LMFDB - Embedded newform 961.2.g.n.448.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(235,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [16,4,-3,6,-3,-11,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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			448.1
Root			$1.83925i$ of defining polynomial
Character	$\chi$	$=$	961.448
Dual form			961.2.g.n.547.1

$q$-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 $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{11}{15}\right)$

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	−0.997695	−	0.0678533i	$-0.978385\pi$
$2$	−0.213065	+	0.655747i	−0.150660	+	0.463683i	0.847036	+	0.531536i	$0.178385\pi$
$3$	0.603824	−	0.670615i	0.348618	−	0.387179i	−0.543178	−	0.839618i	$-0.682779\pi$
$3$	0.603824	−	0.670615i	0.348618	−	0.387179i	0.891796	+	0.452438i	$0.149446\pi$
$4$	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
$7$	−0.0797964	+	0.759212i	−0.0301602	+	0.286955i	0.969038	+	0.246913i	$0.0794160\pi$
$7$	−0.0797964	+	0.759212i	−0.0301602	+	0.286955i	−0.999198	+	0.0400426i	$0.987251\pi$
$8$	−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	0.247832	−	0.968803i	$-0.420282\pi$
$11$	3.75981	−	1.67397i	1.13362	−	0.504722i	0.885793	+	0.464081i	$0.153615\pi$
$12$	1.34574	−	0.286045i	0.388480	−	0.0825741i
$13$	−2.84617	−	0.604971i	−0.789384	−	0.167789i	−0.204458	−	0.978875i	$-0.565543\pi$
$13$	−2.84617	−	0.604971i	−0.789384	−	0.167789i	−0.584926	+	0.811086i	$0.698877\pi$
$14$	−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	0.256620	−	0.966512i	$-0.417391\pi$
$17$	−1.19540	−	0.532225i	−0.289926	−	0.129083i	−0.546546	+	0.837429i	$0.684058\pi$
$18$	−1.47407	−	0.313324i	−0.347443	−	0.0738512i
$19$	3.71651	−	0.789969i	0.852626	−	0.181231i	0.239187	−	0.970973i	$-0.423119\pi$
$19$	3.71651	−	0.789969i	0.852626	−	0.181231i	0.613439	+	0.789742i	$0.289786\pi$
$20$	−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	−0.829187	−	0.558971i	$-0.811196\pi$
$23$	−2.65597	+	1.92967i	−0.553808	+	0.402365i	0.275380	+	0.961336i	$0.411196\pi$
$24$	−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	0.706664	+	0.707549i	$0.250199\pi$
$29$	−1.51283	+	4.65602i	−0.280926	+	0.864602i	−0.987590	+	0.157052i	$0.949801\pi$
$30$	−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	−0.875784	−	0.482704i	$-0.839655\pi$
$37$	−5.20639	−	9.01773i	−0.855925	−	1.48251i	0.0198583	−	0.999803i	$-0.493679\pi$
$38$	−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	0.781347	−	0.624096i	$-0.214533\pi$
$41$	0.505826	+	0.561777i	0.0789968	+	0.0877349i	−0.702351	+	0.711831i	$0.747866\pi$
$42$	−0.433918	+	0.193193i	−0.0669551	+	0.0298103i
$43$	−7.00049	+	1.48800i	−1.06757	+	0.226918i	−0.708008	−	0.706205i	$-0.750406\pi$
$43$	−7.00049	+	1.48800i	−1.06757	+	0.226918i	−0.359558	+	0.933123i	$0.617072\pi$
$44$	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	0.929369	−	0.369152i	$-0.120352\pi$
$47$	−0.270719	−	0.833189i	−0.0394885	−	0.121533i	−0.968857	+	0.247619i	$0.920352\pi$
$48$	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	0.989736	+	0.142908i	$0.0456452\pi$
$53$	0.373763	+	3.55612i	0.0513403	+	0.488470i	−0.938396	+	0.345562i	$0.887688\pi$
$54$	−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	−0.701401	−	0.712767i	$-0.747442\pi$
$59$	0.620465	−	0.689096i	0.0807776	−	0.0897126i	0.782179	+	0.623054i	$0.214108\pi$
$60$	−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	−0.795221	−	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
$69$	−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	0.931527	+	0.363673i	$0.118478\pi$
$71$	0.808641	+	7.69371i	0.0959680	+	0.913075i	−0.835559	+	0.549401i	$0.814856\pi$
$72$	−3.55415	−	3.94728i	−0.418860	−	0.465192i
$73$	5.16836	−	2.30110i	0.604911	−	0.269324i	−0.0813424	−	0.996686i	$-0.525921\pi$
$73$	5.16836	−	2.30110i	0.604911	−	0.269324i	0.686254	+	0.727362i	$0.259254\pi$
$74$	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	0.972192	−	0.234185i	$-0.0752423\pi$
$79$	12.8762	+	5.73284i	1.44868	+	0.644995i	0.476490	+	0.879180i	$0.341909\pi$
$80$	−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	0.988393	+	0.151918i	$0.0485451\pi$
$83$	9.43990	+	10.4841i	1.03616	+	1.15078i	0.0477709	+	0.998858i	$0.484788\pi$
$84$	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	0.381163	−	0.924508i	$-0.375524\pi$
$89$	−3.58784	−	2.60672i	−0.380310	−	0.276311i	−0.761473	+	0.648196i	$0.775524\pi$
$90$	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	0.783056	−	0.621951i	$-0.213660\pi$
$97$	4.26970	+	3.10212i	0.433522	+	0.314972i	−0.349533	+	0.936924i	$0.613660\pi$
$98$	−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	−0.730393	−	0.683027i	$-0.760663\pi$
$101$	−3.08028	+	2.23795i	−0.306499	+	0.222684i	0.423894	+	0.905712i	$0.360663\pi$
$102$	−0.0851031	−	0.809702i	−0.00842646	−	0.0801725i
$103$	−4.17918	−	4.64146i	−0.411787	−	0.457336i	0.501196	−	0.865334i	$-0.332894\pi$
$103$	−4.17918	−	4.64146i	−0.411787	−	0.457336i	−0.912983	+	0.407998i	$0.866227\pi$
$104$	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	0.506927	−	0.861989i	$-0.330781\pi$
$107$	2.12617	+	0.946633i	0.205545	+	0.0915144i	−0.301382	+	0.953503i	$0.597448\pi$
$108$	2.20467	+	6.78526i	0.212144	+	0.652912i
$109$	0.456365	+	1.40455i	0.0437118	+	0.134531i	0.970531	−	0.240978i	$-0.0774680\pi$
$109$	0.456365	+	1.40455i	0.0437118	+	0.134531i	−0.926819	+	0.375509i	$0.877468\pi$
$110$	−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	−0.113818	−	0.993502i	$-0.536308\pi$
$113$	5.82892	−	2.59520i	0.548339	−	0.244136i	0.662157	+	0.749366i	$0.269641\pi$
$114$	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	−0.699130	−	0.714995i	$-0.746429\pi$
$127$	0.958204	−	1.06419i	0.0850269	−	0.0944319i	0.784157	+	0.620563i	$0.213096\pi$
$128$	−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	0.927468	+	0.373902i	$0.121980\pi$
$131$	−0.657787	+	6.25843i	−0.0574711	+	0.546801i	−0.984939	+	0.172900i	$0.944686\pi$
$132$	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	0.707115	−	0.707098i	$-0.249996\pi$
$137$	12.4713	+	2.65085i	1.06549	+	0.226478i	0.358379	+	0.933576i	$0.383330\pi$
$138$	−1.86606	−	0.830822i	−0.158849	−	0.0707242i
$139$	−5.78287	−	17.7978i	−0.490496	−	1.50959i	−0.823860	−	0.566794i	$-0.808184\pi$
$139$	−5.78287	−	17.7978i	−0.490496	−	1.50959i	0.333363	−	0.942798i	$-0.391816\pi$
$140$	−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	0.902092	+	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	0.964643	−	0.263559i	$-0.0848964\pi$
$151$	12.4366	+	9.03571i	1.01207	+	0.735315i	0.0474314	+	0.998874i	$0.484896\pi$
$152$	−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	−0.570876	−	0.821037i	$-0.693396\pi$
$157$	4.68076	−	14.4059i	0.373566	−	1.14972i	0.944441	−	0.328680i	$-0.106604\pi$
$158$	−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	−0.554188	−	0.832392i	$-0.686971\pi$
$163$	0.845317	−	0.614159i	0.0662103	−	0.0481046i	0.620398	+	0.784287i	$0.286971\pi$
$164$	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	−0.614284	−	0.789085i	$-0.710555\pi$
$167$	−11.0427	+	2.34720i	−0.854510	+	0.181632i	−0.240226	+	0.970717i	$0.577222\pi$
$168$	−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	0.896716	−	0.442607i	$-0.145946\pi$
$173$	20.2014	+	4.29393i	1.53588	+	0.326462i	0.639166	+	0.769069i	$0.279280\pi$
$174$	−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	−0.995024	−	0.0996337i	$-0.968233\pi$
$179$	−0.0137625	+	0.130941i	−0.00102866	+	0.00978700i	0.993996	+	0.109421i	$0.0348996\pi$
$180$	−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
$183$	−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	−0.177585	−	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
$193$	−0.591969	+	5.63221i	−0.0426109	+	0.405415i	0.952339	+	0.305042i	$0.0986705\pi$
$193$	−0.591969	+	5.63221i	−0.0426109	+	0.405415i	−0.994950	+	0.100374i	$0.967996\pi$
$194$	−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	−0.852979	−	0.521945i	$-0.825207\pi$
$197$	−14.5389	+	6.47313i	−1.03585	+	0.461192i	−0.182874	+	0.983136i	$0.558540\pi$
$198$	−6.06673	+	1.28952i	−0.431144	+	0.0916424i
$199$	−4.16833	−	0.886006i	−0.295485	−	0.0628073i	0.0577838	−	0.998329i	$-0.481597\pi$
$199$	−4.16833	−	0.886006i	−0.295485	−	0.0628073i	−0.353269	+	0.935522i	$0.614930\pi$
$200$	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	0.993245	−	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
$214$	−1.07376	+	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	0.979551	−	0.201195i	$-0.0644824\pi$
$223$	4.71196	+	8.16135i	0.315536	+	0.546524i	−0.664015	+	0.747719i	$0.731149\pi$
$224$	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	0.997264	+	0.0739173i	$0.0235501\pi$
$227$	14.5623	+	16.1731i	0.966534	+	1.07344i	−0.0307302	+	0.999528i	$0.509783\pi$
$228$	4.77548	−	2.12618i	0.316264	−	0.140810i
$229$	16.5854	−	3.52533i	1.09599	−	0.232960i	0.375776	−	0.926710i	$-0.377376\pi$
$229$	16.5854	−	3.52533i	1.09599	−	0.232960i	0.720216	+	0.693750i	$0.244043\pi$
$230$	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	−0.999904	−	0.0138848i	$-0.995580\pi$
$233$	−3.03952	−	9.35469i	−0.199126	−	0.612846i	0.800778	−	0.598962i	$-0.204420\pi$
$234$	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	0.996337	−	0.0855115i	$-0.0272524\pi$
$239$	0.0617382	+	0.587399i	0.00399351	+	0.0379957i	−0.992344	+	0.123507i	$0.960586\pi$
$240$	−3.71793	+	2.70124i	−0.239992	+	0.174364i
$241$	1.60665	−	15.2862i	0.103493	−	0.984674i	−0.812359	−	0.583158i	$-0.801817\pi$
$241$	1.60665	−	15.2862i	0.103493	−	0.984674i	0.915852	−	0.401516i	$-0.131516\pi$
$242$	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	−0.601673	−	0.798743i	$-0.705499\pi$
$251$	4.04925	−	4.49714i	0.255586	−	0.283857i	0.857259	+	0.514885i	$0.172166\pi$
$252$	−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	0.999317	+	0.0369649i	$0.0117690\pi$
$257$	0.473288	+	4.50304i	0.0295229	+	0.280892i	−0.969794	+	0.243927i	$0.921564\pi$
$258$	−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	0.972110	−	0.234525i	$-0.0753536\pi$
$263$	0.775281	+	2.38607i	0.0478059	+	0.147131i	−0.924304	+	0.381657i	$0.875354\pi$
$264$	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	0.406803	−	0.913516i	$-0.366643\pi$
$269$	−8.92605	−	9.91338i	−0.544231	−	0.604430i	−0.951034	+	0.309086i	$0.899977\pi$
$270$	−1.25041	−	11.8968i	−0.0760974	−	0.724019i
$271$	11.1840	−	8.12564i	0.679379	−	0.493598i	−0.193773	−	0.981046i	$-0.562072\pi$
$271$	11.1840	−	8.12564i	0.679379	−	0.493598i	0.873152	+	0.487449i	$0.162072\pi$
$272$	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	0.784331	+	0.620343i	$0.213006\pi$
$277$	−3.57556	+	11.0044i	−0.214834	+	0.661192i	−0.999165	+	0.0408496i	$0.986994\pi$
$278$	12.9030			0.773870
$279$		0			0
$280$	6.87814			0.411048
$281$	−4.75866	+	14.6457i	−0.283878	+	0.873686i	0.702855	+	0.711333i	$0.251908\pi$
$281$	−4.75866	+	14.6457i	−0.283878	+	0.873686i	−0.986733	+	0.162353i	$0.948092\pi$
$282$	0.364735	−	0.405079i	0.0217196	−	0.0241221i
$283$	18.3612	+	13.3402i	1.09146	+	0.792993i	0.979645	−	0.200736i	$-0.0643333\pi$
$283$	18.3612	+	13.3402i	1.09146	+	0.792993i	0.111816	+	0.993729i	$0.464333\pi$
$284$	−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	0.710030	−	0.704171i	$-0.248681\pi$
$293$	11.3288	+	5.04388i	0.661833	+	0.294667i	−0.0481978	+	0.998838i	$0.515348\pi$
$294$	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	0.229027	−	0.973420i	$-0.426446\pi$
$307$	20.5557	−	22.8294i	1.17317	−	1.30294i	0.944148	−	0.329523i	$-0.106888\pi$
$308$	−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	−0.911254	−	0.411844i	$-0.864885\pi$
$313$	−7.19020	+	7.98553i	−0.406414	+	0.451369i	0.504840	+	0.863213i	$0.331551\pi$
$314$	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	0.938381	+	0.345603i	$0.112326\pi$
$317$	−0.914242	+	8.69844i	−0.0513490	+	0.488553i	−0.989730	+	0.142950i	$0.954341\pi$
$318$	−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	0.934696	+	0.355449i	$0.115672\pi$
$331$	21.6592	+	24.0549i	1.19049	+	1.32218i	0.255799	+	0.966730i	$0.417661\pi$
$332$	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	0.996283	−	0.0861400i	$-0.0274532\pi$
$337$	22.4371	+	16.3015i	1.22223	+	0.888000i	0.225944	+	0.974140i	$0.427453\pi$
$338$	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	−0.969970	−	0.243224i	$-0.921795\pi$
$347$	−12.9580	−	22.4440i	−0.695624	−	1.20486i	0.274347	−	0.961631i	$-0.411538\pi$
$348$	−0.704042	+	6.69851i	−0.0377406	+	0.359078i
$349$	−4.52559	+	3.28803i	−0.242249	+	0.176004i	−0.702285	−	0.711896i	$-0.747837\pi$
$349$	−4.52559	+	3.28803i	−0.242249	+	0.176004i	0.460036	+	0.887900i	$0.347837\pi$
$350$	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	0.106120	−	0.994353i	$-0.466157\pi$
$353$	11.4140	−	2.42612i	0.607505	−	0.129129i	0.501385	+	0.865224i	$0.332824\pi$
$354$	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	−0.526066	−	0.850444i	$-0.676334\pi$
$359$	−25.6273	−	5.44725i	−1.35256	−	0.287495i	−0.826492	+	0.562949i	$0.809667\pi$
$360$	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	−0.261589	−	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
$369$	−1.10557	+	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	−0.974984	−	0.222276i	$-0.928651\pi$
$379$	0.484909	−	4.61360i	0.0249081	−	0.236985i	0.999892	−	0.0147084i	$-0.00468201\pi$
$380$	−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	−0.286178	−	0.958177i	$-0.592385\pi$
$383$	4.58722	−	2.04236i	0.234396	−	0.104360i	0.520574	+	0.853817i	$0.325718\pi$
$384$	−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	−0.0721346	−	0.997395i	$-0.522981\pi$
$389$	−16.9936	−	7.56605i	−0.861611	−	0.383614i	−0.789476	+	0.613781i	$0.789648\pi$
$390$	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	−0.907854	−	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
$400$	8.03833	−	8.92747i	0.401917	−	0.446374i
$401$	3.82880	−	11.7838i	0.191201	−	0.588457i	−0.808799	−	0.588086i	$-0.799882\pi$
$401$	3.82880	−	11.7838i	0.191201	−	0.588457i	1.00000		0.000371451i	$-0.000118236\pi$
$402$	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	0.820249	−	0.572007i	$-0.193835\pi$
$409$	−1.72404	−	2.98613i	−0.0852484	−	0.147654i	−0.905497	+	0.424353i	$0.860502\pi$
$410$	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	−0.499717	−	0.866189i	$-0.666563\pi$
$419$	−12.3752	−	38.0871i	−0.604570	−	1.86068i	−0.104854	−	0.994488i	$-0.533437\pi$
$420$	−3.55727	−	1.58380i	−0.173577	−	0.0772815i
$421$	−21.2106	−	4.50844i	−1.03374	−	0.219728i	−0.340356	−	0.940297i	$-0.610548\pi$
$421$	−21.2106	−	4.50844i	−1.03374	−	0.219728i	−0.693384	+	0.720569i	$0.743881\pi$
$422$	−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	−0.900719	−	0.434403i	$-0.856959\pi$
$431$	−7.77574	+	8.63584i	−0.374544	+	0.415974i	0.526174	+	0.850377i	$0.323626\pi$
$432$	−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	−0.997227	−	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
$441$	−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	−0.945773	−	0.324829i	$-0.894693\pi$
$443$	−1.85646	−	17.6630i	−0.0882031	−	0.839196i	0.857570	−	0.514368i	$-0.171973\pi$
$444$	−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	0.995456	−	0.0952196i	$-0.0303553\pi$
$449$	2.84252	+	8.74836i	0.134147	+	0.412861i	−0.861310	+	0.508080i	$0.830355\pi$
$450$	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	−0.992254	−	0.124222i	$-0.960356\pi$
$457$	−25.2412	+	18.3388i	−1.18074	+	0.857855i	−0.188481	+	0.982077i	$0.560356\pi$
$458$	−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	0.455022	−	0.890480i	$-0.349631\pi$
$461$	−5.39491	−	3.91963i	−0.251266	−	0.182555i	−0.706288	+	0.707925i	$0.749631\pi$
$462$	−1.30805	+	1.45274i	−0.0608560	+	0.0675874i
$463$	−10.9140	+	33.5899i	−0.507217	+	1.56105i	0.289795	+	0.957089i	$0.406413\pi$
$463$	−10.9140	+	33.5899i	−0.507217	+	1.56105i	−0.797011	+	0.603964i	$0.793587\pi$
$464$	−6.72466			−0.312184
$465$		0			0
$466$	6.78192			0.314167
$467$	11.1071	−	34.1842i	0.513977	−	1.58186i	−0.271159	−	0.962535i	$-0.587407\pi$
$467$	11.1071	−	34.1842i	0.513977	−	1.58186i	0.785136	−	0.619324i	$-0.212593\pi$
$468$	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	0.958418	−	0.285369i	$-0.0921163\pi$
$479$	30.3703	+	13.5217i	1.38765	+	0.617823i	0.429236	+	0.903192i	$0.358783\pi$
$480$	−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	0.826624	+	0.562754i	$0.190258\pi$
$487$	2.98067	+	28.3591i	0.135067	+	1.28508i	−0.691557	+	0.722321i	$0.743075\pi$
$488$	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	0.356359	+	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
$493$	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	0.335417	−	0.942070i	$-0.391123\pi$
$499$	27.6384	−	30.6956i	1.23727	−	1.37412i	0.901848	−	0.432053i	$-0.142211\pi$
$500$	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	−0.757235	−	0.653143i	$-0.773450\pi$
$503$	2.67447	−	25.4459i	0.119249	−	1.13458i	0.876483	−	0.481432i	$-0.159883\pi$
$504$	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	−0.355718	−	0.934593i	$-0.615764\pi$
$509$	−23.9331	−	5.08714i	−1.06082	−	0.225483i	−0.705098	+	0.709110i	$0.749097\pi$
$510$	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	0.654253	−	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	0.151559	−	0.988448i	$-0.451571\pi$
$523$	−16.9615	−	12.3233i	−0.741677	−	0.538860i	−0.893236	+	0.449589i	$0.851571\pi$
$524$	−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	0.440454	−	0.897775i	$-0.354817\pi$
$541$	1.58162	+	0.704184i	0.0679993	+	0.0302752i	−0.372455	+	0.928050i	$0.621484\pi$
$542$	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	−0.646670	−	0.762770i	$-0.723839\pi$
$547$	−11.9870	+	5.33697i	−0.512528	+	0.228192i	0.134142	+	0.990962i	$0.457172\pi$
$548$	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	−0.999662	−	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
$565$	−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	0.796256	−	0.604960i	$-0.206811\pi$
$569$	42.4269	−	18.8897i	1.77863	−	0.791896i	0.982372	−	0.186936i	$-0.0598558\pi$
$570$	−8.57330	+	1.82231i	−0.359096	+	0.0763282i
$571$	−12.2252	−	2.59855i	−0.511610	−	0.108746i	−0.0551292	−	0.998479i	$-0.517557\pi$
$571$	−12.2252	−	2.59855i	−0.511610	−	0.108746i	−0.456481	+	0.889733i	$0.650890\pi$
$572$	−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	0.459980	−	0.887929i	$-0.347857\pi$
$577$	29.8181	−	6.33804i	1.24135	−	0.263856i	0.781366	+	0.624073i	$0.214523\pi$
$578$	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	0.469532	+	0.882915i	$0.344423\pi$
$587$	−10.4009	+	32.0107i	−0.429292	+	1.32123i	−0.898824	+	0.438310i	$0.855577\pi$
$588$	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	0.973697	+	0.227847i	$0.0731687\pi$
$593$	36.3151	+	26.3844i	1.49128	+	1.08348i	0.517585	+	0.855632i	$0.326831\pi$
$594$	−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	0.413349	−	0.910573i	$-0.364359\pi$
$599$	−13.1047	−	14.5542i	−0.535442	−	0.594669i	−0.948791	+	0.315904i	$0.897692\pi$
$600$	17.5212	−	7.80092i	0.715298	−	0.318471i
$601$	29.7938	−	6.33288i	1.21532	−	0.258323i	0.444733	−	0.895663i	$-0.353298\pi$
$601$	29.7938	−	6.33288i	1.21532	−	0.258323i	0.770583	+	0.637340i	$0.219965\pi$
$602$	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	0.465604	−	0.884993i	$-0.345837\pi$
$607$	13.0823	+	2.78073i	0.530994	+	0.112866i	0.0653907	+	0.997860i	$0.479171\pi$
$608$	−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	0.978066	+	0.208293i	$0.0667908\pi$
$613$	−0.543047	+	5.16675i	−0.0219335	+	0.208683i	−1.00000		0.000389879i	$0.999876\pi$
$614$	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	−0.996445	−	0.0842517i	$-0.973150\pi$
$617$	−20.0827	+	22.3041i	−0.808498	+	0.897927i	0.187947	+	0.982179i	$0.439817\pi$
$618$	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	−0.585971	−	0.810332i	$-0.699287\pi$
$631$	−9.44169	+	4.20371i	−0.375868	+	0.167347i	0.210103	+	0.977679i	$0.432620\pi$
$632$	−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	0.741805	−	0.670615i	$-0.233970\pi$
$641$	−0.0677508	−	0.0752449i	−0.00267599	−	0.00297199i	−0.744481	+	0.667643i	$0.767303\pi$
$642$	0.151367	+	1.44016i	0.00597399	+	0.0568387i
$643$	−11.0931	+	8.05961i	−0.437469	+	0.317840i	−0.784629	−	0.619966i	$-0.787146\pi$
$643$	−11.0931	+	8.05961i	−0.437469	+	0.317840i	0.347159	+	0.937806i	$0.387146\pi$
$644$	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	0.402003	−	0.915638i	$-0.368314\pi$
$647$	−8.76519	−	6.36828i	−0.344595	−	0.250363i	−0.746598	+	0.665275i	$0.768314\pi$
$648$	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	0.690519	+	0.723314i	$0.257382\pi$
$653$	−7.49434	+	23.0652i	−0.293276	+	0.902611i	−0.983795	+	0.179297i	$0.942618\pi$
$654$	−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	−0.445144	−	0.895459i	$-0.646847\pi$
$659$	6.90374	−	5.01586i	0.268932	−	0.195390i	0.714075	+	0.700069i	$0.246847\pi$
$660$	2.19436	+	20.8780i	0.0854155	+	0.812674i
$661$	25.3495	+	28.1535i	0.985981	+	1.09504i	0.995469	+	0.0950874i	$0.0303130\pi$
$661$	25.3495	+	28.1535i	0.985981	+	1.09504i	−0.00948838	+	0.999955i	$0.503020\pi$
$662$	−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	0.999457	+	0.0329387i	$0.0104866\pi$
$673$	0.744254	+	7.08110i	0.0286889	+	0.272956i	−0.970769	+	0.240018i	$0.922847\pi$
$674$	−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	0.129716	−	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
$679$	−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	−0.904652	−	0.426151i	$-0.859869\pi$
$691$	−2.84872	−	27.1038i	−0.108371	−	1.03108i	0.796282	−	0.604926i	$-0.206797\pi$
$692$	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	−0.362035	−	0.932165i	$-0.617918\pi$
$701$	−8.30364	+	1.76499i	−0.313624	+	0.0666629i	0.0484104	+	0.998828i	$0.484584\pi$
$702$	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	0.172804	−	0.984956i	$-0.444717\pi$
$709$	−18.9198	−	13.7460i	−0.710546	−	0.516242i	−0.883350	+	0.468714i	$0.844717\pi$
$710$	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	0.961278	−	0.275582i	$-0.0888706\pi$
$719$	6.48843	+	11.2383i	0.241978	+	0.419118i	−0.719300	+	0.694700i	$0.755537\pi$
$720$	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	0.185341	−	0.982674i	$-0.440661\pi$
$727$	−11.3490	−	5.05290i	−0.420911	−	0.187402i	−0.606252	+	0.795273i	$0.707328\pi$
$728$	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	−0.891879	−	0.452275i	$-0.850613\pi$
$733$	−31.2043	+	13.8930i	−1.15256	+	0.513151i	−0.260678	+	0.965426i	$0.583946\pi$
$734$	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	−0.957099	−	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
$741$	−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	−0.954491	−	0.298240i	$-0.903600\pi$
$751$	1.12768	−	10.7292i	0.0411497	−	0.391513i	0.995641	−	0.0932730i	$-0.0297329\pi$
$752$	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	0.868851	−	0.495074i	$-0.164859\pi$
$757$	40.2035	+	8.54552i	1.46122	+	0.310592i	0.592370	+	0.805666i	$0.298192\pi$
$758$	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	0.0544972	−	0.998514i	$-0.482644\pi$
$761$	−17.9608	−	7.99665i	−0.651078	−	0.289878i	−0.705575	+	0.708636i	$0.749311\pi$
$762$	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	0.829850	−	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
$772$	−5.77739	+	6.41644i	−0.207933	+	0.230933i
$773$	7.83963	−	24.1279i	0.281972	−	0.867820i	−0.705318	−	0.708891i	$-0.749196\pi$
$773$	7.83963	−	24.1279i	0.281972	−	0.867820i	0.987290	−	0.158929i	$-0.0508041\pi$
$774$	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	−0.636687	−	0.771123i	$-0.719695\pi$
$787$	−25.3796	+	5.39460i	−0.904685	+	0.192297i	−0.267998	+	0.963419i	$0.586362\pi$
$788$	−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	−0.973861	−	0.227146i	$-0.927060\pi$
$797$	−1.93405	−	18.4013i	−0.0685076	−	0.651806i	0.905353	−	0.424660i	$-0.139606\pi$
$798$	−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	−0.999528	−	0.0307106i	$-0.990223\pi$
$809$	−24.5891	+	27.3090i	−0.864507	+	0.960132i	0.135022	+	0.990843i	$0.456890\pi$
$810$	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
$813$	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	0.942755	−	0.333486i	$-0.108225\pi$
$821$	−0.457525	−	1.40812i	−0.0159677	−	0.0491436i	−0.958723	+	0.284342i	$0.908225\pi$
$822$	2.45142	+	7.54471i	0.0855032	+	0.263152i
$823$	35.5051	+	15.8079i	1.23763	+	0.551029i	0.918025	−	0.396521i	$-0.129783\pi$
$823$	35.5051	+	15.8079i	1.23763	+	0.551029i	0.319606	+	0.947551i	$0.396449\pi$
$824$	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	0.205182	−	0.978724i	$-0.434221\pi$
$827$	−22.7078	−	25.2196i	−0.789628	−	0.876971i	−0.994810	+	0.101753i	$0.967555\pi$
$828$	−1.14351	−	10.8798i	−0.0397398	−	0.378099i
$829$	13.3736	−	9.71650i	0.464485	−	0.337468i	−0.330803	−	0.943700i	$-0.607320\pi$
$829$	13.3736	−	9.71650i	0.464485	−	0.337468i	0.795288	+	0.606232i	$0.207320\pi$
$830$	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	0.0525843	+	0.998616i	$0.483254\pi$
$839$	−16.7110	+	51.4313i	−0.576929	+	1.77561i	−0.629514	+	0.776989i	$0.716746\pi$
$840$	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	0.908865	+	0.417091i	$0.136950\pi$
$853$	12.2297	+	37.6392i	0.418738	+	1.28874i	−0.490127	+	0.871651i	$0.663050\pi$
$854$	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	−0.198464	−	0.980108i	$-0.563595\pi$
$857$	11.6249	−	5.17574i	0.397099	−	0.176800i	0.595564	+	0.803308i	$0.296929\pi$
$858$	−4.98576	−	5.53725i	−0.170211	−	0.189039i
$859$	−2.21123	−	21.0385i	−0.0754462	−	0.717823i	−0.965223	−	0.261427i	$-0.915807\pi$
$859$	−2.21123	−	21.0385i	−0.0754462	−	0.717823i	0.889777	−	0.456396i	$-0.150860\pi$
$860$	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	−0.775531	−	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
$865$	−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	−0.960006	−	0.279978i	$-0.909673\pi$
$877$	−2.34512	−	22.3123i	−0.0791892	−	0.753435i	0.880817	−	0.473456i	$-0.156994\pi$
$878$	−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	−0.635520	−	0.772084i	$-0.719214\pi$
$881$	−45.4168	−	9.65365i	−1.53013	−	0.325240i	−0.894612	+	0.446844i	$0.852548\pi$
$882$	−8.83472	−	3.93347i	−0.297480	−	0.132447i
$883$	−11.2913	−	34.7512i	−0.379984	−	1.16947i	−0.940054	−	0.341026i	$-0.889226\pi$
$883$	−11.2913	−	34.7512i	−0.379984	−	1.16947i	0.560070	−	0.828445i	$-0.310774\pi$
$884$	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	−0.653266	−	0.757128i	$-0.726602\pi$
$887$	−28.0582	+	5.96396i	−0.942102	+	0.200250i	−0.288836	+	0.957378i	$0.593268\pi$
$888$	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	−0.248406	−	0.968656i	$-0.579907\pi$
$907$	17.9518	−	13.0427i	0.596079	−	0.433077i	0.844485	+	0.535579i	$0.179907\pi$
$908$	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	−0.649856	−	0.760057i	$-0.725171\pi$
$911$	−28.2024	+	5.99460i	−0.934386	+	0.198610i	−0.284530	+	0.958667i	$0.591838\pi$
$912$	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	0.476238	−	0.879317i	$-0.342000\pi$
$919$	43.9071	−	19.5487i	1.44836	−	0.644853i	0.972125	+	0.234464i	$0.0753335\pi$
$920$	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	−0.950268	−	0.311432i	$-0.899191\pi$
$937$	1.34639	−	12.8101i	0.0439848	−	0.418487i	0.994253	−	0.107055i	$-0.0341421\pi$
$938$	−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	0.509768	−	0.860312i	$-0.329731\pi$
$941$	45.7131	−	20.3528i	1.49021	−	0.663482i	0.980438	+	0.196830i	$0.0630647\pi$
$942$	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	−0.550928	−	0.834553i	$-0.685726\pi$
$947$	−47.3837	−	21.0966i	−1.53976	−	0.685547i	−0.988836	+	0.149006i	$0.952393\pi$
$948$	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	−0.314577	−	0.949232i	$-0.601863\pi$
$953$	15.1571	−	11.0123i	0.490987	−	0.356723i	0.805564	+	0.592509i	$0.201863\pi$
$954$	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	−0.938471	−	0.345358i	$-0.887757\pi$
$967$	−23.8923	−	41.3827i	−0.768324	−	1.33078i	0.170146	−	0.985419i	$-0.445576\pi$
$968$	−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	0.310077	−	0.950711i	$-0.399645\pi$
$971$	−20.8104	−	23.1123i	−0.667838	−	0.741709i	−0.977915	+	0.209002i	$0.932978\pi$
$972$	−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	−0.998904	−	0.0467994i	$-0.985098\pi$
$977$	−6.82283	−	20.9985i	−0.218282	−	0.671802i	0.780623	−	0.625003i	$-0.214902\pi$
$978$	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	−0.858810	−	0.512294i	$-0.828796\pi$
$983$	−3.92785	−	37.3710i	−0.125279	−	1.19195i	0.733531	−	0.679656i	$-0.237871\pi$
$984$	−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	−0.531046	−	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
$999$	5.09338	−	48.4603i	0.161147	−	1.53321i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.18.2	✓	16	31.22	odd	30
31.2.g.a.19.2	yes	16	31.15	odd	10
279.2.y.c.19.1		16	93.77	even	10
279.2.y.c.235.1		16	93.53	even	30
496.2.bg.c.49.1		16	124.115	even	30
496.2.bg.c.81.1		16	124.15	even	10
775.2.bl.a.576.1		16	155.84	odd	30
775.2.bl.a.701.1		16	155.139	odd	10
775.2.ck.a.49.2		32	155.53	even	60
775.2.ck.a.49.3		32	155.22	even	60
775.2.ck.a.174.2		32	155.77	even	20
775.2.ck.a.174.3		32	155.108	even	20
961.2.a.i.1.3		8	31.12	odd	30
961.2.a.j.1.3		8	31.19	even	15
961.2.c.i.439.3		16	31.10	even	15
961.2.c.i.521.3		16	31.2	even	5
961.2.c.j.439.3		16	31.21	odd	30
961.2.c.j.521.3		16	31.29	odd	10
961.2.d.n.374.4		16	31.28	even	15
961.2.d.n.388.4		16	31.14	even	15
961.2.d.o.374.4		16	31.3	odd	30
961.2.d.o.388.4		16	31.17	odd	30
961.2.d.p.531.1		16	31.24	odd	30
961.2.d.p.628.1		16	31.6	odd	6
961.2.d.q.531.1		16	31.7	even	15
961.2.d.q.628.1		16	31.25	even	3
961.2.g.j.338.2		16	31.8	even	5
961.2.g.j.816.2		16	31.18	even	15
961.2.g.k.338.2		16	31.23	odd	10
961.2.g.k.816.2		16	31.13	odd	30
961.2.g.l.235.2		16	31.9	even	15
961.2.g.l.732.2		16	31.16	even	5
961.2.g.m.844.1		16	31.4	even	5
961.2.g.m.846.1		16	31.5	even	3
961.2.g.n.448.1		16	1.1	even	1	trivial
961.2.g.n.547.1		16	31.20	even	15	inner
961.2.g.s.844.1		16	31.27	odd	10
961.2.g.s.846.1		16	31.26	odd	6
961.2.g.t.448.1		16	31.30	odd	2
961.2.g.t.547.1		16	31.11	odd	30
8649.2.a.be.1.6		8	93.50	odd	30
8649.2.a.bf.1.6		8	93.74	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(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

Introduction

L-functions

Modular forms

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