LMFDB - Embedded newform 240.2.t.b.59.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(59,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 2]))

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

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

chi := DirichletCharacter("240.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.t (of order $4$, degree $2$, 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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			59.22
Character	$\chi$	$=$	240.59
Dual form			240.2.t.b.179.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0728709 + 1.41233i) q^{2} +(-0.938373 - 1.45584i) q^{3} +(-1.98938 + 0.205836i) q^{4} +(-1.27753 + 1.83519i) q^{5} +(1.98775 - 1.43139i) q^{6} -2.98852i q^{7} +(-0.435678 - 2.79467i) q^{8} +(-1.23891 + 2.73223i) q^{9} +O(q^{10})$	\(q+(0.0728709 + 1.41233i) q^{2} +(-0.938373 - 1.45584i) q^{3} +(-1.98938 + 0.205836i) q^{4} +(-1.27753 + 1.83519i) q^{5} +(1.98775 - 1.43139i) q^{6} -2.98852i q^{7} +(-0.435678 - 2.79467i) q^{8} +(-1.23891 + 2.73223i) q^{9} +(-2.68499 - 1.67057i) q^{10} +(-2.52400 - 2.52400i) q^{11} +(2.16644 + 2.70306i) q^{12} +(-3.40183 - 3.40183i) q^{13} +(4.22079 - 0.217776i) q^{14} +(3.87053 + 0.137786i) q^{15} +(3.91526 - 0.818973i) q^{16} -0.127067 q^{17} +(-3.94911 - 1.55066i) q^{18} +(-0.587567 - 0.587567i) q^{19} +(2.16375 - 3.91385i) q^{20} +(-4.35079 + 2.80434i) q^{21} +(3.38081 - 3.74866i) q^{22} -2.84152 q^{23} +(-3.65975 + 3.25672i) q^{24} +(-1.73582 - 4.68902i) q^{25} +(4.55663 - 5.05242i) q^{26} +(5.14024 - 0.760202i) q^{27} +(0.615146 + 5.94530i) q^{28} +(-1.31161 - 1.31161i) q^{29} +(0.0874495 + 5.47653i) q^{30} +6.78269i q^{31} +(1.44197 + 5.46998i) q^{32} +(-1.30607 + 6.04298i) q^{33} +(-0.00925951 - 0.179461i) q^{34} +(5.48449 + 3.81793i) q^{35} +(1.90227 - 5.69046i) q^{36} +(-7.14473 + 7.14473i) q^{37} +(0.787025 - 0.872658i) q^{38} +(-1.76032 + 8.14470i) q^{39} +(5.68534 + 2.77073i) q^{40} +7.94027 q^{41} +(-4.27772 - 5.94042i) q^{42} +(2.36290 + 2.36290i) q^{43} +(5.54072 + 4.50166i) q^{44} +(-3.43141 - 5.76415i) q^{45} +(-0.207065 - 4.01318i) q^{46} -7.61054i q^{47} +(-4.86627 - 4.93147i) q^{48} -1.93124 q^{49} +(6.49598 - 2.79326i) q^{50} +(0.119236 + 0.184989i) q^{51} +(7.46776 + 6.06732i) q^{52} +(-1.48747 - 1.48747i) q^{53} +(1.44823 + 7.20435i) q^{54} +(7.85650 - 1.40752i) q^{55} +(-8.35192 + 1.30203i) q^{56} +(-0.304044 + 1.40676i) q^{57} +(1.75685 - 1.94801i) q^{58} +(-7.38294 - 7.38294i) q^{59} +(-7.72832 + 0.522588i) q^{60} +(-4.75537 + 4.75537i) q^{61} +(-9.57943 + 0.494261i) q^{62} +(8.16533 + 3.70251i) q^{63} +(-7.62037 + 2.43515i) q^{64} +(10.5890 - 1.89705i) q^{65} +(-8.62989 - 1.40426i) q^{66} +(3.26749 - 3.26749i) q^{67} +(0.252785 - 0.0261550i) q^{68} +(2.66641 + 4.13679i) q^{69} +(-4.99253 + 8.02415i) q^{70} +8.39116i q^{71} +(8.17546 + 2.27198i) q^{72} -2.60248 q^{73} +(-10.6114 - 9.57010i) q^{74} +(-5.19759 + 6.92712i) q^{75} +(1.28984 + 1.04795i) q^{76} +(-7.54302 + 7.54302i) q^{77} +(-11.6313 - 1.89265i) q^{78} -16.3288i q^{79} +(-3.49890 + 8.23150i) q^{80} +(-5.93019 - 6.76999i) q^{81} +(0.578615 + 11.2143i) q^{82} +(-5.78381 - 5.78381i) q^{83} +(8.07814 - 6.47446i) q^{84} +(0.162332 - 0.233192i) q^{85} +(-3.16502 + 3.50939i) q^{86} +(-0.678708 + 3.14026i) q^{87} +(-5.95410 + 8.15340i) q^{88} +16.9746 q^{89} +(7.89086 - 5.26634i) q^{90} +(-10.1664 + 10.1664i) q^{91} +(5.65287 - 0.584889i) q^{92} +(9.87448 - 6.36470i) q^{93} +(10.7486 - 0.554587i) q^{94} +(1.82893 - 0.327660i) q^{95} +(6.61028 - 7.23216i) q^{96} -12.8285i q^{97} +(-0.140731 - 2.72756i) q^{98} +(10.0232 - 3.76914i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 8 q^{4} - 4 q^{6}+O(q^{10}) $ 80 * q - 8 * q^4 - 4 * q^6	$ 80 q - 8 q^{4} - 4 q^{6} + 16 q^{10} - 32 q^{16} + 16 q^{19} + 8 q^{21} - 56 q^{24} + 8 q^{30} - 16 q^{34} - 40 q^{36} - 8 q^{39} - 8 q^{40} - 12 q^{45} - 24 q^{46} - 112 q^{49} + 32 q^{51} + 60 q^{54} - 40 q^{55} + 40 q^{60} + 16 q^{61} - 32 q^{64} - 56 q^{66} - 40 q^{69} + 48 q^{70} - 36 q^{75} - 128 q^{76} + 64 q^{81} + 128 q^{84} - 64 q^{85} + 72 q^{90} + 48 q^{91} + 56 q^{94} - 24 q^{96} - 8 q^{99}+O(q^{100}) $ 80 * q - 8 * q^4 - 4 * q^6 + 16 * q^10 - 32 * q^16 + 16 * q^19 + 8 * q^21 - 56 * q^24 + 8 * q^30 - 16 * q^34 - 40 * q^36 - 8 * q^39 - 8 * q^40 - 12 * q^45 - 24 * q^46 - 112 * q^49 + 32 * q^51 + 60 * q^54 - 40 * q^55 + 40 * q^60 + 16 * q^61 - 32 * q^64 - 56 * q^66 - 40 * q^69 + 48 * q^70 - 36 * q^75 - 128 * q^76 + 64 * q^81 + 128 * q^84 - 64 * q^85 + 72 * q^90 + 48 * q^91 + 56 * q^94 - 24 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.0728709	+	1.41233i	0.0515275	+	0.998672i
$2$	0.0728709	+	1.41233i	0.0515275	+	0.998672i
$3$	−0.938373	−	1.45584i	−0.541770	−	0.840527i
$3$	−0.938373	−	1.45584i	−0.541770	−	0.840527i
$4$	−1.98938	+	0.205836i	−0.994690	+	0.102918i
$5$	−1.27753	+	1.83519i	−0.571330	+	0.820721i
$5$	−1.27753	+	1.83519i	−0.571330	+	0.820721i
$6$	1.98775	−	1.43139i	0.811494	−	0.584360i
$7$		−	2.98852i		−	1.12955i	−0.825244	−	0.564777i	$-0.808962\pi$
$7$		−	2.98852i		−	1.12955i	0.825244	−	0.564777i	$-0.191038\pi$
$8$	−0.435678	−	2.79467i	−0.154035	−	0.988065i
$9$	−1.23891	+	2.73223i	−0.412971	+	0.910744i
$10$	−2.68499	−	1.67057i	−0.849070	−	0.528281i
$11$	−2.52400	−	2.52400i	−0.761014	−	0.761014i	0.215491	−	0.976506i	$-0.430865\pi$
$11$	−2.52400	−	2.52400i	−0.761014	−	0.761014i	−0.976506	+	0.215491i	$0.930865\pi$
$12$	2.16644	+	2.70306i	0.625399	+	0.780306i
$13$	−3.40183	−	3.40183i	−0.943499	−	0.943499i	0.0549880	−	0.998487i	$-0.482488\pi$
$13$	−3.40183	−	3.40183i	−0.943499	−	0.943499i	−0.998487	+	0.0549880i	$0.982488\pi$
$14$	4.22079	−	0.217776i	1.12805	−	0.0582031i
$15$	3.87053	+	0.137786i	0.999367	+	0.0355762i
$16$	3.91526	−	0.818973i	0.978816	−	0.204743i
$17$	−0.127067			−0.0308183			−0.0154092	−	0.999881i	$-0.504905\pi$
$17$	−0.127067			−0.0308183			−0.0154092	+	0.999881i	$0.504905\pi$
$18$	−3.94911	−	1.55066i	−0.930814	−	0.365494i
$19$	−0.587567	−	0.587567i	−0.134797	−	0.134797i	0.636489	−	0.771286i	$-0.280386\pi$
$19$	−0.587567	−	0.587567i	−0.134797	−	0.134797i	−0.771286	+	0.636489i	$0.780386\pi$
$20$	2.16375	−	3.91385i	0.483829	−	0.875163i
$21$	−4.35079	+	2.80434i	−0.949420	+	0.611958i
$22$	3.38081	−	3.74866i	0.720790	−	0.799217i
$23$	−2.84152			−0.592499			−0.296249	−	0.955111i	$-0.595736\pi$
$23$	−2.84152			−0.592499			−0.296249	+	0.955111i	$0.595736\pi$
$24$	−3.65975	+	3.25672i	−0.747044	+	0.664775i
$25$	−1.73582	−	4.68902i	−0.347165	−	0.937804i
$26$	4.55663	−	5.05242i	0.893629	−	0.990862i
$27$	5.14024	−	0.760202i	0.989240	−	0.146301i
$28$	0.615146	+	5.94530i	0.116252	+	1.12356i
$29$	−1.31161	−	1.31161i	−0.243560	−	0.243560i	0.574761	−	0.818321i	$-0.305095\pi$
$29$	−1.31161	−	1.31161i	−0.243560	−	0.243560i	−0.818321	+	0.574761i	$0.805095\pi$
$30$	0.0874495	+	5.47653i	0.0159660	+	0.999873i
$31$			6.78269i			1.21821i	0.793091	+	0.609104i	$0.208471\pi$
$31$			6.78269i			1.21821i	−0.793091	+	0.609104i	$0.791529\pi$
$32$	1.44197	+	5.46998i	0.254907	+	0.966966i
$33$	−1.30607	+	6.04298i	−0.227358	+	1.05195i
$34$	−0.00925951	−	0.179461i	−0.00158799	−	0.0307774i
$35$	5.48449	+	3.81793i	0.927048	+	0.645347i
$36$	1.90227	−	5.69046i	0.317046	−	0.948410i
$37$	−7.14473	+	7.14473i	−1.17459	+	1.17459i	−0.193482	+	0.981104i	$0.561978\pi$
$37$	−7.14473	+	7.14473i	−1.17459	+	1.17459i	−0.981104	+	0.193482i	$0.938022\pi$
$38$	0.787025	−	0.872658i	0.127672	−	0.141564i
$39$	−1.76032	+	8.14470i	−0.281877	+	1.30420i
$40$	5.68534	+	2.77073i	0.898931	+	0.438091i
$41$	7.94027			1.24006			0.620031	−	0.784577i	$-0.287120\pi$
$41$	7.94027			1.24006			0.620031	+	0.784577i	$0.287120\pi$
$42$	−4.27772	−	5.94042i	−0.660066	−	0.916626i
$43$	2.36290	+	2.36290i	0.360339	+	0.360339i	0.863938	−	0.503599i	$-0.167991\pi$
$43$	2.36290	+	2.36290i	0.360339	+	0.360339i	−0.503599	+	0.863938i	$0.667991\pi$
$44$	5.54072	+	4.50166i	0.835296	+	0.678651i
$45$	−3.43141	−	5.76415i	−0.511524	−	0.859269i
$46$	−0.207065	−	4.01318i	−0.0305300	−	0.591712i
$47$		−	7.61054i		−	1.11011i	−0.831813	−	0.555055i	$-0.812697\pi$
$47$		−	7.61054i		−	1.11011i	0.831813	−	0.555055i	$-0.187303\pi$
$48$	−4.86627	−	4.93147i	−0.702385	−	0.711797i
$49$	−1.93124			−0.275891
$50$	6.49598	−	2.79326i	0.918670	−	0.395026i
$51$	0.119236	+	0.184989i	0.0166964	+	0.0259036i
$52$	7.46776	+	6.06732i	1.03559	+	0.841386i
$53$	−1.48747	−	1.48747i	−0.204319	−	0.204319i	0.597528	−	0.801848i	$-0.296150\pi$
$53$	−1.48747	−	1.48747i	−0.204319	−	0.204319i	−0.801848	+	0.597528i	$0.796150\pi$
$54$	1.44823	+	7.20435i	0.197080	+	0.980387i
$55$	7.85650	−	1.40752i	1.05937	−	0.189790i
$56$	−8.35192	+	1.30203i	−1.11607	+	0.173991i
$57$	−0.304044	+	1.40676i	−0.0402716	+	0.186330i
$58$	1.75685	−	1.94801i	0.230686	−	0.255786i
$59$	−7.38294	−	7.38294i	−0.961177	−	0.961177i	0.0380975	−	0.999274i	$-0.487870\pi$
$59$	−7.38294	−	7.38294i	−0.961177	−	0.961177i	−0.999274	+	0.0380975i	$0.987870\pi$
$60$	−7.72832	+	0.522588i	−0.997722	+	0.0674658i
$61$	−4.75537	+	4.75537i	−0.608862	+	0.608862i	−0.942649	−	0.333786i	$-0.891674\pi$
$61$	−4.75537	+	4.75537i	−0.608862	+	0.608862i	0.333786	+	0.942649i	$0.391674\pi$
$62$	−9.57943	+	0.494261i	−1.21659	+	0.0627712i
$63$	8.16533	+	3.70251i	1.02873	+	0.466473i
$64$	−7.62037	+	2.43515i	−0.952546	+	0.304394i
$65$	10.5890	−	1.89705i	1.31340	−	0.235300i
$66$	−8.62989	−	1.40426i	−1.06227	−	0.172852i
$67$	3.26749	−	3.26749i	0.399187	−	0.399187i	−0.478759	−	0.877946i	$-0.658913\pi$
$67$	3.26749	−	3.26749i	0.399187	−	0.399187i	0.877946	+	0.478759i	$0.158913\pi$
$68$	0.252785	−	0.0261550i	0.0306547	−	0.00317177i
$69$	2.66641	+	4.13679i	0.320998	+	0.498011i
$70$	−4.99253	+	8.02415i	−0.596722	+	0.959070i
$71$			8.39116i			0.995848i	0.867221	+	0.497924i	$0.165904\pi$
$71$			8.39116i			0.995848i	−0.867221	+	0.497924i	$0.834096\pi$
$72$	8.17546	+	2.27198i	0.963487	+	0.267755i
$73$	−2.60248			−0.304597			−0.152299	−	0.988335i	$-0.548668\pi$
$73$	−2.60248			−0.304597			−0.152299	+	0.988335i	$0.548668\pi$
$74$	−10.6114	−	9.57010i	−1.23355	−	1.11250i
$75$	−5.19759	+	6.92712i	−0.600166	+	0.799875i
$76$	1.28984	+	1.04795i	0.147954	+	0.120208i
$77$	−7.54302	+	7.54302i	−0.859607	+	0.859607i
$78$	−11.6313	−	1.89265i	−1.31699	−	0.214300i
$79$		−	16.3288i		−	1.83713i	−0.395268	−	0.918566i	$-0.629348\pi$
$79$		−	16.3288i		−	1.83713i	0.395268	−	0.918566i	$-0.370652\pi$
$80$	−3.49890	+	8.23150i	−0.391189	+	0.920310i
$81$	−5.93019	−	6.76999i	−0.658910	−	0.752221i
$82$	0.578615	+	11.2143i	0.0638973	+	1.23841i
$83$	−5.78381	−	5.78381i	−0.634856	−	0.634856i	0.314426	−	0.949282i	$-0.398188\pi$
$83$	−5.78381	−	5.78381i	−0.634856	−	0.634856i	−0.949282	+	0.314426i	$0.898188\pi$
$84$	8.07814	−	6.47446i	0.881397	−	0.706421i
$85$	0.162332	−	0.233192i	0.0176074	−	0.0252932i
$86$	−3.16502	+	3.50939i	−0.341293	+	0.378428i
$87$	−0.678708	+	3.14026i	−0.0727651	+	0.336672i
$88$	−5.95410	+	8.15340i	−0.634709	+	0.869155i
$89$	16.9746			1.79931			0.899654	−	0.436603i	$-0.143819\pi$
$89$	16.9746			1.79931			0.899654	+	0.436603i	$0.143819\pi$
$90$	7.89086	−	5.26634i	0.831770	−	0.555121i
$91$	−10.1664	+	10.1664i	−1.06573	+	1.06573i
$92$	5.65287	−	0.584889i	0.589353	−	0.0609789i
$93$	9.87448	−	6.36470i	1.02394	−	0.659988i
$94$	10.7486	−	0.554587i	1.10864	−	0.0572013i
$95$	1.82893	−	0.327660i	0.187644	−	0.0336172i
$96$	6.61028	−	7.23216i	0.674659	−	0.738129i
$97$		−	12.8285i		−	1.30253i	−0.758848	−	0.651267i	$-0.774238\pi$
$97$		−	12.8285i		−	1.30253i	0.758848	−	0.651267i	$-0.225762\pi$
$98$	−0.140731	−	2.72756i	−0.0142160	−	0.275525i
$99$	10.0232	−	3.76914i	1.00737	−	0.378813i
$100$	4.41838	+	8.97095i	0.441838	+	0.897095i
$101$	−1.45648	+	1.45648i	−0.144925	+	0.144925i	−0.775847	−	0.630922i	$-0.782677\pi$
$101$	−1.45648	+	1.45648i	−0.144925	+	0.144925i	0.630922	+	0.775847i	$0.282677\pi$
$102$	−0.252577	+	0.181882i	−0.0250089	+	0.0180090i
$103$		−	0.355513i		−	0.0350297i	−0.999847	−	0.0175149i	$-0.994425\pi$
$103$		−	0.355513i		−	0.0350297i	0.999847	−	0.0175149i	$-0.00557544\pi$
$104$	−8.02490	+	10.9891i	−0.786906	+	1.07757i
$105$	0.411776	−	11.5672i	0.0401852	−	1.12884i
$106$	1.99241	−	2.20920i	0.193520	−	0.214576i
$107$	5.54098	−	5.54098i	0.535666	−	0.535666i	−0.386587	−	0.922253i	$-0.626346\pi$
$107$	5.54098	−	5.54098i	0.535666	−	0.535666i	0.922253	+	0.386587i	$0.126346\pi$
$108$	−10.0694	+	2.57038i	−0.968930	+	0.247335i
$109$	9.20725	−	9.20725i	0.881894	−	0.881894i	−0.111833	−	0.993727i	$-0.535672\pi$
$109$	9.20725	−	9.20725i	0.881894	−	0.881894i	0.993727	+	0.111833i	$0.0356721\pi$
$110$	2.56040	+	10.9934i	0.244125	+	1.04818i
$111$	17.1060	+	3.69713i	1.62363	+	0.350916i
$112$	−2.44752	−	11.7008i	−0.231269	−	1.10562i
$113$	−12.8907			−1.21265			−0.606327	−	0.795216i	$-0.707358\pi$
$113$	−12.8907			−1.21265			−0.606327	+	0.795216i	$0.707358\pi$
$114$	−2.00897	−	0.326900i	−0.188157	−	0.0306170i
$115$	3.63014	−	5.21473i	0.338512	−	0.486276i
$116$	2.87926	+	2.33931i	0.267333	+	0.217199i
$117$	13.5092	−	5.08003i	1.24892	−	0.469649i
$118$	9.88918	−	10.9652i	0.910373	−	1.00943i
$119$			0.379743i			0.0348110i
$120$	−1.30124	−	10.8769i	−0.118786	−	0.992920i
$121$			1.74114i			0.158286i
$122$	−7.06270	−	6.36964i	−0.639427	−	0.576680i
$123$	−7.45094	−	11.5597i	−0.671828	−	1.04231i
$124$	−1.39612	−	13.4934i	−0.125376	−	1.21174i
$125$	10.8228	+	2.80481i	0.968021	+	0.250870i
$126$	−4.63417	+	11.8020i	−0.412845	+	1.05140i
$127$	−13.2152			−1.17266			−0.586328	−	0.810074i	$-0.699427\pi$
$127$	−13.2152			−1.17266			−0.586328	+	0.810074i	$0.699427\pi$
$128$	−3.99455	−	10.5851i	−0.353072	−	0.935596i
$129$	1.22271	−	5.65728i	0.107654	−	0.498095i
$130$	3.45090	+	14.8169i	0.302664	+	1.29953i
$131$	6.69769	−	6.69769i	0.585180	−	0.585180i	−0.351142	−	0.936322i	$-0.614207\pi$
$131$	6.69769	−	6.69769i	0.585180	−	0.585180i	0.936322	+	0.351142i	$0.114207\pi$
$132$	1.35441	−	12.2906i	0.117886	−	1.06976i
$133$	−1.75595	+	1.75595i	−0.152261	+	0.152261i
$134$	4.85289	+	4.37668i	0.419226	+	0.378088i
$135$	−5.17171	+	10.4045i	−0.445110	+	0.895476i
$136$	0.0553604	+	0.355111i	0.00474711	+	0.0304505i
$137$			20.0773i			1.71532i	0.514218	+	0.857660i	$0.328082\pi$
$137$			20.0773i			1.71532i	−0.514218	+	0.857660i	$0.671918\pi$
$138$	−5.64823	+	4.06732i	−0.480809	+	0.346233i
$139$	10.9617	−	10.9617i	0.929761	−	0.929761i	−0.0679293	−	0.997690i	$-0.521639\pi$
$139$	10.9617	−	10.9617i	0.929761	−	0.929761i	0.997690	+	0.0679293i	$0.0216392\pi$
$140$	−11.6966	−	6.46640i	−0.988543	−	0.546510i
$141$	−11.0797	+	7.14152i	−0.933078	+	0.601425i
$142$	−11.8511	+	0.611472i	−0.994525	+	0.0513136i
$143$			17.1725i			1.43603i
$144$	−2.61304	+	11.7120i	−0.217753	+	0.976004i
$145$	4.08267	−	0.731425i	0.339047	−	0.0607415i
$146$	−0.189645	−	3.67557i	−0.0156951	−	0.304193i
$147$	1.81222	+	2.81156i	0.149470	+	0.231894i
$148$	12.7429	−	15.6842i	1.04746	−	1.28923i
$149$	−7.93077	+	7.93077i	−0.649714	+	0.649714i	−0.952924	−	0.303210i	$-0.901942\pi$
$149$	−7.93077	+	7.93077i	−0.649714	+	0.649714i	0.303210	+	0.952924i	$0.401942\pi$
$150$	−10.1622	−	6.83595i	−0.829738	−	0.558153i
$151$	−4.02297			−0.327384			−0.163692	−	0.986511i	$-0.552340\pi$
$151$	−4.02297			−0.327384			−0.163692	+	0.986511i	$0.552340\pi$
$152$	−1.38607	+	1.89805i	−0.112425	+	0.153952i
$153$	0.157425	−	0.347177i	0.0127271	−	0.0280676i
$154$	−11.2029	−	10.1036i	−0.902758	−	0.814171i
$155$	−12.4475	−	8.66511i	−0.999808	−	0.695998i
$156$	1.82547	−	16.5652i	0.146155	−	1.32628i
$157$	10.2275	+	10.2275i	0.816245	+	0.816245i	0.985562	−	0.169317i	$-0.0541561\pi$
$157$	10.2275	+	10.2275i	0.816245	+	0.816245i	−0.169317	+	0.985562i	$0.554156\pi$
$158$	23.0617	−	1.18989i	1.83469	−	0.0946628i
$159$	−0.769708	+	3.56131i	−0.0610418	+	0.282430i
$160$	−11.8806	−	4.34179i	−0.939245	−	0.343248i
$161$			8.49195i			0.669259i
$162$	9.12936	−	8.86876i	0.717270	−	0.696795i
$163$	−4.76608	+	4.76608i	−0.373308	+	0.373308i	−0.868681	−	0.495373i	$-0.835032\pi$
$163$	−4.76608	+	4.76608i	−0.373308	+	0.373308i	0.495373	+	0.868681i	$0.335032\pi$
$164$	−15.7962	+	1.63440i	−1.23348	+	0.127625i
$165$	−9.42145	−	10.1170i	−0.733459	−	0.787607i
$166$	7.74720	−	8.59015i	0.601300	−	0.666725i
$167$	12.9105			0.999042			0.499521	−	0.866302i	$-0.333509\pi$
$167$	12.9105			0.999042			0.499521	+	0.866302i	$0.333509\pi$
$168$	9.73276	+	10.9372i	0.750899	+	0.843826i
$169$			10.1450i			0.780381i
$170$	0.341175	+	0.212275i	0.0261669	+	0.0162807i
$171$	2.33331	−	0.877426i	0.178433	−	0.0670985i
$172$	−5.18708	−	4.21434i	−0.395511	−	0.321340i
$173$	8.42120	−	8.42120i	0.640252	−	0.640252i	−0.310365	−	0.950617i	$-0.600451\pi$
$173$	8.42120	−	8.42120i	0.640252	−	0.640252i	0.950617	+	0.310365i	$0.100451\pi$
$174$	−4.48456	−	0.729728i	−0.339974	−	0.0553206i
$175$	−14.0132	+	5.18754i	−1.05930	+	0.392141i
$176$	−11.9492	−	7.81503i	−0.900705	−	0.589080i
$177$	−3.82039	+	17.6763i	−0.287158	+	1.32863i
$178$	1.23696	+	23.9739i	0.0927139	+	1.79692i
$179$	−6.93744	+	6.93744i	−0.518529	+	0.518529i	−0.917126	−	0.398597i	$-0.869497\pi$
$179$	−6.93744	+	6.93744i	−0.518529	+	0.518529i	0.398597	+	0.917126i	$0.369497\pi$
$180$	8.01285	+	10.7608i	0.597242	+	0.802061i
$181$	8.83940	+	8.83940i	0.657028	+	0.657028i	0.954676	−	0.297648i	$-0.0962022\pi$
$181$	8.83940	+	8.83940i	0.657028	+	0.657028i	−0.297648	+	0.954676i	$0.596202\pi$
$182$	−15.0993	−	13.6176i	−1.11923	−	1.00940i
$183$	11.3853	+	2.46072i	0.841629	+	0.181902i
$184$	1.23799	+	7.94112i	0.0912658	+	0.585428i
$185$	−3.98429	−	22.2395i	−0.292931	−	1.63508i
$186$	9.70864	+	13.4823i	0.711872	+	0.988568i
$187$	0.320718	+	0.320718i	0.0234532	+	0.0234532i
$188$	1.56652	+	15.1402i	0.114251	+	1.10422i
$189$	−2.27188	−	15.3617i	−0.165255	−	1.11740i
$190$	0.596041	+	2.55919i	0.0432414	+	0.185663i
$191$	−16.7030			−1.20859			−0.604294	−	0.796762i	$-0.706545\pi$
$191$	−16.7030			−1.20859			−0.604294	+	0.796762i	$0.706545\pi$
$192$	10.6959	+	8.80892i	0.771912	+	0.635729i
$193$		−	12.8577i		−	0.925514i	−0.886485	−	0.462757i	$-0.846860\pi$
$193$		−	12.8577i		−	0.925514i	0.886485	−	0.462757i	$-0.153140\pi$
$194$	18.1181	−	0.934823i	1.30080	−	0.0671164i
$195$	−12.6982	−	13.6356i	−0.909336	−	0.976468i
$196$	3.84197	−	0.397519i	0.274426	−	0.0283942i
$197$	−4.01686	−	4.01686i	−0.286189	−	0.286189i	0.549382	−	0.835571i	$-0.314863\pi$
$197$	−4.01686	−	4.01686i	−0.286189	−	0.286189i	−0.835571	+	0.549382i	$0.814863\pi$
$198$	6.05369	+	13.8814i	0.430217	+	0.986509i
$199$	−18.1309			−1.28527			−0.642633	−	0.766174i	$-0.722158\pi$
$199$	−18.1309			−1.28527			−0.642633	+	0.766174i	$0.722158\pi$
$200$	−12.3480	+	6.89396i	−0.873136	+	0.487476i
$201$	−7.82304	−	1.69080i	−0.551795	−	0.119260i
$202$	−2.16317	−	1.95090i	−0.152200	−	0.137265i
$203$	−3.91976	+	3.91976i	−0.275114	+	0.275114i
$204$	−0.275284	−	0.343470i	−0.0192737	−	0.0240477i
$205$	−10.1440	+	14.5719i	−0.708484	+	1.01774i
$206$	0.502103	−	0.0259065i	0.0349832	−	0.00180499i
$207$	3.52040	−	7.76371i	0.244685	−	0.539615i
$208$	−16.1051	−	10.5331i	−1.11669	−	0.730337i
$209$			2.96604i			0.205165i
$210$	16.3667	−	0.261344i	1.12941	−	0.0180345i
$211$	−5.26322	−	5.26322i	−0.362335	−	0.362335i	0.502337	−	0.864672i	$-0.332474\pi$
$211$	−5.26322	−	5.26322i	−0.362335	−	0.362335i	−0.864672	+	0.502337i	$0.832474\pi$
$212$	3.26531	+	2.65296i	0.224263	+	0.182206i
$213$	12.2162	−	7.87404i	0.837037	−	0.539521i
$214$	8.22949	+	7.42194i	0.562556	+	0.507353i
$215$	−7.35505	+	1.31768i	−0.501610	+	0.0898653i
$216$	−4.36400	−	14.0341i	−0.296933	−	0.954898i
$217$	20.2702			1.37603
$218$	13.6747	+	12.3328i	0.926165	+	0.835281i
$219$	2.44210	+	3.78878i	0.165022	+	0.256022i
$220$	−15.3398	+	4.41725i	−1.03421	+	0.297811i
$221$	0.432262	+	0.432262i	0.0290771	+	0.0290771i
$222$	−3.97505	+	24.4288i	−0.266788	+	1.63955i
$223$	−9.22307			−0.617622			−0.308811	−	0.951123i	$-0.599931\pi$
$223$	−9.22307			−0.617622			−0.308811	+	0.951123i	$0.599931\pi$
$224$	16.3471	−	4.30936i	1.09224	−	0.287931i
$225$	14.9620	+	1.06661i	0.997469	+	0.0711073i
$226$	−0.939356	−	18.2060i	−0.0624850	−	1.21104i
$227$	−2.82027	−	2.82027i	−0.187188	−	0.187188i	0.607291	−	0.794479i	$-0.292256\pi$
$227$	−2.82027	−	2.82027i	−0.187188	−	0.187188i	−0.794479	+	0.607291i	$0.792256\pi$
$228$	0.315297	−	2.86116i	0.0208810	−	0.189485i
$229$	−16.6147	−	16.6147i	−1.09793	−	1.09793i	−0.994653	−	0.103278i	$-0.967067\pi$
$229$	−16.6147	−	16.6147i	−1.09793	−	1.09793i	−0.103278	−	0.994653i	$-0.532933\pi$
$230$	7.62948	+	4.74697i	0.503073	+	0.313006i
$231$	18.0596	+	3.90323i	1.18823	+	0.256813i
$232$	−3.09407	+	4.23695i	−0.203136	+	0.278170i
$233$		−	0.616689i		−	0.0404007i	−0.999796	−	0.0202003i	$-0.993570\pi$
$233$		−	0.616689i		−	0.0404007i	0.999796	−	0.0202003i	$-0.00643040\pi$
$234$	8.15913	+	18.7093i	0.533379	+	1.22306i
$235$	13.9668	+	9.72270i	0.911091	+	0.634239i
$236$	16.2071	+	13.1678i	1.05500	+	0.857150i
$237$	−23.7720	+	15.3225i	−1.54416	+	0.995302i
$238$	−0.536324	+	0.0276722i	−0.0347647	+	0.00179372i
$239$	−5.63705			−0.364631			−0.182315	−	0.983240i	$-0.558359\pi$
$239$	−5.63705			−0.364631			−0.182315	+	0.983240i	$0.558359\pi$
$240$	15.2670	−	2.63039i	0.985480	−	0.169791i
$241$	10.1922			0.656537			0.328269	−	0.944584i	$-0.393535\pi$
$241$	10.1922			0.656537			0.328269	+	0.944584i	$0.393535\pi$
$242$	−2.45908	+	0.126879i	−0.158076	+	0.00815608i
$243$	−4.29126	+	14.9862i	−0.275284	+	0.961363i
$244$	8.48140	−	10.4391i	0.542966	−	0.668292i
$245$	2.46722	−	3.54418i	0.157625	−	0.226430i
$246$	15.7832	−	11.3656i	1.00630	−	0.724643i
$247$			3.99761i			0.254362i
$248$	18.9554	−	2.95507i	1.20367	−	0.187647i
$249$	−2.99290	+	13.8476i	−0.189667	+	0.877559i
$250$	−3.17267	+	15.4898i	−0.200657	+	0.979662i
$251$	2.63211	+	2.63211i	0.166137	+	0.166137i	0.785279	−	0.619142i	$-0.212519\pi$
$251$	2.63211	+	2.63211i	0.166137	+	0.166137i	−0.619142	+	0.785279i	$0.712519\pi$
$252$	−17.0060	−	5.68498i	−1.07128	−	0.358120i
$253$	7.17201	+	7.17201i	0.450900	+	0.450900i
$254$	−0.963001	−	18.6642i	−0.0604240	−	1.17110i
$255$	−0.491818	−	0.0175081i	−0.0307988	−	0.00109640i
$256$	14.6586	−	6.41299i	0.916160	−	0.400812i
$257$	−1.44889			−0.0903796			−0.0451898	−	0.998978i	$-0.514389\pi$
$257$	−1.44889			−0.0903796			−0.0451898	+	0.998978i	$0.514389\pi$
$258$	8.07907	+	1.31463i	0.502981	+	0.0818451i
$259$	21.3521	+	21.3521i	1.32676	+	1.32676i
$260$	−20.6750	+	5.95354i	−1.28221	+	0.369223i
$261$	5.20859	−	1.95865i	0.322403	−	0.121238i
$262$	9.94745	+	8.97132i	0.614556	+	0.554250i
$263$	−10.0540			−0.619958			−0.309979	−	0.950743i	$-0.600322\pi$
$263$	−10.0540			−0.619958			−0.309979	+	0.950743i	$0.600322\pi$
$264$	17.4572	+	1.01726i	1.07441	+	0.0626077i
$265$	4.63007	−	0.829494i	0.284423	−	0.0509554i
$266$	−2.60795	−	2.35204i	−0.159904	−	0.144213i
$267$	−15.9285	−	24.7123i	−0.974811	−	1.51237i
$268$	−5.82770	+	7.17284i	−0.355984	+	0.438151i
$269$	4.70735	+	4.70735i	0.287012	+	0.287012i	0.835898	−	0.548886i	$-0.184948\pi$
$269$	4.70735	+	4.70735i	0.287012	+	0.287012i	−0.548886	+	0.835898i	$0.684948\pi$
$270$	−15.0715	−	6.54600i	−0.917222	−	0.398377i
$271$		−	1.87113i		−	0.113663i	−0.998384	−	0.0568316i	$-0.981900\pi$
$271$		−	1.87113i		−	0.113663i	0.998384	−	0.0568316i	$-0.0180998\pi$
$272$	−0.497502	+	0.104065i	−0.0301655	+	0.00630985i
$273$	24.3406	+	5.26075i	1.47316	+	0.318395i
$274$	−28.3559	+	1.46305i	−1.71304	+	0.0883862i
$275$	−7.45387	+	16.2163i	−0.449485	+	0.977880i
$276$	−6.15600	−	7.68080i	−0.370548	−	0.462330i
$277$	7.54104	−	7.54104i	0.453097	−	0.453097i	−0.443284	−	0.896381i	$-0.646187\pi$
$277$	7.54104	−	7.54104i	0.453097	−	0.453097i	0.896381	+	0.443284i	$0.146187\pi$
$278$	16.2804	+	14.6828i	0.976434	+	0.880617i
$279$	−18.5319	−	8.40316i	−1.10948	−	0.503084i
$280$	8.28038	−	16.9907i	0.494847	−	1.01539i
$281$	−7.32843			−0.437178			−0.218589	−	0.975817i	$-0.570145\pi$
$281$	−7.32843			−0.437178			−0.218589	+	0.975817i	$0.570145\pi$
$282$	−10.8936	−	15.1278i	−0.648705	−	0.900848i
$283$	12.9281	+	12.9281i	0.768498	+	0.768498i	0.977842	−	0.209344i	$-0.0671329\pi$
$283$	12.9281	+	12.9281i	0.768498	+	0.768498i	−0.209344	+	0.977842i	$0.567133\pi$
$284$	−1.72721	−	16.6932i	−0.102491	−	0.990560i
$285$	−2.19324	−	2.35516i	−0.129916	−	0.139507i
$286$	−24.2533	+	1.25137i	−1.43413	+	0.0739952i
$287$		−	23.7296i		−	1.40072i
$288$	−16.7317	−	2.83702i	−0.985928	−	0.167173i
$289$	−16.9839			−0.999050
$290$	1.33053	+	5.71279i	0.0781311	+	0.335467i
$291$	−18.6762	+	12.0379i	−1.09482	+	0.705674i
$292$	5.17732	−	0.535685i	0.302980	−	0.0313486i
$293$	10.7802	+	10.7802i	0.629789	+	0.629789i	0.948015	−	0.318226i	$-0.103087\pi$
$293$	10.7802	+	10.7802i	0.629789	+	0.629789i	−0.318226	+	0.948015i	$0.603087\pi$
$294$	−3.83881	+	2.76435i	−0.223884	+	0.161220i
$295$	22.9810	−	4.11713i	1.33801	−	0.239709i
$296$	23.0800	+	16.8544i	1.34150	+	0.979640i
$297$	−14.8927	−	11.0552i	−0.864163	−	0.641489i
$298$	−11.7788	−	10.6230i	−0.682329	−	0.615373i
$299$	9.66639	+	9.66639i	0.559022	+	0.559022i
$300$	8.91413	−	14.8505i	0.514657	−	0.857396i
$301$	7.06157	−	7.06157i	0.407022	−	0.407022i
$302$	−0.293157	−	5.68178i	−0.0168693	−	0.326950i
$303$	3.48711	+	0.753672i	0.200329	+	0.0432973i
$304$	−2.78168	−	1.81928i	−0.159540	−	0.104343i
$305$	−2.65186	−	14.8021i	−0.151845	−	0.847567i
$306$	0.501802	+	0.197038i	0.0286861	+	0.0112639i
$307$	−12.0423	+	12.0423i	−0.687293	+	0.687293i	−0.961633	−	0.274340i	$-0.911541\pi$
$307$	−12.0423	+	12.0423i	−0.687293	+	0.687293i	0.274340	+	0.961633i	$0.411541\pi$
$308$	13.4533	−	16.5586i	0.766573	−	0.943511i
$309$	−0.517568	+	0.333604i	−0.0294434	+	0.0189780i
$310$	11.3310	−	18.2115i	0.643556	−	1.03434i
$311$		−	25.4739i		−	1.44449i	−0.691635	−	0.722247i	$-0.743110\pi$
$311$		−	25.4739i		−	1.44449i	0.691635	−	0.722247i	$-0.256890\pi$
$312$	23.5287	+	1.37105i	1.33205	+	0.0776205i
$313$	29.5145			1.66826			0.834129	−	0.551569i	$-0.185971\pi$
$313$	29.5145			1.66826			0.834129	+	0.551569i	$0.185971\pi$
$314$	−13.6994	+	15.1900i	−0.773101	+	0.857220i
$315$	−17.2263	+	10.2548i	−0.970590	+	0.577794i
$316$	3.36106	+	32.4841i	0.189074	+	1.82738i
$317$	1.88407	−	1.88407i	0.105820	−	0.105820i	−0.652214	−	0.758035i	$-0.726160\pi$
$317$	1.88407	−	1.88407i	0.105820	−	0.105820i	0.758035	+	0.652214i	$0.226160\pi$
$318$	−5.08585	−	0.827570i	−0.285200	−	0.0464078i
$319$			6.62100i			0.370705i
$320$	5.26631	−	17.0958i	0.294396	−	0.955684i
$321$	−13.2663	−	2.86725i	−0.740450	−	0.160034i
$322$	−11.9935	+	0.618816i	−0.668370	+	0.0344853i
$323$	0.0746605	+	0.0746605i	0.00415422	+	0.00415422i
$324$	13.1909	+	12.2474i	0.732829	+	0.680413i
$325$	−10.0463	+	21.8563i	−0.557268	+	1.21237i
$326$	−7.07861	−	6.38399i	−0.392048	−	0.353577i
$327$	−22.0441	−	4.76440i	−1.21904	−	0.263472i
$328$	−3.45940	−	22.1904i	−0.191013	−	1.22526i
$329$	−22.7442			−1.25393
$330$	13.6020	−	14.0435i	0.748767	−	0.773068i
$331$	−9.55258	+	9.55258i	−0.525057	+	0.525057i	−0.919094	−	0.394037i	$-0.871078\pi$
$331$	−9.55258	+	9.55258i	−0.525057	+	0.525057i	0.394037	+	0.919094i	$0.371078\pi$
$332$	12.6967	+	10.3157i	0.696823	+	0.566146i
$333$	−10.6694	−	28.3727i	−0.584678	−	1.55482i
$334$	0.940798	+	18.2339i	0.0514782	+	0.997715i
$335$	1.82213	+	10.1708i	0.0995537	+	0.555689i
$336$	−14.7378	+	14.5429i	−0.804013	+	0.793382i
$337$			9.53979i			0.519666i	0.965654	+	0.259833i	$0.0836675\pi$
$337$			9.53979i			0.519666i	−0.965654	+	0.259833i	$0.916333\pi$
$338$	−14.3281	+	0.739272i	−0.779344	+	0.0402111i
$339$	12.0963	+	18.7667i	0.656979	+	1.01927i
$340$	−0.274941	+	0.497322i	−0.0149108	+	0.0269710i
$341$	17.1195	−	17.1195i	0.927074	−	0.927074i
$342$	1.40925	+	3.23148i	0.0762035	+	0.174739i
$343$		−	15.1481i		−	0.817920i
$344$	5.57407	−	7.63299i	0.300534	−	0.411543i
$345$	−10.9982	−	0.391522i	−0.592124	−	0.0210788i
$346$	12.5072	+	11.2799i	0.672392	+	0.606411i
$347$	5.26599	−	5.26599i	0.282693	−	0.282693i	−0.551489	−	0.834182i	$-0.685940\pi$
$347$	5.26599	−	5.26599i	0.282693	−	0.282693i	0.834182	+	0.551489i	$0.185940\pi$
$348$	0.703827	−	6.38688i	0.0377291	−	0.342373i
$349$	12.7870	−	12.7870i	0.684470	−	0.684470i	−0.276534	−	0.961004i	$-0.589186\pi$
$349$	12.7870	−	12.7870i	0.684470	−	0.684470i	0.961004	+	0.276534i	$0.0891859\pi$
$350$	−8.34770	−	19.4133i	−0.446203	−	1.03769i
$351$	−20.0723	−	14.9002i	−1.07138	−	0.795312i
$352$	10.1667	−	17.4458i	0.541887	−	0.929863i
$353$	−10.5420			−0.561093			−0.280546	−	0.959840i	$-0.590516\pi$
$353$	−10.5420			−0.561093			−0.280546	+	0.959840i	$0.590516\pi$
$354$	−25.2432	−	4.10758i	−1.34166	−	0.218316i
$355$	−15.3994	−	10.7200i	−0.817313	−	0.568958i
$356$	−33.7690	+	3.49400i	−1.78975	+	0.185182i
$357$	0.552843	−	0.356340i	0.0292595	−	0.0188595i
$358$	−10.3035	−	9.29245i	−0.544558	−	0.491121i
$359$		−	0.701622i		−	0.0370302i	−0.999829	−	0.0185151i	$-0.994106\pi$
$359$		−	0.701622i		−	0.0370302i	0.999829	−	0.0185151i	$-0.00589387\pi$
$360$	−14.6139	+	12.1010i	−0.770221	+	0.637777i
$361$		−	18.3095i		−	0.963659i
$362$	−11.8401	+	13.1283i	−0.622300	+	0.690010i
$363$	2.53482	−	1.63384i	0.133044	−	0.0857545i
$364$	18.1323	−	22.3175i	0.950390	−	1.16976i
$365$	3.32475	−	4.77604i	0.174025	−	0.249989i
$366$	−2.64570	+	16.2592i	−0.138293	+	0.849884i
$367$	11.8327			0.617662			0.308831	−	0.951117i	$-0.400062\pi$
$367$	11.8327			0.617662			0.308831	+	0.951117i	$0.400062\pi$
$368$	−11.1253	+	2.32713i	−0.579947	+	0.121310i
$369$	−9.83730	+	21.6947i	−0.512109	+	1.12938i
$370$	31.1193	−	7.24777i	1.61782	−	0.376794i
$371$	−4.44532	+	4.44532i	−0.230790	+	0.230790i
$372$	−18.3340	+	14.6943i	−0.950574	+	0.761865i
$373$	−11.3071	+	11.3071i	−0.585461	+	0.585461i	−0.936399	−	0.350938i	$-0.885863\pi$
$373$	−11.3071	+	11.3071i	−0.585461	+	0.585461i	0.350938	+	0.936399i	$0.385863\pi$
$374$	−0.429590	+	0.476332i	−0.0222136	+	0.0246305i
$375$	−6.07248	−	18.3882i	−0.313582	−	0.949561i
$376$	−21.2689	+	3.31574i	−1.09686	+	0.170996i
$377$			8.92375i			0.459596i
$378$	21.5303	−	4.32807i	1.10740	−	0.222612i
$379$	−6.65822	+	6.65822i	−0.342010	+	0.342010i	−0.857122	−	0.515113i	$-0.827750\pi$
$379$	−6.65822	+	6.65822i	−0.342010	+	0.342010i	0.515113	+	0.857122i	$0.327750\pi$
$380$	−3.57099	+	1.02830i	−0.183188	+	0.0527507i
$381$	12.4007	+	19.2391i	0.635309	+	0.985648i
$382$	−1.21716	−	23.5902i	−0.0622755	−	1.20698i
$383$			10.2745i			0.525000i	0.964932	+	0.262500i	$0.0845470\pi$
$383$			10.2745i			0.525000i	−0.964932	+	0.262500i	$0.915453\pi$
$384$	−11.6617	+	15.7481i	−0.595110	+	0.803644i
$385$	−4.20640	−	23.4793i	−0.214378	−	1.19662i
$386$	18.1593	−	0.936949i	0.924285	−	0.0476895i
$387$	−9.38342	+	3.52857i	−0.476986	+	0.179367i
$388$	2.64057	+	25.5207i	0.134054	+	1.29562i
$389$	18.2183	−	18.2183i	0.923703	−	0.923703i	−0.0735861	−	0.997289i	$-0.523444\pi$
$389$	18.2183	−	18.2183i	0.923703	−	0.923703i	0.997289	+	0.0735861i	$0.0234444\pi$
$390$	18.3327	−	18.9277i	0.928315	−	0.958443i
$391$	0.361065			0.0182598
$392$	0.841398	+	5.39718i	0.0424970	+	0.272599i
$393$	−16.0357	−	3.46580i	−0.808893	−	0.174827i
$394$	5.38044	−	5.96586i	0.271063	−	0.300556i
$395$	29.9664	+	20.8605i	1.50777	+	1.04961i
$396$	−19.1641	+	9.56138i	−0.963030	+	0.480478i
$397$	−10.3406	−	10.3406i	−0.518981	−	0.518981i	0.398282	−	0.917263i	$-0.369607\pi$
$397$	−10.3406	−	10.3406i	−0.518981	−	0.518981i	−0.917263	+	0.398282i	$0.869607\pi$
$398$	−1.32122	−	25.6069i	−0.0662266	−	1.28356i
$399$	4.20412	+	0.908640i	0.210469	+	0.0454889i
$400$	−10.6364	−	16.9372i	−0.531819	−	0.846858i
$401$			11.1765i			0.558129i	0.960272	+	0.279065i	$0.0900244\pi$
$401$			11.1765i			0.558129i	−0.960272	+	0.279065i	$0.909976\pi$
$402$	1.81790	−	11.1720i	0.0906688	−	0.557207i
$403$	23.0736	−	23.0736i	1.14938	−	1.14938i
$404$	2.59769	−	3.19728i	0.129240	−	0.159071i
$405$	20.0002	−	2.23413i	0.993819	−	0.111015i
$406$	−5.82166	−	5.25038i	−0.288924	−	0.260572i
$407$	36.0666			1.78775
$408$	0.465034	−	0.413822i	0.0230226	−	0.0204873i
$409$			23.4437i			1.15922i	0.814895	+	0.579609i	$0.196795\pi$
$409$			23.4437i			1.15922i	−0.814895	+	0.579609i	$0.803205\pi$
$410$	−21.3196	−	13.2648i	−1.05290	−	0.655101i
$411$	29.2292	−	18.8400i	1.44177	−	0.929308i
$412$	0.0731774	+	0.707250i	0.00360519	+	0.0348437i
$413$	−22.0640	+	22.0640i	−1.08570	+	1.08570i
$414$	11.2215	+	4.40623i	0.551506	+	0.216555i
$415$	18.0034	−	3.22537i	0.883751	−	0.158327i
$416$	13.7026	−	23.5133i	0.671826	−	1.15284i
$417$	−26.2446	−	5.67227i	−1.28521	−	0.277772i
$418$	−4.18904	+	0.216138i	−0.204893	+	0.0105717i
$419$	26.0827	−	26.0827i	1.27422	−	1.27422i	0.330370	−	0.943851i	$-0.392826\pi$
$419$	26.0827	−	26.0827i	1.27422	−	1.27422i	0.943851	−	0.330370i	$-0.107174\pi$
$420$	1.56176	+	23.0962i	0.0762062	+	1.12698i
$421$	−1.31659	−	1.31659i	−0.0641669	−	0.0641669i	0.674295	−	0.738462i	$-0.264448\pi$
$421$	−1.31659	−	1.31659i	−0.0641669	−	0.0641669i	−0.738462	+	0.674295i	$0.764448\pi$
$422$	7.04989	−	7.81696i	0.343183	−	0.380524i
$423$	20.7938	+	9.42878i	1.01103	+	0.458443i
$424$	−3.50893	+	4.80504i	−0.170409	+	0.233353i
$425$	0.220566	+	0.595821i	0.0106990	+	0.0289016i
$426$	12.0110	+	16.6795i	0.581934	+	0.808125i
$427$	14.2115	+	14.2115i	0.687743	+	0.687743i
$428$	−9.88257	+	12.1636i	−0.477692	+	0.587952i
$429$	25.0003	−	16.1142i	1.20702	−	0.777999i
$430$	−2.39698	−	10.2918i	−0.115593	−	0.496313i
$431$	13.2223			0.636896			0.318448	−	0.947940i	$-0.396838\pi$
$431$	13.2223			0.636896			0.318448	+	0.947940i	$0.396838\pi$
$432$	19.5028	−	7.18611i	0.938330	−	0.345742i
$433$			16.6667i			0.800949i	0.916308	+	0.400474i	$0.131155\pi$
$433$			16.6667i			0.800949i	−0.916308	+	0.400474i	$0.868845\pi$
$434$	1.47711	+	28.6283i	0.0709035	+	1.37420i
$435$	−4.89590	−	5.25734i	−0.234740	−	0.252070i
$436$	−16.4215	+	20.2119i	−0.786448	+	0.967974i
$437$	1.66959	+	1.66959i	0.0798671	+	0.0798671i
$438$	−5.17307	+	3.72515i	−0.247179	+	0.177995i
$439$	−3.80511			−0.181608			−0.0908040	−	0.995869i	$-0.528944\pi$
$439$	−3.80511			−0.181608			−0.0908040	+	0.995869i	$0.528944\pi$
$440$	−7.35646	−	21.3431i	−0.350706	−	1.01749i
$441$	2.39263	−	5.27659i	0.113935	−	0.251266i
$442$	−0.578999	+	0.641997i	−0.0275402	+	0.0305367i
$443$	−8.95143	+	8.95143i	−0.425295	+	0.425295i	−0.887022	−	0.461727i	$-0.847230\pi$
$443$	−8.95143	+	8.95143i	−0.425295	+	0.425295i	0.461727	+	0.887022i	$0.347230\pi$
$444$	−34.7913	−	3.83396i	−1.65112	−	0.181952i
$445$	−21.6856	+	31.1516i	−1.02800	+	1.47673i
$446$	−0.672094	−	13.0261i	−0.0318246	−	0.616802i
$447$	18.9879	+	4.10387i	0.898097	+	0.194107i
$448$	7.27749	+	22.7736i	0.343829	+	1.07595i
$449$		−	5.45237i		−	0.257313i	−0.991689	−	0.128657i	$-0.958933\pi$
$449$		−	5.45237i		−	0.257313i	0.991689	−	0.128657i	$-0.0410665\pi$
$450$	−0.416112	+	21.2091i	−0.0196157	+	0.999808i
$451$	−20.0412	−	20.0412i	−0.943705	−	0.943705i
$452$	25.6445	−	2.65337i	1.20621	−	0.124804i
$453$	3.77504	+	5.85678i	0.177367	+	0.275175i
$454$	3.77765	−	4.18868i	0.177294	−	0.196585i
$455$	−5.66937	−	31.6453i	−0.265784	−	1.48355i
$456$	4.06389	+	0.236809i	0.190309	+	0.0110896i
$457$	−26.6690			−1.24752			−0.623762	−	0.781614i	$-0.714397\pi$
$457$	−26.6690			−1.24752			−0.623762	+	0.781614i	$0.714397\pi$
$458$	22.2548	−	24.6763i	1.03990	−	1.15305i
$459$	−0.653156	+	0.0965968i	−0.0304867	+	0.00450875i
$460$	−6.14834	+	11.1213i	−0.286668	+	0.518533i
$461$	0.412379	+	0.412379i	0.0192064	+	0.0192064i	0.716645	−	0.697438i	$-0.245677\pi$
$461$	0.412379	+	0.412379i	0.0192064	+	0.0192064i	−0.697438	+	0.716645i	$0.745677\pi$
$462$	−4.19665	+	25.7906i	−0.195246	+	1.19989i
$463$	−3.85517			−0.179165			−0.0895824	−	0.995979i	$-0.528553\pi$
$463$	−3.85517			−0.179165			−0.0895824	+	0.995979i	$0.528553\pi$
$464$	−6.20946	−	4.06112i	−0.288267	−	0.188533i
$465$	−0.934559	+	26.2526i	−0.0433391	+	1.21744i
$466$	0.870972	−	0.0449387i	0.0403470	−	0.00208175i
$467$	−9.90097	−	9.90097i	−0.458162	−	0.458162i	0.439890	−	0.898052i	$-0.355018\pi$
$467$	−9.90097	−	9.90097i	−0.458162	−	0.458162i	−0.898052	+	0.439890i	$0.855018\pi$
$468$	−25.8292	+	12.8868i	−1.19396	+	0.595692i
$469$	−9.76494	−	9.76494i	−0.450903	−	0.450903i
$470$	−12.7139	+	20.4342i	−0.586450	+	0.942561i
$471$	5.29235	−	24.4868i	0.243859	−	1.12829i
$472$	−17.4163	+	23.8495i	−0.801650	+	1.09776i
$473$		−	11.9279i		−	0.548446i
$474$	−23.3728	−	32.4575i	−1.07355	−	1.49082i
$475$	−1.73520	+	3.77503i	−0.0796165	+	0.173210i
$476$	−0.0781648	−	0.755452i	−0.00358268	−	0.0346261i
$477$	5.90695	−	2.22127i	0.270461	−	0.101705i
$478$	−0.410777	−	7.96141i	−0.0187885	−	0.364146i
$479$	13.8625			0.633394			0.316697	−	0.948527i	$-0.397426\pi$
$479$	13.8625			0.633394			0.316697	+	0.948527i	$0.397426\pi$
$480$	4.82752	+	21.3704i	0.220345	+	0.975422i
$481$	48.6104			2.21644
$482$	0.742715	+	14.3948i	0.0338297	+	0.655665i
$483$	12.3629	−	7.96861i	0.562530	−	0.362584i
$484$	−0.358391	−	3.46380i	−0.0162905	−	0.157445i
$485$	23.5427	+	16.3888i	1.06902	+	0.744177i
$486$	−21.4782	−	4.96864i	−0.974270	−	0.225382i
$487$		−	10.6487i		−	0.482540i	−0.970458	−	0.241270i	$-0.922436\pi$
$487$		−	10.6487i		−	0.482540i	0.970458	−	0.241270i	$-0.0775639\pi$
$488$	15.3615	+	11.2179i	0.695382	+	0.507810i
$489$	11.4110	+	2.46627i	0.516023	+	0.111528i
$490$	5.18536	+	3.22627i	0.234251	+	0.145748i
$491$	15.1731	+	15.1731i	0.684751	+	0.684751i	0.961067	−	0.276316i	$-0.0891137\pi$
$491$	15.1731	+	15.1731i	0.684751	+	0.684751i	−0.276316	+	0.961067i	$0.589114\pi$
$492$	17.2022	+	21.4630i	0.775533	+	0.967627i
$493$	0.166662	+	0.166662i	0.00750610	+	0.00750610i
$494$	−5.64597	+	0.291310i	−0.254024	+	0.0131066i
$495$	−5.88784	+	23.2096i	−0.264639	+	1.04319i
$496$	5.55484	+	26.5560i	0.249420	+	1.19240i
$497$	25.0771			1.12486
$498$	−19.7756	−	3.21789i	−0.886166	−	0.144197i
$499$	17.1415	+	17.1415i	0.767360	+	0.767360i	0.977641	−	0.210281i	$-0.0674378\pi$
$499$	17.1415	+	17.1415i	0.767360	+	0.767360i	−0.210281	+	0.977641i	$0.567438\pi$
$500$	−22.1080	−	3.35211i	−0.988700	−	0.149911i
$501$	−12.1148	−	18.7955i	−0.541251	−	0.839722i
$502$	−3.52562	+	3.90923i	−0.157356	+	0.174477i
$503$	−27.5546			−1.22860			−0.614300	−	0.789073i	$-0.710561\pi$
$503$	−27.5546			−1.22860			−0.614300	+	0.789073i	$0.710561\pi$
$504$	6.78985	−	24.4325i	0.302444	−	1.08831i
$505$	−0.812212	−	4.53361i	−0.0361430	−	0.201743i
$506$	−9.60664	+	10.6519i	−0.427067	+	0.473535i
$507$	14.7694	−	9.51975i	0.655931	−	0.422787i
$508$	26.2900	−	2.72016i	1.16643	−	0.120688i
$509$	−4.28863	−	4.28863i	−0.190090	−	0.190090i	0.605645	−	0.795735i	$-0.292915\pi$
$509$	−4.28863	−	4.28863i	−0.190090	−	0.190090i	−0.795735	+	0.605645i	$0.792915\pi$
$510$	−0.0111120	−	0.695887i	−0.000492046	−	0.0308144i
$511$			7.77756i			0.344059i
$512$	10.1255	+	20.2355i	0.447487	+	0.894290i
$513$	−3.46691	−	2.57357i	−0.153068	−	0.113626i
$514$	−0.105582	−	2.04632i	−0.00465704	−	0.0902595i
$515$	0.652433	+	0.454179i	0.0287496	+	0.0200135i
$516$	−1.26796	+	11.5062i	−0.0558190	+	0.506530i
$517$	−19.2090	+	19.2090i	−0.844810	+	0.844810i
$518$	−28.6004	+	31.7123i	−1.25663	+	1.39336i
$519$	−20.1621	−	4.35765i	−0.885019	−	0.191280i
$520$	−9.91500	−	28.7661i	−0.434802	−	1.26148i
$521$	−19.2799			−0.844668			−0.422334	−	0.906440i	$-0.638789\pi$
$521$	−19.2799			−0.844668			−0.422334	+	0.906440i	$0.638789\pi$
$522$	3.14583	+	7.21354i	0.137689	+	0.315728i
$523$	−3.34042	−	3.34042i	−0.146066	−	0.146066i	0.630292	−	0.776358i	$-0.282935\pi$
$523$	−3.34042	−	3.34042i	−0.146066	−	0.146066i	−0.776358	+	0.630292i	$0.782935\pi$
$524$	−11.9456	+	14.7029i	−0.521847	+	0.642298i
$525$	20.7018	+	15.5331i	0.903502	+	0.677920i
$526$	−0.732647	−	14.1997i	−0.0319449	−	0.619135i
$527$		−	0.861858i		−	0.0375431i
$528$	−0.164585	+	24.7295i	−0.00716263	+	1.07621i
$529$	−14.9257			−0.648945
$530$	1.50892	+	6.47876i	0.0655433	+	0.281419i
$531$	29.3187	−	11.0251i	1.27232	−	0.478448i
$532$	3.13182	−	3.85470i	0.135782	−	0.167122i
$533$	−27.0115	−	27.0115i	−1.17000	−	1.17000i
$534$	33.7413	−	24.2972i	1.46013	−	1.05144i
$535$	3.08995	+	17.2475i	0.133590	+	0.745675i
$536$	−10.5551	−	7.70798i	−0.455912	−	0.332934i
$537$	16.6097	+	3.58986i	0.716761	+	0.154914i
$538$	−6.30532	+	6.99138i	−0.271842	+	0.301420i
$539$	4.87444	+	4.87444i	0.209957	+	0.209957i
$540$	8.14688	−	21.7630i	0.350586	−	0.936531i
$541$	8.05797	−	8.05797i	0.346439	−	0.346439i	−0.512342	−	0.858781i	$-0.671222\pi$
$541$	8.05797	−	8.05797i	0.346439	−	0.346439i	0.858781	+	0.512342i	$0.171222\pi$
$542$	2.64266	−	0.136351i	0.113512	−	0.00585678i
$543$	4.57406	−	21.1634i	0.196292	−	0.908207i
$544$	−0.183228	−	0.695056i	−0.00785582	−	0.0298003i
$545$	5.13447	+	28.6596i	0.219936	+	1.22764i
$546$	−5.65622	+	34.7604i	−0.242064	+	1.48761i
$547$	30.0440	−	30.0440i	1.28459	−	1.28459i	0.346562	−	0.938027i	$-0.387349\pi$
$547$	30.0440	−	30.0440i	1.28459	−	1.28459i	0.938027	−	0.346562i	$-0.112651\pi$
$548$	−4.13264	−	39.9414i	−0.176537	−	1.70621i
$549$	−7.10129	−	18.8843i	−0.303076	−	0.805960i
$550$	−23.4460	−	9.34566i	−0.999742	−	0.398500i
$551$			1.54132i			0.0656623i
$552$	10.3993	−	9.25405i	0.442622	−	0.393878i
$553$	−48.7988			−2.07514
$554$	11.2000	+	10.1009i	0.475842	+	0.429148i
$555$	−28.6383	+	26.6695i	−1.21563	+	1.13206i
$556$	−19.5507	+	24.0633i	−0.829134	+	1.02051i
$557$	12.7025	−	12.7025i	0.538221	−	0.538221i	−0.384785	−	0.923006i	$-0.625724\pi$
$557$	12.7025	−	12.7025i	0.538221	−	0.538221i	0.923006	+	0.384785i	$0.125724\pi$
$558$	10.5176	−	26.7856i	0.445247	−	1.13392i
$559$		−	16.0764i		−	0.679959i
$560$	24.6000	+	10.4565i	1.03954	+	0.441869i
$561$	0.165959	−	0.767865i	0.00700680	−	0.0324193i
$562$	−0.534030	−	10.3502i	−0.0225267	−	0.436597i
$563$	8.03490	+	8.03490i	0.338631	+	0.338631i	0.855852	−	0.517221i	$-0.173033\pi$
$563$	8.03490	+	8.03490i	0.338631	+	0.338631i	−0.517221	+	0.855852i	$0.673033\pi$
$564$	20.5717	−	16.4878i	0.866226	−	0.694262i
$565$	16.4683	−	23.6568i	0.692825	−	0.995250i
$566$	−17.3168	+	19.2009i	−0.727878	+	0.807076i
$567$	−20.2322	+	17.7225i	−0.849674	+	0.744275i
$568$	23.4505	−	3.65584i	0.983963	−	0.153396i
$569$	−30.5559			−1.28097			−0.640486	−	0.767970i	$-0.721267\pi$
$569$	−30.5559			−1.28097			−0.640486	+	0.767970i	$0.721267\pi$
$570$	3.16645	−	3.26921i	0.132628	−	0.136932i
$571$	17.2411	−	17.2411i	0.721519	−	0.721519i	−0.247396	−	0.968914i	$-0.579575\pi$
$571$	17.2411	−	17.2411i	0.721519	−	0.721519i	0.968914	+	0.247396i	$0.0795748\pi$
$572$	−3.53471	−	34.1625i	−0.147794	−	1.42841i
$573$	15.6737	+	24.3168i	0.654776	+	1.01585i
$574$	33.5142	−	1.72920i	1.39886	−	0.0721755i
$575$	4.93239	+	13.3240i	0.205695	+	0.555648i
$576$	2.78757	−	23.8376i	0.116149	−	0.993232i
$577$		−	2.74770i		−	0.114388i	−0.998363	−	0.0571942i	$-0.981785\pi$
$577$		−	2.74770i		−	0.114388i	0.998363	−	0.0571942i	$-0.0182154\pi$
$578$	−1.23763	−	23.9869i	−0.0514786	−	0.997723i
$579$	−18.7186	+	12.0653i	−0.777920	+	0.501416i
$580$	−7.97142	+	2.29544i	−0.330995	+	0.0953131i
$581$	−17.2850	+	17.2850i	−0.717103	+	0.717103i
$582$	−18.3625	−	25.4998i	−0.761150	−	1.05700i
$583$			7.50873i			0.310980i
$584$	1.13384	+	7.27307i	0.0469187	+	0.300962i
$585$	−7.93560	+	31.2818i	−0.328097	+	1.29334i
$586$	−14.4398	+	16.0109i	−0.596501	+	0.661404i
$587$	−27.0914	+	27.0914i	−1.11818	+	1.11818i	−0.126173	+	0.992008i	$0.540269\pi$
$587$	−27.0914	+	27.0914i	−1.11818	+	1.11818i	−0.992008	+	0.126173i	$0.959731\pi$
$588$	−4.18392	−	5.22025i	−0.172542	−	0.215279i
$589$	3.98529	−	3.98529i	0.164211	−	0.164211i
$590$	7.48942	+	32.1569i	0.308334	+	1.32388i
$591$	−2.07857	+	9.61720i	−0.0855011	+	0.395599i
$592$	−22.1221	+	33.8248i	−0.909215	+	1.39019i
$593$	17.1557			0.704500			0.352250	−	0.935906i	$-0.385417\pi$
$593$	17.1557			0.704500			0.352250	+	0.935906i	$0.385417\pi$
$594$	14.5284	−	21.8391i	0.596109	−	0.896069i
$595$	−0.696899	−	0.485133i	−0.0285701	−	0.0198885i
$596$	14.1449	−	17.4098i	0.579396	−	0.713131i
$597$	17.0135	+	26.3956i	0.696318	+	1.08030i
$598$	−12.9478	+	14.3566i	−0.529474	+	0.587084i
$599$			16.2294i			0.663114i	0.943435	+	0.331557i	$0.107574\pi$
$599$			16.2294i			0.663114i	−0.943435	+	0.331557i	$0.892426\pi$
$600$	21.6235	+	11.5076i	0.882776	+	0.469794i
$601$		−	21.5512i		−	0.879093i	−0.898220	−	0.439547i	$-0.855139\pi$
$601$		−	21.5512i		−	0.879093i	0.898220	−	0.439547i	$-0.144861\pi$
$602$	10.4879	+	9.45872i	0.427454	+	0.385509i
$603$	4.87941	+	12.9757i	0.198705	+	0.528410i
$604$	8.00321	−	0.828073i	0.325646	−	0.0336938i
$605$	−3.19533	−	2.22437i	−0.129908	−	0.0904334i
$606$	−0.810328	+	4.97989i	−0.0329173	+	0.202294i
$607$	−30.2087			−1.22613			−0.613067	−	0.790031i	$-0.710064\pi$
$607$	−30.2087			−1.22613			−0.613067	+	0.790031i	$0.710064\pi$
$608$	2.36673	−	4.06124i	0.0959834	−	0.164705i
$609$	9.38473	+	2.02833i	0.380289	+	0.0821921i
$610$	20.7123	−	4.82395i	0.838617	−	0.195316i
$611$	−25.8898	+	25.8898i	−1.04739	+	1.04739i
$612$	−0.241717	+	0.723071i	−0.00977082	+	0.0292284i
$613$	−13.2331	+	13.2331i	−0.534481	+	0.534481i	−0.921903	−	0.387422i	$-0.873366\pi$
$613$	−13.2331	+	13.2331i	−0.534481	+	0.534481i	0.387422	+	0.921903i	$0.373366\pi$
$614$	−17.8854	−	16.1303i	−0.721794	−	0.650965i
$615$	30.7331	+	1.09406i	1.23928	+	0.0441166i
$616$	24.3666	+	17.7939i	0.981757	+	0.716938i
$617$			2.60352i			0.104814i	0.998626	+	0.0524069i	$0.0166893\pi$
$617$			2.60352i			0.104814i	−0.998626	+	0.0524069i	$0.983311\pi$
$618$	−0.508876	−	0.706669i	−0.0204700	−	0.0284264i
$619$	22.1516	−	22.1516i	0.890347	−	0.890347i	−0.104209	−	0.994555i	$-0.533231\pi$
$619$	22.1516	−	22.1516i	0.890347	−	0.890347i	0.994555	+	0.104209i	$0.0332310\pi$
$620$	26.5464	+	14.6760i	1.06613	+	0.589404i
$621$	−14.6061	+	2.16013i	−0.586124	+	0.0866831i
$622$	35.9777	−	1.85631i	1.44257	−	0.0744312i
$623$		−	50.7290i		−	2.03242i
$624$	−0.221827	+	33.3303i	−0.00888017	+	1.33428i
$625$	−18.9738	+	16.2786i	−0.758953	+	0.651145i
$626$	2.15075	+	41.6844i	0.0859612	+	1.66604i
$627$	4.31806	−	2.78325i	0.172447	−	0.111152i
$628$	−22.4516	−	18.2412i	−0.895917	−	0.727904i
$629$	0.907861	−	0.907861i	0.0361988	−	0.0361988i
$630$	−15.7385	−	23.5820i	−0.627039	−	0.939529i
$631$	−4.51364			−0.179685			−0.0898426	−	0.995956i	$-0.528636\pi$
$631$	−4.51364			−0.179685			−0.0898426	+	0.995956i	$0.528636\pi$
$632$	−45.6336	+	7.11409i	−1.81521	+	0.282983i
$633$	−2.72352	+	12.6012i	−0.108250	+	0.500854i
$634$	2.79824	+	2.52365i	0.111132	+	0.100227i
$635$	16.8828	−	24.2523i	0.669973	−	0.962423i
$636$	0.798195	−	7.24323i	0.0316505	−	0.287213i
$637$	6.56975	+	6.56975i	0.260303	+	0.260303i
$638$	−9.35106	+	0.482478i	−0.370212	+	0.0191015i
$639$	−22.9266	−	10.3959i	−0.906963	−	0.411256i
$640$	24.5287	+	6.19200i	0.969584	+	0.244760i
$641$		−	44.6021i		−	1.76168i	−0.473418	−	0.880838i	$-0.656980\pi$
$641$		−	44.6021i		−	1.76168i	0.473418	−	0.880838i	$-0.343020\pi$
$642$	3.08279	−	18.9453i	0.121668	−	0.747712i
$643$	−15.0364	+	15.0364i	−0.592979	+	0.592979i	−0.938435	−	0.345456i	$-0.887724\pi$
$643$	−15.0364	+	15.0364i	−0.592979	+	0.592979i	0.345456	+	0.938435i	$0.387724\pi$
$644$	−1.74795	−	16.8937i	−0.0688789	−	0.665705i
$645$	8.82011	+	9.47126i	0.347291	+	0.372930i
$646$	−0.100005	+	0.110886i	−0.00393465	+	0.00436276i
$647$	8.58088			0.337349			0.168675	−	0.985672i	$-0.446051\pi$
$647$	8.58088			0.337349			0.168675	+	0.985672i	$0.446051\pi$
$648$	−16.3362	+	19.5225i	−0.641748	+	0.766915i
$649$			37.2691i			1.46294i
$650$	−31.6004	−	12.5960i	−1.23947	−	0.494057i
$651$	−19.0210	−	29.5101i	−0.745492	−	1.15659i
$652$	8.50051	−	10.4626i	0.332906	−	0.409746i
$653$	−14.5218	+	14.5218i	−0.568282	+	0.568282i	−0.931647	−	0.363365i	$-0.881628\pi$
$653$	−14.5218	+	14.5218i	−0.568282	+	0.568282i	0.363365	+	0.931647i	$0.381628\pi$
$654$	5.12256	−	31.4808i	0.200308	−	1.23100i
$655$	3.73500	+	20.8480i	0.145939	+	0.814600i
$656$	31.0882	−	6.50287i	1.21379	−	0.253894i
$657$	3.22424	−	7.11058i	0.125790	−	0.277410i
$658$	−1.65739	−	32.1225i	−0.0646119	−	1.25226i
$659$	−12.9343	+	12.9343i	−0.503848	+	0.503848i	−0.912632	−	0.408783i	$-0.865953\pi$
$659$	−12.9343	+	12.9343i	−0.503848	+	0.503848i	0.408783	+	0.912632i	$0.365953\pi$
$660$	20.8253	+	18.1873i	0.810623	+	0.707938i
$661$	2.72210	+	2.72210i	0.105878	+	0.105878i	0.758061	−	0.652184i	$-0.226147\pi$
$661$	2.72210	+	2.72210i	0.105878	+	0.105878i	−0.652184	+	0.758061i	$0.726147\pi$
$662$	−14.1875	−	12.7953i	−0.551415	−	0.497305i
$663$	0.223679	−	1.03492i	0.00868697	−	0.0401931i
$664$	−13.6440	+	18.6837i	−0.529489	+	0.725069i
$665$	−0.979217	−	5.46579i	−0.0379724	−	0.211954i
$666$	39.2943	−	17.1363i	1.52262	−	0.664017i
$667$	3.72697	+	3.72697i	0.144309	+	0.144309i
$668$	−25.6838	+	2.65744i	−0.993737	+	0.102820i
$669$	8.65468	+	13.4273i	0.334609	+	0.519128i
$670$	−14.2318	+	3.31461i	−0.549821	+	0.128055i
$671$	24.0051			0.926706
$672$	−21.6134	−	19.7550i	−0.833756	−	0.762064i
$673$		−	38.9883i		−	1.50289i	−0.659796	−	0.751445i	$-0.729357\pi$
$673$		−	38.9883i		−	1.50289i	0.659796	−	0.751445i	$-0.270643\pi$
$674$	−13.4734	+	0.695174i	−0.518975	+	0.0267771i
$675$	−12.4872	−	22.7831i	−0.480631	−	0.876923i
$676$	−2.08820	−	20.1822i	−0.0803154	−	0.776237i
$677$	−17.8693	−	17.8693i	−0.686773	−	0.686773i	0.274744	−	0.961517i	$-0.411407\pi$
$677$	−17.8693	−	17.8693i	−0.686773	−	0.686773i	−0.961517	+	0.274744i	$0.911407\pi$
$678$	−25.6234	+	18.4515i	−0.984061	+	0.708627i
$679$	−38.3381			−1.47128
$680$	−0.722420	−	0.352069i	−0.0277035	−	0.0135012i
$681$	−1.45938	+	6.75232i	−0.0559237	+	0.258749i
$682$	25.4260	+	22.9310i	0.973612	+	0.878072i
$683$	−4.43249	+	4.43249i	−0.169605	+	0.169605i	−0.786806	−	0.617201i	$-0.788267\pi$
$683$	−4.43249	+	4.43249i	−0.169605	+	0.169605i	0.617201	+	0.786806i	$0.288267\pi$
$684$	−4.46124	+	2.22581i	−0.170580	+	0.0851062i
$685$	−36.8456	−	25.6494i	−1.40780	−	0.980013i
$686$	21.3942	−	1.10386i	0.816833	−	0.0421454i
$687$	−8.59748	+	39.7791i	−0.328014	+	1.51767i
$688$	11.1865	+	7.31623i	0.426482	+	0.278928i
$689$			10.1202i			0.385550i
$690$	−0.248490	−	15.5617i	−0.00945984	−	0.592423i
$691$	−7.10387	−	7.10387i	−0.270244	−	0.270244i	0.558954	−	0.829198i	$-0.311203\pi$
$691$	−7.10387	−	7.10387i	−0.270244	−	0.270244i	−0.829198	+	0.558954i	$0.811203\pi$
$692$	−15.0196	+	18.4864i	−0.570959	+	0.702746i
$693$	−11.2641	−	29.9544i	−0.427889	−	1.13787i
$694$	7.82107	+	7.05360i	0.296884	+	0.267751i
$695$	6.11286	+	34.1208i	0.231874	+	1.29427i
$696$	9.07170	+	0.528621i	0.343862	+	0.0200373i
$697$	−1.00895			−0.0382166
$698$	18.9913	+	17.1277i	0.718830	+	0.648292i
$699$	−0.897798	+	0.578684i	−0.0339578	+	0.0218879i
$700$	26.8098	−	13.2044i	1.01332	−	0.499080i
$701$	−17.8215	−	17.8215i	−0.673110	−	0.673110i	0.285321	−	0.958432i	$-0.407900\pi$
$701$	−17.8215	−	17.8215i	−0.673110	−	0.673110i	−0.958432	+	0.285321i	$0.907900\pi$
$702$	19.5813	−	29.4346i	0.739050	−	1.11094i
$703$	8.39601			0.316662
$704$	25.3801	+	13.0875i	0.956550	+	0.493253i
$705$	1.04862	−	29.4568i	0.0394935	−	1.10941i
$706$	−0.768203	−	14.8888i	−0.0289117	−	0.560347i
$707$	4.35271	+	4.35271i	0.163700	+	0.163700i
$708$	3.96178	−	35.9512i	0.148893	−	1.35113i
$709$	22.3118	+	22.3118i	0.837937	+	0.837937i	0.988587	−	0.150650i	$-0.0481368\pi$
$709$	22.3118	+	22.3118i	0.837937	+	0.837937i	−0.150650	+	0.988587i	$0.548137\pi$
$710$	14.0180	−	22.5302i	0.526088	−	0.845544i
$711$	44.6140	+	20.2299i	1.67316	+	0.758681i
$712$	−7.39547	−	47.4385i	−0.277157	−	1.77783i
$713$		−	19.2732i		−	0.721786i
$714$	0.543558	+	0.754832i	0.0203421	+	0.0282489i
$715$	−31.5147	−	21.9384i	−1.17858	−	0.820448i
$716$	12.3732	−	15.2292i	0.462409	−	0.569141i
$717$	5.28966	+	8.20662i	0.197546	+	0.306482i
$718$	0.990925	−	0.0511278i	0.0369810	−	0.00190807i
$719$	−35.5466			−1.32566			−0.662832	−	0.748769i	$-0.730645\pi$
$719$	−35.5466			−1.32566			−0.662832	+	0.748769i	$0.730645\pi$
$720$	−18.1556	−	19.7579i	−0.676618	−	0.736335i
$721$	−1.06246			−0.0395679
$722$	25.8592	−	1.33423i	0.962379	−	0.0496550i
$723$	−9.56409	−	14.8382i	−0.355692	−	0.551837i
$724$	−19.4044	−	15.7655i	−0.721159	−	0.585919i
$725$	−3.87344	+	8.42688i	−0.143856	+	0.312966i
$726$	2.49225	+	3.46095i	0.0924960	+	0.128448i
$727$		−	20.5691i		−	0.762865i	−0.924397	−	0.381433i	$-0.875431\pi$
$727$		−	20.5691i		−	0.762865i	0.924397	−	0.381433i	$-0.124569\pi$
$728$	32.8412	+	23.9826i	1.21717	+	0.888853i
$729$	25.8442	−	7.81525i	0.957192	−	0.289454i
$730$	6.98764	+	4.34763i	0.258624	+	0.160913i
$731$	−0.300247	−	0.300247i	−0.0111050	−	0.0111050i
$732$	−23.1563	−	2.55180i	−0.855880	−	0.0943171i
$733$	17.9463	+	17.9463i	0.662860	+	0.662860i	0.956053	−	0.293193i	$-0.0947179\pi$
$733$	17.9463	+	17.9463i	0.662860	+	0.662860i	−0.293193	+	0.956053i	$0.594718\pi$
$734$	0.862261	+	16.7118i	0.0318266	+	0.616842i
$735$	−7.47492	−	0.266097i	−0.275717	−	0.00981515i
$736$	−4.09740	−	15.5431i	−0.151032	−	0.572926i
$737$	−16.4943			−0.607574
$738$	−31.3570	−	12.3126i	−1.15427	−	0.453235i
$739$	30.4234	+	30.4234i	1.11914	+	1.11914i	0.991867	+	0.127276i	$0.0406234\pi$
$739$	30.4234	+	30.4234i	1.11914	+	1.11914i	0.127276	+	0.991867i	$0.459377\pi$
$740$	12.5040	+	43.4228i	0.459655	+	1.59625i
$741$	5.81986	−	3.75125i	0.213798	−	0.137806i
$742$	−6.60222	−	5.95435i	−0.242375	−	0.218591i
$743$	−12.9937			−0.476692			−0.238346	−	0.971180i	$-0.576605\pi$
$743$	−12.9937			−0.476692			−0.238346	+	0.971180i	$0.576605\pi$
$744$	−22.0893	−	24.8230i	−0.809834	−	0.910054i
$745$	−4.42263	−	24.6863i	−0.162033	−	0.904434i
$746$	−16.7934	−	15.1455i	−0.614850	−	0.554516i
$747$	22.9683	−	8.63708i	0.840368	−	0.316014i
$748$	−0.704044	−	0.572014i	−0.0257424	−	0.0209149i
$749$	−16.5593	−	16.5593i	−0.605064	−	0.605064i
$750$	25.5278	−	9.91634i	0.932142	−	0.362094i
$751$		−	12.0685i		−	0.440387i	−0.975456	−	0.220193i	$-0.929331\pi$
$751$		−	12.0685i		−	0.440387i	0.975456	−	0.220193i	$-0.0706688\pi$
$752$	−6.23282	−	29.7972i	−0.227288	−	1.08659i
$753$	1.36202	−	6.30182i	0.0496347	−	0.229651i
$754$	−12.6033	+	0.650282i	−0.458986	+	0.0236819i
$755$	5.13947	−	7.38290i	0.187044	−	0.268691i
$756$	7.68162	+	30.0926i	0.279378	+	1.09446i
$757$	24.0233	−	24.0233i	0.873141	−	0.873141i	−0.119673	−	0.992813i	$-0.538184\pi$
$757$	24.0233	−	24.0233i	0.873141	−	0.873141i	0.992813	+	0.119673i	$0.0381845\pi$
$758$	−9.88882	−	8.91844i	−0.359178	−	0.323932i
$759$	3.71124	−	17.1713i	0.134710	−	0.623278i
$760$	−1.71253	−	4.96851i	−0.0621199	−	0.180227i
$761$	−16.9093			−0.612961			−0.306480	−	0.951877i	$-0.599151\pi$
$761$	−16.9093			−0.612961			−0.306480	+	0.951877i	$0.599151\pi$
$762$	−26.2684	+	18.9160i	−0.951603	+	0.685254i
$763$	−27.5160	−	27.5160i	−0.996147	−	0.996147i
$764$	33.2286	−	3.43809i	1.20217	−	0.124386i
$765$	0.436020	+	0.732435i	0.0157643	+	0.0264812i
$766$	−14.5110	+	0.748710i	−0.524303	+	0.0270520i
$767$			50.2311i			1.81374i
$768$	−23.0915	−	15.3227i	−0.833241	−	0.552910i
$769$	−12.2949			−0.443365			−0.221683	−	0.975119i	$-0.571155\pi$
$769$	−12.2949			−0.443365			−0.221683	+	0.975119i	$0.571155\pi$
$770$	32.8541	−	7.65181i	1.18398	−	0.275752i
$771$	1.35960	+	2.10935i	0.0489649	+	0.0759664i
$772$	2.64657	+	25.5788i	0.0952522	+	0.920600i
$773$	17.1391	+	17.1391i	0.616451	+	0.616451i	0.944619	−	0.328169i	$-0.106431\pi$
$773$	17.1391	+	17.1391i	0.616451	+	0.616451i	−0.328169	+	0.944619i	$0.606431\pi$
$774$	−5.66730	−	12.9954i	−0.203707	−	0.467110i
$775$	31.8042	−	11.7736i	1.14244	−	0.422919i
$776$	−35.8514	+	5.58908i	−1.28699	+	0.200636i
$777$	11.0489	−	51.1215i	0.396378	−	1.83397i
$778$	27.0579	+	24.4027i	0.970072	+	0.874880i
$779$	−4.66544	−	4.66544i	−0.167157	−	0.167157i
$780$	28.0682	+	24.5127i	1.00500	+	0.877695i
$781$	21.1793	−	21.1793i	0.757855	−	0.757855i
$782$	0.0263111	+	0.509944i	0.000940883	+	0.0182356i
$783$	−7.73907	−	5.74490i	−0.276572	−	0.205306i
$784$	−7.56131	+	1.58163i	−0.270047	+	0.0564869i
$785$	−31.8354	+	5.70343i	−1.13625	+	0.203564i
$786$	3.72634	−	22.9003i	0.132914	−	0.816826i
$787$	−8.44662	+	8.44662i	−0.301089	+	0.301089i	−0.841440	−	0.540351i	$-0.818292\pi$
$787$	−8.44662	+	8.44662i	−0.301089	+	0.301089i	0.540351	+	0.841440i	$0.318292\pi$
$788$	8.81788	+	7.16424i	0.314124	+	0.255216i
$789$	9.43443	+	14.6370i	0.335875	+	0.521091i
$790$	−27.2784	+	43.8427i	−0.970522	+	1.55985i
$791$			38.5240i			1.36976i
$792$	−14.9004	−	26.3693i	−0.529462	−	0.936993i
$793$	32.3539			1.14892
$794$	13.8509	−	15.3579i	0.491550	−	0.545033i
$795$	−5.55234	−	5.96224i	−0.196921	−	0.211459i
$796$	36.0692	−	3.73200i	1.27844	−	0.132277i
$797$	33.5617	−	33.5617i	1.18882	−	1.18882i	0.211420	−	0.977395i	$-0.432191\pi$
$797$	33.5617	−	33.5617i	1.18882	−	1.18882i	0.977395	−	0.211420i	$-0.0678087\pi$
$798$	−0.976946	+	6.00384i	−0.0345835	+	0.212534i
$799$			0.967050i			0.0342118i
$800$	23.1459	−	16.2564i	0.818329	−	0.574749i
$801$	−21.0301	+	46.3787i	−0.743062	+	1.63871i
$802$	−15.7850	+	0.814444i	−0.557388	+	0.0287590i
$803$	6.56866	+	6.56866i	0.231803	+	0.231803i
$804$	15.9110	+	1.75338i	0.561139	+	0.0618369i
$805$	−15.5843	−	10.8487i	−0.549275	−	0.382368i
$806$	34.2690	+	30.9062i	1.20708	+	1.08863i
$807$	2.43587	−	11.2704i	0.0857468	−	0.396736i
$808$	4.70493	+	3.43582i	0.165519	+	0.120872i
$809$	51.8719			1.82372			0.911859	−	0.410504i	$-0.134647\pi$
$809$	51.8719			1.82372			0.911859	+	0.410504i	$0.134647\pi$
$810$	4.61278	+	28.0842i	0.162077	+	0.986778i
$811$	−25.5812	+	25.5812i	−0.898277	+	0.898277i	−0.995284	−	0.0970070i	$-0.969073\pi$
$811$	−25.5812	+	25.5812i	−0.898277	+	0.898277i	0.0970070	+	0.995284i	$0.469073\pi$
$812$	6.99107	−	8.60473i	0.245338	−	0.301967i
$813$	−2.72406	+	1.75582i	−0.0955369	+	0.0615793i
$814$	2.62820	+	50.9381i	0.0921185	+	1.78538i
$815$	−2.65783	−	14.8355i	−0.0930997	−	0.519664i
$816$	0.618343	+	0.626629i	0.0216463	+	0.0219364i
$817$		−	2.77673i		−	0.0971453i
$818$	−33.1104	+	1.70837i	−1.15768	+	0.0597316i
$819$	−15.1818	−	40.3724i	−0.530494	−	1.41073i
$820$	17.1807	−	31.0770i	0.599978	−	1.08526i
$821$	−12.7761	+	12.7761i	−0.445888	+	0.445888i	−0.893985	−	0.448097i	$-0.852102\pi$
$821$	−12.7761	+	12.7761i	−0.445888	+	0.445888i	0.448097	+	0.893985i	$0.352102\pi$
$822$	28.7383	+	39.9086i	1.00236	+	1.39197i
$823$			24.9850i			0.870924i	0.900207	+	0.435462i	$0.143415\pi$
$823$			24.9850i			0.870924i	−0.900207	+	0.435462i	$0.856585\pi$
$824$	−0.993541	+	0.154889i	−0.0346116	+	0.00539581i
$825$	30.6028	−	4.36534i	1.06545	−	0.151982i
$826$	−32.7696	−	29.5540i	−1.14020	−	1.02831i
$827$	−23.9919	+	23.9919i	−0.834281	+	0.834281i	−0.988099	−	0.153819i	$-0.950843\pi$
$827$	−23.9919	+	23.9919i	−0.834281	+	0.834281i	0.153819	+	0.988099i	$0.450843\pi$
$828$	−5.40536	+	16.1696i	−0.187849	+	0.561932i
$829$	−5.07448	+	5.07448i	−0.176244	+	0.176244i	−0.789716	−	0.613472i	$-0.789772\pi$
$829$	−5.07448	+	5.07448i	−0.176244	+	0.176244i	0.613472	+	0.789716i	$0.289772\pi$
$830$	5.86723	+	25.1918i	0.203654	+	0.874419i
$831$	−18.0548	−	3.90220i	−0.626315	−	0.135366i
$832$	34.2072	+	17.6393i	1.18592	+	0.611531i
$833$	0.245397			0.00850251
$834$	6.09868	−	37.4796i	0.211180	−	1.29781i
$835$	−16.4935	+	23.6931i	−0.570782	+	0.819935i
$836$	−0.610518	−	5.90058i	−0.0211152	−	0.204076i
$837$	5.15622	+	34.8647i	0.178225	+	1.20510i
$838$	38.7381	+	34.9368i	1.33819	+	1.20687i
$839$			1.00441i			0.0346759i	0.999850	+	0.0173380i	$0.00551913\pi$
$839$			1.00441i			0.0346759i	−0.999850	+	0.0173380i	$0.994481\pi$
$840$	−32.5058	+	3.88877i	−1.12156	+	0.134175i
$841$		−	25.5594i		−	0.881358i
$842$	1.76353	−	1.95541i	0.0607753	−	0.0673880i
$843$	6.87681	+	10.6690i	0.236850	+	0.367460i
$844$	11.5539	+	9.38718i	0.397702	+	0.323120i
$845$	−18.6179	−	12.9605i	−0.640475	−	0.445855i
$846$	−11.8013	+	30.0548i	−0.405738	+	1.03331i
$847$	5.20344			0.178792
$848$	−7.04202	−	4.60563i	−0.241824	−	0.158158i
$849$	6.68982	−	30.9526i	0.229594	−	1.06229i
$850$	−0.825426	+	0.354932i	−0.0283119	+	0.0121741i
$851$	20.3019	−	20.3019i	0.695941	−	0.695941i
$852$	−22.6818	+	18.1790i	−0.777066	+	0.622802i
$853$	30.8835	−	30.8835i	1.05743	−	1.05743i	0.0591851	−	0.998247i	$-0.481150\pi$
$853$	30.8835	−	30.8835i	1.05743	−	1.05743i	0.998247	−	0.0591851i	$-0.0188502\pi$
$854$	−19.0358	+	21.1070i	−0.651391	+	0.722267i
$855$	−1.37064	+	5.40301i	−0.0468750	+	0.184779i
$856$	−17.8993	−	13.0711i	−0.611785	−	0.446762i
$857$			39.8295i			1.36055i	0.732958	+	0.680274i	$0.238139\pi$
$857$			39.8295i			1.36055i	−0.732958	+	0.680274i	$0.761861\pi$
$858$	24.5804	+	34.1345i	0.839161	+	1.16533i
$859$	−21.7833	+	21.7833i	−0.743236	+	0.743236i	−0.973199	−	0.229963i	$-0.926139\pi$
$859$	−21.7833	+	21.7833i	−0.743236	+	0.743236i	0.229963	+	0.973199i	$0.426139\pi$
$860$	14.3608	−	4.13531i	0.489698	−	0.141013i
$861$	−34.5464	+	22.2673i	−1.17734	+	0.758866i
$862$	0.963522	+	18.6743i	0.0328177	+	0.636050i
$863$		−	8.01847i		−	0.272952i	−0.990643	−	0.136476i	$-0.956422\pi$
$863$		−	8.01847i		−	0.272952i	0.990643	−	0.136476i	$-0.0435776\pi$
$864$	11.5704	+	27.0208i	0.393632	+	0.919268i
$865$	4.69613	+	26.2128i	0.159673	+	0.891263i
$866$	−23.5389	+	1.21452i	−0.799885	+	0.0412709i
$867$	15.9372	+	24.7257i	0.541255	+	0.839729i
$868$	−40.3251	+	4.17234i	−1.36872	+	0.141619i
$869$	−41.2138	+	41.2138i	−1.39808	+	1.39808i
$870$	7.06836	−	7.29776i	0.239640	−	0.247417i
$871$	−22.2309			−0.753265
$872$	−29.7426	−	21.7198i	−1.00721	−	0.735526i
$873$	35.0504	+	15.8934i	1.18628	+	0.537909i
$874$	−2.23635	+	2.47968i	−0.0756457	+	0.0838764i
$875$	8.38223	−	32.3441i	0.283371	−	1.09343i
$876$	−5.63813	−	7.03465i	−0.190495	−	0.237679i
$877$	−20.0311	−	20.0311i	−0.676401	−	0.676401i	0.282783	−	0.959184i	$-0.408742\pi$
$877$	−20.0311	−	20.0311i	−0.676401	−	0.676401i	−0.959184	+	0.282783i	$0.908742\pi$
$878$	−0.277282	−	5.37409i	−0.00935781	−	0.181367i
$879$	5.57837	−	25.8102i	0.188154	−	0.870555i
$880$	29.6075	−	11.9451i	0.998070	−	0.402669i
$881$		−	8.15726i		−	0.274825i	−0.990514	−	0.137412i	$-0.956121\pi$
$881$		−	8.15726i		−	0.274825i	0.990514	−	0.137412i	$-0.0438786\pi$
$882$	7.62667	+	2.99469i	0.256803	+	0.100836i
$883$	−25.2094	+	25.2094i	−0.848365	+	0.848365i	−0.989929	−	0.141564i	$-0.954787\pi$
$883$	−25.2094	+	25.2094i	−0.848365	+	0.848365i	0.141564	+	0.989929i	$0.454787\pi$
$884$	−0.948908	−	0.770957i	−0.0319152	−	0.0259301i
$885$	−27.5586	−	29.5932i	−0.926373	−	0.994763i
$886$	−13.2947	−	11.9901i	−0.446645	−	0.402816i
$887$	−22.4761			−0.754675			−0.377338	−	0.926076i	$-0.623160\pi$
$887$	−22.4761			−0.754675			−0.377338	+	0.926076i	$0.623160\pi$
$888$	2.87956	−	49.4163i	0.0966317	−	1.65830i
$889$			39.4937i			1.32458i
$890$	−45.5768	−	28.3573i	−1.52774	−	0.950540i
$891$	−2.11965	+	32.0553i	−0.0710110	+	1.07389i
$892$	18.3482	−	1.89844i	0.614343	−	0.0635646i
$893$	−4.47170	+	4.47170i	−0.149640	+	0.149640i
$894$	−4.41238	+	27.1163i	−0.147572	+	0.906906i
$895$	−3.86870	−	21.5943i	−0.129316	−	0.721818i
$896$	−31.6336	+	11.9378i	−1.05681	+	0.398814i
$897$	5.00199	−	23.1434i	0.167012	−	0.772734i
$898$	7.70057	−	0.397319i	0.256972	−	0.0132587i
$899$	8.89624	−	8.89624i	0.296706	−	0.296706i
$900$	−29.9847	+	0.957839i	−0.999490	+	0.0319280i
$901$	0.189008	+	0.189008i	0.00629678	+	0.00629678i
$902$	26.8445	−	29.7654i	0.893825	−	0.991078i
$903$	−16.9069	−	3.65410i	−0.562625	−	0.121601i
$904$	5.61618	+	36.0252i	0.186791	+	1.19818i
$905$	−27.5146	+	4.92934i	−0.914616	+	0.163857i
$906$	−7.99664	+	5.75842i	−0.265671	+	0.191311i
$907$	−5.99135	−	5.99135i	−0.198939	−	0.198939i	0.600606	−	0.799545i	$-0.294926\pi$
$907$	−5.99135	−	5.99135i	−0.198939	−	0.198939i	−0.799545	+	0.600606i	$0.794926\pi$
$908$	6.19110	+	5.03008i	0.205459	+	0.166929i
$909$	−2.17499	−	5.78388i	−0.0721398	−	0.191839i
$910$	44.2806	−	10.3131i	1.46789	−	0.341875i
$911$	2.13853			0.0708526			0.0354263	−	0.999372i	$-0.488721\pi$
$911$	2.13853			0.0708526			0.0354263	+	0.999372i	$0.488721\pi$
$912$	−0.0383140	+	5.75683i	−0.00126870	+	0.190628i
$913$			29.1967i			0.966269i
$914$	−1.94340	−	37.6656i	−0.0642819	−	1.24587i
$915$	−19.0610	+	17.7506i	−0.630138	+	0.586816i
$916$	36.4729	+	29.6330i	1.20510	+	0.979103i
$917$	−20.0162	−	20.0162i	−0.660992	−	0.660992i
$918$	−0.184023	−	0.915436i	−0.00607367	−	0.0302139i
$919$	39.4143			1.30016			0.650080	−	0.759866i	$-0.274736\pi$
$919$	39.4143			1.30016			0.650080	+	0.759866i	$0.274736\pi$
$920$	−16.1550	−	7.87310i	−0.532615	−	0.259568i
$921$	28.8319	+	6.23145i	0.950042	+	0.205333i
$922$	−0.552367	+	0.612468i	−0.0181912	+	0.0201706i
$923$	28.5453	−	28.5453i	0.939582	−	0.939582i
$924$	−36.7307	−	4.04769i	−1.20835	−	0.133159i
$925$	45.9038	+	21.0998i	1.50931	+	0.693757i
$926$	−0.280929	−	5.44478i	−0.00923192	−	0.178927i
$927$	0.971344	+	0.440449i	0.0319031	+	0.0144662i
$928$	5.28317	−	9.06578i	0.173429	−	0.297599i
$929$			2.69933i			0.0885622i	0.999019	+	0.0442811i	$0.0140997\pi$
$929$			2.69933i			0.0885622i	−0.999019	+	0.0442811i	$0.985900\pi$
$930$	−37.1456	+	0.593143i	−1.21805	+	0.0194499i
$931$	1.13473	+	1.13473i	0.0371893	+	0.0371893i
$932$	0.126937	+	1.22683i	0.00415796	+	0.0401861i
$933$	−37.0858	+	23.9040i	−1.21414	+	0.782583i
$934$	13.2620	−	14.7050i	0.433945	−	0.481161i
$935$	−0.998304	+	0.178850i	−0.0326480	+	0.00584901i
$936$	−20.0827	−	35.5404i	−0.656422	−	1.16168i
$937$	28.5020			0.931120			0.465560	−	0.885016i	$-0.345853\pi$
$937$	28.5020			0.931120			0.465560	+	0.885016i	$0.345853\pi$
$938$	13.0798	−	14.5030i	0.427070	−	0.473538i
$939$	−27.6956	−	42.9682i	−0.903812	−	1.40222i
$940$	−29.7865	−	16.4673i	−0.971527	−	0.537103i
$941$	27.2302	+	27.2302i	0.887680	+	0.887680i	0.994300	−	0.106620i	$-0.0340027\pi$
$941$	27.2302	+	27.2302i	0.887680	+	0.887680i	−0.106620	+	0.994300i	$0.534003\pi$
$942$	34.9692	+	5.69020i	1.13936	+	0.185397i
$943$	−22.5625			−0.734735
$944$	−34.9526	−	22.8597i	−1.13761	−	0.744020i
$945$	31.0940	+	15.4558i	1.01149	+	0.502776i
$946$	16.8462	−	0.869199i	0.547718	−	0.0282601i
$947$	−0.842383	−	0.842383i	−0.0273738	−	0.0273738i	0.693287	−	0.720661i	$-0.256162\pi$
$947$	−0.842383	−	0.842383i	−0.0273738	−	0.0273738i	−0.720661	+	0.693287i	$0.756162\pi$
$948$	44.1376	−	35.3754i	1.43352	−	1.14894i
$949$	8.85320	+	8.85320i	0.287387	+	0.287387i
$950$	−5.45805	−	2.17560i	−0.177082	−	0.0705856i
$951$	−4.51086	−	0.974937i	−0.146275	−	0.0316145i
$952$	1.06126	−	0.165445i	0.0343955	−	0.00536212i
$953$		−	2.36649i		−	0.0766582i	−0.999265	−	0.0383291i	$-0.987796\pi$
$953$		−	2.36649i		−	0.0766582i	0.999265	−	0.0383291i	$-0.0122035\pi$
$954$	3.56762	+	8.18073i	0.115506	+	0.264861i
$955$	21.3386	−	30.6532i	0.690502	−	0.991913i
$956$	11.2142	−	1.16031i	0.362694	−	0.0375271i
$957$	9.63908	−	6.21296i	0.311587	−	0.200837i
$958$	1.01017	+	19.5785i	0.0326372	+	0.632552i
$959$	60.0014			1.93754
$960$	−29.8304	+	8.37535i	−0.962772	+	0.270313i
$961$	−15.0049			−0.484030
$962$	3.54228	+	68.6541i	0.114208	+	2.21350i
$963$	8.27446	+	22.0040i	0.266641	+	0.709070i
$964$	−20.2762	+	2.09793i	−0.653051	+	0.0675696i
$965$	23.5962	+	16.4261i	0.759589	+	0.528774i
$966$	12.1552	+	16.8798i	0.391089	+	0.543100i
$967$			42.6028i			1.37001i	0.728536	+	0.685007i	$0.240201\pi$
$967$			42.6028i			1.37001i	−0.728536	+	0.685007i	$0.759799\pi$
$968$	4.86593	−	0.758578i	0.156397	−	0.0243816i
$969$	0.0386340	−	0.178753i	0.00124110	−	0.00574237i
$970$	−21.4309	+	34.4444i	−0.688104	+	1.10594i
$971$	−28.3644	−	28.3644i	−0.910257	−	0.910257i	0.0860348	−	0.996292i	$-0.472580\pi$
$971$	−28.3644	−	28.3644i	−0.910257	−	0.910257i	−0.996292	+	0.0860348i	$0.972580\pi$
$972$	5.45225	−	30.6965i	0.174881	−	0.984590i
$973$	−32.7593	−	32.7593i	−1.05021	−	1.05021i
$974$	15.0396	−	0.775983i	0.481899	−	0.0248641i
$975$	41.2463	−	5.88359i	1.32094	−	0.188426i
$976$	−14.7240	+	22.5130i	−0.471304	+	0.720625i
$977$	33.3357			1.06650			0.533252	−	0.845957i	$-0.320970\pi$
$977$	33.3357			1.06650			0.533252	+	0.845957i	$0.320970\pi$
$978$	−2.65166	+	16.2959i	−0.0847908	+	0.521084i
$979$	−42.8440	−	42.8440i	−1.36930	−	1.36930i
$980$	−4.17871	+	7.55857i	−0.133484	+	0.241450i
$981$	13.7494	+	36.5633i	0.438984	+	1.16738i
$982$	−20.3238	+	22.5351i	−0.648557	+	0.719124i
$983$	23.4948			0.749367			0.374684	−	0.927153i	$-0.377751\pi$
$983$	23.4948			0.749367			0.374684	+	0.927153i	$0.377751\pi$
$984$	−29.0594	+	25.8592i	−0.926381	+	0.824362i
$985$	12.5034	−	2.24002i	0.398390	−	0.0713731i
$986$	−0.223238	+	0.247528i	−0.00710936	+	0.00788290i
$987$	21.3426	+	33.1118i	0.679341	+	1.05396i
$988$	−0.822854	−	7.95277i	−0.0261785	−	0.253011i
$989$	−6.71424	−	6.71424i	−0.213500	−	0.213500i
$990$	−33.2088	−	6.62429i	−1.05544	−	0.210534i
$991$			8.02181i			0.254821i	0.991850	+	0.127411i	$0.0406666\pi$
$991$			8.02181i			0.254821i	−0.991850	+	0.127411i	$0.959333\pi$
$992$	−37.1012	+	9.78046i	−1.17796	+	0.310530i
$993$	22.8709	+	4.94310i	0.725785	+	0.156864i
$994$	1.82739	+	35.4173i	0.0579614	+	1.12337i
$995$	23.1628	−	33.2736i	0.734310	−	1.05484i
$996$	3.10367	−	28.1643i	0.0983436	−	0.892419i
$997$	1.11384	−	1.11384i	0.0352758	−	0.0352758i	−0.689249	−	0.724525i	$-0.742059\pi$
$997$	1.11384	−	1.11384i	0.0352758	−	0.0352758i	0.724525	+	0.689249i	$0.242059\pi$
$998$	−22.9605	+	25.4587i	−0.726801	+	0.805881i
$999$	−31.2942	+	42.1571i	−0.990105	+	1.33379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.t.b.59.22	yes	80
3.2	odd	2	inner	240.2.t.b.59.20	yes	80
4.3	odd	2		960.2.t.b.719.28		80
5.4	even	2	inner	240.2.t.b.59.19	✓	80
12.11	even	2		960.2.t.b.719.8		80
15.14	odd	2	inner	240.2.t.b.59.21	yes	80
16.3	odd	4	inner	240.2.t.b.179.21	yes	80
16.13	even	4		960.2.t.b.239.33		80
20.19	odd	2		960.2.t.b.719.13		80
48.29	odd	4		960.2.t.b.239.13		80
48.35	even	4	inner	240.2.t.b.179.19	yes	80
60.59	even	2		960.2.t.b.719.33		80
80.19	odd	4	inner	240.2.t.b.179.20	yes	80
80.29	even	4		960.2.t.b.239.8		80
240.29	odd	4		960.2.t.b.239.28		80
240.179	even	4	inner	240.2.t.b.179.22	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.t.b.59.19	✓	80	5.4	even	2	inner
240.2.t.b.59.20	yes	80	3.2	odd	2	inner
240.2.t.b.59.21	yes	80	15.14	odd	2	inner
240.2.t.b.59.22	yes	80	1.1	even	1	trivial
240.2.t.b.179.19	yes	80	48.35	even	4	inner
240.2.t.b.179.20	yes	80	80.19	odd	4	inner
240.2.t.b.179.21	yes	80	16.3	odd	4	inner
240.2.t.b.179.22	yes	80	240.179	even	4	inner
960.2.t.b.239.8		80	80.29	even	4
960.2.t.b.239.13		80	48.29	odd	4
960.2.t.b.239.28		80	240.29	odd	4
960.2.t.b.239.33		80	16.13	even	4
960.2.t.b.719.8		80	12.11	even	2
960.2.t.b.719.13		80	20.19	odd	2
960.2.t.b.719.28		80	4.3	odd	2
960.2.t.b.719.33		80	60.59	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0728709 + 1.41233i) q^{2} +(-0.938373 - 1.45584i) q^{3} +(-1.98938 + 0.205836i) q^{4} +(-1.27753 + 1.83519i) q^{5} +(1.98775 - 1.43139i) q^{6} -2.98852i q^{7} +(-0.435678 - 2.79467i) q^{8} +(-1.23891 + 2.73223i) q^{9} +O(q^{10})\)	\(q+(0.0728709 + 1.41233i) q^{2} +(-0.938373 - 1.45584i) q^{3} +(-1.98938 + 0.205836i) q^{4} +(-1.27753 + 1.83519i) q^{5} +(1.98775 - 1.43139i) q^{6} -2.98852i q^{7} +(-0.435678 - 2.79467i) q^{8} +(-1.23891 + 2.73223i) q^{9} +(-2.68499 - 1.67057i) q^{10} +(-2.52400 - 2.52400i) q^{11} +(2.16644 + 2.70306i) q^{12} +(-3.40183 - 3.40183i) q^{13} +(4.22079 - 0.217776i) q^{14} +(3.87053 + 0.137786i) q^{15} +(3.91526 - 0.818973i) q^{16} -0.127067 q^{17} +(-3.94911 - 1.55066i) q^{18} +(-0.587567 - 0.587567i) q^{19} +(2.16375 - 3.91385i) q^{20} +(-4.35079 + 2.80434i) q^{21} +(3.38081 - 3.74866i) q^{22} -2.84152 q^{23} +(-3.65975 + 3.25672i) q^{24} +(-1.73582 - 4.68902i) q^{25} +(4.55663 - 5.05242i) q^{26} +(5.14024 - 0.760202i) q^{27} +(0.615146 + 5.94530i) q^{28} +(-1.31161 - 1.31161i) q^{29} +(0.0874495 + 5.47653i) q^{30} +6.78269i q^{31} +(1.44197 + 5.46998i) q^{32} +(-1.30607 + 6.04298i) q^{33} +(-0.00925951 - 0.179461i) q^{34} +(5.48449 + 3.81793i) q^{35} +(1.90227 - 5.69046i) q^{36} +(-7.14473 + 7.14473i) q^{37} +(0.787025 - 0.872658i) q^{38} +(-1.76032 + 8.14470i) q^{39} +(5.68534 + 2.77073i) q^{40} +7.94027 q^{41} +(-4.27772 - 5.94042i) q^{42} +(2.36290 + 2.36290i) q^{43} +(5.54072 + 4.50166i) q^{44} +(-3.43141 - 5.76415i) q^{45} +(-0.207065 - 4.01318i) q^{46} -7.61054i q^{47} +(-4.86627 - 4.93147i) q^{48} -1.93124 q^{49} +(6.49598 - 2.79326i) q^{50} +(0.119236 + 0.184989i) q^{51} +(7.46776 + 6.06732i) q^{52} +(-1.48747 - 1.48747i) q^{53} +(1.44823 + 7.20435i) q^{54} +(7.85650 - 1.40752i) q^{55} +(-8.35192 + 1.30203i) q^{56} +(-0.304044 + 1.40676i) q^{57} +(1.75685 - 1.94801i) q^{58} +(-7.38294 - 7.38294i) q^{59} +(-7.72832 + 0.522588i) q^{60} +(-4.75537 + 4.75537i) q^{61} +(-9.57943 + 0.494261i) q^{62} +(8.16533 + 3.70251i) q^{63} +(-7.62037 + 2.43515i) q^{64} +(10.5890 - 1.89705i) q^{65} +(-8.62989 - 1.40426i) q^{66} +(3.26749 - 3.26749i) q^{67} +(0.252785 - 0.0261550i) q^{68} +(2.66641 + 4.13679i) q^{69} +(-4.99253 + 8.02415i) q^{70} +8.39116i q^{71} +(8.17546 + 2.27198i) q^{72} -2.60248 q^{73} +(-10.6114 - 9.57010i) q^{74} +(-5.19759 + 6.92712i) q^{75} +(1.28984 + 1.04795i) q^{76} +(-7.54302 + 7.54302i) q^{77} +(-11.6313 - 1.89265i) q^{78} -16.3288i q^{79} +(-3.49890 + 8.23150i) q^{80} +(-5.93019 - 6.76999i) q^{81} +(0.578615 + 11.2143i) q^{82} +(-5.78381 - 5.78381i) q^{83} +(8.07814 - 6.47446i) q^{84} +(0.162332 - 0.233192i) q^{85} +(-3.16502 + 3.50939i) q^{86} +(-0.678708 + 3.14026i) q^{87} +(-5.95410 + 8.15340i) q^{88} +16.9746 q^{89} +(7.89086 - 5.26634i) q^{90} +(-10.1664 + 10.1664i) q^{91} +(5.65287 - 0.584889i) q^{92} +(9.87448 - 6.36470i) q^{93} +(10.7486 - 0.554587i) q^{94} +(1.82893 - 0.327660i) q^{95} +(6.61028 - 7.23216i) q^{96} -12.8285i q^{97} +(-0.140731 - 2.72756i) q^{98} +(10.0232 - 3.76914i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 8 q^{4} - 4 q^{6}+O(q^{10}) \) 80 * q - 8 * q^4 - 4 * q^6	\( 80 q - 8 q^{4} - 4 q^{6} + 16 q^{10} - 32 q^{16} + 16 q^{19} + 8 q^{21} - 56 q^{24} + 8 q^{30} - 16 q^{34} - 40 q^{36} - 8 q^{39} - 8 q^{40} - 12 q^{45} - 24 q^{46} - 112 q^{49} + 32 q^{51} + 60 q^{54} - 40 q^{55} + 40 q^{60} + 16 q^{61} - 32 q^{64} - 56 q^{66} - 40 q^{69} + 48 q^{70} - 36 q^{75} - 128 q^{76} + 64 q^{81} + 128 q^{84} - 64 q^{85} + 72 q^{90} + 48 q^{91} + 56 q^{94} - 24 q^{96} - 8 q^{99}+O(q^{100}) \) 80 * q - 8 * q^4 - 4 * q^6 + 16 * q^10 - 32 * q^16 + 16 * q^19 + 8 * q^21 - 56 * q^24 + 8 * q^30 - 16 * q^34 - 40 * q^36 - 8 * q^39 - 8 * q^40 - 12 * q^45 - 24 * q^46 - 112 * q^49 + 32 * q^51 + 60 * q^54 - 40 * q^55 + 40 * q^60 + 16 * q^61 - 32 * q^64 - 56 * q^66 - 40 * q^69 + 48 * q^70 - 36 * q^75 - 128 * q^76 + 64 * q^81 + 128 * q^84 - 64 * q^85 + 72 * q^90 + 48 * q^91 + 56 * q^94 - 24 * q^96 - 8 * q^99

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