LMFDB - Embedded newform 48.3.i.b.29.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,3,Mod(5,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("48.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	48.i (of order $4$, degree $2$, 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:	$1.30790526893$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + \cdots + 1048576 $ x^20 - 2x^18 + 6x^16 - 24x^14 - 24x^12 + 1216x^10 - 384x^8 - 6144x^6 + 24576x^4 - 131072*x^2 + 1048576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{13} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			29.8
Root			$1.28499 + 1.53258i$ of defining polynomial
Character	$\chi$	$=$	48.29
Dual form			48.3.i.b.5.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28499 - 1.53258i) q^{2} +(-2.17774 - 2.06336i) q^{3} +(-0.697601 - 3.93870i) q^{4} +(3.17955 + 3.17955i) q^{5} +(-5.96063 + 0.686173i) q^{6} -6.03979i q^{7} +(-6.93278 - 3.99206i) q^{8} +(0.485128 + 8.98692i) q^{9} +O(q^{10})$	\(q+(1.28499 - 1.53258i) q^{2} +(-2.17774 - 2.06336i) q^{3} +(-0.697601 - 3.93870i) q^{4} +(3.17955 + 3.17955i) q^{5} +(-5.96063 + 0.686173i) q^{6} -6.03979i q^{7} +(-6.93278 - 3.99206i) q^{8} +(0.485128 + 8.98692i) q^{9} +(8.95859 - 0.787223i) q^{10} +(13.0097 + 13.0097i) q^{11} +(-6.60774 + 10.0169i) q^{12} +(6.39520 + 6.39520i) q^{13} +(-9.25646 - 7.76107i) q^{14} +(-0.363700 - 13.4848i) q^{15} +(-15.0267 + 5.49528i) q^{16} -4.39848i q^{17} +(14.3965 + 10.8046i) q^{18} +(-3.21075 - 3.21075i) q^{19} +(10.3052 - 14.7413i) q^{20} +(-12.4622 + 13.1531i) q^{21} +(36.6557 - 3.22107i) q^{22} -34.0396 q^{23} +(6.86077 + 22.9985i) q^{24} -4.78097i q^{25} +(18.0189 - 1.58339i) q^{26} +(17.4867 - 20.5722i) q^{27} +(-23.7889 + 4.21336i) q^{28} +(-27.9597 + 27.9597i) q^{29} +(-21.1338 - 16.7704i) q^{30} -7.90993 q^{31} +(-10.8872 + 30.0910i) q^{32} +(-1.48814 - 55.1754i) q^{33} +(-6.74102 - 5.65200i) q^{34} +(19.2038 - 19.2038i) q^{35} +(35.0583 - 8.18005i) q^{36} +(20.0443 - 20.0443i) q^{37} +(-9.04650 + 0.794947i) q^{38} +(-0.731530 - 27.1227i) q^{39} +(-9.35016 - 34.7360i) q^{40} +45.1067 q^{41} +(4.14434 + 36.0010i) q^{42} +(-36.0095 + 36.0095i) q^{43} +(42.1657 - 60.3168i) q^{44} +(-27.0318 + 30.1168i) q^{45} +(-43.7406 + 52.1684i) q^{46} +5.08935i q^{47} +(44.0630 + 19.0381i) q^{48} +12.5209 q^{49} +(-7.32721 - 6.14349i) q^{50} +(-9.07563 + 9.57876i) q^{51} +(20.7275 - 29.6501i) q^{52} +(-20.7687 - 20.7687i) q^{53} +(-9.05825 - 53.2348i) q^{54} +82.7299i q^{55} +(-24.1112 + 41.8725i) q^{56} +(0.367268 + 13.6171i) q^{57} +(6.92253 + 78.7784i) q^{58} +(39.0656 + 39.0656i) q^{59} +(-52.8587 + 10.8395i) q^{60} +(-49.8322 - 49.8322i) q^{61} +(-10.1642 + 12.1226i) q^{62} +(54.2791 - 2.93007i) q^{63} +(32.1269 + 55.3522i) q^{64} +40.6677i q^{65} +(-86.4729 - 68.6191i) q^{66} +(44.9162 + 44.9162i) q^{67} +(-17.3243 + 3.06838i) q^{68} +(74.1295 + 70.2358i) q^{69} +(-4.75466 - 54.1080i) q^{70} -46.6947 q^{71} +(32.5130 - 64.2410i) q^{72} -97.3523i q^{73} +(-4.96275 - 56.4761i) q^{74} +(-9.86483 + 10.4117i) q^{75} +(-10.4063 + 14.8860i) q^{76} +(78.5758 - 78.5758i) q^{77} +(-42.5077 - 33.7312i) q^{78} -40.1637 q^{79} +(-65.2506 - 30.3056i) q^{80} +(-80.5293 + 8.71960i) q^{81} +(57.9616 - 69.1296i) q^{82} +(35.5451 - 35.5451i) q^{83} +(60.4998 + 39.9094i) q^{84} +(13.9852 - 13.9852i) q^{85} +(8.91558 + 101.459i) q^{86} +(118.580 - 3.19823i) q^{87} +(-38.2579 - 142.129i) q^{88} -69.6795 q^{89} +(11.4208 + 80.1282i) q^{90} +(38.6257 - 38.6257i) q^{91} +(23.7461 + 134.072i) q^{92} +(17.2258 + 16.3210i) q^{93} +(7.79984 + 6.53977i) q^{94} -20.4174i q^{95} +(85.7980 - 43.0663i) q^{96} +61.0939 q^{97} +(16.0893 - 19.1893i) q^{98} +(-110.606 + 123.228i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{3} + 4 q^{4} - 12 q^{6}+O(q^{10}) $ 20 * q - 6 * q^3 + 4 * q^4 - 12 * q^6	$ 20 q - 6 q^{3} + 4 q^{4} - 12 q^{6} + 32 q^{10} - 88 q^{12} + 92 q^{13} - 116 q^{15} - 16 q^{16} + 4 q^{18} - 52 q^{19} + 48 q^{21} + 24 q^{22} - 8 q^{24} + 18 q^{27} + 56 q^{28} + 28 q^{30} - 80 q^{31} + 60 q^{33} + 104 q^{34} + 92 q^{36} - 116 q^{37} + 88 q^{40} + 304 q^{42} + 172 q^{43} + 60 q^{45} - 424 q^{46} + 176 q^{48} - 364 q^{49} + 128 q^{51} - 208 q^{52} + 40 q^{54} - 512 q^{58} - 240 q^{60} - 244 q^{61} + 296 q^{63} + 88 q^{64} - 492 q^{66} + 356 q^{67} - 20 q^{69} + 200 q^{70} - 472 q^{72} - 146 q^{75} + 328 q^{76} + 84 q^{78} + 384 q^{79} - 188 q^{81} + 560 q^{82} + 816 q^{84} + 48 q^{85} + 416 q^{88} + 616 q^{90} + 136 q^{91} - 132 q^{93} + 32 q^{94} - 24 q^{96} + 472 q^{97} - 452 q^{99}+O(q^{100}) $ 20 * q - 6 * q^3 + 4 * q^4 - 12 * q^6 + 32 * q^10 - 88 * q^12 + 92 * q^13 - 116 * q^15 - 16 * q^16 + 4 * q^18 - 52 * q^19 + 48 * q^21 + 24 * q^22 - 8 * q^24 + 18 * q^27 + 56 * q^28 + 28 * q^30 - 80 * q^31 + 60 * q^33 + 104 * q^34 + 92 * q^36 - 116 * q^37 + 88 * q^40 + 304 * q^42 + 172 * q^43 + 60 * q^45 - 424 * q^46 + 176 * q^48 - 364 * q^49 + 128 * q^51 - 208 * q^52 + 40 * q^54 - 512 * q^58 - 240 * q^60 - 244 * q^61 + 296 * q^63 + 88 * q^64 - 492 * q^66 + 356 * q^67 - 20 * q^69 + 200 * q^70 - 472 * q^72 - 146 * q^75 + 328 * q^76 + 84 * q^78 + 384 * q^79 - 188 * q^81 + 560 * q^82 + 816 * q^84 + 48 * q^85 + 416 * q^88 + 616 * q^90 + 136 * q^91 - 132 * q^93 + 32 * q^94 - 24 * q^96 + 472 * q^97 - 452 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.28499	−	1.53258i	0.642495	−	0.766290i
$2$	1.28499	−	1.53258i	0.642495	−	0.766290i
$3$	−2.17774	−	2.06336i	−0.725914	−	0.687785i
$3$	−2.17774	−	2.06336i	−0.725914	−	0.687785i
$4$	−0.697601	−	3.93870i	−0.174400	−	0.984675i
$5$	3.17955	+	3.17955i	0.635909	+	0.635909i	0.949544	−	0.313634i	$-0.101547\pi$
$5$	3.17955	+	3.17955i	0.635909	+	0.635909i	−0.313634	+	0.949544i	$0.601547\pi$
$6$	−5.96063	+	0.686173i	−0.993439	+	0.114362i
$7$		−	6.03979i		−	0.862827i	−0.902154	−	0.431414i	$-0.858015\pi$
$7$		−	6.03979i		−	0.862827i	0.902154	−	0.431414i	$-0.141985\pi$
$8$	−6.93278	−	3.99206i	−0.866598	−	0.499008i
$9$	0.485128	+	8.98692i	0.0539031	+	0.998546i
$10$	8.95859	−	0.787223i	0.895859	−	0.0787223i
$11$	13.0097	+	13.0097i	1.18270	+	1.18270i	0.979042	+	0.203657i	$0.0652828\pi$
$11$	13.0097	+	13.0097i	1.18270	+	1.18270i	0.203657	+	0.979042i	$0.434717\pi$
$12$	−6.60774	+	10.0169i	−0.550645	+	0.834739i
$13$	6.39520	+	6.39520i	0.491939	+	0.491939i	0.908917	−	0.416978i	$-0.136911\pi$
$13$	6.39520	+	6.39520i	0.491939	+	0.491939i	−0.416978	+	0.908917i	$0.636911\pi$
$14$	−9.25646	−	7.76107i	−0.661176	−	0.554362i
$15$	−0.363700	−	13.4848i	−0.0242466	−	0.898985i
$16$	−15.0267	+	5.49528i	−0.939169	+	0.343455i
$17$		−	4.39848i		−	0.258734i	−0.991597	−	0.129367i	$-0.958705\pi$
$17$		−	4.39848i		−	0.258734i	0.991597	−	0.129367i	$-0.0412945\pi$
$18$	14.3965	+	10.8046i	0.799808	+	0.600256i
$19$	−3.21075	−	3.21075i	−0.168987	−	0.168987i	0.617547	−	0.786534i	$-0.288126\pi$
$19$	−3.21075	−	3.21075i	−0.168987	−	0.168987i	−0.786534	+	0.617547i	$0.788126\pi$
$20$	10.3052	−	14.7413i	0.515261	−	0.737067i
$21$	−12.4622	+	13.1531i	−0.593440	+	0.626339i
$22$	36.6557	−	3.22107i	1.66617	−	0.146412i
$23$	−34.0396			−1.47998			−0.739992	−	0.672616i	$-0.765171\pi$
$23$	−34.0396			−1.47998			−0.739992	+	0.672616i	$0.765171\pi$
$24$	6.86077	+	22.9985i	0.285866	+	0.958270i
$25$		−	4.78097i		−	0.191239i
$26$	18.0189	−	1.58339i	0.693036	−	0.0608994i
$27$	17.4867	−	20.5722i	0.647656	−	0.761933i
$28$	−23.7889	+	4.21336i	−0.849604	+	0.150477i
$29$	−27.9597	+	27.9597i	−0.964128	+	0.964128i	−0.999378	−	0.0352510i	$-0.988777\pi$
$29$	−27.9597	+	27.9597i	−0.964128	+	0.964128i	0.0352510	+	0.999378i	$0.488777\pi$
$30$	−21.1338	−	16.7704i	−0.704461	−	0.559013i
$31$	−7.90993			−0.255159			−0.127580	−	0.991828i	$-0.540721\pi$
$31$	−7.90993			−0.255159			−0.127580	+	0.991828i	$0.540721\pi$
$32$	−10.8872	+	30.0910i	−0.340225	+	0.940344i
$33$	−1.48814	−	55.1754i	−0.0450952	−	1.67198i
$34$	−6.74102	−	5.65200i	−0.198265	−	0.166235i
$35$	19.2038	−	19.2038i	0.548680	−	0.548680i
$36$	35.0583	−	8.18005i	0.973843	−	0.227224i
$37$	20.0443	−	20.0443i	0.541736	−	0.541736i	−0.382301	−	0.924038i	$-0.624868\pi$
$37$	20.0443	−	20.0443i	0.541736	−	0.541736i	0.924038	+	0.382301i	$0.124868\pi$
$38$	−9.04650	+	0.794947i	−0.238066	+	0.0209197i
$39$	−0.731530	−	27.1227i	−0.0187572	−	0.695453i
$40$	−9.35016	−	34.7360i	−0.233754	−	0.868401i
$41$	45.1067			1.10016			0.550081	−	0.835111i	$-0.314597\pi$
$41$	45.1067			1.10016			0.550081	+	0.835111i	$0.314597\pi$
$42$	4.14434	+	36.0010i	0.0986748	+	0.857166i
$43$	−36.0095	+	36.0095i	−0.837431	+	0.837431i	−0.988520	−	0.151089i	$-0.951722\pi$
$43$	−36.0095	+	36.0095i	−0.837431	+	0.837431i	0.151089	+	0.988520i	$0.451722\pi$
$44$	42.1657	−	60.3168i	0.958311	−	1.37084i
$45$	−27.0318	+	30.1168i	−0.600707	+	0.669262i
$46$	−43.7406	+	52.1684i	−0.950882	+	1.13410i
$47$			5.08935i			0.108284i	0.998533	+	0.0541421i	$0.0172424\pi$
$47$			5.08935i			0.108284i	−0.998533	+	0.0541421i	$0.982758\pi$
$48$	44.0630	+	19.0381i	0.917980	+	0.396628i
$49$	12.5209			0.255529
$50$	−7.32721	−	6.14349i	−0.146544	−	0.122870i
$51$	−9.07563	+	9.57876i	−0.177953	+	0.187819i
$52$	20.7275	−	29.6501i	0.398605	−	0.570194i
$53$	−20.7687	−	20.7687i	−0.391863	−	0.391863i	0.483488	−	0.875351i	$-0.339370\pi$
$53$	−20.7687	−	20.7687i	−0.391863	−	0.391863i	−0.875351	+	0.483488i	$0.839370\pi$
$54$	−9.05825	−	53.2348i	−0.167745	−	0.985830i
$55$			82.7299i			1.50418i
$56$	−24.1112	+	41.8725i	−0.430557	+	0.747724i
$57$	0.367268	+	13.6171i	0.00644331	+	0.238896i
$58$	6.92253	+	78.7784i	0.119354	+	1.35825i
$59$	39.0656	+	39.0656i	0.662129	+	0.662129i	0.955881	−	0.293753i	$-0.0949043\pi$
$59$	39.0656	+	39.0656i	0.662129	+	0.662129i	−0.293753	+	0.955881i	$0.594904\pi$
$60$	−52.8587	+	10.8395i	−0.880979	+	0.180658i
$61$	−49.8322	−	49.8322i	−0.816921	−	0.816921i	0.168739	−	0.985661i	$-0.446030\pi$
$61$	−49.8322	−	49.8322i	−0.816921	−	0.816921i	−0.985661	+	0.168739i	$0.946030\pi$
$62$	−10.1642	+	12.1226i	−0.163938	+	0.195526i
$63$	54.2791	−	2.93007i	0.861573	−	0.0465090i
$64$	32.1269	+	55.3522i	0.501983	+	0.864878i
$65$			40.6677i			0.625657i
$66$	−86.4729	−	68.6191i	−1.31020	−	1.03968i
$67$	44.9162	+	44.9162i	0.670390	+	0.670390i	0.957806	−	0.287416i	$-0.0927961\pi$
$67$	44.9162	+	44.9162i	0.670390	+	0.670390i	−0.287416	+	0.957806i	$0.592796\pi$
$68$	−17.3243	+	3.06838i	−0.254769	+	0.0451233i
$69$	74.1295	+	70.2358i	1.07434	+	1.01791i
$70$	−4.75466	−	54.1080i	−0.0679237	−	0.772972i
$71$	−46.6947			−0.657672			−0.328836	−	0.944387i	$-0.606656\pi$
$71$	−46.6947			−0.657672			−0.328836	+	0.944387i	$0.606656\pi$
$72$	32.5130	−	64.2410i	0.451570	−	0.892236i
$73$		−	97.3523i		−	1.33359i	−0.745240	−	0.666797i	$-0.767665\pi$
$73$		−	97.3523i		−	1.33359i	0.745240	−	0.666797i	$-0.232335\pi$
$74$	−4.96275	−	56.4761i	−0.0670642	−	0.763190i
$75$	−9.86483	+	10.4117i	−0.131531	+	0.138823i
$76$	−10.4063	+	14.8860i	−0.136926	+	0.195868i
$77$	78.5758	−	78.5758i	1.02047	−	1.02047i
$78$	−42.5077	−	33.7312i	−0.544970	−	0.432452i
$79$	−40.1637			−0.508402			−0.254201	−	0.967151i	$-0.581812\pi$
$79$	−40.1637			−0.508402			−0.254201	+	0.967151i	$0.581812\pi$
$80$	−65.2506	−	30.3056i	−0.815633	−	0.378820i
$81$	−80.5293	+	8.71960i	−0.994189	+	0.107649i
$82$	57.9616	−	69.1296i	0.706849	−	0.843043i
$83$	35.5451	−	35.5451i	0.428254	−	0.428254i	−0.459779	−	0.888033i	$-0.652071\pi$
$83$	35.5451	−	35.5451i	0.428254	−	0.428254i	0.888033	+	0.459779i	$0.152071\pi$
$84$	60.4998	+	39.9094i	0.720236	+	0.475112i
$85$	13.9852	−	13.9852i	0.164531	−	0.164531i
$86$	8.91558	+	101.459i	0.103670	+	1.17976i
$87$	118.580	−	3.19823i	1.36299	−	0.0367613i
$88$	−38.2579	−	142.129i	−0.434749	−	1.61510i
$89$	−69.6795			−0.782916			−0.391458	−	0.920196i	$-0.628029\pi$
$89$	−69.6795			−0.782916			−0.391458	+	0.920196i	$0.628029\pi$
$90$	11.4208	+	80.1282i	0.126897	+	0.890314i
$91$	38.6257	−	38.6257i	0.424458	−	0.424458i
$92$	23.7461	+	134.072i	0.258109	+	1.45730i
$93$	17.2258	+	16.3210i	0.185224	+	0.175495i
$94$	7.79984	+	6.53977i	0.0829770	+	0.0695720i
$95$		−	20.4174i		−	0.214920i
$96$	85.7980	−	43.0663i	0.893729	−	0.448607i
$97$	61.0939			0.629834			0.314917	−	0.949119i	$-0.398023\pi$
$97$	61.0939			0.629834			0.314917	+	0.949119i	$0.398023\pi$
$98$	16.0893	−	19.1893i	0.164176	−	0.195809i
$99$	−110.606	+	123.228i	−1.11723	+	1.24473i
$100$	−18.8308	+	3.33521i	−0.188308	+	0.0333521i
$101$	−104.036	−	104.036i	−1.03006	−	1.03006i	−0.999534	−	0.0305280i	$-0.990281\pi$
$101$	−104.036	−	104.036i	−1.03006	−	1.03006i	−0.0305280	−	0.999534i	$-0.509719\pi$
$102$	3.01812	+	26.2177i	0.0295894	+	0.257037i
$103$		−	57.2961i		−	0.556272i	−0.960542	−	0.278136i	$-0.910283\pi$
$103$		−	57.2961i		−	0.556272i	0.960542	−	0.278136i	$-0.0897167\pi$
$104$	−18.8065	−	69.8666i	−0.180832	−	0.671794i
$105$	−81.4452	+	2.19667i	−0.775668	+	0.0209207i
$106$	−58.5173	+	5.14212i	−0.552050	+	0.0485105i
$107$	−92.4468	−	92.4468i	−0.863989	−	0.863989i	0.127810	−	0.991799i	$-0.459205\pi$
$107$	−92.4468	−	92.4468i	−0.863989	−	0.863989i	−0.991799	+	0.127810i	$0.959205\pi$
$108$	−93.2264	−	54.5238i	−0.863207	−	0.504850i
$109$	75.3749	+	75.3749i	0.691513	+	0.691513i	0.962565	−	0.271052i	$-0.0873714\pi$
$109$	75.3749	+	75.3749i	0.691513	+	0.691513i	−0.271052	+	0.962565i	$0.587371\pi$
$110$	126.790	+	106.307i	1.15264	+	0.966428i
$111$	−85.0096	+	2.29281i	−0.765853	+	0.0206559i
$112$	33.1903	+	90.7581i	0.296342	+	0.810341i
$113$			112.254i			0.993401i	0.867922	+	0.496701i	$0.165455\pi$
$113$			112.254i			0.993401i	−0.867922	+	0.496701i	$0.834545\pi$
$114$	21.3412	+	16.9350i	0.187204	+	0.148552i
$115$	−108.231	−	108.231i	−0.941135	−	0.941135i
$116$	129.630	+	90.6201i	1.11750	+	0.781208i
$117$	−54.3707	+	60.5756i	−0.464706	+	0.517740i
$118$	110.070	−	9.67223i	0.932797	−	0.0819681i
$119$	−26.5659			−0.223243
$120$	−51.3106	+	94.9389i	−0.427588	+	0.791157i
$121$			217.504i			1.79756i
$122$	−140.406	+	12.3379i	−1.15087	+	0.101131i
$123$	−98.2307	−	93.0711i	−0.798624	−	0.756676i
$124$	5.51798	+	31.1548i	0.0444998	+	0.251249i
$125$	94.6900	−	94.6900i	0.757520	−	0.757520i
$126$	65.2575	−	86.9521i	0.517917	−	0.690096i
$127$	93.6335			0.737272			0.368636	−	0.929574i	$-0.379825\pi$
$127$	93.6335			0.737272			0.368636	+	0.929574i	$0.379825\pi$
$128$	126.114	+	21.8899i	0.985268	+	0.171015i
$129$	152.720	−	4.11903i	1.18388	−	0.0319305i
$130$	62.3265	+	52.2576i	0.479434	+	0.401981i
$131$	81.5208	−	81.5208i	0.622296	−	0.622296i	−0.323822	−	0.946118i	$-0.604968\pi$
$131$	81.5208	−	81.5208i	0.622296	−	0.622296i	0.946118	+	0.323822i	$0.104968\pi$
$132$	−216.281	+	44.3518i	−1.63849	+	0.335998i
$133$	−19.3922	+	19.3922i	−0.145806	+	0.145806i
$134$	126.554	−	11.1208i	0.944436	−	0.0829909i
$135$	121.010	−	9.81037i	0.896371	−	0.0726694i
$136$	−17.5590	+	30.4937i	−0.129110	+	0.224218i
$137$	24.5510			0.179205			0.0896023	−	0.995978i	$-0.471440\pi$
$137$	24.5510			0.179205			0.0896023	+	0.995978i	$0.471440\pi$
$138$	202.898	−	23.3571i	1.47027	−	0.169254i
$139$	3.06917	−	3.06917i	0.0220804	−	0.0220804i	−0.695980	−	0.718061i	$-0.745030\pi$
$139$	3.06917	−	3.06917i	0.0220804	−	0.0220804i	0.718061	+	0.695980i	$0.245030\pi$
$140$	−89.0346	−	62.2414i	−0.635961	−	0.444581i
$141$	10.5011	−	11.0833i	0.0744762	−	0.0786050i
$142$	−60.0022	+	71.5633i	−0.422551	+	0.503967i
$143$			166.399i			1.16363i
$144$	−56.6755	−	132.378i	−0.393580	−	0.919290i
$145$	−177.798			−1.22620
$146$	−149.200	−	125.097i	−1.02192	−	0.856827i
$147$	−27.2674	−	25.8351i	−0.185492	−	0.175749i
$148$	−92.9312	−	64.9654i	−0.627913	−	0.438955i
$149$	−5.86344	−	5.86344i	−0.0393519	−	0.0393519i	0.687157	−	0.726509i	$-0.258858\pi$
$149$	−5.86344	−	5.86344i	−0.0393519	−	0.0393519i	−0.726509	+	0.687157i	$0.758858\pi$
$150$	3.28057	+	28.4976i	0.0218705	+	0.189984i
$151$		−	179.561i		−	1.18914i	−0.804043	−	0.594571i	$-0.797322\pi$
$151$		−	179.561i		−	1.18914i	0.804043	−	0.594571i	$-0.202678\pi$
$152$	9.44191	+	35.0769i	0.0621178	+	0.230769i
$153$	39.5288	−	2.13382i	0.258358	−	0.0139466i
$154$	−19.4546	−	221.393i	−0.126328	−	1.43762i
$155$	−25.1500	−	25.1500i	−0.162258	−	0.162258i
$156$	−106.318	+	21.8021i	−0.681524	+	0.139757i
$157$	−14.8689	−	14.8689i	−0.0947067	−	0.0947067i	0.658166	−	0.752873i	$-0.271332\pi$
$157$	−14.8689	−	14.8689i	−0.0947067	−	0.0947067i	−0.752873	+	0.658166i	$0.771332\pi$
$158$	−51.6100	+	61.5541i	−0.326646	+	0.389583i
$159$	2.37568	+	88.0822i	0.0149414	+	0.553976i
$160$	−130.292	+	61.0594i	−0.814326	+	0.381621i
$161$			205.592i			1.27697i
$162$	−90.1159	+	134.622i	−0.556271	+	0.831001i
$163$	66.1190	+	66.1190i	0.405638	+	0.405638i	0.880214	−	0.474577i	$-0.157399\pi$
$163$	66.1190	+	66.1190i	0.405638	+	0.405638i	−0.474577	+	0.880214i	$0.657399\pi$
$164$	−31.4665	−	177.662i	−0.191869	−	1.08330i
$165$	170.701	−	180.164i	1.03455	−	1.09191i
$166$	−8.80060	−	100.151i	−0.0530156	−	0.603318i
$167$	158.709			0.950353			0.475176	−	0.879891i	$-0.342384\pi$
$167$	158.709			0.950353			0.475176	+	0.879891i	$0.342384\pi$
$168$	138.906	−	41.4376i	0.826821	−	0.246653i
$169$		−	87.2028i		−	0.515993i
$170$	−3.46258	−	39.4042i	−0.0203681	−	0.231789i
$171$	27.2971	−	30.4123i	0.159632	−	0.177850i
$172$	166.951	+	116.710i	0.970645	+	0.678549i
$173$	−76.9955	+	76.9955i	−0.445061	+	0.445061i	−0.893709	−	0.448648i	$-0.851906\pi$
$173$	−76.9955	+	76.9955i	−0.445061	+	0.445061i	0.448648	+	0.893709i	$0.351906\pi$
$174$	147.472	−	185.843i	0.847542	−	1.06806i
$175$	−28.8760			−0.165006
$176$	−266.985	−	124.001i	−1.51696	−	0.704551i
$177$	−4.46861	−	165.681i	−0.0252464	−	0.936051i
$178$	−89.5375	+	106.789i	−0.503020	+	0.599941i
$179$	−101.360	+	101.360i	−0.566257	+	0.566257i	−0.931078	−	0.364821i	$-0.881130\pi$
$179$	−101.360	+	101.360i	−0.566257	+	0.566257i	0.364821	+	0.931078i	$0.381130\pi$
$180$	137.478	+	85.4607i	0.763769	+	0.474782i
$181$	−212.373	+	212.373i	−1.17333	+	1.17333i	−0.191920	+	0.981411i	$0.561471\pi$
$181$	−212.373	+	212.373i	−1.17333	+	1.17333i	−0.981411	+	0.191920i	$0.938529\pi$
$182$	−9.56332	−	108.831i	−0.0525457	−	0.597970i
$183$	5.70017	+	211.343i	0.0311485	+	1.15488i
$184$	235.989	+	135.888i	1.28255	+	0.738523i
$185$	127.463			0.688991
$186$	47.1482	−	5.42758i	0.253485	−	0.0291805i
$187$	57.2229	−	57.2229i	0.306005	−	0.306005i
$188$	20.0454	−	3.55034i	0.106625	−	0.0188848i
$189$	−124.252	−	105.616i	−0.657416	−	0.558815i
$190$	−31.2913	−	26.2362i	−0.164691	−	0.138085i
$191$			36.3314i			0.190217i	0.995467	+	0.0951083i	$0.0303197\pi$
$191$			36.3314i			0.190217i	−0.995467	+	0.0951083i	$0.969680\pi$
$192$	44.2471	−	186.832i	0.230453	−	0.973083i
$193$	47.1090			0.244088			0.122044	−	0.992525i	$-0.461055\pi$
$193$	47.1090			0.244088			0.122044	+	0.992525i	$0.461055\pi$
$194$	78.5050	−	93.6313i	0.404665	−	0.482635i
$195$	83.9119	−	88.5638i	0.430317	−	0.454173i
$196$	−8.73462	−	49.3162i	−0.0445644	−	0.251613i
$197$	32.2783	+	32.2783i	0.163849	+	0.163849i	0.784269	−	0.620420i	$-0.213038\pi$
$197$	32.2783	+	32.2783i	0.163849	+	0.163849i	−0.620420	+	0.784269i	$0.713038\pi$
$198$	46.7301	+	327.859i	0.236011	+	1.65585i
$199$			118.181i			0.593874i	0.954897	+	0.296937i	$0.0959651\pi$
$199$			118.181i			0.593874i	−0.954897	+	0.296937i	$0.904035\pi$
$200$	−19.0859	+	33.1454i	−0.0954295	+	0.165727i
$201$	−5.13784	−	190.494i	−0.0255614	−	0.947731i
$202$	−293.129	+	25.7583i	−1.45114	+	0.127516i
$203$	168.871	+	168.871i	0.831875	+	0.831875i
$204$	44.0590	+	29.0640i	0.215976	+	0.142471i
$205$	143.419	+	143.419i	0.699604	+	0.699604i
$206$	−87.8108	−	73.6249i	−0.426266	−	0.357402i
$207$	−16.5136	−	305.911i	−0.0797756	−	1.47783i
$208$	−131.242	−	60.9554i	−0.630972	−	0.293055i
$209$		−	83.5416i		−	0.399721i
$210$	−101.290	+	127.644i	−0.482332	+	0.607828i
$211$	63.8884	+	63.8884i	0.302789	+	0.302789i	0.842104	−	0.539315i	$-0.181317\pi$
$211$	63.8884	+	63.8884i	0.302789	+	0.302789i	−0.539315	+	0.842104i	$0.681317\pi$
$212$	−67.3134	+	96.2900i	−0.317516	+	0.454198i
$213$	101.689	+	96.3478i	0.477413	+	0.452337i
$214$	−260.475	+	22.8889i	−1.21717	+	0.106957i
$215$	−228.988			−1.06506
$216$	−203.357	+	72.8144i	−0.941468	+	0.337104i
$217$			47.7743i			0.220158i
$218$	212.374	−	18.6621i	0.974193	−	0.0856057i
$219$	−200.872	+	212.008i	−0.917226	+	0.968075i
$220$	325.848	−	57.7124i	1.48113	−	0.262329i
$221$	28.1292	−	28.1292i	0.127281	−	0.127281i
$222$	−105.723	+	133.230i	−0.476228	+	0.600136i
$223$	−42.8886			−0.192326			−0.0961628	−	0.995366i	$-0.530657\pi$
$223$	−42.8886			−0.192326			−0.0961628	+	0.995366i	$0.530657\pi$
$224$	181.743	+	65.7565i	0.811354	+	0.293556i
$225$	42.9661	−	2.31938i	0.190961	−	0.0103084i
$226$	172.039	+	144.246i	0.761233	+	0.638255i
$227$	−23.0035	+	23.0035i	−0.101337	+	0.101337i	−0.755958	−	0.654621i	$-0.772828\pi$
$227$	−23.0035	+	23.0035i	−0.101337	+	0.101337i	0.654621	+	0.755958i	$0.272828\pi$
$228$	53.3774	−	10.9459i	0.234111	−	0.0480081i
$229$	241.282	−	241.282i	1.05363	−	1.05363i	0.0551571	−	0.998478i	$-0.482434\pi$
$229$	241.282	−	241.282i	1.05363	−	1.05363i	0.998478	−	0.0551571i	$-0.0175660\pi$
$230$	−304.947	+	26.7968i	−1.32586	+	0.116508i
$231$	−333.248	+	8.98807i	−1.44263	+	0.0389094i
$232$	305.455	−	82.2217i	1.31662	−	0.354404i
$233$	−240.310			−1.03137			−0.515687	−	0.856777i	$-0.672463\pi$
$233$	−240.310			−1.03137			−0.515687	+	0.856777i	$0.672463\pi$
$234$	22.9712	+	161.166i	0.0981677	+	0.688745i
$235$	−16.1818	+	16.1818i	−0.0688589	+	0.0688589i
$236$	126.615	−	181.120i	0.536506	−	0.767457i
$237$	87.4663	+	82.8721i	0.369056	+	0.349671i
$238$	−34.1369	+	40.7143i	−0.143432	+	0.171069i
$239$		−	218.171i		−	0.912851i	−0.889762	−	0.456425i	$-0.849130\pi$
$239$		−	218.171i		−	0.912851i	0.889762	−	0.456425i	$-0.150870\pi$
$240$	79.5678	+	200.633i	0.331533	+	0.835971i
$241$	−88.9611			−0.369133			−0.184567	−	0.982820i	$-0.559088\pi$
$241$	−88.9611			−0.369133			−0.184567	+	0.982820i	$0.559088\pi$
$242$	333.343	+	279.491i	1.37745	+	1.15492i
$243$	193.364	+	147.172i	0.795736	+	0.605644i
$244$	−161.511	+	231.037i	−0.661931	+	0.946873i
$245$	39.8109	+	39.8109i	0.162493	+	0.162493i
$246$	−268.864	+	30.9510i	−1.09294	+	0.125817i
$247$		−	41.0667i		−	0.166262i
$248$	54.8378	+	31.5769i	0.221120	+	0.127326i
$249$	−150.750	+	4.06591i	−0.605423	+	0.0163289i
$250$	−23.4443	−	266.796i	−0.0937770	−	1.06718i
$251$	169.225	+	169.225i	0.674205	+	0.674205i	0.958683	−	0.284478i	$-0.0918201\pi$
$251$	169.225	+	169.225i	0.674205	+	0.674205i	−0.284478	+	0.958683i	$0.591820\pi$
$252$	−49.4058	−	211.745i	−0.196055	−	0.840258i
$253$	−442.845	−	442.845i	−1.75038	−	1.75038i
$254$	120.318	−	143.501i	0.473693	−	0.564964i
$255$	−59.3125	+	1.59973i	−0.232598	+	0.00627343i
$256$	195.604	−	165.152i	0.764077	−	0.645125i
$257$		−	393.109i		−	1.52961i	−0.644262	−	0.764804i	$-0.722836\pi$
$257$		−	393.109i		−	1.52961i	0.644262	−	0.764804i	$-0.277164\pi$
$258$	189.931	−	239.348i	0.736166	−	0.927707i
$259$	−121.063	−	121.063i	−0.467425	−	0.467425i
$260$	160.178	−	28.3698i	0.616068	−	0.109115i
$261$	−264.835	−	237.707i	−1.01470	−	0.910756i
$262$	−20.1837	−	229.690i	−0.0770370	−	0.876681i
$263$	−179.865			−0.683897			−0.341948	−	0.939719i	$-0.611087\pi$
$263$	−179.865			−0.683897			−0.341948	+	0.939719i	$0.611087\pi$
$264$	−209.947	+	388.460i	−0.795252	+	1.47144i
$265$		−	132.070i		−	0.498378i
$266$	4.80131	+	54.6390i	0.0180501	+	0.205410i
$267$	151.744	+	143.774i	0.568330	+	0.538478i
$268$	145.578	−	208.245i	0.543200	−	0.777033i
$269$	−290.530	+	290.530i	−1.08004	+	1.08004i	−0.0835324	+	0.996505i	$0.526620\pi$
$269$	−290.530	+	290.530i	−1.08004	+	1.08004i	−0.996505	+	0.0835324i	$0.973380\pi$
$270$	140.462	−	198.064i	0.520228	−	0.733570i
$271$	496.550			1.83229			0.916144	−	0.400849i	$-0.131285\pi$
$271$	496.550			1.83229			0.916144	+	0.400849i	$0.131285\pi$
$272$	24.1709	+	66.0947i	0.0888635	+	0.242995i
$273$	−163.815	+	4.41829i	−0.600056	+	0.0161842i
$274$	31.5478	−	37.6264i	0.115138	−	0.137323i
$275$	62.1989	−	62.1989i	0.226178	−	0.226178i
$276$	224.925	−	340.970i	0.814946	−	1.23540i
$277$	−93.0101	+	93.0101i	−0.335776	+	0.335776i	−0.854775	−	0.518999i	$-0.826305\pi$
$277$	−93.0101	+	93.0101i	−0.335776	+	0.335776i	0.518999	+	0.854775i	$0.326305\pi$
$278$	−0.759895	−	8.64760i	−0.00273343	−	0.0311065i
$279$	−3.83733	−	71.0859i	−0.0137539	−	0.254788i
$280$	−209.798	+	56.4730i	−0.749280	+	0.201689i
$281$	300.875			1.07073			0.535365	−	0.844621i	$-0.320174\pi$
$281$	300.875			1.07073			0.535365	+	0.844621i	$0.320174\pi$
$282$	−3.49218	−	30.3358i	−0.0123836	−	0.107574i
$283$	101.469	−	101.469i	0.358549	−	0.358549i	−0.504729	−	0.863278i	$-0.668408\pi$
$283$	101.469	−	101.469i	0.358549	−	0.358549i	0.863278	+	0.504729i	$0.168408\pi$
$284$	32.5743	+	183.916i	0.114698	+	0.647593i
$285$	−42.1284	+	44.4639i	−0.147819	+	0.156014i
$286$	255.020	+	213.821i	0.891679	+	0.747627i
$287$		−	272.435i		−	0.949250i
$288$	−275.707	−	83.2445i	−0.957316	−	0.289043i
$289$	269.653			0.933057
$290$	−228.469	+	272.490i	−0.787824	+	0.939621i
$291$	−133.047	−	126.058i	−0.457205	−	0.433190i
$292$	−383.442	+	67.9131i	−1.31316	+	0.232579i
$293$	321.104	+	321.104i	1.09592	+	1.09592i	0.994883	+	0.101037i	$0.0322160\pi$
$293$	321.104	+	321.104i	1.09592	+	1.09592i	0.101037	+	0.994883i	$0.467784\pi$
$294$	−74.6327	+	8.59153i	−0.253853	+	0.0292229i
$295$			248.422i			0.842107i
$296$	−218.980	+	58.9445i	−0.739798	+	0.199137i
$297$	495.135	−	40.1409i	1.66712	−	0.135155i
$298$	−16.5206	+	1.45173i	−0.0554384	+	0.00487156i
$299$	−217.690	−	217.690i	−0.728061	−	0.728061i
$300$	47.8903	+	31.5914i	0.159634	+	0.105305i
$301$	217.490	+	217.490i	0.722558	+	0.722558i
$302$	−275.191	−	230.733i	−0.911228	−	0.764018i
$303$	11.9004	+	441.228i	0.0392753	+	1.45620i
$304$	65.8909	+	30.6030i	0.216746	+	0.100668i
$305$		−	316.888i		−	1.03898i
$306$	47.5238	−	63.3229i	0.155307	−	0.206938i
$307$	94.2282	+	94.2282i	0.306932	+	0.306932i	0.843718	−	0.536786i	$-0.180362\pi$
$307$	94.2282	+	94.2282i	0.306932	+	0.306932i	−0.536786	+	0.843718i	$0.680362\pi$
$308$	−364.301	−	254.672i	−1.18280	−	0.826857i
$309$	−118.222	+	124.776i	−0.382596	+	0.403806i
$310$	−70.8619	+	6.22688i	−0.228587	+	0.0200867i
$311$	245.712			0.790070			0.395035	−	0.918666i	$-0.370732\pi$
$311$	245.712			0.790070			0.395035	+	0.918666i	$0.370732\pi$
$312$	−103.204	+	190.956i	−0.330782	+	0.612038i
$313$			353.841i			1.13048i	0.824925	+	0.565242i	$0.191217\pi$
$313$			353.841i			1.13048i	−0.824925	+	0.565242i	$0.808783\pi$
$314$	−41.8943	+	3.68140i	−0.133421	+	0.0117242i
$315$	181.899	+	163.267i	0.577458	+	0.518307i
$316$	28.0183	+	158.193i	0.0886654	+	0.500610i
$317$	−234.024	+	234.024i	−0.738245	+	0.738245i	−0.972238	−	0.233994i	$-0.924821\pi$
$317$	−234.024	+	234.024i	−0.738245	+	0.738245i	0.233994	+	0.972238i	$0.424821\pi$
$318$	138.046	+	109.544i	0.434106	+	0.344477i
$319$	−727.494			−2.28055
$320$	−73.8458	+	278.144i	−0.230768	+	0.869199i
$321$	10.5747	+	392.076i	0.0329431	+	1.22142i
$322$	315.086	+	264.184i	0.978529	+	0.820447i
$323$	−14.1224	+	14.1224i	−0.0437226	+	0.0437226i
$324$	90.5212	+	311.098i	0.279386	+	0.960179i
$325$	30.5752	−	30.5752i	0.0940777	−	0.0940777i
$326$	186.295	−	16.3704i	0.571456	−	0.0502158i
$327$	−8.62193	−	319.673i	−0.0263668	−	0.977592i
$328$	−312.715	−	180.069i	−0.953398	−	0.548989i
$329$	30.7386			0.0934305
$330$	−56.7670	−	493.122i	−0.172021	−	1.49431i
$331$	−32.5392	+	32.5392i	−0.0983058	+	0.0983058i	−0.754549	−	0.656243i	$-0.772144\pi$
$331$	−32.5392	+	32.5392i	−0.0983058	+	0.0983058i	0.656243	+	0.754549i	$0.272144\pi$
$332$	−164.798	−	115.205i	−0.496379	−	0.347004i
$333$	189.860	+	170.412i	0.570150	+	0.511748i
$334$	203.939	−	243.234i	0.610597	−	0.728246i
$335$			285.626i			0.852615i
$336$	114.986	−	266.131i	0.342221	−	0.792058i
$337$	−185.573			−0.550660			−0.275330	−	0.961350i	$-0.588787\pi$
$337$	−185.573			−0.550660			−0.275330	+	0.961350i	$0.588787\pi$
$338$	−133.645	−	112.055i	−0.395400	−	0.331523i
$339$	231.621	−	244.461i	0.683247	−	0.721124i
$340$	−64.8395	−	45.3273i	−0.190704	−	0.133316i
$341$	−102.906	−	102.906i	−0.301776	−	0.301776i
$342$	−11.5328	−	80.9145i	−0.0337217	−	0.236592i
$343$		−	371.574i		−	1.08330i
$344$	393.398	−	105.894i	1.14360	−	0.307831i
$345$	12.3802	+	459.016i	0.0358846	+	1.33048i
$346$	19.0633	+	216.940i	0.0550962	+	0.626995i
$347$	−51.9585	−	51.9585i	−0.149736	−	0.149736i	0.628264	−	0.778000i	$-0.283766\pi$
$347$	−51.9585	−	51.9585i	−0.149736	−	0.149736i	−0.778000	+	0.628264i	$0.783766\pi$
$348$	−95.3183	−	464.819i	−0.273903	−	1.33569i
$349$	378.719	+	378.719i	1.08515	+	1.08515i	0.996020	+	0.0891344i	$0.0284101\pi$
$349$	378.719	+	378.719i	1.08515	+	1.08515i	0.0891344	+	0.996020i	$0.471590\pi$
$350$	−37.1054	+	44.2548i	−0.106015	+	0.126442i
$351$	243.394	−	19.7322i	0.693431	−	0.0562170i
$352$	−533.114	+	249.835i	−1.51453	+	0.709760i
$353$		−	326.435i		−	0.924744i	−0.886686	−	0.462372i	$-0.846998\pi$
$353$		−	326.435i		−	0.924744i	0.886686	−	0.462372i	$-0.153002\pi$
$354$	−259.661	−	206.050i	−0.733507	−	0.582062i
$355$	−148.468	−	148.468i	−0.418220	−	0.418220i
$356$	48.6085	+	274.447i	0.136541	+	0.770918i
$357$	57.8537	+	54.8149i	0.162055	+	0.153543i
$358$	25.0957	+	285.589i	0.0700997	+	0.797734i
$359$	254.927			0.710103			0.355051	−	0.934847i	$-0.384463\pi$
$359$	254.927			0.710103			0.355051	+	0.934847i	$0.384463\pi$
$360$	307.634	−	100.880i	0.854539	−	0.280224i
$361$		−	340.382i		−	0.942887i
$362$	52.5813	+	598.375i	0.145252	+	1.65297i
$363$	448.789	−	473.668i	1.23633	−	1.30487i
$364$	−179.080	−	125.190i	−0.491979	−	0.343928i
$365$	309.536	−	309.536i	0.848045	−	0.848045i
$366$	331.225	+	262.838i	0.904986	+	0.718137i
$367$	−124.247			−0.338548			−0.169274	−	0.985569i	$-0.554142\pi$
$367$	−124.247			−0.338548			−0.169274	+	0.985569i	$0.554142\pi$
$368$	511.503	−	187.057i	1.38995	−	0.508308i
$369$	21.8825	+	405.370i	0.0593021	+	1.09856i
$370$	163.789	−	195.348i	0.442673	−	0.527966i
$371$	−125.439	+	125.439i	−0.338110	+	0.338110i
$372$	52.2668	−	79.2328i	0.140502	−	0.212991i
$373$	−201.674	+	201.674i	−0.540680	+	0.540680i	−0.923728	−	0.383048i	$-0.874874\pi$
$373$	−201.674	+	201.674i	−0.540680	+	0.540680i	0.383048	+	0.923728i	$0.374874\pi$
$374$	−14.1678	−	161.229i	−0.0378818	−	0.431095i
$375$	−401.589	+	10.8313i	−1.07091	+	0.0288835i
$376$	20.3170	−	35.2834i	0.0540346	−	0.0938388i
$377$	−357.616			−0.948583
$378$	−321.527	+	54.7099i	−0.850601	+	0.144735i
$379$	−227.541	+	227.541i	−0.600372	+	0.600372i	−0.940411	−	0.340040i	$-0.889560\pi$
$379$	−227.541	+	227.541i	−0.600372	+	0.600372i	0.340040	+	0.940411i	$0.389560\pi$
$380$	−80.4181	+	14.2432i	−0.211627	+	0.0374822i
$381$	−203.910	−	193.199i	−0.535196	−	0.507084i
$382$	55.6807	+	46.6854i	0.145761	+	0.122213i
$383$		−	128.933i		−	0.336641i	−0.985732	−	0.168320i	$-0.946166\pi$
$383$		−	128.933i		−	0.336641i	0.985732	−	0.168320i	$-0.0538343\pi$
$384$	−229.478	−	307.889i	−0.597599	−	0.801795i
$385$	499.671			1.29785
$386$	60.5346	−	72.1982i	0.156825	−	0.187042i
$387$	−341.084	−	306.145i	−0.881353	−	0.791073i
$388$	−42.6192	−	240.630i	−0.109843	−	0.620182i
$389$	−107.474	−	107.474i	−0.276283	−	0.276283i	0.555340	−	0.831623i	$-0.312588\pi$
$389$	−107.474	−	107.474i	−0.276283	−	0.276283i	−0.831623	+	0.555340i	$0.812588\pi$
$390$	−27.9051	−	242.405i	−0.0715515	−	0.621552i
$391$			149.723i			0.382922i
$392$	−86.8049	−	49.9843i	−0.221441	−	0.127511i
$393$	−345.738	+	9.32494i	−0.879739	+	0.0237276i
$394$	90.9463	−	7.99176i	0.230828	−	0.0202837i
$395$	−127.702	−	127.702i	−0.323297	−	0.323297i
$396$	562.518	+	349.678i	1.42050	+	0.883026i
$397$	−259.306	−	259.306i	−0.653163	−	0.653163i	0.300591	−	0.953753i	$-0.402816\pi$
$397$	−259.306	−	259.306i	−0.653163	−	0.653163i	−0.953753	+	0.300591i	$0.902816\pi$
$398$	181.122	+	151.861i	0.455080	+	0.381561i
$399$	82.2444	−	2.21822i	0.206126	−	0.00555946i
$400$	26.2728	+	71.8422i	0.0656819	+	0.179605i
$401$			335.810i			0.837431i	0.908117	+	0.418716i	$0.137520\pi$
$401$			335.810i			0.837431i	−0.908117	+	0.418716i	$0.862480\pi$
$402$	−298.549	−	236.909i	−0.742659	−	0.589325i
$403$	−50.5856	−	50.5856i	−0.125523	−	0.125523i
$404$	−337.192	+	482.343i	−0.834633	+	1.19392i
$405$	−283.771	−	228.322i	−0.700669	−	0.563759i
$406$	475.805	−	41.8106i	1.17193	−	0.102982i
$407$	521.539			1.28142
$408$	101.158	−	30.1770i	0.247937	−	0.0739632i
$409$		−	66.3618i		−	0.162254i	−0.996704	−	0.0811269i	$-0.974148\pi$
$409$		−	66.3618i		−	0.162254i	0.996704	−	0.0811269i	$-0.0258519\pi$
$410$	404.092	−	35.5090i	0.985591	−	0.0866073i
$411$	−53.4658	−	50.6575i	−0.130087	−	0.123254i
$412$	−225.672	+	39.9698i	−0.547747	+	0.0970140i
$413$	235.948	−	235.948i	0.571303	−	0.571303i
$414$	−490.053	−	367.784i	−1.18370	−	0.888368i
$415$	226.035			0.544662
$416$	−262.064	+	122.812i	−0.629961	+	0.295222i
$417$	−13.0167	+	0.351074i	−0.0312150	+	0.000841904i
$418$	−128.034	−	107.350i	−0.306302	−	0.256819i
$419$	−371.566	+	371.566i	−0.886792	+	0.886792i	−0.994214	−	0.107422i	$-0.965740\pi$
$419$	−371.566	+	371.566i	−0.886792	+	0.886792i	0.107422	+	0.994214i	$0.465740\pi$
$420$	65.4683	+	319.256i	0.155877	+	0.760133i
$421$	487.629	−	487.629i	1.15826	−	1.15826i	0.173416	−	0.984849i	$-0.444519\pi$
$421$	487.629	−	487.629i	1.15826	−	1.15826i	0.984849	−	0.173416i	$-0.0554806\pi$
$422$	180.010	−	15.8181i	0.426564	−	0.0374837i
$423$	−45.7376	+	2.46899i	−0.108127	+	0.00583685i
$424$	61.0750	+	226.895i	0.144045	+	0.535129i
$425$	−21.0290			−0.0494800
$426$	278.330	−	32.0406i	0.653357	−	0.0752128i
$427$	−300.976	+	300.976i	−0.704862	+	0.704862i
$428$	−299.629	+	428.611i	−0.700068	+	1.00143i
$429$	343.341	−	362.375i	0.800328	−	0.844696i
$430$	−294.247	+	350.942i	−0.684296	+	0.816145i
$431$		−	505.901i		−	1.17378i	−0.809665	−	0.586892i	$-0.800351\pi$
$431$		−	505.901i		−	1.17378i	0.809665	−	0.586892i	$-0.199649\pi$
$432$	−149.718	+	405.227i	−0.346569	+	0.938024i
$433$	−758.226			−1.75110			−0.875550	−	0.483128i	$-0.839500\pi$
$433$	−758.226			−1.75110			−0.875550	+	0.483128i	$0.839500\pi$
$434$	73.2180	+	61.3895i	0.168705	+	0.141451i
$435$	387.199	+	366.861i	0.890113	+	0.843359i
$436$	244.298	−	349.461i	0.560316	−	0.801516i
$437$	109.293	+	109.293i	0.250097	+	0.250097i
$438$	66.8005	+	580.282i	0.152513	+	1.32484i
$439$			145.760i			0.332026i	0.986124	+	0.166013i	$0.0530895\pi$
$439$			145.760i			0.332026i	−0.986124	+	0.166013i	$0.946911\pi$
$440$	330.263	−	573.548i	0.750597	−	1.30352i
$441$	6.07425	+	112.525i	0.0137738	+	0.255158i
$442$	−6.96449	−	79.2559i	−0.0157568	−	0.179312i
$443$	−607.046	−	607.046i	−1.37031	−	1.37031i	−0.859983	−	0.510323i	$-0.829526\pi$
$443$	−607.046	−	607.046i	−1.37031	−	1.37031i	−0.510323	−	0.859983i	$-0.670474\pi$
$444$	68.3335	+	333.228i	0.153904	+	0.750513i
$445$	−221.549	−	221.549i	−0.497864	−	0.497864i
$446$	−55.1114	+	65.7302i	−0.123568	+	0.147377i
$447$	0.670702	+	24.8674i	0.00150045	+	0.0556318i
$448$	334.315	−	194.040i	0.746240	−	0.433124i
$449$			190.654i			0.424620i	0.977202	+	0.212310i	$0.0680986\pi$
$449$			190.654i			0.424620i	−0.977202	+	0.212310i	$0.931901\pi$
$450$	51.6564	−	68.8294i	0.114792	−	0.152954i
$451$	586.824	+	586.824i	1.30116	+	1.30116i
$452$	442.136	−	78.3087i	0.978177	−	0.173249i
$453$	−370.497	+	391.037i	−0.817875	+	0.863216i
$454$	5.69542	+	64.8139i	0.0125450	+	0.142762i
$455$	245.624			0.539834
$456$	51.8141	−	95.8705i	0.113627	−	0.210242i
$457$		−	128.091i		−	0.280287i	−0.990131	−	0.140143i	$-0.955244\pi$
$457$		−	128.091i		−	0.280287i	0.990131	−	0.140143i	$-0.0447563\pi$
$458$	−59.7390	−	679.830i	−0.130435	−	1.48434i
$459$	−90.4863	−	76.9150i	−0.197138	−	0.167571i
$460$	−350.786	+	501.789i	−0.762578	+	1.09085i
$461$	74.2060	−	74.2060i	0.160968	−	0.160968i	−0.622028	−	0.782995i	$-0.713691\pi$
$461$	74.2060	−	74.2060i	0.160968	−	0.160968i	0.782995	+	0.622028i	$0.213691\pi$
$462$	−414.445	+	522.278i	−0.897067	+	1.13047i
$463$	620.192			1.33951			0.669753	−	0.742584i	$-0.266400\pi$
$463$	620.192			1.33951			0.669753	+	0.742584i	$0.266400\pi$
$464$	266.496	−	573.789i	0.574344	−	1.23661i
$465$	2.87684	+	106.664i	0.00618675	+	0.229384i
$466$	−308.796	+	368.294i	−0.662653	+	0.790331i
$467$	−331.708	+	331.708i	−0.710296	+	0.710296i	−0.966597	−	0.256301i	$-0.917496\pi$
$467$	−331.708	+	331.708i	−0.710296	+	0.710296i	0.256301	+	0.966597i	$0.417496\pi$
$468$	276.518	+	171.892i	0.590851	+	0.367291i
$469$	271.284	−	271.284i	0.578431	−	0.578431i
$470$	4.00646	+	45.5935i	0.00852437	+	0.0970074i
$471$	1.70082	+	63.0607i	0.00361108	+	0.133887i
$472$	−114.881	−	426.785i	−0.243392	−	0.904206i
$473$	−936.946			−1.98086
$474$	239.401	−	27.5593i	0.505066	−	0.0581419i
$475$	−15.3505	+	15.3505i	−0.0323168	+	0.0323168i
$476$	18.5324	+	104.635i	0.0389336	+	0.219822i
$477$	176.571	−	196.722i	0.370170	−	0.412415i
$478$	−334.365	−	280.348i	−0.699508	−	0.586502i
$479$			867.941i			1.81198i	0.423294	+	0.905992i	$0.360874\pi$
$479$			867.941i			1.81198i	−0.423294	+	0.905992i	$0.639126\pi$
$480$	409.730	+	135.867i	0.853604	+	0.283057i
$481$	256.374			0.533002
$482$	−114.314	+	136.340i	−0.237166	+	0.282863i
$483$	424.210	−	447.727i	0.878281	−	0.926970i
$484$	856.684	−	151.731i	1.77001	−	0.313494i
$485$	194.251	+	194.251i	0.400517	+	0.400517i
$486$	474.023	−	107.231i	0.975355	−	0.220641i
$487$			815.778i			1.67511i	0.546354	+	0.837554i	$0.316015\pi$
$487$			815.778i			1.67511i	−0.546354	+	0.837554i	$0.683985\pi$
$488$	146.543	+	544.409i	0.300292	+	1.11559i
$489$	−7.56317	−	280.417i	−0.0154666	−	0.573450i
$490$	112.170	−	9.85676i	0.228918	−	0.0201158i
$491$	337.746	+	337.746i	0.687874	+	0.687874i	0.961762	−	0.273888i	$-0.0883098\pi$
$491$	337.746	+	337.746i	0.687874	+	0.687874i	−0.273888	+	0.961762i	$0.588310\pi$
$492$	−298.053	+	451.828i	−0.605799	+	0.918349i
$493$	122.980	+	122.980i	0.249453	+	0.249453i
$494$	−62.9380	−	52.7703i	−0.127405	−	0.106823i
$495$	−743.486	+	40.1345i	−1.50199	+	0.0810799i
$496$	118.860	−	43.4673i	0.239637	−	0.0876357i
$497$			282.026i			0.567457i
$498$	−187.481	+	236.261i	−0.376468	+	0.474421i
$499$	−515.289	−	515.289i	−1.03264	−	1.03264i	−0.999449	−	0.0331940i	$-0.989432\pi$
$499$	−515.289	−	515.289i	−1.03264	−	1.03264i	−0.0331940	−	0.999449i	$-0.510568\pi$
$500$	−439.011	−	306.900i	−0.878022	−	0.613799i
$501$	−345.627	−	327.473i	−0.689875	−	0.653639i
$502$	476.805	−	41.8985i	0.949810	−	0.0834631i
$503$	196.781			0.391215			0.195607	−	0.980682i	$-0.437332\pi$
$503$	196.781			0.391215			0.195607	+	0.980682i	$0.437332\pi$
$504$	−388.002	−	196.372i	−0.769845	−	0.389627i
$505$		−	661.576i		−	1.31005i
$506$	−1247.75	+	109.644i	−2.46590	+	0.216687i
$507$	−179.930	+	189.905i	−0.354892	+	0.374567i
$508$	−65.3188	−	368.794i	−0.128580	−	0.725973i
$509$	−29.3054	+	29.3054i	−0.0575744	+	0.0575744i	−0.735308	−	0.677733i	$-0.762962\pi$
$509$	−29.3054	+	29.3054i	−0.0575744	+	0.0575744i	0.677733	+	0.735308i	$0.262962\pi$
$510$	−73.7642	+	92.9567i	−0.144636	+	0.182268i
$511$	−587.988			−1.15066
$512$	−1.75962	−	511.997i	−0.00343675	−	0.999994i
$513$	−122.197	+	9.90664i	−0.238202	+	0.0193112i
$514$	−602.472	−	505.142i	−1.17212	−	0.982766i
$515$	182.175	−	182.175i	0.353739	−	0.353739i
$516$	−122.761	−	598.644i	−0.237909	−	1.16016i
$517$	−66.2109	+	66.2109i	−0.128068	+	0.128068i
$518$	−341.104	+	29.9740i	−0.658501	+	0.0578648i
$519$	326.546	−	8.80731i	0.629182	−	0.0169698i
$520$	162.348	−	281.940i	0.312207	−	0.542193i
$521$	770.641			1.47916			0.739578	−	0.673071i	$-0.235025\pi$
$521$	770.641			1.47916			0.739578	+	0.673071i	$0.235025\pi$
$522$	−704.617	+	100.430i	−1.34984	+	0.192394i
$523$	258.725	−	258.725i	0.494694	−	0.494694i	−0.415087	−	0.909782i	$-0.636249\pi$
$523$	258.725	−	258.725i	0.494694	−	0.494694i	0.909782	+	0.415087i	$0.136249\pi$
$524$	−377.955	−	264.217i	−0.721288	−	0.504231i
$525$	62.8846	+	59.5815i	0.119780	+	0.113489i
$526$	−231.125	+	275.657i	−0.439400	+	0.524063i
$527$			34.7917i			0.0660183i
$528$	325.566	+	820.927i	0.616603	+	1.55479i
$529$	629.695			1.19035
$530$	−202.408	−	169.709i	−0.381902	−	0.320205i
$531$	−332.127	+	370.031i	−0.625475	+	0.696857i
$532$	89.9082	+	62.8521i	0.169000	+	0.118143i
$533$	288.466	+	288.466i	0.541212	+	0.541212i
$534$	415.334	−	47.8122i	0.777780	−	0.0895360i
$535$		−	587.878i		−	1.09884i
$536$	−132.086	−	490.702i	−0.246429	−	0.915489i
$537$	429.878	−	11.5943i	0.800517	−	0.0215909i
$538$	71.9322	+	818.589i	0.133703	+	1.52154i
$539$	162.894	+	162.894i	0.302214	+	0.302214i
$540$	−123.057	−	469.778i	−0.227883	−	0.869960i
$541$	−122.667	−	122.667i	−0.226742	−	0.226742i	0.584588	−	0.811330i	$-0.301256\pi$
$541$	−122.667	−	122.667i	−0.226742	−	0.226742i	−0.811330	+	0.584588i	$0.801256\pi$
$542$	638.062	−	761.003i	1.17724	−	1.40406i
$543$	900.694	−	24.2927i	1.65874	−	0.0447380i
$544$	132.355	+	47.8872i	0.243299	+	0.0880279i
$545$			479.316i			0.879479i
$546$	−203.730	+	256.737i	−0.373131	+	0.470215i
$547$	334.075	+	334.075i	0.610740	+	0.610740i	0.943139	−	0.332399i	$-0.107858\pi$
$547$	334.075	+	334.075i	0.610740	+	0.610740i	−0.332399	+	0.943139i	$0.607858\pi$
$548$	−17.1268	−	96.6991i	−0.0312533	−	0.176458i
$549$	423.663	−	472.013i	0.771699	−	0.859768i
$550$	−15.3998	−	175.250i	−0.0279996	−	0.318636i
$551$	179.543			0.325849
$552$	−233.538	−	782.859i	−0.423076	−	1.41822i
$553$			242.581i			0.438663i
$554$	23.0283	+	262.062i	0.0415674	+	0.473037i
$555$	−277.582	−	263.002i	−0.500148	−	0.473878i
$556$	−14.2296	−	9.94748i	−0.0255928	−	0.0178912i
$557$	−159.480	+	159.480i	−0.286320	+	0.286320i	−0.835623	−	0.549303i	$-0.814893\pi$
$557$	−159.480	+	159.480i	−0.286320	+	0.286320i	0.549303	+	0.835623i	$0.314893\pi$
$558$	−113.876	−	85.4636i	−0.204078	−	0.153161i
$559$	−460.576			−0.823929
$560$	−183.040	+	394.100i	−0.326856	+	0.703750i
$561$	−242.688	+	6.54557i	−0.432599	+	0.0116677i
$562$	386.621	−	461.115i	0.687938	−	0.820489i
$563$	341.226	−	341.226i	0.606086	−	0.606086i	−0.335835	−	0.941921i	$-0.609018\pi$
$563$	341.226	−	341.226i	0.606086	−	0.606086i	0.941921	+	0.335835i	$0.109018\pi$
$564$	−50.9794	−	33.6291i	−0.0903890	−	0.0596261i
$565$	−356.918	+	356.918i	−0.631713	+	0.631713i
$566$	−25.1227	−	285.897i	−0.0443865	−	0.505118i
$567$	52.6646	+	486.380i	0.0928828	+	0.857813i
$568$	323.724	+	186.408i	0.569937	+	0.328183i
$569$	882.975			1.55180			0.775901	−	0.630855i	$-0.217296\pi$
$569$	882.975			1.55180			0.775901	+	0.630855i	$0.217296\pi$
$570$	14.0099	+	121.701i	0.0245788	+	0.213510i
$571$	370.112	−	370.112i	0.648181	−	0.648181i	−0.304372	−	0.952553i	$-0.598447\pi$
$571$	370.112	−	370.112i	0.648181	−	0.648181i	0.952553	+	0.304372i	$0.0984466\pi$
$572$	655.397	−	116.080i	1.14580	−	0.202938i
$573$	74.9645	−	79.1204i	0.130828	−	0.138081i
$574$	−417.528	−	350.076i	−0.727401	−	0.609889i
$575$			162.742i			0.283030i
$576$	−481.860	+	315.575i	−0.836562	+	0.547873i
$577$	−698.607			−1.21076			−0.605378	−	0.795938i	$-0.706978\pi$
$577$	−698.607			−1.21076			−0.605378	+	0.795938i	$0.706978\pi$
$578$	346.502	−	413.265i	0.599484	−	0.714992i
$579$	−102.591	−	97.2025i	−0.177187	−	0.167880i
$580$	124.032	+	700.294i	0.213849	+	1.20740i
$581$	−214.685	−	214.685i	−0.369509	−	0.369509i
$582$	−364.158	+	41.9210i	−0.625702	+	0.0720292i
$583$		−	540.389i		−	0.926911i
$584$	−388.636	+	674.922i	−0.665473	+	1.15569i
$585$	−365.477	+	19.7290i	−0.624747	+	0.0337248i
$586$	904.734	−	79.5021i	1.54392	−	0.135669i
$587$	−196.072	−	196.072i	−0.334024	−	0.334024i	0.520088	−	0.854112i	$-0.325899\pi$
$587$	−196.072	−	196.072i	−0.334024	−	0.334024i	−0.854112	+	0.520088i	$0.825899\pi$
$588$	−82.7351	+	125.421i	−0.140706	+	0.213300i
$589$	25.3968	+	25.3968i	0.0431185	+	0.0431185i
$590$	380.726	+	319.219i	0.645298	+	0.541050i
$591$	−3.69222	−	136.895i	−0.00624742	−	0.231633i
$592$	−191.050	+	411.348i	−0.322720	+	0.694844i
$593$		−	774.011i		−	1.30525i	−0.757683	−	0.652623i	$-0.773669\pi$
$593$		−	774.011i		−	1.30525i	0.757683	−	0.652623i	$-0.226331\pi$
$594$	574.724	−	810.414i	0.967549	−	1.36433i
$595$	−84.4675	−	84.4675i	−0.141962	−	0.141962i
$596$	−19.0040	+	27.1847i	−0.0318859	+	0.0456118i
$597$	243.849	−	257.368i	0.408458	−	0.431102i
$598$	−613.357	+	53.8978i	−1.02568	+	0.0901301i
$599$	−783.533			−1.30807			−0.654034	−	0.756465i	$-0.726925\pi$
$599$	−783.533			−1.30807			−0.654034	+	0.756465i	$0.726925\pi$
$600$	109.955	−	32.8011i	0.183258	−	0.0546685i
$601$			797.210i			1.32647i	0.748410	+	0.663236i	$0.230818\pi$
$601$			797.210i			1.32647i	−0.748410	+	0.663236i	$0.769182\pi$
$602$	612.793	−	53.8482i	1.01793	−	0.0894489i
$603$	−381.868	+	425.448i	−0.633280	+	0.705552i
$604$	−707.235	+	125.262i	−1.17092	+	0.207387i
$605$	−691.565	+	691.565i	−1.14308	+	1.14308i
$606$	691.509	+	548.735i	1.14110	+	0.905504i
$607$	433.576			0.714293			0.357146	−	0.934048i	$-0.383750\pi$
$607$	433.576			0.714293			0.357146	+	0.934048i	$0.383750\pi$
$608$	131.571	−	61.6585i	0.216399	−	0.101412i
$609$	−19.3167	−	716.197i	−0.0317186	−	1.17602i
$610$	−485.656	−	407.197i	−0.796157	−	0.667537i
$611$	−32.5475	+	32.5475i	−0.0532692	+	0.0532692i
$612$	−35.9798	−	154.203i	−0.0587905	−	0.251966i
$613$	−493.642	+	493.642i	−0.805289	+	0.805289i	−0.983917	−	0.178628i	$-0.942834\pi$
$613$	−493.642	+	493.642i	−0.805289	+	0.805289i	0.178628	+	0.983917i	$0.442834\pi$
$614$	265.494	−	23.3299i	0.432401	−	0.0379966i
$615$	−16.4053	−	608.253i	−0.0266752	−	0.989029i
$616$	−858.428	+	231.070i	−1.39355	+	0.375113i
$617$	−685.069			−1.11032			−0.555161	−	0.831743i	$-0.687343\pi$
$617$	−685.069			−1.11032			−0.555161	+	0.831743i	$0.687343\pi$
$618$	39.3150	+	341.521i	0.0636165	+	0.552623i
$619$	−379.995	+	379.995i	−0.613885	+	0.613885i	−0.943956	−	0.330071i	$-0.892927\pi$
$619$	−379.995	+	379.995i	−0.613885	+	0.613885i	0.330071	+	0.943956i	$0.392927\pi$
$620$	−81.5136	+	116.603i	−0.131474	+	0.188069i
$621$	−595.241	+	700.269i	−0.958520	+	1.12765i
$622$	315.737	−	376.573i	0.507616	−	0.605422i
$623$			420.850i			0.675521i
$624$	160.039	+	403.545i	0.256473	+	0.646706i
$625$	482.618			0.772189
$626$	542.290	+	454.683i	0.866278	+	0.726330i
$627$	−172.376	+	181.932i	−0.274922	+	0.290163i
$628$	−48.1917	+	68.9369i	−0.0767384	+	0.109772i
$629$	−88.1642	−	88.1642i	−0.140166	−	0.140166i
$630$	483.958	−	68.9790i	0.768187	−	0.109491i
$631$			489.285i			0.775412i	0.921783	+	0.387706i	$0.126732\pi$
$631$			489.285i			0.775412i	−0.921783	+	0.387706i	$0.873268\pi$
$632$	278.446	+	160.336i	0.440580	+	0.253696i
$633$	−7.30802	−	270.957i	−0.0115451	−	0.428052i
$634$	57.9418	+	659.378i	0.0913908	+	1.04003i
$635$	297.712	+	297.712i	0.468838	+	0.468838i
$636$	345.272	−	70.8033i	0.542880	−	0.111326i
$637$	80.0739	+	80.0739i	0.125705	+	0.125705i
$638$	−934.823	+	1114.94i	−1.46524	+	1.74756i
$639$	−22.6529	−	419.641i	−0.0354505	−	0.656716i
$640$	331.386	+	470.587i	0.517791	+	0.735291i
$641$		−	492.158i		−	0.767797i	−0.923375	−	0.383898i	$-0.874581\pi$
$641$		−	492.158i		−	0.767797i	0.923375	−	0.383898i	$-0.125419\pi$
$642$	614.476	+	487.607i	0.957128	+	0.759513i
$643$	−169.985	−	169.985i	−0.264362	−	0.264362i	0.562462	−	0.826823i	$-0.309854\pi$
$643$	−169.985	−	169.985i	−0.264362	−	0.264362i	−0.826823	+	0.562462i	$0.809854\pi$
$644$	809.766	−	143.421i	1.25740	−	0.222704i
$645$	498.677	+	472.483i	0.773142	+	0.732532i
$646$	3.49656	+	39.7908i	0.00541263	+	0.0615957i
$647$	−1003.50			−1.55101			−0.775503	−	0.631343i	$-0.782504\pi$
$647$	−1003.50			−1.55101			−0.775503	+	0.631343i	$0.782504\pi$
$648$	593.101	+	261.027i	0.915280	+	0.402819i
$649$			1016.46i			1.56620i
$650$	−7.57011	−	86.1479i	−0.0116463	−	0.132535i
$651$	98.5754	−	104.040i	0.151422	−	0.159816i
$652$	214.298	−	306.547i	0.328678	−	0.470165i
$653$	407.090	−	407.090i	0.623415	−	0.623415i	−0.322988	−	0.946403i	$-0.604687\pi$
$653$	407.090	−	407.090i	0.623415	−	0.623415i	0.946403	+	0.322988i	$0.104687\pi$
$654$	−501.003	−	397.562i	−0.766059	−	0.607893i
$655$	518.398			0.791448
$656$	−677.805	+	247.874i	−1.03324	+	0.377856i
$657$	874.897	−	47.2283i	1.33165	−	0.0718848i
$658$	39.4988	−	47.1094i	0.0600286	−	0.0715948i
$659$	635.355	−	635.355i	0.964119	−	0.964119i	−0.0352587	−	0.999378i	$-0.511226\pi$
$659$	635.355	−	635.355i	0.964119	−	0.964119i	0.999378	+	0.0352587i	$0.0112255\pi$
$660$	−828.694	−	546.658i	−1.25560	−	0.828269i
$661$	−196.325	+	196.325i	−0.297013	+	0.297013i	−0.839843	−	0.542830i	$-0.817353\pi$
$661$	−196.325	+	196.325i	−0.297013	+	0.297013i	0.542830	+	0.839843i	$0.317353\pi$
$662$	8.05637	+	91.6815i	0.0121697	+	0.138492i
$663$	−119.299	+	3.21762i	−0.179937	+	0.00485312i
$664$	−388.325	+	104.528i	−0.584826	+	0.157422i
$665$	−123.317			−0.185439
$666$	505.138	−	71.9979i	0.758466	−	0.108105i
$667$	951.737	−	951.737i	1.42689	−	1.42689i
$668$	−110.715	−	625.107i	−0.165742	−	0.935788i
$669$	93.4003	+	88.4944i	0.139612	+	0.132279i
$670$	437.745	+	367.027i	0.653350	+	0.547801i
$671$		−	1296.60i		−	1.93234i
$672$	−260.111	−	518.202i	−0.387070	−	0.771134i
$673$	−489.653			−0.727568			−0.363784	−	0.931483i	$-0.618515\pi$
$673$	−489.653			−0.727568			−0.363784	+	0.931483i	$0.618515\pi$
$674$	−238.459	+	284.405i	−0.353797	+	0.421966i
$675$	−98.3549	−	83.6034i	−0.145711	−	0.123857i
$676$	−343.466	+	60.8327i	−0.508085	+	0.0899893i
$677$	−832.940	−	832.940i	−1.23034	−	1.23034i	−0.963833	−	0.266507i	$-0.914131\pi$
$677$	−832.940	−	832.940i	−1.23034	−	1.23034i	−0.266507	−	0.963833i	$-0.585869\pi$
$678$	−77.0259	−	669.107i	−0.113608	−	0.986884i
$679$		−	368.994i		−	0.543438i
$680$	−152.786	+	41.1265i	−0.224685	+	0.0604801i
$681$	97.5600	−	2.63131i	0.143260	−	0.00386388i
$682$	−289.944	+	25.4784i	−0.425138	+	0.0373584i
$683$	773.804	+	773.804i	1.13295	+	1.13295i	0.989684	+	0.143264i	$0.0457599\pi$
$683$	773.804	+	773.804i	1.13295	+	1.13295i	0.143264	+	0.989684i	$0.454240\pi$
$684$	−138.827	−	86.2993i	−0.202964	−	0.126169i
$685$	78.0611	+	78.0611i	0.113958	+	0.113958i
$686$	−569.466	−	477.468i	−0.830125	−	0.696018i
$687$	−1023.30	+	27.5996i	−1.48952	+	0.0401741i
$688$	343.222	−	738.987i	0.498869	−	1.07411i
$689$		−	265.640i		−	0.385545i
$690$	719.388	+	570.858i	1.04259	+	0.827330i
$691$	−840.306	−	840.306i	−1.21607	−	1.21607i	−0.968996	−	0.247077i	$-0.920530\pi$
$691$	−840.306	−	840.306i	−1.21607	−	1.21607i	−0.247077	−	0.968996i	$-0.579470\pi$
$692$	356.974	+	249.550i	0.515859	+	0.360622i
$693$	744.274	+	668.035i	1.07399	+	0.963975i
$694$	−146.397	+	12.8644i	−0.210946	+	0.0185366i
$695$	19.5171			0.0280822
$696$	−834.856	−	451.205i	−1.19951	−	0.648283i
$697$		−	198.401i		−	0.284650i
$698$	1067.07	−	93.7668i	1.52875	−	0.134336i
$699$	523.334	+	495.845i	0.748689	+	0.709364i
$700$	20.1440	+	113.734i	0.0287771	+	0.162477i
$701$	529.432	−	529.432i	0.755253	−	0.755253i	−0.220201	−	0.975454i	$-0.570671\pi$
$701$	529.432	−	529.432i	0.755253	−	0.755253i	0.975454	+	0.220201i	$0.0706715\pi$
$702$	282.518	−	398.377i	0.402448	−	0.567488i
$703$	−128.714			−0.183092
$704$	−302.153	+	1138.08i	−0.429195	+	1.61659i
$705$	68.6288	−	1.85100i	0.0973458	−	0.00262553i
$706$	−500.287	−	419.465i	−0.708622	−	0.594144i
$707$	−628.357	+	628.357i	−0.888765	+	0.888765i
$708$	−649.450	+	133.180i	−0.917303	+	0.188107i
$709$	−56.2182	+	56.2182i	−0.0792923	+	0.0792923i	−0.745641	−	0.666348i	$-0.767856\pi$
$709$	−56.2182	+	56.2182i	−0.0792923	+	0.0792923i	0.666348	+	0.745641i	$0.267856\pi$
$710$	−418.319	+	36.7591i	−0.589181	+	0.0517734i
$711$	−19.4845	−	360.948i	−0.0274044	−	0.507663i
$712$	483.073	+	278.165i	0.678473	+	0.390681i
$713$	269.251			0.377631
$714$	158.350	−	18.2288i	0.221778	−	0.0255305i
$715$	−529.074	+	529.074i	−0.739964	+	0.739964i
$716$	469.936	+	328.518i	0.656335	+	0.458824i
$717$	−450.165	+	475.121i	−0.627845	+	0.662651i
$718$	327.578	−	390.696i	0.456237	−	0.544144i
$719$		−	966.944i		−	1.34485i	−0.740167	−	0.672423i	$-0.765254\pi$
$719$		−	966.944i		−	1.34485i	0.740167	−	0.672423i	$-0.234746\pi$
$720$	240.699	−	601.104i	0.334304	−	0.834866i
$721$	−346.056			−0.479967
$722$	−521.663	−	437.388i	−0.722525	−	0.605800i
$723$	193.734	+	183.558i	0.267959	+	0.253884i
$724$	984.624	+	688.321i	1.35998	+	0.950720i
$725$	133.674	+	133.674i	0.184378	+	0.184378i
$726$	−149.246	−	1296.46i	−0.205572	−	1.78576i
$727$		−	1338.18i		−	1.84069i	−0.391110	−	0.920344i	$-0.627909\pi$
$727$		−	1338.18i		−	1.84069i	0.391110	−	0.920344i	$-0.372091\pi$
$728$	−421.979	+	113.587i	−0.579642	+	0.156027i
$729$	−117.429	−	719.480i	−0.161083	−	0.986941i
$730$	−76.6380	−	872.140i	−0.104984	−	1.19471i
$731$	158.387	+	158.387i	0.216672	+	0.216672i
$732$	828.441	−	169.885i	1.13175	−	0.232083i
$733$	757.046	+	757.046i	1.03280	+	1.03280i	0.999443	+	0.0333615i	$0.0106213\pi$
$733$	757.046	+	757.046i	1.03280	+	1.03280i	0.0333615	+	0.999443i	$0.489379\pi$
$734$	−159.656	+	190.418i	−0.217515	+	0.259426i
$735$	−4.55386	−	168.842i	−0.00619573	−	0.229717i
$736$	370.596	−	1024.29i	0.503528	−	1.39169i
$737$			1168.69i			1.58574i
$738$	649.380	+	487.360i	0.879919	+	0.660379i
$739$	495.335	+	495.335i	0.670278	+	0.670278i	0.957780	−	0.287502i	$-0.0928249\pi$
$739$	495.335	+	495.335i	0.670278	+	0.670278i	−0.287502	+	0.957780i	$0.592825\pi$
$740$	−88.9185	−	502.039i	−0.120160	−	0.678432i
$741$	−84.7353	+	89.4328i	−0.114353	+	0.120692i
$742$	31.0573	+	353.432i	0.0418562	+	0.476324i
$743$	−1421.01			−1.91253			−0.956266	−	0.292500i	$-0.905513\pi$
$743$	−1421.01			−1.91253			−0.956266	+	0.292500i	$0.905513\pi$
$744$	−54.2682	−	181.916i	−0.0729412	−	0.244511i
$745$		−	37.2861i		−	0.0500485i
$746$	49.9323	+	568.230i	0.0669334	+	0.761702i
$747$	336.685	+	302.197i	0.450716	+	0.404547i
$748$	−265.302	−	185.465i	−0.354682	−	0.247948i
$749$	−558.359	+	558.359i	−0.745473	+	0.745473i
$750$	−499.439	+	629.386i	−0.665918	+	0.839181i
$751$	−143.509			−0.191090			−0.0955452	−	0.995425i	$-0.530459\pi$
$751$	−143.509			−0.191090			−0.0955452	+	0.995425i	$0.530459\pi$
$752$	−27.9674	−	76.4762i	−0.0371907	−	0.101697i
$753$	−19.3572	−	717.702i	−0.0257068	−	0.953123i
$754$	−459.533	+	548.075i	−0.609460	+	0.726890i
$755$	570.921	−	570.921i	0.756187	−	0.756187i
$756$	−329.312	+	563.068i	−0.435598	+	0.744799i
$757$	651.883	−	651.883i	0.861140	−	0.861140i	−0.130331	−	0.991471i	$-0.541604\pi$
$757$	651.883	−	651.883i	0.861140	−	0.861140i	0.991471	+	0.130331i	$0.0416040\pi$
$758$	56.3367	+	641.112i	0.0743229	+	0.845794i
$759$	50.6558	+	1878.15i	0.0667402	+	2.47450i
$760$	−81.5076	+	141.550i	−0.107247	+	0.186249i
$761$	434.623			0.571122			0.285561	−	0.958361i	$-0.407820\pi$
$761$	434.623			0.571122			0.285561	+	0.958361i	$0.407820\pi$
$762$	−558.115	+	64.2488i	−0.732434	+	0.0843160i
$763$	455.249	−	455.249i	0.596656	−	0.596656i
$764$	143.098	−	25.3448i	0.187301	−	0.0331738i
$765$	132.468	+	118.899i	0.173161	+	0.155423i
$766$	−197.601	−	165.678i	−0.257964	−	0.216290i
$767$			499.665i			0.651453i
$768$	−766.742	−	43.9417i	−0.998362	−	0.0572157i
$769$	17.1894			0.0223529			0.0111764	−	0.999938i	$-0.496442\pi$
$769$	17.1894			0.0223529			0.0111764	+	0.999938i	$0.496442\pi$
$770$	642.072	−	765.786i	0.833860	−	0.994527i
$771$	−811.125	+	856.091i	−1.05204	+	1.11036i
$772$	−32.8633	−	185.548i	−0.0425690	−	0.240347i
$773$	553.125	+	553.125i	0.715557	+	0.715557i	0.967692	−	0.252135i	$-0.0811328\pi$
$773$	553.125	+	553.125i	0.715557	+	0.715557i	−0.252135	+	0.967692i	$0.581133\pi$
$774$	−907.481	+	129.344i	−1.17246	+	0.167112i
$775$			37.8171i			0.0487963i
$776$	−423.551	−	243.891i	−0.545813	−	0.314292i
$777$	13.8481	+	513.440i	0.0178225	+	0.660798i
$778$	−302.815	+	26.6094i	−0.389223	+	0.0342024i
$779$	−144.826	−	144.826i	−0.185913	−	0.185913i
$780$	−407.363	−	268.722i	−0.522260	−	0.344515i
$781$	−607.484	−	607.484i	−0.777828	−	0.777828i
$782$	229.462	+	192.392i	0.293429	+	0.246026i
$783$	86.2686	+	1064.12i	0.110177	+	1.35902i
$784$	−188.148	+	68.8061i	−0.239985	+	0.0877628i
$785$		−	94.5530i		−	0.120450i
$786$	−429.978	+	541.853i	−0.547046	+	0.689380i
$787$	274.851	+	274.851i	0.349239	+	0.349239i	0.859826	−	0.510587i	$-0.170572\pi$
$787$	274.851	+	274.851i	0.349239	+	0.349239i	−0.510587	+	0.859826i	$0.670572\pi$
$788$	104.617	−	149.652i	0.132763	−	0.189913i
$789$	391.699	+	371.125i	0.496450	+	0.470374i
$790$	−359.811	+	31.6178i	−0.455457	+	0.0400225i
$791$	677.993			0.857134
$792$	1258.74	−	412.771i	1.58932	−	0.521175i
$793$		−	637.374i		−	0.803750i
$794$	−730.612	+	64.2014i	−0.920166	+	0.0808582i
$795$	−272.508	+	287.615i	−0.342777	+	0.361780i
$796$	465.479	−	82.4431i	0.584773	−	0.103572i
$797$	165.770	−	165.770i	0.207993	−	0.207993i	−0.595421	−	0.803414i	$-0.703015\pi$
$797$	165.770	−	165.770i	0.207993	−	0.207993i	0.803414	+	0.595421i	$0.203015\pi$
$798$	102.284	−	128.896i	0.128175	−	0.161524i
$799$	22.3854			0.0280168
$800$	143.864	+	52.0514i	0.179830	+	0.0650642i
$801$	−33.8035	−	626.204i	−0.0422016	−	0.781778i
$802$	514.656	+	431.513i	0.641715	+	0.538046i
$803$	1266.52	−	1266.52i	1.57724	−	1.57724i
$804$	−746.714	+	153.125i	−0.928749	+	0.190454i
$805$	−653.690	+	653.690i	−0.812037	+	0.812037i
$806$	−142.528	+	12.5245i	−0.176834	+	0.0155390i
$807$	1232.17	−	33.2329i	1.52685	−	0.0411808i
$808$	305.942	+	1136.58i	0.378641	+	1.40666i
$809$	184.708			0.228316			0.114158	−	0.993463i	$-0.463583\pi$
$809$	184.708			0.228316			0.114158	+	0.993463i	$0.463583\pi$
$810$	−714.565	+	141.510i	−0.882179	+	0.174704i
$811$	−585.531	+	585.531i	−0.721986	+	0.721986i	−0.969010	−	0.247023i	$-0.920548\pi$
$811$	−585.531	+	585.531i	−0.721986	+	0.721986i	0.247023	+	0.969010i	$0.420548\pi$
$812$	547.327	−	782.935i	0.674048	−	0.964206i
$813$	−1081.36	−	1024.56i	−1.33008	−	1.26022i
$814$	670.173	−	799.300i	0.823308	−	0.981941i
$815$			420.457i			0.515898i
$816$	83.7388	−	193.810i	0.102621	−	0.237513i
$817$	231.235			0.283029
$818$	−101.705	−	85.2742i	−0.124333	−	0.104247i
$819$	365.864	+	328.387i	0.446720	+	0.400961i
$820$	464.834	−	664.932i	0.566871	−	0.810893i
$821$	−659.299	−	659.299i	−0.803044	−	0.803044i	0.180526	−	0.983570i	$-0.442220\pi$
$821$	−659.299	−	659.299i	−0.803044	−	0.803044i	−0.983570	+	0.180526i	$0.942220\pi$
$822$	−146.340	+	16.8462i	−0.178029	+	0.0204942i
$823$			1397.61i			1.69819i	0.528237	+	0.849097i	$0.322853\pi$
$823$			1397.61i			1.69819i	−0.528237	+	0.849097i	$0.677147\pi$
$824$	−228.729	+	397.221i	−0.277584	+	0.482064i
$825$	−263.792	+	7.11476i	−0.319748	+	0.00862395i
$826$	−58.4183	−	664.800i	−0.0707243	−	0.804842i
$827$	78.1971	+	78.1971i	0.0945551	+	0.0945551i	0.752802	−	0.658247i	$-0.228702\pi$
$827$	78.1971	+	78.1971i	0.0945551	+	0.0945551i	−0.658247	+	0.752802i	$0.728702\pi$
$828$	−1193.37	+	278.446i	−1.44127	+	0.336287i
$829$	−30.4254	−	30.4254i	−0.0367014	−	0.0367014i	0.688518	−	0.725219i	$-0.258262\pi$
$829$	−30.4254	−	30.4254i	−0.0367014	−	0.0367014i	−0.725219	+	0.688518i	$0.758262\pi$
$830$	290.452	−	346.416i	0.349942	−	0.417369i
$831$	394.465	−	10.6392i	0.474687	−	0.0128028i
$832$	−148.530	+	559.446i	−0.178522	+	0.672411i
$833$		−	55.0731i		−	0.0661141i
$834$	−16.1882	+	20.4002i	−0.0194103	+	0.0244607i
$835$	504.622	+	504.622i	0.604338	+	0.604338i
$836$	−329.045	+	58.2787i	−0.393595	+	0.0697114i
$837$	−138.319	+	162.725i	−0.165255	+	0.194414i
$838$	91.9958	+	1046.91i	0.109780	+	1.24930i
$839$	694.526			0.827802			0.413901	−	0.910322i	$-0.364166\pi$
$839$	694.526			0.827802			0.413901	+	0.910322i	$0.364166\pi$
$840$	573.411	+	309.905i	0.682632	+	0.368935i
$841$		−	722.489i		−	0.859084i
$842$	−120.732	−	1373.93i	−0.143387	−	1.63175i
$843$	−655.228	−	620.812i	−0.777258	−	0.736432i
$844$	207.069	−	296.206i	0.245342	−	0.350955i
$845$	277.265	−	277.265i	0.328125	−	0.328125i
$846$	−54.9884	+	73.2691i	−0.0649982	+	0.0866065i
$847$	1313.68			1.55098
$848$	426.215	+	197.955i	0.502612	+	0.233438i
$849$	−430.341	+	11.6068i	−0.506880	+	0.0136711i
$850$	−27.0220	+	32.2286i	−0.0317906	+	0.0379160i
$851$	−682.298	+	682.298i	−0.801761	+	0.801761i
$852$	308.546	−	467.735i	0.362144	−	0.548985i
$853$	727.489	−	727.489i	0.852860	−	0.852860i	−0.137625	−	0.990484i	$-0.543947\pi$
$853$	727.489	−	727.489i	0.852860	−	0.852860i	0.990484	+	0.137625i	$0.0439468\pi$
$854$	74.5185	+	848.021i	0.0872582	+	0.992999i
$855$	183.490	−	9.90506i	0.214608	−	0.0115849i
$856$	271.860	+	1009.97i	0.317594	+	1.17987i
$857$	1275.44			1.48826			0.744128	−	0.668037i	$-0.232865\pi$
$857$	1275.44			1.48826			0.744128	+	0.668037i	$0.232865\pi$
$858$	−114.179	−	991.845i	−0.133075	−	1.15600i
$859$	2.20191	−	2.20191i	0.00256334	−	0.00256334i	−0.705824	−	0.708387i	$-0.749423\pi$
$859$	2.20191	−	2.20191i	0.00256334	−	0.00256334i	0.708387	+	0.705824i	$0.249423\pi$
$860$	159.742	+	901.914i	0.185747	+	1.04874i
$861$	−562.130	+	593.293i	−0.652880	+	0.689074i
$862$	−775.334	−	650.078i	−0.899459	−	0.754151i
$863$			1311.55i			1.51976i	0.650063	+	0.759880i	$0.274742\pi$
$863$			1311.55i			1.51976i	−0.650063	+	0.759880i	$0.725258\pi$
$864$	428.656	+	750.167i	0.496130	+	0.868248i
$865$	−489.622			−0.566037
$866$	−974.313	+	1162.04i	−1.12507	+	1.34185i
$867$	−587.236	−	556.391i	−0.677319	−	0.641743i
$868$	188.169	−	33.3274i	0.216784	−	0.0383956i
$869$	−522.518	−	522.518i	−0.601287	−	0.601287i
$870$	1059.79	−	122.000i	1.21815	−	0.140230i
$871$			574.496i			0.659582i
$872$	−221.657	−	823.459i	−0.254193	−	0.944334i
$873$	29.6383	+	549.046i	0.0339500	+	0.628918i
$874$	307.939	−	27.0597i	0.352333	−	0.0309608i
$875$	−571.908	−	571.908i	−0.653609	−	0.653609i
$876$	975.166	+	643.279i	1.11320	+	0.734337i
$877$	−449.158	−	449.158i	−0.512152	−	0.512152i	0.403033	−	0.915185i	$-0.367956\pi$
$877$	−449.158	−	449.158i	−0.512152	−	0.512152i	−0.915185	+	0.403033i	$0.867956\pi$
$878$	223.388	+	187.300i	0.254429	+	0.213325i
$879$	−36.7303	−	1361.84i	−0.0417864	−	1.54930i
$880$	−454.624	−	1243.16i	−0.516618	−	1.41268i
$881$			982.786i			1.11553i	0.829998	+	0.557767i	$0.188342\pi$
$881$			982.786i			1.11553i	−0.829998	+	0.557767i	$0.811658\pi$
$882$	180.258	+	135.284i	0.204374	+	0.153383i
$883$	233.961	+	233.961i	0.264962	+	0.264962i	0.827066	−	0.562104i	$-0.190008\pi$
$883$	233.961	+	233.961i	0.264962	+	0.264962i	−0.562104	+	0.827066i	$0.690008\pi$
$884$	−130.415	−	91.1694i	−0.147529	−	0.103133i
$885$	512.582	−	540.999i	0.579189	−	0.611298i
$886$	−1710.39	+	150.298i	−1.93047	+	0.169637i
$887$	−1421.57			−1.60267			−0.801334	−	0.598217i	$-0.795876\pi$
$887$	−1421.57			−1.60267			−0.801334	+	0.598217i	$0.795876\pi$
$888$	598.506	+	323.468i	0.673994	+	0.364266i
$889$		−	565.527i		−	0.636138i
$890$	−624.231	+	54.8533i	−0.701383	+	0.0616329i
$891$	−1161.10	−	934.222i	−1.30314	−	1.04851i
$892$	29.9191	+	168.925i	0.0335416	+	0.189378i
$893$	16.3406	−	16.3406i	0.0182986	−	0.0182986i
$894$	38.9731	+	30.9265i	0.0435941	+	0.0345934i
$895$	−644.558			−0.720176
$896$	132.211	−	761.704i	0.147557	−	0.850116i
$897$	24.9010	+	923.246i	0.0277603	+	1.02926i
$898$	292.193	+	244.989i	0.325382	+	0.272816i
$899$	221.159	−	221.159i	0.246006	−	0.246006i
$900$	−39.1086	−	167.613i	−0.0434540	−	0.186236i
$901$	−91.3508	+	91.3508i	−0.101388	+	0.101388i
$902$	1653.42	−	145.292i	1.83306	−	0.161077i
$903$	−24.8781	−	922.396i	−0.0275505	−	1.02148i
$904$	448.126	−	778.235i	0.495715	−	0.860879i
$905$	−1350.50			−1.49226
$906$	123.210	+	1070.29i	0.135993	+	1.18134i
$907$	−358.736	+	358.736i	−0.395519	+	0.395519i	−0.876649	−	0.481130i	$-0.840226\pi$
$907$	−358.736	+	358.736i	−0.395519	+	0.395519i	0.481130	+	0.876649i	$0.340226\pi$
$908$	106.651	+	74.5565i	0.117457	+	0.0821107i
$909$	884.494	−	985.436i	0.973041	−	1.08409i
$910$	315.625	−	376.439i	0.346840	−	0.413669i
$911$			353.455i			0.387986i	0.981003	+	0.193993i	$0.0621439\pi$
$911$			353.455i			0.387986i	−0.981003	+	0.193993i	$0.937856\pi$
$912$	−80.3486	−	202.602i	−0.0881015	−	0.222151i
$913$	924.862			1.01299
$914$	−196.310	−	164.596i	−0.214781	−	0.180083i
$915$	−653.852	+	690.100i	−0.714592	+	0.754207i
$916$	−1118.66	−	782.020i	−1.22124	−	0.853734i
$917$	−492.368	−	492.368i	−0.536934	−	0.536934i
$918$	−234.152	+	39.8425i	−0.255068	+	0.0434014i
$919$		−	1519.58i		−	1.65351i	−0.562560	−	0.826757i	$-0.690183\pi$
$919$		−	1519.58i		−	1.65351i	0.562560	−	0.826757i	$-0.309817\pi$
$920$	318.276	+	1182.40i	0.345952	+	1.28522i
$921$	−10.7785	−	399.631i	−0.0117030	−	0.433910i
$922$	−18.3726	−	209.081i	−0.0199269	−	0.226769i
$923$	−298.622	−	298.622i	−0.323534	−	0.323534i
$924$	267.875	+	1306.29i	0.289908	+	1.41374i
$925$	−95.8309	−	95.8309i	−0.103601	−	0.103601i
$926$	796.940	−	950.493i	0.860626	−	1.02645i
$927$	514.915	−	27.7959i	0.555464	−	0.0299848i
$928$	−536.932	−	1145.74i	−0.578591	−	1.23463i
$929$		−	95.2916i		−	0.102574i	−0.998684	−	0.0512872i	$-0.983668\pi$
$929$		−	95.2916i		−	0.102574i	0.998684	−	0.0512872i	$-0.0163324\pi$
$930$	167.167	+	132.653i	0.179750	+	0.142637i
$931$	−40.2015	−	40.2015i	−0.0431810	−	0.0431810i
$932$	167.641	+	946.509i	0.179872	+	1.01557i
$933$	−535.097	−	506.991i	−0.573523	−	0.543398i
$934$	82.1275	+	934.611i	0.0879309	+	1.00065i
$935$	363.886			0.389182
$936$	618.761	−	202.907i	0.661070	−	0.216781i
$937$			701.772i			0.748956i	0.927236	+	0.374478i	$0.122178\pi$
$937$			701.772i			0.748956i	−0.927236	+	0.374478i	$0.877822\pi$
$938$	−67.1671	−	764.362i	−0.0716068	−	0.814885i
$939$	730.101	−	770.576i	0.777530	−	0.820634i
$940$	75.0239	+	52.4469i	0.0798126	+	0.0557946i
$941$	88.8345	−	88.8345i	0.0944044	−	0.0944044i	−0.658327	−	0.752732i	$-0.728736\pi$
$941$	88.8345	−	88.8345i	0.0944044	−	0.0944044i	0.752732	+	0.658327i	$0.228736\pi$
$942$	98.8310	+	78.4257i	0.104916	+	0.0832545i
$943$	−1535.41			−1.62822
$944$	−801.703	−	372.351i	−0.849262	−	0.394439i
$945$	−59.2526	−	730.875i	−0.0627012	−	0.773413i
$946$	−1203.97	+	1435.94i	−1.27269	+	1.51791i
$947$	−345.769	+	345.769i	−0.365120	+	0.365120i	−0.865694	−	0.500574i	$-0.833122\pi$
$947$	−345.769	+	345.769i	−0.365120	+	0.365120i	0.500574	+	0.865694i	$0.333122\pi$
$948$	265.392	−	402.315i	0.279949	−	0.424383i
$949$	622.588	−	622.588i	0.656046	−	0.656046i
$950$	3.80062	+	43.2510i	0.00400065	+	0.0455274i
$951$	992.517	−	26.7693i	1.04366	−	0.0281486i
$952$	184.176	+	106.053i	0.193462	+	0.111400i
$953$	−1627.75			−1.70803			−0.854013	−	0.520251i	$-0.825838\pi$
$953$	−1627.75			−1.70803			−0.854013	+	0.520251i	$0.825838\pi$
$954$	−74.6001	−	523.395i	−0.0781972	−	0.548633i
$955$	−115.517	+	115.517i	−0.120961	+	0.120961i
$956$	−859.311	+	152.197i	−0.898861	+	0.159201i
$957$	1584.30	+	1501.08i	1.65548	+	1.56853i
$958$	1330.19	+	1115.30i	1.38851	+	1.16419i
$959$		−	148.283i		−	0.154623i
$960$	734.727	−	453.355i	0.765340	−	0.472245i
$961$	−898.433			−0.934894
$962$	329.438	−	392.914i	0.342451	−	0.408434i
$963$	785.963	−	875.660i	0.816161	−	0.909304i
$964$	62.0594	+	350.391i	0.0643770	+	0.363476i
$965$	149.785	+	149.785i	0.155218	+	0.155218i
$966$	−141.072	−	1225.46i	−0.146037	−	1.26859i
$967$			1444.31i			1.49360i	0.665049	+	0.746799i	$0.268410\pi$
$967$			1444.31i			1.49360i	−0.665049	+	0.746799i	$0.731590\pi$
$968$	868.290	−	1507.91i	0.896994	−	1.55776i
$969$	59.8945	−	1.61542i	0.0618106	−	0.00166710i
$970$	547.315	−	48.0945i	0.564243	−	0.0495820i
$971$	165.972	+	165.972i	0.170929	+	0.170929i	0.787388	−	0.616458i	$-0.211433\pi$
$971$	165.972	+	165.972i	0.170929	+	0.170929i	−0.616458	+	0.787388i	$0.711433\pi$
$972$	444.774	−	864.269i	0.457586	−	0.889165i
$973$	−18.5371	−	18.5371i	−0.0190515	−	0.0190515i
$974$	1250.24	+	1048.27i	1.28362	+	1.07625i
$975$	−129.673	+	3.49742i	−0.132998	+	0.00358710i
$976$	1022.66	+	474.972i	1.04780	+	0.486651i
$977$			1708.09i			1.74830i	0.485658	+	0.874149i	$0.338580\pi$
$977$			1708.09i			1.74830i	−0.485658	+	0.874149i	$0.661420\pi$
$978$	−439.480	−	348.742i	−0.449366	−	0.356587i
$979$	−906.510	−	906.510i	−0.925955	−	0.925955i
$980$	129.031	−	184.575i	0.131664	−	0.188342i
$981$	−640.822	+	713.955i	−0.653233	+	0.727783i
$982$	951.623	−	83.6224i	0.969066	−	0.0851552i
$983$	285.345			0.290279			0.145140	−	0.989411i	$-0.453637\pi$
$983$	285.345			0.290279			0.145140	+	0.989411i	$0.453637\pi$
$984$	309.467	+	1037.38i	0.314499	+	1.05425i
$985$			205.261i			0.208386i
$986$	346.505	−	30.4486i	0.351425	−	0.0308809i
$987$	−66.9408	−	63.4247i	−0.0678225	−	0.0642601i
$988$	−161.750	+	28.6482i	−0.163714	+	0.0289961i
$989$	1225.75	−	1225.75i	1.23938	−	1.23938i
$990$	−893.863	+	1191.02i	−0.902892	+	1.20305i
$991$	−437.191			−0.441162			−0.220581	−	0.975369i	$-0.570795\pi$
$991$	−437.191			−0.441162			−0.220581	+	0.975369i	$0.570795\pi$
$992$	86.1171	−	238.018i	0.0868116	−	0.239937i
$993$	138.002	−	3.72207i	0.138975	−	0.00374831i
$994$	432.228	+	362.401i	0.434837	+	0.364588i
$995$	−375.762	+	375.762i	−0.377650	+	0.377650i
$996$	121.178	+	590.924i	0.121665	+	0.593297i
$997$	−1029.10	+	1029.10i	−1.03220	+	1.03220i	−0.0327341	+	0.999464i	$0.510421\pi$
$997$	−1029.10	+	1029.10i	−1.03220	+	1.03220i	−0.999464	+	0.0327341i	$0.989579\pi$
$998$	−1451.86	+	127.580i	−1.45477	+	0.127836i
$999$	−61.8458	−	762.862i	−0.0619077	−	0.763626i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.3.i.b.29.8	yes	20
3.2	odd	2	inner	48.3.i.b.29.3	yes	20
4.3	odd	2		192.3.i.b.17.8		20
8.3	odd	2		384.3.i.c.161.3		20
8.5	even	2		384.3.i.d.161.8		20
12.11	even	2		192.3.i.b.17.7		20
16.3	odd	4		384.3.i.c.353.4		20
16.5	even	4	inner	48.3.i.b.5.3	✓	20
16.11	odd	4		192.3.i.b.113.7		20
16.13	even	4		384.3.i.d.353.7		20
24.5	odd	2		384.3.i.d.161.7		20
24.11	even	2		384.3.i.c.161.4		20
48.5	odd	4	inner	48.3.i.b.5.8	yes	20
48.11	even	4		192.3.i.b.113.8		20
48.29	odd	4		384.3.i.d.353.8		20
48.35	even	4		384.3.i.c.353.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.3.i.b.5.3	✓	20	16.5	even	4	inner
48.3.i.b.5.8	yes	20	48.5	odd	4	inner
48.3.i.b.29.3	yes	20	3.2	odd	2	inner
48.3.i.b.29.8	yes	20	1.1	even	1	trivial
192.3.i.b.17.7		20	12.11	even	2
192.3.i.b.17.8		20	4.3	odd	2
192.3.i.b.113.7		20	16.11	odd	4
192.3.i.b.113.8		20	48.11	even	4
384.3.i.c.161.3		20	8.3	odd	2
384.3.i.c.161.4		20	24.11	even	2
384.3.i.c.353.3		20	48.35	even	4
384.3.i.c.353.4		20	16.3	odd	4
384.3.i.d.161.7		20	24.5	odd	2
384.3.i.d.161.8		20	8.5	even	2
384.3.i.d.353.7		20	16.13	even	4
384.3.i.d.353.8		20	48.29	odd	4

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	48.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.28499 - 1.53258i) q^{2} +(-2.17774 - 2.06336i) q^{3} +(-0.697601 - 3.93870i) q^{4} +(3.17955 + 3.17955i) q^{5} +(-5.96063 + 0.686173i) q^{6} -6.03979i q^{7} +(-6.93278 - 3.99206i) q^{8} +(0.485128 + 8.98692i) q^{9} +O(q^{10})\)	\(q+(1.28499 - 1.53258i) q^{2} +(-2.17774 - 2.06336i) q^{3} +(-0.697601 - 3.93870i) q^{4} +(3.17955 + 3.17955i) q^{5} +(-5.96063 + 0.686173i) q^{6} -6.03979i q^{7} +(-6.93278 - 3.99206i) q^{8} +(0.485128 + 8.98692i) q^{9} +(8.95859 - 0.787223i) q^{10} +(13.0097 + 13.0097i) q^{11} +(-6.60774 + 10.0169i) q^{12} +(6.39520 + 6.39520i) q^{13} +(-9.25646 - 7.76107i) q^{14} +(-0.363700 - 13.4848i) q^{15} +(-15.0267 + 5.49528i) q^{16} -4.39848i q^{17} +(14.3965 + 10.8046i) q^{18} +(-3.21075 - 3.21075i) q^{19} +(10.3052 - 14.7413i) q^{20} +(-12.4622 + 13.1531i) q^{21} +(36.6557 - 3.22107i) q^{22} -34.0396 q^{23} +(6.86077 + 22.9985i) q^{24} -4.78097i q^{25} +(18.0189 - 1.58339i) q^{26} +(17.4867 - 20.5722i) q^{27} +(-23.7889 + 4.21336i) q^{28} +(-27.9597 + 27.9597i) q^{29} +(-21.1338 - 16.7704i) q^{30} -7.90993 q^{31} +(-10.8872 + 30.0910i) q^{32} +(-1.48814 - 55.1754i) q^{33} +(-6.74102 - 5.65200i) q^{34} +(19.2038 - 19.2038i) q^{35} +(35.0583 - 8.18005i) q^{36} +(20.0443 - 20.0443i) q^{37} +(-9.04650 + 0.794947i) q^{38} +(-0.731530 - 27.1227i) q^{39} +(-9.35016 - 34.7360i) q^{40} +45.1067 q^{41} +(4.14434 + 36.0010i) q^{42} +(-36.0095 + 36.0095i) q^{43} +(42.1657 - 60.3168i) q^{44} +(-27.0318 + 30.1168i) q^{45} +(-43.7406 + 52.1684i) q^{46} +5.08935i q^{47} +(44.0630 + 19.0381i) q^{48} +12.5209 q^{49} +(-7.32721 - 6.14349i) q^{50} +(-9.07563 + 9.57876i) q^{51} +(20.7275 - 29.6501i) q^{52} +(-20.7687 - 20.7687i) q^{53} +(-9.05825 - 53.2348i) q^{54} +82.7299i q^{55} +(-24.1112 + 41.8725i) q^{56} +(0.367268 + 13.6171i) q^{57} +(6.92253 + 78.7784i) q^{58} +(39.0656 + 39.0656i) q^{59} +(-52.8587 + 10.8395i) q^{60} +(-49.8322 - 49.8322i) q^{61} +(-10.1642 + 12.1226i) q^{62} +(54.2791 - 2.93007i) q^{63} +(32.1269 + 55.3522i) q^{64} +40.6677i q^{65} +(-86.4729 - 68.6191i) q^{66} +(44.9162 + 44.9162i) q^{67} +(-17.3243 + 3.06838i) q^{68} +(74.1295 + 70.2358i) q^{69} +(-4.75466 - 54.1080i) q^{70} -46.6947 q^{71} +(32.5130 - 64.2410i) q^{72} -97.3523i q^{73} +(-4.96275 - 56.4761i) q^{74} +(-9.86483 + 10.4117i) q^{75} +(-10.4063 + 14.8860i) q^{76} +(78.5758 - 78.5758i) q^{77} +(-42.5077 - 33.7312i) q^{78} -40.1637 q^{79} +(-65.2506 - 30.3056i) q^{80} +(-80.5293 + 8.71960i) q^{81} +(57.9616 - 69.1296i) q^{82} +(35.5451 - 35.5451i) q^{83} +(60.4998 + 39.9094i) q^{84} +(13.9852 - 13.9852i) q^{85} +(8.91558 + 101.459i) q^{86} +(118.580 - 3.19823i) q^{87} +(-38.2579 - 142.129i) q^{88} -69.6795 q^{89} +(11.4208 + 80.1282i) q^{90} +(38.6257 - 38.6257i) q^{91} +(23.7461 + 134.072i) q^{92} +(17.2258 + 16.3210i) q^{93} +(7.79984 + 6.53977i) q^{94} -20.4174i q^{95} +(85.7980 - 43.0663i) q^{96} +61.0939 q^{97} +(16.0893 - 19.1893i) q^{98} +(-110.606 + 123.228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{3} + 4 q^{4} - 12 q^{6}+O(q^{10}) \) 20 * q - 6 * q^3 + 4 * q^4 - 12 * q^6	\( 20 q - 6 q^{3} + 4 q^{4} - 12 q^{6} + 32 q^{10} - 88 q^{12} + 92 q^{13} - 116 q^{15} - 16 q^{16} + 4 q^{18} - 52 q^{19} + 48 q^{21} + 24 q^{22} - 8 q^{24} + 18 q^{27} + 56 q^{28} + 28 q^{30} - 80 q^{31} + 60 q^{33} + 104 q^{34} + 92 q^{36} - 116 q^{37} + 88 q^{40} + 304 q^{42} + 172 q^{43} + 60 q^{45} - 424 q^{46} + 176 q^{48} - 364 q^{49} + 128 q^{51} - 208 q^{52} + 40 q^{54} - 512 q^{58} - 240 q^{60} - 244 q^{61} + 296 q^{63} + 88 q^{64} - 492 q^{66} + 356 q^{67} - 20 q^{69} + 200 q^{70} - 472 q^{72} - 146 q^{75} + 328 q^{76} + 84 q^{78} + 384 q^{79} - 188 q^{81} + 560 q^{82} + 816 q^{84} + 48 q^{85} + 416 q^{88} + 616 q^{90} + 136 q^{91} - 132 q^{93} + 32 q^{94} - 24 q^{96} + 472 q^{97} - 452 q^{99}+O(q^{100}) \) 20 * q - 6 * q^3 + 4 * q^4 - 12 * q^6 + 32 * q^10 - 88 * q^12 + 92 * q^13 - 116 * q^15 - 16 * q^16 + 4 * q^18 - 52 * q^19 + 48 * q^21 + 24 * q^22 - 8 * q^24 + 18 * q^27 + 56 * q^28 + 28 * q^30 - 80 * q^31 + 60 * q^33 + 104 * q^34 + 92 * q^36 - 116 * q^37 + 88 * q^40 + 304 * q^42 + 172 * q^43 + 60 * q^45 - 424 * q^46 + 176 * q^48 - 364 * q^49 + 128 * q^51 - 208 * q^52 + 40 * q^54 - 512 * q^58 - 240 * q^60 - 244 * q^61 + 296 * q^63 + 88 * q^64 - 492 * q^66 + 356 * q^67 - 20 * q^69 + 200 * q^70 - 472 * q^72 - 146 * q^75 + 328 * q^76 + 84 * q^78 + 384 * q^79 - 188 * q^81 + 560 * q^82 + 816 * q^84 + 48 * q^85 + 416 * q^88 + 616 * q^90 + 136 * q^91 - 132 * q^93 + 32 * q^94 - 24 * q^96 + 472 * q^97 - 452 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more