LMFDB - Embedded newform 357.2.bl.a.199.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(10,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([0, 8, 9]))

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

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

chi := DirichletCharacter("357.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.bl (of order $48$, degree $16$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$24$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			199.3
Character	$\chi$	$=$	357.199
Dual form			357.2.bl.a.61.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34749 + 1.75608i) q^{2} +(-0.997859 + 0.0654031i) q^{3} +(-0.750463 - 2.80077i) q^{4} +(2.28911 - 0.777050i) q^{5} +(1.22975 - 1.84045i) q^{6} +(-2.05900 + 1.66148i) q^{7} +(1.83962 + 0.761994i) q^{8} +(0.991445 - 0.130526i) q^{9} +(-1.72000 + 5.06695i) q^{10} +(-2.71359 - 5.50261i) q^{11} +(0.932035 + 2.74569i) q^{12} +(1.93919 - 1.93919i) q^{13} +(-0.143218 - 5.85461i) q^{14} +(-2.23339 + 0.925101i) q^{15} +(1.20520 - 0.695825i) q^{16} +(2.42899 - 3.33167i) q^{17} +(-1.10675 + 1.91694i) q^{18} +(1.02425 + 0.785935i) q^{19} +(-3.89423 - 5.82813i) q^{20} +(1.94593 - 1.79259i) q^{21} +(13.3196 + 2.64943i) q^{22} +(0.0873696 - 1.33300i) q^{23} +(-1.88551 - 0.640046i) q^{24} +(0.669471 - 0.513703i) q^{25} +(0.792340 + 6.01842i) q^{26} +(-0.980785 + 0.195090i) q^{27} +(6.19862 + 4.51990i) q^{28} +(0.988225 - 4.96814i) q^{29} +(1.38492 - 5.16859i) q^{30} +(0.0580584 + 0.885800i) q^{31} +(-0.921878 + 7.00236i) q^{32} +(3.06767 + 5.31335i) q^{33} +(2.57765 + 8.75490i) q^{34} +(-3.42223 + 5.40327i) q^{35} +(-1.10962 - 2.67885i) q^{36} +(6.73382 + 3.32075i) q^{37} +(-2.76034 + 0.739630i) q^{38} +(-1.80821 + 2.06187i) q^{39} +(4.80320 + 0.314818i) q^{40} +(-0.303942 - 1.52802i) q^{41} +(0.525821 + 5.83271i) q^{42} +(0.638340 - 1.54109i) q^{43} +(-13.3751 + 11.7296i) q^{44} +(2.16811 - 1.06919i) q^{45} +(2.22314 + 1.94964i) q^{46} +(5.59161 + 1.49827i) q^{47} +(-1.15711 + 0.773159i) q^{48} +(1.47896 - 6.84198i) q^{49} +1.86786i q^{50} +(-2.20589 + 3.48340i) q^{51} +(-6.88650 - 3.97592i) q^{52} +(-0.446791 - 0.0588211i) q^{53} +(0.979004 - 1.98522i) q^{54} +(-10.4875 - 10.4875i) q^{55} +(-5.05381 + 1.48754i) q^{56} +(-1.07346 - 0.717263i) q^{57} +(7.39286 + 8.42994i) q^{58} +(-4.87522 - 6.35351i) q^{59} +(4.26707 + 5.56095i) q^{60} +(-5.24003 - 5.97511i) q^{61} +(-1.63377 - 1.09165i) q^{62} +(-1.82452 + 1.91602i) q^{63} +(-9.08642 - 9.08642i) q^{64} +(2.93218 - 5.94587i) q^{65} +(-13.4644 - 1.77262i) q^{66} +(11.9999 + 6.92817i) q^{67} +(-11.1541 - 4.30274i) q^{68} +1.33586i q^{69} +(-4.87716 - 13.2906i) q^{70} +(6.51440 - 4.35279i) q^{71} +(1.92334 + 0.515357i) q^{72} +(-0.689539 - 0.604709i) q^{73} +(-14.9053 + 7.35047i) q^{74} +(-0.634440 + 0.556389i) q^{75} +(1.43256 - 3.45850i) q^{76} +(14.7298 + 6.82130i) q^{77} +(-1.18427 - 5.95371i) q^{78} +(-8.69432 - 0.569856i) q^{79} +(2.21816 - 2.52932i) q^{80} +(0.965926 - 0.258819i) q^{81} +(3.09289 + 1.52525i) q^{82} +(-5.67933 - 13.7111i) q^{83} +(-6.48097 - 4.10481i) q^{84} +(2.97136 - 9.51401i) q^{85} +(1.84613 + 3.19759i) q^{86} +(-0.661177 + 5.02214i) q^{87} +(-0.799003 - 12.1904i) q^{88} +(-2.81219 + 10.4953i) q^{89} +(-1.04391 + 5.24810i) q^{90} +(-0.770864 + 7.21472i) q^{91} +(-3.79900 + 0.755667i) q^{92} +(-0.115868 - 0.880106i) q^{93} +(-10.1657 + 7.80044i) q^{94} +(2.95534 + 1.00320i) q^{95} +(0.461928 - 7.04766i) q^{96} +(-8.60161 - 1.71097i) q^{97} +(10.0222 + 11.8167i) q^{98} +(-3.40861 - 5.10134i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 16 q^{11} + 32 q^{14} - 64 q^{22} - 16 q^{25} - 48 q^{28} - 64 q^{30} - 64 q^{35} - 32 q^{37} - 48 q^{42} - 64 q^{44} + 32 q^{46} - 64 q^{49} + 80 q^{56} - 32 q^{58} - 288 q^{61} - 528 q^{68} + 176 q^{70}+ \cdots + 32 q^{99}+O(q^{100}) $ 384 * q - 16 * q^11 + 32 * q^14 - 64 * q^22 - 16 * q^25 - 48 * q^28 - 64 * q^30 - 64 * q^35 - 32 * q^37 - 48 * q^42 - 64 * q^44 + 32 * q^46 - 64 * q^49 + 80 * q^56 - 32 * q^58 - 288 * q^61 - 528 * q^68 + 176 * q^70 + 64 * q^71 - 48 * q^73 - 128 * q^74 + 96 * q^77 + 128 * q^78 - 480 * q^80 - 240 * q^82 + 32 * q^85 - 144 * q^87 - 96 * q^88 - 64 * q^91 + 320 * q^92 - 192 * q^94 - 64 * q^95 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{16}\right)$	$1$

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 $

$2$	−1.34749	+	1.75608i	−0.952820	+	1.24174i	0.0174830	+	0.999847i	$0.494435\pi$
$2$	−1.34749	+	1.75608i	−0.952820	+	1.24174i	−0.970303	+	0.241892i	$0.922232\pi$
$3$	−0.997859	+	0.0654031i	−0.576114	+	0.0377605i
$3$	−0.997859	+	0.0654031i	−0.576114	+	0.0377605i
$4$	−0.750463	−	2.80077i	−0.375231	−	1.40038i
$5$	2.28911	−	0.777050i	1.02372	−	0.347507i	0.241430	−	0.970418i	$-0.422383\pi$
$5$	2.28911	−	0.777050i	1.02372	−	0.347507i	0.782293	+	0.622911i	$0.214050\pi$
$6$	1.22975	−	1.84045i	0.502044	−	0.751363i
$7$	−2.05900	+	1.66148i	−0.778229	+	0.627981i
$7$	−2.05900	+	1.66148i	−0.778229	+	0.627981i
$8$	1.83962	+	0.761994i	0.650402	+	0.269406i
$9$	0.991445	−	0.130526i	0.330482	−	0.0435087i
$10$	−1.72000	+	5.06695i	−0.543911	+	1.60231i
$11$	−2.71359	−	5.50261i	−0.818178	−	1.65910i	−0.750010	−	0.661426i	$-0.769952\pi$
$11$	−2.71359	−	5.50261i	−0.818178	−	1.65910i	−0.0681672	−	0.997674i	$-0.521715\pi$
$12$	0.932035	+	2.74569i	0.269055	+	0.792611i
$13$	1.93919	−	1.93919i	0.537834	−	0.537834i	−0.385058	−	0.922892i	$-0.625819\pi$
$13$	1.93919	−	1.93919i	0.537834	−	0.537834i	0.922892	+	0.385058i	$0.125819\pi$
$14$	−0.143218	−	5.85461i	−0.0382765	−	1.56471i
$15$	−2.23339	+	0.925101i	−0.576659	+	0.238860i
$16$	1.20520	−	0.695825i	0.301301	−	0.173956i
$17$	2.42899	−	3.33167i	0.589117	−	0.808048i
$17$	2.42899	−	3.33167i	0.589117	−	0.808048i
$18$	−1.10675	+	1.91694i	−0.260863	+	0.451828i
$19$	1.02425	+	0.785935i	0.234979	+	0.180306i	0.719539	−	0.694452i	$-0.244353\pi$
$19$	1.02425	+	0.785935i	0.234979	+	0.180306i	−0.484559	+	0.874758i	$0.661020\pi$
$20$	−3.89423	−	5.82813i	−0.870776	−	1.30321i
$21$	1.94593	−	1.79259i	0.424636	−	0.391175i
$22$	13.3196	+	2.64943i	2.83975	+	0.564861i
$23$	0.0873696	−	1.33300i	0.0182178	−	0.277950i	−0.979025	−	0.203741i	$-0.934690\pi$
$23$	0.0873696	−	1.33300i	0.0182178	−	0.277950i	0.997243	−	0.0742094i	$-0.0236433\pi$
$24$	−1.88551	−	0.640046i	−0.384879	−	0.130649i
$25$	0.669471	−	0.513703i	0.133894	−	0.102741i
$26$	0.792340	+	6.01842i	0.155391	+	1.18031i
$27$	−0.980785	+	0.195090i	−0.188752	+	0.0375451i
$28$	6.19862	+	4.51990i	1.17143	+	0.854180i
$29$	0.988225	−	4.96814i	0.183509	−	0.922561i	−0.773786	−	0.633447i	$-0.781639\pi$
$29$	0.988225	−	4.96814i	0.183509	−	0.922561i	0.957295	−	0.289114i	$-0.0933606\pi$
$30$	1.38492	−	5.16859i	0.252851	−	0.943651i
$31$	0.0580584	+	0.885800i	0.0104276	+	0.159094i	0.999897	+	0.0143522i	$0.00456860\pi$
$31$	0.0580584	+	0.885800i	0.0104276	+	0.159094i	−0.989469	+	0.144742i	$0.953765\pi$
$32$	−0.921878	+	7.00236i	−0.162967	+	1.23785i
$33$	3.06767	+	5.31335i	0.534012	+	0.924936i
$34$	2.57765	+	8.75490i	0.442063	+	1.50145i
$35$	−3.42223	+	5.40327i	−0.578463	+	0.913318i
$36$	−1.10962	−	2.67885i	−0.184936	−	0.446475i
$37$	6.73382	+	3.32075i	1.10703	+	0.545928i	0.901525	−	0.432727i	$-0.142449\pi$
$37$	6.73382	+	3.32075i	1.10703	+	0.545928i	0.205508	+	0.978655i	$0.434115\pi$
$38$	−2.76034	+	0.739630i	−0.447786	+	0.119984i
$39$	−1.80821	+	2.06187i	−0.289545	+	0.330163i
$40$	4.80320	+	0.314818i	0.759452	+	0.0497771i
$41$	−0.303942	−	1.52802i	−0.0474678	−	0.238637i	0.949766	−	0.312960i	$-0.101320\pi$
$41$	−0.303942	−	1.52802i	−0.0474678	−	0.238637i	−0.997234	+	0.0743229i	$0.976320\pi$
$42$	0.525821	+	5.83271i	0.0811359	+	0.900006i
$43$	0.638340	−	1.54109i	0.0973460	−	0.235014i	−0.867703	−	0.497083i	$-0.834405\pi$
$43$	0.638340	−	1.54109i	0.0973460	−	0.235014i	0.965049	+	0.262068i	$0.0844046\pi$
$44$	−13.3751	+	11.7296i	−2.01637	+	1.76831i
$45$	2.16811	−	1.06919i	0.323202	−	0.159386i
$46$	2.22314	+	1.94964i	0.327783	+	0.287458i
$47$	5.59161	+	1.49827i	0.815620	+	0.218545i	0.642431	−	0.766344i	$-0.277926\pi$
$47$	5.59161	+	1.49827i	0.815620	+	0.218545i	0.173189	+	0.984889i	$0.444593\pi$
$48$	−1.15711	+	0.773159i	−0.167015	+	0.111596i
$49$	1.47896	−	6.84198i	0.211280	−	0.977426i
$50$			1.86786i			0.264155i
$51$	−2.20589	+	3.48340i	−0.308886	+	0.487773i
$52$	−6.88650	−	3.97592i	−0.954986	−	0.551361i
$53$	−0.446791	−	0.0588211i	−0.0613714	−	0.00807970i	0.0997779	−	0.995010i	$-0.468187\pi$
$53$	−0.446791	−	0.0588211i	−0.0613714	−	0.00807970i	−0.161149	+	0.986930i	$0.551520\pi$
$54$	0.979004	−	1.98522i	0.133226	−	0.270155i
$55$	−10.4875	−	10.4875i	−1.41414	−	1.41414i
$56$	−5.05381	+	1.48754i	−0.675343	+	0.198781i
$57$	−1.07346	−	0.717263i	−0.142183	−	0.0950039i
$58$	7.39286	+	8.42994i	0.970730	+	1.10691i
$59$	−4.87522	−	6.35351i	−0.634700	−	0.827157i	0.359675	−	0.933078i	$-0.382888\pi$
$59$	−4.87522	−	6.35351i	−0.634700	−	0.827157i	−0.994375	+	0.105921i	$0.966221\pi$
$60$	4.26707	+	5.56095i	0.550876	+	0.717916i
$61$	−5.24003	−	5.97511i	−0.670917	−	0.765034i	0.311800	−	0.950148i	$-0.399068\pi$
$61$	−5.24003	−	5.97511i	−0.670917	−	0.765034i	−0.982717	+	0.185114i	$0.940735\pi$
$62$	−1.63377	−	1.09165i	−0.207489	−	0.138640i
$63$	−1.82452	+	1.91602i	−0.229868	+	0.241396i
$64$	−9.08642	−	9.08642i	−1.13580	−	1.13580i
$65$	2.93218	−	5.94587i	0.363692	−	0.737494i
$66$	−13.4644	−	1.77262i	−1.65735	−	0.218194i
$67$	11.9999	+	6.92817i	1.46603	+	0.846411i	0.999279	−	0.0379788i	$-0.0120919\pi$
$67$	11.9999	+	6.92817i	1.46603	+	0.846411i	0.466749	+	0.884390i	$0.345425\pi$
$68$	−11.1541	−	4.30274i	−1.35263	−	0.521784i
$69$			1.33586i			0.160819i
$70$	−4.87716	−	13.2906i	−0.582932	−	1.58853i
$71$	6.51440	−	4.35279i	0.773118	−	0.516581i	−0.105320	−	0.994438i	$-0.533587\pi$
$71$	6.51440	−	4.35279i	0.773118	−	0.516581i	0.878437	+	0.477858i	$0.158587\pi$
$72$	1.92334	+	0.515357i	0.226668	+	0.0607354i
$73$	−0.689539	−	0.604709i	−0.0807044	−	0.0707759i	0.618043	−	0.786144i	$-0.287926\pi$
$73$	−0.689539	−	0.604709i	−0.0807044	−	0.0707759i	−0.698748	+	0.715368i	$0.746259\pi$
$74$	−14.9053	+	7.35047i	−1.73270	+	0.854475i
$75$	−0.634440	+	0.556389i	−0.0732588	+	0.0642462i
$76$	1.43256	−	3.45850i	0.164326	−	0.396717i
$77$	14.7298	+	6.82130i	1.67861	+	0.777360i
$78$	−1.18427	−	5.95371i	−0.134092	−	0.674125i
$79$	−8.69432	−	0.569856i	−0.978187	−	0.0641138i	−0.432085	−	0.901833i	$-0.642222\pi$
$79$	−8.69432	−	0.569856i	−0.978187	−	0.0641138i	−0.546102	+	0.837719i	$0.683889\pi$
$80$	2.21816	−	2.52932i	0.247998	−	0.282787i
$81$	0.965926	−	0.258819i	0.107325	−	0.0287577i
$82$	3.09289	+	1.52525i	0.341553	+	0.168435i
$83$	−5.67933	−	13.7111i	−0.623387	−	1.50499i	−0.847702	−	0.530473i	$-0.822014\pi$
$83$	−5.67933	−	13.7111i	−0.623387	−	1.50499i	0.224314	−	0.974517i	$-0.427986\pi$
$84$	−6.48097	−	4.10481i	−0.707131	−	0.447871i
$85$	2.97136	−	9.51401i	0.322290	−	1.03194i
$86$	1.84613	+	3.19759i	0.199073	+	0.344805i
$87$	−0.661177	+	5.02214i	−0.0708856	+	0.538430i
$88$	−0.799003	−	12.1904i	−0.0851740	−	1.29950i
$89$	−2.81219	+	10.4953i	−0.298092	+	1.11249i	0.640639	+	0.767843i	$0.278670\pi$
$89$	−2.81219	+	10.4953i	−0.298092	+	1.11249i	−0.938731	+	0.344652i	$0.887997\pi$
$90$	−1.04391	+	5.24810i	−0.110038	+	0.553199i
$91$	−0.770864	+	7.21472i	−0.0808085	+	0.756308i
$92$	−3.79900	+	0.755667i	−0.396073	+	0.0787838i
$93$	−0.115868	−	0.880106i	−0.0120150	−	0.0912628i
$94$	−10.1657	+	7.80044i	−1.04851	+	0.804554i
$95$	2.95534	+	1.00320i	0.303211	+	0.102926i
$96$	0.461928	−	7.04766i	0.0471453	−	0.719299i
$97$	−8.60161	−	1.71097i	−0.873361	−	0.173722i	−0.261994	−	0.965070i	$-0.584380\pi$
$97$	−8.60161	−	1.71097i	−0.873361	−	0.173722i	−0.611367	+	0.791347i	$0.709380\pi$
$98$	10.0222	+	11.8167i	1.01240	+	1.19367i
$99$	−3.40861	−	5.10134i	−0.342578	−	0.512704i
$100$	−1.94118	−	1.48952i	−0.194118	−	0.148952i
$101$	9.08141	−	15.7295i	0.903634	−	1.56514i	0.0808933	−	0.996723i	$-0.474223\pi$
$101$	9.08141	−	15.7295i	0.903634	−	1.56514i	0.822741	−	0.568417i	$-0.192444\pi$
$102$	−3.14473	−	8.56757i	−0.311374	−	0.848316i
$103$	−14.4466	+	8.34076i	−1.42347	+	0.821839i	−0.996593	−	0.0824722i	$-0.973718\pi$
$103$	−14.4466	+	8.34076i	−1.42347	+	0.821839i	−0.426874	+	0.904311i	$0.640385\pi$
$104$	5.04501	−	2.08971i	0.494704	−	0.204913i
$105$	3.06151	−	5.61552i	0.298773	−	0.548019i
$106$	0.705342	−	0.705342i	0.0685088	−	0.0685088i
$107$	−5.01876	−	14.7848i	−0.485182	−	1.42930i	−0.863842	−	0.503764i	$-0.831948\pi$
$107$	−5.01876	−	14.7848i	−0.485182	−	1.42930i	0.378660	−	0.925536i	$-0.376385\pi$
$108$	1.28245	+	2.60054i	0.123403	+	0.250237i
$109$	3.02681	−	8.91668i	0.289915	−	0.854063i	−0.700217	−	0.713930i	$-0.746914\pi$
$109$	3.02681	−	8.91668i	0.289915	−	0.854063i	0.990133	−	0.140133i	$-0.0447531\pi$
$110$	32.5488	−	4.28513i	3.10341	−	0.408571i
$111$	−6.93659	−	2.87323i	−0.658392	−	0.272715i
$112$	−1.32541	+	3.43513i	−0.125240	+	0.324589i
$113$	−10.5293	+	15.7583i	−0.990518	+	1.48241i	−0.118491	+	0.992955i	$0.537806\pi$
$113$	−10.5293	+	15.7583i	−0.990518	+	1.48241i	−0.872026	+	0.489459i	$0.837194\pi$
$114$	2.70605	−	0.918582i	0.253445	−	0.0860330i
$115$	−0.835810	−	3.11929i	−0.0779397	−	0.290875i
$116$	−14.6562	+	0.960620i	−1.36080	+	0.0891914i
$117$	1.66948	−	2.17571i	0.154344	−	0.201145i
$118$	17.7266			1.63187
$119$	0.534213	+	10.8956i	0.0489712	+	0.998800i
$120$	−4.81350			−0.439411
$121$	−16.2188	+	21.1368i	−1.47444	+	1.92152i
$122$	17.5537	−	1.15053i	1.58924	−	0.104164i
$123$	0.403229	+	1.50487i	0.0363579	+	0.135690i
$124$	2.43735	−	0.827368i	0.218880	−	0.0742998i
$125$	−5.58187	+	8.35386i	−0.499258	+	0.747192i
$126$	−0.906172	−	5.78583i	−0.0807282	−	0.515443i
$127$	17.9361	+	7.42939i	1.59157	+	0.659252i	0.990192	−	0.139710i	$-0.0446172\pi$
$127$	17.9361	+	7.42939i	1.59157	+	0.659252i	0.601382	+	0.798962i	$0.294617\pi$
$128$	14.1957	−	1.86890i	1.25473	−	0.165189i
$129$	−0.536182	+	1.57954i	−0.0472082	+	0.139071i
$130$	6.49037	+	13.1612i	0.569243	+	1.15431i
$131$	2.73766	+	8.06490i	0.239191	+	0.704633i	0.998543	+	0.0539540i	$0.0171824\pi$
$131$	2.73766	+	8.06490i	0.239191	+	0.704633i	−0.759353	+	0.650679i	$0.774484\pi$
$132$	12.5793	−	12.5793i	1.09489	−	1.09489i
$133$	−3.41475	+	0.0835328i	−0.296096	+	0.00724322i
$134$	−28.3363	+	11.7373i	−2.44788	+	1.01395i
$135$	−2.09353	+	1.20870i	−0.180183	+	0.104029i
$136$	7.00712	−	4.27811i	0.600856	−	0.366845i
$137$	0.365057	−	0.632298i	0.0311889	−	0.0540208i	−0.850010	−	0.526767i	$-0.823404\pi$
$137$	0.365057	−	0.632298i	0.0311889	−	0.0540208i	0.881199	+	0.472746i	$0.156737\pi$
$138$	−2.34589	−	1.80006i	−0.199695	−	0.153232i
$139$	−5.33575	−	7.98552i	−0.452573	−	0.677323i	0.533088	−	0.846060i	$-0.321031\pi$
$139$	−5.33575	−	7.98552i	−0.452573	−	0.677323i	−0.985661	+	0.168736i	$0.946031\pi$
$140$	17.7015	+	5.52992i	1.49605	+	0.467364i
$141$	−5.67763	−	1.12935i	−0.478142	−	0.0951084i
$142$	−1.13424	+	17.3052i	−0.0951835	+	1.45222i
$143$	−15.9328	−	5.40844i	−1.33236	−	0.452277i
$144$	1.10407	−	0.847182i	0.0920058	−	0.0705985i
$145$	−1.59833	−	12.1405i	−0.132734	−	1.00822i
$146$	1.99107	−	0.396048i	0.164782	−	0.0327772i
$147$	−1.02831	+	6.92406i	−0.0848133	+	0.571087i
$148$	4.24717	−	21.3519i	0.349115	−	1.75512i
$149$	−2.73968	+	10.2246i	−0.224443	+	0.837633i	0.758184	+	0.652041i	$0.226087\pi$
$149$	−2.73968	+	10.2246i	−0.224443	+	0.837633i	−0.982627	+	0.185592i	$0.940580\pi$
$150$	−0.122164	−	1.86386i	−0.00997463	−	0.152183i
$151$	1.87872	−	14.2703i	0.152888	−	1.16130i	−0.727179	−	0.686448i	$-0.759169\pi$
$151$	1.87872	−	14.2703i	0.152888	−	1.16130i	0.880067	−	0.474850i	$-0.157498\pi$
$152$	1.28535	+	2.22629i	0.104256	+	0.180576i
$153$	1.97334	−	3.62021i	0.159535	−	0.292677i
$154$	−31.8270	+	16.6751i	−2.56469	+	1.34372i
$155$	0.821213	+	1.98258i	0.0659614	+	0.159245i
$156$	7.13180	+	3.51701i	0.571001	+	0.281586i
$157$	−2.53682	+	0.679739i	−0.202460	+	0.0542490i	−0.358624	−	0.933482i	$-0.616754\pi$
$157$	−2.53682	+	0.679739i	−0.202460	+	0.0542490i	0.156164	+	0.987731i	$0.450087\pi$
$158$	12.7162	−	14.5001i	1.01165	−	1.15356i
$159$	0.449681	+	0.0294737i	0.0356620	+	0.00233741i
$160$	3.33090	+	16.7455i	0.263330	+	1.32385i
$161$	2.03486	+	2.88982i	0.160370	+	0.227749i
$162$	−0.847068	+	2.04500i	−0.0665520	+	0.160671i
$163$	−0.579611	+	0.508305i	−0.0453986	+	0.0398135i	−0.681745	−	0.731590i	$-0.738778\pi$
$163$	−0.579611	+	0.508305i	−0.0453986	+	0.0398135i	0.636346	+	0.771404i	$0.280445\pi$
$164$	−4.05153	+	1.99799i	−0.316371	+	0.156017i
$165$	11.1510	+	9.77914i	0.868102	+	0.761305i
$166$	31.7307	+	8.50222i	2.46278	+	0.659900i
$167$	−7.64667	+	5.10934i	−0.591717	+	0.395373i	−0.815068	−	0.579365i	$-0.803300\pi$
$167$	−7.64667	+	5.10934i	−0.591717	+	0.395373i	0.223351	+	0.974738i	$0.428300\pi$
$168$	4.94570	−	1.81489i	0.381569	−	0.140022i
$169$			5.47909i			0.421469i
$170$	12.7035	+	18.0380i	0.974316	+	1.38345i
$171$	1.11807	+	0.645520i	0.0855012	+	0.0493642i
$172$	−4.79528	−	0.631311i	−0.365637	−	0.0481370i
$173$	4.22030	−	8.55793i	0.320864	−	0.650647i	−0.675358	−	0.737490i	$-0.736011\pi$
$173$	4.22030	−	8.55793i	0.320864	−	0.650647i	0.996222	+	0.0868425i	$0.0276777\pi$
$174$	−7.92837	−	7.92837i	−0.601048	−	0.601048i
$175$	−0.524933	+	2.17003i	−0.0396812	+	0.164039i
$176$	−7.09928	−	4.74359i	−0.535128	−	0.357561i
$177$	5.28032	+	6.02105i	0.396893	+	0.452570i
$178$	−14.6411	−	19.0807i	−1.09740	−	1.43016i
$179$	14.3875	+	18.7502i	1.07537	+	1.40146i	0.909696	+	0.415276i	$0.136315\pi$
$179$	14.3875	+	18.7502i	1.07537	+	1.40146i	0.165679	+	0.986180i	$0.447018\pi$
$180$	−4.62164	−	5.26997i	−0.344476	−	0.392800i
$181$	5.57542	+	3.72538i	0.414418	+	0.276905i	0.745251	−	0.666784i	$-0.232330\pi$
$181$	5.57542	+	3.72538i	0.414418	+	0.276905i	−0.330833	+	0.943689i	$0.607330\pi$
$182$	−11.6309	−	11.0755i	−0.862141	−	0.820968i
$183$	5.61960	+	5.61960i	0.415413	+	0.415413i
$184$	1.17647	−	2.38564i	0.0867303	−	0.175872i
$185$	17.9949	+	2.36907i	1.32301	+	0.174177i
$186$	1.70167	+	0.982461i	0.124773	+	0.0720375i
$187$	−24.9242	−	4.32502i	−1.82263	−	0.316277i
$188$		−	16.7852i		−	1.22418i
$189$	1.69530	−	2.03125i	0.123315	−	0.147751i
$190$	−5.74400	+	3.83802i	−0.416714	+	0.278439i
$191$	11.8532	+	3.17607i	0.857671	+	0.229812i	0.660749	−	0.750607i	$-0.270239\pi$
$191$	11.8532	+	3.17607i	0.857671	+	0.229812i	0.196922	+	0.980419i	$0.436905\pi$
$192$	9.66125	+	8.47269i	0.697241	+	0.611464i
$193$	13.9900	−	6.89910i	1.00702	−	0.496608i	0.137499	−	0.990502i	$-0.456094\pi$
$193$	13.9900	−	6.89910i	1.00702	−	0.496608i	0.869522	+	0.493894i	$0.164427\pi$
$194$	14.5952	−	12.7996i	1.04787	−	0.918960i
$195$	−2.53702	+	6.12491i	−0.181680	+	0.438614i
$196$	−20.2727	+	0.992429i	−1.44805	+	0.0708878i
$197$	1.04189	+	5.23793i	0.0742316	+	0.373187i	0.999988	−	0.00493346i	$-0.00157037\pi$
$197$	1.04189	+	5.23793i	0.0742316	+	0.373187i	−0.925756	+	0.378121i	$0.876570\pi$
$198$	13.5515	+	0.888210i	0.963060	+	0.0631223i
$199$	12.0511	−	13.7416i	0.854277	−	0.974117i	−0.145607	−	0.989343i	$-0.546513\pi$
$199$	12.0511	−	13.7416i	0.854277	−	0.974117i	0.999884	+	0.0152258i	$0.00484671\pi$
$200$	1.62301	−	0.434884i	0.114764	−	0.0307509i
$201$	−12.4274	−	6.12851i	−0.876560	−	0.432271i
$202$	15.3851	+	37.1430i	1.08250	+	2.61337i
$203$	6.21972	+	11.8713i	0.436539	+	0.833204i
$204$	11.4116	+	3.56401i	0.798973	+	0.249531i
$205$	−1.88311	−	3.26164i	−0.131522	−	0.227802i
$206$	4.81961	−	36.6086i	0.335798	−	2.55064i
$207$	−0.0873696	−	1.33300i	−0.00607261	−	0.0926501i
$208$	0.987782	−	3.68645i	0.0684903	−	0.255609i
$209$	1.54530	−	7.76876i	0.106891	−	0.537376i
$210$	5.73597	+	12.9431i	0.395819	+	0.893162i
$211$	4.67480	−	0.929876i	0.321827	−	0.0640153i	−0.0315333	−	0.999503i	$-0.510039\pi$
$211$	4.67480	−	0.929876i	0.321827	−	0.0640153i	0.353360	+	0.935487i	$0.385039\pi$
$212$	0.170556	+	1.29550i	0.0117138	+	0.0889753i
$213$	−6.21577	+	4.76953i	−0.425898	+	0.326803i
$214$	32.7261	+	11.1090i	2.23711	+	0.759396i
$215$	0.263731	−	4.02375i	0.0179863	−	0.274418i
$216$	−1.95293	−	0.388461i	−0.132880	−	0.0264314i
$217$	−1.59128	−	1.72740i	−0.108023	−	0.117263i
$218$	11.5799	+	17.3305i	0.784287	+	1.17377i
$219$	0.727612	+	0.558317i	0.0491675	+	0.0377275i
$220$	−21.5026	+	37.2436i	−1.44970	+	2.51096i
$221$	−1.75046	−	11.1710i	−0.117749	−	0.751443i
$222$	14.3926	−	8.30958i	0.965969	−	0.557703i
$223$	12.7830	−	5.29489i	0.856013	−	0.354572i	0.0888659	−	0.996044i	$-0.471676\pi$
$223$	12.7830	−	5.29489i	0.856013	−	0.354572i	0.767147	+	0.641472i	$0.221676\pi$
$224$	−9.73614	−	15.9495i	−0.650523	−	1.06567i
$225$	0.596692	−	0.596692i	0.0397795	−	0.0397795i
$226$	−13.4847	−	39.7246i	−0.896987	−	2.64244i
$227$	6.38390	+	12.9453i	0.423714	+	0.859207i	0.999144	+	0.0413566i	$0.0131680\pi$
$227$	6.38390	+	12.9453i	0.423714	+	0.859207i	−0.575430	+	0.817851i	$0.695165\pi$
$228$	−1.20329	+	3.54479i	−0.0796901	+	0.234760i
$229$	9.43192	−	1.24174i	0.623279	−	0.0820562i	0.187729	−	0.982221i	$-0.439887\pi$
$229$	9.43192	−	1.24174i	0.623279	−	0.0820562i	0.435550	+	0.900165i	$0.356554\pi$
$230$	6.60398	+	2.73546i	0.435453	+	0.180371i
$231$	−15.1444	−	5.84332i	−0.996426	−	0.384463i
$232$	5.60365	−	8.38646i	0.367898	−	0.550598i
$233$	9.95588	−	3.37956i	0.652231	−	0.221403i	0.0243399	−	0.999704i	$-0.492252\pi$
$233$	9.95588	−	3.37956i	0.652231	−	0.221403i	0.627891	+	0.778301i	$0.283918\pi$
$234$	1.57112	+	5.86351i	0.102708	+	0.383310i
$235$	13.9641	−	0.915253i	0.910915	−	0.0597045i
$236$	−14.1360	+	18.4224i	−0.920177	+	1.19920i
$237$	8.71297			0.565968
$238$	−19.8535	−	13.7436i	−1.28691	−	0.890867i
$239$	−2.10674			−0.136274			−0.0681368	−	0.997676i	$-0.521705\pi$
$239$	−2.10674			−0.136274			−0.0681368	+	0.997676i	$0.521705\pi$
$240$	−2.04798	+	2.66898i	−0.132197	+	0.172282i
$241$	−0.290056	+	0.0190113i	−0.0186842	+	0.00122463i	−0.0747423	−	0.997203i	$-0.523813\pi$
$241$	−0.290056	+	0.0190113i	−0.0186842	+	0.00122463i	0.0560582	+	0.998428i	$0.482147\pi$
$242$	−15.2632	−	56.9632i	−0.981158	−	3.66173i
$243$	−0.946930	+	0.321439i	−0.0607456	+	0.0206204i
$244$	−12.8024	+	19.1602i	−0.819591	+	1.22661i
$245$	−1.93105	−	16.8113i	−0.123370	−	1.07403i
$246$	−3.18603	−	1.31970i	−0.203134	−	0.0841407i
$247$	3.51029	−	0.462139i	0.223355	−	0.0294052i
$248$	−0.568169	+	1.67377i	−0.0360788	+	0.106285i
$249$	6.56392	+	13.3103i	0.415971	+	0.843507i
$250$	−7.14856	−	21.0590i	−0.452115	−	1.33189i
$251$	−21.0814	+	21.0814i	−1.33065	+	1.33065i	−0.425856	+	0.904791i	$0.640027\pi$
$251$	−21.0814	+	21.0814i	−1.33065	+	1.33065i	−0.904791	+	0.425856i	$0.859973\pi$
$252$	6.73556	+	3.67215i	0.424300	+	0.231323i
$253$	−7.57208	+	3.13646i	−0.476053	+	0.197187i
$254$	−37.2154	+	21.4863i	−2.33510	+	1.34817i
$255$	−2.34276	+	9.68798i	−0.146709	+	0.606685i
$256$	−2.99648	+	5.19005i	−0.187280	+	0.324378i
$257$	−18.4343	−	14.1452i	−1.14990	−	0.882351i	−0.155482	−	0.987839i	$-0.549693\pi$
$257$	−18.4343	−	14.1452i	−1.14990	−	0.882351i	−0.994421	+	0.105488i	$0.966360\pi$
$258$	−2.05131	−	3.07000i	−0.127709	−	0.191130i
$259$	−19.3823	+	4.35068i	−1.20436	+	0.270338i
$260$	−18.8535	−	3.75019i	−1.16924	−	0.232577i
$261$	0.331298	−	5.05463i	0.0205068	−	0.312874i
$262$	−17.8516	−	6.05981i	−1.10288	−	0.374376i
$263$	−18.3596	+	14.0878i	−1.13210	+	0.868690i	−0.992588	−	0.121531i	$-0.961220\pi$
$263$	−18.3596	+	14.0878i	−1.13210	+	0.868690i	−0.139511	+	0.990221i	$0.544553\pi$
$264$	1.59458	+	12.1121i	0.0981399	+	0.745447i
$265$	−1.06846	+	0.212530i	−0.0656351	+	0.0130556i
$266$	4.45465	−	6.10915i	0.273132	−	0.374576i
$267$	2.11975	−	10.6567i	0.129727	−	0.652180i
$268$	10.3987	−	38.8084i	0.635200	−	2.37060i
$269$	1.01239	+	15.4461i	0.0617266	+	0.941766i	0.910631	+	0.413220i	$0.135596\pi$
$269$	1.01239	+	15.4461i	0.0617266	+	0.941766i	−0.848905	+	0.528546i	$0.822737\pi$
$270$	0.698435	−	5.30514i	0.0425054	−	0.322861i
$271$	9.91021	+	17.1650i	0.602003	+	1.04270i	0.992517	+	0.122102i	$0.0389637\pi$
$271$	9.91021	+	17.1650i	0.602003	+	1.04270i	−0.390515	+	0.920597i	$0.627703\pi$
$272$	0.609171	−	5.70549i	0.0369364	−	0.345946i
$273$	0.297348	−	7.24968i	0.0179963	−	0.438771i
$274$	0.618457	+	1.49309i	0.0373624	+	0.0902007i
$275$	−4.64338	−	2.28986i	−0.280006	−	0.138084i
$276$	3.74144	−	1.00252i	0.225208	−	0.0603443i
$277$	−20.6904	+	23.5929i	−1.24317	+	1.41756i	−0.370796	+	0.928714i	$0.620915\pi$
$277$	−20.6904	+	23.5929i	−1.24317	+	1.41756i	−0.872370	+	0.488846i	$0.837418\pi$
$278$	21.2131	+	1.39038i	1.27228	+	0.0833896i
$279$	0.173182	+	0.870644i	0.0103681	+	0.0521241i
$280$	−10.4128	+	7.33221i	−0.622287	+	0.438184i
$281$	0.200758	−	0.484673i	0.0119762	−	0.0289131i	−0.917778	−	0.397093i	$-0.870019\pi$
$281$	0.200758	−	0.484673i	0.0119762	−	0.0289131i	0.929755	+	0.368180i	$0.120019\pi$
$282$	9.63379	−	8.44860i	0.573684	−	0.503107i
$283$	14.1320	−	6.96914i	0.840062	−	0.414273i	0.0292447	−	0.999572i	$-0.490690\pi$
$283$	14.1320	−	6.96914i	0.840062	−	0.414273i	0.810817	+	0.585300i	$0.199023\pi$
$284$	−17.0800	−	14.9787i	−1.01351	−	0.888823i
$285$	−3.01462	−	0.807766i	−0.178571	−	0.0478479i
$286$	30.9669	−	20.6915i	1.83111	−	1.22351i
$287$	3.16459	+	2.64120i	0.186800	+	0.155905i
$288$			7.06278i			0.416178i
$289$	−5.20001	−	16.1852i	−0.305883	−	0.952069i
$290$	23.4736	+	13.5525i	1.37842	+	0.795829i
$291$	8.69509	+	1.14473i	0.509715	+	0.0671053i
$292$	−1.17618	+	2.38505i	−0.0688305	+	0.139574i
$293$	7.59491	+	7.59491i	0.443699	+	0.443699i	0.893253	−	0.449554i	$-0.148417\pi$
$293$	7.59491	+	7.59491i	0.443699	+	0.443699i	−0.449554	+	0.893253i	$0.648417\pi$
$294$	−10.7736	−	11.1359i	−0.628329	−	0.649459i
$295$	−16.0969	−	10.7556i	−0.937200	−	0.626217i
$296$	9.85724	+	11.2400i	0.572941	+	0.653314i
$297$	3.73495	+	4.86749i	0.216724	+	0.282440i
$298$	−14.2636	−	18.5887i	−0.826268	−	1.07681i
$299$	−2.41552	−	2.75437i	−0.139693	−	0.159289i
$300$	2.03444	+	1.35937i	0.117458	+	0.0784832i
$301$	1.24615	+	4.23370i	0.0718269	+	0.244026i
$302$	22.5282	+	22.5282i	1.29636	+	1.29636i
$303$	−8.03321	+	16.2897i	−0.461496	+	0.935821i
$304$	1.78130	+	0.234513i	0.102165	+	0.0134502i
$305$	−16.6380	−	9.60594i	−0.952688	−	0.550035i
$306$	3.69834	+	8.34355i	0.211420	+	0.476969i
$307$			7.74112i			0.441809i	0.975295	+	0.220905i	$0.0709009\pi$
$307$			7.74112i			0.441809i	−0.975295	+	0.220905i	$0.929099\pi$
$308$	8.05073	−	46.3738i	0.458733	−	2.64239i
$309$	13.8702	−	9.26775i	0.789046	−	0.527224i
$310$	−4.58816	−	1.22939i	−0.260590	−	0.0698249i
$311$	−4.25998	−	3.73590i	−0.241561	−	0.211843i	0.530002	−	0.847997i	$-0.322191\pi$
$311$	−4.25998	−	3.73590i	−0.241561	−	0.211843i	−0.771563	+	0.636153i	$0.780525\pi$
$312$	−4.89754	+	2.41520i	−0.277268	+	0.136734i
$313$	−2.39176	+	2.09752i	−0.135190	+	0.118559i	−0.724271	−	0.689516i	$-0.757823\pi$
$313$	−2.39176	+	2.09752i	−0.135190	+	0.118559i	0.589080	+	0.808074i	$0.299490\pi$
$314$	2.22466	−	5.37081i	0.125545	−	0.303092i
$315$	−2.68769	+	5.80373i	−0.151434	+	0.327003i
$316$	4.92873	+	24.7784i	0.277263	+	1.39389i
$317$	3.05688	+	0.200358i	0.171691	+	0.0112533i	0.151006	−	0.988533i	$-0.451749\pi$
$317$	3.05688	+	0.200358i	0.171691	+	0.0112533i	0.0206851	+	0.999786i	$0.493415\pi$
$318$	−0.657700	+	0.749963i	−0.0368820	+	0.0420558i
$319$	−30.0194	+	8.04368i	−1.68076	+	0.450359i
$320$	−27.8605	−	13.7393i	−1.55745	−	0.768048i
$321$	5.97499	+	14.4249i	0.333491	+	0.805119i
$322$	−7.81672	−	0.320606i	−0.435609	−	0.0178666i
$323$	5.10637	−	1.50343i	0.284126	−	0.0836533i
$324$	−1.44978	−	2.51110i	−0.0805435	−	0.139505i
$325$	0.302063	−	2.29440i	0.0167555	−	0.127270i
$326$	−0.111606	−	1.70278i	−0.00618130	−	0.0943083i
$327$	−2.43715	+	9.09555i	−0.134774	+	0.502985i
$328$	0.605205	−	3.04257i	0.0334169	−	0.167998i
$329$	−14.0025	+	6.20542i	−0.771981	+	0.342116i
$330$	−32.1988	+	6.40475i	−1.77249	+	0.352570i
$331$	1.82591	+	13.8692i	0.100361	+	0.762320i	0.965429	+	0.260665i	$0.0839419\pi$
$331$	1.82591	+	13.8692i	0.100361	+	0.762320i	−0.865068	+	0.501655i	$0.832725\pi$
$332$	−34.1395	+	26.1962i	−1.87365	+	1.43770i
$333$	7.10965	+	2.41340i	0.389607	+	0.132254i
$334$	1.33138	−	20.3130i	0.0728501	−	1.11148i
$335$	32.8528	+	6.53483i	1.79494	+	0.357036i
$336$	1.09791	−	3.51446i	0.0598958	−	0.191729i
$337$	8.72820	+	13.0627i	0.475455	+	0.711569i	0.989232	−	0.146355i	$-0.0467541\pi$
$337$	8.72820	+	13.0627i	0.475455	+	0.711569i	−0.513777	+	0.857924i	$0.671754\pi$
$338$	−9.62175	−	7.38303i	−0.523354	−	0.401584i
$339$	9.47616	−	16.4132i	0.514674	−	0.891442i
$340$	−28.8764	−	1.18218i	−1.56604	−	0.0641129i
$341$	4.71667	−	2.72317i	0.255422	−	0.147468i
$342$	−2.64018	+	1.09360i	−0.142765	+	0.0591351i
$343$	8.32264	+	16.5449i	0.449380	+	0.893341i
$344$	2.34860	−	2.34860i	0.126628	−	0.126628i
$345$	1.03803	+	3.05794i	0.0558857	+	0.164634i
$346$	9.34163	+	18.9429i	0.502209	+	1.01838i
$347$	2.34337	−	6.90334i	0.125799	−	0.370591i	−0.865725	−	0.500521i	$-0.833142\pi$
$347$	2.34337	−	6.90334i	0.125799	−	0.370591i	0.991523	+	0.129930i	$0.0414753\pi$
$348$	14.5620	−	1.91713i	0.780607	−	0.102769i
$349$	5.71825	+	2.36858i	0.306091	+	0.126787i	0.530442	−	0.847721i	$-0.322026\pi$
$349$	5.71825	+	2.36858i	0.306091	+	0.126787i	−0.224351	+	0.974508i	$0.572026\pi$
$350$	−3.10341	−	3.84592i	−0.165884	−	0.205573i
$351$	−1.52361	+	2.28024i	−0.0813243	+	0.121710i
$352$	41.0329	−	13.9288i	2.18706	−	0.742406i
$353$	−6.07275	−	22.6638i	−0.323220	−	1.20627i	−0.916089	−	0.400974i	$-0.868672\pi$
$353$	−6.07275	−	22.6638i	−0.323220	−	1.20627i	0.592870	−	0.805299i	$-0.297995\pi$
$354$	−17.6887	+	1.15938i	−0.940142	+	0.0616202i
$355$	11.5299	−	15.0260i	0.611943	−	0.797499i
$356$	31.5052			1.66977
$357$	−1.24568	−	10.8374i	−0.0659282	−	0.573574i
$358$	−52.3140			−2.76488
$359$	−6.07780	+	7.92075i	−0.320774	+	0.418041i	−0.925711	−	0.378233i	$-0.876532\pi$
$359$	−6.07780	+	7.92075i	−0.320774	+	0.418041i	0.604936	+	0.796274i	$0.293199\pi$
$360$	4.80320	−	0.314818i	0.253151	−	0.0165924i
$361$	−4.48617	−	16.7426i	−0.236114	−	0.881189i
$362$	−14.0549	+	4.77100i	−0.738709	+	0.250758i
$363$	14.8017	−	22.1523i	0.776886	−	1.16269i
$364$	20.7852	−	3.25537i	1.08944	−	0.170628i
$365$	−2.04832	−	0.848443i	−0.107214	−	0.0444095i
$366$	−17.4409	+	2.29613i	−0.911648	+	0.120021i
$367$	2.48091	−	7.30853i	0.129502	−	0.381502i	−0.862767	−	0.505601i	$-0.831271\pi$
$367$	2.48091	−	7.30853i	0.129502	−	0.381502i	0.992270	+	0.124099i	$0.0396041\pi$
$368$	−0.822238	−	1.66733i	−0.0428621	−	0.0869158i
$369$	−0.500789	−	1.47528i	−0.0260700	−	0.0767998i
$370$	−28.4082	+	28.4082i	−1.47687	+	1.47687i
$371$	1.01767	−	0.621222i	0.0528349	−	0.0322522i
$372$	−2.37802	+	0.985007i	−0.123294	+	0.0510702i
$373$	1.15826	−	0.668724i	0.0599726	−	0.0346252i	−0.469714	−	0.882819i	$-0.655643\pi$
$373$	1.15826	−	0.668724i	0.0599726	−	0.0346252i	0.529686	+	0.848194i	$0.322310\pi$
$374$	41.1802	−	37.9410i	2.12938	−	1.96188i
$375$	5.02355	−	8.70104i	0.259415	−	0.449320i
$376$	9.14474	+	7.01701i	0.471604	+	0.361874i
$377$	−7.71781	−	11.5505i	−0.397488	−	0.594882i
$378$	1.28264	+	5.71417i	0.0659721	+	0.293905i
$379$	14.9861	+	2.98092i	0.769783	+	0.153119i	0.564332	−	0.825548i	$-0.309134\pi$
$379$	14.9861	+	2.98092i	0.769783	+	0.153119i	0.205451	+	0.978667i	$0.434134\pi$
$380$	0.591862	−	9.03008i	0.0303619	−	0.463233i
$381$	−18.3836	−	6.24040i	−0.941822	−	0.319705i
$382$	−21.5496	+	16.5356i	−1.10257	+	0.846034i
$383$	3.53986	+	26.8879i	0.180879	+	1.37391i	0.805322	+	0.592838i	$0.201993\pi$
$383$	3.53986	+	26.8879i	0.180879	+	1.37391i	−0.624443	+	0.781070i	$0.714674\pi$
$384$	−14.0431	+	2.79334i	−0.716632	+	0.142547i
$385$	39.0186	+	4.16898i	1.98857	+	0.212471i
$386$	−6.73598	+	33.8641i	−0.342853	+	1.72364i
$387$	0.431727	−	1.61123i	0.0219459	−	0.0819032i
$388$	1.66317	+	25.3751i	0.0844348	+	1.28823i
$389$	−4.55235	+	34.5786i	−0.230813	+	1.75320i	0.347770	+	0.937580i	$0.386939\pi$
$389$	−4.55235	+	34.5786i	−0.230813	+	1.75320i	−0.578584	+	0.815623i	$0.696394\pi$
$390$	−7.33725	−	12.7085i	−0.371536	−	0.643520i
$391$	−4.22890	−	3.52894i	−0.213865	−	0.178466i
$392$	7.93427	−	11.4597i	0.400741	−	0.578800i
$393$	−3.25927	−	7.86858i	−0.164408	−	0.396917i
$394$	−10.6022	−	5.22842i	−0.534131	−	0.263404i
$395$	−20.3451	+	5.45145i	−1.02367	+	0.274292i
$396$	−11.7296	+	13.3751i	−0.589436	+	0.672123i
$397$	3.83924	+	0.251637i	0.192686	+	0.0126293i	0.161441	−	0.986882i	$-0.448386\pi$
$397$	3.83924	+	0.251637i	0.192686	+	0.0126293i	0.0312454	+	0.999512i	$0.490053\pi$
$398$	7.89272	+	39.6794i	0.395626	+	1.98895i
$399$	3.40197	−	0.306689i	0.170312	−	0.0153537i
$400$	0.449401	−	1.08495i	0.0224701	−	0.0542476i
$401$	20.2175	−	17.7303i	1.00961	−	0.885406i	0.0161850	−	0.999869i	$-0.494848\pi$
$401$	20.2175	−	17.7303i	1.00961	−	0.885406i	0.993428	+	0.114463i	$0.0365146\pi$
$402$	27.5080	−	13.5654i	1.37197	−	0.676582i
$403$	1.83032	+	1.60515i	0.0911747	+	0.0799581i
$404$	−50.8698	−	13.6305i	−2.53087	−	0.678144i
$405$	2.01000	−	1.34304i	0.0998777	−	0.0667361i
$406$	−29.2281	−	5.07415i	−1.45056	−	0.251826i
$407$		−	46.0647i		−	2.28334i
$408$	−6.71231	+	4.72724i	−0.332309	+	0.234033i
$409$	11.9304	+	6.88802i	0.589921	+	0.340591i	0.765066	−	0.643952i	$-0.222706\pi$
$409$	11.9304	+	6.88802i	0.589921	+	0.340591i	−0.175145	+	0.984543i	$0.556040\pi$
$410$	8.26518	+	1.08813i	0.408188	+	0.0537390i
$411$	−0.322921	+	0.654820i	−0.0159285	+	0.0322999i
$412$	34.2021	+	34.2021i	1.68502	+	1.68502i
$413$	20.5943	+	4.98179i	1.01338	+	0.245138i
$414$	2.45860	+	1.64278i	0.120833	+	0.0807383i
$415$	−23.6548	−	26.9732i	−1.16117	−	1.32406i
$416$	11.7912	+	15.3666i	0.578111	+	0.753409i
$417$	5.84661	+	7.61945i	0.286310	+	0.373126i
$418$	11.5603	+	13.1820i	0.565434	+	0.644754i
$419$	−23.7931	−	15.8981i	−1.16237	−	0.776671i	−0.183877	−	0.982949i	$-0.558865\pi$
$419$	−23.7931	−	15.8981i	−1.16237	−	0.776671i	−0.978493	+	0.206278i	$0.933865\pi$
$420$	−18.0253	−	4.36035i	−0.879545	−	0.212763i
$421$	−3.32865	−	3.32865i	−0.162229	−	0.162229i	0.621325	−	0.783553i	$-0.286595\pi$
$421$	−3.32865	−	3.32865i	−0.162229	−	0.162229i	−0.783553	+	0.621325i	$0.786595\pi$
$422$	−4.66632	+	9.46235i	−0.227153	+	0.460620i
$423$	5.73933	+	0.755598i	0.279056	+	0.0367384i
$424$	−0.777102	−	0.448660i	−0.0377394	−	0.0217889i
$425$	−0.0853497	−	3.47823i	−0.00414007	−	0.168719i
$426$		−	17.3423i		−	0.840238i
$427$	20.7167	+	3.59654i	1.00255	+	0.174049i
$428$	−37.6423	+	25.1518i	−1.81951	+	1.21576i
$429$	16.2524	+	4.35481i	0.784672	+	0.210252i
$430$	6.71068	+	5.88511i	0.323618	+	0.283805i
$431$	30.4928	−	15.0374i	1.46879	−	0.724326i	0.480509	−	0.876990i	$-0.340452\pi$
$431$	30.4928	−	15.0374i	1.46879	−	0.724326i	0.988278	+	0.152664i	$0.0487851\pi$
$432$	−1.04630	+	0.917578i	−0.0503400	+	0.0441470i
$433$	−11.6445	+	28.1122i	−0.559597	+	1.35099i	0.350489	+	0.936567i	$0.386015\pi$
$433$	−11.6445	+	28.1122i	−0.559597	+	1.35099i	−0.910086	+	0.414419i	$0.863985\pi$
$434$	5.17770	−	0.466771i	0.248537	−	0.0224057i
$435$	2.38894	+	12.0100i	0.114541	+	0.575836i
$436$	−27.2450	−	1.78573i	−1.30480	−	0.0855212i
$437$	1.13714	−	1.29666i	0.0543969	−	0.0620278i
$438$	−1.96090	+	0.525422i	−0.0936956	+	0.0251056i
$439$	−7.79388	−	3.84352i	−0.371982	−	0.183441i	0.246683	−	0.969096i	$-0.420659\pi$
$439$	−7.79388	−	3.84352i	−0.371982	−	0.183441i	−0.618665	+	0.785655i	$0.712326\pi$
$440$	−11.3016	−	27.2844i	−0.538782	−	1.30073i
$441$	0.573250	−	6.97649i	0.0272976	−	0.332214i
$442$	21.9760	+	11.9789i	1.04529	+	0.569777i
$443$	12.1961	+	21.1242i	0.579453	+	1.00364i	0.995542	+	0.0943176i	$0.0300669\pi$
$443$	12.1961	+	21.1242i	0.579453	+	1.00364i	−0.416090	+	0.909324i	$0.636600\pi$
$444$	−2.84159	+	21.5840i	−0.134856	+	1.02433i
$445$	1.71790	+	26.2100i	0.0814361	+	1.24248i
$446$	−7.92670	+	29.5828i	−0.375340	+	1.40079i
$447$	2.06509	−	10.3819i	0.0976754	−	0.491047i
$448$	33.8059	+	3.61202i	1.59718	+	0.170652i
$449$	29.4309	−	5.85416i	1.38893	−	0.276275i	0.556703	−	0.830712i	$-0.312066\pi$
$449$	29.4309	−	5.85416i	1.38893	−	0.276275i	0.832226	+	0.554437i	$0.187066\pi$
$450$	0.243804	+	1.85188i	0.0114931	+	0.0872984i
$451$	−7.58333	+	5.81889i	−0.357085	+	0.274001i
$452$	52.0371	+	17.6642i	2.44762	+	0.830855i
$453$	−0.941374	+	14.3626i	−0.0442296	+	0.674813i
$454$	−31.3352	−	6.23296i	−1.47064	−	0.292528i
$455$	3.84160	+	17.1143i	0.180097	+	0.802331i
$456$	−1.42820	−	2.13746i	−0.0668818	−	0.100096i
$457$	1.60686	+	1.23299i	0.0751660	+	0.0576769i	0.645661	−	0.763624i	$-0.276582\pi$
$457$	1.60686	+	1.23299i	0.0751660	+	0.0576769i	−0.570495	+	0.821301i	$0.693249\pi$
$458$	−10.5288	+	18.2365i	−0.491980	+	0.852134i
$459$	−1.73234	+	3.74152i	−0.0808588	+	0.174639i
$460$	−8.10914	+	4.68182i	−0.378091	+	0.218291i
$461$	10.8365	−	4.48864i	0.504708	−	0.209057i	−0.115777	−	0.993275i	$-0.536936\pi$
$461$	10.8365	−	4.48864i	0.504708	−	0.209057i	0.620485	+	0.784218i	$0.286936\pi$
$462$	30.6683	−	18.7210i	1.42682	−	0.870978i
$463$	8.73024	−	8.73024i	0.405729	−	0.405729i	−0.474517	−	0.880246i	$-0.657377\pi$
$463$	8.73024	−	8.73024i	0.405729	−	0.405729i	0.880246	+	0.474517i	$0.157377\pi$
$464$	−2.26594	−	6.67526i	−0.105194	−	0.309891i
$465$	−0.949122	−	1.92463i	−0.0440145	−	0.0892525i
$466$	−7.48065	+	22.0373i	−0.346535	+	1.02086i
$467$	7.65589	−	1.00792i	0.354272	−	0.0466408i	0.0487100	−	0.998813i	$-0.484489\pi$
$467$	7.65589	−	1.00792i	0.354272	−	0.0466408i	0.305562	+	0.952172i	$0.401156\pi$
$468$	−7.34655	−	3.04304i	−0.339594	−	0.140665i
$469$	−36.2189	+	5.67258i	−1.67243	+	0.261935i
$470$	−17.2092	+	25.7554i	−0.793800	+	1.18801i
$471$	2.48693	−	0.844199i	0.114592	−	0.0388986i
$472$	−4.12720	−	15.4029i	−0.189970	−	0.708977i
$473$	−10.2122	+	0.669344i	−0.469558	+	0.0307765i
$474$	−11.7407	+	15.3007i	−0.539266	+	0.702785i
$475$	1.08944			0.0499871
$476$	30.1152	−	9.67297i	1.38033	−	0.443360i
$477$	−0.450646			−0.0206337
$478$	2.83881	−	3.69961i	0.129844	−	0.169216i
$479$	−32.9824	+	2.16178i	−1.50700	+	0.0987743i	−0.796380	−	0.604797i	$-0.793254\pi$
$479$	−32.9824	+	2.16178i	−1.50700	+	0.0987743i	−0.710625	+	0.703571i	$0.751588\pi$
$480$	−4.41898	−	16.4918i	−0.201698	−	0.752746i
$481$	19.4977	−	6.61858i	0.889019	−	0.301781i
$482$	0.357463	−	0.534981i	0.0162820	−	0.0243677i
$483$	−2.21951	−	2.75054i	−0.100991	−	0.125154i
$484$	71.3707	+	29.5627i	3.24412	+	1.34376i
$485$	−21.0196	+	2.76728i	−0.954449	+	0.125656i
$486$	0.711505	−	2.09603i	0.0322745	−	0.0950777i
$487$	−11.8349	−	23.9989i	−0.536292	−	1.08749i	−0.981393	−	0.192012i	$-0.938499\pi$
$487$	−11.8349	−	23.9989i	−0.536292	−	1.08749i	0.445101	−	0.895480i	$-0.353168\pi$
$488$	−5.08664	−	14.9848i	−0.230262	−	0.678329i
$489$	0.545125	−	0.545125i	0.0246514	−	0.0246514i
$490$	32.1241	+	19.2620i	1.45122	+	0.870168i
$491$	5.39335	−	2.23400i	0.243398	−	0.100819i	−0.257650	−	0.966238i	$-0.582948\pi$
$491$	5.39335	−	2.23400i	0.243398	−	0.100819i	0.501048	+	0.865419i	$0.332948\pi$
$492$	3.91218	−	2.25870i	0.176375	−	0.101830i
$493$	−14.1518	−	15.3600i	−0.637366	−	0.691780i
$494$	−3.91853	+	6.78710i	−0.176303	+	0.305366i
$495$	−11.7667	−	9.02890i	−0.528873	−	0.405819i
$496$	0.686333	+	1.02717i	0.0308173	+	0.0461213i
$497$	−6.18109	+	19.7859i	−0.277260	+	0.887521i
$498$	−32.2189	−	6.40873i	−1.44376	−	0.287182i
$499$	1.95569	−	29.8381i	0.0875488	−	1.33574i	−0.697626	−	0.716462i	$-0.745760\pi$
$499$	1.95569	−	29.8381i	0.0875488	−	1.33574i	0.785175	−	0.619274i	$-0.212573\pi$
$500$	27.5862	+	9.36425i	1.23369	+	0.418782i
$501$	7.29613	−	5.59852i	0.325967	−	0.250123i
$502$	−8.61373	−	65.4278i	−0.384450	−	2.92018i
$503$	−32.4711	+	6.45891i	−1.44782	+	0.287988i	−0.855536	−	0.517744i	$-0.826772\pi$
$503$	−32.4711	+	6.45891i	−1.44782	+	0.287988i	−0.592280	+	0.805732i	$0.701772\pi$
$504$	−4.81641	+	2.13447i	−0.214540	+	0.0950769i
$505$	8.56581	−	43.0632i	0.381174	−	1.91629i
$506$	4.69543	−	17.5236i	0.208737	−	0.779018i
$507$	−0.358350	−	5.46736i	−0.0159149	−	0.242814i
$508$	7.34757	−	55.8104i	0.325996	−	2.47618i
$509$	4.81235	+	8.33523i	0.213304	+	0.369453i	0.952746	−	0.303767i	$-0.0982443\pi$
$509$	4.81235	+	8.33523i	0.213304	+	0.369453i	−0.739443	+	0.673219i	$0.764911\pi$
$510$	−13.8561	−	17.1685i	−0.613557	−	0.760236i
$511$	2.42447	+	0.0994406i	0.107252	+	0.00439899i
$512$	5.88222	+	14.2009i	0.259960	+	0.627598i
$513$	−1.15790	−	0.571012i	−0.0511225	−	0.0252108i
$514$	49.6802	−	13.3118i	2.19130	−	0.587157i
$515$	−26.5888	+	30.3187i	−1.17164	+	1.33600i
$516$	4.82631	+	0.316333i	0.212466	+	0.0139258i
$517$	−6.92894	−	34.8341i	−0.304734	−	1.53200i
$518$	18.4773	−	39.8995i	0.811846	−	1.75308i
$519$	−3.65155	+	8.81563i	−0.160285	+	0.386963i
$520$	9.92480	−	8.70382i	0.435231	−	0.381688i
$521$	19.1018	−	9.41999i	0.836867	−	0.412697i	0.0272308	−	0.999629i	$-0.491331\pi$
$521$	19.1018	−	9.41999i	0.836867	−	0.412697i	0.809636	+	0.586932i	$0.199664\pi$
$522$	8.42994	+	7.39286i	0.368968	+	0.323577i
$523$	23.6469	+	6.33616i	1.03401	+	0.277061i	0.735627	−	0.677387i	$-0.236888\pi$
$523$	23.6469	+	6.33616i	1.03401	+	0.277061i	0.298378	+	0.954448i	$0.403554\pi$
$524$	20.5334	−	13.7200i	0.897004	−	0.599359i
$525$	0.381882	−	2.19971i	0.0166667	−	0.0960034i
$526$		−	51.2241i		−	2.23348i
$527$	3.09221	+	1.95817i	0.134699	+	0.0852991i
$528$	7.39432	+	4.26911i	0.321797	+	0.185789i
$529$	21.0340	+	2.76917i	0.914520	+	0.120399i
$530$	1.06652	−	2.16269i	0.0463268	−	0.0939414i
$531$	−5.66281	−	5.66281i	−0.245745	−	0.245745i
$532$	2.79660	+	9.50122i	0.121248	+	0.411930i
$533$	−3.55252	−	2.37372i	−0.153877	−	0.102817i
$534$	15.8577	+	18.0823i	0.686231	+	0.782497i
$535$	−22.9770	−	29.9442i	−0.993383	−	1.29460i
$536$	16.7961	+	21.8891i	0.725480	+	0.945464i
$537$	−15.5830	−	17.7691i	−0.672458	−	0.766792i
$538$	−28.4889	−	19.0357i	−1.22824	−	0.820685i
$539$	−41.6620	+	10.4282i	−1.79451	+	0.449173i
$540$	4.95641	+	4.95641i	0.213290	+	0.213290i
$541$	−1.91355	+	3.88029i	−0.0822699	+	0.166827i	−0.934120	−	0.356958i	$-0.883814\pi$
$541$	−1.91355	+	3.88029i	−0.0822699	+	0.166827i	0.851850	+	0.523785i	$0.175481\pi$
$542$	−43.4971	−	5.72650i	−1.86836	−	0.245974i
$543$	−5.80713	−	3.35275i	−0.249208	−	0.143880i
$544$	21.0903	+	20.0801i	0.904239	+	0.860925i
$545$		−	22.7633i		−	0.975072i
$546$	12.3304	+	10.2911i	0.527692	+	0.440416i
$547$	8.16676	−	5.45685i	0.349185	−	0.233318i	−0.368591	−	0.929591i	$-0.620160\pi$
$547$	8.16676	−	5.45685i	0.349185	−	0.233318i	0.717777	+	0.696273i	$0.245160\pi$
$548$	−2.04488	−	0.547924i	−0.0873529	−	0.0234061i
$549$	−5.97511	−	5.24003i	−0.255011	−	0.223639i
$550$	10.2781	−	5.06860i	0.438260	−	0.216126i
$551$	4.91683	−	4.31195i	0.209464	−	0.183695i
$552$	−1.01792	+	2.45747i	−0.0433255	+	0.104597i
$553$	18.8484	−	13.2721i	0.801516	−	0.564388i
$554$	−13.5510	−	68.1253i	−0.575726	−	2.89437i
$555$	−18.1113	−	1.18708i	−0.768781	−	0.0503886i
$556$	−18.3613	+	20.9370i	−0.778692	+	0.887928i
$557$	13.6373	−	3.65411i	0.577831	−	0.154829i	0.0419455	−	0.999120i	$-0.486644\pi$
$557$	13.6373	−	3.65411i	0.577831	−	0.154829i	0.535886	+	0.844290i	$0.319978\pi$
$558$	−1.76228	−	0.869063i	−0.0746035	−	0.0367904i
$559$	−1.75060	−	4.22633i	−0.0740426	−	0.178755i
$560$	−0.364762	+	8.89331i	−0.0154140	+	0.375811i
$561$	25.1537	+	2.68564i	1.06199	+	0.113388i
$562$	0.580607	+	1.00564i	0.0244914	+	0.0424204i
$563$	−0.310673	+	2.35980i	−0.0130933	+	0.0994536i	−0.996744	−	0.0806351i	$-0.974305\pi$
$563$	−0.310673	+	2.35980i	−0.0130933	+	0.0994536i	0.983650	+	0.180089i	$0.0576385\pi$
$564$	1.09780	+	16.7492i	0.0462259	+	0.705270i
$565$	−11.8579	+	44.2543i	−0.498866	+	1.86179i
$566$	−6.80437	+	34.2079i	−0.286009	+	1.43786i
$567$	−1.55882	+	2.13778i	−0.0654642	+	0.0897782i
$568$	15.3008	−	3.04352i	0.642007	−	0.127703i
$569$	1.62703	+	12.3585i	0.0682088	+	0.518097i	0.991108	+	0.133057i	$0.0424792\pi$
$569$	1.62703	+	12.3585i	0.0682088	+	0.518097i	−0.922900	+	0.385041i	$0.874187\pi$
$570$	5.48068	−	4.20548i	0.229561	−	0.176148i
$571$	19.2435	+	6.53230i	0.805317	+	0.273368i	0.693590	−	0.720370i	$-0.256028\pi$
$571$	19.2435	+	6.53230i	0.805317	+	0.273368i	0.111728	+	0.993739i	$0.464362\pi$
$572$	−3.19084	+	48.6828i	−0.133416	+	2.03553i
$573$	−12.0356	−	2.39403i	−0.502794	−	0.100012i
$574$	−8.90243	+	1.99830i	−0.371580	+	0.0834075i
$575$	−0.626276	−	0.937289i	−0.0261175	−	0.0390876i
$576$	−10.1947	−	7.82267i	−0.424779	−	0.325945i
$577$	−5.13838	+	8.89994i	−0.213914	+	0.370509i	−0.952936	−	0.303172i	$-0.901954\pi$
$577$	−5.13838	+	8.89994i	−0.213914	+	0.370509i	0.739022	+	0.673681i	$0.235288\pi$
$578$	35.4295	+	12.6777i	1.47367	+	0.527323i
$579$	−13.5088	+	7.79932i	−0.561407	+	0.324128i
$580$	−32.8033	+	13.5876i	−1.36208	+	0.564194i
$581$	34.4745	+	18.7951i	1.43024	+	0.779751i
$582$	−13.7268	+	13.7268i	−0.568994	+	0.568994i
$583$	0.888736	+	2.61813i	0.0368077	+	0.108432i
$584$	−0.807702	−	1.63786i	−0.0334229	−	0.0677750i
$585$	2.13100	−	6.27773i	0.0881061	−	0.259552i
$586$	−23.5714	+	3.10323i	−0.973725	+	0.128193i
$587$	−22.1824	−	9.18825i	−0.915566	−	0.379240i	−0.125381	−	0.992109i	$-0.540015\pi$
$587$	−22.1824	−	9.18825i	−0.915566	−	0.379240i	−0.790185	+	0.612869i	$0.790015\pi$
$588$	20.1644	−	2.31620i	0.831565	−	0.0955185i
$589$	−0.636715	+	0.952912i	−0.0262354	+	0.0392640i
$590$	40.5783	−	13.7745i	1.67058	−	0.567086i
$591$	−1.38224	−	5.15858i	−0.0568576	−	0.212196i
$592$	10.4263	−	0.683374i	0.428517	−	0.0280865i
$593$	−15.7736	+	20.5566i	−0.647745	+	0.844158i	−0.995631	−	0.0933792i	$-0.970233\pi$
$593$	−15.7736	+	20.5566i	−0.647745	+	0.844158i	0.347886	+	0.937537i	$0.386900\pi$
$594$	−13.5805			−0.557216
$595$	9.68931	+	24.5262i	0.397223	+	1.00548i
$596$	30.6928			1.25723
$597$	−11.1265	+	14.5004i	−0.455378	+	0.593460i
$598$	8.09180	−	0.530364i	0.330898	−	0.0216882i
$599$	−6.11987	−	22.8397i	−0.250051	−	0.933204i	−0.970777	−	0.239984i	$-0.922858\pi$
$599$	−6.11987	−	22.8397i	−0.250051	−	0.933204i	0.720726	−	0.693220i	$-0.243809\pi$
$600$	−1.59109	+	0.540102i	−0.0649560	+	0.0220496i
$601$	−8.76475	+	13.1174i	−0.357522	+	0.535069i	−0.966014	−	0.258491i	$-0.916775\pi$
$601$	−8.76475	+	13.1174i	−0.357522	+	0.535069i	0.608492	+	0.793560i	$0.291775\pi$
$602$	−9.11390	−	3.51652i	−0.371455	−	0.143323i
$603$	12.8016	+	5.30259i	0.521321	+	0.215938i
$604$	−41.3776	+	5.44746i	−1.68363	+	0.221654i
$605$	−20.7024	+	60.9873i	−0.841672	+	2.47949i
$606$	−17.7815	−	36.0573i	−0.722323	−	1.46473i
$607$	−14.3864	−	42.3811i	−0.583928	−	1.72020i	−0.688081	−	0.725634i	$-0.741547\pi$
$607$	−14.3864	−	42.3811i	−0.583928	−	1.72020i	0.104154	−	0.994561i	$-0.466787\pi$
$608$	−6.44764	+	6.44764i	−0.261486	+	0.261486i
$609$	−6.98283	−	11.4391i	−0.282958	−	0.463536i
$610$	39.2884	−	16.2738i	1.59074	−	0.658906i
$611$	13.7486	−	7.93776i	0.556209	−	0.321127i
$612$	−11.6203	−	2.81003i	−0.469722	−	0.113589i
$613$	14.8994	−	25.8065i	0.601781	−	1.04231i	−0.390771	−	0.920488i	$-0.627792\pi$
$613$	14.8994	−	25.8065i	0.601781	−	1.04231i	0.992551	−	0.121827i	$-0.0388752\pi$
$614$	−13.5941	−	10.4311i	−0.548612	−	0.420965i
$615$	2.09240	+	3.13149i	0.0843735	+	0.126274i
$616$	21.8993	+	23.7726i	0.882349	+	0.957824i
$617$	−19.7096	−	3.92049i	−0.793479	−	0.157833i	−0.218323	−	0.975877i	$-0.570059\pi$
$617$	−19.7096	−	3.92049i	−0.793479	−	0.157833i	−0.575156	+	0.818044i	$0.695059\pi$
$618$	−2.41498	+	36.8454i	−0.0971446	+	1.48214i
$619$	26.6881	+	9.05940i	1.07269	+	0.364128i	0.801251	−	0.598329i	$-0.204168\pi$
$619$	26.6881	+	9.05940i	1.07269	+	0.364128i	0.271435	+	0.962457i	$0.412502\pi$
$620$	4.93646	−	3.78788i	0.198253	−	0.152125i
$621$	0.174365	+	1.32443i	0.00699703	+	0.0531477i
$622$	12.3008	−	2.44679i	0.493219	−	0.0981073i
$623$	−11.6474	−	26.2821i	−0.466641	−	1.05297i
$624$	−0.744561	+	3.74316i	−0.0298063	+	0.149846i
$625$	−7.37820	+	27.5358i	−0.295128	+	1.10143i
$626$	−0.460543	−	7.02653i	−0.0184070	−	0.280837i
$627$	−1.03389	+	7.85319i	−0.0412897	+	0.313626i
$628$	3.80758	+	6.59492i	0.151939	+	0.263166i
$629$	27.4200	−	14.3688i	1.09331	−	0.572920i
$630$	−6.57021	−	12.5403i	−0.261763	−	0.499617i
$631$	7.69012	+	18.5656i	0.306139	+	0.739085i	0.999823	+	0.0188054i	$0.00598631\pi$
$631$	7.69012	+	18.5656i	0.306139	+	0.739085i	−0.693684	+	0.720279i	$0.744014\pi$
$632$	−15.5600	−	7.67333i	−0.618943	−	0.305229i
$633$	−4.60398	+	1.23363i	−0.182992	+	0.0490325i
$634$	−4.47096	+	5.09816i	−0.177565	+	0.202474i
$635$	46.8308	+	3.06946i	1.85843	+	0.121808i
$636$	−0.254920	−	1.28157i	−0.0101082	−	0.0508176i
$637$	−10.3999	−	16.1359i	−0.412059	−	0.639327i
$638$	26.3255	−	63.5554i	1.04224	−	2.51618i
$639$	5.89052	−	5.16585i	0.233025	−	0.204358i
$640$	31.0433	−	15.3089i	1.22710	−	0.605136i
$641$	11.5477	+	10.1271i	0.456106	+	0.399994i	0.856335	−	0.516421i	$-0.172736\pi$
$641$	11.5477	+	10.1271i	0.456106	+	0.399994i	−0.400229	+	0.916415i	$0.631069\pi$
$642$	−33.3826	−	8.94483i	−1.31750	−	0.353024i
$643$	14.7861	−	9.87978i	0.583108	−	0.389620i	−0.228741	−	0.973487i	$-0.573461\pi$
$643$	14.7861	−	9.87978i	0.583108	−	0.389620i	0.811849	+	0.583867i	$0.198461\pi$
$644$	6.56660	−	7.86788i	0.258760	−	0.310038i
$645$			4.03239i			0.158775i
$646$	−4.24063	+	10.9931i	−0.166845	+	0.432517i
$647$	17.7812	+	10.2660i	0.699051	+	0.403598i	0.806994	−	0.590560i	$-0.201093\pi$
$647$	17.7812	+	10.2660i	0.699051	+	0.403598i	−0.107943	+	0.994157i	$0.534426\pi$
$648$	1.97415	+	0.259902i	0.0775520	+	0.0102099i
$649$	−21.7316	+	44.0673i	−0.853039	+	1.72979i
$650$	3.62213	+	3.62213i	0.142072	+	0.142072i
$651$	1.70085	+	1.61963i	0.0666617	+	0.0634781i
$652$	1.85862	+	1.24189i	0.0727891	+	0.0486361i
$653$	2.73507	+	3.11875i	0.107032	+	0.122046i	0.802875	−	0.596147i	$-0.203303\pi$
$653$	2.73507	+	3.11875i	0.107032	+	0.122046i	−0.695843	+	0.718194i	$0.744969\pi$
$654$	−12.6885	−	16.5360i	−0.496161	−	0.646609i
$655$	12.5336	+	16.3342i	0.489730	+	0.638229i
$656$	−1.42955	−	1.63009i	−0.0558144	−	0.0636441i
$657$	−0.762570	−	0.509533i	−0.0297507	−	0.0198788i
$658$	7.97095	−	32.9513i	0.310740	−	1.28457i
$659$	−7.25275	−	7.25275i	−0.282527	−	0.282527i	0.551589	−	0.834116i	$-0.314022\pi$
$659$	−7.25275	−	7.25275i	−0.282527	−	0.282527i	−0.834116	+	0.551589i	$0.814022\pi$
$660$	19.0207	−	38.5702i	0.740380	−	1.50134i
$661$	−10.4008	−	1.36930i	−0.404546	−	0.0532595i	−0.0744922	−	0.997222i	$-0.523734\pi$
$661$	−10.4008	−	1.36930i	−0.404546	−	0.0532595i	−0.330054	+	0.943962i	$0.607067\pi$
$662$	−26.8159	−	15.4822i	−1.04223	−	0.601731i
$663$	2.47733	+	11.0326i	0.0962116	+	0.428471i
$664$		−	29.5508i		−	1.14679i
$665$	−7.75184	+	2.84465i	−0.300604	+	0.110311i
$666$	−13.8183	+	9.23311i	−0.535450	+	0.357776i
$667$	−6.53621	−	1.75137i	−0.253083	−	0.0678134i
$668$	20.0486	+	17.5822i	0.775704	+	0.680274i
$669$	−12.4093	+	6.11960i	−0.479772	+	0.236597i
$670$	−55.7446	+	48.8867i	−2.15360	+	1.88866i
$671$	−18.6594	+	45.0478i	−0.720339	+	1.73905i
$672$	10.7584	+	15.2786i	0.415016	+	0.589385i
$673$	6.71261	+	33.7466i	0.258752	+	1.30083i	0.863472	+	0.504397i	$0.168285\pi$
$673$	6.71261	+	33.7466i	0.258752	+	1.30083i	−0.604720	+	0.796438i	$0.706715\pi$
$674$	−34.7003	−	2.27438i	−1.33661	−	0.0876058i
$675$	−0.556389	+	0.634440i	−0.0214154	+	0.0244196i
$676$	15.3457	−	4.11186i	0.590218	−	0.158148i
$677$	−29.9604	−	14.7748i	−1.15147	−	0.567842i	−0.236607	−	0.971606i	$-0.576035\pi$
$677$	−29.9604	−	14.7748i	−1.15147	−	0.567842i	−0.914864	+	0.403763i	$0.867702\pi$
$678$	16.0539	+	38.7576i	0.616547	+	1.48848i
$679$	20.5534	−	10.7685i	0.788769	−	0.413258i
$680$	12.7158	−	15.2380i	0.487628	−	0.584349i
$681$	−7.21689	−	12.5000i	−0.276552	−	0.479002i
$682$	−1.57355	+	11.9523i	−0.0602544	+	0.457678i
$683$	2.49959	+	38.1364i	0.0956442	+	1.45925i	0.728535	+	0.685008i	$0.240201\pi$
$683$	2.49959	+	38.1364i	0.0956442	+	1.45925i	−0.632891	+	0.774241i	$0.718132\pi$
$684$	0.968878	−	3.61590i	0.0370460	−	0.138257i
$685$	0.344331	−	1.73107i	0.0131562	−	0.0661408i
$686$	−40.2689	−	7.67884i	−1.53747	−	0.293180i
$687$	−9.33051	+	1.85595i	−0.355981	+	0.0708090i
$688$	−0.302998	−	2.30150i	−0.0115517	−	0.0877439i
$689$	−0.980477	+	0.752346i	−0.0373532	+	0.0286621i
$690$	−6.76874	−	2.29768i	−0.257682	−	0.0874712i
$691$	−2.29304	+	34.9850i	−0.0872313	+	1.33089i	0.699959	+	0.714183i	$0.253202\pi$
$691$	−2.29304	+	34.9850i	−0.0872313	+	1.33089i	−0.787190	+	0.616710i	$0.788465\pi$
$692$	−27.1359	−	5.39767i	−1.03155	−	0.205189i
$693$	15.4941	+	4.84032i	0.588572	+	0.183869i
$694$	8.96518	+	13.4173i	0.340314	+	0.509315i
$695$	−18.4193	−	14.1336i	−0.698684	−	0.536119i
$696$	−5.04315	+	8.73500i	−0.191160	+	0.331099i
$697$	−5.82913	−	2.69891i	−0.220794	−	0.102229i
$698$	−11.8647	+	6.85010i	−0.449086	+	0.259280i
$699$	−9.71353	+	4.02347i	−0.367399	+	0.152182i
$700$	6.47168	−	0.158313i	0.244607	−	0.00598366i
$701$	0.358450	−	0.358450i	0.0135385	−	0.0135385i	−0.700305	−	0.713844i	$-0.746953\pi$
$701$	0.358450	−	0.358450i	0.0135385	−	0.0135385i	0.713844	+	0.700305i	$0.246953\pi$
$702$	−1.95125	−	5.74820i	−0.0736452	−	0.216952i
$703$	4.28722	+	8.69363i	0.161696	+	0.327886i
$704$	−25.3423	+	74.6559i	−0.955122	+	2.81370i
$705$	−13.8743	+	1.82659i	−0.522536	+	0.0687932i
$706$	47.9825	+	19.8750i	1.80585	+	0.748006i
$707$	7.43558	+	47.4755i	0.279644	+	1.78550i
$708$	12.9009	−	19.3075i	0.484845	−	0.725621i
$709$	−1.76803	+	0.600164i	−0.0663996	+	0.0225396i	−0.354442	−	0.935078i	$-0.615329\pi$
$709$	−1.76803	+	0.600164i	−0.0663996	+	0.0225396i	0.288042	+	0.957618i	$0.406996\pi$
$710$	10.8506	+	40.4949i	0.407215	+	1.51975i
$711$	−8.69432	+	0.569856i	−0.326062	+	0.0213713i
$712$	−13.1707	+	17.1644i	−0.493592	+	0.643262i
$713$	1.18585			0.0444103
$714$	20.7099	+	12.4157i	0.775047	+	0.464647i
$715$	−40.6745			−1.52114
$716$	41.7176	−	54.3674i	1.55906	−	2.03181i
$717$	2.10223	−	0.137787i	0.0785092	−	0.00514576i
$718$	−5.71972	−	21.3463i	−0.213458	−	0.796636i
$719$	−2.62797	+	0.892076i	−0.0980068	+	0.0332688i	−0.370012	−	0.929027i	$-0.620646\pi$
$719$	−2.62797	+	0.892076i	−0.0980068	+	0.0332688i	0.272005	+	0.962296i	$0.412313\pi$
$720$	1.86904	−	2.79721i	0.0696549	−	0.104246i
$721$	15.8876	−	41.1764i	0.591684	−	1.53349i
$722$	35.4465	+	14.6824i	1.31918	+	0.546423i
$723$	0.288192	−	0.0379412i	0.0107180	−	0.00141105i
$724$	6.24976	−	18.4112i	0.232270	−	0.684247i
$725$	−1.89056	−	3.83368i	−0.0702138	−	0.142379i
$726$	18.9561	+	55.8430i	0.703528	+	2.07253i
$727$	−17.9107	+	17.9107i	−0.664269	+	0.664269i	−0.956383	−	0.292114i	$-0.905641\pi$
$727$	−17.9107	+	17.9107i	−0.664269	+	0.664269i	0.292114	+	0.956383i	$0.405641\pi$
$728$	−6.91566	+	12.6849i	−0.256311	+	0.470134i
$729$	0.923880	−	0.382683i	0.0342178	−	0.0141735i
$730$	4.25003	−	2.45376i	0.157301	−	0.0908177i
$731$	−3.58388	−	5.87003i	−0.132554	−	0.217111i
$732$	11.5219	−	19.9565i	0.425861	−	0.737613i
$733$	−0.525859	−	0.403506i	−0.0194230	−	0.0149038i	0.599004	−	0.800746i	$-0.295563\pi$
$733$	−0.525859	−	0.403506i	−0.0194230	−	0.0149038i	−0.618427	+	0.785842i	$0.712230\pi$
$734$	9.49139	+	14.2049i	0.350334	+	0.524311i
$735$	3.02642	+	16.6490i	0.111631	+	0.614108i
$736$	9.25362	+	1.84066i	0.341093	+	0.0678476i
$737$	5.56014	−	84.8313i	0.204810	−	3.12480i
$738$	3.26552	+	1.10849i	0.120205	+	0.0408042i
$739$	−13.4931	+	10.3536i	−0.496353	+	0.380865i	−0.826386	−	0.563105i	$-0.809607\pi$
$739$	−13.4931	+	10.3536i	−0.496353	+	0.380865i	0.330033	+	0.943969i	$0.392940\pi$
$740$	−6.86927	−	52.1773i	−0.252519	−	1.91808i
$741$	−3.47255	+	0.690734i	−0.127567	+	0.0253747i
$742$	−0.280386	+	2.62421i	−0.0102933	+	0.0963378i
$743$	1.89588	−	9.53123i	0.0695531	−	0.349667i	−0.930300	−	0.366799i	$-0.880454\pi$
$743$	1.89588	−	9.53123i	0.0695531	−	0.349667i	0.999853	+	0.0171323i	$0.00545364\pi$
$744$	0.457483	−	1.70735i	0.0167721	−	0.0625944i
$745$	1.67360	+	25.5342i	0.0613159	+	0.935500i
$746$	−0.386414	+	2.93511i	−0.0141476	+	0.107462i
$747$	−7.42040	−	12.8525i	−0.271498	−	0.470249i
$748$	6.59129	+	73.0525i	0.241001	+	2.67106i
$749$	34.8983	+	22.1033i	1.27516	+	0.807637i
$750$	8.51058	+	20.5464i	0.310762	+	0.750247i
$751$	14.0724	+	6.93972i	0.513508	+	0.253234i	0.680531	−	0.732719i	$-0.261749\pi$
$751$	14.0724	+	6.93972i	0.513508	+	0.253234i	−0.167024	+	0.985953i	$0.553416\pi$
$752$	7.78156	−	2.08506i	0.283764	−	0.0760344i
$753$	19.6575	−	22.4151i	0.716359	−	0.816850i
$754$	30.6834	+	2.01110i	1.11742	+	0.0732398i
$755$	−6.78811	−	34.1261i	−0.247045	−	1.24198i
$756$	−6.96131	−	3.22376i	−0.253180	−	0.117247i
$757$	−0.673804	+	1.62671i	−0.0244898	+	0.0591236i	−0.935651	−	0.352926i	$-0.885187\pi$
$757$	−0.673804	+	1.62671i	−0.0244898	+	0.0591236i	0.911162	+	0.412049i	$0.135187\pi$
$758$	−25.4284	+	22.3001i	−0.923599	+	0.809975i
$759$	7.35074	−	3.62498i	0.266815	−	0.131578i
$760$	4.67225	+	4.09746i	0.169480	+	0.148630i
$761$	30.6989	+	8.22575i	1.11283	+	0.298183i	0.767981	−	0.640473i	$-0.221262\pi$
$761$	30.6989	+	8.22575i	1.11283	+	0.298183i	0.344854	+	0.938656i	$0.387928\pi$
$762$	35.7305	−	23.8743i	1.29438	−	0.864876i
$763$	8.58271	+	23.3884i	0.310715	+	0.846718i
$764$		−	35.5817i		−	1.28730i
$765$	1.70412	−	9.82046i	0.0616125	−	0.355059i
$766$	−51.9874	−	30.0149i	−1.87838	−	1.08448i
$767$	−21.7746	−	2.86669i	−0.786237	−	0.103510i
$768$	2.65062	−	5.37492i	0.0956459	−	0.193951i
$769$	−28.4755	−	28.4755i	−1.02685	−	1.02685i	−0.999629	−	0.0272230i	$-0.991334\pi$
$769$	−28.4755	−	28.4755i	−1.02685	−	1.02685i	−0.0272230	−	0.999629i	$-0.508666\pi$
$770$	−59.8983	+	62.9023i	−2.15859	+	2.26684i
$771$	19.3200	+	12.9092i	0.695793	+	0.464914i
$772$	−29.8217	−	34.0052i	−1.07331	−	1.22387i
$773$	−24.3365	−	31.7160i	−0.875324	−	1.14074i	−0.989101	−	0.147238i	$-0.952962\pi$
$773$	−24.3365	−	31.7160i	−0.875324	−	1.14074i	0.113777	−	0.993506i	$-0.463705\pi$
$774$	2.24770	+	2.92926i	0.0807920	+	0.105290i
$775$	0.493907	+	0.563193i	0.0177416	+	0.0202305i
$776$	−14.5199	−	9.70189i	−0.521234	−	0.348278i
$777$	19.0562	−	5.60903i	0.683639	−	0.201223i
$778$	−54.5886	−	54.5886i	−1.95710	−	1.95710i
$779$	0.889612	−	1.80396i	0.0318737	−	0.0646334i
$780$	19.0584	+	2.50908i	0.682400	+	0.0898396i
$781$	−41.6291	−	24.0346i	−1.48961	−	0.860025i
$782$	11.8955	−	2.67110i	0.425383	−	0.0955183i
$783$			5.06548i			0.181025i
$784$	−2.97837	−	9.27507i	−0.106370	−	0.331253i
$785$	−5.27888	+	3.52723i	−0.188411	+	0.125892i
$786$	18.2097	+	4.87928i	0.649519	+	0.174038i
$787$	18.2660	+	16.0188i	0.651111	+	0.571009i	0.919882	−	0.392195i	$-0.128284\pi$
$787$	18.2660	+	16.0188i	0.651111	+	0.571009i	−0.268771	+	0.963204i	$0.586618\pi$
$788$	13.8883	−	6.84897i	0.494751	−	0.243984i
$789$	17.3989	−	15.2584i	0.619416	−	0.543213i
$790$	17.8416	−	43.0735i	0.634776	−	1.53249i
$791$	−4.50216	−	49.9406i	−0.160079	−	1.77568i
$792$	−2.38334	−	11.9818i	−0.0846882	−	0.425756i
$793$	−21.7483	−	1.42546i	−0.772303	−	0.0506194i
$794$	−5.61524	+	6.40295i	−0.199277	+	0.227232i
$795$	1.05227	−	0.281956i	0.0373203	−	0.00999995i
$796$	−47.5309	−	23.4396i	−1.68469	−	0.830796i
$797$	−18.5475	−	44.7776i	−0.656985	−	1.58610i	−0.802436	−	0.596738i	$-0.796463\pi$
$797$	−18.5475	−	44.7776i	−0.656985	−	1.58610i	0.145451	−	0.989365i	$-0.453537\pi$
$798$	−4.04556	+	6.38742i	−0.143211	+	0.226112i
$799$	18.5737	−	14.9901i	0.657090	−	0.530312i
$800$	2.97996	+	5.16145i	0.105358	+	0.182485i
$801$	−1.41823	+	10.7725i	−0.0501107	+	0.380629i
$802$	3.89295	+	59.3950i	0.137465	+	2.09731i
$803$	−1.45636	+	5.43520i	−0.0513937	+	0.191804i
$804$	−7.83822	+	39.4054i	−0.276433	+	1.38972i
$805$	6.90357	+	5.03393i	0.243319	+	0.177423i
$806$	−5.28511	+	1.05127i	−0.186160	+	0.0370296i
$807$	−2.02045	−	15.3468i	−0.0711231	−	0.540234i
$808$	28.6921	−	22.0162i	1.00938	−	0.774527i
$809$	−26.0531	−	8.84383i	−0.915978	−	0.310933i	−0.176647	−	0.984274i	$-0.556525\pi$
$809$	−26.0531	−	8.84383i	−0.915978	−	0.310933i	−0.739331	+	0.673342i	$0.764858\pi$
$810$	−0.349967	+	5.33946i	−0.0122966	+	0.187610i
$811$	−9.94901	−	1.97898i	−0.349357	−	0.0694914i	0.0172928	−	0.999850i	$-0.494495\pi$
$811$	−9.94901	−	1.97898i	−0.349357	−	0.0694914i	−0.366650	+	0.930359i	$0.619495\pi$
$812$	28.5811	−	26.3290i	1.00300	−	0.923966i
$813$	−11.0116	−	16.4801i	−0.386195	−	0.577982i
$814$	80.8936	+	62.0718i	2.83532	+	2.17562i
$815$	−0.931817	+	1.61395i	−0.0326401	+	0.0565343i
$816$	−0.234710	+	5.73311i	−0.00821650	+	0.200699i
$817$	1.86502	−	1.07677i	0.0652487	−	0.0376714i
$818$	−28.1721	+	11.6693i	−0.985014	+	0.408006i
$819$	0.177440	+	7.25361i	0.00620027	+	0.253462i
$820$	−7.72188	+	7.72188i	−0.269660	+	0.269660i
$821$	−1.08203	−	3.18757i	−0.0377633	−	0.111247i	0.926413	−	0.376508i	$-0.122875\pi$
$821$	−1.08203	−	3.18757i	−0.0377633	−	0.111247i	−0.964177	+	0.265261i	$0.914542\pi$
$822$	−0.714785	−	1.44944i	−0.0249310	−	0.0505551i
$823$	0.388094	−	1.14329i	0.0135281	−	0.0398525i	−0.939956	−	0.341295i	$-0.889135\pi$
$823$	0.388094	−	1.14329i	0.0135281	−	0.0398525i	0.953485	+	0.301442i	$0.0974680\pi$
$824$	−32.9318	+	4.33556i	−1.14723	+	0.151036i
$825$	4.78320	+	1.98127i	0.166530	+	0.0689788i
$826$	−36.4991	+	29.4525i	−1.26997	+	1.02478i
$827$	−1.21299	+	1.81537i	−0.0421799	+	0.0631267i	−0.851960	−	0.523606i	$-0.824586\pi$
$827$	−1.21299	+	1.81537i	−0.0421799	+	0.0631267i	0.809780	+	0.586733i	$0.199586\pi$
$828$	−3.66786	+	1.24507i	−0.127467	+	0.0432692i
$829$	−2.87701	−	10.7372i	−0.0999227	−	0.372917i	0.897797	−	0.440409i	$-0.145167\pi$
$829$	−2.87701	−	10.7372i	−0.0999227	−	0.372917i	−0.997720	+	0.0674928i	$0.978500\pi$
$830$	79.2419	−	5.19379i	2.75053	−	0.180279i
$831$	19.1031	−	24.8956i	0.662678	−	0.863619i
$832$	−35.2406			−1.22175
$833$	−19.2028	−	21.5465i	−0.665338	−	0.746542i
$834$	−21.2587			−0.736127
$835$	−13.5339	+	17.6377i	−0.468360	+	0.610378i
$836$	−22.9182	+	1.50214i	−0.792642	+	0.0519525i
$837$	−0.229754	−	0.857453i	−0.00794145	−	0.0296379i
$838$	59.9794	−	20.3603i	2.07195	−	0.703333i
$839$	5.51326	−	8.25118i	0.190339	−	0.284862i	−0.724010	−	0.689789i	$-0.757703\pi$
$839$	5.51326	−	8.25118i	0.190339	−	0.284862i	0.914349	+	0.404927i	$0.132703\pi$
$840$	9.91100	−	7.99755i	0.341962	−	0.275942i
$841$	3.08664	+	1.27853i	0.106436	+	0.0440872i
$842$	10.3307	−	1.36007i	0.356020	−	0.0468709i
$843$	−0.168629	+	0.496765i	−0.00580789	+	0.0171095i
$844$	−6.11263	−	12.3952i	−0.210406	−	0.426660i
$845$	4.25753	+	12.5423i	0.146463	+	0.431467i
$846$	−9.06060	+	9.06060i	−0.311510	+	0.311510i
$847$	−1.72381	−	70.4678i	−0.0592308	−	2.42130i
$848$	−0.579403	+	0.239997i	−0.0198968	+	0.00824152i
$849$	−13.6460	+	7.87850i	−0.468328	+	0.270389i
$850$	6.22308	+	4.53701i	0.213450	+	0.155618i
$851$	5.01490	−	8.68606i	0.171909	−	0.297754i
$852$	18.0230	+	13.8296i	0.617459	+	0.473793i
$853$	10.2193	+	15.2943i	0.349902	+	0.523665i	0.964118	−	0.265472i	$-0.0855279\pi$
$853$	10.2193	+	15.2943i	0.349902	+	0.523665i	−0.614217	+	0.789137i	$0.710528\pi$
$854$	−34.2314	+	31.5341i	−1.17138	+	1.07907i
$855$	3.06100	+	0.608871i	0.104684	+	0.0208229i
$856$	2.03333	−	31.0226i	0.0694977	−	1.06033i
$857$	−51.2237	−	17.3881i	−1.74977	−	0.593966i	−0.751902	−	0.659275i	$-0.770863\pi$
$857$	−51.2237	−	17.3881i	−1.74977	−	0.593966i	−0.997865	+	0.0653086i	$0.979197\pi$
$858$	−29.5474	+	22.6725i	−1.00873	+	0.774026i
$859$	−1.05828	−	8.03842i	−0.0361080	−	0.274268i	−0.999969	−	0.00786218i	$-0.997497\pi$
$859$	−1.05828	−	8.03842i	−0.0361080	−	0.274268i	0.963861	−	0.266405i	$-0.0858360\pi$
$860$	−11.4675	+	2.28103i	−0.391039	+	0.0777825i
$861$	−3.33056	−	2.42857i	−0.113505	−	0.0827655i
$862$	−14.6819	+	73.8107i	−0.500066	+	2.51400i
$863$	4.73532	−	17.6724i	0.161192	−	0.601577i	−0.837303	−	0.546739i	$-0.815869\pi$
$863$	4.73532	−	17.6724i	0.161192	−	0.601577i	0.998495	−	0.0548381i	$-0.0174643\pi$
$864$	−0.461928	−	7.04766i	−0.0157151	−	0.239766i
$865$	3.01082	−	22.8695i	0.102371	−	0.777585i
$866$	−33.6766	−	58.3296i	−1.14438	−	1.98212i
$867$	6.24744	+	15.8104i	0.212174	+	0.536950i
$868$	−3.64384	+	5.75316i	−0.123680	+	0.195275i
$869$	20.4571	+	49.3878i	0.693960	+	1.67537i
$870$	−24.3097	−	11.9882i	−0.824176	−	0.406438i
$871$	36.7052	−	9.83513i	1.24371	−	0.333251i
$872$	12.3626	−	14.0969i	0.418651	−	0.477380i
$873$	−8.75134	−	0.573593i	−0.296188	−	0.0194132i
$874$	0.744760	+	3.74416i	0.0251919	+	0.126648i
$875$	−2.38671	−	26.4748i	−0.0806855	−	0.895010i
$876$	1.01767	−	2.45687i	0.0343838	−	0.0830099i
$877$	−6.11349	+	5.36138i	−0.206438	+	0.181041i	−0.756321	−	0.654200i	$-0.773005\pi$
$877$	−6.11349	+	5.36138i	−0.206438	+	0.181041i	0.549884	+	0.835241i	$0.314672\pi$
$878$	17.2517	−	8.50761i	0.582218	−	0.287118i
$879$	−8.07538	−	7.08192i	−0.272376	−	0.238867i
$880$	−19.9371	−	5.34212i	−0.672078	−	0.180083i
$881$	−4.04042	+	2.69972i	−0.136125	+	0.0909560i	−0.621768	−	0.783201i	$-0.713585\pi$
$881$	−4.04042	+	2.69972i	−0.136125	+	0.0909560i	0.485643	+	0.874157i	$0.338585\pi$
$882$	11.4789	+	10.4074i	0.386513	+	0.350436i
$883$			44.7736i			1.50675i	0.657590	+	0.753376i	$0.271576\pi$
$883$			44.7736i			1.50675i	−0.657590	+	0.753376i	$0.728424\pi$
$884$	−29.9737	+	13.2861i	−1.00812	+	0.446858i
$885$	16.7659	+	9.67981i	0.563580	+	0.325383i
$886$	−53.5300	−	7.04736i	−1.79837	−	0.236761i
$887$	2.21036	−	4.48216i	0.0742166	−	0.150496i	−0.856602	−	0.515977i	$-0.827429\pi$
$887$	2.21036	−	4.48216i	0.0742166	−	0.150496i	0.930819	+	0.365481i	$0.119096\pi$
$888$	−10.5713	−	10.5713i	−0.354749	−	0.354749i
$889$	−49.2743	+	14.5034i	−1.65261	+	0.486429i
$890$	−48.3419	−	32.3010i	−1.62042	−	1.08273i
$891$	−4.04531	−	4.61279i	−0.135523	−	0.154534i
$892$	−24.4229	−	31.8286i	−0.817740	−	1.06570i
$893$	4.54967	+	5.92924i	0.152249	+	0.198415i
$894$	15.4488	+	17.6160i	0.516686	+	0.589167i
$895$	47.5045	+	31.7415i	1.58790	+	1.06100i
$896$	−26.1238	+	27.4339i	−0.872734	+	0.916503i
$897$	2.59049	+	2.59049i	0.0864940	+	0.0864940i
$898$	−29.3774	+	59.5715i	−0.980337	+	1.98793i
$899$	4.45816	+	0.586927i	0.148688	+	0.0195751i
$900$	−2.11899	−	1.22340i	−0.0706330	−	0.0407800i
$901$	−1.28122	+	1.34568i	−0.0426837	+	0.0448312i
$902$		−	21.1579i		−	0.704480i
$903$	−1.52038	−	4.14313i	−0.0505950	−	0.137875i
$904$	−31.3777	+	20.9659i	−1.04361	+	0.697315i
$905$	15.6576	+	4.19543i	0.520475	+	0.139461i
$906$	−23.9534	−	21.0066i	−0.795800	−	0.697897i
$907$	28.9530	−	14.2780i	0.961369	−	0.474095i	0.107284	−	0.994228i	$-0.465784\pi$
$907$	28.9530	−	14.2780i	0.961369	−	0.474095i	0.854085	+	0.520134i	$0.174118\pi$
$908$	31.4658	−	27.5947i	1.04423	−	0.915764i
$909$	6.95061	−	16.7803i	0.230537	−	0.556566i
$910$	−35.2307	−	16.3152i	−1.16789	−	0.540844i
$911$	−5.72126	−	28.7627i	−0.189554	−	0.952952i	−0.952046	−	0.305954i	$-0.901024\pi$
$911$	−5.72126	−	28.7627i	−0.189554	−	0.952952i	0.762492	−	0.646997i	$-0.223976\pi$
$912$	−1.79283	−	0.117508i	−0.0593665	−	0.00389108i
$913$	−60.0356	+	68.4575i	−1.98689	+	2.26561i
$914$	−4.33047	+	1.16035i	−0.143239	+	0.0383809i
$915$	17.2306	+	8.49720i	0.569626	+	0.280909i
$916$	−10.5561	−	25.4847i	−0.348784	−	0.842039i
$917$	−19.0365	−	12.0570i	−0.628641	−	0.398159i
$918$	−4.23612	−	8.08381i	−0.139813	−	0.266805i
$919$	4.80832	+	8.32825i	0.158612	+	0.274724i	0.934368	−	0.356309i	$-0.115965\pi$
$919$	4.80832	+	8.32825i	0.158612	+	0.274724i	−0.775757	+	0.631032i	$0.782632\pi$
$920$	0.839307	−	6.37517i	0.0276711	−	0.210183i
$921$	−0.506294	−	7.72455i	−0.0166829	−	0.254532i
$922$	−6.71971	+	25.0783i	−0.221302	+	0.825909i
$923$	4.19179	−	21.0735i	0.137974	−	0.693644i
$924$	−5.00050	+	46.8010i	−0.164504	+	1.53964i
$925$	6.21397	−	1.23604i	0.204314	−	0.0406406i
$926$	3.56712	+	27.0950i	0.117223	+	0.890396i
$927$	−13.2343	+	10.1551i	−0.434673	+	0.333536i
$928$	33.8777	+	11.4999i	1.11209	+	0.377504i
$929$	1.73830	−	26.5213i	0.0570318	−	0.870137i	−0.869503	−	0.493928i	$-0.835561\pi$
$929$	1.73830	−	26.5213i	0.0570318	−	0.870137i	0.926535	−	0.376209i	$-0.122773\pi$
$930$	4.65874	+	0.926682i	0.152766	+	0.0303871i
$931$	6.89218	−	5.84554i	0.225882	−	0.191580i
$932$	−16.9369	−	25.3478i	−0.554786	−	0.830296i
$933$	4.49520	+	3.44928i	0.147166	+	0.112925i
$934$	−8.54625	+	14.8025i	−0.279642	+	0.484354i
$935$	−60.4150	+	9.46684i	−1.97578	+	0.309599i
$936$	4.72909	−	2.73034i	0.154575	−	0.0892440i
$937$	−22.8080	+	9.44737i	−0.745104	+	0.308632i	−0.722742	−	0.691118i	$-0.757119\pi$
$937$	−22.8080	+	9.44737i	−0.745104	+	0.308632i	−0.0223617	+	0.999750i	$0.507119\pi$
$938$	38.8431	−	71.2473i	1.26827	−	2.32631i
$939$	2.24946	−	2.24946i	0.0734083	−	0.0734083i
$940$	−13.0429	−	38.4232i	−0.425413	−	1.25323i
$941$	20.4337	+	41.4355i	0.666120	+	1.35076i	0.923182	+	0.384363i	$0.125579\pi$
$941$	20.4337	+	41.4355i	0.666120	+	1.35076i	−0.257062	+	0.966395i	$0.582754\pi$
$942$	−1.86863	+	5.50481i	−0.0608833	+	0.179356i
$943$	−2.06341	+	0.271653i	−0.0671939	+	0.00884624i
$944$	−10.2966	−	4.26498i	−0.335125	−	0.138813i
$945$	2.30235	−	5.96709i	0.0748955	−	0.194109i
$946$	12.5854	−	18.8355i	0.409188	−	0.612393i
$947$	28.7880	−	9.77221i	0.935484	−	0.317554i	0.188255	−	0.982120i	$-0.439717\pi$
$947$	28.7880	−	9.77221i	0.935484	−	0.317554i	0.747230	+	0.664566i	$0.231384\pi$
$948$	−6.53876	−	24.4030i	−0.212369	−	0.792572i
$949$	−2.50979	+	0.164500i	−0.0814713	+	0.00533991i
$950$	−1.46802	+	1.91316i	−0.0476287	+	0.0620710i
$951$	−3.06344			−0.0993388
$952$	−7.31965	+	20.4508i	−0.237231	+	0.662815i
$953$	32.4072			1.04977			0.524886	−	0.851172i	$-0.324108\pi$
$953$	32.4072			1.04977			0.524886	+	0.851172i	$0.324108\pi$
$954$	0.607242	−	0.791373i	0.0196602	−	0.0256216i
$955$	29.6014	−	1.94018i	0.957879	−	0.0627827i
$956$	1.58103	+	5.90048i	0.0511342	+	0.190835i
$957$	29.4291	−	9.98982i	0.951306	−	0.322925i
$958$	40.6472	−	60.8329i	1.31325	−	1.96542i
$959$	0.298898	+	1.90844i	0.00965192	+	0.0616266i
$960$	28.6994	+	11.8877i	0.926269	+	0.383673i
$961$	29.9535	−	3.94346i	0.966243	−	0.127208i
$962$	−14.6502	+	43.1581i	−0.472341	+	1.39147i
$963$	−6.90563	−	14.0032i	−0.222531	−	0.451248i
$964$	0.270923	+	0.798112i	0.00872583	+	0.0257055i
$965$	26.6637	−	26.6637i	0.858336	−	0.858336i
$966$	7.82096	−	0.191319i	0.251635	−	0.00615559i
$967$	−42.2140	+	17.4856i	−1.35751	+	0.562299i	−0.938373	−	0.345625i	$-0.887667\pi$
$967$	−42.2140	+	17.4856i	−1.35751	+	0.562299i	−0.419136	+	0.907923i	$0.637667\pi$
$968$	−45.9425	+	26.5249i	−1.47665	+	0.852542i
$969$	−4.99711	+	1.83419i	−0.160530	+	0.0589226i
$970$	23.4641	−	40.6410i	0.753387	−	1.30490i
$971$	−20.3350	−	15.6036i	−0.652582	−	0.500743i	0.228601	−	0.973520i	$-0.426585\pi$
$971$	−20.3350	−	15.6036i	−0.652582	−	0.500743i	−0.881182	+	0.472777i	$0.843252\pi$
$972$	1.61091	+	2.41090i	0.0516700	+	0.0773297i
$973$	24.2541	+	7.57693i	0.777551	+	0.242905i
$974$	58.0915	+	11.5551i	1.86137	+	0.370250i
$975$	−0.151356	+	2.30924i	−0.00484726	+	0.0739549i
$976$	−10.4729	−	3.55508i	−0.335230	−	0.113795i
$977$	−4.22545	+	3.24230i	−0.135184	+	0.103730i	−0.674140	−	0.738604i	$-0.735486\pi$
$977$	−4.22545	+	3.24230i	−0.135184	+	0.103730i	0.538956	+	0.842334i	$0.318819\pi$
$978$	0.222734	+	1.69184i	0.00712226	+	0.0540990i
$979$	65.3824	−	13.0054i	2.08963	−	0.415654i
$980$	−45.6353	+	18.0247i	−1.45777	+	0.575777i
$981$	1.83705	−	9.23548i	0.0586525	−	0.294866i
$982$	−3.34440	+	12.4815i	−0.106724	+	0.398300i
$983$	1.29451	+	19.7504i	0.0412885	+	0.629941i	0.967490	+	0.252911i	$0.0813880\pi$
$983$	1.29451	+	19.7504i	0.0412885	+	0.629941i	−0.926201	+	0.377030i	$0.876945\pi$
$984$	−0.404916	+	3.07564i	−0.0129082	+	0.0980479i
$985$	6.45514	+	11.1806i	0.205678	+	0.356245i
$986$	46.0429	−	4.15431i	1.46631	−	0.132300i
$987$	13.5666	−	7.10794i	0.431831	−	0.226248i
$988$	−3.92869	−	9.48469i	−0.124988	−	0.301748i
$989$	−1.99851	−	0.985554i	−0.0635488	−	0.0313388i
$990$	31.7110	−	8.49694i	1.00784	−	0.270051i
$991$	15.6220	−	17.8134i	0.496248	−	0.565862i	−0.448449	−	0.893809i	$-0.648023\pi$
$991$	15.6220	−	17.8134i	0.496248	−	0.565862i	0.944696	+	0.327947i	$0.106357\pi$
$992$	−6.25621	−	0.410054i	−0.198635	−	0.0130192i
$993$	−2.72909	−	13.7201i	−0.0866052	−	0.435394i
$994$	−26.4168	−	37.5159i	−0.837891	−	1.18993i
$995$	16.9084	−	40.8204i	0.536031	−	1.29409i
$996$	32.3531	−	28.3729i	1.02515	−	0.899030i
$997$	−17.7395	+	8.74816i	−0.561816	+	0.277057i	−0.700943	−	0.713218i	$-0.747237\pi$
$997$	−17.7395	+	8.74816i	−0.561816	+	0.277057i	0.139127	+	0.990275i	$0.455570\pi$
$998$	49.7630	+	43.6409i	1.57522	+	1.38143i
$999$	−7.25227	−	1.94324i	−0.229452	−	0.0614814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bl.a.199.3	yes	384
7.5	odd	6	inner	357.2.bl.a.250.22	yes	384
17.10	odd	16	inner	357.2.bl.a.10.22	✓	384
119.61	even	48	inner	357.2.bl.a.61.3	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bl.a.10.22	✓	384	17.10	odd	16	inner
357.2.bl.a.61.3	yes	384	119.61	even	48	inner
357.2.bl.a.199.3	yes	384	1.1	even	1	trivial
357.2.bl.a.250.22	yes	384	7.5	odd	6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.bl (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34749 + 1.75608i) q^{2} +(-0.997859 + 0.0654031i) q^{3} +(-0.750463 - 2.80077i) q^{4} +(2.28911 - 0.777050i) q^{5} +(1.22975 - 1.84045i) q^{6} +(-2.05900 + 1.66148i) q^{7} +(1.83962 + 0.761994i) q^{8} +(0.991445 - 0.130526i) q^{9} +(-1.72000 + 5.06695i) q^{10} +(-2.71359 - 5.50261i) q^{11} +(0.932035 + 2.74569i) q^{12} +(1.93919 - 1.93919i) q^{13} +(-0.143218 - 5.85461i) q^{14} +(-2.23339 + 0.925101i) q^{15} +(1.20520 - 0.695825i) q^{16} +(2.42899 - 3.33167i) q^{17} +(-1.10675 + 1.91694i) q^{18} +(1.02425 + 0.785935i) q^{19} +(-3.89423 - 5.82813i) q^{20} +(1.94593 - 1.79259i) q^{21} +(13.3196 + 2.64943i) q^{22} +(0.0873696 - 1.33300i) q^{23} +(-1.88551 - 0.640046i) q^{24} +(0.669471 - 0.513703i) q^{25} +(0.792340 + 6.01842i) q^{26} +(-0.980785 + 0.195090i) q^{27} +(6.19862 + 4.51990i) q^{28} +(0.988225 - 4.96814i) q^{29} +(1.38492 - 5.16859i) q^{30} +(0.0580584 + 0.885800i) q^{31} +(-0.921878 + 7.00236i) q^{32} +(3.06767 + 5.31335i) q^{33} +(2.57765 + 8.75490i) q^{34} +(-3.42223 + 5.40327i) q^{35} +(-1.10962 - 2.67885i) q^{36} +(6.73382 + 3.32075i) q^{37} +(-2.76034 + 0.739630i) q^{38} +(-1.80821 + 2.06187i) q^{39} +(4.80320 + 0.314818i) q^{40} +(-0.303942 - 1.52802i) q^{41} +(0.525821 + 5.83271i) q^{42} +(0.638340 - 1.54109i) q^{43} +(-13.3751 + 11.7296i) q^{44} +(2.16811 - 1.06919i) q^{45} +(2.22314 + 1.94964i) q^{46} +(5.59161 + 1.49827i) q^{47} +(-1.15711 + 0.773159i) q^{48} +(1.47896 - 6.84198i) q^{49} +1.86786i q^{50} +(-2.20589 + 3.48340i) q^{51} +(-6.88650 - 3.97592i) q^{52} +(-0.446791 - 0.0588211i) q^{53} +(0.979004 - 1.98522i) q^{54} +(-10.4875 - 10.4875i) q^{55} +(-5.05381 + 1.48754i) q^{56} +(-1.07346 - 0.717263i) q^{57} +(7.39286 + 8.42994i) q^{58} +(-4.87522 - 6.35351i) q^{59} +(4.26707 + 5.56095i) q^{60} +(-5.24003 - 5.97511i) q^{61} +(-1.63377 - 1.09165i) q^{62} +(-1.82452 + 1.91602i) q^{63} +(-9.08642 - 9.08642i) q^{64} +(2.93218 - 5.94587i) q^{65} +(-13.4644 - 1.77262i) q^{66} +(11.9999 + 6.92817i) q^{67} +(-11.1541 - 4.30274i) q^{68} +1.33586i q^{69} +(-4.87716 - 13.2906i) q^{70} +(6.51440 - 4.35279i) q^{71} +(1.92334 + 0.515357i) q^{72} +(-0.689539 - 0.604709i) q^{73} +(-14.9053 + 7.35047i) q^{74} +(-0.634440 + 0.556389i) q^{75} +(1.43256 - 3.45850i) q^{76} +(14.7298 + 6.82130i) q^{77} +(-1.18427 - 5.95371i) q^{78} +(-8.69432 - 0.569856i) q^{79} +(2.21816 - 2.52932i) q^{80} +(0.965926 - 0.258819i) q^{81} +(3.09289 + 1.52525i) q^{82} +(-5.67933 - 13.7111i) q^{83} +(-6.48097 - 4.10481i) q^{84} +(2.97136 - 9.51401i) q^{85} +(1.84613 + 3.19759i) q^{86} +(-0.661177 + 5.02214i) q^{87} +(-0.799003 - 12.1904i) q^{88} +(-2.81219 + 10.4953i) q^{89} +(-1.04391 + 5.24810i) q^{90} +(-0.770864 + 7.21472i) q^{91} +(-3.79900 + 0.755667i) q^{92} +(-0.115868 - 0.880106i) q^{93} +(-10.1657 + 7.80044i) q^{94} +(2.95534 + 1.00320i) q^{95} +(0.461928 - 7.04766i) q^{96} +(-8.60161 - 1.71097i) q^{97} +(10.0222 + 11.8167i) q^{98} +(-3.40861 - 5.10134i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 16 q^{11} + 32 q^{14} - 64 q^{22} - 16 q^{25} - 48 q^{28} - 64 q^{30} - 64 q^{35} - 32 q^{37} - 48 q^{42} - 64 q^{44} + 32 q^{46} - 64 q^{49} + 80 q^{56} - 32 q^{58} - 288 q^{61} - 528 q^{68} + 176 q^{70}+ \cdots + 32 q^{99}+O(q^{100}) \) 384 * q - 16 * q^11 + 32 * q^14 - 64 * q^22 - 16 * q^25 - 48 * q^28 - 64 * q^30 - 64 * q^35 - 32 * q^37 - 48 * q^42 - 64 * q^44 + 32 * q^46 - 64 * q^49 + 80 * q^56 - 32 * q^58 - 288 * q^61 - 528 * q^68 + 176 * q^70 + 64 * q^71 - 48 * q^73 - 128 * q^74 + 96 * q^77 + 128 * q^78 - 480 * q^80 - 240 * q^82 + 32 * q^85 - 144 * q^87 - 96 * q^88 - 64 * q^91 + 320 * q^92 - 192 * q^94 - 64 * q^95 + 32 * q^99

Introduction

L-functions

Modular forms

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Database

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