LMFDB - Embedded newform 156.3.l.c.47.19

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			47.19
Character	$\chi$	$=$	156.47
Dual form			156.3.l.c.83.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.685761 + 1.87876i) q^{2} +(-2.74902 - 1.20121i) q^{3} +(-3.05946 - 2.57676i) q^{4} +(-2.23749 + 2.23749i) q^{5} +(4.14196 - 4.34099i) q^{6} +(-1.91723 - 1.91723i) q^{7} +(6.93916 - 3.98095i) q^{8} +(6.11417 + 6.60431i) q^{9} +(-2.66932 - 5.73809i) q^{10} +(6.43837 - 6.43837i) q^{11} +(5.31528 + 10.7586i) 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} +(-16.6008 + 6.95808i) q^{18} +(13.1475 - 13.1475i) q^{19} +(12.6110 - 1.08005i) q^{20} +(2.96749 + 7.57350i) q^{21} +(7.68096 + 16.5113i) q^{22} -13.4703i q^{23} +(-23.8578 + 2.60829i) q^{24} +14.9872i q^{25} +(-7.88675 + 24.7750i) q^{26} +(-8.87477 - 25.4998i) q^{27} +(0.925460 + 10.8059i) q^{28} -10.9793i q^{29} +(0.445336 + 18.9805i) q^{30} +(4.01999 - 4.01999i) q^{31} +(-31.4881 - 5.70096i) q^{32} +(-25.4330 + 9.96532i) q^{33} +(-5.43842 + 14.8995i) q^{34} +8.57958 q^{35} +(-1.68839 - 35.9604i) 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} +(-16.2638 + 0.381593i) q^{42} +46.1935 q^{43} +(-36.2881 + 3.10784i) q^{44} +(-28.4575 - 1.09668i) q^{45} +(25.3074 + 9.23738i) q^{46} +(-45.9388 + 45.9388i) q^{47} +(11.4604 - 46.6118i) q^{48} -41.6485i q^{49} +(-28.1574 - 10.2777i) q^{50} +(-21.8010 - 9.52621i) q^{51} +(-41.1378 - 31.8070i) q^{52} -96.7348i q^{53} +(53.9939 + 0.813197i) q^{54} +28.8116i q^{55} +(-20.9364 - 5.67157i) q^{56} +(-51.9357 + 20.3497i) q^{57} +(20.6274 + 7.52915i) q^{58} +(19.8925 - 19.8925i) q^{59} +(-35.9652 - 12.1794i) 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} +(-1.28145 - 54.6163i) q^{66} +(-57.5421 + 57.5421i) q^{67} +(-24.2631 - 20.4350i) q^{68} +(-16.1807 + 37.0300i) q^{69} +(-5.88354 + 16.1190i) q^{70} +(-15.3918 - 15.3918i) q^{71} +(68.7187 + 21.4881i) q^{72} +(-52.5418 + 52.5418i) q^{73} +(2.03811 + 4.38120i) q^{74} +(18.0029 - 41.2002i) q^{75} +(-74.1023 + 6.34639i) q^{76} -24.6877 q^{77} +(51.4408 - 58.6331i) q^{78} +46.1756i q^{79} +(-41.3660 - 29.1911i) q^{80} +(-6.23379 + 80.7598i) q^{81} +(41.9475 + 90.1721i) q^{82} +(88.7459 + 88.7459i) q^{83} +(10.4361 - 30.8174i) q^{84} +(-17.7444 + 17.7444i) q^{85} +(-31.6777 + 86.7865i) q^{86} +(-13.1884 + 30.1822i) q^{87} +(19.0461 - 70.3077i) q^{88} +(96.2535 + 96.2535i) q^{89} +(21.5754 - 52.7127i) 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} +(79.7131 + 53.4959i) q^{96} +(-42.4947 - 42.4947i) q^{97} +(78.2474 + 28.5609i) 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 $

$2$	−0.685761	+	1.87876i	−0.342880	+	0.939379i
$2$	−0.685761	+	1.87876i	−0.342880	+	0.939379i
$3$	−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	$0.352484\pi$
$6$	4.14196	−	4.34099i	0.690326	−	0.723498i
$7$	−1.91723	−	1.91723i	−0.273890	−	0.273890i	0.556774	−	0.830664i	$-0.312039\pi$
$7$	−1.91723	−	1.91723i	−0.273890	−	0.273890i	−0.830664	+	0.556774i	$0.812039\pi$
$8$	6.93916	−	3.98095i	0.867396	−	0.497619i
$9$	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	−0.351050	−	0.936357i	$-0.614175\pi$
$11$	6.43837	−	6.43837i	0.585306	−	0.585306i	0.936357	+	0.351050i	$0.114175\pi$
$12$	5.31528	+	10.7586i	0.442940	+	0.896551i
$13$	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	$0.425064\pi$
$18$	−16.6008	+	6.95808i	−0.922264	+	0.386560i
$19$	13.1475	−	13.1475i	0.691974	−	0.691974i	−0.270692	−	0.962666i	$-0.587252\pi$
$19$	13.1475	−	13.1475i	0.691974	−	0.691974i	0.962666	+	0.270692i	$0.0872525\pi$
$20$	12.6110	−	1.08005i	0.630550	−	0.0540026i
$21$	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	$-0.905402\pi$
$23$		−	13.4703i		−	0.585664i	0.956164	−	0.292832i	$-0.0945977\pi$
$24$	−23.8578	+	2.60829i	−0.994077	+	0.108679i
$25$			14.9872i			0.599490i
$26$	−7.88675	+	24.7750i	−0.303337	+	0.952883i
$27$	−8.87477	−	25.4998i	−0.328695	−	0.944436i
$28$	0.925460	+	10.8059i	0.0330521	+	0.385926i
$29$		−	10.9793i		−	0.378595i	−0.981920	−	0.189298i	$-0.939379\pi$
$29$		−	10.9793i		−	0.378595i	0.981920	−	0.189298i	$-0.0606211\pi$
$30$	0.445336	+	18.9805i	0.0148445	+	0.632685i
$31$	4.01999	−	4.01999i	0.129677	−	0.129677i	−0.639289	−	0.768966i	$-0.720771\pi$
$31$	4.01999	−	4.01999i	0.129677	−	0.129677i	0.768966	+	0.639289i	$0.220771\pi$
$32$	−31.4881	−	5.70096i	−0.984002	−	0.178155i
$33$	−25.4330	+	9.96532i	−0.770698	+	0.301979i
$34$	−5.43842	+	14.8995i	−0.159954	+	0.438220i
$35$	8.57958			0.245131
$36$	−1.68839	−	35.9604i	−0.0468997	−	0.998900i
$37$	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	$0.0426084\pi$
$42$	−16.2638	+	0.381593i	−0.387233	+	0.00908555i
$43$	46.1935			1.07427			0.537134	−	0.843497i	$-0.319507\pi$
$43$	46.1935			1.07427			0.537134	+	0.843497i	$0.319507\pi$
$44$	−36.2881	+	3.10784i	−0.824729	+	0.0706328i
$45$	−28.4575	−	1.09668i	−0.632389	−	0.0243706i
$46$	25.3074	+	9.23738i	0.550160	+	0.200813i
$47$	−45.9388	+	45.9388i	−0.977422	+	0.977422i	−0.999751	−	0.0223285i	$-0.992892\pi$
$47$	−45.9388	+	45.9388i	−0.977422	+	0.977422i	0.0223285	+	0.999751i	$0.492892\pi$
$48$	11.4604	−	46.6118i	0.238759	−	0.971079i
$49$		−	41.6485i		−	0.849968i
$50$	−28.1574	−	10.2777i	−0.563148	−	0.205553i
$51$	−21.8010	−	9.52621i	−0.427471	−	0.186788i
$52$	−41.1378	−	31.8070i	−0.791111	−	0.611673i
$53$		−	96.7348i		−	1.82518i	−0.408870	−	0.912592i	$-0.634077\pi$
$53$		−	96.7348i		−	1.82518i	0.408870	−	0.912592i	$-0.365923\pi$
$54$	53.9939	+	0.813197i	0.999887	+	0.0150592i
$55$			28.8116i			0.523847i
$56$	−20.9364	−	5.67157i	−0.373864	−	0.101278i
$57$	−51.9357	+	20.3497i	−0.911152	+	0.357013i
$58$	20.6274	+	7.52915i	0.355645	+	0.129813i
$59$	19.8925	−	19.8925i	0.337162	−	0.337162i	−0.518136	−	0.855298i	$-0.673374\pi$
$59$	19.8925	−	19.8925i	0.337162	−	0.337162i	0.855298	+	0.518136i	$0.173374\pi$
$60$	−35.9652	−	12.1794i	−0.599420	−	0.202990i
$61$	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
$66$	−1.28145	−	54.6163i	−0.0194159	−	0.827520i
$67$	−57.5421	+	57.5421i	−0.858838	+	0.858838i	−0.991201	−	0.132364i	$-0.957743\pi$
$67$	−57.5421	+	57.5421i	−0.858838	+	0.858838i	0.132364	+	0.991201i	$0.457743\pi$
$68$	−24.2631	−	20.4350i	−0.356810	−	0.300514i
$69$	−16.1807	+	37.0300i	−0.234502	+	0.536666i
$70$	−5.88354	+	16.1190i	−0.0840506	+	0.230271i
$71$	−15.3918	−	15.3918i	−0.216785	−	0.216785i	0.590357	−	0.807142i	$-0.298987\pi$
$71$	−15.3918	−	15.3918i	−0.216785	−	0.216785i	−0.807142	+	0.590357i	$0.798987\pi$
$72$	68.7187	+	21.4881i	0.954426	+	0.298446i
$73$	−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
$76$	−74.1023	+	6.34639i	−0.975030	+	0.0835051i
$77$	−24.6877			−0.320619
$78$	51.4408	−	58.6331i	0.659498	−	0.751707i
$79$			46.1756i			0.584501i	0.956342	+	0.292251i	$0.0944042\pi$
$79$			46.1756i			0.584501i	−0.956342	+	0.292251i	$0.905596\pi$
$80$	−41.3660	−	29.1911i	−0.517074	−	0.364889i
$81$	−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	$0.0228775\pi$
$83$	88.7459	+	88.7459i	1.06923	+	1.06923i	0.0718100	+	0.997418i	$0.477122\pi$
$84$	10.4361	−	30.8174i	0.124240	−	0.366873i
$85$	−17.7444	+	17.7444i	−0.208758	+	0.208758i
$86$	−31.6777	+	86.7865i	−0.368346	+	1.00915i
$87$	−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	$0.472869\pi$
$90$	21.5754	−	52.7127i	0.239727	−	0.585697i
$91$	−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
$96$	79.7131	+	53.4959i	0.830345	+	0.557249i
$97$	−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	$0.850254\pi$
$98$	78.2474	+	28.5609i	0.798442	+	0.291438i
$99$	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	$0.365728\pi$
$102$	32.8477	−	34.4262i	0.322037	−	0.337512i
$103$	−136.814			−1.32829			−0.664144	−	0.747605i	$-0.731204\pi$
$103$	−136.814			−1.32829			−0.664144	+	0.747605i	$0.731204\pi$
$104$	87.9683	−	55.4759i	0.845849	−	0.533422i
$105$	−23.5854	−	10.3059i	−0.224623	−	0.0981515i
$106$	181.741	+	66.3369i	1.71454	+	0.625820i
$107$	93.4017			0.872913			0.436457	−	0.899725i	$-0.356233\pi$
$107$	93.4017			0.872913			0.436457	+	0.899725i	$0.356233\pi$
$108$	−38.5547	+	100.884i	−0.356988	+	0.934109i
$109$	−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	$0.970567\pi$
$110$	−54.1300	−	19.7579i	−0.492091	−	0.179617i
$111$	−6.74854	+	2.64425i	−0.0607976	+	0.0238221i
$112$	25.0129	−	35.4451i	0.223329	−	0.316474i
$113$		−	85.7284i		−	0.758658i	−0.925262	−	0.379329i	$-0.876155\pi$
$113$		−	85.7284i		−	0.758658i	0.925262	−	0.379329i	$-0.123845\pi$
$114$	−2.61679	−	111.530i	−0.0229543	−	0.978330i
$115$	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
$120$	47.5457	−	59.2178i	0.396215	−	0.493482i
$121$			38.0948i			0.314833i
$122$	−73.9881	+	202.703i	−0.606460	+	1.66150i
$123$	−138.896	+	54.4229i	−1.12923	+	0.442463i
$124$	−22.6576	+	1.94048i	−0.182722	+	0.0156490i
$125$	−89.4712	−	89.4712i	−0.715770	−	0.715770i
$126$	45.1677	+	18.4873i	0.358474	+	0.146724i
$127$	93.7596			0.738265			0.369132	−	0.929377i	$-0.379655\pi$
$127$	93.7596			0.738265			0.369132	+	0.929377i	$0.379655\pi$
$128$	81.6467	+	98.5790i	0.637864	+	0.770149i
$129$	−126.987	−	55.4883i	−0.984394	−	0.430142i
$130$	−37.7873	−	73.0804i	−0.290671	−	0.562157i
$131$	56.4833			0.431170			0.215585	−	0.976485i	$-0.430834\pi$
$131$	56.4833			0.431170			0.215585	+	0.976485i	$0.430834\pi$
$132$	103.490	+	35.0462i	0.784013	+	0.265502i
$133$	−50.4136			−0.379050
$134$	−68.6476	−	147.568i	−0.512295	−	1.10125i
$135$	76.9128	+	37.1983i	0.569725	+	0.275543i
$136$	55.0310	−	31.5709i	0.404640	−	0.232139i
$137$	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	$0.733668\pi$
$138$	−58.4743	−	55.7933i	−0.423727	−	0.404299i
$139$		−	157.438i		−	1.13265i	−0.824183	−	0.566324i	$-0.808365\pi$
$139$		−	157.438i		−	1.13265i	0.824183	−	0.566324i	$-0.191635\pi$
$140$	−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
$144$	−87.4956	+	114.370i	−0.607609	+	0.794237i
$145$	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
$148$	−9.62887	+	0.824652i	−0.0650599	+	0.00557197i
$149$	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	$0.136956\pi$
$150$	65.0595	+	62.0765i	0.433730	+	0.413844i
$151$	95.2616	+	95.2616i	0.630871	+	0.630871i	0.948287	−	0.317415i	$-0.102815\pi$
$151$	95.2616	+	95.2616i	0.630871	+	0.630871i	−0.317415	+	0.948287i	$0.602815\pi$
$152$	38.8931	−	143.572i	0.255876	−	0.944555i
$153$	48.4884	+	52.3754i	0.316918	+	0.342323i
$154$	16.9298	−	46.3822i	0.109934	−	0.301183i
$155$			17.9894i			0.116061i
$156$	74.8813	+	136.853i	0.480008	+	0.877264i
$157$	−174.497			−1.11145			−0.555724	−	0.831367i	$-0.687559\pi$
$157$	−174.497			−1.11145			−0.555724	+	0.831367i	$0.687559\pi$
$158$	−86.7528	−	31.6654i	−0.549068	−	0.200414i
$159$	−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
$162$	−147.453	−	67.0937i	−0.910205	−	0.414158i
$163$	−204.207	−	204.207i	−1.25280	−	1.25280i	−0.954459	−	0.298343i	$-0.903566\pi$
$163$	−204.207	−	204.207i	−1.25280	−	1.25280i	−0.298343	−	0.954459i	$-0.596434\pi$
$164$	−198.178	+	16.9726i	−1.20840	+	0.103492i
$165$	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	−0.891697	−	0.452632i	$-0.850485\pi$
$167$	−73.3239	+	73.3239i	−0.439066	+	0.439066i	0.452632	+	0.891697i	$0.350485\pi$
$168$	50.7417	+	40.7403i	0.302034	+	0.242502i
$169$	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	$0.543912\pi$
$174$	−47.6609	−	45.4756i	−0.273913	−	0.261354i
$175$	28.7340	−	28.7340i	0.164194	−	0.164194i
$176$	119.030	+	83.9972i	0.676308	+	0.477257i
$177$	−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	$-0.573412\pi$
$179$		−	348.521i		−	1.94704i	0.228591	−	0.973522i	$-0.426588\pi$
$180$	84.2389	+	76.6834i	0.467994	+	0.426019i
$181$			170.140i			0.940001i	0.882666	+	0.470000i	$0.155746\pi$
$181$			170.140i			0.940001i	−0.882666	+	0.470000i	$0.844254\pi$
$182$	62.6201	−	32.3786i	0.344066	−	0.177905i
$183$	−296.597	−	129.601i	−1.62075	−	0.708204i
$184$	−53.6245	−	93.4724i	−0.291438	−	0.508002i
$185$			7.64503i			0.0413245i
$186$	−0.800113	−	34.1014i	−0.00430168	−	0.183341i
$187$	51.0594	−	51.0594i	0.273045	−	0.273045i
$188$	258.921	−	22.1750i	1.37724	−	0.117952i
$189$	−31.8740	+	65.9039i	−0.168645	+	0.348698i
$190$	−110.537	−	40.3467i	−0.581771	−	0.212351i
$191$	−364.231			−1.90697			−0.953483	−	0.301445i	$-0.902531\pi$
$191$	−364.231			−1.90697			−0.953483	+	0.301445i	$0.902531\pi$
$192$	−155.170	+	113.076i	−0.808177	+	0.588939i
$193$	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	$0.465989\pi$
$198$	−62.0832	+	151.680i	−0.313551	+	0.766063i
$199$	217.321			1.09207			0.546033	−	0.837764i	$-0.316137\pi$
$199$	217.321			1.09207			0.546033	+	0.837764i	$0.316137\pi$
$200$	59.6635	+	103.999i	0.298318	+	0.519995i
$201$	227.305	−	89.0638i	1.13087	−	0.443103i
$202$	−56.7154	+	155.382i	−0.280769	+	0.769216i
$203$	−21.0498	+	21.0498i	−0.103694	+	0.103694i
$204$	42.1528	+	85.3211i	0.206631	+	0.418241i
$205$			157.347i			0.767546i
$206$	93.8215	−	257.040i	0.455444	−	1.24777i
$207$	88.9618	−	82.3596i	0.429767	−	0.397872i
$208$	43.9006	+	203.314i	0.211060	+	0.977473i
$209$		−	169.297i		−	0.810034i
$210$	35.5363	−	37.2439i	0.169220	−	0.177352i
$211$			16.1284i			0.0764381i	0.999269	+	0.0382191i	$0.0121685\pi$
$211$			16.1284i			0.0764381i	−0.999269	+	0.0382191i	$0.987832\pi$
$212$	−249.262	+	295.957i	−1.17576	+	1.39602i
$213$	23.8234	+	60.8010i	0.111847	+	0.285451i
$214$	−64.0512	+	175.479i	−0.299305	+	0.819996i
$215$	−103.358	+	103.358i	−0.480734	+	0.480734i
$216$	−163.097	−	141.617i	−0.755078	−	0.655635i
$217$	−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
$222$	−0.340027	−	14.4922i	−0.00153165	−	0.0652801i
$223$	−216.887	+	216.887i	−0.972590	+	0.972590i	−0.999634	−	0.0270445i	$-0.991390\pi$
$223$	−216.887	+	216.887i	−0.972590	+	0.972590i	0.0270445	+	0.999634i	$0.491390\pi$
$224$	49.4399	+	71.3000i	0.220714	+	0.318303i
$225$	−98.9804	+	91.6346i	−0.439913	+	0.407265i
$226$	161.063	+	58.7891i	0.712667	+	0.260129i
$227$	170.053	+	170.053i	0.749133	+	0.749133i	0.974316	−	0.225184i	$-0.0722982\pi$
$227$	170.053	+	170.053i	0.749133	+	0.749133i	−0.225184	+	0.974316i	$0.572298\pi$
$228$	211.332	+	71.5663i	0.926893	+	0.313887i
$229$	−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
$232$	−43.7079	−	76.1869i	−0.188396	−	0.328392i
$233$	−127.409			−0.546818			−0.273409	−	0.961898i	$-0.588151\pi$
$233$	−127.409			−0.546818			−0.273409	+	0.961898i	$0.588151\pi$
$234$	−211.843	+	99.3919i	−0.905310	+	0.424752i
$235$		−	205.576i		−	0.874790i
$236$	−112.119	+	9.60226i	−0.475080	+	0.0406875i
$237$	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	0.726535	−	0.687129i	$-0.241129\pi$
$239$	9.41795	+	9.41795i	0.0394057	+	0.0394057i	−0.687129	+	0.726535i	$0.741129\pi$
$240$	78.6509	+	129.936i	0.327712	+	0.541401i
$241$	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	$-0.170167\pi$
$242$	−71.5709	−	26.1239i	−0.295748	−	0.107950i
$243$	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
$246$	−6.99830	−	298.272i	−0.0284484	−	1.21249i
$247$	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	$-0.915485\pi$
$251$		−	131.726i		−	0.524804i	0.964959	−	0.262402i	$-0.0845147\pi$
$252$	−65.7073	+	72.1814i	−0.260743	+	0.286434i
$253$	−86.7266	−	86.7266i	−0.342793	−	0.342793i
$254$	−64.2967	+	176.152i	−0.253137	+	0.693510i
$255$	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	$0.408918\pi$
$258$	191.332	−	200.526i	0.741596	−	0.777232i
$259$	−6.55076			−0.0252925
$260$	163.213	−	20.8775i	0.627744	−	0.0802980i
$261$	72.5105	−	67.1291i	0.277818	−	0.257200i
$262$	−38.7340	+	106.118i	−0.147840	+	0.405032i
$263$	−73.5496			−0.279656			−0.139828	−	0.990176i	$-0.544655\pi$
$263$	−73.5496			−0.279656			−0.139828	+	0.990176i	$0.544655\pi$
$264$	−136.813	+	170.399i	−0.518229	+	0.645450i
$265$	216.443	+	216.443i	0.816768	+	0.816768i
$266$	34.5717	−	94.7150i	0.129969	−	0.356071i
$267$	−148.981	−	380.223i	−0.557982	−	1.42406i
$268$	324.320	−	27.7760i	1.21015	−	0.103642i
$269$			329.441i			1.22469i	0.790591	+	0.612345i	$0.209774\pi$
$269$			329.441i			1.22469i	−0.790591	+	0.612345i	$0.790226\pi$
$270$	−122.630	+	118.991i	−0.454187	+	0.440709i
$271$	−163.971	−	163.971i	−0.605061	−	0.605061i	0.336590	−	0.941651i	$-0.390726\pi$
$271$	−163.971	−	163.971i	−0.605061	−	0.605061i	−0.941651	+	0.336590i	$0.890726\pi$
$272$	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
$276$	144.921	−	71.5982i	0.525078	−	0.259414i
$277$		−	165.945i		−	0.599078i	−0.954084	−	0.299539i	$-0.903167\pi$
$277$		−	165.945i		−	0.599078i	0.954084	−	0.299539i	$-0.0968329\pi$
$278$	295.788	+	107.965i	1.06399	+	0.388363i
$279$	51.1282	+	1.97034i	0.183255	+	0.00706217i
$280$	59.5351	−	34.1549i	0.212625	−	0.121982i
$281$	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	$0.738989\pi$
$282$	9.14337	+	389.697i	0.0324233	+	1.38190i
$283$	330.563			1.16807			0.584033	−	0.811730i	$-0.301474\pi$
$283$	330.563			1.16807			0.584033	+	0.811730i	$0.301474\pi$
$284$	7.42971	+	86.7514i	0.0261609	+	0.305463i
$285$	70.6733	−	161.738i	0.247976	−	0.567502i
$286$	108.733	+	210.288i	0.380184	+	0.735273i
$287$	−134.825			−0.469774
$288$	−154.873	−	242.814i	−0.537752	−	0.843103i
$289$	−226.107			−0.782378
$290$	−63.0001	+	29.3072i	−0.217242	+	0.101059i
$291$	65.7734	+	167.864i	0.226025	+	0.576851i
$292$	296.137	−	25.3623i	1.01417	−	0.0868572i
$293$	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	$0.733974\pi$
$294$	−180.796	−	172.506i	−0.614951	−	0.586755i
$295$			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
$300$	−161.242	+	79.6614i	−0.537473	+	0.265538i
$301$	−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
$304$	243.066	+	171.527i	0.799560	+	0.564234i
$305$	−241.408	+	241.408i	−0.791500	+	0.791500i
$306$	−131.652	+	55.1809i	−0.430236	+	0.180330i
$307$	330.034	+	330.034i	1.07503	+	1.07503i	0.996947	+	0.0780834i	$0.0248800\pi$
$307$	330.034	+	330.034i	1.07503	+	1.07503i	0.0780834	+	0.996947i	$0.475120\pi$
$308$	75.5311	+	63.6142i	0.245231	+	0.206539i
$309$	376.103	+	164.342i	1.21716	+	0.531853i
$310$	−33.7978	−	12.3364i	−0.109025	−	0.0397950i
$311$			291.242i			0.936470i	0.883604	+	0.468235i	$0.155110\pi$
$311$			291.242i			0.936470i	−0.883604	+	0.468235i	$0.844890\pi$
$312$	−308.465	+	46.8354i	−0.988669	+	0.150113i
$313$	342.505			1.09427			0.547133	−	0.837046i	$-0.315719\pi$
$313$	342.505			1.09427			0.547133	+	0.837046i	$0.315719\pi$
$314$	119.663	−	327.838i	0.381094	−	1.04407i
$315$	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	$0.900675\pi$
$318$	−419.925	−	400.671i	−1.32052	−	1.25997i
$319$	−70.6886	−	70.6886i	−0.221594	−	0.221594i
$320$	51.3392	+	195.899i	0.160435	+	0.612185i
$321$	−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
$324$	227.170	−	231.019i	0.701143	−	0.713021i
$325$	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
$330$	125.071	+	119.336i	0.379003	+	0.361626i
$331$	−386.713	+	386.713i	−1.16832	+	1.16832i	−0.185715	+	0.982604i	$0.559460\pi$
$331$	−386.713	+	386.713i	−1.16832	+	1.16832i	−0.982604	+	0.185715i	$0.940540\pi$
$332$	−42.8383	−	500.192i	−0.129031	−	1.50660i
$333$	21.7281	+	0.837344i	0.0652497	+	0.00251455i
$334$	−87.4753	−	188.041i	−0.261902	−	0.562996i
$335$		−	257.500i		−	0.768657i
$336$	−111.338	+	67.3932i	−0.331363	+	0.200575i
$337$		−	61.3087i		−	0.181925i	−0.995854	−	0.0909625i	$-0.971006\pi$
$337$		−	61.3087i		−	0.181925i	0.995854	−	0.0909625i	$-0.0289944\pi$
$338$	−88.9829	+	326.077i	−0.263263	+	0.964724i
$339$	−102.978	+	235.669i	−0.303770	+	0.695188i
$340$	100.011	−	8.56535i	0.294151	−	0.0251922i
$341$		−	51.7644i		−	0.151802i
$342$	−126.777	+	309.740i	−0.370694	+	0.905672i
$343$	−173.794	+	173.794i	−0.506688	+	0.506688i
$344$	320.545	−	183.894i	0.931816	−	0.534577i
$345$	−46.6502	−	119.058i	−0.135218	−	0.345097i
$346$	32.6288	−	89.3921i	0.0943028	−	0.258359i
$347$	27.4780			0.0791872			0.0395936	−	0.999216i	$-0.487394\pi$
$347$	27.4780			0.0791872			0.0395936	+	0.999216i	$0.487394\pi$
$348$	118.122	−	58.3579i	0.339430	−	0.167695i
$349$	−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	$0.430785\pi$
$354$	−3.95928	−	168.747i	−0.0111844	−	0.476687i
$355$	68.8779			0.194022
$356$	−46.4622	−	542.506i	−0.130512	−	1.52389i
$357$	23.5337	+	60.0616i	0.0659207	+	0.168240i
$358$	654.787	+	239.002i	1.82901	+	0.667604i
$359$	−43.0730	+	43.0730i	−0.119981	+	0.119981i	−0.764548	−	0.644567i	$-0.777038\pi$
$359$	−43.0730	+	43.0730i	−0.119981	+	0.119981i	0.644567	+	0.764548i	$0.277038\pi$
$360$	−201.837	+	105.678i	−0.560659	+	0.293550i
$361$			15.2861i			0.0423437i
$362$	−319.652	−	116.675i	−0.883017	−	0.322308i
$363$	45.7600	−	104.723i	0.126061	−	0.288494i
$364$	17.8892	+	139.852i	0.0491462	+	0.384209i
$365$		−	235.124i		−	0.644175i
$366$	446.884	−	468.358i	1.22099	−	1.27967i
$367$			499.591i			1.36128i	0.732616	+	0.680642i	$0.238299\pi$
$367$			499.591i			1.36128i	−0.732616	+	0.680642i	$0.761701\pi$
$368$	212.386	−	36.6478i	0.577135	−	0.0995864i
$369$	447.200	+	17.2339i	1.21192	+	0.0467043i
$370$	−14.3632	−	5.24266i	−0.0388193	−	0.0141694i
$371$	−185.463	+	185.463i	−0.499900	+	0.499900i
$372$	64.6170	+	21.8822i	0.173702	+	0.0588231i
$373$	−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
$378$	−101.960	−	105.078i	−0.269735	−	0.277984i
$379$	−468.317	+	468.317i	−1.23567	+	1.23567i	−0.273911	+	0.961755i	$0.588317\pi$
$379$	−468.317	+	468.317i	−1.23567	+	1.23567i	−0.961755	+	0.273911i	$0.911683\pi$
$380$	151.603	−	180.003i	0.398956	−	0.473693i
$381$	−257.747	−	112.625i	−0.676500	−	0.295605i
$382$	249.775	−	684.301i	0.653862	−	1.79136i
$383$	−101.144	−	101.144i	−0.264083	−	0.264083i	0.562627	−	0.826711i	$-0.309791\pi$
$383$	−101.144	−	101.144i	−0.264083	−	0.264083i	−0.826711	+	0.562627i	$0.809791\pi$
$384$	−106.033	−	369.070i	−0.276129	−	0.961121i
$385$	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
$388$	20.5125	+	239.509i	0.0528672	+	0.617293i
$389$	456.268			1.17293			0.586463	−	0.809976i	$-0.300520\pi$
$389$	456.268			1.17293			0.586463	+	0.809976i	$0.300520\pi$
$390$	16.0927	+	246.290i	0.0412633	+	0.631512i
$391$		−	106.826i		−	0.273212i
$392$	−165.801	−	289.005i	−0.422961	−	0.737259i
$393$	−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
$396$	−242.397	−	220.656i	−0.612113	−	0.557211i
$397$	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	$0.0699189\pi$
$398$	−149.030	+	408.294i	−0.374448	+	1.02586i
$399$	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	$0.896762\pi$
$402$	11.4528	+	488.127i	0.0284896	+	1.21425i
$403$	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
$408$	−189.204	+	20.6850i	−0.463736	+	0.0506985i
$409$	−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	$0.791697\pi$
$410$	−295.617	−	107.902i	−0.721016	−	0.263176i
$411$	−15.3800	−	39.2520i	−0.0374208	−	0.0955036i
$412$	418.577	+	352.536i	1.01596	+	0.855669i
$413$	−76.2772			−0.184691
$414$	93.7272	+	223.617i	0.226394	+	0.540137i
$415$	−397.137			−0.956956
$416$	−412.084	−	56.9465i	−0.990586	−	0.136891i
$417$	−189.117	+	432.799i	−0.453517	+	1.03789i
$418$	318.068	+	116.097i	0.760929	+	0.277745i
$419$	354.855			0.846909			0.423454	−	0.905917i	$-0.360817\pi$
$419$	354.855			0.846909			0.423454	+	0.905917i	$0.360817\pi$
$420$	45.6029	+	92.3044i	0.108578	+	0.219772i
$421$	−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	$0.830143\pi$
$422$	−30.3014	−	11.0603i	−0.0718044	−	0.0262091i
$423$	−584.272	−	22.5163i	−1.38126	−	0.0532300i
$424$	−385.097	−	671.259i	−0.908247	−	1.58316i
$425$			118.856i			0.279662i
$426$	−130.568	+	3.06348i	−0.306496	+	0.00719126i
$427$	−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	0.540376	−	0.841424i	$-0.318282\pi$
$431$	−129.751	−	129.751i	−0.301047	−	0.301047i	−0.841424	+	0.540376i	$0.818282\pi$
$432$	377.910	−	209.304i	0.874791	−	0.484500i
$433$		−	277.129i		−	0.640020i	−0.947414	−	0.320010i	$-0.896314\pi$
$433$		−	277.129i		−	0.640020i	0.947414	−	0.320010i	$-0.103686\pi$
$434$	10.5707	−	28.9601i	0.0243564	−	0.0667285i
$435$	−38.0234	−	97.0414i	−0.0874100	−	0.223084i
$436$	47.5320	+	554.997i	0.109018	+	1.27293i
$437$	−177.101	−	177.101i	−0.405264	−	0.405264i
$438$	10.4576	+	445.710i	0.0238758	+	1.01760i
$439$	824.382			1.87786			0.938932	−	0.344104i	$-0.111817\pi$
$439$	824.382			1.87786			0.938932	+	0.344104i	$0.111817\pi$
$440$	114.698	+	199.929i	0.260677	+	0.454383i
$441$	275.059	−	254.646i	0.623717	−	0.577428i
$442$	−62.5458	+	196.478i	−0.141506	+	0.444520i
$443$	296.524			0.669354			0.334677	−	0.942333i	$-0.391373\pi$
$443$	296.524			0.669354			0.334677	+	0.942333i	$0.391373\pi$
$444$	27.4605	+	9.29935i	0.0618480	+	0.0209445i
$445$	−430.733			−0.967939
$446$	−258.746	−	556.212i	−0.580148	−	1.24711i
$447$	−289.436	+	113.408i	−0.647507	+	0.253710i
$448$	−167.859	+	43.9908i	−0.374686	+	0.0981938i
$449$	−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	$0.801381\pi$
$450$	−104.282	−	248.800i	−0.231739	−	0.552888i
$451$		−	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
$456$	−279.379	+	347.964i	−0.612673	+	0.763078i
$457$	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
$460$	−14.5486	−	169.874i	−0.0316274	−	0.369291i
$461$	−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	$0.404427\pi$
$462$	−102.255	+	107.169i	−0.221332	+	0.231967i
$463$	−141.035	−	141.035i	−0.304612	−	0.304612i	0.538203	−	0.842815i	$-0.319103\pi$
$463$	−141.035	−	141.035i	−0.304612	−	0.304612i	−0.842815	+	0.538203i	$0.819103\pi$
$464$	173.110	−	29.8706i	0.373082	−	0.0643764i
$465$	21.6091	−	49.4532i	0.0464713	−	0.106351i
$466$	87.3718	−	239.370i	0.187493	−	0.513669i
$467$			546.532i			1.17030i	0.810923	+	0.585152i	$0.198965\pi$
$467$			546.532i			1.17030i	−0.810923	+	0.585152i	$0.801035\pi$
$468$	−41.4601	−	466.160i	−0.0885899	−	0.996068i
$469$	220.643			0.470454
$470$	386.227	+	140.976i	0.821760	+	0.299948i
$471$	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
$474$	200.448	+	191.257i	0.422886	+	0.403497i
$475$	197.045	+	197.045i	0.414832	+	0.414832i
$476$	7.33935	+	85.6964i	0.0154188	+	0.180034i
$477$	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	−0.814187	−	0.580602i	$-0.802817\pi$
$479$	−111.887	+	111.887i	−0.233585	+	0.233585i	0.580602	+	0.814187i	$0.302817\pi$
$480$	−298.054	+	58.6608i	−0.620947	+	0.122210i
$481$	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
$486$	324.757	+	361.564i	0.668225	+	0.743959i
$487$	149.033	−	149.033i	0.306022	−	0.306022i	−0.537343	−	0.843364i	$-0.680572\pi$
$487$	149.033	−	149.033i	0.306022	−	0.306022i	0.843364	+	0.537343i	$0.180572\pi$
$488$	748.680	−	429.513i	1.53418	−	0.880149i
$489$	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	$-0.855057\pi$
$491$		−	431.862i		−	0.879555i	0.898107	−	0.439778i	$-0.144943\pi$
$492$	565.181	+	191.395i	1.14874	+	0.389015i
$493$		−	87.0710i		−	0.176615i
$494$	222.038	+	429.420i	0.449470	+	0.869272i
$495$	−190.281	+	176.159i	−0.384406	+	0.355877i
$496$	74.3202	+	52.4463i	0.149839	+	0.105738i
$497$			59.0191i			0.118751i
$498$	752.827	−	17.6634i	1.51170	−	0.0354687i
$499$	249.737	−	249.737i	0.500475	−	0.500475i	−0.411111	−	0.911586i	$-0.634859\pi$
$499$	249.737	−	249.737i	0.500475	−	0.500475i	0.911586	+	0.411111i	$0.134859\pi$
$500$	43.1883	+	504.279i	0.0863767	+	1.00856i
$501$	289.646	−	113.491i	0.578136	−	0.226529i
$502$	247.481	+	90.3324i	0.492990	+	0.179945i
$503$	19.5125			0.0387923			0.0193961	−	0.999812i	$-0.493826\pi$
$503$	19.5125			0.0387923			0.0193961	+	0.999812i	$0.493826\pi$
$504$	−90.5519	−	172.947i	−0.179666	−	0.343150i
$505$	−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	$0.117476\pi$
$510$	3.53173	+	150.525i	0.00692497	+	0.295147i
$511$	201.470			0.394265
$512$	4.21922	−	511.983i	0.00824067	−	0.999966i
$513$	−451.940	−	218.577i	−0.880974	−	0.426077i
$514$	−99.4886	+	272.566i	−0.193558	+	0.530284i
$515$	306.120	−	306.120i	0.594407	−	0.594407i
$516$	245.532	+	496.979i	0.475836	+	0.963137i
$517$			591.542i			1.14418i
$518$	4.49225	−	12.3073i	0.00867231	−	0.0237593i
$519$	130.799	+	57.1542i	0.252022	+	0.110124i
$520$	−72.7016	+	320.955i	−0.139811	+	0.617222i
$521$			554.046i			1.06343i	0.846924	+	0.531714i	$0.178452\pi$
$521$			554.046i			1.06343i	−0.846924	+	0.531714i	$0.821548\pi$
$522$	76.3946	+	182.264i	0.146350	+	0.349165i
$523$		−	565.353i		−	1.08098i	−0.841350	−	0.540491i	$-0.818239\pi$
$523$		−	565.353i		−	1.08098i	0.841350	−	0.540491i	$-0.181761\pi$
$524$	−172.809	−	145.544i	−0.329787	−	0.277755i
$525$	−113.506	+	44.4746i	−0.216202	+	0.0847135i
$526$	50.4374	−	138.182i	0.0958887	−	0.262703i
$527$	31.8805	−	31.8805i	0.0604944	−	0.0604944i
$528$	−226.317	−	373.890i	−0.428631	−	0.708126i
$529$	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
$534$	816.513	−	19.1577i	1.52905	−	0.0358758i
$535$	−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
$538$	−618.941	−	225.918i	−1.15045	−	0.419922i
$539$	−268.148	−	268.148i	−0.497492	−	0.497492i
$540$	−139.461	−	311.993i	−0.258261	−	0.577764i
$541$	−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
$544$	−249.716	−	45.2114i	−0.459037	−	0.0831092i
$545$	440.651			0.808533
$546$	−211.037	+	13.7893i	−0.386515	+	0.0252551i
$547$		−	745.007i		−	1.36199i	−0.732289	−	0.680994i	$-0.761548\pi$
$547$		−	745.007i		−	1.36199i	0.732289	−	0.680994i	$-0.238452\pi$
$548$	−4.79648	−	56.0051i	−0.00875270	−	0.102199i
$549$	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
$552$	35.1343	+	321.372i	0.0636491	+	0.582195i
$553$	88.5293	−	88.5293i	0.160089	−	0.160089i
$554$	311.770	+	113.798i	0.562761	+	0.205412i
$555$	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	$0.606148\pi$
$558$	−38.7635	+	94.7064i	−0.0694687	+	0.169725i
$559$	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	$0.296800\pi$
$563$			904.253i			1.60613i	−0.595890	+	0.803066i	$0.703200\pi$
$564$	−738.416	−	250.061i	−1.30925	−	0.443370i
$565$	191.817	+	191.817i	0.339498	+	0.339498i
$566$	−226.687	+	621.047i	−0.400507	+	1.09726i
$567$	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	$0.808666\pi$
$570$	255.402	+	243.692i	0.448073	+	0.427529i
$571$	−472.192			−0.826956			−0.413478	−	0.910514i	$-0.635686\pi$
$571$	−472.192			−0.826956			−0.413478	+	0.910514i	$0.635686\pi$
$572$	−469.645	+	60.0748i	−0.821058	+	0.105026i
$573$	1001.28	+	437.519i	1.74743	+	0.763558i
$574$	92.4578	−	253.304i	0.161076	−	0.441296i
$575$	201.882			0.351100
$576$	562.394	−	124.456i	0.976378	−	0.216070i
$577$	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	$0.739129\pi$
$578$	155.056	−	424.801i	0.268262	−	0.734950i
$579$	−108.908	+	42.6731i	−0.188097	+	0.0737013i
$580$	−11.8582	−	138.460i	−0.0204451	−	0.238723i
$581$		−	340.293i		−	0.585702i
$582$	−360.480	+	8.45786i	−0.619382	+	0.0145324i
$583$	−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	0.170810	−	0.985304i	$-0.445362\pi$
$587$	−478.108	−	478.108i	−0.814494	−	0.814494i	−0.985304	+	0.170810i	$0.945362\pi$
$588$	448.080	−	221.373i	0.762040	−	0.376485i
$589$		−	105.706i		−	0.179467i
$590$	−167.245	−	61.0456i	−0.283466	−	0.103467i
$591$	690.765	−	270.660i	1.16881	−	0.457969i
$592$	31.5841	+	22.2883i	0.0533515	+	0.0376491i
$593$	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	$0.719214\pi$
$594$	352.868	−	342.397i	0.594054	−	0.576426i
$595$	68.0403			0.114353
$596$	−412.970	+	35.3682i	−0.692902	+	0.0593427i
$597$	−597.419	−	261.049i	−1.00070	−	0.437268i
$598$	333.726	+	106.237i	0.558070	+	0.177653i
$599$	686.856			1.14667			0.573336	−	0.819321i	$-0.305649\pi$
$599$	686.856			1.14667			0.573336	+	0.819321i	$0.305649\pi$
$600$	−39.0910	−	357.563i	−0.0651517	−	0.595939i
$601$	−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
$604$	−45.9834	−	536.915i	−0.0761314	−	0.888933i
$605$	−85.2369	−	85.2369i	−0.140887	−	0.140887i
$606$	342.558	−	359.019i	0.565277	−	0.592440i
$607$		−	834.152i		−	1.37422i	−0.726553	−	0.687110i	$-0.758879\pi$
$607$		−	834.152i		−	1.37422i	0.726553	−	0.687110i	$-0.241121\pi$
$608$	−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
$612$	−13.3898	−	285.183i	−0.0218787	−	0.465986i
$613$	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
$616$	−171.312	+	98.2805i	−0.278104	+	0.159546i
$617$	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	$0.167798\pi$
$618$	−566.676	+	593.907i	−0.916952	+	0.961014i
$619$	534.752	+	534.752i	0.863896	+	0.863896i	0.991788	−	0.127892i	$-0.0408212\pi$
$619$	534.752	+	534.752i	0.863896	+	0.863896i	−0.127892	+	0.991788i	$0.540821\pi$
$620$	46.3544	−	55.0380i	0.0747651	−	0.0887709i
$621$	−343.489	+	119.546i	−0.553122	+	0.192505i
$622$	−547.173	−	199.722i	−0.879700	−	0.321097i
$623$		−	369.080i		−	0.592424i
$624$	123.541	−	611.648i	0.197982	−	0.980206i
$625$	25.7012			0.0411219
$626$	−234.877	+	643.484i	−0.375202	+	1.02793i
$627$	−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
$630$	−142.428	+	59.6974i	−0.226076	+	0.0947577i
$631$	35.0852	+	35.0852i	0.0556025	+	0.0556025i	0.734361	−	0.678759i	$-0.237482\pi$
$631$	35.0852	+	35.0852i	0.0556025	+	0.0556025i	−0.678759	+	0.734361i	$0.737482\pi$
$632$	183.823	+	320.420i	0.290859	+	0.506994i
$633$	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
$636$	1040.73	−	514.172i	1.63637	−	0.808447i
$637$	−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	$0.245784\pi$
$642$	386.866	−	405.456i	0.602595	−	0.631551i
$643$	−174.939	+	174.939i	−0.272066	+	0.272066i	−0.829932	−	0.557865i	$-0.811621\pi$
$643$	−174.939	+	174.939i	−0.272066	+	0.272066i	0.557865	+	0.829932i	$0.311621\pi$
$644$	145.559	−	12.4662i	0.226023	−	0.0193575i
$645$	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	$0.317610\pi$
$647$			1087.32i			1.68056i	−0.542151	+	0.840281i	$0.682390\pi$
$648$	278.244	+	585.222i	0.429388	+	0.903120i
$649$		−	256.151i		−	0.394686i
$650$	−371.309	−	118.201i	−0.571244	−	0.181847i
$651$	42.3747	+	18.5161i	0.0650918	+	0.0284426i
$652$	98.5719	+	1150.95i	0.151184	+	1.76527i
$653$		−	915.597i		−	1.40214i	−0.713093	−	0.701070i	$-0.752706\pi$
$653$		−	915.597i		−	1.40214i	0.713093	−	0.701070i	$-0.247294\pi$
$654$	−835.313	+	19.5988i	−1.27724	+	0.0299675i
$655$	−126.381	+	126.381i	−0.192948	+	0.192948i
$656$	650.051	+	458.728i	0.990932	+	0.699281i
$657$	−668.252	−	25.7526i	−1.01713	−	0.0391973i
$658$	−120.797	+	330.945i	−0.183582	+	0.502955i
$659$	−330.590			−0.501653			−0.250827	−	0.968032i	$-0.580702\pi$
$659$	−330.590			−0.501653			−0.250827	+	0.968032i	$0.580702\pi$
$660$	−309.973	+	153.142i	−0.469656	+	0.232033i
$661$	−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
$666$	−16.4735	+	40.2477i	−0.0247349	+	0.0604320i
$667$	−147.894			−0.221730
$668$	413.270	−	35.3940i	0.618668	−	0.0529850i
$669$	856.755	−	335.699i	1.28065	−	0.501792i
$670$	483.781	+	176.584i	0.722061	+	0.263558i
$671$	694.648	−	694.648i	1.03524	−	1.03524i
$672$	−50.2645	−	255.393i	−0.0747983	−	0.380048i
$673$		−	186.978i		−	0.277827i	−0.990304	−	0.138914i	$-0.955639\pi$
$673$		−	186.978i		−	0.277827i	0.990304	−	0.138914i	$-0.0443611\pi$
$674$	115.184	+	42.0431i	0.170897	+	0.0623785i
$675$	382.171	−	133.008i	0.566180	−	0.197049i
$676$	−551.598	−	390.788i	−0.815974	−	0.578089i
$677$		−	368.883i		−	0.544879i	−0.962173	−	0.272440i	$-0.912170\pi$
$677$		−	368.883i		−	0.544879i	0.962173	−	0.272440i	$-0.0878305\pi$
$678$	−372.146	−	355.083i	−0.548888	−	0.523721i
$679$			162.944i			0.239977i
$680$	−52.4917	+	193.771i	−0.0771937	+	0.284958i
$681$	−263.209	−	671.749i	−0.386503	−	0.986415i
$682$	97.2528	+	35.4980i	0.142599	+	0.0520499i
$683$	−455.745	+	455.745i	−0.667269	+	0.667269i	−0.957083	−	0.289814i	$-0.906407\pi$
$683$	−455.745	+	455.745i	−0.667269	+	0.667269i	0.289814	+	0.957083i	$0.406407\pi$
$684$	−494.988	−	450.591i	−0.723666	−	0.658759i
$685$	−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
$690$	255.673	−	5.99880i	0.370541	−	0.00869391i
$691$	−252.600	+	252.600i	−0.365557	+	0.365557i	−0.865854	−	0.500297i	$-0.833224\pi$
$691$	−252.600	+	252.600i	−0.365557	+	0.365557i	0.500297	+	0.865854i	$0.333224\pi$
$692$	145.571	+	122.603i	0.210362	+	0.177172i
$693$	−150.945	−	163.045i	−0.217813	−	0.235274i
$694$	−18.8433	+	51.6244i	−0.0271517	+	0.0743868i
$695$	352.266	+	352.266i	0.506858	+	0.506858i
$696$	28.6371	+	261.942i	0.0411452	+	0.376353i
$697$	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
$700$	−161.951	+	13.8701i	−0.231359	+	0.0198144i
$701$	−684.290			−0.976162			−0.488081	−	0.872798i	$-0.662303\pi$
$701$	−684.290			−0.976162			−0.488081	+	0.872798i	$0.662303\pi$
$702$	701.749	−	18.7618i	0.999643	−	0.0267263i
$703$		−	44.9222i		−	0.0639007i
$704$	−147.728	−	563.699i	−0.209841	−	0.800708i
$705$	−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
$708$	319.751	+	108.282i	0.451625	+	0.152940i
$709$	−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	$0.955213\pi$
$710$	−47.2338	+	129.405i	−0.0665265	+	0.182261i
$711$	−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
$714$	−128.980	+	3.02622i	−0.180644	+	0.00423840i
$715$	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	$-0.775679\pi$
$719$		−	931.573i		−	1.29565i	0.761789	−	0.647825i	$-0.224321\pi$
$720$	−60.1314	−	451.673i	−0.0835159	−	0.627324i
$721$	262.303	+	262.303i	0.363805	+	0.363805i
$722$	−28.7188	−	10.4826i	−0.0397767	−	0.0145188i
$723$	−1304.22	+	511.026i	−1.80390	+	0.706813i
$724$	438.410	−	520.538i	0.605538	−	0.718975i
$725$	164.549			0.226964
$726$	165.369	+	157.787i	0.227781	+	0.217338i
$727$	364.106			0.500833			0.250417	−	0.968138i	$-0.419432\pi$
$727$	364.106			0.500833			0.250417	+	0.968138i	$0.419432\pi$
$728$	−275.016	−	62.2955i	−0.377769	−	0.0855707i
$729$	−571.477	+	452.609i	−0.783919	+	0.620863i
$730$	441.741	+	161.239i	0.605125	+	0.220875i
$731$	366.337			0.501146
$732$	573.476	+	1160.77i	0.783437	+	1.58575i
$733$	−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	$-0.559998\pi$
$734$	−938.611	−	342.600i	−1.27876	−	0.466758i
$735$	−144.237	−	368.114i	−0.196241	−	0.500836i
$736$	−76.7935	+	424.153i	−0.104339	+	0.576295i
$737$			740.955i			1.00537i
$738$	−339.050	+	828.362i	−0.459418	+	1.12244i
$739$	963.677	+	963.677i	1.30403	+	1.30403i	0.925651	+	0.378378i	$0.123518\pi$
$739$	963.677	+	963.677i	1.30403	+	1.30403i	0.378378	+	0.925651i	$0.376482\pi$
$740$	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	$0.0993803\pi$
$743$	935.304	+	935.304i	1.25882	+	1.25882i	0.307165	+	0.951656i	$0.400620\pi$
$744$	−85.4231	+	106.394i	−0.114816	+	0.143002i
$745$			327.885i			0.440114i
$746$	227.690	−	623.794i	0.305214	−	0.836185i
$747$	−43.4976	+	1128.71i	−0.0582297	+	1.51100i
$748$	−287.782	+	24.6467i	−0.384736	+	0.0329502i
$749$	−179.073	−	179.073i	−0.239082	−	0.239082i
$750$	−758.979	+	17.8078i	−1.01197	+	0.0237437i
$751$	−1140.94			−1.51923			−0.759613	−	0.650376i	$-0.774611\pi$
$751$	−1140.94			−1.51923			−0.759613	+	0.650376i	$0.774611\pi$
$752$	−849.301	−	599.334i	−1.12939	−	0.796987i
$753$	−158.231	+	362.116i	−0.210134	+	0.480898i
$754$	272.011	+	86.5907i	0.360757	+	0.114842i
$755$	−426.294			−0.564628
$756$	267.336	−	119.499i	0.353619	−	0.158068i
$757$	−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
$760$	234.219	+	408.265i	0.308183	+	0.537191i
$761$	−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	$0.751419\pi$
$762$	388.348	−	407.010i	0.509643	−	0.534133i
$763$			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
$768$	766.107	+	53.8827i	0.997536	+	0.0701598i
$769$	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
$772$	−155.391	+	13.3083i	−0.201284	+	0.0172387i
$773$	−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	$0.423509\pi$
$774$	−766.848	+	321.418i	−0.990760	+	0.415269i
$775$	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
$778$	−312.891	+	857.217i	−0.402173	+	1.10182i
$779$		−	924.570i		−	1.18687i
$780$	−473.754	−	138.662i	−0.607378	−	0.177771i
$781$	−198.196			−0.253772
$782$	200.700	+	73.2570i	0.256650	+	0.0936790i
$783$	−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
$786$	233.951	−	245.193i	0.297648	−	0.311951i
$787$	322.116	+	322.116i	0.409296	+	0.409296i	0.881493	−	0.472197i	$-0.156539\pi$
$787$	322.116	+	322.116i	0.409296	+	0.409296i	−0.472197	+	0.881493i	$0.656539\pi$
$788$	985.590	−	84.4095i	1.25075	−	0.107119i
$789$	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
$792$	580.785	−	304.088i	0.733314	−	0.383949i
$793$	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	$0.182704\pi$
$798$	−208.811	+	218.845i	−0.261668	+	0.274242i
$799$	−364.318	+	364.318i	−0.455967	+	0.455967i
$800$	85.4417	−	471.920i	0.106802	−	0.589900i
$801$	−47.1773	+	1224.20i	−0.0588980	+	1.52834i
$802$	647.041	−	300.999i	0.806785	−	0.375311i
$803$			676.567i			0.842550i
$804$	−924.926	−	313.221i	−1.15041	−	0.389578i
$805$		−	115.569i		−	0.143564i
$806$	67.8906	+	131.300i	0.0842315	+	0.162903i
$807$	395.730	−	905.640i	0.490371	−	1.12223i
$808$	573.899	−	329.242i	0.710271	−	0.407478i
$809$			615.167i			0.760404i	0.924903	+	0.380202i	$0.124146\pi$
$809$			615.167i			0.760404i	−0.924903	+	0.380202i	$0.875854\pi$
$810$	480.047	−	179.804i	0.592651	−	0.221980i
$811$	−322.284	+	322.284i	−0.397391	+	0.397391i	−0.877312	−	0.479921i	$-0.840665\pi$
$811$	−322.284	+	322.284i	−0.397391	+	0.397391i	0.479921	+	0.877312i	$0.340665\pi$
$812$	118.641	−	10.1609i	0.146110	−	0.0125134i
$813$	253.795	+	647.725i	0.312171	+	0.796710i
$814$	41.3299	+	15.0857i	0.0507738	+	0.0185328i
$815$	913.822			1.12125
$816$	90.8869	−	369.654i	0.111381	−	0.453008i
$817$	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	$0.348594\pi$
$822$	84.2920	−	1.97772i	0.102545	−	0.00240599i
$823$	155.082			0.188435			0.0942176	−	0.995552i	$-0.469965\pi$
$823$	155.082			0.188435			0.0942176	+	0.995552i	$0.469965\pi$
$824$	−949.373	+	544.649i	−1.15215	+	0.660982i
$825$	−149.353	−	381.171i	−0.181034	−	0.462026i
$826$	52.3079	−	143.306i	0.0633268	−	0.173494i
$827$	453.337	−	453.337i	0.548170	−	0.548170i	−0.377741	−	0.925911i	$-0.623299\pi$
$827$	453.337	−	453.337i	0.548170	−	0.548170i	0.925911	+	0.377741i	$0.123299\pi$
$828$	−484.396	+	22.7431i	−0.585020	+	0.0274675i
$829$			277.026i			0.334169i	0.985943	+	0.167084i	$0.0534352\pi$
$829$			277.026i			0.334169i	−0.985943	+	0.167084i	$0.946565\pi$
$830$	272.341	−	746.124i	0.328122	−	0.898945i
$831$	−199.335	+	456.184i	−0.239874	+	0.548958i
$832$	389.580	−	735.154i	0.468245	−	0.883599i
$833$		−	330.293i		−	0.396510i
$834$	−683.437	−	652.101i	−0.819468	−	0.781896i
$835$		−	328.124i		−	0.392962i
$836$	−436.237	+	517.958i	−0.521815	+	0.619567i
$837$	−138.185	−	66.8324i	−0.165096	−	0.0798476i
$838$	−243.345	+	666.686i	−0.290388	+	0.795568i
$839$	548.135	−	548.135i	0.653319	−	0.653319i	−0.300471	−	0.953791i	$-0.597144\pi$
$839$	548.135	−	548.135i	0.653319	−	0.653319i	0.953791	+	0.300471i	$0.0971440\pi$
$840$	−204.690	+	22.3780i	−0.243679	+	0.0266405i
$841$	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
$846$	442.974	−	1082.27i	0.523610	−	1.27927i
$847$	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
$850$	−223.302	−	81.5069i	−0.262708	−	0.0958905i
$851$	−23.0125	−	23.0125i	−0.0270417	−	0.0270417i
$852$	83.7825	−	247.406i	0.0983363	−	0.290382i
$853$	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
$856$	648.130	−	371.828i	0.757161	−	0.434378i
$857$	−465.906			−0.543647			−0.271824	−	0.962347i	$-0.587627\pi$
$857$	−465.906			−0.543647			−0.271824	+	0.962347i	$0.587627\pi$
$858$	−46.3066	−	708.697i	−0.0539704	−	0.825987i
$859$			646.398i			0.752500i	0.926518	+	0.376250i	$0.122787\pi$
$859$			646.398i			0.752500i	−0.926518	+	0.376250i	$0.877213\pi$
$860$	582.547	−	49.8915i	0.677380	−	0.0580133i
$861$	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	0.659183	−	0.751983i	$-0.270902\pi$
$863$	−80.0865	−	80.0865i	−0.0928001	−	0.0928001i	−0.751983	+	0.659183i	$0.770902\pi$
$864$	134.076	+	853.534i	0.155181	+	0.987886i
$865$	106.461	−	106.461i	0.123076	−	0.123076i
$866$	520.658	+	190.044i	0.601222	+	0.219450i
$867$	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
$870$	208.392	−	4.88946i	0.239531	−	0.00562007i
$871$	−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
$876$	−844.552	−	286.003i	−0.964100	−	0.326487i
$877$	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	$0.620038\pi$
$878$	−565.329	+	1548.81i	−0.643883	+	1.76403i
$879$	−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	$0.607172\pi$
$882$	289.793	+	691.396i	0.328564	+	0.783896i
$883$	−751.578			−0.851164			−0.425582	−	0.904920i	$-0.639931\pi$
$883$	−751.578			−0.851164			−0.425582	+	0.904920i	$0.639931\pi$
$884$	−326.243	−	252.245i	−0.369053	−	0.285345i
$885$	106.931	−	244.714i	0.120826	−	0.276513i
$886$	−203.344	+	557.096i	−0.229508	+	0.628777i
$887$	−227.550			−0.256539			−0.128270	−	0.991739i	$-0.540942\pi$
$887$	−227.550			−0.256539			−0.128270	+	0.991739i	$0.540942\pi$
$888$	−36.3026	+	45.2145i	−0.0408813	+	0.0509172i
$889$	−179.759	−	179.759i	−0.202203	−	0.202203i
$890$	295.380	−	809.243i	0.331887	−	0.909262i
$891$	479.826	+	560.097i	0.538525	+	0.628616i
$892$	1222.43	−	104.693i	1.37043	−	0.117369i
$893$			1207.96i			1.35270i
$894$	−14.5833	−	621.551i	−0.0163124	−	0.695247i
$895$	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
$900$	538.947	−	25.3043i	0.598830	−	0.0281159i
$901$		−	767.154i		−	0.851448i
$902$	850.635	+	310.488i	0.943054	+	0.344222i
$903$	137.079	+	349.847i	0.151804	+	0.387427i
$904$	−341.281	−	594.883i	−0.377523	−	0.658057i
$905$	−380.687	−	380.687i	−0.420649	−	0.420649i
$906$	808.099	−	18.9602i	0.891941	−	0.0209274i
$907$	83.6189			0.0921929			0.0460964	−	0.998937i	$-0.485322\pi$
$907$	83.6189			0.0921929			0.0460964	+	0.998937i	$0.485322\pi$
$908$	−82.0858	−	958.457i	−0.0904028	−	1.05557i
$909$	505.669	+	546.205i	0.556291	+	0.600886i
$910$	−67.6650	+	212.559i	−0.0743572	+	0.233581i
$911$	−141.993			−0.155865			−0.0779323	−	0.996959i	$-0.524832\pi$
$911$	−141.993			−0.155865			−0.0779323	+	0.996959i	$0.524832\pi$
$912$	−462.153	−	763.505i	−0.506746	−	0.837177i
$913$	1142.76			1.25165
$914$	−762.684	+	354.796i	−0.834447	+	0.388179i
$915$	953.615	−	373.651i	1.04220	−	0.408362i
$916$	161.916	−	13.8670i	0.176764	−	0.0151387i
$917$	−108.292	−	108.292i	−0.118093	−	0.118093i
$918$	428.198	+	6.44905i	0.466447	+	0.00702511i
$919$			31.4087i			0.0341771i	0.999854	+	0.0170885i	$0.00543972\pi$
$919$			31.4087i			0.0341771i	−0.999854	+	0.0170885i	$0.994560\pi$
$920$	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
$924$	−131.222	−	265.605i	−0.142015	−	0.287452i
$925$	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
$928$	−62.5923	+	345.716i	−0.0674487	+	0.372539i
$929$	−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	$0.950219\pi$
$930$	78.0919	+	74.5114i	0.0839698	+	0.0801198i
$931$	−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
$934$	−1026.80	−	374.791i	−1.09936	−	0.401275i
$935$			228.490i			0.244375i
$936$	904.233	+	241.781i	0.966061	+	0.258313i
$937$	−1441.85			−1.53879			−0.769395	−	0.638773i	$-0.779442\pi$
$937$	−1441.85			−1.53879			−0.769395	+	0.638773i	$0.779442\pi$
$938$	−151.308	+	414.535i	−0.161310	+	0.441935i
$939$	−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	$0.201041\pi$
$942$	−722.761	+	757.492i	−0.767262	+	0.804131i
$943$	−473.634	−	473.634i	−0.502263	−	0.502263i
$944$	367.766	+	259.525i	0.389583	+	0.274921i
$945$	−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	−0.839318	−	0.543641i	$-0.817045\pi$
$947$	−280.005	+	280.005i	−0.295676	+	0.295676i	0.543641	+	0.839318i	$0.317045\pi$
$948$	−496.786	+	245.436i	−0.524036	+	0.258899i
$949$	−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	$0.211570\pi$
$954$	673.088	+	1605.87i	0.705543	+	1.68330i
$955$	814.964	−	814.964i	0.853365	−	0.853365i
$956$	−4.54611	−	53.0817i	−0.00475534	−	0.0555248i
$957$	109.412	+	279.236i	0.114328	+	0.291783i
$958$	−133.481	−	286.937i	−0.139333	−	0.299517i
$959$		−	38.1017i		−	0.0397306i
$960$	94.1845	−	600.199i	0.0981088	−	0.625208i
$961$			928.679i			0.966368i
$962$	28.8517	+	55.7990i	0.0299914	+	0.0580031i
$963$	571.074	+	616.854i	0.593016	+	0.640554i
$964$	−1860.87	+	159.371i	−1.93036	+	0.165323i
$965$			123.376i			0.127851i
$966$	5.14016	+	219.077i	0.00532108	+	0.226788i
$967$	302.480	−	302.480i	0.312803	−	0.312803i	−0.533192	−	0.845994i	$-0.679008\pi$
$967$	302.480	−	302.480i	0.312803	−	0.312803i	0.845994	+	0.533192i	$0.179008\pi$
$968$	151.654	+	264.346i	0.156667	+	0.273085i
$969$	−411.875	+	161.383i	−0.425052	+	0.166546i
$970$	−130.406	+	357.271i	−0.134440	+	0.368320i
$971$	−1484.57			−1.52891			−0.764453	−	0.644679i	$-0.776991\pi$
$971$	−1484.57			−1.52891			−0.764453	+	0.644679i	$0.776991\pi$
$972$	−901.998	+	362.194i	−0.927981	+	0.372627i
$973$	−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	$0.0861567\pi$
$978$	−1732.27	+	40.6440i	−1.77124	+	0.0415582i
$979$	1239.43			1.26602
$980$	−44.9825	−	525.229i	−0.0459005	−	0.535948i
$981$	48.2636	−	1252.39i	0.0491983	−	1.27664i
$982$	811.363	+	296.154i	0.826236	+	0.301582i
$983$	178.438	−	178.438i	0.181524	−	0.181524i	−0.610496	−	0.792019i	$-0.709030\pi$
$983$	178.438	−	178.438i	0.181524	−	0.181524i	0.792019	+	0.610496i	$0.209030\pi$
$984$	−747.165	+	930.587i	−0.759314	+	0.945718i
$985$		−	782.528i		−	0.794444i
$986$	163.585	+	59.7099i	0.165908	+	0.0605577i
$987$	−484.241	−	211.595i	−0.490619	−	0.214382i
$988$	−959.042	+	122.676i	−0.970690	+	0.124166i
$989$		−	622.240i		−	0.629160i
$990$	−200.473	−	478.295i	−0.202498	−	0.483126i
$991$		−	1209.46i		−	1.22045i	−0.792230	−	0.610223i	$-0.791080\pi$
$991$		−	1209.46i		−	1.22045i	0.792230	−	0.610223i	$-0.208920\pi$
$992$	−149.500	+	103.664i	−0.150705	+	0.104500i
$993$	1527.61	−	598.556i	1.53838	−	0.602775i
$994$	−110.883	−	40.4730i	−0.111552	−	0.0407173i
$995$	−486.255	+	486.255i	−0.488698	+	0.488698i
$996$	−483.074	+	1426.49i	−0.485014	+	1.43222i
$997$	−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.47.19	yes	96
3.2	odd	2	inner	156.3.l.c.47.30	yes	96
4.3	odd	2	inner	156.3.l.c.47.6	✓	96
12.11	even	2	inner	156.3.l.c.47.43	yes	96
13.5	odd	4	inner	156.3.l.c.83.43	yes	96
39.5	even	4	inner	156.3.l.c.83.6	yes	96
52.31	even	4	inner	156.3.l.c.83.30	yes	96
156.83	odd	4	inner	156.3.l.c.83.19	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.3.l.c.47.6	✓	96	4.3	odd	2	inner
156.3.l.c.47.19	yes	96	1.1	even	1	trivial
156.3.l.c.47.30	yes	96	3.2	odd	2	inner
156.3.l.c.47.43	yes	96	12.11	even	2	inner
156.3.l.c.83.6	yes	96	39.5	even	4	inner
156.3.l.c.83.19	yes	96	156.83	odd	4	inner
156.3.l.c.83.30	yes	96	52.31	even	4	inner
156.3.l.c.83.43	yes	96	13.5	odd	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+(-0.685761 + 1.87876i) q^{2} +(-2.74902 - 1.20121i) q^{3} +(-3.05946 - 2.57676i) q^{4} +(-2.23749 + 2.23749i) q^{5} +(4.14196 - 4.34099i) q^{6} +(-1.91723 - 1.91723i) q^{7} +(6.93916 - 3.98095i) q^{8} +(6.11417 + 6.60431i) q^{9} +(-2.66932 - 5.73809i) q^{10} +(6.43837 - 6.43837i) q^{11} +(5.31528 + 10.7586i) 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} +(-16.6008 + 6.95808i) q^{18} +(13.1475 - 13.1475i) q^{19} +(12.6110 - 1.08005i) q^{20} +(2.96749 + 7.57350i) q^{21} +(7.68096 + 16.5113i) q^{22} -13.4703i q^{23} +(-23.8578 + 2.60829i) q^{24} +14.9872i q^{25} +(-7.88675 + 24.7750i) q^{26} +(-8.87477 - 25.4998i) q^{27} +(0.925460 + 10.8059i) q^{28} -10.9793i q^{29} +(0.445336 + 18.9805i) q^{30} +(4.01999 - 4.01999i) q^{31} +(-31.4881 - 5.70096i) q^{32} +(-25.4330 + 9.96532i) q^{33} +(-5.43842 + 14.8995i) q^{34} +8.57958 q^{35} +(-1.68839 - 35.9604i) 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} +(-16.2638 + 0.381593i) q^{42} +46.1935 q^{43} +(-36.2881 + 3.10784i) q^{44} +(-28.4575 - 1.09668i) q^{45} +(25.3074 + 9.23738i) q^{46} +(-45.9388 + 45.9388i) q^{47} +(11.4604 - 46.6118i) q^{48} -41.6485i q^{49} +(-28.1574 - 10.2777i) q^{50} +(-21.8010 - 9.52621i) q^{51} +(-41.1378 - 31.8070i) q^{52} -96.7348i q^{53} +(53.9939 + 0.813197i) q^{54} +28.8116i q^{55} +(-20.9364 - 5.67157i) q^{56} +(-51.9357 + 20.3497i) q^{57} +(20.6274 + 7.52915i) q^{58} +(19.8925 - 19.8925i) q^{59} +(-35.9652 - 12.1794i) 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} +(-1.28145 - 54.6163i) q^{66} +(-57.5421 + 57.5421i) q^{67} +(-24.2631 - 20.4350i) q^{68} +(-16.1807 + 37.0300i) q^{69} +(-5.88354 + 16.1190i) q^{70} +(-15.3918 - 15.3918i) q^{71} +(68.7187 + 21.4881i) q^{72} +(-52.5418 + 52.5418i) q^{73} +(2.03811 + 4.38120i) q^{74} +(18.0029 - 41.2002i) q^{75} +(-74.1023 + 6.34639i) q^{76} -24.6877 q^{77} +(51.4408 - 58.6331i) q^{78} +46.1756i q^{79} +(-41.3660 - 29.1911i) q^{80} +(-6.23379 + 80.7598i) q^{81} +(41.9475 + 90.1721i) q^{82} +(88.7459 + 88.7459i) q^{83} +(10.4361 - 30.8174i) q^{84} +(-17.7444 + 17.7444i) q^{85} +(-31.6777 + 86.7865i) q^{86} +(-13.1884 + 30.1822i) q^{87} +(19.0461 - 70.3077i) q^{88} +(96.2535 + 96.2535i) q^{89} +(21.5754 - 52.7127i) 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} +(79.7131 + 53.4959i) q^{96} +(-42.4947 - 42.4947i) q^{97} +(78.2474 + 28.5609i) 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

Related objects

Downloads

Learn more