10 q^{32} - 2 q^{33} - 10 q^{34} - 14 q^{35} + 10 q^{36} + q^{37} - 15 q^{38} - q^{40} - 5 q^{41} + 10 q^{42} + 26 q^{43} + 2 q^{44} + q^{45} - 19 q^{46} + 14 q^{47} - 10 q^{48} + 20 q^{49} - 19 q^{50} - 10 q^{51} - 2 q^{53} + 10 q^{54} + 4 q^{55} - 10 q^{56} - 15 q^{57} + q^{58} - 10 q^{59} - q^{60} + 4 q^{61} - 15 q^{62} + 10 q^{63} + 10 q^{64} - 20 q^{65} + 2 q^{66} + 15 q^{67} + 10 q^{68} - 19 q^{69} + 14 q^{70} + 14 q^{71} - 10 q^{72} + 43 q^{73} - q^{74} - 19 q^{75} + 15 q^{76} + 20 q^{77} + q^{80} + 10 q^{81} + 5 q^{82} - 4 q^{83} - 10 q^{84} + q^{85} - 26 q^{86} + q^{87} - 2 q^{88} - 22 q^{89} - q^{90} - q^{91} + 19 q^{92} - 15 q^{93} - 14 q^{94} - 37 q^{95} + 10 q^{96} + 37 q^{97} - 20 q^{98} + 2 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + q^5 + 10 * q^6 + 10 * q^7 - 10 * q^8 + 10 * q^9 - q^10 + 2 * q^11 - 10 * q^12 - 10 * q^14 - q^15 + 10 * q^16 + 10 * q^17 - 10 * q^18 + 15 * q^19 + q^20 - 10 * q^21 - 2 * q^22 + 19 * q^23 + 10 * q^24 + 19 * q^25 - 10 * q^27 + 10 * q^28 - q^29 + q^30 + 15 * q^31 - 10 * q^32 - 2 * q^33 - 10 * q^34 - 14 * q^35 + 10 * q^36 + q^37 - 15 * q^38 - q^40 - 5 * q^41 + 10 * q^42 + 26 * q^43 + 2 * q^44 + q^45 - 19 * q^46 + 14 * q^47 - 10 * q^48 + 20 * q^49 - 19 * q^50 - 10 * q^51 - 2 * q^53 + 10 * q^54 + 4 * q^55 - 10 * q^56 - 15 * q^57 + q^58 - 10 * q^59 - q^60 + 4 * q^61 - 15 * q^62 + 10 * q^63 + 10 * q^64 - 20 * q^65 + 2 * q^66 + 15 * q^67 + 10 * q^68 - 19 * q^69 + 14 * q^70 + 14 * q^71 - 10 * q^72 + 43 * q^73 - q^74 - 19 * q^75 + 15 * q^76 + 20 * q^77 + q^80 + 10 * q^81 + 5 * q^82 - 4 * q^83 - 10 * q^84 + q^85 - 26 * q^86 + q^87 - 2 * q^88 - 22 * q^89 - q^90 - q^91 + 19 * q^92 - 15 * q^93 - 14 * q^94 - 37 * q^95 + 10 * q^96 + 37 * q^97 - 20 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more