LMFDB - Embedded newform 820.2.j.c.483.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(483,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.483"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [240,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$120$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			483.12
Character	$\chi$	$=$	820.483
Dual form			820.2.j.c.747.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.35590 + 0.401898i) q^{2} +2.73899i q^{3} +(1.67696 - 1.08987i) q^{4} +(-2.07460 + 0.834293i) q^{5} +(-1.10079 - 3.71381i) q^{6} +0.506296 q^{7} +(-1.83578 + 2.15173i) q^{8} -4.50206 q^{9} +(2.47766 - 1.96500i) q^{10} +(-0.975492 - 0.975492i) q^{11} +(2.98514 + 4.59316i) q^{12} -0.970376 q^{13} +(-0.686490 + 0.203479i) q^{14} +(-2.28512 - 5.68230i) q^{15} +(1.62436 - 3.65533i) q^{16} -2.65685 q^{17} +(6.10436 - 1.80937i) q^{18} +(-0.779817 - 0.779817i) q^{19} +(-2.56974 + 3.66012i) q^{20} +1.38674i q^{21} +(1.71472 + 0.930627i) q^{22} +(-0.0275214 + 0.0275214i) q^{23} +(-5.89355 - 5.02817i) q^{24} +(3.60791 - 3.46164i) q^{25} +(1.31574 - 0.389992i) q^{26} -4.11412i q^{27} +(0.849037 - 0.551797i) q^{28} +(-5.29962 - 5.29962i) q^{29} +(5.38211 + 6.78627i) q^{30} -5.80786i q^{31} +(-0.733415 + 5.60911i) q^{32} +(2.67186 - 2.67186i) q^{33} +(3.60244 - 1.06778i) q^{34} +(-1.05036 + 0.422399i) q^{35} +(-7.54975 + 4.90666i) q^{36} +(-0.173081 + 0.173081i) q^{37} +(1.37076 + 0.743951i) q^{38} -2.65785i q^{39} +(2.01333 - 5.99554i) q^{40} +(-5.89613 + 2.49713i) q^{41} +(-0.557328 - 1.88029i) q^{42} +(2.73516 + 2.73516i) q^{43} +(-2.69902 - 0.572698i) q^{44} +(9.33996 - 3.75604i) q^{45} +(0.0262557 - 0.0483773i) q^{46} -2.79284i q^{47} +(10.0119 + 4.44912i) q^{48} -6.74366 q^{49} +(-3.50076 + 6.14367i) q^{50} -7.27709i q^{51} +(-1.62728 + 1.05758i) q^{52} +1.35261 q^{53} +(1.65346 + 5.57835i) q^{54} +(2.83760 + 1.20991i) q^{55} +(-0.929447 + 1.08941i) q^{56} +(2.13591 - 2.13591i) q^{57} +(9.31569 + 5.05587i) q^{58} +10.0057 q^{59} +(-10.0250 - 7.03848i) q^{60} +7.27577i q^{61} +(2.33416 + 7.87490i) q^{62} -2.27937 q^{63} +(-1.25985 - 7.90018i) q^{64} +(2.01314 - 0.809578i) q^{65} +(-2.54898 + 4.69661i) q^{66} +3.00303i q^{67} +(-4.45543 + 2.89563i) q^{68} +(-0.0753809 - 0.0753809i) q^{69} +(1.25443 - 0.994871i) q^{70} +(-0.285327 - 0.285327i) q^{71} +(8.26477 - 9.68719i) q^{72} +(9.38587 - 9.38587i) q^{73} +(0.165120 - 0.304242i) q^{74} +(9.48141 + 9.88202i) q^{75} +(-2.15762 - 0.457819i) q^{76} +(-0.493888 - 0.493888i) q^{77} +(1.06818 + 3.60379i) q^{78} +(5.35986 - 5.35986i) q^{79} +(-0.320286 + 8.93854i) q^{80} -2.23765 q^{81} +(6.99100 - 5.75551i) q^{82} +(-2.48145 + 2.48145i) q^{83} +(1.51137 + 2.32550i) q^{84} +(5.51190 - 2.21660i) q^{85} +(-4.80788 - 2.60936i) q^{86} +(14.5156 - 14.5156i) q^{87} +(3.88978 - 0.308206i) q^{88} +(8.00574 + 8.00574i) q^{89} +(-11.1546 + 8.84654i) q^{90} -0.491298 q^{91} +(-0.0161574 + 0.0761471i) q^{92} +15.9076 q^{93} +(1.12244 + 3.78682i) q^{94} +(2.26840 + 0.967210i) q^{95} +(-15.3633 - 2.00881i) q^{96} -5.38726 q^{97} +(9.14377 - 2.71026i) q^{98} +(4.39172 + 4.39172i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{6} + 12 q^{8} - 240 q^{9} - 20 q^{10} - 32 q^{13} - 8 q^{14} + 8 q^{16} + 32 q^{17} - 12 q^{18} + 16 q^{20} - 28 q^{22} + 12 q^{24} - 16 q^{25} - 8 q^{28} - 10 q^{30} + 24 q^{33} - 20 q^{34}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q - 4 * q^6 + 12 * q^8 - 240 * q^9 - 20 * q^10 - 32 * q^13 - 8 * q^14 + 8 * q^16 + 32 * q^17 - 12 * q^18 + 16 * q^20 - 28 * q^22 + 12 * q^24 - 16 * q^25 - 8 * q^28 - 10 * q^30 + 24 * q^33 - 20 * q^34 - 8 * q^37 + 16 * q^38 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 + 8 * q^48 + 224 * q^49 - 12 * q^50 - 32 * q^53 + 48 * q^54 + 24 * q^56 - 8 * q^57 + 6 * q^60 - 8 * q^65 - 8 * q^66 + 16 * q^69 + 10 * q^70 - 96 * q^72 - 72 * q^73 + 112 * q^74 + 20 * q^76 - 56 * q^77 + 4 * q^78 + 60 * q^80 + 48 * q^81 - 56 * q^82 - 32 * q^84 - 32 * q^85 - 8 * q^86 - 64 * q^89 + 76 * q^90 + 20 * q^92 - 16 * q^93 + 48 * q^94 + 24 * q^96 - 48 * q^97 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.35590	+	0.401898i	−0.958770	+	0.284185i
$2$	−1.35590	+	0.401898i	−0.958770	+	0.284185i
$3$			2.73899i			1.58136i	0.612232	+	0.790678i	$0.290272\pi$
$3$			2.73899i			1.58136i	−0.612232	+	0.790678i	$0.709728\pi$
$4$	1.67696	−	1.08987i	0.838478	−	0.544935i
$5$	−2.07460	+	0.834293i	−0.927788	+	0.373107i
$5$	−2.07460	+	0.834293i	−0.927788	+	0.373107i
$6$	−1.10079	−	3.71381i	−0.449397	−	1.51616i
$7$	0.506296			0.191362			0.0956810	−	0.995412i	$-0.469497\pi$
$7$	0.506296			0.191362			0.0956810	+	0.995412i	$0.469497\pi$
$8$	−1.83578	+	2.15173i	−0.649045	+	0.760750i
$9$	−4.50206			−1.50069
$10$	2.47766	−	1.96500i	0.783504	−	0.621387i
$11$	−0.975492	−	0.975492i	−0.294122	−	0.294122i	0.544584	−	0.838706i	$-0.316687\pi$
$11$	−0.975492	−	0.975492i	−0.294122	−	0.294122i	−0.838706	+	0.544584i	$0.816687\pi$
$12$	2.98514	+	4.59316i	0.861736	+	1.32593i
$13$	−0.970376			−0.269134			−0.134567	−	0.990905i	$-0.542964\pi$
$13$	−0.970376			−0.269134			−0.134567	+	0.990905i	$0.542964\pi$
$14$	−0.686490	+	0.203479i	−0.183472	+	0.0543821i
$15$	−2.28512	−	5.68230i	−0.590015	−	1.46716i
$16$	1.62436	−	3.65533i	0.406091	−	0.913833i
$17$	−2.65685			−0.644382			−0.322191	−	0.946675i	$-0.604419\pi$
$17$	−2.65685			−0.644382			−0.322191	+	0.946675i	$0.604419\pi$
$18$	6.10436	−	1.80937i	1.43881	−	0.426472i
$19$	−0.779817	−	0.779817i	−0.178902	−	0.178902i	0.611975	−	0.790877i	$-0.290375\pi$
$19$	−0.779817	−	0.779817i	−0.178902	−	0.178902i	−0.790877	+	0.611975i	$0.790375\pi$
$20$	−2.56974	+	3.66012i	−0.574611	+	0.818427i
$21$			1.38674i			0.302611i
$22$	1.71472	+	0.930627i	0.365580	+	0.198410i
$23$	−0.0275214	+	0.0275214i	−0.00573862	+	0.00573862i	−0.709970	−	0.704232i	$-0.751292\pi$
$23$	−0.0275214	+	0.0275214i	−0.00573862	+	0.00573862i	0.704232	+	0.709970i	$0.251292\pi$
$24$	−5.89355	−	5.02817i	−1.20302	−	1.02637i
$25$	3.60791	−	3.46164i	0.721582	−	0.692329i
$26$	1.31574	−	0.389992i	0.258037	−	0.0764837i
$27$		−	4.11412i		−	0.791763i
$28$	0.849037	−	0.551797i	0.160453	−	0.104280i
$29$	−5.29962	−	5.29962i	−0.984115	−	0.984115i	0.0157612	−	0.999876i	$-0.494983\pi$
$29$	−5.29962	−	5.29962i	−0.984115	−	0.984115i	−0.999876	+	0.0157612i	$0.994983\pi$
$30$	5.38211	+	6.78627i	0.982634	+	1.23900i
$31$		−	5.80786i		−	1.04312i	−0.853214	−	0.521561i	$-0.825350\pi$
$31$		−	5.80786i		−	1.04312i	0.853214	−	0.521561i	$-0.174650\pi$
$32$	−0.733415	+	5.60911i	−0.129651	+	0.991560i
$33$	2.67186	−	2.67186i	0.465112	−	0.465112i
$34$	3.60244	−	1.06778i	0.617814	−	0.183123i
$35$	−1.05036	+	0.422399i	−0.177543	+	0.0713985i
$36$	−7.54975	+	4.90666i	−1.25829	+	0.817777i
$37$	−0.173081	+	0.173081i	−0.0284543	+	0.0284543i	−0.721191	−	0.692736i	$-0.756405\pi$
$37$	−0.173081	+	0.173081i	−0.0284543	+	0.0284543i	0.692736	+	0.721191i	$0.256405\pi$
$38$	1.37076	+	0.743951i	0.222367	+	0.120685i
$39$		−	2.65785i		−	0.425596i
$40$	2.01333	−	5.99554i	0.318335	−	0.947978i
$41$	−5.89613	+	2.49713i	−0.920821	+	0.389986i
$41$	−5.89613	+	2.49713i	−0.920821	+	0.389986i
$42$	−0.557328	−	1.88029i	−0.0859975	−	0.290135i
$43$	2.73516	+	2.73516i	0.417108	+	0.417108i	0.884206	−	0.467097i	$-0.154700\pi$
$43$	2.73516	+	2.73516i	0.417108	+	0.417108i	−0.467097	+	0.884206i	$0.654700\pi$
$44$	−2.69902	−	0.572698i	−0.406892	−	0.0863374i
$45$	9.33996	−	3.75604i	1.39232	−	0.559917i
$46$	0.0262557	−	0.0483773i	0.00387119	−	0.00713284i
$47$		−	2.79284i		−	0.407377i	−0.979036	−	0.203689i	$-0.934707\pi$
$47$		−	2.79284i		−	0.407377i	0.979036	−	0.203689i	$-0.0652930\pi$
$48$	10.0119	+	4.44912i	1.44509	+	0.642175i
$49$	−6.74366			−0.963381
$50$	−3.50076	+	6.14367i	−0.495082	+	0.868846i
$51$		−	7.27709i		−	1.01900i
$52$	−1.62728	+	1.05758i	−0.225663	+	0.146661i
$53$	1.35261			0.185795			0.0928976	−	0.995676i	$-0.470387\pi$
$53$	1.35261			0.185795			0.0928976	+	0.995676i	$0.470387\pi$
$54$	1.65346	+	5.57835i	0.225007	+	0.759118i
$55$	2.83760	+	1.20991i	0.382622	+	0.163144i
$56$	−0.929447	+	1.08941i	−0.124203	+	0.145579i
$57$	2.13591	−	2.13591i	0.282908	−	0.282908i
$58$	9.31569	+	5.05587i	1.22321	+	0.663869i
$59$	10.0057			1.30263			0.651313	−	0.758809i	$-0.274218\pi$
$59$	10.0057			1.30263			0.651313	+	0.758809i	$0.274218\pi$
$60$	−10.0250	−	7.03848i	−1.29422	−	0.908664i
$61$			7.27577i			0.931566i	0.884899	+	0.465783i	$0.154227\pi$
$61$			7.27577i			0.931566i	−0.884899	+	0.465783i	$0.845773\pi$
$62$	2.33416	+	7.87490i	0.296439	+	1.00011i
$63$	−2.27937			−0.287174
$64$	−1.25985	−	7.90018i	−0.157481	−	0.987522i
$65$	2.01314	−	0.809578i	0.249699	−	0.100416i
$66$	−2.54898	+	4.69661i	−0.313757	+	0.578112i
$67$			3.00303i			0.366878i	0.983031	+	0.183439i	$0.0587230\pi$
$67$			3.00303i			0.366878i	−0.983031	+	0.183439i	$0.941277\pi$
$68$	−4.45543	+	2.89563i	−0.540300	+	0.351146i
$69$	−0.0753809	−	0.0753809i	−0.00907480	−	0.00907480i
$70$	1.25443	−	0.994871i	0.149933	−	0.118910i
$71$	−0.285327	−	0.285327i	−0.0338621	−	0.0338621i	0.689973	−	0.723835i	$-0.257622\pi$
$71$	−0.285327	−	0.285327i	−0.0338621	−	0.0338621i	−0.723835	+	0.689973i	$0.757622\pi$
$72$	8.26477	−	9.68719i	0.974013	−	1.14165i
$73$	9.38587	−	9.38587i	1.09853	−	1.09853i	0.103950	−	0.994583i	$-0.466852\pi$
$73$	9.38587	−	9.38587i	1.09853	−	1.09853i	0.994583	−	0.103950i	$-0.0331483\pi$
$74$	0.165120	−	0.304242i	0.0191948	−	0.0353674i
$75$	9.48141	+	9.88202i	1.09482	+	1.14108i
$76$	−2.15762	−	0.457819i	−0.247496	−	0.0525155i
$77$	−0.493888	−	0.493888i	−0.0562838	−	0.0562838i
$78$	1.06818	+	3.60379i	0.120948	+	0.408049i
$79$	5.35986	−	5.35986i	0.603032	−	0.603032i	−0.338084	−	0.941116i	$-0.609779\pi$
$79$	5.35986	−	5.35986i	0.603032	−	0.603032i	0.941116	+	0.338084i	$0.109779\pi$
$80$	−0.320286	+	8.93854i	−0.0358091	+	0.999359i
$81$	−2.23765			−0.248628
$82$	6.99100	−	5.75551i	0.772027	−	0.635590i
$83$	−2.48145	+	2.48145i	−0.272375	+	0.272375i	−0.830056	−	0.557681i	$-0.811691\pi$
$83$	−2.48145	+	2.48145i	−0.272375	+	0.272375i	0.557681	+	0.830056i	$0.311691\pi$
$84$	1.51137	+	2.32550i	0.164904	+	0.253733i
$85$	5.51190	−	2.21660i	0.597850	−	0.240424i
$86$	−4.80788	−	2.60936i	−0.518447	−	0.281375i
$87$	14.5156	−	14.5156i	1.55624	−	1.55624i
$88$	3.88978	−	0.308206i	0.414652	−	0.0328549i
$89$	8.00574	+	8.00574i	0.848607	+	0.848607i	0.989959	−	0.141352i	$-0.0451450\pi$
$89$	8.00574	+	8.00574i	0.848607	+	0.848607i	−0.141352	+	0.989959i	$0.545145\pi$
$90$	−11.1546	+	8.84654i	−1.17579	+	0.932507i
$91$	−0.491298			−0.0515020
$92$	−0.0161574	+	0.0761471i	−0.00168453	+	0.00793888i
$93$	15.9076			1.64955
$94$	1.12244	+	3.78682i	0.115770	+	0.390581i
$95$	2.26840	+	0.967210i	0.232733	+	0.0992337i
$96$	−15.3633	−	2.00881i	−1.56801	−	0.205024i
$97$	−5.38726			−0.546994			−0.273497	−	0.961873i	$-0.588180\pi$
$97$	−5.38726			−0.546994			−0.273497	+	0.961873i	$0.588180\pi$
$98$	9.14377	−	2.71026i	0.923660	−	0.273778i
$99$	4.39172	+	4.39172i	0.441385	+	0.441385i
$100$	2.27756	−	9.73718i	0.227756	−	0.973718i
$101$	−12.4093	−	12.4093i	−1.23477	−	1.23477i	−0.962112	−	0.272656i	$-0.912098\pi$
$101$	−12.4093	−	12.4093i	−1.23477	−	1.23477i	−0.272656	−	0.962112i	$-0.587902\pi$
$102$	2.92465	+	9.86705i	0.289583	+	0.976983i
$103$	−9.20940	−	9.20940i	−0.907429	−	0.907429i	0.0886348	−	0.996064i	$-0.471750\pi$
$103$	−9.20940	−	9.20940i	−0.907429	−	0.907429i	−0.996064	+	0.0886348i	$0.971750\pi$
$104$	1.78139	−	2.08798i	0.174680	−	0.204744i
$105$	−1.15695	−	2.87693i	−0.112906	−	0.280759i
$106$	−1.83401	+	0.543611i	−0.178135	+	0.0528001i
$107$	2.40984	+	2.40984i	0.232968	+	0.232968i	0.813930	−	0.580962i	$-0.197324\pi$
$107$	2.40984	+	2.40984i	0.232968	+	0.232968i	−0.580962	+	0.813930i	$0.697324\pi$
$108$	−4.48386	−	6.89920i	−0.431459	−	0.663876i
$109$	−3.34989	+	3.34989i	−0.320861	+	0.320861i	−0.849098	−	0.528236i	$-0.822854\pi$
$109$	−3.34989	+	3.34989i	−0.320861	+	0.320861i	0.528236	+	0.849098i	$0.322854\pi$
$110$	−4.33378	−	0.500094i	−0.413209	−	0.0476821i
$111$	−0.474066	−	0.474066i	−0.0449964	−	0.0449964i
$112$	0.822410	−	1.85068i	0.0777104	−	0.174873i
$113$	−4.56483	−	4.56483i	−0.429423	−	0.429423i	0.459009	−	0.888432i	$-0.348205\pi$
$113$	−4.56483	−	4.56483i	−0.429423	−	0.429423i	−0.888432	+	0.459009i	$0.848205\pi$
$114$	−2.03767	+	3.75451i	−0.190846	+	0.351642i
$115$	0.0341350	−	0.0800569i	0.00318310	−	0.00746534i
$116$	−14.6631	−	3.11133i	−1.36144	−	0.288880i
$117$	4.36869			0.403885
$118$	−13.5667	+	4.02126i	−1.24892	+	0.370187i
$119$	−1.34516			−0.123310
$120$	16.4217	+	5.51448i	1.49909	+	0.503401i
$121$		−	9.09683i		−	0.826984i
$122$	−2.92411	−	9.86525i	−0.264737	−	0.893158i
$123$	−6.83961	−	16.1494i	−0.616707	−	1.45615i
$124$	−6.32981	−	9.73952i	−0.568434	−	0.874635i
$125$	−4.59694	+	10.1916i	−0.411162	+	0.911562i
$126$	3.09062	−	0.916076i	0.275334	−	0.0816105i
$127$	−6.73426	−	6.73426i	−0.597569	−	0.597569i	0.342096	−	0.939665i	$-0.388863\pi$
$127$	−6.73426	−	6.73426i	−0.597569	−	0.597569i	−0.939665	+	0.342096i	$0.888863\pi$
$128$	4.88330	+	10.2056i	0.431627	+	0.902052i
$129$	−7.49158	+	7.49158i	−0.659597	+	0.659597i
$130$	−2.40426	+	1.90679i	−0.210867	+	0.167236i
$131$	−14.1204			−1.23370			−0.616851	−	0.787080i	$-0.711592\pi$
$131$	−14.1204			−1.23370			−0.616851	+	0.787080i	$0.711592\pi$
$132$	1.56861	−	7.39258i	0.136530	−	0.643442i
$133$	−0.394818	−	0.394818i	−0.0342351	−	0.0342351i
$134$	−1.20691	−	4.07182i	−0.104261	−	0.351752i
$135$	3.43238	+	8.53514i	0.295412	+	0.734588i
$136$	4.87739	−	5.71682i	0.418233	−	0.490214i
$137$	−17.3921			−1.48591			−0.742953	−	0.669344i	$-0.766575\pi$
$137$	−17.3921			−1.48591			−0.742953	+	0.669344i	$0.766575\pi$
$138$	0.132505	+	0.0719139i	0.0112796	+	0.00612172i
$139$	17.8470			1.51376			0.756880	−	0.653554i	$-0.226723\pi$
$139$	17.8470			1.51376			0.756880	+	0.653554i	$0.226723\pi$
$140$	−1.30105	+	1.85310i	−0.109959	+	0.156616i
$141$	7.64955			0.644209
$142$	0.501549	+	0.272204i	0.0420890	+	0.0228428i
$143$	0.946594	+	0.946594i	0.0791582	+	0.0791582i
$144$	−7.31298	+	16.4565i	−0.609415	+	1.37138i
$145$	15.4160	+	6.57314i	1.28023	+	0.545870i
$146$	−8.95418	+	16.4985i	−0.741054	+	1.36543i
$147$		−	18.4708i		−	1.52345i
$148$	−0.101613	+	0.478884i	−0.00835255	+	0.0393640i
$149$	−3.93105	+	3.93105i	−0.322045	+	0.322045i	−0.849551	−	0.527506i	$-0.823127\pi$
$149$	−3.93105	+	3.93105i	−0.322045	+	0.322045i	0.527506	+	0.849551i	$0.323127\pi$
$150$	−16.8274	−	9.58853i	−1.37396	−	0.782900i
$151$	5.54646	+	5.54646i	0.451364	+	0.451364i	0.895807	−	0.444443i	$-0.146598\pi$
$151$	5.54646	+	5.54646i	0.451364	+	0.451364i	−0.444443	+	0.895807i	$0.646598\pi$
$152$	3.10952	−	0.246383i	0.252216	−	0.0199843i
$153$	11.9613			0.967015
$154$	0.868158	+	0.471173i	0.0699582	+	0.0379682i
$155$	4.84545	+	12.0490i	0.389196	+	0.967796i
$156$	−2.89671	−	4.45709i	−0.231922	−	0.356853i
$157$			11.2694i			0.899395i	0.893181	+	0.449698i	$0.148468\pi$
$157$			11.2694i			0.899395i	−0.893181	+	0.449698i	$0.851532\pi$
$158$	−5.11335	+	9.42158i	−0.406796	+	0.749541i
$159$			3.70478i			0.293808i
$160$	−3.15810	−	12.2485i	−0.249670	−	0.968331i
$161$	−0.0139340	+	0.0139340i	−0.00109815	+	0.00109815i
$162$	3.03404	−	0.899306i	0.238377	−	0.0706562i
$163$	−12.5159	+	12.5159i	−0.980324	+	0.980324i	−0.999810	−	0.0194860i	$-0.993797\pi$
$163$	−12.5159	+	12.5159i	−0.980324	+	0.980324i	0.0194860	+	0.999810i	$0.493797\pi$
$164$	−7.16600	+	10.6136i	−0.559571	+	0.828782i
$165$	−3.31392	+	7.77216i	−0.257989	+	0.605062i
$166$	2.36733	−	4.36191i	0.183740	−	0.338550i
$167$	5.10460			0.395006			0.197503	−	0.980302i	$-0.436717\pi$
$167$	5.10460			0.395006			0.197503	+	0.980302i	$0.436717\pi$
$168$	−2.98388	−	2.54574i	−0.230212	−	0.196408i
$169$	−12.0584			−0.927567
$170$	−6.58277	+	5.22072i	−0.504876	+	0.400411i
$171$	3.51078	+	3.51078i	0.268476	+	0.268476i
$172$	7.56772	+	1.60578i	0.577033	+	0.122439i
$173$	3.35639	−	3.35639i	0.255182	−	0.255182i	−0.567909	−	0.823091i	$-0.692248\pi$
$173$	3.35639	−	3.35639i	0.255182	−	0.255182i	0.823091	+	0.567909i	$0.192248\pi$
$174$	−13.8480	+	25.5156i	−1.04981	+	1.93433i
$175$	1.82667	−	1.75262i	0.138083	−	0.132485i
$176$	−5.15030	+	1.98119i	−0.388219	+	0.149338i
$177$			27.4054i			2.05992i
$178$	−14.0725	−	7.63754i	−1.05478	−	0.572457i
$179$	0.113859	+	0.113859i	0.00851023	+	0.00851023i	0.711349	−	0.702839i	$-0.248085\pi$
$179$	0.113859	+	0.113859i	0.00851023	+	0.00851023i	−0.702839	+	0.711349i	$0.748085\pi$
$180$	11.5691	−	16.4781i	0.862310	−	1.22820i
$181$	−1.99835	−	1.99835i	−0.148536	−	0.148536i	0.628928	−	0.777464i	$-0.283494\pi$
$181$	−1.99835	−	1.99835i	−0.148536	−	0.148536i	−0.777464	+	0.628928i	$0.783494\pi$
$182$	0.666153	−	0.197451i	0.0493785	−	0.0146361i
$183$	−19.9282			−1.47314
$184$	−0.00869538	−	0.109742i	−0.000641032	−	0.00809028i
$185$	0.214673	−	0.503473i	0.0157831	−	0.0370161i
$186$	−21.5693	+	6.39325i	−1.58153	+	0.468776i
$187$	2.59174	+	2.59174i	0.189527	+	0.189527i
$188$	−3.04383	−	4.68347i	−0.221994	−	0.341577i
$189$		−	2.08296i		−	0.151513i
$190$	−3.46446	−	0.399779i	−0.251338	−	0.0290030i
$191$	19.1254	−	19.1254i	1.38386	−	1.38386i	0.546229	−	0.837636i	$-0.316063\pi$
$191$	19.1254	−	19.1254i	1.38386	−	1.38386i	0.837636	−	0.546229i	$-0.183937\pi$
$192$	21.6385	−	3.45071i	1.56162	−	0.249034i
$193$	−24.3151			−1.75024			−0.875120	−	0.483907i	$-0.839217\pi$
$193$	−24.3151			−1.75024			−0.875120	+	0.483907i	$0.839217\pi$
$194$	7.30461	−	2.16513i	0.524441	−	0.155447i
$195$	2.21742	+	5.51397i	0.158793	+	0.394863i
$196$	−11.3088	+	7.34972i	−0.807774	+	0.524980i
$197$	−8.48564	−	8.48564i	−0.604577	−	0.604577i	0.336947	−	0.941524i	$-0.390606\pi$
$197$	−8.48564	−	8.48564i	−0.604577	−	0.604577i	−0.941524	+	0.336947i	$0.890606\pi$
$198$	−7.71978	−	4.18974i	−0.548621	−	0.297752i
$199$	−12.2856	−	12.2856i	−0.870904	−	0.870904i	0.121667	−	0.992571i	$-0.461176\pi$
$199$	−12.2856	−	12.2856i	−0.870904	−	0.870904i	−0.992571	+	0.121667i	$0.961176\pi$
$200$	0.825193	+	14.1180i	0.0583500	+	0.998296i
$201$	−8.22526			−0.580165
$202$	21.8130	+	11.8385i	1.53476	+	0.832956i
$203$	−2.68318	−	2.68318i	−0.188322	−	0.188322i
$204$	−7.93109	−	12.2034i	−0.555287	−	0.854407i
$205$	10.1488	−	10.0996i	0.708820	−	0.705389i
$206$	16.1883	+	8.78583i	1.12789	+	0.612138i
$207$	0.123903	−	0.123903i	0.00861186	−	0.00861186i
$208$	−1.57624	+	3.54704i	−0.109293	+	0.245943i
$209$			1.52141i			0.105238i
$210$	2.72494	+	3.43586i	0.188039	+	0.237097i
$211$	−20.1412	+	20.1412i	−1.38657	+	1.38657i	−0.554172	+	0.832402i	$0.686965\pi$
$211$	−20.1412	+	20.1412i	−1.38657	+	1.38657i	−0.832402	+	0.554172i	$0.813035\pi$
$212$	2.26827	−	1.47417i	0.155785	−	0.101246i
$213$	0.781507	−	0.781507i	0.0535480	−	0.0535480i
$214$	−4.23603	−	2.29901i	−0.289569	−	0.157157i
$215$	−7.95629	−	3.39243i	−0.542614	−	0.231362i
$216$	8.85246	+	7.55260i	0.602333	+	0.513890i
$217$		−	2.94050i		−	0.199614i
$218$	3.19582	−	5.88845i	0.216448	−	0.398816i
$219$	25.7078	+	25.7078i	1.73717	+	1.73717i
$220$	6.07718	−	1.06366i	0.409723	−	0.0717116i
$221$	2.57815			0.173425
$222$	0.833315	+	0.452262i	0.0559284	+	0.0303539i
$223$	−16.5565	+	16.5565i	−1.10871	+	1.10871i	−0.115386	+	0.993321i	$0.536810\pi$
$223$	−16.5565	+	16.5565i	−1.10871	+	1.10871i	−0.993321	+	0.115386i	$0.963190\pi$
$224$	−0.371325	+	2.83987i	−0.0248102	+	0.189747i
$225$	−16.2430	+	15.5845i	−1.08287	+	1.03897i
$226$	8.02406	+	4.35488i	0.533753	+	0.289682i
$227$			23.2393i			1.54244i	0.636566	+	0.771222i	$0.280354\pi$
$227$			23.2393i			1.54244i	−0.636566	+	0.771222i	$0.719646\pi$
$228$	1.25396	−	5.90969i	0.0830457	−	0.391379i
$229$	15.7883	−	15.7883i	1.04332	−	1.04332i	0.0443006	−	0.999018i	$-0.485894\pi$
$229$	15.7883	−	15.7883i	1.04332	−	1.04332i	0.999018	−	0.0443006i	$-0.0141059\pi$
$230$	−0.0141091	+	0.122268i	−0.000930326	+	0.00806213i
$231$	1.35275	−	1.35275i	0.0890047	−	0.0890047i
$232$	21.1322	−	1.67441i	1.38740	−	0.109930i
$233$	−25.4543			−1.66757			−0.833783	−	0.552092i	$-0.813830\pi$
$233$	−25.4543			−1.66757			−0.833783	+	0.552092i	$0.813830\pi$
$234$	−5.92353	+	1.75577i	−0.387233	+	0.114778i
$235$	2.33005	+	5.79402i	0.151995	+	0.377960i
$236$	16.7791	−	10.9049i	1.09222	−	0.709847i
$237$	14.6806	+	14.6806i	0.953608	+	0.953608i
$238$	1.82390	−	0.540615i	0.118226	−	0.0350429i
$239$	−11.0360	+	11.0360i	−0.713859	+	0.713859i	−0.967340	−	0.253481i	$-0.918424\pi$
$239$	−11.0360	+	11.0360i	−0.713859	+	0.713859i	0.253481	+	0.967340i	$0.418424\pi$
$240$	−24.4825	−	0.877260i	−1.58034	−	0.0566269i
$241$		−	6.73550i		−	0.433872i	−0.976186	−	0.216936i	$-0.930394\pi$
$241$		−	6.73550i		−	0.433872i	0.976186	−	0.216936i	$-0.0696063\pi$
$242$	3.65600	+	12.3344i	0.235016	+	0.792888i
$243$		−	18.4713i		−	1.18493i
$244$	7.92964	+	12.2011i	0.507643	+	0.781098i
$245$	13.9904	−	5.62619i	0.893813	−	0.359444i
$246$	15.7643	+	19.1483i	1.00509	+	1.22085i
$247$	0.756715	+	0.756715i	0.0481486	+	0.0481486i
$248$	12.4969	+	10.6619i	0.793555	+	0.677033i
$249$	−6.79668	−	6.79668i	−0.430722	−	0.430722i
$250$	2.13704	−	15.6663i	0.135158	−	0.990824i
$251$	12.0901			0.763122			0.381561	−	0.924344i	$-0.375387\pi$
$251$	12.0901			0.763122			0.381561	+	0.924344i	$0.375387\pi$
$252$	−3.82241	+	2.48422i	−0.240789	+	0.156491i
$253$	0.0536939			0.00337571
$254$	11.8375	+	6.42453i	0.742751	+	0.403111i
$255$	6.07123	+	15.0970i	0.380195	+	0.945413i
$256$	−10.7229	−	11.8752i	−0.670180	−	0.742199i
$257$		−	4.99518i		−	0.311591i	−0.987789	−	0.155795i	$-0.950206\pi$
$257$		−	4.99518i		−	0.311591i	0.987789	−	0.155795i	$-0.0497941\pi$
$258$	7.14702	−	13.1687i	0.444954	−	0.819849i
$259$	−0.0876301	+	0.0876301i	−0.00544507	+	0.00544507i
$260$	2.49361	−	3.55169i	0.154647	−	0.220266i
$261$	23.8592	+	23.8592i	1.47685	+	1.47685i
$262$	19.1459	−	5.67494i	1.18284	−	0.350599i
$263$	−1.91999			−0.118391			−0.0591957	−	0.998246i	$-0.518854\pi$
$263$	−1.91999			−0.118391			−0.0591957	+	0.998246i	$0.518854\pi$
$264$	0.844173	+	10.6541i	0.0519553	+	0.655712i
$265$	−2.80612	+	1.12847i	−0.172379	+	0.0693215i
$266$	0.694013	+	0.376659i	0.0425527	+	0.0230945i
$267$	−21.9276	+	21.9276i	−1.34195	+	1.34195i
$268$	3.27291	+	5.03595i	0.199925	+	0.307619i
$269$			5.03457i			0.306963i	0.988152	+	0.153481i	$0.0490485\pi$
$269$			5.03457i			0.306963i	−0.988152	+	0.153481i	$0.950951\pi$
$270$	−8.08424	−	10.1934i	−0.491991	−	0.620349i
$271$			6.79803i			0.412951i	0.978452	+	0.206476i	$0.0661994\pi$
$271$			6.79803i			0.412951i	−0.978452	+	0.206476i	$0.933801\pi$
$272$	−4.31570	+	9.71168i	−0.261678	+	0.588857i
$273$		−	1.34566i		−	0.0814430i
$274$	23.5820	−	6.98984i	1.42464	−	0.422272i
$275$	−6.89630	−	0.142681i	−0.415862	−	0.00860398i
$276$	−0.208566	−	0.0442551i	−0.0125542	−	0.00266384i
$277$	8.48229	−	8.48229i	0.509651	−	0.509651i	−0.404768	−	0.914419i	$-0.632648\pi$
$277$	8.48229	−	8.48229i	0.509651	−	0.509651i	0.914419	+	0.404768i	$0.132648\pi$
$278$	−24.1988	+	7.17266i	−1.45135	+	0.430187i
$279$			26.1473i			1.56540i
$280$	1.01934	−	3.03552i	0.0609172	−	0.181407i
$281$	−14.7418	−	14.7418i	−0.879420	−	0.879420i	0.114055	−	0.993474i	$-0.463616\pi$
$281$	−14.7418	−	14.7418i	−0.879420	−	0.879420i	−0.993474	+	0.114055i	$0.963616\pi$
$282$	−10.3721	+	3.07434i	−0.617648	+	0.183074i
$283$	−19.3245	+	19.3245i	−1.14872	+	1.14872i	−0.161917	+	0.986804i	$0.551768\pi$
$283$	−19.3245	+	19.3245i	−1.14872	+	1.14872i	−0.986804	+	0.161917i	$0.948232\pi$
$284$	−0.789450	−	0.167511i	−0.0468453	−	0.00993997i
$285$	−2.64918	+	6.21313i	−0.156924	+	0.368034i
$286$	−1.66393	−	0.903058i	−0.0983900	−	0.0533989i
$287$	−2.98519	+	1.26429i	−0.176210	+	0.0746285i
$288$	3.30187	−	25.2525i	0.194565	−	1.48802i
$289$	−9.94112			−0.584772
$290$	−23.5444	−	2.71689i	−1.38257	−	0.159541i
$291$		−	14.7556i		−	0.864991i
$292$	5.51031	−	25.9691i	0.322466	−	1.51972i
$293$			15.6720i			0.915569i	0.889063	+	0.457784i	$0.151357\pi$
$293$			15.6720i			0.915569i	−0.889063	+	0.457784i	$0.848643\pi$
$294$	7.42338	+	25.0447i	0.432940	+	1.46064i
$295$	−20.7577	+	8.34766i	−1.20856	+	0.486019i
$296$	−0.0546847	−	0.690160i	−0.00317848	−	0.0401147i
$297$	−4.01329	+	4.01329i	−0.232875	+	0.232875i
$298$	3.75025	−	6.91002i	0.217246	−	0.400287i
$299$	0.0267061	−	0.0267061i	0.00154446	−	0.00154446i
$300$	26.6700	+	6.23822i	1.53979	+	0.360164i
$301$	1.38480	+	1.38480i	0.0798187	+	0.0798187i
$302$	−9.74958	−	5.29136i	−0.561025	−	0.304484i
$303$	33.9888	−	33.9888i	1.95261	−	1.95261i
$304$	−4.11720	+	1.58378i	−0.236137	+	0.0908361i
$305$	−6.07012	−	15.0943i	−0.347574	−	0.864296i
$306$	−16.2184	+	4.80723i	−0.927144	+	0.274811i
$307$	−12.8575	+	12.8575i	−0.733814	+	0.733814i	−0.971373	−	0.237559i	$-0.923653\pi$
$307$	−12.8575	+	12.8575i	−0.733814	+	0.733814i	0.237559	+	0.971373i	$0.423653\pi$
$308$	−1.36650	−	0.289955i	−0.0778637	−	0.0165217i
$309$	25.2244	−	25.2244i	1.43497	−	1.43497i
$310$	−11.4124	−	14.3899i	−0.648182	−	0.817290i
$311$	7.23596	−	7.23596i	0.410314	−	0.410314i	−0.471534	−	0.881848i	$-0.656300\pi$
$311$	7.23596	−	7.23596i	0.410314	−	0.410314i	0.881848	+	0.471534i	$0.156300\pi$
$312$	5.71896	+	4.87922i	0.323772	+	0.276231i
$313$		−	6.45336i		−	0.364765i	−0.983228	−	0.182383i	$-0.941619\pi$
$313$		−	6.45336i		−	0.364765i	0.983228	−	0.182383i	$-0.0583810\pi$
$314$	−4.52914	−	15.2802i	−0.255594	−	0.862313i
$315$	4.72879	−	1.90167i	0.266437	−	0.107147i
$316$	3.14670	−	14.8298i	0.177016	−	0.834242i
$317$		−	31.1248i		−	1.74814i	−0.485797	−	0.874072i	$-0.661470\pi$
$317$		−	31.1248i		−	1.74814i	0.485797	−	0.874072i	$-0.338530\pi$
$318$	−1.48894	−	5.02333i	−0.0834958	−	0.281694i
$319$			10.3395i			0.578900i
$320$	9.20474	+	15.3386i	0.514561	+	0.857454i
$321$	−6.60053	+	6.60053i	−0.368406	+	0.368406i
$322$	0.0132931	−	0.0244932i	0.000740798	−	0.00136495i
$323$	2.07186	+	2.07186i	0.115281	+	0.115281i
$324$	−3.75244	+	2.43875i	−0.208469	+	0.135486i
$325$	−3.50103	+	3.35910i	−0.194202	+	0.186329i
$326$	11.9403	−	22.0006i	0.661312	−	1.21850i
$327$	−9.17531	−	9.17531i	−0.507396	−	0.507396i
$328$	5.45084	−	17.2710i	0.300972	−	0.953633i
$329$		−	1.41400i		−	0.0779565i
$330$	1.36975	−	11.8702i	0.0754024	−	0.653431i
$331$	−12.8239	−	12.8239i	−0.704867	−	0.704867i	0.260584	−	0.965451i	$-0.416085\pi$
$331$	−12.8239	−	12.8239i	−0.704867	−	0.704867i	−0.965451	+	0.260584i	$0.916085\pi$
$332$	−1.45683	+	6.86576i	−0.0799538	+	0.376807i
$333$	0.779219	−	0.779219i	0.0427010	−	0.0427010i
$334$	−6.92136	+	2.05153i	−0.378720	+	0.112255i
$335$	−2.50540	−	6.23007i	−0.136885	−	0.340385i
$336$	5.06899	+	2.25257i	0.276536	+	0.122888i
$337$	0.151394	+	0.151394i	0.00824698	+	0.00824698i	0.711218	−	0.702971i	$-0.248144\pi$
$337$	0.151394	+	0.151394i	0.00824698	+	0.00824698i	−0.702971	+	0.711218i	$0.748144\pi$
$338$	16.3500	−	4.84623i	0.889323	−	0.263600i
$339$	12.5030	−	12.5030i	0.679070	−	0.679070i
$340$	6.82742	−	9.72440i	0.370269	−	0.527379i
$341$	−5.66552	+	5.66552i	−0.306805	+	0.306805i
$342$	−6.17126	−	3.34931i	−0.333704	−	0.181110i
$343$	−6.95837			−0.375716
$344$	−10.9065	+	0.864173i	−0.588037	+	0.0465931i
$345$	0.219275	+	0.0934953i	0.0118054	+	0.00503362i
$346$	−3.20202	+	5.89988i	−0.172142	+	0.317180i
$347$		−	16.5869i		−	0.890433i	−0.895423	−	0.445217i	$-0.853127\pi$
$347$		−	16.5869i		−	0.890433i	0.895423	−	0.445217i	$-0.146873\pi$
$348$	8.52190	−	40.1621i	0.456822	−	2.15292i
$349$	18.4133			0.985640			0.492820	−	0.870131i	$-0.335966\pi$
$349$	18.4133			0.985640			0.492820	+	0.870131i	$0.335966\pi$
$350$	−1.77242	+	3.11052i	−0.0947398	+	0.166264i
$351$			3.99224i			0.213090i
$352$	6.18708	−	4.75620i	0.329773	−	0.253506i
$353$	1.54677	+	1.54677i	0.0823261	+	0.0823261i	0.747071	−	0.664745i	$-0.231460\pi$
$353$	1.54677	+	1.54677i	0.0823261	+	0.0823261i	−0.664745	+	0.747071i	$0.731460\pi$
$354$	−11.0142	−	37.1591i	−0.585397	−	1.97499i
$355$	0.829985	+	0.353892i	0.0440510	+	0.0187827i
$356$	22.1505	+	4.70006i	1.17397	+	0.249103i
$357$		−	3.68437i		−	0.194997i
$358$	−0.200142	−	0.108622i	−0.0105778	−	0.00574087i
$359$	12.9866			0.685407			0.342703	−	0.939444i	$-0.388657\pi$
$359$	12.9866			0.685407			0.342703	+	0.939444i	$0.388657\pi$
$360$	−9.06412	+	26.9923i	−0.477721	+	1.42262i
$361$		−	17.7838i		−	0.935988i
$362$	3.51270	+	1.90644i	0.184623	+	0.100200i
$363$	24.9161			1.30776
$364$	−0.823885	+	0.535451i	−0.0431833	+	0.0280652i
$365$	−11.6413	+	27.3025i	−0.609335	+	1.42908i
$366$	27.0208	−	8.00912i	1.41240	−	0.418643i
$367$	19.3087	−	19.3087i	1.00791	−	1.00791i	0.00793712	−	0.999969i	$-0.497474\pi$
$367$	19.3087	−	19.3087i	1.00791	−	1.00791i	0.999969	−	0.00793712i	$-0.00252649\pi$
$368$	0.0558951	+	0.145305i	0.00291373	+	0.00757454i
$369$	26.5447	−	11.2422i	1.38186	−	0.585247i
$370$	−0.0887312	+	0.768938i	−0.00461292	+	0.0399752i
$371$	0.684821			0.0355541
$372$	26.6764	−	17.3373i	1.38311	−	0.898896i
$373$	6.00229	+	6.00229i	0.310787	+	0.310787i	0.845214	−	0.534428i	$-0.179473\pi$
$373$	6.00229	+	6.00229i	0.310787	+	0.310787i	−0.534428	+	0.845214i	$0.679473\pi$
$374$	−4.55577	−	2.47254i	−0.235573	−	0.127852i
$375$	−27.9146	−	12.5910i	−1.44150	−	0.650194i
$376$	6.00942	+	5.12703i	0.309912	+	0.264406i
$377$	5.14262	+	5.14262i	0.264859	+	0.264859i
$378$	0.837138	+	2.82430i	0.0430577	+	0.145266i
$379$	−18.9657			−0.974201			−0.487100	−	0.873346i	$-0.661945\pi$
$379$	−18.9657			−0.974201			−0.487100	+	0.873346i	$0.661945\pi$
$380$	4.85814	−	0.850295i	0.249218	−	0.0436192i
$381$	18.4451	−	18.4451i	0.944969	−	0.944969i
$382$	−18.2458	+	33.6187i	−0.933534	+	1.72008i
$383$	24.6155			1.25779			0.628897	−	0.777489i	$-0.283507\pi$
$383$	24.6155			1.25779			0.628897	+	0.777489i	$0.283507\pi$
$384$	−27.9529	+	13.3753i	−1.42647	+	0.682555i
$385$	1.43667	+	0.612572i	0.0732193	+	0.0312195i
$386$	32.9690	−	9.77219i	1.67808	−	0.497391i
$387$	−12.3139	−	12.3139i	−0.625949	−	0.625949i
$388$	−9.03420	+	5.87142i	−0.458642	+	0.298076i
$389$	−20.8413			−1.05669			−0.528347	−	0.849029i	$-0.677188\pi$
$389$	−20.8413			−1.05669			−0.528347	+	0.849029i	$0.677188\pi$
$390$	−5.22267	−	6.58523i	−0.264460	−	0.333456i
$391$	0.0731205	−	0.0731205i	0.00369786	−	0.00369786i
$392$	12.3799	−	14.5105i	0.625277	−	0.732892i
$393$		−	38.6755i		−	1.95092i
$394$	14.9161	+	8.09536i	0.751462	+	0.407838i
$395$	−6.64786	+	15.5913i	−0.334490	+	0.784481i
$396$	12.1511	+	2.57832i	0.610618	+	0.129565i
$397$		−	10.1917i		−	0.511509i	−0.966742	−	0.255754i	$-0.917676\pi$
$397$		−	10.1917i		−	0.511509i	0.966742	−	0.255754i	$-0.0823238\pi$
$398$	21.5957	+	11.7206i	1.08249	+	0.587499i
$399$	1.08140	−	1.08140i	0.0541379	−	0.0541379i
$400$	−6.79289	−	18.8111i	−0.339645	−	0.940554i
$401$			12.5184i			0.625142i	0.949894	+	0.312571i	$0.101190\pi$
$401$			12.5184i			0.625142i	−0.949894	+	0.312571i	$0.898810\pi$
$402$	11.1527	−	3.30571i	0.556244	−	0.164874i
$403$			5.63580i			0.280739i
$404$	−34.3343	−	7.28530i	−1.70819	−	0.362457i
$405$	4.64222	−	1.86685i	0.230674	−	0.0927648i
$406$	4.71650	+	2.55977i	0.234076	+	0.127039i
$407$	0.337678			0.0167381
$408$	15.6583	+	13.3591i	0.775202	+	0.661375i
$409$			23.6147i			1.16767i	0.811872	+	0.583835i	$0.198449\pi$
$409$			23.6147i			1.16767i	−0.811872	+	0.583835i	$0.801551\pi$
$410$	−9.70173	+	17.7729i	−0.479134	+	0.877742i
$411$		−	47.6367i		−	2.34974i
$412$	−25.4808	−	5.40671i	−1.25535	−	0.266369i
$413$	5.06583			0.249273
$414$	−0.118204	+	0.217797i	−0.00580943	+	0.0107042i
$415$	3.07776	−	7.21828i	0.151081	−	0.354331i
$416$	0.711688	−	5.44294i	0.0348934	−	0.266862i
$417$			48.8826i			2.39379i
$418$	−0.611452	−	2.06289i	−0.0299071	−	0.100899i
$419$			10.4033i			0.508236i	0.967173	+	0.254118i	$0.0817851\pi$
$419$			10.4033i			0.508236i	−0.967173	+	0.254118i	$0.918215\pi$
$420$	−5.07563	−	3.56356i	−0.247665	−	0.173884i
$421$	9.23337	−	9.23337i	0.450007	−	0.450007i	−0.445350	−	0.895357i	$-0.646921\pi$
$421$	9.23337	−	9.23337i	0.450007	−	0.450007i	0.895357	+	0.445350i	$0.146921\pi$
$422$	19.2148	−	35.4042i	0.935362	−	1.72345i
$423$			12.5735i			0.611346i
$424$	−2.48309	+	2.91044i	−0.120589	+	0.141344i
$425$	−9.58569	+	9.19709i	−0.464974	+	0.446124i
$426$	−0.745563	+	1.37374i	−0.0361227	+	0.0665577i
$427$			3.68369i			0.178266i
$428$	6.66762	+	1.41478i	0.322291	+	0.0683862i
$429$	−2.59271	+	2.59271i	−0.125177	+	0.125177i
$430$	12.1514	+	1.40220i	0.585992	+	0.0676203i
$431$	−29.7537			−1.43319			−0.716593	−	0.697491i	$-0.754300\pi$
$431$	−29.7537			−1.43319			−0.716593	+	0.697491i	$0.754300\pi$
$432$	−15.0385	−	6.68283i	−0.723538	−	0.321528i
$433$	24.5015	+	24.5015i	1.17747	+	1.17747i	0.980387	+	0.197080i	$0.0631458\pi$
$433$	24.5015	+	24.5015i	1.17747	+	1.17747i	0.197080	+	0.980387i	$0.436854\pi$
$434$	1.18178	+	3.98703i	0.0567272	+	0.191384i
$435$	−18.0038	+	42.2243i	−0.863214	+	2.02450i
$436$	−1.96667	+	9.26857i	−0.0941866	+	0.443884i
$437$	0.0429234			0.00205330
$438$	−45.1892	−	24.5254i	−2.15922	−	1.17187i
$439$	8.96296	−	8.96296i	0.427779	−	0.427779i	−0.460092	−	0.887871i	$-0.652184\pi$
$439$	8.96296	−	8.96296i	0.427779	−	0.427779i	0.887871	+	0.460092i	$0.152184\pi$
$440$	−7.81259	+	3.88462i	−0.372451	+	0.185192i
$441$	30.3604			1.44573
$442$	−3.49572	+	1.03615i	−0.166275	+	0.0492847i
$443$	22.9626	+	22.9626i	1.09099	+	1.09099i	0.995424	+	0.0955617i	$0.0304647\pi$
$443$	22.9626	+	22.9626i	1.09099	+	1.09099i	0.0955617	+	0.995424i	$0.469535\pi$
$444$	−1.31166	−	0.278317i	−0.0622486	−	0.0132084i
$445$	−23.2878	−	9.92956i	−1.10395	−	0.470706i
$446$	15.7950	−	29.1031i	0.747917	−	1.37807i
$447$	−10.7671	−	10.7671i	−0.509267	−	0.509267i
$448$	−0.637856	−	3.99983i	−0.0301359	−	0.188974i
$449$	37.5738			1.77322			0.886610	−	0.462518i	$-0.153054\pi$
$449$	37.5738			1.77322			0.886610	+	0.462518i	$0.153054\pi$
$450$	15.7606	−	27.6592i	0.742962	−	1.30387i
$451$	8.18756	+	3.31570i	0.385537	+	0.156130i
$452$	−12.6301	−	2.67994i	−0.594069	−	0.126054i
$453$	−15.1917	+	15.1917i	−0.713767	+	0.713767i
$454$	−9.33981	−	31.5102i	−0.438339	−	1.47885i
$455$	1.01924	−	0.409886i	0.0477829	−	0.0192158i
$456$	0.674839	+	8.51694i	0.0316022	+	0.398842i
$457$	9.69803			0.453655			0.226827	−	0.973935i	$-0.427165\pi$
$457$	9.69803			0.453655			0.226827	+	0.973935i	$0.427165\pi$
$458$	−15.0621	+	27.7527i	−0.703807	+	1.29680i
$459$			10.9306i			0.510198i
$460$	−0.0300088	−	0.171455i	−0.00139917	−	0.00799411i
$461$	−8.82193			−0.410878			−0.205439	−	0.978670i	$-0.565862\pi$
$461$	−8.82193			−0.410878			−0.205439	+	0.978670i	$0.565862\pi$
$462$	−1.29054	+	2.37787i	−0.0600412	+	0.110629i
$463$		−	4.22273i		−	0.196247i	−0.995174	−	0.0981235i	$-0.968716\pi$
$463$		−	4.22273i		−	0.196247i	0.995174	−	0.0981235i	$-0.0312840\pi$
$464$	−27.9804	+	10.7633i	−1.29896	+	0.499676i
$465$	−33.0020	+	13.2716i	−1.53043	+	0.615458i
$466$	34.5136	−	10.2300i	1.59881	−	0.473897i
$467$	−10.6127	−	10.6127i	−0.491098	−	0.491098i	0.417554	−	0.908652i	$-0.362887\pi$
$467$	−10.6127	−	10.6127i	−0.491098	−	0.491098i	−0.908652	+	0.417554i	$0.862887\pi$
$468$	7.32610	−	4.76130i	0.338649	−	0.220091i
$469$			1.52042i			0.0702065i
$470$	−5.48792	−	6.91969i	−0.253139	−	0.319182i
$471$	−30.8667			−1.42226
$472$	−18.3682	+	21.5295i	−0.845463	+	0.990973i
$473$		−	5.33626i		−	0.245362i
$474$	−25.8056	−	14.0054i	−1.18529	−	0.643289i
$475$	−5.51296	−	0.114060i	−0.252952	−	0.00523344i
$476$	−2.25577	+	1.46605i	−0.103393	+	0.0671961i
$477$	−6.08952			−0.278820
$478$	10.5284	−	19.3991i	0.481559	−	0.887295i
$479$	−9.98779	+	9.98779i	−0.456354	+	0.456354i	−0.897457	−	0.441103i	$-0.854587\pi$
$479$	−9.98779	+	9.98779i	−0.456354	+	0.456354i	0.441103	+	0.897457i	$0.354587\pi$
$480$	33.5486	−	8.65000i	1.53128	−	0.394817i
$481$	0.167953	−	0.167953i	0.00765801	−	0.00765801i
$482$	2.70698	+	9.13270i	0.123300	+	0.415983i
$483$	−0.0381651	−	0.0381651i	−0.00173657	−	0.00173657i
$484$	−9.91437	−	15.2550i	−0.450653	−	0.693408i
$485$	11.1764	−	4.49456i	0.507494	−	0.204087i
$486$	7.42356	+	25.0453i	0.336739	+	1.13608i
$487$	8.53027	−	8.53027i	0.386543	−	0.386543i	−0.486909	−	0.873453i	$-0.661876\pi$
$487$	8.53027	−	8.53027i	0.386543	−	0.386543i	0.873453	+	0.486909i	$0.161876\pi$
$488$	−15.6555	−	13.3567i	−0.708689	−	0.604629i
$489$	−34.2810	−	34.2810i	−1.55024	−	1.55024i
$490$	−16.7085	+	13.2513i	−0.754812	+	0.598632i
$491$			2.95377i			0.133302i	0.997776	+	0.0666509i	$0.0212314\pi$
$491$			2.95377i			0.133302i	−0.997776	+	0.0666509i	$0.978769\pi$
$492$	−29.0705	−	19.6276i	−1.31060	−	0.884881i
$493$	14.0803	+	14.0803i	0.634146	+	0.634146i
$494$	−1.33016	−	0.721912i	−0.0598466	−	0.0324803i
$495$	−12.7750	−	5.44707i	−0.574195	−	0.244828i
$496$	−21.2296	−	9.43407i	−0.953239	−	0.423602i
$497$	−0.144460	−	0.144460i	−0.00647992	−	0.00647992i
$498$	11.9472	+	6.48408i	0.535368	+	0.290558i
$499$	5.67254	−	5.67254i	0.253938	−	0.253938i	−0.568645	−	0.822583i	$-0.692532\pi$
$499$	5.67254	−	5.67254i	0.253938	−	0.253938i	0.822583	+	0.568645i	$0.192532\pi$
$500$	3.39864	+	22.1009i	0.151992	+	0.988382i
$501$			13.9814i			0.624645i
$502$	−16.3931	+	4.85899i	−0.731658	+	0.216867i
$503$		−	16.6210i		−	0.741094i	−0.928814	−	0.370547i	$-0.879170\pi$
$503$		−	16.6210i		−	0.741094i	0.928814	−	0.370547i	$-0.120830\pi$
$504$	4.18442	−	4.90459i	0.186389	−	0.218468i
$505$	36.0972	+	15.3913i	1.60630	+	0.684902i
$506$	−0.0728039	+	0.0215795i	−0.00323653	+	0.000959325i
$507$		−	33.0277i		−	1.46681i
$508$	−18.6325	−	3.95359i	−0.826685	−	0.175412i
$509$	14.7461	−	14.7461i	0.653610	−	0.653610i	−0.300251	−	0.953860i	$-0.597070\pi$
$509$	14.7461	−	14.7461i	0.653610	−	0.653610i	0.953860	+	0.300251i	$0.0970703\pi$
$510$	−14.2995	−	18.0301i	−0.633192	−	0.798388i
$511$	4.75203	−	4.75203i	0.210217	−	0.210217i
$512$	19.3118	+	11.7921i	0.853470	+	0.521143i
$513$	−3.20826	+	3.20826i	−0.141648	+	0.141648i
$514$	2.00755	+	6.77299i	0.0885494	+	0.298744i
$515$	26.7891	+	11.4225i	1.18047	+	0.503334i
$516$	−4.39820	+	20.7279i	−0.193620	+	0.912495i
$517$	−2.72439	+	2.72439i	−0.119819	+	0.119819i
$518$	0.0835997	−	0.154036i	0.00367316	−	0.00676797i
$519$	9.19313	+	9.19313i	0.403533	+	0.403533i
$520$	−1.95368	+	5.81793i	−0.0856747	+	0.255133i
$521$	0.192870	−	0.192870i	0.00844978	−	0.00844978i	−0.702869	−	0.711319i	$-0.748098\pi$
$521$	0.192870	−	0.192870i	0.00844978	−	0.00844978i	0.711319	+	0.702869i	$0.248098\pi$
$522$	−41.9398	−	22.7618i	−1.83565	−	0.996259i
$523$	−17.3160	+	17.3160i	−0.757176	+	0.757176i	−0.975807	−	0.218632i	$-0.929841\pi$
$523$	−17.3160	+	17.3160i	−0.757176	+	0.757176i	0.218632	+	0.975807i	$0.429841\pi$
$524$	−23.6792	+	15.3894i	−1.03443	+	0.672288i
$525$	4.80040	+	5.00323i	0.209507	+	0.218359i
$526$	2.60332	−	0.771638i	0.113510	−	0.0336450i
$527$			15.4306i			0.672169i
$528$	−5.42646	−	14.1066i	−0.236156	−	0.613912i
$529$			22.9985i			0.999934i
$530$	3.35130	−	2.65787i	0.145571	−	0.115451i
$531$	−45.0461			−1.95483
$532$	−1.09239	−	0.231792i	−0.0473613	−	0.0100495i
$533$	5.72146	−	2.42315i	0.247824	−	0.104958i
$534$	20.9191	−	38.5445i	0.905259	−	1.66798i
$535$	−7.00997	−	2.98894i	−0.303067	−	0.129223i
$536$	−6.46169	−	5.51289i	−0.279103	−	0.238120i
$537$	−0.311859	+	0.311859i	−0.0134577	+	0.0134577i
$538$	−2.02338	−	6.82639i	−0.0872342	−	0.294307i
$539$	6.57839	+	6.57839i	0.283351	+	0.283351i
$540$	15.0582	+	10.5722i	0.648000	+	0.454955i
$541$			28.5162i			1.22601i	0.790081	+	0.613003i	$0.210039\pi$
$541$			28.5162i			1.22601i	−0.790081	+	0.613003i	$0.789961\pi$
$542$	−2.73211	−	9.21749i	−0.117354	−	0.395925i
$543$	5.47345	−	5.47345i	0.234888	−	0.234888i
$544$	1.94858	−	14.9026i	0.0835445	−	0.638943i
$545$	4.15488	−	9.74447i	0.177976	−	0.417407i
$546$	0.540817	+	1.82458i	0.0231448	+	0.0780850i
$547$			4.89489i			0.209291i	0.994510	+	0.104645i	$0.0333707\pi$
$547$			4.89489i			0.209291i	−0.994510	+	0.104645i	$0.966629\pi$
$548$	−29.1658	+	18.9551i	−1.24590	+	0.809722i
$549$		−	32.7559i		−	1.39799i
$550$	9.40807	−	2.57815i	0.401161	−	0.109932i
$551$			8.26547i			0.352121i
$552$	0.300582	−	0.0238165i	0.0127936	−	0.00101370i
$553$	2.71368	−	2.71368i	0.115397	−	0.115397i
$554$	−8.09216	+	14.9102i	−0.343803	+	0.633473i
$555$	1.37901	+	0.587986i	0.0585356	+	0.0249586i
$556$	29.9286	−	19.4509i	1.26925	−	0.824901i
$557$	14.2279			0.602857			0.301429	−	0.953489i	$-0.402537\pi$
$557$	14.2279			0.602857			0.301429	+	0.953489i	$0.402537\pi$
$558$	−10.5085	−	35.4533i	−0.444862	−	1.50086i
$559$	−2.65414	−	2.65414i	−0.112258	−	0.112258i
$560$	−0.162160	+	4.52555i	−0.00685249	+	0.191239i
$561$	−7.09875	+	7.09875i	−0.299709	+	0.299709i
$562$	25.9131	+	14.0637i	1.09308	+	0.593243i
$563$			22.5681i			0.951134i	0.879680	+	0.475567i	$0.157757\pi$
$563$			22.5681i			0.951134i	−0.879680	+	0.475567i	$0.842243\pi$
$564$	12.8280	−	8.33702i	0.540155	−	0.351052i
$565$	13.2786	+	5.66177i	0.558634	+	0.238193i
$566$	18.4357	−	33.9686i	0.774910	−	1.42781i
$567$	−1.13291			−0.0475779
$568$	1.13774	−	0.0901488i	0.0477386	−	0.00378256i
$569$	37.6419			1.57803			0.789015	−	0.614374i	$-0.210592\pi$
$569$	37.6419			1.57803			0.789015	+	0.614374i	$0.210592\pi$
$570$	1.09499	−	9.48911i	0.0458641	−	0.397455i
$571$	7.63312	+	7.63312i	0.319436	+	0.319436i	0.848550	−	0.529115i	$-0.177476\pi$
$571$	7.63312	+	7.63312i	0.319436	+	0.319436i	−0.529115	+	0.848550i	$0.677476\pi$
$572$	2.61906	+	0.555732i	0.109508	+	0.0232363i
$573$	52.3842	+	52.3842i	2.18838	+	2.18838i
$574$	3.53952	−	2.91399i	0.147737	−	0.121628i
$575$	−0.00402544	+	0.194564i	−0.000167872	+	0.00811390i
$576$	5.67191	+	35.5670i	0.236330	+	1.48196i
$577$			38.7552i			1.61340i	0.590960	+	0.806701i	$0.298749\pi$
$577$			38.7552i			1.61340i	−0.590960	+	0.806701i	$0.701251\pi$
$578$	13.4792	−	3.99532i	0.560662	−	0.166183i
$579$		−	66.5988i		−	2.76775i
$580$	33.0159	−	5.77859i	1.37091	−	0.239943i
$581$	−1.25635	+	1.25635i	−0.0521222	+	0.0521222i
$582$	5.93026	+	20.0073i	0.245817	+	0.829327i
$583$	−1.31946	−	1.31946i	−0.0546464	−	0.0546464i
$584$	2.96546	+	37.4262i	0.122712	+	1.54871i
$585$	−9.06327	+	3.64477i	−0.374720	+	0.150693i
$586$	−6.29855	−	21.2498i	−0.260191	−	0.877819i
$587$	−33.6979			−1.39086			−0.695432	−	0.718592i	$-0.744787\pi$
$587$	−33.6979			−1.39086			−0.695432	+	0.718592i	$0.744787\pi$
$588$	−20.1308	−	30.9748i	−0.830180	−	1.27738i
$589$	−4.52906	+	4.52906i	−0.186617	+	0.186617i
$590$	24.7906	−	19.6611i	1.02061	−	0.809435i
$591$	23.2421	−	23.2421i	0.956051	−	0.956051i
$592$	0.351521	+	0.913813i	0.0144474	+	0.0375575i
$593$			27.3857i			1.12460i	0.826935	+	0.562298i	$0.190083\pi$
$593$			27.3857i			1.12460i	−0.826935	+	0.562298i	$0.809917\pi$
$594$	3.82871	−	7.05458i	0.157094	−	0.289453i
$595$	2.79066	−	1.12225i	0.114406	−	0.0460079i
$596$	−2.30787	+	10.8765i	−0.0945339	+	0.445521i
$597$	33.6502	−	33.6502i	1.37721	−	1.37721i
$598$	−0.0254779	+	0.0469441i	−0.00104187	+	0.00191969i
$599$	−4.24282			−0.173357			−0.0866785	−	0.996236i	$-0.527625\pi$
$599$	−4.24282			−0.173357			−0.0866785	+	0.996236i	$0.527625\pi$
$600$	−38.6691	+	2.26020i	−1.57866	+	0.0922721i
$601$	7.81811	+	7.81811i	0.318907	+	0.318907i	0.848347	−	0.529440i	$-0.177598\pi$
$601$	7.81811	+	7.81811i	0.318907	+	0.318907i	−0.529440	+	0.848347i	$0.677598\pi$
$602$	−2.43421	−	1.32111i	−0.0992110	−	0.0538445i
$603$		−	13.5198i		−	0.550569i
$604$	15.3461	+	3.25625i	0.624423	+	0.132495i
$605$	7.58942	+	18.8723i	0.308554	+	0.767266i
$606$	−32.4256	+	59.7456i	−1.31720	+	2.42700i
$607$	1.38399	−	1.38399i	0.0561744	−	0.0561744i	−0.678462	−	0.734636i	$-0.737353\pi$
$607$	1.38399	−	1.38399i	0.0561744	−	0.0561744i	0.734636	+	0.678462i	$0.237353\pi$
$608$	4.94601	−	3.80215i	0.200587	−	0.154197i
$609$	7.34919	−	7.34919i	0.297804	−	0.297804i
$610$	14.2969	+	18.0269i	0.578863	+	0.729886i
$611$			2.71010i			0.109639i
$612$	20.0586	−	13.0363i	0.810821	−	0.526961i
$613$	−12.5008	+	12.5008i	−0.504904	+	0.504904i	−0.912958	−	0.408054i	$-0.866208\pi$
$613$	−12.5008	+	12.5008i	−0.504904	+	0.504904i	0.408054	+	0.912958i	$0.366208\pi$
$614$	12.2661	−	22.6009i	0.495020	−	0.912098i
$615$	27.6628	+	27.7973i	1.11547	+	1.12090i
$616$	1.96938	−	0.156044i	0.0793486	−	0.00628718i
$617$	−12.5111	−	12.5111i	−0.503678	−	0.503678i	0.408901	−	0.912579i	$-0.365912\pi$
$617$	−12.5111	−	12.5111i	−0.503678	−	0.503678i	−0.912579	+	0.408901i	$0.865912\pi$
$618$	−24.0643	+	44.3396i	−0.968008	+	1.78360i
$619$	40.0488			1.60970			0.804848	−	0.593481i	$-0.202247\pi$
$619$	40.0488			1.60970			0.804848	+	0.593481i	$0.202247\pi$
$620$	21.2574	+	14.9247i	0.853719	+	0.599389i
$621$	0.113227	+	0.113227i	0.00454362	+	0.00454362i
$622$	−6.90315	+	12.7194i	−0.276791	+	0.510001i
$623$	4.05328	+	4.05328i	0.162391	+	0.162391i
$624$	−9.71531	−	4.31731i	−0.388924	−	0.172831i
$625$	1.03403	−	24.9786i	0.0413613	−	0.999144i
$626$	2.59359	+	8.75014i	0.103661	+	0.349726i
$627$	−4.16713			−0.166419
$628$	12.2822	+	18.8983i	0.490112	+	0.754123i
$629$	0.459850	−	0.459850i	0.0183354	−	0.0183354i
$630$	−5.64751	+	4.47897i	−0.225002	+	0.178446i
$631$			38.3960i			1.52852i	0.644907	+	0.764261i	$0.276896\pi$
$631$			38.3960i			1.52852i	−0.644907	+	0.764261i	$0.723104\pi$
$632$	1.69345	+	21.3725i	0.0673616	+	0.850151i
$633$	−55.1664	−	55.1664i	−2.19267	−	2.19267i
$634$	12.5090	+	42.2023i	0.496796	+	1.67607i
$635$	19.5892	+	8.35253i	0.777375	+	0.331460i
$636$	4.03773	+	6.21275i	0.160106	+	0.246352i
$637$	6.54389			0.259278
$638$	−4.15541	−	14.0193i	−0.164514	−	0.555031i
$639$	1.28456	+	1.28456i	0.0508163	+	0.0508163i
$640$	−18.6453	−	17.0983i	−0.737020	−	0.675871i
$641$	−6.37039	−	6.37039i	−0.251615	−	0.251615i	0.570017	−	0.821633i	$-0.306936\pi$
$641$	−6.37039	−	6.37039i	−0.251615	−	0.251615i	−0.821633	+	0.570017i	$0.806936\pi$
$642$	6.29695	−	11.6024i	0.248521	−	0.457911i
$643$			37.3655i			1.47355i	0.676136	+	0.736776i	$0.263653\pi$
$643$			37.3655i			1.47355i	−0.676136	+	0.736776i	$0.736347\pi$
$644$	−0.00818046	+	0.0385530i	−0.000322355	+	0.00151920i
$645$	9.29184	−	21.7922i	0.365866	−	0.858066i
$646$	−3.64192	−	1.97657i	−0.143289	−	0.0777671i
$647$	30.6277	−	30.6277i	1.20410	−	1.20410i	0.231192	−	0.972908i	$-0.425738\pi$
$647$	30.6277	−	30.6277i	1.20410	−	1.20410i	0.972908	−	0.231192i	$-0.0742624\pi$
$648$	4.10782	−	4.81481i	0.161371	−	0.189143i
$649$	−9.76045	−	9.76045i	−0.383131	−	0.383131i
$650$	3.39705	−	5.96167i	0.133243	−	0.233836i
$651$	8.05398			0.315660
$652$	−7.34793	+	34.6294i	−0.287767	+	1.35619i
$653$	−25.7433			−1.00741			−0.503707	−	0.863875i	$-0.668031\pi$
$653$	−25.7433			−1.00741			−0.503707	+	0.863875i	$0.668031\pi$
$654$	16.1284	+	8.75331i	0.630670	+	0.342282i
$655$	29.2941	−	11.7805i	1.14461	−	0.460303i
$656$	−0.449632	+	25.6085i	−0.0175552	+	0.999846i
$657$	−42.2557	+	42.2557i	−1.64855	+	1.64855i
$658$	0.568285	+	1.91725i	0.0221541	+	0.0747424i
$659$	28.0296	−	28.0296i	1.09188	−	1.09188i	0.0965521	−	0.995328i	$-0.469219\pi$
$659$	28.0296	−	28.0296i	1.09188	−	1.09188i	0.995328	−	0.0965521i	$-0.0307814\pi$
$660$	2.91334	+	16.6453i	0.113402	+	0.647918i
$661$		−	15.2495i		−	0.593135i	−0.955012	−	0.296567i	$-0.904158\pi$
$661$		−	15.2495i		−	0.593135i	0.955012	−	0.296567i	$-0.0958420\pi$
$662$	22.5419	+	12.2341i	0.876117	+	0.475493i
$663$			7.06152i			0.274247i
$664$	−0.784014	−	9.89481i	−0.0304256	−	0.383993i
$665$	1.14848	+	0.489695i	0.0445363	+	0.0189896i
$666$	−0.743381	+	1.36971i	−0.0288054	+	0.0530753i
$667$	0.291706			0.0112949
$668$	8.56020	−	5.56336i	0.331204	−	0.215253i
$669$	−45.3481	−	45.3481i	−1.75326	−	1.75326i
$670$	5.90094	+	7.44047i	0.227973	+	0.287450i
$671$	7.09746	−	7.09746i	0.273994	−	0.273994i
$672$	−7.77837	−	1.01705i	−0.300057	−	0.0392337i
$673$		−	7.69551i		−	0.296640i	−0.988939	−	0.148320i	$-0.952613\pi$
$673$		−	7.69551i		−	0.296640i	0.988939	−	0.148320i	$-0.0473866\pi$
$674$	−0.266121	−	0.144431i	−0.0102506	−	0.00556329i
$675$	−14.2416	−	14.8434i	−0.548160	−	0.571322i
$676$	−20.2214	+	13.1421i	−0.777745	+	0.505464i
$677$	12.4753	+	12.4753i	0.479467	+	0.479467i	0.904961	−	0.425494i	$-0.139900\pi$
$677$	12.4753	+	12.4753i	0.479467	+	0.479467i	−0.425494	+	0.904961i	$0.639900\pi$
$678$	−11.9280	+	21.9778i	−0.458090	+	0.844053i
$679$	−2.72755			−0.104674
$680$	−5.34912	+	15.9293i	−0.205129	+	0.610860i
$681$	−63.6521			−2.43915
$682$	5.40495	−	9.95887i	0.206966	−	0.381345i
$683$	15.2321			0.582839			0.291419	−	0.956595i	$-0.405872\pi$
$683$	15.2321			0.582839			0.291419	+	0.956595i	$0.405872\pi$
$684$	9.71372	+	2.06113i	0.371413	+	0.0788092i
$685$	36.0816	−	14.5101i	1.37861	−	0.554402i
$686$	9.43488	−	2.79655i	0.360225	−	0.106773i
$687$	43.2439	+	43.2439i	1.64986	+	1.64986i
$688$	14.4408	−	5.55502i	0.550551	−	0.211783i
$689$	−1.31254			−0.0500037
$690$	−0.334891	−	0.0386446i	−0.0127491	−	0.00147118i
$691$	20.4510	−	20.4510i	0.777991	−	0.777991i	−0.201498	−	0.979489i	$-0.564581\pi$
$691$	20.4510	−	20.4510i	0.777991	−	0.777991i	0.979489	+	0.201498i	$0.0645809\pi$
$692$	1.97049	−	9.28656i	0.0749068	−	0.353022i
$693$	2.22351	+	2.22351i	0.0844643	+	0.0844643i
$694$	6.66625	+	22.4903i	0.253047	+	0.853720i
$695$	−37.0253	+	14.8896i	−1.40445	+	0.564795i
$696$	4.58619	+	57.8810i	0.173839	+	2.19397i
$697$	15.6652	−	6.63451i	0.593360	−	0.251300i
$698$	−24.9666	+	7.40025i	−0.945001	+	0.280104i
$699$		−	69.7190i		−	2.63701i
$700$	1.15312	−	4.92990i	0.0435839	−	0.186333i
$701$	−36.6370			−1.38376			−0.691880	−	0.722013i	$-0.743217\pi$
$701$	−36.6370			−1.38376			−0.691880	+	0.722013i	$0.743217\pi$
$702$	−1.60447	−	5.41310i	−0.0605569	−	0.204304i
$703$	0.269942			0.0101811
$704$	−6.47759	+	8.93553i	−0.244133	+	0.336771i
$705$	−15.8697	+	6.38197i	−0.597689	+	0.240359i
$706$	−2.71891	−	1.47563i	−0.102328	−	0.0555359i
$707$	−6.28276	−	6.28276i	−0.236288	−	0.236288i
$708$	29.8683	+	45.9577i	1.12252	+	1.72719i
$709$	−7.99114	−	7.99114i	−0.300114	−	0.300114i	0.540945	−	0.841058i	$-0.318067\pi$
$709$	−7.99114	−	7.99114i	−0.300114	−	0.300114i	−0.841058	+	0.540945i	$0.818067\pi$
$710$	−1.26761	−	0.146275i	−0.0475725	−	0.00548961i
$711$	−24.1304	+	24.1304i	−0.904961	+	0.904961i
$712$	−31.9229	+	2.52941i	−1.19636	+	0.0947936i
$713$	0.159841	+	0.159841i	0.00598608	+	0.00598608i
$714$	1.48074	+	4.99565i	0.0554152	+	0.186957i
$715$	−2.75354	−	1.17407i	−0.102977	−	0.0439075i
$716$	0.315028	+	0.0668450i	0.0117732	+	0.00249812i
$717$	−30.2275	−	30.2275i	−1.12887	−	1.12887i
$718$	−17.6086	+	5.21929i	−0.657147	+	0.194782i
$719$	24.2611	+	24.2611i	0.904785	+	0.904785i	0.995845	−	0.0910603i	$-0.0290256\pi$
$719$	24.2611	+	24.2611i	0.904785	+	0.904785i	−0.0910603	+	0.995845i	$0.529026\pi$
$720$	1.44195	−	40.2418i	0.0537382	−	1.49972i
$721$	−4.66269	−	4.66269i	−0.173647	−	0.173647i
$722$	7.14726	+	24.1131i	0.265993	+	0.897397i
$723$	18.4485			0.686106
$724$	−5.52908	−	1.17320i	−0.205487	−	0.0436017i
$725$	−37.4660	−	0.775151i	−1.39145	−	0.0287884i
$726$	−33.7839	+	10.0137i	−1.25384	+	0.371644i
$727$	−53.4008			−1.98053			−0.990263	−	0.139209i	$-0.955544\pi$
$727$	−53.4008			−1.98053			−0.990263	+	0.139209i	$0.955544\pi$
$728$	0.901913	−	1.05714i	0.0334271	−	0.0391801i
$729$	43.8796			1.62517
$730$	4.81174	−	41.6982i	0.178091	−	1.54332i
$731$	−7.26693	−	7.26693i	−0.268777	−	0.268777i
$732$	−33.4188	+	21.7192i	−1.23519	+	0.802765i
$733$	1.06150	−	1.06150i	0.0392074	−	0.0392074i	−0.687231	−	0.726439i	$-0.741174\pi$
$733$	1.06150	−	1.06150i	0.0392074	−	0.0392074i	0.726439	+	0.687231i	$0.241174\pi$
$734$	−18.4206	+	33.9409i	−0.679918	+	1.25278i
$735$	15.4101	+	38.3195i	0.568409	+	1.41344i
$736$	−0.134186	−	0.174555i	−0.00494617	−	0.00643420i
$737$	2.92943	−	2.92943i	0.107907	−	0.107907i
$738$	−31.4739	+	25.9116i	−1.15857	+	0.953821i
$739$	−16.8153			−0.618561			−0.309280	−	0.950971i	$-0.600088\pi$
$739$	−16.8153			−0.618561			−0.309280	+	0.950971i	$0.600088\pi$
$740$	−0.188723	−	1.07827i	−0.00693761	−	0.0396379i
$741$	−2.07263	+	2.07263i	−0.0761401	+	0.0761401i
$742$	−0.928552	+	0.275228i	−0.0340882	+	0.0101039i
$743$	−15.2017	−	15.2017i	−0.557698	−	0.557698i	0.370953	−	0.928651i	$-0.379031\pi$
$743$	−15.2017	−	15.2017i	−0.557698	−	0.557698i	−0.928651	+	0.370953i	$0.879031\pi$
$744$	−29.2029	+	34.2289i	−1.07063	+	1.25489i
$745$	4.87571	−	11.4350i	0.178632	−	0.418946i
$746$	−10.5508	−	5.72622i	−0.386294	−	0.209652i
$747$	11.1717	−	11.1717i	0.408749	−	0.408749i
$748$	7.17090	+	1.52157i	0.262194	+	0.0556343i
$749$	1.22009	+	1.22009i	0.0445813	+	0.0445813i
$750$	42.9098	+	5.85332i	1.56685	+	0.213733i
$751$	23.2313	+	23.2313i	0.847724	+	0.847724i	0.989849	−	0.142125i	$-0.0453935\pi$
$751$	23.2313	+	23.2313i	0.847724	+	0.847724i	−0.142125	+	0.989849i	$0.545393\pi$
$752$	−10.2087	−	4.53659i	−0.372275	−	0.165432i
$753$			33.1147i			1.20677i
$754$	−9.03972	−	4.90610i	−0.329207	−	0.178670i
$755$	−16.1340	−	6.87930i	−0.587178	−	0.250363i
$756$	−2.27016	−	3.49304i	−0.0825649	−	0.127041i
$757$	−45.6472			−1.65908			−0.829539	−	0.558449i	$-0.811397\pi$
$757$	−45.6472			−1.65908			−0.829539	+	0.558449i	$0.811397\pi$
$758$	25.7156	−	7.62226i	0.934034	−	0.276853i
$759$			0.147067i			0.00533820i
$760$	−6.24545	+	3.10540i	−0.226546	+	0.112645i
$761$	−0.106407			−0.00385725			−0.00192862	−	0.999998i	$-0.500614\pi$
$761$	−0.106407			−0.00385725			−0.00192862	+	0.999998i	$0.500614\pi$
$762$	−17.5967	+	32.4228i	−0.637462	+	1.17455i
$763$	−1.69604	+	1.69604i	−0.0614007	+	0.0614007i
$764$	11.2282	−	52.9166i	0.406224	−	1.91446i
$765$	−24.8149	+	9.97924i	−0.897185	+	0.360800i
$766$	−33.3763	+	9.89291i	−1.20593	+	0.357446i
$767$	−9.70926			−0.350581
$768$	32.5260	−	29.3698i	1.17368	−	1.05979i
$769$			35.7061i			1.28759i	0.765196	+	0.643797i	$0.222642\pi$
$769$			35.7061i			1.28759i	−0.765196	+	0.643797i	$0.777358\pi$
$770$	−2.19417	−	0.253196i	−0.0790726	−	0.00912454i
$771$	13.6817			0.492736
$772$	−40.7754	+	26.5003i	−1.46754	+	0.953767i
$773$			15.8111i			0.568686i	0.958723	+	0.284343i	$0.0917754\pi$
$773$			15.8111i			0.568686i	−0.958723	+	0.284343i	$0.908225\pi$
$774$	21.6453	+	11.7475i	0.778026	+	0.422256i
$775$	−20.1047	−	20.9542i	−0.722183	−	0.752698i
$776$	9.88981	−	11.5919i	0.355023	−	0.416125i
$777$	−0.240018	−	0.240018i	−0.00861059	−	0.00861059i
$778$	28.2588	−	8.37606i	1.01313	−	0.300296i
$779$	6.54520	+	2.65060i	0.234506	+	0.0949675i
$780$	9.72803	+	6.82997i	0.348319	+	0.244552i
$781$			0.556669i			0.0199192i
$782$	−0.0697575	+	0.128531i	−0.00249452	+	0.00459627i
$783$	−21.8033	+	21.8033i	−0.779185	+	0.779185i
$784$	−10.9542	+	24.6503i	−0.391220	+	0.880369i
$785$	−9.40197	−	23.3794i	−0.335571	−	0.834448i
$786$	15.5436	+	52.4403i	0.554422	+	1.87048i
$787$	16.1363	−	16.1363i	0.575196	−	0.575196i	−0.358380	−	0.933576i	$-0.616671\pi$
$787$	16.1363	−	16.1363i	0.575196	−	0.575196i	0.933576	+	0.358380i	$0.116671\pi$
$788$	−23.4783	−	4.98180i	−0.836380	−	0.177469i
$789$		−	5.25882i		−	0.187219i
$790$	2.74778	−	23.8120i	0.0977616	−	0.847194i
$791$	−2.31115	−	2.31115i	−0.0821752	−	0.0821752i
$792$	−17.5120	+	1.38756i	−0.622262	+	0.0493049i
$793$		−	7.06023i		−	0.250716i
$794$	4.09604	+	13.8190i	0.145363	+	0.490419i
$795$	−3.09087	−	7.68593i	−0.109622	−	0.272592i
$796$	−33.9922	−	7.21271i	−1.20482	−	0.255648i
$797$	22.6539	−	22.6539i	0.802442	−	0.802442i	−0.181035	−	0.983477i	$-0.557945\pi$
$797$	22.6539	−	22.6539i	0.802442	−	0.802442i	0.983477	+	0.181035i	$0.0579447\pi$
$798$	−1.03167	+	1.90089i	−0.0365206	+	0.0672909i
$799$			7.42017i			0.262507i
$800$	16.7706	+	22.7760i	0.592932	+	0.805253i
$801$	−36.0423	−	36.0423i	−1.27349	−	1.27349i
$802$	−5.03114	−	16.9738i	−0.177656	−	0.599367i
$803$	−18.3117			−0.646205
$804$	−13.7934	+	8.96446i	−0.486456	+	0.316152i
$805$	0.0172824	−	0.0405325i	0.000609125	−	0.00142858i
$806$	−2.26502	−	7.64161i	−0.0797818	−	0.269164i
$807$	−13.7896			−0.485418
$808$	49.4820	−	3.92070i	1.74077	−	0.137930i
$809$	−16.4566	−	16.4566i	−0.578583	−	0.578583i	0.355930	−	0.934513i	$-0.384164\pi$
$809$	−16.4566	−	16.4566i	−0.578583	−	0.578583i	−0.934513	+	0.355930i	$0.884164\pi$
$810$	−5.54412	+	4.39698i	−0.194801	+	0.154494i
$811$	37.5176			1.31742			0.658711	−	0.752396i	$-0.271102\pi$
$811$	37.5176			1.31742			0.658711	+	0.752396i	$0.271102\pi$
$812$	−7.42389	−	1.57526i	−0.260527	−	0.0552806i
$813$	−18.6197			−0.653023
$814$	−0.457859	+	0.135712i	−0.0160479	+	0.00475670i
$815$	15.5236	−	36.4075i	0.543767	−	1.27530i
$816$	−26.6002	−	11.8207i	−0.931193	−	0.413806i
$817$		−	4.26585i		−	0.149243i
$818$	−9.49068	−	32.0192i	−0.331834	−	1.11953i
$819$	2.21185			0.0772883
$820$	6.01173	−	27.9975i	0.209939	−	0.977715i
$821$	42.3518			1.47809			0.739043	−	0.673658i	$-0.235278\pi$
$821$	42.3518			1.47809			0.739043	+	0.673658i	$0.235278\pi$
$822$	19.1451	+	64.5908i	0.667762	+	2.25286i
$823$			14.6455i			0.510509i	0.966874	+	0.255254i	$0.0821593\pi$
$823$			14.6455i			0.510509i	−0.966874	+	0.255254i	$0.917841\pi$
$824$	36.7225	−	2.90970i	1.27929	−	0.101364i
$825$	0.390801	−	18.8889i	0.0136059	−	0.657626i
$826$	−6.86879	+	2.03595i	−0.238996	+	0.0708396i
$827$	−39.1285			−1.36063			−0.680316	−	0.732919i	$-0.738157\pi$
$827$	−39.1285			−1.36063			−0.680316	+	0.732919i	$0.738157\pi$
$828$	0.0727418	−	0.342819i	0.00252795	−	0.0119138i
$829$	−41.7870			−1.45132			−0.725661	−	0.688052i	$-0.758466\pi$
$829$	−41.7870			−1.45132			−0.725661	+	0.688052i	$0.758466\pi$
$830$	−1.27214	+	11.0242i	−0.0441566	+	0.382657i
$831$	23.2329	+	23.2329i	0.805940	+	0.805940i
$832$	1.22253	+	7.66614i	0.0423835	+	0.265776i
$833$	17.9169			0.620785
$834$	−19.6458	−	66.2802i	−0.680279	−	2.29510i
$835$	−10.5900	+	4.25874i	−0.366482	+	0.147380i
$836$	1.65814	+	2.55134i	0.0573480	+	0.0882399i
$837$	−23.8942			−0.825905
$838$	−4.18107	−	14.1059i	−0.144433	−	0.487281i
$839$	−0.726098	−	0.726098i	−0.0250677	−	0.0250677i	0.694462	−	0.719530i	$-0.255643\pi$
$839$	−0.726098	−	0.726098i	−0.0250677	−	0.0250677i	−0.719530	+	0.694462i	$0.755643\pi$
$840$	8.31425	+	2.79196i	0.286869	+	0.0963318i
$841$			27.1719i			0.936963i
$842$	−8.80870	+	16.2304i	−0.303568	+	0.559338i
$843$	40.3775	−	40.3775i	1.39068	−	1.39068i
$844$	−11.8246	+	55.7271i	−0.407019	+	1.91821i
$845$	25.0163	−	10.0602i	0.860586	−	0.346082i
$846$	−5.05327	−	17.0485i	−0.173735	−	0.586139i
$847$		−	4.60569i		−	0.158253i
$848$	2.19713	−	4.94423i	0.0754497	−	0.169786i
$849$	−52.9295	−	52.9295i	−1.81654	−	1.81654i
$850$	9.30100	−	16.3228i	0.319022	−	0.559869i
$851$		−	0.00952686i		−	0.000326577i
$852$	0.458812	−	2.16230i	0.0157186	−	0.0740790i
$853$	−34.5834	+	34.5834i	−1.18411	+	1.18411i	−0.205444	+	0.978669i	$0.565864\pi$
$853$	−34.5834	+	34.5834i	−1.18411	+	1.18411i	−0.978669	+	0.205444i	$0.934136\pi$
$854$	−1.48047	−	4.99474i	−0.0506606	−	0.170916i
$855$	−10.2125	−	4.35444i	−0.349259	−	0.148919i
$856$	−9.60925	+	0.761388i	−0.328437	+	0.0260237i
$857$	2.96552	−	2.96552i	0.101300	−	0.101300i	−0.654640	−	0.755940i	$-0.727180\pi$
$857$	2.96552	−	2.96552i	0.101300	−	0.101300i	0.755940	+	0.654640i	$0.227180\pi$
$858$	2.47346	−	4.55747i	0.0844427	−	0.155590i
$859$		−	33.3755i		−	1.13876i	−0.822075	−	0.569379i	$-0.807184\pi$
$859$		−	33.3755i		−	1.13876i	0.822075	−	0.569379i	$-0.192816\pi$
$860$	−17.0397	+	2.98236i	−0.581048	+	0.101698i
$861$	−3.46287	−	8.17640i	−0.118014	−	0.278651i
$862$	40.3432	−	11.9580i	1.37410	−	0.407290i
$863$	22.3426	+	22.3426i	0.760552	+	0.760552i	0.976422	−	0.215870i	$-0.0692587\pi$
$863$	22.3426	+	22.3426i	0.760552	+	0.760552i	−0.215870	+	0.976422i	$0.569259\pi$
$864$	23.0765	+	3.01735i	0.785080	+	0.102652i
$865$	−4.16295	+	9.76339i	−0.141545	+	0.331965i
$866$	−43.0688	−	23.3746i	−1.46354	−	0.794302i
$867$		−	27.2286i		−	0.924732i
$868$	−3.20476	−	4.93108i	−0.108777	−	0.167372i
$869$	−10.4570			−0.354730
$870$	7.44154	−	64.4878i	0.252292	−	2.18634i
$871$		−	2.91406i		−	0.0987393i
$872$	−1.05840	−	13.3577i	−0.0358418	−	0.452349i
$873$	24.2538			0.820866
$874$	−0.0582000	+	0.0172508i	−0.00196864	+	0.000583517i
$875$	−2.32741	+	5.15996i	−0.0786809	+	0.174438i
$876$	71.1290	+	15.0927i	2.40323	+	0.509934i
$877$	9.05582	−	9.05582i	0.305793	−	0.305793i	−0.537482	−	0.843275i	$-0.680624\pi$
$877$	9.05582	−	9.05582i	0.305793	−	0.305793i	0.843275	+	0.537482i	$0.180624\pi$
$878$	−8.55073	+	15.7551i	−0.288573	+	0.531709i
$879$	−42.9255			−1.44784
$880$	9.03191	−	8.40704i	0.304466	−	0.283401i
$881$			14.3488i			0.483425i	0.970348	+	0.241712i	$0.0777090\pi$
$881$			14.3488i			0.483425i	−0.970348	+	0.241712i	$0.922291\pi$
$882$	−41.1658	+	12.2018i	−1.38612	+	0.410855i
$883$	−55.8276			−1.87875			−0.939374	−	0.342893i	$-0.888593\pi$
$883$	−55.8276			−1.87875			−0.939374	+	0.342893i	$0.888593\pi$
$884$	4.32344	−	2.80985i	0.145413	−	0.0945054i
$885$	−22.8641	−	56.8552i	−0.768570	−	1.91117i
$886$	−40.3637	−	21.9065i	−1.35604	−	0.735962i
$887$			32.1928i			1.08093i	0.841367	+	0.540464i	$0.181751\pi$
$887$			32.1928i			1.08093i	−0.841367	+	0.540464i	$0.818249\pi$
$888$	1.89034	−	0.149781i	0.0634356	−	0.00502631i
$889$	−3.40953	−	3.40953i	−0.114352	−	0.114352i
$890$	35.5668	+	4.10421i	1.19220	+	0.137573i
$891$	2.18281	+	2.18281i	0.0731269	+	0.0731269i
$892$	−9.72010	+	45.8090i	−0.325453	+	1.53380i
$893$	−2.17790	+	2.17790i	−0.0728807	+	0.0728807i
$894$	18.9265	+	10.2719i	0.632996	+	0.343544i
$895$	−0.331204	−	0.141220i	−0.0110709	−	0.00472046i
$896$	2.47240	+	5.16704i	0.0825969	+	0.172619i
$897$	0.0731478	+	0.0731478i	0.00244233	+	0.00244233i
$898$	−50.9466	+	15.1008i	−1.70011	+	0.503922i
$899$	−30.7794	+	30.7794i	−1.02655	+	1.02655i
$900$	−10.2537	+	43.8374i	−0.341791	+	1.46125i
$901$	−3.59369			−0.119723
$902$	−12.4341	−	1.20521i	−0.414011	−	0.0401291i
$903$	−3.79296	+	3.79296i	−0.126222	+	0.126222i
$904$	18.2023	−	1.44225i	0.605398	−	0.0479686i
$905$	5.81297	+	2.47856i	0.193230	+	0.0823901i
$906$	14.4930	−	26.7040i	0.481497	−	0.887180i
$907$	−2.08557	+	2.08557i	−0.0692501	+	0.0692501i	−0.740884	−	0.671633i	$-0.765593\pi$
$907$	−2.08557	+	2.08557i	−0.0692501	+	0.0692501i	0.671633	+	0.740884i	$0.265593\pi$
$908$	25.3278	+	38.9712i	0.840532	+	1.29331i
$909$	55.8672	+	55.8672i	1.85300	+	1.85300i
$910$	−1.21727	+	0.965399i	−0.0403520	+	0.0320027i
$911$	−7.04564			−0.233433			−0.116716	−	0.993165i	$-0.537237\pi$
$911$	−7.04564			−0.233433			−0.116716	+	0.993165i	$0.537237\pi$
$912$	−4.33796	−	11.2769i	−0.143644	−	0.373417i
$913$	4.84128			0.160223
$914$	−13.1496	+	3.89762i	−0.434950	+	0.128922i
$915$	41.3431	−	16.6260i	1.36676	−	0.549638i
$916$	9.26907	−	43.6834i	0.306259	−	1.44334i
$917$	−7.14909			−0.236084
$918$	−4.39299	−	14.8209i	−0.144990	−	0.489162i
$919$	−31.6419	−	31.6419i	−1.04377	−	1.04377i	−0.998997	−	0.0447739i	$-0.985743\pi$
$919$	−31.6419	−	31.6419i	−1.04377	−	1.04377i	−0.0447739	−	0.998997i	$-0.514257\pi$
$920$	0.109596	+	0.220416i	0.00361328	+	0.00726689i
$921$	−35.2165	−	35.2165i	−1.16042	−	1.16042i
$922$	11.9617	−	3.54551i	0.393938	−	0.116765i
$923$	0.276874	+	0.276874i	0.00911343	+	0.00911343i
$924$	0.794183	−	3.74284i	0.0261267	−	0.123130i
$925$	−0.0253157	+	1.22360i	−0.000832376	+	0.0402318i
$926$	1.69711	+	5.72562i	0.0557704	+	0.188156i
$927$	41.4613	+	41.4613i	1.36177	+	1.36177i
$928$	33.6130	−	25.8393i	1.10340	−	0.848217i
$929$	3.73201	−	3.73201i	0.122443	−	0.122443i	−0.643230	−	0.765673i	$-0.722406\pi$
$929$	3.73201	−	3.73201i	0.122443	−	0.122443i	0.765673	+	0.643230i	$0.222406\pi$
$930$	39.4137	−	31.2585i	1.29243	−	1.02501i
$931$	5.25882	+	5.25882i	0.172351	+	0.172351i
$932$	−42.6857	+	27.7419i	−1.39822	+	0.908715i
$933$	19.8192	+	19.8192i	0.648852	+	0.648852i
$934$	18.6551	+	10.1246i	0.610412	+	0.331287i
$935$	−7.53909	−	3.21455i	−0.246555	−	0.105127i
$936$	−8.01994	+	9.40022i	−0.262140	+	0.307256i
$937$	18.8986			0.617390			0.308695	−	0.951161i	$-0.400108\pi$
$937$	18.8986			0.617390			0.308695	+	0.951161i	$0.400108\pi$
$938$	−0.611054	−	2.06155i	−0.0199516	−	0.0673119i
$939$	17.6757			0.576824
$940$	10.2221	+	7.17686i	0.333409	+	0.234083i
$941$		−	22.9516i		−	0.748200i	−0.927388	−	0.374100i	$-0.877952\pi$
$941$		−	22.9516i		−	0.748200i	0.927388	−	0.374100i	$-0.122048\pi$
$942$	41.8523	−	12.4053i	1.36362	−	0.404186i
$943$	0.0935454	−	0.230995i	0.00304626	−	0.00752222i
$944$	16.2528	−	36.5740i	0.528985	−	1.19038i
$945$	1.73780	+	4.32131i	0.0565307	+	0.140572i
$946$	2.14463	+	7.23546i	0.0697280	+	0.235245i
$947$	−6.56792	−	6.56792i	−0.213429	−	0.213429i	0.592293	−	0.805722i	$-0.298223\pi$
$947$	−6.56792	−	6.56792i	−0.213429	−	0.213429i	−0.805722	+	0.592293i	$0.798223\pi$
$948$	40.6187	+	8.61878i	1.31923	+	0.279925i
$949$	−9.10782	+	9.10782i	−0.295652	+	0.295652i
$950$	7.52089	−	2.06099i	0.244010	−	0.0668674i
$951$	85.2505			2.76444
$952$	2.46941	−	2.89441i	0.0800339	−	0.0938082i
$953$	−7.99435	−	7.99435i	−0.258962	−	0.258962i	0.565670	−	0.824632i	$-0.308618\pi$
$953$	−7.99435	−	7.99435i	−0.258962	−	0.258962i	−0.824632	+	0.565670i	$0.808618\pi$
$954$	8.25681	−	2.44737i	0.267324	−	0.0792364i
$955$	−23.7213	+	55.6337i	−0.767604	+	1.80026i
$956$	−6.47908	+	30.5347i	−0.209548	+	0.987563i
$957$	−28.3197			−0.915446
$958$	9.52842	−	17.5566i	0.307849	−	0.567227i
$959$	−8.80554			−0.284346
$960$	−42.0123	+	25.2117i	−1.35594	+	0.813703i
$961$	−2.73119			−0.0881028
$962$	−0.160229	+	0.295229i	−0.00516598	+	0.00951856i
$963$	−10.8492	−	10.8492i	−0.349612	−	0.349612i
$964$	−7.34083	−	11.2951i	−0.236432	−	0.363792i
$965$	50.4441	−	20.2859i	1.62385	−	0.653027i
$966$	0.0670867	+	0.0364098i	0.00215848	+	0.00117146i
$967$			52.7292i			1.69566i	0.530272	+	0.847828i	$0.322090\pi$
$967$			52.7292i			1.69566i	−0.530272	+	0.847828i	$0.677910\pi$
$968$	19.5739	+	16.6997i	0.629128	+	0.536750i
$969$	−5.67480	+	5.67480i	−0.182301	+	0.182301i
$970$	−13.3478	+	10.5860i	−0.428572	+	0.339895i
$971$	−4.74747	−	4.74747i	−0.152354	−	0.152354i	0.626815	−	0.779168i	$-0.284358\pi$
$971$	−4.74747	−	4.74747i	−0.152354	−	0.152354i	−0.779168	+	0.626815i	$0.784358\pi$
$972$	−20.1313	−	30.9755i	−0.645711	−	0.993539i
$973$	9.03585			0.289676
$974$	−8.13794	+	14.9945i	−0.260756	+	0.480456i
$975$	−9.20053	−	9.58928i	−0.294653	−	0.307103i
$976$	26.5953	+	11.8185i	0.851296	+	0.378301i
$977$		−	2.93492i		−	0.0938964i	−0.998897	−	0.0469482i	$-0.985050\pi$
$977$		−	2.93492i		−	0.0938964i	0.998897	−	0.0469482i	$-0.0149496\pi$
$978$	60.2593	+	32.7043i	1.92688	+	1.04577i
$979$		−	15.6191i		−	0.499188i
$980$	17.3294	−	24.6826i	0.553569	−	0.788456i
$981$	15.0814	−	15.0814i	0.481512	−	0.481512i
$982$	−1.18711	−	4.00503i	−0.0378823	−	0.127806i
$983$	8.88418	−	8.88418i	0.283361	−	0.283361i	−0.551087	−	0.834448i	$-0.685787\pi$
$983$	8.88418	−	8.88418i	0.283361	−	0.283361i	0.834448	+	0.551087i	$0.185787\pi$
$984$	47.3051	+	14.9298i	1.50803	+	0.475944i
$985$	24.6838	+	10.5248i	0.786491	+	0.335347i
$986$	−24.7504	−	13.4327i	−0.788214	−	0.427785i
$987$	3.87294			0.123277
$988$	2.09370	+	0.444257i	0.0666095	+	0.0141337i
$989$	−0.150551			−0.00478725
$990$	19.5109	+	2.25145i	0.620097	+	0.0715559i
$991$	18.0138	+	18.0138i	0.572227	+	0.572227i	0.932750	−	0.360523i	$-0.117402\pi$
$991$	18.0138	+	18.0138i	0.572227	+	0.572227i	−0.360523	+	0.932750i	$0.617402\pi$
$992$	32.5769	+	4.25957i	1.03432	+	0.135241i
$993$	35.1246	−	35.1246i	1.11465	−	1.11465i
$994$	0.253932	+	0.137816i	0.00805424	+	0.00437125i
$995$	35.7375	+	15.2379i	1.13296	+	0.483074i
$996$	−18.8052	−	3.99023i	−0.595866	−	0.126435i
$997$		−	22.7008i		−	0.718942i	−0.933156	−	0.359471i	$-0.882957\pi$
$997$		−	22.7008i		−	0.718942i	0.933156	−	0.359471i	$-0.117043\pi$
$998$	−5.41165	+	9.97122i	−0.171303	+	0.315633i
$999$	0.712075	+	0.712075i	0.0225290	+	0.0225290i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.j.c.483.12	✓	240
4.3	odd	2	inner	820.2.j.c.483.73	yes	240
5.2	odd	4		820.2.s.c.647.48	yes	240
20.7	even	4		820.2.s.c.647.109	yes	240
41.9	even	4		820.2.s.c.583.109	yes	240
164.91	odd	4		820.2.s.c.583.48	yes	240
205.132	odd	4	inner	820.2.j.c.747.73	yes	240
820.747	even	4	inner	820.2.j.c.747.12	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.j.c.483.12	✓	240	1.1	even	1	trivial
820.2.j.c.483.73	yes	240	4.3	odd	2	inner
820.2.j.c.747.12	yes	240	820.747	even	4	inner
820.2.j.c.747.73	yes	240	205.132	odd	4	inner
820.2.s.c.583.48	yes	240	164.91	odd	4
820.2.s.c.583.109	yes	240	41.9	even	4
820.2.s.c.647.48	yes	240	5.2	odd	4
820.2.s.c.647.109	yes	240	20.7	even	4

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:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35590 + 0.401898i) q^{2} +2.73899i q^{3} +(1.67696 - 1.08987i) q^{4} +(-2.07460 + 0.834293i) q^{5} +(-1.10079 - 3.71381i) q^{6} +0.506296 q^{7} +(-1.83578 + 2.15173i) q^{8} -4.50206 q^{9} +(2.47766 - 1.96500i) q^{10} +(-0.975492 - 0.975492i) q^{11} +(2.98514 + 4.59316i) q^{12} -0.970376 q^{13} +(-0.686490 + 0.203479i) q^{14} +(-2.28512 - 5.68230i) q^{15} +(1.62436 - 3.65533i) q^{16} -2.65685 q^{17} +(6.10436 - 1.80937i) q^{18} +(-0.779817 - 0.779817i) q^{19} +(-2.56974 + 3.66012i) q^{20} +1.38674i q^{21} +(1.71472 + 0.930627i) q^{22} +(-0.0275214 + 0.0275214i) q^{23} +(-5.89355 - 5.02817i) q^{24} +(3.60791 - 3.46164i) q^{25} +(1.31574 - 0.389992i) q^{26} -4.11412i q^{27} +(0.849037 - 0.551797i) q^{28} +(-5.29962 - 5.29962i) q^{29} +(5.38211 + 6.78627i) q^{30} -5.80786i q^{31} +(-0.733415 + 5.60911i) q^{32} +(2.67186 - 2.67186i) q^{33} +(3.60244 - 1.06778i) q^{34} +(-1.05036 + 0.422399i) q^{35} +(-7.54975 + 4.90666i) q^{36} +(-0.173081 + 0.173081i) q^{37} +(1.37076 + 0.743951i) q^{38} -2.65785i q^{39} +(2.01333 - 5.99554i) q^{40} +(-5.89613 + 2.49713i) q^{41} +(-0.557328 - 1.88029i) q^{42} +(2.73516 + 2.73516i) q^{43} +(-2.69902 - 0.572698i) q^{44} +(9.33996 - 3.75604i) q^{45} +(0.0262557 - 0.0483773i) q^{46} -2.79284i q^{47} +(10.0119 + 4.44912i) q^{48} -6.74366 q^{49} +(-3.50076 + 6.14367i) q^{50} -7.27709i q^{51} +(-1.62728 + 1.05758i) q^{52} +1.35261 q^{53} +(1.65346 + 5.57835i) q^{54} +(2.83760 + 1.20991i) q^{55} +(-0.929447 + 1.08941i) q^{56} +(2.13591 - 2.13591i) q^{57} +(9.31569 + 5.05587i) q^{58} +10.0057 q^{59} +(-10.0250 - 7.03848i) q^{60} +7.27577i q^{61} +(2.33416 + 7.87490i) q^{62} -2.27937 q^{63} +(-1.25985 - 7.90018i) q^{64} +(2.01314 - 0.809578i) q^{65} +(-2.54898 + 4.69661i) q^{66} +3.00303i q^{67} +(-4.45543 + 2.89563i) q^{68} +(-0.0753809 - 0.0753809i) q^{69} +(1.25443 - 0.994871i) q^{70} +(-0.285327 - 0.285327i) q^{71} +(8.26477 - 9.68719i) q^{72} +(9.38587 - 9.38587i) q^{73} +(0.165120 - 0.304242i) q^{74} +(9.48141 + 9.88202i) q^{75} +(-2.15762 - 0.457819i) q^{76} +(-0.493888 - 0.493888i) q^{77} +(1.06818 + 3.60379i) q^{78} +(5.35986 - 5.35986i) q^{79} +(-0.320286 + 8.93854i) q^{80} -2.23765 q^{81} +(6.99100 - 5.75551i) q^{82} +(-2.48145 + 2.48145i) q^{83} +(1.51137 + 2.32550i) q^{84} +(5.51190 - 2.21660i) q^{85} +(-4.80788 - 2.60936i) q^{86} +(14.5156 - 14.5156i) q^{87} +(3.88978 - 0.308206i) q^{88} +(8.00574 + 8.00574i) q^{89} +(-11.1546 + 8.84654i) q^{90} -0.491298 q^{91} +(-0.0161574 + 0.0761471i) q^{92} +15.9076 q^{93} +(1.12244 + 3.78682i) q^{94} +(2.26840 + 0.967210i) q^{95} +(-15.3633 - 2.00881i) q^{96} -5.38726 q^{97} +(9.14377 - 2.71026i) q^{98} +(4.39172 + 4.39172i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{6} + 12 q^{8} - 240 q^{9} - 20 q^{10} - 32 q^{13} - 8 q^{14} + 8 q^{16} + 32 q^{17} - 12 q^{18} + 16 q^{20} - 28 q^{22} + 12 q^{24} - 16 q^{25} - 8 q^{28} - 10 q^{30} + 24 q^{33} - 20 q^{34}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q - 4 * q^6 + 12 * q^8 - 240 * q^9 - 20 * q^10 - 32 * q^13 - 8 * q^14 + 8 * q^16 + 32 * q^17 - 12 * q^18 + 16 * q^20 - 28 * q^22 + 12 * q^24 - 16 * q^25 - 8 * q^28 - 10 * q^30 + 24 * q^33 - 20 * q^34 - 8 * q^37 + 16 * q^38 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 + 8 * q^48 + 224 * q^49 - 12 * q^50 - 32 * q^53 + 48 * q^54 + 24 * q^56 - 8 * q^57 + 6 * q^60 - 8 * q^65 - 8 * q^66 + 16 * q^69 + 10 * q^70 - 96 * q^72 - 72 * q^73 + 112 * q^74 + 20 * q^76 - 56 * q^77 + 4 * q^78 + 60 * q^80 + 48 * q^81 - 56 * q^82 - 32 * q^84 - 32 * q^85 - 8 * q^86 - 64 * q^89 + 76 * q^90 + 20 * q^92 - 16 * q^93 + 48 * q^94 + 24 * q^96 - 48 * q^97 - 12 * q^98

Introduction

L-functions

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