LMFDB - Embedded newform 961.2.d.f.374.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(374,961)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$4$
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			374.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	961.374
Dual form			961.2.d.f.388.1

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

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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	0.750358	−	0.661031i	$-0.229881\pi$
$2$	0.500000	+	0.363271i	0.353553	+	0.256872i	−0.396805	+	0.917903i	$0.629881\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i	−0.329218	−	0.944254i	$-0.606785\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i	0.796305	+	0.604896i	$0.206785\pi$
$4$	−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	0.958633	+	0.284644i	$0.0918755\pi$
$7$	0.927051	+	2.85317i	0.350392	+	1.07840i	−0.608241	+	0.793752i	$0.708125\pi$
$8$	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	$-0.136740\pi$
$11$	−0.236068	−	0.726543i	−0.0711772	−	0.219061i	−0.980317	+	0.197430i	$0.936740\pi$
$12$	−1.30902	−	0.951057i	−0.377881	−	0.274546i
$13$	−3.92705	+	2.85317i	−1.08917	+	0.791327i	−0.979259	−	0.202615i	$-0.935056\pi$
$13$	−3.92705	+	2.85317i	−1.08917	+	0.791327i	−0.109909	+	0.993942i	$0.535056\pi$
$14$	−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	$-0.890886\pi$
$17$	0.0729490	−	0.224514i	0.0176927	−	0.0544526i	0.959513	+	0.281664i	$0.0908864\pi$
$18$	−1.00000	+	0.726543i	−0.235702	+	0.171248i
$19$	−4.04508	−	2.93893i	−0.928006	−	0.674236i	0.0174977	−	0.999847i	$-0.494430\pi$
$19$	−4.04508	−	2.93893i	−0.928006	−	0.674236i	−0.945504	+	0.325611i	$0.894430\pi$
$20$	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	0.604797	+	0.796380i	$0.293254\pi$
$23$	−1.69098	+	5.20431i	−0.352594	+	1.08517i	−0.957391	+	0.288794i	$0.906746\pi$
$24$	−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	$-0.00474555\pi$
$29$	6.97214	+	5.06555i	1.29469	+	0.940650i	0.294804	+	0.955558i	$0.404746\pi$
$30$	−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	$-0.493823\pi$
$37$	0.236068			0.0388093			0.0194047	+	0.999812i	$0.493823\pi$
$38$	−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	0.0983268	−	0.995154i	$-0.468651\pi$
$41$	−5.23607	−	3.80423i	−0.817736	−	0.594120i	−0.916063	+	0.401034i	$0.868651\pi$
$42$	0.572949	+	1.76336i	0.0884080	+	0.272092i
$43$	3.73607	+	2.71441i	0.569745	+	0.413944i	0.835013	−	0.550231i	$-0.185460\pi$
$43$	3.73607	+	2.71441i	0.569745	+	0.413944i	−0.265268	+	0.964175i	$0.585460\pi$
$44$	−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	−0.370076	−	0.929001i	$-0.620668\pi$
$47$	2.73607	−	1.98787i	0.399097	−	0.289961i	0.769173	+	0.639041i	$0.220668\pi$
$48$	−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	0.194474	+	0.980908i	$0.437700\pi$
$53$	−3.92705	+	12.0862i	−0.539422	+	1.66017i	−0.733896	+	0.679262i	$0.762300\pi$
$54$	−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	−0.961584	−	0.274512i	$-0.911484\pi$
$59$	−7.66312	+	5.56758i	−0.997653	+	0.724837i	−0.0360694	+	0.999349i	$0.511484\pi$
$60$	3.42705	+	2.48990i	0.442430	+	0.321444i
$61$	−6.94427			−0.889123			−0.444561	−	0.895748i	$-0.646640\pi$
$61$	−6.94427			−0.889123			−0.444561	+	0.895748i	$0.646640\pi$
$62$		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	−0.949389	−	0.314101i	$-0.898297\pi$
$71$	0.0278640	−	0.0857567i	0.00330685	−	0.0101774i	0.952696	+	0.303924i	$0.0982968\pi$
$72$	3.61803	+	2.62866i	0.426389	+	0.309790i
$73$	−2.64590	−	8.14324i	−0.309679	−	0.953094i	−0.977890	−	0.209122i	$-0.932940\pi$
$73$	−2.64590	−	8.14324i	−0.309679	−	0.953094i	0.668211	−	0.743972i	$-0.267060\pi$
$74$	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	$-0.900000\pi$
$79$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$80$	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	$-0.227933\pi$
$83$	3.30902	+	2.40414i	0.363212	+	0.263889i	−0.391179	+	0.920315i	$0.627933\pi$
$84$	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	−0.999523	−	0.0308856i	$-0.990167\pi$
$89$	−1.97214	−	6.06961i	−0.209046	−	0.643377i	0.790477	−	0.612492i	$-0.209833\pi$
$90$	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	0.833076	−	0.553158i	$-0.186578\pi$
$97$	−1.63525	−	5.03280i	−0.166035	−	0.511003i	−0.999111	+	0.0421553i	$0.986578\pi$
$98$	−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	−0.850716	−	0.525626i	$-0.823831\pi$
$101$	1.47214	−	4.53077i	0.146483	−	0.450828i	0.997199	+	0.0747977i	$0.0238311\pi$
$102$	0.0450850	−	0.138757i	0.00446408	−	0.0137390i
$103$	0.118034	+	0.0857567i	0.0116302	+	0.00844986i	0.593585	−	0.804771i	$-0.297712\pi$
$103$	0.118034	+	0.0857567i	0.0116302	+	0.00844986i	−0.581955	+	0.813221i	$0.697712\pi$
$104$	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	−0.933451	−	0.358704i	$-0.883219\pi$
$107$	0.336881	−	1.03681i	0.0325675	−	0.100233i	0.966019	+	0.258471i	$0.0832188\pi$
$108$	6.54508	−	4.75528i	0.629801	−	0.457577i
$109$	6.80902	−	4.94704i	0.652186	−	0.473841i	−0.211829	−	0.977307i	$-0.567942\pi$
$109$	6.80902	−	4.94704i	0.652186	−	0.473841i	0.864015	+	0.503466i	$0.167942\pi$
$110$	−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	0.920484	−	0.390781i	$-0.127795\pi$
$113$	−0.572949	−	1.76336i	−0.0538985	−	0.165883i	−0.974382	+	0.224898i	$0.927795\pi$
$114$	−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	$-0.850058\pi$
$127$	−8.28115	+	6.01661i	−0.734833	+	0.533888i	0.156255	+	0.987717i	$0.450058\pi$
$128$	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	0.952266	−	0.305268i	$-0.0987461\pi$
$131$	0.0278640	+	0.0857567i	0.00243449	+	0.00749260i	−0.949832	+	0.312761i	$0.898746\pi$
$132$	−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	$-0.610833\pi$
$137$	5.23607	−	3.80423i	0.447347	−	0.325017i	0.788548	+	0.614974i	$0.210833\pi$
$138$	−1.04508	+	3.21644i	−0.0889635	+	0.273802i
$139$	−4.73607	+	3.44095i	−0.401708	+	0.291858i	−0.770236	−	0.637759i	$-0.779862\pi$
$139$	−4.73607	+	3.44095i	−0.401708	+	0.291858i	0.368528	+	0.929617i	$0.379862\pi$
$140$	−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	−0.823793	−	0.566891i	$-0.808146\pi$
$151$	−6.02786	−	18.5519i	−0.490541	−	1.50973i	0.333252	−	0.942838i	$-0.391854\pi$
$152$	−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	0.228473	−	0.973550i	$-0.426627\pi$
$157$	−7.85410	−	5.70634i	−0.626826	−	0.455415i	−0.855299	+	0.518135i	$0.826627\pi$
$158$		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	0.671108	+	0.741360i	$0.265819\pi$
$163$	−3.92705	+	12.0862i	−0.307590	+	0.946666i	−0.978698	+	0.205306i	$0.934181\pi$
$164$	−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	$-0.183679\pi$
$167$	7.47214	+	5.42882i	0.578211	+	0.420095i	−0.259868	+	0.965644i	$0.583679\pi$
$168$	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	−0.615415	−	0.788204i	$-0.711011\pi$
$173$	−0.736068	+	0.534785i	−0.0559622	+	0.0406589i	0.559452	+	0.828862i	$0.311011\pi$
$174$	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	0.868433	+	0.495806i	$0.165127\pi$
$179$	6.11803	+	18.8294i	0.457283	+	1.40737i	−0.411150	+	0.911568i	$0.634873\pi$
$180$	−8.47214			−0.631476
$181$	17.0000			1.26360			0.631800	−	0.775131i	$-0.282316\pi$
$181$	17.0000			1.26360			0.631800	+	0.775131i	$0.282316\pi$
$182$	−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	0.921064	−	0.389412i	$-0.127322\pi$
$193$	−0.736068	−	2.26538i	−0.0529833	−	0.163066i	−0.974047	+	0.226346i	$0.927322\pi$
$194$	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	0.952185	+	0.305522i	$0.0988311\pi$
$197$	5.07295	+	15.6129i	0.361433	+	1.11238i	−0.590752	+	0.806853i	$0.701169\pi$
$198$	0.763932	+	0.555029i	0.0542903	+	0.0394442i
$199$	21.6074	−	15.6987i	1.53171	−	1.11285i	0.576427	−	0.817149i	$-0.304446\pi$
$199$	21.6074	−	15.6987i	1.53171	−	1.11285i	0.955280	−	0.295702i	$-0.0955535\pi$
$200$	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	$-0.492451\pi$
$223$	0.708204			0.0474248			0.0237124	+	0.999719i	$0.492451\pi$
$224$	−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	0.983259	−	0.182216i	$-0.0583271\pi$
$227$	16.7812	+	12.1922i	1.11380	+	0.809226i	0.130546	+	0.991442i	$0.458327\pi$
$228$	2.50000	+	7.69421i	0.165567	+	0.509561i
$229$	5.85410	+	4.25325i	0.386850	+	0.281063i	0.764163	−	0.645023i	$-0.223152\pi$
$229$	5.85410	+	4.25325i	0.386850	+	0.281063i	−0.377314	+	0.926086i	$0.623152\pi$
$230$	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	−0.961297	−	0.275516i	$-0.911151\pi$
$233$	−15.2082	+	11.0494i	−0.996323	+	0.723871i	−0.0350260	+	0.999386i	$0.511151\pi$
$234$	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	0.722769	+	0.691090i	$0.242869\pi$
$239$	−4.14590	+	12.7598i	−0.268176	+	0.825360i	−0.990945	+	0.134271i	$0.957131\pi$
$240$	1.50000	−	4.61653i	0.0968246	−	0.297995i
$241$	−2.63525	−	8.11048i	−0.169752	−	0.522442i	0.829603	−	0.558353i	$-0.188567\pi$
$241$	−2.63525	−	8.11048i	−0.169752	−	0.522442i	−0.999355	+	0.0359113i	$0.988567\pi$
$242$	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	$-0.709487\pi$
$251$	−0.763932	+	0.555029i	−0.0482190	+	0.0350331i	0.563415	+	0.826174i	$0.309487\pi$
$252$	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	−0.936477	−	0.350730i	$-0.885934\pi$
$257$	0.437694	−	1.34708i	0.0273026	−	0.0840288i	0.963779	+	0.266701i	$0.0859336\pi$
$258$	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	$-0.591963\pi$
$263$	8.73607	−	6.34712i	0.538689	−	0.391380i	0.823598	+	0.567174i	$0.191963\pi$
$264$	−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	$-0.286586\pi$
$269$	1.11803	+	0.812299i	0.0681677	+	0.0495268i	−0.553180	+	0.833062i	$0.686586\pi$
$270$	2.50000	−	7.69421i	0.152145	−	0.468255i
$271$	2.95492	−	9.09429i	0.179498	−	0.552439i	−0.820312	−	0.571916i	$-0.806200\pi$
$271$	2.95492	−	9.09429i	0.179498	−	0.552439i	0.999810	+	0.0194773i	$0.00620021\pi$
$272$	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	$-0.431111\pi$
$277$	−10.7812	−	7.83297i	−0.647777	−	0.470637i	−0.862513	+	0.506035i	$0.831111\pi$
$278$	−3.61803			−0.216995
$279$		0			0
$280$	−17.5623			−1.04955
$281$	−15.3992	−	11.1882i	−0.918638	−	0.667430i	0.0245463	−	0.999699i	$-0.492186\pi$
$281$	−15.3992	−	11.1882i	−0.918638	−	0.667430i	−0.943185	+	0.332269i	$0.892186\pi$
$282$	1.69098	−	1.22857i	0.100697	−	0.0731603i
$283$	2.02786	+	6.24112i	0.120544	+	0.370996i	0.993063	−	0.117584i	$-0.0375149\pi$
$283$	2.02786	+	6.24112i	0.120544	+	0.370996i	−0.872519	+	0.488580i	$0.837515\pi$
$284$	−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	−0.997467	−	0.0711377i	$-0.977337\pi$
$293$	−2.54508	+	7.83297i	−0.148685	+	0.457607i	0.848781	+	0.528744i	$0.177337\pi$
$294$	−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	−0.719441	−	0.694553i	$-0.755602\pi$
$307$	−4.92705	+	3.57971i	−0.281202	+	0.204305i	0.438240	+	0.898858i	$0.355602\pi$
$308$	−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	$-0.711122\pi$
$313$	−1.00000	+	0.726543i	−0.0565233	+	0.0410666i	0.559165	+	0.829057i	$0.311122\pi$
$314$	−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	0.877671	+	0.479265i	$0.159097\pi$
$317$	8.00000	+	24.6215i	0.449325	+	1.38288i	−0.428346	+	0.903615i	$0.640903\pi$
$318$	−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	$-0.400243\pi$
$331$	−9.11803	−	6.62464i	−0.501172	−	0.364123i	−0.809465	+	0.587169i	$0.800243\pi$
$332$	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	0.973874	+	0.227089i	$0.0729209\pi$
$337$	5.86475	+	18.0498i	0.319473	+	0.983237i	−0.654401	+	0.756148i	$0.727079\pi$
$338$	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	$-0.430022\pi$
$347$	8.12461			0.436152			0.218076	+	0.975932i	$0.430022\pi$
$348$	−4.30902	−	13.2618i	−0.230988	−	0.710907i
$349$	−5.16312	+	15.8904i	−0.276375	+	0.850596i	0.712477	+	0.701696i	$0.247573\pi$
$349$	−5.16312	+	15.8904i	−0.276375	+	0.850596i	−0.988852	+	0.148900i	$0.952427\pi$
$350$	−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	0.995372	+	0.0961006i	$0.0306370\pi$
$353$	26.1976	+	19.0336i	1.39436	+	1.01306i	0.398984	+	0.916958i	$0.369363\pi$
$354$	−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	0.103463	−	0.994633i	$-0.467008\pi$
$359$	20.4894	−	14.8864i	1.08139	−	0.785674i	0.977924	+	0.208960i	$0.0670078\pi$
$360$	−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	$-0.895559\pi$
$367$	−36.2705			−1.89331			−0.946653	+	0.322256i	$0.895559\pi$
$368$	−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	−0.984106	−	0.177579i	$-0.943173\pi$
$379$	−5.69098	−	17.5150i	−0.292326	−	0.899687i	0.691780	−	0.722108i	$-0.256827\pi$
$380$	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	−0.991432	−	0.130626i	$-0.958301\pi$
$383$	−5.20820	−	16.0292i	−0.266127	−	0.819054i	0.725305	−	0.688428i	$-0.241699\pi$
$384$	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	0.415167	+	0.909745i	$0.363723\pi$
$389$	−8.98278	+	27.6462i	−0.455445	+	1.40172i	−0.870612	+	0.491970i	$0.836277\pi$
$390$	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	$-0.0325020\pi$
$401$	24.1353	+	17.5353i	1.20526	+	0.875671i	0.210466	+	0.977601i	$0.432502\pi$
$402$	−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	$-0.548829\pi$
$409$	−6.18034			−0.305598			−0.152799	+	0.988257i	$0.548829\pi$
$410$	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	−0.672644	−	0.739966i	$-0.734841\pi$
$419$	−3.61803	+	2.62866i	−0.176753	+	0.128418i	0.495891	+	0.868385i	$0.334841\pi$
$420$	−3.92705	+	12.0862i	−0.191620	+	0.589747i
$421$	−11.9443	+	8.67802i	−0.582128	+	0.422941i	−0.839491	−	0.543374i	$-0.817147\pi$
$421$	−11.9443	+	8.67802i	−0.582128	+	0.422941i	0.257363	+	0.966315i	$0.417147\pi$
$422$	−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	−0.987022	−	0.160588i	$-0.948661\pi$
$431$	−23.6525	+	17.1845i	−1.13930	+	0.827750i	−0.152278	+	0.988338i	$0.548661\pi$
$432$	−7.50000	−	5.44907i	−0.360844	−	0.262168i
$433$	0.583592			0.0280456			0.0140228	−	0.999902i	$-0.495536\pi$
$433$	0.583592			0.0280456			0.0140228	+	0.999902i	$0.495536\pi$
$434$		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	−0.0988488	+	0.995102i	$0.531516\pi$
$443$	−12.7082	+	39.1118i	−0.603785	+	1.85826i	−0.504936	+	0.863157i	$0.668484\pi$
$444$	−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	$-0.892260\pi$
$449$	−19.4721	+	14.1473i	−0.918947	+	0.667654i	0.0243148	+	0.999704i	$0.492260\pi$
$450$	−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	0.770458	+	0.637491i	$0.220028\pi$
$457$	−4.86475	+	14.9721i	−0.227563	+	0.700367i	−0.998021	+	0.0628768i	$0.979972\pi$
$458$	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	$-0.0195143\pi$
$461$	3.31966	+	10.2169i	0.154612	+	0.475847i	−0.843509	+	0.537114i	$0.819514\pi$
$462$	1.14590	−	0.832544i	0.0533120	−	0.0387334i
$463$	25.1803	+	18.2946i	1.17023	+	0.850222i	0.991036	−	0.133592i	$-0.0426513\pi$
$463$	25.1803	+	18.2946i	1.17023	+	0.850222i	0.179193	+	0.983814i	$0.442651\pi$
$464$	−15.9787			−0.741793
$465$		0			0
$466$	−11.6180			−0.538195
$467$	26.5172	+	19.2659i	1.22707	+	0.891519i	0.996667	−	0.0815762i	$-0.0259954\pi$
$467$	26.5172	+	19.2659i	1.22707	+	0.891519i	0.230404	+	0.973095i	$0.425995\pi$
$468$	−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	−0.994133	−	0.108161i	$-0.965504\pi$
$479$	−2.76393	+	8.50651i	−0.126287	+	0.388672i	0.867846	+	0.496833i	$0.165504\pi$
$480$	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	−0.652231	−	0.758020i	$-0.726167\pi$
$487$	7.08359	−	21.8011i	0.320988	−	0.987900i	0.973219	−	0.229880i	$-0.0738333\pi$
$488$	−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	$-0.713969\pi$
$491$	−27.5967			−1.24542			−0.622712	+	0.782451i	$0.713969\pi$
$492$	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	$-0.729581\pi$
$499$	−3.35410	+	2.43690i	−0.150150	+	0.109091i	0.510174	+	0.860071i	$0.329581\pi$
$500$	−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	0.999860	−	0.0167188i	$-0.00532200\pi$
$503$	4.06231	+	12.5025i	0.181129	+	0.557459i	−0.818731	+	0.574177i	$0.805322\pi$
$504$	−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	$-0.686523\pi$
$509$	1.54508	−	1.12257i	0.0684847	−	0.0497570i	0.621501	+	0.783413i	$0.286523\pi$
$510$	−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	0.863816	+	0.503807i	$0.168068\pi$
$523$	10.5451	+	32.4544i	0.461104	+	1.41913i	−0.402712	+	0.915327i	$0.631932\pi$
$524$	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	−0.691835	−	0.722056i	$-0.743197\pi$
$541$	6.79837	−	20.9232i	0.292285	−	0.899560i	0.984120	−	0.177505i	$-0.0568025\pi$
$542$	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	−0.976470	−	0.215654i	$-0.930812\pi$
$547$	−7.32624	−	22.5478i	−0.313247	−	0.964076i	0.663223	−	0.748422i	$-0.269188\pi$
$548$	−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	$-0.225041\pi$
$557$	35.8885			1.52065			0.760323	+	0.649545i	$0.225041\pi$
$558$		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	0.999849	+	0.0173602i	$0.00552620\pi$
$569$	4.79837	+	14.7679i	0.201158	+	0.619102i	−0.798691	+	0.601741i	$0.794474\pi$
$570$	6.54508	+	4.75528i	0.274143	+	0.199177i
$571$	−5.66312	+	4.11450i	−0.236994	+	0.172186i	−0.699943	−	0.714199i	$-0.746791\pi$
$571$	−5.66312	+	4.11450i	−0.236994	+	0.172186i	0.462949	+	0.886385i	$0.346791\pi$
$572$	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	−0.999992	−	0.00398440i	$-0.998732\pi$
$577$	−31.5344	−	22.9111i	−1.31280	−	0.953802i	−0.312804	−	0.949818i	$-0.601268\pi$
$578$	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	$-0.566698\pi$
$587$	−29.1353	−	21.1680i	−1.20254	−	0.873697i	−0.994532	+	0.104430i	$0.966698\pi$
$588$	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	0.982316	−	0.187232i	$-0.0599517\pi$
$593$	1.88854	+	5.81234i	0.0775532	+	0.238684i	−0.904762	+	0.425917i	$0.859952\pi$
$594$	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	−0.0261805	−	0.999657i	$-0.508334\pi$
$599$	−24.1074	−	17.5150i	−0.985001	−	0.715645i	−0.958821	+	0.284012i	$0.908334\pi$
$600$	−1.28115	−	3.94298i	−0.0523029	−	0.160972i
$601$	−17.7984	−	12.9313i	−0.726011	−	0.527478i	0.162288	−	0.986743i	$-0.448113\pi$
$601$	−17.7984	−	12.9313i	−0.726011	−	0.527478i	−0.888299	+	0.459266i	$0.848113\pi$
$602$	−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	−0.0862582	−	0.996273i	$-0.527491\pi$
$607$	20.5623	−	14.9394i	0.834598	−	0.606371i	0.920856	+	0.389902i	$0.127491\pi$
$608$	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	0.976682	+	0.214692i	$0.0688748\pi$
$613$	7.74265	+	23.8294i	0.312723	+	0.962461i	−0.663959	+	0.747769i	$0.731125\pi$
$614$	−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	−0.331302	−	0.943525i	$-0.607488\pi$
$617$	11.5172	−	8.36775i	0.463666	−	0.336873i	0.794968	+	0.606652i	$0.207488\pi$
$618$	0.0729490	+	0.0530006i	0.00293444	+	0.00213200i
$619$	−40.0000			−1.60774			−0.803868	−	0.594808i	$-0.797228\pi$
$619$	−40.0000			−1.60774			−0.803868	+	0.594808i	$0.797228\pi$
$620$		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	$-0.155591\pi$
$631$	−2.69756	−	8.30224i	−0.107388	−	0.330507i	−0.990284	+	0.139063i	$0.955591\pi$
$632$		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	0.999991	+	0.00420601i	$0.00133882\pi$
$641$	33.2426	+	24.1522i	1.31301	+	0.953954i	0.313014	+	0.949748i	$0.398661\pi$
$642$	0.208204	−	0.640786i	0.00821715	−	0.0252898i
$643$	2.51722	−	7.74721i	0.0992695	−	0.305520i	−0.889073	−	0.457765i	$-0.848650\pi$
$643$	2.51722	−	7.74721i	0.0992695	−	0.305520i	0.988343	+	0.152245i	$0.0486502\pi$
$644$	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	−0.951158	−	0.308705i	$-0.900104\pi$
$647$	−9.23607	−	28.4257i	−0.363107	−	1.11753i	0.588050	−	0.808824i	$-0.299896\pi$
$648$	−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	−0.256848	−	0.966452i	$-0.582684\pi$
$653$	−32.0795	−	23.3071i	−1.25537	−	0.912079i	−0.998521	+	0.0543729i	$0.982684\pi$
$654$	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	−0.716621	−	0.697463i	$-0.754312\pi$
$659$	7.01064	−	21.5765i	0.273096	−	0.840503i	0.989717	−	0.143040i	$-0.0456877\pi$
$660$	1.00000	−	3.07768i	0.0389249	−	0.119799i
$661$	13.4443	+	9.76784i	0.522922	+	0.379925i	0.817703	−	0.575640i	$-0.195247\pi$
$661$	13.4443	+	9.76784i	0.522922	+	0.379925i	−0.294782	+	0.955565i	$0.595247\pi$
$662$	−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	$-0.927127\pi$
$673$	−1.36475	+	4.20025i	−0.0526071	+	0.161908i	0.921301	+	0.388849i	$0.127127\pi$
$674$	−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	$-0.314398\pi$
$677$	28.6525			1.10120			0.550602	+	0.834768i	$0.314398\pi$
$678$	−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	−0.925997	−	0.377530i	$-0.876773\pi$
$691$	1.18441	−	3.64522i	0.0450569	−	0.138671i	0.971054	+	0.238859i	$0.0767735\pi$
$692$	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	0.942960	−	0.332907i	$-0.108030\pi$
$701$	24.2984	+	17.6538i	0.917737	+	0.666775i	−0.0252228	+	0.999682i	$0.508030\pi$
$702$	−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	$-0.0751941\pi$
$709$	1.28115	+	3.94298i	0.0481147	+	0.148082i	−0.924113	+	0.382120i	$0.875194\pi$
$710$	−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	$-0.780565\pi$
$719$	−41.3820			−1.54329			−0.771643	+	0.636055i	$0.780565\pi$
$720$	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	0.716561	+	0.697524i	$0.245715\pi$
$727$	−7.36475	+	22.6664i	−0.273143	+	0.840649i	−0.989705	+	0.143125i	$0.954285\pi$
$728$	−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	0.974098	+	0.226127i	$0.0726065\pi$
$733$	8.63525	+	26.5766i	0.318950	+	0.981628i	−0.655147	+	0.755501i	$0.727393\pi$
$734$	−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	$-0.369262\pi$
$739$	21.7082			0.798549			0.399275	+	0.916831i	$0.369262\pi$
$740$	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	$-0.520085\pi$
$743$	−3.43769			−0.126117			−0.0630584	+	0.998010i	$0.520085\pi$
$744$		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	−0.877854	−	0.478929i	$-0.841025\pi$
$751$	−12.3090	−	37.8833i	−0.449162	−	1.38238i	0.428691	−	0.903451i	$-0.358975\pi$
$752$	−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	$-0.986668\pi$
$757$	−34.8885	+	25.3480i	−1.26805	+	0.921289i	−0.268923	+	0.963162i	$0.586668\pi$
$758$	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	$-0.879756\pi$
$761$	1.08359	−	3.33495i	0.0392802	−	0.120892i	0.968774	+	0.247946i	$0.0797556\pi$
$762$	−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	$-0.188451\pi$
$773$	15.4443	+	11.2209i	0.555492	+	0.403588i	−0.274314	+	0.961640i	$0.588451\pi$
$774$	−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	$-0.488322\pi$
$787$	−25.3156	−	18.3929i	−0.902403	−	0.655635i	−0.939082	+	0.343693i	$0.888322\pi$
$788$	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	$-0.848726\pi$
$797$	2.79837	−	8.61251i	0.0991235	−	0.305071i	0.988306	+	0.152481i	$0.0487264\pi$
$798$	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	−0.621561	+	0.783366i	$0.713501\pi$
$809$	−44.3328	+	32.2097i	−1.55866	+	1.13243i	−0.937098	+	0.349066i	$0.886499\pi$
$810$	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	$-0.508242\pi$
$821$	26.2705	−	19.0866i	0.916847	−	0.666128i	0.942737	+	0.333536i	$0.108242\pi$
$822$	3.23607	−	2.35114i	0.112871	−	0.0820055i
$823$	−1.89261	+	5.82485i	−0.0659722	+	0.203042i	−0.978609	−	0.205731i	$-0.934043\pi$
$823$	−1.89261	+	5.82485i	−0.0659722	+	0.203042i	0.912636	+	0.408772i	$0.134043\pi$
$824$	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	$-0.314803\pi$
$827$	−2.16312	−	1.57160i	−0.0752190	−	0.0546498i	−0.624759	+	0.780817i	$0.714803\pi$
$828$	−5.47214	+	16.8415i	−0.190170	+	0.585283i
$829$	−6.70820	+	20.6457i	−0.232986	+	0.717056i	0.764397	+	0.644746i	$0.223037\pi$
$829$	−6.70820	+	20.6457i	−0.232986	+	0.717056i	−0.997382	+	0.0723096i	$0.976963\pi$
$830$	−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	0.420599	−	0.907246i	$-0.361820\pi$
$839$	−9.04508	−	6.57164i	−0.312271	−	0.226878i	−0.732870	+	0.680368i	$0.761820\pi$
$840$	−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	−0.641806	−	0.766867i	$-0.721815\pi$
$853$	−3.23607	+	2.35114i	−0.110801	+	0.0805015i	0.531005	+	0.847369i	$0.321815\pi$
$854$	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	0.898553	−	0.438865i	$-0.144619\pi$
$857$	−2.52786	−	7.77997i	−0.0863502	−	0.265759i	−0.984903	+	0.173107i	$0.944619\pi$
$858$	1.85410	+	1.34708i	0.0632980	+	0.0459887i
$859$	13.3779	−	41.1729i	0.456448	−	1.40480i	−0.412979	−	0.910741i	$-0.635512\pi$
$859$	13.3779	−	41.1729i	0.456448	−	1.40480i	0.869427	−	0.494062i	$-0.164488\pi$
$860$	−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	$-0.486487\pi$
$863$	2.49342			0.0848771			0.0424385	+	0.999099i	$0.486487\pi$
$864$	−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	−0.829369	−	0.558701i	$-0.811300\pi$
$877$	5.03444	−	15.4944i	0.170001	−	0.523209i	0.999370	+	0.0354920i	$0.0112998\pi$
$878$	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	$-0.616687\pi$
$881$	12.4271	−	9.02878i	0.418678	−	0.304187i	0.777106	+	0.629370i	$0.216687\pi$
$882$	0.763932	−	2.35114i	0.0257229	−	0.0791670i
$883$	0.809017	−	0.587785i	0.0272256	−	0.0197805i	−0.574089	−	0.818793i	$-0.694644\pi$
$883$	0.809017	−	0.587785i	0.0272256	−	0.0197805i	0.601315	+	0.799012i	$0.294644\pi$
$884$	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	−0.0877123	−	0.996146i	$-0.527956\pi$
$887$	−31.6353	−	22.9844i	−1.06221	−	0.771739i	−0.974496	+	0.224407i	$0.927956\pi$
$888$	−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	−0.182601	−	0.983187i	$-0.558452\pi$
$907$	16.3541	−	50.3328i	0.543029	−	1.67127i	0.725631	−	0.688085i	$-0.241548\pi$
$908$	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	$-0.343268\pi$
$911$	−6.61803	−	4.80828i	−0.219265	−	0.159306i	−0.691996	+	0.721901i	$0.743268\pi$
$912$	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	0.988689	−	0.149983i	$-0.0479218\pi$
$919$	3.05166	+	9.39205i	0.100665	+	0.309815i	−0.888024	+	0.459798i	$0.847922\pi$
$920$	−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	$-0.314543\pi$
$929$	33.5410			1.10045			0.550223	+	0.835018i	$0.314543\pi$
$930$		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	0.917762	+	0.397131i	$0.129994\pi$
$937$	12.5106	+	38.5038i	0.408705	+	1.25786i	−0.509057	+	0.860733i	$0.670006\pi$
$938$	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	0.985502	+	0.169667i	$0.0542691\pi$
$941$	8.83282	+	27.1846i	0.287942	+	0.886193i	−0.697560	+	0.716526i	$0.745731\pi$
$942$	−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	−0.777009	−	0.629490i	$-0.783264\pi$
$947$	6.81966	−	20.9888i	0.221609	−	0.682043i	0.998618	−	0.0525534i	$-0.0167360\pi$
$948$		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	−0.482729	−	0.875770i	$-0.660354\pi$
$953$	13.0451	−	40.1486i	0.422572	−	1.30054i	0.905300	−	0.424772i	$-0.139646\pi$
$954$	−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	$-0.252342\pi$
$967$	43.6525			1.40377			0.701884	+	0.712291i	$0.252342\pi$
$968$	−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	0.821796	−	0.569782i	$-0.192972\pi$
$971$	16.6353	+	12.0862i	0.533851	+	0.387865i	−0.287945	+	0.957647i	$0.592972\pi$
$972$	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	−0.506469	−	0.862258i	$-0.669050\pi$
$977$	4.90983	−	3.56720i	0.157079	−	0.114125i	0.663549	+	0.748133i	$0.269050\pi$
$978$	−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	−0.792292	−	0.610142i	$-0.791113\pi$
$983$	6.50000	−	20.0049i	0.207318	−	0.638059i	0.999610	−	0.0279171i	$-0.00888743\pi$
$984$	−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	$-0.588449\pi$
$991$	−17.2705			−0.548616			−0.274308	+	0.961642i	$0.588449\pi$
$992$		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.f.374.1		4
31.2	even	5		31.2.d.a.8.1	yes	4
31.3	odd	30		961.2.g.g.235.1		8
31.4	even	5		961.2.a.d.1.1		2
31.5	even	3		961.2.g.f.732.1		8
31.6	odd	6		961.2.g.g.816.1		8
31.7	even	15		961.2.c.f.439.1		4
31.8	even	5		31.2.d.a.4.1	✓	4
31.9	even	15		961.2.g.b.844.1		8
31.10	even	15		961.2.g.b.448.1		8
31.11	odd	30		961.2.c.d.521.1		4
31.12	odd	30		961.2.g.c.846.1		8
31.13	odd	30		961.2.g.g.338.1		8
31.14	even	15		961.2.g.b.547.1		8
31.15	odd	10		961.2.d.e.388.1		4
31.16	even	5	inner	961.2.d.f.388.1		4
31.17	odd	30		961.2.g.c.547.1		8
31.18	even	15		961.2.g.f.338.1		8
31.19	even	15		961.2.g.b.846.1		8
31.20	even	15		961.2.c.f.521.1		4
31.21	odd	30		961.2.g.c.448.1		8
31.22	odd	30		961.2.g.c.844.1		8
31.23	odd	10		961.2.d.b.531.1		4
31.24	odd	30		961.2.c.d.439.1		4
31.25	even	3		961.2.g.f.816.1		8
31.26	odd	6		961.2.g.g.732.1		8
31.27	odd	10		961.2.a.e.1.1		2
31.28	even	15		961.2.g.f.235.1		8
31.29	odd	10		961.2.d.b.628.1		4
31.30	odd	2		961.2.d.e.374.1		4
93.2	odd	10		279.2.i.a.163.1		4
93.8	odd	10		279.2.i.a.190.1		4
93.35	odd	10		8649.2.a.g.1.2		2
93.89	even	10		8649.2.a.f.1.2		2
124.39	odd	10		496.2.n.b.97.1		4
124.95	odd	10		496.2.n.b.225.1		4
155.2	odd	20		775.2.bf.a.349.1		8
155.8	odd	20		775.2.bf.a.624.1		8
155.33	odd	20		775.2.bf.a.349.2		8
155.39	even	10		775.2.k.c.376.1		4
155.64	even	10		775.2.k.c.101.1		4
155.132	odd	20		775.2.bf.a.624.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.d.a.4.1	✓	4	31.8	even	5
31.2.d.a.8.1	yes	4	31.2	even	5
279.2.i.a.163.1		4	93.2	odd	10
279.2.i.a.190.1		4	93.8	odd	10
496.2.n.b.97.1		4	124.39	odd	10
496.2.n.b.225.1		4	124.95	odd	10
775.2.k.c.101.1		4	155.64	even	10
775.2.k.c.376.1		4	155.39	even	10
775.2.bf.a.349.1		8	155.2	odd	20
775.2.bf.a.349.2		8	155.33	odd	20
775.2.bf.a.624.1		8	155.8	odd	20
775.2.bf.a.624.2		8	155.132	odd	20
961.2.a.d.1.1		2	31.4	even	5
961.2.a.e.1.1		2	31.27	odd	10
961.2.c.d.439.1		4	31.24	odd	30
961.2.c.d.521.1		4	31.11	odd	30
961.2.c.f.439.1		4	31.7	even	15
961.2.c.f.521.1		4	31.20	even	15
961.2.d.b.531.1		4	31.23	odd	10
961.2.d.b.628.1		4	31.29	odd	10
961.2.d.e.374.1		4	31.30	odd	2
961.2.d.e.388.1		4	31.15	odd	10
961.2.d.f.374.1		4	1.1	even	1	trivial
961.2.d.f.388.1		4	31.16	even	5	inner
961.2.g.b.448.1		8	31.10	even	15
961.2.g.b.547.1		8	31.14	even	15
961.2.g.b.844.1		8	31.9	even	15
961.2.g.b.846.1		8	31.19	even	15
961.2.g.c.448.1		8	31.21	odd	30
961.2.g.c.547.1		8	31.17	odd	30
961.2.g.c.844.1		8	31.22	odd	30
961.2.g.c.846.1		8	31.12	odd	30
961.2.g.f.235.1		8	31.28	even	15
961.2.g.f.338.1		8	31.18	even	15
961.2.g.f.732.1		8	31.5	even	3
961.2.g.f.816.1		8	31.25	even	3
961.2.g.g.235.1		8	31.3	odd	30
961.2.g.g.338.1		8	31.13	odd	30
961.2.g.g.732.1		8	31.26	odd	6
961.2.g.g.816.1		8	31.6	odd	6
8649.2.a.f.1.2		2	93.89	even	10
8649.2.a.g.1.2		2	93.35	odd	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 $\F_{q}$

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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