LMFDB - Embedded newform 240.2.t.b.179.22

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			179.22
Character	$\chi$	$=$	240.179
Dual form			240.2.t.b.59.22

$q$-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 $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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	$0.191038\pi$
$7$			2.98852i			1.12955i	−0.825244	+	0.564777i	$0.808962\pi$
$8$	−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	−0.976506	−	0.215491i	$-0.930865\pi$
$11$	−2.52400	+	2.52400i	−0.761014	+	0.761014i	0.215491	+	0.976506i	$0.430865\pi$
$12$	2.16644	−	2.70306i	0.625399	−	0.780306i
$13$	−3.40183	+	3.40183i	−0.943499	+	0.943499i	−0.998487	−	0.0549880i	$-0.982488\pi$
$13$	−3.40183	+	3.40183i	−0.943499	+	0.943499i	0.0549880	+	0.998487i	$0.482488\pi$
$14$	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	−0.771286	−	0.636489i	$-0.780386\pi$
$19$	−0.587567	+	0.587567i	−0.134797	+	0.134797i	0.636489	+	0.771286i	$0.280386\pi$
$20$	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	−0.818321	−	0.574761i	$-0.805095\pi$
$29$	−1.31161	+	1.31161i	−0.243560	+	0.243560i	0.574761	+	0.818321i	$0.305095\pi$
$30$	0.0874495	−	5.47653i	0.0159660	−	0.999873i
$31$		−	6.78269i		−	1.21821i	−0.793091	−	0.609104i	$-0.791529\pi$
$31$		−	6.78269i		−	1.21821i	0.793091	−	0.609104i	$-0.208471\pi$
$32$	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	−0.981104	−	0.193482i	$-0.938022\pi$
$37$	−7.14473	−	7.14473i	−1.17459	−	1.17459i	−0.193482	−	0.981104i	$-0.561978\pi$
$38$	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	−0.503599	−	0.863938i	$-0.667991\pi$
$43$	2.36290	−	2.36290i	0.360339	−	0.360339i	0.863938	+	0.503599i	$0.167991\pi$
$44$	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	$0.187303\pi$
$47$			7.61054i			1.11011i	−0.831813	+	0.555055i	$0.812697\pi$
$48$	−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	−0.801848	−	0.597528i	$-0.796150\pi$
$53$	−1.48747	+	1.48747i	−0.204319	+	0.204319i	0.597528	+	0.801848i	$0.296150\pi$
$54$	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	−0.999274	−	0.0380975i	$-0.987870\pi$
$59$	−7.38294	+	7.38294i	−0.961177	+	0.961177i	0.0380975	+	0.999274i	$0.487870\pi$
$60$	−7.72832	−	0.522588i	−0.997722	−	0.0674658i
$61$	−4.75537	−	4.75537i	−0.608862	−	0.608862i	0.333786	−	0.942649i	$-0.391674\pi$
$61$	−4.75537	−	4.75537i	−0.608862	−	0.608862i	−0.942649	+	0.333786i	$0.891674\pi$
$62$	−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	0.877946	−	0.478759i	$-0.158913\pi$
$67$	3.26749	+	3.26749i	0.399187	+	0.399187i	−0.478759	+	0.877946i	$0.658913\pi$
$68$	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	$-0.834096\pi$
$71$		−	8.39116i		−	0.995848i	0.867221	−	0.497924i	$-0.165904\pi$
$72$	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	$0.370652\pi$
$79$			16.3288i			1.83713i	−0.395268	+	0.918566i	$0.629348\pi$
$80$	−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	−0.949282	−	0.314426i	$-0.898188\pi$
$83$	−5.78381	+	5.78381i	−0.634856	+	0.634856i	0.314426	+	0.949282i	$0.398188\pi$
$84$	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	$0.225762\pi$
$97$			12.8285i			1.30253i	−0.758848	+	0.651267i	$0.774238\pi$
$98$	−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	0.630922	−	0.775847i	$-0.282677\pi$
$101$	−1.45648	−	1.45648i	−0.144925	−	0.144925i	−0.775847	+	0.630922i	$0.782677\pi$
$102$	−0.252577	−	0.181882i	−0.0250089	−	0.0180090i
$103$			0.355513i			0.0350297i	0.999847	+	0.0175149i	$0.00557544\pi$
$103$			0.355513i			0.0350297i	−0.999847	+	0.0175149i	$0.994425\pi$
$104$	−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	0.922253	−	0.386587i	$-0.126346\pi$
$107$	5.54098	+	5.54098i	0.535666	+	0.535666i	−0.386587	+	0.922253i	$0.626346\pi$
$108$	−10.0694	−	2.57038i	−0.968930	−	0.247335i
$109$	9.20725	+	9.20725i	0.881894	+	0.881894i	0.993727	−	0.111833i	$-0.0356721\pi$
$109$	9.20725	+	9.20725i	0.881894	+	0.881894i	−0.111833	+	0.993727i	$0.535672\pi$
$110$	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	0.936322	−	0.351142i	$-0.114207\pi$
$131$	6.69769	+	6.69769i	0.585180	+	0.585180i	−0.351142	+	0.936322i	$0.614207\pi$
$132$	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	$-0.671918\pi$
$137$		−	20.0773i		−	1.71532i	0.514218	−	0.857660i	$-0.328082\pi$
$138$	−5.64823	−	4.06732i	−0.480809	−	0.346233i
$139$	10.9617	+	10.9617i	0.929761	+	0.929761i	0.997690	−	0.0679293i	$-0.0216392\pi$
$139$	10.9617	+	10.9617i	0.929761	+	0.929761i	−0.0679293	+	0.997690i	$0.521639\pi$
$140$	−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	0.303210	−	0.952924i	$-0.401942\pi$
$149$	−7.93077	−	7.93077i	−0.649714	−	0.649714i	−0.952924	+	0.303210i	$0.901942\pi$
$150$	−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	−0.169317	−	0.985562i	$-0.554156\pi$
$157$	10.2275	−	10.2275i	0.816245	−	0.816245i	0.985562	+	0.169317i	$0.0541561\pi$
$158$	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	0.495373	−	0.868681i	$-0.335032\pi$
$163$	−4.76608	−	4.76608i	−0.373308	−	0.373308i	−0.868681	+	0.495373i	$0.835032\pi$
$164$	−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	0.950617	−	0.310365i	$-0.100451\pi$
$173$	8.42120	+	8.42120i	0.640252	+	0.640252i	−0.310365	+	0.950617i	$0.600451\pi$
$174$	−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	0.398597	−	0.917126i	$-0.369497\pi$
$179$	−6.93744	−	6.93744i	−0.518529	−	0.518529i	−0.917126	+	0.398597i	$0.869497\pi$
$180$	8.01285	−	10.7608i	0.597242	−	0.802061i
$181$	8.83940	−	8.83940i	0.657028	−	0.657028i	−0.297648	−	0.954676i	$-0.596202\pi$
$181$	8.83940	−	8.83940i	0.657028	−	0.657028i	0.954676	+	0.297648i	$0.0962022\pi$
$182$	−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	$0.153140\pi$
$193$			12.8577i			0.925514i	−0.886485	+	0.462757i	$0.846860\pi$
$194$	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	−0.835571	−	0.549382i	$-0.814863\pi$
$197$	−4.01686	+	4.01686i	−0.286189	+	0.286189i	0.549382	+	0.835571i	$0.314863\pi$
$198$	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	−0.864672	−	0.502337i	$-0.832474\pi$
$211$	−5.26322	+	5.26322i	−0.362335	+	0.362335i	0.502337	+	0.864672i	$0.332474\pi$
$212$	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	−0.794479	−	0.607291i	$-0.792256\pi$
$227$	−2.82027	+	2.82027i	−0.187188	+	0.187188i	0.607291	+	0.794479i	$0.292256\pi$
$228$	0.315297	+	2.86116i	0.0208810	+	0.189485i
$229$	−16.6147	+	16.6147i	−1.09793	+	1.09793i	−0.103278	+	0.994653i	$0.532933\pi$
$229$	−16.6147	+	16.6147i	−1.09793	+	1.09793i	−0.994653	+	0.103278i	$0.967067\pi$
$230$	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	$0.00643040\pi$
$233$			0.616689i			0.0404007i	−0.999796	+	0.0202003i	$0.993570\pi$
$234$	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	−0.619142	−	0.785279i	$-0.712519\pi$
$251$	2.63211	−	2.63211i	0.166137	−	0.166137i	0.785279	+	0.619142i	$0.212519\pi$
$252$	−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	−0.548886	−	0.835898i	$-0.684948\pi$
$269$	4.70735	−	4.70735i	0.287012	−	0.287012i	0.835898	+	0.548886i	$0.184948\pi$
$270$	−15.0715	+	6.54600i	−0.917222	+	0.398377i
$271$			1.87113i			0.113663i	0.998384	+	0.0568316i	$0.0180998\pi$
$271$			1.87113i			0.113663i	−0.998384	+	0.0568316i	$0.981900\pi$
$272$	−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	0.896381	−	0.443284i	$-0.146187\pi$
$277$	7.54104	+	7.54104i	0.453097	+	0.453097i	−0.443284	+	0.896381i	$0.646187\pi$
$278$	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	−0.209344	−	0.977842i	$-0.567133\pi$
$283$	12.9281	−	12.9281i	0.768498	−	0.768498i	0.977842	+	0.209344i	$0.0671329\pi$
$284$	−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	−0.318226	−	0.948015i	$-0.603087\pi$
$293$	10.7802	−	10.7802i	0.629789	−	0.629789i	0.948015	+	0.318226i	$0.103087\pi$
$294$	−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	0.274340	−	0.961633i	$-0.411541\pi$
$307$	−12.0423	−	12.0423i	−0.687293	−	0.687293i	−0.961633	+	0.274340i	$0.911541\pi$
$308$	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	$0.256890\pi$
$311$			25.4739i			1.44449i	−0.691635	+	0.722247i	$0.743110\pi$
$312$	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	0.758035	−	0.652214i	$-0.226160\pi$
$317$	1.88407	+	1.88407i	0.105820	+	0.105820i	−0.652214	+	0.758035i	$0.726160\pi$
$318$	−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	0.394037	−	0.919094i	$-0.371078\pi$
$331$	−9.55258	−	9.55258i	−0.525057	−	0.525057i	−0.919094	+	0.394037i	$0.871078\pi$
$332$	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	$-0.916333\pi$
$337$		−	9.53979i		−	0.519666i	0.965654	−	0.259833i	$-0.0836675\pi$
$338$	−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	0.834182	−	0.551489i	$-0.185940\pi$
$347$	5.26599	+	5.26599i	0.282693	+	0.282693i	−0.551489	+	0.834182i	$0.685940\pi$
$348$	0.703827	+	6.38688i	0.0377291	+	0.342373i
$349$	12.7870	+	12.7870i	0.684470	+	0.684470i	0.961004	−	0.276534i	$-0.0891859\pi$
$349$	12.7870	+	12.7870i	0.684470	+	0.684470i	−0.276534	+	0.961004i	$0.589186\pi$
$350$	−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	$0.00589387\pi$
$359$			0.701622i			0.0370302i	−0.999829	+	0.0185151i	$0.994106\pi$
$360$	−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	0.350938	−	0.936399i	$-0.385863\pi$
$373$	−11.3071	−	11.3071i	−0.585461	−	0.585461i	−0.936399	+	0.350938i	$0.885863\pi$
$374$	−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	0.515113	−	0.857122i	$-0.327750\pi$
$379$	−6.65822	−	6.65822i	−0.342010	−	0.342010i	−0.857122	+	0.515113i	$0.827750\pi$
$380$	−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	$-0.915453\pi$
$383$		−	10.2745i		−	0.525000i	0.964932	−	0.262500i	$-0.0845470\pi$
$384$	−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	0.997289	−	0.0735861i	$-0.0234444\pi$
$389$	18.2183	+	18.2183i	0.923703	+	0.923703i	−0.0735861	+	0.997289i	$0.523444\pi$
$390$	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	−0.917263	−	0.398282i	$-0.869607\pi$
$397$	−10.3406	+	10.3406i	−0.518981	+	0.518981i	0.398282	+	0.917263i	$0.369607\pi$
$398$	−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	$-0.909976\pi$
$401$		−	11.1765i		−	0.558129i	0.960272	−	0.279065i	$-0.0900244\pi$
$402$	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	$-0.803205\pi$
$409$		−	23.4437i		−	1.15922i	0.814895	−	0.579609i	$-0.196795\pi$
$410$	−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	0.943851	+	0.330370i	$0.107174\pi$
$419$	26.0827	+	26.0827i	1.27422	+	1.27422i	0.330370	+	0.943851i	$0.392826\pi$
$420$	1.56176	−	23.0962i	0.0762062	−	1.12698i
$421$	−1.31659	+	1.31659i	−0.0641669	+	0.0641669i	−0.738462	−	0.674295i	$-0.764448\pi$
$421$	−1.31659	+	1.31659i	−0.0641669	+	0.0641669i	0.674295	+	0.738462i	$0.264448\pi$
$422$	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	$-0.868845\pi$
$433$		−	16.6667i		−	0.800949i	0.916308	−	0.400474i	$-0.131155\pi$
$434$	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	0.461727	−	0.887022i	$-0.347230\pi$
$443$	−8.95143	−	8.95143i	−0.425295	−	0.425295i	−0.887022	+	0.461727i	$0.847230\pi$
$444$	−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	$0.0410665\pi$
$449$			5.45237i			0.257313i	−0.991689	+	0.128657i	$0.958933\pi$
$450$	−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	−0.697438	−	0.716645i	$-0.745677\pi$
$461$	0.412379	−	0.412379i	0.0192064	−	0.0192064i	0.716645	+	0.697438i	$0.245677\pi$
$462$	−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	−0.898052	−	0.439890i	$-0.855018\pi$
$467$	−9.90097	+	9.90097i	−0.458162	+	0.458162i	0.439890	+	0.898052i	$0.355018\pi$
$468$	−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	$0.0775639\pi$
$487$			10.6487i			0.482540i	−0.970458	+	0.241270i	$0.922436\pi$
$488$	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	−0.276316	−	0.961067i	$-0.589114\pi$
$491$	15.1731	−	15.1731i	0.684751	−	0.684751i	0.961067	+	0.276316i	$0.0891137\pi$
$492$	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	−0.210281	−	0.977641i	$-0.567438\pi$
$499$	17.1415	−	17.1415i	0.767360	−	0.767360i	0.977641	+	0.210281i	$0.0674378\pi$
$500$	−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	−0.795735	−	0.605645i	$-0.792915\pi$
$509$	−4.28863	+	4.28863i	−0.190090	+	0.190090i	0.605645	+	0.795735i	$0.292915\pi$
$510$	−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	−0.776358	−	0.630292i	$-0.782935\pi$
$523$	−3.34042	+	3.34042i	−0.146066	+	0.146066i	0.630292	+	0.776358i	$0.282935\pi$
$524$	−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	0.858781	−	0.512342i	$-0.171222\pi$
$541$	8.05797	+	8.05797i	0.346439	+	0.346439i	−0.512342	+	0.858781i	$0.671222\pi$
$542$	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	0.938027	+	0.346562i	$0.112651\pi$
$547$	30.0440	+	30.0440i	1.28459	+	1.28459i	0.346562	+	0.938027i	$0.387349\pi$
$548$	−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	0.923006	−	0.384785i	$-0.125724\pi$
$557$	12.7025	+	12.7025i	0.538221	+	0.538221i	−0.384785	+	0.923006i	$0.625724\pi$
$558$	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	−0.517221	−	0.855852i	$-0.673033\pi$
$563$	8.03490	−	8.03490i	0.338631	−	0.338631i	0.855852	+	0.517221i	$0.173033\pi$
$564$	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	0.968914	−	0.247396i	$-0.0795748\pi$
$571$	17.2411	+	17.2411i	0.721519	+	0.721519i	−0.247396	+	0.968914i	$0.579575\pi$
$572$	−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	$0.0182154\pi$
$577$			2.74770i			0.114388i	−0.998363	+	0.0571942i	$0.981785\pi$
$578$	−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	−0.992008	−	0.126173i	$-0.959731\pi$
$587$	−27.0914	−	27.0914i	−1.11818	−	1.11818i	−0.126173	−	0.992008i	$-0.540269\pi$
$588$	−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	$-0.892426\pi$
$599$		−	16.2294i		−	0.663114i	0.943435	−	0.331557i	$-0.107574\pi$
$600$	21.6235	−	11.5076i	0.882776	−	0.469794i
$601$			21.5512i			0.879093i	0.898220	+	0.439547i	$0.144861\pi$
$601$			21.5512i			0.879093i	−0.898220	+	0.439547i	$0.855139\pi$
$602$	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	0.387422	−	0.921903i	$-0.373366\pi$
$613$	−13.2331	−	13.2331i	−0.534481	−	0.534481i	−0.921903	+	0.387422i	$0.873366\pi$
$614$	−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	$-0.983311\pi$
$617$		−	2.60352i		−	0.104814i	0.998626	−	0.0524069i	$-0.0166893\pi$
$618$	−0.508876	+	0.706669i	−0.0204700	+	0.0284264i
$619$	22.1516	+	22.1516i	0.890347	+	0.890347i	0.994555	−	0.104209i	$-0.0332310\pi$
$619$	22.1516	+	22.1516i	0.890347	+	0.890347i	−0.104209	+	0.994555i	$0.533231\pi$
$620$	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	$0.343020\pi$
$641$			44.6021i			1.76168i	−0.473418	+	0.880838i	$0.656980\pi$
$642$	3.08279	+	18.9453i	0.121668	+	0.747712i
$643$	−15.0364	−	15.0364i	−0.592979	−	0.592979i	0.345456	−	0.938435i	$-0.387724\pi$
$643$	−15.0364	−	15.0364i	−0.592979	−	0.592979i	−0.938435	+	0.345456i	$0.887724\pi$
$644$	−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	0.363365	−	0.931647i	$-0.381628\pi$
$653$	−14.5218	−	14.5218i	−0.568282	−	0.568282i	−0.931647	+	0.363365i	$0.881628\pi$
$654$	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	0.408783	−	0.912632i	$-0.365953\pi$
$659$	−12.9343	−	12.9343i	−0.503848	−	0.503848i	−0.912632	+	0.408783i	$0.865953\pi$
$660$	20.8253	−	18.1873i	0.810623	−	0.707938i
$661$	2.72210	−	2.72210i	0.105878	−	0.105878i	−0.652184	−	0.758061i	$-0.726147\pi$
$661$	2.72210	−	2.72210i	0.105878	−	0.105878i	0.758061	+	0.652184i	$0.226147\pi$
$662$	−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	$0.270643\pi$
$673$			38.9883i			1.50289i	−0.659796	+	0.751445i	$0.729357\pi$
$674$	−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	−0.961517	−	0.274744i	$-0.911407\pi$
$677$	−17.8693	+	17.8693i	−0.686773	+	0.686773i	0.274744	+	0.961517i	$0.411407\pi$
$678$	−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	0.617201	−	0.786806i	$-0.288267\pi$
$683$	−4.43249	−	4.43249i	−0.169605	−	0.169605i	−0.786806	+	0.617201i	$0.788267\pi$
$684$	−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	−0.829198	−	0.558954i	$-0.811203\pi$
$691$	−7.10387	+	7.10387i	−0.270244	+	0.270244i	0.558954	+	0.829198i	$0.311203\pi$
$692$	−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	−0.958432	−	0.285321i	$-0.907900\pi$
$701$	−17.8215	+	17.8215i	−0.673110	+	0.673110i	0.285321	+	0.958432i	$0.407900\pi$
$702$	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	−0.150650	−	0.988587i	$-0.548137\pi$
$709$	22.3118	−	22.3118i	0.837937	−	0.837937i	0.988587	+	0.150650i	$0.0481368\pi$
$710$	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	$0.124569\pi$
$727$			20.5691i			0.762865i	−0.924397	+	0.381433i	$0.875431\pi$
$728$	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	−0.293193	−	0.956053i	$-0.594718\pi$
$733$	17.9463	−	17.9463i	0.662860	−	0.662860i	0.956053	+	0.293193i	$0.0947179\pi$
$734$	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	0.127276	−	0.991867i	$-0.459377\pi$
$739$	30.4234	−	30.4234i	1.11914	−	1.11914i	0.991867	−	0.127276i	$-0.0406234\pi$
$740$	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	$0.0706688\pi$
$751$			12.0685i			0.440387i	−0.975456	+	0.220193i	$0.929331\pi$
$752$	−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	0.992813	−	0.119673i	$-0.0381845\pi$
$757$	24.0233	+	24.0233i	0.873141	+	0.873141i	−0.119673	+	0.992813i	$0.538184\pi$
$758$	−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	−0.328169	−	0.944619i	$-0.606431\pi$
$773$	17.1391	−	17.1391i	0.616451	−	0.616451i	0.944619	+	0.328169i	$0.106431\pi$
$774$	−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	0.540351	−	0.841440i	$-0.318292\pi$
$787$	−8.44662	−	8.44662i	−0.301089	−	0.301089i	−0.841440	+	0.540351i	$0.818292\pi$
$788$	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	0.977395	+	0.211420i	$0.0678087\pi$
$797$	33.5617	+	33.5617i	1.18882	+	1.18882i	0.211420	+	0.977395i	$0.432191\pi$
$798$	−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	0.0970070	−	0.995284i	$-0.469073\pi$
$811$	−25.5812	−	25.5812i	−0.898277	−	0.898277i	−0.995284	+	0.0970070i	$0.969073\pi$
$812$	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	0.448097	−	0.893985i	$-0.352102\pi$
$821$	−12.7761	−	12.7761i	−0.445888	−	0.445888i	−0.893985	+	0.448097i	$0.852102\pi$
$822$	28.7383	−	39.9086i	1.00236	−	1.39197i
$823$		−	24.9850i		−	0.870924i	−0.900207	−	0.435462i	$-0.856585\pi$
$823$		−	24.9850i		−	0.870924i	0.900207	−	0.435462i	$-0.143415\pi$
$824$	−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	0.153819	−	0.988099i	$-0.450843\pi$
$827$	−23.9919	−	23.9919i	−0.834281	−	0.834281i	−0.988099	+	0.153819i	$0.950843\pi$
$828$	−5.40536	−	16.1696i	−0.187849	−	0.561932i
$829$	−5.07448	−	5.07448i	−0.176244	−	0.176244i	0.613472	−	0.789716i	$-0.289772\pi$
$829$	−5.07448	−	5.07448i	−0.176244	−	0.176244i	−0.789716	+	0.613472i	$0.789772\pi$
$830$	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	$-0.994481\pi$
$839$		−	1.00441i		−	0.0346759i	0.999850	−	0.0173380i	$-0.00551913\pi$
$840$	−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	0.998247	+	0.0591851i	$0.0188502\pi$
$853$	30.8835	+	30.8835i	1.05743	+	1.05743i	0.0591851	+	0.998247i	$0.481150\pi$
$854$	−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	$-0.761861\pi$
$857$		−	39.8295i		−	1.36055i	0.732958	−	0.680274i	$-0.238139\pi$
$858$	24.5804	−	34.1345i	0.839161	−	1.16533i
$859$	−21.7833	−	21.7833i	−0.743236	−	0.743236i	0.229963	−	0.973199i	$-0.426139\pi$
$859$	−21.7833	−	21.7833i	−0.743236	−	0.743236i	−0.973199	+	0.229963i	$0.926139\pi$
$860$	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	$0.0435776\pi$
$863$			8.01847i			0.272952i	−0.990643	+	0.136476i	$0.956422\pi$
$864$	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	−0.959184	−	0.282783i	$-0.908742\pi$
$877$	−20.0311	+	20.0311i	−0.676401	+	0.676401i	0.282783	+	0.959184i	$0.408742\pi$
$878$	−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	$0.0438786\pi$
$881$			8.15726i			0.274825i	−0.990514	+	0.137412i	$0.956121\pi$
$882$	7.62667	−	2.99469i	0.256803	−	0.100836i
$883$	−25.2094	−	25.2094i	−0.848365	−	0.848365i	0.141564	−	0.989929i	$-0.454787\pi$
$883$	−25.2094	−	25.2094i	−0.848365	−	0.848365i	−0.989929	+	0.141564i	$0.954787\pi$
$884$	−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	−0.799545	−	0.600606i	$-0.794926\pi$
$907$	−5.99135	+	5.99135i	−0.198939	+	0.198939i	0.600606	+	0.799545i	$0.294926\pi$
$908$	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	$-0.985900\pi$
$929$		−	2.69933i		−	0.0885622i	0.999019	−	0.0442811i	$-0.0140997\pi$
$930$	−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	−0.106620	−	0.994300i	$-0.534003\pi$
$941$	27.2302	−	27.2302i	0.887680	−	0.887680i	0.994300	+	0.106620i	$0.0340027\pi$
$942$	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	−0.720661	−	0.693287i	$-0.756162\pi$
$947$	−0.842383	+	0.842383i	−0.0273738	+	0.0273738i	0.693287	+	0.720661i	$0.256162\pi$
$948$	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	$0.0122035\pi$
$953$			2.36649i			0.0766582i	−0.999265	+	0.0383291i	$0.987796\pi$
$954$	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	$-0.759799\pi$
$967$		−	42.6028i		−	1.37001i	0.728536	−	0.685007i	$-0.240201\pi$
$968$	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	−0.996292	−	0.0860348i	$-0.972580\pi$
$971$	−28.3644	+	28.3644i	−0.910257	+	0.910257i	0.0860348	+	0.996292i	$0.472580\pi$
$972$	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	$-0.959333\pi$
$991$		−	8.02181i		−	0.254821i	0.991850	−	0.127411i	$-0.0406666\pi$
$992$	−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	0.724525	−	0.689249i	$-0.242059\pi$
$997$	1.11384	+	1.11384i	0.0352758	+	0.0352758i	−0.689249	+	0.724525i	$0.742059\pi$
$998$	−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.179.22	yes	80
3.2	odd	2	inner	240.2.t.b.179.20	yes	80
4.3	odd	2		960.2.t.b.239.28		80
5.4	even	2	inner	240.2.t.b.179.19	yes	80
12.11	even	2		960.2.t.b.239.8		80
15.14	odd	2	inner	240.2.t.b.179.21	yes	80
16.5	even	4		960.2.t.b.719.33		80
16.11	odd	4	inner	240.2.t.b.59.21	yes	80
20.19	odd	2		960.2.t.b.239.13		80
48.5	odd	4		960.2.t.b.719.13		80
48.11	even	4	inner	240.2.t.b.59.19	✓	80
60.59	even	2		960.2.t.b.239.33		80
80.59	odd	4	inner	240.2.t.b.59.20	yes	80
80.69	even	4		960.2.t.b.719.8		80
240.59	even	4	inner	240.2.t.b.59.22	yes	80
240.149	odd	4		960.2.t.b.719.28		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.t.b.59.19	✓	80	48.11	even	4	inner
240.2.t.b.59.20	yes	80	80.59	odd	4	inner
240.2.t.b.59.21	yes	80	16.11	odd	4	inner
240.2.t.b.59.22	yes	80	240.59	even	4	inner
240.2.t.b.179.19	yes	80	5.4	even	2	inner
240.2.t.b.179.20	yes	80	3.2	odd	2	inner
240.2.t.b.179.21	yes	80	15.14	odd	2	inner
240.2.t.b.179.22	yes	80	1.1	even	1	trivial
960.2.t.b.239.8		80	12.11	even	2
960.2.t.b.239.13		80	20.19	odd	2
960.2.t.b.239.28		80	4.3	odd	2
960.2.t.b.239.33		80	60.59	even	2
960.2.t.b.719.8		80	80.69	even	4
960.2.t.b.719.13		80	48.5	odd	4
960.2.t.b.719.28		80	240.149	odd	4
960.2.t.b.719.33		80	16.5	even	4

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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