LMFDB - Embedded newform 605.2.j.j.124.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(9,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([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("605.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.j (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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.343361479062744140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 3 x^{14} - 8 x^{13} + 8 x^{12} + 7 x^{11} + 6 x^{10} + 56 x^{9} - 137 x^{8} + \cdots + 6561 $ x^16 - x^15 + 3x^14 - 8x^13 + 8x^12 + 7x^11 + 6x^10 + 56x^9 - 137x^8 + 168x^7 + 54x^6 + 189x^5 + 648x^4 - 1944x^3 + 2187x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			124.1
Root			$-0.217724 - 1.71831i$ of defining polynomial
Character	$\chi$	$=$	605.124
Dual form			605.2.j.j.444.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.48377 - 2.04223i) q^{2} +(-0.753510 + 0.244830i) q^{3} +(-1.35111 + 4.15829i) q^{4} +(-1.80602 + 1.31844i) q^{5} +(1.61803 + 1.17557i) q^{6} +(-3.29456 - 1.07047i) q^{7} +(5.69534 - 1.85053i) q^{8} +(-1.91922 + 1.39439i) q^{9} +(5.37228 + 1.73205i) q^{10} -3.46410i q^{12} +(2.70222 + 8.31657i) q^{14} +(1.03806 - 1.43563i) q^{15} +(-5.15528 - 3.74553i) q^{16} +(-0.931389 + 1.28195i) q^{17} +(5.69534 + 1.85053i) q^{18} +(1.23607 + 3.80423i) q^{19} +(-3.04233 - 9.29131i) q^{20} +2.74456 q^{21} -0.792287i q^{23} +(-3.83843 + 2.78878i) q^{24} +(1.52342 - 4.76227i) q^{25} +(2.50184 - 3.44349i) q^{27} +(8.90261 - 12.2534i) q^{28} +(2.70222 - 8.31657i) q^{29} +(-4.47212 + 0.0101793i) q^{30} +(-2.72823 + 1.98218i) q^{31} +4.10891i q^{32} +4.00000 q^{34} +(7.36138 - 2.41040i) q^{35} +(-3.20521 - 9.86463i) q^{36} +(-1.03403 - 0.335976i) q^{37} +(5.93507 - 8.16893i) q^{38} +(-7.84609 + 10.8511i) q^{40} +(-2.70222 - 8.31657i) q^{41} +(-4.07230 - 5.60503i) q^{42} +3.46410i q^{43} +(1.62772 - 5.04868i) q^{45} +(-1.61803 + 1.17557i) q^{46} +(6.30860 - 2.04979i) q^{47} +(4.80158 + 1.56013i) q^{48} +(4.04508 + 2.93893i) q^{49} +(-11.9861 + 3.95492i) q^{50} +(0.387951 - 1.19399i) q^{51} +(5.93507 + 8.16893i) q^{53} -10.7446 q^{54} -20.7446 q^{56} +(-1.86278 - 2.56389i) q^{57} +(-20.9938 + 6.82131i) q^{58} +(2.27816 - 7.01146i) q^{59} +(4.56722 + 6.25624i) q^{60} +(-0.602364 - 0.437643i) q^{61} +(8.09613 + 2.63059i) q^{62} +(7.81561 - 2.53945i) q^{63} +(-1.91922 + 1.39439i) q^{64} +9.30506i q^{67} +(-4.07230 - 5.60503i) q^{68} +(0.193976 + 0.596996i) q^{69} +(-15.8452 - 11.4572i) q^{70} +(8.18470 + 5.94653i) q^{71} +(-8.35023 + 11.4931i) q^{72} +(-6.58911 - 2.14093i) q^{73} +(0.848116 + 2.61023i) q^{74} +(0.0180337 + 3.96139i) q^{75} -17.4891 q^{76} +(-1.01567 + 0.737928i) q^{79} +(14.2488 - 0.0324327i) q^{80} +(1.15713 - 3.56129i) q^{81} +(-12.9749 + 17.8584i) q^{82} +(3.89893 - 5.36641i) q^{83} +(-3.70820 + 11.4127i) q^{84} +(-0.00806494 - 3.54321i) q^{85} +(7.07450 - 5.13992i) q^{86} +6.92820i q^{87} -1.37228 q^{89} +(-12.7257 + 4.16689i) q^{90} +(3.29456 + 1.07047i) q^{92} +(1.57045 - 2.16154i) q^{93} +(-13.5466 - 9.84221i) q^{94} +(-7.24802 - 5.24083i) q^{95} +(-1.00599 - 3.09610i) q^{96} +(-3.43323 - 4.72544i) q^{97} -12.6217i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{4} + 3 q^{5} + 8 q^{6} + 2 q^{9} + 40 q^{10} - 12 q^{14} - q^{15} - 14 q^{16} - 16 q^{19} + 12 q^{20} - 48 q^{21} + 4 q^{24} - q^{25} - 12 q^{29} - 6 q^{30} - 2 q^{31} + 64 q^{34} + 18 q^{35}+ \cdots + 36 q^{96}+O(q^{100}) $ 16 * q + 6 * q^4 + 3 * q^5 + 8 * q^6 + 2 * q^9 + 40 * q^10 - 12 * q^14 - q^15 - 14 * q^16 - 16 * q^19 + 12 * q^20 - 48 * q^21 + 4 * q^24 - q^25 - 12 * q^29 - 6 * q^30 - 2 * q^31 + 64 * q^34 + 18 * q^35 + 30 * q^36 + 28 * q^40 + 12 * q^41 + 72 * q^45 - 8 * q^46 + 20 * q^49 - 18 * q^50 - 28 * q^51 - 80 * q^54 - 240 * q^56 - 18 * q^59 + 18 * q^60 + 20 * q^61 + 2 * q^64 - 14 * q^69 - 24 * q^70 + 6 * q^71 + 12 * q^74 - 15 * q^75 - 96 * q^76 - 28 * q^79 - 6 * q^80 + 8 * q^81 + 48 * q^84 + 2 * q^85 + 12 * q^86 + 24 * q^89 - 28 * q^90 - 44 * q^94 + 12 * q^95 + 36 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−1.48377	−	2.04223i	−1.04918	−	1.44408i	−0.889515	−	0.456905i	$-0.848958\pi$
$2$	−1.48377	−	2.04223i	−1.04918	−	1.44408i	−0.159667	−	0.987171i	$-0.551042\pi$
$3$	−0.753510	+	0.244830i	−0.435039	+	0.141353i	−0.518346	−	0.855171i	$-0.673452\pi$
$3$	−0.753510	+	0.244830i	−0.435039	+	0.141353i	0.0833066	+	0.996524i	$0.473452\pi$
$4$	−1.35111	+	4.15829i	−0.675555	+	2.07914i
$5$	−1.80602	+	1.31844i	−0.807677	+	0.589625i
$5$	−1.80602	+	1.31844i	−0.807677	+	0.589625i
$6$	1.61803	+	1.17557i	0.660560	+	0.479925i
$7$	−3.29456	−	1.07047i	−1.24523	−	0.404598i	−0.389018	−	0.921230i	$-0.627186\pi$
$7$	−3.29456	−	1.07047i	−1.24523	−	0.404598i	−0.856208	+	0.516632i	$0.827186\pi$
$8$	5.69534	−	1.85053i	2.01361	−	0.654261i
$9$	−1.91922	+	1.39439i	−0.639739	+	0.464797i
$10$	5.37228	+	1.73205i	1.69886	+	0.547723i
$11$		0			0
$11$		0			0
$12$		−	3.46410i		−	1.00000i
$13$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$13$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$14$	2.70222	+	8.31657i	0.722198	+	2.22270i
$15$	1.03806	−	1.43563i	0.268026	−	0.370677i
$16$	−5.15528	−	3.74553i	−1.28882	−	0.936383i
$17$	−0.931389	+	1.28195i	−0.225895	+	0.310918i	−0.906888	−	0.421372i	$-0.861549\pi$
$17$	−0.931389	+	1.28195i	−0.225895	+	0.310918i	0.680993	+	0.732290i	$0.261549\pi$
$18$	5.69534	+	1.85053i	1.34241	+	0.436174i
$19$	1.23607	+	3.80423i	0.283573	+	0.872749i	0.986823	+	0.161806i	$0.0517318\pi$
$19$	1.23607	+	3.80423i	0.283573	+	0.872749i	−0.703249	+	0.710943i	$0.748268\pi$
$20$	−3.04233	−	9.29131i	−0.680285	−	2.07760i
$21$	2.74456			0.598913
$22$		0			0
$23$		−	0.792287i		−	0.165203i	−0.996583	−	0.0826016i	$-0.973677\pi$
$23$		−	0.792287i		−	0.165203i	0.996583	−	0.0826016i	$-0.0263229\pi$
$24$	−3.83843	+	2.78878i	−0.783517	+	0.569258i
$25$	1.52342	−	4.76227i	0.304684	−	0.952453i
$26$		0			0
$27$	2.50184	−	3.44349i	0.481480	−	0.662700i
$28$	8.90261	−	12.2534i	1.68244	−	2.31567i
$29$	2.70222	−	8.31657i	0.501789	−	1.54435i	−0.304313	−	0.952572i	$-0.598427\pi$
$29$	2.70222	−	8.31657i	0.501789	−	1.54435i	0.806102	−	0.591777i	$-0.201573\pi$
$30$	−4.47212	+	0.0101793i	−0.816494	+	0.00185848i
$31$	−2.72823	+	1.98218i	−0.490005	+	0.356010i	−0.805186	−	0.593022i	$-0.797935\pi$
$31$	−2.72823	+	1.98218i	−0.490005	+	0.356010i	0.315181	+	0.949032i	$0.397935\pi$
$32$			4.10891i			0.726360i
$33$		0			0
$34$	4.00000			0.685994
$35$	7.36138	−	2.41040i	1.24430	−	0.407432i
$36$	−3.20521	−	9.86463i	−0.534202	−	1.64410i
$37$	−1.03403	−	0.335976i	−0.169993	−	0.0552341i	0.222784	−	0.974868i	$-0.428486\pi$
$37$	−1.03403	−	0.335976i	−0.169993	−	0.0552341i	−0.392777	+	0.919634i	$0.628486\pi$
$38$	5.93507	−	8.16893i	0.962796	−	1.32518i
$39$		0			0
$40$	−7.84609	+	10.8511i	−1.24058	+	1.71571i
$41$	−2.70222	−	8.31657i	−0.422016	−	1.29883i	−0.905823	−	0.423656i	$-0.860747\pi$
$41$	−2.70222	−	8.31657i	−0.422016	−	1.29883i	0.483807	−	0.875174i	$-0.339253\pi$
$42$	−4.07230	−	5.60503i	−0.628369	−	0.864876i
$43$			3.46410i			0.528271i	0.964486	+	0.264135i	$0.0850865\pi$
$43$			3.46410i			0.528271i	−0.964486	+	0.264135i	$0.914913\pi$
$44$		0			0
$45$	1.62772	−	5.04868i	0.242646	−	0.752612i
$46$	−1.61803	+	1.17557i	−0.238566	+	0.173328i
$47$	6.30860	−	2.04979i	0.920203	−	0.298992i	0.189653	−	0.981851i	$-0.439264\pi$
$47$	6.30860	−	2.04979i	0.920203	−	0.298992i	0.730550	+	0.682859i	$0.239264\pi$
$48$	4.80158	+	1.56013i	0.693048	+	0.225185i
$49$	4.04508	+	2.93893i	0.577869	+	0.419847i
$50$	−11.9861	+	3.95492i	−1.69508	+	0.559310i
$51$	0.387951	−	1.19399i	0.0543241	−	0.167192i
$52$		0			0
$53$	5.93507	+	8.16893i	0.815245	+	1.12209i	0.990493	+	0.137564i	$0.0439274\pi$
$53$	5.93507	+	8.16893i	0.815245	+	1.12209i	−0.175248	+	0.984524i	$0.556073\pi$
$54$	−10.7446			−1.46215
$55$		0			0
$56$	−20.7446			−2.77211
$57$	−1.86278	−	2.56389i	−0.246731	−	0.339596i
$58$	−20.9938	+	6.82131i	−2.75663	+	0.895682i
$59$	2.27816	−	7.01146i	0.296591	−	0.912814i	−0.686091	−	0.727516i	$-0.740675\pi$
$59$	2.27816	−	7.01146i	0.296591	−	0.912814i	0.982682	−	0.185298i	$-0.0593251\pi$
$60$	4.56722	+	6.25624i	0.589625	+	0.807677i
$61$	−0.602364	−	0.437643i	−0.0771248	−	0.0560344i	0.548555	−	0.836115i	$-0.315178\pi$
$61$	−0.602364	−	0.437643i	−0.0771248	−	0.0560344i	−0.625680	+	0.780080i	$0.715178\pi$
$62$	8.09613	+	2.63059i	1.02821	+	0.334086i
$63$	7.81561	−	2.53945i	0.984675	−	0.319940i
$64$	−1.91922	+	1.39439i	−0.239902	+	0.174299i
$65$		0			0
$66$		0			0
$67$			9.30506i			1.13679i	0.822754	+	0.568397i	$0.192436\pi$
$67$			9.30506i			1.13679i	−0.822754	+	0.568397i	$0.807564\pi$
$68$	−4.07230	−	5.60503i	−0.493838	−	0.679710i
$69$	0.193976	+	0.596996i	0.0233519	+	0.0718699i
$70$	−15.8452	−	11.4572i	−1.89386	−	1.36940i
$71$	8.18470	+	5.94653i	0.971345	+	0.705723i	0.955758	−	0.294155i	$-0.0950382\pi$
$71$	8.18470	+	5.94653i	0.971345	+	0.705723i	0.0155873	+	0.999879i	$0.495038\pi$
$72$	−8.35023	+	11.4931i	−0.984084	+	1.35448i
$73$	−6.58911	−	2.14093i	−0.771197	−	0.250577i	−0.103120	−	0.994669i	$-0.532883\pi$
$73$	−6.58911	−	2.14093i	−0.771197	−	0.250577i	−0.668077	+	0.744092i	$0.732883\pi$
$74$	0.848116	+	2.61023i	0.0985915	+	0.303434i
$75$	0.0180337	+	3.96139i	0.00208235	+	0.457422i
$76$	−17.4891			−2.00614
$77$		0			0
$78$		0			0
$79$	−1.01567	+	0.737928i	−0.114272	+	0.0830233i	−0.643453	−	0.765485i	$-0.722499\pi$
$79$	−1.01567	+	0.737928i	−0.114272	+	0.0830233i	0.529182	+	0.848509i	$0.322499\pi$
$80$	14.2488	−	0.0324327i	1.59307	−	0.00362609i
$81$	1.15713	−	3.56129i	0.128570	−	0.395699i
$82$	−12.9749	+	17.8584i	−1.43284	+	1.97213i
$83$	3.89893	−	5.36641i	0.427963	−	0.589040i	−0.539521	−	0.841972i	$-0.681395\pi$
$83$	3.89893	−	5.36641i	0.427963	−	0.589040i	0.967484	+	0.252932i	$0.0813948\pi$
$84$	−3.70820	+	11.4127i	−0.404598	+	1.24523i
$85$	−0.00806494	−	3.54321i	−0.000874766	−	0.384315i
$86$	7.07450	−	5.13992i	0.762863	−	0.554252i
$87$			6.92820i			0.742781i
$88$		0			0
$89$	−1.37228			−0.145462			−0.0727308	−	0.997352i	$-0.523171\pi$
$89$	−1.37228			−0.145462			−0.0727308	+	0.997352i	$0.523171\pi$
$90$	−12.7257	+	4.16689i	−1.34141	+	0.439228i
$91$		0			0
$92$	3.29456	+	1.07047i	0.343481	+	0.111604i
$93$	1.57045	−	2.16154i	0.162848	−	0.224142i
$94$	−13.5466	−	9.84221i	−1.39723	−	1.01515i
$95$	−7.24802	−	5.24083i	−0.743631	−	0.537698i
$96$	−1.00599	−	3.09610i	−0.102673	−	0.315995i
$97$	−3.43323	−	4.72544i	−0.348592	−	0.479796i	0.598334	−	0.801247i	$-0.295829\pi$
$97$	−3.43323	−	4.72544i	−0.348592	−	0.479796i	−0.946926	+	0.321451i	$0.895829\pi$
$98$		−	12.6217i		−	1.27498i
$99$		0			0
$100$	17.7446	+	12.7692i	1.77446	+	1.27692i
$101$	4.85410	−	3.52671i	0.483001	−	0.350921i	−0.319485	−	0.947591i	$-0.603510\pi$
$101$	4.85410	−	3.52671i	0.483001	−	0.350921i	0.802486	+	0.596670i	$0.203510\pi$
$102$	−3.01404	+	0.979321i	−0.298434	+	0.0969672i
$103$	9.88367	+	3.21140i	0.973867	+	0.316429i	0.752376	−	0.658734i	$-0.228908\pi$
$103$	9.88367	+	3.21140i	0.973867	+	0.316429i	0.221491	+	0.975162i	$0.428908\pi$
$104$		0			0
$105$	−4.95674	+	3.61855i	−0.483728	+	0.353134i
$106$	7.87657	−	24.2416i	0.765040	−	2.35455i
$107$	−6.30860	+	2.04979i	−0.609875	+	0.198160i	−0.597640	−	0.801765i	$-0.703895\pi$
$107$	−6.30860	+	2.04979i	−0.609875	+	0.198160i	−0.0122352	+	0.999925i	$0.503895\pi$
$108$	10.9388	+	15.0559i	1.05258	+	1.44876i
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$		0			0
$111$	0.861407			0.0817611
$112$	12.9749	+	17.8584i	1.22601	+	1.68746i
$113$	−0.472992	+	0.153684i	−0.0444954	+	0.0144574i	−0.331180	−	0.943568i	$-0.607447\pi$
$113$	−0.472992	+	0.153684i	−0.0444954	+	0.0144574i	0.286685	+	0.958025i	$0.407447\pi$
$114$	−2.47214	+	7.60845i	−0.231537	+	0.712597i
$115$	1.04458	+	1.43089i	0.0974080	+	0.133431i
$116$	30.9317	+	22.4732i	2.87194	+	2.08658i
$117$		0			0
$118$	−17.6993	+	5.75085i	−1.62935	+	0.529408i
$119$	4.44080	−	3.22643i	0.407087	−	0.295766i
$120$	3.25544	−	10.0974i	0.297179	−	0.921758i
$121$		0			0
$122$			1.87953i			0.170164i
$123$	4.07230	+	5.60503i	0.367187	+	0.505389i
$124$	−4.55632	−	14.0229i	−0.409170	−	1.25929i
$125$	3.52744	+	10.6093i	0.315504	+	0.948924i
$126$	−16.7827	−	12.1933i	−1.49512	−	1.08627i
$127$	4.83032	−	6.64836i	0.428621	−	0.589946i	−0.539015	−	0.842296i	$-0.681203\pi$
$127$	4.83032	−	6.64836i	0.428621	−	0.589946i	0.967636	+	0.252350i	$0.0812034\pi$
$128$	13.5110	+	4.38998i	1.19421	+	0.388023i
$129$	−0.848116	−	2.61023i	−0.0746725	−	0.229818i
$130$		0			0
$131$	2.74456			0.239794			0.119897	−	0.992786i	$-0.461744\pi$
$131$	2.74456			0.239794			0.119897	+	0.992786i	$0.461744\pi$
$132$		0			0
$133$		−	13.8564i		−	1.20150i
$134$	19.0031	−	13.8066i	1.64162	−	1.19271i
$135$	0.0216636	+	9.51755i	0.00186450	+	0.819140i
$136$	−2.93230	+	9.02469i	−0.251443	+	0.773861i
$137$	8.43692	−	11.6124i	0.720814	−	0.992116i	−0.278682	−	0.960383i	$-0.589898\pi$
$137$	8.43692	−	11.6124i	0.720814	−	0.992116i	0.999496	−	0.0317325i	$-0.0101025\pi$
$138$	0.931389	−	1.28195i	0.0792851	−	0.109127i
$139$	−5.01649	+	15.4392i	−0.425493	+	1.30953i	0.477029	+	0.878888i	$0.341714\pi$
$139$	−5.01649	+	15.4392i	−0.425493	+	1.30953i	−0.902522	+	0.430644i	$0.858286\pi$
$140$	0.0770881	+	33.8675i	0.00651514	+	2.86232i
$141$	−4.25174	+	3.08907i	−0.358061	+	0.260147i
$142$		−	25.5383i		−	2.14313i
$143$		0			0
$144$	15.1168			1.25974
$145$	6.08466	+	18.5826i	0.505303	+	1.54320i
$146$	5.40444	+	16.6331i	0.447274	+	1.37657i
$147$	−3.76755	−	1.22415i	−0.310742	−	0.100966i
$148$	2.79417	−	3.84584i	0.229679	−	0.316126i
$149$	9.29490	+	6.75314i	0.761468	+	0.553239i	0.899360	−	0.437209i	$-0.144033\pi$
$149$	9.29490	+	6.75314i	0.761468	+	0.553239i	−0.137892	+	0.990447i	$0.544033\pi$
$150$	8.06333	−	5.91462i	0.658368	−	0.482927i
$151$	3.78042	+	11.6349i	0.307646	+	0.946837i	0.978677	+	0.205407i	$0.0658519\pi$
$151$	3.78042	+	11.6349i	0.307646	+	0.946837i	−0.671031	+	0.741430i	$0.734148\pi$
$152$	14.0797	+	19.3790i	1.14201	+	1.57184i
$153$		−	3.75906i		−	0.303902i
$154$		0			0
$155$	2.31386	−	7.17687i	0.185854	−	0.576460i
$156$		0			0
$157$	23.2544	−	7.55580i	1.85590	−	0.603019i	0.860248	−	0.509876i	$-0.170309\pi$
$157$	23.2544	−	7.55580i	1.85590	−	0.603019i	0.995653	−	0.0931428i	$-0.0296913\pi$
$158$	3.01404	+	0.979321i	0.239784	+	0.0779106i
$159$	−6.47214	−	4.70228i	−0.513274	−	0.372915i
$160$	−5.41736	−	7.42078i	−0.428280	−	0.586664i
$161$	−0.848116	+	2.61023i	−0.0668409	+	0.205715i
$162$	−8.98990	+	2.92100i	−0.706313	+	0.229495i
$163$	−2.03615	−	2.80252i	−0.159483	−	0.219510i	0.721796	−	0.692106i	$-0.243317\pi$
$163$	−2.03615	−	2.80252i	−0.159483	−	0.219510i	−0.881279	+	0.472596i	$0.843317\pi$
$164$	38.2337			2.98555
$165$		0			0
$166$	−16.7446			−1.29963
$167$	−9.24935	−	12.7306i	−0.715736	−	0.985126i	−0.999655	−	0.0262779i	$-0.991635\pi$
$167$	−9.24935	−	12.7306i	−0.715736	−	0.985126i	0.283918	−	0.958848i	$-0.408365\pi$
$168$	15.6312	−	5.07889i	1.20598	−	0.391845i
$169$	4.01722	−	12.3637i	0.309017	−	0.951057i
$170$	−7.22408	+	5.27377i	−0.554062	+	0.404480i
$171$	−7.67686	−	5.57757i	−0.587064	−	0.426527i
$172$	−14.4047	−	4.68038i	−1.09835	−	0.356876i
$173$	8.09613	−	2.63059i	0.615538	−	0.200000i	0.0153795	−	0.999882i	$-0.495104\pi$
$173$	8.09613	−	2.63059i	0.615538	−	0.200000i	0.600158	+	0.799881i	$0.295104\pi$
$174$	14.1490	−	10.2798i	1.07263	−	0.779313i
$175$	−10.1168	+	14.0588i	−0.764762	+	1.06274i
$176$		0			0
$177$			5.84096i			0.439034i
$178$	2.03615	+	2.80252i	0.152616	+	0.210058i
$179$	−3.97439	−	12.2319i	−0.297060	−	0.914257i	−0.982522	−	0.186148i	$-0.940400\pi$
$179$	−3.97439	−	12.2319i	−0.297060	−	0.914257i	0.685462	−	0.728109i	$-0.259600\pi$
$180$	18.7946	+	13.5898i	1.40087	+	1.01293i
$181$	−19.5109	−	14.1755i	−1.45024	−	1.05366i	−0.985776	−	0.168065i	$-0.946248\pi$
$181$	−19.5109	−	14.1755i	−1.45024	−	1.05366i	−0.464461	−	0.885594i	$-0.653752\pi$
$182$		0			0
$183$	0.561035	+	0.182291i	0.0414729	+	0.0134754i
$184$	−1.46615	−	4.51235i	−0.108086	−	0.332655i
$185$	2.31044	−	0.756526i	0.169867	−	0.0556209i
$186$	−6.74456			−0.494535
$187$		0			0
$188$			29.0024i			2.11522i
$189$	−11.9286	+	8.66664i	−0.867678	+	0.630405i
$190$	0.0513921	+	22.5783i	0.00372837	+	1.63800i
$191$	−5.98636	+	18.4241i	−0.433158	+	1.33312i	0.461804	+	0.886982i	$0.347202\pi$
$191$	−5.98636	+	18.4241i	−0.433158	+	1.33312i	−0.894962	+	0.446142i	$0.852798\pi$
$192$	1.10476	−	1.52057i	0.0797291	−	0.109738i
$193$	−9.66063	+	13.2967i	−0.695387	+	0.957119i	0.304602	+	0.952480i	$0.401477\pi$
$193$	−9.66063	+	13.2967i	−0.695387	+	0.957119i	−0.999989	+	0.00463891i	$0.998523\pi$
$194$	−4.55632	+	14.0229i	−0.327125	+	1.00679i
$195$		0			0
$196$	−17.6862	+	12.8498i	−1.26330	+	0.917844i
$197$		−	8.51278i		−	0.606510i	−0.952909	−	0.303255i	$-0.901927\pi$
$197$		−	8.51278i		−	0.606510i	0.952909	−	0.303255i	$-0.0980734\pi$
$198$		0			0
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	−0.136306	−	29.9419i	−0.00963832	−	2.11721i
$201$	−2.27816	−	7.01146i	−0.160689	−	0.494550i
$202$	−14.4047	−	4.68038i	−1.01351	−	0.329310i
$203$	−17.8052	+	24.5068i	−1.24968	+	1.72004i
$204$	4.44080	+	3.22643i	0.310918	+	0.225895i
$205$	15.8452	+	11.4572i	1.10668	+	0.800205i
$206$	−8.10666	−	24.9497i	−0.564817	−	1.73833i
$207$	1.10476	+	1.52057i	0.0767860	+	0.105687i
$208$		0			0
$209$		0			0
$210$	14.7446	+	4.75372i	1.01747	+	0.328038i
$211$	1.20473	−	0.875286i	0.0829369	−	0.0602572i	−0.545544	−	0.838082i	$-0.683677\pi$
$211$	1.20473	−	0.875286i	0.0829369	−	0.0602572i	0.628481	+	0.777825i	$0.283677\pi$
$212$	−41.9877	+	13.6426i	−2.88373	+	0.936979i
$213$	−7.62314	−	2.47691i	−0.522329	−	0.169715i
$214$	13.5466	+	9.84221i	0.926029	+	0.672799i
$215$	−4.56722	−	6.25624i	−0.311482	−	0.426672i
$216$	7.87657	−	24.2416i	0.535933	−	1.64943i
$217$	11.1102	−	3.60991i	0.754208	−	0.245057i
$218$	−14.8377	−	20.4223i	−1.00493	−	1.38317i
$219$	5.48913			0.370921
$220$		0			0
$221$		0			0
$222$	−1.27813	−	1.75919i	−0.0857823	−	0.118069i
$223$	−2.26053	+	0.734490i	−0.151376	+	0.0491851i	−0.383725	−	0.923447i	$-0.625359\pi$
$223$	−2.26053	+	0.734490i	−0.151376	+	0.0491851i	0.232349	+	0.972633i	$0.425359\pi$
$224$	4.39845	−	13.5370i	0.293884	−	0.904482i
$225$	3.71669	+	11.2641i	0.247779	+	0.750938i
$226$	1.01567	+	0.737928i	0.0675614	+	0.0490862i
$227$	−15.9117	−	5.17004i	−1.05610	−	0.343148i	−0.271040	−	0.962568i	$-0.587368\pi$
$227$	−15.9117	−	5.17004i	−1.05610	−	0.343148i	−0.785059	+	0.619420i	$0.787368\pi$
$228$	13.1782	−	4.28187i	0.872749	−	0.283573i
$229$	11.8341	−	8.59796i	0.782018	−	0.568169i	−0.123566	−	0.992336i	$-0.539433\pi$
$229$	11.8341	−	8.59796i	0.782018	−	0.568169i	0.905584	+	0.424167i	$0.139433\pi$
$230$	1.37228	−	4.25639i	0.0904856	−	0.280658i
$231$		0			0
$232$		−	52.3663i		−	3.43801i
$233$	2.20952	+	3.04114i	0.144750	+	0.199232i	0.875236	−	0.483697i	$-0.160706\pi$
$233$	2.20952	+	3.04114i	0.144750	+	0.199232i	−0.730485	+	0.682928i	$0.760706\pi$
$234$		0			0
$235$	−8.69093	+	12.0195i	−0.566934	+	0.784064i
$236$	26.0776	+	18.9465i	1.69751	+	1.23331i
$237$	0.584650	−	0.804702i	0.0379771	−	0.0522710i
$238$	−13.1782	−	4.28187i	−0.854217	−	0.277552i
$239$	−4.55632	−	14.0229i	−0.294724	−	0.907067i	−0.983314	−	0.181916i	$-0.941770\pi$
$239$	−4.55632	−	14.0229i	−0.294724	−	0.907067i	0.688590	−	0.725151i	$-0.258230\pi$
$240$	−10.7287	+	3.51298i	−0.692533	+	0.226762i
$241$	−16.7446			−1.07861			−0.539306	−	0.842110i	$-0.681313\pi$
$241$	−16.7446			−1.07861			−0.539306	+	0.842110i	$0.681313\pi$
$242$		0			0
$243$			15.7359i			1.00946i
$244$	2.63370	−	1.91350i	0.168606	−	0.122499i
$245$	−11.1803	+	0.0254483i	−0.714284	+	0.00162583i
$246$	5.40444	−	16.6331i	0.344574	−	1.06049i
$247$		0			0
$248$	−11.8701	+	16.3379i	−0.753755	+	1.03745i
$249$	−1.62402	+	4.99822i	−0.102918	+	0.316749i
$250$	16.4327	−	22.9456i	1.03930	−	1.45121i
$251$	17.8929	−	13.0000i	1.12939	−	0.820550i	0.143784	−	0.989609i	$-0.454073\pi$
$251$	17.8929	−	13.0000i	1.12939	−	0.820550i	0.985606	+	0.169059i	$0.0540729\pi$
$252$			35.9306i			2.26342i
$253$		0			0
$254$	−20.7446			−1.30163
$255$	0.873561	+	2.66787i	0.0547045	+	0.167068i
$256$	−9.61563	−	29.5939i	−0.600977	−	1.84962i
$257$	10.1642	+	3.30254i	0.634025	+	0.206007i	0.608357	−	0.793663i	$-0.291829\pi$
$257$	10.1642	+	3.30254i	0.634025	+	0.206007i	0.0256675	+	0.999671i	$0.491829\pi$
$258$	−4.07230	+	5.60503i	−0.253530	+	0.348954i
$259$	3.04701	+	2.21378i	0.189332	+	0.137558i
$260$		0			0
$261$	6.41042	+	19.7293i	0.396795	+	1.22121i
$262$	−4.07230	−	5.60503i	−0.251587	−	0.346280i
$263$			27.4179i			1.69066i	0.534246	+	0.845329i	$0.320595\pi$
$263$			27.4179i			1.69066i	−0.534246	+	0.845329i	$0.679405\pi$
$264$		0			0
$265$	−21.4891	−	6.92820i	−1.32007	−	0.425596i
$266$	−28.2980	+	20.5597i	−1.73506	+	1.26060i
$267$	1.03403	−	0.335976i	0.0632814	−	0.0205614i
$268$	−38.6931	−	12.5722i	−2.36356	−	0.767967i
$269$	−9.29490	−	6.75314i	−0.566720	−	0.411746i	0.267192	−	0.963643i	$-0.413904\pi$
$269$	−9.29490	−	6.75314i	−0.566720	−	0.411746i	−0.833912	+	0.551897i	$0.813904\pi$
$270$	19.4049	−	14.1661i	1.18094	−	0.862120i
$271$	−4.16837	+	12.8289i	−0.253210	+	0.779301i	0.740967	+	0.671542i	$0.234368\pi$
$271$	−4.16837	+	12.8289i	−0.253210	+	0.779301i	−0.994177	+	0.107760i	$0.965632\pi$
$272$	9.60315	−	3.12025i	0.582277	−	0.189193i
$273$		0			0
$274$	−36.2337			−2.18896
$275$		0			0
$276$	−2.74456			−0.165203
$277$	−6.86646	−	9.45088i	−0.412566	−	0.567848i	0.551276	−	0.834323i	$-0.314141\pi$
$277$	−6.86646	−	9.45088i	−0.412566	−	0.567848i	−0.963842	+	0.266475i	$0.914141\pi$
$278$	38.9736	−	12.6633i	2.33748	−	0.759494i
$279$	2.47214	−	7.60845i	0.148003	−	0.455506i
$280$	37.4651	−	27.3505i	2.23897	−	1.63451i
$281$	−0.413306	−	0.300285i	−0.0246558	−	0.0179135i	0.575389	−	0.817880i	$-0.304851\pi$
$281$	−0.413306	−	0.300285i	−0.0246558	−	0.0179135i	−0.600045	+	0.799966i	$0.704851\pi$
$282$	12.6172	+	4.09957i	0.751343	+	0.244126i
$283$	−14.4047	+	4.68038i	−0.856272	+	0.278220i	−0.704071	−	0.710130i	$-0.748636\pi$
$283$	−14.4047	+	4.68038i	−0.856272	+	0.278220i	−0.152201	+	0.988350i	$0.548636\pi$
$284$	−35.7858	+	25.9999i	−2.12350	+	1.54281i
$285$	6.74456	+	2.17448i	0.399513	+	0.128805i
$286$		0			0
$287$			30.2921i			1.78808i
$288$	−5.72943	−	7.88589i	−0.337610	−	0.464680i
$289$	4.47739	+	13.7800i	0.263376	+	0.810587i
$290$	28.9218	−	39.9986i	1.69835	−	2.34880i
$291$	3.74390	+	2.72010i	0.219471	+	0.159455i
$292$	17.8052	−	24.5068i	1.04197	−	1.43415i
$293$	3.01404	+	0.979321i	0.176082	+	0.0572125i	0.395731	−	0.918366i	$-0.370491\pi$
$293$	3.01404	+	0.979321i	0.176082	+	0.0572125i	−0.219649	+	0.975579i	$0.570491\pi$
$294$	3.09017	+	9.51057i	0.180222	+	0.554667i
$295$	5.12979	+	15.6665i	0.298668	+	0.912136i
$296$	−6.51087			−0.378437
$297$		0			0
$298$		−	29.0024i		−	1.68007i
$299$		0			0
$300$	−16.4970	−	5.27729i	−0.952453	−	0.304684i
$301$	3.70820	−	11.4127i	0.213737	−	0.657816i
$302$	18.1520	−	24.9840i	1.04453	−	1.43767i
$303$	−2.79417	+	3.84584i	−0.160521	+	0.220938i
$304$	7.87657	−	24.2416i	0.451752	−	1.39035i
$305$	1.66489	−	0.00378957i	0.0953312	−	0.000216990i
$306$	−7.67686	+	5.57757i	−0.438857	+	0.318848i
$307$		−	31.5817i		−	1.80246i	−0.433340	−	0.901231i	$-0.642665\pi$
$307$		−	31.5817i		−	1.80246i	0.433340	−	0.901231i	$-0.357335\pi$
$308$		0			0
$309$	−8.23369			−0.468398
$310$	−18.0901	+	5.92338i	−1.02745	+	0.336425i
$311$	1.69623	+	5.22047i	0.0961845	+	0.296026i	0.987561	−	0.157239i	$-0.0502593\pi$
$311$	1.69623	+	5.22047i	0.0961845	+	0.296026i	−0.891376	+	0.453265i	$0.850259\pi$
$312$		0			0
$313$	12.8560	−	17.6947i	0.726661	−	1.00016i	−0.272615	−	0.962123i	$-0.587888\pi$
$313$	12.8560	−	17.6947i	0.726661	−	1.00016i	0.999276	−	0.0380403i	$-0.0121115\pi$
$314$	−49.9348	−	36.2798i	−2.81798	−	2.04739i
$315$	−10.7670	+	14.8907i	−0.606654	+	0.838998i
$316$	−1.69623	−	5.22047i	−0.0954206	−	0.293674i
$317$	−19.3757	−	26.6683i	−1.08825	−	1.49784i	−0.850106	−	0.526612i	$-0.823462\pi$
$317$	−19.3757	−	26.6683i	−1.08825	−	1.49784i	−0.238141	−	0.971231i	$-0.576538\pi$
$318$			20.1947i			1.13246i
$319$		0			0
$320$	1.62772	−	5.04868i	0.0909922	−	0.282230i
$321$	4.25174	−	3.08907i	0.237309	−	0.172415i
$322$	6.58911	−	2.14093i	0.367197	−	0.119310i
$323$	−6.02808	−	1.95864i	−0.335411	−	0.108982i
$324$	13.2455	+	9.62339i	0.735859	+	0.534633i
$325$		0			0
$326$	−2.70222	+	8.31657i	−0.149662	+	0.460612i
$327$	−7.53510	+	2.44830i	−0.416692	+	0.135391i
$328$	−30.7801	−	42.3652i	−1.69955	−	2.33923i
$329$	−22.9783			−1.26683
$330$		0			0
$331$	−14.1168			−0.775932			−0.387966	−	0.921674i	$-0.626822\pi$
$331$	−14.1168			−0.775932			−0.387966	+	0.921674i	$0.626822\pi$
$332$	17.0472	+	23.4635i	0.935587	+	1.28772i
$333$	2.45300	−	0.797029i	0.134424	−	0.0436769i
$334$	−12.2750	+	37.7786i	−0.671659	+	2.06716i
$335$	−12.2682	−	16.8051i	−0.670283	−	0.918163i
$336$	−14.1490	−	10.2798i	−0.771891	−	0.560812i
$337$	30.8775	+	10.0327i	1.68201	+	0.546517i	0.985299	−	0.170840i	$-0.0546481\pi$
$337$	30.8775	+	10.0327i	1.68201	+	0.546517i	0.696706	+	0.717356i	$0.254648\pi$
$338$	−31.2102	+	10.1408i	−1.69761	+	0.551588i
$339$	0.318778	−	0.231605i	0.0173136	−	0.0125791i
$340$	14.7446	+	4.75372i	0.799636	+	0.257807i
$341$		0			0
$342$			23.9538i			1.29527i
$343$	4.07230	+	5.60503i	0.219883	+	0.302643i
$344$	6.41042	+	19.7293i	0.345627	+	1.06373i
$345$	−1.13743	−	0.822441i	−0.0612371	−	0.0442787i
$346$	−17.3851	−	12.6310i	−0.934627	−	0.679046i
$347$	13.3216	−	18.3357i	0.715143	−	0.984310i	−0.284528	−	0.958668i	$-0.591837\pi$
$347$	13.3216	−	18.3357i	0.715143	−	0.984310i	0.999671	−	0.0256427i	$-0.00816321\pi$
$348$	−28.8095	−	9.36076i	−1.54435	−	0.501789i
$349$	4.78640	+	14.7310i	0.256210	+	0.788534i	0.993589	+	0.113054i	$0.0360634\pi$
$349$	4.78640	+	14.7310i	0.256210	+	0.788534i	−0.737379	+	0.675480i	$0.763937\pi$
$350$	43.7224	−	0.199040i	2.33706	−	0.0106391i
$351$		0			0
$352$		0			0
$353$		−	25.0410i		−	1.33280i	−0.745595	−	0.666399i	$-0.767835\pi$
$353$		−	25.0410i		−	1.33280i	0.745595	−	0.666399i	$-0.232165\pi$
$354$	11.9286	−	8.66664i	0.633998	−	0.460627i
$355$	−22.6219	+	0.0514913i	−1.20065	+	0.00273287i
$356$	1.85410	−	5.70634i	0.0982672	−	0.302435i
$357$	−2.55626	+	3.51838i	−0.135291	+	0.186213i
$358$	−19.0834	+	26.2660i	−1.00859	+	1.38820i
$359$	9.11264	−	28.0458i	0.480947	−	1.48020i	−0.356820	−	0.934173i	$-0.616139\pi$
$359$	9.11264	−	28.0458i	0.480947	−	1.48020i	0.837766	−	0.546029i	$-0.183861\pi$
$360$	−0.0723050	−	31.7661i	−0.00381081	−	1.67422i
$361$	2.42705	−	1.76336i	0.127740	−	0.0928082i
$362$			60.8791i			3.19973i
$363$		0			0
$364$		0			0
$365$	14.7228	−	4.82079i	0.770625	−	0.252332i
$366$	−0.460165	−	1.41624i	−0.0240532	−	0.0740282i
$367$	24.4809	+	7.95432i	1.27789	+	0.415212i	0.867837	−	0.496849i	$-0.165510\pi$
$367$	24.4809	+	7.95432i	1.27789	+	0.415212i	0.410054	+	0.912061i	$0.365510\pi$
$368$	−2.96754	+	4.08446i	−0.154694	+	0.212917i
$369$	16.7827	+	12.1933i	0.873673	+	0.634760i
$370$	−4.97316	−	3.59594i	−0.258542	−	0.186944i
$371$	−10.8089	−	33.2663i	−0.561169	−	1.72710i
$372$	6.86646	+	9.45088i	0.356010	+	0.490005i
$373$		−	11.6819i		−	0.604867i	−0.953170	−	0.302434i	$-0.902201\pi$
$373$		−	11.6819i		−	0.604867i	0.953170	−	0.302434i	$-0.0977990\pi$
$374$		0			0
$375$	−5.25544	−	7.13058i	−0.271390	−	0.368222i
$376$	32.1364	−	23.3485i	1.65731	−	1.20411i
$377$		0			0
$378$	35.3986	+	11.5017i	1.82071	+	0.591583i
$379$	−0.507835	−	0.368964i	−0.0260857	−	0.0189524i	0.574666	−	0.818388i	$-0.305132\pi$
$379$	−0.507835	−	0.368964i	−0.0260857	−	0.0189524i	−0.600752	+	0.799436i	$0.705132\pi$
$380$	31.5857	−	23.0584i	1.62031	−	1.18287i
$381$	−2.01197	+	6.19221i	−0.103076	+	0.317237i
$382$	46.5087	−	15.1116i	2.37959	−	0.773177i
$383$	−6.40077	−	8.80990i	−0.327064	−	0.450165i	0.613544	−	0.789661i	$-0.289744\pi$
$383$	−6.40077	−	8.80990i	−0.327064	−	0.450165i	−0.940608	+	0.339496i	$0.889744\pi$
$384$	−11.2554			−0.574377
$385$		0			0
$386$	41.4891			2.11174
$387$	−4.83032	−	6.64836i	−0.245539	−	0.337955i
$388$	24.2884	−	7.89178i	1.23306	−	0.400644i
$389$	−5.82850	+	17.9383i	−0.295516	+	0.909506i	0.687531	+	0.726155i	$0.258695\pi$
$389$	−5.82850	+	17.9383i	−0.295516	+	0.909506i	−0.983047	+	0.183351i	$0.941305\pi$
$390$		0			0
$391$	1.01567	+	0.737928i	0.0513646	+	0.0373186i
$392$	28.4767	+	9.25265i	1.43829	+	0.467329i
$393$	−2.06805	+	0.671952i	−0.104320	+	0.0338955i
$394$	−17.3851	+	12.6310i	−0.875847	+	0.636340i
$395$	0.861407	−	2.67181i	0.0433421	−	0.134434i
$396$		0			0
$397$		−	16.4356i		−	0.824881i	−0.910984	−	0.412441i	$-0.864676\pi$
$397$		−	16.4356i		−	0.824881i	0.910984	−	0.412441i	$-0.135324\pi$
$398$	−11.8701	−	16.3379i	−0.594997	−	0.818943i
$399$	3.39247	+	10.4409i	0.169836	+	0.522701i
$400$	−25.6909	+	18.8448i	−1.28454	+	0.942241i
$401$	9.29490	+	6.75314i	0.464165	+	0.337236i	0.795163	−	0.606396i	$-0.207385\pi$
$401$	9.29490	+	6.75314i	0.464165	+	0.337236i	−0.330998	+	0.943631i	$0.607385\pi$
$402$	−10.9388	+	15.0559i	−0.545576	+	0.750921i
$403$		0			0
$404$	8.10666	+	24.9497i	0.403321	+	1.24129i
$405$	2.60555	+	7.95738i	0.129471	+	0.395405i
$406$	76.4674			3.79501
$407$		0			0
$408$		−	7.51811i		−	0.372202i
$409$	−22.2392	+	16.1577i	−1.09966	+	0.798947i	−0.981004	−	0.193989i	$-0.937857\pi$
$409$	−22.2392	+	16.1577i	−1.09966	+	0.798947i	−0.118652	+	0.992936i	$0.537857\pi$
$410$	−0.112350	−	49.3594i	−0.00554859	−	2.43768i
$411$	−3.51423	+	10.8157i	−0.173344	+	0.533498i
$412$	−26.7078	+	36.7602i	−1.31580	+	1.81104i
$413$	−15.0111	+	20.6609i	−0.738646	+	1.01666i
$414$	1.46615	−	4.51235i	0.0720574	−	0.221770i
$415$	0.0337610	+	14.8324i	0.00165726	+	0.728092i
$416$		0			0
$417$		−	12.8617i		−	0.629842i
$418$		0			0
$419$	22.9783			1.12256			0.561280	−	0.827626i	$-0.310309\pi$
$419$	22.9783			1.12256			0.561280	+	0.827626i	$0.310309\pi$
$420$	−8.34986	−	25.5006i	−0.407432	−	1.24430i
$421$	2.63000	+	8.09432i	0.128179	+	0.394493i	0.994467	−	0.105051i	$-0.0335007\pi$
$421$	2.63000	+	8.09432i	0.128179	+	0.394493i	−0.866288	+	0.499545i	$0.833501\pi$
$422$	−3.57507	−	1.16161i	−0.174032	−	0.0565464i
$423$	−9.24935	+	12.7306i	−0.449719	+	0.618985i
$424$	48.9191	+	35.5418i	2.37572	+	1.72606i
$425$	4.68608	+	6.38847i	0.227308	+	0.309886i
$426$	6.25255	+	19.2434i	0.302937	+	0.932345i
$427$	1.51604	+	2.08665i	0.0733663	+	0.100980i
$428$		−	29.0024i		−	1.40189i
$429$		0			0
$430$	−6.00000	+	18.6101i	−0.289346	+	0.897460i
$431$	−20.8102	+	15.1195i	−1.00239	+	0.728280i	−0.962600	−	0.270928i	$-0.912670\pi$
$431$	−20.8102	+	15.1195i	−1.00239	+	0.728280i	−0.0397920	+	0.999208i	$0.512670\pi$
$432$	−25.7954	+	8.38144i	−1.24108	+	0.403252i
$433$	−27.7754	−	9.02478i	−1.33480	−	0.433703i	−0.447249	−	0.894409i	$-0.647596\pi$
$433$	−27.7754	−	9.02478i	−1.33480	−	0.433703i	−0.887553	+	0.460706i	$0.847596\pi$
$434$	−23.8572	−	17.3333i	−1.14518	−	0.832024i
$435$	−9.13443	−	12.5125i	−0.437963	−	0.599927i
$436$	−13.5111	+	41.5829i	−0.647064	+	1.99146i
$437$	3.01404	−	0.979321i	0.144181	−	0.0468473i
$438$	−8.14459	−	11.2101i	−0.389164	−	0.535638i
$439$	21.4891			1.02562			0.512810	−	0.858502i	$-0.328605\pi$
$439$	21.4891			1.02562			0.512810	+	0.858502i	$0.328605\pi$
$440$		0			0
$441$	−11.8614			−0.564829
$442$		0			0
$443$	−30.1240	+	9.78788i	−1.43123	+	0.465036i	−0.919153	−	0.393901i	$-0.871125\pi$
$443$	−30.1240	+	9.78788i	−1.43123	+	0.465036i	−0.512081	+	0.858937i	$0.671125\pi$
$444$	−1.16385	+	3.58198i	−0.0552341	+	0.169993i
$445$	2.47837	−	1.80927i	0.117486	−	0.0857678i
$446$	4.85410	+	3.52671i	0.229848	+	0.166995i
$447$	−8.65717	−	2.81288i	−0.409470	−	0.133045i
$448$	7.81561	−	2.53945i	0.369253	−	0.119978i
$449$	5.55099	−	4.03303i	0.261968	−	0.190331i	−0.449046	−	0.893508i	$-0.648236\pi$
$449$	5.55099	−	4.03303i	0.261968	−	0.190331i	0.711014	+	0.703178i	$0.248236\pi$
$450$	17.4891	−	24.3036i	0.824445	−	1.14568i
$451$		0			0
$452$		−	2.17448i		−	0.102279i
$453$	−5.69716	−	7.84147i	−0.267676	−	0.368424i
$454$	13.0509	+	40.1666i	0.612510	+	1.88511i
$455$		0			0
$456$	−15.3537	−	11.1551i	−0.719004	−	0.522387i
$457$	12.2169	−	16.8151i	0.571482	−	0.786577i	−0.421247	−	0.906946i	$-0.638408\pi$
$457$	12.2169	−	16.8151i	0.571482	−	0.786577i	0.992729	+	0.120368i	$0.0384076\pi$
$458$	−35.1181	−	11.4105i	−1.64096	−	0.533180i
$459$	2.08418	+	6.41446i	0.0972814	+	0.299401i
$460$	−7.36138	+	2.41040i	−0.343226	+	0.112385i
$461$	−2.23369			−0.104033			−0.0520166	−	0.998646i	$-0.516565\pi$
$461$	−2.23369			−0.104033			−0.0520166	+	0.998646i	$0.516565\pi$
$462$		0			0
$463$			30.0897i			1.39839i	0.714933	+	0.699193i	$0.246457\pi$
$463$			30.0897i			1.39839i	−0.714933	+	0.699193i	$0.753543\pi$
$464$	−45.0807	+	32.7530i	−2.09282	+	1.52052i
$465$	0.0135986	+	5.97434i	0.000630621	+	0.277054i
$466$	2.93230	−	9.02469i	0.135836	−	0.418061i
$467$	−4.53799	+	6.24601i	−0.209993	+	0.289031i	−0.901001	−	0.433816i	$-0.857167\pi$
$467$	−4.53799	+	6.24601i	−0.209993	+	0.289031i	0.691008	+	0.722847i	$0.257167\pi$
$468$		0			0
$469$	9.96076	−	30.6561i	0.459945	−	1.41557i
$470$	37.4419	−	0.0852241i	1.72707	−	0.00393110i
$471$	−15.6725	+	11.3867i	−0.722151	+	0.524673i
$472$		−	44.1485i		−	2.03210i
$473$		0			0
$474$	−2.51087			−0.115328
$475$	19.9998	−	0.0910464i	0.917653	−	0.00417749i
$476$	7.41641	+	22.8254i	0.339930	+	1.04620i
$477$	−22.7814	−	7.40212i	−1.04309	−	0.338920i
$478$	−21.8775	+	30.1118i	−1.00065	+	1.37728i
$479$	4.44080	+	3.22643i	0.202905	+	0.147419i	0.684598	−	0.728921i	$-0.259978\pi$
$479$	4.44080	+	3.22643i	0.202905	+	0.147419i	−0.481693	+	0.876340i	$0.659978\pi$
$480$	5.89887	+	4.26530i	0.269245	+	0.194683i
$481$		0			0
$482$	24.8451	+	34.1963i	1.13166	+	1.55760i
$483$		−	2.17448i		−	0.0989423i
$484$		0			0
$485$	12.4307	+	4.00772i	0.564449	+	0.181981i
$486$	32.1364	−	23.3485i	1.45774	−	1.05911i
$487$	6.78159	−	2.20347i	0.307303	−	0.0998488i	−0.151306	−	0.988487i	$-0.548348\pi$
$487$	6.78159	−	2.20347i	0.307303	−	0.0998488i	0.458609	+	0.888638i	$0.348348\pi$
$488$	−4.24054	−	1.37784i	−0.191960	−	0.0623717i
$489$	2.22040	+	1.61321i	0.100410	+	0.0729520i
$490$	16.6410	+	22.7950i	0.751762	+	1.02977i
$491$	−2.01197	+	6.19221i	−0.0907990	+	0.279451i	−0.986136	−	0.165939i	$-0.946935\pi$
$491$	−2.01197	+	6.19221i	−0.0907990	+	0.279451i	0.895337	+	0.445389i	$0.146935\pi$
$492$	−28.8095	+	9.36076i	−1.29883	+	0.422016i
$493$	8.14459	+	11.2101i	0.366814	+	0.504876i
$494$		0			0
$495$		0			0
$496$	21.4891			0.964890
$497$	−20.5994	−	28.3526i	−0.924009	−	1.27179i
$498$	12.6172	−	4.09957i	0.565390	−	0.183706i
$499$	6.18034	−	19.0211i	0.276670	−	0.851503i	−0.712103	−	0.702075i	$-0.752257\pi$
$499$	6.18034	−	19.0211i	0.276670	−	0.851503i	0.988773	−	0.149427i	$-0.0477430\pi$
$500$	−48.8825	+	0.333799i	−2.18609	+	0.0149279i
$501$	10.0863	+	7.32814i	0.450623	+	0.327397i
$502$	−53.0979	−	17.2525i	−2.36987	−	0.770018i
$503$	−12.8977	+	4.19072i	−0.575080	+	0.186855i	−0.582095	−	0.813120i	$-0.697767\pi$
$503$	−12.8977	+	4.19072i	−0.575080	+	0.186855i	0.00701509	+	0.999975i	$0.497767\pi$
$504$	39.8133	−	28.9261i	1.77343	−	1.28847i
$505$	−4.11684	+	12.7692i	−0.183197	+	0.568220i
$506$		0			0
$507$			10.2997i			0.457427i
$508$	21.1195	+	29.0685i	0.937026	+	1.28971i
$509$	−6.99235	−	21.5202i	−0.309930	−	0.953868i	−0.977791	−	0.209582i	$-0.932790\pi$
$509$	−6.99235	−	21.5202i	−0.309930	−	0.953868i	0.667861	−	0.744286i	$-0.267210\pi$
$510$	4.15224	−	5.74251i	0.183864	−	0.254283i
$511$	19.4164	+	14.1068i	0.858931	+	0.624050i
$512$	−29.4697	+	40.5616i	−1.30239	+	1.79259i
$513$	16.1923	+	5.26119i	0.714906	+	0.232287i
$514$	−8.33674	−	25.6578i	−0.367718	−	1.13172i
$515$	−22.0842	+	7.23119i	−0.973144	+	0.318644i
$516$	12.0000			0.528271
$517$		0			0
$518$		−	9.50744i		−	0.417733i
$519$	−5.45647	+	3.96435i	−0.239512	+	0.174016i
$520$		0			0
$521$	−6.67661	+	20.5485i	−0.292508	+	0.900246i	0.691540	+	0.722339i	$0.256933\pi$
$521$	−6.67661	+	20.5485i	−0.292508	+	0.900246i	−0.984047	+	0.177907i	$0.943067\pi$
$522$	30.7801	−	42.3652i	1.34721	−	1.85428i
$523$	17.0472	−	23.4635i	0.745422	−	1.02599i	−0.252866	−	0.967501i	$-0.581373\pi$
$523$	17.0472	−	23.4635i	0.745422	−	1.02599i	0.998288	−	0.0584843i	$-0.0186268\pi$
$524$	−3.70820	+	11.4127i	−0.161994	+	0.498565i
$525$	4.18113	−	13.0703i	0.182479	−	0.570436i
$526$	55.9936	−	40.6818i	2.44144	−	1.77381i
$527$		−	5.34363i		−	0.232772i
$528$		0			0
$529$	22.3723			0.972708
$530$	17.7359	+	54.1656i	0.770398	+	2.35280i
$531$	5.40444	+	16.6331i	0.234533	+	0.721817i
$532$	57.6189	+	18.7215i	2.49810	+	0.811681i
$533$		0			0
$534$	−2.22040	−	1.61321i	−0.0960860	−	0.0698106i
$535$	8.69093	−	12.0195i	0.375742	−	0.519647i
$536$	17.2193	+	52.9955i	0.743760	+	2.28906i
$537$	5.98949	+	8.24382i	0.258465	+	0.355747i
$538$			29.0024i			1.25038i
$539$		0			0
$540$	−39.6060	−	12.7692i	−1.70437	−	0.549497i
$541$	27.6956	−	20.1221i	1.19073	−	0.865115i	0.197387	−	0.980326i	$-0.436754\pi$
$541$	27.6956	−	20.1221i	1.19073	−	0.865115i	0.993341	+	0.115211i	$0.0367544\pi$
$542$	32.3845	−	10.5224i	1.39103	−	0.451975i
$543$	18.1723	+	5.90453i	0.779847	+	0.253388i
$544$	−5.26741	−	3.82700i	−0.225838	−	0.164081i
$545$	−18.0602	+	13.1844i	−0.773614	+	0.564759i
$546$		0			0
$547$	−27.5830	+	8.96224i	−1.17936	+	0.383198i	−0.832130	−	0.554581i	$-0.812878\pi$
$547$	−27.5830	+	8.96224i	−1.17936	+	0.383198i	−0.347232	+	0.937779i	$0.612878\pi$
$548$	36.8886	+	50.7728i	1.57580	+	2.16891i
$549$	1.76631			0.0753844
$550$		0			0
$551$	34.9783			1.49012
$552$	2.20952	+	3.04114i	0.0940433	+	0.129439i
$553$	4.13611	−	1.34390i	0.175885	−	0.0571486i
$554$	−9.11264	+	28.0458i	−0.387159	+	1.19155i
$555$	−1.55572	+	1.13571i	−0.0660366	+	0.0482084i
$556$	−57.4226	−	41.7200i	−2.43526	−	1.76932i
$557$	0.945984	+	0.307369i	0.0400826	+	0.0130236i	0.328990	−	0.944334i	$-0.393292\pi$
$557$	0.945984	+	0.307369i	0.0400826	+	0.0130236i	−0.288907	+	0.957357i	$0.593292\pi$
$558$	−19.2063	+	6.24051i	−0.813068	+	0.264182i
$559$		0			0
$560$	−46.9783	−	15.1460i	−1.98519	−	0.640036i
$561$		0			0
$562$			1.28962i			0.0543994i
$563$	11.1121	+	15.2945i	0.468320	+	0.644588i	0.976208	−	0.216836i	$-0.0695735\pi$
$563$	11.1121	+	15.2945i	0.468320	+	0.644588i	−0.507888	+	0.861423i	$0.669574\pi$
$564$	−7.10067	−	21.8536i	−0.298992	−	0.920203i
$565$	0.651610	−	0.901170i	0.0274134	−	0.0379125i
$566$	30.9317	+	22.4732i	1.30016	+	0.944619i
$567$	−7.62448	+	10.4942i	−0.320198	+	0.440715i
$568$	57.6189	+	18.7215i	2.41764	+	0.785537i
$569$	−8.42239	−	25.9215i	−0.353085	−	1.08668i	−0.957111	−	0.289720i	$-0.906438\pi$
$569$	−8.42239	−	25.9215i	−0.353085	−	1.08668i	0.604026	−	0.796964i	$-0.293562\pi$
$570$	−5.56657	−	17.0004i	−0.233158	−	0.712068i
$571$	−1.48913			−0.0623180			−0.0311590	−	0.999514i	$-0.509920\pi$
$571$	−1.48913			−0.0623180			−0.0311590	+	0.999514i	$0.509920\pi$
$572$		0			0
$573$		−	15.3484i		−	0.641189i
$574$	61.8634	−	44.9464i	2.58213	−	1.87603i
$575$	−3.77308	−	1.20699i	−0.157348	−	0.0503348i
$576$	1.73906	−	5.35228i	0.0724609	−	0.223012i
$577$	12.8560	−	17.6947i	0.535200	−	0.736640i	−0.452712	−	0.891657i	$-0.649543\pi$
$577$	12.8560	−	17.6947i	0.535200	−	0.736640i	0.987912	+	0.155017i	$0.0495433\pi$
$578$	21.4985	−	29.5902i	0.894220	−	1.23079i
$579$	4.02394	−	12.3844i	0.167229	−	0.514679i
$580$	−85.4929	+	0.194596i	−3.54990	+	0.00808018i
$581$	−18.5898	+	13.5063i	−0.771235	+	0.560335i
$582$		−	11.6819i		−	0.484231i
$583$		0			0
$584$	−41.4891			−1.71683
$585$		0			0
$586$	−2.47214	−	7.60845i	−0.102123	−	0.314302i
$587$	−39.2542	−	12.7544i	−1.62019	−	0.526432i	−0.648205	−	0.761466i	$-0.724480\pi$
$587$	−39.2542	−	12.7544i	−1.62019	−	0.526432i	−0.971987	+	0.235033i	$0.924480\pi$
$588$	10.1807	−	14.0126i	0.419847	−	0.577869i
$589$	−10.9129	−	7.92871i	−0.449660	−	0.326697i
$590$	24.3831	−	33.7216i	1.00384	−	1.38830i
$591$	2.08418	+	6.41446i	0.0857319	+	0.263856i
$592$	4.07230	+	5.60503i	0.167370	+	0.230365i
$593$		−	22.7739i		−	0.935214i	−0.883937	−	0.467607i	$-0.845116\pi$
$593$		−	22.7739i		−	0.935214i	0.883937	−	0.467607i	$-0.154884\pi$
$594$		0			0
$595$	−3.76631	+	11.6819i	−0.154404	+	0.478912i
$596$	−40.6399	+	29.5266i	−1.66468	+	1.20946i
$597$	−6.02808	+	1.95864i	−0.246713	+	0.0801618i
$598$		0			0
$599$	8.88159	+	6.45285i	0.362892	+	0.263656i	0.754257	−	0.656579i	$-0.227997\pi$
$599$	8.88159	+	6.45285i	0.362892	+	0.263656i	−0.391365	+	0.920235i	$0.627997\pi$
$600$	7.43338	+	22.5281i	0.303467	+	0.919707i
$601$	11.8871	−	36.5846i	0.484884	−	1.49232i	−0.347265	−	0.937767i	$-0.612890\pi$
$601$	11.8871	−	36.5846i	0.484884	−	1.49232i	0.832149	−	0.554552i	$-0.187110\pi$
$602$	−28.8095	+	9.36076i	−1.17419	+	0.381516i
$603$	−12.9749	−	17.8584i	−0.528379	−	0.727251i
$604$	−53.4891			−2.17644
$605$		0			0
$606$	12.0000			0.487467
$607$	2.03615	+	2.80252i	0.0826447	+	0.113751i	0.848338	−	0.529456i	$-0.177604\pi$
$607$	2.03615	+	2.80252i	0.0826447	+	0.113751i	−0.765693	+	0.643206i	$0.777604\pi$
$608$	−15.6312	+	5.07889i	−0.633930	+	0.205976i
$609$	7.41641	−	22.8254i	0.300528	−	0.924930i
$610$	−2.47805	−	3.39447i	−0.100333	−	0.137438i
$611$		0			0
$612$	15.6312	+	5.07889i	0.631855	+	0.205302i
$613$	4.13611	−	1.34390i	0.167056	−	0.0542797i	−0.224295	−	0.974521i	$-0.572008\pi$
$613$	4.13611	−	1.34390i	0.167056	−	0.0542797i	0.391351	+	0.920242i	$0.372008\pi$
$614$	−64.4971	+	46.8599i	−2.60289	+	1.89111i
$615$	−14.7446	−	4.75372i	−0.594558	−	0.191689i
$616$		0			0
$617$		−	17.0256i		−	0.685423i	−0.939441	−	0.342712i	$-0.888655\pi$
$617$		−	17.0256i		−	0.685423i	0.939441	−	0.342712i	$-0.111345\pi$
$618$	12.2169	+	16.8151i	0.491435	+	0.676403i
$619$	−4.36234	−	13.4259i	−0.175337	−	0.539633i	0.824311	−	0.566137i	$-0.191563\pi$
$619$	−4.36234	−	13.4259i	−0.175337	−	0.539633i	−0.999649	+	0.0265037i	$0.991563\pi$
$620$	26.7172	+	19.3184i	1.07299	+	0.775847i
$621$	−2.72823	−	1.98218i	−0.109480	−	0.0795420i
$622$	8.14459	−	11.2101i	0.326568	−	0.449483i
$623$	4.52106	+	1.46898i	0.181132	+	0.0588535i
$624$		0			0
$625$	−20.3584	−	14.5099i	−0.814335	−	0.580395i
$626$	−55.2119			−2.20671
$627$		0			0
$628$			106.907i			4.26606i
$629$	1.39379	−	1.01264i	0.0555739	−	0.0403768i
$630$	46.3861	−	0.105583i	1.84807	−	0.00420652i
$631$	7.29465	−	22.4506i	0.290395	−	0.893745i	−0.694334	−	0.719653i	$-0.744301\pi$
$631$	7.29465	−	22.4506i	0.290395	−	0.893745i	0.984729	−	0.174092i	$-0.0556990\pi$
$632$	−4.41903	+	6.08228i	−0.175780	+	0.241940i
$633$	−0.693478	+	0.954490i	−0.0275633	+	0.0379376i
$634$	−25.7139	+	79.1393i	−1.02123	+	3.14302i
$635$	0.0418259	+	18.3756i	0.00165981	+	0.729212i
$636$	28.2980	−	20.5597i	1.12209	−	0.815245i
$637$		0			0
$638$		0			0
$639$	−24.0000			−0.949425
$640$	−30.1890	+	9.88503i	−1.19333	+	0.390740i
$641$	−7.84047	−	24.1305i	−0.309680	−	0.953096i	−0.977889	−	0.209123i	$-0.932939\pi$
$641$	−7.84047	−	24.1305i	−0.309680	−	0.953096i	0.668210	−	0.743973i	$-0.267061\pi$
$642$	−12.6172	−	4.09957i	−0.497961	−	0.161797i
$643$	17.9242	−	24.6705i	0.706861	−	0.972910i	−0.292998	−	0.956113i	$-0.594653\pi$
$643$	17.9242	−	24.6705i	0.706861	−	0.972910i	0.999859	−	0.0167972i	$-0.00534696\pi$
$644$	−9.70820	−	7.05342i	−0.382557	−	0.277944i
$645$	4.97316	+	3.59594i	0.195818	+	0.141590i
$646$	4.94427	+	15.2169i	0.194530	+	0.598701i
$647$	12.9205	+	17.7835i	0.507957	+	0.699143i	0.983573	−	0.180510i	$-0.0577749\pi$
$647$	12.9205	+	17.7835i	0.507957	+	0.699143i	−0.475616	+	0.879653i	$0.657775\pi$
$648$		−	22.4241i		−	0.880901i
$649$		0			0
$650$		0			0
$651$	−7.48781	+	5.44021i	−0.293470	+	0.213219i
$652$	14.4047	−	4.68038i	0.564133	−	0.183298i
$653$	29.2824	+	9.51444i	1.14591	+	0.372329i	0.819601	−	0.572934i	$-0.194195\pi$
$653$	29.2824	+	9.51444i	1.14591	+	0.372329i	0.326309	+	0.945263i	$0.394195\pi$
$654$	16.1803	+	11.7557i	0.632701	+	0.459684i
$655$	−4.95674	+	3.61855i	−0.193676	+	0.141388i
$656$	−17.2193	+	52.9955i	−0.672301	+	2.06913i
$657$	15.6312	−	5.07889i	0.609832	−	0.198147i
$658$	34.0944	+	46.9269i	1.32914	+	1.82940i
$659$	21.2554			0.827994			0.413997	−	0.910278i	$-0.364132\pi$
$659$	21.2554			0.827994			0.413997	+	0.910278i	$0.364132\pi$
$660$		0			0
$661$	−16.3505			−0.635962			−0.317981	−	0.948097i	$-0.603005\pi$
$661$	−16.3505			−0.635962			−0.317981	+	0.948097i	$0.603005\pi$
$662$	20.9461	+	28.8299i	0.814094	+	1.12050i
$663$		0			0
$664$	12.2750	−	37.7786i	0.476363	−	1.46610i
$665$	18.2689	+	25.0250i	0.708436	+	0.970426i
$666$	−5.26741	−	3.82700i	−0.204108	−	0.148293i
$667$	−6.58911	−	2.14093i	−0.255131	−	0.0828972i
$668$	65.4345	−	21.2610i	2.53174	−	0.822611i
$669$	1.52351	−	1.10689i	0.0589021	−	0.0427949i
$670$	−16.1168	+	49.9894i	−0.622648	+	1.93126i
$671$		0			0
$672$			11.2772i			0.435026i
$673$	−10.9388	−	15.0559i	−0.421658	−	0.580363i	0.544355	−	0.838855i	$-0.316774\pi$
$673$	−10.9388	−	15.0559i	−0.421658	−	0.580363i	−0.966013	+	0.258492i	$0.916774\pi$
$674$	−25.3260	−	77.9453i	−0.975519	−	3.00234i
$675$	−12.5875	−	17.1603i	−0.484492	−	0.660501i
$676$	45.9842	+	33.4095i	1.76862	+	1.28498i
$677$	−29.4375	+	40.5172i	−1.13137	+	1.55720i	−0.345939	+	0.938257i	$0.612440\pi$
$677$	−29.4375	+	40.5172i	−1.13137	+	1.55720i	−0.785434	+	0.618945i	$0.787560\pi$
$678$	−0.945984	−	0.307369i	−0.0363303	−	0.0118044i
$679$	6.25255	+	19.2434i	0.239951	+	0.738493i
$680$	−6.60274	−	20.1649i	−0.253204	−	0.773287i
$681$	13.2554			0.507949
$682$		0			0
$683$		−	17.9104i		−	0.685323i	−0.939459	−	0.342661i	$-0.888672\pi$
$683$		−	17.9104i		−	0.685323i	0.939459	−	0.342661i	$-0.111328\pi$
$684$	33.5654	−	24.3867i	1.28341	−	0.932449i
$685$	0.0730557	+	32.0959i	0.00279131	+	1.22632i
$686$	5.40444	−	16.6331i	0.206342	−	0.635056i
$687$	−6.81205	+	9.37598i	−0.259896	+	0.357716i
$688$	12.9749	−	17.8584i	0.494664	−	0.680846i
$689$		0			0
$690$	0.00806494	+	3.54321i	0.000307027	+	0.134888i
$691$	−36.2936	+	26.3689i	−1.38068	+	1.00312i	−0.383858	+	0.923392i	$0.625405\pi$
$691$	−36.2936	+	26.3689i	−1.38068	+	1.00312i	−0.996817	+	0.0797273i	$0.974595\pi$
$692$			37.2203i			1.41490i
$693$		0			0
$694$	−57.2119			−2.17174
$695$	−11.2958	−	34.4974i	−0.428472	−	1.30856i
$696$	12.8208	+	39.4585i	0.485973	+	1.49567i
$697$	13.1782	+	4.28187i	0.499161	+	0.162187i
$698$	22.9823	−	31.6324i	0.869892	−	1.19730i
$699$	−2.40946	−	1.75057i	−0.0911340	−	0.0662127i
$700$	−44.7915	−	61.0637i	−1.69296	−	2.30799i
$701$	3.86607	+	11.8985i	0.146020	+	0.449402i	0.997141	−	0.0755673i	$-0.0240768\pi$
$701$	3.86607	+	11.8985i	0.146020	+	0.449402i	−0.851121	+	0.524969i	$0.824077\pi$
$702$		0			0
$703$		−	4.34896i		−	0.164024i
$704$		0			0
$705$	3.60597	−	11.1846i	0.135809	−	0.421236i
$706$	−51.1395	+	37.1550i	−1.92466	+	1.39835i
$707$	−19.7673	+	6.42280i	−0.743427	+	0.241554i
$708$	−24.2884	−	7.89178i	−0.912814	−	0.296591i
$709$	19.3219	+	14.0382i	0.725648	+	0.527214i	0.888184	−	0.459488i	$-0.151967\pi$
$709$	19.3219	+	14.0382i	0.725648	+	0.527214i	−0.162535	+	0.986703i	$0.551967\pi$
$710$	33.6708	+	46.1228i	1.26364	+	1.73096i
$711$	0.920330	−	2.83248i	0.0345151	−	0.106226i
$712$	−7.81561	+	2.53945i	−0.292903	+	0.0951698i
$713$	1.57045	+	2.16154i	0.0588139	+	0.0809504i
$714$	10.9783			0.410851
$715$		0			0
$716$	56.2337			2.10155
$717$	6.86646	+	9.45088i	0.256433	+	0.352949i
$718$	−70.7971	+	23.0034i	−2.64213	+	0.858479i
$719$	9.37883	−	28.8651i	0.349771	−	1.07649i	−0.609208	−	0.793010i	$-0.708513\pi$
$719$	9.37883	−	28.8651i	0.349771	−	1.07649i	0.958980	−	0.283475i	$-0.0914874\pi$
$720$	−27.3013	+	19.9307i	−1.01746	+	0.742773i
$721$	−29.1246	−	21.1603i	−1.08466	−	0.788050i
$722$	−7.20236	−	2.34019i	−0.268044	−	0.0870928i
$723$	12.6172	−	4.09957i	0.469238	−	0.152465i
$724$	85.3073	−	61.9794i	3.17042	−	2.30345i
$725$	−35.4891	−	25.5383i	−1.31803	−	0.948470i
$726$		0			0
$727$			14.0588i			0.521412i	0.965418	+	0.260706i	$0.0839552\pi$
$727$			14.0588i			0.521412i	−0.965418	+	0.260706i	$0.916045\pi$
$728$		0			0
$729$	−0.381231	−	1.17331i	−0.0141196	−	0.0434558i
$730$	−31.6904	−	22.9144i	−1.17291	−	0.848099i
$731$	−4.44080	−	3.22643i	−0.164249	−	0.119334i
$732$	−1.51604	+	2.08665i	−0.0560344	+	0.0771248i
$733$	−9.04212	−	2.93796i	−0.333978	−	0.108516i	0.137227	−	0.990540i	$-0.456181\pi$
$733$	−9.04212	−	2.93796i	−0.333978	−	0.108516i	−0.471205	+	0.882024i	$0.656181\pi$
$734$	−20.0794	−	61.7980i	−0.741144	−	2.28101i
$735$	8.41824	−	2.75645i	0.310512	−	0.101673i
$736$	3.25544			0.119997
$737$		0			0
$738$		−	52.3663i		−	1.92763i
$739$	8.69253	−	6.31550i	0.319760	−	0.232319i	−0.416313	−	0.909221i	$-0.636678\pi$
$739$	8.69253	−	6.31550i	0.319760	−	0.232319i	0.736073	+	0.676902i	$0.236678\pi$
$740$	0.0241948	+	10.6296i	0.000889420	+	0.390753i
$741$		0			0
$742$	−51.8996	+	71.4337i	−1.90530	+	2.62241i
$743$	6.69309	−	9.21225i	0.245546	−	0.337965i	−0.668399	−	0.743803i	$-0.733020\pi$
$743$	6.69309	−	9.21225i	0.245546	−	0.337965i	0.913945	+	0.405838i	$0.133020\pi$
$744$	4.94427	−	15.2169i	0.181266	−	0.557879i
$745$	−25.6904	+	0.0584757i	−0.941223	+	0.00214239i
$746$	−23.8572	+	17.3333i	−0.873474	+	0.634616i
$747$			15.7359i			0.575748i
$748$		0			0
$749$	22.9783			0.839607
$750$	−6.76445	+	21.3130i	−0.247003	+	0.778239i
$751$	8.45850	+	26.0326i	0.308655	+	0.949943i	0.978288	+	0.207250i	$0.0664515\pi$
$751$	8.45850	+	26.0326i	0.308655	+	0.949943i	−0.669633	+	0.742692i	$0.733549\pi$
$752$	−40.2001	−	13.0618i	−1.46595	−	0.476316i
$753$	−10.2997	+	14.1763i	−0.375342	+	0.516614i
$754$		0			0
$755$	−22.1675	−	16.0287i	−0.806758	−	0.583343i
$756$	−19.9215	−	61.3121i	−0.724538	−	2.22990i
$757$	−23.3936	−	32.1985i	−0.850253	−	1.17027i	−0.983807	−	0.179232i	$-0.942639\pi$
$757$	−23.3936	−	32.1985i	−0.850253	−	1.17027i	0.133554	−	0.991042i	$-0.457361\pi$
$758$			1.58457i			0.0575543i
$759$		0			0
$760$	−50.9783	−	16.4356i	−1.84918	−	0.596184i
$761$	26.4909	−	19.2468i	0.960295	−	0.697695i	0.00707549	−	0.999975i	$-0.497748\pi$
$761$	26.4909	−	19.2468i	0.960295	−	0.697695i	0.953219	+	0.302280i	$0.0977478\pi$
$762$	15.6312	−	5.07889i	0.566260	−	0.183989i
$763$	−32.9456	−	10.7047i	−1.19271	−	0.387535i
$764$	−68.5246	−	49.7860i	−2.47913	−	1.80120i
$765$	4.95610	+	6.78893i	0.179188	+	0.245454i
$766$	−8.49461	+	26.1437i	−0.306923	+	0.944611i
$767$		0			0
$768$	14.4909	+	19.9451i	0.522897	+	0.719706i
$769$	29.2119			1.05341			0.526705	−	0.850048i	$-0.323427\pi$
$769$	29.2119			1.05341			0.526705	+	0.850048i	$0.323427\pi$
$770$		0			0
$771$	−8.46738			−0.304945
$772$	−42.2390	−	58.1370i	−1.52021	−	2.09240i
$773$	−16.7533	+	5.44348i	−0.602574	+	0.195788i	−0.594388	−	0.804178i	$-0.702606\pi$
$773$	−16.7533	+	5.44348i	−0.602574	+	0.195788i	−0.00818608	+	0.999966i	$0.502606\pi$
$774$	−6.41042	+	19.7293i	−0.230418	+	0.709153i
$775$	5.28341	+	16.0123i	0.189786	+	0.575178i
$776$	−28.2980	−	20.5597i	−1.01584	−	0.738050i
$777$	−2.83795	−	0.922107i	−0.101811	−	0.0330804i
$778$	45.2822	−	14.7131i	1.62345	−	0.527490i
$779$	28.2980	−	20.5597i	1.01388	−	0.736628i
$780$		0			0
$781$		0			0
$782$		−	3.16915i		−	0.113328i
$783$	−21.8775	−	30.1118i	−0.781839	−	1.07611i
$784$	−9.84572	−	30.3020i	−0.351633	−	1.08221i
$785$	−32.0360	+	44.3055i	−1.14341	+	1.58133i
$786$	4.44080	+	3.22643i	0.158398	+	0.115083i
$787$	8.90261	−	12.2534i	0.317344	−	0.436786i	−0.620310	−	0.784357i	$-0.712993\pi$
$787$	8.90261	−	12.2534i	0.317344	−	0.436786i	0.937654	+	0.347570i	$0.112993\pi$
$788$	35.3986	+	11.5017i	1.26102	+	0.409731i
$789$	−6.71272	−	20.6596i	−0.238979	−	0.735502i
$790$	−6.73459	+	2.20516i	−0.239606	+	0.0784561i
$791$	1.72281			0.0612562
$792$		0			0
$793$		0			0
$794$	−33.5654	+	24.3867i	−1.19119	+	0.865451i
$795$	17.8885	−	0.0407173i	0.634440	−	0.00144409i
$796$	−10.8089	+	33.2663i	−0.383110	+	1.17909i
$797$	3.08649	−	4.24819i	0.109329	−	0.150479i	−0.750846	−	0.660477i	$-0.770354\pi$
$797$	3.08649	−	4.24819i	0.109329	−	0.150479i	0.860175	+	0.509998i	$0.170354\pi$
$798$	16.2892	−	22.4201i	0.576631	−	0.793664i
$799$	−3.24804	+	9.99644i	−0.114907	+	0.353648i
$800$	19.5677	+	6.25960i	0.691824	+	0.221310i
$801$	2.63370	−	1.91350i	0.0930574	−	0.0676101i
$802$		−	29.0024i		−	1.02411i
$803$		0			0
$804$	32.2337			1.13679
$805$	−1.90973	−	5.83233i	−0.0673090	−	0.205563i
$806$		0			0
$807$	8.65717	+	2.81288i	0.304747	+	0.0990182i
$808$	21.1195	−	29.0685i	0.742981	−	1.02263i
$809$	26.4909	+	19.2468i	0.931371	+	0.676680i	0.946328	−	0.323208i	$-0.104761\pi$
$809$	26.4909	+	19.2468i	0.931371	+	0.676680i	−0.0149573	+	0.999888i	$0.504761\pi$
$810$	12.3848	−	17.1280i	0.435157	−	0.601818i
$811$	0.0722135	+	0.222250i	0.00253576	+	0.00780427i	0.952316	−	0.305112i	$-0.0986940\pi$
$811$	0.0722135	+	0.222250i	0.00253576	+	0.00780427i	−0.949781	+	0.312917i	$0.898694\pi$
$812$	−77.8494	−	107.151i	−2.73198	−	3.76025i
$813$		−	10.6873i		−	0.374819i
$814$		0			0
$815$	7.37228	+	2.37686i	0.258240	+	0.0832578i
$816$	−6.47214	+	4.70228i	−0.226570	+	0.164613i
$817$	−13.1782	+	4.28187i	−0.461048	+	0.149803i
$818$	65.9956	+	21.4433i	2.30748	+	0.749746i
$819$		0			0
$820$	−69.0508	+	50.4089i	−2.41136	+	1.76036i
$821$	5.56231	−	17.1190i	0.194126	−	0.597458i	−0.805860	−	0.592106i	$-0.798297\pi$
$821$	5.56231	−	17.1190i	0.194126	−	0.597458i	0.999986	−	0.00535152i	$-0.00170345\pi$
$822$	27.3024	−	8.87110i	0.952282	−	0.309415i
$823$	32.9352	+	45.3315i	1.14805	+	1.58016i	0.748053	+	0.663639i	$0.230989\pi$
$823$	32.9352	+	45.3315i	1.14805	+	1.58016i	0.399997	+	0.916516i	$0.369011\pi$
$824$	62.2337			2.16801
$825$		0			0
$826$	64.4674			2.24311
$827$	16.7005	+	22.9862i	0.580732	+	0.799309i	0.993775	−	0.111402i	$-0.0355342\pi$
$827$	16.7005	+	22.9862i	0.580732	+	0.799309i	−0.413043	+	0.910711i	$0.635534\pi$
$828$	−7.81561	+	2.53945i	−0.271611	+	0.0882519i
$829$	6.28866	−	19.3545i	0.218414	−	0.672210i	−0.780479	−	0.625182i	$-0.785025\pi$
$829$	6.28866	−	19.3545i	0.218414	−	0.672210i	0.998894	−	0.0470282i	$-0.0149751\pi$
$830$	30.2410	−	22.0767i	1.04968	−	0.766295i
$831$	7.48781	+	5.44021i	0.259749	+	0.188719i
$832$		0			0
$833$	−7.53510	+	2.44830i	−0.261076	+	0.0848286i
$834$	−26.2667	+	19.0838i	−0.909540	+	0.660819i
$835$	33.4891	+	10.7971i	1.15894	+	0.373648i
$836$		0			0
$837$			14.3537i			0.496138i
$838$	−34.0944	−	46.9269i	−1.17777	−	1.62106i
$839$	3.12628	+	9.62169i	0.107931	+	0.332178i	0.990407	−	0.138180i	$-0.0441251\pi$
$839$	3.12628	+	9.62169i	0.107931	+	0.332178i	−0.882476	+	0.470357i	$0.844125\pi$
$840$	−21.5341	+	29.7815i	−0.742997	+	1.02756i
$841$	−38.4019	−	27.9006i	−1.32420	−	0.962090i
$842$	12.6282	−	17.3812i	0.435195	−	0.598995i
$843$	0.384949	+	0.125078i	0.0132583	+	0.00430790i
$844$	2.01197	+	6.19221i	0.0692549	+	0.213145i
$845$	9.04568	+	27.6256i	0.311181	+	0.950351i
$846$	39.7228			1.36570
$847$		0			0
$848$		−	64.3432i		−	2.20955i
$849$	9.70820	−	7.05342i	0.333185	−	0.242073i
$850$	6.09369	−	19.0491i	0.209012	−	0.653378i
$851$	−0.266189	+	0.819246i	−0.00912485	+	0.0280834i
$852$	20.5994	−	28.3526i	0.705723	−	0.971345i
$853$	20.5994	−	28.3526i	0.705310	−	0.970775i	−0.294576	−	0.955628i	$-0.595178\pi$
$853$	20.5994	−	28.3526i	0.705310	−	0.970775i	0.999885	−	0.0151473i	$-0.00482172\pi$
$854$	2.01197	−	6.19221i	0.0688482	−	0.211893i
$855$	21.2183	−	0.0482964i	0.725650	−	0.00165170i
$856$	−32.1364	+	23.3485i	−1.09840	+	0.798035i
$857$			23.9538i			0.818245i	0.912480	+	0.409122i	$0.134165\pi$
$857$			23.9538i			0.818245i	−0.912480	+	0.409122i	$0.865835\pi$
$858$		0			0
$859$	6.11684			0.208704			0.104352	−	0.994540i	$-0.466723\pi$
$859$	6.11684			0.208704			0.104352	+	0.994540i	$0.466723\pi$
$860$	32.1860	−	10.5389i	1.09754	−	0.359375i
$861$	−7.41641	−	22.8254i	−0.252751	−	0.777886i
$862$	61.7550	+	20.0654i	2.10338	+	0.683431i
$863$	1.68941	−	2.32527i	0.0575082	−	0.0791532i	−0.779294	−	0.626658i	$-0.784422\pi$
$863$	1.68941	−	2.32527i	0.0575082	−	0.0791532i	0.836802	+	0.547505i	$0.184422\pi$
$864$	14.1490	+	10.2798i	0.481359	+	0.349728i
$865$	−11.1535	+	15.4252i	−0.379230	+	0.524472i
$866$	22.7816	+	70.1146i	0.774150	+	2.38259i
$867$	−6.74751	−	9.28715i	−0.229157	−	0.315408i
$868$			51.0767i			1.73365i
$869$		0			0
$870$	−12.0000	+	37.2203i	−0.406838	+	1.26188i
$871$		0			0
$872$	56.9534	−	18.5053i	1.92869	−	0.626668i
$873$	13.1782	+	4.28187i	0.446015	+	0.144919i
$874$	−6.47214	−	4.70228i	−0.218923	−	0.159057i
$875$	−0.264465	−	38.7289i	−0.00894054	−	1.30928i
$876$	−7.41641	+	22.8254i	−0.250577	+	0.771197i
$877$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$877$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$878$	−31.8849	−	43.8858i	−1.07606	−	1.48107i
$879$	−2.51087			−0.0846897
$880$		0			0
$881$	−6.86141			−0.231167			−0.115583	−	0.993298i	$-0.536874\pi$
$881$	−6.86141			−0.231167			−0.115583	+	0.993298i	$0.536874\pi$
$882$	17.5996	+	24.2237i	0.592609	+	0.815656i
$883$	23.0619	−	7.49326i	0.776095	−	0.252168i	0.105923	−	0.994374i	$-0.466220\pi$
$883$	23.0619	−	7.49326i	0.776095	−	0.252168i	0.670172	+	0.742206i	$0.266220\pi$
$884$		0			0
$885$	−7.70097	−	10.5489i	−0.258865	−	0.354597i
$886$	64.6862	+	46.9973i	2.17317	+	1.57890i
$887$	26.0759	+	8.47258i	0.875544	+	0.284482i	0.712106	−	0.702072i	$-0.247742\pi$
$887$	26.0759	+	8.47258i	0.875544	+	0.284482i	0.163438	+	0.986554i	$0.447742\pi$
$888$	4.90601	−	1.59406i	0.164635	−	0.0534931i
$889$	−23.0306	+	16.7327i	−0.772421	+	0.561197i
$890$	−7.37228	−	2.37686i	−0.247119	−	0.0796726i
$891$		0			0
$892$		−	10.3923i		−	0.347960i
$893$	15.5957	+	21.4656i	0.521890	+	0.718320i
$894$	7.10067	+	21.8536i	0.237482	+	0.730894i
$895$	23.3049	+	16.8511i	0.778998	+	0.563270i
$896$	−39.8133	−	28.9261i	−1.33007	−	0.966352i
$897$		0			0
$898$	−16.4728	−	5.35233i	−0.549704	−	0.178610i
$899$	9.11264	+	28.0458i	0.303924	+	0.935381i
$900$	−51.8609	+	0.236090i	−1.72870	+	0.00786965i
$901$	−16.0000			−0.533037
$902$		0			0
$903$			9.50744i			0.316388i
$904$	−2.40946	+	1.75057i	−0.0801373	+	0.0582232i
$905$	53.9268	−	0.122747i	1.79259	−	0.00408023i
$906$	−7.56083	+	23.2699i	−0.251192	+	0.773089i
$907$	−11.6968	+	16.0992i	−0.388385	+	0.534566i	−0.957782	−	0.287497i	$-0.907177\pi$
$907$	−11.6968	+	16.0992i	−0.388385	+	0.534566i	0.569396	+	0.822063i	$0.307177\pi$
$908$	42.9970	−	59.1803i	1.42691	−	1.96397i
$909$	−4.39845	+	13.5370i	−0.145887	+	0.448995i
$910$		0			0
$911$	43.2736	−	31.4401i	1.43372	−	1.04166i	0.444410	−	0.895824i	$-0.353413\pi$
$911$	43.2736	−	31.4401i	1.43372	−	1.04166i	0.989309	−	0.145834i	$-0.0465865\pi$
$912$			20.1947i			0.668713i
$913$		0			0
$914$	−52.4674			−1.73547
$915$	−1.25358	+	0.410470i	−0.0414421	+	0.0135697i
$916$	19.7636	+	60.8262i	0.653009	+	2.00976i
$917$	−9.04212	−	2.93796i	−0.298597	−	0.0970200i
$918$	10.0074	−	13.7740i	0.330292	−	0.454609i
$919$	22.8415	+	16.5953i	0.753473	+	0.547430i	0.896901	−	0.442231i	$-0.145813\pi$
$919$	22.8415	+	16.5953i	0.753473	+	0.547430i	−0.143429	+	0.989661i	$0.545813\pi$
$920$	8.59717	+	6.21636i	0.283440	+	0.204947i
$921$	7.73215	+	23.7971i	0.254783	+	0.784141i
$922$	3.31428	+	4.56171i	0.109150	+	0.150232i
$923$		0			0
$924$		0			0
$925$	−3.17527	+	4.41248i	−0.104402	+	0.145081i
$926$	61.4501	−	44.6461i	2.01938	−	1.46716i
$927$	−23.4468	+	7.61834i	−0.770095	+	0.250219i
$928$	34.1721	+	11.1032i	1.12175	+	0.364480i
$929$	−5.68071	−	4.12728i	−0.186378	−	0.135412i	0.490684	−	0.871338i	$-0.336747\pi$
$929$	−5.68071	−	4.12728i	−0.186378	−	0.135412i	−0.677062	+	0.735926i	$0.736747\pi$
$930$	12.1808	−	8.89231i	0.399425	−	0.291590i
$931$	−6.18034	+	19.0211i	−0.202552	+	0.623392i
$932$	−15.6312	+	5.07889i	−0.512018	+	0.166365i
$933$	−2.55626	−	3.51838i	−0.0836881	−	0.115187i
$934$	19.4891			0.637704
$935$		0			0
$936$		0			0
$937$	31.5381	+	43.4085i	1.03031	+	1.41810i	0.904717	+	0.426013i	$0.140082\pi$
$937$	31.5381	+	43.4085i	1.03031	+	1.41810i	0.125589	+	0.992082i	$0.459918\pi$
$938$	−77.3862	+	25.1443i	−2.52675	+	0.820991i
$939$	−5.35489	+	16.4807i	−0.174750	+	0.537826i
$940$	−38.2380	−	52.3790i	−1.24719	−	1.70841i
$941$	−47.3011	−	34.3663i	−1.54197	−	1.12031i	−0.949084	−	0.315023i	$-0.897988\pi$
$941$	−47.3011	−	34.3663i	−1.54197	−	1.12031i	−0.592888	−	0.805285i	$-0.702012\pi$
$942$	46.5087	+	15.1116i	1.51534	+	0.492363i
$943$	−6.58911	+	2.14093i	−0.214571	+	0.0697184i
$944$	−38.0062	+	27.6131i	−1.23700	+	0.898731i
$945$	10.1168	−	31.3793i	0.329101	−	1.02077i
$946$		0			0
$947$		−	26.7354i		−	0.868783i	−0.900724	−	0.434392i	$-0.856963\pi$
$947$		−	26.7354i		−	0.868783i	0.900724	−	0.434392i	$-0.143037\pi$
$948$	2.55626	+	3.51838i	0.0830233	+	0.114272i
$949$		0			0
$950$	−29.8610	−	40.7091i	−0.968819	−	1.32078i
$951$	21.1290	+	15.3511i	0.685154	+	0.497793i
$952$	19.3213	−	26.5934i	0.626206	−	0.861898i
$953$	29.7554	+	9.66813i	0.963873	+	0.313181i	0.748340	−	0.663315i	$-0.230851\pi$
$953$	29.7554	+	9.66813i	0.963873	+	0.313181i	0.215533	+	0.976497i	$0.430851\pi$
$954$	18.6854	+	57.5079i	0.604964	+	1.86189i
$955$	−13.4797	−	41.1670i	−0.436191	−	1.33213i
$956$	64.4674			2.08502
$957$		0			0
$958$		−	13.8564i		−	0.447680i
$959$	−40.2266	+	29.2263i	−1.29898	+	0.943768i
$960$	0.00956616	+	4.20274i	0.000308746	+	0.135643i
$961$	−6.06530	+	18.6671i	−0.195655	+	0.602164i
$962$		0			0
$963$	9.24935	−	12.7306i	0.298056	−	0.410239i
$964$	22.6237	−	69.6287i	0.728661	−	2.24259i
$965$	−0.0836519	−	36.7511i	−0.00269285	−	1.18306i
$966$	−4.44080	+	3.22643i	−0.142880	+	0.103809i
$967$			26.4232i			0.849713i	0.905261	+	0.424856i	$0.139675\pi$
$967$			26.4232i			0.849713i	−0.905261	+	0.424856i	$0.860325\pi$
$968$		0			0
$969$	5.02175			0.161322
$970$	−10.2596	−	31.3329i	−0.329416	−	1.00604i
$971$	−2.81054	−	8.64995i	−0.0901945	−	0.277590i	0.895777	−	0.444504i	$-0.146620\pi$
$971$	−2.81054	−	8.64995i	−0.0901945	−	0.277590i	−0.985972	+	0.166914i	$0.946620\pi$
$972$	−65.4345	−	21.2610i	−2.09881	−	0.681946i
$973$	33.0542	−	45.4952i	1.05967	−	1.45851i
$974$	−14.5623	−	10.5801i	−0.466606	−	0.339009i
$975$		0			0
$976$	1.46615	+	4.51235i	0.0469303	+	0.144437i
$977$	29.7298	+	40.9195i	0.951140	+	1.30913i	0.951019	+	0.309132i	$0.100038\pi$
$977$	29.7298	+	40.9195i	0.951140	+	1.30913i	0.000120920		1.00000i	$0.499962\pi$
$978$		−	6.92820i		−	0.221540i
$979$		0			0
$980$	15.0000	−	46.5253i	0.479157	−	1.48620i
$981$	−19.1922	+	13.9439i	−0.612758	+	0.445195i
$982$	15.6312	−	5.07889i	0.498813	−	0.162074i
$983$	23.5349	+	7.64695i	0.750646	+	0.243900i	0.659259	−	0.751916i	$-0.270870\pi$
$983$	23.5349	+	7.64695i	0.750646	+	0.243900i	0.0913870	+	0.995815i	$0.470870\pi$
$984$	33.5654	+	24.3867i	1.07003	+	0.777419i
$985$	11.2236	+	15.3743i	0.357614	+	0.489864i
$986$	10.8089	−	33.2663i	0.344225	−	1.05941i
$987$	17.3143	−	5.62577i	0.551121	−	0.179070i
$988$		0			0
$989$	2.74456			0.0872720
$990$		0			0
$991$	18.9783			0.602864			0.301432	−	0.953488i	$-0.402535\pi$
$991$	18.9783			0.602864			0.301432	+	0.953488i	$0.402535\pi$
$992$	−8.14459	−	11.2101i	−0.258591	−	0.355920i
$993$	10.6372	−	3.45623i	0.337561	−	0.109680i
$994$	−27.3379	+	84.1375i	−0.867106	+	2.66868i
$995$	−14.4482	+	10.5475i	−0.458038	+	0.334379i
$996$	−18.5898	−	13.5063i	−0.589040	−	0.427963i
$997$	−2.06805	−	0.671952i	−0.0654959	−	0.0212809i	0.276086	−	0.961133i	$-0.410963\pi$
$997$	−2.06805	−	0.671952i	−0.0654959	−	0.0212809i	−0.341582	+	0.939852i	$0.610963\pi$
$998$	−48.0158	+	15.6013i	−1.51991	+	0.493849i
$999$	−3.74390	+	2.72010i	−0.118452	+	0.0860603i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.j.j.124.1		16
5.4	even	2	inner	605.2.j.j.124.4		16
11.2	odd	10		55.2.b.a.34.1	✓	4
11.3	even	5	inner	605.2.j.j.269.1		16
11.4	even	5	inner	605.2.j.j.444.4		16
11.5	even	5	inner	605.2.j.j.9.4		16
11.6	odd	10		605.2.j.i.9.1		16
11.7	odd	10		605.2.j.i.444.1		16
11.8	odd	10		605.2.j.i.269.4		16
11.9	even	5		605.2.b.c.364.4		4
11.10	odd	2		605.2.j.i.124.4		16
33.2	even	10		495.2.c.a.199.4		4
44.35	even	10		880.2.b.h.529.2		4
55.2	even	20		275.2.a.h.1.4		4
55.4	even	10	inner	605.2.j.j.444.1		16
55.9	even	10		605.2.b.c.364.1		4
55.13	even	20		275.2.a.h.1.1		4
55.14	even	10	inner	605.2.j.j.269.4		16
55.19	odd	10		605.2.j.i.269.1		16
55.24	odd	10		55.2.b.a.34.4	yes	4
55.29	odd	10		605.2.j.i.444.4		16
55.39	odd	10		605.2.j.i.9.4		16
55.42	odd	20		3025.2.a.ba.1.1		4
55.49	even	10	inner	605.2.j.j.9.1		16
55.53	odd	20		3025.2.a.ba.1.4		4
55.54	odd	2		605.2.j.i.124.1		16
165.2	odd	20		2475.2.a.bi.1.1		4
165.68	odd	20		2475.2.a.bi.1.4		4
165.134	even	10		495.2.c.a.199.1		4
220.79	even	10		880.2.b.h.529.3		4
220.123	odd	20		4400.2.a.cc.1.3		4
220.167	odd	20		4400.2.a.cc.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.b.a.34.1	✓	4	11.2	odd	10
55.2.b.a.34.4	yes	4	55.24	odd	10
275.2.a.h.1.1		4	55.13	even	20
275.2.a.h.1.4		4	55.2	even	20
495.2.c.a.199.1		4	165.134	even	10
495.2.c.a.199.4		4	33.2	even	10
605.2.b.c.364.1		4	55.9	even	10
605.2.b.c.364.4		4	11.9	even	5
605.2.j.i.9.1		16	11.6	odd	10
605.2.j.i.9.4		16	55.39	odd	10
605.2.j.i.124.1		16	55.54	odd	2
605.2.j.i.124.4		16	11.10	odd	2
605.2.j.i.269.1		16	55.19	odd	10
605.2.j.i.269.4		16	11.8	odd	10
605.2.j.i.444.1		16	11.7	odd	10
605.2.j.i.444.4		16	55.29	odd	10
605.2.j.j.9.1		16	55.49	even	10	inner
605.2.j.j.9.4		16	11.5	even	5	inner
605.2.j.j.124.1		16	1.1	even	1	trivial
605.2.j.j.124.4		16	5.4	even	2	inner
605.2.j.j.269.1		16	11.3	even	5	inner
605.2.j.j.269.4		16	55.14	even	10	inner
605.2.j.j.444.1		16	55.4	even	10	inner
605.2.j.j.444.4		16	11.4	even	5	inner
880.2.b.h.529.2		4	44.35	even	10
880.2.b.h.529.3		4	220.79	even	10
2475.2.a.bi.1.1		4	165.2	odd	20
2475.2.a.bi.1.4		4	165.68	odd	20
3025.2.a.ba.1.1		4	55.42	odd	20
3025.2.a.ba.1.4		4	55.53	odd	20
4400.2.a.cc.1.2		4	220.167	odd	20
4400.2.a.cc.1.3		4	220.123	odd	20

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.j (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.48377 - 2.04223i) q^{2} +(-0.753510 + 0.244830i) q^{3} +(-1.35111 + 4.15829i) q^{4} +(-1.80602 + 1.31844i) q^{5} +(1.61803 + 1.17557i) q^{6} +(-3.29456 - 1.07047i) q^{7} +(5.69534 - 1.85053i) q^{8} +(-1.91922 + 1.39439i) q^{9} +(5.37228 + 1.73205i) q^{10} -3.46410i q^{12} +(2.70222 + 8.31657i) q^{14} +(1.03806 - 1.43563i) q^{15} +(-5.15528 - 3.74553i) q^{16} +(-0.931389 + 1.28195i) q^{17} +(5.69534 + 1.85053i) q^{18} +(1.23607 + 3.80423i) q^{19} +(-3.04233 - 9.29131i) q^{20} +2.74456 q^{21} -0.792287i q^{23} +(-3.83843 + 2.78878i) q^{24} +(1.52342 - 4.76227i) q^{25} +(2.50184 - 3.44349i) q^{27} +(8.90261 - 12.2534i) q^{28} +(2.70222 - 8.31657i) q^{29} +(-4.47212 + 0.0101793i) q^{30} +(-2.72823 + 1.98218i) q^{31} +4.10891i q^{32} +4.00000 q^{34} +(7.36138 - 2.41040i) q^{35} +(-3.20521 - 9.86463i) q^{36} +(-1.03403 - 0.335976i) q^{37} +(5.93507 - 8.16893i) q^{38} +(-7.84609 + 10.8511i) q^{40} +(-2.70222 - 8.31657i) q^{41} +(-4.07230 - 5.60503i) q^{42} +3.46410i q^{43} +(1.62772 - 5.04868i) q^{45} +(-1.61803 + 1.17557i) q^{46} +(6.30860 - 2.04979i) q^{47} +(4.80158 + 1.56013i) q^{48} +(4.04508 + 2.93893i) q^{49} +(-11.9861 + 3.95492i) q^{50} +(0.387951 - 1.19399i) q^{51} +(5.93507 + 8.16893i) q^{53} -10.7446 q^{54} -20.7446 q^{56} +(-1.86278 - 2.56389i) q^{57} +(-20.9938 + 6.82131i) q^{58} +(2.27816 - 7.01146i) q^{59} +(4.56722 + 6.25624i) q^{60} +(-0.602364 - 0.437643i) q^{61} +(8.09613 + 2.63059i) q^{62} +(7.81561 - 2.53945i) q^{63} +(-1.91922 + 1.39439i) q^{64} +9.30506i q^{67} +(-4.07230 - 5.60503i) q^{68} +(0.193976 + 0.596996i) q^{69} +(-15.8452 - 11.4572i) q^{70} +(8.18470 + 5.94653i) q^{71} +(-8.35023 + 11.4931i) q^{72} +(-6.58911 - 2.14093i) q^{73} +(0.848116 + 2.61023i) q^{74} +(0.0180337 + 3.96139i) q^{75} -17.4891 q^{76} +(-1.01567 + 0.737928i) q^{79} +(14.2488 - 0.0324327i) q^{80} +(1.15713 - 3.56129i) q^{81} +(-12.9749 + 17.8584i) q^{82} +(3.89893 - 5.36641i) q^{83} +(-3.70820 + 11.4127i) q^{84} +(-0.00806494 - 3.54321i) q^{85} +(7.07450 - 5.13992i) q^{86} +6.92820i q^{87} -1.37228 q^{89} +(-12.7257 + 4.16689i) q^{90} +(3.29456 + 1.07047i) q^{92} +(1.57045 - 2.16154i) q^{93} +(-13.5466 - 9.84221i) q^{94} +(-7.24802 - 5.24083i) q^{95} +(-1.00599 - 3.09610i) q^{96} +(-3.43323 - 4.72544i) q^{97} -12.6217i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{4} + 3 q^{5} + 8 q^{6} + 2 q^{9} + 40 q^{10} - 12 q^{14} - q^{15} - 14 q^{16} - 16 q^{19} + 12 q^{20} - 48 q^{21} + 4 q^{24} - q^{25} - 12 q^{29} - 6 q^{30} - 2 q^{31} + 64 q^{34} + 18 q^{35}+ \cdots + 36 q^{96}+O(q^{100}) \) 16 * q + 6 * q^4 + 3 * q^5 + 8 * q^6 + 2 * q^9 + 40 * q^10 - 12 * q^14 - q^15 - 14 * q^16 - 16 * q^19 + 12 * q^20 - 48 * q^21 + 4 * q^24 - q^25 - 12 * q^29 - 6 * q^30 - 2 * q^31 + 64 * q^34 + 18 * q^35 + 30 * q^36 + 28 * q^40 + 12 * q^41 + 72 * q^45 - 8 * q^46 + 20 * q^49 - 18 * q^50 - 28 * q^51 - 80 * q^54 - 240 * q^56 - 18 * q^59 + 18 * q^60 + 20 * q^61 + 2 * q^64 - 14 * q^69 - 24 * q^70 + 6 * q^71 + 12 * q^74 - 15 * q^75 - 96 * q^76 - 28 * q^79 - 6 * q^80 + 8 * q^81 + 48 * q^84 + 2 * q^85 + 12 * q^86 + 24 * q^89 - 28 * q^90 - 44 * q^94 + 12 * q^95 + 36 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more