LMFDB - Embedded newform 112.3.u.a.107.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [112,3,Mod(11,112)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(112, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 8])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("112.11"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	112.u (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.05177896084$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$30$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			107.5
Character	$\chi$	$=$	112.107
Dual form			112.3.u.a.67.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.70355 + 1.04781i) q^{2} +(1.42423 - 5.31530i) q^{3} +(1.80419 - 3.57000i) q^{4} +(-1.56586 + 0.419571i) q^{5} +(3.14317 + 10.5472i) q^{6} +(6.45786 - 2.70113i) q^{7} +(0.667143 + 7.97213i) q^{8} +(-18.4298 - 10.6404i) q^{9} +(2.22790 - 2.35548i) q^{10} +(-10.6579 - 2.85576i) q^{11} +(-16.4060 - 14.6743i) q^{12} +(-1.18165 + 1.18165i) q^{13} +(-8.17104 + 11.3681i) q^{14} +8.92058i q^{15} +(-9.48979 - 12.8819i) q^{16} +(-4.47899 - 7.75783i) q^{17} +(42.5452 - 1.18434i) q^{18} +(29.2429 - 7.83562i) q^{19} +(-1.32724 + 6.34710i) q^{20} +(-5.15984 - 38.1725i) q^{21} +(21.1485 - 6.30246i) q^{22} +(-5.11508 + 8.85958i) q^{23} +(43.3245 + 7.80809i) q^{24} +(-19.3748 + 11.1860i) q^{25} +(0.774863 - 3.25116i) q^{26} +(-47.7857 + 47.7857i) q^{27} +(2.00818 - 27.9279i) q^{28} +(31.5544 - 31.5544i) q^{29} +(-9.34707 - 15.1967i) q^{30} +(-8.16065 + 4.71155i) q^{31} +(29.6642 + 12.0016i) q^{32} +(-30.3585 + 52.5825i) q^{33} +(15.7589 + 8.52276i) q^{34} +(-8.97878 + 6.93912i) q^{35} +(-71.2372 + 46.5969i) q^{36} +(51.9889 - 13.9304i) q^{37} +(-41.6067 + 43.9894i) q^{38} +(4.59790 + 7.96380i) q^{39} +(-4.38953 - 12.2033i) q^{40} +53.2158i q^{41} +(48.7876 + 59.6223i) q^{42} +(6.71176 - 6.71176i) q^{43} +(-29.4239 + 32.8962i) q^{44} +(33.3229 + 8.92883i) q^{45} +(-0.569336 - 20.4524i) q^{46} +(4.10186 + 2.36821i) q^{47} +(-81.9869 + 32.0943i) q^{48} +(34.4078 - 34.8870i) q^{49} +(21.2851 - 39.3570i) q^{50} +(-47.6143 + 12.7582i) q^{51} +(2.08658 + 6.35044i) q^{52} +(8.79535 - 32.8247i) q^{53} +(31.3352 - 131.476i) q^{54} +17.8869 q^{55} +(25.8421 + 49.6809i) q^{56} -166.595i q^{57} +(-20.6916 + 86.8176i) q^{58} +(85.6173 + 22.9411i) q^{59} +(31.8465 + 16.0944i) q^{60} +(-4.14213 - 15.4586i) q^{61} +(8.96529 - 16.5772i) q^{62} +(-147.758 - 18.9332i) q^{63} +(-63.1098 + 10.6371i) q^{64} +(1.35452 - 2.34609i) q^{65} +(-3.37906 - 121.387i) q^{66} +(3.84292 - 14.3420i) q^{67} +(-35.7764 + 1.99337i) q^{68} +(39.8063 + 39.8063i) q^{69} +(8.02496 - 21.2292i) q^{70} +93.6627 q^{71} +(72.5317 - 154.023i) q^{72} +(16.5673 - 9.56511i) q^{73} +(-73.9695 + 78.2056i) q^{74} +(31.8630 + 118.914i) q^{75} +(24.7867 - 118.534i) q^{76} +(-76.5407 + 10.3461i) q^{77} +(-16.1773 - 8.74904i) q^{78} +(102.698 + 59.2925i) q^{79} +(20.2646 + 16.1896i) q^{80} +(90.1737 + 156.185i) q^{81} +(-55.7600 - 90.6560i) q^{82} +(-7.54311 - 7.54311i) q^{83} +(-145.585 - 50.4498i) q^{84} +(10.2684 + 10.2684i) q^{85} +(-4.40120 + 18.4665i) q^{86} +(-122.780 - 212.662i) q^{87} +(15.6562 - 86.8711i) q^{88} +(-56.1412 - 32.4131i) q^{89} +(-66.1230 + 19.7053i) q^{90} +(-4.43915 + 10.8228i) q^{91} +(22.4001 + 34.2452i) q^{92} +(13.4207 + 50.0866i) q^{93} +(-9.46916 + 0.263594i) q^{94} +(-42.5027 + 24.5390i) q^{95} +(106.040 - 140.581i) q^{96} -119.381 q^{97} +(-22.0606 + 95.4847i) q^{98} +(166.035 + 166.035i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{7} - 20 q^{8} + 16 q^{10} + 14 q^{11} - 2 q^{12} - 8 q^{13} + 20 q^{14} + 8 q^{16} - 4 q^{17} - 38 q^{18} - 2 q^{19} + 72 q^{20} + 14 q^{21}+ \cdots - 776 q^{99}+O(q^{100}) $ 120 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^7 - 20 * q^8 + 16 * q^10 + 14 * q^11 - 2 * q^12 - 8 * q^13 + 20 * q^14 + 8 * q^16 - 4 * q^17 - 38 * q^18 - 2 * q^19 + 72 * q^20 + 14 * q^21 + 52 * q^22 - 68 * q^23 - 142 * q^24 - 2 * q^26 - 44 * q^27 - 62 * q^28 - 40 * q^29 - 14 * q^30 + 88 * q^32 - 4 * q^33 + 168 * q^34 + 94 * q^35 - 272 * q^36 - 50 * q^37 + 138 * q^38 - 4 * q^39 - 206 * q^40 - 198 * q^42 - 104 * q^43 + 2 * q^44 - 84 * q^45 - 76 * q^46 - 856 * q^48 - 8 * q^49 - 320 * q^50 + 114 * q^51 + 76 * q^52 - 82 * q^53 + 350 * q^54 - 16 * q^55 + 8 * q^56 - 6 * q^58 + 62 * q^59 + 318 * q^60 - 2 * q^61 + 876 * q^62 + 112 * q^64 - 4 * q^65 + 162 * q^66 - 66 * q^67 + 192 * q^68 + 28 * q^69 + 112 * q^70 + 496 * q^71 + 248 * q^72 + 178 * q^74 + 12 * q^75 - 308 * q^76 + 94 * q^77 - 140 * q^78 + 204 * q^80 + 248 * q^81 + 266 * q^82 - 488 * q^83 + 620 * q^84 + 92 * q^85 - 408 * q^86 - 4 * q^87 - 370 * q^88 - 404 * q^90 - 488 * q^91 + 900 * q^92 - 38 * q^93 - 150 * q^94 + 768 * q^96 - 16 * q^97 + 432 * q^98 - 776 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.70355	+	1.04781i	−0.851777	+	0.523905i
$2$	−1.70355	+	1.04781i	−0.851777	+	0.523905i
$3$	1.42423	−	5.31530i	0.474744	−	1.77177i	−0.147626	−	0.989043i	$-0.547163\pi$
$3$	1.42423	−	5.31530i	0.474744	−	1.77177i	0.622369	−	0.782724i	$-0.286170\pi$
$4$	1.80419	−	3.57000i	0.451048	−	0.892500i
$5$	−1.56586	+	0.419571i	−0.313172	+	0.0839142i	−0.411982	−	0.911192i	$-0.635163\pi$
$5$	−1.56586	+	0.419571i	−0.313172	+	0.0839142i	0.0988096	+	0.995106i	$0.468497\pi$
$6$	3.14317	+	10.5472i	0.523862	+	1.75787i
$7$	6.45786	−	2.70113i	0.922551	−	0.385876i
$7$	6.45786	−	2.70113i	0.922551	−	0.385876i
$8$	0.667143	+	7.97213i	0.0833928	+	0.996517i
$9$	−18.4298	−	10.6404i	−2.04775	−	1.18227i
$10$	2.22790	−	2.35548i	0.222790	−	0.235548i
$11$	−10.6579	−	2.85576i	−0.968896	−	0.259615i	−0.260534	−	0.965465i	$-0.583899\pi$
$11$	−10.6579	−	2.85576i	−0.968896	−	0.259615i	−0.708362	+	0.705850i	$0.750565\pi$
$12$	−16.4060	−	14.6743i	−1.36717	−	1.22286i
$13$	−1.18165	+	1.18165i	−0.0908965	+	0.0908965i	−0.751093	−	0.660196i	$-0.770473\pi$
$13$	−1.18165	+	1.18165i	−0.0908965	+	0.0908965i	0.660196	+	0.751093i	$0.270473\pi$
$14$	−8.17104	+	11.3681i	−0.583645	+	0.812009i
$15$			8.92058i			0.594706i
$16$	−9.48979	−	12.8819i	−0.593112	−	0.805120i
$17$	−4.47899	−	7.75783i	−0.263470	−	0.456343i	0.703692	−	0.710505i	$-0.251534\pi$
$17$	−4.47899	−	7.75783i	−0.263470	−	0.456343i	−0.967162	+	0.254162i	$0.918200\pi$
$18$	42.5452	−	1.18434i	2.36362	−	0.0657965i
$19$	29.2429	−	7.83562i	1.53910	−	0.412401i	0.613126	−	0.789985i	$-0.289912\pi$
$19$	29.2429	−	7.83562i	1.53910	−	0.412401i	0.925975	+	0.377584i	$0.123245\pi$
$20$	−1.32724	+	6.34710i	−0.0663621	+	0.317355i
$21$	−5.15984	−	38.1725i	−0.245707	−	1.81774i
$22$	21.1485	−	6.30246i	0.961297	−	0.286475i
$23$	−5.11508	+	8.85958i	−0.222395	+	0.385199i	−0.955535	−	0.294879i	$-0.904721\pi$
$23$	−5.11508	+	8.85958i	−0.222395	+	0.385199i	0.733140	+	0.680078i	$0.238054\pi$
$24$	43.3245	+	7.80809i	1.80519	+	0.325337i
$25$	−19.3748	+	11.1860i	−0.774990	+	0.447441i
$26$	0.774863	−	3.25116i	0.0298024	−	0.125045i
$27$	−47.7857	+	47.7857i	−1.76984	+	1.76984i
$28$	2.00818	−	27.9279i	0.0717205	−	0.997425i
$29$	31.5544	−	31.5544i	1.08808	−	1.08808i	0.0923562	−	0.995726i	$-0.470560\pi$
$29$	31.5544	−	31.5544i	1.08808	−	1.08808i	0.995726	−	0.0923562i	$-0.0294399\pi$
$30$	−9.34707	−	15.1967i	−0.311569	−	0.506556i
$31$	−8.16065	+	4.71155i	−0.263247	+	0.151986i	−0.625815	−	0.779972i	$-0.715233\pi$
$31$	−8.16065	+	4.71155i	−0.263247	+	0.151986i	0.362568	+	0.931957i	$0.381900\pi$
$32$	29.6642	+	12.0016i	0.927005	+	0.375049i
$33$	−30.3585	+	52.5825i	−0.919955	+	1.59341i
$34$	15.7589	+	8.52276i	0.463498	+	0.250669i
$35$	−8.97878	+	6.93912i	−0.256537	+	0.198261i
$36$	−71.2372	+	46.5969i	−1.97881	+	1.29436i
$37$	51.9889	−	13.9304i	1.40511	−	0.376497i	0.524930	−	0.851146i	$-0.324092\pi$
$37$	51.9889	−	13.9304i	1.40511	−	0.376497i	0.880175	+	0.474649i	$0.157425\pi$
$38$	−41.6067	+	43.9894i	−1.09491	+	1.15762i
$39$	4.59790	+	7.96380i	0.117895	+	0.204200i
$40$	−4.38953	−	12.2033i	−0.109738	−	0.305083i
$41$			53.2158i			1.29795i	0.760811	+	0.648974i	$0.224801\pi$
$41$			53.2158i			1.29795i	−0.760811	+	0.648974i	$0.775199\pi$
$42$	48.7876	+	59.6223i	1.16161	+	1.41958i
$43$	6.71176	−	6.71176i	0.156088	−	0.156088i	−0.624743	−	0.780830i	$-0.714796\pi$
$43$	6.71176	−	6.71176i	0.156088	−	0.156088i	0.780830	+	0.624743i	$0.214796\pi$
$44$	−29.4239	+	32.8962i	−0.668725	+	0.747641i
$45$	33.3229	+	8.92883i	0.740508	+	0.198418i
$46$	−0.569336	−	20.4524i	−0.0123769	−	0.444617i
$47$	4.10186	+	2.36821i	0.0872735	+	0.0503874i	0.543002	−	0.839732i	$-0.317288\pi$
$47$	4.10186	+	2.36821i	0.0872735	+	0.0503874i	−0.455728	+	0.890119i	$0.650621\pi$
$48$	−81.9869	+	32.0943i	−1.70806	+	0.668631i
$49$	34.4078	−	34.8870i	0.702200	−	0.711980i
$50$	21.2851	−	39.3570i	0.425702	−	0.787141i
$51$	−47.6143	+	12.7582i	−0.933614	+	0.250161i
$52$	2.08658	+	6.35044i	0.0401265	+	0.122124i
$53$	8.79535	−	32.8247i	0.165950	−	0.619334i	−0.831967	−	0.554825i	$-0.812785\pi$
$53$	8.79535	−	32.8247i	0.165950	−	0.619334i	0.997917	−	0.0645090i	$-0.0205481\pi$
$54$	31.3352	−	131.476i	0.580282	−	2.43474i
$55$	17.8869			0.325217
$56$	25.8421	+	49.6809i	0.461466	+	0.887158i
$57$		−	166.595i		−	2.92271i
$58$	−20.6916	+	86.8176i	−0.356752	+	1.49685i
$59$	85.6173	+	22.9411i	1.45114	+	0.388832i	0.896420	−	0.443205i	$-0.146159\pi$
$59$	85.6173	+	22.9411i	1.45114	+	0.388832i	0.554720	+	0.832037i	$0.312825\pi$
$60$	31.8465	+	16.0944i	0.530775	+	0.268241i
$61$	−4.14213	−	15.4586i	−0.0679037	−	0.253420i	0.923627	−	0.383293i	$-0.125210\pi$
$61$	−4.14213	−	15.4586i	−0.0679037	−	0.253420i	−0.991531	+	0.129872i	$0.958543\pi$
$62$	8.96529	−	16.5772i	0.144602	−	0.267374i
$63$	−147.758	−	18.9332i	−2.34536	−	0.300527i
$64$	−63.1098	+	10.6371i	−0.986091	+	0.166205i
$65$	1.35452	−	2.34609i	0.0208387	−	0.0360937i
$66$	−3.37906	−	121.387i	−0.0511979	−	1.83920i
$67$	3.84292	−	14.3420i	0.0573570	−	0.214059i	−0.931299	−	0.364255i	$-0.881324\pi$
$67$	3.84292	−	14.3420i	0.0573570	−	0.214059i	0.988656	+	0.150196i	$0.0479904\pi$
$68$	−35.7764	+	1.99337i	−0.526124	+	0.0293142i
$69$	39.8063	+	39.8063i	0.576903	+	0.576903i
$70$	8.02496	−	21.2292i	0.114642	−	0.303274i
$71$	93.6627			1.31919			0.659597	−	0.751620i	$-0.270727\pi$
$71$	93.6627			1.31919			0.659597	+	0.751620i	$0.270727\pi$
$72$	72.5317	−	154.023i	1.00738	−	2.13921i
$73$	16.5673	−	9.56511i	0.226949	−	0.131029i	−0.382215	−	0.924073i	$-0.624839\pi$
$73$	16.5673	−	9.56511i	0.226949	−	0.131029i	0.609164	+	0.793045i	$0.291505\pi$
$74$	−73.9695	+	78.2056i	−0.999588	+	1.05683i
$75$	31.8630	+	118.914i	0.424839	+	1.58552i
$76$	24.7867	−	118.534i	0.326140	−	1.55966i
$77$	−76.5407	+	10.3461i	−0.994035	+	0.134365i
$78$	−16.1773	−	8.74904i	−0.207401	−	0.112167i
$79$	102.698	+	59.2925i	1.29997	+	0.750538i	0.980399	−	0.197024i	$-0.0631276\pi$
$79$	102.698	+	59.2925i	1.29997	+	0.750538i	0.319572	+	0.947562i	$0.396461\pi$
$80$	20.2646	+	16.1896i	0.253307	+	0.202371i
$81$	90.1737	+	156.185i	1.11326	+	1.92822i
$82$	−55.7600	−	90.6560i	−0.680001	−	1.10556i
$83$	−7.54311	−	7.54311i	−0.0908809	−	0.0908809i	0.660205	−	0.751086i	$-0.270469\pi$
$83$	−7.54311	−	7.54311i	−0.0908809	−	0.0908809i	−0.751086	+	0.660205i	$0.770469\pi$
$84$	−145.585	−	50.4498i	−1.73316	−	0.600593i
$85$	10.2684	+	10.2684i	0.120805	+	0.120805i
$86$	−4.40120	+	18.4665i	−0.0511768	+	0.214727i
$87$	−122.780	−	212.662i	−1.41127	−	2.44439i
$88$	15.6562	−	86.8711i	0.177912	−	0.987171i
$89$	−56.1412	−	32.4131i	−0.630800	−	0.364192i	0.150262	−	0.988646i	$-0.451988\pi$
$89$	−56.1412	−	32.4131i	−0.630800	−	0.364192i	−0.781062	+	0.624454i	$0.785322\pi$
$90$	−66.1230	+	19.7053i	−0.734700	+	0.218947i
$91$	−4.43915	+	10.8228i	−0.0487819	+	0.118931i
$92$	22.4001	+	34.2452i	0.243480	+	0.372231i
$93$	13.4207	+	50.0866i	0.144308	+	0.538566i
$94$	−9.46916	+	0.263594i	−0.100736	+	0.00280419i
$95$	−42.5027	+	24.5390i	−0.447397	+	0.258305i
$96$	106.040	−	140.581i	1.10459	−	1.46439i
$97$	−119.381			−1.23073			−0.615366	−	0.788242i	$-0.710992\pi$
$97$	−119.381			−1.23073			−0.615366	+	0.788242i	$0.710992\pi$
$98$	−22.0606	+	95.4847i	−0.225108	+	0.974334i
$99$	166.035	+	166.035i	1.67712	+	1.67712i
$100$	4.97833	+	89.3496i	0.0497833	+	0.893496i
$101$	−44.7977	+	167.187i	−0.443542	+	1.65532i	0.276216	+	0.961096i	$0.410920\pi$
$101$	−44.7977	+	167.187i	−0.443542	+	1.65532i	−0.719758	+	0.694225i	$0.755747\pi$
$102$	67.7454	−	71.6251i	0.664171	−	0.702207i
$103$	−21.0109	+	36.3920i	−0.203990	+	0.353321i	−0.949810	−	0.312826i	$-0.898724\pi$
$103$	−21.0109	+	36.3920i	−0.203990	+	0.353321i	0.745821	+	0.666147i	$0.232058\pi$
$104$	−10.2086	−	8.63198i	−0.0981600	−	0.0829998i
$105$	24.0956	+	57.6078i	0.229482	+	0.548646i
$106$	19.4107	+	65.1345i	0.183120	+	0.614476i
$107$	−10.1916	−	38.0354i	−0.0952482	−	0.355471i	0.901809	−	0.432135i	$-0.142240\pi$
$107$	−10.1916	−	38.0354i	−0.0952482	−	0.355471i	−0.997057	+	0.0766641i	$0.975573\pi$
$108$	84.3804	+	256.810i	0.781300	+	2.37787i
$109$	−122.704	−	32.8786i	−1.12573	−	0.301638i	−0.352529	−	0.935801i	$-0.614678\pi$
$109$	−122.704	−	32.8786i	−1.12573	−	0.301638i	−0.773200	+	0.634162i	$0.781345\pi$
$110$	−30.4713	+	18.7421i	−0.277012	+	0.170382i
$111$		−	296.177i		−	2.66826i
$112$	−96.0794	−	57.5564i	−0.857852	−	0.513897i
$113$	−129.391			−1.14506			−0.572528	−	0.819885i	$-0.694037\pi$
$113$	−129.391			−1.14506			−0.572528	+	0.819885i	$0.694037\pi$
$114$	174.560	+	283.803i	1.53122	+	2.48950i
$115$	4.29228	−	16.0190i	0.0373242	−	0.139296i
$116$	−55.7190	−	169.579i	−0.480336	−	1.46189i
$117$	34.3509	−	9.20430i	0.293598	−	0.0786693i
$118$	−169.891	+	50.6292i	−1.43976	+	0.429061i
$119$	−49.8796	−	38.0006i	−0.419156	−	0.319333i
$120$	−71.1161	+	5.95130i	−0.592634	+	0.0495942i
$121$	0.645479	+	0.372667i	0.00533454	+	0.00307990i
$122$	23.2540	+	21.9945i	0.190607	+	0.180282i
$123$	282.858	+	75.7916i	2.29966	+	0.616192i
$124$	2.09687	+	37.6341i	0.0169103	+	0.303500i
$125$	54.3021	−	54.3021i	0.434416	−	0.434416i
$126$	271.552	−	122.568i	2.15517	−	0.972766i
$127$			53.1110i			0.418197i	0.977895	+	0.209099i	$0.0670530\pi$
$127$			53.1110i			0.418197i	−0.977895	+	0.209099i	$0.932947\pi$
$128$	96.3654	−	84.2480i	0.752854	−	0.658187i
$129$	−26.1159	−	45.2341i	−0.202449	−	0.350652i
$130$	0.150765	+	5.41597i	0.00115973	+	0.0416613i
$131$	−14.4395	+	3.86906i	−0.110225	+	0.0295348i	−0.313510	−	0.949585i	$-0.601505\pi$
$131$	−14.4395	+	3.86906i	−0.110225	+	0.0295348i	0.203285	+	0.979120i	$0.434838\pi$
$132$	132.947	+	203.249i	1.00717	+	1.53976i
$133$	167.682	−	129.590i	1.26076	−	0.974363i
$134$	8.48103	+	28.4590i	0.0632913	+	0.212380i
$135$	54.7762	−	94.8752i	0.405750	−	0.702779i
$136$	58.8584	−	40.8827i	0.432782	−	0.300608i
$137$	56.0020	−	32.3328i	0.408774	−	0.236005i	−0.281489	−	0.959564i	$-0.590828\pi$
$137$	56.0020	−	32.3328i	0.408774	−	0.236005i	0.690263	+	0.723559i	$0.257495\pi$
$138$	−109.522	−	26.1027i	−0.793634	−	0.189150i
$139$	30.9038	−	30.9038i	0.222330	−	0.222330i	−0.587149	−	0.809479i	$-0.699750\pi$
$139$	30.9038	−	30.9038i	0.222330	−	0.222330i	0.809479	+	0.587149i	$0.199750\pi$
$140$	8.57321	+	44.5737i	0.0612372	+	0.318384i
$141$	18.4297	−	18.4297i	0.130707	−	0.130707i
$142$	−159.559	+	98.1407i	−1.12366	+	0.691131i
$143$	15.9684	−	9.21938i	0.111667	−	0.0644712i
$144$	37.8254	+	338.386i	0.262677	+	2.34990i
$145$	−36.1704	+	62.6490i	−0.249451	+	0.432062i
$146$	−18.2008	+	33.6540i	−0.124663	+	0.230507i
$147$	−136.430	−	232.575i	−0.928097	−	1.58214i
$148$	44.0664	−	210.733i	0.297746	−	1.42387i
$149$	−86.4420	+	23.1621i	−0.580148	+	0.155450i	−0.536947	−	0.843616i	$-0.680422\pi$
$149$	−86.4420	+	23.1621i	−0.580148	+	0.155450i	−0.0432012	+	0.999066i	$0.513756\pi$
$150$	−178.880	−	169.190i	−1.19253	−	1.12794i
$151$	39.0685	+	67.6686i	0.258732	+	0.448136i	0.965902	−	0.258906i	$-0.0833621\pi$
$151$	39.0685	+	67.6686i	0.258732	+	0.448136i	−0.707171	+	0.707043i	$0.750029\pi$
$152$	81.9758	+	227.901i	0.539315	+	1.49935i
$153$			190.633i			1.24597i
$154$	119.550	−	97.8253i	0.776301	−	0.635229i
$155$	10.8016	−	10.8016i	0.0696878	−	0.0696878i
$156$	36.7262	−	2.04629i	0.235425	−	0.0131173i
$157$	−56.3224	−	15.0915i	−0.358741	−	0.0961244i	0.0749467	−	0.997188i	$-0.476121\pi$
$157$	−56.3224	−	15.0915i	−0.358741	−	0.0961244i	−0.433688	+	0.901063i	$0.642788\pi$
$158$	−237.078	+	6.59958i	−1.50050	+	0.0417695i
$159$	−161.947	−	93.4999i	−1.01853	−	0.588050i
$160$	−51.4854	−	6.34653i	−0.321784	−	0.0396658i
$161$	−9.10159	+	71.0304i	−0.0565316	+	0.441183i
$162$	−317.268	−	171.585i	−1.95845	−	1.05917i
$163$	−265.492	+	71.1385i	−1.62879	+	0.436432i	−0.953566	−	0.301183i	$-0.902618\pi$
$163$	−265.492	+	71.1385i	−1.62879	+	0.436432i	−0.675221	+	0.737616i	$0.735952\pi$
$164$	189.980	+	96.0115i	1.15842	+	0.585436i
$165$	25.4751	−	95.0743i	0.154394	−	0.576208i
$166$	20.7538	+	4.94635i	0.125023	+	0.0297973i
$167$	86.0202			0.515091			0.257546	−	0.966266i	$-0.417086\pi$
$167$	86.0202			0.515091			0.257546	+	0.966266i	$0.417086\pi$
$168$	300.874	−	66.6014i	1.79092	−	0.396437i
$169$			166.207i			0.983476i
$170$	−28.2522	−	6.73346i	−0.166189	−	0.0396086i
$171$	−622.315	−	166.749i	−3.63927	−	0.975139i
$172$	−11.8517	−	36.0703i	−0.0689052	−	0.209711i
$173$	21.2247	+	79.2116i	0.122686	+	0.457871i	0.999747	−	0.0225092i	$-0.00716550\pi$
$173$	21.2247	+	79.2116i	0.122686	+	0.457871i	−0.877061	+	0.480380i	$0.840499\pi$
$174$	431.992	+	233.630i	2.48271	+	1.34270i
$175$	−94.9045	+	124.571i	−0.542311	+	0.711837i
$176$	64.3531	+	164.394i	0.365643	+	0.934058i
$177$	243.877	−	422.408i	1.37784	−	2.38649i
$178$	129.602	−	3.60775i	0.728103	−	0.0202683i
$179$	67.1363	−	250.556i	0.375063	−	1.39975i	−0.478190	−	0.878257i	$-0.658707\pi$
$179$	67.1363	−	250.556i	0.375063	−	1.39975i	0.853253	−	0.521498i	$-0.174626\pi$
$180$	91.9967	−	102.853i	0.511093	−	0.571407i
$181$	207.889	+	207.889i	1.14856	+	1.14856i	0.986836	+	0.161722i	$0.0517049\pi$
$181$	207.889	+	207.889i	1.14856	+	1.14856i	0.161722	+	0.986836i	$0.448295\pi$
$182$	−3.77785	−	23.0885i	−0.0207574	−	0.126860i
$183$	−88.0666			−0.481238
$184$	−74.0423	−	34.8675i	−0.402404	−	0.189497i
$185$	−75.5625	+	43.6260i	−0.408446	+	0.235816i
$186$	−75.3441	−	71.2630i	−0.405076	−	0.383134i
$187$	25.5819	+	95.4728i	0.136801	+	0.510550i
$188$	15.8550	−	10.3709i	0.0843353	−	0.0551645i
$189$	−179.518	+	437.669i	−0.949830	+	2.31571i
$190$	46.6935	−	86.3382i	0.245755	−	0.454412i
$191$	127.283	+	73.4869i	0.666403	+	0.384748i	0.794712	−	0.606986i	$-0.207622\pi$
$191$	127.283	+	73.4869i	0.666403	+	0.384748i	−0.128309	+	0.991734i	$0.540955\pi$
$192$	−33.3436	+	350.598i	−0.173664	+	1.82603i
$193$	63.9196	+	110.712i	0.331190	+	0.573637i	0.982745	−	0.184964i	$-0.0592167\pi$
$193$	63.9196	+	110.712i	0.331190	+	0.573637i	−0.651556	+	0.758601i	$0.725883\pi$
$194$	203.372	−	125.088i	1.04831	−	0.644786i
$195$	−10.5410	−	10.5410i	−0.0540567	−	0.0540567i
$196$	−62.4683	−	185.779i	−0.318716	−	0.947850i
$197$	−98.6531	−	98.6531i	−0.500777	−	0.500777i	0.410902	−	0.911679i	$-0.365214\pi$
$197$	−98.6531	−	98.6531i	−0.500777	−	0.500777i	−0.911679	+	0.410902i	$0.865214\pi$
$198$	−456.823	−	108.877i	−2.30719	−	0.549882i
$199$	191.079	+	330.958i	0.960195	+	1.66311i	0.722004	+	0.691889i	$0.243221\pi$
$199$	191.079	+	330.958i	0.960195	+	1.66311i	0.238191	+	0.971218i	$0.423445\pi$
$200$	−102.102	−	146.995i	−0.510511	−	0.734977i
$201$	−70.7587	−	40.8525i	−0.352033	−	0.203246i
$202$	−98.8652	−	331.752i	−0.489432	−	1.64234i
$203$	118.541	−	289.006i	0.583947	−	1.42368i
$204$	−40.3585	+	193.001i	−0.197836	+	0.946085i
$205$	−22.3278	−	83.3285i	−0.108916	−	0.406481i
$206$	−2.33863	−	84.0113i	−0.0113526	−	0.407822i
$207$	188.540	−	108.853i	0.910819	−	0.525862i
$208$	26.4356	+	4.00833i	0.127094	+	0.0192708i
$209$	−334.044			−1.59830
$210$	−101.410	−	72.8904i	−0.482906	−	0.347097i
$211$	7.41591	+	7.41591i	0.0351465	+	0.0351465i	0.724462	−	0.689315i	$-0.242088\pi$
$211$	7.41591	+	7.41591i	0.0351465	+	0.0351465i	−0.689315	+	0.724462i	$0.742088\pi$
$212$	−101.316	−	90.6214i	−0.477904	−	0.427460i
$213$	133.397	−	497.846i	0.626278	−	2.33730i
$214$	57.2157	+	54.1166i	0.267363	+	0.252881i
$215$	−7.69362	+	13.3257i	−0.0357843	+	0.0619802i
$216$	−412.834	−	349.074i	−1.91127	−	1.61608i
$217$	−39.9738	+	52.4695i	−0.184211	+	0.241795i
$218$	243.484	−	72.5605i	1.11690	−	0.332846i
$219$	−27.2459	−	101.683i	−0.124410	−	0.464306i
$220$	32.2714	−	63.8562i	0.146688	−	0.290256i
$221$	14.4597	+	3.87446i	0.0654285	+	0.0175315i
$222$	310.337	+	504.553i	1.39791	+	2.27276i
$223$			102.258i			0.458557i	0.973361	+	0.229278i	$0.0736366\pi$
$223$			102.258i			0.458557i	−0.973361	+	0.229278i	$0.926363\pi$
$224$	223.985	−	2.62245i	0.999931	−	0.0117074i
$225$	476.096			2.11598
$226$	220.425	−	135.578i	0.975333	−	0.599901i
$227$	−83.5418	+	311.782i	−0.368026	+	1.37349i	0.495247	+	0.868752i	$0.335078\pi$
$227$	−83.5418	+	311.782i	−0.368026	+	1.37349i	−0.863272	+	0.504738i	$0.831589\pi$
$228$	−594.743	−	300.569i	−2.60852	−	1.31828i
$229$	−184.014	+	49.3064i	−0.803554	+	0.215312i	−0.637144	−	0.770745i	$-0.719884\pi$
$229$	−184.014	+	49.3064i	−0.803554	+	0.215312i	−0.166410	+	0.986057i	$0.553218\pi$
$230$	9.47273	+	31.7867i	0.0411858	+	0.138203i
$231$	−54.0188	+	421.572i	−0.233848	+	1.82499i
$232$	272.607	+	230.505i	1.17503	+	0.993554i
$233$	−84.9300	−	49.0344i	−0.364506	−	0.210448i	0.306549	−	0.951855i	$-0.400826\pi$
$233$	−84.9300	−	49.0344i	−0.364506	−	0.210448i	−0.671056	+	0.741407i	$0.734159\pi$
$234$	−48.8743	+	51.6733i	−0.208865	+	0.220826i
$235$	−7.41656	−	1.98726i	−0.0315598	−	0.00845643i
$236$	236.370	−	264.263i	1.00157	−	1.11976i
$237$	461.423	−	461.423i	1.94693	−	1.94693i
$238$	124.790	+	12.4719i	0.524328	+	0.0524028i
$239$		−	158.330i		−	0.662468i	−0.943549	−	0.331234i	$-0.892535\pi$
$239$		−	158.330i		−	0.662468i	0.943549	−	0.331234i	$-0.107465\pi$
$240$	114.914	−	84.6545i	0.478809	−	0.352727i
$241$	−45.5171	−	78.8379i	−0.188868	−	0.327128i	0.756005	−	0.654565i	$-0.227148\pi$
$241$	−45.5171	−	78.8379i	−0.188868	−	0.327128i	−0.944873	+	0.327437i	$0.893815\pi$
$242$	−1.49009	+	0.0414799i	−0.00615741	+	0.000171404i
$243$	371.112	−	99.4393i	1.52721	−	0.409215i
$244$	−62.6605	−	13.1029i	−0.256805	−	0.0537005i
$245$	−39.2402	+	69.0647i	−0.160164	+	0.281897i
$246$	−561.279	+	167.266i	−2.28162	+	0.679945i
$247$	−25.2960	+	43.8140i	−0.102413	+	0.177385i
$248$	−43.0054	−	61.9145i	−0.173409	−	0.249655i
$249$	−50.8371	+	29.3508i	−0.204165	+	0.117875i
$250$	−35.6083	+	149.405i	−0.142433	+	0.597619i
$251$	149.092	−	149.092i	0.593992	−	0.593992i	−0.344715	−	0.938707i	$-0.612025\pi$
$251$	149.092	−	149.092i	0.593992	−	0.593992i	0.938707	+	0.344715i	$0.112025\pi$
$252$	−334.175	+	493.337i	−1.32609	+	1.95769i
$253$	79.8167	−	79.8167i	0.315481	−	0.315481i
$254$	−55.6502	−	90.4775i	−0.219095	−	0.356211i
$255$	69.2044	−	39.9552i	0.271390	−	0.156687i
$256$	−75.8878	+	244.493i	−0.296437	+	0.955053i
$257$	−104.527	+	181.046i	−0.406720	+	0.704460i	−0.994520	−	0.104547i	$-0.966661\pi$
$257$	−104.527	+	181.046i	−0.406720	+	0.704460i	0.587800	+	0.809006i	$0.299994\pi$
$258$	91.8867	+	49.6943i	0.356150	+	0.192613i
$259$	298.109	−	230.389i	1.15100	−	0.889533i
$260$	−5.93174	−	9.06843i	−0.0228144	−	0.0348786i
$261$	−917.292	+	245.788i	−3.51453	+	0.941715i
$262$	20.5445	−	21.7210i	0.0784139	−	0.0829046i
$263$	−140.474	−	243.308i	−0.534122	−	0.925126i	−0.999205	−	0.0398590i	$-0.987309\pi$
$263$	−140.474	−	243.308i	−0.534122	−	0.925126i	0.465084	−	0.885267i	$-0.346024\pi$
$264$	−439.448	−	206.942i	−1.66458	−	0.783871i
$265$			55.0892i			0.207884i
$266$	−149.869	+	396.462i	−0.563416	+	1.49046i
$267$	−252.244	+	252.244i	−0.944732	+	0.944732i
$268$	−44.2675	−	39.5949i	−0.165177	−	0.147742i
$269$	415.356	+	111.294i	1.54407	+	0.413733i	0.927579	−	0.373626i	$-0.121886\pi$
$269$	415.356	+	111.294i	1.54407	+	0.413733i	0.616494	+	0.787359i	$0.288552\pi$
$270$	6.09689	+	219.020i	0.0225811	+	0.811186i
$271$	109.682	+	63.3247i	0.404729	+	0.233671i	0.688523	−	0.725215i	$-0.258260\pi$
$271$	109.682	+	63.3247i	0.404729	+	0.233671i	−0.283793	+	0.958885i	$0.591593\pi$
$272$	−57.4311	+	131.318i	−0.211144	+	0.482787i
$273$	51.2038	+	39.0095i	0.187560	+	0.142892i
$274$	−61.5238	+	113.760i	−0.224539	+	0.415182i
$275$	238.438	−	63.8893i	0.867048	−	0.232325i
$276$	213.927	−	70.2903i	0.775096	−	0.254675i
$277$	−91.8945	+	342.955i	−0.331749	+	1.23810i	0.575602	+	0.817730i	$0.304768\pi$
$277$	−91.8945	+	342.955i	−0.331749	+	1.23810i	−0.907351	+	0.420374i	$0.861899\pi$
$278$	−20.2650	+	85.0276i	−0.0728957	+	0.305855i
$279$	200.532			0.718752
$280$	−61.3097	−	66.9507i	−0.218963	−	0.239110i
$281$		−	203.996i		−	0.725966i	−0.931796	−	0.362983i	$-0.881758\pi$
$281$		−	203.996i		−	0.725966i	0.931796	−	0.362983i	$-0.118242\pi$
$282$	−12.0852	+	50.7069i	−0.0428553	+	0.179812i
$283$	7.20400	+	1.93030i	0.0254558	+	0.00682086i	0.271524	−	0.962432i	$-0.412472\pi$
$283$	7.20400	+	1.93030i	0.0254558	+	0.00682086i	−0.246069	+	0.969252i	$0.579139\pi$
$284$	168.985	−	334.376i	0.595019	−	1.17738i
$285$	69.8983	+	260.864i	0.245257	+	0.915312i
$286$	−17.5429	+	32.4376i	−0.0613389	+	0.113418i
$287$	143.743	+	343.660i	0.500846	+	1.19742i
$288$	−419.002	−	536.825i	−1.45487	−	1.86398i
$289$	104.377	−	180.787i	0.361167	−	0.625560i
$290$	−4.02596	−	144.626i	−0.0138826	−	0.498709i
$291$	−170.026	+	634.546i	−0.584282	+	2.18057i
$292$	−4.25694	−	76.4024i	−0.0145786	−	0.261652i
$293$	−67.6489	−	67.6489i	−0.230884	−	0.230884i	0.582178	−	0.813061i	$-0.302201\pi$
$293$	−67.6489	−	67.6489i	−0.230884	−	0.230884i	−0.813061	+	0.582178i	$0.802201\pi$
$294$	476.111	+	253.251i	1.61942	+	0.861398i
$295$	−143.690			−0.487085
$296$	145.739	+	405.169i	0.492361	+	1.36881i
$297$	645.758	−	372.829i	2.17427	−	1.25532i
$298$	122.989	−	130.033i	0.412715	−	0.436351i
$299$	−4.42470	−	16.5132i	−0.0147983	−	0.0552282i
$300$	482.010	+	100.793i	1.60670	+	0.335977i
$301$	25.2143	−	61.4729i	0.0837683	−	0.204229i
$302$	−137.459	−	74.3408i	−0.455162	−	0.246162i
$303$	824.849	+	476.227i	2.72227	+	1.57171i
$304$	−378.447	−	302.347i	−1.24489	−	0.994562i
$305$	12.9720	+	22.4681i	0.0425311	+	0.0736660i
$306$	−199.748	−	324.754i	−0.652770	−	1.06129i
$307$	−200.976	−	200.976i	−0.654644	−	0.654644i	0.299463	−	0.954108i	$-0.403192\pi$
$307$	−200.976	−	200.976i	−0.654644	−	0.654644i	−0.954108	+	0.299463i	$0.903192\pi$
$308$	−101.158	+	291.917i	−0.328436	+	0.947781i
$309$	163.510	+	163.510i	0.529159	+	0.529159i
$310$	−7.08309	+	29.7191i	−0.0228487	+	0.0958682i
$311$	−117.586	−	203.665i	−0.378090	−	0.654871i	0.612694	−	0.790320i	$-0.290086\pi$
$311$	−117.586	−	203.665i	−0.378090	−	0.654871i	−0.990784	+	0.135449i	$0.956752\pi$
$312$	−60.4210	+	41.9681i	−0.193657	+	0.134513i
$313$	133.891	+	77.3022i	0.427768	+	0.246972i	0.698395	−	0.715712i	$-0.253898\pi$
$313$	133.891	+	77.3022i	0.427768	+	0.246972i	−0.270627	+	0.962684i	$0.587231\pi$
$314$	111.761	−	33.3059i	0.355928	−	0.106070i
$315$	239.312	−	32.3482i	0.759721	−	0.102693i
$316$	396.960	−	259.656i	1.25620	−	0.821695i
$317$	−48.0495	−	179.323i	−0.151576	−	0.565688i	−0.999374	−	0.0353699i	$-0.988739\pi$
$317$	−48.0495	−	179.323i	−0.151576	−	0.565688i	0.847799	−	0.530318i	$-0.177928\pi$
$318$	373.855	−	10.4070i	1.17564	−	0.0327265i
$319$	−426.414	+	246.190i	−1.33672	+	0.771756i
$320$	94.3581	−	43.1353i	0.294869	−	0.134798i
$321$	−216.685			−0.675031
$322$	−58.9213	−	130.541i	−0.182985	−	0.405406i
$323$	−191.766	−	191.766i	−0.593703	−	0.593703i
$324$	720.272	−	40.1317i	2.22306	−	0.123863i
$325$	9.67626	−	36.1123i	0.0297731	−	0.111115i
$326$	377.741	−	399.374i	1.15871	−	1.22507i
$327$	−349.519	+	605.385i	−1.06887	+	1.85133i
$328$	−424.244	+	35.5026i	−1.29343	+	0.108239i
$329$	32.8860	+	4.21390i	0.0999575	+	0.0128082i
$330$	56.2216	+	188.657i	0.170368	+	0.571689i
$331$	51.4949	+	192.182i	0.155574	+	0.580609i	0.999056	+	0.0434513i	$0.0138353\pi$
$331$	51.4949	+	192.182i	0.155574	+	0.580609i	−0.843482	+	0.537158i	$0.819498\pi$
$332$	−40.5381	+	13.3197i	−0.122103	+	0.0401196i
$333$	−1106.37	−	296.451i	−3.32243	−	0.890242i
$334$	−146.540	+	90.1328i	−0.438743	+	0.269859i
$335$			24.0699i			0.0718504i
$336$	−442.769	+	428.718i	−1.31777	+	1.27594i
$337$	9.29790			0.0275902			0.0137951	−	0.999905i	$-0.495609\pi$
$337$	9.29790			0.0275902			0.0137951	+	0.999905i	$0.495609\pi$
$338$	−174.154	−	283.143i	−0.515248	−	0.837702i
$339$	−184.283	+	687.754i	−0.543608	+	2.02877i
$340$	55.1845	−	18.1321i	0.162307	−	0.0533296i
$341$	100.430	−	26.9102i	0.294516	−	0.0789155i
$342$	1234.87	−	368.002i	3.61072	−	1.07603i
$343$	127.966	−	318.235i	0.373080	−	0.927799i
$344$	57.9848	+	49.0294i	0.168560	+	0.142527i
$345$	−79.0326	−	45.6295i	−0.229080	−	0.132259i
$346$	−119.156	−	112.702i	−0.344382	−	0.325728i
$347$	−396.103	−	106.135i	−1.14151	−	0.305866i	−0.361950	−	0.932197i	$-0.617889\pi$
$347$	−396.103	−	106.135i	−1.14151	−	0.305866i	−0.779557	+	0.626332i	$0.784556\pi$
$348$	−980.722	+	54.6433i	−2.81817	+	0.157021i
$349$	−241.381	+	241.381i	−0.691636	+	0.691636i	−0.962592	−	0.270956i	$-0.912660\pi$
$349$	−241.381	+	241.381i	−0.691636	+	0.691636i	0.270956	+	0.962592i	$0.412660\pi$
$350$	31.1478	−	311.656i	0.0889937	−	0.890446i
$351$		−	112.932i		−	0.321745i
$352$	−281.883	−	212.625i	−0.800804	−	0.604048i
$353$	14.3559	+	24.8651i	0.0406682	+	0.0704394i	0.885643	−	0.464367i	$-0.153718\pi$
$353$	14.3559	+	24.8651i	0.0406682	+	0.0704394i	−0.844975	+	0.534806i	$0.820385\pi$
$354$	27.1449	+	975.132i	0.0766804	+	2.75461i
$355$	−146.663	+	39.2981i	−0.413134	+	0.110699i
$356$	−217.004	+	141.945i	−0.609563	+	0.398721i
$357$	−273.025	+	211.003i	−0.764776	+	0.591045i
$358$	148.165	+	497.182i	0.413868	+	1.38878i
$359$	197.795	−	342.591i	0.550962	−	0.954294i	−0.447244	−	0.894412i	$-0.647594\pi$
$359$	197.795	−	342.591i	0.550962	−	0.954294i	0.998205	−	0.0598817i	$-0.0190723\pi$
$360$	−48.9507	+	271.611i	−0.135974	+	0.754475i
$361$	481.117	−	277.773i	1.33273	−	0.769454i
$362$	−571.978	−	136.322i	−1.58005	−	0.376580i
$363$	2.90015	−	2.90015i	0.00798939	−	0.00798939i
$364$	30.6282	+	35.3741i	0.0841433	+	0.0971816i
$365$	−21.9288	+	21.9288i	−0.0600788	+	0.0600788i
$366$	150.026	−	92.2771i	0.409908	−	0.252123i
$367$	−437.898	+	252.821i	−1.19318	+	0.688885i	−0.959027	−	0.283314i	$-0.908566\pi$
$367$	−437.898	+	252.821i	−1.19318	+	0.688885i	−0.234157	+	0.972199i	$0.575233\pi$
$368$	162.669	−	18.1835i	0.442037	−	0.0494117i
$369$	566.239	−	980.755i	1.53452	−	2.65787i
$370$	83.0131	−	153.494i	0.224360	−	0.414850i
$371$	−31.8646	−	235.735i	−0.0858885	−	0.635403i
$372$	203.023	+	42.4541i	0.545760	+	0.114124i
$373$	206.892	−	55.4367i	0.554671	−	0.148624i	0.0294143	−	0.999567i	$-0.490636\pi$
$373$	206.892	−	55.4367i	0.554671	−	0.148624i	0.525257	+	0.850944i	$0.323969\pi$
$374$	−143.617	−	135.838i	−0.384004	−	0.363204i
$375$	−211.293	−	365.970i	−0.563448	−	0.975921i
$376$	−16.1431	+	34.2805i	−0.0429339	+	0.0911715i
$377$			74.5728i			0.197806i
$378$	−152.775	−	933.693i	−0.404167	−	2.47009i
$379$	335.553	−	335.553i	0.885364	−	0.885364i	−0.108709	−	0.994074i	$-0.534672\pi$
$379$	335.553	−	335.553i	0.885364	−	0.885364i	0.994074	+	0.108709i	$0.0346718\pi$
$380$	10.9210	+	196.008i	0.0287396	+	0.515810i
$381$	282.301	+	75.6424i	0.740948	+	0.198536i
$382$	−293.834	+	8.17948i	−0.769198	+	0.0214123i
$383$	48.3341	+	27.9057i	0.126199	+	0.0728609i	0.561770	−	0.827293i	$-0.310120\pi$
$383$	48.3341	+	27.9057i	0.126199	+	0.0728609i	−0.435572	+	0.900154i	$0.643454\pi$
$384$	−310.557	−	632.199i	−0.808742	−	1.64635i
$385$	115.511	−	48.3148i	0.300029	−	0.125493i
$386$	−224.895	−	121.628i	−0.582631	−	0.315099i
$387$	−195.112	+	52.2802i	−0.504166	+	0.135091i
$388$	−215.386	+	426.190i	−0.555119	+	1.09843i
$389$	21.5517	−	80.4320i	0.0554028	−	0.206766i	−0.932676	−	0.360715i	$-0.882533\pi$
$389$	21.5517	−	80.4320i	0.0554028	−	0.206766i	0.988079	+	0.153949i	$0.0491993\pi$
$390$	29.0022	+	6.91223i	0.0743647	+	0.0177237i
$391$	91.6415			0.234377
$392$	301.079	+	251.029i	0.768058	+	0.640380i
$393$			82.2608i			0.209315i
$394$	271.430	+	64.6912i	0.688910	+	0.164191i
$395$	−185.688	−	49.7548i	−0.470095	−	0.125962i
$396$	892.305	−	293.187i	2.25330	−	0.740370i
$397$	−90.7823	−	338.804i	−0.228671	−	0.853411i	−0.980901	−	0.194510i	$-0.937688\pi$
$397$	−90.7823	−	338.804i	−0.228671	−	0.853411i	0.752230	−	0.658901i	$-0.228978\pi$
$398$	−672.294	−	363.591i	−1.68918	−	0.913545i
$399$	−449.994	−	1075.84i	−1.12780	−	2.69635i
$400$	327.960	+	143.431i	0.819900	+	0.358578i
$401$	−199.672	+	345.842i	−0.497934	+	0.862448i	−0.999997	−	0.00238351i	$-0.999241\pi$
$401$	−199.672	+	345.842i	−0.497934	+	0.862448i	0.502063	+	0.864831i	$0.332575\pi$
$402$	163.347	−	4.54711i	0.406336	−	0.0113112i
$403$	4.07564	−	15.2105i	0.0101132	−	0.0377432i
$404$	516.035	+	461.566i	1.27732	+	1.14249i
$405$	−206.730	−	206.730i	−0.510445	−	0.510445i
$406$	100.882	+	616.546i	0.248478	+	1.51859i
$407$	−593.872			−1.45915
$408$	−133.476	−	371.076i	−0.327147	−	0.909501i
$409$	499.745	−	288.528i	1.22187	−	0.705448i	0.256555	−	0.966530i	$-0.417413\pi$
$409$	499.745	−	288.528i	1.22187	−	0.705448i	0.965317	+	0.261082i	$0.0840793\pi$
$410$	125.349	+	118.559i	0.305729	+	0.289169i
$411$	−92.0986	−	343.717i	−0.224084	−	0.836294i
$412$	92.0118	+	140.667i	0.223330	+	0.341425i
$413$	614.871	−	83.1131i	1.48879	−	0.201242i
$414$	−207.130	+	382.991i	−0.500313	+	0.925099i
$415$	14.9763	+	8.64659i	0.0360875	+	0.0208352i
$416$	−49.2345	+	20.8711i	−0.118352	+	0.0501709i
$417$	−120.249	−	208.277i	−0.288367	−	0.499466i
$418$	569.061	−	350.014i	1.36139	−	0.837354i
$419$	104.114	+	104.114i	0.248482	+	0.248482i	0.820348	−	0.571865i	$-0.193780\pi$
$419$	104.114	+	104.114i	0.248482	+	0.248482i	−0.571865	+	0.820348i	$0.693780\pi$
$420$	249.133	+	17.9141i	0.593174	+	0.0426526i
$421$	70.1243	+	70.1243i	0.166566	+	0.166566i	0.785468	−	0.618902i	$-0.212422\pi$
$421$	70.1243	+	70.1243i	0.166566	+	0.166566i	−0.618902	+	0.785468i	$0.712422\pi$
$422$	−20.4039	−	4.86294i	−0.0483504	−	0.0115236i
$423$	−50.3975	−	87.2910i	−0.119143	−	0.206362i
$424$	267.551	+	48.2190i	0.631016	+	0.113724i
$425$	173.559	+	100.204i	0.408373	+	0.235774i
$426$	294.398	+	987.882i	0.691075	+	2.31897i
$427$	−68.5050	−	88.6412i	−0.160433	−	0.207591i
$428$	−154.174	−	32.2393i	−0.360220	−	0.0753255i
$429$	−26.2610	−	98.0076i	−0.0612146	−	0.228456i
$430$	−0.856341	−	30.7626i	−0.00199149	−	0.0715408i
$431$	395.520	−	228.353i	0.917679	−	0.529822i	0.0347851	−	0.999395i	$-0.488925\pi$
$431$	395.520	−	228.353i	0.917679	−	0.529822i	0.882894	+	0.469573i	$0.155592\pi$
$432$	1069.05	+	162.095i	2.47465	+	0.375221i
$433$	−42.2284			−0.0975253			−0.0487626	−	0.998810i	$-0.515528\pi$
$433$	−42.2284			−0.0975253			−0.0487626	+	0.998810i	$0.515528\pi$
$434$	13.1195	−	131.270i	0.0302292	−	0.302464i
$435$	281.484	+	281.484i	0.647089	+	0.647089i
$436$	−338.759	+	378.736i	−0.776970	+	0.868660i
$437$	−80.1597	+	299.160i	−0.183432	+	0.684577i
$438$	152.959	+	144.674i	0.349222	+	0.330306i
$439$	−145.062	+	251.256i	−0.330438	+	0.572336i	−0.982598	−	0.185746i	$-0.940530\pi$
$439$	−145.062	+	251.256i	−0.330438	+	0.572336i	0.652159	+	0.758082i	$0.273863\pi$
$440$	11.9331	+	142.597i	0.0271207	+	0.324084i
$441$	−1005.34	+	276.846i	−2.27968	+	0.627768i
$442$	−28.6926	+	8.55065i	−0.0649153	+	0.0193454i
$443$	5.13914	+	19.1795i	0.0116008	+	0.0432947i	0.971484	−	0.237107i	$-0.0761991\pi$
$443$	5.13914	+	19.1795i	0.0116008	+	0.0432947i	−0.959883	+	0.280401i	$0.909532\pi$
$444$	−1057.35	−	534.359i	−2.38142	−	1.20351i
$445$	101.509	+	27.1992i	0.228110	+	0.0611218i
$446$	−107.147	−	174.202i	−0.240240	−	0.390588i
$447$			492.454i			1.10169i
$448$	−378.822	+	239.161i	−0.845585	+	0.533841i
$449$	−552.102			−1.22963			−0.614813	−	0.788673i	$-0.710769\pi$
$449$	−552.102			−1.22963			−0.614813	+	0.788673i	$0.710769\pi$
$450$	−811.056	+	498.858i	−1.80235	+	1.10857i
$451$	151.972	−	567.167i	0.336966	−	1.25758i
$452$	−233.447	+	461.927i	−0.516475	+	1.02196i
$453$	415.322	−	111.285i	0.916825	−	0.245662i
$454$	−184.371	−	618.674i	−0.406102	−	1.36272i
$455$	2.41018	−	18.8095i	0.00529709	−	0.0413395i
$456$	1328.12	−	111.142i	2.91253	−	0.243733i
$457$	−271.165	−	156.557i	−0.593359	−	0.342576i	0.173066	−	0.984910i	$-0.444633\pi$
$457$	−271.165	−	156.557i	−0.593359	−	0.342576i	−0.766424	+	0.642335i	$0.777966\pi$
$458$	261.814	−	276.808i	0.571646	−	0.604383i
$459$	584.745	+	156.682i	1.27395	+	0.341355i
$460$	−49.4437	−	44.2248i	−0.107486	−	0.0961408i
$461$	−122.341	+	122.341i	−0.265381	+	0.265381i	−0.827236	−	0.561855i	$-0.810088\pi$
$461$	−122.341	+	122.341i	−0.265381	+	0.265381i	0.561855	+	0.827236i	$0.310088\pi$
$462$	−349.703	−	774.772i	−0.756934	−	1.67700i
$463$			125.988i			0.272111i	0.990701	+	0.136056i	$0.0434426\pi$
$463$			125.988i			0.272111i	−0.990701	+	0.136056i	$0.956557\pi$
$464$	−705.926	−	107.037i	−1.52139	−	0.230682i
$465$	−42.0298	−	72.7977i	−0.0903867	−	0.156554i
$466$	196.062	−	5.45779i	0.420733	−	0.0117120i
$467$	340.750	−	91.3037i	0.729657	−	0.195511i	0.125181	−	0.992134i	$-0.460049\pi$
$467$	340.750	−	91.3037i	0.729657	−	0.195511i	0.604477	+	0.796623i	$0.293382\pi$
$468$	29.1163	−	139.239i	0.0622143	−	0.297520i
$469$	−13.9225	−	102.999i	−0.0296855	−	0.219613i
$470$	14.7168	−	4.38574i	0.0313123	−	0.00933135i
$471$	−160.432	+	277.877i	−0.340620	+	0.589972i
$472$	−125.770	+	697.857i	−0.266463	+	1.47851i
$473$	−90.7002	+	52.3658i	−0.191755	+	0.110710i
$474$	−302.575	+	1269.54i	−0.638345	+	2.67836i
$475$	−478.925	+	478.925i	−1.00826	+	1.00826i
$476$	−225.655	+	109.510i	−0.474064	+	0.230062i
$477$	−511.365	+	511.365i	−1.07204	+	1.07204i
$478$	165.899	+	269.723i	0.347070	+	0.564275i
$479$	−179.861	+	103.843i	−0.375492	+	0.216791i	−0.675855	−	0.737034i	$-0.736226\pi$
$479$	−179.861	+	103.843i	−0.375492	+	0.216791i	0.300363	+	0.953825i	$0.402892\pi$
$480$	−107.061	+	264.622i	−0.223043	+	0.551295i
$481$	−44.9720	+	77.8938i	−0.0934969	+	0.161941i
$482$	160.148	+	86.6114i	0.332257	+	0.179692i
$483$	364.585	+	149.541i	0.754835	+	0.309609i
$484$	2.49499	−	1.63200i	0.00515494	−	0.00337189i
$485$	186.934	−	50.0888i	0.385431	−	0.103276i
$486$	−528.016	+	558.255i	−1.08645	+	1.14867i
$487$	228.856	+	396.390i	0.469930	+	0.813943i	0.999409	−	0.0343802i	$-0.0109457\pi$
$487$	228.856	+	396.390i	0.469930	+	0.813943i	−0.529479	+	0.848323i	$0.677612\pi$
$488$	120.475	−	43.3347i	0.246875	−	0.0888006i
$489$			1512.49i			3.09303i
$490$	−5.51878	−	158.772i	−0.0112628	−	0.324024i
$491$	−217.040	+	217.040i	−0.442037	+	0.442037i	−0.892696	−	0.450659i	$-0.851189\pi$
$491$	−217.040	+	217.040i	−0.442037	+	0.442037i	0.450659	+	0.892696i	$0.351189\pi$
$492$	780.906	−	873.061i	1.58721	−	1.77451i
$493$	−386.125	−	103.462i	−0.783216	−	0.209862i
$494$	−2.81559	−	101.145i	−0.00569957	−	0.204747i
$495$	−329.652	−	190.324i	−0.665963	−	0.384494i
$496$	138.137	+	60.4132i	0.278501	+	0.121801i
$497$	604.860	−	252.995i	1.21702	−	0.509044i
$498$	55.8496	−	103.268i	0.112148	−	0.207366i
$499$	335.338	−	89.8535i	0.672019	−	0.180067i	0.0933551	−	0.995633i	$-0.470241\pi$
$499$	335.338	−	89.8535i	0.672019	−	0.180067i	0.578664	+	0.815566i	$0.303574\pi$
$500$	−95.8870	−	291.830i	−0.191774	−	0.583659i
$501$	122.513	−	457.223i	0.244536	−	0.912622i
$502$	−97.7662	+	410.206i	−0.194753	+	0.817144i
$503$	862.625			1.71496			0.857480	−	0.514517i	$-0.172029\pi$
$503$	862.625			1.71496			0.857480	+	0.514517i	$0.172029\pi$
$504$	52.3623	−	1190.58i	0.103893	−	2.36226i
$505$		−	280.588i		−	0.555620i
$506$	−52.3393	+	219.605i	−0.103437	+	0.434001i
$507$	883.442	+	236.718i	1.74249	+	0.466899i
$508$	189.606	+	95.8224i	0.373241	+	0.188627i
$509$	219.511	+	819.225i	0.431259	+	1.60948i	0.749864	+	0.661592i	$0.230119\pi$
$509$	219.511	+	819.225i	0.431259	+	1.60948i	−0.318606	+	0.947887i	$0.603215\pi$
$510$	−76.0280	+	140.579i	−0.149075	+	0.275645i
$511$	81.1524	−	106.520i	0.158811	−	0.208455i
$512$	−126.904	−	496.024i	−0.247859	−	0.968796i
$513$	−1022.96	+	1771.82i	−1.99408	+	3.45385i
$514$	−11.6344	−	417.946i	−0.0226351	−	0.813125i
$515$	17.6312	−	65.8004i	0.0342353	−	0.127768i
$516$	−208.604	+	11.6229i	−0.404271	+	0.0225250i
$517$	−36.9539	−	36.9539i	−0.0714777	−	0.0714777i
$518$	−266.441	+	704.842i	−0.514365	+	1.36070i
$519$	451.262			0.869485
$520$	19.6070	+	9.23322i	0.0377058	+	0.0177562i
$521$	−703.365	+	406.088i	−1.35003	+	0.779439i	−0.988253	−	0.152826i	$-0.951162\pi$
$521$	−703.365	+	406.088i	−1.35003	+	0.779439i	−0.361775	+	0.932265i	$0.617829\pi$
$522$	1305.12	−	1379.86i	2.50023	−	2.64341i
$523$	−143.186	−	534.377i	−0.273778	−	1.02175i	−0.956656	−	0.291221i	$-0.905938\pi$
$523$	−143.186	−	534.377i	−0.273778	−	1.02175i	0.682878	−	0.730533i	$-0.260728\pi$
$524$	−12.2391	+	58.5296i	−0.0233571	+	0.111698i
$525$	526.969	+	681.865i	1.00375	+	1.29879i
$526$	494.245	+	267.298i	0.939630	+	0.508172i
$527$	73.1029	+	42.2060i	0.138715	+	0.0800872i
$528$	965.459	−	107.921i	1.82852	−	0.204395i
$529$	212.172	+	367.492i	0.401081	+	0.694693i
$530$	−57.7229	−	93.8473i	−0.108911	−	0.177070i
$531$	−1333.80	−	1333.80i	−2.51187	−	2.51187i
$532$	−160.107	−	832.429i	−0.300954	−	1.56472i
$533$	−62.8827	−	62.8827i	−0.117979	−	0.117979i
$534$	165.407	−	694.014i	0.309751	−	1.29965i
$535$	31.9171	+	55.2821i	0.0596582	+	0.103331i
$536$	116.900	+	21.0681i	0.218097	+	0.0393062i
$537$	−1236.16	−	713.699i	−2.30198	−	1.32905i
$538$	−824.196	+	245.618i	−1.53196	+	0.456539i
$539$	−466.343	+	273.560i	−0.865200	+	0.507533i
$540$	−239.878	−	366.724i	−0.444218	−	0.679119i
$541$	−201.784	−	753.067i	−0.372983	−	1.39199i	−0.856270	−	0.516528i	$-0.827224\pi$
$541$	−201.784	−	753.067i	−0.372983	−	1.39199i	0.483288	−	0.875462i	$-0.339443\pi$
$542$	−253.201	+	7.04838i	−0.467160	+	0.0130044i
$543$	1401.08	−	808.911i	2.58025	−	1.48971i
$544$	−39.7594	−	283.884i	−0.0730871	−	0.521846i
$545$	205.933			0.377859
$546$	−128.103	−	12.8030i	−0.234621	−	0.0234487i
$547$	−587.801	−	587.801i	−1.07459	−	1.07459i	−0.996984	−	0.0776074i	$-0.975272\pi$
$547$	−587.801	−	587.801i	−1.07459	−	1.07459i	−0.0776074	−	0.996984i	$-0.524728\pi$
$548$	−14.3897	−	258.261i	−0.0262585	−	0.471280i
$549$	−88.1481	+	328.973i	−0.160561	+	0.599222i
$550$	−339.248	+	358.676i	−0.616815	+	0.652139i
$551$	675.495	−	1169.99i	1.22594	−	2.12340i
$552$	−290.785	+	343.898i	−0.526784	+	0.623003i
$553$	823.363	+	105.503i	1.48890	+	0.190783i
$554$	−202.804	−	680.530i	−0.366072	−	1.22839i
$555$	124.267	+	463.771i	0.223905	+	0.835624i
$556$	−54.5702	−	166.083i	−0.0981479	−	0.298710i
$557$	349.938	+	93.7657i	0.628256	+	0.168341i	0.558878	−	0.829250i	$-0.311232\pi$
$557$	349.938	+	93.7657i	0.628256	+	0.168341i	0.0693776	+	0.997590i	$0.477899\pi$
$558$	−341.617	+	210.119i	−0.612216	+	0.376558i
$559$			15.8620i			0.0283756i
$560$	174.596	+	49.8132i	0.311778	+	0.0889521i
$561$	543.901			0.969521
$562$	213.749	+	347.519i	0.380337	+	0.618361i
$563$	−144.531	+	539.397i	−0.256716	+	0.958076i	0.710412	+	0.703786i	$0.248508\pi$
$563$	−144.531	+	539.397i	−0.256716	+	0.958076i	−0.967128	+	0.254290i	$0.918158\pi$
$564$	−32.5434	−	99.0448i	−0.0577010	−	0.175611i
$565$	202.609	−	54.2889i	0.358600	−	0.0960865i
$566$	−14.2950	+	4.26004i	−0.0252562	+	0.00752657i
$567$	1004.21	+	765.052i	1.77109	+	1.34930i
$568$	62.4864	+	746.692i	0.110011	+	1.31460i
$569$	45.7744	+	26.4279i	0.0804471	+	0.0464462i	0.539684	−	0.841868i	$-0.318544\pi$
$569$	45.7744	+	26.4279i	0.0804471	+	0.0464462i	−0.459237	+	0.888314i	$0.651877\pi$
$570$	−392.411	−	371.156i	−0.688441	−	0.651150i
$571$	−539.525	−	144.565i	−0.944878	−	0.253179i	−0.246690	−	0.969094i	$-0.579343\pi$
$571$	−539.525	−	144.565i	−0.944878	−	0.253179i	−0.698187	+	0.715915i	$0.746010\pi$
$572$	−4.10308	−	73.6408i	−0.00717321	−	0.128743i
$573$	571.885	−	571.885i	0.998054	−	0.998054i
$574$	−604.964	−	434.828i	−1.05394	−	0.757541i
$575$		−	228.870i		−	0.398034i
$576$	1276.28	+	475.477i	2.21577	+	0.825480i
$577$	484.594	+	839.341i	0.839851	+	1.45466i	0.890019	+	0.455923i	$0.150691\pi$
$577$	484.594	+	839.341i	0.839851	+	1.45466i	−0.0501683	+	0.998741i	$0.515976\pi$
$578$	11.6178	+	417.348i	0.0200999	+	0.722055i
$579$	679.504	−	182.072i	1.17358	−	0.314460i
$580$	158.399	+	242.159i	0.273101	+	0.417516i
$581$	−69.0873	−	28.3374i	−0.118911	−	0.0487735i
$582$	−375.235	−	1259.14i	−0.644733	−	2.16347i
$583$	−187.479	+	324.724i	−0.321577	+	0.556987i
$584$	87.3071	+	125.695i	0.149498	+	0.215231i
$585$	−49.9269	+	28.8253i	−0.0853451	+	0.0492740i
$586$	186.127	+	44.3604i	0.317622	+	0.0757003i
$587$	532.999	−	532.999i	0.908005	−	0.908005i	−0.0881061	−	0.996111i	$-0.528081\pi$
$587$	532.999	−	532.999i	0.908005	−	0.908005i	0.996111	+	0.0881061i	$0.0280815\pi$
$588$	−1076.44	+	67.4464i	−1.83068	+	0.114705i
$589$	−201.723	+	201.723i	−0.342484	+	0.342484i
$590$	244.784	−	150.560i	0.414888	−	0.255186i
$591$	−664.876	+	383.866i	−1.12500	+	0.649520i
$592$	−672.814	−	537.520i	−1.13651	−	0.907974i
$593$	74.2290	−	128.568i	0.125175	−	0.216810i	−0.796626	−	0.604472i	$-0.793384\pi$
$593$	74.2290	−	128.568i	0.125175	−	0.216810i	0.921801	+	0.387662i	$0.126717\pi$
$594$	−709.430	+	1311.76i	−1.19433	+	2.20836i
$595$	94.0484	+	38.5757i	0.158064	+	0.0648331i
$596$	−73.2693	+	350.387i	−0.122935	+	0.587897i
$597$	2031.28	−	544.281i	3.40249	−	0.911693i
$598$	24.8404	+	23.4949i	0.0415392	+	0.0392892i
$599$	−104.219	−	180.513i	−0.173988	−	0.301357i	0.765822	−	0.643052i	$-0.222332\pi$
$599$	−104.219	−	180.513i	−0.173988	−	0.301357i	−0.939811	+	0.341695i	$0.888999\pi$
$600$	−926.742	+	333.348i	−1.54457	+	0.555581i
$601$		−	295.838i		−	0.492244i	−0.969239	−	0.246122i	$-0.920844\pi$
$601$		−	295.838i		−	0.492244i	0.969239	−	0.246122i	$-0.0791563\pi$
$602$	21.4581	+	131.142i	0.0356446	+	0.217844i
$603$	−223.429	+	223.429i	−0.370529	+	0.370529i
$604$	312.064	−	17.3874i	0.516662	−	0.0287871i
$605$	−1.16709	−	0.312721i	−0.00192907	−	0.000516894i
$606$	−1904.17	+	53.0066i	−3.14220	+	0.0874697i
$607$	−841.395	−	485.780i	−1.38615	−	0.800296i	−0.393274	−	0.919421i	$-0.628658\pi$
$607$	−841.395	−	485.780i	−1.38615	−	0.800296i	−0.992879	+	0.119126i	$0.961991\pi$
$608$	961.507	+	118.523i	1.58143	+	0.194940i
$609$	−1367.32	−	1041.69i	−2.24520	−	1.71050i
$610$	−45.6408	−	24.6835i	−0.0748210	−	0.0404648i
$611$	−7.64538	+	2.04857i	−0.0125129	+	0.00335282i
$612$	680.561	+	343.939i	1.11203	+	0.561992i
$613$	−115.987	+	432.868i	−0.189212	+	0.706147i	0.804478	+	0.593982i	$0.202445\pi$
$613$	−115.987	+	432.868i	−0.189212	+	0.706147i	−0.993690	+	0.112165i	$0.964222\pi$
$614$	552.958	+	131.789i	0.900582	+	0.214640i
$615$	−474.716			−0.771896
$616$	−133.544	−	603.290i	−0.216793	−	0.979367i
$617$			135.380i			0.219416i	0.993964	+	0.109708i	$0.0349916\pi$
$617$			135.380i			0.219416i	−0.993964	+	0.109708i	$0.965008\pi$
$618$	−449.876	−	107.221i	−0.727955	−	0.173497i
$619$	848.164	+	227.265i	1.37022	+	0.367149i	0.867558	−	0.497336i	$-0.165688\pi$
$619$	848.164	+	227.265i	1.37022	+	0.367149i	0.502659	+	0.864485i	$0.332355\pi$
$620$	−19.0736	−	58.0499i	−0.0307638	−	0.0936288i
$621$	−178.934	−	667.789i	−0.288138	−	1.07534i
$622$	413.716	+	223.746i	0.665138	+	0.359721i
$623$	−450.104	−	57.6747i	−0.722478	−	0.0925758i
$624$	58.9559	−	134.805i	0.0944806	−	0.216033i
$625$	217.405	−	376.556i	0.347848	−	0.602490i
$626$	−309.089	+	8.60415i	−0.493753	+	0.0137447i
$627$	−475.755	+	1775.54i	−0.758780	+	2.83181i
$628$	−155.493	+	173.843i	−0.247601	+	0.276820i
$629$	−340.927	−	340.927i	−0.542015	−	0.542015i
$630$	−373.786	+	305.860i	−0.593311	+	0.485493i
$631$	−215.205			−0.341053			−0.170527	−	0.985353i	$-0.554547\pi$
$631$	−215.205			−0.341053			−0.170527	+	0.985353i	$0.554547\pi$
$632$	−404.174	+	858.276i	−0.639516	+	1.35803i
$633$	49.9798	−	28.8558i	0.0789570	−	0.0455859i
$634$	269.751	+	255.140i	0.425475	+	0.402429i
$635$	−22.2838	−	83.1644i	−0.0350927	−	0.130968i
$636$	−625.977	+	409.457i	−0.984241	+	0.643801i
$637$	0.566253	+	81.8825i	0.000888938	+	0.128544i
$638$	468.459	−	866.199i	0.734261	−	1.35768i
$639$	−1726.18	−	996.612i	−2.70138	−	1.55964i
$640$	−115.547	+	172.353i	−0.180542	+	0.269301i
$641$	268.660	+	465.334i	0.419127	+	0.725949i	0.995852	−	0.0909890i	$-0.0290028\pi$
$641$	268.660	+	465.334i	0.419127	+	0.725949i	−0.576725	+	0.816939i	$0.695669\pi$
$642$	369.134	−	227.044i	0.574976	−	0.353652i
$643$	−175.115	−	175.115i	−0.272341	−	0.272341i	0.557701	−	0.830042i	$-0.311684\pi$
$643$	−175.115	−	175.115i	−0.272341	−	0.272341i	−0.830042	+	0.557701i	$0.811684\pi$
$644$	237.157	+	160.645i	0.368257	+	0.249449i
$645$	59.8728	+	59.8728i	0.0928261	+	0.0928261i
$646$	527.618	+	125.750i	0.816747	+	0.194659i
$647$	113.321	+	196.278i	0.175149	+	0.303367i	0.940213	−	0.340587i	$-0.110626\pi$
$647$	113.321	+	196.278i	0.175149	+	0.303367i	−0.765064	+	0.643954i	$0.777293\pi$
$648$	−1184.97	+	823.075i	−1.82866	+	1.27018i
$649$	−846.982	−	489.005i	−1.30506	−	0.753475i
$650$	21.3548	+	71.6581i	0.0328535	+	0.110243i
$651$	221.959	+	287.201i	0.340951	+	0.441170i
$652$	−225.035	+	1076.15i	−0.345145	+	1.65054i
$653$	−50.0052	−	186.622i	−0.0765777	−	0.285792i	0.917009	−	0.398867i	$-0.130597\pi$
$653$	−50.0052	−	186.622i	−0.0765777	−	0.285792i	−0.993586	+	0.113075i	$0.963930\pi$
$654$	−38.9033	−	1397.53i	−0.0594852	−	2.13690i
$655$	20.9869	−	12.1168i	0.0320411	−	0.0184989i
$656$	685.522	−	505.007i	1.04500	−	0.769828i
$657$	−407.108			−0.619646
$658$	−60.4385	+	27.2797i	−0.0918518	+	0.0414585i
$659$	695.484	+	695.484i	1.05536	+	1.05536i	0.998375	+	0.0569882i	$0.0181497\pi$
$659$	695.484	+	695.484i	1.05536	+	1.05536i	0.0569882	+	0.998375i	$0.481850\pi$
$660$	−293.453	−	262.478i	−0.444626	−	0.397694i
$661$	257.009	−	959.171i	0.388819	−	1.45109i	−0.443240	−	0.896403i	$-0.646171\pi$
$661$	257.009	−	959.171i	0.388819	−	1.45109i	0.832059	−	0.554688i	$-0.187162\pi$
$662$	−289.094	−	273.435i	−0.436698	−	0.413043i
$663$	41.1879	−	71.3395i	0.0621235	−	0.107601i
$664$	55.1024	−	65.1671i	0.0829855	−	0.0981432i
$665$	−208.194	+	273.274i	−0.313073	+	0.410939i
$666$	2195.38	−	654.244i	3.29637	−	0.982348i
$667$	118.155	+	440.962i	0.177144	+	0.661112i
$668$	155.197	−	307.092i	0.232331	−	0.459719i
$669$	543.533	+	145.639i	0.812456	+	0.217697i
$670$	−25.2207	−	41.0043i	−0.0376428	−	0.0612005i
$671$			176.585i			0.263167i
$672$	305.067	−	1194.28i	0.453968	−	1.77720i
$673$	−432.324			−0.642383			−0.321192	−	0.947014i	$-0.604083\pi$
$673$	−432.324			−0.642383			−0.321192	+	0.947014i	$0.604083\pi$
$674$	−15.8395	+	9.74243i	−0.0235007	+	0.0144546i
$675$	391.305	−	1460.37i	0.579711	−	2.16351i
$676$	593.360	+	299.870i	0.877752	+	0.443594i
$677$	98.5271	−	26.4003i	0.145535	−	0.0389960i	−0.185316	−	0.982679i	$-0.559331\pi$
$677$	98.5271	−	26.4003i	0.145535	−	0.0389960i	0.330851	+	0.943683i	$0.392664\pi$
$678$	−406.699	−	1364.72i	−0.599851	−	2.01286i
$679$	−770.945	+	322.463i	−1.13541	+	0.474909i
$680$	−75.0108	+	88.7118i	−0.110310	+	0.130459i
$681$	1538.23	+	888.100i	2.25879	+	1.30411i
$682$	−142.891	+	151.075i	−0.209518	+	0.221517i
$683$	271.798	+	72.8281i	0.397947	+	0.106630i	0.452242	−	0.891895i	$-0.350624\pi$
$683$	271.798	+	72.8281i	0.397947	+	0.106630i	−0.0542946	+	0.998525i	$0.517291\pi$
$684$	−1718.07	+	1920.82i	−2.51179	+	2.80821i
$685$	−74.1254	+	74.1254i	−0.108212	+	0.108212i
$686$	115.452	+	676.215i	0.168298	+	0.985736i
$687$			1048.31i			1.52593i
$688$	−150.154	−	22.7672i	−0.218247	−	0.0330918i
$689$	28.3944	+	49.1805i	0.0412110	+	0.0713796i
$690$	182.447	−	5.07881i	0.264416	−	0.00736059i
$691$	−107.916	+	28.9159i	−0.156173	+	0.0418464i	−0.336058	−	0.941841i	$-0.609094\pi$
$691$	−107.916	+	28.9159i	−0.156173	+	0.0418464i	0.179885	+	0.983688i	$0.442427\pi$
$692$	321.079	+	67.1408i	0.463987	+	0.0970242i
$693$	1520.71	+	623.749i	2.19439	+	0.900071i
$694$	785.992	−	234.233i	1.13255	−	0.337511i
$695$	−35.4247	+	61.3574i	−0.0509708	+	0.0882840i
$696$	1613.46	−	1120.70i	2.31818	−	1.61020i
$697$	412.840	−	238.353i	0.592309	−	0.341970i
$698$	158.284	−	664.127i	0.226768	−	0.951471i
$699$	−381.592	+	381.592i	−0.545912	+	0.545912i
$700$	273.494	+	563.560i	0.390706	+	0.805085i
$701$	−35.1689	+	35.1689i	−0.0501696	+	0.0501696i	−0.731747	−	0.681577i	$-0.761295\pi$
$701$	−35.1689	+	35.1689i	−0.0501696	+	0.0501696i	0.681577	+	0.731747i	$0.261295\pi$
$702$	118.332	+	192.386i	0.168564	+	0.274055i
$703$	1411.15	−	814.730i	2.00733	−	1.15893i
$704$	702.993	+	66.8581i	0.998569	+	0.0949689i
$705$	−21.1258	+	36.5909i	−0.0299657	+	0.0519020i
$706$	−50.5099	−	27.3168i	−0.0715437	−	0.0386924i
$707$	162.298	+	1200.68i	0.229558	+	1.69827i
$708$	−1068.00	−	1632.75i	−1.50847	−	2.30614i
$709$	−690.815	+	185.103i	−0.974351	+	0.261076i	−0.710664	−	0.703532i	$-0.751605\pi$
$709$	−690.815	+	185.103i	−0.974351	+	0.261076i	−0.263687	+	0.964608i	$0.584939\pi$
$710$	208.671	−	220.621i	0.293903	−	0.310734i
$711$	−1261.80	−	2185.49i	−1.77468	−	3.07383i
$712$	220.948	−	469.189i	0.310320	−	0.658974i
$713$		−	96.3999i		−	0.135203i
$714$	244.021	−	645.533i	0.341767	−	0.904108i
$715$	−21.1361	+	21.1361i	−0.0295610	+	0.0295610i
$716$	−773.358	−	691.727i	−1.08011	−	0.966100i
$717$	−841.571	−	225.498i	−1.17374	−	0.314502i
$718$	22.0157	+	790.875i	0.0306625	+	1.10150i
$719$	140.229	+	80.9613i	0.195033	+	0.112603i	0.594337	−	0.804216i	$-0.297415\pi$
$719$	140.229	+	80.9613i	0.195033	+	0.112603i	−0.399303	+	0.916819i	$0.630748\pi$
$720$	−201.206	−	513.995i	−0.279453	−	0.713882i
$721$	−37.3861	+	291.768i	−0.0518531	+	0.404671i
$722$	−528.555	+	977.320i	−0.732071	+	1.35363i
$723$	−483.874	+	129.654i	−0.669259	+	0.179327i
$724$	1117.24	−	367.092i	1.54314	−	0.507034i
$725$	−258.391	+	964.327i	−0.356401	+	1.33011i
$726$	−1.90176	+	7.97937i	−0.00261950	+	0.0109909i
$727$	714.589			0.982929			0.491464	−	0.870898i	$-0.336462\pi$
$727$	714.589			0.982929			0.491464	+	0.870898i	$0.336462\pi$
$728$	−89.2420	−	28.1692i	−0.122585	−	0.0386940i
$729$		−	491.072i		−	0.673624i
$730$	14.3797	−	60.3340i	0.0196982	−	0.0826493i
$731$	−82.1306	−	22.0068i	−0.112354	−	0.0301051i
$732$	−158.889	+	314.398i	−0.217062	+	0.429505i
$733$	191.773	+	715.708i	0.261628	+	0.976409i	0.964282	+	0.264878i	$0.0853315\pi$
$733$	191.773	+	715.708i	0.261628	+	0.976409i	−0.702654	+	0.711532i	$0.748002\pi$
$734$	481.076	−	889.528i	0.655416	−	1.21189i
$735$	311.212	+	306.938i	0.423418	+	0.417602i
$736$	−258.063	+	201.423i	−0.350630	+	0.273673i
$737$	−81.9146	+	141.880i	−0.111146	+	0.192510i
$738$	63.0255	+	2264.08i	0.0854004	+	3.06786i
$739$	173.791	−	648.596i	0.235170	−	0.877668i	−0.742902	−	0.669401i	$-0.766551\pi$
$739$	173.791	−	648.596i	0.235170	−	0.877668i	0.978072	−	0.208267i	$-0.0667823\pi$
$740$	19.4157	+	348.468i	0.0262375	+	0.470903i
$741$	196.857	+	196.857i	0.265665	+	0.265665i
$742$	301.288	+	368.198i	0.406049	+	0.496224i
$743$	−881.354			−1.18621			−0.593105	−	0.805125i	$-0.702098\pi$
$743$	−881.354			−1.18621			−0.593105	+	0.805125i	$0.702098\pi$
$744$	−390.344	+	140.406i	−0.524656	+	0.188718i
$745$	125.638	−	72.5371i	0.168642	−	0.0973652i
$746$	−294.365	+	311.223i	−0.394592	+	0.417189i
$747$	58.7559	+	219.280i	0.0786558	+	0.293547i
$748$	386.992	+	80.9240i	0.517370	+	0.108187i
$749$	−168.554	−	218.099i	−0.225039	−	0.291186i
$750$	743.416	+	402.055i	0.991222	+	0.536074i
$751$	−1172.11	−	676.719i	−1.56074	−	0.901091i	−0.997183	−	0.0750109i	$-0.976101\pi$
$751$	−1172.11	−	676.719i	−1.56074	−	0.901091i	−0.563553	−	0.826080i	$-0.690566\pi$
$752$	−8.41869	−	75.3136i	−0.0111951	−	0.100151i
$753$	−580.127	−	1004.81i	−0.770421	−	1.33441i
$754$	−78.1380	−	127.039i	−0.103631	−	0.168486i
$755$	−89.5676	−	89.5676i	−0.118633	−	0.118633i
$756$	1238.59	+	1430.52i	1.63835	+	1.89222i
$757$	−973.785	−	973.785i	−1.28637	−	1.28637i	−0.936974	−	0.349400i	$-0.886386\pi$
$757$	−973.785	−	973.785i	−1.28637	−	1.28637i	−0.349400	−	0.936974i	$-0.613614\pi$
$758$	−220.037	+	923.228i	−0.290286	+	1.21798i
$759$	−310.572	−	537.927i	−0.409186	−	0.708731i
$760$	−223.983	−	322.467i	−0.294715	−	0.424298i
$761$	−303.447	−	175.195i	−0.398748	−	0.230217i	0.287195	−	0.957872i	$-0.407277\pi$
$761$	−303.447	−	175.195i	−0.398748	−	0.230217i	−0.685944	+	0.727655i	$0.740610\pi$
$762$	−560.174	+	166.937i	−0.735136	+	0.219077i
$763$	−881.217	+	119.116i	−1.15494	+	0.156115i
$764$	491.991	−	321.816i	0.643967	−	0.421225i
$765$	−79.9842	−	298.505i	−0.104555	−	0.390203i
$766$	−111.580	+	3.10606i	−0.145665	+	0.00405491i
$767$	−128.278	+	74.0616i	−0.167247	+	0.0965601i
$768$	1191.47	+	751.581i	1.55140	+	0.978622i
$769$	1006.65			1.30904			0.654518	−	0.756046i	$-0.272872\pi$
$769$	1006.65			1.30904			0.654518	+	0.756046i	$0.272872\pi$
$770$	−146.155	+	203.341i	−0.189811	+	0.264079i
$771$	813.444	+	813.444i	1.05505	+	1.05505i
$772$	510.565	−	28.4473i	0.661353	−	0.0368489i
$773$	−185.870	+	693.677i	−0.240453	+	0.897383i	0.735162	+	0.677892i	$0.237106\pi$
$773$	−185.870	+	693.677i	−0.240453	+	0.897383i	−0.975615	+	0.219491i	$0.929560\pi$
$774$	277.605	−	293.503i	0.358662	−	0.379202i
$775$	105.407	−	182.570i	0.136009	−	0.235575i
$776$	−79.6441	−	951.721i	−0.102634	−	1.22644i
$777$	−800.012	−	1912.67i	−1.02962	−	2.46160i
$778$	47.5629	+	159.602i	0.0611349	+	0.205144i
$779$	416.979	+	1556.19i	0.535275	+	1.99767i
$780$	−56.6496	+	18.6135i	−0.0726277	+	0.0238634i
$781$	−998.244	−	267.479i	−1.27816	−	0.342482i
$782$	−156.116	+	96.0229i	−0.199637	+	0.122791i
$783$			3015.70i			3.85147i
$784$	−775.934	−	112.168i	−0.989712	−	0.143072i
$785$	94.5249			0.120414
$786$	−86.1936	−	140.136i	−0.109661	−	0.178290i
$787$	102.531	−	382.652i	0.130281	−	0.486215i	−0.869692	−	0.493595i	$-0.835682\pi$
$787$	102.531	−	382.652i	0.130281	−	0.486215i	0.999973	+	0.00737982i	$0.00234909\pi$
$788$	−530.180	+	174.202i	−0.672818	+	0.221069i
$789$	−1493.32	+	400.135i	−1.89268	+	0.507142i
$790$	368.462	−	109.805i	0.466408	−	0.138994i
$791$	−835.591	+	349.503i	−1.05637	+	0.441850i
$792$	−1212.89	+	1434.42i	−1.53142	+	1.81114i
$793$	23.1613	+	13.3722i	0.0292072	+	0.0168628i
$794$	509.655	+	482.049i	0.641883	+	0.607114i
$795$	292.815	+	78.4597i	0.368321	+	0.0986914i
$796$	1526.26	−	85.0395i	1.91742	−	0.106834i
$797$	−955.509	+	955.509i	−1.19888	+	1.19888i	−0.224381	+	0.974502i	$0.572036\pi$
$797$	−955.509	+	955.509i	−1.19888	+	1.19888i	−0.974502	+	0.224381i	$0.927964\pi$
$798$	1893.87	+	1361.25i	2.37327	+	1.70583i
$799$		−	42.4287i		−	0.0531022i
$800$	−708.986	+	99.2968i	−0.886232	+	0.124121i
$801$	689.779	+	1194.73i	0.861148	+	1.49155i
$802$	−22.2245	−	798.377i	−0.0277114	−	0.995483i
$803$	−203.887	+	54.6314i	−0.253907	+	0.0680341i
$804$	−273.506	+	178.903i	−0.340181	+	0.222516i
$805$	−15.5505	−	115.042i	−0.0193174	−	0.142910i
$806$	8.99463	+	30.1824i	0.0111596	+	0.0374471i
$807$	1183.13	−	2049.23i	1.46608	−	2.53932i
$808$	−1362.73	−	245.596i	−1.68654	−	0.303955i
$809$	895.301	−	516.902i	1.10668	−	0.638939i	0.168709	−	0.985666i	$-0.446040\pi$
$809$	895.301	−	516.902i	1.10668	−	0.638939i	0.937966	+	0.346726i	$0.112707\pi$
$810$	568.790	+	135.562i	0.702210	+	0.167361i
$811$	861.473	−	861.473i	1.06224	−	1.06224i	0.0643058	−	0.997930i	$-0.479517\pi$
$811$	861.473	−	861.473i	1.06224	−	1.06224i	0.997930	−	0.0643058i	$-0.0204833\pi$
$812$	−817.881	−	944.614i	−1.00724	−	1.16332i
$813$	492.802	−	492.802i	0.606153	−	0.606153i
$814$	1011.69	−	622.265i	1.24287	−	0.764453i
$815$	385.876	−	222.786i	0.473468	−	0.273357i
$816$	616.200	+	492.291i	0.755148	+	0.603298i
$817$	143.681	−	248.862i	0.175864	−	0.304605i
$818$	−549.021	+	1015.16i	−0.671174	+	1.24103i
$819$	196.971	−	152.226i	0.240502	−	0.185869i
$820$	−337.766	−	70.6303i	−0.411910	−	0.0861345i
$821$	617.062	−	165.341i	0.751598	−	0.201390i	0.137371	−	0.990520i	$-0.456135\pi$
$821$	617.062	−	165.341i	0.751598	−	0.201390i	0.614227	+	0.789129i	$0.289468\pi$
$822$	517.044	+	489.038i	0.629008	+	0.594937i
$823$	613.463	+	1062.55i	0.745399	+	1.29107i	0.950008	+	0.312225i	$0.101074\pi$
$823$	613.463	+	1062.55i	0.745399	+	1.29107i	−0.204609	+	0.978844i	$0.565592\pi$
$824$	−304.139	−	143.223i	−0.369101	−	0.173815i
$825$		−	1358.36i		−	1.64650i
$826$	−960.379	+	785.855i	−1.16269	+	0.951398i
$827$	105.313	−	105.313i	0.127343	−	0.127343i	−0.640563	−	0.767906i	$-0.721299\pi$
$827$	105.313	−	105.313i	0.127343	−	0.127343i	0.767906	+	0.640563i	$0.221299\pi$
$828$	−48.4451	−	869.478i	−0.0585085	−	1.05009i
$829$	−1192.53	−	319.537i	−1.43851	−	0.385448i	−0.546500	−	0.837459i	$-0.684040\pi$
$829$	−1192.53	−	319.537i	−1.43851	−	0.385448i	−0.892012	+	0.452011i	$0.850707\pi$
$830$	−34.5730	+	0.962412i	−0.0416542	+	0.00115953i
$831$	1692.03	+	976.894i	2.03614	+	1.17556i
$832$	62.0046	−	87.1434i	0.0745248	−	0.104740i
$833$	−424.760	−	110.672i	−0.509916	−	0.132859i
$834$	423.085	+	228.814i	0.507297	+	0.274357i
$835$	−134.696	+	36.0916i	−0.161312	+	0.0432235i
$836$	−602.679	+	1192.54i	−0.720907	+	1.42648i
$837$	164.818	−	615.107i	0.196915	−	0.734895i
$838$	−286.456	−	68.2722i	−0.341833	−	0.0814704i
$839$	275.728			0.328639			0.164319	−	0.986407i	$-0.447457\pi$
$839$	275.728			0.328639			0.164319	+	0.986407i	$0.447457\pi$
$840$	−443.182	+	230.526i	−0.527598	+	0.274436i
$841$		−	1150.36i		−	1.36785i
$842$	−192.937	−	45.9836i	−0.229142	−	0.0546124i
$843$	−1084.30	−	290.538i	−1.28624	−	0.344647i
$844$	39.8545	−	13.0951i	0.0472210	−	0.0155155i
$845$	−69.7358	−	260.257i	−0.0825275	−	0.307997i
$846$	177.319	+	95.8980i	0.209597	+	0.113355i
$847$	5.17503	+	0.663110i	0.00610984	+	0.000782893i
$848$	−506.311	+	198.198i	−0.597065	+	0.233725i
$849$	20.5203	−	35.5422i	0.0241700	−	0.0418636i
$850$	−400.661	+	11.1533i	−0.471366	+	0.0131215i
$851$	−142.510	+	531.855i	−0.167462	+	0.624976i
$852$	−1536.63	−	1374.44i	−1.80356	−	1.61319i
$853$	−0.857543	−	0.857543i	−0.00100533	−	0.00100533i	0.706604	−	0.707609i	$-0.250226\pi$
$853$	−0.857543	−	0.857543i	−0.00100533	−	0.00100533i	−0.707609	+	0.706604i	$0.750226\pi$
$854$	209.581	+	79.2248i	0.245411	+	0.0927691i
$855$	1044.42			1.22154
$856$	296.424	−	106.624i	0.346290	−	0.124560i
$857$	−1066.44	+	615.711i	−1.24439	+	0.718449i	−0.969985	−	0.243165i	$-0.921814\pi$
$857$	−1066.44	+	615.711i	−1.24439	+	0.718449i	−0.274406	+	0.961614i	$0.588481\pi$
$858$	147.430	+	139.445i	0.171830	+	0.162523i
$859$	331.959	+	1238.89i	0.386448	+	1.44224i	0.835872	+	0.548924i	$0.184962\pi$
$859$	331.959	+	1238.89i	0.386448	+	1.44224i	−0.449425	+	0.893318i	$0.648371\pi$
$860$	33.6921	+	51.5084i	0.0391769	+	0.0598935i
$861$	2031.38	−	274.585i	2.35933	−	0.318914i
$862$	−434.518	+	803.441i	−0.504081	+	0.932067i
$863$	−98.8495	−	57.0708i	−0.114542	−	0.0661307i	0.441635	−	0.897195i	$-0.354399\pi$
$863$	−98.8495	−	57.0708i	−0.114542	−	0.0661307i	−0.556176	+	0.831064i	$0.687732\pi$
$864$	−1991.03	+	844.021i	−2.30443	+	0.976876i
$865$	−66.4698	−	115.129i	−0.0768437	−	0.133097i
$866$	71.9384	−	44.2474i	0.0830698	−	0.0510939i
$867$	−812.279	−	812.279i	−0.936885	−	0.936885i
$868$	115.196	+	237.371i	0.132714	+	0.273469i
$869$	−925.212	−	925.212i	−1.06469	−	1.06469i
$870$	−774.463	−	184.581i	−0.890188	−	0.212162i
$871$	12.4062	+	21.4883i	0.0142437	+	0.0246708i
$872$	180.251	−	1000.15i	0.206710	−	1.14696i
$873$	2200.16	+	1270.26i	2.52023	+	1.45506i
$874$	−176.906	−	593.627i	−0.202410	−	0.679207i
$875$	203.998	−	497.352i	0.233141	−	0.568402i
$876$	−412.165	−	86.1877i	−0.470508	−	0.0983878i
$877$	−154.230	−	575.594i	−0.175861	−	0.656321i	−0.996403	−	0.0847361i	$-0.972995\pi$
$877$	−154.230	−	575.594i	−0.175861	−	0.656321i	0.820543	−	0.571585i	$-0.193671\pi$
$878$	−16.1462	−	580.025i	−0.0183898	−	0.660621i
$879$	−455.922	+	263.227i	−0.518682	+	0.299461i
$880$	−169.743	−	230.418i	−0.192890	−	0.261838i
$881$	−722.266			−0.819825			−0.409912	−	0.912125i	$-0.634441\pi$
$881$	−722.266			−0.819825			−0.409912	+	0.912125i	$0.634441\pi$
$882$	1422.57	−	1525.03i	1.61289	−	1.72906i
$883$	384.133	+	384.133i	0.435032	+	0.435032i	0.890336	−	0.455304i	$-0.150469\pi$
$883$	384.133	+	384.133i	0.435032	+	0.435032i	−0.455304	+	0.890336i	$0.650469\pi$
$884$	39.9199	−	44.6308i	0.0451582	−	0.0504874i
$885$	−204.648	+	763.756i	−0.231240	+	0.863001i
$886$	−28.8513	−	27.2885i	−0.0325635	−	0.0307997i
$887$	−464.363	+	804.300i	−0.523521	+	0.906765i	0.476104	+	0.879389i	$0.342048\pi$
$887$	−464.363	+	804.300i	−0.523521	+	0.906765i	−0.999625	+	0.0273760i	$0.991285\pi$
$888$	2361.16	−	197.592i	2.65896	−	0.222514i
$889$	143.460	+	342.983i	0.161372	+	0.385808i
$890$	−201.425	+	60.0266i	−0.226321	+	0.0674456i
$891$	−515.030	−	1922.12i	−0.578036	−	2.15726i
$892$	365.062	+	184.493i	0.409262	+	0.206831i
$893$	138.507	+	37.1127i	0.155103	+	0.0415596i
$894$	−515.997	−	838.921i	−0.577178	−	0.938390i
$895$			420.504i			0.469837i
$896$	394.749	−	804.356i	0.440568	−	0.897719i
$897$	−94.0746			−0.104877
$898$	940.536	−	578.498i	1.04737	−	0.644207i
$899$	−108.834	+	406.174i	−0.121061	+	0.451807i
$900$	858.969	−	1699.66i	0.954410	−	1.88852i
$901$	−294.043	+	78.7885i	−0.326352	+	0.0874457i
$902$	335.390	+	1125.44i	0.371830	+	1.24771i
$903$	−290.836	−	221.573i	−0.322078	−	0.245374i
$904$	−86.3225	−	1031.53i	−0.0954895	−	1.14107i
$905$	−412.749	−	238.301i	−0.456077	−	0.263316i
$906$	−590.917	+	624.758i	−0.652226	+	0.689578i
$907$	−1158.38	−	310.386i	−1.27715	−	0.342212i	−0.444385	−	0.895836i	$-0.646578\pi$
$907$	−1158.38	−	310.386i	−1.27715	−	0.342212i	−0.832767	+	0.553624i	$0.813244\pi$
$908$	962.338	+	860.759i	1.05984	+	0.947973i
$909$	2604.56	−	2604.56i	2.86530	−	2.86530i
$910$	15.6029	+	34.5683i	0.0171460	+	0.0379872i
$911$		−	1018.76i		−	1.11829i	−0.829069	−	0.559146i	$-0.811129\pi$
$911$		−	1018.76i		−	1.11829i	0.829069	−	0.559146i	$-0.188871\pi$
$912$	−2146.06	+	1580.95i	−2.35314	+	1.73350i
$913$	58.8521	+	101.935i	0.0644601	+	0.111648i
$914$	625.986	−	17.4256i	0.684886	−	0.0190653i
$915$	137.900	−	36.9502i	0.150710	−	0.0403827i
$916$	−155.972	+	745.887i	−0.170276	+	0.814288i
$917$	−82.7975	+	63.9888i	−0.0902917	+	0.0697806i
$918$	−1160.32	+	345.785i	−1.26396	+	0.376672i
$919$	−567.923	+	983.672i	−0.617979	+	1.07037i	0.371874	+	0.928283i	$0.378715\pi$
$919$	−567.923	+	983.672i	−0.617979	+	1.07037i	−0.989854	+	0.142089i	$0.954618\pi$
$920$	130.569	+	23.5317i	0.141923	+	0.0255779i
$921$	−1354.48	+	782.011i	−1.47067	+	0.849089i
$922$	80.2242	−	336.604i	0.0870111	−	0.365080i
$923$	−110.677	+	110.677i	−0.119910	+	0.119910i
$924$	1407.55	+	953.444i	1.52332	+	1.03187i
$925$	−851.447	+	851.447i	−0.920483	+	0.920483i
$926$	−132.011	−	214.627i	−0.142560	−	0.231778i
$927$	774.454	−	447.131i	0.835441	−	0.482342i
$928$	1314.74	−	557.333i	1.41674	−	0.600574i
$929$	813.052	−	1408.25i	0.875191	−	1.51587i	0.0186309	−	0.999826i	$-0.494069\pi$
$929$	813.052	−	1408.25i	0.875191	−	1.51587i	0.856560	−	0.516048i	$-0.172597\pi$
$930$	147.878	+	79.9757i	0.159009	+	0.0859953i
$931$	732.824	−	1289.80i	0.787136	−	1.38540i
$932$	−328.283	+	214.733i	−0.352235	+	0.230400i
$933$	−1250.01	+	334.939i	−1.33977	+	0.358992i
$934$	−484.817	+	512.582i	−0.519076	+	0.548803i
$935$	−80.1152	−	138.764i	−0.0856847	−	0.148410i
$936$	96.2949	+	267.710i	0.102879	+	0.286015i
$937$			1091.45i			1.16484i	0.812888	+	0.582419i	$0.197894\pi$
$937$			1091.45i			1.16484i	−0.812888	+	0.582419i	$0.802106\pi$
$938$	131.641	+	160.875i	0.140342	+	0.171509i
$939$	601.577	−	601.577i	0.640657	−	0.640657i
$940$	−20.4754	+	22.8917i	−0.0217824	+	0.0243529i
$941$	292.211	+	78.2976i	0.310532	+	0.0832068i	0.410719	−	0.911762i	$-0.365278\pi$
$941$	292.211	+	78.2976i	0.310532	+	0.0832068i	−0.100187	+	0.994969i	$0.531944\pi$
$942$	−17.8570	−	641.480i	−0.0189564	−	0.680977i
$943$	−471.470	−	272.203i	−0.499968	−	0.288657i
$944$	−516.965	−	1320.62i	−0.547632	−	1.39896i
$945$	97.4668	−	760.648i	0.103139	−	0.804919i
$946$	99.6433	−	184.245i	0.105331	−	0.194762i
$947$	64.5709	−	17.3017i	0.0681847	−	0.0182700i	−0.224565	−	0.974459i	$-0.572096\pi$
$947$	64.5709	−	17.3017i	0.0681847	−	0.0182700i	0.292750	+	0.956189i	$0.405430\pi$
$948$	−814.784	−	2479.77i	−0.859477	−	2.61580i
$949$	−8.27412	+	30.8794i	−0.00871878	+	0.0325389i
$950$	314.053	−	1317.70i	0.330582	−	1.38705i
$951$	−1021.59			−1.07423
$952$	269.669	−	422.998i	0.283266	−	0.444326i
$953$			964.031i			1.01157i	0.862658	+	0.505787i	$0.168798\pi$
$953$			964.031i			1.01157i	−0.862658	+	0.505787i	$0.831202\pi$
$954$	335.325	−	1406.95i	0.351494	−	1.47479i
$955$	−230.140	−	61.6659i	−0.240985	−	0.0645716i
$956$	−565.237	−	285.657i	−0.591252	−	0.298805i
$957$	701.264	+	2617.15i	0.732773	+	2.73475i
$958$	197.595	−	365.362i	0.206258	−	0.381380i
$959$	274.318	−	360.069i	0.286046	−	0.375463i
$960$	−94.8891	−	562.977i	−0.0988429	−	0.586434i
$961$	−436.103	+	755.352i	−0.453801	+	0.786006i
$962$	−5.00563	−	179.818i	−0.00520335	−	0.186921i
$963$	−216.885	+	809.427i	−0.225218	+	0.840526i
$964$	−363.573	+	20.2573i	−0.377150	+	0.0210138i
$965$	−146.541	−	146.541i	−0.151856	−	0.151856i
$966$	−777.781	+	127.264i	−0.805157	+	0.131743i
$967$	1600.68			1.65531			0.827653	−	0.561241i	$-0.189676\pi$
$967$	1600.68			1.65531			0.827653	+	0.561241i	$0.189676\pi$
$968$	−2.54033	+	5.39447i	−0.00262431	+	0.00557280i
$969$	−1292.41	+	746.176i	−1.33376	+	0.770047i
$970$	−265.968	+	281.200i	−0.274194	+	0.289897i
$971$	211.594	+	789.680i	0.217914	+	0.813265i	0.985121	+	0.171865i	$0.0549793\pi$
$971$	211.594	+	789.680i	0.217914	+	0.813265i	−0.767207	+	0.641400i	$0.778354\pi$
$972$	314.559	−	1504.28i	0.323621	−	1.54761i
$973$	116.097	−	283.048i	0.119319	−	0.290902i
$974$	−805.210	−	435.475i	−0.826704	−	0.447099i
$975$	−178.166	−	102.864i	−0.182735	−	0.105502i
$976$	−159.829	+	200.058i	−0.163759	+	0.204977i
$977$	71.5575	+	123.941i	0.0732421	+	0.126859i	0.900320	−	0.435228i	$-0.143332\pi$
$977$	71.5575	+	123.941i	0.0732421	+	0.126859i	−0.827078	+	0.562087i	$0.809999\pi$
$978$	−1584.80	−	2576.61i	−1.62045	−	2.63457i
$979$	505.781	+	505.781i	0.516630	+	0.516630i
$980$	175.764	+	264.693i	0.179351	+	0.270095i
$981$	1911.57	+	1911.57i	1.94860	+	1.94860i
$982$	142.323	−	597.157i	0.144932	−	0.608102i
$983$	305.104	+	528.455i	0.310380	+	0.537594i	0.978445	−	0.206509i	$-0.0662104\pi$
$983$	305.104	+	528.455i	0.310380	+	0.537594i	−0.668065	+	0.744103i	$0.732877\pi$
$984$	−415.514	+	2305.55i	−0.422271	+	2.34304i
$985$	195.869	+	113.085i	0.198852	+	0.114807i
$986$	766.194	−	228.333i	0.777073	−	0.231575i
$987$	69.2354	−	168.798i	0.0701473	−	0.171021i
$988$	110.777	+	169.356i	0.112123	+	0.171413i
$989$	25.1322	+	93.7946i	0.0254117	+	0.0948378i
$990$	761.003	−	21.1841i	0.768690	−	0.0213981i
$991$	−465.910	+	268.993i	−0.470141	+	0.271436i	−0.716299	−	0.697794i	$-0.754165\pi$
$991$	−465.910	+	268.993i	−0.470141	+	0.271436i	0.246158	+	0.969230i	$0.420832\pi$
$992$	−298.625	+	41.8238i	−0.301033	+	0.0421611i
$993$	1094.84			1.10256
$994$	−765.321	+	1064.77i	−0.769941	+	1.07120i
$995$	−438.063	−	438.063i	−0.440265	−	0.440265i
$996$	13.0625	+	234.443i	0.0131150	+	0.235384i
$997$	328.053	−	1224.31i	0.329040	−	1.22800i	−0.581147	−	0.813799i	$-0.697396\pi$
$997$	328.053	−	1224.31i	0.329040	−	1.22800i	0.910187	−	0.414197i	$-0.135937\pi$
$998$	−477.116	+	504.440i	−0.478073	+	0.505451i
$999$	−1818.65	+	3150.00i	−1.82047	+	3.15315i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.3.u.a.107.5	yes	120
7.4	even	3	inner	112.3.u.a.11.16	✓	120
16.3	odd	4	inner	112.3.u.a.51.16	yes	120
112.67	odd	12	inner	112.3.u.a.67.5	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.3.u.a.11.16	✓	120	7.4	even	3	inner
112.3.u.a.51.16	yes	120	16.3	odd	4	inner
112.3.u.a.67.5	yes	120	112.67	odd	12	inner
112.3.u.a.107.5	yes	120	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	112.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70355 + 1.04781i) q^{2} +(1.42423 - 5.31530i) q^{3} +(1.80419 - 3.57000i) q^{4} +(-1.56586 + 0.419571i) q^{5} +(3.14317 + 10.5472i) q^{6} +(6.45786 - 2.70113i) q^{7} +(0.667143 + 7.97213i) q^{8} +(-18.4298 - 10.6404i) q^{9} +(2.22790 - 2.35548i) q^{10} +(-10.6579 - 2.85576i) q^{11} +(-16.4060 - 14.6743i) q^{12} +(-1.18165 + 1.18165i) q^{13} +(-8.17104 + 11.3681i) q^{14} +8.92058i q^{15} +(-9.48979 - 12.8819i) q^{16} +(-4.47899 - 7.75783i) q^{17} +(42.5452 - 1.18434i) q^{18} +(29.2429 - 7.83562i) q^{19} +(-1.32724 + 6.34710i) q^{20} +(-5.15984 - 38.1725i) q^{21} +(21.1485 - 6.30246i) q^{22} +(-5.11508 + 8.85958i) q^{23} +(43.3245 + 7.80809i) q^{24} +(-19.3748 + 11.1860i) q^{25} +(0.774863 - 3.25116i) q^{26} +(-47.7857 + 47.7857i) q^{27} +(2.00818 - 27.9279i) q^{28} +(31.5544 - 31.5544i) q^{29} +(-9.34707 - 15.1967i) q^{30} +(-8.16065 + 4.71155i) q^{31} +(29.6642 + 12.0016i) q^{32} +(-30.3585 + 52.5825i) q^{33} +(15.7589 + 8.52276i) q^{34} +(-8.97878 + 6.93912i) q^{35} +(-71.2372 + 46.5969i) q^{36} +(51.9889 - 13.9304i) q^{37} +(-41.6067 + 43.9894i) q^{38} +(4.59790 + 7.96380i) q^{39} +(-4.38953 - 12.2033i) q^{40} +53.2158i q^{41} +(48.7876 + 59.6223i) q^{42} +(6.71176 - 6.71176i) q^{43} +(-29.4239 + 32.8962i) q^{44} +(33.3229 + 8.92883i) q^{45} +(-0.569336 - 20.4524i) q^{46} +(4.10186 + 2.36821i) q^{47} +(-81.9869 + 32.0943i) q^{48} +(34.4078 - 34.8870i) q^{49} +(21.2851 - 39.3570i) q^{50} +(-47.6143 + 12.7582i) q^{51} +(2.08658 + 6.35044i) q^{52} +(8.79535 - 32.8247i) q^{53} +(31.3352 - 131.476i) q^{54} +17.8869 q^{55} +(25.8421 + 49.6809i) q^{56} -166.595i q^{57} +(-20.6916 + 86.8176i) q^{58} +(85.6173 + 22.9411i) q^{59} +(31.8465 + 16.0944i) q^{60} +(-4.14213 - 15.4586i) q^{61} +(8.96529 - 16.5772i) q^{62} +(-147.758 - 18.9332i) q^{63} +(-63.1098 + 10.6371i) q^{64} +(1.35452 - 2.34609i) q^{65} +(-3.37906 - 121.387i) q^{66} +(3.84292 - 14.3420i) q^{67} +(-35.7764 + 1.99337i) q^{68} +(39.8063 + 39.8063i) q^{69} +(8.02496 - 21.2292i) q^{70} +93.6627 q^{71} +(72.5317 - 154.023i) q^{72} +(16.5673 - 9.56511i) q^{73} +(-73.9695 + 78.2056i) q^{74} +(31.8630 + 118.914i) q^{75} +(24.7867 - 118.534i) q^{76} +(-76.5407 + 10.3461i) q^{77} +(-16.1773 - 8.74904i) q^{78} +(102.698 + 59.2925i) q^{79} +(20.2646 + 16.1896i) q^{80} +(90.1737 + 156.185i) q^{81} +(-55.7600 - 90.6560i) q^{82} +(-7.54311 - 7.54311i) q^{83} +(-145.585 - 50.4498i) q^{84} +(10.2684 + 10.2684i) q^{85} +(-4.40120 + 18.4665i) q^{86} +(-122.780 - 212.662i) q^{87} +(15.6562 - 86.8711i) q^{88} +(-56.1412 - 32.4131i) q^{89} +(-66.1230 + 19.7053i) q^{90} +(-4.43915 + 10.8228i) q^{91} +(22.4001 + 34.2452i) q^{92} +(13.4207 + 50.0866i) q^{93} +(-9.46916 + 0.263594i) q^{94} +(-42.5027 + 24.5390i) q^{95} +(106.040 - 140.581i) q^{96} -119.381 q^{97} +(-22.0606 + 95.4847i) q^{98} +(166.035 + 166.035i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{7} - 20 q^{8} + 16 q^{10} + 14 q^{11} - 2 q^{12} - 8 q^{13} + 20 q^{14} + 8 q^{16} - 4 q^{17} - 38 q^{18} - 2 q^{19} + 72 q^{20} + 14 q^{21}+ \cdots - 776 q^{99}+O(q^{100}) \) 120 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^7 - 20 * q^8 + 16 * q^10 + 14 * q^11 - 2 * q^12 - 8 * q^13 + 20 * q^14 + 8 * q^16 - 4 * q^17 - 38 * q^18 - 2 * q^19 + 72 * q^20 + 14 * q^21 + 52 * q^22 - 68 * q^23 - 142 * q^24 - 2 * q^26 - 44 * q^27 - 62 * q^28 - 40 * q^29 - 14 * q^30 + 88 * q^32 - 4 * q^33 + 168 * q^34 + 94 * q^35 - 272 * q^36 - 50 * q^37 + 138 * q^38 - 4 * q^39 - 206 * q^40 - 198 * q^42 - 104 * q^43 + 2 * q^44 - 84 * q^45 - 76 * q^46 - 856 * q^48 - 8 * q^49 - 320 * q^50 + 114 * q^51 + 76 * q^52 - 82 * q^53 + 350 * q^54 - 16 * q^55 + 8 * q^56 - 6 * q^58 + 62 * q^59 + 318 * q^60 - 2 * q^61 + 876 * q^62 + 112 * q^64 - 4 * q^65 + 162 * q^66 - 66 * q^67 + 192 * q^68 + 28 * q^69 + 112 * q^70 + 496 * q^71 + 248 * q^72 + 178 * q^74 + 12 * q^75 - 308 * q^76 + 94 * q^77 - 140 * q^78 + 204 * q^80 + 248 * q^81 + 266 * q^82 - 488 * q^83 + 620 * q^84 + 92 * q^85 - 408 * q^86 - 4 * q^87 - 370 * q^88 - 404 * q^90 - 488 * q^91 + 900 * q^92 - 38 * q^93 - 150 * q^94 + 768 * q^96 - 16 * q^97 + 432 * q^98 - 776 * q^99

Introduction

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