LMFDB - Embedded newform 1000.2.t.b.901.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(101,1000)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1000, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 6]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1000.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.t (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$56$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			901.30
Character	$\chi$	$=$	1000.901
Dual form			1000.2.t.b.101.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.343193 - 1.37194i) q^{2} +(1.46605 + 2.01785i) q^{3} +(-1.76444 - 0.941679i) q^{4} +(3.27150 - 1.31882i) q^{6} +0.110917 q^{7} +(-1.89747 + 2.09752i) q^{8} +(-0.995348 + 3.06337i) q^{9} +O(q^{10})$	\(q+(0.343193 - 1.37194i) q^{2} +(1.46605 + 2.01785i) q^{3} +(-1.76444 - 0.941679i) q^{4} +(3.27150 - 1.31882i) q^{6} +0.110917 q^{7} +(-1.89747 + 2.09752i) q^{8} +(-0.995348 + 3.06337i) q^{9} +(-1.63700 + 0.531893i) q^{11} +(-0.686591 - 4.94092i) q^{12} +(4.56868 + 1.48445i) q^{13} +(0.0380659 - 0.152171i) q^{14} +(2.22648 + 3.32307i) q^{16} +(0.371056 + 0.269588i) q^{17} +(3.86116 + 2.41688i) q^{18} +(2.40052 - 3.30403i) q^{19} +(0.162610 + 0.223814i) q^{21} +(0.167919 + 2.42841i) q^{22} +(1.98459 + 6.10792i) q^{23} +(-7.01427 - 0.753724i) q^{24} +(3.60452 - 5.75850i) q^{26} +(-0.524271 + 0.170346i) q^{27} +(-0.195706 - 0.104448i) q^{28} +(5.29624 + 7.28964i) q^{29} +(2.87291 + 2.08729i) q^{31} +(5.32316 - 1.91414i) q^{32} +(-3.47320 - 2.52343i) q^{33} +(0.497203 - 0.416546i) q^{34} +(4.64094 - 4.46782i) q^{36} +(1.53972 + 0.500287i) q^{37} +(-3.70909 - 4.42728i) q^{38} +(3.70252 + 11.3952i) q^{39} +(-3.51556 + 10.8198i) q^{41} +(0.362865 - 0.146280i) q^{42} -10.5304i q^{43} +(3.38926 + 0.603036i) q^{44} +(9.06080 - 0.626536i) q^{46} +(-2.51014 + 1.82373i) q^{47} +(-3.44131 + 9.36449i) q^{48} -6.98770 q^{49} +1.14397i q^{51} +(-6.66327 - 6.92145i) q^{52} +(-2.69868 - 3.71441i) q^{53} +(0.0537784 + 0.777730i) q^{54} +(-0.210462 + 0.232651i) q^{56} +10.1863 q^{57} +(11.8186 - 4.76436i) q^{58} +(-3.38621 - 1.10025i) q^{59} +(-11.1816 + 3.63312i) q^{61} +(3.84960 - 3.22512i) q^{62} +(-0.110401 + 0.339779i) q^{63} +(-0.799218 - 7.95998i) q^{64} +(-4.65397 + 3.89900i) q^{66} +(-2.19833 + 3.02574i) q^{67} +(-0.400840 - 0.825088i) q^{68} +(-9.41535 + 12.9591i) q^{69} +(9.04844 - 6.57408i) q^{71} +(-4.53684 - 7.90041i) q^{72} +(-3.20201 - 9.85476i) q^{73} +(1.21479 - 1.94072i) q^{74} +(-7.34690 + 3.56923i) q^{76} +(-0.181571 + 0.0589960i) q^{77} +(16.9042 - 1.16889i) q^{78} +(4.45472 - 3.23655i) q^{79} +(6.70522 + 4.87163i) q^{81} +(13.6376 + 8.53642i) q^{82} +(7.20048 - 9.91061i) q^{83} +(-0.0761547 - 0.548032i) q^{84} +(-14.4471 - 3.61397i) q^{86} +(-6.94483 + 21.3740i) q^{87} +(1.99050 - 4.44290i) q^{88} +(2.07551 + 6.38776i) q^{89} +(0.506744 + 0.164651i) q^{91} +(2.25003 - 12.6459i) q^{92} +8.85717i q^{93} +(1.64058 + 4.06966i) q^{94} +(11.6665 + 7.93510i) q^{96} +(4.54704 - 3.30362i) q^{97} +(-2.39813 + 9.58670i) q^{98} -5.54415i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9}+O(q^{10}) $ 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9	$ 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9} + 6 q^{14} - 30 q^{16} + 32 q^{24} - 28 q^{26} - 36 q^{31} - 18 q^{34} + 82 q^{36} + 20 q^{39} - 20 q^{41} + 64 q^{44} + 26 q^{46} + 160 q^{49} - 86 q^{54} + 72 q^{56} + 72 q^{64} + 80 q^{66} + 44 q^{71} - 8 q^{74} - 72 q^{76} - 28 q^{79} - 12 q^{81} - 156 q^{84} - 118 q^{86} - 48 q^{89} - 90 q^{94} + 92 q^{96}+O(q^{100}) $ 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9 + 6 * q^14 - 30 * q^16 + 32 * q^24 - 28 * q^26 - 36 * q^31 - 18 * q^34 + 82 * q^36 + 20 * q^39 - 20 * q^41 + 64 * q^44 + 26 * q^46 + 160 * q^49 - 86 * q^54 + 72 * q^56 + 72 * q^64 + 80 * q^66 + 44 * q^71 - 8 * q^74 - 72 * q^76 - 28 * q^79 - 12 * q^81 - 156 * q^84 - 118 * q^86 - 48 * q^89 - 90 * q^94 + 92 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.343193	−	1.37194i	0.242674	−	0.970108i
$2$	0.343193	−	1.37194i	0.242674	−	0.970108i
$3$	1.46605	+	2.01785i	0.846425	+	1.16500i	0.984639	+	0.174602i	$0.0558639\pi$
$3$	1.46605	+	2.01785i	0.846425	+	1.16500i	−0.138214	+	0.990402i	$0.544136\pi$
$4$	−1.76444	−	0.941679i	−0.882219	−	0.470840i
$5$		0			0
$5$		0			0
$6$	3.27150	−	1.31882i	1.33559	−	0.538408i
$7$	0.110917			0.0419227			0.0209613	−	0.999780i	$-0.493327\pi$
$7$	0.110917			0.0419227			0.0209613	+	0.999780i	$0.493327\pi$
$8$	−1.89747	+	2.09752i	−0.670857	+	0.741587i
$9$	−0.995348	+	3.06337i	−0.331783	+	1.02112i
$10$		0			0
$11$	−1.63700	+	0.531893i	−0.493574	+	0.160372i	−0.545219	−	0.838294i	$-0.683554\pi$
$11$	−1.63700	+	0.531893i	−0.493574	+	0.160372i	0.0516452	+	0.998665i	$0.483554\pi$
$12$	−0.686591	−	4.94092i	−0.198202	−	1.42632i
$13$	4.56868	+	1.48445i	1.26712	+	0.411713i	0.864027	−	0.503445i	$-0.167934\pi$
$13$	4.56868	+	1.48445i	1.26712	+	0.411713i	0.403096	+	0.915158i	$0.367934\pi$
$14$	0.0380659	−	0.152171i	0.0101735	−	0.0406695i
$15$		0			0
$16$	2.22648	+	3.32307i	0.556620	+	0.830767i
$17$	0.371056	+	0.269588i	0.0899944	+	0.0653848i	0.631873	−	0.775072i	$-0.282287\pi$
$17$	0.371056	+	0.269588i	0.0899944	+	0.0653848i	−0.541878	+	0.840457i	$0.682287\pi$
$18$	3.86116	+	2.41688i	0.910084	+	0.569665i
$19$	2.40052	−	3.30403i	0.550716	−	0.757996i	−0.439393	−	0.898295i	$-0.644806\pi$
$19$	2.40052	−	3.30403i	0.550716	−	0.757996i	0.990109	+	0.140299i	$0.0448064\pi$
$20$		0			0
$21$	0.162610	+	0.223814i	0.0354844	+	0.0488401i
$22$	0.167919	+	2.42841i	0.0358005	+	0.517738i
$23$	1.98459	+	6.10792i	0.413815	+	1.27359i	0.913307	+	0.407272i	$0.133520\pi$
$23$	1.98459	+	6.10792i	0.413815	+	1.27359i	−0.499492	+	0.866318i	$0.666480\pi$
$24$	−7.01427	−	0.753724i	−1.43178	−	0.153853i
$25$		0			0
$26$	3.60452	−	5.75850i	0.706904	−	1.12933i
$27$	−0.524271	+	0.170346i	−0.100896	+	0.0327831i
$28$	−0.195706	−	0.104448i	−0.0369850	−	0.0197389i
$29$	5.29624	+	7.28964i	0.983486	+	1.35365i	0.934930	+	0.354833i	$0.115462\pi$
$29$	5.29624	+	7.28964i	0.983486	+	1.35365i	0.0485566	+	0.998820i	$0.484538\pi$
$30$		0			0
$31$	2.87291	+	2.08729i	0.515990	+	0.374889i	0.815091	−	0.579333i	$-0.196687\pi$
$31$	2.87291	+	2.08729i	0.515990	+	0.374889i	−0.299101	+	0.954221i	$0.596687\pi$
$32$	5.32316	−	1.91414i	0.941011	−	0.338376i
$33$	−3.47320	−	2.52343i	−0.604607	−	0.439273i
$34$	0.497203	−	0.416546i	0.0852696	−	0.0714371i
$35$		0			0
$36$	4.64094	−	4.46782i	0.773490	−	0.744637i
$37$	1.53972	+	0.500287i	0.253129	+	0.0822467i	0.432833	−	0.901474i	$-0.357514\pi$
$37$	1.53972	+	0.500287i	0.253129	+	0.0822467i	−0.179704	+	0.983721i	$0.557514\pi$
$38$	−3.70909	−	4.42728i	−0.601693	−	0.718200i
$39$	3.70252	+	11.3952i	0.592877	+	1.82469i
$40$		0			0
$41$	−3.51556	+	10.8198i	−0.549039	+	1.68977i	0.162149	+	0.986766i	$0.448157\pi$
$41$	−3.51556	+	10.8198i	−0.549039	+	1.68977i	−0.711188	+	0.703002i	$0.751843\pi$
$42$	0.362865	−	0.146280i	0.0559913	−	0.0225715i
$43$		−	10.5304i		−	1.60588i	−0.596063	−	0.802938i	$-0.703269\pi$
$43$		−	10.5304i		−	1.60588i	0.596063	−	0.802938i	$-0.296731\pi$
$44$	3.38926	+	0.603036i	0.510950	+	0.0909111i
$45$		0			0
$46$	9.06080	−	0.626536i	1.33594	−	0.0923777i
$47$	−2.51014	+	1.82373i	−0.366142	+	0.266018i	−0.755609	−	0.655022i	$-0.772659\pi$
$47$	−2.51014	+	1.82373i	−0.366142	+	0.266018i	0.389467	+	0.921040i	$0.372659\pi$
$48$	−3.44131	+	9.36449i	−0.496710	+	1.35165i
$49$	−6.98770			−0.998242
$50$		0			0
$51$			1.14397i			0.160187i
$52$	−6.66327	−	6.92145i	−0.924029	−	0.959833i
$53$	−2.69868	−	3.71441i	−0.370692	−	0.510213i	0.582397	−	0.812905i	$-0.302115\pi$
$53$	−2.69868	−	3.71441i	−0.370692	−	0.510213i	−0.953089	+	0.302691i	$0.902115\pi$
$54$	0.0537784	+	0.777730i	0.00731832	+	0.105836i
$55$		0			0
$56$	−0.210462	+	0.232651i	−0.0281241	+	0.0310893i
$57$	10.1863			1.34921
$58$	11.8186	−	4.76436i	1.55186	−	0.625592i
$59$	−3.38621	−	1.10025i	−0.440847	−	0.143240i	0.0801796	−	0.996780i	$-0.474451\pi$
$59$	−3.38621	−	1.10025i	−0.440847	−	0.143240i	−0.521026	+	0.853541i	$0.674451\pi$
$60$		0			0
$61$	−11.1816	+	3.63312i	−1.43166	+	0.465174i	−0.919286	−	0.393590i	$-0.871233\pi$
$61$	−11.1816	+	3.63312i	−1.43166	+	0.465174i	−0.512372	+	0.858764i	$0.671233\pi$
$62$	3.84960	−	3.22512i	0.488900	−	0.409590i
$63$	−0.110401	+	0.339779i	−0.0139092	+	0.0428082i
$64$	−0.799218	−	7.95998i	−0.0999022	−	0.994997i
$65$		0			0
$66$	−4.65397	+	3.89900i	−0.572865	+	0.479934i
$67$	−2.19833	+	3.02574i	−0.268569	+	0.369653i	−0.921906	−	0.387414i	$-0.873368\pi$
$67$	−2.19833	+	3.02574i	−0.268569	+	0.369653i	0.653337	+	0.757067i	$0.273368\pi$
$68$	−0.400840	−	0.825088i	−0.0486090	−	0.100057i
$69$	−9.41535	+	12.9591i	−1.13348	+	1.56009i
$70$		0			0
$71$	9.04844	−	6.57408i	1.07385	−	0.780200i	0.0972518	−	0.995260i	$-0.468995\pi$
$71$	9.04844	−	6.57408i	1.07385	−	0.780200i	0.976601	+	0.215060i	$0.0689948\pi$
$72$	−4.53684	−	7.90041i	−0.534672	−	0.931072i
$73$	−3.20201	−	9.85476i	−0.374766	−	1.15341i	−0.943636	−	0.330985i	$-0.892619\pi$
$73$	−3.20201	−	9.85476i	−0.374766	−	1.15341i	0.568870	−	0.822428i	$-0.307381\pi$
$74$	1.21479	−	1.94072i	0.141216	−	0.225604i
$75$		0			0
$76$	−7.34690	+	3.56923i	−0.842747	+	0.409419i
$77$	−0.181571	+	0.0589960i	−0.0206919	+	0.00672322i
$78$	16.9042	−	1.16889i	1.91402	−	0.132351i
$79$	4.45472	−	3.23655i	0.501196	−	0.364140i	−0.308278	−	0.951296i	$-0.599753\pi$
$79$	4.45472	−	3.23655i	0.501196	−	0.364140i	0.809474	+	0.587156i	$0.199753\pi$
$80$		0			0
$81$	6.70522	+	4.87163i	0.745025	+	0.541292i
$82$	13.6376	+	8.53642i	1.50602	+	0.942690i
$83$	7.20048	−	9.91061i	0.790356	−	1.08783i	−0.203708	−	0.979032i	$-0.565299\pi$
$83$	7.20048	−	9.91061i	0.790356	−	1.08783i	0.994064	−	0.108800i	$-0.0347007\pi$
$84$	−0.0761547	−	0.548032i	−0.00830915	−	0.0597951i
$85$		0			0
$86$	−14.4471	−	3.61397i	−1.55787	−	0.389704i
$87$	−6.94483	+	21.3740i	−0.744564	+	2.29153i
$88$	1.99050	−	4.44290i	0.212188	−	0.473614i
$89$	2.07551	+	6.38776i	0.220003	+	0.677101i	0.998760	+	0.0497752i	$0.0158505\pi$
$89$	2.07551	+	6.38776i	0.220003	+	0.677101i	−0.778757	+	0.627326i	$0.784150\pi$
$90$		0			0
$91$	0.506744	+	0.164651i	0.0531212	+	0.0172601i
$92$	2.25003	−	12.6459i	0.234582	−	1.31843i
$93$			8.85717i			0.918446i
$94$	1.64058	+	4.06966i	0.169213	+	0.419753i
$95$		0			0
$96$	11.6665	+	7.93510i	1.19070	+	0.809872i
$97$	4.54704	−	3.30362i	0.461682	−	0.335431i	−0.332509	−	0.943100i	$-0.607895\pi$
$97$	4.54704	−	3.30362i	0.461682	−	0.335431i	0.794191	+	0.607669i	$0.207895\pi$
$98$	−2.39813	+	9.58670i	−0.242247	+	0.968403i
$99$		−	5.54415i		−	0.557208i
$100$		0			0
$101$			1.55640i			0.154868i	0.996997	+	0.0774339i	$0.0246727\pi$
$101$			1.55640i			0.154868i	−0.996997	+	0.0774339i	$0.975327\pi$
$102$	1.56945	+	0.392601i	0.155399	+	0.0388733i
$103$	3.81692	−	2.77316i	0.376092	−	0.273247i	−0.383640	−	0.923483i	$-0.625330\pi$
$103$	3.81692	−	2.77316i	0.376092	−	0.273247i	0.759733	+	0.650235i	$0.225330\pi$
$104$	−11.7826	+	6.76621i	−1.15538	+	0.663481i
$105$		0			0
$106$	−6.02211	+	2.42766i	−0.584919	+	0.235796i
$107$		−	11.5454i		−	1.11614i	−0.829794	−	0.558070i	$-0.811542\pi$
$107$		−	11.5454i		−	1.11614i	0.829794	−	0.558070i	$-0.188458\pi$
$108$	1.08545	+	0.193130i	0.104448	+	0.0185840i
$109$	−1.79379	−	0.582837i	−0.171814	−	0.0558256i	0.221847	−	0.975081i	$-0.428791\pi$
$109$	−1.79379	−	0.582837i	−0.171814	−	0.0558256i	−0.393661	+	0.919256i	$0.628791\pi$
$110$		0			0
$111$	1.24781	+	3.84038i	0.118437	+	0.364512i
$112$	0.246954	+	0.368585i	0.0233350	+	0.0348280i
$113$	1.42005	−	4.37045i	0.133587	−	0.411137i	−0.861781	−	0.507281i	$-0.830651\pi$
$113$	1.42005	−	4.37045i	0.133587	−	0.411137i	0.995367	+	0.0961433i	$0.0306507\pi$
$114$	3.49586	−	13.9750i	0.327418	−	1.30888i
$115$		0			0
$116$	−2.48037	−	17.8495i	−0.230297	−	1.65728i
$117$	−9.09485	+	12.5180i	−0.840819	+	1.15729i
$118$	−2.67159	+	4.26808i	−0.245940	+	0.392908i
$119$	0.0411565	+	0.0299019i	0.00377281	+	0.00274111i
$120$		0			0
$121$	−6.50233	+	4.72422i	−0.591121	+	0.429475i
$122$	1.14698	+	16.5873i	0.103843	+	1.50175i
$123$	−26.9867	+	8.76851i	−2.43331	+	0.790630i
$124$	−3.10351	−	6.38826i	−0.278704	−	0.573683i
$125$		0			0
$126$	0.428268	+	0.268073i	0.0381531	+	0.0238819i
$127$	−2.51421	−	7.73794i	−0.223100	−	0.686631i	−0.998479	−	0.0551347i	$-0.982441\pi$
$127$	−2.51421	−	7.73794i	−0.223100	−	0.686631i	0.775379	−	0.631496i	$-0.217559\pi$
$128$	−11.1949	−	1.63533i	−0.989498	−	0.144544i
$129$	21.2488	−	15.4382i	1.87085	−	1.35925i
$130$		0			0
$131$	12.7817	−	17.5926i	1.11675	−	1.53707i	0.305661	−	0.952140i	$-0.401122\pi$
$131$	12.7817	−	17.5926i	1.11675	−	1.53707i	0.811085	−	0.584929i	$-0.198878\pi$
$132$	3.75199	+	7.72308i	0.326569	+	0.672208i
$133$	0.266258	−	0.366473i	0.0230875	−	0.0317772i
$134$	3.39668	+	4.05439i	0.293429	+	0.350246i
$135$		0			0
$136$	−1.26954	+	0.266764i	−0.108862	+	0.0228749i
$137$	−2.83428	+	8.72303i	−0.242149	+	0.745259i	0.753943	+	0.656940i	$0.228149\pi$
$137$	−2.83428	+	8.72303i	−0.242149	+	0.745259i	−0.996092	+	0.0883189i	$0.971851\pi$
$138$	14.5479	+	17.3648i	1.23840	+	1.47819i
$139$	−13.0150	+	4.22884i	−1.10392	+	0.358685i	−0.803610	−	0.595156i	$-0.797090\pi$
$139$	−13.0150	+	4.22884i	−1.10392	+	0.358685i	−0.300310	+	0.953842i	$0.597090\pi$
$140$		0			0
$141$	−7.36000	−	2.39141i	−0.619824	−	0.201393i
$142$	−5.91388	−	14.6701i	−0.496282	−	1.23109i
$143$	−8.26849			−0.691446
$144$	−12.3959	+	3.51291i	−1.03299	+	0.292743i
$145$		0			0
$146$	−14.6190	+	1.01088i	−1.20988	+	0.0836608i
$147$	−10.2443	−	14.1001i	−0.844938	−	1.16296i
$148$	−2.24564	−	2.33265i	−0.184590	−	0.191743i
$149$		−	14.8397i		−	1.21572i	−0.794045	−	0.607859i	$-0.792028\pi$
$149$		−	14.8397i		−	1.21572i	0.794045	−	0.607859i	$-0.207972\pi$
$150$		0			0
$151$	−8.87251			−0.722035			−0.361017	−	0.932559i	$-0.617570\pi$
$151$	−8.87251			−0.722035			−0.361017	+	0.932559i	$0.617570\pi$
$152$	2.37537	+	11.3044i	0.192668	+	0.916911i
$153$	−1.19518	+	0.868348i	−0.0966244	+	0.0702017i
$154$	0.0186251	+	0.269352i	0.00150085	+	0.0217050i
$155$		0			0
$156$	4.19774	−	23.5927i	0.336088	−	1.88892i
$157$		−	4.71374i		−	0.376197i	−0.982150	−	0.188099i	$-0.939768\pi$
$157$		−	4.71374i		−	0.376197i	0.982150	−	0.188099i	$-0.0602325\pi$
$158$	−2.91152	−	7.22237i	−0.231628	−	0.574581i
$159$	3.53871	−	10.8910i	0.280638	−	0.863715i
$160$		0			0
$161$	0.220124	+	0.677473i	0.0173482	+	0.0533923i
$162$	8.98477	−	7.52725i	0.705910	−	0.591397i
$163$	−9.54040	−	3.09987i	−0.747262	−	0.242800i	−0.0894595	−	0.995990i	$-0.528514\pi$
$163$	−9.54040	−	3.09987i	−0.747262	−	0.242800i	−0.657803	+	0.753190i	$0.728514\pi$
$164$	16.3918	−	15.7803i	1.27998	−	1.23224i
$165$		0			0
$166$	−11.1256	−	13.2799i	−0.863515	−	1.03072i
$167$	6.50795	+	4.72830i	0.503601	+	0.365887i	0.810391	−	0.585890i	$-0.199255\pi$
$167$	6.50795	+	4.72830i	0.503601	+	0.365887i	−0.306790	+	0.951777i	$0.599255\pi$
$168$	−0.778002	−	0.0836008i	−0.0600242	−	0.00644994i
$169$	8.15199	+	5.92277i	0.627076	+	0.455597i
$170$		0			0
$171$	7.73210	+	10.6423i	0.591288	+	0.813838i
$172$	−9.91629	+	18.5803i	−0.756110	+	1.41673i
$173$	9.45929	−	3.07351i	0.719176	−	0.233675i	0.0735104	−	0.997294i	$-0.476580\pi$
$173$	9.45929	−	3.07351i	0.719176	−	0.233675i	0.645666	+	0.763620i	$0.276580\pi$
$174$	26.9404	+	16.8633i	2.04235	+	1.27840i
$175$		0			0
$176$	−5.41226	−	4.25561i	−0.407965	−	0.320779i
$177$	−2.74423	−	8.44586i	−0.206269	−	0.634830i
$178$	9.47592	−	0.655240i	0.710250	−	0.0491123i
$179$	−7.39861	−	10.1833i	−0.552998	−	0.761136i	0.437417	−	0.899259i	$-0.355893\pi$
$179$	−7.39861	−	10.1833i	−0.552998	−	0.761136i	−0.990415	+	0.138122i	$0.955893\pi$
$180$		0			0
$181$	7.67562	−	10.5646i	0.570524	−	0.785259i	−0.422092	−	0.906553i	$-0.638704\pi$
$181$	7.67562	−	10.5646i	0.570524	−	0.785259i	0.992617	+	0.121293i	$0.0387042\pi$
$182$	0.399802	−	0.638715i	0.0296353	−	0.0473447i
$183$	−23.7239	−	17.2364i	−1.75372	−	1.27415i
$184$	−16.5772	−	7.42689i	−1.22209	−	0.547517i
$185$		0			0
$186$	12.1515	+	3.03972i	0.890992	+	0.222883i
$187$	−0.750811	−	0.243953i	−0.0549048	−	0.0178396i
$188$	6.14636	−	0.854100i	0.448269	−	0.0622917i
$189$	−0.0581506	+	0.0188943i	−0.00422983	+	0.00137436i
$190$		0			0
$191$	0.889107	−	2.73639i	0.0643335	−	0.197998i	−0.913723	−	0.406337i	$-0.866806\pi$
$191$	0.889107	−	2.73639i	0.0643335	−	0.197998i	0.978057	+	0.208339i	$0.0668058\pi$
$192$	14.8903	−	13.2824i	1.07462	−	0.958577i
$193$	−15.9019			−1.14464			−0.572322	−	0.820029i	$-0.693957\pi$
$193$	−15.9019			−1.14464			−0.572322	+	0.820029i	$0.693957\pi$
$194$	−2.97185	−	7.37204i	−0.213366	−	0.529281i
$195$		0			0
$196$	12.3294	+	6.58017i	0.880668	+	0.470012i
$197$	2.74963	+	3.78454i	0.195903	+	0.269637i	0.895656	−	0.444748i	$-0.146707\pi$
$197$	2.74963	+	3.78454i	0.195903	+	0.269637i	−0.699753	+	0.714385i	$0.746707\pi$
$198$	−7.60623	−	1.90271i	−0.540552	−	0.135220i
$199$	−28.0439			−1.98798			−0.993988	−	0.109488i	$-0.965079\pi$
$199$	−28.0439			−1.98798			−0.993988	+	0.109488i	$0.965079\pi$
$200$		0			0
$201$	−9.32834			−0.657971
$202$	2.13529	+	0.534146i	0.150239	+	0.0375824i
$203$	0.587443	+	0.808546i	0.0412304	+	0.0567488i
$204$	1.07725	−	2.01846i	0.0754225	−	0.141320i
$205$		0			0
$206$	−2.49466	−	6.18831i	−0.173811	−	0.431160i
$207$	−20.6862			−1.43779
$208$	5.23913	+	18.4871i	0.363268	+	1.28185i
$209$	−2.17225	+	6.68551i	−0.150258	+	0.462446i
$210$		0			0
$211$	0.310359	−	0.100842i	0.0213660	−	0.00694223i	−0.298315	−	0.954468i	$-0.596424\pi$
$211$	0.310359	−	0.100842i	0.0213660	−	0.00694223i	0.319680	+	0.947525i	$0.396424\pi$
$212$	1.26386	+	9.09513i	0.0868025	+	0.624656i
$213$	26.5310	+	8.62043i	1.81787	+	0.590662i
$214$	−15.8396	−	3.96231i	−1.08278	−	0.270858i
$215$		0			0
$216$	0.637484	−	1.42290i	0.0433753	−	0.0968159i
$217$	0.318655	+	0.231516i	0.0216317	+	0.0157163i
$218$	−1.41523	+	2.26094i	−0.0958516	+	0.153130i
$219$	15.1911	−	20.9087i	1.02652	−	1.41288i
$220$		0			0
$221$	1.29505	+	1.78248i	0.0871142	+	0.119902i
$222$	5.69700	−	0.393936i	0.382358	−	0.0264393i
$223$	3.64231	+	11.2099i	0.243907	+	0.750669i	0.995814	+	0.0914002i	$0.0291343\pi$
$223$	3.64231	+	11.2099i	0.243907	+	0.750669i	−0.751907	+	0.659269i	$0.770866\pi$
$224$	0.590429	−	0.212311i	0.0394497	−	0.0141856i
$225$		0			0
$226$	−5.50865	−	3.44812i	−0.366430	−	0.229366i
$227$	−0.998051	+	0.324287i	−0.0662430	+	0.0215237i	−0.341951	−	0.939718i	$-0.611088\pi$
$227$	−0.998051	+	0.324287i	−0.0662430	+	0.0215237i	0.275708	+	0.961241i	$0.411088\pi$
$228$	−17.9731	−	9.59223i	−1.19030	−	0.635261i
$229$	11.8902	+	16.3654i	0.785723	+	1.08146i	0.994627	+	0.103519i	$0.0330104\pi$
$229$	11.8902	+	16.3654i	0.785723	+	1.08146i	−0.208904	+	0.977936i	$0.566990\pi$
$230$		0			0
$231$	−0.385237	−	0.279891i	−0.0253468	−	0.0184155i
$232$	−25.3397	−	2.72289i	−1.66363	−	0.178767i
$233$	21.2400	+	15.4318i	1.39148	+	1.01097i	0.995701	+	0.0926216i	$0.0295247\pi$
$233$	21.2400	+	15.4318i	1.39148	+	1.01097i	0.395777	+	0.918347i	$0.370475\pi$
$234$	14.0526	+	16.7737i	0.918649	+	1.09653i
$235$		0			0
$236$	4.93867	+	5.13004i	0.321480	+	0.333937i
$237$	13.0617	+	4.24401i	0.848449	+	0.275678i
$238$	0.0551482	−	0.0462021i	0.00357473	−	0.00299484i
$239$	2.69865	+	8.30559i	0.174561	+	0.537244i	0.999613	−	0.0278129i	$-0.00885425\pi$
$239$	2.69865	+	8.30559i	0.174561	+	0.537244i	−0.825052	+	0.565057i	$0.808854\pi$
$240$		0			0
$241$	0.110550	−	0.340238i	0.00712115	−	0.0219166i	−0.947433	−	0.319955i	$-0.896332\pi$
$241$	0.110550	−	0.340238i	0.00712115	−	0.0219166i	0.954554	+	0.298038i	$0.0963323\pi$
$242$	4.24979	+	10.5421i	0.273187	+	0.677673i
$243$			22.3259i			1.43221i
$244$	23.1505	+	4.11907i	1.48206	+	0.263696i
$245$		0			0
$246$	2.76823	+	40.0334i	0.176496	+	2.55244i
$247$	15.8719	−	11.5316i	1.00990	−	0.733737i
$248$	−9.82941	+	2.06543i	−0.624168	+	0.131155i
$249$	30.5544			1.93631
$250$		0			0
$251$			20.0370i			1.26473i	0.774672	+	0.632363i	$0.217915\pi$
$251$			20.0370i			1.26473i	−0.774672	+	0.632363i	$0.782085\pi$
$252$	0.514759	−	0.495557i	0.0324268	−	0.0312172i
$253$	−6.49753	−	8.94308i	−0.408496	−	0.562247i
$254$	−11.4788	+	0.793738i	−0.720247	+	0.0498036i
$255$		0			0
$256$	−6.08558	+	14.7975i	−0.380349	+	0.924843i
$257$	−18.7305			−1.16838			−0.584190	−	0.811617i	$-0.698588\pi$
$257$	−18.7305			−1.16838			−0.584190	+	0.811617i	$0.698588\pi$
$258$	−13.8878	−	34.4503i	−0.864616	−	2.14478i
$259$	0.170782	+	0.0554903i	0.0106119	+	0.00344800i
$260$		0			0
$261$	−27.6024	+	8.96858i	−1.70855	+	0.555141i
$262$	−19.7493	−	23.5734i	−1.22012	−	1.45637i
$263$	−5.09486	+	15.6804i	−0.314162	+	0.966892i	0.661936	+	0.749561i	$0.269735\pi$
$263$	−5.09486	+	15.6804i	−0.314162	+	0.966892i	−0.976098	+	0.217331i	$0.930265\pi$
$264$	11.8833	−	2.49700i	0.731364	−	0.153680i
$265$		0			0
$266$	−0.411401	−	0.491061i	−0.0252246	−	0.0301089i
$267$	−9.84671	+	13.5528i	−0.602609	+	0.829420i
$268$	6.72809	−	3.26861i	0.410984	−	0.199662i
$269$	−0.0856192	+	0.117845i	−0.00522029	+	0.00718512i	−0.811619	−	0.584187i	$-0.801414\pi$
$269$	−0.0856192	+	0.117845i	−0.00522029	+	0.00718512i	0.806399	+	0.591372i	$0.201414\pi$
$270$		0			0
$271$	−12.4072	+	9.01437i	−0.753684	+	0.547584i	−0.896967	−	0.442098i	$-0.854234\pi$
$271$	−12.4072	+	9.01437i	−0.753684	+	0.547584i	0.143282	+	0.989682i	$0.454234\pi$
$272$	−0.0697110	+	1.83328i	−0.00422685	+	0.111159i
$273$	0.410672	+	1.26392i	0.0248550	+	0.0764958i
$274$	10.9948	+	6.88215i	0.664218	+	0.415766i
$275$		0			0
$276$	28.8161	−	13.9993i	1.73453	−	0.842660i
$277$	19.6954	−	6.39942i	1.18338	−	0.384504i	0.349759	−	0.936840i	$-0.386263\pi$
$277$	19.6954	−	6.39942i	1.18338	−	0.384504i	0.833622	+	0.552336i	$0.186263\pi$
$278$	1.33505	+	19.3071i	0.0800709	+	1.15797i
$279$	−9.25369	+	6.72320i	−0.554004	+	0.402507i
$280$		0			0
$281$	−8.56374	−	6.22192i	−0.510870	−	0.371169i	0.302284	−	0.953218i	$-0.402251\pi$
$281$	−8.56374	−	6.22192i	−0.510870	−	0.371169i	−0.813153	+	0.582049i	$0.802251\pi$
$282$	−5.80677	+	9.27677i	−0.345788	+	0.552423i
$283$	12.0915	−	16.6426i	0.718767	−	0.989298i	−0.280797	−	0.959767i	$-0.590599\pi$
$283$	12.0915	−	16.6426i	0.718767	−	0.989298i	0.999564	−	0.0295305i	$-0.00940123\pi$
$284$	−22.1561	+	3.07882i	−1.31472	+	0.182694i
$285$		0			0
$286$	−2.83769	+	11.3439i	−0.167796	+	0.670777i
$287$	−0.389936	+	1.20010i	−0.0230172	+	0.0708396i
$288$	0.565321	+	18.2120i	0.0333118	+	1.07315i
$289$	−5.18828	−	15.9679i	−0.305193	−	0.939288i
$290$		0			0
$291$	13.3324	+	4.33195i	0.781558	+	0.253944i
$292$	−3.63029	+	20.4034i	−0.212446	+	1.19402i
$293$		−	0.603128i		−	0.0352351i	−0.999845	−	0.0176176i	$-0.994392\pi$
$293$		−	0.603128i		−	0.0352351i	0.999845	−	0.0176176i	$-0.00560813\pi$
$294$	−22.8603	+	9.21554i	−1.33324	+	0.537461i
$295$		0			0
$296$	−3.97095	+	2.28033i	−0.230807	+	0.132542i
$297$	0.767625	−	0.557713i	0.0445421	−	0.0323618i
$298$	−20.3592	−	5.09289i	−1.17938	−	0.295023i
$299$			30.8512i			1.78417i
$300$		0			0
$301$		−	1.16800i		−	0.0673226i
$302$	−3.04498	+	12.1726i	−0.175219	+	0.700452i
$303$	−3.14058	+	2.28177i	−0.180422	+	0.131084i
$304$	16.3242	+	0.620733i	0.936258	+	0.0356015i
$305$		0			0
$306$	0.781144	+	1.93772i	0.0446550	+	0.110772i
$307$		−	9.96251i		−	0.568591i	−0.958737	−	0.284295i	$-0.908240\pi$
$307$		−	9.96251i		−	0.568591i	0.958737	−	0.284295i	$-0.0917596\pi$
$308$	0.375926	+	0.0668870i	0.0214204	+	0.00381124i
$309$	11.1916	+	3.63637i	0.636668	+	0.206866i
$310$		0			0
$311$	−7.52782	−	23.1683i	−0.426864	−	1.31375i	−0.901198	−	0.433407i	$-0.857311\pi$
$311$	−7.52782	−	23.1683i	−0.426864	−	1.31375i	0.474335	−	0.880344i	$-0.342689\pi$
$312$	−30.9271	−	13.8559i	−1.75090	−	0.784435i
$313$	5.78333	−	17.7993i	0.326893	−	1.00607i	−0.643686	−	0.765290i	$-0.722596\pi$
$313$	5.78333	−	17.7993i	0.326893	−	1.00607i	0.970579	−	0.240784i	$-0.0774045\pi$
$314$	−6.46697	−	1.61772i	−0.364952	−	0.0912933i
$315$		0			0
$316$	−10.9079	+	1.51576i	−0.613616	+	0.0852683i
$317$	−16.7789	+	23.0942i	−0.942397	+	1.29710i	0.0124261	+	0.999923i	$0.496045\pi$
$317$	−16.7789	+	23.0942i	−0.942397	+	1.29710i	−0.954823	+	0.297175i	$0.903955\pi$
$318$	−13.7274	−	8.59262i	−0.769793	−	0.481850i
$319$	−12.5472	−	9.11611i	−0.702511	−	0.510404i
$320$		0			0
$321$	23.2969	−	16.9262i	1.30031	−	0.944728i
$322$	1.00500	−	0.0694935i	0.0560063	−	0.00387272i
$323$	1.78145	−	0.578830i	0.0991228	−	0.0322069i
$324$	−7.24343	−	14.9099i	−0.402413	−	0.828325i
$325$		0			0
$326$	−7.52703	+	12.0250i	−0.416883	+	0.666004i
$327$	−1.45371	−	4.47406i	−0.0803903	−	0.247416i
$328$	−16.0241	−	27.9042i	−0.884783	−	1.54075i
$329$	−0.278418	+	0.202282i	−0.0153497	+	0.0111522i
$330$		0			0
$331$	2.10228	−	2.89354i	0.115552	−	0.159043i	−0.747323	−	0.664461i	$-0.768661\pi$
$331$	2.10228	−	2.89354i	0.115552	−	0.159043i	0.862875	+	0.505417i	$0.168661\pi$
$332$	−22.0374	+	10.7061i	−1.20946	+	0.587574i
$333$	−3.06512	+	4.21878i	−0.167968	+	0.231188i
$334$	8.72043	−	7.30580i	0.477161	−	0.399756i
$335$		0			0
$336$	−0.381700	+	1.03868i	−0.0208234	+	0.0566647i
$337$	3.03819	−	9.35059i	0.165501	−	0.509359i	−0.833572	−	0.552411i	$-0.813708\pi$
$337$	3.03819	−	9.35059i	0.165501	−	0.509359i	0.999073	+	0.0430517i	$0.0137080\pi$
$338$	10.9234	−	9.15139i	0.594154	−	0.497770i
$339$	10.9008	−	3.54187i	0.592048	−	0.192368i
$340$		0			0
$341$	−5.81317	−	1.88881i	−0.314801	−	0.102285i
$342$	17.2542	−	6.95560i	0.933001	−	0.376116i
$343$	−1.55147			−0.0837717
$344$	22.0878	+	19.9812i	1.19090	+	1.07731i
$345$		0			0
$346$	−0.970311	−	14.0324i	−0.0521642	−	0.754386i
$347$	−9.28373	−	12.7780i	−0.498377	−	0.685957i	0.483529	−	0.875329i	$-0.339355\pi$
$347$	−9.28373	−	12.7780i	−0.498377	−	0.685957i	−0.981905	+	0.189372i	$0.939355\pi$
$348$	32.3812	−	31.1733i	1.73581	−	1.67106i
$349$			7.78786i			0.416875i	0.978036	+	0.208437i	$0.0668377\pi$
$349$			7.78786i			0.416875i	−0.978036	+	0.208437i	$0.933162\pi$
$350$		0			0
$351$	−2.64810			−0.141345
$352$	−7.69589	+	5.96480i	−0.410192	+	0.317925i
$353$	−9.09643	+	6.60894i	−0.484154	+	0.351759i	−0.802932	−	0.596071i	$-0.796728\pi$
$353$	−9.09643	+	6.60894i	−0.484154	+	0.351759i	0.318778	+	0.947830i	$0.396728\pi$
$354$	−12.5290	+	0.866356i	−0.665910	+	0.0460463i
$355$		0			0
$356$	2.35312	−	13.2253i	0.124715	−	0.700937i
$357$			0.126885i			0.00671548i
$358$	−16.5100	+	6.65560i	−0.872582	+	0.351760i
$359$	3.14405	−	9.67639i	0.165937	−	0.510700i	−0.833167	−	0.553021i	$-0.813475\pi$
$359$	3.14405	−	9.67639i	0.165937	−	0.510700i	0.999104	+	0.0423204i	$0.0134750\pi$
$360$		0			0
$361$	0.717206	+	2.20733i	0.0377477	+	0.116175i
$362$	−11.8598	−	14.1562i	−0.623335	−	0.744032i
$363$	−19.0655	−	6.19476i	−1.00068	−	0.325141i
$364$	−0.739070	−	0.767707i	−0.0387378	−	0.0402388i
$365$		0			0
$366$	−31.7892	+	26.6323i	−1.66165	+	1.39209i
$367$	−9.81851	−	7.13356i	−0.512522	−	0.372369i	0.301257	−	0.953543i	$-0.402594\pi$
$367$	−9.81851	−	7.13356i	−0.512522	−	0.372369i	−0.813779	+	0.581174i	$0.802594\pi$
$368$	−15.8784	+	20.1941i	−0.827720	+	1.05269i
$369$	−29.6458	−	21.5389i	−1.54330	−	1.12127i
$370$		0			0
$371$	−0.299329	−	0.411991i	−0.0155404	−	0.0213895i
$372$	8.34062	−	15.6279i	0.432441	−	0.810270i
$373$	7.08589	−	2.30235i	0.366894	−	0.119211i	−0.119767	−	0.992802i	$-0.538215\pi$
$373$	7.08589	−	2.30235i	0.366894	−	0.119211i	0.486661	+	0.873591i	$0.338215\pi$
$374$	−0.592362	+	0.946345i	−0.0306303	+	0.0489343i
$375$		0			0
$376$	0.937612	−	8.72556i	0.0483536	−	0.449986i
$377$	13.3757	+	41.1660i	0.688881	+	2.12016i
$378$	0.00596494	+	0.0862635i	0.000306804	+	0.00443691i
$379$	3.70220	+	5.09564i	0.190169	+	0.261746i	0.893446	−	0.449171i	$-0.148281\pi$
$379$	3.70220	+	5.09564i	0.190169	+	0.261746i	−0.703277	+	0.710916i	$0.748281\pi$
$380$		0			0
$381$	11.9280	−	16.4175i	0.611091	−	0.841094i
$382$	−3.44903	−	2.15891i	−0.176468	−	0.110460i
$383$	23.1761	+	16.8385i	1.18425	+	0.860405i	0.992644	−	0.121068i	$-0.0386319\pi$
$383$	23.1761	+	16.8385i	1.18425	+	0.860405i	0.191601	+	0.981473i	$0.438632\pi$
$384$	−13.1125	−	24.9871i	−0.669142	−	1.27512i
$385$		0			0
$386$	−5.45742	+	21.8164i	−0.277775	+	1.11043i
$387$	32.2586	+	10.4814i	1.63979	+	0.532802i
$388$	−11.1339	+	1.54717i	−0.565239	+	0.0785457i
$389$	0.660483	−	0.214604i	0.0334878	−	0.0108808i	−0.292225	−	0.956350i	$-0.594396\pi$
$389$	0.660483	−	0.214604i	0.0334878	−	0.0108808i	0.325713	+	0.945469i	$0.394396\pi$
$390$		0			0
$391$	−0.910232	+	2.80141i	−0.0460324	+	0.141673i
$392$	13.2589	−	14.6569i	0.669678	−	0.740284i
$393$	54.2378			2.73593
$394$	6.13581	−	2.47350i	0.309118	−	0.124613i
$395$		0			0
$396$	−5.22081	+	9.78230i	−0.262356	+	0.491579i
$397$	12.3352	+	16.9780i	0.619086	+	0.852099i	0.997286	−	0.0736250i	$-0.0234568\pi$
$397$	12.3352	+	16.9780i	0.619086	+	0.852099i	−0.378200	+	0.925724i	$0.623457\pi$
$398$	−9.62445	+	38.4745i	−0.482430	+	1.92855i
$399$	1.12983			0.0565625
$400$		0			0
$401$	18.7715			0.937404			0.468702	−	0.883356i	$-0.344722\pi$
$401$	18.7715			0.937404			0.468702	+	0.883356i	$0.344722\pi$
$402$	−3.20142	+	12.7979i	−0.159672	+	0.638302i
$403$	10.0269	+	13.8009i	0.499476	+	0.687470i
$404$	1.46563	−	2.74617i	0.0729179	−	0.136627i
$405$		0			0
$406$	1.31088	−	0.528449i	0.0650580	−	0.0262265i
$407$	−2.78663			−0.138128
$408$	−2.39950	−	2.17064i	−0.118793	−	0.107463i
$409$	−11.2943	+	34.7602i	−0.558465	+	1.71878i	0.128146	+	0.991755i	$0.459097\pi$
$409$	−11.2943	+	34.7602i	−0.558465	+	1.71878i	−0.686611	+	0.727025i	$0.740903\pi$
$410$		0			0
$411$	−21.7569	+	7.06926i	−1.07319	+	0.348701i
$412$	−9.34614	+	1.29874i	−0.460451	+	0.0639845i
$413$	−0.375588	−	0.122036i	−0.0184815	−	0.00600499i
$414$	−7.09934	+	28.3802i	−0.348914	+	1.39481i
$415$		0			0
$416$	27.1613	−	0.843114i	1.33169	−	0.0413371i
$417$	−27.6138	−	20.0626i	−1.35226	−	0.982471i
$418$	8.42661	+	5.27462i	0.412159	+	0.257990i
$419$	−6.06690	+	8.35037i	−0.296387	+	0.407942i	−0.931076	−	0.364826i	$-0.881128\pi$
$419$	−6.06690	+	8.35037i	−0.296387	+	0.407942i	0.634688	+	0.772768i	$0.281128\pi$
$420$		0			0
$421$	−7.12906	−	9.81232i	−0.347449	−	0.478223i	0.599149	−	0.800637i	$-0.295506\pi$
$421$	−7.12906	−	9.81232i	−0.347449	−	0.478223i	−0.946599	+	0.322414i	$0.895506\pi$
$422$	−0.0318358	−	0.460402i	−0.00154974	−	0.0224120i
$423$	−3.08828	−	9.50473i	−0.150157	−	0.462136i
$424$	12.9117	+	1.38744i	0.627049	+	0.0673800i
$425$		0			0
$426$	20.9320	−	33.4404i	1.01416	−	1.62019i
$427$	−1.24023	+	0.402975i	−0.0600189	+	0.0195013i
$428$	−10.8721	+	20.3712i	−0.525523	+	0.984679i
$429$	−12.1220	−	16.6845i	−0.585257	−	0.805538i
$430$		0			0
$431$	−24.8747	−	18.0726i	−1.19817	−	0.870525i	−0.204070	−	0.978956i	$-0.565417\pi$
$431$	−24.8747	−	18.0726i	−1.19817	−	0.870525i	−0.994104	+	0.108432i	$0.965417\pi$
$432$	−1.73335	−	1.36292i	−0.0833959	−	0.0655734i
$433$	−3.64760	−	2.65013i	−0.175292	−	0.127357i	0.496680	−	0.867934i	$-0.334552\pi$
$433$	−3.64760	−	2.65013i	−0.175292	−	0.127357i	−0.671972	+	0.740577i	$0.734552\pi$
$434$	0.426986	−	0.357720i	0.0204960	−	0.0171711i
$435$		0			0
$436$	2.61618	+	2.71755i	0.125292	+	0.130147i
$437$	24.9448	+	8.10505i	1.19327	+	0.387717i
$438$	−23.4721	−	28.0170i	−1.12154	−	1.33870i
$439$	−3.68407	−	11.3384i	−0.175831	−	0.541153i	0.823839	−	0.566824i	$-0.191828\pi$
$439$	−3.68407	−	11.3384i	−0.175831	−	0.541153i	−0.999670	+	0.0256706i	$0.991828\pi$
$440$		0			0
$441$	6.95519	−	21.4059i	0.331200	−	1.01933i
$442$	2.88990	−	1.16499i	0.137459	−	0.0554130i
$443$			4.00502i			0.190284i	0.995464	+	0.0951422i	$0.0303306\pi$
$443$			4.00502i			0.190284i	−0.995464	+	0.0951422i	$0.969669\pi$
$444$	1.41471	−	7.95114i	0.0671393	−	0.377345i
$445$		0			0
$446$	16.6293	−	1.14988i	0.787420	−	0.0544485i
$447$	29.9443	−	21.7558i	1.41632	−	1.02902i
$448$	−0.0886468	−	0.882897i	−0.00418817	−	0.0417130i
$449$	−6.20695			−0.292924			−0.146462	−	0.989216i	$-0.546789\pi$
$449$	−6.20695			−0.292924			−0.146462	+	0.989216i	$0.546789\pi$
$450$		0			0
$451$		−	19.5819i		−	0.922076i
$452$	−6.62115	+	6.37416i	−0.311432	+	0.299815i
$453$	−13.0076	−	17.9034i	−0.611148	−	0.841174i
$454$	0.102378	+	1.48056i	0.00480482	+	0.0694861i
$455$		0			0
$456$	−19.3282	+	21.3660i	−0.905126	+	1.00056i
$457$	34.1526			1.59759			0.798795	−	0.601604i	$-0.205471\pi$
$457$	34.1526			1.59759			0.798795	+	0.601604i	$0.205471\pi$
$458$	26.5329	−	10.6961i	1.23980	−	0.499795i
$459$	−0.240457	−	0.0781294i	−0.0112236	−	0.00364677i
$460$		0			0
$461$	12.3750	−	4.02087i	0.576359	−	0.187271i	−0.00630961	−	0.999980i	$-0.502008\pi$
$461$	12.3750	−	4.02087i	0.576359	−	0.187271i	0.582669	+	0.812710i	$0.302008\pi$
$462$	−0.516205	+	0.432466i	−0.0240160	+	0.0201201i
$463$	−0.154016	+	0.474013i	−0.00715774	+	0.0220292i	−0.954572	−	0.297982i	$-0.903687\pi$
$463$	−0.154016	+	0.474013i	−0.00715774	+	0.0220292i	0.947414	+	0.320011i	$0.103687\pi$
$464$	−12.4320	+	33.8300i	−0.577143	+	1.57052i
$465$		0			0
$466$	28.4609	−	23.8439i	1.31842	−	1.10455i
$467$	16.0152	−	22.0431i	0.741096	−	1.02003i	−0.257459	−	0.966289i	$-0.582885\pi$
$467$	16.0152	−	22.0431i	0.741096	−	1.02003i	0.998555	−	0.0537419i	$-0.0171148\pi$
$468$	27.8352	−	13.5228i	1.28668	−	0.625090i
$469$	−0.243832	+	0.335606i	−0.0112591	+	0.0154968i
$470$		0			0
$471$	9.51161	−	6.91059i	0.438272	−	0.318423i
$472$	8.73302	−	5.01497i	0.401970	−	0.230833i
$473$	5.60106	+	17.2383i	0.257537	+	0.792618i
$474$	10.3052	−	16.4634i	0.473334	−	0.756188i
$475$		0			0
$476$	−0.0444600	−	0.0915163i	−0.00203782	−	0.00419464i
$477$	14.0647	−	4.56990i	0.643979	−	0.209242i
$478$	12.3209	−	0.851967i	0.563546	−	0.0389681i
$479$	−23.5204	+	17.0886i	−1.07468	+	0.780797i	−0.976747	−	0.214396i	$-0.931222\pi$
$479$	−23.5204	+	17.0886i	−1.07468	+	0.780797i	−0.0979285	+	0.995193i	$0.531222\pi$
$480$		0			0
$481$	6.29185	+	4.57130i	0.286884	+	0.208433i
$482$	−0.428846	−	0.268435i	−0.0195334	−	0.0122269i
$483$	−1.04432	+	1.43739i	−0.0475183	+	0.0654034i
$484$	15.9217	−	2.21248i	0.723712	−	0.100567i
$485$		0			0
$486$	30.6298	+	7.66210i	1.38940	+	0.347560i
$487$	8.04647	−	24.7645i	0.364620	−	1.12219i	−0.585598	−	0.810601i	$-0.699140\pi$
$487$	8.04647	−	24.7645i	0.364620	−	1.12219i	0.950219	−	0.311584i	$-0.100860\pi$
$488$	13.5962	−	30.3474i	0.615471	−	1.37376i
$489$	−7.73167	−	23.7956i	−0.349638	−	1.07608i
$490$		0			0
$491$	23.4217	+	7.61016i	1.05700	+	0.343442i	0.785414	−	0.618971i	$-0.212450\pi$
$491$	23.4217	+	7.61016i	1.05700	+	0.343442i	0.271591	+	0.962413i	$0.412450\pi$
$492$	55.8735	+	9.94133i	2.51897	+	0.448190i
$493$			4.13267i			0.186126i
$494$	−10.3735	−	25.7328i	−0.466727	−	1.15777i
$495$		0			0
$496$	−0.539738	+	14.1942i	−0.0242350	+	0.637338i
$497$	1.00363	−	0.729177i	0.0450188	−	0.0327081i
$498$	10.4860	−	41.9188i	0.469891	−	1.87843i
$499$		−	18.4619i		−	0.826469i	−0.910625	−	0.413234i	$-0.864399\pi$
$499$		−	18.4619i		−	0.826469i	0.910625	−	0.413234i	$-0.135601\pi$
$500$		0			0
$501$			20.0640i			0.896393i
$502$	27.4896	+	6.87656i	1.22692	+	0.306916i
$503$	19.4694	−	14.1453i	0.868097	−	0.630709i	−0.0619786	−	0.998077i	$-0.519741\pi$
$503$	19.4694	−	14.1453i	0.868097	−	0.630709i	0.930076	+	0.367368i	$0.119741\pi$
$504$	−0.503213	−	0.876290i	−0.0224149	−	0.0390331i
$505$		0			0
$506$	−14.4993	+	5.84502i	−0.644571	+	0.259843i
$507$			25.1325i			1.11618i
$508$	−2.85049	+	16.0207i	−0.126470	+	0.710803i
$509$	−0.950881	−	0.308960i	−0.0421471	−	0.0136944i	0.287868	−	0.957670i	$-0.407054\pi$
$509$	−0.950881	−	0.308960i	−0.0421471	−	0.0136944i	−0.330015	+	0.943976i	$0.607054\pi$
$510$		0			0
$511$	−0.355157	−	1.09306i	−0.0157112	−	0.0483541i
$512$	18.2127	+	13.4274i	0.804897	+	0.593415i
$513$	−0.695693	+	2.14112i	−0.0307156	+	0.0945330i
$514$	−6.42819	+	25.6972i	−0.283535	+	1.13345i
$515$		0			0
$516$	−52.0300	+	7.23010i	−2.29049	+	0.318288i
$517$	3.13908	−	4.32057i	0.138056	−	0.190018i
$518$	0.134740	−	0.215258i	0.00592015	−	0.00945791i
$519$	20.0697	+	14.5815i	0.880961	+	0.640056i
$520$		0			0
$521$	−13.1276	+	9.53774i	−0.575129	+	0.417856i	−0.836965	−	0.547257i	$-0.815672\pi$
$521$	−13.1276	+	9.53774i	−0.575129	+	0.417856i	0.261836	+	0.965112i	$0.415672\pi$
$522$	2.83139	+	40.9468i	0.123927	+	1.79219i
$523$	−1.04250	+	0.338728i	−0.0455852	+	0.0148115i	−0.331721	−	0.943378i	$-0.607629\pi$
$523$	−1.04250	+	0.338728i	−0.0455852	+	0.0148115i	0.286136	+	0.958189i	$0.407629\pi$
$524$	−39.1191	+	19.0047i	−1.70893	+	0.830223i
$525$		0			0
$526$	19.7640	+	12.3712i	0.861751	+	0.539411i
$527$	0.503303	+	1.54901i	0.0219242	+	0.0674758i
$528$	0.652517	−	17.1601i	0.0283971	−	0.746796i
$529$	−14.7608	+	10.7243i	−0.641773	+	0.466275i
$530$		0			0
$531$	6.74091	−	9.27806i	0.292530	−	0.402634i
$532$	−0.814896	+	0.395889i	−0.0353302	+	0.0171639i
$533$	−32.1230	+	44.2135i	−1.39140	+	1.91510i
$534$	15.2144	+	18.1603i	0.658390	+	0.785874i
$535$		0			0
$536$	−2.17530	−	10.3523i	−0.0939587	−	0.447151i
$537$	9.70162	−	29.8585i	0.418656	−	1.28849i
$538$	0.132292	+	0.157908i	0.00570351	+	0.00680789i
$539$	11.4389	−	3.71671i	0.492706	−	0.160090i
$540$		0			0
$541$	22.8256	+	7.41649i	0.981349	+	0.318860i	0.755389	−	0.655277i	$-0.227448\pi$
$541$	22.8256	+	7.41649i	0.981349	+	0.318860i	0.225961	+	0.974136i	$0.427448\pi$
$542$	8.10910	+	20.1156i	0.348316	+	0.864040i
$543$	32.5706			1.39774
$544$	2.49122	+	0.724807i	0.106810	+	0.0310759i
$545$		0			0
$546$	1.87496	−	0.129650i	0.0802409	−	0.00554849i
$547$	−15.0286	−	20.6852i	−0.642579	−	0.884434i	0.356171	−	0.934421i	$-0.384082\pi$
$547$	−15.0286	−	20.6852i	−0.642579	−	0.884434i	−0.998750	+	0.0499871i	$0.984082\pi$
$548$	13.2152	−	12.7223i	0.564526	−	0.543468i
$549$		−	37.8696i		−	1.61623i
$550$		0			0
$551$	36.7989			1.56769
$552$	−9.31673	−	44.3385i	−0.396546	−	1.88717i
$553$	0.494105	−	0.358988i	0.0210115	−	0.0152657i
$554$	−2.02030	−	29.2171i	−0.0858345	−	1.24132i
$555$		0			0
$556$	26.9464	+	4.79446i	1.14278	+	0.203330i
$557$		−	39.1180i		−	1.65748i	−0.559631	−	0.828742i	$-0.689057\pi$
$557$		−	39.1180i		−	1.65748i	0.559631	−	0.828742i	$-0.310943\pi$
$558$	6.04802	+	15.0029i	0.256033	+	0.635121i
$559$	15.6319	−	48.1101i	0.661160	−	2.03484i
$560$		0			0
$561$	−0.608468	−	1.87267i	−0.0256895	−	0.0790642i
$562$	−11.4751	+	9.61362i	−0.484049	+	0.405526i
$563$	29.0845	+	9.45014i	1.22577	+	0.398276i	0.849179	−	0.528105i	$-0.177097\pi$
$563$	29.0845	+	9.45014i	1.22577	+	0.398276i	0.376588	+	0.926381i	$0.377097\pi$
$564$	10.7343	+	11.1503i	0.451997	+	0.469511i
$565$		0			0
$566$	−18.6829	−	22.3005i	−0.785300	−	0.937358i
$567$	0.743723	+	0.540347i	0.0312334	+	0.0226924i
$568$	−3.37986	+	31.4534i	−0.141816	+	1.31976i
$569$	−0.511882	−	0.371904i	−0.0214592	−	0.0155910i	0.577004	−	0.816741i	$-0.304222\pi$
$569$	−0.511882	−	0.371904i	−0.0214592	−	0.0155910i	−0.598463	+	0.801150i	$0.704222\pi$
$570$		0			0
$571$	−2.91121	−	4.00694i	−0.121830	−	0.167685i	0.743746	−	0.668463i	$-0.233047\pi$
$571$	−2.91121	−	4.00694i	−0.121830	−	0.167685i	−0.865576	+	0.500778i	$0.833047\pi$
$572$	14.5892	+	7.78627i	0.610007	+	0.325560i
$573$	6.82510	−	2.21761i	0.285122	−	0.0926419i
$574$	1.51264	+	0.946834i	0.0631364	+	0.0395201i
$575$		0			0
$576$	25.1798	+	5.47465i	1.04916	+	0.228110i
$577$	−4.95951	−	15.2638i	−0.206467	−	0.635440i	−0.999650	−	0.0264569i	$-0.991578\pi$
$577$	−4.95951	−	15.2638i	−0.206467	−	0.635440i	0.793183	−	0.608984i	$-0.208422\pi$
$578$	−23.6876	+	1.63795i	−0.985273	+	0.0681296i
$579$	−23.3130	−	32.0876i	−0.968855	−	1.33352i
$580$		0			0
$581$	0.798656	−	1.09926i	0.0331338	−	0.0456048i
$582$	10.5188	−	16.8045i	0.436016	−	0.696570i
$583$	6.39340	+	4.64508i	0.264788	+	0.192379i
$584$	26.7463	+	11.9828i	1.10677	+	0.495853i
$585$		0			0
$586$	−0.827455	−	0.206989i	−0.0341819	−	0.00855064i
$587$	22.2461	+	7.22818i	0.918193	+	0.298339i	0.729725	−	0.683740i	$-0.239648\pi$
$587$	22.2461	+	7.22818i	0.918193	+	0.298339i	0.188468	+	0.982079i	$0.439648\pi$
$588$	4.79769	+	34.5256i	0.197854	+	1.42381i
$589$	13.7929	−	4.48160i	0.568328	−	0.184661i
$590$		0			0
$591$	−3.60552	+	11.0967i	−0.148311	+	0.456455i
$592$	1.76568	+	6.23049i	0.0725689	+	0.256072i
$593$	−7.54773			−0.309948			−0.154974	−	0.987919i	$-0.549529\pi$
$593$	−7.54773			−0.309948			−0.154974	+	0.987919i	$0.549529\pi$
$594$	−0.501705	−	1.24454i	−0.0205852	−	0.0510640i
$595$		0			0
$596$	−13.9743	+	26.1838i	−0.572409	+	1.07253i
$597$	−41.1137	−	56.5882i	−1.68267	−	2.31600i
$598$	42.3259	+	10.5879i	1.73084	+	0.432971i
$599$	−0.302745			−0.0123698			−0.00618491	−	0.999981i	$-0.501969\pi$
$599$	−0.302745			−0.0123698			−0.00618491	+	0.999981i	$0.501969\pi$
$600$		0			0
$601$	−32.7273			−1.33497			−0.667487	−	0.744622i	$-0.732630\pi$
$601$	−32.7273			−1.33497			−0.667487	+	0.744622i	$0.732630\pi$
$602$	−1.60243	−	0.400850i	−0.0653102	−	0.0163374i
$603$	−7.08085	−	9.74595i	−0.288354	−	0.396886i
$604$	15.6550	+	8.35506i	0.636993	+	0.339963i
$605$		0			0
$606$	2.05262	+	5.09177i	0.0833820	+	0.206839i
$607$	26.9091			1.09221			0.546103	−	0.837718i	$-0.316111\pi$
$607$	26.9091			1.09221			0.546103	+	0.837718i	$0.316111\pi$
$608$	6.45396	−	22.1828i	0.261743	−	0.899631i
$609$	−0.770300	+	2.37074i	−0.0312141	+	0.0960672i
$610$		0			0
$611$	−14.1753	+	4.60583i	−0.573470	+	0.186332i
$612$	2.92652	−	0.406671i	0.118298	−	0.0164387i
$613$	−8.04187	−	2.61296i	−0.324808	−	0.105537i	0.142074	−	0.989856i	$-0.454623\pi$
$613$	−8.04187	−	2.61296i	−0.324808	−	0.105537i	−0.466882	+	0.884319i	$0.654623\pi$
$614$	−13.6680	−	3.41906i	−0.551594	−	0.137982i
$615$		0			0
$616$	0.220780	−	0.492793i	0.00889548	−	0.0198552i
$617$	−15.5720	−	11.3137i	−0.626904	−	0.455472i	0.228422	−	0.973562i	$-0.426643\pi$
$617$	−15.5720	−	11.3137i	−0.626904	−	0.455472i	−0.855326	+	0.518090i	$0.826643\pi$
$618$	8.82976	−	14.1062i	0.355185	−	0.567436i
$619$	19.2261	−	26.4625i	0.772763	−	1.06362i	−0.223281	−	0.974754i	$-0.571677\pi$
$619$	19.2261	−	26.4625i	0.772763	−	1.06362i	0.996044	−	0.0888631i	$-0.0283233\pi$
$620$		0			0
$621$	−2.08092	−	2.86414i	−0.0835045	−	0.114934i
$622$	−34.3689	+	2.37654i	−1.37807	+	0.0952907i
$623$	0.230209	+	0.708511i	0.00922313	+	0.0283859i
$624$	−29.6234	+	37.6748i	−1.18588	+	1.50820i
$625$		0			0
$626$	−22.4347	−	14.0430i	−0.896672	−	0.561270i
$627$	−16.6750	+	5.41803i	−0.665934	+	0.216375i
$628$	−4.43883	+	8.31710i	−0.177129	+	0.331888i
$629$	0.436453	+	0.600727i	0.0174025	+	0.0239525i
$630$		0			0
$631$	29.3548	+	21.3275i	1.16860	+	0.849035i	0.990840	−	0.135040i	$-0.0431162\pi$
$631$	29.3548	+	21.3275i	1.16860	+	0.849035i	0.177756	+	0.984075i	$0.443116\pi$
$632$	−1.66397	+	15.4851i	−0.0661891	+	0.615966i
$633$	0.658485	+	0.478417i	0.0261724	+	0.0190154i
$634$	25.9254	+	30.9454i	1.02963	+	1.22900i
$635$		0			0
$636$	−16.4997	+	15.8842i	−0.654256	+	0.629850i
$637$	−31.9245	−	10.3729i	−1.26490	−	0.410990i
$638$	−16.8129	+	14.0855i	−0.665628	+	0.557650i
$639$	11.1325	+	34.2622i	0.440393	+	1.35539i
$640$		0			0
$641$	−0.0519999	+	0.160039i	−0.00205387	+	0.00632117i	−0.952078	−	0.305855i	$-0.901058\pi$
$641$	−0.0519999	+	0.160039i	−0.00205387	+	0.00632117i	0.950024	+	0.312176i	$0.101058\pi$
$642$	−15.2264	−	37.7709i	−0.600938	−	1.49070i
$643$		−	6.95566i		−	0.274305i	−0.990550	−	0.137152i	$-0.956205\pi$
$643$		−	6.95566i		−	0.274305i	0.990550	−	0.137152i	$-0.0437950\pi$
$644$	0.249567	−	1.40264i	0.00983431	−	0.0552719i
$645$		0			0
$646$	−0.182737	−	2.64270i	−0.00718970	−	0.103976i
$647$	−20.9935	+	15.2526i	−0.825338	+	0.599643i	−0.918237	−	0.396032i	$-0.870387\pi$
$647$	−20.9935	+	15.2526i	−0.825338	+	0.599643i	0.0928983	+	0.995676i	$0.470387\pi$
$648$	−22.9413	+	4.82060i	−0.901220	+	0.189371i
$649$	6.12843			0.240562
$650$		0			0
$651$			0.982411i			0.0385037i
$652$	13.9144	+	14.4535i	0.544929	+	0.566044i
$653$	−10.8488	−	14.9322i	−0.424548	−	0.584340i	0.542143	−	0.840286i	$-0.317613\pi$
$653$	−10.8488	−	14.9322i	−0.424548	−	0.584340i	−0.966691	+	0.255946i	$0.917613\pi$
$654$	−6.63704	+	0.458938i	−0.259529	+	0.0179459i
$655$		0			0
$656$	−43.7823	+	12.4076i	−1.70941	+	0.484435i
$657$	33.3758			1.30212
$658$	0.181968	+	0.451394i	0.00709386	+	0.0175972i
$659$	−8.10100	−	2.63217i	−0.315570	−	0.102535i	0.146950	−	0.989144i	$-0.453055\pi$
$659$	−8.10100	−	2.63217i	−0.315570	−	0.102535i	−0.462520	+	0.886609i	$0.653055\pi$
$660$		0			0
$661$	38.1202	−	12.3860i	1.48270	−	0.481760i	0.547785	−	0.836619i	$-0.315471\pi$
$661$	38.1202	−	12.3860i	1.48270	−	0.481760i	0.934920	+	0.354859i	$0.115471\pi$
$662$	−3.24828	−	3.87724i	−0.126248	−	0.150693i
$663$	−1.69816	+	5.22641i	−0.0659512	+	0.202977i
$664$	7.12506	+	33.9083i	0.276506	+	1.31590i
$665$		0			0
$666$	4.73599	+	5.65302i	0.183516	+	0.219050i
$667$	−34.0138	+	46.8159i	−1.31702	+	1.81272i
$668$	−7.03033	−	14.4712i	−0.272012	−	0.559908i
$669$	−17.2800	+	23.7839i	−0.668084	+	0.919539i
$670$		0			0
$671$	16.3718	−	11.8948i	0.632028	−	0.459195i
$672$	1.29401	+	0.880137i	0.0499175	+	0.0339520i
$673$	−13.9092	−	42.8082i	−0.536162	−	1.65014i	−0.741125	−	0.671367i	$-0.765708\pi$
$673$	−13.9092	−	42.8082i	−0.536162	−	1.65014i	0.204964	−	0.978770i	$-0.434292\pi$
$674$	−11.7858	−	7.37727i	−0.453970	−	0.284162i
$675$		0			0
$676$	−8.80633	−	18.1269i	−0.338705	−	0.697189i
$677$	−42.8382	+	13.9190i	−1.64641	+	0.534950i	−0.977957	−	0.208808i	$-0.933042\pi$
$677$	−42.8382	+	13.9190i	−1.64641	+	0.534950i	−0.668450	+	0.743758i	$0.733042\pi$
$678$	−1.11817	−	16.1707i	−0.0429432	−	0.621033i
$679$	0.504344	−	0.366427i	0.0193549	−	0.0140622i
$680$		0			0
$681$	−2.11756	−	1.53849i	−0.0811449	−	0.0589552i
$682$	−4.58638	+	7.32709i	−0.175621	+	0.280569i
$683$	−4.29498	+	5.91153i	−0.164343	+	0.226199i	−0.883244	−	0.468914i	$-0.844645\pi$
$683$	−4.29498	+	5.91153i	−0.164343	+	0.226199i	0.718901	+	0.695112i	$0.244645\pi$
$684$	−3.62115	−	26.0589i	−0.138458	−	0.996385i
$685$		0			0
$686$	−0.532454	+	2.12853i	−0.0203292	+	0.0812676i
$687$	−15.5913	+	47.9850i	−0.594844	+	1.83074i
$688$	34.9933	−	23.4458i	1.33411	−	0.893862i
$689$	−6.81552	−	20.9760i	−0.259650	−	0.799122i
$690$		0			0
$691$	−33.1194	−	10.7611i	−1.25992	−	0.409373i	−0.398455	−	0.917188i	$-0.630454\pi$
$691$	−33.1194	−	10.7611i	−1.25992	−	0.409373i	−0.861467	+	0.507814i	$0.830454\pi$
$692$	−19.5846	−	3.48460i	−0.744494	−	0.132465i
$693$		−	0.614940i		−	0.0233596i
$694$	−20.7167	+	8.35142i	−0.786395	+	0.317015i
$695$		0			0
$696$	−31.6549	−	55.1234i	−1.19987	−	2.08945i
$697$	−4.22136	+	3.06700i	−0.159896	+	0.116171i
$698$	10.6845	+	2.67274i	0.404413	+	0.101165i
$699$			65.4828i			2.47679i
$700$		0			0
$701$			22.3659i			0.844750i	0.906421	+	0.422375i	$0.138803\pi$
$701$			22.3659i			0.844750i	−0.906421	+	0.422375i	$0.861197\pi$
$702$	−0.908807	+	3.63303i	−0.0343007	+	0.137120i
$703$	5.34910	−	3.88635i	0.201745	−	0.146576i
$704$	5.54218	+	12.6054i	0.208879	+	0.475083i
$705$		0			0
$706$	5.94524	+	14.7479i	0.223752	+	0.555044i
$707$			0.172631i			0.00649248i
$708$	−3.11128	+	17.4864i	−0.116929	+	0.657178i
$709$	17.1971	+	5.58767i	0.645849	+	0.209849i	0.613583	−	0.789630i	$-0.289728\pi$
$709$	17.1971	+	5.58767i	0.645849	+	0.209849i	0.0322662	+	0.999479i	$0.489728\pi$
$710$		0			0
$711$	5.48073	+	16.8679i	0.205543	+	0.632597i
$712$	−17.3367	−	7.76714i	−0.649720	−	0.291086i
$713$	−7.04749	+	21.6899i	−0.263930	+	0.812294i
$714$	0.174079	+	0.0435461i	0.00651474	+	0.00162967i
$715$		0			0
$716$	3.46497	+	24.9349i	0.129492	+	0.931862i
$717$	−12.8030	+	17.6219i	−0.478139	+	0.658101i
$718$	−12.1964	−	7.63431i	−0.455166	−	0.284910i
$719$	31.8411	+	23.1339i	1.18747	+	0.862749i	0.992995	−	0.118158i	$-0.0376991\pi$
$719$	31.8411	+	23.1339i	1.18747	+	0.862749i	0.194477	+	0.980907i	$0.437699\pi$
$720$		0			0
$721$	0.423362	−	0.307590i	0.0157668	−	0.0114553i
$722$	3.27447	−	0.226423i	0.121863	−	0.00842658i
$723$	0.848620	−	0.275733i	0.0315605	−	0.0102546i
$724$	−23.4916	+	11.4126i	−0.873059	+	0.424145i
$725$		0			0
$726$	−15.0420	+	24.0307i	−0.558260	+	0.891864i
$727$	−5.45658	−	16.7936i	−0.202373	−	0.622841i	−0.999811	−	0.0194399i	$-0.993812\pi$
$727$	−5.45658	−	16.7936i	−0.202373	−	0.622841i	0.797438	−	0.603401i	$-0.206188\pi$
$728$	−1.30689	+	0.750487i	−0.0484366	+	0.0278149i
$729$	−24.9346	+	18.1161i	−0.923505	+	0.670966i
$730$		0			0
$731$	2.83888	−	3.90738i	0.105000	−	0.144520i
$732$	25.6281	+	52.7529i	0.947244	+	1.94980i
$733$	5.28165	−	7.26956i	0.195082	−	0.268507i	−0.700259	−	0.713889i	$-0.746932\pi$
$733$	5.28165	−	7.26956i	0.195082	−	0.268507i	0.895341	+	0.445382i	$0.146932\pi$
$734$	−13.1565	+	11.0222i	−0.485614	+	0.406837i
$735$		0			0
$736$	22.2557	+	28.7147i	0.820356	+	1.05844i
$737$	1.98929	−	6.12241i	0.0732765	−	0.225522i
$738$	−39.7243	+	33.2802i	−1.46227	+	1.22506i
$739$	−20.0852	+	6.52609i	−0.738848	+	0.240066i	−0.654176	−	0.756343i	$-0.726984\pi$
$739$	−20.0852	+	6.52609i	−0.738848	+	0.240066i	−0.0846720	+	0.996409i	$0.526984\pi$
$740$		0			0
$741$	46.5379	+	15.1211i	1.70961	+	0.555487i
$742$	−0.667955	+	0.269269i	−0.0245214	+	0.00988518i
$743$	8.50903			0.312166			0.156083	−	0.987744i	$-0.450113\pi$
$743$	8.50903			0.312166			0.156083	+	0.987744i	$0.450113\pi$
$744$	−18.5781	−	16.8062i	−0.681108	−	0.616146i
$745$		0			0
$746$	−0.726854	−	10.5116i	−0.0266120	−	0.384856i
$747$	23.1929	+	31.9222i	0.848582	+	1.16797i
$748$	1.09503	+	1.13746i	0.0400384	+	0.0415898i
$749$		−	1.28058i		−	0.0467916i
$750$		0			0
$751$	−17.1075			−0.624262			−0.312131	−	0.950039i	$-0.601043\pi$
$751$	−17.1075			−0.624262			−0.312131	+	0.950039i	$0.601043\pi$
$752$	−11.6492	−	4.28089i	−0.424801	−	0.156108i
$753$	−40.4317	+	29.3753i	−1.47341	+	1.07050i
$754$	61.0678	−	4.22271i	2.22396	−	0.153782i
$755$		0			0
$756$	0.120395	+	0.0214215i	0.00437874	+	0.000779091i
$757$			2.28693i			0.0831199i	0.999136	+	0.0415599i	$0.0132328\pi$
$757$			2.28693i			0.0831199i	−0.999136	+	0.0415599i	$0.986767\pi$
$758$	8.26148	−	3.33041i	0.300070	−	0.120966i
$759$	8.52006	−	26.2220i	0.309258	−	0.951800i
$760$		0			0
$761$	−6.05917	−	18.6482i	−0.219645	−	0.675997i	−0.998791	−	0.0491552i	$-0.984347\pi$
$761$	−6.05917	−	18.6482i	−0.219645	−	0.675997i	0.779146	−	0.626842i	$-0.215653\pi$
$762$	−18.4302	−	21.9989i	−0.667656	−	0.796935i
$763$	−0.198961	−	0.0646465i	−0.00720289	−	0.00234036i
$764$	−4.14558	+	3.99094i	−0.149982	+	0.144387i
$765$		0			0
$766$	31.0552	−	26.0174i	1.12207	−	0.940048i
$767$	−13.8372	−	10.0533i	−0.499633	−	0.363005i
$768$	−38.7808	+	9.41412i	−1.39938	+	0.339703i
$769$	−15.2893	−	11.1083i	−0.551345	−	0.400576i	0.276936	−	0.960888i	$-0.410681\pi$
$769$	−15.2893	−	11.1083i	−0.551345	−	0.400576i	−0.828281	+	0.560313i	$0.810681\pi$
$770$		0			0
$771$	−27.4599	−	37.7954i	−0.988946	−	1.36117i
$772$	28.0579	+	14.9745i	1.00983	+	0.538944i
$773$	−7.19893	+	2.33908i	−0.258928	+	0.0841307i	−0.435604	−	0.900138i	$-0.643465\pi$
$773$	−7.19893	+	2.33908i	−0.258928	+	0.0841307i	0.176677	+	0.984269i	$0.443465\pi$
$774$	25.4508	−	40.6597i	0.914811	−	1.46148i
$775$		0			0
$776$	−1.69845	+	15.8060i	−0.0609708	+	0.567403i
$777$	0.138404	+	0.425963i	0.00496521	+	0.0152813i
$778$	−0.0677507	−	0.979793i	−0.00242898	−	0.0351273i
$779$	27.3097	+	37.5886i	0.978473	+	1.34675i
$780$		0			0
$781$	−11.3156	+	15.5746i	−0.404903	+	0.557302i
$782$	3.53098	+	2.21021i	0.126267	+	0.0790368i
$783$	−4.01843	−	2.91956i	−0.143607	−	0.104336i
$784$	−15.5580	−	23.2206i	−0.555642	−	0.829307i
$785$		0			0
$786$	18.6140	−	74.4110i	0.663940	−	2.65415i
$787$	38.7769	+	12.5994i	1.38225	+	0.449119i	0.903407	−	0.428784i	$-0.141058\pi$
$787$	38.7769	+	12.5994i	1.38225	+	0.449119i	0.478839	+	0.877903i	$0.341058\pi$
$788$	−1.28772	−	9.26684i	−0.0458733	−	0.330118i
$789$	−39.1099	+	12.7076i	−1.39235	+	0.452401i
$790$		0			0
$791$	0.157507	−	0.484757i	0.00560031	−	0.0172360i
$792$	11.6290	+	10.5198i	0.413218	+	0.373807i
$793$	−56.4783			−2.00560
$794$	27.5261	−	11.0964i	0.976864	−	0.393798i
$795$		0			0
$796$	49.4816	+	26.4083i	1.75383	+	0.936018i
$797$	2.91212	+	4.00819i	0.103153	+	0.141977i	0.857473	−	0.514529i	$-0.172033\pi$
$797$	2.91212	+	4.00819i	0.103153	+	0.141977i	−0.754320	+	0.656507i	$0.772033\pi$
$798$	0.387751	−	1.55006i	0.0137262	−	0.0548717i
$799$	−1.42306			−0.0503443
$800$		0			0
$801$	−21.6339			−0.764396
$802$	6.44224	−	25.7534i	0.227484	−	0.909383i
$803$	10.4834	+	14.4291i	0.369950	+	0.509192i
$804$	16.4593	+	8.78431i	0.580474	+	0.309799i
$805$		0			0
$806$	22.3751	−	9.01997i	0.788130	−	0.317715i
$807$	−0.363315			−0.0127893
$808$	−3.26459	−	2.95323i	−0.114848	−	0.103894i
$809$	−7.58506	+	23.3444i	−0.266676	+	0.820746i	0.724626	+	0.689142i	$0.242013\pi$
$809$	−7.58506	+	23.3444i	−0.266676	+	0.820746i	−0.991302	+	0.131603i	$0.957987\pi$
$810$		0			0
$811$	−0.736311	+	0.239242i	−0.0258554	+	0.00840092i	−0.321916	−	0.946768i	$-0.604327\pi$
$811$	−0.736311	+	0.239242i	−0.0258554	+	0.00840092i	0.296061	+	0.955169i	$0.404327\pi$
$812$	−0.275115	−	1.97981i	−0.00965465	−	0.0694777i
$813$	−36.3792	−	11.8203i	−1.27588	−	0.414557i
$814$	−0.956350	+	3.82309i	−0.0335201	+	0.133999i
$815$		0			0
$816$	−3.80148	+	2.54702i	−0.133078	+	0.0891634i
$817$	−34.7928	−	25.2785i	−1.21725	−	0.884382i
$818$	43.8128	+	27.4245i	1.53188	+	0.958875i
$819$	−1.00877	+	1.38846i	−0.0352494	+	0.0485166i
$820$		0			0
$821$	−4.17446	−	5.74566i	−0.145690	−	0.200525i	0.729935	−	0.683516i	$-0.239550\pi$
$821$	−4.17446	−	5.74566i	−0.145690	−	0.200525i	−0.875625	+	0.482992i	$0.839550\pi$
$822$	2.23177	+	32.2753i	0.0778420	+	1.12573i
$823$	−2.42963	−	7.47765i	−0.0846917	−	0.260654i	0.899739	−	0.436429i	$-0.143757\pi$
$823$	−2.42963	−	7.47765i	−0.0846917	−	0.260654i	−0.984430	+	0.175775i	$0.943757\pi$
$824$	−1.42573	+	13.2681i	−0.0496677	+	0.462215i
$825$		0			0
$826$	−0.296325	+	0.473402i	−0.0103105	+	0.0164718i
$827$	3.13777	−	1.01952i	0.109111	−	0.0354523i	−0.253953	−	0.967217i	$-0.581731\pi$
$827$	3.13777	−	1.01952i	0.109111	−	0.0354523i	0.363064	+	0.931764i	$0.381731\pi$
$828$	36.4994	+	19.4797i	1.26844	+	0.676968i
$829$	−19.0835	−	26.2662i	−0.662798	−	0.912263i	0.336772	−	0.941586i	$-0.390665\pi$
$829$	−19.0835	−	26.2662i	−0.662798	−	0.912263i	−0.999570	+	0.0293232i	$0.990665\pi$
$830$		0			0
$831$	41.7875	+	30.3604i	1.44959	+	1.05319i
$832$	8.16485	−	37.5530i	0.283065	−	1.30192i
$833$	−2.59283	−	1.88380i	−0.0898362	−	0.0652699i
$834$	−37.0016	+	30.9992i	−1.28126	+	1.07341i
$835$		0			0
$836$	10.1284	−	9.75059i	0.350298	−	0.337231i
$837$	−1.86175	−	0.604918i	−0.0643514	−	0.0209090i
$838$	9.37409	+	11.1892i	0.323823	+	0.386525i
$839$	−3.32108	−	10.2212i	−0.114656	−	0.352876i	0.877219	−	0.480091i	$-0.159396\pi$
$839$	−3.32108	−	10.2212i	−0.114656	−	0.352876i	−0.991875	+	0.127215i	$0.959396\pi$
$840$		0			0
$841$	−16.1273	+	49.6347i	−0.556114	+	1.71154i
$842$	−15.9085	+	6.41313i	−0.548245	+	0.221011i
$843$		−	26.4020i		−	0.909332i
$844$	−0.642569	−	0.114330i	−0.0221181	−	0.00393539i
$845$		0			0
$846$	−14.0998	+	0.974972i	−0.484761	+	0.0335202i
$847$	−0.721219	+	0.523996i	−0.0247814	+	0.0180047i
$848$	6.33469	−	17.2379i	0.217534	−	0.591954i
$849$	51.3090			1.76092
$850$		0			0
$851$			10.3974i			0.356418i
$852$	−38.6945	−	40.1939i	−1.32565	−	1.37702i
$853$	13.5909	+	18.7063i	0.465344	+	0.640491i	0.975606	−	0.219528i	$-0.0704517\pi$
$853$	13.5909	+	18.7063i	0.465344	+	0.640491i	−0.510262	+	0.860019i	$0.670452\pi$
$854$	0.127220	+	1.83982i	0.00435337	+	0.0629573i
$855$		0			0
$856$	24.2168	+	21.9071i	0.827714	+	0.748770i
$857$	15.8941			0.542932			0.271466	−	0.962448i	$-0.412492\pi$
$857$	15.8941			0.542932			0.271466	+	0.962448i	$0.412492\pi$
$858$	−27.0504	+	10.9047i	−0.923485	+	0.372280i
$859$	−3.46524	−	1.12593i	−0.118233	−	0.0384161i	0.249303	−	0.968425i	$-0.419798\pi$
$859$	−3.46524	−	1.12593i	−0.118233	−	0.0384161i	−0.367536	+	0.930009i	$0.619798\pi$
$860$		0			0
$861$	−2.99328	+	0.972577i	−0.102011	+	0.0331453i
$862$	−33.3313	+	27.9243i	−1.13527	+	0.951105i
$863$	12.9507	−	39.8580i	0.440845	−	1.35678i	−0.446131	−	0.894968i	$-0.647198\pi$
$863$	12.9507	−	39.8580i	0.440845	−	1.35678i	0.886976	−	0.461815i	$-0.152802\pi$
$864$	−2.46471	+	1.91031i	−0.0838513	+	0.0649900i
$865$		0			0
$866$	−4.88765	+	4.09477i	−0.166089	+	0.139146i
$867$	24.6145	−	33.8789i	0.835951	−	1.15059i
$868$	−0.344232	−	0.708566i	−0.0116840	−	0.0240503i
$869$	−5.57088	+	7.66766i	−0.188979	+	0.260108i
$870$		0			0
$871$	−14.5350	+	10.5603i	−0.492500	+	0.357823i
$872$	4.62617	−	2.65660i	0.156662	−	0.0899637i
$873$	5.59430	+	17.2175i	0.189338	+	0.582723i
$874$	19.6805	−	31.4411i	0.665703	−	1.06351i
$875$		0			0
$876$	−46.4931	+	22.5870i	−1.57086	+	0.763145i
$877$	27.2067	−	8.84000i	0.918705	−	0.298505i	0.188770	−	0.982021i	$-0.439550\pi$
$877$	27.2067	−	8.84000i	0.918705	−	0.298505i	0.729936	+	0.683516i	$0.239550\pi$
$878$	−16.8200	+	1.16307i	−0.567646	+	0.0392516i
$879$	1.21702	−	0.884217i	0.0410491	−	0.0298239i
$880$		0			0
$881$	15.5718	+	11.3135i	0.524626	+	0.381163i	0.818344	−	0.574729i	$-0.194893\pi$
$881$	15.5718	+	11.3135i	0.524626	+	0.381163i	−0.293718	+	0.955892i	$0.594893\pi$
$882$	−26.9806	−	16.8884i	−0.908484	−	0.568663i
$883$	−7.63372	+	10.5069i	−0.256895	+	0.353586i	−0.917911	−	0.396786i	$-0.870126\pi$
$883$	−7.63372	+	10.5069i	−0.256895	+	0.353586i	0.661016	+	0.750372i	$0.270126\pi$
$884$	−0.606505	−	4.36459i	−0.0203990	−	0.146797i
$885$		0			0
$886$	5.49465	+	1.37450i	0.184596	+	0.0461771i
$887$	−5.22346	+	16.0762i	−0.175387	+	0.539785i	−0.999651	−	0.0264205i	$-0.991589\pi$
$887$	−5.22346	+	16.0762i	−0.175387	+	0.539785i	0.824264	+	0.566205i	$0.191589\pi$
$888$	−10.4230	−	4.66968i	−0.349772	−	0.156704i
$889$	−0.278868	−	0.858269i	−0.00935295	−	0.0287854i
$890$		0			0
$891$	−13.5676	−	4.40839i	−0.454533	−	0.147687i
$892$	4.12949	−	23.2090i	0.138265	−	0.777096i
$893$			12.6715i			0.424035i
$894$	−19.5710	−	48.5483i	−0.654552	−	1.62370i
$895$		0			0
$896$	−1.24170	−	0.181386i	−0.0414824	−	0.00605967i
$897$	−62.2529	+	45.2294i	−2.07856	+	1.51017i
$898$	−2.13018	+	8.51557i	−0.0710851	+	0.284168i
$899$			31.9973i			1.06717i
$900$		0			0
$901$		−	2.10579i		−	0.0701540i
$902$	−26.8652	−	6.72037i	−0.894513	−	0.223764i
$903$	2.35685	−	1.71235i	0.0784312	−	0.0569836i
$904$	6.47263	+	11.2714i	0.215277	+	0.374880i
$905$		0			0
$906$	−29.0264	+	11.7013i	−0.964339	+	0.388749i
$907$			36.2209i			1.20269i	0.798988	+	0.601347i	$0.205369\pi$
$907$			36.2209i			1.20269i	−0.798988	+	0.601347i	$0.794631\pi$
$908$	2.06637	+	0.367661i	0.0685750	+	0.0122013i
$909$	−4.76783	−	1.54916i	−0.158139	−	0.0513825i
$910$		0			0
$911$	−3.31491	−	10.2022i	−0.109828	−	0.338015i	0.881005	−	0.473106i	$-0.156867\pi$
$911$	−3.31491	−	10.2022i	−0.109828	−	0.338015i	−0.990833	+	0.135091i	$0.956867\pi$
$912$	22.6796	+	33.8498i	0.750996	+	1.12088i
$913$	−6.51579	+	20.0536i	−0.215641	+	0.663676i
$914$	11.7209	−	46.8553i	0.387693	−	1.54983i
$915$		0			0
$916$	−5.56848	−	40.0724i	−0.183988	−	1.32403i
$917$	1.41771	−	1.95131i	0.0468170	−	0.0644381i
$918$	−0.189712	+	0.303080i	−0.00626143	+	0.0100031i
$919$	32.1024	+	23.3238i	1.05896	+	0.769380i	0.973896	−	0.226995i	$-0.0728901\pi$
$919$	32.1024	+	23.3238i	1.05896	+	0.769380i	0.0850654	+	0.996375i	$0.472890\pi$
$920$		0			0
$921$	20.1028	−	14.6056i	0.662411	−	0.481270i
$922$	−1.26939	−	18.3576i	−0.0418052	−	0.604576i
$923$	51.0983	−	16.6029i	1.68192	−	0.546490i
$924$	0.416159	+	0.856621i	0.0136906	+	0.0281808i
$925$		0			0
$926$	0.597460	+	0.373979i	0.0196338	+	0.0122897i
$927$	4.69603	+	14.4529i	0.154238	+	0.474695i
$928$	42.1461	+	28.6662i	1.38352	+	0.941014i
$929$	−17.2005	+	12.4969i	−0.564331	+	0.410011i	−0.833042	−	0.553210i	$-0.813403\pi$
$929$	−17.2005	+	12.4969i	−0.564331	+	0.410011i	0.268710	+	0.963221i	$0.413403\pi$
$930$		0			0
$931$	−16.7741	+	23.0875i	−0.549748	+	0.756664i
$932$	−22.9449	−	47.2296i	−0.751584	−	1.54706i
$933$	35.7138	−	49.1558i	1.16922	−	1.60929i
$934$	−24.7454	−	29.5369i	−0.809696	−	0.966478i
$935$		0			0
$936$	−8.99958	−	42.8292i	−0.294160	−	1.39991i
$937$	−9.26796	+	28.5238i	−0.302771	+	0.931833i	0.677729	+	0.735312i	$0.262964\pi$
$937$	−9.26796	+	28.5238i	−0.302771	+	0.931833i	−0.980500	+	0.196521i	$0.937036\pi$
$938$	0.376750	+	0.449700i	0.0123013	+	0.0146832i
$939$	44.3948	−	14.4248i	1.44877	−	0.470734i
$940$		0			0
$941$	−20.6829	−	6.72027i	−0.674242	−	0.219075i	−0.0481695	−	0.998839i	$-0.515339\pi$
$941$	−20.6829	−	6.72027i	−0.674242	−	0.219075i	−0.626073	+	0.779765i	$0.715339\pi$
$942$	−6.21659	−	15.4210i	−0.202548	−	0.502444i
$943$	−73.0634			−2.37927
$944$	−3.88313	−	13.7023i	−0.126385	−	0.445971i
$945$		0			0
$946$	25.5722	−	1.76826i	0.831423	−	0.0574912i
$947$	−13.8628	−	19.0805i	−0.450481	−	0.620034i	0.522020	−	0.852934i	$-0.325179\pi$
$947$	−13.8628	−	19.0805i	−0.450481	−	0.620034i	−0.972501	+	0.232899i	$0.925179\pi$
$948$	−19.0501	−	19.7882i	−0.618718	−	0.642692i
$949$		−	49.7764i		−	1.61581i
$950$		0			0
$951$	−71.1992			−2.30879
$952$	−0.140813	+	0.0295887i	−0.00456378	+	0.000958976i
$953$	22.5241	−	16.3647i	0.729629	−	0.530106i	−0.159817	−	0.987147i	$-0.551091\pi$
$953$	22.5241	−	16.3647i	0.729629	−	0.530106i	0.889446	+	0.457040i	$0.151091\pi$
$954$	−1.44272	−	20.8643i	−0.0467099	−	0.675507i
$955$		0			0
$956$	3.05960	−	17.1960i	0.0989547	−	0.556157i
$957$		−	38.6831i		−	1.25045i
$958$	15.3725	+	38.1333i	0.496662	+	1.23203i
$959$	−0.314370	+	0.967532i	−0.0101515	+	0.0312432i
$960$		0			0
$961$	−5.68270	−	17.4895i	−0.183313	−	0.564179i
$962$	8.43087	−	7.06321i	0.271822	−	0.227727i
$963$	35.3679	+	11.4917i	1.13971	+	0.370316i
$964$	−0.515453	+	0.496226i	−0.0166016	+	0.0159823i
$965$		0			0
$966$	1.61360	+	1.92605i	0.0519169	+	0.0619696i
$967$	49.5079	+	35.9696i	1.59207	+	1.15671i	0.900914	+	0.433998i	$0.142897\pi$
$967$	49.5079	+	35.9696i	1.59207	+	1.15671i	0.691154	+	0.722707i	$0.257103\pi$
$968$	2.42881	−	22.6029i	0.0780649	−	0.726484i
$969$	3.77969	+	2.74611i	0.121421	+	0.0882177i
$970$		0			0
$971$	−19.9841	−	27.5058i	−0.641321	−	0.882703i	0.357364	−	0.933965i	$-0.383676\pi$
$971$	−19.9841	−	27.5058i	−0.641321	−	0.882703i	−0.998685	+	0.0512621i	$0.983676\pi$
$972$	21.0239	−	39.3927i	0.674341	−	1.26352i
$973$	−1.44359	+	0.469050i	−0.0462793	+	0.0150371i
$974$	−31.2139	−	19.5383i	−1.00016	−	0.626046i
$975$		0			0
$976$	−36.9687	−	29.0682i	−1.18334	−	0.930449i
$977$	16.4081	+	50.4988i	0.524940	+	1.61560i	0.764434	+	0.644702i	$0.223018\pi$
$977$	16.4081	+	50.4988i	0.524940	+	1.61560i	−0.239494	+	0.970898i	$0.576982\pi$
$978$	−35.2996	+	2.44090i	−1.12876	+	0.0780513i
$979$	−6.79521	−	9.35280i	−0.217176	−	0.298917i
$980$		0			0
$981$	3.57088	−	4.91490i	0.114010	−	0.156921i
$982$	18.4788	−	29.5214i	0.589683	−	0.942065i
$983$	−24.8942	−	18.0867i	−0.794003	−	0.576877i	0.115146	−	0.993349i	$-0.463266\pi$
$983$	−24.8942	−	18.0867i	−0.794003	−	0.576877i	−0.909149	+	0.416472i	$0.863266\pi$
$984$	32.8143	−	73.2432i	1.04608	−	2.33491i
$985$		0			0
$986$	5.66978	+	1.41830i	0.180563	+	0.0451680i
$987$	−0.816350	−	0.265248i	−0.0259847	−	0.00844294i
$988$	−38.8640	+	5.40055i	−1.23643	+	0.171814i
$989$	64.3191	−	20.8985i	2.04523	−	0.664535i
$990$		0			0
$991$	−3.86953	+	11.9092i	−0.122920	+	0.378308i	−0.993516	−	0.113690i	$-0.963733\pi$
$991$	−3.86953	+	11.9092i	−0.122920	+	0.378308i	0.870597	+	0.491997i	$0.163733\pi$
$992$	19.2883	+	5.61183i	0.612406	+	0.178176i
$993$	8.92077			0.283092
$994$	−0.655950	−	1.62716i	−0.0208055	−	0.0516105i
$995$		0			0
$996$	−53.9113	−	28.7724i	−1.70824	−	0.911689i
$997$	7.25948	+	9.99182i	0.229910	+	0.316444i	0.908349	−	0.418212i	$-0.137343\pi$
$997$	7.25948	+	9.99182i	0.229910	+	0.316444i	−0.678439	+	0.734657i	$0.737343\pi$
$998$	−25.3286	−	6.33599i	−0.801764	−	0.200562i
$999$	−0.892455			−0.0282360

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.t.b.901.30		224
5.2	odd	4		1000.2.o.a.349.27		112
5.3	odd	4		200.2.o.a.69.2	yes	112
5.4	even	2	inner	1000.2.t.b.901.27		224
8.5	even	2	inner	1000.2.t.b.901.14		224
20.3	even	4		800.2.be.a.369.24		112
25.3	odd	20		1000.2.o.a.149.20		112
25.4	even	10	inner	1000.2.t.b.101.43		224
25.21	even	5	inner	1000.2.t.b.101.14		224
25.22	odd	20		200.2.o.a.29.9	yes	112
40.3	even	4		800.2.be.a.369.5		112
40.13	odd	4		200.2.o.a.69.9	yes	112
40.29	even	2	inner	1000.2.t.b.901.43		224
40.37	odd	4		1000.2.o.a.349.20		112
100.47	even	20		800.2.be.a.529.5		112
200.21	even	10	inner	1000.2.t.b.101.30		224
200.29	even	10	inner	1000.2.t.b.101.27		224
200.53	odd	20		1000.2.o.a.149.27		112
200.147	even	20		800.2.be.a.529.24		112
200.197	odd	20		200.2.o.a.29.2	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.2	✓	112	200.197	odd	20
200.2.o.a.29.9	yes	112	25.22	odd	20
200.2.o.a.69.2	yes	112	5.3	odd	4
200.2.o.a.69.9	yes	112	40.13	odd	4
800.2.be.a.369.5		112	40.3	even	4
800.2.be.a.369.24		112	20.3	even	4
800.2.be.a.529.5		112	100.47	even	20
800.2.be.a.529.24		112	200.147	even	20
1000.2.o.a.149.20		112	25.3	odd	20
1000.2.o.a.149.27		112	200.53	odd	20
1000.2.o.a.349.20		112	40.37	odd	4
1000.2.o.a.349.27		112	5.2	odd	4
1000.2.t.b.101.14		224	25.21	even	5	inner
1000.2.t.b.101.27		224	200.29	even	10	inner
1000.2.t.b.101.30		224	200.21	even	10	inner
1000.2.t.b.101.43		224	25.4	even	10	inner
1000.2.t.b.901.14		224	8.5	even	2	inner
1000.2.t.b.901.27		224	5.4	even	2	inner
1000.2.t.b.901.30		224	1.1	even	1	trivial
1000.2.t.b.901.43		224	40.29	even	2	inner

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:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.t (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.343193 - 1.37194i) q^{2} +(1.46605 + 2.01785i) q^{3} +(-1.76444 - 0.941679i) q^{4} +(3.27150 - 1.31882i) q^{6} +0.110917 q^{7} +(-1.89747 + 2.09752i) q^{8} +(-0.995348 + 3.06337i) q^{9} +O(q^{10})\)	\(q+(0.343193 - 1.37194i) q^{2} +(1.46605 + 2.01785i) q^{3} +(-1.76444 - 0.941679i) q^{4} +(3.27150 - 1.31882i) q^{6} +0.110917 q^{7} +(-1.89747 + 2.09752i) q^{8} +(-0.995348 + 3.06337i) q^{9} +(-1.63700 + 0.531893i) q^{11} +(-0.686591 - 4.94092i) q^{12} +(4.56868 + 1.48445i) q^{13} +(0.0380659 - 0.152171i) q^{14} +(2.22648 + 3.32307i) q^{16} +(0.371056 + 0.269588i) q^{17} +(3.86116 + 2.41688i) q^{18} +(2.40052 - 3.30403i) q^{19} +(0.162610 + 0.223814i) q^{21} +(0.167919 + 2.42841i) q^{22} +(1.98459 + 6.10792i) q^{23} +(-7.01427 - 0.753724i) q^{24} +(3.60452 - 5.75850i) q^{26} +(-0.524271 + 0.170346i) q^{27} +(-0.195706 - 0.104448i) q^{28} +(5.29624 + 7.28964i) q^{29} +(2.87291 + 2.08729i) q^{31} +(5.32316 - 1.91414i) q^{32} +(-3.47320 - 2.52343i) q^{33} +(0.497203 - 0.416546i) q^{34} +(4.64094 - 4.46782i) q^{36} +(1.53972 + 0.500287i) q^{37} +(-3.70909 - 4.42728i) q^{38} +(3.70252 + 11.3952i) q^{39} +(-3.51556 + 10.8198i) q^{41} +(0.362865 - 0.146280i) q^{42} -10.5304i q^{43} +(3.38926 + 0.603036i) q^{44} +(9.06080 - 0.626536i) q^{46} +(-2.51014 + 1.82373i) q^{47} +(-3.44131 + 9.36449i) q^{48} -6.98770 q^{49} +1.14397i q^{51} +(-6.66327 - 6.92145i) q^{52} +(-2.69868 - 3.71441i) q^{53} +(0.0537784 + 0.777730i) q^{54} +(-0.210462 + 0.232651i) q^{56} +10.1863 q^{57} +(11.8186 - 4.76436i) q^{58} +(-3.38621 - 1.10025i) q^{59} +(-11.1816 + 3.63312i) q^{61} +(3.84960 - 3.22512i) q^{62} +(-0.110401 + 0.339779i) q^{63} +(-0.799218 - 7.95998i) q^{64} +(-4.65397 + 3.89900i) q^{66} +(-2.19833 + 3.02574i) q^{67} +(-0.400840 - 0.825088i) q^{68} +(-9.41535 + 12.9591i) q^{69} +(9.04844 - 6.57408i) q^{71} +(-4.53684 - 7.90041i) q^{72} +(-3.20201 - 9.85476i) q^{73} +(1.21479 - 1.94072i) q^{74} +(-7.34690 + 3.56923i) q^{76} +(-0.181571 + 0.0589960i) q^{77} +(16.9042 - 1.16889i) q^{78} +(4.45472 - 3.23655i) q^{79} +(6.70522 + 4.87163i) q^{81} +(13.6376 + 8.53642i) q^{82} +(7.20048 - 9.91061i) q^{83} +(-0.0761547 - 0.548032i) q^{84} +(-14.4471 - 3.61397i) q^{86} +(-6.94483 + 21.3740i) q^{87} +(1.99050 - 4.44290i) q^{88} +(2.07551 + 6.38776i) q^{89} +(0.506744 + 0.164651i) q^{91} +(2.25003 - 12.6459i) q^{92} +8.85717i q^{93} +(1.64058 + 4.06966i) q^{94} +(11.6665 + 7.93510i) q^{96} +(4.54704 - 3.30362i) q^{97} +(-2.39813 + 9.58670i) q^{98} -5.54415i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9}+O(q^{10}) \) 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9	\( 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9} + 6 q^{14} - 30 q^{16} + 32 q^{24} - 28 q^{26} - 36 q^{31} - 18 q^{34} + 82 q^{36} + 20 q^{39} - 20 q^{41} + 64 q^{44} + 26 q^{46} + 160 q^{49} - 86 q^{54} + 72 q^{56} + 72 q^{64} + 80 q^{66} + 44 q^{71} - 8 q^{74} - 72 q^{76} - 28 q^{79} - 12 q^{81} - 156 q^{84} - 118 q^{86} - 48 q^{89} - 90 q^{94} + 92 q^{96}+O(q^{100}) \) 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9 + 6 * q^14 - 30 * q^16 + 32 * q^24 - 28 * q^26 - 36 * q^31 - 18 * q^34 + 82 * q^36 + 20 * q^39 - 20 * q^41 + 64 * q^44 + 26 * q^46 + 160 * q^49 - 86 * q^54 + 72 * q^56 + 72 * q^64 + 80 * q^66 + 44 * q^71 - 8 * q^74 - 72 * q^76 - 28 * q^79 - 12 * q^81 - 156 * q^84 - 118 * q^86 - 48 * q^89 - 90 * q^94 + 92 * q^96

Introduction

L-functions

Modular forms

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