LMFDB - Embedded newform 459.2.y.a.62.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [459,2,Mod(44,459)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(459, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([40, 9]))

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

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

chi := DirichletCharacter("459.44");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$459 = 3^{3} \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	459.y (of order $48$ , degree $16$ , not minimal)

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:	no
Analytic conductor:	$3.66513345278$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{48})$
Twist minimal:	no (minimal twist has level 153)
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			62.6
Character	$\chi$	$=$	459.62
Dual form			459.2.y.a.422.6

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.260648 - 0.339683i) q^{2} +(0.470191 - 1.75478i) q^{4} +(-1.46900 - 0.0962834i) q^{5} +(-0.0205877 - 0.314107i) q^{7} +(-1.50976 + 0.625364i) q^{8} +(0.350186 + 0.524091i) q^{10} +(-1.30742 - 1.14658i) q^{11} +(-4.45178 - 1.19285i) q^{13} +(-0.101331 + 0.0888647i) q^{14} +(-2.54064 - 1.46684i) q^{16} +(0.980810 - 4.00475i) q^{17} +(2.71326 + 1.12387i) q^{19} +(-0.859666 + 2.53250i) q^{20} +(-0.0486964 + 0.742964i) q^{22} +(1.15753 + 3.40999i) q^{23} +(-2.80853 - 0.369750i) q^{25} +(0.755157 + 1.82311i) q^{26} +(-0.560867 - 0.111563i) q^{28} +(-6.45120 + 3.18138i) q^{29} +(-6.04943 - 6.89806i) q^{31} +(0.590552 + 4.48569i) q^{32} +(-1.61599 + 0.710666i) q^{34} +0.463405i q^{35} +(0.433080 + 2.17724i) q^{37} +(-0.325446 - 1.21458i) q^{38} +(2.27805 - 0.773295i) q^{40} +(1.97235 - 3.99953i) q^{41} +(0.375298 - 2.85067i) q^{43} +(-2.62673 + 1.75512i) q^{44} +(0.856606 - 1.28200i) q^{46} +(4.65071 - 1.24615i) q^{47} +(6.84187 - 0.900750i) q^{49} +(0.606441 + 1.05039i) q^{50} +(-4.18637 + 7.25101i) q^{52} +(4.06143 - 9.80516i) q^{53} +(1.81021 + 1.81021i) q^{55} +(0.227514 + 0.461352i) q^{56} +(2.76216 + 1.36214i) q^{58} +(-5.20950 - 3.99739i) q^{59} +(-3.81967 + 0.250355i) q^{61} +(-0.766381 + 3.85286i) q^{62} +(-2.77905 + 2.77905i) q^{64} +(6.42482 + 2.18093i) q^{65} +(4.04083 - 2.33298i) q^{67} +(-6.56627 - 3.60410i) q^{68} +(0.157411 - 0.120786i) q^{70} +(-5.89482 + 1.17255i) q^{71} +(6.74041 + 4.50380i) q^{73} +(0.626690 - 0.714603i) q^{74} +(3.24788 - 4.23273i) q^{76} +(-0.333232 + 0.434276i) q^{77} +(5.06005 - 5.76989i) q^{79} +(3.59096 + 2.39940i) q^{80} +(-1.87266 + 0.372496i) q^{82} +(3.29965 - 2.53191i) q^{83} +(-1.82640 + 5.78854i) q^{85} +(-1.06615 + 0.615539i) q^{86} +(2.69093 + 0.913447i) q^{88} +(2.40264 - 2.40264i) q^{89} +(-0.283031 + 1.42289i) q^{91} +(6.52802 - 0.427869i) q^{92} +(-1.63550 - 1.25496i) q^{94} +(-3.87757 - 1.91220i) q^{95} +(8.28805 + 16.8065i) q^{97} +(-2.08929 - 2.08929i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$256 q + 24 q^{2} - 8 q^{4} + 24 q^{5} - 8 q^{7} - 32 q^{10} + 24 q^{11} - 8 q^{13} + 24 q^{14} - 32 q^{19} + 24 q^{20} - 8 q^{22} + 24 q^{23} - 8 q^{25} - 32 q^{28} + 24 q^{29} - 8 q^{31} + 24 q^{32} - 56 q^{34}+ \cdots - 8 q^{97}+O(q^{100})$ 256 * q + 24 * q^2 - 8 * q^4 + 24 * q^5 - 8 * q^7 - 32 * q^10 + 24 * q^11 - 8 * q^13 + 24 * q^14 - 32 * q^19 + 24 * q^20 - 8 * q^22 + 24 * q^23 - 8 * q^25 - 32 * q^28 + 24 * q^29 - 8 * q^31 + 24 * q^32 - 56 * q^34 - 32 * q^37 - 8 * q^40 + 24 * q^41 + 16 * q^43 - 32 * q^46 - 96 * q^47 - 8 * q^49 - 16 * q^52 - 32 * q^55 - 216 * q^56 - 8 * q^58 + 24 * q^59 - 8 * q^61 - 96 * q^64 - 24 * q^65 + 24 * q^68 + 8 * q^70 - 32 * q^73 + 24 * q^74 - 8 * q^76 + 24 * q^77 - 8 * q^79 + 160 * q^82 + 24 * q^83 - 8 * q^85 - 192 * q^86 - 8 * q^88 - 128 * q^91 + 24 * q^92 - 8 * q^94 - 216 * q^95 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$ .

$n$	$137$	$190$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{16}\right)$

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

)

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

$2$	−0.260648	−	0.339683i	−0.184306	−	0.240192i	0.692058	−	0.721842i	$-0.256704\pi$
$2$	−0.260648	−	0.339683i	−0.184306	−	0.240192i	−0.876364	+	0.481650i	$0.840038\pi$
$3$		0			0
$3$		0			0
$4$	0.470191	−	1.75478i	0.235095	−	0.877388i
$5$	−1.46900	−	0.0962834i	−0.656957	−	0.0430592i	−0.266721	−	0.963774i	$-0.585940\pi$
$5$	−1.46900	−	0.0962834i	−0.656957	−	0.0430592i	−0.390236	+	0.920715i	$0.627607\pi$
$6$		0			0
$7$	−0.0205877	−	0.314107i	−0.00778140	−	0.118721i	0.992201	−	0.124648i	$-0.0397801\pi$
$7$	−0.0205877	−	0.314107i	−0.00778140	−	0.118721i	−0.999982	+	0.00592667i	$0.998113\pi$
$8$	−1.50976	+	0.625364i	−0.533781	+	0.221099i
$9$		0			0
$10$	0.350186	+	0.524091i	0.110739	+	0.165732i
$11$	−1.30742	−	1.14658i	−0.394203	−	0.345707i	0.439183	−	0.898397i	$-0.355268\pi$
$11$	−1.30742	−	1.14658i	−0.394203	−	0.345707i	−0.833387	+	0.552691i	$0.813601\pi$
$12$		0			0
$13$	−4.45178	−	1.19285i	−1.23470	−	0.330837i	−0.418294	−	0.908312i	$-0.637372\pi$
$13$	−4.45178	−	1.19285i	−1.23470	−	0.330837i	−0.816409	+	0.577474i	$0.804038\pi$
$14$	−0.101331	+	0.0888647i	−0.0270818	+	0.0237501i
$15$		0			0
$16$	−2.54064	−	1.46684i	−0.635159	−	0.366709i
$17$	0.980810	−	4.00475i	0.237881	−	0.971294i
$17$	0.980810	−	4.00475i	0.237881	−	0.971294i
$18$		0			0
$19$	2.71326	+	1.12387i	0.622464	+	0.257833i	0.671547	−	0.740962i	$-0.265630\pi$
$19$	2.71326	+	1.12387i	0.622464	+	0.257833i	−0.0490835	+	0.998795i	$0.515630\pi$
$20$	−0.859666	+	2.53250i	−0.192227	+	0.566283i
$21$		0			0
$22$	−0.0486964	+	0.742964i	−0.0103821	+	0.158400i
$23$	1.15753	+	3.40999i	0.241363	+	0.711031i	0.998340	+	0.0575906i	$0.0183418\pi$
$23$	1.15753	+	3.40999i	0.241363	+	0.711031i	−0.756978	+	0.653441i	$0.773325\pi$
$24$		0			0
$25$	−2.80853	−	0.369750i	−0.561707	−	0.0739501i
$26$	0.755157	+	1.82311i	0.148099	+	0.357541i
$27$		0			0
$28$	−0.560867	−	0.111563i	−0.105994	−	0.0210835i
$29$	−6.45120	+	3.18138i	−1.19796	+	0.590767i	−0.928172	−	0.372153i	$-0.878620\pi$
$29$	−6.45120	+	3.18138i	−1.19796	+	0.590767i	−0.269786	+	0.962920i	$0.586953\pi$
$30$		0			0
$31$	−6.04943	−	6.89806i	−1.08651	−	1.23893i	−0.969316	−	0.245819i	$-0.920943\pi$
$31$	−6.04943	−	6.89806i	−1.08651	−	1.23893i	−0.117194	−	0.993109i	$-0.537390\pi$
$32$	0.590552	+	4.48569i	0.104396	+	0.792965i
$33$		0			0
$34$	−1.61599	+	0.710666i	−0.277140	+	0.121878i
$35$			0.463405i			0.0783298i
$36$		0			0
$37$	0.433080	+	2.17724i	0.0711978	+	0.357936i	0.999917	−	0.0128470i	$-0.00408945\pi$
$37$	0.433080	+	2.17724i	0.0711978	+	0.357936i	−0.928720	+	0.370783i	$0.879089\pi$
$38$	−0.325446	−	1.21458i	−0.0527944	−	0.197031i
$39$		0			0
$40$	2.27805	−	0.773295i	0.360192	−	0.122269i
$41$	1.97235	−	3.99953i	0.308029	−	0.624622i	−0.686725	−	0.726918i	$-0.740952\pi$
$41$	1.97235	−	3.99953i	0.308029	−	0.624622i	0.994754	+	0.102296i	$0.0326188\pi$
$42$		0			0
$43$	0.375298	−	2.85067i	0.0572324	−	0.434723i	−0.938708	−	0.344712i	$-0.887977\pi$
$43$	0.375298	−	2.85067i	0.0572324	−	0.434723i	0.995941	−	0.0900108i	$-0.0286902\pi$
$44$	−2.62673	+	1.75512i	−0.395994	+	0.264595i
$45$		0			0
$46$	0.856606	−	1.28200i	0.126300	−	0.189021i
$47$	4.65071	−	1.24615i	0.678376	−	0.181770i	0.0968512	−	0.995299i	$-0.469123\pi$
$47$	4.65071	−	1.24615i	0.678376	−	0.181770i	0.581525	+	0.813528i	$0.302456\pi$
$48$		0			0
$49$	6.84187	−	0.900750i	0.977411	−	0.128679i
$50$	0.606441	+	1.05039i	0.0857637	+	0.148547i
$51$		0			0
$52$	−4.18637	+	7.25101i	−0.580546	+	1.00553i
$53$	4.06143	−	9.80516i	0.557881	−	1.34684i	−0.353560	−	0.935412i	$-0.615029\pi$
$53$	4.06143	−	9.80516i	0.557881	−	1.34684i	0.911441	−	0.411431i	$-0.134971\pi$
$54$		0			0
$55$	1.81021	+	1.81021i	0.244089	+	0.244089i
$56$	0.227514	+	0.461352i	0.0304028	+	0.0616507i
$57$		0			0
$58$	2.76216	+	1.36214i	0.362689	+	0.178858i
$59$	−5.20950	−	3.99739i	−0.678220	−	0.520416i	0.211238	−	0.977435i	$-0.432251\pi$
$59$	−5.20950	−	3.99739i	−0.678220	−	0.520416i	−0.889457	+	0.457019i	$0.848917\pi$
$60$		0			0
$61$	−3.81967	+	0.250355i	−0.489059	+	0.0320546i	−0.307938	−	0.951406i	$-0.599639\pi$
$61$	−3.81967	+	0.250355i	−0.489059	+	0.0320546i	−0.181120	+	0.983461i	$0.557972\pi$
$62$	−0.766381	+	3.85286i	−0.0973305	+	0.489313i
$63$		0			0
$64$	−2.77905	+	2.77905i	−0.347382	+	0.347382i
$65$	6.42482	+	2.18093i	0.796901	+	0.270511i
$66$		0			0
$67$	4.04083	−	2.33298i	0.493666	−	0.285018i	−0.232428	−	0.972614i	$-0.574667\pi$
$67$	4.04083	−	2.33298i	0.493666	−	0.285018i	0.726094	+	0.687595i	$0.241334\pi$
$68$	−6.56627	−	3.60410i	−0.796277	−	0.437061i
$69$		0			0
$70$	0.157411	−	0.120786i	0.0188142	−	0.0144367i
$71$	−5.89482	+	1.17255i	−0.699586	+	0.139156i	−0.532054	−	0.846710i	$-0.678580\pi$
$71$	−5.89482	+	1.17255i	−0.699586	+	0.139156i	−0.167532	+	0.985867i	$0.553580\pi$
$72$		0			0
$73$	6.74041	+	4.50380i	0.788905	+	0.527130i	0.883525	−	0.468384i	$-0.155164\pi$
$73$	6.74041	+	4.50380i	0.788905	+	0.527130i	−0.0946199	+	0.995513i	$0.530164\pi$
$74$	0.626690	−	0.714603i	0.0728512	−	0.0830709i
$75$		0			0
$76$	3.24788	−	4.23273i	0.372558	−	0.485527i
$77$	−0.333232	+	0.434276i	−0.0379753	+	0.0494904i
$78$		0			0
$79$	5.06005	−	5.76989i	0.569301	−	0.649163i	−0.393516	−	0.919318i	$-0.628742\pi$
$79$	5.06005	−	5.76989i	0.569301	−	0.649163i	0.962817	+	0.270155i	$0.0870748\pi$
$80$	3.59096	+	2.39940i	0.401482	+	0.268262i
$81$		0			0
$82$	−1.87266	+	0.372496i	−0.206801	+	0.0411353i
$83$	3.29965	−	2.53191i	0.362184	−	0.277913i	−0.411598	−	0.911365i	$-0.635029\pi$
$83$	3.29965	−	2.53191i	0.362184	−	0.277913i	0.773782	+	0.633452i	$0.218363\pi$
$84$		0			0
$85$	−1.82640	+	5.78854i	−0.198101	+	0.627855i
$86$	−1.06615	+	0.615539i	−0.114965	+	0.0663753i
$87$		0			0
$88$	2.69093	+	0.913447i	0.286854	+	0.0973738i
$89$	2.40264	−	2.40264i	0.254680	−	0.254680i	−0.568206	−	0.822886i	$-0.692363\pi$
$89$	2.40264	−	2.40264i	0.254680	−	0.254680i	0.822886	+	0.568206i	$0.192363\pi$
$90$		0			0
$91$	−0.283031	+	1.42289i	−0.0296697	+	0.149160i
$92$	6.52802	−	0.427869i	0.680594	−	0.0446085i
$93$		0			0
$94$	−1.63550	−	1.25496i	−0.168689	−	0.129439i
$95$	−3.87757	−	1.91220i	−0.397830	−	0.196188i
$96$		0			0
$97$	8.28805	+	16.8065i	0.841524	+	1.70644i	0.697157	+	0.716919i	$0.254448\pi$
$97$	8.28805	+	16.8065i	0.841524	+	1.70644i	0.144367	+	0.989524i	$0.453885\pi$
$98$	−2.08929	−	2.08929i	−0.211050	−	0.211050i
$99$		0			0
$100$	−1.96938	+	4.75449i	−0.196938	+	0.475449i
$101$	1.81085	−	3.13649i	0.180187	−	0.312092i	−0.761757	−	0.647862i	$-0.775663\pi$
$101$	1.81085	−	3.13649i	0.180187	−	0.312092i	0.941944	+	0.335770i	$0.108996\pi$
$102$		0			0
$103$	6.75574	+	11.7013i	0.665663	+	1.15296i	0.979105	+	0.203355i	$0.0651844\pi$
$103$	6.75574	+	11.7013i	0.665663	+	1.15296i	−0.313442	+	0.949607i	$0.601482\pi$
$104$	7.46710	−	0.983062i	0.732209	−	0.0963972i
$105$		0			0
$106$	−4.38926	+	1.17610i	−0.426322	+	0.114233i
$107$	−2.01958	+	3.02251i	−0.195240	+	0.292197i	−0.916153	−	0.400828i	$-0.868723\pi$
$107$	−2.01958	+	3.02251i	−0.195240	+	0.292197i	0.720913	+	0.693025i	$0.243723\pi$
$108$		0			0
$109$	6.81952	−	4.55666i	0.653192	−	0.436449i	−0.184321	−	0.982866i	$-0.559009\pi$
$109$	6.81952	−	4.55666i	0.653192	−	0.436449i	0.837513	+	0.546417i	$0.184009\pi$
$110$	0.143070	−	1.08673i	0.0136412	−	0.103615i
$111$		0			0
$112$	−0.408438	+	0.828230i	−0.0385938	+	0.0782604i
$113$	17.8320	−	6.05316i	1.67750	−	0.569434i	0.689552	−	0.724236i	$-0.257807\pi$
$113$	17.8320	−	6.05316i	1.67750	−	0.569434i	0.987945	+	0.154802i	$0.0494741\pi$
$114$		0			0
$115$	−1.37209	−	5.12072i	−0.127948	−	0.477510i
$116$	2.54931	+	12.8163i	0.236698	+	1.18996i
$117$		0			0
$118$			2.81149i			0.258819i
$119$	−1.27811	−	0.225631i	−0.117164	−	0.0206835i
$120$		0			0
$121$	−1.04108	−	7.90776i	−0.0946433	−	0.718887i
$122$	1.08063	+	1.23222i	0.0978358	+	0.111560i
$123$		0			0
$124$	−14.9489	+	7.37200i	−1.34245	+	0.662025i
$125$	11.3095	+	2.24959i	1.01155	+	0.201210i
$126$		0			0
$127$	−6.18204	−	14.9248i	−0.548568	−	1.32436i	−0.918544	−	0.395318i	$-0.870634\pi$
$127$	−6.18204	−	14.9248i	−0.548568	−	1.32436i	0.369977	−	0.929041i	$-0.379366\pi$
$128$	10.6397	+	1.40075i	0.940428	+	0.123810i
$129$		0			0
$130$	−0.933791	−	2.75086i	−0.0818989	−	0.241266i
$131$	−0.471269	+	7.19017i	−0.0411750	+	0.628209i	0.926546	+	0.376183i	$0.122763\pi$
$131$	−0.471269	+	7.19017i	−0.0411750	+	0.628209i	−0.967720	+	0.252026i	$0.918903\pi$
$132$		0			0
$133$	0.297155	−	0.875391i	0.0257666	−	0.0759060i
$134$	−1.84571	−	0.764518i	−0.159445	−	0.0660443i
$135$		0			0
$136$	1.02364	+	6.65958i	0.0877760	+	0.571054i
$137$	−16.9099	−	9.76295i	−1.44471	−	0.834105i	−0.446553	−	0.894757i	$-0.647349\pi$
$137$	−16.9099	−	9.76295i	−1.44471	−	0.834105i	−0.998159	+	0.0606525i	$0.980682\pi$
$138$		0			0
$139$	7.89024	−	6.91956i	0.669242	−	0.586909i	−0.255821	−	0.966724i	$-0.582346\pi$
$139$	7.89024	−	6.91956i	0.669242	−	0.586909i	0.925062	+	0.379815i	$0.124012\pi$
$140$	0.813173	+	0.217889i	0.0687256	+	0.0184150i
$141$		0			0
$142$	1.93477	+	1.69675i	0.162362	+	0.142388i
$143$	4.45267	+	6.66389i	0.372351	+	0.557262i
$144$		0			0
$145$	9.78313	−	4.05231i	0.812445	−	0.336526i
$146$	−0.227010	−	3.46351i	−0.0187875	−	0.286642i
$147$		0			0
$148$	4.02419	+	0.263760i	0.330787	+	0.0216809i
$149$	0.760197	−	2.83710i	0.0622778	−	0.232424i	−0.927771	−	0.373151i	$-0.878277\pi$
$149$	0.760197	−	2.83710i	0.0622778	−	0.232424i	0.990048	+	0.140727i	$0.0449440\pi$
$150$		0			0
$151$	−2.39553	−	3.12191i	−0.194945	−	0.254058i	0.685645	−	0.727936i	$-0.259520\pi$
$151$	−2.39553	−	3.12191i	−0.194945	−	0.254058i	−0.880590	+	0.473878i	$0.842854\pi$
$152$	−4.79920			−0.389266
$153$		0			0
$154$	0.234373			0.0188863
$155$	8.22245	+	10.7157i	0.660443	+	0.860706i
$156$		0			0
$157$	−1.50636	+	5.62181i	−0.120221	+	0.448669i	−0.999624	−	0.0274075i	$-0.991275\pi$
$157$	−1.50636	+	5.62181i	−0.120221	+	0.448669i	0.879404	+	0.476077i	$0.157941\pi$
$158$	−3.27883	−	0.214906i	−0.260850	−	0.0170970i
$159$		0			0
$160$	−0.435624	−	6.64634i	−0.0344391	−	0.525439i
$161$	1.04727	−	0.433793i	0.0825364	−	0.0341877i
$162$		0			0
$163$	−4.31689	−	6.46068i	−0.338125	−	0.506039i	0.622975	−	0.782242i	$-0.285924\pi$
$163$	−4.31689	−	6.46068i	−0.338125	−	0.506039i	−0.961099	+	0.276203i	$0.910924\pi$
$164$	−6.09090	−	5.34158i	−0.475619	−	0.417107i
$165$		0			0
$166$	−1.72010	−	0.460898i	−0.133505	−	0.0357727i
$167$	2.26505	−	1.98640i	0.175275	−	0.153712i	−0.567214	−	0.823571i	$-0.691979\pi$
$167$	2.26505	−	1.98640i	0.175275	−	0.153712i	0.742489	+	0.669859i	$0.233645\pi$
$168$		0			0
$169$	7.13714	+	4.12063i	0.549011	+	0.316972i
$170$	2.44232	−	0.888375i	0.187317	−	0.0681352i
$171$		0			0
$172$	−4.82582	−	1.99892i	−0.367966	−	0.152416i
$173$	−7.99671	+	23.5575i	−0.607978	+	1.79105i	0.00376823	+	0.999993i	$0.498801\pi$
$173$	−7.99671	+	23.5575i	−0.607978	+	1.79105i	−0.611747	+	0.791054i	$0.709533\pi$
$174$		0			0
$175$	−0.0583200	+	0.889792i	−0.00440858	+	0.0672619i
$176$	1.63984	+	4.83082i	0.123608	+	0.364137i
$177$		0			0
$178$	−1.44238	−	0.189893i	−0.108111	−	0.0142331i
$179$	−5.98135	−	14.4403i	−0.447067	−	1.07932i	−0.973415	−	0.229047i	$-0.926439\pi$
$179$	−5.98135	−	14.4403i	−0.447067	−	1.07932i	0.526348	−	0.850269i	$-0.323561\pi$
$180$		0			0
$181$	−0.871620	−	0.173376i	−0.0647870	−	0.0128869i	0.162590	−	0.986694i	$-0.448015\pi$
$181$	−0.871620	−	0.173376i	−0.0647870	−	0.0128869i	−0.227377	+	0.973807i	$0.573015\pi$
$182$	0.557105	−	0.274734i	0.0412954	−	0.0203646i
$183$		0			0
$184$	−3.88008	−	4.42439i	−0.286044	−	0.326170i
$185$	−0.426562	−	3.24006i	−0.0313615	−	0.238214i
$186$		0			0
$187$	−5.87410	+	4.11133i	−0.429557	+	0.300650i
$188$		−	8.74689i		−	0.637933i
$189$		0			0
$190$	0.361137	+	1.81556i	0.0261996	+	0.131714i
$191$	−5.51673	−	20.5887i	−0.399177	−	1.48975i	−0.814548	−	0.580096i	$-0.803015\pi$
$191$	−5.51673	−	20.5887i	−0.399177	−	1.48975i	0.415372	−	0.909652i	$-0.363651\pi$
$192$		0			0
$193$	−6.94554	+	2.35769i	−0.499951	+	0.169710i	−0.560012	−	0.828484i	$-0.689204\pi$
$193$	−6.94554	+	2.35769i	−0.499951	+	0.169710i	0.0600615	+	0.998195i	$0.480870\pi$
$194$	3.54863	−	7.19590i	0.254776	−	0.516636i
$195$		0			0
$196$	1.63637	−	12.4295i	0.116884	−	0.887820i
$197$	−17.8237	+	11.9094i	−1.26988	+	0.848509i	−0.993643	−	0.112579i	$-0.964089\pi$
$197$	−17.8237	+	11.9094i	−1.26988	+	0.848509i	−0.276241	+	0.961088i	$0.589089\pi$
$198$		0			0
$199$	−1.58466	+	2.37161i	−0.112333	+	0.168119i	−0.883376	−	0.468664i	$-0.844735\pi$
$199$	−1.58466	+	2.37161i	−0.112333	+	0.168119i	0.771043	+	0.636783i	$0.219735\pi$
$200$	4.47144	−	1.19812i	0.316179	−	0.0847199i
$201$		0			0
$202$	−1.53741	+	0.202404i	−0.108172	+	0.0142411i
$203$	1.13211	+	1.96087i	0.0794585	+	0.137626i
$204$		0			0
$205$	−3.28247	+	5.68541i	−0.229258	+	0.397086i
$206$	2.21386	−	5.34473i	0.154247	−	0.372385i
$207$		0			0
$208$	9.56064	+	9.56064i	0.662911	+	0.662911i
$209$	−2.25877	−	4.58034i	−0.156243	−	0.316829i
$210$		0			0
$211$	−20.0517	−	9.88840i	−1.38042	−	0.680746i	−0.407780	−	0.913080i	$-0.633697\pi$
$211$	−20.0517	−	9.88840i	−1.38042	−	0.680746i	−0.972636	+	0.232334i	$0.925364\pi$
$212$	−15.2962	−	11.7372i	−1.05055	−	0.806114i
$213$		0			0
$214$	1.55310	−	0.101795i	0.106168	−	0.00695859i
$215$	−0.825785	+	4.15150i	−0.0563180	+	0.283130i
$216$		0			0
$217$	−2.04218	+	2.04218i	−0.138632	+	0.138632i
$218$	−3.32532	−	1.12879i	−0.225219	−	0.0764515i
$219$		0			0
$220$	4.02766	−	2.32537i	0.271545	−	0.156776i
$221$	−9.14342	+	16.6583i	−0.615053	+	1.12056i
$222$		0			0
$223$	16.3407	−	12.5387i	1.09426	−	0.839653i	0.106293	−	0.994335i	$-0.466102\pi$
$223$	16.3407	−	12.5387i	1.09426	−	0.839653i	0.987964	+	0.154682i	$0.0494353\pi$
$224$	1.39683	−	0.277846i	0.0933295	−	0.0185644i
$225$		0			0
$226$	−6.70405	−	4.47950i	−0.445947	−	0.297972i
$227$	−8.45193	+	9.63758i	−0.560975	+	0.639669i	−0.960906	−	0.276876i	$-0.910701\pi$
$227$	−8.45193	+	9.63758i	−0.560975	+	0.639669i	0.399931	+	0.916545i	$0.369034\pi$
$228$		0			0
$229$	−16.7037	+	21.7687i	−1.10381	+	1.43852i	−0.217128	+	0.976143i	$0.569669\pi$
$229$	−16.7037	+	21.7687i	−1.10381	+	1.43852i	−0.886685	+	0.462374i	$0.846998\pi$
$230$	−1.38179	+	1.80078i	−0.0911126	+	0.118740i
$231$		0			0
$232$	7.75026	−	8.83747i	0.508829	−	0.580209i
$233$	−7.36408	−	4.92052i	−0.482437	−	0.322354i	0.290458	−	0.956888i	$-0.406192\pi$
$233$	−7.36408	−	4.92052i	−0.482437	−	0.322354i	−0.772895	+	0.634533i	$0.781192\pi$
$234$		0			0
$235$	−6.95188	+	1.38282i	−0.453491	+	0.0902049i
$236$	−9.46399	+	7.26197i	−0.616053	+	0.472714i
$237$		0			0
$238$	0.256495	+	0.492964i	0.0166261	+	0.0319541i
$239$	−17.0123	+	9.82203i	−1.10043	+	0.635334i	−0.936334	−	0.351110i	$-0.885804\pi$
$239$	−17.0123	+	9.82203i	−1.10043	+	0.635334i	−0.164097	+	0.986444i	$0.552471\pi$
$240$		0			0
$241$	17.3786	+	5.89925i	1.11946	+	0.380004i	0.819001	−	0.573792i	$-0.194528\pi$
$241$	17.3786	+	5.89925i	1.11946	+	0.380004i	0.300455	+	0.953796i	$0.402861\pi$
$242$	−2.41478	+	2.41478i	−0.155228	+	0.155228i
$243$		0			0
$244$	−1.35666	+	6.82038i	−0.0868512	+	0.436630i
$245$	−10.1374	+	0.664443i	−0.647658	+	0.0424497i
$246$		0			0
$247$	−10.7382	−	8.23973i	−0.683257	−	0.524281i
$248$	13.4470	+	6.63133i	0.853885	+	0.421090i
$249$		0			0
$250$	−2.18364	−	4.42799i	−0.138106	−	0.280051i
$251$	8.88797	+	8.88797i	0.561004	+	0.561004i	0.929593	−	0.368589i	$-0.120159\pi$
$251$	8.88797	+	8.88797i	0.561004	+	0.561004i	−0.368589	+	0.929593i	$0.620159\pi$
$252$		0			0
$253$	2.39643	−	5.78550i	0.150663	−	0.363731i
$254$	−3.45836	+	5.99005i	−0.216997	+	0.375849i
$255$		0			0
$256$	1.63276	+	2.82802i	0.102048	+	0.176751i
$257$	−5.18162	+	0.682173i	−0.323220	+	0.0425528i	−0.290391	−	0.956908i	$-0.593785\pi$
$257$	−5.18162	+	0.682173i	−0.323220	+	0.0425528i	−0.0328297	+	0.999461i	$0.510452\pi$
$258$		0			0
$259$	0.674969	−	0.180858i	0.0419406	−	0.0112379i
$260$	6.84794	−	10.2487i	0.424691	−	0.635595i
$261$		0			0
$262$	2.56522	−	1.71402i	0.158480	−	0.105893i
$263$	1.34155	−	10.1901i	0.0827238	−	0.628350i	−0.898988	−	0.437974i	$-0.855696\pi$
$263$	1.34155	−	10.1901i	0.0827238	−	0.628350i	0.981711	−	0.190375i	$-0.0609705\pi$
$264$		0			0
$265$	−6.91032	+	14.0127i	−0.424498	+	0.860796i
$266$	−0.374809	+	0.127230i	−0.0229810	+	0.00780099i
$267$		0			0
$268$	−2.19389	−	8.18770i	−0.134013	−	0.500144i
$269$	−2.69186	−	13.5329i	−0.164126	−	0.825116i	−0.971858	−	0.235567i	$-0.924305\pi$
$269$	−2.69186	−	13.5329i	−0.164126	−	0.825116i	0.807733	−	0.589549i	$-0.200695\pi$
$270$		0			0
$271$		−	9.45664i		−	0.574450i	−0.957863	−	0.287225i	$-0.907267\pi$
$271$		−	9.45664i		−	0.574450i	0.957863	−	0.287225i	$-0.0927327\pi$
$272$	−8.36619	+	8.73592i	−0.507275	+	0.529693i
$273$		0			0
$274$	1.09123	+	8.28871i	0.0659236	+	0.500739i
$275$	3.24799	+	3.70363i	0.195861	+	0.223337i
$276$		0			0
$277$	7.96652	−	3.92865i	0.478662	−	0.236050i	−0.186920	−	0.982375i	$-0.559850\pi$
$277$	7.96652	−	3.92865i	0.478662	−	0.236050i	0.665581	+	0.746325i	$0.268184\pi$
$278$	−4.40703	−	0.876614i	−0.264316	−	0.0525758i
$279$		0			0
$280$	−0.289797	−	0.699632i	−0.0173187	−	0.0418110i
$281$	29.8332	+	3.92761i	1.77970	+	0.234302i	0.947405	−	0.320036i	$-0.103695\pi$
$281$	29.8332	+	3.92761i	1.77970	+	0.234302i	0.832292	+	0.554338i	$0.187028\pi$
$282$		0			0
$283$	4.56871	+	13.4590i	0.271581	+	0.800053i	0.994077	+	0.108677i	$0.0346616\pi$
$283$	4.56871	+	13.4590i	0.271581	+	0.800053i	−0.722496	+	0.691375i	$0.757005\pi$
$284$	−0.714123	+	10.8954i	−0.0423754	+	0.646524i
$285$		0			0
$286$	1.10303	−	3.24943i	0.0652236	−	0.192143i
$287$	−1.29689	−	0.537188i	−0.0765528	−	0.0317092i
$288$		0			0
$289$	−15.0760	−	7.85579i	−0.886825	−	0.462106i
$290$	−3.92646	−	2.26694i	−0.230569	−	0.133119i
$291$		0			0
$292$	11.0724	−	9.71026i	0.647965	−	0.568250i
$293$	30.3108	+	8.12175i	1.77078	+	0.474478i	0.988853	−	0.148897i	$-0.0475723\pi$
$293$	30.3108	+	8.12175i	1.77078	+	0.474478i	0.781923	+	0.623375i	$0.214239\pi$
$294$		0			0
$295$	7.26788	+	6.37376i	0.423152	+	0.371095i
$296$	−2.01541	−	3.01628i	−0.117143	−	0.175318i
$297$		0			0
$298$	−1.16186	+	0.481257i	−0.0673046	+	0.0278785i
$299$	−1.08548	−	16.5613i	−0.0627752	−	0.957764i
$300$		0			0
$301$	−0.903142	−	0.0591950i	−0.0520562	−	0.00341194i
$302$	−0.436072	+	1.62744i	−0.0250931	+	0.0936488i
$303$		0			0
$304$	−5.24487	−	6.83524i	−0.300814	−	0.392028i
$305$	5.63520			0.322671
$306$		0			0
$307$	−31.8168			−1.81588			−0.907940	−	0.419101i	$-0.862345\pi$
$307$	−31.8168			−1.81588			−0.907940	+	0.419101i	$0.862345\pi$
$308$	0.605375	+	0.788940i	0.0344944	+	0.0449540i
$309$		0			0
$310$	1.49678	−	5.58606i	0.0850114	−	0.317267i
$311$	−32.1576	−	2.10772i	−1.82349	−	0.119518i	−0.885165	−	0.465277i	$-0.845955\pi$
$311$	−32.1576	−	2.10772i	−1.82349	−	0.119518i	−0.938323	+	0.345759i	$0.887621\pi$
$312$		0			0
$313$	−0.853948	−	13.0287i	−0.0482680	−	0.736427i	−0.951572	−	0.307426i	$-0.900532\pi$
$313$	−0.853948	−	13.0287i	−0.0482680	−	0.736427i	0.903304	−	0.429001i	$-0.141134\pi$
$314$	2.30226	−	0.953629i	0.129924	−	0.0538164i
$315$		0			0
$316$	−7.74567	−	11.5922i	−0.435728	−	0.652113i
$317$	14.4524	+	12.6744i	0.811729	+	0.711868i	0.960885	−	0.276946i	$-0.0893224\pi$
$317$	14.4524	+	12.6744i	0.811729	+	0.711868i	−0.149156	+	0.988814i	$0.547656\pi$
$318$		0			0
$319$	12.0822	+	3.23740i	0.676471	+	0.181260i
$320$	4.35001	−	3.81485i	0.243173	−	0.213257i
$321$		0			0
$322$	−0.420321	−	0.242673i	−0.0234236	−	0.0135236i
$323$	7.16200	−	9.76361i	0.398504	−	0.543262i
$324$		0			0
$325$	12.0619	+	4.99621i	0.669075	+	0.277140i
$326$	−1.06940	+	3.15034i	−0.0592284	+	0.174481i
$327$		0			0
$328$	−0.476617	+	7.27178i	−0.0263168	+	0.401517i
$329$	−0.487173	−	1.43517i	−0.0268587	−	0.0791233i
$330$		0			0
$331$	−27.6154	−	3.63564i	−1.51788	−	0.199833i	−0.674953	−	0.737861i	$-0.735836\pi$
$331$	−27.6154	−	3.63564i	−1.51788	−	0.199833i	−0.842927	+	0.538029i	$0.819169\pi$
$332$	−2.89147	−	6.98063i	−0.158690	−	0.383112i
$333$		0			0
$334$	−1.26513	−	0.251650i	−0.0692248	−	0.0137697i
$335$	−6.16061	+	3.03808i	−0.336590	+	0.165988i
$336$		0			0
$337$	8.38319	+	9.55920i	0.456662	+	0.520723i	0.933650	−	0.358187i	$-0.116605\pi$
$337$	8.38319	+	9.55920i	0.456662	+	0.520723i	−0.476988	+	0.878910i	$0.658272\pi$
$338$	−0.460573	−	3.49840i	−0.0250519	−	0.190288i
$339$		0			0
$340$	9.29884	+	5.92664i	0.504300	+	0.321417i
$341$			15.9548i			0.864003i
$342$		0			0
$343$	−0.853665	−	4.29166i	−0.0460936	−	0.231728i
$344$	1.21610	+	4.53853i	0.0655675	+	0.244701i
$345$		0			0
$346$	10.0864	−	3.42388i	0.542250	−	0.184069i
$347$	13.4709	−	27.3162i	0.723154	−	1.46641i	−0.154941	−	0.987924i	$-0.549519\pi$
$347$	13.4709	−	27.3162i	0.723154	−	1.46641i	0.878095	−	0.478487i	$-0.158815\pi$
$348$		0			0
$349$	2.54288	−	19.3151i	0.136117	−	1.03391i	−0.777943	−	0.628335i	$-0.783737\pi$
$349$	2.54288	−	19.3151i	0.136117	−	1.03391i	0.914060	−	0.405578i	$-0.132930\pi$
$350$	0.317448	−	0.212112i	0.0169683	−	0.0113379i
$351$		0			0
$352$	4.37110	−	6.54181i	0.232980	−	0.348680i
$353$	5.37930	−	1.44138i	0.286311	−	0.0767169i	−0.112805	−	0.993617i	$-0.535984\pi$
$353$	5.37930	−	1.44138i	0.286311	−	0.0767169i	0.399116	+	0.916900i	$0.369317\pi$
$354$		0			0
$355$	8.77239	−	1.15491i	0.465590	−	0.0612961i
$356$	−3.08640	−	5.34580i	−0.163579	−	0.283327i
$357$		0			0
$358$	−3.34609	+	5.79559i	−0.176846	+	0.306307i
$359$	−12.0601	+	29.1158i	−0.636510	+	1.53667i	0.194789	+	0.980845i	$0.437598\pi$
$359$	−12.0601	+	29.1158i	−0.636510	+	1.53667i	−0.831299	+	0.555826i	$0.812402\pi$
$360$		0			0
$361$	−7.33635	−	7.33635i	−0.386123	−	0.386123i
$362$	0.168293	+	0.341265i	0.00884530	+	0.0179365i
$363$		0			0
$364$	2.36378	+	1.16569i	0.123896	+	0.0610986i
$365$	−9.46802	−	7.26507i	−0.495579	−	0.380271i
$366$		0			0
$367$	9.89647	−	0.648649i	0.516592	−	0.0338592i	0.195122	−	0.980779i	$-0.437490\pi$
$367$	9.89647	−	0.648649i	0.516592	−	0.0338592i	0.321470	+	0.946920i	$0.395823\pi$
$368$	2.06102	−	10.3614i	0.107438	−	0.540128i
$369$		0			0
$370$	−0.989412	+	0.989412i	−0.0514371	+	0.0514371i
$371$	−3.16349	−	1.07386i	−0.164240	−	0.0557520i
$372$		0			0
$373$	−24.3815	+	14.0767i	−1.26243	+	0.728863i	−0.973544	−	0.228501i	$-0.926618\pi$
$373$	−24.3815	+	14.0767i	−1.26243	+	0.728863i	−0.288884	+	0.957364i	$0.593284\pi$
$374$	2.92762	+	0.923723i	0.151384	+	0.0477646i
$375$		0			0
$376$	−6.24217	+	4.78978i	−0.321915	+	0.247014i
$377$	32.5143	−	6.46749i	1.67457	−	0.333093i
$378$		0			0
$379$	−19.3719	−	12.9439i	−0.995067	−	0.664883i	−0.0524031	−	0.998626i	$-0.516688\pi$
$379$	−19.3719	−	12.9439i	−0.995067	−	0.664883i	−0.942664	+	0.333743i	$0.891688\pi$
$380$	−5.17868	+	5.90516i	−0.265661	+	0.302928i
$381$		0			0
$382$	−5.55572	+	7.24035i	−0.284255	+	0.370449i
$383$	12.4032	−	16.1641i	0.633772	−	0.825947i	−0.360508	−	0.932756i	$-0.617397\pi$
$383$	12.4032	−	16.1641i	0.633772	−	0.825947i	0.994280	+	0.106809i	$0.0340633\pi$
$384$		0			0
$385$	0.531331	−	0.605867i	0.0270792	−	0.0308779i
$386$	2.61121	+	1.74476i	0.132907	+	0.0888057i
$387$		0			0
$388$	33.3886	−	6.64141i	1.69505	−	0.337167i
$389$	19.8781	−	15.2530i	1.00786	−	0.773359i	0.0337501	−	0.999430i	$-0.489255\pi$
$389$	19.8781	−	15.2530i	1.00786	−	0.773359i	0.974111	+	0.226071i	$0.0725883\pi$
$390$		0			0
$391$	14.7915	−	1.29109i	0.748036	−	0.0652930i
$392$	−9.76630	+	5.63858i	−0.493273	+	0.284791i
$393$		0			0
$394$	8.69113	+	2.95024i	0.437853	+	0.148631i
$395$	−7.98877	+	7.98877i	−0.401958	+	0.401958i
$396$		0			0
$397$	−0.535806	+	2.69368i	−0.0268914	+	0.135192i	−0.991899	−	0.127030i	$-0.959455\pi$
$397$	−0.535806	+	2.69368i	−0.0268914	+	0.135192i	0.965007	+	0.262222i	$0.0844554\pi$
$398$	1.21863	−	0.0798735i	0.0610846	−	0.00400370i
$399$		0			0
$400$	6.59310	+	5.05906i	0.329655	+	0.252953i
$401$	14.3340	+	7.06875i	0.715806	+	0.352997i	0.763449	−	0.645868i	$-0.223504\pi$
$401$	14.3340	+	7.06875i	0.715806	+	0.352997i	−0.0476429	+	0.998864i	$0.515171\pi$
$402$		0			0
$403$	18.7024	+	37.9247i	0.931633	+	1.88917i
$404$	−4.65239	−	4.65239i	−0.231465	−	0.231465i
$405$		0			0
$406$	0.370993	−	0.895656i	0.0184121	−	0.0444506i
$407$	1.93016	−	3.34313i	0.0956744	−	0.165713i
$408$		0			0
$409$	4.21393	+	7.29874i	0.208365	+	0.360899i	0.951200	−	0.308576i	$-0.0998523\pi$
$409$	4.21393	+	7.29874i	0.208365	+	0.360899i	−0.742834	+	0.669475i	$0.766519\pi$
$410$	2.78681	−	0.366890i	0.137631	−	0.0181194i
$411$		0			0
$412$	23.7096	−	6.35297i	1.16809	−	0.312989i
$413$	−1.14836	+	1.71864i	−0.0565070	+	0.0845687i
$414$		0			0
$415$	−5.09097	+	3.40168i	−0.249906	+	0.166982i
$416$	2.72175	−	20.6737i	0.133445	−	1.01361i
$417$		0			0
$418$	−0.967119	+	1.96112i	−0.0473033	+	0.0959217i
$419$	−10.8486	+	3.68261i	−0.529989	+	0.179907i	−0.573591	−	0.819142i	$-0.694450\pi$
$419$	−10.8486	+	3.68261i	−0.529989	+	0.179907i	0.0436016	+	0.999049i	$0.486117\pi$
$420$		0			0
$421$	3.00563	+	11.2172i	0.146485	+	0.546691i	0.999685	+	0.0251059i	$0.00799230\pi$
$421$	3.00563	+	11.2172i	0.146485	+	0.546691i	−0.853199	+	0.521585i	$0.825341\pi$
$422$	1.86751	+	9.38862i	0.0909091	+	0.457031i
$423$		0			0
$424$			17.3433i			0.842267i
$425$	−4.23539	+	10.8848i	−0.205447	+	0.527991i
$426$		0			0
$427$	0.157276	+	1.19463i	0.00761113	+	0.0578123i
$428$	4.35425	+	4.96507i	0.210470	+	0.239996i
$429$		0			0
$430$	1.62543	−	0.801576i	0.0783854	−	0.0386554i
$431$	−16.3546	−	3.25313i	−0.787772	−	0.156698i	−0.215220	−	0.976566i	$-0.569047\pi$
$431$	−16.3546	−	3.25313i	−0.787772	−	0.156698i	−0.572552	+	0.819868i	$0.694047\pi$
$432$		0			0
$433$	2.99292	+	7.22556i	0.143831	+	0.347238i	0.979335	−	0.202246i	$-0.0648242\pi$
$433$	2.99292	+	7.22556i	0.143831	+	0.347238i	−0.835504	+	0.549484i	$0.814824\pi$
$434$	1.22599	+	0.161404i	0.0588493	+	0.00774765i
$435$		0			0
$436$	−4.78944	−	14.1092i	−0.229373	−	0.675710i
$437$	−0.691686	+	10.5531i	−0.0330878	+	0.504823i
$438$		0			0
$439$	−6.41610	+	18.9012i	−0.306224	+	0.902106i	0.679491	+	0.733684i	$0.262201\pi$
$439$	−6.41610	+	18.9012i	−0.306224	+	0.902106i	−0.985715	+	0.168422i	$0.946133\pi$
$440$	−3.86502	−	1.60095i	−0.184258	−	0.0763221i
$441$		0			0
$442$	8.04177	−	1.23609i	0.382508	−	0.0587948i
$443$	23.4193	+	13.5212i	1.11269	+	0.642410i	0.939524	−	0.342483i	$-0.111268\pi$
$443$	23.4193	+	13.5212i	1.11269	+	0.642410i	0.173163	+	0.984893i	$0.444601\pi$
$444$		0			0
$445$	−3.76082	+	3.29815i	−0.178280	+	0.156347i
$446$	−8.51837	−	2.28249i	−0.403356	−	0.108079i
$447$		0			0
$448$	0.930134	+	0.815706i	0.0439447	+	0.0385385i
$449$	19.2189	+	28.7631i	0.906996	+	1.35741i	0.933808	+	0.357774i	$0.116464\pi$
$449$	19.2189	+	28.7631i	0.906996	+	1.35741i	−0.0268124	+	0.999640i	$0.508536\pi$
$450$		0			0
$451$	−7.16448	+	2.96762i	−0.337362	+	0.139740i
$452$	−2.23748	−	34.1374i	−0.105242	−	1.60569i
$453$		0			0
$454$	5.47671	+	0.358962i	0.257035	+	0.0168469i
$455$	0.552774	−	2.06298i	0.0259144	−	0.0967140i
$456$		0			0
$457$	−0.429092	−	0.559204i	−0.0200721	−	0.0261584i	0.783209	−	0.621758i	$-0.213581\pi$
$457$	−0.429092	−	0.559204i	−0.0200721	−	0.0261584i	−0.803282	+	0.595599i	$0.796915\pi$
$458$	11.7483			0.548960
$459$		0			0
$460$	−9.63087			−0.449041
$461$	9.18375	+	11.9685i	0.427730	+	0.557428i	0.956649	−	0.291244i	$-0.0940692\pi$
$461$	9.18375	+	11.9685i	0.427730	+	0.557428i	−0.528919	+	0.848672i	$0.677402\pi$
$462$		0			0
$463$	0.430077	−	1.60507i	0.0199874	−	0.0745938i	−0.955212	−	0.295923i	$-0.904373\pi$
$463$	0.430077	−	1.60507i	0.0199874	−	0.0745938i	0.975199	+	0.221329i	$0.0710395\pi$
$464$	21.0567	+	1.38013i	0.977534	+	0.0640709i
$465$		0			0
$466$	0.248015	+	3.78398i	0.0114891	+	0.175290i
$467$	−7.68148	+	3.18177i	−0.355457	+	0.147235i	−0.553264	−	0.833006i	$-0.686618\pi$
$467$	−7.68148	+	3.18177i	−0.355457	+	0.147235i	0.197807	+	0.980241i	$0.436618\pi$
$468$		0			0
$469$	−0.815995	−	1.22122i	−0.0376792	−	0.0563909i
$470$	2.28172	+	2.00101i	0.105248	+	0.0922997i
$471$		0			0
$472$	10.3649	+	2.77728i	0.477085	+	0.127834i
$473$	−3.75919	+	3.29672i	−0.172848	+	0.151584i
$474$		0			0
$475$	−7.20472	−	4.15965i	−0.330575	−	0.190858i
$476$	−0.996888	+	2.13671i	−0.0456923	+	0.0979360i
$477$		0			0
$478$	7.77059	+	3.21868i	0.355419	+	0.147219i
$479$	−4.44762	+	13.1023i	−0.203217	+	0.598658i	−0.999984	−	0.00562848i	$-0.998208\pi$
$479$	−4.44762	+	13.1023i	−0.203217	+	0.598658i	0.796767	+	0.604286i	$0.206542\pi$
$480$		0			0
$481$	0.669146	−	10.2092i	0.0305104	−	0.465499i
$482$	−2.52583	−	7.44086i	−0.115049	−	0.338922i
$483$		0			0
$484$	−14.3659	−	1.89130i	−0.652993	−	0.0859682i
$485$	−10.5570	−	25.4868i	−0.479367	−	1.15729i
$486$		0			0
$487$	23.3311	+	4.64084i	1.05723	+	0.210296i	0.692945	−	0.720991i	$-0.256313\pi$
$487$	23.3311	+	4.64084i	1.05723	+	0.210296i	0.364286	+	0.931287i	$0.381313\pi$
$488$	5.61023	−	2.76666i	0.253963	−	0.125241i
$489$		0			0
$490$	2.86801	+	3.27033i	0.129563	+	0.147739i
$491$	−3.45165	−	26.2179i	−0.155771	−	1.18320i	−0.873483	−	0.486855i	$-0.838144\pi$
$491$	−3.45165	−	26.2179i	−0.155771	−	1.18320i	0.717712	−	0.696340i	$-0.245189\pi$
$492$		0			0
$493$	6.41323	+	28.9558i	0.288837	+	1.30410i
$494$			5.79526i			0.260741i
$495$		0			0
$496$	5.25108	+	26.3990i	0.235781	+	1.18535i
$497$	0.489667	+	1.82746i	0.0219646	+	0.0819730i
$498$		0			0
$499$	28.9006	−	9.81042i	1.29377	−	0.439175i	0.412140	−	0.911121i	$-0.364782\pi$
$499$	28.9006	−	9.81042i	1.29377	−	0.439175i	0.881627	+	0.471946i	$0.156448\pi$
$500$	9.26513	−	18.7878i	0.414349	−	0.840217i
$501$		0			0
$502$	0.702462	−	5.33573i	0.0313524	−	0.238145i
$503$	10.6641	−	7.12553i	0.475489	−	0.317712i	−0.294630	−	0.955611i	$-0.595197\pi$
$503$	10.6641	−	7.12553i	0.475489	−	0.317712i	0.770119	+	0.637900i	$0.220197\pi$
$504$		0			0
$505$	−2.96214	+	4.43315i	−0.131813	+	0.197273i
$506$	−2.58987	+	0.693952i	−0.115134	+	0.0308499i
$507$		0			0
$508$	−29.0964	+	3.83061i	−1.29094	+	0.169956i
$509$	4.49484	+	7.78528i	0.199230	+	0.345077i	0.948279	−	0.317438i	$-0.102823\pi$
$509$	4.49484	+	7.78528i	0.199230	+	0.345077i	−0.749049	+	0.662515i	$0.769489\pi$
$510$		0			0
$511$	1.27590	−	2.20993i	0.0564427	−	0.0977616i
$512$	8.74862	−	21.1210i	0.386638	−	0.933427i
$513$		0			0
$514$	1.58230	+	1.58230i	0.0697923	+	0.0697923i
$515$	−8.79754	−	17.8397i	−0.387666	−	0.786109i
$516$		0			0
$517$	−7.50927	−	3.70316i	−0.330257	−	0.162865i
$518$	−0.237364	−	0.182136i	−0.0104292	−	0.00800258i
$519$		0			0
$520$	−11.0638	+	0.725161i	−0.485181	+	0.0318004i
$521$	−2.27564	+	11.4404i	−0.0996976	+	0.501214i	0.898379	+	0.439221i	$0.144745\pi$
$521$	−2.27564	+	11.4404i	−0.0996976	+	0.501214i	−0.998077	+	0.0619925i	$0.980255\pi$
$522$		0			0
$523$	12.3418	−	12.3418i	0.539671	−	0.539671i	−0.383761	−	0.923432i	$-0.625371\pi$
$523$	12.3418	−	12.3418i	0.539671	−	0.539671i	0.923432	+	0.383761i	$0.125371\pi$
$524$	12.3956	+	4.20773i	0.541503	+	0.183815i
$525$		0			0
$526$	−3.81109	+	2.20033i	−0.166171	+	0.0959390i
$527$	−33.5583	+	17.4608i	−1.46182	+	0.760603i
$528$		0			0
$529$	7.95900	−	6.10716i	0.346044	−	0.265529i
$530$	6.56106	−	1.30508i	0.284994	−	0.0566888i
$531$		0			0
$532$	−1.39639	−	0.933041i	−0.0605414	−	0.0404525i
$533$	−13.5513	+	15.4523i	−0.586973	+	0.669314i
$534$		0			0
$535$	3.25778	−	4.24562i	0.140846	−	0.183554i
$536$	−4.64174	+	6.04923i	−0.200493	+	0.261287i
$537$		0			0
$538$	−3.89527	+	4.44171i	−0.167937	+	0.191496i
$539$	−9.97801	−	6.66709i	−0.429783	−	0.287172i
$540$		0			0
$541$	−4.00985	+	0.797608i	−0.172397	+	0.0342918i	−0.280534	−	0.959844i	$-0.590511\pi$
$541$	−4.00985	+	0.797608i	−0.172397	+	0.0342918i	0.108137	+	0.994136i	$0.465511\pi$
$542$	−3.21226	+	2.46486i	−0.137978	+	0.105875i
$543$		0			0
$544$	18.5433	+	2.03460i	0.795036	+	0.0872325i
$545$	−10.4566	+	6.03713i	−0.447912	+	0.258602i
$546$		0			0
$547$	−18.3367	−	6.22446i	−0.784019	−	0.266139i	−0.0994077	−	0.995047i	$-0.531695\pi$
$547$	−18.3367	−	6.22446i	−0.784019	−	0.266139i	−0.684612	+	0.728908i	$0.740028\pi$
$548$	−25.0827	+	25.0827i	−1.07148	+	1.07148i
$549$		0			0
$550$	0.411477	−	2.06863i	0.0175454	−	0.0882068i
$551$	−21.0792	+	1.38160i	−0.898005	+	0.0588583i
$552$		0			0
$553$	−1.91654	−	1.47061i	−0.0814994	−	0.0625367i
$554$	−3.41096	−	1.68210i	−0.144918	−	0.0714655i
$555$		0			0
$556$	−8.43235	−	17.0991i	−0.357611	−	0.725164i
$557$	−2.32543	−	2.32543i	−0.0985316	−	0.0985316i	0.656123	−	0.754654i	$-0.272195\pi$
$557$	−2.32543	−	2.32543i	−0.0985316	−	0.0985316i	−0.754654	+	0.656123i	$0.772195\pi$
$558$		0			0
$559$	−5.07117	+	12.2429i	−0.214488	+	0.517819i
$560$	0.679740	−	1.17734i	0.0287243	−	0.0497519i
$561$		0			0
$562$	−6.44181	−	11.1575i	−0.271732	−	0.470653i
$563$	9.97726	−	1.31353i	0.420491	−	0.0553587i	0.0826881	−	0.996575i	$-0.473649\pi$
$563$	9.97726	−	1.31353i	0.420491	−	0.0553587i	0.337803	+	0.941217i	$0.390316\pi$
$564$		0			0
$565$	−26.7781	+	7.17517i	−1.12656	+	0.301862i
$566$	3.38096	−	5.05997i	0.142113	−	0.212686i
$567$		0			0
$568$	8.16650	−	5.45668i	0.342659	−	0.228957i
$569$	3.11503	−	23.6610i	0.130589	−	0.991921i	−0.793185	−	0.608981i	$-0.791578\pi$
$569$	3.11503	−	23.6610i	0.130589	−	0.991921i	0.923773	−	0.382940i	$-0.125088\pi$
$570$		0			0
$571$	8.08248	−	16.3896i	0.338241	−	0.685885i	−0.659596	−	0.751620i	$-0.729273\pi$
$571$	8.08248	−	16.3896i	0.338241	−	0.685885i	0.997837	+	0.0657352i	$0.0209393\pi$
$572$	13.7872	−	4.68013i	0.576473	−	0.195686i
$573$		0			0
$574$	0.155557	+	0.580548i	0.00649284	+	0.0242316i
$575$	−1.99013	−	10.0051i	−0.0829941	−	0.417240i
$576$		0			0
$577$		−	22.3597i		−	0.930846i	−0.885088	−	0.465423i	$-0.845902\pi$
$577$		−	22.3597i		−	0.930846i	0.885088	−	0.465423i	$-0.154098\pi$
$578$	1.26106	+	7.16867i	0.0524530	+	0.298177i
$579$		0			0
$580$	−2.51095	−	19.0726i	−0.104262	−	0.791945i
$581$	−0.863223	−	0.984317i	−0.0358125	−	0.0408364i
$582$		0			0
$583$	−16.5524	+	8.16275i	−0.685531	+	0.338066i
$584$	−12.9929	−	2.58445i	−0.537651	−	0.106945i
$585$		0			0
$586$	−5.14163	−	12.4130i	−0.212399	−	0.512776i
$587$	25.3285	+	3.33456i	1.04542	+	0.137632i	0.633621	−	0.773644i	$-0.281568\pi$
$587$	25.3285	+	3.33456i	1.04542	+	0.137632i	0.411797	+	0.911276i	$0.364901\pi$
$588$		0			0
$589$	−8.66116	−	25.5150i	−0.356877	−	1.05133i
$590$	0.270700	−	4.13009i	0.0111446	−	0.170033i
$591$		0			0
$592$	2.09336	−	6.16683i	0.0860364	−	0.253455i
$593$	8.60925	+	3.56607i	0.353539	+	0.146441i	0.552383	−	0.833590i	$-0.313719\pi$
$593$	8.60925	+	3.56607i	0.353539	+	0.146441i	−0.198844	+	0.980031i	$0.563719\pi$
$594$		0			0
$595$	1.85582	+	0.454513i	0.0760813	+	0.0186332i
$596$	−4.62103	−	2.66795i	−0.189285	−	0.109284i
$597$		0			0
$598$	−5.34266	+	4.68539i	−0.218478	+	0.191600i
$599$	17.7417	+	4.75389i	0.724908	+	0.194239i	0.602361	−	0.798224i	$-0.294227\pi$
$599$	17.7417	+	4.75389i	0.724908	+	0.194239i	0.122548	+	0.992463i	$0.460894\pi$
$600$		0			0
$601$	19.9125	+	17.4628i	0.812249	+	0.712323i	0.960999	−	0.276552i	$-0.0891917\pi$
$601$	19.9125	+	17.4628i	0.812249	+	0.712323i	−0.148750	+	0.988875i	$0.547525\pi$
$602$	0.215295	+	0.322211i	0.00877475	+	0.0131323i
$603$		0			0
$604$	−6.60461	+	2.73572i	−0.268738	+	0.111315i
$605$	0.767956	+	11.7167i	0.0312218	+	0.476353i
$606$		0			0
$607$	−25.5436	−	1.67422i	−1.03678	−	0.0679544i	−0.462507	−	0.886616i	$-0.653050\pi$
$607$	−25.5436	−	1.67422i	−1.03678	−	0.0679544i	−0.574276	+	0.818661i	$0.694717\pi$
$608$	−3.43900	+	12.8345i	−0.139470	+	0.520509i
$609$		0			0
$610$	−1.46881	−	1.91418i	−0.0594702	−	0.0775031i
$611$	−22.1904			−0.897729
$612$		0			0
$613$	30.5459			1.23374			0.616869	−	0.787066i	$-0.288401\pi$
$613$	30.5459			1.23374			0.616869	+	0.787066i	$0.288401\pi$
$614$	8.29299	+	10.8076i	0.334678	+	0.436160i
$615$		0			0
$616$	0.231520	−	0.864045i	0.00932821	−	0.0348134i
$617$	7.17371	+	0.470190i	0.288803	+	0.0189291i	0.209116	−	0.977891i	$-0.432941\pi$
$617$	7.17371	+	0.470190i	0.288803	+	0.0189291i	0.0796868	+	0.996820i	$0.474608\pi$
$618$		0			0
$619$	−1.61113	−	24.5811i	−0.0647569	−	0.987999i	−0.899377	−	0.437173i	$-0.855980\pi$
$619$	−1.61113	−	24.5811i	−0.0647569	−	0.987999i	0.834620	−	0.550826i	$-0.185687\pi$
$620$	22.6698	−	9.39013i	0.910441	−	0.377117i
$621$		0			0
$622$	7.66585	+	11.4728i	0.307373	+	0.460016i
$623$	−0.804151	−	0.705222i	−0.0322176	−	0.0282541i
$624$		0			0
$625$	−2.71579	−	0.727694i	−0.108632	−	0.0291077i
$626$	−4.20306	+	3.68599i	−0.167988	+	0.147322i
$627$		0			0
$628$	9.15674	+	5.28664i	0.365394	+	0.210960i
$629$	9.14406	+	0.401082i	0.364598	+	0.0159922i
$630$		0			0
$631$	−4.23320	−	1.75345i	−0.168521	−	0.0698036i	0.296828	−	0.954931i	$-0.404071\pi$
$631$	−4.23320	−	1.75345i	−0.168521	−	0.0698036i	−0.465349	+	0.885127i	$0.654071\pi$
$632$	−4.03120	+	11.8755i	−0.160352	+	0.472383i
$633$		0			0
$634$	0.538297	−	8.21282i	0.0213785	−	0.326173i
$635$	7.64442	+	22.5197i	0.303359	+	0.893668i
$636$		0			0
$637$	−31.5330	−	4.15140i	−1.24938	−	0.164484i
$638$	−2.04950	−	4.94793i	−0.0811405	−	0.195890i
$639$		0			0
$640$	−15.4949	−	3.08213i	−0.612490	−	0.121832i
$641$	−9.60317	+	4.73576i	−0.379303	+	0.187051i	−0.621938	−	0.783066i	$-0.713655\pi$
$641$	−9.60317	+	4.73576i	−0.379303	+	0.187051i	0.242636	+	0.970117i	$0.421988\pi$
$642$		0			0
$643$	16.4527	+	18.7607i	0.648831	+	0.739850i	0.978952	−	0.204089i	$-0.0654231\pi$
$643$	16.4527	+	18.7607i	0.648831	+	0.739850i	−0.330122	+	0.943938i	$0.607090\pi$
$644$	−0.268793	−	2.04169i	−0.0105919	−	0.0804538i
$645$		0			0
$646$	−5.18330	+	0.112056i	−0.203934	+	0.00440880i
$647$		−	23.7610i		−	0.934140i	−0.884220	−	0.467070i	$-0.845310\pi$
$647$		−	23.7610i		−	0.934140i	0.884220	−	0.467070i	$-0.154690\pi$
$648$		0			0
$649$	2.22770	+	11.1994i	0.0874448	+	0.439615i
$650$	−1.44679	−	5.39949i	−0.0567477	−	0.211785i
$651$		0			0
$652$	−13.3668	+	4.53742i	−0.523484	+	0.177699i
$653$	8.64330	−	17.5269i	0.338239	−	0.685880i	−0.659598	−	0.751618i	$-0.729274\pi$
$653$	8.64330	−	17.5269i	0.338239	−	0.685880i	0.997837	+	0.0657383i	$0.0209403\pi$
$654$		0			0
$655$	1.38459	−	10.5170i	0.0541004	−	0.410933i
$656$	−10.8777	+	7.26824i	−0.424702	+	0.283777i
$657$		0			0
$658$	−0.360521	+	0.539558i	−0.0140546	+	0.0210342i
$659$	−33.1069	+	8.87097i	−1.28966	+	0.345564i	−0.837532	−	0.546388i	$-0.816003\pi$
$659$	−33.1069	+	8.87097i	−1.28966	+	0.345564i	−0.452130	+	0.891952i	$0.649336\pi$
$660$		0			0
$661$	−18.5673	+	2.44443i	−0.722183	+	0.0950772i	−0.482653	−	0.875812i	$-0.660327\pi$
$661$	−18.5673	+	2.44443i	−0.722183	+	0.0950772i	−0.239530	+	0.970889i	$0.576993\pi$
$662$	5.96294	+	10.3281i	0.231756	+	0.401413i
$663$		0			0
$664$	−3.39832	+	5.88607i	−0.131880	+	0.228424i
$665$	−0.520806	+	1.25734i	−0.0201960	+	0.0487575i
$666$		0			0
$667$	−18.3160	−	18.3160i	−0.709196	−	0.709196i
$668$	−2.42068	−	4.90865i	−0.0936589	−	0.189921i
$669$		0			0
$670$	2.63774	+	1.30079i	0.101905	+	0.0502538i
$671$	5.28098	+	4.05224i	0.203870	+	0.156435i
$672$		0			0
$673$	−3.40591	+	0.223235i	−0.131288	+	0.00860507i	−0.130905	−	0.991395i	$-0.541788\pi$
$673$	−3.40591	+	0.223235i	−0.131288	+	0.00860507i	−0.000382578		1.00000i	$0.500122\pi$
$674$	1.06204	−	5.33922i	0.0409081	−	0.205659i
$675$		0			0
$676$	10.5866	−	10.5866i	0.407177	−	0.407177i
$677$	−47.9069	−	16.2622i	−1.84121	−	0.625007i	−0.995871	−	0.0907793i	$-0.971064\pi$
$677$	−47.9069	−	16.2622i	−1.84121	−	0.625007i	−0.845341	−	0.534228i	$-0.820602\pi$
$678$		0			0
$679$	5.10841	−	2.94934i	0.196043	−	0.113185i
$680$	−0.862514	−	9.88148i	−0.0330759	−	0.378938i
$681$		0			0
$682$	5.41959	−	4.15860i	0.207527	−	0.159241i
$683$	25.0946	−	4.99162i	0.960218	−	0.190999i	0.309991	−	0.950739i	$-0.399674\pi$
$683$	25.0946	−	4.99162i	0.960218	−	0.190999i	0.650227	+	0.759740i	$0.274674\pi$
$684$		0			0
$685$	23.9007	+	15.9699i	0.913198	+	0.610179i
$686$	−1.23530	+	1.40859i	−0.0471640	+	0.0537802i
$687$		0			0
$688$	−5.13496	+	6.69201i	−0.195769	+	0.255131i
$689$	−29.7767	+	38.8058i	−1.13440	+	1.47838i
$690$		0			0
$691$	8.54287	−	9.74128i	0.324986	−	0.370576i	−0.566157	−	0.824297i	$-0.691571\pi$
$691$	8.54287	−	9.74128i	0.324986	−	0.370576i	0.891144	+	0.453721i	$0.149904\pi$
$692$	37.5782	+	25.1090i	1.42851	+	0.954500i
$693$		0			0
$694$	−12.7900	+	2.54409i	−0.485502	+	0.0965724i
$695$	−12.2570	+	9.40513i	−0.464935	+	0.356757i
$696$		0			0
$697$	−14.0826	−	11.8215i	−0.533417	−	0.447773i
$698$	−7.22381	+	4.17067i	−0.273425	+	0.157862i
$699$		0			0
$700$	1.53396	+	0.520711i	0.0579784	+	0.0196810i
$701$	−11.6445	+	11.6445i	−0.439808	+	0.439808i	−0.891947	−	0.452139i	$-0.850661\pi$
$701$	−11.6445	+	11.6445i	−0.439808	+	0.439808i	0.452139	+	0.891947i	$0.350661\pi$
$702$		0			0
$703$	−1.27187	+	6.39413i	−0.0479695	+	0.241159i
$704$	6.81981	−	0.446994i	0.257031	−	0.0168467i
$705$		0			0
$706$	−1.89172	−	1.45157i	−0.0711957	−	0.0546304i
$707$	−1.02247	−	0.504229i	−0.0384541	−	0.0189635i
$708$		0			0
$709$	−10.0166	−	20.3117i	−0.376182	−	0.762822i	0.623639	−	0.781712i	$-0.285653\pi$
$709$	−10.0166	−	20.3117i	−0.376182	−	0.762822i	−0.999822	+	0.0188899i	$0.993987\pi$
$710$	−2.67881	−	2.67881i	−0.100534	−	0.100534i
$711$		0			0
$712$	−2.12489	+	5.12994i	−0.0796337	+	0.192253i
$713$	16.5199	−	28.6132i	0.618673	−	1.07157i
$714$		0			0
$715$	−5.89935	−	10.2180i	−0.220623	−	0.382130i
$716$	−28.1518	+	3.70625i	−1.05208	+	0.138509i
$717$		0			0
$718$	13.0336	−	3.49234i	0.486409	−	0.130333i
$719$	−6.76012	+	10.1172i	−0.252110	+	0.377309i	−0.935840	−	0.352426i	$-0.885357\pi$
$719$	−6.76012	+	10.1172i	−0.252110	+	0.377309i	0.683730	+	0.729735i	$0.260357\pi$
$720$		0			0
$721$	3.53637	−	2.36293i	0.131701	−	0.0880000i
$722$	−0.579829	+	4.40424i	−0.0215790	+	0.163909i
$723$		0			0
$724$	−0.714064	+	1.44798i	−0.0265380	+	0.0538137i
$725$	19.2947	−	6.54968i	0.716588	−	0.243249i
$726$		0			0
$727$	−7.64487	−	28.5310i	−0.283533	−	1.05816i	−0.949905	−	0.312539i	$-0.898821\pi$
$727$	−7.64487	−	28.5310i	−0.283533	−	1.05816i	0.666372	−	0.745619i	$-0.267846\pi$
$728$	−0.462517	−	2.32523i	−0.0171420	−	0.0861787i
$729$		0			0
$730$			5.10976i			0.189121i
$731$	−11.0481	−	4.29894i	−0.408629	−	0.159002i
$732$		0			0
$733$	−1.78939	−	13.5918i	−0.0660927	−	0.502024i	−0.992190	−	0.124738i	$-0.960191\pi$
$733$	−1.78939	−	13.5918i	−0.0660927	−	0.502024i	0.926097	−	0.377285i	$-0.123142\pi$
$734$	−2.79983	−	3.19260i	−0.103344	−	0.117841i
$735$		0			0
$736$	−14.6126	+	7.20611i	−0.538626	+	0.265621i
$737$	−7.95803	−	1.58295i	−0.293138	−	0.0583087i
$738$		0			0
$739$	18.6853	+	45.1102i	0.687349	+	1.65941i	0.750055	+	0.661375i	$0.230027\pi$
$739$	18.6853	+	45.1102i	0.687349	+	1.65941i	−0.0627066	+	0.998032i	$0.519973\pi$
$740$	−5.88615	−	0.774926i	−0.216379	−	0.0284869i
$741$		0			0
$742$	0.459785	+	1.35448i	0.0168792	+	0.0497246i
$743$	0.0945344	−	1.44232i	0.00346813	−	0.0529135i	−0.995774	−	0.0918369i	$-0.970726\pi$
$743$	0.0945344	−	1.44232i	0.00346813	−	0.0529135i	0.999242	+	0.0389234i	$0.0123928\pi$
$744$		0			0
$745$	−1.38990	+	4.09450i	−0.0509218	+	0.150011i
$746$	11.1366	+	4.61294i	0.407741	+	0.168892i
$747$		0			0
$748$	4.45251	+	12.2408i	0.162800	+	0.447569i
$749$	0.990971	+	0.572137i	0.0362093	+	0.0209054i
$750$		0			0
$751$	20.4355	−	17.9214i	0.745700	−	0.653962i	−0.199706	−	0.979856i	$-0.563999\pi$
$751$	20.4355	−	17.9214i	0.745700	−	0.653962i	0.945406	+	0.325894i	$0.105665\pi$
$752$	−13.6437	−	3.65581i	−0.497534	−	0.133314i
$753$		0			0
$754$	−10.6717	−	9.35881i	−0.388640	−	0.340828i
$755$	3.21844	+	4.81674i	0.117131	+	0.175299i
$756$		0			0
$757$	17.6756	−	7.32147i	0.642430	−	0.266103i	−0.0375938	−	0.999293i	$-0.511969\pi$
$757$	17.6756	−	7.32147i	0.642430	−	0.266103i	0.680024	+	0.733190i	$0.261969\pi$
$758$	0.652427	+	9.95411i	0.0236972	+	0.361549i
$759$		0			0
$760$	7.05002	+	0.462083i	0.255731	+	0.0167615i
$761$	8.72766	−	32.5721i	0.316377	−	1.18074i	−0.606323	−	0.795218i	$-0.707356\pi$
$761$	8.72766	−	32.5721i	0.316377	−	1.18074i	0.922700	−	0.385518i	$-0.125977\pi$
$762$		0			0
$763$	−1.57168	−	2.04825i	−0.0568985	−	0.0741516i
$764$	−38.7225			−1.40093
$765$		0			0
$766$	−8.72354			−0.315194
$767$	18.4233	+	24.0097i	0.665226	+	0.866940i
$768$		0			0
$769$	6.36164	−	23.7420i	0.229407	−	0.856157i	−0.751184	−	0.660093i	$-0.770517\pi$
$769$	6.36164	−	23.7420i	0.229407	−	0.856157i	0.980591	−	0.196065i	$-0.0628163\pi$
$770$	−0.344294	−	0.0225662i	−0.0124075	−	0.000813229i
$771$		0			0
$772$	0.871494	+	13.2964i	0.0313658	+	0.478549i
$773$	−14.8745	+	6.16122i	−0.534999	+	0.221604i	−0.633791	−	0.773504i	$-0.718502\pi$
$773$	−14.8745	+	6.16122i	−0.534999	+	0.221604i	0.0987921	+	0.995108i	$0.468502\pi$
$774$		0			0
$775$	14.4395	+	21.6102i	0.518681	+	0.776261i
$776$	−23.0232	−	20.1908i	−0.826484	−	0.724807i
$777$		0			0
$778$	−10.3624	−	2.77659i	−0.371510	−	0.0995457i
$779$	9.84644	−	8.63509i	0.352785	−	0.309384i
$780$		0			0
$781$	9.05145	+	5.22586i	0.323886	+	0.186996i
$782$	−4.29393	−	4.68789i	−0.153551	−	0.167639i
$783$		0			0
$784$	−18.7040	−	7.74744i	−0.667999	−	0.276694i
$785$	2.75413	−	8.11340i	0.0982991	−	0.289580i
$786$		0			0
$787$	−1.04438	+	15.9342i	−0.0372282	+	0.567993i	0.937978	+	0.346695i	$0.112696\pi$
$787$	−1.04438	+	15.9342i	−0.0372282	+	0.567993i	−0.975206	+	0.221298i	$0.928971\pi$
$788$	12.5178	+	36.8762i	0.445928	+	1.31366i
$789$		0			0
$790$	4.79591	+	0.631393i	0.170631	+	0.0224640i
$791$	−2.26846	−	5.47655i	−0.0806572	−	0.194724i
$792$		0			0
$793$	17.3030	+	3.44178i	0.614447	+	0.122221i
$794$	1.05466	−	0.520098i	0.0374283	−	0.0184576i
$795$		0			0
$796$	3.41655	+	3.89583i	0.121096	+	0.138084i
$797$	1.10425	+	8.38761i	0.0391145	+	0.297104i	0.999810	+	0.0194995i	$0.00620727\pi$
$797$	1.10425	+	8.38761i	0.0391145	+	0.297104i	−0.960695	+	0.277605i	$0.910459\pi$
$798$		0			0
$799$	−0.429071	−	19.8472i	−0.0151794	−	0.702143i
$800$		−	12.8166i		−	0.453134i
$801$		0			0
$802$	−1.33500	−	6.71148i	−0.0471404	−	0.236991i
$803$	−3.64861	−	13.6168i	−0.128757	−	0.480526i
$804$		0			0
$805$	−1.58021	+	0.536408i	−0.0556950	+	0.0189059i
$806$	8.00765	−	16.2379i	0.282057	−	0.571956i
$807$		0			0
$808$	−0.772510	+	5.86779i	−0.0271768	+	0.206428i
$809$	−6.98362	+	4.66631i	−0.245531	+	0.164059i	−0.672247	−	0.740327i	$-0.734671\pi$
$809$	−6.98362	+	4.66631i	−0.245531	+	0.164059i	0.426716	+	0.904386i	$0.359671\pi$
$810$		0			0
$811$	−19.3160	+	28.9084i	−0.678276	+	1.01511i	0.319443	+	0.947606i	$0.396504\pi$
$811$	−19.3160	+	28.9084i	−0.678276	+	1.01511i	−0.997719	+	0.0675061i	$0.978496\pi$
$812$	3.97319	−	1.06461i	0.139432	−	0.0373606i
$813$		0			0
$814$	−1.63870	+	0.215739i	−0.0574364	+	0.00756164i
$815$	5.71945	+	9.90638i	0.200344	+	0.347005i
$816$		0			0
$817$	4.22205	−	7.31281i	0.147711	−	0.255843i
$818$	1.38091	−	3.33380i	0.0482823	−	0.116564i
$819$		0			0
$820$	8.43323	+	8.43323i	0.294501	+	0.294501i
$821$	3.09953	+	6.28523i	0.108175	+	0.219356i	0.944228	−	0.329291i	$-0.106810\pi$
$821$	3.09953	+	6.28523i	0.108175	+	0.219356i	−0.836054	+	0.548647i	$0.815143\pi$
$822$		0			0
$823$	−4.13996	−	2.04160i	−0.144310	−	0.0711658i	0.368700	−	0.929548i	$-0.379803\pi$
$823$	−4.13996	−	2.04160i	−0.144310	−	0.0711658i	−0.513010	+	0.858383i	$0.671470\pi$
$824$	−17.5171	−	13.4414i	−0.610238	−	0.468252i
$825$		0			0
$826$	0.883110	−	0.0578821i	0.0307273	−	0.00201398i
$827$	−4.28494	+	21.5419i	−0.149002	+	0.749084i	0.831953	+	0.554847i	$0.187223\pi$
$827$	−4.28494	+	21.5419i	−0.149002	+	0.749084i	−0.980955	+	0.194237i	$0.937777\pi$
$828$		0			0
$829$	−23.5987	+	23.5987i	−0.819616	+	0.819616i	−0.986052	−	0.166437i	$-0.946774\pi$
$829$	−23.5987	+	23.5987i	−0.819616	+	0.819616i	0.166437	+	0.986052i	$0.446774\pi$
$830$	2.48245	+	0.842677i	0.0861669	+	0.0292497i
$831$		0			0
$832$	15.6867	−	9.05675i	0.543840	−	0.313986i
$833$	3.10330	−	28.2835i	0.107523	−	0.979964i
$834$		0			0
$835$	−3.51862	+	2.69993i	−0.121767	+	0.0934351i
$836$	−9.09952	+	1.81001i	−0.314713	+	0.0626004i
$837$		0			0
$838$	4.07859	+	2.72523i	0.140893	+	0.0941414i
$839$	33.9713	−	38.7369i	1.17282	−	1.33734i	0.242694	−	0.970103i	$-0.421969\pi$
$839$	33.9713	−	38.7369i	1.17282	−	1.33734i	0.930125	−	0.367242i	$-0.119698\pi$
$840$		0			0
$841$	13.8427	−	18.0402i	0.477336	−	0.622076i
$842$	3.02687	−	3.94469i	0.104313	−	0.135943i
$843$		0			0
$844$	−26.7801	+	30.5368i	−0.921808	+	1.05112i
$845$	−10.0877	−	6.74040i	−0.347028	−	0.231877i
$846$		0			0
$847$	−2.46245	+	0.489812i	−0.0846108	+	0.0168301i
$848$	−24.7012	+	18.9539i	−0.848242	+	0.650879i
$849$		0			0
$850$	4.80134	−	1.39841i	0.164685	−	0.0479652i
$851$	−6.92305	+	3.99702i	−0.237319	+	0.137016i
$852$		0			0
$853$	6.66902	+	2.26383i	0.228343	+	0.0775120i	0.433266	−	0.901266i	$-0.357361\pi$
$853$	6.66902	+	2.26383i	0.228343	+	0.0775120i	−0.204923	+	0.978778i	$0.565694\pi$
$854$	0.364803	−	0.364803i	0.0124833	−	0.0124833i
$855$		0			0
$856$	1.15891	−	5.82625i	0.0396108	−	0.199137i
$857$	−21.2926	+	1.39559i	−0.727340	+	0.0476724i	−0.424575	−	0.905393i	$-0.639576\pi$
$857$	−21.2926	+	1.39559i	−0.727340	+	0.0476724i	−0.302765	+	0.953065i	$0.597910\pi$
$858$		0			0
$859$	16.1417	+	12.3859i	0.550747	+	0.422603i	0.846287	−	0.532727i	$-0.178833\pi$
$859$	16.1417	+	12.3859i	0.550747	+	0.422603i	−0.295540	+	0.955330i	$0.595500\pi$
$860$	6.89668	+	3.40106i	0.235175	+	0.115975i
$861$		0			0
$862$	3.15776	+	6.40330i	0.107554	+	0.218097i
$863$	−8.04291	−	8.04291i	−0.273784	−	0.273784i	0.556837	−	0.830621i	$-0.312015\pi$
$863$	−8.04291	−	8.04291i	−0.273784	−	0.273784i	−0.830621	+	0.556837i	$0.812015\pi$
$864$		0			0
$865$	14.0154	−	33.8361i	0.476537	−	1.15046i
$866$	1.67430	−	2.89997i	0.0568951	−	0.0985452i
$867$		0			0
$868$	2.62336	+	4.54379i	0.0890426	+	0.154226i
$869$	−13.2313	+	1.74193i	−0.448840	+	0.0590909i
$870$		0			0
$871$	−20.7718	+	5.56579i	−0.703826	+	0.188590i
$872$	−7.44629	+	11.1442i	−0.252163	+	0.377389i
$873$		0			0
$874$	3.76499	−	2.51569i	0.127353	−	0.0850944i
$875$	0.473777	−	3.59869i	0.0160166	−	0.121658i
$876$		0			0
$877$	−5.31252	+	10.7727i	−0.179391	+	0.363769i	−0.967932	−	0.251214i	$-0.919170\pi$
$877$	−5.31252	+	10.7727i	−0.179391	+	0.363769i	0.788541	+	0.614983i	$0.210837\pi$
$878$	8.09277	−	2.74713i	0.273118	−	0.0927110i
$879$		0			0
$880$	−1.94380	−	7.25436i	−0.0655255	−	0.244545i
$881$	−9.38269	−	47.1700i	−0.316111	−	1.58920i	−0.732993	−	0.680236i	$-0.761877\pi$
$881$	−9.38269	−	47.1700i	−0.316111	−	1.58920i	0.416882	−	0.908960i	$-0.363123\pi$
$882$		0			0
$883$		−	20.2173i		−	0.680366i	−0.940359	−	0.340183i	$-0.889511\pi$
$883$		−	20.2173i		−	0.680366i	0.940359	−	0.340183i	$-0.110489\pi$
$884$	24.9324	+	23.8772i	0.838569	+	0.803079i
$885$		0			0
$886$	−1.51129	−	11.4794i	−0.0507729	−	0.385659i
$887$	−16.0199	−	18.2672i	−0.537896	−	0.613353i	0.417501	−	0.908676i	$-0.362906\pi$
$887$	−16.0199	−	18.2672i	−0.537896	−	0.613353i	−0.955397	+	0.295324i	$0.904573\pi$
$888$		0			0
$889$	−4.56070	+	2.24909i	−0.152961	+	0.0754320i
$890$	2.10058	+	0.417830i	0.0704114	+	0.0140057i
$891$		0			0
$892$	−14.3193	−	34.5699i	−0.479447	−	1.15749i
$893$	14.0191	+	1.84565i	0.469131	+	0.0617623i
$894$		0			0
$895$	7.39625	+	21.7887i	0.247229	+	0.728314i
$896$	0.220937	−	3.37085i	0.00738100	−	0.112612i
$897$		0			0
$898$	4.76098	−	14.0254i	0.158876	−	0.468033i
$899$	60.9715	+	25.2552i	2.03351	+	0.842308i
$900$		0			0
$901$	−35.2837	−	25.8820i	−1.17547	−	0.862255i
$902$	2.87546	+	1.66015i	0.0957424	+	0.0552769i
$903$		0			0
$904$	−23.1367	+	20.2903i	−0.769515	+	0.674847i
$905$	1.26372	+	0.338612i	0.0420074	+	0.0112558i
$906$		0			0
$907$	−2.33961	−	2.05178i	−0.0776855	−	0.0681283i	0.619623	−	0.784900i	$-0.287286\pi$
$907$	−2.33961	−	2.05178i	−0.0776855	−	0.0681283i	−0.697308	+	0.716772i	$0.745619\pi$
$908$	12.9378	+	19.3628i	0.429355	+	0.642576i
$909$		0			0
$910$	−0.844840	+	0.349944i	−0.0280062	+	0.0116005i
$911$	−0.871769	−	13.3006i	−0.0288830	−	0.440669i	−0.987671	−	0.156546i	$-0.949964\pi$
$911$	−0.871769	−	13.3006i	−0.0288830	−	0.440669i	0.958788	−	0.284123i	$-0.0917026\pi$
$912$		0			0
$913$	−7.21708	−	0.473033i	−0.238851	−	0.0156551i
$914$	−0.0781101	+	0.291511i	−0.00258365	+	0.00964232i
$915$		0			0
$916$	30.3453	+	39.5467i	1.00264	+	1.30666i
$917$	2.26819			0.0749021
$918$		0			0
$919$	23.5802			0.777841			0.388920	−	0.921271i	$-0.372848\pi$
$919$	23.5802			0.777841			0.388920	+	0.921271i	$0.372848\pi$
$920$	5.27385	+	6.87301i	0.173874	+	0.226597i
$921$		0			0
$922$	1.67177	−	6.23913i	0.0550568	−	0.205475i
$923$	27.6411	+	1.81170i	0.909819	+	0.0596327i
$924$		0			0
$925$	−0.411284	−	6.27498i	−0.0135229	−	0.206320i
$926$	−0.657313	+	0.272268i	−0.0216007	+	0.00894729i
$927$		0			0
$928$	−18.0804	−	27.0593i	−0.593520	−	0.888265i
$929$	13.1610	+	11.5419i	0.431797	+	0.378676i	0.847474	−	0.530836i	$-0.178122\pi$
$929$	13.1610	+	11.5419i	0.431797	+	0.378676i	−0.415677	+	0.909512i	$0.636455\pi$
$930$		0			0
$931$	19.5761	+	5.24540i	0.641580	+	0.171911i
$932$	−12.0969	+	10.6087i	−0.396248	+	0.347501i
$933$		0			0
$934$	3.08296	+	1.77995i	0.100878	+	0.0582417i
$935$	9.02491	−	5.47396i	0.295146	−	0.179018i
$936$		0			0
$937$	38.3879	+	15.9008i	1.25408	+	0.519456i	0.908087	−	0.418782i	$-0.137543\pi$
$937$	38.3879	+	15.9008i	1.25408	+	0.519456i	0.345991	+	0.938238i	$0.387543\pi$
$938$	−0.202142	+	0.595490i	−0.00660015	+	0.0194434i
$939$		0			0
$940$	−0.842180	+	12.8492i	−0.0274689	+	0.419094i
$941$	4.96592	+	14.6291i	0.161884	+	0.476896i	0.997359	−	0.0726337i	$-0.0231404\pi$
$941$	4.96592	+	14.6291i	0.161884	+	0.476896i	−0.835474	+	0.549529i	$0.814807\pi$
$942$		0			0
$943$	15.9214	+	2.09609i	0.518473	+	0.0682582i
$944$	7.37193	+	17.7974i	0.239936	+	0.579256i
$945$		0			0
$946$	2.09967	+	0.417650i	0.0682661	+	0.0135790i
$947$	−4.97929	+	2.45551i	−0.161805	+	0.0797935i	−0.521388	−	0.853320i	$-0.674586\pi$
$947$	−4.97929	+	2.45551i	−0.161805	+	0.0797935i	0.359583	+	0.933113i	$0.382919\pi$
$948$		0			0
$949$	−24.6345	−	28.0902i	−0.799669	−	0.911847i
$950$	0.464934	+	3.53153i	0.0150845	+	0.114578i
$951$		0			0
$952$	2.07075	−	0.458636i	0.0671133	−	0.0148645i
$953$		−	15.3612i		−	0.497600i	−0.968555	−	0.248800i	$-0.919964\pi$
$953$		−	15.3612i		−	0.497600i	0.968555	−	0.248800i	$-0.0800361\pi$
$954$		0			0
$955$	6.12173	+	30.7760i	0.198094	+	0.995888i
$956$	9.23645	+	34.4709i	0.298728	+	1.11487i
$957$		0			0
$958$	5.60989	−	1.90430i	0.181247	−	0.0615251i
$959$	−2.71847	+	5.51252i	−0.0877841	+	0.178009i
$960$		0			0
$961$	−6.94123	+	52.7239i	−0.223911	+	1.70077i
$962$	−3.64230	+	2.43371i	−0.117433	+	0.0784659i
$963$		0			0
$964$	18.5231	−	27.7218i	0.596590	−	0.892861i
$965$	10.4300	−	2.79471i	0.335754	−	0.0899650i
$966$		0			0
$967$	27.1102	−	3.56913i	0.871806	−	0.114775i	0.318669	−	0.947866i	$-0.396764\pi$
$967$	27.1102	−	3.56913i	0.871806	−	0.114775i	0.553137	+	0.833091i	$0.313431\pi$
$968$	6.51701	+	11.2878i	0.209464	+	0.362803i
$969$		0			0
$970$	−5.90578	+	10.2291i	−0.189623	+	0.328437i
$971$	15.7860	−	38.1109i	0.506598	−	1.22304i	−0.439232	−	0.898374i	$-0.644749\pi$
$971$	15.7860	−	38.1109i	0.506598	−	1.22304i	0.945830	−	0.324662i	$-0.105251\pi$
$972$		0			0
$973$	−2.33592	−	2.33592i	−0.0748862	−	0.0748862i
$974$	−4.50478	−	9.13480i	−0.144343	−	0.292698i
$975$		0			0
$976$	10.0716	+	4.96678i	0.322385	+	0.158983i
$977$	18.0637	+	13.8608i	0.577911	+	0.443446i	0.855903	−	0.517137i	$-0.173002\pi$
$977$	18.0637	+	13.8608i	0.577911	+	0.443446i	−0.277992	+	0.960583i	$0.589669\pi$
$978$		0			0
$979$	−5.89609	+	0.386450i	−0.188440	+	0.0123510i
$980$	−3.60058	+	18.1014i	−0.115016	+	0.578227i
$981$		0			0
$982$	−8.00610	+	8.00610i	−0.255485	+	0.255485i
$983$	35.3341	+	11.9943i	1.12698	+	0.382560i	0.821824	−	0.569741i	$-0.192957\pi$
$983$	35.3341	+	11.9943i	1.12698	+	0.382560i	0.305160	+	0.952301i	$0.401290\pi$
$984$		0			0
$985$	27.3297	−	15.7788i	0.870795	−	0.502754i
$986$	8.16420	−	9.72573i	0.260001	−	0.309730i
$987$		0			0
$988$	−19.5079	+	14.9689i	−0.620629	+	0.476225i
$989$	10.1552	−	2.01999i	0.322915	−	0.0642319i
$990$		0			0
$991$	30.8345	+	20.6029i	0.979489	+	0.654474i	0.938715	−	0.344695i	$-0.112018\pi$
$991$	30.8345	+	20.6029i	0.979489	+	0.654474i	0.0407744	+	0.999168i	$0.487018\pi$
$992$	27.3700	−	31.2095i	0.868999	−	0.990904i
$993$		0			0
$994$	0.493128	−	0.642657i	0.0156411	−	0.0203838i
$995$	2.55621	−	3.33132i	0.0810373	−	0.105610i
$996$		0			0
$997$	−7.02794	+	8.01383i	−0.222577	+	0.253800i	−0.852341	−	0.522986i	$-0.824818\pi$
$997$	−7.02794	+	8.01383i	−0.222577	+	0.253800i	0.629764	+	0.776786i	$0.283151\pi$
$998$	−10.8653	−	7.25997i	−0.343936	−	0.229810i
$999$		0			0

Display

a_p

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p

up to: 50 250 1000 (See

a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.2.y.a.62.6		256
3.2	odd	2		153.2.s.a.11.11	✓	256
9.4	even	3		153.2.s.a.113.11	yes	256
9.5	odd	6	inner	459.2.y.a.368.6		256
17.14	odd	16	inner	459.2.y.a.116.6		256
51.14	even	16		153.2.s.a.65.11	yes	256
153.14	even	48	inner	459.2.y.a.422.6		256
153.31	odd	48		153.2.s.a.14.11	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.s.a.11.11	✓	256	3.2	odd	2
153.2.s.a.14.11	yes	256	153.31	odd	48
153.2.s.a.65.11	yes	256	51.14	even	16
153.2.s.a.113.11	yes	256	9.4	even	3
459.2.y.a.62.6		256	1.1	even	1	trivial
459.2.y.a.116.6		256	17.14	odd	16	inner
459.2.y.a.368.6		256	9.5	odd	6	inner
459.2.y.a.422.6		256	153.14	even	48	inner

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

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	459.2.y.a.62.6

Level	$459$
Weight	$2$
Character	459.62
Analytic conductor	$3.665$
Analytic rank	$0$
Dimension	$256$
Inner twists	$4$