LMFDB - Embedded newform 740.2.u.a.31.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(31,740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("740.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.u (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$76$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.18
Character	$\chi$	$=$	740.31
Dual form			740.2.u.a.191.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.07503 + 0.918861i) q^{2} +0.615294 q^{3} +(0.311387 - 1.97561i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.661461 + 0.565370i) q^{6} +3.79949i q^{7} +(1.48056 + 2.40997i) q^{8} -2.62141 q^{9} +(-0.110429 + 1.40990i) q^{10} -1.28930 q^{11} +(0.191595 - 1.21558i) q^{12} +(-2.04663 + 2.04663i) q^{13} +(-3.49120 - 4.08457i) q^{14} +(0.435079 - 0.435079i) q^{15} +(-3.80608 - 1.23036i) q^{16} +(-0.482222 + 0.482222i) q^{17} +(2.81810 - 2.40872i) q^{18} +(-1.08422 - 1.08422i) q^{19} +(-1.17678 - 1.61715i) q^{20} +2.33780i q^{21} +(1.38604 - 1.18469i) q^{22} +(1.07857 + 1.07857i) q^{23} +(0.910981 + 1.48284i) q^{24} -1.00000i q^{25} +(0.319623 - 4.08076i) q^{26} -3.45882 q^{27} +(7.50631 + 1.18311i) q^{28} +(-0.779940 - 0.779940i) q^{29} +(-0.0679464 + 0.867501i) q^{30} +(-4.58150 + 4.58150i) q^{31} +(5.22218 - 2.17458i) q^{32} -0.793298 q^{33} +(0.0753089 - 0.961500i) q^{34} +(2.68664 + 2.68664i) q^{35} +(-0.816274 + 5.17889i) q^{36} +(-5.91033 - 1.43804i) q^{37} +(2.16182 + 0.169324i) q^{38} +(-1.25928 + 1.25928i) q^{39} +(2.75102 + 0.657188i) q^{40} +4.34206i q^{41} +(-2.14812 - 2.51321i) q^{42} +(3.97078 + 3.97078i) q^{43} +(-0.401471 + 2.54715i) q^{44} +(-1.85362 + 1.85362i) q^{45} +(-2.15056 - 0.168441i) q^{46} +11.1672i q^{47} +(-2.34186 - 0.757033i) q^{48} -7.43612 q^{49} +(0.918861 + 1.07503i) q^{50} +(-0.296709 + 0.296709i) q^{51} +(3.40605 + 4.68064i) q^{52} +3.28494 q^{53} +(3.71835 - 3.17818i) q^{54} +(-0.911672 + 0.911672i) q^{55} +(-9.15664 + 5.62538i) q^{56} +(-0.667116 - 0.667116i) q^{57} +(1.55512 + 0.121804i) q^{58} +(-1.39099 - 1.39099i) q^{59} +(-0.724068 - 0.995024i) q^{60} +(0.396109 + 0.396109i) q^{61} +(0.715495 - 9.13503i) q^{62} -9.96003i q^{63} +(-3.61588 + 7.13621i) q^{64} +2.89437i q^{65} +(0.852821 - 0.728931i) q^{66} -7.18162 q^{67} +(0.802526 + 1.10284i) q^{68} +(0.663639 + 0.663639i) q^{69} +(-5.35688 - 0.419574i) q^{70} +8.26090i q^{71} +(-3.88116 - 6.31752i) q^{72} -14.2805i q^{73} +(7.67515 - 3.88484i) q^{74} -0.615294i q^{75} +(-2.47962 + 1.80439i) q^{76} -4.89868i q^{77} +(0.196662 - 2.51087i) q^{78} +(-1.41474 - 1.41474i) q^{79} +(-3.56130 + 1.82131i) q^{80} +5.73604 q^{81} +(-3.98975 - 4.66785i) q^{82} -6.76042i q^{83} +(4.61859 + 0.727962i) q^{84} +0.681966i q^{85} +(-7.91732 - 0.620119i) q^{86} +(-0.479893 - 0.479893i) q^{87} +(-1.90889 - 3.10717i) q^{88} +(4.04522 + 4.04522i) q^{89} +(0.289480 - 3.69592i) q^{90} +(-7.77615 - 7.77615i) q^{91} +(2.46669 - 1.79498i) q^{92} +(-2.81897 + 2.81897i) q^{93} +(-10.2611 - 12.0051i) q^{94} -1.53332 q^{95} +(3.21318 - 1.33801i) q^{96} +(-0.0212823 + 0.0212823i) q^{97} +(7.99406 - 6.83276i) q^{98} +3.37978 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q - 4 q^{2} - 4 q^{8} + 152 q^{9} - 16 q^{13} + 24 q^{14} + 40 q^{16} + 16 q^{22} - 36 q^{24} + 32 q^{29} - 4 q^{32} - 16 q^{37} - 40 q^{38} - 20 q^{42} - 72 q^{44} + 8 q^{46} - 248 q^{49} - 4 q^{50}+ \cdots + 24 q^{98}+O(q^{100}) $ 152 * q - 4 * q^2 - 4 * q^8 + 152 * q^9 - 16 * q^13 + 24 * q^14 + 40 * q^16 + 16 * q^22 - 36 * q^24 + 32 * q^29 - 4 * q^32 - 16 * q^37 - 40 * q^38 - 20 * q^42 - 72 * q^44 + 8 * q^46 - 248 * q^49 - 4 * q^50 - 20 * q^52 + 8 * q^54 - 4 * q^56 + 48 * q^57 + 28 * q^60 + 16 * q^61 + 16 * q^66 - 28 * q^68 - 128 * q^72 - 80 * q^74 + 76 * q^76 + 152 * q^81 + 16 * q^82 - 56 * q^84 - 96 * q^86 - 72 * q^88 + 8 * q^89 - 152 * q^92 + 16 * q^93 + 28 * q^94 + 48 * q^96 - 48 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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 $

$2$	−1.07503	+	0.918861i	−0.760162	+	0.649733i
$2$	−1.07503	+	0.918861i	−0.760162	+	0.649733i
$3$	0.615294			0.355240			0.177620	−	0.984099i	$-0.443160\pi$
$3$	0.615294			0.355240			0.177620	+	0.984099i	$0.443160\pi$
$4$	0.311387	−	1.97561i	0.155694	−	0.987805i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	−0.661461	+	0.565370i	−0.270040	+	0.230811i
$7$			3.79949i			1.43607i	0.696006	+	0.718036i	$0.254959\pi$
$7$			3.79949i			1.43607i	−0.696006	+	0.718036i	$0.745041\pi$
$8$	1.48056	+	2.40997i	0.523458	+	0.852052i
$9$	−2.62141			−0.873804
$10$	−0.110429	+	1.40990i	−0.0349208	+	0.445848i
$11$	−1.28930			−0.388738			−0.194369	−	0.980928i	$-0.562266\pi$
$11$	−1.28930			−0.388738			−0.194369	+	0.980928i	$0.562266\pi$
$12$	0.191595	−	1.21558i	0.0553086	−	0.350908i
$13$	−2.04663	+	2.04663i	−0.567633	+	0.567633i	−0.931465	−	0.363832i	$-0.881468\pi$
$13$	−2.04663	+	2.04663i	−0.567633	+	0.567633i	0.363832	+	0.931465i	$0.381468\pi$
$14$	−3.49120	−	4.08457i	−0.933063	−	1.09165i
$15$	0.435079	−	0.435079i	0.112337	−	0.112337i
$16$	−3.80608	−	1.23036i	−0.951519	−	0.307590i
$17$	−0.482222	+	0.482222i	−0.116956	+	0.116956i	−0.763163	−	0.646206i	$-0.776354\pi$
$17$	−0.482222	+	0.482222i	−0.116956	+	0.116956i	0.646206	+	0.763163i	$0.276354\pi$
$18$	2.81810	−	2.40872i	0.664233	−	0.567740i
$19$	−1.08422	−	1.08422i	−0.248738	−	0.248738i	0.571715	−	0.820452i	$-0.306278\pi$
$19$	−1.08422	−	1.08422i	−0.248738	−	0.248738i	−0.820452	+	0.571715i	$0.806278\pi$
$20$	−1.17678	−	1.61715i	−0.263137	−	0.361606i
$21$			2.33780i			0.510151i
$22$	1.38604	−	1.18469i	0.295504	−	0.252576i
$23$	1.07857	+	1.07857i	0.224898	+	0.224898i	0.810557	−	0.585660i	$-0.199164\pi$
$23$	1.07857	+	1.07857i	0.224898	+	0.224898i	−0.585660	+	0.810557i	$0.699164\pi$
$24$	0.910981	+	1.48284i	0.185953	+	0.302683i
$25$		−	1.00000i		−	0.200000i
$26$	0.319623	−	4.08076i	0.0626833	−	0.800303i
$27$	−3.45882			−0.665651
$28$	7.50631	+	1.18311i	1.41856	+	0.223587i
$29$	−0.779940	−	0.779940i	−0.144831	−	0.144831i	0.630973	−	0.775805i	$-0.282656\pi$
$29$	−0.779940	−	0.779940i	−0.144831	−	0.144831i	−0.775805	+	0.630973i	$0.782656\pi$
$30$	−0.0679464	+	0.867501i	−0.0124053	+	0.158383i
$31$	−4.58150	+	4.58150i	−0.822862	+	0.822862i	−0.986518	−	0.163655i	$-0.947672\pi$
$31$	−4.58150	+	4.58150i	−0.822862	+	0.822862i	0.163655	+	0.986518i	$0.447672\pi$
$32$	5.22218	−	2.17458i	0.923160	−	0.384415i
$33$	−0.793298			−0.138095
$34$	0.0753089	−	0.961500i	0.0129154	−	0.164896i
$35$	2.68664	+	2.68664i	0.454126	+	0.454126i
$36$	−0.816274	+	5.17889i	−0.136046	+	0.863149i
$37$	−5.91033	−	1.43804i	−0.971653	−	0.236412i
$37$	−5.91033	−	1.43804i	−0.971653	−	0.236412i
$38$	2.16182	+	0.169324i	0.350694	+	0.0274679i
$39$	−1.25928	+	1.25928i	−0.201646	+	0.201646i
$40$	2.75102	+	0.657188i	0.434974	+	0.103911i
$41$			4.34206i			0.678116i	0.940765	+	0.339058i	$0.110108\pi$
$41$			4.34206i			0.678116i	−0.940765	+	0.339058i	$0.889892\pi$
$42$	−2.14812	−	2.51321i	−0.331462	−	0.387797i
$43$	3.97078	+	3.97078i	0.605539	+	0.605539i	0.941777	−	0.336238i	$-0.109155\pi$
$43$	3.97078	+	3.97078i	0.605539	+	0.605539i	−0.336238	+	0.941777i	$0.609155\pi$
$44$	−0.401471	+	2.54715i	−0.0605240	+	0.383998i
$45$	−1.85362	+	1.85362i	−0.276321	+	0.276321i
$46$	−2.15056	−	0.168441i	−0.317082	−	0.0248353i
$47$			11.1672i			1.62890i	0.580231	+	0.814452i	$0.302962\pi$
$47$			11.1672i			1.62890i	−0.580231	+	0.814452i	$0.697038\pi$
$48$	−2.34186	−	0.757033i	−0.338018	−	0.109268i
$49$	−7.43612			−1.06230
$50$	0.918861	+	1.07503i	0.129947	+	0.152032i
$51$	−0.296709	+	0.296709i	−0.0415475	+	0.0415475i
$52$	3.40605	+	4.68064i	0.472334	+	0.649088i
$53$	3.28494			0.451221			0.225610	−	0.974218i	$-0.427562\pi$
$53$	3.28494			0.451221			0.225610	+	0.974218i	$0.427562\pi$
$54$	3.71835	−	3.17818i	0.506003	−	0.432495i
$55$	−0.911672	+	0.911672i	−0.122930	+	0.122930i
$56$	−9.15664	+	5.62538i	−1.22361	+	0.751723i
$57$	−0.667116	−	0.667116i	−0.0883617	−	0.0883617i
$58$	1.55512	+	0.121804i	0.204197	+	0.0159936i
$59$	−1.39099	−	1.39099i	−0.181091	−	0.181091i	0.610740	−	0.791831i	$-0.290872\pi$
$59$	−1.39099	−	1.39099i	−0.181091	−	0.181091i	−0.791831	+	0.610740i	$0.790872\pi$
$60$	−0.724068	−	0.995024i	−0.0934768	−	0.128457i
$61$	0.396109	+	0.396109i	0.0507165	+	0.0507165i	0.732010	−	0.681294i	$-0.238582\pi$
$61$	0.396109	+	0.396109i	0.0507165	+	0.0507165i	−0.681294	+	0.732010i	$0.738582\pi$
$62$	0.715495	−	9.13503i	0.0908680	−	1.16015i
$63$		−	9.96003i		−	1.25485i
$64$	−3.61588	+	7.13621i	−0.451984	+	0.892026i
$65$			2.89437i			0.359003i
$66$	0.852821	−	0.728931i	0.104975	−	0.0897252i
$67$	−7.18162			−0.877374			−0.438687	−	0.898640i	$-0.644556\pi$
$67$	−7.18162			−0.877374			−0.438687	+	0.898640i	$0.644556\pi$
$68$	0.802526	+	1.10284i	0.0973206	+	0.133739i
$69$	0.663639	+	0.663639i	0.0798927	+	0.0798927i
$70$	−5.35688	−	0.419574i	−0.640270	−	0.0501487i
$71$			8.26090i			0.980388i	0.871613	+	0.490194i	$0.163074\pi$
$71$			8.26090i			0.980388i	−0.871613	+	0.490194i	$0.836926\pi$
$72$	−3.88116	−	6.31752i	−0.457399	−	0.744526i
$73$		−	14.2805i		−	1.67140i	−0.549183	−	0.835702i	$-0.685061\pi$
$73$		−	14.2805i		−	1.67140i	0.549183	−	0.835702i	$-0.314939\pi$
$74$	7.67515	−	3.88484i	0.892219	−	0.451604i
$75$		−	0.615294i		−	0.0710481i
$76$	−2.47962	+	1.80439i	−0.284431	+	0.206978i
$77$		−	4.89868i		−	0.558256i
$78$	0.196662	−	2.51087i	0.0222676	−	0.284300i
$79$	−1.41474	−	1.41474i	−0.159171	−	0.159171i	0.623028	−	0.782199i	$-0.285902\pi$
$79$	−1.41474	−	1.41474i	−0.159171	−	0.159171i	−0.782199	+	0.623028i	$0.785902\pi$
$80$	−3.56130	+	1.82131i	−0.398165	+	0.203628i
$81$	5.73604			0.637338
$82$	−3.98975	−	4.66785i	−0.440595	−	0.515478i
$83$		−	6.76042i		−	0.742052i	−0.928622	−	0.371026i	$-0.879006\pi$
$83$		−	6.76042i		−	0.742052i	0.928622	−	0.371026i	$-0.120994\pi$
$84$	4.61859	+	0.727962i	0.503930	+	0.0794272i
$85$			0.681966i			0.0739695i
$86$	−7.91732	−	0.620119i	−0.853747	−	0.0668692i
$87$	−0.479893	−	0.479893i	−0.0514499	−	0.0514499i
$88$	−1.90889	−	3.10717i	−0.203488	−	0.331225i
$89$	4.04522	+	4.04522i	0.428793	+	0.428793i	0.888217	−	0.459424i	$-0.151944\pi$
$89$	4.04522	+	4.04522i	0.428793	+	0.428793i	−0.459424	+	0.888217i	$0.651944\pi$
$90$	0.289480	−	3.69592i	0.0305139	−	0.389584i
$91$	−7.77615	−	7.77615i	−0.815162	−	0.815162i
$92$	2.46669	−	1.79498i	0.257170	−	0.187140i
$93$	−2.81897	+	2.81897i	−0.292314	+	0.292314i
$94$	−10.2611	−	12.0051i	−1.05835	−	1.23823i
$95$	−1.53332			−0.157316
$96$	3.21318	−	1.33801i	0.327944	−	0.136560i
$97$	−0.0212823	+	0.0212823i	−0.00216089	+	0.00216089i	−0.708186	−	0.706026i	$-0.750486\pi$
$97$	−0.0212823	+	0.0212823i	−0.00216089	+	0.00216089i	0.706026	+	0.708186i	$0.250486\pi$
$98$	7.99406	−	6.83276i	0.807522	−	0.690213i
$99$	3.37978			0.339681
$100$	−1.97561	−	0.311387i	−0.197561	−	0.0311387i
$101$			2.62491i			0.261188i	0.991436	+	0.130594i	$0.0416884\pi$
$101$			2.62491i			0.261188i	−0.991436	+	0.130594i	$0.958312\pi$
$102$	0.0463371	−	0.591606i	0.00458806	−	0.0585777i
$103$	−3.86584	+	3.86584i	−0.380912	+	0.380912i	−0.871431	−	0.490519i	$-0.836807\pi$
$103$	−3.86584	+	3.86584i	−0.380912	+	0.380912i	0.490519	+	0.871431i	$0.336807\pi$
$104$	−7.96247	−	1.90215i	−0.780785	−	0.186521i
$105$	1.65308	+	1.65308i	0.161324	+	0.161324i
$106$	−3.53141	+	3.01840i	−0.343001	+	0.293173i
$107$			4.98247i			0.481674i	0.970566	+	0.240837i	$0.0774219\pi$
$107$			4.98247i			0.481674i	−0.970566	+	0.240837i	$0.922578\pi$
$108$	−1.07703	+	6.83329i	−0.103638	+	0.657534i
$109$	5.49220	−	5.49220i	0.526057	−	0.526057i	−0.393337	−	0.919394i	$-0.628679\pi$
$109$	5.49220	−	5.49220i	0.526057	−	0.526057i	0.919394	+	0.393337i	$0.128679\pi$
$110$	0.142376	−	1.81778i	0.0135750	−	0.173318i
$111$	−3.63660	−	0.884816i	−0.345170	−	0.0839830i
$112$	4.67474	−	14.4611i	0.441721	−	1.36645i
$113$	7.17133	+	7.17133i	0.674622	+	0.674622i	0.958778	−	0.284156i	$-0.0917134\pi$
$113$	7.17133	+	7.17133i	0.674622	+	0.674622i	−0.284156	+	0.958778i	$0.591713\pi$
$114$	1.33016	+	0.104184i	0.124581	+	0.00975771i
$115$	1.52533			0.142238
$116$	−1.78372	+	1.29799i	−0.165614	+	0.120516i
$117$	5.36506	−	5.36506i	0.496000	−	0.496000i
$118$	2.77348	+	0.217231i	0.255320	+	0.0199978i
$119$	−1.83220	−	1.83220i	−0.167957	−	0.167957i
$120$	1.69269	+	0.404364i	0.154520	+	0.0369132i
$121$	−9.33771			−0.848883
$122$	−0.789798	−	0.0618605i	−0.0715050	−	0.00560058i
$123$			2.67165i			0.240894i
$124$	7.62465	+	10.4779i	0.684713	+	0.940942i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	9.15189	+	10.7073i	0.815315	+	0.953886i
$127$			3.99044i			0.354095i	0.984202	+	0.177047i	$0.0566545\pi$
$127$			3.99044i			0.354095i	−0.984202	+	0.177047i	$0.943345\pi$
$128$	−2.67000	−	10.9941i	−0.235997	−	0.971754i
$129$	2.44320	+	2.44320i	0.215112	+	0.215112i
$130$	−2.65953	−	3.11154i	−0.233256	−	0.272900i
$131$	−4.76334	+	4.76334i	−0.416175	+	0.416175i	−0.883883	−	0.467708i	$-0.845080\pi$
$131$	−4.76334	+	4.76334i	−0.416175	+	0.416175i	0.467708	+	0.883883i	$0.345080\pi$
$132$	−0.247023	+	1.56725i	−0.0215006	+	0.136411i
$133$	4.11949	−	4.11949i	0.357205	−	0.357205i
$134$	7.72047	−	6.59891i	0.666947	−	0.570059i
$135$	−2.44576	+	2.44576i	−0.210497	+	0.210497i
$136$	−1.87610	−	0.448180i	−0.160874	−	0.0384311i
$137$	19.7401			1.68651			0.843254	−	0.537515i	$-0.180637\pi$
$137$	19.7401			1.68651			0.843254	+	0.537515i	$0.180637\pi$
$138$	−1.32322	−	0.103641i	−0.112640	−	0.00882248i
$139$	−18.9693			−1.60896			−0.804478	−	0.593982i	$-0.797555\pi$
$139$	−18.9693			−1.60896			−0.804478	+	0.593982i	$0.797555\pi$
$140$	6.14435	−	4.47118i	0.519292	−	0.377883i
$141$			6.87112i			0.578652i
$142$	−7.59062	−	8.88073i	−0.636991	−	0.745254i
$143$	2.63872	−	2.63872i	0.220661	−	0.220661i
$144$	9.97730	+	3.22528i	0.831441	+	0.268773i
$145$	−1.10300			−0.0915993
$146$	13.1218	+	15.3520i	1.08597	+	1.27054i
$147$	−4.57540			−0.377373
$148$	−4.68140	+	11.2287i	−0.384809	+	0.922996i
$149$	11.0074			0.901764			0.450882	−	0.892584i	$-0.351109\pi$
$149$	11.0074			0.901764			0.450882	+	0.892584i	$0.351109\pi$
$150$	0.565370	+	0.661461i	0.0461623	+	0.0540081i
$151$	16.8387			1.37031			0.685155	−	0.728397i	$-0.259734\pi$
$151$	16.8387			1.37031			0.685155	+	0.728397i	$0.259734\pi$
$152$	1.00768	−	4.21820i	0.0817338	−	0.342141i
$153$	1.26410	−	1.26410i	0.102197	−	0.102197i
$154$	4.50120	+	5.26623i	0.362717	+	0.424365i
$155$			6.47922i			0.520424i
$156$	2.09572	+	2.87997i	0.167792	+	0.230582i
$157$	15.2829			1.21971			0.609855	−	0.792513i	$-0.291228\pi$
$157$	15.2829			1.21971			0.609855	+	0.792513i	$0.291228\pi$
$158$	2.82085	+	0.220941i	0.224415	+	0.0175771i
$159$	2.02120			0.160292
$160$	2.15498	−	5.23030i	0.170366	−	0.413492i
$161$	−4.09802	+	4.09802i	−0.322969	+	0.322969i
$162$	−6.16643	+	5.27063i	−0.484481	+	0.414100i
$163$	−2.64285	+	2.64285i	−0.207004	+	0.207004i	−0.802993	−	0.595989i	$-0.796760\pi$
$163$	−2.64285	+	2.64285i	−0.207004	+	0.207004i	0.595989	+	0.802993i	$0.296760\pi$
$164$	8.57822	+	1.35206i	0.669847	+	0.105578i
$165$	−0.560947	+	0.560947i	−0.0436696	+	0.0436696i
$166$	6.21189	+	7.26767i	0.482136	+	0.564080i
$167$	10.4117	+	10.4117i	0.805685	+	0.805685i	0.983978	−	0.178292i	$-0.0570572\pi$
$167$	10.4117	+	10.4117i	0.805685	+	0.805685i	−0.178292	+	0.983978i	$0.557057\pi$
$168$	−5.63403	+	3.46126i	−0.434675	+	0.267042i
$169$			4.62261i			0.355585i
$170$	−0.626632	−	0.733135i	−0.0480605	−	0.0562289i
$171$	2.84220	+	2.84220i	0.217348	+	0.217348i
$172$	9.08118	−	6.60827i	0.692433	−	0.503876i
$173$		−	15.1003i		−	1.14806i	−0.818836	−	0.574028i	$-0.805380\pi$
$173$		−	15.1003i		−	1.14806i	0.818836	−	0.574028i	$-0.194620\pi$
$174$	0.956855	+	0.0749450i	0.0725390	+	0.00568157i
$175$	3.79949			0.287214
$176$	4.90717	+	1.58630i	0.369892	+	0.119572i
$177$	−0.855868	−	0.855868i	−0.0643310	−	0.0643310i
$178$	−8.06575	−	0.631745i	−0.604553	−	0.0473513i
$179$	5.40899	−	5.40899i	0.404287	−	0.404287i	−0.475454	−	0.879741i	$-0.657716\pi$
$179$	5.40899	−	5.40899i	0.404287	−	0.404287i	0.879741	+	0.475454i	$0.157716\pi$
$180$	3.08484	+	4.23922i	0.229930	+	0.315973i
$181$	−19.4221			−1.44363			−0.721817	−	0.692084i	$-0.756693\pi$
$181$	−19.4221			−1.44363			−0.721817	+	0.692084i	$0.756693\pi$
$182$	15.5048	+	1.21440i	1.14929	+	0.0900177i
$183$	0.243723	+	0.243723i	0.0180166	+	0.0180166i
$184$	−1.00243	+	4.19621i	−0.0739000	+	0.309349i
$185$	−5.19608	+	3.16239i	−0.382024	+	0.232504i
$186$	0.440240	−	5.62073i	0.0322800	−	0.412132i
$187$	0.621729	−	0.621729i	0.0454653	−	0.0454653i
$188$	22.0620	+	3.47732i	1.60904	+	0.253610i
$189$		−	13.1418i		−	0.955922i
$190$	1.64837	−	1.40891i	0.119585	−	0.102213i
$191$	4.01795	+	4.01795i	0.290729	+	0.290729i	0.837368	−	0.546639i	$-0.184093\pi$
$191$	4.01795	+	4.01795i	0.290729	+	0.290729i	−0.546639	+	0.837368i	$0.684093\pi$
$192$	−2.22483	+	4.39087i	−0.160563	+	0.316884i
$193$	−15.9909	+	15.9909i	−1.15105	+	1.15105i	−0.164704	+	0.986343i	$0.552667\pi$
$193$	−15.9909	+	15.9909i	−1.15105	+	1.15105i	−0.986343	+	0.164704i	$0.947333\pi$
$194$	0.00332366	−	0.0424346i	0.000238625	−	0.00304662i
$195$			1.78089i			0.127532i
$196$	−2.31551	+	14.6909i	−0.165394	+	1.04935i
$197$	16.8129			1.19787			0.598934	−	0.800799i	$-0.295591\pi$
$197$	16.8129			1.19787			0.598934	+	0.800799i	$0.295591\pi$
$198$	−3.63338	+	3.10555i	−0.258213	+	0.220702i
$199$	12.1507	−	12.1507i	0.861342	−	0.861342i	−0.130152	−	0.991494i	$-0.541547\pi$
$199$	12.1507	−	12.1507i	0.861342	−	0.861342i	0.991494	+	0.130152i	$0.0415466\pi$
$200$	2.40997	−	1.48056i	0.170410	−	0.104692i
$201$	−4.41881			−0.311679
$202$	−2.41193	−	2.82186i	−0.169702	−	0.198545i
$203$	2.96337	−	2.96337i	0.207988	−	0.207988i
$204$	0.493790	+	0.678572i	0.0345722	+	0.0475096i
$205$	3.07030	+	3.07030i	0.214439	+	0.214439i
$206$	0.603729	−	7.70807i	0.0420638	−	0.537046i
$207$	−2.82738	−	2.82738i	−0.196516	−	0.196516i
$208$	10.3077	−	5.27154i	0.714712	−	0.365515i
$209$	1.39789	+	1.39789i	0.0966939	+	0.0966939i
$210$	−3.29606	−	0.258162i	−0.227450	−	0.0178149i
$211$		−	26.9632i		−	1.85622i	−0.372303	−	0.928111i	$-0.621432\pi$
$211$		−	26.9632i		−	1.85622i	0.372303	−	0.928111i	$-0.378568\pi$
$212$	1.02289	−	6.48975i	0.0702522	−	0.445718i
$213$			5.08288i			0.348273i
$214$	−4.57820	−	5.35632i	−0.312959	−	0.366150i
$215$	5.61554			0.382976
$216$	−5.12100	−	8.33565i	−0.348440	−	0.567169i
$217$	−17.4074	−	17.4074i	−1.18169	−	1.18169i
$218$	−0.857719	+	10.9509i	−0.0580921	+	0.741686i
$219$		−	8.78670i		−	0.593750i
$220$	1.51723	+	2.08499i	0.102291	+	0.140570i
$221$		−	1.97386i		−	0.132776i
$222$	4.72248	−	2.39032i	0.316952	−	0.160428i
$223$		−	6.22149i		−	0.416622i	−0.978063	−	0.208311i	$-0.933203\pi$
$223$		−	6.22149i		−	0.416622i	0.978063	−	0.208311i	$-0.0667965\pi$
$224$	8.26229	+	19.8416i	0.552048	+	1.32572i
$225$			2.62141i			0.174761i
$226$	−14.2989	−	1.11995i	−0.951147	−	0.0744980i
$227$	15.8281	+	15.8281i	1.05055	+	1.05055i	0.998652	+	0.0518970i	$0.0165268\pi$
$227$	15.8281	+	15.8281i	1.05055	+	1.05055i	0.0518970	+	0.998652i	$0.483473\pi$
$228$	−1.52569	+	1.11023i	−0.101042	+	0.0735268i
$229$	28.9936			1.91595			0.957975	−	0.286852i	$-0.0926088\pi$
$229$	28.9936			1.91595			0.957975	+	0.286852i	$0.0926088\pi$
$230$	−1.63978	+	1.40157i	−0.108124	+	0.0924166i
$231$		−	3.01413i		−	0.198315i
$232$	0.724880	−	3.03438i	0.0475907	−	0.199217i
$233$		−	28.2070i		−	1.84790i	−0.382513	−	0.923950i	$-0.624941\pi$
$233$		−	28.2070i		−	1.84790i	0.382513	−	0.923950i	$-0.375059\pi$
$234$	−0.837864	+	10.6974i	−0.0547729	+	0.699309i
$235$	7.89641	+	7.89641i	0.515105	+	0.515105i
$236$	−3.18119	+	2.31492i	−0.207078	+	0.150688i
$237$	−0.870484	−	0.870484i	−0.0565440	−	0.0565440i
$238$	3.65321	+	0.286135i	0.236802	+	0.0185474i
$239$	−12.1066	−	12.1066i	−0.783112	−	0.783112i	0.197243	−	0.980355i	$-0.436801\pi$
$239$	−12.1066	−	12.1066i	−0.783112	−	0.783112i	−0.980355	+	0.197243i	$0.936801\pi$
$240$	−2.19125	+	1.12064i	−0.141444	+	0.0723370i
$241$	−13.7429	+	13.7429i	−0.885256	+	0.885256i	−0.994063	−	0.108807i	$-0.965297\pi$
$241$	−13.7429	+	13.7429i	−0.885256	+	0.885256i	0.108807	+	0.994063i	$0.465297\pi$
$242$	10.0383	−	8.58006i	0.645289	−	0.551547i
$243$	13.9058			0.892059
$244$	0.905900	−	0.659213i	0.0579943	−	0.0422018i
$245$	−5.25813	+	5.25813i	−0.335929	+	0.335929i
$246$	−2.45487	−	2.87210i	−0.156517	−	0.183119i
$247$	4.43801			0.282384
$248$	−17.8245	−	4.25807i	−1.13185	−	0.270388i
$249$		−	4.15965i		−	0.263607i
$250$	1.40990	+	0.110429i	0.0891696	+	0.00698415i
$251$	−12.2371	+	12.2371i	−0.772400	+	0.772400i	−0.978526	−	0.206125i	$-0.933915\pi$
$251$	−12.2371	+	12.2371i	−0.772400	+	0.772400i	0.206125	+	0.978526i	$0.433915\pi$
$252$	−19.6771	−	3.10143i	−1.23954	−	0.195371i
$253$	−1.39060	−	1.39060i	−0.0874263	−	0.0874263i
$254$	−3.66666	−	4.28985i	−0.230067	−	0.269169i
$255$			0.419610i			0.0262770i
$256$	12.9724	+	9.36569i	0.810777	+	0.585355i
$257$	5.01406	−	5.01406i	0.312769	−	0.312769i	−0.533213	−	0.845981i	$-0.679015\pi$
$257$	5.01406	−	5.01406i	0.312769	−	0.312769i	0.845981	+	0.533213i	$0.179015\pi$
$258$	−4.87148	−	0.381556i	−0.303285	−	0.0237546i
$259$	5.46380	−	22.4562i	0.339504	−	1.39536i
$260$	5.71815	+	0.901271i	0.354625	+	0.0558944i
$261$	2.04454	+	2.04454i	0.126554	+	0.126554i
$262$	0.743893	−	9.49759i	0.0459579	−	0.586763i
$263$	−8.59046			−0.529711			−0.264855	−	0.964288i	$-0.585324\pi$
$263$	−8.59046			−0.529711			−0.264855	+	0.964288i	$0.585324\pi$
$264$	−1.17453	−	1.91182i	−0.0722871	−	0.117665i
$265$	2.32280	−	2.32280i	0.142688	−	0.142688i
$266$	−0.643343	+	8.21383i	−0.0394459	+	0.503622i
$267$	2.48900	+	2.48900i	0.152325	+	0.152325i
$268$	−2.23626	+	14.1881i	−0.136602	+	0.866675i
$269$	−2.78784			−0.169978			−0.0849888	−	0.996382i	$-0.527085\pi$
$269$	−2.78784			−0.169978			−0.0849888	+	0.996382i	$0.527085\pi$
$270$	0.381955	−	4.87658i	0.0232450	−	0.296779i
$271$		−	11.3856i		−	0.691629i	−0.938303	−	0.345814i	$-0.887603\pi$
$271$		−	11.3856i		−	0.691629i	0.938303	−	0.345814i	$-0.112397\pi$
$272$	2.42868	−	1.24207i	0.147261	−	0.0753114i
$273$	−4.78462	−	4.78462i	−0.289578	−	0.289578i
$274$	−21.2212	+	18.1384i	−1.28202	+	1.09578i
$275$			1.28930i			0.0777476i
$276$	1.51774	−	1.10444i	0.0913572	−	0.0664797i
$277$	−2.84695	−	2.84695i	−0.171057	−	0.171057i	0.616387	−	0.787444i	$-0.288596\pi$
$277$	−2.84695	−	2.84695i	−0.171057	−	0.171057i	−0.787444	+	0.616387i	$0.788596\pi$
$278$	20.3926	−	17.4302i	1.22307	−	1.04539i
$279$	12.0100	−	12.0100i	0.719021	−	0.719021i
$280$	−2.49698	+	10.4525i	−0.149223	+	0.624654i
$281$	1.19742	−	1.19742i	0.0714320	−	0.0714320i	−0.670488	−	0.741920i	$-0.733915\pi$
$281$	1.19742	−	1.19742i	0.0714320	−	0.0714320i	0.741920	+	0.670488i	$0.233915\pi$
$282$	−6.31360	−	7.38667i	−0.375970	−	0.439870i
$283$	−4.15097	+	4.15097i	−0.246750	+	0.246750i	−0.819635	−	0.572886i	$-0.805824\pi$
$283$	−4.15097	+	4.15097i	−0.246750	+	0.246750i	0.572886	+	0.819635i	$0.305824\pi$
$284$	16.3203	+	2.57234i	0.968432	+	0.152640i
$285$	−0.943445			−0.0558848
$286$	−0.412090	+	5.26132i	−0.0243674	+	0.311109i
$287$	−16.4976			−0.973823
$288$	−13.6895	+	5.70047i	−0.806661	+	0.335904i
$289$			16.5349i			0.972643i
$290$	1.18576	−	1.01351i	0.0696303	−	0.0595151i
$291$	−0.0130949	+	0.0130949i	−0.000767634	+	0.000767634i
$292$	−28.2127	−	4.44676i	−1.65102	−	0.260227i
$293$	10.1319			0.591910			0.295955	−	0.955202i	$-0.404362\pi$
$293$	10.1319			0.591910			0.295955	+	0.955202i	$0.404362\pi$
$294$	4.91870	−	4.20416i	0.286864	−	0.245192i
$295$	−1.96716			−0.114532
$296$	−5.28499	−	16.3728i	−0.307184	−	0.951650i
$297$	4.45946			0.258764
$298$	−11.8333	+	10.1143i	−0.685487	+	0.585906i
$299$	−4.41487			−0.255319
$300$	−1.21558	−	0.191595i	−0.0701817	−	0.0110617i
$301$	−15.0870	+	15.0870i	−0.869597	+	0.869597i
$302$	−18.1021	+	15.4724i	−1.04166	+	0.890336i
$303$			1.61509i			0.0927845i
$304$	2.79265	+	5.46062i	0.160169	+	0.313188i
$305$	0.560182			0.0320759
$306$	−0.197416	+	2.52049i	−0.0112855	+	0.144087i
$307$	22.0225			1.25689			0.628445	−	0.777854i	$-0.283692\pi$
$307$	22.0225			1.25689			0.628445	+	0.777854i	$0.283692\pi$
$308$	−9.67788	−	1.52538i	−0.551448	−	0.0869169i
$309$	−2.37863	+	2.37863i	−0.135315	+	0.135315i
$310$	−5.95351	−	6.96537i	−0.338137	−	0.395607i
$311$	17.8591	−	17.8591i	1.01270	−	1.01270i	0.0127805	−	0.999918i	$-0.495932\pi$
$311$	17.8591	−	17.8591i	1.01270	−	1.01270i	0.999918	−	0.0127805i	$-0.00406827\pi$
$312$	−4.89926	−	1.17038i	−0.277366	−	0.0662598i
$313$	−16.7487	+	16.7487i	−0.946695	+	0.946695i	−0.998649	−	0.0519544i	$-0.983455\pi$
$313$	−16.7487	+	16.7487i	−0.946695	+	0.946695i	0.0519544	+	0.998649i	$0.483455\pi$
$314$	−16.4296	+	14.0429i	−0.927178	+	0.792487i
$315$	−7.04280	−	7.04280i	−0.396817	−	0.396817i
$316$	−3.23552	+	2.35445i	−0.182012	+	0.132448i
$317$			1.64636i			0.0924689i	0.998931	+	0.0462345i	$0.0147221\pi$
$317$			1.64636i			0.0924689i	−0.998931	+	0.0462345i	$0.985278\pi$
$318$	−2.17286	+	1.85720i	−0.121848	+	0.104147i
$319$	1.00558	+	1.00558i	0.0563014	+	0.0563014i
$320$	2.48925	+	7.60287i	0.139153	+	0.425013i
$321$			3.06569i			0.171110i
$322$	0.639989	−	8.17101i	0.0356652	−	0.455353i
$323$	1.04567			0.0581828
$324$	1.78613	−	11.3322i	0.0992295	−	0.629566i
$325$	2.04663	+	2.04663i	0.113527	+	0.113527i
$326$	0.412735	−	5.26956i	0.0228593	−	0.291854i
$327$	3.37932	−	3.37932i	0.186877	−	0.186877i
$328$	−10.4642	+	6.42869i	−0.577790	+	0.354965i
$329$	−42.4297			−2.33922
$330$	0.0876033	−	1.11847i	0.00482240	−	0.0615696i
$331$	2.02323	+	2.02323i	0.111207	+	0.111207i	0.760520	−	0.649314i	$-0.224944\pi$
$331$	2.02323	+	2.02323i	0.111207	+	0.111207i	−0.649314	+	0.760520i	$0.724944\pi$
$332$	−13.3560	−	2.10511i	−0.733003	−	0.115533i
$333$	15.4934	+	3.76969i	0.849035	+	0.206578i
$334$	−20.7599	−	1.62601i	−1.13593	−	0.0889712i
$335$	−5.07817	+	5.07817i	−0.277450	+	0.277450i
$336$	2.87634	−	8.89786i	0.156917	−	0.485418i
$337$			12.7710i			0.695683i	0.937553	+	0.347842i	$0.113085\pi$
$337$			12.7710i			0.695683i	−0.937553	+	0.347842i	$0.886915\pi$
$338$	−4.24754	−	4.96945i	−0.231035	−	0.270302i
$339$	4.41248	+	4.41248i	0.239653	+	0.239653i
$340$	1.34730	+	0.212355i	0.0730675	+	0.0115166i
$341$	5.90693	−	5.90693i	0.319878	−	0.319878i
$342$	−5.66704	−	0.443867i	−0.306438	−	0.0240016i
$343$		−	1.65701i		−	0.0894704i
$344$	−3.69047	+	15.4484i	−0.198977	+	0.832924i
$345$	0.938527			0.0505286
$346$	13.8751	+	16.2333i	0.745930	+	0.872709i
$347$	−6.34871	+	6.34871i	−0.340817	+	0.340817i	−0.856674	−	0.515858i	$-0.827473\pi$
$347$	−6.34871	+	6.34871i	−0.340817	+	0.340817i	0.515858	+	0.856674i	$0.327473\pi$
$348$	−1.09751	+	0.798649i	−0.0588329	+	0.0428121i
$349$	12.8596			0.688358			0.344179	−	0.938904i	$-0.388157\pi$
$349$	12.8596			0.688358			0.344179	+	0.938904i	$0.388157\pi$
$350$	−4.08457	+	3.49120i	−0.218330	+	0.186613i
$351$	7.07893	−	7.07893i	0.377846	−	0.377846i
$352$	−6.73295	+	2.80368i	−0.358868	+	0.149437i
$353$	18.9558	+	18.9558i	1.00892	+	1.00892i	0.999960	+	0.00895814i	$0.00285150\pi$
$353$	18.9558	+	18.9558i	1.00892	+	1.00892i	0.00895814	+	0.999960i	$0.497148\pi$
$354$	1.70651	+	0.133661i	0.0906999	+	0.00710402i
$355$	5.84134	+	5.84134i	0.310026	+	0.310026i
$356$	9.25142	−	6.73216i	0.490324	−	0.356804i
$357$	−1.12734	−	1.12734i	−0.0596652	−	0.0596652i
$358$	−0.844725	+	10.7850i	−0.0446451	+	0.570002i
$359$		−	13.3600i		−	0.705113i	−0.935790	−	0.352557i	$-0.885312\pi$
$359$		−	13.3600i		−	0.705113i	0.935790	−	0.352557i	$-0.114688\pi$
$360$	−7.21156	−	1.72276i	−0.380082	−	0.0907975i
$361$		−	16.6489i		−	0.876259i
$362$	20.8794	−	17.8462i	1.09740	−	0.937977i
$363$	−5.74544			−0.301557
$364$	−17.7840	+	12.9413i	−0.932137	+	0.678306i
$365$	−10.0978	−	10.0978i	−0.528545	−	0.528545i
$366$	−0.485959	−	0.0380624i	−0.0254015	−	0.00198955i
$367$			14.5379i			0.758873i	0.925218	+	0.379436i	$0.123882\pi$
$367$			14.5379i			0.758873i	−0.925218	+	0.379436i	$0.876118\pi$
$368$	−2.77809	−	5.43215i	−0.144818	−	0.283171i
$369$		−	11.3823i		−	0.592541i
$370$	2.68016	−	8.17415i	0.139335	−	0.424954i
$371$			12.4811i			0.647985i
$372$	4.69140	+	6.44699i	0.243238	+	0.334261i
$373$			19.0877i			0.988326i	0.869369	+	0.494163i	$0.164525\pi$
$373$			19.0877i			0.988326i	−0.869369	+	0.494163i	$0.835475\pi$
$374$	−0.0970956	+	1.23966i	−0.00502070	+	0.0641013i
$375$	−0.435079	−	0.435079i	−0.0224674	−	0.0224674i
$376$	−26.9126	+	16.5337i	−1.38791	+	0.852662i
$377$	3.19250			0.164422
$378$	12.0755	+	14.1278i	0.621095	+	0.726656i
$379$		−	17.1511i		−	0.880995i	−0.897754	−	0.440497i	$-0.854802\pi$
$379$		−	17.1511i		−	0.880995i	0.897754	−	0.440497i	$-0.145198\pi$
$380$	−0.477457	+	3.02925i	−0.0244930	+	0.155397i
$381$			2.45530i			0.125789i
$382$	−8.01137	−	0.627485i	−0.409897	−	0.0321049i
$383$	−17.9283	−	17.9283i	−0.916096	−	0.916096i	0.0806470	−	0.996743i	$-0.474301\pi$
$383$	−17.9283	−	17.9283i	−0.916096	−	0.916096i	−0.996743	+	0.0806470i	$0.974301\pi$
$384$	−1.64284	−	6.76463i	−0.0838357	−	0.345206i
$385$	−3.46389	−	3.46389i	−0.176536	−	0.176536i
$386$	2.49730	−	31.8841i	0.127109	−	1.62286i
$387$	−10.4091	−	10.4091i	−0.529123	−	0.529123i
$388$	0.0354184	+	0.0486725i	0.00179810	+	0.00247097i
$389$	−5.51362	+	5.51362i	−0.279552	+	0.279552i	−0.832930	−	0.553378i	$-0.813338\pi$
$389$	−5.51362	+	5.51362i	−0.279552	+	0.279552i	0.553378	+	0.832930i	$0.313338\pi$
$390$	−1.63639	−	1.91451i	−0.0828619	−	0.0969452i
$391$	−1.04022			−0.0526063
$392$	−11.0096	−	17.9208i	−0.556070	−	0.905136i
$393$	−2.93086	+	2.93086i	−0.147842	+	0.147842i
$394$	−18.0744	+	15.4487i	−0.910574	+	0.778294i
$395$	−2.00075			−0.100669
$396$	1.05242	−	6.67714i	0.0528862	−	0.335539i
$397$		−	11.9756i		−	0.601036i	−0.953776	−	0.300518i	$-0.902840\pi$
$397$		−	11.9756i		−	0.601036i	0.953776	−	0.300518i	$-0.0971595\pi$
$398$	−1.89758	+	24.2272i	−0.0951173	+	1.21440i
$399$	2.53470	−	2.53470i	0.126894	−	0.126894i
$400$	−1.23036	+	3.80608i	−0.0615180	+	0.190304i
$401$	−19.4322	−	19.4322i	−0.970398	−	0.970398i	0.0291764	−	0.999574i	$-0.490712\pi$
$401$	−19.4322	−	19.4322i	−0.970398	−	0.970398i	−0.999574	+	0.0291764i	$0.990712\pi$
$402$	4.75036	−	4.06027i	0.236926	−	0.202508i
$403$		−	18.7533i		−	0.934168i
$404$	5.18579	+	0.817362i	0.258003	+	0.0406653i
$405$	4.05600	−	4.05600i	0.201544	−	0.201544i
$406$	−0.462791	+	5.90865i	−0.0229679	+	0.293241i
$407$	7.62019	+	1.85406i	0.377719	+	0.0919023i
$408$	−1.15435	−	0.275763i	−0.0571490	−	0.0136523i
$409$	−17.1369	−	17.1369i	−0.847365	−	0.847365i	0.142439	−	0.989804i	$-0.454506\pi$
$409$	−17.1369	−	17.1369i	−0.847365	−	0.847365i	−0.989804	+	0.142439i	$0.954506\pi$
$410$	−6.12185	−	0.479490i	−0.302337	−	0.0236803i
$411$	12.1460			0.599116
$412$	6.43362	+	8.84116i	0.316962	+	0.435573i
$413$	5.28505	−	5.28505i	0.260060	−	0.260060i
$414$	5.63749	+	0.441553i	0.277068	+	0.0217012i
$415$	−4.78034	−	4.78034i	−0.234658	−	0.234658i
$416$	−6.23732	+	15.1384i	−0.305810	+	0.742223i
$417$	−11.6717			−0.571566
$418$	−2.78724	−	0.218309i	−0.136328	−	0.0106778i
$419$			6.67619i			0.326153i	0.986613	+	0.163077i	$0.0521418\pi$
$419$			6.67619i			0.326153i	−0.986613	+	0.163077i	$0.947858\pi$
$420$	3.78058	−	2.75109i	0.184474	−	0.134239i
$421$	20.0281	+	20.0281i	0.976109	+	0.976109i	0.999721	−	0.0236118i	$-0.00751658\pi$
$421$	20.0281	+	20.0281i	0.976109	+	0.976109i	−0.0236118	+	0.999721i	$0.507517\pi$
$422$	24.7754	+	28.9863i	1.20605	+	1.41103i
$423$		−	29.2739i		−	1.42334i
$424$	4.86355	+	7.91658i	0.236195	+	0.384463i
$425$	0.482222	+	0.482222i	0.0233912	+	0.0233912i
$426$	−4.67046	−	5.46426i	−0.226285	−	0.264744i
$427$	−1.50501	+	1.50501i	−0.0728326	+	0.0728326i
$428$	9.84343	+	1.55148i	0.475800	+	0.0749935i
$429$	1.62359	−	1.62359i	0.0783876	−	0.0783876i
$430$	−6.03688	+	5.15990i	−0.291124	+	0.248833i
$431$	−11.6621	+	11.6621i	−0.561744	+	0.561744i	−0.929803	−	0.368059i	$-0.880023\pi$
$431$	−11.6621	+	11.6621i	−0.561744	+	0.561744i	0.368059	+	0.929803i	$0.380023\pi$
$432$	13.1645	+	4.25560i	0.633379	+	0.204748i
$433$	−40.2202			−1.93286			−0.966431	−	0.256928i	$-0.917290\pi$
$433$	−40.2202			−1.93286			−0.966431	+	0.256928i	$0.917290\pi$
$434$	34.7084	+	2.71852i	1.66606	+	0.130493i
$435$	−0.678671			−0.0325398
$436$	−9.14025	−	12.5606i	−0.437738	−	0.601546i
$437$		−	2.33882i		−	0.111881i
$438$	8.07376	+	9.44599i	0.385779	+	0.451347i
$439$	−7.12323	+	7.12323i	−0.339973	+	0.339973i	−0.856357	−	0.516384i	$-0.827278\pi$
$439$	−7.12323	+	7.12323i	−0.339973	+	0.339973i	0.516384	+	0.856357i	$0.327278\pi$
$440$	−3.54688	−	0.847312i	−0.169091	−	0.0403940i
$441$	19.4931			0.928244
$442$	1.81371	+	2.12196i	0.0862692	+	0.100932i
$443$	−15.2038			−0.722355			−0.361177	−	0.932497i	$-0.617625\pi$
$443$	−15.2038			−0.722355			−0.361177	+	0.932497i	$0.617625\pi$
$444$	−2.88044	+	6.90898i	−0.136700	+	0.327886i
$445$	5.72081			0.271192
$446$	5.71668	+	6.68830i	0.270693	+	0.316700i
$447$	6.77281			0.320343
$448$	−27.1139	−	13.7385i	−1.28101	−	0.649082i
$449$	−28.1784	+	28.1784i	−1.32982	+	1.32982i	−0.424296	+	0.905524i	$0.639478\pi$
$449$	−28.1784	+	28.1784i	−1.32982	+	1.32982i	−0.905524	+	0.424296i	$0.860522\pi$
$450$	−2.40872	−	2.81810i	−0.113548	−	0.132847i
$451$		−	5.59821i		−	0.263610i
$452$	16.4008	−	11.9347i	0.771430	−	0.561361i
$453$	10.3607			0.486790
$454$	−31.5596	−	2.47188i	−1.48116	−	0.116011i
$455$	−10.9971			−0.515554
$456$	0.620021	−	2.59543i	0.0290351	−	0.121542i
$457$	−18.9496	+	18.9496i	−0.886425	+	0.886425i	−0.994178	−	0.107752i	$-0.965635\pi$
$457$	−18.9496	+	18.9496i	−0.886425	+	0.886425i	0.107752	+	0.994178i	$0.465635\pi$
$458$	−31.1690	+	26.6411i	−1.45643	+	1.24486i
$459$	1.66792	−	1.66792i	0.0778519	−	0.0778519i
$460$	0.474968	−	3.01346i	0.0221455	−	0.140503i
$461$	2.98278	−	2.98278i	0.138922	−	0.138922i	−0.634226	−	0.773148i	$-0.718681\pi$
$461$	2.98278	−	2.98278i	0.138922	−	0.138922i	0.773148	+	0.634226i	$0.218681\pi$
$462$	2.76957	+	3.24028i	0.128852	+	0.150752i
$463$	−9.13928	−	9.13928i	−0.424738	−	0.424738i	0.462093	−	0.886831i	$-0.347099\pi$
$463$	−9.13928	−	9.13928i	−0.424738	−	0.424738i	−0.886831	+	0.462093i	$0.847099\pi$
$464$	2.00890	+	3.92812i	0.0932610	+	0.182358i
$465$			3.98663i			0.184876i
$466$	25.9183	+	30.3234i	1.20064	+	1.40470i
$467$	12.2178	+	12.2178i	0.565371	+	0.565371i	0.930828	−	0.365457i	$-0.119087\pi$
$467$	12.2178	+	12.2178i	0.565371	+	0.565371i	−0.365457	+	0.930828i	$0.619087\pi$
$468$	−8.92867	−	12.2699i	−0.412728	−	0.567176i
$469$		−	27.2865i		−	1.25997i
$470$	−15.7446	−	1.23318i	−0.726244	−	0.0568826i
$471$	9.40350			0.433291
$472$	1.29279	−	5.41168i	0.0595056	−	0.249093i
$473$	−5.11953	−	5.11953i	−0.235396	−	0.235396i
$474$	1.73565	+	0.135944i	0.0797211	+	0.00624411i
$475$	−1.08422	+	1.08422i	−0.0497476	+	0.0497476i
$476$	−4.19023	+	3.04919i	−0.192059	+	0.139759i
$477$	−8.61117			−0.394279
$478$	24.1393	+	1.89070i	1.10411	+	0.0864784i
$479$	3.39874	+	3.39874i	0.155292	+	0.155292i	0.780477	−	0.625185i	$-0.214976\pi$
$479$	3.39874	+	3.39874i	0.155292	+	0.155292i	−0.625185	+	0.780477i	$0.714976\pi$
$480$	1.32595	−	3.21818i	0.0605209	−	0.146889i
$481$	15.0394	−	9.15314i	0.685738	−	0.417347i
$482$	2.14623	−	27.4018i	0.0977581	−	1.24812i
$483$	−2.52149	+	2.52149i	−0.114732	+	0.114732i
$484$	−2.90764	+	18.4477i	−0.132166	+	0.838531i
$485$			0.0300977i			0.00136666i
$486$	−14.9492	+	12.7775i	−0.678110	+	0.579600i
$487$	26.2429	+	26.2429i	1.18918	+	1.18918i	0.977294	+	0.211887i	$0.0679609\pi$
$487$	26.2429	+	26.2429i	1.18918	+	1.18918i	0.211887	+	0.977294i	$0.432039\pi$
$488$	−0.368145	+	1.54107i	−0.0166652	+	0.0697610i
$489$	−1.62613	+	1.62613i	−0.0735361	+	0.0735361i
$490$	0.821164	−	10.4841i	0.0370964	−	0.473625i
$491$			17.7808i			0.802435i	0.915983	+	0.401217i	$0.131413\pi$
$491$			17.7808i			0.802435i	−0.915983	+	0.401217i	$0.868587\pi$
$492$	5.27813	+	0.831916i	0.237957	+	0.0375057i
$493$	0.752209			0.0338778
$494$	−4.77100	+	4.07791i	−0.214657	+	0.183474i
$495$	2.38987	−	2.38987i	0.107417	−	0.107417i
$496$	23.0744	−	11.8007i	1.03607	−	0.529865i
$497$	−31.3872			−1.40791
$498$	3.82214	+	4.47175i	0.171274	+	0.200384i
$499$	−21.4887	+	21.4887i	−0.961966	+	0.961966i	−0.999303	−	0.0373366i	$-0.988113\pi$
$499$	−21.4887	+	21.4887i	−0.961966	+	0.961966i	0.0373366	+	0.999303i	$0.488113\pi$
$500$	−1.61715	+	1.17678i	−0.0723212	+	0.0526274i
$501$	6.40629	+	6.40629i	0.286212	+	0.286212i
$502$	1.91108	−	24.3995i	0.0852955	−	1.08900i
$503$	−19.5798	−	19.5798i	−0.873019	−	0.873019i	0.119781	−	0.992800i	$-0.461781\pi$
$503$	−19.5798	−	19.5798i	−0.873019	−	0.873019i	−0.992800	+	0.119781i	$0.961781\pi$
$504$	24.0033	−	14.7464i	1.06919	−	0.656858i
$505$	1.85609	+	1.85609i	0.0825949	+	0.0825949i
$506$	2.77271	+	0.217171i	0.123262	+	0.00965441i
$507$			2.84426i			0.126318i
$508$	7.88356	+	1.24257i	0.349776	+	0.0551302i
$509$		−	11.6048i		−	0.514372i	−0.966362	−	0.257186i	$-0.917205\pi$
$509$		−	11.6048i		−	0.514372i	0.966362	−	0.257186i	$-0.0827953\pi$
$510$	−0.385563	−	0.451094i	−0.0170730	−	0.0199748i
$511$	54.2585			2.40026
$512$	−22.5515	+	1.85145i	−0.996647	+	0.0818235i
$513$	3.75014	+	3.75014i	0.165573	+	0.165573i
$514$	−0.783048	+	9.99750i	−0.0345388	+	0.440971i
$515$			5.46712i			0.240910i
$516$	5.58760	−	4.06603i	0.245980	−	0.178997i
$517$		−	14.3979i		−	0.633217i
$518$	14.7604	+	29.1617i	0.648535	+	1.28129i
$519$		−	9.29114i		−	0.407836i
$520$	−6.97534	+	4.28530i	−0.305889	+	0.187923i
$521$		−	28.0050i		−	1.22692i	−0.789725	−	0.613461i	$-0.789777\pi$
$521$		−	28.0050i		−	1.22692i	0.789725	−	0.613461i	$-0.210223\pi$
$522$	−4.07660	−	0.319297i	−0.178428	−	0.0139753i
$523$	21.6362	+	21.6362i	0.946084	+	0.946084i	0.998619	−	0.0525348i	$-0.0167300\pi$
$523$	21.6362	+	21.6362i	0.946084	+	0.946084i	−0.0525348	+	0.998619i	$0.516730\pi$
$524$	7.92726	+	10.8937i	0.346304	+	0.475896i
$525$	2.33780			0.102030
$526$	9.23502	−	7.89344i	0.402666	−	0.344171i
$527$		−	4.41861i		−	0.192478i
$528$	3.01935	+	0.976042i	0.131400	+	0.0424768i
$529$		−	20.6734i		−	0.898842i
$530$	−0.362753	+	4.63142i	−0.0157570	+	0.201176i
$531$	3.64636	+	3.64636i	0.158238	+	0.158238i
$532$	−6.85576	−	9.42127i	−0.297235	−	0.408464i
$533$	−8.88660	−	8.88660i	−0.384921	−	0.384921i
$534$	−4.96281	−	0.388709i	−0.214762	−	0.0168211i
$535$	3.52314	+	3.52314i	0.152319	+	0.152319i
$536$	−10.6328	−	17.3075i	−0.459268	−	0.747568i
$537$	3.32812	−	3.32812i	0.143619	−	0.143619i
$538$	2.99702	−	2.56164i	0.129211	−	0.110440i
$539$	9.58737			0.412957
$540$	4.07029	+	5.59344i	0.175157	+	0.240703i
$541$	6.18325	−	6.18325i	0.265839	−	0.265839i	−0.561582	−	0.827421i	$-0.689807\pi$
$541$	6.18325	−	6.18325i	0.265839	−	0.265839i	0.827421	+	0.561582i	$0.189807\pi$
$542$	10.4618	+	12.2399i	0.449374	+	0.525750i
$543$	−11.9503			−0.512837
$544$	−1.46962	+	3.56689i	−0.0630095	+	0.152929i
$545$		−	7.76714i		−	0.332708i
$546$	9.54002	+	0.747216i	0.408275	+	0.0319779i
$547$	23.2981	−	23.2981i	0.996156	−	0.996156i	−0.00383635	−	0.999993i	$-0.501221\pi$
$547$	23.2981	−	23.2981i	0.996156	−	0.996156i	0.999993	+	0.00383635i	$0.00122115\pi$
$548$	6.14681	−	38.9987i	0.262579	−	1.66594i
$549$	−1.03836	−	1.03836i	−0.0443163	−	0.0443163i
$550$	−1.18469	−	1.38604i	−0.0505152	−	0.0591008i
$551$			1.69126i			0.0720500i
$552$	−0.616789	+	2.58190i	−0.0262523	+	0.109893i
$553$	5.37530	−	5.37530i	0.228581	−	0.228581i
$554$	5.67652	+	0.444610i	0.241172	+	0.0188897i
$555$	−3.19712	+	1.94580i	−0.135710	+	0.0825947i
$556$	−5.90680	+	37.4760i	−0.250504	+	1.58934i
$557$	23.3828	+	23.3828i	0.990763	+	0.990763i	0.999958	−	0.00919506i	$-0.00292692\pi$
$557$	23.3828	+	23.3828i	0.990763	+	0.990763i	−0.00919506	+	0.999958i	$0.502927\pi$
$558$	−1.87561	+	23.9467i	−0.0794009	+	1.01374i
$559$	−16.2535			−0.687448
$560$	−6.92003	−	13.5311i	−0.292425	−	0.571794i
$561$	0.382546	−	0.382546i	0.0161511	−	0.0161511i
$562$	−0.187001	+	2.38752i	−0.00788817	+	0.100712i
$563$	13.8108	+	13.8108i	0.582054	+	0.582054i	0.935467	−	0.353413i	$-0.114979\pi$
$563$	13.8108	+	13.8108i	0.582054	+	0.582054i	−0.353413	+	0.935467i	$0.614979\pi$
$564$	13.5747	+	2.13958i	0.571596	+	0.0900925i
$565$	10.1418			0.426668
$566$	0.648259	−	8.27659i	0.0272483	−	0.347891i
$567$			21.7940i			0.915263i
$568$	−19.9085	+	12.2308i	−0.835341	+	0.513191i
$569$	17.2605	+	17.2605i	0.723599	+	0.723599i	0.969336	−	0.245738i	$-0.0790302\pi$
$569$	17.2605	+	17.2605i	0.723599	+	0.723599i	−0.245738	+	0.969336i	$0.579030\pi$
$570$	1.01423	−	0.866895i	0.0424816	−	0.0363102i
$571$		−	21.1069i		−	0.883295i	−0.897189	−	0.441647i	$-0.854394\pi$
$571$		−	21.1069i		−	0.883295i	0.897189	−	0.441647i	$-0.145606\pi$
$572$	−4.39142	−	6.03474i	−0.183614	−	0.252325i
$573$	2.47222	+	2.47222i	0.103279	+	0.103279i
$574$	17.7355	−	15.1590i	0.740264	−	0.632725i
$575$	1.07857	−	1.07857i	0.0449795	−	0.0449795i
$576$	9.47870	−	18.7069i	0.394946	−	0.779456i
$577$	−16.8161	+	16.8161i	−0.700064	+	0.700064i	−0.964424	−	0.264360i	$-0.914839\pi$
$577$	−16.8161	+	16.8161i	−0.700064	+	0.700064i	0.264360	+	0.964424i	$0.414839\pi$
$578$	−15.1933	−	17.7756i	−0.631958	−	0.739366i
$579$	−9.83908	+	9.83908i	−0.408898	+	0.408898i
$580$	−0.343461	+	2.17910i	−0.0142614	+	0.0904823i
$581$	25.6861			1.06564
$582$	0.00204503	−	0.0261097i	8.47692e−5	−	0.00108228i
$583$	−4.23526			−0.175407
$584$	34.4155	−	21.1431i	1.42412	−	0.874909i
$585$		−	7.58735i		−	0.313698i
$586$	−10.8921	+	9.30978i	−0.449948	+	0.384584i
$587$	−27.0065	+	27.0065i	−1.11468	+	1.11468i	−0.122168	+	0.992509i	$0.538985\pi$
$587$	−27.0065	+	27.0065i	−1.11468	+	1.11468i	−0.992509	+	0.122168i	$0.961015\pi$
$588$	−1.42472	+	9.03921i	−0.0587545	+	0.372771i
$589$	9.93474			0.409354
$590$	2.11476	−	1.80754i	0.0870631	−	0.0744154i
$591$	10.3449			0.425531
$592$	20.7259	+	12.7451i	0.851828	+	0.523821i
$593$	30.1275			1.23719			0.618593	−	0.785711i	$-0.287703\pi$
$593$	30.1275			1.23719			0.618593	+	0.785711i	$0.287703\pi$
$594$	−4.79406	+	4.09762i	−0.196703	+	0.168128i
$595$	−2.59112			−0.106226
$596$	3.42757	−	21.7464i	0.140399	−	0.890767i
$597$	7.47627	−	7.47627i	0.305983	−	0.305983i
$598$	4.74613	−	4.05666i	0.194084	−	0.165889i
$599$		−	11.7895i		−	0.481707i	−0.970562	−	0.240853i	$-0.922573\pi$
$599$		−	11.7895i		−	0.481707i	0.970562	−	0.240853i	$-0.0774273\pi$
$600$	1.48284	−	0.910981i	0.0605366	−	0.0371906i
$601$	10.8714			0.443453			0.221726	−	0.975109i	$-0.428831\pi$
$601$	10.8714			0.443453			0.221726	+	0.975109i	$0.428831\pi$
$602$	2.35614	−	30.0818i	0.0960289	−	1.22604i
$603$	18.8260			0.766654
$604$	5.24334	−	33.2666i	0.213349	−	1.35360i
$605$	−6.60276	+	6.60276i	−0.268440	+	0.268440i
$606$	−1.48404	−	1.73627i	−0.0602852	−	0.0705313i
$607$	−6.87992	+	6.87992i	−0.279247	+	0.279247i	−0.832809	−	0.553561i	$-0.813268\pi$
$607$	−6.87992	+	6.87992i	−0.279247	+	0.279247i	0.553561	+	0.832809i	$0.313268\pi$
$608$	−8.01974	−	3.30428i	−0.325243	−	0.134006i
$609$	1.82335	−	1.82335i	0.0738857	−	0.0738857i
$610$	−0.602214	+	0.514730i	−0.0243829	+	0.0208408i
$611$	−22.8551	−	22.8551i	−0.924620	−	0.924620i
$612$	−2.10375	−	2.89100i	−0.0850391	−	0.116862i
$613$			35.7133i			1.44245i	0.692702	+	0.721224i	$0.256420\pi$
$613$			35.7133i			1.44245i	−0.692702	+	0.721224i	$0.743580\pi$
$614$	−23.6749	+	20.2356i	−0.955441	+	0.816643i
$615$	1.88914	+	1.88914i	0.0761774	+	0.0761774i
$616$	11.8056	−	7.25279i	0.475663	−	0.292223i
$617$			5.36901i			0.216148i	0.994143	+	0.108074i	$0.0344684\pi$
$617$			5.36901i			0.216148i	−0.994143	+	0.108074i	$0.965532\pi$
$618$	0.371471	−	4.74273i	0.0149428	−	0.190781i
$619$	45.1109			1.81316			0.906580	−	0.422033i	$-0.138683\pi$
$619$	45.1109			1.81316			0.906580	+	0.422033i	$0.138683\pi$
$620$	12.8004	+	2.01755i	0.514077	+	0.0810267i
$621$	−3.73059	−	3.73059i	−0.149703	−	0.149703i
$622$	−2.78907	+	35.6092i	−0.111831	+	1.42780i
$623$	−15.3698	+	15.3698i	−0.615778	+	0.615778i
$624$	6.34228	−	3.24355i	0.253895	−	0.129846i
$625$	−1.00000			−0.0400000
$626$	2.61566	−	33.3952i	0.104543	−	1.33474i
$627$	0.860112	+	0.860112i	0.0343496	+	0.0343496i
$628$	4.75891	−	30.1931i	0.189901	−	1.20484i
$629$	3.54355	−	2.15664i	0.141291	−	0.0859910i
$630$	14.0426	+	1.09988i	0.559471	+	0.0438202i
$631$	−20.4575	+	20.4575i	−0.814399	+	0.814399i	−0.985290	−	0.170891i	$-0.945335\pi$
$631$	−20.4575	+	20.4575i	−0.814399	+	0.814399i	0.170891	+	0.985290i	$0.445335\pi$
$632$	1.31487	−	5.50410i	0.0523027	−	0.218941i
$633$		−	16.5903i		−	0.659405i
$634$	−1.51278	−	1.76989i	−0.0600801	−	0.0702914i
$635$	2.82167	+	2.82167i	0.111975	+	0.111975i
$636$	0.629377	−	3.99311i	0.0249564	−	0.158337i
$637$	15.2190	−	15.2190i	0.602998	−	0.602998i
$638$	−2.00501	−	0.157041i	−0.0793791	−	0.00621732i
$639$		−	21.6552i		−	0.856667i
$640$	−9.66201	−	5.88605i	−0.381924	−	0.232667i
$641$	12.8712			0.508383			0.254192	−	0.967154i	$-0.418191\pi$
$641$	12.8712			0.508383			0.254192	+	0.967154i	$0.418191\pi$
$642$	−2.81694	−	3.29571i	−0.111176	−	0.130071i
$643$	12.0189	−	12.0189i	0.473978	−	0.473978i	−0.429221	−	0.903199i	$-0.641212\pi$
$643$	12.0189	−	12.0189i	0.473978	−	0.473978i	0.903199	+	0.429221i	$0.141212\pi$
$644$	6.82002	+	9.37216i	0.268746	+	0.369315i
$645$	3.45521			0.136049
$646$	−1.12413	+	0.960829i	−0.0442284	+	0.0378033i
$647$	−28.7670	+	28.7670i	−1.13095	+	1.13095i	−0.140926	+	0.990020i	$0.545008\pi$
$647$	−28.7670	+	28.7670i	−1.13095	+	1.13095i	−0.990020	+	0.140926i	$0.954992\pi$
$648$	8.49257	+	13.8237i	0.333619	+	0.543045i
$649$	1.79340	+	1.79340i	0.0703971	+	0.0703971i
$650$	−4.08076	−	0.319623i	−0.160061	−	0.0125367i
$651$	−10.7107	−	10.7107i	−0.419784	−	0.419784i
$652$	4.39829	+	6.04419i	0.172250	+	0.236709i
$653$	−0.0103565	−	0.0103565i	−0.000405281	−	0.000405281i	0.706904	−	0.707309i	$-0.250091\pi$
$653$	−0.0103565	−	0.0103565i	−0.000405281	−	0.000405281i	−0.707309	+	0.706904i	$0.750091\pi$
$654$	−0.527750	+	6.73800i	−0.0206366	+	0.263477i
$655$			6.73638i			0.263212i
$656$	5.34230	−	16.5262i	0.208582	−	0.645240i
$657$			37.4351i			1.46048i
$658$	45.6132	−	38.9870i	1.77819	−	1.51987i
$659$	−6.57880			−0.256273			−0.128137	−	0.991757i	$-0.540900\pi$
$659$	−6.57880			−0.256273			−0.128137	+	0.991757i	$0.540900\pi$
$660$	0.933540	+	1.28288i	0.0363380	+	0.0499362i
$661$	15.7458	+	15.7458i	0.612441	+	0.612441i	0.943581	−	0.331141i	$-0.107434\pi$
$661$	15.7458	+	15.7458i	0.612441	+	0.612441i	−0.331141	+	0.943581i	$0.607434\pi$
$662$	−4.03409	−	0.315968i	−0.156790	−	0.0122804i
$663$		−	1.21451i		−	0.0471675i
$664$	16.2924	−	10.0092i	0.632267	−	0.388433i
$665$		−	5.82584i		−	0.225916i
$666$	−20.1197	+	10.1838i	−0.779624	+	0.394613i
$667$		−	1.68244i		−	0.0651444i
$668$	23.8116	−	17.3275i	0.921300	−	0.670420i
$669$		−	3.82805i		−	0.148001i
$670$	0.793060	−	10.1253i	0.0306386	−	0.391176i
$671$	−0.510702	−	0.510702i	−0.0197154	−	0.0197154i
$672$	5.08374	+	12.2084i	0.196110	+	0.470951i
$673$	14.4159			0.555693			0.277846	−	0.960626i	$-0.410379\pi$
$673$	14.4159			0.555693			0.277846	+	0.960626i	$0.410379\pi$
$674$	−11.7348	−	13.7293i	−0.452009	−	0.528832i
$675$			3.45882i			0.133130i
$676$	9.13247	+	1.43942i	0.351249	+	0.0553623i
$677$			25.8717i			0.994331i	0.867656	+	0.497166i	$0.165626\pi$
$677$			25.8717i			0.994331i	−0.867656	+	0.497166i	$0.834374\pi$
$678$	−8.79801	−	0.689099i	−0.337886	−	0.0264647i
$679$	−0.0808617	−	0.0808617i	−0.00310319	−	0.00310319i
$680$	−1.64351	+	1.00969i	−0.0630259	+	0.0387199i
$681$	9.73895	+	9.73895i	0.373198	+	0.373198i
$682$	−0.922487	+	11.7778i	−0.0353239	+	0.450995i
$683$	−6.00111	−	6.00111i	−0.229626	−	0.229626i	0.582910	−	0.812536i	$-0.301914\pi$
$683$	−6.00111	−	6.00111i	−0.229626	−	0.229626i	−0.812536	+	0.582910i	$0.801914\pi$
$684$	6.50010	−	4.73005i	0.248537	−	0.180858i
$685$	13.9583	−	13.9583i	0.533321	−	0.533321i
$686$	1.52257	+	1.78134i	0.0581319	+	0.0680120i
$687$	17.8396			0.680623
$688$	−10.2276	−	19.9986i	−0.389924	−	0.762439i
$689$	−6.72305	+	6.72305i	−0.256128	+	0.256128i
$690$	−1.00895	+	0.862376i	−0.0384099	+	0.0328301i
$691$	−31.4969			−1.19820			−0.599100	−	0.800674i	$-0.704475\pi$
$691$	−31.4969			−1.19820			−0.599100	+	0.800674i	$0.704475\pi$
$692$	−29.8324	−	4.70205i	−1.13406	−	0.178745i
$693$			12.8415i			0.487806i
$694$	0.991481	−	12.6587i	0.0376361	−	0.480516i
$695$	−13.4133	+	13.4133i	−0.508797	+	0.508797i
$696$	0.446015	−	1.86704i	0.0169061	−	0.0707698i
$697$	−2.09384	−	2.09384i	−0.0793098	−	0.0793098i
$698$	−13.8245	+	11.8162i	−0.523264	+	0.447249i
$699$		−	17.3556i		−	0.656449i
$700$	1.18311	−	7.50631i	0.0447174	−	0.283712i
$701$	17.2397	−	17.2397i	0.651134	−	0.651134i	−0.302132	−	0.953266i	$-0.597698\pi$
$701$	17.2397	−	17.2397i	0.651134	−	0.651134i	0.953266	+	0.302132i	$0.0976983\pi$
$702$	−1.10552	+	14.1146i	−0.0417252	+	0.532723i
$703$	4.84897	+	7.96727i	0.182882	+	0.300491i
$704$	4.66194	−	9.20070i	0.175704	−	0.346764i
$705$	4.85861	+	4.85861i	0.182986	+	0.182986i
$706$	−37.7959	−	2.96034i	−1.42247	−	0.111414i
$707$	−9.97330			−0.375085
$708$	−1.95737	+	1.42436i	−0.0735624	+	0.0535306i
$709$	−4.27773	+	4.27773i	−0.160654	+	0.160654i	−0.782856	−	0.622203i	$-0.786238\pi$
$709$	−4.27773	+	4.27773i	−0.160654	+	0.160654i	0.622203	+	0.782856i	$0.286238\pi$
$710$	−11.6470	−	0.912244i	−0.437104	−	0.0342359i
$711$	3.70863	+	3.70863i	0.139084	+	0.139084i
$712$	−3.75965	+	15.7381i	−0.140899	+	0.589809i
$713$	−9.88295			−0.370120
$714$	2.24780	+	0.176057i	0.0841218	+	0.00658878i
$715$		−	3.73171i		−	0.139558i
$716$	−9.00177	−	12.3704i	−0.336412	−	0.462302i
$717$	−7.44913	−	7.44913i	−0.278193	−	0.278193i
$718$	12.2760	+	14.3624i	0.458136	+	0.536001i
$719$			28.4619i			1.06145i	0.847544	+	0.530725i	$0.178080\pi$
$719$			28.4619i			1.06145i	−0.847544	+	0.530725i	$0.821920\pi$
$720$	9.33563	−	4.77440i	0.347918	−	0.177931i
$721$	−14.6882	−	14.6882i	−0.547017	−	0.547017i
$722$	15.2981	+	17.8981i	0.569335	+	0.666099i
$723$	−8.45591	+	8.45591i	−0.314479	+	0.314479i
$724$	−6.04779	+	38.3705i	−0.224764	+	1.42603i
$725$	−0.779940	+	0.779940i	−0.0289662	+	0.0289662i
$726$	6.17653	−	5.27926i	0.229233	−	0.195932i
$727$	−21.6825	+	21.6825i	−0.804158	+	0.804158i	−0.983743	−	0.179584i	$-0.942525\pi$
$727$	−21.6825	+	21.6825i	−0.804158	+	0.804158i	0.179584	+	0.983743i	$0.442525\pi$
$728$	7.22719	−	30.2533i	0.267858	−	1.12126i
$729$	−8.65196			−0.320443
$730$	20.1340	+	1.57698i	0.745193	+	0.0583667i
$731$	−3.82960			−0.141643
$732$	0.557395	−	0.405610i	0.0206019	−	0.0149918i
$733$		−	1.06667i		−	0.0393985i	−0.999806	−	0.0196993i	$-0.993729\pi$
$733$		−	1.06667i		−	0.0393985i	0.999806	−	0.0196993i	$-0.00627087\pi$
$734$	−13.3583	−	15.6287i	−0.493065	−	0.576867i
$735$	−3.23530	+	3.23530i	−0.119336	+	0.119336i
$736$	7.97793	+	3.28706i	0.294071	+	0.121162i
$737$	9.25925			0.341069
$738$	10.4588	+	12.2364i	0.384993	+	0.450427i
$739$	−43.3409			−1.59432			−0.797161	−	0.603767i	$-0.793666\pi$
$739$	−43.3409			−1.59432			−0.797161	+	0.603767i	$0.793666\pi$
$740$	4.62966	+	11.2502i	0.170190	+	0.413564i
$741$	2.73068			0.100314
$742$	−11.4684	−	13.4176i	−0.421017	−	0.492574i
$743$	21.8137			0.800266			0.400133	−	0.916457i	$-0.368964\pi$
$743$	21.8137			0.800266			0.400133	+	0.916457i	$0.368964\pi$
$744$	−10.9673	−	2.61997i	−0.402081	−	0.0960527i
$745$	7.78343	−	7.78343i	0.285163	−	0.285163i
$746$	−17.5390	−	20.5199i	−0.642148	−	0.751288i
$747$			17.7218i			0.648408i
$748$	−1.03470	−	1.42189i	−0.0378322	−	0.0519895i
$749$	−18.9308			−0.691718
$750$	0.867501	+	0.0679464i	0.0316766	+	0.00248105i
$751$	−41.7274			−1.52265			−0.761327	−	0.648368i	$-0.775452\pi$
$751$	−41.7274			−1.52265			−0.761327	+	0.648368i	$0.775452\pi$
$752$	13.7397	−	42.5032i	0.501034	−	1.54993i
$753$	−7.52943	+	7.52943i	−0.274388	+	0.274388i
$754$	−3.43204	+	2.93346i	−0.124987	+	0.106830i
$755$	11.9067	−	11.9067i	0.433330	−	0.433330i
$756$	−25.9630	−	4.09218i	−0.944265	−	0.148831i
$757$	−28.7982	+	28.7982i	−1.04669	+	1.04669i	−0.0478321	+	0.998855i	$0.515231\pi$
$757$	−28.7982	+	28.7982i	−1.04669	+	1.04669i	−0.998855	+	0.0478321i	$0.984769\pi$
$758$	15.7595	+	18.4380i	0.572411	+	0.669699i
$759$	−0.855628	−	0.855628i	−0.0310573	−	0.0310573i
$760$	−2.27018	−	3.69526i	−0.0823480	−	0.134041i
$761$			2.69410i			0.0976610i	0.998807	+	0.0488305i	$0.0155494\pi$
$761$			2.69410i			0.0976610i	−0.998807	+	0.0488305i	$0.984451\pi$
$762$	−2.25608	−	2.63952i	−0.0817291	−	0.0956198i
$763$	20.8675	+	20.8675i	0.755456	+	0.755456i
$764$	9.18905	−	6.68677i	0.332448	−	0.241919i
$765$		−	1.78771i		−	0.0646349i
$766$	35.7472	+	2.79988i	1.29160	+	0.101164i
$767$	5.69368			0.205587
$768$	7.98186	+	5.76265i	0.288021	+	0.207942i
$769$	4.59297	+	4.59297i	0.165627	+	0.165627i	0.785054	−	0.619427i	$-0.212635\pi$
$769$	4.59297	+	4.59297i	0.165627	+	0.165627i	−0.619427	+	0.785054i	$0.712635\pi$
$770$	6.90662	+	0.540957i	0.248897	+	0.0194947i
$771$	3.08512	−	3.08512i	0.111108	−	0.111108i
$772$	26.6124	+	36.5711i	0.957800	+	1.31622i
$773$	−22.6397			−0.814294			−0.407147	−	0.913363i	$-0.633476\pi$
$773$	−22.6397			−0.814294			−0.407147	+	0.913363i	$0.633476\pi$
$774$	20.7546	+	1.62559i	0.746007	+	0.0584306i
$775$	4.58150	+	4.58150i	0.164572	+	0.164572i
$776$	−0.0827992	−	0.0197798i	−0.00297232	−	0.000710055i
$777$	3.36185	−	13.8172i	0.120606	−	0.495689i
$778$	0.861065	−	10.9936i	0.0308707	−	0.394139i
$779$	4.70776	−	4.70776i	0.168673	−	0.168673i
$780$	3.51835	+	0.554547i	0.125977	+	0.0198560i
$781$		−	10.6508i		−	0.381114i
$782$	1.11827	−	0.955820i	0.0399893	−	0.0341801i
$783$	2.69767	+	2.69767i	0.0964070	+	0.0964070i
$784$	28.3024	+	9.14910i	1.01080	+	0.326753i
$785$	10.8067	−	10.8067i	0.385706	−	0.385706i
$786$	0.457713	−	5.84381i	0.0163261	−	0.208442i
$787$		−	42.6435i		−	1.52008i	−0.649878	−	0.760038i	$-0.725180\pi$
$787$		−	42.6435i		−	1.52008i	0.649878	−	0.760038i	$-0.274820\pi$
$788$	5.23531	−	33.2157i	0.186500	−	1.18326i
$789$	−5.28566			−0.188175
$790$	2.15087	−	1.83841i	0.0765245	−	0.0654078i
$791$	−27.2474	+	27.2474i	−0.968806	+	0.968806i
$792$	5.00398	+	8.14517i	0.177809	+	0.289426i
$793$	−1.62138			−0.0575768
$794$	11.0039	+	12.8741i	0.390513	+	0.456885i
$795$	1.42921	−	1.42921i	0.0506887	−	0.0506887i
$796$	−20.2215	−	27.7887i	−0.716733	−	0.984943i
$797$	1.61072	+	1.61072i	0.0570546	+	0.0570546i	0.735058	−	0.678004i	$-0.237155\pi$
$797$	1.61072	+	1.61072i	0.0570546	+	0.0570546i	−0.678004	+	0.735058i	$0.737155\pi$
$798$	−0.395845	+	5.05392i	−0.0140128	+	0.178907i
$799$	−5.38508	−	5.38508i	−0.190510	−	0.190510i
$800$	−2.17458	−	5.22218i	−0.0768830	−	0.184632i
$801$	−10.6042	−	10.6042i	−0.374681	−	0.374681i
$802$	38.7457	+	3.03474i	1.36816	+	0.107160i
$803$			18.4118i			0.649739i
$804$	−1.37596	+	8.72985i	−0.0485264	+	0.307878i
$805$			5.79547i			0.204264i
$806$	17.2317	+	20.1604i	0.606960	+	0.710119i
$807$	−1.71534			−0.0603829
$808$	−6.32594	+	3.88634i	−0.222546	+	0.136721i
$809$	28.8901	+	28.8901i	1.01572	+	1.01572i	0.999874	+	0.0158465i	$0.00504430\pi$
$809$	28.8901	+	28.8901i	1.01572	+	1.01572i	0.0158465	+	0.999874i	$0.494956\pi$
$810$	−0.633427	+	8.08722i	−0.0222563	+	0.284156i
$811$		−	1.47828i		−	0.0519094i	−0.999663	−	0.0259547i	$-0.991737\pi$
$811$		−	1.47828i		−	0.0519094i	0.999663	−	0.0259547i	$-0.00826256\pi$
$812$	−4.93172	−	6.77723i	−0.173069	−	0.237834i
$813$		−	7.00553i		−	0.245695i
$814$	−9.89557	+	5.00872i	−0.346839	+	0.175556i
$815$			3.73755i			0.130921i
$816$	1.49435	−	0.764238i	0.0523129	−	0.0267537i
$817$		−	8.61043i		−	0.301241i
$818$	34.1691	+	2.67628i	1.19470	+	0.0935738i
$819$	20.3845	+	20.3845i	0.712292	+	0.712292i
$820$	7.02177	−	5.10967i	0.245211	−	0.178437i
$821$	−0.822634			−0.0287101			−0.0143551	−	0.999897i	$-0.504570\pi$
$821$	−0.822634			−0.0287101			−0.0143551	+	0.999897i	$0.504570\pi$
$822$	−13.0573	+	11.1605i	−0.455425	+	0.389266i
$823$			35.1429i			1.22501i	0.790468	+	0.612503i	$0.209837\pi$
$823$			35.1429i			1.22501i	−0.790468	+	0.612503i	$0.790163\pi$
$824$	−15.0401	−	3.59293i	−0.523948	−	0.125166i
$825$			0.793298i			0.0276191i
$826$	−0.825368	+	10.5378i	−0.0287182	+	0.366658i
$827$	−32.1482	−	32.1482i	−1.11790	−	1.11790i	−0.992049	−	0.125855i	$-0.959833\pi$
$827$	−32.1482	−	32.1482i	−1.11790	−	1.11790i	−0.125855	−	0.992049i	$-0.540167\pi$
$828$	−6.46621	+	4.70539i	−0.224716	+	0.163524i
$829$	4.64161	+	4.64161i	0.161210	+	0.161210i	0.783103	−	0.621893i	$-0.213636\pi$
$829$	4.64161	+	4.64161i	0.161210	+	0.161210i	−0.621893	+	0.783103i	$0.713636\pi$
$830$	9.53148	+	0.746547i	0.330843	+	0.0259130i
$831$	−1.75171	−	1.75171i	−0.0607663	−	0.0607663i
$832$	−7.20482	−	22.0055i	−0.249782	−	0.762905i
$833$	3.58586	−	3.58586i	0.124243	−	0.124243i
$834$	12.5475	−	10.7247i	0.434483	−	0.371366i
$835$	14.7244			0.509560
$836$	3.19697	−	2.32640i	0.110569	−	0.0804601i
$837$	15.8466	−	15.8466i	0.547739	−	0.547739i
$838$	−6.13450	−	7.17712i	−0.211913	−	0.247929i
$839$	−0.477230			−0.0164758			−0.00823791	−	0.999966i	$-0.502622\pi$
$839$	−0.477230			−0.0164758			−0.00823791	+	0.999966i	$0.502622\pi$
$840$	−1.53638	+	6.43134i	−0.0530101	+	0.221902i
$841$		−	27.7834i		−	0.958048i
$842$	−39.9339	−	3.12780i	−1.37621	−	0.107791i
$843$	0.736764	−	0.736764i	0.0253755	−	0.0253755i
$844$	−53.2688	−	8.39599i	−1.83359	−	0.289002i
$845$	3.26868	+	3.26868i	0.112446	+	0.112446i
$846$	26.8986	+	31.4703i	0.924793	+	1.08197i
$847$		−	35.4785i		−	1.21906i
$848$	−12.5027	−	4.04165i	−0.429345	−	0.138791i
$849$	−2.55407	+	2.55407i	−0.0876554	+	0.0876554i
$850$	−0.961500	−	0.0753089i	−0.0329792	−	0.00258307i
$851$	−4.82369	−	7.92574i	−0.165354	−	0.271691i
$852$	10.0418	+	1.58274i	0.344026	+	0.0542239i
$853$	−12.4097	−	12.4097i	−0.424899	−	0.424899i	0.461987	−	0.886887i	$-0.347137\pi$
$853$	−12.4097	−	12.4097i	−0.424899	−	0.424899i	−0.886887	+	0.461987i	$0.847137\pi$
$854$	0.235038	−	3.00083i	0.00804284	−	0.102686i
$855$	4.01947			0.137463
$856$	−12.0076	+	7.37686i	−0.410411	+	0.252136i
$857$	−36.8850	+	36.8850i	−1.25997	+	1.25997i	−0.308861	+	0.951107i	$0.599948\pi$
$857$	−36.8850	+	36.8850i	−1.25997	+	1.25997i	−0.951107	+	0.308861i	$0.900052\pi$
$858$	−0.253556	+	3.23726i	−0.00865628	+	0.110518i
$859$	−31.1441	−	31.1441i	−1.06262	−	1.06262i	−0.997904	−	0.0647193i	$-0.979385\pi$
$859$	−31.1441	−	31.1441i	−1.06262	−	1.06262i	−0.0647193	−	0.997904i	$-0.520615\pi$
$860$	1.74861	−	11.0941i	0.0596270	−	0.378306i
$861$	−10.1509			−0.345941
$862$	1.82128	−	23.2530i	0.0620329	−	0.792000i
$863$			6.76121i			0.230154i	0.993357	+	0.115077i	$0.0367115\pi$
$863$			6.76121i			0.230154i	−0.993357	+	0.115077i	$0.963288\pi$
$864$	−18.0626	+	7.52149i	−0.614502	+	0.255886i
$865$	−10.6775	−	10.6775i	−0.363047	−	0.363047i
$866$	43.2380	−	36.9568i	1.46929	−	1.25584i
$867$			10.1738i			0.345522i
$868$	−39.8106	+	28.9698i	−1.35126	+	0.983298i
$869$	1.82403	+	1.82403i	0.0618759	+	0.0618759i
$870$	0.729593	−	0.623604i	0.0247355	−	0.0211422i
$871$	14.6981	−	14.6981i	0.498027	−	0.498027i
$872$	21.3675	+	5.10448i	0.723597	+	0.172859i
$873$	0.0557896	−	0.0557896i	0.00188819	−	0.00188819i
$874$	2.14905	+	2.51431i	0.0726928	+	0.0850478i
$875$	2.68664	−	2.68664i	0.0908252	−	0.0908252i
$876$	−17.3591	−	2.73607i	−0.586510	−	0.0924431i
$877$	55.4786			1.87338			0.936690	−	0.350159i	$-0.113872\pi$
$877$	55.4786			1.87338			0.936690	+	0.350159i	$0.113872\pi$
$878$	1.11244	−	14.2030i	0.0375430	−	0.479327i
$879$	6.23408			0.210270
$880$	4.59158	−	2.34821i	0.154782	−	0.0791581i
$881$		−	15.3137i		−	0.515930i	−0.966154	−	0.257965i	$-0.916948\pi$
$881$		−	15.3137i		−	0.515930i	0.966154	−	0.257965i	$-0.0830520\pi$
$882$	−20.9557	+	17.9115i	−0.705616	+	0.603111i
$883$	−13.5444	+	13.5444i	−0.455805	+	0.455805i	−0.897276	−	0.441471i	$-0.854457\pi$
$883$	−13.5444	+	13.5444i	−0.455805	+	0.455805i	0.441471	+	0.897276i	$0.354457\pi$
$884$	−3.89958	−	0.614635i	−0.131157	−	0.0206724i
$885$	−1.21038			−0.0406865
$886$	16.3446	−	13.9702i	0.549107	−	0.469338i
$887$	−45.2686			−1.51997			−0.759985	−	0.649940i	$-0.774794\pi$
$887$	−45.2686			−1.51997			−0.759985	+	0.649940i	$0.774794\pi$
$888$	−3.25183	−	10.0741i	−0.109124	−	0.338065i
$889$	−15.1616			−0.508505
$890$	−6.15006	+	5.25663i	−0.206150	+	0.176203i
$891$	−7.39547			−0.247758
$892$	−12.2912	−	1.93729i	−0.411541	−	0.0648653i
$893$	12.1077	−	12.1077i	0.405170	−	0.405170i
$894$	−7.28099	+	6.22328i	−0.243513	+	0.208137i
$895$		−	7.64947i		−	0.255694i
$896$	41.7721	−	10.1447i	1.39551	−	0.338909i
$897$	−2.71645			−0.0906995
$898$	4.40063	−	56.1847i	0.146851	−	1.87491i
$899$	7.14660			0.238352
$900$	5.17889	+	0.816274i	0.172630	+	0.0272091i
$901$	−1.58407	+	1.58407i	−0.0527730	+	0.0527730i
$902$	5.14398	+	6.01826i	0.171276	+	0.200386i
$903$	−9.28292	+	9.28292i	−0.308916	+	0.308916i
$904$	−6.66507	+	27.9003i	−0.221677	+	0.927949i
$905$	−13.7335	+	13.7335i	−0.456517	+	0.456517i
$906$	−11.1381	+	9.52008i	−0.370039	+	0.316283i
$907$	34.3098	+	34.3098i	1.13924	+	1.13924i	0.988587	+	0.150651i	$0.0481370\pi$
$907$	34.3098	+	34.3098i	1.13924	+	1.13924i	0.150651	+	0.988587i	$0.451863\pi$
$908$	36.1989	−	26.3415i	1.20130	−	0.874175i
$909$		−	6.88096i		−	0.228227i
$910$	11.8223	−	10.1048i	0.391905	−	0.334972i
$911$	−30.2541	−	30.2541i	−1.00236	−	1.00236i	−0.999997	−	0.00236571i	$-0.999247\pi$
$911$	−30.2541	−	30.2541i	−1.00236	−	1.00236i	−0.00236571	−	0.999997i	$-0.500753\pi$
$912$	1.71830	+	3.35989i	0.0568987	+	0.111257i
$913$			8.71620i			0.288464i
$914$	2.95937	−	37.7835i	0.0978872	−	1.24977i
$915$	0.344677			0.0113947
$916$	9.02823	−	57.2800i	0.298301	−	1.89259i
$917$	−18.0983	−	18.0983i	−0.597657	−	0.597657i
$918$	−0.260480	+	3.32566i	−0.00859713	+	0.109763i
$919$	16.3454	−	16.3454i	0.539185	−	0.539185i	−0.384105	−	0.923290i	$-0.625490\pi$
$919$	16.3454	−	16.3454i	0.539185	−	0.539185i	0.923290	+	0.384105i	$0.125490\pi$
$920$	2.25834	+	3.67599i	0.0744554	+	0.121194i
$921$	13.5503			0.446498
$922$	−0.465823	+	5.94735i	−0.0153411	+	0.195866i
$923$	−16.9070	−	16.9070i	−0.556501	−	0.556501i
$924$	−5.95474	−	0.938561i	−0.195897	−	0.0308764i
$925$	−1.43804	+	5.91033i	−0.0472824	+	0.194331i
$926$	18.2227	+	1.42728i	0.598836	+	0.0469035i
$927$	10.1340	−	10.1340i	0.332843	−	0.332843i
$928$	−5.76903	−	2.37695i	−0.189378	−	0.0780271i
$929$			9.78758i			0.321120i	0.987026	+	0.160560i	$0.0513300\pi$
$929$			9.78758i			0.321120i	−0.987026	+	0.160560i	$0.948670\pi$
$930$	−3.66316	−	4.28575i	−0.120120	−	0.140535i
$931$	8.06241	+	8.06241i	0.264235	+	0.264235i
$932$	−55.7260	−	8.78329i	−1.82537	−	0.287706i
$933$	10.9886	−	10.9886i	0.359751	−	0.359751i
$934$	−24.3609	−	1.90806i	−0.797114	−	0.0624335i
$935$		−	0.879257i		−	0.0287548i
$936$	20.8729	+	4.98632i	0.682253	+	0.162983i
$937$	−57.7545			−1.88676			−0.943379	−	0.331718i	$-0.892372\pi$
$937$	−57.7545			−1.88676			−0.943379	+	0.331718i	$0.892372\pi$
$938$	25.0725	+	29.3338i	0.818646	+	0.957784i
$939$	−10.3054	+	10.3054i	−0.336304	+	0.336304i
$940$	18.0591	−	13.1414i	0.589022	−	0.428625i
$941$	−39.6163			−1.29146			−0.645728	−	0.763568i	$-0.723446\pi$
$941$	−39.6163			−1.29146			−0.645728	+	0.763568i	$0.723446\pi$
$942$	−10.1091	+	8.64052i	−0.329371	+	0.281523i
$943$	−4.68322	+	4.68322i	−0.152507	+	0.152507i
$944$	3.58279	+	7.00563i	0.116610	+	0.228014i
$945$	−9.29263	−	9.29263i	−0.302289	−	0.302289i
$946$	10.2078	+	0.799519i	0.331884	+	0.0259946i
$947$	−12.2495	−	12.2495i	−0.398057	−	0.398057i	0.479490	−	0.877547i	$-0.340822\pi$
$947$	−12.2495	−	12.2495i	−0.398057	−	0.398057i	−0.877547	+	0.479490i	$0.840822\pi$
$948$	−1.99080	+	1.44868i	−0.0646580	+	0.0470509i
$949$	29.2269	+	29.2269i	0.948745	+	0.948745i
$950$	0.169324	−	2.16182i	0.00549358	−	0.0701389i
$951$			1.01300i			0.0328487i
$952$	1.70285	−	7.12822i	0.0551898	−	0.231027i
$953$			3.50871i			0.113658i	0.998384	+	0.0568292i	$0.0180990\pi$
$953$			3.50871i			0.113658i	−0.998384	+	0.0568292i	$0.981901\pi$
$954$	9.25729	−	7.91247i	0.299716	−	0.256176i
$955$	5.68224			0.183873
$956$	−27.6878	+	20.1481i	−0.895488	+	0.651637i
$957$	0.618725	+	0.618725i	0.0200005	+	0.0200005i
$958$	−6.77672	−	0.530782i	−0.218946	−	0.0171488i
$959$			75.0022i			2.42195i
$960$	1.53162	+	4.67800i	0.0494329	+	0.150982i
$961$		−	10.9804i		−	0.354205i
$962$	−7.75737	+	23.6590i	−0.250108	+	0.762798i
$963$		−	13.0611i		−	0.420889i
$964$	22.8712	+	31.4299i	0.736632	+	1.01229i
$965$			22.6145i			0.727986i
$966$	0.393782	−	5.02758i	0.0126697	−	0.161760i
$967$	7.80942	+	7.80942i	0.251134	+	0.251134i	0.821435	−	0.570302i	$-0.193174\pi$
$967$	7.80942	+	7.80942i	0.251134	+	0.251134i	−0.570302	+	0.821435i	$0.693174\pi$
$968$	−13.8251	−	22.5036i	−0.444354	−	0.723292i
$969$	0.643397			0.0206689
$970$	−0.0276556	−	0.0323559i	−0.000887967	−	0.00103889i
$971$			38.4528i			1.23401i	0.786959	+	0.617005i	$0.211654\pi$
$971$			38.4528i			1.23401i	−0.786959	+	0.617005i	$0.788346\pi$
$972$	4.33010	−	27.4725i	0.138888	−	0.881181i
$973$		−	72.0737i		−	2.31058i
$974$	−52.3256	−	4.09837i	−1.67662	−	0.131320i
$975$	1.25928	+	1.25928i	0.0403292	+	0.0403292i
$976$	−1.02026	−	1.99498i	−0.0326578	−	0.0638576i
$977$	42.9033	+	42.9033i	1.37260	+	1.37260i	0.856576	+	0.516021i	$0.172587\pi$
$977$	42.9033	+	42.9033i	1.37260	+	1.37260i	0.516021	+	0.856576i	$0.327413\pi$
$978$	0.253953	−	3.24233i	0.00812053	−	0.103678i
$979$	−5.21550	−	5.21550i	−0.166688	−	0.166688i
$980$	8.75070	+	12.0253i	0.279531	+	0.384135i
$981$	−14.3973	+	14.3973i	−0.459671	+	0.459671i
$982$	−16.3381	−	19.1149i	−0.521369	−	0.609981i
$983$	50.4618			1.60948			0.804741	−	0.593626i	$-0.202304\pi$
$983$	50.4618			1.60948			0.804741	+	0.593626i	$0.202304\pi$
$984$	−6.43858	+	3.95554i	−0.205254	+	0.126098i
$985$	11.8885	−	11.8885i	0.378799	−	0.378799i
$986$	−0.808649	+	0.691176i	−0.0257526	+	0.0220115i
$987$	−26.1067			−0.830986
$988$	1.38194	−	8.76777i	0.0439653	−	0.278940i
$989$			8.56555i			0.272368i
$990$	−0.373227	+	4.76514i	−0.0118619	+	0.151446i
$991$	−23.7810	+	23.7810i	−0.755429	+	0.755429i	−0.975487	−	0.220058i	$-0.929375\pi$
$991$	−23.7810	+	23.7810i	−0.755429	+	0.755429i	0.220058	+	0.975487i	$0.429375\pi$
$992$	−13.9626	+	33.8883i	−0.443313	+	1.07595i
$993$	1.24488	+	1.24488i	0.0395050	+	0.0395050i
$994$	33.7422	−	28.8405i	1.07024	−	0.914764i
$995$		−	17.1837i		−	0.544760i
$996$	−8.21784	−	1.29526i	−0.260392	−	0.0410419i
$997$	42.5964	−	42.5964i	1.34904	−	1.34904i	0.462339	−	0.886703i	$-0.347010\pi$
$997$	42.5964	−	42.5964i	1.34904	−	1.34904i	0.886703	−	0.462339i	$-0.152990\pi$
$998$	3.35590	−	42.8462i	0.106229	−	1.35627i
$999$	20.4428	+	4.97392i	0.646782	+	0.157368i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.u.a.31.18	✓	152
4.3	odd	2	inner	740.2.u.a.31.56	yes	152
37.6	odd	4	inner	740.2.u.a.191.56	yes	152
148.43	even	4	inner	740.2.u.a.191.18	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.u.a.31.18	✓	152	1.1	even	1	trivial
740.2.u.a.31.56	yes	152	4.3	odd	2	inner
740.2.u.a.191.18	yes	152	148.43	even	4	inner
740.2.u.a.191.56	yes	152	37.6	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07503 + 0.918861i) q^{2} +0.615294 q^{3} +(0.311387 - 1.97561i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.661461 + 0.565370i) q^{6} +3.79949i q^{7} +(1.48056 + 2.40997i) q^{8} -2.62141 q^{9} +(-0.110429 + 1.40990i) q^{10} -1.28930 q^{11} +(0.191595 - 1.21558i) q^{12} +(-2.04663 + 2.04663i) q^{13} +(-3.49120 - 4.08457i) q^{14} +(0.435079 - 0.435079i) q^{15} +(-3.80608 - 1.23036i) q^{16} +(-0.482222 + 0.482222i) q^{17} +(2.81810 - 2.40872i) q^{18} +(-1.08422 - 1.08422i) q^{19} +(-1.17678 - 1.61715i) q^{20} +2.33780i q^{21} +(1.38604 - 1.18469i) q^{22} +(1.07857 + 1.07857i) q^{23} +(0.910981 + 1.48284i) q^{24} -1.00000i q^{25} +(0.319623 - 4.08076i) q^{26} -3.45882 q^{27} +(7.50631 + 1.18311i) q^{28} +(-0.779940 - 0.779940i) q^{29} +(-0.0679464 + 0.867501i) q^{30} +(-4.58150 + 4.58150i) q^{31} +(5.22218 - 2.17458i) q^{32} -0.793298 q^{33} +(0.0753089 - 0.961500i) q^{34} +(2.68664 + 2.68664i) q^{35} +(-0.816274 + 5.17889i) q^{36} +(-5.91033 - 1.43804i) q^{37} +(2.16182 + 0.169324i) q^{38} +(-1.25928 + 1.25928i) q^{39} +(2.75102 + 0.657188i) q^{40} +4.34206i q^{41} +(-2.14812 - 2.51321i) q^{42} +(3.97078 + 3.97078i) q^{43} +(-0.401471 + 2.54715i) q^{44} +(-1.85362 + 1.85362i) q^{45} +(-2.15056 - 0.168441i) q^{46} +11.1672i q^{47} +(-2.34186 - 0.757033i) q^{48} -7.43612 q^{49} +(0.918861 + 1.07503i) q^{50} +(-0.296709 + 0.296709i) q^{51} +(3.40605 + 4.68064i) q^{52} +3.28494 q^{53} +(3.71835 - 3.17818i) q^{54} +(-0.911672 + 0.911672i) q^{55} +(-9.15664 + 5.62538i) q^{56} +(-0.667116 - 0.667116i) q^{57} +(1.55512 + 0.121804i) q^{58} +(-1.39099 - 1.39099i) q^{59} +(-0.724068 - 0.995024i) q^{60} +(0.396109 + 0.396109i) q^{61} +(0.715495 - 9.13503i) q^{62} -9.96003i q^{63} +(-3.61588 + 7.13621i) q^{64} +2.89437i q^{65} +(0.852821 - 0.728931i) q^{66} -7.18162 q^{67} +(0.802526 + 1.10284i) q^{68} +(0.663639 + 0.663639i) q^{69} +(-5.35688 - 0.419574i) q^{70} +8.26090i q^{71} +(-3.88116 - 6.31752i) q^{72} -14.2805i q^{73} +(7.67515 - 3.88484i) q^{74} -0.615294i q^{75} +(-2.47962 + 1.80439i) q^{76} -4.89868i q^{77} +(0.196662 - 2.51087i) q^{78} +(-1.41474 - 1.41474i) q^{79} +(-3.56130 + 1.82131i) q^{80} +5.73604 q^{81} +(-3.98975 - 4.66785i) q^{82} -6.76042i q^{83} +(4.61859 + 0.727962i) q^{84} +0.681966i q^{85} +(-7.91732 - 0.620119i) q^{86} +(-0.479893 - 0.479893i) q^{87} +(-1.90889 - 3.10717i) q^{88} +(4.04522 + 4.04522i) q^{89} +(0.289480 - 3.69592i) q^{90} +(-7.77615 - 7.77615i) q^{91} +(2.46669 - 1.79498i) q^{92} +(-2.81897 + 2.81897i) q^{93} +(-10.2611 - 12.0051i) q^{94} -1.53332 q^{95} +(3.21318 - 1.33801i) q^{96} +(-0.0212823 + 0.0212823i) q^{97} +(7.99406 - 6.83276i) q^{98} +3.37978 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q - 4 q^{2} - 4 q^{8} + 152 q^{9} - 16 q^{13} + 24 q^{14} + 40 q^{16} + 16 q^{22} - 36 q^{24} + 32 q^{29} - 4 q^{32} - 16 q^{37} - 40 q^{38} - 20 q^{42} - 72 q^{44} + 8 q^{46} - 248 q^{49} - 4 q^{50}+ \cdots + 24 q^{98}+O(q^{100}) \) 152 * q - 4 * q^2 - 4 * q^8 + 152 * q^9 - 16 * q^13 + 24 * q^14 + 40 * q^16 + 16 * q^22 - 36 * q^24 + 32 * q^29 - 4 * q^32 - 16 * q^37 - 40 * q^38 - 20 * q^42 - 72 * q^44 + 8 * q^46 - 248 * q^49 - 4 * q^50 - 20 * q^52 + 8 * q^54 - 4 * q^56 + 48 * q^57 + 28 * q^60 + 16 * q^61 + 16 * q^66 - 28 * q^68 - 128 * q^72 - 80 * q^74 + 76 * q^76 + 152 * q^81 + 16 * q^82 - 56 * q^84 - 96 * q^86 - 72 * q^88 + 8 * q^89 - 152 * q^92 + 16 * q^93 + 28 * q^94 + 48 * q^96 - 48 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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