LMFDB - Embedded newform 605.2.j.j.444.4

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			444.4
Root			$-1.70149 - 0.323920i$ of defining polynomial
Character	$\chi$	$=$	605.444
Dual form			605.2.j.j.124.4

$q$-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} +(0.695822 + 2.12505i) 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} +(0.00403247 + 1.77160i) 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} +(7.89643 - 5.76460i) q^{20} +2.74456 q^{21} -0.792287i q^{23} +(-3.83843 - 2.78878i) q^{24} +(-4.03166 + 2.95731i) q^{25} +(-2.50184 - 3.44349i) q^{27} +(-8.90261 - 12.2534i) q^{28} +(2.70222 + 8.31657i) q^{29} +(3.62401 + 2.62041i) q^{30} +(-2.72823 - 1.98218i) q^{31} +4.10891i q^{32} +4.00000 q^{34} +(4.56722 + 6.25624i) q^{35} +(-3.20521 + 9.86463i) q^{36} +(1.03403 - 0.335976i) q^{37} +(-5.93507 - 8.16893i) q^{38} +(-0.0304791 - 13.3905i) 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} +(0.0574579 + 12.6216i) 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} +(7.36138 - 2.41040i) 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} +(19.5534 - 0.0445068i) 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} +(-3.76194 + 1.24129i) q^{75} -17.4891 q^{76} +(-1.01567 - 0.737928i) q^{79} +(-11.5466 - 8.34901i) 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} +(-2.07612 + 2.87125i) q^{85} +(7.07450 + 5.13992i) q^{86} +6.92820i q^{87} -1.37228 q^{89} +(-7.89541 - 10.8152i) q^{90} +(-3.29456 + 1.07047i) q^{92} +(-1.57045 - 2.16154i) q^{93} +(-13.5466 + 9.84221i) q^{94} +(8.94425 - 0.0203586i) 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 $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

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

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	0.159667	−	0.987171i	$-0.448958\pi$
$2$	1.48377	−	2.04223i	1.04918	−	1.44408i	0.889515	−	0.456905i	$-0.151042\pi$
$3$	0.753510	+	0.244830i	0.435039	+	0.141353i	0.518346	−	0.855171i	$-0.326548\pi$
$3$	0.753510	+	0.244830i	0.435039	+	0.141353i	−0.0833066	+	0.996524i	$0.526548\pi$
$4$	−1.35111	−	4.15829i	−0.675555	−	2.07914i
$5$	0.695822	+	2.12505i	0.311181	+	0.950351i
$5$	0.695822	+	2.12505i	0.311181	+	0.950351i
$6$	1.61803	−	1.17557i	0.660560	−	0.479925i
$7$	3.29456	−	1.07047i	1.24523	−	0.404598i	0.389018	−	0.921230i	$-0.372814\pi$
$7$	3.29456	−	1.07047i	1.24523	−	0.404598i	0.856208	+	0.516632i	$0.172814\pi$
$8$	−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	$-0.800000\pi$
$13$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$14$	2.70222	−	8.31657i	0.722198	−	2.22270i
$15$	0.00403247	+	1.77160i	0.00104118	+	0.457426i
$16$	−5.15528	+	3.74553i	−1.28882	+	0.936383i
$17$	0.931389	+	1.28195i	0.225895	+	0.310918i	0.906888	−	0.421372i	$-0.138451\pi$
$17$	0.931389	+	1.28195i	0.225895	+	0.310918i	−0.680993	+	0.732290i	$0.738451\pi$
$18$	−5.69534	+	1.85053i	−1.34241	+	0.436174i
$19$	1.23607	−	3.80423i	0.283573	−	0.872749i	−0.703249	−	0.710943i	$-0.748268\pi$
$19$	1.23607	−	3.80423i	0.283573	−	0.872749i	0.986823	−	0.161806i	$-0.0517318\pi$
$20$	7.89643	−	5.76460i	1.76570	−	1.28900i
$21$	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
$25$	−4.03166	+	2.95731i	−0.806333	+	0.591462i
$26$		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	0.806102	+	0.591777i	$0.201573\pi$
$29$	2.70222	+	8.31657i	0.501789	+	1.54435i	−0.304313	+	0.952572i	$0.598427\pi$
$30$	3.62401	+	2.62041i	0.661650	+	0.478420i
$31$	−2.72823	−	1.98218i	−0.490005	−	0.356010i	0.315181	−	0.949032i	$-0.397935\pi$
$31$	−2.72823	−	1.98218i	−0.490005	−	0.356010i	−0.805186	+	0.593022i	$0.797935\pi$
$32$			4.10891i			0.726360i
$33$		0			0
$34$	4.00000			0.685994
$35$	4.56722	+	6.25624i	0.772001	+	1.05750i
$36$	−3.20521	+	9.86463i	−0.534202	+	1.64410i
$37$	1.03403	−	0.335976i	0.169993	−	0.0552341i	−0.222784	−	0.974868i	$-0.571514\pi$
$37$	1.03403	−	0.335976i	0.169993	−	0.0552341i	0.392777	+	0.919634i	$0.371514\pi$
$38$	−5.93507	−	8.16893i	−0.962796	−	1.32518i
$39$		0			0
$40$	−0.0304791	−	13.3905i	−0.00481917	−	2.11723i
$41$	−2.70222	+	8.31657i	−0.422016	+	1.29883i	0.483807	+	0.875174i	$0.339253\pi$
$41$	−2.70222	+	8.31657i	−0.422016	+	1.29883i	−0.905823	+	0.423656i	$0.860747\pi$
$42$	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	$-0.560736\pi$
$47$	−6.30860	−	2.04979i	−0.920203	−	0.298992i	−0.730550	+	0.682859i	$0.760736\pi$
$48$	−4.80158	+	1.56013i	−0.693048	+	0.225185i
$49$	4.04508	−	2.93893i	0.577869	−	0.419847i
$50$	0.0574579	+	12.6216i	0.00812578	+	1.78496i
$51$	0.387951	+	1.19399i	0.0543241	+	0.167192i
$52$		0			0
$53$	−5.93507	+	8.16893i	−0.815245	+	1.12209i	0.175248	+	0.984524i	$0.443927\pi$
$53$	−5.93507	+	8.16893i	−0.815245	+	1.12209i	−0.990493	+	0.137564i	$0.956073\pi$
$54$	−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	0.982682	+	0.185298i	$0.0593251\pi$
$59$	2.27816	+	7.01146i	0.296591	+	0.912814i	−0.686091	+	0.727516i	$0.740675\pi$
$60$	7.36138	−	2.41040i	0.950351	−	0.311181i
$61$	−0.602364	+	0.437643i	−0.0771248	+	0.0560344i	−0.625680	−	0.780080i	$-0.715178\pi$
$61$	−0.602364	+	0.437643i	−0.0771248	+	0.0560344i	0.548555	+	0.836115i	$0.315178\pi$
$62$	−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
$70$	19.5534	−	0.0445068i	2.33708	−	0.00531959i
$71$	8.18470	−	5.94653i	0.971345	−	0.705723i	0.0155873	−	0.999879i	$-0.495038\pi$
$71$	8.18470	−	5.94653i	0.971345	−	0.705723i	0.955758	+	0.294155i	$0.0950382\pi$
$72$	8.35023	+	11.4931i	0.984084	+	1.35448i
$73$	6.58911	−	2.14093i	0.771197	−	0.250577i	0.103120	−	0.994669i	$-0.467117\pi$
$73$	6.58911	−	2.14093i	0.771197	−	0.250577i	0.668077	+	0.744092i	$0.267117\pi$
$74$	0.848116	−	2.61023i	0.0985915	−	0.303434i
$75$	−3.76194	+	1.24129i	−0.434391	+	0.143332i
$76$	−17.4891			−2.00614
$77$		0			0
$78$		0			0
$79$	−1.01567	−	0.737928i	−0.114272	−	0.0830233i	0.529182	−	0.848509i	$-0.322499\pi$
$79$	−1.01567	−	0.737928i	−0.114272	−	0.0830233i	−0.643453	+	0.765485i	$0.722499\pi$
$80$	−11.5466	−	8.34901i	−1.29095	−	0.933447i
$81$	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	$-0.318605\pi$
$83$	−3.89893	−	5.36641i	−0.427963	−	0.589040i	−0.967484	+	0.252932i	$0.918605\pi$
$84$	−3.70820	−	11.4127i	−0.404598	−	1.24523i
$85$	−2.07612	+	2.87125i	−0.225187	+	0.311431i
$86$	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	$0.523171\pi$
$90$	−7.89541	−	10.8152i	−0.832249	−	1.14003i
$91$		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
$95$	8.94425	−	0.0203586i	0.917661	−	0.00208875i
$96$	−1.00599	+	3.09610i	−0.102673	+	0.315995i
$97$	3.43323	−	4.72544i	0.348592	−	0.479796i	−0.598334	−	0.801247i	$-0.704171\pi$
$97$	3.43323	−	4.72544i	0.348592	−	0.479796i	0.946926	+	0.321451i	$0.104171\pi$
$98$		−	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	0.802486	−	0.596670i	$-0.203510\pi$
$101$	4.85410	+	3.52671i	0.483001	+	0.350921i	−0.319485	+	0.947591i	$0.603510\pi$
$102$	3.01404	+	0.979321i	0.298434	+	0.0969672i
$103$	−9.88367	+	3.21140i	−0.973867	+	0.316429i	−0.752376	−	0.658734i	$-0.771092\pi$
$103$	−9.88367	+	3.21140i	−0.973867	+	0.316429i	−0.221491	+	0.975162i	$0.571092\pi$
$104$		0			0
$105$	1.90973	+	5.83233i	0.186370	+	0.569177i
$106$	7.87657	+	24.2416i	0.765040	+	2.35455i
$107$	6.30860	+	2.04979i	0.609875	+	0.198160i	0.597640	−	0.801765i	$-0.296105\pi$
$107$	6.30860	+	2.04979i	0.609875	+	0.198160i	0.0122352	+	0.999925i	$0.496105\pi$
$108$	−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	$-0.392553\pi$
$113$	0.472992	+	0.153684i	0.0444954	+	0.0144574i	−0.286685	+	0.958025i	$0.592553\pi$
$114$	−2.47214	−	7.60845i	−0.231537	−	0.712597i
$115$	1.68365	−	0.551291i	0.157001	−	0.0514081i
$116$	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
$125$	−9.08975	−	6.50972i	−0.813012	−	0.582247i
$126$	−16.7827	+	12.1933i	−1.49512	+	1.08627i
$127$	−4.83032	−	6.64836i	−0.428621	−	0.589946i	0.539015	−	0.842296i	$-0.318797\pi$
$127$	−4.83032	−	6.64836i	−0.428621	−	0.589946i	−0.967636	+	0.252350i	$0.918797\pi$
$128$	−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
$135$	5.57675	−	7.71259i	0.479970	−	0.663794i
$136$	−2.93230	−	9.02469i	−0.251443	−	0.773861i
$137$	−8.43692	−	11.6124i	−0.720814	−	0.992116i	−0.999496	−	0.0317325i	$-0.989898\pi$
$137$	−8.43692	−	11.6124i	−0.720814	−	0.992116i	0.278682	−	0.960383i	$-0.410102\pi$
$138$	−0.931389	−	1.28195i	−0.0792851	−	0.109127i
$139$	−5.01649	−	15.4392i	−0.425493	−	1.30953i	−0.902522	−	0.430644i	$-0.858286\pi$
$139$	−5.01649	−	15.4392i	−0.425493	−	1.30953i	0.477029	−	0.878888i	$-0.341714\pi$
$140$	19.8444	−	27.4447i	1.67716	−	2.31950i
$141$	−4.25174	−	3.08907i	−0.358061	−	0.260147i
$142$		−	25.5383i		−	2.14313i
$143$		0			0
$144$	15.1168			1.25974
$145$	−15.7929	+	11.5292i	−1.31153	+	0.957448i
$146$	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	−0.137892	−	0.990447i	$-0.544033\pi$
$149$	9.29490	−	6.75314i	0.761468	−	0.553239i	0.899360	+	0.437209i	$0.144033\pi$
$150$	−3.04684	+	9.52453i	−0.248774	+	0.777675i
$151$	3.78042	−	11.6349i	0.307646	−	0.946837i	−0.671031	−	0.741430i	$-0.734148\pi$
$151$	3.78042	−	11.6349i	0.307646	−	0.946837i	0.978677	−	0.205407i	$-0.0658519\pi$
$152$	−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	−0.995653	−	0.0931428i	$-0.970309\pi$
$157$	−23.2544	−	7.55580i	−1.85590	−	0.603019i	−0.860248	−	0.509876i	$-0.829691\pi$
$158$	−3.01404	+	0.979321i	−0.239784	+	0.0779106i
$159$	−6.47214	+	4.70228i	−0.513274	+	0.372915i
$160$	−8.73164	+	2.85907i	−0.690297	+	0.226029i
$161$	−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	$-0.756683\pi$
$163$	2.03615	−	2.80252i	0.159483	−	0.219510i	0.881279	+	0.472596i	$0.156683\pi$
$164$	38.2337			2.98555
$165$		0			0
$166$	−16.7446			−1.29963
$167$	9.24935	−	12.7306i	0.715736	−	0.985126i	−0.283918	−	0.958848i	$-0.591635\pi$
$167$	9.24935	−	12.7306i	0.715736	−	0.985126i	0.999655	−	0.0262779i	$-0.00836549\pi$
$168$	−15.6312	−	5.07889i	−1.20598	−	0.391845i
$169$	4.01722	+	12.3637i	0.309017	+	0.951057i
$170$	2.78329	+	8.50019i	0.213468	+	0.651935i
$171$	−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	$-0.504896\pi$
$173$	−8.09613	−	2.63059i	−0.615538	−	0.200000i	−0.600158	+	0.799881i	$0.704896\pi$
$174$	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	0.685462	+	0.728109i	$0.259600\pi$
$179$	−3.97439	+	12.2319i	−0.297060	+	0.914257i	−0.982522	+	0.186148i	$0.940400\pi$
$180$	−23.1931	+	0.0527914i	−1.72871	+	0.00393484i
$181$	−19.5109	+	14.1755i	−1.45024	+	1.05366i	−0.464461	+	0.885594i	$0.653752\pi$
$181$	−19.5109	+	14.1755i	−1.45024	+	1.05366i	−0.985776	+	0.168065i	$0.946248\pi$
$182$		0			0
$183$	−0.561035	+	0.182291i	−0.0414729	+	0.0134754i
$184$	−1.46615	+	4.51235i	−0.108086	+	0.332655i
$185$	1.43346	+	1.96358i	0.105390	+	0.144365i
$186$	−6.74456			−0.494535
$187$		0			0
$188$			29.0024i			2.11522i
$189$	−11.9286	−	8.66664i	−0.867678	−	0.630405i
$190$	13.2296	−	18.2964i	0.959777	−	1.32736i
$191$	−5.98636	−	18.4241i	−0.433158	−	1.33312i	−0.894962	−	0.446142i	$-0.852798\pi$
$191$	−5.98636	−	18.4241i	−0.433158	−	1.33312i	0.461804	−	0.886982i	$-0.347202\pi$
$192$	−1.10476	−	1.52057i	−0.0797291	−	0.109738i
$193$	9.66063	+	13.2967i	0.695387	+	0.957119i	0.999989	+	0.00463891i	$0.00147662\pi$
$193$	9.66063	+	13.2967i	0.695387	+	0.957119i	−0.304602	+	0.952480i	$0.598523\pi$
$194$	−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	$0.408487\pi$
$200$	28.4343	−	9.38219i	2.01061	−	0.663421i
$201$	−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
$205$	−19.5534	+	0.0445068i	−1.36567	+	0.00310849i
$206$	−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	0.628481	−	0.777825i	$-0.283677\pi$
$211$	1.20473	+	0.875286i	0.0829369	+	0.0602572i	−0.545544	+	0.838082i	$0.683677\pi$
$212$	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
$215$	−7.36138	+	2.41040i	−0.502042	+	0.164388i
$216$	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	$-0.374641\pi$
$223$	2.26053	+	0.734490i	0.151376	+	0.0491851i	−0.232349	+	0.972633i	$0.574641\pi$
$224$	4.39845	+	13.5370i	0.293884	+	0.904482i
$225$	11.8613	−	0.0539969i	0.790752	−	0.00359979i
$226$	1.01567	−	0.737928i	0.0675614	−	0.0490862i
$227$	15.9117	−	5.17004i	1.05610	−	0.343148i	0.271040	−	0.962568i	$-0.412632\pi$
$227$	15.9117	−	5.17004i	1.05610	−	0.343148i	0.785059	+	0.619420i	$0.212632\pi$
$228$	−13.1782	−	4.28187i	−0.872749	−	0.283573i
$229$	11.8341	+	8.59796i	0.782018	+	0.568169i	0.905584	−	0.424167i	$-0.139433\pi$
$229$	11.8341	+	8.59796i	0.782018	+	0.568169i	−0.123566	+	0.992336i	$0.539433\pi$
$230$	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	$-0.839294\pi$
$233$	−2.20952	+	3.04114i	−0.144750	+	0.199232i	0.730485	+	0.682928i	$0.239294\pi$
$234$		0			0
$235$	−0.0337610	−	14.8324i	−0.00220232	−	0.967556i
$236$	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	0.688590	+	0.725151i	$0.258230\pi$
$239$	−4.55632	+	14.0229i	−0.294724	+	0.907067i	−0.983314	+	0.181916i	$0.941770\pi$
$240$	−6.65639	−	9.11801i	−0.429668	−	0.588565i
$241$	−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
$245$	9.06002	+	6.55103i	0.578823	+	0.418530i
$246$	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
$250$	−26.7814	+	8.90446i	−1.69381	+	0.563167i
$251$	17.8929	+	13.0000i	1.12939	+	0.820550i	0.985606	−	0.169059i	$-0.0540729\pi$
$251$	17.8929	+	13.0000i	1.12939	+	0.820550i	0.143784	+	0.989609i	$0.454073\pi$
$252$			35.9306i			2.26342i
$253$		0			0
$254$	−20.7446			−1.30163
$255$	−2.26735	+	1.65522i	−0.141987	+	0.103654i
$256$	−9.61563	+	29.5939i	−0.600977	+	1.84962i
$257$	−10.1642	+	3.30254i	−0.634025	+	0.206007i	−0.608357	−	0.793663i	$-0.708171\pi$
$257$	−10.1642	+	3.30254i	−0.634025	+	0.206007i	−0.0256675	+	0.999671i	$0.508171\pi$
$258$	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	−0.833912	−	0.551897i	$-0.813904\pi$
$269$	−9.29490	+	6.75314i	−0.566720	+	0.411746i	0.267192	+	0.963643i	$0.413904\pi$
$270$	−7.47630	−	22.8327i	−0.454993	−	1.38956i
$271$	−4.16837	−	12.8289i	−0.253210	−	0.779301i	−0.994177	−	0.107760i	$-0.965632\pi$
$271$	−4.16837	−	12.8289i	−0.253210	−	0.779301i	0.740967	−	0.671542i	$-0.234368\pi$
$272$	−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	$-0.685859\pi$
$277$	6.86646	−	9.45088i	0.412566	−	0.567848i	0.963842	+	0.266475i	$0.0858589\pi$
$278$	−38.9736	−	12.6633i	−2.33748	−	0.759494i
$279$	2.47214	+	7.60845i	0.148003	+	0.455506i
$280$	−14.4345	−	44.0832i	−0.862627	−	2.63448i
$281$	−0.413306	+	0.300285i	−0.0246558	+	0.0179135i	−0.600045	−	0.799966i	$-0.704851\pi$
$281$	−0.413306	+	0.300285i	−0.0246558	+	0.0179135i	0.575389	+	0.817880i	$0.304851\pi$
$282$	−12.6172	+	4.09957i	−0.751343	+	0.244126i
$283$	14.4047	+	4.68038i	0.856272	+	0.278220i	0.704071	−	0.710130i	$-0.251364\pi$
$283$	14.4047	+	4.68038i	0.856272	+	0.278220i	0.152201	+	0.988350i	$0.451364\pi$
$284$	−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
$290$	0.112350	+	49.3594i	0.00659744	+	2.89848i
$291$	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	$-0.629509\pi$
$293$	−3.01404	+	0.979321i	−0.176082	+	0.0572125i	0.219649	+	0.975579i	$0.429509\pi$
$294$	3.09017	−	9.51057i	0.180222	−	0.554667i
$295$	−13.3145	+	9.71993i	−0.775200	+	0.565916i
$296$	−6.51087			−0.378437
$297$		0			0
$298$		−	29.0024i		−	1.68007i
$299$		0			0
$300$	10.2444	+	13.9661i	0.591462	+	0.806333i
$301$	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
$305$	−1.34915	−	0.975531i	−0.0772521	−	0.0558587i
$306$	−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
$310$	−11.2236	−	15.3743i	−0.637458	−	0.873199i
$311$	1.69623	−	5.22047i	0.0961845	−	0.296026i	−0.891376	−	0.453265i	$-0.850259\pi$
$311$	1.69623	−	5.22047i	0.0961845	−	0.296026i	0.987561	+	0.157239i	$0.0502593\pi$
$312$		0			0
$313$	−12.8560	−	17.6947i	−0.726661	−	1.00016i	−0.999276	−	0.0380403i	$-0.987888\pi$
$313$	−12.8560	−	17.6947i	−0.726661	−	1.00016i	0.272615	−	0.962123i	$-0.412112\pi$
$314$	−49.9348	+	36.2798i	−2.81798	+	2.04739i
$315$	−0.0418259	−	18.3756i	−0.00235662	−	1.03535i
$316$	−1.69623	+	5.22047i	−0.0954206	+	0.293674i
$317$	19.3757	−	26.6683i	1.08825	−	1.49784i	0.238141	−	0.971231i	$-0.423462\pi$
$317$	19.3757	−	26.6683i	1.08825	−	1.49784i	0.850106	−	0.526612i	$-0.176538\pi$
$318$			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
$335$	−19.7737	+	6.47467i	−1.08035	+	0.353749i
$336$	−14.1490	+	10.2798i	−0.771891	+	0.560812i
$337$	−30.8775	+	10.0327i	−1.68201	+	0.546517i	−0.985299	−	0.170840i	$-0.945352\pi$
$337$	−30.8775	+	10.0327i	−1.68201	+	0.546517i	−0.696706	+	0.717356i	$0.745352\pi$
$338$	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
$345$	1.40362	−	0.00319487i	0.0755683	−	0.000172006i
$346$	−17.3851	+	12.6310i	−0.934627	+	0.679046i
$347$	−13.3216	−	18.3357i	−0.715143	−	0.984310i	−0.999671	−	0.0256427i	$-0.991837\pi$
$347$	−13.3216	−	18.3357i	−0.715143	−	0.984310i	0.284528	−	0.958668i	$-0.408163\pi$
$348$	28.8095	−	9.36076i	1.54435	−	0.501789i
$349$	4.78640	−	14.7310i	0.256210	−	0.788534i	−0.737379	−	0.675480i	$-0.763937\pi$
$349$	4.78640	−	14.7310i	0.256210	−	0.788534i	0.993589	−	0.113054i	$-0.0360634\pi$
$350$	13.7003	+	41.5209i	0.732309	+	2.21939i
$351$		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
$355$	18.3318	+	13.2552i	0.972949	+	0.703511i
$356$	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	0.837766	+	0.546029i	$0.183861\pi$
$359$	9.11264	+	28.0458i	0.480947	+	1.48020i	−0.356820	+	0.934173i	$0.616139\pi$
$360$	−18.6131	+	25.7418i	−0.980999	+	1.35671i
$361$	2.42705	+	1.76336i	0.127740	+	0.0928082i
$362$			60.8791i			3.19973i
$363$		0			0
$364$		0			0
$365$	9.13443	+	12.5125i	0.478118	+	0.654933i
$366$	−0.460165	+	1.41624i	−0.0240532	+	0.0740282i
$367$	−24.4809	+	7.95432i	−1.27789	+	0.415212i	−0.867837	−	0.496849i	$-0.834490\pi$
$367$	−24.4809	+	7.95432i	−1.27789	+	0.415212i	−0.410054	+	0.912061i	$0.634490\pi$
$368$	2.96754	+	4.08446i	0.154694	+	0.212917i
$369$	16.7827	−	12.1933i	0.873673	−	0.634760i
$370$	6.13701	−	0.0139689i	0.319048	−	0.000726208i
$371$	−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	−0.600752	−	0.799436i	$-0.705132\pi$
$379$	−0.507835	+	0.368964i	−0.0260857	+	0.0189524i	0.574666	+	0.818388i	$0.305132\pi$
$380$	−12.1693	−	37.1652i	−0.624273	−	1.90654i
$381$	−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	$-0.710256\pi$
$383$	6.40077	−	8.80990i	0.327064	−	0.450165i	0.940608	+	0.339496i	$0.110256\pi$
$384$	−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	−0.983047	−	0.183351i	$-0.941305\pi$
$389$	−5.82850	−	17.9383i	−0.295516	−	0.909506i	0.687531	−	0.726155i	$-0.258695\pi$
$390$		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
$400$	9.70767	−	30.3465i	0.485383	−	1.51733i
$401$	9.29490	−	6.75314i	0.464165	−	0.337236i	−0.330998	−	0.943631i	$-0.607385\pi$
$401$	9.29490	−	6.75314i	0.464165	−	0.337236i	0.795163	+	0.606396i	$0.207385\pi$
$402$	10.9388	+	15.0559i	0.545576	+	0.750921i
$403$		0			0
$404$	8.10666	−	24.9497i	0.403321	−	1.24129i
$405$	−6.76276	+	4.93699i	−0.336044	+	0.245321i
$406$	76.4674			3.79501
$407$		0			0
$408$		−	7.51811i		−	0.372202i
$409$	−22.2392	−	16.1577i	−1.09966	−	0.798947i	−0.118652	−	0.992936i	$-0.537857\pi$
$409$	−22.2392	−	16.1577i	−1.09966	−	0.798947i	−0.981004	+	0.193989i	$0.937857\pi$
$410$	−28.9218	+	39.9986i	−1.42835	+	1.97539i
$411$	−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
$415$	8.69093	−	12.0195i	0.426621	−	0.590013i
$416$		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	$0.310309\pi$
$420$	21.6722	−	15.8213i	1.05750	−	0.772001i
$421$	2.63000	−	8.09432i	0.128179	−	0.394493i	−0.866288	−	0.499545i	$-0.833501\pi$
$421$	2.63000	−	8.09432i	0.128179	−	0.394493i	0.994467	+	0.105051i	$0.0335007\pi$
$422$	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
$425$	−7.54616	−	2.41397i	−0.366043	−	0.117095i
$426$	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	−0.0397920	−	0.999208i	$-0.512670\pi$
$431$	−20.8102	−	15.1195i	−1.00239	−	0.728280i	−0.962600	+	0.270928i	$0.912670\pi$
$432$	25.7954	+	8.38144i	1.24108	+	0.403252i
$433$	27.7754	−	9.02478i	1.33480	−	0.433703i	0.447249	−	0.894409i	$-0.352404\pi$
$433$	27.7754	−	9.02478i	1.33480	−	0.433703i	0.887553	+	0.460706i	$0.152404\pi$
$434$	−23.8572	+	17.3333i	−1.14518	+	0.832024i
$435$	−14.7228	+	4.82079i	−0.705903	+	0.231139i
$436$	−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	$-0.128875\pi$
$443$	30.1240	+	9.78788i	1.43123	+	0.465036i	0.512081	+	0.858937i	$0.328875\pi$
$444$	−1.16385	−	3.58198i	−0.0552341	−	0.169993i
$445$	−0.954863	−	2.91616i	−0.0452649	−	0.138239i
$446$	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	0.711014	−	0.703178i	$-0.248236\pi$
$449$	5.55099	+	4.03303i	0.261968	+	0.190331i	−0.449046	+	0.893508i	$0.648236\pi$
$450$	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	$-0.361592\pi$
$457$	−12.2169	−	16.8151i	−0.571482	−	0.786577i	−0.992729	+	0.120368i	$0.961592\pi$
$458$	35.1181	−	11.4105i	1.64096	−	0.533180i
$459$	2.08418	−	6.41446i	0.0972814	−	0.299401i
$460$	−4.56722	−	6.25624i	−0.212948	−	0.291699i
$461$	−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
$465$	3.50063	−	4.84134i	0.162338	−	0.224512i
$466$	2.93230	+	9.02469i	0.135836	+	0.418061i
$467$	4.53799	+	6.24601i	0.209993	+	0.289031i	0.901001	−	0.433816i	$-0.142833\pi$
$467$	4.53799	+	6.24601i	0.209993	+	0.289031i	−0.691008	+	0.722847i	$0.742833\pi$
$468$		0			0
$469$	9.96076	+	30.6561i	0.459945	+	1.41557i
$470$	−30.3412	−	21.9388i	−1.39954	−	1.01196i
$471$	−15.6725	−	11.3867i	−0.722151	−	0.524673i
$472$		−	44.1485i		−	2.03210i
$473$		0			0
$474$	−2.51087			−0.115328
$475$	6.26687	+	18.9928i	0.287544	+	0.871449i
$476$	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	−0.481693	−	0.876340i	$-0.659978\pi$
$479$	4.44080	−	3.22643i	0.202905	−	0.147419i	0.684598	+	0.728921i	$0.259978\pi$
$480$	−7.27936	+	0.0165691i	−0.332256	+	0.000756271i
$481$		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	$-0.451652\pi$
$487$	−6.78159	−	2.20347i	−0.307303	−	0.0998488i	−0.458609	+	0.888638i	$0.651652\pi$
$488$	4.24054	−	1.37784i	0.191960	−	0.0623717i
$489$	2.22040	−	1.61321i	0.100410	−	0.0729520i
$490$	26.8217	−	8.78245i	1.21168	−	0.396750i
$491$	−2.01197	−	6.19221i	−0.0907990	−	0.279451i	0.895337	−	0.445389i	$-0.146935\pi$
$491$	−2.01197	−	6.19221i	−0.0907990	−	0.279451i	−0.986136	+	0.165939i	$0.946935\pi$
$492$	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	0.988773	+	0.149427i	$0.0477430\pi$
$499$	6.18034	+	19.0211i	0.276670	+	0.851503i	−0.712103	+	0.702075i	$0.752257\pi$
$500$	−14.7880	+	46.5931i	−0.661342	+	2.08371i
$501$	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	$-0.302233\pi$
$503$	12.8977	+	4.19072i	0.575080	+	0.186855i	−0.00701509	+	0.999975i	$0.502233\pi$
$504$	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	0.667861	+	0.744286i	$0.267210\pi$
$509$	−6.99235	+	21.5202i	−0.309930	+	0.953868i	−0.977791	+	0.209582i	$0.932790\pi$
$510$	0.0161299	+	7.08641i	0.000714243	+	0.313792i
$511$	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
$515$	−13.7017	−	18.7687i	−0.603767	−	0.827049i
$516$	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	−0.984047	−	0.177907i	$-0.943067\pi$
$521$	−6.67661	−	20.5485i	−0.292508	−	0.900246i	0.691540	−	0.722339i	$-0.256933\pi$
$522$	−30.7801	−	42.3652i	−1.34721	−	1.85428i
$523$	−17.0472	−	23.4635i	−0.745422	−	1.02599i	−0.998288	−	0.0584843i	$-0.981373\pi$
$523$	−17.0472	−	23.4635i	−0.745422	−	1.02599i	0.252866	−	0.967501i	$-0.418627\pi$
$524$	−3.70820	−	11.4127i	−0.161994	−	0.498565i
$525$	−11.0652	+	8.11652i	−0.482923	+	0.354234i
$526$	55.9936	+	40.6818i	2.44144	+	1.77381i
$527$		−	5.34363i		−	0.232772i
$528$		0			0
$529$	22.3723			0.972708
$530$	−46.0339	+	33.6059i	−1.99958	+	1.45975i
$531$	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
$535$	0.0337610	+	14.8324i	0.00145961	+	0.641259i
$536$	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	0.993341	−	0.115211i	$-0.0367544\pi$
$541$	27.6956	+	20.1221i	1.19073	+	0.865115i	0.197387	+	0.980326i	$0.436754\pi$
$542$	−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
$545$	6.95822	+	21.2505i	0.298057	+	0.910271i
$546$		0			0
$547$	27.5830	+	8.96224i	1.17936	+	0.383198i	0.832130	−	0.554581i	$-0.187122\pi$
$547$	27.5830	+	8.96224i	1.17936	+	0.383198i	0.347232	+	0.937779i	$0.387122\pi$
$548$	−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
$555$	0.599385	+	1.83053i	0.0254425	+	0.0777017i
$556$	−57.4226	+	41.7200i	−2.43526	+	1.76932i
$557$	−0.945984	+	0.307369i	−0.0400826	+	0.0130236i	−0.328990	−	0.944334i	$-0.606708\pi$
$557$	−0.945984	+	0.307369i	−0.0400826	+	0.0130236i	0.288907	+	0.957357i	$0.406708\pi$
$558$	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	$-0.930426\pi$
$563$	−11.1121	+	15.2945i	−0.468320	+	0.644588i	0.507888	+	0.861423i	$0.330426\pi$
$564$	−7.10067	+	21.8536i	−0.298992	+	0.920203i
$565$	0.00253126	+	1.11207i	0.000106491	+	0.0467851i
$566$	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	0.604026	+	0.796964i	$0.293562\pi$
$569$	−8.42239	+	25.9215i	−0.353085	+	1.08668i	−0.957111	+	0.289720i	$0.906438\pi$
$570$	14.4482	−	10.5475i	0.605167	−	0.441788i
$571$	−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
$575$	2.34304	+	3.19424i	0.0977115	+	0.133209i
$576$	1.73906	+	5.35228i	0.0724609	+	0.223012i
$577$	−12.8560	−	17.6947i	−0.535200	−	0.736640i	0.452712	−	0.891657i	$-0.350457\pi$
$577$	−12.8560	−	17.6947i	−0.535200	−	0.736640i	−0.987912	+	0.155017i	$0.950457\pi$
$578$	−21.4985	−	29.5902i	−0.894220	−	1.23079i
$579$	4.02394	+	12.3844i	0.167229	+	0.514679i
$580$	69.2796	+	50.0940i	2.87668	+	2.08004i
$581$	−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	$-0.275520\pi$
$587$	39.2542	−	12.7544i	1.62019	−	0.526432i	0.971987	+	0.235033i	$0.0755199\pi$
$588$	−10.1807	−	14.0126i	−0.419847	−	0.577869i
$589$	−10.9129	+	7.92871i	−0.449660	+	0.326697i
$590$	0.0947192	+	41.6134i	0.00389953	+	1.71320i
$591$	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	−0.391365	−	0.920235i	$-0.627997\pi$
$599$	8.88159	−	6.45285i	0.362892	−	0.263656i	0.754257	+	0.656579i	$0.227997\pi$
$600$	23.7226	−	0.107994i	0.968470	−	0.00440883i
$601$	11.8871	+	36.5846i	0.484884	+	1.49232i	0.832149	+	0.554552i	$0.187110\pi$
$601$	11.8871	+	36.5846i	0.484884	+	1.49232i	−0.347265	+	0.937767i	$0.612890\pi$
$602$	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	$-0.822396\pi$
$607$	−2.03615	+	2.80252i	−0.0826447	+	0.113751i	0.765693	+	0.643206i	$0.222396\pi$
$608$	15.6312	+	5.07889i	0.633930	+	0.205976i
$609$	7.41641	+	22.8254i	0.300528	+	0.924930i
$610$	−3.99409	+	1.30782i	−0.161716	+	0.0529519i
$611$		0			0
$612$	−15.6312	+	5.07889i	−0.631855	+	0.205302i
$613$	−4.13611	−	1.34390i	−0.167056	−	0.0542797i	0.224295	−	0.974521i	$-0.427992\pi$
$613$	−4.13611	−	1.34390i	−0.167056	−	0.0542797i	−0.391351	+	0.920242i	$0.627992\pi$
$614$	−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	−0.999649	−	0.0265037i	$-0.991563\pi$
$619$	−4.36234	+	13.4259i	−0.175337	+	0.539633i	0.824311	+	0.566137i	$0.191563\pi$
$620$	−32.9698	+	0.0750448i	−1.32410	+	0.00301387i
$621$	−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
$625$	7.50863	−	23.8458i	0.300345	−	0.953831i
$626$	−55.2119			−2.20671
$627$		0			0
$628$			106.907i			4.26606i
$629$	1.39379	+	1.01264i	0.0555739	+	0.0403768i
$630$	−37.5892	−	27.1797i	−1.49759	−	1.08286i
$631$	7.29465	+	22.4506i	0.290395	+	0.893745i	0.984729	+	0.174092i	$0.0556990\pi$
$631$	7.29465	+	22.4506i	0.290395	+	0.893745i	−0.694334	+	0.719653i	$0.744301\pi$
$632$	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
$635$	10.7670	−	14.8907i	0.427277	−	0.590921i
$636$	28.2980	+	20.5597i	1.12209	+	0.815245i
$637$		0			0
$638$		0			0
$639$	−24.0000			−0.949425
$640$	−18.7301	−	25.6568i	−0.740374	−	1.01417i
$641$	−7.84047	+	24.1305i	−0.309680	+	0.953096i	0.668210	+	0.743973i	$0.267061\pi$
$641$	−7.84047	+	24.1305i	−0.309680	+	0.953096i	−0.977889	+	0.209123i	$0.932939\pi$
$642$	12.6172	−	4.09957i	0.497961	−	0.161797i
$643$	−17.9242	−	24.6705i	−0.706861	−	0.972910i	−0.999859	−	0.0167972i	$-0.994653\pi$
$643$	−17.9242	−	24.6705i	−0.706861	−	0.972910i	0.292998	−	0.956113i	$-0.405347\pi$
$644$	−9.70820	+	7.05342i	−0.382557	+	0.277944i
$645$	−6.13701	+	0.0139689i	−0.241645	+	0.000550025i
$646$	4.94427	−	15.2169i	0.194530	−	0.598701i
$647$	−12.9205	+	17.7835i	−0.507957	+	0.699143i	−0.983573	−	0.180510i	$-0.942225\pi$
$647$	−12.9205	+	17.7835i	−0.507957	+	0.699143i	0.475616	+	0.879653i	$0.342225\pi$
$648$		−	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	$-0.805805\pi$
$653$	−29.2824	+	9.51444i	−1.14591	+	0.372329i	−0.326309	+	0.945263i	$0.605805\pi$
$654$	16.1803	−	11.7557i	0.632701	−	0.459684i
$655$	1.90973	+	5.83233i	0.0746192	+	0.227888i
$656$	−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
$665$	29.4455	−	9.64159i	1.14185	−	0.373885i
$666$	−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	$-0.683226\pi$
$673$	10.9388	−	15.0559i	0.421658	−	0.580363i	0.966013	+	0.258492i	$0.0832256\pi$
$674$	−25.3260	+	77.9453i	−0.975519	+	3.00234i
$675$	20.2701	+	6.48427i	0.780195	+	0.249580i
$676$	45.9842	−	33.4095i	1.76862	−	1.28498i
$677$	29.4375	+	40.5172i	1.13137	+	1.55720i	0.785434	+	0.618945i	$0.212440\pi$
$677$	29.4375	+	40.5172i	1.13137	+	1.55720i	0.345939	+	0.938257i	$0.387560\pi$
$678$	0.945984	−	0.307369i	0.0363303	−	0.0118044i
$679$	6.25255	−	19.2434i	0.239951	−	0.738493i
$680$	17.1376	−	12.5109i	0.657195	−	0.479770i
$681$	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
$685$	18.8064	−	26.0090i	0.718554	−	0.993754i
$686$	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
$690$	2.07612	−	2.87125i	0.0790365	−	0.109307i
$691$	−36.2936	−	26.3689i	−1.38068	−	1.00312i	−0.996817	−	0.0797273i	$-0.974595\pi$
$691$	−36.2936	−	26.3689i	−1.38068	−	1.00312i	−0.383858	−	0.923392i	$-0.625405\pi$
$692$			37.2203i			1.41490i
$693$		0			0
$694$	−57.2119			−2.17174
$695$	29.3184	−	21.4032i	1.11211	−	0.811869i
$696$	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
$700$	72.1294	+	23.0738i	2.72624	+	0.872107i
$701$	3.86607	−	11.8985i	0.146020	−	0.449402i	−0.851121	−	0.524969i	$-0.824077\pi$
$701$	3.86607	−	11.8985i	0.146020	−	0.449402i	0.997141	+	0.0755673i	$0.0240768\pi$
$702$		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	−0.162535	−	0.986703i	$-0.551967\pi$
$709$	19.3219	−	14.0382i	0.725648	−	0.527214i	0.888184	+	0.459488i	$0.151967\pi$
$710$	54.2702	−	17.7701i	2.03672	−	0.666901i
$711$	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	0.958980	+	0.283475i	$0.0914874\pi$
$719$	9.37883	+	28.8651i	0.349771	+	1.07649i	−0.609208	+	0.793010i	$0.708513\pi$
$720$	10.5186	+	32.1240i	0.392006	+	1.19719i
$721$	−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
$730$	39.1068	−	0.0890137i	1.44741	−	0.00329454i
$731$	−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	$-0.543819\pi$
$733$	9.04212	−	2.93796i	0.333978	−	0.108516i	0.471205	+	0.882024i	$0.343819\pi$
$734$	−20.0794	+	61.7980i	−0.741144	+	2.28101i
$735$	5.22292	+	7.15443i	0.192650	+	0.263895i
$736$	3.25544			0.119997
$737$		0			0
$738$		−	52.3663i		−	1.92763i
$739$	8.69253	+	6.31550i	0.319760	+	0.232319i	0.736073	−	0.676902i	$-0.236678\pi$
$739$	8.69253	+	6.31550i	0.319760	+	0.232319i	−0.416313	+	0.909221i	$0.636678\pi$
$740$	6.22836	−	8.61376i	0.228959	−	0.316648i
$741$		0			0
$742$	51.8996	+	71.4337i	1.90530	+	2.62241i
$743$	−6.69309	−	9.21225i	−0.245546	−	0.337965i	0.668399	−	0.743803i	$-0.266980\pi$
$743$	−6.69309	−	9.21225i	−0.245546	−	0.337965i	−0.913945	+	0.405838i	$0.866980\pi$
$744$	4.94427	+	15.2169i	0.181266	+	0.557879i
$745$	20.8183	+	15.0531i	0.762725	+	0.551504i
$746$	−23.8572	−	17.3333i	−0.873474	−	0.634616i
$747$			15.7359i			0.575748i
$748$		0			0
$749$	22.9783			0.839607
$750$	−22.3602	+	0.152689i	−0.816478	+	0.00557540i
$751$	8.45850	−	26.0326i	0.308655	−	0.949943i	−0.669633	−	0.742692i	$-0.733549\pi$
$751$	8.45850	−	26.0326i	0.308655	−	0.949943i	0.978288	−	0.207250i	$-0.0664515\pi$
$752$	40.2001	−	13.0618i	1.46595	−	0.476316i
$753$	10.2997	+	14.1763i	0.375342	+	0.516614i
$754$		0			0
$755$	27.3553	−	0.0622653i	0.995561	−	0.00226607i
$756$	−19.9215	+	61.3121i	−0.724538	+	2.22990i
$757$	23.3936	−	32.1985i	0.850253	−	1.17027i	−0.133554	−	0.991042i	$-0.542639\pi$
$757$	23.3936	−	32.1985i	0.850253	−	1.17027i	0.983807	−	0.179232i	$-0.0573612\pi$
$758$			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	0.953219	−	0.302280i	$-0.0977478\pi$
$761$	26.4909	+	19.2468i	0.960295	+	0.697695i	0.00707549	+	0.999975i	$0.497748\pi$
$762$	−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
$765$	7.98818	−	2.61563i	0.288813	−	0.0945684i
$766$	−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	$-0.297394\pi$
$773$	16.7533	+	5.44348i	0.602574	+	0.195788i	0.00818608	+	0.999966i	$0.497394\pi$
$774$	−6.41042	−	19.7293i	−0.230418	−	0.709153i
$775$	16.8612	−	0.0767585i	0.605673	−	0.00275725i
$776$	−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
$785$	−0.124448	−	54.6742i	−0.00444173	−	1.95140i
$786$	4.44080	−	3.22643i	0.158398	−	0.115083i
$787$	−8.90261	−	12.2534i	−0.317344	−	0.436786i	0.620310	−	0.784357i	$-0.287007\pi$
$787$	−8.90261	−	12.2534i	−0.317344	−	0.436786i	−0.937654	+	0.347570i	$0.887007\pi$
$788$	−35.3986	+	11.5017i	−1.26102	+	0.409731i
$789$	−6.71272	+	20.6596i	−0.238979	+	0.735502i
$790$	−4.17834	−	5.72355i	−0.148659	−	0.203635i
$791$	1.72281			0.0612562
$792$		0			0
$793$		0			0
$794$	−33.5654	−	24.3867i	−1.19119	−	0.865451i
$795$	−14.4960	−	10.4817i	−0.514121	−	0.371746i
$796$	−10.8089	−	33.2663i	−0.383110	−	1.17909i
$797$	−3.08649	−	4.24819i	−0.109329	−	0.150479i	0.750846	−	0.660477i	$-0.229646\pi$
$797$	−3.08649	−	4.24819i	−0.109329	−	0.150479i	−0.860175	+	0.509998i	$0.829646\pi$
$798$	−16.2892	−	22.4201i	−0.576631	−	0.793664i
$799$	−3.24804	−	9.99644i	−0.114907	−	0.353648i
$800$	−12.1513	−	16.5658i	−0.429614	−	0.585688i
$801$	2.63370	+	1.91350i	0.0930574	+	0.0676101i
$802$		−	29.0024i		−	1.02411i
$803$		0			0
$804$	32.2337			1.13679
$805$	4.95674	−	3.61855i	0.174702	−	0.127537i
$806$		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	−0.0149573	−	0.999888i	$-0.504761\pi$
$809$	26.4909	−	19.2468i	0.931371	−	0.676680i	0.946328	+	0.323208i	$0.104761\pi$
$810$	0.0481102	+	21.1365i	0.00169042	+	0.742660i
$811$	0.0722135	−	0.222250i	0.00253576	−	0.00780427i	−0.949781	−	0.312917i	$-0.898694\pi$
$811$	0.0722135	−	0.222250i	0.00253576	−	0.00780427i	0.952316	+	0.305112i	$0.0986940\pi$
$812$	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
$820$	26.6038	+	81.2484i	0.929046	+	2.83732i
$821$	5.56231	+	17.1190i	0.194126	+	0.597458i	0.999986	+	0.00535152i	$0.00170345\pi$
$821$	5.56231	+	17.1190i	0.194126	+	0.597458i	−0.805860	+	0.592106i	$0.798297\pi$
$822$	−27.3024	−	8.87110i	−0.952282	−	0.309415i
$823$	−32.9352	+	45.3315i	−1.14805	+	1.58016i	−0.399997	+	0.916516i	$0.630989\pi$
$823$	−32.9352	+	45.3315i	−1.14805	+	1.58016i	−0.748053	+	0.663639i	$0.769011\pi$
$824$	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	$-0.964466\pi$
$827$	−16.7005	+	22.9862i	−0.580732	+	0.799309i	0.413043	+	0.910711i	$0.364466\pi$
$828$	7.81561	+	2.53945i	0.271611	+	0.0882519i
$829$	6.28866	+	19.3545i	0.218414	+	0.672210i	0.998894	+	0.0470282i	$0.0149751\pi$
$829$	6.28866	+	19.3545i	0.218414	+	0.672210i	−0.780479	+	0.625182i	$0.785025\pi$
$830$	−11.6512	−	35.5830i	−0.404420	−	1.23510i
$831$	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	−0.882476	−	0.470357i	$-0.844125\pi$
$839$	3.12628	−	9.62169i	0.107931	−	0.332178i	0.990407	+	0.138180i	$0.0441251\pi$
$840$	−0.0836519	−	36.7511i	−0.00288626	−	1.26803i
$841$	−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
$845$	−23.4783	+	17.1397i	−0.807677	+	0.589625i
$846$	39.7228			1.36570
$847$		0			0
$848$		−	64.3432i		−	2.20955i
$849$	9.70820	+	7.05342i	0.333185	+	0.242073i
$850$	−16.1267	+	11.8292i	−0.553140	+	0.405740i
$851$	−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	−0.999885	−	0.0151473i	$-0.995178\pi$
$853$	−20.5994	−	28.3526i	−0.705310	−	0.970775i	0.294576	−	0.955628i	$-0.404822\pi$
$854$	2.01197	+	6.19221i	0.0688482	+	0.211893i
$855$	−17.1943	−	12.4327i	−0.588034	−	0.425190i
$856$	−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	$0.466723\pi$
$860$	19.9692	+	27.3540i	0.680943	+	0.932765i
$861$	−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	$-0.215578\pi$
$863$	−1.68941	−	2.32527i	−0.0575082	−	0.0791532i	−0.836802	+	0.547505i	$0.815578\pi$
$864$	14.1490	−	10.2798i	0.481359	−	0.349728i
$865$	−0.0433271	−	19.0351i	−0.00147317	−	0.647213i
$866$	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
$875$	−36.9151	−	11.7164i	−1.24796	−	0.396086i
$876$	−7.41641	−	22.8254i	−0.250577	−	0.771197i
$877$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$877$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$878$	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	$-0.533780\pi$
$883$	−23.0619	−	7.49326i	−0.776095	−	0.252168i	−0.670172	+	0.742206i	$0.733780\pi$
$884$		0			0
$885$	−12.4123	+	4.06427i	−0.417236	+	0.136619i
$886$	64.6862	−	46.9973i	2.17317	−	1.57890i
$887$	−26.0759	+	8.47258i	−0.875544	+	0.284482i	−0.712106	−	0.702072i	$-0.752258\pi$
$887$	−26.0759	+	8.47258i	−0.875544	+	0.284482i	−0.163438	+	0.986554i	$0.552258\pi$
$888$	−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
$895$	−28.7589	+	0.0654602i	−0.961304	+	0.00218809i
$896$	−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
$900$	−16.2504	−	49.2497i	−0.541681	−	1.64166i
$901$	−16.0000			−0.533037
$902$		0			0
$903$			9.50744i			0.316388i
$904$	−2.40946	−	1.75057i	−0.0801373	−	0.0582232i
$905$	−43.6998	−	31.5981i	−1.45263	−	1.05035i
$906$	−7.56083	−	23.2699i	−0.251192	−	0.773089i
$907$	11.6968	+	16.0992i	0.388385	+	0.534566i	0.957782	−	0.287497i	$-0.0928230\pi$
$907$	11.6968	+	16.0992i	0.388385	+	0.534566i	−0.569396	+	0.822063i	$0.692823\pi$
$908$	−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	0.989309	+	0.145834i	$0.0465865\pi$
$911$	43.2736	+	31.4401i	1.43372	+	1.04166i	0.444410	+	0.895824i	$0.353413\pi$
$912$			20.1947i			0.668713i
$913$		0			0
$914$	−52.4674			−1.73547
$915$	−0.777759	−	1.06538i	−0.0257119	−	0.0352205i
$916$	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	−0.143429	−	0.989661i	$-0.545813\pi$
$919$	22.8415	−	16.5953i	0.753473	−	0.547430i	0.896901	+	0.442231i	$0.145813\pi$
$920$	−10.6091	+	0.0241482i	−0.349773	+	0.000796143i
$921$	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	−0.677062	−	0.735926i	$-0.736747\pi$
$929$	−5.68071	+	4.12728i	−0.186378	+	0.135412i	0.490684	+	0.871338i	$0.336747\pi$
$930$	−4.69301	−	14.3325i	−0.153890	−	0.469982i
$931$	−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	−0.125589	+	0.992082i	$0.540082\pi$
$937$	−31.5381	+	43.4085i	−1.03031	+	1.41810i	−0.904717	+	0.426013i	$0.859918\pi$
$938$	77.3862	+	25.1443i	2.52675	+	0.820991i
$939$	−5.35489	−	16.4807i	−0.174750	−	0.537826i
$940$	−61.6316	+	20.1805i	−2.01020	+	0.658216i
$941$	−47.3011	+	34.3663i	−1.54197	+	1.12031i	−0.592888	+	0.805285i	$0.702012\pi$
$941$	−47.3011	+	34.3663i	−1.54197	+	1.12031i	−0.949084	+	0.315023i	$0.897988\pi$
$942$	−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
$950$	48.0863	+	15.3825i	1.56013	+	0.499075i
$951$	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	$-0.769149\pi$
$953$	−29.7554	+	9.66813i	−0.963873	+	0.313181i	−0.215533	+	0.976497i	$0.569149\pi$
$954$	18.6854	−	57.5079i	0.604964	−	1.86189i
$955$	34.9867	−	25.5412i	1.13214	−	0.826495i
$956$	64.4674			2.08502
$957$		0			0
$958$		−	13.8564i		−	0.447680i
$959$	−40.2266	−	29.2263i	−1.29898	−	0.943768i
$960$	2.46257	−	3.40571i	0.0794791	−	0.109919i
$961$	−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
$965$	−21.5341	+	29.7815i	−0.693207	+	0.958699i
$966$	−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
$970$	26.6290	−	19.4399i	0.855005	−	0.624176i
$971$	−2.81054	+	8.64995i	−0.0901945	+	0.277590i	−0.985972	−	0.166914i	$-0.946620\pi$
$971$	−2.81054	+	8.64995i	−0.0901945	+	0.277590i	0.895777	+	0.444504i	$0.146620\pi$
$972$	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	−0.000120920		1.00000i	$0.500038\pi$
$977$	−29.7298	+	40.9195i	−0.951140	+	1.30913i	−0.951019	+	0.309132i	$0.899962\pi$
$978$		−	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	$-0.729130\pi$
$983$	−23.5349	+	7.64695i	−0.750646	+	0.243900i	−0.0913870	+	0.995815i	$0.529130\pi$
$984$	33.5654	−	24.3867i	1.07003	−	0.777419i
$985$	18.0901	−	5.92338i	0.576397	−	0.188734i
$986$	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
$995$	5.56657	+	17.0004i	0.176472	+	0.538949i
$996$	−18.5898	+	13.5063i	−0.589040	+	0.427963i
$997$	2.06805	−	0.671952i	0.0654959	−	0.0212809i	−0.276086	−	0.961133i	$-0.589037\pi$
$997$	2.06805	−	0.671952i	0.0654959	−	0.0212809i	0.341582	+	0.939852i	$0.389037\pi$
$998$	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.444.4		16
5.4	even	2	inner	605.2.j.j.444.1		16
11.2	odd	10		605.2.j.i.269.4		16
11.3	even	5	inner	605.2.j.j.124.1		16
11.4	even	5	inner	605.2.j.j.9.4		16
11.5	even	5		605.2.b.c.364.4		4
11.6	odd	10		55.2.b.a.34.1	✓	4
11.7	odd	10		605.2.j.i.9.1		16
11.8	odd	10		605.2.j.i.124.4		16
11.9	even	5	inner	605.2.j.j.269.1		16
11.10	odd	2		605.2.j.i.444.1		16
33.17	even	10		495.2.c.a.199.4		4
44.39	even	10		880.2.b.h.529.2		4
55.4	even	10	inner	605.2.j.j.9.1		16
55.9	even	10	inner	605.2.j.j.269.4		16
55.14	even	10	inner	605.2.j.j.124.4		16
55.17	even	20		275.2.a.h.1.4		4
55.19	odd	10		605.2.j.i.124.1		16
55.24	odd	10		605.2.j.i.269.1		16
55.27	odd	20		3025.2.a.ba.1.1		4
55.28	even	20		275.2.a.h.1.1		4
55.29	odd	10		605.2.j.i.9.4		16
55.38	odd	20		3025.2.a.ba.1.4		4
55.39	odd	10		55.2.b.a.34.4	yes	4
55.49	even	10		605.2.b.c.364.1		4
55.54	odd	2		605.2.j.i.444.4		16
165.17	odd	20		2475.2.a.bi.1.1		4
165.83	odd	20		2475.2.a.bi.1.4		4
165.149	even	10		495.2.c.a.199.1		4
220.39	even	10		880.2.b.h.529.3		4
220.83	odd	20		4400.2.a.cc.1.3		4
220.127	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	11.6	odd	10
55.2.b.a.34.4	yes	4	55.39	odd	10
275.2.a.h.1.1		4	55.28	even	20
275.2.a.h.1.4		4	55.17	even	20
495.2.c.a.199.1		4	165.149	even	10
495.2.c.a.199.4		4	33.17	even	10
605.2.b.c.364.1		4	55.49	even	10
605.2.b.c.364.4		4	11.5	even	5
605.2.j.i.9.1		16	11.7	odd	10
605.2.j.i.9.4		16	55.29	odd	10
605.2.j.i.124.1		16	55.19	odd	10
605.2.j.i.124.4		16	11.8	odd	10
605.2.j.i.269.1		16	55.24	odd	10
605.2.j.i.269.4		16	11.2	odd	10
605.2.j.i.444.1		16	11.10	odd	2
605.2.j.i.444.4		16	55.54	odd	2
605.2.j.j.9.1		16	55.4	even	10	inner
605.2.j.j.9.4		16	11.4	even	5	inner
605.2.j.j.124.1		16	11.3	even	5	inner
605.2.j.j.124.4		16	55.14	even	10	inner
605.2.j.j.269.1		16	11.9	even	5	inner
605.2.j.j.269.4		16	55.9	even	10	inner
605.2.j.j.444.1		16	5.4	even	2	inner
605.2.j.j.444.4		16	1.1	even	1	trivial
880.2.b.h.529.2		4	44.39	even	10
880.2.b.h.529.3		4	220.39	even	10
2475.2.a.bi.1.1		4	165.17	odd	20
2475.2.a.bi.1.4		4	165.83	odd	20
3025.2.a.ba.1.1		4	55.27	odd	20
3025.2.a.ba.1.4		4	55.38	odd	20
4400.2.a.cc.1.2		4	220.127	odd	20
4400.2.a.cc.1.3		4	220.83	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} +(0.695822 + 2.12505i) 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} +(0.00403247 + 1.77160i) 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} +(7.89643 - 5.76460i) q^{20} +2.74456 q^{21} -0.792287i q^{23} +(-3.83843 - 2.78878i) q^{24} +(-4.03166 + 2.95731i) q^{25} +(-2.50184 - 3.44349i) q^{27} +(-8.90261 - 12.2534i) q^{28} +(2.70222 + 8.31657i) q^{29} +(3.62401 + 2.62041i) q^{30} +(-2.72823 - 1.98218i) q^{31} +4.10891i q^{32} +4.00000 q^{34} +(4.56722 + 6.25624i) q^{35} +(-3.20521 + 9.86463i) q^{36} +(1.03403 - 0.335976i) q^{37} +(-5.93507 - 8.16893i) q^{38} +(-0.0304791 - 13.3905i) 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} +(0.0574579 + 12.6216i) 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} +(7.36138 - 2.41040i) 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} +(19.5534 - 0.0445068i) 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} +(-3.76194 + 1.24129i) q^{75} -17.4891 q^{76} +(-1.01567 - 0.737928i) q^{79} +(-11.5466 - 8.34901i) 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} +(-2.07612 + 2.87125i) q^{85} +(7.07450 + 5.13992i) q^{86} +6.92820i q^{87} -1.37228 q^{89} +(-7.89541 - 10.8152i) q^{90} +(-3.29456 + 1.07047i) q^{92} +(-1.57045 - 2.16154i) q^{93} +(-13.5466 + 9.84221i) q^{94} +(8.94425 - 0.0203586i) 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

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