LMFDB - Embedded newform 247.2.z.a.141.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [247,2,Mod(141,247)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("247.141"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(247, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([7, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 247 = 13 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	247.z (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.97230492993$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			141.10
Character	$\chi$	$=$	247.141
Dual form			247.2.z.a.240.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.273277 + 0.273277i) q^{2} +1.58138i q^{3} +1.85064i q^{4} +(-1.36285 + 0.365175i) q^{5} +(-0.432157 - 0.432157i) q^{6} +(0.171253 + 0.639124i) q^{7} +(-1.05229 - 1.05229i) q^{8} +0.499222 q^{9} +(0.272642 - 0.472230i) q^{10} +(-0.965805 - 0.258787i) q^{11} -2.92657 q^{12} +(-3.00572 + 1.99140i) q^{13} +(-0.221457 - 0.127859i) q^{14} +(-0.577481 - 2.15519i) q^{15} -3.12614 q^{16} +(5.10151 - 2.94536i) q^{17} +(-0.136426 + 0.136426i) q^{18} +(-4.11106 + 1.44884i) q^{19} +(-0.675806 - 2.52214i) q^{20} +(-1.01070 + 0.270816i) q^{21} +(0.334653 - 0.193212i) q^{22} +(-0.401540 - 0.231829i) q^{23} +(1.66408 - 1.66408i) q^{24} +(-2.60612 + 1.50464i) q^{25} +(0.277189 - 1.36560i) q^{26} +5.53362i q^{27} +(-1.18279 + 0.316927i) q^{28} +(9.08639 + 5.24603i) q^{29} +(0.746777 + 0.431152i) q^{30} +(5.77984 - 5.77984i) q^{31} +(2.95889 - 2.95889i) q^{32} +(0.409241 - 1.52731i) q^{33} +(-0.589228 + 2.19903i) q^{34} +(-0.466783 - 0.808492i) q^{35} +0.923879i q^{36} +(-2.31834 + 8.65218i) q^{37} +(0.727525 - 1.51940i) q^{38} +(-3.14917 - 4.75319i) q^{39} +(1.81839 + 1.04985i) q^{40} +(-4.11747 + 4.11747i) q^{41} +(0.202194 - 0.350209i) q^{42} +(-1.71044 + 0.987525i) q^{43} +(0.478921 - 1.78736i) q^{44} +(-0.680364 + 0.182303i) q^{45} +(0.173086 - 0.0463782i) q^{46} +(9.33773 + 2.50204i) q^{47} -4.94363i q^{48} +(5.68303 - 3.28110i) q^{49} +(0.301008 - 1.12338i) q^{50} +(4.65775 + 8.06745i) q^{51} +(-3.68536 - 5.56249i) q^{52} +(0.164497 - 0.0949726i) q^{53} +(-1.51221 - 1.51221i) q^{54} +1.41075 q^{55} +(0.492337 - 0.852753i) q^{56} +(-2.29118 - 6.50118i) q^{57} +(-3.91672 + 1.04948i) q^{58} +(1.52455 - 5.68970i) q^{59} +(3.98848 - 1.06871i) q^{60} +11.8397 q^{61} +3.15900i q^{62} +(0.0854930 + 0.319064i) q^{63} -4.63509i q^{64} +(3.36913 - 3.81159i) q^{65} +(0.305543 + 0.529216i) q^{66} +(0.384465 + 1.43484i) q^{67} +(5.45080 + 9.44106i) q^{68} +(0.366612 - 0.634990i) q^{69} +(0.348504 + 0.0933813i) q^{70} +(-12.9129 - 3.46000i) q^{71} +(-0.525327 - 0.525327i) q^{72} +(-0.199486 - 0.744491i) q^{73} +(-1.73089 - 2.99799i) q^{74} +(-2.37942 - 4.12128i) q^{75} +(-2.68129 - 7.60810i) q^{76} -0.661587i q^{77} +(2.15954 + 0.438343i) q^{78} +(8.07597 + 4.66267i) q^{79} +(4.26046 - 1.14159i) q^{80} -7.25311 q^{81} -2.25043i q^{82} +(-5.07743 - 5.07743i) q^{83} +(-0.501183 - 1.87044i) q^{84} +(-5.87702 + 5.87702i) q^{85} +(0.197557 - 0.737294i) q^{86} +(-8.29599 + 14.3691i) q^{87} +(0.743990 + 1.28863i) q^{88} +(10.4864 - 2.80983i) q^{89} +(0.136109 - 0.235747i) q^{90} +(-1.78749 - 1.57999i) q^{91} +(0.429033 - 0.743106i) q^{92} +(9.14015 + 9.14015i) q^{93} +(-3.23554 + 1.86804i) q^{94} +(5.07368 - 3.47581i) q^{95} +(4.67914 + 4.67914i) q^{96} +(2.18470 + 0.585387i) q^{97} +(-0.656393 + 2.44969i) q^{98} +(-0.482151 - 0.129192i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 6 q^{2} - 2 q^{5} + 14 q^{6} - 12 q^{7} + 12 q^{8} - 84 q^{9} - 6 q^{10} - 4 q^{11} + 36 q^{12} - 6 q^{13} - 12 q^{14} + 30 q^{15} - 92 q^{16} - 6 q^{17} + 6 q^{18} - 14 q^{19} - 24 q^{20} - 18 q^{22}+ \cdots + 28 q^{99}+O(q^{100}) $ 88 * q - 6 * q^2 - 2 * q^5 + 14 * q^6 - 12 * q^7 + 12 * q^8 - 84 * q^9 - 6 * q^10 - 4 * q^11 + 36 * q^12 - 6 * q^13 - 12 * q^14 + 30 * q^15 - 92 * q^16 - 6 * q^17 + 6 * q^18 - 14 * q^19 - 24 * q^20 - 18 * q^22 - 30 * q^23 + 48 * q^24 + 12 * q^25 + 32 * q^26 + 18 * q^28 + 18 * q^29 + 60 * q^30 - 30 * q^31 - 12 * q^32 - 6 * q^33 - 6 * q^34 - 6 * q^35 - 12 * q^37 - 36 * q^38 + 18 * q^39 - 12 * q^40 - 6 * q^41 + 6 * q^42 + 12 * q^43 + 64 * q^44 - 38 * q^45 + 24 * q^46 + 64 * q^47 - 42 * q^49 - 24 * q^51 + 18 * q^52 - 66 * q^53 - 96 * q^54 - 36 * q^55 + 60 * q^56 + 64 * q^57 - 24 * q^58 - 6 * q^59 + 54 * q^60 - 28 * q^61 - 6 * q^63 + 44 * q^66 - 36 * q^67 - 12 * q^68 - 36 * q^69 + 114 * q^70 - 30 * q^71 - 66 * q^72 + 22 * q^73 + 6 * q^74 - 12 * q^75 + 38 * q^76 + 12 * q^78 - 24 * q^79 + 14 * q^80 + 64 * q^81 - 6 * q^83 - 18 * q^84 - 18 * q^85 - 6 * q^86 + 32 * q^87 + 42 * q^88 + 66 * q^89 + 18 * q^90 - 18 * q^91 + 104 * q^92 - 2 * q^93 - 84 * q^94 - 42 * q^95 - 174 * q^96 + 30 * q^97 - 60 * q^98 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/247\mathbb{Z}\right)^\times$.

$n$	$40$	$210$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	−0.273277	+	0.273277i	−0.193236	+	0.193236i	−0.797093	−	0.603857i	$-0.793630\pi$
$2$	−0.273277	+	0.273277i	−0.193236	+	0.193236i	0.603857	+	0.797093i	$0.293630\pi$
$3$			1.58138i			0.913013i	0.889720	+	0.456507i	$0.150899\pi$
$3$			1.58138i			0.913013i	−0.889720	+	0.456507i	$0.849101\pi$
$4$			1.85064i			0.925319i
$5$	−1.36285	+	0.365175i	−0.609485	+	0.163311i	−0.550343	−	0.834939i	$-0.685503\pi$
$5$	−1.36285	+	0.365175i	−0.609485	+	0.163311i	−0.0591418	+	0.998250i	$0.518836\pi$
$6$	−0.432157	−	0.432157i	−0.176427	−	0.176427i
$7$	0.171253	+	0.639124i	0.0647274	+	0.241566i	0.990708	−	0.136005i	$-0.0434262\pi$
$7$	0.171253	+	0.639124i	0.0647274	+	0.241566i	−0.925981	+	0.377571i	$0.876760\pi$
$8$	−1.05229	−	1.05229i	−0.372042	−	0.372042i
$9$	0.499222			0.166407
$10$	0.272642	−	0.472230i	0.0862170	−	0.149332i
$11$	−0.965805	−	0.258787i	−0.291201	−	0.0780271i	0.110261	−	0.993903i	$-0.464831\pi$
$11$	−0.965805	−	0.258787i	−0.291201	−	0.0780271i	−0.401462	+	0.915876i	$0.631498\pi$
$12$	−2.92657			−0.844829
$13$	−3.00572	+	1.99140i	−0.833635	+	0.552315i
$13$	−3.00572	+	1.99140i	−0.833635	+	0.552315i
$14$	−0.221457	−	0.127859i	−0.0591870	−	0.0341716i
$15$	−0.577481	−	2.15519i	−0.149105	−	0.556468i
$16$	−3.12614			−0.781536
$17$	5.10151	−	2.94536i	1.23730	−	0.714355i	0.268757	−	0.963208i	$-0.413387\pi$
$17$	5.10151	−	2.94536i	1.23730	−	0.714355i	0.968541	+	0.248853i	$0.0800538\pi$
$18$	−0.136426	+	0.136426i	−0.0321559	+	0.0321559i
$19$	−4.11106	+	1.44884i	−0.943143	+	0.332387i
$19$	−4.11106	+	1.44884i	−0.943143	+	0.332387i
$20$	−0.675806	−	2.52214i	−0.151115	−	0.563968i
$21$	−1.01070	+	0.270816i	−0.220553	+	0.0590970i
$22$	0.334653	−	0.193212i	0.0713483	−	0.0411930i
$23$	−0.401540	−	0.231829i	−0.0837270	−	0.0483398i	0.457552	−	0.889183i	$-0.348726\pi$
$23$	−0.401540	−	0.231829i	−0.0837270	−	0.0483398i	−0.541279	+	0.840843i	$0.682060\pi$
$24$	1.66408	−	1.66408i	0.339679	−	0.339679i
$25$	−2.60612	+	1.50464i	−0.521224	+	0.300929i
$26$	0.277189	−	1.36560i	0.0543613	−	0.267816i
$27$			5.53362i			1.06494i
$28$	−1.18279	+	0.316927i	−0.223526	+	0.0598935i
$29$	9.08639	+	5.24603i	1.68730	+	0.974163i	0.956573	+	0.291492i	$0.0941517\pi$
$29$	9.08639	+	5.24603i	1.68730	+	0.974163i	0.730726	+	0.682671i	$0.239182\pi$
$30$	0.746777	+	0.431152i	0.136342	+	0.0787172i
$31$	5.77984	−	5.77984i	1.03809	−	1.03809i	0.0388441	−	0.999245i	$-0.487632\pi$
$31$	5.77984	−	5.77984i	1.03809	−	1.03809i	0.999245	−	0.0388441i	$-0.0123676\pi$
$32$	2.95889	−	2.95889i	0.523063	−	0.523063i
$33$	0.409241	−	1.52731i	0.0712398	−	0.265871i
$34$	−0.589228	+	2.19903i	−0.101052	+	0.377130i
$35$	−0.466783	−	0.808492i	−0.0789008	−	0.136660i
$36$			0.923879i			0.153980i
$37$	−2.31834	+	8.65218i	−0.381133	+	1.42241i	0.463039	+	0.886338i	$0.346759\pi$
$37$	−2.31834	+	8.65218i	−0.381133	+	1.42241i	−0.844173	+	0.536071i	$0.819908\pi$
$38$	0.727525	−	1.51940i	0.118020	−	0.246479i
$39$	−3.14917	−	4.75319i	−0.504271	−	0.761120i
$40$	1.81839	+	1.04985i	0.287512	+	0.165995i
$41$	−4.11747	+	4.11747i	−0.643042	+	0.643042i	−0.951302	−	0.308260i	$-0.900253\pi$
$41$	−4.11747	+	4.11747i	−0.643042	+	0.643042i	0.308260	+	0.951302i	$0.400253\pi$
$42$	0.202194	−	0.350209i	0.0311991	−	0.0540385i
$43$	−1.71044	+	0.987525i	−0.260840	+	0.150596i	−0.624718	−	0.780851i	$-0.714786\pi$
$43$	−1.71044	+	0.987525i	−0.260840	+	0.150596i	0.363878	+	0.931447i	$0.381453\pi$
$44$	0.478921	−	1.78736i	0.0722000	−	0.269454i
$45$	−0.680364	+	0.182303i	−0.101423	+	0.0271761i
$46$	0.173086	−	0.0463782i	0.0255201	−	0.00683809i
$47$	9.33773	+	2.50204i	1.36205	+	0.364959i	0.864568	−	0.502516i	$-0.167592\pi$
$47$	9.33773	+	2.50204i	1.36205	+	0.364959i	0.497480	+	0.867476i	$0.334259\pi$
$48$		−	4.94363i		−	0.713552i
$49$	5.68303	−	3.28110i	0.811861	−	0.468728i
$50$	0.301008	−	1.12338i	0.0425690	−	0.158870i
$51$	4.65775	+	8.06745i	0.652215	+	1.12967i
$52$	−3.68536	−	5.56249i	−0.511068	−	0.771379i
$53$	0.164497	−	0.0949726i	0.0225955	−	0.0130455i	−0.488660	−	0.872474i	$-0.662514\pi$
$53$	0.164497	−	0.0949726i	0.0225955	−	0.0130455i	0.511255	+	0.859429i	$0.329181\pi$
$54$	−1.51221	−	1.51221i	−0.205786	−	0.205786i
$55$	1.41075			0.190225
$56$	0.492337	−	0.852753i	0.0657913	−	0.113954i
$57$	−2.29118	−	6.50118i	−0.303474	−	0.861102i
$58$	−3.91672	+	1.04948i	−0.514291	+	0.137804i
$59$	1.52455	−	5.68970i	0.198479	−	0.740735i	−0.792859	−	0.609405i	$-0.791408\pi$
$59$	1.52455	−	5.68970i	0.198479	−	0.740735i	0.991339	−	0.131331i	$-0.0419249\pi$
$60$	3.98848	−	1.06871i	0.514910	−	0.137970i
$61$	11.8397			1.51592			0.757958	−	0.652303i	$-0.226197\pi$
$61$	11.8397			1.51592			0.757958	+	0.652303i	$0.226197\pi$
$62$			3.15900i			0.401193i
$63$	0.0854930	+	0.319064i	0.0107711	+	0.0401983i
$64$		−	4.63509i		−	0.579386i
$65$	3.36913	−	3.81159i	0.417889	−	0.472770i
$66$	0.305543	+	0.529216i	0.0376097	+	0.0651419i
$67$	0.384465	+	1.43484i	0.0469699	+	0.175294i	0.985426	−	0.170104i	$-0.0544105\pi$
$67$	0.384465	+	1.43484i	0.0469699	+	0.175294i	−0.938456	+	0.345398i	$0.887744\pi$
$68$	5.45080	+	9.44106i	0.661006	+	1.14490i
$69$	0.366612	−	0.634990i	0.0441348	−	0.0764438i
$70$	0.348504	+	0.0933813i	0.0416542	+	0.0111612i
$71$	−12.9129	−	3.46000i	−1.53248	−	0.410626i	−0.608651	−	0.793438i	$-0.708289\pi$
$71$	−12.9129	−	3.46000i	−1.53248	−	0.410626i	−0.923826	+	0.382812i	$0.874956\pi$
$72$	−0.525327	−	0.525327i	−0.0619104	−	0.0619104i
$73$	−0.199486	−	0.744491i	−0.0233480	−	0.0871361i	0.953269	−	0.302124i	$-0.0976956\pi$
$73$	−0.199486	−	0.744491i	−0.0233480	−	0.0871361i	−0.976617	+	0.214988i	$0.931029\pi$
$74$	−1.73089	−	2.99799i	−0.201212	−	0.348510i
$75$	−2.37942	−	4.12128i	−0.274752	−	0.475884i
$76$	−2.68129	−	7.60810i	−0.307565	−	0.872709i
$77$		−	0.661587i		−	0.0753948i
$78$	2.15954	+	0.438343i	0.244519	+	0.0496326i
$79$	8.07597	+	4.66267i	0.908618	+	0.524591i	0.879986	−	0.474999i	$-0.157552\pi$
$79$	8.07597	+	4.66267i	0.908618	+	0.524591i	0.0286318	+	0.999590i	$0.490885\pi$
$80$	4.26046	−	1.14159i	0.476334	−	0.127633i
$81$	−7.25311			−0.805901
$82$		−	2.25043i		−	0.248518i
$83$	−5.07743	−	5.07743i	−0.557320	−	0.557320i	0.371223	−	0.928544i	$-0.378938\pi$
$83$	−5.07743	−	5.07743i	−0.557320	−	0.557320i	−0.928544	+	0.371223i	$0.878938\pi$
$84$	−0.501183	−	1.87044i	−0.0546836	−	0.204082i
$85$	−5.87702	+	5.87702i	−0.637453	+	0.637453i
$86$	0.197557	−	0.737294i	0.0213031	−	0.0795044i
$87$	−8.29599	+	14.3691i	−0.889423	+	1.54053i
$88$	0.743990	+	1.28863i	0.0793096	+	0.137368i
$89$	10.4864	−	2.80983i	1.11156	−	0.297841i	0.344095	−	0.938935i	$-0.388186\pi$
$89$	10.4864	−	2.80983i	1.11156	−	0.297841i	0.767463	+	0.641094i	$0.221519\pi$
$90$	0.136109	−	0.235747i	0.0143471	−	0.0248500i
$91$	−1.78749	−	1.57999i	−0.187380	−	0.165628i
$92$	0.429033	−	0.743106i	0.0447297	−	0.0774742i
$93$	9.14015	+	9.14015i	0.947789	+	0.947789i
$94$	−3.23554	+	1.86804i	−0.333720	+	0.192674i
$95$	5.07368	−	3.47581i	0.520549	−	0.356611i
$96$	4.67914	+	4.67914i	0.477563	+	0.477563i
$97$	2.18470	+	0.585387i	0.221822	+	0.0594371i	0.368018	−	0.929819i	$-0.380036\pi$
$97$	2.18470	+	0.585387i	0.221822	+	0.0594371i	−0.146196	+	0.989256i	$0.546703\pi$
$98$	−0.656393	+	2.44969i	−0.0663057	+	0.247456i
$99$	−0.482151	−	0.129192i	−0.0484580	−	0.0129843i
$100$	−2.78455	−	4.82299i	−0.278455	−	0.482299i
$101$	10.7066	+	6.18143i	1.06534	+	0.615075i	0.926905	−	0.375296i	$-0.122459\pi$
$101$	10.7066	+	6.18143i	1.06534	+	0.615075i	0.138437	+	0.990371i	$0.455792\pi$
$102$	−3.47751	−	0.931796i	−0.344325	−	0.0922615i
$103$	−17.1566			−1.69049			−0.845243	−	0.534382i	$-0.820544\pi$
$103$	−17.1566			−1.69049			−0.845243	+	0.534382i	$0.820544\pi$
$104$	5.25843	+	1.06736i	0.515631	+	0.104663i
$105$	1.27854	−	0.738164i	0.124772	−	0.0720374i
$106$	−0.0189996	+	0.0709073i	−0.00184540	+	0.00688713i
$107$	−6.79069	+	3.92061i	−0.656481	+	0.379019i	−0.790935	−	0.611900i	$-0.790405\pi$
$107$	−6.79069	+	3.92061i	−0.656481	+	0.379019i	0.134454	+	0.990920i	$0.457072\pi$
$108$	−10.2407			−0.985414
$109$	0.278050	+	1.03770i	0.0266323	+	0.0993932i	0.977963	−	0.208780i	$-0.0669491\pi$
$109$	0.278050	+	1.03770i	0.0266323	+	0.0993932i	−0.951330	+	0.308173i	$0.900282\pi$
$110$	−0.385526	+	0.385526i	−0.0367585	+	0.0367585i
$111$	−13.6824	−	3.66619i	−1.29868	−	0.347980i
$112$	−0.535360	−	1.99799i	−0.0505868	−	0.188792i
$113$	−5.92136	−	3.41870i	−0.557035	−	0.321604i	0.194920	−	0.980819i	$-0.437555\pi$
$113$	−5.92136	−	3.41870i	−0.557035	−	0.321604i	−0.751955	+	0.659215i	$0.770889\pi$
$114$	2.40275	+	1.15050i	0.225038	+	0.107754i
$115$	0.631897	+	0.169316i	0.0589247	+	0.0157888i
$116$	−9.70850	+	16.8156i	−0.901412	+	1.56129i
$117$	−1.50052	+	0.994150i	−0.138723	+	0.0919092i
$118$	1.13824	+	1.97149i	0.104784	+	0.181490i
$119$	2.75610	+	2.75610i	0.252651	+	0.252651i
$120$	−1.66021	+	2.87557i	−0.151556	+	0.262502i
$121$	−8.66047	−	5.00012i	−0.787315	−	0.454557i
$122$	−3.23552	+	3.23552i	−0.292930	+	0.292930i
$123$	−6.51131	−	6.51131i	−0.587105	−	0.587105i
$124$	10.6964	+	10.6964i	0.960564	+	0.960564i
$125$	7.99067	−	7.99067i	0.714707	−	0.714707i
$126$	−0.110556	−	0.0638297i	−0.00984914	−	0.00568641i
$127$	−3.01025	+	5.21390i	−0.267116	+	0.462659i	−0.968116	−	0.250503i	$-0.919404\pi$
$127$	−3.01025	+	5.21390i	−0.267116	+	0.462659i	0.701000	+	0.713162i	$0.252737\pi$
$128$	7.18444	+	7.18444i	0.635021	+	0.635021i
$129$	−1.56166	−	2.70487i	−0.137496	−	0.238150i
$130$	0.120914	+	1.96233i	0.0106049	+	0.172108i
$131$	4.35687	−	7.54632i	0.380662	−	0.659325i	−0.610495	−	0.792020i	$-0.709030\pi$
$131$	4.35687	−	7.54632i	0.380662	−	0.659325i	0.991157	+	0.132695i	$0.0423630\pi$
$132$	2.82650	+	0.757358i	0.246015	+	0.0659196i
$133$	−1.63002	−	2.37936i	−0.141341	−	0.206317i
$134$	−0.497176	−	0.287045i	−0.0429495	−	0.0247969i
$135$	−2.02074	−	7.54149i	−0.173917	−	0.649068i
$136$	−8.46766	−	2.26890i	−0.726096	−	0.194557i
$137$	2.74247	−	2.74247i	0.234305	−	0.234305i	−0.580182	−	0.814487i	$-0.697019\pi$
$137$	2.74247	−	2.74247i	0.234305	−	0.234305i	0.814487	+	0.580182i	$0.197019\pi$
$138$	0.0733417	+	0.273715i	0.00624326	+	0.0233002i
$139$	−11.0251			−0.935135			−0.467567	−	0.883957i	$-0.654870\pi$
$139$	−11.0251			−0.935135			−0.467567	+	0.883957i	$0.654870\pi$
$140$	1.49623	−	0.863847i	0.126454	−	0.0730084i
$141$	−3.95668	+	14.7665i	−0.333213	+	1.24357i
$142$	4.47434	−	2.58326i	0.375478	−	0.216782i
$143$	3.41828	−	1.14547i	0.285851	−	0.0957886i
$144$	−1.56064			−0.130053
$145$	−14.2991	−	3.83143i	−1.18748	−	0.318183i
$146$	0.257967	+	0.148938i	0.0213495	+	0.0123262i
$147$	5.18868	+	8.98705i	0.427955	+	0.741240i
$148$	−16.0121	−	4.29042i	−1.31618	−	0.352670i
$149$	3.80194	−	14.1890i	0.311467	−	1.16241i	−0.615766	−	0.787929i	$-0.711153\pi$
$149$	3.80194	−	14.1890i	0.311467	−	1.16241i	0.927234	−	0.374483i	$-0.122180\pi$
$150$	1.77649	+	0.476010i	0.145050	+	0.0388661i
$151$	11.1605	+	11.1605i	0.908231	+	0.908231i	0.996129	−	0.0878981i	$-0.0280150\pi$
$151$	11.1605	+	11.1605i	0.908231	+	0.908231i	−0.0878981	+	0.996129i	$0.528015\pi$
$152$	5.85065	+	2.80144i	0.474550	+	0.227226i
$153$	2.54679	−	1.47039i	0.205895	−	0.118874i
$154$	0.180797	+	0.180797i	0.0145690	+	0.0145690i
$155$	−5.76640	+	9.98770i	−0.463168	+	0.802231i
$156$	8.79644	−	5.82798i	0.704279	−	0.466612i
$157$	4.26392	−	7.38532i	0.340298	−	0.589413i	−0.644190	−	0.764865i	$-0.722805\pi$
$157$	4.26392	−	7.38532i	0.340298	−	0.589413i	0.984488	+	0.175452i	$0.0561388\pi$
$158$	−3.48118	+	0.932780i	−0.276948	+	0.0742080i
$159$	0.150188	+	0.260134i	0.0119107	+	0.0206299i
$160$	−2.95201	+	5.11303i	−0.233377	+	0.404221i
$161$	0.0794028	−	0.296335i	0.00625782	−	0.0233545i
$162$	1.98211	−	1.98211i	0.155729	−	0.155729i
$163$	2.62814	+	9.80835i	0.205852	+	0.768249i	0.989188	+	0.146651i	$0.0468495\pi$
$163$	2.62814	+	9.80835i	0.205852	+	0.768249i	−0.783337	+	0.621598i	$0.786484\pi$
$164$	−7.61996	−	7.61996i	−0.595019	−	0.595019i
$165$			2.23094i			0.173678i
$166$	2.77509			0.215389
$167$	0.933835	−	0.250220i	0.0722623	−	0.0193626i	−0.222507	−	0.974931i	$-0.571424\pi$
$167$	0.933835	−	0.250220i	0.0722623	−	0.0193626i	0.294769	+	0.955569i	$0.404757\pi$
$168$	1.34853	+	0.778574i	0.104041	+	0.0600683i
$169$	5.06865	−	11.9712i	0.389896	−	0.920859i
$170$		−	3.21212i		−	0.246358i
$171$	−2.05233	+	0.723294i	−0.156946	+	0.0553117i
$172$	−1.82755	−	3.16541i	−0.139350	−	0.241360i
$173$	−7.61376	−	13.1874i	−0.578863	−	1.00262i	−0.995610	−	0.0935982i	$-0.970163\pi$
$173$	−7.61376	−	13.1874i	−0.578863	−	1.00262i	0.416747	−	0.909023i	$-0.363170\pi$
$174$	−1.65964	−	6.19385i	−0.125817	−	0.469554i
$175$	−1.40796	−	1.40796i	−0.106432	−	0.106432i
$176$	3.01924	+	0.809004i	0.227584	+	0.0609810i
$177$	8.99760	+	2.41090i	0.676301	+	0.181214i
$178$	−2.09784	+	3.63356i	−0.157240	+	0.272347i
$179$	−3.61350	−	6.25877i	−0.270086	−	0.467803i	0.698798	−	0.715319i	$-0.253719\pi$
$179$	−3.61350	−	6.25877i	−0.270086	−	0.467803i	−0.968884	+	0.247517i	$0.920385\pi$
$180$	−0.337377	−	1.25911i	−0.0251466	−	0.0938484i
$181$	8.85929	+	15.3447i	0.658506	+	1.14057i	0.981003	+	0.193995i	$0.0621445\pi$
$181$	8.85929	+	15.3447i	0.658506	+	1.14057i	−0.322497	+	0.946570i	$0.604522\pi$
$182$	0.920256	−	0.0567040i	0.0682139	−	0.00420318i
$183$			18.7231i			1.38405i
$184$	0.178586	+	0.666490i	0.0131655	+	0.0491343i
$185$		−	12.6382i		−	0.929180i
$186$	−4.99559			−0.366294
$187$	−5.68929	+	1.52444i	−0.416042	+	0.111478i
$188$	−4.63037	+	17.2808i	−0.337704	+	1.26033i
$189$	−3.53666	+	0.947646i	−0.257254	+	0.0689311i
$190$	−0.436662	+	2.33638i	−0.0316788	+	0.169499i
$191$	−0.106245	+	0.184021i	−0.00768759	+	0.0133153i	−0.869844	−	0.493328i	$-0.835780\pi$
$191$	−0.106245	+	0.184021i	−0.00768759	+	0.0133153i	0.862156	+	0.506643i	$0.169114\pi$
$192$	7.32986			0.528987
$193$	4.98651	+	4.98651i	0.358937	+	0.358937i	0.863421	−	0.504484i	$-0.168317\pi$
$193$	4.98651	+	4.98651i	0.358937	+	0.358937i	−0.504484	+	0.863421i	$0.668317\pi$
$194$	−0.757001	+	0.437055i	−0.0543495	+	0.0313787i
$195$	6.02759	+	5.32789i	0.431645	+	0.381538i
$196$	6.07213	+	10.5172i	0.433723	+	0.751231i
$197$	4.40483	−	16.4390i	0.313831	−	1.17123i	−0.611242	−	0.791444i	$-0.709330\pi$
$197$	4.40483	−	16.4390i	0.313831	−	1.17123i	0.925073	−	0.379789i	$-0.124003\pi$
$198$	0.167066	−	0.0964557i	0.0118729	−	0.00685481i
$199$		−	20.0357i		−	1.42029i	−0.704056	−	0.710145i	$-0.748629\pi$
$199$		−	20.0357i		−	1.42029i	0.704056	−	0.710145i	$-0.251371\pi$
$200$	4.32573	+	1.15907i	0.305875	+	0.0819590i
$201$	−2.26904	+	0.607988i	−0.160046	+	0.0428841i
$202$	−4.61510	+	1.23661i	−0.324718	+	0.0870078i
$203$	−1.79679	+	6.70572i	−0.126110	+	0.470649i
$204$	−14.9299	+	8.61981i	−1.04531	+	0.603507i
$205$	4.10790	−	7.11510i	0.286908	−	0.496940i
$206$	4.68850	−	4.68850i	0.326663	−	0.326663i
$207$	−0.200458	−	0.115734i	−0.0139328	−	0.00804409i
$208$	9.39630	−	6.22540i	0.651516	−	0.431654i
$209$	4.34543	−	0.335411i	0.300580	−	0.0232009i
$210$	−0.147672	+	0.551119i	−0.0101903	+	0.0380308i
$211$		−	1.30145i		−	0.0895952i	−0.998996	−	0.0447976i	$-0.985736\pi$
$211$		−	1.30145i		−	0.0895952i	0.998996	−	0.0447976i	$-0.0142643\pi$
$212$	0.175760	+	0.304425i	0.0120713	+	0.0209080i
$213$	5.47159	−	20.4202i	0.374907	−	1.39917i
$214$	0.784329	−	2.92715i	0.0536156	−	0.200096i
$215$	1.97046	−	1.97046i	0.134384	−	0.134384i
$216$	5.82298	−	5.82298i	0.396204	−	0.396204i
$217$	4.68384	+	2.70422i	0.317960	+	0.183574i
$218$	−0.359563	−	0.207594i	−0.0243527	−	0.0140600i
$219$	1.17733	−	0.315464i	0.0795564	−	0.0213171i
$220$			2.61079i			0.176019i
$221$	−9.46830	+	19.0121i	−0.636907	+	1.27889i
$222$	4.74098	−	2.73721i	0.318194	−	0.183709i
$223$	14.1786	−	14.1786i	0.949467	−	0.949467i	−0.0493167	−	0.998783i	$-0.515704\pi$
$223$	14.1786	−	14.1786i	0.949467	−	0.949467i	0.998783	+	0.0493167i	$0.0157044\pi$
$224$	2.39781	+	1.38438i	0.160211	+	0.0924976i
$225$	−1.30103	+	0.751151i	−0.0867354	+	0.0500767i
$226$	2.55243	−	0.683921i	0.169785	−	0.0454937i
$227$	−2.79249	−	10.4217i	−0.185344	−	0.691713i	−0.994557	−	0.104197i	$-0.966773\pi$
$227$	−2.79249	−	10.4217i	−0.185344	−	0.691713i	0.809213	−	0.587516i	$-0.199894\pi$
$228$	12.0313	−	4.24014i	0.796794	−	0.280810i
$229$	15.4050	−	15.4050i	1.01799	−	1.01799i	0.0181565	−	0.999835i	$-0.494220\pi$
$229$	15.4050	−	15.4050i	1.01799	−	1.01799i	0.999835	−	0.0181565i	$-0.00577970\pi$
$230$	−0.218954	+	0.126413i	−0.0144374	+	0.00833542i
$231$	1.04622			0.0688364
$232$	−4.04118	−	15.0819i	−0.265316	−	0.990175i
$233$	−2.76866	−	1.59849i	−0.181381	−	0.104720i	0.406560	−	0.913624i	$-0.366728\pi$
$233$	−2.76866	−	1.59849i	−0.181381	−	0.104720i	−0.587941	+	0.808904i	$0.700061\pi$
$234$	0.138379	−	0.681736i	0.00904612	−	0.0445665i
$235$	−13.6396			−0.889749
$236$	10.5296	+	2.82139i	0.685417	+	0.183657i
$237$	−7.37347	+	12.7712i	−0.478958	+	0.829580i
$238$	−1.50636			−0.0976426
$239$	12.6019	+	12.6019i	0.815150	+	0.815150i	0.985401	−	0.170251i	$-0.0544578\pi$
$239$	12.6019	+	12.6019i	0.815150	+	0.815150i	−0.170251	+	0.985401i	$0.554458\pi$
$240$	1.80529	+	6.73743i	0.116531	+	0.434899i
$241$	0.0263630	+	0.0263630i	0.00169819	+	0.00169819i	0.707955	−	0.706257i	$-0.249618\pi$
$241$	0.0263630	+	0.0263630i	0.00169819	+	0.00169819i	−0.706257	+	0.707955i	$0.749618\pi$
$242$	3.73313	−	1.00029i	0.239975	−	0.0643010i
$243$			5.13089i			0.329147i
$244$			21.9110i			1.40271i
$245$	−6.54694	+	6.54694i	−0.418269	+	0.418269i
$246$	3.55879			0.226900
$247$	9.47146	−	12.5416i	0.602655	−	0.798002i
$248$	−12.1642			−0.772425
$249$	8.02937	−	8.02937i	0.508841	−	0.508841i
$250$			4.36734i			0.276215i
$251$		−	30.2918i		−	1.91200i	−0.293366	−	0.956000i	$-0.594775\pi$
$251$		−	30.2918i		−	1.91200i	0.293366	−	0.956000i	$-0.405225\pi$
$252$	−0.590473	+	0.158217i	−0.0371963	+	0.00996672i
$253$	0.327815	+	0.327815i	0.0206096	+	0.0206096i
$254$	−0.602209	−	2.24747i	−0.0377860	−	0.141019i
$255$	−9.29384	−	9.29384i	−0.582003	−	0.582003i
$256$	5.34349			0.333968
$257$	−5.30887	+	9.19523i	−0.331158	+	0.573583i	−0.982739	−	0.184996i	$-0.940773\pi$
$257$	−5.30887	+	9.19523i	−0.331158	+	0.573583i	0.651581	+	0.758579i	$0.274106\pi$
$258$	1.16594	+	0.312414i	0.0725886	+	0.0194500i
$259$	−5.92683			−0.368275
$260$	7.05388	+	6.23504i	0.437463	+	0.386681i
$261$	4.53612	+	2.61893i	0.280779	+	0.162108i
$262$	0.871605	+	3.25287i	0.0538479	+	0.200963i
$263$	−4.57922			−0.282367			−0.141183	−	0.989983i	$-0.545091\pi$
$263$	−4.57922			−0.282367			−0.141183	+	0.989983i	$0.545091\pi$
$264$	−2.03782	+	1.17653i	−0.125419	+	0.0724107i
$265$	−0.189504	+	0.189504i	−0.0116411	+	0.0116411i
$266$	1.09567	+	0.204778i	0.0671800	+	0.0125557i
$267$	4.44342	+	16.5831i	0.271933	+	1.01487i
$268$	−2.65538	+	0.711506i	−0.162203	+	0.0434622i
$269$	15.1303	−	8.73550i	0.922512	−	0.532613i	0.0380765	−	0.999275i	$-0.487877\pi$
$269$	15.1303	−	8.73550i	0.922512	−	0.532613i	0.884436	+	0.466662i	$0.154544\pi$
$270$	2.61314	+	1.50870i	0.159031	+	0.0918164i
$271$	−9.00738	+	9.00738i	−0.547159	+	0.547159i	−0.925618	−	0.378459i	$-0.876454\pi$
$271$	−9.00738	+	9.00738i	−0.547159	+	0.547159i	0.378459	+	0.925618i	$0.376454\pi$
$272$	−15.9481	+	9.20761i	−0.966993	+	0.558294i
$273$	2.49857	−	2.82671i	0.151221	−	0.171080i
$274$			1.49891i			0.0905525i
$275$	2.90639	−	0.778764i	0.175262	−	0.0469612i
$276$	1.17514	+	0.678466i	0.0707349	+	0.0408388i
$277$	−0.0723826	−	0.0417901i	−0.00434905	−	0.00251092i	0.497824	−	0.867278i	$-0.334133\pi$
$277$	−0.0723826	−	0.0417901i	−0.00434905	−	0.00251092i	−0.502173	+	0.864767i	$0.667466\pi$
$278$	3.01290	−	3.01290i	0.180702	−	0.180702i
$279$	2.88542	−	2.88542i	0.172746	−	0.172746i
$280$	−0.359578	+	1.34196i	−0.0214889	+	0.0801976i
$281$	2.16815	−	8.09164i	0.129341	−	0.482707i	−0.870616	−	0.491963i	$-0.836280\pi$
$281$	2.16815	−	8.09164i	0.129341	−	0.482707i	0.999957	+	0.00925595i	$0.00294630\pi$
$282$	−2.95409	−	5.11663i	−0.175913	−	0.304691i
$283$			20.4016i			1.21275i	0.795178	+	0.606376i	$0.207377\pi$
$283$			20.4016i			1.21275i	−0.795178	+	0.606376i	$0.792623\pi$
$284$	6.40320	−	23.8971i	0.379960	−	1.41803i
$285$	5.49660	+	8.02345i	0.325590	+	0.475268i
$286$	−0.621110	+	1.24717i	−0.0367270	+	0.0737467i
$287$	−3.33670	−	1.92645i	−0.196959	−	0.113715i
$288$	1.47714	−	1.47714i	0.0870414	−	0.0870414i
$289$	8.85028	−	15.3291i	0.520605	−	0.901714i
$290$	4.95466	−	2.86058i	0.290948	−	0.167979i
$291$	−0.925723	+	3.45484i	−0.0542668	+	0.202527i
$292$	1.37778	−	0.369176i	0.0806287	−	0.0216044i
$293$	−24.7539	+	6.63278i	−1.44614	+	0.387491i	−0.894678	−	0.446711i	$-0.852595\pi$
$293$	−24.7539	+	6.63278i	−1.44614	+	0.387491i	−0.551459	+	0.834202i	$0.685929\pi$
$294$	−3.87391	−	1.03801i	−0.225931	−	0.0605380i
$295$			8.31093i			0.483881i
$296$	11.5442	−	6.66504i	0.670993	−	0.387398i
$297$	1.43203	−	5.34440i	0.0830946	−	0.310113i
$298$	2.83856	+	4.91653i	0.164433	+	0.284807i
$299$	1.66858	−	0.102814i	0.0964965	−	0.00594590i
$300$	7.62700	−	4.40345i	0.440345	−	0.254233i
$301$	−0.924068	−	0.924068i	−0.0532624	−	0.0532624i
$302$	−6.09984			−0.351007
$303$	−9.77522	+	16.9312i	−0.561572	+	0.972671i
$304$	12.8518	−	4.52929i	0.737100	−	0.259773i
$305$	−16.1357	+	4.32355i	−0.923928	+	0.247566i
$306$	−0.294155	+	1.09780i	−0.0168157	+	0.0627572i
$307$	−33.2043	+	8.89706i	−1.89507	+	0.507782i	−0.897267	+	0.441488i	$0.854451\pi$
$307$	−33.2043	+	8.89706i	−1.89507	+	0.507782i	−0.997800	+	0.0662941i	$0.978882\pi$
$308$	1.22436			0.0697643
$309$		−	27.1311i		−	1.54344i
$310$	−1.15359	−	4.30524i	−0.0655192	−	0.244521i
$311$		−	3.19974i		−	0.181441i	−0.995876	−	0.0907204i	$-0.971083\pi$
$311$		−	3.19974i		−	0.181441i	0.995876	−	0.0907204i	$-0.0289169\pi$
$312$	−1.68790	+	8.31560i	−0.0955586	+	0.470778i
$313$	4.01667	+	6.95707i	0.227035	+	0.393237i	0.956928	−	0.290325i	$-0.0937634\pi$
$313$	4.01667	+	6.95707i	0.227035	+	0.393237i	−0.729893	+	0.683562i	$0.760430\pi$
$314$	0.853009	+	3.18347i	0.0481381	+	0.179654i
$315$	−0.233028	−	0.403617i	−0.0131297	−	0.0227412i
$316$	−8.62891	+	14.9457i	−0.485414	+	0.840762i
$317$	−9.05584	−	2.42650i	−0.508626	−	0.136286i	−0.00462573	−	0.999989i	$-0.501472\pi$
$317$	−9.05584	−	2.42650i	−0.508626	−	0.136286i	−0.504001	+	0.863703i	$0.668139\pi$
$318$	−0.112132	−	0.0300456i	−0.00628804	−	0.00168487i
$319$	−7.41808	−	7.41808i	−0.415333	−	0.415333i
$320$	1.69262	+	6.31693i	0.0946202	+	0.353127i
$321$	−6.19999	−	10.7387i	−0.346050	−	0.599375i
$322$	0.0592827	+	0.102681i	0.00330370	+	0.00572217i
$323$	−16.7053	+	19.4999i	−0.929507	+	1.08500i
$324$		−	13.4229i		−	0.745716i
$325$	4.83691	−	9.71236i	0.268303	−	0.538745i
$326$	−3.39861	−	1.96219i	−0.188232	−	0.108676i
$327$	−1.64100	+	0.439704i	−0.0907473	+	0.0243157i
$328$	8.66558			0.478476
$329$			6.39644i			0.352647i
$330$	−0.609665	−	0.609665i	−0.0335609	−	0.0335609i
$331$	−0.0260252	−	0.0971273i	−0.00143047	−	0.00533860i	0.965207	−	0.261487i	$-0.0842130\pi$
$331$	−0.0260252	−	0.0971273i	−0.00143047	−	0.00533860i	−0.966637	+	0.256149i	$0.917546\pi$
$332$	9.39649	−	9.39649i	0.515699	−	0.515699i
$333$	−1.15737	+	4.31935i	−0.0634233	+	0.236699i
$334$	−0.186816	+	0.323575i	−0.0102221	+	0.0177053i
$335$	−1.04794	−	1.81508i	−0.0572549	−	0.0991684i
$336$	3.15959	−	0.846610i	0.172370	−	0.0461864i
$337$	−8.73127	+	15.1230i	−0.475623	+	0.823803i	−0.999610	−	0.0279233i	$-0.991111\pi$
$337$	−8.73127	+	15.1230i	−0.475623	+	0.823803i	0.523987	+	0.851726i	$0.324444\pi$
$338$	1.88630	+	4.65660i	0.102601	+	0.253285i
$339$	5.40628	−	9.36395i	0.293629	−	0.508580i
$340$	−10.8762	−	10.8762i	−0.589847	−	0.589847i
$341$	−7.07794	+	4.08645i	−0.383292	+	0.221294i
$342$	0.363196	−	0.758516i	0.0196394	−	0.0410158i
$343$	6.34536	+	6.34536i	0.342617	+	0.342617i
$344$	2.83905	+	0.760722i	0.153071	+	0.0410154i
$345$	−0.267754	+	0.999273i	−0.0144154	+	0.0537990i
$346$	5.68449	+	1.52315i	0.305600	+	0.0818853i
$347$	5.30731	+	9.19254i	0.284912	+	0.493481i	0.972588	−	0.232536i	$-0.0747024\pi$
$347$	5.30731	+	9.19254i	0.284912	+	0.493481i	−0.687676	+	0.726018i	$0.741369\pi$
$348$	−26.5920	−	15.3529i	−1.42548	−	0.823001i
$349$	16.3992	+	4.39415i	0.877829	+	0.235214i	0.669470	−	0.742839i	$-0.266521\pi$
$349$	16.3992	+	4.39415i	0.877829	+	0.235214i	0.208359	+	0.978052i	$0.433188\pi$
$350$	0.769526			0.0411329
$351$	−11.0196	−	16.6325i	−0.588185	−	0.887776i
$352$	−3.62343	+	2.09199i	−0.193130	+	0.111503i
$353$	−2.94292	+	10.9831i	−0.156636	+	0.584573i	0.842324	+	0.538972i	$0.181187\pi$
$353$	−2.94292	+	10.9831i	−0.156636	+	0.584573i	−0.998960	+	0.0456015i	$0.985480\pi$
$354$	−3.11768	+	1.80000i	−0.165703	+	0.0956687i
$355$	18.8618			1.00108
$356$	5.19997	+	19.4066i	0.275598	+	1.02855i
$357$	−4.35845	+	4.35845i	−0.230674	+	0.230674i
$358$	2.69787	+	0.722892i	0.142587	+	0.0382060i
$359$	2.02847	+	7.57037i	0.107059	+	0.399549i	0.998571	−	0.0534486i	$-0.0170213\pi$
$359$	2.02847	+	7.57037i	0.107059	+	0.399549i	−0.891512	+	0.452997i	$0.850355\pi$
$360$	0.907778	+	0.524106i	0.0478441	+	0.0276228i
$361$	14.8017	−	11.9126i	0.779037	−	0.626978i
$362$	−6.61441	−	1.77233i	−0.347646	−	0.0931514i
$363$	7.90712	−	13.6955i	0.415016	−	0.718829i
$364$	2.92399	−	3.30799i	0.153259	−	0.173386i
$365$	0.543738	+	0.941782i	0.0284606	+	0.0492951i
$366$	−5.11660	−	5.11660i	−0.267449	−	0.267449i
$367$	3.40742	−	5.90182i	0.177866	−	0.308072i	−0.763284	−	0.646064i	$-0.776414\pi$
$367$	3.40742	−	5.90182i	0.177866	−	0.308072i	0.941149	+	0.337991i	$0.109747\pi$
$368$	1.25527	+	0.724732i	0.0654356	+	0.0377793i
$369$	−2.05553	+	2.05553i	−0.107007	+	0.107007i
$370$	3.45374	+	3.45374i	0.179551	+	0.179551i
$371$	0.0888699	+	0.0888699i	0.00461389	+	0.00461389i
$372$	−16.9151	+	16.9151i	−0.877008	+	0.877008i
$373$	15.1134	+	8.72571i	0.782540	+	0.451800i	0.837330	−	0.546698i	$-0.184115\pi$
$373$	15.1134	+	8.72571i	0.782540	+	0.451800i	−0.0547894	+	0.998498i	$0.517449\pi$
$374$	1.13816	−	1.97135i	0.0588528	−	0.101936i
$375$	12.6363	+	12.6363i	0.652537	+	0.652537i
$376$	−7.19315	−	12.4589i	−0.370958	−	0.642518i
$377$	−37.7580	+	2.32656i	−1.94464	+	0.119824i
$378$	0.707520	−	1.22546i	0.0363909	−	0.0630309i
$379$	−29.6305	−	7.93946i	−1.52202	−	0.407823i	−0.601611	−	0.798790i	$-0.705474\pi$
$379$	−29.6305	−	7.93946i	−1.52202	−	0.407823i	−0.920405	+	0.390967i	$0.872141\pi$
$380$	6.43247	+	9.38956i	0.329979	+	0.481674i
$381$	−8.24519	−	4.76036i	−0.422414	−	0.243881i
$382$	−0.0212545	−	0.0793230i	−0.00108748	−	0.00405852i
$383$	15.3770	+	4.12027i	0.785730	+	0.210536i	0.629310	−	0.777155i	$-0.283338\pi$
$383$	15.3770	+	4.12027i	0.785730	+	0.210536i	0.156421	+	0.987691i	$0.450004\pi$
$384$	−11.3614	+	11.3614i	−0.579782	+	0.579782i
$385$	0.241595	+	0.901643i	0.0123128	+	0.0459520i
$386$	−2.72540			−0.138719
$387$	−0.853890	+	0.492994i	−0.0434057	+	0.0250603i
$388$	−1.08334	+	4.04308i	−0.0549983	+	0.205256i
$389$	−15.9979	+	9.23640i	−0.811126	+	0.468304i	−0.847347	−	0.531040i	$-0.821801\pi$
$389$	−15.9979	+	9.23640i	−0.811126	+	0.468304i	0.0362204	+	0.999344i	$0.488468\pi$
$390$	−3.10320	+	0.191212i	−0.157136	+	0.00968239i
$391$	−2.73128			−0.138127
$392$	−9.43288	−	2.52753i	−0.476432	−	0.127660i
$393$	11.9336	+	6.88989i	0.601972	+	0.347549i
$394$	3.28868	+	5.69616i	0.165681	+	0.286968i
$395$	−12.7090	−	3.40537i	−0.639460	−	0.171343i
$396$	0.239088	−	0.892287i	0.0120146	−	0.0448391i
$397$	10.6456	+	2.85249i	0.534289	+	0.143162i	0.515868	−	0.856668i	$-0.327469\pi$
$397$	10.6456	+	2.85249i	0.534289	+	0.143162i	0.0184210	+	0.999830i	$0.494136\pi$
$398$	5.47529	+	5.47529i	0.274451	+	0.274451i
$399$	3.76268	−	2.57769i	0.188370	−	0.129046i
$400$	8.14710	−	4.70373i	0.407355	−	0.235187i
$401$	−18.6142	−	18.6142i	−0.929547	−	0.929547i	0.0681292	−	0.997677i	$-0.478297\pi$
$401$	−18.6142	−	18.6142i	−0.929547	−	0.929547i	−0.997677	+	0.0681292i	$0.978297\pi$
$402$	0.453928	−	0.786227i	0.0226399	−	0.0392134i
$403$	−5.86258	+	28.8825i	−0.292036	+	1.43874i
$404$	−11.4396	+	19.8140i	−0.569141	+	0.985781i
$405$	9.88490	−	2.64865i	0.491185	−	0.131613i
$406$	−1.34150	−	2.32354i	−0.0665775	−	0.115316i
$407$	4.47814	−	7.75636i	0.221973	−	0.384468i
$408$	3.58801	−	13.3906i	0.177633	−	0.662935i
$409$	−0.655426	+	0.655426i	−0.0324087	+	0.0324087i	−0.723125	−	0.690717i	$-0.757295\pi$
$409$	−0.655426	+	0.655426i	−0.0324087	+	0.0324087i	0.690717	+	0.723125i	$0.257295\pi$
$410$	0.821798	+	3.06699i	0.0405857	+	0.151468i
$411$	4.33690	+	4.33690i	0.213924	+	0.213924i
$412$		−	31.7506i		−	1.56424i
$413$	3.89750			0.191784
$414$	0.0864081	−	0.0231530i	0.00424673	−	0.00113791i
$415$	8.77392	+	5.06563i	0.430695	+	0.248662i
$416$	−3.00125	+	14.7859i	−0.147148	+	0.724939i
$417$		−	17.4349i		−	0.853790i
$418$	−1.09585	+	1.27917i	−0.0535996	+	0.0625661i
$419$	2.29070	+	3.96761i	0.111908	+	0.193831i	0.916540	−	0.399944i	$-0.130970\pi$
$419$	2.29070	+	3.96761i	0.111908	+	0.193831i	−0.804631	+	0.593775i	$0.797637\pi$
$420$	1.36607	+	2.36611i	0.0666576	+	0.115454i
$421$	2.90592	+	10.8450i	0.141626	+	0.528555i	0.999882	+	0.0153339i	$0.00488111\pi$
$421$	2.90592	+	10.8450i	0.141626	+	0.528555i	−0.858257	+	0.513221i	$0.828452\pi$
$422$	0.355656	+	0.355656i	0.0173130	+	0.0173130i
$423$	4.66160	+	1.24907i	0.226655	+	0.0607319i
$424$	−0.273038	−	0.0731604i	−0.0132599	−	0.00355298i
$425$	−8.86343	+	15.3519i	−0.429940	+	0.744677i
$426$	4.08513	+	7.07565i	0.197925	+	0.342816i
$427$	2.02758	+	7.56702i	0.0981213	+	0.366194i
$428$	−7.25563	−	12.5671i	−0.350714	−	0.607454i
$429$	1.81142	+	5.40562i	0.0874563	+	0.260986i
$430$			1.07696i			0.0519358i
$431$	4.96325	+	18.5231i	0.239071	+	0.892226i	0.976271	+	0.216552i	$0.0694809\pi$
$431$	4.96325	+	18.5231i	0.239071	+	0.892226i	−0.737200	+	0.675675i	$0.763852\pi$
$432$		−	17.2989i		−	0.832292i
$433$	25.6484			1.23258			0.616291	−	0.787518i	$-0.288634\pi$
$433$	25.6484			1.23258			0.616291	+	0.787518i	$0.288634\pi$
$434$	−2.01899	+	0.540987i	−0.0969146	+	0.0259682i
$435$	6.05897	−	22.6124i	0.290505	−	1.08418i
$436$	−1.92040	+	0.514570i	−0.0919705	+	0.0246434i
$437$	1.98664	+	0.371297i	0.0950340	+	0.0177615i
$438$	−0.235528	+	0.407946i	−0.0112539	+	0.0194924i
$439$	−9.01763			−0.430388			−0.215194	−	0.976571i	$-0.569038\pi$
$439$	−9.01763			−0.430388			−0.215194	+	0.976571i	$0.569038\pi$
$440$	−1.48452	−	1.48452i	−0.0707718	−	0.0707718i
$441$	2.83709	−	1.63799i	0.135100	−	0.0779998i
$442$	−2.60809	−	7.78304i	−0.124054	−	0.370201i
$443$	−2.44333	−	4.23197i	−0.116086	−	0.201067i	0.802127	−	0.597153i	$-0.203701\pi$
$443$	−2.44333	−	4.23197i	−0.116086	−	0.201067i	−0.918213	+	0.396086i	$0.870368\pi$
$444$	6.78480	−	25.3212i	0.321992	−	1.20169i
$445$	−13.2653	+	7.65874i	−0.628837	+	0.363059i
$446$			7.74936i			0.366943i
$447$	22.4383	+	6.01234i	1.06130	+	0.284374i
$448$	2.96240	−	0.793771i	0.139960	−	0.0375022i
$449$	6.54244	−	1.75304i	0.308757	−	0.0827312i	−0.101114	−	0.994875i	$-0.532241\pi$
$449$	6.54244	−	1.75304i	0.308757	−	0.0827312i	0.409871	+	0.912144i	$0.365574\pi$
$450$	0.150270	−	0.560815i	0.00708379	−	0.0264371i
$451$	5.04223	−	2.91113i	0.237429	−	0.137080i
$452$	6.32678	−	10.9583i	0.297587	−	0.515435i
$453$	−17.6491	+	17.6491i	−0.829227	+	0.829227i
$454$	3.61114	+	2.08489i	0.169479	+	0.0978489i
$455$	3.01305	+	1.50055i	0.141254	+	0.0703467i
$456$	−4.43015	+	9.25213i	−0.207461	+	0.433271i
$457$	−2.23648	+	8.34667i	−0.104618	+	0.390441i	−0.998302	−	0.0582576i	$-0.981446\pi$
$457$	−2.23648	+	8.34667i	−0.104618	+	0.390441i	0.893683	+	0.448698i	$0.148112\pi$
$458$			8.41968i			0.393426i
$459$	16.2985	+	28.2298i	0.760748	+	1.31765i
$460$	−0.313344	+	1.16941i	−0.0146097	+	0.0545242i
$461$	−8.84384	+	33.0056i	−0.411899	+	1.53723i	0.379069	+	0.925368i	$0.376244\pi$
$461$	−8.84384	+	33.0056i	−0.411899	+	1.53723i	−0.790968	+	0.611858i	$0.790422\pi$
$462$	−0.285909	+	0.285909i	−0.0133017	+	0.0133017i
$463$	−9.54853	+	9.54853i	−0.443758	+	0.443758i	−0.893273	−	0.449515i	$-0.851597\pi$
$463$	−9.54853	+	9.54853i	−0.443758	+	0.443758i	0.449515	+	0.893273i	$0.351597\pi$
$464$	−28.4053	−	16.3998i	−1.31868	−	0.761343i
$465$	−15.7944	−	9.11890i	−0.732448	−	0.422879i
$466$	1.19344	−	0.319782i	0.0552852	−	0.0148136i
$467$		−	31.7096i		−	1.46735i	−0.679502	−	0.733674i	$-0.737804\pi$
$467$		−	31.7096i		−	1.46735i	0.679502	−	0.733674i	$-0.262196\pi$
$468$	−1.83981	−	2.77692i	−0.0850454	−	0.128363i
$469$	−0.851202	+	0.491442i	−0.0393049	+	0.0226927i
$470$	3.72739	−	3.72739i	0.171932	−	0.171932i
$471$	11.6790	+	6.74290i	0.538142	+	0.310696i
$472$	−7.59150	+	4.38295i	−0.349427	+	0.201742i
$473$	1.90751	−	0.511117i	0.0877076	−	0.0235012i
$474$	−1.47508	−	5.50509i	−0.0677528	−	0.252857i
$475$	8.53393	−	9.96155i	0.391564	−	0.457067i
$476$	−5.10054	+	5.10054i	−0.233783	+	0.233783i
$477$	0.0821207	−	0.0474124i	0.00376005	−	0.00217086i
$478$	−6.88763			−0.315033
$479$	−6.91420	−	25.8041i	−0.315918	−	1.17902i	−0.923132	−	0.384483i	$-0.874380\pi$
$479$	−6.91420	−	25.8041i	−0.315918	−	1.17902i	0.607214	−	0.794538i	$-0.292287\pi$
$480$	−8.08567	−	4.66826i	−0.369059	−	0.213076i
$481$	−10.2617	−	30.6227i	−0.467892	−	1.39628i
$482$	−0.0144088			−0.000656303
$483$	0.468620	+	0.125566i	0.0213230	+	0.00571347i
$484$	9.25343	−	16.0274i	0.420610	−	0.728518i
$485$	−3.19118			−0.144904
$486$	−1.40216	−	1.40216i	−0.0636030	−	0.0636030i
$487$	−1.49325	−	5.57289i	−0.0676657	−	0.252532i	0.923805	−	0.382864i	$-0.125062\pi$
$487$	−1.49325	−	5.57289i	−0.0676657	−	0.252532i	−0.991470	+	0.130332i	$0.958396\pi$
$488$	−12.4588	−	12.4588i	−0.563984	−	0.563984i
$489$	−15.5108	+	4.15610i	−0.701421	+	0.187945i
$490$		−	3.57826i		−	0.161649i
$491$			32.5441i			1.46869i	0.678775	+	0.734347i	$0.262511\pi$
$491$			32.5441i			1.46869i	−0.678775	+	0.734347i	$0.737489\pi$
$492$	12.0501	−	12.0501i	0.543260	−	0.543260i
$493$	61.8057			2.78359
$494$	0.838994	+	6.01567i	0.0377481	+	0.270658i
$495$	0.704277			0.0316549
$496$	−18.0686	+	18.0686i	−0.811304	+	0.811304i
$497$		−	8.84546i		−	0.396773i
$498$			4.38849i			0.196653i
$499$	19.5092	−	5.22747i	0.873351	−	0.234014i	0.205815	−	0.978591i	$-0.434016\pi$
$499$	19.5092	−	5.22747i	0.873351	−	0.234014i	0.667536	+	0.744577i	$0.267349\pi$
$500$	14.7878	+	14.7878i	0.661332	+	0.661332i
$501$	0.395695	+	1.47675i	0.0176783	+	0.0659764i
$502$	8.27806	+	8.27806i	0.369468	+	0.369468i
$503$	34.6648			1.54563			0.772813	−	0.634633i	$-0.218849\pi$
$503$	34.6648			1.54563			0.772813	+	0.634633i	$0.218849\pi$
$504$	0.245785	−	0.425713i	0.0109481	−	0.0189627i
$505$	−16.8487	−	4.51460i	−0.749758	−	0.200897i
$506$	−0.179169			−0.00796504
$507$	18.9310	+	8.01549i	0.840756	+	0.355980i
$508$	−9.64905	−	5.57088i	−0.428108	−	0.247168i
$509$	8.97123	+	33.4811i	0.397643	+	1.48402i	0.817232	+	0.576309i	$0.195508\pi$
$509$	8.97123	+	33.4811i	0.397643	+	1.48402i	−0.419589	+	0.907714i	$0.637826\pi$
$510$	5.07959			0.224928
$511$	0.441659	−	0.254992i	0.0195379	−	0.0112802i
$512$	−15.8291	+	15.8291i	−0.699556	+	0.699556i
$513$	−8.01734	−	22.7491i	−0.353974	−	1.00440i
$514$	−1.06206	−	3.96364i	−0.0468452	−	0.174829i
$515$	23.3818	−	6.26514i	1.03033	−	0.276075i
$516$	5.00574	−	2.89006i	0.220365	−	0.127228i
$517$	−8.37093	−	4.83296i	−0.368153	−	0.212553i
$518$	1.61967	−	1.61967i	0.0711642	−	0.0711642i
$519$	20.8544	−	12.0403i	0.915406	−	0.528510i
$520$	−7.55622	+	0.465597i	−0.331362	+	0.0204178i
$521$		−	21.3515i		−	0.935427i	−0.883880	−	0.467714i	$-0.845078\pi$
$521$		−	21.3515i		−	0.935427i	0.883880	−	0.467714i	$-0.154922\pi$
$522$	−1.95531	+	0.523925i	−0.0855818	+	0.0229316i
$523$	−8.07260	−	4.66072i	−0.352990	−	0.203799i	0.313011	−	0.949749i	$-0.398662\pi$
$523$	−8.07260	−	4.66072i	−0.352990	−	0.203799i	−0.666002	+	0.745950i	$0.731996\pi$
$524$	13.9655	+	8.06299i	0.610086	+	0.352234i
$525$	2.22652	−	2.22652i	0.0971735	−	0.0971735i
$526$	1.25140	−	1.25140i	0.0545635	−	0.0545635i
$527$	12.4622	−	46.5096i	0.542862	−	2.02599i
$528$	−1.27935	+	4.77459i	−0.0556764	+	0.207787i
$529$	−11.3925	−	19.7324i	−0.495327	−	0.857931i
$530$		−	0.103574i		−	0.00449897i
$531$	0.761088	−	2.84042i	0.0330284	−	0.123264i
$532$	4.40334	−	3.01658i	0.190909	−	0.130785i
$533$	4.17642	−	20.5755i	0.180901	−	0.891224i
$534$	−5.74606	−	3.31749i	−0.248656	−	0.143562i
$535$	7.82298	−	7.82298i	0.338217	−	0.338217i
$536$	1.10531	−	1.91445i	0.0477419	−	0.0826914i
$537$	9.89753	−	5.71434i	0.427110	−	0.246592i
$538$	−1.74756	+	6.52199i	−0.0753427	+	0.281183i
$539$	−6.33780	+	1.69821i	−0.272988	+	0.0731470i
$540$	13.9566	−	3.73965i	0.600595	−	0.160929i
$541$	−20.9118	−	5.60330i	−0.899069	−	0.240905i	−0.220453	−	0.975398i	$-0.570753\pi$
$541$	−20.9118	−	5.60330i	−0.899069	−	0.240905i	−0.678616	+	0.734493i	$0.737420\pi$
$542$		−	4.92302i		−	0.211462i
$543$	−24.2659	+	14.0099i	−1.04135	+	0.601224i
$544$	6.37982	−	23.8098i	0.273532	−	1.02084i
$545$	−0.757880	−	1.31269i	−0.0324640	−	0.0562293i
$546$	0.0896709	+	1.45528i	0.00383756	+	0.0622802i
$547$	0.682495	−	0.394039i	0.0291814	−	0.0168479i	−0.485338	−	0.874326i	$-0.661304\pi$
$547$	0.682495	−	0.394039i	0.0291814	−	0.0168479i	0.514520	+	0.857479i	$0.327970\pi$
$548$	5.07532	+	5.07532i	0.216807	+	0.216807i
$549$	5.91063			0.252259
$550$	−0.581431	+	1.00707i	−0.0247923	+	0.0429415i
$551$	−44.9554	−	8.40201i	−1.91516	−	0.357938i
$552$	−1.05398	+	0.282412i	−0.0448603	+	0.0120203i
$553$	−1.59699	+	5.96004i	−0.0679108	+	0.253447i
$554$	0.0312008	−	0.00836023i	0.00132559	−	0.000355192i
$555$	19.9859			0.848353
$556$		−	20.4034i		−	0.865299i
$557$	9.79606	+	36.5594i	0.415073	+	1.54907i	0.784690	+	0.619888i	$0.212822\pi$
$557$	9.79606	+	36.5594i	0.415073	+	1.54907i	−0.369618	+	0.929184i	$0.620511\pi$
$558$			1.57704i			0.0667614i
$559$	3.17455	−	6.37440i	0.134269	−	0.269608i
$560$	1.45923	+	2.52746i	0.0616638	+	0.106805i
$561$	−2.41073	−	8.99695i	−0.101781	−	0.379852i
$562$	1.61876	+	2.80377i	0.0682831	+	0.118270i
$563$	4.87241	−	8.43927i	0.205348	−	0.355673i	−0.744896	−	0.667181i	$-0.767501\pi$
$563$	4.87241	−	8.43927i	0.205348	−	0.355673i	0.950243	+	0.311508i	$0.100834\pi$
$564$	−27.3275	−	7.32239i	−1.15070	−	0.308328i
$565$	9.31835	+	2.49684i	0.392026	+	0.105043i
$566$	−5.57531	−	5.57531i	−0.234348	−	0.234348i
$567$	−1.24211	−	4.63563i	−0.0521639	−	0.194678i
$568$	9.94720	+	17.2291i	0.417375	+	0.722915i
$569$	9.44605	+	16.3610i	0.395999	+	0.685891i	0.993228	−	0.116180i	$-0.0370650\pi$
$569$	9.44605	+	16.3610i	0.395999	+	0.685891i	−0.597229	+	0.802071i	$0.703732\pi$
$570$	−3.69472	−	0.690531i	−0.154755	−	0.0289232i
$571$		−	24.4065i		−	1.02138i	−0.859765	−	0.510690i	$-0.829390\pi$
$571$		−	24.4065i		−	1.02138i	0.859765	−	0.510690i	$-0.170610\pi$
$572$	2.11984	+	6.32601i	0.0886351	+	0.264504i
$573$	−0.291008	−	0.168014i	−0.0121570	−	0.00701887i
$574$	1.43830	−	0.385391i	0.0600335	−	0.0160859i
$575$	1.39528			0.0581873
$576$		−	2.31394i		−	0.0964141i
$577$	19.1615	+	19.1615i	0.797705	+	0.797705i	0.982733	−	0.185028i	$-0.0592377\pi$
$577$	19.1615	+	19.1615i	0.797705	+	0.797705i	−0.185028	+	0.982733i	$0.559238\pi$
$578$	1.77052	+	6.60769i	0.0736441	+	0.274844i
$579$	−7.88559	+	7.88559i	−0.327714	+	0.327714i
$580$	7.09060	−	26.4625i	0.294421	−	1.09879i
$581$	2.37558	−	4.11463i	0.0985557	−	0.170704i
$582$	−0.691152	−	1.19711i	−0.0286492	−	0.0496218i
$583$	−0.183450	+	0.0491553i	−0.00759773	+	0.00203581i
$584$	−0.573505	+	0.993340i	−0.0237318	+	0.0411047i
$585$	1.68194	−	1.90283i	0.0695398	−	0.0786723i
$586$	4.95209	−	8.57727i	0.204569	−	0.354324i
$587$	11.9711	+	11.9711i	0.494099	+	0.494099i	0.909595	−	0.415496i	$-0.136392\pi$
$587$	11.9711	+	11.9711i	0.494099	+	0.494099i	−0.415496	+	0.909595i	$0.636392\pi$
$588$	−16.6318	+	9.60237i	−0.685883	+	0.395995i
$589$	−15.3872	+	32.1354i	−0.634019	+	1.32411i
$590$	−2.27119	−	2.27119i	−0.0935034	−	0.0935034i
$591$	25.9964	+	6.96573i	1.06935	+	0.286532i
$592$	7.24747	−	27.0479i	0.297869	−	1.11166i
$593$	−25.9894	−	6.96384i	−1.06726	−	0.285971i	−0.317892	−	0.948127i	$-0.602975\pi$
$593$	−25.9894	−	6.96384i	−1.06726	−	0.285971i	−0.749366	+	0.662156i	$0.769641\pi$
$594$	1.06916	+	1.85184i	0.0438682	+	0.0759820i
$595$	−4.76260	−	2.74969i	−0.195248	−	0.112726i
$596$	26.2588	+	7.03603i	1.07560	+	0.288207i
$597$	31.6841			1.29674
$598$	−0.427889	+	0.484082i	−0.0174977	+	0.0197956i
$599$	−6.66436	+	3.84767i	−0.272298	+	0.157212i	−0.629932	−	0.776651i	$-0.716917\pi$
$599$	−6.66436	+	3.84767i	−0.272298	+	0.157212i	0.357633	+	0.933862i	$0.383584\pi$
$600$	−1.83294	+	6.84064i	−0.0748296	+	0.279268i
$601$	18.3741	−	10.6083i	0.749495	−	0.432721i	−0.0760166	−	0.997107i	$-0.524220\pi$
$601$	18.3741	−	10.6083i	0.749495	−	0.432721i	0.825511	+	0.564386i	$0.190887\pi$
$602$	0.505054			0.0205845
$603$	0.191933	+	0.716305i	0.00781613	+	0.0291702i
$604$	−20.6541	+	20.6541i	−0.840404	+	0.840404i
$605$	13.6288	+	3.65184i	0.554091	+	0.148468i
$606$	−1.95556	−	7.29825i	−0.0794393	−	0.296471i
$607$	6.71795	+	3.87861i	0.272673	+	0.157428i	0.630102	−	0.776513i	$-0.283013\pi$
$607$	6.71795	+	3.87861i	0.272673	+	0.157428i	−0.357429	+	0.933940i	$0.616346\pi$
$608$	−7.87722	+	16.4511i	−0.319463	+	0.667182i
$609$	−10.6043	−	2.84142i	−0.429709	−	0.115140i
$610$	3.22800	−	5.59105i	0.130698	−	0.226375i
$611$	−33.0491	+	11.0747i	−1.33702	+	0.448036i
$612$	2.72116	+	4.71318i	0.109996	+	0.190519i
$613$	15.9108	+	15.9108i	0.642631	+	0.642631i	0.951202	−	0.308570i	$-0.0998505\pi$
$613$	15.9108	+	15.9108i	0.642631	+	0.642631i	−0.308570	+	0.951202i	$0.599850\pi$
$614$	6.64261	−	11.5053i	0.268074	−	0.464318i
$615$	11.2517	+	6.49618i	0.453713	+	0.261951i
$616$	−0.696183	+	0.696183i	−0.0280500	+	0.0280500i
$617$	21.3076	+	21.3076i	0.857812	+	0.857812i	0.991080	−	0.133268i	$-0.0425472\pi$
$617$	21.3076	+	21.3076i	0.857812	+	0.857812i	−0.133268	+	0.991080i	$0.542547\pi$
$618$	7.41432	+	7.41432i	0.298248	+	0.298248i
$619$	18.0503	−	18.0503i	0.725503	−	0.725503i	−0.244218	−	0.969720i	$-0.578531\pi$
$619$	18.0503	−	18.0503i	0.725503	−	0.725503i	0.969720	+	0.244218i	$0.0785312\pi$
$620$	−18.4836	−	10.6715i	−0.742320	−	0.428579i
$621$	1.28286	−	2.22197i	0.0514792	−	0.0891646i
$622$	0.874417	+	0.874417i	0.0350609	+	0.0350609i
$623$	3.59165	+	6.22092i	0.143896	+	0.249236i
$624$	9.84475	+	14.8592i	0.394106	+	0.594842i
$625$	−0.448873	+	0.777470i	−0.0179549	+	0.0310988i
$626$	−2.99887	−	0.803546i	−0.119859	−	0.0321161i
$627$	0.530415	+	6.87180i	0.0211827	+	0.274433i
$628$	13.6676	+	7.89098i	0.545395	+	0.314884i
$629$	13.6567	+	50.9675i	0.544529	+	2.03221i
$630$	0.173981	+	0.0466180i	0.00693156	+	0.00185731i
$631$	−30.4433	+	30.4433i	−1.21193	+	1.21193i	−0.241537	+	0.970392i	$0.577651\pi$
$631$	−30.4433	+	30.4433i	−1.21193	+	1.21193i	−0.970392	+	0.241537i	$0.922349\pi$
$632$	−3.59180	−	13.4048i	−0.142874	−	0.533213i
$633$	2.05809			0.0818016
$634$	3.13786	−	1.81165i	0.124620	−	0.0719497i
$635$	2.19853	−	8.20503i	0.0872461	−	0.325607i
$636$	−0.481414	+	0.277944i	−0.0190893	+	0.0110212i
$637$	−10.5476	+	21.1792i	−0.417911	+	0.839151i
$638$	4.05438			0.160515
$639$	−6.44639	−	1.72731i	−0.255015	−	0.0683311i
$640$	−12.4149	−	7.16774i	−0.490742	−	0.283330i
$641$	0.413215	+	0.715709i	0.0163210	+	0.0282688i	0.874071	−	0.485799i	$-0.161471\pi$
$641$	0.413215	+	0.715709i	0.0163210	+	0.0282688i	−0.857750	+	0.514068i	$0.828138\pi$
$642$	4.62896	+	1.24033i	0.182690	+	0.0489517i
$643$	5.09016	−	18.9967i	0.200736	−	0.749158i	−0.789971	−	0.613145i	$-0.789904\pi$
$643$	5.09016	−	18.9967i	0.200736	−	0.749158i	0.990707	−	0.136013i	$-0.0434290\pi$
$644$	0.548410	+	0.146946i	0.0216104	+	0.00579048i
$645$	3.11605	+	3.11605i	0.122694	+	0.122694i
$646$	−0.763693	−	9.89404i	−0.0300471	−	0.389276i
$647$	−27.5492	+	15.9055i	−1.08307	+	0.625311i	−0.931723	−	0.363170i	$-0.881695\pi$
$647$	−27.5492	+	15.9055i	−1.08307	+	0.625311i	−0.151347	+	0.988481i	$0.548361\pi$
$648$	7.63240	+	7.63240i	0.299829	+	0.299829i
$649$	−2.94484	+	5.10061i	−0.115595	+	0.200216i
$650$	1.33235	+	3.97598i	0.0522591	+	0.155951i
$651$	−4.27641	+	7.40696i	−0.167606	+	0.290302i
$652$	−18.1517	+	4.86373i	−0.710876	+	0.190479i
$653$	−16.2191	−	28.0924i	−0.634704	−	1.09934i	−0.986578	−	0.163292i	$-0.947789\pi$
$653$	−16.2191	−	28.0924i	−0.634704	−	1.09934i	0.351874	−	0.936047i	$-0.385544\pi$
$654$	0.328286	−	0.568608i	0.0128370	−	0.0222343i
$655$	−3.18204	+	11.8755i	−0.124332	+	0.464015i
$656$	12.8718	−	12.8718i	0.502560	−	0.502560i
$657$	−0.0995876	−	0.371666i	−0.00388528	−	0.0145001i
$658$	−1.74800	−	1.74800i	−0.0681442	−	0.0681442i
$659$		−	7.55332i		−	0.294236i	−0.989119	−	0.147118i	$-0.953000\pi$
$659$		−	7.55332i		−	0.294236i	0.989119	−	0.147118i	$-0.0469997\pi$
$660$	−4.12866			−0.160708
$661$	−8.97930	+	2.40600i	−0.349254	+	0.0935824i	−0.429181	−	0.903218i	$-0.641198\pi$
$661$	−8.97930	+	2.40600i	−0.349254	+	0.0935824i	0.0799271	+	0.996801i	$0.474531\pi$
$662$	0.0336548	+	0.0194306i	0.00130803	+	0.000755192i
$663$	−30.0654	−	14.9730i	−1.16764	−	0.581504i
$664$			10.6859i			0.414693i
$665$	3.09035	+	2.64747i	0.119839	+	0.102664i
$666$	−0.864099	−	1.49666i	−0.0334832	−	0.0579945i
$667$	−2.43237	−	4.21298i	−0.0941816	−	0.163127i
$668$	0.463067	+	1.72819i	0.0179166	+	0.0668657i
$669$	22.4218	+	22.4218i	0.866875	+	0.866875i
$670$	0.782398	+	0.209643i	0.0302267	+	0.00809921i
$671$	−11.4348	−	3.06395i	−0.441437	−	0.118283i
$672$	−2.18923	+	3.79187i	−0.0844516	+	0.146274i
$673$	−3.22030	−	5.57772i	−0.124133	−	0.215005i	0.797260	−	0.603635i	$-0.206282\pi$
$673$	−3.22030	−	5.57772i	−0.124133	−	0.215005i	−0.921394	+	0.388630i	$0.872948\pi$
$674$	−1.74672	−	6.51884i	−0.0672810	−	0.251096i
$675$	−8.32612	−	14.4213i	−0.320473	−	0.555075i
$676$	22.1543	+	9.38024i	0.852089	+	0.360779i
$677$		−	32.6758i		−	1.25583i	−0.778281	−	0.627916i	$-0.783908\pi$
$677$		−	32.6758i		−	1.25583i	0.778281	−	0.627916i	$-0.216092\pi$
$678$	1.08154	+	4.03637i	0.0415364	+	0.155016i
$679$			1.49654i			0.0574319i
$680$	12.3687			0.474318
$681$	16.4807	−	4.41600i	0.631543	−	0.169221i
$682$	0.817507	−	3.05098i	0.0313039	−	0.116828i
$683$	−49.8434	+	13.3555i	−1.90720	+	0.511034i	−0.912391	+	0.409320i	$0.865766\pi$
$683$	−49.8434	+	13.3555i	−1.90720	+	0.511034i	−0.994814	+	0.101714i	$0.967567\pi$
$684$	−1.33856	−	3.79813i	−0.0511810	−	0.145225i
$685$	−2.73610	+	4.73906i	−0.104541	+	0.181070i
$686$	−3.46808			−0.132412
$687$	24.3612	+	24.3612i	0.929440	+	0.929440i
$688$	5.34709	−	3.08714i	0.203856	−	0.117696i
$689$	−0.305304	+	0.613041i	−0.0116312	+	0.0233550i
$690$	−0.199907	−	0.346250i	−0.00761035	−	0.0131815i
$691$	0.278104	−	1.03790i	0.0105796	−	0.0394835i	−0.960434	−	0.278507i	$-0.910161\pi$
$691$	0.278104	−	1.03790i	0.0105796	−	0.0394835i	0.971014	+	0.239023i	$0.0768272\pi$
$692$	24.4052	−	14.0903i	0.927745	−	0.535634i
$693$		−	0.330278i		−	0.0125462i
$694$	−3.96248	−	1.06174i	−0.150414	−	0.0403032i
$695$	15.0255	−	4.02608i	0.569951	−	0.152718i
$696$	23.8503	−	6.39066i	0.904042	−	0.242237i
$697$	−8.87790	+	33.1328i	−0.336275	+	1.25499i
$698$	−5.68235	+	3.28071i	−0.215080	+	0.124177i
$699$	2.52782	−	4.37832i	0.0956111	−	0.165603i
$700$	2.60562	−	2.60562i	0.0984833	−	0.0984833i
$701$	−23.2759	−	13.4384i	−0.879119	−	0.507560i	−0.00875130	−	0.999962i	$-0.502786\pi$
$701$	−23.2759	−	13.4384i	−0.879119	−	0.507560i	−0.870368	+	0.492402i	$0.836119\pi$
$702$	7.55670	+	1.53386i	0.285209	+	0.0578918i
$703$	−3.00479	−	38.9286i	−0.113328	−	1.46822i
$704$	−1.19950	+	4.47659i	−0.0452079	+	0.168718i
$705$		−	21.5695i		−	0.812353i
$706$	−2.19721	−	3.80568i	−0.0826930	−	0.143229i
$707$	−2.11717	+	7.90140i	−0.0796245	+	0.297163i
$708$	−4.46170	+	16.6513i	−0.167681	+	0.625795i
$709$	11.4634	−	11.4634i	0.430515	−	0.430515i	−0.458288	−	0.888804i	$-0.651537\pi$
$709$	11.4634	−	11.4634i	0.430515	−	0.430515i	0.888804	+	0.458288i	$0.151537\pi$
$710$	−5.15451	+	5.15451i	−0.193445	+	0.193445i
$711$	4.03170	+	2.32770i	0.151201	+	0.0872957i
$712$	−13.9915	−	8.07802i	−0.524355	−	0.302736i
$713$	−3.66077	+	0.980902i	−0.137097	+	0.0367351i
$714$		−	2.38213i		−	0.0891490i
$715$	−4.24031	+	2.80937i	−0.158579	+	0.105064i
$716$	11.5827	−	6.68729i	0.432867	−	0.249916i
$717$	−19.9285	+	19.9285i	−0.744243	+	0.744243i
$718$	−2.62315	−	1.51447i	−0.0978950	−	0.0565197i
$719$	10.3731	−	5.98891i	0.386851	−	0.223349i	−0.293944	−	0.955823i	$-0.594968\pi$
$719$	10.3731	−	5.98891i	0.386851	−	0.223349i	0.680795	+	0.732474i	$0.261634\pi$
$720$	2.12692	−	0.569905i	0.0792655	−	0.0212391i
$721$	−2.93811	−	10.9652i	−0.109421	−	0.408364i
$722$	−0.789534	+	7.30041i	−0.0293834	+	0.271693i
$723$	−0.0416900	+	0.0416900i	−0.00155047	+	0.00155047i
$724$	−28.3976	+	16.3953i	−1.05539	+	0.609328i
$725$	−31.5736			−1.17261
$726$	1.58184	+	5.90352i	0.0587077	+	0.219100i
$727$	−43.0014	−	24.8269i	−1.59483	−	0.920777i	−0.992461	−	0.122562i	$-0.960889\pi$
$727$	−43.0014	−	24.8269i	−1.59483	−	0.920777i	−0.602372	−	0.798215i	$-0.705778\pi$
$728$	0.218347	+	3.54357i	0.00809247	+	0.131334i
$729$	−29.8732			−1.10642
$730$	−0.405959	−	0.108776i	−0.0150252	−	0.00402600i
$731$	−5.81723	+	10.0757i	−0.215158	+	0.372665i
$732$	−34.6497			−1.28069
$733$	−26.4010	−	26.4010i	−0.975142	−	0.975142i	0.0245562	−	0.999698i	$-0.492183\pi$
$733$	−26.4010	−	26.4010i	−0.975142	−	0.975142i	−0.999698	+	0.0245562i	$0.992183\pi$
$734$	0.681664	+	2.54400i	0.0251607	+	0.0939009i
$735$	−10.3532	−	10.3532i	−0.381885	−	0.381885i
$736$	−1.87407	+	0.502156i	−0.0690792	+	0.0185097i
$737$		−	1.48527i		−	0.0547108i
$738$		−	1.12346i		−	0.0413552i
$739$	−8.92389	+	8.92389i	−0.328270	+	0.328270i	−0.851929	−	0.523658i	$-0.824567\pi$
$739$	−8.92389	+	8.92389i	−0.328270	+	0.328270i	0.523658	+	0.851929i	$0.324567\pi$
$740$	23.3888			0.859788
$741$	19.8331	+	14.9780i	0.728586	+	0.550232i
$742$	−0.0485722			−0.00178314
$743$	20.0980	−	20.0980i	0.737324	−	0.737324i	−0.234736	−	0.972059i	$-0.575422\pi$
$743$	20.0980	−	20.0980i	0.737324	−	0.737324i	0.972059	+	0.234736i	$0.0754224\pi$
$744$		−	19.2362i		−	0.705234i
$745$			20.7259i			0.759339i
$746$	−6.51468	+	1.74560i	−0.238519	+	0.0639111i
$747$	−2.53476	−	2.53476i	−0.0927421	−	0.0927421i
$748$	−2.82119	−	10.5288i	−0.103153	−	0.384972i
$749$	−3.66868	−	3.66868i	−0.134050	−	0.134050i
$750$	−6.90644			−0.252188
$751$	3.02126	−	5.23298i	0.110248	−	0.190954i	−0.805622	−	0.592429i	$-0.798169\pi$
$751$	3.02126	−	5.23298i	0.110248	−	0.190954i	0.915870	+	0.401475i	$0.131502\pi$
$752$	−29.1911	−	7.82172i	−1.06449	−	0.285229i
$753$	47.9030			1.74568
$754$	9.68262	−	10.9542i	0.352620	−	0.398929i
$755$	−19.2857	−	11.1346i	−0.701878	−	0.405229i
$756$	−1.75375	−	6.54509i	−0.0637833	−	0.238043i
$757$	−31.6368			−1.14986			−0.574930	−	0.818202i	$-0.694971\pi$
$757$	−31.6368			−1.14986			−0.574930	+	0.818202i	$0.694971\pi$
$758$	10.2670	−	5.92766i	0.372915	−	0.215302i
$759$	−0.518402	+	0.518402i	−0.0188168	+	0.0188168i
$760$	−8.99657	−	1.68143i	−0.326340	−	0.0609918i
$761$	1.84999	+	6.90426i	0.0670621	+	0.250279i	0.991316	−	0.131498i	$-0.0419788\pi$
$761$	1.84999	+	6.90426i	0.0670621	+	0.250279i	−0.924254	+	0.381777i	$0.875312\pi$
$762$	3.55412	−	0.952324i	0.128752	−	0.0344991i
$763$	−0.615599	+	0.355416i	−0.0222862	+	0.0128669i
$764$	−0.340557	−	0.196620i	−0.0123209	−	0.00711348i
$765$	−2.93394	+	2.93394i	−0.106077	+	0.106077i
$766$	−5.32817	+	3.07622i	−0.192515	+	0.111148i
$767$	6.74810	+	20.1376i	0.243660	+	0.727126i
$768$			8.45011i			0.304917i
$769$	−44.8183	+	12.0090i	−1.61619	+	0.433057i	−0.949879	−	0.312616i	$-0.898795\pi$
$769$	−44.8183	+	12.0090i	−1.61619	+	0.433057i	−0.666312	+	0.745673i	$0.732128\pi$
$770$	−0.312421	−	0.180376i	−0.0112589	−	0.00650031i
$771$	−14.5412	−	8.39537i	−0.523689	−	0.302352i
$772$	−9.22822	+	9.22822i	−0.332131	+	0.332131i
$773$	0.250240	−	0.250240i	0.00900050	−	0.00900050i	−0.702592	−	0.711593i	$-0.747974\pi$
$773$	0.250240	−	0.250240i	0.00900050	−	0.00900050i	0.711593	+	0.702592i	$0.247974\pi$
$774$	0.0986249	−	0.368073i	0.00354500	−	0.0132301i
$775$	−6.36635	+	23.7595i	−0.228686	+	0.853468i
$776$	−1.68294	−	2.91494i	−0.0604140	−	0.104640i
$777$		−	9.37260i		−	0.336240i
$778$	1.84777	−	6.89597i	0.0662457	−	0.247232i
$779$	10.9616	−	22.8928i	0.392741	−	0.820219i
$780$	−9.86000	+	11.1549i	−0.353045	+	0.399409i
$781$	11.5759	+	6.68336i	0.414219	+	0.239150i
$782$	0.746398	−	0.746398i	0.0266911	−	0.0266911i
$783$	−29.0295	+	50.2806i	−1.03743	+	1.79688i
$784$	−17.7660	+	10.2572i	−0.634498	+	0.366328i
$785$	−3.11415	+	11.6222i	−0.111149	+	0.414813i
$786$	−5.14404	+	1.37834i	−0.183482	+	0.0491638i
$787$	21.2818	−	5.70243i	0.758613	−	0.203270i	0.141278	−	0.989970i	$-0.454879\pi$
$787$	21.2818	−	5.70243i	0.758613	−	0.203270i	0.617335	+	0.786700i	$0.288212\pi$
$788$	30.4227	+	8.15174i	1.08376	+	0.290394i
$789$		−	7.24151i		−	0.257804i
$790$	4.40370	−	2.54248i	0.156677	−	0.0904573i
$791$	1.17092	−	4.36994i	0.0416332	−	0.155377i
$792$	0.371416	+	0.643311i	0.0131977	+	0.0228591i
$793$	−35.5867	+	23.5775i	−1.26372	+	0.837263i
$794$	−3.68873	+	2.12969i	−0.130908	+	0.0755799i
$795$	−0.299678	−	0.299678i	−0.0106285	−	0.0106285i
$796$	37.0788			1.31422
$797$	−1.51887	+	2.63077i	−0.0538012	+	0.0931865i	−0.891672	−	0.452683i	$-0.850467\pi$
$797$	−1.51887	+	2.63077i	−0.0538012	+	0.0931865i	0.837870	+	0.545869i	$0.183800\pi$
$798$	−0.323832	+	1.73268i	−0.0114635	+	0.0613362i
$799$	55.0059	−	14.7388i	1.94597	−	0.521421i
$800$	−3.25914	+	12.1633i	−0.115228	+	0.430037i
$801$	5.23505	−	1.40273i	0.184971	−	0.0495629i
$802$	10.1737			0.359245
$803$			0.770658i			0.0271959i
$804$	−1.12517	−	4.19918i	−0.0396815	−	0.148093i
$805$			0.432856i			0.0152562i
$806$	−6.29083	−	9.49505i	−0.221585	−	0.334449i
$807$	13.8142	+	23.9269i	0.486282	+	0.842266i
$808$	−4.76175	−	17.7711i	−0.167518	−	0.625185i
$809$	−2.56551	−	4.44360i	−0.0901987	−	0.156229i	0.817396	−	0.576076i	$-0.195417\pi$
$809$	−2.56551	−	4.44360i	−0.0901987	−	0.156229i	−0.907595	+	0.419848i	$0.862084\pi$
$810$	−1.97750	+	3.42514i	−0.0694824	+	0.120347i
$811$	−21.9224	−	5.87410i	−0.769801	−	0.206268i	−0.147517	−	0.989059i	$-0.547128\pi$
$811$	−21.9224	−	5.87410i	−0.769801	−	0.206268i	−0.622284	+	0.782792i	$0.713795\pi$
$812$	−12.4099	−	3.32521i	−0.435501	−	0.116692i
$813$	−14.2441	−	14.2441i	−0.499563	−	0.499563i
$814$	0.895864	+	3.34341i	0.0314000	+	0.117186i
$815$	−7.16352	−	12.4076i	−0.250927	−	0.434618i
$816$	−14.5608	−	25.2200i	−0.509729	−	0.882877i
$817$	5.60097	−	6.53794i	0.195953	−	0.228734i
$818$		−	0.358226i		−	0.0125251i
$819$	−0.892352	−	0.788766i	−0.0311813	−	0.0275617i
$820$	13.1675	+	7.60225i	0.459828	+	0.265482i
$821$	−39.9554	+	10.7060i	−1.39445	+	0.373643i	−0.876350	−	0.481675i	$-0.840029\pi$
$821$	−39.9554	+	10.7060i	−1.39445	+	0.373643i	−0.518104	+	0.855318i	$0.673362\pi$
$822$	−2.37035			−0.0826756
$823$			11.2683i			0.392788i	0.980525	+	0.196394i	$0.0629231\pi$
$823$			11.2683i			0.392788i	−0.980525	+	0.196394i	$0.937077\pi$
$824$	18.0537	+	18.0537i	0.628931	+	0.628931i
$825$	1.23153	+	4.59611i	0.0428762	+	0.160016i
$826$	−1.06510	+	1.06510i	−0.0370595	+	0.0370595i
$827$	4.16458	−	15.5424i	0.144817	−	0.540464i	−0.854947	−	0.518716i	$-0.826410\pi$
$827$	4.16458	−	15.5424i	0.144817	−	0.540464i	0.999763	−	0.0217477i	$-0.00692307\pi$
$828$	0.214182	−	0.370975i	0.00744335	−	0.0128923i
$829$	12.1990	+	21.1293i	0.423690	+	0.733853i	0.996297	−	0.0859773i	$-0.0274013\pi$
$829$	12.1990	+	21.1293i	0.423690	+	0.733853i	−0.572607	+	0.819830i	$0.694068\pi$
$830$	−3.78203	+	1.01339i	−0.131276	+	0.0351754i
$831$	0.0660862	−	0.114465i	0.00229251	−	0.00397074i
$832$	9.23032	+	13.9318i	0.320004	+	0.482997i
$833$	19.3280	−	33.4771i	0.669676	−	1.15991i
$834$	4.76456	+	4.76456i	0.164983	+	0.164983i
$835$	−1.18130	+	0.682025i	−0.0408807	+	0.0236025i
$836$	0.620725	+	8.04182i	0.0214682	+	0.278132i
$837$	31.9834	+	31.9834i	1.10551	+	1.10551i
$838$	−1.71026	−	0.458262i	−0.0590798	−	0.0158304i
$839$	11.0823	−	41.3596i	0.382602	−	1.42789i	−0.459309	−	0.888276i	$-0.651903\pi$
$839$	11.0823	−	41.3596i	0.382602	−	1.42789i	0.841912	−	0.539615i	$-0.181430\pi$
$840$	−2.12216	−	0.568631i	−0.0732215	−	0.0196196i
$841$	40.5416	+	70.2201i	1.39799	+	2.42138i
$842$	−3.75782	−	2.16958i	−0.129503	−	0.0747687i
$843$	12.7960	+	3.42868i	0.440718	+	0.118090i
$844$	2.40851			0.0829042
$845$	−2.53625	+	18.1658i	−0.0872496	+	0.624924i
$846$	−1.61525	+	0.932566i	−0.0555335	+	0.0320623i
$847$	1.71257	−	6.39139i	0.0588446	−	0.219611i
$848$	−0.514242	+	0.296898i	−0.0176592	+	0.0101955i
$849$	−32.2629			−1.10726
$850$	−1.77316	−	6.61751i	−0.0608187	−	0.226979i
$851$	2.93674	−	2.93674i	0.100670	−	0.100670i
$852$	37.7905	+	10.1259i	1.29468	+	0.346909i
$853$	−13.3535	−	49.8360i	−0.457216	−	1.70635i	−0.681491	−	0.731826i	$-0.738668\pi$
$853$	−13.3535	−	49.8360i	−0.457216	−	1.70635i	0.224276	−	0.974526i	$-0.427998\pi$
$854$	−2.62199	−	1.51380i	−0.0897225	−	0.0518013i
$855$	2.53289	−	1.73520i	0.0866231	−	0.0593426i
$856$	11.2714	+	3.02017i	0.385249	+	0.103227i
$857$	−8.52346	+	14.7631i	−0.291156	+	0.504297i	−0.974083	−	0.226189i	$-0.927373\pi$
$857$	−8.52346	+	14.7631i	−0.291156	+	0.504297i	0.682927	+	0.730486i	$0.260707\pi$
$858$	−1.97225	−	0.982214i	−0.0673317	−	0.0335322i
$859$	9.40026	+	16.2817i	0.320733	+	0.555525i	0.980639	−	0.195822i	$-0.0627376\pi$
$859$	9.40026	+	16.2817i	0.320733	+	0.555525i	−0.659907	+	0.751348i	$0.729404\pi$
$860$	3.64661	+	3.64661i	0.124348	+	0.124348i
$861$	3.04645	−	5.27661i	0.103823	−	0.179826i
$862$	−6.41829	−	3.70560i	−0.218608	−	0.126213i
$863$	18.6928	−	18.6928i	0.636309	−	0.636309i	−0.313334	−	0.949643i	$-0.601446\pi$
$863$	18.6928	−	18.6928i	0.636309	−	0.636309i	0.949643	+	0.313334i	$0.101446\pi$
$864$	16.3734	+	16.3734i	0.557033	+	0.557033i
$865$	15.1921	+	15.1921i	0.516548	+	0.516548i
$866$	−7.00912	+	7.00912i	−0.238180	+	0.238180i
$867$	24.2413	+	13.9957i	0.823277	+	0.475319i
$868$	−5.00453	+	8.66810i	−0.169865	+	0.294215i
$869$	−6.59318	−	6.59318i	−0.223658	−	0.223658i
$870$	4.52367	+	7.83523i	0.153367	+	0.265639i
$871$	−4.01294	−	3.54711i	−0.135973	−	0.120189i
$872$	0.799370	−	1.38455i	0.0270701	−	0.0468867i
$873$	1.09065	+	0.292238i	0.0369128	+	0.00989076i
$874$	−0.644372	+	0.441438i	−0.0217962	+	0.0149318i
$875$	6.47545	+	3.73860i	0.218910	+	0.126388i
$876$	0.583810	+	2.17881i	0.0197251	+	0.0736151i
$877$	12.2712	+	3.28806i	0.414369	+	0.111030i	0.459980	−	0.887929i	$-0.347857\pi$
$877$	12.2712	+	3.28806i	0.414369	+	0.111030i	−0.0456106	+	0.998959i	$0.514523\pi$
$878$	2.46431	−	2.46431i	0.0831665	−	0.0831665i
$879$	−10.4890	−	39.1454i	−0.353785	−	1.32034i
$880$	−4.41020			−0.148668
$881$	−9.77060	+	5.64106i	−0.329180	+	0.190052i	−0.655477	−	0.755215i	$-0.727532\pi$
$881$	−9.77060	+	5.64106i	−0.329180	+	0.190052i	0.326297	+	0.945267i	$0.394199\pi$
$882$	−0.327686	+	1.22294i	−0.0110337	+	0.0411785i
$883$	22.5559	−	13.0227i	0.759067	−	0.438248i	−0.0698936	−	0.997554i	$-0.522266\pi$
$883$	22.5559	−	13.0227i	0.759067	−	0.438248i	0.828961	+	0.559307i	$0.188933\pi$
$884$	−35.1845	−	17.5224i	−1.18338	−	0.589343i
$885$	−13.1428			−0.441790
$886$	1.82421	+	0.488795i	0.0612854	+	0.0164214i
$887$	−13.5225	−	7.80722i	−0.454041	−	0.262141i	0.255494	−	0.966811i	$-0.417762\pi$
$887$	−13.5225	−	7.80722i	−0.454041	−	0.262141i	−0.709535	+	0.704670i	$0.751095\pi$
$888$	10.5400	+	18.2558i	0.353699	+	0.612625i
$889$	−3.84784	−	1.03103i	−0.129052	−	0.0345795i
$890$	1.53215	−	5.71807i	0.0513579	−	0.191670i
$891$	7.00509	+	1.87701i	0.234679	+	0.0628822i
$892$	26.2394	+	26.2394i	0.878560	+	0.878560i
$893$	−42.0131	+	3.24287i	−1.40591	+	0.108518i
$894$	−7.77493	+	4.48886i	−0.260032	+	0.150130i
$895$	7.21021	+	7.21021i	0.241011	+	0.241011i
$896$	−3.36139	+	5.82210i	−0.112296	+	0.194503i
$897$	0.162589	+	2.63867i	0.00542868	+	0.0881026i
$898$	−1.30883	+	2.26697i	−0.0436764	+	0.0756497i
$899$	82.8390	−	22.1966i	2.76284	−	0.740300i
$900$	−1.39011	−	2.40774i	−0.0463370	−	0.0802580i
$901$	0.559457	−	0.969008i	0.0186382	−	0.0322823i
$902$	−0.582380	+	2.17347i	−0.0193911	+	0.0723687i
$903$	1.46131	−	1.46131i	0.0486293	−	0.0486293i
$904$	2.63353	+	9.82848i	0.0875900	+	0.326890i
$905$	−17.6774	−	17.6774i	−0.587616	−	0.587616i
$906$		−	9.64620i		−	0.320474i
$907$	59.0791			1.96169			0.980845	−	0.194789i	$-0.0624021\pi$
$907$	59.0791			1.96169			0.980845	+	0.194789i	$0.0624021\pi$
$908$	19.2868	−	5.16789i	0.640056	−	0.171502i
$909$	5.34494	+	3.08590i	0.177281	+	0.102353i
$910$	−1.23346	+	0.413333i	−0.0408889	+	0.0137019i
$911$		−	5.53264i		−	0.183305i	−0.995791	−	0.0916523i	$-0.970785\pi$
$911$		−	5.53264i		−	0.183305i	0.995791	−	0.0916523i	$-0.0292148\pi$
$912$	7.16255	+	20.3236i	0.237176	+	0.672982i
$913$	3.58984	+	6.21778i	0.118806	+	0.205778i
$914$	−1.66978	−	2.89214i	−0.0552313	−	0.0956633i
$915$	−6.83720	−	25.5168i	−0.226031	−	0.843558i
$916$	28.5091	+	28.5091i	0.941967	+	0.941967i
$917$	5.56916	+	1.49225i	0.183910	+	0.0492785i
$918$	−12.1686	−	3.26056i	−0.401623	−	0.107615i
$919$	−25.2815	+	43.7888i	−0.833959	+	1.44446i	0.0609168	+	0.998143i	$0.480598\pi$
$919$	−25.2815	+	43.7888i	−0.833959	+	1.44446i	−0.894875	+	0.446316i	$0.852736\pi$
$920$	−0.486770	−	0.843111i	−0.0160483	−	0.0277966i
$921$	−14.0697	−	52.5087i	−0.463611	−	1.73022i
$922$	−6.60288	−	11.4365i	−0.217454	−	0.376642i
$923$	45.7027	−	15.3149i	1.50432	−	0.504098i
$924$			1.93618i			0.0636957i
$925$	−6.97656	−	26.0369i	−0.229388	−	0.856088i
$926$		−	5.21880i		−	0.171500i
$927$	−8.56493			−0.281309
$928$	42.4080	−	11.3632i	1.39211	−	0.373015i
$929$	−10.3910	+	38.7798i	−0.340918	+	1.27232i	0.556390	+	0.830921i	$0.312186\pi$
$929$	−10.3910	+	38.7798i	−0.340918	+	1.27232i	−0.897309	+	0.441404i	$0.854481\pi$
$930$	6.80824	−	1.82426i	0.223251	−	0.0598199i
$931$	−18.6095	+	21.7226i	−0.609902	+	0.711930i
$932$	2.95822	−	5.12379i	0.0968998	−	0.167835i
$933$	5.06002			0.165658
$934$	8.66553	+	8.66553i	0.283545	+	0.283545i
$935$	7.19696	−	4.15516i	0.235366	−	0.135888i
$936$	2.62512	+	0.532848i	0.0858048	+	0.0174167i
$937$	−22.8863	−	39.6402i	−0.747662	−	1.29499i	−0.948941	−	0.315454i	$-0.897843\pi$
$937$	−22.8863	−	39.6402i	−0.747662	−	1.29499i	0.201279	−	0.979534i	$-0.435490\pi$
$938$	0.0983143	−	0.366914i	0.00321008	−	0.0119802i
$939$	−11.0018	+	6.35189i	−0.359030	+	0.207286i
$940$		−	25.2420i		−	0.823302i
$941$	23.5420	+	6.30806i	0.767448	+	0.205637i	0.621244	−	0.783618i	$-0.286628\pi$
$941$	23.5420	+	6.30806i	0.767448	+	0.205637i	0.146204	+	0.989254i	$0.453294\pi$
$942$	−5.03430	+	1.34894i	−0.164026	+	0.0439507i
$943$	2.60788	−	0.698780i	0.0849244	−	0.0227554i
$944$	−4.76596	+	17.7868i	−0.155119	+	0.578911i
$945$	4.47389	−	2.58300i	0.145536	−	0.0840250i
$946$	−0.381604	+	0.660957i	−0.0124070	+	0.0214896i
$947$	37.5524	−	37.5524i	1.22029	−	1.22029i	0.252760	−	0.967529i	$-0.418662\pi$
$947$	37.5524	−	37.5524i	1.22029	−	1.22029i	0.967529	−	0.252760i	$-0.0813382\pi$
$948$	−23.6349	−	13.6456i	−0.767627	−	0.443189i
$949$	2.08218	+	1.84047i	0.0675903	+	0.0597443i
$950$	0.390135	+	5.05440i	0.0126576	+	0.163986i
$951$	3.83724	−	14.3208i	0.124431	−	0.464383i
$952$		−	5.80044i		−	0.187993i
$953$	−26.2389	−	45.4471i	−0.849961	−	1.47217i	−0.881243	−	0.472664i	$-0.843292\pi$
$953$	−26.2389	−	45.4471i	−0.849961	−	1.47217i	0.0312819	−	0.999511i	$-0.490041\pi$
$954$	−0.00948499	+	0.0353985i	−0.000307088	+	0.00114607i
$955$	0.0775957	−	0.289591i	0.00251094	−	0.00937094i
$956$	−23.3216	+	23.3216i	−0.754274	+	0.754274i
$957$	11.7308	−	11.7308i	0.379204	−	0.379204i
$958$	8.94118	+	5.16219i	0.288876	+	0.166783i
$959$	2.22243	+	1.28312i	0.0717661	+	0.0414342i
$960$	−9.98950	+	2.67668i	−0.322410	+	0.0863894i
$961$		−	35.8130i		−	1.15526i
$962$	11.1728	+	5.56422i	0.360225	+	0.179398i
$963$	−3.39006	+	1.95725i	−0.109243	+	0.0630716i
$964$	−0.0487884	+	0.0487884i	−0.00157137	+	0.00157137i
$965$	−8.61680	−	4.97491i	−0.277385	−	0.160148i
$966$	−0.162378	+	0.0937488i	−0.00522442	+	0.00301632i
$967$	−22.4957	+	6.02769i	−0.723412	+	0.193838i	−0.601693	−	0.798727i	$-0.705507\pi$
$967$	−22.4957	+	6.02769i	−0.723412	+	0.193838i	−0.121718	+	0.992565i	$0.538840\pi$
$968$	3.85175	+	14.3749i	0.123800	+	0.462028i
$969$	−30.8368	−	26.4175i	−0.990620	−	0.848652i
$970$	0.872077	−	0.872077i	0.0280007	−	0.0280007i
$971$	16.0012	−	9.23833i	0.513505	−	0.296472i	−0.220769	−	0.975326i	$-0.570857\pi$
$971$	16.0012	−	9.23833i	0.513505	−	0.296472i	0.734273	+	0.678854i	$0.237523\pi$
$972$	−9.49542			−0.304566
$973$	−1.88807	−	7.04639i	−0.0605289	−	0.225897i
$974$	1.93102	+	1.11487i	0.0618737	+	0.0357228i
$975$	15.3590	+	7.64901i	0.491881	+	0.244964i
$976$	−37.0125			−1.18474
$977$	42.0772	+	11.2745i	1.34617	+	0.360705i	0.858719	−	0.512447i	$-0.171261\pi$
$977$	42.0772	+	11.2745i	1.34617	+	0.360705i	0.487449	+	0.873151i	$0.337927\pi$
$978$	3.10297	−	5.37451i	0.0992222	−	0.171858i
$979$	−10.8550			−0.346927
$980$	−12.1160	−	12.1160i	−0.387032	−	0.387032i
$981$	0.138808	+	0.518040i	0.00443181	+	0.0165398i
$982$	−8.89356	−	8.89356i	−0.283805	−	0.283805i
$983$	−18.5990	+	4.98358i	−0.593215	+	0.158951i	−0.542922	−	0.839783i	$-0.682682\pi$
$983$	−18.5990	+	4.98358i	−0.593215	+	0.158951i	−0.0502928	+	0.998735i	$0.516015\pi$
$984$			13.7036i			0.436855i
$985$			24.0125i			0.765101i
$986$	−16.8901	+	16.8901i	−0.537891	+	0.537891i
$987$	−10.1152			−0.321971
$988$	23.2099	+	17.5283i	0.738407	+	0.557648i
$989$	0.915749			0.0291191
$990$	−0.192463	+	0.192463i	−0.00611687	+	0.00611687i
$991$		−	39.7950i		−	1.26413i	−0.774916	−	0.632065i	$-0.782208\pi$
$991$		−	39.7950i		−	1.26413i	0.774916	−	0.632065i	$-0.217792\pi$
$992$		−	34.2038i		−	1.08597i
$993$	0.153596	−	0.0411558i	0.00487421	−	0.00130604i
$994$	2.41726	+	2.41726i	0.0766710	+	0.0766710i
$995$	7.31651	+	27.3056i	0.231949	+	0.865645i
$996$	14.8595	+	14.8595i	0.470840	+	0.470840i
$997$	37.4910			1.18735			0.593677	−	0.804704i	$-0.297676\pi$
$997$	37.4910			1.18735			0.593677	+	0.804704i	$0.297676\pi$
$998$	−3.90287	+	6.75997i	−0.123543	+	0.213983i
$999$	−47.8778	−	12.8288i	−1.51479	−	0.405886i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	247.2.z.a.141.10	✓	88
13.6	odd	12		247.2.bf.a.84.13	yes	88
19.12	odd	6		247.2.bf.a.50.13	yes	88
247.240	even	12	inner	247.2.z.a.240.10	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
247.2.z.a.141.10	✓	88	1.1	even	1	trivial
247.2.z.a.240.10	yes	88	247.240	even	12	inner
247.2.bf.a.50.13	yes	88	19.12	odd	6
247.2.bf.a.84.13	yes	88	13.6	odd	12

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:	\( N \)	\(=\)	\( 247 = 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	247.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.273277 + 0.273277i) q^{2} +1.58138i q^{3} +1.85064i q^{4} +(-1.36285 + 0.365175i) q^{5} +(-0.432157 - 0.432157i) q^{6} +(0.171253 + 0.639124i) q^{7} +(-1.05229 - 1.05229i) q^{8} +0.499222 q^{9} +(0.272642 - 0.472230i) q^{10} +(-0.965805 - 0.258787i) q^{11} -2.92657 q^{12} +(-3.00572 + 1.99140i) q^{13} +(-0.221457 - 0.127859i) q^{14} +(-0.577481 - 2.15519i) q^{15} -3.12614 q^{16} +(5.10151 - 2.94536i) q^{17} +(-0.136426 + 0.136426i) q^{18} +(-4.11106 + 1.44884i) q^{19} +(-0.675806 - 2.52214i) q^{20} +(-1.01070 + 0.270816i) q^{21} +(0.334653 - 0.193212i) q^{22} +(-0.401540 - 0.231829i) q^{23} +(1.66408 - 1.66408i) q^{24} +(-2.60612 + 1.50464i) q^{25} +(0.277189 - 1.36560i) q^{26} +5.53362i q^{27} +(-1.18279 + 0.316927i) q^{28} +(9.08639 + 5.24603i) q^{29} +(0.746777 + 0.431152i) q^{30} +(5.77984 - 5.77984i) q^{31} +(2.95889 - 2.95889i) q^{32} +(0.409241 - 1.52731i) q^{33} +(-0.589228 + 2.19903i) q^{34} +(-0.466783 - 0.808492i) q^{35} +0.923879i q^{36} +(-2.31834 + 8.65218i) q^{37} +(0.727525 - 1.51940i) q^{38} +(-3.14917 - 4.75319i) q^{39} +(1.81839 + 1.04985i) q^{40} +(-4.11747 + 4.11747i) q^{41} +(0.202194 - 0.350209i) q^{42} +(-1.71044 + 0.987525i) q^{43} +(0.478921 - 1.78736i) q^{44} +(-0.680364 + 0.182303i) q^{45} +(0.173086 - 0.0463782i) q^{46} +(9.33773 + 2.50204i) q^{47} -4.94363i q^{48} +(5.68303 - 3.28110i) q^{49} +(0.301008 - 1.12338i) q^{50} +(4.65775 + 8.06745i) q^{51} +(-3.68536 - 5.56249i) q^{52} +(0.164497 - 0.0949726i) q^{53} +(-1.51221 - 1.51221i) q^{54} +1.41075 q^{55} +(0.492337 - 0.852753i) q^{56} +(-2.29118 - 6.50118i) q^{57} +(-3.91672 + 1.04948i) q^{58} +(1.52455 - 5.68970i) q^{59} +(3.98848 - 1.06871i) q^{60} +11.8397 q^{61} +3.15900i q^{62} +(0.0854930 + 0.319064i) q^{63} -4.63509i q^{64} +(3.36913 - 3.81159i) q^{65} +(0.305543 + 0.529216i) q^{66} +(0.384465 + 1.43484i) q^{67} +(5.45080 + 9.44106i) q^{68} +(0.366612 - 0.634990i) q^{69} +(0.348504 + 0.0933813i) q^{70} +(-12.9129 - 3.46000i) q^{71} +(-0.525327 - 0.525327i) q^{72} +(-0.199486 - 0.744491i) q^{73} +(-1.73089 - 2.99799i) q^{74} +(-2.37942 - 4.12128i) q^{75} +(-2.68129 - 7.60810i) q^{76} -0.661587i q^{77} +(2.15954 + 0.438343i) q^{78} +(8.07597 + 4.66267i) q^{79} +(4.26046 - 1.14159i) q^{80} -7.25311 q^{81} -2.25043i q^{82} +(-5.07743 - 5.07743i) q^{83} +(-0.501183 - 1.87044i) q^{84} +(-5.87702 + 5.87702i) q^{85} +(0.197557 - 0.737294i) q^{86} +(-8.29599 + 14.3691i) q^{87} +(0.743990 + 1.28863i) q^{88} +(10.4864 - 2.80983i) q^{89} +(0.136109 - 0.235747i) q^{90} +(-1.78749 - 1.57999i) q^{91} +(0.429033 - 0.743106i) q^{92} +(9.14015 + 9.14015i) q^{93} +(-3.23554 + 1.86804i) q^{94} +(5.07368 - 3.47581i) q^{95} +(4.67914 + 4.67914i) q^{96} +(2.18470 + 0.585387i) q^{97} +(-0.656393 + 2.44969i) q^{98} +(-0.482151 - 0.129192i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 6 q^{2} - 2 q^{5} + 14 q^{6} - 12 q^{7} + 12 q^{8} - 84 q^{9} - 6 q^{10} - 4 q^{11} + 36 q^{12} - 6 q^{13} - 12 q^{14} + 30 q^{15} - 92 q^{16} - 6 q^{17} + 6 q^{18} - 14 q^{19} - 24 q^{20} - 18 q^{22}+ \cdots + 28 q^{99}+O(q^{100}) \) 88 * q - 6 * q^2 - 2 * q^5 + 14 * q^6 - 12 * q^7 + 12 * q^8 - 84 * q^9 - 6 * q^10 - 4 * q^11 + 36 * q^12 - 6 * q^13 - 12 * q^14 + 30 * q^15 - 92 * q^16 - 6 * q^17 + 6 * q^18 - 14 * q^19 - 24 * q^20 - 18 * q^22 - 30 * q^23 + 48 * q^24 + 12 * q^25 + 32 * q^26 + 18 * q^28 + 18 * q^29 + 60 * q^30 - 30 * q^31 - 12 * q^32 - 6 * q^33 - 6 * q^34 - 6 * q^35 - 12 * q^37 - 36 * q^38 + 18 * q^39 - 12 * q^40 - 6 * q^41 + 6 * q^42 + 12 * q^43 + 64 * q^44 - 38 * q^45 + 24 * q^46 + 64 * q^47 - 42 * q^49 - 24 * q^51 + 18 * q^52 - 66 * q^53 - 96 * q^54 - 36 * q^55 + 60 * q^56 + 64 * q^57 - 24 * q^58 - 6 * q^59 + 54 * q^60 - 28 * q^61 - 6 * q^63 + 44 * q^66 - 36 * q^67 - 12 * q^68 - 36 * q^69 + 114 * q^70 - 30 * q^71 - 66 * q^72 + 22 * q^73 + 6 * q^74 - 12 * q^75 + 38 * q^76 + 12 * q^78 - 24 * q^79 + 14 * q^80 + 64 * q^81 - 6 * q^83 - 18 * q^84 - 18 * q^85 - 6 * q^86 + 32 * q^87 + 42 * q^88 + 66 * q^89 + 18 * q^90 - 18 * q^91 + 104 * q^92 - 2 * q^93 - 84 * q^94 - 42 * q^95 - 174 * q^96 + 30 * q^97 - 60 * q^98 + 28 * q^99

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