LMFDB - Embedded newform 5610.2.a.bq.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5610,2,Mod(1,5610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5610, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("5610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5610.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:	$44.7960755339$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{33}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 8 $ x^2 - x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.37228$ of defining polynomial
Character	$\chi$	$=$	5610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -3.37228 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -3.37228 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} -4.00000 q^{13} +3.37228 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +4.00000 q^{19} +1.00000 q^{20} +3.37228 q^{21} -1.00000 q^{22} -7.37228 q^{23} +1.00000 q^{24} +1.00000 q^{25} +4.00000 q^{26} -1.00000 q^{27} -3.37228 q^{28} -0.627719 q^{29} +1.00000 q^{30} +8.11684 q^{31} -1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} -3.37228 q^{35} +1.00000 q^{36} -2.74456 q^{37} -4.00000 q^{38} +4.00000 q^{39} -1.00000 q^{40} -0.744563 q^{41} -3.37228 q^{42} -4.62772 q^{43} +1.00000 q^{44} +1.00000 q^{45} +7.37228 q^{46} -0.744563 q^{47} -1.00000 q^{48} +4.37228 q^{49} -1.00000 q^{50} -1.00000 q^{51} -4.00000 q^{52} +1.00000 q^{54} +1.00000 q^{55} +3.37228 q^{56} -4.00000 q^{57} +0.627719 q^{58} +1.25544 q^{59} -1.00000 q^{60} -11.4891 q^{61} -8.11684 q^{62} -3.37228 q^{63} +1.00000 q^{64} -4.00000 q^{65} +1.00000 q^{66} +4.00000 q^{67} +1.00000 q^{68} +7.37228 q^{69} +3.37228 q^{70} -6.74456 q^{71} -1.00000 q^{72} -6.00000 q^{73} +2.74456 q^{74} -1.00000 q^{75} +4.00000 q^{76} -3.37228 q^{77} -4.00000 q^{78} +1.00000 q^{80} +1.00000 q^{81} +0.744563 q^{82} +9.48913 q^{83} +3.37228 q^{84} +1.00000 q^{85} +4.62772 q^{86} +0.627719 q^{87} -1.00000 q^{88} +8.74456 q^{89} -1.00000 q^{90} +13.4891 q^{91} -7.37228 q^{92} -8.11684 q^{93} +0.744563 q^{94} +4.00000 q^{95} +1.00000 q^{96} +10.8614 q^{97} -4.37228 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - q^{7} - 2 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} - 8 q^{13} + q^{14} - 2 q^{15} + 2 q^{16} + 2 q^{17} - 2 q^{18} + 8 q^{19} + 2 q^{20} + q^{21} - 2 q^{22} - 9 q^{23} + 2 q^{24} + 2 q^{25} + 8 q^{26} - 2 q^{27} - q^{28} - 7 q^{29} + 2 q^{30} - q^{31} - 2 q^{32} - 2 q^{33} - 2 q^{34} - q^{35} + 2 q^{36} + 6 q^{37} - 8 q^{38} + 8 q^{39} - 2 q^{40} + 10 q^{41} - q^{42} - 15 q^{43} + 2 q^{44} + 2 q^{45} + 9 q^{46} + 10 q^{47} - 2 q^{48} + 3 q^{49} - 2 q^{50} - 2 q^{51} - 8 q^{52} + 2 q^{54} + 2 q^{55} + q^{56} - 8 q^{57} + 7 q^{58} + 14 q^{59} - 2 q^{60} + q^{62} - q^{63} + 2 q^{64} - 8 q^{65} + 2 q^{66} + 8 q^{67} + 2 q^{68} + 9 q^{69} + q^{70} - 2 q^{71} - 2 q^{72} - 12 q^{73} - 6 q^{74} - 2 q^{75} + 8 q^{76} - q^{77} - 8 q^{78} + 2 q^{80} + 2 q^{81} - 10 q^{82} - 4 q^{83} + q^{84} + 2 q^{85} + 15 q^{86} + 7 q^{87} - 2 q^{88} + 6 q^{89} - 2 q^{90} + 4 q^{91} - 9 q^{92} + q^{93} - 10 q^{94} + 8 q^{95} + 2 q^{96} - 7 q^{97} - 3 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - q^7 - 2 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 - 8 * q^13 + q^14 - 2 * q^15 + 2 * q^16 + 2 * q^17 - 2 * q^18 + 8 * q^19 + 2 * q^20 + q^21 - 2 * q^22 - 9 * q^23 + 2 * q^24 + 2 * q^25 + 8 * q^26 - 2 * q^27 - q^28 - 7 * q^29 + 2 * q^30 - q^31 - 2 * q^32 - 2 * q^33 - 2 * q^34 - q^35 + 2 * q^36 + 6 * q^37 - 8 * q^38 + 8 * q^39 - 2 * q^40 + 10 * q^41 - q^42 - 15 * q^43 + 2 * q^44 + 2 * q^45 + 9 * q^46 + 10 * q^47 - 2 * q^48 + 3 * q^49 - 2 * q^50 - 2 * q^51 - 8 * q^52 + 2 * q^54 + 2 * q^55 + q^56 - 8 * q^57 + 7 * q^58 + 14 * q^59 - 2 * q^60 + q^62 - q^63 + 2 * q^64 - 8 * q^65 + 2 * q^66 + 8 * q^67 + 2 * q^68 + 9 * q^69 + q^70 - 2 * q^71 - 2 * q^72 - 12 * q^73 - 6 * q^74 - 2 * q^75 + 8 * q^76 - q^77 - 8 * q^78 + 2 * q^80 + 2 * q^81 - 10 * q^82 - 4 * q^83 + q^84 + 2 * q^85 + 15 * q^86 + 7 * q^87 - 2 * q^88 + 6 * q^89 - 2 * q^90 + 4 * q^91 - 9 * q^92 + q^93 - 10 * q^94 + 8 * q^95 + 2 * q^96 - 7 * q^97 - 3 * 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
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.00000	0.408248
$7$	−3.37228	−1.27460	−0.637301	−	0.770615i	$-0.719949\pi$
$7$	−3.37228	−1.27460	−0.637301	+	0.770615i	$0.719949\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	3.37228	0.901280
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	1.00000	0.223607
$21$	3.37228	0.735892
$22$	−1.00000	−0.213201
$23$	−7.37228	−1.53723	−0.768613	−	0.639713i	$-0.779053\pi$
$23$	−7.37228	−1.53723	−0.768613	+	0.639713i	$0.779053\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	4.00000	0.784465
$27$	−1.00000	−0.192450
$28$	−3.37228	−0.637301
$29$	−0.627719	−0.116564	−0.0582822	−	0.998300i	$-0.518562\pi$
$29$	−0.627719	−0.116564	−0.0582822	+	0.998300i	$0.518562\pi$
$30$	1.00000	0.182574
$31$	8.11684	1.45783	0.728914	−	0.684605i	$-0.240025\pi$
$31$	8.11684	1.45783	0.728914	+	0.684605i	$0.240025\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	−1.00000	−0.171499
$35$	−3.37228	−0.570020
$36$	1.00000	0.166667
$37$	−2.74456	−0.451203	−0.225602	−	0.974220i	$-0.572435\pi$
$37$	−2.74456	−0.451203	−0.225602	+	0.974220i	$0.572435\pi$
$38$	−4.00000	−0.648886
$39$	4.00000	0.640513
$40$	−1.00000	−0.158114
$41$	−0.744563	−0.116281	−0.0581406	−	0.998308i	$-0.518517\pi$
$41$	−0.744563	−0.116281	−0.0581406	+	0.998308i	$0.518517\pi$
$42$	−3.37228	−0.520354
$43$	−4.62772	−0.705720	−0.352860	−	0.935676i	$-0.614791\pi$
$43$	−4.62772	−0.705720	−0.352860	+	0.935676i	$0.614791\pi$
$44$	1.00000	0.150756
$45$	1.00000	0.149071
$46$	7.37228	1.08698
$47$	−0.744563	−0.108606	−0.0543028	−	0.998525i	$-0.517294\pi$
$47$	−0.744563	−0.108606	−0.0543028	+	0.998525i	$0.517294\pi$
$48$	−1.00000	−0.144338
$49$	4.37228	0.624612
$50$	−1.00000	−0.141421
$51$	−1.00000	−0.140028
$52$	−4.00000	−0.554700
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	1.00000	0.136083
$55$	1.00000	0.134840
$56$	3.37228	0.450640
$57$	−4.00000	−0.529813
$58$	0.627719	0.0824235
$59$	1.25544	0.163444	0.0817220	−	0.996655i	$-0.473958\pi$
$59$	1.25544	0.163444	0.0817220	+	0.996655i	$0.473958\pi$
$60$	−1.00000	−0.129099
$61$	−11.4891	−1.47103	−0.735516	−	0.677507i	$-0.763060\pi$
$61$	−11.4891	−1.47103	−0.735516	+	0.677507i	$0.763060\pi$
$62$	−8.11684	−1.03084
$63$	−3.37228	−0.424868
$64$	1.00000	0.125000
$65$	−4.00000	−0.496139
$66$	1.00000	0.123091
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	1.00000	0.121268
$69$	7.37228	0.887518
$70$	3.37228	0.403065
$71$	−6.74456	−0.800432	−0.400216	−	0.916421i	$-0.631065\pi$
$71$	−6.74456	−0.800432	−0.400216	+	0.916421i	$0.631065\pi$
$72$	−1.00000	−0.117851
$73$	−6.00000	−0.702247	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000	−0.702247	−0.351123	+	0.936329i	$0.614200\pi$
$74$	2.74456	0.319049
$75$	−1.00000	−0.115470
$76$	4.00000	0.458831
$77$	−3.37228	−0.384307
$78$	−4.00000	−0.452911
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	0.744563	0.0822232
$83$	9.48913	1.04157	0.520783	−	0.853689i	$-0.325640\pi$
$83$	9.48913	1.04157	0.520783	+	0.853689i	$0.325640\pi$
$84$	3.37228	0.367946
$85$	1.00000	0.108465
$86$	4.62772	0.499020
$87$	0.627719	0.0672985
$88$	−1.00000	−0.106600
$89$	8.74456	0.926922	0.463461	−	0.886117i	$-0.346607\pi$
$89$	8.74456	0.926922	0.463461	+	0.886117i	$0.346607\pi$
$90$	−1.00000	−0.105409
$91$	13.4891	1.41404
$92$	−7.37228	−0.768613
$93$	−8.11684	−0.841678
$94$	0.744563	0.0767958
$95$	4.00000	0.410391
$96$	1.00000	0.102062
$97$	10.8614	1.10281	0.551404	−	0.834238i	$-0.314092\pi$
$97$	10.8614	1.10281	0.551404	+	0.834238i	$0.314092\pi$
$98$	−4.37228	−0.441667
$99$	1.00000	0.100504
$100$	1.00000	0.100000
$101$	2.00000	0.199007	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	2.00000	0.199007	0.0995037	+	0.995037i	$0.468274\pi$
$102$	1.00000	0.0990148
$103$	12.6277	1.24425	0.622123	−	0.782919i	$-0.286270\pi$
$103$	12.6277	1.24425	0.622123	+	0.782919i	$0.286270\pi$
$104$	4.00000	0.392232
$105$	3.37228	0.329101
$106$	0	0
$107$	4.62772	0.447378	0.223689	−	0.974661i	$-0.428190\pi$
$107$	4.62772	0.447378	0.223689	+	0.974661i	$0.428190\pi$
$108$	−1.00000	−0.0962250
$109$	−18.2337	−1.74647	−0.873235	−	0.487299i	$-0.837982\pi$
$109$	−18.2337	−1.74647	−0.873235	+	0.487299i	$0.837982\pi$
$110$	−1.00000	−0.0953463
$111$	2.74456	0.260502
$112$	−3.37228	−0.318651
$113$	−15.4891	−1.45709	−0.728547	−	0.684996i	$-0.759804\pi$
$113$	−15.4891	−1.45709	−0.728547	+	0.684996i	$0.759804\pi$
$114$	4.00000	0.374634
$115$	−7.37228	−0.687469
$116$	−0.627719	−0.0582822
$117$	−4.00000	−0.369800
$118$	−1.25544	−0.115572
$119$	−3.37228	−0.309137
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	11.4891	1.04018
$123$	0.744563	0.0671350
$124$	8.11684	0.728914
$125$	1.00000	0.0894427
$126$	3.37228	0.300427
$127$	11.4891	1.01950	0.509748	−	0.860324i	$-0.329739\pi$
$127$	11.4891	1.01950	0.509748	+	0.860324i	$0.329739\pi$
$128$	−1.00000	−0.0883883
$129$	4.62772	0.407448
$130$	4.00000	0.350823
$131$	8.00000	0.698963	0.349482	−	0.936943i	$-0.386358\pi$
$131$	8.00000	0.698963	0.349482	+	0.936943i	$0.386358\pi$
$132$	−1.00000	−0.0870388
$133$	−13.4891	−1.16966
$134$	−4.00000	−0.345547
$135$	−1.00000	−0.0860663
$136$	−1.00000	−0.0857493
$137$	−16.1168	−1.37695	−0.688477	−	0.725258i	$-0.741721\pi$
$137$	−16.1168	−1.37695	−0.688477	+	0.725258i	$0.741721\pi$
$138$	−7.37228	−0.627570
$139$	7.37228	0.625309	0.312654	−	0.949867i	$-0.398782\pi$
$139$	7.37228	0.625309	0.312654	+	0.949867i	$0.398782\pi$
$140$	−3.37228	−0.285010
$141$	0.744563	0.0627035
$142$	6.74456	0.565991
$143$	−4.00000	−0.334497
$144$	1.00000	0.0833333
$145$	−0.627719	−0.0521292
$146$	6.00000	0.496564
$147$	−4.37228	−0.360620
$148$	−2.74456	−0.225602
$149$	3.25544	0.266696	0.133348	−	0.991069i	$-0.457427\pi$
$149$	3.25544	0.266696	0.133348	+	0.991069i	$0.457427\pi$
$150$	1.00000	0.0816497
$151$	−18.2337	−1.48384	−0.741918	−	0.670490i	$-0.766084\pi$
$151$	−18.2337	−1.48384	−0.741918	+	0.670490i	$0.766084\pi$
$152$	−4.00000	−0.324443
$153$	1.00000	0.0808452
$154$	3.37228	0.271746
$155$	8.11684	0.651961
$156$	4.00000	0.320256
$157$	10.0000	0.798087	0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000	0.798087	0.399043	+	0.916932i	$0.369342\pi$
$158$	0	0
$159$	0	0
$160$	−1.00000	−0.0790569
$161$	24.8614	1.95935
$162$	−1.00000	−0.0785674
$163$	20.8614	1.63399	0.816996	−	0.576644i	$-0.195638\pi$
$163$	20.8614	1.63399	0.816996	+	0.576644i	$0.195638\pi$
$164$	−0.744563	−0.0581406
$165$	−1.00000	−0.0778499
$166$	−9.48913	−0.736499
$167$	−3.48913	−0.269997	−0.134998	−	0.990846i	$-0.543103\pi$
$167$	−3.48913	−0.269997	−0.134998	+	0.990846i	$0.543103\pi$
$168$	−3.37228	−0.260177
$169$	3.00000	0.230769
$170$	−1.00000	−0.0766965
$171$	4.00000	0.305888
$172$	−4.62772	−0.352860
$173$	20.2337	1.53834	0.769169	−	0.639045i	$-0.220670\pi$
$173$	20.2337	1.53834	0.769169	+	0.639045i	$0.220670\pi$
$174$	−0.627719	−0.0475872
$175$	−3.37228	−0.254921
$176$	1.00000	0.0753778
$177$	−1.25544	−0.0943645
$178$	−8.74456	−0.655433
$179$	10.7446	0.803086	0.401543	−	0.915840i	$-0.368474\pi$
$179$	10.7446	0.803086	0.401543	+	0.915840i	$0.368474\pi$
$180$	1.00000	0.0745356
$181$	−8.62772	−0.641293	−0.320647	−	0.947199i	$-0.603900\pi$
$181$	−8.62772	−0.641293	−0.320647	+	0.947199i	$0.603900\pi$
$182$	−13.4891	−0.999880
$183$	11.4891	0.849301
$184$	7.37228	0.543492
$185$	−2.74456	−0.201784
$186$	8.11684	0.595156
$187$	1.00000	0.0731272
$188$	−0.744563	−0.0543028
$189$	3.37228	0.245297
$190$	−4.00000	−0.290191
$191$	13.3723	0.967584	0.483792	−	0.875183i	$-0.339259\pi$
$191$	13.3723	0.967584	0.483792	+	0.875183i	$0.339259\pi$
$192$	−1.00000	−0.0721688
$193$	19.4891	1.40286	0.701429	−	0.712739i	$-0.252546\pi$
$193$	19.4891	1.40286	0.701429	+	0.712739i	$0.252546\pi$
$194$	−10.8614	−0.779804
$195$	4.00000	0.286446
$196$	4.37228	0.312306
$197$	9.48913	0.676072	0.338036	−	0.941133i	$-0.390237\pi$
$197$	9.48913	0.676072	0.338036	+	0.941133i	$0.390237\pi$
$198$	−1.00000	−0.0710669
$199$	−3.25544	−0.230772	−0.115386	−	0.993321i	$-0.536810\pi$
$199$	−3.25544	−0.230772	−0.115386	+	0.993321i	$0.536810\pi$
$200$	−1.00000	−0.0707107
$201$	−4.00000	−0.282138
$202$	−2.00000	−0.140720
$203$	2.11684	0.148573
$204$	−1.00000	−0.0700140
$205$	−0.744563	−0.0520025
$206$	−12.6277	−0.879815
$207$	−7.37228	−0.512409
$208$	−4.00000	−0.277350
$209$	4.00000	0.276686
$210$	−3.37228	−0.232710
$211$	−15.3723	−1.05827	−0.529136	−	0.848537i	$-0.677484\pi$
$211$	−15.3723	−1.05827	−0.529136	+	0.848537i	$0.677484\pi$
$212$	0	0
$213$	6.74456	0.462130
$214$	−4.62772	−0.316344
$215$	−4.62772	−0.315608
$216$	1.00000	0.0680414
$217$	−27.3723	−1.85815
$218$	18.2337	1.23494
$219$	6.00000	0.405442
$220$	1.00000	0.0674200
$221$	−4.00000	−0.269069
$222$	−2.74456	−0.184203
$223$	14.1168	0.945334	0.472667	−	0.881241i	$-0.343291\pi$
$223$	14.1168	0.945334	0.472667	+	0.881241i	$0.343291\pi$
$224$	3.37228	0.225320
$225$	1.00000	0.0666667
$226$	15.4891	1.03032
$227$	−4.86141	−0.322663	−0.161331	−	0.986900i	$-0.551579\pi$
$227$	−4.86141	−0.322663	−0.161331	+	0.986900i	$0.551579\pi$
$228$	−4.00000	−0.264906
$229$	−12.7446	−0.842184	−0.421092	−	0.907018i	$-0.638353\pi$
$229$	−12.7446	−0.842184	−0.421092	+	0.907018i	$0.638353\pi$
$230$	7.37228	0.486114
$231$	3.37228	0.221880
$232$	0.627719	0.0412118
$233$	16.1168	1.05585	0.527925	−	0.849291i	$-0.322970\pi$
$233$	16.1168	1.05585	0.527925	+	0.849291i	$0.322970\pi$
$234$	4.00000	0.261488
$235$	−0.744563	−0.0485699
$236$	1.25544	0.0817220
$237$	0	0
$238$	3.37228	0.218593
$239$	4.23369	0.273855	0.136927	−	0.990581i	$-0.456277\pi$
$239$	4.23369	0.273855	0.136927	+	0.990581i	$0.456277\pi$
$240$	−1.00000	−0.0645497
$241$	−17.6060	−1.13410	−0.567050	−	0.823683i	$-0.691915\pi$
$241$	−17.6060	−1.13410	−0.567050	+	0.823683i	$0.691915\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	−11.4891	−0.735516
$245$	4.37228	0.279335
$246$	−0.744563	−0.0474716
$247$	−16.0000	−1.01806
$248$	−8.11684	−0.515420
$249$	−9.48913	−0.601349
$250$	−1.00000	−0.0632456
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	−3.37228	−0.212434
$253$	−7.37228	−0.463491
$254$	−11.4891	−0.720892
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	8.11684	0.506315	0.253157	−	0.967425i	$-0.418531\pi$
$257$	8.11684	0.506315	0.253157	+	0.967425i	$0.418531\pi$
$258$	−4.62772	−0.288109
$259$	9.25544	0.575105
$260$	−4.00000	−0.248069
$261$	−0.627719	−0.0388548
$262$	−8.00000	−0.494242
$263$	−1.88316	−0.116120	−0.0580602	−	0.998313i	$-0.518492\pi$
$263$	−1.88316	−0.116120	−0.0580602	+	0.998313i	$0.518492\pi$
$264$	1.00000	0.0615457
$265$	0	0
$266$	13.4891	0.827071
$267$	−8.74456	−0.535159
$268$	4.00000	0.244339
$269$	14.0000	0.853595	0.426798	−	0.904347i	$-0.359642\pi$
$269$	14.0000	0.853595	0.426798	+	0.904347i	$0.359642\pi$
$270$	1.00000	0.0608581
$271$	−13.3723	−0.812308	−0.406154	−	0.913805i	$-0.633130\pi$
$271$	−13.3723	−0.812308	−0.406154	+	0.913805i	$0.633130\pi$
$272$	1.00000	0.0606339
$273$	−13.4891	−0.816399
$274$	16.1168	0.973654
$275$	1.00000	0.0603023
$276$	7.37228	0.443759
$277$	−7.48913	−0.449978	−0.224989	−	0.974361i	$-0.572235\pi$
$277$	−7.48913	−0.449978	−0.224989	+	0.974361i	$0.572235\pi$
$278$	−7.37228	−0.442160
$279$	8.11684	0.485943
$280$	3.37228	0.201532
$281$	−14.8614	−0.886557	−0.443279	−	0.896384i	$-0.646185\pi$
$281$	−14.8614	−0.886557	−0.443279	+	0.896384i	$0.646185\pi$
$282$	−0.744563	−0.0443381
$283$	−13.2554	−0.787954	−0.393977	−	0.919120i	$-0.628901\pi$
$283$	−13.2554	−0.787954	−0.393977	+	0.919120i	$0.628901\pi$
$284$	−6.74456	−0.400216
$285$	−4.00000	−0.236940
$286$	4.00000	0.236525
$287$	2.51087	0.148212
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	0.627719	0.0368609
$291$	−10.8614	−0.636707
$292$	−6.00000	−0.351123
$293$	20.1168	1.17524	0.587619	−	0.809138i	$-0.300065\pi$
$293$	20.1168	1.17524	0.587619	+	0.809138i	$0.300065\pi$
$294$	4.37228	0.254997
$295$	1.25544	0.0730944
$296$	2.74456	0.159524
$297$	−1.00000	−0.0580259
$298$	−3.25544	−0.188582
$299$	29.4891	1.70540
$300$	−1.00000	−0.0577350
$301$	15.6060	0.899513
$302$	18.2337	1.04923
$303$	−2.00000	−0.114897
$304$	4.00000	0.229416
$305$	−11.4891	−0.657865
$306$	−1.00000	−0.0571662
$307$	−12.0000	−0.684876	−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000	−0.684876	−0.342438	+	0.939540i	$0.611253\pi$
$308$	−3.37228	−0.192154
$309$	−12.6277	−0.718366
$310$	−8.11684	−0.461006
$311$	33.4891	1.89899	0.949497	−	0.313776i	$-0.101594\pi$
$311$	33.4891	1.89899	0.949497	+	0.313776i	$0.101594\pi$
$312$	−4.00000	−0.226455
$313$	−1.37228	−0.0775659	−0.0387830	−	0.999248i	$-0.512348\pi$
$313$	−1.37228	−0.0775659	−0.0387830	+	0.999248i	$0.512348\pi$
$314$	−10.0000	−0.564333
$315$	−3.37228	−0.190007
$316$	0	0
$317$	16.1168	0.905212	0.452606	−	0.891711i	$-0.350494\pi$
$317$	16.1168	0.905212	0.452606	+	0.891711i	$0.350494\pi$
$318$	0	0
$319$	−0.627719	−0.0351455
$320$	1.00000	0.0559017
$321$	−4.62772	−0.258294
$322$	−24.8614	−1.38547
$323$	4.00000	0.222566
$324$	1.00000	0.0555556
$325$	−4.00000	−0.221880
$326$	−20.8614	−1.15541
$327$	18.2337	1.00833
$328$	0.744563	0.0411116
$329$	2.51087	0.138429
$330$	1.00000	0.0550482
$331$	9.88316	0.543227	0.271614	−	0.962406i	$-0.412443\pi$
$331$	9.88316	0.543227	0.271614	+	0.962406i	$0.412443\pi$
$332$	9.48913	0.520783
$333$	−2.74456	−0.150401
$334$	3.48913	0.190916
$335$	4.00000	0.218543
$336$	3.37228	0.183973
$337$	11.4891	0.625853	0.312926	−	0.949777i	$-0.398691\pi$
$337$	11.4891	0.625853	0.312926	+	0.949777i	$0.398691\pi$
$338$	−3.00000	−0.163178
$339$	15.4891	0.841254
$340$	1.00000	0.0542326
$341$	8.11684	0.439552
$342$	−4.00000	−0.216295
$343$	8.86141	0.478471
$344$	4.62772	0.249510
$345$	7.37228	0.396910
$346$	−20.2337	−1.08777
$347$	−5.48913	−0.294672	−0.147336	−	0.989087i	$-0.547070\pi$
$347$	−5.48913	−0.294672	−0.147336	+	0.989087i	$0.547070\pi$
$348$	0.627719	0.0336493
$349$	4.23369	0.226624	0.113312	−	0.993559i	$-0.463854\pi$
$349$	4.23369	0.226624	0.113312	+	0.993559i	$0.463854\pi$
$350$	3.37228	0.180256
$351$	4.00000	0.213504
$352$	−1.00000	−0.0533002
$353$	25.3723	1.35043	0.675215	−	0.737621i	$-0.264051\pi$
$353$	25.3723	1.35043	0.675215	+	0.737621i	$0.264051\pi$
$354$	1.25544	0.0667257
$355$	−6.74456	−0.357964
$356$	8.74456	0.463461
$357$	3.37228	0.178480
$358$	−10.7446	−0.567868
$359$	13.2554	0.699595	0.349798	−	0.936825i	$-0.386250\pi$
$359$	13.2554	0.699595	0.349798	+	0.936825i	$0.386250\pi$
$360$	−1.00000	−0.0527046
$361$	−3.00000	−0.157895
$362$	8.62772	0.453463
$363$	−1.00000	−0.0524864
$364$	13.4891	0.707022
$365$	−6.00000	−0.314054
$366$	−11.4891	−0.600546
$367$	23.4891	1.22612	0.613061	−	0.790035i	$-0.289938\pi$
$367$	23.4891	1.22612	0.613061	+	0.790035i	$0.289938\pi$
$368$	−7.37228	−0.384307
$369$	−0.744563	−0.0387604
$370$	2.74456	0.142683
$371$	0	0
$372$	−8.11684	−0.420839
$373$	−21.7228	−1.12476	−0.562382	−	0.826877i	$-0.690115\pi$
$373$	−21.7228	−1.12476	−0.562382	+	0.826877i	$0.690115\pi$
$374$	−1.00000	−0.0517088
$375$	−1.00000	−0.0516398
$376$	0.744563	0.0383979
$377$	2.51087	0.129317
$378$	−3.37228	−0.173451
$379$	0	0		−	1.00000i	$-0.5\pi$
$379$	0	0			1.00000i	$0.5\pi$
$380$	4.00000	0.205196
$381$	−11.4891	−0.588606
$382$	−13.3723	−0.684185
$383$	8.74456	0.446826	0.223413	−	0.974724i	$-0.428280\pi$
$383$	8.74456	0.446826	0.223413	+	0.974724i	$0.428280\pi$
$384$	1.00000	0.0510310
$385$	−3.37228	−0.171867
$386$	−19.4891	−0.991970
$387$	−4.62772	−0.235240
$388$	10.8614	0.551404
$389$	9.25544	0.469269	0.234635	−	0.972084i	$-0.424611\pi$
$389$	9.25544	0.469269	0.234635	+	0.972084i	$0.424611\pi$
$390$	−4.00000	−0.202548
$391$	−7.37228	−0.372832
$392$	−4.37228	−0.220834
$393$	−8.00000	−0.403547
$394$	−9.48913	−0.478055
$395$	0	0
$396$	1.00000	0.0502519
$397$	−12.2337	−0.613991	−0.306996	−	0.951711i	$-0.599324\pi$
$397$	−12.2337	−0.613991	−0.306996	+	0.951711i	$0.599324\pi$
$398$	3.25544	0.163180
$399$	13.4891	0.675301
$400$	1.00000	0.0500000
$401$	1.13859	0.0568586	0.0284293	−	0.999596i	$-0.490949\pi$
$401$	1.13859	0.0568586	0.0284293	+	0.999596i	$0.490949\pi$
$402$	4.00000	0.199502
$403$	−32.4674	−1.61732
$404$	2.00000	0.0995037
$405$	1.00000	0.0496904
$406$	−2.11684	−0.105057
$407$	−2.74456	−0.136043
$408$	1.00000	0.0495074
$409$	−22.2337	−1.09939	−0.549693	−	0.835367i	$-0.685255\pi$
$409$	−22.2337	−1.09939	−0.549693	+	0.835367i	$0.685255\pi$
$410$	0.744563	0.0367713
$411$	16.1168	0.794985
$412$	12.6277	0.622123
$413$	−4.23369	−0.208326
$414$	7.37228	0.362328
$415$	9.48913	0.465803
$416$	4.00000	0.196116
$417$	−7.37228	−0.361022
$418$	−4.00000	−0.195646
$419$	32.6277	1.59397	0.796984	−	0.604000i	$-0.206427\pi$
$419$	32.6277	1.59397	0.796984	+	0.604000i	$0.206427\pi$
$420$	3.37228	0.164550
$421$	−36.7446	−1.79082	−0.895410	−	0.445242i	$-0.853118\pi$
$421$	−36.7446	−1.79082	−0.895410	+	0.445242i	$0.853118\pi$
$422$	15.3723	0.748311
$423$	−0.744563	−0.0362019
$424$	0	0
$425$	1.00000	0.0485071
$426$	−6.74456	−0.326775
$427$	38.7446	1.87498
$428$	4.62772	0.223689
$429$	4.00000	0.193122
$430$	4.62772	0.223168
$431$	10.8614	0.523176	0.261588	−	0.965180i	$-0.415754\pi$
$431$	10.8614	0.523176	0.261588	+	0.965180i	$0.415754\pi$
$432$	−1.00000	−0.0481125
$433$	7.25544	0.348674	0.174337	−	0.984686i	$-0.444222\pi$
$433$	7.25544	0.348674	0.174337	+	0.984686i	$0.444222\pi$
$434$	27.3723	1.31391
$435$	0.627719	0.0300968
$436$	−18.2337	−0.873235
$437$	−29.4891	−1.41066
$438$	−6.00000	−0.286691
$439$	21.2554	1.01447	0.507233	−	0.861809i	$-0.330668\pi$
$439$	21.2554	1.01447	0.507233	+	0.861809i	$0.330668\pi$
$440$	−1.00000	−0.0476731
$441$	4.37228	0.208204
$442$	4.00000	0.190261
$443$	4.62772	0.219870	0.109935	−	0.993939i	$-0.464936\pi$
$443$	4.62772	0.219870	0.109935	+	0.993939i	$0.464936\pi$
$444$	2.74456	0.130251
$445$	8.74456	0.414532
$446$	−14.1168	−0.668452
$447$	−3.25544	−0.153977
$448$	−3.37228	−0.159325
$449$	26.8614	1.26767	0.633834	−	0.773469i	$-0.281480\pi$
$449$	26.8614	1.26767	0.633834	+	0.773469i	$0.281480\pi$
$450$	−1.00000	−0.0471405
$451$	−0.744563	−0.0350601
$452$	−15.4891	−0.728547
$453$	18.2337	0.856693
$454$	4.86141	0.228157
$455$	13.4891	0.632380
$456$	4.00000	0.187317
$457$	28.9783	1.35555	0.677773	−	0.735271i	$-0.262945\pi$
$457$	28.9783	1.35555	0.677773	+	0.735271i	$0.262945\pi$
$458$	12.7446	0.595514
$459$	−1.00000	−0.0466760
$460$	−7.37228	−0.343734
$461$	0.510875	0.0237938	0.0118969	−	0.999929i	$-0.496213\pi$
$461$	0.510875	0.0237938	0.0118969	+	0.999929i	$0.496213\pi$
$462$	−3.37228	−0.156893
$463$	8.00000	0.371792	0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000	0.371792	0.185896	+	0.982569i	$0.440481\pi$
$464$	−0.627719	−0.0291411
$465$	−8.11684	−0.376410
$466$	−16.1168	−0.746598
$467$	−14.9783	−0.693111	−0.346555	−	0.938030i	$-0.612649\pi$
$467$	−14.9783	−0.693111	−0.346555	+	0.938030i	$0.612649\pi$
$468$	−4.00000	−0.184900
$469$	−13.4891	−0.622870
$470$	0.744563	0.0343441
$471$	−10.0000	−0.460776
$472$	−1.25544	−0.0577862
$473$	−4.62772	−0.212783
$474$	0	0
$475$	4.00000	0.183533
$476$	−3.37228	−0.154568
$477$	0	0
$478$	−4.23369	−0.193644
$479$	−15.8832	−0.725720	−0.362860	−	0.931844i	$-0.618200\pi$
$479$	−15.8832	−0.725720	−0.362860	+	0.931844i	$0.618200\pi$
$480$	1.00000	0.0456435
$481$	10.9783	0.500565
$482$	17.6060	0.801930
$483$	−24.8614	−1.13123
$484$	1.00000	0.0454545
$485$	10.8614	0.493191
$486$	1.00000	0.0453609
$487$	−15.4891	−0.701879	−0.350940	−	0.936398i	$-0.614138\pi$
$487$	−15.4891	−0.701879	−0.350940	+	0.936398i	$0.614138\pi$
$488$	11.4891	0.520088
$489$	−20.8614	−0.943385
$490$	−4.37228	−0.197520
$491$	41.4891	1.87238	0.936189	−	0.351497i	$-0.114327\pi$
$491$	41.4891	1.87238	0.936189	+	0.351497i	$0.114327\pi$
$492$	0.744563	0.0335675
$493$	−0.627719	−0.0282710
$494$	16.0000	0.719874
$495$	1.00000	0.0449467
$496$	8.11684	0.364457
$497$	22.7446	1.02023
$498$	9.48913	0.425218
$499$	36.0000	1.61158	0.805791	−	0.592200i	$-0.201741\pi$
$499$	36.0000	1.61158	0.805791	+	0.592200i	$0.201741\pi$
$500$	1.00000	0.0447214
$501$	3.48913	0.155883
$502$	−12.0000	−0.535586
$503$	−23.7228	−1.05775	−0.528874	−	0.848700i	$-0.677386\pi$
$503$	−23.7228	−1.05775	−0.528874	+	0.848700i	$0.677386\pi$
$504$	3.37228	0.150213
$505$	2.00000	0.0889988
$506$	7.37228	0.327738
$507$	−3.00000	−0.133235
$508$	11.4891	0.509748
$509$	9.25544	0.410240	0.205120	−	0.978737i	$-0.434242\pi$
$509$	9.25544	0.410240	0.205120	+	0.978737i	$0.434242\pi$
$510$	1.00000	0.0442807
$511$	20.2337	0.895086
$512$	−1.00000	−0.0441942
$513$	−4.00000	−0.176604
$514$	−8.11684	−0.358019
$515$	12.6277	0.556444
$516$	4.62772	0.203724
$517$	−0.744563	−0.0327458
$518$	−9.25544	−0.406661
$519$	−20.2337	−0.888160
$520$	4.00000	0.175412
$521$	2.00000	0.0876216	0.0438108	−	0.999040i	$-0.486050\pi$
$521$	2.00000	0.0876216	0.0438108	+	0.999040i	$0.486050\pi$
$522$	0.627719	0.0274745
$523$	−14.1168	−0.617286	−0.308643	−	0.951178i	$-0.599875\pi$
$523$	−14.1168	−0.617286	−0.308643	+	0.951178i	$0.599875\pi$
$524$	8.00000	0.349482
$525$	3.37228	0.147178
$526$	1.88316	0.0821095
$527$	8.11684	0.353575
$528$	−1.00000	−0.0435194
$529$	31.3505	1.36307
$530$	0	0
$531$	1.25544	0.0544813
$532$	−13.4891	−0.584828
$533$	2.97825	0.129002
$534$	8.74456	0.378414
$535$	4.62772	0.200074
$536$	−4.00000	−0.172774
$537$	−10.7446	−0.463662
$538$	−14.0000	−0.603583
$539$	4.37228	0.188327
$540$	−1.00000	−0.0430331
$541$	2.23369	0.0960337	0.0480169	−	0.998847i	$-0.484710\pi$
$541$	2.23369	0.0960337	0.0480169	+	0.998847i	$0.484710\pi$
$542$	13.3723	0.574389
$543$	8.62772	0.370251
$544$	−1.00000	−0.0428746
$545$	−18.2337	−0.781045
$546$	13.4891	0.577281
$547$	5.25544	0.224706	0.112353	−	0.993668i	$-0.464161\pi$
$547$	5.25544	0.224706	0.112353	+	0.993668i	$0.464161\pi$
$548$	−16.1168	−0.688477
$549$	−11.4891	−0.490344
$550$	−1.00000	−0.0426401
$551$	−2.51087	−0.106967
$552$	−7.37228	−0.313785
$553$	0	0
$554$	7.48913	0.318182
$555$	2.74456	0.116500
$556$	7.37228	0.312654
$557$	−1.13859	−0.0482437	−0.0241219	−	0.999709i	$-0.507679\pi$
$557$	−1.13859	−0.0482437	−0.0241219	+	0.999709i	$0.507679\pi$
$558$	−8.11684	−0.343613
$559$	18.5109	0.782927
$560$	−3.37228	−0.142505
$561$	−1.00000	−0.0422200
$562$	14.8614	0.626891
$563$	33.4891	1.41140	0.705699	−	0.708512i	$-0.250633\pi$
$563$	33.4891	1.41140	0.705699	+	0.708512i	$0.250633\pi$
$564$	0.744563	0.0313517
$565$	−15.4891	−0.651632
$566$	13.2554	0.557168
$567$	−3.37228	−0.141623
$568$	6.74456	0.282996
$569$	6.00000	0.251533	0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000	0.251533	0.125767	+	0.992060i	$0.459861\pi$
$570$	4.00000	0.167542
$571$	4.00000	0.167395	0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000	0.167395	0.0836974	+	0.996491i	$0.473327\pi$
$572$	−4.00000	−0.167248
$573$	−13.3723	−0.558635
$574$	−2.51087	−0.104802
$575$	−7.37228	−0.307445
$576$	1.00000	0.0416667
$577$	38.4674	1.60142	0.800709	−	0.599054i	$-0.204456\pi$
$577$	38.4674	1.60142	0.800709	+	0.599054i	$0.204456\pi$
$578$	−1.00000	−0.0415945
$579$	−19.4891	−0.809940
$580$	−0.627719	−0.0260646
$581$	−32.0000	−1.32758
$582$	10.8614	0.450220
$583$	0	0
$584$	6.00000	0.248282
$585$	−4.00000	−0.165380
$586$	−20.1168	−0.831019
$587$	22.3505	0.922505	0.461253	−	0.887269i	$-0.347400\pi$
$587$	22.3505	0.922505	0.461253	+	0.887269i	$0.347400\pi$
$588$	−4.37228	−0.180310
$589$	32.4674	1.33779
$590$	−1.25544	−0.0516855
$591$	−9.48913	−0.390330
$592$	−2.74456	−0.112801
$593$	40.9783	1.68278	0.841388	−	0.540432i	$-0.181739\pi$
$593$	40.9783	1.68278	0.841388	+	0.540432i	$0.181739\pi$
$594$	1.00000	0.0410305
$595$	−3.37228	−0.138250
$596$	3.25544	0.133348
$597$	3.25544	0.133236
$598$	−29.4891	−1.20590
$599$	44.1168	1.80257	0.901283	−	0.433231i	$-0.142627\pi$
$599$	44.1168	1.80257	0.901283	+	0.433231i	$0.142627\pi$
$600$	1.00000	0.0408248
$601$	36.9783	1.50837	0.754187	−	0.656660i	$-0.228031\pi$
$601$	36.9783	1.50837	0.754187	+	0.656660i	$0.228031\pi$
$602$	−15.6060	−0.636052
$603$	4.00000	0.162893
$604$	−18.2337	−0.741918
$605$	1.00000	0.0406558
$606$	2.00000	0.0812444
$607$	8.00000	0.324710	0.162355	−	0.986732i	$-0.448091\pi$
$607$	8.00000	0.324710	0.162355	+	0.986732i	$0.448091\pi$
$608$	−4.00000	−0.162221
$609$	−2.11684	−0.0857788
$610$	11.4891	0.465181
$611$	2.97825	0.120487
$612$	1.00000	0.0404226
$613$	−5.25544	−0.212265	−0.106133	−	0.994352i	$-0.533847\pi$
$613$	−5.25544	−0.212265	−0.106133	+	0.994352i	$0.533847\pi$
$614$	12.0000	0.484281
$615$	0.744563	0.0300237
$616$	3.37228	0.135873
$617$	26.4674	1.06554	0.532768	−	0.846261i	$-0.321152\pi$
$617$	26.4674	1.06554	0.532768	+	0.846261i	$0.321152\pi$
$618$	12.6277	0.507961
$619$	−16.2337	−0.652487	−0.326244	−	0.945286i	$-0.605783\pi$
$619$	−16.2337	−0.652487	−0.326244	+	0.945286i	$0.605783\pi$
$620$	8.11684	0.325980
$621$	7.37228	0.295839
$622$	−33.4891	−1.34279
$623$	−29.4891	−1.18146
$624$	4.00000	0.160128
$625$	1.00000	0.0400000
$626$	1.37228	0.0548474
$627$	−4.00000	−0.159745
$628$	10.0000	0.399043
$629$	−2.74456	−0.109433
$630$	3.37228	0.134355
$631$	−0.233688	−0.00930297	−0.00465148	−	0.999989i	$-0.501481\pi$
$631$	−0.233688	−0.00930297	−0.00465148	+	0.999989i	$0.501481\pi$
$632$	0	0
$633$	15.3723	0.610993
$634$	−16.1168	−0.640082
$635$	11.4891	0.455932
$636$	0	0
$637$	−17.4891	−0.692944
$638$	0.627719	0.0248516
$639$	−6.74456	−0.266811
$640$	−1.00000	−0.0395285
$641$	−36.1168	−1.42653	−0.713265	−	0.700895i	$-0.752784\pi$
$641$	−36.1168	−1.42653	−0.713265	+	0.700895i	$0.752784\pi$
$642$	4.62772	0.182641
$643$	4.62772	0.182499	0.0912497	−	0.995828i	$-0.470914\pi$
$643$	4.62772	0.182499	0.0912497	+	0.995828i	$0.470914\pi$
$644$	24.8614	0.979677
$645$	4.62772	0.182216
$646$	−4.00000	−0.157378
$647$	12.9783	0.510228	0.255114	−	0.966911i	$-0.417887\pi$
$647$	12.9783	0.510228	0.255114	+	0.966911i	$0.417887\pi$
$648$	−1.00000	−0.0392837
$649$	1.25544	0.0492802
$650$	4.00000	0.156893
$651$	27.3723	1.07280
$652$	20.8614	0.816996
$653$	22.6277	0.885491	0.442746	−	0.896647i	$-0.354005\pi$
$653$	22.6277	0.885491	0.442746	+	0.896647i	$0.354005\pi$
$654$	−18.2337	−0.712994
$655$	8.00000	0.312586
$656$	−0.744563	−0.0290703
$657$	−6.00000	−0.234082
$658$	−2.51087	−0.0978841
$659$	8.62772	0.336088	0.168044	−	0.985779i	$-0.446255\pi$
$659$	8.62772	0.336088	0.168044	+	0.985779i	$0.446255\pi$
$660$	−1.00000	−0.0389249
$661$	28.7446	1.11803	0.559017	−	0.829156i	$-0.311179\pi$
$661$	28.7446	1.11803	0.559017	+	0.829156i	$0.311179\pi$
$662$	−9.88316	−0.384120
$663$	4.00000	0.155347
$664$	−9.48913	−0.368249
$665$	−13.4891	−0.523086
$666$	2.74456	0.106350
$667$	4.62772	0.179186
$668$	−3.48913	−0.134998
$669$	−14.1168	−0.545789
$670$	−4.00000	−0.154533
$671$	−11.4891	−0.443533
$672$	−3.37228	−0.130089
$673$	10.2337	0.394480	0.197240	−	0.980355i	$-0.436802\pi$
$673$	10.2337	0.394480	0.197240	+	0.980355i	$0.436802\pi$
$674$	−11.4891	−0.442545
$675$	−1.00000	−0.0384900
$676$	3.00000	0.115385
$677$	−34.7446	−1.33534	−0.667671	−	0.744456i	$-0.732709\pi$
$677$	−34.7446	−1.33534	−0.667671	+	0.744456i	$0.732709\pi$
$678$	−15.4891	−0.594856
$679$	−36.6277	−1.40564
$680$	−1.00000	−0.0383482
$681$	4.86141	0.186290
$682$	−8.11684	−0.310810
$683$	1.02175	0.0390962	0.0195481	−	0.999809i	$-0.493777\pi$
$683$	1.02175	0.0390962	0.0195481	+	0.999809i	$0.493777\pi$
$684$	4.00000	0.152944
$685$	−16.1168	−0.615793
$686$	−8.86141	−0.338330
$687$	12.7446	0.486235
$688$	−4.62772	−0.176430
$689$	0	0
$690$	−7.37228	−0.280658
$691$	8.00000	0.304334	0.152167	−	0.988355i	$-0.451375\pi$
$691$	8.00000	0.304334	0.152167	+	0.988355i	$0.451375\pi$
$692$	20.2337	0.769169
$693$	−3.37228	−0.128102
$694$	5.48913	0.208364
$695$	7.37228	0.279647
$696$	−0.627719	−0.0237936
$697$	−0.744563	−0.0282023
$698$	−4.23369	−0.160247
$699$	−16.1168	−0.609595
$700$	−3.37228	−0.127460
$701$	6.00000	0.226617	0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000	0.226617	0.113308	+	0.993560i	$0.463855\pi$
$702$	−4.00000	−0.150970
$703$	−10.9783	−0.414053
$704$	1.00000	0.0376889
$705$	0.744563	0.0280419
$706$	−25.3723	−0.954898
$707$	−6.74456	−0.253655
$708$	−1.25544	−0.0471822
$709$	−22.7446	−0.854190	−0.427095	−	0.904207i	$-0.640463\pi$
$709$	−22.7446	−0.854190	−0.427095	+	0.904207i	$0.640463\pi$
$710$	6.74456	0.253119
$711$	0	0
$712$	−8.74456	−0.327716
$713$	−59.8397	−2.24101
$714$	−3.37228	−0.126204
$715$	−4.00000	−0.149592
$716$	10.7446	0.401543
$717$	−4.23369	−0.158110
$718$	−13.2554	−0.494689
$719$	12.2337	0.456240	0.228120	−	0.973633i	$-0.426742\pi$
$719$	12.2337	0.456240	0.228120	+	0.973633i	$0.426742\pi$
$720$	1.00000	0.0372678
$721$	−42.5842	−1.58592
$722$	3.00000	0.111648
$723$	17.6060	0.654773
$724$	−8.62772	−0.320647
$725$	−0.627719	−0.0233129
$726$	1.00000	0.0371135
$727$	6.11684	0.226861	0.113431	−	0.993546i	$-0.463816\pi$
$727$	6.11684	0.226861	0.113431	+	0.993546i	$0.463816\pi$
$728$	−13.4891	−0.499940
$729$	1.00000	0.0370370
$730$	6.00000	0.222070
$731$	−4.62772	−0.171162
$732$	11.4891	0.424650
$733$	9.48913	0.350489	0.175244	−	0.984525i	$-0.443928\pi$
$733$	9.48913	0.350489	0.175244	+	0.984525i	$0.443928\pi$
$734$	−23.4891	−0.866999
$735$	−4.37228	−0.161274
$736$	7.37228	0.271746
$737$	4.00000	0.147342
$738$	0.744563	0.0274077
$739$	36.2337	1.33288	0.666439	−	0.745560i	$-0.267818\pi$
$739$	36.2337	1.33288	0.666439	+	0.745560i	$0.267818\pi$
$740$	−2.74456	−0.100892
$741$	16.0000	0.587775
$742$	0	0
$743$	−45.2119	−1.65867	−0.829333	−	0.558755i	$-0.811279\pi$
$743$	−45.2119	−1.65867	−0.829333	+	0.558755i	$0.811279\pi$
$744$	8.11684	0.297578
$745$	3.25544	0.119270
$746$	21.7228	0.795329
$747$	9.48913	0.347189
$748$	1.00000	0.0365636
$749$	−15.6060	−0.570230
$750$	1.00000	0.0365148
$751$	−0.116844	−0.00426370	−0.00213185	−	0.999998i	$-0.500679\pi$
$751$	−0.116844	−0.00426370	−0.00213185	+	0.999998i	$0.500679\pi$
$752$	−0.744563	−0.0271514
$753$	−12.0000	−0.437304
$754$	−2.51087	−0.0914407
$755$	−18.2337	−0.663592
$756$	3.37228	0.122649
$757$	−14.6277	−0.531653	−0.265827	−	0.964021i	$-0.585645\pi$
$757$	−14.6277	−0.531653	−0.265827	+	0.964021i	$0.585645\pi$
$758$	0	0
$759$	7.37228	0.267597
$760$	−4.00000	−0.145095
$761$	−39.0951	−1.41720	−0.708598	−	0.705612i	$-0.750672\pi$
$761$	−39.0951	−1.41720	−0.708598	+	0.705612i	$0.750672\pi$
$762$	11.4891	0.416207
$763$	61.4891	2.22606
$764$	13.3723	0.483792
$765$	1.00000	0.0361551
$766$	−8.74456	−0.315954
$767$	−5.02175	−0.181325
$768$	−1.00000	−0.0360844
$769$	24.9783	0.900739	0.450369	−	0.892842i	$-0.351292\pi$
$769$	24.9783	0.900739	0.450369	+	0.892842i	$0.351292\pi$
$770$	3.37228	0.121529
$771$	−8.11684	−0.292321
$772$	19.4891	0.701429
$773$	−33.4891	−1.20452	−0.602260	−	0.798300i	$-0.705733\pi$
$773$	−33.4891	−1.20452	−0.602260	+	0.798300i	$0.705733\pi$
$774$	4.62772	0.166340
$775$	8.11684	0.291566
$776$	−10.8614	−0.389902
$777$	−9.25544	−0.332037
$778$	−9.25544	−0.331824
$779$	−2.97825	−0.106707
$780$	4.00000	0.143223
$781$	−6.74456	−0.241339
$782$	7.37228	0.263632
$783$	0.627719	0.0224328
$784$	4.37228	0.156153
$785$	10.0000	0.356915
$786$	8.00000	0.285351
$787$	−9.48913	−0.338251	−0.169125	−	0.985595i	$-0.554094\pi$
$787$	−9.48913	−0.338251	−0.169125	+	0.985595i	$0.554094\pi$
$788$	9.48913	0.338036
$789$	1.88316	0.0670421
$790$	0	0
$791$	52.2337	1.85722
$792$	−1.00000	−0.0355335
$793$	45.9565	1.63196
$794$	12.2337	0.434157
$795$	0	0
$796$	−3.25544	−0.115386
$797$	−5.48913	−0.194435	−0.0972174	−	0.995263i	$-0.530994\pi$
$797$	−5.48913	−0.194435	−0.0972174	+	0.995263i	$0.530994\pi$
$798$	−13.4891	−0.477510
$799$	−0.744563	−0.0263407
$800$	−1.00000	−0.0353553
$801$	8.74456	0.308974
$802$	−1.13859	−0.0402051
$803$	−6.00000	−0.211735
$804$	−4.00000	−0.141069
$805$	24.8614	0.876249
$806$	32.4674	1.14361
$807$	−14.0000	−0.492823
$808$	−2.00000	−0.0703598
$809$	40.9783	1.44072	0.720359	−	0.693601i	$-0.243977\pi$
$809$	40.9783	1.44072	0.720359	+	0.693601i	$0.243977\pi$
$810$	−1.00000	−0.0351364
$811$	−9.48913	−0.333208	−0.166604	−	0.986024i	$-0.553280\pi$
$811$	−9.48913	−0.333208	−0.166604	+	0.986024i	$0.553280\pi$
$812$	2.11684	0.0742867
$813$	13.3723	0.468986
$814$	2.74456	0.0961969
$815$	20.8614	0.730743
$816$	−1.00000	−0.0350070
$817$	−18.5109	−0.647614
$818$	22.2337	0.777383
$819$	13.4891	0.471348
$820$	−0.744563	−0.0260013
$821$	−27.3723	−0.955299	−0.477650	−	0.878550i	$-0.658511\pi$
$821$	−27.3723	−0.955299	−0.477650	+	0.878550i	$0.658511\pi$
$822$	−16.1168	−0.562139
$823$	10.0000	0.348578	0.174289	−	0.984695i	$-0.444237\pi$
$823$	10.0000	0.348578	0.174289	+	0.984695i	$0.444237\pi$
$824$	−12.6277	−0.439907
$825$	−1.00000	−0.0348155
$826$	4.23369	0.147309
$827$	23.8397	0.828986	0.414493	−	0.910052i	$-0.363959\pi$
$827$	23.8397	0.828986	0.414493	+	0.910052i	$0.363959\pi$
$828$	−7.37228	−0.256204
$829$	24.9783	0.867531	0.433765	−	0.901026i	$-0.357185\pi$
$829$	24.9783	0.867531	0.433765	+	0.901026i	$0.357185\pi$
$830$	−9.48913	−0.329372
$831$	7.48913	0.259795
$832$	−4.00000	−0.138675
$833$	4.37228	0.151491
$834$	7.37228	0.255281
$835$	−3.48913	−0.120746
$836$	4.00000	0.138343
$837$	−8.11684	−0.280559
$838$	−32.6277	−1.12711
$839$	−13.7228	−0.473764	−0.236882	−	0.971538i	$-0.576125\pi$
$839$	−13.7228	−0.473764	−0.236882	+	0.971538i	$0.576125\pi$
$840$	−3.37228	−0.116355
$841$	−28.6060	−0.986413
$842$	36.7446	1.26630
$843$	14.8614	0.511854
$844$	−15.3723	−0.529136
$845$	3.00000	0.103203
$846$	0.744563	0.0255986
$847$	−3.37228	−0.115873
$848$	0	0
$849$	13.2554	0.454925
$850$	−1.00000	−0.0342997
$851$	20.2337	0.693602
$852$	6.74456	0.231065
$853$	−4.11684	−0.140958	−0.0704790	−	0.997513i	$-0.522453\pi$
$853$	−4.11684	−0.140958	−0.0704790	+	0.997513i	$0.522453\pi$
$854$	−38.7446	−1.32581
$855$	4.00000	0.136797
$856$	−4.62772	−0.158172
$857$	18.8614	0.644293	0.322147	−	0.946690i	$-0.395596\pi$
$857$	18.8614	0.644293	0.322147	+	0.946690i	$0.395596\pi$
$858$	−4.00000	−0.136558
$859$	−39.8397	−1.35931	−0.679656	−	0.733531i	$-0.737871\pi$
$859$	−39.8397	−1.35931	−0.679656	+	0.733531i	$0.737871\pi$
$860$	−4.62772	−0.157804
$861$	−2.51087	−0.0855704
$862$	−10.8614	−0.369941
$863$	19.7228	0.671372	0.335686	−	0.941974i	$-0.391032\pi$
$863$	19.7228	0.671372	0.335686	+	0.941974i	$0.391032\pi$
$864$	1.00000	0.0340207
$865$	20.2337	0.687966
$866$	−7.25544	−0.246550
$867$	−1.00000	−0.0339618
$868$	−27.3723	−0.929076
$869$	0	0
$870$	−0.627719	−0.0212817
$871$	−16.0000	−0.542139
$872$	18.2337	0.617471
$873$	10.8614	0.367603
$874$	29.4891	0.997485
$875$	−3.37228	−0.114004
$876$	6.00000	0.202721
$877$	−18.6277	−0.629013	−0.314507	−	0.949255i	$-0.601839\pi$
$877$	−18.6277	−0.629013	−0.314507	+	0.949255i	$0.601839\pi$
$878$	−21.2554	−0.717336
$879$	−20.1168	−0.678524
$880$	1.00000	0.0337100
$881$	−11.8832	−0.400354	−0.200177	−	0.979760i	$-0.564152\pi$
$881$	−11.8832	−0.400354	−0.200177	+	0.979760i	$0.564152\pi$
$882$	−4.37228	−0.147222
$883$	1.48913	0.0501131	0.0250565	−	0.999686i	$-0.492023\pi$
$883$	1.48913	0.0501131	0.0250565	+	0.999686i	$0.492023\pi$
$884$	−4.00000	−0.134535
$885$	−1.25544	−0.0422011
$886$	−4.62772	−0.155471
$887$	−11.7228	−0.393614	−0.196807	−	0.980442i	$-0.563057\pi$
$887$	−11.7228	−0.393614	−0.196807	+	0.980442i	$0.563057\pi$
$888$	−2.74456	−0.0921015
$889$	−38.7446	−1.29945
$890$	−8.74456	−0.293118
$891$	1.00000	0.0335013
$892$	14.1168	0.472667
$893$	−2.97825	−0.0996634
$894$	3.25544	0.108878
$895$	10.7446	0.359151
$896$	3.37228	0.112660
$897$	−29.4891	−0.984613
$898$	−26.8614	−0.896377
$899$	−5.09509	−0.169931
$900$	1.00000	0.0333333
$901$	0	0
$902$	0.744563	0.0247912
$903$	−15.6060	−0.519334
$904$	15.4891	0.515161
$905$	−8.62772	−0.286795
$906$	−18.2337	−0.605774
$907$	19.1386	0.635487	0.317743	−	0.948177i	$-0.397075\pi$
$907$	19.1386	0.635487	0.317743	+	0.948177i	$0.397075\pi$
$908$	−4.86141	−0.161331
$909$	2.00000	0.0663358
$910$	−13.4891	−0.447160
$911$	−40.4674	−1.34074	−0.670372	−	0.742025i	$-0.733865\pi$
$911$	−40.4674	−1.34074	−0.670372	+	0.742025i	$0.733865\pi$
$912$	−4.00000	−0.132453
$913$	9.48913	0.314044
$914$	−28.9783	−0.958515
$915$	11.4891	0.379819
$916$	−12.7446	−0.421092
$917$	−26.9783	−0.890900
$918$	1.00000	0.0330049
$919$	27.8832	0.919780	0.459890	−	0.887976i	$-0.347889\pi$
$919$	27.8832	0.919780	0.459890	+	0.887976i	$0.347889\pi$
$920$	7.37228	0.243057
$921$	12.0000	0.395413
$922$	−0.510875	−0.0168248
$923$	26.9783	0.888000
$924$	3.37228	0.110940
$925$	−2.74456	−0.0902407
$926$	−8.00000	−0.262896
$927$	12.6277	0.414749
$928$	0.627719	0.0206059
$929$	25.3723	0.832438	0.416219	−	0.909265i	$-0.363355\pi$
$929$	25.3723	0.832438	0.416219	+	0.909265i	$0.363355\pi$
$930$	8.11684	0.266162
$931$	17.4891	0.573183
$932$	16.1168	0.527925
$933$	−33.4891	−1.09638
$934$	14.9783	0.490103
$935$	1.00000	0.0327035
$936$	4.00000	0.130744
$937$	−34.4674	−1.12600	−0.563000	−	0.826457i	$-0.690353\pi$
$937$	−34.4674	−1.12600	−0.563000	+	0.826457i	$0.690353\pi$
$938$	13.4891	0.440436
$939$	1.37228	0.0447827
$940$	−0.744563	−0.0242850
$941$	−14.7446	−0.480659	−0.240330	−	0.970691i	$-0.577255\pi$
$941$	−14.7446	−0.480659	−0.240330	+	0.970691i	$0.577255\pi$
$942$	10.0000	0.325818
$943$	5.48913	0.178751
$944$	1.25544	0.0408610
$945$	3.37228	0.109700
$946$	4.62772	0.150460
$947$	−34.7446	−1.12905	−0.564523	−	0.825417i	$-0.690940\pi$
$947$	−34.7446	−1.12905	−0.564523	+	0.825417i	$0.690940\pi$
$948$	0	0
$949$	24.0000	0.779073
$950$	−4.00000	−0.129777
$951$	−16.1168	−0.522624
$952$	3.37228	0.109296
$953$	−7.02175	−0.227457	−0.113728	−	0.993512i	$-0.536279\pi$
$953$	−7.02175	−0.227457	−0.113728	+	0.993512i	$0.536279\pi$
$954$	0	0
$955$	13.3723	0.432717
$956$	4.23369	0.136927
$957$	0.627719	0.0202913
$958$	15.8832	0.513161
$959$	54.3505	1.75507
$960$	−1.00000	−0.0322749
$961$	34.8832	1.12526
$962$	−10.9783	−0.353953
$963$	4.62772	0.149126
$964$	−17.6060	−0.567050
$965$	19.4891	0.627377
$966$	24.8614	0.799903
$967$	26.4674	0.851133	0.425567	−	0.904927i	$-0.360075\pi$
$967$	26.4674	0.851133	0.425567	+	0.904927i	$0.360075\pi$
$968$	−1.00000	−0.0321412
$969$	−4.00000	−0.128499
$970$	−10.8614	−0.348739
$971$	48.4674	1.55539	0.777696	−	0.628640i	$-0.216388\pi$
$971$	48.4674	1.55539	0.777696	+	0.628640i	$0.216388\pi$
$972$	−1.00000	−0.0320750
$973$	−24.8614	−0.797020
$974$	15.4891	0.496304
$975$	4.00000	0.128103
$976$	−11.4891	−0.367758
$977$	−11.4891	−0.367570	−0.183785	−	0.982966i	$-0.558835\pi$
$977$	−11.4891	−0.367570	−0.183785	+	0.982966i	$0.558835\pi$
$978$	20.8614	0.667074
$979$	8.74456	0.279477
$980$	4.37228	0.139667
$981$	−18.2337	−0.582157
$982$	−41.4891	−1.32397
$983$	−5.88316	−0.187644	−0.0938218	−	0.995589i	$-0.529908\pi$
$983$	−5.88316	−0.187644	−0.0938218	+	0.995589i	$0.529908\pi$
$984$	−0.744563	−0.0237358
$985$	9.48913	0.302349
$986$	0.627719	0.0199906
$987$	−2.51087	−0.0799220
$988$	−16.0000	−0.509028
$989$	34.1168	1.08485
$990$	−1.00000	−0.0317821
$991$	13.3723	0.424785	0.212392	−	0.977184i	$-0.431875\pi$
$991$	13.3723	0.424785	0.212392	+	0.977184i	$0.431875\pi$
$992$	−8.11684	−0.257710
$993$	−9.88316	−0.313632
$994$	−22.7446	−0.721414
$995$	−3.25544	−0.103204
$996$	−9.48913	−0.300674
$997$	24.1168	0.763788	0.381894	−	0.924206i	$-0.375272\pi$
$997$	24.1168	0.763788	0.381894	+	0.924206i	$0.375272\pi$
$998$	−36.0000	−1.13956
$999$	2.74456	0.0868341

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.bq.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.bq.1.1	✓	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5610.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -3.37228 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -3.37228 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} -4.00000 q^{13} +3.37228 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +4.00000 q^{19} +1.00000 q^{20} +3.37228 q^{21} -1.00000 q^{22} -7.37228 q^{23} +1.00000 q^{24} +1.00000 q^{25} +4.00000 q^{26} -1.00000 q^{27} -3.37228 q^{28} -0.627719 q^{29} +1.00000 q^{30} +8.11684 q^{31} -1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} -3.37228 q^{35} +1.00000 q^{36} -2.74456 q^{37} -4.00000 q^{38} +4.00000 q^{39} -1.00000 q^{40} -0.744563 q^{41} -3.37228 q^{42} -4.62772 q^{43} +1.00000 q^{44} +1.00000 q^{45} +7.37228 q^{46} -0.744563 q^{47} -1.00000 q^{48} +4.37228 q^{49} -1.00000 q^{50} -1.00000 q^{51} -4.00000 q^{52} +1.00000 q^{54} +1.00000 q^{55} +3.37228 q^{56} -4.00000 q^{57} +0.627719 q^{58} +1.25544 q^{59} -1.00000 q^{60} -11.4891 q^{61} -8.11684 q^{62} -3.37228 q^{63} +1.00000 q^{64} -4.00000 q^{65} +1.00000 q^{66} +4.00000 q^{67} +1.00000 q^{68} +7.37228 q^{69} +3.37228 q^{70} -6.74456 q^{71} -1.00000 q^{72} -6.00000 q^{73} +2.74456 q^{74} -1.00000 q^{75} +4.00000 q^{76} -3.37228 q^{77} -4.00000 q^{78} +1.00000 q^{80} +1.00000 q^{81} +0.744563 q^{82} +9.48913 q^{83} +3.37228 q^{84} +1.00000 q^{85} +4.62772 q^{86} +0.627719 q^{87} -1.00000 q^{88} +8.74456 q^{89} -1.00000 q^{90} +13.4891 q^{91} -7.37228 q^{92} -8.11684 q^{93} +0.744563 q^{94} +4.00000 q^{95} +1.00000 q^{96} +10.8614 q^{97} -4.37228 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - q^{7} - 2 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} - 8 q^{13} + q^{14} - 2 q^{15} + 2 q^{16} + 2 q^{17} - 2 q^{18} + 8 q^{19} + 2 q^{20} + q^{21} - 2 q^{22} - 9 q^{23} + 2 q^{24} + 2 q^{25} + 8 q^{26} - 2 q^{27} - q^{28} - 7 q^{29} + 2 q^{30} - q^{31} - 2 q^{32} - 2 q^{33} - 2 q^{34} - q^{35} + 2 q^{36} + 6 q^{37} - 8 q^{38} + 8 q^{39} - 2 q^{40} + 10 q^{41} - q^{42} - 15 q^{43} + 2 q^{44} + 2 q^{45} + 9 q^{46} + 10 q^{47} - 2 q^{48} + 3 q^{49} - 2 q^{50} - 2 q^{51} - 8 q^{52} + 2 q^{54} + 2 q^{55} + q^{56} - 8 q^{57} + 7 q^{58} + 14 q^{59} - 2 q^{60} + q^{62} - q^{63} + 2 q^{64} - 8 q^{65} + 2 q^{66} + 8 q^{67} + 2 q^{68} + 9 q^{69} + q^{70} - 2 q^{71} - 2 q^{72} - 12 q^{73} - 6 q^{74} - 2 q^{75} + 8 q^{76} - q^{77} - 8 q^{78} + 2 q^{80} + 2 q^{81} - 10 q^{82} - 4 q^{83} + q^{84} + 2 q^{85} + 15 q^{86} + 7 q^{87} - 2 q^{88} + 6 q^{89} - 2 q^{90} + 4 q^{91} - 9 q^{92} + q^{93} - 10 q^{94} + 8 q^{95} + 2 q^{96} - 7 q^{97} - 3 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - q^7 - 2 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 - 8 * q^13 + q^14 - 2 * q^15 + 2 * q^16 + 2 * q^17 - 2 * q^18 + 8 * q^19 + 2 * q^20 + q^21 - 2 * q^22 - 9 * q^23 + 2 * q^24 + 2 * q^25 + 8 * q^26 - 2 * q^27 - q^28 - 7 * q^29 + 2 * q^30 - q^31 - 2 * q^32 - 2 * q^33 - 2 * q^34 - q^35 + 2 * q^36 + 6 * q^37 - 8 * q^38 + 8 * q^39 - 2 * q^40 + 10 * q^41 - q^42 - 15 * q^43 + 2 * q^44 + 2 * q^45 + 9 * q^46 + 10 * q^47 - 2 * q^48 + 3 * q^49 - 2 * q^50 - 2 * q^51 - 8 * q^52 + 2 * q^54 + 2 * q^55 + q^56 - 8 * q^57 + 7 * q^58 + 14 * q^59 - 2 * q^60 + q^62 - q^63 + 2 * q^64 - 8 * q^65 + 2 * q^66 + 8 * q^67 + 2 * q^68 + 9 * q^69 + q^70 - 2 * q^71 - 2 * q^72 - 12 * q^73 - 6 * q^74 - 2 * q^75 + 8 * q^76 - q^77 - 8 * q^78 + 2 * q^80 + 2 * q^81 - 10 * q^82 - 4 * q^83 + q^84 + 2 * q^85 + 15 * q^86 + 7 * q^87 - 2 * q^88 + 6 * q^89 - 2 * q^90 + 4 * q^91 - 9 * q^92 + q^93 - 10 * q^94 + 8 * q^95 + 2 * q^96 - 7 * q^97 - 3 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more