LMFDB - Embedded newform 475.2.e.d.201.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(26,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("475.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$475 = 5^{2} \cdot 19$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	475.e (of order $3$ , degree $2$ , 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.3518667.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{6} - x^{5} + 7x^{4} - 8x^{3} + 43x^{2} - 42x + 49$ x^6 - x^5 + 7x^4 - 8x^3 + 43x^2 - 42x + 49
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.3
Root			$1.14257 - 1.97899i$ of defining polynomial
Character	$\chi$	$=$	475.201
Dual form			475.2.e.d.26.3

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.14257 - 1.97899i) q^{2} +(-1.25351 + 2.17114i) q^{3} +(-1.61094 - 2.79023i) q^{4} +(2.86445 + 4.96137i) q^{6} -3.50702 q^{7} -2.79216 q^{8} +(-1.64257 - 2.84502i) q^{9} -4.50702 q^{11} +8.07730 q^{12} +(-2.50000 - 4.33013i) q^{13} +(-4.00702 + 6.94036i) q^{14} +(0.0316332 - 0.0547902i) q^{16} +(0.0793049 - 0.137360i) q^{17} -7.50702 q^{18} +(-4.26053 + 0.920816i) q^{19} +(4.39608 - 7.61423i) q^{21} +(-5.14959 + 8.91935i) q^{22} +(0.579305 + 1.00339i) q^{23} +(3.50000 - 6.06218i) q^{24} -11.4257 q^{26} +0.714858 q^{27} +(5.64959 + 9.78538i) q^{28} +(1.75351 + 3.03717i) q^{29} -2.28514 q^{31} +(-2.86445 - 4.96137i) q^{32} +(5.64959 - 9.78538i) q^{33} +(-0.181223 - 0.313888i) q^{34} +(-5.29216 + 9.16629i) q^{36} +10.9648 q^{37} +(-3.04567 + 9.48365i) q^{38} +12.5351 q^{39} +(-3.03865 + 5.26310i) q^{41} +(-10.0457 - 17.3996i) q^{42} +(-1.67420 + 2.89981i) q^{43} +(7.26053 + 12.5756i) q^{44} +2.64759 q^{46} +(1.53163 + 2.65287i) q^{47} +(0.0793049 + 0.137360i) q^{48} +5.29918 q^{49} +(0.198819 + 0.344364i) q^{51} +(-8.05469 + 13.9511i) q^{52} +(-2.87147 - 4.97353i) q^{53} +(0.816776 - 1.41470i) q^{54} +9.79216 q^{56} +(3.34139 - 10.4045i) q^{57} +8.01404 q^{58} +(-1.53163 + 2.65287i) q^{59} +(0.436734 + 0.756445i) q^{61} +(-2.61094 + 4.52228i) q^{62} +(5.76053 + 9.97753i) q^{63} -12.9648 q^{64} +(-12.9101 - 22.3610i) q^{66} +(-4.22188 - 7.31250i) q^{67} -0.511021 q^{68} -2.90466 q^{69} +(8.11796 - 14.0607i) q^{71} +(4.58632 + 7.94375i) q^{72} +(-3.57930 + 6.19954i) q^{73} +(12.5281 - 21.6993i) q^{74} +(9.43273 + 10.4045i) q^{76} +15.8062 q^{77} +(14.3222 - 24.8068i) q^{78} +(5.06327 - 8.76983i) q^{79} +(4.03163 - 6.98299i) q^{81} +(6.94375 + 12.0269i) q^{82} -4.85543 q^{83} -28.3273 q^{84} +(3.82580 + 6.62647i) q^{86} -8.79216 q^{87} +12.5843 q^{88} +(0.556248 + 0.963449i) q^{89} +(8.76755 + 15.1858i) q^{91} +(1.86645 - 3.23278i) q^{92} +(2.86445 - 4.96137i) q^{93} +7.00000 q^{94} +14.3624 q^{96} +(0.809757 - 1.40254i) q^{97} +(6.05469 - 10.4870i) q^{98} +(7.40310 + 12.8225i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$6 q + q^{2} + q^{3} - 7 q^{4} + 6 q^{6} - 4 q^{7} + 12 q^{8} - 4 q^{9} - 10 q^{11} + 8 q^{12} - 15 q^{13} - 7 q^{14} - 3 q^{16} + q^{17} - 28 q^{18} + 12 q^{21} - 8 q^{22} + 4 q^{23} + 21 q^{24} - 10 q^{26}+ \cdots + 13 q^{99}+O(q^{100})$ 6 * q + q^2 + q^3 - 7 * q^4 + 6 * q^6 - 4 * q^7 + 12 * q^8 - 4 * q^9 - 10 * q^11 + 8 * q^12 - 15 * q^13 - 7 * q^14 - 3 * q^16 + q^17 - 28 * q^18 + 12 * q^21 - 8 * q^22 + 4 * q^23 + 21 * q^24 - 10 * q^26 + 16 * q^27 + 11 * q^28 + 2 * q^29 - 2 * q^31 - 6 * q^32 + 11 * q^33 + 25 * q^34 - 3 * q^36 + 4 * q^37 + 19 * q^38 - 10 * q^39 + 2 * q^41 - 23 * q^42 - q^43 + 18 * q^44 - 48 * q^46 + 6 * q^47 + q^48 - 14 * q^49 + 6 * q^51 - 35 * q^52 + 11 * q^53 - 10 * q^54 + 30 * q^56 + 19 * q^57 + 14 * q^58 - 6 * q^59 + 9 * q^61 - 13 * q^62 + 9 * q^63 - 16 * q^64 - 29 * q^66 - 20 * q^67 - 68 * q^68 - 10 * q^69 + 29 * q^71 + 11 * q^72 - 22 * q^73 + 7 * q^74 - 19 * q^76 + 32 * q^77 + 30 * q^78 + 24 * q^79 + 21 * q^81 + 31 * q^82 + 6 * q^83 - 56 * q^84 + 32 * q^86 - 24 * q^87 + 18 * q^88 + 14 * q^89 + 10 * q^91 + 41 * q^92 + 6 * q^93 + 42 * q^94 + 34 * q^96 + 7 * q^97 + 23 * q^98 + 13 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$ .

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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

)

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

$2$	1.14257	−	1.97899i	0.807920	−	1.39936i	−0.106382	−	0.994325i	$-0.533927\pi$
$2$	1.14257	−	1.97899i	0.807920	−	1.39936i	0.914302	−	0.405033i	$-0.132740\pi$
$3$	−1.25351	+	2.17114i	−0.723714	+	1.25351i	0.235787	+	0.971805i	$0.424233\pi$
$3$	−1.25351	+	2.17114i	−0.723714	+	1.25351i	−0.959501	+	0.281705i	$0.909100\pi$
$4$	−1.61094	−	2.79023i	−0.805469	−	1.39511i
$5$		0			0
$5$		0			0
$6$	2.86445	+	4.96137i	1.16941	+	2.02547i
$7$	−3.50702			−1.32553			−0.662764	−	0.748828i	$-0.730617\pi$
$7$	−3.50702			−1.32553			−0.662764	+	0.748828i	$0.730617\pi$
$8$	−2.79216			−0.987178
$9$	−1.64257	−	2.84502i	−0.547524	−	0.948339i
$10$		0			0
$11$	−4.50702			−1.35892			−0.679459	−	0.733714i	$-0.737785\pi$
$11$	−4.50702			−1.35892			−0.679459	+	0.733714i	$0.737785\pi$
$12$	8.07730			2.33172
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	0.277350	−	0.960769i	$-0.410544\pi$
$14$	−4.00702	+	6.94036i	−1.07092	+	1.85489i
$15$		0			0
$16$	0.0316332	−	0.0547902i	0.00790829	−	0.0136976i
$17$	0.0793049	−	0.137360i	0.0192343	−	0.0333147i	−0.856248	−	0.516565i	$-0.827210\pi$
$17$	0.0793049	−	0.137360i	0.0192343	−	0.0333147i	0.875482	+	0.483250i	$0.160544\pi$
$18$	−7.50702			−1.76942
$19$	−4.26053	+	0.920816i	−0.977432	+	0.211250i
$19$	−4.26053	+	0.920816i	−0.977432	+	0.211250i
$20$		0			0
$21$	4.39608	−	7.61423i	0.959303	−	1.66156i
$22$	−5.14959	+	8.91935i	−1.09790	+	1.90161i
$23$	0.579305	+	1.00339i	0.120793	+	0.209220i	0.920081	−	0.391729i	$-0.128123\pi$
$23$	0.579305	+	1.00339i	0.120793	+	0.209220i	−0.799287	+	0.600949i	$0.794789\pi$
$24$	3.50000	−	6.06218i	0.714435	−	1.23744i
$25$		0			0
$26$	−11.4257			−2.24077
$27$	0.714858			0.137574
$28$	5.64959	+	9.78538i	1.06767	+	1.84926i
$29$	1.75351	+	3.03717i	0.325619	+	0.563988i	0.981637	−	0.190757i	$-0.0610942\pi$
$29$	1.75351	+	3.03717i	0.325619	+	0.563988i	−0.656019	+	0.754745i	$0.727761\pi$
$30$		0			0
$31$	−2.28514			−0.410424			−0.205212	−	0.978718i	$-0.565788\pi$
$31$	−2.28514			−0.410424			−0.205212	+	0.978718i	$0.565788\pi$
$32$	−2.86445	−	4.96137i	−0.506368	−	0.877054i
$33$	5.64959	−	9.78538i	0.983467	−	1.70342i
$34$	−0.181223	−	0.313888i	−0.0310795	−	0.0538313i
$35$		0			0
$36$	−5.29216	+	9.16629i	−0.882027	+	1.52772i
$37$	10.9648			1.80260			0.901302	−	0.433192i	$-0.142613\pi$
$37$	10.9648			1.80260			0.901302	+	0.433192i	$0.142613\pi$
$38$	−3.04567	+	9.48365i	−0.494073	+	1.53845i
$39$	12.5351			2.00722
$40$		0			0
$41$	−3.03865	+	5.26310i	−0.474558	+	0.821958i	−0.999576	−	0.0291332i	$-0.990725\pi$
$41$	−3.03865	+	5.26310i	−0.474558	+	0.821958i	0.525018	+	0.851091i	$0.324059\pi$
$42$	−10.0457	−	17.3996i	−1.55008	−	2.68482i
$43$	−1.67420	+	2.89981i	−0.255314	+	0.442216i	−0.964981	−	0.262321i	$-0.915512\pi$
$43$	−1.67420	+	2.89981i	−0.255314	+	0.442216i	0.709667	+	0.704537i	$0.248845\pi$
$44$	7.26053	+	12.5756i	1.09457	+	1.89584i
$45$		0			0
$46$	2.64759			0.390366
$47$	1.53163	+	2.65287i	0.223412	+	0.386960i	0.955842	−	0.293882i	$-0.0949472\pi$
$47$	1.53163	+	2.65287i	0.223412	+	0.386960i	−0.732430	+	0.680842i	$0.761614\pi$
$48$	0.0793049	+	0.137360i	0.0114467	+	0.0198262i
$49$	5.29918			0.757026
$50$		0			0
$51$	0.198819	+	0.344364i	0.0278402	+	0.0482207i
$52$	−8.05469	+	13.9511i	−1.11698	+	1.93467i
$53$	−2.87147	−	4.97353i	−0.394426	−	0.683166i	0.598602	−	0.801047i	$-0.295723\pi$
$53$	−2.87147	−	4.97353i	−0.394426	−	0.683166i	−0.993028	+	0.117881i	$0.962390\pi$
$54$	0.816776	−	1.41470i	0.111149	−	0.192516i
$55$		0			0
$56$	9.79216			1.30853
$57$	3.34139	−	10.4045i	0.442578	−	1.37810i
$58$	8.01404			1.05229
$59$	−1.53163	+	2.65287i	−0.199402	+	0.345374i	−0.948335	−	0.317272i	$-0.897233\pi$
$59$	−1.53163	+	2.65287i	−0.199402	+	0.345374i	0.748933	+	0.662646i	$0.230567\pi$
$60$		0			0
$61$	0.436734	+	0.756445i	0.0559180	+	0.0968528i	0.892629	−	0.450791i	$-0.148858\pi$
$61$	0.436734	+	0.756445i	0.0559180	+	0.0968528i	−0.836711	+	0.547644i	$0.815525\pi$
$62$	−2.61094	+	4.52228i	−0.331589	+	0.574330i
$63$	5.76053	+	9.97753i	0.725758	+	1.25705i
$64$	−12.9648			−1.62060
$65$		0			0
$66$	−12.9101	−	22.3610i	−1.58913	−	2.75245i
$67$	−4.22188	−	7.31250i	−0.515784	−	0.893365i	−0.999832	−	0.0183230i	$-0.994167\pi$
$67$	−4.22188	−	7.31250i	−0.515784	−	0.893365i	0.484048	−	0.875042i	$-0.339166\pi$
$68$	−0.511021			−0.0619704
$69$	−2.90466			−0.349680
$70$		0			0
$71$	8.11796	−	14.0607i	0.963424	−	1.66870i	0.249634	−	0.968340i	$-0.419690\pi$
$71$	8.11796	−	14.0607i	0.963424	−	1.66870i	0.713790	−	0.700359i	$-0.246977\pi$
$72$	4.58632	+	7.94375i	0.540503	+	0.936179i
$73$	−3.57930	+	6.19954i	−0.418926	+	0.725601i	−0.995832	−	0.0912097i	$-0.970927\pi$
$73$	−3.57930	+	6.19954i	−0.418926	+	0.725601i	0.576906	+	0.816811i	$0.304260\pi$
$74$	12.5281	−	21.6993i	1.45636	−	2.52249i
$75$		0			0
$76$	9.43273	+	10.4045i	1.08201	+	1.19347i
$77$	15.8062			1.80128
$78$	14.3222	−	24.8068i	1.62167	−	2.80882i
$79$	5.06327	−	8.76983i	0.569662	−	0.986683i	−0.426937	−	0.904281i	$-0.640407\pi$
$79$	5.06327	−	8.76983i	0.569662	−	0.986683i	0.996599	−	0.0824022i	$-0.0262592\pi$
$80$		0			0
$81$	4.03163	−	6.98299i	0.447959	−	0.775888i
$82$	6.94375	+	12.0269i	0.766809	+	1.32815i
$83$	−4.85543			−0.532952			−0.266476	−	0.963841i	$-0.585859\pi$
$83$	−4.85543			−0.532952			−0.266476	+	0.963841i	$0.585859\pi$
$84$	−28.3273			−3.09076
$85$		0			0
$86$	3.82580	+	6.62647i	0.412546	+	0.714551i
$87$	−8.79216			−0.942619
$88$	12.5843			1.34149
$89$	0.556248	+	0.963449i	0.0589621	+	0.102125i	0.894000	−	0.448067i	$-0.147888\pi$
$89$	0.556248	+	0.963449i	0.0589621	+	0.102125i	−0.835038	+	0.550193i	$0.814554\pi$
$90$		0			0
$91$	8.76755	+	15.1858i	0.919089	+	1.59191i
$92$	1.86645	−	3.23278i	0.194591	−	0.337041i
$93$	2.86445	−	4.96137i	0.297029	−	0.514470i
$94$	7.00000			0.721995
$95$		0			0
$96$	14.3624			1.46586
$97$	0.809757	−	1.40254i	0.0822184	−	0.142406i	−0.821984	−	0.569510i	$-0.807133\pi$
$97$	0.809757	−	1.40254i	0.0822184	−	0.142406i	0.904203	+	0.427104i	$0.140466\pi$
$98$	6.05469	−	10.4870i	0.611616	−	1.05935i
$99$	7.40310	+	12.8225i	0.744039	+	1.28871i
$100$		0			0
$101$	−6.15661	−	10.6636i	−0.612605	−	1.06106i	−0.990800	−	0.135337i	$-0.956788\pi$
$101$	−6.15661	−	10.6636i	−0.612605	−	1.06106i	0.378194	−	0.925726i	$-0.376545\pi$
$102$	0.908659			0.0899707
$103$	−10.6164			−1.04606			−0.523032	−	0.852313i	$-0.675199\pi$
$103$	−10.6164			−1.04606			−0.523032	+	0.852313i	$0.675199\pi$
$104$	6.98040	+	12.0904i	0.684485	+	1.18556i
$105$		0			0
$106$	−13.1234			−1.27466
$107$	2.17265			0.210038			0.105019	−	0.994470i	$-0.466510\pi$
$107$	2.17265			0.210038			0.105019	+	0.994470i	$0.466510\pi$
$108$	−1.15159	−	1.99461i	−0.110812	−	0.191932i
$109$	−7.91012	+	13.7007i	−0.757652	+	1.31229i	0.186393	+	0.982475i	$0.440320\pi$
$109$	−7.91012	+	13.7007i	−0.757652	+	1.31229i	−0.944045	+	0.329816i	$0.893013\pi$
$110$		0			0
$111$	−13.7445	+	23.8062i	−1.30457	+	2.25958i
$112$	−0.110938	+	0.192150i	−0.0104827	+	0.0181565i
$113$	−9.83828			−0.925507			−0.462754	−	0.886487i	$-0.653139\pi$
$113$	−9.83828			−0.925507			−0.462754	+	0.886487i	$0.653139\pi$
$114$	−16.7726	−	18.5004i	−1.57089	−	1.73272i
$115$		0			0
$116$	5.64959	−	9.78538i	0.524551	−	0.908549i
$117$	−8.21286	+	14.2251i	−0.759279	+	1.31511i
$118$	3.50000	+	6.06218i	0.322201	+	0.558069i
$119$	−0.278124	+	0.481725i	−0.0254956	+	0.0441596i
$120$		0			0
$121$	9.31322			0.846656
$122$	1.99600			0.180709
$123$	−7.61796	−	13.1947i	−0.686888	−	1.18972i
$124$	3.68122	+	6.37607i	0.330584	+	0.572588i
$125$		0			0
$126$	26.3273			2.34542
$127$	7.85543	+	13.6060i	0.697056	+	1.20734i	0.969483	+	0.245160i	$0.0788407\pi$
$127$	7.85543	+	13.6060i	0.697056	+	1.20734i	−0.272426	+	0.962177i	$0.587826\pi$
$128$	−9.08432	+	15.7345i	−0.802948	+	1.39075i
$129$	−4.19726	−	7.26987i	−0.369548	−	0.640076i
$130$		0			0
$131$	5.76755	−	9.98968i	0.503913	−	0.872803i	−0.496077	−	0.868279i	$-0.665227\pi$
$131$	5.76755	−	9.98968i	0.503913	−	0.872803i	0.999990	−	0.00452412i	$-0.00144008\pi$
$132$	−36.4046			−3.16861
$133$	14.9418	−	3.22932i	1.29561	−	0.280017i
$134$	−19.2952			−1.66685
$135$		0			0
$136$	−0.221432	+	0.383532i	−0.0189876	+	0.0328876i
$137$	0.0546904	+	0.0947266i	0.00467252	+	0.00809304i	0.868352	−	0.495948i	$-0.165179\pi$
$137$	0.0546904	+	0.0947266i	0.00467252	+	0.00809304i	−0.863680	+	0.504041i	$0.831846\pi$
$138$	−3.31878	+	5.74829i	−0.282513	+	0.489327i
$139$	−0.721876	−	1.25033i	−0.0612287	−	0.106051i	0.833786	−	0.552088i	$-0.186169\pi$
$139$	−0.721876	−	1.25033i	−0.0612287	−	0.106051i	−0.895015	+	0.446036i	$0.852835\pi$
$140$		0			0
$141$	−7.67967			−0.646745
$142$	−18.5507	−	32.1307i	−1.55674	−	2.69635i
$143$	11.2675	+	19.5160i	0.942240	+	1.63201i
$144$	−0.207839			−0.0173199
$145$		0			0
$146$	8.17922	+	14.1668i	0.676917	+	1.17245i
$147$	−6.64257	+	11.5053i	−0.547870	+	0.948939i
$148$	−17.6636	−	30.5943i	−1.45194	−	2.51484i
$149$	−0.864447	+	1.49727i	−0.0708183	+	0.122661i	−0.899260	−	0.437414i	$-0.855894\pi$
$149$	−0.864447	+	1.49727i	−0.0708183	+	0.122661i	0.828442	+	0.560075i	$0.189228\pi$
$150$		0			0
$151$	−20.1406			−1.63902			−0.819508	−	0.573068i	$-0.805753\pi$
$151$	−20.1406			−1.63902			−0.819508	+	0.573068i	$0.805753\pi$
$152$	11.8961	−	2.57107i	0.964900	−	0.208541i
$153$	−0.521056			−0.0421249
$154$	18.0597	−	31.2803i	1.45529	−	2.52064i
$155$		0			0
$156$	−20.1933	−	34.9758i	−1.61675	−	2.80030i
$157$	1.88906	−	3.27195i	0.150764	−	0.261130i	−0.780745	−	0.624850i	$-0.785160\pi$
$157$	1.88906	−	3.27195i	0.150764	−	0.261130i	0.931508	+	0.363720i	$0.118493\pi$
$158$	−11.5703	−	20.0403i	−0.920482	−	1.59432i
$159$	14.3976			1.14181
$160$		0			0
$161$	−2.03163	−	3.51889i	−0.160115	−	0.277328i
$162$	−9.21286	−	15.9571i	−0.723830	−	1.25371i
$163$	1.61640			0.126606			0.0633031	−	0.997994i	$-0.479837\pi$
$163$	1.61640			0.126606			0.0633031	+	0.997994i	$0.479837\pi$
$164$	19.5803			1.52897
$165$		0			0
$166$	−5.54767	+	9.60885i	−0.430583	+	0.745791i
$167$	3.24649	+	5.62309i	0.251221	+	0.435128i	0.963862	−	0.266401i	$-0.0858346\pi$
$167$	3.24649	+	5.62309i	0.251221	+	0.435128i	−0.712641	+	0.701529i	$0.752501\pi$
$168$	−12.2746	+	21.2602i	−0.947003	+	1.64026i
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$		0			0
$171$	9.61796	+	10.6088i	0.735504	+	0.811273i
$172$	10.7882			0.822589
$173$	4.26053	−	7.37945i	0.323922	−	0.561049i	−0.657372	−	0.753567i	$-0.728332\pi$
$173$	4.26053	−	7.37945i	0.323922	−	0.561049i	0.981294	+	0.192517i	$0.0616651\pi$
$174$	−10.0457	+	17.3996i	−0.761560	+	1.31906i
$175$		0			0
$176$	−0.142571	+	0.246941i	−0.0107467	+	0.0186139i
$177$	−3.83983	−	6.65079i	−0.288620	−	0.499904i
$178$	2.54221			0.190547
$179$	−10.2711			−0.767698			−0.383849	−	0.923396i	$-0.625402\pi$
$179$	−10.2711			−0.767698			−0.383849	+	0.923396i	$0.625402\pi$
$180$		0			0
$181$	−6.13355	−	10.6236i	−0.455903	−	0.789648i	0.542836	−	0.839838i	$-0.317350\pi$
$181$	−6.13355	−	10.6236i	−0.455903	−	0.789648i	−0.998740	+	0.0501908i	$0.984017\pi$
$182$	40.0702			2.97020
$183$	−2.18980			−0.161875
$184$	−1.61751	−	2.80161i	−0.119245	−	0.206538i
$185$		0			0
$186$	−6.54567	−	11.3374i	−0.479952	−	0.831301i
$187$	−0.357429	+	0.619085i	−0.0261378	+	0.0452720i
$188$	4.93473	−	8.54721i	0.359902	−	0.623369i
$189$	−2.50702			−0.182359
$190$		0			0
$191$	5.71085			0.413223			0.206611	−	0.978423i	$-0.433756\pi$
$191$	5.71085			0.413223			0.206611	+	0.978423i	$0.433756\pi$
$192$	16.2515	−	28.1484i	1.17285	−	2.03144i
$193$	−5.07930	+	8.79761i	−0.365616	+	0.633266i	−0.988875	−	0.148750i	$-0.952475\pi$
$193$	−5.07930	+	8.79761i	−0.365616	+	0.633266i	0.623259	+	0.782016i	$0.285808\pi$
$194$	−1.85041	−	3.20500i	−0.132852	−	0.230106i
$195$		0			0
$196$	−8.53665	−	14.7859i	−0.609761	−	1.05614i
$197$	−16.2038			−1.15448			−0.577238	−	0.816576i	$-0.695869\pi$
$197$	−16.2038			−1.15448			−0.577238	+	0.816576i	$0.695869\pi$
$198$	33.8343			2.40450
$199$	−0.167186	−	0.289574i	−0.0118515	−	0.0205274i	0.860039	−	0.510229i	$-0.170439\pi$
$199$	−0.167186	−	0.289574i	−0.0118515	−	0.0205274i	−0.871890	+	0.489701i	$0.837106\pi$
$200$		0			0
$201$	21.1686			1.49312
$202$	−28.1375			−1.97974
$203$	−6.14959	−	10.6514i	−0.431617	−	0.747582i
$204$	0.640570	−	1.10950i	0.0448489	−	0.0776805i
$205$		0			0
$206$	−12.1300	+	21.0098i	−0.845137	+	1.46382i
$207$	1.90310	−	3.29626i	0.132275	−	0.229106i
$208$	−0.316332			−0.0219336
$209$	19.2023	−	4.15013i	1.32825	−	0.287071i
$210$		0			0
$211$	−1.01404	+	1.75636i	−0.0698092	+	0.120913i	−0.898817	−	0.438324i	$-0.855572\pi$
$211$	−1.01404	+	1.75636i	−0.0698092	+	0.120913i	0.829008	+	0.559237i	$0.188906\pi$
$212$	−9.25151	+	16.0241i	−0.635396	+	1.10054i
$213$	20.3519	+	35.2505i	1.39449	+	2.41532i
$214$	2.48240	−	4.29965i	0.169694	−	0.293918i
$215$		0			0
$216$	−1.99600			−0.135810
$217$	8.01404			0.544028
$218$	18.0757	+	31.3081i	1.22424	+	2.12045i
$219$	−8.97338	−	15.5424i	−0.606365	−	1.05026i
$220$		0			0
$221$	−0.793049			−0.0533463
$222$	31.4081	+	54.4005i	2.10797	+	3.65112i
$223$	−9.61596	+	16.6553i	−0.643932	+	1.11532i	0.340615	+	0.940203i	$0.389365\pi$
$223$	−9.61596	+	16.6553i	−0.643932	+	1.11532i	−0.984547	+	0.175120i	$0.943969\pi$
$224$	10.0457	+	17.3996i	0.671205	+	1.16256i
$225$		0			0
$226$	−11.2409	+	19.4699i	−0.747736	+	1.29512i
$227$	−4.00000			−0.265489			−0.132745	−	0.991150i	$-0.542379\pi$
$227$	−4.00000			−0.265489			−0.132745	+	0.991150i	$0.542379\pi$
$228$	−34.4136	+	7.43771i	−2.27909	+	0.492574i
$229$	−12.9788			−0.857666			−0.428833	−	0.903384i	$-0.641075\pi$
$229$	−12.9788			−0.857666			−0.428833	+	0.903384i	$0.641075\pi$
$230$		0			0
$231$	−19.8132	+	34.3175i	−1.30361	+	2.25793i
$232$	−4.89608	−	8.48026i	−0.321443	−	0.556756i
$233$	13.5367	−	23.4462i	0.886815	−	1.53601i	0.0431968	−	0.999067i	$-0.486246\pi$
$233$	13.5367	−	23.4462i	0.886815	−	1.53601i	0.843619	−	0.536943i	$-0.180421\pi$
$234$	18.7675	+	32.5063i	1.22687	+	2.12501i
$235$		0			0
$236$	9.86946			0.642447
$237$	12.6937	+	21.9861i	0.824545	+	1.42815i
$238$	0.635553	+	1.10081i	0.0411968	+	0.0713549i
$239$	20.0602			1.29758			0.648792	−	0.760966i	$-0.275275\pi$
$239$	20.0602			1.29758			0.648792	+	0.760966i	$0.275275\pi$
$240$		0			0
$241$	10.7922	+	18.6926i	0.695184	+	1.20409i	0.970119	+	0.242631i	$0.0780105\pi$
$241$	10.7922	+	18.6926i	0.695184	+	1.20409i	−0.274934	+	0.961463i	$0.588656\pi$
$242$	10.6410	−	18.4308i	0.684030	−	1.18478i
$243$	11.1797	+	19.3637i	0.717176	+	1.24219i
$244$	1.40710	−	2.43717i	0.0900805	−	0.156024i
$245$		0			0
$246$	−34.8162			−2.21980
$247$	14.6386	+	16.1466i	0.931430	+	1.02738i
$248$	6.38049			0.405161
$249$	6.08632	−	10.5418i	0.385705	−	0.668061i
$250$		0			0
$251$	3.63400	+	6.29426i	0.229376	+	0.397290i	0.957623	−	0.288024i	$-0.0929982\pi$
$251$	3.63400	+	6.29426i	0.229376	+	0.397290i	−0.728248	+	0.685314i	$0.759665\pi$
$252$	18.5597	−	32.1464i	1.16915	−	2.02503i
$253$	−2.61094	−	4.52228i	−0.164148	−	0.284313i
$254$	35.9015			2.25266
$255$		0			0
$256$	7.79416	+	13.4999i	0.487135	+	0.843743i
$257$	7.53865	+	13.0573i	0.470248	+	0.814494i	0.999421	−	0.0340202i	$-0.0108311\pi$
$257$	7.53865	+	13.0573i	0.470248	+	0.814494i	−0.529173	+	0.848514i	$0.677498\pi$
$258$	−19.1827			−1.19426
$259$	−38.4538			−2.38940
$260$		0			0
$261$	5.76053	−	9.97753i	0.356568	−	0.617593i
$262$	−13.1797	−	22.8279i	−0.814242	−	1.41031i
$263$	10.0773	−	17.4544i	0.621393	−	1.07628i	−0.367833	−	0.929892i	$-0.619900\pi$
$263$	10.0773	−	17.4544i	0.621393	−	1.07628i	0.989227	−	0.146393i	$-0.0467663\pi$
$264$	−15.7746	+	27.3223i	−0.970857	+	1.68157i
$265$		0			0
$266$	10.6812	−	33.2593i	0.654908	−	2.03926i
$267$	−2.78905			−0.170687
$268$	−13.6024	+	23.5600i	−0.830897	+	1.43915i
$269$	3.86245	−	6.68995i	0.235497	−	0.407894i	−0.723920	−	0.689884i	$-0.757661\pi$
$269$	3.86245	−	6.68995i	0.235497	−	0.407894i	0.959417	+	0.281991i	$0.0909947\pi$
$270$		0			0
$271$	2.64257	−	4.57707i	0.160525	−	0.278037i	−0.774532	−	0.632534i	$-0.782015\pi$
$271$	2.64257	−	4.57707i	0.160525	−	0.278037i	0.935057	+	0.354497i	$0.115348\pi$
$272$	−0.00501733	−	0.00869027i	−0.000304220	−	0.000526925i
$273$	−43.9608			−2.66063
$274$	0.249951			0.0151001
$275$		0			0
$276$	4.67922	+	8.10465i	0.281656	+	0.487843i
$277$	−30.6264			−1.84016			−0.920082	−	0.391726i	$-0.871878\pi$
$277$	−30.6264			−1.84016			−0.920082	+	0.391726i	$0.871878\pi$
$278$	−3.29918			−0.197872
$279$	3.75351	+	6.50127i	0.224717	+	0.389221i
$280$		0			0
$281$	−6.68122	−	11.5722i	−0.398568	−	0.690341i	0.594981	−	0.803740i	$-0.297159\pi$
$281$	−6.68122	−	11.5722i	−0.398568	−	0.690341i	−0.993550	+	0.113399i	$0.963826\pi$
$282$	−8.77457	+	15.1980i	−0.522518	+	0.905027i
$283$	2.04767	−	3.54667i	0.121721	−	0.210828i	−0.798725	−	0.601696i	$-0.794492\pi$
$283$	2.04767	−	3.54667i	0.121721	−	0.210828i	0.920447	+	0.390868i	$0.127825\pi$
$284$	−52.3101			−3.10403
$285$		0			0
$286$	51.4959			3.04502
$287$	10.6566	−	18.4578i	0.629040	−	1.08953i
$288$	−9.41012	+	16.2988i	−0.554497	+	0.960416i
$289$	8.48742	+	14.7006i	0.499260	+	0.864744i
$290$		0			0
$291$	2.03008	+	3.51619i	0.119005	+	0.206123i
$292$	23.0642			1.34973
$293$	−12.1726			−0.711134			−0.355567	−	0.934651i	$-0.615712\pi$
$293$	−12.1726			−0.711134			−0.355567	+	0.934651i	$0.615712\pi$
$294$	15.1792	+	26.2912i	0.885270	+	1.53333i
$295$		0			0
$296$	−30.6155			−1.77949
$297$	−3.22188			−0.186952
$298$	1.97539	+	3.42147i	0.114431	+	0.198200i
$299$	2.89652	−	5.01693i	0.167510	−	0.290136i
$300$		0			0
$301$	5.87147	−	10.1697i	0.338426	−	0.586170i
$302$	−23.0120	+	39.8580i	−1.32419	+	2.29357i
$303$	30.8695			1.77340
$304$	−0.0843223	+	0.262564i	−0.00483621	+	0.0150591i
$305$		0			0
$306$	−0.595344	+	1.03117i	−0.0340335	+	0.0589478i
$307$	12.2675	−	21.2480i	0.700146	−	1.21269i	−0.268269	−	0.963344i	$-0.586452\pi$
$307$	12.2675	−	21.2480i	0.700146	−	1.21269i	0.968415	−	0.249344i	$-0.0802150\pi$
$308$	−25.4628	−	44.1029i	−1.45088	−	2.51299i
$309$	13.3078	−	23.0497i	0.757052	−	1.31125i
$310$		0			0
$311$	−10.2038			−0.578606			−0.289303	−	0.957238i	$-0.593424\pi$
$311$	−10.2038			−0.578606			−0.289303	+	0.957238i	$0.593424\pi$
$312$	−35.0000			−1.98148
$313$	−15.9910	−	27.6972i	−0.903864	−	1.56554i	−0.822435	−	0.568859i	$-0.807385\pi$
$313$	−15.9910	−	27.6972i	−0.903864	−	1.56554i	−0.0814282	−	0.996679i	$-0.525948\pi$
$314$	−4.31678	−	7.47687i	−0.243610	−	0.421944i
$315$		0			0
$316$	−32.6264			−1.83538
$317$	1.11796	+	1.93636i	0.0627907	+	0.108757i	0.895712	−	0.444635i	$-0.146667\pi$
$317$	1.11796	+	1.93636i	0.0627907	+	0.108757i	−0.832921	+	0.553392i	$0.813333\pi$
$318$	16.4503	−	28.4928i	0.922489	−	1.59780i
$319$	−7.90310	−	13.6886i	−0.442489	−	0.766413i
$320$		0			0
$321$	−2.72343	+	4.71713i	−0.152007	+	0.263284i
$322$	−9.28514			−0.517441
$323$	−0.211397	+	0.658252i	−0.0117625	+	0.0366261i
$324$	−25.9788			−1.44327
$325$		0			0
$326$	1.84685	−	3.19884i	0.102288	−	0.177167i
$327$	−19.8308	−	34.3480i	−1.09665	−	1.89945i
$328$	8.48441	−	14.6954i	0.468473	−	0.811419i
$329$	−5.37147	−	9.30365i	−0.296139	−	0.512927i
$330$		0			0
$331$	−10.0913			−0.554670			−0.277335	−	0.960773i	$-0.589451\pi$
$331$	−10.0913			−0.554670			−0.277335	+	0.960773i	$0.589451\pi$
$332$	7.82179	+	13.5477i	0.429277	+	0.743529i
$333$	−18.0105	−	31.1951i	−0.986968	−	1.70948i
$334$	14.8374			0.811866
$335$		0			0
$336$	−0.278124	−	0.481725i	−0.0151729	−	0.0262802i
$337$	2.80620	−	4.86048i	0.152863	−	0.264767i	−0.779416	−	0.626507i	$-0.784484\pi$
$337$	2.80620	−	4.86048i	0.152863	−	0.264767i	0.932279	+	0.361740i	$0.117817\pi$
$338$	13.7109	+	23.7479i	0.745772	+	1.29172i
$339$	12.3324	−	21.3603i	0.669802	−	1.16013i
$340$		0			0
$341$	10.2992			0.557732
$342$	31.9839	−	6.91258i	1.72949	−	0.373790i
$343$	5.96481			0.322069
$344$	4.67465	−	8.09673i	0.252040	−	0.436546i
$345$		0			0
$346$	−9.73591	−	16.8631i	−0.523406	−	0.906566i
$347$	2.73747	−	4.74144i	0.146955	−	0.254534i	−0.783146	−	0.621838i	$-0.786386\pi$
$347$	2.73747	−	4.74144i	0.146955	−	0.254534i	0.930101	+	0.367305i	$0.119719\pi$
$348$	14.1636	+	24.5321i	0.759250	+	1.31506i
$349$	−18.8202			−1.00742			−0.503712	−	0.863872i	$-0.668033\pi$
$349$	−18.8202			−1.00742			−0.503712	+	0.863872i	$0.668033\pi$
$350$		0			0
$351$	−1.78714	−	3.09542i	−0.0953907	−	0.165222i
$352$	12.9101	+	22.3610i	0.688112	+	1.19184i
$353$	12.7008			0.675996			0.337998	−	0.941147i	$-0.390250\pi$
$353$	12.7008			0.675996			0.337998	+	0.941147i	$0.390250\pi$
$354$	−17.5491			−0.932726
$355$		0			0
$356$	1.79216	−	3.10411i	0.0949843	−	0.164518i
$357$	−0.697262	−	1.20769i	−0.0369030	−	0.0639179i
$358$	−11.7355	+	20.3264i	−0.620239	+	1.07429i
$359$	5.54021	−	9.59592i	0.292401	−	0.506453i	−0.681976	−	0.731375i	$-0.738879\pi$
$359$	5.54021	−	9.59592i	0.292401	−	0.506453i	0.974377	+	0.224921i	$0.0722125\pi$
$360$		0			0
$361$	17.3042	−	7.84632i	0.910747	−	0.412964i
$362$	−28.0321			−1.47333
$363$	−11.6742	+	20.2203i	−0.612737	+	1.06129i
$364$	28.2479	−	48.9269i	1.48059	−	2.56447i
$365$		0			0
$366$	−2.50200	+	4.33359i	−0.130782	+	0.226521i
$367$	−10.3202	−	17.8752i	−0.538712	−	0.933076i	−0.998974	−	0.0452932i	$-0.985578\pi$
$367$	−10.3202	−	17.8752i	−0.538712	−	0.933076i	0.460262	−	0.887783i	$-0.347756\pi$
$368$	0.0733010			0.00382108
$369$	19.9648			1.03933
$370$		0			0
$371$	10.0703	+	17.4422i	0.522823	+	0.905556i
$372$	−18.4578			−0.956992
$373$	−4.55313			−0.235752			−0.117876	−	0.993028i	$-0.537609\pi$
$373$	−4.55313			−0.235752			−0.117876	+	0.993028i	$0.537609\pi$
$374$	0.816776	+	1.41470i	0.0422345	+	0.0731522i
$375$		0			0
$376$	−4.27657	−	7.40723i	−0.220547	−	0.381999i
$377$	8.76755	−	15.1858i	0.451552	−	0.782110i
$378$	−2.86445	+	4.96137i	−0.147331	+	0.255185i
$379$	−19.9187			−1.02315			−0.511577	−	0.859237i	$-0.670939\pi$
$379$	−19.9187			−1.02315			−0.511577	+	0.859237i	$0.670939\pi$
$380$		0			0
$381$	−39.3874			−2.01788
$382$	6.52506	−	11.3017i	0.333851	−	0.578247i
$383$	−9.98742	+	17.2987i	−0.510333	+	0.883923i	0.489595	+	0.871950i	$0.337145\pi$
$383$	−9.98742	+	17.2987i	−0.510333	+	0.883923i	−0.999928	+	0.0119734i	$0.996189\pi$
$384$	−22.7746	−	39.4467i	−1.16221	−	2.01301i
$385$		0			0
$386$	11.6069	+	20.1038i	0.590777	+	1.02326i
$387$	11.0000			0.559161
$388$	−5.21787			−0.264897
$389$	−6.90110	−	11.9531i	−0.349900	−	0.606044i	0.636332	−	0.771416i	$-0.280451\pi$
$389$	−6.90110	−	11.9531i	−0.349900	−	0.606044i	−0.986231	+	0.165372i	$0.947118\pi$
$390$		0			0
$391$	0.183767			0.00929349
$392$	−14.7962			−0.747319
$393$	14.4593	+	25.0443i	0.729378	+	1.26332i
$394$	−18.5140	+	32.0673i	−0.932724	+	1.61552i
$395$		0			0
$396$	23.8519	−	41.3126i	1.19860	−	2.07604i
$397$	−8.27457	+	14.3320i	−0.415289	+	0.719301i	−0.995459	−	0.0951945i	$-0.969653\pi$
$397$	−8.27457	+	14.3320i	−0.415289	+	0.719301i	0.580170	+	0.814495i	$0.302986\pi$
$398$	−0.764087			−0.0383002
$399$	−11.7183	+	36.4886i	−0.586650	+	1.82672i
$400$		0			0
$401$	−4.26253	+	7.38292i	−0.212861	+	0.368685i	−0.952609	−	0.304199i	$-0.901611\pi$
$401$	−4.26253	+	7.38292i	−0.212861	+	0.368685i	0.739748	+	0.672884i	$0.234945\pi$
$402$	24.1867	−	41.8926i	1.20632	−	2.08941i
$403$	5.71286	+	9.89496i	0.284578	+	0.492903i
$404$	−19.8358	+	34.3567i	−0.986869	+	1.70931i
$405$		0			0
$406$	−28.1054			−1.39485
$407$	−49.4186			−2.44959
$408$	−0.555134	−	0.961521i	−0.0274833	−	0.0476024i
$409$	5.78314	+	10.0167i	0.285958	+	0.495294i	0.972841	−	0.231474i	$-0.0743549\pi$
$409$	5.78314	+	10.0167i	0.285958	+	0.495294i	−0.686883	+	0.726768i	$0.741022\pi$
$410$		0			0
$411$	−0.274220			−0.0135263
$412$	17.1024	+	29.6222i	0.842573	+	1.45938i
$413$	5.37147	−	9.30365i	0.264313	−	0.457803i
$414$	−4.34885	−	7.53243i	−0.213734	−	0.370199i
$415$		0			0
$416$	−14.3222	+	24.8068i	−0.702205	+	1.21626i
$417$	3.61951			0.177248
$418$	13.7269	−	42.7430i	0.671404	−	2.09063i
$419$	−21.7149			−1.06084			−0.530420	−	0.847735i	$-0.677966\pi$
$419$	−21.7149			−1.06084			−0.530420	+	0.847735i	$0.677966\pi$
$420$		0			0
$421$	3.46135	−	5.99523i	0.168696	−	0.292190i	−0.769266	−	0.638929i	$-0.779378\pi$
$421$	3.46135	−	5.99523i	0.168696	−	0.292190i	0.937962	+	0.346739i	$0.112711\pi$
$422$	2.31722	+	4.01354i	0.112800	+	0.195376i
$423$	5.03163	−	8.71504i	0.244646	−	0.423740i
$424$	8.01760	+	13.8869i	0.389369	+	0.674407i
$425$		0			0
$426$	93.0138			4.50654
$427$	−1.53163	−	2.65287i	−0.0741209	−	0.128381i
$428$	−3.50000	−	6.06218i	−0.169179	−	0.293026i
$429$	−56.4959			−2.72765
$430$		0			0
$431$	13.9894	+	24.2304i	0.673847	+	1.16714i	0.976805	+	0.214133i	$0.0686926\pi$
$431$	13.9894	+	24.2304i	0.673847	+	1.16714i	−0.302958	+	0.953004i	$0.597974\pi$
$432$	0.0226132	−	0.0391672i	0.00108798	−	0.00188443i
$433$	3.12698	+	5.41608i	0.150273	+	0.260280i	0.931328	−	0.364182i	$-0.118651\pi$
$433$	3.12698	+	5.41608i	0.150273	+	0.260280i	−0.781055	+	0.624462i	$0.785318\pi$
$434$	9.15661	−	15.8597i	0.439531	−	0.761290i
$435$		0			0
$436$	50.9708			2.44106
$437$	−3.39208	−	3.74152i	−0.162265	−	0.178981i
$438$	−41.0109			−1.95958
$439$	−15.5988	+	27.0179i	−0.744490	+	1.28949i	0.205942	+	0.978564i	$0.433974\pi$
$439$	−15.5988	+	27.0179i	−0.744490	+	1.28949i	−0.950433	+	0.310931i	$0.899359\pi$
$440$		0			0
$441$	−8.70428	−	15.0763i	−0.414490	−	0.717917i
$442$	−0.906115	+	1.56944i	−0.0430995	+	0.0746505i
$443$	−16.3519	−	28.3223i	−0.776901	−	1.34563i	−0.933720	−	0.358004i	$-0.883457\pi$
$443$	−16.3519	−	28.3223i	−0.776901	−	1.34563i	0.156819	−	0.987627i	$-0.449876\pi$
$444$	88.5661			4.20316
$445$		0			0
$446$	21.9738	+	38.0598i	1.04049	+	1.80218i
$447$	−2.16719	−	3.75368i	−0.102504	−	0.177543i
$448$	45.4678			2.14815
$449$	25.6304			1.20958			0.604788	−	0.796387i	$-0.293258\pi$
$449$	25.6304			1.20958			0.604788	+	0.796387i	$0.293258\pi$
$450$		0			0
$451$	13.6953	−	23.7209i	0.644885	−	1.11697i
$452$	15.8489	+	27.4510i	0.745467	+	1.29119i
$453$	25.2464	−	43.7280i	1.18618	−	2.05452i
$454$	−4.57028	+	7.91597i	−0.214494	+	0.371515i
$455$		0			0
$456$	−9.32970	+	29.0509i	−0.436903	+	1.36043i
$457$	−33.1646			−1.55138			−0.775688	−	0.631116i	$-0.782597\pi$
$457$	−33.1646			−1.55138			−0.775688	+	0.631116i	$0.782597\pi$
$458$	−14.8293	+	25.6850i	−0.692926	+	1.20018i
$459$	0.0566917	−	0.0981929i	0.00264614	−	0.00458325i
$460$		0			0
$461$	−1.08788	+	1.88426i	−0.0506677	+	0.0877590i	−0.890247	−	0.455478i	$-0.849468\pi$
$461$	−1.08788	+	1.88426i	−0.0506677	+	0.0877590i	0.839579	+	0.543237i	$0.182802\pi$
$462$	45.2760	+	78.4204i	2.10643	+	3.64845i
$463$	6.20072			0.288172			0.144086	−	0.989565i	$-0.453976\pi$
$463$	6.20072			0.288172			0.144086	+	0.989565i	$0.453976\pi$
$464$	0.221876			0.0103003
$465$		0			0
$466$	−30.9332	−	53.5778i	−1.43295	−	2.48195i
$467$	17.1546			0.793821			0.396910	−	0.917857i	$-0.370082\pi$
$467$	17.1546			0.793821			0.396910	+	0.917857i	$0.370082\pi$
$468$	52.9216			2.44630
$469$	14.8062	+	25.6451i	0.683687	+	1.18418i
$470$		0			0
$471$	4.73591	+	8.20284i	0.218219	+	0.377967i
$472$	4.27657	−	7.40723i	0.196845	−	0.340945i
$473$	7.54567	−	13.0695i	0.346950	−	0.600936i
$474$	58.0138			2.66466
$475$		0			0
$476$	1.79216			0.0821436
$477$	−9.43318	+	16.3387i	−0.431915	+	0.748099i
$478$	22.9202	−	39.6989i	1.04834	−	1.81578i
$479$	17.8891	+	30.9848i	0.817372	+	1.41573i	0.907612	+	0.419810i	$0.137903\pi$
$479$	17.8891	+	30.9848i	0.817372	+	1.41573i	−0.0902399	+	0.995920i	$0.528763\pi$
$480$		0			0
$481$	−27.4120	−	47.4790i	−1.24988	−	2.16486i
$482$	49.3233			2.24661
$483$	10.1867			0.463510
$484$	−15.0030	−	25.9860i	−0.681955	−	1.18118i
$485$		0			0
$486$	51.0943			2.31768
$487$	23.7149			1.07462			0.537311	−	0.843384i	$-0.319440\pi$
$487$	23.7149			1.07462			0.537311	+	0.843384i	$0.319440\pi$
$488$	−1.21943	−	2.11212i	−0.0552010	−	0.0956110i
$489$	−2.02617	+	3.50943i	−0.0916267	+	0.158702i
$490$		0			0
$491$	19.5933	−	33.9367i	0.884235	−	1.53154i	0.0376474	−	0.999291i	$-0.488014\pi$
$491$	19.5933	−	33.9367i	0.884235	−	1.53154i	0.846588	−	0.532249i	$-0.178653\pi$
$492$	−24.5441	+	42.5117i	−1.10653	+	1.91657i
$493$	0.556248			0.0250521
$494$	48.6796	−	10.5210i	2.19020	−	0.473361i
$495$		0			0
$496$	−0.0722863	+	0.125204i	−0.00324575	+	0.00562180i
$497$	−28.4698	+	49.3112i	−1.27705	+	2.21191i
$498$	−13.9081	−	24.0896i	−0.623238	−	1.07948i
$499$	4.68824	−	8.12027i	0.209875	−	0.363513i	−0.741800	−	0.670621i	$-0.766028\pi$
$499$	4.68824	−	8.12027i	0.209875	−	0.363513i	0.951675	+	0.307107i	$0.0993611\pi$
$500$		0			0
$501$	−16.2780			−0.727249
$502$	16.6084			0.741269
$503$	6.74649	+	11.6853i	0.300811	+	0.521020i	0.976320	−	0.216332i	$-0.0694093\pi$
$503$	6.74649	+	11.6853i	0.300811	+	0.521020i	−0.675509	+	0.737352i	$0.736076\pi$
$504$	−16.0843	−	27.8589i	−0.716453	−	1.24093i
$505$		0			0
$506$	−11.9327			−0.530475
$507$	−15.0421	−	26.0537i	−0.668044	−	1.15709i
$508$	25.3092	−	43.8368i	1.12291	−	1.94495i
$509$	−12.8534	−	22.2628i	−0.569718	−	0.986781i	−0.996594	−	0.0824703i	$-0.973719\pi$
$509$	−12.8534	−	22.2628i	−0.569718	−	0.986781i	0.426875	−	0.904310i	$-0.359614\pi$
$510$		0			0
$511$	12.5527	−	21.7419i	0.555298	−	0.961805i
$512$	−0.715746			−0.0316318
$513$	−3.04567	+	0.658252i	−0.134470	+	0.0290625i
$514$	34.4538			1.51969
$515$		0			0
$516$	−13.5231	+	23.4226i	−0.595319	+	1.03112i
$517$	−6.90310	−	11.9565i	−0.303598	−	0.525847i
$518$	−43.9362	+	76.0997i	−1.93045	+	3.34363i
$519$	10.6812	+	18.5004i	0.468854	+	0.812078i
$520$		0			0
$521$	−37.7358			−1.65324			−0.826618	−	0.562763i	$-0.809738\pi$
$521$	−37.7358			−1.65324			−0.826618	+	0.562763i	$0.809738\pi$
$522$	−13.1636	−	22.8001i	−0.576156	−	0.997932i
$523$	19.2003	+	33.2559i	0.839570	+	1.45418i	0.890255	+	0.455462i	$0.150526\pi$
$523$	19.2003	+	33.2559i	0.839570	+	1.45418i	−0.0506855	+	0.998715i	$0.516141\pi$
$524$	−37.1646			−1.62354
$525$		0			0
$526$	−23.0281	−	39.8858i	−1.00407	−	1.73910i
$527$	−0.181223	+	0.313888i	−0.00789420	+	0.0136732i
$528$	−0.357429	−	0.619085i	−0.0155551	−	0.0269422i
$529$	10.8288	−	18.7561i	0.470818	−	0.815481i
$530$		0			0
$531$	10.0633			0.436709
$532$	−33.0808	−	36.4886i	−1.43423	−	1.58198i
$533$	30.3865			1.31619
$534$	−3.18668	+	5.51950i	−0.137901	+	0.238852i
$535$		0			0
$536$	11.7882	+	20.4177i	0.509171	+	0.881910i
$537$	12.8749	−	22.3000i	0.555594	−	0.962317i
$538$	−8.82624	−	15.2875i	−0.380526	−	0.659091i
$539$	−23.8835			−1.02874
$540$		0			0
$541$	6.40310	+	11.0905i	0.275291	+	0.476818i	0.970208	−	0.242272i	$-0.0778926\pi$
$541$	6.40310	+	11.0905i	0.275291	+	0.476818i	−0.694918	+	0.719089i	$0.744559\pi$
$542$	−6.03865	−	10.4593i	−0.259382	−	0.449263i
$543$	30.7539			1.31977
$544$	−0.908659			−0.0389584
$545$		0			0
$546$	−50.2284	+	86.9981i	−2.14958	+	3.72317i
$547$	−9.12853	−	15.8111i	−0.390308	−	0.676033i	0.602182	−	0.798359i	$-0.294298\pi$
$547$	−9.12853	−	15.8111i	−0.390308	−	0.676033i	−0.992490	+	0.122326i	$0.960965\pi$
$548$	0.176206	−	0.305197i	0.00752714	−	0.0130374i
$549$	1.43473	−	2.48503i	0.0612329	−	0.106058i
$550$		0			0
$551$	−10.2675	−	11.3253i	−0.437412	−	0.482473i
$552$	8.11027			0.345196
$553$	−17.7570	+	30.7560i	−0.755103	+	1.30788i
$554$	−34.9929	+	60.6095i	−1.48671	+	2.57505i
$555$		0			0
$556$	−2.32580	+	4.02840i	−0.0986357	+	0.170842i
$557$	7.45233	+	12.9078i	0.315765	+	0.546922i	0.979600	−	0.200958i	$-0.0644054\pi$
$557$	7.45233	+	12.9078i	0.315765	+	0.546922i	−0.663835	+	0.747879i	$0.731072\pi$
$558$	17.1546			0.726212
$559$	16.7420			0.708113
$560$		0			0
$561$	−0.896081	−	1.55206i	−0.0378326	−	0.0655279i
$562$	−30.5351			−1.28805
$563$	−45.7810			−1.92944			−0.964720	−	0.263276i	$-0.915197\pi$
$563$	−45.7810			−1.92944			−0.964720	+	0.263276i	$0.915197\pi$
$564$	12.3715	+	21.4280i	0.520933	+	0.902282i
$565$		0			0
$566$	−4.67922	−	8.10465i	−0.196682	−	0.340664i
$567$	−14.1390	+	24.4895i	−0.593783	+	1.02846i
$568$	−22.6666	+	39.2598i	−0.951071	+	1.64730i
$569$	0.379598			0.0159136			0.00795679	−	0.999968i	$-0.497467\pi$
$569$	0.379598			0.0159136			0.00795679	+	0.999968i	$0.497467\pi$
$570$		0			0
$571$	−15.8514			−0.663361			−0.331681	−	0.943392i	$-0.607616\pi$
$571$	−15.8514			−0.663361			−0.331681	+	0.943392i	$0.607616\pi$
$572$	36.3026	−	62.8780i	1.51789	−	2.62906i
$573$	−7.15861	+	12.3991i	−0.299055	+	0.517979i
$574$	−24.3519	−	42.1787i	−1.01643	−	1.76050i
$575$		0			0
$576$	21.2956	+	36.8851i	0.887318	+	1.53688i
$577$	19.2350			0.800765			0.400382	−	0.916348i	$-0.368877\pi$
$577$	19.2350			0.800765			0.400382	+	0.916348i	$0.368877\pi$
$578$	38.7899			1.61345
$579$	−12.7339	−	22.0558i	−0.529203	−	0.916607i
$580$		0			0
$581$	17.0281			0.706444
$582$	9.27803			0.384587
$583$	12.9418	+	22.4158i	0.535993	+	0.928366i
$584$	9.99400	−	17.3101i	0.413554	−	0.716297i
$585$		0			0
$586$	−13.9081	+	24.0896i	−0.574539	+	0.995131i
$587$	20.4242	−	35.3757i	0.842995	−	1.46011i	−0.0443559	−	0.999016i	$-0.514124\pi$
$587$	20.4242	−	35.3757i	0.842995	−	1.46011i	0.887351	−	0.461095i	$-0.152543\pi$
$588$	42.8031			1.76517
$589$	9.73591	−	2.10419i	0.401161	−	0.0867018i
$590$		0			0
$591$	20.3117	−	35.1808i	0.835510	−	1.44715i
$592$	0.346852	−	0.600764i	0.0142555	−	0.0246913i
$593$	−7.12342	−	12.3381i	−0.292524	−	0.506666i	0.681882	−	0.731462i	$-0.261162\pi$
$593$	−7.12342	−	12.3381i	−0.292524	−	0.506666i	−0.974406	+	0.224796i	$0.927828\pi$
$594$	−3.68122	+	6.37607i	−0.151042	+	0.261613i
$595$		0			0
$596$	5.57028			0.228168
$597$	0.838276			0.0343083
$598$	−6.61897	−	11.4644i	−0.270670	−	0.468814i
$599$	7.92571	+	13.7277i	0.323836	+	0.560900i	0.981276	−	0.192607i	$-0.0616941\pi$
$599$	7.92571	+	13.7277i	0.323836	+	0.560900i	−0.657440	+	0.753507i	$0.728361\pi$
$600$		0			0
$601$	16.4718			0.671900			0.335950	−	0.941880i	$-0.390943\pi$
$601$	16.4718			0.671900			0.335950	+	0.941880i	$0.390943\pi$
$602$	−13.4171	−	23.2392i	−0.546842	−	0.947158i
$603$	−13.8695	+	24.0226i	−0.564808	+	0.978277i
$604$	32.4452	+	56.1968i	1.32018	+	2.28661i
$605$		0			0
$606$	35.2706	−	61.0904i	1.43277	−	2.48163i
$607$	10.3914			0.421774			0.210887	−	0.977510i	$-0.432365\pi$
$607$	10.3914			0.421774			0.210887	+	0.977510i	$0.432365\pi$
$608$	16.7726	+	18.5004i	0.680217	+	0.750291i
$609$	30.8343			1.24947
$610$		0			0
$611$	7.65817	−	13.2643i	0.309816	−	0.536617i
$612$	0.839389	+	1.45386i	0.0339303	+	0.0587690i
$613$	−10.8925	+	18.8664i	−0.439945	+	0.762007i	−0.997685	−	0.0680090i	$-0.978335\pi$
$613$	−10.8925	+	18.8664i	−0.439945	+	0.762007i	0.557740	+	0.830016i	$0.311669\pi$
$614$	−28.0331	−	48.5547i	−1.13132	−	1.95951i
$615$		0			0
$616$	−44.1335			−1.77819
$617$	−21.3855	−	37.0408i	−0.860948	−	1.49121i	−0.871015	−	0.491256i	$-0.836538\pi$
$617$	−21.3855	−	37.0408i	−0.860948	−	1.49121i	0.0100671	−	0.999949i	$-0.496795\pi$
$618$	−30.4101	−	52.6719i	−1.22327	−	2.11877i
$619$	28.7882			1.15709			0.578547	−	0.815649i	$-0.303620\pi$
$619$	28.7882			1.15709			0.578547	+	0.815649i	$0.303620\pi$
$620$		0			0
$621$	0.414120	+	0.717278i	0.0166181	+	0.0287834i
$622$	−11.6586	+	20.1933i	−0.467468	+	0.809678i
$623$	−1.95077	−	3.37883i	−0.0781560	−	0.135370i
$624$	0.396525	−	0.686801i	0.0158737	−	0.0274940i
$625$		0			0
$626$	−73.0833			−2.92100
$627$	−15.0597	+	46.8931i	−0.601427	+	1.87273i
$628$	−12.1726			−0.485742
$629$	0.869563	−	1.50613i	0.0346718	−	0.0600532i
$630$		0			0
$631$	9.69370	+	16.7900i	0.385900	+	0.668399i	0.991894	−	0.127071i	$-0.0405576\pi$
$631$	9.69370	+	16.7900i	0.385900	+	0.668399i	−0.605993	+	0.795470i	$0.707224\pi$
$632$	−14.1375	+	24.4868i	−0.562358	+	0.974032i
$633$	−2.54221	−	4.40324i	−0.101044	−	0.175013i
$634$	5.10938			0.202919
$635$		0			0
$636$	−23.1937	−	40.1727i	−0.919690	−	1.59295i
$637$	−13.2479	−	22.9461i	−0.524903	−	0.909158i
$638$	−36.1194			−1.42998
$639$	−53.3373			−2.10999
$640$		0			0
$641$	−20.3433	+	35.2356i	−0.803512	+	1.39172i	0.113779	+	0.993506i	$0.463704\pi$
$641$	−20.3433	+	35.2356i	−0.803512	+	1.39172i	−0.917291	+	0.398217i	$0.869629\pi$
$642$	6.22343	+	10.7793i	0.245619	+	0.425425i
$643$	−17.0527	+	29.5361i	−0.672492	+	1.16479i	0.304703	+	0.952448i	$0.401443\pi$
$643$	−17.0527	+	29.5361i	−0.672492	+	1.16479i	−0.977195	+	0.212344i	$0.931890\pi$
$644$	−6.54567	+	11.3374i	−0.257936	+	0.446757i
$645$		0			0
$646$	1.06114	+	1.17045i	0.0417499	+	0.0460509i
$647$	48.0029			1.88719			0.943595	−	0.331103i	$-0.107421\pi$
$647$	48.0029			1.88719			0.943595	+	0.331103i	$0.107421\pi$
$648$	−11.2570	+	19.4976i	−0.442216	+	0.765940i
$649$	6.90310	−	11.9565i	0.270970	−	0.469334i
$650$		0			0
$651$	−10.0457	+	17.3996i	−0.393721	+	0.681945i
$652$	−2.60392	−	4.51012i	−0.101977	−	0.176630i
$653$	−3.90866			−0.152958			−0.0764788	−	0.997071i	$-0.524368\pi$
$653$	−3.90866			−0.152958			−0.0764788	+	0.997071i	$0.524368\pi$
$654$	−90.6325			−3.54401
$655$		0			0
$656$	0.192244	+	0.332977i	0.00750588	+	0.0130006i
$657$	23.5171			0.917488
$658$	−24.5491			−0.957025
$659$	−6.54411	−	11.3347i	−0.254922	−	0.441539i	0.709952	−	0.704250i	$-0.248717\pi$
$659$	−6.54411	−	11.3347i	−0.254922	−	0.441539i	−0.964874	+	0.262711i	$0.915383\pi$
$660$		0			0
$661$	11.9714	+	20.7350i	0.465633	+	0.806500i	0.999230	−	0.0392391i	$-0.0124934\pi$
$661$	11.9714	+	20.7350i	0.465633	+	0.806500i	−0.533597	+	0.845739i	$0.679160\pi$
$662$	−11.5301	+	19.9707i	−0.448129	+	0.776182i
$663$	0.994095	−	1.72182i	0.0386074	−	0.0668700i
$664$	13.5571			0.526119
$665$		0			0
$666$	−82.3130			−3.18956
$667$	−2.03163	+	3.51889i	−0.0786652	+	0.136252i
$668$	10.4598	−	18.1169i	0.404701	−	0.700963i
$669$	−24.1074	−	41.7552i	−0.932045	−	1.61435i
$670$		0			0
$671$	−1.96837	−	3.40931i	−0.0759880	−	0.131615i
$672$	−50.3694			−1.94304
$673$	11.3304			0.436754			0.218377	−	0.975865i	$-0.429924\pi$
$673$	11.3304			0.436754			0.218377	+	0.975865i	$0.429924\pi$
$674$	−6.41256	−	11.1069i	−0.247003	−	0.427821i
$675$		0			0
$676$	38.6625			1.48702
$677$	−8.90466			−0.342234			−0.171117	−	0.985251i	$-0.554738\pi$
$677$	−8.90466			−0.342234			−0.171117	+	0.985251i	$0.554738\pi$
$678$	−28.1812	−	48.8113i	−1.08229	−	1.87459i
$679$	−2.83983	+	4.91873i	−0.108983	+	0.188764i
$680$		0			0
$681$	5.01404	−	8.68457i	0.192138	−	0.332793i
$682$	11.7675	−	20.3820i	0.450603	−	0.780467i
$683$	26.6977			1.02156			0.510780	−	0.859712i	$-0.329357\pi$
$683$	26.6977			1.02156			0.510780	+	0.859712i	$0.329357\pi$
$684$	14.1069	−	43.9263i	0.539392	−	1.67957i
$685$		0			0
$686$	6.81522	−	11.8043i	0.260206	−	0.450690i
$687$	16.2691	−	28.1789i	0.620705	−	1.07509i
$688$	0.105921	+	0.183460i	0.00403819	+	0.00699435i
$689$	−14.3573	+	24.8676i	−0.546971	+	0.947381i
$690$		0			0
$691$	35.9708			1.36840			0.684198	−	0.729297i	$-0.260153\pi$
$691$	35.9708			1.36840			0.684198	+	0.729297i	$0.260153\pi$
$692$	−27.4538			−1.04364
$693$	−25.9628	−	44.9689i	−0.986245	−	1.70823i
$694$	−6.25551	−	10.8349i	−0.237456	−	0.411286i
$695$		0			0
$696$	24.5491			0.930532
$697$	0.481960	+	0.834779i	0.0182555	+	0.0316195i
$698$	−21.5035	+	37.2451i	−0.813918	+	1.40975i
$699$	33.9366	+	58.7800i	1.28360	+	2.22326i
$700$		0			0
$701$	−1.22543	+	2.12252i	−0.0462840	+	0.0801663i	−0.888239	−	0.459381i	$-0.848071\pi$
$701$	−1.22543	+	2.12252i	−0.0462840	+	0.0801663i	0.841955	+	0.539547i	$0.181405\pi$
$702$	−8.16776			−0.308272
$703$	−46.7159	+	10.0966i	−1.76192	+	0.380799i
$704$	58.4326			2.20226
$705$		0			0
$706$	14.5116	−	25.1348i	0.546151	−	0.945961i
$707$	21.5913	+	37.3973i	0.812026	+	1.40647i
$708$	−12.3715	+	21.4280i	−0.464948	+	0.805314i
$709$	25.1440	+	43.5507i	0.944304	+	1.63558i	0.757139	+	0.653254i	$0.226597\pi$
$709$	25.1440	+	43.5507i	0.944304	+	1.63558i	0.187165	+	0.982329i	$0.440070\pi$
$710$		0			0
$711$	−33.2671			−1.24761
$712$	−1.55313	−	2.69011i	−0.0582061	−	0.100816i
$713$	−1.32379	−	2.29288i	−0.0495765	−	0.0858690i
$714$	−3.18668			−0.119259
$715$		0			0
$716$	16.5461	+	28.6587i	0.618357	+	1.07103i
$717$	−25.1456	+	43.5534i	−0.939079	+	1.62653i
$718$	−12.6602	−	21.9281i	−0.472473	−	0.818348i
$719$	24.0491	−	41.6543i	0.896881	−	1.55344i	0.0654223	−	0.997858i	$-0.479161\pi$
$719$	24.0491	−	41.6543i	0.896881	−	1.55344i	0.831459	−	0.555586i	$-0.187506\pi$
$720$		0			0
$721$	37.2319			1.38659
$722$	4.24347	−	43.2098i	0.157926	−	1.60810i
$723$	−54.1123			−2.01246
$724$	−19.7615	+	34.2280i	−0.734432	+	1.27207i
$725$		0			0
$726$	26.6772	+	46.2063i	0.990085	+	1.71488i
$727$	−8.33983	+	14.4450i	−0.309307	+	0.535736i	−0.978211	−	0.207613i	$-0.933430\pi$
$727$	−8.33983	+	14.4450i	−0.309307	+	0.535736i	0.668904	+	0.743349i	$0.266764\pi$
$728$	−24.4804	−	42.4013i	−0.907304	−	1.57150i
$729$	−31.8655			−1.18020
$730$		0			0
$731$	0.265545	+	0.459938i	0.00982155	+	0.0170114i
$732$	3.52763	+	6.11004i	0.130385	+	0.225833i
$733$	4.13365			0.152680			0.0763399	−	0.997082i	$-0.475677\pi$
$733$	4.13365			0.152680			0.0763399	+	0.997082i	$0.475677\pi$
$734$	−47.1664			−1.74094
$735$		0			0
$736$	3.31878	−	5.74829i	0.122332	−	0.211885i
$737$	19.0281	+	32.9576i	0.700908	+	1.21401i
$738$	22.8112	−	39.5102i	0.839692	−	1.45439i
$739$	−23.4870	+	40.6806i	−0.863982	+	1.49646i	0.00407159	+	0.999992i	$0.498704\pi$
$739$	−23.4870	+	40.6806i	−0.863982	+	1.49646i	−0.868054	+	0.496470i	$0.834629\pi$
$740$		0			0
$741$	−53.4061	+	11.5425i	−1.96192	+	0.424025i
$742$	46.0241			1.68960
$743$	20.6069	−	35.6923i	0.755995	−	1.30942i	−0.188883	−	0.982000i	$-0.560487\pi$
$743$	20.6069	−	35.6923i	0.755995	−	1.30942i	0.944878	−	0.327422i	$-0.106180\pi$
$744$	−7.99800	+	13.8529i	−0.293221	+	0.507873i
$745$		0			0
$746$	−5.20228	+	9.01061i	−0.190469	+	0.329902i
$747$	7.97539	+	13.8138i	0.291804	+	0.505420i
$748$	2.30318			0.0842127
$749$	−7.61951			−0.278411
$750$		0			0
$751$	−2.98942	−	5.17783i	−0.109086	−	0.188942i	0.806314	−	0.591487i	$-0.201459\pi$
$751$	−2.98942	−	5.17783i	−0.109086	−	0.188942i	−0.915400	+	0.402545i	$0.868126\pi$
$752$	0.193802			0.00706722
$753$	−18.2210			−0.664010
$754$	−20.0351	−	34.7018i	−0.729635	−	1.26376i
$755$		0			0
$756$	4.03865	+	6.99515i	0.146884	+	0.254411i
$757$	18.1968	−	31.5178i	0.661375	−	1.14553i	−0.318880	−	0.947795i	$-0.603307\pi$
$757$	18.1968	−	31.5178i	0.661375	−	1.14553i	0.980255	−	0.197739i	$-0.0633599\pi$
$758$	−22.7585	+	39.4189i	−0.826627	+	1.43176i
$759$	13.0913			0.475186
$760$		0			0
$761$	−2.71397			−0.0983813			−0.0491907	−	0.998789i	$-0.515664\pi$
$761$	−2.71397			−0.0983813			−0.0491907	+	0.998789i	$0.515664\pi$
$762$	−45.0029	+	77.9473i	−1.63028	+	2.82373i
$763$	27.7409	−	48.0487i	1.00429	−	1.73948i
$764$	−9.19983	−	15.9346i	−0.332838	−	0.576493i
$765$		0			0
$766$	22.8227	+	39.5300i	0.824617	+	1.42828i
$767$	15.3163			0.553041
$768$	−39.0802			−1.41019
$769$	−19.8995	−	34.4670i	−0.717596	−	1.24291i	−0.961950	−	0.273226i	$-0.911909\pi$
$769$	−19.8995	−	34.4670i	−0.717596	−	1.24291i	0.244354	−	0.969686i	$-0.421424\pi$
$770$		0			0
$771$	−37.7991			−1.36130
$772$	32.7298			1.17797
$773$	22.4874	+	38.9494i	0.808816	+	1.40091i	0.913684	+	0.406425i	$0.133225\pi$
$773$	22.4874	+	38.9494i	0.808816	+	1.40091i	−0.104868	+	0.994486i	$0.533442\pi$
$774$	12.5683	−	21.7689i	0.451758	−	0.782467i
$775$		0			0
$776$	−2.26097	+	3.91612i	−0.0811642	+	0.140580i
$777$	48.2022	−	83.4886i	1.72924	−	2.99514i
$778$	−31.5400			−1.13076
$779$	8.09992	−	25.2216i	0.290210	−	0.903658i
$780$		0			0
$781$	−36.5878	+	63.3719i	−1.30921	+	2.26762i
$782$	0.209967	−	0.363673i	0.00750840	−	0.0130049i
$783$	1.25351	+	2.17114i	0.0447968	+	0.0775903i
$784$	0.167630	−	0.290343i	0.00598678	−	0.0103694i
$785$		0			0
$786$	66.0833			2.35711
$787$	17.7149			0.631466			0.315733	−	0.948848i	$-0.397750\pi$
$787$	17.7149			0.631466			0.315733	+	0.948848i	$0.397750\pi$
$788$	26.1034	+	45.2124i	0.929894	+	1.61062i
$789$	25.2640	+	43.7585i	0.899422	+	1.55784i
$790$		0			0
$791$	34.5030			1.22679
$792$	−20.6706	−	35.8026i	−0.734499	−	1.27219i
$793$	2.18367	−	3.78222i	0.0775443	−	0.134311i
$794$	18.9086	+	32.7506i	0.671040	+	1.16227i
$795$		0			0
$796$	−0.538652	+	0.932972i	−0.0190920	+	0.0330683i
$797$	−25.4930			−0.903008			−0.451504	−	0.892269i	$-0.649112\pi$
$797$	−25.4930			−0.903008			−0.451504	+	0.892269i	$0.649112\pi$
$798$	58.8217	+	64.8813i	2.08227	+	2.29677i
$799$	0.485864			0.0171886
$800$		0			0
$801$	1.82735	−	3.16507i	0.0645663	−	0.111832i
$802$	9.74049	+	16.8710i	0.343949	+	0.595736i
$803$	16.1320	−	27.9414i	0.569286	−	0.986032i
$804$	−34.1014	−	59.0653i	−1.20266	−	2.08307i
$805$		0			0
$806$	26.1094			0.919664
$807$	9.68322	+	16.7718i	0.340866	+	0.590397i
$808$	17.1902	+	29.7744i	0.604751	+	1.04746i
$809$	−20.4678			−0.719610			−0.359805	−	0.933027i	$-0.617157\pi$
$809$	−20.4678			−0.719610			−0.359805	+	0.933027i	$0.617157\pi$
$810$		0			0
$811$	11.4508	+	19.8333i	0.402091	+	0.696442i	0.993978	−	0.109579i	$-0.0349502\pi$
$811$	11.4508	+	19.8333i	0.402091	+	0.696442i	−0.591887	+	0.806021i	$0.701617\pi$
$812$	−19.8132	+	34.3175i	−0.695308	+	1.20431i
$813$	6.62498	+	11.4748i	0.232348	+	0.402439i
$814$	−56.4643	+	97.7990i	−1.97907	+	3.42785i
$815$		0			0
$816$	0.0251571			0.000880674
$817$	4.46281	−	13.8963i	0.156134	−	0.486171i
$818$	26.4306			0.924124
$819$	28.8026	−	49.8876i	1.00645	−	1.74322i
$820$		0			0
$821$	−15.3609	−	26.6058i	−0.536099	−	0.928550i	−0.999109	−	0.0421975i	$-0.986564\pi$
$821$	−15.3609	−	26.6058i	−0.536099	−	0.928550i	0.463011	−	0.886353i	$-0.346769\pi$
$822$	−0.313316	+	0.542679i	−0.0109281	+	0.0189281i
$823$	2.09846	+	3.63464i	0.0731476	+	0.126695i	0.900279	−	0.435313i	$-0.143362\pi$
$823$	2.09846	+	3.63464i	0.0731476	+	0.126695i	−0.827132	+	0.562008i	$0.810029\pi$
$824$	29.6427			1.03265
$825$		0			0
$826$	−12.2746	−	21.2602i	−0.427087	−	0.739736i
$827$	−10.6652	−	18.4726i	−0.370865	−	0.642357i	0.618834	−	0.785522i	$-0.287605\pi$
$827$	−10.6652	−	18.4726i	−0.370865	−	0.642357i	−0.989699	+	0.143165i	$0.954272\pi$
$828$	−12.2631			−0.426172
$829$	34.0390			1.18222			0.591112	−	0.806590i	$-0.298689\pi$
$829$	34.0390			1.18222			0.591112	+	0.806590i	$0.298689\pi$
$830$		0			0
$831$	38.3905	−	66.4943i	1.33175	−	2.30666i
$832$	32.4120	+	56.1393i	1.12368	+	1.94628i
$833$	0.420251	−	0.727896i	0.0145608	−	0.0252201i
$834$	4.13555	−	7.16299i	0.143202	−	0.248034i
$835$		0			0
$836$	−42.5135	−	46.8931i	−1.47036	−	1.62183i
$837$	−1.63355			−0.0564638
$838$	−24.8108	+	42.9735i	−0.857074	+	1.48450i
$839$	−5.20584	+	9.01678i	−0.179725	+	0.311294i	−0.941786	−	0.336212i	$-0.890854\pi$
$839$	−5.20584	+	9.01678i	−0.179725	+	0.311294i	0.762061	+	0.647505i	$0.224188\pi$
$840$		0			0
$841$	8.35041	−	14.4633i	0.287945	−	0.498736i
$842$	−7.90967	−	13.7000i	−0.272585	−	0.472132i
$843$	33.4999			1.15380
$844$	6.53421			0.224917
$845$		0			0
$846$	−11.4980	−	19.9151i	−0.395309	−	0.684696i
$847$	−32.6616			−1.12227
$848$	−0.363334			−0.0124769
$849$	5.13355	+	8.89157i	0.176183	+	0.305158i
$850$		0			0
$851$	6.35197	+	11.0019i	0.217743	+	0.377141i
$852$	65.5712	−	113.573i	2.24643	−	3.89093i
$853$	−6.56527	+	11.3714i	−0.224790	+	0.389349i	−0.956257	−	0.292529i	$-0.905503\pi$
$853$	−6.56527	+	11.3714i	−0.224790	+	0.389349i	0.731466	+	0.681878i	$0.238836\pi$
$854$	−7.00000			−0.239535
$855$		0			0
$856$	−6.06638			−0.207345
$857$	−21.6230	+	37.4521i	−0.738627	+	1.27934i	0.214487	+	0.976727i	$0.431192\pi$
$857$	−21.6230	+	37.4521i	−0.738627	+	1.27934i	−0.953114	+	0.302612i	$0.902141\pi$
$858$	−64.5506	+	111.805i	−2.20372	+	3.81696i
$859$	−15.7344	−	27.2527i	−0.536849	−	0.929850i	−0.999071	−	0.0430861i	$-0.986281\pi$
$859$	−15.7344	−	27.2527i	−0.536849	−	0.929850i	0.462222	−	0.886764i	$-0.347052\pi$
$860$		0			0
$861$	26.7163	+	46.2740i	0.910490	+	1.57701i
$862$	63.9356			2.17766
$863$	23.7842			0.809622			0.404811	−	0.914400i	$-0.367337\pi$
$863$	23.7842			0.809622			0.404811	+	0.914400i	$0.367337\pi$
$864$	−2.04767	−	3.54667i	−0.0696632	−	0.120660i
$865$		0			0
$866$	14.2912			0.485634
$867$	−42.5562			−1.44529
$868$	−12.9101	−	22.3610i	−0.438198	−	0.758981i
$869$	−22.8202	+	39.5258i	−0.774123	+	1.34082i
$870$		0			0
$871$	−21.1094	+	36.5625i	−0.715264	+	1.23887i
$872$	22.0863	−	38.2546i	0.747937	−	1.29547i
$873$	−5.32033			−0.180066
$874$	−11.2801	+	2.43794i	−0.381556	+	0.0824646i
$875$		0			0
$876$	−28.9111	+	50.0756i	−0.976817	+	1.69190i
$877$	−19.0848	+	33.0558i	−0.644447	+	1.11621i	0.339982	+	0.940432i	$0.389579\pi$
$877$	−19.0848	+	33.0558i	−0.644447	+	1.11621i	−0.984429	+	0.175783i	$0.943754\pi$
$878$	35.6455	+	61.7398i	1.20298	+	2.08362i
$879$	15.2585	−	26.4285i	0.514657	−	0.891413i
$880$		0			0
$881$	5.49209			0.185033			0.0925167	−	0.995711i	$-0.470509\pi$
$881$	5.49209			0.185033			0.0925167	+	0.995711i	$0.470509\pi$
$882$	−39.7810			−1.33950
$883$	−17.1491	−	29.7032i	−0.577115	−	0.999592i	−0.995808	−	0.0914644i	$-0.970845\pi$
$883$	−17.1491	−	29.7032i	−0.577115	−	0.999592i	0.418694	−	0.908128i	$-0.362488\pi$
$884$	1.27755	+	2.21279i	0.0429688	+	0.0744241i
$885$		0			0
$886$	−74.7327			−2.51069
$887$	−18.7585	−	32.4907i	−0.629850	−	1.09093i	−0.987582	−	0.157107i	$-0.949783\pi$
$887$	−18.7585	−	32.4907i	−0.629850	−	1.09093i	0.357732	−	0.933824i	$-0.383550\pi$
$888$	38.3768	−	66.4706i	1.28784	−	2.23061i
$889$	−27.5491	−	47.7165i	−0.923968	−	1.60036i
$890$		0			0
$891$	−18.1706	+	31.4725i	−0.608740	+	1.05437i
$892$	61.9628			2.07467
$893$	−8.96837	−	9.89226i	−0.300115	−	0.331032i
$894$	−9.90466			−0.331261
$895$		0			0
$896$	31.8589	−	55.1812i	1.06433	−	1.84347i
$897$	7.26164	+	12.5775i	0.242459	+	0.419952i
$898$	29.2846	−	50.7224i	0.977240	−	1.69263i
$899$	−4.00702	−	6.94036i	−0.133642	−	0.231474i
$900$		0			0
$901$	−0.910886			−0.0303460
$902$	−31.2956	−	54.2056i	−1.04203	−	1.80485i
$903$	14.7199	+	25.4956i	0.489847	+	0.848439i
$904$	27.4701			0.913640
$905$		0			0
$906$	−57.6916	−	99.9248i	−1.91668	−	3.31978i
$907$	−11.1265	+	19.2717i	−0.369450	+	0.639907i	−0.989480	−	0.144672i	$-0.953787\pi$
$907$	−11.1265	+	19.2717i	−0.369450	+	0.639907i	0.620029	+	0.784579i	$0.287121\pi$
$908$	6.44375	+	11.1609i	0.213843	+	0.370388i
$909$	−20.2253	+	35.0313i	−0.670832	+	1.16192i
$910$		0			0
$911$	10.0421			0.332710			0.166355	−	0.986066i	$-0.446800\pi$
$911$	10.0421			0.332710			0.166355	+	0.986066i	$0.446800\pi$
$912$	−0.464364	−	0.512202i	−0.0153766	−	0.0169607i
$913$	21.8835			0.724238
$914$	−37.8930	+	65.6325i	−1.25339	+	2.17093i
$915$		0			0
$916$	20.9081	+	36.2139i	0.690824	+	1.19654i
$917$	−20.2269	+	35.0340i	−0.667951	+	1.15692i
$918$	−0.129549	−	0.224385i	−0.00427574	−	0.00740580i
$919$	6.06104			0.199935			0.0999676	−	0.994991i	$-0.468126\pi$
$919$	6.06104			0.199935			0.0999676	+	0.994991i	$0.468126\pi$
$920$		0			0
$921$	30.7550	+	53.2692i	1.01341	+	1.75528i
$922$	2.48596	+	4.30581i	0.0818708	+	0.141804i
$923$	−81.1796			−2.67206
$924$	127.671			4.20008
$925$		0			0
$926$	7.08477	−	12.2712i	0.232820	−	0.403256i
$927$	17.4382	+	30.2038i	0.572745	+	0.992024i
$928$	10.0457	−	17.3996i	0.329765	−	0.571170i
$929$	25.9382	−	44.9263i	0.851004	−	1.47398i	−0.0292983	−	0.999571i	$-0.509327\pi$
$929$	25.9382	−	44.9263i	0.851004	−	1.47398i	0.880303	−	0.474412i	$-0.157339\pi$
$930$		0			0
$931$	−22.5773	+	4.87957i	−0.739941	+	0.159921i
$932$	−87.2268			−2.85721
$933$	12.7906	−	22.1540i	0.418746	−	0.725289i
$934$	19.6004	−	33.9488i	0.641343	−	1.11084i
$935$		0			0
$936$	22.9316	−	39.7187i	0.749543	−	1.29825i
$937$	12.5999	+	21.8237i	0.411621	+	0.712949i	0.995067	−	0.0992029i	$-0.0316293\pi$
$937$	12.5999	+	21.8237i	0.411621	+	0.712949i	−0.583446	+	0.812152i	$0.698296\pi$
$938$	67.6685			2.20946
$939$	80.1794			2.61655
$940$		0			0
$941$	0.967923	+	1.67649i	0.0315534	+	0.0546521i	0.881371	−	0.472425i	$-0.156621\pi$
$941$	0.967923	+	1.67649i	0.0315534	+	0.0546521i	−0.849817	+	0.527077i	$0.823288\pi$
$942$	21.6445			0.705215
$943$	−7.04122			−0.229294
$944$	0.0969008	+	0.167837i	0.00315385	+	0.00546263i
$945$		0			0
$946$	−17.2429	−	29.8656i	−0.560616	−	0.971016i
$947$	15.6812	−	27.1607i	0.509571	−	0.882603i	−0.490367	−	0.871516i	$-0.663137\pi$
$947$	15.6812	−	27.1607i	0.509571	−	0.882603i	0.999939	−	0.0110875i	$-0.00352932\pi$
$948$	40.8975	−	70.8366i	1.32829	−	2.30067i
$949$	35.7930			1.16189
$950$		0			0
$951$	−5.60548			−0.181770
$952$	0.776567	−	1.34505i	0.0251687	−	0.0435934i
$953$	26.4542	−	45.8201i	0.856937	−	1.48426i	−0.0179001	−	0.999840i	$-0.505698\pi$
$953$	26.4542	−	45.8201i	0.856937	−	1.48426i	0.874837	−	0.484418i	$-0.160969\pi$
$954$	21.5561	+	37.3363i	0.697906	+	1.20881i
$955$		0			0
$956$	−32.3157	−	55.9724i	−1.04516	−	1.81028i
$957$	39.6264			1.28094
$958$	81.7581			2.64148
$959$	−0.191800	−	0.332208i	−0.00619355	−	0.0107275i
$960$		0			0
$961$	−25.7781			−0.831552
$962$	−125.281			−4.03921
$963$	−3.56873	−	6.18122i	−0.115001	−	0.199187i
$964$	34.7710	−	60.2252i	1.11990	−	1.93972i
$965$		0			0
$966$	11.6390	−	20.1594i	0.374479	−	0.648617i
$967$	−30.0140	+	51.9858i	−0.965186	+	1.67175i	−0.256073	+	0.966657i	$0.582429\pi$
$967$	−30.0140	+	51.9858i	−0.965186	+	1.67175i	−0.709113	+	0.705094i	$0.750905\pi$
$968$	−26.0040			−0.835800
$969$	−1.16417	−	1.28410i	−0.0373985	−	0.0412512i
$970$		0			0
$971$	−0.875025	+	1.51559i	−0.0280809	+	0.0486375i	−0.879724	−	0.475484i	$-0.842273\pi$
$971$	−0.875025	+	1.51559i	−0.0280809	+	0.0486375i	0.851643	+	0.524122i	$0.175606\pi$
$972$	36.0195	−	62.3876i	1.15533	−	2.00108i
$973$	2.53163	+	4.38492i	0.0811604	+	0.140574i
$974$	27.0959	−	46.9315i	0.868209	−	1.50378i
$975$		0			0
$976$	0.0552611			0.00176886
$977$	−5.47583			−0.175187			−0.0875937	−	0.996156i	$-0.527918\pi$
$977$	−5.47583			−0.175187			−0.0875937	+	0.996156i	$0.527918\pi$
$978$	4.63009	+	8.01955i	0.148054	+	0.256437i
$979$	−2.50702	−	4.34228i	−0.0801247	−	0.138780i
$980$		0			0
$981$	51.9717			1.65933
$982$	−44.7736	−	77.5501i	−1.42878	−	2.47472i
$983$	2.52963	−	4.38145i	0.0806827	−	0.139747i	−0.822861	−	0.568243i	$-0.807623\pi$
$983$	2.52963	−	4.38145i	0.0806827	−	0.139747i	0.903543	+	0.428497i	$0.140957\pi$
$984$	21.2706	+	36.8417i	0.678081	+	1.17447i
$985$		0			0
$986$	0.635553	−	1.10081i	0.0202401	−	0.0350569i
$987$	26.9327			0.857278
$988$	21.4708	−	66.8561i	0.683078	−	2.12698i
$989$	−3.87950			−0.123361
$990$		0			0
$991$	−0.0492290	+	0.0852672i	−0.00156381	+	0.00270860i	−0.866806	−	0.498645i	$-0.833831\pi$
$991$	−0.0492290	+	0.0852672i	−0.00156381	+	0.00270860i	0.865242	+	0.501354i	$0.167164\pi$
$992$	6.54567	+	11.3374i	0.207825	+	0.359964i
$993$	12.6496	−	21.9097i	0.401423	−	0.695284i
$994$	65.0576	+	112.683i	2.06350	+	3.57409i
$995$		0			0
$996$	−39.2188			−1.24269
$997$	9.17967	+	15.8996i	0.290723	+	0.503547i	0.973981	−	0.226630i	$-0.0727709\pi$
$997$	9.17967	+	15.8996i	0.290723	+	0.503547i	−0.683258	+	0.730177i	$0.739438\pi$
$998$	−10.7133	−	18.5560i	−0.339124	−	0.587379i
$999$	7.83828			0.247992

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.e.d.201.3		6
5.2	odd	4		475.2.j.b.49.5		12
5.3	odd	4		475.2.j.b.49.2		12
5.4	even	2		95.2.e.b.11.1	✓	6
15.14	odd	2		855.2.k.g.676.3		6
19.7	even	3	inner	475.2.e.d.26.3		6
19.8	odd	6		9025.2.a.ba.1.3		3
19.11	even	3		9025.2.a.z.1.1		3
20.19	odd	2		1520.2.q.j.961.1		6
95.7	odd	12		475.2.j.b.349.2		12
95.49	even	6		1805.2.a.h.1.3		3
95.64	even	6		95.2.e.b.26.1	yes	6
95.83	odd	12		475.2.j.b.349.5		12
95.84	odd	6		1805.2.a.g.1.1		3
285.254	odd	6		855.2.k.g.406.3		6
380.159	odd	6		1520.2.q.j.881.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.b.11.1	✓	6	5.4	even	2
95.2.e.b.26.1	yes	6	95.64	even	6
475.2.e.d.26.3		6	19.7	even	3	inner
475.2.e.d.201.3		6	1.1	even	1	trivial
475.2.j.b.49.2		12	5.3	odd	4
475.2.j.b.49.5		12	5.2	odd	4
475.2.j.b.349.2		12	95.7	odd	12
475.2.j.b.349.5		12	95.83	odd	12
855.2.k.g.406.3		6	285.254	odd	6
855.2.k.g.676.3		6	15.14	odd	2
1520.2.q.j.881.1		6	380.159	odd	6
1520.2.q.j.961.1		6	20.19	odd	2
1805.2.a.g.1.1		3	95.84	odd	6
1805.2.a.h.1.3		3	95.49	even	6
9025.2.a.z.1.1		3	19.11	even	3
9025.2.a.ba.1.3		3	19.8	odd	6

Overview	Random
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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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Database

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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	475.2.e.d.201.3

Level	$475$
Weight	$2$
Character	475.201
Analytic conductor	$3.793$
Analytic rank	$0$
Dimension	$6$
Inner twists	$2$