LMFDB - Embedded newform 880.2.w.a.221.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(221,880)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("880.221"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.w (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			221.7
Character	$\chi$	$=$	880.221
Dual form			880.2.w.a.661.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.27571 + 0.610390i) q^{2} +(0.191372 + 0.191372i) q^{3} +(1.25485 - 1.55736i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.360945 - 0.127322i) q^{6} +1.72361i q^{7} +(-0.650220 + 2.75267i) q^{8} -2.92675i q^{9} +(-0.470449 + 1.33367i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(0.538176 - 0.0578916i) q^{12} +(2.10654 + 2.10654i) q^{13} +(-1.05208 - 2.19882i) q^{14} +0.270640 q^{15} +(-0.850716 - 3.90849i) q^{16} +2.15875 q^{17} +(1.78646 + 3.73367i) q^{18} +(0.960096 + 0.960096i) q^{19} +(-0.213906 - 1.98853i) q^{20} +(-0.329851 + 0.329851i) q^{21} +(0.470449 - 1.33367i) q^{22} +4.90055i q^{23} +(-0.651217 + 0.402350i) q^{24} -1.00000i q^{25} +(-3.97313 - 1.40151i) q^{26} +(1.13421 - 1.13421i) q^{27} +(2.68428 + 2.16287i) q^{28} +(1.71672 + 1.71672i) q^{29} +(-0.345257 + 0.165196i) q^{30} +0.278102 q^{31} +(3.47097 + 4.46681i) q^{32} -0.270640 q^{33} +(-2.75393 + 1.31768i) q^{34} +(1.21878 + 1.21878i) q^{35} +(-4.55800 - 3.67263i) q^{36} +(5.65605 - 5.65605i) q^{37} +(-1.81083 - 0.638766i) q^{38} +0.806263i q^{39} +(1.48666 + 2.40621i) q^{40} -2.17914i q^{41} +(0.219455 - 0.622130i) q^{42} +(3.48058 - 3.48058i) q^{43} +(0.213906 + 1.98853i) q^{44} +(-2.06953 - 2.06953i) q^{45} +(-2.99125 - 6.25165i) q^{46} +1.06451 q^{47} +(0.585171 - 0.910777i) q^{48} +4.02916 q^{49} +(0.610390 + 1.27571i) q^{50} +(0.413124 + 0.413124i) q^{51} +(5.92401 - 0.637246i) q^{52} +(2.76868 - 2.76868i) q^{53} +(-0.754608 + 2.13923i) q^{54} +1.00000i q^{55} +(-4.74455 - 1.12073i) q^{56} +0.367470i q^{57} +(-3.23790 - 1.14216i) q^{58} +(-0.814977 + 0.814977i) q^{59} +(0.339612 - 0.421483i) q^{60} +(3.44842 + 3.44842i) q^{61} +(-0.354776 + 0.169751i) q^{62} +5.04459 q^{63} +(-7.15443 - 3.57969i) q^{64} +2.97909 q^{65} +(0.345257 - 0.165196i) q^{66} +(1.79605 + 1.79605i) q^{67} +(2.70891 - 3.36195i) q^{68} +(-0.937826 + 0.937826i) q^{69} +(-2.29873 - 0.810872i) q^{70} +3.26305i q^{71} +(8.05640 + 1.90303i) q^{72} +5.36462i q^{73} +(-3.76306 + 10.6679i) q^{74} +(0.191372 - 0.191372i) q^{75} +(2.69998 - 0.290437i) q^{76} +(-1.21878 - 1.21878i) q^{77} +(-0.492135 - 1.02855i) q^{78} +12.9535 q^{79} +(-3.36527 - 2.16217i) q^{80} -8.34615 q^{81} +(1.33012 + 2.77993i) q^{82} +(4.27228 + 4.27228i) q^{83} +(0.0997827 + 0.927607i) q^{84} +(1.52647 - 1.52647i) q^{85} +(-2.31568 + 6.56471i) q^{86} +0.657063i q^{87} +(-1.48666 - 2.40621i) q^{88} +2.22599i q^{89} +(3.90333 + 1.37689i) q^{90} +(-3.63086 + 3.63086i) q^{91} +(7.63190 + 6.14944i) q^{92} +(0.0532208 + 0.0532208i) q^{93} +(-1.35800 + 0.649768i) q^{94} +1.35778 q^{95} +(-0.190576 + 1.51907i) q^{96} +12.7002 q^{97} +(-5.14001 + 2.45936i) q^{98} +(2.06953 + 2.06953i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 12 q^{6} - 4 q^{10} + 12 q^{12} - 8 q^{14} + 8 q^{15} + 4 q^{16} + 56 q^{17} + 20 q^{18} + 8 q^{19} - 8 q^{20} + 4 q^{22} - 24 q^{24} - 24 q^{27} + 20 q^{28} - 20 q^{30} + 20 q^{32} - 8 q^{33} + 4 q^{34}+ \cdots - 60 q^{98}+O(q^{100}) $ 72 * q + 12 * q^6 - 4 * q^10 + 12 * q^12 - 8 * q^14 + 8 * q^15 + 4 * q^16 + 56 * q^17 + 20 * q^18 + 8 * q^19 - 8 * q^20 + 4 * q^22 - 24 * q^24 - 24 * q^27 + 20 * q^28 - 20 * q^30 + 20 * q^32 - 8 * q^33 + 4 * q^34 - 60 * q^36 + 12 * q^38 - 40 * q^42 + 8 * q^44 - 20 * q^46 + 40 * q^47 + 20 * q^48 - 24 * q^49 + 32 * q^51 - 84 * q^52 + 72 * q^54 + 8 * q^56 - 8 * q^58 + 32 * q^60 - 16 * q^61 - 96 * q^62 + 36 * q^64 - 40 * q^65 + 20 * q^66 - 76 * q^68 - 16 * q^69 + 24 * q^70 + 20 * q^72 + 56 * q^74 + 56 * q^76 - 132 * q^78 - 16 * q^79 + 56 * q^81 + 36 * q^82 - 40 * q^83 - 152 * q^84 + 16 * q^85 + 56 * q^86 - 36 * q^90 + 88 * q^91 + 80 * q^92 + 48 * q^93 - 76 * q^94 - 32 * q^96 - 64 * q^97 - 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.27571	+	0.610390i	−0.902060	+	0.431611i
$2$	−1.27571	+	0.610390i	−0.902060	+	0.431611i
$3$	0.191372	+	0.191372i	0.110488	+	0.110488i	0.760190	−	0.649701i	$-0.225106\pi$
$3$	0.191372	+	0.191372i	0.110488	+	0.110488i	−0.649701	+	0.760190i	$0.725106\pi$
$4$	1.25485	−	1.55736i	0.627424	−	0.778678i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	−0.360945	−	0.127322i	−0.147355	−	0.0519791i
$7$			1.72361i			0.651465i	0.945462	+	0.325732i	$0.105611\pi$
$7$			1.72361i			0.651465i	−0.945462	+	0.325732i	$0.894389\pi$
$8$	−0.650220	+	2.75267i	−0.229888	+	0.973217i
$9$		−	2.92675i		−	0.975585i
$10$	−0.470449	+	1.33367i	−0.148769	+	0.421744i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$12$	0.538176	−	0.0578916i	0.155358	−	0.0167119i
$13$	2.10654	+	2.10654i	0.584248	+	0.584248i	0.936068	−	0.351820i	$-0.114437\pi$
$13$	2.10654	+	2.10654i	0.584248	+	0.584248i	−0.351820	+	0.936068i	$0.614437\pi$
$14$	−1.05208	−	2.19882i	−0.281179	−	0.587660i
$15$	0.270640			0.0698790
$16$	−0.850716	−	3.90849i	−0.212679	−	0.977122i
$17$	2.15875			0.523574			0.261787	−	0.965126i	$-0.415688\pi$
$17$	2.15875			0.523574			0.261787	+	0.965126i	$0.415688\pi$
$18$	1.78646	+	3.73367i	0.421073	+	0.880036i
$19$	0.960096	+	0.960096i	0.220261	+	0.220261i	0.808608	−	0.588347i	$-0.200221\pi$
$19$	0.960096	+	0.960096i	0.220261	+	0.220261i	−0.588347	+	0.808608i	$0.700221\pi$
$20$	−0.213906	−	1.98853i	−0.0478308	−	0.444648i
$21$	−0.329851	+	0.329851i	−0.0719793	+	0.0719793i
$22$	0.470449	−	1.33367i	0.100300	−	0.284340i
$23$			4.90055i			1.02183i	0.859630	+	0.510917i	$0.170694\pi$
$23$			4.90055i			1.02183i	−0.859630	+	0.510917i	$0.829306\pi$
$24$	−0.651217	+	0.402350i	−0.132929	+	0.0821293i
$25$		−	1.00000i		−	0.200000i
$26$	−3.97313	−	1.40151i	−0.779195	−	0.274859i
$27$	1.13421	−	1.13421i	0.218279	−	0.218279i
$28$	2.68428	+	2.16287i	0.507281	+	0.408744i
$29$	1.71672	+	1.71672i	0.318787	+	0.318787i	0.848301	−	0.529514i	$-0.177626\pi$
$29$	1.71672	+	1.71672i	0.318787	+	0.318787i	−0.529514	+	0.848301i	$0.677626\pi$
$30$	−0.345257	+	0.165196i	−0.0630351	+	0.0301606i
$31$	0.278102			0.0499485			0.0249743	−	0.999688i	$-0.492050\pi$
$31$	0.278102			0.0499485			0.0249743	+	0.999688i	$0.492050\pi$
$32$	3.47097	+	4.46681i	0.613586	+	0.789628i
$33$	−0.270640			−0.0471124
$34$	−2.75393	+	1.31768i	−0.472295	+	0.225981i
$35$	1.21878	+	1.21878i	0.206011	+	0.206011i
$36$	−4.55800	−	3.67263i	−0.759666	−	0.612105i
$37$	5.65605	−	5.65605i	0.929850	−	0.929850i	−0.0678462	−	0.997696i	$-0.521613\pi$
$37$	5.65605	−	5.65605i	0.929850	−	0.929850i	0.997696	+	0.0678462i	$0.0216127\pi$
$38$	−1.81083	−	0.638766i	−0.293756	−	0.103622i
$39$			0.806263i			0.129105i
$40$	1.48666	+	2.40621i	0.235061	+	0.380455i
$41$		−	2.17914i		−	0.340324i	−0.985416	−	0.170162i	$-0.945571\pi$
$41$		−	2.17914i		−	0.340324i	0.985416	−	0.170162i	$-0.0544291\pi$
$42$	0.219455	−	0.622130i	0.0338626	−	0.0959967i
$43$	3.48058	−	3.48058i	0.530784	−	0.530784i	−0.390022	−	0.920806i	$-0.627532\pi$
$43$	3.48058	−	3.48058i	0.530784	−	0.530784i	0.920806	+	0.390022i	$0.127532\pi$
$44$	0.213906	+	1.98853i	0.0322475	+	0.299782i
$45$	−2.06953	−	2.06953i	−0.308507	−	0.308507i
$46$	−2.99125	−	6.25165i	−0.441035	−	0.921756i
$47$	1.06451			0.155275			0.0776375	−	0.996982i	$-0.475262\pi$
$47$	1.06451			0.155275			0.0776375	+	0.996982i	$0.475262\pi$
$48$	0.585171	−	0.910777i	0.0844621	−	0.131459i
$49$	4.02916			0.575594
$50$	0.610390	+	1.27571i	0.0863222	+	0.180412i
$51$	0.413124	+	0.413124i	0.0578489	+	0.0578489i
$52$	5.92401	−	0.637246i	0.821512	−	0.0883701i
$53$	2.76868	−	2.76868i	0.380307	−	0.380307i	−0.490905	−	0.871213i	$-0.663334\pi$
$53$	2.76868	−	2.76868i	0.380307	−	0.380307i	0.871213	+	0.490905i	$0.163334\pi$
$54$	−0.754608	+	2.13923i	−0.102689	+	0.291113i
$55$			1.00000i			0.134840i
$56$	−4.74455	−	1.12073i	−0.634017	−	0.149764i
$57$			0.367470i			0.0486726i
$58$	−3.23790	−	1.14216i	−0.425157	−	0.149973i
$59$	−0.814977	+	0.814977i	−0.106101	+	0.106101i	−0.758164	−	0.652063i	$-0.773904\pi$
$59$	−0.814977	+	0.814977i	−0.106101	+	0.106101i	0.652063	+	0.758164i	$0.273904\pi$
$60$	0.339612	−	0.421483i	0.0438438	−	0.0544133i
$61$	3.44842	+	3.44842i	0.441525	+	0.441525i	0.892524	−	0.450999i	$-0.148932\pi$
$61$	3.44842	+	3.44842i	0.441525	+	0.441525i	−0.450999	+	0.892524i	$0.648932\pi$
$62$	−0.354776	+	0.169751i	−0.0450566	+	0.0215583i
$63$	5.04459			0.635559
$64$	−7.15443	−	3.57969i	−0.894303	−	0.447461i
$65$	2.97909			0.369511
$66$	0.345257	−	0.165196i	0.0424982	−	0.0203343i
$67$	1.79605	+	1.79605i	0.219423	+	0.219423i	0.808255	−	0.588833i	$-0.200412\pi$
$67$	1.79605	+	1.79605i	0.219423	+	0.219423i	−0.588833	+	0.808255i	$0.700412\pi$
$68$	2.70891	−	3.36195i	0.328503	−	0.407696i
$69$	−0.937826	+	0.937826i	−0.112901	+	0.112901i
$70$	−2.29873	−	0.810872i	−0.274751	−	0.0969177i
$71$			3.26305i			0.387253i	0.981075	+	0.193626i	$0.0620249\pi$
$71$			3.26305i			0.387253i	−0.981075	+	0.193626i	$0.937975\pi$
$72$	8.05640	+	1.90303i	0.949456	+	0.224275i
$73$			5.36462i			0.627881i	0.949443	+	0.313941i	$0.101649\pi$
$73$			5.36462i			0.627881i	−0.949443	+	0.313941i	$0.898351\pi$
$74$	−3.76306	+	10.6679i	−0.437446	+	1.24011i
$75$	0.191372	−	0.191372i	0.0220977	−	0.0220977i
$76$	2.69998	−	0.290437i	0.309710	−	0.0333154i
$77$	−1.21878	−	1.21878i	−0.138893	−	0.138893i
$78$	−0.492135	−	1.02855i	−0.0557233	−	0.116461i
$79$	12.9535			1.45738			0.728690	−	0.684844i	$-0.240130\pi$
$79$	12.9535			1.45738			0.728690	+	0.684844i	$0.240130\pi$
$80$	−3.36527	−	2.16217i	−0.376248	−	0.241738i
$81$	−8.34615			−0.927350
$82$	1.33012	+	2.77993i	0.146888	+	0.306992i
$83$	4.27228	+	4.27228i	0.468943	+	0.468943i	0.901572	−	0.432629i	$-0.142414\pi$
$83$	4.27228	+	4.27228i	0.468943	+	0.468943i	−0.432629	+	0.901572i	$0.642414\pi$
$84$	0.0997827	+	0.927607i	0.0108872	+	0.101210i
$85$	1.52647	−	1.52647i	0.165569	−	0.165569i
$86$	−2.31568	+	6.56471i	−0.249707	+	0.707891i
$87$			0.657063i			0.0704445i
$88$	−1.48666	−	2.40621i	−0.158478	−	0.256503i
$89$			2.22599i			0.235955i	0.993016	+	0.117977i	$0.0376410\pi$
$89$			2.22599i			0.235955i	−0.993016	+	0.117977i	$0.962359\pi$
$90$	3.90333	+	1.37689i	0.411447	+	0.145137i
$91$	−3.63086	+	3.63086i	−0.380617	+	0.380617i
$92$	7.63190	+	6.14944i	0.795680	+	0.641123i
$93$	0.0532208	+	0.0532208i	0.00551874	+	0.00551874i
$94$	−1.35800	+	0.649768i	−0.140067	+	0.0670184i
$95$	1.35778			0.139305
$96$	−0.190576	+	1.51907i	−0.0194506	+	0.155039i
$97$	12.7002			1.28951			0.644753	−	0.764391i	$-0.276960\pi$
$97$	12.7002			1.28951			0.644753	+	0.764391i	$0.276960\pi$
$98$	−5.14001	+	2.45936i	−0.519220	+	0.248433i
$99$	2.06953	+	2.06953i	0.207995	+	0.207995i
$100$	−1.55736	−	1.25485i	−0.155736	−	0.125485i
$101$	−5.22426	+	5.22426i	−0.519833	+	0.519833i	−0.917521	−	0.397688i	$-0.869813\pi$
$101$	−5.22426	+	5.22426i	−0.519833	+	0.519833i	0.397688	+	0.917521i	$0.369813\pi$
$102$	−0.779191	−	0.274858i	−0.0771514	−	0.0272150i
$103$			8.29929i			0.817754i	0.912590	+	0.408877i	$0.134079\pi$
$103$			8.29929i			0.817754i	−0.912590	+	0.408877i	$0.865921\pi$
$104$	−7.16832	+	4.42890i	−0.702912	+	0.434289i
$105$			0.466479i			0.0455237i
$106$	−1.84204	+	5.22199i	−0.178915	+	0.507205i
$107$	−5.63504	+	5.63504i	−0.544760	+	0.544760i	−0.924921	−	0.380160i	$-0.875869\pi$
$107$	−5.63504	+	5.63504i	−0.544760	+	0.544760i	0.380160	+	0.924921i	$0.375869\pi$
$108$	−0.343109	−	3.18964i	−0.0330157	−	0.306923i
$109$	−5.19573	−	5.19573i	−0.497661	−	0.497661i	0.413048	−	0.910709i	$-0.364464\pi$
$109$	−5.19573	−	5.19573i	−0.497661	−	0.497661i	−0.910709	+	0.413048i	$0.864464\pi$
$110$	−0.610390	−	1.27571i	−0.0581984	−	0.121634i
$111$	2.16482			0.205475
$112$	6.73672	−	1.46631i	0.636561	−	0.138553i
$113$	−20.0749			−1.88848			−0.944242	−	0.329251i	$-0.893204\pi$
$113$	−20.0749			−1.88848			−0.944242	+	0.329251i	$0.893204\pi$
$114$	−0.224300	−	0.468784i	−0.0210076	−	0.0439056i
$115$	3.46521	+	3.46521i	0.323132	+	0.323132i
$116$	4.82776	−	0.519322i	0.448247	−	0.0482179i
$117$	6.16531	−	6.16531i	0.569983	−	0.569983i
$118$	0.542216	−	1.53712i	0.0499151	−	0.141504i
$119$			3.72086i			0.341090i
$120$	−0.175976	+	0.744985i	−0.0160643	+	0.0680075i
$121$		−	1.00000i		−	0.0909091i
$122$	−6.50405	−	2.29429i	−0.588849	−	0.207715i
$123$	0.417025	−	0.417025i	0.0376018	−	0.0376018i
$124$	0.348975	−	0.433103i	0.0313389	−	0.0388938i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	−6.43541	+	3.07917i	−0.573312	+	0.274314i
$127$	19.8296			1.75959			0.879795	−	0.475354i	$-0.157680\pi$
$127$	19.8296			1.75959			0.879795	+	0.475354i	$0.157680\pi$
$128$	11.3119	+	0.199635i	0.999844	+	0.0176454i
$129$	1.33217			0.117291
$130$	−3.80044	+	1.81841i	−0.333321	+	0.159485i
$131$	−5.10598	−	5.10598i	−0.446111	−	0.446111i	0.447948	−	0.894059i	$-0.352155\pi$
$131$	−5.10598	−	5.10598i	−0.446111	−	0.446111i	−0.894059	+	0.447948i	$0.852155\pi$
$132$	−0.339612	+	0.421483i	−0.0295595	+	0.0366854i
$133$	−1.65483	+	1.65483i	−0.143492	+	0.143492i
$134$	−3.38752	−	1.19494i	−0.292637	−	0.103227i
$135$		−	1.60402i		−	0.138052i
$136$	−1.40367	+	5.94234i	−0.120363	+	0.509552i
$137$			8.18160i			0.699001i	0.936936	+	0.349501i	$0.113649\pi$
$137$			8.18160i			0.699001i	−0.936936	+	0.349501i	$0.886351\pi$
$138$	0.623949	−	1.76883i	0.0531141	−	0.150573i
$139$	−0.628022	+	0.628022i	−0.0532681	+	0.0532681i	−0.733239	−	0.679971i	$-0.761992\pi$
$139$	−0.628022	+	0.628022i	−0.0532681	+	0.0532681i	0.679971	+	0.733239i	$0.261992\pi$
$140$	3.42745	−	0.368691i	0.289673	−	0.0311601i
$141$	0.203717	+	0.203717i	0.0171561	+	0.0171561i
$142$	−1.99173	−	4.16269i	−0.167143	−	0.349325i
$143$	−2.97909			−0.249124
$144$	−11.4392	+	2.48984i	−0.953265	+	0.207486i
$145$	2.42781			0.201618
$146$	−3.27451	−	6.84367i	−0.271000	−	0.566386i
$147$	0.771066	+	0.771066i	0.0635965	+	0.0635965i
$148$	−1.71101	−	15.9060i	−0.140644	−	1.30746i
$149$	7.87635	−	7.87635i	0.645255	−	0.645255i	−0.306587	−	0.951843i	$-0.599187\pi$
$149$	7.87635	−	7.87635i	0.645255	−	0.645255i	0.951843	+	0.306587i	$0.0991871\pi$
$150$	−0.127322	+	0.360945i	−0.0103958	+	0.0294710i
$151$			1.93200i			0.157224i	0.996905	+	0.0786118i	$0.0250488\pi$
$151$			1.93200i			0.157224i	−0.996905	+	0.0786118i	$0.974951\pi$
$152$	−3.26710	+	2.01856i	−0.264997	+	0.163727i
$153$		−	6.31814i		−	0.510791i
$154$	2.29873	+	0.810872i	0.185237	+	0.0653419i
$155$	0.196648	−	0.196648i	0.0157951	−	0.0157951i
$156$	1.25564	+	1.01174i	0.100531	+	0.0810038i
$157$	−5.42164	−	5.42164i	−0.432694	−	0.432694i	0.456850	−	0.889544i	$-0.348978\pi$
$157$	−5.42164	−	5.42164i	−0.432694	−	0.432694i	−0.889544	+	0.456850i	$0.848978\pi$
$158$	−16.5248	+	7.90667i	−1.31464	+	0.629021i
$159$	1.05969			0.0840391
$160$	5.61286	+	0.704168i	0.443735	+	0.0556694i
$161$	−8.44665			−0.665689
$162$	10.6472	−	5.09441i	0.836525	−	0.400255i
$163$	0.880518	+	0.880518i	0.0689675	+	0.0689675i	0.740749	−	0.671782i	$-0.234471\pi$
$163$	0.880518	+	0.880518i	0.0689675	+	0.0689675i	−0.671782	+	0.740749i	$0.734471\pi$
$164$	−3.39369	−	2.73448i	−0.265003	−	0.213527i
$165$	−0.191372	+	0.191372i	−0.0148983	+	0.0148983i
$166$	−8.05792	−	2.84241i	−0.625416	−	0.220614i
$167$			10.2521i			0.793330i	0.917963	+	0.396665i	$0.129833\pi$
$167$			10.2521i			0.793330i	−0.917963	+	0.396665i	$0.870167\pi$
$168$	−0.693496	−	1.12245i	−0.0535044	−	0.0865987i
$169$		−	4.12501i		−	0.317308i
$170$	−1.01558	+	2.87907i	−0.0778916	+	0.220814i
$171$	2.80996	−	2.80996i	0.214883	−	0.214883i
$172$	−1.05291	−	9.78811i	−0.0802834	−	0.746336i
$173$	−14.0460	−	14.0460i	−1.06789	−	1.06789i	−0.997521	−	0.0703742i	$-0.977581\pi$
$173$	−14.0460	−	14.0460i	−1.06789	−	1.06789i	−0.0703742	−	0.997521i	$-0.522419\pi$
$174$	−0.401065	−	0.838218i	−0.0304046	−	0.0635452i
$175$	1.72361			0.130293
$176$	3.36527	+	2.16217i	0.253666	+	0.162980i
$177$	−0.311927			−0.0234459
$178$	−1.35872	−	2.83971i	−0.101841	−	0.212845i
$179$	−8.95892	−	8.95892i	−0.669621	−	0.669621i	0.288007	−	0.957628i	$-0.407007\pi$
$179$	−8.95892	−	8.95892i	−0.669621	−	0.669621i	−0.957628	+	0.288007i	$0.907007\pi$
$180$	−5.81993	+	0.626050i	−0.433792	+	0.0466630i
$181$	9.69069	−	9.69069i	0.720303	−	0.720303i	−0.248363	−	0.968667i	$-0.579893\pi$
$181$	9.69069	−	9.69069i	0.720303	−	0.720303i	0.968667	+	0.248363i	$0.0798927\pi$
$182$	2.41566	−	6.84814i	0.179061	−	0.507618i
$183$			1.31986i			0.0975669i
$184$	−13.4896	−	3.18644i	−0.994467	−	0.234907i
$185$		−	7.99887i		−	0.588088i
$186$	−0.100379	−	0.0354086i	−0.00736018	−	0.00259628i
$187$	−1.52647	+	1.52647i	−0.111626	+	0.111626i
$188$	1.33580	−	1.65782i	0.0974233	−	0.120909i
$189$	1.95494	+	1.95494i	0.142201	+	0.142201i
$190$	−1.73213	+	0.828776i	−0.125662	+	0.0601257i
$191$	−0.679908			−0.0491964			−0.0245982	−	0.999697i	$-0.507831\pi$
$191$	−0.679908			−0.0491964			−0.0245982	+	0.999697i	$0.507831\pi$
$192$	−0.684103	−	2.05421i	−0.0493709	−	0.148249i
$193$	−19.0426			−1.37072			−0.685360	−	0.728205i	$-0.740355\pi$
$193$	−19.0426			−1.37072			−0.685360	+	0.728205i	$0.740355\pi$
$194$	−16.2017	+	7.75205i	−1.16321	+	0.556565i
$195$	0.570114	+	0.570114i	0.0408267	+	0.0408267i
$196$	5.05598	−	6.27483i	0.361141	−	0.448202i
$197$	15.1051	−	15.1051i	1.07619	−	1.07619i	0.0793432	−	0.996847i	$-0.474718\pi$
$197$	15.1051	−	15.1051i	1.07619	−	1.07619i	0.996847	−	0.0793432i	$-0.0252823\pi$
$198$	−3.90333	−	1.37689i	−0.277397	−	0.0978511i
$199$		−	2.61124i		−	0.185106i	−0.995708	−	0.0925531i	$-0.970497\pi$
$199$		−	2.61124i		−	0.185106i	0.995708	−	0.0925531i	$-0.0295028\pi$
$200$	2.75267	+	0.650220i	0.194643	+	0.0459775i
$201$			0.687426i			0.0484873i
$202$	3.47577	−	9.85344i	0.244555	−	0.693286i
$203$	−2.95896	+	2.95896i	−0.207678	+	0.207678i
$204$	1.16179	−	0.124974i	0.0813415	−	0.00874990i
$205$	−1.54088	−	1.54088i	−0.107620	−	0.107620i
$206$	−5.06581	−	10.5875i	−0.352952	−	0.737663i
$207$	14.3427			0.996886
$208$	6.44131	−	10.0254i	0.446624	−	0.695139i
$209$	−1.35778			−0.0939196
$210$	−0.284735	−	0.595090i	−0.0196485	−	0.0410651i
$211$	−17.3860	−	17.3860i	−1.19690	−	1.19690i	−0.975089	−	0.221816i	$-0.928802\pi$
$211$	−17.3860	−	17.3860i	−1.19690	−	1.19690i	−0.221816	−	0.975089i	$-0.571198\pi$
$212$	−0.837549	−	7.78609i	−0.0575231	−	0.534751i
$213$	−0.624455	+	0.624455i	−0.0427870	+	0.0427870i
$214$	3.74908	−	10.6282i	0.256282	−	0.726531i
$215$		−	4.92229i		−	0.335697i
$216$	2.38463	+	3.85961i	0.162253	+	0.262613i
$217$			0.479340i			0.0325397i
$218$	9.79965	+	3.45680i	0.663716	+	0.234124i
$219$	−1.02664	+	1.02664i	−0.0693736	+	0.0693736i
$220$	1.55736	+	1.25485i	0.104997	+	0.0846018i
$221$	4.54749	+	4.54749i	0.305897	+	0.305897i
$222$	−2.76167	+	1.32138i	−0.185351	+	0.0886854i
$223$	−15.1229			−1.01270			−0.506351	−	0.862327i	$-0.669006\pi$
$223$	−15.1229			−1.01270			−0.506351	+	0.862327i	$0.669006\pi$
$224$	−7.69906	+	5.98261i	−0.514415	+	0.399730i
$225$	−2.92675			−0.195117
$226$	25.6096	−	12.2535i	1.70353	−	0.815091i
$227$	−9.26858	−	9.26858i	−0.615177	−	0.615177i	0.329113	−	0.944290i	$-0.393250\pi$
$227$	−9.26858	−	9.26858i	−0.615177	−	0.615177i	−0.944290	+	0.329113i	$0.893250\pi$
$228$	0.572282	+	0.461119i	0.0379003	+	0.0305384i
$229$	13.6250	−	13.6250i	0.900366	−	0.900366i	−0.0951016	−	0.995468i	$-0.530318\pi$
$229$	13.6250	−	13.6250i	0.900366	−	0.900366i	0.995468	+	0.0951016i	$0.0303176\pi$
$230$	−6.53572	−	2.30546i	−0.430952	−	0.152017i
$231$		−	0.466479i		−	0.0306921i
$232$	−5.84181	+	3.60932i	−0.383534	+	0.236964i
$233$			10.9217i			0.715505i	0.933816	+	0.357753i	$0.116457\pi$
$233$			10.9217i			0.715505i	−0.933816	+	0.357753i	$0.883543\pi$
$234$	−4.10187	+	11.6284i	−0.268148	+	0.760170i
$235$	0.752724	−	0.752724i	0.0491023	−	0.0491023i
$236$	0.246538	+	2.29188i	0.0160482	+	0.149189i
$237$	2.47893	+	2.47893i	0.161024	+	0.161024i
$238$	−2.27117	−	4.74672i	−0.147218	−	0.307684i
$239$	−10.0633			−0.650938			−0.325469	−	0.945553i	$-0.605522\pi$
$239$	−10.0633			−0.650938			−0.325469	+	0.945553i	$0.605522\pi$
$240$	−0.230238	−	1.05779i	−0.0148618	−	0.0682804i
$241$	−2.30792			−0.148666			−0.0743332	−	0.997233i	$-0.523683\pi$
$241$	−2.30792			−0.148666			−0.0743332	+	0.997233i	$0.523683\pi$
$242$	0.610390	+	1.27571i	0.0392374	+	0.0820054i
$243$	−4.99985	−	4.99985i	−0.320741	−	0.320741i
$244$	9.69766	−	1.04318i	0.620829	−	0.0667826i
$245$	2.84904	−	2.84904i	0.182019	−	0.182019i
$246$	−0.277453	+	0.786548i	−0.0176897	+	0.0501485i
$247$			4.04495i			0.257374i
$248$	−0.180827	+	0.765523i	−0.0114826	+	0.0486108i
$249$			1.63519i			0.103626i
$250$	1.33367	+	0.470449i	0.0843488	+	0.0297538i
$251$	−13.5660	+	13.5660i	−0.856276	+	0.856276i	−0.990897	−	0.134621i	$-0.957018\pi$
$251$	−13.5660	+	13.5660i	−0.856276	+	0.856276i	0.134621	+	0.990897i	$0.457018\pi$
$252$	6.33019	−	7.85623i	0.398765	−	0.494896i
$253$	−3.46521	−	3.46521i	−0.217856	−	0.217856i
$254$	−25.2967	+	12.1038i	−1.58725	+	0.759458i
$255$	0.584246			0.0365869
$256$	−14.5526	+	6.65003i	−0.909535	+	0.415627i
$257$	−11.9931			−0.748111			−0.374055	−	0.927406i	$-0.622033\pi$
$257$	−11.9931			−0.748111			−0.374055	+	0.927406i	$0.622033\pi$
$258$	−1.69946	+	0.813143i	−0.105803	+	0.0506241i
$259$	9.74885	+	9.74885i	0.605764	+	0.605764i
$260$	3.73831	−	4.63951i	0.231840	−	0.287730i
$261$	5.02441	−	5.02441i	0.311003	−	0.311003i
$262$	9.63036	+	3.39708i	0.594966	+	0.209872i
$263$			14.1938i			0.875226i	0.899163	+	0.437613i	$0.144176\pi$
$263$			14.1938i			0.875226i	−0.899163	+	0.437613i	$0.855824\pi$
$264$	0.175976	−	0.744985i	0.0108306	−	0.0458506i
$265$		−	3.91550i		−	0.240527i
$266$	1.10099	−	3.12118i	0.0675058	−	0.191372i
$267$	−0.425992	+	0.425992i	−0.0260703	+	0.0260703i
$268$	5.05086	−	0.543321i	0.308530	−	0.0331886i
$269$	−17.6243	−	17.6243i	−1.07457	−	1.07457i	−0.996985	−	0.0775891i	$-0.975278\pi$
$269$	−17.6243	−	17.6243i	−1.07457	−	1.07457i	−0.0775891	−	0.996985i	$-0.524722\pi$
$270$	0.979077	+	2.04625i	0.0595848	+	0.124531i
$271$	−26.3421			−1.60017			−0.800086	−	0.599886i	$-0.795213\pi$
$271$	−26.3421			−1.60017			−0.800086	+	0.599886i	$0.795213\pi$
$272$	−1.83649	−	8.43746i	−0.111353	−	0.511596i
$273$	−1.38969			−0.0841076
$274$	−4.99397	−	10.4373i	−0.301697	−	0.630541i
$275$	0.707107	+	0.707107i	0.0426401	+	0.0426401i
$276$	0.283700	+	2.63736i	0.0170768	+	0.158750i
$277$	−11.8709	+	11.8709i	−0.713251	+	0.713251i	−0.967214	−	0.253963i	$-0.918266\pi$
$277$	−11.8709	+	11.8709i	−0.713251	+	0.713251i	0.253963	+	0.967214i	$0.418266\pi$
$278$	0.417832	−	1.18451i	0.0250599	−	0.0710422i
$279$		−	0.813935i		−	0.0487290i
$280$	−4.14738	+	2.56243i	−0.247853	+	0.153134i
$281$			3.13340i			0.186923i	0.995623	+	0.0934615i	$0.0297932\pi$
$281$			3.13340i			0.186923i	−0.995623	+	0.0934615i	$0.970207\pi$
$282$	−0.384230	−	0.135536i	−0.0228806	−	0.00807107i
$283$	0.231924	−	0.231924i	0.0137865	−	0.0137865i	−0.700180	−	0.713966i	$-0.746897\pi$
$283$	0.231924	−	0.231924i	0.0137865	−	0.0137865i	0.713966	+	0.700180i	$0.246897\pi$
$284$	5.08173	+	4.09463i	0.301545	+	0.242972i
$285$	0.259841	+	0.259841i	0.0153916	+	0.0153916i
$286$	3.80044	−	1.81841i	0.224725	−	0.107525i
$287$	3.75599			0.221709
$288$	13.0733	−	10.1587i	0.770349	−	0.598605i
$289$	−12.3398			−0.725870
$290$	−3.09717	+	1.48191i	−0.181872	+	0.0870208i
$291$	2.43045	+	2.43045i	0.142475	+	0.142475i
$292$	8.35462	+	6.73178i	0.488917	+	0.393947i
$293$	2.57259	−	2.57259i	0.150292	−	0.150292i	−0.627956	−	0.778249i	$-0.716108\pi$
$293$	2.57259	−	2.57259i	0.150292	−	0.150292i	0.778249	+	0.627956i	$0.216108\pi$
$294$	−1.45430	−	0.513002i	−0.0848167	−	0.0299189i
$295$			1.15255i			0.0671041i
$296$	11.8916	+	19.2470i	0.691185	+	1.11871i
$297$			1.60402i			0.0930746i
$298$	−5.24025	+	14.8555i	−0.303560	+	0.860558i
$299$	−10.3232	+	10.3232i	−0.597005	+	0.597005i
$300$	−0.0578916	−	0.538176i	−0.00334237	−	0.0310716i
$301$	5.99918	+	5.99918i	0.345787	+	0.345787i
$302$	−1.17927	−	2.46466i	−0.0678595	−	0.141825i
$303$	−1.99955			−0.114871
$304$	2.93575	−	4.56929i	0.168377	−	0.262067i
$305$	4.87680			0.279245
$306$	3.85653	+	8.06008i	0.220463	+	0.460764i
$307$	−0.0220202	−	0.0220202i	−0.00125676	−	0.00125676i	0.706478	−	0.707735i	$-0.250283\pi$
$307$	−0.0220202	−	0.0220202i	−0.00125676	−	0.00125676i	−0.707735	+	0.706478i	$0.750283\pi$
$308$	−3.42745	+	0.368691i	−0.195297	+	0.0210081i
$309$	−1.58825	+	1.58825i	−0.0903523	+	0.0903523i
$310$	−0.130833	+	0.370896i	−0.00743079	+	0.0210655i
$311$			19.2884i			1.09374i	0.837217	+	0.546871i	$0.184181\pi$
$311$			19.2884i			1.09374i	−0.837217	+	0.546871i	$0.815819\pi$
$312$	−2.21938	−	0.524248i	−0.125648	−	0.0296797i
$313$			4.42358i			0.250035i	0.992155	+	0.125018i	$0.0398988\pi$
$313$			4.42358i			0.250035i	−0.992155	+	0.125018i	$0.960101\pi$
$314$	10.2257	+	3.60710i	0.577071	+	0.203560i
$315$	3.56707	−	3.56707i	0.200981	−	0.200981i
$316$	16.2546	−	20.1732i	0.914394	−	1.13483i
$317$	19.4164	+	19.4164i	1.09053	+	1.09053i	0.995471	+	0.0950624i	$0.0303051\pi$
$317$	19.4164	+	19.4164i	1.09053	+	1.09053i	0.0950624	+	0.995471i	$0.469695\pi$
$318$	−1.35186	+	0.646826i	−0.0758083	+	0.0362722i
$319$	−2.42781			−0.135931
$320$	−7.59017	+	2.52772i	−0.424303	+	0.141304i
$321$	−2.15677			−0.120379
$322$	10.7754	−	5.15575i	0.600492	−	0.287319i
$323$	2.07261	+	2.07261i	0.115323	+	0.115323i
$324$	−10.4731	+	12.9979i	−0.581841	+	0.722107i
$325$	2.10654	−	2.10654i	0.116850	−	0.116850i
$326$	−1.66074	−	0.585822i	−0.0919800	−	0.0324457i
$327$		−	1.98863i		−	0.109972i
$328$	5.99845	+	1.41692i	0.331209	+	0.0782362i
$329$			1.83481i			0.101156i
$330$	0.127322	−	0.360945i	0.00700887	−	0.0198694i
$331$	9.92339	−	9.92339i	0.545439	−	0.545439i	−0.379679	−	0.925118i	$-0.623966\pi$
$331$	9.92339	−	9.92339i	0.545439	−	0.545439i	0.925118	+	0.379679i	$0.123966\pi$
$332$	12.0145	−	1.29240i	0.659382	−	0.0709297i
$333$	−16.5539	−	16.5539i	−0.907147	−	0.907147i
$334$	−6.25777	−	13.0786i	−0.342410	−	0.715631i
$335$	2.54000			0.138775
$336$	1.56983	+	1.00861i	0.0856411	+	0.0550241i
$337$	−11.4051			−0.621277			−0.310638	−	0.950528i	$-0.600543\pi$
$337$	−11.4051			−0.621277			−0.310638	+	0.950528i	$0.600543\pi$
$338$	2.51787	+	5.26229i	0.136954	+	0.286231i
$339$	−3.84176	−	3.84176i	−0.208656	−	0.208656i
$340$	−0.461770	−	4.29274i	−0.0250430	−	0.232807i
$341$	−0.196648	+	0.196648i	−0.0106491	+	0.0106491i
$342$	−1.86951	+	5.29986i	−0.101092	+	0.286584i
$343$			19.0100i			1.02644i
$344$	7.31776	+	11.8441i	0.394547	+	0.638589i
$345$			1.32629i			0.0714048i
$346$	26.4920	+	9.34499i	1.42422	+	0.502390i
$347$	10.5111	−	10.5111i	0.564267	−	0.564267i	−0.366249	−	0.930517i	$-0.619358\pi$
$347$	10.5111	−	10.5111i	0.564267	−	0.564267i	0.930517	+	0.366249i	$0.119358\pi$
$348$	1.02328	+	0.824513i	0.0548536	+	0.0441986i
$349$	4.48143	+	4.48143i	0.239886	+	0.239886i	0.816803	−	0.576917i	$-0.195744\pi$
$349$	4.48143	+	4.48143i	0.239886	+	0.239886i	−0.576917	+	0.816803i	$0.695744\pi$
$350$	−2.19882	+	1.05208i	−0.117532	+	0.0562359i
$351$	4.77852			0.255059
$352$	−5.61286	−	0.704168i	−0.299166	−	0.0375323i
$353$	−28.4761			−1.51563			−0.757815	−	0.652469i	$-0.773733\pi$
$353$	−28.4761			−1.51563			−0.757815	+	0.652469i	$0.773733\pi$
$354$	0.397927	−	0.190397i	0.0211496	−	0.0101195i
$355$	2.30732	+	2.30732i	0.122460	+	0.122460i
$356$	3.46666	+	2.79328i	0.183733	+	0.148044i
$357$	−0.712066	+	0.712066i	−0.0376865	+	0.0376865i
$358$	16.8974	+	5.96051i	0.893055	+	0.315023i
$359$		−	11.0087i		−	0.581018i	−0.956872	−	0.290509i	$-0.906175\pi$
$359$		−	11.0087i		−	0.581018i	0.956872	−	0.290509i	$-0.0938247\pi$
$360$	7.04238	−	4.35109i	0.371166	−	0.229322i
$361$		−	17.1564i		−	0.902970i
$362$	−6.44736	+	18.2776i	−0.338866	+	0.960648i
$363$	0.191372	−	0.191372i	0.0100444	−	0.0100444i
$364$	1.09837	+	10.2107i	0.0575700	+	0.535186i
$365$	3.79336	+	3.79336i	0.198553	+	0.198553i
$366$	−0.805630	−	1.68375i	−0.0421109	−	0.0880111i
$367$	7.07292			0.369203			0.184602	−	0.982813i	$-0.440900\pi$
$367$	7.07292			0.369203			0.184602	+	0.982813i	$0.440900\pi$
$368$	19.1537	−	4.16897i	0.998457	−	0.217323i
$369$	−6.37779			−0.332015
$370$	4.88243	+	10.2042i	0.253826	+	0.530491i
$371$	4.77213	+	4.77213i	0.247757	+	0.247757i
$372$	0.149668	−	0.0160997i	0.00775991	−	0.000834733i
$373$	7.53386	−	7.53386i	0.390089	−	0.390089i	−0.484630	−	0.874719i	$-0.661046\pi$
$373$	7.53386	−	7.53386i	0.390089	−	0.390089i	0.874719	+	0.484630i	$0.161046\pi$
$374$	1.01558	−	2.87907i	0.0525145	−	0.148873i
$375$		−	0.270640i		−	0.0139758i
$376$	−0.692167	+	2.93025i	−0.0356958	+	0.151116i
$377$			7.23266i			0.372501i
$378$	−3.68721	−	1.30065i	−0.189650	−	0.0668984i
$379$	23.4231	−	23.4231i	1.20317	−	1.20317i	0.229967	−	0.973198i	$-0.426138\pi$
$379$	23.4231	−	23.4231i	1.20317	−	1.20317i	0.973198	−	0.229967i	$-0.0738619\pi$
$380$	1.70381	−	2.11455i	0.0874035	−	0.108474i
$381$	3.79482	+	3.79482i	0.194414	+	0.194414i
$382$	0.867362	−	0.415009i	0.0443781	−	0.0212337i
$383$	22.6204			1.15585			0.577924	−	0.816091i	$-0.303863\pi$
$383$	22.6204			1.15585			0.577924	+	0.816091i	$0.303863\pi$
$384$	2.12658	+	2.20299i	0.108522	+	0.112421i
$385$	−1.72361			−0.0878435
$386$	24.2928	−	11.6234i	1.23647	−	0.591618i
$387$	−10.1868	−	10.1868i	−0.517825	−	0.517825i
$388$	15.9368	−	19.7787i	0.809066	−	1.00411i
$389$	9.39630	−	9.39630i	0.476411	−	0.476411i	−0.427571	−	0.903982i	$-0.640630\pi$
$389$	9.39630	−	9.39630i	0.476411	−	0.476411i	0.903982	+	0.427571i	$0.140630\pi$
$390$	−1.07529	−	0.379305i	−0.0544494	−	0.0192069i
$391$			10.5791i			0.535007i
$392$	−2.61984	+	11.0910i	−0.132322	+	0.560178i
$393$		−	1.95428i		−	0.0985803i
$394$	−10.0496	+	28.4896i	−0.506292	+	1.43528i
$395$	9.15949	−	9.15949i	0.460864	−	0.460864i
$396$	5.81993	−	0.626050i	0.292463	−	0.0314602i
$397$	−11.2541	−	11.2541i	−0.564826	−	0.564826i	0.365848	−	0.930674i	$-0.380779\pi$
$397$	−11.2541	−	11.2541i	−0.564826	−	0.564826i	−0.930674	+	0.365848i	$0.880779\pi$
$398$	1.59388	+	3.33118i	0.0798939	+	0.166977i
$399$	−0.633377			−0.0317085
$400$	−3.90849	+	0.850716i	−0.195424	+	0.0425358i
$401$	19.4462			0.971098			0.485549	−	0.874210i	$-0.338620\pi$
$401$	19.4462			0.971098			0.485549	+	0.874210i	$0.338620\pi$
$402$	−0.419598	−	0.876953i	−0.0209277	−	0.0437385i
$403$	0.585831	+	0.585831i	0.0291823	+	0.0291823i
$404$	1.58038	+	14.6917i	0.0786270	+	0.730938i
$405$	−5.90162	+	5.90162i	−0.293254	+	0.293254i
$406$	1.96864	−	5.58088i	0.0977020	−	0.276975i
$407$			7.99887i			0.396489i
$408$	−1.40582	+	0.868574i	−0.0695983	+	0.0430008i
$409$			2.28872i			0.113170i	0.998398	+	0.0565850i	$0.0180212\pi$
$409$			2.28872i			0.113170i	−0.998398	+	0.0565850i	$0.981979\pi$
$410$	2.90625	+	1.02517i	0.143529	+	0.0506296i
$411$	−1.56573	+	1.56573i	−0.0772316	+	0.0772316i
$412$	12.9250	+	10.4143i	0.636767	+	0.513078i
$413$	−1.40471	−	1.40471i	−0.0691210	−	0.0691210i
$414$	−18.2970	+	8.75464i	−0.899251	+	0.430267i
$415$	6.04191			0.296586
$416$	−2.09778	+	16.7212i	−0.102852	+	0.819825i
$417$	−0.240371			−0.0117710
$418$	1.73213	−	0.828776i	0.0847211	−	0.0405368i
$419$	−20.7009	−	20.7009i	−1.01131	−	1.01131i	−0.999935	−	0.0113704i	$-0.996381\pi$
$419$	−20.7009	−	20.7009i	−1.01131	−	1.01131i	−0.0113704	−	0.999935i	$-0.503619\pi$
$420$	0.726475	+	0.585361i	0.0354483	+	0.0285627i
$421$	−10.7884	+	10.7884i	−0.525793	+	0.525793i	−0.919315	−	0.393522i	$-0.871256\pi$
$421$	−10.7884	+	10.7884i	−0.525793	+	0.525793i	0.393522	+	0.919315i	$0.371256\pi$
$422$	32.7917	+	11.5672i	1.59628	+	0.563082i
$423$		−	3.11557i		−	0.151484i
$424$	5.82102	+	9.42152i	0.282694	+	0.457550i
$425$		−	2.15875i		−	0.104715i
$426$	0.415459	−	1.17778i	0.0201291	−	0.0570637i
$427$	−5.94375	+	5.94375i	−0.287638	+	0.287638i
$428$	1.70465	+	15.8469i	0.0823973	+	0.765988i
$429$	−0.570114	−	0.570114i	−0.0275254	−	0.0275254i
$430$	3.00452	+	6.27939i	0.144891	+	0.302819i
$431$	−29.4096			−1.41661			−0.708305	−	0.705906i	$-0.750540\pi$
$431$	−29.4096			−1.41661			−0.708305	+	0.705906i	$0.750540\pi$
$432$	−5.39795	−	3.46816i	−0.259709	−	0.166862i
$433$	−24.5084			−1.17780			−0.588898	−	0.808207i	$-0.700438\pi$
$433$	−24.5084			−1.17780			−0.588898	+	0.808207i	$0.700438\pi$
$434$	−0.292584	−	0.611497i	−0.0140445	−	0.0293528i
$435$	0.464613	+	0.464613i	0.0222765	+	0.0222765i
$436$	−14.6115	+	1.57175i	−0.699762	+	0.0752734i
$437$	−4.70499	+	4.70499i	−0.225070	+	0.225070i
$438$	0.683036	−	1.93633i	0.0326367	−	0.0925216i
$439$			16.1927i			0.772837i	0.922324	+	0.386419i	$0.126288\pi$
$439$			16.1927i			0.772837i	−0.922324	+	0.386419i	$0.873712\pi$
$440$	−2.75267	−	0.650220i	−0.131229	−	0.0309980i
$441$		−	11.7923i		−	0.561540i
$442$	−8.57700	−	3.02551i	−0.407966	−	0.143909i
$443$	−11.6595	+	11.6595i	−0.553959	+	0.553959i	−0.927581	−	0.373622i	$-0.878116\pi$
$443$	−11.6595	+	11.6595i	−0.553959	+	0.553959i	0.373622	+	0.927581i	$0.378116\pi$
$444$	2.71651	−	3.37139i	0.128920	−	0.159999i
$445$	1.57401	+	1.57401i	0.0746154	+	0.0746154i
$446$	19.2923	−	9.23085i	0.913518	−	0.437093i
$447$	3.01462			0.142587
$448$	6.17000	−	12.3315i	0.291505	−	0.582607i
$449$	13.5095			0.637553			0.318776	−	0.947830i	$-0.396728\pi$
$449$	13.5095			0.637553			0.318776	+	0.947830i	$0.396728\pi$
$450$	3.73367	−	1.78646i	0.176007	−	0.0842146i
$451$	1.54088	+	1.54088i	0.0725573	+	0.0725573i
$452$	−25.1909	+	31.2637i	−1.18488	+	1.47052i
$453$	−0.369729	+	0.369729i	−0.0173714	+	0.0173714i
$454$	17.4814	+	6.16652i	0.820444	+	0.289409i
$455$			5.13480i			0.240723i
$456$	−1.01153	−	0.238937i	−0.0473690	−	0.0111892i
$457$			26.7237i			1.25008i	0.780592	+	0.625041i	$0.214918\pi$
$457$			26.7237i			1.25008i	−0.780592	+	0.625041i	$0.785082\pi$
$458$	−9.06492	+	25.6981i	−0.423576	+	1.20079i
$459$	2.44848	−	2.44848i	0.114285	−	0.114285i
$460$	9.74488	−	1.04826i	0.454357	−	0.0488752i
$461$	25.1701	+	25.1701i	1.17229	+	1.17229i	0.981662	+	0.190627i	$0.0610522\pi$
$461$	25.1701	+	25.1701i	1.17229	+	1.17229i	0.190627	+	0.981662i	$0.438948\pi$
$462$	0.284735	+	0.595090i	0.0132470	+	0.0276861i
$463$	15.4560			0.718299			0.359150	−	0.933280i	$-0.383067\pi$
$463$	15.4560			0.718299			0.359150	+	0.933280i	$0.383067\pi$
$464$	5.24934	−	8.17022i	0.243694	−	0.379293i
$465$	0.0752655			0.00349036
$466$	−6.66651	−	13.9329i	−0.308820	−	0.645429i
$467$	−27.4025	−	27.4025i	−1.26804	−	1.26804i	−0.947100	−	0.320938i	$-0.896002\pi$
$467$	−27.4025	−	27.4025i	−1.26804	−	1.26804i	−0.320938	−	0.947100i	$-0.603998\pi$
$468$	−1.86506	−	17.3381i	−0.0862125	−	0.801455i
$469$	−3.09570	+	3.09570i	−0.142946	+	0.142946i
$470$	−0.500798	+	1.41971i	−0.0231001	+	0.0654863i
$471$		−	2.07510i		−	0.0956154i
$472$	−1.71345	−	2.77328i	−0.0788680	−	0.127651i
$473$			4.92229i			0.226327i
$474$	−4.67549	−	1.64927i	−0.214753	−	0.0757533i
$475$	0.960096	−	0.960096i	0.0440522	−	0.0440522i
$476$	5.79470	+	4.66911i	0.265600	+	0.214008i
$477$	−8.10324	−	8.10324i	−0.371022	−	0.371022i
$478$	12.8377	−	6.14251i	0.587185	−	0.280952i
$479$	28.3248			1.29419			0.647097	−	0.762408i	$-0.275983\pi$
$479$	28.3248			1.29419			0.647097	+	0.762408i	$0.275983\pi$
$480$	0.939383	+	1.20890i	0.0428768	+	0.0551784i
$481$	23.8294			1.08653
$482$	2.94423	−	1.40873i	0.134106	−	0.0641660i
$483$	−1.61645	−	1.61645i	−0.0735510	−	0.0735510i
$484$	−1.55736	−	1.25485i	−0.0707889	−	0.0570385i
$485$	8.98037	−	8.98037i	0.407777	−	0.407777i
$486$	9.43020	+	3.32648i	0.427763	+	0.150892i
$487$			9.35621i			0.423970i	0.977273	+	0.211985i	$0.0679929\pi$
$487$			9.35621i			0.423970i	−0.977273	+	0.211985i	$0.932007\pi$
$488$	−11.7346	+	7.25015i	−0.531201	+	0.328199i
$489$			0.337012i			0.0152402i
$490$	−1.89551	+	5.37357i	−0.0856305	+	0.242753i
$491$	−8.99034	+	8.99034i	−0.405728	+	0.405728i	−0.880246	−	0.474518i	$-0.842623\pi$
$491$	−8.99034	+	8.99034i	−0.405728	+	0.405728i	0.474518	+	0.880246i	$0.342623\pi$
$492$	−0.126154	−	1.17276i	−0.00568744	−	0.0528720i
$493$	3.70597	+	3.70597i	0.166909	+	0.166909i
$494$	−2.46900	−	5.16017i	−0.111086	−	0.232167i
$495$	2.92675			0.131548
$496$	−0.236586	−	1.08696i	−0.0106230	−	0.0488058i
$497$	−5.62424			−0.252282
$498$	−0.998101	−	2.08601i	−0.0447260	−	0.0934765i
$499$	4.09347	+	4.09347i	0.183249	+	0.183249i	0.792770	−	0.609521i	$-0.208638\pi$
$499$	4.09347	+	4.09347i	0.183249	+	0.183249i	−0.609521	+	0.792770i	$0.708638\pi$
$500$	−1.98853	+	0.213906i	−0.0889297	+	0.00956616i
$501$	−1.96196	+	1.96196i	−0.0876538	+	0.0876538i
$502$	9.02564	−	25.5867i	0.402834	−	1.14199i
$503$			19.2925i			0.860210i	0.902779	+	0.430105i	$0.141523\pi$
$503$			19.2925i			0.860210i	−0.902779	+	0.430105i	$0.858477\pi$
$504$	−3.28010	+	13.8861i	−0.146107	+	0.618537i
$505$			7.38821i			0.328771i
$506$	6.53572	+	2.30546i	0.290548	+	0.102490i
$507$	0.789410	−	0.789410i	0.0350589	−	0.0350589i
$508$	24.8831	−	30.8817i	1.10401	−	1.37015i
$509$	9.45873	+	9.45873i	0.419251	+	0.419251i	0.884946	−	0.465695i	$-0.154195\pi$
$509$	9.45873	+	9.45873i	0.419251	+	0.419251i	−0.465695	+	0.884946i	$0.654195\pi$
$510$	−0.745325	+	0.356618i	−0.0330036	+	0.0157913i
$511$	−9.24653			−0.409042
$512$	14.5057	−	17.3662i	0.641066	−	0.767486i
$513$	2.17791			0.0961569
$514$	15.2997	−	7.32049i	0.674841	−	0.322893i
$515$	5.86849	+	5.86849i	0.258596	+	0.258596i
$516$	1.67167	−	2.07466i	0.0735912	−	0.0913319i
$517$	−0.752724	+	0.752724i	−0.0331048	+	0.0331048i
$518$	−18.3873	−	6.48606i	−0.807890	−	0.284981i
$519$		−	5.37600i		−	0.235980i
$520$	−1.93707	+	8.20047i	−0.0849460	+	0.359614i
$521$		−	0.222314i		−	0.00973975i	−0.999988	−	0.00486988i	$-0.998450\pi$
$521$		−	0.222314i		−	0.00973975i	0.999988	−	0.00486988i	$-0.00155014\pi$
$522$	−3.34282	+	9.47653i	−0.146311	+	0.414776i
$523$	−11.2065	+	11.2065i	−0.490028	+	0.490028i	−0.908315	−	0.418287i	$-0.862631\pi$
$523$	−11.2065	+	11.2065i	−0.490028	+	0.490028i	0.418287	+	0.908315i	$0.362631\pi$
$524$	−14.3590	+	1.54460i	−0.627278	+	0.0674763i
$525$	0.329851	+	0.329851i	0.0143959	+	0.0143959i
$526$	−8.66375	−	18.1071i	−0.377757	−	0.789507i
$527$	0.600353			0.0261518
$528$	0.230238	+	1.05779i	0.0100198	+	0.0460346i
$529$	−1.01536			−0.0441461
$530$	2.38999	+	4.99503i	0.103814	+	0.216970i
$531$	2.38524	+	2.38524i	0.103510	+	0.103510i
$532$	0.500602	+	4.65373i	0.0217038	+	0.201765i
$533$	4.59043	−	4.59043i	0.198833	−	0.198833i
$534$	0.283419	−	0.803461i	0.0122647	−	0.0347692i
$535$			7.96915i			0.344537i
$536$	−6.11177	+	3.77611i	−0.263988	+	0.163103i
$537$		−	3.42897i		−	0.147971i
$538$	33.2412	+	11.7257i	1.43313	+	0.505532i
$539$	−2.84904	+	2.84904i	−0.122717	+	0.122717i
$540$	−2.49803	−	2.01280i	−0.107498	−	0.0866171i
$541$	9.42376	+	9.42376i	0.405159	+	0.405159i	0.880047	−	0.474887i	$-0.157511\pi$
$541$	9.42376	+	9.42376i	0.405159	+	0.405159i	−0.474887	+	0.880047i	$0.657511\pi$
$542$	33.6048	−	16.0790i	1.44345	−	0.690652i
$543$	3.70905			0.159170
$544$	7.49296	+	9.64274i	0.321258	+	0.413429i
$545$	−7.34788			−0.314748
$546$	1.77283	−	0.848250i	0.0758701	−	0.0363018i
$547$	−25.0238	−	25.0238i	−1.06994	−	1.06994i	−0.997363	−	0.0725778i	$-0.976877\pi$
$547$	−25.0238	−	25.0238i	−1.06994	−	1.06994i	−0.0725778	−	0.997363i	$-0.523123\pi$
$548$	12.7417	+	10.2667i	0.544297	+	0.438570i
$549$	10.0927	−	10.0927i	0.430745	−	0.430745i
$550$	−1.33367	−	0.470449i	−0.0568679	−	0.0200600i
$551$			3.29643i			0.140433i
$552$	−1.97173	−	3.19132i	−0.0839226	−	0.135832i
$553$			22.3268i			0.949431i
$554$	7.89786	−	22.3896i	0.335548	−	0.951241i
$555$	1.53076	−	1.53076i	0.0649770	−	0.0649770i
$556$	0.189982	+	1.76613i	0.00805704	+	0.0749004i
$557$	−5.12617	−	5.12617i	−0.217203	−	0.217203i	0.590116	−	0.807319i	$-0.299082\pi$
$557$	−5.12617	−	5.12617i	−0.217203	−	0.217203i	−0.807319	+	0.590116i	$0.799082\pi$
$558$	0.496818	+	1.03834i	0.0210320	+	0.0439565i
$559$	14.6640			0.620219
$560$	3.72675	−	5.80042i	0.157484	−	0.245112i
$561$	−0.584246			−0.0246669
$562$	−1.91260	−	3.99730i	−0.0806780	−	0.168616i
$563$	−19.3267	−	19.3267i	−0.814524	−	0.814524i	0.170784	−	0.985308i	$-0.445370\pi$
$563$	−19.3267	−	19.3267i	−0.814524	−	0.814524i	−0.985308	+	0.170784i	$0.945370\pi$
$564$	0.572895	−	0.0616263i	0.0241232	−	0.00259493i
$565$	−14.1951	+	14.1951i	−0.597191	+	0.597191i
$566$	−0.154303	+	0.437431i	−0.00648582	+	0.0183866i
$567$		−	14.3855i		−	0.604136i
$568$	−8.98211	−	2.12170i	−0.376881	−	0.0890246i
$569$			35.7496i			1.49870i	0.662172	+	0.749351i	$0.269635\pi$
$569$			35.7496i			1.49870i	−0.662172	+	0.749351i	$0.730365\pi$
$570$	−0.490084	−	0.172876i	−0.0205274	−	0.00724097i
$571$	17.2797	−	17.2797i	0.723135	−	0.723135i	−0.246108	−	0.969242i	$-0.579152\pi$
$571$	17.2797	−	17.2797i	0.723135	−	0.723135i	0.969242	+	0.246108i	$0.0791518\pi$
$572$	−3.73831	+	4.63951i	−0.156306	+	0.193988i
$573$	−0.130115	−	0.130115i	−0.00543563	−	0.00543563i
$574$	−4.79153	+	2.29262i	−0.199995	+	0.0956920i
$575$	4.90055			0.204367
$576$	−10.4769	+	20.9392i	−0.436536	+	0.872469i
$577$	−6.19829			−0.258038			−0.129019	−	0.991642i	$-0.541183\pi$
$577$	−6.19829			−0.258038			−0.129019	+	0.991642i	$0.541183\pi$
$578$	15.7419	−	7.53209i	0.654778	−	0.313293i
$579$	−3.64422	−	3.64422i	−0.151449	−	0.151449i
$580$	3.04653	−	3.78096i	0.126500	−	0.156996i
$581$	−7.36376	+	7.36376i	−0.305500	+	0.305500i
$582$	−4.58406	−	1.61701i	−0.190015	−	0.0670274i
$583$			3.91550i			0.162164i
$584$	−14.7670	−	3.48818i	−0.611065	−	0.144342i
$585$		−	8.71907i		−	0.360489i
$586$	−1.71158	+	4.85215i	−0.0707048	+	0.200440i
$587$	−11.6202	+	11.6202i	−0.479617	+	0.479617i	−0.905009	−	0.425392i	$-0.860136\pi$
$587$	−11.6202	+	11.6202i	−0.479617	+	0.479617i	0.425392	+	0.905009i	$0.360136\pi$
$588$	2.16839	−	0.233254i	0.0894231	−	0.00961924i
$589$	0.267004	+	0.267004i	0.0110017	+	0.0110017i
$590$	−0.703506	−	1.47032i	−0.0289629	−	0.0605319i
$591$	5.78136			0.237813
$592$	−26.9183	−	17.2949i	−1.10634	−	0.710817i
$593$	23.9613			0.983971			0.491985	−	0.870603i	$-0.336271\pi$
$593$	23.9613			0.983971			0.491985	+	0.870603i	$0.336271\pi$
$594$	−0.979077	−	2.04625i	−0.0401720	−	0.0839589i
$595$	2.63104	+	2.63104i	0.107862	+	0.107862i
$596$	−2.38266	−	22.1499i	−0.0975977	−	0.907295i
$597$	0.499718	−	0.499718i	0.0204521	−	0.0204521i
$598$	6.86817	−	19.4705i	0.280860	−	0.796208i
$599$		−	40.0187i		−	1.63512i	−0.575845	−	0.817559i	$-0.695327\pi$
$599$		−	40.0187i		−	1.63512i	0.575845	−	0.817559i	$-0.304673\pi$
$600$	0.402350	+	0.651217i	0.0164259	+	0.0265858i
$601$			30.7523i			1.25441i	0.778853	+	0.627206i	$0.215802\pi$
$601$			30.7523i			1.25441i	−0.778853	+	0.627206i	$0.784198\pi$
$602$	−11.3150	−	3.99134i	−0.461166	−	0.162675i
$603$	5.25660	−	5.25660i	0.214065	−	0.214065i
$604$	3.00881	+	2.42436i	0.122427	+	0.0986458i
$605$	−0.707107	−	0.707107i	−0.0287480	−	0.0287480i
$606$	2.55083	−	1.22050i	0.103621	−	0.0495796i
$607$	−47.9139			−1.94476			−0.972382	−	0.233394i	$-0.925017\pi$
$607$	−47.9139			−1.94476			−0.972382	+	0.233394i	$0.925017\pi$
$608$	−0.956106	+	7.62103i	−0.0387752	+	0.309073i
$609$	−1.13252			−0.0458921
$610$	−6.22137	+	2.97675i	−0.251896	+	0.120525i
$611$	2.24243	+	2.24243i	0.0907192	+	0.0907192i
$612$	−9.83959	−	7.92830i	−0.397742	−	0.320483i
$613$	−22.7751	+	22.7751i	−0.919876	+	0.919876i	−0.997020	−	0.0771437i	$-0.975420\pi$
$613$	−22.7751	+	22.7751i	−0.919876	+	0.919876i	0.0771437	+	0.997020i	$0.475420\pi$
$614$	0.0415322	+	0.0146504i	0.00167610	+	0.000591241i
$615$		−	0.589762i		−	0.0237815i
$616$	4.14738	−	2.56243i	0.167103	−	0.103243i
$617$		−	3.41048i		−	0.137301i	−0.997641	−	0.0686503i	$-0.978131\pi$
$617$		−	3.41048i		−	0.137301i	0.997641	−	0.0686503i	$-0.0218693\pi$
$618$	1.05669	−	2.99559i	0.0425061	−	0.120500i
$619$	−11.8100	+	11.8100i	−0.474685	+	0.474685i	−0.903427	−	0.428742i	$-0.858957\pi$
$619$	−11.8100	+	11.8100i	−0.474685	+	0.474685i	0.428742	+	0.903427i	$0.358957\pi$
$620$	−0.0594876	−	0.553013i	−0.00238908	−	0.0222095i
$621$	5.55826	+	5.55826i	0.223045	+	0.223045i
$622$	−11.7734	−	24.6063i	−0.472071	−	0.986621i
$623$	−3.83675			−0.153716
$624$	3.15127	−	0.685900i	0.126152	−	0.0274580i
$625$	−1.00000			−0.0400000
$626$	−2.70011	−	5.64318i	−0.107918	−	0.225547i
$627$	−0.259841	−	0.259841i	−0.0103770	−	0.0103770i
$628$	−15.2468	+	1.64009i	−0.608412	+	0.0654468i
$629$	12.2100	−	12.2100i	0.486846	−	0.486846i
$630$	−2.37322	+	6.72783i	−0.0945514	+	0.268043i
$631$		−	26.0544i		−	1.03721i	−0.855014	−	0.518604i	$-0.826452\pi$
$631$		−	26.0544i		−	1.03721i	0.855014	−	0.518604i	$-0.173548\pi$
$632$	−8.42261	+	35.6567i	−0.335033	+	1.41835i
$633$		−	6.65439i		−	0.264488i
$634$	−36.6212	−	12.9180i	−1.45441	−	0.513040i
$635$	14.0216	−	14.0216i	0.556431	−	0.556431i
$636$	1.32975	−	1.65032i	0.0527281	−	0.0654394i
$637$	8.48756	+	8.48756i	0.336289	+	0.336289i
$638$	3.09717	−	1.48191i	0.122618	−	0.0586694i
$639$	9.55014			0.377798
$640$	8.13992	−	7.85759i	0.321759	−	0.310599i
$641$	11.6549			0.460342			0.230171	−	0.973150i	$-0.426071\pi$
$641$	11.6549			0.460342			0.230171	+	0.973150i	$0.426071\pi$
$642$	2.75141	−	1.31647i	0.108589	−	0.0519571i
$643$	34.0658	+	34.0658i	1.34343	+	1.34343i	0.892624	+	0.450801i	$0.148862\pi$
$643$	34.0658	+	34.0658i	1.34343	+	1.34343i	0.450801	+	0.892624i	$0.351138\pi$
$644$	−10.5993	+	13.1544i	−0.417669	+	0.518358i
$645$	0.941986	−	0.941986i	0.0370907	−	0.0370907i
$646$	−3.90914	−	1.37894i	−0.153803	−	0.0542536i
$647$		−	47.8518i		−	1.88125i	−0.339447	−	0.940625i	$-0.610240\pi$
$647$		−	47.8518i		−	1.88125i	0.339447	−	0.940625i	$-0.389760\pi$
$648$	5.42684	−	22.9742i	0.213186	−	0.902513i
$649$		−	1.15255i		−	0.0452416i
$650$	−1.40151	+	3.97313i	−0.0549717	+	0.155839i
$651$	−0.0917321	+	0.0917321i	−0.00359526	+	0.00359526i
$652$	2.47620	−	0.266364i	0.0969753	−	0.0104316i
$653$	−26.1520	−	26.1520i	−1.02341	−	1.02341i	−0.999719	−	0.0236891i	$-0.992459\pi$
$653$	−26.1520	−	26.1520i	−1.02341	−	1.02341i	−0.0236891	−	0.999719i	$-0.507541\pi$
$654$	1.21384	+	2.53691i	0.0474650	+	0.0992009i
$655$	−7.22094			−0.282146
$656$	−8.51712	+	1.85382i	−0.332538	+	0.0723797i
$657$	15.7009			0.612551
$658$	−1.11995	−	2.34067i	−0.0436602	−	0.0912490i
$659$	−0.786446	−	0.786446i	−0.0306356	−	0.0306356i	0.691623	−	0.722259i	$-0.256896\pi$
$659$	−0.786446	−	0.786446i	−0.0306356	−	0.0306356i	−0.722259	+	0.691623i	$0.756896\pi$
$660$	0.0578916	+	0.538176i	0.00225343	+	0.0209485i
$661$	−12.5912	+	12.5912i	−0.489739	+	0.489739i	−0.908224	−	0.418485i	$-0.862561\pi$
$661$	−12.5912	+	12.5912i	−0.489739	+	0.489739i	0.418485	+	0.908224i	$0.362561\pi$
$662$	−6.60218	+	18.7165i	−0.256601	+	0.727436i
$663$			1.74052i			0.0675963i
$664$	−14.5381	+	8.98226i	−0.564188	+	0.348579i
$665$			2.34029i			0.0907525i
$666$	31.2222	+	11.0135i	1.20984	+	0.426766i
$667$	−8.41286	+	8.41286i	−0.325747	+	0.325747i
$668$	15.9661	+	12.8648i	0.617749	+	0.497754i
$669$	−2.89409	−	2.89409i	−0.111892	−	0.111892i
$670$	−3.24029	+	1.55039i	−0.125183	+	0.0598968i
$671$	−4.87680			−0.188267
$672$	−2.61828	−	0.328480i	−0.101002	−	0.0126714i
$673$	7.75847			0.299067			0.149533	−	0.988757i	$-0.452223\pi$
$673$	7.75847			0.299067			0.149533	+	0.988757i	$0.452223\pi$
$674$	14.5496	−	6.96158i	0.560429	−	0.268150i
$675$	−1.13421	−	1.13421i	−0.0436559	−	0.0436559i
$676$	−6.42411	−	5.17626i	−0.247081	−	0.199087i
$677$	20.7713	−	20.7713i	0.798307	−	0.798307i	−0.184522	−	0.982828i	$-0.559074\pi$
$677$	20.7713	−	20.7713i	0.798307	−	0.798307i	0.982828	+	0.184522i	$0.0590736\pi$
$678$	7.24593	+	2.55598i	0.278278	+	0.0981618i
$679$			21.8902i			0.840067i
$680$	3.20933	+	5.19441i	0.123072	+	0.199197i
$681$		−	3.54749i		−	0.135940i
$682$	0.130833	−	0.370896i	0.00500984	−	0.0142023i
$683$	−10.4992	+	10.4992i	−0.401742	+	0.401742i	−0.878847	−	0.477105i	$-0.841686\pi$
$683$	−10.4992	+	10.4992i	−0.401742	+	0.401742i	0.477105	+	0.878847i	$0.341686\pi$
$684$	−0.850038	−	7.90219i	−0.0325020	−	0.302148i
$685$	5.78527	+	5.78527i	0.221044	+	0.221044i
$686$	−11.6035	−	24.2512i	−0.443025	−	0.925914i
$687$	5.21488			0.198960
$688$	−16.5648	−	10.6428i	−0.631527	−	0.405754i
$689$	11.6646			0.444388
$690$	−0.809552	−	1.69195i	−0.0308191	−	0.0644114i
$691$	−27.2587	−	27.2587i	−1.03697	−	1.03697i	−0.999290	−	0.0376780i	$-0.988004\pi$
$691$	−27.2587	−	27.2587i	−1.03697	−	1.03697i	−0.0376780	−	0.999290i	$-0.511996\pi$
$692$	−39.5001	+	4.24903i	−1.50157	+	0.161524i
$693$	−3.56707	+	3.56707i	−0.135502	+	0.135502i
$694$	−6.99322	+	19.8250i	−0.265459	+	0.752547i
$695$			0.888157i			0.0336897i
$696$	−1.80868	−	0.427236i	−0.0685578	−	0.0161943i
$697$		−	4.70421i		−	0.178185i
$698$	−8.45241	−	2.98156i	−0.319928	−	0.112854i
$699$	−2.09011	+	2.09011i	−0.0790551	+	0.0790551i
$700$	2.16287	−	2.68428i	0.0817489	−	0.101456i
$701$	8.62775	+	8.62775i	0.325866	+	0.325866i	0.851012	−	0.525146i	$-0.175989\pi$
$701$	8.62775	+	8.62775i	0.325866	+	0.325866i	−0.525146	+	0.851012i	$0.675989\pi$
$702$	−6.09598	+	2.91676i	−0.230078	+	0.110086i
$703$	10.8607			0.409619
$704$	7.59017	−	2.52772i	0.286065	−	0.0952671i
$705$	0.288100			0.0108505
$706$	36.3271	−	17.3815i	1.36719	−	0.654163i
$707$	−9.00460	−	9.00460i	−0.338653	−	0.338653i
$708$	−0.391421	+	0.485781i	−0.0147105	+	0.0182568i
$709$	20.3851	−	20.3851i	0.765578	−	0.765578i	−0.211747	−	0.977325i	$-0.567915\pi$
$709$	20.3851	−	20.3851i	0.765578	−	0.765578i	0.977325	+	0.211747i	$0.0679152\pi$
$710$	−4.35183	−	1.53510i	−0.163321	−	0.0576112i
$711$		−	37.9116i		−	1.42180i
$712$	−6.12743	−	1.44739i	−0.229635	−	0.0542431i
$713$			1.36285i			0.0510392i
$714$	0.473748	−	1.34303i	0.0177296	−	0.0502614i
$715$	−2.10654	+	2.10654i	−0.0787800	+	0.0787800i
$716$	−25.1943	+	2.71015i	−0.941556	+	0.101283i
$717$	−1.92582	−	1.92582i	−0.0719211	−	0.0719211i
$718$	6.71962	+	14.0439i	0.250774	+	0.524113i
$719$	28.0790			1.04717			0.523585	−	0.851973i	$-0.324594\pi$
$719$	28.0790			1.04717			0.523585	+	0.851973i	$0.324594\pi$
$720$	−6.32814	+	9.84930i	−0.235836	+	0.367062i
$721$	−14.3048			−0.532738
$722$	10.4721	+	21.8865i	0.389732	+	0.814533i
$723$	−0.441671	−	0.441671i	−0.0164259	−	0.0164259i
$724$	−2.93152	−	27.2522i	−0.108949	−	1.01282i
$725$	1.71672	−	1.71672i	0.0637574	−	0.0637574i
$726$	−0.127322	+	0.360945i	−0.00472538	+	0.0133959i
$727$			31.1195i			1.15416i	0.816689	+	0.577079i	$0.195807\pi$
$727$			31.1195i			1.15416i	−0.816689	+	0.577079i	$0.804193\pi$
$728$	−7.63370	−	12.3554i	−0.282924	−	0.457922i
$729$			23.1248i			0.856474i
$730$	−7.15463	−	2.52378i	−0.264805	−	0.0934092i
$731$	7.51372	−	7.51372i	0.277905	−	0.277905i
$732$	2.05549	+	1.65622i	0.0759732	+	0.0612158i
$733$	12.2019	+	12.2019i	0.450688	+	0.450688i	0.895583	−	0.444895i	$-0.146759\pi$
$733$	12.2019	+	12.2019i	0.450688	+	0.450688i	−0.444895	+	0.895583i	$0.646759\pi$
$734$	−9.02296	+	4.31724i	−0.333044	+	0.159352i
$735$	1.09045			0.0402219
$736$	−21.8898	+	17.0096i	−0.806869	+	0.626983i
$737$	−2.54000			−0.0935621
$738$	8.13618	−	3.89294i	0.299497	−	0.143301i
$739$	−29.5702	−	29.5702i	−1.08776	−	1.08776i	−0.995759	−	0.0919974i	$-0.970675\pi$
$739$	−29.5702	−	29.5702i	−1.08776	−	1.08776i	−0.0919974	−	0.995759i	$-0.529325\pi$
$740$	−12.4571	−	10.0374i	−0.457932	−	0.368981i
$741$	−0.774089	+	0.774089i	−0.0284369	+	0.0284369i
$742$	−9.00070	−	3.17497i	−0.330426	−	0.116557i
$743$			9.51666i			0.349132i	0.984645	+	0.174566i	$0.0558523\pi$
$743$			9.51666i			0.349132i	−0.984645	+	0.174566i	$0.944148\pi$
$744$	−0.181105	+	0.111894i	−0.00663962	+	0.00410224i
$745$		−	11.1388i		−	0.408095i
$746$	−5.01239	+	14.2096i	−0.183517	+	0.520250i
$747$	12.5039	−	12.5039i	0.457494	−	0.457494i
$748$	0.461770	+	4.29274i	0.0168840	+	0.156958i
$749$	−9.71264	−	9.71264i	−0.354892	−	0.354892i
$750$	0.165196	+	0.345257i	0.00603211	+	0.0126070i
$751$	−51.1834			−1.86771			−0.933854	−	0.357655i	$-0.883576\pi$
$751$	−51.1834			−1.86771			−0.933854	+	0.357655i	$0.883576\pi$
$752$	−0.905597	−	4.16063i	−0.0330237	−	0.151723i
$753$	−5.19228			−0.189217
$754$	−4.41475	−	9.22675i	−0.160776	−	0.336018i
$755$	1.36613	+	1.36613i	0.0497185	+	0.0497185i
$756$	5.49770	−	0.591388i	0.199949	−	0.0215086i
$757$	−6.18062	+	6.18062i	−0.224638	+	0.224638i	−0.810448	−	0.585810i	$-0.800776\pi$
$757$	−6.18062	+	6.18062i	−0.224638	+	0.224638i	0.585810	+	0.810448i	$0.300776\pi$
$758$	−15.5838	+	44.1783i	−0.566028	+	1.60463i
$759$		−	1.32629i		−	0.0481411i
$760$	−0.882857	+	3.73753i	−0.0320246	+	0.135574i
$761$			11.3786i			0.412475i	0.978502	+	0.206237i	$0.0661219\pi$
$761$			11.3786i			0.412475i	−0.978502	+	0.206237i	$0.933878\pi$
$762$	−7.15739	−	2.52475i	−0.259285	−	0.0914620i
$763$	8.95544	−	8.95544i	0.324209	−	0.324209i
$764$	−0.853180	+	1.05886i	−0.0308670	+	0.0383082i
$765$	−4.46760	−	4.46760i	−0.161526	−	0.161526i
$766$	−28.8569	+	13.8073i	−1.04264	+	0.498876i
$767$	−3.43356			−0.123979
$768$	−4.05757	−	1.51232i	−0.146415	−	0.0545712i
$769$	8.82078			0.318085			0.159043	−	0.987272i	$-0.449159\pi$
$769$	8.82078			0.318085			0.159043	+	0.987272i	$0.449159\pi$
$770$	2.19882	−	1.05208i	0.0792401	−	0.0379142i
$771$	−2.29514	−	2.29514i	−0.0826576	−	0.0826576i
$772$	−23.8956	+	29.6562i	−0.860022	+	1.06735i
$773$	−0.826114	+	0.826114i	−0.0297132	+	0.0297132i	−0.721807	−	0.692094i	$-0.756688\pi$
$773$	−0.826114	+	0.826114i	−0.0297132	+	0.0297132i	0.692094	+	0.721807i	$0.256688\pi$
$774$	19.2133	+	6.77744i	0.690608	+	0.243610i
$775$		−	0.278102i		−	0.00998971i
$776$	−8.25790	+	34.9594i	−0.296441	+	1.25497i
$777$			3.73131i			0.133860i
$778$	−6.25150	+	17.7223i	−0.224127	+	0.635376i
$779$	2.09218	−	2.09218i	0.0749601	−	0.0749601i
$780$	1.60328	−	0.172464i	0.0574065	−	0.00617521i
$781$	−2.30732	−	2.30732i	−0.0825626	−	0.0825626i
$782$	−6.45736	−	13.4958i	−0.230915	−	0.482608i
$783$	3.89425			0.139169
$784$	−3.42767	−	15.7479i	−0.122417	−	0.562425i
$785$	−7.66736			−0.273660
$786$	1.19287	+	2.49308i	0.0425483	+	0.0889253i
$787$	−9.18632	−	9.18632i	−0.327457	−	0.327457i	0.524162	−	0.851619i	$-0.324379\pi$
$787$	−9.18632	−	9.18632i	−0.327457	−	0.327457i	−0.851619	+	0.524162i	$0.824379\pi$
$788$	−4.56941	−	42.4785i	−0.162778	−	1.51323i
$789$	−2.71629	+	2.71629i	−0.0967024	+	0.0967024i
$790$	−6.09394	+	17.2757i	−0.216813	+	0.614641i
$791$		−	34.6013i		−	1.23028i
$792$	−7.04238	+	4.35109i	−0.250240	+	0.154609i
$793$			14.5285i			0.515920i
$794$	21.2263	+	7.48751i	0.753292	+	0.265722i
$795$	0.749316	−	0.749316i	0.0265755	−	0.0265755i
$796$	−4.06664	−	3.27671i	−0.144138	−	0.116140i
$797$	3.73245	+	3.73245i	0.132210	+	0.132210i	0.770115	−	0.637905i	$-0.220199\pi$
$797$	3.73245	+	3.73245i	0.132210	+	0.132210i	−0.637905	+	0.770115i	$0.720199\pi$
$798$	0.808002	−	0.386607i	0.0286030	−	0.0136857i
$799$	2.29802			0.0812981
$800$	4.46681	−	3.47097i	0.157926	−	0.122717i
$801$	6.51493			0.230194
$802$	−24.8076	+	11.8698i	−0.875988	+	0.419137i
$803$	−3.79336	−	3.79336i	−0.133865	−	0.133865i
$804$	1.07057	+	0.862615i	0.0377560	+	0.0304221i
$805$	−5.97268	+	5.97268i	−0.210509	+	0.210509i
$806$	−1.10493	−	0.389762i	−0.0389196	−	0.0137288i
$807$		−	6.74559i		−	0.237456i
$808$	−10.9838	−	17.7776i	−0.386407	−	0.625413i
$809$		−	49.3142i		−	1.73379i	−0.498487	−	0.866897i	$-0.666111\pi$
$809$		−	49.3142i		−	1.73379i	0.498487	−	0.866897i	$-0.333889\pi$
$810$	3.92643	−	11.1310i	0.137961	−	0.391104i
$811$	36.1368	−	36.1368i	1.26894	−	1.26894i	0.322297	−	0.946639i	$-0.395545\pi$
$811$	36.1368	−	36.1368i	1.26894	−	1.26894i	0.946639	−	0.322297i	$-0.104455\pi$
$812$	0.895111	+	8.32120i	0.0314123	+	0.292017i
$813$	−5.04114	−	5.04114i	−0.176800	−	0.176800i
$814$	−4.88243	−	10.2042i	−0.171129	−	0.357657i
$815$	1.24524			0.0436189
$816$	1.26324	−	1.96614i	0.0442222	−	0.0688287i
$817$	6.68339			0.233822
$818$	−1.39701	−	2.91973i	−0.0488454	−	0.102086i
$819$	10.6266	+	10.6266i	0.371324	+	0.371324i
$820$	−4.33327	+	0.466130i	−0.151324	+	0.0162780i
$821$	−8.28757	+	8.28757i	−0.289238	+	0.289238i	−0.836779	−	0.547541i	$-0.815564\pi$
$821$	−8.28757	+	8.28757i	−0.289238	+	0.289238i	0.547541	+	0.836779i	$0.315564\pi$
$822$	1.04170	−	2.95311i	0.0363335	−	0.103002i
$823$		−	49.1488i		−	1.71322i	−0.515965	−	0.856610i	$-0.672567\pi$
$823$		−	49.1488i		−	1.71322i	0.515965	−	0.856610i	$-0.327433\pi$
$824$	−22.8452	−	5.39637i	−0.795852	−	0.187991i
$825$			0.270640i			0.00942249i
$826$	2.64941	+	0.934572i	0.0921847	+	0.0325179i
$827$	−32.6137	+	32.6137i	−1.13409	+	1.13409i	−0.144600	+	0.989490i	$0.546189\pi$
$827$	−32.6137	+	32.6137i	−1.13409	+	1.13409i	−0.989490	+	0.144600i	$0.953811\pi$
$828$	17.9979	−	22.3367i	0.625470	−	0.776253i
$829$	18.2168	+	18.2168i	0.632697	+	0.632697i	0.948744	−	0.316047i	$-0.102356\pi$
$829$	18.2168	+	18.2168i	0.632697	+	0.632697i	−0.316047	+	0.948744i	$0.602356\pi$
$830$	−7.70770	+	3.68792i	−0.267538	+	0.128010i
$831$	−4.54349			−0.157612
$832$	−7.53032	−	22.6118i	−0.261067	−	0.783923i
$833$	8.69795			0.301366
$834$	0.306643	−	0.146720i	0.0106182	−	0.00508051i
$835$	7.24932	+	7.24932i	0.250873	+	0.250873i
$836$	−1.70381	+	2.11455i	−0.0589274	+	0.0731332i
$837$	0.315426	−	0.315426i	0.0109027	−	0.0109027i
$838$	39.0439	+	13.7726i	1.34875	+	0.475767i
$839$		−	43.8533i		−	1.51399i	−0.653423	−	0.756993i	$-0.726668\pi$
$839$		−	43.8533i		−	1.51399i	0.653423	−	0.756993i	$-0.273332\pi$
$840$	−1.28407	−	0.303314i	−0.0443045	−	0.0104653i
$841$		−	23.1057i		−	0.796750i
$842$	7.17766	−	20.3479i	0.247358	−	0.701234i
$843$	−0.599644	+	0.599644i	−0.0206528	+	0.0206528i
$844$	−48.8931	+	5.25943i	−1.68297	+	0.181037i
$845$	−2.91682	−	2.91682i	−0.100342	−	0.100342i
$846$	1.90171	+	3.97454i	0.0653822	+	0.136648i
$847$	1.72361			0.0592241
$848$	−13.1767	−	8.46599i	−0.452490	−	0.290723i
$849$	0.0887674			0.00304649
$850$	1.31768	+	2.75393i	0.0451961	+	0.0944591i
$851$	27.7178	+	27.7178i	0.950153	+	0.950153i
$852$	0.188903	+	1.75609i	0.00647171	+	0.0601628i
$853$	−31.5120	+	31.5120i	−1.07895	+	1.07895i	−0.0823448	+	0.996604i	$0.526241\pi$
$853$	−31.5120	+	31.5120i	−1.07895	+	1.07895i	−0.996604	+	0.0823448i	$0.973759\pi$
$854$	3.95446	−	11.2105i	0.135319	−	0.383615i
$855$		−	3.97389i		−	0.135904i
$856$	−11.8474	−	19.1755i	−0.404936	−	0.655404i
$857$			20.1381i			0.687904i	0.938987	+	0.343952i	$0.111766\pi$
$857$			20.1381i			0.687904i	−0.938987	+	0.343952i	$0.888234\pi$
$858$	1.07529	+	0.379305i	0.0367098	+	0.0129493i
$859$	36.8679	−	36.8679i	1.25792	−	1.25792i	0.305832	−	0.952086i	$-0.401066\pi$
$859$	36.8679	−	36.8679i	1.25792	−	1.25792i	0.952086	−	0.305832i	$-0.0989345\pi$
$860$	−7.66576	−	6.17672i	−0.261400	−	0.210624i
$861$	0.718789	+	0.718789i	0.0244963	+	0.0244963i
$862$	37.5180	−	17.9513i	1.27787	−	0.611425i
$863$	33.9081			1.15425			0.577123	−	0.816657i	$-0.304175\pi$
$863$	33.9081			1.15425			0.577123	+	0.816657i	$0.304175\pi$
$864$	9.00313	+	1.12950i	0.306293	+	0.0384263i
$865$	−19.8640			−0.675396
$866$	31.2654	−	14.9597i	1.06244	−	0.508350i
$867$	−2.36148	−	2.36148i	−0.0802002	−	0.0802002i
$868$	0.746503	+	0.601499i	0.0253380	+	0.0204162i
$869$	−9.15949	+	9.15949i	−0.310714	+	0.310714i
$870$	−0.876305	−	0.309114i	−0.0297095	−	0.0104800i
$871$			7.56689i			0.256394i
$872$	17.6805	−	10.9238i	0.598738	−	0.369926i
$873$		−	37.1702i		−	1.25802i
$874$	3.13030	−	8.87407i	0.105884	−	0.300170i
$875$	1.21878	−	1.21878i	0.0412023	−	0.0412023i
$876$	0.310566	+	2.88711i	0.0104931	+	0.0975464i
$877$	−5.77647	−	5.77647i	−0.195058	−	0.195058i	0.602820	−	0.797877i	$-0.294044\pi$
$877$	−5.77647	−	5.77647i	−0.195058	−	0.195058i	−0.797877	+	0.602820i	$0.794044\pi$
$878$	−9.88389	−	20.6572i	−0.333565	−	0.697145i
$879$	0.984641			0.0332111
$880$	3.90849	−	0.850716i	0.131755	−	0.0286776i
$881$	56.4984			1.90348			0.951740	−	0.306905i	$-0.0992933\pi$
$881$	56.4984			1.90348			0.951740	+	0.306905i	$0.0992933\pi$
$882$	7.19793	+	15.0436i	0.242367	+	0.506543i
$883$	33.0787	+	33.0787i	1.11319	+	1.11319i	0.992717	+	0.120469i	$0.0384398\pi$
$883$	33.0787	+	33.0787i	1.11319	+	1.11319i	0.120469	+	0.992717i	$0.461560\pi$
$884$	12.7885	−	1.37566i	0.430123	−	0.0462683i
$885$	−0.220566	+	0.220566i	−0.00741423	+	0.00741423i
$886$	7.75723	−	21.9909i	0.260609	−	0.738799i
$887$		−	16.3645i		−	0.549467i	−0.961520	−	0.274733i	$-0.911410\pi$
$887$		−	16.3645i		−	0.549467i	0.961520	−	0.274733i	$-0.0885896\pi$
$888$	−1.40761	+	5.95903i	−0.0472362	+	0.199972i
$889$			34.1785i			1.14631i
$890$	−2.96874	−	1.04722i	−0.0995124	−	0.0351027i
$891$	5.90162	−	5.90162i	0.197712	−	0.197712i
$892$	−18.9769	+	23.5517i	−0.635393	+	0.788569i
$893$	1.02203	+	1.02203i	0.0342011	+	0.0342011i
$894$	−3.84576	+	1.84009i	−0.128622	+	0.0615419i
$895$	−12.6698			−0.423506
$896$	−0.344094	+	19.4974i	−0.0114954	+	0.651363i
$897$	−3.95113			−0.131924
$898$	−17.2341	+	8.24607i	−0.575111	+	0.275175i
$899$	0.477423	+	0.477423i	0.0159229	+	0.0159229i
$900$	−3.67263	+	4.55800i	−0.122421	+	0.151933i
$901$	5.97689	−	5.97689i	0.199119	−	0.199119i
$902$	−2.90625	−	1.02517i	−0.0967675	−	0.0341345i
$903$			2.29615i			0.0764110i
$904$	13.0531	−	55.2596i	0.434139	−	1.83791i
$905$		−	13.7047i		−	0.455560i
$906$	0.245986	−	0.697345i	0.00817235	−	0.0231677i
$907$	−7.79416	+	7.79416i	−0.258801	+	0.258801i	−0.824566	−	0.565765i	$-0.808581\pi$
$907$	−7.79416	+	7.79416i	−0.258801	+	0.258801i	0.565765	+	0.824566i	$0.308581\pi$
$908$	−26.0651	+	2.80383i	−0.865002	+	0.0930482i
$909$	15.2901	+	15.2901i	0.507141	+	0.507141i
$910$	−3.13423	−	6.55050i	−0.103899	−	0.217147i
$911$	−44.4377			−1.47229			−0.736144	−	0.676825i	$-0.763355\pi$
$911$	−44.4377			−1.47229			−0.736144	+	0.676825i	$0.763355\pi$
$912$	1.43625	−	0.312613i	0.0475591	−	0.0103516i
$913$	−6.04191			−0.199958
$914$	−16.3119	−	34.0916i	−0.539549	−	1.12765i
$915$	0.933282	+	0.933282i	0.0308534	+	0.0308534i
$916$	−4.12168	−	38.3163i	−0.136184	−	1.26601i
$917$	8.80073	−	8.80073i	0.290626	−	0.290626i
$918$	−1.62901	+	4.61808i	−0.0537654	+	0.152419i
$919$			34.8620i			1.14999i	0.818157	+	0.574996i	$0.194996\pi$
$919$			34.8620i			1.14999i	−0.818157	+	0.574996i	$0.805004\pi$
$920$	−11.7917	+	7.28544i	−0.388762	+	0.240194i
$921$		−	0.00842809i		−	0.000277715i
$922$	−47.4733	−	16.7461i	−1.56345	−	0.551502i
$923$	−6.87373	+	6.87373i	−0.226252	+	0.226252i
$924$	−0.726475	−	0.585361i	−0.0238993	−	0.0192569i
$925$	−5.65605	−	5.65605i	−0.185970	−	0.185970i
$926$	−19.7172	+	9.43417i	−0.647949	+	0.310026i
$927$	24.2900			0.797788
$928$	−1.70958	+	13.6269i	−0.0561199	+	0.447326i
$929$	55.0264			1.80536			0.902678	−	0.430317i	$-0.141598\pi$
$929$	55.0264			1.80536			0.902678	+	0.430317i	$0.141598\pi$
$930$	−0.0960167	+	0.0459414i	−0.00314851	+	0.00150648i
$931$	3.86838	+	3.86838i	0.126781	+	0.126781i
$932$	17.0090	+	13.7051i	0.557148	+	0.448925i
$933$	−3.69124	+	3.69124i	−0.120846	+	0.120846i
$934$	51.6838	+	18.2313i	1.69115	+	0.596547i
$935$			2.15875i			0.0705988i
$936$	12.9623	+	20.9799i	0.423686	+	0.685750i
$937$			60.4530i			1.97491i	0.157889	+	0.987457i	$0.449531\pi$
$937$			60.4530i			1.97491i	−0.157889	+	0.987457i	$0.550469\pi$
$938$	2.05961	−	5.83878i	0.0672488	−	0.190643i
$939$	−0.846547	+	0.846547i	−0.0276260	+	0.0276260i
$940$	−0.227705	−	2.11681i	−0.00742693	−	0.0690428i
$941$	−3.84120	−	3.84120i	−0.125220	−	0.125220i	0.641720	−	0.766939i	$-0.278221\pi$
$941$	−3.84120	−	3.84120i	−0.125220	−	0.125220i	−0.766939	+	0.641720i	$0.778221\pi$
$942$	1.26662	+	2.64721i	0.0412687	+	0.0862508i
$943$	10.6790			0.347755
$944$	3.87864	+	2.49201i	0.126239	+	0.0811082i
$945$	2.76471			0.0899360
$946$	−3.00452	−	6.27939i	−0.0976853	−	0.204161i
$947$	15.1478	+	15.1478i	0.492237	+	0.492237i	0.909010	−	0.416773i	$-0.136839\pi$
$947$	15.1478	+	15.1478i	0.492237	+	0.492237i	−0.416773	+	0.909010i	$0.636839\pi$
$948$	6.97125	−	0.749897i	0.226416	−	0.0243555i
$949$	−11.3008	+	11.3008i	−0.366838	+	0.366838i
$950$	−0.638766	+	1.81083i	−0.0207243	+	0.0587512i
$951$			7.43150i			0.240983i
$952$	−10.2423	−	2.41938i	−0.331955	−	0.0784124i
$953$			2.80427i			0.0908394i	0.998968	+	0.0454197i	$0.0144625\pi$
$953$			2.80427i			0.0908394i	−0.998968	+	0.0454197i	$0.985537\pi$
$954$	15.2835	+	5.39121i	0.494821	+	0.174547i
$955$	−0.480767	+	0.480767i	−0.0155573	+	0.0155573i
$956$	−12.6279	+	15.6721i	−0.408414	+	0.506871i
$957$	−0.464613	−	0.464613i	−0.0150188	−	0.0150188i
$958$	−36.1341	+	17.2892i	−1.16744	+	0.558588i
$959$	−14.1019			−0.455375
$960$	−1.93628	−	0.968808i	−0.0624931	−	0.0312682i
$961$	−30.9227			−0.997505
$962$	−30.3992	+	14.5452i	−0.980111	+	0.468957i
$963$	16.4924	+	16.4924i	0.531460	+	0.531460i
$964$	−2.89609	+	3.59426i	−0.0932768	+	0.115763i
$965$	−13.4652	+	13.4652i	−0.433460	+	0.433460i
$966$	3.04878	+	1.07545i	0.0980928	+	0.0346020i
$967$			15.6916i			0.504609i	0.967648	+	0.252305i	$0.0811885\pi$
$967$			15.6916i			0.504609i	−0.967648	+	0.252305i	$0.918812\pi$
$968$	2.75267	+	0.650220i	0.0884743	+	0.0208989i
$969$			0.793277i			0.0254837i
$970$	−5.97477	+	16.9378i	−0.191838	+	0.543841i
$971$	−15.8222	+	15.8222i	−0.507758	+	0.507758i	−0.913838	−	0.406080i	$-0.866896\pi$
$971$	−15.8222	+	15.8222i	−0.507758	+	0.507758i	0.406080	+	0.913838i	$0.366896\pi$
$972$	−14.0606	+	1.51250i	−0.450994	+	0.0485134i
$973$	−1.08247	−	1.08247i	−0.0347023	−	0.0347023i
$974$	−5.71094	−	11.9358i	−0.182990	−	0.382447i
$975$	0.806263			0.0258211
$976$	10.5445	−	16.4117i	0.337521	−	0.525327i
$977$	13.3084			0.425774			0.212887	−	0.977077i	$-0.431713\pi$
$977$	13.3084			0.425774			0.212887	+	0.977077i	$0.431713\pi$
$978$	−0.205709	−	0.429928i	−0.00657785	−	0.0137476i
$979$	−1.57401	−	1.57401i	−0.0503057	−	0.0503057i
$980$	−0.861860	−	8.01209i	−0.0275311	−	0.255937i
$981$	−15.2066	+	15.2066i	−0.485510	+	0.485510i
$982$	5.98141	−	16.9566i	0.190874	−	0.541108i
$983$		−	1.20397i		−	0.0384005i	−0.999816	−	0.0192003i	$-0.993888\pi$
$983$		−	1.20397i		−	0.0384005i	0.999816	−	0.0192003i	$-0.00611201\pi$
$984$	0.876775	+	1.41909i	0.0279506	+	0.0452390i
$985$		−	21.3618i		−	0.680643i
$986$	−6.98982	−	2.46564i	−0.222601	−	0.0785219i
$987$	−0.351130	+	0.351130i	−0.0111766	+	0.0111766i
$988$	6.29943	+	5.07580i	0.200412	+	0.161483i
$989$	17.0568	+	17.0568i	0.542373	+	0.542373i
$990$	−3.73367	+	1.78646i	−0.118664	+	0.0567775i
$991$	0.482712			0.0153339			0.00766693	−	0.999971i	$-0.497560\pi$
$991$	0.482712			0.0153339			0.00766693	+	0.999971i	$0.497560\pi$
$992$	0.965282	+	1.24223i	0.0306477	+	0.0394408i
$993$	3.79811			0.120529
$994$	7.17487	−	3.43298i	0.227573	−	0.108887i
$995$	−1.84643	−	1.84643i	−0.0585357	−	0.0585357i
$996$	2.54657	+	2.05191i	0.0806910	+	0.0650172i
$997$	29.3431	−	29.3431i	0.929306	−	0.929306i	−0.0683555	−	0.997661i	$-0.521775\pi$
$997$	29.3431	−	29.3431i	0.929306	−	0.929306i	0.997661	+	0.0683555i	$0.0217752\pi$
$998$	−7.72068	−	2.72345i	−0.244394	−	0.0862092i
$999$		−	12.8303i		−	0.405934i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.w.a.221.7	✓	72
16.5	even	4	inner	880.2.w.a.661.7	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
880.2.w.a.221.7	✓	72	1.1	even	1	trivial
880.2.w.a.661.7	yes	72	16.5	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27571 + 0.610390i) q^{2} +(0.191372 + 0.191372i) q^{3} +(1.25485 - 1.55736i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.360945 - 0.127322i) q^{6} +1.72361i q^{7} +(-0.650220 + 2.75267i) q^{8} -2.92675i q^{9} +(-0.470449 + 1.33367i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(0.538176 - 0.0578916i) q^{12} +(2.10654 + 2.10654i) q^{13} +(-1.05208 - 2.19882i) q^{14} +0.270640 q^{15} +(-0.850716 - 3.90849i) q^{16} +2.15875 q^{17} +(1.78646 + 3.73367i) q^{18} +(0.960096 + 0.960096i) q^{19} +(-0.213906 - 1.98853i) q^{20} +(-0.329851 + 0.329851i) q^{21} +(0.470449 - 1.33367i) q^{22} +4.90055i q^{23} +(-0.651217 + 0.402350i) q^{24} -1.00000i q^{25} +(-3.97313 - 1.40151i) q^{26} +(1.13421 - 1.13421i) q^{27} +(2.68428 + 2.16287i) q^{28} +(1.71672 + 1.71672i) q^{29} +(-0.345257 + 0.165196i) q^{30} +0.278102 q^{31} +(3.47097 + 4.46681i) q^{32} -0.270640 q^{33} +(-2.75393 + 1.31768i) q^{34} +(1.21878 + 1.21878i) q^{35} +(-4.55800 - 3.67263i) q^{36} +(5.65605 - 5.65605i) q^{37} +(-1.81083 - 0.638766i) q^{38} +0.806263i q^{39} +(1.48666 + 2.40621i) q^{40} -2.17914i q^{41} +(0.219455 - 0.622130i) q^{42} +(3.48058 - 3.48058i) q^{43} +(0.213906 + 1.98853i) q^{44} +(-2.06953 - 2.06953i) q^{45} +(-2.99125 - 6.25165i) q^{46} +1.06451 q^{47} +(0.585171 - 0.910777i) q^{48} +4.02916 q^{49} +(0.610390 + 1.27571i) q^{50} +(0.413124 + 0.413124i) q^{51} +(5.92401 - 0.637246i) q^{52} +(2.76868 - 2.76868i) q^{53} +(-0.754608 + 2.13923i) q^{54} +1.00000i q^{55} +(-4.74455 - 1.12073i) q^{56} +0.367470i q^{57} +(-3.23790 - 1.14216i) q^{58} +(-0.814977 + 0.814977i) q^{59} +(0.339612 - 0.421483i) q^{60} +(3.44842 + 3.44842i) q^{61} +(-0.354776 + 0.169751i) q^{62} +5.04459 q^{63} +(-7.15443 - 3.57969i) q^{64} +2.97909 q^{65} +(0.345257 - 0.165196i) q^{66} +(1.79605 + 1.79605i) q^{67} +(2.70891 - 3.36195i) q^{68} +(-0.937826 + 0.937826i) q^{69} +(-2.29873 - 0.810872i) q^{70} +3.26305i q^{71} +(8.05640 + 1.90303i) q^{72} +5.36462i q^{73} +(-3.76306 + 10.6679i) q^{74} +(0.191372 - 0.191372i) q^{75} +(2.69998 - 0.290437i) q^{76} +(-1.21878 - 1.21878i) q^{77} +(-0.492135 - 1.02855i) q^{78} +12.9535 q^{79} +(-3.36527 - 2.16217i) q^{80} -8.34615 q^{81} +(1.33012 + 2.77993i) q^{82} +(4.27228 + 4.27228i) q^{83} +(0.0997827 + 0.927607i) q^{84} +(1.52647 - 1.52647i) q^{85} +(-2.31568 + 6.56471i) q^{86} +0.657063i q^{87} +(-1.48666 - 2.40621i) q^{88} +2.22599i q^{89} +(3.90333 + 1.37689i) q^{90} +(-3.63086 + 3.63086i) q^{91} +(7.63190 + 6.14944i) q^{92} +(0.0532208 + 0.0532208i) q^{93} +(-1.35800 + 0.649768i) q^{94} +1.35778 q^{95} +(-0.190576 + 1.51907i) q^{96} +12.7002 q^{97} +(-5.14001 + 2.45936i) q^{98} +(2.06953 + 2.06953i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 12 q^{6} - 4 q^{10} + 12 q^{12} - 8 q^{14} + 8 q^{15} + 4 q^{16} + 56 q^{17} + 20 q^{18} + 8 q^{19} - 8 q^{20} + 4 q^{22} - 24 q^{24} - 24 q^{27} + 20 q^{28} - 20 q^{30} + 20 q^{32} - 8 q^{33} + 4 q^{34}+ \cdots - 60 q^{98}+O(q^{100}) \) 72 * q + 12 * q^6 - 4 * q^10 + 12 * q^12 - 8 * q^14 + 8 * q^15 + 4 * q^16 + 56 * q^17 + 20 * q^18 + 8 * q^19 - 8 * q^20 + 4 * q^22 - 24 * q^24 - 24 * q^27 + 20 * q^28 - 20 * q^30 + 20 * q^32 - 8 * q^33 + 4 * q^34 - 60 * q^36 + 12 * q^38 - 40 * q^42 + 8 * q^44 - 20 * q^46 + 40 * q^47 + 20 * q^48 - 24 * q^49 + 32 * q^51 - 84 * q^52 + 72 * q^54 + 8 * q^56 - 8 * q^58 + 32 * q^60 - 16 * q^61 - 96 * q^62 + 36 * q^64 - 40 * q^65 + 20 * q^66 - 76 * q^68 - 16 * q^69 + 24 * q^70 + 20 * q^72 + 56 * q^74 + 56 * q^76 - 132 * q^78 - 16 * q^79 + 56 * q^81 + 36 * q^82 - 40 * q^83 - 152 * q^84 + 16 * q^85 + 56 * q^86 - 36 * q^90 + 88 * q^91 + 80 * q^92 + 48 * q^93 - 76 * q^94 - 32 * q^96 - 64 * q^97 - 60 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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