LMFDB - Embedded newform 5610.2.a.bp.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:	$1$
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			$-2.37228$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -2.37228 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -2.37228 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} +4.37228 q^{13} +2.37228 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +2.37228 q^{19} -1.00000 q^{20} +2.37228 q^{21} +1.00000 q^{22} -2.37228 q^{23} +1.00000 q^{24} +1.00000 q^{25} -4.37228 q^{26} -1.00000 q^{27} -2.37228 q^{28} -2.00000 q^{29} -1.00000 q^{30} +1.62772 q^{31} -1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} +2.37228 q^{35} +1.00000 q^{36} -8.37228 q^{37} -2.37228 q^{38} -4.37228 q^{39} +1.00000 q^{40} -6.00000 q^{41} -2.37228 q^{42} +4.00000 q^{43} -1.00000 q^{44} -1.00000 q^{45} +2.37228 q^{46} -8.74456 q^{47} -1.00000 q^{48} -1.37228 q^{49} -1.00000 q^{50} +1.00000 q^{51} +4.37228 q^{52} +11.4891 q^{53} +1.00000 q^{54} +1.00000 q^{55} +2.37228 q^{56} -2.37228 q^{57} +2.00000 q^{58} +4.00000 q^{59} +1.00000 q^{60} +13.1168 q^{61} -1.62772 q^{62} -2.37228 q^{63} +1.00000 q^{64} -4.37228 q^{65} -1.00000 q^{66} +6.37228 q^{67} -1.00000 q^{68} +2.37228 q^{69} -2.37228 q^{70} +4.74456 q^{71} -1.00000 q^{72} -1.25544 q^{73} +8.37228 q^{74} -1.00000 q^{75} +2.37228 q^{76} +2.37228 q^{77} +4.37228 q^{78} +4.74456 q^{79} -1.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} -1.62772 q^{83} +2.37228 q^{84} +1.00000 q^{85} -4.00000 q^{86} +2.00000 q^{87} +1.00000 q^{88} +10.0000 q^{89} +1.00000 q^{90} -10.3723 q^{91} -2.37228 q^{92} -1.62772 q^{93} +8.74456 q^{94} -2.37228 q^{95} +1.00000 q^{96} +3.62772 q^{97} +1.37228 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} - 2 q^{12} + 3 q^{13} - q^{14} + 2 q^{15} + 2 q^{16} - 2 q^{17} - 2 q^{18} - q^{19} - 2 q^{20} - q^{21} + 2 q^{22} + q^{23} + 2 q^{24} + 2 q^{25} - 3 q^{26} - 2 q^{27} + q^{28} - 4 q^{29} - 2 q^{30} + 9 q^{31} - 2 q^{32} + 2 q^{33} + 2 q^{34} - q^{35} + 2 q^{36} - 11 q^{37} + q^{38} - 3 q^{39} + 2 q^{40} - 12 q^{41} + q^{42} + 8 q^{43} - 2 q^{44} - 2 q^{45} - q^{46} - 6 q^{47} - 2 q^{48} + 3 q^{49} - 2 q^{50} + 2 q^{51} + 3 q^{52} + 2 q^{54} + 2 q^{55} - q^{56} + q^{57} + 4 q^{58} + 8 q^{59} + 2 q^{60} + 9 q^{61} - 9 q^{62} + q^{63} + 2 q^{64} - 3 q^{65} - 2 q^{66} + 7 q^{67} - 2 q^{68} - q^{69} + q^{70} - 2 q^{71} - 2 q^{72} - 14 q^{73} + 11 q^{74} - 2 q^{75} - q^{76} - q^{77} + 3 q^{78} - 2 q^{79} - 2 q^{80} + 2 q^{81} + 12 q^{82} - 9 q^{83} - q^{84} + 2 q^{85} - 8 q^{86} + 4 q^{87} + 2 q^{88} + 20 q^{89} + 2 q^{90} - 15 q^{91} + q^{92} - 9 q^{93} + 6 q^{94} + q^{95} + 2 q^{96} + 13 q^{97} - 3 q^{98} - 2 q^{99}+O(q^{100}) \) 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 + 3 * q^13 - q^14 + 2 * q^15 + 2 * q^16 - 2 * q^17 - 2 * q^18 - q^19 - 2 * q^20 - q^21 + 2 * q^22 + q^23 + 2 * q^24 + 2 * q^25 - 3 * q^26 - 2 * q^27 + q^28 - 4 * q^29 - 2 * q^30 + 9 * q^31 - 2 * q^32 + 2 * q^33 + 2 * q^34 - q^35 + 2 * q^36 - 11 * q^37 + q^38 - 3 * q^39 + 2 * q^40 - 12 * q^41 + q^42 + 8 * q^43 - 2 * q^44 - 2 * q^45 - q^46 - 6 * q^47 - 2 * q^48 + 3 * q^49 - 2 * q^50 + 2 * q^51 + 3 * q^52 + 2 * q^54 + 2 * q^55 - q^56 + q^57 + 4 * q^58 + 8 * q^59 + 2 * q^60 + 9 * q^61 - 9 * q^62 + q^63 + 2 * q^64 - 3 * q^65 - 2 * q^66 + 7 * q^67 - 2 * q^68 - q^69 + q^70 - 2 * q^71 - 2 * q^72 - 14 * q^73 + 11 * q^74 - 2 * q^75 - q^76 - q^77 + 3 * q^78 - 2 * q^79 - 2 * q^80 + 2 * q^81 + 12 * q^82 - 9 * q^83 - q^84 + 2 * q^85 - 8 * q^86 + 4 * q^87 + 2 * q^88 + 20 * q^89 + 2 * q^90 - 15 * q^91 + q^92 - 9 * q^93 + 6 * q^94 + q^95 + 2 * q^96 + 13 * 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
$7$	−2.37228	−0.896638	−0.448319	−	0.893874i	$-0.647977\pi$
$7$	−2.37228	−0.896638	−0.448319	+	0.893874i	$0.647977\pi$
$8$	−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
$13$	4.37228	1.21265	0.606326	−	0.795216i	$-0.292643\pi$
$13$	4.37228	1.21265	0.606326	+	0.795216i	$0.292643\pi$
$14$	2.37228	0.634019
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	2.37228	0.544239	0.272119	−	0.962264i	$-0.412275\pi$
$19$	2.37228	0.544239	0.272119	+	0.962264i	$0.412275\pi$
$20$	−1.00000	−0.223607
$21$	2.37228	0.517674
$22$	1.00000	0.213201
$23$	−2.37228	−0.494655	−0.247327	−	0.968932i	$-0.579552\pi$
$23$	−2.37228	−0.494655	−0.247327	+	0.968932i	$0.579552\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−4.37228	−0.857475
$27$	−1.00000	−0.192450
$28$	−2.37228	−0.448319
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	−1.00000	−0.182574
$31$	1.62772	0.292347	0.146173	−	0.989259i	$-0.453304\pi$
$31$	1.62772	0.292347	0.146173	+	0.989259i	$0.453304\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	1.00000	0.171499
$35$	2.37228	0.400989
$36$	1.00000	0.166667
$37$	−8.37228	−1.37639	−0.688197	−	0.725524i	$-0.741598\pi$
$37$	−8.37228	−1.37639	−0.688197	+	0.725524i	$0.741598\pi$
$38$	−2.37228	−0.384835
$39$	−4.37228	−0.700125
$40$	1.00000	0.158114
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	−2.37228	−0.366051
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	−1.00000	−0.150756
$45$	−1.00000	−0.149071
$46$	2.37228	0.349774
$47$	−8.74456	−1.27553	−0.637763	−	0.770233i	$-0.720140\pi$
$47$	−8.74456	−1.27553	−0.637763	+	0.770233i	$0.720140\pi$
$48$	−1.00000	−0.144338
$49$	−1.37228	−0.196040
$50$	−1.00000	−0.141421
$51$	1.00000	0.140028
$52$	4.37228	0.606326
$53$	11.4891	1.57815	0.789076	−	0.614295i	$-0.210560\pi$
$53$	11.4891	1.57815	0.789076	+	0.614295i	$0.210560\pi$
$54$	1.00000	0.136083
$55$	1.00000	0.134840
$56$	2.37228	0.317009
$57$	−2.37228	−0.314216
$58$	2.00000	0.262613
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	1.00000	0.129099
$61$	13.1168	1.67944	0.839720	−	0.543020i	$-0.182719\pi$
$61$	13.1168	1.67944	0.839720	+	0.543020i	$0.182719\pi$
$62$	−1.62772	−0.206720
$63$	−2.37228	−0.298879
$64$	1.00000	0.125000
$65$	−4.37228	−0.542315
$66$	−1.00000	−0.123091
$67$	6.37228	0.778498	0.389249	−	0.921133i	$-0.372735\pi$
$67$	6.37228	0.778498	0.389249	+	0.921133i	$0.372735\pi$
$68$	−1.00000	−0.121268
$69$	2.37228	0.285589
$70$	−2.37228	−0.283542
$71$	4.74456	0.563076	0.281538	−	0.959550i	$-0.409155\pi$
$71$	4.74456	0.563076	0.281538	+	0.959550i	$0.409155\pi$
$72$	−1.00000	−0.117851
$73$	−1.25544	−0.146938	−0.0734689	−	0.997298i	$-0.523407\pi$
$73$	−1.25544	−0.146938	−0.0734689	+	0.997298i	$0.523407\pi$
$74$	8.37228	0.973258
$75$	−1.00000	−0.115470
$76$	2.37228	0.272119
$77$	2.37228	0.270347
$78$	4.37228	0.495063
$79$	4.74456	0.533805	0.266903	−	0.963724i	$-0.414000\pi$
$79$	4.74456	0.533805	0.266903	+	0.963724i	$0.414000\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	6.00000	0.662589
$83$	−1.62772	−0.178665	−0.0893327	−	0.996002i	$-0.528473\pi$
$83$	−1.62772	−0.178665	−0.0893327	+	0.996002i	$0.528473\pi$
$84$	2.37228	0.258837
$85$	1.00000	0.108465
$86$	−4.00000	−0.431331
$87$	2.00000	0.214423
$88$	1.00000	0.106600
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	1.00000	0.105409
$91$	−10.3723	−1.08731
$92$	−2.37228	−0.247327
$93$	−1.62772	−0.168787
$94$	8.74456	0.901933
$95$	−2.37228	−0.243391
$96$	1.00000	0.102062
$97$	3.62772	0.368339	0.184170	−	0.982894i	$-0.441040\pi$
$97$	3.62772	0.368339	0.184170	+	0.982894i	$0.441040\pi$
$98$	1.37228	0.138621
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	11.4891	1.14321	0.571605	−	0.820529i	$-0.306321\pi$
$101$	11.4891	1.14321	0.571605	+	0.820529i	$0.306321\pi$
$102$	−1.00000	−0.0990148
$103$	−7.11684	−0.701243	−0.350622	−	0.936517i	$-0.614030\pi$
$103$	−7.11684	−0.701243	−0.350622	+	0.936517i	$0.614030\pi$
$104$	−4.37228	−0.428737
$105$	−2.37228	−0.231511
$106$	−11.4891	−1.11592
$107$	−3.25544	−0.314715	−0.157358	−	0.987542i	$-0.550297\pi$
$107$	−3.25544	−0.314715	−0.157358	+	0.987542i	$0.550297\pi$
$108$	−1.00000	−0.0962250
$109$	−1.11684	−0.106974	−0.0534871	−	0.998569i	$-0.517034\pi$
$109$	−1.11684	−0.106974	−0.0534871	+	0.998569i	$0.517034\pi$
$110$	−1.00000	−0.0953463
$111$	8.37228	0.794662
$112$	−2.37228	−0.224160
$113$	−2.00000	−0.188144	−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000	−0.188144	−0.0940721	+	0.995565i	$0.529988\pi$
$114$	2.37228	0.222185
$115$	2.37228	0.221216
$116$	−2.00000	−0.185695
$117$	4.37228	0.404218
$118$	−4.00000	−0.368230
$119$	2.37228	0.217467
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	−13.1168	−1.18754
$123$	6.00000	0.541002
$124$	1.62772	0.146173
$125$	−1.00000	−0.0894427
$126$	2.37228	0.211340
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	−1.00000	−0.0883883
$129$	−4.00000	−0.352180
$130$	4.37228	0.383474
$131$	1.62772	0.142214	0.0711072	−	0.997469i	$-0.477347\pi$
$131$	1.62772	0.142214	0.0711072	+	0.997469i	$0.477347\pi$
$132$	1.00000	0.0870388
$133$	−5.62772	−0.487985
$134$	−6.37228	−0.550481
$135$	1.00000	0.0860663
$136$	1.00000	0.0857493
$137$	−17.1168	−1.46239	−0.731195	−	0.682168i	$-0.761037\pi$
$137$	−17.1168	−1.46239	−0.731195	+	0.682168i	$0.761037\pi$
$138$	−2.37228	−0.201942
$139$	−0.744563	−0.0631530	−0.0315765	−	0.999501i	$-0.510053\pi$
$139$	−0.744563	−0.0631530	−0.0315765	+	0.999501i	$0.510053\pi$
$140$	2.37228	0.200494
$141$	8.74456	0.736425
$142$	−4.74456	−0.398155
$143$	−4.37228	−0.365629
$144$	1.00000	0.0833333
$145$	2.00000	0.166091
$146$	1.25544	0.103901
$147$	1.37228	0.113184
$148$	−8.37228	−0.688197
$149$	−13.1168	−1.07457	−0.537287	−	0.843400i	$-0.680551\pi$
$149$	−13.1168	−1.07457	−0.537287	+	0.843400i	$0.680551\pi$
$150$	1.00000	0.0816497
$151$	9.62772	0.783493	0.391746	−	0.920073i	$-0.371871\pi$
$151$	9.62772	0.783493	0.391746	+	0.920073i	$0.371871\pi$
$152$	−2.37228	−0.192417
$153$	−1.00000	−0.0808452
$154$	−2.37228	−0.191164
$155$	−1.62772	−0.130742
$156$	−4.37228	−0.350063
$157$	10.7446	0.857509	0.428755	−	0.903421i	$-0.358952\pi$
$157$	10.7446	0.857509	0.428755	+	0.903421i	$0.358952\pi$
$158$	−4.74456	−0.377457
$159$	−11.4891	−0.911147
$160$	1.00000	0.0790569
$161$	5.62772	0.443526
$162$	−1.00000	−0.0785674
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	−6.00000	−0.468521
$165$	−1.00000	−0.0778499
$166$	1.62772	0.126335
$167$	−21.4891	−1.66288	−0.831439	−	0.555616i	$-0.812483\pi$
$167$	−21.4891	−1.66288	−0.831439	+	0.555616i	$0.812483\pi$
$168$	−2.37228	−0.183025
$169$	6.11684	0.470526
$170$	−1.00000	−0.0766965
$171$	2.37228	0.181413
$172$	4.00000	0.304997
$173$	5.86141	0.445634	0.222817	−	0.974860i	$-0.428475\pi$
$173$	5.86141	0.445634	0.222817	+	0.974860i	$0.428475\pi$
$174$	−2.00000	−0.151620
$175$	−2.37228	−0.179328
$176$	−1.00000	−0.0753778
$177$	−4.00000	−0.300658
$178$	−10.0000	−0.749532
$179$	3.11684	0.232964	0.116482	−	0.993193i	$-0.462838\pi$
$179$	3.11684	0.232964	0.116482	+	0.993193i	$0.462838\pi$
$180$	−1.00000	−0.0745356
$181$	1.25544	0.0933159	0.0466580	−	0.998911i	$-0.485143\pi$
$181$	1.25544	0.0933159	0.0466580	+	0.998911i	$0.485143\pi$
$182$	10.3723	0.768845
$183$	−13.1168	−0.969625
$184$	2.37228	0.174887
$185$	8.37228	0.615542
$186$	1.62772	0.119350
$187$	1.00000	0.0731272
$188$	−8.74456	−0.637763
$189$	2.37228	0.172558
$190$	2.37228	0.172103
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	−1.00000	−0.0721688
$193$	22.7446	1.63719	0.818595	−	0.574372i	$-0.194754\pi$
$193$	22.7446	1.63719	0.818595	+	0.574372i	$0.194754\pi$
$194$	−3.62772	−0.260455
$195$	4.37228	0.313106
$196$	−1.37228	−0.0980201
$197$	−14.6060	−1.04063	−0.520316	−	0.853974i	$-0.674186\pi$
$197$	−14.6060	−1.04063	−0.520316	+	0.853974i	$0.674186\pi$
$198$	1.00000	0.0710669
$199$	−14.3723	−1.01882	−0.509412	−	0.860523i	$-0.670137\pi$
$199$	−14.3723	−1.01882	−0.509412	+	0.860523i	$0.670137\pi$
$200$	−1.00000	−0.0707107
$201$	−6.37228	−0.449466
$202$	−11.4891	−0.808372
$203$	4.74456	0.333003
$204$	1.00000	0.0700140
$205$	6.00000	0.419058
$206$	7.11684	0.495854
$207$	−2.37228	−0.164885
$208$	4.37228	0.303163
$209$	−2.37228	−0.164094
$210$	2.37228	0.163703
$211$	−8.74456	−0.602001	−0.301000	−	0.953624i	$-0.597321\pi$
$211$	−8.74456	−0.602001	−0.301000	+	0.953624i	$0.597321\pi$
$212$	11.4891	0.789076
$213$	−4.74456	−0.325092
$214$	3.25544	0.222537
$215$	−4.00000	−0.272798
$216$	1.00000	0.0680414
$217$	−3.86141	−0.262129
$218$	1.11684	0.0756422
$219$	1.25544	0.0848346
$220$	1.00000	0.0674200
$221$	−4.37228	−0.294111
$222$	−8.37228	−0.561911
$223$	−19.8614	−1.33002	−0.665009	−	0.746835i	$-0.731572\pi$
$223$	−19.8614	−1.33002	−0.665009	+	0.746835i	$0.731572\pi$
$224$	2.37228	0.158505
$225$	1.00000	0.0666667
$226$	2.00000	0.133038
$227$	−12.7446	−0.845886	−0.422943	−	0.906156i	$-0.639003\pi$
$227$	−12.7446	−0.845886	−0.422943	+	0.906156i	$0.639003\pi$
$228$	−2.37228	−0.157108
$229$	5.11684	0.338131	0.169065	−	0.985605i	$-0.445925\pi$
$229$	5.11684	0.338131	0.169065	+	0.985605i	$0.445925\pi$
$230$	−2.37228	−0.156424
$231$	−2.37228	−0.156085
$232$	2.00000	0.131306
$233$	−0.510875	−0.0334685	−0.0167343	−	0.999860i	$-0.505327\pi$
$233$	−0.510875	−0.0334685	−0.0167343	+	0.999860i	$0.505327\pi$
$234$	−4.37228	−0.285825
$235$	8.74456	0.570432
$236$	4.00000	0.260378
$237$	−4.74456	−0.308192
$238$	−2.37228	−0.153772
$239$	12.7446	0.824377	0.412189	−	0.911099i	$-0.364764\pi$
$239$	12.7446	0.824377	0.412189	+	0.911099i	$0.364764\pi$
$240$	1.00000	0.0645497
$241$	−22.6060	−1.45618	−0.728089	−	0.685482i	$-0.759591\pi$
$241$	−22.6060	−1.45618	−0.728089	+	0.685482i	$0.759591\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	13.1168	0.839720
$245$	1.37228	0.0876718
$246$	−6.00000	−0.382546
$247$	10.3723	0.659972
$248$	−1.62772	−0.103360
$249$	1.62772	0.103152
$250$	1.00000	0.0632456
$251$	−22.3723	−1.41213	−0.706063	−	0.708149i	$-0.749530\pi$
$251$	−22.3723	−1.41213	−0.706063	+	0.708149i	$0.749530\pi$
$252$	−2.37228	−0.149440
$253$	2.37228	0.149144
$254$	8.00000	0.501965
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	−0.510875	−0.0318675	−0.0159337	−	0.999873i	$-0.505072\pi$
$257$	−0.510875	−0.0318675	−0.0159337	+	0.999873i	$0.505072\pi$
$258$	4.00000	0.249029
$259$	19.8614	1.23413
$260$	−4.37228	−0.271157
$261$	−2.00000	−0.123797
$262$	−1.62772	−0.100561
$263$	−13.6277	−0.840321	−0.420161	−	0.907450i	$-0.638026\pi$
$263$	−13.6277	−0.840321	−0.420161	+	0.907450i	$0.638026\pi$
$264$	−1.00000	−0.0615457
$265$	−11.4891	−0.705771
$266$	5.62772	0.345058
$267$	−10.0000	−0.611990
$268$	6.37228	0.389249
$269$	7.62772	0.465070	0.232535	−	0.972588i	$-0.425298\pi$
$269$	7.62772	0.465070	0.232535	+	0.972588i	$0.425298\pi$
$270$	−1.00000	−0.0608581
$271$	−20.0000	−1.21491	−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000	−1.21491	−0.607457	+	0.794353i	$0.707810\pi$
$272$	−1.00000	−0.0606339
$273$	10.3723	0.627759
$274$	17.1168	1.03407
$275$	−1.00000	−0.0603023
$276$	2.37228	0.142795
$277$	4.23369	0.254378	0.127189	−	0.991879i	$-0.459405\pi$
$277$	4.23369	0.254378	0.127189	+	0.991879i	$0.459405\pi$
$278$	0.744563	0.0446559
$279$	1.62772	0.0974490
$280$	−2.37228	−0.141771
$281$	14.0000	0.835170	0.417585	−	0.908638i	$-0.362877\pi$
$281$	14.0000	0.835170	0.417585	+	0.908638i	$0.362877\pi$
$282$	−8.74456	−0.520731
$283$	−28.0000	−1.66443	−0.832214	−	0.554455i	$-0.812927\pi$
$283$	−28.0000	−1.66443	−0.832214	+	0.554455i	$0.812927\pi$
$284$	4.74456	0.281538
$285$	2.37228	0.140522
$286$	4.37228	0.258538
$287$	14.2337	0.840188
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−2.00000	−0.117444
$291$	−3.62772	−0.212661
$292$	−1.25544	−0.0734689
$293$	−26.7446	−1.56243	−0.781217	−	0.624260i	$-0.785401\pi$
$293$	−26.7446	−1.56243	−0.781217	+	0.624260i	$0.785401\pi$
$294$	−1.37228	−0.0800331
$295$	−4.00000	−0.232889
$296$	8.37228	0.486629
$297$	1.00000	0.0580259
$298$	13.1168	0.759838
$299$	−10.3723	−0.599845
$300$	−1.00000	−0.0577350
$301$	−9.48913	−0.546944
$302$	−9.62772	−0.554013
$303$	−11.4891	−0.660033
$304$	2.37228	0.136060
$305$	−13.1168	−0.751068
$306$	1.00000	0.0571662
$307$	−21.4891	−1.22645	−0.613225	−	0.789909i	$-0.710128\pi$
$307$	−21.4891	−1.22645	−0.613225	+	0.789909i	$0.710128\pi$
$308$	2.37228	0.135173
$309$	7.11684	0.404863
$310$	1.62772	0.0924482
$311$	−30.2337	−1.71440	−0.857198	−	0.514988i	$-0.827796\pi$
$311$	−30.2337	−1.71440	−0.857198	+	0.514988i	$0.827796\pi$
$312$	4.37228	0.247532
$313$	−9.11684	−0.515314	−0.257657	−	0.966236i	$-0.582951\pi$
$313$	−9.11684	−0.515314	−0.257657	+	0.966236i	$0.582951\pi$
$314$	−10.7446	−0.606351
$315$	2.37228	0.133663
$316$	4.74456	0.266903
$317$	2.00000	0.112331	0.0561656	−	0.998421i	$-0.482113\pi$
$317$	2.00000	0.112331	0.0561656	+	0.998421i	$0.482113\pi$
$318$	11.4891	0.644278
$319$	2.00000	0.111979
$320$	−1.00000	−0.0559017
$321$	3.25544	0.181701
$322$	−5.62772	−0.313621
$323$	−2.37228	−0.131997
$324$	1.00000	0.0555556
$325$	4.37228	0.242531
$326$	4.00000	0.221540
$327$	1.11684	0.0617616
$328$	6.00000	0.331295
$329$	20.7446	1.14368
$330$	1.00000	0.0550482
$331$	21.4891	1.18115	0.590575	−	0.806983i	$-0.298901\pi$
$331$	21.4891	1.18115	0.590575	+	0.806983i	$0.298901\pi$
$332$	−1.62772	−0.0893327
$333$	−8.37228	−0.458798
$334$	21.4891	1.17583
$335$	−6.37228	−0.348155
$336$	2.37228	0.129419
$337$	0.233688	0.0127298	0.00636490	−	0.999980i	$-0.497974\pi$
$337$	0.233688	0.0127298	0.00636490	+	0.999980i	$0.497974\pi$
$338$	−6.11684	−0.332712
$339$	2.00000	0.108625
$340$	1.00000	0.0542326
$341$	−1.62772	−0.0881459
$342$	−2.37228	−0.128278
$343$	19.8614	1.07242
$344$	−4.00000	−0.215666
$345$	−2.37228	−0.127719
$346$	−5.86141	−0.315111
$347$	−31.7228	−1.70297	−0.851485	−	0.524379i	$-0.824297\pi$
$347$	−31.7228	−1.70297	−0.851485	+	0.524379i	$0.824297\pi$
$348$	2.00000	0.107211
$349$	16.9783	0.908825	0.454412	−	0.890791i	$-0.349849\pi$
$349$	16.9783	0.908825	0.454412	+	0.890791i	$0.349849\pi$
$350$	2.37228	0.126804
$351$	−4.37228	−0.233375
$352$	1.00000	0.0533002
$353$	22.6060	1.20319	0.601597	−	0.798800i	$-0.294531\pi$
$353$	22.6060	1.20319	0.601597	+	0.798800i	$0.294531\pi$
$354$	4.00000	0.212598
$355$	−4.74456	−0.251815
$356$	10.0000	0.529999
$357$	−2.37228	−0.125554
$358$	−3.11684	−0.164730
$359$	−14.2337	−0.751225	−0.375613	−	0.926777i	$-0.622568\pi$
$359$	−14.2337	−0.751225	−0.375613	+	0.926777i	$0.622568\pi$
$360$	1.00000	0.0527046
$361$	−13.3723	−0.703804
$362$	−1.25544	−0.0659843
$363$	−1.00000	−0.0524864
$364$	−10.3723	−0.543655
$365$	1.25544	0.0657126
$366$	13.1168	0.685628
$367$	25.4891	1.33052	0.665261	−	0.746611i	$-0.268320\pi$
$367$	25.4891	1.33052	0.665261	+	0.746611i	$0.268320\pi$
$368$	−2.37228	−0.123664
$369$	−6.00000	−0.312348
$370$	−8.37228	−0.435254
$371$	−27.2554	−1.41503
$372$	−1.62772	−0.0843933
$373$	3.48913	0.180660	0.0903300	−	0.995912i	$-0.471208\pi$
$373$	3.48913	0.180660	0.0903300	+	0.995912i	$0.471208\pi$
$374$	−1.00000	−0.0517088
$375$	1.00000	0.0516398
$376$	8.74456	0.450966
$377$	−8.74456	−0.450368
$378$	−2.37228	−0.122017
$379$	−0.883156	−0.0453647	−0.0226823	−	0.999743i	$-0.507221\pi$
$379$	−0.883156	−0.0453647	−0.0226823	+	0.999743i	$0.507221\pi$
$380$	−2.37228	−0.121695
$381$	8.00000	0.409852
$382$	0	0
$383$	2.23369	0.114136	0.0570681	−	0.998370i	$-0.481825\pi$
$383$	2.23369	0.114136	0.0570681	+	0.998370i	$0.481825\pi$
$384$	1.00000	0.0510310
$385$	−2.37228	−0.120903
$386$	−22.7446	−1.15767
$387$	4.00000	0.203331
$388$	3.62772	0.184170
$389$	28.2337	1.43150	0.715752	−	0.698354i	$-0.246084\pi$
$389$	28.2337	1.43150	0.715752	+	0.698354i	$0.246084\pi$
$390$	−4.37228	−0.221399
$391$	2.37228	0.119971
$392$	1.37228	0.0693107
$393$	−1.62772	−0.0821075
$394$	14.6060	0.735838
$395$	−4.74456	−0.238725
$396$	−1.00000	−0.0502519
$397$	11.4891	0.576623	0.288311	−	0.957537i	$-0.406906\pi$
$397$	11.4891	0.576623	0.288311	+	0.957537i	$0.406906\pi$
$398$	14.3723	0.720417
$399$	5.62772	0.281738
$400$	1.00000	0.0500000
$401$	9.86141	0.492455	0.246228	−	0.969212i	$-0.420809\pi$
$401$	9.86141	0.492455	0.246228	+	0.969212i	$0.420809\pi$
$402$	6.37228	0.317821
$403$	7.11684	0.354515
$404$	11.4891	0.571605
$405$	−1.00000	−0.0496904
$406$	−4.74456	−0.235469
$407$	8.37228	0.414999
$408$	−1.00000	−0.0495074
$409$	−16.9783	−0.839520	−0.419760	−	0.907635i	$-0.637886\pi$
$409$	−16.9783	−0.839520	−0.419760	+	0.907635i	$0.637886\pi$
$410$	−6.00000	−0.296319
$411$	17.1168	0.844312
$412$	−7.11684	−0.350622
$413$	−9.48913	−0.466929
$414$	2.37228	0.116591
$415$	1.62772	0.0799016
$416$	−4.37228	−0.214369
$417$	0.744563	0.0364614
$418$	2.37228	0.116032
$419$	−13.4891	−0.658987	−0.329493	−	0.944158i	$-0.606878\pi$
$419$	−13.4891	−0.658987	−0.329493	+	0.944158i	$0.606878\pi$
$420$	−2.37228	−0.115755
$421$	24.0951	1.17432	0.587162	−	0.809470i	$-0.300245\pi$
$421$	24.0951	1.17432	0.587162	+	0.809470i	$0.300245\pi$
$422$	8.74456	0.425679
$423$	−8.74456	−0.425175
$424$	−11.4891	−0.557961
$425$	−1.00000	−0.0485071
$426$	4.74456	0.229875
$427$	−31.1168	−1.50585
$428$	−3.25544	−0.157358
$429$	4.37228	0.211096
$430$	4.00000	0.192897
$431$	−8.00000	−0.385346	−0.192673	−	0.981263i	$-0.561716\pi$
$431$	−8.00000	−0.385346	−0.192673	+	0.981263i	$0.561716\pi$
$432$	−1.00000	−0.0481125
$433$	10.0000	0.480569	0.240285	−	0.970702i	$-0.422759\pi$
$433$	10.0000	0.480569	0.240285	+	0.970702i	$0.422759\pi$
$434$	3.86141	0.185353
$435$	−2.00000	−0.0958927
$436$	−1.11684	−0.0534871
$437$	−5.62772	−0.269210
$438$	−1.25544	−0.0599871
$439$	28.7446	1.37190	0.685952	−	0.727647i	$-0.259386\pi$
$439$	28.7446	1.37190	0.685952	+	0.727647i	$0.259386\pi$
$440$	−1.00000	−0.0476731
$441$	−1.37228	−0.0653467
$442$	4.37228	0.207968
$443$	−22.2337	−1.05635	−0.528177	−	0.849134i	$-0.677124\pi$
$443$	−22.2337	−1.05635	−0.528177	+	0.849134i	$0.677124\pi$
$444$	8.37228	0.397331
$445$	−10.0000	−0.474045
$446$	19.8614	0.940465
$447$	13.1168	0.620405
$448$	−2.37228	−0.112080
$449$	−40.8397	−1.92734	−0.963671	−	0.267091i	$-0.913938\pi$
$449$	−40.8397	−1.92734	−0.963671	+	0.267091i	$0.913938\pi$
$450$	−1.00000	−0.0471405
$451$	6.00000	0.282529
$452$	−2.00000	−0.0940721
$453$	−9.62772	−0.452350
$454$	12.7446	0.598132
$455$	10.3723	0.486260
$456$	2.37228	0.111092
$457$	−4.37228	−0.204527	−0.102263	−	0.994757i	$-0.532608\pi$
$457$	−4.37228	−0.204527	−0.102263	+	0.994757i	$0.532608\pi$
$458$	−5.11684	−0.239094
$459$	1.00000	0.0466760
$460$	2.37228	0.110608
$461$	11.4891	0.535102	0.267551	−	0.963544i	$-0.413786\pi$
$461$	11.4891	0.535102	0.267551	+	0.963544i	$0.413786\pi$
$462$	2.37228	0.110369
$463$	−26.3723	−1.22562	−0.612812	−	0.790229i	$-0.709962\pi$
$463$	−26.3723	−1.22562	−0.612812	+	0.790229i	$0.709962\pi$
$464$	−2.00000	−0.0928477
$465$	1.62772	0.0754836
$466$	0.510875	0.0236658
$467$	−10.9783	−0.508013	−0.254006	−	0.967203i	$-0.581748\pi$
$467$	−10.9783	−0.508013	−0.254006	+	0.967203i	$0.581748\pi$
$468$	4.37228	0.202109
$469$	−15.1168	−0.698031
$470$	−8.74456	−0.403357
$471$	−10.7446	−0.495083
$472$	−4.00000	−0.184115
$473$	−4.00000	−0.183920
$474$	4.74456	0.217925
$475$	2.37228	0.108848
$476$	2.37228	0.108733
$477$	11.4891	0.526051
$478$	−12.7446	−0.582923
$479$	−24.6060	−1.12428	−0.562138	−	0.827044i	$-0.690021\pi$
$479$	−24.6060	−1.12428	−0.562138	+	0.827044i	$0.690021\pi$
$480$	−1.00000	−0.0456435
$481$	−36.6060	−1.66909
$482$	22.6060	1.02967
$483$	−5.62772	−0.256070
$484$	1.00000	0.0454545
$485$	−3.62772	−0.164726
$486$	1.00000	0.0453609
$487$	−6.51087	−0.295036	−0.147518	−	0.989059i	$-0.547128\pi$
$487$	−6.51087	−0.295036	−0.147518	+	0.989059i	$0.547128\pi$
$488$	−13.1168	−0.593772
$489$	4.00000	0.180886
$490$	−1.37228	−0.0619934
$491$	−15.2554	−0.688468	−0.344234	−	0.938884i	$-0.611861\pi$
$491$	−15.2554	−0.688468	−0.344234	+	0.938884i	$0.611861\pi$
$492$	6.00000	0.270501
$493$	2.00000	0.0900755
$494$	−10.3723	−0.466671
$495$	1.00000	0.0449467
$496$	1.62772	0.0730867
$497$	−11.2554	−0.504875
$498$	−1.62772	−0.0729398
$499$	33.4891	1.49918	0.749590	−	0.661903i	$-0.230251\pi$
$499$	33.4891	1.49918	0.749590	+	0.661903i	$0.230251\pi$
$500$	−1.00000	−0.0447214
$501$	21.4891	0.960063
$502$	22.3723	0.998524
$503$	−21.4891	−0.958153	−0.479076	−	0.877773i	$-0.659028\pi$
$503$	−21.4891	−0.958153	−0.479076	+	0.877773i	$0.659028\pi$
$504$	2.37228	0.105670
$505$	−11.4891	−0.511259
$506$	−2.37228	−0.105461
$507$	−6.11684	−0.271659
$508$	−8.00000	−0.354943
$509$	−35.4891	−1.57303	−0.786514	−	0.617573i	$-0.788116\pi$
$509$	−35.4891	−1.57303	−0.786514	+	0.617573i	$0.788116\pi$
$510$	1.00000	0.0442807
$511$	2.97825	0.131750
$512$	−1.00000	−0.0441942
$513$	−2.37228	−0.104739
$514$	0.510875	0.0225337
$515$	7.11684	0.313606
$516$	−4.00000	−0.176090
$517$	8.74456	0.384585
$518$	−19.8614	−0.872660
$519$	−5.86141	−0.257287
$520$	4.37228	0.191737
$521$	1.86141	0.0815497	0.0407749	−	0.999168i	$-0.487017\pi$
$521$	1.86141	0.0815497	0.0407749	+	0.999168i	$0.487017\pi$
$522$	2.00000	0.0875376
$523$	4.00000	0.174908	0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000	0.174908	0.0874539	+	0.996169i	$0.472127\pi$
$524$	1.62772	0.0711072
$525$	2.37228	0.103535
$526$	13.6277	0.594197
$527$	−1.62772	−0.0709045
$528$	1.00000	0.0435194
$529$	−17.3723	−0.755317
$530$	11.4891	0.499056
$531$	4.00000	0.173585
$532$	−5.62772	−0.243993
$533$	−26.2337	−1.13631
$534$	10.0000	0.432742
$535$	3.25544	0.140745
$536$	−6.37228	−0.275241
$537$	−3.11684	−0.134502
$538$	−7.62772	−0.328854
$539$	1.37228	0.0591083
$540$	1.00000	0.0430331
$541$	−11.4891	−0.493956	−0.246978	−	0.969021i	$-0.579438\pi$
$541$	−11.4891	−0.493956	−0.246978	+	0.969021i	$0.579438\pi$
$542$	20.0000	0.859074
$543$	−1.25544	−0.0538760
$544$	1.00000	0.0428746
$545$	1.11684	0.0478403
$546$	−10.3723	−0.443893
$547$	−25.6277	−1.09576	−0.547881	−	0.836556i	$-0.684565\pi$
$547$	−25.6277	−1.09576	−0.547881	+	0.836556i	$0.684565\pi$
$548$	−17.1168	−0.731195
$549$	13.1168	0.559813
$550$	1.00000	0.0426401
$551$	−4.74456	−0.202125
$552$	−2.37228	−0.100971
$553$	−11.2554	−0.478630
$554$	−4.23369	−0.179872
$555$	−8.37228	−0.355384
$556$	−0.744563	−0.0315765
$557$	−44.2337	−1.87424	−0.937121	−	0.349005i	$-0.886520\pi$
$557$	−44.2337	−1.87424	−0.937121	+	0.349005i	$0.886520\pi$
$558$	−1.62772	−0.0689068
$559$	17.4891	0.739711
$560$	2.37228	0.100247
$561$	−1.00000	−0.0422200
$562$	−14.0000	−0.590554
$563$	−4.88316	−0.205800	−0.102900	−	0.994692i	$-0.532812\pi$
$563$	−4.88316	−0.205800	−0.102900	+	0.994692i	$0.532812\pi$
$564$	8.74456	0.368213
$565$	2.00000	0.0841406
$566$	28.0000	1.17693
$567$	−2.37228	−0.0996265
$568$	−4.74456	−0.199077
$569$	−32.8397	−1.37671	−0.688355	−	0.725374i	$-0.741667\pi$
$569$	−32.8397	−1.37671	−0.688355	+	0.725374i	$0.741667\pi$
$570$	−2.37228	−0.0993639
$571$	15.2554	0.638420	0.319210	−	0.947684i	$-0.396582\pi$
$571$	15.2554	0.638420	0.319210	+	0.947684i	$0.396582\pi$
$572$	−4.37228	−0.182814
$573$	0	0
$574$	−14.2337	−0.594103
$575$	−2.37228	−0.0989310
$576$	1.00000	0.0416667
$577$	27.4891	1.14439	0.572194	−	0.820119i	$-0.306093\pi$
$577$	27.4891	1.14439	0.572194	+	0.820119i	$0.306093\pi$
$578$	−1.00000	−0.0415945
$579$	−22.7446	−0.945232
$580$	2.00000	0.0830455
$581$	3.86141	0.160198
$582$	3.62772	0.150374
$583$	−11.4891	−0.475831
$584$	1.25544	0.0519504
$585$	−4.37228	−0.180772
$586$	26.7446	1.10481
$587$	12.7446	0.526024	0.263012	−	0.964793i	$-0.415284\pi$
$587$	12.7446	0.526024	0.263012	+	0.964793i	$0.415284\pi$
$588$	1.37228	0.0565919
$589$	3.86141	0.159106
$590$	4.00000	0.164677
$591$	14.6060	0.600809
$592$	−8.37228	−0.344099
$593$	39.4891	1.62162	0.810812	−	0.585307i	$-0.199026\pi$
$593$	39.4891	1.62162	0.810812	+	0.585307i	$0.199026\pi$
$594$	−1.00000	−0.0410305
$595$	−2.37228	−0.0972541
$596$	−13.1168	−0.537287
$597$	14.3723	0.588218
$598$	10.3723	0.424154
$599$	38.8397	1.58695	0.793473	−	0.608606i	$-0.208271\pi$
$599$	38.8397	1.58695	0.793473	+	0.608606i	$0.208271\pi$
$600$	1.00000	0.0408248
$601$	4.37228	0.178349	0.0891745	−	0.996016i	$-0.471577\pi$
$601$	4.37228	0.178349	0.0891745	+	0.996016i	$0.471577\pi$
$602$	9.48913	0.386748
$603$	6.37228	0.259499
$604$	9.62772	0.391746
$605$	−1.00000	−0.0406558
$606$	11.4891	0.466714
$607$	16.6060	0.674016	0.337008	−	0.941502i	$-0.390585\pi$
$607$	16.6060	0.674016	0.337008	+	0.941502i	$0.390585\pi$
$608$	−2.37228	−0.0962087
$609$	−4.74456	−0.192259
$610$	13.1168	0.531085
$611$	−38.2337	−1.54677
$612$	−1.00000	−0.0404226
$613$	−48.9783	−1.97821	−0.989106	−	0.147202i	$-0.952973\pi$
$613$	−48.9783	−1.97821	−0.989106	+	0.147202i	$0.952973\pi$
$614$	21.4891	0.867231
$615$	−6.00000	−0.241943
$616$	−2.37228	−0.0955819
$617$	−10.0000	−0.402585	−0.201292	−	0.979531i	$-0.564514\pi$
$617$	−10.0000	−0.402585	−0.201292	+	0.979531i	$0.564514\pi$
$618$	−7.11684	−0.286281
$619$	−7.11684	−0.286050	−0.143025	−	0.989719i	$-0.545683\pi$
$619$	−7.11684	−0.286050	−0.143025	+	0.989719i	$0.545683\pi$
$620$	−1.62772	−0.0653708
$621$	2.37228	0.0951964
$622$	30.2337	1.21226
$623$	−23.7228	−0.950434
$624$	−4.37228	−0.175031
$625$	1.00000	0.0400000
$626$	9.11684	0.364382
$627$	2.37228	0.0947398
$628$	10.7446	0.428755
$629$	8.37228	0.333825
$630$	−2.37228	−0.0945140
$631$	14.2337	0.566634	0.283317	−	0.959026i	$-0.408565\pi$
$631$	14.2337	0.566634	0.283317	+	0.959026i	$0.408565\pi$
$632$	−4.74456	−0.188729
$633$	8.74456	0.347565
$634$	−2.00000	−0.0794301
$635$	8.00000	0.317470
$636$	−11.4891	−0.455573
$637$	−6.00000	−0.237729
$638$	−2.00000	−0.0791808
$639$	4.74456	0.187692
$640$	1.00000	0.0395285
$641$	−44.9783	−1.77653	−0.888267	−	0.459327i	$-0.848090\pi$
$641$	−44.9783	−1.77653	−0.888267	+	0.459327i	$0.848090\pi$
$642$	−3.25544	−0.128482
$643$	−28.0000	−1.10421	−0.552106	−	0.833774i	$-0.686176\pi$
$643$	−28.0000	−1.10421	−0.552106	+	0.833774i	$0.686176\pi$
$644$	5.62772	0.221763
$645$	4.00000	0.157500
$646$	2.37228	0.0933362
$647$	−18.2337	−0.716840	−0.358420	−	0.933560i	$-0.616684\pi$
$647$	−18.2337	−0.716840	−0.358420	+	0.933560i	$0.616684\pi$
$648$	−1.00000	−0.0392837
$649$	−4.00000	−0.157014
$650$	−4.37228	−0.171495
$651$	3.86141	0.151340
$652$	−4.00000	−0.156652
$653$	32.2337	1.26140	0.630701	−	0.776026i	$-0.282768\pi$
$653$	32.2337	1.26140	0.630701	+	0.776026i	$0.282768\pi$
$654$	−1.11684	−0.0436721
$655$	−1.62772	−0.0636002
$656$	−6.00000	−0.234261
$657$	−1.25544	−0.0489793
$658$	−20.7446	−0.808707
$659$	26.2337	1.02192	0.510960	−	0.859605i	$-0.329290\pi$
$659$	26.2337	1.02192	0.510960	+	0.859605i	$0.329290\pi$
$660$	−1.00000	−0.0389249
$661$	−34.6060	−1.34602	−0.673008	−	0.739635i	$-0.734998\pi$
$661$	−34.6060	−1.34602	−0.673008	+	0.739635i	$0.734998\pi$
$662$	−21.4891	−0.835199
$663$	4.37228	0.169805
$664$	1.62772	0.0631677
$665$	5.62772	0.218234
$666$	8.37228	0.324419
$667$	4.74456	0.183710
$668$	−21.4891	−0.831439
$669$	19.8614	0.767886
$670$	6.37228	0.246183
$671$	−13.1168	−0.506370
$672$	−2.37228	−0.0915127
$673$	6.74456	0.259984	0.129992	−	0.991515i	$-0.458505\pi$
$673$	6.74456	0.259984	0.129992	+	0.991515i	$0.458505\pi$
$674$	−0.233688	−0.00900132
$675$	−1.00000	−0.0384900
$676$	6.11684	0.235263
$677$	11.4891	0.441563	0.220781	−	0.975323i	$-0.429139\pi$
$677$	11.4891	0.441563	0.220781	+	0.975323i	$0.429139\pi$
$678$	−2.00000	−0.0768095
$679$	−8.60597	−0.330267
$680$	−1.00000	−0.0383482
$681$	12.7446	0.488373
$682$	1.62772	0.0623286
$683$	−22.3723	−0.856052	−0.428026	−	0.903767i	$-0.640791\pi$
$683$	−22.3723	−0.856052	−0.428026	+	0.903767i	$0.640791\pi$
$684$	2.37228	0.0907064
$685$	17.1168	0.654001
$686$	−19.8614	−0.758312
$687$	−5.11684	−0.195220
$688$	4.00000	0.152499
$689$	50.2337	1.91375
$690$	2.37228	0.0903112
$691$	21.3505	0.812213	0.406106	−	0.913826i	$-0.366886\pi$
$691$	21.3505	0.812213	0.406106	+	0.913826i	$0.366886\pi$
$692$	5.86141	0.222817
$693$	2.37228	0.0901155
$694$	31.7228	1.20418
$695$	0.744563	0.0282429
$696$	−2.00000	−0.0758098
$697$	6.00000	0.227266
$698$	−16.9783	−0.642636
$699$	0.510875	0.0193231
$700$	−2.37228	−0.0896638
$701$	−7.48913	−0.282860	−0.141430	−	0.989948i	$-0.545170\pi$
$701$	−7.48913	−0.282860	−0.141430	+	0.989948i	$0.545170\pi$
$702$	4.37228	0.165021
$703$	−19.8614	−0.749087
$704$	−1.00000	−0.0376889
$705$	−8.74456	−0.329339
$706$	−22.6060	−0.850787
$707$	−27.2554	−1.02505
$708$	−4.00000	−0.150329
$709$	14.0000	0.525781	0.262891	−	0.964826i	$-0.415324\pi$
$709$	14.0000	0.525781	0.262891	+	0.964826i	$0.415324\pi$
$710$	4.74456	0.178060
$711$	4.74456	0.177935
$712$	−10.0000	−0.374766
$713$	−3.86141	−0.144611
$714$	2.37228	0.0887804
$715$	4.37228	0.163514
$716$	3.11684	0.116482
$717$	−12.7446	−0.475954
$718$	14.2337	0.531197
$719$	4.74456	0.176942	0.0884712	−	0.996079i	$-0.471802\pi$
$719$	4.74456	0.176942	0.0884712	+	0.996079i	$0.471802\pi$
$720$	−1.00000	−0.0372678
$721$	16.8832	0.628762
$722$	13.3723	0.497665
$723$	22.6060	0.840725
$724$	1.25544	0.0466580
$725$	−2.00000	−0.0742781
$726$	1.00000	0.0371135
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	10.3723	0.384422
$729$	1.00000	0.0370370
$730$	−1.25544	−0.0464658
$731$	−4.00000	−0.147945
$732$	−13.1168	−0.484813
$733$	−46.3288	−1.71119	−0.855596	−	0.517644i	$-0.826809\pi$
$733$	−46.3288	−1.71119	−0.855596	+	0.517644i	$0.826809\pi$
$734$	−25.4891	−0.940821
$735$	−1.37228	−0.0506174
$736$	2.37228	0.0874434
$737$	−6.37228	−0.234726
$738$	6.00000	0.220863
$739$	−29.3505	−1.07968	−0.539838	−	0.841769i	$-0.681515\pi$
$739$	−29.3505	−1.07968	−0.539838	+	0.841769i	$0.681515\pi$
$740$	8.37228	0.307771
$741$	−10.3723	−0.381035
$742$	27.2554	1.00058
$743$	−18.5109	−0.679098	−0.339549	−	0.940588i	$-0.610274\pi$
$743$	−18.5109	−0.679098	−0.339549	+	0.940588i	$0.610274\pi$
$744$	1.62772	0.0596751
$745$	13.1168	0.480564
$746$	−3.48913	−0.127746
$747$	−1.62772	−0.0595551
$748$	1.00000	0.0365636
$749$	7.72281	0.282185
$750$	−1.00000	−0.0365148
$751$	−13.4891	−0.492225	−0.246113	−	0.969241i	$-0.579153\pi$
$751$	−13.4891	−0.492225	−0.246113	+	0.969241i	$0.579153\pi$
$752$	−8.74456	−0.318881
$753$	22.3723	0.815291
$754$	8.74456	0.318458
$755$	−9.62772	−0.350389
$756$	2.37228	0.0862790
$757$	−12.9783	−0.471703	−0.235851	−	0.971789i	$-0.575788\pi$
$757$	−12.9783	−0.471703	−0.235851	+	0.971789i	$0.575788\pi$
$758$	0.883156	0.0320777
$759$	−2.37228	−0.0861084
$760$	2.37228	0.0860517
$761$	21.1168	0.765485	0.382742	−	0.923855i	$-0.374980\pi$
$761$	21.1168	0.765485	0.382742	+	0.923855i	$0.374980\pi$
$762$	−8.00000	−0.289809
$763$	2.64947	0.0959172
$764$	0	0
$765$	1.00000	0.0361551
$766$	−2.23369	−0.0807064
$767$	17.4891	0.631496
$768$	−1.00000	−0.0360844
$769$	−55.2119	−1.99099	−0.995497	−	0.0947961i	$-0.969780\pi$
$769$	−55.2119	−1.99099	−0.995497	+	0.0947961i	$0.969780\pi$
$770$	2.37228	0.0854911
$771$	0.510875	0.0183987
$772$	22.7446	0.818595
$773$	−5.39403	−0.194010	−0.0970049	−	0.995284i	$-0.530926\pi$
$773$	−5.39403	−0.194010	−0.0970049	+	0.995284i	$0.530926\pi$
$774$	−4.00000	−0.143777
$775$	1.62772	0.0584694
$776$	−3.62772	−0.130228
$777$	−19.8614	−0.712524
$778$	−28.2337	−1.01223
$779$	−14.2337	−0.509975
$780$	4.37228	0.156553
$781$	−4.74456	−0.169774
$782$	−2.37228	−0.0848326
$783$	2.00000	0.0714742
$784$	−1.37228	−0.0490100
$785$	−10.7446	−0.383490
$786$	1.62772	0.0580588
$787$	3.11684	0.111103	0.0555517	−	0.998456i	$-0.482308\pi$
$787$	3.11684	0.111103	0.0555517	+	0.998456i	$0.482308\pi$
$788$	−14.6060	−0.520316
$789$	13.6277	0.485160
$790$	4.74456	0.168804
$791$	4.74456	0.168697
$792$	1.00000	0.0355335
$793$	57.3505	2.03658
$794$	−11.4891	−0.407734
$795$	11.4891	0.407477
$796$	−14.3723	−0.509412
$797$	28.3723	1.00500	0.502499	−	0.864578i	$-0.332414\pi$
$797$	28.3723	1.00500	0.502499	+	0.864578i	$0.332414\pi$
$798$	−5.62772	−0.199219
$799$	8.74456	0.309360
$800$	−1.00000	−0.0353553
$801$	10.0000	0.353333
$802$	−9.86141	−0.348218
$803$	1.25544	0.0443034
$804$	−6.37228	−0.224733
$805$	−5.62772	−0.198351
$806$	−7.11684	−0.250680
$807$	−7.62772	−0.268508
$808$	−11.4891	−0.404186
$809$	18.0000	0.632846	0.316423	−	0.948618i	$-0.397518\pi$
$809$	18.0000	0.632846	0.316423	+	0.948618i	$0.397518\pi$
$810$	1.00000	0.0351364
$811$	−40.7446	−1.43074	−0.715368	−	0.698748i	$-0.753741\pi$
$811$	−40.7446	−1.43074	−0.715368	+	0.698748i	$0.753741\pi$
$812$	4.74456	0.166502
$813$	20.0000	0.701431
$814$	−8.37228	−0.293448
$815$	4.00000	0.140114
$816$	1.00000	0.0350070
$817$	9.48913	0.331982
$818$	16.9783	0.593631
$819$	−10.3723	−0.362437
$820$	6.00000	0.209529
$821$	0.978251	0.0341412	0.0170706	−	0.999854i	$-0.494566\pi$
$821$	0.978251	0.0341412	0.0170706	+	0.999854i	$0.494566\pi$
$822$	−17.1168	−0.597018
$823$	4.74456	0.165385	0.0826925	−	0.996575i	$-0.473648\pi$
$823$	4.74456	0.165385	0.0826925	+	0.996575i	$0.473648\pi$
$824$	7.11684	0.247927
$825$	1.00000	0.0348155
$826$	9.48913	0.330169
$827$	−1.76631	−0.0614207	−0.0307103	−	0.999528i	$-0.509777\pi$
$827$	−1.76631	−0.0614207	−0.0307103	+	0.999528i	$0.509777\pi$
$828$	−2.37228	−0.0824425
$829$	−5.86141	−0.203575	−0.101788	−	0.994806i	$-0.532456\pi$
$829$	−5.86141	−0.203575	−0.101788	+	0.994806i	$0.532456\pi$
$830$	−1.62772	−0.0564989
$831$	−4.23369	−0.146865
$832$	4.37228	0.151582
$833$	1.37228	0.0475467
$834$	−0.744563	−0.0257821
$835$	21.4891	0.743662
$836$	−2.37228	−0.0820471
$837$	−1.62772	−0.0562622
$838$	13.4891	0.465974
$839$	−8.00000	−0.276191	−0.138095	−	0.990419i	$-0.544098\pi$
$839$	−8.00000	−0.276191	−0.138095	+	0.990419i	$0.544098\pi$
$840$	2.37228	0.0818515
$841$	−25.0000	−0.862069
$842$	−24.0951	−0.830372
$843$	−14.0000	−0.482186
$844$	−8.74456	−0.301000
$845$	−6.11684	−0.210426
$846$	8.74456	0.300644
$847$	−2.37228	−0.0815126
$848$	11.4891	0.394538
$849$	28.0000	0.960958
$850$	1.00000	0.0342997
$851$	19.8614	0.680840
$852$	−4.74456	−0.162546
$853$	−40.2337	−1.37758	−0.688788	−	0.724963i	$-0.741857\pi$
$853$	−40.2337	−1.37758	−0.688788	+	0.724963i	$0.741857\pi$
$854$	31.1168	1.06480
$855$	−2.37228	−0.0811303
$856$	3.25544	0.111269
$857$	32.3723	1.10582	0.552908	−	0.833242i	$-0.313518\pi$
$857$	32.3723	1.10582	0.552908	+	0.833242i	$0.313518\pi$
$858$	−4.37228	−0.149267
$859$	2.51087	0.0856699	0.0428350	−	0.999082i	$-0.486361\pi$
$859$	2.51087	0.0856699	0.0428350	+	0.999082i	$0.486361\pi$
$860$	−4.00000	−0.136399
$861$	−14.2337	−0.485083
$862$	8.00000	0.272481
$863$	5.48913	0.186852	0.0934260	−	0.995626i	$-0.470218\pi$
$863$	5.48913	0.186852	0.0934260	+	0.995626i	$0.470218\pi$
$864$	1.00000	0.0340207
$865$	−5.86141	−0.199294
$866$	−10.0000	−0.339814
$867$	−1.00000	−0.0339618
$868$	−3.86141	−0.131065
$869$	−4.74456	−0.160948
$870$	2.00000	0.0678064
$871$	27.8614	0.944048
$872$	1.11684	0.0378211
$873$	3.62772	0.122780
$874$	5.62772	0.190360
$875$	2.37228	0.0801977
$876$	1.25544	0.0424173
$877$	−11.7663	−0.397320	−0.198660	−	0.980068i	$-0.563659\pi$
$877$	−11.7663	−0.397320	−0.198660	+	0.980068i	$0.563659\pi$
$878$	−28.7446	−0.970082
$879$	26.7446	0.902072
$880$	1.00000	0.0337100
$881$	−22.4674	−0.756945	−0.378473	−	0.925613i	$-0.623551\pi$
$881$	−22.4674	−0.756945	−0.378473	+	0.925613i	$0.623551\pi$
$882$	1.37228	0.0462071
$883$	52.0000	1.74994	0.874970	−	0.484178i	$-0.160881\pi$
$883$	52.0000	1.74994	0.874970	+	0.484178i	$0.160881\pi$
$884$	−4.37228	−0.147056
$885$	4.00000	0.134459
$886$	22.2337	0.746955
$887$	−5.48913	−0.184307	−0.0921534	−	0.995745i	$-0.529375\pi$
$887$	−5.48913	−0.184307	−0.0921534	+	0.995745i	$0.529375\pi$
$888$	−8.37228	−0.280955
$889$	18.9783	0.636510
$890$	10.0000	0.335201
$891$	−1.00000	−0.0335013
$892$	−19.8614	−0.665009
$893$	−20.7446	−0.694190
$894$	−13.1168	−0.438693
$895$	−3.11684	−0.104185
$896$	2.37228	0.0792524
$897$	10.3723	0.346320
$898$	40.8397	1.36284
$899$	−3.25544	−0.108575
$900$	1.00000	0.0333333
$901$	−11.4891	−0.382758
$902$	−6.00000	−0.199778
$903$	9.48913	0.315778
$904$	2.00000	0.0665190
$905$	−1.25544	−0.0417321
$906$	9.62772	0.319860
$907$	2.51087	0.0833722	0.0416861	−	0.999131i	$-0.486727\pi$
$907$	2.51087	0.0833722	0.0416861	+	0.999131i	$0.486727\pi$
$908$	−12.7446	−0.422943
$909$	11.4891	0.381070
$910$	−10.3723	−0.343838
$911$	0	0		−	1.00000i	$-0.5\pi$
$911$	0	0			1.00000i	$0.5\pi$
$912$	−2.37228	−0.0785541
$913$	1.62772	0.0538696
$914$	4.37228	0.144622
$915$	13.1168	0.433629
$916$	5.11684	0.169065
$917$	−3.86141	−0.127515
$918$	−1.00000	−0.0330049
$919$	11.1168	0.366711	0.183355	−	0.983047i	$-0.441304\pi$
$919$	11.1168	0.366711	0.183355	+	0.983047i	$0.441304\pi$
$920$	−2.37228	−0.0782118
$921$	21.4891	0.708091
$922$	−11.4891	−0.378374
$923$	20.7446	0.682816
$924$	−2.37228	−0.0780423
$925$	−8.37228	−0.275279
$926$	26.3723	0.866647
$927$	−7.11684	−0.233748
$928$	2.00000	0.0656532
$929$	38.6060	1.26662	0.633310	−	0.773898i	$-0.281696\pi$
$929$	38.6060	1.26662	0.633310	+	0.773898i	$0.281696\pi$
$930$	−1.62772	−0.0533750
$931$	−3.25544	−0.106693
$932$	−0.510875	−0.0167343
$933$	30.2337	0.989807
$934$	10.9783	0.359219
$935$	−1.00000	−0.0327035
$936$	−4.37228	−0.142912
$937$	25.5842	0.835800	0.417900	−	0.908493i	$-0.362766\pi$
$937$	25.5842	0.835800	0.417900	+	0.908493i	$0.362766\pi$
$938$	15.1168	0.493582
$939$	9.11684	0.297517
$940$	8.74456	0.285216
$941$	13.7228	0.447351	0.223675	−	0.974664i	$-0.428194\pi$
$941$	13.7228	0.447351	0.223675	+	0.974664i	$0.428194\pi$
$942$	10.7446	0.350077
$943$	14.2337	0.463513
$944$	4.00000	0.130189
$945$	−2.37228	−0.0771703
$946$	4.00000	0.130051
$947$	−28.0000	−0.909878	−0.454939	−	0.890523i	$-0.650339\pi$
$947$	−28.0000	−0.909878	−0.454939	+	0.890523i	$0.650339\pi$
$948$	−4.74456	−0.154096
$949$	−5.48913	−0.178185
$950$	−2.37228	−0.0769670
$951$	−2.00000	−0.0648544
$952$	−2.37228	−0.0768861
$953$	4.23369	0.137143	0.0685713	−	0.997646i	$-0.478156\pi$
$953$	4.23369	0.137143	0.0685713	+	0.997646i	$0.478156\pi$
$954$	−11.4891	−0.371974
$955$	0	0
$956$	12.7446	0.412189
$957$	−2.00000	−0.0646508
$958$	24.6060	0.794983
$959$	40.6060	1.31124
$960$	1.00000	0.0322749
$961$	−28.3505	−0.914533
$962$	36.6060	1.18022
$963$	−3.25544	−0.104905
$964$	−22.6060	−0.728089
$965$	−22.7446	−0.732173
$966$	5.62772	0.181069
$967$	54.2337	1.74404	0.872019	−	0.489472i	$-0.162811\pi$
$967$	54.2337	1.74404	0.872019	+	0.489472i	$0.162811\pi$
$968$	−1.00000	−0.0321412
$969$	2.37228	0.0762087
$970$	3.62772	0.116479
$971$	−36.6060	−1.17474	−0.587371	−	0.809318i	$-0.699837\pi$
$971$	−36.6060	−1.17474	−0.587371	+	0.809318i	$0.699837\pi$
$972$	−1.00000	−0.0320750
$973$	1.76631	0.0566254
$974$	6.51087	0.208622
$975$	−4.37228	−0.140025
$976$	13.1168	0.419860
$977$	−5.86141	−0.187523	−0.0937615	−	0.995595i	$-0.529889\pi$
$977$	−5.86141	−0.187523	−0.0937615	+	0.995595i	$0.529889\pi$
$978$	−4.00000	−0.127906
$979$	−10.0000	−0.319601
$980$	1.37228	0.0438359
$981$	−1.11684	−0.0356581
$982$	15.2554	0.486821
$983$	30.5109	0.973146	0.486573	−	0.873640i	$-0.338247\pi$
$983$	30.5109	0.973146	0.486573	+	0.873640i	$0.338247\pi$
$984$	−6.00000	−0.191273
$985$	14.6060	0.465385
$986$	−2.00000	−0.0636930
$987$	−20.7446	−0.660307
$988$	10.3723	0.329986
$989$	−9.48913	−0.301737
$990$	−1.00000	−0.0317821
$991$	−8.13859	−0.258531	−0.129265	−	0.991610i	$-0.541262\pi$
$991$	−8.13859	−0.258531	−0.129265	+	0.991610i	$0.541262\pi$
$992$	−1.62772	−0.0516801
$993$	−21.4891	−0.681937
$994$	11.2554	0.357001
$995$	14.3723	0.455632
$996$	1.62772	0.0515762
$997$	8.97825	0.284344	0.142172	−	0.989842i	$-0.454591\pi$
$997$	8.97825	0.284344	0.142172	+	0.989842i	$0.454591\pi$
$998$	−33.4891	−1.06008
$999$	8.37228	0.264887

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.bp.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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -2.37228 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -2.37228 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} +4.37228 q^{13} +2.37228 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +2.37228 q^{19} -1.00000 q^{20} +2.37228 q^{21} +1.00000 q^{22} -2.37228 q^{23} +1.00000 q^{24} +1.00000 q^{25} -4.37228 q^{26} -1.00000 q^{27} -2.37228 q^{28} -2.00000 q^{29} -1.00000 q^{30} +1.62772 q^{31} -1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} +2.37228 q^{35} +1.00000 q^{36} -8.37228 q^{37} -2.37228 q^{38} -4.37228 q^{39} +1.00000 q^{40} -6.00000 q^{41} -2.37228 q^{42} +4.00000 q^{43} -1.00000 q^{44} -1.00000 q^{45} +2.37228 q^{46} -8.74456 q^{47} -1.00000 q^{48} -1.37228 q^{49} -1.00000 q^{50} +1.00000 q^{51} +4.37228 q^{52} +11.4891 q^{53} +1.00000 q^{54} +1.00000 q^{55} +2.37228 q^{56} -2.37228 q^{57} +2.00000 q^{58} +4.00000 q^{59} +1.00000 q^{60} +13.1168 q^{61} -1.62772 q^{62} -2.37228 q^{63} +1.00000 q^{64} -4.37228 q^{65} -1.00000 q^{66} +6.37228 q^{67} -1.00000 q^{68} +2.37228 q^{69} -2.37228 q^{70} +4.74456 q^{71} -1.00000 q^{72} -1.25544 q^{73} +8.37228 q^{74} -1.00000 q^{75} +2.37228 q^{76} +2.37228 q^{77} +4.37228 q^{78} +4.74456 q^{79} -1.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} -1.62772 q^{83} +2.37228 q^{84} +1.00000 q^{85} -4.00000 q^{86} +2.00000 q^{87} +1.00000 q^{88} +10.0000 q^{89} +1.00000 q^{90} -10.3723 q^{91} -2.37228 q^{92} -1.62772 q^{93} +8.74456 q^{94} -2.37228 q^{95} +1.00000 q^{96} +3.62772 q^{97} +1.37228 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} - 2 q^{12} + 3 q^{13} - q^{14} + 2 q^{15} + 2 q^{16} - 2 q^{17} - 2 q^{18} - q^{19} - 2 q^{20} - q^{21} + 2 q^{22} + q^{23} + 2 q^{24} + 2 q^{25} - 3 q^{26} - 2 q^{27} + q^{28} - 4 q^{29} - 2 q^{30} + 9 q^{31} - 2 q^{32} + 2 q^{33} + 2 q^{34} - q^{35} + 2 q^{36} - 11 q^{37} + q^{38} - 3 q^{39} + 2 q^{40} - 12 q^{41} + q^{42} + 8 q^{43} - 2 q^{44} - 2 q^{45} - q^{46} - 6 q^{47} - 2 q^{48} + 3 q^{49} - 2 q^{50} + 2 q^{51} + 3 q^{52} + 2 q^{54} + 2 q^{55} - q^{56} + q^{57} + 4 q^{58} + 8 q^{59} + 2 q^{60} + 9 q^{61} - 9 q^{62} + q^{63} + 2 q^{64} - 3 q^{65} - 2 q^{66} + 7 q^{67} - 2 q^{68} - q^{69} + q^{70} - 2 q^{71} - 2 q^{72} - 14 q^{73} + 11 q^{74} - 2 q^{75} - q^{76} - q^{77} + 3 q^{78} - 2 q^{79} - 2 q^{80} + 2 q^{81} + 12 q^{82} - 9 q^{83} - q^{84} + 2 q^{85} - 8 q^{86} + 4 q^{87} + 2 q^{88} + 20 q^{89} + 2 q^{90} - 15 q^{91} + q^{92} - 9 q^{93} + 6 q^{94} + q^{95} + 2 q^{96} + 13 q^{97} - 3 q^{98} - 2 q^{99}+O(q^{100}) \) 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 + 3 * q^13 - q^14 + 2 * q^15 + 2 * q^16 - 2 * q^17 - 2 * q^18 - q^19 - 2 * q^20 - q^21 + 2 * q^22 + q^23 + 2 * q^24 + 2 * q^25 - 3 * q^26 - 2 * q^27 + q^28 - 4 * q^29 - 2 * q^30 + 9 * q^31 - 2 * q^32 + 2 * q^33 + 2 * q^34 - q^35 + 2 * q^36 - 11 * q^37 + q^38 - 3 * q^39 + 2 * q^40 - 12 * q^41 + q^42 + 8 * q^43 - 2 * q^44 - 2 * q^45 - q^46 - 6 * q^47 - 2 * q^48 + 3 * q^49 - 2 * q^50 + 2 * q^51 + 3 * q^52 + 2 * q^54 + 2 * q^55 - q^56 + q^57 + 4 * q^58 + 8 * q^59 + 2 * q^60 + 9 * q^61 - 9 * q^62 + q^63 + 2 * q^64 - 3 * q^65 - 2 * q^66 + 7 * q^67 - 2 * q^68 - q^69 + q^70 - 2 * q^71 - 2 * q^72 - 14 * q^73 + 11 * q^74 - 2 * q^75 - q^76 - q^77 + 3 * q^78 - 2 * q^79 - 2 * q^80 + 2 * q^81 + 12 * q^82 - 9 * q^83 - q^84 + 2 * q^85 - 8 * q^86 + 4 * q^87 + 2 * q^88 + 20 * q^89 + 2 * q^90 - 15 * q^91 + q^92 - 9 * q^93 + 6 * q^94 + q^95 + 2 * q^96 + 13 * q^97 - 3 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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