LMFDB - Embedded newform 961.2.g.i.732.1

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)

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")

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);

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,-16,0,24,0,0,-2] 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:	16.0.26873856000000000000.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} + 8x^{10} - 16x^{8} + 32x^{6} - 128x^{2} + 256 $ x^16 - 2x^14 + 8x^10 - 16x^8 + 32x^6 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			732.1
Root			$0.147826 + 1.40647i$ of defining polynomial
Character	$\chi$	$=$	961.732
Dual form			961.2.g.i.235.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.11803 - 1.53884i) q^{2} +(-0.798468 - 0.355501i) q^{3} +(1.50000 + 4.61653i) q^{4} +(-1.11803 + 1.93649i) q^{5} +(1.14412 + 1.98168i) q^{6} +(-0.669131 + 0.743145i) q^{7} +(2.30902 - 7.10642i) q^{8} +(-1.49622 - 1.66172i) q^{9} +(5.34799 - 2.38108i) q^{10} +(-4.14993 - 0.882095i) q^{11} +(0.443477 - 4.21940i) q^{12} +(0.274084 + 2.60773i) q^{13} +(2.56082 - 0.544320i) q^{14} +(1.58114 - 1.14876i) q^{15} +(-7.97214 + 5.79210i) q^{16} +(-3.62155 + 0.769785i) q^{17} +(0.611920 + 5.82203i) q^{18} +(-0.104528 + 0.994522i) q^{19} +(-10.6169 - 2.25669i) q^{20} +(0.798468 - 0.355501i) q^{21} +(7.43229 + 8.25439i) q^{22} +(-0.810272 + 2.49376i) q^{23} +(-4.37002 + 4.85339i) q^{24} +(3.43237 - 5.94504i) q^{26} +(1.41421 + 4.35250i) q^{27} +(-4.43444 - 1.97434i) q^{28} +(0.437016 + 0.317511i) q^{29} -5.11667 q^{30} +10.8541 q^{32} +(3.00000 + 2.17963i) q^{33} +(8.85515 + 3.94256i) q^{34} +(-0.690983 - 2.12663i) q^{35} +(5.42705 - 9.39993i) q^{36} +(-2.12132 - 3.67423i) q^{37} +(1.75181 - 1.94558i) q^{38} +(0.708204 - 2.17963i) q^{39} +(11.1800 + 12.4166i) q^{40} +(-1.34486 + 0.598772i) q^{41} +(-2.23824 - 0.475753i) q^{42} +(1.01321 - 9.64006i) q^{43} +(-2.15268 - 20.4814i) q^{44} +(4.89074 - 1.03956i) q^{45} +(5.55369 - 4.03499i) q^{46} +(7.85410 - 5.70634i) q^{47} +(8.42459 - 1.79070i) q^{48} +(0.627171 + 5.96713i) q^{49} +(3.16535 + 0.672816i) q^{51} +(-11.6275 + 5.17691i) q^{52} +(-9.18681 - 10.2030i) q^{53} +(3.70246 - 11.3950i) q^{54} +(6.34793 - 7.05009i) q^{55} +(3.73607 + 6.47106i) q^{56} +(0.437016 - 0.756934i) q^{57} +(-0.437016 - 1.34500i) q^{58} +(10.9116 + 4.85817i) q^{59} +(7.67501 + 5.57622i) q^{60} +13.9358 q^{61} +2.23607 q^{63} +(-7.04508 - 5.11855i) q^{64} +(-5.35629 - 2.38477i) q^{65} +(-3.00000 - 9.23305i) q^{66} +(-3.00000 + 5.19615i) q^{67} +(-8.98606 - 15.5643i) q^{68} +(1.53351 - 1.70314i) q^{69} +(-1.80902 + 5.56758i) q^{70} +(-0.985051 - 1.09401i) q^{71} +(-15.2637 + 6.79584i) q^{72} +(-4.14993 - 0.882095i) q^{73} +(-1.16104 + 11.0465i) q^{74} +(-4.74803 + 1.00922i) q^{76} +(3.43237 - 2.49376i) q^{77} +(-4.85410 + 3.52671i) q^{78} +(1.58513 - 0.336930i) q^{79} +(-2.30323 - 21.9137i) q^{80} +(-0.283084 + 2.69337i) q^{81} +(3.76988 + 0.801313i) q^{82} +(-2.88888 + 1.28621i) q^{83} +(2.83888 + 3.15290i) q^{84} +(2.55834 - 7.87375i) q^{85} +(-16.9805 + 18.8588i) q^{86} +(-0.236068 - 0.408882i) q^{87} +(-15.8508 + 27.4544i) q^{88} +(-4.74342 - 14.5987i) q^{89} +(-11.9585 - 5.32425i) q^{90} +(-2.12132 - 1.54123i) q^{91} -12.7279 q^{92} -25.4164 q^{94} +(-1.80902 - 1.31433i) q^{95} +(-8.66665 - 3.85864i) q^{96} +(-2.16312 - 6.65740i) q^{97} +(7.85410 - 13.6037i) q^{98} +(4.74342 + 8.21584i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} + 24 q^{4} - 2 q^{7} + 28 q^{8} + 10 q^{9} + 20 q^{10} + 2 q^{14} - 56 q^{16} - 20 q^{18} + 2 q^{19} - 18 q^{28} + 120 q^{32} + 48 q^{33} - 20 q^{35} + 60 q^{36} - 2 q^{38} - 96 q^{39} - 10 q^{40}+ \cdots + 72 q^{98}+O(q^{100}) $ 16 * q - 16 * q^2 + 24 * q^4 - 2 * q^7 + 28 * q^8 + 10 * q^9 + 20 * q^10 + 2 * q^14 - 56 * q^16 - 20 * q^18 + 2 * q^19 - 18 * q^28 + 120 * q^32 + 48 * q^33 - 20 * q^35 + 60 * q^36 - 2 * q^38 - 96 * q^39 - 10 * q^40 - 14 * q^41 - 10 * q^45 + 72 * q^47 - 12 * q^49 + 8 * q^51 + 24 * q^56 + 46 * q^59 - 68 * q^64 - 48 * q^66 - 48 * q^67 + 48 * q^69 - 20 * q^70 + 26 * q^71 - 50 * q^72 - 12 * q^76 - 24 * q^78 + 80 * q^80 + 22 * q^81 + 14 * q^82 + 32 * q^87 - 40 * q^90 - 192 * q^94 - 20 * q^95 + 28 * q^97 + 72 * q^98

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{15}\right)$

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 $

$2$	−2.11803	−	1.53884i	−1.49768	−	1.08813i	−0.971295	−	0.237877i	$-0.923549\pi$
$2$	−2.11803	−	1.53884i	−1.49768	−	1.08813i	−0.526381	−	0.850249i	$-0.676451\pi$
$3$	−0.798468	−	0.355501i	−0.460996	−	0.205249i	0.163079	−	0.986613i	$-0.447857\pi$
$3$	−0.798468	−	0.355501i	−0.460996	−	0.205249i	−0.624075	+	0.781364i	$0.714524\pi$
$4$	1.50000	+	4.61653i	0.750000	+	2.30826i
$5$	−1.11803	+	1.93649i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$5$	−1.11803	+	1.93649i	−0.500000	+	0.866025i	−1.00000			$\pi$
$6$	1.14412	+	1.98168i	0.467086	+	0.809017i
$7$	−0.669131	+	0.743145i	−0.252908	+	0.280882i	−0.856208	−	0.516632i	$-0.827186\pi$
$7$	−0.669131	+	0.743145i	−0.252908	+	0.280882i	0.603300	+	0.797514i	$0.293852\pi$
$8$	2.30902	−	7.10642i	0.816361	−	2.51250i
$9$	−1.49622	−	1.66172i	−0.498741	−	0.553907i
$10$	5.34799	−	2.38108i	1.69118	−	0.752963i
$11$	−4.14993	−	0.882095i	−1.25125	−	0.265962i	−0.465802	−	0.884889i	$-0.654234\pi$
$11$	−4.14993	−	0.882095i	−1.25125	−	0.265962i	−0.785448	+	0.618927i	$0.787568\pi$
$12$	0.443477	−	4.21940i	0.128021	−	1.21804i
$13$	0.274084	+	2.60773i	0.0760171	+	0.723255i	0.964453	+	0.264254i	$0.0851258\pi$
$13$	0.274084	+	2.60773i	0.0760171	+	0.723255i	−0.888436	+	0.459001i	$0.848208\pi$
$14$	2.56082	−	0.544320i	0.684409	−	0.145476i
$15$	1.58114	−	1.14876i	0.408248	−	0.296610i
$16$	−7.97214	+	5.79210i	−1.99303	+	1.44802i
$17$	−3.62155	+	0.769785i	−0.878355	+	0.186700i	−0.624954	−	0.780661i	$-0.714882\pi$
$17$	−3.62155	+	0.769785i	−0.878355	+	0.186700i	−0.253401	+	0.967361i	$0.581549\pi$
$18$	0.611920	+	5.82203i	0.144231	+	1.37227i
$19$	−0.104528	+	0.994522i	−0.0239805	+	0.228159i	0.975967	+	0.217918i	$0.0699265\pi$
$19$	−0.104528	+	0.994522i	−0.0239805	+	0.228159i	−0.999948	+	0.0102410i	$0.996740\pi$
$20$	−10.6169	−	2.25669i	−2.37401	−	0.504612i
$21$	0.798468	−	0.355501i	0.174240	−	0.0775766i
$22$	7.43229	+	8.25439i	1.58457	+	1.75984i
$23$	−0.810272	+	2.49376i	−0.168953	+	0.519985i	−0.999306	−	0.0372534i	$-0.988139\pi$
$23$	−0.810272	+	2.49376i	−0.168953	+	0.519985i	0.830352	+	0.557239i	$0.188139\pi$
$24$	−4.37002	+	4.85339i	−0.892026	+	0.990695i
$25$		0			0
$26$	3.43237	−	5.94504i	0.673143	−	1.16592i
$27$	1.41421	+	4.35250i	0.272166	+	0.837639i
$28$	−4.43444	−	1.97434i	−0.838031	−	0.373115i
$29$	0.437016	+	0.317511i	0.0811518	+	0.0589603i	0.627621	−	0.778519i	$-0.284029\pi$
$29$	0.437016	+	0.317511i	0.0811518	+	0.0589603i	−0.546470	+	0.837479i	$0.684029\pi$
$30$	−5.11667			−0.934172
$31$		0			0
$31$		0			0
$32$	10.8541			1.91875
$33$	3.00000	+	2.17963i	0.522233	+	0.379424i
$34$	8.85515	+	3.94256i	1.51864	+	0.676144i
$35$	−0.690983	−	2.12663i	−0.116797	−	0.359466i
$36$	5.42705	−	9.39993i	0.904508	−	1.56665i
$37$	−2.12132	−	3.67423i	−0.348743	−	0.604040i	0.637284	−	0.770629i	$-0.280058\pi$
$37$	−2.12132	−	3.67423i	−0.348743	−	0.604040i	−0.986026	+	0.166589i	$0.946725\pi$
$38$	1.75181	−	1.94558i	0.284181	−	0.315614i
$39$	0.708204	−	2.17963i	0.113403	−	0.349020i
$40$	11.1800	+	12.4166i	1.76771	+	1.96324i
$41$	−1.34486	+	0.598772i	−0.210032	+	0.0935124i	−0.509056	−	0.860733i	$-0.670006\pi$
$41$	−1.34486	+	0.598772i	−0.210032	+	0.0935124i	0.299024	+	0.954246i	$0.403339\pi$
$42$	−2.23824	−	0.475753i	−0.345368	−	0.0734103i
$43$	1.01321	−	9.64006i	0.154513	−	1.47010i	−0.592653	−	0.805458i	$-0.701919\pi$
$43$	1.01321	−	9.64006i	0.154513	−	1.47010i	0.747166	−	0.664638i	$-0.231414\pi$
$44$	−2.15268	−	20.4814i	−0.324529	−	3.08769i
$45$	4.89074	−	1.03956i	0.729068	−	0.154968i
$46$	5.55369	−	4.03499i	0.818847	−	0.594927i
$47$	7.85410	−	5.70634i	1.14564	−	0.832355i	0.157744	−	0.987480i	$-0.449578\pi$
$47$	7.85410	−	5.70634i	1.14564	−	0.832355i	0.987895	+	0.155125i	$0.0495780\pi$
$48$	8.42459	−	1.79070i	1.21598	−	0.258466i
$49$	0.627171	+	5.96713i	0.0895958	+	0.852447i
$50$		0			0
$51$	3.16535	+	0.672816i	0.443238	+	0.0942131i
$52$	−11.6275	+	5.17691i	−1.61245	+	0.717909i
$53$	−9.18681	−	10.2030i	−1.26191	−	1.40149i	−0.878384	−	0.477956i	$-0.841378\pi$
$53$	−9.18681	−	10.2030i	−1.26191	−	1.40149i	−0.383522	−	0.923532i	$-0.625289\pi$
$54$	3.70246	−	11.3950i	0.503841	−	1.55066i
$55$	6.34793	−	7.05009i	0.855955	−	0.950634i
$56$	3.73607	+	6.47106i	0.499253	+	0.864732i
$57$	0.437016	−	0.756934i	0.0578842	−	0.100258i
$58$	−0.437016	−	1.34500i	−0.0573830	−	0.176607i
$59$	10.9116	+	4.85817i	1.42057	+	0.632480i	0.966074	−	0.258266i	$-0.0831512\pi$
$59$	10.9116	+	4.85817i	1.42057	+	0.632480i	0.454500	+	0.890747i	$0.349818\pi$
$60$	7.67501	+	5.57622i	0.990839	+	0.719887i
$61$	13.9358			1.78430			0.892148	−	0.451742i	$-0.149197\pi$
$61$	13.9358			1.78430			0.892148	+	0.451742i	$0.149197\pi$
$62$		0			0
$63$	2.23607			0.281718
$64$	−7.04508	−	5.11855i	−0.880636	−	0.639819i
$65$	−5.35629	−	2.38477i	−0.664366	−	0.295795i
$66$	−3.00000	−	9.23305i	−0.369274	−	1.13651i
$67$	−3.00000	+	5.19615i	−0.366508	+	0.634811i	−0.989017	−	0.147802i	$-0.952780\pi$
$67$	−3.00000	+	5.19615i	−0.366508	+	0.634811i	0.622509	+	0.782613i	$0.286114\pi$
$68$	−8.98606	−	15.5643i	−1.08972	−	1.88745i
$69$	1.53351	−	1.70314i	0.184613	−	0.205034i
$70$	−1.80902	+	5.56758i	−0.216219	+	0.665453i
$71$	−0.985051	−	1.09401i	−0.116904	−	0.129835i	0.681852	−	0.731490i	$-0.261175\pi$
$71$	−0.985051	−	1.09401i	−0.116904	−	0.129835i	−0.798756	+	0.601655i	$0.794508\pi$
$72$	−15.2637	+	6.79584i	−1.79884	+	0.800897i
$73$	−4.14993	−	0.882095i	−0.485712	−	0.103241i	−0.0414547	−	0.999140i	$-0.513199\pi$
$73$	−4.14993	−	0.882095i	−0.485712	−	0.103241i	−0.444258	+	0.895899i	$0.646533\pi$
$74$	−1.16104	+	11.0465i	−0.134968	+	1.28413i
$75$		0			0
$76$	−4.74803	+	1.00922i	−0.544636	+	0.115766i
$77$	3.43237	−	2.49376i	0.391155	−	0.284191i
$78$	−4.85410	+	3.52671i	−0.549619	+	0.399321i
$79$	1.58513	−	0.336930i	0.178341	−	0.0379076i	−0.117875	−	0.993028i	$-0.537608\pi$
$79$	1.58513	−	0.336930i	0.178341	−	0.0379076i	0.296217	+	0.955121i	$0.404275\pi$
$80$	−2.30323	−	21.9137i	−0.257509	−	2.45003i
$81$	−0.283084	+	2.69337i	−0.0314538	+	0.299263i
$82$	3.76988	+	0.801313i	0.416314	+	0.0884902i
$83$	−2.88888	+	1.28621i	−0.317096	+	0.141180i	−0.559112	−	0.829092i	$-0.688858\pi$
$83$	−2.88888	+	1.28621i	−0.317096	+	0.141180i	0.242016	+	0.970272i	$0.422191\pi$
$84$	2.83888	+	3.15290i	0.309747	+	0.344009i
$85$	2.55834	−	7.87375i	0.277491	−	0.854028i
$86$	−16.9805	+	18.8588i	−1.83106	+	2.03360i
$87$	−0.236068	−	0.408882i	−0.0253091	−	0.0438367i
$88$	−15.8508	+	27.4544i	−1.68970	+	2.92665i
$89$	−4.74342	−	14.5987i	−0.502801	−	1.54746i	−0.804436	−	0.594039i	$-0.797532\pi$
$89$	−4.74342	−	14.5987i	−0.502801	−	1.54746i	0.301635	−	0.953424i	$-0.402468\pi$
$90$	−11.9585	−	5.32425i	−1.26053	−	0.561225i
$91$	−2.12132	−	1.54123i	−0.222375	−	0.161565i
$92$	−12.7279			−1.32698
$93$		0			0
$94$	−25.4164			−2.62150
$95$	−1.80902	−	1.31433i	−0.185601	−	0.134847i
$96$	−8.66665	−	3.85864i	−0.884537	−	0.393821i
$97$	−2.16312	−	6.65740i	−0.219631	−	0.675956i	−0.998792	−	0.0491321i	$-0.984354\pi$
$97$	−2.16312	−	6.65740i	−0.219631	−	0.675956i	0.779161	−	0.626824i	$-0.215646\pi$
$98$	7.85410	−	13.6037i	0.793384	−	1.37418i
$99$	4.74342	+	8.21584i	0.476731	+	0.825723i
$100$		0			0
$101$	0.690983	−	2.12663i	0.0687554	−	0.211607i	−0.910775	−	0.412902i	$-0.864515\pi$
$101$	0.690983	−	2.12663i	0.0687554	−	0.211607i	0.979531	+	0.201295i	$0.0645150\pi$
$102$	−5.66897	−	6.29602i	−0.561311	−	0.623399i
$103$	9.78243	−	4.35542i	0.963892	−	0.429152i	0.136415	−	0.990652i	$-0.456442\pi$
$103$	9.78243	−	4.35542i	0.963892	−	0.429152i	0.827477	+	0.561500i	$0.189775\pi$
$104$	19.1645	+	4.07354i	1.87924	+	0.399444i
$105$	−0.204290	+	1.94369i	−0.0199367	+	0.189685i
$106$	3.75719	+	35.7473i	0.364931	+	3.47209i
$107$	−1.43997	+	0.306074i	−0.139207	+	0.0295893i	−0.276988	−	0.960873i	$-0.589336\pi$
$107$	−1.43997	+	0.306074i	−0.139207	+	0.0295893i	0.137781	+	0.990463i	$0.456003\pi$
$108$	−17.9721	+	13.0575i	−1.72937	+	1.25646i
$109$	1.04508	−	0.759299i	0.100101	−	0.0727276i	−0.536609	−	0.843831i	$-0.680295\pi$
$109$	1.04508	−	0.759299i	0.100101	−	0.0727276i	0.636710	+	0.771103i	$0.280295\pi$
$110$	−24.2941	+	5.16387i	−2.31635	+	0.492356i
$111$	0.387613	+	3.68789i	0.0367906	+	0.350039i
$112$	1.03003	−	9.80012i	0.0973291	−	0.926024i
$113$	9.55057	+	2.03004i	0.898442	+	0.190970i	0.633910	−	0.773407i	$-0.281449\pi$
$113$	9.55057	+	2.03004i	0.898442	+	0.190970i	0.264532	+	0.964377i	$0.414782\pi$
$114$	−2.09042	+	0.930713i	−0.195785	+	0.0871693i
$115$	−3.92324	−	4.35720i	−0.365844	−	0.406311i
$116$	−0.810272	+	2.49376i	−0.0752319	+	0.231540i
$117$	3.92324	−	4.35720i	0.362703	−	0.402823i
$118$	−15.6353	−	27.0811i	−1.43934	−	2.49301i
$119$	1.85123	−	3.20642i	0.169702	−	0.293932i
$120$	−4.51273	−	13.8888i	−0.411954	−	1.26786i
$121$	6.39482	+	2.84716i	0.581347	+	0.258832i
$122$	−29.5165	−	21.4450i	−2.67230	−	1.94154i
$123$	1.28669			0.116017
$124$		0			0
$125$	−11.1803			−1.00000
$126$	−4.73607	−	3.44095i	−0.421922	−	0.306545i
$127$	−8.66665	−	3.85864i	−0.769041	−	0.342399i	−0.0155688	−	0.999879i	$-0.504956\pi$
$127$	−8.66665	−	3.85864i	−0.769041	−	0.342399i	−0.753472	+	0.657480i	$0.771623\pi$
$128$	0.336881	+	1.03681i	0.0297764	+	0.0916422i
$129$	−4.23607	+	7.33708i	−0.372965	+	0.645994i
$130$	7.67501	+	13.2935i	0.673143	+	1.16592i
$131$	4.96255	−	5.51147i	0.433580	−	0.481539i	−0.486271	−	0.873808i	$-0.661643\pi$
$131$	4.96255	−	5.51147i	0.433580	−	0.481539i	0.919850	+	0.392269i	$0.128310\pi$
$132$	−5.56231	+	17.1190i	−0.484137	+	1.49002i
$133$	−0.669131	−	0.743145i	−0.0580210	−	0.0644388i
$134$	14.3502	−	6.38910i	1.23966	−	0.551934i
$135$	−10.0097	−	2.12763i	−0.861500	−	0.183117i
$136$	−2.89181	+	27.5137i	−0.247971	+	2.35928i
$137$	0.274084	+	2.60773i	0.0234165	+	0.222794i	0.999972	+	0.00752612i	$0.00239566\pi$
$137$	0.274084	+	2.60773i	0.0234165	+	0.222794i	−0.976555	+	0.215267i	$0.930938\pi$
$138$	−5.86889	+	1.24747i	−0.499593	+	0.106192i
$139$	14.5397	−	10.5637i	1.23325	−	0.896005i	0.236116	−	0.971725i	$-0.424125\pi$
$139$	14.5397	−	10.5637i	1.23325	−	0.896005i	0.997129	+	0.0757198i	$0.0241255\pi$
$140$	8.78115	−	6.37988i	0.742143	−	0.539198i
$141$	−8.29986	+	1.76419i	−0.698974	+	0.148572i
$142$	0.402863	+	3.83299i	0.0338075	+	0.321657i
$143$	1.16284	−	11.0637i	0.0972414	−	0.925191i
$144$	21.5529	+	4.58122i	1.79608	+	0.381768i
$145$	−1.10346	+	0.491290i	−0.0916370	+	0.0407994i
$146$	7.43229	+	8.25439i	0.615100	+	0.683138i
$147$	1.62054	−	4.98752i	0.133660	−	0.411364i
$148$	13.7802	−	15.3045i	1.13273	−	1.25802i
$149$	6.70820	+	11.6190i	0.549557	+	0.951861i	0.998305	+	0.0582028i	$0.0185370\pi$
$149$	6.70820	+	11.6190i	0.549557	+	0.951861i	−0.448747	+	0.893659i	$0.648130\pi$
$150$		0			0
$151$	3.86938	+	11.9087i	0.314886	+	0.969120i	0.975801	+	0.218659i	$0.0701683\pi$
$151$	3.86938	+	11.9087i	0.314886	+	0.969120i	−0.660915	+	0.750461i	$0.729832\pi$
$152$	6.82614	+	3.03919i	0.553673	+	0.246511i
$153$	6.69781	+	4.86624i	0.541486	+	0.393413i
$154$	−11.1074			−0.895058
$155$		0			0
$156$	11.1246			0.890682
$157$	−7.04508	−	5.11855i	−0.562259	−	0.408505i	0.270026	−	0.962853i	$-0.412968\pi$
$157$	−7.04508	−	5.11855i	−0.562259	−	0.408505i	−0.832285	+	0.554348i	$0.812968\pi$
$158$	−3.87585	−	1.72564i	−0.308346	−	0.137284i
$159$	3.70820	+	11.4127i	0.294080	+	0.905084i
$160$	−12.1353	+	21.0189i	−0.959376	+	1.66169i
$161$	−1.31105	−	2.27080i	−0.103325	−	0.178964i
$162$	4.74425	−	5.26902i	0.372743	−	0.413974i
$163$	4.45492	−	13.7108i	0.348936	−	1.07391i	−0.610507	−	0.792011i	$-0.709034\pi$
$163$	4.45492	−	13.7108i	0.348936	−	1.07391i	0.959443	−	0.281903i	$-0.0909657\pi$
$164$	−4.78154	−	5.31044i	−0.373375	−	0.414675i
$165$	−7.57493	+	3.37258i	−0.589708	+	0.262555i
$166$	8.09804	+	1.72129i	0.628529	+	0.133598i
$167$	0.112929	−	1.07444i	0.00873868	−	0.0831430i	−0.989283	−	0.146009i	$-0.953357\pi$
$167$	0.112929	−	1.07444i	0.00873868	−	0.0831430i	0.998022	+	0.0628656i	$0.0200239\pi$
$168$	−0.682664	−	6.49511i	−0.0526686	−	0.501109i
$169$	5.99077	−	1.27338i	0.460829	−	0.0979522i
$170$	−17.5351	+	12.7400i	−1.34488	+	0.977113i
$171$	1.80902	−	1.31433i	0.138339	−	0.100509i
$172$	46.0234	−	9.78258i	3.50925	−	0.745915i
$173$	−1.88151	−	17.9014i	−0.143049	−	1.36102i	−0.796770	−	0.604282i	$-0.793460\pi$
$173$	−1.88151	−	17.9014i	−0.143049	−	1.36102i	0.653721	−	0.756735i	$-0.273207\pi$
$174$	−0.129204	+	1.22930i	−0.00979495	+	0.0931927i
$175$		0			0
$176$	38.1930	−	17.0046i	2.87890	−	1.28177i
$177$	−6.98551	−	7.75819i	−0.525063	−	0.583141i
$178$	−12.4184	+	38.2200i	−0.930800	+	2.86471i
$179$	8.87809	−	9.86012i	0.663580	−	0.736980i	−0.313562	−	0.949568i	$-0.601522\pi$
$179$	8.87809	−	9.86012i	0.663580	−	0.736980i	0.977142	+	0.212588i	$0.0681891\pi$
$180$	12.1353	+	21.0189i	0.904508	+	1.56665i
$181$	−4.34581	+	7.52716i	−0.323021	+	0.559489i	−0.981110	−	0.193451i	$-0.938032\pi$
$181$	−4.34581	+	7.52716i	−0.323021	+	0.559489i	0.658089	+	0.752940i	$0.271365\pi$
$182$	2.12132	+	6.52875i	0.157243	+	0.483943i
$183$	−11.1273	−	4.95419i	−0.822553	−	0.366224i
$184$	15.8508	+	11.5163i	1.16854	+	0.848991i
$185$	9.48683			0.697486
$186$		0			0
$187$	15.7082			1.14870
$188$	38.1246	+	27.6992i	2.78052	+	2.02017i
$189$	−4.18083	−	1.86143i	−0.304111	−	0.135399i
$190$	1.80902	+	5.56758i	0.131240	+	0.403915i
$191$	−4.88197	+	8.45581i	−0.353247	+	0.611841i	−0.986816	−	0.161845i	$-0.948256\pi$
$191$	−4.88197	+	8.45581i	−0.353247	+	0.611841i	0.633570	+	0.773686i	$0.281589\pi$
$192$	3.80562	+	6.59154i	0.274647	+	0.475703i
$193$	−13.8565	+	15.3892i	−0.997412	+	1.10774i	−0.00323349	+	0.999995i	$0.501029\pi$
$193$	−13.8565	+	15.3892i	−0.997412	+	1.10774i	−0.994179	+	0.107744i	$0.965637\pi$
$194$	−5.66312	+	17.4293i	−0.406588	+	1.25135i
$195$	3.42903	+	3.80833i	0.245558	+	0.272720i
$196$	−26.6067	+	11.8460i	−1.90048	+	0.846146i
$197$	1.05675	+	0.224620i	0.0752906	+	0.0160035i	0.245403	−	0.969421i	$-0.421080\pi$
$197$	1.05675	+	0.224620i	0.0752906	+	0.0160035i	−0.170112	+	0.985425i	$0.554413\pi$
$198$	2.59616	−	24.7008i	0.184501	−	1.75541i
$199$	−2.42676	−	23.0891i	−0.172029	−	1.63674i	−0.651117	−	0.758978i	$-0.725699\pi$
$199$	−2.42676	−	23.0891i	−0.172029	−	1.63674i	0.479088	−	0.877767i	$-0.340968\pi$
$200$		0			0
$201$	4.24264	−	3.08246i	0.299253	−	0.217420i
$202$	−4.73607	+	3.44095i	−0.333229	+	0.242105i
$203$	−0.528377	+	0.112310i	−0.0370848	+	0.00788262i
$204$	1.64195	+	15.6222i	0.114960	+	1.09377i
$205$	0.344086	−	3.27376i	0.0240320	−	0.228650i
$206$	−27.4218	−	5.82869i	−1.91057	−	0.406104i
$207$	5.35629	−	2.38477i	0.372288	−	0.165753i
$208$	−17.2893	−	19.2017i	−1.19879	−	1.33140i
$209$	1.31105	−	4.03499i	0.0906871	−	0.279106i
$210$	3.42372	−	3.80243i	0.236259	−	0.262393i
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	0.939156	−	0.343490i	$-0.111609\pi$
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	−0.767049	+	0.641588i	$0.778276\pi$
$212$	33.3221	−	57.7156i	2.28857	−	3.96393i
$213$	0.397610	+	1.22372i	0.0272438	+	0.0838478i
$214$	3.52090	+	1.56760i	0.240684	+	0.107159i
$215$	17.5351	+	12.7400i	1.19588	+	0.868860i
$216$	34.1962			2.32675
$217$		0			0
$218$	−3.38197			−0.229056
$219$	3.00000	+	2.17963i	0.202721	+	0.147286i
$220$	42.0688	+	18.7302i	2.83628	+	1.26279i
$221$	−3.00000	−	9.23305i	−0.201802	−	0.621082i
$222$	4.85410	−	8.40755i	0.325786	−	0.564278i
$223$	−8.07262	−	13.9822i	−0.540583	−	0.936316i	−0.998871	−	0.0475128i	$-0.984871\pi$
$223$	−8.07262	−	13.9822i	−0.540583	−	0.936316i	0.458288	−	0.888804i	$-0.348463\pi$
$224$	−7.26281	+	8.06617i	−0.485267	+	0.538944i
$225$		0			0
$226$	−17.1045	−	18.9965i	−1.13778	−	1.26363i
$227$	2.09366	−	0.932157i	0.138961	−	0.0618695i	−0.336078	−	0.941834i	$-0.609101\pi$
$227$	2.09366	−	0.932157i	0.138961	−	0.0618695i	0.475039	+	0.879965i	$0.342434\pi$
$228$	4.14993	+	0.882095i	0.274836	+	0.0584181i
$229$	−0.443477	+	4.21940i	−0.0293058	+	0.278826i	0.970049	+	0.242909i	$0.0781017\pi$
$229$	−0.443477	+	4.21940i	−0.0293058	+	0.278826i	−0.999355	+	0.0359165i	$0.988565\pi$
$230$	1.60451	+	15.2659i	0.105799	+	1.00661i
$231$	−3.62717	+	0.770979i	−0.238650	+	0.0507267i
$232$	3.26544	−	2.37248i	0.214387	−	0.155761i
$233$	10.8992	−	7.91872i	0.714029	−	0.518773i	−0.170442	−	0.985368i	$-0.554519\pi$
$233$	10.8992	−	7.91872i	0.714029	−	0.518773i	0.884471	+	0.466595i	$0.154519\pi$
$234$	−15.0146	+	3.19145i	−0.981534	+	0.208631i
$235$	2.26913	+	21.5893i	0.148021	+	1.40833i
$236$	−6.06043	+	57.6611i	−0.394500	+	3.75342i
$237$	−1.38546	−	0.294488i	−0.0899950	−	0.0191290i
$238$	−8.85515	+	3.94256i	−0.573994	+	0.255559i
$239$	8.10246	+	8.99869i	0.524104	+	0.582077i	0.945836	−	0.324644i	$-0.105244\pi$
$239$	8.10246	+	8.99869i	0.524104	+	0.582077i	−0.421732	+	0.906720i	$0.638578\pi$
$240$	−5.95130	+	18.3162i	−0.384155	+	1.18231i
$241$	−15.5347	+	17.2531i	−1.00068	+	1.11137i	−0.00690415	+	0.999976i	$0.502198\pi$
$241$	−15.5347	+	17.2531i	−1.00068	+	1.11137i	−0.993777	+	0.111392i	$0.964469\pi$
$242$	−9.16312	−	15.8710i	−0.589028	−	1.02023i
$243$	8.04827	−	13.9400i	0.516296	−	0.894252i
$244$	20.9037	+	64.3350i	1.33822	+	4.11863i
$245$	−12.2565	−	5.45694i	−0.783039	−	0.348631i
$246$	−2.72526	−	1.98002i	−0.173756	−	0.126241i
$247$	−2.62210			−0.166840
$248$		0			0
$249$	2.76393			0.175157
$250$	23.6803	+	17.2048i	1.49768	+	1.08813i
$251$	10.0751	+	4.48572i	0.635934	+	0.283136i	0.699272	−	0.714856i	$-0.253508\pi$
$251$	10.0751	+	4.48572i	0.635934	+	0.283136i	−0.0633373	+	0.997992i	$0.520174\pi$
$252$	3.35410	+	10.3229i	0.211289	+	0.650279i
$253$	5.56231	−	9.63420i	0.349699	−	0.605697i
$254$	12.4184	+	21.5093i	0.779201	+	1.34962i
$255$	−4.84187	+	5.37745i	−0.303210	+	0.336749i
$256$	−4.50000	+	13.8496i	−0.281250	+	0.865598i
$257$	4.05207	+	4.50028i	0.252761	+	0.280720i	0.856150	−	0.516727i	$-0.172850\pi$
$257$	4.05207	+	4.50028i	0.252761	+	0.280720i	−0.603389	+	0.797447i	$0.706183\pi$
$258$	20.2627	−	9.02156i	1.26150	−	0.561658i
$259$	4.14993	+	0.882095i	0.257864	+	0.0548107i
$260$	2.97493	−	28.3046i	0.184497	−	1.75538i
$261$	−0.126258	−	1.20127i	−0.00781518	−	0.0743565i
$262$	−18.9921	+	4.03690i	−1.17334	+	0.249400i
$263$	−14.9768	+	10.8813i	−0.923507	+	0.670967i	−0.944394	−	0.328815i	$-0.893351\pi$
$263$	−14.9768	+	10.8813i	−0.923507	+	0.670967i	0.0208877	+	0.999782i	$0.493351\pi$
$264$	22.4164	−	16.2865i	1.37963	−	1.00236i
$265$	30.0292	−	6.38290i	1.84468	−	0.392098i
$266$	0.273659	+	2.60369i	0.0167791	+	0.159643i
$267$	−1.40240	+	13.3429i	−0.0858253	+	0.816573i
$268$	−28.4882	−	6.05535i	−1.74019	−	0.369889i
$269$	1.97392	−	0.878846i	0.120352	−	0.0535842i	−0.345677	−	0.938353i	$-0.612351\pi$
$269$	1.97392	−	0.878846i	0.120352	−	0.0535842i	0.466029	+	0.884769i	$0.345684\pi$
$270$	17.9268	+	19.9098i	1.09099	+	1.21167i
$271$	−5.74497	+	17.6812i	−0.348982	+	1.07406i	0.610435	+	0.792066i	$0.290994\pi$
$271$	−5.74497	+	17.6812i	−0.348982	+	1.07406i	−0.959417	+	0.281990i	$0.909006\pi$
$272$	24.4128	−	27.1132i	1.48025	−	1.64398i
$273$	1.14590	+	1.98475i	0.0693529	+	0.120123i
$274$	3.43237	−	5.94504i	0.207357	−	0.359153i
$275$		0			0
$276$	10.1628	+	4.52479i	0.611731	+	0.272360i
$277$	−8.17578	−	5.94006i	−0.491235	−	0.356903i	0.314424	−	0.949283i	$-0.398189\pi$
$277$	−8.17578	−	5.94006i	−0.491235	−	0.356903i	−0.805659	+	0.592379i	$0.798189\pi$
$278$	−47.0516			−2.82197
$279$		0			0
$280$	−16.7082			−0.998506
$281$	−10.8090	−	7.85321i	−0.644812	−	0.468483i	0.216688	−	0.976241i	$-0.430475\pi$
$281$	−10.8090	−	7.85321i	−0.644812	−	0.468483i	−0.861500	+	0.507758i	$0.830475\pi$
$282$	20.2942	+	9.03555i	1.20850	+	0.538059i
$283$	7.41641	+	22.8254i	0.440860	+	1.35683i	0.886961	+	0.461844i	$0.152812\pi$
$283$	7.41641	+	22.8254i	0.440860	+	1.35683i	−0.446101	+	0.894982i	$0.647188\pi$
$284$	3.57295	−	6.18853i	0.212016	−	0.367222i
$285$	0.977198	+	1.69256i	0.0578842	+	0.100258i
$286$	−19.4882	+	21.6438i	−1.15236	+	1.27982i
$287$	0.454915	−	1.40008i	0.0268528	−	0.0826444i
$288$	−16.2401	−	18.0365i	−0.956959	−	1.06281i
$289$	−3.00721	+	1.33889i	−0.176894	+	0.0787585i
$290$	3.09317	+	0.657474i	0.181637	+	0.0386082i
$291$	−0.639529	+	6.08471i	−0.0374898	+	0.356692i
$292$	−2.15268	−	20.4814i	−0.125976	−	1.19858i
$293$	2.24171	−	0.476491i	0.130962	−	0.0278369i	−0.141964	−	0.989872i	$-0.545342\pi$
$293$	2.24171	−	0.476491i	0.130962	−	0.0278369i	0.272926	+	0.962035i	$0.412008\pi$
$294$	−11.1074	+	8.06998i	−0.647795	+	0.470651i
$295$	−21.6074	+	15.6987i	−1.25803	+	0.914013i
$296$	−31.0088	+	6.59113i	−1.80235	+	0.383102i
$297$	−2.02957	−	19.3100i	−0.117767	−	1.12048i
$298$	3.67152	−	34.9322i	0.212686	−	2.02357i
$299$	−6.72514	−	1.42947i	−0.388925	−	0.0826686i
$300$		0			0
$301$	6.48599	+	7.20342i	0.373846	+	0.415198i
$302$	10.1302	−	31.1775i	0.582926	−	1.79406i
$303$	−1.30775	+	1.45240i	−0.0751280	+	0.0834381i
$304$	−4.92705	−	8.53390i	−0.282586	−	0.489453i
$305$	−15.5807	+	26.9866i	−0.892148	+	1.54525i
$306$	−6.69781	−	20.6137i	−0.382888	−	1.17841i
$307$	22.0389	+	9.81236i	1.25783	+	0.560021i	0.923920	−	0.382585i	$-0.124966\pi$
$307$	22.0389	+	9.81236i	1.25783	+	0.560021i	0.333908	+	0.942606i	$0.391633\pi$
$308$	16.6611	+	12.1050i	0.949352	+	0.689745i
$309$	−9.35931			−0.532433
$310$		0			0
$311$	25.4721			1.44439			0.722196	−	0.691688i	$-0.243133\pi$
$311$	25.4721			1.44439			0.722196	+	0.691688i	$0.243133\pi$
$312$	−13.8541	−	10.0656i	−0.784334	−	0.569852i
$313$	−10.5241	−	4.68562i	−0.594856	−	0.264847i	0.0871479	−	0.996195i	$-0.472225\pi$
$313$	−10.5241	−	4.68562i	−0.594856	−	0.264847i	−0.682004	+	0.731348i	$0.738891\pi$
$314$	7.04508	+	21.6825i	0.397577	+	1.22362i
$315$	−2.50000	+	4.33013i	−0.140859	+	0.243975i
$316$	3.93314	+	6.81241i	0.221257	+	0.383228i
$317$	17.5554	−	19.4972i	0.986007	−	1.09507i	−0.00945912	−	0.999955i	$-0.503011\pi$
$317$	17.5554	−	19.4972i	0.986007	−	1.09507i	0.995466	−	0.0951165i	$-0.0303224\pi$
$318$	9.70820	−	29.8788i	0.544409	−	1.67552i
$319$	−1.53351	−	1.70314i	−0.0858601	−	0.0953573i
$320$	17.7887	−	7.92003i	0.994418	−	0.442743i
$321$	1.25858	+	0.267519i	0.0702469	+	0.0149314i
$322$	−0.717560	+	6.82713i	−0.0399881	+	0.380461i
$323$	−0.387012	−	3.68218i	−0.0215339	−	0.204882i
$324$	−12.8586	+	2.73319i	−0.714368	+	0.151844i
$325$		0			0
$326$	−30.5344	+	22.1846i	−1.69115	+	1.22869i
$327$	−1.10440	+	0.234747i	−0.0610734	+	0.0129815i
$328$	1.14981	+	10.9397i	0.0634878	+	0.604046i
$329$	−1.01478	+	9.65502i	−0.0559468	+	0.532299i
$330$	21.2338	+	4.51339i	1.16888	+	0.248454i
$331$	28.5839	−	12.7264i	1.57111	−	0.699504i	0.577930	−	0.816086i	$-0.303861\pi$
$331$	28.5839	−	12.7264i	1.57111	−	0.699504i	0.993181	+	0.116583i	$0.0371940\pi$
$332$	−10.2712	−	11.4073i	−0.563704	−	0.626056i
$333$	−2.93159	+	9.02251i	−0.160650	+	0.494431i
$334$	−1.89259	+	2.10193i	−0.103558	+	0.115013i
$335$	−6.70820	−	11.6190i	−0.366508	−	0.634811i
$336$	−4.30640	+	7.45890i	−0.234933	+	0.406917i
$337$	−4.74342	−	14.5987i	−0.258390	−	0.795244i	−0.993143	−	0.116908i	$-0.962702\pi$
$337$	−4.74342	−	14.5987i	−0.258390	−	0.795244i	0.734752	−	0.678335i	$-0.237298\pi$
$338$	−14.6482	−	6.52180i	−0.796757	−	0.354739i
$339$	−6.90414	−	5.01615i	−0.374982	−	0.272440i
$340$	40.1869			2.17944
$341$		0			0
$342$	−5.85410			−0.316554
$343$	−10.5172	−	7.64121i	−0.567877	−	0.412586i
$344$	−66.1669	−	29.4594i	−3.56748	−	1.58834i
$345$	1.58359	+	4.87380i	0.0852577	+	0.262396i
$346$	−23.5623	+	40.8111i	−1.26672	+	2.19402i
$347$	10.7979	+	18.7025i	0.579661	+	1.00400i	0.995518	+	0.0945718i	$0.0301482\pi$
$347$	10.7979	+	18.7025i	0.579661	+	1.00400i	−0.415857	+	0.909430i	$0.636518\pi$
$348$	1.53351	−	1.70314i	0.0822048	−	0.0912977i
$349$	1.85410	−	5.70634i	0.0992478	−	0.305453i	−0.889090	−	0.457733i	$-0.848662\pi$
$349$	1.85410	−	5.70634i	0.0992478	−	0.305453i	0.988337	+	0.152280i	$0.0486615\pi$
$350$		0			0
$351$	−10.9625	+	4.88084i	−0.585137	+	0.260520i
$352$	−45.0438	−	9.57434i	−2.40084	−	0.510314i
$353$	−0.999882	+	9.51324i	−0.0532184	+	0.506339i	0.935149	+	0.354254i	$0.115265\pi$
$353$	−0.999882	+	9.51324i	−0.0532184	+	0.506339i	−0.988367	+	0.152085i	$0.951401\pi$
$354$	2.85691	+	27.1817i	0.151843	+	1.44469i
$355$	3.21986	−	0.684403i	0.170893	−	0.0363243i
$356$	60.2803	−	43.7962i	3.19485	−	2.32119i
$357$	−2.61803	+	1.90211i	−0.138561	+	0.100670i
$358$	−33.9773	+	7.22209i	−1.79575	+	0.381699i
$359$	−1.48807	−	14.1581i	−0.0785376	−	0.747235i	−0.960943	−	0.276746i	$-0.910744\pi$
$359$	−1.48807	−	14.1581i	−0.0785376	−	0.747235i	0.882406	−	0.470489i	$-0.155923\pi$
$360$	3.90525	−	37.1560i	0.205825	−	1.95829i
$361$	17.6067	+	3.74241i	0.926666	+	0.196969i
$362$	20.7877	−	9.25527i	1.09258	−	0.486446i
$363$	−4.09389	−	4.54673i	−0.214874	−	0.238641i
$364$	3.93314	−	12.1050i	0.206153	−	0.634473i
$365$	6.34793	−	7.05009i	0.332266	−	0.369019i
$366$	15.9443	+	27.6163i	0.833420	+	1.44353i
$367$	−3.32920	+	5.76635i	−0.173783	+	0.301001i	−0.939739	−	0.341892i	$-0.888932\pi$
$367$	−3.32920	+	5.76635i	−0.173783	+	0.301001i	0.765956	+	0.642892i	$0.222266\pi$
$368$	−7.98451	−	24.5738i	−0.416221	−	1.28100i
$369$	3.00721	+	1.33889i	0.156549	+	0.0697000i
$370$	−20.0934	−	14.5987i	−1.04461	−	0.758952i
$371$	13.7295			0.712799
$372$		0			0
$373$	−9.29180			−0.481111			−0.240555	−	0.970635i	$-0.577330\pi$
$373$	−9.29180			−0.481111			−0.240555	+	0.970635i	$0.577330\pi$
$374$	−33.2705	−	24.1724i	−1.72038	−	1.24993i
$375$	8.92714	+	3.97462i	0.460996	+	0.205249i
$376$	−22.4164	−	68.9906i	−1.15604	−	3.55792i
$377$	−0.708204	+	1.22665i	−0.0364744	+	0.0631754i
$378$	5.99070	+	10.3762i	0.308129	+	0.533694i
$379$	4.96255	−	5.51147i	0.254909	−	0.283105i	−0.602085	−	0.798432i	$-0.705663\pi$
$379$	4.96255	−	5.51147i	0.254909	−	0.283105i	0.856993	+	0.515327i	$0.172330\pi$
$380$	3.35410	−	10.3229i	0.172062	−	0.529552i
$381$	5.54829	+	6.16201i	0.284248	+	0.315689i
$382$	23.3523	−	10.3971i	1.19481	−	0.531963i
$383$	6.26344	+	1.33133i	0.320047	+	0.0680280i	0.365134	−	0.930955i	$-0.381023\pi$
$383$	6.26344	+	1.33133i	0.320047	+	0.0680280i	−0.0450871	+	0.998983i	$0.514357\pi$
$384$	0.0995993	−	0.947624i	0.00508265	−	0.0483582i
$385$	0.991644	+	9.43486i	0.0505389	+	0.480845i
$386$	53.0301	−	11.2719i	2.69916	−	0.573724i
$387$	−17.5351	+	12.7400i	−0.891359	+	0.647610i
$388$	27.4894	−	19.9722i	1.39556	−	1.01393i
$389$	16.4455	−	3.49561i	0.833822	−	0.177234i	0.228830	−	0.973466i	$-0.426510\pi$
$389$	16.4455	−	3.49561i	0.833822	−	0.177234i	0.604991	+	0.796232i	$0.293177\pi$
$390$	−1.40240	−	13.3429i	−0.0710131	−	0.675645i
$391$	1.01478	−	9.65502i	0.0513198	−	0.488275i
$392$	43.8531	+	9.32127i	2.21492	+	0.470795i
$393$	−5.92176	+	2.63654i	−0.298714	+	0.132996i
$394$	−1.89259	−	2.10193i	−0.0953472	−	0.105894i
$395$	−1.11977	+	3.44629i	−0.0563417	+	0.173402i
$396$	−30.8135	+	34.2219i	−1.54844	+	1.71971i
$397$	−7.35410	−	12.7377i	−0.369092	−	0.639286i	0.620332	−	0.784339i	$-0.286998\pi$
$397$	−7.35410	−	12.7377i	−0.369092	−	0.639286i	−0.989424	+	0.145054i	$0.953665\pi$
$398$	−30.3905	+	52.6380i	−1.52334	+	2.63850i
$399$	0.270091	+	0.831254i	0.0135215	+	0.0416147i
$400$		0			0
$401$	0.437016	+	0.317511i	0.0218235	+	0.0158557i	0.598644	−	0.801016i	$-0.295707\pi$
$401$	0.437016	+	0.317511i	0.0218235	+	0.0158557i	−0.576820	+	0.816871i	$0.695707\pi$
$402$	−13.7295			−0.684764
$403$		0			0
$404$	10.8541			0.540012
$405$	−4.89919	−	3.55947i	−0.243443	−	0.176871i
$406$	1.29195	+	0.575212i	0.0641183	+	0.0285473i
$407$	5.56231	+	17.1190i	0.275713	+	0.848558i
$408$	12.0902	−	20.9408i	0.598553	−	1.03672i
$409$	−15.0405	−	26.0509i	−0.743706	−	1.28814i	−0.950797	−	0.309815i	$-0.899733\pi$
$409$	−15.0405	−	26.0509i	−0.743706	−	1.28814i	0.207091	−	0.978322i	$-0.433600\pi$
$410$	−5.76659	+	6.40445i	−0.284792	+	0.316293i
$411$	0.708204	−	2.17963i	0.0349331	−	0.107513i
$412$	34.7805	+	38.6277i	1.71351	+	1.90305i
$413$	−10.9116	+	4.85817i	−0.536926	+	0.239055i
$414$	−15.0146	−	3.19145i	−0.737927	−	0.156851i
$415$	0.739128	−	7.03233i	0.0362824	−	0.345204i
$416$	2.97493	+	28.3046i	0.145858	+	1.38775i
$417$	−15.3649	+	3.26592i	−0.752424	+	0.159933i
$418$	−8.98606	+	6.52875i	−0.439522	+	0.319332i
$419$	−24.7533	+	17.9843i	−1.20928	+	0.878591i	−0.995165	−	0.0982177i	$-0.968686\pi$
$419$	−24.7533	+	17.9843i	−1.20928	+	0.878591i	−0.214112	+	0.976809i	$0.568686\pi$
$420$	−9.27952	+	1.97242i	−0.452794	+	0.0962444i
$421$	−2.76127	−	26.2717i	−0.134576	−	1.28040i	−0.828350	−	0.560211i	$-0.810720\pi$
$421$	−2.76127	−	26.2717i	−0.134576	−	1.28040i	0.693774	−	0.720193i	$-0.255947\pi$
$422$	1.36830	−	13.0185i	0.0666076	−	0.633729i
$423$	−21.2338	−	4.51339i	−1.03242	−	0.219449i
$424$	−93.7193	+	41.7265i	−4.55141	+	2.02642i
$425$		0			0
$426$	1.04096	−	3.20374i	0.0504345	−	0.155222i
$427$	−9.32487	+	10.3563i	−0.451262	+	0.501178i
$428$	−3.57295	−	6.18853i	−0.172705	−	0.299134i
$429$	−4.86163	+	8.42060i	−0.234722	+	0.406550i
$430$	−17.5351	−	53.9675i	−0.845618	−	2.60254i
$431$	−32.7858	−	14.5972i	−1.57924	−	0.703122i	−0.585071	−	0.810982i	$-0.698933\pi$
$431$	−32.7858	−	14.5972i	−1.57924	−	0.703122i	−0.994166	+	0.107860i	$0.965600\pi$
$432$	−36.4844	−	26.5075i	−1.75536	−	1.27534i
$433$	−25.8384			−1.24171			−0.620857	−	0.783924i	$-0.713215\pi$
$433$	−25.8384			−1.24171			−0.620857	+	0.783924i	$0.713215\pi$
$434$		0			0
$435$	1.05573			0.0506183
$436$	5.07295	+	3.68571i	0.242950	+	0.176514i
$437$	−2.39540	−	1.06650i	−0.114588	−	0.0510177i
$438$	−3.00000	−	9.23305i	−0.143346	−	0.441172i
$439$	12.5000	−	21.6506i	0.596592	−	1.03333i	−0.396728	−	0.917936i	$-0.629854\pi$
$439$	12.5000	−	21.6506i	0.596592	−	1.03333i	0.993320	−	0.115392i	$-0.0368124\pi$
$440$	−35.4435	−	61.3899i	−1.68970	−	2.92665i
$441$	8.97733	−	9.97033i	0.427492	−	0.474778i
$442$	−7.85410	+	24.1724i	−0.373582	+	1.14977i
$443$	4.05207	+	4.50028i	0.192520	+	0.213815i	0.831675	−	0.555263i	$-0.187382\pi$
$443$	4.05207	+	4.50028i	0.192520	+	0.213815i	−0.639155	+	0.769078i	$0.720716\pi$
$444$	−16.4438	+	7.32126i	−0.780389	+	0.347452i
$445$	33.5736	+	7.13630i	1.59154	+	0.338293i
$446$	−4.41829	+	42.0372i	−0.209212	+	1.99052i
$447$	−1.22574	−	11.6621i	−0.0579755	−	0.551600i
$448$	8.51791	−	1.81054i	0.402433	−	0.0855399i
$449$	−27.2677	+	19.8111i	−1.28684	+	0.934945i	−0.999737	−	0.0229547i	$-0.992693\pi$
$449$	−27.2677	+	19.8111i	−1.28684	+	0.934945i	−0.287104	+	0.957899i	$0.592693\pi$
$450$		0			0
$451$	6.10926	−	1.29856i	0.287674	−	0.0611470i
$452$	4.95414	+	47.1355i	0.233023	+	2.21707i
$453$	1.14399	−	10.8843i	0.0537492	−	0.511390i
$454$	−5.86889	−	1.24747i	−0.275440	−	0.0585467i
$455$	5.35629	−	2.38477i	0.251107	−	0.111800i
$456$	−4.37002	−	4.85339i	−0.204645	−	0.227281i
$457$	3.49613	−	10.7600i	0.163542	−	0.503330i	−0.835384	−	0.549667i	$-0.814755\pi$
$457$	3.49613	−	10.7600i	0.163542	−	0.503330i	0.998926	+	0.0463365i	$0.0147546\pi$
$458$	7.43229	−	8.25439i	0.347288	−	0.385702i
$459$	−8.47214	−	14.6742i	−0.395445	−	0.684932i
$460$	14.2302	−	24.6475i	0.663489	−	1.14920i
$461$	1.59619	+	4.91257i	0.0743420	+	0.228801i	0.981322	−	0.192373i	$-0.0616182\pi$
$461$	1.59619	+	4.91257i	0.0743420	+	0.228801i	−0.906980	+	0.421174i	$0.861618\pi$
$462$	8.86889	+	3.94868i	0.412618	+	0.183709i
$463$	3.09852	+	2.25121i	0.144000	+	0.104622i	0.657453	−	0.753496i	$-0.271634\pi$
$463$	3.09852	+	2.25121i	0.144000	+	0.104622i	−0.513453	+	0.858118i	$0.671634\pi$
$464$	−5.32300			−0.247114
$465$		0			0
$466$	−35.2705			−1.63387
$467$	12.6631	+	9.20029i	0.585979	+	0.425739i	0.840875	−	0.541230i	$-0.182041\pi$
$467$	12.6631	+	9.20029i	0.585979	+	0.425739i	−0.254895	+	0.966969i	$0.582041\pi$
$468$	26.0000	+	11.5759i	1.20185	+	0.535097i
$469$	−1.85410	−	5.70634i	−0.0856145	−	0.263494i
$470$	28.4164	−	49.2187i	1.31075	−	2.27029i
$471$	3.80562	+	6.59154i	0.175354	+	0.303722i
$472$	59.7194	−	66.3251i	2.74881	−	3.05286i
$473$	−12.7082	+	39.1118i	−0.584324	+	1.79836i
$474$	2.48127	+	2.75573i	0.113969	+	0.126575i
$475$		0			0
$476$	17.5794	+	3.73661i	0.805750	+	0.171267i
$477$	−3.20903	+	30.5319i	−0.146931	+	1.39796i
$478$	−3.31372	−	31.5279i	−0.151566	−	1.44205i
$479$	−16.1667	+	3.43634i	−0.738675	+	0.157010i	−0.561858	−	0.827234i	$-0.689913\pi$
$479$	−16.1667	+	3.43634i	−0.738675	+	0.157010i	−0.176817	+	0.984244i	$0.556580\pi$
$480$	17.1618	−	12.4688i	0.783327	−	0.569121i
$481$	9.00000	−	6.53888i	0.410365	−	0.298147i
$482$	59.4529	−	12.6371i	2.70800	−	0.575604i
$483$	0.239558	+	2.27924i	0.0109003	+	0.103709i
$484$	−3.55174	+	33.7926i	−0.161443	+	1.53603i
$485$	15.3104	+	3.25433i	0.695211	+	0.147772i
$486$	−38.4980	+	17.1404i	−1.74630	+	0.777504i
$487$	18.7878	+	20.8660i	0.851357	+	0.945528i	0.999053	−	0.0435051i	$-0.0138525\pi$
$487$	18.7878	+	20.8660i	0.851357	+	0.945528i	−0.147696	+	0.989033i	$0.547186\pi$
$488$	32.1780	−	99.0337i	1.45663	−	4.48305i
$489$	−8.43131	+	9.36392i	−0.381277	+	0.423451i
$490$	17.5623	+	30.4188i	0.793384	+	1.37418i
$491$	7.94510	−	13.7613i	0.358557	−	0.621040i	−0.629163	−	0.777274i	$-0.716602\pi$
$491$	7.94510	−	13.7613i	0.358557	−	0.621040i	0.987720	+	0.156234i	$0.0499354\pi$
$492$	1.93004	+	5.94006i	0.0870130	+	0.267798i
$493$	−1.82709	−	0.813473i	−0.0822880	−	0.0366370i
$494$	5.55369	+	4.03499i	0.249872	+	0.181543i
$495$	−21.2132			−0.953463
$496$		0			0
$497$	1.47214			0.0660343
$498$	−5.85410	−	4.25325i	−0.262329	−	0.190593i
$499$	16.7953	+	7.47776i	0.751862	+	0.334751i	0.746633	−	0.665236i	$-0.231669\pi$
$499$	16.7953	+	7.47776i	0.751862	+	0.334751i	0.00522878	+	0.999986i	$0.498336\pi$
$500$	−16.7705	−	51.6143i	−0.750000	−	2.30826i
$501$	−0.472136	+	0.817763i	−0.0210935	+	0.0365350i
$502$	−14.4366	−	25.0049i	−0.644336	−	1.11602i
$503$	−22.0067	+	24.4410i	−0.981232	+	1.08977i	0.0147213	+	0.999892i	$0.495314\pi$
$503$	−22.0067	+	24.4410i	−0.981232	+	1.08977i	−0.995953	+	0.0898765i	$0.971353\pi$
$504$	5.16312	−	15.8904i	0.229984	−	0.707817i
$505$	3.34565	+	3.71572i	0.148880	+	0.165348i
$506$	−26.6067	+	11.8460i	−1.18281	+	0.526621i
$507$	−5.23613	−	1.11297i	−0.232545	−	0.0494289i
$508$	4.81354	−	45.7978i	0.213566	−	2.03195i
$509$	0.830489	+	7.90158i	0.0368108	+	0.350231i	0.997389	+	0.0722203i	$0.0230085\pi$
$509$	0.830489	+	7.90158i	0.0368108	+	0.350231i	−0.960578	+	0.278011i	$0.910325\pi$
$510$	18.5303	−	3.93874i	0.820535	−	0.174410i
$511$	3.43237	−	2.49376i	0.151839	−	0.110318i
$512$	32.6074	−	23.6907i	1.44106	−	1.04699i
$513$	−4.47648	+	0.951506i	−0.197642	+	0.0420100i
$514$	−1.65720	−	15.7673i	−0.0730962	−	0.695464i
$515$	−2.50286	+	23.8131i	−0.110289	+	1.04933i
$516$	−40.2259	−	8.55029i	−1.77085	−	0.376405i
$517$	−37.6275	+	16.7528i	−1.65486	+	0.736789i
$518$	−7.43229	−	8.25439i	−0.326556	−	0.362677i
$519$	−4.86163	+	14.9626i	−0.213402	+	0.656784i
$520$	−29.3150	+	32.5576i	−1.28555	+	1.42774i
$521$	6.70820	+	11.6190i	0.293892	+	0.509035i	0.974726	−	0.223402i	$-0.0717161\pi$
$521$	6.70820	+	11.6190i	0.293892	+	0.509035i	−0.680835	+	0.732437i	$0.738383\pi$
$522$	−1.58114	+	2.73861i	−0.0692046	+	0.119866i
$523$	0.191279	+	0.588697i	0.00836406	+	0.0257419i	0.955151	−	0.296118i	$-0.0956921\pi$
$523$	0.191279	+	0.588697i	0.00836406	+	0.0257419i	−0.946787	+	0.321860i	$0.895692\pi$
$524$	32.8876	+	14.6425i	1.43670	+	0.639661i
$525$		0			0
$526$	48.4658			2.11321
$527$		0			0
$528$	−36.5410			−1.59024
$529$	13.0451	+	9.47781i	0.567178	+	0.412079i
$530$	−73.4251	−	32.6909i	−3.18938	−	1.42000i
$531$	−8.25329	−	25.4010i	−0.358162	−	1.10231i
$532$	2.42705	−	4.20378i	0.105226	−	0.182257i
$533$	−1.93004	−	3.34293i	−0.0835994	−	0.144798i
$534$	23.5030	−	26.1027i	1.01707	−	1.12957i
$535$	1.01722	−	3.13068i	0.0439783	−	0.135351i
$536$	29.9990	+	33.3173i	1.29576	+	1.43909i
$537$	−10.5942	+	4.71682i	−0.457172	+	0.203546i
$538$	−5.53324	−	1.17613i	−0.238555	−	0.0507064i
$539$	2.66086	−	25.3164i	0.114611	−	1.09045i
$540$	−5.19232	−	49.4016i	−0.223442	−	2.12591i
$541$	−25.2683	+	5.37094i	−1.08637	+	0.230915i	−0.716092	−	0.698006i	$-0.754071\pi$
$541$	−25.2683	+	5.37094i	−1.08637	+	0.230915i	−0.370278	+	0.928921i	$0.620737\pi$
$542$	39.3766	−	28.6088i	1.69137	−	1.22885i
$543$	6.14590	−	4.46526i	0.263746	−	0.191622i
$544$	−39.3087	+	8.35532i	−1.68535	+	0.358231i
$545$	0.301935	+	2.87272i	0.0129335	+	0.123054i
$546$	0.627171	−	5.96713i	0.0268404	−	0.255370i
$547$	−2.36360	−	0.502399i	−0.101060	−	0.0214810i	0.157104	−	0.987582i	$-0.449784\pi$
$547$	−2.36360	−	0.502399i	−0.101060	−	0.0214810i	−0.258164	+	0.966101i	$0.583118\pi$
$548$	−11.6275	+	5.17691i	−0.496704	+	0.221147i
$549$	−20.8511	−	23.1574i	−0.889901	−	0.988335i
$550$		0			0
$551$	−0.361452	+	0.401433i	−0.0153984	+	0.0171016i
$552$	−8.56231	−	14.8303i	−0.364436	−	0.631222i
$553$	−0.810272	+	1.40343i	−0.0344563	+	0.0596800i
$554$	8.17578	+	25.1625i	0.347356	+	1.06905i
$555$	−7.57493	−	3.37258i	−0.321538	−	0.143158i
$556$	70.5774	+	51.2775i	2.99315	+	2.17465i
$557$	−10.6460			−0.451086			−0.225543	−	0.974233i	$-0.572416\pi$
$557$	−10.6460			−0.451086			−0.225543	+	0.974233i	$0.572416\pi$
$558$		0			0
$559$	25.4164			1.07500
$560$	17.8262	+	12.9515i	0.753296	+	0.547302i
$561$	−12.5425	−	5.58428i	−0.529545	−	0.235768i
$562$	10.8090	+	33.2667i	0.455951	+	1.40327i
$563$	−4.88197	+	8.45581i	−0.205750	+	0.356370i	−0.950372	−	0.311117i	$-0.899297\pi$
$563$	−4.88197	+	8.45581i	−0.205750	+	0.356370i	0.744621	+	0.667487i	$0.232630\pi$
$564$	−20.5942	−	35.6702i	−0.867173	−	1.50199i
$565$	−14.6090	+	16.2249i	−0.614605	+	0.682589i
$566$	19.4164	−	59.7576i	0.816132	−	2.51180i
$567$	−1.81214	−	2.01259i	−0.0761028	−	0.0845207i
$568$	−10.0490	+	4.47410i	−0.421647	+	0.187729i
$569$	11.4701	+	2.43805i	0.480852	+	0.102208i	0.441959	−	0.897035i	$-0.354284\pi$
$569$	11.4701	+	2.43805i	0.480852	+	0.102208i	0.0388930	+	0.999243i	$0.487617\pi$
$570$	0.534838	−	5.08864i	0.0224019	−	0.213140i
$571$	0.274084	+	2.60773i	0.0114700	+	0.109130i	0.998759	−	0.0498059i	$-0.0158603\pi$
$571$	0.274084	+	2.60773i	0.0114700	+	0.109130i	−0.987289	+	0.158936i	$0.949194\pi$
$572$	52.8200	−	11.2272i	2.20851	−	0.469434i
$573$	6.90414	−	5.01615i	0.288425	−	0.209553i
$574$	−3.11803	+	2.26538i	−0.130144	+	0.0945553i
$575$		0			0
$576$	2.03539	+	19.3655i	0.0848080	+	0.806894i
$577$	3.13585	−	29.8357i	0.130547	−	1.24207i	−0.711506	−	0.702680i	$-0.751987\pi$
$577$	3.13585	−	29.8357i	0.130547	−	1.24207i	0.842053	−	0.539395i	$-0.181347\pi$
$578$	8.42971	+	1.79179i	0.350630	+	0.0745286i
$579$	16.5348	−	7.36178i	0.687164	−	0.305945i
$580$	−3.92324	−	4.35720i	−0.162904	−	0.180923i
$581$	0.977198	−	3.00750i	0.0405410	−	0.124772i
$582$	10.7179	−	11.9035i	0.444273	−	0.493415i
$583$	29.1246	+	50.4453i	1.20622	+	2.08923i
$584$	−15.8508	+	27.4544i	−0.655911	+	1.13607i
$585$	4.05136	+	12.4688i	0.167503	+	0.515522i
$586$	−5.48127	−	2.44042i	−0.226429	−	0.100813i
$587$	12.7279	+	9.24738i	0.525338	+	0.381680i	0.818611	−	0.574349i	$-0.194745\pi$
$587$	12.7279	+	9.24738i	0.525338	+	0.381680i	−0.293273	+	0.956029i	$0.594745\pi$
$588$	25.4558			1.04978
$589$		0			0
$590$	69.9230			2.87868
$591$	−0.763932	−	0.555029i	−0.0314240	−	0.0228308i
$592$	38.1930	+	17.0046i	1.56972	+	0.698885i
$593$	1.60081	+	4.92680i	0.0657375	+	0.202319i	0.978530	−	0.206104i	$-0.0660786\pi$
$593$	1.60081	+	4.92680i	0.0657375	+	0.202319i	−0.912793	+	0.408424i	$0.866079\pi$
$594$	−25.4164	+	44.0225i	−1.04285	+	1.80627i
$595$	4.13948	+	7.16978i	0.169702	+	0.293932i
$596$	−43.5769	+	48.3970i	−1.78498	+	1.98242i
$597$	−6.27051	+	19.2986i	−0.256635	+	0.789841i
$598$	12.0444	+	13.3766i	0.492530	+	0.547010i
$599$	5.53218	−	2.46309i	0.226039	−	0.100639i	−0.290593	−	0.956847i	$-0.593852\pi$
$599$	5.53218	−	2.46309i	0.226039	−	0.100639i	0.516631	+	0.856208i	$0.327186\pi$
$600$		0			0
$601$	−1.90016	+	18.0789i	−0.0775093	+	0.737452i	0.884888	+	0.465805i	$0.154235\pi$
$601$	−1.90016	+	18.0789i	−0.0775093	+	0.737452i	−0.962397	+	0.271647i	$0.912432\pi$
$602$	−2.65262	−	25.2380i	−0.108113	−	1.02862i
$603$	13.1232	−	2.78943i	0.534419	−	0.113594i
$604$	−49.1729	+	35.7262i	−2.00082	+	1.45368i
$605$	−12.6631	+	9.20029i	−0.514829	+	0.374045i
$606$	5.00486	−	1.06382i	0.203309	−	0.0432146i
$607$	−1.58095	−	15.0418i	−0.0641689	−	0.610526i	−0.978598	−	0.205780i	$-0.934027\pi$
$607$	−1.58095	−	15.0418i	−0.0641689	−	0.610526i	0.914429	−	0.404746i	$-0.132640\pi$
$608$	−1.13456	+	10.7946i	−0.0460126	+	0.437781i
$609$	0.461819	+	0.0981626i	0.0187138	+	0.00397775i
$610$	74.5285	−	33.1822i	3.01757	−	1.34351i
$611$	17.0333	+	18.9174i	0.689093	+	0.765315i
$612$	−12.4184	+	38.2200i	−0.501985	+	1.54495i
$613$	0.394044	−	0.437630i	0.0159153	−	0.0176757i	−0.735135	−	0.677921i	$-0.762881\pi$
$613$	0.394044	−	0.437630i	0.0159153	−	0.0176757i	0.751050	+	0.660245i	$0.229548\pi$
$614$	−31.5795	−	54.6973i	−1.27445	−	2.20741i
$615$	−1.43857	+	2.49167i	−0.0580086	+	0.100474i
$616$	−9.79633	−	30.1500i	−0.394705	−	1.21478i
$617$	−6.28098	−	2.79647i	−0.252863	−	0.112582i	0.276391	−	0.961045i	$-0.410861\pi$
$617$	−6.28098	−	2.79647i	−0.252863	−	0.112582i	−0.529254	+	0.848463i	$0.677528\pi$
$618$	19.8233	+	14.4025i	0.797412	+	0.579354i
$619$	25.8384			1.03853			0.519267	−	0.854612i	$-0.326205\pi$
$619$	25.8384			1.03853			0.519267	+	0.854612i	$0.326205\pi$
$620$		0			0
$621$	−12.0000			−0.481543
$622$	−53.9508	−	39.1976i	−2.16323	−	1.57168i
$623$	14.0229	+	6.24341i	0.561817	+	0.250137i
$624$	6.97871	+	21.4783i	0.279372	+	0.859819i
$625$	12.5000	−	21.6506i	0.500000	−	0.866025i
$626$	15.0799	+	26.1192i	0.602715	+	1.04393i
$627$	−2.48127	+	2.75573i	−0.0990925	+	0.110053i
$628$	13.0623	−	40.2016i	0.521243	−	1.60422i
$629$	10.5108	+	11.6735i	0.419095	+	0.465452i
$630$	11.9585	−	5.32425i	0.476437	−	0.212123i
$631$	23.1126	+	4.91274i	0.920099	+	0.195573i	0.643530	−	0.765421i	$-0.277469\pi$
$631$	23.1126	+	4.91274i	0.920099	+	0.195573i	0.276569	+	0.960994i	$0.410803\pi$
$632$	1.26573	−	12.0426i	0.0503479	−	0.479029i
$633$	−0.456806	−	4.34622i	−0.0181564	−	0.172747i
$634$	−67.1859	+	14.2808i	−2.66829	+	0.567164i
$635$	17.1618	−	12.4688i	0.681047	−	0.494810i
$636$	−47.1246	+	34.2380i	−1.86861	+	1.35763i
$637$	−15.3888	+	3.27099i	−0.609726	+	0.129601i
$638$	0.627171	+	5.96713i	0.0248299	+	0.236241i
$639$	−0.344086	+	3.27376i	−0.0136118	+	0.129508i
$640$	−2.38442	−	0.506825i	−0.0942527	−	0.0200340i
$641$	−7.75169	+	3.45127i	−0.306173	+	0.136317i	−0.554072	−	0.832469i	$-0.686927\pi$
$641$	−7.75169	+	3.45127i	−0.306173	+	0.136317i	0.247898	+	0.968786i	$0.420260\pi$
$642$	−2.25404	−	2.50336i	−0.0889598	−	0.0987999i
$643$	−1.43857	+	4.42746i	−0.0567316	+	0.174602i	−0.975407	−	0.220411i	$-0.929260\pi$
$643$	−1.43857	+	4.42746i	−0.0567316	+	0.174602i	0.918675	+	0.395013i	$0.129260\pi$
$644$	8.51664	−	9.45869i	0.335603	−	0.372725i
$645$	−9.47214	−	16.4062i	−0.372965	−	0.645994i
$646$	−4.84658	+	8.39453i	−0.190686	+	0.330278i
$647$	9.82068	+	30.2250i	0.386091	+	1.18827i	0.935686	+	0.352834i	$0.114782\pi$
$647$	9.82068	+	30.2250i	0.386091	+	1.18827i	−0.549595	+	0.835431i	$0.685218\pi$
$648$	18.4866	+	8.23075i	0.726221	+	0.323334i
$649$	−40.9971	−	29.7862i	−1.60928	−	1.16921i
$650$		0			0
$651$		0			0
$652$	69.9787			2.74058
$653$	−19.9443	−	14.4904i	−0.780480	−	0.567052i	0.124643	−	0.992202i	$-0.460221\pi$
$653$	−19.9443	−	14.4904i	−0.780480	−	0.567052i	−0.905123	+	0.425150i	$0.860221\pi$
$654$	2.70039	+	1.20229i	0.105594	+	0.0470133i
$655$	5.12461	+	15.7719i	0.200235	+	0.616260i
$656$	7.25329	−	12.5631i	0.283193	−	0.490505i
$657$	4.74342	+	8.21584i	0.185058	+	0.320530i
$658$	17.0069	−	18.8881i	0.662998	−	0.736334i
$659$	7.66970	−	23.6049i	0.298769	−	0.919516i	−0.683160	−	0.730268i	$-0.739395\pi$
$659$	7.66970	−	23.6049i	0.298769	−	0.919516i	0.981929	−	0.189248i	$-0.0606050\pi$
$660$	−26.9320	−	29.9110i	−1.04833	−	1.16428i
$661$	7.15563	−	3.18589i	0.278322	−	0.123917i	−0.262829	−	0.964842i	$-0.584655\pi$
$661$	7.15563	−	3.18589i	0.278322	−	0.123917i	0.541151	+	0.840926i	$0.317989\pi$
$662$	−80.1254	−	17.0312i	−3.11416	−	0.661936i
$663$	−0.886953	+	8.43880i	−0.0344464	+	0.327736i
$664$	2.46990	+	23.4995i	0.0958507	+	0.911958i
$665$	2.18720	−	0.464905i	0.0848162	−	0.0180282i
$666$	20.0934	−	14.5987i	0.778605	−	0.565689i
$667$	−1.14590	+	0.832544i	−0.0443693	+	0.0322362i
$668$	5.12959	−	1.09033i	0.198470	−	0.0421861i
$669$	1.47505	+	14.0342i	0.0570287	+	0.542592i
$670$	−3.67152	+	34.9322i	−0.141843	+	1.34955i
$671$	−57.8326	−	12.2927i	−2.23260	−	0.474554i
$672$	8.66665	−	3.85864i	0.334323	−	0.148850i
$673$	26.7522	+	29.7113i	1.03122	+	1.14529i	0.989260	+	0.146168i	$0.0466941\pi$
$673$	26.7522	+	29.7113i	1.03122	+	1.14529i	0.0419619	+	0.999119i	$0.486639\pi$
$674$	−12.4184	+	38.2200i	−0.478340	+	1.47218i
$675$		0			0
$676$	14.8647	+	25.7465i	0.571721	+	0.990250i
$677$	10.6066	−	18.3712i	0.407645	−	0.706062i	−0.586981	−	0.809601i	$-0.699683\pi$
$677$	10.6066	−	18.3712i	0.407645	−	0.706062i	0.994625	+	0.103540i	$0.0330168\pi$
$678$	6.90414	+	21.2488i	0.265152	+	0.816054i
$679$	6.39482	+	2.84716i	0.245411	+	0.109264i
$680$	−50.0470	−	36.3612i	−1.91921	−	1.39439i
$681$	−2.00310			−0.0767591
$682$		0			0
$683$	−41.1803			−1.57572			−0.787861	−	0.615853i	$-0.788811\pi$
$683$	−41.1803			−1.57572			−0.787861	+	0.615853i	$0.788811\pi$
$684$	8.78115	+	6.37988i	0.335756	+	0.243941i
$685$	−5.35629	−	2.38477i	−0.204653	−	0.0911175i
$686$	10.5172	+	32.3687i	0.401549	+	1.23584i
$687$	1.85410	−	3.21140i	0.0707384	−	0.122523i
$688$	47.7587	+	82.7205i	1.82078	+	3.15369i
$689$	24.0887	−	26.7532i	0.917706	−	1.01922i
$690$	4.14590	−	12.7598i	0.157832	−	0.485756i
$691$	−32.3969	−	35.9804i	−1.23244	−	1.36876i	−0.905854	−	0.423590i	$-0.860770\pi$
$691$	−32.3969	−	35.9804i	−1.23244	−	1.36876i	−0.326582	−	0.945169i	$-0.605897\pi$
$692$	79.8200	−	35.5381i	3.03430	−	1.35096i
$693$	−9.27952	−	1.97242i	−0.352500	−	0.0749262i
$694$	5.90988	−	56.2287i	0.224336	−	2.13441i
$695$	4.20067	+	39.9667i	0.159341	+	1.51602i
$696$	−3.45077	+	0.733484i	−0.130801	+	0.0278026i
$697$	4.40957	−	3.20374i	0.167024	−	0.121350i
$698$	−12.7082	+	9.23305i	−0.481013	+	0.349476i
$699$	−11.5178	+	2.44818i	−0.435642	+	0.0925985i
$700$		0			0
$701$	0.381788	−	3.63247i	0.0144199	−	0.137196i	−0.984943	−	0.172878i	$-0.944693\pi$
$701$	0.381788	−	3.63247i	0.0144199	−	0.137196i	0.999363	+	0.0356813i	$0.0113601\pi$
$702$	30.7299	+	6.53184i	1.15982	+	0.246528i
$703$	3.87585	−	1.72564i	0.146180	−	0.0650836i
$704$	24.7216	+	27.4561i	0.931729	+	1.03479i
$705$	5.86319	−	18.0450i	0.220820	−	0.679615i
$706$	16.7572	−	18.6107i	0.630664	−	0.700423i
$707$	1.11803	+	1.93649i	0.0420480	+	0.0728293i
$708$	25.3376	−	43.8861i	0.952246	−	1.64934i
$709$	−12.7279	−	39.1725i	−0.478007	−	1.47115i	−0.841859	−	0.539698i	$-0.818538\pi$
$709$	−12.7279	−	39.1725i	−0.478007	−	1.47115i	0.363852	−	0.931457i	$-0.381462\pi$
$710$	−7.87297	−	3.50527i	−0.295467	−	0.131550i
$711$	−2.93159	−	2.12993i	−0.109943	−	0.0798785i
$712$	−114.697			−4.29847
$713$		0			0
$714$	8.47214			0.317062
$715$	20.1246	+	14.6214i	0.752618	+	0.546809i
$716$	58.8366	+	26.1958i	2.19883	+	0.978982i
$717$	−3.27051	−	10.0656i	−0.122139	−	0.375907i
$718$	−18.6353	+	32.2772i	−0.695462	+	1.20457i
$719$	18.7824	+	32.5320i	0.700465	+	1.21324i	0.968303	+	0.249777i	$0.0803573\pi$
$719$	18.7824	+	32.5320i	0.700465	+	1.21324i	−0.267839	+	0.963464i	$0.586309\pi$
$720$	−32.9684	+	36.6151i	−1.22866	+	1.36457i
$721$	−3.30902	+	10.1841i	−0.123234	+	0.379276i
$722$	−31.5325	−	35.0204i	−1.17352	−	1.30332i
$723$	18.5375	−	8.25342i	0.689416	−	0.306948i
$724$	−41.2680	−	8.77179i	−1.53371	−	0.326001i
$725$		0			0
$726$	1.67431	+	15.9300i	0.0621394	+	0.591217i
$727$	29.7517	−	6.32393i	1.10343	−	0.234541i	0.380033	−	0.924973i	$-0.375913\pi$
$727$	29.7517	−	6.32393i	1.10343	−	0.234541i	0.723398	+	0.690431i	$0.242579\pi$
$728$	−15.8508	+	11.5163i	−0.587470	+	0.426822i
$729$	−4.80902	+	3.49396i	−0.178112	+	0.129406i
$730$	−24.2941	+	5.16387i	−0.899165	+	0.191123i
$731$	3.75137	+	35.6919i	0.138750	+	1.32011i
$732$	6.18020	−	58.8007i	0.228427	−	2.17334i
$733$	14.1014	+	2.99734i	0.520846	+	0.110709i	0.460831	−	0.887488i	$-0.347552\pi$
$733$	14.1014	+	2.99734i	0.520846	+	0.110709i	0.0600157	+	0.998197i	$0.480885\pi$
$734$	15.9249	−	7.09021i	0.587797	−	0.261704i
$735$	7.84647	+	8.71439i	0.289422	+	0.321435i
$736$	−8.79478	+	27.0675i	−0.324180	+	0.997723i
$737$	17.0333	−	18.9174i	0.627429	−	0.696831i
$738$	−4.30902	−	7.46344i	−0.158617	−	0.274733i
$739$	17.5745	−	30.4399i	0.646489	−	1.11975i	−0.337467	−	0.941337i	$-0.609570\pi$
$739$	17.5745	−	30.4399i	0.646489	−	1.11975i	0.983956	−	0.178414i	$-0.0570965\pi$
$740$	14.2302	+	43.7962i	0.523114	+	1.60998i
$741$	2.09366	+	0.932157i	0.0769125	+	0.0342437i
$742$	−29.0795	−	21.1275i	−1.06754	−	0.775614i
$743$	−36.4844			−1.33848			−0.669242	−	0.743045i	$-0.733381\pi$
$743$	−36.4844			−1.33848			−0.669242	+	0.743045i	$0.733381\pi$
$744$		0			0
$745$	−30.0000			−1.09911
$746$	19.6803	+	14.2986i	0.720548	+	0.523509i
$747$	6.45974	+	2.87606i	0.236350	+	0.105230i
$748$	23.5623	+	72.5173i	0.861523	+	2.65150i
$749$	0.736068	−	1.27491i	0.0268953	−	0.0465841i
$750$	−12.7917	−	22.1558i	−0.467086	−	0.809017i
$751$	−25.1198	+	27.8984i	−0.916636	+	1.01803i	0.0831329	+	0.996538i	$0.473507\pi$
$751$	−25.1198	+	27.8984i	−0.916636	+	1.01803i	−0.999769	+	0.0214891i	$0.993159\pi$
$752$	−29.5623	+	90.9834i	−1.07803	+	3.31782i
$753$	−6.44996	−	7.16341i	−0.235050	−	0.261049i
$754$	3.38761	−	1.50826i	0.123370	−	0.0549277i
$755$	−27.3873	−	5.82135i	−0.996725	−	0.211860i
$756$	2.32207	−	22.0931i	0.0844530	−	0.803517i
$757$	−0.970077	−	9.22966i	−0.0352580	−	0.335458i	−0.997905	−	0.0646977i	$-0.979392\pi$
$757$	−0.970077	−	9.22966i	−0.0352580	−	0.335458i	0.962647	−	0.270760i	$-0.0872750\pi$
$758$	−18.9921	+	4.03690i	−0.689825	+	0.146627i
$759$	−7.86629	+	5.71519i	−0.285528	+	0.207448i
$760$	−13.5172	+	9.82084i	−0.490321	+	0.356239i
$761$	−39.3087	+	8.35532i	−1.42494	+	0.302880i	−0.854924	−	0.518754i	$-0.826396\pi$
$761$	−39.3087	+	8.35532i	−1.42494	+	0.302880i	−0.570015	+	0.821634i	$0.693063\pi$
$762$	−2.26913	−	21.5893i	−0.0822017	−	0.782097i
$763$	−0.135029	+	1.28472i	−0.00488839	+	0.0465100i
$764$	−46.3594	−	9.85400i	−1.67723	−	0.356505i
$765$	−16.9118	+	7.52963i	−0.611448	+	0.272234i
$766$	−11.2175	−	12.4583i	−0.405303	−	0.450135i
$767$	−9.67811	+	29.7862i	−0.349456	+	1.07552i
$768$	8.51664	−	9.45869i	0.307318	−	0.341311i
$769$	−27.0623	−	46.8733i	−0.975892	−	1.69029i	−0.676960	−	0.736019i	$-0.736703\pi$
$769$	−27.0623	−	46.8733i	−0.975892	−	1.69029i	−0.298931	−	0.954275i	$-0.596630\pi$
$770$	12.4184	−	21.5093i	0.447529	−	0.775143i
$771$	−1.63560	−	5.03385i	−0.0589046	−	0.181290i
$772$	−91.8293	−	40.8851i	−3.30501	−	1.47149i
$773$	9.04982	+	6.57508i	0.325499	+	0.236489i	0.738518	−	0.674233i	$-0.235526\pi$
$773$	9.04982	+	6.57508i	0.325499	+	0.236489i	−0.413019	+	0.910722i	$0.635526\pi$
$774$	56.7448			2.03965
$775$		0			0
$776$	−52.3050			−1.87764
$777$	−3.00000	−	2.17963i	−0.107624	−	0.0781937i
$778$	−40.2114	−	17.9033i	−1.44165	−	0.641863i
$779$	−0.454915	−	1.40008i	−0.0162990	−	0.0501632i
$780$	−12.4377	+	21.5427i	−0.445341	+	0.771353i
$781$	3.12287	+	5.40897i	0.111745	+	0.193548i
$782$	−17.0069	+	18.8881i	−0.608165	+	0.675436i
$783$	−0.763932	+	2.35114i	−0.0273007	+	0.0840229i
$784$	−39.5621	−	43.9381i	−1.41293	−	1.56922i
$785$	17.7887	−	7.92003i	0.634905	−	0.282678i
$786$	16.5997	+	3.52838i	0.592092	+	0.125853i
$787$	3.92659	−	37.3590i	0.139968	−	1.33170i	−0.668741	−	0.743495i	$-0.733167\pi$
$787$	3.92659	−	37.3590i	0.139968	−	1.33170i	0.808709	−	0.588209i	$-0.200167\pi$
$788$	0.548167	+	5.21546i	0.0195277	+	0.185793i
$789$	15.8268	−	3.36408i	0.563448	−	0.119764i
$790$	7.67501	−	5.57622i	0.273065	−	0.198393i
$791$	−7.89919	+	5.73910i	−0.280863	+	0.204059i
$792$	69.3379	−	14.7382i	2.46381	−	0.523700i
$793$	3.81958	+	36.3408i	0.135637	+	1.29050i
$794$	−4.02503	+	38.2956i	−0.142843	+	1.35906i
$795$	−26.2465	−	5.57886i	−0.930866	−	0.197862i
$796$	102.951	−	45.8369i	3.64902	−	1.62465i
$797$	−9.18681	−	10.2030i	−0.325414	−	0.361408i	0.558133	−	0.829751i	$-0.311518\pi$
$797$	−9.18681	−	10.2030i	−0.325414	−	0.361408i	−0.883547	+	0.468343i	$0.844851\pi$
$798$	0.707107	−	2.17625i	0.0250313	−	0.0770384i
$799$	−24.0514	+	26.7118i	−0.850877	+	0.944994i
$800$		0			0
$801$	−17.1618	+	29.7252i	−0.606384	+	1.05029i
$802$	−0.437016	−	1.34500i	−0.0154316	−	0.0474935i
$803$	16.4438	+	7.32126i	0.580290	+	0.258362i
$804$	20.5942	+	14.9626i	0.726302	+	0.527689i
$805$	5.86319			0.206650
$806$		0			0
$807$	−1.88854			−0.0664799
$808$	−13.5172	−	9.82084i	−0.475534	−	0.345496i
$809$	43.4053	+	19.3253i	1.52605	+	0.679440i	0.986686	−	0.162634i	$-0.0519990\pi$
$809$	43.4053	+	19.3253i	1.52605	+	0.679440i	0.539361	+	0.842074i	$0.318666\pi$
$810$	4.89919	+	15.0781i	0.172140	+	0.529792i
$811$	8.29180	−	14.3618i	0.291164	−	0.504311i	−0.682921	−	0.730492i	$-0.739291\pi$
$811$	8.29180	−	14.3618i	0.291164	−	0.504311i	0.974085	+	0.226181i	$0.0726240\pi$
$812$	−1.31105	−	2.27080i	−0.0460088	−	0.0796895i
$813$	10.8729	−	12.0755i	0.381328	−	0.423507i
$814$	14.5623	−	44.8182i	0.510409	−	1.57088i
$815$	21.5701	+	23.9561i	0.755569	+	0.839144i
$816$	−29.1316	+	12.9702i	−1.01981	+	0.454049i
$817$	9.48135	+	2.01532i	0.331710	+	0.0705072i
$818$	−8.23195	+	78.3218i	−0.287823	+	2.73846i
$819$	0.612870	+	5.83107i	0.0214154	+	0.203754i
$820$	15.6295	−	3.32216i	0.545807	−	0.116015i
$821$	−19.2832	+	14.0100i	−0.672987	+	0.488954i	−0.871024	−	0.491241i	$-0.836543\pi$
$821$	−19.2832	+	14.0100i	−0.672987	+	0.488954i	0.198037	+	0.980195i	$0.436543\pi$
$822$	−4.85410	+	3.52671i	−0.169306	+	0.123008i
$823$	13.2276	−	2.81162i	0.461086	−	0.0980069i	0.0284888	−	0.999594i	$-0.490931\pi$
$823$	13.2276	−	2.81162i	0.461086	−	0.0980069i	0.432597	+	0.901587i	$0.357597\pi$
$824$	−8.36365	−	79.5748i	−0.291362	−	2.77212i
$825$		0			0
$826$	30.5872	+	6.50150i	1.06426	+	0.226216i
$827$	−16.7678	+	7.46552i	−0.583075	+	0.259601i	−0.677006	−	0.735977i	$-0.736723\pi$
$827$	−16.7678	+	7.46552i	−0.583075	+	0.259601i	0.0939319	+	0.995579i	$0.470056\pi$
$828$	19.0438	+	21.1503i	0.661817	+	0.735023i
$829$	15.7870	−	48.5875i	0.548306	−	1.68751i	−0.164690	−	0.986345i	$-0.552662\pi$
$829$	15.7870	−	48.5875i	0.548306	−	1.68751i	0.712996	−	0.701168i	$-0.247338\pi$
$830$	−12.3871	+	13.7573i	−0.429964	+	0.477523i
$831$	4.41641	+	7.64944i	0.153203	+	0.265356i
$832$	11.4169	−	19.7746i	0.395809	−	0.685561i
$833$	−6.86474	−	21.1275i	−0.237849	−	0.732024i
$834$	37.5692	+	16.7269i	1.30092	+	0.579205i
$835$	1.95440	+	1.41995i	0.0676346	+	0.0491394i
$836$	20.5942			0.712266
$837$		0			0
$838$	80.1033			2.76712
$839$	15.7082	+	11.4127i	0.542307	+	0.394009i	0.824941	−	0.565218i	$-0.191208\pi$
$839$	15.7082	+	11.4127i	0.542307	+	0.394009i	−0.282634	+	0.959228i	$0.591208\pi$
$840$	13.3410	+	5.93978i	0.460307	+	0.204942i
$841$	−8.87132	−	27.3031i	−0.305908	−	0.941487i
$842$	−34.5795	+	59.8935i	−1.19169	+	2.06407i
$843$	5.83883	+	10.1132i	0.201100	+	0.348315i
$844$	−16.2401	+	18.0365i	−0.559009	+	0.620842i
$845$	−4.23200	+	13.0248i	−0.145585	+	0.448066i
$846$	38.0286	+	42.2350i	1.30745	+	1.45207i
$847$	−6.39482	+	2.84716i	−0.219729	+	0.0978295i
$848$	132.335	+	28.1287i	4.54441	+	0.965944i
$849$	2.19267	−	20.8619i	0.0752522	−	0.715977i
$850$		0			0
$851$	10.8815	−	2.31294i	0.373013	−	0.0792865i
$852$	−5.05291	+	3.67116i	−0.173110	+	0.125772i
$853$	26.1246	−	18.9806i	0.894490	−	0.649885i	−0.0425551	−	0.999094i	$-0.513550\pi$
$853$	26.1246	−	18.9806i	0.894490	−	0.649885i	0.937045	+	0.349209i	$0.113550\pi$
$854$	35.6871	−	7.58554i	1.22119	−	0.259572i
$855$	0.522642	+	4.97261i	0.0178740	+	0.170060i
$856$	−1.14981	+	10.9397i	−0.0392998	+	0.373913i
$857$	5.86889	+	1.24747i	0.200477	+	0.0426128i	0.307056	−	0.951692i	$-0.400656\pi$
$857$	5.86889	+	1.24747i	0.200477	+	0.0426128i	−0.106578	+	0.994304i	$0.533990\pi$
$858$	23.2551	−	10.3538i	0.793915	−	0.353474i
$859$	−27.8366	−	30.9156i	−0.949771	−	1.05483i	−0.998430	−	0.0560122i	$-0.982161\pi$
$859$	−27.8366	−	30.9156i	−0.949771	−	1.05483i	0.0486590	−	0.998815i	$-0.484505\pi$
$860$	−32.5119	+	100.061i	−1.10865	+	3.41206i
$861$	−0.860966	+	0.956200i	−0.0293417	+	0.0325872i
$862$	46.9787	+	81.3695i	1.60010	+	2.77146i
$863$	15.5413	−	26.9183i	0.529032	−	0.916310i	−0.470395	−	0.882456i	$-0.655889\pi$
$863$	15.5413	−	26.9183i	0.529032	−	0.916310i	0.999427	−	0.0338541i	$-0.0107782\pi$
$864$	15.3500	+	47.2425i	0.522218	+	1.60722i
$865$	36.7695	+	16.3708i	1.25020	+	0.556625i
$866$	54.7266	+	39.7612i	1.85969	+	1.35114i
$867$	2.87714			0.0977126
$868$		0			0
$869$	−6.87539			−0.233232
$870$	−2.23607	−	1.62460i	−0.0758098	−	0.0550790i
$871$	−14.3724	−	6.39902i	−0.486991	−	0.216822i
$872$	−2.98278	−	9.18005i	−0.101010	−	0.310876i
$873$	−7.82624	+	13.5554i	−0.264878	+	0.458782i
$874$	3.43237	+	5.94504i	0.116102	+	0.201094i
$875$	7.48111	−	8.30861i	0.252908	−	0.280882i
$876$	−5.56231	+	17.1190i	−0.187933	+	0.578398i
$877$	−19.2095	−	21.3344i	−0.648660	−	0.720410i	0.325683	−	0.945479i	$-0.394406\pi$
$877$	−19.2095	−	21.3344i	−0.648660	−	0.720410i	−0.974343	+	0.225069i	$0.927739\pi$
$878$	−59.7923	+	26.6213i	−2.01789	+	0.898424i
$879$	−1.95933	−	0.416469i	−0.0660866	−	0.0140471i
$880$	−9.77176	+	92.9721i	−0.329406	+	3.13409i
$881$	−0.757549	−	7.20759i	−0.0255225	−	0.242830i	−0.999844	−	0.0176684i	$-0.994376\pi$
$881$	−0.757549	−	7.20759i	−0.0255225	−	0.242830i	0.974321	−	0.225162i	$-0.0722910\pi$
$882$	−34.3571	+	7.30282i	−1.15686	+	0.245899i
$883$	27.4589	−	19.9501i	0.924067	−	0.671374i	−0.0204659	−	0.999791i	$-0.506515\pi$
$883$	27.4589	−	19.9501i	0.924067	−	0.671374i	0.944533	+	0.328416i	$0.106515\pi$
$884$	38.1246	−	27.6992i	1.28227	−	0.931623i
$885$	22.8337	−	4.85345i	0.767547	−	0.163147i
$886$	−1.65720	−	15.7673i	−0.0556749	−	0.529711i
$887$	−2.65091	+	25.2218i	−0.0890089	+	0.846864i	0.855373	+	0.518013i	$0.173328\pi$
$887$	−2.65091	+	25.2218i	−0.0890089	+	0.846864i	−0.944382	+	0.328851i	$0.893339\pi$
$888$	27.1027	+	5.76086i	0.909508	+	0.193322i
$889$	8.66665	−	3.85864i	0.290670	−	0.129415i
$890$	−60.1285	−	66.7794i	−2.01551	−	2.23845i
$891$	3.55059	−	10.9276i	0.118949	−	0.366088i
$892$	52.4402	−	58.2407i	1.75583	−	1.95004i
$893$	4.85410	+	8.40755i	0.162436	+	0.281348i
$894$	−15.3500	+	26.5870i	−0.513381	+	0.889203i
$895$	9.16803	+	28.2163i	0.306454	+	0.943167i
$896$	−0.995920	−	0.443412i	−0.0332713	−	0.0148134i
$897$	4.86163	+	3.53218i	0.162325	+	0.117936i
$898$	88.2400			2.94461
$899$		0			0
$900$		0			0
$901$	41.1246	+	29.8788i	1.37006	+	0.995406i
$902$	−14.9379	−	6.65078i	−0.497378	−	0.221447i
$903$	−2.61803	−	8.05748i	−0.0871227	−	0.268136i
$904$	36.4787	−	63.1830i	1.21326	−	2.10143i
$905$	−9.71752	−	16.8312i	−0.323021	−	0.559489i
$906$	−19.1722	+	21.2929i	−0.636955	+	0.707411i
$907$	3.56637	−	10.9762i	0.118419	−	0.364457i	−0.874225	−	0.485520i	$-0.838630\pi$
$907$	3.56637	−	10.9762i	0.118419	−	0.364457i	0.992645	+	0.121063i	$0.0386302\pi$
$908$	7.44382	+	8.26720i	0.247032	+	0.274357i
$909$	−4.56773	+	2.03368i	−0.151502	+	0.0674530i
$910$	−15.0146	−	3.19145i	−0.497729	−	0.105795i
$911$	2.81378	−	26.7713i	0.0932246	−	0.886973i	−0.843553	−	0.537047i	$-0.819540\pi$
$911$	2.81378	−	26.7713i	0.0932246	−	0.886973i	0.936777	−	0.349926i	$-0.113793\pi$
$912$	0.900283	+	8.56562i	0.0298113	+	0.283636i
$913$	13.1232	−	2.78943i	0.434315	−	0.0923166i
$914$	−23.9628	+	17.4100i	−0.792620	+	0.575872i
$915$	22.0344	−	16.0090i	0.728436	−	0.529240i
$916$	−20.1442	+	4.28178i	−0.665582	+	0.141474i
$917$	0.775226	+	7.37578i	0.0256002	+	0.243570i
$918$	−4.63695	+	44.1177i	−0.153042	+	1.45610i
$919$	41.6114	+	8.84478i	1.37263	+	0.291762i	0.834458	−	0.551071i	$-0.185781\pi$
$919$	41.6114	+	8.84478i	1.37263	+	0.291762i	0.538175	+	0.842833i	$0.319114\pi$
$920$	−40.0229	+	17.8193i	−1.31952	+	0.587486i
$921$	−14.1091	−	15.6697i	−0.464910	−	0.516335i
$922$	4.17888	−	12.8613i	0.137624	−	0.423563i
$923$	2.58290	−	2.86860i	0.0850172	−	0.0944211i
$924$	−9.00000	−	15.5885i	−0.296078	−	0.512823i
$925$		0			0
$926$	−3.09852	−	9.53626i	−0.101824	−	0.313381i
$927$	−21.8742	−	9.73901i	−0.718442	−	0.319871i
$928$	4.74342	+	3.44629i	0.155710	+	0.113130i
$929$	10.6460			0.349284			0.174642	−	0.984632i	$-0.444123\pi$
$929$	10.6460			0.349284			0.174642	+	0.984632i	$0.444123\pi$
$930$		0			0
$931$	−6.00000			−0.196642
$932$	52.9058	+	38.4383i	1.73299	+	1.25909i
$933$	−20.3387	−	9.05537i	−0.665859	−	0.296459i
$934$	−12.6631	−	38.9731i	−0.414350	−	1.27524i
$935$	−17.5623	+	30.4188i	−0.574349	+	0.994801i
$936$	−21.9053	−	37.9410i	−0.715996	−	1.24014i
$937$	16.2259	−	18.0207i	0.530077	−	0.588710i	−0.417325	−	0.908758i	$-0.637032\pi$
$937$	16.2259	−	18.0207i	0.530077	−	0.588710i	0.947402	+	0.320047i	$0.103699\pi$
$938$	−4.85410	+	14.9394i	−0.158492	+	0.487788i
$939$	6.73740	+	7.48264i	0.219867	+	0.244187i
$940$	−96.2638	+	42.8594i	−3.13978	+	1.39792i
$941$	−24.9767	−	5.30895i	−0.814216	−	0.173067i	−0.218060	−	0.975935i	$-0.569973\pi$
$941$	−24.9767	−	5.30895i	−0.814216	−	0.173067i	−0.596156	+	0.802868i	$0.703306\pi$
$942$	2.08289	−	19.8173i	0.0678641	−	0.645684i
$943$	−0.403488	−	3.83894i	−0.0131394	−	0.125013i
$944$	−115.128	+	24.4712i	−3.74710	+	0.796470i
$945$	8.27895	−	6.01501i	0.269314	−	0.195668i
$946$	87.1033	−	63.2843i	2.83197	−	2.05755i
$947$	−39.3087	+	8.35532i	−1.27736	+	0.271511i	−0.796153	−	0.605095i	$-0.793135\pi$
$947$	−39.3087	+	8.35532i	−1.27736	+	0.271511i	−0.481208	+	0.876607i	$0.659802\pi$
$948$	−0.718674	−	6.83772i	−0.0233414	−	0.222079i
$949$	1.16284	−	11.0637i	0.0377473	−	0.359142i
$950$		0			0
$951$	−20.9487	+	9.32694i	−0.679307	+	0.302447i
$952$	−18.5117	−	20.5593i	−0.599967	−	0.666331i
$953$	5.76932	−	17.7561i	0.186887	−	0.575178i	−0.813089	−	0.582139i	$-0.802216\pi$
$953$	5.76932	−	17.7561i	0.186887	−	0.575178i	0.999976	+	0.00696122i	$0.00221584\pi$
$954$	53.7805	−	59.7293i	1.74121	−	1.93381i
$955$	−10.9164	−	18.9078i	−0.353247	−	0.611841i
$956$	−29.3890	+	50.9032i	−0.950508	+	1.64633i
$957$	0.618993	+	1.90506i	0.0200092	+	0.0615820i
$958$	39.5296	+	17.5997i	1.27714	+	0.568621i
$959$	−2.12132	−	1.54123i	−0.0685010	−	0.0497689i
$960$	−17.0193			−0.549295
$961$		0			0
$962$	−29.1246			−0.939015
$963$	2.66312	+	1.93487i	0.0858178	+	0.0623503i
$964$	−102.951	−	45.8369i	−3.31584	−	1.47631i
$965$	−14.3090	−	44.0386i	−0.460624	−	1.41765i
$966$	3.00000	−	5.19615i	0.0965234	−	0.167183i
$967$	−22.0084	−	38.1197i	−0.707743	−	1.22585i	−0.965692	−	0.259689i	$-0.916380\pi$
$967$	−22.0084	−	38.1197i	−0.707743	−	1.22585i	0.257949	−	0.966158i	$-0.416953\pi$
$968$	34.9988	−	38.8702i	1.12491	−	1.24933i
$969$	−1.00000	+	3.07768i	−0.0321246	+	0.0988694i
$970$	−27.4201	−	30.4531i	−0.880407	−	0.977791i
$971$	49.2296	−	21.9184i	1.57985	−	0.703396i	0.585616	−	0.810589i	$-0.300853\pi$
$971$	49.2296	−	21.9184i	1.57985	−	0.703396i	0.994238	+	0.107192i	$0.0341861\pi$
$972$	76.4268	+	16.2450i	2.45139	+	0.521059i
$973$	−1.87860	+	17.8737i	−0.0602251	+	0.573003i
$974$	−7.68378	−	73.1063i	−0.246204	−	2.34248i
$975$		0			0
$976$	−111.098	+	80.7175i	−3.55616	+	2.58370i
$977$	34.3713	−	24.9722i	1.09964	−	0.798932i	0.118636	−	0.992938i	$-0.462148\pi$
$977$	34.3713	−	24.9722i	1.09964	−	0.798932i	0.981000	+	0.194006i	$0.0621480\pi$
$978$	32.2674	−	6.85865i	1.03180	−	0.219315i
$979$	6.80738	+	64.7679i	0.217565	+	2.06999i
$980$	6.80738	−	64.7679i	0.217454	−	2.06893i
$981$	−2.82542	−	0.600562i	−0.0902088	−	0.0191745i
$982$	−38.0045	+	16.9207i	−1.21277	+	0.539961i
$983$	36.0771	+	40.0677i	1.15068	+	1.27796i	0.954773	+	0.297337i	$0.0960986\pi$
$983$	36.0771	+	40.0677i	1.15068	+	1.27796i	0.195907	+	0.980622i	$0.437235\pi$
$984$	2.97100	−	9.14379i	0.0947120	−	0.291493i
$985$	−1.61646	+	1.79526i	−0.0515048	+	0.0572018i
$986$	2.61803	+	4.53457i	0.0833752	+	0.144410i
$987$	4.24264	−	7.34847i	0.135045	−	0.233904i
$988$	−3.93314	−	12.1050i	−0.125130	−	0.385111i
$989$	23.2190	+	10.3378i	0.738323	+	0.328722i
$990$	44.9303	+	32.6438i	1.42798	+	1.03749i
$991$	−13.9358			−0.442685			−0.221343	−	0.975196i	$-0.571044\pi$
$991$	−13.9358			−0.442685			−0.221343	+	0.975196i	$0.571044\pi$
$992$		0			0
$993$	−27.3475			−0.867847
$994$	−3.11803	−	2.26538i	−0.0988980	−	0.0718536i
$995$	47.4251	+	21.1150i	1.50348	+	0.669391i
$996$	4.14590	+	12.7598i	0.131368	+	0.404309i
$997$	29.3328	−	50.8059i	0.928980	−	1.60904i	0.143947	−	0.989585i	$-0.454021\pi$
$997$	29.3328	−	50.8059i	0.928980	−	1.60904i	0.785033	−	0.619454i	$-0.212646\pi$
$998$	−24.0660	−	41.6835i	−0.761795	−	1.31947i
$999$	12.9921	−	14.4292i	0.411052	−	0.456520i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.i.732.1		16
31.2	even	5		961.2.g.p.448.1		16
31.3	odd	30		961.2.d.h.388.1		8
31.4	even	5		961.2.c.h.521.4		8
31.5	even	3	inner	961.2.g.i.816.2		16
31.6	odd	6		961.2.d.h.374.1		8
31.7	even	15		961.2.a.h.1.3	✓	4
31.8	even	5		961.2.g.p.844.2		16
31.9	even	15		961.2.g.p.547.1		16
31.10	even	15		961.2.g.p.846.2		16
31.11	odd	30		961.2.c.h.439.3		8
31.12	odd	30		961.2.d.j.628.2		8
31.13	odd	30	inner	961.2.g.i.235.2		16
31.14	even	15		961.2.d.j.531.1		8
31.15	odd	10	inner	961.2.g.i.338.1		16
31.16	even	5	inner	961.2.g.i.338.2		16
31.17	odd	30		961.2.d.j.531.2		8
31.18	even	15	inner	961.2.g.i.235.1		16
31.19	even	15		961.2.d.j.628.1		8
31.20	even	15		961.2.c.h.439.4		8
31.21	odd	30		961.2.g.p.846.1		16
31.22	odd	30		961.2.g.p.547.2		16
31.23	odd	10		961.2.g.p.844.1		16
31.24	odd	30		961.2.a.h.1.4	yes	4
31.25	even	3		961.2.d.h.374.2		8
31.26	odd	6	inner	961.2.g.i.816.1		16
31.27	odd	10		961.2.c.h.521.3		8
31.28	even	15		961.2.d.h.388.2		8
31.29	odd	10		961.2.g.p.448.2		16
31.30	odd	2	inner	961.2.g.i.732.2		16
93.38	odd	30		8649.2.a.r.1.1		4
93.86	even	30		8649.2.a.r.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.h.1.3	✓	4	31.7	even	15
961.2.a.h.1.4	yes	4	31.24	odd	30
961.2.c.h.439.3		8	31.11	odd	30
961.2.c.h.439.4		8	31.20	even	15
961.2.c.h.521.3		8	31.27	odd	10
961.2.c.h.521.4		8	31.4	even	5
961.2.d.h.374.1		8	31.6	odd	6
961.2.d.h.374.2		8	31.25	even	3
961.2.d.h.388.1		8	31.3	odd	30
961.2.d.h.388.2		8	31.28	even	15
961.2.d.j.531.1		8	31.14	even	15
961.2.d.j.531.2		8	31.17	odd	30
961.2.d.j.628.1		8	31.19	even	15
961.2.d.j.628.2		8	31.12	odd	30
961.2.g.i.235.1		16	31.18	even	15	inner
961.2.g.i.235.2		16	31.13	odd	30	inner
961.2.g.i.338.1		16	31.15	odd	10	inner
961.2.g.i.338.2		16	31.16	even	5	inner
961.2.g.i.732.1		16	1.1	even	1	trivial
961.2.g.i.732.2		16	31.30	odd	2	inner
961.2.g.i.816.1		16	31.26	odd	6	inner
961.2.g.i.816.2		16	31.5	even	3	inner
961.2.g.p.448.1		16	31.2	even	5
961.2.g.p.448.2		16	31.29	odd	10
961.2.g.p.547.1		16	31.9	even	15
961.2.g.p.547.2		16	31.22	odd	30
961.2.g.p.844.1		16	31.23	odd	10
961.2.g.p.844.2		16	31.8	even	5
961.2.g.p.846.1		16	31.21	odd	30
961.2.g.p.846.2		16	31.10	even	15
8649.2.a.r.1.1		4	93.38	odd	30
8649.2.a.r.1.2		4	93.86	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+(-2.11803 - 1.53884i) q^{2} +(-0.798468 - 0.355501i) q^{3} +(1.50000 + 4.61653i) q^{4} +(-1.11803 + 1.93649i) q^{5} +(1.14412 + 1.98168i) q^{6} +(-0.669131 + 0.743145i) q^{7} +(2.30902 - 7.10642i) q^{8} +(-1.49622 - 1.66172i) q^{9} +(5.34799 - 2.38108i) q^{10} +(-4.14993 - 0.882095i) q^{11} +(0.443477 - 4.21940i) q^{12} +(0.274084 + 2.60773i) q^{13} +(2.56082 - 0.544320i) q^{14} +(1.58114 - 1.14876i) q^{15} +(-7.97214 + 5.79210i) q^{16} +(-3.62155 + 0.769785i) q^{17} +(0.611920 + 5.82203i) q^{18} +(-0.104528 + 0.994522i) q^{19} +(-10.6169 - 2.25669i) q^{20} +(0.798468 - 0.355501i) q^{21} +(7.43229 + 8.25439i) q^{22} +(-0.810272 + 2.49376i) q^{23} +(-4.37002 + 4.85339i) q^{24} +(3.43237 - 5.94504i) q^{26} +(1.41421 + 4.35250i) q^{27} +(-4.43444 - 1.97434i) q^{28} +(0.437016 + 0.317511i) q^{29} -5.11667 q^{30} +10.8541 q^{32} +(3.00000 + 2.17963i) q^{33} +(8.85515 + 3.94256i) q^{34} +(-0.690983 - 2.12663i) q^{35} +(5.42705 - 9.39993i) q^{36} +(-2.12132 - 3.67423i) q^{37} +(1.75181 - 1.94558i) q^{38} +(0.708204 - 2.17963i) q^{39} +(11.1800 + 12.4166i) q^{40} +(-1.34486 + 0.598772i) q^{41} +(-2.23824 - 0.475753i) q^{42} +(1.01321 - 9.64006i) q^{43} +(-2.15268 - 20.4814i) q^{44} +(4.89074 - 1.03956i) q^{45} +(5.55369 - 4.03499i) q^{46} +(7.85410 - 5.70634i) q^{47} +(8.42459 - 1.79070i) q^{48} +(0.627171 + 5.96713i) q^{49} +(3.16535 + 0.672816i) q^{51} +(-11.6275 + 5.17691i) q^{52} +(-9.18681 - 10.2030i) q^{53} +(3.70246 - 11.3950i) q^{54} +(6.34793 - 7.05009i) q^{55} +(3.73607 + 6.47106i) q^{56} +(0.437016 - 0.756934i) q^{57} +(-0.437016 - 1.34500i) q^{58} +(10.9116 + 4.85817i) q^{59} +(7.67501 + 5.57622i) q^{60} +13.9358 q^{61} +2.23607 q^{63} +(-7.04508 - 5.11855i) q^{64} +(-5.35629 - 2.38477i) q^{65} +(-3.00000 - 9.23305i) q^{66} +(-3.00000 + 5.19615i) q^{67} +(-8.98606 - 15.5643i) q^{68} +(1.53351 - 1.70314i) q^{69} +(-1.80902 + 5.56758i) q^{70} +(-0.985051 - 1.09401i) q^{71} +(-15.2637 + 6.79584i) q^{72} +(-4.14993 - 0.882095i) q^{73} +(-1.16104 + 11.0465i) q^{74} +(-4.74803 + 1.00922i) q^{76} +(3.43237 - 2.49376i) q^{77} +(-4.85410 + 3.52671i) q^{78} +(1.58513 - 0.336930i) q^{79} +(-2.30323 - 21.9137i) q^{80} +(-0.283084 + 2.69337i) q^{81} +(3.76988 + 0.801313i) q^{82} +(-2.88888 + 1.28621i) q^{83} +(2.83888 + 3.15290i) q^{84} +(2.55834 - 7.87375i) q^{85} +(-16.9805 + 18.8588i) q^{86} +(-0.236068 - 0.408882i) q^{87} +(-15.8508 + 27.4544i) q^{88} +(-4.74342 - 14.5987i) q^{89} +(-11.9585 - 5.32425i) q^{90} +(-2.12132 - 1.54123i) q^{91} -12.7279 q^{92} -25.4164 q^{94} +(-1.80902 - 1.31433i) q^{95} +(-8.66665 - 3.85864i) q^{96} +(-2.16312 - 6.65740i) q^{97} +(7.85410 - 13.6037i) q^{98} +(4.74342 + 8.21584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} + 24 q^{4} - 2 q^{7} + 28 q^{8} + 10 q^{9} + 20 q^{10} + 2 q^{14} - 56 q^{16} - 20 q^{18} + 2 q^{19} - 18 q^{28} + 120 q^{32} + 48 q^{33} - 20 q^{35} + 60 q^{36} - 2 q^{38} - 96 q^{39} - 10 q^{40}+ \cdots + 72 q^{98}+O(q^{100}) \) 16 * q - 16 * q^2 + 24 * q^4 - 2 * q^7 + 28 * q^8 + 10 * q^9 + 20 * q^10 + 2 * q^14 - 56 * q^16 - 20 * q^18 + 2 * q^19 - 18 * q^28 + 120 * q^32 + 48 * q^33 - 20 * q^35 + 60 * q^36 - 2 * q^38 - 96 * q^39 - 10 * q^40 - 14 * q^41 - 10 * q^45 + 72 * q^47 - 12 * q^49 + 8 * q^51 + 24 * q^56 + 46 * q^59 - 68 * q^64 - 48 * q^66 - 48 * q^67 + 48 * q^69 - 20 * q^70 + 26 * q^71 - 50 * q^72 - 12 * q^76 - 24 * q^78 + 80 * q^80 + 22 * q^81 + 14 * q^82 + 32 * q^87 - 40 * q^90 - 192 * q^94 - 20 * q^95 + 28 * q^97 + 72 * q^98

Introduction

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