LMFDB - Embedded newform 168.2.ba.c.5.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(5,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))

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

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

chi := DirichletCharacter("168.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$168 = 2^{3} \cdot 3 \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	168.ba (of order $6$ , degree $2$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.5
Character	$\chi$	$=$	168.5
Dual form			168.2.ba.c.101.5

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26535 + 0.631567i) q^{2} +(0.528554 - 1.64943i) q^{3} +(1.20225 - 1.59831i) q^{4} +(2.66818 + 1.54047i) q^{5} +(0.372919 + 2.42094i) q^{6} +(-1.46307 - 2.20441i) q^{7} +(-0.511826 + 2.78173i) q^{8} +(-2.44126 - 1.74363i) q^{9} +(-4.34911 - 0.264112i) q^{10} +(-0.621780 - 1.07696i) q^{11} +(-2.00086 - 2.82782i) q^{12} +5.98957 q^{13} +(3.24353 + 1.86534i) q^{14} +(3.95119 - 3.58676i) q^{15} +(-1.10921 - 3.84313i) q^{16} +(-0.595854 - 1.03205i) q^{17} +(4.19028 + 0.664491i) q^{18} +(-0.614126 + 1.06370i) q^{19} +(5.66997 - 2.41256i) q^{20} +(-4.40934 + 1.24808i) q^{21} +(1.46694 + 0.970035i) q^{22} +(2.56956 + 1.48354i) q^{23} +(4.31775 + 2.31452i) q^{24} +(2.24612 + 3.89040i) q^{25} +(-7.57893 + 3.78282i) q^{26} +(-4.16634 + 3.10509i) q^{27} +(-5.28231 - 0.311808i) q^{28} -3.19900 q^{29} +(-2.73438 + 7.03397i) q^{30} +(1.33987 - 0.773574i) q^{31} +(3.83074 + 4.16238i) q^{32} +(-2.10501 + 0.456356i) q^{33} +(1.40578 + 0.929587i) q^{34} +(-0.507883 - 8.13559i) q^{35} +(-5.72186 + 1.80563i) q^{36} +(0.334978 + 0.193399i) q^{37} +(0.105291 - 1.73382i) q^{38} +(3.16581 - 9.87940i) q^{39} +(-5.65083 + 6.63371i) q^{40} -9.44060 q^{41} +(4.79114 - 4.36406i) q^{42} +8.29057i q^{43} +(-2.46884 - 0.300965i) q^{44} +(-3.82770 - 8.41302i) q^{45} +(-4.18836 - 0.254350i) q^{46} +(-3.34244 + 5.78928i) q^{47} +(-6.92527 - 0.201736i) q^{48} +(-2.71887 + 6.45041i) q^{49} +(-5.29919 - 3.50416i) q^{50} +(-2.01724 + 0.437327i) q^{51} +(7.20094 - 9.57321i) q^{52} +(5.25317 + 9.09875i) q^{53} +(3.31083 - 6.56037i) q^{54} -3.83135i q^{55} +(6.88092 - 2.94158i) q^{56} +(1.42990 + 1.57518i) q^{57} +(4.04788 - 2.02039i) q^{58} +(-3.22898 + 1.86425i) q^{59} +(-0.982467 - 10.6274i) q^{60} +(-3.16493 + 5.48181i) q^{61} +(-1.20685 + 1.82506i) q^{62} +(-0.271956 + 7.93259i) q^{63} +(-7.47607 - 2.84752i) q^{64} +(15.9813 + 9.22678i) q^{65} +(2.37537 - 1.90691i) q^{66} +(10.7324 - 6.19634i) q^{67} +(-2.36590 - 0.288416i) q^{68} +(3.80515 - 3.45419i) q^{69} +(5.78082 + 9.97364i) q^{70} -6.21100i q^{71} +(6.09981 - 5.89850i) q^{72} +(-8.92963 + 5.15552i) q^{73} +(-0.546010 - 0.0331580i) q^{74} +(7.60415 - 1.64854i) q^{75} +(0.961791 + 2.26039i) q^{76} +(-1.46435 + 2.94632i) q^{77} +(2.23362 + 14.5004i) q^{78} +(-6.41425 + 11.1098i) q^{79} +(2.96067 - 11.9629i) q^{80} +(2.91950 + 8.51331i) q^{81} +(11.9457 - 5.96237i) q^{82} -5.22882i q^{83} +(-3.30629 + 8.54801i) q^{84} -3.67159i q^{85} +(-5.23605 - 10.4905i) q^{86} +(-1.69085 + 5.27654i) q^{87} +(3.31404 - 1.17841i) q^{88} +(6.94090 - 12.0220i) q^{89} +(10.1568 + 8.22800i) q^{90} +(-8.76314 - 13.2035i) q^{91} +(5.46040 - 2.32339i) q^{92} +(-0.567765 - 2.61890i) q^{93} +(0.573057 - 9.43648i) q^{94} +(-3.27720 + 1.89209i) q^{95} +(8.89033 - 4.11850i) q^{96} -17.1489i q^{97} +(-0.633524 - 9.87920i) q^{98} +(-0.359884 + 3.71328i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42}+ \cdots + 90 q^{96}+O(q^{100})$ 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$ .

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	−1.26535	+	0.631567i	−0.894741	+	0.446585i
$2$	−1.26535	+	0.631567i	−0.894741	+	0.446585i
$3$	0.528554	−	1.64943i	0.305161	−	0.952301i
$3$	0.528554	−	1.64943i	0.305161	−	0.952301i
$4$	1.20225	−	1.59831i	0.601123	−	0.799157i
$5$	2.66818	+	1.54047i	1.19325	+	0.688921i	0.959041	−	0.283266i	$-0.0914180\pi$
$5$	2.66818	+	1.54047i	1.19325	+	0.688921i	0.234205	+	0.972187i	$0.424751\pi$
$6$	0.372919	+	2.42094i	0.152244	+	0.988343i
$7$	−1.46307	−	2.20441i	−0.552987	−	0.833190i
$7$	−1.46307	−	2.20441i	−0.552987	−	0.833190i
$8$	−0.511826	+	2.78173i	−0.180958	+	0.983491i
$9$	−2.44126	−	1.74363i	−0.813753	−	0.581210i
$10$	−4.34911	−	0.264112i	−1.37531	−	0.0835195i
$11$	−0.621780	−	1.07696i	−0.187474	−	0.324714i	0.756933	−	0.653492i	$-0.226697\pi$
$11$	−0.621780	−	1.07696i	−0.187474	−	0.324714i	−0.944407	+	0.328778i	$0.893363\pi$
$12$	−2.00086	−	2.82782i	−0.577598	−	0.816321i
$13$	5.98957			1.66121			0.830604	−	0.556864i	$-0.187995\pi$
$13$	5.98957			1.66121			0.830604	+	0.556864i	$0.187995\pi$
$14$	3.24353	+	1.86534i	0.866871	+	0.498533i
$15$	3.95119	−	3.58676i	1.02019	−	0.926098i
$16$	−1.10921	−	3.84313i	−0.277302	−	0.960783i
$17$	−0.595854	−	1.03205i	−0.144516	−	0.250309i	0.784676	−	0.619906i	$-0.212829\pi$
$17$	−0.595854	−	1.03205i	−0.144516	−	0.250309i	−0.929192	+	0.369597i	$0.879496\pi$
$18$	4.19028	+	0.664491i	0.987659	+	0.156622i
$19$	−0.614126	+	1.06370i	−0.140890	+	0.244029i	−0.927832	−	0.372998i	$-0.878330\pi$
$19$	−0.614126	+	1.06370i	−0.140890	+	0.244029i	0.786942	+	0.617027i	$0.211663\pi$
$20$	5.66997	−	2.41256i	1.26784	−	0.539464i
$21$	−4.40934	+	1.24808i	−0.962197	+	0.272353i
$22$	1.46694	+	0.970035i	0.312753	+	0.206812i
$23$	2.56956	+	1.48354i	0.535791	+	0.309339i	0.743371	−	0.668879i	$-0.233226\pi$
$23$	2.56956	+	1.48354i	0.535791	+	0.309339i	−0.207581	+	0.978218i	$0.566559\pi$
$24$	4.31775	+	2.31452i	0.881358	+	0.472449i
$25$	2.24612	+	3.89040i	0.449225	+	0.778080i
$26$	−7.57893	+	3.78282i	−1.48635	+	0.741871i
$27$	−4.16634	+	3.10509i	−0.801813	+	0.597575i
$28$	−5.28231	−	0.311808i	−0.998262	−	0.0589262i
$29$	−3.19900			−0.594040			−0.297020	−	0.954871i	$-0.595993\pi$
$29$	−3.19900			−0.594040			−0.297020	+	0.954871i	$0.595993\pi$
$30$	−2.73438	+	7.03397i	−0.499226	+	1.28422i
$31$	1.33987	−	0.773574i	0.240648	−	0.138938i	−0.374827	−	0.927095i	$-0.622298\pi$
$31$	1.33987	−	0.773574i	0.240648	−	0.138938i	0.615474	+	0.788157i	$0.288964\pi$
$32$	3.83074	+	4.16238i	0.677185	+	0.735812i
$33$	−2.10501	+	0.456356i	−0.366435	+	0.0794414i
$34$	1.40578	+	0.929587i	0.241088	+	0.159423i
$35$	−0.507883	−	8.13559i	−0.0858478	−	1.37517i
$36$	−5.72186	+	1.80563i	−0.953644	+	0.300938i
$37$	0.334978	+	0.193399i	0.0550700	+	0.0317947i	0.527282	−	0.849690i	$-0.323211\pi$
$37$	0.334978	+	0.193399i	0.0550700	+	0.0317947i	−0.472212	+	0.881485i	$0.656544\pi$
$38$	0.105291	−	1.73382i	0.0170804	−	0.281262i
$39$	3.16581	−	9.87940i	0.506936	−	1.58197i
$40$	−5.65083	+	6.63371i	−0.893475	+	1.04888i
$41$	−9.44060			−1.47437			−0.737187	−	0.675689i	$-0.763846\pi$
$41$	−9.44060			−1.47437			−0.737187	+	0.675689i	$0.763846\pi$
$42$	4.79114	−	4.36406i	0.739289	−	0.673389i
$43$			8.29057i			1.26430i	0.774846	+	0.632150i	$0.217827\pi$
$43$			8.29057i			1.26430i	−0.774846	+	0.632150i	$0.782173\pi$
$44$	−2.46884	−	0.300965i	−0.372192	−	0.0453722i
$45$	−3.82770	−	8.41302i	−0.570600	−	1.25414i
$46$	−4.18836	−	0.254350i	−0.617540	−	0.0375019i
$47$	−3.34244	+	5.78928i	−0.487546	+	0.844454i	−0.999897	−	0.0143219i	$-0.995441\pi$
$47$	−3.34244	+	5.78928i	−0.487546	+	0.844454i	0.512352	+	0.858776i	$0.328774\pi$
$48$	−6.92527	−	0.201736i	−0.999576	−	0.0291181i
$49$	−2.71887	+	6.45041i	−0.388410	+	0.921486i
$50$	−5.29919	−	3.50416i	−0.749419	−	0.495563i
$51$	−2.01724	+	0.437327i	−0.282470	+	0.0612380i
$52$	7.20094	−	9.57321i	0.998590	−	1.32757i
$53$	5.25317	+	9.09875i	0.721578	+	1.24981i	0.960367	+	0.278738i	$0.0899162\pi$
$53$	5.25317	+	9.09875i	0.721578	+	1.24981i	−0.238789	+	0.971071i	$0.576750\pi$
$54$	3.31083	−	6.56037i	0.450546	−	0.892753i
$55$		−	3.83135i		−	0.516619i
$56$	6.88092	−	2.94158i	0.919502	−	0.393086i
$57$	1.42990	+	1.57518i	0.189395	+	0.208638i
$58$	4.04788	−	2.02039i	0.531512	−	0.265290i
$59$	−3.22898	+	1.86425i	−0.420377	+	0.242705i	−0.695238	−	0.718779i	$-0.744701\pi$
$59$	−3.22898	+	1.86425i	−0.420377	+	0.242705i	0.274862	+	0.961484i	$0.411368\pi$
$60$	−0.982467	−	10.6274i	−0.126836	−	1.37199i
$61$	−3.16493	+	5.48181i	−0.405227	+	0.701874i	−0.994348	−	0.106171i	$-0.966141\pi$
$61$	−3.16493	+	5.48181i	−0.405227	+	0.701874i	0.589121	+	0.808045i	$0.299474\pi$
$62$	−1.20685	+	1.82506i	−0.153270	+	0.231783i
$63$	−0.271956	+	7.93259i	−0.0342632	+	0.999413i
$64$	−7.47607	−	2.84752i	−0.934509	−	0.355940i
$65$	15.9813	+	9.22678i	1.98223	+	1.14444i
$66$	2.37537	−	1.90691i	0.292387	−	0.234724i
$67$	10.7324	−	6.19634i	1.31117	−	0.757003i	0.328878	−	0.944372i	$-0.393329\pi$
$67$	10.7324	−	6.19634i	1.31117	−	0.757003i	0.982290	+	0.187369i	$0.0599961\pi$
$68$	−2.36590	−	0.288416i	−0.286908	−	0.0349755i
$69$	3.80515	−	3.45419i	0.458086	−	0.415836i
$70$	5.78082	+	9.97364i	0.690940	+	1.19208i
$71$		−	6.21100i		−	0.737110i	−0.929606	−	0.368555i	$-0.879853\pi$
$71$		−	6.21100i		−	0.737110i	0.929606	−	0.368555i	$-0.120147\pi$
$72$	6.09981	−	5.89850i	0.718870	−	0.695145i
$73$	−8.92963	+	5.15552i	−1.04513	+	0.603408i	−0.921283	−	0.388893i	$-0.872858\pi$
$73$	−8.92963	+	5.15552i	−1.04513	+	0.603408i	−0.123851	+	0.992301i	$0.539524\pi$
$74$	−0.546010	−	0.0331580i	−0.0634724	−	0.00385454i
$75$	7.60415	−	1.64854i	0.878052	−	0.190357i
$76$	0.961791	+	2.26039i	0.110325	+	0.259285i
$77$	−1.46435	+	2.94632i	−0.166878	+	0.335764i
$78$	2.23362	+	14.5004i	0.252908	+	1.64184i
$79$	−6.41425	+	11.1098i	−0.721660	+	1.24995i	0.238674	+	0.971100i	$0.423287\pi$
$79$	−6.41425	+	11.1098i	−0.721660	+	1.24995i	−0.960334	+	0.278852i	$0.910046\pi$
$80$	2.96067	−	11.9629i	0.331013	−	1.33749i
$81$	2.91950	+	8.51331i	0.324389	+	0.945924i
$82$	11.9457	−	5.96237i	1.31918	−	0.658434i
$83$		−	5.22882i		−	0.573938i	−0.957940	−	0.286969i	$-0.907352\pi$
$83$		−	5.22882i		−	0.573938i	0.957940	−	0.286969i	$-0.0926476\pi$
$84$	−3.30629	+	8.54801i	−0.360746	+	0.932664i
$85$		−	3.67159i		−	0.398240i
$86$	−5.23605	−	10.4905i	−0.564618	−	1.13122i
$87$	−1.69085	+	5.27654i	−0.181278	+	0.565705i
$88$	3.31404	−	1.17841i	0.353278	−	0.125619i
$89$	6.94090	−	12.0220i	0.735734	−	1.27433i	−0.218666	−	0.975800i	$-0.570171\pi$
$89$	6.94090	−	12.0220i	0.735734	−	1.27433i	0.954400	−	0.298529i	$-0.0964960\pi$
$90$	10.1568	+	8.22800i	1.07062	+	0.867308i
$91$	−8.76314	−	13.2035i	−0.918627	−	1.38410i
$92$	5.46040	−	2.32339i	0.569286	−	0.242230i
$93$	−0.567765	−	2.61890i	−0.0588745	−	0.271567i
$94$	0.573057	−	9.43648i	0.0591063	−	0.973298i
$95$	−3.27720	+	1.89209i	−0.336233	+	0.194124i
$96$	8.89033	−	4.11850i	0.907365	−	0.420343i
$97$		−	17.1489i		−	1.74120i	−0.491989	−	0.870601i	$-0.663730\pi$
$97$		−	17.1489i		−	1.74120i	0.491989	−	0.870601i	$-0.336270\pi$
$98$	−0.633524	−	9.87920i	−0.0639956	−	0.997950i
$99$	−0.359884	+	3.71328i	−0.0361697	+	0.373199i
$100$	8.91847	+	1.08721i	0.891847	+	0.108721i
$101$	2.87413	−	1.65938i	0.285986	−	0.165114i	−0.350144	−	0.936696i	$-0.613867\pi$
$101$	2.87413	−	1.65938i	0.285986	−	0.165114i	0.636130	+	0.771582i	$0.280534\pi$
$102$	2.27632	−	1.82739i	0.225389	−	0.180939i
$103$	10.7667	+	6.21615i	1.06087	+	0.612496i	0.925674	−	0.378322i	$-0.123499\pi$
$103$	10.7667	+	6.21615i	1.06087	+	0.612496i	0.135200	+	0.990818i	$0.456832\pi$
$104$	−3.06561	+	16.6614i	−0.300608	+	1.63378i
$105$	−13.6876	−	3.46238i	−1.33577	−	0.337894i
$106$	−12.3936	−	8.19542i	−1.20377	−	0.796010i
$107$	−4.79031	+	8.29706i	−0.463097	+	0.802107i	−0.999113	−	0.0421002i	$-0.986595\pi$
$107$	−4.79031	+	8.29706i	−0.463097	+	0.802107i	0.536017	+	0.844207i	$0.319928\pi$
$108$	−0.0460561	+	10.3922i	−0.00443175	+	0.999990i
$109$	0.510424	−	0.294693i	0.0488898	−	0.0282265i	−0.475356	−	0.879794i	$-0.657681\pi$
$109$	0.510424	−	0.294693i	0.0488898	−	0.0282265i	0.524246	+	0.851567i	$0.324347\pi$
$110$	2.41975	+	4.84801i	0.230714	+	0.462240i
$111$	0.496053	−	0.450301i	0.0470833	−	0.0427407i
$112$	−6.84900	+	8.06791i	−0.647170	+	0.762346i
$113$		−	7.02041i		−	0.660425i	−0.943907	−	0.330212i	$-0.892880\pi$
$113$		−	7.02041i		−	0.660425i	0.943907	−	0.330212i	$-0.107120\pi$
$114$	−2.80416	−	1.09009i	−0.262634	−	0.102096i
$115$	4.57070	+	7.91669i	0.426220	+	0.738235i
$116$	−3.84599	+	5.11301i	−0.357091	+	0.474731i
$117$	−14.6221	−	10.4436i	−1.35181	−	0.965511i
$118$	2.90840	−	4.39825i	0.267740	−	0.404892i
$119$	−1.40329	+	2.82346i	−0.128639	+	0.258827i
$120$	7.95509	+	12.8269i	0.726197	+	1.17093i
$121$	4.72678	−	8.18702i	0.429707	−	0.744275i
$122$	0.542622	−	8.93530i	0.0491267	−	0.808964i
$123$	−4.98987	+	15.5716i	−0.449921	+	1.40405i
$124$	0.374439	−	3.07156i	0.0336256	−	0.275834i
$125$		−	1.56436i		−	0.139921i
$126$	−4.66585	−	10.2093i	−0.415667	−	0.909517i
$127$	−5.88744			−0.522426			−0.261213	−	0.965281i	$-0.584123\pi$
$127$	−5.88744			−0.522426			−0.261213	+	0.965281i	$0.584123\pi$
$128$	11.2583	−	1.11851i	0.995101	−	0.0988635i
$129$	13.6747	+	4.38201i	1.20399	+	0.385815i
$130$	−26.0493	−	1.58192i	−2.28467	−	0.138743i
$131$	−3.67922	−	2.12420i	−0.321455	−	0.185592i	0.330586	−	0.943776i	$-0.392754\pi$
$131$	−3.67922	−	2.12420i	−0.321455	−	0.185592i	−0.652041	+	0.758184i	$0.726087\pi$
$132$	−1.80134	+	3.91312i	−0.156787	+	0.340593i
$133$	3.24333	−	0.202473i	0.281233	−	0.0175566i
$134$	−9.66685	+	14.6188i	−0.835089	+	1.26287i
$135$	−15.8999	+	1.86680i	−1.36844	+	0.160669i
$136$	3.17586	−	1.12928i	0.272328	−	0.0968347i
$137$	0.674838	−	0.389618i	0.0576553	−	0.0332873i	−0.470895	−	0.882189i	$-0.656069\pi$
$137$	0.674838	−	0.389618i	0.0576553	−	0.0332873i	0.528551	+	0.848902i	$0.322736\pi$
$138$	−2.63331	+	6.77398i	−0.224162	+	0.576640i
$139$	−5.54714			−0.470502			−0.235251	−	0.971935i	$-0.575591\pi$
$139$	−5.54714			−0.470502			−0.235251	+	0.971935i	$0.575591\pi$
$140$	−13.6138	−	8.96922i	−1.15058	−	0.758037i
$141$	7.78237	+	8.57309i	0.655394	+	0.721984i
$142$	3.92266	+	7.85911i	0.329182	+	0.659522i
$143$	−3.72420	−	6.45050i	−0.311433	−	0.539418i
$144$	−3.99313	+	11.3161i	−0.332761	+	0.943011i
$145$	−8.53552	−	4.92798i	−0.708836	−	0.409247i
$146$	8.04309	−	12.1632i	0.665651	−	1.00664i
$147$	9.20244	+	7.89399i	0.759005	+	0.651085i
$148$	0.711838	−	0.302886i	0.0585128	−	0.0248970i
$149$	2.07219	−	3.58914i	0.169761	−	0.294034i	−0.768575	−	0.639760i	$-0.779034\pi$
$149$	2.07219	−	3.58914i	0.169761	−	0.294034i	0.938336	+	0.345726i	$0.112367\pi$
$150$	−8.58079	+	6.88852i	−0.700618	+	0.562446i
$151$	2.16486	+	3.74965i	0.176174	+	0.305142i	0.940567	−	0.339608i	$-0.110295\pi$
$151$	2.16486	+	3.74965i	0.176174	+	0.305142i	−0.764393	+	0.644751i	$0.776961\pi$
$152$	−2.64459	−	2.25276i	−0.214505	−	0.182723i
$153$	−0.344878	+	3.55845i	−0.0278817	+	0.287684i
$154$	−0.00787757	−	4.65297i	−0.000634793	−	0.374947i
$155$	4.76668			0.382869
$156$	−11.9843	−	16.9374i	−0.959511	−	1.35608i
$157$	3.21017	+	5.56018i	0.256200	+	0.443751i	0.965221	−	0.261437i	$-0.0841963\pi$
$157$	3.21017	+	5.56018i	0.256200	+	0.443751i	−0.709021	+	0.705187i	$0.750863\pi$
$158$	1.09971	−	18.1089i	0.0874885	−	1.44067i
$159$	17.7844	−	3.85556i	1.41039	−	0.305766i
$160$	3.80906	+	17.0071i	0.301132	+	1.34453i
$161$	−0.489111	−	7.83489i	−0.0385473	−	0.617476i
$162$	−9.07094	−	8.92850i	−0.712680	−	0.701489i
$163$	9.18195	+	5.30120i	0.719186	+	0.415222i	0.814453	−	0.580230i	$-0.197037\pi$
$163$	9.18195	+	5.30120i	0.719186	+	0.415222i	−0.0952672	+	0.995452i	$0.530371\pi$
$164$	−11.3499	+	15.0890i	−0.886280	+	1.17826i
$165$	−6.31955	−	2.02508i	−0.491977	−	0.157652i
$166$	3.30235	+	6.61631i	0.256312	+	0.513526i
$167$	−15.5718			−1.20498			−0.602492	−	0.798125i	$-0.705825\pi$
$167$	−15.5718			−1.20498			−0.602492	+	0.798125i	$0.705825\pi$
$168$	−1.21501	−	12.9044i	−0.0937397	−	0.995597i
$169$	22.8750			1.75961
$170$	2.31886	+	4.64587i	0.177848	+	0.356322i
$171$	3.35394	−	1.52595i	0.256482	−	0.116693i
$172$	13.2509	+	9.96730i	1.01037	+	0.759999i
$173$	−1.61807	−	0.934192i	−0.123019	−	0.0710253i	0.437228	−	0.899351i	$-0.355960\pi$
$173$	−1.61807	−	0.934192i	−0.123019	−	0.0710253i	−0.560247	+	0.828326i	$0.689294\pi$
$174$	−1.19297	−	7.74459i	−0.0904388	−	0.587116i
$175$	5.28982	−	10.6433i	0.399873	−	0.804558i
$176$	−3.44920	+	3.58415i	−0.259993	+	0.270166i
$177$	1.36827	+	6.31134i	0.102845	+	0.474389i
$178$	−1.19001	+	19.5957i	−0.0891948	+	1.46876i
$179$	−7.73124	−	13.3909i	−0.577860	−	1.00088i	−0.995724	−	0.0923734i	$-0.970555\pi$
$179$	−7.73124	−	13.3909i	−0.577860	−	1.00088i	0.417864	−	0.908509i	$-0.362779\pi$
$180$	−18.0485	−	3.99665i	−1.34525	−	0.297893i
$181$	−16.6129			−1.23483			−0.617415	−	0.786638i	$-0.711820\pi$
$181$	−16.6129			−1.23483			−0.617415	+	0.786638i	$0.711820\pi$
$182$	19.4274	+	11.1726i	1.44005	+	0.828167i
$183$	7.36905	+	8.11777i	0.544736	+	0.600083i
$184$	−5.44197	+	6.38852i	−0.401187	+	0.470968i
$185$	0.595854	+	1.03205i	0.0438081	+	0.0758778i
$186$	2.37244	+	2.95526i	0.173955	+	0.216690i
$187$	−0.740981	+	1.28342i	−0.0541859	+	0.0938527i
$188$	5.23465	+	12.3024i	0.381776	+	0.897246i
$189$	12.9405	+	4.64138i	0.941286	+	0.337611i
$190$	2.95183	−	4.46393i	0.214149	−	0.323848i
$191$	−0.391130	−	0.225819i	−0.0283012	−	0.0163397i	0.485783	−	0.874080i	$-0.338535\pi$
$191$	−0.391130	−	0.225819i	−0.0283012	−	0.0163397i	−0.514084	+	0.857740i	$0.671868\pi$
$192$	−8.64831	+	10.8262i	−0.624138	+	0.781314i
$193$	0.859277	+	1.48831i	0.0618521	+	0.107131i	0.895293	−	0.445477i	$-0.146966\pi$
$193$	0.859277	+	1.48831i	0.0618521	+	0.107131i	−0.833441	+	0.552608i	$0.813633\pi$
$194$	10.8307	+	21.6994i	0.777596	+	1.55793i
$195$	23.6659	−	21.4832i	1.69475	−	1.53844i
$196$	7.04101	+	12.1006i	0.502930	+	0.864327i
$197$	16.4222			1.17003			0.585017	−	0.811021i	$-0.301088\pi$
$197$	16.4222			1.17003			0.585017	+	0.811021i	$0.301088\pi$
$198$	−1.88981	−	4.92591i	−0.134303	−	0.350069i
$199$	0.839396	−	0.484625i	0.0595032	−	0.0343542i	−0.469953	−	0.882691i	$-0.655729\pi$
$199$	0.839396	−	0.484625i	0.0595032	−	0.0343542i	0.529456	+	0.848337i	$0.322396\pi$
$200$	−11.9717	+	4.25691i	−0.846525	+	0.301009i
$201$	−4.54780	−	20.9774i	−0.320777	−	1.47963i
$202$	−2.58878	+	3.91491i	−0.182146	+	0.275452i
$203$	4.68036	+	7.05193i	0.328497	+	0.494948i
$204$	−1.72623	+	3.74995i	−0.120860	+	0.262549i
$205$	−25.1892	−	14.5430i	−1.75929	−	1.01573i
$206$	−17.5496	−	1.06575i	−1.22274	−	0.0742543i
$207$	−3.68623	−	8.10207i	−0.256211	−	0.563132i
$208$	−6.64369	−	23.0187i	−0.460657	−	1.59606i
$209$	1.52741			0.105653
$210$	19.5063	−	4.26347i	1.34607	−	0.294207i
$211$		−	9.99340i		−	0.687974i	−0.938974	−	0.343987i	$-0.888222\pi$
$211$		−	9.99340i		−	0.687974i	0.938974	−	0.343987i	$-0.111778\pi$
$212$	20.8583	+	2.54273i	1.43255	+	0.174635i
$213$	−10.2446	−	3.28285i	−0.701950	−	0.224937i
$214$	0.821291	−	13.5241i	0.0561423	−	0.924491i
$215$	−12.7714	+	22.1207i	−0.871003	+	1.50862i
$216$	−6.50510	−	13.1789i	−0.442616	−	0.896711i
$217$	−3.66559	−	1.82184i	−0.248837	−	0.123674i
$218$	−0.459749	+	0.695259i	−0.0311381	+	0.0470889i
$219$	3.78390	+	17.4538i	0.255692	+	1.17942i
$220$	−6.12369	−	4.60622i	−0.412859	−	0.310551i
$221$	−3.56891	−	6.18153i	−0.240071	−	0.415815i
$222$	−0.343288	+	0.883082i	−0.0230400	+	0.0592686i
$223$		−	13.7534i		−	0.920996i	−0.887661	−	0.460498i	$-0.847671\pi$
$223$		−	13.7534i		−	0.920996i	0.887661	−	0.460498i	$-0.152329\pi$
$224$	3.57099	−	14.5344i	0.238597	−	0.971119i
$225$	1.30005	−	13.4139i	0.0866699	−	0.894259i
$226$	4.43386	+	8.88331i	0.294936	+	0.590909i
$227$	4.13075	−	2.38489i	0.274167	−	0.158291i	−0.356613	−	0.934252i	$-0.616068\pi$
$227$	4.13075	−	2.38489i	0.274167	−	0.158291i	0.630780	+	0.775962i	$0.282735\pi$
$228$	4.23672	−	0.391670i	0.280584	−	0.0259390i
$229$	−0.743202	+	1.28726i	−0.0491122	+	0.0850648i	−0.889536	−	0.456864i	$-0.848973\pi$
$229$	−0.743202	+	1.28726i	−0.0491122	+	0.0850648i	0.840424	+	0.541929i	$0.182306\pi$
$230$	−10.7835	−	7.13071i	−0.711042	−	0.470185i
$231$	4.08577	+	3.97263i	0.268824	+	0.261380i
$232$	1.63733	−	8.89877i	0.107496	−	0.584233i
$233$	2.00188	+	1.15579i	0.131148	+	0.0757182i	0.564139	−	0.825680i	$-0.309208\pi$
$233$	2.00188	+	1.15579i	0.131148	+	0.0757182i	−0.432991	+	0.901398i	$0.642542\pi$
$234$	25.0980	+	3.98002i	1.64071	+	0.260182i
$235$	−17.8365	+	10.2979i	−1.16352	+	0.671761i
$236$	−0.902367	+	7.40220i	−0.0587391	+	0.481842i
$237$	14.9346	+	16.4520i	0.970108	+	1.06867i
$238$	−0.00754910	−	4.45896i	−0.000489335	−	0.289031i
$239$		−	21.6031i		−	1.39739i	−0.715420	−	0.698695i	$-0.753765\pi$
$239$		−	21.6031i		−	1.39739i	0.715420	−	0.698695i	$-0.246235\pi$
$240$	−18.1671	−	11.2065i	−1.17268	−	0.723374i
$241$	3.38489	−	1.95427i	0.218040	−	0.125885i	−0.387002	−	0.922079i	$-0.626489\pi$
$241$	3.38489	−	1.95427i	0.218040	−	0.125885i	0.605042	+	0.796193i	$0.293156\pi$
$242$	−0.810399	+	13.3448i	−0.0520944	+	0.857834i
$243$	15.5853	−	0.315780i	0.999795	−	0.0202573i
$244$	4.95663	+	11.6490i	0.317316	+	0.745753i
$245$	−17.1911	+	13.0225i	−1.09830	+	0.831976i
$246$	−3.52058	−	22.8551i	−0.224464	−	1.45719i
$247$	−3.67835	+	6.37109i	−0.234048	+	0.405383i
$248$	1.46610	+	4.12309i	0.0930972	+	0.261817i
$249$	−8.62459	−	2.76372i	−0.546561	−	0.175143i
$250$	0.988000	+	1.97947i	0.0624866	+	0.125193i
$251$			15.6528i			0.987995i	0.869463	+	0.493997i	$0.164465\pi$
$251$			15.6528i			0.987995i	−0.869463	+	0.493997i	$0.835535\pi$
$252$	12.3518	+	9.97160i	0.778091	+	0.628152i
$253$		−	3.68974i		−	0.231972i
$254$	7.44970	−	3.71832i	0.467436	−	0.233308i
$255$	−6.05604	−	1.94064i	−0.379244	−	0.121527i
$256$	−13.5393	+	8.52568i	−0.846207	+	0.532855i
$257$	−6.53148	+	11.3128i	−0.407422	+	0.705676i	−0.994600	−	0.103782i	$-0.966906\pi$
$257$	−6.53148	+	11.3128i	−0.407422	+	0.705676i	0.587178	+	0.809458i	$0.300239\pi$
$258$	−20.0709	+	3.09171i	−1.24956	+	0.192481i
$259$	−0.0637623	−	1.02139i	−0.00396200	−	0.0634658i
$260$	33.9607	−	14.4502i	2.10615	−	0.896163i
$261$	7.80960	+	5.57788i	0.483402	+	0.345262i
$262$	5.99710	+	0.364191i	0.370502	+	0.0224998i
$263$	26.2857	−	15.1761i	1.62085	−	0.935796i	0.634151	−	0.773209i	$-0.281350\pi$
$263$	26.2857	−	15.1761i	1.62085	−	0.935796i	0.986694	−	0.162586i	$-0.0519836\pi$
$264$	−0.192062	−	6.08915i	−0.0118206	−	0.374761i
$265$			32.3695i			1.98844i
$266$	−3.97609	+	2.30458i	−0.243790	+	0.141303i
$267$	−16.1608	−	17.8028i	−0.989027	−	1.08952i
$268$	2.99926	−	24.6032i	0.183209	−	1.50288i
$269$	0.684713	−	0.395319i	0.0417477	−	0.0241030i	−0.478981	−	0.877825i	$-0.658994\pi$
$269$	0.684713	−	0.395319i	0.0417477	−	0.0241030i	0.520729	+	0.853722i	$0.325660\pi$
$270$	18.9400	−	12.4040i	1.15265	−	0.754884i
$271$	−4.95134	−	2.85866i	−0.300773	−	0.173651i	0.342017	−	0.939694i	$-0.388890\pi$
$271$	−4.95134	−	2.85866i	−0.300773	−	0.173651i	−0.642790	+	0.766043i	$0.722223\pi$
$272$	−3.30537	+	3.43470i	−0.200418	+	0.208259i
$273$	−26.4101	+	7.47545i	−1.59841	+	0.452435i
$274$	−0.607840	+	0.919211i	−0.0367209	+	0.0555315i
$275$	2.79319	−	4.83795i	0.168436	−	0.291739i
$276$	−0.946154	−	10.2346i	−0.0569518	−	0.616051i
$277$	15.4143	−	8.89945i	0.926156	−	0.534716i	0.0405619	−	0.999177i	$-0.487085\pi$
$277$	15.4143	−	8.89945i	0.926156	−	0.534716i	0.885594	+	0.464461i	$0.153752\pi$
$278$	7.01910	−	3.50339i	0.420977	−	0.210119i
$279$	−4.61980	−	0.447742i	−0.276580	−	0.0268056i
$280$	22.8910	+	2.75121i	1.36800	+	0.164416i
$281$			27.9140i			1.66521i	0.553866	+	0.832606i	$0.313152\pi$
$281$			27.9140i			1.66521i	−0.553866	+	0.832606i	$0.686848\pi$
$282$	−15.2619	−	5.93291i	−0.908836	−	0.353300i
$283$	−1.81190	−	3.13830i	−0.107706	−	0.186552i	0.807134	−	0.590368i	$-0.201017\pi$
$283$	−1.81190	−	3.13830i	−0.107706	−	0.186552i	−0.914841	+	0.403815i	$0.867684\pi$
$284$	−9.92712	−	7.46714i	−0.589066	−	0.443094i
$285$	1.38870	+	6.40559i	0.0822595	+	0.379434i
$286$	8.78636	+	5.81009i	0.519548	+	0.343558i
$287$	13.8122	+	20.8110i	0.815309	+	1.22843i
$288$	−2.09417	−	16.8409i	−0.123400	−	0.992357i
$289$	7.78992	−	13.4925i	0.458230	−	0.793678i
$290$	13.9128	+	0.844895i	0.816989	+	0.0496140i
$291$	−28.2859	−	9.06411i	−1.65815	−	0.531347i
$292$	−2.49547	+	20.4705i	−0.146036	+	1.19795i
$293$		−	9.77037i		−	0.570791i	−0.958410	−	0.285396i	$-0.907875\pi$
$293$		−	9.77037i		−	0.570791i	0.958410	−	0.285396i	$-0.0921250\pi$
$294$	−16.6299	−	4.17674i	−0.969878	−	0.243592i
$295$	−11.4873			−0.668817
$296$	−0.709436	+	0.832832i	−0.0412351	+	0.0484074i
$297$	5.93460	+	2.55628i	0.344360	+	0.148330i
$298$	−0.355274	+	5.85026i	−0.0205805	+	0.338897i
$299$	15.3906	+	8.88575i	0.890059	+	0.513876i
$300$	6.50717	−	14.1358i	0.375692	−	0.816129i
$301$	18.2758	−	12.1296i	1.05340	−	0.699141i
$302$	−5.10747	−	3.37738i	−0.293902	−	0.194347i
$303$	−1.21790	−	5.61775i	−0.0699666	−	0.322731i
$304$	4.76912	+	1.18030i	0.273528	+	0.0676950i
$305$	−16.8892	+	9.75098i	−0.967072	+	0.558339i
$306$	−1.81101	−	4.72052i	−0.103528	−	0.269854i
$307$	−9.56907			−0.546136			−0.273068	−	0.961995i	$-0.588038\pi$
$307$	−9.56907			−0.546136			−0.273068	+	0.961995i	$0.588038\pi$
$308$	2.94863	+	5.88269i	0.168014	+	0.335197i
$309$	15.9439	−	14.4734i	0.907018	−	0.823361i
$310$	−6.03155	+	3.01048i	−0.342569	+	0.170984i
$311$	8.85168	+	15.3316i	0.501933	+	0.869373i	0.999998	+	0.00223345i	$0.000710930\pi$
$311$	8.85168	+	15.3316i	0.501933	+	0.869373i	−0.498065	+	0.867140i	$0.665956\pi$
$312$	25.8615	+	13.8630i	1.46412	+	0.784836i
$313$	−9.93451	−	5.73569i	−0.561532	−	0.324200i	0.192228	−	0.981350i	$-0.438429\pi$
$313$	−9.93451	−	5.73569i	−0.561532	−	0.324200i	−0.753760	+	0.657150i	$0.771762\pi$
$314$	−7.57363	−	5.00816i	−0.427405	−	0.282627i
$315$	−12.9456	+	20.7466i	−0.729401	+	1.16894i
$316$	10.0455	+	23.6087i	0.565101	+	1.32809i
$317$	1.15640	−	2.00294i	0.0649499	−	0.112497i	−0.831722	−	0.555193i	$-0.812645\pi$
$317$	1.15640	−	2.00294i	0.0649499	−	0.112497i	0.896672	+	0.442696i	$0.145978\pi$
$318$	−20.0685	+	16.1107i	−1.12539	+	0.903442i
$319$	1.98908	+	3.44519i	0.111367	+	0.192893i
$320$	−15.5610	−	19.1144i	−0.869884	−	1.06853i
$321$	11.1535	+	12.2867i	0.622528	+	0.685779i
$322$	5.56716	+	9.60501i	0.310245	+	0.535266i
$323$	1.46372			0.0814434
$324$	17.1169	+	5.56881i	0.950939	+	0.309378i
$325$	13.4533	+	23.3018i	0.746256	+	1.29255i
$326$	−14.9665	−	0.908883i	−0.828917	−	0.0503383i
$327$	−0.216290	−	0.997672i	−0.0119609	−	0.0551714i
$328$	4.83194	−	26.2612i	0.266799	−	1.45003i
$329$	17.6522	−	1.10198i	0.973197	−	0.0607540i
$330$	9.27545	−	1.42878i	0.510597	−	0.0786519i
$331$	−20.7165	−	11.9607i	−1.13868	−	0.657418i	−0.192578	−	0.981282i	$-0.561685\pi$
$331$	−20.7165	−	11.9607i	−1.13868	−	0.657418i	−0.946104	+	0.323863i	$0.895018\pi$
$332$	−8.35729	−	6.28633i	−0.458666	−	0.345007i
$333$	−0.480551	−	1.05622i	−0.0263340	−	0.0578803i
$334$	19.7039	−	9.83465i	1.07815	−	0.538128i
$335$	38.1812			2.08606
$336$	9.68741	+	15.5613i	0.528492	+	0.848938i
$337$	−25.6463			−1.39704			−0.698522	−	0.715589i	$-0.746159\pi$
$337$	−25.6463			−1.39704			−0.698522	+	0.715589i	$0.746159\pi$
$338$	−28.9449	+	14.4471i	−1.57440	+	0.785817i
$339$	−11.5797	−	3.71067i	−0.628923	−	0.201536i
$340$	−5.86835	−	4.41415i	−0.318256	−	0.239391i
$341$	−1.66621	−	0.961986i	−0.0902303	−	0.0520945i
$342$	−3.28018	+	4.04911i	−0.177372	+	0.218951i
$343$	18.1972	−	3.44385i	0.982559	−	0.185950i
$344$	−23.0621	−	4.24332i	−1.24343	−	0.228785i
$345$	15.4739	−	3.35467i	0.833087	−	0.180609i
$346$	2.63744	+	0.160166i	0.141789	+	0.00861057i
$347$	−0.473950	−	0.820906i	−0.0254430	−	0.0440686i	0.853024	−	0.521872i	$-0.174766\pi$
$347$	−0.473950	−	0.820906i	−0.0254430	−	0.0440686i	−0.878467	+	0.477804i	$0.841433\pi$
$348$	6.40076	+	9.04621i	0.343117	+	0.484928i
$349$	−14.1965			−0.759919			−0.379960	−	0.925003i	$-0.624062\pi$
$349$	−14.1965			−0.759919			−0.379960	+	0.925003i	$0.624062\pi$
$350$	0.0284570	+	16.8084i	0.00152109	+	0.898448i
$351$	−24.9546	+	18.5982i	−1.33198	+	0.992697i
$352$	2.10082	−	6.71362i	0.111974	−	0.357837i
$353$	−7.75978	−	13.4403i	−0.413011	−	0.715356i	0.582206	−	0.813041i	$-0.302190\pi$
$353$	−7.75978	−	13.4403i	−0.413011	−	0.715356i	−0.995217	+	0.0976847i	$0.968856\pi$
$354$	−5.71738	−	7.12193i	−0.303875	−	0.378526i
$355$	9.56788	−	16.5721i	0.507810	−	0.879553i
$356$	−10.8702	−	25.5471i	−0.576122	−	1.35400i
$357$	3.91540	+	3.80699i	0.207225	+	0.201487i
$358$	18.2400	+	12.0614i	0.964015	+	0.637467i
$359$	−12.2735	−	7.08613i	−0.647772	−	0.373991i	0.139830	−	0.990176i	$-0.455344\pi$
$359$	−12.2735	−	7.08613i	−0.647772	−	0.373991i	−0.787602	+	0.616184i	$0.788678\pi$
$360$	25.3619	−	6.34165i	1.33669	−	0.334234i
$361$	8.74570	+	15.1480i	0.460300	+	0.797263i
$362$	21.0213	−	10.4922i	1.10485	−	0.551457i
$363$	−11.0056	−	12.1238i	−0.577643	−	0.636334i
$364$	−31.6388	−	1.86760i	−1.65832	−	0.0978886i
$365$	−31.7678			−1.66280
$366$	−14.4514	−	5.61781i	−0.755386	−	0.293648i
$367$	−11.5602	+	6.67430i	−0.603439	+	0.348396i	−0.770393	−	0.637569i	$-0.779940\pi$
$367$	−11.5602	+	6.67430i	−0.603439	+	0.348396i	0.166954	+	0.985965i	$0.446607\pi$
$368$	2.85124	−	11.5207i	0.148631	−	0.600559i
$369$	23.0470	+	16.4609i	1.19978	+	0.856921i
$370$	−1.40578	−	0.929587i	−0.0730828	−	0.0483269i
$371$	12.3717	−	24.8922i	0.642305	−	1.29234i
$372$	−4.86842	−	2.24110i	−0.252416	−	0.116195i
$373$	4.56967	+	2.63830i	0.236609	+	0.136606i	0.613617	−	0.789604i	$-0.289714\pi$
$373$	4.56967	+	2.63830i	0.236609	+	0.136606i	−0.377008	+	0.926210i	$0.623047\pi$
$374$	0.127040	−	2.09196i	0.00656908	−	0.108172i
$375$	−2.58031	−	0.826851i	−0.133247	−	0.0426984i
$376$	−14.3935	−	12.2609i	−0.742287	−	0.632307i
$377$	−19.1607			−0.986824
$378$	−19.3057	+	2.29983i	−0.992979	+	0.118290i
$379$			15.3619i			0.789086i	0.918877	+	0.394543i	$0.129097\pi$
$379$			15.3619i			0.789086i	−0.918877	+	0.394543i	$0.870903\pi$
$380$	−0.915843	+	7.51274i	−0.0469817	+	0.385396i
$381$	−3.11183	+	9.71094i	−0.159424	+	0.497507i
$382$	0.637538	+	0.0387163i	0.0326193	+	0.00198090i
$383$	−1.35424	+	2.34561i	−0.0691983	+	0.119855i	−0.898549	−	0.438874i	$-0.855377\pi$
$383$	−1.35424	+	2.34561i	−0.0691983	+	0.119855i	0.829350	+	0.558729i	$0.188711\pi$
$384$	4.10570	−	19.1610i	0.209518	−	0.977805i
$385$	−8.44587	+	5.60552i	−0.430442	+	0.285684i
$386$	−2.02726	−	1.34055i	−0.103185	−	0.0682323i
$387$	14.4557	−	20.2394i	0.734824	−	1.02883i
$388$	−27.4092	−	20.6171i	−1.39149	−	1.04668i
$389$	6.35306	+	11.0038i	0.322113	+	0.557916i	0.980924	−	0.194393i	$-0.0622736\pi$
$389$	6.35306	+	11.0038i	0.322113	+	0.557916i	−0.658811	+	0.752308i	$0.728940\pi$
$390$	−16.3777	+	42.1304i	−0.829319	+	2.13336i
$391$		−	3.53589i		−	0.178817i
$392$	−16.5517	−	10.8647i	−0.835988	−	0.548748i
$393$	−5.44840	+	4.94588i	−0.274835	+	0.249487i
$394$	−20.7799	+	10.3717i	−1.04688	+	0.522520i
$395$	−34.2288	+	19.7620i	−1.72224	+	0.994334i
$396$	5.50232	+	5.03949i	0.276502	+	0.253244i
$397$	−11.9617	+	20.7184i	−0.600343	+	1.03982i	0.392426	+	0.919784i	$0.371636\pi$
$397$	−11.9617	+	20.7184i	−0.600343	+	1.03982i	−0.992769	+	0.120041i	$0.961697\pi$
$398$	−0.756060	+	1.14336i	−0.0378979	+	0.0573113i
$399$	1.38031	−	5.45668i	0.0691021	−	0.273176i
$400$	12.4599	−	12.9474i	0.622995	−	0.647371i
$401$	−23.5968	−	13.6236i	−1.17837	−	0.680331i	−0.222731	−	0.974880i	$-0.571497\pi$
$401$	−23.5968	−	13.6236i	−1.17837	−	0.680331i	−0.955636	+	0.294549i	$0.904831\pi$
$402$	19.0032	+	23.6717i	0.947796	+	1.18063i
$403$	8.02524	−	4.63338i	0.399766	−	0.230805i
$404$	0.803202	−	6.58874i	0.0399608	−	0.327802i
$405$	−5.32478	+	27.2125i	−0.264590	+	1.35220i
$406$	−10.3761	−	5.96723i	−0.514956	−	0.296149i
$407$		−	0.481008i		−	0.0238427i
$408$	−0.184053	−	5.83525i	−0.00911199	−	0.288888i
$409$	6.82328	−	3.93942i	0.337390	−	0.194792i	−0.321727	−	0.946832i	$-0.604263\pi$
$409$	6.82328	−	3.93942i	0.337390	−	0.194792i	0.659117	+	0.752040i	$0.270930\pi$
$410$	41.0582	+	2.49337i	2.02772	+	0.123139i
$411$	−0.285960	−	1.31903i	−0.0141054	−	0.0650632i
$412$	22.8796	−	9.73520i	1.12720	−	0.479619i
$413$	8.83378	+	4.39047i	0.434682	+	0.216041i
$414$	9.78138	+	7.92389i	0.480729	+	0.389438i
$415$	8.05487	−	13.9514i	0.395398	−	0.684849i
$416$	22.9445	+	24.9309i	1.12495	+	1.22234i
$417$	−2.93196	+	9.14963i	−0.143579	+	0.448059i
$418$	−1.93271	+	0.964659i	−0.0945319	+	0.0471830i
$419$			19.8589i			0.970173i	0.874466	+	0.485086i	$0.161212\pi$
$419$			19.8589i			0.970173i	−0.874466	+	0.485086i	$0.838788\pi$
$420$	−21.9898	+	17.7144i	−1.07299	+	0.864372i
$421$			16.6507i			0.811505i	0.913983	+	0.405753i	$0.132991\pi$
$421$			16.6507i			0.811505i	−0.913983	+	0.405753i	$0.867009\pi$
$422$	6.31150	+	12.6452i	0.307239	+	0.615559i
$423$	18.2541	−	8.30516i	0.887547	−	0.403811i
$424$	−27.9990	+	9.95593i	−1.35975	+	0.483503i
$425$	2.67672	−	4.63622i	0.129840	−	0.224890i
$426$	15.0364	−	2.31620i	0.728517	−	0.112220i
$427$	16.7147	−	1.04345i	0.808880	−	0.0504962i
$428$	7.50217	+	17.6315i	0.362631	+	0.852252i
$429$	−12.6081	+	2.73338i	−0.608725	+	0.131969i
$430$	2.18964	−	36.0566i	0.105594	−	1.73880i
$431$	−19.8541	+	11.4628i	−0.956339	+	0.552142i	−0.895044	−	0.445977i	$-0.852856\pi$
$431$	−19.8541	+	11.4628i	−0.956339	+	0.552142i	−0.0612944	+	0.998120i	$0.519523\pi$
$432$	16.5546	+	12.5676i	0.796485	+	0.604659i
$433$		−	10.5825i		−	0.508564i	−0.967130	−	0.254282i	$-0.918161\pi$
$433$		−	10.5825i		−	0.508564i	0.967130	−	0.254282i	$-0.0818392\pi$
$434$	5.78889	−	0.00980070i	0.277876	−	0.000470449i
$435$	−12.6399	+	11.4741i	−0.606035	+	0.550139i
$436$	0.142643	−	1.17011i	0.00683135	−	0.0560382i
$437$	−3.15607	+	1.82216i	−0.150975	+	0.0871656i
$438$	−15.8112	−	19.6955i	−0.755489	−	0.941086i
$439$	−6.69332	−	3.86439i	−0.319455	−	0.184437i	0.331695	−	0.943387i	$-0.392380\pi$
$439$	−6.69332	−	3.86439i	−0.319455	−	0.184437i	−0.651150	+	0.758949i	$0.725713\pi$
$440$	10.6578	+	1.96098i	0.508090	+	0.0934861i
$441$	17.8846	−	11.0064i	0.851648	−	0.524115i
$442$	8.41999	+	5.56783i	0.400498	+	0.264834i
$443$	2.28548	−	3.95856i	0.108586	−	0.188077i	−0.806611	−	0.591082i	$-0.798701\pi$
$443$	2.28548	−	3.95856i	0.108586	−	0.188077i	0.915198	+	0.403005i	$0.132034\pi$
$444$	−0.123344	−	1.33422i	−0.00585366	−	0.0633194i
$445$	37.0392	−	21.3846i	1.75582	−	1.01373i
$446$	8.68620	+	17.4029i	0.411303	+	0.824053i
$447$	−4.82478	−	5.31500i	−0.228204	−	0.251391i
$448$	4.66087	+	20.6465i	0.220205	+	0.975454i
$449$			4.33700i			0.204676i	0.994750	+	0.102338i	$0.0326323\pi$
$449$			4.33700i			0.204676i	−0.994750	+	0.102338i	$0.967368\pi$
$450$	6.82675	+	17.7944i	0.321816	+	0.838836i
$451$	5.86998	+	10.1671i	0.276406	+	0.478750i
$452$	−11.2208	−	8.44026i	−0.527783	−	0.396996i
$453$	7.32905	−	1.58890i	0.344349	−	0.0746531i
$454$	−3.72065	+	5.62658i	−0.174619	+	0.264068i
$455$	−3.04200	−	48.7287i	−0.142611	−	2.28444i
$456$	−5.11359	+	3.17138i	−0.239466	+	0.148513i
$457$	−9.88462	+	17.1207i	−0.462383	+	0.800871i	−0.999079	−	0.0429048i	$-0.986339\pi$
$457$	−9.88462	+	17.1207i	−0.462383	+	0.800871i	0.536696	+	0.843776i	$0.319672\pi$
$458$	0.127421	−	2.09823i	0.00595398	−	0.0980437i
$459$	5.68714	+	2.44969i	0.265453	+	0.114342i
$460$	18.1485	+	2.21239i	0.846176	+	0.103153i
$461$		−	25.3326i		−	1.17986i	−0.807455	−	0.589929i	$-0.799156\pi$
$461$		−	25.3326i		−	1.17986i	0.807455	−	0.589929i	$-0.200844\pi$
$462$	−7.67893	−	2.44636i	−0.357256	−	0.113815i
$463$	20.9574			0.973975			0.486988	−	0.873409i	$-0.338096\pi$
$463$	20.9574			0.973975			0.486988	+	0.873409i	$0.338096\pi$
$464$	3.54837	+	12.2942i	0.164729	+	0.570744i
$465$	2.51945	−	7.86233i	0.116837	−	0.364607i
$466$	−3.26305	−	0.198158i	−0.151158	−	0.00917950i
$467$	−26.9170	−	15.5406i	−1.24557	−	0.719131i	−0.275348	−	0.961345i	$-0.588793\pi$
$467$	−26.9170	−	15.5406i	−1.24557	−	0.719131i	−0.970223	+	0.242214i	$0.922127\pi$
$468$	−34.2715	+	10.8149i	−1.58420	+	0.499920i
$469$	−29.3615	−	14.5929i	−1.35579	−	0.673839i
$470$	16.0657	−	24.2954i	0.741054	−	1.12066i
$471$	10.8679	−	2.35611i	0.500766	−	0.108564i
$472$	−3.53317	−	9.93632i	−0.162627	−	0.457356i
$473$	8.92857	−	5.15491i	0.410536	−	0.237023i
$474$	−29.2881	−	11.3854i	−1.34525	−	0.522951i
$475$	−5.51761			−0.253165
$476$	2.82568	+	5.63739i	0.129515	+	0.258390i
$477$	3.04051	−	31.3720i	0.139216	−	1.43643i
$478$	13.6438	+	27.3356i	0.624054	+	1.25030i
$479$	−17.0894	−	29.5997i	−0.780835	−	1.35245i	−0.931456	−	0.363855i	$-0.881460\pi$
$479$	−17.0894	−	29.5997i	−0.780835	−	1.35245i	0.150620	−	0.988592i	$-0.451873\pi$
$480$	30.0654	+	2.70642i	1.37229	+	0.123530i
$481$	2.00637	+	1.15838i	0.0914827	+	0.0528176i
$482$	−3.04884	+	4.61063i	−0.138871	+	0.210008i
$483$	−13.1816	−	3.33441i	−0.599786	−	0.151721i
$484$	−7.40267	−	17.3977i	−0.336485	−	0.790804i
$485$	26.4174	−	45.7562i	1.19955	−	2.07768i
$486$	−19.5214	+	10.2427i	−0.885511	+	0.464619i
$487$	−12.3371	−	21.3684i	−0.559046	−	0.968296i	−0.997576	−	0.0695795i	$-0.977834\pi$
$487$	−12.3371	−	21.3684i	−0.559046	−	0.968296i	0.438531	−	0.898716i	$-0.355499\pi$
$488$	−13.6290	−	11.6097i	−0.616958	−	0.525547i
$489$	13.5971	−	12.3430i	0.614884	−	0.558171i
$490$	13.5283	−	27.3354i	0.611146	−	1.23489i
$491$	43.3064			1.95439			0.977196	−	0.212339i	$-0.0681079\pi$
$491$	43.3064			1.95439			0.977196	+	0.212339i	$0.0681079\pi$
$492$	18.8893	+	26.6963i	0.851595	+	1.20356i
$493$	1.90614	+	3.30153i	0.0858482	+	0.148693i
$494$	0.630647	−	10.3848i	0.0283742	−	0.467235i
$495$	−6.68046	+	9.35332i	−0.300264	+	0.420400i
$496$	−4.45914	−	4.29124i	−0.200221	−	0.192682i
$497$	−13.6916	+	9.08710i	−0.614152	+	0.407612i
$498$	12.6586	−	1.94993i	0.567247	−	0.0873783i
$499$	32.3258	+	18.6633i	1.44710	+	0.835485i	0.998308	−	0.0581497i	$-0.0185201\pi$
$499$	32.3258	+	18.6633i	1.44710	+	0.835485i	0.448795	+	0.893635i	$0.351853\pi$
$500$	−2.50034	−	1.88075i	−0.111819	−	0.0841096i
$501$	−8.23056	+	25.6847i	−0.367714	+	1.14751i
$502$	−9.88578	−	19.8063i	−0.441224	−	0.883999i
$503$	34.2432			1.52683			0.763414	−	0.645910i	$-0.223522\pi$
$503$	34.2432			1.52683			0.763414	+	0.645910i	$0.223522\pi$
$504$	−21.9272	−	4.81661i	−0.976713	−	0.214549i
$505$	10.2249			0.455003
$506$	2.33032	+	4.66883i	0.103595	+	0.207555i
$507$	12.0907	−	37.7307i	0.536965	−	1.67568i
$508$	−7.07815	+	9.40998i	−0.314042	+	0.417500i
$509$	24.1054	+	13.9173i	1.06845	+	0.616871i	0.927758	−	0.373182i	$-0.121733\pi$
$509$	24.1054	+	13.9173i	1.06845	+	0.616871i	0.140694	+	0.990053i	$0.455067\pi$
$510$	8.88869	−	1.36921i	0.393598	−	0.0606295i
$511$	24.4295	+	12.1417i	1.08070	+	0.537118i
$512$	11.7475	−	19.3390i	0.519171	−	0.854671i
$513$	−0.744220	−	6.33864i	−0.0328581	−	0.279858i
$514$	1.11981	−	18.4398i	0.0493928	−	0.813346i
$515$	19.1517	+	33.1716i	0.843923	+	1.46172i
$516$	23.4442	−	16.5882i	1.03207	−	0.730257i
$517$	8.31307			0.365608
$518$	0.725756	+	1.25214i	0.0318879	+	0.0550161i
$519$	−2.39612	+	2.17512i	−0.105178	+	0.0954774i
$520$	−33.8460	+	39.7331i	−1.48425	+	1.74241i
$521$	−8.13261	−	14.0861i	−0.356296	−	0.617123i	0.631043	−	0.775748i	$-0.282627\pi$
$521$	−8.13261	−	14.0861i	−0.356296	−	0.617123i	−0.987339	+	0.158625i	$0.949294\pi$
$522$	−13.4047	−	2.12571i	−0.586709	−	0.0930399i
$523$	−6.98922	+	12.1057i	−0.305617	+	0.529345i	−0.977399	−	0.211405i	$-0.932196\pi$
$523$	−6.98922	+	12.1057i	−0.305617	+	0.529345i	0.671781	+	0.740750i	$0.265530\pi$
$524$	−7.81847	+	3.32674i	−0.341551	+	0.145329i
$525$	−14.7594	−	14.3508i	−0.644155	−	0.626319i
$526$	−23.6760	+	35.8043i	−1.03232	+	1.56114i
$527$	−1.59673	−	0.921874i	−0.0695548	−	0.0401575i
$528$	4.08873	+	7.58364i	0.177939	+	0.330035i
$529$	−7.09824	−	12.2945i	−0.308619	−	0.534544i
$530$	−20.4435	−	40.9589i	−0.888009	−	1.77914i
$531$	11.1333	+	1.07902i	0.483145	+	0.0468255i
$532$	3.57567	−	5.42729i	0.155025	−	0.235303i
$533$	−56.5451			−2.44924
$534$	31.6929	+	12.3202i	1.37148	+	0.533149i
$535$	−25.5628	+	14.7587i	−1.10518	+	0.638074i
$536$	11.7435	+	33.0260i	0.507240	+	1.42651i
$537$	−26.1738	+	5.67434i	−1.12948	+	0.244866i
$538$	−0.616734	+	0.932661i	−0.0265893	+	0.0402099i
$539$	8.63734	−	1.08263i	0.372037	−	0.0466322i
$540$	−16.1318	+	27.6573i	−0.694203	+	1.19018i
$541$	18.9287	+	10.9285i	0.813810	+	0.469853i	0.848277	−	0.529552i	$-0.177640\pi$
$541$	18.9287	+	10.9285i	0.813810	+	0.469853i	−0.0344673	+	0.999406i	$0.510973\pi$
$542$	8.07064	+	0.490112i	0.346664	+	0.0210521i
$543$	−8.78084	+	27.4019i	−0.376822	+	1.17593i
$544$	2.01322	−	6.43368i	0.0863163	−	0.275842i
$545$	1.81587			0.0777834
$546$	28.6969	−	26.1388i	1.22811	−	1.11864i
$547$			9.11111i			0.389563i	0.980847	+	0.194782i	$0.0623998\pi$
$547$			9.11111i			0.389563i	−0.980847	+	0.194782i	$0.937600\pi$
$548$	0.188590	−	1.54702i	0.00805616	−	0.0660854i
$549$	17.2847	−	7.86407i	0.737692	−	0.335630i
$550$	−0.478888	+	7.88581i	−0.0204199	+	0.336252i
$551$	1.96459	−	3.40277i	0.0836944	−	0.144963i
$552$	7.66106	+	12.3528i	0.326076	+	0.525772i
$553$	33.8751	−	2.11473i	1.44052	−	0.0899275i
$554$	−13.8840	+	20.9961i	−0.589873	+	0.892040i
$555$	2.01724	−	0.437327i	0.0856270	−	0.0185635i
$556$	−6.66902	+	8.86606i	−0.282830	+	0.376005i
$557$	−2.14436	−	3.71415i	−0.0908596	−	0.157373i	0.817013	−	0.576619i	$-0.195628\pi$
$557$	−2.14436	−	3.71415i	−0.0908596	−	0.157373i	−0.907873	+	0.419245i	$0.862295\pi$
$558$	6.12846	−	2.35116i	0.259438	−	0.0995325i
$559$			49.6569i			2.10026i
$560$	−30.7028	+	10.9759i	−1.29743	+	0.463818i
$561$	1.72526	+	1.90055i	0.0728406	+	0.0802414i
$562$	−17.6296	−	35.3212i	−0.743659	−	1.48993i
$563$	27.2512	−	15.7335i	1.14850	−	0.663087i	0.199979	−	0.979800i	$-0.435913\pi$
$563$	27.2512	−	15.7335i	1.14850	−	0.663087i	0.948521	+	0.316713i	$0.102579\pi$
$564$	23.0588	−	2.13171i	0.970951	−	0.0897611i
$565$	10.8148	−	18.7317i	0.454981	−	0.788049i
$566$	4.27474	+	2.82673i	0.179681	+	0.118816i
$567$	14.4954	−	18.8913i	0.608751	−	0.793362i
$568$	17.2773	+	3.17895i	0.724941	+	0.133386i
$569$	8.62592	+	4.98018i	0.361617	+	0.208780i	0.669790	−	0.742551i	$-0.266384\pi$
$569$	8.62592	+	4.98018i	0.361617	+	0.208780i	−0.308173	+	0.951330i	$0.599717\pi$
$570$	−5.80276	−	7.22829i	−0.243051	−	0.302760i
$571$	29.5465	−	17.0587i	1.23648	−	0.713883i	0.268108	−	0.963389i	$-0.413601\pi$
$571$	29.5465	−	17.0587i	1.23648	−	0.713883i	0.968373	+	0.249506i	$0.0802681\pi$
$572$	−14.7873	−	1.80265i	−0.618289	−	0.0753727i
$573$	−0.579206	+	0.525785i	−0.0241967	+	0.0219650i
$574$	−30.6209	−	17.6099i	−1.27809	−	0.735024i
$575$			13.3288i			0.555851i
$576$	13.2860	+	19.9870i	0.553583	+	0.832794i
$577$	0.843668	−	0.487092i	0.0351224	−	0.0202779i	−0.482336	−	0.875986i	$-0.660212\pi$
$577$	0.843668	−	0.487092i	0.0351224	−	0.0202779i	0.517458	+	0.855708i	$0.326878\pi$
$578$	−1.33557	+	21.9927i	−0.0555523	+	0.914775i
$579$	2.90905	−	0.630667i	0.120896	−	0.0262096i
$580$	−18.1383	+	7.71779i	−0.753150	+	0.320464i
$581$	−11.5265	+	7.65011i	−0.478199	+	0.317380i
$582$	41.5163	−	6.39514i	1.72091	−	0.265087i
$583$	6.53263	−	11.3149i	0.270554	−	0.468613i
$584$	−9.77087	−	27.4786i	−0.404322	−	1.13707i
$585$	−22.9263	−	50.3904i	−0.947886	−	2.08339i
$586$	6.17064	+	12.3630i	0.254907	+	0.510710i
$587$			25.9212i			1.06988i	0.844890	+	0.534940i	$0.179666\pi$
$587$			25.9212i			1.06988i	−0.844890	+	0.534940i	$0.820334\pi$
$588$	23.6807	−	5.21786i	0.976574	−	0.215181i
$589$			1.90029i			0.0782999i
$590$	14.5355	−	7.25501i	0.598418	−	0.298684i
$591$	8.68003	−	27.0873i	0.357049	−	1.11422i
$592$	0.371699	−	1.50188i	0.0152767	−	0.0617270i
$593$	22.1118	−	38.2987i	0.908022	−	1.57274i	0.0912135	−	0.995831i	$-0.470925\pi$
$593$	22.1118	−	38.2987i	0.908022	−	1.57274i	0.816808	−	0.576909i	$-0.195741\pi$
$594$	−9.12383	+	0.513497i	−0.374355	+	0.0210691i
$595$	−8.09370	+	5.37178i	−0.331809	+	0.220222i
$596$	−3.24529	−	7.62704i	−0.132932	−	0.312416i
$597$	−0.355691	−	1.64068i	−0.0145575	−	0.0671485i
$598$	−25.0865	−	1.52345i	−1.02586	−	0.0622984i
$599$	−8.58632	+	4.95731i	−0.350827	+	0.202550i	−0.665050	−	0.746799i	$-0.731590\pi$
$599$	−8.58632	+	4.95731i	−0.350827	+	0.202550i	0.314222	+	0.949349i	$0.398256\pi$
$600$	0.693805	+	21.9965i	0.0283245	+	0.898003i
$601$			11.8235i			0.482292i	0.970489	+	0.241146i	$0.0775233\pi$
$601$			11.8235i			0.482292i	−0.970489	+	0.241146i	$0.922477\pi$
$602$	−15.4647	+	26.8907i	−0.630295	+	1.09598i
$603$	−37.0046	−	3.58642i	−1.50695	−	0.146050i
$604$	8.59581	+	1.04787i	0.349759	+	0.0426374i
$605$	25.2238	−	14.5630i	1.02549	−	0.592069i
$606$	5.08906	+	6.33926i	0.206729	+	0.257515i
$607$	5.56281	+	3.21169i	0.225788	+	0.130359i	0.608627	−	0.793456i	$-0.291721\pi$
$607$	5.56281	+	3.21169i	0.225788	+	0.130359i	−0.382840	+	0.923815i	$0.625054\pi$
$608$	−6.78007	+	1.51852i	−0.274968	+	0.0615841i
$609$	14.1055	−	3.99261i	0.571584	−	0.161789i
$610$	15.2124	−	23.0051i	0.615933	−	0.931449i
$611$	−20.0198	+	34.6753i	−0.809915	+	1.40281i
$612$	5.27289	+	4.82935i	0.213144	+	0.195215i
$613$	−17.5740	+	10.1463i	−0.709805	+	0.409806i	−0.810989	−	0.585061i	$-0.801070\pi$
$613$	−17.5740	+	10.1463i	−0.709805	+	0.409806i	0.101184	+	0.994868i	$0.467737\pi$
$614$	12.1083	−	6.04351i	0.488650	−	0.243896i
$615$	−37.3016	+	33.8612i	−1.50414	+	1.36541i
$616$	−7.44638	−	5.58143i	−0.300023	−	0.224882i
$617$			26.7202i			1.07571i	0.843036	+	0.537856i	$0.180766\pi$
$617$			26.7202i			1.07571i	−0.843036	+	0.537856i	$0.819234\pi$
$618$	−11.0338	+	28.3836i	−0.443845	+	1.14176i
$619$	7.12358	+	12.3384i	0.286321	+	0.495922i	0.972929	−	0.231106i	$-0.0742343\pi$
$619$	7.12358	+	12.3384i	0.286321	+	0.495922i	−0.686608	+	0.727028i	$0.740901\pi$
$620$	5.73073	−	7.61865i	0.230151	−	0.305972i
$621$	−15.3122	+	1.79780i	−0.614457	+	0.0721434i
$622$	−20.8834	−	13.8094i	−0.837350	−	0.553708i
$623$	−36.6564	+	2.28836i	−1.46861	+	0.0916813i
$624$	−41.4794	−	1.20831i	−1.66050	−	0.0483712i
$625$	13.6405	−	23.6260i	0.545619	−	0.945040i
$626$	16.1932	+	0.983375i	0.647209	+	0.0393036i
$627$	0.807317	−	2.51935i	0.0322411	−	0.100613i
$628$	12.7463	+	1.55384i	0.508634	+	0.0620051i
$629$		−	0.460951i		−	0.0183793i
$630$	3.27786	−	34.4279i	0.130593	−	1.37164i
$631$	−13.9775			−0.556436			−0.278218	−	0.960518i	$-0.589744\pi$
$631$	−13.9775			−0.556436			−0.278218	+	0.960518i	$0.589744\pi$
$632$	−27.6216	−	23.5290i	−1.09873	−	0.935934i
$633$	−16.4834	−	5.28206i	−0.655158	−	0.209943i
$634$	−0.198263	+	3.26478i	−0.00787403	+	0.129661i
$635$	−15.7088	−	9.06945i	−0.623383	−	0.359910i
$636$	15.2188	−	33.0603i	0.603464	−	1.31093i
$637$	−16.2849	+	38.6352i	−0.645231	+	1.53078i
$638$	−4.69276	−	3.10315i	−0.185788	−	0.122855i
$639$	−10.8297	+	15.1627i	−0.428416	+	0.599826i
$640$	31.7622	+	14.3587i	1.25551	+	0.567578i
$641$	6.31225	−	3.64438i	0.249319	−	0.143944i	−0.370133	−	0.928979i	$-0.620688\pi$
$641$	6.31225	−	3.64438i	0.249319	−	0.143944i	0.619452	+	0.785034i	$0.287355\pi$
$642$	−21.8731	−	8.50290i	−0.863261	−	0.335583i
$643$	−25.1189			−0.990594			−0.495297	−	0.868724i	$-0.664941\pi$
$643$	−25.1189			−0.990594			−0.495297	+	0.868724i	$0.664941\pi$
$644$	−13.1106	−	8.63771i	−0.516631	−	0.340373i
$645$	29.7363	+	32.7576i	1.17086	+	1.28983i
$646$	−1.85212	+	0.924435i	−0.0728707	+	0.0363714i
$647$	20.2246	+	35.0301i	0.795112	+	1.37717i	0.922768	+	0.385355i	$0.125921\pi$
$647$	20.2246	+	35.0301i	0.795112	+	1.37717i	−0.127657	+	0.991818i	$0.540746\pi$
$648$	−25.1760	+	3.76395i	−0.989008	+	0.147862i
$649$	4.01543	+	2.31831i	0.157619	+	0.0910016i
$650$	−31.7399	−	20.9884i	−1.24494	−	0.823233i
$651$	−4.94246	+	5.08321i	−0.193710	+	0.199227i
$652$	19.5119	−	8.30228i	0.764146	−	0.325142i
$653$	−22.0316	+	38.1599i	−0.862164	+	1.49331i	0.00767187	+	0.999971i	$0.497558\pi$
$653$	−22.0316	+	38.1599i	−0.862164	+	1.49331i	−0.869836	+	0.493341i	$0.835775\pi$
$654$	0.903781	+	1.12581i	0.0353406	+	0.0440225i
$655$	−6.54455	−	11.3355i	−0.255717	−	0.442915i
$656$	10.4716	+	36.2814i	0.408847	+	1.41655i
$657$	30.7889	+	2.98400i	1.20119	+	0.116417i
$658$	−21.6403	+	12.5429i	−0.843627	+	0.488975i
$659$	−5.89051			−0.229462			−0.114731	−	0.993397i	$-0.536601\pi$
$659$	−5.89051			−0.229462			−0.114731	+	0.993397i	$0.536601\pi$
$660$	−10.8344	+	7.66599i	−0.421727	+	0.298398i
$661$	−21.0993	−	36.5450i	−0.820667	−	1.42144i	−0.905186	−	0.425015i	$-0.860269\pi$
$661$	−21.0993	−	36.5450i	−0.820667	−	1.42144i	0.0845192	−	0.996422i	$-0.473065\pi$
$662$	33.7677	+	2.05064i	1.31242	+	0.0797004i
$663$	−12.0824	+	2.61940i	−0.469241	+	0.101729i
$664$	14.5452	+	2.67624i	0.564462	+	0.103858i
$665$	8.96570	+	4.45604i	0.347675	+	0.172798i
$666$	1.27514	+	1.03299i	0.0494106	+	0.0400275i
$667$	−8.22004	−	4.74584i	−0.318281	−	0.183760i
$668$	−18.7212	+	24.8887i	−0.724344	+	0.962971i
$669$	−22.6853	−	7.26942i	−0.877065	−	0.281052i
$670$	−48.3128	+	24.1140i	−1.86648	+	0.931605i
$671$	7.87156			0.303878
$672$	−22.0860	−	13.5723i	−0.851987	−	0.523563i
$673$	−46.7729			−1.80296			−0.901481	−	0.432818i	$-0.857519\pi$
$673$	−46.7729			−1.80296			−0.901481	+	0.432818i	$0.857519\pi$
$674$	32.4517	−	16.1974i	1.24999	−	0.623899i
$675$	−21.4382	−	9.23431i	−0.825155	−	0.355429i
$676$	27.5013	−	36.5613i	1.05774	−	1.40621i
$677$	−35.7518	−	20.6413i	−1.37405	−	0.793310i	−0.382618	−	0.923907i	$-0.624977\pi$
$677$	−35.7518	−	20.6413i	−1.37405	−	0.793310i	−0.991436	+	0.130596i	$0.958311\pi$
$678$	16.9960	−	2.61804i	0.652726	−	0.100545i
$679$	−37.8032	+	25.0899i	−1.45075	+	0.962863i
$680$	10.2134	+	1.87921i	0.391665	+	0.0720646i
$681$	−1.75039	−	8.07394i	−0.0670751	−	0.309394i
$682$	2.71591	+	0.164931i	0.103997	+	0.00631554i
$683$	−17.1346	−	29.6781i	−0.655638	−	1.13560i	−0.981733	−	0.190262i	$-0.939066\pi$
$683$	−17.1346	−	29.6781i	−0.655638	−	1.13560i	0.326095	−	0.945337i	$-0.394267\pi$
$684$	1.59330	−	7.19521i	0.0609215	−	0.275116i
$685$	2.40079			0.0917293
$686$	−20.8510	+	15.8505i	−0.796093	+	0.605174i
$687$	1.73043	+	1.90625i	0.0660201	+	0.0727280i
$688$	31.8617	−	9.19598i	1.21472	−	0.350593i
$689$	31.4642	+	54.4976i	1.19869	+	2.07619i
$690$	−17.4613	+	14.0177i	−0.664740	+	0.533643i
$691$	3.57575	−	6.19338i	0.136028	−	0.235607i	−0.789962	−	0.613156i	$-0.789900\pi$
$691$	3.57575	−	6.19338i	0.136028	−	0.235607i	0.925990	+	0.377549i	$0.123233\pi$
$692$	−3.43845	+	1.46305i	−0.130710	+	0.0556169i
$693$	8.71215	−	4.63945i	0.330947	−	0.176238i
$694$	1.11817	+	0.739406i	0.0424453	+	0.0280675i
$695$	−14.8008	−	8.54522i	−0.561425	−	0.324139i
$696$	−13.8125	−	7.40416i	−0.523562	−	0.280654i
$697$	5.62522	+	9.74316i	0.213070	+	0.369048i
$698$	17.9636	−	8.96602i	0.679931	−	0.339369i
$699$	2.96450	−	2.69108i	0.112128	−	0.101786i
$700$	−10.6517	−	21.2506i	−0.402595	−	0.803199i
$701$	12.4116			0.468778			0.234389	−	0.972143i	$-0.424691\pi$
$701$	12.4116			0.468778			0.234389	+	0.972143i	$0.424691\pi$
$702$	19.8304	−	39.2938i	0.748451	−	1.48305i
$703$	−0.411437	+	0.237543i	−0.0155176	+	0.00895911i
$704$	1.58182	+	9.82193i	0.0596170	+	0.370178i
$705$	7.55815	+	34.8631i	0.284656	+	1.31302i
$706$	18.3073	+	12.1060i	0.689006	+	0.455614i
$707$	−7.86299	−	3.90798i	−0.295718	−	0.146975i
$708$	11.7325	+	5.40086i	0.440934	+	0.202977i
$709$	30.5908	+	17.6616i	1.14886	+	0.663295i	0.948609	−	0.316450i	$-0.102491\pi$
$709$	30.5908	+	17.6616i	1.14886	+	0.663295i	0.200251	+	0.979745i	$0.435824\pi$
$710$	−1.64040	+	27.0123i	−0.0615631	+	1.01375i
$711$	35.0303	−	15.9379i	1.31374	−	0.597717i
$712$	29.8894	+	25.4609i	1.12015	+	0.954187i
$713$	4.59050			0.171916
$714$	−7.35874	−	2.34435i	−0.275394	−	0.0877351i
$715$		−	22.9481i		−	0.858211i
$716$	−30.6977	−	3.74221i	−1.14723	−	0.139853i
$717$	−35.6329	−	11.4184i	−1.33073	−	0.426429i
$718$	20.0057	+	1.21491i	0.746607	+	0.0453399i
$719$	12.1803	−	21.0969i	0.454250	−	0.786783i	−0.544395	−	0.838829i	$-0.683241\pi$
$719$	12.1803	−	21.0969i	0.454250	−	0.786783i	0.998645	+	0.0520455i	$0.0165741\pi$
$720$	−28.0866	+	24.0422i	−1.04673	+	0.895999i
$721$	−2.04942	−	32.8289i	−0.0763243	−	1.22261i
$722$	−20.6334	−	13.6441i	−0.767895	−	0.507781i
$723$	−1.43434	−	6.61609i	−0.0533435	−	0.246055i
$724$	−19.9728	+	26.5527i	−0.742284	+	0.986822i
$725$	−7.18536	−	12.4454i	−0.266858	−	0.462211i
$726$	21.5830	+	8.39013i	0.801019	+	0.311387i
$727$		−	5.15142i		−	0.191055i	−0.995427	−	0.0955277i	$-0.969546\pi$
$727$		−	5.15142i		−	0.191055i	0.995427	−	0.0955277i	$-0.0304539\pi$
$728$	41.2138	−	17.6188i	1.52748	−	0.652997i
$729$	7.71680	−	25.8738i	0.285807	−	0.958287i
$730$	40.1975	−	20.0635i	1.48778	−	0.742583i
$731$	8.55627	−	4.93997i	0.316465	−	0.182711i
$732$	21.8342	−	2.01849i	0.807013	−	0.0746056i
$733$	−3.74171	+	6.48083i	−0.138203	+	0.239375i	−0.926817	−	0.375514i	$-0.877466\pi$
$733$	−3.74171	+	6.48083i	−0.138203	+	0.239375i	0.788613	+	0.614889i	$0.210799\pi$
$734$	10.4125	−	15.7464i	0.384333	−	0.581211i
$735$	12.3933	+	35.2387i	0.457133	+	1.29980i
$736$	3.66827	+	16.3785i	0.135214	+	0.603721i
$737$	−13.3464	−	7.70552i	−0.491619	−	0.283837i
$738$	−39.5587	−	6.27320i	−1.45618	−	0.230920i
$739$	−2.26360	+	1.30689i	−0.0832679	+	0.0480747i	−0.541056	−	0.840987i	$-0.681975\pi$
$739$	−2.26360	+	1.30689i	−0.0832679	+	0.0480747i	0.457788	+	0.889061i	$0.348642\pi$
$740$	2.36590	+	0.288416i	0.0869722	+	0.0106024i
$741$	8.56448	+	9.43466i	0.314624	+	0.346591i
$742$	0.0665544	+	39.3110i	0.00244329	+	1.44315i
$743$			23.6093i			0.866140i	0.901360	+	0.433070i	$0.142570\pi$
$743$			23.6093i			0.866140i	−0.901360	+	0.433070i	$0.857430\pi$
$744$	7.57568	−	0.238949i	0.277738	−	0.00876030i
$745$	11.0580	−	6.38431i	0.405132	−	0.233903i
$746$	−7.44852	−	0.452332i	−0.272710	−	0.0165611i
$747$	−9.11713	+	12.7649i	−0.333578	+	0.467044i
$748$	1.16046	+	2.72730i	0.0424306	+	0.0997200i
$749$	25.2987	−	1.57933i	0.924394	−	0.0577074i
$750$	3.78722	−	0.583380i	0.138290	−	0.0213020i
$751$	0.504993	−	0.874673i	0.0184275	−	0.0319173i	−0.856665	−	0.515874i	$-0.827467\pi$
$751$	0.504993	−	0.874673i	0.0184275	−	0.0319173i	0.875092	+	0.483956i	$0.160801\pi$
$752$	25.9564	+	6.42392i	0.946534	+	0.234256i
$753$	25.8182	+	8.27335i	0.940868	+	0.301497i
$754$	24.2450	−	12.1012i	0.882952	−	0.440701i
$755$			13.3397i			0.485480i
$756$	22.9761	−	15.1030i	0.835632	−	0.549289i
$757$		−	11.1837i		−	0.406478i	−0.979129	−	0.203239i	$-0.934853\pi$
$757$		−	11.1837i		−	0.406478i	0.979129	−	0.203239i	$-0.0651469\pi$
$758$	−9.70205	−	19.4382i	−0.352394	−	0.706028i
$759$	−6.08598	−	1.95023i	−0.220907	−	0.0707888i
$760$	−3.58594	−	10.0847i	−0.130076	−	0.365811i
$761$	−3.99009	+	6.91104i	−0.144641	+	0.250525i	−0.929239	−	0.369480i	$-0.879536\pi$
$761$	−3.99009	+	6.91104i	−0.144641	+	0.250525i	0.784598	+	0.620005i	$0.212869\pi$
$762$	−2.19554	−	14.2531i	−0.0795360	−	0.516336i
$763$	−1.39641	−	0.694029i	−0.0505534	−	0.0251255i
$764$	−0.831163	+	0.353658i	−0.0300704	+	0.0127949i
$765$	−6.40190	+	8.96331i	−0.231461	+	0.324069i
$766$	0.232182	−	3.82332i	0.00838907	−	0.138142i
$767$	−19.3402	+	11.1661i	−0.698333	+	0.403183i
$768$	6.90628	+	26.8385i	0.249209	+	0.968450i
$769$		−	11.8900i		−	0.428766i	−0.976750	−	0.214383i	$-0.931226\pi$
$769$		−	11.8900i		−	0.428766i	0.976750	−	0.214383i	$-0.0687740\pi$
$770$	7.14677	−	12.4271i	0.257552	−	0.447842i
$771$	15.2075	+	16.7527i	0.547686	+	0.603333i
$772$	3.41185	+	0.415923i	0.122795	+	0.0149694i
$773$	31.4449	−	18.1547i	1.13099	−	0.652979i	0.186809	−	0.982396i	$-0.440186\pi$
$773$	31.4449	−	18.1547i	1.13099	−	0.652979i	0.944185	+	0.329417i	$0.106852\pi$
$774$	−5.50901	+	34.7398i	−0.198017	+	1.24870i
$775$	6.01902	+	3.47508i	0.216210	+	0.124829i
$776$	47.7035	+	8.77722i	1.71246	+	0.315084i
$777$	−1.71841	−	0.434686i	−0.0616476	−	0.0155943i
$778$	−14.9885	−	9.91135i	−0.537364	−	0.355339i
$779$	5.79771	−	10.0419i	0.207725	−	0.359790i
$780$	−5.88455	−	63.6536i	−0.210701	−	2.27916i
$781$	−6.68897	+	3.86188i	−0.239350	+	0.138189i
$782$	2.23315	+	4.47415i	0.0798572	+	0.159995i
$783$	13.3281	−	9.93321i	0.476309	−	0.354984i
$784$	27.8056	+	3.29413i	0.993055	+	0.117648i
$785$			19.7807i			0.706005i
$786$	3.77050	−	9.69932i	0.134489	−	0.345963i
$787$	6.73055	+	11.6577i	0.239918	+	0.415551i	0.960691	−	0.277621i	$-0.0895460\pi$
$787$	6.73055	+	11.6577i	0.239918	+	0.415551i	−0.720772	+	0.693172i	$0.756213\pi$
$788$	19.7435	−	26.2478i	0.703334	−	0.935040i
$789$	−11.1385	−	51.3779i	−0.396540	−	1.82910i
$790$	30.8305	−	46.6237i	1.09690	−	1.65880i
$791$	−15.4759	+	10.2713i	−0.550259	+	0.365206i
$792$	−10.1452	−	2.90166i	−0.360493	−	0.103106i
$793$	−18.9565	+	32.8337i	−0.673167	+	1.16596i
$794$	2.05082	−	33.7707i	0.0727810	−	1.19848i
$795$	53.3913	+	17.1090i	1.89359	+	0.606795i
$796$	0.234577	−	1.92426i	0.00831436	−	0.0682034i
$797$		−	13.9811i		−	0.495236i	−0.968858	−	0.247618i	$-0.920352\pi$
$797$		−	13.9811i		−	0.495236i	0.968858	−	0.247618i	$-0.0796479\pi$
$798$	1.69967	+	7.77640i	0.0601678	+	0.275282i
$799$	7.96643			0.281832
$800$	−7.58902	+	24.2523i	−0.268312	+	0.857449i
$801$	−37.9065	+	17.2465i	−1.33936	+	0.609373i
$802$	38.4625	+	2.33575i	1.35816	+	0.0824781i
$803$	11.1045	+	6.41121i	0.391871	+	0.226247i
$804$	−38.9961	−	17.9512i	−1.37529	−	0.633091i
$805$	10.7644	−	21.6584i	0.379396	−	0.763357i
$806$	−7.22849	+	10.9313i	−0.254613	+	0.385040i
$807$	−0.290145	−	1.33834i	−0.0102136	−	0.0471117i
$808$	3.14489	+	8.84436i	0.110637	+	0.311144i
$809$	−2.99316	+	1.72810i	−0.105234	+	0.0607569i	−0.551693	−	0.834047i	$-0.686018\pi$
$809$	−2.99316	+	1.72810i	−0.105234	+	0.0607569i	0.446459	+	0.894804i	$0.352685\pi$
$810$	−10.4488	−	37.7964i	−0.367132	−	1.32803i
$811$	45.3167			1.59129			0.795643	−	0.605766i	$-0.207133\pi$
$811$	45.3167			1.59129			0.795643	+	0.605766i	$0.207133\pi$
$812$	16.8981	+	0.997475i	0.593008	+	0.0350045i
$813$	−7.33222	+	6.65595i	−0.257152	+	0.233434i
$814$	0.303789	+	0.608646i	0.0106478	+	0.0213330i
$815$	16.3327	+	28.2891i	0.572111	+	0.990924i
$816$	3.91825	+	7.26742i	0.137166	+	0.254411i
$817$	−8.81865	−	5.09145i	−0.308525	−	0.178127i
$818$	−6.14586	+	9.29413i	−0.214885	+	0.324962i
$819$	−1.62890	+	47.5128i	−0.0569183	+	1.66023i
$820$	−53.5279	+	22.7760i	−1.86927	+	0.795372i
$821$	−22.3394	+	38.6931i	−0.779652	+	1.35040i	0.152490	+	0.988305i	$0.451271\pi$
$821$	−22.3394	+	38.6931i	−0.779652	+	1.35040i	−0.932142	+	0.362092i	$0.882063\pi$
$822$	1.19490	+	1.48844i	0.0416769	+	0.0519154i
$823$	21.1932	+	36.7076i	0.738747	+	1.27955i	0.953060	+	0.302783i	$0.0979157\pi$
$823$	21.1932	+	36.7076i	0.738747	+	1.27955i	−0.214312	+	0.976765i	$0.568751\pi$
$824$	−22.8023	+	26.7685i	−0.794357	+	0.932524i
$825$	−6.50352	−	7.16430i	−0.226424	−	0.249429i
$826$	−13.9507	+	0.0236189i	−0.485409	+	0.000821806i
$827$	−9.18843			−0.319513			−0.159757	−	0.987156i	$-0.551071\pi$
$827$	−9.18843			−0.319513			−0.159757	+	0.987156i	$0.551071\pi$
$828$	−17.3814	−	3.84893i	−0.604045	−	0.133759i
$829$	−13.0225	−	22.5556i	−0.452290	−	0.783389i	0.546238	−	0.837630i	$-0.316059\pi$
$829$	−13.0225	−	22.5556i	−0.452290	−	0.783389i	−0.998528	+	0.0542413i	$0.982726\pi$
$830$	−1.38099	+	22.7407i	−0.0479350	+	0.789341i
$831$	−6.53175	−	30.1287i	−0.226584	−	1.04515i
$832$	−44.7784	−	17.0554i	−1.55241	−	0.591291i
$833$	8.27719	−	1.03749i	0.286788	−	0.0359468i
$834$	−2.06863	−	13.4293i	−0.0716309	−	0.465017i
$835$	−41.5484	−	23.9880i	−1.43784	−	0.830139i
$836$	1.83632	−	2.44127i	0.0635103	−	0.0844332i
$837$	−3.18033	+	7.38339i	−0.109928	+	0.255207i
$838$	−12.5423	−	25.1286i	−0.433265	−	0.868053i
$839$	−31.2096			−1.07748			−0.538738	−	0.842473i	$-0.681099\pi$
$839$	−31.2096			−1.07748			−0.538738	+	0.842473i	$0.681099\pi$
$840$	16.6371	−	36.3030i	0.574033	−	1.25257i
$841$	−18.7664			−0.647116
$842$	−10.5160	−	21.0690i	−0.362406	−	0.726087i
$843$	46.0423	+	14.7541i	1.58578	+	0.508158i
$844$	−15.9726	−	12.0145i	−0.549799	−	0.413557i
$845$	61.0345	+	35.2383i	2.09965	+	1.21223i
$846$	−17.8527	+	22.0377i	−0.613789	+	0.757672i
$847$	−24.9632	+	1.55838i	−0.857744	+	0.0535467i
$848$	29.1408	−	30.2810i	1.00070	−	1.03985i
$849$	−6.13410	+	1.32984i	−0.210522	+	0.0456401i
$850$	−0.458920	+	7.55699i	−0.0157408	+	0.259203i
$851$	0.573831	+	0.993904i	0.0196707	+	0.0340706i
$852$	−17.5636	+	12.4273i	−0.601718	+	0.425753i
$853$	−4.78201			−0.163733			−0.0818665	−	0.996643i	$-0.526088\pi$
$853$	−4.78201			−0.163733			−0.0818665	+	0.996643i	$0.526088\pi$
$854$	−20.4910	+	11.8768i	−0.701187	+	0.406415i
$855$	11.2996	+	1.09513i	0.386438	+	0.0374528i
$856$	−20.6284	−	17.5720i	−0.705064	−	0.600599i
$857$	−15.2965	−	26.4944i	−0.522520	−	0.905031i	−0.999657	−	0.0262016i	$-0.991659\pi$
$857$	−15.2965	−	26.4944i	−0.522520	−	0.905031i	0.477137	−	0.878829i	$-0.341675\pi$
$858$	14.2274	−	11.4216i	0.485716	−	0.389926i
$859$	−12.2711	+	21.2542i	−0.418684	+	0.725183i	−0.995807	−	0.0914746i	$-0.970842\pi$
$859$	−12.2711	+	21.2542i	−0.418684	+	0.725183i	0.577123	+	0.816657i	$0.304175\pi$
$860$	20.0015	+	47.0072i	0.682045	+	1.60293i
$861$	41.6268	−	11.7826i	1.41864	−	0.401550i
$862$	17.8830	−	27.0437i	0.609097	−	0.921111i
$863$	32.1415	+	18.5569i	1.09411	+	0.631684i	0.934667	−	0.355523i	$-0.115697\pi$
$863$	32.1415	+	18.5569i	1.09411	+	0.631684i	0.159441	+	0.987207i	$0.449031\pi$
$864$	−28.8848	−	5.44711i	−0.982679	−	0.185314i
$865$	−2.87820	−	4.98519i	−0.0978617	−	0.169501i
$866$	6.68358	+	13.3907i	0.227117	+	0.455033i
$867$	−18.1376	−	19.9805i	−0.615986	−	0.678573i
$868$	−7.31881	+	3.66847i	−0.248417	+	0.124516i
$869$	15.9530			0.541170
$870$	8.74728	−	22.5017i	0.296561	−	0.762879i
$871$	64.2823	−	37.1134i	2.17812	−	1.25754i
$872$	0.558510	+	1.57069i	0.0189135	+	0.0531904i
$873$	−29.9013	+	41.8648i	−1.01200	+	1.41691i
$874$	2.84273	−	4.29894i	0.0961568	−	0.145414i
$875$	−3.44850	+	2.28877i	−0.116581	+	0.0773744i
$876$	32.4458	+	14.9359i	1.09624	+	0.504637i
$877$	−28.4107	−	16.4029i	−0.959360	−	0.553887i	−0.0633837	−	0.997989i	$-0.520189\pi$
$877$	−28.4107	−	16.4029i	−0.959360	−	0.553887i	−0.895976	+	0.444103i	$0.853523\pi$
$878$	10.9101	+	0.662544i	0.368196	+	0.0223598i
$879$	−16.1156	−	5.16417i	−0.543565	−	0.174183i
$880$	−14.7244	+	4.24977i	−0.496358	+	0.143260i
$881$	27.1405			0.914385			0.457193	−	0.889368i	$-0.348855\pi$
$881$	27.1405			0.914385			0.457193	+	0.889368i	$0.348855\pi$
$882$	−15.6791	+	25.2223i	−0.527942	+	0.849280i
$883$		−	47.9537i		−	1.61377i	−0.590709	−	0.806884i	$-0.701152\pi$
$883$		−	47.9537i		−	1.61377i	0.590709	−	0.806884i	$-0.298848\pi$
$884$	−14.1707	−	1.72749i	−0.476613	−	0.0581017i
$885$	−6.07167	+	18.9476i	−0.204097	+	0.636915i
$886$	−0.391841	+	6.45242i	−0.0131642	+	0.216773i
$887$	14.5502	−	25.2017i	0.488548	−	0.846190i	−0.511365	−	0.859364i	$-0.670860\pi$
$887$	14.5502	−	25.2017i	0.488548	−	0.846190i	0.999913	+	0.0131735i	$0.00419338\pi$
$888$	0.998725	+	1.61036i	0.0335150	+	0.0540403i
$889$	8.61372	+	12.9784i	0.288895	+	0.435280i
$890$	−33.3619	+	50.4518i	−1.11829	+	1.69115i
$891$	7.35317	−	8.43759i	0.246340	−	0.282670i
$892$	−21.9823	−	16.5350i	−0.736020	−	0.553632i
$893$	−4.10536	−	7.11070i	−0.137381	−	0.237950i
$894$	9.46184	+	3.67818i	0.316451	+	0.123017i
$895$		−	47.6391i		−	1.59240i
$896$	−18.9373	−	23.1814i	−0.632650	−	0.774438i
$897$	22.7912	−	20.6891i	0.760976	−	0.690789i
$898$	−2.73911	−	5.48784i	−0.0914051	−	0.183132i
$899$	−4.28625	+	2.47467i	−0.142954	+	0.0825348i
$900$	−19.8766	−	18.2047i	−0.662554	−	0.606822i
$901$	6.26024	−	10.8431i	0.208559	−	0.361235i
$902$	−13.8488	−	9.15770i	−0.461115	−	0.304918i
$903$	−10.3473	−	36.5559i	−0.344336	−	1.21651i
$904$	19.5289	+	3.59323i	0.649522	+	0.119509i
$905$	−44.3263	−	25.5918i	−1.47346	−	0.850700i
$906$	−8.27035	+	6.63931i	−0.274764	+	0.220576i
$907$	−1.60692	+	0.927757i	−0.0533570	+	0.0308057i	−0.526441	−	0.850212i	$-0.676474\pi$
$907$	−1.60692	+	0.927757i	−0.0533570	+	0.0308057i	0.473084	+	0.881017i	$0.343141\pi$
$908$	1.15438	−	9.46945i	0.0383093	−	0.314255i
$909$	−9.90984	−	0.960442i	−0.328688	−	0.0318558i
$910$	34.6246	+	59.7378i	1.14780	+	1.98029i
$911$		−	12.2209i		−	0.404896i	−0.979293	−	0.202448i	$-0.935110\pi$
$911$		−	12.2209i		−	0.404896i	0.979293	−	0.202448i	$-0.0648897\pi$
$912$	4.46757	−	7.24249i	0.147936	−	0.239823i
$913$	−5.63121	+	3.25118i	−0.186366	+	0.107598i
$914$	1.69470	−	27.9065i	0.0560558	−	0.923065i
$915$	7.15673	+	33.0115i	0.236594	+	1.09133i
$916$	1.16394	+	2.73548i	0.0384576	+	0.0903827i
$917$	0.700333	+	11.2184i	0.0231270	+	0.370463i
$918$	−8.74339	+	0.492086i	−0.288575	+	0.0162413i
$919$	14.5126	−	25.1365i	0.478726	−	0.829177i	−0.520977	−	0.853571i	$-0.674432\pi$
$919$	14.5126	−	25.1365i	0.478726	−	0.829177i	0.999702	+	0.0243939i	$0.00776558\pi$
$920$	−24.3615	+	8.66251i	−0.803175	+	0.285594i
$921$	−5.05777	+	15.7835i	−0.166659	+	0.520085i
$922$	15.9993	+	32.0548i	0.526907	+	1.05567i
$923$		−	37.2012i		−	1.22449i
$924$	11.2616	−	1.75425i	0.370480	−	0.0577107i
$925$			1.73760i			0.0571318i
$926$	−26.5186	+	13.2360i	−0.871456	+	0.434963i
$927$	−15.4456	−	33.9484i	−0.507301	−	1.11501i
$928$	−12.2546	−	13.3155i	−0.402275	−	0.437102i
$929$	−14.7335	+	25.5191i	−0.483390	+	0.837255i	−0.999818	−	0.0190749i	$-0.993928\pi$
$929$	−14.7335	+	25.5191i	−0.483390	+	0.837255i	0.516428	+	0.856330i	$0.327261\pi$
$930$	1.77759	+	11.5398i	0.0582894	+	0.378406i
$931$	−5.19155	−	6.85342i	−0.170146	−	0.224612i
$932$	4.25407	−	1.81010i	0.139347	−	0.0592917i
$933$	29.9670	−	6.49670i	0.981075	−	0.212692i
$934$	43.8745	+	2.66440i	1.43562	+	0.0871819i
$935$	−3.95414	+	2.28292i	−0.129314	+	0.0746596i
$936$	36.5353	−	35.3295i	1.19419	−	1.15478i
$937$		−	23.9964i		−	0.783929i	−0.919980	−	0.391965i	$-0.871796\pi$
$937$		−	23.9964i		−	0.783929i	0.919980	−	0.391965i	$-0.128204\pi$
$938$	46.3691	−	0.0785037i	1.51400	−	0.00256324i
$939$	−14.7116	+	13.3547i	−0.480094	+	0.435814i
$940$	−4.98457	+	40.8889i	−0.162579	+	1.33365i
$941$	−37.8505	+	21.8530i	−1.23389	+	0.712387i	−0.967839	−	0.251571i	$-0.919053\pi$
$941$	−37.8505	+	21.8530i	−1.23389	+	0.712387i	−0.266052	+	0.963959i	$0.585719\pi$
$942$	−12.2637	+	9.84511i	−0.399573	+	0.320771i
$943$	−24.2582	−	14.0055i	−0.789955	−	0.456081i
$944$	10.7462	+	10.3415i	0.349758	+	0.336588i
$945$	27.3778	+	32.3186i	0.890599	+	1.05132i
$946$	−8.04214	+	12.1618i	−0.261472	+	0.395414i
$947$	15.9345	−	27.5994i	0.517802	−	0.896859i	−0.481984	−	0.876180i	$-0.660084\pi$
$947$	15.9345	−	27.5994i	0.517802	−	0.896859i	0.999786	−	0.0206793i	$-0.00658291\pi$
$948$	44.2506	−	4.09081i	1.43719	−	0.132863i
$949$	−53.4846	+	30.8794i	−1.73618	+	1.00239i
$950$	6.98173	−	3.48474i	0.226517	−	0.113060i
$951$	−2.69250	−	2.96607i	−0.0873103	−	0.0961814i
$952$	−7.13588	−	5.34870i	−0.231275	−	0.173352i
$953$		−	49.4699i		−	1.60249i	−0.598338	−	0.801243i	$-0.704172\pi$
$953$		−	49.4699i		−	1.60249i	0.598338	−	0.801243i	$-0.295828\pi$
$954$	15.9662	+	41.6170i	0.516925	+	1.34740i
$955$	−0.695736	−	1.20505i	−0.0225135	−	0.0389945i
$956$	−34.5285	−	25.9723i	−1.11673	−	0.840003i
$957$	6.73394	−	1.45988i	0.217677	−	0.0471914i
$958$	40.3184	+	26.6611i	1.30263	+	0.861380i
$959$	−1.84621	−	0.917585i	−0.0596173	−	0.0296304i
$960$	−39.7527	+	15.5638i	−1.28301	+	0.502319i
$961$	−14.3032	+	24.7738i	−0.461392	+	0.799155i
$962$	−3.27037	−	0.198602i	−0.105441	−	0.00640320i
$963$	26.1614	−	11.9028i	0.843040	−	0.383561i
$964$	0.945939	−	7.75963i	0.0304667	−	0.249921i
$965$			5.29478i			0.170445i
$966$	18.7854	−	4.10588i	0.604409	−	0.132105i
$967$	18.5748			0.597324			0.298662	−	0.954359i	$-0.403460\pi$
$967$	18.5748			0.597324			0.298662	+	0.954359i	$0.403460\pi$
$968$	20.3548	+	17.3390i	0.654228	+	0.557295i
$969$	0.773654	−	2.41430i	0.0248533	−	0.0775586i
$970$	−4.52922	+	74.5822i	−0.145424	+	2.39469i
$971$	−41.9333	−	24.2102i	−1.34570	−	0.776943i	−0.358067	−	0.933696i	$-0.616564\pi$
$971$	−41.9333	−	24.2102i	−1.34570	−	0.776943i	−0.987638	+	0.156753i	$0.949897\pi$
$972$	18.2326	−	25.2898i	0.584811	−	0.811170i
$973$	8.11583	+	12.2282i	0.260182	+	0.392018i
$974$	29.1064	+	19.2470i	0.932628	+	0.616712i
$975$	45.5456	−	9.87406i	1.45863	−	0.316223i
$976$	24.5779	+	6.08274i	0.786719	+	0.194704i
$977$	46.0630	−	26.5945i	1.47369	−	0.850833i	0.474125	−	0.880458i	$-0.342765\pi$
$977$	46.0630	−	26.5945i	1.47369	−	0.850833i	0.999561	+	0.0296250i	$0.00943130\pi$
$978$	−9.40974	+	24.2058i	−0.300890	+	0.774017i
$979$	−17.2629			−0.551724
$980$	0.146051	+	43.1330i	0.00466541	+	1.37783i
$981$	−1.75991	−	0.170567i	−0.0561897	−	0.00544580i
$982$	−54.7980	+	27.3509i	−1.74867	+	0.872803i
$983$	−7.97962	−	13.8211i	−0.254510	−	0.440825i	0.710252	−	0.703947i	$-0.248581\pi$
$983$	−7.97962	−	13.8211i	−0.254510	−	0.440825i	−0.964762	+	0.263123i	$0.915248\pi$
$984$	−40.7622	−	21.8504i	−1.29945	−	0.696567i
$985$	43.8174	+	25.2980i	1.39614	+	0.806061i
$986$	−4.49708	−	2.97375i	−0.143216	−	0.0947036i
$987$	7.51250	−	29.6986i	0.239126	−	0.945316i
$988$	5.76071	+	13.5388i	0.183273	+	0.430726i
$989$	−12.2994	+	21.3031i	−0.391097	+	0.677400i
$990$	2.54590	−	16.0544i	0.0809139	−	0.510243i
$991$	−4.26387	−	7.38524i	−0.135446	−	0.234600i	0.790322	−	0.612692i	$-0.209914\pi$
$991$	−4.26387	−	7.38524i	−0.135446	−	0.234600i	−0.925768	+	0.378092i	$0.876580\pi$
$992$	8.35260	+	2.61369i	0.265195	+	0.0829847i
$993$	−30.6781	+	27.8486i	−0.973541	+	0.883749i
$994$	11.5856	−	20.1456i	0.367474	−	0.638979i
$995$	2.98621			0.0946693
$996$	−14.7862	+	10.4621i	−0.468518	+	0.331505i
$997$	13.8974	+	24.0710i	0.440136	+	0.762337i	0.997699	−	0.0677970i	$-0.0215970\pi$
$997$	13.8974	+	24.0710i	0.440136	+	0.762337i	−0.557564	+	0.830134i	$0.688264\pi$
$998$	−52.6908	−	3.19980i	−1.66790	−	0.101288i
$999$	−1.99615	+	0.234369i	−0.0631555	+	0.00741509i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.ba.c.5.5	✓	48
3.2	odd	2	inner	168.2.ba.c.5.20	yes	48
4.3	odd	2		672.2.bi.c.593.10		48
7.3	odd	6	inner	168.2.ba.c.101.13	yes	48
8.3	odd	2		672.2.bi.c.593.15		48
8.5	even	2	inner	168.2.ba.c.5.12	yes	48
12.11	even	2		672.2.bi.c.593.22		48
21.17	even	6	inner	168.2.ba.c.101.12	yes	48
24.5	odd	2	inner	168.2.ba.c.5.13	yes	48
24.11	even	2		672.2.bi.c.593.3		48
28.3	even	6		672.2.bi.c.17.3		48
56.3	even	6		672.2.bi.c.17.22		48
56.45	odd	6	inner	168.2.ba.c.101.20	yes	48
84.59	odd	6		672.2.bi.c.17.15		48
168.59	odd	6		672.2.bi.c.17.10		48
168.101	even	6	inner	168.2.ba.c.101.5	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.5	✓	48	1.1	even	1	trivial
168.2.ba.c.5.12	yes	48	8.5	even	2	inner
168.2.ba.c.5.13	yes	48	24.5	odd	2	inner
168.2.ba.c.5.20	yes	48	3.2	odd	2	inner
168.2.ba.c.101.5	yes	48	168.101	even	6	inner
168.2.ba.c.101.12	yes	48	21.17	even	6	inner
168.2.ba.c.101.13	yes	48	7.3	odd	6	inner
168.2.ba.c.101.20	yes	48	56.45	odd	6	inner
672.2.bi.c.17.3		48	28.3	even	6
672.2.bi.c.17.10		48	168.59	odd	6
672.2.bi.c.17.15		48	84.59	odd	6
672.2.bi.c.17.22		48	56.3	even	6
672.2.bi.c.593.3		48	24.11	even	2
672.2.bi.c.593.10		48	4.3	odd	2
672.2.bi.c.593.15		48	8.3	odd	2
672.2.bi.c.593.22		48	12.11	even	2

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	168.2.ba.c.5.5

Level	$168$
Weight	$2$
Character	168.5
Analytic conductor	$1.341$
Analytic rank	$0$
Dimension	$48$
Inner twists	$8$