LMFDB - Embedded newform 618.2.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [618,2,Mod(1,618)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(618, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("618.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 618 = 2 \cdot 3 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	618.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:	$4.93475484492$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	618.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.41421 q^{5} -1.00000 q^{6} +1.41421 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.41421 q^{5} -1.00000 q^{6} +1.41421 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.41421 q^{10} +4.41421 q^{11} +1.00000 q^{12} +1.41421 q^{13} -1.41421 q^{14} +3.41421 q^{15} +1.00000 q^{16} -7.07107 q^{17} -1.00000 q^{18} -5.24264 q^{19} +3.41421 q^{20} +1.41421 q^{21} -4.41421 q^{22} +3.58579 q^{23} -1.00000 q^{24} +6.65685 q^{25} -1.41421 q^{26} +1.00000 q^{27} +1.41421 q^{28} +1.00000 q^{29} -3.41421 q^{30} -9.24264 q^{31} -1.00000 q^{32} +4.41421 q^{33} +7.07107 q^{34} +4.82843 q^{35} +1.00000 q^{36} -3.82843 q^{37} +5.24264 q^{38} +1.41421 q^{39} -3.41421 q^{40} -6.24264 q^{41} -1.41421 q^{42} -10.4853 q^{43} +4.41421 q^{44} +3.41421 q^{45} -3.58579 q^{46} +13.0711 q^{47} +1.00000 q^{48} -5.00000 q^{49} -6.65685 q^{50} -7.07107 q^{51} +1.41421 q^{52} +6.24264 q^{53} -1.00000 q^{54} +15.0711 q^{55} -1.41421 q^{56} -5.24264 q^{57} -1.00000 q^{58} +5.41421 q^{59} +3.41421 q^{60} -4.00000 q^{61} +9.24264 q^{62} +1.41421 q^{63} +1.00000 q^{64} +4.82843 q^{65} -4.41421 q^{66} +3.41421 q^{67} -7.07107 q^{68} +3.58579 q^{69} -4.82843 q^{70} -0.242641 q^{71} -1.00000 q^{72} +10.2426 q^{73} +3.82843 q^{74} +6.65685 q^{75} -5.24264 q^{76} +6.24264 q^{77} -1.41421 q^{78} +16.1421 q^{79} +3.41421 q^{80} +1.00000 q^{81} +6.24264 q^{82} +12.0000 q^{83} +1.41421 q^{84} -24.1421 q^{85} +10.4853 q^{86} +1.00000 q^{87} -4.41421 q^{88} -1.00000 q^{89} -3.41421 q^{90} +2.00000 q^{91} +3.58579 q^{92} -9.24264 q^{93} -13.0711 q^{94} -17.8995 q^{95} -1.00000 q^{96} -7.48528 q^{97} +5.00000 q^{98} +4.41421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} - 4 q^{10} + 6 q^{11} + 2 q^{12} + 4 q^{15} + 2 q^{16} - 2 q^{18} - 2 q^{19} + 4 q^{20} - 6 q^{22} + 10 q^{23} - 2 q^{24} + 2 q^{25} + 2 q^{27} + 2 q^{29} - 4 q^{30} - 10 q^{31} - 2 q^{32} + 6 q^{33} + 4 q^{35} + 2 q^{36} - 2 q^{37} + 2 q^{38} - 4 q^{40} - 4 q^{41} - 4 q^{43} + 6 q^{44} + 4 q^{45} - 10 q^{46} + 12 q^{47} + 2 q^{48} - 10 q^{49} - 2 q^{50} + 4 q^{53} - 2 q^{54} + 16 q^{55} - 2 q^{57} - 2 q^{58} + 8 q^{59} + 4 q^{60} - 8 q^{61} + 10 q^{62} + 2 q^{64} + 4 q^{65} - 6 q^{66} + 4 q^{67} + 10 q^{69} - 4 q^{70} + 8 q^{71} - 2 q^{72} + 12 q^{73} + 2 q^{74} + 2 q^{75} - 2 q^{76} + 4 q^{77} + 4 q^{79} + 4 q^{80} + 2 q^{81} + 4 q^{82} + 24 q^{83} - 20 q^{85} + 4 q^{86} + 2 q^{87} - 6 q^{88} - 2 q^{89} - 4 q^{90} + 4 q^{91} + 10 q^{92} - 10 q^{93} - 12 q^{94} - 16 q^{95} - 2 q^{96} + 2 q^{97} + 10 q^{98} + 6 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 - 4 * q^10 + 6 * q^11 + 2 * q^12 + 4 * q^15 + 2 * q^16 - 2 * q^18 - 2 * q^19 + 4 * q^20 - 6 * q^22 + 10 * q^23 - 2 * q^24 + 2 * q^25 + 2 * q^27 + 2 * q^29 - 4 * q^30 - 10 * q^31 - 2 * q^32 + 6 * q^33 + 4 * q^35 + 2 * q^36 - 2 * q^37 + 2 * q^38 - 4 * q^40 - 4 * q^41 - 4 * q^43 + 6 * q^44 + 4 * q^45 - 10 * q^46 + 12 * q^47 + 2 * q^48 - 10 * q^49 - 2 * q^50 + 4 * q^53 - 2 * q^54 + 16 * q^55 - 2 * q^57 - 2 * q^58 + 8 * q^59 + 4 * q^60 - 8 * q^61 + 10 * q^62 + 2 * q^64 + 4 * q^65 - 6 * q^66 + 4 * q^67 + 10 * q^69 - 4 * q^70 + 8 * q^71 - 2 * q^72 + 12 * q^73 + 2 * q^74 + 2 * q^75 - 2 * q^76 + 4 * q^77 + 4 * q^79 + 4 * q^80 + 2 * q^81 + 4 * q^82 + 24 * q^83 - 20 * q^85 + 4 * q^86 + 2 * q^87 - 6 * q^88 - 2 * q^89 - 4 * q^90 + 4 * q^91 + 10 * q^92 - 10 * q^93 - 12 * q^94 - 16 * q^95 - 2 * q^96 + 2 * q^97 + 10 * q^98 + 6 * 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
$5$	3.41421	1.52688	0.763441	−	0.645877i	$-0.223508\pi$
$5$	3.41421	1.52688	0.763441	+	0.645877i	$0.223508\pi$
$6$	−1.00000	−0.408248
$7$	1.41421	0.534522	0.267261	−	0.963624i	$-0.413881\pi$
$7$	1.41421	0.534522	0.267261	+	0.963624i	$0.413881\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.41421	−1.07967
$11$	4.41421	1.33094	0.665468	−	0.746427i	$-0.268232\pi$
$11$	4.41421	1.33094	0.665468	+	0.746427i	$0.268232\pi$
$12$	1.00000	0.288675
$13$	1.41421	0.392232	0.196116	−	0.980581i	$-0.437167\pi$
$13$	1.41421	0.392232	0.196116	+	0.980581i	$0.437167\pi$
$14$	−1.41421	−0.377964
$15$	3.41421	0.881546
$16$	1.00000	0.250000
$17$	−7.07107	−1.71499	−0.857493	−	0.514496i	$-0.827979\pi$
$17$	−7.07107	−1.71499	−0.857493	+	0.514496i	$0.827979\pi$
$18$	−1.00000	−0.235702
$19$	−5.24264	−1.20274	−0.601372	−	0.798969i	$-0.705379\pi$
$19$	−5.24264	−1.20274	−0.601372	+	0.798969i	$0.705379\pi$
$20$	3.41421	0.763441
$21$	1.41421	0.308607
$22$	−4.41421	−0.941113
$23$	3.58579	0.747688	0.373844	−	0.927492i	$-0.378040\pi$
$23$	3.58579	0.747688	0.373844	+	0.927492i	$0.378040\pi$
$24$	−1.00000	−0.204124
$25$	6.65685	1.33137
$26$	−1.41421	−0.277350
$27$	1.00000	0.192450
$28$	1.41421	0.267261
$29$	1.00000	0.185695	0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000	0.185695	0.0928477	+	0.995680i	$0.470403\pi$
$30$	−3.41421	−0.623347
$31$	−9.24264	−1.66003	−0.830014	−	0.557743i	$-0.811667\pi$
$31$	−9.24264	−1.66003	−0.830014	+	0.557743i	$0.811667\pi$
$32$	−1.00000	−0.176777
$33$	4.41421	0.768416
$34$	7.07107	1.21268
$35$	4.82843	0.816153
$36$	1.00000	0.166667
$37$	−3.82843	−0.629390	−0.314695	−	0.949193i	$-0.601902\pi$
$37$	−3.82843	−0.629390	−0.314695	+	0.949193i	$0.601902\pi$
$38$	5.24264	0.850469
$39$	1.41421	0.226455
$40$	−3.41421	−0.539835
$41$	−6.24264	−0.974937	−0.487468	−	0.873141i	$-0.662080\pi$
$41$	−6.24264	−0.974937	−0.487468	+	0.873141i	$0.662080\pi$
$42$	−1.41421	−0.218218
$43$	−10.4853	−1.59899	−0.799495	−	0.600672i	$-0.794900\pi$
$43$	−10.4853	−1.59899	−0.799495	+	0.600672i	$0.794900\pi$
$44$	4.41421	0.665468
$45$	3.41421	0.508961
$46$	−3.58579	−0.528695
$47$	13.0711	1.90661	0.953306	−	0.302007i	$-0.0976567\pi$
$47$	13.0711	1.90661	0.953306	+	0.302007i	$0.0976567\pi$
$48$	1.00000	0.144338
$49$	−5.00000	−0.714286
$50$	−6.65685	−0.941421
$51$	−7.07107	−0.990148
$52$	1.41421	0.196116
$53$	6.24264	0.857493	0.428746	−	0.903425i	$-0.358955\pi$
$53$	6.24264	0.857493	0.428746	+	0.903425i	$0.358955\pi$
$54$	−1.00000	−0.136083
$55$	15.0711	2.03218
$56$	−1.41421	−0.188982
$57$	−5.24264	−0.694405
$58$	−1.00000	−0.131306
$59$	5.41421	0.704871	0.352435	−	0.935836i	$-0.385354\pi$
$59$	5.41421	0.704871	0.352435	+	0.935836i	$0.385354\pi$
$60$	3.41421	0.440773
$61$	−4.00000	−0.512148	−0.256074	−	0.966657i	$-0.582429\pi$
$61$	−4.00000	−0.512148	−0.256074	+	0.966657i	$0.582429\pi$
$62$	9.24264	1.17382
$63$	1.41421	0.178174
$64$	1.00000	0.125000
$65$	4.82843	0.598893
$66$	−4.41421	−0.543352
$67$	3.41421	0.417113	0.208556	−	0.978010i	$-0.433124\pi$
$67$	3.41421	0.417113	0.208556	+	0.978010i	$0.433124\pi$
$68$	−7.07107	−0.857493
$69$	3.58579	0.431678
$70$	−4.82843	−0.577107
$71$	−0.242641	−0.0287962	−0.0143981	−	0.999896i	$-0.504583\pi$
$71$	−0.242641	−0.0287962	−0.0143981	+	0.999896i	$0.504583\pi$
$72$	−1.00000	−0.117851
$73$	10.2426	1.19881	0.599405	−	0.800446i	$-0.295404\pi$
$73$	10.2426	1.19881	0.599405	+	0.800446i	$0.295404\pi$
$74$	3.82843	0.445046
$75$	6.65685	0.768667
$76$	−5.24264	−0.601372
$77$	6.24264	0.711415
$78$	−1.41421	−0.160128
$79$	16.1421	1.81613	0.908066	−	0.418827i	$-0.137559\pi$
$79$	16.1421	1.81613	0.908066	+	0.418827i	$0.137559\pi$
$80$	3.41421	0.381721
$81$	1.00000	0.111111
$82$	6.24264	0.689384
$83$	12.0000	1.31717	0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000	1.31717	0.658586	+	0.752506i	$0.271155\pi$
$84$	1.41421	0.154303
$85$	−24.1421	−2.61858
$86$	10.4853	1.13066
$87$	1.00000	0.107211
$88$	−4.41421	−0.470557
$89$	−1.00000	−0.106000	−0.0529999	−	0.998595i	$-0.516878\pi$
$89$	−1.00000	−0.106000	−0.0529999	+	0.998595i	$0.516878\pi$
$90$	−3.41421	−0.359890
$91$	2.00000	0.209657
$92$	3.58579	0.373844
$93$	−9.24264	−0.958417
$94$	−13.0711	−1.34818
$95$	−17.8995	−1.83645
$96$	−1.00000	−0.102062
$97$	−7.48528	−0.760015	−0.380008	−	0.924983i	$-0.624079\pi$
$97$	−7.48528	−0.760015	−0.380008	+	0.924983i	$0.624079\pi$
$98$	5.00000	0.505076
$99$	4.41421	0.443645
$100$	6.65685	0.665685
$101$	−14.0000	−1.39305	−0.696526	−	0.717532i	$-0.745272\pi$
$101$	−14.0000	−1.39305	−0.696526	+	0.717532i	$0.745272\pi$
$102$	7.07107	0.700140
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.41421	−0.138675
$105$	4.82843	0.471206
$106$	−6.24264	−0.606339
$107$	−19.3137	−1.86713	−0.933563	−	0.358412i	$-0.883318\pi$
$107$	−19.3137	−1.86713	−0.933563	+	0.358412i	$0.883318\pi$
$108$	1.00000	0.0962250
$109$	−16.4853	−1.57900	−0.789502	−	0.613748i	$-0.789661\pi$
$109$	−16.4853	−1.57900	−0.789502	+	0.613748i	$0.789661\pi$
$110$	−15.0711	−1.43697
$111$	−3.82843	−0.363378
$112$	1.41421	0.133631
$113$	3.82843	0.360148	0.180074	−	0.983653i	$-0.442366\pi$
$113$	3.82843	0.360148	0.180074	+	0.983653i	$0.442366\pi$
$114$	5.24264	0.491018
$115$	12.2426	1.14163
$116$	1.00000	0.0928477
$117$	1.41421	0.130744
$118$	−5.41421	−0.498419
$119$	−10.0000	−0.916698
$120$	−3.41421	−0.311674
$121$	8.48528	0.771389
$122$	4.00000	0.362143
$123$	−6.24264	−0.562880
$124$	−9.24264	−0.830014
$125$	5.65685	0.505964
$126$	−1.41421	−0.125988
$127$	−0.343146	−0.0304493	−0.0152246	−	0.999884i	$-0.504846\pi$
$127$	−0.343146	−0.0304493	−0.0152246	+	0.999884i	$0.504846\pi$
$128$	−1.00000	−0.0883883
$129$	−10.4853	−0.923178
$130$	−4.82843	−0.423481
$131$	12.9706	1.13324	0.566622	−	0.823978i	$-0.308250\pi$
$131$	12.9706	1.13324	0.566622	+	0.823978i	$0.308250\pi$
$132$	4.41421	0.384208
$133$	−7.41421	−0.642894
$134$	−3.41421	−0.294943
$135$	3.41421	0.293849
$136$	7.07107	0.606339
$137$	−8.00000	−0.683486	−0.341743	−	0.939793i	$-0.611017\pi$
$137$	−8.00000	−0.683486	−0.341743	+	0.939793i	$0.611017\pi$
$138$	−3.58579	−0.305242
$139$	12.5563	1.06502	0.532508	−	0.846425i	$-0.321250\pi$
$139$	12.5563	1.06502	0.532508	+	0.846425i	$0.321250\pi$
$140$	4.82843	0.408077
$141$	13.0711	1.10078
$142$	0.242641	0.0203620
$143$	6.24264	0.522036
$144$	1.00000	0.0833333
$145$	3.41421	0.283535
$146$	−10.2426	−0.847687
$147$	−5.00000	−0.412393
$148$	−3.82843	−0.314695
$149$	−13.4853	−1.10476	−0.552379	−	0.833593i	$-0.686280\pi$
$149$	−13.4853	−1.10476	−0.552379	+	0.833593i	$0.686280\pi$
$150$	−6.65685	−0.543530
$151$	−15.2426	−1.24043	−0.620214	−	0.784432i	$-0.712954\pi$
$151$	−15.2426	−1.24043	−0.620214	+	0.784432i	$0.712954\pi$
$152$	5.24264	0.425234
$153$	−7.07107	−0.571662
$154$	−6.24264	−0.503046
$155$	−31.5563	−2.53467
$156$	1.41421	0.113228
$157$	8.48528	0.677199	0.338600	−	0.940931i	$-0.390047\pi$
$157$	8.48528	0.677199	0.338600	+	0.940931i	$0.390047\pi$
$158$	−16.1421	−1.28420
$159$	6.24264	0.495074
$160$	−3.41421	−0.269917
$161$	5.07107	0.399656
$162$	−1.00000	−0.0785674
$163$	−13.3848	−1.04838	−0.524188	−	0.851602i	$-0.675631\pi$
$163$	−13.3848	−1.04838	−0.524188	+	0.851602i	$0.675631\pi$
$164$	−6.24264	−0.487468
$165$	15.0711	1.17328
$166$	−12.0000	−0.931381
$167$	6.07107	0.469793	0.234897	−	0.972020i	$-0.424525\pi$
$167$	6.07107	0.469793	0.234897	+	0.972020i	$0.424525\pi$
$168$	−1.41421	−0.109109
$169$	−11.0000	−0.846154
$170$	24.1421	1.85162
$171$	−5.24264	−0.400915
$172$	−10.4853	−0.799495
$173$	20.6274	1.56827	0.784137	−	0.620588i	$-0.213106\pi$
$173$	20.6274	1.56827	0.784137	+	0.620588i	$0.213106\pi$
$174$	−1.00000	−0.0758098
$175$	9.41421	0.711648
$176$	4.41421	0.332734
$177$	5.41421	0.406957
$178$	1.00000	0.0749532
$179$	−11.3137	−0.845626	−0.422813	−	0.906217i	$-0.638957\pi$
$179$	−11.3137	−0.845626	−0.422813	+	0.906217i	$0.638957\pi$
$180$	3.41421	0.254480
$181$	9.48528	0.705035	0.352518	−	0.935805i	$-0.385326\pi$
$181$	9.48528	0.705035	0.352518	+	0.935805i	$0.385326\pi$
$182$	−2.00000	−0.148250
$183$	−4.00000	−0.295689
$184$	−3.58579	−0.264348
$185$	−13.0711	−0.961004
$186$	9.24264	0.677703
$187$	−31.2132	−2.28254
$188$	13.0711	0.953306
$189$	1.41421	0.102869
$190$	17.8995	1.29857
$191$	−1.07107	−0.0774997	−0.0387499	−	0.999249i	$-0.512338\pi$
$191$	−1.07107	−0.0774997	−0.0387499	+	0.999249i	$0.512338\pi$
$192$	1.00000	0.0721688
$193$	−3.07107	−0.221060	−0.110530	−	0.993873i	$-0.535255\pi$
$193$	−3.07107	−0.221060	−0.110530	+	0.993873i	$0.535255\pi$
$194$	7.48528	0.537412
$195$	4.82843	0.345771
$196$	−5.00000	−0.357143
$197$	−6.34315	−0.451930	−0.225965	−	0.974135i	$-0.572554\pi$
$197$	−6.34315	−0.451930	−0.225965	+	0.974135i	$0.572554\pi$
$198$	−4.41421	−0.313704
$199$	21.6569	1.53521	0.767607	−	0.640921i	$-0.221447\pi$
$199$	21.6569	1.53521	0.767607	+	0.640921i	$0.221447\pi$
$200$	−6.65685	−0.470711
$201$	3.41421	0.240820
$202$	14.0000	0.985037
$203$	1.41421	0.0992583
$204$	−7.07107	−0.495074
$205$	−21.3137	−1.48861
$206$	1.00000	0.0696733
$207$	3.58579	0.249229
$208$	1.41421	0.0980581
$209$	−23.1421	−1.60077
$210$	−4.82843	−0.333193
$211$	−0.100505	−0.00691905	−0.00345953	−	0.999994i	$-0.501101\pi$
$211$	−0.100505	−0.00691905	−0.00345953	+	0.999994i	$0.501101\pi$
$212$	6.24264	0.428746
$213$	−0.242641	−0.0166255
$214$	19.3137	1.32026
$215$	−35.7990	−2.44147
$216$	−1.00000	−0.0680414
$217$	−13.0711	−0.887322
$218$	16.4853	1.11652
$219$	10.2426	0.692134
$220$	15.0711	1.01609
$221$	−10.0000	−0.672673
$222$	3.82843	0.256947
$223$	6.58579	0.441017	0.220508	−	0.975385i	$-0.429228\pi$
$223$	6.58579	0.441017	0.220508	+	0.975385i	$0.429228\pi$
$224$	−1.41421	−0.0944911
$225$	6.65685	0.443790
$226$	−3.82843	−0.254663
$227$	−2.75736	−0.183012	−0.0915062	−	0.995805i	$-0.529168\pi$
$227$	−2.75736	−0.183012	−0.0915062	+	0.995805i	$0.529168\pi$
$228$	−5.24264	−0.347202
$229$	−15.3137	−1.01196	−0.505979	−	0.862546i	$-0.668869\pi$
$229$	−15.3137	−1.01196	−0.505979	+	0.862546i	$0.668869\pi$
$230$	−12.2426	−0.807256
$231$	6.24264	0.410736
$232$	−1.00000	−0.0656532
$233$	7.31371	0.479137	0.239568	−	0.970879i	$-0.422994\pi$
$233$	7.31371	0.479137	0.239568	+	0.970879i	$0.422994\pi$
$234$	−1.41421	−0.0924500
$235$	44.6274	2.91117
$236$	5.41421	0.352435
$237$	16.1421	1.04854
$238$	10.0000	0.648204
$239$	18.4142	1.19112	0.595558	−	0.803312i	$-0.296931\pi$
$239$	18.4142	1.19112	0.595558	+	0.803312i	$0.296931\pi$
$240$	3.41421	0.220387
$241$	23.3137	1.50177	0.750884	−	0.660434i	$-0.229628\pi$
$241$	23.3137	1.50177	0.750884	+	0.660434i	$0.229628\pi$
$242$	−8.48528	−0.545455
$243$	1.00000	0.0641500
$244$	−4.00000	−0.256074
$245$	−17.0711	−1.09063
$246$	6.24264	0.398016
$247$	−7.41421	−0.471755
$248$	9.24264	0.586908
$249$	12.0000	0.760469
$250$	−5.65685	−0.357771
$251$	−10.5563	−0.666311	−0.333155	−	0.942872i	$-0.608113\pi$
$251$	−10.5563	−0.666311	−0.333155	+	0.942872i	$0.608113\pi$
$252$	1.41421	0.0890871
$253$	15.8284	0.995125
$254$	0.343146	0.0215309
$255$	−24.1421	−1.51184
$256$	1.00000	0.0625000
$257$	−7.00000	−0.436648	−0.218324	−	0.975876i	$-0.570059\pi$
$257$	−7.00000	−0.436648	−0.218324	+	0.975876i	$0.570059\pi$
$258$	10.4853	0.652785
$259$	−5.41421	−0.336423
$260$	4.82843	0.299446
$261$	1.00000	0.0618984
$262$	−12.9706	−0.801324
$263$	5.65685	0.348817	0.174408	−	0.984673i	$-0.444199\pi$
$263$	5.65685	0.348817	0.174408	+	0.984673i	$0.444199\pi$
$264$	−4.41421	−0.271676
$265$	21.3137	1.30929
$266$	7.41421	0.454595
$267$	−1.00000	−0.0611990
$268$	3.41421	0.208556
$269$	−21.1421	−1.28906	−0.644529	−	0.764580i	$-0.722947\pi$
$269$	−21.1421	−1.28906	−0.644529	+	0.764580i	$0.722947\pi$
$270$	−3.41421	−0.207782
$271$	1.24264	0.0754850	0.0377425	−	0.999287i	$-0.487983\pi$
$271$	1.24264	0.0754850	0.0377425	+	0.999287i	$0.487983\pi$
$272$	−7.07107	−0.428746
$273$	2.00000	0.121046
$274$	8.00000	0.483298
$275$	29.3848	1.77197
$276$	3.58579	0.215839
$277$	2.65685	0.159635	0.0798175	−	0.996809i	$-0.474566\pi$
$277$	2.65685	0.159635	0.0798175	+	0.996809i	$0.474566\pi$
$278$	−12.5563	−0.753080
$279$	−9.24264	−0.553342
$280$	−4.82843	−0.288554
$281$	−17.1716	−1.02437	−0.512185	−	0.858875i	$-0.671164\pi$
$281$	−17.1716	−1.02437	−0.512185	+	0.858875i	$0.671164\pi$
$282$	−13.0711	−0.778371
$283$	11.7574	0.698902	0.349451	−	0.936955i	$-0.386368\pi$
$283$	11.7574	0.698902	0.349451	+	0.936955i	$0.386368\pi$
$284$	−0.242641	−0.0143981
$285$	−17.8995	−1.06027
$286$	−6.24264	−0.369135
$287$	−8.82843	−0.521126
$288$	−1.00000	−0.0589256
$289$	33.0000	1.94118
$290$	−3.41421	−0.200490
$291$	−7.48528	−0.438795
$292$	10.2426	0.599405
$293$	8.68629	0.507459	0.253729	−	0.967275i	$-0.418343\pi$
$293$	8.68629	0.507459	0.253729	+	0.967275i	$0.418343\pi$
$294$	5.00000	0.291606
$295$	18.4853	1.07625
$296$	3.82843	0.222523
$297$	4.41421	0.256139
$298$	13.4853	0.781181
$299$	5.07107	0.293267
$300$	6.65685	0.384334
$301$	−14.8284	−0.854696
$302$	15.2426	0.877115
$303$	−14.0000	−0.804279
$304$	−5.24264	−0.300686
$305$	−13.6569	−0.781989
$306$	7.07107	0.404226
$307$	21.5563	1.23029	0.615143	−	0.788416i	$-0.289098\pi$
$307$	21.5563	1.23029	0.615143	+	0.788416i	$0.289098\pi$
$308$	6.24264	0.355707
$309$	−1.00000	−0.0568880
$310$	31.5563	1.79228
$311$	4.34315	0.246277	0.123139	−	0.992389i	$-0.460704\pi$
$311$	4.34315	0.246277	0.123139	+	0.992389i	$0.460704\pi$
$312$	−1.41421	−0.0800641
$313$	−2.65685	−0.150174	−0.0750871	−	0.997177i	$-0.523923\pi$
$313$	−2.65685	−0.150174	−0.0750871	+	0.997177i	$0.523923\pi$
$314$	−8.48528	−0.478852
$315$	4.82843	0.272051
$316$	16.1421	0.908066
$317$	19.7990	1.11202	0.556011	−	0.831175i	$-0.312331\pi$
$317$	19.7990	1.11202	0.556011	+	0.831175i	$0.312331\pi$
$318$	−6.24264	−0.350070
$319$	4.41421	0.247149
$320$	3.41421	0.190860
$321$	−19.3137	−1.07799
$322$	−5.07107	−0.282600
$323$	37.0711	2.06269
$324$	1.00000	0.0555556
$325$	9.41421	0.522207
$326$	13.3848	0.741314
$327$	−16.4853	−0.911638
$328$	6.24264	0.344692
$329$	18.4853	1.01913
$330$	−15.0711	−0.829635
$331$	−8.82843	−0.485254	−0.242627	−	0.970120i	$-0.578009\pi$
$331$	−8.82843	−0.485254	−0.242627	+	0.970120i	$0.578009\pi$
$332$	12.0000	0.658586
$333$	−3.82843	−0.209797
$334$	−6.07107	−0.332194
$335$	11.6569	0.636882
$336$	1.41421	0.0771517
$337$	−34.7990	−1.89562	−0.947811	−	0.318833i	$-0.896709\pi$
$337$	−34.7990	−1.89562	−0.947811	+	0.318833i	$0.896709\pi$
$338$	11.0000	0.598321
$339$	3.82843	0.207932
$340$	−24.1421	−1.30929
$341$	−40.7990	−2.20939
$342$	5.24264	0.283490
$343$	−16.9706	−0.916324
$344$	10.4853	0.565328
$345$	12.2426	0.659122
$346$	−20.6274	−1.10894
$347$	18.2426	0.979316	0.489658	−	0.871915i	$-0.337122\pi$
$347$	18.2426	0.979316	0.489658	+	0.871915i	$0.337122\pi$
$348$	1.00000	0.0536056
$349$	−24.6569	−1.31985	−0.659926	−	0.751331i	$-0.729412\pi$
$349$	−24.6569	−1.31985	−0.659926	+	0.751331i	$0.729412\pi$
$350$	−9.41421	−0.503211
$351$	1.41421	0.0754851
$352$	−4.41421	−0.235278
$353$	21.3137	1.13441	0.567207	−	0.823575i	$-0.308024\pi$
$353$	21.3137	1.13441	0.567207	+	0.823575i	$0.308024\pi$
$354$	−5.41421	−0.287762
$355$	−0.828427	−0.0439683
$356$	−1.00000	−0.0529999
$357$	−10.0000	−0.529256
$358$	11.3137	0.597948
$359$	32.9706	1.74012	0.870060	−	0.492946i	$-0.164080\pi$
$359$	32.9706	1.74012	0.870060	+	0.492946i	$0.164080\pi$
$360$	−3.41421	−0.179945
$361$	8.48528	0.446594
$362$	−9.48528	−0.498535
$363$	8.48528	0.445362
$364$	2.00000	0.104828
$365$	34.9706	1.83044
$366$	4.00000	0.209083
$367$	6.58579	0.343775	0.171888	−	0.985117i	$-0.445013\pi$
$367$	6.58579	0.343775	0.171888	+	0.985117i	$0.445013\pi$
$368$	3.58579	0.186922
$369$	−6.24264	−0.324979
$370$	13.0711	0.679532
$371$	8.82843	0.458349
$372$	−9.24264	−0.479209
$373$	−13.8995	−0.719689	−0.359844	−	0.933012i	$-0.617170\pi$
$373$	−13.8995	−0.719689	−0.359844	+	0.933012i	$0.617170\pi$
$374$	31.2132	1.61400
$375$	5.65685	0.292119
$376$	−13.0711	−0.674089
$377$	1.41421	0.0728357
$378$	−1.41421	−0.0727393
$379$	1.27208	0.0653423	0.0326711	−	0.999466i	$-0.489599\pi$
$379$	1.27208	0.0653423	0.0326711	+	0.999466i	$0.489599\pi$
$380$	−17.8995	−0.918225
$381$	−0.343146	−0.0175799
$382$	1.07107	0.0548006
$383$	−29.7990	−1.52266	−0.761329	−	0.648366i	$-0.775453\pi$
$383$	−29.7990	−1.52266	−0.761329	+	0.648366i	$0.775453\pi$
$384$	−1.00000	−0.0510310
$385$	21.3137	1.08625
$386$	3.07107	0.156313
$387$	−10.4853	−0.532997
$388$	−7.48528	−0.380008
$389$	−1.65685	−0.0840058	−0.0420029	−	0.999117i	$-0.513374\pi$
$389$	−1.65685	−0.0840058	−0.0420029	+	0.999117i	$0.513374\pi$
$390$	−4.82843	−0.244497
$391$	−25.3553	−1.28227
$392$	5.00000	0.252538
$393$	12.9706	0.654278
$394$	6.34315	0.319563
$395$	55.1127	2.77302
$396$	4.41421	0.221823
$397$	22.0000	1.10415	0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000	1.10415	0.552074	+	0.833795i	$0.313837\pi$
$398$	−21.6569	−1.08556
$399$	−7.41421	−0.371175
$400$	6.65685	0.332843
$401$	−17.3137	−0.864605	−0.432303	−	0.901729i	$-0.642299\pi$
$401$	−17.3137	−0.864605	−0.432303	+	0.901729i	$0.642299\pi$
$402$	−3.41421	−0.170285
$403$	−13.0711	−0.651116
$404$	−14.0000	−0.696526
$405$	3.41421	0.169654
$406$	−1.41421	−0.0701862
$407$	−16.8995	−0.837677
$408$	7.07107	0.350070
$409$	21.9706	1.08637	0.543187	−	0.839612i	$-0.317217\pi$
$409$	21.9706	1.08637	0.543187	+	0.839612i	$0.317217\pi$
$410$	21.3137	1.05261
$411$	−8.00000	−0.394611
$412$	−1.00000	−0.0492665
$413$	7.65685	0.376769
$414$	−3.58579	−0.176232
$415$	40.9706	2.01117
$416$	−1.41421	−0.0693375
$417$	12.5563	0.614887
$418$	23.1421	1.13192
$419$	18.7279	0.914919	0.457459	−	0.889230i	$-0.348759\pi$
$419$	18.7279	0.914919	0.457459	+	0.889230i	$0.348759\pi$
$420$	4.82843	0.235603
$421$	−27.4142	−1.33609	−0.668044	−	0.744122i	$-0.732868\pi$
$421$	−27.4142	−1.33609	−0.668044	+	0.744122i	$0.732868\pi$
$422$	0.100505	0.00489251
$423$	13.0711	0.635537
$424$	−6.24264	−0.303169
$425$	−47.0711	−2.28328
$426$	0.242641	0.0117560
$427$	−5.65685	−0.273754
$428$	−19.3137	−0.933563
$429$	6.24264	0.301398
$430$	35.7990	1.72638
$431$	−36.0711	−1.73748	−0.868741	−	0.495266i	$-0.835070\pi$
$431$	−36.0711	−1.73748	−0.868741	+	0.495266i	$0.835070\pi$
$432$	1.00000	0.0481125
$433$	17.5563	0.843704	0.421852	−	0.906665i	$-0.361380\pi$
$433$	17.5563	0.843704	0.421852	+	0.906665i	$0.361380\pi$
$434$	13.0711	0.627431
$435$	3.41421	0.163699
$436$	−16.4853	−0.789502
$437$	−18.7990	−0.899278
$438$	−10.2426	−0.489412
$439$	0.556349	0.0265531	0.0132765	−	0.999912i	$-0.495774\pi$
$439$	0.556349	0.0265531	0.0132765	+	0.999912i	$0.495774\pi$
$440$	−15.0711	−0.718485
$441$	−5.00000	−0.238095
$442$	10.0000	0.475651
$443$	12.7574	0.606120	0.303060	−	0.952971i	$-0.401992\pi$
$443$	12.7574	0.606120	0.303060	+	0.952971i	$0.401992\pi$
$444$	−3.82843	−0.181689
$445$	−3.41421	−0.161849
$446$	−6.58579	−0.311846
$447$	−13.4853	−0.637832
$448$	1.41421	0.0668153
$449$	33.9411	1.60178	0.800890	−	0.598811i	$-0.204360\pi$
$449$	33.9411	1.60178	0.800890	+	0.598811i	$0.204360\pi$
$450$	−6.65685	−0.313807
$451$	−27.5563	−1.29758
$452$	3.82843	0.180074
$453$	−15.2426	−0.716162
$454$	2.75736	0.129409
$455$	6.82843	0.320122
$456$	5.24264	0.245509
$457$	14.3848	0.672891	0.336446	−	0.941703i	$-0.390775\pi$
$457$	14.3848	0.672891	0.336446	+	0.941703i	$0.390775\pi$
$458$	15.3137	0.715563
$459$	−7.07107	−0.330049
$460$	12.2426	0.570816
$461$	−23.4853	−1.09382	−0.546909	−	0.837192i	$-0.684196\pi$
$461$	−23.4853	−1.09382	−0.546909	+	0.837192i	$0.684196\pi$
$462$	−6.24264	−0.290434
$463$	1.24264	0.0577504	0.0288752	−	0.999583i	$-0.490807\pi$
$463$	1.24264	0.0577504	0.0288752	+	0.999583i	$0.490807\pi$
$464$	1.00000	0.0464238
$465$	−31.5563	−1.46339
$466$	−7.31371	−0.338801
$467$	−4.82843	−0.223433	−0.111716	−	0.993740i	$-0.535635\pi$
$467$	−4.82843	−0.223433	−0.111716	+	0.993740i	$0.535635\pi$
$468$	1.41421	0.0653720
$469$	4.82843	0.222956
$470$	−44.6274	−2.05851
$471$	8.48528	0.390981
$472$	−5.41421	−0.249209
$473$	−46.2843	−2.12815
$474$	−16.1421	−0.741433
$475$	−34.8995	−1.60130
$476$	−10.0000	−0.458349
$477$	6.24264	0.285831
$478$	−18.4142	−0.842247
$479$	−32.8701	−1.50187	−0.750936	−	0.660375i	$-0.770397\pi$
$479$	−32.8701	−1.50187	−0.750936	+	0.660375i	$0.770397\pi$
$480$	−3.41421	−0.155837
$481$	−5.41421	−0.246867
$482$	−23.3137	−1.06191
$483$	5.07107	0.230742
$484$	8.48528	0.385695
$485$	−25.5563	−1.16045
$486$	−1.00000	−0.0453609
$487$	−19.3137	−0.875188	−0.437594	−	0.899173i	$-0.644169\pi$
$487$	−19.3137	−0.875188	−0.437594	+	0.899173i	$0.644169\pi$
$488$	4.00000	0.181071
$489$	−13.3848	−0.605281
$490$	17.0711	0.771192
$491$	8.10051	0.365571	0.182785	−	0.983153i	$-0.441489\pi$
$491$	8.10051	0.365571	0.182785	+	0.983153i	$0.441489\pi$
$492$	−6.24264	−0.281440
$493$	−7.07107	−0.318465
$494$	7.41421	0.333581
$495$	15.0711	0.677394
$496$	−9.24264	−0.415007
$497$	−0.343146	−0.0153922
$498$	−12.0000	−0.537733
$499$	21.0711	0.943271	0.471635	−	0.881794i	$-0.343664\pi$
$499$	21.0711	0.943271	0.471635	+	0.881794i	$0.343664\pi$
$500$	5.65685	0.252982
$501$	6.07107	0.271235
$502$	10.5563	0.471153
$503$	−9.44365	−0.421072	−0.210536	−	0.977586i	$-0.567521\pi$
$503$	−9.44365	−0.421072	−0.210536	+	0.977586i	$0.567521\pi$
$504$	−1.41421	−0.0629941
$505$	−47.7990	−2.12703
$506$	−15.8284	−0.703659
$507$	−11.0000	−0.488527
$508$	−0.343146	−0.0152246
$509$	−6.00000	−0.265945	−0.132973	−	0.991120i	$-0.542452\pi$
$509$	−6.00000	−0.265945	−0.132973	+	0.991120i	$0.542452\pi$
$510$	24.1421	1.06903
$511$	14.4853	0.640791
$512$	−1.00000	−0.0441942
$513$	−5.24264	−0.231468
$514$	7.00000	0.308757
$515$	−3.41421	−0.150448
$516$	−10.4853	−0.461589
$517$	57.6985	2.53758
$518$	5.41421	0.237887
$519$	20.6274	0.905443
$520$	−4.82843	−0.211741
$521$	3.14214	0.137659	0.0688297	−	0.997628i	$-0.478073\pi$
$521$	3.14214	0.137659	0.0688297	+	0.997628i	$0.478073\pi$
$522$	−1.00000	−0.0437688
$523$	2.27208	0.0993510	0.0496755	−	0.998765i	$-0.484181\pi$
$523$	2.27208	0.0993510	0.0496755	+	0.998765i	$0.484181\pi$
$524$	12.9706	0.566622
$525$	9.41421	0.410870
$526$	−5.65685	−0.246651
$527$	65.3553	2.84692
$528$	4.41421	0.192104
$529$	−10.1421	−0.440962
$530$	−21.3137	−0.925808
$531$	5.41421	0.234957
$532$	−7.41421	−0.321447
$533$	−8.82843	−0.382402
$534$	1.00000	0.0432742
$535$	−65.9411	−2.85088
$536$	−3.41421	−0.147472
$537$	−11.3137	−0.488223
$538$	21.1421	0.911502
$539$	−22.0711	−0.950668
$540$	3.41421	0.146924
$541$	−16.0000	−0.687894	−0.343947	−	0.938989i	$-0.611764\pi$
$541$	−16.0000	−0.687894	−0.343947	+	0.938989i	$0.611764\pi$
$542$	−1.24264	−0.0533760
$543$	9.48528	0.407052
$544$	7.07107	0.303170
$545$	−56.2843	−2.41095
$546$	−2.00000	−0.0855921
$547$	15.7279	0.672477	0.336239	−	0.941777i	$-0.390845\pi$
$547$	15.7279	0.672477	0.336239	+	0.941777i	$0.390845\pi$
$548$	−8.00000	−0.341743
$549$	−4.00000	−0.170716
$550$	−29.3848	−1.25297
$551$	−5.24264	−0.223344
$552$	−3.58579	−0.152621
$553$	22.8284	0.970763
$554$	−2.65685	−0.112879
$555$	−13.0711	−0.554836
$556$	12.5563	0.532508
$557$	12.9289	0.547816	0.273908	−	0.961756i	$-0.411684\pi$
$557$	12.9289	0.547816	0.273908	+	0.961756i	$0.411684\pi$
$558$	9.24264	0.391272
$559$	−14.8284	−0.627176
$560$	4.82843	0.204038
$561$	−31.2132	−1.31782
$562$	17.1716	0.724339
$563$	30.4142	1.28181	0.640903	−	0.767622i	$-0.278560\pi$
$563$	30.4142	1.28181	0.640903	+	0.767622i	$0.278560\pi$
$564$	13.0711	0.550391
$565$	13.0711	0.549904
$566$	−11.7574	−0.494199
$567$	1.41421	0.0593914
$568$	0.242641	0.0101810
$569$	−29.4558	−1.23485	−0.617427	−	0.786628i	$-0.711825\pi$
$569$	−29.4558	−1.23485	−0.617427	+	0.786628i	$0.711825\pi$
$570$	17.8995	0.749727
$571$	1.24264	0.0520029	0.0260014	−	0.999662i	$-0.491723\pi$
$571$	1.24264	0.0520029	0.0260014	+	0.999662i	$0.491723\pi$
$572$	6.24264	0.261018
$573$	−1.07107	−0.0447445
$574$	8.82843	0.368491
$575$	23.8701	0.995450
$576$	1.00000	0.0416667
$577$	42.0000	1.74848	0.874241	−	0.485491i	$-0.161359\pi$
$577$	42.0000	1.74848	0.874241	+	0.485491i	$0.161359\pi$
$578$	−33.0000	−1.37262
$579$	−3.07107	−0.127629
$580$	3.41421	0.141768
$581$	16.9706	0.704058
$582$	7.48528	0.310275
$583$	27.5563	1.14127
$584$	−10.2426	−0.423843
$585$	4.82843	0.199631
$586$	−8.68629	−0.358827
$587$	29.8995	1.23408	0.617042	−	0.786930i	$-0.288331\pi$
$587$	29.8995	1.23408	0.617042	+	0.786930i	$0.288331\pi$
$588$	−5.00000	−0.206197
$589$	48.4558	1.99659
$590$	−18.4853	−0.761027
$591$	−6.34315	−0.260922
$592$	−3.82843	−0.157347
$593$	31.6274	1.29878	0.649391	−	0.760455i	$-0.275024\pi$
$593$	31.6274	1.29878	0.649391	+	0.760455i	$0.275024\pi$
$594$	−4.41421	−0.181117
$595$	−34.1421	−1.39969
$596$	−13.4853	−0.552379
$597$	21.6569	0.886356
$598$	−5.07107	−0.207371
$599$	46.8701	1.91506	0.957529	−	0.288336i	$-0.0931020\pi$
$599$	46.8701	1.91506	0.957529	+	0.288336i	$0.0931020\pi$
$600$	−6.65685	−0.271765
$601$	−41.3553	−1.68692	−0.843460	−	0.537192i	$-0.819485\pi$
$601$	−41.3553	−1.68692	−0.843460	+	0.537192i	$0.819485\pi$
$602$	14.8284	0.604362
$603$	3.41421	0.139038
$604$	−15.2426	−0.620214
$605$	28.9706	1.17782
$606$	14.0000	0.568711
$607$	−21.5147	−0.873255	−0.436628	−	0.899642i	$-0.643827\pi$
$607$	−21.5147	−0.873255	−0.436628	+	0.899642i	$0.643827\pi$
$608$	5.24264	0.212617
$609$	1.41421	0.0573068
$610$	13.6569	0.552950
$611$	18.4853	0.747834
$612$	−7.07107	−0.285831
$613$	40.1838	1.62301	0.811504	−	0.584348i	$-0.198649\pi$
$613$	40.1838	1.62301	0.811504	+	0.584348i	$0.198649\pi$
$614$	−21.5563	−0.869943
$615$	−21.3137	−0.859452
$616$	−6.24264	−0.251523
$617$	−13.6274	−0.548619	−0.274310	−	0.961641i	$-0.588449\pi$
$617$	−13.6274	−0.548619	−0.274310	+	0.961641i	$0.588449\pi$
$618$	1.00000	0.0402259
$619$	6.68629	0.268745	0.134372	−	0.990931i	$-0.457098\pi$
$619$	6.68629	0.268745	0.134372	+	0.990931i	$0.457098\pi$
$620$	−31.5563	−1.26733
$621$	3.58579	0.143893
$622$	−4.34315	−0.174144
$623$	−1.41421	−0.0566593
$624$	1.41421	0.0566139
$625$	−13.9706	−0.558823
$626$	2.65685	0.106189
$627$	−23.1421	−0.924208
$628$	8.48528	0.338600
$629$	27.0711	1.07939
$630$	−4.82843	−0.192369
$631$	−42.2426	−1.68165	−0.840826	−	0.541305i	$-0.817931\pi$
$631$	−42.2426	−1.68165	−0.840826	+	0.541305i	$0.817931\pi$
$632$	−16.1421	−0.642100
$633$	−0.100505	−0.00399472
$634$	−19.7990	−0.786318
$635$	−1.17157	−0.0464925
$636$	6.24264	0.247537
$637$	−7.07107	−0.280166
$638$	−4.41421	−0.174760
$639$	−0.242641	−0.00959872
$640$	−3.41421	−0.134959
$641$	28.9706	1.14427	0.572134	−	0.820160i	$-0.306116\pi$
$641$	28.9706	1.14427	0.572134	+	0.820160i	$0.306116\pi$
$642$	19.3137	0.762251
$643$	24.6274	0.971211	0.485605	−	0.874178i	$-0.338599\pi$
$643$	24.6274	0.971211	0.485605	+	0.874178i	$0.338599\pi$
$644$	5.07107	0.199828
$645$	−35.7990	−1.40958
$646$	−37.0711	−1.45854
$647$	−27.1127	−1.06591	−0.532955	−	0.846144i	$-0.678919\pi$
$647$	−27.1127	−1.06591	−0.532955	+	0.846144i	$0.678919\pi$
$648$	−1.00000	−0.0392837
$649$	23.8995	0.938137
$650$	−9.41421	−0.369256
$651$	−13.0711	−0.512296
$652$	−13.3848	−0.524188
$653$	−25.3553	−0.992231	−0.496116	−	0.868257i	$-0.665241\pi$
$653$	−25.3553	−0.992231	−0.496116	+	0.868257i	$0.665241\pi$
$654$	16.4853	0.644626
$655$	44.2843	1.73033
$656$	−6.24264	−0.243734
$657$	10.2426	0.399603
$658$	−18.4853	−0.720631
$659$	−45.2132	−1.76126	−0.880628	−	0.473808i	$-0.842879\pi$
$659$	−45.2132	−1.76126	−0.880628	+	0.473808i	$0.842879\pi$
$660$	15.0711	0.586641
$661$	28.3137	1.10128	0.550638	−	0.834744i	$-0.314385\pi$
$661$	28.3137	1.10128	0.550638	+	0.834744i	$0.314385\pi$
$662$	8.82843	0.343127
$663$	−10.0000	−0.388368
$664$	−12.0000	−0.465690
$665$	−25.3137	−0.981624
$666$	3.82843	0.148349
$667$	3.58579	0.138842
$668$	6.07107	0.234897
$669$	6.58579	0.254621
$670$	−11.6569	−0.450344
$671$	−17.6569	−0.681635
$672$	−1.41421	−0.0545545
$673$	24.3137	0.937225	0.468612	−	0.883404i	$-0.344754\pi$
$673$	24.3137	0.937225	0.468612	+	0.883404i	$0.344754\pi$
$674$	34.7990	1.34041
$675$	6.65685	0.256222
$676$	−11.0000	−0.423077
$677$	−0.656854	−0.0252450	−0.0126225	−	0.999920i	$-0.504018\pi$
$677$	−0.656854	−0.0252450	−0.0126225	+	0.999920i	$0.504018\pi$
$678$	−3.82843	−0.147030
$679$	−10.5858	−0.406245
$680$	24.1421	0.925809
$681$	−2.75736	−0.105662
$682$	40.7990	1.56227
$683$	−12.2132	−0.467325	−0.233663	−	0.972318i	$-0.575071\pi$
$683$	−12.2132	−0.467325	−0.233663	+	0.972318i	$0.575071\pi$
$684$	−5.24264	−0.200457
$685$	−27.3137	−1.04360
$686$	16.9706	0.647939
$687$	−15.3137	−0.584254
$688$	−10.4853	−0.399748
$689$	8.82843	0.336336
$690$	−12.2426	−0.466069
$691$	20.5269	0.780881	0.390440	−	0.920628i	$-0.372323\pi$
$691$	20.5269	0.780881	0.390440	+	0.920628i	$0.372323\pi$
$692$	20.6274	0.784137
$693$	6.24264	0.237138
$694$	−18.2426	−0.692481
$695$	42.8701	1.62615
$696$	−1.00000	−0.0379049
$697$	44.1421	1.67200
$698$	24.6569	0.933276
$699$	7.31371	0.276630
$700$	9.41421	0.355824
$701$	34.8284	1.31545	0.657726	−	0.753257i	$-0.271519\pi$
$701$	34.8284	1.31545	0.657726	+	0.753257i	$0.271519\pi$
$702$	−1.41421	−0.0533761
$703$	20.0711	0.756995
$704$	4.41421	0.166367
$705$	44.6274	1.68077
$706$	−21.3137	−0.802152
$707$	−19.7990	−0.744618
$708$	5.41421	0.203479
$709$	−38.3848	−1.44157	−0.720785	−	0.693158i	$-0.756219\pi$
$709$	−38.3848	−1.44157	−0.720785	+	0.693158i	$0.756219\pi$
$710$	0.828427	0.0310903
$711$	16.1421	0.605377
$712$	1.00000	0.0374766
$713$	−33.1421	−1.24118
$714$	10.0000	0.374241
$715$	21.3137	0.797088
$716$	−11.3137	−0.422813
$717$	18.4142	0.687691
$718$	−32.9706	−1.23045
$719$	−1.27208	−0.0474405	−0.0237203	−	0.999719i	$-0.507551\pi$
$719$	−1.27208	−0.0474405	−0.0237203	+	0.999719i	$0.507551\pi$
$720$	3.41421	0.127240
$721$	−1.41421	−0.0526681
$722$	−8.48528	−0.315789
$723$	23.3137	0.867046
$724$	9.48528	0.352518
$725$	6.65685	0.247229
$726$	−8.48528	−0.314918
$727$	0.0710678	0.00263576	0.00131788	−	0.999999i	$-0.499581\pi$
$727$	0.0710678	0.00263576	0.00131788	+	0.999999i	$0.499581\pi$
$728$	−2.00000	−0.0741249
$729$	1.00000	0.0370370
$730$	−34.9706	−1.29432
$731$	74.1421	2.74225
$732$	−4.00000	−0.147844
$733$	1.34315	0.0496102	0.0248051	−	0.999692i	$-0.492103\pi$
$733$	1.34315	0.0496102	0.0248051	+	0.999692i	$0.492103\pi$
$734$	−6.58579	−0.243086
$735$	−17.0711	−0.629676
$736$	−3.58579	−0.132174
$737$	15.0711	0.555150
$738$	6.24264	0.229795
$739$	5.37258	0.197634	0.0988168	−	0.995106i	$-0.468494\pi$
$739$	5.37258	0.197634	0.0988168	+	0.995106i	$0.468494\pi$
$740$	−13.0711	−0.480502
$741$	−7.41421	−0.272368
$742$	−8.82843	−0.324102
$743$	20.1005	0.737416	0.368708	−	0.929545i	$-0.379800\pi$
$743$	20.1005	0.737416	0.368708	+	0.929545i	$0.379800\pi$
$744$	9.24264	0.338852
$745$	−46.0416	−1.68683
$746$	13.8995	0.508897
$747$	12.0000	0.439057
$748$	−31.2132	−1.14127
$749$	−27.3137	−0.998021
$750$	−5.65685	−0.206559
$751$	−28.5858	−1.04311	−0.521555	−	0.853218i	$-0.674648\pi$
$751$	−28.5858	−1.04311	−0.521555	+	0.853218i	$0.674648\pi$
$752$	13.0711	0.476653
$753$	−10.5563	−0.384695
$754$	−1.41421	−0.0515026
$755$	−52.0416	−1.89399
$756$	1.41421	0.0514344
$757$	−38.2843	−1.39147	−0.695733	−	0.718301i	$-0.744920\pi$
$757$	−38.2843	−1.39147	−0.695733	+	0.718301i	$0.744920\pi$
$758$	−1.27208	−0.0462040
$759$	15.8284	0.574536
$760$	17.8995	0.649283
$761$	−9.97056	−0.361433	−0.180716	−	0.983535i	$-0.557842\pi$
$761$	−9.97056	−0.361433	−0.180716	+	0.983535i	$0.557842\pi$
$762$	0.343146	0.0124309
$763$	−23.3137	−0.844013
$764$	−1.07107	−0.0387499
$765$	−24.1421	−0.872861
$766$	29.7990	1.07668
$767$	7.65685	0.276473
$768$	1.00000	0.0360844
$769$	10.5858	0.381733	0.190867	−	0.981616i	$-0.438870\pi$
$769$	10.5858	0.381733	0.190867	+	0.981616i	$0.438870\pi$
$770$	−21.3137	−0.768093
$771$	−7.00000	−0.252099
$772$	−3.07107	−0.110530
$773$	16.7990	0.604218	0.302109	−	0.953273i	$-0.402309\pi$
$773$	16.7990	0.604218	0.302109	+	0.953273i	$0.402309\pi$
$774$	10.4853	0.376886
$775$	−61.5269	−2.21011
$776$	7.48528	0.268706
$777$	−5.41421	−0.194234
$778$	1.65685	0.0594011
$779$	32.7279	1.17260
$780$	4.82843	0.172885
$781$	−1.07107	−0.0383258
$782$	25.3553	0.906705
$783$	1.00000	0.0357371
$784$	−5.00000	−0.178571
$785$	28.9706	1.03400
$786$	−12.9706	−0.462645
$787$	−26.8284	−0.956330	−0.478165	−	0.878270i	$-0.658698\pi$
$787$	−26.8284	−0.956330	−0.478165	+	0.878270i	$0.658698\pi$
$788$	−6.34315	−0.225965
$789$	5.65685	0.201389
$790$	−55.1127	−1.96082
$791$	5.41421	0.192507
$792$	−4.41421	−0.156852
$793$	−5.65685	−0.200881
$794$	−22.0000	−0.780751
$795$	21.3137	0.755919
$796$	21.6569	0.767607
$797$	17.8284	0.631515	0.315758	−	0.948840i	$-0.397741\pi$
$797$	17.8284	0.631515	0.315758	+	0.948840i	$0.397741\pi$
$798$	7.41421	0.262460
$799$	−92.4264	−3.26981
$800$	−6.65685	−0.235355
$801$	−1.00000	−0.0353333
$802$	17.3137	0.611368
$803$	45.2132	1.59554
$804$	3.41421	0.120410
$805$	17.3137	0.610228
$806$	13.0711	0.460409
$807$	−21.1421	−0.744238
$808$	14.0000	0.492518
$809$	45.9706	1.61624	0.808119	−	0.589019i	$-0.200486\pi$
$809$	45.9706	1.61624	0.808119	+	0.589019i	$0.200486\pi$
$810$	−3.41421	−0.119963
$811$	1.79899	0.0631711	0.0315855	−	0.999501i	$-0.489944\pi$
$811$	1.79899	0.0631711	0.0315855	+	0.999501i	$0.489944\pi$
$812$	1.41421	0.0496292
$813$	1.24264	0.0435813
$814$	16.8995	0.592327
$815$	−45.6985	−1.60075
$816$	−7.07107	−0.247537
$817$	54.9706	1.92318
$818$	−21.9706	−0.768183
$819$	2.00000	0.0698857
$820$	−21.3137	−0.744307
$821$	2.62742	0.0916975	0.0458487	−	0.998948i	$-0.485401\pi$
$821$	2.62742	0.0916975	0.0458487	+	0.998948i	$0.485401\pi$
$822$	8.00000	0.279032
$823$	9.87006	0.344049	0.172024	−	0.985093i	$-0.444969\pi$
$823$	9.87006	0.344049	0.172024	+	0.985093i	$0.444969\pi$
$824$	1.00000	0.0348367
$825$	29.3848	1.02305
$826$	−7.65685	−0.266416
$827$	−44.7696	−1.55679	−0.778395	−	0.627775i	$-0.783966\pi$
$827$	−44.7696	−1.55679	−0.778395	+	0.627775i	$0.783966\pi$
$828$	3.58579	0.124615
$829$	24.4853	0.850409	0.425204	−	0.905097i	$-0.360202\pi$
$829$	24.4853	0.850409	0.425204	+	0.905097i	$0.360202\pi$
$830$	−40.9706	−1.42211
$831$	2.65685	0.0921653
$832$	1.41421	0.0490290
$833$	35.3553	1.22499
$834$	−12.5563	−0.434791
$835$	20.7279	0.717319
$836$	−23.1421	−0.800387
$837$	−9.24264	−0.319472
$838$	−18.7279	−0.646945
$839$	−1.78680	−0.0616871	−0.0308435	−	0.999524i	$-0.509819\pi$
$839$	−1.78680	−0.0616871	−0.0308435	+	0.999524i	$0.509819\pi$
$840$	−4.82843	−0.166597
$841$	−28.0000	−0.965517
$842$	27.4142	0.944756
$843$	−17.1716	−0.591420
$844$	−0.100505	−0.00345953
$845$	−37.5563	−1.29198
$846$	−13.0711	−0.449393
$847$	12.0000	0.412325
$848$	6.24264	0.214373
$849$	11.7574	0.403512
$850$	47.0711	1.61452
$851$	−13.7279	−0.470587
$852$	−0.242641	−0.00831273
$853$	3.61522	0.123783	0.0618915	−	0.998083i	$-0.480287\pi$
$853$	3.61522	0.123783	0.0618915	+	0.998083i	$0.480287\pi$
$854$	5.65685	0.193574
$855$	−17.8995	−0.612150
$856$	19.3137	0.660129
$857$	−26.3848	−0.901287	−0.450643	−	0.892704i	$-0.648805\pi$
$857$	−26.3848	−0.901287	−0.450643	+	0.892704i	$0.648805\pi$
$858$	−6.24264	−0.213120
$859$	14.1005	0.481103	0.240552	−	0.970636i	$-0.422672\pi$
$859$	14.1005	0.481103	0.240552	+	0.970636i	$0.422672\pi$
$860$	−35.7990	−1.22074
$861$	−8.82843	−0.300872
$862$	36.0711	1.22859
$863$	−1.65685	−0.0564000	−0.0282000	−	0.999602i	$-0.508978\pi$
$863$	−1.65685	−0.0564000	−0.0282000	+	0.999602i	$0.508978\pi$
$864$	−1.00000	−0.0340207
$865$	70.4264	2.39457
$866$	−17.5563	−0.596589
$867$	33.0000	1.12074
$868$	−13.0711	−0.443661
$869$	71.2548	2.41715
$870$	−3.41421	−0.115753
$871$	4.82843	0.163605
$872$	16.4853	0.558262
$873$	−7.48528	−0.253338
$874$	18.7990	0.635885
$875$	8.00000	0.270449
$876$	10.2426	0.346067
$877$	−31.0000	−1.04680	−0.523398	−	0.852088i	$-0.675336\pi$
$877$	−31.0000	−1.04680	−0.523398	+	0.852088i	$0.675336\pi$
$878$	−0.556349	−0.0187759
$879$	8.68629	0.292981
$880$	15.0711	0.508046
$881$	6.62742	0.223283	0.111642	−	0.993749i	$-0.464389\pi$
$881$	6.62742	0.223283	0.111642	+	0.993749i	$0.464389\pi$
$882$	5.00000	0.168359
$883$	−38.8995	−1.30907	−0.654536	−	0.756031i	$-0.727136\pi$
$883$	−38.8995	−1.30907	−0.654536	+	0.756031i	$0.727136\pi$
$884$	−10.0000	−0.336336
$885$	18.4853	0.621376
$886$	−12.7574	−0.428592
$887$	54.4264	1.82746	0.913730	−	0.406322i	$-0.133189\pi$
$887$	54.4264	1.82746	0.913730	+	0.406322i	$0.133189\pi$
$888$	3.82843	0.128474
$889$	−0.485281	−0.0162758
$890$	3.41421	0.114445
$891$	4.41421	0.147882
$892$	6.58579	0.220508
$893$	−68.5269	−2.29317
$894$	13.4853	0.451015
$895$	−38.6274	−1.29117
$896$	−1.41421	−0.0472456
$897$	5.07107	0.169318
$898$	−33.9411	−1.13263
$899$	−9.24264	−0.308259
$900$	6.65685	0.221895
$901$	−44.1421	−1.47059
$902$	27.5563	0.917526
$903$	−14.8284	−0.493459
$904$	−3.82843	−0.127332
$905$	32.3848	1.07651
$906$	15.2426	0.506403
$907$	48.2843	1.60325	0.801626	−	0.597825i	$-0.203968\pi$
$907$	48.2843	1.60325	0.801626	+	0.597825i	$0.203968\pi$
$908$	−2.75736	−0.0915062
$909$	−14.0000	−0.464351
$910$	−6.82843	−0.226360
$911$	−52.2843	−1.73226	−0.866128	−	0.499823i	$-0.833398\pi$
$911$	−52.2843	−1.73226	−0.866128	+	0.499823i	$0.833398\pi$
$912$	−5.24264	−0.173601
$913$	52.9706	1.75307
$914$	−14.3848	−0.475806
$915$	−13.6569	−0.451482
$916$	−15.3137	−0.505979
$917$	18.3431	0.605744
$918$	7.07107	0.233380
$919$	2.07107	0.0683182	0.0341591	−	0.999416i	$-0.489125\pi$
$919$	2.07107	0.0683182	0.0341591	+	0.999416i	$0.489125\pi$
$920$	−12.2426	−0.403628
$921$	21.5563	0.710306
$922$	23.4853	0.773447
$923$	−0.343146	−0.0112948
$924$	6.24264	0.205368
$925$	−25.4853	−0.837951
$926$	−1.24264	−0.0408357
$927$	−1.00000	−0.0328443
$928$	−1.00000	−0.0328266
$929$	2.68629	0.0881344	0.0440672	−	0.999029i	$-0.485968\pi$
$929$	2.68629	0.0881344	0.0440672	+	0.999029i	$0.485968\pi$
$930$	31.5563	1.03477
$931$	26.2132	0.859103
$932$	7.31371	0.239568
$933$	4.34315	0.142188
$934$	4.82843	0.157991
$935$	−106.569	−3.48516
$936$	−1.41421	−0.0462250
$937$	−35.6569	−1.16486	−0.582429	−	0.812881i	$-0.697898\pi$
$937$	−35.6569	−1.16486	−0.582429	+	0.812881i	$0.697898\pi$
$938$	−4.82843	−0.157654
$939$	−2.65685	−0.0867032
$940$	44.6274	1.45559
$941$	57.4853	1.87397	0.936983	−	0.349374i	$-0.113606\pi$
$941$	57.4853	1.87397	0.936983	+	0.349374i	$0.113606\pi$
$942$	−8.48528	−0.276465
$943$	−22.3848	−0.728949
$944$	5.41421	0.176218
$945$	4.82843	0.157069
$946$	46.2843	1.50483
$947$	44.5563	1.44789	0.723943	−	0.689859i	$-0.242328\pi$
$947$	44.5563	1.44789	0.723943	+	0.689859i	$0.242328\pi$
$948$	16.1421	0.524272
$949$	14.4853	0.470212
$950$	34.8995	1.13229
$951$	19.7990	0.642026
$952$	10.0000	0.324102
$953$	35.6569	1.15504	0.577519	−	0.816377i	$-0.304021\pi$
$953$	35.6569	1.15504	0.577519	+	0.816377i	$0.304021\pi$
$954$	−6.24264	−0.202113
$955$	−3.65685	−0.118333
$956$	18.4142	0.595558
$957$	4.41421	0.142691
$958$	32.8701	1.06198
$959$	−11.3137	−0.365339
$960$	3.41421	0.110193
$961$	54.4264	1.75569
$962$	5.41421	0.174561
$963$	−19.3137	−0.622376
$964$	23.3137	0.750884
$965$	−10.4853	−0.337533
$966$	−5.07107	−0.163159
$967$	−42.3431	−1.36166	−0.680832	−	0.732440i	$-0.738382\pi$
$967$	−42.3431	−1.36166	−0.680832	+	0.732440i	$0.738382\pi$
$968$	−8.48528	−0.272727
$969$	37.0711	1.19089
$970$	25.5563	0.820565
$971$	12.9706	0.416245	0.208123	−	0.978103i	$-0.433265\pi$
$971$	12.9706	0.416245	0.208123	+	0.978103i	$0.433265\pi$
$972$	1.00000	0.0320750
$973$	17.7574	0.569275
$974$	19.3137	0.618851
$975$	9.41421	0.301496
$976$	−4.00000	−0.128037
$977$	12.2843	0.393009	0.196504	−	0.980503i	$-0.437041\pi$
$977$	12.2843	0.393009	0.196504	+	0.980503i	$0.437041\pi$
$978$	13.3848	0.427998
$979$	−4.41421	−0.141079
$980$	−17.0711	−0.545315
$981$	−16.4853	−0.526335
$982$	−8.10051	−0.258498
$983$	−28.2132	−0.899861	−0.449931	−	0.893063i	$-0.648551\pi$
$983$	−28.2132	−0.899861	−0.449931	+	0.893063i	$0.648551\pi$
$984$	6.24264	0.199008
$985$	−21.6569	−0.690045
$986$	7.07107	0.225189
$987$	18.4853	0.588393
$988$	−7.41421	−0.235878
$989$	−37.5980	−1.19555
$990$	−15.0711	−0.478990
$991$	−56.9706	−1.80973	−0.904865	−	0.425699i	$-0.860028\pi$
$991$	−56.9706	−1.80973	−0.904865	+	0.425699i	$0.860028\pi$
$992$	9.24264	0.293454
$993$	−8.82843	−0.280162
$994$	0.343146	0.0108839
$995$	73.9411	2.34409
$996$	12.0000	0.380235
$997$	18.8579	0.597235	0.298617	−	0.954373i	$-0.403475\pi$
$997$	18.8579	0.597235	0.298617	+	0.954373i	$0.403475\pi$
$998$	−21.0711	−0.666993
$999$	−3.82843	−0.121126

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	618.2.a.i.1.2	✓	2
3.2	odd	2		1854.2.a.l.1.1		2
4.3	odd	2		4944.2.a.q.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
618.2.a.i.1.2	✓	2	1.1	even	1	trivial
1854.2.a.l.1.1		2	3.2	odd	2
4944.2.a.q.1.2		2	4.3	odd	2

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:	\( N \)	\(=\)	\( 618 = 2 \cdot 3 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	618.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.41421 q^{5} -1.00000 q^{6} +1.41421 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.41421 q^{5} -1.00000 q^{6} +1.41421 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.41421 q^{10} +4.41421 q^{11} +1.00000 q^{12} +1.41421 q^{13} -1.41421 q^{14} +3.41421 q^{15} +1.00000 q^{16} -7.07107 q^{17} -1.00000 q^{18} -5.24264 q^{19} +3.41421 q^{20} +1.41421 q^{21} -4.41421 q^{22} +3.58579 q^{23} -1.00000 q^{24} +6.65685 q^{25} -1.41421 q^{26} +1.00000 q^{27} +1.41421 q^{28} +1.00000 q^{29} -3.41421 q^{30} -9.24264 q^{31} -1.00000 q^{32} +4.41421 q^{33} +7.07107 q^{34} +4.82843 q^{35} +1.00000 q^{36} -3.82843 q^{37} +5.24264 q^{38} +1.41421 q^{39} -3.41421 q^{40} -6.24264 q^{41} -1.41421 q^{42} -10.4853 q^{43} +4.41421 q^{44} +3.41421 q^{45} -3.58579 q^{46} +13.0711 q^{47} +1.00000 q^{48} -5.00000 q^{49} -6.65685 q^{50} -7.07107 q^{51} +1.41421 q^{52} +6.24264 q^{53} -1.00000 q^{54} +15.0711 q^{55} -1.41421 q^{56} -5.24264 q^{57} -1.00000 q^{58} +5.41421 q^{59} +3.41421 q^{60} -4.00000 q^{61} +9.24264 q^{62} +1.41421 q^{63} +1.00000 q^{64} +4.82843 q^{65} -4.41421 q^{66} +3.41421 q^{67} -7.07107 q^{68} +3.58579 q^{69} -4.82843 q^{70} -0.242641 q^{71} -1.00000 q^{72} +10.2426 q^{73} +3.82843 q^{74} +6.65685 q^{75} -5.24264 q^{76} +6.24264 q^{77} -1.41421 q^{78} +16.1421 q^{79} +3.41421 q^{80} +1.00000 q^{81} +6.24264 q^{82} +12.0000 q^{83} +1.41421 q^{84} -24.1421 q^{85} +10.4853 q^{86} +1.00000 q^{87} -4.41421 q^{88} -1.00000 q^{89} -3.41421 q^{90} +2.00000 q^{91} +3.58579 q^{92} -9.24264 q^{93} -13.0711 q^{94} -17.8995 q^{95} -1.00000 q^{96} -7.48528 q^{97} +5.00000 q^{98} +4.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} - 4 q^{10} + 6 q^{11} + 2 q^{12} + 4 q^{15} + 2 q^{16} - 2 q^{18} - 2 q^{19} + 4 q^{20} - 6 q^{22} + 10 q^{23} - 2 q^{24} + 2 q^{25} + 2 q^{27} + 2 q^{29} - 4 q^{30} - 10 q^{31} - 2 q^{32} + 6 q^{33} + 4 q^{35} + 2 q^{36} - 2 q^{37} + 2 q^{38} - 4 q^{40} - 4 q^{41} - 4 q^{43} + 6 q^{44} + 4 q^{45} - 10 q^{46} + 12 q^{47} + 2 q^{48} - 10 q^{49} - 2 q^{50} + 4 q^{53} - 2 q^{54} + 16 q^{55} - 2 q^{57} - 2 q^{58} + 8 q^{59} + 4 q^{60} - 8 q^{61} + 10 q^{62} + 2 q^{64} + 4 q^{65} - 6 q^{66} + 4 q^{67} + 10 q^{69} - 4 q^{70} + 8 q^{71} - 2 q^{72} + 12 q^{73} + 2 q^{74} + 2 q^{75} - 2 q^{76} + 4 q^{77} + 4 q^{79} + 4 q^{80} + 2 q^{81} + 4 q^{82} + 24 q^{83} - 20 q^{85} + 4 q^{86} + 2 q^{87} - 6 q^{88} - 2 q^{89} - 4 q^{90} + 4 q^{91} + 10 q^{92} - 10 q^{93} - 12 q^{94} - 16 q^{95} - 2 q^{96} + 2 q^{97} + 10 q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 - 4 * q^10 + 6 * q^11 + 2 * q^12 + 4 * q^15 + 2 * q^16 - 2 * q^18 - 2 * q^19 + 4 * q^20 - 6 * q^22 + 10 * q^23 - 2 * q^24 + 2 * q^25 + 2 * q^27 + 2 * q^29 - 4 * q^30 - 10 * q^31 - 2 * q^32 + 6 * q^33 + 4 * q^35 + 2 * q^36 - 2 * q^37 + 2 * q^38 - 4 * q^40 - 4 * q^41 - 4 * q^43 + 6 * q^44 + 4 * q^45 - 10 * q^46 + 12 * q^47 + 2 * q^48 - 10 * q^49 - 2 * q^50 + 4 * q^53 - 2 * q^54 + 16 * q^55 - 2 * q^57 - 2 * q^58 + 8 * q^59 + 4 * q^60 - 8 * q^61 + 10 * q^62 + 2 * q^64 + 4 * q^65 - 6 * q^66 + 4 * q^67 + 10 * q^69 - 4 * q^70 + 8 * q^71 - 2 * q^72 + 12 * q^73 + 2 * q^74 + 2 * q^75 - 2 * q^76 + 4 * q^77 + 4 * q^79 + 4 * q^80 + 2 * q^81 + 4 * q^82 + 24 * q^83 - 20 * q^85 + 4 * q^86 + 2 * q^87 - 6 * q^88 - 2 * q^89 - 4 * q^90 + 4 * q^91 + 10 * q^92 - 10 * q^93 - 12 * q^94 - 16 * q^95 - 2 * q^96 + 2 * q^97 + 10 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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