LMFDB - Embedded newform 656.2.n.f.493.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [656,2,Mod(165,656)] 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("656.165"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(656, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 656 = 2^{4} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	656.n (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [66,-2,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.23818637260$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$33$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			493.11
Character	$\chi$	$=$	656.493
Dual form			656.2.n.f.165.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.526430 + 1.31258i) q^{2} +(0.868344 + 0.868344i) q^{3} +(-1.44574 - 1.38196i) q^{4} +(-0.218916 + 0.218916i) q^{5} +(-1.59689 + 0.682651i) q^{6} +2.55903i q^{7} +(2.57502 - 1.17015i) q^{8} -1.49196i q^{9} +(-0.172101 - 0.402589i) q^{10} +(-3.62852 + 3.62852i) q^{11} +(-0.0553819 - 2.45542i) q^{12} +(-2.19620 - 2.19620i) q^{13} +(-3.35893 - 1.34715i) q^{14} -0.380189 q^{15} +(0.180348 + 3.99593i) q^{16} -5.97463 q^{17} +(1.95832 + 0.785411i) q^{18} +(2.91040 + 2.91040i) q^{19} +(0.619031 - 0.0139622i) q^{20} +(-2.22211 + 2.22211i) q^{21} +(-2.85257 - 6.67289i) q^{22} +3.65990i q^{23} +(3.25210 + 1.21991i) q^{24} +4.90415i q^{25} +(4.03883 - 1.72654i) q^{26} +(3.90056 - 3.90056i) q^{27} +(3.53648 - 3.69969i) q^{28} +(-1.12861 - 1.12861i) q^{29} +(0.200143 - 0.499029i) q^{30} -5.06366 q^{31} +(-5.33993 - 1.86686i) q^{32} -6.30160 q^{33} +(3.14522 - 7.84219i) q^{34} +(-0.560212 - 0.560212i) q^{35} +(-2.06183 + 2.15699i) q^{36} +(-3.63678 + 3.63678i) q^{37} +(-5.35225 + 2.28801i) q^{38} -3.81411i q^{39} +(-0.307550 + 0.819879i) q^{40} -1.00000i q^{41} +(-1.74692 - 4.08649i) q^{42} +(0.225812 - 0.225812i) q^{43} +(10.2604 - 0.231422i) q^{44} +(0.326614 + 0.326614i) q^{45} +(-4.80392 - 1.92668i) q^{46} -9.42737 q^{47} +(-3.31324 + 3.62645i) q^{48} +0.451388 q^{49} +(-6.43710 - 2.58169i) q^{50} +(-5.18803 - 5.18803i) q^{51} +(0.140071 + 6.21020i) q^{52} +(6.63179 - 6.63179i) q^{53} +(3.06644 + 7.17318i) q^{54} -1.58868i q^{55} +(2.99444 + 6.58955i) q^{56} +5.05445i q^{57} +(2.07553 - 0.887260i) q^{58} +(0.727412 - 0.727412i) q^{59} +(0.549656 + 0.525408i) q^{60} +(2.49664 + 2.49664i) q^{61} +(2.66566 - 6.64646i) q^{62} +3.81796 q^{63} +(5.26150 - 6.02633i) q^{64} +0.961565 q^{65} +(3.31735 - 8.27137i) q^{66} +(5.07091 + 5.07091i) q^{67} +(8.63778 + 8.25672i) q^{68} +(-3.17805 + 3.17805i) q^{69} +(1.03024 - 0.440412i) q^{70} -12.5284i q^{71} +(-1.74581 - 3.84183i) q^{72} +1.92731i q^{73} +(-2.85907 - 6.68809i) q^{74} +(-4.25849 + 4.25849i) q^{75} +(-0.185621 - 8.22975i) q^{76} +(-9.28547 - 9.28547i) q^{77} +(5.00633 + 2.00786i) q^{78} +3.47482 q^{79} +(-0.914255 - 0.835293i) q^{80} +2.29819 q^{81} +(1.31258 + 0.526430i) q^{82} +(6.23773 + 6.23773i) q^{83} +(6.28349 - 0.141724i) q^{84} +(1.30794 - 1.30794i) q^{85} +(0.177523 + 0.415271i) q^{86} -1.96004i q^{87} +(-5.09761 + 13.5894i) q^{88} +14.9007i q^{89} +(-0.600646 + 0.256768i) q^{90} +(5.62012 - 5.62012i) q^{91} +(5.05785 - 5.29127i) q^{92} +(-4.39699 - 4.39699i) q^{93} +(4.96285 - 12.3742i) q^{94} -1.27427 q^{95} +(-3.01582 - 6.25797i) q^{96} +12.0281 q^{97} +(-0.237624 + 0.592484i) q^{98} +(5.41360 + 5.41360i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 2 q^{2} + 8 q^{3} - 8 q^{4} - 6 q^{5} + 2 q^{6} + 4 q^{8} + 6 q^{10} - 8 q^{11} - 16 q^{12} + 16 q^{14} + 32 q^{15} + 44 q^{16} - 4 q^{17} - 20 q^{18} - 16 q^{19} + 4 q^{20} - 24 q^{21} - 12 q^{22}+ \cdots - 40 q^{99}+O(q^{100}) $ 66 * q - 2 * q^2 + 8 * q^3 - 8 * q^4 - 6 * q^5 + 2 * q^6 + 4 * q^8 + 6 * q^10 - 8 * q^11 - 16 * q^12 + 16 * q^14 + 32 * q^15 + 44 * q^16 - 4 * q^17 - 20 * q^18 - 16 * q^19 + 4 * q^20 - 24 * q^21 - 12 * q^22 + 24 * q^24 + 20 * q^26 + 32 * q^27 - 16 * q^28 - 12 * q^29 - 42 * q^30 - 28 * q^31 - 12 * q^32 - 32 * q^33 - 56 * q^34 + 48 * q^36 + 10 * q^37 - 18 * q^38 + 40 * q^40 + 30 * q^42 + 58 * q^43 - 84 * q^44 - 14 * q^45 + 16 * q^46 + 16 * q^47 - 4 * q^48 - 66 * q^49 - 26 * q^50 - 4 * q^51 - 4 * q^52 - 8 * q^53 - 2 * q^54 + 28 * q^56 + 60 * q^58 + 6 * q^59 - 68 * q^60 + 30 * q^61 - 8 * q^62 - 56 * q^63 + 4 * q^64 + 32 * q^65 - 110 * q^66 + 44 * q^67 + 36 * q^68 + 40 * q^69 + 62 * q^70 + 52 * q^72 - 18 * q^74 + 12 * q^75 - 76 * q^76 + 48 * q^77 + 16 * q^78 + 128 * q^79 - 32 * q^80 - 98 * q^81 - 2 * q^82 - 6 * q^83 + 112 * q^84 + 12 * q^85 - 36 * q^86 + 182 * q^90 + 24 * q^91 - 24 * q^92 + 8 * q^93 + 54 * q^94 + 48 * q^95 + 56 * q^96 + 36 * q^97 - 48 * q^98 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/656\mathbb{Z}\right)^\times$.

$n$	$129$	$165$	$575$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.526430	+	1.31258i	−0.372242	+	0.928136i
$2$	−0.526430	+	1.31258i	−0.372242	+	0.928136i
$3$	0.868344	+	0.868344i	0.501339	+	0.501339i	0.911854	−	0.410515i	$-0.134651\pi$
$3$	0.868344	+	0.868344i	0.501339	+	0.501339i	−0.410515	+	0.911854i	$0.634651\pi$
$4$	−1.44574	−	1.38196i	−0.722872	−	0.690982i
$5$	−0.218916	+	0.218916i	−0.0979023	+	0.0979023i	−0.754362	−	0.656459i	$-0.772053\pi$
$5$	−0.218916	+	0.218916i	−0.0979023	+	0.0979023i	0.656459	+	0.754362i	$0.272053\pi$
$6$	−1.59689	+	0.682651i	−0.651930	+	0.278691i
$7$			2.55903i			0.967221i	0.875283	+	0.483610i	$0.160675\pi$
$7$			2.55903i			0.967221i	−0.875283	+	0.483610i	$0.839325\pi$
$8$	2.57502	−	1.17015i	0.910409	−	0.413710i
$9$		−	1.49196i		−	0.497319i
$10$	−0.172101	−	0.402589i	−0.0544233	−	0.127310i
$11$	−3.62852	+	3.62852i	−1.09404	+	1.09404i	−0.0989466	+	0.995093i	$0.531547\pi$
$11$	−3.62852	+	3.62852i	−1.09404	+	1.09404i	−0.995093	+	0.0989466i	$0.968453\pi$
$12$	−0.0553819	−	2.45542i	−0.0159874	−	0.708820i
$13$	−2.19620	−	2.19620i	−0.609115	−	0.609115i	0.333600	−	0.942715i	$-0.391737\pi$
$13$	−2.19620	−	2.19620i	−0.609115	−	0.609115i	−0.942715	+	0.333600i	$0.891737\pi$
$14$	−3.35893	−	1.34715i	−0.897712	−	0.360040i
$15$	−0.380189			−0.0981644
$16$	0.180348	+	3.99593i	0.0450869	+	0.998983i
$17$	−5.97463			−1.44906			−0.724530	−	0.689243i	$-0.757943\pi$
$17$	−5.97463			−1.44906			−0.724530	+	0.689243i	$0.757943\pi$
$18$	1.95832	+	0.785411i	0.461580	+	0.185123i
$19$	2.91040	+	2.91040i	0.667691	+	0.667691i	0.957181	−	0.289490i	$-0.0934858\pi$
$19$	2.91040	+	2.91040i	0.667691	+	0.667691i	−0.289490	+	0.957181i	$0.593486\pi$
$20$	0.619031	−	0.0139622i	0.138420	−	0.00312204i
$21$	−2.22211	+	2.22211i	−0.484905	+	0.484905i
$22$	−2.85257	−	6.67289i	−0.608169	−	1.42266i
$23$			3.65990i			0.763141i	0.924340	+	0.381571i	$0.124617\pi$
$23$			3.65990i			0.763141i	−0.924340	+	0.381571i	$0.875383\pi$
$24$	3.25210	+	1.21991i	0.663832	+	0.249014i
$25$			4.90415i			0.980830i
$26$	4.03883	−	1.72654i	0.792080	−	0.338603i
$27$	3.90056	−	3.90056i	0.750664	−	0.750664i
$28$	3.53648	−	3.69969i	0.668332	−	0.699177i
$29$	−1.12861	−	1.12861i	−0.209578	−	0.209578i	0.594510	−	0.804088i	$-0.297346\pi$
$29$	−1.12861	−	1.12861i	−0.209578	−	0.209578i	−0.804088	+	0.594510i	$0.797346\pi$
$30$	0.200143	−	0.499029i	0.0365409	−	0.0911099i
$31$	−5.06366			−0.909459			−0.454730	−	0.890630i	$-0.650264\pi$
$31$	−5.06366			−0.909459			−0.454730	+	0.890630i	$0.650264\pi$
$32$	−5.33993	−	1.86686i	−0.943975	−	0.330017i
$33$	−6.30160			−1.09697
$34$	3.14522	−	7.84219i	0.539401	−	1.34492i
$35$	−0.560212	−	0.560212i	−0.0946931	−	0.0946931i
$36$	−2.06183	+	2.15699i	−0.343639	+	0.359498i
$37$	−3.63678	+	3.63678i	−0.597883	+	0.597883i	−0.939749	−	0.341865i	$-0.888941\pi$
$37$	−3.63678	+	3.63678i	−0.597883	+	0.597883i	0.341865	+	0.939749i	$0.388941\pi$
$38$	−5.35225	+	2.28801i	−0.868250	+	0.371165i
$39$		−	3.81411i		−	0.610746i
$40$	−0.307550	+	0.819879i	−0.0486279	+	0.129634i
$41$		−	1.00000i		−	0.156174i
$41$		−	1.00000i		−	0.156174i
$42$	−1.74692	−	4.08649i	−0.269556	−	0.630560i
$43$	0.225812	−	0.225812i	0.0344360	−	0.0344360i	−0.689679	−	0.724115i	$-0.742248\pi$
$43$	0.225812	−	0.225812i	0.0344360	−	0.0344360i	0.724115	+	0.689679i	$0.242248\pi$
$44$	10.2604	−	0.231422i	1.54681	−	0.0348882i
$45$	0.326614	+	0.326614i	0.0486887	+	0.0486887i
$46$	−4.80392	−	1.92668i	−0.708299	−	0.284073i
$47$	−9.42737			−1.37512			−0.687562	−	0.726126i	$-0.741319\pi$
$47$	−9.42737			−1.37512			−0.687562	+	0.726126i	$0.741319\pi$
$48$	−3.31324	+	3.62645i	−0.478225	+	0.523433i
$49$	0.451388			0.0644840
$50$	−6.43710	−	2.58169i	−0.910344	−	0.365106i
$51$	−5.18803	−	5.18803i	−0.726470	−	0.726470i
$52$	0.140071	+	6.21020i	0.0194243	+	0.861200i
$53$	6.63179	−	6.63179i	0.910946	−	0.910946i	−0.0854005	−	0.996347i	$-0.527217\pi$
$53$	6.63179	−	6.63179i	0.910946	−	0.910946i	0.996347	+	0.0854005i	$0.0272170\pi$
$54$	3.06644	+	7.17318i	0.417289	+	0.976147i
$55$		−	1.58868i		−	0.214218i
$56$	2.99444	+	6.58955i	0.400149	+	0.880566i
$57$			5.05445i			0.669478i
$58$	2.07553	−	0.887260i	0.272530	−	0.116503i
$59$	0.727412	−	0.727412i	0.0947009	−	0.0947009i	−0.658169	−	0.752870i	$-0.728669\pi$
$59$	0.727412	−	0.727412i	0.0947009	−	0.0947009i	0.752870	+	0.658169i	$0.228669\pi$
$60$	0.549656	+	0.525408i	0.0709603	+	0.0678299i
$61$	2.49664	+	2.49664i	0.319663	+	0.319663i	0.848637	−	0.528975i	$-0.177423\pi$
$61$	2.49664	+	2.49664i	0.319663	+	0.319663i	−0.528975	+	0.848637i	$0.677423\pi$
$62$	2.66566	−	6.64646i	0.338539	−	0.844102i
$63$	3.81796			0.481017
$64$	5.26150	−	6.02633i	0.657688	−	0.753291i
$65$	0.961565			0.119268
$66$	3.31735	−	8.27137i	0.408338	−	1.01814i
$67$	5.07091	+	5.07091i	0.619510	+	0.619510i	0.945406	−	0.325896i	$-0.105666\pi$
$67$	5.07091	+	5.07091i	0.619510	+	0.619510i	−0.325896	+	0.945406i	$0.605666\pi$
$68$	8.63778	+	8.25672i	1.04748	+	1.00127i
$69$	−3.17805	+	3.17805i	−0.382592	+	0.382592i
$70$	1.03024	−	0.440412i	0.123137	−	0.0526393i
$71$		−	12.5284i		−	1.48685i	−0.668821	−	0.743424i	$-0.733201\pi$
$71$		−	12.5284i		−	1.48685i	0.668821	−	0.743424i	$-0.266799\pi$
$72$	−1.74581	−	3.84183i	−0.205746	−	0.452764i
$73$			1.92731i			0.225575i	0.993619	+	0.112787i	$0.0359779\pi$
$73$			1.92731i			0.225575i	−0.993619	+	0.112787i	$0.964022\pi$
$74$	−2.85907	−	6.68809i	−0.332360	−	0.777474i
$75$	−4.25849	+	4.25849i	−0.491728	+	0.491728i
$76$	−0.185621	−	8.22975i	−0.0212922	−	0.944017i
$77$	−9.28547	−	9.28547i	−1.05818	−	1.05818i
$78$	5.00633	+	2.00786i	0.566855	+	0.227345i
$79$	3.47482			0.390948			0.195474	−	0.980709i	$-0.437376\pi$
$79$	3.47482			0.390948			0.195474	+	0.980709i	$0.437376\pi$
$80$	−0.914255	−	0.835293i	−0.102217	−	0.0933886i
$81$	2.29819			0.255354
$82$	1.31258	+	0.526430i	0.144950	+	0.0581344i
$83$	6.23773	+	6.23773i	0.684680	+	0.684680i	0.961051	−	0.276371i	$-0.0891319\pi$
$83$	6.23773	+	6.23773i	0.684680	+	0.684680i	−0.276371	+	0.961051i	$0.589132\pi$
$84$	6.28349	−	0.141724i	0.685585	−	0.0154633i
$85$	1.30794	−	1.30794i	0.141866	−	0.141866i
$86$	0.177523	+	0.415271i	0.0191428	+	0.0447799i
$87$		−	1.96004i		−	0.210139i
$88$	−5.09761	+	13.5894i	−0.543407	+	1.44864i
$89$			14.9007i			1.57947i	0.613450	+	0.789733i	$0.289781\pi$
$89$			14.9007i			1.57947i	−0.613450	+	0.789733i	$0.710219\pi$
$90$	−0.600646	+	0.256768i	−0.0633137	+	0.0270657i
$91$	5.62012	−	5.62012i	0.589149	−	0.589149i
$92$	5.05785	−	5.29127i	0.527317	−	0.551653i
$93$	−4.39699	−	4.39699i	−0.455947	−	0.455947i
$94$	4.96285	−	12.3742i	0.511879	−	1.27630i
$95$	−1.27427			−0.130737
$96$	−3.01582	−	6.25797i	−0.307801	−	0.638701i
$97$	12.0281			1.22127			0.610634	−	0.791913i	$-0.290915\pi$
$97$	12.0281			1.22127			0.610634	+	0.791913i	$0.290915\pi$
$98$	−0.237624	+	0.592484i	−0.0240037	+	0.0598499i
$99$	5.41360	+	5.41360i	0.544087	+	0.544087i
$100$	6.77736	−	7.09014i	0.677736	−	0.709014i
$101$	−4.71903	+	4.71903i	−0.469561	+	0.469561i	−0.901772	−	0.432211i	$-0.857733\pi$
$101$	−4.71903	+	4.71903i	−0.469561	+	0.469561i	0.432211	+	0.901772i	$0.357733\pi$
$102$	9.54085	−	4.07858i	0.944685	−	0.403840i
$103$			12.4982i			1.23149i	0.787946	+	0.615744i	$0.211145\pi$
$103$			12.4982i			1.23149i	−0.787946	+	0.615744i	$0.788855\pi$
$104$	−8.22513	−	3.08538i	−0.806541	−	0.302546i
$105$		−	0.972914i		−	0.0949467i
$106$	5.21360	+	12.1959i	0.506389	+	1.18457i
$107$	4.41285	−	4.41285i	0.426607	−	0.426607i	−0.460864	−	0.887471i	$-0.652460\pi$
$107$	4.41285	−	4.41285i	0.426607	−	0.426607i	0.887471	+	0.460864i	$0.152460\pi$
$108$	−11.0297	+	0.248773i	−1.06133	+	0.0239382i
$109$	−2.36910	−	2.36910i	−0.226918	−	0.226918i	0.584486	−	0.811404i	$-0.301296\pi$
$109$	−2.36910	−	2.36910i	−0.226918	−	0.226918i	−0.811404	+	0.584486i	$0.801296\pi$
$110$	2.08528	+	0.836330i	0.198823	+	0.0797409i
$111$	−6.31596			−0.599484
$112$	−10.2257	+	0.461515i	−0.966237	+	0.0436090i
$113$	−15.7767			−1.48415			−0.742074	−	0.670318i	$-0.766158\pi$
$113$	−15.7767			−1.48415			−0.742074	+	0.670318i	$0.766158\pi$
$114$	−6.63438	−	2.66081i	−0.621367	−	0.249208i
$115$	−0.801211	−	0.801211i	−0.0747133	−	0.0747133i
$116$	0.0719814	+	3.19138i	0.00668330	+	0.296312i
$117$	−3.27663	+	3.27663i	−0.302925	+	0.302925i
$118$	0.571856	+	1.33772i	0.0526437	+	0.123147i
$119$		−	15.2892i		−	1.40156i
$120$	−0.978996	+	0.444878i	−0.0893697	+	0.0406116i
$121$		−	15.3323i		−	1.39384i
$122$	−4.59136	+	1.96274i	−0.415682	+	0.177698i
$123$	0.868344	−	0.868344i	0.0782959	−	0.0782959i
$124$	7.32075	+	6.99779i	0.657422	+	0.628420i
$125$	−2.16818	−	2.16818i	−0.193928	−	0.193928i
$126$	−2.00989	+	5.01138i	−0.179055	+	0.446449i
$127$	2.44046			0.216556			0.108278	−	0.994121i	$-0.465466\pi$
$127$	2.44046			0.216556			0.108278	+	0.994121i	$0.465466\pi$
$128$	5.14024	+	10.0786i	0.454337	+	0.890830i
$129$	0.392165			0.0345282
$130$	−0.506197	+	1.26213i	−0.0443964	+	0.110696i
$131$	7.04367	+	7.04367i	0.615408	+	0.615408i	0.944350	−	0.328942i	$-0.106692\pi$
$131$	7.04367	+	7.04367i	0.615408	+	0.615408i	−0.328942	+	0.944350i	$0.606692\pi$
$132$	9.11050	+	8.70859i	0.792967	+	0.757986i
$133$	−7.44778	+	7.44778i	−0.645804	+	0.645804i
$134$	−9.32546	+	3.98651i	−0.805597	+	0.344382i
$135$			1.70779i			0.146983i
$136$	−15.3848	+	6.99121i	−1.31924	+	0.599491i
$137$			20.3281i			1.73675i	0.495910	+	0.868374i	$0.334834\pi$
$137$			20.3281i			1.73675i	−0.495910	+	0.868374i	$0.665166\pi$
$138$	−2.49843	−	5.84447i	−0.212681	−	0.497514i
$139$	6.51610	−	6.51610i	0.552689	−	0.552689i	−0.374527	−	0.927216i	$-0.622195\pi$
$139$	6.51610	−	6.51610i	0.552689	−	0.552689i	0.927216	+	0.374527i	$0.122195\pi$
$140$	0.0357296	+	1.58412i	0.00301971	+	0.133882i
$141$	−8.18620	−	8.18620i	−0.689402	−	0.689402i
$142$	16.4446	+	6.59532i	1.38000	+	0.553467i
$143$	15.9379			1.33279
$144$	5.96176	−	0.269071i	0.496813	−	0.0224226i
$145$	0.494142			0.0410363
$146$	−2.52975	−	1.01459i	−0.209364	−	0.0839684i
$147$	0.391960	+	0.391960i	0.0323283	+	0.0323283i
$148$	10.2838	−	0.231950i	0.845320	−	0.0190661i
$149$	−6.34662	+	6.34662i	−0.519935	+	0.519935i	−0.917552	−	0.397617i	$-0.869837\pi$
$149$	−6.34662	+	6.34662i	−0.519935	+	0.519935i	0.397617	+	0.917552i	$0.369837\pi$
$150$	−3.34782	−	7.83141i	−0.273348	−	0.639432i
$151$		−	7.60329i		−	0.618747i	−0.950941	−	0.309373i	$-0.899881\pi$
$151$		−	7.60329i		−	0.618747i	0.950941	−	0.309373i	$-0.100119\pi$
$152$	10.8999	+	4.08874i	0.884102	+	0.331641i
$153$			8.91389i			0.720645i
$154$	17.0761	−	7.29979i	1.37603	−	0.588234i
$155$	1.10852	−	1.10852i	0.0890382	−	0.0890382i
$156$	−5.27096	+	5.51422i	−0.422014	+	0.441491i
$157$	3.79336	+	3.79336i	0.302743	+	0.302743i	0.842086	−	0.539343i	$-0.181327\pi$
$157$	3.79336	+	3.79336i	0.302743	+	0.302743i	−0.539343	+	0.842086i	$0.681327\pi$
$158$	−1.82925	+	4.56098i	−0.145527	+	0.362852i
$159$	11.5173			0.913385
$160$	1.57768	−	0.760312i	0.124727	−	0.0601079i
$161$	−9.36577			−0.738126
$162$	−1.20984	+	3.01656i	−0.0950536	+	0.237004i
$163$	13.5964	+	13.5964i	1.06495	+	1.06495i	0.997739	+	0.0672094i	$0.0214096\pi$
$163$	13.5964	+	13.5964i	1.06495	+	1.06495i	0.0672094	+	0.997739i	$0.478590\pi$
$164$	−1.38196	+	1.44574i	−0.107913	+	0.112894i
$165$	1.37952	−	1.37952i	0.107396	−	0.107396i
$166$	−11.4713	+	4.90381i	−0.890343	+	0.380609i
$167$			20.9034i			1.61755i	0.588117	+	0.808776i	$0.299869\pi$
$167$			20.9034i			1.61755i	−0.588117	+	0.808776i	$0.700131\pi$
$168$	−3.12179	+	8.32220i	−0.240852	+	0.642072i
$169$		−	3.35345i		−	0.257958i
$170$	1.02824	+	2.40532i	0.0788626	+	0.184480i
$171$	4.34219	−	4.34219i	0.332055	−	0.332055i
$172$	−0.638531	+	0.0144020i	−0.0486875	+	0.00109814i
$173$	1.89939	+	1.89939i	0.144408	+	0.144408i	0.775615	−	0.631207i	$-0.217440\pi$
$173$	1.89939	+	1.89939i	0.144408	+	0.144408i	−0.631207	+	0.775615i	$0.717440\pi$
$174$	2.57272	+	1.03183i	0.195037	+	0.0782225i
$175$	−12.5498			−0.948679
$176$	−15.1537	−	13.8449i	−1.14225	−	1.04360i
$177$	1.26329			0.0949545
$178$	−19.5583	−	7.84415i	−1.46596	−	0.587944i
$179$	4.33461	+	4.33461i	0.323984	+	0.323984i	0.850293	−	0.526309i	$-0.176425\pi$
$179$	4.33461	+	4.33461i	0.323984	+	0.323984i	−0.526309	+	0.850293i	$0.676425\pi$
$180$	−0.0208310	−	0.923568i	−0.00155265	−	0.0688387i
$181$	−8.07560	+	8.07560i	−0.600255	+	0.600255i	−0.940380	−	0.340125i	$-0.889531\pi$
$181$	−8.07560	+	8.07560i	−0.600255	+	0.600255i	0.340125	+	0.940380i	$0.389531\pi$
$182$	4.41827	+	10.3355i	0.327504	+	0.766116i
$183$			4.33589i			0.320518i
$184$	4.28263	+	9.42433i	0.315720	+	0.694771i
$185$		−	1.59230i		−	0.117068i
$186$	8.08612	−	3.45671i	0.592903	−	0.253458i
$187$	21.6790	−	21.6790i	1.58533	−	1.58533i
$188$	13.6296	+	13.0283i	0.994038	+	0.950186i
$189$	9.98164	+	9.98164i	0.726058	+	0.726058i
$190$	0.670811	−	1.67258i	0.0486658	−	0.121342i
$191$	−25.0047			−1.80928			−0.904639	−	0.426178i	$-0.859860\pi$
$191$	−25.0047			−1.80928			−0.904639	+	0.426178i	$0.859860\pi$
$192$	9.80172	−	0.664132i	0.707378	−	0.0479296i
$193$	25.1799			1.81249			0.906243	−	0.422757i	$-0.138938\pi$
$193$	25.1799			1.81249			0.906243	+	0.422757i	$0.138938\pi$
$194$	−6.33195	+	15.7879i	−0.454607	+	1.13350i
$195$	0.834970	+	0.834970i	0.0597934	+	0.0597934i
$196$	−0.652591	−	0.623802i	−0.0466136	−	0.0445573i
$197$	10.5221	−	10.5221i	0.749667	−	0.749667i	−0.224750	−	0.974416i	$-0.572157\pi$
$197$	10.5221	−	10.5221i	0.749667	−	0.749667i	0.974416	+	0.224750i	$0.0721565\pi$
$198$	−9.95567	+	4.25591i	−0.707518	+	0.302454i
$199$		−	4.85177i		−	0.343933i	−0.985103	−	0.171966i	$-0.944988\pi$
$199$		−	4.85177i		−	0.343933i	0.985103	−	0.171966i	$-0.0550121\pi$
$200$	5.73859	+	12.6283i	0.405780	+	0.892956i
$201$			8.80658i			0.621168i
$202$	−3.70987	−	8.67835i	−0.261026	−	0.610606i
$203$	2.88814	−	2.88814i	0.202708	−	0.202708i
$204$	0.330886	+	14.6702i	0.0231667	+	1.02712i
$205$	0.218916	+	0.218916i	0.0152898	+	0.0152898i
$206$	−16.4050	−	6.57945i	−1.14299	−	0.458412i
$207$	5.46041			0.379525
$208$	8.37977	−	9.17193i	0.581032	−	0.635959i
$209$	−21.1208			−1.46096
$210$	1.27703	+	0.512171i	0.0881234	+	0.0353431i
$211$	6.41924	+	6.41924i	0.441919	+	0.441919i	0.892657	−	0.450738i	$-0.148839\pi$
$211$	6.41924	+	6.41924i	0.441919	+	0.441919i	−0.450738	+	0.892657i	$0.648839\pi$
$212$	−18.7528	+	0.422967i	−1.28794	+	0.0290495i
$213$	10.8790	−	10.8790i	0.745414	−	0.745414i
$214$	3.46918	+	8.11529i	0.237148	+	0.554750i
$215$			0.0988679i			0.00674273i
$216$	5.47980	−	14.6083i	0.372853	−	0.993968i
$217$		−	12.9580i		−	0.879648i
$218$	4.35680	−	1.86247i	0.295080	−	0.126142i
$219$	−1.67357	+	1.67357i	−0.113089	+	0.113089i
$220$	−2.19550	+	2.29683i	−0.148021	+	0.154852i
$221$	13.1214	+	13.1214i	0.882644	+	0.882644i
$222$	3.32491	−	8.29021i	0.223153	−	0.556403i
$223$	−11.6797			−0.782128			−0.391064	−	0.920363i	$-0.627893\pi$
$223$	−11.6797			−0.782128			−0.391064	+	0.920363i	$0.627893\pi$
$224$	4.77733	−	13.6650i	0.319199	−	0.913032i
$225$	7.31679			0.487786
$226$	8.30533	−	20.7082i	0.552462	−	1.37749i
$227$	4.44346	+	4.44346i	0.294923	+	0.294923i	0.839021	−	0.544099i	$-0.183128\pi$
$227$	4.44346	+	4.44346i	0.294923	+	0.294923i	−0.544099	+	0.839021i	$0.683128\pi$
$228$	6.98507	−	7.30744i	0.462598	−	0.483947i
$229$	8.80443	−	8.80443i	0.581813	−	0.581813i	−0.353588	−	0.935401i	$-0.615038\pi$
$229$	8.80443	−	8.80443i	0.581813	−	0.581813i	0.935401	+	0.353588i	$0.115038\pi$
$230$	1.47344	−	0.629874i	0.0971555	−	0.0415327i
$231$		−	16.1260i		−	1.06101i
$232$	−4.22684	−	1.58556i	−0.277506	−	0.104097i
$233$		−	14.3469i		−	0.939897i	−0.882694	−	0.469948i	$-0.844272\pi$
$233$		−	14.3469i		−	0.939897i	0.882694	−	0.469948i	$-0.155728\pi$
$234$	−2.57593	−	6.02576i	−0.168394	−	0.393916i
$235$	2.06380	−	2.06380i	0.134628	−	0.134628i
$236$	−2.05691	+	0.0463934i	−0.133893	+	0.00301996i
$237$	3.01734	+	3.01734i	0.195997	+	0.195997i
$238$	20.0684	+	8.04870i	1.30084	+	0.521720i
$239$	−15.6376			−1.01152			−0.505758	−	0.862676i	$-0.668787\pi$
$239$	−15.6376			−1.01152			−0.505758	+	0.862676i	$0.668787\pi$
$240$	−0.0685663	−	1.51921i	−0.00442593	−	0.0980646i
$241$	−8.65892			−0.557770			−0.278885	−	0.960325i	$-0.589965\pi$
$241$	−8.65892			−0.557770			−0.278885	+	0.960325i	$0.589965\pi$
$242$	20.1249	+	8.07137i	1.29368	+	0.518847i
$243$	−9.70607	−	9.70607i	−0.622645	−	0.622645i
$244$	−0.159233	−	7.05978i	−0.0101938	−	0.451956i
$245$	−0.0988161	+	0.0988161i	−0.00631313	+	0.00631313i
$246$	0.682651	+	1.59689i	0.0435242	+	0.101814i
$247$		−	12.7836i		−	0.813401i
$248$	−13.0390	+	5.92523i	−0.827980	+	0.376253i
$249$			10.8330i			0.686513i
$250$	3.98731	−	1.70452i	0.252179	−	0.107803i
$251$	18.9552	−	18.9552i	1.19644	−	1.19644i	0.221221	−	0.975224i	$-0.428996\pi$
$251$	18.9552	−	18.9552i	1.19644	−	1.19644i	0.975224	−	0.221221i	$-0.0710041\pi$
$252$	−5.51979	−	5.27628i	−0.347714	−	0.332375i
$253$	−13.2800	−	13.2800i	−0.834907	−	0.834907i
$254$	−1.28473	+	3.20330i	−0.0806112	+	0.200993i
$255$	2.27149			0.142246
$256$	−15.9349	+	1.44131i	−0.995934	+	0.0900822i
$257$	−14.8963			−0.929204			−0.464602	−	0.885520i	$-0.653803\pi$
$257$	−14.8963			−0.929204			−0.464602	+	0.885520i	$0.653803\pi$
$258$	−0.206447	+	0.514749i	−0.0128529	+	0.0320469i
$259$	−9.30662	−	9.30662i	−0.578285	−	0.578285i
$260$	−1.39018	−	1.32885i	−0.0862151	−	0.0824117i
$261$	−1.68384	+	1.68384i	−0.104227	+	0.104227i
$262$	−12.9534	+	5.53740i	−0.800264	+	0.342102i
$263$			30.8174i			1.90028i	0.311822	+	0.950140i	$0.399061\pi$
$263$			30.8174i			1.90028i	−0.311822	+	0.950140i	$0.600939\pi$
$264$	−16.2268	+	7.37382i	−0.998689	+	0.453827i
$265$			2.90361i			0.178367i
$266$	−5.85509	−	13.6966i	−0.358998	−	0.839789i
$267$	−12.9389	+	12.9389i	−0.791847	+	0.791847i
$268$	−0.323416	−	14.3390i	−0.0197558	−	0.875897i
$269$	−17.0095	−	17.0095i	−1.03709	−	1.03709i	−0.999285	−	0.0377998i	$-0.987965\pi$
$269$	−17.0095	−	17.0095i	−1.03709	−	1.03709i	−0.0377998	−	0.999285i	$-0.512035\pi$
$270$	−2.24162	−	0.899033i	−0.136421	−	0.0547134i
$271$	15.3971			0.935305			0.467653	−	0.883912i	$-0.345100\pi$
$271$	15.3971			0.935305			0.467653	+	0.883912i	$0.345100\pi$
$272$	−1.07751	−	23.8742i	−0.0653337	−	1.44759i
$273$	9.76039			0.590726
$274$	−26.6823	−	10.7013i	−1.61194	−	0.646490i
$275$	−17.7948	−	17.7948i	−1.07307	−	1.07307i
$276$	8.98660	−	0.202692i	0.540930	−	0.0122006i
$277$	15.5010	−	15.5010i	0.931365	−	0.931365i	−0.0664260	−	0.997791i	$-0.521160\pi$
$277$	15.5010	−	15.5010i	0.931365	−	0.931365i	0.997791	+	0.0664260i	$0.0211596\pi$
$278$	5.12265	+	11.9832i	0.307236	+	0.718704i
$279$			7.55476i			0.452292i
$280$	−2.09809	−	0.787028i	−0.125385	−	0.0470339i
$281$			31.3069i			1.86762i	0.357776	+	0.933808i	$0.383535\pi$
$281$			31.3069i			1.86762i	−0.357776	+	0.933808i	$0.616465\pi$
$282$	15.0545	−	6.43560i	0.896484	−	0.383234i
$283$	11.9399	−	11.9399i	0.709756	−	0.709756i	−0.256728	−	0.966484i	$-0.582644\pi$
$283$	11.9399	−	11.9399i	0.709756	−	0.709756i	0.966484	+	0.256728i	$0.0826443\pi$
$284$	−17.3138	+	18.1128i	−1.02739	+	1.07480i
$285$	−1.10650	−	1.10650i	−0.0655435	−	0.0655435i
$286$	−8.39017	+	20.9198i	−0.496121	+	1.23701i
$287$	2.55903			0.151055
$288$	−2.78527	+	7.96695i	−0.164124	+	0.469457i
$289$	18.6962			1.09977
$290$	−0.260131	+	0.648602i	−0.0152754	+	0.0380872i
$291$	10.4445	+	10.4445i	0.612269	+	0.612269i
$292$	2.66348	−	2.78640i	0.155868	−	0.163062i
$293$	5.88002	−	5.88002i	0.343515	−	0.343515i	−0.514172	−	0.857687i	$-0.671901\pi$
$293$	5.88002	−	5.88002i	0.343515	−	0.343515i	0.857687	+	0.514172i	$0.171901\pi$
$294$	−0.720819	+	0.308140i	−0.0420390	+	0.0179711i
$295$			0.318484i			0.0185429i
$296$	−5.10922	+	13.6204i	−0.296968	+	0.791669i
$297$			28.3065i			1.64251i
$298$	−4.98941	−	11.6715i	−0.289029	−	0.676112i
$299$	8.03785	−	8.03785i	0.464841	−	0.464841i
$300$	12.0418	−	0.271601i	0.695232	−	0.0156809i
$301$	0.577859	+	0.577859i	0.0333073	+	0.0333073i
$302$	9.97994	+	4.00260i	0.574281	+	0.230324i
$303$	−8.19548			−0.470818
$304$	−11.1049	+	12.1546i	−0.636907	+	0.697116i
$305$	−1.09311			−0.0625914
$306$	−11.7002	−	4.69254i	−0.668857	−	0.268255i
$307$	12.1309	+	12.1309i	0.692345	+	0.692345i	0.962747	−	0.270402i	$-0.0871568\pi$
$307$	12.1309	+	12.1309i	0.692345	+	0.692345i	−0.270402	+	0.962747i	$0.587157\pi$
$308$	0.592216	+	26.2566i	0.0337446	+	1.49611i
$309$	−10.8528	+	10.8528i	−0.617393	+	0.617393i
$310$	0.871462	+	2.03857i	0.0494957	+	0.115783i
$311$		−	24.1098i		−	1.36714i	−0.729885	−	0.683570i	$-0.760426\pi$
$311$		−	24.1098i		−	1.36714i	0.729885	−	0.683570i	$-0.239574\pi$
$312$	−4.46307	−	9.82141i	−0.252672	−	0.556028i
$313$			4.68539i			0.264834i	0.991194	+	0.132417i	$0.0422737\pi$
$313$			4.68539i			0.264834i	−0.991194	+	0.132417i	$0.957726\pi$
$314$	−6.97603	+	2.98216i	−0.393680	+	0.168293i
$315$	−0.835813	+	0.835813i	−0.0470927	+	0.0470927i
$316$	−5.02369	−	4.80207i	−0.282605	−	0.270138i
$317$	−1.76120	−	1.76120i	−0.0989189	−	0.0989189i	0.655915	−	0.754834i	$-0.272283\pi$
$317$	−1.76120	−	1.76120i	−0.0989189	−	0.0989189i	−0.754834	+	0.655915i	$0.772283\pi$
$318$	−6.06307	+	15.1175i	−0.340000	+	0.847745i
$319$	8.19037			0.458572
$320$	0.167433	+	2.47109i	0.00935978	+	0.138138i
$321$	7.66375			0.427749
$322$	4.93042	−	12.2933i	0.274762	−	0.685081i
$323$	−17.3885	−	17.3885i	−0.967524	−	0.967524i
$324$	−3.32259	−	3.17602i	−0.184588	−	0.176445i
$325$	10.7705	−	10.7705i	0.597438	−	0.597438i
$326$	−25.0038	+	10.6888i	−1.38484	+	0.591998i
$327$		−	4.11438i		−	0.227526i
$328$	−1.17015	−	2.57502i	−0.0646107	−	0.142182i
$329$		−	24.1249i		−	1.33005i
$330$	1.08452	+	2.53696i	0.0597006	+	0.139655i
$331$	−16.9778	+	16.9778i	−0.933183	+	0.933183i	−0.997903	−	0.0647202i	$-0.979385\pi$
$331$	−16.9778	+	16.9778i	−0.933183	+	0.933183i	0.0647202	+	0.997903i	$0.479385\pi$
$332$	−0.397835	−	17.6385i	−0.0218340	−	0.968037i
$333$	5.42593	+	5.42593i	0.297339	+	0.297339i
$334$	−27.4374	−	11.0042i	−1.50131	−	0.602121i
$335$	−2.22021			−0.121303
$336$	−9.28017	−	8.47867i	−0.506275	−	0.462549i
$337$	−14.1568			−0.771171			−0.385585	−	0.922672i	$-0.626000\pi$
$337$	−14.1568			−0.771171			−0.385585	+	0.922672i	$0.626000\pi$
$338$	4.40168	+	1.76536i	0.239420	+	0.0960228i
$339$	−13.6996	−	13.6996i	−0.744060	−	0.744060i
$340$	−3.69848	+	0.0834190i	−0.200578	+	0.00452403i
$341$	18.3736	−	18.3736i	0.994984	−	0.994984i
$342$	3.41362	+	7.98533i	0.184587	+	0.431797i
$343$			19.0683i			1.02959i
$344$	0.317238	−	0.845706i	0.0171043	−	0.0455974i
$345$		−	1.39145i		−	0.0749133i
$346$	−3.49301	+	1.49321i	−0.187785	+	0.0802756i
$347$	3.61897	−	3.61897i	0.194276	−	0.194276i	−0.603265	−	0.797541i	$-0.706134\pi$
$347$	3.61897	−	3.61897i	0.194276	−	0.194276i	0.797541	+	0.603265i	$0.206134\pi$
$348$	−2.70871	+	2.83372i	−0.145202	+	0.151903i
$349$	−21.8985	−	21.8985i	−1.17220	−	1.17220i	−0.981684	−	0.190517i	$-0.938984\pi$
$349$	−21.8985	−	21.8985i	−1.17220	−	1.17220i	−0.190517	−	0.981684i	$-0.561016\pi$
$350$	6.60661	−	16.4727i	0.353138	−	0.880503i
$351$	−17.1328			−0.914481
$352$	26.1500	−	12.6021i	1.39380	−	0.671695i
$353$	−30.9347			−1.64649			−0.823245	−	0.567686i	$-0.807839\pi$
$353$	−30.9347			−1.64649			−0.823245	+	0.567686i	$0.807839\pi$
$354$	−0.665032	+	1.65817i	−0.0353461	+	0.0881306i
$355$	2.74267	+	2.74267i	0.145566	+	0.145566i
$356$	20.5922	−	21.5425i	1.09138	−	1.14175i
$357$	13.2763	−	13.2763i	0.702657	−	0.702657i
$358$	−7.97141	+	3.40767i	−0.421302	+	0.180101i
$359$		−	14.6257i		−	0.771914i	−0.922517	−	0.385957i	$-0.873871\pi$
$359$		−	14.6257i		−	0.771914i	0.922517	−	0.385957i	$-0.126129\pi$
$360$	1.22323	+	0.458851i	0.0644696	+	0.0241836i
$361$		−	2.05919i		−	0.108378i
$362$	−6.34865	−	14.8511i	−0.333678	−	0.780558i
$363$	13.3137	−	13.3137i	0.698788	−	0.698788i
$364$	−15.8921	+	0.358444i	−0.832970	+	0.0187876i
$365$	−0.421920	−	0.421920i	−0.0220843	−	0.0220843i
$366$	−5.69121	−	2.28254i	−0.297485	−	0.119310i
$367$	6.24009			0.325730			0.162865	−	0.986648i	$-0.447927\pi$
$367$	6.24009			0.325730			0.162865	+	0.986648i	$0.447927\pi$
$368$	−14.6247	+	0.660054i	−0.762365	+	0.0344077i
$369$	−1.49196			−0.0776682
$370$	2.09003	+	0.838235i	0.108655	+	0.0435778i
$371$	16.9709	+	16.9709i	0.881086	+	0.881086i
$372$	0.280435	+	12.4334i	0.0145399	+	0.644643i
$373$	−7.90117	+	7.90117i	−0.409107	+	0.409107i	−0.881427	−	0.472320i	$-0.843417\pi$
$373$	−7.90117	+	7.90117i	−0.409107	+	0.409107i	0.472320	+	0.881427i	$0.343417\pi$
$374$	17.0430	+	39.8680i	0.881274	+	2.06153i
$375$		−	3.76545i		−	0.194447i
$376$	−24.2757	+	11.0314i	−1.25192	+	0.568903i
$377$			4.95730i			0.255314i
$378$	−18.3564	+	7.84709i	−0.944149	+	0.403611i
$379$	−9.15392	+	9.15392i	−0.470206	+	0.470206i	−0.901981	−	0.431776i	$-0.857887\pi$
$379$	−9.15392	+	9.15392i	−0.470206	+	0.470206i	0.431776	+	0.901981i	$0.357887\pi$
$380$	1.84226	+	1.76099i	0.0945060	+	0.0903369i
$381$	2.11916	+	2.11916i	0.108568	+	0.108568i
$382$	13.1632	−	32.8208i	0.673490	−	1.67926i
$383$	7.34802			0.375466			0.187733	−	0.982220i	$-0.439886\pi$
$383$	7.34802			0.375466			0.187733	+	0.982220i	$0.439886\pi$
$384$	−4.28819	+	13.2152i	−0.218831	+	0.674384i
$385$	4.06548			0.207196
$386$	−13.2554	+	33.0506i	−0.674684	+	1.68223i
$387$	−0.336902	−	0.336902i	−0.0171257	−	0.0171257i
$388$	−17.3895	−	16.6224i	−0.882820	−	0.843874i
$389$	27.2871	−	27.2871i	1.38351	−	1.38351i	0.545207	−	0.838301i	$-0.316451\pi$
$389$	27.2871	−	27.2871i	1.38351	−	1.38351i	0.838301	−	0.545207i	$-0.183549\pi$
$390$	−1.53552	+	0.656413i	−0.0777540	+	0.0332388i
$391$		−	21.8665i		−	1.10584i
$392$	1.16233	−	0.528191i	0.0587068	−	0.0266777i
$393$			12.2327i			0.617056i
$394$	8.27195	+	19.3502i	0.416735	+	0.974850i
$395$	−0.760694	+	0.760694i	−0.0382747	+	0.0382747i
$396$	−0.345272	−	15.3081i	−0.0173506	−	0.769259i
$397$	−19.6809	−	19.6809i	−0.987755	−	0.987755i	0.0121707	−	0.999926i	$-0.496126\pi$
$397$	−19.6809	−	19.6809i	−0.987755	−	0.987755i	−0.999926	+	0.0121707i	$0.996126\pi$
$398$	6.36835	+	2.55412i	0.319216	+	0.128026i
$399$	−12.9345			−0.647533
$400$	−19.5967	+	0.884453i	−0.979833	+	0.0442226i
$401$	13.1634			0.657347			0.328673	−	0.944444i	$-0.393399\pi$
$401$	13.1634			0.657347			0.328673	+	0.944444i	$0.393399\pi$
$402$	−11.5594	−	4.63605i	−0.576529	−	0.231225i
$403$	11.1208	+	11.1208i	0.553965	+	0.553965i
$404$	13.3440	−	0.300974i	0.663890	−	0.0149740i
$405$	−0.503111	+	0.503111i	−0.0249998	+	0.0249998i
$406$	2.27052	+	5.31133i	0.112684	+	0.263597i
$407$		−	26.3923i		−	1.30822i
$408$	−19.4301	−	7.28853i	−0.961932	−	0.360836i
$409$		−	2.47574i		−	0.122417i	−0.998125	−	0.0612087i	$-0.980504\pi$
$409$		−	2.47574i		−	0.122417i	0.998125	−	0.0612087i	$-0.0194955\pi$
$410$	−0.402589	+	0.172101i	−0.0198825	+	0.00849949i
$411$	−17.6518	+	17.6518i	−0.870699	+	0.870699i
$412$	17.2721	−	18.0693i	0.850937	−	0.890208i
$413$	1.86147	+	1.86147i	0.0915967	+	0.0915967i
$414$	−2.87452	+	7.16724i	−0.141275	+	0.352251i
$415$	−2.73108			−0.134063
$416$	7.62755	+	15.8275i	0.373971	+	0.776007i
$417$	11.3164			0.554168
$418$	11.1186	−	27.7228i	0.543831	−	1.35597i
$419$	−24.5748	−	24.5748i	−1.20056	−	1.20056i	−0.973997	−	0.226560i	$-0.927252\pi$
$419$	−24.5748	−	24.5748i	−1.20056	−	1.20056i	−0.226560	−	0.973997i	$-0.572748\pi$
$420$	−1.34453	+	1.40658i	−0.0656065	+	0.0686342i
$421$	18.3945	−	18.3945i	0.896493	−	0.896493i	−0.0986315	−	0.995124i	$-0.531446\pi$
$421$	18.3945	−	18.3945i	0.896493	−	0.896493i	0.995124	+	0.0986315i	$0.0314465\pi$
$422$	−11.8051	+	5.04650i	−0.574662	+	0.245660i
$423$			14.0652i			0.683875i
$424$	9.31683	−	24.8372i	0.452465	−	1.20620i
$425$		−	29.3005i		−	1.42128i
$426$	8.55252	+	20.0065i	0.414371	+	0.969320i
$427$	−6.38898	+	6.38898i	−0.309184	+	0.309184i
$428$	−12.4783	+	0.281446i	−0.603160	+	0.0136042i
$429$	13.8396	+	13.8396i	0.668180	+	0.668180i
$430$	−0.129772	−	0.0520470i	−0.00625817	−	0.00250993i
$431$	11.5651			0.557071			0.278536	−	0.960426i	$-0.410151\pi$
$431$	11.5651			0.557071			0.278536	+	0.960426i	$0.410151\pi$
$432$	16.2898	+	14.8829i	0.783746	+	0.716055i
$433$	−39.6951			−1.90763			−0.953813	−	0.300400i	$-0.902880\pi$
$433$	−39.6951			−1.90763			−0.953813	+	0.300400i	$0.902880\pi$
$434$	17.0085	+	6.82149i	0.816433	+	0.327442i
$435$	0.429085	+	0.429085i	0.0205731	+	0.0205731i
$436$	0.151098	+	6.69912i	0.00723629	+	0.320829i
$437$	−10.6518	+	10.6518i	−0.509542	+	0.509542i
$438$	−1.31568	−	3.07771i	−0.0628656	−	0.147059i
$439$			35.0806i			1.67430i	0.546970	+	0.837152i	$0.315781\pi$
$439$			35.0806i			1.67430i	−0.546970	+	0.837152i	$0.684219\pi$
$440$	−1.85900	−	4.09090i	−0.0886242	−	0.195026i
$441$		−	0.673452i		−	0.0320691i
$442$	−24.1305	+	10.3155i	−1.14777	+	0.490656i
$443$	−5.89997	+	5.89997i	−0.280316	+	0.280316i	−0.833235	−	0.552919i	$-0.813514\pi$
$443$	−5.89997	+	5.89997i	−0.280316	+	0.280316i	0.552919	+	0.833235i	$0.313514\pi$
$444$	9.13125	+	8.72843i	0.433350	+	0.414233i
$445$	−3.26199	−	3.26199i	−0.154633	−	0.154633i
$446$	6.14852	−	15.3305i	0.291141	−	0.725921i
$447$	−11.0221			−0.521327
$448$	15.4215	+	13.4643i	0.728599	+	0.636129i
$449$	20.7901			0.981146			0.490573	−	0.871400i	$-0.336788\pi$
$449$	20.7901			0.981146			0.490573	+	0.871400i	$0.336788\pi$
$450$	−3.85177	+	9.60388i	−0.181574	+	0.452731i
$451$	3.62852	+	3.62852i	0.170860	+	0.170860i
$452$	22.8091	+	21.8028i	1.07285	+	1.02552i
$453$	6.60227	−	6.60227i	0.310202	−	0.310202i
$454$	−8.17157	+	3.49323i	−0.383511	+	0.163946i
$455$			2.46067i			0.115358i
$456$	5.91446	+	13.0153i	0.276970	+	0.609499i
$457$		−	23.7191i		−	1.10953i	−0.832005	−	0.554767i	$-0.812807\pi$
$457$		−	23.7191i		−	1.10953i	0.832005	−	0.554767i	$-0.187193\pi$
$458$	6.92163	+	16.1915i	0.323426	+	0.756577i
$459$	−23.3044	+	23.3044i	−1.08776	+	1.08776i
$460$	0.0511003	+	2.26559i	0.00238256	+	0.105634i
$461$	11.5518	+	11.5518i	0.538023	+	0.538023i	0.922948	−	0.384925i	$-0.125773\pi$
$461$	11.5518	+	11.5518i	0.538023	+	0.538023i	−0.384925	+	0.922948i	$0.625773\pi$
$462$	21.1667	+	8.48919i	0.984762	+	0.394953i
$463$	13.9111			0.646503			0.323252	−	0.946313i	$-0.395224\pi$
$463$	13.9111			0.646503			0.323252	+	0.946313i	$0.395224\pi$
$464$	4.30631	−	4.71339i	0.199915	−	0.218814i
$465$	1.92515			0.0892765
$466$	18.8315	+	7.55264i	0.872352	+	0.349869i
$467$	−18.7970	−	18.7970i	−0.869821	−	0.869821i	0.122631	−	0.992452i	$-0.460867\pi$
$467$	−18.7970	−	18.7970i	−0.869821	−	0.869821i	−0.992452	+	0.122631i	$0.960867\pi$
$468$	9.26535	−	0.208979i	0.428291	−	0.00966008i
$469$	−12.9766	+	12.9766i	−0.599203	+	0.599203i
$470$	1.62246	+	3.79536i	0.0748387	+	0.175067i
$471$			6.58788i			0.303554i
$472$	1.02192	−	2.72428i	0.0470378	−	0.125395i
$473$			1.63873i			0.0753488i
$474$	−5.54892	+	2.37209i	−0.254870	+	0.108954i
$475$	−14.2730	+	14.2730i	−0.654891	+	0.654891i
$476$	−21.1292	+	22.1043i	−0.968454	+	1.01315i
$477$	−9.89435	−	9.89435i	−0.453031	−	0.453031i
$478$	8.23212	−	20.5257i	0.376528	−	0.938823i
$479$	−10.3339			−0.472166			−0.236083	−	0.971733i	$-0.575864\pi$
$479$	−10.3339			−0.472166			−0.236083	+	0.971733i	$0.575864\pi$
$480$	2.03018	+	0.709759i	0.0926648	+	0.0323959i
$481$	15.9742			0.728360
$482$	4.55831	−	11.3655i	0.207625	−	0.517686i
$483$	−8.13271	−	8.13271i	−0.370051	−	0.370051i
$484$	−21.1887	+	22.1665i	−0.963122	+	1.00757i
$485$	−2.63314	+	2.63314i	−0.119565	+	0.119565i
$486$	17.8496	−	7.63045i	0.809674	−	0.346124i
$487$		−	5.49464i		−	0.248986i	−0.992220	−	0.124493i	$-0.960270\pi$
$487$		−	5.49464i		−	0.248986i	0.992220	−	0.124493i	$-0.0397304\pi$
$488$	9.35037	+	3.50747i	0.423271	+	0.158776i
$489$			23.6126i			1.06780i
$490$	−0.0776845	−	0.181724i	−0.00350943	−	0.00820945i
$491$	−9.86596	+	9.86596i	−0.445245	+	0.445245i	−0.893770	−	0.448525i	$-0.851949\pi$
$491$	−9.86596	+	9.86596i	−0.445245	+	0.445245i	0.448525	+	0.893770i	$0.351949\pi$
$492$	−2.45542	+	0.0553819i	−0.110699	+	0.00249681i
$493$	6.74303	+	6.74303i	0.303691	+	0.303691i
$494$	16.7795	+	6.72967i	0.754946	+	0.302782i
$495$	−2.37025			−0.106535
$496$	−0.913219	−	20.2340i	−0.0410047	−	0.908534i
$497$	32.0605			1.43811
$498$	−14.2192	−	5.70281i	−0.637177	−	0.255549i
$499$	1.36698	+	1.36698i	0.0611943	+	0.0611943i	0.737042	−	0.675847i	$-0.236222\pi$
$499$	1.36698	+	1.36698i	0.0611943	+	0.0611943i	−0.675847	+	0.737042i	$0.736222\pi$
$500$	0.138284	+	6.13098i	0.00618424	+	0.274186i
$501$	−18.1513	+	18.1513i	−0.810941	+	0.810941i
$502$	14.9017	+	34.8589i	0.665096	+	1.55583i
$503$			21.6743i			0.966411i	0.875507	+	0.483206i	$0.160528\pi$
$503$			21.6743i			0.966411i	−0.875507	+	0.483206i	$0.839472\pi$
$504$	9.83133	−	4.46758i	0.437922	−	0.199002i
$505$		−	2.06614i		−	0.0919422i
$506$	24.4221	−	10.4401i	1.08569	−	0.464119i
$507$	2.91195	−	2.91195i	0.129324	−	0.129324i
$508$	−3.52828	−	3.37263i	−0.156542	−	0.149636i
$509$	15.3746	+	15.3746i	0.681466	+	0.681466i	0.960330	−	0.278865i	$-0.0899581\pi$
$509$	15.3746	+	15.3746i	0.681466	+	0.681466i	−0.278865	+	0.960330i	$0.589958\pi$
$510$	−1.19578	+	2.98151i	−0.0529500	+	0.132024i
$511$	−4.93204			−0.218181
$512$	6.49679	−	21.6747i	0.287120	−	0.957895i
$513$	22.7044			1.00242
$514$	7.84184	−	19.5526i	0.345889	−	0.862428i
$515$	−2.73607	−	2.73607i	−0.120566	−	0.120566i
$516$	−0.566970	−	0.541959i	−0.0249595	−	0.0238584i
$517$	34.2074	−	34.2074i	1.50444	−	1.50444i
$518$	17.1150	−	7.31642i	0.751989	−	0.321465i
$519$			3.29865i			0.144795i
$520$	2.47605	−	1.12518i	0.108582	−	0.0493422i
$521$			26.2392i			1.14956i	0.818308	+	0.574780i	$0.194912\pi$
$521$			26.2392i			1.14956i	−0.818308	+	0.574780i	$0.805088\pi$
$522$	−1.32375	−	3.09660i	−0.0579391	−	0.135534i
$523$	8.75690	−	8.75690i	0.382912	−	0.382912i	−0.489238	−	0.872150i	$-0.662725\pi$
$523$	8.75690	−	8.75690i	0.382912	−	0.382912i	0.872150	+	0.489238i	$0.162725\pi$
$524$	−0.449237	−	19.9174i	−0.0196250	−	0.870098i
$525$	−10.8976	−	10.8976i	−0.475610	−	0.475610i
$526$	−40.4503	−	16.2232i	−1.76372	−	0.707364i
$527$	30.2535			1.31786
$528$	−1.13648	−	25.1808i	−0.0494589	−	1.09585i
$529$	9.60515			0.417615
$530$	−3.81123	−	1.52855i	−0.165549	−	0.0663959i
$531$	−1.08527	−	1.08527i	−0.0470966	−	0.0470966i
$532$	21.0601	−	0.475010i	0.913073	−	0.0205943i
$533$	−2.19620	+	2.19620i	−0.0951278	+	0.0951278i
$534$	−10.1719	−	23.7948i	−0.440183	−	1.02970i
$535$			1.93209i			0.0835316i
$536$	18.9914	+	7.12399i	0.820305	+	0.307709i
$537$			7.52787i			0.324852i
$538$	31.2806	−	13.3720i	1.34860	−	0.576509i
$539$	−1.63787	+	1.63787i	−0.0705480	+	0.0705480i
$540$	2.36011	−	2.46903i	0.101563	−	0.106250i
$541$	−2.23302	−	2.23302i	−0.0960052	−	0.0960052i	0.657473	−	0.753478i	$-0.271625\pi$
$541$	−2.23302	−	2.23302i	−0.0960052	−	0.0960052i	−0.753478	+	0.657473i	$0.771625\pi$
$542$	−8.10547	+	20.2099i	−0.348160	+	0.868090i
$543$	−14.0248			−0.601862
$544$	31.9041	+	11.1538i	1.36788	+	0.478214i
$545$	1.03727			0.0444317
$546$	−5.13816	+	12.8113i	−0.219893	+	0.548274i
$547$	−4.24298	−	4.24298i	−0.181417	−	0.181417i	0.610556	−	0.791973i	$-0.290946\pi$
$547$	−4.24298	−	4.24298i	−0.181417	−	0.181417i	−0.791973	+	0.610556i	$0.790946\pi$
$548$	28.0927	−	29.3892i	1.20006	−	1.25545i
$549$	3.72489	−	3.72489i	0.158974	−	0.158974i
$550$	32.7249	−	13.9894i	1.39539	−	0.596511i
$551$		−	6.56941i		−	0.279866i
$552$	−4.46476	+	11.9024i	−0.190033	+	0.506598i
$553$			8.89215i			0.378133i
$554$	12.1862	+	28.5065i	0.517740	+	1.21113i
$555$	1.38267	−	1.38267i	0.0586909	−	0.0586909i
$556$	−18.4256	+	0.415589i	−0.781421	+	0.0176249i
$557$	24.6420	+	24.6420i	1.04411	+	1.04411i	0.998981	+	0.0451338i	$0.0143714\pi$
$557$	24.6420	+	24.6420i	1.04411	+	1.04411i	0.0451338	+	0.998981i	$0.485629\pi$
$558$	−9.91624	−	3.97705i	−0.419788	−	0.168362i
$559$	−0.991855			−0.0419510
$560$	2.13754	−	2.33960i	0.0903274	−	0.0988663i
$561$	37.6497			1.58957
$562$	−41.0929	−	16.4809i	−1.73340	−	0.695205i
$563$	23.3514	+	23.3514i	0.984146	+	0.984146i	0.999876	−	0.0157303i	$-0.00500733\pi$
$563$	23.3514	+	23.3514i	0.984146	+	0.984146i	−0.0157303	+	0.999876i	$0.505007\pi$
$564$	0.522106	+	23.1482i	0.0219846	+	0.974714i
$565$	3.45378	−	3.45378i	0.145301	−	0.145301i
$566$	9.38662	+	21.9577i	0.394549	+	0.922951i
$567$			5.88113i			0.246984i
$568$	−14.6601	−	32.2609i	−0.615124	−	1.35364i
$569$		−	20.8572i		−	0.874381i	−0.899369	−	0.437191i	$-0.855973\pi$
$569$		−	20.8572i		−	0.874381i	0.899369	−	0.437191i	$-0.144027\pi$
$570$	2.03487	−	0.869878i	0.0852312	−	0.0364352i
$571$	−18.1403	+	18.1403i	−0.759148	+	0.759148i	−0.976167	−	0.217019i	$-0.930366\pi$
$571$	−18.1403	+	18.1403i	−0.759148	+	0.759148i	0.217019	+	0.976167i	$0.430366\pi$
$572$	−23.0421	−	22.0256i	−0.963437	−	0.920935i
$573$	−21.7127	−	21.7127i	−0.907061	−	0.907061i
$574$	−1.34715	+	3.35893i	−0.0562288	+	0.140199i
$575$	−17.9487			−0.748512
$576$	−8.99102	−	7.84994i	−0.374626	−	0.327081i
$577$	−2.46103			−0.102454			−0.0512271	−	0.998687i	$-0.516313\pi$
$577$	−2.46103			−0.102454			−0.0512271	+	0.998687i	$0.516313\pi$
$578$	−9.84222	+	24.5403i	−0.409382	+	1.02074i
$579$	21.8648	+	21.8648i	0.908669	+	0.908669i
$580$	−0.714403	−	0.682887i	−0.0296640	−	0.0283553i
$581$	−15.9625	+	15.9625i	−0.662237	+	0.662237i
$582$	−19.2076	+	8.21098i	−0.796181	+	0.340356i
$583$			48.1271i			1.99322i
$584$	2.25524	+	4.96287i	0.0933226	+	0.205365i
$585$		−	1.43461i		−	0.0593140i
$586$	4.62259	+	10.8134i	0.190958	+	0.446699i
$587$	13.3950	−	13.3950i	0.552871	−	0.552871i	−0.374397	−	0.927268i	$-0.622150\pi$
$587$	13.3950	−	13.3950i	0.552871	−	0.552871i	0.927268	+	0.374397i	$0.122150\pi$
$588$	−0.0249987	−	1.10835i	−0.00103093	−	0.0457075i
$589$	−14.7372	−	14.7372i	−0.607237	−	0.607237i
$590$	−0.418037	−	0.167660i	−0.0172103	−	0.00690244i
$591$	18.2736			0.751674
$592$	−15.1882	−	13.8765i	−0.624232	−	0.570319i
$593$	−9.14983			−0.375738			−0.187869	−	0.982194i	$-0.560158\pi$
$593$	−9.14983			−0.375738			−0.187869	+	0.982194i	$0.560158\pi$
$594$	−37.1546	−	14.9014i	−1.52447	−	0.611412i
$595$	3.34706	+	3.34706i	0.137216	+	0.137216i
$596$	17.9464	−	0.404779i	0.735112	−	0.0165804i
$597$	4.21300	−	4.21300i	0.172427	−	0.172427i
$598$	6.31897	+	14.7817i	0.258402	+	0.604469i
$599$			19.2655i			0.787165i	0.919289	+	0.393583i	$0.128765\pi$
$599$			19.2655i			0.787165i	−0.919289	+	0.393583i	$0.871235\pi$
$600$	−5.98265	+	15.9488i	−0.244240	+	0.651106i
$601$			4.15907i			0.169652i	0.996396	+	0.0848261i	$0.0270335\pi$
$601$			4.15907i			0.169652i	−0.996396	+	0.0848261i	$0.972967\pi$
$602$	−1.06269	+	0.454285i	−0.0433120	+	0.0185153i
$603$	7.56558	−	7.56558i	0.308094	−	0.308094i
$604$	−10.5075	+	10.9924i	−0.427543	+	0.447274i
$605$	3.35649	+	3.35649i	0.136461	+	0.136461i
$606$	4.31434	−	10.7572i	0.175258	−	0.436983i
$607$	−3.07772			−0.124921			−0.0624604	−	0.998047i	$-0.519895\pi$
$607$	−3.07772			−0.124921			−0.0624604	+	0.998047i	$0.519895\pi$
$608$	−10.1080	−	20.9746i	−0.409934	−	0.850632i
$609$	5.01580			0.203251
$610$	0.575447	−	1.43480i	0.0232992	−	0.0580933i
$611$	20.7043	+	20.7043i	0.837608	+	0.837608i
$612$	12.3187	−	12.8872i	0.497953	−	0.520934i
$613$	−21.0812	+	21.0812i	−0.851460	+	0.851460i	−0.990313	−	0.138853i	$-0.955659\pi$
$613$	−21.0812	+	21.0812i	−0.851460	+	0.851460i	0.138853	+	0.990313i	$0.455659\pi$
$614$	−22.3088	+	9.53671i	−0.900310	+	0.384870i
$615$			0.380189i			0.0153307i
$616$	−34.7757	−	13.0449i	−1.40115	−	0.525595i
$617$		−	6.54181i		−	0.263363i	−0.991292	−	0.131682i	$-0.957962\pi$
$617$		−	6.54181i		−	0.263363i	0.991292	−	0.131682i	$-0.0420376\pi$
$618$	−8.53193	−	19.9584i	−0.343205	−	0.802844i
$619$	−17.9520	+	17.9520i	−0.721553	+	0.721553i	−0.968922	−	0.247368i	$-0.920434\pi$
$619$	−17.9520	+	17.9520i	−0.721553	+	0.721553i	0.247368	+	0.968922i	$0.420434\pi$
$620$	−3.13456	+	0.0706998i	−0.125887	+	0.00283937i
$621$	14.2757	+	14.2757i	0.572863	+	0.572863i
$622$	31.6461	+	12.6921i	1.26889	+	0.508907i
$623$	−38.1312			−1.52769
$624$	15.2409	−	0.687865i	0.610125	−	0.0275367i
$625$	−23.5715			−0.942858
$626$	−6.14995	−	2.46653i	−0.245802	−	0.0985822i
$627$	−18.3402	−	18.3402i	−0.732435	−	0.732435i
$628$	−0.241936	−	10.7265i	−0.00965429	−	0.428035i
$629$	21.7284	−	21.7284i	0.866369	−	0.866369i
$630$	−0.657076	−	1.53707i	−0.0261785	−	0.0612383i
$631$		−	2.89723i		−	0.115337i	−0.998336	−	0.0576684i	$-0.981633\pi$
$631$		−	2.89723i		−	0.115337i	0.998336	−	0.0576684i	$-0.0183666\pi$
$632$	8.94774	−	4.06606i	0.355922	−	0.161739i
$633$			11.1482i			0.443102i
$634$	3.23887	−	1.38457i	0.128632	−	0.0549884i
$635$	−0.534256	+	0.534256i	−0.0212013	+	0.0212013i
$636$	−16.6511	−	15.9166i	−0.660260	−	0.631133i
$637$	−0.991336	−	0.991336i	−0.0392782	−	0.0392782i
$638$	−4.31165	+	10.7505i	−0.170700	+	0.425617i
$639$	−18.6918			−0.739438
$640$	−3.33165	−	1.08109i	−0.131695	−	0.0427336i
$641$	−24.7441			−0.977332			−0.488666	−	0.872471i	$-0.662516\pi$
$641$	−24.7441			−0.977332			−0.488666	+	0.872471i	$0.662516\pi$
$642$	−4.03443	+	10.0593i	−0.159226	+	0.397009i
$643$	−0.242784	−	0.242784i	−0.00957446	−	0.00957446i	0.702303	−	0.711878i	$-0.252155\pi$
$643$	−0.242784	−	0.242784i	−0.00957446	−	0.00957446i	−0.711878	+	0.702303i	$0.752155\pi$
$644$	13.5405	+	12.9432i	0.533571	+	0.510032i
$645$	−0.0858513	+	0.0858513i	−0.00338039	+	0.00338039i
$646$	31.9777	−	13.6700i	1.25815	−	0.537840i
$647$		−	1.38545i		−	0.0544678i	−0.999629	−	0.0272339i	$-0.991330\pi$
$647$		−	1.38545i		−	0.0544678i	0.999629	−	0.0272339i	$-0.00866988\pi$
$648$	5.91789	−	2.68923i	0.232477	−	0.105643i
$649$			5.27885i			0.207213i
$650$	8.46723	+	19.8070i	0.332112	+	0.776896i
$651$	11.2520	−	11.2520i	0.441001	−	0.441001i
$652$	−0.867159	−	38.4465i	−0.0339606	−	1.50568i
$653$	20.8682	+	20.8682i	0.816637	+	0.816637i	0.985619	−	0.168982i	$-0.0540480\pi$
$653$	20.8682	+	20.8682i	0.816637	+	0.816637i	−0.168982	+	0.985619i	$0.554048\pi$
$654$	5.40046	+	2.16593i	0.211175	+	0.0846947i
$655$	−3.08395			−0.120500
$656$	3.99593	−	0.180348i	0.156015	−	0.00704140i
$657$	2.87547			0.112183
$658$	31.6659	+	12.7001i	1.23446	+	0.495100i
$659$	−24.1341	−	24.1341i	−0.940130	−	0.940130i	0.0581764	−	0.998306i	$-0.481471\pi$
$659$	−24.1341	−	24.1341i	−0.940130	−	0.940130i	−0.998306	+	0.0581764i	$0.981471\pi$
$660$	−3.90089	+	0.0879843i	−0.151842	+	0.00342478i
$661$	−13.5545	+	13.5545i	−0.527209	+	0.527209i	−0.919739	−	0.392530i	$-0.871600\pi$
$661$	−13.5545	+	13.5545i	−0.527209	+	0.527209i	0.392530	+	0.919739i	$0.371600\pi$
$662$	−13.3471	−	31.2223i	−0.518751	−	1.21349i
$663$			22.7879i			0.885007i
$664$	23.3614	+	8.76323i	0.906598	+	0.340079i
$665$		−	3.26088i		−	0.126451i
$666$	−9.97834	+	4.26560i	−0.386653	+	0.165289i
$667$	4.13060	−	4.13060i	0.159937	−	0.159937i
$668$	28.8877	−	30.2209i	1.11770	−	1.16928i
$669$	−10.1420	−	10.1420i	−0.392111	−	0.392111i
$670$	1.16878	−	2.91420i	0.0451540	−	0.112586i
$671$	−18.1182			−0.699447
$672$	16.0143	−	7.71757i	0.617765	−	0.297712i
$673$	21.0358			0.810869			0.405435	−	0.914124i	$-0.367120\pi$
$673$	21.0358			0.810869			0.405435	+	0.914124i	$0.367120\pi$
$674$	7.45257	−	18.5820i	0.287062	−	0.715751i
$675$	19.1290	+	19.1290i	0.736274	+	0.736274i
$676$	−4.63435	+	4.84823i	−0.178244	+	0.186470i
$677$	2.83374	−	2.83374i	0.108910	−	0.108910i	−0.650552	−	0.759462i	$-0.725462\pi$
$677$	2.83374	−	2.83374i	0.108910	−	0.108910i	0.759462	+	0.650552i	$0.225462\pi$
$678$	25.1937	−	10.7700i	0.967560	−	0.413618i
$679$			30.7802i			1.18124i
$680$	1.83750	−	4.89847i	0.0704647	−	0.187848i
$681$			7.71690i			0.295712i
$682$	14.4444	+	33.7892i	0.553105	+	1.29386i
$683$	−10.9152	+	10.9152i	−0.417658	+	0.417658i	−0.884396	−	0.466738i	$-0.845429\pi$
$683$	−10.9152	+	10.9152i	−0.417658	+	0.417658i	0.466738	+	0.884396i	$0.345429\pi$
$684$	−12.2784	+	0.276939i	−0.469478	+	0.0105890i
$685$	−4.45015	−	4.45015i	−0.170032	−	0.170032i
$686$	−25.0287	−	10.0381i	−0.955600	−	0.383257i
$687$	15.2906			0.583371
$688$	0.943055	+	0.861606i	0.0359536	+	0.0328484i
$689$	−29.1294			−1.10974
$690$	1.82640	+	0.732503i	0.0695297	+	0.0278859i
$691$	−9.75576	−	9.75576i	−0.371127	−	0.371127i	0.496761	−	0.867887i	$-0.334523\pi$
$691$	−9.75576	−	9.75576i	−0.371127	−	0.371127i	−0.867887	+	0.496761i	$0.834523\pi$
$692$	−0.121141	−	5.37093i	−0.00460509	−	0.204172i
$693$	−13.8535	+	13.8535i	−0.526252	+	0.526252i
$694$	2.84506	+	6.65533i	0.107997	+	0.252633i
$695$			2.85296i			0.108219i
$696$	−2.29354	−	5.04716i	−0.0869366	−	0.191312i
$697$			5.97463i			0.226305i
$698$	40.2716	−	17.2156i	1.52430	−	0.651619i
$699$	12.4580	−	12.4580i	0.471207	−	0.471207i
$700$	18.1439	+	17.3434i	0.685773	+	0.655521i
$701$	6.53420	+	6.53420i	0.246793	+	0.246793i	0.819653	−	0.572860i	$-0.194166\pi$
$701$	6.53420	+	6.53420i	0.246793	+	0.246793i	−0.572860	+	0.819653i	$0.694166\pi$
$702$	9.01922	−	22.4882i	0.340408	−	0.848763i
$703$	−21.1690			−0.798402
$704$	2.77519	+	40.9581i	0.104594	+	1.54367i
$705$	3.58418			0.134988
$706$	16.2850	−	40.6044i	0.612893	−	1.52817i
$707$	−12.0761	−	12.0761i	−0.454169	−	0.454169i
$708$	−1.82639	−	1.74582i	−0.0686399	−	0.0656119i
$709$	−18.7273	+	18.7273i	−0.703320	+	0.703320i	−0.965122	−	0.261802i	$-0.915683\pi$
$709$	−18.7273	+	18.7273i	−0.703320	+	0.703320i	0.261802	+	0.965122i	$0.415683\pi$
$710$	−5.04380	+	2.15616i	−0.189291	+	0.0809191i
$711$		−	5.18428i		−	0.194426i
$712$	17.4360	+	38.3696i	0.653442	+	1.43796i
$713$		−	18.5325i		−	0.694046i
$714$	10.4372	+	24.4153i	0.390602	+	0.913719i
$715$	−3.48906	+	3.48906i	−0.130483	+	0.130483i
$716$	−0.276456	−	12.2570i	−0.0103317	−	0.458066i
$717$	−13.5789	−	13.5789i	−0.507112	−	0.507112i
$718$	19.1974	+	7.69939i	0.716441	+	0.287339i
$719$	−36.0694			−1.34516			−0.672581	−	0.740024i	$-0.734814\pi$
$719$	−36.0694			−1.34516			−0.672581	+	0.740024i	$0.734814\pi$
$720$	−1.24622	+	1.36403i	−0.0464440	+	0.0508344i
$721$	−31.9833			−1.19112
$722$	2.70286	+	1.08402i	0.100590	+	0.0403430i
$723$	−7.51892	−	7.51892i	−0.279632	−	0.279632i
$724$	22.8354	−	0.515052i	0.848673	−	0.0191418i
$725$	5.53488	−	5.53488i	0.205560	−	0.205560i
$726$	10.4666	+	24.4840i	0.388452	+	0.908688i
$727$			26.0414i			0.965821i	0.875670	+	0.482910i	$0.160420\pi$
$727$			26.0414i			0.965821i	−0.875670	+	0.482910i	$0.839580\pi$
$728$	7.89556	−	21.0483i	0.292629	−	0.780103i
$729$		−	23.7510i		−	0.879666i
$730$	0.775915	−	0.331693i	0.0287179	−	0.0122765i
$731$	−1.34914	+	1.34914i	−0.0498999	+	0.0498999i
$732$	5.99205	−	6.26859i	0.221473	−	0.231694i
$733$	36.5248	+	36.5248i	1.34907	+	1.34907i	0.886668	+	0.462407i	$0.153014\pi$
$733$	36.5248	+	36.5248i	1.34907	+	1.34907i	0.462407	+	0.886668i	$0.346986\pi$
$734$	−3.28497	+	8.19063i	−0.121250	+	0.302321i
$735$	−0.171613			−0.00633003
$736$	6.83250	−	19.5436i	0.251849	−	0.720387i
$737$	−36.7998			−1.35554
$738$	0.785411	−	1.95832i	0.0289114	−	0.0720866i
$739$	16.0393	+	16.0393i	0.590014	+	0.590014i	0.937635	−	0.347621i	$-0.113010\pi$
$739$	16.0393	+	16.0393i	0.590014	+	0.590014i	−0.347621	+	0.937635i	$0.613010\pi$
$740$	−2.20050	+	2.30206i	−0.0808921	+	0.0846254i
$741$	11.1006	−	11.1006i	0.407789	−	0.407789i
$742$	−31.2097	+	13.3417i	−1.14574	+	0.489790i
$743$		−	40.5434i		−	1.48739i	−0.668518	−	0.743696i	$-0.733071\pi$
$743$		−	40.5434i		−	1.48739i	0.668518	−	0.743696i	$-0.266929\pi$
$744$	−16.4675	−	6.17723i	−0.603728	−	0.226468i
$745$		−	2.77875i		−	0.101806i
$746$	−6.21152	−	14.5303i	−0.227420	−	0.531994i
$747$	9.30643	−	9.30643i	0.340504	−	0.340504i
$748$	−61.3020	+	1.38266i	−2.24142	+	0.0505552i
$749$	11.2926	+	11.2926i	0.412623	+	0.412623i
$750$	4.94246	+	1.98225i	0.180473	+	0.0723814i
$751$	−37.9825			−1.38600			−0.693001	−	0.720936i	$-0.743712\pi$
$751$	−37.9825			−1.38600			−0.693001	+	0.720936i	$0.743712\pi$
$752$	−1.70021	−	37.6711i	−0.0620001	−	1.37373i
$753$	32.9193			1.19965
$754$	−6.50686	−	2.60967i	−0.236966	−	0.0950385i
$755$	1.66448	+	1.66448i	0.0605767	+	0.0605767i
$756$	−0.636617	−	28.2252i	−0.0231535	−	1.02654i
$757$	23.4413	−	23.4413i	0.851989	−	0.851989i	−0.138389	−	0.990378i	$-0.544192\pi$
$757$	23.4413	−	23.4413i	0.851989	−	0.851989i	0.990378	+	0.138389i	$0.0441924\pi$
$758$	−7.19638	−	16.8342i	−0.261384	−	0.611445i
$759$		−	23.0632i		−	0.837142i
$760$	−3.28127	+	1.49108i	−0.119024	+	0.0540872i
$761$		−	18.4381i		−	0.668381i	−0.942506	−	0.334190i	$-0.891537\pi$
$761$		−	18.4381i		−	0.668381i	0.942506	−	0.334190i	$-0.108463\pi$
$762$	−3.89716	+	1.66598i	−0.141179	+	0.0603521i
$763$	6.06258	−	6.06258i	0.219480	−	0.219480i
$764$	36.1504	+	34.5557i	1.30788	+	1.25018i
$765$	−1.95140	−	1.95140i	−0.0705528	−	0.0705528i
$766$	−3.86822	+	9.64488i	−0.139764	+	0.348484i
$767$	−3.19508			−0.115368
$768$	−15.0886	−	12.5855i	−0.544462	−	0.454139i
$769$	−3.21262			−0.115850			−0.0579251	−	0.998321i	$-0.518448\pi$
$769$	−3.21262			−0.115850			−0.0579251	+	0.998321i	$0.518448\pi$
$770$	−2.14019	+	5.33628i	−0.0771271	+	0.192306i
$771$	−12.9351	−	12.9351i	−0.465846	−	0.465846i
$772$	−36.4036	−	34.7977i	−1.31020	−	1.25240i
$773$	−30.2772	+	30.2772i	−1.08900	+	1.08900i	−0.0933650	+	0.995632i	$0.529762\pi$
$773$	−30.2772	+	30.2772i	−1.08900	+	1.08900i	−0.995632	+	0.0933650i	$0.970238\pi$
$774$	0.619567	−	0.264856i	0.0222699	−	0.00952007i
$775$		−	24.8329i		−	0.892025i
$776$	30.9726	−	14.0747i	1.11185	−	0.505251i
$777$		−	16.1627i		−	0.579833i
$778$	21.4518	+	50.1812i	0.769084	+	1.79908i
$779$	2.91040	−	2.91040i	0.104276	−	0.104276i
$780$	−0.0532533	−	2.36105i	−0.00190678	−	0.0845392i
$781$	45.4595	+	45.4595i	1.62667	+	1.62667i
$782$	28.7016	+	11.5112i	1.02637	+	0.411639i
$783$	−8.80443			−0.314645
$784$	0.0814068	+	1.80372i	0.00290739	+	0.0644184i
$785$	−1.66086			−0.0592785
$786$	−16.0564	−	6.43964i	−0.572712	−	0.229694i
$787$	22.0863	+	22.0863i	0.787290	+	0.787290i	0.981049	−	0.193759i	$-0.0620679\pi$
$787$	22.0863	+	22.0863i	0.787290	+	0.787290i	−0.193759	+	0.981049i	$0.562068\pi$
$788$	−29.7533	+	0.671085i	−1.05992	+	0.0239064i
$789$	−26.7601	+	26.7601i	−0.952684	+	0.952684i
$790$	−0.598021	−	1.39893i	−0.0212766	−	0.0497715i
$791$		−	40.3730i		−	1.43550i
$792$	20.2749	+	7.60542i	0.720436	+	0.270247i
$793$		−	10.9662i		−	0.389423i
$794$	36.1934	−	15.4722i	1.28445	−	0.549087i
$795$	−2.52133	+	2.52133i	−0.0894225	+	0.0894225i
$796$	−6.70497	+	7.01441i	−0.237651	+	0.248619i
$797$	−11.2555	−	11.2555i	−0.398691	−	0.398691i	0.479080	−	0.877771i	$-0.340970\pi$
$797$	−11.2555	−	11.2555i	−0.398691	−	0.398691i	−0.877771	+	0.479080i	$0.840970\pi$
$798$	6.80909	−	16.9775i	0.241039	−	0.600999i
$799$	56.3250			1.99264
$800$	9.15535	−	26.1878i	0.323690	−	0.925879i
$801$	22.2311			0.785499
$802$	−6.92958	+	17.2780i	−0.244692	+	0.610107i
$803$	−6.99328	−	6.99328i	−0.246788	−	0.246788i
$804$	12.1704	−	12.7321i	0.429216	−	0.449025i
$805$	2.05032	−	2.05032i	0.0722643	−	0.0722643i
$806$	−20.4512	+	8.74262i	−0.720364	+	0.307946i
$807$		−	29.5401i		−	1.03986i
$808$	−6.62964	+	17.6736i	−0.233230	+	0.621754i
$809$		−	2.64773i		−	0.0930892i	−0.998916	−	0.0465446i	$-0.985179\pi$
$809$		−	2.64773i		−	0.0930892i	0.998916	−	0.0465446i	$-0.0148210\pi$
$810$	−0.395522	−	0.925227i	−0.0138972	−	0.0325092i
$811$	16.7257	−	16.7257i	0.587317	−	0.587317i	−0.349587	−	0.936904i	$-0.613678\pi$
$811$	16.7257	−	16.7257i	0.587317	−	0.587317i	0.936904	+	0.349587i	$0.113678\pi$
$812$	−8.16682	+	0.184202i	−0.286599	+	0.00646423i
$813$	13.3699	+	13.3699i	0.468905	+	0.468905i
$814$	34.6420	+	13.8937i	1.21420	+	0.486973i
$815$	−5.95292			−0.208522
$816$	19.7954	−	21.6667i	0.692977	−	0.758485i
$817$	1.31441			0.0459852
$818$	3.24961	+	1.30330i	0.113620	+	0.0455689i
$819$	−8.38498	−	8.38498i	−0.292995	−	0.292995i
$820$	−0.0139622	−	0.619031i	−0.000487581	−	0.0216175i
$821$	−16.2301	+	16.2301i	−0.566436	+	0.566436i	−0.931128	−	0.364692i	$-0.881174\pi$
$821$	−16.2301	+	16.2301i	−0.566436	+	0.566436i	0.364692	+	0.931128i	$0.381174\pi$
$822$	−13.8770	−	32.4618i	−0.484016	−	1.13224i
$823$		−	13.1785i		−	0.459374i	−0.973265	−	0.229687i	$-0.926230\pi$
$823$		−	13.1785i		−	0.459374i	0.973265	−	0.229687i	$-0.0737703\pi$
$824$	14.6248	+	32.1833i	0.509480	+	1.12116i
$825$		−	30.9040i		−	1.07594i
$826$	−3.42326	+	1.46340i	−0.119110	+	0.0509180i
$827$	−25.2430	+	25.2430i	−0.877786	+	0.877786i	−0.993305	−	0.115519i	$-0.963147\pi$
$827$	−25.2430	+	25.2430i	−0.877786	+	0.877786i	0.115519	+	0.993305i	$0.463147\pi$
$828$	−7.89436	−	7.54610i	−0.274348	−	0.262245i
$829$	8.68647	+	8.68647i	0.301694	+	0.301694i	0.841676	−	0.539983i	$-0.181569\pi$
$829$	8.68647	+	8.68647i	0.301694	+	0.301694i	−0.539983	+	0.841676i	$0.681569\pi$
$830$	1.43772	−	3.58477i	0.0499041	−	0.124429i
$831$	26.9204			0.933859
$832$	−24.7903	+	1.67971i	−0.859448	+	0.0582334i
$833$	−2.69687			−0.0934412
$834$	−5.95731	+	14.8538i	−0.206285	+	0.514343i
$835$	−4.57609	−	4.57609i	−0.158362	−	0.158362i
$836$	30.5353	+	29.1883i	1.05609	+	1.00950i
$837$	−19.7511	+	19.7511i	−0.682698	+	0.682698i
$838$	45.1933	−	19.3195i	1.56118	−	0.667382i
$839$			29.1174i			1.00524i	0.864506	+	0.502622i	$0.167631\pi$
$839$			29.1174i			1.00524i	−0.864506	+	0.502622i	$0.832369\pi$
$840$	−1.13845	−	2.50528i	−0.0392804	−	0.0864402i
$841$		−	26.4525i		−	0.912154i
$842$	14.4609	+	33.8277i	0.498354	+	1.16578i
$843$	−27.1852	+	27.1852i	−0.936308	+	0.936308i
$844$	−0.409412	−	18.1517i	−0.0140925	−	0.624809i
$845$	0.734125	+	0.734125i	0.0252547	+	0.0252547i
$846$	−18.4618	−	7.40436i	−0.634729	−	0.254567i
$847$	39.2357			1.34815
$848$	27.6962	+	25.3041i	0.951092	+	0.868948i
$849$	20.7360			0.711656
$850$	38.4593	+	15.4246i	1.31914	+	0.529061i
$851$	−13.3103	−	13.3103i	−0.456270	−	0.456270i
$852$	−30.7625	+	0.693847i	−1.05391	+	0.0237708i
$853$	14.8030	−	14.8030i	0.506844	−	0.506844i	−0.406713	−	0.913556i	$-0.633325\pi$
$853$	14.8030	−	14.8030i	0.506844	−	0.506844i	0.913556	+	0.406713i	$0.133325\pi$
$854$	−5.02271	−	11.7494i	−0.171874	−	0.402056i
$855$			1.90115i			0.0650180i
$856$	6.19951	−	16.5269i	0.211895	−	0.564878i
$857$			8.99709i			0.307335i	0.988123	+	0.153667i	$0.0491084\pi$
$857$			8.99709i			0.307335i	−0.988123	+	0.153667i	$0.950892\pi$
$858$	−25.4511	+	10.8800i	−0.868886	+	0.371437i
$859$	5.82477	−	5.82477i	0.198739	−	0.198739i	−0.600721	−	0.799459i	$-0.705120\pi$
$859$	5.82477	−	5.82477i	0.198739	−	0.198739i	0.799459	+	0.600721i	$0.205120\pi$
$860$	0.136632	−	0.142938i	0.00465911	−	0.00487413i
$861$	2.22211	+	2.22211i	0.0757295	+	0.0757295i
$862$	−6.08821	+	15.1801i	−0.207365	+	0.517038i
$863$	−1.41766			−0.0482578			−0.0241289	−	0.999709i	$-0.507681\pi$
$863$	−1.41766			−0.0482578			−0.0241289	+	0.999709i	$0.507681\pi$
$864$	−28.1105	+	13.5469i	−0.956340	+	0.460876i
$865$	−0.831616			−0.0282758
$866$	20.8967	−	52.1031i	0.710099	−	1.77054i
$867$	16.2347	+	16.2347i	0.551359	+	0.551359i
$868$	−17.9075	+	18.7340i	−0.607821	+	0.635873i
$869$	−12.6084	+	12.6084i	−0.427712	+	0.427712i
$870$	−0.789093	+	0.337326i	−0.0267528	+	0.0114364i
$871$		−	22.2734i		−	0.754706i
$872$	−8.87268	−	3.32829i	−0.300467	−	0.112710i
$873$		−	17.9454i		−	0.607360i
$874$	−8.37390	−	19.5887i	−0.283251	−	0.662598i
$875$	5.54843	−	5.54843i	0.187571	−	0.187571i
$876$	4.73236	−	0.106738i	0.159892	−	0.00360635i
$877$	26.9895	+	26.9895i	0.911372	+	0.911372i	0.996380	−	0.0850084i	$-0.0270917\pi$
$877$	26.9895	+	26.9895i	0.911372	+	0.911372i	−0.0850084	+	0.996380i	$0.527092\pi$
$878$	−46.0461	−	18.4675i	−1.55398	−	0.623247i
$879$	10.2118			0.344434
$880$	6.34827	−	0.286515i	0.214000	−	0.00965843i
$881$	45.0143			1.51657			0.758285	−	0.651923i	$-0.226038\pi$
$881$	45.0143			1.51657			0.758285	+	0.651923i	$0.226038\pi$
$882$	0.883961	+	0.354525i	0.0297645	+	0.0119375i
$883$	15.1744	+	15.1744i	0.510658	+	0.510658i	0.914728	−	0.404070i	$-0.132405\pi$
$883$	15.1744	+	15.1744i	0.510658	+	0.510658i	−0.404070	+	0.914728i	$0.632405\pi$
$884$	−0.836870	−	37.1036i	−0.0281470	−	1.24793i
$885$	−0.276554	+	0.276554i	−0.00929626	+	0.00929626i
$886$	−4.63827	−	10.8501i	−0.155826	−	0.364517i
$887$		−	53.0117i		−	1.77996i	−0.456002	−	0.889979i	$-0.650719\pi$
$887$		−	53.0117i		−	1.77996i	0.456002	−	0.889979i	$-0.349281\pi$
$888$	−16.2637	+	7.39061i	−0.545775	+	0.248013i
$889$			6.24520i			0.209457i
$890$	5.99885	−	2.56442i	0.201082	−	0.0859597i
$891$	−8.33902	+	8.33902i	−0.279368	+	0.279368i
$892$	16.8858	+	16.1409i	0.565378	+	0.540437i
$893$	−27.4374	−	27.4374i	−0.918157	−	0.918157i
$894$	5.80236	−	14.4674i	0.194060	−	0.483862i
$895$	−1.89783			−0.0634376
$896$	−25.7914	+	13.1540i	−0.861629	+	0.439444i
$897$	13.9592			0.466085
$898$	−10.9445	+	27.2887i	−0.365224	+	0.910636i
$899$	5.71489	+	5.71489i	0.190602	+	0.190602i
$900$	−10.5782	−	10.1115i	−0.352607	−	0.337051i
$901$	−39.6225	+	39.6225i	−1.32002	+	1.32002i
$902$	−6.67289	+	2.85257i	−0.222183	+	0.0949801i
$903$			1.00356i			0.0333964i
$904$	−40.6254	+	18.4611i	−1.35118	+	0.614007i
$905$		−	3.53576i		−	0.117533i
$906$	5.19039	+	12.1416i	0.172439	+	0.403379i
$907$	−16.3795	+	16.3795i	−0.543872	+	0.543872i	−0.924662	−	0.380790i	$-0.875652\pi$
$907$	−16.3795	+	16.3795i	−0.543872	+	0.543872i	0.380790	+	0.924662i	$0.375652\pi$
$908$	−0.283398	−	12.5648i	−0.00940490	−	0.416977i
$909$	7.04059	+	7.04059i	0.233522	+	0.233522i
$910$	−3.22983	−	1.29537i	−0.107068	−	0.0429411i
$911$	44.9463			1.48914			0.744568	−	0.667546i	$-0.232655\pi$
$911$	44.9463			1.48914			0.744568	+	0.667546i	$0.232655\pi$
$912$	−20.1972	+	0.911559i	−0.668797	+	0.0301847i
$913$	−45.2674			−1.49813
$914$	31.1333	+	12.4865i	1.02980	+	0.413016i
$915$	−0.949197	−	0.949197i	−0.0313795	−	0.0313795i
$916$	−24.8964	+	0.561536i	−0.822599	+	0.0185537i
$917$	−18.0249	+	18.0249i	−0.595236	+	0.595236i
$918$	−18.3208	−	42.8571i	−0.604677	−	1.41450i
$919$			13.1081i			0.432395i	0.976350	+	0.216198i	$0.0693656\pi$
$919$			13.1081i			0.432395i	−0.976350	+	0.216198i	$0.930634\pi$
$920$	−3.00067	−	1.12560i	−0.0989293	−	0.0371100i
$921$			21.0675i			0.694198i
$922$	−21.2440	+	9.08151i	−0.699633	+	0.299084i
$923$	−27.5148	+	27.5148i	−0.905661	+	0.905661i
$924$	−22.2855	+	23.3140i	−0.733139	+	0.766974i
$925$	−17.8353	−	17.8353i	−0.586422	−	0.586422i
$926$	−7.32321	+	18.2594i	−0.240656	+	0.600043i
$927$	18.6469			0.612443
$928$	3.91975	+	8.13365i	0.128672	+	0.267000i
$929$	−33.7893			−1.10859			−0.554296	−	0.832320i	$-0.687012\pi$
$929$	−33.7893			−1.10859			−0.554296	+	0.832320i	$0.687012\pi$
$930$	−1.01345	+	2.52691i	−0.0332325	+	0.0828607i
$931$	1.31372	+	1.31372i	0.0430554	+	0.0430554i
$932$	−19.8269	+	20.7419i	−0.649452	+	0.679425i
$933$	20.9356	−	20.9356i	0.685400	−	0.685400i
$934$	34.5679	−	14.7773i	1.13110	−	0.483528i
$935$			9.49179i			0.310415i
$936$	−4.60326	+	12.2716i	−0.150462	+	0.401108i
$937$			3.91442i			0.127879i	0.997954	+	0.0639393i	$0.0203664\pi$
$937$			3.91442i			0.127879i	−0.997954	+	0.0639393i	$0.979634\pi$
$938$	−10.2016	−	23.8641i	−0.333093	−	0.779190i
$939$	−4.06853	+	4.06853i	−0.132771	+	0.132771i
$940$	−5.83584	+	0.131627i	−0.190344	+	0.00429320i
$941$	4.06482	+	4.06482i	0.132509	+	0.132509i	0.770251	−	0.637741i	$-0.220131\pi$
$941$	4.06482	+	4.06482i	0.132509	+	0.132509i	−0.637741	+	0.770251i	$0.720131\pi$
$942$	−8.64714	−	3.46806i	−0.281739	−	0.112995i
$943$	3.65990			0.119183
$944$	3.03788	+	2.77550i	0.0988744	+	0.0903349i
$945$	−4.37029			−0.142165
$946$	−2.15096	−	0.862675i	−0.0699339	−	0.0280480i
$947$	−4.66579	−	4.66579i	−0.151618	−	0.151618i	0.627222	−	0.778840i	$-0.284192\pi$
$947$	−4.66579	−	4.66579i	−0.151618	−	0.151618i	−0.778840	+	0.627222i	$0.784192\pi$
$948$	−0.192442	−	8.53215i	−0.00625023	−	0.277111i
$949$	4.23275	−	4.23275i	0.137401	−	0.137401i
$950$	−11.2208	−	26.2483i	−0.364050	−	0.851606i
$951$		−	3.05866i		−	0.0991837i
$952$	−17.8907	−	39.3701i	−0.579840	−	1.27599i
$953$		−	17.6438i		−	0.571539i	−0.958298	−	0.285769i	$-0.907751\pi$
$953$		−	17.6438i		−	0.571539i	0.958298	−	0.285769i	$-0.0922491\pi$
$954$	18.1958	−	7.77846i	0.589111	−	0.251837i
$955$	5.47394	−	5.47394i	0.177133	−	0.177133i
$956$	22.6080	+	21.6107i	0.731196	+	0.698939i
$957$	7.11205	+	7.11205i	0.229900	+	0.229900i
$958$	5.44006	−	13.5640i	0.175760	−	0.438235i
$959$	−52.0201			−1.67982
$960$	−2.00037	+	2.29114i	−0.0645615	+	0.0739463i
$961$	−5.35940			−0.172884
$962$	−8.40928	+	20.9674i	−0.271126	+	0.676016i
$963$	−6.58379	−	6.58379i	−0.212160	−	0.212160i
$964$	12.5186	+	11.9663i	0.403196	+	0.385409i
$965$	−5.51228	+	5.51228i	−0.177447	+	0.177447i
$966$	14.9562	−	6.39355i	0.481206	−	0.205709i
$967$			21.8739i			0.703417i	0.936110	+	0.351708i	$0.114399\pi$
$967$			21.8739i			0.703417i	−0.936110	+	0.351708i	$0.885601\pi$
$968$	−17.9411	−	39.4810i	−0.576648	−	1.26897i
$969$		−	30.1984i		−	0.970114i
$970$	−2.07005	−	4.84238i	−0.0664654	−	0.155480i
$971$	−21.0612	+	21.0612i	−0.675885	+	0.675885i	−0.959066	−	0.283182i	$-0.908610\pi$
$971$	−21.0612	+	21.0612i	−0.675885	+	0.675885i	0.283182	+	0.959066i	$0.408610\pi$
$972$	0.619042	+	27.4459i	0.0198558	+	0.880329i
$973$	16.6749	+	16.6749i	0.534572	+	0.534572i
$974$	7.21217	+	2.89254i	0.231093	+	0.0926831i
$975$	18.7050			0.599038
$976$	−9.52616	+	10.4267i	−0.304925	+	0.333750i
$977$	51.3633			1.64326			0.821628	−	0.570024i	$-0.193066\pi$
$977$	51.3633			1.64326			0.821628	+	0.570024i	$0.193066\pi$
$978$	−30.9935	−	12.4304i	−0.991063	−	0.397480i
$979$	−54.0673	−	54.0673i	−1.72800	−	1.72800i
$980$	0.279423	−	0.00630237i	0.00892585	−	0.000201322i
$981$	−3.53459	+	3.53459i	−0.112851	+	0.112851i
$982$	−7.75615	−	18.1436i	−0.247509	−	0.578986i
$983$		−	48.8409i		−	1.55778i	−0.627159	−	0.778891i	$-0.715782\pi$
$983$		−	48.8409i		−	1.55778i	0.627159	−	0.778891i	$-0.284218\pi$
$984$	1.21991	−	3.25210i	0.0388895	−	0.103673i
$985$			4.60690i			0.146788i
$986$	−12.4005	+	5.30104i	−0.394912	+	0.168820i
$987$	20.9487	−	20.9487i	0.666804	−	0.666804i
$988$	−17.6665	+	18.4818i	−0.562045	+	0.587984i
$989$	0.826450	+	0.826450i	0.0262796	+	0.0262796i
$990$	1.24777	−	3.11114i	0.0396567	−	0.0988787i
$991$	−57.6644			−1.83177			−0.915885	−	0.401440i	$-0.868510\pi$
$991$	−57.6644			−1.83177			−0.915885	+	0.401440i	$0.868510\pi$
$992$	27.0396	+	9.45312i	0.858507	+	0.300137i
$993$	−29.4851			−0.935682
$994$	−16.8776	+	42.0820i	−0.535325	+	1.33476i
$995$	1.06213	+	1.06213i	0.0336718	+	0.0336718i
$996$	14.9708	−	15.6617i	0.474368	−	0.496261i
$997$	−13.1724	+	13.1724i	−0.417175	+	0.417175i	−0.884229	−	0.467054i	$-0.845315\pi$
$997$	−13.1724	+	13.1724i	−0.417175	+	0.417175i	0.467054	+	0.884229i	$0.345315\pi$
$998$	−2.51389	+	1.07465i	−0.0795757	+	0.0340175i
$999$			28.3710i			0.897619i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	656.2.n.f.493.11	yes	66
16.5	even	4	inner	656.2.n.f.165.11	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
656.2.n.f.165.11	✓	66	16.5	even	4	inner
656.2.n.f.493.11	yes	66	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 656 = 2^{4} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	656.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.526430 + 1.31258i) q^{2} +(0.868344 + 0.868344i) q^{3} +(-1.44574 - 1.38196i) q^{4} +(-0.218916 + 0.218916i) q^{5} +(-1.59689 + 0.682651i) q^{6} +2.55903i q^{7} +(2.57502 - 1.17015i) q^{8} -1.49196i q^{9} +(-0.172101 - 0.402589i) q^{10} +(-3.62852 + 3.62852i) q^{11} +(-0.0553819 - 2.45542i) q^{12} +(-2.19620 - 2.19620i) q^{13} +(-3.35893 - 1.34715i) q^{14} -0.380189 q^{15} +(0.180348 + 3.99593i) q^{16} -5.97463 q^{17} +(1.95832 + 0.785411i) q^{18} +(2.91040 + 2.91040i) q^{19} +(0.619031 - 0.0139622i) q^{20} +(-2.22211 + 2.22211i) q^{21} +(-2.85257 - 6.67289i) q^{22} +3.65990i q^{23} +(3.25210 + 1.21991i) q^{24} +4.90415i q^{25} +(4.03883 - 1.72654i) q^{26} +(3.90056 - 3.90056i) q^{27} +(3.53648 - 3.69969i) q^{28} +(-1.12861 - 1.12861i) q^{29} +(0.200143 - 0.499029i) q^{30} -5.06366 q^{31} +(-5.33993 - 1.86686i) q^{32} -6.30160 q^{33} +(3.14522 - 7.84219i) q^{34} +(-0.560212 - 0.560212i) q^{35} +(-2.06183 + 2.15699i) q^{36} +(-3.63678 + 3.63678i) q^{37} +(-5.35225 + 2.28801i) q^{38} -3.81411i q^{39} +(-0.307550 + 0.819879i) q^{40} -1.00000i q^{41} +(-1.74692 - 4.08649i) q^{42} +(0.225812 - 0.225812i) q^{43} +(10.2604 - 0.231422i) q^{44} +(0.326614 + 0.326614i) q^{45} +(-4.80392 - 1.92668i) q^{46} -9.42737 q^{47} +(-3.31324 + 3.62645i) q^{48} +0.451388 q^{49} +(-6.43710 - 2.58169i) q^{50} +(-5.18803 - 5.18803i) q^{51} +(0.140071 + 6.21020i) q^{52} +(6.63179 - 6.63179i) q^{53} +(3.06644 + 7.17318i) q^{54} -1.58868i q^{55} +(2.99444 + 6.58955i) q^{56} +5.05445i q^{57} +(2.07553 - 0.887260i) q^{58} +(0.727412 - 0.727412i) q^{59} +(0.549656 + 0.525408i) q^{60} +(2.49664 + 2.49664i) q^{61} +(2.66566 - 6.64646i) q^{62} +3.81796 q^{63} +(5.26150 - 6.02633i) q^{64} +0.961565 q^{65} +(3.31735 - 8.27137i) q^{66} +(5.07091 + 5.07091i) q^{67} +(8.63778 + 8.25672i) q^{68} +(-3.17805 + 3.17805i) q^{69} +(1.03024 - 0.440412i) q^{70} -12.5284i q^{71} +(-1.74581 - 3.84183i) q^{72} +1.92731i q^{73} +(-2.85907 - 6.68809i) q^{74} +(-4.25849 + 4.25849i) q^{75} +(-0.185621 - 8.22975i) q^{76} +(-9.28547 - 9.28547i) q^{77} +(5.00633 + 2.00786i) q^{78} +3.47482 q^{79} +(-0.914255 - 0.835293i) q^{80} +2.29819 q^{81} +(1.31258 + 0.526430i) q^{82} +(6.23773 + 6.23773i) q^{83} +(6.28349 - 0.141724i) q^{84} +(1.30794 - 1.30794i) q^{85} +(0.177523 + 0.415271i) q^{86} -1.96004i q^{87} +(-5.09761 + 13.5894i) q^{88} +14.9007i q^{89} +(-0.600646 + 0.256768i) q^{90} +(5.62012 - 5.62012i) q^{91} +(5.05785 - 5.29127i) q^{92} +(-4.39699 - 4.39699i) q^{93} +(4.96285 - 12.3742i) q^{94} -1.27427 q^{95} +(-3.01582 - 6.25797i) q^{96} +12.0281 q^{97} +(-0.237624 + 0.592484i) q^{98} +(5.41360 + 5.41360i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 2 q^{2} + 8 q^{3} - 8 q^{4} - 6 q^{5} + 2 q^{6} + 4 q^{8} + 6 q^{10} - 8 q^{11} - 16 q^{12} + 16 q^{14} + 32 q^{15} + 44 q^{16} - 4 q^{17} - 20 q^{18} - 16 q^{19} + 4 q^{20} - 24 q^{21} - 12 q^{22}+ \cdots - 40 q^{99}+O(q^{100}) \) 66 * q - 2 * q^2 + 8 * q^3 - 8 * q^4 - 6 * q^5 + 2 * q^6 + 4 * q^8 + 6 * q^10 - 8 * q^11 - 16 * q^12 + 16 * q^14 + 32 * q^15 + 44 * q^16 - 4 * q^17 - 20 * q^18 - 16 * q^19 + 4 * q^20 - 24 * q^21 - 12 * q^22 + 24 * q^24 + 20 * q^26 + 32 * q^27 - 16 * q^28 - 12 * q^29 - 42 * q^30 - 28 * q^31 - 12 * q^32 - 32 * q^33 - 56 * q^34 + 48 * q^36 + 10 * q^37 - 18 * q^38 + 40 * q^40 + 30 * q^42 + 58 * q^43 - 84 * q^44 - 14 * q^45 + 16 * q^46 + 16 * q^47 - 4 * q^48 - 66 * q^49 - 26 * q^50 - 4 * q^51 - 4 * q^52 - 8 * q^53 - 2 * q^54 + 28 * q^56 + 60 * q^58 + 6 * q^59 - 68 * q^60 + 30 * q^61 - 8 * q^62 - 56 * q^63 + 4 * q^64 + 32 * q^65 - 110 * q^66 + 44 * q^67 + 36 * q^68 + 40 * q^69 + 62 * q^70 + 52 * q^72 - 18 * q^74 + 12 * q^75 - 76 * q^76 + 48 * q^77 + 16 * q^78 + 128 * q^79 - 32 * q^80 - 98 * q^81 - 2 * q^82 - 6 * q^83 + 112 * q^84 + 12 * q^85 - 36 * q^86 + 182 * q^90 + 24 * q^91 - 24 * q^92 + 8 * q^93 + 54 * q^94 + 48 * q^95 + 56 * q^96 + 36 * q^97 - 48 * q^98 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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