LMFDB - Embedded newform 230.2.g.d.31.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(31,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.g (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [30,-3,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			31.3
Character	$\chi$	$=$	230.31
Dual form			230.2.g.d.141.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.142315 + 0.989821i) q^{2} +(1.30924 + 2.86684i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(-3.02398 + 0.887921i) q^{6} +(-0.493060 - 0.316870i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-4.54006 + 5.23951i) q^{9} +(-0.841254 + 0.540641i) q^{10} +(-0.242232 - 1.68476i) q^{11} +(-0.448526 - 3.11956i) q^{12} +(5.25515 - 3.37728i) q^{13} +(0.383815 - 0.442946i) q^{14} +(-1.30924 + 2.86684i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-2.14296 + 0.629229i) q^{17} +(-4.54006 - 5.23951i) q^{18} +(1.47258 + 0.432387i) q^{19} +(-0.415415 - 0.909632i) q^{20} +(0.262882 - 1.82838i) q^{21} +1.70208 q^{22} +(-1.29994 - 4.61629i) q^{23} +3.15164 q^{24} +(-0.142315 + 0.989821i) q^{25} +(2.59502 + 5.68230i) q^{26} +(-11.8929 - 3.49207i) q^{27} +(0.383815 + 0.442946i) q^{28} +(0.262809 - 0.0771677i) q^{29} +(-2.65133 - 1.70391i) q^{30} +(-3.69829 + 8.09813i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(4.51279 - 2.90019i) q^{33} +(-0.317850 - 2.21069i) q^{34} +(-0.0834109 - 0.580136i) q^{35} +(5.83229 - 3.74819i) q^{36} +(5.54390 - 6.39800i) q^{37} +(-0.637555 + 1.39605i) q^{38} +(16.5624 + 10.6440i) q^{39} +(0.959493 - 0.281733i) q^{40} +(2.02311 + 2.33479i) q^{41} +(1.77236 + 0.520412i) q^{42} +(3.08429 + 6.75365i) q^{43} +(-0.242232 + 1.68476i) q^{44} -6.93286 q^{45} +(4.75431 - 0.629743i) q^{46} -5.72656 q^{47} +(-0.448526 + 3.11956i) q^{48} +(-2.76520 - 6.05495i) q^{49} +(-0.959493 - 0.281733i) q^{50} +(-4.60954 - 5.31969i) q^{51} +(-5.99377 + 1.75993i) q^{52} +(8.65325 + 5.56110i) q^{53} +(5.14906 - 11.2749i) q^{54} +(1.11463 - 1.28635i) q^{55} +(-0.493060 + 0.316870i) q^{56} +(0.688372 + 4.78773i) q^{57} +(0.0389806 + 0.271116i) q^{58} +(-5.47617 + 3.51932i) q^{59} +(2.06389 - 2.38185i) q^{60} +(4.86419 - 10.6511i) q^{61} +(-7.48938 - 4.81313i) q^{62} +(3.89876 - 1.14478i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(5.99377 + 1.75993i) q^{65} +(2.22844 + 4.87959i) q^{66} +(1.87379 - 13.0325i) q^{67} +2.23343 q^{68} +(11.5322 - 9.77055i) q^{69} +0.586101 q^{70} +(-1.13073 + 7.86440i) q^{71} +(2.88001 + 6.30635i) q^{72} +(-1.37667 - 0.404227i) q^{73} +(5.54390 + 6.39800i) q^{74} +(-3.02398 + 0.887921i) q^{75} +(-1.29111 - 0.829745i) q^{76} +(-0.414415 + 0.907443i) q^{77} +(-12.8927 + 14.8790i) q^{78} +(9.95391 - 6.39699i) q^{79} +(0.142315 + 0.989821i) q^{80} +(-2.59952 - 18.0800i) q^{81} +(-2.59894 + 1.67024i) q^{82} +(-2.84544 + 3.28382i) q^{83} +(-0.767348 + 1.68026i) q^{84} +(-1.87888 - 1.20748i) q^{85} +(-7.12385 + 2.09175i) q^{86} +(0.565307 + 0.652399i) q^{87} +(-1.63314 - 0.479532i) q^{88} +(-4.46450 - 9.77589i) q^{89} +(0.986649 - 6.86229i) q^{90} -3.66127 q^{91} +(-0.0532753 + 4.79554i) q^{92} -28.0580 q^{93} +(0.814974 - 5.66827i) q^{94} +(0.637555 + 1.39605i) q^{95} +(-3.02398 - 0.887921i) q^{96} +(-2.54448 - 2.93648i) q^{97} +(6.38685 - 1.87535i) q^{98} +(9.92705 + 6.37973i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{2} - q^{3} - 3 q^{4} + 3 q^{5} - q^{6} + 8 q^{7} - 3 q^{8} + 12 q^{9} + 3 q^{10} - 3 q^{11} - q^{12} + 12 q^{13} - 3 q^{14} + q^{15} - 3 q^{16} - 26 q^{17} + 12 q^{18} - 25 q^{19} + 3 q^{20}+ \cdots + 97 q^{99}+O(q^{100}) $ 30 * q - 3 * q^2 - q^3 - 3 * q^4 + 3 * q^5 - q^6 + 8 * q^7 - 3 * q^8 + 12 * q^9 + 3 * q^10 - 3 * q^11 - q^12 + 12 * q^13 - 3 * q^14 + q^15 - 3 * q^16 - 26 * q^17 + 12 * q^18 - 25 * q^19 + 3 * q^20 - 11 * q^21 - 14 * q^22 + 14 * q^23 + 10 * q^24 - 3 * q^25 - 10 * q^26 - 52 * q^27 - 3 * q^28 + 4 * q^29 + q^30 + 5 * q^31 - 3 * q^32 + 9 * q^33 + 7 * q^34 + 3 * q^35 + 12 * q^36 - 20 * q^37 + 19 * q^38 + 41 * q^39 + 3 * q^40 + 32 * q^41 + 22 * q^42 - 46 * q^43 - 3 * q^44 - 56 * q^45 + 3 * q^46 + 80 * q^47 - q^48 - 41 * q^49 - 3 * q^50 - 34 * q^51 - 21 * q^52 + 29 * q^53 + 47 * q^54 + 3 * q^55 + 8 * q^56 - 33 * q^57 - 7 * q^58 - 3 * q^59 + q^60 - q^61 - 28 * q^62 - 8 * q^63 - 3 * q^64 + 21 * q^65 - 46 * q^66 - 63 * q^67 - 4 * q^68 + 78 * q^69 - 8 * q^70 + 55 * q^71 - 32 * q^72 - 36 * q^73 - 20 * q^74 - q^75 - 3 * q^76 - 9 * q^77 - 80 * q^78 - 29 * q^79 + 3 * q^80 + 15 * q^81 - 23 * q^82 - 63 * q^83 + 4 * q^85 + 31 * q^86 + 63 * q^87 - 3 * q^88 - 95 * q^89 + 10 * q^90 - 12 * q^91 + 14 * q^92 + 126 * q^93 + 3 * q^94 - 19 * q^95 - q^96 + 11 * q^97 + 58 * q^98 + 97 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{3}{11}\right)$

Coefficient data

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

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

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

$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$3$	1.30924	+	2.86684i	0.755890	+	1.65517i	0.755483	+	0.655169i	$0.227402\pi$
$3$	1.30924	+	2.86684i	0.755890	+	1.65517i	0.000407523		1.00000i	$0.499870\pi$
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	0.654861	+	0.755750i	0.292863	+	0.337981i
$5$	0.654861	+	0.755750i	0.292863	+	0.337981i
$6$	−3.02398	+	0.887921i	−1.23453	+	0.362492i
$7$	−0.493060	−	0.316870i	−0.186359	−	0.119766i	0.444135	−	0.895960i	$-0.353511\pi$
$7$	−0.493060	−	0.316870i	−0.186359	−	0.119766i	−0.630494	+	0.776194i	$0.717148\pi$
$8$	0.415415	−	0.909632i	0.146871	−	0.321603i
$9$	−4.54006	+	5.23951i	−1.51335	+	1.74650i
$10$	−0.841254	+	0.540641i	−0.266028	+	0.170966i
$11$	−0.242232	−	1.68476i	−0.0730356	−	0.507974i	−0.993198	−	0.116437i	$-0.962853\pi$
$11$	−0.242232	−	1.68476i	−0.0730356	−	0.507974i	0.920162	−	0.391537i	$-0.128056\pi$
$12$	−0.448526	−	3.11956i	−0.129478	−	0.900541i
$13$	5.25515	−	3.37728i	1.45752	−	0.936689i	0.458674	−	0.888605i	$-0.348325\pi$
$13$	5.25515	−	3.37728i	1.45752	−	0.936689i	0.998843	−	0.0480845i	$-0.0153117\pi$
$14$	0.383815	−	0.442946i	0.102579	−	0.118382i
$15$	−1.30924	+	2.86684i	−0.338044	+	0.740214i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	−2.14296	+	0.629229i	−0.519743	+	0.152610i	−0.531074	−	0.847325i	$-0.678211\pi$
$17$	−2.14296	+	0.629229i	−0.519743	+	0.152610i	0.0113308	+	0.999936i	$0.496393\pi$
$18$	−4.54006	−	5.23951i	−1.07010	−	1.23496i
$19$	1.47258	+	0.432387i	0.337832	+	0.0991964i	0.446248	−	0.894909i	$-0.352760\pi$
$19$	1.47258	+	0.432387i	0.337832	+	0.0991964i	−0.108416	+	0.994106i	$0.534578\pi$
$20$	−0.415415	−	0.909632i	−0.0928896	−	0.203400i
$21$	0.262882	−	1.82838i	0.0573655	−	0.398986i
$22$	1.70208			0.362885
$23$	−1.29994	−	4.61629i	−0.271056	−	0.962563i
$23$	−1.29994	−	4.61629i	−0.271056	−	0.962563i
$24$	3.15164			0.643327
$25$	−0.142315	+	0.989821i	−0.0284630	+	0.197964i
$26$	2.59502	+	5.68230i	0.508925	+	1.11439i
$27$	−11.8929	−	3.49207i	−2.28879	−	0.672049i
$28$	0.383815	+	0.442946i	0.0725342	+	0.0837089i
$29$	0.262809	−	0.0771677i	0.0488024	−	0.0143297i	−0.257240	−	0.966347i	$-0.582813\pi$
$29$	0.262809	−	0.0771677i	0.0488024	−	0.0143297i	0.306043	+	0.952018i	$0.400995\pi$
$30$	−2.65133	−	1.70391i	−0.484065	−	0.311089i
$31$	−3.69829	+	8.09813i	−0.664233	+	1.45447i	0.214292	+	0.976770i	$0.431256\pi$
$31$	−3.69829	+	8.09813i	−0.664233	+	1.45447i	−0.878525	+	0.477697i	$0.841472\pi$
$32$	−0.654861	+	0.755750i	−0.115764	+	0.133599i
$33$	4.51279	−	2.90019i	0.785576	−	0.504859i
$34$	−0.317850	−	2.21069i	−0.0545108	−	0.379131i
$35$	−0.0834109	−	0.580136i	−0.0140990	−	0.0980608i
$36$	5.83229	−	3.74819i	0.972049	−	0.624698i
$37$	5.54390	−	6.39800i	0.911411	−	1.05182i	−0.0870412	−	0.996205i	$-0.527741\pi$
$37$	5.54390	−	6.39800i	0.911411	−	1.05182i	0.998452	−	0.0556194i	$-0.0177134\pi$
$38$	−0.637555	+	1.39605i	−0.103425	+	0.226469i
$39$	16.5624	+	10.6440i	2.65210	+	1.70440i
$40$	0.959493	−	0.281733i	0.151709	−	0.0445458i
$41$	2.02311	+	2.33479i	0.315956	+	0.364633i	0.891407	−	0.453204i	$-0.149719\pi$
$41$	2.02311	+	2.33479i	0.315956	+	0.364633i	−0.575451	+	0.817836i	$0.695173\pi$
$42$	1.77236	+	0.520412i	0.273481	+	0.0803012i
$43$	3.08429	+	6.75365i	0.470350	+	1.02992i	0.985005	+	0.172525i	$0.0551926\pi$
$43$	3.08429	+	6.75365i	0.470350	+	1.02992i	−0.514656	+	0.857397i	$0.672080\pi$
$44$	−0.242232	+	1.68476i	−0.0365178	+	0.253987i
$45$	−6.93286			−1.03349
$46$	4.75431	−	0.629743i	0.700984	−	0.0928505i
$47$	−5.72656			−0.835304			−0.417652	−	0.908607i	$-0.637147\pi$
$47$	−5.72656			−0.835304			−0.417652	+	0.908607i	$0.637147\pi$
$48$	−0.448526	+	3.11956i	−0.0647391	+	0.450270i
$49$	−2.76520	−	6.05495i	−0.395029	−	0.864993i
$50$	−0.959493	−	0.281733i	−0.135693	−	0.0398430i
$51$	−4.60954	−	5.31969i	−0.645465	−	0.744906i
$52$	−5.99377	+	1.75993i	−0.831187	+	0.244058i
$53$	8.65325	+	5.56110i	1.18861	+	0.763876i	0.976950	−	0.213466i	$-0.0684753\pi$
$53$	8.65325	+	5.56110i	1.18861	+	0.763876i	0.211664	+	0.977342i	$0.432112\pi$
$54$	5.14906	−	11.2749i	0.700698	−	1.53431i
$55$	1.11463	−	1.28635i	0.150296	−	0.173451i
$56$	−0.493060	+	0.316870i	−0.0658879	+	0.0423436i
$57$	0.688372	+	4.78773i	0.0911771	+	0.634150i
$58$	0.0389806	+	0.271116i	0.00511840	+	0.0355993i
$59$	−5.47617	+	3.51932i	−0.712936	+	0.458176i	−0.846173	−	0.532908i	$-0.821099\pi$
$59$	−5.47617	+	3.51932i	−0.712936	+	0.458176i	0.133237	+	0.991084i	$0.457463\pi$
$60$	2.06389	−	2.38185i	0.266447	−	0.307496i
$61$	4.86419	−	10.6511i	0.622795	−	1.36373i	−0.290674	−	0.956822i	$-0.593879\pi$
$61$	4.86419	−	10.6511i	0.622795	−	1.36373i	0.913469	−	0.406909i	$-0.133393\pi$
$62$	−7.48938	−	4.81313i	−0.951152	−	0.611268i
$63$	3.89876	−	1.14478i	0.491198	−	0.144229i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	5.99377	+	1.75993i	0.743436	+	0.218292i
$66$	2.22844	+	4.87959i	0.274302	+	0.600637i
$67$	1.87379	−	13.0325i	0.228920	−	1.59217i	−0.473754	−	0.880657i	$-0.657101\pi$
$67$	1.87379	−	13.0325i	0.228920	−	1.59217i	0.702673	−	0.711513i	$-0.251990\pi$
$68$	2.23343			0.270843
$69$	11.5322	−	9.77055i	1.38832	−	1.17624i
$70$	0.586101			0.0700525
$71$	−1.13073	+	7.86440i	−0.134193	+	0.933332i	0.805812	+	0.592171i	$0.201729\pi$
$71$	−1.13073	+	7.86440i	−0.134193	+	0.933332i	−0.940005	+	0.341161i	$0.889180\pi$
$72$	2.88001	+	6.30635i	0.339413	+	0.743211i
$73$	−1.37667	−	0.404227i	−0.161127	−	0.0473112i	0.200174	−	0.979760i	$-0.435849\pi$
$73$	−1.37667	−	0.404227i	−0.161127	−	0.0473112i	−0.361301	+	0.932449i	$0.617667\pi$
$74$	5.54390	+	6.39800i	0.644465	+	0.743752i
$75$	−3.02398	+	0.887921i	−0.349179	+	0.102528i
$76$	−1.29111	−	0.829745i	−0.148100	−	0.0951783i
$77$	−0.414415	+	0.907443i	−0.0472270	+	0.103413i
$78$	−12.8927	+	14.8790i	−1.45981	+	1.68471i
$79$	9.95391	−	6.39699i	1.11990	−	0.719718i	0.156474	−	0.987682i	$-0.449987\pi$
$79$	9.95391	−	6.39699i	1.11990	−	0.719718i	0.963429	+	0.267964i	$0.0863509\pi$
$80$	0.142315	+	0.989821i	0.0159113	+	0.110665i
$81$	−2.59952	−	18.0800i	−0.288835	−	2.00889i
$82$	−2.59894	+	1.67024i	−0.287005	+	0.184447i
$83$	−2.84544	+	3.28382i	−0.312328	+	0.360446i	−0.890110	−	0.455745i	$-0.849373\pi$
$83$	−2.84544	+	3.28382i	−0.312328	+	0.360446i	0.577782	+	0.816191i	$0.303918\pi$
$84$	−0.767348	+	1.68026i	−0.0837245	+	0.183331i
$85$	−1.87888	−	1.20748i	−0.203793	−	0.130970i
$86$	−7.12385	+	2.09175i	−0.768184	+	0.225559i
$87$	0.565307	+	0.652399i	0.0606073	+	0.0699445i
$88$	−1.63314	−	0.479532i	−0.174093	−	0.0511183i
$89$	−4.46450	−	9.77589i	−0.473236	−	1.03624i	−0.984268	−	0.176681i	$-0.943464\pi$
$89$	−4.46450	−	9.77589i	−0.473236	−	1.03624i	0.511032	−	0.859561i	$-0.329263\pi$
$90$	0.986649	−	6.86229i	0.104002	−	0.723349i
$91$	−3.66127			−0.383805
$92$	−0.0532753	+	4.79554i	−0.00555433	+	0.499969i
$93$	−28.0580			−2.90948
$94$	0.814974	−	5.66827i	0.0840582	−	0.584637i
$95$	0.637555	+	1.39605i	0.0654118	+	0.143232i
$96$	−3.02398	−	0.887921i	−0.308634	−	0.0906230i
$97$	−2.54448	−	2.93648i	−0.258353	−	0.298155i	0.611724	−	0.791071i	$-0.290476\pi$
$97$	−2.54448	−	2.93648i	−0.258353	−	0.298155i	−0.870077	+	0.492916i	$0.835931\pi$
$98$	6.38685	−	1.87535i	0.645169	−	0.189439i
$99$	9.92705	+	6.37973i	0.997706	+	0.641187i
$100$	0.415415	−	0.909632i	0.0415415	−	0.0909632i
$101$	−11.3182	+	13.0619i	−1.12621	+	1.29971i	−0.177298	+	0.984157i	$0.556736\pi$
$101$	−11.3182	+	13.0619i	−1.12621	+	1.29971i	−0.948908	+	0.315553i	$0.897810\pi$
$102$	5.92155	−	3.80555i	0.586321	−	0.376806i
$103$	0.220091	+	1.53077i	0.0216862	+	0.150831i	0.997787	−	0.0664856i	$-0.0211787\pi$
$103$	0.220091	+	1.53077i	0.0216862	+	0.150831i	−0.976101	+	0.217317i	$0.930270\pi$
$104$	−0.889014	−	6.18323i	−0.0871750	−	0.606315i
$105$	1.55395	−	0.998662i	0.151650	−	0.0974595i
$106$	−6.73599	+	7.77374i	−0.654257	+	0.755052i
$107$	−1.74238	+	3.81528i	−0.168442	+	0.368837i	−0.974962	−	0.222369i	$-0.928621\pi$
$107$	−1.74238	+	3.81528i	−0.168442	+	0.368837i	0.806520	+	0.591206i	$0.201348\pi$
$108$	10.4273	+	6.70123i	1.00337	+	0.644826i
$109$	−19.3101	+	5.66996i	−1.84957	+	0.543084i	−0.849700	+	0.527267i	$0.823217\pi$
$109$	−19.3101	+	5.66996i	−1.84957	+	0.543084i	−0.999875	+	0.0158169i	$0.994965\pi$
$110$	1.11463	+	1.28635i	0.106276	+	0.122649i
$111$	25.6003	+	7.51693i	2.42987	+	0.713475i
$112$	−0.243475	−	0.533137i	−0.0230063	−	0.0503767i
$113$	2.87342	−	19.9851i	0.270309	−	1.88004i	−0.174861	−	0.984593i	$-0.555948\pi$
$113$	2.87342	−	19.9851i	0.270309	−	1.88004i	0.445170	−	0.895446i	$-0.353143\pi$
$114$	−4.83696			−0.453023
$115$	2.63748	−	4.00546i	0.245946	−	0.373511i
$116$	−0.273904			−0.0254313
$117$	−6.16341	+	42.8674i	−0.569807	+	3.96310i
$118$	−2.70416	−	5.92128i	−0.248938	−	0.545098i
$119$	1.25599	+	0.368792i	0.115136	+	0.0338071i
$120$	2.06389	+	2.38185i	0.188406	+	0.217432i
$121$	7.77469	−	2.28285i	0.706790	−	0.207532i
$122$	9.85042	+	6.33048i	0.891815	+	0.573135i
$123$	−4.04472	+	8.85671i	−0.364700	+	0.798583i
$124$	5.82999	−	6.72817i	0.523549	−	0.604207i
$125$	−0.841254	+	0.540641i	−0.0752440	+	0.0483564i
$126$	0.578276	+	4.02200i	0.0515169	+	0.358308i
$127$	−0.440666	−	3.06490i	−0.0391028	−	0.271966i	0.960885	−	0.276949i	$-0.0893231\pi$
$127$	−0.440666	−	3.06490i	−0.0391028	−	0.271966i	−0.999988	+	0.00498237i	$0.998414\pi$
$128$	0.841254	−	0.540641i	0.0743570	−	0.0477863i
$129$	−15.3235	+	17.6843i	−1.34916	+	1.55702i
$130$	−2.59502	+	5.68230i	−0.227598	+	0.498371i
$131$	−2.36509	−	1.51995i	−0.206639	−	0.132799i	0.433228	−	0.901284i	$-0.357374\pi$
$131$	−2.36509	−	1.51995i	−0.206639	−	0.132799i	−0.639867	+	0.768485i	$0.721011\pi$
$132$	−5.14707	+	1.51132i	−0.447995	+	0.131543i
$133$	−0.589057	−	0.679808i	−0.0510777	−	0.0589468i
$134$	12.6332	+	3.70943i	1.09134	+	0.320446i
$135$	−5.14906	−	11.2749i	−0.443160	−	0.970386i
$136$	−0.317850	+	2.21069i	−0.0272554	+	0.189565i
$137$	−11.7641			−1.00508			−0.502539	−	0.864555i	$-0.667601\pi$
$137$	−11.7641			−1.00508			−0.502539	+	0.864555i	$0.667601\pi$
$138$	8.02990	+	12.8053i	0.683550	+	1.09006i
$139$	−16.1372			−1.36874			−0.684368	−	0.729137i	$-0.739922\pi$
$139$	−16.1372			−1.36874			−0.684368	+	0.729137i	$0.739922\pi$
$140$	−0.0834109	+	0.580136i	−0.00704951	+	0.0490304i
$141$	−7.49744	−	16.4171i	−0.631398	−	1.38257i
$142$	−7.62343	−	2.23844i	−0.639744	−	0.187846i
$143$	−6.96287	−	8.03558i	−0.582264	−	0.671969i
$144$	−6.65203	+	1.95321i	−0.554336	+	0.162768i
$145$	0.230423	+	0.148084i	0.0191356	+	0.0122977i
$146$	0.596033	−	1.30513i	0.0493281	−	0.108013i
$147$	13.7382	−	15.8548i	1.13311	−	1.30768i
$148$	−7.12185	+	4.57694i	−0.585413	+	0.376222i
$149$	0.680101	+	4.73020i	0.0557160	+	0.387513i	0.998530	+	0.0541951i	$0.0172593\pi$
$149$	0.680101	+	4.73020i	0.0557160	+	0.387513i	−0.942814	+	0.333318i	$0.891832\pi$
$150$	−0.448526	−	3.11956i	−0.0366220	−	0.254711i
$151$	4.58931	−	2.94937i	0.373473	−	0.240016i	−0.340417	−	0.940275i	$-0.610568\pi$
$151$	4.58931	−	2.94937i	0.373473	−	0.240016i	0.713890	+	0.700258i	$0.246932\pi$
$152$	1.00504	−	1.15988i	0.0815198	−	0.0940788i
$153$	6.43230	−	14.0848i	0.520020	−	1.13869i
$154$	−0.839229	−	0.539340i	−0.0676270	−	0.0434612i
$155$	−8.54202	+	2.50816i	−0.686112	+	0.201461i
$156$	−12.8927	−	14.8790i	−1.03224	−	1.19127i
$157$	5.22176	+	1.53325i	0.416742	+	0.122367i	0.483380	−	0.875411i	$-0.339409\pi$
$157$	5.22176	+	1.53325i	0.416742	+	0.122367i	−0.0666377	+	0.997777i	$0.521227\pi$
$158$	4.91529	+	10.7630i	0.391039	+	0.856257i
$159$	−4.61360	+	32.0883i	−0.365882	+	2.54476i
$160$	−1.00000			−0.0790569
$161$	−0.821817	+	2.68802i	−0.0647683	+	0.211846i
$162$	18.2660			1.43511
$163$	0.456880	−	3.17767i	0.0357856	−	0.248895i	−0.964074	−	0.265633i	$-0.914419\pi$
$163$	0.456880	−	3.17767i	0.0357856	−	0.248895i	0.999860	+	0.0167383i	$0.00532821\pi$
$164$	−1.28337	−	2.81019i	−0.100214	−	0.219439i
$165$	5.14707	+	1.51132i	0.400699	+	0.117656i
$166$	−2.84544	−	3.28382i	−0.220849	−	0.254874i
$167$	8.20807	−	2.41011i	0.635160	−	0.186500i	0.0517272	−	0.998661i	$-0.483527\pi$
$167$	8.20807	−	2.41011i	0.635160	−	0.186500i	0.583433	+	0.812161i	$0.301709\pi$
$168$	−1.55395	−	0.998662i	−0.119890	−	0.0770485i
$169$	10.8102	−	23.6710i	0.831554	−	1.82085i
$170$	1.46258	−	1.68791i	0.112175	−	0.129457i
$171$	−8.95107	+	5.75250i	−0.684505	+	0.439905i
$172$	−1.05663	−	7.34902i	−0.0805673	−	0.560358i
$173$	−2.28391	−	15.8850i	−0.173643	−	1.20771i	−0.871108	−	0.491092i	$-0.836598\pi$
$173$	−2.28391	−	15.8850i	−0.173643	−	1.20771i	0.697465	−	0.716619i	$-0.254311\pi$
$174$	−0.726210	+	0.466707i	−0.0550539	+	0.0353810i
$175$	0.383815	−	0.442946i	0.0290137	−	0.0334836i
$176$	0.707071	−	1.54827i	0.0532975	−	0.116705i
$177$	−17.2589	−	11.0916i	−1.29726	−	0.833698i
$178$	10.3117	−	3.02780i	0.772898	−	0.226943i
$179$	0.578725	+	0.667884i	0.0432559	+	0.0499200i	0.776965	−	0.629543i	$-0.216758\pi$
$179$	0.578725	+	0.667884i	0.0432559	+	0.0499200i	−0.733709	+	0.679463i	$0.762213\pi$
$180$	6.65203	+	1.95321i	0.495813	+	0.145584i
$181$	2.42646	+	5.31321i	0.180358	+	0.394928i	0.978119	−	0.208045i	$-0.0667100\pi$
$181$	2.42646	+	5.31321i	0.180358	+	0.394928i	−0.797762	+	0.602973i	$0.793983\pi$
$182$	0.521052	−	3.62400i	0.0386230	−	0.268629i
$183$	36.9033			2.72797
$184$	−4.73914	−	0.735209i	−0.349374	−	0.0542003i
$185$	8.46576			0.622415
$186$	3.99306	−	27.7724i	0.292786	−	2.03637i
$187$	1.57919	+	3.45795i	0.115482	+	0.252870i
$188$	5.49459	+	1.61336i	0.400734	+	0.117666i
$189$	4.75737	+	5.49030i	0.346048	+	0.399361i
$190$	−1.47258	+	0.432387i	−0.106832	+	0.0313687i
$191$	−10.9385	−	7.02977i	−0.791484	−	0.508656i	0.0813425	−	0.996686i	$-0.474079\pi$
$191$	−10.9385	−	7.02977i	−0.791484	−	0.508656i	−0.872827	+	0.488030i	$0.837716\pi$
$192$	1.30924	−	2.86684i	0.0944863	−	0.206896i
$193$	1.47901	−	1.70687i	0.106461	−	0.122863i	−0.700018	−	0.714125i	$-0.746825\pi$
$193$	1.47901	−	1.70687i	0.106461	−	0.122863i	0.806479	+	0.591262i	$0.201370\pi$
$194$	3.26871	−	2.10067i	0.234680	−	0.150820i
$195$	2.80186	+	19.4873i	0.200645	+	1.39552i
$196$	0.947317	+	6.58873i	0.0676655	+	0.470624i
$197$	5.00593	−	3.21711i	0.356657	−	0.229210i	−0.350026	−	0.936740i	$-0.613827\pi$
$197$	5.00593	−	3.21711i	0.356657	−	0.229210i	0.706683	+	0.707530i	$0.250191\pi$
$198$	−7.72756	+	8.91808i	−0.549174	+	0.633780i
$199$	−8.56360	+	18.7517i	−0.607058	+	1.32927i	0.317511	+	0.948255i	$0.397153\pi$
$199$	−8.56360	+	18.7517i	−0.607058	+	1.32927i	−0.924568	+	0.381016i	$0.875574\pi$
$200$	0.841254	+	0.540641i	0.0594856	+	0.0382291i
$201$	39.8152	−	11.6908i	2.80835	−	0.824605i
$202$	−11.3182	−	13.0619i	−0.796348	−	0.919034i
$203$	−0.154033	−	0.0452281i	−0.0108110	−	0.00317439i
$204$	2.92409	+	6.40287i	0.204727	+	0.448290i
$205$	−0.439663	+	3.05792i	−0.0307074	+	0.213575i
$206$	−1.54651			−0.107750
$207$	30.0889	+	14.1472i	2.09132	+	0.983297i
$208$	6.24681			0.433138
$209$	0.371763	−	2.58567i	0.0257154	−	0.178855i
$210$	0.767348	+	1.68026i	0.0529520	+	0.115949i
$211$	−0.291024	−	0.0854525i	−0.0200349	−	0.00588279i	0.271700	−	0.962382i	$-0.412414\pi$
$211$	−0.291024	−	0.0854525i	−0.0200349	−	0.00588279i	−0.291735	+	0.956499i	$0.594232\pi$
$212$	−6.73599	−	7.77374i	−0.462629	−	0.533903i
$213$	−24.0263	+	7.05477i	−1.64626	+	0.483385i
$214$	−3.52848	−	2.26762i	−0.241202	−	0.155011i
$215$	−3.08429	+	6.75365i	−0.210347	+	0.460595i
$216$	−8.11698	+	9.36749i	−0.552291	+	0.637377i
$217$	4.38954	−	2.82098i	0.297981	−	0.191501i
$218$	−2.86413	−	19.9205i	−0.193984	−	1.34919i
$219$	−0.643540	−	4.47592i	−0.0434864	−	0.302455i
$220$	−1.43188	+	0.920216i	−0.0965376	+	0.0620409i
$221$	−9.13648	+	10.5441i	−0.614586	+	0.709270i
$222$	−11.0837	+	24.2700i	−0.743890	+	1.62889i
$223$	−11.0096	−	7.07545i	−0.737259	−	0.473807i	0.117343	−	0.993091i	$-0.462562\pi$
$223$	−11.0096	−	7.07545i	−0.737259	−	0.473807i	−0.854602	+	0.519284i	$0.826199\pi$
$224$	0.562360	−	0.165124i	0.0375743	−	0.0110328i
$225$	−4.54006	−	5.23951i	−0.302670	−	0.349300i
$226$	19.3727	+	5.68835i	1.28866	+	0.378383i
$227$	−8.94360	−	19.5838i	−0.593608	−	1.29982i	−0.933237	−	0.359260i	$-0.883029\pi$
$227$	−8.94360	−	19.5838i	−0.593608	−	1.29982i	0.339630	−	0.940559i	$-0.389698\pi$
$228$	0.688372	−	4.78773i	0.0455885	−	0.317075i
$229$	11.6468			0.769640			0.384820	−	0.922992i	$-0.374263\pi$
$229$	11.6468			0.769640			0.384820	+	0.922992i	$0.374263\pi$
$230$	3.58934	+	3.18067i	0.236674	+	0.209727i
$231$	−3.14406			−0.206864
$232$	0.0389806	−	0.271116i	0.00255920	−	0.0177996i
$233$	6.19002	+	13.5543i	0.405522	+	0.887969i	0.996680	+	0.0814135i	$0.0259434\pi$
$233$	6.19002	+	13.5543i	0.405522	+	0.887969i	−0.591159	+	0.806555i	$0.701329\pi$
$234$	−41.5540	−	12.2013i	−2.71647	−	0.797627i
$235$	−3.75010	−	4.32784i	−0.244629	−	0.282317i
$236$	6.24585	−	1.83395i	0.406570	−	0.119380i
$237$	31.3712	+	20.1610i	2.03778	+	1.30960i
$238$	−0.543784	+	1.19072i	−0.0352483	+	0.0771830i
$239$	−9.22524	+	10.6465i	−0.596731	+	0.688665i	−0.971116	−	0.238609i	$-0.923309\pi$
$239$	−9.22524	+	10.6465i	−0.596731	+	0.688665i	0.374384	+	0.927274i	$0.377854\pi$
$240$	−2.65133	+	1.70391i	−0.171143	+	0.109987i
$241$	−0.114663	−	0.797502i	−0.00738612	−	0.0513716i	0.985795	−	0.167953i	$-0.0537156\pi$
$241$	−0.114663	−	0.797502i	−0.00738612	−	0.0513716i	−0.993181	+	0.116581i	$0.962807\pi$
$242$	1.15316	+	8.02044i	0.0741282	+	0.515573i
$243$	17.1472	−	11.0198i	1.09999	−	0.706921i
$244$	−7.66791	+	8.84924i	−0.490887	+	0.566514i
$245$	2.76520	−	6.05495i	0.176662	−	0.386837i
$246$	−8.19094	−	5.26399i	−0.522235	−	0.335620i
$247$	9.19890	−	2.70104i	0.585312	−	0.171863i
$248$	5.82999	+	6.72817i	0.370205	+	0.427239i
$249$	−13.1395	−	3.85811i	−0.832684	−	0.244498i
$250$	−0.415415	−	0.909632i	−0.0262732	−	0.0575302i
$251$	−2.58783	+	17.9987i	−0.163342	+	1.13607i	0.728935	+	0.684583i	$0.240016\pi$
$251$	−2.58783	+	17.9987i	−0.163342	+	1.13607i	−0.892277	+	0.451488i	$0.850894\pi$
$252$	−4.06336			−0.255968
$253$	−7.46245	+	3.30830i	−0.469160	+	0.207991i
$254$	3.09642			0.194287
$255$	1.00175	−	6.96732i	0.0627320	−	0.436310i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	15.4095	+	4.52463i	0.961216	+	0.282239i	0.724450	−	0.689328i	$-0.242094\pi$
$257$	15.4095	+	4.52463i	0.961216	+	0.282239i	0.236767	+	0.971566i	$0.423912\pi$
$258$	−15.3235	−	17.6843i	−0.954002	−	1.10098i
$259$	−4.76081	+	1.39790i	−0.295822	+	0.0868612i
$260$	−5.25515	−	3.37728i	−0.325911	−	0.209450i
$261$	−0.788847	+	1.72733i	−0.0488284	+	0.106919i
$262$	1.84107	−	2.12471i	0.113742	−	0.131265i
$263$	6.70950	−	4.31194i	0.413726	−	0.265885i	−0.317178	−	0.948366i	$-0.602735\pi$
$263$	6.70950	−	4.31194i	0.413726	−	0.265885i	0.730904	+	0.682481i	$0.239099\pi$
$264$	−0.763428	−	5.30976i	−0.0469858	−	0.326793i
$265$	1.46387	+	10.1814i	0.0899248	+	0.625441i
$266$	0.756720	−	0.486315i	0.0463975	−	0.0298179i
$267$	22.1808	−	25.5980i	1.35744	−	1.56657i
$268$	−5.46956	+	11.9767i	−0.334106	+	0.731591i
$269$	15.1847	+	9.75864i	0.925829	+	0.594994i	0.914343	−	0.404940i	$-0.132707\pi$
$269$	15.1847	+	9.75864i	0.925829	+	0.594994i	0.0114860	+	0.999934i	$0.496344\pi$
$270$	11.8929	−	3.49207i	0.723778	−	0.212520i
$271$	14.9602	+	17.2649i	0.908765	+	1.04877i	0.998604	+	0.0528146i	$0.0168192\pi$
$271$	14.9602	+	17.2649i	0.908765	+	1.04877i	−0.0898392	+	0.995956i	$0.528635\pi$
$272$	−2.14296	−	0.629229i	−0.129936	−	0.0381526i
$273$	−4.79348	−	10.4962i	−0.290114	−	0.635262i
$274$	1.67421	−	11.6444i	0.101143	−	0.703463i
$275$	1.70208			0.102640
$276$	−13.8178	+	6.12578i	−0.831732	+	0.368728i
$277$	20.9373			1.25800			0.629000	−	0.777405i	$-0.283465\pi$
$277$	20.9373			1.25800			0.629000	+	0.777405i	$0.283465\pi$
$278$	2.29656	−	15.9729i	0.137738	−	0.957991i
$279$	−25.6397	−	56.1432i	−1.53501	−	3.36120i
$280$	−0.562360	−	0.165124i	−0.0336074	−	0.00986804i
$281$	−1.89023	−	2.18144i	−0.112762	−	0.130134i	0.696562	−	0.717496i	$-0.254712\pi$
$281$	−1.89023	−	2.18144i	−0.112762	−	0.130134i	−0.809324	+	0.587362i	$0.800166\pi$
$282$	17.3170	−	5.08473i	1.03121	−	0.302791i
$283$	−2.40666	−	1.54667i	−0.143061	−	0.0919398i	0.467152	−	0.884177i	$-0.345280\pi$
$283$	−2.40666	−	1.54667i	−0.143061	−	0.0919398i	−0.610213	+	0.792237i	$0.708916\pi$
$284$	3.30058	−	7.22727i	0.195854	−	0.428860i
$285$	−3.16754	+	3.65553i	−0.187629	+	0.216535i
$286$	8.94471	−	5.74841i	0.528912	−	0.339911i
$287$	−0.257687	−	1.79225i	−0.0152108	−	0.105793i
$288$	−0.986649	−	6.86229i	−0.0581388	−	0.404364i
$289$	−10.1050	+	6.49407i	−0.594410	+	0.382004i
$290$	−0.179369	+	0.207003i	−0.0105329	+	0.0121556i
$291$	5.08708	−	11.1392i	0.298210	−	0.652989i
$292$	1.20702	+	0.775706i	0.0706356	+	0.0453948i
$293$	−2.68442	+	0.788217i	−0.156826	+	0.0460482i	−0.359203	−	0.933259i	$-0.616951\pi$
$293$	−2.68442	+	0.788217i	−0.156826	+	0.0460482i	0.202377	+	0.979308i	$0.435133\pi$
$294$	13.7382	+	15.8548i	0.801230	+	0.924669i
$295$	−6.24585	−	1.83395i	−0.363647	−	0.106776i
$296$	−3.51680	−	7.70073i	−0.204410	−	0.447596i
$297$	−3.00246	+	20.8825i	−0.174220	+	1.21173i
$298$	−4.77884			−0.276831
$299$	−22.4219	−	19.8691i	−1.29669	−	1.14906i
$300$	3.15164			0.181960
$301$	0.619292	−	4.30727i	0.0356954	−	0.248267i
$302$	2.26622	+	4.96234i	0.130406	+	0.285550i
$303$	−52.2647	−	15.3463i	−3.00253	−	0.881622i
$304$	1.00504	+	1.15988i	0.0576432	+	0.0665238i
$305$	11.2349	−	3.29887i	0.643309	−	0.188893i
$306$	13.0260	+	8.37130i	0.744646	+	0.478555i
$307$	−11.8778	+	26.0087i	−0.677902	+	1.48440i	0.186950	+	0.982369i	$0.440140\pi$
$307$	−11.8778	+	26.0087i	−0.677902	+	1.48440i	−0.864851	+	0.502028i	$0.832587\pi$
$308$	0.653285	−	0.753931i	0.0372244	−	0.0429592i
$309$	−4.10031	+	2.63511i	−0.233258	+	0.149906i
$310$	−1.26698	−	8.81203i	−0.0719595	−	0.500490i
$311$	2.45615	+	17.0829i	0.139276	+	0.968684i	0.932864	+	0.360229i	$0.117301\pi$
$311$	2.45615	+	17.0829i	0.139276	+	0.968684i	−0.793588	+	0.608455i	$0.791790\pi$
$312$	16.5624	−	10.6440i	0.937659	−	0.602597i
$313$	−19.9457	+	23.0185i	−1.12740	+	1.30108i	−0.179052	+	0.983840i	$0.557303\pi$
$313$	−19.9457	+	23.0185i	−1.12740	+	1.30108i	−0.948344	+	0.317245i	$0.897242\pi$
$314$	−2.26078	+	4.95041i	−0.127583	+	0.279368i
$315$	3.41831	+	2.19682i	0.192600	+	0.123777i
$316$	−11.3530	+	3.33353i	−0.638653	+	0.187526i
$317$	−5.77890	−	6.66921i	−0.324576	−	0.374580i	0.569887	−	0.821723i	$-0.306987\pi$
$317$	−5.77890	−	6.66921i	−0.324576	−	0.374580i	−0.894463	+	0.447143i	$0.852442\pi$
$318$	−31.1051	−	9.13327i	−1.74429	−	0.512168i
$319$	−0.193670	−	0.424077i	−0.0108434	−	0.0237438i
$320$	0.142315	−	0.989821i	0.00795564	−	0.0553327i
$321$	−13.2190			−0.737811
$322$	−2.54370	−	1.19600i	−0.141755	−	0.0666503i
$323$	−3.42774			−0.190724
$324$	−2.59952	+	18.0800i	−0.144418	+	1.00445i
$325$	2.59502	+	5.68230i	0.143946	+	0.315197i
$326$	3.08031	+	0.904460i	0.170602	+	0.0500934i
$327$	−41.5364	−	47.9356i	−2.29697	−	2.65085i
$328$	2.96423	−	0.870375i	0.163672	−	0.0480584i
$329$	2.82354	+	1.81458i	0.155667	+	0.100041i
$330$	−2.22844	+	4.87959i	−0.122671	+	0.268613i
$331$	−3.88592	+	4.48459i	−0.213590	+	0.246496i	−0.852427	−	0.522846i	$-0.824870\pi$
$331$	−3.88592	+	4.48459i	−0.213590	+	0.246496i	0.638837	+	0.769342i	$0.279416\pi$
$332$	3.65534	−	2.34914i	0.200613	−	0.128926i
$333$	8.35273	+	58.0945i	0.457727	+	3.18356i
$334$	1.21745	+	8.46752i	0.0666157	+	0.463322i
$335$	11.0764	−	7.11834i	0.605166	−	0.388917i
$336$	1.20965	−	1.39601i	0.0659917	−	0.0761585i
$337$	−10.7220	+	23.4779i	−0.584064	+	1.27892i	0.354899	+	0.934905i	$0.384515\pi$
$337$	−10.7220	+	23.4779i	−0.584064	+	1.27892i	−0.938963	+	0.344017i	$0.888212\pi$
$338$	21.8916	+	14.0689i	1.19075	+	0.765248i
$339$	61.0560	−	17.9277i	3.31611	−	0.973697i
$340$	1.46258	+	1.68791i	0.0793197	+	0.0915398i
$341$	14.5392	+	4.26911i	0.787344	+	0.231185i
$342$	−4.42008	−	9.67863i	−0.239011	−	0.523360i
$343$	−1.13910	+	7.92262i	−0.0615056	+	0.427781i
$344$	7.42460			0.400307
$345$	14.9361	+	2.31712i	0.804132	+	0.124749i
$346$	16.0483			0.862762
$347$	−3.90388	+	27.1521i	−0.209572	+	1.45760i	0.564987	+	0.825100i	$0.308881\pi$
$347$	−3.90388	+	27.1521i	−0.209572	+	1.45760i	−0.774559	+	0.632502i	$0.782028\pi$
$348$	−0.358606	−	0.785238i	−0.0192233	−	0.0420932i
$349$	−3.41364	−	1.00234i	−0.182728	−	0.0536538i	0.189088	−	0.981960i	$-0.439447\pi$
$349$	−3.41364	−	1.00234i	−0.182728	−	0.0536538i	−0.371816	+	0.928306i	$0.621265\pi$
$350$	0.383815	+	0.442946i	0.0205158	+	0.0236765i
$351$	−74.2926	+	21.8143i	−3.96545	+	1.16436i
$352$	1.43188	+	0.920216i	0.0763197	+	0.0490477i
$353$	5.57039	−	12.1974i	0.296482	−	0.649205i	−0.701502	−	0.712667i	$-0.747487\pi$
$353$	5.57039	−	12.1974i	0.296482	−	0.649205i	0.997984	+	0.0634625i	$0.0202143\pi$
$354$	13.4349	−	15.5047i	0.714059	−	0.824068i
$355$	−6.68399	+	4.29554i	−0.354749	+	0.227983i
$356$	1.52947	+	10.6377i	0.0810617	+	0.563796i
$357$	0.587126	+	4.08355i	0.0310740	+	0.216125i
$358$	−0.743447	+	0.477784i	−0.0392924	+	0.0252517i
$359$	−1.64868	+	1.90267i	−0.0870138	+	0.100419i	−0.797587	−	0.603204i	$-0.793890\pi$
$359$	−1.64868	+	1.90267i	−0.0870138	+	0.100419i	0.710573	+	0.703624i	$0.248436\pi$
$360$	−2.88001	+	6.30635i	−0.151790	+	0.332374i
$361$	−14.0023	−	8.99873i	−0.736963	−	0.473617i
$362$	−5.60445	+	1.64562i	−0.294564	+	0.0864917i
$363$	16.7235	+	19.2999i	0.877756	+	1.01298i
$364$	3.51296	+	1.03150i	0.184129	+	0.0540652i
$365$	−0.596033	−	1.30513i	−0.0311978	−	0.0683137i
$366$	−5.25189	+	36.5277i	−0.274520	+	1.90933i
$367$	30.4898			1.59155			0.795777	−	0.605590i	$-0.207063\pi$
$367$	30.4898			1.59155			0.795777	+	0.605590i	$0.207063\pi$
$368$	1.40218	−	4.58627i	0.0730935	−	0.239076i
$369$	−21.4181			−1.11498
$370$	−1.20480	+	8.37959i	−0.0626348	+	0.435634i
$371$	−2.50442	−	5.48391i	−0.130023	−	0.284711i
$372$	26.9214	+	7.90484i	1.39581	+	0.409847i
$373$	18.5936	+	21.4582i	0.962742	+	1.11106i	0.993759	+	0.111544i	$0.0355797\pi$
$373$	18.5936	+	21.4582i	0.962742	+	1.11106i	−0.0310178	+	0.999519i	$0.509875\pi$
$374$	−3.64749	+	1.07100i	−0.188607	+	0.0553801i
$375$	−2.65133	−	1.70391i	−0.136914	−	0.0879894i
$376$	−2.37890	+	5.20906i	−0.122682	+	0.268637i
$377$	1.12048	−	1.29311i	0.0577079	−	0.0665984i
$378$	−6.11146	+	3.92760i	−0.314340	+	0.202014i
$379$	−2.64486	−	18.3954i	−0.135857	−	0.944907i	−0.937718	−	0.347396i	$-0.887066\pi$
$379$	−2.64486	−	18.3954i	−0.135857	−	0.944907i	0.801861	−	0.597510i	$-0.203843\pi$
$380$	−0.218417	−	1.51912i	−0.0112045	−	0.0779293i
$381$	8.20964	−	5.27601i	0.420592	−	0.270298i
$382$	8.51493	−	9.82675i	0.435662	−	0.502780i
$383$	−3.52909	+	7.72764i	−0.180328	+	0.394864i	−0.978112	−	0.208080i	$-0.933278\pi$
$383$	−3.52909	+	7.72764i	−0.180328	+	0.394864i	0.797784	+	0.602944i	$0.206006\pi$
$384$	2.65133	+	1.70391i	0.135300	+	0.0869522i
$385$	−0.957184	+	0.281055i	−0.0487826	+	0.0143239i
$386$	1.47901	+	1.70687i	0.0752795	+	0.0868772i
$387$	−49.3886	−	14.5018i	−2.51057	−	0.737169i
$388$	1.61411	+	3.53440i	0.0819438	+	0.179432i
$389$	0.843026	−	5.86337i	0.0427431	−	0.297285i	−0.957225	−	0.289343i	$-0.906563\pi$
$389$	0.843026	−	5.86337i	0.0427431	−	0.297285i	0.999968	−	0.00794138i	$-0.00252785\pi$
$390$	−19.6877			−0.996927
$391$	5.69042	+	9.07455i	0.287777	+	0.458920i
$392$	−6.65649			−0.336203
$393$	1.26098	−	8.77031i	0.0636080	−	0.442404i
$394$	2.47195	+	5.41282i	0.124535	+	0.272694i
$395$	11.3530	+	3.33353i	0.571229	+	0.167728i
$396$	−7.72756	−	8.91808i	−0.388324	−	0.448150i
$397$	10.8547	−	3.18723i	0.544782	−	0.159962i	0.00224971	−	0.999997i	$-0.499284\pi$
$397$	10.8547	−	3.18723i	0.544782	−	0.159962i	0.542532	+	0.840035i	$0.317466\pi$
$398$	−17.3421	−	11.1451i	−0.869280	−	0.558652i
$399$	1.17768	−	2.57876i	0.0589578	−	0.129100i
$400$	−0.654861	+	0.755750i	−0.0327430	+	0.0377875i
$401$	1.87055	−	1.20213i	0.0934106	−	0.0600313i	−0.493102	−	0.869972i	$-0.664137\pi$
$401$	1.87055	−	1.20213i	0.0934106	−	0.0600313i	0.586512	+	0.809940i	$0.300501\pi$
$402$	5.90551	+	41.0737i	0.294540	+	2.04857i
$403$	7.91457	+	55.0471i	0.394253	+	2.74209i
$404$	14.5397	−	9.34412i	0.723379	−	0.464887i
$405$	11.9617	−	13.8045i	0.594380	−	0.685951i
$406$	0.0666889	−	0.146028i	0.00330971	−	0.00724726i
$407$	−12.1220	−	7.79033i	−0.600865	−	0.386152i
$408$	−6.75384	+	1.98311i	−0.334365	+	0.0981783i
$409$	11.5538	+	13.3338i	0.571299	+	0.659315i	0.965711	−	0.259619i	$-0.0835970\pi$
$409$	11.5538	+	13.3338i	0.571299	+	0.659315i	−0.394412	+	0.918934i	$0.629052\pi$
$410$	−2.96423	−	0.870375i	−0.146393	−	0.0429848i
$411$	−15.4021	−	33.7258i	−0.759728	−	1.66357i
$412$	0.220091	−	1.53077i	0.0108431	−	0.0754155i
$413$	3.81524			0.187736
$414$	−18.2853	+	27.7693i	−0.898672	+	1.36479i
$415$	−4.34511			−0.213293
$416$	−0.889014	+	6.18323i	−0.0435875	+	0.303158i
$417$	−21.1274	−	46.2626i	−1.03461	−	2.26549i
$418$	2.50645	+	0.735959i	0.122594	+	0.0359969i
$419$	−0.540649	−	0.623942i	−0.0264124	−	0.0304816i	0.742390	−	0.669968i	$-0.233692\pi$
$419$	−0.540649	−	0.623942i	−0.0264124	−	0.0304816i	−0.768802	+	0.639487i	$0.779147\pi$
$420$	−1.77236	+	0.520412i	−0.0864823	+	0.0253935i
$421$	−15.1693	−	9.74872i	−0.739307	−	0.475124i	0.115998	−	0.993249i	$-0.462994\pi$
$421$	−15.1693	−	9.74872i	−0.739307	−	0.475124i	−0.855304	+	0.518126i	$0.826630\pi$
$422$	0.126000	−	0.275901i	0.00613357	−	0.0134307i
$423$	25.9989	−	30.0043i	1.26411	−	1.45886i
$424$	8.65325	−	5.56110i	0.420239	−	0.270071i
$425$	−0.317850	−	2.21069i	−0.0154180	−	0.107234i
$426$	−3.56366	−	24.7858i	−0.172660	−	1.20088i
$427$	−5.77335	+	3.71030i	−0.279392	+	0.179554i
$428$	2.74669	−	3.16985i	0.132766	−	0.153220i
$429$	13.9206	−	30.4819i	0.672094	−	1.47168i
$430$	−6.24597	−	4.01404i	−0.301207	−	0.193574i
$431$	6.14302	−	1.80375i	0.295899	−	0.0868838i	−0.130414	−	0.991460i	$-0.541631\pi$
$431$	6.14302	−	1.80375i	0.295899	−	0.0868838i	0.426313	+	0.904576i	$0.359812\pi$
$432$	−8.11698	−	9.36749i	−0.390528	−	0.450694i
$433$	19.0903	+	5.60543i	0.917423	+	0.269380i	0.706162	−	0.708050i	$-0.250425\pi$
$433$	19.0903	+	5.60543i	0.917423	+	0.269380i	0.211261	+	0.977430i	$0.432243\pi$
$434$	2.16757	+	4.74633i	0.104047	+	0.227831i
$435$	−0.122853	+	0.854461i	−0.00589035	+	0.0409683i
$436$	20.1253			0.963829
$437$	0.0817639	−	7.35992i	0.00391130	−	0.352072i
$438$	4.52195			0.216067
$439$	3.10998	−	21.6304i	0.148431	−	1.03236i	−0.770357	−	0.637612i	$-0.779922\pi$
$439$	3.10998	−	21.6304i	0.148431	−	1.03236i	0.918789	−	0.394750i	$-0.129169\pi$
$440$	−0.707071	−	1.54827i	−0.0337083	−	0.0738109i
$441$	44.2791	+	13.0015i	2.10853	+	0.619120i
$442$	−9.13648	−	10.5441i	−0.434578	−	0.501530i
$443$	−8.50110	+	2.49615i	−0.403899	+	0.118596i	−0.477371	−	0.878702i	$-0.658410\pi$
$443$	−8.50110	+	2.49615i	−0.403899	+	0.118596i	0.0734719	+	0.997297i	$0.476592\pi$
$444$	−22.4455	−	14.4249i	−1.06522	−	0.684574i
$445$	4.46450	−	9.77589i	0.211638	−	0.463421i
$446$	8.57027	−	9.89061i	0.405814	−	0.468334i
$447$	−12.6703	+	8.14271i	−0.599285	+	0.385137i
$448$	0.0834109	+	0.580136i	0.00394080	+	0.0274088i
$449$	1.26035	+	8.76591i	0.0594795	+	0.413689i	0.997708	+	0.0676717i	$0.0215571\pi$
$449$	1.26035	+	8.76591i	0.0594795	+	0.413689i	−0.938228	+	0.346017i	$0.887534\pi$
$450$	5.83229	−	3.74819i	0.274937	−	0.176691i
$451$	3.44349	−	3.97400i	0.162148	−	0.187129i
$452$	−8.38748	+	18.3660i	−0.394514	+	0.863865i
$453$	14.4639	+	9.29536i	0.679572	+	0.436734i
$454$	20.6572	−	6.06551i	0.969492	−	0.284668i
$455$	−2.39762	−	2.76700i	−0.112402	−	0.129719i
$456$	4.64103	+	1.36273i	0.217336	+	0.0638157i
$457$	3.72783	+	8.16282i	0.174381	+	0.381840i	0.976561	−	0.215242i	$-0.0690539\pi$
$457$	3.72783	+	8.16282i	0.174381	+	0.381840i	−0.802180	+	0.597082i	$0.796327\pi$
$458$	−1.65751	+	11.5282i	−0.0774503	+	0.538679i
$459$	27.6832			1.29214
$460$	−3.65911	+	3.10015i	−0.170607	+	0.144545i
$461$	−17.5927			−0.819374			−0.409687	−	0.912226i	$-0.634362\pi$
$461$	−17.5927			−0.819374			−0.409687	+	0.912226i	$0.634362\pi$
$462$	0.447446	−	3.11206i	0.0208171	−	0.144786i
$463$	−13.9596	−	30.5672i	−0.648757	−	1.42058i	−0.892638	−	0.450774i	$-0.851148\pi$
$463$	−13.9596	−	30.5672i	−0.648757	−	1.42058i	0.243881	−	0.969805i	$-0.421579\pi$
$464$	0.262809	+	0.0771677i	0.0122006	+	0.00358242i
$465$	−18.3741	−	21.2048i	−0.852076	−	0.983349i
$466$	−14.2972	+	4.19804i	−0.662306	+	0.194471i
$467$	−3.41192	−	2.19271i	−0.157885	−	0.101466i	0.459313	−	0.888275i	$-0.348096\pi$
$467$	−3.41192	−	2.19271i	−0.157885	−	0.101466i	−0.617198	+	0.786808i	$0.711732\pi$
$468$	17.9909	−	39.3946i	0.831630	−	1.82102i
$469$	−5.05349	+	5.83204i	−0.233349	+	0.269299i
$470$	4.81749	−	3.09601i	0.222214	−	0.142808i
$471$	2.44097	+	16.9773i	0.112474	+	0.782274i
$472$	0.926403	+	6.44327i	0.0426411	+	0.296576i
$473$	10.6312	−	6.83223i	0.488821	−	0.314146i
$474$	−24.4204	+	28.1827i	−1.12167	+	1.29447i
$475$	−0.637555	+	1.39605i	−0.0292530	+	0.0640552i
$476$	−1.10121	−	0.707706i	−0.0504740	−	0.0324377i
$477$	−68.4237	+	20.0910i	−3.13290	+	0.919904i
$478$	−9.22524	−	10.6465i	−0.421953	−	0.486959i
$479$	−0.0905902	−	0.0265997i	−0.00413917	−	0.00121537i	0.279662	−	0.960098i	$-0.409777\pi$
$479$	−0.0905902	−	0.0265997i	−0.00413917	−	0.00121537i	−0.283801	+	0.958883i	$0.591596\pi$
$480$	−1.30924	−	2.86684i	−0.0597584	−	0.130853i
$481$	7.52618	−	52.3457i	0.343164	−	2.38676i
$482$	0.805703			0.0366988
$483$	−8.78207	+	1.16325i	−0.399598	+	0.0529297i
$484$	−8.10291			−0.368314
$485$	0.552968	−	3.84598i	0.0251090	−	0.174637i
$486$	8.46735	+	18.5409i	0.384087	+	0.841033i
$487$	15.5293	+	4.55982i	0.703701	+	0.206625i	0.613957	−	0.789340i	$-0.289577\pi$
$487$	15.5293	+	4.55982i	0.703701	+	0.206625i	0.0897443	+	0.995965i	$0.471395\pi$
$488$	−7.66791	−	8.84924i	−0.347110	−	0.400586i
$489$	9.70803	−	2.85054i	0.439012	−	0.128906i
$490$	5.59979	+	3.59877i	0.252973	+	0.162576i
$491$	3.62841	−	7.94511i	0.163748	−	0.358558i	−0.809916	−	0.586546i	$-0.800487\pi$
$491$	3.62841	−	7.94511i	0.163748	−	0.358558i	0.973664	+	0.227988i	$0.0732147\pi$
$492$	6.37611	−	7.35842i	0.287457	−	0.331743i
$493$	−0.514632	+	0.330734i	−0.0231779	+	0.0148955i
$494$	1.36441	+	9.48967i	0.0613876	+	0.426960i
$495$	1.67936	+	11.6802i	0.0754816	+	0.524986i
$496$	−7.48938	+	4.81313i	−0.336283	+	0.216116i
$497$	3.04951	−	3.51932i	0.136789	−	0.157863i
$498$	5.68879	−	12.4567i	0.254921	−	0.558199i
$499$	−9.27457	−	5.96041i	−0.415187	−	0.266824i	0.316328	−	0.948650i	$-0.397550\pi$
$499$	−9.27457	−	5.96041i	−0.415187	−	0.266824i	−0.731515	+	0.681825i	$0.761186\pi$
$500$	0.959493	−	0.281733i	0.0429098	−	0.0125995i
$501$	17.6557	+	20.3758i	0.788800	+	0.910323i
$502$	−17.4473	−	5.12298i	−0.778709	−	0.228650i
$503$	−10.8246	−	23.7026i	−0.482646	−	1.05685i	−0.981727	−	0.190292i	$-0.939056\pi$
$503$	−10.8246	−	23.7026i	−0.482646	−	1.05685i	0.499081	−	0.866555i	$-0.333671\pi$
$504$	0.578276	−	4.02200i	0.0257585	−	0.179154i
$505$	−17.2834			−0.769102
$506$	−2.21261	−	7.85731i	−0.0983625	−	0.349300i
$507$	82.0141			3.64238
$508$	−0.440666	+	3.06490i	−0.0195514	+	0.135983i
$509$	−5.49248	−	12.0269i	−0.243450	−	0.533081i	0.747980	−	0.663721i	$-0.231024\pi$
$509$	−5.49248	−	12.0269i	−0.243450	−	0.533081i	−0.991430	+	0.130640i	$0.958297\pi$
$510$	6.75384	+	1.98311i	0.299065	+	0.0878134i
$511$	0.550694	+	0.635534i	0.0243613	+	0.0281144i
$512$	−0.959493	+	0.281733i	−0.0424040	+	0.0124509i
$513$	−16.0032	−	10.2847i	−0.706561	−	0.454079i
$514$	−6.67157	+	14.6087i	−0.294270	+	0.644362i
$515$	−1.01275	+	1.16877i	−0.0446270	+	0.0515023i
$516$	19.6851	−	12.6508i	0.866587	−	0.556921i
$517$	1.38715	+	9.64787i	0.0610070	+	0.424313i
$518$	−0.706137	−	4.91129i	−0.0310259	−	0.215790i
$519$	42.5494	−	27.3448i	1.86771	−	1.20030i
$520$	4.09079	−	4.72103i	0.179393	−	0.207031i
$521$	−6.07332	+	13.2987i	−0.266077	+	0.582628i	−0.994762	−	0.102222i	$-0.967405\pi$
$521$	−6.07332	+	13.2987i	−0.266077	+	0.582628i	0.728684	+	0.684850i	$0.240132\pi$
$522$	−1.59749	−	1.02664i	−0.0699201	−	0.0449349i
$523$	−2.22535	+	0.653421i	−0.0973077	+	0.0285721i	−0.330024	−	0.943973i	$-0.607057\pi$
$523$	−2.22535	+	0.653421i	−0.0973077	+	0.0285721i	0.232716	+	0.972545i	$0.425239\pi$
$524$	1.84107	+	2.12471i	0.0804274	+	0.0928182i
$525$	1.77236	+	0.520412i	0.0773521	+	0.0227126i
$526$	3.31318	+	7.25486i	0.144462	+	0.316327i
$527$	2.82970	−	19.6810i	0.123264	−	0.857318i
$528$	5.36436			0.233454
$529$	−19.6203	+	12.0018i	−0.853057	+	0.521818i
$530$	−10.2861			−0.446801
$531$	6.42262	−	44.6703i	0.278718	−	1.93853i
$532$	0.373672	+	0.818228i	0.0162007	+	0.0354747i
$533$	18.5170	+	5.43707i	0.802059	+	0.235506i
$534$	22.1808	+	25.5980i	0.959856	+	1.10773i
$535$	−4.02441	+	1.18167i	−0.173991	+	0.0510882i
$536$	−11.0764	−	7.11834i	−0.478426	−	0.307466i
$537$	−1.15702	+	2.53353i	−0.0499293	+	0.109330i
$538$	−11.8203	+	13.6414i	−0.509610	+	0.588121i
$539$	−9.53131	+	6.12540i	−0.410543	+	0.263840i
$540$	1.76399	+	12.2688i	0.0759100	+	0.527965i
$541$	−1.55679	−	10.8277i	−0.0669318	−	0.465521i	−0.995531	−	0.0944363i	$-0.969895\pi$
$541$	−1.55679	−	10.8277i	−0.0669318	−	0.465521i	0.928599	−	0.371084i	$-0.121014\pi$
$542$	−19.2183	+	12.3508i	−0.825495	+	0.530514i
$543$	−12.0553	+	13.9125i	−0.517342	+	0.597045i
$544$	0.927799	−	2.03160i	0.0397790	−	0.0871039i
$545$	−16.9305	−	10.8806i	−0.725224	−	0.466073i
$546$	11.0716	−	3.25091i	0.473820	−	0.139126i
$547$	18.8252	+	21.7254i	0.804908	+	0.928913i	0.998640	−	0.0521415i	$-0.0166047\pi$
$547$	18.8252	+	21.7254i	0.804908	+	0.928913i	−0.193732	+	0.981054i	$0.562059\pi$
$548$	11.2876	+	3.31434i	0.482182	+	0.141582i
$549$	33.7227	+	73.8424i	1.43925	+	3.15152i
$550$	−0.242232	+	1.68476i	−0.0103288	+	0.0718384i
$551$	0.420372			0.0179085
$552$	−4.09695	−	14.5489i	−0.174378	−	0.619243i
$553$	−6.93489			−0.294902
$554$	−2.97969	+	20.7242i	−0.126595	+	0.880486i
$555$	11.0837	+	24.2700i	0.470478	+	1.03020i
$556$	15.4835	+	4.54636i	0.656646	+	0.192809i
$557$	4.44923	+	5.13469i	0.188520	+	0.217564i	0.842140	−	0.539259i	$-0.181296\pi$
$557$	4.44923	+	5.13469i	0.188520	+	0.217564i	−0.653620	+	0.756823i	$0.726750\pi$
$558$	59.2206	−	17.3888i	2.50701	−	0.736125i
$559$	39.0174	+	25.0750i	1.65026	+	1.06056i
$560$	0.243475	−	0.533137i	0.0102887	−	0.0225291i
$561$	−7.84582	+	9.05456i	−0.331251	+	0.382284i
$562$	2.42825	−	1.56054i	0.102429	−	0.0658274i
$563$	−5.55049	−	38.6045i	−0.233925	−	1.62698i	−0.680857	−	0.732417i	$-0.738392\pi$
$563$	−5.55049	−	38.6045i	−0.233925	−	1.62698i	0.446932	−	0.894568i	$-0.352517\pi$
$564$	2.56851	+	17.8644i	0.108154	+	0.752226i
$565$	16.9854	−	10.9159i	0.714582	−	0.459234i
$566$	1.87343	−	2.16205i	0.0787460	−	0.0908777i
$567$	−4.44731	+	9.73825i	−0.186769	+	0.408968i
$568$	6.68399	+	4.29554i	0.280454	+	0.180237i
$569$	−42.6683	+	12.5285i	−1.78875	+	0.525223i	−0.996394	−	0.0848412i	$-0.972962\pi$
$569$	−42.6683	+	12.5285i	−1.78875	+	0.525223i	−0.792352	+	0.610065i	$0.791144\pi$
$570$	−3.16754	−	3.65553i	−0.132674	−	0.153113i
$571$	−0.231157	−	0.0678737i	−0.00967361	−	0.00284043i	0.276892	−	0.960901i	$-0.410696\pi$
$571$	−0.231157	−	0.0678737i	−0.00967361	−	0.00284043i	−0.286566	+	0.958061i	$0.592514\pi$
$572$	4.41694	+	9.67175i	0.184682	+	0.404396i
$573$	5.83202	−	40.5626i	0.243636	−	1.69453i
$574$	1.81068			0.0755764
$575$	4.75431	−	0.629743i	0.198268	−	0.0262621i
$576$	6.93286			0.288869
$577$	1.00718	−	7.00512i	0.0419296	−	0.291627i	−0.958058	−	0.286576i	$-0.907483\pi$
$577$	1.00718	−	7.00512i	0.0419296	−	0.291627i	0.999987	−	0.00505123i	$-0.00160786\pi$
$578$	−4.98989	−	10.9263i	−0.207552	−	0.454475i
$579$	6.82968	+	2.00538i	0.283832	+	0.0833406i
$580$	−0.179369	−	0.207003i	−0.00744789	−	0.00859532i
$581$	2.44352	−	0.717482i	0.101374	−	0.0297662i
$582$	10.3018	+	6.62057i	0.427024	+	0.274432i
$583$	7.27303	−	15.9257i	0.301218	−	0.659575i
$584$	−0.939588	+	1.08434i	−0.0388804	+	0.0448704i
$585$	−36.4332	+	23.4142i	−1.50633	+	0.968059i
$586$	−0.398161	−	2.76927i	−0.0164479	−	0.114398i
$587$	−3.78442	−	26.3212i	−0.156200	−	1.08639i	−0.905556	−	0.424226i	$-0.860546\pi$
$587$	−3.78442	−	26.3212i	−0.156200	−	1.08639i	0.749357	−	0.662166i	$-0.230363\pi$
$588$	−17.6485	+	11.3420i	−0.727814	+	0.467738i
$589$	−8.94754	+	10.3260i	−0.368677	+	0.425476i
$590$	2.70416	−	5.92128i	0.111328	−	0.243775i
$591$	15.7769	+	10.1392i	0.648975	+	0.417071i
$592$	8.12284	−	2.38508i	0.333847	−	0.0980262i
$593$	23.9141	+	27.5983i	0.982034	+	1.13333i	0.991067	+	0.133368i	$0.0425793\pi$
$593$	23.9141	+	27.5983i	0.982034	+	1.13333i	−0.00903271	+	0.999959i	$0.502875\pi$
$594$	−20.2427	−	5.94379i	−0.830568	−	0.243877i
$595$	0.543784	+	1.19072i	0.0222930	+	0.0488148i
$596$	0.680101	−	4.73020i	0.0278580	−	0.193757i
$597$	−64.9698			−2.65904
$598$	22.8578	−	19.3660i	0.934724	−	0.791936i
$599$	−21.6301			−0.883783			−0.441892	−	0.897068i	$-0.645692\pi$
$599$	−21.6301			−0.883783			−0.441892	+	0.897068i	$0.645692\pi$
$600$	−0.448526	+	3.11956i	−0.0183110	+	0.127356i
$601$	−6.37117	−	13.9509i	−0.259885	−	0.569070i	0.734042	−	0.679104i	$-0.237631\pi$
$601$	−6.37117	−	13.9509i	−0.259885	−	0.569070i	−0.993928	+	0.110034i	$0.964904\pi$
$602$	4.17530	+	1.22598i	0.170172	+	0.0499671i
$603$	59.7766	+	68.9859i	2.43429	+	2.80932i
$604$	−5.23434	+	1.53694i	−0.212982	+	0.0625373i
$605$	6.81660	+	4.38076i	0.277134	+	0.178103i
$606$	22.6281	−	49.5487i	0.919205	−	2.01278i
$607$	−15.9126	+	18.3641i	−0.645871	+	0.745375i	−0.980402	−	0.197010i	$-0.936877\pi$
$607$	−15.9126	+	18.3641i	−0.645871	+	0.745375i	0.334530	+	0.942385i	$0.391422\pi$
$608$	−1.29111	+	0.829745i	−0.0523613	+	0.0336506i
$609$	−0.0720043	−	0.500801i	−0.00291776	−	0.0202935i
$610$	1.66640	+	11.5900i	0.0674704	+	0.469267i
$611$	−30.0939	+	19.3402i	−1.21747	+	0.782421i
$612$	−10.1399	+	11.7020i	−0.409880	+	0.473027i
$613$	−13.9221	+	30.4852i	−0.562309	+	1.23128i	0.388483	+	0.921456i	$0.372999\pi$
$613$	−13.9221	+	30.4852i	−0.562309	+	1.23128i	−0.950792	+	0.309829i	$0.899728\pi$
$614$	−24.0536	−	15.4583i	−0.970725	−	0.623847i
$615$	−9.34218	+	2.74311i	−0.376713	+	0.110613i
$616$	0.653285	+	0.753931i	0.0263216	+	0.0303767i
$617$	25.8505	+	7.59040i	1.04070	+	0.305578i	0.757055	−	0.653351i	$-0.226637\pi$
$617$	25.8505	+	7.59040i	1.04070	+	0.305578i	0.283647	+	0.958929i	$0.408456\pi$
$618$	−2.02475	−	4.43359i	−0.0814475	−	0.178345i
$619$	1.09859	−	7.64085i	0.0441560	−	0.307112i	−0.955760	−	0.294148i	$-0.904964\pi$
$619$	1.09859	−	7.64085i	0.0441560	−	0.307112i	0.999916	−	0.0129639i	$-0.00412667\pi$
$620$	8.90264			0.357539
$621$	−0.660345	+	59.4405i	−0.0264987	+	2.38527i
$622$	−17.2586			−0.692007
$623$	−0.896424	+	6.23476i	−0.0359145	+	0.249791i
$624$	8.17858	+	17.9086i	0.327405	+	0.716917i
$625$	−0.959493	−	0.281733i	−0.0383797	−	0.0112693i
$626$	−19.9457	−	23.0185i	−0.797189	−	0.920005i
$627$	7.89943	−	2.31948i	0.315473	−	0.0926311i
$628$	−4.57828	−	2.94228i	−0.182693	−	0.117410i
$629$	−7.85452	+	17.1990i	−0.313180	+	0.685769i
$630$	−2.66093	+	3.07088i	−0.106014	+	0.122347i
$631$	3.18392	−	2.04618i	0.126750	−	0.0814571i	−0.475730	−	0.879592i	$-0.657816\pi$
$631$	3.18392	−	2.04618i	0.126750	−	0.0814571i	0.602479	+	0.798134i	$0.294180\pi$
$632$	−1.68390	−	11.7118i	−0.0669821	−	0.465871i
$633$	−0.136043	−	0.946197i	−0.00540721	−	0.0376080i
$634$	7.42375	−	4.77096i	0.294835	−	0.189479i
$635$	2.02772	−	2.34012i	0.0804678	−	0.0928647i
$636$	13.4670	−	29.4887i	0.534002	−	1.16930i
$637$	−34.9808	−	22.4808i	−1.38599	−	0.890723i
$638$	0.447323	−	0.131346i	0.0177097	−	0.00520003i
$639$	−36.0720	−	41.6293i	−1.42699	−	1.64683i
$640$	0.959493	+	0.281733i	0.0379273	+	0.0111365i
$641$	−2.97557	−	6.51560i	−0.117528	−	0.257351i	0.841721	−	0.539913i	$-0.181543\pi$
$641$	−2.97557	−	6.51560i	−0.117528	−	0.257351i	−0.959249	+	0.282562i	$0.908816\pi$
$642$	1.88126	−	13.0844i	0.0742473	−	0.516401i
$643$	−42.6671			−1.68263			−0.841313	−	0.540548i	$-0.818217\pi$
$643$	−42.6671			−1.68263			−0.841313	+	0.540548i	$0.818217\pi$
$644$	1.54583	−	2.34760i	0.0609143	−	0.0925086i
$645$	−23.3997			−0.921362
$646$	0.487818	−	3.39285i	0.0191929	−	0.133490i
$647$	8.96510	+	19.6308i	0.352455	+	0.771768i	0.999953	+	0.00970096i	$0.00308796\pi$
$647$	8.96510	+	19.6308i	0.352455	+	0.771768i	−0.647498	+	0.762067i	$0.724185\pi$
$648$	−17.5261	−	5.14611i	−0.688489	−	0.202158i
$649$	7.25570	+	8.37353i	0.284811	+	0.328690i
$650$	−5.99377	+	1.75993i	−0.235095	+	0.0690301i
$651$	13.8343	+	8.89074i	0.542207	+	0.348455i
$652$	−1.33363	+	2.92024i	−0.0522289	+	0.114365i
$653$	11.8584	−	13.6854i	0.464056	−	0.535550i	−0.474692	−	0.880152i	$-0.657441\pi$
$653$	11.8584	−	13.6854i	0.464056	−	0.535550i	0.938749	+	0.344602i	$0.111986\pi$
$654$	53.3590	−	34.2917i	2.08650	−	1.34091i
$655$	−0.400102	−	2.78277i	−0.0156333	−	0.108732i
$656$	0.439663	+	3.05792i	0.0171659	+	0.119392i
$657$	8.36811	−	5.37786i	0.326471	−	0.209810i
$658$	−2.19794	+	2.53656i	−0.0856845	+	0.0988852i
$659$	3.38546	−	7.41312i	0.131879	−	0.288774i	−0.832160	−	0.554535i	$-0.812896\pi$
$659$	3.38546	−	7.41312i	0.131879	−	0.288774i	0.964039	+	0.265761i	$0.0856233\pi$
$660$	−4.51279	−	2.90019i	−0.175660	−	0.112890i
$661$	−17.1226	+	5.02766i	−0.665993	+	0.195553i	−0.597218	−	0.802079i	$-0.703727\pi$
$661$	−17.1226	+	5.02766i	−0.665993	+	0.195553i	−0.0687752	+	0.997632i	$0.521909\pi$
$662$	−3.88592	−	4.48459i	−0.151031	−	0.174299i
$663$	−42.1899	−	12.3881i	−1.63852	−	0.481113i
$664$	1.80502	+	3.95245i	0.0700485	+	0.153385i
$665$	0.128014	−	0.890359i	0.00496418	−	0.0345267i
$666$	−58.6919			−2.27427
$667$	−0.697865	−	1.11289i	−0.0270214	−	0.0430912i
$668$	−8.55460			−0.330987
$669$	5.86993	−	40.8262i	0.226944	−	1.57843i
$670$	5.46956	+	11.9767i	0.211307	+	0.462699i
$671$	−19.1228	−	5.61495i	−0.738226	−	0.216763i
$672$	1.20965	+	1.39601i	0.0466632	+	0.0538522i
$673$	−9.19327	+	2.69939i	−0.354375	+	0.104054i	−0.454074	−	0.890964i	$-0.650030\pi$
$673$	−9.19327	+	2.69939i	−0.354375	+	0.104054i	0.0996998	+	0.995018i	$0.468212\pi$
$674$	−21.7130	−	13.9541i	−0.836354	−	0.537492i
$675$	5.14906	−	11.2749i	0.198187	−	0.433970i
$676$	−17.0412	+	19.6666i	−0.655431	+	0.756408i
$677$	−21.3256	+	13.7051i	−0.819610	+	0.526731i	−0.881961	−	0.471323i	$-0.843777\pi$
$677$	−21.3256	+	13.7051i	−0.819610	+	0.526731i	0.0623509	+	0.998054i	$0.480140\pi$
$678$	9.05600	+	62.9859i	0.347794	+	2.41896i
$679$	0.324095	+	2.25413i	0.0124376	+	0.0865056i
$680$	−1.87888	+	1.20748i	−0.0720517	+	0.0463048i
$681$	44.4341	−	51.2797i	1.70272	−	1.96504i
$682$	−6.29480	+	13.7837i	−0.241040	+	0.527805i
$683$	15.7957	+	10.1513i	0.604405	+	0.388427i	0.806755	−	0.590886i	$-0.201222\pi$
$683$	15.7957	+	10.1513i	0.604405	+	0.388427i	−0.202350	+	0.979313i	$0.564858\pi$
$684$	10.2092	−	2.99768i	0.390357	−	0.114619i
$685$	−7.70387	−	8.89074i	−0.294350	−	0.339698i
$686$	−7.67986	−	2.25501i	−0.293219	−	0.0860967i
$687$	15.2484	+	33.3894i	0.581764	+	1.27388i
$688$	−1.05663	+	7.34902i	−0.0402837	+	0.280179i
$689$	64.2555			2.44794
$690$	−4.41916	+	14.4543i	−0.168234	+	0.550266i
$691$	46.2070			1.75780			0.878898	−	0.477010i	$-0.158280\pi$
$691$	46.2070			1.75780			0.878898	+	0.477010i	$0.158280\pi$
$692$	−2.28391	+	15.8850i	−0.0868213	+	0.603856i
$693$	−2.87308	−	6.29117i	−0.109139	−	0.238982i
$694$	−26.3202	−	7.72830i	−0.999100	−	0.293362i
$695$	−10.5676	−	12.1956i	−0.400852	−	0.462607i
$696$	0.828280	−	0.243205i	0.0313959	−	0.00921866i
$697$	−5.80454	−	3.73035i	−0.219863	−	0.141297i
$698$	1.47795	−	3.23625i	0.0559411	−	0.122494i
$699$	−30.7536	+	35.4915i	−1.16321	+	1.34241i
$700$	−0.493060	+	0.316870i	−0.0186359	+	0.0119766i
$701$	−7.07288	−	49.1930i	−0.267139	−	1.85799i	−0.475202	−	0.879877i	$-0.657625\pi$
$701$	−7.07288	−	49.1930i	−0.267139	−	1.85799i	0.208063	−	0.978116i	$-0.433284\pi$
$702$	−11.0193	−	76.6409i	−0.415897	−	2.89263i
$703$	10.9302	−	7.02442i	0.412241	−	0.264931i
$704$	−1.11463	+	1.28635i	−0.0420091	+	0.0484811i
$705$	7.49744	−	16.4171i	0.282370	−	0.618304i
$706$	11.2805	+	7.24957i	0.424549	+	0.272841i
$707$	9.71950	−	2.85390i	0.365540	−	0.107332i
$708$	13.4349	+	15.5047i	0.504916	+	0.582704i
$709$	5.37148	+	1.57721i	0.201730	+	0.0592333i	0.381037	−	0.924560i	$-0.375567\pi$
$709$	5.37148	+	1.57721i	0.201730	+	0.0592333i	−0.179306	+	0.983793i	$0.557385\pi$
$710$	−3.30058	−	7.22727i	−0.123869	−	0.271235i
$711$	−11.6743	+	81.1963i	−0.437819	+	3.04510i
$712$	−10.7471			−0.402764
$713$	42.1909	+	6.54530i	1.58006	+	0.245124i
$714$	−4.12555			−0.154395
$715$	1.51318	−	10.5244i	0.0565896	−	0.393589i
$716$	−0.367118	−	0.803875i	−0.0137198	−	0.0300422i
$717$	−42.5998	−	12.5084i	−1.59092	−	0.467136i
$718$	−1.64868	−	1.90267i	−0.0615280	−	0.0710071i
$719$	31.2124	−	9.16477i	1.16402	−	0.341788i	0.358029	−	0.933710i	$-0.383449\pi$
$719$	31.2124	−	9.16477i	1.16402	−	0.341788i	0.805995	+	0.591922i	$0.201631\pi$
$720$	−5.83229	−	3.74819i	−0.217357	−	0.139687i
$721$	0.376537	−	0.824501i	0.0140230	−	0.0307060i
$722$	10.8999	−	12.5791i	0.405651	−	0.468146i
$723$	2.13619	−	1.37284i	0.0794456	−	0.0510566i
$724$	−0.831269	−	5.78161i	−0.0308939	−	0.214872i
$725$	0.0389806	+	0.271116i	0.00144770	+	0.0100690i
$726$	−21.4835	+	13.8066i	−0.797328	+	0.512411i
$727$	−3.28289	+	3.78866i	−0.121756	+	0.140514i	−0.813355	−	0.581768i	$-0.802361\pi$
$727$	−3.28289	+	3.78866i	−0.121756	+	0.140514i	0.691599	+	0.722282i	$0.256907\pi$
$728$	−1.52094	+	3.33040i	−0.0563700	+	0.123433i
$729$	7.94286	+	5.10457i	0.294180	+	0.189058i
$730$	1.37667	−	0.404227i	0.0509529	−	0.0149611i
$731$	−10.8591	−	12.5321i	−0.401638	−	0.463515i
$732$	−35.4084	−	10.3969i	−1.30873	−	0.384279i
$733$	−8.26980	−	18.1083i	−0.305452	−	0.668847i	0.693200	−	0.720745i	$-0.256200\pi$
$733$	−8.26980	−	18.1083i	−0.305452	−	0.668847i	−0.998652	+	0.0518981i	$0.983473\pi$
$734$	−4.33915	+	30.1794i	−0.160161	+	1.11394i
$735$	20.9789			0.773817
$736$	4.34004	+	2.04060i	0.159976	+	0.0752175i
$737$	−22.4105			−0.825500
$738$	3.04812	−	21.2001i	0.112203	−	0.780388i
$739$	8.37565	+	18.3401i	0.308103	+	0.674652i	0.998825	−	0.0484690i	$-0.0154342\pi$
$739$	8.37565	+	18.3401i	0.308103	+	0.674652i	−0.690721	+	0.723121i	$0.742707\pi$
$740$	−8.12284	−	2.38508i	−0.298602	−	0.0876773i
$741$	19.7870	+	22.8354i	0.726894	+	0.838880i
$742$	5.78451	−	1.69849i	0.212356	−	0.0623534i
$743$	−31.2553	−	20.0866i	−1.14665	−	0.736905i	−0.177678	−	0.984089i	$-0.556858\pi$
$743$	−31.2553	−	20.0866i	−1.14665	−	0.736905i	−0.968969	+	0.247184i	$0.920495\pi$
$744$	−11.6557	+	25.5224i	−0.427319	+	0.935697i
$745$	−3.12948	+	3.61161i	−0.114655	+	0.132319i
$746$	−23.8859	+	15.3506i	−0.874526	+	0.562024i
$747$	−4.28710	−	29.8174i	−0.156857	−	1.09096i
$748$	−0.541007	−	3.76278i	−0.0197812	−	0.137581i
$749$	2.06805	−	1.32905i	0.0755648	−	0.0485625i
$750$	2.06389	−	2.38185i	0.0753625	−	0.0869730i
$751$	2.65933	−	5.82312i	0.0970404	−	0.212489i	−0.854886	−	0.518816i	$-0.826373\pi$
$751$	2.65933	−	5.82312i	0.0970404	−	0.212489i	0.951926	+	0.306327i	$0.0991002\pi$
$752$	−4.81749	−	3.09601i	−0.175676	−	0.112900i
$753$	−54.9875	+	16.1458i	−2.00386	+	0.588385i
$754$	1.12048	+	1.29311i	0.0408056	+	0.0470922i
$755$	5.23434	+	1.53694i	0.190497	+	0.0559350i
$756$	−3.01787	−	6.60821i	−0.109759	−	0.240338i
$757$	0.512476	−	3.56435i	0.0186263	−	0.129548i	−0.978387	−	0.206784i	$-0.933700\pi$
$757$	0.512476	−	3.56435i	0.0186263	−	0.129548i	0.997013	+	0.0772355i	$0.0246093\pi$
$758$	18.5845			0.675021
$759$	−19.2545	−	17.0623i	−0.698894	−	0.619321i
$760$	1.53474			0.0556710
$761$	−3.15524	+	21.9452i	−0.114377	+	0.795512i	0.849198	+	0.528075i	$0.177086\pi$
$761$	−3.15524	+	21.9452i	−0.114377	+	0.795512i	−0.963575	+	0.267437i	$0.913823\pi$
$762$	4.05396	+	8.87693i	0.146859	+	0.321577i
$763$	11.3177	+	3.32317i	0.409728	+	0.120307i
$764$	8.51493	+	9.82675i	0.308059	+	0.355519i
$765$	14.8568	−	4.36235i	0.537149	−	0.157721i
$766$	−7.14674	−	4.59293i	−0.258222	−	0.165949i
$767$	−16.8924	+	36.9891i	−0.609948	+	1.33560i
$768$	−2.06389	+	2.38185i	−0.0744741	+	0.0859477i
$769$	−1.19825	+	0.770067i	−0.0432099	+	0.0277693i	−0.562067	−	0.827091i	$-0.689994\pi$
$769$	−1.19825	+	0.770067i	−0.0432099	+	0.0277693i	0.518858	+	0.854861i	$0.326358\pi$
$770$	−0.141972	−	0.987440i	−0.00511633	−	0.0355849i
$771$	7.20333	+	50.1003i	0.259422	+	1.80432i
$772$	−1.89998	+	1.22104i	−0.0683817	+	0.0439462i
$773$	−4.15042	+	4.78984i	−0.149280	+	0.172278i	−0.825465	−	0.564454i	$-0.809087\pi$
$773$	−4.15042	+	4.78984i	−0.149280	+	0.172278i	0.676184	+	0.736732i	$0.263632\pi$
$774$	21.3829	−	46.8221i	0.768594	−	1.68299i
$775$	−7.48938	−	4.81313i	−0.269026	−	0.172893i
$776$	−3.72813	+	1.09468i	−0.133832	+	0.0392967i
$777$	−10.2406	−	11.8183i	−0.367379	−	0.423978i
$778$	5.68372	+	1.66889i	0.203771	+	0.0598326i
$779$	1.96964	+	4.31291i	0.0705698	+	0.154526i
$780$	2.80186	−	19.4873i	0.100323	−	0.697758i
$781$	13.5235			0.483909
$782$	−9.79202	+	4.34106i	−0.350162	+	0.155236i
$783$	−3.39503			−0.121329
$784$	0.947317	−	6.58873i	0.0338327	−	0.235312i
$785$	2.26078	+	4.95041i	0.0806906	+	0.176688i
$786$	8.50158	+	2.49629i	0.303241	+	0.0890397i
$787$	9.45634	+	10.9132i	0.337082	+	0.389014i	0.898832	−	0.438294i	$-0.144417\pi$
$787$	9.45634	+	10.9132i	0.337082	+	0.389014i	−0.561750	+	0.827307i	$0.689872\pi$
$788$	−5.70952	+	1.67647i	−0.203393	+	0.0597216i
$789$	21.1460	+	13.5897i	0.752816	+	0.483806i
$790$	−4.91529	+	10.7630i	−0.174878	+	0.382930i
$791$	−7.74945	+	8.94335i	−0.275539	+	0.317989i
$792$	9.92705	−	6.37973i	0.352742	−	0.226694i
$793$	−10.4097	−	72.4008i	−0.369658	−	2.57103i
$794$	1.61000	+	11.1978i	0.0571368	+	0.397395i
$795$	−27.2720	+	17.5266i	−0.967236	+	0.621605i
$796$	13.4997	−	15.5795i	0.478483	−	0.552199i
$797$	−12.4488	+	27.2591i	−0.440960	+	0.965567i	0.550461	+	0.834861i	$0.314452\pi$
$797$	−12.4488	+	27.2591i	−0.440960	+	0.965567i	−0.991421	+	0.130707i	$0.958275\pi$
$798$	2.38491	+	1.53269i	0.0844250	+	0.0542567i
$799$	12.2718	−	3.60332i	0.434144	−	0.127476i
$800$	−0.654861	−	0.755750i	−0.0231528	−	0.0267198i
$801$	71.4899	+	20.9913i	2.52597	+	0.741692i
$802$	0.923684	+	2.02259i	0.0326164	+	0.0714200i
$803$	−0.347552	+	2.41728i	−0.0122648	+	0.0853038i
$804$	−41.4961			−1.46345
$805$	−2.56965	+	1.13919i	−0.0905681	+	0.0401512i
$806$	−55.6131			−1.95889
$807$	−8.09595	+	56.3085i	−0.284991	+	1.98215i
$808$	7.17979	+	15.7215i	0.252584	+	0.553082i
$809$	30.9522	+	9.08838i	1.08822	+	0.319530i	0.776162	−	0.630533i	$-0.217164\pi$
$809$	30.9522	+	9.08838i	1.08822	+	0.319530i	0.312058	+	0.950063i	$0.398982\pi$
$810$	11.9617	+	13.8045i	0.420290	+	0.485040i
$811$	0.200133	−	0.0587644i	0.00702763	−	0.00206350i	−0.278217	−	0.960518i	$-0.589743\pi$
$811$	0.200133	−	0.0587644i	0.00702763	−	0.00206350i	0.285244	+	0.958455i	$0.407925\pi$
$812$	0.135051	+	0.0867920i	0.00473936	+	0.00304580i
$813$	−29.9093	+	65.4923i	−1.04897	+	2.29692i
$814$	9.43617	−	10.8899i	0.330738	−	0.381692i
$815$	2.70072	−	1.73565i	0.0946020	−	0.0607970i
$816$	−1.00175	−	6.96732i	−0.0350682	−	0.243905i
$817$	1.62166	+	11.2789i	0.0567346	+	0.394598i
$818$	−14.8424	+	9.53862i	−0.518952	+	0.333510i
$819$	16.6224	−	19.1832i	0.580832	−	0.670316i
$820$	1.28337	−	2.81019i	0.0448172	−	0.0981360i
$821$	20.6488	+	13.2702i	0.720648	+	0.463132i	0.848862	−	0.528614i	$-0.177288\pi$
$821$	20.6488	+	13.2702i	0.720648	+	0.463132i	−0.128214	+	0.991746i	$0.540925\pi$
$822$	35.5745	−	10.4456i	1.24080	−	0.364333i
$823$	8.88545	+	10.2544i	0.309727	+	0.357444i	0.889177	−	0.457564i	$-0.151278\pi$
$823$	8.88545	+	10.2544i	0.309727	+	0.357444i	−0.579450	+	0.815008i	$0.696732\pi$
$824$	1.48386	+	0.435702i	0.0516929	+	0.0151784i
$825$	2.22844	+	4.87959i	0.0775842	+	0.169886i
$826$	−0.542966	+	3.77641i	−0.0188922	+	0.131398i
$827$	36.3082			1.26256			0.631280	−	0.775555i	$-0.282530\pi$
$827$	36.3082			1.26256			0.631280	+	0.775555i	$0.282530\pi$
$828$	−24.8844	−	22.0511i	−0.864791	−	0.766330i
$829$	23.1362			0.803555			0.401777	−	0.915737i	$-0.368393\pi$
$829$	23.1362			0.803555			0.401777	+	0.915737i	$0.368393\pi$
$830$	0.618374	−	4.30088i	0.0214641	−	0.149286i
$831$	27.4119	+	60.0238i	0.950910	+	2.08220i
$832$	−5.99377	−	1.75993i	−0.207797	−	0.0610146i
$833$	9.73566	+	11.2356i	0.337321	+	0.389289i
$834$	48.7984	−	14.3285i	1.68975	−	0.496156i
$835$	7.19658	+	4.62496i	0.249048	+	0.160053i
$836$	−1.08517	+	2.37620i	−0.0375315	+	0.0821825i
$837$	72.2626	−	83.3955i	2.49776	−	2.88257i
$838$	0.694534	−	0.446350i	0.0239923	−	0.0154189i
$839$	−2.48982	−	17.3171i	−0.0859582	−	0.597853i	−0.986584	−	0.163256i	$-0.947800\pi$
$839$	−2.48982	−	17.3171i	−0.0859582	−	0.597853i	0.900625	−	0.434596i	$-0.143109\pi$
$840$	−0.262882	−	1.82838i	−0.00907027	−	0.0630851i
$841$	−24.3332	+	15.6380i	−0.839077	+	0.539242i
$842$	11.8083	−	13.6275i	0.406941	−	0.469635i
$843$	3.77907	−	8.27502i	0.130158	−	0.285007i
$844$	0.255161	+	0.163982i	0.00878301	+	0.00564450i
$845$	24.9686	−	7.33143i	0.858944	−	0.252209i
$846$	25.9989	+	30.0043i	0.893861	+	1.03157i
$847$	−4.55675	−	1.33798i	−0.156572	−	0.0459737i
$848$	4.27301	+	9.35660i	0.146736	+	0.321307i
$849$	1.28314	−	8.92446i	0.0440374	−	0.306287i
$850$	2.23343			0.0766059
$851$	−36.7418	−	17.2752i	−1.25949	−	0.592187i
$852$	25.0407			0.857879
$853$	−0.00779563	+	0.0542198i	−0.000266917	+	0.00185645i	−0.989954	−	0.141387i	$-0.954844\pi$
$853$	−0.00779563	+	0.0542198i	−0.000266917	+	0.00185645i	0.989688	+	0.143243i	$0.0457530\pi$
$854$	−2.85091	−	6.24261i	−0.0975560	−	0.213618i
$855$	−10.2092	−	2.99768i	−0.349146	−	0.102518i
$856$	2.74669	+	3.16985i	0.0938799	+	0.108343i
$857$	30.0882	−	8.83469i	1.02779	−	0.301787i	0.275980	−	0.961163i	$-0.410998\pi$
$857$	30.0882	−	8.83469i	1.02779	−	0.301787i	0.751813	+	0.659376i	$0.229179\pi$
$858$	28.1905	+	18.1170i	0.962409	+	0.618503i
$859$	2.48522	−	5.44186i	0.0847945	−	0.185674i	−0.862485	−	0.506083i	$-0.831093\pi$
$859$	2.48522	−	5.44186i	0.0847945	−	0.185674i	0.947279	+	0.320409i	$0.103820\pi$
$860$	4.86208	−	5.61114i	0.165795	−	0.191338i
$861$	4.80072	−	3.08523i	0.163608	−	0.105145i
$862$	0.911152	+	6.33720i	0.0310339	+	0.215846i
$863$	−7.73420	−	53.7926i	−0.263275	−	1.83112i	−0.507797	−	0.861477i	$-0.669540\pi$
$863$	−7.73420	−	53.7926i	−0.263275	−	1.83112i	0.244522	−	0.969644i	$-0.421369\pi$
$864$	10.4273	−	6.70123i	0.354744	−	0.227980i
$865$	10.5094	−	12.1285i	0.357331	−	0.412381i
$866$	−8.26521	+	18.0983i	−0.280863	+	0.615005i
$867$	−31.8473	−	20.4670i	−1.08159	−	0.695096i
$868$	−5.00649	+	1.47004i	−0.169931	+	0.0498964i
$869$	−13.1885	−	15.2204i	−0.447391	−	0.516316i
$870$	−0.828280	−	0.243205i	−0.0280813	−	0.00824542i
$871$	−34.1673	−	74.8159i	−1.15771	−	2.53504i
$872$	−2.86413	+	19.9205i	−0.0969918	+	0.674593i
$873$	26.9378			0.911706
$874$	7.27337	+	1.12836i	0.246025	+	0.0381672i
$875$	0.586101			0.0198138
$876$	−0.643540	+	4.47592i	−0.0217432	+	0.151227i
$877$	11.0898	+	24.2833i	0.374476	+	0.819987i	0.999233	+	0.0391680i	$0.0124708\pi$
$877$	11.0898	+	24.2833i	0.374476	+	0.819987i	−0.624757	+	0.780819i	$0.714802\pi$
$878$	20.9676	+	6.15665i	0.707623	+	0.207777i
$879$	−5.77424	−	6.66383i	−0.194760	−	0.224765i
$880$	1.63314	−	0.479532i	0.0550530	−	0.0161650i
$881$	16.4728	+	10.5864i	0.554983	+	0.356666i	0.787873	−	0.615837i	$-0.211182\pi$
$881$	16.4728	+	10.5864i	0.554983	+	0.356666i	−0.232891	+	0.972503i	$0.574818\pi$
$882$	−19.1708	+	41.9781i	−0.645513	+	1.41348i
$883$	−27.0780	+	31.2496i	−0.911246	+	1.05163i	0.0872159	+	0.996189i	$0.472203\pi$
$883$	−27.0780	+	31.2496i	−0.911246	+	1.05163i	−0.998462	+	0.0554444i	$0.982342\pi$
$884$	11.7370	−	7.54291i	0.394758	−	0.253695i
$885$	−2.91969	−	20.3069i	−0.0981444	−	0.682609i
$886$	−1.26091	−	8.76981i	−0.0423610	−	0.294627i
$887$	28.1181	−	18.0704i	0.944114	−	0.606745i	0.0245557	−	0.999698i	$-0.492183\pi$
$887$	28.1181	−	18.0704i	0.944114	−	0.606745i	0.919559	+	0.392953i	$0.128547\pi$
$888$	17.4724	−	20.1642i	0.586335	−	0.676666i
$889$	−0.753902	+	1.65081i	−0.0252851	+	0.0553665i
$890$	9.04102	+	5.81031i	0.303056	+	0.194762i
$891$	−29.8308	+	8.75912i	−0.999370	+	0.293441i
$892$	8.57027	+	9.89061i	0.286954	+	0.331162i
$893$	−8.43279	−	2.47609i	−0.282192	−	0.0828592i
$894$	−6.25666	−	13.7002i	−0.209254	−	0.458202i
$895$	−0.125769	+	0.874742i	−0.00420399	+	0.0292394i
$896$	−0.586101			−0.0195803
$897$	27.6057	−	90.2933i	0.921726	−	3.01481i
$898$	−8.85606			−0.295530
$899$	−0.347030	+	2.41365i	−0.0115741	+	0.0804997i
$900$	2.88001	+	6.30635i	0.0960005	+	0.210212i
$901$	−22.0427	−	6.47233i	−0.734350	−	0.215625i
$902$	3.44349	+	3.97400i	0.114656	+	0.132320i
$903$	13.1591	−	3.86385i	0.437906	−	0.128581i
$904$	−16.9854	−	10.9159i	−0.564927	−	0.363056i
$905$	−2.42646	+	5.31321i	−0.0806584	+	0.176617i
$906$	−11.2592	+	12.9938i	−0.374061	+	0.431689i
$907$	−6.00754	+	3.86081i	−0.199477	+	0.128196i	−0.636566	−	0.771222i	$-0.719646\pi$
$907$	−6.00754	+	3.86081i	−0.199477	+	0.128196i	0.437089	+	0.899418i	$0.356009\pi$
$908$	3.06394	+	21.3102i	0.101680	+	0.707203i
$909$	−17.0527	−	118.604i	−0.565601	−	3.93384i
$910$	3.08005	−	1.97943i	0.102103	−	0.0656174i
$911$	26.9041	−	31.0490i	0.891374	−	1.02870i	−0.108029	−	0.994148i	$-0.534454\pi$
$911$	26.9041	−	31.0490i	0.891374	−	1.02870i	0.999403	−	0.0345525i	$-0.0110006\pi$
$912$	−2.00935	+	4.39986i	−0.0665361	+	0.145694i
$913$	6.22170	+	3.99844i	0.205908	+	0.132329i
$914$	−8.61026	+	2.52820i	−0.284802	+	0.0836254i
$915$	24.1665	+	27.8896i	0.798920	+	0.922003i
$916$	−11.1750	−	3.28127i	−0.369232	−	0.108416i
$917$	0.684504	+	1.49885i	0.0226043	+	0.0494965i
$918$	−3.93974	+	27.4015i	−0.130031	+	0.904383i
$919$	1.24485			0.0410639			0.0205319	−	0.999789i	$-0.493464\pi$
$919$	1.24485			0.0410639			0.0205319	+	0.999789i	$0.493464\pi$
$920$	−2.54784	−	4.06306i	−0.0839999	−	0.133955i
$921$	−90.1137			−2.96935
$922$	2.50370	−	17.4136i	0.0824551	−	0.573488i
$923$	20.6181	+	45.1474i	0.678654	+	1.48604i
$924$	3.01670	+	0.885784i	0.0992422	+	0.0291402i
$925$	5.54390	+	6.39800i	0.182282	+	0.210365i
$926$	32.2427	−	9.46732i	1.05956	−	0.311116i
$927$	−9.01969	−	5.79660i	−0.296246	−	0.190385i
$928$	−0.113784	+	0.249152i	−0.00373514	+	0.00817881i
$929$	−24.9616	+	28.8072i	−0.818963	+	0.945133i	−0.999259	−	0.0384790i	$-0.987749\pi$
$929$	−24.9616	+	28.8072i	−0.818963	+	0.945133i	0.180297	+	0.983612i	$0.442294\pi$
$930$	23.6039	−	15.1693i	0.774001	−	0.497420i
$931$	−1.45389	−	10.1120i	−0.0476492	−	0.331408i
$932$	−2.12061	−	14.7491i	−0.0694628	−	0.483124i
$933$	−45.7583	+	29.4070i	−1.49806	+	0.962743i
$934$	2.65596	−	3.06514i	0.0869055	−	0.100294i
$935$	−1.57919	+	3.45795i	−0.0516451	+	0.113087i
$936$	36.4332	+	23.4142i	1.19086	+	0.765318i
$937$	−38.9443	+	11.4351i	−1.27226	+	0.373568i	−0.847042	−	0.531525i	$-0.821619\pi$
$937$	−38.9443	+	11.4351i	−1.27226	+	0.373568i	−0.425213	+	0.905093i	$0.639801\pi$
$938$	−5.05349	−	5.83204i	−0.165002	−	0.190423i
$939$	−92.1040	−	27.0442i	−3.00570	−	0.882553i
$940$	2.37890	+	5.20906i	0.0775911	+	0.169901i
$941$	−6.66893	+	46.3834i	−0.217401	+	1.51206i	0.530179	+	0.847885i	$0.322125\pi$
$941$	−6.66893	+	46.3834i	−0.217401	+	1.51206i	−0.747580	+	0.664171i	$0.768785\pi$
$942$	−17.1519			−0.558840
$943$	8.14814	−	12.3743i	0.265340	−	0.402964i
$944$	−6.50953			−0.211867
$945$	−1.03388	+	7.19077i	−0.0336320	+	0.233916i
$946$	5.24972	+	11.4953i	0.170683	+	0.373744i
$947$	−20.3315	−	5.96985i	−0.660683	−	0.193994i	−0.0658331	−	0.997831i	$-0.520970\pi$
$947$	−20.3315	−	5.96985i	−0.660683	−	0.193994i	−0.594850	+	0.803836i	$0.702789\pi$
$948$	−24.4204	−	28.1827i	−0.793138	−	0.915330i
$949$	−8.59980	+	2.52513i	−0.279161	+	0.0819692i
$950$	−1.29111	−	0.829745i	−0.0418891	−	0.0269205i
$951$	11.5536	−	25.2988i	0.374650	−	0.820369i
$952$	0.857222	−	0.989287i	0.0277827	−	0.0320630i
$953$	15.1463	−	9.73394i	0.490637	−	0.315313i	−0.271824	−	0.962347i	$-0.587627\pi$
$953$	15.1463	−	9.73394i	0.490637	−	0.315313i	0.762462	+	0.647034i	$0.223991\pi$
$954$	−10.1488	−	70.5865i	−0.328580	−	2.28532i
$955$	−1.85047	−	12.8703i	−0.0598798	−	0.416473i
$956$	11.8510	−	7.61619i	0.383289	−	0.246325i
$957$	0.962200	−	1.11044i	0.0311035	−	0.0358954i
$958$	0.0392213	−	0.0858826i	0.00126718	−	0.00277474i
$959$	5.80042	+	3.72770i	0.187305	+	0.120374i
$960$	3.02398	−	0.887921i	0.0975985	−	0.0286575i
$961$	−31.6017	−	36.4703i	−1.01941	−	1.17646i
$962$	50.7418	+	14.8992i	1.63598	+	0.480368i
$963$	−12.0797	−	26.4508i	−0.389262	−	0.852365i
$964$	−0.114663	+	0.797502i	−0.00369306	+	0.0256858i
$965$	2.25851			0.0727039
$966$	0.0984092	−	8.85823i	0.00316626	−	0.285009i
$967$	44.5708			1.43330			0.716650	−	0.697433i	$-0.245674\pi$
$967$	44.5708			1.43330			0.716650	+	0.697433i	$0.245674\pi$
$968$	1.15316	−	8.02044i	0.0370641	−	0.257787i
$969$	−4.48773	−	9.82675i	−0.144167	−	0.315681i
$970$	3.72813	+	1.09468i	0.119703	+	0.0351480i
$971$	39.4885	+	45.5721i	1.26725	+	1.46248i	0.824531	+	0.565817i	$0.191439\pi$
$971$	39.4885	+	45.5721i	1.26725	+	1.46248i	0.442714	+	0.896663i	$0.354016\pi$
$972$	−19.5572	+	5.74252i	−0.627298	+	0.184191i
$973$	7.95658	+	5.11339i	0.255076	+	0.163928i
$974$	−6.72347	+	14.7223i	−0.215434	+	0.471734i
$975$	−12.8927	+	14.8790i	−0.412897	+	0.476509i
$976$	9.85042	−	6.33048i	0.315304	−	0.202634i
$977$	−0.161337	−	1.12212i	−0.00516162	−	0.0358998i	0.987078	−	0.160241i	$-0.0512273\pi$
$977$	−0.161337	−	1.12212i	−0.00516162	−	0.0358998i	−0.992239	+	0.124342i	$0.960318\pi$
$978$	1.43992	+	10.0149i	0.0460437	+	0.320241i
$979$	−15.3886	+	9.88963i	−0.491821	+	0.316074i
$980$	−4.35907	+	5.03064i	−0.139245	+	0.160698i
$981$	57.9613	−	126.917i	1.85056	−	4.05216i
$982$	7.34787	+	4.72219i	0.234480	+	0.150691i
$983$	33.9881	−	9.97980i	1.08405	−	0.318306i	0.309553	−	0.950882i	$-0.399821\pi$
$983$	33.9881	−	9.97980i	1.08405	−	0.318306i	0.774498	+	0.632576i	$0.218002\pi$
$984$	6.37611	+	7.35842i	0.203263	+	0.234578i
$985$	5.70952	+	1.67647i	0.181920	+	0.0534166i
$986$	−0.254128	−	0.556462i	−0.00809308	−	0.0177214i
$987$	−1.50541	+	10.4703i	−0.0479176	+	0.333274i
$988$	−9.58725			−0.305011
$989$	27.1674	−	23.0173i	0.863874	−	0.731908i
$990$	−11.8003			−0.375038
$991$	3.70584	−	25.7747i	0.117720	−	0.818759i	−0.842337	−	0.538952i	$-0.818820\pi$
$991$	3.70584	−	25.7747i	0.117720	−	0.818759i	0.960056	−	0.279807i	$-0.0902705\pi$
$992$	−3.69829	−	8.09813i	−0.117421	−	0.257116i
$993$	−17.9442	−	5.26889i	−0.569442	−	0.167203i
$994$	3.04951	+	3.51932i	0.0967247	+	0.111626i
$995$	−19.7795	+	5.80780i	−0.627053	+	0.184120i
$996$	11.5203	+	7.40367i	0.365036	+	0.234594i
$997$	16.5669	−	36.2765i	0.524680	−	1.14889i	−0.442957	−	0.896543i	$-0.646070\pi$
$997$	16.5669	−	36.2765i	0.524680	−	1.14889i	0.967637	−	0.252346i	$-0.0812022\pi$
$998$	7.21965	−	8.33192i	0.228534	−	0.263742i
$999$	−88.2752	+	56.7310i	−2.79290	+	1.79489i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.g.d.31.3	✓	30
23.3	even	11	inner	230.2.g.d.141.3	yes	30
23.7	odd	22		5290.2.a.bl.1.14		15
23.16	even	11		5290.2.a.bk.1.14		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.d.31.3	✓	30	1.1	even	1	trivial
230.2.g.d.141.3	yes	30	23.3	even	11	inner
5290.2.a.bk.1.14		15	23.16	even	11
5290.2.a.bl.1.14		15	23.7	odd	22

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{2} +(1.30924 + 2.86684i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(-3.02398 + 0.887921i) q^{6} +(-0.493060 - 0.316870i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-4.54006 + 5.23951i) q^{9} +(-0.841254 + 0.540641i) q^{10} +(-0.242232 - 1.68476i) q^{11} +(-0.448526 - 3.11956i) q^{12} +(5.25515 - 3.37728i) q^{13} +(0.383815 - 0.442946i) q^{14} +(-1.30924 + 2.86684i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-2.14296 + 0.629229i) q^{17} +(-4.54006 - 5.23951i) q^{18} +(1.47258 + 0.432387i) q^{19} +(-0.415415 - 0.909632i) q^{20} +(0.262882 - 1.82838i) q^{21} +1.70208 q^{22} +(-1.29994 - 4.61629i) q^{23} +3.15164 q^{24} +(-0.142315 + 0.989821i) q^{25} +(2.59502 + 5.68230i) q^{26} +(-11.8929 - 3.49207i) q^{27} +(0.383815 + 0.442946i) q^{28} +(0.262809 - 0.0771677i) q^{29} +(-2.65133 - 1.70391i) q^{30} +(-3.69829 + 8.09813i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(4.51279 - 2.90019i) q^{33} +(-0.317850 - 2.21069i) q^{34} +(-0.0834109 - 0.580136i) q^{35} +(5.83229 - 3.74819i) q^{36} +(5.54390 - 6.39800i) q^{37} +(-0.637555 + 1.39605i) q^{38} +(16.5624 + 10.6440i) q^{39} +(0.959493 - 0.281733i) q^{40} +(2.02311 + 2.33479i) q^{41} +(1.77236 + 0.520412i) q^{42} +(3.08429 + 6.75365i) q^{43} +(-0.242232 + 1.68476i) q^{44} -6.93286 q^{45} +(4.75431 - 0.629743i) q^{46} -5.72656 q^{47} +(-0.448526 + 3.11956i) q^{48} +(-2.76520 - 6.05495i) q^{49} +(-0.959493 - 0.281733i) q^{50} +(-4.60954 - 5.31969i) q^{51} +(-5.99377 + 1.75993i) q^{52} +(8.65325 + 5.56110i) q^{53} +(5.14906 - 11.2749i) q^{54} +(1.11463 - 1.28635i) q^{55} +(-0.493060 + 0.316870i) q^{56} +(0.688372 + 4.78773i) q^{57} +(0.0389806 + 0.271116i) q^{58} +(-5.47617 + 3.51932i) q^{59} +(2.06389 - 2.38185i) q^{60} +(4.86419 - 10.6511i) q^{61} +(-7.48938 - 4.81313i) q^{62} +(3.89876 - 1.14478i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(5.99377 + 1.75993i) q^{65} +(2.22844 + 4.87959i) q^{66} +(1.87379 - 13.0325i) q^{67} +2.23343 q^{68} +(11.5322 - 9.77055i) q^{69} +0.586101 q^{70} +(-1.13073 + 7.86440i) q^{71} +(2.88001 + 6.30635i) q^{72} +(-1.37667 - 0.404227i) q^{73} +(5.54390 + 6.39800i) q^{74} +(-3.02398 + 0.887921i) q^{75} +(-1.29111 - 0.829745i) q^{76} +(-0.414415 + 0.907443i) q^{77} +(-12.8927 + 14.8790i) q^{78} +(9.95391 - 6.39699i) q^{79} +(0.142315 + 0.989821i) q^{80} +(-2.59952 - 18.0800i) q^{81} +(-2.59894 + 1.67024i) q^{82} +(-2.84544 + 3.28382i) q^{83} +(-0.767348 + 1.68026i) q^{84} +(-1.87888 - 1.20748i) q^{85} +(-7.12385 + 2.09175i) q^{86} +(0.565307 + 0.652399i) q^{87} +(-1.63314 - 0.479532i) q^{88} +(-4.46450 - 9.77589i) q^{89} +(0.986649 - 6.86229i) q^{90} -3.66127 q^{91} +(-0.0532753 + 4.79554i) q^{92} -28.0580 q^{93} +(0.814974 - 5.66827i) q^{94} +(0.637555 + 1.39605i) q^{95} +(-3.02398 - 0.887921i) q^{96} +(-2.54448 - 2.93648i) q^{97} +(6.38685 - 1.87535i) q^{98} +(9.92705 + 6.37973i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{2} - q^{3} - 3 q^{4} + 3 q^{5} - q^{6} + 8 q^{7} - 3 q^{8} + 12 q^{9} + 3 q^{10} - 3 q^{11} - q^{12} + 12 q^{13} - 3 q^{14} + q^{15} - 3 q^{16} - 26 q^{17} + 12 q^{18} - 25 q^{19} + 3 q^{20}+ \cdots + 97 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - q^3 - 3 * q^4 + 3 * q^5 - q^6 + 8 * q^7 - 3 * q^8 + 12 * q^9 + 3 * q^10 - 3 * q^11 - q^12 + 12 * q^13 - 3 * q^14 + q^15 - 3 * q^16 - 26 * q^17 + 12 * q^18 - 25 * q^19 + 3 * q^20 - 11 * q^21 - 14 * q^22 + 14 * q^23 + 10 * q^24 - 3 * q^25 - 10 * q^26 - 52 * q^27 - 3 * q^28 + 4 * q^29 + q^30 + 5 * q^31 - 3 * q^32 + 9 * q^33 + 7 * q^34 + 3 * q^35 + 12 * q^36 - 20 * q^37 + 19 * q^38 + 41 * q^39 + 3 * q^40 + 32 * q^41 + 22 * q^42 - 46 * q^43 - 3 * q^44 - 56 * q^45 + 3 * q^46 + 80 * q^47 - q^48 - 41 * q^49 - 3 * q^50 - 34 * q^51 - 21 * q^52 + 29 * q^53 + 47 * q^54 + 3 * q^55 + 8 * q^56 - 33 * q^57 - 7 * q^58 - 3 * q^59 + q^60 - q^61 - 28 * q^62 - 8 * q^63 - 3 * q^64 + 21 * q^65 - 46 * q^66 - 63 * q^67 - 4 * q^68 + 78 * q^69 - 8 * q^70 + 55 * q^71 - 32 * q^72 - 36 * q^73 - 20 * q^74 - q^75 - 3 * q^76 - 9 * q^77 - 80 * q^78 - 29 * q^79 + 3 * q^80 + 15 * q^81 - 23 * q^82 - 63 * q^83 + 4 * q^85 + 31 * q^86 + 63 * q^87 - 3 * q^88 - 95 * q^89 + 10 * q^90 - 12 * q^91 + 14 * q^92 + 126 * q^93 + 3 * q^94 - 19 * q^95 - q^96 + 11 * q^97 + 58 * q^98 + 97 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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