LMFDB - Embedded newform 961.2.d.e.388.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(374,961)] 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("961.374"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,2,-1,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			388.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	961.388
Dual form			961.2.d.e.374.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.363271i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.500000 + 1.53884i) q^{4} -2.61803 q^{5} -0.618034 q^{6} +(0.927051 - 2.85317i) q^{7} +(0.690983 + 2.12663i) q^{8} +(-0.618034 - 1.90211i) q^{9} +(-1.30902 + 0.951057i) q^{10} +(0.236068 - 0.726543i) q^{11} +(1.30902 - 0.951057i) q^{12} +(3.92705 + 2.85317i) q^{13} +(-0.572949 - 1.76336i) q^{14} +(2.11803 + 1.53884i) q^{15} +(-1.50000 - 1.08981i) q^{16} +(-0.0729490 - 0.224514i) q^{17} +(-1.00000 - 0.726543i) q^{18} +(-4.04508 + 2.93893i) q^{19} +(1.30902 - 4.02874i) q^{20} +(-2.42705 + 1.76336i) q^{21} +(-0.145898 - 0.449028i) q^{22} +(1.69098 + 5.20431i) q^{23} +(0.690983 - 2.12663i) q^{24} +1.85410 q^{25} +3.00000 q^{26} +(-1.54508 + 4.75528i) q^{27} +(3.92705 + 2.85317i) q^{28} +(-6.97214 + 5.06555i) q^{29} +1.61803 q^{30} -5.61803 q^{32} +(-0.618034 + 0.449028i) q^{33} +(-0.118034 - 0.0857567i) q^{34} +(-2.42705 + 7.46969i) q^{35} +3.23607 q^{36} -0.236068 q^{37} +(-0.954915 + 2.93893i) q^{38} +(-1.50000 - 4.61653i) q^{39} +(-1.80902 - 5.56758i) q^{40} +(-5.23607 + 3.80423i) q^{41} +(-0.572949 + 1.76336i) q^{42} +(-3.73607 + 2.71441i) q^{43} +(1.00000 + 0.726543i) q^{44} +(1.61803 + 4.97980i) q^{45} +(2.73607 + 1.98787i) q^{46} +(2.73607 + 1.98787i) q^{47} +(0.572949 + 1.76336i) q^{48} +(-1.61803 - 1.17557i) q^{49} +(0.927051 - 0.673542i) q^{50} +(-0.0729490 + 0.224514i) q^{51} +(-6.35410 + 4.61653i) q^{52} +(3.92705 + 12.0862i) q^{53} +(0.954915 + 2.93893i) q^{54} +(-0.618034 + 1.90211i) q^{55} +6.70820 q^{56} +5.00000 q^{57} +(-1.64590 + 5.06555i) q^{58} +(-7.66312 - 5.56758i) q^{59} +(-3.42705 + 2.48990i) q^{60} +6.94427 q^{61} -6.00000 q^{63} +(0.190983 - 0.138757i) q^{64} +(-10.2812 - 7.46969i) q^{65} +(-0.145898 + 0.449028i) q^{66} -4.23607 q^{67} +0.381966 q^{68} +(1.69098 - 5.20431i) q^{69} +(1.50000 + 4.61653i) q^{70} +(0.0278640 + 0.0857567i) q^{71} +(3.61803 - 2.62866i) q^{72} +(2.64590 - 8.14324i) q^{73} +(-0.118034 + 0.0857567i) q^{74} +(-1.50000 - 1.08981i) q^{75} +(-2.50000 - 7.69421i) q^{76} +(-1.85410 - 1.34708i) q^{77} +(-2.42705 - 1.76336i) q^{78} +(3.92705 + 2.85317i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-1.23607 + 3.80423i) q^{82} +(-3.30902 + 2.40414i) q^{83} +(-1.50000 - 4.61653i) q^{84} +(0.190983 + 0.587785i) q^{85} +(-0.881966 + 2.71441i) q^{86} +8.61803 q^{87} +1.70820 q^{88} +(1.97214 - 6.06961i) q^{89} +(2.61803 + 1.90211i) q^{90} +(11.7812 - 8.55951i) q^{91} -8.85410 q^{92} +2.09017 q^{94} +(10.5902 - 7.69421i) q^{95} +(4.54508 + 3.30220i) q^{96} +(-1.63525 + 5.03280i) q^{97} -1.23607 q^{98} -1.52786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} - 3 q^{7} + 5 q^{8} + 2 q^{9} - 3 q^{10} - 8 q^{11} + 3 q^{12} + 9 q^{13} - 9 q^{14} + 4 q^{15} - 6 q^{16} - 7 q^{17} - 4 q^{18} - 5 q^{19} + 3 q^{20}+ \cdots - 24 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 - 3 * q^7 + 5 * q^8 + 2 * q^9 - 3 * q^10 - 8 * q^11 + 3 * q^12 + 9 * q^13 - 9 * q^14 + 4 * q^15 - 6 * q^16 - 7 * q^17 - 4 * q^18 - 5 * q^19 + 3 * q^20 - 3 * q^21 - 14 * q^22 + 9 * q^23 + 5 * q^24 - 6 * q^25 + 12 * q^26 + 5 * q^27 + 9 * q^28 - 10 * q^29 + 2 * q^30 - 18 * q^32 + 2 * q^33 + 4 * q^34 - 3 * q^35 + 4 * q^36 + 8 * q^37 - 15 * q^38 - 6 * q^39 - 5 * q^40 - 12 * q^41 - 9 * q^42 - 6 * q^43 + 4 * q^44 + 2 * q^45 + 2 * q^46 + 2 * q^47 + 9 * q^48 - 2 * q^49 - 3 * q^50 - 7 * q^51 - 12 * q^52 + 9 * q^53 + 15 * q^54 + 2 * q^55 + 20 * q^57 - 20 * q^58 - 15 * q^59 - 7 * q^60 - 8 * q^61 - 24 * q^63 + 3 * q^64 - 21 * q^65 - 14 * q^66 - 8 * q^67 + 6 * q^68 + 9 * q^69 + 6 * q^70 + 18 * q^71 + 10 * q^72 + 24 * q^73 + 4 * q^74 - 6 * q^75 - 10 * q^76 + 6 * q^77 - 3 * q^78 + 9 * q^80 - q^81 + 4 * q^82 - 11 * q^83 - 6 * q^84 + 3 * q^85 - 8 * q^86 + 30 * q^87 - 20 * q^88 - 10 * q^89 + 6 * q^90 + 27 * q^91 - 22 * q^92 - 14 * q^94 + 20 * q^95 + 7 * q^96 + 27 * q^97 + 4 * q^98 - 24 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.500000	−	0.363271i	0.353553	−	0.256872i	−0.396805	−	0.917903i	$-0.629881\pi$
$2$	0.500000	−	0.363271i	0.353553	−	0.256872i	0.750358	+	0.661031i	$0.229881\pi$
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i	0.329218	−	0.944254i	$-0.393215\pi$
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i	−0.796305	+	0.604896i	$0.793215\pi$
$4$	−0.500000	+	1.53884i	−0.250000	+	0.769421i
$5$	−2.61803			−1.17082			−0.585410	−	0.810737i	$-0.699067\pi$
$5$	−2.61803			−1.17082			−0.585410	+	0.810737i	$0.699067\pi$
$6$	−0.618034			−0.252311
$7$	0.927051	−	2.85317i	0.350392	−	1.07840i	−0.608241	−	0.793752i	$-0.708125\pi$
$7$	0.927051	−	2.85317i	0.350392	−	1.07840i	0.958633	−	0.284644i	$-0.0918755\pi$
$8$	0.690983	+	2.12663i	0.244299	+	0.751876i
$9$	−0.618034	−	1.90211i	−0.206011	−	0.634038i
$10$	−1.30902	+	0.951057i	−0.413948	+	0.300750i
$11$	0.236068	−	0.726543i	0.0711772	−	0.219061i	−0.909140	−	0.416491i	$-0.863260\pi$
$11$	0.236068	−	0.726543i	0.0711772	−	0.219061i	0.980317	+	0.197430i	$0.0632597\pi$
$12$	1.30902	−	0.951057i	0.377881	−	0.274546i
$13$	3.92705	+	2.85317i	1.08917	+	0.791327i	0.979259	−	0.202615i	$-0.0649439\pi$
$13$	3.92705	+	2.85317i	1.08917	+	0.791327i	0.109909	+	0.993942i	$0.464944\pi$
$14$	−0.572949	−	1.76336i	−0.153127	−	0.471277i
$15$	2.11803	+	1.53884i	0.546874	+	0.397327i
$16$	−1.50000	−	1.08981i	−0.375000	−	0.272453i
$17$	−0.0729490	−	0.224514i	−0.0176927	−	0.0544526i	0.941820	−	0.336117i	$-0.109114\pi$
$17$	−0.0729490	−	0.224514i	−0.0176927	−	0.0544526i	−0.959513	+	0.281664i	$0.909114\pi$
$18$	−1.00000	−	0.726543i	−0.235702	−	0.171248i
$19$	−4.04508	+	2.93893i	−0.928006	+	0.674236i	−0.945504	−	0.325611i	$-0.894430\pi$
$19$	−4.04508	+	2.93893i	−0.928006	+	0.674236i	0.0174977	+	0.999847i	$0.494430\pi$
$20$	1.30902	−	4.02874i	0.292705	−	0.900854i
$21$	−2.42705	+	1.76336i	−0.529626	+	0.384796i
$22$	−0.145898	−	0.449028i	−0.0311056	−	0.0957331i
$23$	1.69098	+	5.20431i	0.352594	+	1.08517i	0.957391	+	0.288794i	$0.0932543\pi$
$23$	1.69098	+	5.20431i	0.352594	+	1.08517i	−0.604797	+	0.796380i	$0.706746\pi$
$24$	0.690983	−	2.12663i	0.141046	−	0.434096i
$25$	1.85410			0.370820
$26$	3.00000			0.588348
$27$	−1.54508	+	4.75528i	−0.297352	+	0.915155i
$28$	3.92705	+	2.85317i	0.742143	+	0.539198i
$29$	−6.97214	+	5.06555i	−1.29469	+	0.940650i	−0.999889	−	0.0149080i	$-0.995254\pi$
$29$	−6.97214	+	5.06555i	−1.29469	+	0.940650i	−0.294804	+	0.955558i	$0.595254\pi$
$30$	1.61803			0.295411
$31$		0			0
$31$		0			0
$32$	−5.61803			−0.993137
$33$	−0.618034	+	0.449028i	−0.107586	+	0.0781657i
$34$	−0.118034	−	0.0857567i	−0.0202427	−	0.0147072i
$35$	−2.42705	+	7.46969i	−0.410246	+	1.26261i
$36$	3.23607			0.539345
$37$	−0.236068			−0.0388093			−0.0194047	−	0.999812i	$-0.506177\pi$
$37$	−0.236068			−0.0388093			−0.0194047	+	0.999812i	$0.506177\pi$
$38$	−0.954915	+	2.93893i	−0.154908	+	0.476757i
$39$	−1.50000	−	4.61653i	−0.240192	−	0.739236i
$40$	−1.80902	−	5.56758i	−0.286031	−	0.880312i
$41$	−5.23607	+	3.80423i	−0.817736	+	0.594120i	−0.916063	−	0.401034i	$-0.868651\pi$
$41$	−5.23607	+	3.80423i	−0.817736	+	0.594120i	0.0983268	+	0.995154i	$0.468651\pi$
$42$	−0.572949	+	1.76336i	−0.0884080	+	0.272092i
$43$	−3.73607	+	2.71441i	−0.569745	+	0.413944i	−0.835013	−	0.550231i	$-0.814540\pi$
$43$	−3.73607	+	2.71441i	−0.569745	+	0.413944i	0.265268	+	0.964175i	$0.414540\pi$
$44$	1.00000	+	0.726543i	0.150756	+	0.109530i
$45$	1.61803	+	4.97980i	0.241202	+	0.742344i
$46$	2.73607	+	1.98787i	0.403411	+	0.293095i
$47$	2.73607	+	1.98787i	0.399097	+	0.289961i	0.769173	−	0.639041i	$-0.220668\pi$
$47$	2.73607	+	1.98787i	0.399097	+	0.289961i	−0.370076	+	0.929001i	$0.620668\pi$
$48$	0.572949	+	1.76336i	0.0826981	+	0.254518i
$49$	−1.61803	−	1.17557i	−0.231148	−	0.167939i
$50$	0.927051	−	0.673542i	0.131105	−	0.0952532i
$51$	−0.0729490	+	0.224514i	−0.0102149	+	0.0314382i
$52$	−6.35410	+	4.61653i	−0.881155	+	0.640197i
$53$	3.92705	+	12.0862i	0.539422	+	1.66017i	0.733896	+	0.679262i	$0.237700\pi$
$53$	3.92705	+	12.0862i	0.539422	+	1.66017i	−0.194474	+	0.980908i	$0.562300\pi$
$54$	0.954915	+	2.93893i	0.129947	+	0.399937i
$55$	−0.618034	+	1.90211i	−0.0833357	+	0.256481i
$56$	6.70820			0.896421
$57$	5.00000			0.662266
$58$	−1.64590	+	5.06555i	−0.216117	+	0.665140i
$59$	−7.66312	−	5.56758i	−0.997653	−	0.724837i	−0.0360694	−	0.999349i	$-0.511484\pi$
$59$	−7.66312	−	5.56758i	−0.997653	−	0.724837i	−0.961584	+	0.274512i	$0.911484\pi$
$60$	−3.42705	+	2.48990i	−0.442430	+	0.321444i
$61$	6.94427			0.889123			0.444561	−	0.895748i	$-0.353360\pi$
$61$	6.94427			0.889123			0.444561	+	0.895748i	$0.353360\pi$
$62$		0			0
$63$	−6.00000			−0.755929
$64$	0.190983	−	0.138757i	0.0238729	−	0.0173447i
$65$	−10.2812	−	7.46969i	−1.27522	−	0.926502i
$66$	−0.145898	+	0.449028i	−0.0179588	+	0.0552715i
$67$	−4.23607			−0.517518			−0.258759	−	0.965942i	$-0.583314\pi$
$67$	−4.23607			−0.517518			−0.258759	+	0.965942i	$0.583314\pi$
$68$	0.381966			0.0463202
$69$	1.69098	−	5.20431i	0.203570	−	0.626525i
$70$	1.50000	+	4.61653i	0.179284	+	0.551780i
$71$	0.0278640	+	0.0857567i	0.00330685	+	0.0101774i	0.952696	−	0.303924i	$-0.0982968\pi$
$71$	0.0278640	+	0.0857567i	0.00330685	+	0.0101774i	−0.949389	+	0.314101i	$0.898297\pi$
$72$	3.61803	−	2.62866i	0.426389	−	0.309790i
$73$	2.64590	−	8.14324i	0.309679	−	0.953094i	−0.668211	−	0.743972i	$-0.732940\pi$
$73$	2.64590	−	8.14324i	0.309679	−	0.953094i	0.977890	−	0.209122i	$-0.0670605\pi$
$74$	−0.118034	+	0.0857567i	−0.0137212	+	0.00996902i
$75$	−1.50000	−	1.08981i	−0.173205	−	0.125841i
$76$	−2.50000	−	7.69421i	−0.286770	−	0.882586i
$77$	−1.85410	−	1.34708i	−0.211295	−	0.153514i
$78$	−2.42705	−	1.76336i	−0.274809	−	0.199661i
$79$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$79$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$80$	3.92705	+	2.85317i	0.439058	+	0.318994i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−1.23607	+	3.80423i	−0.136501	+	0.420106i
$83$	−3.30902	+	2.40414i	−0.363212	+	0.263889i	−0.754390	−	0.656426i	$-0.772067\pi$
$83$	−3.30902	+	2.40414i	−0.363212	+	0.263889i	0.391179	+	0.920315i	$0.372067\pi$
$84$	−1.50000	−	4.61653i	−0.163663	−	0.503704i
$85$	0.190983	+	0.587785i	0.0207150	+	0.0637543i
$86$	−0.881966	+	2.71441i	−0.0951048	+	0.292703i
$87$	8.61803			0.923950
$88$	1.70820			0.182095
$89$	1.97214	−	6.06961i	0.209046	−	0.643377i	−0.790477	−	0.612492i	$-0.790167\pi$
$89$	1.97214	−	6.06961i	0.209046	−	0.643377i	0.999523	−	0.0308856i	$-0.00983276\pi$
$90$	2.61803	+	1.90211i	0.275965	+	0.200500i
$91$	11.7812	−	8.55951i	1.23500	−	0.897280i
$92$	−8.85410			−0.923104
$93$		0			0
$94$	2.09017			0.215585
$95$	10.5902	−	7.69421i	1.08653	−	0.789409i
$96$	4.54508	+	3.30220i	0.463881	+	0.337029i
$97$	−1.63525	+	5.03280i	−0.166035	+	0.511003i	−0.999111	−	0.0421553i	$-0.986578\pi$
$97$	−1.63525	+	5.03280i	−0.166035	+	0.511003i	0.833076	+	0.553158i	$0.186578\pi$
$98$	−1.23607			−0.124862
$99$	−1.52786			−0.153556
$100$	−0.927051	+	2.85317i	−0.0927051	+	0.285317i
$101$	1.47214	+	4.53077i	0.146483	+	0.450828i	0.997199	−	0.0747977i	$-0.0238311\pi$
$101$	1.47214	+	4.53077i	0.146483	+	0.450828i	−0.850716	+	0.525626i	$0.823831\pi$
$102$	0.0450850	+	0.138757i	0.00446408	+	0.0137390i
$103$	0.118034	−	0.0857567i	0.0116302	−	0.00844986i	−0.581955	−	0.813221i	$-0.697712\pi$
$103$	0.118034	−	0.0857567i	0.0116302	−	0.00844986i	0.593585	+	0.804771i	$0.297712\pi$
$104$	−3.35410	+	10.3229i	−0.328897	+	1.01224i
$105$	6.35410	−	4.61653i	0.620097	−	0.450527i
$106$	6.35410	+	4.61653i	0.617165	+	0.448397i
$107$	0.336881	+	1.03681i	0.0325675	+	0.100233i	0.966019	−	0.258471i	$-0.0832188\pi$
$107$	0.336881	+	1.03681i	0.0325675	+	0.100233i	−0.933451	+	0.358704i	$0.883219\pi$
$108$	−6.54508	−	4.75528i	−0.629801	−	0.457577i
$109$	6.80902	+	4.94704i	0.652186	+	0.473841i	0.864015	−	0.503466i	$-0.167942\pi$
$109$	6.80902	+	4.94704i	0.652186	+	0.473841i	−0.211829	+	0.977307i	$0.567942\pi$
$110$	0.381966	+	1.17557i	0.0364190	+	0.112086i
$111$	0.190983	+	0.138757i	0.0181273	+	0.0131703i
$112$	−4.50000	+	3.26944i	−0.425210	+	0.308933i
$113$	−0.572949	+	1.76336i	−0.0538985	+	0.165883i	−0.974382	−	0.224898i	$-0.927795\pi$
$113$	−0.572949	+	1.76336i	−0.0538985	+	0.165883i	0.920484	+	0.390781i	$0.127795\pi$
$114$	2.50000	−	1.81636i	0.234146	−	0.170117i
$115$	−4.42705	−	13.6251i	−0.412825	−	1.27054i
$116$	−4.30902	−	13.2618i	−0.400082	−	1.23133i
$117$	3.00000	−	9.23305i	0.277350	−	0.853596i
$118$	−5.85410			−0.538914
$119$	−0.708204			−0.0649209
$120$	−1.80902	+	5.56758i	−0.165140	+	0.508248i
$121$	8.42705	+	6.12261i	0.766096	+	0.556601i
$122$	3.47214	−	2.52265i	0.314352	−	0.228390i
$123$	6.47214			0.583573
$124$		0			0
$125$	8.23607			0.736656
$126$	−3.00000	+	2.17963i	−0.267261	+	0.194177i
$127$	8.28115	+	6.01661i	0.734833	+	0.533888i	0.891089	−	0.453829i	$-0.149942\pi$
$127$	8.28115	+	6.01661i	0.734833	+	0.533888i	−0.156255	+	0.987717i	$0.549942\pi$
$128$	3.51722	−	10.8249i	0.310881	−	0.956794i
$129$	4.61803			0.406595
$130$	−7.85410			−0.688850
$131$	0.0278640	−	0.0857567i	0.00243449	−	0.00749260i	−0.949832	−	0.312761i	$-0.898746\pi$
$131$	0.0278640	−	0.0857567i	0.00243449	−	0.00749260i	0.952266	+	0.305268i	$0.0987461\pi$
$132$	−0.381966	−	1.17557i	−0.0332459	−	0.102320i
$133$	4.63525	+	14.2658i	0.401928	+	1.23701i
$134$	−2.11803	+	1.53884i	−0.182970	+	0.132936i
$135$	4.04508	−	12.4495i	0.348145	−	1.07148i
$136$	0.427051	−	0.310271i	0.0366193	−	0.0266055i
$137$	−5.23607	−	3.80423i	−0.447347	−	0.325017i	0.341200	−	0.939991i	$-0.389167\pi$
$137$	−5.23607	−	3.80423i	−0.447347	−	0.325017i	−0.788548	+	0.614974i	$0.789167\pi$
$138$	−1.04508	−	3.21644i	−0.0889635	−	0.273802i
$139$	4.73607	+	3.44095i	0.401708	+	0.291858i	0.770236	−	0.637759i	$-0.220138\pi$
$139$	4.73607	+	3.44095i	0.401708	+	0.291858i	−0.368528	+	0.929617i	$0.620138\pi$
$140$	−10.2812	−	7.46969i	−0.868916	−	0.631304i
$141$	−1.04508	−	3.21644i	−0.0880120	−	0.270873i
$142$	0.0450850	+	0.0327561i	0.00378345	+	0.00274883i
$143$	3.00000	−	2.17963i	0.250873	−	0.182270i
$144$	−1.14590	+	3.52671i	−0.0954915	+	0.293893i
$145$	18.2533	−	13.2618i	1.51585	−	1.10133i
$146$	−1.63525	−	5.03280i	−0.135335	−	0.416517i
$147$	0.618034	+	1.90211i	0.0509746	+	0.156884i
$148$	0.118034	−	0.363271i	0.00970233	−	0.0298607i
$149$	−17.0344			−1.39552			−0.697758	−	0.716334i	$-0.745819\pi$
$149$	−17.0344			−1.39552			−0.697758	+	0.716334i	$0.745819\pi$
$150$	−1.14590			−0.0935622
$151$	6.02786	−	18.5519i	0.490541	−	1.50973i	−0.333252	−	0.942838i	$-0.608146\pi$
$151$	6.02786	−	18.5519i	0.490541	−	1.50973i	0.823793	−	0.566891i	$-0.191854\pi$
$152$	−9.04508	−	6.57164i	−0.733653	−	0.533030i
$153$	−0.381966	+	0.277515i	−0.0308801	+	0.0224357i
$154$	−1.41641			−0.114137
$155$		0			0
$156$	7.85410			0.628831
$157$	−7.85410	+	5.70634i	−0.626826	+	0.455415i	−0.855299	−	0.518135i	$-0.826627\pi$
$157$	−7.85410	+	5.70634i	−0.626826	+	0.455415i	0.228473	+	0.973550i	$0.426627\pi$
$158$		0			0
$159$	3.92705	−	12.0862i	0.311435	−	0.958500i
$160$	14.7082			1.16279
$161$	16.4164			1.29379
$162$	−0.190983	+	0.587785i	−0.0150050	+	0.0461808i
$163$	−3.92705	−	12.0862i	−0.307590	−	0.946666i	−0.978698	−	0.205306i	$-0.934181\pi$
$163$	−3.92705	−	12.0862i	−0.307590	−	0.946666i	0.671108	−	0.741360i	$-0.265819\pi$
$164$	−3.23607	−	9.95959i	−0.252694	−	0.777714i
$165$	1.61803	−	1.17557i	0.125964	−	0.0915180i
$166$	−0.781153	+	2.40414i	−0.0606292	+	0.186598i
$167$	−7.47214	+	5.42882i	−0.578211	+	0.420095i	−0.838079	−	0.545549i	$-0.816321\pi$
$167$	−7.47214	+	5.42882i	−0.578211	+	0.420095i	0.259868	+	0.965644i	$0.416321\pi$
$168$	−5.42705	−	3.94298i	−0.418706	−	0.304208i
$169$	3.26393	+	10.0453i	0.251072	+	0.772719i
$170$	0.309017	+	0.224514i	0.0237005	+	0.0172194i
$171$	8.09017	+	5.87785i	0.618671	+	0.449491i
$172$	−2.30902	−	7.10642i	−0.176061	−	0.541860i
$173$	−0.736068	−	0.534785i	−0.0559622	−	0.0406589i	0.559452	−	0.828862i	$-0.311011\pi$
$173$	−0.736068	−	0.534785i	−0.0559622	−	0.0406589i	−0.615415	+	0.788204i	$0.711011\pi$
$174$	4.30902	−	3.13068i	0.326666	−	0.237337i
$175$	1.71885	−	5.29007i	0.129933	−	0.399891i
$176$	−1.14590	+	0.832544i	−0.0863753	+	0.0627553i
$177$	2.92705	+	9.00854i	0.220011	+	0.677123i
$178$	−1.21885	−	3.75123i	−0.0913564	−	0.281166i
$179$	−6.11803	+	18.8294i	−0.457283	+	1.40737i	0.411150	+	0.911568i	$0.365127\pi$
$179$	−6.11803	+	18.8294i	−0.457283	+	1.40737i	−0.868433	+	0.495806i	$0.834873\pi$
$180$	−8.47214			−0.631476
$181$	−17.0000			−1.26360			−0.631800	−	0.775131i	$-0.717684\pi$
$181$	−17.0000			−1.26360			−0.631800	+	0.775131i	$0.717684\pi$
$182$	2.78115	−	8.55951i	0.206153	−	0.634473i
$183$	−5.61803	−	4.08174i	−0.415297	−	0.301731i
$184$	−9.89919	+	7.19218i	−0.729778	+	0.530215i
$185$	0.618034			0.0454388
$186$		0			0
$187$	−0.180340			−0.0131878
$188$	−4.42705	+	3.21644i	−0.322876	+	0.234583i
$189$	12.1353	+	8.81678i	0.882710	+	0.641326i
$190$	2.50000	−	7.69421i	0.181369	−	0.558197i
$191$	−16.0902			−1.16424			−0.582122	−	0.813102i	$-0.697777\pi$
$191$	−16.0902			−1.16424			−0.582122	+	0.813102i	$0.697777\pi$
$192$	−0.236068			−0.0170367
$193$	−0.736068	+	2.26538i	−0.0529833	+	0.163066i	−0.974047	−	0.226346i	$-0.927322\pi$
$193$	−0.736068	+	2.26538i	−0.0529833	+	0.163066i	0.921064	+	0.389412i	$0.127322\pi$
$194$	1.01064	+	3.11044i	0.0725599	+	0.223317i
$195$	3.92705	+	12.0862i	0.281222	+	0.865512i
$196$	2.61803	−	1.90211i	0.187002	−	0.135865i
$197$	−5.07295	+	15.6129i	−0.361433	+	1.11238i	0.590752	+	0.806853i	$0.298831\pi$
$197$	−5.07295	+	15.6129i	−0.361433	+	1.11238i	−0.952185	+	0.305522i	$0.901169\pi$
$198$	−0.763932	+	0.555029i	−0.0542903	+	0.0394442i
$199$	−21.6074	−	15.6987i	−1.53171	−	1.11285i	−0.955280	−	0.295702i	$-0.904446\pi$
$199$	−21.6074	−	15.6987i	−1.53171	−	1.11285i	−0.576427	−	0.817149i	$-0.695554\pi$
$200$	1.28115	+	3.94298i	0.0905912	+	0.278811i
$201$	3.42705	+	2.48990i	0.241726	+	0.175624i
$202$	2.38197	+	1.73060i	0.167595	+	0.121765i
$203$	7.98936	+	24.5887i	0.560743	+	1.72579i
$204$	−0.309017	−	0.224514i	−0.0216355	−	0.0157191i
$205$	13.7082	−	9.95959i	0.957422	−	0.695608i
$206$	0.0278640	−	0.0857567i	0.00194138	−	0.00597495i
$207$	8.85410	−	6.43288i	0.615403	−	0.447116i
$208$	−2.78115	−	8.55951i	−0.192838	−	0.593495i
$209$	1.18034	+	3.63271i	0.0816458	+	0.251280i
$210$	1.50000	−	4.61653i	0.103510	−	0.318571i
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$	−20.5623			−1.41222
$213$	0.0278640	−	0.0857567i	0.00190921	−	0.00587595i
$214$	0.545085	+	0.396027i	0.0372612	+	0.0270719i
$215$	9.78115	−	7.10642i	0.667069	−	0.484654i
$216$	−11.1803			−0.760726
$217$		0			0
$218$	5.20163			0.352299
$219$	−6.92705	+	5.03280i	−0.468087	+	0.340085i
$220$	−2.61803	−	1.90211i	−0.176508	−	0.128240i
$221$	0.354102	−	1.08981i	0.0238195	−	0.0733088i
$222$	0.145898			0.00979203
$223$	−0.708204			−0.0474248			−0.0237124	−	0.999719i	$-0.507549\pi$
$223$	−0.708204			−0.0474248			−0.0237124	+	0.999719i	$0.507549\pi$
$224$	−5.20820	+	16.0292i	−0.347988	+	1.07100i
$225$	−1.14590	−	3.52671i	−0.0763932	−	0.235114i
$226$	0.354102	+	1.08981i	0.0235545	+	0.0724933i
$227$	16.7812	−	12.1922i	1.11380	−	0.809226i	0.130546	−	0.991442i	$-0.458327\pi$
$227$	16.7812	−	12.1922i	1.11380	−	0.809226i	0.983259	+	0.182216i	$0.0583271\pi$
$228$	−2.50000	+	7.69421i	−0.165567	+	0.509561i
$229$	−5.85410	+	4.25325i	−0.386850	+	0.281063i	−0.764163	−	0.645023i	$-0.776848\pi$
$229$	−5.85410	+	4.25325i	−0.386850	+	0.281063i	0.377314	+	0.926086i	$0.376848\pi$
$230$	−7.16312	−	5.20431i	−0.472322	−	0.343162i
$231$	0.708204	+	2.17963i	0.0465964	+	0.143409i
$232$	−15.5902	−	11.3269i	−1.02354	−	0.743649i
$233$	−15.2082	−	11.0494i	−0.996323	−	0.723871i	−0.0350260	−	0.999386i	$-0.511151\pi$
$233$	−15.2082	−	11.0494i	−0.996323	−	0.723871i	−0.961297	+	0.275516i	$0.911151\pi$
$234$	−1.85410	−	5.70634i	−0.121206	−	0.373035i
$235$	−7.16312	−	5.20431i	−0.467270	−	0.339492i
$236$	12.3992	−	9.00854i	0.807118	−	0.586406i
$237$		0			0
$238$	−0.354102	+	0.257270i	−0.0229530	+	0.0166763i
$239$	4.14590	+	12.7598i	0.268176	+	0.825360i	0.990945	+	0.134271i	$0.0428691\pi$
$239$	4.14590	+	12.7598i	0.268176	+	0.825360i	−0.722769	+	0.691090i	$0.757131\pi$
$240$	−1.50000	−	4.61653i	−0.0968246	−	0.297995i
$241$	2.63525	−	8.11048i	0.169752	−	0.522442i	−0.829603	−	0.558353i	$-0.811433\pi$
$241$	2.63525	−	8.11048i	0.169752	−	0.522442i	0.999355	+	0.0359113i	$0.0114334\pi$
$242$	6.43769			0.413831
$243$	16.0000			1.02640
$244$	−3.47214	+	10.6861i	−0.222281	+	0.684110i
$245$	4.23607	+	3.07768i	0.270632	+	0.196626i
$246$	3.23607	−	2.35114i	0.206324	−	0.149903i
$247$	−24.2705			−1.54430
$248$		0			0
$249$	4.09017			0.259204
$250$	4.11803	−	2.99193i	0.260447	−	0.189226i
$251$	0.763932	+	0.555029i	0.0482190	+	0.0350331i	0.611634	−	0.791141i	$-0.290513\pi$
$251$	0.763932	+	0.555029i	0.0482190	+	0.0350331i	−0.563415	+	0.826174i	$0.690513\pi$
$252$	3.00000	−	9.23305i	0.188982	−	0.581628i
$253$	4.18034			0.262816
$254$	6.32624			0.396943
$255$	0.190983	−	0.587785i	0.0119598	−	0.0368085i
$256$	−2.02786	−	6.24112i	−0.126742	−	0.390070i
$257$	0.437694	+	1.34708i	0.0273026	+	0.0840288i	0.963779	−	0.266701i	$-0.0859336\pi$
$257$	0.437694	+	1.34708i	0.0273026	+	0.0840288i	−0.936477	+	0.350730i	$0.885934\pi$
$258$	2.30902	−	1.67760i	0.143753	−	0.104443i
$259$	−0.218847	+	0.673542i	−0.0135985	+	0.0418519i
$260$	16.6353	−	12.0862i	1.03167	−	0.749556i
$261$	13.9443	+	10.1311i	0.863129	+	0.627100i
$262$	−0.0172209	−	0.0530006i	−0.00106391	−	0.00327439i
$263$	−8.73607	−	6.34712i	−0.538689	−	0.391380i	0.284909	−	0.958555i	$-0.408037\pi$
$263$	−8.73607	−	6.34712i	−0.538689	−	0.391380i	−0.823598	+	0.567174i	$0.808037\pi$
$264$	−1.38197	−	1.00406i	−0.0850541	−	0.0617954i
$265$	−10.2812	−	31.6421i	−0.631566	−	1.94376i
$266$	7.50000	+	5.44907i	0.459855	+	0.334104i
$267$	−5.16312	+	3.75123i	−0.315978	+	0.229571i
$268$	2.11803	−	6.51864i	0.129380	−	0.398189i
$269$	−1.11803	+	0.812299i	−0.0681677	+	0.0495268i	−0.621347	−	0.783535i	$-0.713414\pi$
$269$	−1.11803	+	0.812299i	−0.0681677	+	0.0495268i	0.553180	+	0.833062i	$0.313414\pi$
$270$	−2.50000	−	7.69421i	−0.152145	−	0.468255i
$271$	−2.95492	−	9.09429i	−0.179498	−	0.552439i	0.820312	−	0.571916i	$-0.193800\pi$
$271$	−2.95492	−	9.09429i	−0.179498	−	0.552439i	−0.999810	+	0.0194773i	$0.993800\pi$
$272$	−0.135255	+	0.416272i	−0.00820103	+	0.0252402i
$273$	−14.5623			−0.881351
$274$	−4.00000			−0.241649
$275$	0.437694	−	1.34708i	0.0263939	−	0.0812322i
$276$	7.16312	+	5.20431i	0.431169	+	0.313263i
$277$	10.7812	−	7.83297i	0.647777	−	0.470637i	−0.214736	−	0.976672i	$-0.568889\pi$
$277$	10.7812	−	7.83297i	0.647777	−	0.470637i	0.862513	+	0.506035i	$0.168889\pi$
$278$	3.61803			0.216995
$279$		0			0
$280$	−17.5623			−1.04955
$281$	−15.3992	+	11.1882i	−0.918638	+	0.667430i	−0.943185	−	0.332269i	$-0.892186\pi$
$281$	−15.3992	+	11.1882i	−0.918638	+	0.667430i	0.0245463	+	0.999699i	$0.492186\pi$
$282$	−1.69098	−	1.22857i	−0.100697	−	0.0731603i
$283$	2.02786	−	6.24112i	0.120544	−	0.370996i	−0.872519	−	0.488580i	$-0.837515\pi$
$283$	2.02786	−	6.24112i	0.120544	−	0.370996i	0.993063	+	0.117584i	$0.0375149\pi$
$284$	−0.145898			−0.00865746
$285$	−13.0902			−0.775395
$286$	0.708204	−	2.17963i	0.0418770	−	0.128884i
$287$	6.00000	+	18.4661i	0.354169	+	1.09002i
$288$	3.47214	+	10.6861i	0.204598	+	0.629687i
$289$	13.7082	−	9.95959i	0.806365	−	0.585858i
$290$	4.30902	−	13.2618i	0.253034	−	0.778759i
$291$	4.28115	−	3.11044i	0.250966	−	0.182337i
$292$	11.2082	+	8.14324i	0.655911	+	0.476547i
$293$	−2.54508	−	7.83297i	−0.148685	−	0.457607i	0.848781	−	0.528744i	$-0.177337\pi$
$293$	−2.54508	−	7.83297i	−0.148685	−	0.457607i	−0.997467	+	0.0711377i	$0.977337\pi$
$294$	1.00000	+	0.726543i	0.0583212	+	0.0423728i
$295$	20.0623	+	14.5761i	1.16807	+	0.848654i
$296$	−0.163119	−	0.502029i	−0.00948110	−	0.0291798i
$297$	3.09017	+	2.24514i	0.179310	+	0.130276i
$298$	−8.51722	+	6.18812i	−0.493389	+	0.358468i
$299$	−8.20820	+	25.2623i	−0.474693	+	1.46095i
$300$	2.42705	−	1.76336i	0.140126	−	0.101807i
$301$	4.28115	+	13.1760i	0.246762	+	0.759454i
$302$	−3.72542	−	11.4657i	−0.214374	−	0.659776i
$303$	1.47214	−	4.53077i	0.0845720	−	0.260286i
$304$	9.27051			0.531700
$305$	−18.1803			−1.04100
$306$	−0.0901699	+	0.277515i	−0.00515467	+	0.0158645i
$307$	−4.92705	−	3.57971i	−0.281202	−	0.204305i	0.438240	−	0.898858i	$-0.355602\pi$
$307$	−4.92705	−	3.57971i	−0.281202	−	0.204305i	−0.719441	+	0.694553i	$0.755602\pi$
$308$	3.00000	−	2.17963i	0.170941	−	0.124196i
$309$	−0.145898			−0.00829985
$310$		0			0
$311$	16.4721			0.934049			0.467025	−	0.884244i	$-0.345326\pi$
$311$	16.4721			0.934049			0.467025	+	0.884244i	$0.345326\pi$
$312$	8.78115	−	6.37988i	0.497135	−	0.361190i
$313$	1.00000	+	0.726543i	0.0565233	+	0.0410666i	0.615688	−	0.787990i	$-0.288878\pi$
$313$	1.00000	+	0.726543i	0.0565233	+	0.0410666i	−0.559165	+	0.829057i	$0.688878\pi$
$314$	−1.85410	+	5.70634i	−0.104633	+	0.322027i
$315$	15.7082			0.885057
$316$		0			0
$317$	8.00000	−	24.6215i	0.449325	−	1.38288i	−0.428346	−	0.903615i	$-0.640903\pi$
$317$	8.00000	−	24.6215i	0.449325	−	1.38288i	0.877671	−	0.479265i	$-0.159097\pi$
$318$	−2.42705	−	7.46969i	−0.136102	−	0.418880i
$319$	2.03444	+	6.26137i	0.113907	+	0.350569i
$320$	−0.500000	+	0.363271i	−0.0279508	+	0.0203075i
$321$	0.336881	−	1.03681i	0.0188029	−	0.0578693i
$322$	8.20820	−	5.96361i	0.457425	−	0.332339i
$323$	0.954915	+	0.693786i	0.0531329	+	0.0386033i
$324$	−0.500000	−	1.53884i	−0.0277778	−	0.0854912i
$325$	7.28115	+	5.29007i	0.403886	+	0.293440i
$326$	−6.35410	−	4.61653i	−0.351921	−	0.255686i
$327$	−2.60081	−	8.00448i	−0.143825	−	0.442649i
$328$	−11.7082	−	8.50651i	−0.646477	−	0.469693i
$329$	8.20820	−	5.96361i	0.452533	−	0.328784i
$330$	0.381966	−	1.17557i	0.0210265	−	0.0647130i
$331$	9.11803	−	6.62464i	0.501172	−	0.364123i	−0.308292	−	0.951292i	$-0.599757\pi$
$331$	9.11803	−	6.62464i	0.501172	−	0.364123i	0.809465	+	0.587169i	$0.199757\pi$
$332$	−2.04508	−	6.29412i	−0.112239	−	0.345435i
$333$	0.145898	+	0.449028i	0.00799516	+	0.0246066i
$334$	−1.76393	+	5.42882i	−0.0965181	+	0.297052i
$335$	11.0902			0.605921
$336$	5.56231			0.303449
$337$	−5.86475	+	18.0498i	−0.319473	+	0.983237i	0.654401	+	0.756148i	$0.272921\pi$
$337$	−5.86475	+	18.0498i	−0.319473	+	0.983237i	−0.973874	+	0.227089i	$0.927079\pi$
$338$	5.28115	+	3.83698i	0.287257	+	0.208704i
$339$	1.50000	−	1.08981i	0.0814688	−	0.0591906i
$340$	−1.00000			−0.0542326
$341$		0			0
$342$	6.18034			0.334195
$343$	12.1353	−	8.81678i	0.655242	−	0.476061i
$344$	−8.35410	−	6.06961i	−0.450423	−	0.327251i
$345$	−4.42705	+	13.6251i	−0.238344	+	0.733549i
$346$	−0.562306			−0.0302298
$347$	−8.12461			−0.436152			−0.218076	−	0.975932i	$-0.569978\pi$
$347$	−8.12461			−0.436152			−0.218076	+	0.975932i	$0.569978\pi$
$348$	−4.30902	+	13.2618i	−0.230988	+	0.710907i
$349$	−5.16312	−	15.8904i	−0.276375	−	0.850596i	−0.988852	−	0.148900i	$-0.952427\pi$
$349$	−5.16312	−	15.8904i	−0.276375	−	0.850596i	0.712477	−	0.701696i	$-0.247573\pi$
$350$	−1.06231	−	3.26944i	−0.0567826	−	0.174759i
$351$	−19.6353	+	14.2658i	−1.04805	+	0.761455i
$352$	−1.32624	+	4.08174i	−0.0706887	+	0.217558i
$353$	−26.1976	+	19.0336i	−1.39436	+	1.01306i	−0.398984	+	0.916958i	$0.630637\pi$
$353$	−26.1976	+	19.0336i	−1.39436	+	1.01306i	−0.995372	+	0.0961006i	$0.969363\pi$
$354$	4.73607	+	3.44095i	0.251719	+	0.182885i
$355$	−0.0729490	−	0.224514i	−0.00387173	−	0.0119160i
$356$	8.35410	+	6.06961i	0.442767	+	0.321689i
$357$	0.572949	+	0.416272i	0.0303237	+	0.0220314i
$358$	3.78115	+	11.6372i	0.199840	+	0.615045i
$359$	20.4894	+	14.8864i	1.08139	+	0.785674i	0.977924	−	0.208960i	$-0.0670078\pi$
$359$	20.4894	+	14.8864i	1.08139	+	0.785674i	0.103463	+	0.994633i	$0.467008\pi$
$360$	−9.47214	+	6.88191i	−0.499225	+	0.362708i
$361$	1.85410	−	5.70634i	0.0975843	−	0.300334i
$362$	−8.50000	+	6.17561i	−0.446750	+	0.324583i
$363$	−3.21885	−	9.90659i	−0.168946	−	0.519961i
$364$	7.28115	+	22.4091i	0.381636	+	1.17456i
$365$	−6.92705	+	21.3193i	−0.362578	+	1.11590i
$366$	−4.29180			−0.224336
$367$	36.2705			1.89331			0.946653	−	0.322256i	$-0.104441\pi$
$367$	36.2705			1.89331			0.946653	+	0.322256i	$0.104441\pi$
$368$	3.13525	−	9.64932i	0.163436	−	0.503006i
$369$	10.4721	+	7.60845i	0.545158	+	0.396080i
$370$	0.309017	−	0.224514i	0.0160650	−	0.0116719i
$371$	38.1246			1.97933
$372$		0			0
$373$	−0.347524			−0.0179941			−0.00899706	−	0.999960i	$-0.502864\pi$
$373$	−0.347524			−0.0179941			−0.00899706	+	0.999960i	$0.502864\pi$
$374$	−0.0901699	+	0.0655123i	−0.00466258	+	0.00338756i
$375$	−6.66312	−	4.84104i	−0.344082	−	0.249990i
$376$	−2.33688	+	7.19218i	−0.120515	+	0.370908i
$377$	−41.8328			−2.15450
$378$	9.27051			0.476824
$379$	−5.69098	+	17.5150i	−0.292326	+	0.899687i	0.691780	+	0.722108i	$0.256827\pi$
$379$	−5.69098	+	17.5150i	−0.292326	+	0.899687i	−0.984106	+	0.177579i	$0.943173\pi$
$380$	6.54508	+	20.1437i	0.335756	+	1.03335i
$381$	−3.16312	−	9.73508i	−0.162051	−	0.498743i
$382$	−8.04508	+	5.84510i	−0.411622	+	0.299061i
$383$	5.20820	−	16.0292i	0.266127	−	0.819054i	−0.725305	−	0.688428i	$-0.758301\pi$
$383$	5.20820	−	16.0292i	0.266127	−	0.819054i	0.991432	−	0.130626i	$-0.0416988\pi$
$384$	−9.20820	+	6.69015i	−0.469904	+	0.341405i
$385$	4.85410	+	3.52671i	0.247388	+	0.179738i
$386$	0.454915	+	1.40008i	0.0231546	+	0.0712624i
$387$	7.47214	+	5.42882i	0.379830	+	0.275963i
$388$	−6.92705	−	5.03280i	−0.351668	−	0.255502i
$389$	8.98278	+	27.6462i	0.455445	+	1.40172i	0.870612	+	0.491970i	$0.163723\pi$
$389$	8.98278	+	27.6462i	0.455445	+	1.40172i	−0.415167	+	0.909745i	$0.636277\pi$
$390$	6.35410	+	4.61653i	0.321752	+	0.233767i
$391$	1.04508	−	0.759299i	0.0528522	−	0.0383994i
$392$	1.38197	−	4.25325i	0.0697998	−	0.214822i
$393$	−0.0729490	+	0.0530006i	−0.00367979	+	0.00267352i
$394$	3.13525	+	9.64932i	0.157952	+	0.486126i
$395$		0			0
$396$	0.763932	−	2.35114i	0.0383890	−	0.118149i
$397$	16.2918			0.817662			0.408831	−	0.912610i	$-0.365937\pi$
$397$	16.2918			0.817662			0.408831	+	0.912610i	$0.365937\pi$
$398$	−16.5066			−0.827400
$399$	4.63525	−	14.2658i	0.232053	−	0.714186i
$400$	−2.78115	−	2.02063i	−0.139058	−	0.101031i
$401$	−24.1353	+	17.5353i	−1.20526	+	0.875671i	−0.994792	−	0.101931i	$-0.967498\pi$
$401$	−24.1353	+	17.5353i	−1.20526	+	0.875671i	−0.210466	+	0.977601i	$0.567498\pi$
$402$	2.61803			0.130576
$403$		0			0
$404$	−7.70820			−0.383497
$405$	2.11803	−	1.53884i	0.105246	−	0.0764657i
$406$	12.9271	+	9.39205i	0.641559	+	0.466120i
$407$	−0.0557281	+	0.171513i	−0.00276234	+	0.00850160i
$408$	−0.527864			−0.0261332
$409$	6.18034			0.305598			0.152799	−	0.988257i	$-0.451171\pi$
$409$	6.18034			0.305598			0.152799	+	0.988257i	$0.451171\pi$
$410$	3.23607	−	9.95959i	0.159818	−	0.491869i
$411$	2.00000	+	6.15537i	0.0986527	+	0.303622i
$412$	0.0729490	+	0.224514i	0.00359394	+	0.0110610i
$413$	−22.9894	+	16.7027i	−1.13123	+	0.821888i
$414$	2.09017	−	6.43288i	0.102726	−	0.316159i
$415$	8.66312	−	6.29412i	0.425256	−	0.308966i
$416$	−22.0623	−	16.0292i	−1.08169	−	0.785896i
$417$	−1.80902	−	5.56758i	−0.0885879	−	0.272646i
$418$	1.90983	+	1.38757i	0.0934128	+	0.0678684i
$419$	−3.61803	−	2.62866i	−0.176753	−	0.128418i	0.495891	−	0.868385i	$-0.334841\pi$
$419$	−3.61803	−	2.62866i	−0.176753	−	0.128418i	−0.672644	+	0.739966i	$0.734841\pi$
$420$	3.92705	+	12.0862i	0.191620	+	0.589747i
$421$	−11.9443	−	8.67802i	−0.582128	−	0.422941i	0.257363	−	0.966315i	$-0.417147\pi$
$421$	−11.9443	−	8.67802i	−0.582128	−	0.422941i	−0.839491	+	0.543374i	$0.817147\pi$
$422$	−4.00000	+	2.90617i	−0.194717	+	0.141470i
$423$	2.09017	−	6.43288i	0.101628	−	0.312777i
$424$	−22.9894	+	16.7027i	−1.11646	+	0.811157i
$425$	−0.135255	−	0.416272i	−0.00656083	−	0.0201921i
$426$	−0.0172209	−	0.0530006i	−0.000834357	−	0.00256789i
$427$	6.43769	−	19.8132i	0.311542	−	0.958827i
$428$	−1.76393			−0.0852629
$429$	−3.70820			−0.179034
$430$	2.30902	−	7.10642i	0.111351	−	0.342702i
$431$	−23.6525	−	17.1845i	−1.13930	−	0.827750i	−0.152278	−	0.988338i	$-0.548661\pi$
$431$	−23.6525	−	17.1845i	−1.13930	−	0.827750i	−0.987022	+	0.160588i	$0.948661\pi$
$432$	7.50000	−	5.44907i	0.360844	−	0.262168i
$433$	−0.583592			−0.0280456			−0.0140228	−	0.999902i	$-0.504464\pi$
$433$	−0.583592			−0.0280456			−0.0140228	+	0.999902i	$0.504464\pi$
$434$		0			0
$435$	−22.5623			−1.08178
$436$	−11.0172	+	8.00448i	−0.527629	+	0.383345i
$437$	−22.1353	−	16.0822i	−1.05887	−	0.769316i
$438$	−1.63525	+	5.03280i	−0.0781355	+	0.240476i
$439$	41.8328			1.99657			0.998286	−	0.0585295i	$-0.0186412\pi$
$439$	41.8328			1.99657			0.998286	+	0.0585295i	$0.0186412\pi$
$440$	−4.47214			−0.213201
$441$	−1.23607	+	3.80423i	−0.0588604	+	0.181154i
$442$	−0.218847	−	0.673542i	−0.0104095	−	0.0320371i
$443$	−12.7082	−	39.1118i	−0.603785	−	1.85826i	−0.504936	−	0.863157i	$-0.668484\pi$
$443$	−12.7082	−	39.1118i	−0.603785	−	1.85826i	−0.0988488	−	0.995102i	$-0.531516\pi$
$444$	−0.309017	+	0.224514i	−0.0146653	+	0.0106550i
$445$	−5.16312	+	15.8904i	−0.244755	+	0.753279i
$446$	−0.354102	+	0.257270i	−0.0167672	+	0.0121821i
$447$	13.7812	+	10.0126i	0.651826	+	0.473579i
$448$	−0.218847	−	0.673542i	−0.0103396	−	0.0318219i
$449$	19.4721	+	14.1473i	0.918947	+	0.667654i	0.943262	−	0.332050i	$-0.107740\pi$
$449$	19.4721	+	14.1473i	0.918947	+	0.667654i	−0.0243148	+	0.999704i	$0.507740\pi$
$450$	−1.85410	−	1.34708i	−0.0874032	−	0.0635021i
$451$	1.52786	+	4.70228i	0.0719443	+	0.221422i
$452$	−2.42705	−	1.76336i	−0.114159	−	0.0829413i
$453$	−15.7812	+	11.4657i	−0.741463	+	0.538705i
$454$	3.96149	−	12.1922i	0.185922	−	0.572209i
$455$	−30.8435	+	22.4091i	−1.44596	+	1.05055i
$456$	3.45492	+	10.6331i	0.161791	+	0.497942i
$457$	4.86475	+	14.9721i	0.227563	+	0.700367i	0.998021	+	0.0628768i	$0.0200275\pi$
$457$	4.86475	+	14.9721i	0.227563	+	0.700367i	−0.770458	+	0.637491i	$0.779972\pi$
$458$	−1.38197	+	4.25325i	−0.0645750	+	0.198742i
$459$	1.18034			0.0550935
$460$	23.1803			1.08079
$461$	−3.31966	+	10.2169i	−0.154612	+	0.475847i	−0.998121	−	0.0612677i	$-0.980486\pi$
$461$	−3.31966	+	10.2169i	−0.154612	+	0.475847i	0.843509	+	0.537114i	$0.180486\pi$
$462$	1.14590	+	0.832544i	0.0533120	+	0.0387334i
$463$	−25.1803	+	18.2946i	−1.17023	+	0.850222i	−0.991036	−	0.133592i	$-0.957349\pi$
$463$	−25.1803	+	18.2946i	−1.17023	+	0.850222i	−0.179193	+	0.983814i	$0.557349\pi$
$464$	15.9787			0.741793
$465$		0			0
$466$	−11.6180			−0.538195
$467$	26.5172	−	19.2659i	1.22707	−	0.891519i	0.230404	−	0.973095i	$-0.425995\pi$
$467$	26.5172	−	19.2659i	1.22707	−	0.891519i	0.996667	+	0.0815762i	$0.0259954\pi$
$468$	12.7082	+	9.23305i	0.587437	+	0.426798i
$469$	−3.92705	+	12.0862i	−0.181334	+	0.558090i
$470$	−5.47214			−0.252411
$471$	9.70820			0.447330
$472$	6.54508	−	20.1437i	0.301262	−	0.927189i
$473$	1.09017	+	3.35520i	0.0501261	+	0.154272i
$474$		0			0
$475$	−7.50000	+	5.44907i	−0.344124	+	0.250020i
$476$	0.354102	−	1.08981i	0.0162302	−	0.0499515i
$477$	20.5623	−	14.9394i	0.941483	−	0.684028i
$478$	6.70820	+	4.87380i	0.306826	+	0.222922i
$479$	−2.76393	−	8.50651i	−0.126287	−	0.388672i	0.867846	−	0.496833i	$-0.165504\pi$
$479$	−2.76393	−	8.50651i	−0.126287	−	0.388672i	−0.994133	+	0.108161i	$0.965504\pi$
$480$	−11.8992	−	8.64527i	−0.543121	−	0.394601i
$481$	−0.927051	−	0.673542i	−0.0422699	−	0.0307109i
$482$	−1.62868	−	5.01255i	−0.0741842	−	0.228316i
$483$	−13.2812	−	9.64932i	−0.604313	−	0.439059i
$484$	−13.6353	+	9.90659i	−0.619784	+	0.450300i
$485$	4.28115	−	13.1760i	0.194397	−	0.598293i
$486$	8.00000	−	5.81234i	0.362887	−	0.263653i
$487$	−7.08359	−	21.8011i	−0.320988	−	0.987900i	−0.973219	−	0.229880i	$-0.926167\pi$
$487$	−7.08359	−	21.8011i	−0.320988	−	0.987900i	0.652231	−	0.758020i	$-0.273833\pi$
$488$	4.79837	+	14.7679i	0.217212	+	0.668510i
$489$	−3.92705	+	12.0862i	−0.177587	+	0.546558i
$490$	3.23607			0.146191
$491$	27.5967			1.24542			0.622712	−	0.782451i	$-0.286031\pi$
$491$	27.5967			1.24542			0.622712	+	0.782451i	$0.286031\pi$
$492$	−3.23607	+	9.95959i	−0.145893	+	0.449013i
$493$	1.64590	+	1.19581i	0.0741275	+	0.0538568i
$494$	−12.1353	+	8.81678i	−0.545991	+	0.396686i
$495$	4.00000			0.179787
$496$		0			0
$497$	0.270510			0.0121340
$498$	2.04508	−	1.48584i	0.0916424	−	0.0665821i
$499$	3.35410	+	2.43690i	0.150150	+	0.109091i	0.660324	−	0.750981i	$-0.270419\pi$
$499$	3.35410	+	2.43690i	0.150150	+	0.109091i	−0.510174	+	0.860071i	$0.670419\pi$
$500$	−4.11803	+	12.6740i	−0.184164	+	0.566799i
$501$	9.23607			0.412637
$502$	0.583592			0.0260470
$503$	4.06231	−	12.5025i	0.181129	−	0.557459i	−0.818731	−	0.574177i	$-0.805322\pi$
$503$	4.06231	−	12.5025i	0.181129	−	0.557459i	0.999860	+	0.0167188i	$0.00532200\pi$
$504$	−4.14590	−	12.7598i	−0.184673	−	0.568365i
$505$	−3.85410	−	11.8617i	−0.171505	−	0.527839i
$506$	2.09017	−	1.51860i	0.0929194	−	0.0675099i
$507$	3.26393	−	10.0453i	0.144956	−	0.446130i
$508$	−13.3992	+	9.73508i	−0.594493	+	0.431924i
$509$	−1.54508	−	1.12257i	−0.0684847	−	0.0497570i	0.553016	−	0.833171i	$-0.313477\pi$
$509$	−1.54508	−	1.12257i	−0.0684847	−	0.0497570i	−0.621501	+	0.783413i	$0.713477\pi$
$510$	−0.118034	−	0.363271i	−0.00522663	−	0.0160859i
$511$	−20.7812	−	15.0984i	−0.919304	−	0.667914i
$512$	15.1353	+	10.9964i	0.668890	+	0.485977i
$513$	−7.72542	−	23.7764i	−0.341086	−	1.04975i
$514$	0.708204	+	0.514540i	0.0312375	+	0.0226954i
$515$	−0.309017	+	0.224514i	−0.0136169	+	0.00989327i
$516$	−2.30902	+	7.10642i	−0.101649	+	0.312843i
$517$	2.09017	−	1.51860i	0.0919256	−	0.0667878i
$518$	0.135255	+	0.416272i	0.00594276	+	0.0182899i
$519$	0.281153	+	0.865300i	0.0123412	+	0.0379824i
$520$	8.78115	−	27.0256i	0.385079	−	1.18515i
$521$	31.0689			1.36115			0.680576	−	0.732677i	$-0.261729\pi$
$521$	31.0689			1.36115			0.680576	+	0.732677i	$0.261729\pi$
$522$	10.6525			0.466246
$523$	−10.5451	+	32.4544i	−0.461104	+	1.41913i	0.402712	+	0.915327i	$0.368068\pi$
$523$	−10.5451	+	32.4544i	−0.461104	+	1.41913i	−0.863816	+	0.503807i	$0.831932\pi$
$524$	0.118034	+	0.0857567i	0.00515634	+	0.00374630i
$525$	−4.50000	+	3.26944i	−0.196396	+	0.142690i
$526$	−6.67376			−0.290990
$527$		0			0
$528$	1.41641			0.0616412
$529$	−5.61803	+	4.08174i	−0.244262	+	0.177467i
$530$	−16.6353	−	12.0862i	−0.722589	−	0.524992i
$531$	−5.85410	+	18.0171i	−0.254046	+	0.781874i
$532$	−24.2705			−1.05226
$533$	−31.4164			−1.36080
$534$	−1.21885	+	3.75123i	−0.0527447	+	0.162331i
$535$	−0.881966	−	2.71441i	−0.0381307	−	0.117354i
$536$	−2.92705	−	9.00854i	−0.126429	−	0.389110i
$537$	16.0172	−	11.6372i	0.691194	−	0.502182i
$538$	−0.263932	+	0.812299i	−0.0113789	+	0.0350207i
$539$	−1.23607	+	0.898056i	−0.0532412	+	0.0386820i
$540$	17.1353	+	12.4495i	0.737384	+	0.535741i
$541$	6.79837	+	20.9232i	0.292285	+	0.899560i	0.984120	+	0.177505i	$0.0568025\pi$
$541$	6.79837	+	20.9232i	0.292285	+	0.899560i	−0.691835	+	0.722056i	$0.743197\pi$
$542$	−4.78115	−	3.47371i	−0.205368	−	0.149209i
$543$	13.7533	+	9.99235i	0.590210	+	0.428813i
$544$	0.409830	+	1.26133i	0.0175713	+	0.0540790i
$545$	−17.8262	−	12.9515i	−0.763592	−	0.554782i
$546$	−7.28115	+	5.29007i	−0.311605	+	0.226394i
$547$	−7.32624	+	22.5478i	−0.313247	+	0.964076i	0.663223	+	0.748422i	$0.269188\pi$
$547$	−7.32624	+	22.5478i	−0.313247	+	0.964076i	−0.976470	+	0.215654i	$0.930812\pi$
$548$	8.47214	−	6.15537i	0.361912	−	0.262944i
$549$	−4.29180	−	13.2088i	−0.183169	−	0.563737i
$550$	−0.270510	−	0.832544i	−0.0115346	−	0.0354998i
$551$	13.3156	−	40.9812i	0.567263	−	1.74586i
$552$	12.2361			0.520802
$553$		0			0
$554$	2.54508	−	7.83297i	0.108130	−	0.332791i
$555$	−0.500000	−	0.363271i	−0.0212238	−	0.0154200i
$556$	−7.66312	+	5.56758i	−0.324989	+	0.236118i
$557$	−35.8885			−1.52065			−0.760323	−	0.649545i	$-0.774959\pi$
$557$	−35.8885			−1.52065			−0.760323	+	0.649545i	$0.774959\pi$
$558$		0			0
$559$	−22.4164			−0.948113
$560$	11.7812	−	8.55951i	0.497845	−	0.361705i
$561$	0.145898	+	0.106001i	0.00615982	+	0.00447537i
$562$	−3.63525	+	11.1882i	−0.153344	+	0.471944i
$563$	−8.56231			−0.360858			−0.180429	−	0.983588i	$-0.557749\pi$
$563$	−8.56231			−0.360858			−0.180429	+	0.983588i	$0.557749\pi$
$564$	5.47214			0.230418
$565$	1.50000	−	4.61653i	0.0631055	−	0.194219i
$566$	−1.25329	−	3.85723i	−0.0526797	−	0.162131i
$567$	0.927051	+	2.85317i	0.0389325	+	0.119822i
$568$	−0.163119	+	0.118513i	−0.00684432	+	0.00497269i
$569$	−4.79837	+	14.7679i	−0.201158	+	0.619102i	0.798691	+	0.601741i	$0.205526\pi$
$569$	−4.79837	+	14.7679i	−0.201158	+	0.619102i	−0.999849	+	0.0173602i	$0.994474\pi$
$570$	−6.54508	+	4.75528i	−0.274143	+	0.199177i
$571$	5.66312	+	4.11450i	0.236994	+	0.172186i	0.699943	−	0.714199i	$-0.253209\pi$
$571$	5.66312	+	4.11450i	0.236994	+	0.172186i	−0.462949	+	0.886385i	$0.653209\pi$
$572$	1.85410	+	5.70634i	0.0775239	+	0.238594i
$573$	13.0172	+	9.45756i	0.543802	+	0.395095i
$574$	9.70820	+	7.05342i	0.405213	+	0.294404i
$575$	3.13525	+	9.64932i	0.130749	+	0.402405i
$576$	−0.381966	−	0.277515i	−0.0159153	−	0.0115631i
$577$	−31.5344	+	22.9111i	−1.31280	+	0.953802i	−0.312804	+	0.949818i	$0.601268\pi$
$577$	−31.5344	+	22.9111i	−1.31280	+	0.953802i	−0.999992	+	0.00398440i	$0.998732\pi$
$578$	3.23607	−	9.95959i	0.134603	−	0.414264i
$579$	1.92705	−	1.40008i	0.0800855	−	0.0581855i
$580$	11.2812	+	34.7198i	0.468424	+	1.44166i
$581$	3.79180	+	11.6699i	0.157310	+	0.484151i
$582$	1.01064	−	3.11044i	0.0418925	−	0.128932i
$583$	9.70820			0.402073
$584$	19.1459			0.792263
$585$	−7.85410	+	24.1724i	−0.324727	+	0.999407i
$586$	−4.11803	−	2.99193i	−0.170114	−	0.123595i
$587$	29.1353	−	21.1680i	1.20254	−	0.873697i	0.208008	−	0.978127i	$-0.433302\pi$
$587$	29.1353	−	21.1680i	1.20254	−	0.873697i	0.994532	+	0.104430i	$0.0333018\pi$
$588$	−3.23607			−0.133453
$589$		0			0
$590$	15.3262			0.630971
$591$	13.2812	−	9.64932i	0.546314	−	0.396920i
$592$	0.354102	+	0.257270i	0.0145535	+	0.0105737i
$593$	1.88854	−	5.81234i	0.0775532	−	0.238684i	−0.904762	−	0.425917i	$-0.859952\pi$
$593$	1.88854	−	5.81234i	0.0775532	−	0.238684i	0.982316	+	0.187232i	$0.0599517\pi$
$594$	2.36068			0.0968599
$595$	1.85410			0.0760108
$596$	8.51722	−	26.2133i	0.348879	−	1.07374i
$597$	8.25329	+	25.4010i	0.337785	+	1.03959i
$598$	5.07295	+	15.6129i	0.207448	+	0.638460i
$599$	−24.1074	+	17.5150i	−0.985001	+	0.715645i	−0.958821	−	0.284012i	$-0.908334\pi$
$599$	−24.1074	+	17.5150i	−0.985001	+	0.715645i	−0.0261805	+	0.999657i	$0.508334\pi$
$600$	1.28115	−	3.94298i	0.0523029	−	0.160972i
$601$	17.7984	−	12.9313i	0.726011	−	0.527478i	−0.162288	−	0.986743i	$-0.551887\pi$
$601$	17.7984	−	12.9313i	0.726011	−	0.527478i	0.888299	+	0.459266i	$0.151887\pi$
$602$	6.92705	+	5.03280i	0.282326	+	0.205121i
$603$	2.61803	+	8.05748i	0.106615	+	0.328126i
$604$	25.5344	+	18.5519i	1.03898	+	0.754864i
$605$	−22.0623	−	16.0292i	−0.896960	−	0.651680i
$606$	−0.909830	−	2.80017i	−0.0369593	−	0.113749i
$607$	20.5623	+	14.9394i	0.834598	+	0.606371i	0.920856	−	0.389902i	$-0.127491\pi$
$607$	20.5623	+	14.9394i	0.834598	+	0.606371i	−0.0862582	+	0.996273i	$0.527491\pi$
$608$	22.7254	−	16.5110i	0.921638	−	0.669609i
$609$	7.98936	−	24.5887i	0.323745	−	0.996385i
$610$	−9.09017	+	6.60440i	−0.368050	+	0.267404i
$611$	5.07295	+	15.6129i	0.205230	+	0.631632i
$612$	−0.236068	−	0.726543i	−0.00954248	−	0.0293687i
$613$	−7.74265	+	23.8294i	−0.312723	+	0.962461i	0.663959	+	0.747769i	$0.268875\pi$
$613$	−7.74265	+	23.8294i	−0.312723	+	0.962461i	−0.976682	+	0.214692i	$0.931125\pi$
$614$	−3.76393			−0.151900
$615$	−16.9443			−0.683259
$616$	1.58359	−	4.87380i	0.0638047	−	0.196371i
$617$	11.5172	+	8.36775i	0.463666	+	0.336873i	0.794968	−	0.606652i	$-0.207488\pi$
$617$	11.5172	+	8.36775i	0.463666	+	0.336873i	−0.331302	+	0.943525i	$0.607488\pi$
$618$	−0.0729490	+	0.0530006i	−0.00293444	+	0.00213200i
$619$	40.0000			1.60774			0.803868	−	0.594808i	$-0.202772\pi$
$619$	40.0000			1.60774			0.803868	+	0.594808i	$0.202772\pi$
$620$		0			0
$621$	−27.3607			−1.09795
$622$	8.23607	−	5.98385i	0.330236	−	0.239931i
$623$	−15.4894	−	11.2537i	−0.620568	−	0.450869i
$624$	−2.78115	+	8.55951i	−0.111335	+	0.342655i
$625$	−30.8328			−1.23331
$626$	0.763932			0.0305329
$627$	1.18034	−	3.63271i	0.0471382	−	0.145077i
$628$	−4.85410	−	14.9394i	−0.193700	−	0.596147i
$629$	0.0172209	+	0.0530006i	0.000686643	+	0.00211327i
$630$	7.85410	−	5.70634i	0.312915	−	0.227346i
$631$	2.69756	−	8.30224i	0.107388	−	0.330507i	−0.882895	−	0.469570i	$-0.844409\pi$
$631$	2.69756	−	8.30224i	0.107388	−	0.330507i	0.990284	+	0.139063i	$0.0444090\pi$
$632$		0			0
$633$	6.47214	+	4.70228i	0.257244	+	0.186899i
$634$	−4.94427	−	15.2169i	−0.196362	−	0.604340i
$635$	−21.6803	−	15.7517i	−0.860358	−	0.625087i
$636$	16.6353	+	12.0862i	0.659631	+	0.479250i
$637$	−3.00000	−	9.23305i	−0.118864	−	0.365827i
$638$	3.29180	+	2.39163i	0.130323	+	0.0946855i
$639$	0.145898	−	0.106001i	0.00577164	−	0.00419334i
$640$	−9.20820	+	28.3399i	−0.363986	+	1.12023i
$641$	−33.2426	+	24.1522i	−1.31301	+	0.953954i	−0.313014	+	0.949748i	$0.601339\pi$
$641$	−33.2426	+	24.1522i	−1.31301	+	0.953954i	−0.999991	+	0.00420601i	$0.998661\pi$
$642$	−0.208204	−	0.640786i	−0.00821715	−	0.0252898i
$643$	−2.51722	−	7.74721i	−0.0992695	−	0.305520i	0.889073	−	0.457765i	$-0.151350\pi$
$643$	−2.51722	−	7.74721i	−0.0992695	−	0.305520i	−0.988343	+	0.152245i	$0.951350\pi$
$644$	−8.20820	+	25.2623i	−0.323449	+	0.995472i
$645$	−12.0902			−0.476050
$646$	0.729490			0.0287014
$647$	9.23607	−	28.4257i	0.363107	−	1.11753i	−0.588050	−	0.808824i	$-0.700104\pi$
$647$	9.23607	−	28.4257i	0.363107	−	1.11753i	0.951158	−	0.308705i	$-0.0998956\pi$
$648$	−1.80902	−	1.31433i	−0.0710649	−	0.0516317i
$649$	−5.85410	+	4.25325i	−0.229794	+	0.166955i
$650$	5.56231			0.218172
$651$		0			0
$652$	20.5623			0.805282
$653$	−32.0795	+	23.3071i	−1.25537	+	0.912079i	−0.998521	−	0.0543729i	$-0.982684\pi$
$653$	−32.0795	+	23.3071i	−1.25537	+	0.912079i	−0.256848	+	0.966452i	$0.582684\pi$
$654$	−4.20820	−	3.05744i	−0.164554	−	0.119555i
$655$	−0.0729490	+	0.224514i	−0.00285035	+	0.00877249i
$656$	12.0000			0.468521
$657$	−17.1246			−0.668095
$658$	1.93769	−	5.96361i	0.0755392	−	0.232486i
$659$	7.01064	+	21.5765i	0.273096	+	0.840503i	0.989717	+	0.143040i	$0.0456877\pi$
$659$	7.01064	+	21.5765i	0.273096	+	0.840503i	−0.716621	+	0.697463i	$0.754312\pi$
$660$	1.00000	+	3.07768i	0.0389249	+	0.119799i
$661$	13.4443	−	9.76784i	0.522922	−	0.379925i	−0.294782	−	0.955565i	$-0.595247\pi$
$661$	13.4443	−	9.76784i	0.522922	−	0.379925i	0.817703	+	0.575640i	$0.195247\pi$
$662$	2.15248	−	6.62464i	0.0836583	−	0.257474i
$663$	−0.927051	+	0.673542i	−0.0360037	+	0.0261582i
$664$	−7.39919	−	5.37582i	−0.287144	−	0.208622i
$665$	−12.1353	−	37.3485i	−0.470585	−	1.44831i
$666$	0.236068	+	0.171513i	0.00914745	+	0.00664601i
$667$	−38.1525	−	27.7194i	−1.47727	−	1.07330i
$668$	−4.61803	−	14.2128i	−0.178677	−	0.549912i
$669$	0.572949	+	0.416272i	0.0221515	+	0.0160940i
$670$	5.54508	−	4.02874i	0.214225	−	0.155644i
$671$	1.63932	−	5.04531i	0.0632853	−	0.194772i
$672$	13.6353	−	9.90659i	0.525991	−	0.382155i
$673$	1.36475	+	4.20025i	0.0526071	+	0.161908i	0.973908	−	0.226942i	$-0.0728726\pi$
$673$	1.36475	+	4.20025i	0.0526071	+	0.161908i	−0.921301	+	0.388849i	$0.872873\pi$
$674$	3.62461	+	11.1554i	0.139615	+	0.429690i
$675$	−2.86475	+	8.81678i	−0.110264	+	0.339358i
$676$	−17.0902			−0.657314
$677$	−28.6525			−1.10120			−0.550602	−	0.834768i	$-0.685602\pi$
$677$	−28.6525			−1.10120			−0.550602	+	0.834768i	$0.685602\pi$
$678$	0.354102	−	1.08981i	0.0135992	−	0.0418540i
$679$	12.8435	+	9.33132i	0.492887	+	0.358103i
$680$	−1.11803	+	0.812299i	−0.0428746	+	0.0311503i
$681$	−20.7426			−0.794860
$682$		0			0
$683$	10.0557			0.384772			0.192386	−	0.981319i	$-0.438377\pi$
$683$	10.0557			0.384772			0.192386	+	0.981319i	$0.438377\pi$
$684$	−13.0902	+	9.51057i	−0.500515	+	0.363646i
$685$	13.7082	+	9.95959i	0.523764	+	0.380536i
$686$	2.86475	−	8.81678i	0.109376	−	0.336626i
$687$	7.23607			0.276073
$688$	8.56231			0.326435
$689$	−19.0623	+	58.6677i	−0.726216	+	2.23506i
$690$	2.73607	+	8.42075i	0.104160	+	0.320573i
$691$	1.18441	+	3.64522i	0.0450569	+	0.138671i	0.971054	−	0.238859i	$-0.0767735\pi$
$691$	1.18441	+	3.64522i	0.0450569	+	0.138671i	−0.925997	+	0.377530i	$0.876773\pi$
$692$	1.19098	−	0.865300i	0.0452744	−	0.0328938i
$693$	−1.41641	+	4.35926i	−0.0538049	+	0.165594i
$694$	−4.06231	+	2.95144i	−0.154203	+	0.112035i
$695$	−12.3992	−	9.00854i	−0.470328	−	0.341713i
$696$	5.95492	+	18.3273i	0.225720	+	0.694696i
$697$	1.23607	+	0.898056i	0.0468194	+	0.0340163i
$698$	−8.35410	−	6.06961i	−0.316207	−	0.229738i
$699$	5.80902	+	17.8783i	0.219717	+	0.676220i
$700$	7.28115	+	5.29007i	0.275202	+	0.199946i
$701$	24.2984	−	17.6538i	0.917737	−	0.666775i	−0.0252228	−	0.999682i	$-0.508030\pi$
$701$	24.2984	−	17.6538i	0.917737	−	0.666775i	0.942960	+	0.332907i	$0.108030\pi$
$702$	−4.63525	+	14.2658i	−0.174946	+	0.538430i
$703$	0.954915	−	0.693786i	0.0360153	−	0.0261666i
$704$	−0.0557281	−	0.171513i	−0.00210033	−	0.00646416i
$705$	2.73607	+	8.42075i	0.103046	+	0.317144i
$706$	−6.18441	+	19.0336i	−0.232753	+	0.716341i
$707$	14.2918			0.537498
$708$	−15.3262			−0.575995
$709$	−1.28115	+	3.94298i	−0.0481147	+	0.148082i	−0.972227	−	0.234038i	$-0.924806\pi$
$709$	−1.28115	+	3.94298i	−0.0481147	+	0.148082i	0.924113	+	0.382120i	$0.124806\pi$
$710$	−0.118034	−	0.0857567i	−0.00442974	−	0.00321839i
$711$		0			0
$712$	14.2705			0.534810
$713$		0			0
$714$	0.437694			0.0163803
$715$	−7.85410	+	5.70634i	−0.293727	+	0.213405i
$716$	−25.9164	−	18.8294i	−0.968542	−	0.703687i
$717$	4.14590	−	12.7598i	0.154831	−	0.476522i
$718$	15.6525			0.584145
$719$	41.3820			1.54329			0.771643	−	0.636055i	$-0.219435\pi$
$719$	41.3820			1.54329			0.771643	+	0.636055i	$0.219435\pi$
$720$	3.00000	−	9.23305i	0.111803	−	0.344095i
$721$	−0.135255	−	0.416272i	−0.00503716	−	0.0155028i
$722$	−1.14590	−	3.52671i	−0.0426459	−	0.131251i
$723$	−6.89919	+	5.01255i	−0.256584	+	0.186419i
$724$	8.50000	−	26.1603i	0.315900	−	0.972240i
$725$	−12.9271	+	9.39205i	−0.480099	+	0.348812i
$726$	−5.20820	−	3.78398i	−0.193295	−	0.140437i
$727$	−7.36475	−	22.6664i	−0.273143	−	0.840649i	−0.989705	−	0.143125i	$-0.954285\pi$
$727$	−7.36475	−	22.6664i	−0.273143	−	0.840649i	0.716561	−	0.697524i	$-0.245715\pi$
$728$	26.3435	+	19.1396i	0.976354	+	0.709362i
$729$	−10.5172	−	7.64121i	−0.389527	−	0.283008i
$730$	4.28115	+	13.1760i	0.158453	+	0.487667i
$731$	0.881966	+	0.640786i	0.0326207	+	0.0237003i
$732$	9.09017	−	6.60440i	0.335982	−	0.244105i
$733$	8.63525	−	26.5766i	0.318950	−	0.981628i	−0.655147	−	0.755501i	$-0.727393\pi$
$733$	8.63525	−	26.5766i	0.318950	−	0.981628i	0.974098	−	0.226127i	$-0.0726065\pi$
$734$	18.1353	−	13.1760i	0.669384	−	0.486336i
$735$	−1.61803	−	4.97980i	−0.0596821	−	0.183683i
$736$	−9.50000	−	29.2380i	−0.350175	−	1.07773i
$737$	−1.00000	+	3.07768i	−0.0368355	+	0.113368i
$738$	8.00000			0.294484
$739$	−21.7082			−0.798549			−0.399275	−	0.916831i	$-0.630738\pi$
$739$	−21.7082			−0.798549			−0.399275	+	0.916831i	$0.630738\pi$
$740$	−0.309017	+	0.951057i	−0.0113597	+	0.0349615i
$741$	19.6353	+	14.2658i	0.721319	+	0.524069i
$742$	19.0623	−	13.8496i	0.699799	−	0.508434i
$743$	3.43769			0.126117			0.0630584	−	0.998010i	$-0.479915\pi$
$743$	3.43769			0.126117			0.0630584	+	0.998010i	$0.479915\pi$
$744$		0			0
$745$	44.5967			1.63390
$746$	−0.173762	+	0.126246i	−0.00636188	+	0.00462218i
$747$	6.61803	+	4.80828i	0.242141	+	0.175926i
$748$	0.0901699	−	0.277515i	0.00329694	−	0.0101469i
$749$	3.27051			0.119502
$750$	−5.09017			−0.185867
$751$	−12.3090	+	37.8833i	−0.449162	+	1.38238i	0.428691	+	0.903451i	$0.358975\pi$
$751$	−12.3090	+	37.8833i	−0.449162	+	1.38238i	−0.877854	+	0.478929i	$0.841025\pi$
$752$	−1.93769	−	5.96361i	−0.0706604	−	0.217470i
$753$	−0.291796	−	0.898056i	−0.0106336	−	0.0327270i
$754$	−20.9164	+	15.1967i	−0.761731	+	0.553430i
$755$	−15.7812	+	48.5694i	−0.574335	+	1.76762i
$756$	−19.6353	+	14.2658i	−0.714127	+	0.518844i
$757$	34.8885	+	25.3480i	1.26805	+	0.921289i	0.999123	−	0.0418726i	$-0.0133324\pi$
$757$	34.8885	+	25.3480i	1.26805	+	0.921289i	0.268923	+	0.963162i	$0.413332\pi$
$758$	3.51722	+	10.8249i	0.127751	+	0.393178i
$759$	−3.38197	−	2.45714i	−0.122758	−	0.0891886i
$760$	23.6803	+	17.2048i	0.858976	+	0.624083i
$761$	−1.08359	−	3.33495i	−0.0392802	−	0.120892i	0.929494	−	0.368838i	$-0.120244\pi$
$761$	−1.08359	−	3.33495i	−0.0392802	−	0.120892i	−0.968774	+	0.247946i	$0.920244\pi$
$762$	−5.11803	−	3.71847i	−0.185407	−	0.134706i
$763$	20.4271	−	14.8411i	0.739509	−	0.537285i
$764$	8.04508	−	24.7602i	0.291061	−	0.895794i
$765$	1.00000	−	0.726543i	0.0361551	−	0.0262682i
$766$	−3.21885	−	9.90659i	−0.116302	−	0.357940i
$767$	−14.2082	−	43.7284i	−0.513029	−	1.57894i
$768$	−2.02786	+	6.24112i	−0.0731742	+	0.225207i
$769$	−53.7426			−1.93801			−0.969005	−	0.247042i	$-0.920541\pi$
$769$	−53.7426			−1.93801			−0.969005	+	0.247042i	$0.920541\pi$
$770$	3.70820			0.133634
$771$	0.437694	−	1.34708i	0.0157632	−	0.0485140i
$772$	−3.11803	−	2.26538i	−0.112220	−	0.0815330i
$773$	−15.4443	+	11.2209i	−0.555492	+	0.403588i	−0.829806	−	0.558052i	$-0.811549\pi$
$773$	−15.4443	+	11.2209i	−0.555492	+	0.403588i	0.274314	+	0.961640i	$0.411549\pi$
$774$	5.70820			0.205177
$775$		0			0
$776$	−11.8328			−0.424773
$777$	0.572949	−	0.416272i	0.0205544	−	0.0149337i
$778$	14.5344	+	10.5599i	0.521085	+	0.378590i
$779$	10.0000	−	30.7768i	0.358287	−	1.10269i
$780$	−20.5623			−0.736249
$781$	0.0688837			0.00246485
$782$	0.246711	−	0.759299i	0.00882237	−	0.0271525i
$783$	−13.3156	−	40.9812i	−0.475861	−	1.46455i
$784$	1.14590	+	3.52671i	0.0409249	+	0.125954i
$785$	20.5623	−	14.9394i	0.733900	−	0.533210i
$786$	−0.0172209	+	0.0530006i	−0.000614250	+	0.00189047i
$787$	25.3156	−	18.3929i	0.902403	−	0.655635i	−0.0366787	−	0.999327i	$-0.511678\pi$
$787$	25.3156	−	18.3929i	0.902403	−	0.655635i	0.939082	+	0.343693i	$0.111678\pi$
$788$	−21.4894	−	15.6129i	−0.765527	−	0.556188i
$789$	3.33688	+	10.2699i	0.118796	+	0.365617i
$790$		0			0
$791$	4.50000	+	3.26944i	0.160002	+	0.116248i
$792$	−1.05573	−	3.24920i	−0.0375137	−	0.115455i
$793$	27.2705	+	19.8132i	0.968404	+	0.703587i
$794$	8.14590	−	5.91834i	0.289087	−	0.210034i
$795$	−10.2812	+	31.6421i	−0.364635	+	1.12223i
$796$	34.9615	−	25.4010i	1.23918	−	0.900315i
$797$	−2.79837	−	8.61251i	−0.0991235	−	0.305071i	0.889183	−	0.457552i	$-0.151274\pi$
$797$	−2.79837	−	8.61251i	−0.0991235	−	0.305071i	−0.988306	+	0.152481i	$0.951274\pi$
$798$	−2.86475	−	8.81678i	−0.101411	−	0.312111i
$799$	0.246711	−	0.759299i	0.00872801	−	0.0268621i
$800$	−10.4164			−0.368276
$801$	−12.7639			−0.450991
$802$	−5.69756	+	17.5353i	−0.201188	+	0.619193i
$803$	−5.29180	−	3.84471i	−0.186743	−	0.135677i
$804$	−5.54508	+	4.02874i	−0.195560	+	0.142083i
$805$	−42.9787			−1.51480
$806$		0			0
$807$	1.38197			0.0486475
$808$	−8.61803	+	6.26137i	−0.303181	+	0.220274i
$809$	44.3328	+	32.2097i	1.55866	+	1.13243i	0.937098	+	0.349066i	$0.113501\pi$
$809$	44.3328	+	32.2097i	1.55866	+	1.13243i	0.621561	+	0.783366i	$0.286499\pi$
$810$	0.500000	−	1.53884i	0.0175682	−	0.0540694i
$811$	42.7771			1.50211			0.751053	−	0.660242i	$-0.229546\pi$
$811$	42.7771			1.50211			0.751053	+	0.660242i	$0.229546\pi$
$812$	−41.8328			−1.46804
$813$	−2.95492	+	9.09429i	−0.103633	+	0.318951i
$814$	0.0344419	+	0.106001i	0.00120719	+	0.00371534i
$815$	10.2812	+	31.6421i	0.360133	+	1.10838i
$816$	0.354102	−	0.257270i	0.0123960	−	0.00900626i
$817$	7.13525	−	21.9601i	0.249631	−	0.768285i
$818$	3.09017	−	2.24514i	0.108045	−	0.0784995i
$819$	−23.5623	−	17.1190i	−0.823334	−	0.598187i
$820$	8.47214	+	26.0746i	0.295860	+	0.910563i
$821$	−26.2705	−	19.0866i	−0.916847	−	0.666128i	0.0258901	−	0.999665i	$-0.491758\pi$
$821$	−26.2705	−	19.0866i	−0.916847	−	0.666128i	−0.942737	+	0.333536i	$0.891758\pi$
$822$	3.23607	+	2.35114i	0.112871	+	0.0820055i
$823$	1.89261	+	5.82485i	0.0659722	+	0.203042i	0.978609	−	0.205731i	$-0.0659571\pi$
$823$	1.89261	+	5.82485i	0.0659722	+	0.203042i	−0.912636	+	0.408772i	$0.865957\pi$
$824$	0.263932	+	0.191758i	0.00919451	+	0.00668020i
$825$	−1.14590	+	0.832544i	−0.0398950	+	0.0289854i
$826$	−5.42705	+	16.7027i	−0.188831	+	0.581163i
$827$	2.16312	−	1.57160i	0.0752190	−	0.0546498i	−0.549540	−	0.835467i	$-0.685197\pi$
$827$	2.16312	−	1.57160i	0.0752190	−	0.0546498i	0.624759	+	0.780817i	$0.285197\pi$
$828$	5.47214	+	16.8415i	0.190170	+	0.585283i
$829$	6.70820	+	20.6457i	0.232986	+	0.717056i	0.997382	+	0.0723096i	$0.0230370\pi$
$829$	6.70820	+	20.6457i	0.232986	+	0.717056i	−0.764397	+	0.644746i	$0.776963\pi$
$830$	2.04508	−	6.29412i	0.0709859	−	0.218472i
$831$	−13.3262			−0.462282
$832$	1.14590			0.0397269
$833$	−0.145898	+	0.449028i	−0.00505507	+	0.0155579i
$834$	−2.92705	−	2.12663i	−0.101355	−	0.0736391i
$835$	19.5623	−	14.2128i	0.676982	−	0.491856i
$836$	−6.18034			−0.213752
$837$		0			0
$838$	−2.76393			−0.0954784
$839$	−9.04508	+	6.57164i	−0.312271	+	0.226878i	−0.732870	−	0.680368i	$-0.761820\pi$
$839$	−9.04508	+	6.57164i	−0.312271	+	0.226878i	0.420599	+	0.907246i	$0.361820\pi$
$840$	14.2082	+	10.3229i	0.490230	+	0.356173i
$841$	13.9894	−	43.0548i	0.482392	−	1.48465i
$842$	−9.12461			−0.314455
$843$	19.0344			0.655581
$844$	4.00000	−	12.3107i	0.137686	−	0.423753i
$845$	−8.54508	−	26.2991i	−0.293960	−	0.904715i
$846$	−1.29180	−	3.97574i	−0.0444129	−	0.136689i
$847$	25.2812	−	18.3678i	0.868671	−	0.631126i
$848$	7.28115	−	22.4091i	0.250036	−	0.769531i
$849$	−5.30902	+	3.85723i	−0.182205	+	0.132380i
$850$	−0.218847	−	0.159002i	−0.00750639	−	0.00545371i
$851$	−0.399187	−	1.22857i	−0.0136840	−	0.0421149i
$852$	0.118034	+	0.0857567i	0.00404378	+	0.00293798i
$853$	−3.23607	−	2.35114i	−0.110801	−	0.0805015i	0.531005	−	0.847369i	$-0.321815\pi$
$853$	−3.23607	−	2.35114i	−0.110801	−	0.0805015i	−0.641806	+	0.766867i	$0.721815\pi$
$854$	−3.97871	−	12.2452i	−0.136149	−	0.419023i
$855$	−21.1803	−	15.3884i	−0.724352	−	0.526273i
$856$	−1.97214	+	1.43284i	−0.0674062	+	0.0489735i
$857$	−2.52786	+	7.77997i	−0.0863502	+	0.265759i	−0.984903	−	0.173107i	$-0.944619\pi$
$857$	−2.52786	+	7.77997i	−0.0863502	+	0.265759i	0.898553	+	0.438865i	$0.144619\pi$
$858$	−1.85410	+	1.34708i	−0.0632980	+	0.0459887i
$859$	−13.3779	−	41.1729i	−0.456448	−	1.40480i	−0.869427	−	0.494062i	$-0.835512\pi$
$859$	−13.3779	−	41.1729i	−0.456448	−	1.40480i	0.412979	−	0.910741i	$-0.364488\pi$
$860$	6.04508	+	18.6049i	0.206136	+	0.634420i
$861$	6.00000	−	18.4661i	0.204479	−	0.629323i
$862$	−18.0689			−0.615429
$863$	−2.49342			−0.0848771			−0.0424385	−	0.999099i	$-0.513513\pi$
$863$	−2.49342			−0.0848771			−0.0424385	+	0.999099i	$0.513513\pi$
$864$	8.68034	−	26.7153i	0.295311	−	0.908874i
$865$	1.92705	+	1.40008i	0.0655217	+	0.0476043i
$866$	−0.291796	+	0.212002i	−0.00991563	+	0.00720413i
$867$	−16.9443			−0.575458
$868$		0			0
$869$		0			0
$870$	−11.2812	+	8.19624i	−0.382467	+	0.277878i
$871$	−16.6353	−	12.0862i	−0.563664	−	0.409526i
$872$	−5.81559	+	17.8986i	−0.196941	+	0.606122i
$873$	10.5836			0.358200
$874$	−16.9098			−0.571984
$875$	7.63525	−	23.4989i	0.258119	−	0.794408i
$876$	−4.28115	−	13.1760i	−0.144647	−	0.445177i
$877$	5.03444	+	15.4944i	0.170001	+	0.523209i	0.999370	−	0.0354920i	$-0.0112998\pi$
$877$	5.03444	+	15.4944i	0.170001	+	0.523209i	−0.829369	+	0.558701i	$0.811300\pi$
$878$	20.9164	−	15.1967i	0.705895	−	0.512862i
$879$	−2.54508	+	7.83297i	−0.0858436	+	0.264199i
$880$	3.00000	−	2.17963i	0.101130	−	0.0734752i
$881$	−12.4271	−	9.02878i	−0.418678	−	0.304187i	0.358428	−	0.933557i	$-0.383313\pi$
$881$	−12.4271	−	9.02878i	−0.418678	−	0.304187i	−0.777106	+	0.629370i	$0.783313\pi$
$882$	0.763932	+	2.35114i	0.0257229	+	0.0791670i
$883$	−0.809017	−	0.587785i	−0.0272256	−	0.0197805i	0.574089	−	0.818793i	$-0.305356\pi$
$883$	−0.809017	−	0.587785i	−0.0272256	−	0.0197805i	−0.601315	+	0.799012i	$0.705356\pi$
$884$	1.50000	+	1.08981i	0.0504505	+	0.0366544i
$885$	−7.66312	−	23.5847i	−0.257593	−	0.792790i
$886$	−20.5623	−	14.9394i	−0.690804	−	0.501899i
$887$	−31.6353	+	22.9844i	−1.06221	+	0.771739i	−0.974496	−	0.224407i	$-0.927956\pi$
$887$	−31.6353	+	22.9844i	−1.06221	+	0.771739i	−0.0877123	+	0.996146i	$0.527956\pi$
$888$	−0.163119	+	0.502029i	−0.00547391	+	0.0168470i
$889$	24.8435	−	18.0498i	0.833223	−	0.605372i
$890$	3.19098	+	9.82084i	0.106962	+	0.329195i
$891$	0.236068	+	0.726543i	0.00790857	+	0.0243401i
$892$	0.354102	−	1.08981i	0.0118562	−	0.0364897i
$893$	−16.9098			−0.565866
$894$	10.5279			0.352104
$895$	16.0172	−	49.2959i	0.535397	−	1.64778i
$896$	−27.6246	−	20.0705i	−0.922874	−	0.670507i
$897$	21.4894	−	15.6129i	0.717509	−	0.521301i
$898$	14.8754			0.496398
$899$		0			0
$900$	6.00000			0.200000
$901$	2.42705	−	1.76336i	0.0808568	−	0.0587459i
$902$	2.47214	+	1.79611i	0.0823131	+	0.0598040i
$903$	4.28115	−	13.1760i	0.142468	−	0.438471i
$904$	−4.14590			−0.137891
$905$	44.5066			1.47945
$906$	−3.72542	+	11.4657i	−0.123769	+	0.380922i
$907$	16.3541	+	50.3328i	0.543029	+	1.67127i	0.725631	+	0.688085i	$0.241548\pi$
$907$	16.3541	+	50.3328i	0.543029	+	1.67127i	−0.182601	+	0.983187i	$0.558452\pi$
$908$	10.3713	+	31.9196i	0.344184	+	1.05929i
$909$	7.70820	−	5.60034i	0.255665	−	0.185751i
$910$	−7.28115	+	22.4091i	−0.241368	+	0.742854i
$911$	6.61803	−	4.80828i	0.219265	−	0.159306i	−0.472731	−	0.881207i	$-0.656732\pi$
$911$	6.61803	−	4.80828i	0.219265	−	0.159306i	0.691996	+	0.721901i	$0.256732\pi$
$912$	−7.50000	−	5.44907i	−0.248350	−	0.180437i
$913$	0.965558	+	2.97168i	0.0319553	+	0.0983483i
$914$	7.87132	+	5.71885i	0.260360	+	0.189163i
$915$	14.7082	+	10.6861i	0.486238	+	0.353273i
$916$	−3.61803	−	11.1352i	−0.119543	−	0.367916i
$917$	−0.218847	−	0.159002i	−0.00722697	−	0.00525070i
$918$	0.590170	−	0.428784i	0.0194785	−	0.0141520i
$919$	3.05166	−	9.39205i	0.100665	−	0.309815i	−0.888024	−	0.459798i	$-0.847922\pi$
$919$	3.05166	−	9.39205i	0.100665	−	0.309815i	0.988689	+	0.149983i	$0.0479218\pi$
$920$	25.9164	−	18.8294i	0.854439	−	0.620786i
$921$	1.88197	+	5.79210i	0.0620129	+	0.190856i
$922$	2.05166	+	6.31437i	0.0675679	+	0.207953i
$923$	−0.135255	+	0.416272i	−0.00445197	+	0.0137018i
$924$	−3.70820			−0.121991
$925$	−0.437694			−0.0143913
$926$	−5.94427	+	18.2946i	−0.195341	+	0.601197i
$927$	−0.236068	−	0.171513i	−0.00775349	−	0.00563324i
$928$	39.1697	−	28.4585i	1.28581	−	0.934194i
$929$	−33.5410			−1.10045			−0.550223	−	0.835018i	$-0.685457\pi$
$929$	−33.5410			−1.10045			−0.550223	+	0.835018i	$0.685457\pi$
$930$		0			0
$931$	10.0000			0.327737
$932$	24.6074	−	17.8783i	0.806042	−	0.585624i
$933$	−13.3262	−	9.68208i	−0.436281	−	0.316977i
$934$	6.25987	−	19.2659i	0.204829	−	0.630399i
$935$	0.472136			0.0154405
$936$	21.7082			0.709555
$937$	12.5106	−	38.5038i	0.408705	−	1.25786i	−0.509057	−	0.860733i	$-0.670006\pi$
$937$	12.5106	−	38.5038i	0.408705	−	1.25786i	0.917762	−	0.397131i	$-0.129994\pi$
$938$	2.42705	+	7.46969i	0.0792460	+	0.243894i
$939$	−0.381966	−	1.17557i	−0.0124650	−	0.0383633i
$940$	11.5902	−	8.42075i	0.378030	−	0.274655i
$941$	−8.83282	+	27.1846i	−0.287942	+	0.886193i	0.697560	+	0.716526i	$0.254269\pi$
$941$	−8.83282	+	27.1846i	−0.287942	+	0.886193i	−0.985502	+	0.169667i	$0.945731\pi$
$942$	4.85410	−	3.52671i	0.158155	−	0.114906i
$943$	−28.6525	−	20.8172i	−0.933053	−	0.677903i
$944$	5.42705	+	16.7027i	0.176635	+	0.543628i
$945$	−31.7705	−	23.0826i	−1.03349	−	0.750878i
$946$	1.76393	+	1.28157i	0.0573504	+	0.0416675i
$947$	−6.81966	−	20.9888i	−0.221609	−	0.682043i	−0.998618	−	0.0525534i	$-0.983264\pi$
$947$	−6.81966	−	20.9888i	−0.221609	−	0.682043i	0.777009	−	0.629490i	$-0.216736\pi$
$948$		0			0
$949$	33.6246	−	24.4297i	1.09150	−	0.793022i
$950$	−1.77051	+	5.44907i	−0.0574429	+	0.176791i
$951$	−20.9443	+	15.2169i	−0.679165	+	0.493442i
$952$	−0.489357	−	1.50609i	−0.0158601	−	0.0488125i
$953$	−13.0451	−	40.1486i	−0.422572	−	1.30054i	−0.905300	−	0.424772i	$-0.860354\pi$
$953$	−13.0451	−	40.1486i	−0.422572	−	1.30054i	0.482729	−	0.875770i	$-0.339646\pi$
$954$	4.85410	−	14.9394i	0.157157	−	0.483681i
$955$	42.1246			1.36312
$956$	−21.7082			−0.702093
$957$	2.03444	−	6.26137i	0.0657642	−	0.202401i
$958$	−4.47214	−	3.24920i	−0.144488	−	0.104977i
$959$	−15.7082	+	11.4127i	−0.507244	+	0.368535i
$960$	0.618034			0.0199470
$961$		0			0
$962$	−0.708204			−0.0228334
$963$	1.76393	−	1.28157i	0.0568419	−	0.0412981i
$964$	11.1631	+	8.11048i	0.359540	+	0.261221i
$965$	1.92705	−	5.93085i	0.0620340	−	0.190921i
$966$	−10.1459			−0.326439
$967$	−43.6525			−1.40377			−0.701884	−	0.712291i	$-0.747658\pi$
$967$	−43.6525			−1.40377			−0.701884	+	0.712291i	$0.747658\pi$
$968$	−7.19756	+	22.1518i	−0.231338	+	0.711986i
$969$	−0.364745	−	1.12257i	−0.0117173	−	0.0360621i
$970$	−2.64590	−	8.14324i	−0.0849547	−	0.261464i
$971$	16.6353	−	12.0862i	0.533851	−	0.387865i	−0.287945	−	0.957647i	$-0.592972\pi$
$971$	16.6353	−	12.0862i	0.533851	−	0.387865i	0.821796	+	0.569782i	$0.192972\pi$
$972$	−8.00000	+	24.6215i	−0.256600	+	0.789734i
$973$	14.2082	−	10.3229i	0.455494	−	0.330936i
$974$	−11.4615	−	8.32726i	−0.367250	−	0.266823i
$975$	−2.78115	−	8.55951i	−0.0890682	−	0.274124i
$976$	−10.4164	−	7.56796i	−0.333421	−	0.242245i
$977$	4.90983	+	3.56720i	0.157079	+	0.114125i	0.663549	−	0.748133i	$-0.269050\pi$
$977$	4.90983	+	3.56720i	0.157079	+	0.114125i	−0.506469	+	0.862258i	$0.669050\pi$
$978$	2.42705	+	7.46969i	0.0776085	+	0.238855i
$979$	−3.94427	−	2.86568i	−0.126059	−	0.0915876i
$980$	−6.85410	+	4.97980i	−0.218946	+	0.159074i
$981$	5.20163	−	16.0090i	0.166075	−	0.511127i
$982$	13.7984	−	10.0251i	0.440324	−	0.319914i
$983$	−6.50000	−	20.0049i	−0.207318	−	0.638059i	−0.999610	−	0.0279171i	$-0.991113\pi$
$983$	−6.50000	−	20.0049i	−0.207318	−	0.638059i	0.792292	−	0.610142i	$-0.208887\pi$
$984$	4.47214	+	13.7638i	0.142566	+	0.438775i
$985$	13.2812	−	40.8752i	0.423173	−	1.30239i
$986$	1.25735			0.0400423
$987$	−10.1459			−0.322947
$988$	12.1353	−	37.3485i	0.386074	−	1.18821i
$989$	−20.4443	−	14.8536i	−0.650090	−	0.472318i
$990$	2.00000	−	1.45309i	0.0635642	−	0.0461821i
$991$	17.2705			0.548616			0.274308	−	0.961642i	$-0.411551\pi$
$991$	17.2705			0.548616			0.274308	+	0.961642i	$0.411551\pi$
$992$		0			0
$993$	−11.2705			−0.357659
$994$	0.135255	−	0.0982684i	0.00429003	−	0.00311689i
$995$	56.5689	+	41.0997i	1.79335	+	1.30295i
$996$	−2.04508	+	6.29412i	−0.0648010	+	0.199437i
$997$	−27.2492			−0.862992			−0.431496	−	0.902115i	$-0.642014\pi$
$997$	−27.2492			−0.862992			−0.431496	+	0.902115i	$0.642014\pi$
$998$	2.56231			0.0811084
$999$	0.364745	−	1.12257i	0.0115400	−	0.0355165i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.e.388.1		4
31.2	even	5	inner	961.2.d.e.374.1		4
31.3	odd	30		961.2.g.b.547.1		8
31.4	even	5		961.2.d.b.628.1		4
31.5	even	3		961.2.g.g.338.1		8
31.6	odd	6		961.2.g.f.235.1		8
31.7	even	15		961.2.g.c.846.1		8
31.8	even	5		961.2.a.e.1.1		2
31.9	even	15		961.2.c.d.521.1		4
31.10	even	15		961.2.g.g.732.1		8
31.11	odd	30		961.2.g.b.448.1		8
31.12	odd	30		961.2.g.f.816.1		8
31.13	odd	30		961.2.g.b.844.1		8
31.14	even	15		961.2.c.d.439.1		4
31.15	odd	10		31.2.d.a.4.1	✓	4
31.16	even	5		961.2.d.b.531.1		4
31.17	odd	30		961.2.c.f.439.1		4
31.18	even	15		961.2.g.c.844.1		8
31.19	even	15		961.2.g.g.816.1		8
31.20	even	15		961.2.g.c.448.1		8
31.21	odd	30		961.2.g.f.732.1		8
31.22	odd	30		961.2.c.f.521.1		4
31.23	odd	10		961.2.a.d.1.1		2
31.24	odd	30		961.2.g.b.846.1		8
31.25	even	3		961.2.g.g.235.1		8
31.26	odd	6		961.2.g.f.338.1		8
31.27	odd	10		31.2.d.a.8.1	yes	4
31.28	even	15		961.2.g.c.547.1		8
31.29	odd	10		961.2.d.f.374.1		4
31.30	odd	2		961.2.d.f.388.1		4
93.8	odd	10		8649.2.a.f.1.2		2
93.23	even	10		8649.2.a.g.1.2		2
93.77	even	10		279.2.i.a.190.1		4
93.89	even	10		279.2.i.a.163.1		4
124.15	even	10		496.2.n.b.97.1		4
124.27	even	10		496.2.n.b.225.1		4
155.27	even	20		775.2.bf.a.349.1		8
155.58	even	20		775.2.bf.a.349.2		8
155.77	even	20		775.2.bf.a.624.2		8
155.89	odd	10		775.2.k.c.101.1		4
155.108	even	20		775.2.bf.a.624.1		8
155.139	odd	10		775.2.k.c.376.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.d.a.4.1	✓	4	31.15	odd	10
31.2.d.a.8.1	yes	4	31.27	odd	10
279.2.i.a.163.1		4	93.89	even	10
279.2.i.a.190.1		4	93.77	even	10
496.2.n.b.97.1		4	124.15	even	10
496.2.n.b.225.1		4	124.27	even	10
775.2.k.c.101.1		4	155.89	odd	10
775.2.k.c.376.1		4	155.139	odd	10
775.2.bf.a.349.1		8	155.27	even	20
775.2.bf.a.349.2		8	155.58	even	20
775.2.bf.a.624.1		8	155.108	even	20
775.2.bf.a.624.2		8	155.77	even	20
961.2.a.d.1.1		2	31.23	odd	10
961.2.a.e.1.1		2	31.8	even	5
961.2.c.d.439.1		4	31.14	even	15
961.2.c.d.521.1		4	31.9	even	15
961.2.c.f.439.1		4	31.17	odd	30
961.2.c.f.521.1		4	31.22	odd	30
961.2.d.b.531.1		4	31.16	even	5
961.2.d.b.628.1		4	31.4	even	5
961.2.d.e.374.1		4	31.2	even	5	inner
961.2.d.e.388.1		4	1.1	even	1	trivial
961.2.d.f.374.1		4	31.29	odd	10
961.2.d.f.388.1		4	31.30	odd	2
961.2.g.b.448.1		8	31.11	odd	30
961.2.g.b.547.1		8	31.3	odd	30
961.2.g.b.844.1		8	31.13	odd	30
961.2.g.b.846.1		8	31.24	odd	30
961.2.g.c.448.1		8	31.20	even	15
961.2.g.c.547.1		8	31.28	even	15
961.2.g.c.844.1		8	31.18	even	15
961.2.g.c.846.1		8	31.7	even	15
961.2.g.f.235.1		8	31.6	odd	6
961.2.g.f.338.1		8	31.26	odd	6
961.2.g.f.732.1		8	31.21	odd	30
961.2.g.f.816.1		8	31.12	odd	30
961.2.g.g.235.1		8	31.25	even	3
961.2.g.g.338.1		8	31.5	even	3
961.2.g.g.732.1		8	31.10	even	15
961.2.g.g.816.1		8	31.19	even	15
8649.2.a.f.1.2		2	93.8	odd	10
8649.2.a.g.1.2		2	93.23	even	10

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.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.363271i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.500000 + 1.53884i) q^{4} -2.61803 q^{5} -0.618034 q^{6} +(0.927051 - 2.85317i) q^{7} +(0.690983 + 2.12663i) q^{8} +(-0.618034 - 1.90211i) q^{9} +(-1.30902 + 0.951057i) q^{10} +(0.236068 - 0.726543i) q^{11} +(1.30902 - 0.951057i) q^{12} +(3.92705 + 2.85317i) q^{13} +(-0.572949 - 1.76336i) q^{14} +(2.11803 + 1.53884i) q^{15} +(-1.50000 - 1.08981i) q^{16} +(-0.0729490 - 0.224514i) q^{17} +(-1.00000 - 0.726543i) q^{18} +(-4.04508 + 2.93893i) q^{19} +(1.30902 - 4.02874i) q^{20} +(-2.42705 + 1.76336i) q^{21} +(-0.145898 - 0.449028i) q^{22} +(1.69098 + 5.20431i) q^{23} +(0.690983 - 2.12663i) q^{24} +1.85410 q^{25} +3.00000 q^{26} +(-1.54508 + 4.75528i) q^{27} +(3.92705 + 2.85317i) q^{28} +(-6.97214 + 5.06555i) q^{29} +1.61803 q^{30} -5.61803 q^{32} +(-0.618034 + 0.449028i) q^{33} +(-0.118034 - 0.0857567i) q^{34} +(-2.42705 + 7.46969i) q^{35} +3.23607 q^{36} -0.236068 q^{37} +(-0.954915 + 2.93893i) q^{38} +(-1.50000 - 4.61653i) q^{39} +(-1.80902 - 5.56758i) q^{40} +(-5.23607 + 3.80423i) q^{41} +(-0.572949 + 1.76336i) q^{42} +(-3.73607 + 2.71441i) q^{43} +(1.00000 + 0.726543i) q^{44} +(1.61803 + 4.97980i) q^{45} +(2.73607 + 1.98787i) q^{46} +(2.73607 + 1.98787i) q^{47} +(0.572949 + 1.76336i) q^{48} +(-1.61803 - 1.17557i) q^{49} +(0.927051 - 0.673542i) q^{50} +(-0.0729490 + 0.224514i) q^{51} +(-6.35410 + 4.61653i) q^{52} +(3.92705 + 12.0862i) q^{53} +(0.954915 + 2.93893i) q^{54} +(-0.618034 + 1.90211i) q^{55} +6.70820 q^{56} +5.00000 q^{57} +(-1.64590 + 5.06555i) q^{58} +(-7.66312 - 5.56758i) q^{59} +(-3.42705 + 2.48990i) q^{60} +6.94427 q^{61} -6.00000 q^{63} +(0.190983 - 0.138757i) q^{64} +(-10.2812 - 7.46969i) q^{65} +(-0.145898 + 0.449028i) q^{66} -4.23607 q^{67} +0.381966 q^{68} +(1.69098 - 5.20431i) q^{69} +(1.50000 + 4.61653i) q^{70} +(0.0278640 + 0.0857567i) q^{71} +(3.61803 - 2.62866i) q^{72} +(2.64590 - 8.14324i) q^{73} +(-0.118034 + 0.0857567i) q^{74} +(-1.50000 - 1.08981i) q^{75} +(-2.50000 - 7.69421i) q^{76} +(-1.85410 - 1.34708i) q^{77} +(-2.42705 - 1.76336i) q^{78} +(3.92705 + 2.85317i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-1.23607 + 3.80423i) q^{82} +(-3.30902 + 2.40414i) q^{83} +(-1.50000 - 4.61653i) q^{84} +(0.190983 + 0.587785i) q^{85} +(-0.881966 + 2.71441i) q^{86} +8.61803 q^{87} +1.70820 q^{88} +(1.97214 - 6.06961i) q^{89} +(2.61803 + 1.90211i) q^{90} +(11.7812 - 8.55951i) q^{91} -8.85410 q^{92} +2.09017 q^{94} +(10.5902 - 7.69421i) q^{95} +(4.54508 + 3.30220i) q^{96} +(-1.63525 + 5.03280i) q^{97} -1.23607 q^{98} -1.52786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} - 3 q^{7} + 5 q^{8} + 2 q^{9} - 3 q^{10} - 8 q^{11} + 3 q^{12} + 9 q^{13} - 9 q^{14} + 4 q^{15} - 6 q^{16} - 7 q^{17} - 4 q^{18} - 5 q^{19} + 3 q^{20}+ \cdots - 24 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 - 3 * q^7 + 5 * q^8 + 2 * q^9 - 3 * q^10 - 8 * q^11 + 3 * q^12 + 9 * q^13 - 9 * q^14 + 4 * q^15 - 6 * q^16 - 7 * q^17 - 4 * q^18 - 5 * q^19 + 3 * q^20 - 3 * q^21 - 14 * q^22 + 9 * q^23 + 5 * q^24 - 6 * q^25 + 12 * q^26 + 5 * q^27 + 9 * q^28 - 10 * q^29 + 2 * q^30 - 18 * q^32 + 2 * q^33 + 4 * q^34 - 3 * q^35 + 4 * q^36 + 8 * q^37 - 15 * q^38 - 6 * q^39 - 5 * q^40 - 12 * q^41 - 9 * q^42 - 6 * q^43 + 4 * q^44 + 2 * q^45 + 2 * q^46 + 2 * q^47 + 9 * q^48 - 2 * q^49 - 3 * q^50 - 7 * q^51 - 12 * q^52 + 9 * q^53 + 15 * q^54 + 2 * q^55 + 20 * q^57 - 20 * q^58 - 15 * q^59 - 7 * q^60 - 8 * q^61 - 24 * q^63 + 3 * q^64 - 21 * q^65 - 14 * q^66 - 8 * q^67 + 6 * q^68 + 9 * q^69 + 6 * q^70 + 18 * q^71 + 10 * q^72 + 24 * q^73 + 4 * q^74 - 6 * q^75 - 10 * q^76 + 6 * q^77 - 3 * q^78 + 9 * q^80 - q^81 + 4 * q^82 - 11 * q^83 - 6 * q^84 + 3 * q^85 - 8 * q^86 + 30 * q^87 - 20 * q^88 - 10 * q^89 + 6 * q^90 + 27 * q^91 - 22 * q^92 - 14 * q^94 + 20 * q^95 + 7 * q^96 + 27 * q^97 + 4 * q^98 - 24 * q^99

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