LMFDB - Embedded newform 841.2.d.o.190.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(190,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("841.190");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.d (of order $7$, degree $6$, not 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:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			190.5
Character	$\chi$	$=$	841.190
Dual form			841.2.d.o.571.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.75304 + 0.844219i) q^{2} +(-1.41628 + 1.77596i) q^{3} +(1.11346 + 1.39624i) q^{4} +(-2.89865 - 1.39592i) q^{5} +(-3.98209 + 1.91767i) q^{6} +(-1.57757 + 1.97820i) q^{7} +(-0.0927185 - 0.406226i) q^{8} +(-0.480617 - 2.10572i) q^{9} +(-3.90299 - 4.89420i) q^{10} +(0.249954 - 1.09512i) q^{11} -4.05663 q^{12} +(0.344690 - 1.51019i) q^{13} +(-4.43557 + 2.13606i) q^{14} +(6.58439 - 3.17088i) q^{15} +(0.975184 - 4.27256i) q^{16} +4.41979 q^{17} +(0.935150 - 4.09716i) q^{18} +(-3.06344 - 3.84143i) q^{19} +(-1.27851 - 5.60150i) q^{20} +(-1.27893 - 5.60338i) q^{21} +(1.36270 - 1.70877i) q^{22} +(-2.22905 + 1.07345i) q^{23} +(0.852756 + 0.410666i) q^{24} +(3.33615 + 4.18341i) q^{25} +(1.87918 - 2.35642i) q^{26} +(-1.71939 - 0.828013i) q^{27} -4.51860 q^{28} +14.2196 q^{30} +(-1.43038 - 0.688836i) q^{31} +(4.79693 - 6.01516i) q^{32} +(1.59088 + 1.99490i) q^{33} +(7.74806 + 3.73127i) q^{34} +(7.33422 - 3.53198i) q^{35} +(2.40494 - 3.01569i) q^{36} +(-1.84330 - 8.07603i) q^{37} +(-2.12732 - 9.32039i) q^{38} +(2.19385 + 2.75100i) q^{39} +(-0.298300 + 1.30694i) q^{40} -11.7882 q^{41} +(2.48846 - 10.9026i) q^{42} +(-1.69733 + 0.817393i) q^{43} +(1.80736 - 0.870379i) q^{44} +(-1.54627 + 6.77466i) q^{45} -4.81385 q^{46} +(0.214209 - 0.938513i) q^{47} +(6.20675 + 7.78302i) q^{48} +(0.133067 + 0.583004i) q^{49} +(2.31670 + 10.1501i) q^{50} +(-6.25965 + 7.84936i) q^{51} +(2.49237 - 1.20026i) q^{52} +(-1.45786 - 0.702068i) q^{53} +(-2.31513 - 2.90308i) q^{54} +(-2.25323 + 2.82546i) q^{55} +(0.949867 + 0.457432i) q^{56} +11.1609 q^{57} -13.3686 q^{59} +(11.7588 + 5.66272i) q^{60} +(-1.19861 + 1.50300i) q^{61} +(-1.92599 - 2.41511i) q^{62} +(4.92375 + 2.37115i) q^{63} +(5.59044 - 2.69221i) q^{64} +(-3.10723 + 3.89635i) q^{65} +(1.10474 + 4.84020i) q^{66} +(0.672869 + 2.94803i) q^{67} +(4.92126 + 6.17106i) q^{68} +(1.25055 - 5.47901i) q^{69} +15.8389 q^{70} +(-0.921826 + 4.03878i) q^{71} +(-0.810837 + 0.390479i) q^{72} +(3.42082 - 1.64738i) q^{73} +(3.58656 - 15.7137i) q^{74} -12.1545 q^{75} +(1.95252 - 8.55456i) q^{76} +(1.77205 + 2.22208i) q^{77} +(1.52346 + 6.67470i) q^{78} +(2.94521 + 12.9038i) q^{79} +(-8.79086 + 11.0234i) q^{80} +(9.74359 - 4.69226i) q^{81} +(-20.6652 - 9.95183i) q^{82} +(-6.05305 - 7.59028i) q^{83} +(6.39959 - 8.02484i) q^{84} +(-12.8114 - 6.16966i) q^{85} -3.66555 q^{86} -0.468042 q^{88} +(-4.39654 - 2.11726i) q^{89} +(-8.42997 + 10.5709i) q^{90} +(2.44369 + 3.06428i) q^{91} +(-3.98076 - 1.91703i) q^{92} +(3.24917 - 1.56472i) q^{93} +(1.16783 - 1.46441i) q^{94} +(3.51752 + 15.4113i) q^{95} +(3.88888 + 17.0383i) q^{96} +(-9.73579 - 12.2083i) q^{97} +(-0.258912 + 1.13437i) q^{98} -2.42615 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 2 q^{2} + 2 q^{3} - 8 q^{4} + 2 q^{5} + 3 q^{6} + 4 q^{7} + 3 q^{8} - 6 q^{9} + 15 q^{10} + 13 q^{11} + 24 q^{12} + 6 q^{13} - 6 q^{14} + 19 q^{15} - 4 q^{16} - 18 q^{17} + 17 q^{18} - 6 q^{19} + 5 q^{20}+ \cdots - 36 q^{99}+O(q^{100}) $ 36 * q + 2 * q^2 + 2 * q^3 - 8 * q^4 + 2 * q^5 + 3 * q^6 + 4 * q^7 + 3 * q^8 - 6 * q^9 + 15 * q^10 + 13 * q^11 + 24 * q^12 + 6 * q^13 - 6 * q^14 + 19 * q^15 - 4 * q^16 - 18 * q^17 + 17 * q^18 - 6 * q^19 + 5 * q^20 - 2 * q^21 + 4 * q^22 + 5 * q^23 + 10 * q^24 - 6 * q^25 + 9 * q^26 - q^27 - 30 * q^28 + 156 * q^30 + 16 * q^31 + 33 * q^32 - 27 * q^33 + 4 * q^35 + 21 * q^36 - 10 * q^37 - 41 * q^38 + 17 * q^39 + 7 * q^40 - 180 * q^41 + 21 * q^42 - 2 * q^43 + 16 * q^44 - 16 * q^45 + 120 * q^46 + 5 * q^47 - 30 * q^48 + 12 * q^49 - 8 * q^50 + 23 * q^51 + 13 * q^53 - 19 * q^54 + 10 * q^55 + 16 * q^56 - 96 * q^57 - 102 * q^59 - 9 * q^60 - 4 * q^61 + 9 * q^63 - q^64 - 32 * q^65 - 8 * q^66 + 9 * q^67 + 16 * q^68 + 26 * q^69 + 168 * q^70 - 21 * q^72 + 9 * q^73 + 36 * q^74 - 42 * q^75 + 24 * q^76 + 13 * q^77 + 6 * q^79 - 5 * q^80 + 22 * q^81 - 19 * q^82 + 24 * q^83 - 26 * q^85 + 102 * q^86 + 126 * q^88 + 9 * q^89 - 16 * q^90 - 16 * q^91 + 23 * q^92 + 12 * q^93 + 37 * q^94 + 31 * q^95 + 37 * q^96 - 10 * q^97 - 42 * q^98 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{7}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	1.75304	+	0.844219i	1.23959	+	0.596953i	0.934701	−	0.355436i	$-0.115668\pi$
$2$	1.75304	+	0.844219i	1.23959	+	0.596953i	0.304885	+	0.952389i	$0.401382\pi$
$3$	−1.41628	+	1.77596i	−0.817689	+	1.02535i	0.181431	+	0.983404i	$0.441927\pi$
$3$	−1.41628	+	1.77596i	−0.817689	+	1.02535i	−0.999120	+	0.0419461i	$0.986644\pi$
$4$	1.11346	+	1.39624i	0.556730	+	0.698118i
$5$	−2.89865	−	1.39592i	−1.29632	−	0.624273i	−0.346785	−	0.937944i	$-0.612727\pi$
$5$	−2.89865	−	1.39592i	−1.29632	−	0.624273i	−0.949532	+	0.313671i	$0.898441\pi$
$6$	−3.98209	+	1.91767i	−1.62568	+	0.782887i
$7$	−1.57757	+	1.97820i	−0.596264	+	0.747691i	−0.984790	−	0.173747i	$-0.944413\pi$
$7$	−1.57757	+	1.97820i	−0.596264	+	0.747691i	0.388527	+	0.921437i	$0.372984\pi$
$8$	−0.0927185	−	0.406226i	−0.0327809	−	0.143623i
$9$	−0.480617	−	2.10572i	−0.160206	−	0.701907i
$10$	−3.90299	−	4.89420i	−1.23423	−	1.54768i
$11$	0.249954	−	1.09512i	0.0753640	−	0.330191i	−0.923165	−	0.384403i	$-0.874407\pi$
$11$	0.249954	−	1.09512i	0.0753640	−	0.330191i	0.998529	+	0.0542115i	$0.0172645\pi$
$12$	−4.05663			−1.17105
$13$	0.344690	−	1.51019i	0.0955998	−	0.418850i	−0.904369	−	0.426751i	$-0.859658\pi$
$13$	0.344690	−	1.51019i	0.0955998	−	0.418850i	0.999969	+	0.00790118i	$0.00251505\pi$
$14$	−4.43557	+	2.13606i	−1.18546	+	0.570886i
$15$	6.58439	−	3.17088i	1.70008	−	0.818717i
$16$	0.975184	−	4.27256i	0.243796	−	1.06814i
$17$	4.41979			1.07196			0.535978	−	0.844232i	$-0.319943\pi$
$17$	4.41979			1.07196			0.535978	+	0.844232i	$0.319943\pi$
$18$	0.935150	−	4.09716i	0.220417	−	0.965710i
$19$	−3.06344	−	3.84143i	−0.702801	−	0.881285i	0.294428	−	0.955674i	$-0.404871\pi$
$19$	−3.06344	−	3.84143i	−0.702801	−	0.881285i	−0.997229	+	0.0743890i	$0.976299\pi$
$20$	−1.27851	−	5.60150i	−0.285883	−	1.25253i
$21$	−1.27893	−	5.60338i	−0.279086	−	1.22276i
$22$	1.36270	−	1.70877i	0.290529	−	0.364312i
$23$	−2.22905	+	1.07345i	−0.464789	+	0.223831i	−0.651596	−	0.758566i	$-0.725900\pi$
$23$	−2.22905	+	1.07345i	−0.464789	+	0.223831i	0.186807	+	0.982397i	$0.440186\pi$
$24$	0.852756	+	0.410666i	0.174068	+	0.0838267i
$25$	3.33615	+	4.18341i	0.667231	+	0.836681i
$26$	1.87918	−	2.35642i	0.368538	−	0.462132i
$27$	−1.71939	−	0.828013i	−0.330896	−	0.159351i
$28$	−4.51860			−0.853934
$29$		0			0
$29$		0			0
$30$	14.2196			2.59613
$31$	−1.43038	−	0.688836i	−0.256904	−	0.123719i	0.300999	−	0.953624i	$-0.402680\pi$
$31$	−1.43038	−	0.688836i	−0.256904	−	0.123719i	−0.557904	+	0.829906i	$0.688394\pi$
$32$	4.79693	−	6.01516i	0.847985	−	1.06334i
$33$	1.59088	+	1.99490i	0.276937	+	0.347268i
$34$	7.74806	+	3.73127i	1.32878	+	0.639907i
$35$	7.33422	−	3.53198i	1.23971	−	0.597013i
$36$	2.40494	−	3.01569i	0.400823	−	0.502616i
$37$	−1.84330	−	8.07603i	−0.303037	−	1.32769i	−0.865517	−	0.500880i	$-0.833010\pi$
$37$	−1.84330	−	8.07603i	−0.303037	−	1.32769i	0.562480	−	0.826811i	$-0.309847\pi$
$38$	−2.12732	−	9.32039i	−0.345097	−	1.51197i
$39$	2.19385	+	2.75100i	0.351297	+	0.440513i
$40$	−0.298300	+	1.30694i	−0.0471653	+	0.206645i
$41$	−11.7882			−1.84101			−0.920504	−	0.390733i	$-0.872222\pi$
$41$	−11.7882			−1.84101			−0.920504	+	0.390733i	$0.872222\pi$
$42$	2.48846	−	10.9026i	0.383977	−	1.68231i
$43$	−1.69733	+	0.817393i	−0.258841	+	0.124651i	−0.558805	−	0.829299i	$-0.688740\pi$
$43$	−1.69733	+	0.817393i	−0.258841	+	0.124651i	0.299963	+	0.953951i	$0.403026\pi$
$44$	1.80736	−	0.870379i	0.272470	−	0.131215i
$45$	−1.54627	+	6.77466i	−0.230505	+	1.00991i
$46$	−4.81385			−0.709763
$47$	0.214209	−	0.938513i	0.0312457	−	0.136896i	−0.956899	−	0.290420i	$-0.906205\pi$
$47$	0.214209	−	0.938513i	0.0312457	−	0.136896i	0.988145	+	0.153524i	$0.0490622\pi$
$48$	6.20675	+	7.78302i	0.895868	+	1.12338i
$49$	0.133067	+	0.583004i	0.0190096	+	0.0832863i
$50$	2.31670	+	10.1501i	0.327631	+	1.43544i
$51$	−6.25965	+	7.84936i	−0.876527	+	1.09913i
$52$	2.49237	−	1.20026i	0.345630	−	0.166447i
$53$	−1.45786	−	0.702068i	−0.200252	−	0.0964364i	0.331070	−	0.943606i	$-0.392590\pi$
$53$	−1.45786	−	0.702068i	−0.200252	−	0.0964364i	−0.531322	+	0.847170i	$0.678305\pi$
$54$	−2.31513	−	2.90308i	−0.315049	−	0.395059i
$55$	−2.25323	+	2.82546i	−0.303825	+	0.380985i
$56$	0.949867	+	0.457432i	0.126931	+	0.0611269i
$57$	11.1609			1.47830
$58$		0			0
$59$	−13.3686			−1.74045			−0.870224	−	0.492657i	$-0.836026\pi$
$59$	−13.3686			−1.74045			−0.870224	+	0.492657i	$0.836026\pi$
$60$	11.7588	+	5.66272i	1.51805	+	0.731054i
$61$	−1.19861	+	1.50300i	−0.153466	+	0.192440i	−0.852621	−	0.522530i	$-0.824988\pi$
$61$	−1.19861	+	1.50300i	−0.153466	+	0.192440i	0.699155	+	0.714970i	$0.253560\pi$
$62$	−1.92599	−	2.41511i	−0.244601	−	0.306720i
$63$	4.92375	+	2.37115i	0.620334	+	0.298737i
$64$	5.59044	−	2.69221i	0.698805	−	0.336527i
$65$	−3.10723	+	3.89635i	−0.385405	+	0.483282i
$66$	1.10474	+	4.84020i	0.135985	+	0.595788i
$67$	0.672869	+	2.94803i	0.0822040	+	0.360159i	0.999254	−	0.0386123i	$-0.0122937\pi$
$67$	0.672869	+	2.94803i	0.0822040	+	0.360159i	−0.917050	+	0.398772i	$0.869437\pi$
$68$	4.92126	+	6.17106i	0.596790	+	0.748351i
$69$	1.25055	−	5.47901i	0.150548	−	0.659596i
$70$	15.8389			1.89312
$71$	−0.921826	+	4.03878i	−0.109401	+	0.479315i	0.890312	+	0.455351i	$0.150486\pi$
$71$	−0.921826	+	4.03878i	−0.109401	+	0.479315i	−0.999713	+	0.0239648i	$0.992371\pi$
$72$	−0.810837	+	0.390479i	−0.0955581	+	0.0460183i
$73$	3.42082	−	1.64738i	0.400377	−	0.192811i	−0.222850	−	0.974853i	$-0.571536\pi$
$73$	3.42082	−	1.64738i	0.400377	−	0.192811i	0.623226	+	0.782042i	$0.285822\pi$
$74$	3.58656	−	15.7137i	0.416929	−	1.82669i
$75$	−12.1545			−1.40348
$76$	1.95252	−	8.55456i	0.223970	−	0.981276i
$77$	1.77205	+	2.22208i	0.201944	+	0.253230i
$78$	1.52346	+	6.67470i	0.172498	+	0.755761i
$79$	2.94521	+	12.9038i	0.331362	+	1.45179i	0.816496	+	0.577351i	$0.195914\pi$
$79$	2.94521	+	12.9038i	0.331362	+	1.45179i	−0.485134	+	0.874440i	$0.661229\pi$
$80$	−8.79086	+	11.0234i	−0.982848	+	1.23245i
$81$	9.74359	−	4.69226i	1.08262	−	0.521363i
$82$	−20.6652	−	9.95183i	−2.28209	−	1.09900i
$83$	−6.05305	−	7.59028i	−0.664408	−	0.833142i	0.329407	−	0.944188i	$-0.393151\pi$
$83$	−6.05305	−	7.59028i	−0.664408	−	0.833142i	−0.993815	+	0.111046i	$0.964580\pi$
$84$	6.39959	−	8.02484i	0.698253	−	0.875581i
$85$	−12.8114	−	6.16966i	−1.38959	−	0.669194i
$86$	−3.66555			−0.395267
$87$		0			0
$88$	−0.468042			−0.0498934
$89$	−4.39654	−	2.11726i	−0.466032	−	0.224429i	0.186106	−	0.982530i	$-0.440413\pi$
$89$	−4.39654	−	2.11726i	−0.466032	−	0.224429i	−0.652138	+	0.758100i	$0.726128\pi$
$90$	−8.42997	+	10.5709i	−0.888597	+	1.11427i
$91$	2.44369	+	3.06428i	0.256168	+	0.321224i
$92$	−3.98076	−	1.91703i	−0.415023	−	0.199864i
$93$	3.24917	−	1.56472i	0.336923	−	0.162254i
$94$	1.16783	−	1.46441i	0.120452	−	0.151042i
$95$	3.51752	+	15.4113i	0.360890	+	1.58116i
$96$	3.88888	+	17.0383i	0.396907	+	1.73896i
$97$	−9.73579	−	12.2083i	−0.988520	−	1.23956i	−0.970842	−	0.239721i	$-0.922944\pi$
$97$	−9.73579	−	12.2083i	−0.988520	−	1.23956i	−0.0176778	−	0.999844i	$-0.505627\pi$
$98$	−0.258912	+	1.13437i	−0.0261541	+	0.114588i
$99$	−2.42615			−0.243837
$100$	−2.12634	+	9.31612i	−0.212634	+	0.931612i
$101$	10.2658	−	4.94374i	1.02148	−	0.491920i	0.153308	−	0.988179i	$-0.451007\pi$
$101$	10.2658	−	4.94374i	1.02148	−	0.491920i	0.868175	+	0.496258i	$0.165293\pi$
$102$	−17.6000	+	8.47571i	−1.74266	+	0.839220i
$103$	−1.64423	+	7.20385i	−0.162011	+	0.709816i	0.827028	+	0.562161i	$0.190030\pi$
$103$	−1.64423	+	7.20385i	−0.162011	+	0.709816i	−0.989039	+	0.147655i	$0.952827\pi$
$104$	−0.645436			−0.0632902
$105$	−4.11467	+	18.0275i	−0.401551	+	1.75931i
$106$	−1.96298	−	2.46150i	−0.190662	−	0.239082i
$107$	2.65249	+	11.6213i	0.256426	+	1.12347i	0.925042	+	0.379866i	$0.124030\pi$
$107$	2.65249	+	11.6213i	0.256426	+	1.12347i	−0.668616	+	0.743608i	$0.733113\pi$
$108$	−0.758368	−	3.32263i	−0.0729740	−	0.319720i
$109$	10.0830	−	12.6437i	0.965776	−	1.21104i	−0.0116856	−	0.999932i	$-0.503720\pi$
$109$	10.0830	−	12.6437i	0.965776	−	1.21104i	0.977462	−	0.211113i	$-0.0677089\pi$
$110$	−6.33531	+	3.05092i	−0.604048	+	0.290894i
$111$	16.9533	+	8.16429i	1.60914	+	0.774920i
$112$	6.91358	+	8.66935i	0.653272	+	0.819177i
$113$	−3.95801	+	4.96319i	−0.372338	+	0.466898i	−0.932334	−	0.361598i	$-0.882231\pi$
$113$	−3.95801	+	4.96319i	−0.372338	+	0.466898i	0.559996	+	0.828495i	$0.310803\pi$
$114$	19.5655	+	9.42225i	1.83248	+	0.882474i
$115$	7.95970			0.742246
$116$		0			0
$117$	−3.34570			−0.309310
$118$	−23.4357	−	11.2861i	−2.15743	−	1.03897i
$119$	−6.97250	+	8.74324i	−0.639168	+	0.801492i
$120$	−1.89859	−	2.38075i	−0.173317	−	0.217332i
$121$	8.77385	+	4.22526i	0.797622	+	0.384115i
$122$	−3.37007	+	1.62294i	−0.305112	+	0.146934i
$123$	16.6954	−	20.9354i	1.50537	−	1.88768i
$124$	−0.630898	−	2.76414i	−0.0566563	−	0.248227i
$125$	−0.251124	−	1.10025i	−0.0224612	−	0.0984091i
$126$	6.62976	+	8.31345i	0.590626	+	0.740621i
$127$	3.97011	−	17.3942i	0.352291	−	1.54349i	−0.419587	−	0.907715i	$-0.637825\pi$
$127$	3.97011	−	17.3942i	0.352291	−	1.54349i	0.771878	−	0.635771i	$-0.219318\pi$
$128$	−3.31428			−0.292943
$129$	0.952244	−	4.17205i	0.0838404	−	0.367329i
$130$	−8.73647	+	4.20726i	−0.766239	+	0.369001i
$131$	−0.517814	+	0.249366i	−0.0452416	+	0.0217872i	−0.456368	−	0.889791i	$-0.650850\pi$
$131$	−0.517814	+	0.249366i	−0.0452416	+	0.0217872i	0.411126	+	0.911578i	$0.365136\pi$
$132$	−1.01397	+	4.44250i	−0.0882548	+	0.386670i
$133$	12.4319			1.07798
$134$	−1.30922	+	5.73606i	−0.113099	+	0.495520i
$135$	3.82807	+	4.80025i	0.329468	+	0.413139i
$136$	−0.409796	−	1.79543i	−0.0351397	−	0.153957i
$137$	−3.06697	−	13.4373i	−0.262029	−	1.14803i	−0.919046	−	0.394149i	$-0.871039\pi$
$137$	−3.06697	−	13.4373i	−0.262029	−	1.14803i	0.657017	−	0.753876i	$-0.271818\pi$
$138$	6.81775	−	8.54919i	0.580366	−	0.727755i
$139$	−9.55146	+	4.59974i	−0.810144	+	0.390145i	−0.792631	−	0.609702i	$-0.791289\pi$
$139$	−9.55146	+	4.59974i	−0.810144	+	0.390145i	−0.0175134	+	0.999847i	$0.505575\pi$
$140$	13.0978	+	6.30759i	1.10697	+	0.533088i
$141$	1.36338	+	1.70962i	0.114817	+	0.143976i
$142$	−5.02562	+	6.30192i	−0.421740	+	0.528846i
$143$	−1.56768	−	0.754955i	−0.131096	−	0.0631325i
$144$	−9.46551			−0.788793
$145$		0			0
$146$	7.38758			0.611400
$147$	−1.22385	−	0.589376i	−0.100942	−	0.0486109i
$148$	9.22359	−	11.5660i	0.758175	−	0.950721i
$149$	1.47553	+	1.85025i	0.120880	+	0.151579i	0.838589	−	0.544764i	$-0.183381\pi$
$149$	1.47553	+	1.85025i	0.120880	+	0.151579i	−0.717709	+	0.696343i	$0.754809\pi$
$150$	−21.3073	−	10.2610i	−1.73973	−	0.837811i
$151$	−8.78385	+	4.23008i	−0.714820	+	0.344239i	−0.755694	−	0.654925i	$-0.772700\pi$
$151$	−8.78385	+	4.23008i	−0.714820	+	0.344239i	0.0408740	+	0.999164i	$0.486986\pi$
$152$	−1.27645	+	1.60062i	−0.103534	+	0.129827i
$153$	−2.12423	−	9.30684i	−0.171734	−	0.752414i
$154$	1.23055	+	5.39140i	0.0991607	+	0.434452i
$155$	3.18463	+	3.99340i	0.255795	+	0.320757i
$156$	−1.39828	+	6.12626i	−0.111952	+	0.490494i
$157$	18.7547			1.49679			0.748396	−	0.663252i	$-0.230824\pi$
$157$	18.7547			1.49679			0.748396	+	0.663252i	$0.230824\pi$
$158$	−5.73057	+	25.1073i	−0.455900	+	1.99743i
$159$	3.31158	−	1.59477i	0.262625	−	0.126474i
$160$	−22.3013	+	10.7397i	−1.76307	+	0.849051i
$161$	1.39296	−	6.10296i	0.109781	−	0.480981i
$162$	21.0422			1.65323
$163$	2.14783	−	9.41026i	0.168231	−	0.737068i	−0.818474	−	0.574544i	$-0.805179\pi$
$163$	2.14783	−	9.41026i	0.168231	−	0.737068i	0.986705	−	0.162524i	$-0.0519635\pi$
$164$	−13.1257	−	16.4591i	−1.02495	−	1.28524i
$165$	−1.82670	−	8.00328i	−0.142208	−	0.623055i
$166$	−4.20337	−	18.4162i	−0.326245	−	1.42937i
$167$	0.289826	−	0.363430i	0.0224274	−	0.0281231i	−0.770491	−	0.637450i	$-0.779989\pi$
$167$	0.289826	−	0.363430i	0.0224274	−	0.0281231i	0.792919	+	0.609327i	$0.208560\pi$
$168$	−2.15766	+	1.03907i	−0.166467	+	0.0801662i
$169$	9.55074	+	4.59940i	0.734673	+	0.353800i
$170$	−17.2504	−	21.6313i	−1.32304	−	1.65905i
$171$	−6.61664	+	8.29701i	−0.505987	+	0.634488i
$172$	−3.03119	−	1.45974i	−0.231126	−	0.111304i
$173$	−22.2914			−1.69478			−0.847392	−	0.530968i	$-0.821828\pi$
$173$	−22.2914			−1.69478			−0.847392	+	0.530968i	$0.821828\pi$
$174$		0			0
$175$	−13.5386			−1.02342
$176$	−4.43522	−	2.13589i	−0.334317	−	0.160999i
$177$	18.9337	−	23.7421i	1.42315	−	1.78457i
$178$	−5.91987	−	7.42328i	−0.443713	−	0.556399i
$179$	−6.76622	−	3.25844i	−0.505731	−	0.243547i	0.163579	−	0.986530i	$-0.447696\pi$
$179$	−6.76622	−	3.25844i	−0.505731	−	0.243547i	−0.669310	+	0.742983i	$0.733410\pi$
$180$	−11.1807	+	5.38436i	−0.833363	+	0.401326i
$181$	−14.9245	+	18.7148i	−1.10933	+	1.39106i	−0.197595	+	0.980284i	$0.563313\pi$
$181$	−14.9245	+	18.7148i	−1.10933	+	1.39106i	−0.911737	+	0.410775i	$0.865258\pi$
$182$	1.69695	+	7.43482i	0.125786	+	0.551105i
$183$	−0.971712	−	4.25735i	−0.0718310	−	0.314712i
$184$	0.642740	+	0.805970i	0.0473834	+	0.0594169i
$185$	−5.93038	+	25.9827i	−0.436010	+	1.91029i
$186$	7.01688			0.514503
$187$	1.10474	−	4.84020i	0.0807869	−	0.353951i
$188$	1.54890	−	0.745910i	0.112965	−	0.0544011i
$189$	4.35042	−	2.09505i	0.316447	−	0.152393i
$190$	−6.84414	+	29.9861i	−0.496526	+	2.17542i
$191$	−13.4059			−0.970016			−0.485008	−	0.874510i	$-0.661183\pi$
$191$	−13.4059			−0.970016			−0.485008	+	0.874510i	$0.661183\pi$
$192$	−3.13637	+	13.7413i	−0.226348	+	0.991694i
$193$	−7.96230	−	9.98441i	−0.573139	−	0.718693i	0.407787	−	0.913077i	$-0.366301\pi$
$193$	−7.96230	−	9.98441i	−0.573139	−	0.718693i	−0.980926	+	0.194384i	$0.937729\pi$
$194$	−6.76074	−	29.6208i	−0.485393	−	2.12665i
$195$	−2.51904	−	11.0366i	−0.180392	−	0.790350i
$196$	−0.665847	+	0.834945i	−0.0475605	+	0.0596389i
$197$	3.67334	−	1.76899i	0.261715	−	0.126035i	−0.298426	−	0.954433i	$-0.596462\pi$
$197$	3.67334	−	1.76899i	0.261715	−	0.126035i	0.560140	+	0.828398i	$0.310747\pi$
$198$	−4.25314	−	2.04820i	−0.302257	−	0.145560i
$199$	10.5793	+	13.2660i	0.749945	+	0.940402i	0.999610	−	0.0279307i	$-0.00889178\pi$
$199$	10.5793	+	13.2660i	0.749945	+	0.940402i	−0.249665	+	0.968332i	$0.580320\pi$
$200$	1.39009	−	1.74311i	0.0982939	−	0.123257i
$201$	−6.18855	−	2.98025i	−0.436507	−	0.210211i
$202$	22.1699			1.55987
$203$		0			0
$204$	−17.9294			−1.25531
$205$	34.1699	+	16.4554i	2.38653	+	1.14929i
$206$	−8.96403	+	11.2405i	−0.624553	+	0.783165i
$207$	3.33172	+	4.17784i	0.231570	+	0.290380i
$208$	−6.11622	−	2.94542i	−0.424084	−	0.204228i
$209$	−4.97255	+	2.39465i	−0.343958	+	0.165642i
$210$	−22.4324	+	28.1293i	−1.54798	+	1.94111i
$211$	0.982698	+	4.30548i	0.0676517	+	0.296402i	0.997424	−	0.0717341i	$-0.0228533\pi$
$211$	0.982698	+	4.30548i	0.0676517	+	0.296402i	−0.929772	+	0.368136i	$0.879996\pi$
$212$	−0.643016	−	2.81724i	−0.0441625	−	0.193489i
$213$	−5.86715	−	7.35717i	−0.402010	−	0.504105i
$214$	−5.16101	+	22.6119i	−0.352800	+	1.54572i
$215$	6.06100			0.413357
$216$	−0.176942	+	0.775232i	−0.0120394	+	0.0527478i
$217$	3.61918	−	1.74291i	0.245686	−	0.118316i
$218$	28.3499	−	13.6526i	1.92010	−	0.924671i
$219$	−1.91916	+	8.40838i	−0.129685	+	0.568186i
$220$	−6.45389			−0.435121
$221$	1.52346	−	6.67470i	0.102479	−	0.448989i
$222$	22.8274	+	28.6246i	1.53207	+	1.92116i
$223$	3.79805	+	16.6403i	0.254336	+	1.11432i	0.927204	+	0.374556i	$0.122205\pi$
$223$	3.79805	+	16.6403i	0.254336	+	1.11432i	−0.672868	+	0.739762i	$0.734938\pi$
$224$	4.33174	+	18.9786i	0.289427	+	1.26806i
$225$	7.20568	−	9.03563i	0.480378	−	0.602375i
$226$	−11.1286	+	5.35924i	−0.740261	+	0.356491i
$227$	8.81155	+	4.24342i	0.584843	+	0.281645i	0.702816	−	0.711371i	$-0.251926\pi$
$227$	8.81155	+	4.24342i	0.584843	+	0.281645i	−0.117974	+	0.993017i	$0.537640\pi$
$228$	12.4272	+	15.5833i	0.823013	+	1.03203i
$229$	2.14430	−	2.68887i	0.141699	−	0.177686i	−0.705918	−	0.708294i	$-0.749465\pi$
$229$	2.14430	−	2.68887i	0.141699	−	0.177686i	0.847617	+	0.530608i	$0.178037\pi$
$230$	13.9537	+	6.71973i	0.920078	+	0.443086i
$231$	−6.45605			−0.424777
$232$		0			0
$233$	−4.39157			−0.287702			−0.143851	−	0.989599i	$-0.545949\pi$
$233$	−4.39157			−0.287702			−0.143851	+	0.989599i	$0.545949\pi$
$234$	−5.86514	−	2.82450i	−0.383416	−	0.184643i
$235$	−1.93101	+	2.42140i	−0.125965	+	0.157955i
$236$	−14.8854	−	18.6658i	−0.968960	−	1.21504i
$237$	−27.0879	−	13.0448i	−1.75954	−	0.847352i
$238$	−19.6043	+	9.44092i	−1.27076	+	0.611964i
$239$	11.0235	−	13.8230i	0.713050	−	0.894136i	−0.284873	−	0.958565i	$-0.591951\pi$
$239$	11.0235	−	13.8230i	0.713050	−	0.894136i	0.997922	+	0.0644294i	$0.0205227\pi$
$240$	−7.12677	−	31.2244i	−0.460031	−	2.01553i
$241$	−2.53826	−	11.1208i	−0.163503	−	0.716355i	−0.988500	−	0.151218i	$-0.951680\pi$
$241$	−2.53826	−	11.1208i	−0.163503	−	0.716355i	0.824997	−	0.565137i	$-0.191177\pi$
$242$	11.8138	+	14.8141i	0.759423	+	0.952286i
$243$	−4.19242	+	18.3682i	−0.268944	+	1.17832i
$244$	−3.43315			−0.219785
$245$	0.428111	−	1.87568i	0.0273510	−	0.119833i
$246$	46.9417	−	22.6059i	2.99289	−	1.44130i
$247$	−6.85721	+	3.30226i	−0.436314	+	0.210118i
$248$	−0.147200	+	0.644927i	−0.00934723	+	0.0409529i
$249$	22.0528			1.39754
$250$	0.488619	−	2.14078i	0.0309030	−	0.135395i
$251$	−15.9212	−	19.9646i	−1.00494	−	1.26015i	−0.965356	−	0.260935i	$-0.915969\pi$
$251$	−15.9212	−	19.9646i	−1.00494	−	1.26015i	−0.0395807	−	0.999216i	$-0.512602\pi$
$252$	2.17171	+	9.51490i	0.136805	+	0.599383i
$253$	0.618402	+	2.70940i	0.0388786	+	0.170338i
$254$	21.6443	−	27.1411i	1.35808	−	1.70298i
$255$	29.1016	−	14.0146i	1.82241	−	0.877629i
$256$	−16.9909	−	8.18240i	−1.06193	−	0.511400i
$257$	0.111366	+	0.139648i	0.00694681	+	0.00871103i	0.785293	−	0.619125i	$-0.212512\pi$
$257$	0.111366	+	0.139648i	0.00694681	+	0.00871103i	−0.778346	+	0.627836i	$0.783941\pi$
$258$	5.19145	−	6.50987i	0.323205	−	0.405287i
$259$	18.8840	+	9.09403i	1.17339	+	0.565076i
$260$	−8.90000			−0.551955
$261$		0			0
$262$	−1.11827			−0.0690869
$263$	5.07453	+	2.44376i	0.312909	+	0.150689i	0.583746	−	0.811936i	$-0.301586\pi$
$263$	5.07453	+	2.44376i	0.312909	+	0.150689i	−0.270837	+	0.962625i	$0.587301\pi$
$264$	0.662878	−	0.831223i	0.0407973	−	0.0511582i
$265$	3.24580	+	4.07010i	0.199388	+	0.250024i
$266$	21.7936	+	10.4953i	1.33625	+	0.643505i
$267$	9.98689	−	4.80943i	0.611188	−	0.294333i
$268$	−3.36693	+	4.22200i	−0.205668	+	0.257900i
$269$	−0.433544	−	1.89948i	−0.0264336	−	0.115813i	0.959990	−	0.280035i	$-0.0903460\pi$
$269$	−0.433544	−	1.89948i	−0.0264336	−	0.115813i	−0.986423	+	0.164221i	$0.947489\pi$
$270$	2.65829	+	11.6467i	0.161779	+	0.708798i
$271$	10.8748	+	13.6365i	0.660595	+	0.828359i	0.993408	−	0.114633i	$-0.0365693\pi$
$271$	10.8748	+	13.6365i	0.660595	+	0.828359i	−0.332813	+	0.942993i	$0.607998\pi$
$272$	4.31011	−	18.8838i	0.261339	−	1.14500i
$273$	−8.90298			−0.538833
$274$	5.96749	−	26.1453i	0.360509	−	1.57949i
$275$	5.41522	−	2.60783i	0.326550	−	0.157258i
$276$	9.04243	−	4.35461i	0.544290	−	0.262116i
$277$	3.41448	−	14.9598i	0.205156	−	0.898849i	−0.762582	−	0.646892i	$-0.776069\pi$
$277$	3.41448	−	14.9598i	0.205156	−	0.898849i	0.967738	−	0.251957i	$-0.0810742\pi$
$278$	−20.6273			−1.23714
$279$	−0.763031	+	3.34306i	−0.0456815	+	0.200144i
$280$	−2.11480	−	2.65187i	−0.126383	−	0.158480i
$281$	2.93977	+	12.8800i	0.175372	+	0.768354i	0.983729	+	0.179661i	$0.0575001\pi$
$281$	2.93977	+	12.8800i	0.175372	+	0.768354i	−0.808357	+	0.588693i	$0.799643\pi$
$282$	0.946760	+	4.14803i	0.0563788	+	0.247011i
$283$	−6.95581	+	8.72231i	−0.413480	+	0.518488i	−0.944340	−	0.328972i	$-0.893298\pi$
$283$	−6.95581	+	8.72231i	−0.413480	+	0.518488i	0.530860	+	0.847460i	$0.321869\pi$
$284$	−6.66551	+	3.20994i	−0.395525	+	0.190475i
$285$	−32.3516	−	15.5797i	−1.91634	−	0.922862i
$286$	−2.11086	−	2.64693i	−0.124818	−	0.156516i
$287$	18.5967	−	23.3195i	1.09773	−	1.37651i
$288$	−14.9717	−	7.21001i	−0.882218	−	0.424854i
$289$	2.53452			0.149090
$290$		0			0
$291$	35.4700			2.07929
$292$	6.10908	+	2.94198i	0.357507	+	0.172166i
$293$	4.24146	−	5.31862i	0.247789	−	0.310717i	−0.642346	−	0.766415i	$-0.722039\pi$
$293$	4.24146	−	5.31862i	0.247789	−	0.310717i	0.890135	+	0.455698i	$0.150610\pi$
$294$	−1.64790	−	2.06640i	−0.0961073	−	0.120515i
$295$	38.7510	+	18.6615i	2.25617	+	1.08651i
$296$	−3.10978	+	1.49759i	−0.180753	+	0.0870459i
$297$	−1.33654	+	1.67597i	−0.0775540	+	0.0972497i
$298$	1.02464	+	4.48923i	0.0593557	+	0.260054i
$299$	0.852784	+	3.73629i	0.0493178	+	0.216075i
$300$	−13.5335	−	16.9705i	−0.781359	−	0.979793i
$301$	1.06069	−	4.64717i	0.0611369	−	0.267858i
$302$	−18.9695			−1.09157
$303$	−5.75933	+	25.2333i	−0.330865	+	1.44961i
$304$	−19.4002	+	9.34262i	−1.11268	+	0.535836i
$305$	5.57241	−	2.68353i	0.319075	−	0.153659i
$306$	4.13316	−	18.1086i	0.236277	−	1.03520i
$307$	16.1578			0.922176			0.461088	−	0.887354i	$-0.347459\pi$
$307$	16.1578			0.922176			0.461088	+	0.887354i	$0.347459\pi$
$308$	−1.12944	+	4.94841i	−0.0643559	+	0.281962i
$309$	−10.4650	−	13.1227i	−0.595335	−	0.746527i
$310$	2.21147	+	9.68910i	0.125603	+	0.550304i
$311$	−0.965638	−	4.23074i	−0.0547563	−	0.239903i	0.940142	−	0.340782i	$-0.110692\pi$
$311$	−0.965638	−	4.23074i	−0.0547563	−	0.239903i	−0.994899	+	0.100879i	$0.967835\pi$
$312$	0.914118	−	1.14627i	0.0517517	−	0.0648946i
$313$	−0.967103	+	0.465732i	−0.0546639	+	0.0263247i	−0.461016	−	0.887392i	$-0.652515\pi$
$313$	−0.967103	+	0.465732i	−0.0546639	+	0.0263247i	0.406352	+	0.913717i	$0.366801\pi$
$314$	32.8778	+	15.8331i	1.85540	+	0.893514i
$315$	−10.9623	−	13.7463i	−0.617656	−	0.774517i
$316$	−14.7374	+	18.4801i	−0.829042	+	1.03959i
$317$	7.02229	+	3.38175i	0.394411	+	0.189938i	0.620568	−	0.784153i	$-0.286902\pi$
$317$	7.02229	+	3.38175i	0.394411	+	0.189938i	−0.226157	+	0.974091i	$0.572616\pi$
$318$	7.15166			0.401045
$319$		0			0
$320$	−19.9629			−1.11596
$321$	−24.3956	−	11.7483i	−1.36163	−	0.655727i
$322$	7.59416	−	9.52277i	0.423206	−	0.530683i
$323$	−13.5397	−	16.9783i	−0.753372	−	0.944698i
$324$	17.4006	+	8.37969i	0.966700	+	0.465538i
$325$	7.46766	−	3.59624i	0.414231	−	0.199483i
$326$	11.7095	−	14.6833i	0.648532	−	0.813233i
$327$	8.17430	+	35.8140i	0.452040	+	1.98052i
$328$	1.09298	+	4.78868i	0.0603500	+	0.264410i
$329$	1.51864	+	1.90432i	0.0837254	+	0.104988i
$330$	3.55425	−	15.5722i	0.195655	−	0.857221i
$331$	9.95716			0.547295			0.273648	−	0.961830i	$-0.411770\pi$
$331$	9.95716			0.547295			0.273648	+	0.961830i	$0.411770\pi$
$332$	3.85799	−	16.9030i	0.211735	−	0.927670i
$333$	−16.1199	+	7.76296i	−0.883368	+	0.425407i
$334$	0.814891	−	0.392431i	0.0445889	−	0.0214729i
$335$	2.16480	−	9.48459i	0.118275	−	0.518198i
$336$	−25.1880			−1.37412
$337$	−4.75303	+	20.8244i	−0.258914	+	1.13438i	0.663501	+	0.748175i	$0.269070\pi$
$337$	−4.75303	+	20.8244i	−0.258914	+	1.13438i	−0.922415	+	0.386200i	$0.873787\pi$
$338$	12.8599	+	16.1258i	0.699488	+	0.877130i
$339$	−3.20877	−	14.0585i	−0.174276	−	0.763554i
$340$	−5.65073	−	24.7575i	−0.306454	−	1.34266i
$341$	−1.11189	+	1.39427i	−0.0602122	+	0.0755037i
$342$	−18.6037	+	8.95908i	−1.00597	+	0.484452i
$343$	−17.3208	−	8.34124i	−0.935233	−	0.450384i
$344$	0.489421	+	0.613714i	0.0263878	+	0.0330892i
$345$	−11.2732	+	14.1361i	−0.606927	+	0.761062i
$346$	−39.0777	−	18.8188i	−2.10083	−	1.01171i
$347$	26.9149			1.44487			0.722434	−	0.691440i	$-0.243023\pi$
$347$	26.9149			1.44487			0.722434	+	0.691440i	$0.243023\pi$
$348$		0			0
$349$	18.7783			1.00518			0.502591	−	0.864524i	$-0.332380\pi$
$349$	18.7783			1.00518			0.502591	+	0.864524i	$0.332380\pi$
$350$	−23.7338	−	11.4296i	−1.26862	−	0.610936i
$351$	−1.84311	+	2.31119i	−0.0983779	+	0.123362i
$352$	−5.38831	−	6.75673i	−0.287198	−	0.360135i
$353$	−26.6474	−	12.8327i	−1.41830	−	0.683016i	−0.441515	−	0.897254i	$-0.645559\pi$
$353$	−26.6474	−	12.8327i	−1.41830	−	0.683016i	−0.976782	+	0.214238i	$0.931273\pi$
$354$	53.2351	−	25.6367i	2.82941	−	1.36257i
$355$	8.30986	−	10.4202i	0.441042	−	0.553049i
$356$	−1.93918	−	8.49609i	−0.102776	−	0.450292i
$357$	−5.65262	−	24.7657i	−0.299168	−	1.31074i
$358$	−9.11061	−	11.4243i	−0.481511	−	0.603795i
$359$	4.51356	−	19.7752i	0.238216	−	1.04369i	−0.704396	−	0.709807i	$-0.748782\pi$
$359$	4.51356	−	19.7752i	0.238216	−	1.04369i	0.942613	−	0.333888i	$-0.108361\pi$
$360$	2.89541			0.152602
$361$	−1.14403	+	5.01234i	−0.0602123	+	0.263807i
$362$	−41.9627	+	20.2082i	−2.20551	+	1.06212i
$363$	−19.9301	+	9.59783i	−1.04606	+	0.503756i
$364$	−1.55752	+	6.82392i	−0.0816360	+	0.357671i
$365$	−12.2154			−0.639382
$366$	1.89069	−	8.28364i	0.0988277	−	0.432993i
$367$	10.5952	+	13.2859i	0.553063	+	0.693519i	0.977259	−	0.212051i	$-0.0680144\pi$
$367$	10.5952	+	13.2859i	0.553063	+	0.693519i	−0.424195	+	0.905571i	$0.639443\pi$
$368$	2.41266	+	10.5706i	0.125769	+	0.551029i
$369$	5.66562	+	24.8227i	0.294940	+	1.29222i
$370$	−32.3313	+	40.5421i	−1.68082	+	2.10769i
$371$	3.68870	−	1.77638i	0.191508	−	0.0922253i
$372$	5.80253	+	2.79435i	0.300847	+	0.144880i
$373$	−6.49402	−	8.14325i	−0.336248	−	0.421641i	0.584747	−	0.811215i	$-0.301194\pi$
$373$	−6.49402	−	8.14325i	−0.336248	−	0.421641i	−0.920995	+	0.389574i	$0.872622\pi$
$374$	6.02285	−	7.55242i	0.311434	−	0.390526i
$375$	2.30965	+	1.11227i	0.119270	+	0.0574374i
$376$	−0.401110			−0.0206856
$377$		0			0
$378$	9.39515			0.483234
$379$	20.6304	+	9.93509i	1.05971	+	0.510331i	0.880778	−	0.473529i	$-0.157020\pi$
$379$	20.6304	+	9.93509i	1.05971	+	0.510331i	0.178936	+	0.983861i	$0.442734\pi$
$380$	−17.6012	+	22.0711i	−0.902920	+	1.13223i
$381$	25.2686	+	31.6858i	1.29455	+	1.62331i
$382$	−23.5011	−	11.3175i	−1.20242	−	0.579054i
$383$	2.61523	−	1.25943i	0.133632	−	0.0643538i	−0.365873	−	0.930665i	$-0.619230\pi$
$383$	2.61523	−	1.25943i	0.133632	−	0.0643538i	0.499505	+	0.866311i	$0.333515\pi$
$384$	4.69394	−	5.88601i	0.239537	−	0.300369i
$385$	−2.03472	−	8.91469i	−0.103699	−	0.454335i
$386$	−5.52919	−	24.2250i	−0.281429	−	1.23302i
$387$	2.53697	+	3.18126i	0.128961	+	0.161713i
$388$	6.20524	−	27.1869i	0.315023	−	1.38021i
$389$	3.15385			0.159907			0.0799533	−	0.996799i	$-0.474523\pi$
$389$	3.15385			0.159907			0.0799533	+	0.996799i	$0.474523\pi$
$390$	4.90136	−	21.4743i	0.248190	−	1.08739i
$391$	−9.85194	+	4.74444i	−0.498234	+	0.239937i
$392$	0.224494	−	0.108111i	0.0113386	−	0.00546041i
$393$	0.290506	−	1.27279i	0.0146541	−	0.0642037i
$394$	7.93292			0.399655
$395$	9.47551	−	41.5149i	0.476765	−	2.08884i
$396$	−2.70142	−	3.38748i	−0.135752	−	0.170227i
$397$	−4.71764	−	20.6693i	−0.236772	−	1.03736i	−0.943888	−	0.330267i	$-0.892861\pi$
$397$	−4.71764	−	20.6693i	−0.236772	−	1.03736i	0.707116	−	0.707098i	$-0.249996\pi$
$398$	7.34648	+	32.1870i	0.368246	+	1.61339i
$399$	−17.6071	+	22.0785i	−0.881455	+	1.10531i
$400$	21.1272	−	10.1743i	1.05636	−	0.508717i
$401$	3.87409	+	1.86566i	0.193463	+	0.0931668i	0.528107	−	0.849178i	$-0.322902\pi$
$401$	3.87409	+	1.86566i	0.193463	+	0.0931668i	−0.334644	+	0.942344i	$0.608616\pi$
$402$	−8.33279	−	10.4490i	−0.415602	−	0.521148i
$403$	−1.53331	+	1.92271i	−0.0763796	+	0.0957770i
$404$	18.3332	+	8.82878i	0.912108	+	0.439248i
$405$	−34.7933			−1.72889
$406$		0			0
$407$	−9.30497			−0.461230
$408$	3.76900	+	1.81505i	0.186593	+	0.0898586i
$409$	−15.8979	+	19.9353i	−0.786099	+	0.985737i	0.213861	+	0.976864i	$0.431396\pi$
$409$	−15.8979	+	19.9353i	−0.786099	+	0.985737i	−0.999961	+	0.00887325i	$0.997176\pi$
$410$	46.0093	+	57.6938i	2.27224	+	2.84929i
$411$	28.2078	+	13.5841i	1.39139	+	0.670056i
$412$	−11.8891	+	5.72547i	−0.585732	+	0.282074i
$413$	21.0899	−	26.4459i	1.03777	−	1.30132i
$414$	2.31362	+	10.1366i	0.113708	+	0.498188i
$415$	6.95028	+	30.4511i	0.341176	+	1.49479i
$416$	−7.43056	−	9.31762i	−0.364313	−	0.456834i
$417$	5.35859	−	23.4775i	0.262411	−	1.14970i
$418$	−10.7387			−0.525246
$419$	−1.50119	+	6.57714i	−0.0733379	+	0.321314i	−0.998269	−	0.0588216i	$-0.981266\pi$
$419$	−1.50119	+	6.57714i	−0.0733379	+	0.321314i	0.924931	+	0.380136i	$0.124123\pi$
$420$	−29.7522	+	14.3279i	−1.45176	+	0.699130i
$421$	−31.1254	+	14.9892i	−1.51696	+	0.730530i	−0.992653	−	0.120999i	$-0.961390\pi$
$421$	−31.1254	+	14.9892i	−1.51696	+	0.730530i	−0.524308	+	0.851529i	$0.675676\pi$
$422$	−1.91206	+	8.37729i	−0.0930777	+	0.407800i
$423$	−2.07920			−0.101094
$424$	−0.150028	+	0.657315i	−0.00728599	+	0.0319220i
$425$	14.7451	+	18.4898i	0.715242	+	0.896885i
$426$	−4.07427	−	17.8506i	−0.197399	−	0.864863i
$427$	−1.08237	−	4.74217i	−0.0523796	−	0.229490i
$428$	−13.2726	+	16.6434i	−0.641557	+	0.804487i
$429$	3.56104	−	1.71491i	0.171929	−	0.0827965i
$430$	10.6252	+	5.11681i	0.512391	+	0.246755i
$431$	6.15982	+	7.72416i	0.296708	+	0.372060i	0.907731	−	0.419553i	$-0.137813\pi$
$431$	6.15982	+	7.72416i	0.296708	+	0.372060i	−0.611023	+	0.791613i	$0.709242\pi$
$432$	−5.21445	+	6.53872i	−0.250880	+	0.314594i
$433$	2.88480	+	1.38924i	0.138634	+	0.0667628i	0.501915	−	0.864917i	$-0.332629\pi$
$433$	2.88480	+	1.38924i	0.138634	+	0.0667628i	−0.363280	+	0.931680i	$0.618343\pi$
$434$	7.81596			0.375178
$435$		0			0
$436$	28.8806			1.38313
$437$	10.9522	+	5.27428i	0.523913	+	0.252303i
$438$	−10.4629	+	13.1200i	−0.499935	+	0.626899i
$439$	3.99930	+	5.01496i	0.190876	+	0.239351i	0.868056	−	0.496467i	$-0.165370\pi$
$439$	3.99930	+	5.01496i	0.190876	+	0.239351i	−0.677180	+	0.735818i	$0.736798\pi$
$440$	1.35669	+	0.653348i	0.0646777	+	0.0311471i
$441$	1.16369	−	0.560404i	0.0554138	−	0.0266859i
$442$	8.30559	−	10.4149i	0.395057	−	0.495385i
$443$	−1.89131	−	8.28639i	−0.0898590	−	0.393698i	0.909919	−	0.414787i	$-0.136144\pi$
$443$	−1.89131	−	8.28639i	−0.0898590	−	0.393698i	−0.999778	+	0.0210888i	$0.993287\pi$
$444$	7.47758	+	32.7614i	0.354870	+	1.55479i
$445$	9.78852	+	12.2744i	0.464020	+	0.581863i
$446$	−7.38996	+	32.3775i	−0.349925	+	1.53312i
$447$	−5.37573			−0.254263
$448$	−3.49353	+	15.3062i	−0.165054	+	0.723149i
$449$	15.2645	−	7.35098i	0.720374	−	0.346914i	−0.0375159	−	0.999296i	$-0.511944\pi$
$449$	15.2645	−	7.35098i	0.720374	−	0.346914i	0.757890	+	0.652382i	$0.226230\pi$
$450$	20.2599	−	9.75665i	0.955060	−	0.459933i
$451$	−2.94651	+	12.9095i	−0.138746	+	0.607885i
$452$	−11.3369			−0.533242
$453$	4.92794	−	21.5907i	0.231535	−	1.01442i
$454$	11.8646	+	14.8778i	0.556834	+	0.698247i
$455$	−2.80591	−	12.2935i	−0.131543	−	0.576327i
$456$	−1.03482	−	4.53385i	−0.0484600	−	0.212317i
$457$	0.315430	−	0.395537i	0.0147552	−	0.0185024i	−0.774399	−	0.632697i	$-0.781948\pi$
$457$	0.315430	−	0.395537i	0.0147552	−	0.0185024i	0.789154	+	0.614195i	$0.210519\pi$
$458$	6.02904	−	2.90343i	0.281719	−	0.135669i
$459$	−7.59932	−	3.65964i	−0.354706	−	0.170817i
$460$	8.86282	+	11.1136i	0.413231	+	0.518175i
$461$	−3.42974	+	4.30076i	−0.159739	+	0.200306i	−0.855260	−	0.518200i	$-0.826602\pi$
$461$	−3.42974	+	4.30076i	−0.159739	+	0.200306i	0.695521	+	0.718506i	$0.255174\pi$
$462$	−11.3177	−	5.45032i	−0.526548	−	0.253572i
$463$	−6.56599			−0.305148			−0.152574	−	0.988292i	$-0.548756\pi$
$463$	−6.56599			−0.305148			−0.152574	+	0.988292i	$0.548756\pi$
$464$		0			0
$465$	−11.6024			−0.538050
$466$	−7.69860	−	3.70745i	−0.356631	−	0.171744i
$467$	2.79211	−	3.50119i	0.129203	−	0.162016i	−0.713022	−	0.701142i	$-0.752674\pi$
$467$	2.79211	−	3.50119i	0.129203	−	0.162016i	0.842225	+	0.539126i	$0.181245\pi$
$468$	−3.72530	−	4.67138i	−0.172202	−	0.215935i
$469$	−6.89330	−	3.31964i	−0.318303	−	0.153287i
$470$	−5.42933	+	2.61463i	−0.250436	+	0.120604i
$471$	−26.5620	+	33.3076i	−1.22391	+	1.53474i
$472$	1.23952	+	5.43069i	0.0570535	+	0.249968i
$473$	0.470888	+	2.06310i	0.0216515	+	0.0948613i
$474$	−36.4734	−	45.7362i	−1.67528	−	2.10073i
$475$	5.85016	−	25.6312i	0.268424	−	1.17604i
$476$	−19.9712			−0.915380
$477$	−0.777687	+	3.40727i	−0.0356079	+	0.156008i
$478$	30.9942	−	14.9260i	1.41764	−	0.682701i
$479$	8.35822	−	4.02511i	0.381897	−	0.183912i	−0.233079	−	0.972458i	$-0.574880\pi$
$479$	8.35822	−	4.02511i	0.381897	−	0.183912i	0.614976	+	0.788546i	$0.289166\pi$
$480$	12.5115	−	54.8167i	0.571071	−	2.50203i
$481$	−12.8317			−0.585074
$482$	4.93875	−	21.6381i	0.224954	−	0.985588i
$483$	8.86579	+	11.1173i	0.403407	+	0.505857i
$484$	3.86987	+	16.9550i	0.175903	+	0.770683i
$485$	11.1789	+	48.9780i	0.507608	+	2.22398i
$486$	−22.8562	+	28.6608i	−1.03678	+	1.30008i
$487$	−34.3122	+	16.5239i	−1.55484	+	0.748770i	−0.996715	−	0.0809897i	$-0.974192\pi$
$487$	−34.3122	+	16.5239i	−1.55484	+	0.748770i	−0.558121	+	0.829759i	$0.688478\pi$
$488$	0.721693	+	0.347549i	0.0326695	+	0.0157328i
$489$	13.6703	+	17.1420i	0.618192	+	0.775188i
$490$	2.33398	−	2.92672i	0.105438	−	0.132216i
$491$	−28.4650	−	13.7080i	−1.28461	−	0.618635i	−0.338038	−	0.941132i	$-0.609763\pi$
$491$	−28.4650	−	13.7080i	−1.28461	−	0.618635i	−0.946570	+	0.322498i	$0.895478\pi$
$492$	47.8204			2.15591
$493$		0			0
$494$	−14.8088			−0.666279
$495$	7.03257	+	3.38671i	0.316091	+	0.152221i
$496$	−4.33798	+	5.43966i	−0.194781	+	0.244248i
$497$	−6.53530	−	8.19500i	−0.293148	−	0.367596i
$498$	38.6595	+	18.6174i	1.73237	+	0.834267i
$499$	18.9792	−	9.13992i	0.849628	−	0.409159i	0.0421883	−	0.999110i	$-0.486567\pi$
$499$	18.9792	−	9.13992i	0.849628	−	0.409159i	0.807439	+	0.589951i	$0.200853\pi$
$500$	1.25659	−	1.57571i	0.0561963	−	0.0704679i
$501$	0.234962	+	1.02944i	0.0104973	+	0.0459919i
$502$	−11.0560	−	48.4396i	−0.493455	−	2.16197i
$503$	−16.3582	−	20.5126i	−0.729377	−	0.914610i	0.269451	−	0.963014i	$-0.413158\pi$
$503$	−16.3582	−	20.5126i	−0.729377	−	0.914610i	−0.998828	+	0.0484045i	$0.984586\pi$
$504$	0.506702	−	2.22001i	0.0225703	−	0.0988869i
$505$	−36.6580			−1.63126
$506$	−1.20324	+	5.27174i	−0.0534906	+	0.234358i
$507$	−21.6949	+	10.4477i	−0.963502	+	0.463998i
$508$	28.7070	−	13.8245i	1.27367	−	0.613365i
$509$	4.67072	−	20.4637i	0.207026	−	0.907040i	−0.759507	−	0.650499i	$-0.774560\pi$
$509$	4.67072	−	20.4637i	0.207026	−	0.907040i	0.966533	−	0.256541i	$-0.0825829\pi$
$510$	62.8477			2.78294
$511$	−2.13771	+	9.36593i	−0.0945668	+	0.414324i
$512$	−18.7452	−	23.5057i	−0.828429	−	1.03882i
$513$	2.08648	+	9.14147i	0.0921204	+	0.403606i
$514$	0.0773349	+	0.338826i	0.00341110	+	0.0149450i
$515$	14.8220	−	18.5862i	0.653137	−	0.819008i
$516$	6.88545	−	3.31586i	0.303115	−	0.145973i
$517$	−0.974243	−	0.469170i	−0.0428471	−	0.0206341i
$518$	25.4270	+	31.8844i	1.11720	+	1.40092i
$519$	31.5708	−	39.5886i	1.38581	−	1.73775i
$520$	1.87090	+	0.900976i	0.0820442	+	0.0395104i
$521$	−37.4112			−1.63901			−0.819507	−	0.573069i	$-0.805753\pi$
$521$	−37.4112			−1.63901			−0.819507	+	0.573069i	$0.805753\pi$
$522$		0			0
$523$	17.4633			0.763618			0.381809	−	0.924241i	$-0.375301\pi$
$523$	17.4633			0.763618			0.381809	+	0.924241i	$0.375301\pi$
$524$	−0.924740	−	0.445331i	−0.0403974	−	0.0194544i
$525$	19.1745	−	24.0440i	0.836843	−	1.04937i
$526$	6.83277	+	8.56803i	0.297923	+	0.373584i
$527$	−6.32199	−	3.04451i	−0.275390	−	0.132621i
$528$	10.0748	−	4.85175i	0.438447	−	0.211145i
$529$	−10.5239	+	13.1966i	−0.457561	+	0.573763i
$530$	2.25395	+	9.87521i	0.0979054	+	0.428952i
$531$	6.42519	+	28.1506i	0.278830	+	1.22163i
$532$	13.8424	+	17.3579i	0.600146	+	0.752559i
$533$	−4.06328	+	17.8024i	−0.176000	+	0.771107i
$534$	21.5676			0.933323
$535$	8.53375	−	37.3888i	0.368946	−	1.61646i
$536$	1.13518	−	0.546674i	0.0490323	−	0.0236127i
$537$	15.3697	−	7.40166i	0.663252	−	0.319405i
$538$	0.843557	−	3.69587i	0.0363683	−	0.159340i
$539$	0.671721			0.0289331
$540$	−2.43987	+	10.6898i	−0.104995	+	0.460014i
$541$	3.55074	+	4.45248i	0.152658	+	0.191427i	0.852280	−	0.523086i	$-0.175219\pi$
$541$	3.55074	+	4.45248i	0.152658	+	0.191427i	−0.699622	+	0.714514i	$0.746648\pi$
$542$	7.55167	+	33.0860i	0.324372	+	1.42117i
$543$	−12.0993	−	53.0107i	−0.519233	−	2.27491i
$544$	21.2014	−	26.5857i	0.909003	−	1.13985i
$545$	−46.8767	+	22.5746i	−2.00798	+	0.966990i
$546$	−15.6073	−	7.51607i	−0.667930	−	0.321658i
$547$	−16.2807	−	20.4153i	−0.696111	−	0.872896i	0.300615	−	0.953746i	$-0.402808\pi$
$547$	−16.2807	−	20.4153i	−0.696111	−	0.872896i	−0.996726	+	0.0808494i	$0.974237\pi$
$548$	15.3467	−	19.2441i	0.655577	−	0.822068i
$549$	3.74098	+	1.80156i	0.159661	+	0.0768888i
$550$	11.6947			0.498663
$551$		0			0
$552$	−2.34167			−0.0996680
$553$	−30.1726	−	14.5304i	−1.28307	−	0.617894i
$554$	18.6151	−	23.3426i	0.790880	−	0.991732i
$555$	−37.7451	−	47.3309i	−1.60219	−	2.00908i
$556$	−17.0575	−	8.21446i	−0.723399	−	0.348371i
$557$	−25.8140	+	12.4314i	−1.09377	+	0.526734i	−0.891695	−	0.452636i	$-0.850484\pi$
$557$	−25.8140	+	12.4314i	−1.09377	+	0.526734i	−0.202078	+	0.979369i	$0.564769\pi$
$558$	−4.15990	+	5.21634i	−0.176102	+	0.220825i
$559$	0.649362	+	2.84504i	0.0274651	+	0.120332i
$560$	−7.93836	−	34.7802i	−0.335457	−	1.46973i
$561$	7.03137	+	8.81706i	0.296865	+	0.372256i
$562$	−5.71998	+	25.0609i	−0.241283	+	1.05713i
$563$	2.23595			0.0942341			0.0471170	−	0.998889i	$-0.484997\pi$
$563$	2.23595			0.0942341			0.0471170	+	0.998889i	$0.484997\pi$
$564$	−0.868968	+	3.80720i	−0.0365902	+	0.160312i
$565$	18.4011	−	8.86151i	0.774140	−	0.372806i
$566$	−19.5574	+	9.41832i	−0.822057	+	0.395882i
$567$	−6.08889	+	26.6772i	−0.255709	+	1.12034i
$568$	1.72613			0.0724268
$569$	−3.26643	+	14.3112i	−0.136936	+	0.599956i	0.859162	+	0.511704i	$0.170985\pi$
$569$	−3.26643	+	14.3112i	−0.136936	+	0.599956i	−0.996098	+	0.0882525i	$0.971872\pi$
$570$	−43.5609	−	54.6237i	−1.82457	−	2.28793i
$571$	−4.64178	−	20.3369i	−0.194252	−	0.851075i	−0.974282	−	0.225332i	$-0.927653\pi$
$571$	−4.64178	−	20.3369i	−0.194252	−	0.851075i	0.780030	−	0.625743i	$-0.215204\pi$
$572$	−0.691455	−	3.02946i	−0.0289112	−	0.126668i
$573$	18.9865	−	23.8083i	0.793172	−	0.994606i
$574$	52.2874	−	25.1803i	2.18243	−	1.05101i
$575$	−11.9272	−	5.74382i	−0.497397	−	0.239534i
$576$	−8.35592	−	10.4780i	−0.348163	−	0.436583i
$577$	14.0234	−	17.5848i	0.583804	−	0.732066i	−0.398953	−	0.916971i	$-0.630626\pi$
$577$	14.0234	−	17.5848i	0.583804	−	0.732066i	0.982756	+	0.184905i	$0.0591977\pi$
$578$	4.44312	+	2.13969i	0.184809	+	0.0889995i
$579$	29.0087			1.20556
$580$		0			0
$581$	24.5642			1.01909
$582$	62.1803	+	29.9445i	2.57746	+	1.24124i
$583$	−1.13325	+	1.42105i	−0.0469343	+	0.0588537i
$584$	−0.986381	−	1.23688i	−0.0408168	−	0.0511826i
$585$	9.69801	+	4.67032i	0.400963	+	0.193094i
$586$	11.9255	−	5.74303i	0.492639	−	0.237242i
$587$	10.2851	−	12.8971i	0.424512	−	0.532321i	−0.522876	−	0.852409i	$-0.675141\pi$
$587$	10.2851	−	12.8971i	0.424512	−	0.532321i	0.947388	+	0.320088i	$0.103712\pi$
$588$	−0.539803	−	2.36503i	−0.0222611	−	0.0975322i
$589$	1.73577	+	7.60493i	0.0715214	+	0.313356i
$590$	52.1777	+	65.4287i	2.14812	+	2.69366i
$591$	−2.06083	+	9.02907i	−0.0847711	+	0.371406i
$592$	−36.3029			−1.49204
$593$	10.0362	−	43.9714i	0.412136	−	1.80569i	−0.161841	−	0.986817i	$-0.551743\pi$
$593$	10.0362	−	43.9714i	0.412136	−	1.80569i	0.573977	−	0.818871i	$-0.305400\pi$
$594$	−3.75790	+	1.80971i	−0.154188	+	0.0742532i
$595$	32.4157	−	15.6106i	1.32891	−	0.639972i
$596$	−0.940446	+	4.12036i	−0.0385222	+	0.168777i
$597$	−38.5431			−1.57746
$598$	−1.65929	+	7.26980i	−0.0678532	+	0.297284i
$599$	6.59100	+	8.26485i	0.269301	+	0.337693i	0.898032	−	0.439930i	$-0.144997\pi$
$599$	6.59100	+	8.26485i	0.269301	+	0.337693i	−0.628731	+	0.777623i	$0.716425\pi$
$600$	1.12694	+	4.93747i	0.0460073	+	0.201571i
$601$	0.165422	+	0.724760i	0.00674770	+	0.0295636i	0.978190	−	0.207714i	$-0.0666022\pi$
$601$	0.165422	+	0.724760i	0.00674770	+	0.0295636i	−0.971442	+	0.237277i	$0.923745\pi$
$602$	5.78265	−	7.25121i	0.235683	−	0.295537i
$603$	5.88434	−	2.83375i	0.239629	−	0.115399i
$604$	−15.6867	−	7.55430i	−0.638281	−	0.307380i
$605$	−19.5342	−	24.4951i	−0.794179	−	0.995869i
$606$	−31.3988	+	39.3728i	−1.27549	+	1.59941i
$607$	29.3874	+	14.1522i	1.19280	+	0.574420i	0.921614	−	0.388108i	$-0.126871\pi$
$607$	29.3874	+	14.1522i	1.19280	+	0.574420i	0.271182	+	0.962528i	$0.412585\pi$
$608$	−37.8019			−1.53307
$609$		0			0
$610$	12.0342			0.487248
$611$	−1.34349	−	0.646992i	−0.0543519	−	0.0261745i
$612$	10.6293	−	13.3287i	0.429664	−	0.538782i
$613$	9.35574	+	11.7317i	0.377875	+	0.473840i	0.934007	−	0.357254i	$-0.116287\pi$
$613$	9.35574	+	11.7317i	0.377875	+	0.473840i	−0.556133	+	0.831094i	$0.687715\pi$
$614$	28.3253	+	13.6408i	1.14312	+	0.550496i
$615$	−77.6182	+	37.3790i	−3.12987	+	1.50726i
$616$	0.738367	−	0.925882i	0.0297496	−	0.0373049i
$617$	−9.24015	−	40.4838i	−0.371995	−	1.62981i	−0.721171	−	0.692757i	$-0.756396\pi$
$617$	−9.24015	−	40.4838i	−0.371995	−	1.62981i	0.349176	−	0.937057i	$-0.386461\pi$
$618$	−7.26715	−	31.8395i	−0.292328	−	1.28077i
$619$	−13.3292	−	16.7143i	−0.535745	−	0.671803i	0.438124	−	0.898915i	$-0.355643\pi$
$619$	−13.3292	−	16.7143i	−0.535745	−	0.671803i	−0.973869	+	0.227112i	$0.927072\pi$
$620$	−2.02976	+	8.89298i	−0.0815173	+	0.357151i
$621$	4.72144			0.189465
$622$	1.87887	−	8.23186i	0.0753357	−	0.330067i
$623$	11.1242	−	5.35713i	0.445682	−	0.214629i
$624$	13.8932	−	6.69062i	0.556174	−	0.267839i
$625$	5.14537	−	22.5433i	0.205815	−	0.901733i
$626$	−2.08855			−0.0834752
$627$	2.78971	−	12.2225i	0.111410	−	0.488121i
$628$	20.8827	+	26.1860i	0.833309	+	1.04494i
$629$	−8.14700	−	35.6943i	−0.324842	−	1.42323i
$630$	−7.61247	−	33.3524i	−0.303288	−	1.32879i
$631$	13.8934	−	17.4218i	0.553088	−	0.693551i	−0.424175	−	0.905580i	$-0.639436\pi$
$631$	13.8934	−	17.4218i	0.553088	−	0.693551i	0.977263	+	0.212029i	$0.0680073\pi$
$632$	4.96879	−	2.39284i	0.197648	−	0.0951821i
$633$	−9.03813	−	4.35254i	−0.359234	−	0.172998i
$634$	9.45540	+	11.8567i	0.375522	+	0.470890i
$635$	−35.7889	+	44.8778i	−1.42024	+	1.78092i
$636$	5.91399	+	2.84803i	0.234505	+	0.112932i
$637$	0.926312			0.0367018
$638$		0			0
$639$	8.94760			0.353962
$640$	9.60693	+	4.62646i	0.379747	+	0.182877i
$641$	−16.5807	+	20.7916i	−0.654899	+	0.821217i	−0.992777	−	0.119972i	$-0.961719\pi$
$641$	−16.5807	+	20.7916i	−0.654899	+	0.821217i	0.337878	+	0.941190i	$0.390291\pi$
$642$	−32.8483	−	41.1905i	−1.29642	−	1.62566i
$643$	−34.4384	−	16.5847i	−1.35812	−	0.654035i	−0.393902	−	0.919153i	$-0.628875\pi$
$643$	−34.4384	−	16.5847i	−1.35812	−	0.654035i	−0.964216	+	0.265117i	$0.914589\pi$
$644$	10.0722	−	4.85051i	0.396900	−	0.191137i
$645$	−8.58407	+	10.7641i	−0.337997	+	0.423835i
$646$	−9.40230	−	41.1941i	−0.369928	−	1.62076i
$647$	−7.30612	−	32.0102i	−0.287233	−	1.25845i	−0.888304	−	0.459255i	$-0.848116\pi$
$647$	−7.30612	−	32.0102i	−0.287233	−	1.25845i	0.601071	−	0.799195i	$-0.294741\pi$
$648$	−2.80953	−	3.52304i	−0.110369	−	0.138398i
$649$	−3.34154	+	14.6403i	−0.131167	+	0.574681i
$650$	16.1271			0.632558
$651$	−2.03044	+	8.89596i	−0.0795794	+	0.348660i
$652$	15.5305	−	7.47907i	0.608220	−	0.292903i
$653$	−1.17449	+	0.565603i	−0.0459612	+	0.0221338i	−0.456723	−	0.889609i	$-0.650977\pi$
$653$	−1.17449	+	0.565603i	−0.0459612	+	0.0221338i	0.410762	+	0.911743i	$0.365263\pi$
$654$	−15.9050	+	69.6842i	−0.621933	+	2.72487i
$655$	1.84906			0.0722487
$656$	−11.4957	+	50.3658i	−0.448830	+	1.96645i
$657$	−5.11303	−	6.41153i	−0.199478	−	0.250138i
$658$	1.05458	+	4.62041i	0.0411117	+	0.180122i
$659$	−4.39431	−	19.2527i	−0.171178	−	0.749980i	−0.985515	−	0.169588i	$-0.945756\pi$
$659$	−4.39431	−	19.2527i	−0.171178	−	0.749980i	0.814337	−	0.580392i	$-0.197101\pi$
$660$	9.14051	−	11.4618i	0.355794	−	0.446151i
$661$	37.9985	−	18.2991i	1.47797	−	0.711753i	0.490778	−	0.871284i	$-0.336713\pi$
$661$	37.9985	−	18.2991i	1.47797	−	0.711753i	0.987193	+	0.159531i	$0.0509982\pi$
$662$	17.4553	+	8.40603i	0.678419	+	0.326710i
$663$	9.69635	+	12.1588i	0.376575	+	0.472210i
$664$	−2.52214	+	3.16266i	−0.0978781	+	0.122735i
$665$	−36.0358	−	17.3539i	−1.39741	−	0.672956i
$666$	−34.8125			−1.34896
$667$		0			0
$668$	0.830144			0.0321192
$669$	−34.9316	−	16.8222i	−1.35053	−	0.650383i
$670$	11.8020	−	14.7993i	0.455953	−	0.571747i
$671$	1.34637	+	1.68830i	0.0519762	+	0.0651761i
$672$	−39.8402	−	19.1860i	−1.53687	−	0.740117i
$673$	37.5590	−	18.0875i	1.44779	−	0.697220i	0.465582	−	0.885005i	$-0.345845\pi$
$673$	37.5590	−	18.0875i	1.44779	−	0.697220i	0.982210	+	0.187784i	$0.0601306\pi$
$674$	−25.9126	+	32.4933i	−0.998115	+	1.25160i
$675$	−2.27223	−	9.95527i	−0.0874580	−	0.383179i
$676$	4.21254	+	18.4563i	0.162021	+	0.709859i
$677$	15.3214	+	19.2125i	0.588850	+	0.738395i	0.983594	−	0.180396i	$-0.0577380\pi$
$677$	15.3214	+	19.2125i	0.588850	+	0.738395i	−0.394744	+	0.918791i	$0.629167\pi$
$678$	6.24338	−	27.3541i	0.239776	−	1.05053i
$679$	39.5093			1.51623
$680$	−1.31842	+	5.77638i	−0.0505591	+	0.221514i
$681$	−20.0157	+	9.63907i	−0.767005	+	0.369370i
$682$	−3.12625	+	1.50552i	−0.119710	+	0.0576495i
$683$	−9.59756	+	42.0497i	−0.367241	+	1.60899i	0.367084	+	0.930188i	$0.380356\pi$
$683$	−9.59756	+	42.0497i	−0.367241	+	1.60899i	−0.734325	+	0.678798i	$0.762501\pi$
$684$	−18.9519			−0.724646
$685$	−9.86726	+	43.2313i	−0.377009	+	1.65178i
$686$	−23.3221	−	29.2450i	−0.890443	−	1.11658i
$687$	1.73839	+	7.61638i	0.0663237	+	0.290583i
$688$	1.83715	+	8.04907i	0.0700406	+	0.306868i
$689$	−1.56276	+	1.95964i	−0.0595365	+	0.0746564i
$690$	−31.6963	+	15.2641i	−1.20666	+	0.581095i
$691$	36.9937	+	17.8152i	1.40731	+	0.677723i	0.974629	−	0.223826i	$-0.0718549\pi$
$691$	36.9937	+	17.8152i	1.40731	+	0.677723i	0.432677	+	0.901549i	$0.357569\pi$
$692$	−24.8206	−	31.1240i	−0.943537	−	1.18316i
$693$	3.82741	−	4.79942i	0.145391	−	0.182315i
$694$	47.1829	+	22.7221i	1.79104	+	0.862518i
$695$	34.1072			1.29376
$696$		0			0
$697$	−52.1014			−1.97348
$698$	32.9192	+	15.8530i	1.24601	+	0.600046i
$699$	6.21970	−	7.79925i	0.235251	−	0.294995i
$700$	−15.0747	−	18.9031i	−0.569771	−	0.714471i
$701$	−1.00176	−	0.482425i	−0.0378361	−	0.0182209i	0.414870	−	0.909881i	$-0.363827\pi$
$701$	−1.00176	−	0.482425i	−0.0378361	−	0.0182209i	−0.452706	+	0.891660i	$0.649541\pi$
$702$	−5.18219	+	2.49561i	−0.195589	+	0.0941908i
$703$	−25.3767	+	31.8213i	−0.957099	+	1.20016i
$704$	−1.55095	−	6.79514i	−0.0584535	−	0.256101i
$705$	−1.56547	−	6.85877i	−0.0589590	−	0.258316i
$706$	−35.8803	−	44.9925i	−1.35037	−	1.69331i
$707$	−6.41521	+	28.1069i	−0.241269	+	1.05707i
$708$	54.2315			2.03815
$709$	−6.66195	+	29.1879i	−0.250195	+	1.09618i	0.681181	+	0.732115i	$0.261467\pi$
$709$	−6.66195	+	29.1879i	−0.250195	+	1.09618i	−0.931375	+	0.364060i	$0.881390\pi$
$710$	23.3645	−	11.2517i	0.876853	−	0.422270i
$711$	25.7563	−	12.4036i	0.965937	−	0.465171i
$712$	−0.452447	+	1.98230i	−0.0169562	+	0.0742897i
$713$	3.92783			0.147099
$714$	10.9985	−	48.1874i	0.411607	−	1.80337i
$715$	3.49030	+	4.37670i	0.130530	+	0.163679i
$716$	−2.98437	−	13.0754i	−0.111531	−	0.488650i
$717$	8.93675	+	39.1545i	0.333749	+	1.46225i
$718$	24.6070	−	30.8562i	0.918326	−	1.15154i
$719$	4.53255	−	2.18276i	0.169036	−	0.0814032i	−0.347453	−	0.937698i	$-0.612953\pi$
$719$	4.53255	−	2.18276i	0.169036	−	0.0814032i	0.516488	+	0.856294i	$0.327239\pi$
$720$	27.4372	+	13.2131i	1.02253	+	0.492422i
$721$	−11.6568	−	14.6172i	−0.434122	−	0.544372i
$722$	−6.23705	+	7.82101i	−0.232119	+	0.291068i
$723$	23.3450	+	11.2424i	0.868210	+	0.418108i
$724$	−42.7481			−1.58872
$725$		0			0
$726$	−43.0409			−1.59740
$727$	0.586285	+	0.282340i	0.0217441	+	0.0104714i	0.444724	−	0.895668i	$-0.353302\pi$
$727$	0.586285	+	0.282340i	0.0217441	+	0.0104714i	−0.422980	+	0.906139i	$0.639016\pi$
$728$	1.01822	−	1.27680i	0.0377377	−	0.0473215i
$729$	−6.45516	−	8.09452i	−0.239080	−	0.299797i
$730$	−21.4140	−	10.3125i	−0.792569	−	0.381681i
$731$	−7.50186	+	3.61270i	−0.277466	+	0.133621i
$732$	4.86230	−	6.09713i	0.179716	−	0.225356i
$733$	2.53302	+	11.0979i	0.0935591	+	0.409909i	0.999921	−	0.0125937i	$-0.00400879\pi$
$733$	2.53302	+	11.0979i	0.0935591	+	0.409909i	−0.906362	+	0.422503i	$0.861152\pi$
$734$	7.35751	+	32.2354i	0.271571	+	1.18983i
$735$	2.72480	+	3.41679i	0.100506	+	0.126030i
$736$	−4.23560	+	18.5574i	−0.156126	+	0.684034i
$737$	3.39664			0.125117
$738$	−11.0237	+	48.2982i	−0.405789	+	1.77788i
$739$	−17.2786	+	8.32091i	−0.635602	+	0.306090i	−0.723797	−	0.690013i	$-0.757605\pi$
$739$	−17.2786	+	8.32091i	−0.635602	+	0.306090i	0.0881945	+	0.996103i	$0.471890\pi$
$740$	−42.8812	+	20.6505i	−1.57634	+	0.759128i
$741$	3.84705	−	16.8550i	0.141325	−	0.619185i
$742$	7.96609			0.292444
$743$	7.15673	−	31.3557i	0.262555	−	1.15033i	−0.655914	−	0.754836i	$-0.727717\pi$
$743$	7.15673	−	31.3557i	0.262555	−	1.15033i	0.918469	−	0.395493i	$-0.129426\pi$
$744$	−0.936886	−	1.17482i	−0.0343479	−	0.0430709i
$745$	−1.69424	−	7.42295i	−0.0620722	−	0.271956i
$746$	−4.50959	−	19.7578i	−0.165108	−	0.723385i
$747$	−13.0738	+	16.3941i	−0.478346	+	0.599827i
$748$	7.98815	−	3.84689i	0.292076	−	0.140656i
$749$	−27.1738	−	13.0862i	−0.992908	−	0.478159i
$750$	3.10991	+	3.89971i	0.113558	+	0.142397i
$751$	23.8850	−	29.9508i	0.871575	−	1.09292i	−0.123356	−	0.992362i	$-0.539366\pi$
$751$	23.8850	−	29.9508i	0.871575	−	1.09292i	0.994931	−	0.100558i	$-0.0320628\pi$
$752$	−3.80096	−	1.83045i	−0.138607	−	0.0667495i
$753$	58.0051			2.11382
$754$		0			0
$755$	31.3662			1.14153
$756$	7.76921	+	3.74146i	0.282564	+	0.136075i
$757$	7.08436	−	8.88351i	0.257485	−	0.322877i	−0.636240	−	0.771491i	$-0.719511\pi$
$757$	7.08436	−	8.88351i	0.257485	−	0.322877i	0.893725	+	0.448615i	$0.148082\pi$
$758$	27.7786	+	34.8332i	1.00896	+	1.26520i
$759$	−5.68760	−	2.73900i	−0.206447	−	0.0994196i
$760$	5.93433	−	2.85782i	0.215261	−	0.103664i
$761$	−9.73857	+	12.2118i	−0.353023	+	0.442677i	−0.926358	−	0.376644i	$-0.877078\pi$
$761$	−9.73857	+	12.2118i	−0.353023	+	0.442677i	0.573335	+	0.819321i	$0.305649\pi$
$762$	17.5471	+	76.8787i	0.635663	+	2.78502i
$763$	9.10519	+	39.8925i	0.329630	+	1.44420i
$764$	−14.9269	−	18.7178i	−0.540037	−	0.677186i
$765$	−6.83419	+	29.9426i	−0.247091	+	1.08258i
$766$	5.64784			0.204065
$767$	−4.60803	+	20.1891i	−0.166386	+	0.728987i
$768$	38.5955	−	18.5866i	1.39270	−	0.670687i
$769$	−8.69727	+	4.18838i	−0.313631	+	0.151037i	−0.584077	−	0.811698i	$-0.698543\pi$
$769$	−8.69727	+	4.18838i	−0.313631	+	0.151037i	0.270445	+	0.962735i	$0.412829\pi$
$770$	3.95901	−	17.3456i	0.142673	−	0.625090i
$771$	−0.405735			−0.0146122
$772$	5.07488	−	22.2345i	0.182649	−	0.800237i
$773$	−9.79782	−	12.2861i	−0.352403	−	0.441899i	0.573760	−	0.819024i	$-0.305484\pi$
$773$	−9.79782	−	12.2861i	−0.352403	−	0.441899i	−0.926163	+	0.377124i	$0.876913\pi$
$774$	1.76173	+	7.71864i	0.0633240	+	0.277441i
$775$	−1.89030	−	8.28194i	−0.0679015	−	0.297496i
$776$	−4.05664	+	5.08687i	−0.145625	+	0.182608i
$777$	−42.8956	+	20.6574i	−1.53887	+	0.741081i
$778$	5.52882	+	2.66254i	0.198218	+	0.0954567i
$779$	36.1124	+	45.2836i	1.29386	+	1.62245i
$780$	12.6049	−	15.8060i	0.451327	−	0.565947i
$781$	4.19254	+	2.01902i	0.150021	+	0.0722463i
$782$	−21.2762			−0.760835
$783$		0			0
$784$	2.62069			0.0935959
$785$	−54.3635	−	26.1801i	−1.94032	−	0.934407i
$786$	1.58378	−	1.98600i	0.0564916	−	0.0708382i
$787$	3.19583	+	4.00745i	0.113919	+	0.142850i	0.835522	−	0.549458i	$-0.185166\pi$
$787$	3.19583	+	4.00745i	0.113919	+	0.142850i	−0.721603	+	0.692308i	$0.756594\pi$
$788$	6.56004	+	3.15915i	0.233692	+	0.112540i
$789$	−11.5270	+	5.55110i	−0.410371	+	0.197624i
$790$	51.6586	−	64.7779i	1.83793	−	2.30469i
$791$	−3.57418	−	15.6595i	−0.127083	−	0.556788i
$792$	0.224949	+	0.985566i	0.00799322	+	0.0350206i
$793$	1.85667	+	2.32819i	0.0659322	+	0.0826764i
$794$	9.17924	−	40.2169i	0.325759	−	1.42724i
$795$	−11.8253			−0.419400
$796$	−6.74285	+	29.5423i	−0.238994	+	1.04710i
$797$	−36.5490	+	17.6011i	−1.29463	+	0.623462i	−0.949109	−	0.314949i	$-0.898013\pi$
$797$	−36.5490	+	17.6011i	−1.29463	+	0.623462i	−0.345523	+	0.938410i	$0.612298\pi$
$798$	−49.5050	+	23.8403i	−1.75246	+	0.843939i
$799$	0.946760	−	4.14803i	0.0334940	−	0.146747i
$800$	41.1672			1.45548
$801$	−2.34531	+	10.2755i	−0.0828675	+	0.363066i
$802$	5.21640	+	6.54116i	0.184198	+	0.230976i
$803$	−0.949031	−	4.15798i	−0.0334906	−	0.146732i
$804$	−2.72958	−	11.9591i	−0.0962648	−	0.421764i
$805$	−12.5569	+	15.7459i	−0.442574	+	0.554971i
$806$	−4.31114	+	2.07614i	−0.151853	+	0.0731288i
$807$	3.98741	+	1.92024i	0.140364	+	0.0675955i
$808$	−2.96010	−	3.71185i	−0.104136	−	0.130582i
$809$	−19.3417	+	24.2537i	−0.680018	+	0.852716i	−0.995356	−	0.0962636i	$-0.969311\pi$
$809$	−19.3417	+	24.2537i	−0.680018	+	0.852716i	0.315338	+	0.948980i	$0.397882\pi$
$810$	−60.9940	−	29.3732i	−2.14311	−	1.03207i
$811$	−45.3970			−1.59410			−0.797052	−	0.603910i	$-0.793609\pi$
$811$	−45.3970			−1.59410			−0.797052	+	0.603910i	$0.793609\pi$
$812$		0			0
$813$	−39.6196			−1.38952
$814$	−16.3120	−	7.85543i	−0.571734	−	0.275333i
$815$	−19.3618	+	24.2789i	−0.678213	+	0.850452i
$816$	27.4325	+	34.3993i	0.960331	+	1.20422i
$817$	8.33964	+	4.01616i	0.291767	+	0.140508i
$818$	−44.6994	+	21.5261i	−1.56288	+	0.752642i
$819$	5.27805	−	6.61847i	0.184430	−	0.231268i
$820$	15.0713	+	66.0317i	0.526312	+	2.30593i
$821$	5.87646	+	25.7464i	0.205090	+	0.898557i	0.967781	+	0.251794i	$0.0810206\pi$
$821$	5.87646	+	25.7464i	0.205090	+	0.898557i	−0.762691	+	0.646763i	$0.776122\pi$
$822$	37.9813	+	47.6271i	1.32475	+	1.66118i
$823$	−7.64881	+	33.5116i	−0.266621	+	1.16814i	0.647295	+	0.762239i	$0.275900\pi$
$823$	−7.64881	+	33.5116i	−0.266621	+	1.16814i	−0.913916	+	0.405903i	$0.866957\pi$
$824$	3.07884			0.107257
$825$	−3.03806	+	13.3106i	−0.105772	+	0.463416i
$826$	59.2975	−	28.5562i	2.06322	−	0.993596i
$827$	−36.3536	+	17.5070i	−1.26414	+	0.608778i	−0.941266	−	0.337665i	$-0.890363\pi$
$827$	−36.3536	+	17.5070i	−1.26414	+	0.608778i	−0.322873	+	0.946442i	$0.604649\pi$
$828$	−2.12351	+	9.30373i	−0.0737972	+	0.323327i
$829$	41.4695			1.44029			0.720147	−	0.693821i	$-0.244074\pi$
$829$	41.4695			1.44029			0.720147	+	0.693821i	$0.244074\pi$
$830$	−13.5233	+	59.2496i	−0.469402	+	2.05658i
$831$	21.7322	+	27.2513i	0.753880	+	0.945336i
$832$	−2.13877	−	9.37059i	−0.0741487	−	0.324867i
$833$	0.588128	+	2.57676i	0.0203774	+	0.0892793i
$834$	29.2140	−	36.6332i	1.01160	−	1.26850i
$835$	−1.34742	+	0.648885i	−0.0466295	+	0.0224556i
$836$	−8.88024	−	4.27650i	−0.307129	−	0.147906i
$837$	1.88902	+	2.36875i	0.0652940	+	0.0818761i
$838$	−8.18419	+	10.2627i	−0.282718	+	0.354517i
$839$	11.6980	+	5.63345i	0.403859	+	0.194488i	0.624775	−	0.780805i	$-0.285191\pi$
$839$	11.6980	+	5.63345i	0.403859	+	0.194488i	−0.220916	+	0.975293i	$0.570905\pi$
$840$	7.70476			0.265840
$841$		0			0
$842$	−67.2183			−2.31649
$843$	−27.0378	−	13.0207i	−0.931231	−	0.448457i
$844$	−4.91727	+	6.16606i	−0.169259	+	0.212245i
$845$	−21.2639	−	26.6641i	−0.731501	−	0.917273i
$846$	−3.64492	−	1.75530i	−0.125315	−	0.0603485i
$847$	−22.1997	+	10.6908i	−0.762792	+	0.367341i
$848$	−4.42131	+	5.54414i	−0.151828	+	0.190387i
$849$	−5.63909	−	24.7065i	−0.193533	−	0.847923i
$850$	10.2393	+	44.8614i	0.351206	+	1.53873i
$851$	12.7781	+	16.0232i	0.438026	+	0.549268i
$852$	3.73950	−	16.3838i	0.128113	−	0.561301i
$853$	−8.15508			−0.279225			−0.139612	−	0.990206i	$-0.544586\pi$
$853$	−8.15508			−0.279225			−0.139612	+	0.990206i	$0.544586\pi$
$854$	2.10600	−	9.22698i	0.0720657	−	0.315741i
$855$	30.7613	−	14.8139i	1.05201	−	0.506623i
$856$	4.47494	−	2.15502i	0.152950	−	0.0736570i
$857$	6.53525	−	28.6328i	0.223240	−	0.978078i	−0.731781	−	0.681540i	$-0.761311\pi$
$857$	6.53525	−	28.6328i	0.223240	−	0.978078i	0.955021	−	0.296538i	$-0.0958322\pi$
$858$	7.69040			0.262546
$859$	−4.31916	+	18.9235i	−0.147368	+	0.645661i	0.846243	+	0.532798i	$0.178859\pi$
$859$	−4.31916	+	18.9235i	−0.147368	+	0.645661i	−0.993611	+	0.112863i	$0.963998\pi$
$860$	6.74868	+	8.46258i	0.230128	+	0.288572i
$861$	15.0763	+	66.0538i	0.513800	+	2.25111i
$862$	4.27751	+	18.7410i	0.145693	+	0.638321i
$863$	−31.5587	+	39.5734i	−1.07427	+	1.34709i	−0.140153	+	0.990130i	$0.544759\pi$
$863$	−31.5587	+	39.5734i	−1.07427	+	1.34709i	−0.934118	+	0.356963i	$0.883812\pi$
$864$	−13.2284	+	6.37046i	−0.450040	+	0.216728i
$865$	64.6150	+	31.1170i	2.19698	+	1.05801i
$866$	3.88433	+	4.87080i	0.131995	+	0.165517i
$867$	−3.58959	+	4.50121i	−0.121909	+	0.152869i
$868$	6.46332	+	3.11257i	0.219380	+	0.105648i
$869$	14.8674			0.504342
$870$		0			0
$871$	4.68401			0.158712
$872$	−6.07107	−	2.92367i	−0.205592	−	0.0990081i
$873$	−21.0281	+	26.3684i	−0.711693	+	0.892435i
$874$	14.7469	+	18.4921i	0.498822	+	0.625503i
$875$	2.57268	+	1.23894i	0.0869724	+	0.0418837i
$876$	−13.8770	+	6.68280i	−0.468860	+	0.225791i
$877$	21.8982	−	27.4595i	0.739450	−	0.927240i	−0.259812	−	0.965659i	$-0.583661\pi$
$877$	21.8982	−	27.4595i	0.739450	−	0.927240i	0.999262	+	0.0384188i	$0.0122321\pi$
$878$	2.77720	+	12.1677i	0.0937259	+	0.410640i
$879$	3.43856	+	15.0653i	0.115980	+	0.508140i
$880$	9.87463	+	12.3824i	0.332874	+	0.417411i
$881$	7.16142	−	31.3762i	0.241274	−	1.05709i	−0.698584	−	0.715528i	$-0.746186\pi$
$881$	7.16142	−	31.3762i	0.241274	−	1.05709i	0.939859	−	0.341564i	$-0.110957\pi$
$882$	2.51310			0.0846204
$883$	10.4224	−	45.6637i	0.350743	−	1.53671i	−0.424726	−	0.905322i	$-0.639630\pi$
$883$	10.4224	−	45.6637i	0.350743	−	1.53671i	0.775469	−	0.631385i	$-0.217513\pi$
$884$	11.0158	−	5.30491i	0.370500	−	0.178424i
$885$	−88.0243	+	42.3903i	−2.95891	+	1.42493i
$886$	3.67998	−	16.1230i	0.123631	−	0.541664i
$887$	6.85131			0.230045			0.115022	−	0.993363i	$-0.463306\pi$
$887$	6.85131			0.230045			0.115022	+	0.993363i	$0.463306\pi$
$888$	1.74466	−	7.64386i	0.0585470	−	0.256511i
$889$	28.1462	+	35.2942i	0.943992	+	1.18373i
$890$	6.79736	+	29.7812i	0.227848	+	0.998267i
$891$	−2.70315	−	11.8433i	−0.0905588	−	0.396764i
$892$	−19.0048	+	23.8313i	−0.636329	+	0.797932i
$893$	−4.26145	+	2.05221i	−0.142604	+	0.0686745i
$894$	−9.42386	−	4.53829i	−0.315181	−	0.151783i
$895$	15.0644	+	18.8902i	0.503548	+	0.631429i
$896$	5.22848	−	6.55631i	0.174671	−	0.219031i
$897$	−7.84328	−	3.77712i	−0.261880	−	0.126115i
$898$	32.9650			1.10006
$899$		0			0
$900$	20.6391			0.687970
$901$	−6.44342	−	3.10299i	−0.214662	−	0.103376i
$902$	−16.0638	+	20.1434i	−0.534866	+	0.670701i
$903$	6.75094	+	8.46542i	0.224657	+	0.281711i
$904$	2.38316	+	1.14767i	0.0792627	+	0.0381709i
$905$	69.3853	−	33.4142i	2.30645	−	1.11073i
$906$	26.8662	−	33.6891i	0.892569	−	1.11925i
$907$	−2.72594	−	11.9431i	−0.0905135	−	0.396565i	0.909295	−	0.416153i	$-0.136622\pi$
$907$	−2.72594	−	11.9431i	−0.0905135	−	0.396565i	−0.999808	+	0.0195874i	$0.993765\pi$
$908$	3.88650	+	17.0279i	0.128978	+	0.565090i
$909$	−15.3440	−	19.2408i	−0.508930	−	0.638178i
$910$	5.45953	−	23.9198i	0.180982	−	0.792932i
$911$	−19.8474			−0.657572			−0.328786	−	0.944404i	$-0.606640\pi$
$911$	−19.8474			−0.657572			−0.328786	+	0.944404i	$0.606640\pi$
$912$	10.8839	−	47.6856i	0.360403	−	1.57903i
$913$	−9.82526	+	4.73160i	−0.325169	+	0.156593i
$914$	0.886882	−	0.427100i	0.0293354	−	0.0141272i
$915$	−3.12625	+	13.6970i	−0.103351	+	0.452809i
$916$	6.14189			0.202934
$917$	0.323588	−	1.41773i	0.0106858	−	0.0468177i
$918$	−10.2324	−	12.8310i	−0.337719	−	0.423486i
$919$	6.79540	+	29.7726i	0.224160	+	0.982107i	0.954309	+	0.298820i	$0.0965931\pi$
$919$	6.79540	+	29.7726i	0.224160	+	0.982107i	−0.730150	+	0.683287i	$0.760550\pi$
$920$	−0.738011	−	3.23344i	−0.0243315	−	0.106603i
$921$	−22.8840	+	28.6956i	−0.754054	+	0.945553i
$922$	−9.64326	+	4.64395i	−0.317584	+	0.152940i
$923$	5.78157	+	2.78426i	0.190303	+	0.0916450i
$924$	−7.18856	−	9.01417i	−0.236486	−	0.296544i
$925$	27.6358	−	34.6542i	0.908658	−	1.13942i
$926$	−11.5104	−	5.54314i	−0.378257	−	0.182159i
$927$	15.9595			0.524180
$928$		0			0
$929$	−8.90962			−0.292315			−0.146158	−	0.989261i	$-0.546691\pi$
$929$	−8.90962			−0.292315			−0.146158	+	0.989261i	$0.546691\pi$
$930$	−20.3395	−	9.79499i	−0.666959	−	0.321190i
$931$	1.83193	−	2.29717i	0.0600390	−	0.0752865i
$932$	−4.88985	−	6.13167i	−0.160172	−	0.200850i
$933$	8.88123	+	4.27697i	0.290758	+	0.140022i
$934$	7.85044	−	3.78057i	0.256874	−	0.123704i
$935$	−9.95879	+	12.4879i	−0.325687	+	0.408399i
$936$	0.310208	+	1.35911i	0.0101395	+	0.0444239i
$937$	−3.42621	−	15.0112i	−0.111929	−	0.490395i	−0.999555	−	0.0298290i	$-0.990504\pi$
$937$	−3.42621	−	15.0112i	−0.111929	−	0.490395i	0.887626	−	0.460566i	$-0.152353\pi$
$938$	−9.28172	−	11.6389i	−0.303059	−	0.380024i
$939$	0.542567	−	2.37714i	0.0177060	−	0.0775751i
$940$	−5.53095			−0.180400
$941$	−10.3500	+	45.3464i	−0.337401	+	1.47825i	0.467050	+	0.884231i	$0.345317\pi$
$941$	−10.3500	+	45.3464i	−0.337401	+	1.47825i	−0.804451	+	0.594020i	$0.797540\pi$
$942$	−74.6831	+	35.9655i	−2.43331	+	1.17182i
$943$	26.2765	−	12.6541i	0.855681	−	0.412074i
$944$	−13.0369	+	57.1183i	−0.424314	+	1.85904i
$945$	−15.5349			−0.505350
$946$	−0.916220	+	4.01422i	−0.0297889	+	0.130514i
$947$	−19.4641	−	24.4072i	−0.632498	−	0.793127i	0.357545	−	0.933896i	$-0.383614\pi$
$947$	−19.4641	−	24.4072i	−0.632498	−	0.793127i	−0.990043	+	0.140769i	$0.955043\pi$
$948$	−11.9476	−	52.3459i	−0.388040	−	1.70012i
$949$	−1.30873	−	5.73391i	−0.0424831	−	0.186131i
$950$	31.8939	−	39.9937i	1.03478	−	1.29757i
$951$	−15.9514	+	7.68178i	−0.517259	+	0.249099i
$952$	4.19821	+	2.02175i	0.136065	+	0.0655254i
$953$	−15.3163	−	19.2060i	−0.496144	−	0.622144i	0.469211	−	0.883086i	$-0.344538\pi$
$953$	−15.3163	−	19.2060i	−0.496144	−	0.622144i	−0.965355	+	0.260942i	$0.915967\pi$
$954$	−4.23980	+	5.31654i	−0.137269	+	0.172129i
$955$	38.8590	+	18.7135i	1.25745	+	0.605555i
$956$	31.5744			1.02119
$957$		0			0
$958$	18.0504			0.583181
$959$	31.4200	+	15.1311i	1.01461	+	0.488609i
$960$	28.2730	−	35.4532i	0.912507	−	1.14425i
$961$	−17.7567	−	22.2662i	−0.572796	−	0.718264i
$962$	−22.4944	−	10.8327i	−0.725249	−	0.349262i
$963$	23.1964	−	11.1708i	0.747494	−	0.359974i
$964$	12.7010	−	15.9266i	0.409073	−	0.512961i
$965$	9.14253	+	40.0561i	0.294309	+	1.28945i
$966$	6.15659	+	26.9738i	0.198085	+	0.867868i
$967$	15.8225	+	19.8408i	0.508819	+	0.638039i	0.968193	−	0.250204i	$-0.0804977\pi$
$967$	15.8225	+	19.8408i	0.508819	+	0.638039i	−0.459374	+	0.888243i	$0.651926\pi$
$968$	0.902914	−	3.95592i	0.0290208	−	0.127148i
$969$	49.3288			1.58467
$970$	−21.7511	+	95.2978i	−0.698385	+	3.05983i
$971$	−9.94178	+	4.78771i	−0.319047	+	0.153645i	−0.586552	−	0.809912i	$-0.699515\pi$
$971$	−9.94178	+	4.78771i	−0.319047	+	0.153645i	0.267505	+	0.963556i	$0.413801\pi$
$972$	−30.3144	+	14.5986i	−0.972334	+	0.468252i
$973$	5.96882	−	26.1511i	0.191352	−	0.838367i
$974$	−74.1005			−2.37433
$975$	−4.18953	+	18.3555i	−0.134172	+	0.587847i
$976$	5.25281	+	6.58682i	0.168138	+	0.210839i
$977$	11.6763	+	51.1574i	0.373559	+	1.63667i	0.716697	+	0.697384i	$0.245653\pi$
$977$	11.6763	+	51.1574i	0.373559	+	1.63667i	−0.343138	+	0.939285i	$0.611490\pi$
$978$	9.49295	+	41.5913i	0.303551	+	1.32994i
$979$	−3.41759	+	4.28552i	−0.109227	+	0.136966i
$980$	3.09557	−	1.49075i	0.0988845	−	0.0476202i
$981$	−31.4701	−	15.1552i	−1.00476	−	0.483869i
$982$	−38.3277	−	48.0614i	−1.22309	−	1.53370i
$983$	−28.7287	+	36.0246i	−0.916302	+	1.14901i	0.0721376	+	0.997395i	$0.477018\pi$
$983$	−28.7287	+	36.0246i	−0.916302	+	1.14901i	−0.988440	+	0.151612i	$0.951553\pi$
$984$	−10.0525	−	4.84101i	−0.320461	−	0.154326i
$985$	−13.1171			−0.417945
$986$		0			0
$987$	−5.53280			−0.176111
$988$	−12.2460	−	5.89735i	−0.389596	−	0.187620i
$989$	2.90601	−	3.64402i	0.0924058	−	0.115873i
$990$	9.46925	+	11.8741i	0.300953	+	0.377383i
$991$	−0.727211	−	0.350206i	−0.0231006	−	0.0111247i	0.422298	−	0.906457i	$-0.361224\pi$
$991$	−0.727211	−	0.350206i	−0.0231006	−	0.0111247i	−0.445398	+	0.895332i	$0.646938\pi$
$992$	−11.0049	+	5.29968i	−0.349406	+	0.168265i
$993$	−14.1021	+	17.6835i	−0.447517	+	0.561169i
$994$	−4.53825	−	19.8834i	−0.143945	−	0.630663i
$995$	−12.1474	−	53.2213i	−0.385099	−	1.68723i
$996$	24.5550	+	30.7909i	0.778054	+	0.975648i
$997$	6.81025	−	29.8377i	0.215683	−	0.944969i	−0.744944	−	0.667127i	$-0.767524\pi$
$997$	6.81025	−	29.8377i	0.215683	−	0.944969i	0.960627	−	0.277842i	$-0.0896190\pi$
$998$	40.9875			1.29744
$999$	−3.51771	+	15.4121i	−0.111295	+	0.487617i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.d.o.190.5		36
29.2	odd	28		841.2.e.l.267.10		72
29.3	odd	28		841.2.b.d.840.10		12
29.4	even	14		841.2.d.n.778.5		36
29.5	even	14		841.2.d.n.574.5		36
29.6	even	14		841.2.d.n.605.2		36
29.7	even	7		841.2.a.g.1.2	✓	6
29.8	odd	28		841.2.e.l.270.10		72
29.9	even	14		841.2.d.n.571.2		36
29.10	odd	28		841.2.e.l.63.10		72
29.11	odd	28		841.2.e.l.196.10		72
29.12	odd	4		841.2.e.l.651.3		72
29.13	even	14		841.2.d.n.645.2		36
29.14	odd	28		841.2.e.l.236.3		72
29.15	odd	28		841.2.e.l.236.10		72
29.16	even	7	inner	841.2.d.o.645.5		36
29.17	odd	4		841.2.e.l.651.10		72
29.18	odd	28		841.2.e.l.196.3		72
29.19	odd	28		841.2.e.l.63.3		72
29.20	even	7	inner	841.2.d.o.571.5		36
29.21	odd	28		841.2.e.l.270.3		72
29.22	even	14		841.2.a.h.1.5	yes	6
29.23	even	7	inner	841.2.d.o.605.5		36
29.24	even	7	inner	841.2.d.o.574.2		36
29.25	even	7	inner	841.2.d.o.778.2		36
29.26	odd	28		841.2.b.d.840.3		12
29.27	odd	28		841.2.e.l.267.3		72
29.28	even	2		841.2.d.n.190.2		36
87.65	odd	14		7569.2.a.bc.1.5		6
87.80	odd	14		7569.2.a.y.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
841.2.a.g.1.2	✓	6	29.7	even	7
841.2.a.h.1.5	yes	6	29.22	even	14
841.2.b.d.840.3		12	29.26	odd	28
841.2.b.d.840.10		12	29.3	odd	28
841.2.d.n.190.2		36	29.28	even	2
841.2.d.n.571.2		36	29.9	even	14
841.2.d.n.574.5		36	29.5	even	14
841.2.d.n.605.2		36	29.6	even	14
841.2.d.n.645.2		36	29.13	even	14
841.2.d.n.778.5		36	29.4	even	14
841.2.d.o.190.5		36	1.1	even	1	trivial
841.2.d.o.571.5		36	29.20	even	7	inner
841.2.d.o.574.2		36	29.24	even	7	inner
841.2.d.o.605.5		36	29.23	even	7	inner
841.2.d.o.645.5		36	29.16	even	7	inner
841.2.d.o.778.2		36	29.25	even	7	inner
841.2.e.l.63.3		72	29.19	odd	28
841.2.e.l.63.10		72	29.10	odd	28
841.2.e.l.196.3		72	29.18	odd	28
841.2.e.l.196.10		72	29.11	odd	28
841.2.e.l.236.3		72	29.14	odd	28
841.2.e.l.236.10		72	29.15	odd	28
841.2.e.l.267.3		72	29.27	odd	28
841.2.e.l.267.10		72	29.2	odd	28
841.2.e.l.270.3		72	29.21	odd	28
841.2.e.l.270.10		72	29.8	odd	28
841.2.e.l.651.3		72	29.12	odd	4
841.2.e.l.651.10		72	29.17	odd	4
7569.2.a.y.1.2		6	87.80	odd	14
7569.2.a.bc.1.5		6	87.65	odd	14

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.d (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.75304 + 0.844219i) q^{2} +(-1.41628 + 1.77596i) q^{3} +(1.11346 + 1.39624i) q^{4} +(-2.89865 - 1.39592i) q^{5} +(-3.98209 + 1.91767i) q^{6} +(-1.57757 + 1.97820i) q^{7} +(-0.0927185 - 0.406226i) q^{8} +(-0.480617 - 2.10572i) q^{9} +(-3.90299 - 4.89420i) q^{10} +(0.249954 - 1.09512i) q^{11} -4.05663 q^{12} +(0.344690 - 1.51019i) q^{13} +(-4.43557 + 2.13606i) q^{14} +(6.58439 - 3.17088i) q^{15} +(0.975184 - 4.27256i) q^{16} +4.41979 q^{17} +(0.935150 - 4.09716i) q^{18} +(-3.06344 - 3.84143i) q^{19} +(-1.27851 - 5.60150i) q^{20} +(-1.27893 - 5.60338i) q^{21} +(1.36270 - 1.70877i) q^{22} +(-2.22905 + 1.07345i) q^{23} +(0.852756 + 0.410666i) q^{24} +(3.33615 + 4.18341i) q^{25} +(1.87918 - 2.35642i) q^{26} +(-1.71939 - 0.828013i) q^{27} -4.51860 q^{28} +14.2196 q^{30} +(-1.43038 - 0.688836i) q^{31} +(4.79693 - 6.01516i) q^{32} +(1.59088 + 1.99490i) q^{33} +(7.74806 + 3.73127i) q^{34} +(7.33422 - 3.53198i) q^{35} +(2.40494 - 3.01569i) q^{36} +(-1.84330 - 8.07603i) q^{37} +(-2.12732 - 9.32039i) q^{38} +(2.19385 + 2.75100i) q^{39} +(-0.298300 + 1.30694i) q^{40} -11.7882 q^{41} +(2.48846 - 10.9026i) q^{42} +(-1.69733 + 0.817393i) q^{43} +(1.80736 - 0.870379i) q^{44} +(-1.54627 + 6.77466i) q^{45} -4.81385 q^{46} +(0.214209 - 0.938513i) q^{47} +(6.20675 + 7.78302i) q^{48} +(0.133067 + 0.583004i) q^{49} +(2.31670 + 10.1501i) q^{50} +(-6.25965 + 7.84936i) q^{51} +(2.49237 - 1.20026i) q^{52} +(-1.45786 - 0.702068i) q^{53} +(-2.31513 - 2.90308i) q^{54} +(-2.25323 + 2.82546i) q^{55} +(0.949867 + 0.457432i) q^{56} +11.1609 q^{57} -13.3686 q^{59} +(11.7588 + 5.66272i) q^{60} +(-1.19861 + 1.50300i) q^{61} +(-1.92599 - 2.41511i) q^{62} +(4.92375 + 2.37115i) q^{63} +(5.59044 - 2.69221i) q^{64} +(-3.10723 + 3.89635i) q^{65} +(1.10474 + 4.84020i) q^{66} +(0.672869 + 2.94803i) q^{67} +(4.92126 + 6.17106i) q^{68} +(1.25055 - 5.47901i) q^{69} +15.8389 q^{70} +(-0.921826 + 4.03878i) q^{71} +(-0.810837 + 0.390479i) q^{72} +(3.42082 - 1.64738i) q^{73} +(3.58656 - 15.7137i) q^{74} -12.1545 q^{75} +(1.95252 - 8.55456i) q^{76} +(1.77205 + 2.22208i) q^{77} +(1.52346 + 6.67470i) q^{78} +(2.94521 + 12.9038i) q^{79} +(-8.79086 + 11.0234i) q^{80} +(9.74359 - 4.69226i) q^{81} +(-20.6652 - 9.95183i) q^{82} +(-6.05305 - 7.59028i) q^{83} +(6.39959 - 8.02484i) q^{84} +(-12.8114 - 6.16966i) q^{85} -3.66555 q^{86} -0.468042 q^{88} +(-4.39654 - 2.11726i) q^{89} +(-8.42997 + 10.5709i) q^{90} +(2.44369 + 3.06428i) q^{91} +(-3.98076 - 1.91703i) q^{92} +(3.24917 - 1.56472i) q^{93} +(1.16783 - 1.46441i) q^{94} +(3.51752 + 15.4113i) q^{95} +(3.88888 + 17.0383i) q^{96} +(-9.73579 - 12.2083i) q^{97} +(-0.258912 + 1.13437i) q^{98} -2.42615 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 2 q^{2} + 2 q^{3} - 8 q^{4} + 2 q^{5} + 3 q^{6} + 4 q^{7} + 3 q^{8} - 6 q^{9} + 15 q^{10} + 13 q^{11} + 24 q^{12} + 6 q^{13} - 6 q^{14} + 19 q^{15} - 4 q^{16} - 18 q^{17} + 17 q^{18} - 6 q^{19} + 5 q^{20}+ \cdots - 36 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 + 2 * q^3 - 8 * q^4 + 2 * q^5 + 3 * q^6 + 4 * q^7 + 3 * q^8 - 6 * q^9 + 15 * q^10 + 13 * q^11 + 24 * q^12 + 6 * q^13 - 6 * q^14 + 19 * q^15 - 4 * q^16 - 18 * q^17 + 17 * q^18 - 6 * q^19 + 5 * q^20 - 2 * q^21 + 4 * q^22 + 5 * q^23 + 10 * q^24 - 6 * q^25 + 9 * q^26 - q^27 - 30 * q^28 + 156 * q^30 + 16 * q^31 + 33 * q^32 - 27 * q^33 + 4 * q^35 + 21 * q^36 - 10 * q^37 - 41 * q^38 + 17 * q^39 + 7 * q^40 - 180 * q^41 + 21 * q^42 - 2 * q^43 + 16 * q^44 - 16 * q^45 + 120 * q^46 + 5 * q^47 - 30 * q^48 + 12 * q^49 - 8 * q^50 + 23 * q^51 + 13 * q^53 - 19 * q^54 + 10 * q^55 + 16 * q^56 - 96 * q^57 - 102 * q^59 - 9 * q^60 - 4 * q^61 + 9 * q^63 - q^64 - 32 * q^65 - 8 * q^66 + 9 * q^67 + 16 * q^68 + 26 * q^69 + 168 * q^70 - 21 * q^72 + 9 * q^73 + 36 * q^74 - 42 * q^75 + 24 * q^76 + 13 * q^77 + 6 * q^79 - 5 * q^80 + 22 * q^81 - 19 * q^82 + 24 * q^83 - 26 * q^85 + 102 * q^86 + 126 * q^88 + 9 * q^89 - 16 * q^90 - 16 * q^91 + 23 * q^92 + 12 * q^93 + 37 * q^94 + 31 * q^95 + 37 * q^96 - 10 * q^97 - 42 * q^98 - 36 * q^99

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