LMFDB - Embedded newform 475.2.n.a.39.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(39,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("475.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.n (of order $10$, degree $4$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.16
Character	$\chi$	$=$	475.39
Dual form			475.2.n.a.134.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06731 + 1.46902i) q^{2} +(1.88156 + 0.611355i) q^{3} +(-0.400851 + 1.23369i) q^{4} +(-0.796184 + 2.08952i) q^{5} +(1.11011 + 3.41656i) q^{6} -1.51173i q^{7} +(1.21373 - 0.394364i) q^{8} +(0.739455 + 0.537245i) q^{9} +O(q^{10})$	\(q+(1.06731 + 1.46902i) q^{2} +(1.88156 + 0.611355i) q^{3} +(-0.400851 + 1.23369i) q^{4} +(-0.796184 + 2.08952i) q^{5} +(1.11011 + 3.41656i) q^{6} -1.51173i q^{7} +(1.21373 - 0.394364i) q^{8} +(0.739455 + 0.537245i) q^{9} +(-3.91933 + 1.06055i) q^{10} +(-0.617978 + 0.448987i) q^{11} +(-1.50845 + 2.07620i) q^{12} +(-3.89825 + 5.36547i) q^{13} +(2.22076 - 1.61348i) q^{14} +(-2.77550 + 3.44480i) q^{15} +(3.97364 + 2.88702i) q^{16} +(5.50553 - 1.78885i) q^{17} +1.65968i q^{18} +(-0.309017 - 0.951057i) q^{19} +(-2.25867 - 1.81983i) q^{20} +(0.924202 - 2.84440i) q^{21} +(-1.31915 - 0.428617i) q^{22} +(2.24922 + 3.09578i) q^{23} +2.52480 q^{24} +(-3.73218 - 3.32728i) q^{25} -12.0426 q^{26} +(-2.42572 - 3.33872i) q^{27} +(1.86500 + 0.605977i) q^{28} +(3.05663 - 9.40735i) q^{29} +(-8.02282 - 0.400617i) q^{30} +(-1.47261 - 4.53222i) q^{31} +6.36632i q^{32} +(-1.43725 + 0.466992i) q^{33} +(8.50397 + 6.17850i) q^{34} +(3.15878 + 1.20361i) q^{35} +(-0.959206 + 0.696904i) q^{36} +(-0.374095 + 0.514898i) q^{37} +(1.06731 - 1.46902i) q^{38} +(-10.6150 + 7.71224i) q^{39} +(-0.142319 + 2.85010i) q^{40} +(-7.04416 - 5.11788i) q^{41} +(5.16490 - 1.67818i) q^{42} -6.61002i q^{43} +(-0.306195 - 0.942372i) q^{44} +(-1.71133 + 1.11736i) q^{45} +(-2.14717 + 6.60831i) q^{46} +(9.00036 + 2.92439i) q^{47} +(5.71163 + 7.86139i) q^{48} +4.71468 q^{49} +(0.904467 - 9.03391i) q^{50} +11.4526 q^{51} +(-5.05673 - 6.95999i) q^{52} +(-8.77849 - 2.85230i) q^{53} +(2.31567 - 7.12689i) q^{54} +(-0.446144 - 1.64875i) q^{55} +(-0.596171 - 1.83483i) q^{56} -1.97839i q^{57} +(17.0820 - 5.55028i) q^{58} +(-1.08856 - 0.790887i) q^{59} +(-3.13726 - 4.80497i) q^{60} +(-4.38712 + 3.18743i) q^{61} +(5.08622 - 7.00058i) q^{62} +(0.812168 - 1.11785i) q^{63} +(-1.40502 + 1.02080i) q^{64} +(-8.10754 - 12.4174i) q^{65} +(-2.22001 - 1.61293i) q^{66} +(10.4460 - 3.39410i) q^{67} +7.50919i q^{68} +(2.33941 + 7.19997i) q^{69} +(1.60326 + 5.92495i) q^{70} +(-3.81652 + 11.7460i) q^{71} +(1.10937 + 0.360455i) q^{72} +(5.65453 + 7.78280i) q^{73} -1.15567 q^{74} +(-4.98817 - 8.54217i) q^{75} +1.29718 q^{76} +(0.678746 + 0.934214i) q^{77} +(-22.6589 - 7.36233i) q^{78} +(-1.24836 + 3.84206i) q^{79} +(-9.19622 + 6.00439i) q^{80} +(-3.37033 - 10.3728i) q^{81} -15.8104i q^{82} +(-16.8126 + 5.46275i) q^{83} +(3.13865 + 2.28036i) q^{84} +(-0.645565 + 12.9282i) q^{85} +(9.71029 - 7.05494i) q^{86} +(11.5025 - 15.8318i) q^{87} +(-0.572993 + 0.788657i) q^{88} +(-3.83802 + 2.78849i) q^{89} +(-3.46794 - 1.32141i) q^{90} +(8.11113 + 5.89308i) q^{91} +(-4.72084 + 1.53390i) q^{92} -9.42793i q^{93} +(5.31016 + 16.3430i) q^{94} +(2.23329 + 0.111519i) q^{95} +(-3.89209 + 11.9786i) q^{96} +(-10.8821 - 3.53582i) q^{97} +(5.03202 + 6.92598i) q^{98} -0.698183 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9}+O(q^{10}) $ 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9	$ 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9} - 36 q^{10} + 20 q^{11} + 45 q^{12} - 10 q^{14} - 20 q^{16} - 15 q^{17} + 20 q^{19} + 12 q^{20} + 16 q^{21} + 15 q^{23} + 72 q^{24} + 41 q^{25} - 84 q^{26} + 15 q^{27} + 30 q^{28} - 24 q^{29} - 40 q^{30} + 8 q^{31} - 75 q^{33} - 24 q^{34} - 33 q^{35} - 32 q^{36} - 15 q^{37} - 30 q^{39} - 28 q^{40} + 13 q^{41} - 130 q^{42} - 24 q^{44} + 6 q^{45} + 30 q^{46} + 145 q^{48} - 28 q^{49} + 77 q^{50} - 36 q^{51} - 5 q^{52} - 10 q^{53} + 15 q^{54} - 8 q^{55} + 48 q^{56} - 60 q^{58} - 19 q^{59} - 110 q^{60} + 8 q^{61} + 110 q^{62} + 55 q^{63} + 16 q^{64} - 43 q^{65} - 17 q^{66} - 65 q^{67} - 42 q^{69} + 4 q^{70} + 18 q^{71} + 100 q^{73} + 22 q^{74} + 115 q^{75} + 64 q^{76} - 145 q^{78} - 16 q^{79} - 97 q^{80} + q^{81} - 70 q^{83} - 46 q^{84} - 16 q^{85} + 64 q^{86} + 10 q^{87} + 30 q^{88} + 4 q^{89} - 8 q^{90} + 16 q^{91} - 135 q^{92} + 38 q^{94} - 2 q^{95} + 50 q^{96} + 150 q^{97} + 130 q^{98} + 178 q^{99}+O(q^{100}) $ 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9 - 36 * q^10 + 20 * q^11 + 45 * q^12 - 10 * q^14 - 20 * q^16 - 15 * q^17 + 20 * q^19 + 12 * q^20 + 16 * q^21 + 15 * q^23 + 72 * q^24 + 41 * q^25 - 84 * q^26 + 15 * q^27 + 30 * q^28 - 24 * q^29 - 40 * q^30 + 8 * q^31 - 75 * q^33 - 24 * q^34 - 33 * q^35 - 32 * q^36 - 15 * q^37 - 30 * q^39 - 28 * q^40 + 13 * q^41 - 130 * q^42 - 24 * q^44 + 6 * q^45 + 30 * q^46 + 145 * q^48 - 28 * q^49 + 77 * q^50 - 36 * q^51 - 5 * q^52 - 10 * q^53 + 15 * q^54 - 8 * q^55 + 48 * q^56 - 60 * q^58 - 19 * q^59 - 110 * q^60 + 8 * q^61 + 110 * q^62 + 55 * q^63 + 16 * q^64 - 43 * q^65 - 17 * q^66 - 65 * q^67 - 42 * q^69 + 4 * q^70 + 18 * q^71 + 100 * q^73 + 22 * q^74 + 115 * q^75 + 64 * q^76 - 145 * q^78 - 16 * q^79 - 97 * q^80 + q^81 - 70 * q^83 - 46 * q^84 - 16 * q^85 + 64 * q^86 + 10 * q^87 + 30 * q^88 + 4 * q^89 - 8 * q^90 + 16 * q^91 - 135 * q^92 + 38 * q^94 - 2 * q^95 + 50 * q^96 + 150 * q^97 + 130 * q^98 + 178 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	1.06731	+	1.46902i	0.754701	+	1.03876i	0.997636	+	0.0687146i	$0.0218898\pi$
$2$	1.06731	+	1.46902i	0.754701	+	1.03876i	−0.242935	+	0.970043i	$0.578110\pi$
$3$	1.88156	+	0.611355i	1.08632	+	0.352966i	0.796823	−	0.604213i	$-0.206512\pi$
$3$	1.88156	+	0.611355i	1.08632	+	0.352966i	0.289495	+	0.957179i	$0.406512\pi$
$4$	−0.400851	+	1.23369i	−0.200425	+	0.616846i
$5$	−0.796184	+	2.08952i	−0.356064	+	0.934462i
$5$	−0.796184	+	2.08952i	−0.356064	+	0.934462i
$6$	1.11011	+	3.41656i	0.453199	+	1.39480i
$7$		−	1.51173i		−	0.571379i	−0.958322	−	0.285689i	$-0.907777\pi$
$7$		−	1.51173i		−	0.571379i	0.958322	−	0.285689i	$-0.0922226\pi$
$8$	1.21373	−	0.394364i	0.429118	−	0.139429i
$9$	0.739455	+	0.537245i	0.246485	+	0.179082i
$10$	−3.91933	+	1.06055i	−1.23940	+	0.335375i
$11$	−0.617978	+	0.448987i	−0.186327	+	0.135375i	−0.677039	−	0.735947i	$-0.736737\pi$
$11$	−0.617978	+	0.448987i	−0.186327	+	0.135375i	0.490711	+	0.871322i	$0.336737\pi$
$12$	−1.50845	+	2.07620i	−0.435451	+	0.599348i
$13$	−3.89825	+	5.36547i	−1.08118	+	1.48811i	−0.222962	+	0.974827i	$0.571573\pi$
$13$	−3.89825	+	5.36547i	−1.08118	+	1.48811i	−0.858217	+	0.513288i	$0.828427\pi$
$14$	2.22076	−	1.61348i	0.593524	−	0.431220i
$15$	−2.77550	+	3.44480i	−0.716632	+	0.889444i
$16$	3.97364	+	2.88702i	0.993409	+	0.721754i
$17$	5.50553	−	1.78885i	1.33529	−	0.433861i	0.447569	−	0.894249i	$-0.352290\pi$
$17$	5.50553	−	1.78885i	1.33529	−	0.433861i	0.887718	+	0.460388i	$0.152290\pi$
$18$			1.65968i			0.391191i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$20$	−2.25867	−	1.81983i	−0.505055	−	0.406927i
$21$	0.924202	−	2.84440i	0.201677	−	0.620699i
$22$	−1.31915	−	0.428617i	−0.281243	−	0.0913814i
$23$	2.24922	+	3.09578i	0.468994	+	0.645515i	0.976344	−	0.216225i	$-0.0693745\pi$
$23$	2.24922	+	3.09578i	0.468994	+	0.645515i	−0.507349	+	0.861741i	$0.669375\pi$
$24$	2.52480			0.515372
$25$	−3.73218	−	3.32728i	−0.746437	−	0.665456i
$26$	−12.0426			−2.36176
$27$	−2.42572	−	3.33872i	−0.466830	−	0.642537i
$28$	1.86500	+	0.605977i	0.352453	+	0.114519i
$29$	3.05663	−	9.40735i	0.567603	−	1.74690i	−0.0924857	−	0.995714i	$-0.529481\pi$
$29$	3.05663	−	9.40735i	0.567603	−	1.74690i	0.660089	−	0.751188i	$-0.270519\pi$
$30$	−8.02282	−	0.400617i	−1.46476	−	0.0731424i
$31$	−1.47261	−	4.53222i	−0.264488	−	0.814012i	−0.991811	−	0.127716i	$-0.959236\pi$
$31$	−1.47261	−	4.53222i	−0.264488	−	0.814012i	0.727322	−	0.686296i	$-0.240764\pi$
$32$			6.36632i			1.12542i
$33$	−1.43725	+	0.466992i	−0.250194	+	0.0812928i
$34$	8.50397	+	6.17850i	1.45842	+	1.05960i
$35$	3.15878	+	1.20361i	0.533932	+	0.203448i
$36$	−0.959206	+	0.696904i	−0.159868	+	0.116151i
$37$	−0.374095	+	0.514898i	−0.0615009	+	0.0846487i	−0.838660	−	0.544656i	$-0.816660\pi$
$37$	−0.374095	+	0.514898i	−0.0615009	+	0.0846487i	0.777159	+	0.629305i	$0.216660\pi$
$38$	1.06731	−	1.46902i	0.173140	−	0.238307i
$39$	−10.6150	+	7.71224i	−1.69976	+	1.23495i
$40$	−0.142319	+	2.85010i	−0.0225026	+	0.450640i
$41$	−7.04416	−	5.11788i	−1.10011	−	0.799278i	−0.119034	−	0.992890i	$-0.537980\pi$
$41$	−7.04416	−	5.11788i	−1.10011	−	0.799278i	−0.981078	+	0.193612i	$0.937980\pi$
$42$	5.16490	−	1.67818i	0.796962	−	0.258949i
$43$		−	6.61002i		−	1.00802i	−0.863698	−	0.504010i	$-0.831858\pi$
$43$		−	6.61002i		−	1.00802i	0.863698	−	0.504010i	$-0.168142\pi$
$44$	−0.306195	−	0.942372i	−0.0461606	−	0.142068i
$45$	−1.71133	+	1.11736i	−0.255109	+	0.166566i
$46$	−2.14717	+	6.60831i	−0.316583	+	0.974343i
$47$	9.00036	+	2.92439i	1.31284	+	0.426567i	0.880029	−	0.474919i	$-0.157523\pi$
$47$	9.00036	+	2.92439i	1.31284	+	0.426567i	0.432808	+	0.901486i	$0.357523\pi$
$48$	5.71163	+	7.86139i	0.824403	+	1.13469i
$49$	4.71468			0.673526
$50$	0.904467	−	9.03391i	0.127911	−	1.27759i
$51$	11.4526			1.60368
$52$	−5.05673	−	6.95999i	−0.701242	−	0.965177i
$53$	−8.77849	−	2.85230i	−1.20582	−	0.391794i	−0.363920	−	0.931430i	$-0.618562\pi$
$53$	−8.77849	−	2.85230i	−1.20582	−	0.391794i	−0.841898	+	0.539636i	$0.818562\pi$
$54$	2.31567	−	7.12689i	0.315122	−	0.969847i
$55$	−0.446144	−	1.64875i	−0.0601580	−	0.222318i
$56$	−0.596171	−	1.83483i	−0.0796667	−	0.245189i
$57$		−	1.97839i		−	0.262044i
$58$	17.0820	−	5.55028i	2.24298	−	0.728787i
$59$	−1.08856	−	0.790887i	−0.141719	−	0.102965i	0.514667	−	0.857390i	$-0.327916\pi$
$59$	−1.08856	−	0.790887i	−0.141719	−	0.102965i	−0.656386	+	0.754425i	$0.727916\pi$
$60$	−3.13726	−	4.80497i	−0.405019	−	0.620319i
$61$	−4.38712	+	3.18743i	−0.561713	+	0.408108i	−0.832085	−	0.554648i	$-0.812853\pi$
$61$	−4.38712	+	3.18743i	−0.561713	+	0.408108i	0.270373	+	0.962756i	$0.412853\pi$
$62$	5.08622	−	7.00058i	0.645951	−	0.889075i
$63$	0.812168	−	1.11785i	0.102324	−	0.140836i
$64$	−1.40502	+	1.02080i	−0.175627	+	0.127600i
$65$	−8.10754	−	12.4174i	−1.00562	−	1.54018i
$66$	−2.22001	−	1.61293i	−0.273265	−	0.198539i
$67$	10.4460	−	3.39410i	1.27618	−	0.414655i	0.408945	−	0.912559i	$-0.365897\pi$
$67$	10.4460	−	3.39410i	1.27618	−	0.414655i	0.867232	+	0.497904i	$0.165897\pi$
$68$			7.50919i			0.910623i
$69$	2.33941	+	7.19997i	0.281632	+	0.866774i
$70$	1.60326	+	5.92495i	0.191626	+	0.708167i
$71$	−3.81652	+	11.7460i	−0.452938	+	1.39400i	0.420602	+	0.907245i	$0.361819\pi$
$71$	−3.81652	+	11.7460i	−0.452938	+	1.39400i	−0.873539	+	0.486754i	$0.838181\pi$
$72$	1.10937	+	0.360455i	0.130740	+	0.0424801i
$73$	5.65453	+	7.78280i	0.661813	+	0.910908i	0.999540	−	0.0303367i	$-0.00965795\pi$
$73$	5.65453	+	7.78280i	0.661813	+	0.910908i	−0.337727	+	0.941244i	$0.609658\pi$
$74$	−1.15567			−0.134344
$75$	−4.98817	−	8.54217i	−0.575984	−	0.986364i
$76$	1.29718			0.148797
$77$	0.678746	+	0.934214i	0.0773503	+	0.106464i
$78$	−22.6589	−	7.36233i	−2.56562	−	0.833620i
$79$	−1.24836	+	3.84206i	−0.140452	+	0.432266i	−0.996398	−	0.0847987i	$-0.972975\pi$
$79$	−1.24836	+	3.84206i	−0.140452	+	0.432266i	0.855946	+	0.517065i	$0.172975\pi$
$80$	−9.19622	+	6.00439i	−1.02817	+	0.671312i
$81$	−3.37033	−	10.3728i	−0.374481	−	1.15254i
$82$		−	15.8104i		−	1.74597i
$83$	−16.8126	+	5.46275i	−1.84542	+	0.599615i	−0.847832	+	0.530264i	$0.822093\pi$
$83$	−16.8126	+	5.46275i	−1.84542	+	0.599615i	−0.997592	+	0.0693507i	$0.977907\pi$
$84$	3.13865	+	2.28036i	0.342455	+	0.248808i
$85$	−0.645565	+	12.9282i	−0.0700213	+	1.40226i
$86$	9.71029	−	7.05494i	1.04709	−	0.760753i
$87$	11.5025	−	15.8318i	1.23319	−	1.69735i
$88$	−0.572993	+	0.788657i	−0.0610813	+	0.0840712i
$89$	−3.83802	+	2.78849i	−0.406829	+	0.295579i	−0.772317	−	0.635237i	$-0.780902\pi$
$89$	−3.83802	+	2.78849i	−0.406829	+	0.295579i	0.365488	+	0.930816i	$0.380902\pi$
$90$	−3.46794	−	1.32141i	−0.365553	−	0.139289i
$91$	8.11113	+	5.89308i	0.850277	+	0.617763i
$92$	−4.72084	+	1.53390i	−0.492182	+	0.159920i
$93$		−	9.42793i		−	0.977631i
$94$	5.31016	+	16.3430i	0.547701	+	1.68565i
$95$	2.23329	+	0.111519i	0.229130	+	0.0114416i
$96$	−3.89209	+	11.9786i	−0.397234	+	1.22256i
$97$	−10.8821	−	3.53582i	−1.10491	−	0.359008i	−0.300922	−	0.953649i	$-0.597294\pi$
$97$	−10.8821	−	3.53582i	−1.10491	−	0.359008i	−0.803992	+	0.594640i	$0.797294\pi$
$98$	5.03202	+	6.92598i	0.508311	+	0.699630i
$99$	−0.698183			−0.0701701
$100$	5.60089	−	3.27062i	0.560089	−	0.327062i
$101$	−8.70986			−0.866663			−0.433332	−	0.901235i	$-0.642662\pi$
$101$	−8.70986			−0.866663			−0.433332	+	0.901235i	$0.642662\pi$
$102$	12.2235	+	16.8241i	1.21030	+	1.66584i
$103$	10.0099	+	3.25240i	0.986302	+	0.320469i	0.757379	−	0.652976i	$-0.226480\pi$
$103$	10.0099	+	3.25240i	0.986302	+	0.320469i	0.228923	+	0.973445i	$0.426480\pi$
$104$	−2.61546	+	8.04956i	−0.256467	+	0.789324i
$105$	5.20760	+	4.19580i	0.508209	+	0.409469i
$106$	−5.17925	−	15.9401i	−0.503054	−	1.54824i
$107$		−	4.06660i		−	0.393133i	−0.980490	−	0.196567i	$-0.937021\pi$
$107$		−	4.06660i		−	0.393133i	0.980490	−	0.196567i	$-0.0629792\pi$
$108$	5.09130	−	1.65426i	0.489911	−	0.159182i
$109$	5.00135	+	3.63369i	0.479042	+	0.348045i	0.800955	−	0.598725i	$-0.204326\pi$
$109$	5.00135	+	3.63369i	0.479042	+	0.348045i	−0.321913	+	0.946769i	$0.604326\pi$
$110$	1.94589	−	2.41513i	0.185533	−	0.230273i
$111$	−1.01867	+	0.740105i	−0.0966877	+	0.0702477i
$112$	4.36438	−	6.00705i	0.412395	−	0.567613i
$113$	9.15627	−	12.6025i	0.861349	−	1.18555i	−0.119897	−	0.992786i	$-0.538256\pi$
$113$	9.15627	−	12.6025i	0.861349	−	1.18555i	0.981246	−	0.192759i	$-0.0617437\pi$
$114$	2.90630	−	2.11155i	0.272200	−	0.197765i
$115$	−8.25949	+	2.23497i	−0.770201	+	0.208412i
$116$	10.3805	+	7.54189i	0.963807	+	0.700247i
$117$	−5.76515	+	1.87321i	−0.532989	+	0.173178i
$118$		−	2.44325i		−	0.224919i
$119$	−2.70426	−	8.32285i	−0.247899	−	0.762955i
$120$	−2.01020	+	5.27561i	−0.183506	+	0.481595i
$121$	−3.21888	+	9.90669i	−0.292625	+	0.900608i
$122$	−9.36482	−	3.04281i	−0.847851	−	0.275483i
$123$	−10.1251	−	13.9361i	−0.912954	−	1.25657i
$124$	6.18167			0.555130
$125$	9.92392	−	5.14934i	0.887623	−	0.460571i
$126$	2.50899			0.223518
$127$	−4.55683	−	6.27194i	−0.404354	−	0.556545i	0.557476	−	0.830193i	$-0.311770\pi$
$127$	−4.55683	−	6.27194i	−0.404354	−	0.556545i	−0.961830	+	0.273648i	$0.911770\pi$
$128$	9.11030	+	2.96012i	0.805244	+	0.261640i
$129$	4.04107	−	12.4371i	0.355797	−	1.09503i
$130$	9.58816	−	25.1633i	0.840937	−	2.20697i
$131$	1.34486	+	4.13904i	0.117501	+	0.361629i	0.992460	−	0.122566i	$-0.0391123\pi$
$131$	1.34486	+	4.13904i	0.117501	+	0.361629i	−0.874960	+	0.484196i	$0.839112\pi$
$132$		−	1.96032i		−	0.170624i
$133$	−1.43774	+	0.467149i	−0.124668	+	0.0405070i
$134$	16.1351	+	11.7228i	1.39386	+	1.01270i
$135$	8.90764	−	2.41036i	0.766647	−	0.207451i
$136$	5.97676	−	4.34237i	0.512503	−	0.372355i
$137$	2.75204	−	3.78785i	0.235122	−	0.323618i	−0.675109	−	0.737718i	$-0.735903\pi$
$137$	2.75204	−	3.78785i	0.235122	−	0.323618i	0.910232	+	0.414100i	$0.135903\pi$
$138$	−8.08005	+	11.1212i	−0.687820	+	0.946703i
$139$	−8.67387	+	6.30193i	−0.735708	+	0.534523i	−0.891364	−	0.453288i	$-0.850251\pi$
$139$	−8.67387	+	6.30193i	−0.735708	+	0.534523i	0.155656	+	0.987811i	$0.450251\pi$
$140$	−2.75109	+	3.41450i	−0.232509	+	0.288578i
$141$	15.1469	+	11.0048i	1.27560	+	0.926774i
$142$	−21.3286	+	6.93009i	−1.78986	+	0.581560i
$143$		−	5.06601i		−	0.423641i
$144$	1.38729	+	4.26963i	0.115607	+	0.355803i
$145$	17.2232	+	13.8769i	1.43031	+	1.15241i
$146$	−5.39799	+	16.6133i	−0.446741	+	1.37493i
$147$	8.87095	+	2.88235i	0.731664	+	0.237732i
$148$	−0.485269	−	0.667916i	−0.0398889	−	0.0549023i
$149$	−6.11999			−0.501369			−0.250685	−	0.968069i	$-0.580656\pi$
$149$	−6.11999			−0.501369			−0.250685	+	0.968069i	$0.580656\pi$
$150$	7.22473	−	16.4449i	0.589897	−	1.34272i
$151$	17.6672			1.43773			0.718867	−	0.695147i	$-0.244661\pi$
$151$	17.6672			1.43773			0.718867	+	0.695147i	$0.244661\pi$
$152$	−0.750125	−	1.03246i	−0.0608432	−	0.0837435i
$153$	5.03214	+	1.63504i	0.406825	+	0.132185i
$154$	−0.647951	+	1.99419i	−0.0522134	+	0.160696i
$155$	10.6426	+	0.531438i	0.854837	+	0.0426861i
$156$	−5.25950	−	16.1871i	−0.421097	−	1.29600i
$157$			8.86986i			0.707892i	0.935266	+	0.353946i	$0.115160\pi$
$157$			8.86986i			0.707892i	−0.935266	+	0.353946i	$0.884840\pi$
$158$	−6.97647	+	2.26679i	−0.555018	+	0.180336i
$159$	−14.7735	−	10.7336i	−1.17161	−	0.851226i
$160$	−13.3026	−	5.06876i	−1.05166	−	0.400721i
$161$	4.67998	−	3.40020i	0.368834	−	0.267974i
$162$	11.6407	−	16.0221i	0.914582	−	1.25881i
$163$	−13.2593	+	18.2499i	−1.03855	+	1.42944i	−0.140217	+	0.990121i	$0.544780\pi$
$163$	−13.2593	+	18.2499i	−1.03855	+	1.42944i	−0.898331	+	0.439319i	$0.855220\pi$
$164$	9.13754	−	6.63881i	0.713522	−	0.518404i
$165$	0.168529	−	3.37498i	0.0131199	−	0.262742i
$166$	−25.9692	−	18.8677i	−2.01560	−	1.46442i
$167$	−6.95605	+	2.26016i	−0.538275	+	0.174896i	−0.565523	−	0.824732i	$-0.691326\pi$
$167$	−6.95605	+	2.26016i	−0.538275	+	0.174896i	0.0272478	+	0.999629i	$0.491326\pi$
$168$		−	3.81680i		−	0.294473i
$169$	−9.57478	−	29.4681i	−0.736521	−	2.26678i
$170$	−19.6808	+	12.8500i	−1.50945	+	0.985549i
$171$	0.282447	−	0.869281i	0.0215992	−	0.0664756i
$172$	8.15473	+	2.64963i	0.621792	+	0.202033i
$173$	5.12513	+	7.05414i	0.389656	+	0.536316i	0.958110	−	0.286399i	$-0.0924583\pi$
$173$	5.12513	+	7.05414i	0.389656	+	0.536316i	−0.568454	+	0.822715i	$0.692458\pi$
$174$	35.5340			2.69382
$175$	−5.02994	+	5.64204i	−0.380228	+	0.426498i
$176$	−3.75185			−0.282807
$177$	−1.56468	−	2.15360i	−0.117609	−	0.161874i
$178$	−8.19271	−	2.66197i	−0.614069	−	0.199523i
$179$	0.541725	−	1.66726i	0.0404904	−	0.124617i	−0.928768	−	0.370661i	$-0.879131\pi$
$179$	0.541725	−	1.66726i	0.0404904	−	0.124617i	0.969258	+	0.246045i	$0.0791310\pi$
$180$	−0.692491	−	2.55914i	−0.0516152	−	0.190747i
$181$	2.58947	+	7.96956i	0.192474	+	0.592373i	0.999997	+	0.00253684i	$0.000807504\pi$
$181$	2.58947	+	7.96956i	0.192474	+	0.592373i	−0.807523	+	0.589836i	$0.799192\pi$
$182$			18.2052i			1.34946i
$183$	−10.2033	+	3.31524i	−0.754247	+	0.245070i
$184$	3.95081	+	2.87043i	0.291257	+	0.211611i
$185$	−0.778041	−	1.19163i	−0.0572027	−	0.0876106i
$186$	13.8499	−	10.0625i	1.01552	−	0.737819i
$187$	−2.59912	+	3.57739i	−0.190067	+	0.261604i
$188$	−7.21560	+	9.93143i	−0.526252	+	0.724324i
$189$	−5.04723	+	3.66703i	−0.367132	+	0.266737i
$190$	2.21978	+	3.39978i	0.161040	+	0.246646i
$191$	−0.554339	−	0.402751i	−0.0401106	−	0.0291420i	0.567549	−	0.823339i	$-0.307892\pi$
$191$	−0.554339	−	0.402751i	−0.0401106	−	0.0291420i	−0.607660	+	0.794197i	$0.707892\pi$
$192$	−3.26769	+	1.06174i	−0.235825	+	0.0766243i
$193$			10.6285i			0.765055i	0.923944	+	0.382527i	$0.124946\pi$
$193$			10.6285i			0.765055i	−0.923944	+	0.382527i	$0.875054\pi$
$194$	−6.42040	−	19.7599i	−0.460958	−	1.41868i
$195$	−7.66340	−	28.3206i	−0.548787	−	2.02808i
$196$	−1.88988	+	5.81647i	−0.134992	+	0.415462i
$197$	−15.9641	−	5.18704i	−1.13739	−	0.369562i	−0.321012	−	0.947075i	$-0.604023\pi$
$197$	−15.9641	−	5.18704i	−1.13739	−	0.369562i	−0.816381	+	0.577513i	$0.804023\pi$
$198$	−0.745177	−	1.02565i	−0.0529574	−	0.0728897i
$199$	2.49959			0.177191			0.0885956	−	0.996068i	$-0.471762\pi$
$199$	2.49959			0.177191			0.0885956	+	0.996068i	$0.471762\pi$
$200$	−5.84202	−	2.56658i	−0.413093	−	0.181484i
$201$	21.7297			1.53269
$202$	−9.29611	−	12.7950i	−0.654072	−	0.900253i
$203$	−14.2213	−	4.62080i	−0.998143	−	0.324316i
$204$	−4.59078	+	14.1290i	−0.321419	+	0.989226i
$205$	16.3023	−	10.6441i	1.13861	−	0.743418i
$206$	5.90576	+	18.1761i	0.411474	+	1.26639i
$207$			3.49757i			0.243098i
$208$	−30.9804	+	10.0661i	−2.14811	+	0.697962i
$209$	0.617978	+	0.448987i	0.0427464	+	0.0310571i
$210$	−0.605624	+	12.1283i	−0.0417920	+	0.836933i
$211$	−2.51552	+	1.82763i	−0.173175	+	0.125819i	−0.670997	−	0.741460i	$-0.734134\pi$
$211$	−2.51552	+	1.82763i	−0.173175	+	0.125819i	0.497821	+	0.867280i	$0.334134\pi$
$212$	7.03773	−	9.68660i	0.483353	−	0.665279i
$213$	−14.3620	+	19.7676i	−0.984069	+	1.35445i
$214$	5.97394	−	4.34032i	0.408370	−	0.296698i
$215$	13.8118	+	5.26279i	0.941955	+	0.358919i
$216$	−4.26084	−	3.09568i	−0.289913	−	0.210634i
$217$	−6.85148	+	2.22618i	−0.465109	+	0.151123i
$218$			11.2254i			0.760278i
$219$	5.88128	+	18.1007i	0.397420	+	1.22313i
$220$	2.21289	+	0.110500i	0.149193	+	0.00744992i
$221$	−11.8638	+	36.5132i	−0.798049	+	2.45614i
$222$	−2.17447	−	0.706527i	−0.145941	−	0.0474190i
$223$	−5.65349	−	7.78135i	−0.378585	−	0.521078i	0.576624	−	0.817010i	$-0.304370\pi$
$223$	−5.65349	−	7.78135i	−0.378585	−	0.521078i	−0.955209	+	0.295932i	$0.904370\pi$
$224$	9.62414			0.643040
$225$	−0.972214	−	4.46547i	−0.0648143	−	0.297698i
$226$	28.2860			1.88156
$227$	−8.89022	−	12.2363i	−0.590064	−	0.812154i	0.404689	−	0.914454i	$-0.367380\pi$
$227$	−8.89022	−	12.2363i	−0.590064	−	0.812154i	−0.994754	+	0.102300i	$0.967380\pi$
$228$	2.44072	+	0.793038i	0.161641	+	0.0525202i
$229$	−3.46820	+	10.6740i	−0.229185	+	0.705360i	0.768655	+	0.639664i	$0.220927\pi$
$229$	−3.46820	+	10.6740i	−0.229185	+	0.705360i	−0.997840	+	0.0656954i	$0.979073\pi$
$230$	−12.0987	−	9.74799i	−0.797762	−	0.642763i
$231$	0.705964	+	2.17273i	0.0464490	+	0.142955i
$232$		−	12.6234i		−	0.828767i
$233$	13.9867	−	4.54457i	0.916302	−	0.297725i	0.187353	−	0.982293i	$-0.440009\pi$
$233$	13.9867	−	4.54457i	0.916302	−	0.297725i	0.728949	+	0.684568i	$0.240009\pi$
$234$	−8.90499	−	6.46985i	−0.582137	−	0.422948i
$235$	−13.2765	+	16.4781i	−0.866065	+	1.07491i
$236$	1.41206	−	1.02592i	0.0919174	−	0.0667819i
$237$	−4.69773	+	6.46587i	−0.305150	+	0.420003i
$238$	9.34020	−	12.8557i	0.605435	−	0.833310i
$239$	−5.88512	+	4.27579i	−0.380677	+	0.276578i	−0.761624	−	0.648019i	$-0.775598\pi$
$239$	−5.88512	+	4.27579i	−0.380677	+	0.276578i	0.380948	+	0.924597i	$0.375598\pi$
$240$	−20.9740	+	5.67546i	−1.35387	+	0.366349i
$241$	13.8992	+	10.0984i	0.895326	+	0.650493i	0.937261	−	0.348628i	$-0.113352\pi$
$241$	13.8992	+	10.0984i	0.895326	+	0.650493i	−0.0419349	+	0.999120i	$0.513352\pi$
$242$	−17.9887	+	5.84489i	−1.15636	+	0.375724i
$243$		−	9.19687i		−	0.589980i
$244$	−2.17372	−	6.69003i	−0.139158	−	0.428286i
$245$	−3.75375	+	9.85142i	−0.239818	+	0.629384i
$246$	9.66577	−	29.7482i	0.616267	−	1.89667i
$247$	6.30749	+	2.04943i	0.401336	+	0.130402i
$248$	−3.57470	−	4.92015i	−0.226993	−	0.312430i
$249$	−34.9736			−2.21636
$250$	18.1564	+	9.08255i	1.14831	+	0.574431i
$251$	−2.61515			−0.165067			−0.0825334	−	0.996588i	$-0.526301\pi$
$251$	−2.61515			−0.165067			−0.0825334	+	0.996588i	$0.526301\pi$
$252$	1.05353	+	1.45006i	0.0663661	+	0.0913450i
$253$	−2.77994	−	0.903256i	−0.174773	−	0.0567872i
$254$	4.35009	−	13.3882i	0.272949	−	0.840050i
$255$	−9.11837	+	23.9304i	−0.571015	+	1.49858i
$256$	6.44836	+	19.8460i	0.403022	+	1.24037i
$257$		−	4.01230i		−	0.250280i	−0.992139	−	0.125140i	$-0.960062\pi$
$257$		−	4.01230i		−	0.250280i	0.992139	−	0.125140i	$-0.0399381\pi$
$258$	22.5835	−	7.33784i	1.40599	−	0.456834i
$259$	0.778385	+	0.565530i	0.0483665	+	0.0351403i
$260$	18.5691	−	5.02470i	1.15161	−	0.311619i
$261$	7.31430	−	5.31415i	0.452744	−	0.328938i
$262$	−4.64497	+	6.39326i	−0.286967	+	0.394977i
$263$	3.34619	−	4.60563i	0.206335	−	0.283995i	−0.693291	−	0.720658i	$-0.743840\pi$
$263$	3.34619	−	4.60563i	0.206335	−	0.283995i	0.899625	+	0.436663i	$0.143840\pi$
$264$	−1.56027	+	1.13360i	−0.0960280	+	0.0697684i
$265$	12.9492	−	16.0719i	0.795465	−	0.987287i
$266$	−2.22076	−	1.61348i	−0.136164	−	0.0989287i
$267$	−8.92622	+	2.90030i	−0.546276	+	0.177496i
$268$			14.2476i			0.870312i
$269$	−4.08111	−	12.5604i	−0.248829	−	0.765818i	−0.994983	−	0.100044i	$-0.968102\pi$
$269$	−4.08111	−	12.5604i	−0.248829	−	0.765818i	0.746154	−	0.665774i	$-0.231898\pi$
$270$	13.0481	+	10.5129i	0.794081	+	0.639797i
$271$	−7.77513	+	23.9294i	−0.472305	+	1.45361i	0.377252	+	0.926111i	$0.376869\pi$
$271$	−7.77513	+	23.9294i	−0.472305	+	1.45361i	−0.849558	+	0.527496i	$0.823131\pi$
$272$	27.0414	+	8.78629i	1.63963	+	0.532747i
$273$	11.6588	+	16.0470i	0.705622	+	0.971206i
$274$	8.50172			0.513608
$275$	3.80032	+	0.380484i	0.229168	+	0.0229441i
$276$	−9.82030			−0.591112
$277$	−7.80438	−	10.7418i	−0.468920	−	0.645413i	0.507409	−	0.861705i	$-0.330603\pi$
$277$	−7.80438	−	10.7418i	−0.468920	−	0.645413i	−0.976329	+	0.216293i	$0.930603\pi$
$278$	−18.5154	−	6.01601i	−1.11048	−	0.360816i
$279$	1.34599	−	4.14253i	0.0805822	−	0.248007i
$280$	4.30857	+	0.215147i	0.257486	+	0.0128575i
$281$	−4.78643	−	14.7311i	−0.285535	−	0.878785i	−0.986238	−	0.165332i	$-0.947130\pi$
$281$	−4.78643	−	14.7311i	−0.285535	−	0.878785i	0.700703	−	0.713453i	$-0.252870\pi$
$282$			33.9967i			2.02447i
$283$	−8.98670	+	2.91996i	−0.534204	+	0.173573i	−0.563682	−	0.825992i	$-0.690616\pi$
$283$	−8.98670	+	2.91996i	−0.534204	+	0.173573i	0.0294778	+	0.999565i	$0.490616\pi$
$284$	−12.9611	−	9.41682i	−0.769102	−	0.558786i
$285$	4.13388	+	1.57516i	0.244870	+	0.0933044i
$286$	7.44209	−	5.40700i	0.440060	−	0.319722i
$287$	−7.73683	+	10.6488i	−0.456691	+	0.628581i
$288$	−3.42028	+	4.70761i	−0.201542	+	0.277399i
$289$	13.3576	−	9.70483i	0.785739	−	0.570872i
$290$	−2.00299	+	40.1122i	−0.117620	+	2.35547i
$291$	−18.3137	−	13.3057i	−1.07357	−	0.779995i
$292$	−11.8682	+	3.85621i	−0.694534	+	0.225668i
$293$		−	18.6907i		−	1.09192i	−0.837810	−	0.545962i	$-0.816164\pi$
$293$		−	18.6907i		−	1.09192i	0.837810	−	0.545962i	$-0.183836\pi$
$294$	5.23380	+	16.1080i	0.305242	+	0.939437i
$295$	2.51927	−	1.64488i	0.146678	−	0.0957687i
$296$	−0.250993	+	0.772476i	−0.0145887	+	0.0448993i
$297$	2.99809	+	0.974137i	0.173967	+	0.0565252i
$298$	−6.53192	−	8.99042i	−0.378384	−	0.520801i
$299$	−25.3784			−1.46767
$300$	12.5379	−	2.72973i	0.723877	−	0.157601i
$301$	−9.99255			−0.575961
$302$	18.8563	+	25.9535i	1.08506	+	1.49346i
$303$	−16.3881	−	5.32482i	−0.941472	−	0.305903i
$304$	1.51779	−	4.67129i	0.0870514	−	0.267917i
$305$	−3.16724	−	11.7047i	−0.181356	−	0.670212i
$306$	2.96893	+	9.13744i	0.169723	+	0.522352i
$307$		−	14.4375i		−	0.823993i	−0.911186	−	0.411996i	$-0.864832\pi$
$307$		−	14.4375i		−	0.823993i	0.911186	−	0.411996i	$-0.135168\pi$
$308$	−1.42461	+	0.462883i	−0.0811746	+	0.0263752i
$309$	16.8458	+	12.2392i	0.958323	+	0.696262i
$310$	10.5783	+	16.2015i	0.600806	+	0.920184i
$311$	−12.4810	+	9.06794i	−0.707730	+	0.514196i	−0.882441	−	0.470424i	$-0.844101\pi$
$311$	−12.4810	+	9.06794i	−0.707730	+	0.514196i	0.174711	+	0.984620i	$0.444101\pi$
$312$	−9.84228	+	13.5467i	−0.557209	+	0.766933i
$313$	5.45082	−	7.50241i	0.308099	−	0.424061i	−0.626689	−	0.779270i	$-0.715590\pi$
$313$	5.45082	−	7.50241i	0.308099	−	0.424061i	0.934787	+	0.355209i	$0.115590\pi$
$314$	−13.0300	+	9.46687i	−0.735327	+	0.534247i
$315$	1.68914	+	2.58706i	0.0951724	+	0.145764i
$316$	−4.23951	−	3.08019i	−0.238491	−	0.173274i
$317$	1.46426	−	0.475768i	0.0822412	−	0.0267218i	−0.267607	−	0.963528i	$-0.586233\pi$
$317$	1.46426	−	0.475768i	0.0822412	−	0.0267218i	0.349849	+	0.936806i	$0.386233\pi$
$318$		−	33.1586i		−	1.85944i
$319$	2.33485	+	7.18593i	0.130727	+	0.402335i
$320$	−1.01434	−	3.74855i	−0.0567032	−	0.209550i
$321$	2.48614	−	7.65155i	0.138763	−	0.427068i
$322$	9.98996	+	3.24594i	0.556719	+	0.180889i
$323$	−3.40260	−	4.68328i	−0.189326	−	0.260585i
$324$	14.1479			0.785992
$325$	32.4014	−	7.05437i	1.79731	−	0.391306i
$326$	−40.9613			−2.26863
$327$	7.18885	+	9.89460i	0.397544	+	0.547173i
$328$	−10.5680	−	3.43375i	−0.583520	−	0.189597i
$329$	4.42088	−	13.6061i	0.243731	−	0.750128i
$330$	5.13780	−	3.35457i	0.282826	−	0.184663i
$331$	−2.61465	−	8.04707i	−0.143714	−	0.442307i	0.853129	−	0.521700i	$-0.174702\pi$
$331$	−2.61465	−	8.04707i	−0.143714	−	0.442307i	−0.996843	+	0.0793928i	$0.974702\pi$
$332$		−	22.9313i		−	1.25852i
$333$	−0.553253	+	0.179763i	−0.0303181	+	0.00985094i
$334$	−10.7445	−	7.80632i	−0.587912	−	0.427143i
$335$	−1.22487	+	24.5294i	−0.0669217	+	1.34018i
$336$	11.8843	−	8.63443i	0.648340	−	0.471047i
$337$	4.38889	−	6.04079i	0.239078	−	0.329063i	−0.672571	−	0.740033i	$-0.734810\pi$
$337$	4.38889	−	6.04079i	0.239078	−	0.329063i	0.911649	+	0.410970i	$0.134810\pi$
$338$	33.0702	−	45.5172i	1.79878	−	2.47581i
$339$	24.9327	−	18.1146i	1.35416	−	0.983853i
$340$	−15.6906	−	5.97869i	−0.850942	−	0.324240i
$341$	2.94495	+	2.13963i	0.159478	+	0.115868i
$342$	1.57845	−	0.512870i	0.0853530	−	0.0277329i
$343$		−	17.7094i		−	0.956218i
$344$	−2.60676	−	8.02277i	−0.140547	−	0.432559i
$345$	−16.9071	−	0.844251i	−0.910246	−	0.0454529i
$346$	−4.89260	+	15.0579i	−0.263028	+	0.809517i
$347$	4.93510	+	1.60351i	0.264930	+	0.0860811i	0.438470	−	0.898746i	$-0.355521\pi$
$347$	4.93510	+	1.60351i	0.264930	+	0.0860811i	−0.173540	+	0.984827i	$0.555521\pi$
$348$	14.9208	+	20.5367i	0.799838	+	1.10088i
$349$	27.0547			1.44820			0.724102	−	0.689693i	$-0.242255\pi$
$349$	27.0547			1.44820			0.724102	+	0.689693i	$0.242255\pi$
$350$	−13.6568	−	1.36731i	−0.729986	−	0.0730856i
$351$	27.3699			1.46090
$352$	−2.85840	−	3.93425i	−0.152353	−	0.209696i
$353$	−5.25771	−	1.70833i	−0.279839	−	0.0909253i	0.165735	−	0.986170i	$-0.447000\pi$
$353$	−5.25771	−	1.70833i	−0.279839	−	0.0909253i	−0.445574	+	0.895245i	$0.647000\pi$
$354$	1.49369	−	4.59711i	0.0793888	−	0.244334i
$355$	−21.5049	−	17.3267i	−1.14136	−	0.919606i
$356$	−1.90166	−	5.85270i	−0.100788	−	0.310193i
$357$		−	17.3132i		−	0.916312i
$358$	3.02743	−	0.983671i	0.160005	−	0.0519886i
$359$	14.0872	+	10.2350i	0.743495	+	0.540181i	0.893804	−	0.448458i	$-0.148027\pi$
$359$	14.0872	+	10.2350i	0.743495	+	0.540181i	−0.150309	+	0.988639i	$0.548027\pi$
$360$	−1.63644	+	2.03106i	−0.0862479	+	0.107046i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	−8.94371	+	12.3100i	−0.470071	+	0.646998i
$363$	−12.1130	+	16.6721i	−0.635769	+	0.875060i
$364$	−10.5216	+	7.64439i	−0.551482	+	0.400675i
$365$	−20.7644	+	5.61872i	−1.08686	+	0.294097i
$366$	−15.7602	−	11.4505i	−0.823799	−	0.598525i
$367$	−19.6254	+	6.37666i	−1.02444	+	0.332859i	−0.772588	−	0.634908i	$-0.781038\pi$
$367$	−19.6254	+	6.37666i	−1.02444	+	0.332859i	−0.251847	+	0.967767i	$0.581038\pi$
$368$			18.7950i			0.979759i
$369$	−2.45928	−	7.56888i	−0.128025	−	0.394020i
$370$	0.920128	−	2.41480i	0.0478352	−	0.125540i
$371$	−4.31190	+	13.2707i	−0.223863	+	0.688979i
$372$	11.6312	+	3.77919i	0.603048	+	0.195942i
$373$	11.0687	+	15.2348i	0.573116	+	0.788827i	0.992920	−	0.118788i	$-0.0379010\pi$
$373$	11.0687	+	15.2348i	0.573116	+	0.788827i	−0.419804	+	0.907615i	$0.637901\pi$
$374$	−8.02933			−0.415187
$375$	21.8205	−	3.62174i	1.12681	−	0.187026i
$376$	12.0773			0.622838
$377$	38.5594	+	53.0725i	1.98591	+	2.73337i
$378$	−10.7739	−	3.50065i	−0.554150	−	0.180054i
$379$	−10.0692	+	30.9897i	−0.517218	+	1.59183i	0.261992	+	0.965070i	$0.415621\pi$
$379$	−10.0692	+	30.9897i	−0.517218	+	1.59183i	−0.779210	+	0.626763i	$0.784379\pi$
$380$	−1.03279	+	2.71048i	−0.0529812	+	0.139045i
$381$	−4.73956	−	14.5869i	−0.242815	−	0.747308i
$382$		−	1.24420i		−	0.0636587i
$383$	27.0611	−	8.79268i	1.38276	−	0.449285i	0.479182	−	0.877716i	$-0.340933\pi$
$383$	27.0611	−	8.79268i	1.38276	−	0.449285i	0.903575	+	0.428431i	$0.140933\pi$
$384$	15.3319	+	11.1393i	0.782402	+	0.568448i
$385$	−2.49246	+	0.674448i	−0.127028	+	0.0343730i
$386$	−15.6135	+	11.3439i	−0.794706	+	0.577388i
$387$	3.55120	−	4.88781i	0.180518	−	0.248462i
$388$	8.72423	−	12.0079i	0.442906	−	0.609607i
$389$	−27.1132	+	19.6989i	−1.37469	+	0.998774i	−0.377340	+	0.926075i	$0.623161\pi$
$389$	−27.1132	+	19.6989i	−1.37469	+	0.998774i	−0.997354	+	0.0726992i	$0.976839\pi$
$390$	33.4244	−	41.4845i	1.69251	−	2.10065i
$391$	17.9210	+	13.0204i	0.906306	+	0.658470i
$392$	5.72234	−	1.85930i	0.289022	−	0.0939090i
$393$			8.61003i			0.434318i
$394$	−9.41871	−	28.9878i	−0.474508	−	1.46038i
$395$	−7.03414	−	5.66746i	−0.353926	−	0.285161i
$396$	0.279867	−	0.861343i	0.0140639	−	0.0432841i
$397$	31.1875	+	10.1334i	1.56526	+	0.508583i	0.958206	−	0.286080i	$-0.0923523\pi$
$397$	31.1875	+	10.1334i	1.56526	+	0.508583i	0.607051	+	0.794663i	$0.292352\pi$
$398$	2.66783	+	3.67196i	0.133726	+	0.184059i
$399$	−2.99078			−0.149726
$400$	−5.22442	−	23.9963i	−0.261221	−	1.19981i
$401$	0.834332			0.0416646			0.0208323	−	0.999783i	$-0.493368\pi$
$401$	0.834332			0.0416646			0.0208323	+	0.999783i	$0.493368\pi$
$402$	23.1923	+	31.9214i	1.15673	+	1.59210i
$403$	30.0581	+	9.76648i	1.49730	+	0.486503i
$404$	3.49135	−	10.7453i	0.173701	−	0.534598i
$405$	24.3576	+	1.21629i	1.21034	+	0.0604380i
$406$	−8.39051	−	25.8233i	−0.416414	−	1.28159i
$407$		−	0.486160i		−	0.0240980i
$408$	13.9003	−	4.51650i	0.688170	−	0.223600i
$409$	−14.6921	−	10.6744i	−0.726476	−	0.527816i	0.161970	−	0.986796i	$-0.448215\pi$
$409$	−14.6921	−	10.6744i	−0.726476	−	0.527816i	−0.888447	+	0.458980i	$0.848215\pi$
$410$	33.0361	+	12.5880i	1.63154	+	0.621676i
$411$	7.49384	−	5.44459i	0.369644	−	0.268562i
$412$	−8.02493	+	11.0454i	−0.395360	+	0.544166i
$413$	−1.19560	+	1.64561i	−0.0588319	+	0.0809751i
$414$	−5.13802	+	3.73299i	−0.252520	+	0.183466i
$415$	1.97141	−	39.4797i	0.0967726	−	1.93798i
$416$	−34.1584	−	24.8175i	−1.67475	−	1.21678i
$417$	−20.1731	+	6.55464i	−0.987881	+	0.320982i
$418$			1.38703i			0.0678420i
$419$	−1.52196	−	4.68412i	−0.0743528	−	0.228834i	0.906973	−	0.421190i	$-0.138387\pi$
$419$	−1.52196	−	4.68412i	−0.0743528	−	0.228834i	−0.981325	+	0.192355i	$0.938387\pi$
$420$	−7.26380	+	4.74268i	−0.354437	+	0.231419i
$421$	5.11309	−	15.7365i	0.249197	−	0.766949i	−0.745721	−	0.666258i	$-0.767895\pi$
$421$	5.11309	−	15.7365i	0.249197	−	0.766949i	0.994918	−	0.100690i	$-0.0321051\pi$
$422$	−5.36967	−	1.74471i	−0.261391	−	0.0849312i
$423$	5.08424	+	6.99786i	0.247204	+	0.340248i
$424$	−11.7796			−0.572066
$425$	−26.4997	−	11.6421i	−1.28542	−	0.564725i
$426$	−44.3678			−2.14963
$427$	4.81852	+	6.63212i	0.233184	+	0.320951i
$428$	5.01694	+	1.63010i	0.242503	+	0.0787939i
$429$	3.09713	−	9.53199i	0.149531	−	0.460209i
$430$	7.01025	+	25.9069i	0.338065	+	1.24934i
$431$	2.86773	+	8.82595i	0.138133	+	0.425131i	0.996064	−	0.0886341i	$-0.0282502\pi$
$431$	2.86773	+	8.82595i	0.138133	+	0.425131i	−0.857931	+	0.513765i	$0.828250\pi$
$432$		−	20.2699i		−	0.975238i
$433$	28.8293	−	9.36721i	1.38545	−	0.450159i	0.480992	−	0.876725i	$-0.340277\pi$
$433$	28.8293	−	9.36721i	1.38545	−	0.450159i	0.904457	+	0.426566i	$0.140277\pi$
$434$	−10.5830	−	7.68897i	−0.507999	−	0.369083i
$435$	23.9228	+	36.6397i	1.14701	+	1.75674i
$436$	−6.48765	+	4.71355i	−0.310702	+	0.225738i
$437$	2.24922	−	3.09578i	0.107595	−	0.148091i
$438$	−20.3133	+	27.9588i	−0.970605	+	1.33592i
$439$	−16.2144	+	11.7805i	−0.773873	+	0.562252i	−0.903134	−	0.429359i	$-0.858740\pi$
$439$	−16.2144	+	11.7805i	−0.773873	+	0.562252i	0.129261	+	0.991611i	$0.458740\pi$
$440$	−1.19171	−	1.82520i	−0.0568124	−	0.0870128i
$441$	3.48629	+	2.53294i	0.166014	+	0.120616i
$442$	−66.3011	+	21.5425i	−3.15362	+	1.02467i
$443$		−	12.3109i		−	0.584911i	−0.956279	−	0.292455i	$-0.905528\pi$
$443$		−	12.3109i		−	0.584911i	0.956279	−	0.292455i	$-0.0944723\pi$
$444$	−0.504728	−	1.55339i	−0.0239533	−	0.0737208i
$445$	−2.77083	−	10.2398i	−0.131350	−	0.485412i
$446$	5.39699	−	16.6102i	0.255555	−	0.786516i
$447$	−11.5151	−	3.74149i	−0.544647	−	0.176966i
$448$	1.54318	+	2.12400i	0.0729082	+	0.100350i
$449$	24.4015			1.15158			0.575790	−	0.817598i	$-0.304695\pi$
$449$	24.4015			1.15158			0.575790	+	0.817598i	$0.304695\pi$
$450$	5.52224	−	6.19424i	0.260321	−	0.291999i
$451$	6.65100			0.313183
$452$	11.8773	+	16.3477i	0.558663	+	0.768933i
$453$	33.2418	+	10.8009i	1.56184	+	0.507472i
$454$	8.48687	−	26.1199i	0.398308	−	1.22587i
$455$	−18.7717	+	12.2564i	−0.880029	+	0.574588i
$456$	−0.780205	−	2.40122i	−0.0365365	−	0.112448i
$457$		−	2.28287i		−	0.106788i	−0.998574	−	0.0533940i	$-0.982996\pi$
$457$		−	2.28287i		−	0.106788i	0.998574	−	0.0533940i	$-0.0170039\pi$
$458$	−19.3820	+	6.29761i	−0.905664	+	0.294268i
$459$	−19.3274	−	14.0421i	−0.902124	−	0.655431i
$460$	0.553555	−	11.0856i	0.0258096	−	0.516867i
$461$	5.13039	−	3.72745i	0.238946	−	0.173605i	−0.461868	−	0.886949i	$-0.652820\pi$
$461$	5.13039	−	3.72745i	0.238946	−	0.173605i	0.700814	+	0.713344i	$0.252820\pi$
$462$	−2.43832	+	3.35605i	−0.113441	+	0.156138i
$463$	2.68993	−	3.70237i	0.125012	−	0.172064i	−0.741924	−	0.670484i	$-0.766086\pi$
$463$	2.68993	−	3.70237i	0.125012	−	0.172064i	0.866935	+	0.498420i	$0.166086\pi$
$464$	39.3051	−	28.5568i	1.82469	−	1.32572i
$465$	19.6998	+	7.50636i	0.913559	+	0.348099i
$466$	21.6043	+	15.6964i	1.00080	+	0.727122i
$467$	11.9358	−	3.87818i	0.552323	−	0.179461i	−0.0195410	−	0.999809i	$-0.506220\pi$
$467$	11.9358	−	3.87818i	0.552323	−	0.179461i	0.571864	+	0.820348i	$0.306220\pi$
$468$		−	7.86330i		−	0.363481i
$469$	−5.13095	−	15.7914i	−0.236925	−	0.729181i
$470$	−38.3768	−	1.91634i	−1.77019	−	0.0883941i
$471$	−5.42263	+	16.6892i	−0.249862	+	0.768995i
$472$	−1.63312	−	0.530632i	−0.0751703	−	0.0244243i
$473$	2.96782	+	4.08485i	0.136460	+	0.187822i
$474$	−14.5125			−0.666579
$475$	−2.01113	+	4.57770i	−0.0922768	+	0.210039i
$476$	11.3518			0.520311
$477$	−4.95891	−	6.82535i	−0.227053	−	0.312511i
$478$	−12.5625	−	4.08179i	−0.574594	−	0.186697i
$479$	−2.25985	+	6.95510i	−0.103255	+	0.317787i	−0.989317	−	0.145780i	$-0.953431\pi$
$479$	−2.25985	+	6.95510i	−0.103255	+	0.317787i	0.886062	+	0.463567i	$0.153431\pi$
$480$	−21.9307	−	17.6698i	−1.00100	−	0.806511i
$481$	−1.30436	−	4.01440i	−0.0594736	−	0.183041i
$482$			31.1963i			1.42095i
$483$	10.8844	−	3.53655i	0.495257	−	0.160919i
$484$	−10.9315	−	7.94221i	−0.496887	−	0.361010i
$485$	16.0524	−	19.9233i	0.728900	−	0.904670i
$486$	13.5104	−	9.81590i	0.612846	−	0.445258i
$487$	13.7695	−	18.9521i	0.623955	−	0.858800i	−0.373679	−	0.927558i	$-0.621904\pi$
$487$	13.7695	−	18.9521i	0.623955	−	0.858800i	0.997633	+	0.0687584i	$0.0219038\pi$
$488$	−4.06776	+	5.59879i	−0.184139	+	0.253445i
$489$	−36.1053	+	26.2320i	−1.63274	+	1.18625i
$490$	−18.4784	+	5.00015i	−0.834769	+	0.225884i
$491$	−11.7889	−	8.56514i	−0.532026	−	0.386539i	0.289089	−	0.957302i	$-0.406648\pi$
$491$	−11.7889	−	8.56514i	−0.532026	−	0.386539i	−0.821115	+	0.570763i	$0.806648\pi$
$492$	21.2515	−	6.90503i	0.958091	−	0.311303i
$493$		−	57.2603i		−	2.57888i
$494$	3.72138	+	11.4532i	0.167433	+	0.515305i
$495$	0.555882	−	1.45887i	0.0249850	−	0.0655712i
$496$	7.23299	−	22.2609i	0.324771	−	0.999542i
$497$	17.7568	+	5.76954i	0.796502	+	0.258799i
$498$	−37.3276	−	51.3771i	−1.67269	−	2.30226i
$499$	−40.9744			−1.83427			−0.917134	−	0.398580i	$-0.869503\pi$
$499$	−40.9744			−1.83427			−0.917134	+	0.398580i	$0.869503\pi$
$500$	2.37469	+	14.3072i	0.106199	+	0.639837i
$501$	−14.4700			−0.646471
$502$	−2.79117	−	3.84172i	−0.124576	−	0.171464i
$503$	6.16452	+	2.00297i	0.274862	+	0.0893082i	0.443205	−	0.896420i	$-0.353841\pi$
$503$	6.16452	+	2.00297i	0.274862	+	0.0893082i	−0.168342	+	0.985729i	$0.553841\pi$
$504$	0.544910	−	1.67706i	0.0242722	−	0.0747022i
$505$	6.93465	−	18.1994i	0.308588	−	0.809863i
$506$	−1.64014	−	5.04785i	−0.0729133	−	0.224404i
$507$		−	61.2996i		−	2.72241i
$508$	9.56425	−	3.10761i	0.424345	−	0.137878i
$509$	19.3359	+	14.0484i	0.857049	+	0.622683i	0.927081	−	0.374862i	$-0.122310\pi$
$509$	19.3359	+	14.0484i	0.857049	+	0.622683i	−0.0700312	+	0.997545i	$0.522310\pi$
$510$	−44.8865	+	12.1460i	−1.98761	+	0.537836i
$511$	11.7655	−	8.54811i	0.520473	−	0.378146i
$512$	−11.0109	+	15.1552i	−0.486618	+	0.669773i
$513$	−2.42572	+	3.33872i	−0.107098	+	0.147408i
$514$	5.89417	−	4.28236i	0.259981	−	0.188887i
$515$	−14.7657	+	18.3263i	−0.650652	+	0.807553i
$516$	13.7237	+	9.97088i	0.604154	+	0.438943i
$517$	−6.87504	+	2.23384i	−0.302364	+	0.0982440i
$518$			1.74706i			0.0767615i
$519$	5.33065	+	16.4060i	0.233989	+	0.720145i
$520$	−14.7373	−	11.8740i	−0.646274	−	0.520708i
$521$	5.74327	−	17.6760i	0.251617	−	0.774398i	−0.742860	−	0.669447i	$-0.766531\pi$
$521$	5.74327	−	17.6760i	0.251617	−	0.774398i	0.994477	−	0.104951i	$-0.0334687\pi$
$522$	15.6132	+	5.07305i	0.683373	+	0.222041i
$523$	19.6182	+	27.0022i	0.857845	+	1.18072i	0.982079	+	0.188470i	$0.0603527\pi$
$523$	19.6182	+	27.0022i	0.857845	+	1.18072i	−0.124234	+	0.992253i	$0.539647\pi$
$524$	−5.64538			−0.246620
$525$	−12.9134	+	7.54075i	−0.563588	+	0.329105i
$526$	10.3372			0.450723
$527$	−16.2150	−	22.3180i	−0.706336	−	0.972188i
$528$	−7.05933	−	2.29372i	−0.307218	−	0.0998212i
$529$	2.58250	−	7.94812i	0.112283	−	0.345570i
$530$	37.4308	+	1.86910i	1.62589	+	0.0811884i
$531$	−0.380042	−	1.16965i	−0.0164924	−	0.0507585i
$532$		−	1.96098i		−	0.0850194i
$533$	54.9197	−	17.8445i	2.37884	−	0.772931i
$534$	−13.7876	−	10.0173i	−0.596650	−	0.433491i
$535$	8.49725	+	3.23776i	0.367368	+	0.139981i
$536$	11.3401	−	8.23903i	0.489816	−	0.355872i
$537$	2.03857	−	2.80586i	0.0879709	−	0.121082i
$538$	14.0957	−	19.4010i	0.607707	−	0.836437i
$539$	−2.91357	+	2.11683i	−0.125496	+	0.0911785i
$540$	−0.596994	+	11.9555i	−0.0256905	+	0.514482i
$541$	−12.2988	−	8.93560i	−0.528766	−	0.384171i	0.291130	−	0.956684i	$-0.405969\pi$
$541$	−12.2988	−	8.93560i	−0.528766	−	0.384171i	−0.819896	+	0.572512i	$0.805969\pi$
$542$	−43.4513	+	14.1182i	−1.86639	+	0.606428i
$543$			16.5783i			0.711442i
$544$	11.3884	+	35.0500i	0.488275	+	1.50276i
$545$	−11.5747	+	7.55733i	−0.495804	+	0.323720i
$546$	−11.1298	+	34.2541i	−0.476313	+	1.46594i
$547$	−24.6008	−	7.99328i	−1.05185	−	0.341768i	−0.268458	−	0.963291i	$-0.586514\pi$
$547$	−24.6008	−	7.99328i	−1.05185	−	0.341768i	−0.783395	+	0.621524i	$0.786514\pi$
$548$	3.56989	+	4.91353i	0.152498	+	0.209896i
$549$	−4.95651			−0.211538
$550$	3.49717	+	5.98885i	0.149120	+	0.255365i
$551$	−9.89148			−0.421391
$552$	5.67882	+	7.81623i	0.241707	+	0.332681i
$553$	5.80815	+	1.88718i	0.246988	+	0.0802511i
$554$	7.45029	−	22.9297i	0.316533	−	0.974187i
$555$	−0.735418	−	2.71779i	−0.0312168	−	0.115364i
$556$	−4.29772	−	13.2270i	−0.182264	−	0.560950i
$557$		−	46.0919i		−	1.95297i	−0.215575	−	0.976487i	$-0.569163\pi$
$557$		−	46.0919i		−	1.95297i	0.215575	−	0.976487i	$-0.430837\pi$
$558$	7.52206	−	2.44407i	0.318434	−	0.103466i
$559$	35.4659	+	25.7675i	1.50005	+	1.08985i
$560$	9.07700	+	13.9022i	0.383573	+	0.587474i
$561$	−7.07746	+	5.14207i	−0.298810	+	0.217098i
$562$	16.5318	−	22.7540i	0.697351	−	0.959821i
$563$	10.9789	−	15.1112i	0.462707	−	0.636861i	−0.512361	−	0.858770i	$-0.671229\pi$
$563$	10.9789	−	15.1112i	0.462707	−	0.636861i	0.975067	+	0.221909i	$0.0712289\pi$
$564$	−19.6482	+	14.2753i	−0.827339	+	0.601097i
$565$	19.0431	+	29.1661i	0.801151	+	1.22703i
$566$	−13.8811	−	10.0852i	−0.583465	−	0.423912i
$567$	−15.6809	+	5.09502i	−0.658534	+	0.213971i
$568$			15.7616i			0.661342i
$569$	−7.33311	−	22.5690i	−0.307420	−	0.946141i	−0.978763	−	0.204994i	$-0.934282\pi$
$569$	−7.33311	−	22.5690i	−0.307420	−	0.946141i	0.671343	−	0.741147i	$-0.265718\pi$
$570$	2.09818	+	7.75395i	0.0878830	+	0.324777i
$571$	−3.02713	+	9.31655i	−0.126681	+	0.389886i	−0.994204	−	0.107513i	$-0.965711\pi$
$571$	−3.02713	+	9.31655i	−0.126681	+	0.389886i	0.867522	+	0.497398i	$0.165711\pi$
$572$	6.24989	+	2.03071i	0.261321	+	0.0849084i
$573$	−0.796798	−	1.09670i	−0.0332867	−	0.0458152i
$574$	−23.9010			−0.997608
$575$	1.90605	−	19.0378i	0.0794878	−	0.793932i
$576$	−1.58737			−0.0661403
$577$	23.7124	+	32.6373i	0.987159	+	1.35871i	0.932882	+	0.360182i	$0.117286\pi$
$577$	23.7124	+	32.6373i	0.987159	+	1.35871i	0.0542774	+	0.998526i	$0.482714\pi$
$578$	28.5133	+	9.26452i	1.18600	+	0.385353i
$579$	−6.49778	+	19.9981i	−0.270038	+	0.831093i
$580$	−24.0237	+	15.6856i	−0.997531	+	0.651308i
$581$	8.25819	+	25.4161i	0.342607	+	1.05444i
$582$		−	41.1046i		−	1.70384i
$583$	6.70556	−	2.17877i	0.277716	−	0.0902354i
$584$	9.93233	+	7.21626i	0.411003	+	0.298611i
$585$	0.676008	−	13.5378i	0.0279495	−	0.559720i
$586$	27.4571	−	19.9488i	1.13424	−	0.824076i
$587$	−2.68276	+	3.69250i	−0.110729	+	0.152406i	−0.860785	−	0.508969i	$-0.830027\pi$
$587$	−2.68276	+	3.69250i	−0.110729	+	0.152406i	0.750056	+	0.661375i	$0.230027\pi$
$588$	−7.11185	+	9.78863i	−0.293288	+	0.403676i
$589$	−3.85534	+	2.80107i	−0.158857	+	0.115416i
$590$	5.10521	+	1.94527i	0.210178	+	0.0800856i
$591$	−26.8662	−	19.5194i	−1.10513	−	0.802923i
$592$	−2.97304	+	0.965998i	−0.122191	+	0.0397023i
$593$			38.0905i			1.56419i	0.623158	+	0.782096i	$0.285849\pi$
$593$			38.0905i			1.56419i	−0.623158	+	0.782096i	$0.714151\pi$
$594$	1.76885	+	5.44397i	0.0725769	+	0.223369i
$595$	19.5439	+	0.975918i	0.801220	+	0.0400087i
$596$	2.45320	−	7.55019i	0.100487	−	0.309268i
$597$	4.70312	+	1.52814i	0.192486	+	0.0625425i
$598$	−27.0865	−	37.2814i	−1.10765	−	1.52455i
$599$	2.67085			0.109128			0.0545640	−	0.998510i	$-0.482623\pi$
$599$	2.67085			0.109128			0.0545640	+	0.998510i	$0.482623\pi$
$600$	−9.42301	−	8.40071i	−0.384693	−	0.342958i
$601$	0.242716			0.00990058			0.00495029	−	0.999988i	$-0.498424\pi$
$601$	0.242716			0.00990058			0.00495029	+	0.999988i	$0.498424\pi$
$602$	−10.6651	−	14.6793i	−0.434678	−	0.598283i
$603$	9.54778	+	3.10226i	0.388816	+	0.126334i
$604$	−7.08190	+	21.7959i	−0.288159	+	0.886861i
$605$	−18.1374	−	14.6135i	−0.737391	−	0.594122i
$606$	−9.66888	−	29.7577i	−0.392771	−	1.20883i
$607$		−	3.88106i		−	0.157528i	−0.996893	−	0.0787638i	$-0.974903\pi$
$607$		−	3.88106i		−	0.157528i	0.996893	−	0.0787638i	$-0.0250973\pi$
$608$	6.05473	−	1.96730i	0.245552	−	0.0797847i
$609$	−23.9333	−	17.3886i	−0.969828	−	0.704621i
$610$	13.8141	−	17.1453i	0.559318	−	0.694194i
$611$	−50.7764	+	36.8912i	−2.05419	+	1.49246i
$612$	−4.03428	+	5.55271i	−0.163076	+	0.224455i
$613$	5.94361	−	8.18068i	0.240060	−	0.330415i	−0.671939	−	0.740607i	$-0.734538\pi$
$613$	5.94361	−	8.18068i	0.240060	−	0.330415i	0.911999	+	0.410192i	$0.134538\pi$
$614$	21.2091	−	15.4093i	0.855928	−	0.621868i
$615$	37.1812	−	10.0610i	1.49929	−	0.405700i
$616$	1.19223	+	0.866209i	0.0480365	+	0.0349005i
$617$	37.0890	−	12.0509i	1.49315	−	0.485153i	0.555136	−	0.831759i	$-0.312666\pi$
$617$	37.0890	−	12.0509i	1.49315	−	0.485153i	0.938011	+	0.346607i	$0.112666\pi$
$618$			37.8098i			1.52093i
$619$	2.71930	+	8.36914i	0.109298	+	0.336384i	0.990715	−	0.135954i	$-0.0434100\pi$
$619$	2.71930	+	8.36914i	0.109298	+	0.336384i	−0.881417	+	0.472338i	$0.843410\pi$
$620$	−4.92174	+	12.9167i	−0.197662	+	0.518748i
$621$	4.87997	−	15.0190i	0.195827	−	0.602692i
$622$	−26.6421	−	8.65653i	−1.06825	−	0.347095i
$623$	4.21543	+	5.80204i	0.168888	+	0.232454i
$624$	−64.4454			−2.57988
$625$	2.85839	+	24.8361i	0.114335	+	0.993442i
$626$	16.8389			0.673019
$627$	0.888271	+	1.22260i	0.0354741	+	0.0488259i
$628$	−10.9427	−	3.55549i	−0.436660	−	0.141879i
$629$	−1.13851	+	3.50399i	−0.0453956	+	0.139713i
$630$	−1.99762	+	5.24258i	−0.0795869	+	0.208869i
$631$	4.13775	+	12.7347i	0.164721	+	0.506960i	0.999016	−	0.0443594i	$-0.0141247\pi$
$631$	4.13775	+	12.7347i	0.164721	+	0.506960i	−0.834294	+	0.551319i	$0.814125\pi$
$632$			5.15553i			0.205076i
$633$	−5.85043	+	1.90092i	−0.232534	+	0.0755547i
$634$	2.26174	+	1.64325i	0.0898250	+	0.0652617i
$635$	16.7334	−	4.52797i	0.664046	−	0.179687i
$636$	19.1639	−	13.9234i	0.759896	−	0.552097i
$637$	−18.3790	+	25.2965i	−0.728202	+	1.00228i
$638$	−8.06430	+	11.0996i	−0.319269	+	0.439436i
$639$	−9.13265	+	6.63526i	−0.361282	+	0.262487i
$640$	−13.4387	+	16.6794i	−0.531211	+	0.659309i
$641$	26.1462	+	18.9963i	1.03271	+	0.750309i	0.968850	−	0.247650i	$-0.0796581\pi$
$641$	26.1462	+	18.9963i	1.03271	+	0.750309i	0.0638623	+	0.997959i	$0.479658\pi$
$642$	13.8938	−	4.51437i	0.548344	−	0.178168i
$643$			7.51693i			0.296439i	0.988954	+	0.148219i	$0.0473542\pi$
$643$			7.51693i			0.296439i	−0.988954	+	0.148219i	$0.952646\pi$
$644$	2.31883	+	7.13662i	0.0913747	+	0.281222i
$645$	22.7702	+	18.3461i	0.896576	+	0.722379i
$646$	3.24823	−	9.99702i	0.127800	−	0.393327i
$647$	−7.83076	−	2.54437i	−0.307859	−	0.100029i	0.151013	−	0.988532i	$-0.451746\pi$
$647$	−7.83076	−	2.54437i	−0.307859	−	0.100029i	−0.458872	+	0.888502i	$0.651746\pi$
$648$	−8.18134	−	11.2606i	−0.321393	−	0.442360i
$649$	1.02781			0.0403449
$650$	44.9454	+	40.0693i	1.76290	+	1.57165i
$651$	−14.2525			−0.558598
$652$	−17.1997	−	23.6734i	−0.673593	−	0.927121i
$653$	28.0199	+	9.10421i	1.09650	+	0.356275i	0.800756	−	0.598991i	$-0.204431\pi$
$653$	28.0199	+	9.10421i	1.09650	+	0.356275i	0.295747	+	0.955266i	$0.404431\pi$
$654$	−6.86269	+	21.1212i	−0.268352	+	0.825904i
$655$	−9.71935	−	0.485334i	−0.379767	−	0.0189636i
$656$	−13.2155	−	40.6732i	−0.515979	−	1.58802i
$657$			8.79290i			0.343044i
$658$	24.7061	−	8.02750i	0.963145	−	0.312945i
$659$	2.38804	+	1.73501i	0.0930248	+	0.0675865i	0.633325	−	0.773886i	$-0.281689\pi$
$659$	2.38804	+	1.73501i	0.0930248	+	0.0675865i	−0.540301	+	0.841472i	$0.681689\pi$
$660$	4.09613	+	1.56078i	0.159442	+	0.0607531i
$661$	−0.0575326	+	0.0417999i	−0.00223776	+	0.00162583i	−0.588904	−	0.808203i	$-0.700440\pi$
$661$	−0.0575326	+	0.0417999i	−0.00223776	+	0.00162583i	0.586666	+	0.809829i	$0.300440\pi$
$662$	9.03070	−	12.4297i	0.350988	−	0.483094i
$663$	−44.6450	+	61.4486i	−1.73387	+	2.38647i
$664$	−18.2516	+	13.2606i	−0.708301	+	0.514611i
$665$	0.168586	−	3.37612i	0.00653747	−	0.130920i
$666$	−0.854568	−	0.620880i	−0.0331138	−	0.0240586i
$667$	35.9982	−	11.6965i	1.39385	−	0.452891i
$668$		−	9.48761i		−	0.367087i
$669$	−5.88019	−	18.0974i	−0.227341	−	0.699684i
$670$	−37.3416	+	24.3811i	−1.44263	+	0.941922i
$671$	1.28003	−	3.93952i	0.0494149	−	0.152084i
$672$	18.1084	+	5.88377i	0.698546	+	0.226971i
$673$	−20.3555	−	28.0169i	−0.784646	−	1.07997i	−0.994754	−	0.102295i	$-0.967381\pi$
$673$	−20.3555	−	28.0169i	−0.784646	−	1.07997i	0.210108	−	0.977678i	$-0.432619\pi$
$674$	13.5584			0.522249
$675$	−2.05562	+	20.5318i	−0.0791210	+	0.790268i
$676$	40.1927			1.54587
$677$	−7.92643	−	10.9098i	−0.304638	−	0.419298i	0.629062	−	0.777355i	$-0.283439\pi$
$677$	−7.92643	−	10.9098i	−0.304638	−	0.419298i	−0.933700	+	0.358057i	$0.883439\pi$
$678$	53.2217	+	17.2928i	2.04397	+	0.664125i
$679$	−5.34520	+	16.4508i	−0.205130	+	0.631325i
$680$	4.31487	+	15.9459i	0.165468	+	0.611496i
$681$	−9.24671	−	28.4585i	−0.354335	−	1.09053i
$682$			6.60986i			0.253104i
$683$	−41.4340	+	13.4627i	−1.58543	+	0.515136i	−0.963447	−	0.267898i	$-0.913671\pi$
$683$	−41.4340	+	13.4627i	−1.58543	+	0.515136i	−0.621979	+	0.783034i	$0.713671\pi$
$684$	0.959206	+	0.696904i	0.0366762	+	0.0266468i
$685$	5.72367	+	8.76626i	0.218690	+	0.334942i
$686$	26.0155	−	18.9014i	0.993278	−	0.721659i
$687$	−13.0512	+	17.9635i	−0.497936	+	0.685350i
$688$	19.0832	−	26.2658i	0.727542	−	1.00138i
$689$	49.5247	−	35.9818i	1.88674	−	1.37080i
$690$	−16.8048	−	25.7380i	−0.639749	−	0.979828i
$691$	3.17648	+	2.30785i	0.120839	+	0.0877946i	0.646563	−	0.762860i	$-0.276206\pi$
$691$	3.17648	+	2.30785i	0.120839	+	0.0877946i	−0.525724	+	0.850655i	$0.676206\pi$
$692$	−10.7570	+	3.49518i	−0.408921	+	0.132867i
$693$			1.05546i			0.0400937i
$694$	2.91168	+	8.96123i	0.110526	+	0.340164i
$695$	−6.26202	−	23.1417i	−0.237532	−	0.877815i
$696$	7.71738	−	23.7517i	0.292527	−	0.900304i
$697$	−47.9369	−	15.5757i	−1.81574	−	0.589970i
$698$	28.8757	+	39.7440i	1.09296	+	1.50433i
$699$	29.0952			1.10048
$700$	−4.94428	−	8.46701i	−0.186876	−	0.320023i
$701$	10.6292			0.401461			0.200730	−	0.979647i	$-0.435668\pi$
$701$	10.6292			0.401461			0.200730	+	0.979647i	$0.435668\pi$
$702$	29.2121	+	40.2070i	1.10254	+	1.51752i
$703$	0.605299	+	0.196674i	0.0228293	+	0.00741768i
$704$	0.409941	−	1.26167i	0.0154502	−	0.0475509i
$705$	−35.0545	+	22.8878i	−1.32023	+	0.862004i
$706$	−3.10201	−	9.54701i	−0.116746	−	0.359307i
$707$			13.1669i			0.495193i
$708$	3.28408	−	1.06706i	0.123423	−	0.0401027i
$709$	8.04131	+	5.84235i	0.301998	+	0.219414i	0.728455	−	0.685093i	$-0.240239\pi$
$709$	8.04131	+	5.84235i	0.301998	+	0.219414i	−0.426458	+	0.904508i	$0.640239\pi$
$710$	2.50094	−	50.0842i	0.0938587	−	1.87963i
$711$	−2.98724	+	2.17036i	−0.112030	+	0.0813947i
$712$	−3.55864	+	4.89804i	−0.133366	+	0.183562i
$713$	10.7186	−	14.7528i	0.401413	−	0.552498i
$714$	25.4335	−	18.4785i	0.951825	−	0.691541i
$715$	10.5855	+	4.03347i	0.395876	+	0.150843i
$716$	1.83973	+	1.33664i	0.0687540	+	0.0499527i
$717$	−13.6872	+	4.44725i	−0.511158	+	0.166085i
$718$			31.6183i			1.17999i
$719$	12.4721	+	38.3853i	0.465132	+	1.43153i	0.858816	+	0.512284i	$0.171201\pi$
$719$	12.4721	+	38.3853i	0.465132	+	1.43153i	−0.393684	+	0.919246i	$0.628799\pi$
$720$	−10.0260	−	0.500647i	−0.373648	−	0.0186580i
$721$	4.91674	−	15.1322i	0.183109	−	0.563552i
$722$	−1.72694	−	0.561117i	−0.0642701	−	0.0208826i
$723$	19.9785	+	27.4980i	0.743007	+	1.02266i
$724$	−10.8700			−0.403979
$725$	−42.7088	+	24.9397i	−1.58617	+	0.926237i
$726$	−37.4201			−1.38879
$727$	13.8448	+	19.0557i	0.513475	+	0.706737i	0.984500	−	0.175382i	$-0.0561161\pi$
$727$	13.8448	+	19.0557i	0.513475	+	0.706737i	−0.471026	+	0.882119i	$0.656116\pi$
$728$	12.1687	+	3.95386i	0.451003	+	0.146540i
$729$	−4.48844	+	13.8140i	−0.166238	+	0.511629i
$730$	−30.4160	−	24.5064i	−1.12575	−	0.907024i
$731$	−11.8244	−	36.3917i	−0.437340	−	1.34599i
$732$		−	13.9166i		−	0.514372i
$733$	9.12968	−	2.96641i	0.337212	−	0.109567i	−0.135516	−	0.990775i	$-0.543269\pi$
$733$	9.12968	−	2.96641i	0.337212	−	0.109567i	0.472728	+	0.881208i	$0.343269\pi$
$734$	−30.3138	−	22.0243i	−1.11890	−	0.812930i
$735$	−13.0856	+	16.2411i	−0.482671	+	0.599064i
$736$	−19.7088	+	14.3193i	−0.726475	+	0.527815i
$737$	−4.93147	+	6.78759i	−0.181653	+	0.250024i
$738$	8.49406	−	11.6911i	0.312671	−	0.430354i
$739$	−13.4480	+	9.77058i	−0.494694	+	0.359416i	−0.806987	−	0.590570i	$-0.798903\pi$
$739$	−13.4480	+	9.77058i	−0.494694	+	0.359416i	0.312292	+	0.949986i	$0.398903\pi$
$740$	1.78199	−	0.482196i	0.0655071	−	0.0177259i
$741$	10.6150	+	7.71224i	0.389951	+	0.283316i
$742$	−24.0971	+	7.82962i	−0.884632	+	0.287434i
$743$		−	1.53662i		−	0.0563732i	−0.999603	−	0.0281866i	$-0.991027\pi$
$743$		−	1.53662i		−	0.0563732i	0.999603	−	0.0281866i	$-0.00897325\pi$
$744$	−3.71804	−	11.4429i	−0.136310	−	0.419519i
$745$	4.87264	−	12.7878i	0.178520	−	0.468510i
$746$	−10.5665	+	32.5204i	−0.386868	+	1.19066i
$747$	−15.3670	−	4.99304i	−0.562250	−	0.182686i
$748$	−3.37153	−	4.64052i	−0.123275	−	0.169674i
$749$	−6.14759			−0.224628
$750$	28.6097	+	28.1894i	1.04468	+	1.02933i
$751$	−16.1229			−0.588332			−0.294166	−	0.955754i	$-0.595042\pi$
$751$	−16.1229			−0.588332			−0.294166	+	0.955754i	$0.595042\pi$
$752$	27.3214	+	37.6047i	0.996308	+	1.37130i
$753$	−4.92056	−	1.59879i	−0.179315	−	0.0582630i
$754$	−36.8100	+	113.289i	−1.34054	+	4.12576i
$755$	−14.0663	+	36.9159i	−0.511926	+	1.34351i
$756$	−2.50080	−	7.69666i	−0.0909531	−	0.279925i
$757$			4.48872i			0.163145i	0.996667	+	0.0815726i	$0.0259943\pi$
$757$			4.48872i			0.163145i	−0.996667	+	0.0815726i	$0.974006\pi$
$758$	−56.2715	+	18.2837i	−2.04387	+	0.664095i
$759$	−4.67840	−	3.39906i	−0.169815	−	0.123378i
$760$	2.75458	−	0.745375i	0.0999192	−	0.0270376i
$761$	−7.63579	+	5.54773i	−0.276797	+	0.201105i	−0.717519	−	0.696539i	$-0.754722\pi$
$761$	−7.63579	+	5.54773i	−0.276797	+	0.201105i	0.440722	+	0.897644i	$0.354722\pi$
$762$	16.3699	−	22.5312i	0.593019	−	0.816220i
$763$	5.49315	−	7.56067i	0.198865	−	0.273715i
$764$	0.719078	−	0.522441i	0.0260153	−	0.0189012i
$765$	−7.42296	+	9.21297i	−0.268378	+	0.333096i
$766$	41.7992	+	30.3689i	1.51027	+	1.09727i
$767$	8.48697	−	2.75758i	0.306447	−	0.0995706i
$768$			41.2836i			1.48969i
$769$	9.74734	+	29.9992i	0.351498	+	1.08180i	0.958012	+	0.286727i	$0.0925672\pi$
$769$	9.74734	+	29.9992i	0.351498	+	1.08180i	−0.606514	+	0.795072i	$0.707433\pi$
$770$	−3.65101	−	2.94165i	−0.131573	−	0.106010i
$771$	2.45294	−	7.54938i	0.0883405	−	0.271884i
$772$	−13.1123	−	4.26043i	−0.471921	−	0.153336i
$773$	11.5855	+	15.9461i	0.416701	+	0.573540i	0.964837	−	0.262850i	$-0.0846623\pi$
$773$	11.5855	+	15.9461i	0.416701	+	0.573540i	−0.548136	+	0.836389i	$0.684662\pi$
$774$	10.9705			0.394328
$775$	−9.58394	+	21.8149i	−0.344265	+	0.783614i
$776$	−14.6024			−0.524194
$777$	1.11884	+	1.53995i	0.0401381	+	0.0552453i
$778$	−57.8763	−	18.8052i	−2.07497	−	0.674198i
$779$	−2.69063	+	8.28090i	−0.0964017	+	0.296694i
$780$	38.0107	+	1.89806i	1.36100	+	0.0679614i
$781$	−2.91530	−	8.97237i	−0.104318	−	0.321057i
$782$			40.2232i			1.43838i
$783$	−38.8231	+	12.6144i	−1.38742	+	0.450801i
$784$	18.7344	+	13.6114i	0.669087	+	0.486120i
$785$	−18.5337	−	7.06203i	−0.661497	−	0.252055i
$786$	−12.6483	+	9.18955i	−0.451151	+	0.327781i
$787$	23.1472	−	31.8594i	0.825108	−	1.13566i	−0.163706	−	0.986509i	$-0.552345\pi$
$787$	23.1472	−	31.8594i	0.825108	−	1.13566i	0.988814	−	0.149154i	$-0.0476551\pi$
$788$	12.7984	−	17.6155i	0.455925	−	0.627527i
$789$	9.11172	−	6.62005i	0.324386	−	0.235680i
$790$	0.818044	−	16.3823i	0.0291047	−	0.582854i
$791$	−19.0516	−	13.8418i	−0.677396	−	0.492157i
$792$	−0.847405	+	0.275339i	−0.0301112	+	0.00978373i
$793$		−	35.9643i		−	1.27713i
$794$	18.4004	+	56.6307i	0.653007	+	2.00975i
$795$	34.1904	−	22.3236i	1.21261	−	0.791736i
$796$	−1.00196	+	3.08372i	−0.0355136	+	0.109300i
$797$	−5.80071	−	1.88477i	−0.205472	−	0.0667618i	0.204473	−	0.978872i	$-0.434452\pi$
$797$	−5.80071	−	1.88477i	−0.205472	−	0.0667618i	−0.409945	+	0.912110i	$0.634452\pi$
$798$	−3.19209	−	4.39353i	−0.112999	−	0.155529i
$799$	54.7831			1.93809
$800$	21.1826	−	23.7603i	0.748917	−	0.840053i
$801$	−4.33614			−0.153210
$802$	0.890490	+	1.22565i	0.0314443	+	0.0432794i
$803$	−6.98876	−	2.27078i	−0.246628	−	0.0801342i
$804$	−8.71036	+	26.8077i	−0.307191	+	0.945436i
$805$	3.37867	+	12.4861i	0.119082	+	0.440077i
$806$	17.7341	+	54.5800i	0.624657	+	1.92250i
$807$		−	26.1280i		−	0.919751i
$808$	−10.5714	+	3.43486i	−0.371901	+	0.120838i
$809$	−18.6548	−	13.5535i	−0.655869	−	0.476516i	0.209397	−	0.977831i	$-0.432850\pi$
$809$	−18.6548	−	13.5535i	−0.655869	−	0.476516i	−0.865265	+	0.501314i	$0.832850\pi$
$810$	24.2103	+	37.0801i	0.850664	+	1.30286i
$811$	21.2429	−	15.4339i	0.745940	−	0.541957i	−0.148626	−	0.988894i	$-0.547485\pi$
$811$	21.2429	−	15.4339i	0.745940	−	0.541957i	0.894566	+	0.446936i	$0.147485\pi$
$812$	11.4013	−	15.6925i	0.400106	−	0.550699i
$813$	−29.2587	+	40.2712i	−1.02615	+	1.41237i
$814$	0.714181	−	0.518883i	0.0250320	−	0.0181868i
$815$	−27.5766	−	42.2358i	−0.965966	−	1.47946i
$816$	45.5085	+	33.0638i	1.59311	+	1.15747i
$817$	−6.28651	+	2.04261i	−0.219937	+	0.0714619i
$818$		−	32.9759i		−	1.15298i
$819$	2.83178	+	8.71533i	0.0989505	+	0.304538i
$820$	6.59677	+	24.3788i	0.230369	+	0.851344i
$821$	−1.75121	+	5.38968i	−0.0611178	+	0.188101i	−0.976954	−	0.213452i	$-0.931529\pi$
$821$	−1.75121	+	5.38968i	−0.0611178	+	0.188101i	0.915836	+	0.401553i	$0.131529\pi$
$822$	15.9965	+	5.19757i	0.557941	+	0.181286i
$823$	4.57168	+	6.29238i	0.159359	+	0.219339i	0.881229	−	0.472690i	$-0.156717\pi$
$823$	4.57168	+	6.29238i	0.159359	+	0.219339i	−0.721870	+	0.692029i	$0.756717\pi$
$824$	13.4319			0.467922
$825$	6.91790	+	3.03925i	0.240851	+	0.105813i
$826$	−3.69352			−0.128514
$827$	0.339330	+	0.467048i	0.0117997	+	0.0162408i	0.814876	−	0.579635i	$-0.196805\pi$
$827$	0.339330	+	0.467048i	0.0117997	+	0.0162408i	−0.803076	+	0.595876i	$0.796805\pi$
$828$	−4.31493	−	1.40201i	−0.149954	−	0.0487231i
$829$	3.11708	−	9.59338i	0.108261	−	0.333192i	−0.882221	−	0.470835i	$-0.843953\pi$
$829$	3.11708	−	9.59338i	0.108261	−	0.333192i	0.990482	+	0.137643i	$0.0439527\pi$
$830$	60.1007	−	39.2409i	2.08612	−	1.36207i
$831$	−8.11733	−	24.9826i	−0.281587	−	0.866636i
$832$		−	11.5179i		−	0.399312i
$833$	25.9568	−	8.43388i	0.899351	−	0.292217i
$834$	−31.1598	−	22.6390i	−1.07898	−	0.783923i
$835$	0.815649	−	16.3343i	0.0282267	−	0.565272i
$836$	−0.801629	+	0.582418i	−0.0277249	+	0.0201433i
$837$	−11.5597	+	15.9105i	−0.399561	+	0.549949i
$838$	5.25669	−	7.23521i	0.181589	−	0.249936i
$839$	26.0646	−	18.9370i	0.899849	−	0.653778i	−0.0385783	−	0.999256i	$-0.512283\pi$
$839$	26.0646	−	18.9370i	0.899849	−	0.653778i	0.938427	+	0.345477i	$0.112283\pi$
$840$	7.97528	+	3.03888i	0.275173	+	0.104851i
$841$	−55.6938	−	40.4639i	−1.92048	−	1.39531i
$842$	28.5745	−	9.28442i	0.984742	−	0.319962i
$843$		−	30.6437i		−	1.05542i
$844$	−1.24639	−	3.83598i	−0.0429024	−	0.132040i
$845$	69.1975	+	3.45536i	2.38047	+	0.118868i
$846$	−4.85357	+	14.9378i	−0.166869	+	0.513570i
$847$	14.9762	+	4.86607i	0.514589	+	0.167200i
$848$	−26.6479	−	36.6777i	−0.915092	−	1.25952i
$849$	−18.6941			−0.641581
$850$	−11.1808	−	51.3544i	−0.383497	−	1.76144i
$851$	−2.43543			−0.0834856
$852$	−18.6301	−	25.6422i	−0.638258	−	0.878486i
$853$	−2.66623	−	0.866310i	−0.0912899	−	0.0296619i	0.263016	−	0.964791i	$-0.415283\pi$
$853$	−2.66623	−	0.866310i	−0.0912899	−	0.0296619i	−0.354306	+	0.935130i	$0.615283\pi$
$854$	−4.59990	+	14.1570i	−0.157405	+	0.484444i
$855$	1.59150	+	1.28229i	0.0544282	+	0.0438532i
$856$	−1.60372	−	4.93575i	−0.0548141	−	0.168701i
$857$		−	2.76018i		−	0.0942860i	−0.998888	−	0.0471430i	$-0.984988\pi$
$857$		−	2.76018i		−	0.0942860i	0.998888	−	0.0471430i	$-0.0150116\pi$
$858$	17.3083	−	5.62382i	0.590896	−	0.191994i
$859$	28.6710	+	20.8307i	0.978241	+	0.710733i	0.957315	−	0.289048i	$-0.0933386\pi$
$859$	28.6710	+	20.8307i	0.978241	+	0.710733i	0.0209259	+	0.999781i	$0.493339\pi$
$860$	−12.0291	+	14.9299i	−0.410190	+	0.509105i
$861$	−21.0675	+	15.3065i	−0.717979	+	0.521642i
$862$	−9.90479	+	13.6328i	−0.337359	+	0.464334i
$863$	−23.2183	+	31.9572i	−0.790359	+	1.08784i	0.203705	+	0.979032i	$0.434702\pi$
$863$	−23.2183	+	31.9572i	−0.790359	+	1.08784i	−0.994063	+	0.108803i	$0.965298\pi$
$864$	21.2554	−	15.4429i	0.723122	−	0.525379i
$865$	−18.8203	+	5.09267i	−0.639909	+	0.173156i
$866$	44.5304	+	32.3533i	1.51321	+	1.09941i
$867$	31.0661	−	10.0940i	1.05506	−	0.342810i
$868$		−	9.34499i		−	0.317190i
$869$	−0.953577	−	2.93481i	−0.0323479	−	0.0995566i
$870$	−28.2916	+	74.2489i	−0.959174	+	2.51727i
$871$	−22.5100	+	69.2786i	−0.762722	+	2.34742i
$872$	7.50328	+	2.43796i	0.254093	+	0.0825598i
$873$	−6.14725	−	8.46096i	−0.208053	−	0.286360i
$874$	6.94839			0.235033
$875$	−7.78440	−	15.0023i	−0.263161	−	0.507169i
$876$	−24.6882			−0.834138
$877$	−2.86200	−	3.93921i	−0.0966429	−	0.133018i	0.757957	−	0.652304i	$-0.226198\pi$
$877$	−2.86200	−	3.93921i	−0.0966429	−	0.133018i	−0.854600	+	0.519287i	$0.826198\pi$
$878$	−34.6116	−	11.2460i	−1.16809	−	0.379534i
$879$	11.4267	−	35.1677i	0.385412	−	1.18618i
$880$	2.98716	−	7.83957i	0.100697	−	0.264272i
$881$	−17.9091	−	55.1185i	−0.603372	−	1.85699i	−0.507617	−	0.861583i	$-0.669473\pi$
$881$	−17.9091	−	55.1185i	−0.603372	−	1.85699i	−0.0957552	−	0.995405i	$-0.530527\pi$
$882$			7.82488i			0.263478i
$883$	4.81712	−	1.56518i	0.162109	−	0.0526725i	−0.226838	−	0.973932i	$-0.572839\pi$
$883$	4.81712	−	1.56518i	0.162109	−	0.0526725i	0.388947	+	0.921260i	$0.372839\pi$
$884$	−40.2904	−	29.2727i	−1.35511	−	0.984546i
$885$	5.74576	−	1.55477i	0.193142	−	0.0522631i
$886$	18.0851	−	13.1396i	0.607580	−	0.441433i
$887$	17.0256	−	23.4337i	0.571664	−	0.786828i	−0.421087	−	0.907020i	$-0.638351\pi$
$887$	17.0256	−	23.4337i	0.571664	−	0.786828i	0.992751	+	0.120193i	$0.0383513\pi$
$888$	−0.944515	+	1.30001i	−0.0316958	+	0.0436256i
$889$	−9.48146	+	6.88869i	−0.317998	+	0.231039i
$890$	12.0851	−	14.9994i	0.405095	−	0.502781i
$891$	6.74006	+	4.89694i	0.225800	+	0.164054i
$892$	11.8660	−	3.85550i	0.397303	−	0.129092i
$893$		−	9.46354i		−	0.316685i
$894$	−6.79385	−	20.9093i	−0.227220	−	0.699312i
$895$	3.05245	+	2.45939i	0.102032	+	0.0822082i
$896$	4.47489	−	13.7723i	0.149495	−	0.460100i
$897$	−47.7508	−	15.5152i	−1.59435	−	0.518037i
$898$	26.0440	+	35.8465i	0.869099	+	1.19621i
$899$	−47.1375			−1.57212
$900$	5.89873	+	0.590576i	0.196624	+	0.0196859i
$901$	−53.4326			−1.78010
$902$	7.09867	+	9.77048i	0.236360	+	0.325321i
$903$	−18.8016	−	6.10900i	−0.625677	−	0.203295i
$904$	6.14324	−	18.9069i	0.204321	−	0.628836i
$905$	−18.7142	−	0.934491i	−0.622082	−	0.0310635i
$906$	19.6125	+	60.3610i	0.651581	+	2.00536i
$907$			37.4126i			1.24227i	0.783705	+	0.621133i	$0.213327\pi$
$907$			37.4126i			1.24227i	−0.783705	+	0.621133i	$0.786673\pi$
$908$	18.6595	−	6.06285i	0.619238	−	0.201203i
$909$	−6.44055	−	4.67933i	−0.213619	−	0.155204i
$910$	−38.0401	−	14.4947i	−1.26102	−	0.480494i
$911$	38.6923	−	28.1116i	1.28193	−	0.931379i	0.282324	−	0.959319i	$-0.408895\pi$
$911$	38.6923	−	28.1116i	1.28193	−	0.931379i	0.999610	+	0.0279402i	$0.00889480\pi$
$912$	5.71163	−	7.86139i	0.189131	−	0.260317i
$913$	7.93713	−	10.9245i	0.262681	−	0.361549i
$914$	3.35359	−	2.43652i	0.110927	−	0.0805930i
$915$	1.19641	−	23.9595i	0.0395521	−	0.792075i
$916$	−11.7782	−	8.55738i	−0.389164	−	0.282744i
$917$	6.25709	−	2.03305i	0.206627	−	0.0671373i
$918$		−	43.3797i		−	1.43174i
$919$	−11.2288	−	34.5587i	−0.370405	−	1.13999i	−0.946527	−	0.322625i	$-0.895435\pi$
$919$	−11.2288	−	34.5587i	−0.370405	−	1.13999i	0.576123	−	0.817363i	$-0.304565\pi$
$920$	−9.14338	+	5.96990i	−0.301448	+	0.196822i
$921$	8.82645	−	27.1650i	0.290842	−	0.895118i
$922$	10.9514	+	3.55833i	0.360666	+	0.117187i
$923$	−48.1454	−	66.2664i	−1.58472	−	2.18119i
$924$	−2.96347			−0.0974910
$925$	3.10940	−	0.676973i	0.102237	−	0.0222587i
$926$	8.30986			0.273079
$927$	5.65451	+	7.78276i	0.185718	+	0.255619i
$928$	59.8903	+	19.4595i	1.96599	+	0.638790i
$929$	2.74948	−	8.46204i	0.0902076	−	0.277630i	−0.895768	−	0.444523i	$-0.853373\pi$
$929$	2.74948	−	8.46204i	0.0902076	−	0.277630i	0.985975	+	0.166892i	$0.0533732\pi$
$930$	9.99879	+	36.9512i	0.327873	+	1.21168i
$931$	−1.45692	−	4.48393i	−0.0477485	−	0.146955i
$932$			19.0770i			0.624889i
$933$	−29.0274	+	9.43156i	−0.950313	+	0.308776i
$934$	18.4363	+	13.3948i	0.603255	+	0.438290i
$935$	−5.40564	−	8.27917i	−0.176783	−	0.270758i
$936$	−6.25860	+	4.54714i	−0.204569	+	0.148628i
$937$	−8.48435	+	11.6777i	−0.277172	+	0.381494i	−0.924795	−	0.380467i	$-0.875763\pi$
$937$	−8.48435	+	11.6777i	−0.277172	+	0.381494i	0.647623	+	0.761961i	$0.275763\pi$
$938$	17.7217	−	24.3918i	0.578634	−	0.796422i
$939$	14.8427	−	10.7838i	0.484372	−	0.351917i
$940$	−15.0070	−	22.9844i	−0.489473	−	0.749668i
$941$	−5.37458	−	3.90486i	−0.175206	−	0.127295i	0.496726	−	0.867907i	$-0.334535\pi$
$941$	−5.37458	−	3.90486i	−0.175206	−	0.127295i	−0.671932	+	0.740613i	$0.734535\pi$
$942$	−30.3044	+	9.84649i	−0.987370	+	0.320816i
$943$		−	33.3184i		−	1.08500i
$944$	−2.04225	−	6.28539i	−0.0664695	−	0.204572i
$945$	−3.64380	−	13.4659i	−0.118533	−	0.438046i
$946$	−2.83317	+	8.71959i	−0.0921142	+	0.283498i
$947$	−30.8964	−	10.0389i	−1.00400	−	0.326219i	−0.239537	−	0.970887i	$-0.576996\pi$
$947$	−30.8964	−	10.0389i	−1.00400	−	0.326219i	−0.764462	+	0.644668i	$0.776996\pi$
$948$	−6.09380	−	8.38740i	−0.197918	−	0.272410i
$949$	−63.8012			−2.07107
$950$	−8.87125	+	1.93143i	−0.287821	+	0.0626639i
$951$	3.04596			0.0987720
$952$	−6.56447	−	9.03522i	−0.212756	−	0.292833i
$953$	23.7565	+	7.71896i	0.769549	+	0.250042i	0.667372	−	0.744725i	$-0.267419\pi$
$953$	23.7565	+	7.71896i	0.769549	+	0.250042i	0.102177	+	0.994766i	$0.467419\pi$
$954$	4.73392	−	14.5695i	0.153266	−	0.471706i
$955$	1.28291	−	0.837639i	0.0415141	−	0.0271054i
$956$	−2.91595	−	8.97437i	−0.0943086	−	0.290252i
$957$			14.9482i			0.483206i
$958$	−12.6292	+	4.10346i	−0.408030	+	0.132577i
$959$	−5.72620	−	4.16033i	−0.184909	−	0.134344i
$960$	0.383162	−	7.67324i	0.0123665	−	0.247653i
$961$	6.70704	−	4.87295i	0.216356	−	0.157192i
$962$	4.50510	−	6.20073i	0.145250	−	0.199920i
$963$	2.18476	−	3.00707i	0.0704030	−	0.0969015i
$964$	−18.0298	+	13.0994i	−0.580700	+	0.421903i
$965$	−22.2084	−	8.46222i	−0.714914	−	0.272409i
$966$	16.8123	+	12.2148i	0.540926	+	0.393006i
$967$	−44.1087	+	14.3318i	−1.41844	+	0.460879i	−0.915106	−	0.403213i	$-0.867893\pi$
$967$	−44.1087	+	14.3318i	−1.41844	+	0.460879i	−0.503334	+	0.864092i	$0.667893\pi$
$968$			13.2934i			0.427268i
$969$	−3.53905	−	10.8921i	−0.113691	−	0.349904i
$970$	46.4006	+	2.31700i	1.48983	+	0.0743945i
$971$	10.5025	−	32.3234i	0.337042	−	1.03731i	−0.628666	−	0.777675i	$-0.716399\pi$
$971$	10.5025	−	32.3234i	0.337042	−	1.03731i	0.965708	−	0.259632i	$-0.0836013\pi$
$972$	11.3461	+	3.68657i	0.363927	+	0.118247i
$973$	9.52680	+	13.1125i	0.305415	+	0.420368i
$974$	42.5373			1.36298
$975$	65.2779	+	6.53557i	2.09057	+	0.209306i
$976$	−26.6350			−0.852564
$977$	−0.983937	−	1.35427i	−0.0314789	−	0.0433271i	0.792987	−	0.609238i	$-0.208525\pi$
$977$	−0.983937	−	1.35427i	−0.0314789	−	0.0433271i	−0.824466	+	0.565911i	$0.808525\pi$
$978$	−77.0710	−	25.0419i	−2.46446	−	0.800751i
$979$	1.11982	−	3.44645i	0.0357896	−	0.110149i
$980$	−10.6489	−	8.57993i	−0.340167	−	0.274076i
$981$	1.74609	+	5.37390i	0.0557482	+	0.171575i
$982$		−	26.4598i		−	0.844367i
$983$	−51.7541	+	16.8159i	−1.65070	+	0.536345i	−0.978892	−	0.204379i	$-0.934482\pi$
$983$	−51.7541	+	16.8159i	−1.65070	+	0.536345i	−0.671809	+	0.740724i	$0.734482\pi$
$984$	−17.7851	−	12.9216i	−0.566967	−	0.411926i
$985$	23.5488	−	29.2274i	0.750326	−	0.931263i
$986$	84.1168	−	61.1145i	2.67883	−	1.94628i
$987$	16.6363	−	22.8979i	0.529539	−	0.728848i
$988$	−5.05673	+	6.95999i	−0.160876	+	0.221427i
$989$	20.4632	−	14.8674i	0.650692	−	0.472755i
$990$	2.73641	−	0.740458i	0.0869688	−	0.0235333i
$991$	−1.66476	−	1.20952i	−0.0528829	−	0.0384217i	0.561030	−	0.827796i	$-0.310405\pi$
$991$	−1.66476	−	1.20952i	−0.0528829	−	0.0384217i	−0.613913	+	0.789374i	$0.710405\pi$
$992$	28.8536	−	9.37511i	0.916103	−	0.297660i
$993$		−	16.7395i		−	0.531212i
$994$	10.4764	+	32.2431i	0.332291	+	1.02269i
$995$	−1.99013	+	5.22294i	−0.0630914	+	0.165578i
$996$	14.0192	−	43.1467i	0.444215	−	1.36715i
$997$	−11.7095	−	3.80465i	−0.370844	−	0.120494i	0.117665	−	0.993053i	$-0.462459\pi$
$997$	−11.7095	−	3.80465i	−0.370844	−	0.120494i	−0.488509	+	0.872559i	$0.662459\pi$
$998$	−43.7324	−	60.1924i	−1.38432	−	1.90536i
$999$	2.62655			0.0831004

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.n.a.39.16	✓	80
25.9	even	10	inner	475.2.n.a.134.16	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.n.a.39.16	✓	80	1.1	even	1	trivial
475.2.n.a.134.16	yes	80	25.9	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.06731 + 1.46902i) q^{2} +(1.88156 + 0.611355i) q^{3} +(-0.400851 + 1.23369i) q^{4} +(-0.796184 + 2.08952i) q^{5} +(1.11011 + 3.41656i) q^{6} -1.51173i q^{7} +(1.21373 - 0.394364i) q^{8} +(0.739455 + 0.537245i) q^{9} +O(q^{10})\)	\(q+(1.06731 + 1.46902i) q^{2} +(1.88156 + 0.611355i) q^{3} +(-0.400851 + 1.23369i) q^{4} +(-0.796184 + 2.08952i) q^{5} +(1.11011 + 3.41656i) q^{6} -1.51173i q^{7} +(1.21373 - 0.394364i) q^{8} +(0.739455 + 0.537245i) q^{9} +(-3.91933 + 1.06055i) q^{10} +(-0.617978 + 0.448987i) q^{11} +(-1.50845 + 2.07620i) q^{12} +(-3.89825 + 5.36547i) q^{13} +(2.22076 - 1.61348i) q^{14} +(-2.77550 + 3.44480i) q^{15} +(3.97364 + 2.88702i) q^{16} +(5.50553 - 1.78885i) q^{17} +1.65968i q^{18} +(-0.309017 - 0.951057i) q^{19} +(-2.25867 - 1.81983i) q^{20} +(0.924202 - 2.84440i) q^{21} +(-1.31915 - 0.428617i) q^{22} +(2.24922 + 3.09578i) q^{23} +2.52480 q^{24} +(-3.73218 - 3.32728i) q^{25} -12.0426 q^{26} +(-2.42572 - 3.33872i) q^{27} +(1.86500 + 0.605977i) q^{28} +(3.05663 - 9.40735i) q^{29} +(-8.02282 - 0.400617i) q^{30} +(-1.47261 - 4.53222i) q^{31} +6.36632i q^{32} +(-1.43725 + 0.466992i) q^{33} +(8.50397 + 6.17850i) q^{34} +(3.15878 + 1.20361i) q^{35} +(-0.959206 + 0.696904i) q^{36} +(-0.374095 + 0.514898i) q^{37} +(1.06731 - 1.46902i) q^{38} +(-10.6150 + 7.71224i) q^{39} +(-0.142319 + 2.85010i) q^{40} +(-7.04416 - 5.11788i) q^{41} +(5.16490 - 1.67818i) q^{42} -6.61002i q^{43} +(-0.306195 - 0.942372i) q^{44} +(-1.71133 + 1.11736i) q^{45} +(-2.14717 + 6.60831i) q^{46} +(9.00036 + 2.92439i) q^{47} +(5.71163 + 7.86139i) q^{48} +4.71468 q^{49} +(0.904467 - 9.03391i) q^{50} +11.4526 q^{51} +(-5.05673 - 6.95999i) q^{52} +(-8.77849 - 2.85230i) q^{53} +(2.31567 - 7.12689i) q^{54} +(-0.446144 - 1.64875i) q^{55} +(-0.596171 - 1.83483i) q^{56} -1.97839i q^{57} +(17.0820 - 5.55028i) q^{58} +(-1.08856 - 0.790887i) q^{59} +(-3.13726 - 4.80497i) q^{60} +(-4.38712 + 3.18743i) q^{61} +(5.08622 - 7.00058i) q^{62} +(0.812168 - 1.11785i) q^{63} +(-1.40502 + 1.02080i) q^{64} +(-8.10754 - 12.4174i) q^{65} +(-2.22001 - 1.61293i) q^{66} +(10.4460 - 3.39410i) q^{67} +7.50919i q^{68} +(2.33941 + 7.19997i) q^{69} +(1.60326 + 5.92495i) q^{70} +(-3.81652 + 11.7460i) q^{71} +(1.10937 + 0.360455i) q^{72} +(5.65453 + 7.78280i) q^{73} -1.15567 q^{74} +(-4.98817 - 8.54217i) q^{75} +1.29718 q^{76} +(0.678746 + 0.934214i) q^{77} +(-22.6589 - 7.36233i) q^{78} +(-1.24836 + 3.84206i) q^{79} +(-9.19622 + 6.00439i) q^{80} +(-3.37033 - 10.3728i) q^{81} -15.8104i q^{82} +(-16.8126 + 5.46275i) q^{83} +(3.13865 + 2.28036i) q^{84} +(-0.645565 + 12.9282i) q^{85} +(9.71029 - 7.05494i) q^{86} +(11.5025 - 15.8318i) q^{87} +(-0.572993 + 0.788657i) q^{88} +(-3.83802 + 2.78849i) q^{89} +(-3.46794 - 1.32141i) q^{90} +(8.11113 + 5.89308i) q^{91} +(-4.72084 + 1.53390i) q^{92} -9.42793i q^{93} +(5.31016 + 16.3430i) q^{94} +(2.23329 + 0.111519i) q^{95} +(-3.89209 + 11.9786i) q^{96} +(-10.8821 - 3.53582i) q^{97} +(5.03202 + 6.92598i) q^{98} -0.698183 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9}+O(q^{10}) \) 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9	\( 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9} - 36 q^{10} + 20 q^{11} + 45 q^{12} - 10 q^{14} - 20 q^{16} - 15 q^{17} + 20 q^{19} + 12 q^{20} + 16 q^{21} + 15 q^{23} + 72 q^{24} + 41 q^{25} - 84 q^{26} + 15 q^{27} + 30 q^{28} - 24 q^{29} - 40 q^{30} + 8 q^{31} - 75 q^{33} - 24 q^{34} - 33 q^{35} - 32 q^{36} - 15 q^{37} - 30 q^{39} - 28 q^{40} + 13 q^{41} - 130 q^{42} - 24 q^{44} + 6 q^{45} + 30 q^{46} + 145 q^{48} - 28 q^{49} + 77 q^{50} - 36 q^{51} - 5 q^{52} - 10 q^{53} + 15 q^{54} - 8 q^{55} + 48 q^{56} - 60 q^{58} - 19 q^{59} - 110 q^{60} + 8 q^{61} + 110 q^{62} + 55 q^{63} + 16 q^{64} - 43 q^{65} - 17 q^{66} - 65 q^{67} - 42 q^{69} + 4 q^{70} + 18 q^{71} + 100 q^{73} + 22 q^{74} + 115 q^{75} + 64 q^{76} - 145 q^{78} - 16 q^{79} - 97 q^{80} + q^{81} - 70 q^{83} - 46 q^{84} - 16 q^{85} + 64 q^{86} + 10 q^{87} + 30 q^{88} + 4 q^{89} - 8 q^{90} + 16 q^{91} - 135 q^{92} + 38 q^{94} - 2 q^{95} + 50 q^{96} + 150 q^{97} + 130 q^{98} + 178 q^{99}+O(q^{100}) \) 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9 - 36 * q^10 + 20 * q^11 + 45 * q^12 - 10 * q^14 - 20 * q^16 - 15 * q^17 + 20 * q^19 + 12 * q^20 + 16 * q^21 + 15 * q^23 + 72 * q^24 + 41 * q^25 - 84 * q^26 + 15 * q^27 + 30 * q^28 - 24 * q^29 - 40 * q^30 + 8 * q^31 - 75 * q^33 - 24 * q^34 - 33 * q^35 - 32 * q^36 - 15 * q^37 - 30 * q^39 - 28 * q^40 + 13 * q^41 - 130 * q^42 - 24 * q^44 + 6 * q^45 + 30 * q^46 + 145 * q^48 - 28 * q^49 + 77 * q^50 - 36 * q^51 - 5 * q^52 - 10 * q^53 + 15 * q^54 - 8 * q^55 + 48 * q^56 - 60 * q^58 - 19 * q^59 - 110 * q^60 + 8 * q^61 + 110 * q^62 + 55 * q^63 + 16 * q^64 - 43 * q^65 - 17 * q^66 - 65 * q^67 - 42 * q^69 + 4 * q^70 + 18 * q^71 + 100 * q^73 + 22 * q^74 + 115 * q^75 + 64 * q^76 - 145 * q^78 - 16 * q^79 - 97 * q^80 + q^81 - 70 * q^83 - 46 * q^84 - 16 * q^85 + 64 * q^86 + 10 * q^87 + 30 * q^88 + 4 * q^89 - 8 * q^90 + 16 * q^91 - 135 * q^92 + 38 * q^94 - 2 * q^95 + 50 * q^96 + 150 * q^97 + 130 * q^98 + 178 * q^99

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