LMFDB - Embedded newform 5610.2.a.bm.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{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.56155$ of defining polynomial
Character	$\chi$	$=$	5610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -5.12311 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -5.12311 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} -3.12311 q^{13} +5.12311 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -5.12311 q^{19} -1.00000 q^{20} +5.12311 q^{21} +1.00000 q^{22} +5.12311 q^{23} +1.00000 q^{24} +1.00000 q^{25} +3.12311 q^{26} -1.00000 q^{27} -5.12311 q^{28} +8.24621 q^{29} -1.00000 q^{30} +6.24621 q^{31} -1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} +5.12311 q^{35} +1.00000 q^{36} +2.00000 q^{37} +5.12311 q^{38} +3.12311 q^{39} +1.00000 q^{40} +10.0000 q^{41} -5.12311 q^{42} +1.12311 q^{43} -1.00000 q^{44} -1.00000 q^{45} -5.12311 q^{46} -4.00000 q^{47} -1.00000 q^{48} +19.2462 q^{49} -1.00000 q^{50} +1.00000 q^{51} -3.12311 q^{52} -0.876894 q^{53} +1.00000 q^{54} +1.00000 q^{55} +5.12311 q^{56} +5.12311 q^{57} -8.24621 q^{58} +1.12311 q^{59} +1.00000 q^{60} -2.00000 q^{61} -6.24621 q^{62} -5.12311 q^{63} +1.00000 q^{64} +3.12311 q^{65} -1.00000 q^{66} -4.00000 q^{67} -1.00000 q^{68} -5.12311 q^{69} -5.12311 q^{70} -13.1231 q^{71} -1.00000 q^{72} +7.12311 q^{73} -2.00000 q^{74} -1.00000 q^{75} -5.12311 q^{76} +5.12311 q^{77} -3.12311 q^{78} +2.87689 q^{79} -1.00000 q^{80} +1.00000 q^{81} -10.0000 q^{82} +4.00000 q^{83} +5.12311 q^{84} +1.00000 q^{85} -1.12311 q^{86} -8.24621 q^{87} +1.00000 q^{88} +4.24621 q^{89} +1.00000 q^{90} +16.0000 q^{91} +5.12311 q^{92} -6.24621 q^{93} +4.00000 q^{94} +5.12311 q^{95} +1.00000 q^{96} +8.24621 q^{97} -19.2462 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 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 - 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} - 2 q^{12} + 2 q^{13} + 2 q^{14} + 2 q^{15} + 2 q^{16} - 2 q^{17} - 2 q^{18} - 2 q^{19} - 2 q^{20} + 2 q^{21} + 2 q^{22} + 2 q^{23} + 2 q^{24} + 2 q^{25} - 2 q^{26} - 2 q^{27} - 2 q^{28} - 2 q^{30} - 4 q^{31} - 2 q^{32} + 2 q^{33} + 2 q^{34} + 2 q^{35} + 2 q^{36} + 4 q^{37} + 2 q^{38} - 2 q^{39} + 2 q^{40} + 20 q^{41} - 2 q^{42} - 6 q^{43} - 2 q^{44} - 2 q^{45} - 2 q^{46} - 8 q^{47} - 2 q^{48} + 22 q^{49} - 2 q^{50} + 2 q^{51} + 2 q^{52} - 10 q^{53} + 2 q^{54} + 2 q^{55} + 2 q^{56} + 2 q^{57} - 6 q^{59} + 2 q^{60} - 4 q^{61} + 4 q^{62} - 2 q^{63} + 2 q^{64} - 2 q^{65} - 2 q^{66} - 8 q^{67} - 2 q^{68} - 2 q^{69} - 2 q^{70} - 18 q^{71} - 2 q^{72} + 6 q^{73} - 4 q^{74} - 2 q^{75} - 2 q^{76} + 2 q^{77} + 2 q^{78} + 14 q^{79} - 2 q^{80} + 2 q^{81} - 20 q^{82} + 8 q^{83} + 2 q^{84} + 2 q^{85} + 6 q^{86} + 2 q^{88} - 8 q^{89} + 2 q^{90} + 32 q^{91} + 2 q^{92} + 4 q^{93} + 8 q^{94} + 2 q^{95} + 2 q^{96} - 22 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 - 2 * q^12 + 2 * q^13 + 2 * q^14 + 2 * q^15 + 2 * q^16 - 2 * q^17 - 2 * q^18 - 2 * q^19 - 2 * q^20 + 2 * q^21 + 2 * q^22 + 2 * q^23 + 2 * q^24 + 2 * q^25 - 2 * q^26 - 2 * q^27 - 2 * q^28 - 2 * q^30 - 4 * q^31 - 2 * q^32 + 2 * q^33 + 2 * q^34 + 2 * q^35 + 2 * q^36 + 4 * q^37 + 2 * q^38 - 2 * q^39 + 2 * q^40 + 20 * q^41 - 2 * q^42 - 6 * q^43 - 2 * q^44 - 2 * q^45 - 2 * q^46 - 8 * q^47 - 2 * q^48 + 22 * q^49 - 2 * q^50 + 2 * q^51 + 2 * q^52 - 10 * q^53 + 2 * q^54 + 2 * q^55 + 2 * q^56 + 2 * q^57 - 6 * q^59 + 2 * q^60 - 4 * q^61 + 4 * q^62 - 2 * q^63 + 2 * q^64 - 2 * q^65 - 2 * q^66 - 8 * q^67 - 2 * q^68 - 2 * q^69 - 2 * q^70 - 18 * q^71 - 2 * q^72 + 6 * q^73 - 4 * q^74 - 2 * q^75 - 2 * q^76 + 2 * q^77 + 2 * q^78 + 14 * q^79 - 2 * q^80 + 2 * q^81 - 20 * q^82 + 8 * q^83 + 2 * q^84 + 2 * q^85 + 6 * q^86 + 2 * q^88 - 8 * q^89 + 2 * q^90 + 32 * q^91 + 2 * q^92 + 4 * q^93 + 8 * q^94 + 2 * q^95 + 2 * q^96 - 22 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.00000	0.408248
$7$	−5.12311	−1.93635	−0.968176	−	0.250270i	$-0.919480\pi$
$7$	−5.12311	−1.93635	−0.968176	+	0.250270i	$0.919480\pi$
$8$	−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
$13$	−3.12311	−0.866194	−0.433097	−	0.901347i	$-0.642579\pi$
$13$	−3.12311	−0.866194	−0.433097	+	0.901347i	$0.642579\pi$
$14$	5.12311	1.36921
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	−5.12311	−1.17532	−0.587661	−	0.809108i	$-0.699951\pi$
$19$	−5.12311	−1.17532	−0.587661	+	0.809108i	$0.699951\pi$
$20$	−1.00000	−0.223607
$21$	5.12311	1.11795
$22$	1.00000	0.213201
$23$	5.12311	1.06824	0.534121	−	0.845408i	$-0.320643\pi$
$23$	5.12311	1.06824	0.534121	+	0.845408i	$0.320643\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	3.12311	0.612491
$27$	−1.00000	−0.192450
$28$	−5.12311	−0.968176
$29$	8.24621	1.53128	0.765641	−	0.643268i	$-0.222422\pi$
$29$	8.24621	1.53128	0.765641	+	0.643268i	$0.222422\pi$
$30$	−1.00000	−0.182574
$31$	6.24621	1.12185	0.560926	−	0.827866i	$-0.310445\pi$
$31$	6.24621	1.12185	0.560926	+	0.827866i	$0.310445\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	1.00000	0.171499
$35$	5.12311	0.865963
$36$	1.00000	0.166667
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	5.12311	0.831077
$39$	3.12311	0.500097
$40$	1.00000	0.158114
$41$	10.0000	1.56174	0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000	1.56174	0.780869	+	0.624695i	$0.214777\pi$
$42$	−5.12311	−0.790512
$43$	1.12311	0.171272	0.0856360	−	0.996326i	$-0.472708\pi$
$43$	1.12311	0.171272	0.0856360	+	0.996326i	$0.472708\pi$
$44$	−1.00000	−0.150756
$45$	−1.00000	−0.149071
$46$	−5.12311	−0.755361
$47$	−4.00000	−0.583460	−0.291730	−	0.956501i	$-0.594231\pi$
$47$	−4.00000	−0.583460	−0.291730	+	0.956501i	$0.594231\pi$
$48$	−1.00000	−0.144338
$49$	19.2462	2.74946
$50$	−1.00000	−0.141421
$51$	1.00000	0.140028
$52$	−3.12311	−0.433097
$53$	−0.876894	−0.120451	−0.0602254	−	0.998185i	$-0.519182\pi$
$53$	−0.876894	−0.120451	−0.0602254	+	0.998185i	$0.519182\pi$
$54$	1.00000	0.136083
$55$	1.00000	0.134840
$56$	5.12311	0.684604
$57$	5.12311	0.678572
$58$	−8.24621	−1.08278
$59$	1.12311	0.146216	0.0731079	−	0.997324i	$-0.476708\pi$
$59$	1.12311	0.146216	0.0731079	+	0.997324i	$0.476708\pi$
$60$	1.00000	0.129099
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	−6.24621	−0.793270
$63$	−5.12311	−0.645451
$64$	1.00000	0.125000
$65$	3.12311	0.387374
$66$	−1.00000	−0.123091
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	−1.00000	−0.121268
$69$	−5.12311	−0.616749
$70$	−5.12311	−0.612328
$71$	−13.1231	−1.55743	−0.778713	−	0.627380i	$-0.784127\pi$
$71$	−13.1231	−1.55743	−0.778713	+	0.627380i	$0.784127\pi$
$72$	−1.00000	−0.117851
$73$	7.12311	0.833696	0.416848	−	0.908976i	$-0.363135\pi$
$73$	7.12311	0.833696	0.416848	+	0.908976i	$0.363135\pi$
$74$	−2.00000	−0.232495
$75$	−1.00000	−0.115470
$76$	−5.12311	−0.587661
$77$	5.12311	0.583832
$78$	−3.12311	−0.353622
$79$	2.87689	0.323676	0.161838	−	0.986817i	$-0.448258\pi$
$79$	2.87689	0.323676	0.161838	+	0.986817i	$0.448258\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−10.0000	−1.10432
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	5.12311	0.558977
$85$	1.00000	0.108465
$86$	−1.12311	−0.121108
$87$	−8.24621	−0.884087
$88$	1.00000	0.106600
$89$	4.24621	0.450097	0.225049	−	0.974348i	$-0.427746\pi$
$89$	4.24621	0.450097	0.225049	+	0.974348i	$0.427746\pi$
$90$	1.00000	0.105409
$91$	16.0000	1.67726
$92$	5.12311	0.534121
$93$	−6.24621	−0.647702
$94$	4.00000	0.412568
$95$	5.12311	0.525620
$96$	1.00000	0.102062
$97$	8.24621	0.837276	0.418638	−	0.908153i	$-0.362508\pi$
$97$	8.24621	0.837276	0.418638	+	0.908153i	$0.362508\pi$
$98$	−19.2462	−1.94416
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	−8.24621	−0.820529	−0.410264	−	0.911967i	$-0.634564\pi$
$101$	−8.24621	−0.820529	−0.410264	+	0.911967i	$0.634564\pi$
$102$	−1.00000	−0.0990148
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	3.12311	0.306246
$105$	−5.12311	−0.499964
$106$	0.876894	0.0851715
$107$	−18.2462	−1.76393	−0.881964	−	0.471317i	$-0.843779\pi$
$107$	−18.2462	−1.76393	−0.881964	+	0.471317i	$0.843779\pi$
$108$	−1.00000	−0.0962250
$109$	−12.2462	−1.17297	−0.586487	−	0.809959i	$-0.699490\pi$
$109$	−12.2462	−1.17297	−0.586487	+	0.809959i	$0.699490\pi$
$110$	−1.00000	−0.0953463
$111$	−2.00000	−0.189832
$112$	−5.12311	−0.484088
$113$	−15.1231	−1.42266	−0.711331	−	0.702857i	$-0.751907\pi$
$113$	−15.1231	−1.42266	−0.711331	+	0.702857i	$0.751907\pi$
$114$	−5.12311	−0.479823
$115$	−5.12311	−0.477732
$116$	8.24621	0.765641
$117$	−3.12311	−0.288731
$118$	−1.12311	−0.103390
$119$	5.12311	0.469634
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	2.00000	0.181071
$123$	−10.0000	−0.901670
$124$	6.24621	0.560926
$125$	−1.00000	−0.0894427
$126$	5.12311	0.456403
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	−1.00000	−0.0883883
$129$	−1.12311	−0.0988839
$130$	−3.12311	−0.273914
$131$	−4.00000	−0.349482	−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000	−0.349482	−0.174741	+	0.984614i	$0.555909\pi$
$132$	1.00000	0.0870388
$133$	26.2462	2.27584
$134$	4.00000	0.345547
$135$	1.00000	0.0860663
$136$	1.00000	0.0857493
$137$	3.75379	0.320708	0.160354	−	0.987060i	$-0.448736\pi$
$137$	3.75379	0.320708	0.160354	+	0.987060i	$0.448736\pi$
$138$	5.12311	0.436108
$139$	−12.0000	−1.01783	−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000	−1.01783	−0.508913	+	0.860818i	$0.669953\pi$
$140$	5.12311	0.432981
$141$	4.00000	0.336861
$142$	13.1231	1.10127
$143$	3.12311	0.261167
$144$	1.00000	0.0833333
$145$	−8.24621	−0.684811
$146$	−7.12311	−0.589512
$147$	−19.2462	−1.58740
$148$	2.00000	0.164399
$149$	18.0000	1.47462	0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000	1.47462	0.737309	+	0.675556i	$0.236096\pi$
$150$	1.00000	0.0816497
$151$	8.49242	0.691104	0.345552	−	0.938400i	$-0.387692\pi$
$151$	8.49242	0.691104	0.345552	+	0.938400i	$0.387692\pi$
$152$	5.12311	0.415539
$153$	−1.00000	−0.0808452
$154$	−5.12311	−0.412832
$155$	−6.24621	−0.501708
$156$	3.12311	0.250049
$157$	0.246211	0.0196498	0.00982490	−	0.999952i	$-0.496873\pi$
$157$	0.246211	0.0196498	0.00982490	+	0.999952i	$0.496873\pi$
$158$	−2.87689	−0.228873
$159$	0.876894	0.0695422
$160$	1.00000	0.0790569
$161$	−26.2462	−2.06849
$162$	−1.00000	−0.0785674
$163$	16.4924	1.29179	0.645893	−	0.763428i	$-0.276485\pi$
$163$	16.4924	1.29179	0.645893	+	0.763428i	$0.276485\pi$
$164$	10.0000	0.780869
$165$	−1.00000	−0.0778499
$166$	−4.00000	−0.310460
$167$	−1.75379	−0.135712	−0.0678561	−	0.997695i	$-0.521616\pi$
$167$	−1.75379	−0.135712	−0.0678561	+	0.997695i	$0.521616\pi$
$168$	−5.12311	−0.395256
$169$	−3.24621	−0.249709
$170$	−1.00000	−0.0766965
$171$	−5.12311	−0.391774
$172$	1.12311	0.0856360
$173$	−8.24621	−0.626948	−0.313474	−	0.949597i	$-0.601493\pi$
$173$	−8.24621	−0.626948	−0.313474	+	0.949597i	$0.601493\pi$
$174$	8.24621	0.625144
$175$	−5.12311	−0.387270
$176$	−1.00000	−0.0753778
$177$	−1.12311	−0.0844178
$178$	−4.24621	−0.318267
$179$	−9.12311	−0.681893	−0.340946	−	0.940083i	$-0.610747\pi$
$179$	−9.12311	−0.681893	−0.340946	+	0.940083i	$0.610747\pi$
$180$	−1.00000	−0.0745356
$181$	0.246211	0.0183007	0.00915037	−	0.999958i	$-0.497087\pi$
$181$	0.246211	0.0183007	0.00915037	+	0.999958i	$0.497087\pi$
$182$	−16.0000	−1.18600
$183$	2.00000	0.147844
$184$	−5.12311	−0.377680
$185$	−2.00000	−0.147043
$186$	6.24621	0.457994
$187$	1.00000	0.0731272
$188$	−4.00000	−0.291730
$189$	5.12311	0.372651
$190$	−5.12311	−0.371669
$191$	16.0000	1.15772	0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000	1.15772	0.578860	+	0.815427i	$0.303498\pi$
$192$	−1.00000	−0.0721688
$193$	−27.1231	−1.95236	−0.976182	−	0.216954i	$-0.930388\pi$
$193$	−27.1231	−1.95236	−0.976182	+	0.216954i	$0.930388\pi$
$194$	−8.24621	−0.592043
$195$	−3.12311	−0.223650
$196$	19.2462	1.37473
$197$	−26.4924	−1.88751	−0.943753	−	0.330650i	$-0.892732\pi$
$197$	−26.4924	−1.88751	−0.943753	+	0.330650i	$0.892732\pi$
$198$	1.00000	0.0710669
$199$	1.75379	0.124323	0.0621614	−	0.998066i	$-0.480201\pi$
$199$	1.75379	0.124323	0.0621614	+	0.998066i	$0.480201\pi$
$200$	−1.00000	−0.0707107
$201$	4.00000	0.282138
$202$	8.24621	0.580201
$203$	−42.2462	−2.96510
$204$	1.00000	0.0700140
$205$	−10.0000	−0.698430
$206$	−8.00000	−0.557386
$207$	5.12311	0.356080
$208$	−3.12311	−0.216548
$209$	5.12311	0.354373
$210$	5.12311	0.353528
$211$	−8.49242	−0.584642	−0.292321	−	0.956320i	$-0.594428\pi$
$211$	−8.49242	−0.584642	−0.292321	+	0.956320i	$0.594428\pi$
$212$	−0.876894	−0.0602254
$213$	13.1231	0.899180
$214$	18.2462	1.24729
$215$	−1.12311	−0.0765952
$216$	1.00000	0.0680414
$217$	−32.0000	−2.17230
$218$	12.2462	0.829418
$219$	−7.12311	−0.481335
$220$	1.00000	0.0674200
$221$	3.12311	0.210083
$222$	2.00000	0.134231
$223$	4.49242	0.300835	0.150417	−	0.988623i	$-0.451938\pi$
$223$	4.49242	0.300835	0.150417	+	0.988623i	$0.451938\pi$
$224$	5.12311	0.342302
$225$	1.00000	0.0666667
$226$	15.1231	1.00597
$227$	−18.2462	−1.21104	−0.605522	−	0.795829i	$-0.707036\pi$
$227$	−18.2462	−1.21104	−0.605522	+	0.795829i	$0.707036\pi$
$228$	5.12311	0.339286
$229$	16.2462	1.07358	0.536790	−	0.843716i	$-0.319637\pi$
$229$	16.2462	1.07358	0.536790	+	0.843716i	$0.319637\pi$
$230$	5.12311	0.337808
$231$	−5.12311	−0.337076
$232$	−8.24621	−0.541390
$233$	16.2462	1.06432	0.532162	−	0.846642i	$-0.321380\pi$
$233$	16.2462	1.06432	0.532162	+	0.846642i	$0.321380\pi$
$234$	3.12311	0.204164
$235$	4.00000	0.260931
$236$	1.12311	0.0731079
$237$	−2.87689	−0.186874
$238$	−5.12311	−0.332082
$239$	−28.4924	−1.84302	−0.921511	−	0.388353i	$-0.873044\pi$
$239$	−28.4924	−1.84302	−0.921511	+	0.388353i	$0.873044\pi$
$240$	1.00000	0.0645497
$241$	20.8769	1.34480	0.672399	−	0.740188i	$-0.265264\pi$
$241$	20.8769	1.34480	0.672399	+	0.740188i	$0.265264\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	−2.00000	−0.128037
$245$	−19.2462	−1.22960
$246$	10.0000	0.637577
$247$	16.0000	1.01806
$248$	−6.24621	−0.396635
$249$	−4.00000	−0.253490
$250$	1.00000	0.0632456
$251$	27.3693	1.72754	0.863768	−	0.503890i	$-0.168098\pi$
$251$	27.3693	1.72754	0.863768	+	0.503890i	$0.168098\pi$
$252$	−5.12311	−0.322725
$253$	−5.12311	−0.322087
$254$	−8.00000	−0.501965
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	16.2462	1.01341	0.506705	−	0.862119i	$-0.330863\pi$
$257$	16.2462	1.01341	0.506705	+	0.862119i	$0.330863\pi$
$258$	1.12311	0.0699215
$259$	−10.2462	−0.636669
$260$	3.12311	0.193687
$261$	8.24621	0.510428
$262$	4.00000	0.247121
$263$	24.0000	1.47990	0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000	1.47990	0.739952	+	0.672660i	$0.234848\pi$
$264$	−1.00000	−0.0615457
$265$	0.876894	0.0538672
$266$	−26.2462	−1.60926
$267$	−4.24621	−0.259864
$268$	−4.00000	−0.244339
$269$	2.00000	0.121942	0.0609711	−	0.998140i	$-0.480580\pi$
$269$	2.00000	0.121942	0.0609711	+	0.998140i	$0.480580\pi$
$270$	−1.00000	−0.0608581
$271$	1.75379	0.106535	0.0532675	−	0.998580i	$-0.483036\pi$
$271$	1.75379	0.106535	0.0532675	+	0.998580i	$0.483036\pi$
$272$	−1.00000	−0.0606339
$273$	−16.0000	−0.968364
$274$	−3.75379	−0.226775
$275$	−1.00000	−0.0603023
$276$	−5.12311	−0.308375
$277$	20.7386	1.24606	0.623032	−	0.782196i	$-0.285901\pi$
$277$	20.7386	1.24606	0.623032	+	0.782196i	$0.285901\pi$
$278$	12.0000	0.719712
$279$	6.24621	0.373951
$280$	−5.12311	−0.306164
$281$	−12.2462	−0.730548	−0.365274	−	0.930900i	$-0.619025\pi$
$281$	−12.2462	−0.730548	−0.365274	+	0.930900i	$0.619025\pi$
$282$	−4.00000	−0.238197
$283$	24.4924	1.45592	0.727962	−	0.685618i	$-0.240468\pi$
$283$	24.4924	1.45592	0.727962	+	0.685618i	$0.240468\pi$
$284$	−13.1231	−0.778713
$285$	−5.12311	−0.303467
$286$	−3.12311	−0.184673
$287$	−51.2311	−3.02407
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	8.24621	0.484234
$291$	−8.24621	−0.483401
$292$	7.12311	0.416848
$293$	14.4924	0.846656	0.423328	−	0.905976i	$-0.360862\pi$
$293$	14.4924	0.846656	0.423328	+	0.905976i	$0.360862\pi$
$294$	19.2462	1.12246
$295$	−1.12311	−0.0653897
$296$	−2.00000	−0.116248
$297$	1.00000	0.0580259
$298$	−18.0000	−1.04271
$299$	−16.0000	−0.925304
$300$	−1.00000	−0.0577350
$301$	−5.75379	−0.331643
$302$	−8.49242	−0.488684
$303$	8.24621	0.473732
$304$	−5.12311	−0.293830
$305$	2.00000	0.114520
$306$	1.00000	0.0571662
$307$	−29.6155	−1.69025	−0.845124	−	0.534571i	$-0.820473\pi$
$307$	−29.6155	−1.69025	−0.845124	+	0.534571i	$0.820473\pi$
$308$	5.12311	0.291916
$309$	−8.00000	−0.455104
$310$	6.24621	0.354761
$311$	−29.1231	−1.65142	−0.825710	−	0.564095i	$-0.809225\pi$
$311$	−29.1231	−1.65142	−0.825710	+	0.564095i	$0.809225\pi$
$312$	−3.12311	−0.176811
$313$	−15.7538	−0.890457	−0.445228	−	0.895417i	$-0.646878\pi$
$313$	−15.7538	−0.890457	−0.445228	+	0.895417i	$0.646878\pi$
$314$	−0.246211	−0.0138945
$315$	5.12311	0.288654
$316$	2.87689	0.161838
$317$	−24.2462	−1.36180	−0.680901	−	0.732375i	$-0.738412\pi$
$317$	−24.2462	−1.36180	−0.680901	+	0.732375i	$0.738412\pi$
$318$	−0.876894	−0.0491738
$319$	−8.24621	−0.461699
$320$	−1.00000	−0.0559017
$321$	18.2462	1.01840
$322$	26.2462	1.46264
$323$	5.12311	0.285057
$324$	1.00000	0.0555556
$325$	−3.12311	−0.173239
$326$	−16.4924	−0.913431
$327$	12.2462	0.677217
$328$	−10.0000	−0.552158
$329$	20.4924	1.12978
$330$	1.00000	0.0550482
$331$	−20.0000	−1.09930	−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000	−1.09930	−0.549650	+	0.835395i	$0.685239\pi$
$332$	4.00000	0.219529
$333$	2.00000	0.109599
$334$	1.75379	0.0959631
$335$	4.00000	0.218543
$336$	5.12311	0.279488
$337$	−21.3693	−1.16406	−0.582030	−	0.813167i	$-0.697742\pi$
$337$	−21.3693	−1.16406	−0.582030	+	0.813167i	$0.697742\pi$
$338$	3.24621	0.176571
$339$	15.1231	0.821374
$340$	1.00000	0.0542326
$341$	−6.24621	−0.338251
$342$	5.12311	0.277026
$343$	−62.7386	−3.38757
$344$	−1.12311	−0.0605538
$345$	5.12311	0.275819
$346$	8.24621	0.443319
$347$	2.24621	0.120583	0.0602915	−	0.998181i	$-0.480797\pi$
$347$	2.24621	0.120583	0.0602915	+	0.998181i	$0.480797\pi$
$348$	−8.24621	−0.442043
$349$	27.1231	1.45187	0.725933	−	0.687765i	$-0.241408\pi$
$349$	27.1231	1.45187	0.725933	+	0.687765i	$0.241408\pi$
$350$	5.12311	0.273842
$351$	3.12311	0.166699
$352$	1.00000	0.0533002
$353$	−7.75379	−0.412693	−0.206346	−	0.978479i	$-0.566157\pi$
$353$	−7.75379	−0.412693	−0.206346	+	0.978479i	$0.566157\pi$
$354$	1.12311	0.0596924
$355$	13.1231	0.696502
$356$	4.24621	0.225049
$357$	−5.12311	−0.271144
$358$	9.12311	0.482171
$359$	16.0000	0.844448	0.422224	−	0.906492i	$-0.361250\pi$
$359$	16.0000	0.844448	0.422224	+	0.906492i	$0.361250\pi$
$360$	1.00000	0.0527046
$361$	7.24621	0.381380
$362$	−0.246211	−0.0129406
$363$	−1.00000	−0.0524864
$364$	16.0000	0.838628
$365$	−7.12311	−0.372840
$366$	−2.00000	−0.104542
$367$	16.0000	0.835193	0.417597	−	0.908633i	$-0.362873\pi$
$367$	16.0000	0.835193	0.417597	+	0.908633i	$0.362873\pi$
$368$	5.12311	0.267060
$369$	10.0000	0.520579
$370$	2.00000	0.103975
$371$	4.49242	0.233235
$372$	−6.24621	−0.323851
$373$	−7.61553	−0.394317	−0.197159	−	0.980372i	$-0.563171\pi$
$373$	−7.61553	−0.394317	−0.197159	+	0.980372i	$0.563171\pi$
$374$	−1.00000	−0.0517088
$375$	1.00000	0.0516398
$376$	4.00000	0.206284
$377$	−25.7538	−1.32639
$378$	−5.12311	−0.263504
$379$	10.2462	0.526313	0.263156	−	0.964753i	$-0.415237\pi$
$379$	10.2462	0.526313	0.263156	+	0.964753i	$0.415237\pi$
$380$	5.12311	0.262810
$381$	−8.00000	−0.409852
$382$	−16.0000	−0.818631
$383$	14.2462	0.727947	0.363974	−	0.931409i	$-0.381420\pi$
$383$	14.2462	0.727947	0.363974	+	0.931409i	$0.381420\pi$
$384$	1.00000	0.0510310
$385$	−5.12311	−0.261098
$386$	27.1231	1.38053
$387$	1.12311	0.0570907
$388$	8.24621	0.418638
$389$	31.6155	1.60297	0.801485	−	0.598014i	$-0.204043\pi$
$389$	31.6155	1.60297	0.801485	+	0.598014i	$0.204043\pi$
$390$	3.12311	0.158145
$391$	−5.12311	−0.259087
$392$	−19.2462	−0.972080
$393$	4.00000	0.201773
$394$	26.4924	1.33467
$395$	−2.87689	−0.144752
$396$	−1.00000	−0.0502519
$397$	32.7386	1.64310	0.821552	−	0.570133i	$-0.193108\pi$
$397$	32.7386	1.64310	0.821552	+	0.570133i	$0.193108\pi$
$398$	−1.75379	−0.0879095
$399$	−26.2462	−1.31395
$400$	1.00000	0.0500000
$401$	8.87689	0.443291	0.221645	−	0.975127i	$-0.428857\pi$
$401$	8.87689	0.443291	0.221645	+	0.975127i	$0.428857\pi$
$402$	−4.00000	−0.199502
$403$	−19.5076	−0.971742
$404$	−8.24621	−0.410264
$405$	−1.00000	−0.0496904
$406$	42.2462	2.09664
$407$	−2.00000	−0.0991363
$408$	−1.00000	−0.0495074
$409$	−3.75379	−0.185613	−0.0928065	−	0.995684i	$-0.529584\pi$
$409$	−3.75379	−0.185613	−0.0928065	+	0.995684i	$0.529584\pi$
$410$	10.0000	0.493865
$411$	−3.75379	−0.185161
$412$	8.00000	0.394132
$413$	−5.75379	−0.283125
$414$	−5.12311	−0.251787
$415$	−4.00000	−0.196352
$416$	3.12311	0.153123
$417$	12.0000	0.587643
$418$	−5.12311	−0.250579
$419$	−4.00000	−0.195413	−0.0977064	−	0.995215i	$-0.531151\pi$
$419$	−4.00000	−0.195413	−0.0977064	+	0.995215i	$0.531151\pi$
$420$	−5.12311	−0.249982
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	8.49242	0.413405
$423$	−4.00000	−0.194487
$424$	0.876894	0.0425858
$425$	−1.00000	−0.0485071
$426$	−13.1231	−0.635817
$427$	10.2462	0.495849
$428$	−18.2462	−0.881964
$429$	−3.12311	−0.150785
$430$	1.12311	0.0541610
$431$	−13.7538	−0.662497	−0.331248	−	0.943544i	$-0.607470\pi$
$431$	−13.7538	−0.662497	−0.331248	+	0.943544i	$0.607470\pi$
$432$	−1.00000	−0.0481125
$433$	4.24621	0.204060	0.102030	−	0.994781i	$-0.467466\pi$
$433$	4.24621	0.204060	0.102030	+	0.994781i	$0.467466\pi$
$434$	32.0000	1.53605
$435$	8.24621	0.395376
$436$	−12.2462	−0.586487
$437$	−26.2462	−1.25553
$438$	7.12311	0.340355
$439$	−5.12311	−0.244512	−0.122256	−	0.992499i	$-0.539013\pi$
$439$	−5.12311	−0.244512	−0.122256	+	0.992499i	$0.539013\pi$
$440$	−1.00000	−0.0476731
$441$	19.2462	0.916486
$442$	−3.12311	−0.148551
$443$	−37.1231	−1.76377	−0.881886	−	0.471463i	$-0.843726\pi$
$443$	−37.1231	−1.76377	−0.881886	+	0.471463i	$0.843726\pi$
$444$	−2.00000	−0.0949158
$445$	−4.24621	−0.201290
$446$	−4.49242	−0.212722
$447$	−18.0000	−0.851371
$448$	−5.12311	−0.242044
$449$	11.1231	0.524932	0.262466	−	0.964941i	$-0.415464\pi$
$449$	11.1231	0.524932	0.262466	+	0.964941i	$0.415464\pi$
$450$	−1.00000	−0.0471405
$451$	−10.0000	−0.470882
$452$	−15.1231	−0.711331
$453$	−8.49242	−0.399009
$454$	18.2462	0.856337
$455$	−16.0000	−0.750092
$456$	−5.12311	−0.239911
$457$	1.50758	0.0705215	0.0352608	−	0.999378i	$-0.488774\pi$
$457$	1.50758	0.0705215	0.0352608	+	0.999378i	$0.488774\pi$
$458$	−16.2462	−0.759136
$459$	1.00000	0.0466760
$460$	−5.12311	−0.238866
$461$	6.49242	0.302382	0.151191	−	0.988505i	$-0.451689\pi$
$461$	6.49242	0.302382	0.151191	+	0.988505i	$0.451689\pi$
$462$	5.12311	0.238348
$463$	0	0		−	1.00000i	$-0.5\pi$
$463$	0	0			1.00000i	$0.5\pi$
$464$	8.24621	0.382821
$465$	6.24621	0.289661
$466$	−16.2462	−0.752591
$467$	−37.1231	−1.71785	−0.858926	−	0.512099i	$-0.828868\pi$
$467$	−37.1231	−1.71785	−0.858926	+	0.512099i	$0.828868\pi$
$468$	−3.12311	−0.144366
$469$	20.4924	0.946252
$470$	−4.00000	−0.184506
$471$	−0.246211	−0.0113448
$472$	−1.12311	−0.0516951
$473$	−1.12311	−0.0516405
$474$	2.87689	0.132140
$475$	−5.12311	−0.235064
$476$	5.12311	0.234817
$477$	−0.876894	−0.0401502
$478$	28.4924	1.30321
$479$	−20.4924	−0.936323	−0.468161	−	0.883643i	$-0.655083\pi$
$479$	−20.4924	−0.936323	−0.468161	+	0.883643i	$0.655083\pi$
$480$	−1.00000	−0.0456435
$481$	−6.24621	−0.284803
$482$	−20.8769	−0.950916
$483$	26.2462	1.19424
$484$	1.00000	0.0454545
$485$	−8.24621	−0.374441
$486$	1.00000	0.0453609
$487$	36.4924	1.65363	0.826815	−	0.562474i	$-0.190150\pi$
$487$	36.4924	1.65363	0.826815	+	0.562474i	$0.190150\pi$
$488$	2.00000	0.0905357
$489$	−16.4924	−0.745813
$490$	19.2462	0.869455
$491$	−34.7386	−1.56773	−0.783866	−	0.620930i	$-0.786755\pi$
$491$	−34.7386	−1.56773	−0.783866	+	0.620930i	$0.786755\pi$
$492$	−10.0000	−0.450835
$493$	−8.24621	−0.371391
$494$	−16.0000	−0.719874
$495$	1.00000	0.0449467
$496$	6.24621	0.280463
$497$	67.2311	3.01573
$498$	4.00000	0.179244
$499$	−2.24621	−0.100554	−0.0502771	−	0.998735i	$-0.516010\pi$
$499$	−2.24621	−0.100554	−0.0502771	+	0.998735i	$0.516010\pi$
$500$	−1.00000	−0.0447214
$501$	1.75379	0.0783535
$502$	−27.3693	−1.22155
$503$	−7.50758	−0.334746	−0.167373	−	0.985894i	$-0.553528\pi$
$503$	−7.50758	−0.334746	−0.167373	+	0.985894i	$0.553528\pi$
$504$	5.12311	0.228201
$505$	8.24621	0.366952
$506$	5.12311	0.227750
$507$	3.24621	0.144169
$508$	8.00000	0.354943
$509$	−1.36932	−0.0606939	−0.0303470	−	0.999539i	$-0.509661\pi$
$509$	−1.36932	−0.0606939	−0.0303470	+	0.999539i	$0.509661\pi$
$510$	1.00000	0.0442807
$511$	−36.4924	−1.61433
$512$	−1.00000	−0.0441942
$513$	5.12311	0.226191
$514$	−16.2462	−0.716590
$515$	−8.00000	−0.352522
$516$	−1.12311	−0.0494420
$517$	4.00000	0.175920
$518$	10.2462	0.450193
$519$	8.24621	0.361968
$520$	−3.12311	−0.136957
$521$	41.8617	1.83400	0.916998	−	0.398892i	$-0.130605\pi$
$521$	41.8617	1.83400	0.916998	+	0.398892i	$0.130605\pi$
$522$	−8.24621	−0.360927
$523$	27.3693	1.19678	0.598388	−	0.801206i	$-0.295808\pi$
$523$	27.3693	1.19678	0.598388	+	0.801206i	$0.295808\pi$
$524$	−4.00000	−0.174741
$525$	5.12311	0.223591
$526$	−24.0000	−1.04645
$527$	−6.24621	−0.272089
$528$	1.00000	0.0435194
$529$	3.24621	0.141140
$530$	−0.876894	−0.0380899
$531$	1.12311	0.0487386
$532$	26.2462	1.13792
$533$	−31.2311	−1.35277
$534$	4.24621	0.183752
$535$	18.2462	0.788853
$536$	4.00000	0.172774
$537$	9.12311	0.393691
$538$	−2.00000	−0.0862261
$539$	−19.2462	−0.828993
$540$	1.00000	0.0430331
$541$	−22.4924	−0.967025	−0.483512	−	0.875338i	$-0.660639\pi$
$541$	−22.4924	−0.967025	−0.483512	+	0.875338i	$0.660639\pi$
$542$	−1.75379	−0.0753317
$543$	−0.246211	−0.0105659
$544$	1.00000	0.0428746
$545$	12.2462	0.524570
$546$	16.0000	0.684737
$547$	26.7386	1.14326	0.571631	−	0.820511i	$-0.306311\pi$
$547$	26.7386	1.14326	0.571631	+	0.820511i	$0.306311\pi$
$548$	3.75379	0.160354
$549$	−2.00000	−0.0853579
$550$	1.00000	0.0426401
$551$	−42.2462	−1.79975
$552$	5.12311	0.218054
$553$	−14.7386	−0.626750
$554$	−20.7386	−0.881100
$555$	2.00000	0.0848953
$556$	−12.0000	−0.508913
$557$	−2.49242	−0.105607	−0.0528037	−	0.998605i	$-0.516816\pi$
$557$	−2.49242	−0.105607	−0.0528037	+	0.998605i	$0.516816\pi$
$558$	−6.24621	−0.264423
$559$	−3.50758	−0.148355
$560$	5.12311	0.216491
$561$	−1.00000	−0.0422200
$562$	12.2462	0.516575
$563$	32.4924	1.36939	0.684696	−	0.728829i	$-0.259935\pi$
$563$	32.4924	1.36939	0.684696	+	0.728829i	$0.259935\pi$
$564$	4.00000	0.168430
$565$	15.1231	0.636234
$566$	−24.4924	−1.02949
$567$	−5.12311	−0.215150
$568$	13.1231	0.550633
$569$	−10.0000	−0.419222	−0.209611	−	0.977785i	$-0.567220\pi$
$569$	−10.0000	−0.419222	−0.209611	+	0.977785i	$0.567220\pi$
$570$	5.12311	0.214583
$571$	−28.0000	−1.17176	−0.585882	−	0.810397i	$-0.699252\pi$
$571$	−28.0000	−1.17176	−0.585882	+	0.810397i	$0.699252\pi$
$572$	3.12311	0.130584
$573$	−16.0000	−0.668410
$574$	51.2311	2.13834
$575$	5.12311	0.213648
$576$	1.00000	0.0416667
$577$	−8.24621	−0.343294	−0.171647	−	0.985158i	$-0.554909\pi$
$577$	−8.24621	−0.343294	−0.171647	+	0.985158i	$0.554909\pi$
$578$	−1.00000	−0.0415945
$579$	27.1231	1.12720
$580$	−8.24621	−0.342405
$581$	−20.4924	−0.850169
$582$	8.24621	0.341816
$583$	0.876894	0.0363173
$584$	−7.12311	−0.294756
$585$	3.12311	0.129125
$586$	−14.4924	−0.598676
$587$	−21.1231	−0.871844	−0.435922	−	0.899984i	$-0.643578\pi$
$587$	−21.1231	−0.871844	−0.435922	+	0.899984i	$0.643578\pi$
$588$	−19.2462	−0.793700
$589$	−32.0000	−1.31854
$590$	1.12311	0.0462375
$591$	26.4924	1.08975
$592$	2.00000	0.0821995
$593$	−16.7386	−0.687373	−0.343687	−	0.939084i	$-0.611676\pi$
$593$	−16.7386	−0.687373	−0.343687	+	0.939084i	$0.611676\pi$
$594$	−1.00000	−0.0410305
$595$	−5.12311	−0.210027
$596$	18.0000	0.737309
$597$	−1.75379	−0.0717778
$598$	16.0000	0.654289
$599$	−40.9848	−1.67460	−0.837298	−	0.546747i	$-0.815866\pi$
$599$	−40.9848	−1.67460	−0.837298	+	0.546747i	$0.815866\pi$
$600$	1.00000	0.0408248
$601$	−17.8617	−0.728596	−0.364298	−	0.931283i	$-0.618691\pi$
$601$	−17.8617	−0.728596	−0.364298	+	0.931283i	$0.618691\pi$
$602$	5.75379	0.234507
$603$	−4.00000	−0.162893
$604$	8.49242	0.345552
$605$	−1.00000	−0.0406558
$606$	−8.24621	−0.334979
$607$	−16.6307	−0.675019	−0.337509	−	0.941322i	$-0.609584\pi$
$607$	−16.6307	−0.675019	−0.337509	+	0.941322i	$0.609584\pi$
$608$	5.12311	0.207769
$609$	42.2462	1.71190
$610$	−2.00000	−0.0809776
$611$	12.4924	0.505389
$612$	−1.00000	−0.0404226
$613$	−22.6307	−0.914045	−0.457022	−	0.889455i	$-0.651084\pi$
$613$	−22.6307	−0.914045	−0.457022	+	0.889455i	$0.651084\pi$
$614$	29.6155	1.19519
$615$	10.0000	0.403239
$616$	−5.12311	−0.206416
$617$	23.6155	0.950725	0.475363	−	0.879790i	$-0.342317\pi$
$617$	23.6155	0.950725	0.475363	+	0.879790i	$0.342317\pi$
$618$	8.00000	0.321807
$619$	−6.73863	−0.270849	−0.135424	−	0.990788i	$-0.543240\pi$
$619$	−6.73863	−0.270849	−0.135424	+	0.990788i	$0.543240\pi$
$620$	−6.24621	−0.250854
$621$	−5.12311	−0.205583
$622$	29.1231	1.16773
$623$	−21.7538	−0.871547
$624$	3.12311	0.125024
$625$	1.00000	0.0400000
$626$	15.7538	0.629648
$627$	−5.12311	−0.204597
$628$	0.246211	0.00982490
$629$	−2.00000	−0.0797452
$630$	−5.12311	−0.204109
$631$	−36.4924	−1.45274	−0.726370	−	0.687304i	$-0.758794\pi$
$631$	−36.4924	−1.45274	−0.726370	+	0.687304i	$0.758794\pi$
$632$	−2.87689	−0.114437
$633$	8.49242	0.337543
$634$	24.2462	0.962940
$635$	−8.00000	−0.317470
$636$	0.876894	0.0347711
$637$	−60.1080	−2.38156
$638$	8.24621	0.326471
$639$	−13.1231	−0.519142
$640$	1.00000	0.0395285
$641$	−43.6155	−1.72271	−0.861355	−	0.508004i	$-0.830384\pi$
$641$	−43.6155	−1.72271	−0.861355	+	0.508004i	$0.830384\pi$
$642$	−18.2462	−0.720121
$643$	24.4924	0.965887	0.482943	−	0.875652i	$-0.339568\pi$
$643$	24.4924	0.965887	0.482943	+	0.875652i	$0.339568\pi$
$644$	−26.2462	−1.03425
$645$	1.12311	0.0442222
$646$	−5.12311	−0.201566
$647$	−24.4924	−0.962896	−0.481448	−	0.876475i	$-0.659889\pi$
$647$	−24.4924	−0.962896	−0.481448	+	0.876475i	$0.659889\pi$
$648$	−1.00000	−0.0392837
$649$	−1.12311	−0.0440858
$650$	3.12311	0.122498
$651$	32.0000	1.25418
$652$	16.4924	0.645893
$653$	−18.4924	−0.723664	−0.361832	−	0.932243i	$-0.617849\pi$
$653$	−18.4924	−0.723664	−0.361832	+	0.932243i	$0.617849\pi$
$654$	−12.2462	−0.478865
$655$	4.00000	0.156293
$656$	10.0000	0.390434
$657$	7.12311	0.277899
$658$	−20.4924	−0.798878
$659$	26.7386	1.04159	0.520795	−	0.853682i	$-0.325636\pi$
$659$	26.7386	1.04159	0.520795	+	0.853682i	$0.325636\pi$
$660$	−1.00000	−0.0389249
$661$	36.7386	1.42897	0.714484	−	0.699652i	$-0.246662\pi$
$661$	36.7386	1.42897	0.714484	+	0.699652i	$0.246662\pi$
$662$	20.0000	0.777322
$663$	−3.12311	−0.121291
$664$	−4.00000	−0.155230
$665$	−26.2462	−1.01778
$666$	−2.00000	−0.0774984
$667$	42.2462	1.63578
$668$	−1.75379	−0.0678561
$669$	−4.49242	−0.173687
$670$	−4.00000	−0.154533
$671$	2.00000	0.0772091
$672$	−5.12311	−0.197628
$673$	20.8769	0.804745	0.402373	−	0.915476i	$-0.368186\pi$
$673$	20.8769	0.804745	0.402373	+	0.915476i	$0.368186\pi$
$674$	21.3693	0.823115
$675$	−1.00000	−0.0384900
$676$	−3.24621	−0.124854
$677$	−14.0000	−0.538064	−0.269032	−	0.963131i	$-0.586704\pi$
$677$	−14.0000	−0.538064	−0.269032	+	0.963131i	$0.586704\pi$
$678$	−15.1231	−0.580799
$679$	−42.2462	−1.62126
$680$	−1.00000	−0.0383482
$681$	18.2462	0.699196
$682$	6.24621	0.239180
$683$	−36.9848	−1.41519	−0.707593	−	0.706620i	$-0.750219\pi$
$683$	−36.9848	−1.41519	−0.707593	+	0.706620i	$0.750219\pi$
$684$	−5.12311	−0.195887
$685$	−3.75379	−0.143425
$686$	62.7386	2.39537
$687$	−16.2462	−0.619832
$688$	1.12311	0.0428180
$689$	2.73863	0.104334
$690$	−5.12311	−0.195033
$691$	−29.7538	−1.13189	−0.565944	−	0.824444i	$-0.691488\pi$
$691$	−29.7538	−1.13189	−0.565944	+	0.824444i	$0.691488\pi$
$692$	−8.24621	−0.313474
$693$	5.12311	0.194611
$694$	−2.24621	−0.0852650
$695$	12.0000	0.455186
$696$	8.24621	0.312572
$697$	−10.0000	−0.378777
$698$	−27.1231	−1.02662
$699$	−16.2462	−0.614488
$700$	−5.12311	−0.193635
$701$	−46.0000	−1.73740	−0.868698	−	0.495342i	$-0.835043\pi$
$701$	−46.0000	−1.73740	−0.868698	+	0.495342i	$0.835043\pi$
$702$	−3.12311	−0.117874
$703$	−10.2462	−0.386443
$704$	−1.00000	−0.0376889
$705$	−4.00000	−0.150649
$706$	7.75379	0.291818
$707$	42.2462	1.58883
$708$	−1.12311	−0.0422089
$709$	−34.0000	−1.27690	−0.638448	−	0.769665i	$-0.720423\pi$
$709$	−34.0000	−1.27690	−0.638448	+	0.769665i	$0.720423\pi$
$710$	−13.1231	−0.492501
$711$	2.87689	0.107892
$712$	−4.24621	−0.159133
$713$	32.0000	1.19841
$714$	5.12311	0.191727
$715$	−3.12311	−0.116798
$716$	−9.12311	−0.340946
$717$	28.4924	1.06407
$718$	−16.0000	−0.597115
$719$	24.6307	0.918569	0.459285	−	0.888289i	$-0.348106\pi$
$719$	24.6307	0.918569	0.459285	+	0.888289i	$0.348106\pi$
$720$	−1.00000	−0.0372678
$721$	−40.9848	−1.52636
$722$	−7.24621	−0.269676
$723$	−20.8769	−0.776420
$724$	0.246211	0.00915037
$725$	8.24621	0.306257
$726$	1.00000	0.0371135
$727$	40.9848	1.52004	0.760022	−	0.649897i	$-0.225188\pi$
$727$	40.9848	1.52004	0.760022	+	0.649897i	$0.225188\pi$
$728$	−16.0000	−0.592999
$729$	1.00000	0.0370370
$730$	7.12311	0.263638
$731$	−1.12311	−0.0415396
$732$	2.00000	0.0739221
$733$	4.87689	0.180132	0.0900661	−	0.995936i	$-0.471292\pi$
$733$	4.87689	0.180132	0.0900661	+	0.995936i	$0.471292\pi$
$734$	−16.0000	−0.590571
$735$	19.2462	0.709907
$736$	−5.12311	−0.188840
$737$	4.00000	0.147342
$738$	−10.0000	−0.368105
$739$	34.8769	1.28297	0.641484	−	0.767137i	$-0.278319\pi$
$739$	34.8769	1.28297	0.641484	+	0.767137i	$0.278319\pi$
$740$	−2.00000	−0.0735215
$741$	−16.0000	−0.587775
$742$	−4.49242	−0.164922
$743$	−44.0000	−1.61420	−0.807102	−	0.590412i	$-0.798965\pi$
$743$	−44.0000	−1.61420	−0.807102	+	0.590412i	$0.798965\pi$
$744$	6.24621	0.228997
$745$	−18.0000	−0.659469
$746$	7.61553	0.278824
$747$	4.00000	0.146352
$748$	1.00000	0.0365636
$749$	93.4773	3.41559
$750$	−1.00000	−0.0365148
$751$	−40.4924	−1.47759	−0.738795	−	0.673931i	$-0.764605\pi$
$751$	−40.4924	−1.47759	−0.738795	+	0.673931i	$0.764605\pi$
$752$	−4.00000	−0.145865
$753$	−27.3693	−0.997393
$754$	25.7538	0.937898
$755$	−8.49242	−0.309071
$756$	5.12311	0.186326
$757$	−10.0000	−0.363456	−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000	−0.363456	−0.181728	+	0.983349i	$0.558169\pi$
$758$	−10.2462	−0.372159
$759$	5.12311	0.185957
$760$	−5.12311	−0.185835
$761$	−31.7538	−1.15107	−0.575537	−	0.817776i	$-0.695207\pi$
$761$	−31.7538	−1.15107	−0.575537	+	0.817776i	$0.695207\pi$
$762$	8.00000	0.289809
$763$	62.7386	2.27129
$764$	16.0000	0.578860
$765$	1.00000	0.0361551
$766$	−14.2462	−0.514737
$767$	−3.50758	−0.126651
$768$	−1.00000	−0.0360844
$769$	−14.9848	−0.540367	−0.270184	−	0.962809i	$-0.587084\pi$
$769$	−14.9848	−0.540367	−0.270184	+	0.962809i	$0.587084\pi$
$770$	5.12311	0.184624
$771$	−16.2462	−0.585093
$772$	−27.1231	−0.976182
$773$	−36.1080	−1.29871	−0.649356	−	0.760484i	$-0.724962\pi$
$773$	−36.1080	−1.29871	−0.649356	+	0.760484i	$0.724962\pi$
$774$	−1.12311	−0.0403692
$775$	6.24621	0.224371
$776$	−8.24621	−0.296022
$777$	10.2462	0.367581
$778$	−31.6155	−1.13347
$779$	−51.2311	−1.83554
$780$	−3.12311	−0.111825
$781$	13.1231	0.469582
$782$	5.12311	0.183202
$783$	−8.24621	−0.294696
$784$	19.2462	0.687365
$785$	−0.246211	−0.00878766
$786$	−4.00000	−0.142675
$787$	2.73863	0.0976218	0.0488109	−	0.998808i	$-0.484457\pi$
$787$	2.73863	0.0976218	0.0488109	+	0.998808i	$0.484457\pi$
$788$	−26.4924	−0.943753
$789$	−24.0000	−0.854423
$790$	2.87689	0.102355
$791$	77.4773	2.75477
$792$	1.00000	0.0355335
$793$	6.24621	0.221809
$794$	−32.7386	−1.16185
$795$	−0.876894	−0.0311002
$796$	1.75379	0.0621614
$797$	31.1231	1.10244	0.551218	−	0.834361i	$-0.314163\pi$
$797$	31.1231	1.10244	0.551218	+	0.834361i	$0.314163\pi$
$798$	26.2462	0.929106
$799$	4.00000	0.141510
$800$	−1.00000	−0.0353553
$801$	4.24621	0.150032
$802$	−8.87689	−0.313454
$803$	−7.12311	−0.251369
$804$	4.00000	0.141069
$805$	26.2462	0.925057
$806$	19.5076	0.687125
$807$	−2.00000	−0.0704033
$808$	8.24621	0.290101
$809$	−33.2311	−1.16834	−0.584171	−	0.811631i	$-0.698580\pi$
$809$	−33.2311	−1.16834	−0.584171	+	0.811631i	$0.698580\pi$
$810$	1.00000	0.0351364
$811$	−14.2462	−0.500252	−0.250126	−	0.968213i	$-0.580472\pi$
$811$	−14.2462	−0.500252	−0.250126	+	0.968213i	$0.580472\pi$
$812$	−42.2462	−1.48255
$813$	−1.75379	−0.0615081
$814$	2.00000	0.0701000
$815$	−16.4924	−0.577704
$816$	1.00000	0.0350070
$817$	−5.75379	−0.201300
$818$	3.75379	0.131248
$819$	16.0000	0.559085
$820$	−10.0000	−0.349215
$821$	−22.4924	−0.784991	−0.392495	−	0.919754i	$-0.628388\pi$
$821$	−22.4924	−0.784991	−0.392495	+	0.919754i	$0.628388\pi$
$822$	3.75379	0.130928
$823$	−30.7386	−1.07148	−0.535741	−	0.844383i	$-0.679968\pi$
$823$	−30.7386	−1.07148	−0.535741	+	0.844383i	$0.679968\pi$
$824$	−8.00000	−0.278693
$825$	1.00000	0.0348155
$826$	5.75379	0.200200
$827$	−5.75379	−0.200079	−0.100039	−	0.994983i	$-0.531897\pi$
$827$	−5.75379	−0.200079	−0.100039	+	0.994983i	$0.531897\pi$
$828$	5.12311	0.178040
$829$	50.4924	1.75367	0.876837	−	0.480787i	$-0.159649\pi$
$829$	50.4924	1.75367	0.876837	+	0.480787i	$0.159649\pi$
$830$	4.00000	0.138842
$831$	−20.7386	−0.719415
$832$	−3.12311	−0.108274
$833$	−19.2462	−0.666842
$834$	−12.0000	−0.415526
$835$	1.75379	0.0606924
$836$	5.12311	0.177186
$837$	−6.24621	−0.215901
$838$	4.00000	0.138178
$839$	15.3693	0.530608	0.265304	−	0.964165i	$-0.414528\pi$
$839$	15.3693	0.530608	0.265304	+	0.964165i	$0.414528\pi$
$840$	5.12311	0.176764
$841$	39.0000	1.34483
$842$	10.0000	0.344623
$843$	12.2462	0.421782
$844$	−8.49242	−0.292321
$845$	3.24621	0.111673
$846$	4.00000	0.137523
$847$	−5.12311	−0.176032
$848$	−0.876894	−0.0301127
$849$	−24.4924	−0.840578
$850$	1.00000	0.0342997
$851$	10.2462	0.351236
$852$	13.1231	0.449590
$853$	7.26137	0.248624	0.124312	−	0.992243i	$-0.460328\pi$
$853$	7.26137	0.248624	0.124312	+	0.992243i	$0.460328\pi$
$854$	−10.2462	−0.350618
$855$	5.12311	0.175207
$856$	18.2462	0.623643
$857$	26.4924	0.904964	0.452482	−	0.891774i	$-0.350539\pi$
$857$	26.4924	0.904964	0.452482	+	0.891774i	$0.350539\pi$
$858$	3.12311	0.106621
$859$	−8.49242	−0.289758	−0.144879	−	0.989449i	$-0.546279\pi$
$859$	−8.49242	−0.289758	−0.144879	+	0.989449i	$0.546279\pi$
$860$	−1.12311	−0.0382976
$861$	51.2311	1.74595
$862$	13.7538	0.468456
$863$	38.2462	1.30192	0.650958	−	0.759114i	$-0.274367\pi$
$863$	38.2462	1.30192	0.650958	+	0.759114i	$0.274367\pi$
$864$	1.00000	0.0340207
$865$	8.24621	0.280380
$866$	−4.24621	−0.144292
$867$	−1.00000	−0.0339618
$868$	−32.0000	−1.08615
$869$	−2.87689	−0.0975920
$870$	−8.24621	−0.279573
$871$	12.4924	0.423290
$872$	12.2462	0.414709
$873$	8.24621	0.279092
$874$	26.2462	0.887791
$875$	5.12311	0.173193
$876$	−7.12311	−0.240667
$877$	−15.7538	−0.531968	−0.265984	−	0.963977i	$-0.585697\pi$
$877$	−15.7538	−0.531968	−0.265984	+	0.963977i	$0.585697\pi$
$878$	5.12311	0.172896
$879$	−14.4924	−0.488817
$880$	1.00000	0.0337100
$881$	−28.8769	−0.972887	−0.486444	−	0.873712i	$-0.661706\pi$
$881$	−28.8769	−0.972887	−0.486444	+	0.873712i	$0.661706\pi$
$882$	−19.2462	−0.648054
$883$	−33.7538	−1.13591	−0.567953	−	0.823061i	$-0.692264\pi$
$883$	−33.7538	−1.13591	−0.567953	+	0.823061i	$0.692264\pi$
$884$	3.12311	0.105041
$885$	1.12311	0.0377528
$886$	37.1231	1.24718
$887$	2.73863	0.0919543	0.0459772	−	0.998942i	$-0.485360\pi$
$887$	2.73863	0.0919543	0.0459772	+	0.998942i	$0.485360\pi$
$888$	2.00000	0.0671156
$889$	−40.9848	−1.37459
$890$	4.24621	0.142333
$891$	−1.00000	−0.0335013
$892$	4.49242	0.150417
$893$	20.4924	0.685753
$894$	18.0000	0.602010
$895$	9.12311	0.304952
$896$	5.12311	0.171151
$897$	16.0000	0.534224
$898$	−11.1231	−0.371183
$899$	51.5076	1.71787
$900$	1.00000	0.0333333
$901$	0.876894	0.0292136
$902$	10.0000	0.332964
$903$	5.75379	0.191474
$904$	15.1231	0.502987
$905$	−0.246211	−0.00818434
$906$	8.49242	0.282142
$907$	12.0000	0.398453	0.199227	−	0.979953i	$-0.436157\pi$
$907$	12.0000	0.398453	0.199227	+	0.979953i	$0.436157\pi$
$908$	−18.2462	−0.605522
$909$	−8.24621	−0.273510
$910$	16.0000	0.530395
$911$	11.8617	0.392997	0.196498	−	0.980504i	$-0.437043\pi$
$911$	11.8617	0.392997	0.196498	+	0.980504i	$0.437043\pi$
$912$	5.12311	0.169643
$913$	−4.00000	−0.132381
$914$	−1.50758	−0.0498662
$915$	−2.00000	−0.0661180
$916$	16.2462	0.536790
$917$	20.4924	0.676719
$918$	−1.00000	−0.0330049
$919$	41.4773	1.36821	0.684104	−	0.729384i	$-0.260193\pi$
$919$	41.4773	1.36821	0.684104	+	0.729384i	$0.260193\pi$
$920$	5.12311	0.168904
$921$	29.6155	0.975865
$922$	−6.49242	−0.213817
$923$	40.9848	1.34903
$924$	−5.12311	−0.168538
$925$	2.00000	0.0657596
$926$	0	0
$927$	8.00000	0.262754
$928$	−8.24621	−0.270695
$929$	43.1231	1.41482	0.707412	−	0.706802i	$-0.249863\pi$
$929$	43.1231	1.41482	0.707412	+	0.706802i	$0.249863\pi$
$930$	−6.24621	−0.204821
$931$	−98.6004	−3.23150
$932$	16.2462	0.532162
$933$	29.1231	0.953448
$934$	37.1231	1.21471
$935$	−1.00000	−0.0327035
$936$	3.12311	0.102082
$937$	14.0000	0.457360	0.228680	−	0.973502i	$-0.426559\pi$
$937$	14.0000	0.457360	0.228680	+	0.973502i	$0.426559\pi$
$938$	−20.4924	−0.669101
$939$	15.7538	0.514105
$940$	4.00000	0.130466
$941$	1.50758	0.0491456	0.0245728	−	0.999698i	$-0.492177\pi$
$941$	1.50758	0.0491456	0.0245728	+	0.999698i	$0.492177\pi$
$942$	0.246211	0.00802200
$943$	51.2311	1.66831
$944$	1.12311	0.0365540
$945$	−5.12311	−0.166655
$946$	1.12311	0.0365153
$947$	−42.7386	−1.38882	−0.694409	−	0.719580i	$-0.744334\pi$
$947$	−42.7386	−1.38882	−0.694409	+	0.719580i	$0.744334\pi$
$948$	−2.87689	−0.0934372
$949$	−22.2462	−0.722143
$950$	5.12311	0.166215
$951$	24.2462	0.786237
$952$	−5.12311	−0.166041
$953$	41.2311	1.33560	0.667802	−	0.744339i	$-0.267235\pi$
$953$	41.2311	1.33560	0.667802	+	0.744339i	$0.267235\pi$
$954$	0.876894	0.0283905
$955$	−16.0000	−0.517748
$956$	−28.4924	−0.921511
$957$	8.24621	0.266562
$958$	20.4924	0.662080
$959$	−19.2311	−0.621003
$960$	1.00000	0.0322749
$961$	8.01515	0.258553
$962$	6.24621	0.201386
$963$	−18.2462	−0.587976
$964$	20.8769	0.672399
$965$	27.1231	0.873124
$966$	−26.2462	−0.844458
$967$	−53.4773	−1.71971	−0.859856	−	0.510536i	$-0.829447\pi$
$967$	−53.4773	−1.71971	−0.859856	+	0.510536i	$0.829447\pi$
$968$	−1.00000	−0.0321412
$969$	−5.12311	−0.164578
$970$	8.24621	0.264770
$971$	5.61553	0.180211	0.0901054	−	0.995932i	$-0.471280\pi$
$971$	5.61553	0.180211	0.0901054	+	0.995932i	$0.471280\pi$
$972$	−1.00000	−0.0320750
$973$	61.4773	1.97087
$974$	−36.4924	−1.16929
$975$	3.12311	0.100019
$976$	−2.00000	−0.0640184
$977$	3.75379	0.120094	0.0600472	−	0.998196i	$-0.480875\pi$
$977$	3.75379	0.120094	0.0600472	+	0.998196i	$0.480875\pi$
$978$	16.4924	0.527370
$979$	−4.24621	−0.135710
$980$	−19.2462	−0.614798
$981$	−12.2462	−0.390991
$982$	34.7386	1.10855
$983$	−31.3693	−1.00053	−0.500263	−	0.865874i	$-0.666763\pi$
$983$	−31.3693	−1.00053	−0.500263	+	0.865874i	$0.666763\pi$
$984$	10.0000	0.318788
$985$	26.4924	0.844119
$986$	8.24621	0.262613
$987$	−20.4924	−0.652281
$988$	16.0000	0.509028
$989$	5.75379	0.182960
$990$	−1.00000	−0.0317821
$991$	24.4924	0.778027	0.389014	−	0.921232i	$-0.372816\pi$
$991$	24.4924	0.778027	0.389014	+	0.921232i	$0.372816\pi$
$992$	−6.24621	−0.198317
$993$	20.0000	0.634681
$994$	−67.2311	−2.13244
$995$	−1.75379	−0.0555988
$996$	−4.00000	−0.126745
$997$	30.9848	0.981300	0.490650	−	0.871357i	$-0.336759\pi$
$997$	30.9848	0.981300	0.490650	+	0.871357i	$0.336759\pi$
$998$	2.24621	0.0711026
$999$	−2.00000	−0.0632772

Twists

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -5.12311 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -5.12311 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} -3.12311 q^{13} +5.12311 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -5.12311 q^{19} -1.00000 q^{20} +5.12311 q^{21} +1.00000 q^{22} +5.12311 q^{23} +1.00000 q^{24} +1.00000 q^{25} +3.12311 q^{26} -1.00000 q^{27} -5.12311 q^{28} +8.24621 q^{29} -1.00000 q^{30} +6.24621 q^{31} -1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} +5.12311 q^{35} +1.00000 q^{36} +2.00000 q^{37} +5.12311 q^{38} +3.12311 q^{39} +1.00000 q^{40} +10.0000 q^{41} -5.12311 q^{42} +1.12311 q^{43} -1.00000 q^{44} -1.00000 q^{45} -5.12311 q^{46} -4.00000 q^{47} -1.00000 q^{48} +19.2462 q^{49} -1.00000 q^{50} +1.00000 q^{51} -3.12311 q^{52} -0.876894 q^{53} +1.00000 q^{54} +1.00000 q^{55} +5.12311 q^{56} +5.12311 q^{57} -8.24621 q^{58} +1.12311 q^{59} +1.00000 q^{60} -2.00000 q^{61} -6.24621 q^{62} -5.12311 q^{63} +1.00000 q^{64} +3.12311 q^{65} -1.00000 q^{66} -4.00000 q^{67} -1.00000 q^{68} -5.12311 q^{69} -5.12311 q^{70} -13.1231 q^{71} -1.00000 q^{72} +7.12311 q^{73} -2.00000 q^{74} -1.00000 q^{75} -5.12311 q^{76} +5.12311 q^{77} -3.12311 q^{78} +2.87689 q^{79} -1.00000 q^{80} +1.00000 q^{81} -10.0000 q^{82} +4.00000 q^{83} +5.12311 q^{84} +1.00000 q^{85} -1.12311 q^{86} -8.24621 q^{87} +1.00000 q^{88} +4.24621 q^{89} +1.00000 q^{90} +16.0000 q^{91} +5.12311 q^{92} -6.24621 q^{93} +4.00000 q^{94} +5.12311 q^{95} +1.00000 q^{96} +8.24621 q^{97} -19.2462 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} - 2 q^{12} + 2 q^{13} + 2 q^{14} + 2 q^{15} + 2 q^{16} - 2 q^{17} - 2 q^{18} - 2 q^{19} - 2 q^{20} + 2 q^{21} + 2 q^{22} + 2 q^{23} + 2 q^{24} + 2 q^{25} - 2 q^{26} - 2 q^{27} - 2 q^{28} - 2 q^{30} - 4 q^{31} - 2 q^{32} + 2 q^{33} + 2 q^{34} + 2 q^{35} + 2 q^{36} + 4 q^{37} + 2 q^{38} - 2 q^{39} + 2 q^{40} + 20 q^{41} - 2 q^{42} - 6 q^{43} - 2 q^{44} - 2 q^{45} - 2 q^{46} - 8 q^{47} - 2 q^{48} + 22 q^{49} - 2 q^{50} + 2 q^{51} + 2 q^{52} - 10 q^{53} + 2 q^{54} + 2 q^{55} + 2 q^{56} + 2 q^{57} - 6 q^{59} + 2 q^{60} - 4 q^{61} + 4 q^{62} - 2 q^{63} + 2 q^{64} - 2 q^{65} - 2 q^{66} - 8 q^{67} - 2 q^{68} - 2 q^{69} - 2 q^{70} - 18 q^{71} - 2 q^{72} + 6 q^{73} - 4 q^{74} - 2 q^{75} - 2 q^{76} + 2 q^{77} + 2 q^{78} + 14 q^{79} - 2 q^{80} + 2 q^{81} - 20 q^{82} + 8 q^{83} + 2 q^{84} + 2 q^{85} + 6 q^{86} + 2 q^{88} - 8 q^{89} + 2 q^{90} + 32 q^{91} + 2 q^{92} + 4 q^{93} + 8 q^{94} + 2 q^{95} + 2 q^{96} - 22 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 - 2 * q^12 + 2 * q^13 + 2 * q^14 + 2 * q^15 + 2 * q^16 - 2 * q^17 - 2 * q^18 - 2 * q^19 - 2 * q^20 + 2 * q^21 + 2 * q^22 + 2 * q^23 + 2 * q^24 + 2 * q^25 - 2 * q^26 - 2 * q^27 - 2 * q^28 - 2 * q^30 - 4 * q^31 - 2 * q^32 + 2 * q^33 + 2 * q^34 + 2 * q^35 + 2 * q^36 + 4 * q^37 + 2 * q^38 - 2 * q^39 + 2 * q^40 + 20 * q^41 - 2 * q^42 - 6 * q^43 - 2 * q^44 - 2 * q^45 - 2 * q^46 - 8 * q^47 - 2 * q^48 + 22 * q^49 - 2 * q^50 + 2 * q^51 + 2 * q^52 - 10 * q^53 + 2 * q^54 + 2 * q^55 + 2 * q^56 + 2 * q^57 - 6 * q^59 + 2 * q^60 - 4 * q^61 + 4 * q^62 - 2 * q^63 + 2 * q^64 - 2 * q^65 - 2 * q^66 - 8 * q^67 - 2 * q^68 - 2 * q^69 - 2 * q^70 - 18 * q^71 - 2 * q^72 + 6 * q^73 - 4 * q^74 - 2 * q^75 - 2 * q^76 + 2 * q^77 + 2 * q^78 + 14 * q^79 - 2 * q^80 + 2 * q^81 - 20 * q^82 + 8 * q^83 + 2 * q^84 + 2 * q^85 + 6 * q^86 + 2 * q^88 - 8 * q^89 + 2 * q^90 + 32 * q^91 + 2 * q^92 + 4 * q^93 + 8 * q^94 + 2 * q^95 + 2 * q^96 - 22 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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