LMFDB - Embedded newform 156.3.l.c.47.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [156,3,Mod(47,156)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("156.47"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(156, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	156.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,0,0,-36,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.25069212402$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.6
Character	$\chi$	$=$	156.47
Dual form			156.3.l.c.83.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.87876 + 0.685761i) q^{2} +(2.74902 + 1.20121i) q^{3} +(3.05946 - 2.57676i) q^{4} +(-2.23749 + 2.23749i) q^{5} +(-5.98848 - 0.371622i) q^{6} +(1.91723 + 1.91723i) q^{7} +(-3.98095 + 6.93916i) q^{8} +(6.11417 + 6.60431i) q^{9} +(2.66932 - 5.73809i) q^{10} +(-6.43837 + 6.43837i) q^{11} +(11.5058 - 3.40848i) q^{12} +(12.9887 - 0.543102i) q^{13} +(-4.91678 - 2.28725i) q^{14} +(-8.83861 + 3.46320i) q^{15} +(2.72064 - 15.7670i) q^{16} +7.93049 q^{17} +(-16.0160 - 8.21504i) q^{18} +(-13.1475 + 13.1475i) q^{19} +(-1.08005 + 12.6110i) q^{20} +(2.96749 + 7.57350i) q^{21} +(7.68096 - 16.5113i) q^{22} +13.4703i q^{23} +(-19.2791 + 14.2939i) q^{24} +14.9872i q^{25} +(-24.0301 + 9.92747i) q^{26} +(8.87477 + 25.4998i) q^{27} +(10.8059 + 0.925460i) q^{28} -10.9793i q^{29} +(14.2307 - 12.5677i) q^{30} +(-4.01999 + 4.01999i) q^{31} +(5.70096 + 31.4881i) q^{32} +(-25.4330 + 9.96532i) q^{33} +(-14.8995 + 5.43842i) q^{34} -8.57958 q^{35} +(35.7238 + 4.45091i) q^{36} +(1.70839 - 1.70839i) q^{37} +(15.6849 - 33.7170i) q^{38} +(36.3584 + 14.1091i) q^{39} +(-6.61898 - 24.4337i) q^{40} +(35.1614 - 35.1614i) q^{41} +(-10.7688 - 12.1938i) q^{42} -46.1935 q^{43} +(-3.10784 + 36.2881i) q^{44} +(-28.4575 - 1.09668i) q^{45} +(-9.23738 - 25.3074i) q^{46} +(45.9388 - 45.9388i) q^{47} +(26.4186 - 40.0756i) q^{48} -41.6485i q^{49} +(-10.2777 - 28.1574i) q^{50} +(21.8010 + 9.52621i) q^{51} +(38.3389 - 35.1302i) q^{52} -96.7348i q^{53} +(-34.1603 - 41.8219i) q^{54} -28.8116i q^{55} +(-20.9364 + 5.67157i) q^{56} +(-51.9357 + 20.3497i) q^{57} +(7.52915 + 20.6274i) q^{58} +(-19.8925 + 19.8925i) q^{59} +(-18.1176 + 33.3705i) q^{60} +107.892 q^{61} +(4.79584 - 10.3094i) q^{62} +(-0.939704 + 24.3843i) q^{63} +(-32.3040 - 55.2490i) q^{64} +(-27.8468 + 30.2772i) q^{65} +(40.9487 - 36.1634i) q^{66} +(57.5421 - 57.5421i) q^{67} +(24.2631 - 20.4350i) q^{68} +(-16.1807 + 37.0300i) q^{69} +(16.1190 - 5.88354i) q^{70} +(15.3918 + 15.3918i) q^{71} +(-70.1686 + 16.1358i) q^{72} +(-52.5418 + 52.5418i) q^{73} +(-2.03811 + 4.38120i) q^{74} +(-18.0029 + 41.2002i) q^{75} +(-6.34639 + 74.1023i) q^{76} -24.6877 q^{77} +(-77.9841 - 1.57452i) q^{78} -46.1756i q^{79} +(29.1911 + 41.3660i) q^{80} +(-6.23379 + 80.7598i) q^{81} +(-41.9475 + 90.1721i) q^{82} +(-88.7459 - 88.7459i) q^{83} +(28.5940 + 15.5243i) q^{84} +(-17.7444 + 17.7444i) q^{85} +(86.7865 - 31.6777i) q^{86} +(13.1884 - 30.1822i) q^{87} +(-19.0461 - 70.3077i) q^{88} +(96.2535 + 96.2535i) q^{89} +(54.2168 - 17.4547i) q^{90} +(25.9435 + 23.8610i) q^{91} +(34.7096 + 41.2118i) q^{92} +(-15.8799 + 6.22216i) q^{93} +(-54.8049 + 117.811i) q^{94} -58.8349i q^{95} +(-22.1519 + 93.4093i) q^{96} +(-42.4947 - 42.4947i) q^{97} +(28.5609 + 78.2474i) q^{98} +(-81.8863 - 3.15568i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 36 q^{6} - 64 q^{9} - 8 q^{13} + 80 q^{16} + 48 q^{18} + 8 q^{21} + 124 q^{24} - 8 q^{28} + 24 q^{33} + 64 q^{34} - 128 q^{37} - 136 q^{40} - 140 q^{42} - 160 q^{45} + 88 q^{46} - 108 q^{48} - 320 q^{52}+ \cdots + 336 q^{97}+O(q^{100}) $ 96 * q - 36 * q^6 - 64 * q^9 - 8 * q^13 + 80 * q^16 + 48 * q^18 + 8 * q^21 + 124 * q^24 - 8 * q^28 + 24 * q^33 + 64 * q^34 - 128 * q^37 - 136 * q^40 - 140 * q^42 - 160 * q^45 + 88 * q^46 - 108 * q^48 - 320 * q^52 - 216 * q^54 + 136 * q^57 + 280 * q^58 + 80 * q^60 - 464 * q^61 - 240 * q^66 - 120 * q^70 - 32 * q^72 + 288 * q^73 + 88 * q^76 - 296 * q^78 - 144 * q^81 + 204 * q^84 + 848 * q^85 - 392 * q^93 + 1384 * q^94 - 204 * q^96 + 336 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.87876	+	0.685761i	−0.939379	+	0.342880i
$2$	−1.87876	+	0.685761i	−0.939379	+	0.342880i
$3$	2.74902	+	1.20121i	0.916339	+	0.400404i
$3$	2.74902	+	1.20121i	0.916339	+	0.400404i
$4$	3.05946	−	2.57676i	0.764866	−	0.644189i
$5$	−2.23749	+	2.23749i	−0.447499	+	0.447499i	−0.894522	−	0.447024i	$-0.852484\pi$
$5$	−2.23749	+	2.23749i	−0.447499	+	0.447499i	0.447024	+	0.894522i	$0.352484\pi$
$6$	−5.98848	−	0.371622i	−0.998080	−	0.0619370i
$7$	1.91723	+	1.91723i	0.273890	+	0.273890i	0.830664	−	0.556774i	$-0.187961\pi$
$7$	1.91723	+	1.91723i	0.273890	+	0.273890i	−0.556774	+	0.830664i	$0.687961\pi$
$8$	−3.98095	+	6.93916i	−0.497619	+	0.867396i
$9$	6.11417	+	6.60431i	0.679353	+	0.733812i
$10$	2.66932	−	5.73809i	0.266932	−	0.573809i
$11$	−6.43837	+	6.43837i	−0.585306	+	0.585306i	−0.936357	−	0.351050i	$-0.885825\pi$
$11$	−6.43837	+	6.43837i	−0.585306	+	0.585306i	0.351050	+	0.936357i	$0.385825\pi$
$12$	11.5058	−	3.40848i	0.958813	−	0.284040i
$13$	12.9887	−	0.543102i	0.999127	−	0.0417771i
$13$	12.9887	−	0.543102i	0.999127	−	0.0417771i
$14$	−4.91678	−	2.28725i	−0.351198	−	0.163375i
$15$	−8.83861	+	3.46320i	−0.589241	+	0.230880i
$16$	2.72064	−	15.7670i	0.170040	−	0.985437i
$17$	7.93049			0.466499			0.233250	−	0.972417i	$-0.425064\pi$
$17$	7.93049			0.466499			0.233250	+	0.972417i	$0.425064\pi$
$18$	−16.0160	−	8.21504i	−0.889779	−	0.456391i
$19$	−13.1475	+	13.1475i	−0.691974	+	0.691974i	−0.962666	−	0.270692i	$-0.912748\pi$
$19$	−13.1475	+	13.1475i	−0.691974	+	0.691974i	0.270692	+	0.962666i	$0.412748\pi$
$20$	−1.08005	+	12.6110i	−0.0540026	+	0.630550i
$21$	2.96749	+	7.57350i	0.141309	+	0.360643i
$22$	7.68096	−	16.5113i	0.349134	−	0.750514i
$23$			13.4703i			0.585664i	0.956164	+	0.292832i	$0.0945977\pi$
$23$			13.4703i			0.585664i	−0.956164	+	0.292832i	$0.905402\pi$
$24$	−19.2791	+	14.2939i	−0.803297	+	0.595579i
$25$			14.9872i			0.599490i
$26$	−24.0301	+	9.92747i	−0.924234	+	0.381826i
$27$	8.87477	+	25.4998i	0.328695	+	0.944436i
$28$	10.8059	+	0.925460i	0.385926	+	0.0330521i
$29$		−	10.9793i		−	0.378595i	−0.981920	−	0.189298i	$-0.939379\pi$
$29$		−	10.9793i		−	0.378595i	0.981920	−	0.189298i	$-0.0606211\pi$
$30$	14.2307	−	12.5677i	0.474356	−	0.418923i
$31$	−4.01999	+	4.01999i	−0.129677	+	0.129677i	−0.768966	−	0.639289i	$-0.779229\pi$
$31$	−4.01999	+	4.01999i	−0.129677	+	0.129677i	0.639289	+	0.768966i	$0.279229\pi$
$32$	5.70096	+	31.4881i	0.178155	+	0.984002i
$33$	−25.4330	+	9.96532i	−0.770698	+	0.301979i
$34$	−14.8995	+	5.43842i	−0.438220	+	0.159954i
$35$	−8.57958			−0.245131
$36$	35.7238	+	4.45091i	0.992328	+	0.123636i
$37$	1.70839	−	1.70839i	0.0461727	−	0.0461727i	−0.683643	−	0.729816i	$-0.739606\pi$
$37$	1.70839	−	1.70839i	0.0461727	−	0.0461727i	0.729816	+	0.683643i	$0.239606\pi$
$38$	15.6849	−	33.7170i	0.412762	−	0.887290i
$39$	36.3584	+	14.1091i	0.932266	+	0.361773i
$40$	−6.61898	−	24.4337i	−0.165474	−	0.610842i
$41$	35.1614	−	35.1614i	0.857595	−	0.857595i	−0.133459	−	0.991054i	$-0.542608\pi$
$41$	35.1614	−	35.1614i	0.857595	−	0.857595i	0.991054	+	0.133459i	$0.0426084\pi$
$42$	−10.7688	−	12.1938i	−0.256400	−	0.290328i
$43$	−46.1935			−1.07427			−0.537134	−	0.843497i	$-0.680493\pi$
$43$	−46.1935			−1.07427			−0.537134	+	0.843497i	$0.680493\pi$
$44$	−3.10784	+	36.2881i	−0.0706328	+	0.824729i
$45$	−28.4575	−	1.09668i	−0.632389	−	0.0243706i
$46$	−9.23738	−	25.3074i	−0.200813	−	0.550160i
$47$	45.9388	−	45.9388i	0.977422	−	0.977422i	−0.0223285	−	0.999751i	$-0.507108\pi$
$47$	45.9388	−	45.9388i	0.977422	−	0.977422i	0.999751	+	0.0223285i	$0.00710798\pi$
$48$	26.4186	−	40.0756i	0.550388	−	0.834909i
$49$		−	41.6485i		−	0.849968i
$50$	−10.2777	−	28.1574i	−0.205553	−	0.563148i
$51$	21.8010	+	9.52621i	0.427471	+	0.186788i
$52$	38.3389	−	35.1302i	0.737286	−	0.675581i
$53$		−	96.7348i		−	1.82518i	−0.408870	−	0.912592i	$-0.634077\pi$
$53$		−	96.7348i		−	1.82518i	0.408870	−	0.912592i	$-0.365923\pi$
$54$	−34.1603	−	41.8219i	−0.632598	−	0.774480i
$55$		−	28.8116i		−	0.523847i
$56$	−20.9364	+	5.67157i	−0.373864	+	0.101278i
$57$	−51.9357	+	20.3497i	−0.911152	+	0.357013i
$58$	7.52915	+	20.6274i	0.129813	+	0.355645i
$59$	−19.8925	+	19.8925i	−0.337162	+	0.337162i	−0.855298	−	0.518136i	$-0.826626\pi$
$59$	−19.8925	+	19.8925i	−0.337162	+	0.337162i	0.518136	+	0.855298i	$0.326626\pi$
$60$	−18.1176	+	33.3705i	−0.301960	+	0.556175i
$61$	107.892			1.76872			0.884360	−	0.466805i	$-0.154595\pi$
$61$	107.892			1.76872			0.884360	+	0.466805i	$0.154595\pi$
$62$	4.79584	−	10.3094i	0.0773523	−	0.166280i
$63$	−0.939704	+	24.3843i	−0.0149159	+	0.387052i
$64$	−32.3040	−	55.2490i	−0.504750	−	0.863265i
$65$	−27.8468	+	30.2772i	−0.428413	+	0.465803i
$66$	40.9487	−	36.1634i	0.620435	−	0.547930i
$67$	57.5421	−	57.5421i	0.858838	−	0.858838i	−0.132364	−	0.991201i	$-0.542257\pi$
$67$	57.5421	−	57.5421i	0.858838	−	0.858838i	0.991201	+	0.132364i	$0.0422567\pi$
$68$	24.2631	−	20.4350i	0.356810	−	0.300514i
$69$	−16.1807	+	37.0300i	−0.234502	+	0.536666i
$70$	16.1190	−	5.88354i	0.230271	−	0.0840506i
$71$	15.3918	+	15.3918i	0.216785	+	0.216785i	0.807142	−	0.590357i	$-0.201013\pi$
$71$	15.3918	+	15.3918i	0.216785	+	0.216785i	−0.590357	+	0.807142i	$0.701013\pi$
$72$	−70.1686	+	16.1358i	−0.974564	+	0.224108i
$73$	−52.5418	+	52.5418i	−0.719751	+	0.719751i	−0.968554	−	0.248803i	$-0.919963\pi$
$73$	−52.5418	+	52.5418i	−0.719751	+	0.719751i	0.248803	+	0.968554i	$0.419963\pi$
$74$	−2.03811	+	4.38120i	−0.0275420	+	0.0592054i
$75$	−18.0029	+	41.2002i	−0.240038	+	0.549336i
$76$	−6.34639	+	74.1023i	−0.0835051	+	0.975030i
$77$	−24.6877			−0.320619
$78$	−77.9841	−	1.57452i	−0.999796	−	0.0201861i
$79$		−	46.1756i		−	0.584501i	−0.956342	−	0.292251i	$-0.905596\pi$
$79$		−	46.1756i		−	0.584501i	0.956342	−	0.292251i	$-0.0944042\pi$
$80$	29.1911	+	41.3660i	0.364889	+	0.517074i
$81$	−6.23379	+	80.7598i	−0.0769603	+	0.997034i
$82$	−41.9475	+	90.1721i	−0.511555	+	1.09966i
$83$	−88.7459	−	88.7459i	−1.06923	−	1.06923i	−0.997418	−	0.0718100i	$-0.977122\pi$
$83$	−88.7459	−	88.7459i	−1.06923	−	1.06923i	−0.0718100	−	0.997418i	$-0.522878\pi$
$84$	28.5940	+	15.5243i	0.340405	+	0.184814i
$85$	−17.7444	+	17.7444i	−0.208758	+	0.208758i
$86$	86.7865	−	31.6777i	1.00915	−	0.368346i
$87$	13.1884	−	30.1822i	0.151591	−	0.346922i
$88$	−19.0461	−	70.3077i	−0.216432	−	0.798952i
$89$	96.2535	+	96.2535i	1.08150	+	1.08150i	0.996370	+	0.0851298i	$0.0271305\pi$
$89$	96.2535	+	96.2535i	1.08150	+	1.08150i	0.0851298	+	0.996370i	$0.472869\pi$
$90$	54.2168	−	17.4547i	0.602409	−	0.193941i
$91$	25.9435	+	23.8610i	0.285093	+	0.262209i
$92$	34.7096	+	41.2118i	0.377279	+	0.447954i
$93$	−15.8799	+	6.22216i	−0.170752	+	0.0669049i
$94$	−54.8049	+	117.811i	−0.583031	+	1.25331i
$95$		−	58.8349i		−	0.619315i
$96$	−22.1519	+	93.4093i	−0.230749	+	0.973013i
$97$	−42.4947	−	42.4947i	−0.438090	−	0.438090i	0.453279	−	0.891369i	$-0.350254\pi$
$97$	−42.4947	−	42.4947i	−0.438090	−	0.438090i	−0.891369	+	0.453279i	$0.850254\pi$
$98$	28.5609	+	78.2474i	0.291438	+	0.798442i
$99$	−81.8863	−	3.15568i	−0.827134	−	0.0318755i
$100$	38.6185	+	45.8529i	0.386185	+	0.458529i
$101$	82.7044			0.818855			0.409428	−	0.912343i	$-0.365728\pi$
$101$	82.7044			0.818855			0.409428	+	0.912343i	$0.365728\pi$
$102$	−47.4916	−	2.94715i	−0.465604	−	0.0288936i
$103$	136.814			1.32829			0.664144	−	0.747605i	$-0.268796\pi$
$103$	136.814			1.32829			0.664144	+	0.747605i	$0.268796\pi$
$104$	−47.9385	+	92.2924i	−0.460948	+	0.887427i
$105$	−23.5854	−	10.3059i	−0.224623	−	0.0981515i
$106$	66.3369	+	181.741i	0.625820	+	1.71454i
$107$	−93.4017			−0.872913			−0.436457	−	0.899725i	$-0.643767\pi$
$107$	−93.4017			−0.872913			−0.436457	+	0.899725i	$0.643767\pi$
$108$	92.8588	+	55.1475i	0.859803	+	0.510625i
$109$	−98.4697	−	98.4697i	−0.903392	−	0.903392i	0.0923359	−	0.995728i	$-0.470567\pi$
$109$	−98.4697	−	98.4697i	−0.903392	−	0.903392i	−0.995728	+	0.0923359i	$0.970567\pi$
$110$	19.7579	+	54.1300i	0.179617	+	0.492091i
$111$	6.74854	−	2.64425i	0.0607976	−	0.0238221i
$112$	35.4451	−	25.0129i	0.316474	−	0.223329i
$113$		−	85.7284i		−	0.758658i	−0.925262	−	0.379329i	$-0.876155\pi$
$113$		−	85.7284i		−	0.758658i	0.925262	−	0.379329i	$-0.123845\pi$
$114$	83.6195	−	73.8477i	0.733504	−	0.647787i
$115$	−30.1396	−	30.1396i	−0.262084	−	0.262084i
$116$	−28.2909	−	33.5907i	−0.243887	−	0.289575i
$117$	83.0017	+	82.4604i	0.709416	+	0.704790i
$118$	23.7317	−	51.0148i	0.201116	−	0.432329i
$119$	15.2046	+	15.2046i	0.127770	+	0.127770i
$120$	11.1544	−	75.1194i	0.0929534	−	0.625995i
$121$			38.0948i			0.314833i
$122$	−202.703	+	73.9881i	−1.66150	+	0.606460i
$123$	138.896	−	54.4229i	1.12923	−	0.442463i
$124$	−1.94048	+	22.6576i	−0.0156490	+	0.182722i
$125$	−89.4712	−	89.4712i	−0.715770	−	0.715770i
$126$	−14.9563	−	46.4566i	−0.118701	−	0.368703i
$127$	−93.7596			−0.738265			−0.369132	−	0.929377i	$-0.620345\pi$
$127$	−93.7596			−0.738265			−0.369132	+	0.929377i	$0.620345\pi$
$128$	98.5790	+	81.6467i	0.770149	+	0.637864i
$129$	−126.987	−	55.4883i	−0.984394	−	0.430142i
$130$	31.5545	−	75.9798i	0.242727	−	0.584460i
$131$	−56.4833			−0.431170			−0.215585	−	0.976485i	$-0.569166\pi$
$131$	−56.4833			−0.431170			−0.215585	+	0.976485i	$0.569166\pi$
$132$	−52.1332	+	96.0233i	−0.394949	+	0.727449i
$133$	−50.4136			−0.379050
$134$	−68.6476	+	147.568i	−0.512295	+	1.10125i
$135$	−76.9128	−	37.1983i	−0.569725	−	0.275543i
$136$	−31.5709	+	55.0310i	−0.232139	+	0.404640i
$137$	9.93664	+	9.93664i	0.0725302	+	0.0725302i	0.742441	−	0.669911i	$-0.233668\pi$
$137$	9.93664	+	9.93664i	0.0725302	+	0.0725302i	−0.669911	+	0.742441i	$0.733668\pi$
$138$	5.00585	−	80.6665i	0.0362743	−	0.584540i
$139$			157.438i			1.13265i	0.824183	+	0.566324i	$0.191635\pi$
$139$			157.438i			1.13265i	−0.824183	+	0.566324i	$0.808365\pi$
$140$	−26.2489	+	22.1075i	−0.187492	+	0.157911i
$141$	181.469	−	71.1042i	1.28701	−	0.504285i
$142$	−39.4725	−	18.3623i	−0.277975	−	0.129312i
$143$	−80.1290	+	87.1224i	−0.560343	+	0.609248i
$144$	120.765	−	78.4342i	0.838643	−	0.544682i
$145$	24.5660	+	24.5660i	0.169421	+	0.169421i
$146$	62.6823	−	134.745i	0.429331	−	0.922908i
$147$	50.0287	−	114.492i	0.340331	−	0.778859i
$148$	0.824652	−	9.62887i	0.00557197	−	0.0650599i
$149$	73.2706	−	73.2706i	0.491749	−	0.491749i	−0.417108	−	0.908857i	$-0.636956\pi$
$149$	73.2706	−	73.2706i	0.491749	−	0.491749i	0.908857	+	0.417108i	$0.136956\pi$
$150$	5.56960	−	89.7508i	0.0371306	−	0.598339i
$151$	−95.2616	−	95.2616i	−0.630871	−	0.630871i	0.317415	−	0.948287i	$-0.397185\pi$
$151$	−95.2616	−	95.2616i	−0.630871	−	0.630871i	−0.948287	+	0.317415i	$0.897185\pi$
$152$	−38.8931	−	143.572i	−0.255876	−	0.944555i
$153$	48.4884	+	52.3754i	0.316918	+	0.342323i
$154$	46.3822	−	16.9298i	0.301183	−	0.109934i
$155$		−	17.9894i		−	0.116061i
$156$	147.593	−	50.5203i	0.946109	−	0.323848i
$157$	−174.497			−1.11145			−0.555724	−	0.831367i	$-0.687559\pi$
$157$	−174.497			−1.11145			−0.555724	+	0.831367i	$0.687559\pi$
$158$	31.6654	+	86.7528i	0.200414	+	0.549068i
$159$	116.199	−	265.925i	0.730812	−	1.67249i
$160$	−83.2102	−	57.6985i	−0.520064	−	0.360616i
$161$	−25.8256	+	25.8256i	−0.160408	+	0.160408i
$162$	−43.6701	−	156.003i	−0.269569	−	0.962981i
$163$	204.207	+	204.207i	1.25280	+	1.25280i	0.954459	+	0.298343i	$0.0964340\pi$
$163$	204.207	+	204.207i	1.25280	+	1.25280i	0.298343	+	0.954459i	$0.403566\pi$
$164$	16.9726	−	198.178i	0.103492	−	1.20840i
$165$	34.6089	−	79.2036i	0.209751	−	0.480022i
$166$	227.591	+	105.874i	1.37103	+	0.637793i
$167$	73.3239	−	73.3239i	0.439066	−	0.439066i	−0.452632	−	0.891697i	$-0.649515\pi$
$167$	73.3239	−	73.3239i	0.439066	−	0.439066i	0.891697	+	0.452632i	$0.149515\pi$
$168$	−64.3672	−	9.55783i	−0.383138	−	0.0568918i
$169$	168.410	−	14.1083i	0.996509	−	0.0834812i
$170$	21.1690	−	45.5059i	0.124524	−	0.267682i
$171$	−167.216	−	6.44407i	−0.977873	−	0.0376846i
$172$	−141.328	+	119.030i	−0.821672	+	0.692032i
$173$	−47.5804			−0.275031			−0.137516	−	0.990500i	$-0.543912\pi$
$173$	−47.5804			−0.275031			−0.137516	+	0.990500i	$0.543912\pi$
$174$	−4.08014	+	65.7491i	−0.0234491	+	0.377868i
$175$	−28.7340	+	28.7340i	−0.164194	+	0.164194i
$176$	83.9972	+	119.030i	0.477257	+	0.676308i
$177$	−78.5801	+	30.7897i	−0.443955	+	0.173953i
$178$	−246.844	−	114.830i	−1.38676	−	0.645113i
$179$			348.521i			1.94704i	0.228591	+	0.973522i	$0.426588\pi$
$179$			348.521i			1.94704i	−0.228591	+	0.973522i	$0.573412\pi$
$180$	−89.8906	+	69.9729i	−0.499392	+	0.388738i
$181$			170.140i			0.940001i	0.882666	+	0.470000i	$0.155746\pi$
$181$			170.140i			0.940001i	−0.882666	+	0.470000i	$0.844254\pi$
$182$	−65.1045	−	27.0380i	−0.357717	−	0.148560i
$183$	296.597	+	129.601i	1.62075	+	0.708204i
$184$	−93.4724	−	53.6245i	−0.508002	−	0.291438i
$185$			7.64503i			0.0413245i
$186$	25.5676	−	22.5797i	0.137460	−	0.121396i
$187$	−51.0594	+	51.0594i	−0.273045	+	0.273045i
$188$	22.1750	−	258.921i	0.117952	−	1.37724i
$189$	−31.8740	+	65.9039i	−0.168645	+	0.348698i
$190$	40.3467	+	110.537i	0.212351	+	0.581771i
$191$	364.231			1.90697			0.953483	−	0.301445i	$-0.0974691\pi$
$191$	364.231			1.90697			0.953483	+	0.301445i	$0.0974691\pi$
$192$	−22.4384	−	190.684i	−0.116867	−	0.993148i
$193$	27.5701	−	27.5701i	0.142850	−	0.142850i	−0.632065	−	0.774915i	$-0.717792\pi$
$193$	27.5701	−	27.5701i	0.142850	−	0.142850i	0.774915	+	0.632065i	$0.217792\pi$
$194$	108.978	+	50.6961i	0.561745	+	0.261320i
$195$	−112.921	+	49.7825i	−0.579081	+	0.255295i
$196$	−107.318	−	127.422i	−0.547541	−	0.650112i
$197$	−174.867	+	174.867i	−0.887650	+	0.887650i	−0.994297	−	0.106647i	$-0.965989\pi$
$197$	−174.867	+	174.867i	−0.887650	+	0.887650i	0.106647	+	0.994297i	$0.465989\pi$
$198$	156.009	−	50.2256i	0.787922	−	0.253665i
$199$	−217.321			−1.09207			−0.546033	−	0.837764i	$-0.683863\pi$
$199$	−217.321			−1.09207			−0.546033	+	0.837764i	$0.683863\pi$
$200$	−103.999	−	59.6635i	−0.519995	−	0.298318i
$201$	227.305	−	89.0638i	1.13087	−	0.443103i
$202$	−155.382	+	56.7154i	−0.769216	+	0.280769i
$203$	21.0498	−	21.0498i	0.103694	−	0.103694i
$204$	91.2462	−	27.0309i	0.447285	−	0.132504i
$205$			157.347i			0.767546i
$206$	−257.040	+	93.8215i	−1.24777	+	0.455444i
$207$	−88.9618	+	82.3596i	−0.429767	+	0.397872i
$208$	26.7744	−	206.270i	0.128723	−	0.991681i
$209$		−	169.297i		−	0.810034i
$210$	51.3787	+	3.18836i	0.244660	+	0.0151827i
$211$		−	16.1284i		−	0.0764381i	−0.999269	−	0.0382191i	$-0.987832\pi$
$211$		−	16.1284i		−	0.0764381i	0.999269	−	0.0382191i	$-0.0121685\pi$
$212$	−249.262	−	295.957i	−1.17576	−	1.39602i
$213$	23.8234	+	60.8010i	0.111847	+	0.285451i
$214$	175.479	−	64.0512i	0.819996	−	0.299305i
$215$	103.358	−	103.358i	0.480734	−	0.480734i
$216$	−212.277	−	39.9299i	−0.982765	−	0.184861i
$217$	−15.4145			−0.0710346
$218$	252.527	+	117.474i	1.15838	+	0.538872i
$219$	−207.552	+	81.3244i	−0.947727	+	0.371344i
$220$	−74.2405	−	88.1481i	−0.337457	−	0.400673i
$221$	103.006	−	4.30707i	0.466092	−	0.0194890i
$222$	−10.8655	+	9.59579i	−0.0489439	+	0.0432243i
$223$	216.887	−	216.887i	0.972590	−	0.972590i	−0.0270445	−	0.999634i	$-0.508610\pi$
$223$	216.887	−	216.887i	0.972590	−	0.972590i	0.999634	+	0.0270445i	$0.00860960\pi$
$224$	−49.4399	+	71.3000i	−0.220714	+	0.318303i
$225$	−98.9804	+	91.6346i	−0.439913	+	0.407265i
$226$	58.7891	+	161.063i	0.260129	+	0.712667i
$227$	−170.053	−	170.053i	−0.749133	−	0.749133i	0.225184	−	0.974316i	$-0.427702\pi$
$227$	−170.053	−	170.053i	−0.749133	−	0.749133i	−0.974316	+	0.225184i	$0.927702\pi$
$228$	−106.459	+	196.085i	−0.466925	+	0.860022i
$229$	−28.7277	+	28.7277i	−0.125448	+	0.125448i	−0.767044	−	0.641595i	$-0.778273\pi$
$229$	−28.7277	+	28.7277i	−0.125448	+	0.125448i	0.641595	+	0.767044i	$0.278273\pi$
$230$	77.2937	+	35.9565i	0.336059	+	0.156333i
$231$	−67.8668	−	29.6552i	−0.293796	−	0.128377i
$232$	76.1869	+	43.7079i	0.328392	+	0.188396i
$233$	−127.409			−0.546818			−0.273409	−	0.961898i	$-0.588151\pi$
$233$	−127.409			−0.546818			−0.273409	+	0.961898i	$0.588151\pi$
$234$	−212.488	−	98.0039i	−0.908069	−	0.418820i
$235$			205.576i			0.874790i
$236$	−9.60226	+	112.119i	−0.0406875	+	0.475080i
$237$	55.4668	−	126.937i	0.234037	−	0.535601i
$238$	−38.9924	−	18.1390i	−0.163834	−	0.0762144i
$239$	−9.41795	−	9.41795i	−0.0394057	−	0.0394057i	0.687129	−	0.726535i	$-0.258871\pi$
$239$	−9.41795	−	9.41795i	−0.0394057	−	0.0394057i	−0.726535	+	0.687129i	$0.758871\pi$
$240$	30.5575	+	148.780i	0.127323	+	0.619918i
$241$	330.162	−	330.162i	1.36997	−	1.36997i	0.509492	−	0.860475i	$-0.329833\pi$
$241$	330.162	−	330.162i	1.36997	−	1.36997i	0.860475	−	0.509492i	$-0.170167\pi$
$242$	−26.1239	−	71.5709i	−0.107950	−	0.295748i
$243$	−114.146	+	214.522i	−0.469739	+	0.882806i
$244$	330.092	−	278.011i	1.35283	−	1.13939i
$245$	93.1881	+	93.1881i	0.380360	+	0.380360i
$246$	−223.630	+	197.497i	−0.909066	+	0.802832i
$247$	−163.628	+	177.909i	−0.662461	+	0.720279i
$248$	−11.8920	−	43.8988i	−0.0479516	−	0.177011i
$249$	−137.361	−	350.567i	−0.551651	−	1.40790i
$250$	229.451	+	106.739i	0.917802	+	0.426956i
$251$			131.726i			0.524804i	0.964959	+	0.262402i	$0.0845147\pi$
$251$			131.726i			0.524804i	−0.964959	+	0.262402i	$0.915485\pi$
$252$	59.9574	+	77.0242i	0.237926	+	0.305652i
$253$	−86.7266	−	86.7266i	−0.342793	−	0.342793i
$254$	176.152	−	64.2967i	0.693510	−	0.253137i
$255$	−70.0945	+	27.4648i	−0.274880	+	0.107705i
$256$	−241.196	−	85.7927i	−0.942173	−	0.335128i
$257$	145.078			0.564505			0.282252	−	0.959340i	$-0.408918\pi$
$257$	145.078			0.564505			0.282252	+	0.959340i	$0.408918\pi$
$258$	276.629	+	17.1666i	1.07221	+	0.0665370i
$259$	6.55076			0.0252925
$260$	−7.17936	+	164.387i	−0.0276129	+	0.632256i
$261$	72.5105	−	67.1291i	0.277818	−	0.257200i
$262$	106.118	−	38.7340i	0.405032	−	0.147840i
$263$	73.5496			0.279656			0.139828	−	0.990176i	$-0.455345\pi$
$263$	73.5496			0.279656			0.139828	+	0.990176i	$0.455345\pi$
$264$	32.0967	−	216.155i	0.121578	−	0.818771i
$265$	216.443	+	216.443i	0.816768	+	0.816768i
$266$	94.7150	−	34.5717i	0.356071	−	0.129969i
$267$	148.981	+	380.223i	0.557982	+	1.42406i
$268$	27.7760	−	324.320i	0.103642	−	1.21015i
$269$			329.441i			1.22469i	0.790591	+	0.612345i	$0.209774\pi$
$269$			329.441i			1.22469i	−0.790591	+	0.612345i	$0.790226\pi$
$270$	170.010	+	17.1429i	0.629666	+	0.0634921i
$271$	163.971	+	163.971i	0.605061	+	0.605061i	0.941651	−	0.336590i	$-0.109274\pi$
$271$	163.971	+	163.971i	0.605061	+	0.605061i	−0.336590	+	0.941651i	$0.609274\pi$
$272$	21.5760	−	125.040i	0.0793236	−	0.459706i
$273$	42.6569	+	96.7579i	0.156252	+	0.354425i
$274$	−25.4827	−	11.8544i	−0.0930026	−	0.0432642i
$275$	−96.4934	−	96.4934i	−0.350885	−	0.350885i
$276$	45.9131	+	154.986i	0.166352	+	0.561542i
$277$		−	165.945i		−	0.599078i	−0.954084	−	0.299539i	$-0.903167\pi$
$277$		−	165.945i		−	0.599078i	0.954084	−	0.299539i	$-0.0968329\pi$
$278$	−107.965	−	295.788i	−0.388363	−	1.06399i
$279$	−51.1282	−	1.97034i	−0.183255	−	0.00706217i
$280$	34.1549	−	59.5351i	0.121982	−	0.212625i
$281$	13.7443	+	13.7443i	0.0489121	+	0.0489121i	0.731140	−	0.682228i	$-0.238989\pi$
$281$	13.7443	+	13.7443i	0.0489121	+	0.0489121i	−0.682228	+	0.731140i	$0.738989\pi$
$282$	−292.176	+	258.032i	−1.03608	+	0.915007i
$283$	−330.563			−1.16807			−0.584033	−	0.811730i	$-0.698526\pi$
$283$	−330.563			−1.16807			−0.584033	+	0.811730i	$0.698526\pi$
$284$	86.7514	+	7.42971i	0.305463	+	0.0261609i
$285$	70.6733	−	161.738i	0.247976	−	0.567502i
$286$	90.7979	−	218.631i	0.317475	−	0.764445i
$287$	134.825			0.469774
$288$	−173.100	+	230.174i	−0.601043	+	0.799217i
$289$	−226.107			−0.782378
$290$	−63.0001	−	29.3072i	−0.217242	−	0.101059i
$291$	−65.7734	−	167.864i	−0.226025	−	0.576851i
$292$	−25.3623	+	296.137i	−0.0868572	+	1.01417i
$293$	20.8531	+	20.8531i	0.0711711	+	0.0711711i	0.741796	−	0.670625i	$-0.233974\pi$
$293$	20.8531	+	20.8531i	0.0711711	+	0.0711711i	−0.670625	+	0.741796i	$0.733974\pi$
$294$	−15.4775	+	249.411i	−0.0526445	+	0.848336i
$295$		−	89.0188i		−	0.301759i
$296$	5.05378	+	18.6558i	0.0170736	+	0.0630265i
$297$	−221.316	−	107.038i	−0.745172	−	0.360397i
$298$	−87.4117	+	187.904i	−0.293328	+	0.630550i
$299$	7.31573	+	174.961i	0.0244673	+	0.585153i
$300$	51.0837	+	172.440i	0.170279	+	0.574798i
$301$	−88.5637	−	88.5637i	−0.294232	−	0.294232i
$302$	244.300	+	113.647i	0.808941	+	0.376314i
$303$	227.356	+	99.3456i	0.750349	+	0.327873i
$304$	171.527	+	243.066i	0.564234	+	0.799560i
$305$	−241.408	+	241.408i	−0.791500	+	0.791500i
$306$	−127.015	−	65.1493i	−0.415082	−	0.212906i
$307$	−330.034	−	330.034i	−1.07503	−	1.07503i	−0.996947	−	0.0780834i	$-0.975120\pi$
$307$	−330.034	−	330.034i	−1.07503	−	1.07503i	−0.0780834	−	0.996947i	$-0.524880\pi$
$308$	−75.5311	+	63.6142i	−0.245231	+	0.206539i
$309$	376.103	+	164.342i	1.21716	+	0.531853i
$310$	12.3364	+	33.7978i	0.0397950	+	0.109025i
$311$		−	291.242i		−	0.936470i	−0.883604	−	0.468235i	$-0.844890\pi$
$311$		−	291.242i		−	0.936470i	0.883604	−	0.468235i	$-0.155110\pi$
$312$	−242.647	+	196.129i	−0.777714	+	0.628618i
$313$	342.505			1.09427			0.547133	−	0.837046i	$-0.315719\pi$
$313$	342.505			1.09427			0.547133	+	0.837046i	$0.315719\pi$
$314$	327.838	−	119.663i	1.04407	−	0.381094i
$315$	−52.4570	−	56.6622i	−0.166530	−	0.179880i
$316$	−118.983	−	141.273i	−0.376530	−	0.447065i
$317$	−399.011	+	399.011i	−1.25871	+	1.25871i	−0.306999	+	0.951710i	$0.599325\pi$
$317$	−399.011	+	399.011i	−1.25871	+	1.25871i	−0.951710	+	0.306999i	$0.900675\pi$
$318$	−35.9488	+	579.294i	−0.113047	+	1.82168i
$319$	70.6886	+	70.6886i	0.221594	+	0.221594i
$320$	195.899	+	51.3392i	0.612185	+	0.160435i
$321$	−256.763	−	112.195i	−0.799884	−	0.349518i
$322$	30.8099	−	66.2303i	0.0956829	−	0.205684i
$323$	−104.266	+	104.266i	−0.322806	+	0.322806i
$324$	189.026	+	263.145i	0.583414	+	0.812175i
$325$	8.13961	+	194.664i	0.0250449	+	0.598967i
$326$	−523.692	−	243.618i	−1.60642	−	0.747295i
$327$	−152.412	−	388.978i	−0.466091	−	1.18954i
$328$	104.015	+	383.967i	0.317119	+	1.17063i
$329$	176.151			0.535413
$330$	−10.7070	+	172.538i	−0.0324456	+	0.522842i
$331$	386.713	−	386.713i	1.16832	−	1.16832i	0.185715	−	0.982604i	$-0.440540\pi$
$331$	386.713	−	386.713i	1.16832	−	1.16832i	0.982604	−	0.185715i	$-0.0594601\pi$
$332$	−500.192	−	42.8383i	−1.50660	−	0.129031i
$333$	21.7281	+	0.837344i	0.0652497	+	0.00251455i
$334$	−87.4753	+	188.041i	−0.261902	+	0.562996i
$335$			257.500i			0.768657i
$336$	127.485	−	26.1837i	0.379419	−	0.0779276i
$337$		−	61.3087i		−	0.181925i	−0.995854	−	0.0909625i	$-0.971006\pi$
$337$		−	61.3087i		−	0.181925i	0.995854	−	0.0909625i	$-0.0289944\pi$
$338$	−306.727	+	141.995i	−0.907476	+	0.420104i
$339$	102.978	−	235.669i	0.303770	−	0.695188i
$340$	−8.56535	+	100.011i	−0.0251922	+	0.294151i
$341$		−	51.7644i		−	0.151802i
$342$	318.578	−	102.564i	0.931515	−	0.299893i
$343$	173.794	−	173.794i	0.506688	−	0.506688i
$344$	183.894	−	320.545i	0.534577	−	0.931816i
$345$	−46.6502	−	119.058i	−0.135218	−	0.345097i
$346$	89.3921	−	32.6288i	0.258359	−	0.0943028i
$347$	−27.4780			−0.0791872			−0.0395936	−	0.999216i	$-0.512606\pi$
$347$	−27.4780			−0.0791872			−0.0395936	+	0.999216i	$0.512606\pi$
$348$	−37.4226	−	126.325i	−0.107536	−	0.363002i
$349$	−241.315	+	241.315i	−0.691447	+	0.691447i	−0.962550	−	0.271103i	$-0.912612\pi$
$349$	−241.315	+	241.315i	−0.691447	+	0.691447i	0.271103	+	0.962550i	$0.412612\pi$
$350$	34.2796	−	73.6889i	0.0979417	−	0.210540i
$351$	129.120	+	326.388i	0.367864	+	0.929880i
$352$	−239.437	−	166.027i	−0.680218	−	0.471668i
$353$	−268.532	+	268.532i	−0.760715	+	0.760715i	−0.976452	−	0.215737i	$-0.930785\pi$
$353$	−268.532	+	268.532i	−0.760715	+	0.760715i	0.215737	+	0.976452i	$0.430785\pi$
$354$	126.519	−	111.734i	0.357397	−	0.315632i
$355$	−68.8779			−0.194022
$356$	542.506	+	46.4622i	1.52389	+	0.130512i
$357$	23.5337	+	60.0616i	0.0659207	+	0.168240i
$358$	−239.002	−	654.787i	−0.667604	−	1.82901i
$359$	43.0730	−	43.0730i	0.119981	−	0.119981i	−0.644567	−	0.764548i	$-0.722962\pi$
$359$	43.0730	−	43.0730i	0.119981	−	0.119981i	0.764548	+	0.644567i	$0.222962\pi$
$360$	120.898	−	193.106i	0.335828	−	0.536404i
$361$			15.2861i			0.0423437i
$362$	−116.675	−	319.652i	−0.322308	−	0.883017i
$363$	−45.7600	+	104.723i	−0.126061	+	0.288494i
$364$	140.857	+	6.15175i	0.386970	+	0.0169004i
$365$		−	235.124i		−	0.644175i
$366$	−646.109	−	40.0951i	−1.76532	−	0.109549i
$367$		−	499.591i		−	1.36128i	−0.732616	−	0.680642i	$-0.761701\pi$
$367$		−	499.591i		−	1.36128i	0.732616	−	0.680642i	$-0.238299\pi$
$368$	212.386	+	36.6478i	0.577135	+	0.0995864i
$369$	447.200	+	17.2339i	1.21192	+	0.0467043i
$370$	−5.24266	−	14.3632i	−0.0141694	−	0.0388193i
$371$	185.463	−	185.463i	0.499900	−	0.499900i
$372$	−32.5510	+	59.9551i	−0.0875027	+	0.161170i
$373$	−332.025			−0.890147			−0.445073	−	0.895494i	$-0.646822\pi$
$373$	−332.025			−0.890147			−0.445073	+	0.895494i	$0.646822\pi$
$374$	60.9138	−	130.943i	0.162871	−	0.350115i
$375$	−138.484	−	353.432i	−0.369290	−	0.942485i
$376$	135.897	+	501.658i	0.361428	+	1.33420i
$377$	−5.96286	−	142.606i	−0.0158166	−	0.378265i
$378$	14.6891	−	145.675i	0.0388601	−	0.385385i
$379$	468.317	−	468.317i	1.23567	−	1.23567i	0.273911	−	0.961755i	$-0.411683\pi$
$379$	468.317	−	468.317i	1.23567	−	1.23567i	0.961755	−	0.273911i	$-0.0883173\pi$
$380$	−151.603	−	180.003i	−0.398956	−	0.473693i
$381$	−257.747	−	112.625i	−0.676500	−	0.295605i
$382$	−684.301	+	249.775i	−1.79136	+	0.653862i
$383$	101.144	+	101.144i	0.264083	+	0.264083i	0.826711	−	0.562627i	$-0.190209\pi$
$383$	101.144	+	101.144i	0.264083	+	0.264083i	−0.562627	+	0.826711i	$0.690209\pi$
$384$	172.920	+	342.862i	0.450313	+	0.892871i
$385$	55.2385	−	55.2385i	0.143477	−	0.143477i
$386$	−32.8911	+	70.7041i	−0.0852100	+	0.183171i
$387$	−282.435	−	305.076i	−0.729807	−	0.788311i
$388$	−239.509	−	20.5125i	−0.617293	−	0.0528672i
$389$	456.268			1.17293			0.586463	−	0.809976i	$-0.300520\pi$
$389$	456.268			1.17293			0.586463	+	0.809976i	$0.300520\pi$
$390$	178.012	−	170.966i	0.456441	−	0.438374i
$391$			106.826i			0.273212i
$392$	289.005	+	165.801i	0.737259	+	0.422961i
$393$	−155.273	−	67.8485i	−0.395098	−	0.172642i
$394$	208.616	−	448.450i	0.529482	−	1.13820i
$395$	103.318	+	103.318i	0.261564	+	0.261564i
$396$	−258.660	+	201.346i	−0.653181	+	0.508450i
$397$	300.957	−	300.957i	0.758078	−	0.758078i	−0.217895	−	0.975972i	$-0.569919\pi$
$397$	300.957	−	300.957i	0.758078	−	0.758078i	0.975972	+	0.217895i	$0.0699189\pi$
$398$	408.294	−	149.030i	1.02586	−	0.374448i
$399$	−138.588	−	60.5575i	−0.347338	−	0.151773i
$400$	236.304	+	40.7749i	0.590760	+	0.101937i
$401$	−252.305	−	252.305i	−0.629190	−	0.629190i	0.318674	−	0.947864i	$-0.396762\pi$
$401$	−252.305	−	252.305i	−0.629190	−	0.629190i	−0.947864	+	0.318674i	$0.896762\pi$
$402$	−365.974	+	323.206i	−0.910382	+	0.803995i
$403$	−50.0310	+	54.3976i	−0.124146	+	0.134982i
$404$	253.031	−	213.109i	0.626315	−	0.527498i
$405$	−166.751	−	194.647i	−0.411732	−	0.480611i
$406$	−25.1123	+	53.9826i	−0.0618531	+	0.132962i
$407$			21.9985i			0.0540504i
$408$	−152.893	+	113.358i	−0.374737	+	0.277837i
$409$	−75.5531	−	75.5531i	−0.184726	−	0.184726i	0.608685	−	0.793412i	$-0.291697\pi$
$409$	−75.5531	−	75.5531i	−0.184726	−	0.184726i	−0.793412	+	0.608685i	$0.791697\pi$
$410$	−107.902	−	295.617i	−0.263176	−	0.721016i
$411$	15.3800	+	39.2520i	0.0374208	+	0.0955036i
$412$	418.577	−	352.536i	1.01596	−	0.855669i
$413$	−76.2772			−0.184691
$414$	110.659	−	215.740i	0.267292	−	0.521112i
$415$	397.137			0.956956
$416$	91.1490	+	405.891i	0.219108	+	0.975701i
$417$	−189.117	+	432.799i	−0.453517	+	1.03789i
$418$	116.097	+	318.068i	0.277745	+	0.760929i
$419$	−354.855			−0.846909			−0.423454	−	0.905917i	$-0.639183\pi$
$419$	−354.855			−0.846909			−0.423454	+	0.905917i	$0.639183\pi$
$420$	−98.7145	+	29.2433i	−0.235035	+	0.0696269i
$421$	−148.325	−	148.325i	−0.352315	−	0.352315i	0.508655	−	0.860970i	$-0.330143\pi$
$421$	−148.325	−	148.325i	−0.352315	−	0.352315i	−0.860970	+	0.508655i	$0.830143\pi$
$422$	11.0603	+	30.3014i	0.0262091	+	0.0718044i
$423$	584.272	+	22.5163i	1.38126	+	0.0532300i
$424$	671.259	+	385.097i	1.58316	+	0.908247i
$425$			118.856i			0.279662i
$426$	−86.4533	−	97.8932i	−0.202942	−	0.229796i
$427$	206.854	+	206.854i	0.484435	+	0.484435i
$428$	−285.759	+	240.674i	−0.667662	+	0.562321i
$429$	−324.929	+	143.249i	−0.757409	+	0.333913i
$430$	−123.306	+	265.063i	−0.286757	+	0.616425i
$431$	129.751	+	129.751i	0.301047	+	0.301047i	0.841424	−	0.540376i	$-0.181718\pi$
$431$	129.751	+	129.751i	0.301047	+	0.301047i	−0.540376	+	0.841424i	$0.681718\pi$
$432$	426.200	−	70.5527i	0.986574	−	0.163316i
$433$		−	277.129i		−	0.640020i	−0.947414	−	0.320010i	$-0.896314\pi$
$433$		−	277.129i		−	0.640020i	0.947414	−	0.320010i	$-0.103686\pi$
$434$	28.9601	−	10.5707i	0.0667285	−	0.0243564i
$435$	38.0234	+	97.0414i	0.0874100	+	0.223084i
$436$	−554.997	−	47.5320i	−1.27293	−	0.109018i
$437$	−177.101	−	177.101i	−0.405264	−	0.405264i
$438$	334.171	−	295.120i	0.762948	−	0.673790i
$439$	−824.382			−1.87786			−0.938932	−	0.344104i	$-0.888183\pi$
$439$	−824.382			−1.87786			−0.938932	+	0.344104i	$0.888183\pi$
$440$	199.929	+	114.698i	0.454383	+	0.260677i
$441$	275.059	−	254.646i	0.623717	−	0.577428i
$442$	−190.570	+	78.7297i	−0.431155	+	0.178121i
$443$	−296.524			−0.669354			−0.334677	−	0.942333i	$-0.608627\pi$
$443$	−296.524			−0.669354			−0.334677	+	0.942333i	$0.608627\pi$
$444$	13.8333	−	25.4793i	0.0311561	−	0.0573859i
$445$	−430.733			−0.967939
$446$	−258.746	+	556.212i	−0.580148	+	1.24711i
$447$	289.436	−	113.408i	0.647507	−	0.253710i
$448$	43.9908	−	167.859i	0.0981938	−	0.374686i
$449$	−102.052	−	102.052i	−0.227288	−	0.227288i	0.584271	−	0.811559i	$-0.301381\pi$
$449$	−102.052	−	102.052i	−0.227288	−	0.227288i	−0.811559	+	0.584271i	$0.801381\pi$
$450$	123.121	−	240.036i	0.273602	−	0.533414i
$451$			452.764i			1.00391i
$452$	−220.901	−	262.283i	−0.488719	−	0.580272i
$453$	−147.446	−	376.305i	−0.325488	−	0.830695i
$454$	436.104	+	202.873i	0.960583	+	0.446857i
$455$	−111.437	+	4.65959i	−0.244917	+	0.0102409i
$456$	65.5433	−	441.402i	0.143735	−	0.967986i
$457$	297.399	+	297.399i	0.650763	+	0.650763i	0.953177	−	0.302414i	$-0.0977925\pi$
$457$	297.399	+	297.399i	0.650763	+	0.650763i	−0.302414	+	0.953177i	$0.597792\pi$
$458$	34.2721	−	73.6727i	0.0748298	−	0.160857i
$459$	70.3813	+	202.226i	0.153336	+	0.440579i
$460$	−169.874	−	14.5486i	−0.369291	−	0.0316274i
$461$	−304.031	+	304.031i	−0.659503	+	0.659503i	−0.955262	−	0.295759i	$-0.904427\pi$
$461$	−304.031	+	304.031i	−0.659503	+	0.659503i	0.295759	+	0.955262i	$0.404427\pi$
$462$	147.842	+	9.17449i	0.320004	+	0.0198582i
$463$	141.035	+	141.035i	0.304612	+	0.304612i	0.842815	−	0.538203i	$-0.180897\pi$
$463$	141.035	+	141.035i	0.304612	+	0.304612i	−0.538203	+	0.842815i	$0.680897\pi$
$464$	−173.110	−	29.8706i	−0.373082	−	0.0643764i
$465$	21.6091	−	49.4532i	0.0464713	−	0.106351i
$466$	239.370	−	87.3718i	0.513669	−	0.187493i
$467$		−	546.532i		−	1.17030i	−0.810923	−	0.585152i	$-0.801035\pi$
$467$		−	546.532i		−	1.17030i	0.810923	−	0.585152i	$-0.198965\pi$
$468$	466.421	+	38.4096i	0.996626	+	0.0820718i
$469$	220.643			0.470454
$470$	−140.976	−	386.227i	−0.299948	−	0.821760i
$471$	−479.696	−	209.609i	−1.01846	−	0.445029i
$472$	−58.8463	−	217.229i	−0.124674	−	0.460231i
$473$	297.411	−	297.411i	0.628776	−	0.628776i
$474$	−17.1599	+	276.522i	−0.0362023	+	0.583379i
$475$	−197.045	−	197.045i	−0.414832	−	0.414832i
$476$	85.6964	+	7.33935i	0.180034	+	0.0154188i
$477$	638.866	−	591.453i	1.33934	−	1.23994i
$478$	24.1525	+	11.2356i	0.0505283	+	0.0235054i
$479$	111.887	−	111.887i	0.233585	−	0.233585i	−0.580602	−	0.814187i	$-0.697183\pi$
$479$	111.887	−	111.887i	0.233585	−	0.233585i	0.814187	+	0.580602i	$0.197183\pi$
$480$	−159.438	−	258.567i	−0.332162	−	0.538682i
$481$	21.2619	−	23.1175i	0.0442035	−	0.0480614i
$482$	−393.883	+	846.707i	−0.817184	+	1.75665i
$483$	−102.017	+	39.9730i	−0.211216	+	0.0827597i
$484$	98.1611	+	116.550i	0.202812	+	0.240805i
$485$	190.163			0.392089
$486$	67.3430	−	481.312i	0.138566	−	0.990353i
$487$	−149.033	+	149.033i	−0.306022	+	0.306022i	−0.843364	−	0.537343i	$-0.819428\pi$
$487$	−149.033	+	149.033i	−0.306022	+	0.306022i	0.537343	+	0.843364i	$0.319428\pi$
$488$	−429.513	+	748.680i	−0.880149	+	1.53418i
$489$	316.072	+	806.663i	0.646363	+	1.64962i
$490$	−238.983	−	111.173i	−0.487720	−	0.226884i
$491$			431.862i			0.879555i	0.898107	+	0.439778i	$0.144943\pi$
$491$			431.862i			0.879555i	−0.898107	+	0.439778i	$0.855057\pi$
$492$	284.712	−	524.405i	0.578682	−	1.06586i
$493$		−	87.0710i		−	0.176615i
$494$	185.414	−	446.457i	0.375333	−	0.903760i
$495$	190.281	−	176.159i	0.384406	−	0.355877i
$496$	52.4463	+	74.3202i	0.105738	+	0.149839i
$497$			59.0191i			0.118751i
$498$	498.473	+	564.433i	1.00095	+	1.13340i
$499$	−249.737	+	249.737i	−0.500475	+	0.500475i	−0.911586	−	0.411111i	$-0.865141\pi$
$499$	−249.737	+	249.737i	−0.500475	+	0.500475i	0.411111	+	0.911586i	$0.365141\pi$
$500$	−504.279	−	43.1883i	−1.00856	−	0.0863767i
$501$	289.646	−	113.491i	0.578136	−	0.226529i
$502$	−90.3324	−	247.481i	−0.179945	−	0.492990i
$503$	−19.5125			−0.0387923			−0.0193961	−	0.999812i	$-0.506174\pi$
$503$	−19.5125			−0.0387923			−0.0193961	+	0.999812i	$0.506174\pi$
$504$	−165.466	−	103.593i	−0.328305	−	0.205542i
$505$	−185.051	+	185.051i	−0.366437	+	0.366437i
$506$	222.412	+	103.465i	0.439549	+	0.204475i
$507$	479.909	+	163.512i	0.946566	+	0.322510i
$508$	−286.854	+	241.596i	−0.564674	+	0.475582i
$509$	291.110	−	291.110i	0.571926	−	0.571926i	−0.360740	−	0.932666i	$-0.617476\pi$
$509$	291.110	−	291.110i	0.571926	−	0.571926i	0.932666	+	0.360740i	$0.117476\pi$
$510$	112.856	−	99.6679i	0.221287	−	0.195427i
$511$	−201.470			−0.394265
$512$	511.983	−	4.21922i	0.999966	−	0.00824067i
$513$	−451.940	−	218.577i	−0.880974	−	0.426077i
$514$	−272.566	+	99.4886i	−0.530284	+	0.193558i
$515$	−306.120	+	306.120i	−0.594407	+	0.594407i
$516$	−531.491	+	157.450i	−1.03002	+	0.305135i
$517$			591.542i			1.14418i
$518$	−12.3073	+	4.49225i	−0.0237593	+	0.00867231i
$519$	−130.799	−	57.1542i	−0.252022	−	0.110124i
$520$	−99.2416	−	313.766i	−0.190849	−	0.603396i
$521$			554.046i			1.06343i	0.846924	+	0.531714i	$0.178452\pi$
$521$			554.046i			1.06343i	−0.846924	+	0.531714i	$0.821548\pi$
$522$	−90.1951	+	175.844i	−0.172788	+	0.336866i
$523$			565.353i			1.08098i	0.841350	+	0.540491i	$0.181761\pi$
$523$			565.353i			1.08098i	−0.841350	+	0.540491i	$0.818239\pi$
$524$	−172.809	+	145.544i	−0.329787	+	0.277755i
$525$	−113.506	+	44.4746i	−0.216202	+	0.0847135i
$526$	−138.182	+	50.4374i	−0.262703	+	0.0958887i
$527$	−31.8805	+	31.8805i	−0.0604944	+	0.0604944i
$528$	87.9290	+	428.115i	0.166532	+	0.810823i
$529$	347.552			0.656998
$530$	−555.073	−	258.216i	−1.04731	−	0.487201i
$531$	−253.003	−	9.75005i	−0.476465	−	0.0183617i
$532$	−154.239	+	129.904i	−0.289922	+	0.244180i
$533$	437.603	−	475.796i	0.821019	−	0.892675i
$534$	−540.642	−	612.182i	−1.01244	−	1.14641i
$535$	208.986	−	208.986i	0.390627	−	0.390627i
$536$	170.222	+	628.367i	0.317578	+	1.17233i
$537$	−418.648	+	958.090i	−0.779606	+	1.78415i
$538$	−225.918	−	618.941i	−0.419922	−	1.15045i
$539$	268.148	+	268.148i	0.497492	+	0.497492i
$540$	−331.163	+	84.3787i	−0.613265	+	0.156257i
$541$	−173.050	+	173.050i	−0.319870	+	0.319870i	−0.848717	−	0.528847i	$-0.822624\pi$
$541$	−173.050	+	173.050i	−0.319870	+	0.319870i	0.528847	+	0.848717i	$0.322624\pi$
$542$	−420.508	−	195.618i	−0.775845	−	0.360918i
$543$	−204.375	+	467.718i	−0.376380	+	0.861359i
$544$	45.2114	+	249.716i	0.0831092	+	0.459037i
$545$	440.651			0.808533
$546$	−146.495	−	152.532i	−0.268306	−	0.279363i
$547$			745.007i			1.36199i	0.732289	+	0.680994i	$0.238452\pi$
$547$			745.007i			1.36199i	−0.732289	+	0.680994i	$0.761548\pi$
$548$	56.0051	+	4.79648i	0.102199	+	0.00875270i
$549$	659.670	+	712.552i	1.20158	+	1.29791i
$550$	247.459	+	115.116i	0.449926	+	0.209303i
$551$	144.350	+	144.350i	0.261978	+	0.261978i
$552$	−192.543	−	259.695i	−0.348809	−	0.470462i
$553$	88.5293	−	88.5293i	0.160089	−	0.160089i
$554$	113.798	+	311.770i	0.205412	+	0.562761i
$555$	−9.18331	+	21.0163i	−0.0165465	+	0.0378672i
$556$	405.679	+	481.676i	0.729639	+	0.866323i
$557$	343.993	+	343.993i	0.617582	+	0.617582i	0.944911	−	0.327328i	$-0.106148\pi$
$557$	343.993	+	343.993i	0.617582	+	0.617582i	−0.327328	+	0.944911i	$0.606148\pi$
$558$	97.4088	−	31.3599i	0.174568	−	0.0562006i
$559$	−599.992	+	25.0878i	−1.07333	+	0.0448798i
$560$	−23.3420	+	135.274i	−0.0416821	+	0.241561i
$561$	−201.696	+	79.0299i	−0.359530	+	0.140873i
$562$	−35.2475	−	16.3969i	−0.0627180	−	0.0291760i
$563$		−	904.253i		−	1.60613i	−0.595890	−	0.803066i	$-0.703200\pi$
$563$		−	904.253i		−	1.60613i	0.595890	−	0.803066i	$-0.296800\pi$
$564$	371.979	−	685.142i	0.659538	−	1.21479i
$565$	191.817	+	191.817i	0.339498	+	0.339498i
$566$	621.047	−	226.687i	1.09726	−	0.400507i
$567$	−166.787	+	142.884i	−0.294157	+	0.251999i
$568$	−168.080	+	45.5321i	−0.295915	+	0.0801621i
$569$	−938.529			−1.64944			−0.824718	−	0.565545i	$-0.808666\pi$
$569$	−938.529			−1.64944			−0.824718	+	0.565545i	$0.808666\pi$
$570$	−21.8644	+	352.332i	−0.0383585	+	0.618126i
$571$	472.192			0.826956			0.413478	−	0.910514i	$-0.364314\pi$
$571$	472.192			0.826956			0.413478	+	0.910514i	$0.364314\pi$
$572$	−20.6586	+	473.021i	−0.0361164	+	0.826960i
$573$	1001.28	+	437.519i	1.74743	+	0.763558i
$574$	−253.304	+	92.4578i	−0.441296	+	0.161076i
$575$	−201.882			−0.351100
$576$	167.369	−	551.148i	0.290571	−	0.956853i
$577$	27.8631	+	27.8631i	0.0482896	+	0.0482896i	0.730839	−	0.682550i	$-0.239129\pi$
$577$	27.8631	+	27.8631i	0.0482896	+	0.0482896i	−0.682550	+	0.730839i	$0.739129\pi$
$578$	424.801	−	155.056i	0.734950	−	0.268262i
$579$	108.908	−	42.6731i	0.188097	−	0.0737013i
$580$	138.460	+	11.8582i	0.238723	+	0.0204451i
$581$		−	340.293i		−	0.585702i
$582$	238.687	+	270.271i	0.410115	+	0.464382i
$583$	622.814	+	622.814i	1.06829	+	1.06829i
$584$	−155.430	−	573.763i	−0.266147	−	0.982471i
$585$	−370.220	+	1.21099i	−0.632855	+	0.00207007i
$586$	−53.4783	−	24.8777i	−0.0912598	−	0.0424535i
$587$	478.108	+	478.108i	0.814494	+	0.814494i	0.985304	−	0.170810i	$-0.0546384\pi$
$587$	478.108	+	478.108i	0.814494	+	0.814494i	−0.170810	+	0.985304i	$0.554638\pi$
$588$	−141.958	−	479.197i	−0.241425	−	0.814960i
$589$		−	105.706i		−	0.179467i
$590$	61.0456	+	167.245i	0.103467	+	0.283466i
$591$	−690.765	+	270.660i	−1.16881	+	0.457969i
$592$	−22.2883	−	31.5841i	−0.0376491	−	0.0533515i
$593$	80.9828	+	80.9828i	0.136565	+	0.136565i	0.772084	−	0.635520i	$-0.219214\pi$
$593$	80.9828	+	80.9828i	0.136565	+	0.136565i	−0.635520	+	0.772084i	$0.719214\pi$
$594$	489.202	+	49.3285i	0.823572	+	0.0830446i
$595$	−68.0403			−0.114353
$596$	35.3682	−	412.970i	0.0593427	−	0.692902i
$597$	−597.419	−	261.049i	−1.00070	−	0.437268i
$598$	−133.726	−	323.692i	−0.223621	−	0.541291i
$599$	−686.856			−1.14667			−0.573336	−	0.819321i	$-0.694351\pi$
$599$	−686.856			−1.14667			−0.573336	+	0.819321i	$0.694351\pi$
$600$	−214.226	−	288.941i	−0.357044	−	0.481568i
$601$	−294.571			−0.490135			−0.245067	−	0.969506i	$-0.578810\pi$
$601$	−294.571			−0.490135			−0.245067	+	0.969506i	$0.578810\pi$
$602$	227.123	+	105.656i	0.377281	+	0.175509i
$603$	731.848	+	28.2035i	1.21368	+	0.0467719i
$604$	−536.915	−	45.9834i	−0.888933	−	0.0761314i
$605$	−85.2369	−	85.2369i	−0.140887	−	0.140887i
$606$	−495.274	−	30.7348i	−0.817283	−	0.0507175i
$607$			834.152i			1.37422i	0.726553	+	0.687110i	$0.241121\pi$
$607$			834.152i			1.37422i	−0.726553	+	0.687110i	$0.758879\pi$
$608$	−488.943	−	339.036i	−0.804183	−	0.557626i
$609$	83.1515	−	32.5809i	0.136538	−	0.0534990i
$610$	287.999	−	619.094i	0.472129	−	1.01491i
$611$	571.734	−	621.633i	0.935735	−	1.01740i
$612$	283.307	+	35.2979i	0.462920	+	0.0576762i
$613$	71.3441	+	71.3441i	0.116385	+	0.116385i	0.762901	−	0.646516i	$-0.223774\pi$
$613$	71.3441	+	71.3441i	0.116385	+	0.116385i	−0.646516	+	0.762901i	$0.723774\pi$
$614$	846.379	+	393.730i	1.37847	+	0.641254i
$615$	−189.007	+	432.549i	−0.307329	+	0.703332i
$616$	98.2805	−	171.312i	0.159546	−	0.278104i
$617$	222.842	−	222.842i	0.361169	−	0.361169i	−0.503074	−	0.864243i	$-0.667798\pi$
$617$	222.842	−	222.842i	0.361169	−	0.361169i	0.864243	+	0.503074i	$0.167798\pi$
$618$	−819.306	−	50.8430i	−1.32574	−	0.0822703i
$619$	−534.752	−	534.752i	−0.863896	−	0.863896i	0.127892	−	0.991788i	$-0.459179\pi$
$619$	−534.752	−	534.752i	−0.863896	−	0.863896i	−0.991788	+	0.127892i	$0.959179\pi$
$620$	−46.3544	−	55.0380i	−0.0747651	−	0.0887709i
$621$	−343.489	+	119.546i	−0.553122	+	0.192505i
$622$	199.722	+	547.173i	0.321097	+	0.879700i
$623$			369.080i			0.592424i
$624$	321.377	−	534.876i	0.515027	−	0.857174i
$625$	25.7012			0.0411219
$626$	−643.484	+	234.877i	−1.02793	+	0.375202i
$627$	203.362	−	465.400i	0.324341	−	0.742265i
$628$	−533.869	+	449.638i	−0.850109	+	0.715983i
$629$	13.5484	−	13.5484i	0.0215396	−	0.0215396i
$630$	137.411	+	70.4816i	0.218112	+	0.111876i
$631$	−35.0852	−	35.0852i	−0.0556025	−	0.0556025i	0.678759	−	0.734361i	$-0.262518\pi$
$631$	−35.0852	−	35.0852i	−0.0556025	−	0.0556025i	−0.734361	+	0.678759i	$0.762518\pi$
$632$	320.420	+	183.823i	0.506994	+	0.290859i
$633$	19.3737	−	44.3373i	0.0306062	−	0.0700432i
$634$	476.019	−	1023.27i	0.750818	−	1.61399i
$635$	209.787	−	209.787i	0.330372	−	0.330372i
$636$	−329.718	−	1113.01i	−0.518425	−	1.75001i
$637$	−22.6194	−	540.957i	−0.0355092	−	0.849226i
$638$	−181.282	−	84.3313i	−0.284141	−	0.132181i
$639$	−7.54406	+	195.760i	−0.0118060	+	0.306353i
$640$	−403.254	+	37.8861i	−0.630084	+	0.0591970i
$641$	918.436			1.43282			0.716409	−	0.697680i	$-0.245784\pi$
$641$	918.436			1.43282			0.716409	+	0.697680i	$0.245784\pi$
$642$	559.334	+	34.7102i	0.871237	+	0.0540657i
$643$	174.939	−	174.939i	0.272066	−	0.272066i	−0.557865	−	0.829932i	$-0.688379\pi$
$643$	174.939	−	174.939i	0.272066	−	0.272066i	0.829932	+	0.557865i	$0.188379\pi$
$644$	−12.4662	+	145.559i	−0.0193575	+	0.226023i
$645$	408.287	−	159.977i	0.633003	−	0.248027i
$646$	124.389	−	267.393i	0.192553	−	0.413920i
$647$		−	1087.32i		−	1.68056i	−0.542151	−	0.840281i	$-0.682390\pi$
$647$		−	1087.32i		−	1.68056i	0.542151	−	0.840281i	$-0.317610\pi$
$648$	−535.589	−	364.758i	−0.826526	−	0.562898i
$649$		−	256.151i		−	0.394686i
$650$	−148.785	−	360.145i	−0.228901	−	0.554069i
$651$	−42.3747	−	18.5161i	−0.0650918	−	0.0284426i
$652$	1150.95	+	98.5719i	1.76527	+	0.151184i
$653$		−	915.597i		−	1.40214i	−0.713093	−	0.701070i	$-0.752706\pi$
$653$		−	915.597i		−	1.40214i	0.713093	−	0.701070i	$-0.247294\pi$
$654$	553.090	+	626.278i	0.845704	+	0.957611i
$655$	126.381	−	126.381i	0.192948	−	0.192948i
$656$	−458.728	−	650.051i	−0.699281	−	0.990932i
$657$	−668.252	−	25.7526i	−1.01713	−	0.0391973i
$658$	−330.945	+	120.797i	−0.502955	+	0.183582i
$659$	330.590			0.501653			0.250827	−	0.968032i	$-0.419298\pi$
$659$	330.590			0.501653			0.250827	+	0.968032i	$0.419298\pi$
$660$	−98.2037	−	331.499i	−0.148794	−	0.502272i
$661$	−388.081	+	388.081i	−0.587112	+	0.587112i	−0.936848	−	0.349736i	$-0.886271\pi$
$661$	−388.081	+	388.081i	−0.587112	+	0.587112i	0.349736	+	0.936848i	$0.386271\pi$
$662$	−461.348	+	991.734i	−0.696900	+	1.49809i
$663$	288.340	+	111.892i	0.434902	+	0.168767i
$664$	969.116	−	262.529i	1.45951	−	0.395375i
$665$	112.800	−	112.800i	0.169624	−	0.169624i
$666$	−41.3961	+	13.3271i	−0.0621564	+	0.0200107i
$667$	147.894			0.221730
$668$	35.3940	−	413.270i	0.0529850	−	0.618668i
$669$	856.755	−	335.699i	1.28065	−	0.501792i
$670$	−176.584	−	483.781i	−0.263558	−	0.722061i
$671$	−694.648	+	694.648i	−1.03524	+	1.03524i
$672$	−221.557	+	136.617i	−0.329699	+	0.203299i
$673$		−	186.978i		−	0.277827i	−0.990304	−	0.138914i	$-0.955639\pi$
$673$		−	186.978i		−	0.277827i	0.990304	−	0.138914i	$-0.0443611\pi$
$674$	42.0431	+	115.184i	0.0623785	+	0.170897i
$675$	−382.171	+	133.008i	−0.566180	+	0.197049i
$676$	478.891	−	477.116i	0.708418	−	0.705793i
$677$		−	368.883i		−	0.544879i	−0.962173	−	0.272440i	$-0.912170\pi$
$677$		−	368.883i		−	0.544879i	0.962173	−	0.272440i	$-0.0878305\pi$
$678$	−31.8586	+	513.383i	−0.0469890	+	0.757201i
$679$		−	162.944i		−	0.239977i
$680$	−52.4917	−	193.771i	−0.0771937	−	0.284958i
$681$	−263.209	−	671.749i	−0.386503	−	0.986415i
$682$	35.4980	+	97.2528i	0.0520499	+	0.142599i
$683$	455.745	−	455.745i	0.667269	−	0.667269i	−0.289814	−	0.957083i	$-0.593593\pi$
$683$	455.745	−	455.745i	0.667269	−	0.667269i	0.957083	+	0.289814i	$0.0935934\pi$
$684$	−528.197	+	411.161i	−0.772218	+	0.601112i
$685$	−44.4663			−0.0649143
$686$	−207.336	+	445.698i	−0.302239	+	0.649706i
$687$	−113.481	+	44.4648i	−0.165183	+	0.0647231i
$688$	−125.676	+	728.333i	−0.182669	+	1.05862i
$689$	−52.5369	−	1256.45i	−0.0762509	−	1.82359i
$690$	169.290	+	191.691i	0.245348	+	0.277813i
$691$	252.600	−	252.600i	0.365557	−	0.365557i	−0.500297	−	0.865854i	$-0.666776\pi$
$691$	252.600	−	252.600i	0.365557	−	0.365557i	0.865854	+	0.500297i	$0.166776\pi$
$692$	−145.571	+	122.603i	−0.210362	+	0.177172i
$693$	−150.945	−	163.045i	−0.217813	−	0.235274i
$694$	51.6244	−	18.8433i	0.0743868	−	0.0271517i
$695$	−352.266	−	352.266i	−0.506858	−	0.506858i
$696$	156.936	+	211.671i	0.225483	+	0.304124i
$697$	278.847	−	278.847i	0.400068	−	0.400068i
$698$	287.888	−	618.857i	0.412447	−	0.886615i
$699$	−350.248	−	153.045i	−0.501070	−	0.218948i
$700$	−13.8701	+	161.951i	−0.0198144	+	0.231359i
$701$	−684.290			−0.976162			−0.488081	−	0.872798i	$-0.662303\pi$
$701$	−684.290			−0.976162			−0.488081	+	0.872798i	$0.662303\pi$
$702$	−466.410	−	524.658i	−0.664401	−	0.747376i
$703$			44.9222i			0.0639007i
$704$	563.699	+	147.728i	0.800708	+	0.209841i
$705$	−246.940	+	565.131i	−0.350270	+	0.801604i
$706$	320.358	−	688.656i	0.453765	−	0.975434i
$707$	158.563	+	158.563i	0.224276	+	0.224276i
$708$	−161.075	+	296.682i	−0.227508	+	0.419042i
$709$	−801.423	+	801.423i	−1.13036	+	1.13036i	−0.140240	+	0.990118i	$0.544787\pi$
$709$	−801.423	+	801.423i	−1.13036	+	1.13036i	−0.990118	+	0.140240i	$0.955213\pi$
$710$	129.405	−	47.2338i	0.182261	−	0.0665265i
$711$	304.958	−	282.326i	0.428914	−	0.397083i
$712$	−1051.10	+	284.738i	−1.47626	+	0.399913i
$713$	−54.1504	−	54.1504i	−0.0759473	−	0.0759473i
$714$	−85.4020	−	96.7027i	−0.119611	−	0.135438i
$715$	−15.6476	−	374.224i	−0.0218848	−	0.523390i
$716$	898.054	+	1066.29i	1.25427	+	1.48923i
$717$	−14.5771	−	37.2031i	−0.0203307	−	0.0518871i
$718$	−51.3860	+	110.462i	−0.0715683	+	0.153846i
$719$			931.573i			1.29565i	0.761789	+	0.647825i	$0.224321\pi$
$719$			931.573i			1.29565i	−0.761789	+	0.647825i	$0.775679\pi$
$720$	−94.7140	+	445.706i	−0.131547	+	0.619036i
$721$	262.303	+	262.303i	0.363805	+	0.363805i
$722$	−10.4826	−	28.7188i	−0.0145188	−	0.0397767i
$723$	1304.22	−	511.026i	1.80390	−	0.706813i
$724$	438.410	+	520.538i	0.605538	+	0.718975i
$725$	164.549			0.226964
$726$	14.1569	−	228.130i	0.0194998	−	0.314229i
$727$	−364.106			−0.500833			−0.250417	−	0.968138i	$-0.580568\pi$
$727$	−364.106			−0.500833			−0.250417	+	0.968138i	$0.580568\pi$
$728$	−268.855	+	85.0367i	−0.369307	+	0.116809i
$729$	−571.477	+	452.609i	−0.783919	+	0.620863i
$730$	161.239	+	441.741i	0.220875	+	0.605125i
$731$	−366.337			−0.501146
$732$	1241.38	−	367.747i	1.69587	−	0.502387i
$733$	−857.363	−	857.363i	−1.16966	−	1.16966i	−0.982288	−	0.187375i	$-0.940002\pi$
$733$	−857.363	−	857.363i	−1.16966	−	1.16966i	−0.187375	−	0.982288i	$-0.559998\pi$
$734$	342.600	+	938.611i	0.466758	+	1.27876i
$735$	144.237	+	368.114i	0.196241	+	0.500836i
$736$	−424.153	+	76.7935i	−0.576295	+	0.104339i
$737$			740.955i			1.00537i
$738$	−851.999	+	274.294i	−1.15447	+	0.371672i
$739$	−963.677	−	963.677i	−1.30403	−	1.30403i	−0.925651	−	0.378378i	$-0.876482\pi$
$739$	−963.677	−	963.677i	−1.30403	−	1.30403i	−0.378378	−	0.925651i	$-0.623518\pi$
$740$	19.6994	+	23.3897i	0.0266208	+	0.0316077i
$741$	−663.522	+	292.522i	−0.895442	+	0.394767i
$742$	−221.257	+	475.623i	−0.298190	+	0.641002i
$743$	−935.304	−	935.304i	−1.25882	−	1.25882i	−0.951656	−	0.307165i	$-0.900620\pi$
$743$	−935.304	−	935.304i	−1.25882	−	1.25882i	−0.307165	−	0.951656i	$-0.599380\pi$
$744$	20.0406	−	134.963i	0.0269363	−	0.181402i
$745$			327.885i			0.440114i
$746$	623.794	−	227.690i	0.836185	−	0.305214i
$747$	43.4976	−	1128.71i	0.0582297	−	1.51100i
$748$	−24.6467	+	287.782i	−0.0329502	+	0.384736i
$749$	−179.073	−	179.073i	−0.239082	−	0.239082i
$750$	502.547	+	569.046i	0.670063	+	0.758728i
$751$	1140.94			1.51923			0.759613	−	0.650376i	$-0.225389\pi$
$751$	1140.94			1.51923			0.759613	+	0.650376i	$0.225389\pi$
$752$	−599.334	−	849.301i	−0.796987	−	1.12939i
$753$	−158.231	+	362.116i	−0.210134	+	0.480898i
$754$	108.996	+	263.833i	0.144557	+	0.349911i
$755$	426.294			0.564628
$756$	72.3012	+	283.762i	0.0956365	+	0.375347i
$757$	−383.846			−0.507062			−0.253531	−	0.967327i	$-0.581592\pi$
$757$	−383.846			−0.507062			−0.253531	+	0.967327i	$0.581592\pi$
$758$	−558.701	+	1201.01i	−0.737073	+	1.58444i
$759$	−134.236	−	342.590i	−0.176858	−	0.451370i
$760$	408.265	+	234.219i	0.537191	+	0.308183i
$761$	−4.79917	−	4.79917i	−0.00630639	−	0.00630639i	0.703947	−	0.710253i	$-0.251419\pi$
$761$	−4.79917	−	4.79917i	−0.00630639	−	0.00630639i	−0.710253	+	0.703947i	$0.751419\pi$
$762$	561.478	+	34.8432i	0.736847	+	0.0457259i
$763$		−	377.578i		−	0.494860i
$764$	1114.35	−	938.534i	1.45857	−	1.22845i
$765$	−225.682	−	8.69718i	−0.295009	−	0.0113689i
$766$	−259.385	−	120.664i	−0.338623	−	0.157525i
$767$	−247.574	+	269.181i	−0.322782	+	0.350953i
$768$	−559.997	−	525.574i	−0.729163	−	0.684341i
$769$	7.46155	+	7.46155i	0.00970292	+	0.00970292i	0.711942	−	0.702239i	$-0.247816\pi$
$769$	7.46155	+	7.46155i	0.00970292	+	0.00970292i	−0.702239	+	0.711942i	$0.747816\pi$
$770$	−65.8994	+	141.660i	−0.0855836	+	0.183974i
$771$	398.821	+	174.269i	0.517277	+	0.226030i
$772$	13.3083	−	155.391i	0.0172387	−	0.201284i
$773$	−566.815	+	566.815i	−0.733267	+	0.733267i	−0.971266	−	0.237999i	$-0.923509\pi$
$773$	−566.815	+	566.815i	−0.733267	+	0.733267i	0.237999	+	0.971266i	$0.423509\pi$
$774$	739.837	+	379.482i	0.955862	+	0.490287i
$775$	−60.2487	−	60.2487i	−0.0777402	−	0.0777402i
$776$	464.047	−	125.708i	0.597999	−	0.161995i
$777$	18.0081	+	7.86886i	0.0231765	+	0.0101272i
$778$	−857.217	+	312.891i	−1.10182	+	0.402173i
$779$			924.570i			1.18687i
$780$	−217.200	+	443.277i	−0.278461	+	0.568304i
$781$	−198.196			−0.253772
$782$	−73.2570	−	200.700i	−0.0936790	−	0.256650i
$783$	279.969	−	97.4385i	0.357559	−	0.124442i
$784$	−656.671	−	113.311i	−0.837590	−	0.144529i
$785$	390.437	−	390.437i	0.497372	−	0.497372i
$786$	338.249	+	20.9905i	0.430342	+	0.0267054i
$787$	−322.116	−	322.116i	−0.409296	−	0.409296i	0.472197	−	0.881493i	$-0.343461\pi$
$787$	−322.116	−	322.116i	−0.409296	−	0.409296i	−0.881493	+	0.472197i	$0.843461\pi$
$788$	−84.4095	+	985.590i	−0.107119	+	1.25075i
$789$	202.189	+	88.3488i	0.256260	+	0.111976i
$790$	−264.960	−	123.258i	−0.335392	−	0.156022i
$791$	164.361	−	164.361i	0.207789	−	0.207789i
$792$	347.883	−	555.660i	0.439246	−	0.701591i
$793$	1401.37	−	58.5964i	1.76718	−	0.0738920i
$794$	−359.041	+	771.810i	−0.452192	+	0.972052i
$795$	335.012	+	855.001i	0.421398	+	1.07547i
$796$	−664.886	+	559.984i	−0.835284	+	0.703498i
$797$	1338.55			1.67949			0.839746	−	0.542980i	$-0.182704\pi$
$797$	1338.55			1.67949			0.839746	+	0.542980i	$0.182704\pi$
$798$	301.901	+	18.7348i	0.378322	+	0.0234772i
$799$	364.318	−	364.318i	0.455967	−	0.455967i
$800$	−471.920	+	85.4417i	−0.589900	+	0.106802i
$801$	−47.1773	+	1224.20i	−0.0588980	+	1.52834i
$802$	647.041	+	300.999i	0.806785	+	0.375311i
$803$		−	676.567i		−	0.842550i
$804$	465.934	−	858.196i	0.579520	−	1.06741i
$805$		−	115.569i		−	0.143564i
$806$	56.6925	−	136.509i	0.0703381	−	0.169366i
$807$	−395.730	+	905.640i	−0.490371	+	1.12223i
$808$	−329.242	+	573.899i	−0.407478	+	0.710271i
$809$			615.167i			0.760404i	0.924903	+	0.380202i	$0.124146\pi$
$809$			615.167i			0.760404i	−0.924903	+	0.380202i	$0.875854\pi$
$810$	446.767	+	251.344i	0.551564	+	0.310301i
$811$	322.284	−	322.284i	0.397391	−	0.397391i	−0.479921	−	0.877312i	$-0.659335\pi$
$811$	322.284	−	322.284i	0.397391	−	0.397391i	0.877312	+	0.479921i	$0.159335\pi$
$812$	10.1609	−	118.641i	0.0125134	−	0.146110i
$813$	253.795	+	647.725i	0.312171	+	0.796710i
$814$	−15.0857	−	41.3299i	−0.0185328	−	0.0507738i
$815$	−913.822			−1.12125
$816$	209.513	−	317.819i	0.256756	−	0.389485i
$817$	607.330	−	607.330i	0.743366	−	0.743366i
$818$	193.757	+	90.1346i	0.236867	+	0.110189i
$819$	1.03766	+	317.229i	0.00126698	+	0.387337i
$820$	405.445	+	481.397i	0.494445	+	0.587070i
$821$	−353.910	+	353.910i	−0.431072	+	0.431072i	−0.888993	−	0.457921i	$-0.848594\pi$
$821$	−353.910	+	353.910i	−0.431072	+	0.431072i	0.457921	+	0.888993i	$0.348594\pi$
$822$	−55.8127	−	63.1980i	−0.0678987	−	0.0768833i
$823$	−155.082			−0.188435			−0.0942176	−	0.995552i	$-0.530035\pi$
$823$	−155.082			−0.188435			−0.0942176	+	0.995552i	$0.530035\pi$
$824$	−544.649	+	949.373i	−0.660982	+	1.15215i
$825$	−149.353	−	381.171i	−0.181034	−	0.462026i
$826$	143.306	−	52.3079i	0.173494	−	0.0633268i
$827$	−453.337	+	453.337i	−0.548170	+	0.548170i	−0.925911	−	0.377741i	$-0.876701\pi$
$827$	−453.337	+	453.337i	−0.548170	+	0.548170i	0.377741	+	0.925911i	$0.376701\pi$
$828$	−59.9549	+	481.209i	−0.0724093	+	0.581171i
$829$			277.026i			0.334169i	0.985943	+	0.167084i	$0.0534352\pi$
$829$			277.026i			0.334169i	−0.985943	+	0.167084i	$0.946565\pi$
$830$	−746.124	+	272.341i	−0.898945	+	0.328122i
$831$	199.335	−	456.184i	0.239874	−	0.548958i
$832$	−449.591	−	700.065i	−0.540374	−	0.841425i
$833$		−	330.293i		−	0.396510i
$834$	58.5075	−	942.814i	0.0701528	−	1.13047i
$835$			328.124i			0.392962i
$836$	−436.237	−	517.958i	−0.521815	−	0.619567i
$837$	−138.185	−	66.8324i	−0.165096	−	0.0798476i
$838$	666.686	−	243.345i	0.795568	−	0.290388i
$839$	−548.135	+	548.135i	−0.653319	+	0.653319i	−0.953791	−	0.300471i	$-0.902856\pi$
$839$	−548.135	+	548.135i	−0.653319	+	0.653319i	0.300471	+	0.953791i	$0.402856\pi$
$840$	165.407	−	122.636i	0.196913	−	0.145995i
$841$	720.456			0.856666
$842$	380.382	+	176.951i	0.451760	+	0.210156i
$843$	21.2735	+	54.2932i	0.0252354	+	0.0644047i
$844$	−41.5591	−	49.3444i	−0.0492406	−	0.0584649i
$845$	−345.249	+	408.384i	−0.408579	+	0.483294i
$846$	−1113.15	+	358.368i	−1.31578	+	0.423603i
$847$	−73.0366	+	73.0366i	−0.0862297	+	0.0862297i
$848$	−1525.22	−	263.181i	−1.79861	−	0.310355i
$849$	−908.722	−	397.076i	−1.07034	−	0.467699i
$850$	−81.5069	−	223.302i	−0.0958905	−	0.262708i
$851$	23.0125	+	23.0125i	0.0270417	+	0.0270417i
$852$	229.556	+	124.631i	0.269432	+	0.146281i
$853$	671.485	−	671.485i	0.787204	−	0.787204i	−0.193831	−	0.981035i	$-0.562091\pi$
$853$	671.485	−	671.485i	0.787204	−	0.787204i	0.981035	+	0.193831i	$0.0620913\pi$
$854$	−530.481	−	246.776i	−0.621172	−	0.288965i
$855$	388.564	−	359.727i	0.454461	−	0.420733i
$856$	371.828	−	648.130i	0.434378	−	0.757161i
$857$	−465.906			−0.543647			−0.271824	−	0.962347i	$-0.587627\pi$
$857$	−465.906			−0.543647			−0.271824	+	0.962347i	$0.587627\pi$
$858$	512.228	−	491.953i	0.597002	−	0.573372i
$859$		−	646.398i		−	0.752500i	−0.926518	−	0.376250i	$-0.877213\pi$
$859$		−	646.398i		−	0.752500i	0.926518	−	0.376250i	$-0.122787\pi$
$860$	49.8915	−	582.547i	0.0580133	−	0.677380i
$861$	370.636	+	161.954i	0.430472	+	0.188100i
$862$	−332.750	−	154.793i	−0.386021	−	0.179574i
$863$	80.0865	+	80.0865i	0.0928001	+	0.0928001i	0.751983	−	0.659183i	$-0.229098\pi$
$863$	80.0865	+	80.0865i	0.0928001	+	0.0928001i	−0.659183	+	0.751983i	$0.729098\pi$
$864$	−752.344	+	424.823i	−0.870769	+	0.491693i
$865$	106.461	−	106.461i	0.123076	−	0.123076i
$866$	190.044	+	520.658i	0.219450	+	0.601222i
$867$	−621.573	−	271.603i	−0.716923	−	0.313268i
$868$	−47.1602	+	39.7195i	−0.0543320	+	0.0457598i
$869$	297.296	+	297.296i	0.342112	+	0.342112i
$870$	−137.984	−	156.242i	−0.158602	−	0.179589i
$871$	716.143	−	778.646i	0.822208	−	0.893967i
$872$	1075.30	−	291.294i	1.23314	−	0.334053i
$873$	20.8282	−	540.468i	0.0238582	−	0.619093i
$874$	454.178	+	211.280i	0.519654	+	0.241740i
$875$		−	343.074i		−	0.392084i
$876$	−425.446	+	783.621i	−0.485668	+	0.894544i
$877$	492.434	+	492.434i	0.561498	+	0.561498i	0.929733	−	0.368235i	$-0.120038\pi$
$877$	492.434	+	492.434i	0.561498	+	0.561498i	−0.368235	+	0.929733i	$0.620038\pi$
$878$	1548.81	−	565.329i	1.76403	−	0.643883i
$879$	32.2765	+	82.3747i	0.0367196	+	0.0937141i
$880$	−454.273	−	78.3861i	−0.516219	−	0.0890751i
$881$	−582.104			−0.660730			−0.330365	−	0.943853i	$-0.607172\pi$
$881$	−582.104			−0.660730			−0.330365	+	0.943853i	$0.607172\pi$
$882$	−342.144	+	667.043i	−0.387918	+	0.756284i
$883$	751.578			0.851164			0.425582	−	0.904920i	$-0.360069\pi$
$883$	751.578			0.851164			0.425582	+	0.904920i	$0.360069\pi$
$884$	304.046	−	278.600i	0.343943	−	0.315158i
$885$	106.931	−	244.714i	0.120826	−	0.276513i
$886$	557.096	−	203.344i	0.628777	−	0.229508i
$887$	227.550			0.256539			0.128270	−	0.991739i	$-0.459058\pi$
$887$	227.550			0.256539			0.128270	+	0.991739i	$0.459058\pi$
$888$	−8.51671	+	57.3558i	−0.00959089	+	0.0645899i
$889$	−179.759	−	179.759i	−0.202203	−	0.202203i
$890$	809.243	−	295.380i	0.909262	−	0.331887i
$891$	−479.826	−	560.097i	−0.538525	−	0.628616i
$892$	104.693	−	1222.43i	0.117369	−	1.37043i
$893$			1207.96i			1.35270i
$894$	−466.009	+	411.551i	−0.521263	+	0.460348i
$895$	−779.813	−	779.813i	−0.871300	−	0.871300i
$896$	32.4633	+	345.534i	0.0362313	+	0.385641i
$897$	−190.054	+	489.757i	−0.211877	+	0.545995i
$898$	261.715	+	121.748i	0.291442	+	0.135577i
$899$	44.1366	+	44.1366i	0.0490952	+	0.0490952i
$900$	−66.7068	+	535.401i	−0.0741187	+	0.594890i
$901$		−	767.154i		−	0.851448i
$902$	−310.488	−	850.635i	−0.344222	−	0.943054i
$903$	−137.079	−	349.847i	−0.151804	−	0.387427i
$904$	594.883	+	341.281i	0.658057	+	0.377523i
$905$	−380.687	−	380.687i	−0.420649	−	0.420649i
$906$	535.071	+	605.873i	0.590586	+	0.668734i
$907$	−83.6189			−0.0921929			−0.0460964	−	0.998937i	$-0.514678\pi$
$907$	−83.6189			−0.0921929			−0.0460964	+	0.998937i	$0.514678\pi$
$908$	−958.457	−	82.0858i	−1.05557	−	0.0904028i
$909$	505.669	+	546.205i	0.556291	+	0.600886i
$910$	206.168	−	85.1735i	0.226558	−	0.0935973i
$911$	141.993			0.155865			0.0779323	−	0.996959i	$-0.475168\pi$
$911$	141.993			0.155865			0.0779323	+	0.996959i	$0.475168\pi$
$912$	179.556	+	874.234i	0.196881	+	0.958590i
$913$	1142.76			1.25165
$914$	−762.684	−	354.796i	−0.834447	−	0.388179i
$915$	−953.615	+	373.651i	−1.04220	+	0.408362i
$916$	−13.8670	+	161.916i	−0.0151387	+	0.176764i
$917$	−108.292	−	108.292i	−0.118093	−	0.118093i
$918$	−270.908	−	331.668i	−0.295107	−	0.361295i
$919$		−	31.4087i		−	0.0341771i	−0.999854	−	0.0170885i	$-0.994560\pi$
$919$		−	31.4087i		−	0.0341771i	0.999854	−	0.0170885i	$-0.00543972\pi$
$920$	329.128	−	89.1594i	0.357748	−	0.0969124i
$921$	−510.828	−	1303.71i	−0.554645	−	1.41554i
$922$	362.708	−	779.693i	0.393393	−	0.845654i
$923$	208.278	+	191.559i	0.225653	+	0.207539i
$924$	−284.050	+	84.1474i	−0.307414	+	0.0910686i
$925$	25.6041	+	25.6041i	0.0276801	+	0.0276801i
$926$	−361.688	−	168.255i	−0.390592	−	0.181701i
$927$	836.503	+	903.560i	0.902376	+	0.974714i
$928$	345.716	−	62.5923i	0.372539	−	0.0674487i
$929$	−1062.36	+	1062.36i	−1.14355	+	1.14355i	−0.155755	+	0.987796i	$0.549781\pi$
$929$	−1062.36	+	1062.36i	−1.14355	+	1.14355i	−0.987796	+	0.155755i	$0.950219\pi$
$930$	−6.68527	+	107.729i	−0.00718846	+	0.115838i
$931$	547.573	+	547.573i	0.588156	+	0.588156i
$932$	−389.802	+	328.301i	−0.418243	+	0.352254i
$933$	349.844	−	800.629i	0.374967	−	0.858123i
$934$	374.791	+	1026.80i	0.401275	+	1.09936i
$935$		−	228.490i		−	0.244375i
$936$	−902.632	+	247.691i	−0.964351	+	0.264627i
$937$	−1441.85			−1.53879			−0.769395	−	0.638773i	$-0.779442\pi$
$937$	−1441.85			−1.53879			−0.769395	+	0.638773i	$0.779442\pi$
$938$	−414.535	+	151.308i	−0.441935	+	0.161310i
$939$	941.552	+	411.422i	1.00272	+	0.438149i
$940$	529.719	+	628.951i	0.563531	+	0.669097i
$941$	203.881	−	203.881i	0.216664	−	0.216664i	−0.590427	−	0.807091i	$-0.701041\pi$
$941$	203.881	−	203.881i	0.216664	−	0.216664i	0.807091	+	0.590427i	$0.201041\pi$
$942$	1044.97	+	64.8471i	1.10931	+	0.0688398i
$943$	473.634	+	473.634i	0.502263	+	0.502263i
$944$	259.525	+	367.766i	0.274921	+	0.389583i
$945$	−76.1418	−	218.777i	−0.0805734	−	0.231510i
$946$	−354.811	+	762.716i	−0.375064	+	0.806254i
$947$	280.005	−	280.005i	0.295676	−	0.295676i	−0.543641	−	0.839318i	$-0.682955\pi$
$947$	280.005	−	280.005i	0.295676	−	0.295676i	0.839318	+	0.543641i	$0.182955\pi$
$948$	−157.389	−	531.285i	−0.166022	−	0.560427i
$949$	−653.912	+	710.983i	−0.689054	+	0.749192i
$950$	505.326	+	235.074i	0.531922	+	0.247446i
$951$	−1576.18	+	617.590i	−1.65740	+	0.649411i
$952$	−166.036	+	44.9784i	−0.174407	+	0.0472462i
$953$	1500.26			1.57425			0.787123	−	0.616796i	$-0.211570\pi$
$953$	1500.26			1.57425			0.787123	+	0.616796i	$0.211570\pi$
$954$	−794.680	+	1549.31i	−0.832998	+	1.62401i
$955$	−814.964	+	814.964i	−0.853365	+	0.853365i
$956$	−53.0817	−	4.54611i	−0.0555248	−	0.00475534i
$957$	109.412	+	279.236i	0.114328	+	0.291783i
$958$	−133.481	+	286.937i	−0.139333	+	0.299517i
$959$			38.1017i			0.0397306i
$960$	476.861	+	376.449i	0.496730	+	0.392134i
$961$			928.679i			0.966368i
$962$	−24.0928	+	58.0128i	−0.0250445	+	0.0603044i
$963$	−571.074	−	616.854i	−0.593016	−	0.640554i
$964$	159.371	−	1860.87i	0.165323	−	1.93036i
$965$			123.376i			0.127851i
$966$	164.254	−	145.059i	0.170035	−	0.150164i
$967$	−302.480	+	302.480i	−0.312803	+	0.312803i	−0.845994	−	0.533192i	$-0.820992\pi$
$967$	−302.480	+	302.480i	−0.312803	+	0.312803i	0.533192	+	0.845994i	$0.320992\pi$
$968$	−264.346	−	151.654i	−0.273085	−	0.156667i
$969$	−411.875	+	161.383i	−0.425052	+	0.166546i
$970$	−357.271	+	130.406i	−0.368320	+	0.134440i
$971$	1484.57			1.52891			0.764453	−	0.644679i	$-0.223009\pi$
$971$	1484.57			1.52891			0.764453	+	0.644679i	$0.223009\pi$
$972$	203.543	+	950.449i	0.209407	+	0.977829i
$973$	−301.845	+	301.845i	−0.310221	+	0.310221i
$974$	177.795	−	382.197i	0.182541	−	0.392399i
$975$	−211.457	+	544.912i	−0.216879	+	0.558884i
$976$	293.535	−	1701.13i	0.300753	−	1.74296i
$977$	680.203	−	680.203i	0.696216	−	0.696216i	−0.267376	−	0.963592i	$-0.586157\pi$
$977$	680.203	−	680.203i	0.696216	−	0.696216i	0.963592	+	0.267376i	$0.0861567\pi$
$978$	−1147.00	−	1298.78i	−1.17280	−	1.32799i
$979$	−1239.43			−1.26602
$980$	525.229	+	44.9825i	0.535948	+	0.0459005i
$981$	48.2636	−	1252.39i	0.0491983	−	1.27664i
$982$	−296.154	−	811.363i	−0.301582	−	0.826236i
$983$	−178.438	+	178.438i	−0.181524	+	0.181524i	−0.792019	−	0.610496i	$-0.790970\pi$
$983$	−178.438	+	178.438i	−0.181524	+	0.181524i	0.610496	+	0.792019i	$0.290970\pi$
$984$	−175.288	+	1180.47i	−0.178138	+	1.19967i
$985$		−	782.528i		−	0.794444i
$986$	59.7099	+	163.585i	0.0605577	+	0.165908i
$987$	484.241	+	211.595i	0.490619	+	0.214382i
$988$	−42.1859	+	965.935i	−0.0426983	+	0.977667i
$989$		−	622.240i		−	0.629160i
$990$	−236.688	+	461.448i	−0.239079	+	0.466109i
$991$			1209.46i			1.22045i	0.792230	+	0.610223i	$0.208920\pi$
$991$			1209.46i			1.22045i	−0.792230	+	0.610223i	$0.791080\pi$
$992$	−149.500	−	103.664i	−0.150705	−	0.104500i
$993$	1527.61	−	598.556i	1.53838	−	0.602775i
$994$	−40.4730	−	110.883i	−0.0407173	−	0.111552i
$995$	486.255	−	486.255i	0.488698	−	0.488698i
$996$	−1323.58	−	718.600i	−1.32889	−	0.721486i
$997$	−901.595			−0.904308			−0.452154	−	0.891940i	$-0.649344\pi$
$997$	−901.595			−0.904308			−0.452154	+	0.891940i	$0.649344\pi$
$998$	297.936	−	640.455i	0.298533	−	0.641739i
$999$	58.7252	+	28.4020i	0.0587839	+	0.0284304i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.3.l.c.47.6	✓	96
3.2	odd	2	inner	156.3.l.c.47.43	yes	96
4.3	odd	2	inner	156.3.l.c.47.19	yes	96
12.11	even	2	inner	156.3.l.c.47.30	yes	96
13.5	odd	4	inner	156.3.l.c.83.30	yes	96
39.5	even	4	inner	156.3.l.c.83.19	yes	96
52.31	even	4	inner	156.3.l.c.83.43	yes	96
156.83	odd	4	inner	156.3.l.c.83.6	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.3.l.c.47.6	✓	96	1.1	even	1	trivial
156.3.l.c.47.19	yes	96	4.3	odd	2	inner
156.3.l.c.47.30	yes	96	12.11	even	2	inner
156.3.l.c.47.43	yes	96	3.2	odd	2	inner
156.3.l.c.83.6	yes	96	156.83	odd	4	inner
156.3.l.c.83.19	yes	96	39.5	even	4	inner
156.3.l.c.83.30	yes	96	13.5	odd	4	inner
156.3.l.c.83.43	yes	96	52.31	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	156.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.87876 + 0.685761i) q^{2} +(2.74902 + 1.20121i) q^{3} +(3.05946 - 2.57676i) q^{4} +(-2.23749 + 2.23749i) q^{5} +(-5.98848 - 0.371622i) q^{6} +(1.91723 + 1.91723i) q^{7} +(-3.98095 + 6.93916i) q^{8} +(6.11417 + 6.60431i) q^{9} +(2.66932 - 5.73809i) q^{10} +(-6.43837 + 6.43837i) q^{11} +(11.5058 - 3.40848i) q^{12} +(12.9887 - 0.543102i) q^{13} +(-4.91678 - 2.28725i) q^{14} +(-8.83861 + 3.46320i) q^{15} +(2.72064 - 15.7670i) q^{16} +7.93049 q^{17} +(-16.0160 - 8.21504i) q^{18} +(-13.1475 + 13.1475i) q^{19} +(-1.08005 + 12.6110i) q^{20} +(2.96749 + 7.57350i) q^{21} +(7.68096 - 16.5113i) q^{22} +13.4703i q^{23} +(-19.2791 + 14.2939i) q^{24} +14.9872i q^{25} +(-24.0301 + 9.92747i) q^{26} +(8.87477 + 25.4998i) q^{27} +(10.8059 + 0.925460i) q^{28} -10.9793i q^{29} +(14.2307 - 12.5677i) q^{30} +(-4.01999 + 4.01999i) q^{31} +(5.70096 + 31.4881i) q^{32} +(-25.4330 + 9.96532i) q^{33} +(-14.8995 + 5.43842i) q^{34} -8.57958 q^{35} +(35.7238 + 4.45091i) q^{36} +(1.70839 - 1.70839i) q^{37} +(15.6849 - 33.7170i) q^{38} +(36.3584 + 14.1091i) q^{39} +(-6.61898 - 24.4337i) q^{40} +(35.1614 - 35.1614i) q^{41} +(-10.7688 - 12.1938i) q^{42} -46.1935 q^{43} +(-3.10784 + 36.2881i) q^{44} +(-28.4575 - 1.09668i) q^{45} +(-9.23738 - 25.3074i) q^{46} +(45.9388 - 45.9388i) q^{47} +(26.4186 - 40.0756i) q^{48} -41.6485i q^{49} +(-10.2777 - 28.1574i) q^{50} +(21.8010 + 9.52621i) q^{51} +(38.3389 - 35.1302i) q^{52} -96.7348i q^{53} +(-34.1603 - 41.8219i) q^{54} -28.8116i q^{55} +(-20.9364 + 5.67157i) q^{56} +(-51.9357 + 20.3497i) q^{57} +(7.52915 + 20.6274i) q^{58} +(-19.8925 + 19.8925i) q^{59} +(-18.1176 + 33.3705i) q^{60} +107.892 q^{61} +(4.79584 - 10.3094i) q^{62} +(-0.939704 + 24.3843i) q^{63} +(-32.3040 - 55.2490i) q^{64} +(-27.8468 + 30.2772i) q^{65} +(40.9487 - 36.1634i) q^{66} +(57.5421 - 57.5421i) q^{67} +(24.2631 - 20.4350i) q^{68} +(-16.1807 + 37.0300i) q^{69} +(16.1190 - 5.88354i) q^{70} +(15.3918 + 15.3918i) q^{71} +(-70.1686 + 16.1358i) q^{72} +(-52.5418 + 52.5418i) q^{73} +(-2.03811 + 4.38120i) q^{74} +(-18.0029 + 41.2002i) q^{75} +(-6.34639 + 74.1023i) q^{76} -24.6877 q^{77} +(-77.9841 - 1.57452i) q^{78} -46.1756i q^{79} +(29.1911 + 41.3660i) q^{80} +(-6.23379 + 80.7598i) q^{81} +(-41.9475 + 90.1721i) q^{82} +(-88.7459 - 88.7459i) q^{83} +(28.5940 + 15.5243i) q^{84} +(-17.7444 + 17.7444i) q^{85} +(86.7865 - 31.6777i) q^{86} +(13.1884 - 30.1822i) q^{87} +(-19.0461 - 70.3077i) q^{88} +(96.2535 + 96.2535i) q^{89} +(54.2168 - 17.4547i) q^{90} +(25.9435 + 23.8610i) q^{91} +(34.7096 + 41.2118i) q^{92} +(-15.8799 + 6.22216i) q^{93} +(-54.8049 + 117.811i) q^{94} -58.8349i q^{95} +(-22.1519 + 93.4093i) q^{96} +(-42.4947 - 42.4947i) q^{97} +(28.5609 + 78.2474i) q^{98} +(-81.8863 - 3.15568i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 36 q^{6} - 64 q^{9} - 8 q^{13} + 80 q^{16} + 48 q^{18} + 8 q^{21} + 124 q^{24} - 8 q^{28} + 24 q^{33} + 64 q^{34} - 128 q^{37} - 136 q^{40} - 140 q^{42} - 160 q^{45} + 88 q^{46} - 108 q^{48} - 320 q^{52}+ \cdots + 336 q^{97}+O(q^{100}) \) 96 * q - 36 * q^6 - 64 * q^9 - 8 * q^13 + 80 * q^16 + 48 * q^18 + 8 * q^21 + 124 * q^24 - 8 * q^28 + 24 * q^33 + 64 * q^34 - 128 * q^37 - 136 * q^40 - 140 * q^42 - 160 * q^45 + 88 * q^46 - 108 * q^48 - 320 * q^52 - 216 * q^54 + 136 * q^57 + 280 * q^58 + 80 * q^60 - 464 * q^61 - 240 * q^66 - 120 * q^70 - 32 * q^72 + 288 * q^73 + 88 * q^76 - 296 * q^78 - 144 * q^81 + 204 * q^84 + 848 * q^85 - 392 * q^93 + 1384 * q^94 - 204 * q^96 + 336 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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