LMFDB - Embedded newform 961.2.g.m.844.1

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			844.1
Root			$-1.83925i$ of defining polynomial
Character	$\chi$	$=$	961.844
Dual form			961.2.g.m.846.1

$q$ -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} +(-0.882681 + 0.187620i) q^{3} +(1.23343 - 0.896137i) q^{4} +(-1.85376 + 3.21080i) q^{5} +(0.311099 + 0.538840i) q^{6} +(0.697395 + 0.310500i) q^{7} +(-1.96606 - 1.42843i) q^{8} +(-1.99671 + 0.888993i) q^{9} +(2.50044 + 0.531486i) q^{10} +(-0.430200 - 4.09308i) q^{11} +(-0.920590 + 1.02242i) q^{12} +(1.94700 + 2.16237i) q^{13} +(0.0550190 - 0.523471i) q^{14} +(1.03387 - 3.18192i) q^{15} +(0.424467 - 1.30637i) q^{16} +(0.136778 - 1.30136i) q^{17} +(1.00838 + 1.11992i) q^{18} +(-2.54239 + 2.82361i) q^{19} +(0.590845 + 5.62151i) q^{20} +(-0.673833 - 0.143228i) q^{21} +(-2.59236 + 1.15419i) q^{22} +(-2.65597 - 1.92967i) q^{23} +(2.00341 + 0.891974i) q^{24} +(-4.37284 - 7.57398i) q^{25} +(1.00313 - 1.73747i) q^{26} +(3.78584 - 2.75057i) q^{27} +(1.13844 - 0.241982i) q^{28} +(-1.51283 - 4.65602i) q^{29} -2.30681 q^{30} -5.80746 q^{32} +(1.14767 + 3.53217i) q^{33} +(-0.882502 + 0.187582i) q^{34} +(-2.28976 + 1.66361i) q^{35} +(-1.66614 + 2.88584i) q^{36} +(-5.20639 - 9.01773i) q^{37} +(2.39327 + 1.06555i) q^{38} +(-2.12429 - 1.54338i) q^{39} +(8.23100 - 3.66468i) q^{40} +(-0.739427 - 0.157170i) q^{41} +(0.0496492 + 0.472381i) q^{42} +(4.78889 - 5.31861i) q^{43} +(-4.19858 - 4.66299i) q^{44} +(0.847038 - 8.05903i) q^{45} +(-0.699483 + 2.15279i) q^{46} +(-0.270719 + 0.833189i) q^{47} +(-0.129567 + 1.23275i) q^{48} +(-4.29396 - 4.76893i) q^{49} +(-4.03491 + 4.48122i) q^{50} +(0.123429 + 1.17434i) q^{51} +(4.33926 + 0.922339i) q^{52} +(-3.26657 + 1.45437i) q^{53} +(-2.61031 - 1.89650i) q^{54} +(13.9396 + 6.20629i) q^{55} +(-0.927595 - 1.60664i) q^{56} +(1.71435 - 2.96935i) q^{57} +(-2.73084 + 1.98407i) q^{58} +(-0.907007 + 0.192790i) q^{59} +(-1.57623 - 4.85115i) q^{60} -2.31704 q^{61} -1.66853 q^{63} +(0.388433 + 1.19547i) q^{64} +(-10.5522 + 2.24294i) q^{65} +(2.07168 - 1.50516i) q^{66} +(1.04345 - 1.80731i) q^{67} +(-0.997488 - 1.72770i) q^{68} +(2.70642 + 1.20498i) q^{69} +(1.57877 + 1.14704i) q^{70} +(-7.06726 + 3.14655i) q^{71} +(5.19552 + 1.10434i) q^{72} +(-0.591367 - 5.62649i) q^{73} +(-4.80405 + 5.33544i) q^{74} +(5.28085 + 5.86498i) q^{75} +(-0.605510 + 5.76105i) q^{76} +(0.970882 - 2.98807i) q^{77} +(-0.559458 + 1.72183i) q^{78} +(-1.47330 + 14.0175i) q^{79} +(3.40765 + 3.78458i) q^{80} +(1.56187 - 1.73464i) q^{81} +(0.0544822 + 0.518364i) q^{82} +(-13.7994 - 2.93316i) q^{83} +(-0.959476 + 0.427186i) q^{84} +(3.92484 + 2.85157i) q^{85} +(-4.50800 - 2.00709i) q^{86} +(2.20891 + 3.82595i) q^{87} +(-5.00086 + 8.66175i) q^{88} +(-3.58784 + 2.60672i) q^{89} +(-5.46515 + 1.16165i) q^{90} +(0.686415 + 2.11257i) q^{91} -5.00520 q^{92} +0.604042 q^{94} +(-4.35308 - 13.3974i) q^{95} +(5.12614 - 1.08959i) q^{96} +(4.26970 - 3.10212i) q^{97} +(-2.21232 + 3.83184i) q^{98} +(4.49770 + 7.79025i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q + 4 q^{2} - 3 q^{3} + 6 q^{4} - 3 q^{5} - 11 q^{6} - 3 q^{7} - 8 q^{8} + 5 q^{9} + 18 q^{10} + 2 q^{11} + 20 q^{12} + 27 q^{13} - 6 q^{14} - 4 q^{15} - 2 q^{16} + 16 q^{17} + 22 q^{18} - 4 q^{19} - 18 q^{20}+ \cdots - 6 q^{99}+O(q^{100})$ 16 * q + 4 * q^2 - 3 * q^3 + 6 * q^4 - 3 * q^5 - 11 * q^6 - 3 * q^7 - 8 * q^8 + 5 * q^9 + 18 * q^10 + 2 * q^11 + 20 * q^12 + 27 * q^13 - 6 * q^14 - 4 * q^15 - 2 * q^16 + 16 * q^17 + 22 * q^18 - 4 * q^19 - 18 * q^20 - 29 * q^21 - 4 * q^22 - 21 * q^23 + 25 * q^24 - 13 * q^25 - 9 * q^26 - 9 * q^27 - 40 * 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 - 27 * q^38 + 2 * q^39 - 16 * q^40 - 3 * q^41 + 51 * q^42 - 8 * q^43 - 4 * q^44 + 25 * q^45 + 16 * q^46 + 4 * q^47 + 86 * q^48 + 27 * q^49 - 27 * q^50 + 13 * q^51 - 24 * q^52 - 66 * q^53 - 39 * q^54 + 52 * q^55 - 30 * q^56 + 17 * q^57 - 10 * q^58 - 51 * q^59 - 35 * q^60 + 60 * q^61 - 46 * q^63 - 32 * q^64 - 18 * q^65 + 20 * q^66 + 13 * q^67 - 30 * q^68 + 48 * q^69 + 27 * q^70 - 24 * q^71 + 2 * q^72 - 27 * q^73 - 28 * q^74 + 32 * q^75 + 18 * q^76 + 42 * q^77 + 15 * q^78 - 8 * q^79 - 39 * q^80 - 7 * q^81 + 29 * q^82 - 4 * q^83 + 27 * q^84 + 63 * q^85 - 34 * q^86 + 15 * q^87 + 17 * q^88 - 26 * q^89 + 57 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 + 28 * q^95 + 62 * q^96 - 37 * q^97 - 10 * q^98 - 6 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{14}{15}\right)$

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	$0.978385\pi$
$3$	−0.882681	+	0.187620i	−0.509616	+	0.108322i	−0.455541	−	0.890215i	$-0.650554\pi$
$3$	−0.882681	+	0.187620i	−0.509616	+	0.108322i	−0.0540749	+	0.998537i	$0.517221\pi$
$4$	1.23343	−	0.896137i	0.616714	−	0.448069i
$5$	−1.85376	+	3.21080i	−0.829026	+	1.43591i	0.0697774	+	0.997563i	$0.477771\pi$
$5$	−1.85376	+	3.21080i	−0.829026	+	1.43591i	−0.898803	+	0.438352i	$0.855562\pi$
$6$	0.311099	+	0.538840i	0.127006	+	0.219981i
$7$	0.697395	+	0.310500i	0.263591	+	0.117358i	0.534277	−	0.845310i	$-0.320584\pi$
$7$	0.697395	+	0.310500i	0.263591	+	0.117358i	−0.270686	+	0.962668i	$0.587251\pi$
$8$	−1.96606	−	1.42843i	−0.695108	−	0.505025i
$9$	−1.99671	+	0.888993i	−0.665570	+	0.296331i
$10$	2.50044	+	0.531486i	0.790710	+	0.168071i
$11$	−0.430200	−	4.09308i	−0.129710	−	1.23411i	−0.844802	−	0.535079i	$-0.820282\pi$
$11$	−0.430200	−	4.09308i	−0.129710	−	1.23411i	0.715092	−	0.699030i	$-0.246385\pi$
$12$	−0.920590	+	1.02242i	−0.265751	+	0.295147i
$13$	1.94700	+	2.16237i	0.540002	+	0.599733i	0.949960	−	0.312372i	$-0.101123\pi$
$13$	1.94700	+	2.16237i	0.540002	+	0.599733i	−0.409958	+	0.912104i	$0.634457\pi$
$14$	0.0550190	−	0.523471i	0.0147045	−	0.139904i
$15$	1.03387	−	3.18192i	0.266943	−	0.821568i
$16$	0.424467	−	1.30637i	0.106117	−	0.326594i
$17$	0.136778	−	1.30136i	0.0331735	−	0.315625i	−0.965334	−	0.261017i	$-0.915942\pi$
$17$	0.136778	−	1.30136i	0.0331735	−	0.315625i	0.998508	−	0.0546085i	$-0.0173911\pi$
$18$	1.00838	+	1.11992i	0.237678	+	0.263968i
$19$	−2.54239	+	2.82361i	−0.583264	+	0.647781i	−0.960481	−	0.278344i	$-0.910214\pi$
$19$	−2.54239	+	2.82361i	−0.583264	+	0.647781i	0.377217	+	0.926125i	$0.376881\pi$
$20$	0.590845	+	5.62151i	0.132117	+	1.25701i
$21$	−0.673833	−	0.143228i	−0.147043	−	0.0312549i
$22$	−2.59236	+	1.15419i	−0.552693	+	0.246075i
$23$	−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	$0.811196\pi$
$24$	2.00341	+	0.891974i	0.408944	+	0.182073i
$25$	−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
$28$	1.13844	−	0.241982i	0.215144	−	0.0457303i
$29$	−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
$34$	−0.882502	+	0.187582i	−0.151348	+	0.0321700i
$35$	−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	−0.875784	−	0.482704i	$-0.839655\pi$
$37$	−5.20639	−	9.01773i	−0.855925	−	1.48251i	0.0198583	−	0.999803i	$-0.493679\pi$
$38$	2.39327	+	1.06555i	0.388239	+	0.172855i
$39$	−2.12429	−	1.54338i	−0.340158	−	0.247139i
$40$	8.23100	−	3.66468i	1.30144	−	0.579437i
$41$	−0.739427	−	0.157170i	−0.115479	−	0.0245458i	0.149810	−	0.988715i	$-0.452134\pi$
$41$	−0.739427	−	0.157170i	−0.115479	−	0.0245458i	−0.265289	+	0.964169i	$0.585467\pi$
$42$	0.0496492	+	0.472381i	0.00766104	+	0.0728899i
$43$	4.78889	−	5.31861i	0.730299	−	0.811080i	−0.257588	−	0.966255i	$-0.582928\pi$
$43$	4.78889	−	5.31861i	0.730299	−	0.811080i	0.987887	+	0.155175i	$0.0495942\pi$
$44$	−4.19858	−	4.66299i	−0.632960	−	0.702973i
$45$	0.847038	−	8.05903i	0.126269	−	1.20137i
$46$	−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	$0.120352\pi$
$48$	−0.129567	+	1.23275i	−0.0187014	+	0.177932i
$49$	−4.29396	−	4.76893i	−0.613424	−	0.681276i
$50$	−4.03491	+	4.48122i	−0.570623	+	0.633741i
$51$	0.123429	+	1.17434i	0.0172835	+	0.164441i
$52$	4.33926	+	0.922339i	0.601748	+	0.127905i
$53$	−3.26657	+	1.45437i	−0.448698	+	0.199773i	−0.618630	−	0.785683i	$-0.712312\pi$
$53$	−3.26657	+	1.45437i	−0.448698	+	0.199773i	0.169932	+	0.985456i	$0.445645\pi$
$54$	−2.61031	−	1.89650i	−0.355218	−	0.258081i
$55$	13.9396	+	6.20629i	1.87961	+	0.836856i
$56$	−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
$59$	−0.907007	+	0.192790i	−0.118082	+	0.0250992i	−0.266574	−	0.963815i	$-0.585892\pi$
$59$	−0.907007	+	0.192790i	−0.118082	+	0.0250992i	0.148491	+	0.988914i	$0.452558\pi$
$60$	−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
$65$	−10.5522	+	2.24294i	−1.30884	+	0.278203i
$66$	2.07168	−	1.50516i	0.255006	−	0.185273i
$67$	1.04345	−	1.80731i	0.127478	−	0.220798i	−0.795221	−	0.606320i	$-0.792645\pi$
$67$	1.04345	−	1.80731i	0.127478	−	0.220798i	0.922699	+	0.385522i	$0.125979\pi$
$68$	−0.997488	−	1.72770i	−0.120963	−	0.209514i
$69$	2.70642	+	1.20498i	0.325815	+	0.145062i
$70$	1.57877	+	1.14704i	0.188699	+	0.137098i
$71$	−7.06726	+	3.14655i	−0.838730	+	0.373427i	−0.780714	−	0.624889i	$-0.785144\pi$
$71$	−7.06726	+	3.14655i	−0.838730	+	0.373427i	−0.0580164	+	0.998316i	$0.518478\pi$
$72$	5.19552	+	1.10434i	0.612298	+	0.130148i
$73$	−0.591367	−	5.62649i	−0.0692143	−	0.658530i	−0.973041	−	0.230632i	$-0.925921\pi$
$73$	−0.591367	−	5.62649i	−0.0692143	−	0.658530i	0.903827	−	0.427899i	$-0.140746\pi$
$74$	−4.80405	+	5.33544i	−0.558459	+	0.620232i
$75$	5.28085	+	5.86498i	0.609780	+	0.677229i
$76$	−0.605510	+	5.76105i	−0.0694568	+	0.660837i
$77$	0.970882	−	2.98807i	0.110642	−	0.340522i
$78$	−0.559458	+	1.72183i	−0.0633461	+	0.194959i
$79$	−1.47330	+	14.0175i	−0.165759	+	1.57709i	0.523147	+	0.852242i	$0.324758\pi$
$79$	−1.47330	+	14.0175i	−0.165759	+	1.57709i	−0.688906	+	0.724850i	$0.741909\pi$
$80$	3.40765	+	3.78458i	0.380987	+	0.423129i
$81$	1.56187	−	1.73464i	0.173541	−	0.192737i
$82$	0.0544822	+	0.518364i	0.00601656	+	0.0572437i
$83$	−13.7994	−	2.93316i	−1.51468	−	0.321956i	−0.625762	−	0.780014i	$-0.715212\pi$
$83$	−13.7994	−	2.93316i	−1.51468	−	0.321956i	−0.888922	+	0.458058i	$0.848545\pi$
$84$	−0.959476	+	0.427186i	−0.104687	+	0.0466098i
$85$	3.92484	+	2.85157i	0.425709	+	0.309296i
$86$	−4.50800	−	2.00709i	−0.486110	−	0.216430i
$87$	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	$0.375524\pi$
$90$	−5.46515	+	1.16165i	−0.576078	+	0.122449i
$91$	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
$96$	5.12614	−	1.08959i	0.523184	−	0.111206i
$97$	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
$100$	−12.1809	−	5.42329i	−1.21809	−	0.542329i
$101$	−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	$0.760663\pi$
$102$	0.743774	−	0.331150i	0.0736446	−	0.0327887i
$103$	6.10921	+	1.29855i	0.601958	+	0.127950i	0.498804	−	0.866715i	$-0.333773\pi$
$103$	6.10921	+	1.29855i	0.601958	+	0.127950i	0.103155	+	0.994665i	$0.467106\pi$
$104$	−0.739145	−	7.03250i	−0.0724792	−	0.689593i
$105$	1.70900	−	1.89804i	0.166781	−	0.185229i
$106$	1.64969	+	1.83217i	0.160232	+	0.177956i
$107$	−0.243278	+	2.31464i	−0.0235186	+	0.223764i	0.976449	+	0.215747i	$0.0692186\pi$
$107$	−0.243278	+	2.31464i	−0.0235186	+	0.223764i	−0.999968	+	0.00801720i	$0.997448\pi$
$108$	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	$0.0774680\pi$
$110$	1.09972	−	10.4632i	0.104854	−	0.997623i
$111$	6.28749	+	6.98296i	0.596782	+	0.662794i
$112$	0.701651	−	0.779262i	0.0662998	−	0.0736334i
$113$	−0.666949	−	6.34559i	−0.0627413	−	0.596943i	−0.980048	−	0.198762i	$-0.936308\pi$
$113$	−0.666949	−	6.34559i	−0.0627413	−	0.596943i	0.917307	−	0.398182i	$-0.130359\pi$
$114$	−2.31241	−	0.491518i	−0.216577	−	0.0460349i
$115$	11.1193	−	4.95064i	1.03688	−	0.461650i
$116$	−6.03840	−	4.38716i	−0.560652	−	0.407337i
$117$	−5.80993	−	2.58675i	−0.537128	−	0.239145i
$118$	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
$121$	−5.80858	+	1.23465i	−0.528053	+	0.112241i
$122$	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
$127$	−1.40072	+	0.297732i	−0.124294	+	0.0264195i	−0.269639	−	0.962962i	$-0.586904\pi$
$127$	−1.40072	+	0.297732i	−0.124294	+	0.0264195i	0.145345	+	0.989381i	$0.453571\pi$
$128$	−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
$131$	5.74885	+	2.55955i	0.502279	+	0.223629i	0.642205	−	0.766533i	$-0.278020\pi$
$131$	5.74885	+	2.55955i	0.502279	+	0.223629i	−0.139926	+	0.990162i	$0.544686\pi$
$132$	4.58088	+	3.32820i	0.398714	+	0.289683i
$133$	−2.64978	+	1.17976i	−0.229765	+	0.102298i
$134$	−1.40746	−	0.299164i	−0.121586	−	0.0258439i
$135$	1.81352	+	17.2545i	0.156083	+	1.48503i
$136$	−2.12781	+	2.36317i	−0.182458	+	0.202640i
$137$	−8.53135	−	9.47503i	−0.728883	−	0.809506i	0.258808	−	0.965929i	$-0.416670\pi$
$137$	−8.53135	−	9.47503i	−0.728883	−	0.809506i	−0.987690	+	0.156423i	$0.950004\pi$
$138$	0.213515	−	2.03146i	0.0181756	−	0.172930i
$139$	−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
$141$	0.0826364	−	0.786233i	0.00695924	−	0.0662127i
$142$	3.56913	+	3.96392i	0.299514	+	0.332644i
$143$	8.01313	−	8.89948i	0.670092	−	0.744212i
$144$	0.313820	+	2.98580i	0.0261517	+	0.248817i
$145$	17.7540	+	3.77373i	1.47439	+	0.313391i
$146$	−3.56355	+	1.58659i	−0.294921	+	0.131307i
$147$	4.68495	+	3.40381i	0.386408	+	0.280742i
$148$	−14.5028	−	6.45708i	−1.19213	−	0.530768i
$149$	10.0677	+	17.4377i	0.824774	+	1.42855i	0.902092	+	0.431545i	$0.142031\pi$
$149$	10.0677	+	17.4377i	0.824774	+	1.42855i	−0.0773172	+	0.997007i	$0.524635\pi$
$150$	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	$0.0848964\pi$
$152$	9.03182	−	1.91977i	0.732577	−	0.155714i
$153$	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	$0.693396\pi$
$158$	9.50584	−	2.02053i	0.756244	−	0.160745i
$159$	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
$162$	−1.47026	−	0.654603i	−0.115515	−	0.0514305i
$163$	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	$0.686971\pi$
$164$	−1.05287	+	0.468770i	−0.0822157	+	0.0366048i
$165$	−13.4686	−	2.86284i	−1.04853	−	0.222872i
$166$	1.01677	+	9.67388i	0.0789163	+	0.750839i
$167$	7.55409	−	8.38966i	0.584553	−	0.649212i	−0.376226	−	0.926528i	$-0.622778\pi$
$167$	7.55409	−	8.38966i	0.584553	−	0.649212i	0.960779	+	0.277316i	$0.0894450\pi$
$168$	1.12021	+	1.24412i	0.0864259	+	0.0959857i
$169$	0.473864	−	4.50851i	0.0364511	−	0.346809i
$170$	1.03366	−	3.18127i	0.0792779	−	0.243992i
$171$	2.56625	−	7.89810i	0.196246	−	0.603983i
$172$	1.14055	−	10.8516i	0.0869662	−	0.827428i
$173$	−13.8193	−	15.3479i	−1.05067	−	1.16688i	−0.985616	−	0.169000i	$-0.945946\pi$
$173$	−13.8193	−	15.3479i	−1.05067	−	1.16688i	−0.0650489	−	0.997882i	$-0.520720\pi$
$174$	2.03821	−	2.26366i	0.154516	−	0.171608i
$175$	−0.697873	−	6.63982i	−0.0527543	−	0.501923i
$176$	−5.52970	−	1.17537i	−0.416817	−	0.0885971i
$177$	0.764427	−	0.340345i	0.0574578	−	0.0255819i
$178$	2.47379	+	1.79731i	0.185418	+	0.134714i
$179$	0.120280	+	0.0535519i	0.00899012	+	0.00400266i	0.411227	−	0.911533i	$-0.365100\pi$
$179$	0.120280	+	0.0535519i	0.00899012	+	0.00400266i	−0.402237	+	0.915536i	$0.631767\pi$
$180$	−6.17723	−	10.6993i	−0.460424	−	0.797477i
$181$	3.86599	−	6.69610i	0.287357	−	0.497717i	−0.685821	−	0.727770i	$-0.740557\pi$
$181$	3.86599	−	6.69610i	0.287357	−	0.497717i	0.973178	+	0.230053i	$0.0738901\pi$
$182$	1.23906	−	0.900229i	0.0918451	−	0.0667294i
$183$	2.04521	−	0.434722i	0.151186	−	0.0321356i
$184$	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
$189$	3.49428	−	0.742732i	0.254171	−	0.0540258i
$190$	−7.85781	+	5.70903i	−0.570066	+	0.414177i
$191$	10.5513	−	18.2755i	0.763468	−	1.32237i	−0.177585	−	0.984106i	$-0.556828\pi$
$191$	10.5513	−	18.2755i	0.763468	−	1.32237i	0.941053	−	0.338260i	$-0.109838\pi$
$192$	−0.567157	−	0.982344i	−0.0409310	−	0.0708946i
$193$	5.17362	+	2.30345i	0.372406	+	0.165806i	0.584401	−	0.811465i	$-0.301330\pi$
$193$	5.17362	+	2.30345i	0.372406	+	0.165806i	−0.211995	+	0.977271i	$0.567996\pi$
$194$	−2.94393	−	2.13889i	−0.211362	−	0.153563i
$195$	8.89342	−	3.95960i	0.636871	−	0.283553i
$196$	−9.56991	−	2.03415i	−0.683565	−	0.145296i
$197$	1.66355	+	15.8276i	0.118523	+	1.12767i	0.878507	+	0.477729i	$0.158540\pi$
$197$	1.66355	+	15.8276i	0.118523	+	1.12767i	−0.759984	+	0.649942i	$0.774793\pi$
$198$	4.15013	−	4.60918i	0.294937	−	0.327560i
$199$	2.85147	+	3.16688i	0.202135	+	0.224494i	0.835686	−	0.549207i	$-0.185070\pi$
$199$	2.85147	+	3.16688i	0.202135	+	0.224494i	−0.633551	+	0.773701i	$0.718403\pi$
$200$	−2.22161	+	21.1372i	−0.157091	+	1.49463i
$201$	−0.581946	+	1.79105i	−0.0410473	+	0.126331i
$202$	−0.811230	+	2.49671i	−0.0570779	+	0.175668i
$203$	0.390654	−	3.71682i	0.0274185	−	0.260870i
$204$	1.20461	+	1.33786i	0.0843399	+	0.0936689i
$205$	1.87536	−	2.08280i	0.130981	−	0.145469i
$206$	−0.450137	−	4.28277i	−0.0313625	−	0.298395i
$207$	7.01867	+	1.49186i	0.487831	+	0.103692i
$208$	3.65130	−	1.62566i	0.253172	−	0.112719i
$209$	12.6510	+	9.19148i	0.875087	+	0.635788i
$210$	−1.60876	−	0.716266i	−0.111015	−	0.0494270i
$211$	5.75414	+	9.96646i	0.396131	+	0.686120i	0.993245	−	0.116037i	$-0.0370191\pi$
$211$	5.75414	+	9.96646i	0.396131	+	0.686120i	−0.597113	+	0.802157i	$0.703686\pi$
$212$	−2.72576	+	4.72115i	−0.187206	+	0.324250i
$213$	5.64779	−	4.10336i	0.386980	−	0.281157i
$214$	1.56965	−	0.333639i	0.107299	−	0.0228071i
$215$	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
$220$	22.7551	−	4.83675i	1.53415	−	0.326093i
$221$	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	0.979551	−	0.201195i	$-0.0644824\pi$
$223$	4.71196	+	8.16135i	0.315536	+	0.546524i	−0.664015	+	0.747719i	$0.731149\pi$
$224$	−4.05010	−	1.80322i	−0.270608	−	0.120483i
$225$	15.4645	+	11.2356i	1.03097	+	0.749042i
$226$	−4.01900	+	1.78937i	−0.267340	+	0.119027i
$227$	−21.2875	−	4.52479i	−1.41290	−	0.300321i	−0.562646	−	0.826698i	$-0.690217\pi$
$227$	−21.2875	−	4.52479i	−1.41290	−	0.300321i	−0.850251	+	0.526377i	$0.823550\pi$
$228$	−0.546413	−	5.19877i	−0.0361871	−	0.344297i
$229$	−11.3457	+	12.6007i	−0.749745	+	0.832677i	−0.990443	−	0.137924i	$-0.955957\pi$
$229$	−11.3457	+	12.6007i	−0.749745	+	0.832677i	0.240697	+	0.970600i	$0.422624\pi$
$230$	−5.61551	−	6.23665i	−0.370276	−	0.411233i
$231$	−0.296359	+	2.81967i	−0.0194990	+	0.185521i
$232$	−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	$0.995580\pi$
$234$	−0.458358	+	4.36099i	−0.0299638	+	0.285087i
$235$	−2.17336	−	2.41376i	−0.141774	−	0.157456i
$236$	−0.945960	+	1.05060i	−0.0615768	+	0.0683879i
$237$	−1.32951	−	12.6494i	−0.0863607	−	0.821667i
$238$	−0.673697	−	0.143199i	−0.0436693	−	0.00928219i
$239$	−0.539572	+	0.240233i	−0.0349020	+	0.0155394i	−0.424113	−	0.905609i	$-0.639414\pi$
$239$	−0.539572	+	0.240233i	−0.0349020	+	0.0155394i	0.389211	+	0.921148i	$0.372748\pi$
$240$	−3.71793	−	2.70124i	−0.239992	−	0.174364i
$241$	−14.0416	−	6.25172i	−0.904499	−	0.402709i	−0.0988501	−	0.995102i	$-0.531516\pi$
$241$	−14.0416	−	6.25172i	−0.904499	−	0.402709i	−0.805649	+	0.592393i	$0.798183\pi$
$242$	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
$245$	23.2721	−	4.94663i	1.48680	−	0.316029i
$246$	−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
$251$	−5.91926	+	1.25818i	−0.373621	+	0.0794155i	−0.390895	−	0.920435i	$-0.627834\pi$
$251$	−5.91926	+	1.25818i	−0.373621	+	0.0794155i	0.0172744	+	0.999851i	$0.494501\pi$
$252$	−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
$255$	−3.99940	−	1.78065i	−0.250452	−	0.111508i
$256$	8.02935	+	5.83366i	0.501834	+	0.364604i
$257$	−4.13639	+	1.84164i	−0.258021	+	0.114878i	−0.531671	−	0.846951i	$-0.678436\pi$
$257$	−4.13639	+	1.84164i	−0.258021	+	0.114878i	0.273650	+	0.961829i	$0.411769\pi$
$258$	4.35570	+	0.925833i	0.271174	+	0.0576398i
$259$	−0.830903	−	7.90551i	−0.0516298	−	0.491224i
$260$	−11.0054	+	12.2227i	−0.682526	+	0.758022i
$261$	7.15986	+	7.95183i	0.443184	+	0.492206i
$262$	0.453539	−	4.31514i	0.0280198	−	0.266590i
$263$	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
$265$	1.38573	−	13.1844i	0.0851248	−	0.809909i
$266$	1.33820	+	1.48622i	0.0820502	+	0.0911260i
$267$	2.67785	−	2.97405i	0.163882	−	0.182009i
$268$	−0.332576	−	3.16425i	−0.0203153	−	0.193288i
$269$	13.0483	+	2.77349i	0.795567	+	0.169103i	0.587726	−	0.809060i	$-0.300023\pi$
$269$	13.0483	+	2.77349i	0.795567	+	0.169103i	0.207840	+	0.978163i	$0.433357\pi$
$270$	10.9282	−	4.86554i	0.665067	−	0.296107i
$271$	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	$0.562072\pi$
$272$	−1.64200	−	0.731066i	−0.0995609	−	0.0443274i
$273$	−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
$276$	4.41799	−	0.939074i	0.265932	−	0.0565256i
$277$	−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	$-0.251908\pi$
$282$	−0.533176	+	0.113330i	−0.0317502	+	0.00674871i
$283$	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
$286$	−7.54312	−	3.35842i	−0.446034	−	0.198587i
$287$	−0.466871	−	0.339202i	−0.0275585	−	0.0200224i
$288$	11.5958	−	5.16279i	0.683291	−	0.304221i
$289$	14.9537	+	3.17851i	0.879629	+	0.186971i
$290$	−1.30815	−	12.4462i	−0.0768169	−	0.730864i
$291$	−3.18677	+	3.53926i	−0.186812	+	0.207475i
$292$	−5.77151	−	6.40991i	−0.337752	−	0.375112i
$293$	−1.29624	+	12.3329i	−0.0757273	+	0.720497i	0.889118	+	0.457678i	$0.151319\pi$
$293$	−1.29624	+	12.3329i	−0.0757273	+	0.720497i	−0.964845	+	0.262819i	$0.915348\pi$
$294$	1.23384	−	3.79737i	0.0719591	−	0.221467i
$295$	1.06236	−	3.26961i	0.0618530	−	0.190364i
$296$	−2.64509	+	25.1664i	−0.153743	+	1.46277i
$297$	−12.8870	−	14.3124i	−0.747778	−	0.830492i
$298$	9.28964	−	10.3172i	0.538134	−	0.597659i
$299$	−0.998518	−	9.50026i	−0.0577458	−	0.549414i
$300$	11.7694	+	2.50166i	0.679505	+	0.144433i
$301$	4.99118	−	2.22222i	0.287687	−	0.128086i
$302$	−8.57493	−	6.23005i	−0.493432	−	0.358499i
$303$	3.13878	+	1.39748i	0.180318	+	0.0802830i
$304$	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
$307$	−30.0487	+	6.38704i	−1.71497	+	0.364528i	−0.957520	−	0.288367i	$-0.906888\pi$
$307$	−30.0487	+	6.38704i	−1.71497	+	0.364528i	−0.757449	+	0.652894i	$0.773554\pi$
$308$	−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
$313$	10.5108	−	2.23413i	0.594104	−	0.126281i	0.0989597	−	0.995091i	$-0.468449\pi$
$313$	10.5108	−	2.23413i	0.594104	−	0.126281i	0.495144	+	0.868811i	$0.335115\pi$
$314$	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
$317$	7.99019	+	3.55746i	0.448774	+	0.199807i	0.618663	−	0.785656i	$-0.287674\pi$
$317$	7.99019	+	3.55746i	0.448774	+	0.199807i	−0.169890	+	0.985463i	$0.554341\pi$
$318$	−1.79990	−	1.30770i	−0.100933	−	0.0733324i
$319$	−18.4066	+	8.19516i	−1.03057	+	0.458841i
$320$	−4.55849	−	0.968937i	−0.254827	−	0.0541652i
$321$	−0.219534	−	2.08873i	−0.0122532	−	0.116581i
$322$	−1.15626	+	1.28415i	−0.0644357	+	0.0715631i
$323$	3.32678	+	3.69476i	0.185107	+	0.205582i
$324$	0.371985	−	3.53920i	0.0206658	−	0.196622i
$325$	7.86379	−	24.2022i	0.436204	−	1.34250i
$326$	0.222625	−	0.685170i	0.0123301	−	0.0379480i
$327$	−0.139304	+	1.32539i	−0.00770353	+	0.0732942i
$328$	1.22925	+	1.36522i	0.0678741	+	0.0753818i
$329$	−0.447504	+	0.497003i	−0.0246717	+	0.0274007i
$330$	0.992390	+	9.44196i	0.0546293	+	0.519763i
$331$	−31.6618	−	6.72991i	−1.74029	−	0.369910i	−0.775175	−	0.631746i	$-0.782339\pi$
$331$	−31.6618	−	6.72991i	−1.74029	−	0.369910i	−0.965112	+	0.261837i	$0.915672\pi$
$332$	−19.6491	+	8.74834i	−1.07838	+	0.480128i
$333$	18.4124	+	13.3774i	1.00899	+	0.733075i
$334$	−7.11100	−	3.16602i	−0.389097	−	0.173237i
$335$	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	$0.0274532\pi$
$338$	−3.05741	+	0.649872i	−0.166301	+	0.0353484i
$339$	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
$344$	−17.0125	+	3.61612i	−0.917253	+	0.194968i
$345$	−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	−0.969970	−	0.243224i	$-0.921795\pi$
$347$	−12.9580	−	22.4440i	−0.695624	−	1.20486i	0.274347	−	0.961631i	$-0.411538\pi$
$348$	6.15310	+	2.73954i	0.329841	+	0.146855i
$349$	−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	$0.747837\pi$
$350$	−4.20535	+	1.87234i	−0.224785	+	0.100081i
$351$	13.3188	+	2.83100i	0.710905	+	0.151107i
$352$	2.49837	+	23.7704i	0.133163	+	1.26697i
$353$	−7.80807	+	8.67174i	−0.415582	+	0.461550i	−0.914195	−	0.405274i	$-0.867176\pi$
$353$	−7.80807	+	8.67174i	−0.415582	+	0.461550i	0.498614	+	0.866824i	$0.333843\pi$
$354$	−0.386052	−	0.428755i	−0.0205185	−	0.0227881i
$355$	2.99805	−	28.5245i	0.159120	−	1.51393i
$356$	−2.08936	+	6.43039i	−0.110736	+	0.340810i
$357$	−0.278556	+	0.857307i	−0.0147427	+	0.0453735i
$358$	0.00948912	−	0.0902830i	0.000501516	−	0.00477160i
$359$	17.5311	+	19.4703i	0.925257	+	1.02760i	0.999539	+	0.0303649i	$0.00966692\pi$
$359$	17.5311	+	19.4703i	0.925257	+	1.02760i	−0.0742818	+	0.997237i	$0.523666\pi$
$360$	−13.1771	+	14.6346i	−0.694492	+	0.771312i
$361$	0.477014	+	4.53848i	0.0251060	+	0.238868i
$362$	−5.21465	−	1.10841i	−0.274076	−	0.0582566i
$363$	4.89548	−	2.17961i	0.256946	−	0.114400i
$364$	2.73979	+	1.99058i	0.143604	+	0.104335i
$365$	19.1618	+	8.53138i	1.00297	+	0.446553i
$366$	−0.720830	−	1.24851i	−0.0376784	−	0.0652608i
$367$	13.5073	−	23.3953i	0.705076	−	1.22123i	−0.261589	−	0.965179i	$-0.584246\pi$
$367$	13.5073	−	23.3953i	0.705076	−	1.22123i	0.966664	−	0.256047i	$-0.0824203\pi$
$368$	−3.64825	+	2.65061i	−0.190178	+	0.138173i
$369$	1.61614	−	0.343522i	0.0841331	−	0.0178830i
$370$	−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
$375$	−12.2579	+	2.60550i	−0.632997	+	0.134548i
$376$	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
$379$	−4.23795	−	1.88686i	−0.217689	−	0.0969213i	0.294995	−	0.955499i	$-0.404682\pi$
$379$	−4.23795	−	1.88686i	−0.217689	−	0.0969213i	−0.512684	+	0.858577i	$0.671349\pi$
$380$	−17.3751	−	12.6238i	−0.891325	−	0.647585i
$381$	1.18053	−	0.525606i	0.0604804	−	0.0269276i
$382$	−14.2322	−	3.02514i	−0.728182	−	0.154780i
$383$	−0.524872	−	4.99383i	−0.0268197	−	0.255173i	−0.999714	−	0.0239216i	$-0.992385\pi$
$383$	−0.524872	−	4.99383i	−0.0268197	−	0.255173i	0.972894	−	0.231251i	$-0.0742819\pi$
$384$	6.49004	−	7.20792i	0.331194	−	0.367828i
$385$	7.79432	+	8.65647i	0.397235	+	0.441175i
$386$	0.408159	−	3.88337i	0.0207747	−	0.197658i
$387$	−4.83383	+	14.8770i	−0.245718	+	0.756241i
$388$	2.48644	−	7.65247i	0.126230	−	0.388496i
$389$	1.94442	−	18.4999i	0.0985861	−	0.937984i	−0.827702	−	0.561168i	$-0.810352\pi$
$389$	1.94442	−	18.4999i	0.0985861	−	0.937984i	0.926288	−	0.376816i	$-0.122981\pi$
$390$	−4.49137	−	4.98817i	−0.227429	−	0.252586i
$391$	−2.87447	+	3.19242i	−0.145368	+	0.161448i
$392$	1.63013	+	15.5096i	0.0823339	+	0.783355i
$393$	−5.55462	−	1.18067i	−0.280194	−	0.0595570i
$394$	10.0245	−	4.46318i	0.505025	−	0.224852i
$395$	−42.2763	−	30.7155i	−2.12715	−	1.54547i
$396$	12.5287	+	5.57815i	0.629592	+	0.280312i
$397$	−16.2794	−	28.1968i	−0.817040	−	1.41515i	−0.907854	−	0.419287i	$-0.862280\pi$
$397$	−16.2794	−	28.1968i	−0.817040	−	1.41515i	0.0908142	−	0.995868i	$-0.471053\pi$
$398$	1.46912	−	2.54459i	0.0736404	−	0.127549i
$399$	2.11757	−	1.53850i	0.106011	−	0.0770214i
$400$	−11.7506	+	2.49766i	−0.587529	+	0.124883i
$401$	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
$406$	−2.52053	+	0.535755i	−0.125092	+	0.0265891i
$407$	−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	0.820249	−	0.572007i	$-0.193835\pi$
$409$	−1.72404	−	2.98613i	−0.0852484	−	0.147654i	−0.905497	+	0.424353i	$0.860502\pi$
$410$	−1.76536	−	0.785989i	−0.0871850	−	0.0388173i
$411$	9.30817	+	6.76278i	0.459138	+	0.333583i
$412$	8.69895	−	3.87302i	0.428566	−	0.190810i
$413$	−0.692404	−	0.147175i	−0.0340709	−	0.00724200i
$414$	−0.517148	−	4.92033i	−0.0254164	−	0.241821i
$415$	34.9986	−	38.8699i	1.71801	−	1.90805i
$416$	−11.3071	−	12.5579i	−0.554379	−	0.615700i
$417$	1.76520	−	16.7948i	0.0864424	−	0.822444i
$418$	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	$0.666563\pi$
$420$	0.407026	−	3.87259i	0.0198608	−	0.188963i
$421$	14.5097	+	16.1147i	0.707160	+	0.785381i	0.984499	−	0.175392i	$-0.0561191\pi$
$421$	14.5097	+	16.1147i	0.707160	+	0.785381i	−0.277339	+	0.960772i	$0.589452\pi$
$422$	5.30947	−	5.89676i	0.258461	−	0.287050i
$423$	−0.200151	−	1.90431i	−0.00973165	−	0.0925905i
$424$	8.49974	+	1.80667i	0.412784	+	0.0877399i
$425$	−10.4545	+	4.65467i	−0.507120	+	0.225784i
$426$	−3.89411	−	2.82924i	−0.188670	−	0.137077i
$427$	−1.61589	−	0.719441i	−0.0781985	−	0.0348162i
$428$	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
$431$	11.3667	−	2.41607i	0.547516	−	0.116378i	0.0741552	−	0.997247i	$-0.476374\pi$
$431$	11.3667	−	2.41607i	0.547516	−	0.116378i	0.473361	+	0.880869i	$0.343041\pi$
$432$	−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
$437$	12.2012	−	2.59344i	0.583660	−	0.124061i
$438$	2.84780	−	2.06905i	0.136073	−	0.0988630i
$439$	−9.09662	+	15.7558i	−0.434158	+	0.751984i	−0.997227	−	0.0744265i	$-0.976287\pi$
$439$	−9.09662	+	15.7558i	−0.434158	+	0.751984i	0.563068	+	0.826410i	$0.309621\pi$
$440$	−18.5408	−	32.1136i	−0.883897	−	1.53096i
$441$	12.8134	+	5.70487i	0.610160	+	0.271661i
$442$	−2.12386	−	1.54307i	−0.101021	−	0.0733964i
$443$	16.2249	−	7.22378i	0.770867	−	0.343212i	0.0166706	−	0.999861i	$-0.494693\pi$
$443$	16.2249	−	7.22378i	0.770867	−	0.343212i	0.754196	+	0.656649i	$0.228027\pi$
$444$	14.0129	+	2.97852i	0.665021	+	0.141354i
$445$	−1.71867	−	16.3521i	−0.0814728	−	0.775162i
$446$	4.34782	−	4.82875i	0.205875	−	0.228648i
$447$	−12.1582	−	13.5030i	−0.575062	−	0.638671i
$448$	−0.100304	+	0.954326i	−0.00473890	+	0.0450876i
$449$	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
$451$	−0.325208	+	3.09414i	−0.0153134	+	0.145698i
$452$	−6.50915	−	7.22915i	−0.306165	−	0.340031i
$453$	−9.28226	+	10.3090i	−0.436119	+	0.484359i
$454$	1.56850	+	14.9232i	0.0736132	+	0.700383i
$455$	−8.05549	−	1.71225i	−0.377647	−	0.0802714i
$456$	−7.61203	+	3.38909i	−0.356466	+	0.158709i
$457$	−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	$0.960356\pi$
$458$	10.6802	+	4.75514i	0.499054	+	0.222193i
$459$	−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	$0.349631\pi$
$462$	1.91213	−	0.406436i	0.0889604	−	0.0189091i
$463$	−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	$0.587407\pi$
$468$	−9.48421	+	2.01593i	−0.438408	+	0.0931865i
$469$	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
$472$	2.05862	+	0.916556i	0.0947556	+	0.0421879i
$473$	−23.8296	−	17.3132i	−1.09569	−	0.796064i
$474$	−8.01154	+	3.56697i	−0.367982	+	0.163836i
$475$	32.5034	+	6.90882i	1.49136	+	0.316998i
$476$	−0.159192	−	1.51461i	−0.00729655	−	0.0694220i
$477$	5.22947	−	5.80791i	0.239441	−	0.265926i
$478$	0.272496	+	0.302637i	0.0124637	+	0.0138423i
$479$	−3.47499	+	33.0623i	−0.158776	+	1.51065i	0.567570	+	0.823325i	$0.307884\pi$
$479$	−3.47499	+	33.0623i	−0.158776	+	1.51065i	−0.726346	+	0.687329i	$0.758783\pi$
$480$	−6.00415	+	18.4789i	−0.274051	+	0.843441i
$481$	9.36278	−	28.8157i	0.426906	−	1.31388i
$482$	−1.10777	+	10.5398i	−0.0504577	+	0.480073i
$483$	1.51330	+	1.68069i	0.0688574	+	0.0764739i
$484$	−6.05805	+	6.72814i	−0.275366	+	0.305825i
$485$	2.04530	+	19.4597i	0.0928724	+	0.883621i
$486$	10.8886	+	2.31445i	0.493918	+	0.104986i
$487$	−26.0501	+	11.5982i	−1.18044	+	0.525566i	−0.900672	−	0.434501i	$-0.856925\pi$
$487$	−26.0501	+	11.5982i	−1.18044	+	0.525566i	−0.279770	+	0.960067i	$0.590258\pi$
$488$	4.55544	+	3.30972i	0.206215	+	0.149824i
$489$	−0.861374	−	0.383508i	−0.0389527	−	0.0173428i
$490$	−8.20220	−	14.2066i	−0.370538	−	0.641790i
$491$	−13.9818	+	24.2172i	−0.630991	+	1.09291i	0.356359	+	0.934349i	$0.384018\pi$
$491$	−13.9818	+	24.2172i	−0.630991	+	1.09291i	−0.987350	+	0.158559i	$0.949315\pi$
$492$	0.841402	−	0.611315i	0.0379333	−	0.0275602i
$493$	−6.26606	+	1.33189i	−0.282209	+	0.0599854i
$494$	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
$499$	−40.4024	+	8.58778i	−1.80866	+	0.384442i	−0.983565	−	0.180555i	$-0.942211\pi$
$499$	−40.4024	+	8.58778i	−1.80866	+	0.384442i	−0.825093	+	0.564997i	$0.808877\pi$
$500$	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
$503$	−23.3740	−	10.4068i	−1.04220	−	0.464015i	−0.187021	−	0.982356i	$-0.559883\pi$
$503$	−23.3740	−	10.4068i	−1.04220	−	0.464015i	−0.855174	+	0.518341i	$0.826550\pi$
$504$	3.28043	+	2.38337i	0.146122	+	0.106164i
$505$	12.8957	−	5.74154i	0.573851	−	0.255495i
$506$	9.11245	+	1.93691i	0.405098	+	0.0861062i
$507$	0.427615	+	4.06849i	0.0189911	+	0.180688i
$508$	−1.46088	+	1.62247i	−0.0648160	+	0.0719855i
$509$	16.3721	+	18.1831i	0.725683	+	0.805952i	0.987241	−	0.159236i	$-0.0509030\pi$
$509$	16.3721	+	18.1831i	0.725683	+	0.805952i	−0.261558	+	0.965188i	$0.584236\pi$
$510$	−0.315521	+	3.00198i	−0.0139715	+	0.132930i
$511$	1.33461	−	4.10750i	0.0590396	−	0.181705i
$512$	−4.52814	+	13.9362i	−0.200118	+	0.615898i
$513$	−1.85853	+	17.6828i	−0.0820563	+	0.780713i
$514$	2.08897	+	2.32003i	0.0921404	+	0.102332i
$515$	−15.4944	+	17.2083i	−0.682765	+	0.758287i
$516$	1.02923	+	9.79251i	0.0453095	+	0.431091i
$517$	3.52677	+	0.749638i	0.155107	+	0.0329690i
$518$	−5.00697	+	2.22925i	−0.219994	+	0.0979476i
$519$	15.0776	+	10.9546i	0.661835	+	0.480851i
$520$	23.9502	+	10.6633i	1.05028	+	0.467617i
$521$	−7.48279	−	12.9606i	−0.327827	−	0.567813i	0.654253	−	0.756275i	$-0.272983\pi$
$521$	−7.48279	−	12.9606i	−0.327827	−	0.567813i	−0.982080	+	0.188462i	$0.939650\pi$
$522$	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	$0.451571\pi$
$524$	9.38450	−	1.99474i	0.409964	−	0.0871405i
$525$	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
$530$	−8.94085	+	1.90044i	−0.388366	+	0.0825497i
$531$	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
$534$	−2.52078	−	1.12232i	−0.109085	−	0.0485676i
$535$	−6.98086	−	5.07189i	−0.301809	−	0.219277i
$536$	−4.63309	+	2.06278i	−0.200119	+	0.0890987i
$537$	−0.116216	−	0.0247025i	−0.00501509	−	0.00106599i
$538$	−0.961419	−	9.14729i	−0.0414497	−	0.394368i
$539$	−17.6723	+	19.6271i	−0.761202	+	0.845400i
$540$	17.6992	+	19.6570i	0.761654	+	0.845902i
$541$	−0.180970	+	1.72182i	−0.00778052	+	0.0740267i	−0.997723	−	0.0674427i	$-0.978516\pi$
$541$	−0.180970	+	1.72182i	−0.00778052	+	0.0740267i	0.989943	+	0.141469i	$0.0451827\pi$
$542$	2.94545	−	9.06515i	0.126518	−	0.389382i
$543$	−2.15612	+	6.63586i	−0.0925280	+	0.284772i
$544$	−0.794333	+	7.55757i	−0.0340567	+	0.324028i
$545$	3.66373	+	4.06898i	0.156937	+	0.174296i
$546$	−0.924793	+	1.02709i	−0.0395775	+	0.0439553i
$547$	1.37156	+	13.0495i	0.0586438	+	0.557958i	0.983913	+	0.178648i	$0.0571722\pi$
$547$	1.37156	+	13.0495i	0.0586438	+	0.557958i	−0.925269	+	0.379311i	$0.876161\pi$
$548$	−19.0137	−	4.04149i	−0.812226	−	0.172644i
$549$	4.62646	−	2.05983i	0.197452	−	0.0879115i
$550$	20.0778	+	14.5874i	0.856121	+	0.622008i
$551$	16.9930	+	7.56577i	0.723926	+	0.322313i
$552$	−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
$555$	−34.0764	+	7.24316i	−1.44646	+	0.307455i
$556$	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
$561$	4.75358	−	1.01041i	0.200696	−	0.0426594i
$562$	−8.58993	+	6.24095i	−0.362344	+	0.263259i
$563$	−11.3259	+	19.6171i	−0.477331	+	0.826762i	−0.999662	−	0.0259808i	$-0.991729\pi$
$563$	−11.3259	+	19.6171i	−0.477331	+	0.826762i	0.522331	+	0.852743i	$0.325062\pi$
$564$	−0.602646	−	1.04381i	−0.0253760	−	0.0439525i
$565$	21.6108	+	9.62175i	0.909174	+	0.404790i
$566$	−12.6599	−	9.19798i	−0.532136	−	0.386620i
$567$	1.62785	−	0.724764i	0.0683632	−	0.0304372i
$568$	18.3893	+	3.90877i	0.771598	+	0.164008i
$569$	−4.85451	−	46.1876i	−0.203512	−	1.93629i	−0.329294	−	0.944227i	$-0.606811\pi$
$569$	−4.85451	−	46.1876i	−0.203512	−	1.93629i	0.125783	−	0.992058i	$-0.459856\pi$
$570$	5.86482	−	6.51354i	0.245650	−	0.272822i
$571$	8.36303	+	9.28809i	0.349982	+	0.388694i	0.892273	−	0.451496i	$-0.149110\pi$
$571$	8.36303	+	9.28809i	0.349982	+	0.388694i	−0.542291	+	0.840191i	$0.682443\pi$
$572$	1.90845	−	18.1577i	0.0797965	−	0.759213i
$573$	−5.88463	+	18.1110i	−0.245834	+	0.756600i
$574$	−0.122956	+	0.378421i	−0.00513210	+	0.0157950i
$575$	−3.00119	+	28.5544i	−0.125158	+	1.19080i
$576$	−1.83836	−	2.04170i	−0.0765982	−	0.0850709i
$577$	−20.3980	+	22.6542i	−0.849179	+	0.943109i	−0.998959	−	0.0456107i	$-0.985477\pi$
$577$	−20.3980	+	22.6542i	−0.849179	+	0.943109i	0.149780	+	0.988719i	$0.452143\pi$
$578$	−1.10181	−	10.4831i	−0.0458294	−	0.436038i
$579$	−4.99883	−	1.06253i	−0.207744	−	0.0441574i
$580$	25.2800	−	11.2554i	1.04970	−	0.467355i
$581$	−8.71290	−	6.33030i	−0.361472	−	0.262625i
$582$	2.99985	+	1.33562i	0.124348	+	0.0553631i
$583$	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
$586$	8.36346	−	1.77771i	0.345491	−	0.0734364i
$587$	−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
$592$	−13.9905	+	2.97377i	−0.575005	+	0.122221i
$593$	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
$596$	28.0443	+	12.4861i	1.14874	+	0.511451i
$597$	−3.11111	−	2.26035i	−0.127329	−	0.0925100i
$598$	−6.01701	+	2.67895i	−0.246054	+	0.109550i
$599$	19.1566	+	4.07187i	0.782719	+	0.166372i	0.581905	−	0.813257i	$-0.302308\pi$
$599$	19.1566	+	4.07187i	0.782719	+	0.166372i	0.200815	+	0.979629i	$0.435641\pi$
$600$	−2.00478	−	19.0742i	−0.0818449	−	0.778702i
$601$	−20.3814	+	22.6358i	−0.831373	+	0.923333i	−0.998034	−	0.0626811i	$-0.980035\pi$
$601$	−20.3814	+	22.6358i	−0.831373	+	0.923333i	0.166661	+	0.986014i	$0.446702\pi$
$602$	−2.52066	−	2.79947i	−0.102734	−	0.114098i
$603$	−0.476783	+	4.53629i	−0.0194161	+	0.184732i
$604$	7.24238	−	22.2898i	0.294688	−	0.906958i
$605$	6.80348	−	20.9390i	0.276601	−	0.851290i
$606$	0.247626	−	2.35600i	0.0100591	−	0.0957060i
$607$	−8.94933	−	9.93924i	−0.363242	−	0.403421i	0.533625	−	0.845721i	$-0.320829\pi$
$607$	−8.94933	−	9.93924i	−0.363242	−	0.403421i	−0.896867	+	0.442300i	$0.854163\pi$
$608$	14.7648	−	16.3980i	0.598793	−	0.665027i
$609$	0.352526	+	3.35406i	0.0142851	+	0.135914i
$610$	−5.79363	−	1.23147i	−0.234577	−	0.0498609i
$611$	−2.32875	+	1.03683i	−0.0942112	+	0.0419455i
$612$	3.52761	+	2.56296i	0.142595	+	0.103601i
$613$	4.74606	+	2.11308i	0.191691	+	0.0853465i	0.500338	−	0.865830i	$-0.333209\pi$
$613$	4.74606	+	2.11308i	0.191691	+	0.0853465i	−0.308646	+	0.951177i	$0.599876\pi$
$614$	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
$617$	29.3572	−	6.24007i	1.18188	−	0.251216i	0.425258	−	0.905072i	$-0.360183\pi$
$617$	29.3572	−	6.24007i	1.18188	−	0.251216i	0.756619	+	0.653856i	$0.226850\pi$
$618$	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
$623$	−3.31153	+	0.703887i	−0.132674	+	0.0282006i
$624$	−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
$627$	−12.8913	−	5.73957i	−0.514829	−	0.229216i
$628$	18.6831	+	13.5740i	0.745535	+	0.541663i
$629$	−12.4474	+	5.54194i	−0.496310	+	0.220972i
$630$	−4.17206	−	0.886800i	−0.166219	−	0.0353309i
$631$	1.08032	+	10.2786i	0.0430070	+	0.409184i	0.994754	+	0.102299i	$0.0326200\pi$
$631$	1.08032	+	10.2786i	0.0430070	+	0.409184i	−0.951747	+	0.306885i	$0.900713\pi$
$632$	22.9196	−	25.4548i	0.911692	−	1.01254i
$633$	−6.94898	−	7.71762i	−0.276197	−	0.306748i
$634$	0.630363	−	5.99751i	0.0250349	−	0.238191i
$635$	1.64064	−	5.04936i	0.0651067	−	0.200378i
$636$	1.52020	−	4.67868i	0.0602797	−	0.185522i
$637$	1.95181	−	18.5703i	0.0773336	−	0.735780i
$638$	9.29576	+	10.3240i	0.368023	+	0.408731i
$639$	11.3140	−	12.5655i	0.447576	−	0.497083i
$640$	−4.16538	−	39.6310i	−0.164651	−	1.56655i
$641$	0.0990394	+	0.0210515i	0.00391182	+	0.000831483i	0.209867	−	0.977730i	$-0.432697\pi$
$641$	0.0990394	+	0.0210515i	0.00391182	+	0.000831483i	−0.205955	+	0.978561i	$0.566030\pi$
$642$	−1.32290	+	0.588994i	−0.0522108	+	0.0232457i
$643$	−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	$0.787146\pi$
$644$	−3.49060	−	1.55412i	−0.137549	−	0.0612407i
$645$	−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	$0.368314\pi$
$648$	−5.54854	+	1.17938i	−0.217967	+	0.0463304i
$649$	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	$-0.257382\pi$
$654$	0.898800	−	0.191046i	0.0351459	−	0.00747049i
$655$	−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
$658$	0.421256	+	0.187555i	0.0164223	+	0.00731166i
$659$	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	$0.646847\pi$
$660$	−19.1780	+	8.53861i	−0.746504	+	0.332365i
$661$	−37.0563	−	7.87657i	−1.44132	−	0.306363i	−0.580083	−	0.814558i	$-0.696980\pi$
$661$	−37.0563	−	7.87657i	−1.44132	−	0.306363i	−0.861242	+	0.508195i	$0.830313\pi$
$662$	2.33289	+	22.1960i	0.0906705	+	0.862672i
$663$	−2.29905	+	2.55335i	−0.0892876	+	0.0991639i
$664$	22.9407	+	25.4783i	0.890273	+	0.988748i
$665$	1.12408	−	10.6949i	0.0435900	−	0.414731i
$666$	4.84913	−	14.9241i	0.187900	−	0.578297i
$667$	−4.96657	+	15.2855i	−0.192306	+	0.591858i
$668$	1.79913	−	17.1175i	0.0696102	−	0.662297i
$669$	−5.69038	−	6.31981i	−0.220003	−	0.244338i
$670$	3.56964	−	3.96449i	0.137907	−	0.153162i
$671$	0.996790	+	9.48382i	0.0384806	+	0.366119i
$672$	3.91326	+	0.831790i	0.150957	+	0.0320870i
$673$	−6.50454	+	2.89601i	−0.250732	+	0.111633i	−0.528254	−	0.849086i	$-0.677153\pi$
$673$	−6.50454	+	2.89601i	−0.250732	+	0.111633i	0.277523	+	0.960719i	$0.410487\pi$
$674$	−15.4702	−	11.2398i	−0.595891	−	0.432940i
$675$	−37.3877	−	16.6461i	−1.43905	−	0.640707i
$676$	−3.45577	−	5.98557i	−0.132914	−	0.230214i
$677$	24.0305	−	41.6220i	0.923567	−	1.59966i	0.129716	−	0.991551i	$-0.458593\pi$
$677$	24.0305	−	41.6220i	0.923567	−	1.59966i	0.793850	−	0.608113i	$-0.208073\pi$
$678$	3.21177	−	2.33349i	0.123347	−	0.0896171i
$679$	3.94088	−	0.837659i	0.151237	−	0.0321464i
$680$	−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
$685$	46.2375	−	9.82809i	1.76664	−	0.375512i
$686$	−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
$689$	−9.50490	−	4.23185i	−0.362108	−	0.161221i
$690$	6.12682	+	4.45140i	0.233244	+	0.169462i
$691$	24.8969	−	11.0848i	0.947124	−	0.421687i	0.125740	−	0.992063i	$-0.459869\pi$
$691$	24.8969	−	11.0848i	0.947124	−	0.421687i	0.821383	+	0.570376i	$0.193203\pi$
$692$	−30.7990	−	6.54653i	−1.17080	−	0.248862i
$693$	0.717801	+	6.82942i	0.0272670	+	0.259428i
$694$	−11.9567	+	13.2792i	−0.453868	+	0.504072i
$695$	−46.4253	−	51.5605i	−1.76101	−	1.95580i
$696$	1.12223	−	10.6773i	0.0425381	−	0.404723i
$697$	−0.305671	+	0.940760i	−0.0115781	+	0.0356338i
$698$	−1.19187	+	3.66820i	−0.0451130	+	0.138844i
$699$	0.927806	−	8.82749i	0.0350929	−	0.333886i
$700$	−6.81097	−	7.56435i	−0.257430	−	0.285905i
$701$	5.68035	−	6.30867i	0.214544	−	0.238275i	−0.626261	−	0.779614i	$-0.715416\pi$
$701$	5.68035	−	6.30867i	0.214544	−	0.238275i	0.840805	+	0.541338i	$0.182082\pi$
$702$	−0.981352	−	9.33694i	−0.0370387	−	0.352400i
$703$	38.6992	+	8.22578i	1.45957	+	0.310241i
$704$	4.72606	−	2.10418i	0.178120	−	0.0793042i
$705$	2.37125	+	1.72281i	0.0893065	+	0.0648849i
$706$	7.35009	+	3.27247i	0.276624	+	0.123161i
$707$	−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	$0.444717\pi$
$710$	−19.3436	+	4.11162i	−0.725954	+	0.154306i
$711$	−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
$716$	0.196346	−	0.0417346i	0.00733779	−	0.00155970i
$717$	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	0.961278	−	0.275582i	$-0.0888706\pi$
$719$	6.48843	+	11.2383i	0.241978	+	0.419118i	−0.719300	+	0.694700i	$0.755537\pi$
$720$	−10.1686	−	4.52734i	−0.378960	−	0.168724i
$721$	3.85733	+	2.80252i	0.143655	+	0.104371i
$722$	2.87446	−	1.27979i	0.106976	−	0.0476289i
$723$	13.5672	+	2.88380i	0.504570	+	0.107250i
$724$	−1.23220	−	11.7236i	−0.0457944	−	0.435704i
$725$	−28.6492	+	31.8182i	−1.06401	+	1.18170i
$726$	−2.47233	−	2.74580i	−0.0917567	−	0.101906i
$727$	1.29856	−	12.3550i	0.0481609	−	0.458220i	−0.943691	−	0.330827i	$-0.892672\pi$
$727$	1.29856	−	12.3550i	0.0481609	−	0.458220i	0.991852	−	0.127393i	$-0.0406610\pi$
$728$	1.66812	−	5.13393i	0.0618245	−	0.190276i
$729$	2.33825	−	7.19640i	0.0866020	−	0.266533i
$730$	1.51172	−	14.3830i	0.0559511	−	0.532339i
$731$	−6.26638	−	6.95952i	−0.231771	−	0.257407i
$732$	2.13304	−	2.36898i	0.0788395	−	0.0875602i
$733$	3.57041	+	33.9702i	0.131876	+	1.25472i	0.837621	+	0.546252i	$0.183946\pi$
$733$	3.57041	+	33.9702i	0.131876	+	1.25472i	−0.705744	+	0.708467i	$0.749387\pi$
$734$	−18.2193	−	3.87264i	−0.672488	−	0.142942i
$735$	−19.6137	+	8.73260i	−0.723464	+	0.322107i
$736$	15.4244	+	11.2065i	0.568552	+	0.413077i
$737$	−7.84633	−	3.49341i	−0.289023	−	0.128682i
$738$	−0.569607	−	0.986589i	−0.0209675	−	0.0363168i
$739$	−6.18747	+	10.7170i	−0.227610	+	0.394231i	−0.957099	−	0.289761i	$-0.906424\pi$
$739$	−6.18747	+	10.7170i	−0.227610	+	0.394231i	0.729490	+	0.683992i	$0.239758\pi$
$740$	47.6171	−	34.5959i	1.75044	−	1.27177i
$741$	9.75868	−	2.07427i	0.358494	−	0.0762002i
$742$	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
$747$	30.1610	−	6.41092i	1.10353	−	0.234563i
$748$	−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
$751$	−9.85558	−	4.38799i	−0.359635	−	0.160120i	0.218962	−	0.975733i	$-0.429733\pi$
$751$	−9.85558	−	4.38799i	−0.359635	−	0.160120i	−0.578597	+	0.815614i	$0.696400\pi$
$752$	0.973546	+	0.707322i	0.0355016	+	0.0257934i
$753$	4.98876	−	2.22114i	0.181801	−	0.0809429i
$754$	−9.60724	−	2.04208i	−0.349875	−	0.0743682i
$755$	5.95746	+	56.6814i	0.216814	+	2.06285i
$756$	3.64435	−	4.04746i	0.132544	−	0.147205i
$757$	−27.5024	−	30.5445i	−0.999591	−	1.11016i	−0.993912	−	0.110175i	$-0.964859\pi$
$757$	−27.5024	−	30.5445i	−0.999591	−	1.11016i	−0.00567884	−	0.999984i	$-0.501808\pi$
$758$	−0.334341	+	3.18104i	−0.0121438	+	0.115541i
$759$	3.76776	−	11.5960i	0.136761	−	0.420907i
$760$	−10.5788	+	32.5582i	−0.383733	+	1.18101i
$761$	2.05508	−	19.5528i	0.0744967	−	0.708789i	−0.891987	−	0.452061i	$-0.850689\pi$
$761$	2.05508	−	19.5528i	0.0744967	−	0.708789i	0.966484	−	0.256728i	$-0.0826444\pi$
$762$	−0.596194	−	0.662140i	−0.0215978	−	0.0239868i
$763$	0.754378	−	0.837822i	0.0273103	−	0.0303312i
$764$	−3.36301	−	31.9969i	−0.121669	−	1.15761i
$765$	−10.3718	−	2.20459i	−0.374993	−	0.0797073i
$766$	−3.16285	+	1.40819i	−0.114279	+	0.0508801i
$767$	−2.18283	−	1.58592i	−0.0788174	−	0.0572642i
$768$	−8.18186	−	3.64280i	−0.295238	−	0.131448i
$769$	−1.89417	−	3.28080i	−0.0683055	−	0.118309i	0.829850	−	0.557986i	$-0.188426\pi$
$769$	−1.89417	−	3.28080i	−0.0683055	−	0.118309i	−0.898155	+	0.439678i	$0.855093\pi$
$770$	4.01575	−	6.95549i	0.144718	−	0.250658i
$771$	3.30558	−	2.40165i	0.119048	−	0.0864932i
$772$	8.44549	−	1.79514i	0.303960	−	0.0646087i
$773$	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
$778$	−12.5456	+	2.66664i	−0.449780	+	0.0956037i
$779$	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
$782$	2.70587	+	1.20473i	0.0967617	+	0.0430811i
$783$	−18.5341	−	13.4658i	−0.662354	−	0.481228i
$784$	−8.05266	+	3.58527i	−0.287595	+	0.128046i
$785$	−54.9316	−	11.6761i	−1.96059	−	0.416737i
$786$	0.409274	+	3.89399i	0.0145983	+	0.138894i
$787$	17.3617	−	19.2821i	0.618876	−	0.687332i	−0.349469	−	0.936948i	$-0.613638\pi$
$787$	17.3617	−	19.2821i	0.618876	−	0.687332i	0.968345	+	0.249616i	$0.0803045\pi$
$788$	16.2356	+	18.0314i	0.578369	+	0.642344i
$789$	−0.236653	+	2.25160i	−0.00842505	+	0.0801590i
$790$	−11.1340	+	34.2670i	−0.396130	+	1.21916i
$791$	1.50518	−	4.63247i	0.0535181	−	0.164712i
$792$	2.28504	−	21.7408i	0.0811955	−	0.772524i
$793$	−4.51128	−	5.01029i	−0.160200	−	0.177921i
$794$	−15.0214	+	16.6829i	−0.533088	+	0.592054i
$795$	1.25049	+	11.8976i	0.0443502	+	0.421964i
$796$	6.35504	+	1.35080i	0.225248	+	0.0478780i
$797$	16.9030	−	7.52569i	0.598734	−	0.266574i	−0.0849105	−	0.996389i	$-0.527060\pi$
$797$	16.9030	−	7.52569i	0.598734	−	0.266574i	0.683645	+	0.729815i	$0.260394\pi$
$798$	−1.46005	−	1.06079i	−0.0516851	−	0.0375514i
$799$	1.04725	+	0.466264i	0.0370489	+	0.0164952i
$800$	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
$803$	−22.7752	+	4.84102i	−0.803720	+	0.170836i
$804$	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
$809$	35.9448	−	7.64030i	1.26375	−	0.268619i	0.473168	−	0.880972i	$-0.343110\pi$
$809$	35.9448	−	7.64030i	1.26375	−	0.268619i	0.790584	+	0.612353i	$0.209777\pi$
$810$	4.82731	−	3.50725i	0.169614	−	0.123232i
$811$	19.7151	−	34.1475i	0.692289	−	1.19908i	−0.278797	−	0.960350i	$-0.589936\pi$
$811$	19.7151	−	34.1475i	0.692289	−	1.19908i	0.971086	−	0.238730i	$-0.0767310\pi$
$812$	−2.84894	−	4.93451i	−0.0999782	−	0.173167i
$813$	−11.3964	−	5.07402i	−0.399690	−	0.177954i
$814$	23.9051	+	17.3680i	0.837872	+	0.608749i
$815$	−3.53896	+	1.57565i	−0.123964	+	0.0551924i
$816$	1.58653	+	0.337226i	0.0555395	+	0.0118053i
$817$	2.84243	+	27.0439i	0.0994441	+	0.946147i
$818$	−1.59081	+	1.76677i	−0.0556214	+	0.0617738i
$819$	−3.24863	−	3.60797i	−0.113516	−	0.126073i
$820$	0.446647	−	4.24956i	0.0155976	−	0.148401i
$821$	−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
$823$	−4.06252	+	38.6523i	−0.141611	+	1.34733i	0.660800	+	0.750562i	$0.270217\pi$
$823$	−4.06252	+	38.6523i	−0.141611	+	1.34733i	−0.802410	+	0.596773i	$0.796449\pi$
$824$	−10.1562	−	11.2796i	−0.353808	−	0.392943i
$825$	21.7340	−	24.1380i	0.756680	−	0.840379i
$826$	0.0510175	+	0.485399i	0.00177513	+	0.0168892i
$827$	33.1947	+	7.05575i	1.15429	+	0.245352i	0.745009	−	0.667055i	$-0.232445\pi$
$827$	33.1947	+	7.05575i	1.15429	+	0.245352i	0.409284	+	0.912407i	$0.365779\pi$
$828$	9.99393	−	4.44959i	0.347313	−	0.154634i
$829$	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	$0.607320\pi$
$830$	−32.9458	−	14.6684i	−1.14356	−	0.509148i
$831$	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
$834$	−11.3892	+	2.42086i	−0.394377	+	0.0838274i
$835$	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	$-0.483254\pi$
$840$	−6.07121	+	1.29048i	−0.209477	+	0.0445256i
$841$	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
$844$	16.0286	+	7.13641i	0.551728	+	0.245645i
$845$	13.5975	+	9.87918i	0.467769	+	0.339854i
$846$	−1.20610	+	0.536989i	−0.0414665	+	0.0184621i
$847$	−4.43424	−	0.942526i	−0.152362	−	0.0323856i
$848$	0.513402	+	4.88470i	0.0176303	+	0.167741i
$849$	−13.7042	+	15.2201i	−0.470328	+	0.522352i
$850$	5.27978	+	5.86379i	0.181095	+	0.201126i
$851$	−3.57328	+	33.9975i	−0.122490	+	1.16542i
$852$	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	$-0.136950\pi$
$854$	−0.127481	+	1.21290i	−0.00436232	+	0.0415047i
$855$	20.6020	+	22.8809i	0.704575	+	0.782510i
$856$	3.78459	−	4.20321i	0.129355	−	0.143663i
$857$	−1.33013	−	12.6553i	−0.0454363	−	0.432298i	−0.993467	−	0.114119i	$-0.963595\pi$
$857$	−1.33013	−	12.6553i	−0.0454363	−	0.432298i	0.948031	−	0.318179i	$-0.103071\pi$
$858$	7.28828	+	1.54917i	0.248818	+	0.0528878i
$859$	19.3255	−	8.60425i	0.659376	−	0.293573i	−0.0496383	−	0.998767i	$-0.515807\pi$
$859$	19.3255	−	8.60425i	0.659376	−	0.293573i	0.709014	+	0.705194i	$0.249140\pi$
$860$	32.7281	+	23.7784i	1.11602	+	0.810835i
$861$	0.475739	+	0.211813i	0.0162132	+	0.00721856i
$862$	−4.00618	−	6.93891i	−0.136451	−	0.236340i
$863$	4.66987	−	8.08845i	0.158964	−	0.275334i	−0.775531	−	0.631309i	$-0.782518\pi$
$863$	4.66987	−	8.08845i	0.158964	−	0.275334i	0.934495	+	0.355975i	$0.115851\pi$
$864$	−21.9861	+	15.9739i	−0.747983	+	0.543441i
$865$	74.8969	−	15.9198i	2.54657	−	0.541290i
$866$	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
$871$	5.93966	−	1.26251i	0.201258	−	0.0427786i
$872$	−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
$875$	9.68484	+	4.31197i	0.327407	+	0.145771i
$876$	6.29703	+	4.57506i	0.212757	+	0.154577i
$877$	20.4956	−	9.12524i	0.692088	−	0.308137i	−0.0303833	−	0.999538i	$-0.509673\pi$
$877$	20.4956	−	9.12524i	0.692088	−	0.308137i	0.722471	+	0.691401i	$0.243006\pi$
$878$	12.2700	+	2.60807i	0.414092	+	0.0880180i
$879$	−1.16973	−	11.1292i	−0.0394540	−	0.375380i
$880$	14.0246	−	15.5759i	0.472770	−	0.525064i
$881$	31.0687	+	34.5053i	1.04673	+	1.16251i	0.986405	+	0.164335i	$0.0525477\pi$
$881$	31.0687	+	34.5053i	1.04673	+	1.16251i	0.0603272	+	0.998179i	$0.480786\pi$
$882$	1.01087	−	9.61782i	0.0340379	−	0.323849i
$883$	−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
$885$	−0.324282	+	3.08534i	−0.0109006	+	0.103713i
$886$	−8.19392	−	9.10027i	−0.275280	−	0.305730i
$887$	19.1940	−	21.3171i	0.644473	−	0.715760i	−0.329059	−	0.944309i	$-0.606732\pi$
$887$	19.1940	−	21.3171i	0.644473	−	0.715760i	0.973532	+	0.228550i	$0.0733983\pi$
$888$	−2.38693	−	22.7102i	−0.0801003	−	0.762103i
$889$	−1.06930	−	0.227287i	−0.0358632	−	0.00762297i
$890$	−10.3566	+	4.61107i	−0.347155	+	0.154563i
$891$	−7.77192	−	5.64663i	−0.260369	−	0.189169i
$892$	13.1255	+	5.84387i	0.439476	+	0.195667i
$893$	−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
$896$	−8.02583	+	1.70594i	−0.268124	+	0.0569916i
$897$	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
$902$	2.09826	−	0.446000i	0.0698646	−	0.0148502i
$903$	−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
$906$	8.73781	+	3.89032i	0.290294	+	0.129247i
$907$	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	$0.579907\pi$
$908$	−30.3113	+	13.4955i	−1.00592	+	0.447863i
$909$	8.13994	+	1.73020i	0.269985	+	0.0573871i
$910$	0.593543	+	5.64718i	0.0196757	+	0.187202i
$911$	19.2927	−	21.4267i	0.639194	−	0.709897i	−0.333301	−	0.942821i	$-0.608162\pi$
$911$	19.2927	−	21.4267i	0.639194	−	0.709897i	0.972495	+	0.232923i	$0.0748291\pi$
$912$	−3.15140	−	3.49998i	−0.104353	−	0.115896i
$913$	−6.06913	+	57.7440i	−0.200859	+	1.91105i
$914$	−6.64760	+	20.4592i	−0.219883	+	0.676731i
$915$	−2.39551	+	7.37263i	−0.0791932	+	0.243732i
$916$	−2.70216	+	25.7093i	−0.0892819	+	0.849460i
$917$	3.21448	+	3.57004i	0.106151	+	0.117893i
$918$	−2.82505	+	3.13754i	−0.0932407	+	0.103554i
$919$	−5.02388	−	47.7990i	−0.165723	−	1.57675i	−0.689114	−	0.724653i	$-0.742000\pi$
$919$	−5.02388	−	47.7990i	−0.165723	−	1.57675i	0.523392	−	0.852092i	$-0.324667\pi$
$920$	−28.9329	−	6.14988i	−0.953890	−	0.202756i
$921$	25.3251	−	11.2754i	0.834490	−	0.371539i
$922$	3.71975	+	2.70256i	0.122503	+	0.0890039i
$923$	−20.5640	−	9.15567i	−0.676872	−	0.301363i
$924$	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
$927$	−13.3527	+	2.83821i	−0.438561	+	0.0932191i
$928$	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
$933$	−2.10203	+	0.446800i	−0.0688173	+	0.0146276i
$934$	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
$937$	−11.7671	−	5.23903i	−0.384413	−	0.171152i	0.205426	−	0.978673i	$-0.434142\pi$
$937$	−11.7671	−	5.23903i	−0.384413	−	0.171152i	−0.589839	+	0.807521i	$0.700809\pi$
$938$	−0.888663	−	0.645651i	−0.0290159	−	0.0210813i
$939$	−8.85850	+	3.94406i	−0.289086	+	0.128709i
$940$	−4.84374	−	1.02957i	−0.157985	−	0.0335808i
$941$	−5.23053	−	49.7651i	−0.170510	−	1.62230i	−0.660679	−	0.750669i	$-0.729731\pi$
$941$	−5.23053	−	49.7651i	−0.170510	−	1.62230i	0.490168	−	0.871628i	$-0.336935\pi$
$942$	−6.30630	+	7.00385i	−0.205470	+	0.228198i
$943$	1.66061	+	1.84429i	0.0540768	+	0.0600584i
$944$	−0.133138	+	1.26672i	−0.00433328	+	0.0412284i
$945$	−4.09278	+	12.5963i	−0.133138	+	0.409757i
$946$	−6.27584	+	19.3151i	−0.204045	+	0.627987i
$947$	5.42168	−	51.5838i	0.176181	−	1.67625i	−0.447280	−	0.894394i	$-0.647607\pi$
$947$	5.42168	−	51.5838i	0.176181	−	1.67625i	0.623461	−	0.781854i	$-0.285726\pi$
$948$	−12.9755	−	14.4107i	−0.421423	−	0.468038i
$949$	11.0151	−	12.2335i	0.357566	−	0.397118i
$950$	−2.39491	−	22.7860i	−0.0777011	−	0.739277i
$951$	−7.72024	−	1.64099i	−0.250346	−	0.0532127i
$952$	−2.21769	+	0.987377i	−0.0718756	+	0.0320011i
$953$	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	$0.601863\pi$
$954$	−4.92274	−	2.19174i	−0.159379	−	0.0709603i
$955$	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
$958$	22.4209	−	4.76571i	0.724386	−	0.153973i
$959$	−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
$964$	−22.9217	+	4.87216i	−0.738258	+	0.156922i
$965$	−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	−0.938471	−	0.345358i	$-0.887757\pi$
$967$	−23.8923	−	41.3827i	−0.768324	−	1.33078i	0.170146	−	0.985419i	$-0.445576\pi$
$968$	13.1836	+	5.86974i	0.423738	+	0.188660i
$969$	−3.62969	−	2.63713i	−0.116603	−	0.0847167i
$970$	12.3249	−	5.48739i	0.395728	−	0.176189i
$971$	30.4210	+	6.46619i	0.976257	+	0.207510i	0.668301	−	0.743891i	$-0.267022\pi$
$971$	30.4210	+	6.46619i	0.976257	+	0.207510i	0.307956	+	0.951401i	$0.400355\pi$
$972$	2.57294	+	24.4799i	0.0825270	+	0.785192i
$973$	−9.55917	+	10.6165i	−0.306453	+	0.340351i
$974$	13.1559	+	14.6111i	0.421541	+	0.468169i
$975$	−2.40040	+	22.8383i	−0.0768743	+	0.731410i
$976$	−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	$0.985098\pi$
$978$	−0.0679557	+	0.646555i	−0.00217298	+	0.0206746i
$979$	12.2130	+	13.5639i	0.390329	+	0.433504i
$980$	24.2715	−	26.9563i	0.775326	−	0.861087i
$981$	0.337403	+	3.21018i	0.0107725	+	0.102493i
$982$	18.8594	+	4.00869i	0.601828	+	0.127922i
$983$	34.3282	−	15.2839i	1.09490	−	0.487480i	0.221834	−	0.975084i	$-0.428796\pi$
$983$	34.3282	−	15.2839i	1.09490	−	0.487480i	0.873065	+	0.487604i	$0.162129\pi$
$984$	−1.34118	−	0.974425i	−0.0427553	−	0.0310635i
$985$	−53.9032	−	23.9992i	−1.71750	−	0.764679i
$986$	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
$989$	−22.9823	+	4.88504i	−0.730796	+	0.155335i
$990$	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
$995$	−15.4542	+	3.28488i	−0.489930	+	0.104138i
$996$	15.7025	−	11.4086i	0.497554	−	0.361494i
$997$	14.7866	−	25.6112i	0.468298	−	0.811115i	−0.531046	−	0.847343i	$-0.678201\pi$
$997$	14.7866	−	25.6112i	0.468298	−	0.811115i	0.999344	+	0.0362278i	$0.0115342\pi$
$998$	14.2397	+	24.6639i	0.450751	+	0.780724i
$999$	−44.5145	−	19.8191i	−1.40838	−	0.627050i

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.18.2	✓	16	31.21	odd	30
31.2.g.a.19.2	yes	16	31.27	odd	10
279.2.y.c.19.1		16	93.89	even	10
279.2.y.c.235.1		16	93.83	even	30
496.2.bg.c.49.1		16	124.83	even	30
496.2.bg.c.81.1		16	124.27	even	10
775.2.bl.a.576.1		16	155.114	odd	30
775.2.bl.a.701.1		16	155.89	odd	10
775.2.ck.a.49.2		32	155.83	even	60
775.2.ck.a.49.3		32	155.52	even	60
775.2.ck.a.174.2		32	155.27	even	20
775.2.ck.a.174.3		32	155.58	even	20
961.2.a.i.1.3		8	31.3	odd	30
961.2.a.j.1.3		8	31.28	even	15
961.2.c.i.439.3		16	31.18	even	15
961.2.c.i.521.3		16	31.16	even	5
961.2.c.j.439.3		16	31.13	odd	30
961.2.c.j.521.3		16	31.15	odd	10
961.2.d.n.374.4		16	31.7	even	15
961.2.d.n.388.4		16	31.19	even	15
961.2.d.o.374.4		16	31.24	odd	30
961.2.d.o.388.4		16	31.12	odd	30
961.2.d.p.531.1		16	31.6	odd	6
961.2.d.p.628.1		16	31.17	odd	30
961.2.d.q.531.1		16	31.25	even	3
961.2.d.q.628.1		16	31.14	even	15
961.2.g.j.338.2		16	31.2	even	5
961.2.g.j.816.2		16	31.20	even	15
961.2.g.k.338.2		16	31.29	odd	10
961.2.g.k.816.2		16	31.11	odd	30
961.2.g.l.235.2		16	31.10	even	15
961.2.g.l.732.2		16	31.4	even	5
961.2.g.m.844.1		16	1.1	even	1	trivial
961.2.g.m.846.1		16	31.9	even	15	inner
961.2.g.n.448.1		16	31.8	even	5
961.2.g.n.547.1		16	31.5	even	3
961.2.g.s.844.1		16	31.30	odd	2
961.2.g.s.846.1		16	31.22	odd	30
961.2.g.t.448.1		16	31.23	odd	10
961.2.g.t.547.1		16	31.26	odd	6
8649.2.a.be.1.6		8	93.59	odd	30
8649.2.a.bf.1.6		8	93.65	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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Varieties

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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.m.844.1

Level	$961$
Weight	$2$
Character	961.844
Analytic conductor	$7.674$
Analytic rank	$0$
Dimension	$16$
Inner twists	$2$