LMFDB - Embedded newform 961.2.g.n.547.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(235,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([26]))

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

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

chi := DirichletCharacter("961.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$961 = 31^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	961.g (of order $15$ , degree $8$ , 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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1$ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			547.1
Root			$-1.83925i$ of defining polynomial
Character	$\chi$	$=$	961.547
Dual form			961.2.g.n.448.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.213065 - 0.655747i) q^{2} +(0.603824 + 0.670615i) q^{3} +(1.23343 - 0.896137i) q^{4} +(-1.85376 - 3.21080i) q^{5} +(0.311099 - 0.538840i) q^{6} +(-0.0797964 - 0.759212i) q^{7} +(-1.96606 - 1.42843i) q^{8} +(0.228465 - 2.17370i) q^{9} +(-1.71050 + 1.89971i) q^{10} +(3.75981 + 1.67397i) q^{11} +(1.34574 + 0.286045i) q^{12} +(-2.84617 + 0.604971i) q^{13} +(-0.480849 + 0.214088i) q^{14} +(1.03387 - 3.18192i) q^{15} +(0.424467 - 1.30637i) q^{16} +(-1.19540 + 0.532225i) q^{17} +(-1.47407 + 0.313324i) q^{18} +(3.71651 + 0.789969i) q^{19} +(-5.16380 - 2.29907i) q^{20} +(0.460956 - 0.511943i) q^{21} +(0.296620 - 2.82215i) q^{22} +(-2.65597 - 1.92967i) q^{23} +(-0.229231 - 2.18099i) q^{24} +(-4.37284 + 7.57398i) q^{25} +(1.00313 + 1.73747i) q^{26} +(3.78584 - 2.75057i) q^{27} +(-0.778781 - 0.864924i) q^{28} +(-1.51283 - 4.65602i) q^{29} -2.30681 q^{30} -5.80746 q^{32} +(1.14767 + 3.53217i) q^{33} +(0.603702 + 0.670478i) q^{34} +(-2.28976 + 1.66361i) q^{35} +(-1.66614 - 2.88584i) q^{36} +(-5.20639 + 9.01773i) q^{37} +(-0.273839 - 2.60541i) q^{38} +(-2.12429 - 1.54338i) q^{39} +(-0.941797 + 8.96060i) q^{40} +(0.505826 - 0.561777i) q^{41} +(-0.433918 - 0.193193i) q^{42} +(-7.00049 - 1.48800i) q^{43} +(6.13756 - 1.30458i) q^{44} +(-7.40284 + 3.29596i) q^{45} +(-0.699483 + 2.15279i) q^{46} +(-0.270719 + 0.833189i) q^{47} +(1.13238 - 0.504167i) q^{48} +(6.27700 - 1.33422i) q^{49} +(5.89831 + 1.25372i) q^{50} +(-1.07873 - 0.480280i) q^{51} +(-2.96840 + 3.29674i) q^{52} +(0.373763 - 3.55612i) q^{53} +(-2.61031 - 1.89650i) q^{54} +(-1.59497 - 15.1751i) q^{55} +(-0.927595 + 1.60664i) q^{56} +(1.71435 + 2.96935i) q^{57} +(-2.73084 + 1.98407i) q^{58} +(0.620465 + 0.689096i) q^{59} +(-1.57623 - 4.85115i) q^{60} -2.31704 q^{61} -1.66853 q^{63} +(0.388433 + 1.19547i) q^{64} +(7.21855 + 8.01701i) q^{65} +(2.07168 - 1.50516i) q^{66} +(1.04345 + 1.80731i) q^{67} +(-0.997488 + 1.72770i) q^{68} +(-0.309670 - 2.94632i) q^{69} +(1.57877 + 1.14704i) q^{70} +(0.808641 - 7.69371i) q^{71} +(-3.55415 + 3.94728i) q^{72} +(5.16836 + 2.30110i) q^{73} +(7.02265 + 1.49271i) q^{74} +(-7.71965 + 1.64086i) q^{75} +(5.29197 - 2.35614i) q^{76} +(0.970882 - 2.98807i) q^{77} +(-0.559458 + 1.72183i) q^{78} +(12.8762 - 5.73284i) q^{79} +(-4.98137 + 1.05882i) q^{80} +(-2.28318 - 0.485304i) q^{81} +(-0.476157 - 0.211999i) q^{82} +(9.43990 - 10.4841i) q^{83} +(0.109784 - 1.04452i) q^{84} +(3.92484 + 2.85157i) q^{85} +(0.515809 + 4.90759i) q^{86} +(2.20891 - 3.82595i) q^{87} +(-5.00086 - 8.66175i) q^{88} +(-3.58784 + 2.60672i) q^{89} +(3.73860 + 4.15213i) q^{90} +(0.686415 + 2.11257i) q^{91} -5.00520 q^{92} +0.604042 q^{94} +(-4.35308 - 13.3974i) q^{95} +(-3.50669 - 3.89457i) q^{96} +(4.26970 - 3.10212i) q^{97} +(-2.21232 - 3.83184i) q^{98} +(4.49770 - 7.79025i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q + 4 q^{2} - 3 q^{3} + 6 q^{4} - 3 q^{5} - 11 q^{6} + 12 q^{7} - 8 q^{8} + 5 q^{9} - 12 q^{10} + 2 q^{11} - 25 q^{12} - 18 q^{13} + 24 q^{14} - 4 q^{15} - 2 q^{16} + q^{17} - 8 q^{18} + 11 q^{19} - 18 q^{20}+ \cdots - 6 q^{99}+O(q^{100})$ 16 * q + 4 * q^2 - 3 * q^3 + 6 * q^4 - 3 * q^5 - 11 * q^6 + 12 * q^7 - 8 * q^8 + 5 * q^9 - 12 * q^10 + 2 * q^11 - 25 * q^12 - 18 * q^13 + 24 * q^14 - 4 * q^15 - 2 * q^16 + q^17 - 8 * q^18 + 11 * q^19 - 18 * q^20 + 31 * q^21 - 4 * q^22 - 21 * q^23 - 20 * q^24 - 13 * q^25 - 9 * q^26 - 9 * q^27 + 20 * q^28 - 26 * q^29 + 22 * q^30 - 42 * q^32 + 7 * q^33 - 28 * q^34 + 21 * q^35 + q^36 + 8 * q^37 + 3 * q^38 + 2 * q^39 + 29 * q^40 - 3 * q^41 - 39 * q^42 - 8 * q^43 + 41 * q^44 - 20 * q^45 + 16 * q^46 + 4 * q^47 - 49 * q^48 + 12 * q^49 + 48 * q^50 - 2 * q^51 + 6 * q^52 + 69 * q^53 - 39 * q^54 - 23 * q^55 - 30 * q^56 + 17 * q^57 - 10 * q^58 + 54 * q^59 - 35 * q^60 + 60 * q^61 - 46 * q^63 - 32 * q^64 + 27 * q^65 + 20 * q^66 + 13 * q^67 - 30 * q^68 - 27 * q^69 + 27 * q^70 + 6 * q^71 + 2 * q^72 + 18 * q^73 + 92 * q^74 - 13 * q^75 - 27 * q^76 + 42 * q^77 + 15 * q^78 + 22 * q^79 + 21 * q^80 - 22 * q^81 - 61 * q^82 + 71 * q^83 + 12 * q^84 + 63 * q^85 + 11 * q^86 + 15 * q^87 + 17 * q^88 - 26 * q^89 - 33 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 + 28 * q^95 - 58 * q^96 - 37 * q^97 - 10 * q^98 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$ .

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{15}\right)$

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

)

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

$2$	−0.213065	−	0.655747i	−0.150660	−	0.463683i	0.847036	−	0.531536i	$-0.178385\pi$
$2$	−0.213065	−	0.655747i	−0.150660	−	0.463683i	−0.997695	+	0.0678533i	$0.978385\pi$
$3$	0.603824	+	0.670615i	0.348618	+	0.387179i	0.891796	−	0.452438i	$-0.149446\pi$
$3$	0.603824	+	0.670615i	0.348618	+	0.387179i	−0.543178	+	0.839618i	$0.682779\pi$
$4$	1.23343	−	0.896137i	0.616714	−	0.448069i
$5$	−1.85376	−	3.21080i	−0.829026	−	1.43591i	−0.898803	−	0.438352i	$-0.855562\pi$
$5$	−1.85376	−	3.21080i	−0.829026	−	1.43591i	0.0697774	−	0.997563i	$-0.477771\pi$
$6$	0.311099	−	0.538840i	0.127006	−	0.219981i
$7$	−0.0797964	−	0.759212i	−0.0301602	−	0.286955i	−0.999198	−	0.0400426i	$-0.987251\pi$
$7$	−0.0797964	−	0.759212i	−0.0301602	−	0.286955i	0.969038	−	0.246913i	$-0.0794160\pi$
$8$	−1.96606	−	1.42843i	−0.695108	−	0.505025i
$9$	0.228465	−	2.17370i	0.0761550	−	0.724566i
$10$	−1.71050	+	1.89971i	−0.540908	+	0.600740i
$11$	3.75981	+	1.67397i	1.13362	+	0.504722i	0.885793	−	0.464081i	$-0.153615\pi$
$11$	3.75981	+	1.67397i	1.13362	+	0.504722i	0.247832	+	0.968803i	$0.420282\pi$
$12$	1.34574	+	0.286045i	0.388480	+	0.0825741i
$13$	−2.84617	+	0.604971i	−0.789384	+	0.167789i	−0.584926	−	0.811086i	$-0.698877\pi$
$13$	−2.84617	+	0.604971i	−0.789384	+	0.167789i	−0.204458	+	0.978875i	$0.565543\pi$
$14$	−0.480849	+	0.214088i	−0.128512	+	0.0572173i
$15$	1.03387	−	3.18192i	0.266943	−	0.821568i
$16$	0.424467	−	1.30637i	0.106117	−	0.326594i
$17$	−1.19540	+	0.532225i	−0.289926	+	0.129083i	−0.546546	−	0.837429i	$-0.684058\pi$
$17$	−1.19540	+	0.532225i	−0.289926	+	0.129083i	0.256620	+	0.966512i	$0.417391\pi$
$18$	−1.47407	+	0.313324i	−0.347443	+	0.0738512i
$19$	3.71651	+	0.789969i	0.852626	+	0.181231i	0.613439	−	0.789742i	$-0.289786\pi$
$19$	3.71651	+	0.789969i	0.852626	+	0.181231i	0.239187	+	0.970973i	$0.423119\pi$
$20$	−5.16380	−	2.29907i	−1.15466	−	0.514088i
$21$	0.460956	−	0.511943i	0.100589	−	0.111715i
$22$	0.296620	−	2.82215i	0.0632395	−	0.601684i
$23$	−2.65597	−	1.92967i	−0.553808	−	0.402365i	0.275380	−	0.961336i	$-0.411196\pi$
$23$	−2.65597	−	1.92967i	−0.553808	−	0.402365i	−0.829187	+	0.558971i	$0.811196\pi$
$24$	−0.229231	−	2.18099i	−0.0467916	−	0.445192i
$25$	−4.37284	+	7.57398i	−0.874568	+	1.51480i
$26$	1.00313	+	1.73747i	0.196729	+	0.340745i
$27$	3.78584	−	2.75057i	0.728585	−	0.529348i
$28$	−0.778781	−	0.864924i	−0.147176	−	0.163455i
$29$	−1.51283	−	4.65602i	−0.280926	−	0.864602i	−0.987590	−	0.157052i	$-0.949801\pi$
$29$	−1.51283	−	4.65602i	−0.280926	−	0.864602i	0.706664	−	0.707549i	$-0.250199\pi$
$30$	−2.30681			−0.421164
$31$		0			0
$31$		0			0
$32$	−5.80746			−1.02662
$33$	1.14767	+	3.53217i	0.199784	+	0.614872i
$34$	0.603702	+	0.670478i	0.103534	+	0.114986i
$35$	−2.28976	+	1.66361i	−0.387040	+	0.281201i
$36$	−1.66614	−	2.88584i	−0.277690	−	0.480973i
$37$	−5.20639	+	9.01773i	−0.855925	+	1.48251i	0.0198583	+	0.999803i	$0.493679\pi$
$37$	−5.20639	+	9.01773i	−0.855925	+	1.48251i	−0.875784	+	0.482704i	$0.839655\pi$
$38$	−0.273839	−	2.60541i	−0.0444226	−	0.422653i
$39$	−2.12429	−	1.54338i	−0.340158	−	0.247139i
$40$	−0.941797	+	8.96060i	−0.148911	+	1.41679i
$41$	0.505826	−	0.561777i	0.0789968	−	0.0877349i	−0.702351	−	0.711831i	$-0.747866\pi$
$41$	0.505826	−	0.561777i	0.0789968	−	0.0877349i	0.781347	+	0.624096i	$0.214533\pi$
$42$	−0.433918	−	0.193193i	−0.0669551	−	0.0298103i
$43$	−7.00049	−	1.48800i	−1.06757	−	0.226918i	−0.359558	−	0.933123i	$-0.617072\pi$
$43$	−7.00049	−	1.48800i	−1.06757	−	0.226918i	−0.708008	+	0.706205i	$0.750406\pi$
$44$	6.13756	−	1.30458i	0.925272	−	0.196673i
$45$	−7.40284	+	3.29596i	−1.10355	+	0.491332i
$46$	−0.699483	+	2.15279i	−0.103133	+	0.317411i
$47$	−0.270719	+	0.833189i	−0.0394885	+	0.121533i	−0.968857	−	0.247619i	$-0.920352\pi$
$47$	−0.270719	+	0.833189i	−0.0394885	+	0.121533i	0.929369	+	0.369152i	$0.120352\pi$
$48$	1.13238	−	0.504167i	0.163445	−	0.0727702i
$49$	6.27700	−	1.33422i	0.896714	−	0.190602i
$50$	5.89831	+	1.25372i	0.834147	+	0.177303i
$51$	−1.07873	−	0.480280i	−0.151052	−	0.0672527i
$52$	−2.96840	+	3.29674i	−0.411643	+	0.457176i
$53$	0.373763	−	3.55612i	0.0513403	−	0.488470i	−0.938396	−	0.345562i	$-0.887688\pi$
$53$	0.373763	−	3.55612i	0.0513403	−	0.488470i	0.989736	−	0.142908i	$-0.0456452\pi$
$54$	−2.61031	−	1.89650i	−0.355218	−	0.258081i
$55$	−1.59497	−	15.1751i	−0.215066	−	2.04622i
$56$	−0.927595	+	1.60664i	−0.123955	+	0.214696i
$57$	1.71435	+	2.96935i	0.227072	+	0.393300i
$58$	−2.73084	+	1.98407i	−0.358577	+	0.260521i
$59$	0.620465	+	0.689096i	0.0807776	+	0.0897126i	0.782179	−	0.623054i	$-0.214108\pi$
$59$	0.620465	+	0.689096i	0.0807776	+	0.0897126i	−0.701401	+	0.712767i	$0.747442\pi$
$60$	−1.57623	−	4.85115i	−0.203491	−	0.626281i
$61$	−2.31704			−0.296666			−0.148333	−	0.988937i	$-0.547391\pi$
$61$	−2.31704			−0.296666			−0.148333	+	0.988937i	$0.547391\pi$
$62$		0			0
$63$	−1.66853			−0.210215
$64$	0.388433	+	1.19547i	0.0485541	+	0.149434i
$65$	7.21855	+	8.01701i	0.895351	+	0.994388i
$66$	2.07168	−	1.50516i	0.255006	−	0.185273i
$67$	1.04345	+	1.80731i	0.127478	+	0.220798i	0.922699	−	0.385522i	$-0.125979\pi$
$67$	1.04345	+	1.80731i	0.127478	+	0.220798i	−0.795221	+	0.606320i	$0.792645\pi$
$68$	−0.997488	+	1.72770i	−0.120963	+	0.209514i
$69$	−0.309670	−	2.94632i	−0.0372799	−	0.354695i
$70$	1.57877	+	1.14704i	0.188699	+	0.137098i
$71$	0.808641	−	7.69371i	0.0959680	−	0.913075i	−0.835559	−	0.549401i	$-0.814856\pi$
$71$	0.808641	−	7.69371i	0.0959680	−	0.913075i	0.931527	−	0.363673i	$-0.118478\pi$
$72$	−3.55415	+	3.94728i	−0.418860	+	0.465192i
$73$	5.16836	+	2.30110i	0.604911	+	0.269324i	0.686254	−	0.727362i	$-0.259254\pi$
$73$	5.16836	+	2.30110i	0.604911	+	0.269324i	−0.0813424	+	0.996686i	$0.525921\pi$
$74$	7.02265	+	1.49271i	0.816366	+	0.173524i
$75$	−7.71965	+	1.64086i	−0.891388	+	0.189470i
$76$	5.29197	−	2.35614i	0.607030	−	0.270267i
$77$	0.970882	−	2.98807i	0.110642	−	0.340522i
$78$	−0.559458	+	1.72183i	−0.0633461	+	0.194959i
$79$	12.8762	−	5.73284i	1.44868	−	0.644995i	0.476490	−	0.879180i	$-0.341909\pi$
$79$	12.8762	−	5.73284i	1.44868	−	0.644995i	0.972192	+	0.234185i	$0.0752423\pi$
$80$	−4.98137	+	1.05882i	−0.556934	+	0.118380i
$81$	−2.28318	−	0.485304i	−0.253686	−	0.0539227i
$82$	−0.476157	−	0.211999i	−0.0525828	−	0.0234114i
$83$	9.43990	−	10.4841i	1.03616	−	1.15078i	0.0477709	−	0.998858i	$-0.484788\pi$
$83$	9.43990	−	10.4841i	1.03616	−	1.15078i	0.988393	−	0.151918i	$-0.0485451\pi$
$84$	0.109784	−	1.04452i	0.0119784	−	0.113967i
$85$	3.92484	+	2.85157i	0.425709	+	0.309296i
$86$	0.515809	+	4.90759i	0.0556211	+	0.529199i
$87$	2.20891	−	3.82595i	0.236820	−	0.410184i
$88$	−5.00086	−	8.66175i	−0.533094	−	0.923346i
$89$	−3.58784	+	2.60672i	−0.380310	+	0.276311i	−0.761473	−	0.648196i	$-0.775524\pi$
$89$	−3.58784	+	2.60672i	−0.380310	+	0.276311i	0.381163	+	0.924508i	$0.375524\pi$
$90$	3.73860	+	4.15213i	0.394083	+	0.437673i
$91$	0.686415	+	2.11257i	0.0719559	+	0.221457i
$92$	−5.00520			−0.521828
$93$		0			0
$94$	0.604042			0.0623021
$95$	−4.35308	−	13.3974i	−0.446617	−	1.37454i
$96$	−3.50669	−	3.89457i	−0.357900	−	0.397488i
$97$	4.26970	−	3.10212i	0.433522	−	0.314972i	−0.349533	−	0.936924i	$-0.613660\pi$
$97$	4.26970	−	3.10212i	0.433522	−	0.314972i	0.783056	+	0.621951i	$0.213660\pi$
$98$	−2.21232	−	3.83184i	−0.223478	−	0.387075i
$99$	4.49770	−	7.79025i	0.452036	−	0.782949i
$100$	1.39375	+	13.2606i	0.139375	+	1.32606i
$101$	−3.08028	−	2.23795i	−0.306499	−	0.222684i	0.423894	−	0.905712i	$-0.360663\pi$
$101$	−3.08028	−	2.23795i	−0.306499	−	0.222684i	−0.730393	+	0.683027i	$0.760663\pi$
$102$	−0.0851031	+	0.809702i	−0.00842646	+	0.0801725i
$103$	−4.17918	+	4.64146i	−0.411787	+	0.457336i	−0.912983	−	0.407998i	$-0.866227\pi$
$103$	−4.17918	+	4.64146i	−0.411787	+	0.457336i	0.501196	+	0.865334i	$0.332894\pi$
$104$	6.45990	+	2.87613i	0.633445	+	0.282028i
$105$	−2.49825	−	0.531019i	−0.243804	−	0.0518222i
$106$	−2.41155	+	0.512590i	−0.234230	+	0.0497872i
$107$	2.12617	−	0.946633i	0.205545	−	0.0915144i	−0.301382	−	0.953503i	$-0.597448\pi$
$107$	2.12617	−	0.946633i	0.205545	−	0.0915144i	0.506927	+	0.861989i	$0.330781\pi$
$108$	2.20467	−	6.78526i	0.212144	−	0.652912i
$109$	0.456365	−	1.40455i	0.0437118	−	0.134531i	−0.926819	−	0.375509i	$-0.877468\pi$
$109$	0.456365	−	1.40455i	0.0437118	−	0.134531i	0.970531	+	0.240978i	$0.0774680\pi$
$110$	−9.61122	+	4.27919i	−0.916394	+	0.408005i
$111$	−9.19117	+	1.95364i	−0.872387	+	0.185432i
$112$	−1.02569	−	0.218016i	−0.0969183	−	0.0206006i
$113$	5.82892	+	2.59520i	0.548339	+	0.244136i	0.662157	−	0.749366i	$-0.269641\pi$
$113$	5.82892	+	2.59520i	0.548339	+	0.244136i	−0.113818	+	0.993502i	$0.536308\pi$
$114$	1.58187	−	1.75685i	0.148156	−	0.164544i
$115$	−1.27228	+	12.1049i	−0.118641	+	1.12879i
$116$	−6.03840	−	4.38716i	−0.560652	−	0.407337i
$117$	0.664776	+	6.32492i	0.0614586	+	0.584739i
$118$	0.319673	−	0.553690i	0.0294283	−	0.0509713i
$119$	0.499460	+	0.865089i	0.0457854	+	0.0793026i
$120$	−6.57779	+	4.77904i	−0.600467	+	0.436265i
$121$	3.97353	+	4.41305i	0.361230	+	0.401187i
$122$	0.493680	+	1.51939i	0.0446957	+	0.137559i
$123$	0.682166			0.0615089
$124$		0			0
$125$	13.8872			1.24211
$126$	0.355505	+	1.09413i	0.0316709	+	0.0974730i
$127$	0.958204	+	1.06419i	0.0850269	+	0.0944319i	0.784157	−	0.620563i	$-0.213096\pi$
$127$	0.958204	+	1.06419i	0.0850269	+	0.0944319i	−0.699130	+	0.714995i	$0.746429\pi$
$128$	−8.69550	+	6.31765i	−0.768581	+	0.558407i
$129$	−3.22919	−	5.59312i	−0.284314	−	0.492447i
$130$	3.71911	−	6.44168i	0.326187	−	0.564973i
$131$	−0.657787	−	6.25843i	−0.0574711	−	0.546801i	−0.984939	−	0.172900i	$-0.944686\pi$
$131$	−0.657787	−	6.25843i	−0.0574711	−	0.546801i	0.927468	−	0.373902i	$-0.121980\pi$
$132$	4.58088	+	3.32820i	0.398714	+	0.289683i
$133$	0.303190	−	2.88466i	0.0262899	−	0.250132i
$134$	0.962812	−	1.06931i	0.0831743	−	0.0923744i
$135$	−15.8496	−	7.05669i	−1.36411	−	0.607343i
$136$	3.11047	+	0.661150i	0.266720	+	0.0566932i
$137$	12.4713	−	2.65085i	1.06549	−	0.226478i	0.358379	−	0.933576i	$-0.383330\pi$
$137$	12.4713	−	2.65085i	1.06549	−	0.226478i	0.707115	+	0.707098i	$0.249996\pi$
$138$	−1.86606	+	0.830822i	−0.158849	+	0.0707242i
$139$	−5.78287	+	17.7978i	−0.490496	+	1.50959i	0.333363	+	0.942798i	$0.391816\pi$
$139$	−5.78287	+	17.7978i	−0.490496	+	1.50959i	−0.823860	+	0.566794i	$0.808184\pi$
$140$	−1.33343	+	4.10387i	−0.112695	+	0.346841i
$141$	−0.722216	+	0.321551i	−0.0608215	+	0.0270795i
$142$	−5.21741	+	1.10900i	−0.437836	+	0.0930648i
$143$	−11.7137	−	2.48983i	−0.979553	−	0.208210i
$144$	−2.74269	−	1.22112i	−0.228558	−	0.101760i
$145$	−12.1451	+	13.4885i	−1.00860	+	1.12016i
$146$	0.407744	−	3.87942i	0.0337451	−	0.321063i
$147$	4.68495	+	3.40381i	0.386408	+	0.280742i
$148$	1.65942	+	15.7884i	0.136404	+	1.29780i
$149$	10.0677	−	17.4377i	0.824774	−	1.42855i	−0.0773172	−	0.997007i	$-0.524635\pi$
$149$	10.0677	−	17.4377i	0.824774	−	1.42855i	0.902092	−	0.431545i	$-0.142031\pi$
$150$	2.72078	+	4.71252i	0.222150	+	0.384776i
$151$	12.4366	−	9.03571i	1.01207	−	0.735315i	0.0474314	−	0.998874i	$-0.484896\pi$
$151$	12.4366	−	9.03571i	1.01207	−	0.735315i	0.964643	+	0.263559i	$0.0848964\pi$
$152$	−6.17848	−	6.86190i	−0.501141	−	0.556573i
$153$	0.883790	+	2.72003i	0.0714502	+	0.219901i
$154$	−2.16628			−0.174564
$155$		0			0
$156$	−4.00324			−0.320515
$157$	4.68076	+	14.4059i	0.373566	+	1.14972i	0.944441	+	0.328680i	$0.106604\pi$
$157$	4.68076	+	14.4059i	0.373566	+	1.14972i	−0.570876	+	0.821037i	$0.693396\pi$
$158$	−6.50275	−	7.22203i	−0.517331	−	0.574554i
$159$	2.61047	−	1.89662i	0.207024	−	0.150412i
$160$	10.7656	+	18.6466i	0.851098	+	1.47414i
$161$	−1.25310	+	2.17042i	−0.0987577	+	0.171053i
$162$	0.168228	+	1.60059i	0.0132173	+	0.125754i
$163$	0.845317	+	0.614159i	0.0662103	+	0.0481046i	0.620398	−	0.784287i	$-0.286971\pi$
$163$	0.845317	+	0.614159i	0.0662103	+	0.0481046i	−0.554188	+	0.832392i	$0.686971\pi$
$164$	0.120471	−	1.14620i	0.00940717	−	0.0895033i
$165$	9.21359	−	10.2327i	0.717277	−	0.796617i
$166$	−8.88621	−	3.95639i	−0.689704	−	0.307076i
$167$	−11.0427	−	2.34720i	−0.854510	−	0.181632i	−0.240226	−	0.970717i	$-0.577222\pi$
$167$	−11.0427	−	2.34720i	−0.854510	−	0.181632i	−0.614284	+	0.789085i	$0.710555\pi$
$168$	−1.63754	+	0.348070i	−0.126339	+	0.0268542i
$169$	−4.14142	+	1.84388i	−0.318571	+	0.141837i
$170$	1.03366	−	3.18127i	0.0792779	−	0.243992i
$171$	2.56625	−	7.89810i	0.196246	−	0.603983i
$172$	−9.96805	+	4.43806i	−0.760057	+	0.338399i
$173$	20.2014	−	4.29393i	1.53588	−	0.326462i	0.639166	−	0.769069i	$-0.279280\pi$
$173$	20.2014	−	4.29393i	1.53588	−	0.326462i	0.896716	+	0.442607i	$0.145946\pi$
$174$	−2.97949	−	0.633311i	−0.225875	−	0.0480112i
$175$	6.09919	+	2.71554i	0.461056	+	0.205275i
$176$	3.78275	−	4.20117i	0.285136	−	0.316675i
$177$	−0.0874662	+	0.832185i	−0.00657436	+	0.0625509i
$178$	2.47379	+	1.79731i	0.185418	+	0.134714i
$179$	−0.0137625	−	0.130941i	−0.00102866	−	0.00978700i	0.993996	−	0.109421i	$-0.0348996\pi$
$179$	−0.0137625	−	0.130941i	−0.00102866	−	0.00978700i	−0.995024	+	0.0996337i	$0.968233\pi$
$180$	−6.17723	+	10.6993i	−0.460424	+	0.797477i
$181$	3.86599	+	6.69610i	0.287357	+	0.497717i	0.973178	−	0.230053i	$-0.0738901\pi$
$181$	3.86599	+	6.69610i	0.287357	+	0.497717i	−0.685821	+	0.727770i	$0.740557\pi$
$182$	1.23906	−	0.900229i	0.0918451	−	0.0667294i
$183$	−1.39908	−	1.55384i	−0.103423	−	0.114863i
$184$	2.46540	+	7.58772i	0.181752	+	0.559374i
$185$	38.6056			2.83834
$186$		0			0
$187$	−5.38539			−0.393819
$188$	0.412739	+	1.27028i	0.0301021	+	0.0926447i
$189$	−2.39036	−	2.65477i	−0.173873	−	0.193106i
$190$	−7.85781	+	5.70903i	−0.570066	+	0.414177i
$191$	10.5513	+	18.2755i	0.763468	+	1.32237i	0.941053	+	0.338260i	$0.109838\pi$
$191$	10.5513	+	18.2755i	0.763468	+	1.32237i	−0.177585	+	0.984106i	$0.556828\pi$
$192$	−0.567157	+	0.982344i	−0.0409310	+	0.0708946i
$193$	−0.591969	−	5.63221i	−0.0426109	−	0.405415i	−0.994950	−	0.100374i	$-0.967996\pi$
$193$	−0.591969	−	5.63221i	−0.0426109	−	0.405415i	0.952339	−	0.305042i	$-0.0986705\pi$
$194$	−2.94393	−	2.13889i	−0.211362	−	0.153563i
$195$	−1.01759	+	9.68173i	−0.0728712	+	0.693323i
$196$	6.54658	−	7.27071i	0.467613	−	0.519337i
$197$	−14.5389	−	6.47313i	−1.03585	−	0.461192i	−0.182874	−	0.983136i	$-0.558540\pi$
$197$	−14.5389	−	6.47313i	−1.03585	−	0.461192i	−0.852979	+	0.521945i	$0.825207\pi$
$198$	−6.06673	−	1.28952i	−0.431144	−	0.0916424i
$199$	−4.16833	+	0.886006i	−0.295485	+	0.0628073i	−0.353269	−	0.935522i	$-0.614930\pi$
$199$	−4.16833	+	0.886006i	−0.295485	+	0.0628073i	0.0577838	+	0.998329i	$0.481597\pi$
$200$	19.4162	−	8.64463i	1.37293	−	0.611267i
$201$	−0.581946	+	1.79105i	−0.0410473	+	0.126331i
$202$	−0.811230	+	2.49671i	−0.0570779	+	0.175668i
$203$	−3.41419	+	1.52009i	−0.239629	+	0.106690i
$204$	−1.76093	+	0.374297i	−0.123290	+	0.0262060i
$205$	−2.74144	−	0.582710i	−0.191470	−	0.0406982i
$206$	3.93406	+	1.75155i	0.274099	+	0.122037i
$207$	−4.80133	+	5.33241i	−0.333715	+	0.370628i
$208$	−0.417784	+	3.97495i	−0.0289681	+	0.275613i
$209$	12.6510	+	9.19148i	0.875087	+	0.635788i
$210$	0.184075	+	1.75136i	0.0127024	+	0.120855i
$211$	5.75414	−	9.96646i	0.396131	−	0.686120i	−0.597113	−	0.802157i	$-0.703686\pi$
$211$	5.75414	−	9.96646i	0.396131	−	0.686120i	0.993245	+	0.116037i	$0.0370191\pi$
$212$	−2.72576	−	4.72115i	−0.187206	−	0.324250i
$213$	5.64779	−	4.10336i	0.386980	−	0.281157i
$214$	−1.07376	−	1.19254i	−0.0734010	−	0.0815201i
$215$	8.19954	+	25.2356i	0.559204	+	1.72105i
$216$	−11.3722			−0.773780
$217$		0			0
$218$	−1.01826			−0.0689654
$219$	1.57763	+	4.85544i	0.106606	+	0.328100i
$220$	−15.5663	−	17.2881i	−1.04948	−	1.16557i
$221$	3.08032	−	2.23798i	0.207204	−	0.150543i
$222$	3.23941	+	5.61082i	0.217415	+	0.376574i
$223$	4.71196	−	8.16135i	0.315536	−	0.546524i	−0.664015	−	0.747719i	$-0.731149\pi$
$223$	4.71196	−	8.16135i	0.315536	−	0.546524i	0.979551	+	0.201195i	$0.0644824\pi$
$224$	0.463414	+	4.40909i	0.0309632	+	0.294595i
$225$	15.4645	+	11.2356i	1.03097	+	0.749042i
$226$	0.459856	−	4.37524i	0.0305892	−	0.291037i
$227$	14.5623	−	16.1731i	0.966534	−	1.07344i	−0.0307302	−	0.999528i	$-0.509783\pi$
$227$	14.5623	−	16.1731i	0.966534	−	1.07344i	0.997264	−	0.0739173i	$-0.0235501\pi$
$228$	4.77548	+	2.12618i	0.316264	+	0.140810i
$229$	16.5854	+	3.52533i	1.09599	+	0.232960i	0.720216	−	0.693750i	$-0.244043\pi$
$229$	16.5854	+	3.52533i	1.09599	+	0.232960i	0.375776	+	0.926710i	$0.377376\pi$
$230$	8.20885	−	1.74485i	0.541276	−	0.115052i
$231$	2.59008	−	1.15318i	0.170415	−	0.0758737i
$232$	−3.67647	+	11.3150i	−0.241372	+	0.742866i
$233$	−3.03952	+	9.35469i	−0.199126	+	0.612846i	0.800778	+	0.598962i	$0.204420\pi$
$233$	−3.03952	+	9.35469i	−0.199126	+	0.612846i	−0.999904	+	0.0138848i	$0.995580\pi$
$234$	4.00591	−	1.78354i	0.261874	−	0.116594i
$235$	3.17705	−	0.675304i	0.207248	−	0.0440520i
$236$	1.38282	+	0.293928i	0.0900141	+	0.0191331i
$237$	11.6195	+	5.17332i	0.754765	+	0.336043i
$238$	0.460862	−	0.511839i	0.0298733	−	0.0331776i
$239$	0.0617382	−	0.587399i	0.00399351	−	0.0379957i	−0.992344	−	0.123507i	$-0.960586\pi$
$239$	0.0617382	−	0.587399i	0.00399351	−	0.0379957i	0.996337	+	0.0855115i	$0.0272524\pi$
$240$	−3.71793	−	2.70124i	−0.239992	−	0.174364i
$241$	1.60665	+	15.2862i	0.103493	+	0.984674i	0.915852	+	0.401516i	$0.131516\pi$
$241$	1.60665	+	15.2862i	0.103493	+	0.984674i	−0.812359	+	0.583158i	$0.801817\pi$
$242$	2.04722	−	3.54590i	0.131601	−	0.227939i
$243$	−8.07252	−	13.9820i	−0.517852	−	0.896946i
$244$	−2.85790	+	2.07639i	−0.182958	+	0.132927i
$245$	−15.9199	−	17.6809i	−1.01709	−	1.12959i
$246$	−0.145346	−	0.447328i	−0.00926690	−	0.0285206i
$247$	−11.0557			−0.703459
$248$		0			0
$249$	12.7308			0.806783
$250$	−2.95887	−	9.10646i	−0.187135	−	0.575943i
$251$	4.04925	+	4.49714i	0.255586	+	0.283857i	0.857259	−	0.514885i	$-0.172166\pi$
$251$	4.04925	+	4.49714i	0.255586	+	0.283857i	−0.601673	+	0.798743i	$0.705499\pi$
$252$	−2.05801	+	1.49523i	−0.129642	+	0.0941907i
$253$	−6.75571	−	11.7012i	−0.424728	−	0.735650i
$254$	0.493682	−	0.855082i	0.0309763	−	0.0536526i
$255$	0.457614	+	4.35390i	0.0286569	+	0.272652i
$256$	8.02935	+	5.83366i	0.501834	+	0.364604i
$257$	0.473288	−	4.50304i	0.0295229	−	0.280892i	−0.969794	−	0.243927i	$-0.921564\pi$
$257$	0.473288	−	4.50304i	0.0295229	−	0.280892i	0.999317	−	0.0369649i	$-0.0117690\pi$
$258$	−2.97964	+	3.30923i	−0.185505	+	0.206024i
$259$	7.26182	+	3.23317i	0.451228	+	0.200900i
$260$	16.0879	+	3.41959i	0.997729	+	0.212074i
$261$	−10.4664	+	2.22471i	−0.647855	+	0.137706i
$262$	−3.96379	+	1.76479i	−0.244884	+	0.109029i
$263$	0.775281	−	2.38607i	0.0478059	−	0.147131i	−0.924304	−	0.381657i	$-0.875354\pi$
$263$	0.775281	−	2.38607i	0.0478059	−	0.147131i	0.972110	+	0.234525i	$0.0753536\pi$
$264$	2.78905	−	8.58383i	0.171654	−	0.528298i
$265$	−12.1109	+	5.39210i	−0.743964	+	0.331234i
$266$	−1.95620	+	0.415804i	−0.119943	+	0.0254946i
$267$	−3.91453	−	0.832058i	−0.239565	−	0.0509211i
$268$	2.90661	+	1.29411i	0.177550	+	0.0790502i
$269$	−8.92605	+	9.91338i	−0.544231	+	0.604430i	−0.951034	−	0.309086i	$-0.899977\pi$
$269$	−8.92605	+	9.91338i	−0.544231	+	0.604430i	0.406803	+	0.913516i	$0.366643\pi$
$270$	−1.25041	+	11.8968i	−0.0760974	+	0.724019i
$271$	11.1840	+	8.12564i	0.679379	+	0.493598i	0.873152	−	0.487449i	$-0.162072\pi$
$271$	11.1840	+	8.12564i	0.679379	+	0.493598i	−0.193773	+	0.981046i	$0.562072\pi$
$272$	0.187879	+	1.78755i	0.0113918	+	0.108386i
$273$	−1.00225	+	1.73594i	−0.0606586	+	0.105064i
$274$	−4.39548	−	7.61320i	−0.265541	−	0.459930i
$275$	−29.1197	+	21.1567i	−1.75598	+	1.27580i
$276$	−3.02226	−	3.35656i	−0.181919	−	0.202041i
$277$	−3.57556	−	11.0044i	−0.214834	−	0.661192i	−0.999165	−	0.0408496i	$-0.986994\pi$
$277$	−3.57556	−	11.0044i	−0.214834	−	0.661192i	0.784331	−	0.620343i	$-0.213006\pi$
$278$	12.9030			0.773870
$279$		0			0
$280$	6.87814			0.411048
$281$	−4.75866	−	14.6457i	−0.283878	−	0.873686i	−0.986733	−	0.162353i	$-0.948092\pi$
$281$	−4.75866	−	14.6457i	−0.283878	−	0.873686i	0.702855	−	0.711333i	$-0.251908\pi$
$282$	0.364735	+	0.405079i	0.0217196	+	0.0241221i
$283$	18.3612	−	13.3402i	1.09146	−	0.792993i	0.111816	−	0.993729i	$-0.464333\pi$
$283$	18.3612	−	13.3402i	1.09146	−	0.792993i	0.979645	+	0.200736i	$0.0643333\pi$
$284$	−5.89722	−	10.2143i	−0.349935	−	0.606106i
$285$	6.35600	−	11.0089i	0.376497	−	0.652112i
$286$	0.863089	+	8.21174i	0.0510355	+	0.485571i
$287$	−0.466871	−	0.339202i	−0.0275585	−	0.0200224i
$288$	−1.32680	+	12.6237i	−0.0781825	+	0.743857i
$289$	−10.2295	+	11.3610i	−0.601736	+	0.668295i
$290$	11.4328	+	5.09020i	0.671356	+	0.298907i
$291$	4.65847	+	0.990189i	0.273085	+	0.0580459i
$292$	8.43690	−	1.79332i	0.493732	−	0.104946i
$293$	11.3288	−	5.04388i	0.661833	−	0.294667i	−0.0481978	−	0.998838i	$-0.515348\pi$
$293$	11.3288	−	5.04388i	0.661833	−	0.294667i	0.710030	+	0.704171i	$0.248681\pi$
$294$	1.23384	−	3.79737i	0.0719591	−	0.221467i
$295$	1.06236	−	3.26961i	0.0618530	−	0.190364i
$296$	23.1173	−	10.2925i	1.34366	−	0.598238i
$297$	18.8384	−	4.00423i	1.09312	−	0.232349i
$298$	−13.5798	−	2.88647i	−0.786655	−	0.167209i
$299$	8.72673	+	3.88539i	0.504680	+	0.224698i
$300$	−8.05118	+	8.94174i	−0.464835	+	0.516252i
$301$	−0.571094	+	5.43360i	−0.0329173	+	0.313187i
$302$	−8.57493	−	6.23005i	−0.493432	−	0.358499i
$303$	−0.359142	−	3.41701i	−0.0206322	−	0.196302i
$304$	2.60953	−	4.51984i	0.149667	−	0.259231i
$305$	4.29523	+	7.43956i	0.245944	+	0.425988i
$306$	1.59534	−	1.15908i	0.0911997	−	0.0662605i
$307$	20.5557	+	22.8294i	1.17317	+	1.30294i	0.944148	+	0.329523i	$0.106888\pi$
$307$	20.5557	+	22.8294i	1.17317	+	1.30294i	0.229027	+	0.973420i	$0.426446\pi$
$308$	−1.48021	−	4.55561i	−0.0843426	−	0.259580i
$309$	−5.63612			−0.320628
$310$		0			0
$311$	2.38141			0.135037			0.0675187	−	0.997718i	$-0.478492\pi$
$311$	2.38141			0.135037			0.0675187	+	0.997718i	$0.478492\pi$
$312$	1.97187	+	6.06878i	0.111635	+	0.343577i
$313$	−7.19020	−	7.98553i	−0.406414	−	0.451369i	0.504840	−	0.863213i	$-0.331551\pi$
$313$	−7.19020	−	7.98553i	−0.406414	−	0.451369i	−0.911254	+	0.411844i	$0.864885\pi$
$314$	8.44932	−	6.13879i	0.476823	−	0.346432i
$315$	3.09305	+	5.35732i	0.174274	+	0.301851i
$316$	10.7444	−	18.6098i	0.604420	−	1.04689i
$317$	−0.914242	−	8.69844i	−0.0513490	−	0.488553i	−0.989730	−	0.142950i	$-0.954341\pi$
$317$	−0.914242	−	8.69844i	−0.0513490	−	0.488553i	0.938381	−	0.345603i	$-0.112326\pi$
$318$	−1.79990	−	1.30770i	−0.100933	−	0.0733324i
$319$	2.10610	−	20.0382i	0.117919	−	1.12192i
$320$	3.11837	−	3.46330i	0.174322	−	0.193604i
$321$	1.91866	+	0.854242i	0.107089	+	0.0476791i
$322$	1.69024	+	0.359271i	0.0941933	+	0.0200214i
$323$	−4.86315	+	1.03369i	−0.270593	+	0.0575162i
$324$	−3.25103	+	1.44745i	−0.180613	+	0.0804140i
$325$	7.86379	−	24.2022i	0.436204	−	1.34250i
$326$	0.222625	−	0.685170i	0.0123301	−	0.0379480i
$327$	1.21747	−	0.542054i	0.0673264	−	0.0299756i
$328$	−1.79694	+	0.381952i	−0.0992196	+	0.0210898i
$329$	0.654169	+	0.139048i	0.0360655	+	0.00766596i
$330$	−8.67317	−	3.86155i	−0.477442	−	0.212571i
$331$	21.6592	−	24.0549i	1.19049	−	1.32218i	0.255799	−	0.966730i	$-0.417661\pi$
$331$	21.6592	−	24.0549i	1.19049	−	1.32218i	0.934696	−	0.355449i	$-0.115672\pi$
$332$	2.24826	−	21.3908i	0.123389	−	1.17397i
$333$	18.4124	+	13.3774i	1.00899	+	0.733075i
$334$	0.813646	+	7.74132i	0.0445207	+	0.423586i
$335$	3.86860	−	6.70062i	0.211364	−	0.366094i
$336$	−0.473129	−	0.819484i	−0.0258113	−	0.0447065i
$337$	22.4371	−	16.3015i	1.22223	−	0.888000i	0.225944	−	0.974140i	$-0.427453\pi$
$337$	22.4371	−	16.3015i	1.22223	−	0.888000i	0.996283	+	0.0861400i	$0.0274532\pi$
$338$	2.09151	+	2.32286i	0.113763	+	0.126347i
$339$	1.77926	+	5.47600i	0.0966362	+	0.297416i
$340$	7.39640			0.401126
$341$		0			0
$342$	−5.72593			−0.309623
$343$	−3.16515	−	9.74132i	−0.170902	−	0.525982i
$344$	11.6379	+	12.9252i	0.627474	+	0.696880i
$345$	−8.88598	+	6.45605i	−0.478405	+	0.347582i
$346$	−7.11994	−	12.3321i	−0.382770	−	0.662977i
$347$	−12.9580	+	22.4440i	−0.695624	+	1.20486i	0.274347	+	0.961631i	$0.411538\pi$
$347$	−12.9580	+	22.4440i	−0.695624	+	1.20486i	−0.969970	+	0.243224i	$0.921795\pi$
$348$	−0.704042	−	6.69851i	−0.0377406	−	0.359078i
$349$	−4.52559	−	3.28803i	−0.242249	−	0.176004i	0.460036	−	0.887900i	$-0.347837\pi$
$349$	−4.52559	−	3.28803i	−0.242249	−	0.176004i	−0.702285	+	0.711896i	$0.747837\pi$
$350$	0.481179	−	4.57811i	0.0257201	−	0.244710i
$351$	−9.11111	+	10.1189i	−0.486315	+	0.540108i
$352$	−21.8349	−	9.72154i	−1.16381	−	0.518160i
$353$	11.4140	+	2.42612i	0.607505	+	0.129129i	0.501385	−	0.865224i	$-0.332824\pi$
$353$	11.4140	+	2.42612i	0.607505	+	0.129129i	0.106120	+	0.994353i	$0.466157\pi$
$354$	0.564339	−	0.119954i	0.0299943	−	0.00637548i
$355$	−26.2020	+	11.6659i	−1.39066	+	0.619161i
$356$	−2.08936	+	6.43039i	−0.110736	+	0.340810i
$357$	−0.278556	+	0.857307i	−0.0147427	+	0.0453735i
$358$	−0.0829319	+	0.0369237i	−0.00438309	+	0.00195148i
$359$	−25.6273	+	5.44725i	−1.35256	+	0.287495i	−0.826492	−	0.562949i	$-0.809667\pi$
$359$	−25.6273	+	5.44725i	−1.35256	+	0.287495i	−0.526066	+	0.850444i	$0.676334\pi$
$360$	19.2625	+	4.09437i	1.01522	+	0.215792i
$361$	−4.16895	−	1.85614i	−0.219418	−	0.0976913i
$362$	3.56723	−	3.96182i	0.187490	−	0.208228i
$363$	−0.560144	+	5.32942i	−0.0293999	+	0.279722i
$364$	2.73979	+	1.99058i	0.143604	+	0.104335i
$365$	−2.19250	−	20.8603i	−0.114761	−	1.09188i
$366$	−0.720830	+	1.24851i	−0.0376784	+	0.0652608i
$367$	13.5073	+	23.3953i	0.705076	+	1.22123i	0.966664	+	0.256047i	$0.0824203\pi$
$367$	13.5073	+	23.3953i	0.705076	+	1.22123i	−0.261589	+	0.965179i	$0.584246\pi$
$368$	−3.64825	+	2.65061i	−0.190178	+	0.138173i
$369$	−1.10557	−	1.22786i	−0.0575537	−	0.0639199i
$370$	−8.22549	−	25.3155i	−0.427623	−	1.31609i
$371$	−2.72967			−0.141717
$372$		0			0
$373$	−12.4058			−0.642351			−0.321175	−	0.947020i	$-0.604078\pi$
$373$	−12.4058			−0.642351			−0.321175	+	0.947020i	$0.604078\pi$
$374$	1.14744	+	3.53145i	0.0593326	+	0.182607i
$375$	8.38540	+	9.31293i	0.433020	+	0.480918i
$376$	1.72240	−	1.25140i	0.0888261	−	0.0645359i
$377$	7.12253	+	12.3366i	0.366829	+	0.635367i
$378$	−1.23155	+	2.13311i	−0.0633442	+	0.109715i
$379$	0.484909	+	4.61360i	0.0249081	+	0.236985i	0.999892	+	0.0147084i	$0.00468201\pi$
$379$	0.484909	+	4.61360i	0.0249081	+	0.236985i	−0.974984	+	0.222276i	$0.928651\pi$
$380$	−17.3751	−	12.6238i	−0.891325	−	0.647585i
$381$	−0.135077	+	1.28517i	−0.00692020	+	0.0658413i
$382$	9.73595	−	10.8129i	0.498134	−	0.553234i
$383$	4.58722	+	2.04236i	0.234396	+	0.104360i	0.520574	−	0.853817i	$-0.325718\pi$
$383$	4.58722	+	2.04236i	0.234396	+	0.104360i	−0.286178	+	0.958177i	$0.592385\pi$
$384$	−9.48727	−	2.01658i	−0.484145	−	0.102908i
$385$	−11.3939	+	2.42184i	−0.580686	+	0.123429i
$386$	−3.56718	+	1.58821i	−0.181564	+	0.0808377i
$387$	−4.83383	+	14.8770i	−0.245718	+	0.756241i
$388$	2.48644	−	7.65247i	0.126230	−	0.388496i
$389$	−16.9936	+	7.56605i	−0.861611	+	0.383614i	−0.789476	−	0.613781i	$-0.789648\pi$
$389$	−16.9936	+	7.56605i	−0.861611	+	0.383614i	−0.0721346	+	0.997395i	$0.522981\pi$
$390$	6.56557	−	1.39556i	0.332461	−	0.0706667i
$391$	4.20196	+	0.893153i	0.212502	+	0.0451687i
$392$	−14.2468	−	6.34308i	−0.719572	−	0.320374i
$393$	3.79980	−	4.22011i	0.191675	−	0.212876i
$394$	−1.14701	+	10.9130i	−0.0577853	+	0.549790i
$395$	−42.2763	−	30.7155i	−2.12715	−	1.54547i
$396$	−1.43354	−	13.6393i	−0.0720383	−	0.685399i
$397$	−16.2794	+	28.1968i	−0.817040	+	1.41515i	0.0908142	+	0.995868i	$0.471053\pi$
$397$	−16.2794	+	28.1968i	−0.817040	+	1.41515i	−0.907854	+	0.419287i	$0.862280\pi$
$398$	1.46912	+	2.54459i	0.0736404	+	0.127549i
$399$	2.11757	−	1.53850i	0.106011	−	0.0770214i
$400$	8.03833	+	8.92747i	0.401917	+	0.446374i
$401$	3.82880	+	11.7838i	0.191201	+	0.588457i	1.00000		0.000371451i	$0.000118236\pi$
$401$	3.82880	+	11.7838i	0.191201	+	0.588457i	−0.808799	+	0.588086i	$0.799882\pi$
$402$	1.29847			0.0647616
$403$		0			0
$404$	−5.80481			−0.288800
$405$	2.67424	+	8.23046i	0.132884	+	0.408975i
$406$	1.72424	+	1.91496i	0.0855726	+	0.0950381i
$407$	−34.6705	+	25.1896i	−1.71855	+	1.24860i
$408$	1.43480	+	2.48514i	0.0710331	+	0.123033i
$409$	−1.72404	+	2.98613i	−0.0852484	+	0.147654i	−0.905497	−	0.424353i	$-0.860502\pi$
$409$	−1.72404	+	2.98613i	−0.0852484	+	0.147654i	0.820249	+	0.572007i	$0.193835\pi$
$410$	0.201994	+	1.92184i	0.00997576	+	0.0949130i
$411$	9.30817	+	6.76278i	0.459138	+	0.333583i
$412$	−0.995339	+	9.47002i	−0.0490368	+	0.466554i
$413$	0.473659	−	0.526052i	0.0233072	−	0.0258853i
$414$	4.51971	+	2.01230i	0.222131	+	0.0988993i
$415$	−51.1616	−	10.8747i	−2.51142	−	0.533820i
$416$	16.5290	−	3.51335i	0.810401	−	0.172256i
$417$	−15.4273	+	6.86868i	−0.755479	+	0.336361i
$418$	3.33180	−	10.2542i	0.162964	−	0.501550i
$419$	−12.3752	+	38.0871i	−0.604570	+	1.86068i	−0.104854	+	0.994488i	$0.533437\pi$
$419$	−12.3752	+	38.0871i	−0.604570	+	1.86068i	−0.499717	+	0.866189i	$0.666563\pi$
$420$	−3.55727	+	1.58380i	−0.173577	+	0.0772815i
$421$	−21.2106	+	4.50844i	−1.03374	+	0.219728i	−0.693384	−	0.720569i	$-0.743881\pi$
$421$	−21.2106	+	4.50844i	−1.03374	+	0.219728i	−0.340356	+	0.940297i	$0.610548\pi$
$422$	−7.76148	−	1.64975i	−0.377823	−	0.0803088i
$423$	1.74925	+	0.778817i	0.0850516	+	0.0378674i
$424$	−5.81449	+	6.45765i	−0.282377	+	0.313611i
$425$	1.19622	−	11.3812i	0.0580250	−	0.552071i
$426$	−3.89411	−	2.82924i	−0.188670	−	0.137077i
$427$	0.184891	+	1.75912i	0.00894752	+	0.0851300i
$428$	1.77417	−	3.07294i	0.0857575	−	0.148536i
$429$	−5.40332	−	9.35883i	−0.260875	−	0.451849i
$430$	14.8011	−	10.7536i	0.713774	−	0.518587i
$431$	−7.77574	−	8.63584i	−0.374544	−	0.415974i	0.526174	−	0.850377i	$-0.323626\pi$
$431$	−7.77574	−	8.63584i	−0.374544	−	0.415974i	−0.900719	+	0.434403i	$0.856959\pi$
$432$	−1.98632	−	6.11325i	−0.0955667	−	0.294124i
$433$	−24.5964			−1.18203			−0.591015	−	0.806661i	$-0.701272\pi$
$433$	−24.5964			−1.18203			−0.591015	+	0.806661i	$0.701272\pi$
$434$		0			0
$435$	−16.3791			−0.785320
$436$	−0.695773	−	2.14137i	−0.0333215	−	0.102553i
$437$	−8.34656	−	9.26979i	−0.399270	−	0.443434i
$438$	2.84780	−	2.06905i	0.136073	−	0.0988630i
$439$	−9.09662	−	15.7558i	−0.434158	−	0.751984i	0.563068	−	0.826410i	$-0.309621\pi$
$439$	−9.09662	−	15.7558i	−0.434158	−	0.751984i	−0.997227	+	0.0744265i	$0.976287\pi$
$440$	−18.5408	+	32.1136i	−0.883897	+	1.53096i
$441$	−1.46611	−	13.9491i	−0.0698149	−	0.664244i
$442$	−2.12386	−	1.54307i	−0.101021	−	0.0733964i
$443$	−1.85646	+	17.6630i	−0.0882031	+	0.839196i	0.857570	+	0.514368i	$0.171973\pi$
$443$	−1.85646	+	17.6630i	−0.0882031	+	0.839196i	−0.945773	+	0.324829i	$0.894693\pi$
$444$	−9.58590	+	10.6462i	−0.454927	+	0.505247i
$445$	15.0206	+	6.68762i	0.712047	+	0.317024i
$446$	−6.35573	−	1.35095i	−0.300952	−	0.0639694i
$447$	17.7731	−	3.77778i	0.840637	−	0.178683i
$448$	0.876622	−	0.390297i	0.0414165	−	0.0184398i
$449$	2.84252	−	8.74836i	0.134147	−	0.412861i	−0.861310	−	0.508080i	$-0.830355\pi$
$449$	2.84252	−	8.74836i	0.134147	−	0.412861i	0.995456	+	0.0952196i	$0.0303553\pi$
$450$	4.07278	−	12.5347i	0.191993	−	0.590892i
$451$	2.84221	−	1.26543i	0.133835	−	0.0595870i
$452$	9.51520	−	2.02252i	0.447558	−	0.0951313i
$453$	13.5690	+	2.88418i	0.637526	+	0.135510i
$454$	−13.7082	−	6.10327i	−0.643356	−	0.286440i
$455$	5.51059	−	6.12014i	0.258341	−	0.286916i
$456$	0.870973	−	8.28676i	0.0407871	−	0.388063i
$457$	−25.2412	−	18.3388i	−1.18074	−	0.857855i	−0.188481	−	0.982077i	$-0.560356\pi$
$457$	−25.2412	−	18.3388i	−1.18074	−	0.857855i	−0.992254	+	0.124222i	$0.960356\pi$
$458$	−1.22204	−	11.6269i	−0.0571021	−	0.543290i
$459$	−3.06166	+	5.30294i	−0.142906	+	0.247520i
$460$	9.27842	+	16.0707i	0.432609	+	0.749300i
$461$	−5.39491	+	3.91963i	−0.251266	+	0.182555i	−0.706288	−	0.707925i	$-0.749631\pi$
$461$	−5.39491	+	3.91963i	−0.251266	+	0.182555i	0.455022	+	0.890480i	$0.349631\pi$
$462$	−1.30805	−	1.45274i	−0.0608560	−	0.0675874i
$463$	−10.9140	−	33.5899i	−0.507217	−	1.56105i	−0.797011	−	0.603964i	$-0.793587\pi$
$463$	−10.9140	−	33.5899i	−0.507217	−	1.56105i	0.289795	−	0.957089i	$-0.406413\pi$
$464$	−6.72466			−0.312184
$465$		0			0
$466$	6.78192			0.314167
$467$	11.1071	+	34.1842i	0.513977	+	1.58186i	0.785136	+	0.619324i	$0.212593\pi$
$467$	11.1071	+	34.1842i	0.513977	+	1.58186i	−0.271159	+	0.962535i	$0.587407\pi$
$468$	6.48795	+	7.20560i	0.299906	+	0.333079i
$469$	1.28886	−	0.936415i	0.0595143	−	0.0432396i
$470$	−1.11975	−	1.93946i	−0.0516501	−	0.0894606i
$471$	−6.83446	+	11.8376i	−0.314915	+	0.545449i
$472$	−0.235548	−	2.24109i	−0.0108420	−	0.103155i
$473$	−23.8296	−	17.3132i	−1.09569	−	0.796064i
$474$	0.916685	−	8.72168i	0.0421047	−	0.400600i
$475$	−22.2349	+	24.6944i	−1.02021	+	1.13306i
$476$	1.39129	+	0.619440i	0.0637695	+	0.0283920i
$477$	−7.64454	−	1.62490i	−0.350019	−	0.0743989i
$478$	−0.398339	+	0.0846697i	−0.0182196	+	0.00387270i
$479$	30.3703	−	13.5217i	1.38765	−	0.617823i	0.429236	−	0.903192i	$-0.358783\pi$
$479$	30.3703	−	13.5217i	1.38765	−	0.617823i	0.958418	+	0.285369i	$0.0921163\pi$
$480$	−6.00415	+	18.4789i	−0.274051	+	0.843441i
$481$	9.36278	−	28.8157i	0.426906	−	1.31388i
$482$	9.68158	−	4.31052i	0.440984	−	0.196339i
$483$	−2.21217	+	0.470211i	−0.100657	+	0.0213953i
$484$	8.85576	+	1.88235i	0.402535	+	0.0855614i
$485$	−17.8753	−	7.95859i	−0.811675	−	0.361381i
$486$	−7.44868	+	8.27260i	−0.337879	+	0.375253i
$487$	2.98067	−	28.3591i	0.135067	−	1.28508i	−0.691557	−	0.722321i	$-0.743075\pi$
$487$	2.98067	−	28.3591i	0.135067	−	1.28508i	0.826624	−	0.562754i	$-0.190258\pi$
$488$	4.55544	+	3.30972i	0.206215	+	0.149824i
$489$	0.0985590	+	0.937726i	0.00445699	+	0.0424054i
$490$	−8.20220	+	14.2066i	−0.370538	+	0.641790i
$491$	−13.9818	−	24.2172i	−0.630991	−	1.09291i	−0.987350	−	0.158559i	$-0.949315\pi$
$491$	−13.9818	−	24.2172i	−0.630991	−	1.09291i	0.356359	−	0.934349i	$-0.384018\pi$
$492$	0.841402	−	0.611315i	0.0379333	−	0.0275602i
$493$	4.28648	+	4.76062i	0.193054	+	0.214408i
$494$	2.35559	+	7.24975i	0.105983	+	0.326182i
$495$	−33.3506			−1.49900
$496$		0			0
$497$	−5.90568			−0.264906
$498$	−2.71249	−	8.34819i	−0.121550	−	0.374091i
$499$	27.6384	+	30.6956i	1.23727	+	1.37412i	0.901848	+	0.432053i	$0.142211\pi$
$499$	27.6384	+	30.6956i	1.23727	+	1.37412i	0.335417	+	0.942070i	$0.391123\pi$
$500$	17.1288	−	12.4448i	0.766023	−	0.556548i
$501$	−5.09378	−	8.82269i	−0.227573	−	0.394169i
$502$	2.08623	−	3.61346i	0.0931132	−	0.161277i
$503$	2.67447	+	25.4459i	0.119249	+	1.13458i	0.876483	+	0.481432i	$0.159883\pi$
$503$	2.67447	+	25.4459i	0.119249	+	1.13458i	−0.757235	+	0.653143i	$0.773450\pi$
$504$	3.28043	+	2.38337i	0.146122	+	0.106164i
$505$	−1.47554	+	14.0388i	−0.0656604	+	0.624717i
$506$	−6.23364	+	6.92315i	−0.277119	+	0.307772i
$507$	−3.73722	−	1.66392i	−0.165976	−	0.0738972i
$508$	2.13554	+	0.453923i	0.0947492	+	0.0201396i
$509$	−23.9331	+	5.08714i	−1.06082	+	0.225483i	−0.705098	−	0.709110i	$-0.749097\pi$
$509$	−23.9331	+	5.08714i	−1.06082	+	0.225483i	−0.355718	+	0.934593i	$0.615764\pi$
$510$	2.75755	−	1.22774i	0.122107	−	0.0543654i
$511$	1.33461	−	4.10750i	0.0590396	−	0.181705i
$512$	−4.52814	+	13.9362i	−0.200118	+	0.615898i
$513$	16.2430	−	7.23185i	0.717146	−	0.319294i
$514$	−3.05369	+	0.649082i	−0.134693	+	0.0286298i
$515$	22.6500	+	4.81441i	0.998078	+	0.212148i
$516$	−8.99518	−	4.00491i	−0.395991	−	0.176306i
$517$	−2.41259	+	2.67945i	−0.106106	+	0.117842i
$518$	0.572901	−	5.45079i	0.0251718	−	0.239494i
$519$	15.0776	+	10.9546i	0.661835	+	0.480851i
$520$	−2.74039	−	26.0731i	−0.120174	−	1.14338i
$521$	−7.48279	+	12.9606i	−0.327827	+	0.567813i	−0.982080	−	0.188462i	$-0.939650\pi$
$521$	−7.48279	+	12.9606i	−0.327827	+	0.567813i	0.654253	+	0.756275i	$0.272983\pi$
$522$	3.68887	+	6.38931i	0.161458	+	0.279653i
$523$	−16.9615	+	12.3233i	−0.741677	+	0.538860i	−0.893236	−	0.449589i	$-0.851571\pi$
$523$	−16.9615	+	12.3233i	−0.741677	+	0.538860i	0.151559	+	0.988448i	$0.451571\pi$
$524$	−6.41974	−	7.12985i	−0.280448	−	0.311469i
$525$	1.86176	+	5.72991i	0.0812539	+	0.250074i
$526$	−1.72984			−0.0754247
$527$		0			0
$528$	5.10148			0.222014
$529$	−3.77686	−	11.6240i	−0.164211	−	0.505391i
$530$	6.11625	+	6.79278i	0.265673	+	0.295060i
$531$	1.63964	−	1.19127i	0.0711544	−	0.0516967i
$532$	−2.21109	−	3.82971i	−0.0958628	−	0.166039i
$533$	−1.09981	+	1.90492i	−0.0476379	+	0.0825113i
$534$	0.288429	+	2.74422i	0.0124815	+	0.118754i
$535$	−6.98086	−	5.07189i	−0.301809	−	0.219277i
$536$	0.530121	−	5.04377i	0.0228977	−	0.217858i
$537$	0.0795009	−	0.0882947i	0.00343072	−	0.00381020i
$538$	8.40250	+	3.74103i	0.362257	+	0.161287i
$539$	25.8338	+	5.49113i	1.11274	+	0.236520i
$540$	−25.8731	+	5.49949i	−1.11340	+	0.236660i
$541$	1.58162	−	0.704184i	0.0679993	−	0.0302752i	−0.372455	−	0.928050i	$-0.621484\pi$
$541$	1.58162	−	0.704184i	0.0679993	−	0.0302752i	0.440454	+	0.897775i	$0.354817\pi$
$542$	2.94545	−	9.06515i	0.126518	−	0.389382i
$543$	−2.15612	+	6.63586i	−0.0925280	+	0.284772i
$544$	6.94222	−	3.09087i	0.297645	−	0.132520i
$545$	−5.35571	+	1.13839i	−0.229413	+	0.0487633i
$546$	1.35188	+	0.287351i	0.0578551	+	0.0122975i
$547$	−11.9870	−	5.33697i	−0.512528	−	0.228192i	0.134142	−	0.990962i	$-0.457172\pi$
$547$	−11.9870	−	5.33697i	−0.512528	−	0.228192i	−0.646670	+	0.762770i	$0.723839\pi$
$548$	13.0069	−	14.4456i	0.555627	−	0.617086i
$549$	−0.529362	+	5.03655i	−0.0225926	+	0.214955i
$550$	20.0778	+	14.5874i	0.856121	+	0.622008i
$551$	−1.94435	−	18.4993i	−0.0828321	−	0.788095i
$552$	−3.59977	+	6.23498i	−0.153216	+	0.265378i
$553$	−5.37991	−	9.31828i	−0.228777	−	0.396254i
$554$	−6.45429	+	4.68932i	−0.274217	+	0.199230i
$555$	23.3110	+	25.8895i	0.989495	+	1.09895i
$556$	8.81656	+	27.1346i	0.373905	+	1.15076i
$557$	28.0246			1.18744			0.593721	−	0.804671i	$-0.297658\pi$
$557$	28.0246			1.18744			0.593721	+	0.804671i	$0.297658\pi$
$558$		0			0
$559$	20.8248			0.880794
$560$	1.20137	+	3.69743i	0.0507670	+	0.156245i
$561$	−3.25183	−	3.61152i	−0.137292	−	0.152479i
$562$	−8.58993	+	6.24095i	−0.362344	+	0.263259i
$563$	−11.3259	−	19.6171i	−0.477331	−	0.826762i	0.522331	−	0.852743i	$-0.325062\pi$
$563$	−11.3259	−	19.6171i	−0.477331	−	0.826762i	−0.999662	+	0.0259808i	$0.991729\pi$
$564$	−0.602646	+	1.04381i	−0.0253760	+	0.0439525i
$565$	−2.47272	−	23.5264i	−0.104028	−	0.989763i
$566$	−12.6599	−	9.19798i	−0.532136	−	0.386620i
$567$	−0.186259	+	1.77214i	−0.00782216	+	0.0744229i
$568$	−12.5797	+	13.9712i	−0.527834	+	0.586219i
$569$	42.4269	+	18.8897i	1.77863	+	0.791896i	0.982372	+	0.186936i	$0.0598558\pi$
$569$	42.4269	+	18.8897i	1.77863	+	0.791896i	0.796256	+	0.604960i	$0.206811\pi$
$570$	−8.57330	−	1.82231i	−0.359096	−	0.0763282i
$571$	−12.2252	+	2.59855i	−0.511610	+	0.108746i	−0.456481	−	0.889733i	$-0.650890\pi$
$571$	−12.2252	+	2.59855i	−0.511610	+	0.108746i	−0.0551292	+	0.998479i	$0.517557\pi$
$572$	−16.6793	+	7.42610i	−0.697396	+	0.310501i
$573$	−5.88463	+	18.1110i	−0.245834	+	0.756600i
$574$	−0.122956	+	0.378421i	−0.00513210	+	0.0157950i
$575$	26.2294	−	11.6781i	1.09384	−	0.487010i
$576$	2.68734	−	0.571212i	0.111973	−	0.0238005i
$577$	29.8181	+	6.33804i	1.24135	+	0.263856i	0.781366	−	0.624073i	$-0.214523\pi$
$577$	29.8181	+	6.33804i	1.24135	+	0.263856i	0.459980	+	0.887929i	$0.347857\pi$
$578$	9.62950	+	4.28733i	0.400535	+	0.178329i
$579$	3.41960	−	3.79785i	0.142114	−	0.157833i
$580$	−2.89256	+	27.5209i	−0.120107	+	1.14274i
$581$	−8.71290	−	6.33030i	−0.361472	−	0.262625i
$582$	−0.343244	−	3.26575i	−0.0142279	−	0.135370i
$583$	7.35812	−	12.7446i	0.304742	−	0.527829i
$584$	−6.87436	−	11.9067i	−0.284463	−	0.492705i
$585$	19.0758	−	13.8593i	0.788685	−	0.573013i
$586$	−5.72127	−	6.35411i	−0.236343	−	0.262486i
$587$	−10.4009	−	32.0107i	−0.429292	−	1.32123i	−0.898824	−	0.438310i	$-0.855577\pi$
$587$	−10.4009	−	32.0107i	−0.429292	−	1.32123i	0.469532	−	0.882915i	$-0.344423\pi$
$588$	8.82883			0.364095
$589$		0			0
$590$	−2.37039			−0.0975872
$591$	−4.43796	−	13.6586i	−0.182553	−	0.561841i
$592$	9.57060	+	10.6292i	0.393349	+	0.436859i
$593$	36.3151	−	26.3844i	1.49128	−	1.08348i	0.517585	−	0.855632i	$-0.326831\pi$
$593$	36.3151	−	26.3844i	1.49128	−	1.08348i	0.973697	−	0.227847i	$-0.0731687\pi$
$594$	−6.63957	−	11.5001i	−0.272425	−	0.471854i
$595$	1.85175	−	3.20733i	0.0759145	−	0.131488i
$596$	−3.20884	−	30.5301i	−0.131439	−	1.25056i
$597$	−3.11111	−	2.26035i	−0.127329	−	0.0925100i
$598$	0.688471	−	6.55036i	0.0281537	−	0.267864i
$599$	−13.1047	+	14.5542i	−0.535442	+	0.594669i	−0.948791	−	0.315904i	$-0.897692\pi$
$599$	−13.1047	+	14.5542i	−0.535442	+	0.594669i	0.413349	+	0.910573i	$0.364359\pi$
$600$	17.5212	+	7.80092i	0.715298	+	0.318471i
$601$	29.7938	+	6.33288i	1.21532	+	0.258323i	0.770583	−	0.637340i	$-0.219965\pi$
$601$	29.7938	+	6.33288i	1.21532	+	0.258323i	0.444733	+	0.895663i	$0.353298\pi$
$602$	3.68474	−	0.783216i	0.150179	−	0.0319215i
$603$	4.16693	−	1.85524i	0.169691	−	0.0755511i
$604$	7.24238	−	22.2898i	0.294688	−	0.906958i
$605$	6.80348	−	20.9390i	0.276601	−	0.851290i
$606$	−2.16417	+	0.963550i	−0.0879134	+	0.0391416i
$607$	13.0823	−	2.78073i	0.530994	−	0.112866i	0.0653907	−	0.997860i	$-0.479171\pi$
$607$	13.0823	−	2.78073i	0.530994	−	0.112866i	0.465604	+	0.884993i	$0.345837\pi$
$608$	−21.5835	−	4.58772i	−0.875327	−	0.186056i
$609$	−3.08097	−	1.37173i	−0.124847	−	0.0555855i
$610$	3.96330	−	4.40169i	0.160469	−	0.178219i
$611$	0.266457	−	2.53517i	0.0107797	−	0.102562i
$612$	3.52761	+	2.56296i	0.142595	+	0.103601i
$613$	−0.543047	−	5.16675i	−0.0219335	−	0.208683i	−1.00000		0.000389879i	$-0.999876\pi$
$613$	−0.543047	−	5.16675i	−0.0219335	−	0.208683i	0.978066	−	0.208293i	$-0.0667908\pi$
$614$	10.5906	−	18.3435i	0.427402	−	0.740282i
$615$	−1.26457	−	2.19030i	−0.0509924	−	0.0883215i
$616$	−6.17705	+	4.48789i	−0.248881	+	0.180822i
$617$	−20.0827	−	22.3041i	−0.808498	−	0.897927i	0.187947	−	0.982179i	$-0.439817\pi$
$617$	−20.0827	−	22.3041i	−0.808498	−	0.897927i	−0.996445	+	0.0842517i	$0.973150\pi$
$618$	1.20086	+	3.69587i	0.0483057	+	0.148670i
$619$	−18.3260			−0.736584			−0.368292	−	0.929710i	$-0.620057\pi$
$619$	−18.3260			−0.736584			−0.368292	+	0.929710i	$0.620057\pi$
$620$		0			0
$621$	−15.3628			−0.616487
$622$	−0.507396	−	1.56160i	−0.0203447	−	0.0626146i
$623$	2.26535	+	2.51592i	0.0907592	+	0.100798i
$624$	−2.91793	+	2.12000i	−0.116811	+	0.0848679i
$625$	−3.87924	−	6.71905i	−0.155170	−	0.268762i
$626$	−3.70450	+	6.41639i	−0.148062	+	0.256450i
$627$	1.47503	+	14.0340i	0.0589070	+	0.560463i
$628$	18.6831	+	13.5740i	0.745535	+	0.541663i
$629$	1.42424	−	13.5507i	0.0567882	−	0.540303i
$630$	2.85402	−	3.16971i	0.113707	−	0.126284i
$631$	−9.44169	−	4.20371i	−0.375868	−	0.167347i	0.210103	−	0.977679i	$-0.432620\pi$
$631$	−9.44169	−	4.20371i	−0.375868	−	0.167347i	−0.585971	+	0.810332i	$0.699287\pi$
$632$	−33.5043	−	7.12155i	−1.33273	−	0.283280i
$633$	10.1581	−	2.15918i	0.403750	−	0.0858197i
$634$	−5.50918	+	2.45284i	−0.218797	+	0.0974148i
$635$	1.64064	−	5.04936i	0.0651067	−	0.200378i
$636$	1.52020	−	4.67868i	0.0602797	−	0.185522i
$637$	−17.0582	+	7.59481i	−0.675871	+	0.300917i
$638$	−13.5887	+	2.88837i	−0.537982	+	0.114352i
$639$	−16.5391	−	3.51548i	−0.654275	−	0.139070i
$640$	36.4041	+	16.2082i	1.43900	+	0.640683i
$641$	−0.0677508	+	0.0752449i	−0.00267599	+	0.00297199i	−0.744481	−	0.667643i	$-0.767303\pi$
$641$	−0.0677508	+	0.0752449i	−0.00267599	+	0.00297199i	0.741805	+	0.670615i	$0.233970\pi$
$642$	0.151367	−	1.44016i	0.00597399	−	0.0568387i
$643$	−11.0931	−	8.05961i	−0.437469	−	0.317840i	0.347159	−	0.937806i	$-0.387146\pi$
$643$	−11.0931	−	8.05961i	−0.437469	−	0.317840i	−0.784629	+	0.619966i	$0.787146\pi$
$644$	0.399397	+	3.80001i	0.0157384	+	0.149741i
$645$	−11.9723	+	20.7366i	−0.471408	+	0.816503i
$646$	1.71401	+	2.96875i	0.0674367	+	0.116804i
$647$	−8.76519	+	6.36828i	−0.344595	+	0.250363i	−0.746598	−	0.665275i	$-0.768314\pi$
$647$	−8.76519	+	6.36828i	−0.344595	+	0.250363i	0.402003	+	0.915638i	$0.368314\pi$
$648$	3.79564	+	4.21549i	0.149107	+	0.165600i
$649$	1.17930	+	3.62951i	0.0462916	+	0.142471i
$650$	−17.5460			−0.688212
$651$		0			0
$652$	1.59301			0.0623870
$653$	−7.49434	−	23.0652i	−0.293276	−	0.902611i	−0.983795	−	0.179297i	$-0.942618\pi$
$653$	−7.49434	−	23.0652i	−0.293276	−	0.902611i	0.690519	−	0.723314i	$-0.257382\pi$
$654$	−0.614851	−	0.682861i	−0.0240426	−	0.0267020i
$655$	−18.8752	+	13.7136i	−0.737515	+	0.535836i
$656$	−0.519185	−	0.899255i	−0.0202708	−	0.0351100i
$657$	6.18270	−	10.7087i	0.241210	−	0.417788i
$658$	−0.0482003	−	0.458596i	−0.00187904	−	0.0178779i
$659$	6.90374	+	5.01586i	0.268932	+	0.195390i	0.714075	−	0.700069i	$-0.246847\pi$
$659$	6.90374	+	5.01586i	0.268932	+	0.195390i	−0.445144	+	0.895459i	$0.646847\pi$
$660$	2.19436	−	20.8780i	0.0854155	−	0.812674i
$661$	25.3495	−	28.1535i	0.985981	−	1.09504i	−0.00948838	−	0.999955i	$-0.503020\pi$
$661$	25.3495	−	28.1535i	0.985981	−	1.09504i	0.995469	−	0.0950874i	$-0.0303130\pi$
$662$	−20.3887	−	9.07765i	−0.792431	−	0.352813i
$663$	3.36079	+	0.714358i	0.130522	+	0.0277434i
$664$	−33.5352	+	7.12812i	−1.30142	+	0.276625i
$665$	−9.82411	+	4.37397i	−0.380963	+	0.169615i
$666$	4.84913	−	14.9241i	0.187900	−	0.578297i
$667$	−4.96657	+	15.2855i	−0.192306	+	0.591858i
$668$	−15.7238	+	7.00068i	−0.608371	+	0.270864i
$669$	8.31831	−	1.76811i	0.321604	−	0.0683591i
$670$	−5.21817	−	1.10916i	−0.201596	−	0.0428504i
$671$	−8.71162	−	3.87867i	−0.336309	−	0.149734i
$672$	−2.67698	+	2.97309i	−0.103267	+	0.114689i
$673$	0.744254	−	7.08110i	0.0286889	−	0.272956i	−0.970769	−	0.240018i	$-0.922847\pi$
$673$	0.744254	−	7.08110i	0.0286889	−	0.272956i	0.999457	−	0.0329387i	$-0.0104866\pi$
$674$	−15.4702	−	11.2398i	−0.595891	−	0.432940i
$675$	4.27792	+	40.7017i	0.164657	+	1.56661i
$676$	−3.45577	+	5.98557i	−0.132914	+	0.230214i
$677$	24.0305	+	41.6220i	0.923567	+	1.59966i	0.793850	+	0.608113i	$0.208073\pi$
$677$	24.0305	+	41.6220i	0.923567	+	1.59966i	0.129716	+	0.991551i	$0.458593\pi$
$678$	3.21177	−	2.33349i	0.123347	−	0.0896171i
$679$	−2.69587	−	2.99407i	−0.103458	−	0.114902i
$680$	−3.64323	−	11.2127i	−0.139712	−	0.429988i
$681$	19.6390			0.752567
$682$		0			0
$683$	32.5731			1.24638			0.623188	−	0.782072i	$-0.285837\pi$
$683$	32.5731			1.24638			0.623188	+	0.782072i	$0.285837\pi$
$684$	−3.91250	−	12.0414i	−0.149598	−	0.460416i
$685$	−31.6301	−	35.1288i	−1.20852	−	1.34220i
$686$	−5.71346	+	4.15107i	−0.218141	+	0.158489i
$687$	7.65051	+	13.2511i	0.291885	+	0.505560i
$688$	−4.91537	+	8.51366i	−0.187397	+	0.324580i
$689$	1.08756	+	10.3474i	0.0414326	+	0.394205i
$690$	6.12682	+	4.45140i	0.233244	+	0.169462i
$691$	−2.84872	+	27.1038i	−0.108371	+	1.03108i	0.796282	+	0.604926i	$0.206797\pi$
$691$	−2.84872	+	27.1038i	−0.108371	+	1.03108i	−0.904652	+	0.426151i	$0.859869\pi$
$692$	21.0690	−	23.3995i	0.800922	−	0.889514i
$693$	−6.27335	−	2.79308i	−0.238305	−	0.106100i
$694$	17.4785	+	3.71516i	0.663473	+	0.141026i
$695$	67.8654	−	14.4252i	2.57428	−	0.547180i
$696$	−9.80794	+	4.36678i	−0.371769	+	0.165522i
$697$	−0.305671	+	0.940760i	−0.0115781	+	0.0356338i
$698$	−1.19187	+	3.66820i	−0.0451130	+	0.138844i
$699$	−8.10873	+	3.61024i	−0.306700	+	0.136552i
$700$	9.95640	−	2.11630i	0.376317	−	0.0799886i
$701$	−8.30364	−	1.76499i	−0.313624	−	0.0666629i	0.0484104	−	0.998828i	$-0.484584\pi$
$701$	−8.30364	−	1.76499i	−0.313624	−	0.0666629i	−0.362035	+	0.932165i	$0.617918\pi$
$702$	8.57670	+	3.81859i	0.323707	+	0.144124i
$703$	−26.4734	+	29.4016i	−0.998461	+	1.10890i
$704$	−0.540759	+	5.14498i	−0.0203806	+	0.193909i
$705$	2.37125	+	1.72281i	0.0893065	+	0.0648849i
$706$	−0.841002	−	8.00160i	−0.0316515	−	0.301144i
$707$	−1.45328	+	2.51716i	−0.0546564	+	0.0946676i
$708$	0.637869	+	1.10482i	0.0239726	+	0.0415217i
$709$	−18.9198	+	13.7460i	−0.710546	+	0.516242i	−0.883350	−	0.468714i	$-0.844717\pi$
$709$	−18.9198	+	13.7460i	−0.710546	+	0.516242i	0.172804	+	0.984956i	$0.444717\pi$
$710$	13.2326	+	14.6963i	0.496610	+	0.551542i
$711$	−9.51971	−	29.2987i	−0.357017	−	1.09879i
$712$	10.7774			0.403901
$713$		0			0
$714$	0.621526			0.0232600
$715$	13.7201	+	42.2261i	0.513102	+	1.57917i
$716$	−0.134316	−	0.149173i	−0.00501963	−	0.00557487i
$717$	0.431198	−	0.313283i	0.0161034	−	0.0116998i
$718$	9.03230	+	15.6444i	0.337083	+	0.583844i
$719$	6.48843	−	11.2383i	0.241978	−	0.419118i	−0.719300	−	0.694700i	$-0.755537\pi$
$719$	6.48843	−	11.2383i	0.241978	−	0.419118i	0.961278	+	0.275582i	$0.0888706\pi$
$720$	1.16349	+	11.0699i	0.0433609	+	0.412551i
$721$	3.85733	+	2.80252i	0.143655	+	0.104371i
$722$	−0.328898	+	3.12925i	−0.0122403	+	0.116459i
$723$	−9.28104	+	10.3076i	−0.345166	+	0.383345i
$724$	10.7690	+	4.79469i	0.400228	+	0.178193i
$725$	41.8800	+	8.90187i	1.55538	+	0.330607i
$726$	3.61409	−	0.768199i	0.134132	−	0.0285106i
$727$	−11.3490	+	5.05290i	−0.420911	+	0.187402i	−0.606252	−	0.795273i	$-0.707328\pi$
$727$	−11.3490	+	5.05290i	−0.420911	+	0.187402i	0.185341	+	0.982674i	$0.440661\pi$
$728$	1.66812	−	5.13393i	0.0618245	−	0.190276i
$729$	2.33825	−	7.19640i	0.0866020	−	0.266533i
$730$	−13.2119	+	5.88232i	−0.488995	+	0.217715i
$731$	9.16031	−	1.94708i	0.338806	−	0.0720155i
$732$	−3.11812	−	0.662777i	−0.115249	−	0.0244970i
$733$	−31.2043	−	13.8930i	−1.15256	−	0.513151i	−0.260678	−	0.965426i	$-0.583946\pi$
$733$	−31.2043	−	13.8930i	−1.15256	−	0.513151i	−0.891879	+	0.452275i	$0.850613\pi$
$734$	12.4635	−	13.8421i	0.460035	−	0.510921i
$735$	2.24422	−	21.3523i	0.0827792	−	0.787591i
$736$	15.4244	+	11.2065i	0.568552	+	0.413077i
$737$	0.897783	+	8.54183i	0.0330702	+	0.314642i
$738$	−0.569607	+	0.986589i	−0.0209675	+	0.0363168i
$739$	−6.18747	−	10.7170i	−0.227610	−	0.394231i	0.729490	−	0.683992i	$-0.239758\pi$
$739$	−6.18747	−	10.7170i	−0.227610	−	0.394231i	−0.957099	+	0.289761i	$0.906424\pi$
$740$	47.6171	−	34.5959i	1.75044	−	1.27177i
$741$	−6.67571	−	7.41413i	−0.245238	−	0.272365i
$742$	0.581597	+	1.78997i	0.0213511	+	0.0657119i
$743$	16.2455			0.595990			0.297995	−	0.954567i	$-0.403682\pi$
$743$	16.2455			0.595990			0.297995	+	0.954567i	$0.403682\pi$
$744$		0			0
$745$	−74.6520			−2.73504
$746$	2.64325	+	8.13509i	0.0967763	+	0.297847i
$747$	−20.6325	−	22.9148i	−0.754905	−	0.838407i
$748$	−6.64249	+	4.82605i	−0.242873	+	0.176458i
$749$	−0.888356	−	1.53868i	−0.0324598	−	0.0562220i
$750$	4.32029	−	7.48296i	0.157755	−	0.273239i
$751$	1.12768	+	10.7292i	0.0411497	+	0.391513i	0.995641	+	0.0932730i	$0.0297329\pi$
$751$	1.12768	+	10.7292i	0.0411497	+	0.391513i	−0.954491	+	0.298240i	$0.903600\pi$
$752$	0.973546	+	0.707322i	0.0355016	+	0.0257934i
$753$	−0.570817	+	5.43097i	−0.0208017	+	0.197915i
$754$	6.57211	−	7.29907i	0.239342	−	0.265817i
$755$	−52.0663	−	23.1814i	−1.89489	−	0.843658i
$756$	−5.32738	−	1.13237i	−0.193755	−	0.0411839i
$757$	40.2035	−	8.54552i	1.46122	−	0.310592i	0.592370	−	0.805666i	$-0.298192\pi$
$757$	40.2035	−	8.54552i	1.46122	−	0.310592i	0.868851	+	0.495074i	$0.164859\pi$
$758$	2.92203	−	1.30097i	0.106133	−	0.0472535i
$759$	3.76776	−	11.5960i	0.136761	−	0.420907i
$760$	−10.5788	+	32.5582i	−0.383733	+	1.18101i
$761$	−17.9608	+	7.99665i	−0.651078	+	0.289878i	−0.705575	−	0.708636i	$-0.749311\pi$
$761$	−17.9608	+	7.99665i	−0.651078	+	0.289878i	0.0544972	+	0.998514i	$0.482644\pi$
$762$	0.871527	−	0.185249i	0.0315721	−	0.00671086i
$763$	−1.10276	−	0.234400i	−0.0399227	−	0.00848584i
$764$	29.3916	+	13.0860i	1.06335	+	0.473435i
$765$	7.09514	−	7.87995i	0.256525	−	0.284900i
$766$	0.361896	−	3.44321i	0.0130758	−	0.124408i
$767$	−2.18283	−	1.58592i	−0.0788174	−	0.0572642i
$768$	0.936174	+	8.90710i	0.0337813	+	0.321407i
$769$	−1.89417	+	3.28080i	−0.0683055	+	0.118309i	−0.898155	−	0.439678i	$-0.855093\pi$
$769$	−1.89417	+	3.28080i	−0.0683055	+	0.118309i	0.829850	+	0.557986i	$0.188426\pi$
$770$	4.01575	+	6.95549i	0.144718	+	0.250658i
$771$	3.30558	−	2.40165i	0.119048	−	0.0864932i
$772$	−5.77739	−	6.41644i	−0.207933	−	0.230933i
$773$	7.83963	+	24.1279i	0.281972	+	0.867820i	0.987290	+	0.158929i	$0.0508041\pi$
$773$	7.83963	+	24.1279i	0.281972	+	0.867820i	−0.705318	+	0.708891i	$0.749196\pi$
$774$	10.7855			0.387676
$775$		0			0
$776$	−12.8256			−0.460414
$777$	2.21665	+	6.82215i	0.0795219	+	0.244743i
$778$	8.58216	+	9.53145i	0.307685	+	0.341719i
$779$	2.32370	−	1.68826i	0.0832551	−	0.0604884i
$780$	7.42103	+	12.8536i	0.265716	+	0.460233i
$781$	15.9194	−	27.5732i	0.569641	−	0.986647i
$782$	−0.309607	−	2.94572i	−0.0110715	−	0.105339i
$783$	−18.5341	−	13.4658i	−0.662354	−	0.481228i
$784$	0.921390	−	8.76644i	0.0329068	−	0.313087i
$785$	37.5775	−	41.7341i	1.34120	−	1.48955i
$786$	−3.57693	−	1.59255i	−0.127585	−	0.0568044i
$787$	−25.3796	−	5.39460i	−0.904685	−	0.192297i	−0.267998	−	0.963419i	$-0.586362\pi$
$787$	−25.3796	−	5.39460i	−0.904685	−	0.192297i	−0.636687	+	0.771123i	$0.719695\pi$
$788$	−23.7335	+	5.04471i	−0.845470	+	0.179710i
$789$	2.06827	−	0.920852i	0.0736323	−	0.0327832i
$790$	−11.1340	+	34.2670i	−0.396130	+	1.21916i
$791$	1.50518	−	4.63247i	0.0535181	−	0.164712i
$792$	−19.9706	+	8.89147i	−0.709623	+	0.315945i
$793$	6.59468	−	1.40174i	0.234184	−	0.0497773i
$794$	21.9585	+	4.66742i	0.779278	+	0.165641i
$795$	−10.9288	−	4.86584i	−0.387606	−	0.172573i
$796$	−4.34735	+	4.82822i	−0.154088	+	0.171132i
$797$	−1.93405	+	18.4013i	−0.0685076	+	0.651806i	0.905353	+	0.424660i	$0.139606\pi$
$797$	−1.93405	+	18.4013i	−0.0685076	+	0.651806i	−0.973861	+	0.227146i	$0.927060\pi$
$798$	−1.46005	−	1.06079i	−0.0516851	−	0.0375514i
$799$	−0.119827	−	1.14007i	−0.00423916	−	0.0403329i
$800$	25.3951	−	43.9856i	0.897852	−	1.55513i
$801$	4.84652	+	8.39442i	0.171243	+	0.296602i
$802$	6.91143	−	5.02145i	0.244051	−	0.177314i
$803$	15.5801	+	17.3034i	0.549809	+	0.610624i
$804$	0.887235	+	2.73063i	0.0312904	+	0.0963019i
$805$	9.29174			0.327491
$806$		0			0
$807$	−12.0378			−0.423751
$808$	2.85926	+	8.79990i	0.100588	+	0.309579i
$809$	−24.5891	−	27.3090i	−0.864507	−	0.960132i	0.135022	−	0.990843i	$-0.456890\pi$
$809$	−24.5891	−	27.3090i	−0.864507	−	0.960132i	−0.999528	+	0.0307106i	$0.990223\pi$
$810$	4.82731	−	3.50725i	0.169614	−	0.123232i
$811$	19.7151	+	34.1475i	0.692289	+	1.19908i	0.971086	+	0.238730i	$0.0767310\pi$
$811$	19.7151	+	34.1475i	0.692289	+	1.19908i	−0.278797	+	0.960350i	$0.589936\pi$
$812$	−2.84894	+	4.93451i	−0.0999782	+	0.173167i
$813$	1.30399	+	12.4066i	0.0457328	+	0.435119i
$814$	23.9051	+	17.3680i	0.837872	+	0.608749i
$815$	0.404930	−	3.85265i	0.0141841	−	0.134952i
$816$	−1.08531	+	1.20536i	−0.0379934	+	0.0421960i
$817$	−24.8420	−	11.0603i	−0.869110	−	0.386953i
$818$	2.32548	+	0.494295i	0.0813083	+	0.0172826i
$819$	4.74891	−	1.00941i	0.165940	−	0.0352717i
$820$	−3.90355	+	1.73797i	−0.136318	+	0.0606926i
$821$	−0.457525	+	1.40812i	−0.0159677	+	0.0491436i	−0.958723	−	0.284342i	$-0.908225\pi$
$821$	−0.457525	+	1.40812i	−0.0159677	+	0.0491436i	0.942755	+	0.333486i	$0.108225\pi$
$822$	2.45142	−	7.54471i	0.0855032	−	0.263152i
$823$	35.5051	−	15.8079i	1.23763	−	0.551029i	0.319606	−	0.947551i	$-0.396449\pi$
$823$	35.5051	−	15.8079i	1.23763	−	0.551029i	0.918025	+	0.396521i	$0.129783\pi$
$824$	14.8465	−	3.15572i	0.517203	−	0.109935i
$825$	−31.7711	−	6.75317i	−1.10613	−	0.235115i
$826$	−0.445877	−	0.198517i	−0.0155140	−	0.00690729i
$827$	−22.7078	+	25.2196i	−0.789628	+	0.876971i	−0.994810	−	0.101753i	$-0.967555\pi$
$827$	−22.7078	+	25.2196i	−0.789628	+	0.876971i	0.205182	+	0.978724i	$0.434221\pi$
$828$	−1.14351	+	10.8798i	−0.0397398	+	0.378099i
$829$	13.3736	+	9.71650i	0.464485	+	0.337468i	0.795288	−	0.606232i	$-0.207320\pi$
$829$	13.3736	+	9.71650i	0.464485	+	0.337468i	−0.330803	+	0.943700i	$0.607320\pi$
$830$	3.76968	+	35.8661i	0.130847	+	1.24493i
$831$	5.22073	−	9.04256i	0.181105	−	0.313683i
$832$	−1.82877	−	3.16752i	−0.0634012	−	0.109814i
$833$	−6.79340	+	4.93569i	−0.235377	+	0.171012i
$834$	7.79114	+	8.65293i	0.269785	+	0.299627i
$835$	12.9341	+	39.8071i	0.447603	+	1.37758i
$836$	23.8409			0.824555
$837$		0			0
$838$	27.6122			0.953848
$839$	−16.7110	−	51.4313i	−0.576929	−	1.77561i	−0.629514	−	0.776989i	$-0.716746\pi$
$839$	−16.7110	−	51.4313i	−0.576929	−	1.77561i	0.0525843	−	0.998616i	$-0.483254\pi$
$840$	4.15319	+	4.61258i	0.143299	+	0.159149i
$841$	4.07162	−	2.95820i	0.140401	−	0.102007i
$842$	7.47562	+	12.9482i	0.257627	+	0.446223i
$843$	6.94819	−	12.0346i	0.239308	−	0.414494i
$844$	−1.83401	−	17.4494i	−0.0631291	−	0.600633i
$845$	13.5975	+	9.87918i	0.467769	+	0.339854i
$846$	0.138002	−	1.31300i	0.00474462	−	0.0451420i
$847$	3.03337	−	3.36890i	0.104228	−	0.115757i
$848$	−4.48697	−	1.99773i	−0.154083	−	0.0686023i
$849$	20.0331	+	4.25816i	0.687534	+	0.146140i
$850$	−7.71808	+	1.64053i	−0.264728	+	0.0562697i
$851$	31.2293	−	13.9042i	1.07053	−	0.476629i
$852$	3.28896	−	10.1224i	0.112678	−	0.346787i
$853$	12.2297	−	37.6392i	0.418738	−	1.28874i	−0.490127	−	0.871651i	$-0.663050\pi$
$853$	12.2297	−	37.6392i	0.418738	−	1.28874i	0.908865	−	0.417091i	$-0.136950\pi$
$854$	1.11415	−	0.496050i	0.0381253	−	0.0169745i
$855$	−30.1165	+	6.40145i	−1.02996	+	0.218925i
$856$	−5.53238	−	1.17594i	−0.189093	−	0.0401929i
$857$	11.6249	+	5.17574i	0.397099	+	0.176800i	0.595564	−	0.803308i	$-0.296929\pi$
$857$	11.6249	+	5.17574i	0.397099	+	0.176800i	−0.198464	+	0.980108i	$0.563595\pi$
$858$	−4.98576	+	5.53725i	−0.170211	+	0.189039i
$859$	−2.21123	+	21.0385i	−0.0754462	+	0.717823i	0.889777	+	0.456396i	$0.150860\pi$
$859$	−2.21123	+	21.0385i	−0.0754462	+	0.717823i	−0.965223	+	0.261427i	$0.915807\pi$
$860$	32.7281	+	23.7784i	1.11602	+	0.810835i
$861$	−0.0544344	−	0.517909i	−0.00185512	−	0.0176503i
$862$	−4.00618	+	6.93891i	−0.136451	+	0.236340i
$863$	4.66987	+	8.08845i	0.158964	+	0.275334i	0.934495	−	0.355975i	$-0.115851\pi$
$863$	4.66987	+	8.08845i	0.158964	+	0.275334i	−0.775531	+	0.631309i	$0.782518\pi$
$864$	−21.9861	+	15.9739i	−0.747983	+	0.543441i
$865$	−51.2354	−	56.9027i	−1.74206	−	1.93475i
$866$	5.24064	+	16.1290i	0.178084	+	0.548087i
$867$	−13.7957			−0.468526
$868$		0			0
$869$	58.0085			1.96780
$870$	3.48982	+	10.7406i	0.118316	+	0.364139i
$871$	−4.06320	−	4.51264i	−0.137676	−	0.152905i
$872$	−2.90353	+	2.10954i	−0.0983260	+	0.0714380i
$873$	−5.76760	−	9.98977i	−0.195204	−	0.338102i
$874$	−4.30028	+	7.44830i	−0.145459	+	0.251942i
$875$	−1.10815	−	10.5433i	−0.0374621	−	0.356429i
$876$	6.29703	+	4.57506i	0.212757	+	0.154577i
$877$	−2.34512	+	22.3123i	−0.0791892	+	0.753435i	0.880817	+	0.473456i	$0.156994\pi$
$877$	−2.34512	+	22.3123i	−0.0791892	+	0.753435i	−0.960006	+	0.279978i	$0.909673\pi$
$878$	−8.39365	+	9.32209i	−0.283272	+	0.314605i
$879$	10.2231	+	4.55161i	0.344816	+	0.153522i
$880$	−20.5014	−	4.35772i	−0.691104	−	0.146899i
$881$	−45.4168	+	9.65365i	−1.53013	+	0.325240i	−0.894612	−	0.446844i	$-0.852548\pi$
$881$	−45.4168	+	9.65365i	−1.53013	+	0.325240i	−0.635520	+	0.772084i	$0.719214\pi$
$882$	−8.83472	+	3.93347i	−0.297480	+	0.132447i
$883$	−11.2913	+	34.7512i	−0.379984	+	1.16947i	0.560070	+	0.828445i	$0.310774\pi$
$883$	−11.2913	+	34.7512i	−0.379984	+	1.16947i	−0.940054	+	0.341026i	$0.889226\pi$
$884$	1.79381	−	5.52077i	0.0603323	−	0.185684i
$885$	2.83412	−	1.26183i	0.0952681	−	0.0424161i
$886$	11.9780	−	2.54601i	0.402410	−	0.0855348i
$887$	−28.0582	−	5.96396i	−0.942102	−	0.200250i	−0.288836	−	0.957378i	$-0.593268\pi$
$887$	−28.0582	−	5.96396i	−0.942102	−	0.200250i	−0.653266	+	0.757128i	$0.726602\pi$
$888$	20.8610	+	9.28793i	0.700051	+	0.311683i
$889$	0.731487	−	0.812399i	0.0245333	−	0.0272470i
$890$	1.18501	−	11.2746i	0.0397217	−	0.377926i
$891$	−7.77192	−	5.64663i	−0.260369	−	0.189169i
$892$	−1.50183	−	14.2890i	−0.0502851	−	0.478431i
$893$	−1.66433	+	2.88270i	−0.0556945	+	0.0964658i
$894$	−6.26408	−	10.8497i	−0.209502	−	0.362869i
$895$	−0.394914	+	0.286922i	−0.0132005	+	0.00959074i
$896$	5.49031	+	6.09761i	0.183418	+	0.203707i
$897$	2.66381	+	8.19836i	0.0889420	+	0.273735i
$898$	−6.34235			−0.211647
$899$		0			0
$900$	29.1430			0.971434
$901$	1.44586	+	4.44989i	0.0481685	+	0.148247i
$902$	−1.43538	−	1.59415i	−0.0477929	−	0.0530794i
$903$	−3.98869	+	2.89795i	−0.132735	+	0.0964378i
$904$	−7.75296	−	13.4285i	−0.257860	−	0.446626i
$905$	14.3332	−	24.8259i	0.476453	−	0.825240i
$906$	−0.999786	−	9.51233i	−0.0332157	−	0.316026i
$907$	17.9518	+	13.0427i	0.596079	+	0.433077i	0.844485	−	0.535579i	$-0.179907\pi$
$907$	17.9518	+	13.0427i	0.596079	+	0.433077i	−0.248406	+	0.968656i	$0.579907\pi$
$908$	3.46824	−	32.9981i	0.115098	−	1.09508i
$909$	−5.56837	+	6.18430i	−0.184691	+	0.205120i
$910$	−5.18737	−	2.30957i	−0.171960	−	0.0765614i
$911$	−28.2024	−	5.99460i	−0.934386	−	0.198610i	−0.284530	−	0.958667i	$-0.591838\pi$
$911$	−28.2024	−	5.99460i	−0.934386	−	0.198610i	−0.649856	+	0.760057i	$0.725171\pi$
$912$	4.60677	−	0.979199i	0.152545	−	0.0324245i
$913$	53.0423	−	23.6160i	1.75544	−	0.781574i
$914$	−6.64760	+	20.4592i	−0.219883	+	0.676731i
$915$	−2.39551	+	7.37263i	−0.0791932	+	0.243732i
$916$	23.6160	−	10.5145i	0.780295	−	0.347410i
$917$	−4.69898	+	0.998800i	−0.155174	+	0.0329833i
$918$	4.12972	+	0.877799i	0.136301	+	0.0289717i
$919$	43.9071	+	19.5487i	1.44836	+	0.644853i	0.972125	−	0.234464i	$-0.0753335\pi$
$919$	43.9071	+	19.5487i	1.44836	+	0.644853i	0.476238	+	0.879317i	$0.342000\pi$
$920$	19.7924	−	21.9817i	0.652537	−	0.724715i
$921$	−2.89771	+	27.5699i	−0.0954828	+	0.908459i
$922$	3.71975	+	2.70256i	0.122503	+	0.0890039i
$923$	2.35294	+	22.3868i	0.0774481	+	0.736869i
$924$	2.16127	−	3.74343i	0.0711007	−	0.123150i
$925$	−45.5334	−	78.8662i	−1.49713	−	2.59310i
$926$	−19.7010	+	14.3136i	−0.647416	+	0.470376i
$927$	9.13433	+	10.1447i	0.300011	+	0.333196i
$928$	8.78572	+	27.0397i	0.288405	+	0.887621i
$929$	−7.01617			−0.230193			−0.115097	−	0.993354i	$-0.536718\pi$
$929$	−7.01617			−0.230193			−0.115097	+	0.993354i	$0.536718\pi$
$930$		0			0
$931$	24.3825			0.799105
$932$	4.63406	+	14.2622i	0.151794	+	0.467173i
$933$	1.43795	+	1.59701i	0.0470765	+	0.0522837i
$934$	20.0497	−	14.5669i	0.656045	−	0.476644i
$935$	9.98321	+	17.2914i	0.326486	+	0.565490i
$936$	7.72770	−	13.3848i	0.252588	−	0.437495i
$937$	1.34639	+	12.8101i	0.0439848	+	0.418487i	0.994253	+	0.107055i	$0.0341421\pi$
$937$	1.34639	+	12.8101i	0.0439848	+	0.418487i	−0.950268	+	0.311432i	$0.899191\pi$
$938$	−0.888663	−	0.645651i	−0.0290159	−	0.0210813i
$939$	1.01359	−	9.64371i	0.0330774	−	0.314711i
$940$	3.31350	−	3.68001i	0.108074	−	0.120029i
$941$	45.7131	+	20.3528i	1.49021	+	0.663482i	0.980438	−	0.196830i	$-0.0630647\pi$
$941$	45.7131	+	20.3528i	1.49021	+	0.663482i	0.509768	+	0.860312i	$0.329731\pi$
$942$	9.21866	+	1.95949i	0.300360	+	0.0638436i
$943$	−2.42751	+	0.515982i	−0.0790505	+	0.0168027i
$944$	1.16358	−	0.518061i	0.0378714	−	0.0168615i
$945$	−4.09278	+	12.5963i	−0.133138	+	0.409757i
$946$	−6.27584	+	19.3151i	−0.204045	+	0.627987i
$947$	−47.3837	+	21.0966i	−1.53976	+	0.685547i	−0.988836	−	0.149006i	$-0.952393\pi$
$947$	−47.3837	+	21.0966i	−1.53976	+	0.685547i	−0.550928	+	0.834553i	$0.685726\pi$
$948$	18.9678	−	4.03172i	0.616044	−	0.130944i
$949$	−16.1021	−	3.42261i	−0.522697	−	0.111103i
$950$	20.9307	+	9.31896i	0.679083	+	0.302347i
$951$	5.28126	−	5.86543i	0.171256	−	0.190200i
$952$	0.253749	−	2.41426i	0.00822405	−	0.0782467i
$953$	15.1571	+	11.0123i	0.490987	+	0.356723i	0.805564	−	0.592509i	$-0.201863\pi$
$953$	15.1571	+	11.0123i	0.490987	+	0.356723i	−0.314577	+	0.949232i	$0.601863\pi$
$954$	0.563263	+	5.35909i	0.0182363	+	0.173507i
$955$	39.1193	−	67.7565i	1.26587	−	2.19255i
$956$	−0.450241	−	0.779840i	−0.0145618	−	0.0252218i
$957$	14.7096	−	10.6872i	0.475494	−	0.345467i
$958$	−15.3377	−	17.0342i	−0.495537	−	0.550350i
$959$	−3.00772	−	9.25682i	−0.0971245	−	0.298918i
$960$	4.20549			0.135731
$961$		0			0
$962$	−20.8907			−0.673542
$963$	−1.57194	−	4.83793i	−0.0506550	−	0.155900i
$964$	15.6803	+	17.4147i	0.505027	+	0.560889i
$965$	−16.9866	+	12.3415i	−0.546817	+	0.397285i
$966$	0.779674	+	1.35044i	0.0250856	+	0.0434496i
$967$	−23.8923	+	41.3827i	−0.768324	+	1.33078i	0.170146	+	0.985419i	$0.445576\pi$
$967$	−23.8923	+	41.3827i	−0.768324	+	1.33078i	−0.938471	+	0.345358i	$0.887757\pi$
$968$	−1.50848	−	14.3522i	−0.0484844	−	0.461298i
$969$	−3.62969	−	2.63713i	−0.116603	−	0.0847167i
$970$	−1.41022	+	13.4174i	−0.0452795	+	0.430805i
$971$	−20.8104	+	23.1123i	−0.667838	+	0.741709i	−0.977915	−	0.209002i	$-0.932978\pi$
$971$	−20.8104	+	23.1123i	−0.667838	+	0.741709i	0.310077	+	0.950711i	$0.399645\pi$
$972$	−22.4867	−	10.0117i	−0.721260	−	0.321126i
$973$	13.9738	+	2.97022i	0.447979	+	0.0952208i
$974$	−19.2315	+	4.08778i	−0.616217	+	0.130981i
$975$	20.9787	−	9.34033i	0.671857	−	0.299130i
$976$	−0.983507	+	3.02692i	−0.0314813	+	0.0968894i
$977$	−6.82283	+	20.9985i	−0.218282	+	0.671802i	0.780623	+	0.625003i	$0.214902\pi$
$977$	−6.82283	+	20.9985i	−0.218282	+	0.671802i	−0.998904	+	0.0467994i	$0.985098\pi$
$978$	0.593911	−	0.264426i	0.0189912	−	0.00845542i
$979$	−17.8532	+	3.79481i	−0.570590	+	0.121283i
$980$	−35.4806	−	7.54163i	−1.13339	−	0.240909i
$981$	−2.94880	−	1.31289i	−0.0941478	−	0.0419173i
$982$	−12.9013	+	14.3284i	−0.411698	+	0.457237i
$983$	−3.92785	+	37.3710i	−0.125279	+	1.19195i	0.733531	+	0.679656i	$0.237871\pi$
$983$	−3.92785	+	37.3710i	−0.125279	+	1.19195i	−0.858810	+	0.512294i	$0.828796\pi$
$984$	−1.34118	−	0.974425i	−0.0427553	−	0.0310635i
$985$	6.16764	+	58.6811i	0.196517	+	1.86974i
$986$	2.20846	−	3.82517i	0.0703318	−	0.121818i
$987$	0.301756	+	0.522656i	0.00960499	+	0.0166363i
$988$	−13.6364	+	9.90744i	−0.433832	+	0.315198i
$989$	15.7217	+	17.4608i	0.499922	+	0.555220i
$990$	7.10585	+	21.8695i	0.225839	+	0.695060i
$991$	6.77397			0.215182			0.107591	−	0.994195i	$-0.465686\pi$
$991$	6.77397			0.215182			0.107591	+	0.994195i	$0.465686\pi$
$992$		0			0
$993$	29.2099			0.926948
$994$	1.25829	+	3.87263i	0.0399106	+	0.122832i
$995$	10.5719	+	11.7413i	0.335151	+	0.372223i
$996$	15.7025	−	11.4086i	0.497554	−	0.361494i
$997$	14.7866	+	25.6112i	0.468298	+	0.811115i	0.999344	−	0.0362278i	$-0.0115342\pi$
$997$	14.7866	+	25.6112i	0.468298	+	0.811115i	−0.531046	+	0.847343i	$0.678201\pi$
$998$	14.2397	−	24.6639i	0.450751	−	0.780724i
$999$	5.09338	+	48.4603i	0.161147	+	1.53321i

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	961.2.g.n.547.1		16
31.2	even	5		961.2.g.l.235.2		16
31.3	odd	30		961.2.c.j.521.3		16
31.4	even	5		961.2.g.j.816.2		16
31.5	even	3		961.2.d.q.531.1		16
31.6	odd	6		961.2.g.s.844.1		16
31.7	even	15		961.2.g.l.732.2		16
31.8	even	5		961.2.g.m.846.1		16
31.9	even	15		961.2.d.q.628.1		16
31.10	even	15		961.2.d.n.388.4		16
31.11	odd	30		961.2.d.o.374.4		16
31.12	odd	30		961.2.g.k.338.2		16
31.13	odd	30		961.2.a.i.1.3		8
31.14	even	15	inner	961.2.g.n.448.1		16
31.15	odd	10		961.2.c.j.439.3		16
31.16	even	5		961.2.c.i.439.3		16
31.17	odd	30		961.2.g.t.448.1		16
31.18	even	15		961.2.a.j.1.3		8
31.19	even	15		961.2.g.j.338.2		16
31.20	even	15		961.2.d.n.374.4		16
31.21	odd	30		961.2.d.o.388.4		16
31.22	odd	30		961.2.d.p.628.1		16
31.23	odd	10		961.2.g.s.846.1		16
31.24	odd	30		31.2.g.a.19.2	yes	16
31.25	even	3		961.2.g.m.844.1		16
31.26	odd	6		961.2.d.p.531.1		16
31.27	odd	10		961.2.g.k.816.2		16
31.28	even	15		961.2.c.i.521.3		16
31.29	odd	10		31.2.g.a.18.2	✓	16
31.30	odd	2		961.2.g.t.547.1		16
93.29	even	10		279.2.y.c.235.1		16
93.44	even	30		8649.2.a.bf.1.6		8
93.80	odd	30		8649.2.a.be.1.6		8
93.86	even	30		279.2.y.c.19.1		16
124.55	even	30		496.2.bg.c.81.1		16
124.91	even	10		496.2.bg.c.49.1		16
155.24	odd	30		775.2.bl.a.701.1		16
155.29	odd	10		775.2.bl.a.576.1		16
155.117	even	60		775.2.ck.a.174.2		32
155.122	even	20		775.2.ck.a.49.3		32
155.148	even	60		775.2.ck.a.174.3		32
155.153	even	20		775.2.ck.a.49.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.18.2	✓	16	31.29	odd	10
31.2.g.a.19.2	yes	16	31.24	odd	30
279.2.y.c.19.1		16	93.86	even	30
279.2.y.c.235.1		16	93.29	even	10
496.2.bg.c.49.1		16	124.91	even	10
496.2.bg.c.81.1		16	124.55	even	30
775.2.bl.a.576.1		16	155.29	odd	10
775.2.bl.a.701.1		16	155.24	odd	30
775.2.ck.a.49.2		32	155.153	even	20
775.2.ck.a.49.3		32	155.122	even	20
775.2.ck.a.174.2		32	155.117	even	60
775.2.ck.a.174.3		32	155.148	even	60
961.2.a.i.1.3		8	31.13	odd	30
961.2.a.j.1.3		8	31.18	even	15
961.2.c.i.439.3		16	31.16	even	5
961.2.c.i.521.3		16	31.28	even	15
961.2.c.j.439.3		16	31.15	odd	10
961.2.c.j.521.3		16	31.3	odd	30
961.2.d.n.374.4		16	31.20	even	15
961.2.d.n.388.4		16	31.10	even	15
961.2.d.o.374.4		16	31.11	odd	30
961.2.d.o.388.4		16	31.21	odd	30
961.2.d.p.531.1		16	31.26	odd	6
961.2.d.p.628.1		16	31.22	odd	30
961.2.d.q.531.1		16	31.5	even	3
961.2.d.q.628.1		16	31.9	even	15
961.2.g.j.338.2		16	31.19	even	15
961.2.g.j.816.2		16	31.4	even	5
961.2.g.k.338.2		16	31.12	odd	30
961.2.g.k.816.2		16	31.27	odd	10
961.2.g.l.235.2		16	31.2	even	5
961.2.g.l.732.2		16	31.7	even	15
961.2.g.m.844.1		16	31.25	even	3
961.2.g.m.846.1		16	31.8	even	5
961.2.g.n.448.1		16	31.14	even	15	inner
961.2.g.n.547.1		16	1.1	even	1	trivial
961.2.g.s.844.1		16	31.6	odd	6
961.2.g.s.846.1		16	31.23	odd	10
961.2.g.t.448.1		16	31.17	odd	30
961.2.g.t.547.1		16	31.30	odd	2
8649.2.a.be.1.6		8	93.80	odd	30
8649.2.a.bf.1.6		8	93.44	even	30

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

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Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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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	961.2.g.n.547.1

Level	$961$
Weight	$2$
Character	961.547
Analytic conductor	$7.674$
Analytic rank	$0$
Dimension	$16$
Inner twists	$2$