LMFDB - Embedded newform 483.2.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(1,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("483.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$483 = 3 \cdot 7 \cdot 23$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	483.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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{2} - x - 1$ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	483.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.618034 q^{2} +1.00000 q^{3} -1.61803 q^{4} +3.61803 q^{5} +0.618034 q^{6} +1.00000 q^{7} -2.23607 q^{8} +1.00000 q^{9} +2.23607 q^{10} +1.00000 q^{11} -1.61803 q^{12} +0.618034 q^{13} +0.618034 q^{14} +3.61803 q^{15} +1.85410 q^{16} -5.47214 q^{17} +0.618034 q^{18} +4.23607 q^{19} -5.85410 q^{20} +1.00000 q^{21} +0.618034 q^{22} +1.00000 q^{23} -2.23607 q^{24} +8.09017 q^{25} +0.381966 q^{26} +1.00000 q^{27} -1.61803 q^{28} +1.76393 q^{29} +2.23607 q^{30} -8.70820 q^{31} +5.61803 q^{32} +1.00000 q^{33} -3.38197 q^{34} +3.61803 q^{35} -1.61803 q^{36} +0.236068 q^{37} +2.61803 q^{38} +0.618034 q^{39} -8.09017 q^{40} -3.47214 q^{41} +0.618034 q^{42} -3.85410 q^{43} -1.61803 q^{44} +3.61803 q^{45} +0.618034 q^{46} +11.7082 q^{47} +1.85410 q^{48} +1.00000 q^{49} +5.00000 q^{50} -5.47214 q^{51} -1.00000 q^{52} -0.0901699 q^{53} +0.618034 q^{54} +3.61803 q^{55} -2.23607 q^{56} +4.23607 q^{57} +1.09017 q^{58} -3.61803 q^{59} -5.85410 q^{60} -7.85410 q^{61} -5.38197 q^{62} +1.00000 q^{63} -0.236068 q^{64} +2.23607 q^{65} +0.618034 q^{66} -8.09017 q^{67} +8.85410 q^{68} +1.00000 q^{69} +2.23607 q^{70} -10.3262 q^{71} -2.23607 q^{72} +1.76393 q^{73} +0.145898 q^{74} +8.09017 q^{75} -6.85410 q^{76} +1.00000 q^{77} +0.381966 q^{78} -14.2361 q^{79} +6.70820 q^{80} +1.00000 q^{81} -2.14590 q^{82} -17.9443 q^{83} -1.61803 q^{84} -19.7984 q^{85} -2.38197 q^{86} +1.76393 q^{87} -2.23607 q^{88} +13.5623 q^{89} +2.23607 q^{90} +0.618034 q^{91} -1.61803 q^{92} -8.70820 q^{93} +7.23607 q^{94} +15.3262 q^{95} +5.61803 q^{96} +6.70820 q^{97} +0.618034 q^{98} +1.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q - q^{2} + 2 q^{3} - q^{4} + 5 q^{5} - q^{6} + 2 q^{7} + 2 q^{9} + 2 q^{11} - q^{12} - q^{13} - q^{14} + 5 q^{15} - 3 q^{16} - 2 q^{17} - q^{18} + 4 q^{19} - 5 q^{20} + 2 q^{21} - q^{22} + 2 q^{23}+ \cdots + 2 q^{99}+O(q^{100})$ 2 * q - q^2 + 2 * q^3 - q^4 + 5 * q^5 - q^6 + 2 * q^7 + 2 * q^9 + 2 * q^11 - q^12 - q^13 - q^14 + 5 * q^15 - 3 * q^16 - 2 * q^17 - q^18 + 4 * q^19 - 5 * q^20 + 2 * q^21 - q^22 + 2 * q^23 + 5 * q^25 + 3 * q^26 + 2 * q^27 - q^28 + 8 * q^29 - 4 * q^31 + 9 * q^32 + 2 * q^33 - 9 * q^34 + 5 * q^35 - q^36 - 4 * q^37 + 3 * q^38 - q^39 - 5 * q^40 + 2 * q^41 - q^42 - q^43 - q^44 + 5 * q^45 - q^46 + 10 * q^47 - 3 * q^48 + 2 * q^49 + 10 * q^50 - 2 * q^51 - 2 * q^52 + 11 * q^53 - q^54 + 5 * q^55 + 4 * q^57 - 9 * q^58 - 5 * q^59 - 5 * q^60 - 9 * q^61 - 13 * q^62 + 2 * q^63 + 4 * q^64 - q^66 - 5 * q^67 + 11 * q^68 + 2 * q^69 - 5 * q^71 + 8 * q^73 + 7 * q^74 + 5 * q^75 - 7 * q^76 + 2 * q^77 + 3 * q^78 - 24 * q^79 + 2 * q^81 - 11 * q^82 - 18 * q^83 - q^84 - 15 * q^85 - 7 * q^86 + 8 * q^87 + 7 * q^89 - q^91 - q^92 - 4 * q^93 + 10 * q^94 + 15 * q^95 + 9 * q^96 - q^98 + 2 * q^99

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

)

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

$2$	0.618034	0.437016	0.218508	−	0.975835i	$-0.429881\pi$
$2$	0.618034	0.437016	0.218508	+	0.975835i	$0.429881\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.61803	−0.809017
$5$	3.61803	1.61803	0.809017	−	0.587785i	$-0.200000\pi$
$5$	3.61803	1.61803	0.809017	+	0.587785i	$0.200000\pi$
$6$	0.618034	0.252311
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.23607	−0.790569
$9$	1.00000	0.333333
$10$	2.23607	0.707107
$11$	1.00000	0.301511	0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000	0.301511	0.150756	+	0.988571i	$0.451829\pi$
$12$	−1.61803	−0.467086
$13$	0.618034	0.171412	0.0857059	−	0.996320i	$-0.472685\pi$
$13$	0.618034	0.171412	0.0857059	+	0.996320i	$0.472685\pi$
$14$	0.618034	0.165177
$15$	3.61803	0.934172
$16$	1.85410	0.463525
$17$	−5.47214	−1.32719	−0.663594	−	0.748093i	$-0.730970\pi$
$17$	−5.47214	−1.32719	−0.663594	+	0.748093i	$0.730970\pi$
$18$	0.618034	0.145672
$19$	4.23607	0.971821	0.485910	−	0.874009i	$-0.338488\pi$
$19$	4.23607	0.971821	0.485910	+	0.874009i	$0.338488\pi$
$20$	−5.85410	−1.30902
$21$	1.00000	0.218218
$22$	0.618034	0.131765
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.23607	−0.456435
$25$	8.09017	1.61803
$26$	0.381966	0.0749097
$27$	1.00000	0.192450
$28$	−1.61803	−0.305780
$29$	1.76393	0.327554	0.163777	−	0.986497i	$-0.447632\pi$
$29$	1.76393	0.327554	0.163777	+	0.986497i	$0.447632\pi$
$30$	2.23607	0.408248
$31$	−8.70820	−1.56404	−0.782020	−	0.623254i	$-0.785810\pi$
$31$	−8.70820	−1.56404	−0.782020	+	0.623254i	$0.785810\pi$
$32$	5.61803	0.993137
$33$	1.00000	0.174078
$34$	−3.38197	−0.580002
$35$	3.61803	0.611559
$36$	−1.61803	−0.269672
$37$	0.236068	0.0388093	0.0194047	−	0.999812i	$-0.493823\pi$
$37$	0.236068	0.0388093	0.0194047	+	0.999812i	$0.493823\pi$
$38$	2.61803	0.424701
$39$	0.618034	0.0989646
$40$	−8.09017	−1.27917
$41$	−3.47214	−0.542257	−0.271128	−	0.962543i	$-0.587397\pi$
$41$	−3.47214	−0.542257	−0.271128	+	0.962543i	$0.587397\pi$
$42$	0.618034	0.0953647
$43$	−3.85410	−0.587745	−0.293873	−	0.955845i	$-0.594944\pi$
$43$	−3.85410	−0.587745	−0.293873	+	0.955845i	$0.594944\pi$
$44$	−1.61803	−0.243928
$45$	3.61803	0.539345
$46$	0.618034	0.0911241
$47$	11.7082	1.70782	0.853909	−	0.520423i	$-0.174226\pi$
$47$	11.7082	1.70782	0.853909	+	0.520423i	$0.174226\pi$
$48$	1.85410	0.267617
$49$	1.00000	0.142857
$50$	5.00000	0.707107
$51$	−5.47214	−0.766252
$52$	−1.00000	−0.138675
$53$	−0.0901699	−0.0123858	−0.00619290	−	0.999981i	$-0.501971\pi$
$53$	−0.0901699	−0.0123858	−0.00619290	+	0.999981i	$0.501971\pi$
$54$	0.618034	0.0841038
$55$	3.61803	0.487856
$56$	−2.23607	−0.298807
$57$	4.23607	0.561081
$58$	1.09017	0.143146
$59$	−3.61803	−0.471028	−0.235514	−	0.971871i	$-0.575677\pi$
$59$	−3.61803	−0.471028	−0.235514	+	0.971871i	$0.575677\pi$
$60$	−5.85410	−0.755761
$61$	−7.85410	−1.00561	−0.502807	−	0.864398i	$-0.667699\pi$
$61$	−7.85410	−1.00561	−0.502807	+	0.864398i	$0.667699\pi$
$62$	−5.38197	−0.683510
$63$	1.00000	0.125988
$64$	−0.236068	−0.0295085
$65$	2.23607	0.277350
$66$	0.618034	0.0760747
$67$	−8.09017	−0.988372	−0.494186	−	0.869356i	$-0.664534\pi$
$67$	−8.09017	−0.988372	−0.494186	+	0.869356i	$0.664534\pi$
$68$	8.85410	1.07372
$69$	1.00000	0.120386
$70$	2.23607	0.267261
$71$	−10.3262	−1.22550	−0.612749	−	0.790277i	$-0.709937\pi$
$71$	−10.3262	−1.22550	−0.612749	+	0.790277i	$0.709937\pi$
$72$	−2.23607	−0.263523
$73$	1.76393	0.206453	0.103226	−	0.994658i	$-0.467083\pi$
$73$	1.76393	0.206453	0.103226	+	0.994658i	$0.467083\pi$
$74$	0.145898	0.0169603
$75$	8.09017	0.934172
$76$	−6.85410	−0.786219
$77$	1.00000	0.113961
$78$	0.381966	0.0432491
$79$	−14.2361	−1.60168	−0.800841	−	0.598877i	$-0.795614\pi$
$79$	−14.2361	−1.60168	−0.800841	+	0.598877i	$0.795614\pi$
$80$	6.70820	0.750000
$81$	1.00000	0.111111
$82$	−2.14590	−0.236975
$83$	−17.9443	−1.96964	−0.984820	−	0.173579i	$-0.944467\pi$
$83$	−17.9443	−1.96964	−0.984820	+	0.173579i	$0.944467\pi$
$84$	−1.61803	−0.176542
$85$	−19.7984	−2.14744
$86$	−2.38197	−0.256854
$87$	1.76393	0.189113
$88$	−2.23607	−0.238366
$89$	13.5623	1.43760	0.718801	−	0.695216i	$-0.244691\pi$
$89$	13.5623	1.43760	0.718801	+	0.695216i	$0.244691\pi$
$90$	2.23607	0.235702
$91$	0.618034	0.0647876
$92$	−1.61803	−0.168692
$93$	−8.70820	−0.902999
$94$	7.23607	0.746343
$95$	15.3262	1.57244
$96$	5.61803	0.573388
$97$	6.70820	0.681115	0.340557	−	0.940224i	$-0.389384\pi$
$97$	6.70820	0.681115	0.340557	+	0.940224i	$0.389384\pi$
$98$	0.618034	0.0624309
$99$	1.00000	0.100504
$100$	−13.0902	−1.30902
$101$	2.09017	0.207980	0.103990	−	0.994578i	$-0.466839\pi$
$101$	2.09017	0.207980	0.103990	+	0.994578i	$0.466839\pi$
$102$	−3.38197	−0.334865
$103$	−18.4721	−1.82011	−0.910057	−	0.414484i	$-0.863962\pi$
$103$	−18.4721	−1.82011	−0.910057	+	0.414484i	$0.863962\pi$
$104$	−1.38197	−0.135513
$105$	3.61803	0.353084
$106$	−0.0557281	−0.00541279
$107$	−2.90983	−0.281304	−0.140652	−	0.990059i	$-0.544920\pi$
$107$	−2.90983	−0.281304	−0.140652	+	0.990059i	$0.544920\pi$
$108$	−1.61803	−0.155695
$109$	2.38197	0.228151	0.114075	−	0.993472i	$-0.463609\pi$
$109$	2.38197	0.228151	0.114075	+	0.993472i	$0.463609\pi$
$110$	2.23607	0.213201
$111$	0.236068	0.0224066
$112$	1.85410	0.175196
$113$	14.0902	1.32549	0.662746	−	0.748844i	$-0.269391\pi$
$113$	14.0902	1.32549	0.662746	+	0.748844i	$0.269391\pi$
$114$	2.61803	0.245201
$115$	3.61803	0.337383
$116$	−2.85410	−0.264997
$117$	0.618034	0.0571373
$118$	−2.23607	−0.205847
$119$	−5.47214	−0.501630
$120$	−8.09017	−0.738528
$121$	−10.0000	−0.909091
$122$	−4.85410	−0.439470
$123$	−3.47214	−0.313072
$124$	14.0902	1.26533
$125$	11.1803	1.00000
$126$	0.618034	0.0550588
$127$	−7.85410	−0.696939	−0.348469	−	0.937320i	$-0.613298\pi$
$127$	−7.85410	−0.696939	−0.348469	+	0.937320i	$0.613298\pi$
$128$	−11.3820	−1.00603
$129$	−3.85410	−0.339335
$130$	1.38197	0.121206
$131$	−3.29180	−0.287606	−0.143803	−	0.989606i	$-0.545933\pi$
$131$	−3.29180	−0.287606	−0.143803	+	0.989606i	$0.545933\pi$
$132$	−1.61803	−0.140832
$133$	4.23607	0.367314
$134$	−5.00000	−0.431934
$135$	3.61803	0.311391
$136$	12.2361	1.04923
$137$	15.1803	1.29694	0.648472	−	0.761239i	$-0.275408\pi$
$137$	15.1803	1.29694	0.648472	+	0.761239i	$0.275408\pi$
$138$	0.618034	0.0526105
$139$	21.0344	1.78412	0.892059	−	0.451919i	$-0.149260\pi$
$139$	21.0344	1.78412	0.892059	+	0.451919i	$0.149260\pi$
$140$	−5.85410	−0.494762
$141$	11.7082	0.986009
$142$	−6.38197	−0.535563
$143$	0.618034	0.0516826
$144$	1.85410	0.154508
$145$	6.38197	0.529993
$146$	1.09017	0.0902231
$147$	1.00000	0.0824786
$148$	−0.381966	−0.0313974
$149$	3.70820	0.303788	0.151894	−	0.988397i	$-0.451463\pi$
$149$	3.70820	0.303788	0.151894	+	0.988397i	$0.451463\pi$
$150$	5.00000	0.408248
$151$	8.65248	0.704128	0.352064	−	0.935976i	$-0.385480\pi$
$151$	8.65248	0.704128	0.352064	+	0.935976i	$0.385480\pi$
$152$	−9.47214	−0.768292
$153$	−5.47214	−0.442396
$154$	0.618034	0.0498026
$155$	−31.5066	−2.53067
$156$	−1.00000	−0.0800641
$157$	8.76393	0.699438	0.349719	−	0.936855i	$-0.386277\pi$
$157$	8.76393	0.699438	0.349719	+	0.936855i	$0.386277\pi$
$158$	−8.79837	−0.699961
$159$	−0.0901699	−0.00715094
$160$	20.3262	1.60693
$161$	1.00000	0.0788110
$162$	0.618034	0.0485573
$163$	−20.2705	−1.58771	−0.793854	−	0.608108i	$-0.791929\pi$
$163$	−20.2705	−1.58771	−0.793854	+	0.608108i	$0.791929\pi$
$164$	5.61803	0.438695
$165$	3.61803	0.281664
$166$	−11.0902	−0.860764
$167$	10.7082	0.828626	0.414313	−	0.910135i	$-0.364022\pi$
$167$	10.7082	0.828626	0.414313	+	0.910135i	$0.364022\pi$
$168$	−2.23607	−0.172516
$169$	−12.6180	−0.970618
$170$	−12.2361	−0.938464
$171$	4.23607	0.323940
$172$	6.23607	0.475496
$173$	−6.41641	−0.487830	−0.243915	−	0.969797i	$-0.578432\pi$
$173$	−6.41641	−0.487830	−0.243915	+	0.969797i	$0.578432\pi$
$174$	1.09017	0.0826456
$175$	8.09017	0.611559
$176$	1.85410	0.139758
$177$	−3.61803	−0.271948
$178$	8.38197	0.628255
$179$	−13.7984	−1.03134	−0.515669	−	0.856788i	$-0.672457\pi$
$179$	−13.7984	−1.03134	−0.515669	+	0.856788i	$0.672457\pi$
$180$	−5.85410	−0.436339
$181$	−3.18034	−0.236393	−0.118196	−	0.992990i	$-0.537711\pi$
$181$	−3.18034	−0.236393	−0.118196	+	0.992990i	$0.537711\pi$
$182$	0.381966	0.0283132
$183$	−7.85410	−0.580592
$184$	−2.23607	−0.164845
$185$	0.854102	0.0627948
$186$	−5.38197	−0.394625
$187$	−5.47214	−0.400162
$188$	−18.9443	−1.38165
$189$	1.00000	0.0727393
$190$	9.47214	0.687181
$191$	14.1803	1.02605	0.513027	−	0.858373i	$-0.328524\pi$
$191$	14.1803	1.02605	0.513027	+	0.858373i	$0.328524\pi$
$192$	−0.236068	−0.0170367
$193$	0.763932	0.0549890	0.0274945	−	0.999622i	$-0.491247\pi$
$193$	0.763932	0.0549890	0.0274945	+	0.999622i	$0.491247\pi$
$194$	4.14590	0.297658
$195$	2.23607	0.160128
$196$	−1.61803	−0.115574
$197$	11.5623	0.823780	0.411890	−	0.911234i	$-0.364869\pi$
$197$	11.5623	0.823780	0.411890	+	0.911234i	$0.364869\pi$
$198$	0.618034	0.0439218
$199$	1.43769	0.101915	0.0509577	−	0.998701i	$-0.483773\pi$
$199$	1.43769	0.101915	0.0509577	+	0.998701i	$0.483773\pi$
$200$	−18.0902	−1.27917
$201$	−8.09017	−0.570637
$202$	1.29180	0.0908905
$203$	1.76393	0.123804
$204$	8.85410	0.619911
$205$	−12.5623	−0.877390
$206$	−11.4164	−0.795419
$207$	1.00000	0.0695048
$208$	1.14590	0.0794537
$209$	4.23607	0.293015
$210$	2.23607	0.154303
$211$	8.88854	0.611913	0.305956	−	0.952046i	$-0.401024\pi$
$211$	8.88854	0.611913	0.305956	+	0.952046i	$0.401024\pi$
$212$	0.145898	0.0100203
$213$	−10.3262	−0.707542
$214$	−1.79837	−0.122934
$215$	−13.9443	−0.950991
$216$	−2.23607	−0.152145
$217$	−8.70820	−0.591151
$218$	1.47214	0.0997056
$219$	1.76393	0.119195
$220$	−5.85410	−0.394683
$221$	−3.38197	−0.227496
$222$	0.145898	0.00979203
$223$	1.61803	0.108352	0.0541758	−	0.998531i	$-0.482747\pi$
$223$	1.61803	0.108352	0.0541758	+	0.998531i	$0.482747\pi$
$224$	5.61803	0.375371
$225$	8.09017	0.539345
$226$	8.70820	0.579261
$227$	23.9787	1.59152	0.795762	−	0.605610i	$-0.207071\pi$
$227$	23.9787	1.59152	0.795762	+	0.605610i	$0.207071\pi$
$228$	−6.85410	−0.453924
$229$	27.7984	1.83697	0.918484	−	0.395458i	$-0.129414\pi$
$229$	27.7984	1.83697	0.918484	+	0.395458i	$0.129414\pi$
$230$	2.23607	0.147442
$231$	1.00000	0.0657952
$232$	−3.94427	−0.258954
$233$	8.67376	0.568237	0.284119	−	0.958789i	$-0.408299\pi$
$233$	8.67376	0.568237	0.284119	+	0.958789i	$0.408299\pi$
$234$	0.381966	0.0249699
$235$	42.3607	2.76331
$236$	5.85410	0.381070
$237$	−14.2361	−0.924732
$238$	−3.38197	−0.219220
$239$	15.7984	1.02191	0.510956	−	0.859607i	$-0.329292\pi$
$239$	15.7984	1.02191	0.510956	+	0.859607i	$0.329292\pi$
$240$	6.70820	0.433013
$241$	−3.29180	−0.212043	−0.106022	−	0.994364i	$-0.533811\pi$
$241$	−3.29180	−0.212043	−0.106022	+	0.994364i	$0.533811\pi$
$242$	−6.18034	−0.397287
$243$	1.00000	0.0641500
$244$	12.7082	0.813559
$245$	3.61803	0.231148
$246$	−2.14590	−0.136817
$247$	2.61803	0.166582
$248$	19.4721	1.23648
$249$	−17.9443	−1.13717
$250$	6.90983	0.437016
$251$	17.7082	1.11773	0.558866	−	0.829258i	$-0.311237\pi$
$251$	17.7082	1.11773	0.558866	+	0.829258i	$0.311237\pi$
$252$	−1.61803	−0.101927
$253$	1.00000	0.0628695
$254$	−4.85410	−0.304573
$255$	−19.7984	−1.23982
$256$	−6.56231	−0.410144
$257$	23.7082	1.47888	0.739439	−	0.673224i	$-0.235091\pi$
$257$	23.7082	1.47888	0.739439	+	0.673224i	$0.235091\pi$
$258$	−2.38197	−0.148295
$259$	0.236068	0.0146686
$260$	−3.61803	−0.224381
$261$	1.76393	0.109185
$262$	−2.03444	−0.125688
$263$	21.6525	1.33515	0.667574	−	0.744543i	$-0.267333\pi$
$263$	21.6525	1.33515	0.667574	+	0.744543i	$0.267333\pi$
$264$	−2.23607	−0.137620
$265$	−0.326238	−0.0200406
$266$	2.61803	0.160522
$267$	13.5623	0.830000
$268$	13.0902	0.799609
$269$	15.7426	0.959846	0.479923	−	0.877311i	$-0.340665\pi$
$269$	15.7426	0.959846	0.479923	+	0.877311i	$0.340665\pi$
$270$	2.23607	0.136083
$271$	−15.4721	−0.939865	−0.469933	−	0.882702i	$-0.655722\pi$
$271$	−15.4721	−0.939865	−0.469933	+	0.882702i	$0.655722\pi$
$272$	−10.1459	−0.615185
$273$	0.618034	0.0374051
$274$	9.38197	0.566785
$275$	8.09017	0.487856
$276$	−1.61803	−0.0973942
$277$	−24.3262	−1.46162	−0.730811	−	0.682580i	$-0.760858\pi$
$277$	−24.3262	−1.46162	−0.730811	+	0.682580i	$0.760858\pi$
$278$	13.0000	0.779688
$279$	−8.70820	−0.521347
$280$	−8.09017	−0.483480
$281$	−14.6525	−0.874093	−0.437047	−	0.899439i	$-0.643976\pi$
$281$	−14.6525	−0.874093	−0.437047	+	0.899439i	$0.643976\pi$
$282$	7.23607	0.430902
$283$	25.3262	1.50549	0.752744	−	0.658313i	$-0.228730\pi$
$283$	25.3262	1.50549	0.752744	+	0.658313i	$0.228730\pi$
$284$	16.7082	0.991449
$285$	15.3262	0.907848
$286$	0.381966	0.0225861
$287$	−3.47214	−0.204954
$288$	5.61803	0.331046
$289$	12.9443	0.761428
$290$	3.94427	0.231616
$291$	6.70820	0.393242
$292$	−2.85410	−0.167024
$293$	−22.8328	−1.33391	−0.666954	−	0.745099i	$-0.732402\pi$
$293$	−22.8328	−1.33391	−0.666954	+	0.745099i	$0.732402\pi$
$294$	0.618034	0.0360445
$295$	−13.0902	−0.762139
$296$	−0.527864	−0.0306815
$297$	1.00000	0.0580259
$298$	2.29180	0.132760
$299$	0.618034	0.0357418
$300$	−13.0902	−0.755761
$301$	−3.85410	−0.222147
$302$	5.34752	0.307715
$303$	2.09017	0.120077
$304$	7.85410	0.450464
$305$	−28.4164	−1.62712
$306$	−3.38197	−0.193334
$307$	−34.1246	−1.94759	−0.973797	−	0.227418i	$-0.926972\pi$
$307$	−34.1246	−1.94759	−0.973797	+	0.227418i	$0.926972\pi$
$308$	−1.61803	−0.0921960
$309$	−18.4721	−1.05084
$310$	−19.4721	−1.10594
$311$	−10.5066	−0.595773	−0.297887	−	0.954601i	$-0.596282\pi$
$311$	−10.5066	−0.595773	−0.297887	+	0.954601i	$0.596282\pi$
$312$	−1.38197	−0.0782384
$313$	33.8885	1.91549	0.957747	−	0.287612i	$-0.0928615\pi$
$313$	33.8885	1.91549	0.957747	+	0.287612i	$0.0928615\pi$
$314$	5.41641	0.305666
$315$	3.61803	0.203853
$316$	23.0344	1.29579
$317$	−0.0901699	−0.00506445	−0.00253222	−	0.999997i	$-0.500806\pi$
$317$	−0.0901699	−0.00506445	−0.00253222	+	0.999997i	$0.500806\pi$
$318$	−0.0557281	−0.00312508
$319$	1.76393	0.0987612
$320$	−0.854102	−0.0477458
$321$	−2.90983	−0.162411
$322$	0.618034	0.0344417
$323$	−23.1803	−1.28979
$324$	−1.61803	−0.0898908
$325$	5.00000	0.277350
$326$	−12.5279	−0.693854
$327$	2.38197	0.131723
$328$	7.76393	0.428691
$329$	11.7082	0.645494
$330$	2.23607	0.123091
$331$	7.88854	0.433594	0.216797	−	0.976217i	$-0.430439\pi$
$331$	7.88854	0.433594	0.216797	+	0.976217i	$0.430439\pi$
$332$	29.0344	1.59347
$333$	0.236068	0.0129364
$334$	6.61803	0.362123
$335$	−29.2705	−1.59922
$336$	1.85410	0.101150
$337$	10.0344	0.546611	0.273305	−	0.961927i	$-0.411883\pi$
$337$	10.0344	0.546611	0.273305	+	0.961927i	$0.411883\pi$
$338$	−7.79837	−0.424176
$339$	14.0902	0.765273
$340$	32.0344	1.73731
$341$	−8.70820	−0.471576
$342$	2.61803	0.141567
$343$	1.00000	0.0539949
$344$	8.61803	0.464653
$345$	3.61803	0.194788
$346$	−3.96556	−0.213190
$347$	−7.29180	−0.391444	−0.195722	−	0.980659i	$-0.562705\pi$
$347$	−7.29180	−0.391444	−0.195722	+	0.980659i	$0.562705\pi$
$348$	−2.85410	−0.152996
$349$	−19.7984	−1.05978	−0.529891	−	0.848066i	$-0.677767\pi$
$349$	−19.7984	−1.05978	−0.529891	+	0.848066i	$0.677767\pi$
$350$	5.00000	0.267261
$351$	0.618034	0.0329882
$352$	5.61803	0.299442
$353$	6.41641	0.341511	0.170755	−	0.985313i	$-0.445379\pi$
$353$	6.41641	0.341511	0.170755	+	0.985313i	$0.445379\pi$
$354$	−2.23607	−0.118846
$355$	−37.3607	−1.98290
$356$	−21.9443	−1.16304
$357$	−5.47214	−0.289616
$358$	−8.52786	−0.450712
$359$	8.56231	0.451901	0.225951	−	0.974139i	$-0.427451\pi$
$359$	8.56231	0.451901	0.225951	+	0.974139i	$0.427451\pi$
$360$	−8.09017	−0.426389
$361$	−1.05573	−0.0555646
$362$	−1.96556	−0.103307
$363$	−10.0000	−0.524864
$364$	−1.00000	−0.0524142
$365$	6.38197	0.334047
$366$	−4.85410	−0.253728
$367$	13.2705	0.692715	0.346357	−	0.938103i	$-0.387418\pi$
$367$	13.2705	0.692715	0.346357	+	0.938103i	$0.387418\pi$
$368$	1.85410	0.0966517
$369$	−3.47214	−0.180752
$370$	0.527864	0.0274423
$371$	−0.0901699	−0.00468139
$372$	14.0902	0.730541
$373$	34.1246	1.76691	0.883453	−	0.468520i	$-0.155213\pi$
$373$	34.1246	1.76691	0.883453	+	0.468520i	$0.155213\pi$
$374$	−3.38197	−0.174877
$375$	11.1803	0.577350
$376$	−26.1803	−1.35015
$377$	1.09017	0.0561466
$378$	0.618034	0.0317882
$379$	−25.5279	−1.31128	−0.655639	−	0.755074i	$-0.727601\pi$
$379$	−25.5279	−1.31128	−0.655639	+	0.755074i	$0.727601\pi$
$380$	−24.7984	−1.27213
$381$	−7.85410	−0.402378
$382$	8.76393	0.448402
$383$	−3.94427	−0.201543	−0.100771	−	0.994910i	$-0.532131\pi$
$383$	−3.94427	−0.201543	−0.100771	+	0.994910i	$0.532131\pi$
$384$	−11.3820	−0.580834
$385$	3.61803	0.184392
$386$	0.472136	0.0240311
$387$	−3.85410	−0.195915
$388$	−10.8541	−0.551034
$389$	−19.9443	−1.01121	−0.505607	−	0.862764i	$-0.668732\pi$
$389$	−19.9443	−1.01121	−0.505607	+	0.862764i	$0.668732\pi$
$390$	1.38197	0.0699786
$391$	−5.47214	−0.276738
$392$	−2.23607	−0.112938
$393$	−3.29180	−0.166049
$394$	7.14590	0.360005
$395$	−51.5066	−2.59158
$396$	−1.61803	−0.0813093
$397$	22.1803	1.11320	0.556600	−	0.830781i	$-0.312106\pi$
$397$	22.1803	1.11320	0.556600	+	0.830781i	$0.312106\pi$
$398$	0.888544	0.0445387
$399$	4.23607	0.212069
$400$	15.0000	0.750000
$401$	−5.00000	−0.249688	−0.124844	−	0.992176i	$-0.539843\pi$
$401$	−5.00000	−0.249688	−0.124844	+	0.992176i	$0.539843\pi$
$402$	−5.00000	−0.249377
$403$	−5.38197	−0.268095
$404$	−3.38197	−0.168259
$405$	3.61803	0.179782
$406$	1.09017	0.0541042
$407$	0.236068	0.0117015
$408$	12.2361	0.605776
$409$	−24.8885	−1.23066	−0.615330	−	0.788270i	$-0.710977\pi$
$409$	−24.8885	−1.23066	−0.615330	+	0.788270i	$0.710977\pi$
$410$	−7.76393	−0.383433
$411$	15.1803	0.748791
$412$	29.8885	1.47250
$413$	−3.61803	−0.178032
$414$	0.618034	0.0303747
$415$	−64.9230	−3.18694
$416$	3.47214	0.170235
$417$	21.0344	1.03006
$418$	2.61803	0.128052
$419$	13.9098	0.679540	0.339770	−	0.940509i	$-0.389651\pi$
$419$	13.9098	0.679540	0.339770	+	0.940509i	$0.389651\pi$
$420$	−5.85410	−0.285651
$421$	−29.5623	−1.44078	−0.720389	−	0.693570i	$-0.756037\pi$
$421$	−29.5623	−1.44078	−0.720389	+	0.693570i	$0.756037\pi$
$422$	5.49342	0.267416
$423$	11.7082	0.569272
$424$	0.201626	0.00979183
$425$	−44.2705	−2.14744
$426$	−6.38197	−0.309207
$427$	−7.85410	−0.380087
$428$	4.70820	0.227580
$429$	0.618034	0.0298390
$430$	−8.61803	−0.415599
$431$	11.2705	0.542881	0.271441	−	0.962455i	$-0.412500\pi$
$431$	11.2705	0.542881	0.271441	+	0.962455i	$0.412500\pi$
$432$	1.85410	0.0892055
$433$	20.7639	0.997851	0.498925	−	0.866645i	$-0.333728\pi$
$433$	20.7639	0.997851	0.498925	+	0.866645i	$0.333728\pi$
$434$	−5.38197	−0.258343
$435$	6.38197	0.305992
$436$	−3.85410	−0.184578
$437$	4.23607	0.202639
$438$	1.09017	0.0520903
$439$	9.18034	0.438154	0.219077	−	0.975708i	$-0.429695\pi$
$439$	9.18034	0.438154	0.219077	+	0.975708i	$0.429695\pi$
$440$	−8.09017	−0.385684
$441$	1.00000	0.0476190
$442$	−2.09017	−0.0994192
$443$	−26.8328	−1.27487	−0.637433	−	0.770506i	$-0.720004\pi$
$443$	−26.8328	−1.27487	−0.637433	+	0.770506i	$0.720004\pi$
$444$	−0.381966	−0.0181273
$445$	49.0689	2.32609
$446$	1.00000	0.0473514
$447$	3.70820	0.175392
$448$	−0.236068	−0.0111532
$449$	40.2705	1.90048	0.950241	−	0.311514i	$-0.100836\pi$
$449$	40.2705	1.90048	0.950241	+	0.311514i	$0.100836\pi$
$450$	5.00000	0.235702
$451$	−3.47214	−0.163496
$452$	−22.7984	−1.07235
$453$	8.65248	0.406529
$454$	14.8197	0.695521
$455$	2.23607	0.104828
$456$	−9.47214	−0.443573
$457$	−2.74265	−0.128296	−0.0641478	−	0.997940i	$-0.520433\pi$
$457$	−2.74265	−0.128296	−0.0641478	+	0.997940i	$0.520433\pi$
$458$	17.1803	0.802785
$459$	−5.47214	−0.255417
$460$	−5.85410	−0.272949
$461$	−5.32624	−0.248068	−0.124034	−	0.992278i	$-0.539583\pi$
$461$	−5.32624	−0.248068	−0.124034	+	0.992278i	$0.539583\pi$
$462$	0.618034	0.0287535
$463$	14.1246	0.656426	0.328213	−	0.944604i	$-0.393554\pi$
$463$	14.1246	0.656426	0.328213	+	0.944604i	$0.393554\pi$
$464$	3.27051	0.151830
$465$	−31.5066	−1.46108
$466$	5.36068	0.248329
$467$	−32.8885	−1.52190	−0.760950	−	0.648810i	$-0.775267\pi$
$467$	−32.8885	−1.52190	−0.760950	+	0.648810i	$0.775267\pi$
$468$	−1.00000	−0.0462250
$469$	−8.09017	−0.373569
$470$	26.1803	1.20761
$471$	8.76393	0.403821
$472$	8.09017	0.372380
$473$	−3.85410	−0.177212
$474$	−8.79837	−0.404123
$475$	34.2705	1.57244
$476$	8.85410	0.405827
$477$	−0.0901699	−0.00412860
$478$	9.76393	0.446592
$479$	−22.7082	−1.03756	−0.518782	−	0.854906i	$-0.673614\pi$
$479$	−22.7082	−1.03756	−0.518782	+	0.854906i	$0.673614\pi$
$480$	20.3262	0.927762
$481$	0.145898	0.00665238
$482$	−2.03444	−0.0926663
$483$	1.00000	0.0455016
$484$	16.1803	0.735470
$485$	24.2705	1.10207
$486$	0.618034	0.0280346
$487$	−30.1246	−1.36508	−0.682538	−	0.730850i	$-0.739124\pi$
$487$	−30.1246	−1.36508	−0.682538	+	0.730850i	$0.739124\pi$
$488$	17.5623	0.795008
$489$	−20.2705	−0.916664
$490$	2.23607	0.101015
$491$	−2.43769	−0.110012	−0.0550058	−	0.998486i	$-0.517518\pi$
$491$	−2.43769	−0.110012	−0.0550058	+	0.998486i	$0.517518\pi$
$492$	5.61803	0.253281
$493$	−9.65248	−0.434726
$494$	1.61803	0.0727988
$495$	3.61803	0.162619
$496$	−16.1459	−0.724972
$497$	−10.3262	−0.463195
$498$	−11.0902	−0.496962
$499$	16.5623	0.741431	0.370715	−	0.928747i	$-0.379113\pi$
$499$	16.5623	0.741431	0.370715	+	0.928747i	$0.379113\pi$
$500$	−18.0902	−0.809017
$501$	10.7082	0.478407
$502$	10.9443	0.488467
$503$	−25.6869	−1.14532	−0.572662	−	0.819792i	$-0.694089\pi$
$503$	−25.6869	−1.14532	−0.572662	+	0.819792i	$0.694089\pi$
$504$	−2.23607	−0.0996024
$505$	7.56231	0.336518
$506$	0.618034	0.0274750
$507$	−12.6180	−0.560387
$508$	12.7082	0.563835
$509$	30.7639	1.36359	0.681794	−	0.731545i	$-0.261200\pi$
$509$	30.7639	1.36359	0.681794	+	0.731545i	$0.261200\pi$
$510$	−12.2361	−0.541822
$511$	1.76393	0.0780318
$512$	18.7082	0.826794
$513$	4.23607	0.187027
$514$	14.6525	0.646293
$515$	−66.8328	−2.94501
$516$	6.23607	0.274528
$517$	11.7082	0.514926
$518$	0.145898	0.00641039
$519$	−6.41641	−0.281649
$520$	−5.00000	−0.219265
$521$	−21.4164	−0.938270	−0.469135	−	0.883127i	$-0.655434\pi$
$521$	−21.4164	−0.938270	−0.469135	+	0.883127i	$0.655434\pi$
$522$	1.09017	0.0477154
$523$	−10.5836	−0.462788	−0.231394	−	0.972860i	$-0.574329\pi$
$523$	−10.5836	−0.462788	−0.231394	+	0.972860i	$0.574329\pi$
$524$	5.32624	0.232678
$525$	8.09017	0.353084
$526$	13.3820	0.583481
$527$	47.6525	2.07577
$528$	1.85410	0.0806894
$529$	1.00000	0.0434783
$530$	−0.201626	−0.00875808
$531$	−3.61803	−0.157009
$532$	−6.85410	−0.297163
$533$	−2.14590	−0.0929492
$534$	8.38197	0.362723
$535$	−10.5279	−0.455159
$536$	18.0902	0.781376
$537$	−13.7984	−0.595444
$538$	9.72949	0.419468
$539$	1.00000	0.0430730
$540$	−5.85410	−0.251920
$541$	−15.7082	−0.675348	−0.337674	−	0.941263i	$-0.609640\pi$
$541$	−15.7082	−0.675348	−0.337674	+	0.941263i	$0.609640\pi$
$542$	−9.56231	−0.410736
$543$	−3.18034	−0.136481
$544$	−30.7426	−1.31808
$545$	8.61803	0.369156
$546$	0.381966	0.0163466
$547$	−38.8541	−1.66128	−0.830641	−	0.556809i	$-0.812026\pi$
$547$	−38.8541	−1.66128	−0.830641	+	0.556809i	$0.812026\pi$
$548$	−24.5623	−1.04925
$549$	−7.85410	−0.335205
$550$	5.00000	0.213201
$551$	7.47214	0.318324
$552$	−2.23607	−0.0951734
$553$	−14.2361	−0.605379
$554$	−15.0344	−0.638752
$555$	0.854102	0.0362546
$556$	−34.0344	−1.44338
$557$	12.7639	0.540825	0.270413	−	0.962745i	$-0.412840\pi$
$557$	12.7639	0.540825	0.270413	+	0.962745i	$0.412840\pi$
$558$	−5.38197	−0.227837
$559$	−2.38197	−0.100746
$560$	6.70820	0.283473
$561$	−5.47214	−0.231034
$562$	−9.05573	−0.381993
$563$	36.2148	1.52627	0.763136	−	0.646238i	$-0.223659\pi$
$563$	36.2148	1.52627	0.763136	+	0.646238i	$0.223659\pi$
$564$	−18.9443	−0.797698
$565$	50.9787	2.14469
$566$	15.6525	0.657923
$567$	1.00000	0.0419961
$568$	23.0902	0.968842
$569$	25.8885	1.08530	0.542652	−	0.839958i	$-0.317420\pi$
$569$	25.8885	1.08530	0.542652	+	0.839958i	$0.317420\pi$
$570$	9.47214	0.396744
$571$	−24.5967	−1.02934	−0.514671	−	0.857388i	$-0.672086\pi$
$571$	−24.5967	−1.02934	−0.514671	+	0.857388i	$0.672086\pi$
$572$	−1.00000	−0.0418121
$573$	14.1803	0.592392
$574$	−2.14590	−0.0895681
$575$	8.09017	0.337383
$576$	−0.236068	−0.00983617
$577$	−40.2492	−1.67560	−0.837799	−	0.545979i	$-0.816158\pi$
$577$	−40.2492	−1.67560	−0.837799	+	0.545979i	$0.816158\pi$
$578$	8.00000	0.332756
$579$	0.763932	0.0317479
$580$	−10.3262	−0.428774
$581$	−17.9443	−0.744454
$582$	4.14590	0.171853
$583$	−0.0901699	−0.00373446
$584$	−3.94427	−0.163215
$585$	2.23607	0.0924500
$586$	−14.1115	−0.582939
$587$	44.7984	1.84903	0.924513	−	0.381150i	$-0.124472\pi$
$587$	44.7984	1.84903	0.924513	+	0.381150i	$0.124472\pi$
$588$	−1.61803	−0.0667266
$589$	−36.8885	−1.51997
$590$	−8.09017	−0.333067
$591$	11.5623	0.475610
$592$	0.437694	0.0179891
$593$	−45.1246	−1.85305	−0.926523	−	0.376238i	$-0.877217\pi$
$593$	−45.1246	−1.85305	−0.926523	+	0.376238i	$0.877217\pi$
$594$	0.618034	0.0253582
$595$	−19.7984	−0.811654
$596$	−6.00000	−0.245770
$597$	1.43769	0.0588409
$598$	0.381966	0.0156198
$599$	−7.38197	−0.301619	−0.150809	−	0.988563i	$-0.548188\pi$
$599$	−7.38197	−0.301619	−0.150809	+	0.988563i	$0.548188\pi$
$600$	−18.0902	−0.738528
$601$	31.6869	1.29254	0.646268	−	0.763110i	$-0.276329\pi$
$601$	31.6869	1.29254	0.646268	+	0.763110i	$0.276329\pi$
$602$	−2.38197	−0.0970817
$603$	−8.09017	−0.329457
$604$	−14.0000	−0.569652
$605$	−36.1803	−1.47094
$606$	1.29180	0.0524756
$607$	6.50658	0.264094	0.132047	−	0.991243i	$-0.457845\pi$
$607$	6.50658	0.264094	0.132047	+	0.991243i	$0.457845\pi$
$608$	23.7984	0.965152
$609$	1.76393	0.0714781
$610$	−17.5623	−0.711077
$611$	7.23607	0.292740
$612$	8.85410	0.357906
$613$	−21.8328	−0.881819	−0.440910	−	0.897552i	$-0.645344\pi$
$613$	−21.8328	−0.881819	−0.440910	+	0.897552i	$0.645344\pi$
$614$	−21.0902	−0.851130
$615$	−12.5623	−0.506561
$616$	−2.23607	−0.0900937
$617$	−7.74265	−0.311707	−0.155854	−	0.987780i	$-0.549813\pi$
$617$	−7.74265	−0.311707	−0.155854	+	0.987780i	$0.549813\pi$
$618$	−11.4164	−0.459235
$619$	4.90983	0.197343	0.0986714	−	0.995120i	$-0.468541\pi$
$619$	4.90983	0.197343	0.0986714	+	0.995120i	$0.468541\pi$
$620$	50.9787	2.04735
$621$	1.00000	0.0401286
$622$	−6.49342	−0.260363
$623$	13.5623	0.543362
$624$	1.14590	0.0458726
$625$	0	0
$626$	20.9443	0.837101
$627$	4.23607	0.169172
$628$	−14.1803	−0.565857
$629$	−1.29180	−0.0515073
$630$	2.23607	0.0890871
$631$	5.00000	0.199047	0.0995234	−	0.995035i	$-0.468268\pi$
$631$	5.00000	0.199047	0.0995234	+	0.995035i	$0.468268\pi$
$632$	31.8328	1.26624
$633$	8.88854	0.353288
$634$	−0.0557281	−0.00221325
$635$	−28.4164	−1.12767
$636$	0.145898	0.00578523
$637$	0.618034	0.0244874
$638$	1.09017	0.0431602
$639$	−10.3262	−0.408500
$640$	−41.1803	−1.62780
$641$	−24.7984	−0.979477	−0.489738	−	0.871869i	$-0.662908\pi$
$641$	−24.7984	−0.979477	−0.489738	+	0.871869i	$0.662908\pi$
$642$	−1.79837	−0.0709762
$643$	3.96556	0.156386	0.0781932	−	0.996938i	$-0.475085\pi$
$643$	3.96556	0.156386	0.0781932	+	0.996938i	$0.475085\pi$
$644$	−1.61803	−0.0637595
$645$	−13.9443	−0.549055
$646$	−14.3262	−0.563658
$647$	40.2705	1.58320	0.791599	−	0.611042i	$-0.209249\pi$
$647$	40.2705	1.58320	0.791599	+	0.611042i	$0.209249\pi$
$648$	−2.23607	−0.0878410
$649$	−3.61803	−0.142020
$650$	3.09017	0.121206
$651$	−8.70820	−0.341301
$652$	32.7984	1.28448
$653$	4.09017	0.160061	0.0800304	−	0.996792i	$-0.474498\pi$
$653$	4.09017	0.160061	0.0800304	+	0.996792i	$0.474498\pi$
$654$	1.47214	0.0575651
$655$	−11.9098	−0.465356
$656$	−6.43769	−0.251350
$657$	1.76393	0.0688175
$658$	7.23607	0.282091
$659$	−35.9443	−1.40019	−0.700095	−	0.714050i	$-0.746859\pi$
$659$	−35.9443	−1.40019	−0.700095	+	0.714050i	$0.746859\pi$
$660$	−5.85410	−0.227871
$661$	23.6525	0.919975	0.459987	−	0.887925i	$-0.347854\pi$
$661$	23.6525	0.919975	0.459987	+	0.887925i	$0.347854\pi$
$662$	4.87539	0.189487
$663$	−3.38197	−0.131345
$664$	40.1246	1.55714
$665$	15.3262	0.594326
$666$	0.145898	0.00565343
$667$	1.76393	0.0682997
$668$	−17.3262	−0.670372
$669$	1.61803	0.0625568
$670$	−18.0902	−0.698884
$671$	−7.85410	−0.303204
$672$	5.61803	0.216720
$673$	−34.4164	−1.32666	−0.663328	−	0.748329i	$-0.730856\pi$
$673$	−34.4164	−1.32666	−0.663328	+	0.748329i	$0.730856\pi$
$674$	6.20163	0.238878
$675$	8.09017	0.311391
$676$	20.4164	0.785246
$677$	34.3262	1.31926	0.659632	−	0.751589i	$-0.270712\pi$
$677$	34.3262	1.31926	0.659632	+	0.751589i	$0.270712\pi$
$678$	8.70820	0.334437
$679$	6.70820	0.257437
$680$	44.2705	1.69770
$681$	23.9787	0.918866
$682$	−5.38197	−0.206086
$683$	14.1246	0.540463	0.270232	−	0.962795i	$-0.412900\pi$
$683$	14.1246	0.540463	0.270232	+	0.962795i	$0.412900\pi$
$684$	−6.85410	−0.262073
$685$	54.9230	2.09850
$686$	0.618034	0.0235966
$687$	27.7984	1.06057
$688$	−7.14590	−0.272435
$689$	−0.0557281	−0.00212307
$690$	2.23607	0.0851257
$691$	−20.6180	−0.784347	−0.392173	−	0.919891i	$-0.628277\pi$
$691$	−20.6180	−0.784347	−0.392173	+	0.919891i	$0.628277\pi$
$692$	10.3820	0.394663
$693$	1.00000	0.0379869
$694$	−4.50658	−0.171067
$695$	76.1033	2.88676
$696$	−3.94427	−0.149507
$697$	19.0000	0.719676
$698$	−12.2361	−0.463142
$699$	8.67376	0.328072
$700$	−13.0902	−0.494762
$701$	8.09017	0.305562	0.152781	−	0.988260i	$-0.451177\pi$
$701$	8.09017	0.305562	0.152781	+	0.988260i	$0.451177\pi$
$702$	0.381966	0.0144164
$703$	1.00000	0.0377157
$704$	−0.236068	−0.00889715
$705$	42.3607	1.59540
$706$	3.96556	0.149246
$707$	2.09017	0.0786089
$708$	5.85410	0.220011
$709$	8.72949	0.327843	0.163921	−	0.986473i	$-0.447586\pi$
$709$	8.72949	0.327843	0.163921	+	0.986473i	$0.447586\pi$
$710$	−23.0902	−0.866559
$711$	−14.2361	−0.533894
$712$	−30.3262	−1.13652
$713$	−8.70820	−0.326125
$714$	−3.38197	−0.126567
$715$	2.23607	0.0836242
$716$	22.3262	0.834371
$717$	15.7984	0.590001
$718$	5.29180	0.197488
$719$	32.8885	1.22654	0.613268	−	0.789875i	$-0.289855\pi$
$719$	32.8885	1.22654	0.613268	+	0.789875i	$0.289855\pi$
$720$	6.70820	0.250000
$721$	−18.4721	−0.687938
$722$	−0.652476	−0.0242826
$723$	−3.29180	−0.122423
$724$	5.14590	0.191246
$725$	14.2705	0.529993
$726$	−6.18034	−0.229374
$727$	51.5410	1.91155	0.955775	−	0.294098i	$-0.0950192\pi$
$727$	51.5410	1.91155	0.955775	+	0.294098i	$0.0950192\pi$
$728$	−1.38197	−0.0512191
$729$	1.00000	0.0370370
$730$	3.94427	0.145984
$731$	21.0902	0.780048
$732$	12.7082	0.469709
$733$	47.2361	1.74470	0.872352	−	0.488878i	$-0.162594\pi$
$733$	47.2361	1.74470	0.872352	+	0.488878i	$0.162594\pi$
$734$	8.20163	0.302728
$735$	3.61803	0.133453
$736$	5.61803	0.207083
$737$	−8.09017	−0.298005
$738$	−2.14590	−0.0789916
$739$	−31.4721	−1.15772	−0.578861	−	0.815427i	$-0.696502\pi$
$739$	−31.4721	−1.15772	−0.578861	+	0.815427i	$0.696502\pi$
$740$	−1.38197	−0.0508021
$741$	2.61803	0.0961759
$742$	−0.0557281	−0.00204584
$743$	15.6180	0.572970	0.286485	−	0.958085i	$-0.407513\pi$
$743$	15.6180	0.572970	0.286485	+	0.958085i	$0.407513\pi$
$744$	19.4721	0.713883
$745$	13.4164	0.491539
$746$	21.0902	0.772166
$747$	−17.9443	−0.656547
$748$	8.85410	0.323738
$749$	−2.90983	−0.106323
$750$	6.90983	0.252311
$751$	10.4508	0.381357	0.190678	−	0.981653i	$-0.438931\pi$
$751$	10.4508	0.381357	0.190678	+	0.981653i	$0.438931\pi$
$752$	21.7082	0.791617
$753$	17.7082	0.645323
$754$	0.673762	0.0245370
$755$	31.3050	1.13930
$756$	−1.61803	−0.0588473
$757$	53.6525	1.95003	0.975016	−	0.222134i	$-0.0713022\pi$
$757$	53.6525	1.95003	0.975016	+	0.222134i	$0.0713022\pi$
$758$	−15.7771	−0.573050
$759$	1.00000	0.0362977
$760$	−34.2705	−1.24312
$761$	41.8885	1.51846	0.759229	−	0.650823i	$-0.225576\pi$
$761$	41.8885	1.51846	0.759229	+	0.650823i	$0.225576\pi$
$762$	−4.85410	−0.175846
$763$	2.38197	0.0862330
$764$	−22.9443	−0.830095
$765$	−19.7984	−0.715812
$766$	−2.43769	−0.0880775
$767$	−2.23607	−0.0807397
$768$	−6.56231	−0.236797
$769$	−10.6525	−0.384138	−0.192069	−	0.981381i	$-0.561520\pi$
$769$	−10.6525	−0.384138	−0.192069	+	0.981381i	$0.561520\pi$
$770$	2.23607	0.0805823
$771$	23.7082	0.853830
$772$	−1.23607	−0.0444871
$773$	−20.5967	−0.740814	−0.370407	−	0.928870i	$-0.620782\pi$
$773$	−20.5967	−0.740814	−0.370407	+	0.928870i	$0.620782\pi$
$774$	−2.38197	−0.0856180
$775$	−70.4508	−2.53067
$776$	−15.0000	−0.538469
$777$	0.236068	0.00846889
$778$	−12.3262	−0.441917
$779$	−14.7082	−0.526976
$780$	−3.61803	−0.129546
$781$	−10.3262	−0.369502
$782$	−3.38197	−0.120939
$783$	1.76393	0.0630378
$784$	1.85410	0.0662179
$785$	31.7082	1.13171
$786$	−2.03444	−0.0725661
$787$	13.7984	0.491859	0.245929	−	0.969288i	$-0.420907\pi$
$787$	13.7984	0.491859	0.245929	+	0.969288i	$0.420907\pi$
$788$	−18.7082	−0.666452
$789$	21.6525	0.770849
$790$	−31.8328	−1.13256
$791$	14.0902	0.500989
$792$	−2.23607	−0.0794552
$793$	−4.85410	−0.172374
$794$	13.7082	0.486486
$795$	−0.326238	−0.0115705
$796$	−2.32624	−0.0824513
$797$	7.12461	0.252367	0.126183	−	0.992007i	$-0.459727\pi$
$797$	7.12461	0.252367	0.126183	+	0.992007i	$0.459727\pi$
$798$	2.61803	0.0926774
$799$	−64.0689	−2.26659
$800$	45.4508	1.60693
$801$	13.5623	0.479201
$802$	−3.09017	−0.109118
$803$	1.76393	0.0622478
$804$	13.0902	0.461655
$805$	3.61803	0.127519
$806$	−3.32624	−0.117162
$807$	15.7426	0.554167
$808$	−4.67376	−0.164422
$809$	−6.72949	−0.236596	−0.118298	−	0.992978i	$-0.537744\pi$
$809$	−6.72949	−0.236596	−0.118298	+	0.992978i	$0.537744\pi$
$810$	2.23607	0.0785674
$811$	−12.3050	−0.432085	−0.216043	−	0.976384i	$-0.569315\pi$
$811$	−12.3050	−0.432085	−0.216043	+	0.976384i	$0.569315\pi$
$812$	−2.85410	−0.100159
$813$	−15.4721	−0.542631
$814$	0.145898	0.00511372
$815$	−73.3394	−2.56897
$816$	−10.1459	−0.355177
$817$	−16.3262	−0.571183
$818$	−15.3820	−0.537818
$819$	0.618034	0.0215959
$820$	20.3262	0.709823
$821$	−30.5410	−1.06589	−0.532944	−	0.846150i	$-0.678915\pi$
$821$	−30.5410	−1.06589	−0.532944	+	0.846150i	$0.678915\pi$
$822$	9.38197	0.327234
$823$	43.2148	1.50637	0.753186	−	0.657807i	$-0.228516\pi$
$823$	43.2148	1.50637	0.753186	+	0.657807i	$0.228516\pi$
$824$	41.3050	1.43893
$825$	8.09017	0.281664
$826$	−2.23607	−0.0778028
$827$	−0.854102	−0.0297000	−0.0148500	−	0.999890i	$-0.504727\pi$
$827$	−0.854102	−0.0297000	−0.0148500	+	0.999890i	$0.504727\pi$
$828$	−1.61803	−0.0562306
$829$	38.7771	1.34678	0.673392	−	0.739286i	$-0.264837\pi$
$829$	38.7771	1.34678	0.673392	+	0.739286i	$0.264837\pi$
$830$	−40.1246	−1.39275
$831$	−24.3262	−0.843868
$832$	−0.145898	−0.00505810
$833$	−5.47214	−0.189598
$834$	13.0000	0.450153
$835$	38.7426	1.34074
$836$	−6.85410	−0.237054
$837$	−8.70820	−0.301000
$838$	8.59675	0.296970
$839$	−0.978714	−0.0337890	−0.0168945	−	0.999857i	$-0.505378\pi$
$839$	−0.978714	−0.0337890	−0.0168945	+	0.999857i	$0.505378\pi$
$840$	−8.09017	−0.279137
$841$	−25.8885	−0.892708
$842$	−18.2705	−0.629643
$843$	−14.6525	−0.504658
$844$	−14.3820	−0.495048
$845$	−45.6525	−1.57049
$846$	7.23607	0.248781
$847$	−10.0000	−0.343604
$848$	−0.167184	−0.00574113
$849$	25.3262	0.869194
$850$	−27.3607	−0.938464
$851$	0.236068	0.00809231
$852$	16.7082	0.572414
$853$	22.0689	0.755624	0.377812	−	0.925882i	$-0.376677\pi$
$853$	22.0689	0.755624	0.377812	+	0.925882i	$0.376677\pi$
$854$	−4.85410	−0.166104
$855$	15.3262	0.524146
$856$	6.50658	0.222390
$857$	1.12461	0.0384160	0.0192080	−	0.999816i	$-0.493886\pi$
$857$	1.12461	0.0384160	0.0192080	+	0.999816i	$0.493886\pi$
$858$	0.381966	0.0130401
$859$	−1.63932	−0.0559329	−0.0279664	−	0.999609i	$-0.508903\pi$
$859$	−1.63932	−0.0559329	−0.0279664	+	0.999609i	$0.508903\pi$
$860$	22.5623	0.769368
$861$	−3.47214	−0.118330
$862$	6.96556	0.237248
$863$	7.81966	0.266184	0.133092	−	0.991104i	$-0.457509\pi$
$863$	7.81966	0.266184	0.133092	+	0.991104i	$0.457509\pi$
$864$	5.61803	0.191129
$865$	−23.2148	−0.789326
$866$	12.8328	0.436077
$867$	12.9443	0.439611
$868$	14.0902	0.478252
$869$	−14.2361	−0.482926
$870$	3.94427	0.133723
$871$	−5.00000	−0.169419
$872$	−5.32624	−0.180369
$873$	6.70820	0.227038
$874$	2.61803	0.0885563
$875$	11.1803	0.377964
$876$	−2.85410	−0.0964312
$877$	20.0000	0.675352	0.337676	−	0.941262i	$-0.390359\pi$
$877$	20.0000	0.675352	0.337676	+	0.941262i	$0.390359\pi$
$878$	5.67376	0.191480
$879$	−22.8328	−0.770132
$880$	6.70820	0.226134
$881$	−34.2918	−1.15532	−0.577660	−	0.816277i	$-0.696034\pi$
$881$	−34.2918	−1.15532	−0.577660	+	0.816277i	$0.696034\pi$
$882$	0.618034	0.0208103
$883$	4.90983	0.165229	0.0826145	−	0.996582i	$-0.473673\pi$
$883$	4.90983	0.165229	0.0826145	+	0.996582i	$0.473673\pi$
$884$	5.47214	0.184048
$885$	−13.0902	−0.440021
$886$	−16.5836	−0.557137
$887$	3.02129	0.101445	0.0507224	−	0.998713i	$-0.483848\pi$
$887$	3.02129	0.101445	0.0507224	+	0.998713i	$0.483848\pi$
$888$	−0.527864	−0.0177140
$889$	−7.85410	−0.263418
$890$	30.3262	1.01654
$891$	1.00000	0.0335013
$892$	−2.61803	−0.0876583
$893$	49.5967	1.65969
$894$	2.29180	0.0766491
$895$	−49.9230	−1.66874
$896$	−11.3820	−0.380245
$897$	0.618034	0.0206356
$898$	24.8885	0.830541
$899$	−15.3607	−0.512307
$900$	−13.0902	−0.436339
$901$	0.493422	0.0164383
$902$	−2.14590	−0.0714506
$903$	−3.85410	−0.128256
$904$	−31.5066	−1.04789
$905$	−11.5066	−0.382492
$906$	5.34752	0.177660
$907$	−2.27051	−0.0753910	−0.0376955	−	0.999289i	$-0.512002\pi$
$907$	−2.27051	−0.0753910	−0.0376955	+	0.999289i	$0.512002\pi$
$908$	−38.7984	−1.28757
$909$	2.09017	0.0693266
$910$	1.38197	0.0458117
$911$	−41.0132	−1.35883	−0.679413	−	0.733756i	$-0.737766\pi$
$911$	−41.0132	−1.35883	−0.679413	+	0.733756i	$0.737766\pi$
$912$	7.85410	0.260075
$913$	−17.9443	−0.593869
$914$	−1.69505	−0.0560672
$915$	−28.4164	−0.939417
$916$	−44.9787	−1.48614
$917$	−3.29180	−0.108705
$918$	−3.38197	−0.111622
$919$	−42.1935	−1.39183	−0.695917	−	0.718122i	$-0.745002\pi$
$919$	−42.1935	−1.39183	−0.695917	+	0.718122i	$0.745002\pi$
$920$	−8.09017	−0.266725
$921$	−34.1246	−1.12444
$922$	−3.29180	−0.108410
$923$	−6.38197	−0.210065
$924$	−1.61803	−0.0532294
$925$	1.90983	0.0627948
$926$	8.72949	0.286869
$927$	−18.4721	−0.606705
$928$	9.90983	0.325306
$929$	−34.9230	−1.14579	−0.572893	−	0.819630i	$-0.694179\pi$
$929$	−34.9230	−1.14579	−0.572893	+	0.819630i	$0.694179\pi$
$930$	−19.4721	−0.638516
$931$	4.23607	0.138832
$932$	−14.0344	−0.459713
$933$	−10.5066	−0.343970
$934$	−20.3262	−0.665095
$935$	−19.7984	−0.647476
$936$	−1.38197	−0.0451710
$937$	21.3607	0.697823	0.348911	−	0.937156i	$-0.386551\pi$
$937$	21.3607	0.697823	0.348911	+	0.937156i	$0.386551\pi$
$938$	−5.00000	−0.163256
$939$	33.8885	1.10591
$940$	−68.5410	−2.23556
$941$	−0.360680	−0.0117578	−0.00587891	−	0.999983i	$-0.501871\pi$
$941$	−0.360680	−0.0117578	−0.00587891	+	0.999983i	$0.501871\pi$
$942$	5.41641	0.176476
$943$	−3.47214	−0.113068
$944$	−6.70820	−0.218333
$945$	3.61803	0.117695
$946$	−2.38197	−0.0774444
$947$	−26.5836	−0.863851	−0.431925	−	0.901909i	$-0.642166\pi$
$947$	−26.5836	−0.863851	−0.431925	+	0.901909i	$0.642166\pi$
$948$	23.0344	0.748124
$949$	1.09017	0.0353884
$950$	21.1803	0.687181
$951$	−0.0901699	−0.00292396
$952$	12.2361	0.396573
$953$	12.9787	0.420422	0.210211	−	0.977656i	$-0.432585\pi$
$953$	12.9787	0.420422	0.210211	+	0.977656i	$0.432585\pi$
$954$	−0.0557281	−0.00180426
$955$	51.3050	1.66019
$956$	−25.5623	−0.826744
$957$	1.76393	0.0570198
$958$	−14.0344	−0.453432
$959$	15.1803	0.490199
$960$	−0.854102	−0.0275660
$961$	44.8328	1.44622
$962$	0.0901699	0.00290720
$963$	−2.90983	−0.0937680
$964$	5.32624	0.171547
$965$	2.76393	0.0889741
$966$	0.618034	0.0198849
$967$	27.8885	0.896835	0.448418	−	0.893824i	$-0.351988\pi$
$967$	27.8885	0.896835	0.448418	+	0.893824i	$0.351988\pi$
$968$	22.3607	0.718699
$969$	−23.1803	−0.744660
$970$	15.0000	0.481621
$971$	50.0344	1.60568	0.802841	−	0.596193i	$-0.203321\pi$
$971$	50.0344	1.60568	0.802841	+	0.596193i	$0.203321\pi$
$972$	−1.61803	−0.0518985
$973$	21.0344	0.674333
$974$	−18.6180	−0.596560
$975$	5.00000	0.160128
$976$	−14.5623	−0.466128
$977$	−12.2148	−0.390785	−0.195393	−	0.980725i	$-0.562598\pi$
$977$	−12.2148	−0.390785	−0.195393	+	0.980725i	$0.562598\pi$
$978$	−12.5279	−0.400597
$979$	13.5623	0.433453
$980$	−5.85410	−0.187002
$981$	2.38197	0.0760503
$982$	−1.50658	−0.0480768
$983$	5.00000	0.159475	0.0797376	−	0.996816i	$-0.474592\pi$
$983$	5.00000	0.159475	0.0797376	+	0.996816i	$0.474592\pi$
$984$	7.76393	0.247505
$985$	41.8328	1.33290
$986$	−5.96556	−0.189982
$987$	11.7082	0.372676
$988$	−4.23607	−0.134767
$989$	−3.85410	−0.122553
$990$	2.23607	0.0710669
$991$	−50.6180	−1.60793	−0.803967	−	0.594673i	$-0.797281\pi$
$991$	−50.6180	−1.60793	−0.803967	+	0.594673i	$0.797281\pi$
$992$	−48.9230	−1.55331
$993$	7.88854	0.250335
$994$	−6.38197	−0.202424
$995$	5.20163	0.164903
$996$	29.0344	0.919991
$997$	40.3050	1.27647	0.638235	−	0.769841i	$-0.279665\pi$
$997$	40.3050	1.27647	0.638235	+	0.769841i	$0.279665\pi$
$998$	10.2361	0.324017
$999$	0.236068	0.00746886

Display

a_p

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a_n

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a_n

instead) (See

a_n

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a_n

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a_p

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a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.a.e.1.2	✓	2
3.2	odd	2		1449.2.a.g.1.1		2
4.3	odd	2		7728.2.a.be.1.2		2
7.6	odd	2		3381.2.a.o.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.a.e.1.2	✓	2	1.1	even	1	trivial
1449.2.a.g.1.1		2	3.2	odd	2
3381.2.a.o.1.2		2	7.6	odd	2
7728.2.a.be.1.2		2	4.3	odd	2

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Classical	Maass
Hilbert	Bianchi

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

Introduction

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	483.2.a.e.1.2

Level	$483$
Weight	$2$
Character	483.1
Self dual	yes
Analytic conductor	$3.857$
Analytic rank	$0$
Dimension	$2$
CM	no
Inner twists	$1$