LMFDB - Embedded newform 51.3.j.a.46.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,3,Mod(7,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 11])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.7"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	51.j (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.38964934824$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			46.6
Character	$\chi$	$=$	51.46
Dual form			51.3.j.a.10.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.37830 + 3.32751i) q^{2} +(1.44015 - 0.962276i) q^{3} +(-6.34417 + 6.34417i) q^{4} +(-5.25707 - 1.04570i) q^{5} +(5.18693 + 3.46580i) q^{6} +(12.7656 - 2.53924i) q^{7} +(-16.5444 - 6.85292i) q^{8} +(1.14805 - 2.77164i) q^{9} +(-3.76625 - 18.9342i) q^{10} +(0.348948 - 0.522238i) q^{11} +(-3.03170 + 15.2414i) q^{12} +(-6.14688 - 6.14688i) q^{13} +(26.0442 + 38.9779i) q^{14} +(-8.57721 + 3.55280i) q^{15} -28.6090i q^{16} +(-14.0276 - 9.60351i) q^{17} +10.8050 q^{18} +(3.15481 + 7.61639i) q^{19} +(39.9859 - 26.7177i) q^{20} +(15.9409 - 15.9409i) q^{21} +(2.21870 + 0.441328i) q^{22} +(3.09133 + 2.06556i) q^{23} +(-30.4208 + 6.05107i) q^{24} +(3.44634 + 1.42752i) q^{25} +(11.9816 - 28.9260i) q^{26} +(-1.01372 - 5.09631i) q^{27} +(-64.8779 + 97.0967i) q^{28} +(-8.76324 + 44.0558i) q^{29} +(-23.6439 - 23.6439i) q^{30} +(-16.0127 - 23.9647i) q^{31} +(29.0190 - 12.0200i) q^{32} -1.08788i q^{33} +(12.6216 - 59.9133i) q^{34} -69.7651 q^{35} +(10.3003 + 24.8672i) q^{36} +(-11.8321 + 7.90593i) q^{37} +(-20.9953 + 20.9953i) q^{38} +(-14.7674 - 2.93742i) q^{39} +(79.8091 + 53.3267i) q^{40} +(41.9836 - 8.35106i) q^{41} +(75.0150 + 31.0722i) q^{42} +(-3.58037 + 8.64378i) q^{43} +(1.09938 + 5.52695i) q^{44} +(-8.93368 + 13.3702i) q^{45} +(-2.61239 + 13.1334i) q^{46} +(0.164599 + 0.164599i) q^{47} +(-27.5297 - 41.2012i) q^{48} +(111.243 - 46.0785i) q^{49} +13.4353i q^{50} +(-29.4430 - 0.332084i) q^{51} +77.9937 q^{52} +(-7.24464 - 17.4901i) q^{53} +(15.5608 - 10.3974i) q^{54} +(-2.38055 + 2.38055i) q^{55} +(-228.601 - 45.4716i) q^{56} +(11.8725 + 7.93293i) q^{57} +(-158.674 + 31.5623i) q^{58} +(-19.5979 - 8.11773i) q^{59} +(31.8757 - 76.9548i) q^{60} +(15.0720 + 75.7718i) q^{61} +(57.6724 - 86.3128i) q^{62} +(7.61772 - 38.2969i) q^{63} +(-0.924849 - 0.924849i) q^{64} +(25.8868 + 38.7424i) q^{65} +(3.61994 - 1.49943i) q^{66} +79.7985i q^{67} +(149.920 - 28.0670i) q^{68} +6.43960 q^{69} +(-96.1571 - 232.144i) q^{70} +(39.2316 - 26.2137i) q^{71} +(-37.9876 + 37.9876i) q^{72} +(92.6478 + 18.4288i) q^{73} +(-42.6151 - 28.4745i) q^{74} +(6.33691 - 1.26049i) q^{75} +(-68.3344 - 28.3050i) q^{76} +(3.12845 - 7.55275i) q^{77} +(-10.5796 - 53.1873i) q^{78} +(-29.9439 + 44.8141i) q^{79} +(-29.9163 + 150.400i) q^{80} +(-6.36396 - 6.36396i) q^{81} +(85.6542 + 128.191i) q^{82} +(95.7939 - 39.6791i) q^{83} +202.264i q^{84} +(63.7016 + 65.1549i) q^{85} -33.6971 q^{86} +(29.7735 + 71.8795i) q^{87} +(-9.35200 + 6.24880i) q^{88} +(-58.1264 + 58.1264i) q^{89} +(-56.8027 - 11.2988i) q^{90} +(-94.0772 - 62.8604i) q^{91} +(-32.7162 + 6.50765i) q^{92} +(-46.1213 - 19.1041i) q^{93} +(-0.320837 + 0.774569i) q^{94} +(-8.62065 - 43.3389i) q^{95} +(30.2250 - 45.2349i) q^{96} +(36.8737 - 185.377i) q^{97} +(306.653 + 306.653i) q^{98} +(-1.04684 - 1.56671i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{10} - 80 q^{11} - 48 q^{13} - 64 q^{14} + 16 q^{17} + 48 q^{19} + 224 q^{20} + 192 q^{22} + 112 q^{23} - 144 q^{24} + 80 q^{25} - 368 q^{26} - 240 q^{28} - 160 q^{29} - 192 q^{30} - 64 q^{31}+ \cdots + 240 q^{99}+O(q^{100}) $ 48 * q - 48 * q^10 - 80 * q^11 - 48 * q^13 - 64 * q^14 + 16 * q^17 + 48 * q^19 + 224 * q^20 + 192 * q^22 + 112 * q^23 - 144 * q^24 + 80 * q^25 - 368 * q^26 - 240 * q^28 - 160 * q^29 - 192 * q^30 - 64 * q^31 - 80 * q^32 + 16 * q^34 + 128 * q^35 + 48 * q^36 + 128 * q^37 + 400 * q^38 + 192 * q^39 + 128 * q^40 + 320 * q^41 + 432 * q^42 - 112 * q^43 + 704 * q^44 + 96 * q^45 + 80 * q^46 - 32 * q^49 + 128 * q^52 - 336 * q^53 - 608 * q^55 - 880 * q^56 - 752 * q^58 - 512 * q^59 - 400 * q^61 - 560 * q^62 + 160 * q^64 - 240 * q^65 - 208 * q^68 - 240 * q^69 + 80 * q^70 - 160 * q^71 - 288 * q^72 + 544 * q^73 - 48 * q^74 - 288 * q^75 + 496 * q^76 + 512 * q^77 - 384 * q^78 + 608 * q^79 + 816 * q^80 + 1184 * q^82 + 976 * q^83 - 32 * q^85 + 128 * q^86 + 144 * q^87 - 448 * q^88 + 240 * q^89 + 48 * q^90 - 640 * q^91 + 1280 * q^92 + 288 * q^93 - 32 * q^94 + 704 * q^95 + 768 * q^96 + 288 * q^97 + 1008 * q^98 + 240 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$1$	$e\left(\frac{13}{16}\right)$

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 $

$2$	1.37830	+	3.32751i	0.689149	+	1.66375i	0.746488	+	0.665399i	$0.231739\pi$
$2$	1.37830	+	3.32751i	0.689149	+	1.66375i	−0.0573385	+	0.998355i	$0.518261\pi$
$3$	1.44015	−	0.962276i	0.480049	−	0.320759i
$3$	1.44015	−	0.962276i	0.480049	−	0.320759i
$4$	−6.34417	+	6.34417i	−1.58604	+	1.58604i
$5$	−5.25707	−	1.04570i	−1.05141	−	0.209139i	−0.361009	−	0.932562i	$-0.617568\pi$
$5$	−5.25707	−	1.04570i	−1.05141	−	0.209139i	−0.690405	+	0.723423i	$0.742568\pi$
$6$	5.18693	+	3.46580i	0.864489	+	0.577633i
$7$	12.7656	−	2.53924i	1.82366	−	0.362749i	0.839972	−	0.542629i	$-0.182571\pi$
$7$	12.7656	−	2.53924i	1.82366	−	0.362749i	0.983688	+	0.179881i	$0.0575711\pi$
$8$	−16.5444	−	6.85292i	−2.06805	−	0.856615i
$9$	1.14805	−	2.77164i	0.127561	−	0.307960i
$10$	−3.76625	−	18.9342i	−0.376625	−	1.89342i
$11$	0.348948	−	0.522238i	0.0317226	−	0.0474762i	−0.815269	−	0.579082i	$-0.803411\pi$
$11$	0.348948	−	0.522238i	0.0317226	−	0.0474762i	0.846992	+	0.531606i	$0.178411\pi$
$12$	−3.03170	+	15.2414i	−0.252642	+	1.27012i
$13$	−6.14688	−	6.14688i	−0.472837	−	0.472837i	0.429994	−	0.902832i	$-0.358515\pi$
$13$	−6.14688	−	6.14688i	−0.472837	−	0.472837i	−0.902832	+	0.429994i	$0.858515\pi$
$14$	26.0442	+	38.9779i	1.86030	+	2.78413i
$15$	−8.57721	+	3.55280i	−0.571814	+	0.236853i
$16$		−	28.6090i		−	1.78806i
$17$	−14.0276	−	9.60351i	−0.825151	−	0.564912i
$17$	−14.0276	−	9.60351i	−0.825151	−	0.564912i
$18$	10.8050			0.600278
$19$	3.15481	+	7.61639i	0.166043	+	0.400863i	0.984898	−	0.173138i	$-0.0553906\pi$
$19$	3.15481	+	7.61639i	0.166043	+	0.400863i	−0.818855	+	0.574001i	$0.805391\pi$
$20$	39.9859	−	26.7177i	1.99929	−	1.33588i
$21$	15.9409	−	15.9409i	0.759092	−	0.759092i
$22$	2.21870	+	0.441328i	0.100850	+	0.0200604i
$23$	3.09133	+	2.06556i	0.134405	+	0.0898069i	0.620955	−	0.783846i	$-0.286745\pi$
$23$	3.09133	+	2.06556i	0.134405	+	0.0898069i	−0.486550	+	0.873653i	$0.661745\pi$
$24$	−30.4208	+	6.05107i	−1.26753	+	0.252128i
$25$	3.44634	+	1.42752i	0.137854	+	0.0571008i
$26$	11.9816	−	28.9260i	0.460829	−	1.11254i
$27$	−1.01372	−	5.09631i	−0.0375451	−	0.188752i
$28$	−64.8779	+	97.0967i	−2.31707	+	3.46774i
$29$	−8.76324	+	44.0558i	−0.302181	+	1.51917i	0.469372	+	0.883000i	$0.344480\pi$
$29$	−8.76324	+	44.0558i	−0.302181	+	1.51917i	−0.771553	+	0.636165i	$0.780520\pi$
$30$	−23.6439	−	23.6439i	−0.788130	−	0.788130i
$31$	−16.0127	−	23.9647i	−0.516538	−	0.773054i	0.477896	−	0.878417i	$-0.341400\pi$
$31$	−16.0127	−	23.9647i	−0.516538	−	0.773054i	−0.994434	+	0.105363i	$0.966400\pi$
$32$	29.0190	−	12.0200i	0.906842	−	0.375626i
$33$		−	1.08788i		−	0.0329662i
$34$	12.6216	−	59.9133i	0.371223	−	1.76216i
$35$	−69.7651			−1.99329
$36$	10.3003	+	24.8672i	0.286120	+	0.690755i
$37$	−11.8321	+	7.90593i	−0.319785	+	0.213674i	−0.705094	−	0.709114i	$-0.749095\pi$
$37$	−11.8321	+	7.90593i	−0.319785	+	0.213674i	0.385308	+	0.922788i	$0.374095\pi$
$38$	−20.9953	+	20.9953i	−0.552509	+	0.552509i
$39$	−14.7674	−	2.93742i	−0.378652	−	0.0753185i
$40$	79.8091	+	53.3267i	1.99523	+	1.33317i
$41$	41.9836	−	8.35106i	1.02399	−	0.203684i	0.345597	−	0.938383i	$-0.387676\pi$
$41$	41.9836	−	8.35106i	1.02399	−	0.203684i	0.678394	+	0.734698i	$0.262676\pi$
$42$	75.0150	+	31.0722i	1.78607	+	0.739815i
$43$	−3.58037	+	8.64378i	−0.0832645	+	0.201018i	−0.960028	−	0.279903i	$-0.909698\pi$
$43$	−3.58037	+	8.64378i	−0.0832645	+	0.201018i	0.876764	+	0.480921i	$0.159698\pi$
$44$	1.09938	+	5.52695i	0.0249859	+	0.125613i
$45$	−8.93368	+	13.3702i	−0.198526	+	0.297115i
$46$	−2.61239	+	13.1334i	−0.0567911	+	0.285508i
$47$	0.164599	+	0.164599i	0.00350210	+	0.00350210i	0.708856	−	0.705354i	$-0.249212\pi$
$47$	0.164599	+	0.164599i	0.00350210	+	0.00350210i	−0.705354	+	0.708856i	$0.749212\pi$
$48$	−27.5297	−	41.2012i	−0.573536	−	0.858358i
$49$	111.243	−	46.0785i	2.27027	−	0.940378i
$50$			13.4353i			0.268706i
$51$	−29.4430	−	0.332084i	−0.577314	−	0.00651145i
$52$	77.9937			1.49988
$53$	−7.24464	−	17.4901i	−0.136691	−	0.330002i	0.840680	−	0.541532i	$-0.182155\pi$
$53$	−7.24464	−	17.4901i	−0.136691	−	0.330002i	−0.977372	+	0.211530i	$0.932155\pi$
$54$	15.5608	−	10.3974i	0.288163	−	0.192544i
$55$	−2.38055	+	2.38055i	−0.0432827	+	0.0432827i
$56$	−228.601	−	45.4716i	−4.08216	−	0.811992i
$57$	11.8725	+	7.93293i	0.208289	+	0.139174i
$58$	−158.674	+	31.5623i	−2.73576	+	0.544177i
$59$	−19.5979	−	8.11773i	−0.332168	−	0.137589i	0.210365	−	0.977623i	$-0.432535\pi$
$59$	−19.5979	−	8.11773i	−0.332168	−	0.137589i	−0.542533	+	0.840034i	$0.682535\pi$
$60$	31.8757	−	76.9548i	0.531262	−	1.28258i
$61$	15.0720	+	75.7718i	0.247081	+	1.24216i	0.882618	+	0.470091i	$0.155779\pi$
$61$	15.0720	+	75.7718i	0.247081	+	1.24216i	−0.635537	+	0.772071i	$0.719221\pi$
$62$	57.6724	−	86.3128i	0.930200	−	1.39214i
$63$	7.61772	−	38.2969i	0.120916	−	0.607887i
$64$	−0.924849	−	0.924849i	−0.0144508	−	0.0144508i
$65$	25.8868	+	38.7424i	0.398259	+	0.596037i
$66$	3.61994	−	1.49943i	0.0548476	−	0.0227186i
$67$			79.7985i			1.19102i	0.803347	+	0.595511i	$0.203051\pi$
$67$			79.7985i			1.19102i	−0.803347	+	0.595511i	$0.796949\pi$
$68$	149.920	−	28.0670i	2.20470	−	0.412750i
$69$	6.43960			0.0933276
$70$	−96.1571	−	232.144i	−1.37367	−	3.31634i
$71$	39.2316	−	26.2137i	0.552557	−	0.369207i	−0.247725	−	0.968830i	$-0.579683\pi$
$71$	39.2316	−	26.2137i	0.552557	−	0.369207i	0.800282	+	0.599623i	$0.204683\pi$
$72$	−37.9876	+	37.9876i	−0.527606	+	0.527606i
$73$	92.6478	+	18.4288i	1.26915	+	0.252449i	0.783327	−	0.621609i	$-0.213521\pi$
$73$	92.6478	+	18.4288i	1.26915	+	0.252449i	0.485821	+	0.874059i	$0.338521\pi$
$74$	−42.6151	−	28.4745i	−0.575880	−	0.384791i
$75$	6.33691	−	1.26049i	0.0844921	−	0.0168065i
$76$	−68.3344	−	28.3050i	−0.899137	−	0.372435i
$77$	3.12845	−	7.55275i	0.0406293	−	0.0980877i
$78$	−10.5796	−	53.1873i	−0.135636	−	0.681889i
$79$	−29.9439	+	44.8141i	−0.379036	+	0.567268i	−0.971115	−	0.238612i	$-0.923307\pi$
$79$	−29.9439	+	44.8141i	−0.379036	+	0.567268i	0.592079	+	0.805880i	$0.298307\pi$
$80$	−29.9163	+	150.400i	−0.373954	+	1.87999i
$81$	−6.36396	−	6.36396i	−0.0785674	−	0.0785674i
$82$	85.6542	+	128.191i	1.04456	+	1.56330i
$83$	95.7939	−	39.6791i	1.15414	−	0.478062i	0.278223	−	0.960517i	$-0.410255\pi$
$83$	95.7939	−	39.6791i	1.15414	−	0.478062i	0.875921	+	0.482455i	$0.160255\pi$
$84$			202.264i			2.40791i
$85$	63.7016	+	65.1549i	0.749430	+	0.766529i
$86$	−33.6971			−0.391827
$87$	29.7735	+	71.8795i	0.342224	+	0.826201i
$88$	−9.35200	+	6.24880i	−0.106273	+	0.0710091i
$89$	−58.1264	+	58.1264i	−0.653105	+	0.653105i	−0.953739	−	0.300634i	$-0.902802\pi$
$89$	−58.1264	+	58.1264i	−0.653105	+	0.653105i	0.300634	+	0.953739i	$0.402802\pi$
$90$	−56.8027	−	11.2988i	−0.631141	−	0.125542i
$91$	−94.0772	−	62.8604i	−1.03382	−	0.690773i
$92$	−32.7162	+	6.50765i	−0.355610	+	0.0707353i
$93$	−46.1213	−	19.1041i	−0.495928	−	0.205420i
$94$	−0.320837	+	0.774569i	−0.00341316	+	0.00824010i
$95$	−8.62065	−	43.3389i	−0.0907436	−	0.456199i
$96$	30.2250	−	45.2349i	0.314844	−	0.471197i
$97$	36.8737	−	185.377i	0.380141	−	1.91110i	−0.0309849	−	0.999520i	$-0.509864\pi$
$97$	36.8737	−	185.377i	0.380141	−	1.91110i	0.411126	−	0.911579i	$-0.365136\pi$
$98$	306.653	+	306.653i	3.12911	+	3.12911i
$99$	−1.04684	−	1.56671i	−0.0105742	−	0.0158254i
$100$	−30.9206	+	12.8077i	−0.309206	+	0.128077i
$101$		−	52.7047i		−	0.521828i	−0.965362	−	0.260914i	$-0.915976\pi$
$101$		−	52.7047i		−	0.521828i	0.965362	−	0.260914i	$-0.0840239\pi$
$102$	−39.4762	−	98.4295i	−0.387022	−	0.964995i
$103$	−123.387			−1.19793			−0.598965	−	0.800775i	$-0.704421\pi$
$103$	−123.387			−1.19793			−0.598965	+	0.800775i	$0.704421\pi$
$104$	59.5725	+	143.821i	0.572812	+	1.38289i
$105$	−100.472	+	67.1333i	−0.956877	+	0.639364i
$106$	48.2132	−	48.2132i	0.454841	−	0.454841i
$107$	92.3846	+	18.3764i	0.863407	+	0.171742i	0.606879	−	0.794794i	$-0.292421\pi$
$107$	92.3846	+	18.3764i	0.863407	+	0.171742i	0.256528	+	0.966537i	$0.417421\pi$
$108$	38.7631	+	25.9007i	0.358917	+	0.239821i
$109$	−117.667	+	23.4054i	−1.07951	+	0.214729i	−0.702647	−	0.711539i	$-0.747999\pi$
$109$	−117.667	+	23.4054i	−1.07951	+	0.214729i	−0.376867	+	0.926267i	$0.622999\pi$
$110$	−11.2024	−	4.64018i	−0.101840	−	0.0421835i
$111$	−9.43222	+	22.7714i	−0.0849750	+	0.205148i
$112$	−72.6451	−	365.212i	−0.648617	−	3.26082i
$113$	46.5699	−	69.6968i	0.412123	−	0.616786i	−0.566101	−	0.824336i	$-0.691549\pi$
$113$	46.5699	−	69.6968i	0.412123	−	0.616786i	0.978224	+	0.207550i	$0.0665489\pi$
$114$	−10.0331	+	50.4397i	−0.0880094	+	0.442453i
$115$	−14.0914	−	14.0914i	−0.122534	−	0.122534i
$116$	−223.902	−	335.093i	−1.93019	−	2.88873i
$117$	−24.0939	+	9.98000i	−0.205930	+	0.0852992i
$118$		−	76.4009i		−	0.647465i
$119$	−203.456	−	86.9754i	−1.70972	−	0.730886i
$120$	166.252			1.38543
$121$	46.1537	+	111.425i	0.381436	+	0.920867i
$122$	−231.358	+	154.588i	−1.89637	+	1.26712i
$123$	52.4266	−	52.4266i	0.426233	−	0.426233i
$124$	253.623	+	50.4488i	2.04535	+	0.406845i
$125$	94.7934	+	63.3389i	0.758347	+	0.506711i
$126$	137.933	−	27.4365i	1.09470	−	0.217750i
$127$	−75.6934	−	31.3532i	−0.596011	−	0.246876i	0.0642232	−	0.997936i	$-0.479543\pi$
$127$	−75.6934	−	31.3532i	−0.596011	−	0.246876i	−0.660234	+	0.751060i	$0.729543\pi$
$128$	49.8829	−	120.428i	0.389710	−	0.940844i
$129$	3.16144	+	15.8936i	0.0245073	+	0.123206i
$130$	−93.2358	+	139.537i	−0.717198	+	1.07336i
$131$	−0.271809	+	1.36648i	−0.00207488	+	0.0104311i	−0.981809	−	0.189872i	$-0.939193\pi$
$131$	−0.271809	+	1.36648i	−0.00207488	+	0.0104311i	0.979734	+	0.200303i	$0.0641927\pi$
$132$	6.90172	+	6.90172i	0.0522858	+	0.0522858i
$133$	59.6130	+	89.2172i	0.448218	+	0.670806i
$134$	−265.530	+	109.986i	−1.98157	+	0.820793i
$135$			27.8517i			0.206309i
$136$	166.266	+	255.014i	1.22254	+	1.87510i
$137$	−39.1428			−0.285714			−0.142857	−	0.989743i	$-0.545629\pi$
$137$	−39.1428			−0.285714			−0.142857	+	0.989743i	$0.545629\pi$
$138$	8.87570	+	21.4278i	0.0643166	+	0.155274i
$139$	−32.2956	+	21.5792i	−0.232342	+	0.155246i	−0.666292	−	0.745691i	$-0.732120\pi$
$139$	−32.2956	+	21.5792i	−0.232342	+	0.155246i	0.433950	+	0.900937i	$0.357120\pi$
$140$	442.602	−	442.602i	3.16144	−	3.16144i
$141$	0.395436	+	0.0786570i	0.00280451	+	0.000557851i
$142$	141.299	+	94.4131i	0.995064	+	0.664881i
$143$	−5.35508	+	1.06519i	−0.0374481	+	0.00744889i
$144$	−79.2938	−	32.8446i	−0.550651	−	0.228087i
$145$	92.1380	−	222.441i	0.635434	−	1.53407i
$146$	66.3744	+	333.687i	0.454619	+	2.28553i
$147$	115.867	−	173.407i	0.788208	−	1.17964i
$148$	24.9080	−	125.221i	0.168298	−	0.846089i
$149$	−132.110	−	132.110i	−0.886647	−	0.886647i	0.107552	−	0.994199i	$-0.465699\pi$
$149$	−132.110	−	132.110i	−0.886647	−	0.886647i	−0.994199	+	0.107552i	$0.965699\pi$
$150$	12.9284	+	19.3488i	0.0861896	+	0.128992i
$151$	−164.931	+	68.3168i	−1.09226	+	0.452429i	−0.854794	−	0.518967i	$-0.826317\pi$
$151$	−164.931	+	68.3168i	−1.09226	+	0.452429i	−0.237466	+	0.971396i	$0.576317\pi$
$152$		−	147.628i		−	0.971240i
$153$	−42.7218	+	27.8540i	−0.279228	+	0.182052i
$154$	29.4438			0.191193
$155$	59.1201	+	142.728i	0.381420	+	0.920829i
$156$	112.323	−	75.0515i	0.720016	−	0.481099i
$157$	−39.5031	+	39.5031i	−0.251612	+	0.251612i	−0.821631	−	0.570019i	$-0.806936\pi$
$157$	−39.5031	+	39.5031i	−0.251612	+	0.251612i	0.570019	+	0.821631i	$0.306936\pi$
$158$	−190.391	−	37.8711i	−1.20501	−	0.239691i
$159$	−27.2637	−	18.2170i	−0.171469	−	0.114572i
$160$	−165.124	+	32.8452i	−1.03203	+	0.205283i
$161$	44.7077	+	18.5185i	0.277687	+	0.115022i
$162$	12.4047	−	29.9476i	0.0765722	−	0.184862i
$163$	−18.0962	−	90.9758i	−0.111020	−	0.558134i	−0.995755	−	0.0920405i	$-0.970661\pi$
$163$	−18.0962	−	90.9758i	−0.111020	−	0.558134i	0.884736	−	0.466093i	$-0.154339\pi$
$164$	−213.371	+	319.332i	−1.30104	+	1.94715i
$165$	−1.13760	+	5.71908i	−0.00689452	+	0.0346611i
$166$	264.065	+	264.065i	1.59075	+	1.59075i
$167$	52.8828	+	79.1448i	0.316664	+	0.473921i	0.955321	−	0.295571i	$-0.0955098\pi$
$167$	52.8828	+	79.1448i	0.316664	+	0.473921i	−0.638657	+	0.769491i	$0.720510\pi$
$168$	−372.975	+	154.491i	−2.22009	+	0.919592i
$169$		−	93.4317i		−	0.552850i
$170$	−129.004	+	301.770i	−0.758845	+	1.77512i
$171$	24.7318			0.144630
$172$	−32.1232	−	77.5522i	−0.186763	−	0.450885i
$173$	−52.3942	+	35.0087i	−0.302857	+	0.202362i	−0.697707	−	0.716383i	$-0.745796\pi$
$173$	−52.3942	+	35.0087i	−0.302857	+	0.202362i	0.394851	+	0.918745i	$0.370796\pi$
$174$	−198.143	+	198.143i	−1.13875	+	1.13875i
$175$	47.6195	+	9.47211i	0.272112	+	0.0541264i
$176$	−14.9407	−	9.98305i	−0.0848903	−	0.0567219i
$177$	−36.0354	+	7.16789i	−0.203590	+	0.0404965i
$178$	−273.531	−	113.300i	−1.53669	−	0.636519i
$179$	79.6246	−	192.231i	0.444830	−	1.07391i	−0.529403	−	0.848371i	$-0.677584\pi$
$179$	79.6246	−	192.231i	0.444830	−	1.07391i	0.974233	−	0.225544i	$-0.0724160\pi$
$180$	−28.1460	−	141.500i	−0.156367	−	0.786109i
$181$	68.3259	−	102.257i	0.377491	−	0.564955i	−0.593270	−	0.805004i	$-0.702163\pi$
$181$	68.3259	−	102.257i	0.377491	−	0.564955i	0.970761	+	0.240048i	$0.0771633\pi$
$182$	79.5019	−	399.683i	0.436824	−	2.19606i
$183$	94.6192	+	94.6192i	0.517045	+	0.517045i
$184$	−36.9891	−	55.3581i	−0.201028	−	0.300859i
$185$	70.4692	−	29.1893i	0.380914	−	0.157780i
$186$		−	179.800i		−	0.966666i
$187$	−9.91021	+	3.97460i	−0.0529958	+	0.0212545i
$188$	−2.08848			−0.0111090
$189$	−25.8815	−	62.4835i	−0.136939	−	0.330601i
$190$	132.329	−	88.4192i	0.696467	−	0.465364i
$191$	75.7487	−	75.7487i	0.396590	−	0.396590i	−0.480439	−	0.877028i	$-0.659522\pi$
$191$	75.7487	−	75.7487i	0.396590	−	0.396590i	0.877028	+	0.480439i	$0.159522\pi$
$192$	−2.22188	−	0.441959i	−0.0115723	−	0.00230187i
$193$	197.499	+	131.965i	1.02331	+	0.683755i	0.949580	−	0.313524i	$-0.101510\pi$
$193$	197.499	+	131.965i	1.02331	+	0.683755i	0.0737306	+	0.997278i	$0.476510\pi$
$194$	667.665	−	132.807i	3.44157	−	0.684571i
$195$	74.5617	+	30.8845i	0.382368	+	0.158382i
$196$	−413.417	+	998.077i	−2.10927	+	5.09223i
$197$	10.3772	+	52.1696i	0.0526761	+	0.264820i	0.998144	−	0.0608941i	$-0.0193952\pi$
$197$	10.3772	+	52.1696i	0.0526761	+	0.264820i	−0.945468	+	0.325714i	$0.894395\pi$
$198$	3.77039	−	5.64278i	0.0190424	−	0.0284989i
$199$	13.1096	−	65.9066i	0.0658776	−	0.331189i	−0.933766	−	0.357884i	$-0.883498\pi$
$199$	13.1096	−	65.9066i	0.0658776	−	0.331189i	0.999644	+	0.0266951i	$0.00849831\pi$
$200$	−47.2350	−	47.2350i	−0.236175	−	0.236175i
$201$	76.7882	+	114.922i	0.382031	+	0.571750i
$202$	175.375	−	72.6428i	0.868194	−	0.359618i
$203$			584.652i			2.88006i
$204$	188.898	−	184.685i	0.925972	−	0.905317i
$205$	−229.444			−1.11924
$206$	−170.064	−	410.571i	−0.825553	−	1.99306i
$207$	9.27398	−	6.19667i	0.0448018	−	0.0299356i
$208$	−175.856	+	175.856i	−0.845462	+	0.845462i
$209$	5.07843	+	1.01016i	0.0242987	+	0.00483332i
$210$	−361.867	−	241.792i	−1.72318	−	1.15139i
$211$	274.630	−	54.6272i	1.30156	−	0.258897i	0.504824	−	0.863222i	$-0.331557\pi$
$211$	274.630	−	54.6272i	1.30156	−	0.258897i	0.796738	+	0.604325i	$0.206557\pi$
$212$	156.921	+	64.9990i	0.740196	+	0.306599i
$213$	31.2745	−	75.5032i	0.146828	−	0.354475i
$214$	66.1858	+	332.739i	0.309280	+	1.55485i
$215$	27.8611	−	41.6970i	0.129586	−	0.193940i
$216$	−18.1532	+	91.2624i	−0.0840427	+	0.422511i
$217$	−265.264	−	265.264i	−1.22241	−	1.22241i
$218$	−240.062	−	359.278i	−1.10120	−	1.64807i
$219$	151.160	−	62.6126i	0.690229	−	0.285902i
$220$		−	30.2052i		−	0.137296i
$221$	27.1941	+	145.257i	0.123050	+	0.657273i
$222$	−88.7724			−0.399876
$223$	124.230	+	299.917i	0.557084	+	1.34492i	0.912065	+	0.410046i	$0.134487\pi$
$223$	124.230	+	299.917i	0.557084	+	1.34492i	−0.354981	+	0.934873i	$0.615513\pi$
$224$	339.923	−	227.130i	1.51751	−	1.01397i
$225$	7.91315	−	7.91315i	0.0351695	−	0.0351695i
$226$	296.104	+	58.8987i	1.31019	+	0.260614i
$227$	−56.6534	−	37.8546i	−0.249574	−	0.166760i	0.424491	−	0.905432i	$-0.360453\pi$
$227$	−56.6534	−	37.8546i	−0.249574	−	0.166760i	−0.674065	+	0.738672i	$0.735453\pi$
$228$	−125.649	+	24.9931i	−0.551092	+	0.109619i
$229$	−303.570	−	125.743i	−1.32563	−	0.549095i	−0.396227	−	0.918153i	$-0.629681\pi$
$229$	−303.570	−	125.743i	−1.32563	−	0.549095i	−0.929407	+	0.369058i	$0.879681\pi$
$230$	27.4670	−	66.3113i	0.119422	−	0.288310i
$231$	−2.76240	−	13.8875i	−0.0119584	−	0.0601191i
$232$	446.894	−	668.824i	1.92627	−	2.88286i
$233$	−9.10685	+	45.7832i	−0.0390852	+	0.196494i	−0.995395	−	0.0958618i	$-0.969439\pi$
$233$	−9.10685	+	45.7832i	−0.0390852	+	0.196494i	0.956309	+	0.292356i	$0.0944393\pi$
$234$	−66.4171	−	66.4171i	−0.283834	−	0.283834i
$235$	−0.693187	−	1.03743i	−0.00294973	−	0.00441458i
$236$	175.833	−	72.8324i	0.745055	−	0.308612i
$237$			93.3532i			0.393895i
$238$	8.98792	−	796.880i	0.0377644	−	3.34824i
$239$	−147.044			−0.615247			−0.307624	−	0.951508i	$-0.599534\pi$
$239$	−147.044			−0.615247			−0.307624	+	0.951508i	$0.599534\pi$
$240$	101.642	+	245.385i	0.423508	+	1.02244i
$241$	87.8599	−	58.7061i	0.364564	−	0.243594i	−0.359773	−	0.933040i	$-0.617146\pi$
$241$	87.8599	−	58.7061i	0.364564	−	0.243594i	0.724337	+	0.689446i	$0.242146\pi$
$242$	−307.154	+	307.154i	−1.26923	+	1.26923i
$243$	−15.2889	−	3.04116i	−0.0629174	−	0.0125150i
$244$	−576.329	−	385.090i	−2.36200	−	1.57824i
$245$	−632.999	+	125.911i	−2.58367	+	0.513923i
$246$	246.709	+	102.190i	1.00288	+	0.415408i
$247$	27.4248	−	66.2093i	0.111032	−	0.268054i
$248$	100.692	+	506.215i	0.406018	+	2.04119i
$249$	99.7751	−	149.324i	0.400703	−	0.599695i
$250$	−80.1071	+	402.726i	−0.320428	+	1.61090i
$251$	−156.137	−	156.137i	−0.622061	−	0.622061i	0.323997	−	0.946058i	$-0.394973\pi$
$251$	−156.137	−	156.137i	−0.622061	−	0.622061i	−0.946058	+	0.323997i	$0.894973\pi$
$252$	194.634	+	291.290i	0.772357	+	1.15591i
$253$	2.15742	−	0.893635i	0.00852737	−	0.00353215i
$254$		−	295.085i		−	1.16175i
$255$	154.437	+	32.5342i	0.605634	+	0.127585i
$256$	464.247			1.81346
$257$	−96.8954	−	233.926i	−0.377025	−	0.910218i	−0.992521	−	0.122078i	$-0.961044\pi$
$257$	−96.8954	−	233.926i	−0.377025	−	0.910218i	0.615496	−	0.788140i	$-0.288956\pi$
$258$	−48.5288	+	32.4259i	−0.188096	+	0.125682i
$259$	−130.969	+	130.969i	−0.505670	+	0.505670i
$260$	−410.019	−	81.5578i	−1.57700	−	0.313684i
$261$	112.046	+	74.8668i	0.429295	+	0.286846i
$262$	−4.92160	+	0.978967i	−0.0187847	+	0.00373652i
$263$	431.111	+	178.572i	1.63920	+	0.678981i	0.996217	−	0.0868961i	$-0.0276948\pi$
$263$	431.111	+	178.572i	1.63920	+	0.678981i	0.642987	+	0.765877i	$0.277695\pi$
$264$	−7.45518	+	17.9984i	−0.0282393	+	0.0681758i
$265$	19.7962	+	99.5224i	0.0747028	+	0.375556i
$266$	−214.706	+	321.331i	−0.807167	+	1.20801i
$267$	−27.7769	+	139.644i	−0.104033	+	0.523012i
$268$	−506.256	−	506.256i	−1.88901	−	1.88901i
$269$	88.2143	+	132.022i	0.327934	+	0.490788i	0.958400	−	0.285429i	$-0.0921361\pi$
$269$	88.2143	+	132.022i	0.327934	+	0.490788i	−0.630466	+	0.776217i	$0.717136\pi$
$270$	−92.6768	+	38.3880i	−0.343247	+	0.142178i
$271$		−	167.181i		−	0.616903i	−0.951240	−	0.308452i	$-0.900189\pi$
$271$		−	167.181i		−	0.616903i	0.951240	−	0.308452i	$-0.0998108\pi$
$272$	−274.747	+	401.314i	−1.01010	+	1.47542i
$273$	−195.974			−0.717854
$274$	−53.9505	−	130.248i	−0.196900	−	0.475358i
$275$	1.94810	−	1.30168i	0.00708400	−	0.00473338i
$276$	−40.8539	+	40.8539i	−0.148022	+	0.148022i
$277$	189.955	+	37.7843i	0.685757	+	0.136406i	0.525659	−	0.850696i	$-0.323819\pi$
$277$	189.955	+	37.7843i	0.685757	+	0.136406i	0.160098	+	0.987101i	$0.448819\pi$
$278$	−116.318	−	77.7212i	−0.418410	−	0.279573i
$279$	−84.8048	+	16.8687i	−0.303960	+	0.0604614i
$280$	1154.22	+	478.095i	4.12222	+	1.70748i
$281$	−187.355	+	452.315i	−0.666743	+	1.60966i	0.120282	+	0.992740i	$0.461620\pi$
$281$	−187.355	+	452.315i	−0.666743	+	1.60966i	−0.787025	+	0.616921i	$0.788380\pi$
$282$	0.283297	+	1.42423i	0.00100460	+	0.00505045i
$283$	−176.641	+	264.362i	−0.624174	+	0.934142i	0.375798	+	0.926701i	$0.377368\pi$
$283$	−176.641	+	264.362i	−0.624174	+	0.934142i	−0.999972	+	0.00744074i	$0.997632\pi$
$284$	−82.5877	+	415.196i	−0.290802	+	1.46196i
$285$	−54.1190	−	54.1190i	−0.189891	−	0.189891i
$286$	−10.9253	−	16.3509i	−0.0382004	−	0.0571710i
$287$	514.742	−	213.213i	1.79353	−	0.742903i
$288$		−	94.2297i		−	0.327186i
$289$	104.545	+	269.428i	0.361748	+	0.932276i
$290$	867.167			2.99023
$291$	−125.280	−	302.452i	−0.430515	−	1.03935i
$292$	−704.689	+	470.858i	−2.41332	+	1.61253i
$293$	194.121	−	194.121i	0.662529	−	0.662529i	−0.293446	−	0.955976i	$-0.594802\pi$
$293$	194.121	−	194.121i	0.662529	−	0.662529i	0.955976	+	0.293446i	$0.0948022\pi$
$294$	736.711	+	146.541i	2.50582	+	0.498438i
$295$	94.5391	+	63.1690i	0.320471	+	0.214132i
$296$	249.933	−	49.7148i	0.844369	−	0.167955i
$297$	−3.01522	−	1.24895i	−0.0101523	−	0.00420520i
$298$	257.511	−	621.686i	0.864130	−	2.08619i
$299$	−6.30527	−	31.6988i	−0.0210879	−	0.106016i
$300$	−32.2057	+	48.1992i	−0.107352	+	0.160664i
$301$	−23.7570	+	119.435i	−0.0789271	+	0.396793i
$302$	−454.649	−	454.649i	−1.50546	−	1.50546i
$303$	−50.7164	−	75.9025i	−0.167381	−	0.250503i
$304$	217.897	−	90.2560i	0.716767	−	0.296895i
$305$		−	414.099i		−	1.35770i
$306$	−151.568	−	103.766i	−0.495320	−	0.339104i
$307$	−472.647			−1.53957			−0.769783	−	0.638306i	$-0.779636\pi$
$307$	−472.647			−1.53957			−0.769783	+	0.638306i	$0.779636\pi$
$308$	28.0685	+	67.7634i	0.0911316	+	0.220011i
$309$	−177.695	+	118.732i	−0.575066	+	0.384247i
$310$	−393.445	+	393.445i	−1.26918	+	1.26918i
$311$	−133.244	−	26.5039i	−0.428438	−	0.0852217i	−0.0238391	−	0.999716i	$-0.507589\pi$
$311$	−133.244	−	26.5039i	−0.428438	−	0.0852217i	−0.404599	+	0.914494i	$0.632589\pi$
$312$	224.188	+	149.798i	0.718552	+	0.480121i
$313$	88.7346	−	17.6504i	0.283497	−	0.0563911i	−0.0512935	−	0.998684i	$-0.516334\pi$
$313$	88.7346	−	17.6504i	0.283497	−	0.0563911i	0.334791	+	0.942293i	$0.391334\pi$
$314$	−185.894	−	76.9997i	−0.592018	−	0.245222i
$315$	−80.0938	+	193.364i	−0.254266	+	0.613853i
$316$	−94.3397	−	474.278i	−0.298543	−	1.50088i
$317$	−31.7092	+	47.4561i	−0.100029	+	0.149704i	−0.878108	−	0.478462i	$-0.841194\pi$
$317$	−31.7092	+	47.4561i	−0.100029	+	0.149704i	0.778079	+	0.628166i	$0.216194\pi$
$318$	23.0397	−	115.828i	0.0724519	−	0.364240i
$319$	19.9497	+	19.9497i	0.0625382	+	0.0625382i
$320$	3.89489	+	5.82911i	0.0121715	+	0.0182160i
$321$	150.731	−	62.4347i	0.469566	−	0.194501i
$322$			174.289i			0.541271i
$323$	28.8898	−	137.137i	0.0894420	−	0.424572i
$324$	80.7481			0.249223
$325$	−12.4094	−	29.9591i	−0.0381829	−	0.0921817i
$326$	277.781	−	185.607i	0.852088	−	0.569347i
$327$	−146.935	+	146.935i	−0.449344	+	0.449344i
$328$	−751.824	−	149.547i	−2.29215	−	0.455936i
$329$	2.51916	+	1.68325i	0.00765702	+	0.00511626i
$330$	−20.5982	+	4.09725i	−0.0624189	+	0.0124159i
$331$	83.8678	+	34.7392i	0.253377	+	0.104952i	0.505757	−	0.862676i	$-0.331213\pi$
$331$	83.8678	+	34.7392i	0.253377	+	0.104952i	−0.252380	+	0.967628i	$0.581213\pi$
$332$	−356.002	+	859.464i	−1.07229	+	2.58875i
$333$	8.32858	+	41.8706i	0.0250107	+	0.125737i
$334$	−190.466	+	285.053i	−0.570259	+	0.853453i
$335$	83.4451	−	419.507i	0.249090	−	1.25226i
$336$	−456.054	−	456.054i	−1.35730	−	1.35730i
$337$	−88.7546	−	132.831i	−0.263367	−	0.394156i	0.676093	−	0.736817i	$-0.263672\pi$
$337$	−88.7546	−	132.831i	−0.263367	−	0.394156i	−0.939459	+	0.342660i	$0.888672\pi$
$338$	310.895	−	128.777i	0.919807	−	0.380996i
$339$		−	145.187i		−	0.428280i
$340$	−817.488	−	9.22035i	−2.40438	−	0.0271187i
$341$	−18.1029			−0.0530876
$342$	34.0878	+	82.2952i	0.0996719	+	0.240629i
$343$	772.800	−	516.368i	2.25306	−	1.50545i
$344$	118.470	−	118.470i	0.344391	−	0.344391i
$345$	−33.8535	−	6.73387i	−0.0981260	−	0.0195185i
$346$	−188.706	−	126.090i	−0.545394	−	0.364421i
$347$	462.102	−	91.9177i	1.33170	−	0.264893i	0.522611	−	0.852571i	$-0.324958\pi$
$347$	462.102	−	91.9177i	1.33170	−	0.264893i	0.809094	+	0.587679i	$0.199958\pi$
$348$	−644.904	−	267.128i	−1.85317	−	0.767609i
$349$	132.734	−	320.448i	0.380326	−	0.918189i	−0.611576	−	0.791186i	$-0.709464\pi$
$349$	132.734	−	320.448i	0.380326	−	0.918189i	0.991902	−	0.127003i	$-0.0405359\pi$
$350$	34.1154	+	171.510i	0.0974726	+	0.490028i
$351$	−25.0952	+	37.5576i	−0.0714963	+	0.107002i
$352$	3.84879	−	19.3492i	0.0109341	−	0.0549692i
$353$	392.814	+	392.814i	1.11279	+	1.11279i	0.992772	+	0.120015i	$0.0382942\pi$
$353$	392.814	+	392.814i	1.11279	+	1.11279i	0.120015	+	0.992772i	$0.461706\pi$
$354$	−73.5188	−	110.029i	−0.207680	−	0.310815i
$355$	−233.655	+	96.7830i	−0.658183	+	0.272628i
$356$		−	737.527i		−	2.07171i
$357$	−376.701	+	70.5236i	−1.05519	+	0.197545i
$358$	749.396			2.09328
$359$	121.701	+	293.811i	0.338999	+	0.818415i	0.997812	+	0.0661092i	$0.0210586\pi$
$359$	121.701	+	293.811i	0.338999	+	0.818415i	−0.658814	+	0.752306i	$0.728941\pi$
$360$	239.427	−	159.980i	0.665076	−	0.444390i
$361$	207.209	−	207.209i	0.573986	−	0.573986i
$362$	434.434	+	86.4143i	1.20009	+	0.238714i
$363$	173.690	+	116.056i	0.478484	+	0.319713i
$364$	995.639	−	198.045i	2.73527	−	0.544079i
$365$	−467.785	−	193.763i	−1.28160	−	0.530858i
$366$	−184.433	+	445.260i	−0.503914	+	1.21656i
$367$	38.6227	+	194.169i	0.105239	+	0.529072i	0.997056	+	0.0766756i	$0.0244306\pi$
$367$	38.6227	+	194.169i	0.105239	+	0.529072i	−0.891817	+	0.452396i	$0.850569\pi$
$368$	59.0935	−	88.4397i	0.160580	−	0.240325i
$369$	25.0532	−	125.951i	0.0678948	−	0.341330i
$370$	194.255	+	194.255i	0.525014	+	0.525014i
$371$	−136.894	−	204.876i	−0.368986	−	0.552227i
$372$	413.801	−	171.402i	1.11237	−	0.460758i
$373$			287.625i			0.771111i	0.922685	+	0.385556i	$0.125990\pi$
$373$			287.625i			0.771111i	−0.922685	+	0.385556i	$0.874010\pi$
$374$	−26.8847	−	27.4981i	−0.0718843	−	0.0735244i
$375$	197.466			0.526576
$376$	−1.59521	−	3.85117i	−0.00424257	−	0.0102425i
$377$	324.672	−	216.939i	0.861200	−	0.575435i
$378$	172.242	−	172.242i	0.455666	−	0.455666i
$379$	−595.668	−	118.486i	−1.57168	−	0.312627i	−0.669111	−	0.743163i	$-0.733325\pi$
$379$	−595.668	−	118.486i	−1.57168	−	0.312627i	−0.902574	+	0.430535i	$0.858325\pi$
$380$	329.640	+	220.259i	0.867475	+	0.579628i
$381$	−139.180	+	27.6847i	−0.365302	+	0.0726631i
$382$	356.458	+	147.650i	0.933137	+	0.386518i
$383$	−130.778	+	315.727i	−0.341458	+	0.824352i	0.656111	+	0.754664i	$0.272200\pi$
$383$	−130.778	+	315.727i	−0.341458	+	0.824352i	−0.997569	+	0.0696879i	$0.977800\pi$
$384$	−44.0462	−	221.435i	−0.114704	−	0.576654i
$385$	−24.3444	+	36.4340i	−0.0632322	+	0.0946337i
$386$	−166.901	+	839.066i	−0.432385	+	2.17375i
$387$	19.8470	+	19.8470i	0.0512842	+	0.0512842i
$388$	942.128	+	1409.99i	2.42816	+	3.63400i
$389$	−354.712	+	146.927i	−0.911856	+	0.377703i	−0.788767	−	0.614692i	$-0.789280\pi$
$389$	−354.712	+	146.927i	−0.911856	+	0.377703i	−0.123089	+	0.992396i	$0.539280\pi$
$390$			290.673i			0.745315i
$391$	−23.5272	−	58.6623i	−0.0601718	−	0.150032i
$392$	−2156.23			−5.50058
$393$	0.923483	+	2.22949i	0.00234983	+	0.00567299i
$394$	−159.292	+	106.435i	−0.404294	+	0.270141i
$395$	204.279	−	204.279i	0.517162	−	0.517162i
$396$	16.5809	+	3.29814i	0.0418709	+	0.00832863i
$397$	−63.9507	−	42.7305i	−0.161085	−	0.107633i	0.472415	−	0.881376i	$-0.343382\pi$
$397$	−63.9507	−	42.7305i	−0.161085	−	0.107633i	−0.633500	+	0.773743i	$0.718382\pi$
$398$	237.374	−	47.2166i	0.596416	−	0.118635i
$399$	171.703	+	71.1218i	0.430334	+	0.178250i
$400$	40.8399	−	98.5963i	0.102100	−	0.246491i
$401$	−150.571	−	756.971i	−0.375488	−	1.88771i	−0.454353	−	0.890822i	$-0.650129\pi$
$401$	−150.571	−	756.971i	−0.375488	−	1.88771i	0.0788642	−	0.996885i	$-0.474871\pi$
$402$	−276.566	+	413.910i	−0.687974	+	1.02963i
$403$	−48.8800	+	245.736i	−0.121290	+	0.609767i
$404$	334.367	+	334.367i	0.827642	+	0.827642i
$405$	26.8010	+	40.1106i	0.0661754	+	0.0990385i
$406$	−1945.43	+	805.825i	−4.79171	+	1.98479i
$407$			8.93790i			0.0219605i
$408$	484.841	+	207.265i	1.18834	+	0.508002i
$409$	343.320			0.839413			0.419706	−	0.907660i	$-0.362133\pi$
$409$	343.320			0.839413			0.419706	+	0.907660i	$0.362133\pi$
$410$	−316.242	−	763.476i	−0.771322	−	1.86214i
$411$	−56.3715	+	37.6662i	−0.137157	+	0.0916453i
$412$	782.787	−	782.787i	1.89997	−	1.89997i
$413$	−270.793	−	53.8640i	−0.655672	−	0.130421i
$414$	33.4018	+	22.3184i	0.0806807	+	0.0539091i
$415$	−545.088	+	108.425i	−1.31346	+	0.261264i
$416$	−252.262	−	104.490i	−0.606399	−	0.251179i
$417$	−25.7452	+	62.1545i	−0.0617392	+	0.149052i
$418$	3.63827	+	18.2908i	0.00870400	+	0.0437580i
$419$	244.312	−	365.639i	0.583084	−	0.872646i	−0.416246	−	0.909252i	$-0.636655\pi$
$419$	244.312	−	365.639i	0.583084	−	0.872646i	0.999330	+	0.0366056i	$0.0116545\pi$
$420$	211.507	−	1063.32i	0.503588	−	2.53171i
$421$	−135.174	−	135.174i	−0.321077	−	0.321077i	0.528103	−	0.849180i	$-0.322903\pi$
$421$	−135.174	−	135.174i	−0.321077	−	0.321077i	−0.849180	+	0.528103i	$0.822903\pi$
$422$	560.294	+	838.539i	1.32771	+	1.98706i
$423$	0.645175	−	0.267240i	0.00152524	−	0.000631774i
$424$			339.010i			0.799553i
$425$	−34.6346	−	53.1216i	−0.0814931	−	0.124992i
$426$	294.343			0.690946
$427$	384.806	+	929.004i	0.901185	+	2.17565i
$428$	−702.687	+	469.520i	−1.64179	+	1.09701i
$429$	−6.68709	+	6.68709i	−0.0155876	+	0.0155876i
$430$	177.148	+	35.2369i	0.411972	+	0.0819463i
$431$	−323.745	−	216.320i	−0.751149	−	0.501902i	0.120089	−	0.992763i	$-0.461682\pi$
$431$	−323.745	−	216.320i	−0.751149	−	0.501902i	−0.871238	+	0.490861i	$0.836682\pi$
$432$	−145.800	+	29.0015i	−0.337501	+	0.0671330i
$433$	350.486	+	145.176i	0.809437	+	0.335280i	0.748729	−	0.662876i	$-0.230664\pi$
$433$	350.486	+	145.176i	0.809437	+	0.335280i	0.0607076	+	0.998156i	$0.480664\pi$
$434$	517.055	−	1248.28i	1.19137	−	2.87622i
$435$	−81.3571	−	409.010i	−0.187028	−	0.940252i
$436$	598.012	−	894.988i	1.37159	−	2.05273i
$437$	−5.97955	+	30.0612i	−0.0136832	+	0.0687899i
$438$	416.688	+	416.688i	0.951342	+	0.951342i
$439$	−468.801	−	701.610i	−1.06788	−	1.59820i	−0.763683	−	0.645591i	$-0.776611\pi$
$439$	−468.801	−	701.610i	−1.06788	−	1.59820i	−0.304200	−	0.952608i	$-0.598389\pi$
$440$	55.6985	−	23.0711i	0.126587	−	0.0524342i
$441$		−	361.227i		−	0.819108i
$442$	−445.864	+	290.697i	−1.00874	+	0.657685i
$443$	−712.389			−1.60810			−0.804051	−	0.594561i	$-0.797326\pi$
$443$	−712.389			−1.60810			−0.804051	+	0.594561i	$0.797326\pi$
$444$	−84.6260	−	204.305i	−0.190599	−	0.460147i
$445$	366.357	−	244.792i	0.823274	−	0.550094i
$446$	−826.750	+	826.750i	−1.85370	+	1.85370i
$447$	−317.385	−	63.1318i	−0.710034	−	0.141235i
$448$	−14.1547	−	9.45786i	−0.0315953	−	0.0211113i
$449$	−106.862	+	21.2562i	−0.238000	+	0.0473411i	−0.312649	−	0.949869i	$-0.601216\pi$
$449$	−106.862	+	21.2562i	−0.238000	+	0.0473411i	0.0746491	+	0.997210i	$0.476216\pi$
$450$	37.2377	+	15.4244i	0.0827505	+	0.0342764i
$451$	10.2889	−	24.8395i	0.0228135	−	0.0550765i
$452$	146.721	+	737.616i	0.324604	+	1.63189i
$453$	−171.786	+	257.096i	−0.379218	+	0.567540i
$454$	47.8761	−	240.689i	0.105454	−	0.530153i
$455$	428.838	+	428.838i	0.942501	+	0.942501i
$456$	−142.059	−	212.607i	−0.311534	−	0.466243i
$457$	63.3580	−	26.2438i	0.138639	−	0.0574262i	−0.312285	−	0.949988i	$-0.601094\pi$
$457$	63.3580	−	26.2438i	0.138639	−	0.0574262i	0.450924	+	0.892562i	$0.351094\pi$
$458$		−	1183.44i		−	2.58394i
$459$	−34.7225	+	81.2241i	−0.0756480	+	0.176959i
$460$	178.796			0.388687
$461$	213.726	+	515.979i	0.463613	+	1.11926i	0.966903	+	0.255144i	$0.0821227\pi$
$461$	213.726	+	515.979i	0.463613	+	1.11926i	−0.503290	+	0.864118i	$0.667877\pi$
$462$	42.4034	−	28.3331i	0.0917823	−	0.0613269i
$463$	−411.865	+	411.865i	−0.889557	+	0.889557i	−0.994480	−	0.104924i	$-0.966540\pi$
$463$	−411.865	+	411.865i	−0.889557	+	0.889557i	0.104924	+	0.994480i	$0.466540\pi$
$464$	1260.39	+	250.707i	2.71636	+	0.540318i
$465$	222.486	+	148.660i	0.478464	+	0.319699i
$466$	−164.896	+	32.7998i	−0.353854	+	0.0703859i
$467$	−53.1145	−	22.0007i	−0.113736	−	0.0471108i	0.325090	−	0.945683i	$-0.394605\pi$
$467$	−53.1145	−	22.0007i	−0.113736	−	0.0471108i	−0.438826	+	0.898572i	$0.644605\pi$
$468$	89.5407	−	216.170i	0.191326	−	0.461903i
$469$	202.628	+	1018.68i	0.432042	+	2.17202i
$470$	2.49663	−	3.73647i	0.00531198	−	0.00794993i
$471$	−18.8774	+	94.9031i	−0.0400794	+	0.201493i
$472$	268.606	+	268.606i	0.569081	+	0.569081i
$473$	3.26475	+	4.88604i	0.00690221	+	0.0103299i
$474$	−310.634	+	128.669i	−0.655345	+	0.271453i
$475$			30.7523i			0.0647416i
$476$	1842.55	−	738.974i	3.87090	−	1.55247i
$477$	−56.7934			−0.119064
$478$	−202.671	−	489.290i	−0.423997	−	1.02362i
$479$	−767.502	+	512.828i	−1.60230	+	1.07062i	−0.652490	+	0.757798i	$0.726275\pi$
$479$	−767.502	+	512.828i	−1.60230	+	1.07062i	−0.949811	+	0.312825i	$0.898725\pi$
$480$	−206.197	+	206.197i	−0.429577	+	0.429577i
$481$	121.327	+	24.1334i	0.252239	+	0.0501735i
$482$	316.442	+	211.440i	0.656519	+	0.438672i
$483$	82.2055	−	16.3517i	0.170198	−	0.0338545i
$484$	−999.706	−	414.092i	−2.06551	−	0.855562i
$485$	−387.695	+	935.979i	−0.799372	+	1.92985i
$486$	−10.9532	−	55.0657i	−0.0225375	−	0.113304i
$487$	373.481	−	558.954i	0.766902	−	1.14775i	−0.218221	−	0.975899i	$-0.570025\pi$
$487$	373.481	−	558.954i	0.766902	−	1.14775i	0.985123	−	0.171850i	$-0.0549746\pi$
$488$	269.902	−	1356.89i	0.553077	−	2.78051i
$489$	−113.605	−	113.605i	−0.232321	−	0.232321i
$490$	−1291.43	−	1932.76i	−2.63557	−	3.94442i
$491$	−335.513	+	138.974i	−0.683327	+	0.283043i	−0.697217	−	0.716860i	$-0.745579\pi$
$491$	−335.513	+	138.974i	−0.683327	+	0.283043i	0.0138900	+	0.999904i	$0.495579\pi$
$492$			665.207i			1.35205i
$493$	546.017	−	533.838i	1.10754	−	1.08283i
$494$	258.112			0.522493
$495$	3.86503	+	9.33101i	0.00780814	+	0.0188505i
$496$	−685.605	+	458.107i	−1.38227	+	0.923602i
$497$	434.253	−	434.253i	0.873748	−	0.873748i
$498$	634.397	+	126.189i	1.27389	+	0.253392i
$499$	571.975	+	382.181i	1.14624	+	0.765894i	0.975625	−	0.219443i	$-0.0704240\pi$
$499$	571.975	+	382.181i	1.14624	+	0.765894i	0.170617	+	0.985337i	$0.445424\pi$
$500$	−1003.22	+	199.553i	−2.00644	+	0.399105i
$501$	152.318	+	63.0923i	0.304028	+	0.125933i
$502$	304.344	−	734.752i	0.606263	−	1.46365i
$503$	−71.4425	−	359.166i	−0.142033	−	0.714048i	−0.984512	−	0.175318i	$-0.943905\pi$
$503$	−71.4425	−	359.166i	−0.142033	−	0.714048i	0.842479	−	0.538729i	$-0.181095\pi$
$504$	−388.476	+	581.396i	−0.770786	+	1.15356i
$505$	−55.1131	+	277.072i	−0.109135	+	0.548658i
$506$	5.94715	+	5.94715i	0.0117533	+	0.0117533i
$507$	−89.9071	−	134.555i	−0.177331	−	0.265395i
$508$	679.122	−	281.302i	1.33686	−	0.553743i
$509$			402.647i			0.791056i	0.918454	+	0.395528i	$0.129438\pi$
$509$			402.647i			0.791056i	−0.918454	+	0.395528i	$0.870562\pi$
$510$	104.602	+	558.731i	0.205102	+	1.09555i
$511$	1229.50			2.40607
$512$	440.339	+	1063.07i	0.860038	+	2.07631i
$513$	35.6174	−	23.7988i	0.0694296	−	0.0463914i
$514$	644.840	−	644.840i	1.25455	−	1.25455i
$515$	648.654	+	129.025i	1.25952	+	0.250534i
$516$	−120.889	−	80.7752i	−0.234280	−	0.156541i
$517$	0.143396	−	0.0285232i	0.000277362	−	5.51707e-5i
$518$	−616.313	−	255.285i	−1.18979	−	0.492828i
$519$	−41.7674	+	100.835i	−0.0804766	+	0.194288i
$520$	−162.784	−	818.370i	−0.313046	−	1.57379i
$521$	268.408	−	401.701i	0.515178	−	0.771019i	−0.479109	−	0.877755i	$-0.659040\pi$
$521$	268.408	−	401.701i	0.515178	−	0.771019i	0.994287	+	0.106736i	$0.0340401\pi$
$522$	−94.6869	+	476.023i	−0.181392	+	0.911922i
$523$	−336.118	−	336.118i	−0.642672	−	0.642672i	0.308539	−	0.951212i	$-0.400160\pi$
$523$	−336.118	−	336.118i	−0.642672	−	0.642672i	−0.951212	+	0.308539i	$0.900160\pi$
$524$	−6.94477	−	10.3936i	−0.0132534	−	0.0198351i
$525$	77.6939	−	32.1819i	0.147988	−	0.0612988i
$526$			1680.65i			3.19515i
$527$	−5.52602	+	489.944i	−0.0104858	+	0.929685i
$528$	−31.1233			−0.0589456
$529$	−197.150	−	475.962i	−0.372684	−	0.899738i
$530$	−303.877	+	203.044i	−0.573352	+	0.383101i
$531$	−44.9988	+	44.9988i	−0.0847435	+	0.0847435i
$532$	−944.205	−	187.814i	−1.77482	−	0.353034i
$533$	−309.401	−	206.735i	−0.580490	−	0.387871i
$534$	−502.952	+	100.043i	−0.941857	+	0.187347i
$535$	−466.456	−	193.213i	−0.871881	−	0.361145i
$536$	546.853	−	1320.22i	1.02025	−	2.46310i
$537$	−70.3079	−	353.461i	−0.130927	−	0.658215i
$538$	−317.719	+	475.499i	−0.590555	+	0.883828i
$539$	14.7542	−	74.1745i	0.0273733	−	0.137615i
$540$	−176.696	−	176.696i	−0.327215	−	0.327215i
$541$	−362.060	−	541.861i	−0.669242	−	1.00159i	−0.998357	−	0.0573011i	$-0.981750\pi$
$541$	−362.060	−	541.861i	−0.669242	−	1.00159i	0.329115	−	0.944290i	$-0.393250\pi$
$542$	556.295	−	230.425i	1.02638	−	0.425138i
$543$		−	213.013i		−	0.392290i
$544$	−522.500	−	110.072i	−0.960478	−	0.202338i
$545$	643.059			1.17993
$546$	−270.111	−	652.105i	−0.494708	−	1.19433i
$547$	−232.929	+	155.638i	−0.425830	+	0.284531i	−0.749962	−	0.661481i	$-0.769928\pi$
$547$	−232.929	+	155.638i	−0.425830	+	0.284531i	0.324131	+	0.946012i	$0.394928\pi$
$548$	248.329	−	248.329i	0.453155	−	0.453155i
$549$	227.316	+	45.2159i	0.414054	+	0.0823604i
$550$	7.01641	+	4.68821i	0.0127571	+	0.00852403i
$551$	−363.193	+	72.2435i	−0.659152	+	0.131113i
$552$	−106.539	−	44.1301i	−0.193006	−	0.0799458i
$553$	−268.458	+	648.115i	−0.485458	+	1.17200i
$554$	136.087	+	684.154i	0.245644	+	1.23493i
$555$	73.3979	−	109.848i	0.132248	−	0.197924i
$556$	67.9864	−	341.791i	0.122278	−	0.614732i
$557$	559.813	+	559.813i	1.00505	+	1.00505i	0.999987	+	0.00506358i	$0.00161180\pi$
$557$	559.813	+	559.813i	1.00505	+	1.00505i	0.00506358	+	0.999987i	$0.498388\pi$
$558$	−173.017	−	258.938i	−0.310067	−	0.464047i
$559$	75.1404	−	31.1242i	0.134419	−	0.0556783i
$560$			1995.91i			3.56412i
$561$	−10.4475	+	15.2604i	−0.0186230	+	0.0272021i
$562$	−1763.31			−3.13756
$563$	−324.348	−	783.046i	−0.576107	−	1.39085i	−0.896281	−	0.443487i	$-0.853741\pi$
$563$	−324.348	−	783.046i	−0.576107	−	1.39085i	0.320174	−	0.947359i	$-0.396259\pi$
$564$	−3.00773	+	2.00970i	−0.00533285	+	0.00356329i
$565$	−317.703	+	317.703i	−0.562306	+	0.562306i
$566$	−1123.13	−	223.405i	−1.98433	−	0.394708i
$567$	−97.3996	−	65.0803i	−0.171781	−	0.114780i
$568$	−828.704	+	164.839i	−1.45899	+	0.290210i
$569$	465.556	+	192.840i	0.818201	+	0.338910i	0.752221	−	0.658911i	$-0.228983\pi$
$569$	465.556	+	192.840i	0.818201	+	0.338910i	0.0659798	+	0.997821i	$0.478983\pi$
$570$	105.489	−	254.673i	0.185069	−	0.446796i
$571$	−146.741	−	737.716i	−0.256989	−	1.29197i	−0.866493	−	0.499189i	$-0.833631\pi$
$571$	−146.741	−	737.716i	−0.256989	−	1.29197i	0.609504	−	0.792783i	$-0.291369\pi$
$572$	27.2158	−	40.7313i	0.0475800	−	0.0712085i
$573$	36.1981	−	181.980i	0.0631730	−	0.317592i
$574$	1418.94	+	1418.94i	2.47201	+	2.47201i
$575$	7.70514	+	11.5316i	0.0134002	+	0.0200549i
$576$	−3.62512	+	1.50157i	−0.00629361	+	0.00260690i
$577$			922.774i			1.59926i	0.600492	+	0.799631i	$0.294972\pi$
$577$			922.774i			1.59926i	−0.600492	+	0.799631i	$0.705028\pi$
$578$	−752.428	+	719.227i	−1.30178	+	1.24434i
$579$	411.414			0.710560
$580$	826.663	+	1995.74i	1.42528	+	3.44093i
$581$	1122.11	−	749.773i	1.93135	−	1.29049i
$582$	833.739	−	833.739i	1.43254	−	1.43254i
$583$	−11.6620	−	2.31971i	−0.0200034	−	0.00397893i
$584$	−1406.51	−	939.802i	−2.40841	−	1.60925i
$585$	137.099	−	27.2707i	0.234358	−	0.0466166i
$586$	913.496	+	378.383i	1.55887	+	0.645704i
$587$	18.4318	−	44.4983i	0.0314000	−	0.0758063i	−0.907402	−	0.420264i	$-0.861937\pi$
$587$	18.4318	−	44.4983i	0.0314000	−	0.0758063i	0.938802	+	0.344458i	$0.111937\pi$
$588$	365.044	+	1835.20i	0.620823	+	3.12109i
$589$	132.007	−	197.563i	0.224121	−	0.335421i
$590$	−79.8922	+	401.645i	−0.135411	+	0.680755i
$591$	65.1462	+	65.1462i	0.110231	+	0.110231i
$592$	226.181	+	338.503i	0.382062	+	0.571796i
$593$	−514.778	+	213.228i	−0.868090	+	0.359575i	−0.771866	−	0.635785i	$-0.780677\pi$
$593$	−514.778	+	213.228i	−0.868090	+	0.359575i	−0.0962241	+	0.995360i	$0.530677\pi$
$594$		−	11.7546i		−	0.0197889i
$595$	978.634	+	669.990i	1.64476	+	1.12603i
$596$	1676.26			2.81252
$597$	−44.5405	−	107.530i	−0.0746072	−	0.180118i
$598$	96.7873	−	64.6712i	0.161852	−	0.108146i
$599$	−824.786	+	824.786i	−1.37694	+	1.37694i	−0.527192	+	0.849746i	$0.676755\pi$
$599$	−824.786	+	824.786i	−1.37694	+	1.37694i	−0.849746	+	0.527192i	$0.823245\pi$
$600$	−113.478	−	22.5723i	−0.189131	−	0.0376205i
$601$	−396.011	−	264.606i	−0.658921	−	0.440277i	0.180635	−	0.983550i	$-0.442185\pi$
$601$	−396.011	−	264.606i	−0.658921	−	0.440277i	−0.839556	+	0.543273i	$0.817185\pi$
$602$	−430.164	+	85.5650i	−0.714559	+	0.142135i
$603$	221.173	+	91.6127i	0.366787	+	0.151928i
$604$	612.939	−	1479.77i	1.01480	−	2.44994i
$605$	−126.117	−	634.032i	−0.208457	−	1.04799i
$606$	182.664	−	273.376i	0.301425	−	0.451115i
$607$	82.7307	−	415.915i	0.136294	−	0.685198i	−0.850855	−	0.525400i	$-0.823916\pi$
$607$	82.7307	−	415.915i	0.136294	−	0.685198i	0.987150	−	0.159798i	$-0.0510843\pi$
$608$	183.099	+	183.099i	0.301149	+	0.301149i
$609$	562.596	+	841.985i	0.923803	+	1.38257i
$610$	1377.92	−	570.752i	2.25888	−	0.935659i
$611$		−	2.02354i		−	0.00331184i
$612$	94.3238	−	447.745i	0.154124	−	0.731610i
$613$	108.618			0.177191			0.0885955	−	0.996068i	$-0.471762\pi$
$613$	108.618			0.177191			0.0885955	+	0.996068i	$0.471762\pi$
$614$	−651.449	−	1572.74i	−1.06099	−	2.56146i
$615$	−330.433	+	220.788i	−0.537289	+	0.359005i
$616$	−103.517	+	103.517i	−0.168047	+	0.168047i
$617$	299.101	+	59.4949i	0.484767	+	0.0964261i	0.431422	−	0.902150i	$-0.358012\pi$
$617$	299.101	+	59.4949i	0.484767	+	0.0964261i	0.0533443	+	0.998576i	$0.483012\pi$
$618$	−639.999	−	427.634i	−1.03560	−	0.691964i
$619$	838.449	−	166.778i	1.35452	−	0.269431i	0.536151	−	0.844122i	$-0.319878\pi$
$619$	838.449	−	166.778i	1.35452	−	0.269431i	0.818371	+	0.574691i	$0.194878\pi$
$620$	−1280.56	−	530.426i	−2.06542	−	0.855526i
$621$	7.39299	−	17.8482i	0.0119050	−	0.0287411i
$622$	−95.4584	−	479.902i	−0.153470	−	0.771546i
$623$	−594.422	+	889.616i	−0.954129	+	1.42796i
$624$	−84.0366	+	422.481i	−0.134674	+	0.677052i
$625$	−498.045	−	498.045i	−0.796872	−	0.796872i
$626$	181.035	+	270.938i	0.289193	+	0.432808i
$627$	8.28575	−	3.43207i	0.0132149	−	0.00547380i
$628$		−	501.229i		−	0.798135i
$629$	241.900	+	2.72836i	0.384578	+	0.00433761i
$630$	−753.812			−1.19653
$631$	44.6811	+	107.870i	0.0708099	+	0.170950i	0.955322	−	0.295567i	$-0.0955085\pi$
$631$	44.6811	+	107.870i	0.0708099	+	0.170950i	−0.884512	+	0.466517i	$0.845509\pi$
$632$	802.511	−	536.221i	1.26980	−	0.848451i
$633$	342.941	−	342.941i	0.541770	−	0.541770i
$634$	−201.615	−	40.1038i	−0.318005	−	0.0632552i
$635$	365.140	+	243.979i	0.575023	+	0.384218i
$636$	288.537	−	57.3936i	0.453675	−	0.0902415i
$637$	−967.039	−	400.561i	−1.51811	−	0.628824i
$638$	−38.8861	+	93.8793i	−0.0609500	+	0.147146i
$639$	−27.6151	−	138.830i	−0.0432161	−	0.217262i
$640$	−388.169	+	580.936i	−0.606514	+	0.907713i
$641$	−248.642	+	1250.01i	−0.387897	+	1.95009i	−0.0879831	+	0.996122i	$0.528042\pi$
$641$	−248.642	+	1250.01i	−0.387897	+	1.95009i	−0.299914	+	0.953966i	$0.596958\pi$
$642$	415.504	+	415.504i	0.647202	+	0.647202i
$643$	−113.962	−	170.557i	−0.177235	−	0.265251i	0.732206	−	0.681083i	$-0.238491\pi$
$643$	−113.962	−	170.557i	−0.177235	−	0.265251i	−0.909442	+	0.415831i	$0.863491\pi$
$644$	−401.118	+	166.148i	−0.622854	+	0.257994i
$645$		−	86.8599i		−	0.134666i
$646$	496.142	−	92.8845i	0.768022	−	0.143784i
$647$	−564.561			−0.872582			−0.436291	−	0.899806i	$-0.643708\pi$
$647$	−564.561			−0.872582			−0.436291	+	0.899806i	$0.643708\pi$
$648$	61.6763	+	148.900i	0.0951795	+	0.229784i
$649$	−11.0780	+	7.40211i	−0.0170694	+	0.0114054i
$650$	82.5851	−	82.5851i	0.127054	−	0.127054i
$651$	−637.277	−	126.762i	−0.978919	−	0.194719i
$652$	691.972	+	462.361i	1.06131	+	0.709142i
$653$	−6.32354	+	1.25783i	−0.00968382	+	0.00192623i	−0.199930	−	0.979810i	$-0.564071\pi$
$653$	−6.32354	+	1.25783i	−0.00968382	+	0.00192623i	0.190246	+	0.981736i	$0.439071\pi$
$654$	−691.450	−	286.408i	−1.05726	−	0.437933i
$655$	2.85784	−	6.89944i	0.00436312	−	0.0105335i
$656$	−238.915	−	1201.11i	−0.364200	−	1.83096i
$657$	157.442	−	235.629i	0.239638	−	0.358644i
$658$	−2.12887	+	10.7025i	−0.00323536	+	0.0162653i
$659$	−623.968	−	623.968i	−0.946841	−	0.946841i	0.0518159	−	0.998657i	$-0.483499\pi$
$659$	−623.968	−	623.968i	−0.946841	−	0.946841i	−0.998657	+	0.0518159i	$0.983499\pi$
$660$	−29.0657	−	43.5000i	−0.0440390	−	0.0659090i
$661$	−106.167	+	43.9758i	−0.160616	+	0.0665292i	−0.461543	−	0.887118i	$-0.652704\pi$
$661$	−106.167	+	43.9758i	−0.160616	+	0.0665292i	0.300927	+	0.953647i	$0.402704\pi$
$662$			326.952i			0.493885i
$663$	178.941	+	183.024i	0.269896	+	0.276054i
$664$	−1856.77			−2.79634
$665$	−220.096	−	531.358i	−0.330971	−	0.799035i
$666$	−127.845	+	85.4236i	−0.191960	+	0.128264i
$667$	−118.090	+	118.090i	−0.177046	+	0.177046i
$668$	−837.606	−	166.610i	−1.25390	−	0.249416i
$669$	467.512	+	312.382i	0.698822	+	0.466938i
$670$	1510.92	−	300.541i	2.25511	−	0.448569i
$671$	44.8302	+	18.5693i	0.0668111	+	0.0276741i
$672$	270.979	−	654.200i	0.403242	−	0.973512i
$673$	119.601	+	601.276i	0.177714	+	0.893427i	0.962004	+	0.273034i	$0.0880270\pi$
$673$	119.601	+	601.276i	0.177714	+	0.893427i	−0.784291	+	0.620393i	$0.786973\pi$
$674$	319.665	−	478.412i	0.474280	−	0.709810i
$675$	3.78147	−	19.0107i	0.00560218	−	0.0281640i
$676$	592.747	+	592.747i	0.876844	+	0.876844i
$677$	−731.412	−	1094.63i	−1.08037	−	1.61689i	−0.734500	−	0.678609i	$-0.762583\pi$
$677$	−731.412	−	1094.63i	−1.08037	−	1.61689i	−0.345872	−	0.938282i	$-0.612417\pi$
$678$	483.110	−	200.111i	0.712552	−	0.295149i
$679$		−	2460.08i		−	3.62309i
$680$	−607.404	−	1514.49i	−0.893241	−	2.22719i
$681$	−118.016			−0.173298
$682$	−24.9511	−	60.2374i	−0.0365853	−	0.0883246i
$683$	−438.371	+	292.910i	−0.641832	+	0.428858i	−0.833437	−	0.552614i	$-0.813630\pi$
$683$	−438.371	+	292.910i	−0.641832	+	0.428858i	0.191606	+	0.981472i	$0.438630\pi$
$684$	−156.903	+	156.903i	−0.229390	+	0.229390i
$685$	205.777	+	40.9315i	0.300404	+	0.0597541i
$686$	2783.37	+	1859.79i	4.05739	+	2.71106i
$687$	−558.185	+	111.030i	−0.812496	+	0.161616i
$688$	247.290	+	102.431i	0.359433	+	0.148882i
$689$	−62.9777	+	152.042i	−0.0914044	+	0.220670i
$690$	−24.2532	−	121.929i	−0.0351495	−	0.176709i
$691$	−642.811	+	962.035i	−0.930262	+	1.39224i	−0.0104209	+	0.999946i	$0.503317\pi$
$691$	−642.811	+	962.035i	−0.930262	+	1.39224i	−0.919841	+	0.392290i	$0.871683\pi$
$692$	110.297	−	554.499i	0.159388	−	0.801299i
$693$	−17.3419	−	17.3419i	−0.0250244	−	0.0250244i
$694$	942.771	+	1410.96i	1.35846	+	2.03308i
$695$	192.345	−	79.6721i	0.276756	−	0.114636i
$696$		−	1393.24i		−	2.00178i
$697$	−669.128	−	286.045i	−0.960011	−	0.410395i
$698$	1249.24			1.78974
$699$	30.9409	+	74.6979i	0.0442645	+	0.106864i
$700$	−362.199	+	242.014i	−0.517427	+	0.345734i
$701$	745.783	−	745.783i	1.06388	−	1.06388i	0.0660700	−	0.997815i	$-0.478954\pi$
$701$	745.783	−	745.783i	1.06388	−	1.06388i	0.997815	−	0.0660700i	$-0.0210461\pi$
$702$	−159.562	−	31.7388i	−0.227296	−	0.0452120i
$703$	−97.5426	−	65.1759i	−0.138752	−	0.0927110i
$704$	−0.805715	+	0.160267i	−0.00114448	+	0.000227652i
$705$	−1.99658	−	0.827012i	−0.00283203	−	0.00117307i
$706$	−765.676	+	1848.51i	−1.08453	+	2.61828i
$707$	−133.830	−	672.808i	−0.189293	−	0.951638i
$708$	183.141	−	274.089i	0.258673	−	0.387132i
$709$	−165.977	+	834.423i	−0.234100	+	1.17690i	0.667594	+	0.744526i	$0.267324\pi$
$709$	−165.977	+	834.423i	−0.234100	+	1.17690i	−0.901694	+	0.432375i	$0.857676\pi$
$710$	−644.092	−	644.092i	−0.907172	−	0.907172i
$711$	89.8316	+	134.442i	0.126345	+	0.189089i
$712$	1360.00	−	563.331i	1.91012	−	0.791196i
$713$		−	107.158i		−	0.150291i
$714$	−753.875	−	1156.27i	−1.05585	−	1.61943i
$715$	29.2659			0.0409313
$716$	714.393	+	1724.70i	0.997755	+	2.40879i
$717$	−211.765	+	141.497i	−0.295349	+	0.197346i
$718$	−809.919	+	809.919i	−1.12802	+	1.12802i
$719$	−73.7205	−	14.6639i	−0.102532	−	0.0203949i	0.143558	−	0.989642i	$-0.454146\pi$
$719$	−73.7205	−	14.6639i	−0.102532	−	0.0203949i	−0.246090	+	0.969247i	$0.579146\pi$
$720$	382.508	+	255.583i	0.531261	+	0.354977i
$721$	−1575.11	+	313.309i	−2.18462	+	0.434548i
$722$	975.085	+	403.894i	1.35053	+	0.559409i
$723$	70.0397	−	169.091i	0.0968738	−	0.233874i
$724$	215.264	+	1082.21i	0.297326	+	1.49476i
$725$	−93.0917	+	139.322i	−0.128402	+	0.192168i
$726$	−146.780	+	737.913i	−0.202176	+	1.01641i
$727$	−96.0782	−	96.0782i	−0.132157	−	0.132157i	0.637934	−	0.770091i	$-0.279789\pi$
$727$	−96.0782	−	96.0782i	−0.132157	−	0.132157i	−0.770091	+	0.637934i	$0.779789\pi$
$728$	1125.68	+	1684.69i	1.54626	+	2.31414i
$729$	−24.9447	+	10.3325i	−0.0342178	+	0.0141735i
$730$		−	1823.62i		−	2.49811i
$731$	133.235	−	86.8671i	0.182263	−	0.118833i
$732$	−1200.56			−1.64011
$733$	92.9466	+	224.393i	0.126803	+	0.306130i	0.974513	−	0.224330i	$-0.0720194\pi$
$733$	92.9466	+	224.393i	0.126803	+	0.306130i	−0.847710	+	0.530460i	$0.822019\pi$
$734$	−592.866	+	396.140i	−0.807719	+	0.539701i
$735$	−790.450	+	790.450i	−1.07544	+	1.07544i
$736$	114.535	+	22.7825i	0.155618	+	0.0309544i
$737$	41.6738	+	27.8455i	0.0565452	+	0.0377823i
$738$	453.633	−	90.2333i	0.614679	−	0.122267i
$739$	75.0000	+	31.0660i	0.101489	+	0.0420379i	0.432850	−	0.901466i	$-0.357508\pi$
$739$	75.0000	+	31.0660i	0.101489	+	0.0420379i	−0.331361	+	0.943504i	$0.607508\pi$
$740$	−261.887	+	632.250i	−0.353901	+	0.854392i
$741$	−24.2159	−	121.741i	−0.0326800	−	0.164293i
$742$	493.046	−	737.896i	0.664483	−	0.994469i
$743$	161.153	−	810.170i	0.216895	−	1.09040i	−0.706841	−	0.707373i	$-0.749880\pi$
$743$	161.153	−	810.170i	0.216895	−	1.09040i	0.923735	−	0.383031i	$-0.125120\pi$
$744$	632.131	+	632.131i	0.849638	+	0.849638i
$745$	556.366	+	832.661i	0.746801	+	1.11767i
$746$	−957.073	+	396.433i	−1.28294	+	0.531411i
$747$		−	311.060i		−	0.416412i
$748$	37.6565	−	88.0876i	0.0503430	−	0.117764i
$749$	1226.01			1.63686
$750$	272.167	+	657.069i	0.362889	+	0.876092i
$751$	288.724	−	192.919i	0.384453	−	0.256883i	−0.348293	−	0.937386i	$-0.613238\pi$
$751$	288.724	−	192.919i	0.384453	−	0.256883i	0.732746	+	0.680503i	$0.238238\pi$
$752$	4.70900	−	4.70900i	0.00626197	−	0.00626197i
$753$	−375.108	−	74.6136i	−0.498151	−	0.0990885i
$754$	1169.36	+	781.343i	1.55088	+	1.03626i
$755$	938.494	−	186.678i	1.24304	−	0.247256i
$756$	560.603	+	232.209i	0.741538	+	0.307155i
$757$	169.613	−	409.481i	0.224059	−	0.540926i	−0.771375	−	0.636381i	$-0.780431\pi$
$757$	169.613	−	409.481i	0.224059	−	0.540926i	0.995434	+	0.0954548i	$0.0304305\pi$
$758$	−426.747	−	2145.40i	−0.562990	−	2.83034i
$759$	2.24709	−	3.36300i	0.00296059	−	0.00443083i
$760$	−154.375	+	776.094i	−0.203124	+	1.02118i
$761$	522.483	+	522.483i	0.686574	+	0.686574i	0.961473	−	0.274899i	$-0.0886444\pi$
$761$	522.483	+	522.483i	0.686574	+	0.686574i	−0.274899	+	0.961473i	$0.588644\pi$
$762$	−283.953	−	424.965i	−0.372641	−	0.557697i
$763$	−1442.66	+	597.570i	−1.89078	+	0.783185i
$764$			961.125i			1.25802i
$765$	253.719	−	101.757i	0.331658	−	0.133015i
$766$	−1230.84			−1.60684
$767$	70.5674	+	170.365i	0.0920045	+	0.222118i
$768$	668.584	−	446.734i	0.870552	−	0.581684i
$769$	669.907	−	669.907i	0.871140	−	0.871140i	−0.121456	−	0.992597i	$-0.538756\pi$
$769$	669.907	−	669.907i	0.871140	−	0.871140i	0.992597	+	0.121456i	$0.0387564\pi$
$770$	−154.788	−	30.7893i	−0.201024	−	0.0399861i
$771$	−364.645	−	243.648i	−0.472951	−	0.316016i
$772$	−2090.17	+	415.761i	−2.70748	+	0.538551i
$773$	929.368	+	384.957i	1.20229	+	0.498004i	0.891737	−	0.452553i	$-0.149487\pi$
$773$	929.368	+	384.957i	1.20229	+	0.498004i	0.310550	+	0.950557i	$0.399487\pi$
$774$	−38.6859	+	93.3961i	−0.0499818	+	0.120667i
$775$	−20.9751	−	105.449i	−0.0270646	−	0.136063i
$776$	−1880.42	+	2814.25i	−2.42323	+	3.62662i
$777$	−62.5862	+	314.642i	−0.0805485	+	0.404944i
$778$	−977.798	−	977.798i	−1.25681	−	1.25681i
$779$	196.056	+	293.418i	0.251676	+	0.376660i
$780$	−668.969	+	277.096i	−0.857652	+	0.355251i
$781$		−	29.6354i		−	0.0379455i
$782$	162.772	−	159.141i	0.208148	−	0.203505i
$783$	233.405			0.298091
$784$	−1318.26	−	3182.56i	−1.68145	−	4.05939i
$785$	248.979	−	166.362i	0.317170	−	0.211926i
$786$	−6.14579	+	6.14579i	−0.00781908	+	0.00781908i
$787$	−176.230	−	35.0543i	−0.223926	−	0.0445417i	0.0818519	−	0.996645i	$-0.473917\pi$
$787$	−176.230	−	35.0543i	−0.223926	−	0.0445417i	−0.305778	+	0.952103i	$0.598917\pi$
$788$	−396.808	−	265.138i	−0.503563	−	0.336470i
$789$	792.699	−	157.678i	1.00469	−	0.199845i
$790$	961.297	+	398.182i	1.21683	+	0.504028i
$791$	417.517	−	1007.98i	0.527835	−	1.27431i
$792$	6.58286	+	33.0943i	0.00831170	+	0.0417857i
$793$	373.115	−	558.406i	0.470511	−	0.704169i
$794$	54.0428	−	271.692i	0.0680640	−	0.342181i
$795$	124.278	+	124.278i	0.156324	+	0.156324i
$796$	334.953	+	501.293i	0.420795	+	0.629765i
$797$	461.180	−	191.027i	0.578645	−	0.239682i	−0.0741123	−	0.997250i	$-0.523612\pi$
$797$	461.180	−	191.027i	0.578645	−	0.239682i	0.652757	+	0.757567i	$0.273612\pi$
$798$			669.370i			0.838810i
$799$	−0.728194	−	3.88964i	−0.000911381	−	0.00486814i
$800$	117.168			0.146460
$801$	94.3733	+	227.837i	0.117819	+	0.284441i
$802$	2311.29	−	1544.36i	2.88191	−	1.92563i
$803$	41.9535	−	41.9535i	0.0522459	−	0.0522459i
$804$	−1216.24	−	241.925i	−1.51274	−	0.300902i
$805$	−215.667	−	144.104i	−0.267909	−	0.179011i
$806$	−885.060	+	176.049i	−1.09809	+	0.218424i
$807$	254.083	+	105.245i	0.314849	+	0.130415i
$808$	−361.181	+	871.968i	−0.447006	+	1.07917i
$809$	115.250	+	579.401i	0.142460	+	0.716195i	0.984305	+	0.176475i	$0.0564696\pi$
$809$	115.250	+	579.401i	0.142460	+	0.716195i	−0.841845	+	0.539719i	$0.818530\pi$
$810$	−96.5284	+	144.465i	−0.119171	+	0.178352i
$811$	−158.366	+	796.160i	−0.195273	+	0.981702i	0.751484	+	0.659752i	$0.229339\pi$
$811$	−158.366	+	796.160i	−0.195273	+	0.981702i	−0.946756	+	0.321951i	$0.895661\pi$
$812$	−3709.13	−	3709.13i	−4.56790	−	4.56790i
$813$	−160.874	−	240.765i	−0.197877	−	0.296144i
$814$	−29.7409	+	12.3191i	−0.0365368	+	0.0151340i
$815$			497.190i			0.610049i
$816$	−9.50059	+	842.334i	−0.0116429	+	1.03227i
$817$	−77.1299			−0.0944062
$818$	473.197	+	1142.40i	0.578481	+	1.39658i
$819$	−282.232	+	188.581i	−0.344605	+	0.230258i
$820$	1455.63	−	1455.63i	1.77516	−	1.77516i
$821$	−243.851	−	48.5050i	−0.297017	−	0.0590804i	0.0443324	−	0.999017i	$-0.485884\pi$
$821$	−243.851	−	48.5050i	−0.297017	−	0.0590804i	−0.341349	+	0.939936i	$0.610884\pi$
$822$	−203.031	−	135.661i	−0.246997	−	0.165038i
$823$	747.810	−	148.749i	0.908639	−	0.180740i	0.281422	−	0.959584i	$-0.409194\pi$
$823$	747.810	−	148.749i	0.908639	−	0.180740i	0.627217	+	0.778844i	$0.284194\pi$
$824$	2041.36	+	845.560i	2.47738	+	1.02617i
$825$	1.55298	−	3.74922i	0.00188240	−	0.00454451i
$826$	−194.000	−	975.306i	−0.234867	−	1.18076i
$827$	83.5690	−	125.070i	0.101051	−	0.151233i	−0.777499	−	0.628885i	$-0.783512\pi$
$827$	83.5690	−	125.070i	0.101051	−	0.151233i	0.878549	+	0.477651i	$0.158512\pi$
$828$	−19.5229	+	98.1485i	−0.0235784	+	0.118537i
$829$	−53.6142	−	53.6142i	−0.0646734	−	0.0646734i	0.674030	−	0.738704i	$-0.264562\pi$
$829$	−53.6142	−	53.6142i	−0.0646734	−	0.0646734i	−0.738704	+	0.674030i	$0.764562\pi$
$830$	−1112.08	−	1664.34i	−1.33985	−	2.00523i
$831$	309.922	−	128.374i	0.372950	−	0.154481i
$832$			11.3699i			0.0136657i
$833$	−2002.99	−	421.957i	−2.40455	−	0.506551i
$834$	−242.304			−0.290533
$835$	−195.247	−	471.369i	−0.233829	−	0.564514i
$836$	−38.6271	+	25.8098i	−0.0462047	+	0.0308730i
$837$	−105.899	+	105.899i	−0.126522	+	0.126522i
$838$	1553.40	+	308.991i	1.85370	+	0.368724i
$839$	−436.985	−	291.984i	−0.520840	−	0.348014i	0.267197	−	0.963642i	$-0.413903\pi$
$839$	−436.985	−	291.984i	−0.520840	−	0.348014i	−0.788037	+	0.615627i	$0.788903\pi$
$840$	2122.31	−	422.154i	2.52656	−	0.502564i
$841$	−1087.14	−	450.306i	−1.29267	−	0.535442i
$842$	263.481	−	636.100i	0.312923	−	0.755464i
$843$	165.433	+	831.687i	0.196243	+	0.986580i
$844$	−1395.73	+	2088.86i	−1.65371	+	2.47495i
$845$	−97.7012	+	491.177i	−0.115623	+	0.581275i
$846$	1.77849	+	1.77849i	0.00210223	+	0.00210223i
$847$	872.116	+	1305.21i	1.02965	+	1.54098i
$848$	−500.374	+	207.262i	−0.590064	+	0.244412i
$849$			550.698i			0.648643i
$850$	129.026	−	188.464i	0.151795	−	0.221723i
$851$	−52.9069			−0.0621703
$852$	280.595	+	677.416i	0.329337	+	0.795089i
$853$	193.320	−	129.172i	0.226635	−	0.151433i	−0.437069	−	0.899428i	$-0.643983\pi$
$853$	193.320	−	129.172i	0.226635	−	0.151433i	0.663704	+	0.747995i	$0.268983\pi$
$854$	−2560.89	+	2560.89i	−2.99870	+	2.99870i
$855$	−130.017	−	25.8619i	−0.152066	−	0.0302479i
$856$	−1402.52	−	937.132i	−1.63845	−	1.09478i
$857$	−334.809	+	66.5977i	−0.390676	+	0.0777103i	−0.386520	−	0.922281i	$-0.626323\pi$
$857$	−334.809	+	66.5977i	−0.390676	+	0.0777103i	−0.00415619	+	0.999991i	$0.501323\pi$
$858$	−31.4682	−	13.0345i	−0.0366762	−	0.0151918i
$859$	282.676	−	682.440i	0.329076	−	0.794459i	−0.669586	−	0.742735i	$-0.733528\pi$
$859$	282.676	−	682.440i	0.329076	−	0.794459i	0.998661	−	0.0517240i	$-0.0164716\pi$
$860$	87.7777	+	441.288i	0.102067	+	0.513126i
$861$	536.135	−	802.382i	0.622688	−	0.931919i
$862$	273.588	−	1375.42i	0.317387	−	1.59561i
$863$	854.260	+	854.260i	0.989872	+	0.989872i	0.999949	−	0.0100770i	$-0.00320765\pi$
$863$	854.260	+	854.260i	0.989872	+	0.989872i	−0.0100770	+	0.999949i	$0.503208\pi$
$864$	−90.6749	−	135.705i	−0.104948	−	0.157066i
$865$	312.048	−	129.255i	0.360750	−	0.149427i
$866$			1366.34i			1.57776i
$867$	409.824	+	287.414i	0.472692	+	0.331504i
$868$	3365.76			3.87761
$869$	12.9548	+	31.2756i	0.0149077	+	0.0359904i
$870$	1248.85	−	834.454i	1.43546	−	0.959143i
$871$	490.512	−	490.512i	0.563160	−	0.563160i
$872$	2107.13	+	419.134i	2.41643	+	0.480658i
$873$	−471.464	−	315.022i	−0.540050	−	0.360850i
$874$	−108.270	+	21.5363i	−0.123879	+	0.0246411i
$875$	1370.93	+	567.857i	1.56678	+	0.648980i
$876$	−561.761	+	1356.21i	−0.641280	+	1.54819i
$877$	148.725	+	747.693i	0.169584	+	0.852558i	0.968096	+	0.250579i	$0.0806209\pi$
$877$	148.725	+	747.693i	0.169584	+	0.852558i	−0.798512	+	0.601979i	$0.794379\pi$
$878$	1688.46	−	2526.97i	1.92308	−	2.87809i
$879$	92.7650	−	466.361i	0.105535	−	0.530559i
$880$	68.1051	+	68.1051i	0.0773921	+	0.0773921i
$881$	−236.268	−	353.599i	−0.268181	−	0.401361i	0.672798	−	0.739826i	$-0.265092\pi$
$881$	−236.268	−	353.599i	−0.268181	−	0.401361i	−0.940979	+	0.338465i	$0.890092\pi$
$882$	1201.98	−	497.878i	1.36279	−	0.564488i
$883$			52.7625i			0.0597537i	0.999554	+	0.0298768i	$0.00951151\pi$
$883$			52.7625i			0.0597537i	−0.999554	+	0.0298768i	$0.990488\pi$
$884$	−1094.06	−	749.014i	−1.23763	−	0.847301i
$885$	196.936			0.222527
$886$	−981.885	−	2370.48i	−1.10822	−	2.67548i
$887$	1154.65	−	771.510i	1.30174	−	0.869797i	0.305153	−	0.952303i	$-0.401293\pi$
$887$	1154.65	−	771.510i	1.30174	−	0.869797i	0.996591	+	0.0825066i	$0.0262926\pi$
$888$	312.101	−	312.101i	0.351465	−	0.351465i
$889$	−1045.89	−	208.040i	−1.17648	−	0.234016i
$890$	1319.50	+	881.659i	1.48258	+	0.990628i
$891$	−5.54419	+	1.10281i	−0.00622244	+	0.00123772i
$892$	−2690.86	−	1114.59i	−3.01666	−	1.24954i
$893$	−0.734370	+	1.77293i	−0.000822363	+	0.00198536i
$894$	−227.380	−	1143.12i	−0.254340	−	1.27865i
$895$	−619.607	+	927.308i	−0.692299	+	1.03610i
$896$	330.991	−	1664.00i	0.369409	−	1.85715i
$897$	−39.5835	−	39.5835i	−0.0441287	−	0.0441287i
$898$	−218.018	−	326.287i	−0.242781	−	0.363348i
$899$	1196.11	−	495.443i	1.33048	−	0.551105i
$900$			100.405i			0.111561i
$901$	−66.3417	+	314.918i	−0.0736312	+	0.349520i
$902$	96.8348			0.107356
$903$	80.7155	+	194.864i	0.0893860	+	0.215797i
$904$	−1248.10	+	833.953i	−1.38064	+	0.922514i
$905$	−466.124	+	466.124i	−0.515054	+	0.515054i
$906$	−1092.26	−	217.264i	−1.20558	−	0.239806i
$907$	713.035	+	476.435i	0.786146	+	0.525286i	0.882641	−	0.470047i	$-0.155763\pi$
$907$	713.035	+	476.435i	0.786146	+	0.525286i	−0.0964948	+	0.995333i	$0.530763\pi$
$908$	599.575	−	119.263i	0.660325	−	0.131347i
$909$	−146.078	−	60.5076i	−0.160702	−	0.0665650i
$910$	−835.894	+	2018.03i	−0.918565	+	2.21761i
$911$	282.374	+	1419.59i	0.309960	+	1.55827i	0.750702	+	0.660641i	$0.229715\pi$
$911$	282.374	+	1419.59i	0.309960	+	1.55827i	−0.440742	+	0.897634i	$0.645285\pi$
$912$	226.953	−	339.659i	0.248852	−	0.372433i
$913$	12.7052	−	63.8732i	0.0139158	−	0.0699596i
$914$	174.653	+	174.653i	0.191086	+	0.191086i
$915$	−398.477	−	596.363i	−0.435494	−	0.651763i
$916$	2723.63	−	1128.17i	2.97340	−	1.23162i
$917$			18.1341i			0.0197755i
$918$	−318.132	−	3.58817i	−0.346549	−	0.00390868i
$919$	449.711			0.489349			0.244674	−	0.969605i	$-0.421319\pi$
$919$	449.711			0.489349			0.244674	+	0.969605i	$0.421319\pi$
$920$	136.567	+	329.701i	0.148442	+	0.358370i
$921$	−680.681	+	454.817i	−0.739068	+	0.493829i
$922$	−1422.35	+	1422.35i	−1.54268	+	1.54268i
$923$	−402.284	−	80.0193i	−0.435844	−	0.0866948i
$924$	105.630	+	70.5797i	0.114318	+	0.0763849i
$925$	−52.0632	+	10.3560i	−0.0562845	+	0.0111957i
$926$	−1938.16	−	802.810i	−2.09304	−	0.866966i
$927$	−141.654	+	341.984i	−0.152809	+	0.368915i
$928$	275.252	+	1383.79i	0.296608	+	1.49115i
$929$	−503.194	+	753.082i	−0.541651	+	0.810638i	−0.996813	−	0.0797708i	$-0.974581\pi$
$929$	−503.194	+	753.082i	−0.541651	+	0.810638i	0.455162	+	0.890408i	$0.349581\pi$
$930$	−188.016	+	945.221i	−0.202168	+	1.01637i
$931$	701.904	+	701.904i	0.753925	+	0.753925i
$932$	−232.681	−	348.232i	−0.249658	−	0.373639i
$933$	−217.396	+	90.0482i	−0.233007	+	0.0965147i
$934$		−	207.062i		−	0.221694i
$935$	56.2549	−	10.5317i	0.0601657	−	0.0112638i
$936$	467.011			0.498943
$937$	73.0367	+	176.326i	0.0779474	+	0.188182i	0.958049	−	0.286603i	$-0.0925260\pi$
$937$	73.0367	+	176.326i	0.0779474	+	0.188182i	−0.880102	+	0.474784i	$0.842526\pi$
$938$	−3110.38	+	2078.29i	−3.31597	+	2.21566i
$939$	110.806	−	110.806i	0.118005	−	0.118005i
$940$	10.9793	+	2.18392i	0.0116801	+	0.00232332i
$941$	−1481.73	−	990.061i	−1.57463	−	1.05214i	−0.965952	−	0.258722i	$-0.916698\pi$
$941$	−1481.73	−	990.061i	−1.57463	−	1.05214i	−0.608682	−	0.793414i	$-0.708302\pi$
$942$	−341.810	+	67.9901i	−0.362855	+	0.0721764i
$943$	147.035	+	60.9038i	0.155922	+	0.0645851i
$944$	−232.240	+	560.677i	−0.246017	+	0.593937i
$945$	70.7222	+	355.545i	0.0748383	+	0.376238i
$946$	−11.7585	+	17.5979i	−0.0124297	+	0.0186024i
$947$	−112.682	+	566.488i	−0.118988	+	0.598192i	0.874573	+	0.484894i	$0.161142\pi$
$947$	−112.682	+	566.488i	−0.118988	+	0.598192i	−0.993561	+	0.113299i	$0.963858\pi$
$948$	−592.249	−	592.249i	−0.624735	−	0.624735i
$949$	−456.215	−	682.775i	−0.480733	−	0.719468i
$950$	−102.328	+	42.3858i	−0.107714	+	0.0446166i
$951$			98.8568i			0.103950i
$952$	2770.03	+	2833.23i	2.90969	+	2.97608i
$953$	−830.396			−0.871350			−0.435675	−	0.900104i	$-0.643490\pi$
$953$	−830.396			−0.871350			−0.435675	+	0.900104i	$0.643490\pi$
$954$	−78.2783	−	188.981i	−0.0820528	−	0.198093i
$955$	−477.426	+	319.006i	−0.499923	+	0.334038i
$956$	932.873	−	932.873i	0.975809	−	0.975809i
$957$	47.9276	+	9.53339i	0.0500811	+	0.00996174i
$958$	−2764.29	−	1847.04i	−2.88548	−	1.92801i
$959$	−499.683	+	99.3931i	−0.521046	+	0.103642i
$960$	11.2184	+	4.64682i	0.0116859	+	0.00484044i
$961$	49.8591	−	120.371i	0.0518825	−	0.125255i
$962$	86.9207	+	436.980i	0.0903541	+	0.454241i
$963$	156.995	−	234.960i	0.163027	−	0.243987i
$964$	−184.957	+	929.840i	−0.191864	+	0.964564i
$965$	−900.272	−	900.272i	−0.932924	−	0.932924i
$966$	167.714	+	251.002i	0.173617	+	0.259837i
$967$	309.359	−	128.141i	0.319916	−	0.132513i	−0.216946	−	0.976184i	$-0.569610\pi$
$967$	309.359	−	128.141i	0.319916	−	0.132513i	0.536862	+	0.843670i	$0.319610\pi$
$968$		−	2159.75i		−	2.23115i
$969$	−90.3579	−	225.297i	−0.0932486	−	0.232505i
$970$	−3648.84			−3.76169
$971$	−200.079	−	483.034i	−0.206055	−	0.497461i	0.786740	−	0.617284i	$-0.211767\pi$
$971$	−200.079	−	483.034i	−0.206055	−	0.497461i	−0.992795	+	0.119824i	$0.961767\pi$
$972$	116.289	−	77.7020i	0.119639	−	0.0799403i
$973$	−357.478	+	357.478i	−0.367398	+	0.367398i
$974$	2374.69	+	472.356i	2.43808	+	0.484965i
$975$	−46.7003	−	31.2041i	−0.0478978	−	0.0320043i
$976$	2167.76	−	431.193i	2.22106	−	0.441796i
$977$	−789.818	−	327.153i	−0.808411	−	0.334855i	−0.0600914	−	0.998193i	$-0.519139\pi$
$977$	−789.818	−	327.153i	−0.808411	−	0.334855i	−0.748320	+	0.663338i	$0.769139\pi$
$978$	221.440	−	534.604i	0.226421	−	0.546629i
$979$	10.0727	+	50.6389i	0.0102888	+	0.0517251i
$980$	3217.05	−	4814.65i	3.28270	−	4.91291i
$981$	−70.2163	+	353.001i	−0.0715762	+	0.359838i
$982$	−924.876	−	924.876i	−0.941828	−	0.941828i
$983$	301.609	+	451.390i	0.306825	+	0.459196i	0.952554	−	0.304371i	$-0.0984463\pi$
$983$	301.609	+	451.390i	0.306825	+	0.459196i	−0.645729	+	0.763567i	$0.723446\pi$
$984$	−1226.64	+	508.092i	−1.24659	+	0.516354i
$985$		−	285.111i		−	0.289453i
$986$	2528.92	+	1081.09i	2.56483	+	1.09644i
$987$	5.24771			0.00531683
$988$	246.056	+	594.031i	0.249044	+	0.601246i
$989$	−28.9223	+	19.3253i	−0.0292440	+	0.0195402i
$990$	−25.7218	+	25.7218i	−0.0259816	+	0.0259816i
$991$	1680.50	+	334.272i	1.69576	+	0.337308i	0.945942	−	0.324335i	$-0.105140\pi$
$991$	1680.50	+	334.272i	1.69576	+	0.337308i	0.749819	+	0.661643i	$0.230140\pi$
$992$	−752.728	−	502.957i	−0.758798	−	0.507013i
$993$	154.211	−	30.6744i	0.155298	−	0.0308907i
$994$	2043.51	+	846.449i	2.05584	+	0.851559i
$995$	−137.837	+	332.767i	−0.138529	+	0.334439i
$996$	314.347	+	1580.33i	0.315609	+	1.58667i
$997$	111.276	−	166.536i	0.111610	−	0.167037i	−0.771459	−	0.636279i	$-0.780473\pi$
$997$	111.276	−	166.536i	0.111610	−	0.167037i	0.883070	+	0.469242i	$0.155473\pi$
$998$	−483.359	+	2430.01i	−0.484328	+	2.43488i
$999$	52.2854	+	52.2854i	0.0523378	+	0.0523378i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.3.j.a.46.6	yes	48
3.2	odd	2		153.3.p.c.46.1		48
17.10	odd	16	inner	51.3.j.a.10.6	✓	48
51.44	even	16		153.3.p.c.10.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.3.j.a.10.6	✓	48	17.10	odd	16	inner
51.3.j.a.46.6	yes	48	1.1	even	1	trivial
153.3.p.c.10.1		48	51.44	even	16
153.3.p.c.46.1		48	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	51.j (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37830 + 3.32751i) q^{2} +(1.44015 - 0.962276i) q^{3} +(-6.34417 + 6.34417i) q^{4} +(-5.25707 - 1.04570i) q^{5} +(5.18693 + 3.46580i) q^{6} +(12.7656 - 2.53924i) q^{7} +(-16.5444 - 6.85292i) q^{8} +(1.14805 - 2.77164i) q^{9} +(-3.76625 - 18.9342i) q^{10} +(0.348948 - 0.522238i) q^{11} +(-3.03170 + 15.2414i) q^{12} +(-6.14688 - 6.14688i) q^{13} +(26.0442 + 38.9779i) q^{14} +(-8.57721 + 3.55280i) q^{15} -28.6090i q^{16} +(-14.0276 - 9.60351i) q^{17} +10.8050 q^{18} +(3.15481 + 7.61639i) q^{19} +(39.9859 - 26.7177i) q^{20} +(15.9409 - 15.9409i) q^{21} +(2.21870 + 0.441328i) q^{22} +(3.09133 + 2.06556i) q^{23} +(-30.4208 + 6.05107i) q^{24} +(3.44634 + 1.42752i) q^{25} +(11.9816 - 28.9260i) q^{26} +(-1.01372 - 5.09631i) q^{27} +(-64.8779 + 97.0967i) q^{28} +(-8.76324 + 44.0558i) q^{29} +(-23.6439 - 23.6439i) q^{30} +(-16.0127 - 23.9647i) q^{31} +(29.0190 - 12.0200i) q^{32} -1.08788i q^{33} +(12.6216 - 59.9133i) q^{34} -69.7651 q^{35} +(10.3003 + 24.8672i) q^{36} +(-11.8321 + 7.90593i) q^{37} +(-20.9953 + 20.9953i) q^{38} +(-14.7674 - 2.93742i) q^{39} +(79.8091 + 53.3267i) q^{40} +(41.9836 - 8.35106i) q^{41} +(75.0150 + 31.0722i) q^{42} +(-3.58037 + 8.64378i) q^{43} +(1.09938 + 5.52695i) q^{44} +(-8.93368 + 13.3702i) q^{45} +(-2.61239 + 13.1334i) q^{46} +(0.164599 + 0.164599i) q^{47} +(-27.5297 - 41.2012i) q^{48} +(111.243 - 46.0785i) q^{49} +13.4353i q^{50} +(-29.4430 - 0.332084i) q^{51} +77.9937 q^{52} +(-7.24464 - 17.4901i) q^{53} +(15.5608 - 10.3974i) q^{54} +(-2.38055 + 2.38055i) q^{55} +(-228.601 - 45.4716i) q^{56} +(11.8725 + 7.93293i) q^{57} +(-158.674 + 31.5623i) q^{58} +(-19.5979 - 8.11773i) q^{59} +(31.8757 - 76.9548i) q^{60} +(15.0720 + 75.7718i) q^{61} +(57.6724 - 86.3128i) q^{62} +(7.61772 - 38.2969i) q^{63} +(-0.924849 - 0.924849i) q^{64} +(25.8868 + 38.7424i) q^{65} +(3.61994 - 1.49943i) q^{66} +79.7985i q^{67} +(149.920 - 28.0670i) q^{68} +6.43960 q^{69} +(-96.1571 - 232.144i) q^{70} +(39.2316 - 26.2137i) q^{71} +(-37.9876 + 37.9876i) q^{72} +(92.6478 + 18.4288i) q^{73} +(-42.6151 - 28.4745i) q^{74} +(6.33691 - 1.26049i) q^{75} +(-68.3344 - 28.3050i) q^{76} +(3.12845 - 7.55275i) q^{77} +(-10.5796 - 53.1873i) q^{78} +(-29.9439 + 44.8141i) q^{79} +(-29.9163 + 150.400i) q^{80} +(-6.36396 - 6.36396i) q^{81} +(85.6542 + 128.191i) q^{82} +(95.7939 - 39.6791i) q^{83} +202.264i q^{84} +(63.7016 + 65.1549i) q^{85} -33.6971 q^{86} +(29.7735 + 71.8795i) q^{87} +(-9.35200 + 6.24880i) q^{88} +(-58.1264 + 58.1264i) q^{89} +(-56.8027 - 11.2988i) q^{90} +(-94.0772 - 62.8604i) q^{91} +(-32.7162 + 6.50765i) q^{92} +(-46.1213 - 19.1041i) q^{93} +(-0.320837 + 0.774569i) q^{94} +(-8.62065 - 43.3389i) q^{95} +(30.2250 - 45.2349i) q^{96} +(36.8737 - 185.377i) q^{97} +(306.653 + 306.653i) q^{98} +(-1.04684 - 1.56671i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{10} - 80 q^{11} - 48 q^{13} - 64 q^{14} + 16 q^{17} + 48 q^{19} + 224 q^{20} + 192 q^{22} + 112 q^{23} - 144 q^{24} + 80 q^{25} - 368 q^{26} - 240 q^{28} - 160 q^{29} - 192 q^{30} - 64 q^{31}+ \cdots + 240 q^{99}+O(q^{100}) \) 48 * q - 48 * q^10 - 80 * q^11 - 48 * q^13 - 64 * q^14 + 16 * q^17 + 48 * q^19 + 224 * q^20 + 192 * q^22 + 112 * q^23 - 144 * q^24 + 80 * q^25 - 368 * q^26 - 240 * q^28 - 160 * q^29 - 192 * q^30 - 64 * q^31 - 80 * q^32 + 16 * q^34 + 128 * q^35 + 48 * q^36 + 128 * q^37 + 400 * q^38 + 192 * q^39 + 128 * q^40 + 320 * q^41 + 432 * q^42 - 112 * q^43 + 704 * q^44 + 96 * q^45 + 80 * q^46 - 32 * q^49 + 128 * q^52 - 336 * q^53 - 608 * q^55 - 880 * q^56 - 752 * q^58 - 512 * q^59 - 400 * q^61 - 560 * q^62 + 160 * q^64 - 240 * q^65 - 208 * q^68 - 240 * q^69 + 80 * q^70 - 160 * q^71 - 288 * q^72 + 544 * q^73 - 48 * q^74 - 288 * q^75 + 496 * q^76 + 512 * q^77 - 384 * q^78 + 608 * q^79 + 816 * q^80 + 1184 * q^82 + 976 * q^83 - 32 * q^85 + 128 * q^86 + 144 * q^87 - 448 * q^88 + 240 * q^89 + 48 * q^90 - 640 * q^91 + 1280 * q^92 + 288 * q^93 - 32 * q^94 + 704 * q^95 + 768 * q^96 + 288 * q^97 + 1008 * q^98 + 240 * q^99

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