LMFDB - Embedded newform 384.2.v.a.13.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (of order $32$, degree $16$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			13.6
Character	$\chi$	$=$	384.13
Dual form			384.2.v.a.325.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21456 + 0.724467i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(0.950294 - 1.75981i) q^{4} +(-0.290371 - 2.94818i) q^{5} +(1.04584 + 0.951956i) q^{6} +(1.76246 - 2.63771i) q^{7} +(0.120741 + 2.82585i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})$	\(q+(-1.21456 + 0.724467i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(0.950294 - 1.75981i) q^{4} +(-0.290371 - 2.94818i) q^{5} +(1.04584 + 0.951956i) q^{6} +(1.76246 - 2.63771i) q^{7} +(0.120741 + 2.82585i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(2.48853 + 3.37037i) q^{10} +(-0.576974 + 0.308399i) q^{11} +(-1.95989 - 0.398528i) q^{12} +(1.00968 + 0.0994446i) q^{13} +(-0.229674 + 4.48049i) q^{14} +(-2.73695 + 1.13368i) q^{15} +(-2.19388 - 3.34468i) q^{16} +(-4.88892 - 2.02506i) q^{17} +(0.607374 - 1.27714i) q^{18} +(-1.37648 + 1.12965i) q^{19} +(-5.46419 - 2.29064i) q^{20} +(-3.03575 - 0.920883i) q^{21} +(0.477343 - 0.792567i) q^{22} +(-0.883122 + 4.43975i) q^{23} +(2.66912 - 0.935842i) q^{24} +(-3.70354 + 0.736680i) q^{25} +(-1.29836 + 0.610698i) q^{26} +(0.773010 + 0.634393i) q^{27} +(-2.96702 - 5.60820i) q^{28} +(2.92351 - 5.46950i) q^{29} +(2.50286 - 3.35975i) q^{30} +(-0.401871 + 0.401871i) q^{31} +(5.08770 + 2.47291i) q^{32} +(0.462607 + 0.462607i) q^{33} +(7.40495 - 1.08232i) q^{34} +(-8.28822 - 4.43014i) q^{35} +(0.187559 + 1.99119i) q^{36} +(2.94469 - 3.58812i) q^{37} +(0.853418 - 2.36923i) q^{38} +(-0.197932 - 0.995069i) q^{39} +(8.29606 - 1.17651i) q^{40} +(-3.18376 - 0.633289i) q^{41} +(4.35423 - 1.08083i) q^{42} +(1.77667 - 5.85691i) q^{43} +(-0.00557052 + 1.30844i) q^{44} +(1.87936 + 2.29000i) q^{45} +(-2.14385 - 6.03212i) q^{46} +(-4.18716 + 10.1087i) q^{47} +(-2.56381 + 3.07032i) q^{48} +(-1.17246 - 2.83056i) q^{49} +(3.96446 - 3.57784i) q^{50} +(-0.518680 + 5.26625i) q^{51} +(1.13450 - 1.68234i) q^{52} +(-6.69708 - 12.5294i) q^{53} +(-1.39846 - 0.210486i) q^{54} +(1.07675 + 1.61148i) q^{55} +(7.66657 + 4.66197i) q^{56} +(1.48057 + 0.989288i) q^{57} +(0.411708 + 8.76100i) q^{58} +(11.6902 - 1.15138i) q^{59} +(-0.605839 + 5.89384i) q^{60} +(0.684673 - 0.207693i) q^{61} +(0.196953 - 0.779238i) q^{62} +3.17235i q^{63} +(-7.97084 + 0.682391i) q^{64} -3.00559i q^{65} +(-0.897005 - 0.226718i) q^{66} +(-1.83581 + 0.556887i) q^{67} +(-8.20963 + 6.67918i) q^{68} +(4.50493 - 0.443697i) q^{69} +(13.2760 - 0.623882i) q^{70} +(4.06956 + 2.71919i) q^{71} +(-1.67035 - 2.28253i) q^{72} +(-6.01310 - 8.99924i) q^{73} +(-0.977020 + 6.49130i) q^{74} +(1.78004 + 3.33022i) q^{75} +(0.679906 + 3.49584i) q^{76} +(-0.203427 + 2.06543i) q^{77} +(0.961294 + 1.06517i) q^{78} +(6.27556 + 15.1505i) q^{79} +(-9.22369 + 7.43916i) q^{80} +(0.382683 - 0.923880i) q^{81} +(4.32565 - 1.53736i) q^{82} +(-7.62763 - 9.29430i) q^{83} +(-4.50543 + 4.46723i) q^{84} +(-4.55064 + 15.0014i) q^{85} +(2.08527 + 8.40068i) q^{86} +(-6.08263 - 1.20991i) q^{87} +(-0.941154 - 1.59321i) q^{88} +(0.275374 + 1.38440i) q^{89} +(-3.94162 - 1.41981i) q^{90} +(2.04182 - 2.48797i) q^{91} +(6.97391 + 5.77320i) q^{92} +(0.501224 + 0.267910i) q^{93} +(-2.23788 - 15.3110i) q^{94} +(3.73009 + 3.73009i) q^{95} +(0.889541 - 5.58648i) q^{96} +(6.62150 - 6.62150i) q^{97} +(3.47467 + 2.58847i) q^{98} +(0.308399 - 0.576974i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{15}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.21456	+	0.724467i	−0.858821	+	0.512276i
$2$	−1.21456	+	0.724467i	−0.858821	+	0.512276i
$3$	−0.290285	−	0.956940i	−0.167596	−	0.552490i
$3$	−0.290285	−	0.956940i	−0.167596	−	0.552490i
$4$	0.950294	−	1.75981i	0.475147	−	0.879906i
$5$	−0.290371	−	2.94818i	−0.129858	−	1.31847i	−0.810451	−	0.585806i	$-0.800778\pi$
$5$	−0.290371	−	2.94818i	−0.129858	−	1.31847i	0.680593	−	0.732661i	$-0.261722\pi$
$6$	1.04584	+	0.951956i	0.426962	+	0.388634i
$7$	1.76246	−	2.63771i	0.666148	−	0.996960i	−0.332403	−	0.943137i	$-0.607859\pi$
$7$	1.76246	−	2.63771i	0.666148	−	0.996960i	0.998550	−	0.0538229i	$-0.0171406\pi$
$8$	0.120741	+	2.82585i	0.0426884	+	0.999088i
$9$	−0.831470	+	0.555570i	−0.277157	+	0.185190i
$10$	2.48853	+	3.37037i	0.786944	+	1.06580i
$11$	−0.576974	+	0.308399i	−0.173964	+	0.0929859i	−0.556081	−	0.831128i	$-0.687695\pi$
$11$	−0.576974	+	0.308399i	−0.173964	+	0.0929859i	0.382116	+	0.924114i	$0.375195\pi$
$12$	−1.95989	−	0.398528i	−0.565772	−	0.115045i
$13$	1.00968	+	0.0994446i	0.280034	+	0.0275810i	0.237059	−	0.971495i	$-0.423816\pi$
$13$	1.00968	+	0.0994446i	0.280034	+	0.0275810i	0.0429750	+	0.999076i	$0.486316\pi$
$14$	−0.229674	+	4.48049i	−0.0613830	+	1.19746i
$15$	−2.73695	+	1.13368i	−0.706676	+	0.292715i
$16$	−2.19388	−	3.34468i	−0.548470	−	0.836170i
$17$	−4.88892	−	2.02506i	−1.18574	−	0.491148i	−0.299372	−	0.954136i	$-0.596777\pi$
$17$	−4.88892	−	2.02506i	−1.18574	−	0.491148i	−0.886365	+	0.462988i	$0.846777\pi$
$18$	0.607374	−	1.27714i	0.143159	−	0.301026i
$19$	−1.37648	+	1.12965i	−0.315785	+	0.259158i	−0.778911	−	0.627134i	$-0.784228\pi$
$19$	−1.37648	+	1.12965i	−0.315785	+	0.259158i	0.463126	+	0.886293i	$0.346728\pi$
$20$	−5.46419	−	2.29064i	−1.22183	−	0.512203i
$21$	−3.03575	−	0.920883i	−0.662454	−	0.200953i
$22$	0.477343	−	0.792567i	0.101770	−	0.168976i
$23$	−0.883122	+	4.43975i	−0.184144	+	0.925752i	0.772616	+	0.634873i	$0.218948\pi$
$23$	−0.883122	+	4.43975i	−0.184144	+	0.925752i	−0.956760	+	0.290879i	$0.906052\pi$
$24$	2.66912	−	0.935842i	0.544832	−	0.191028i
$25$	−3.70354	+	0.736680i	−0.740708	+	0.147336i
$26$	−1.29836	+	0.610698i	−0.254629	+	0.119768i
$27$	0.773010	+	0.634393i	0.148766	+	0.122089i
$28$	−2.96702	−	5.60820i	−0.560714	−	1.05985i
$29$	2.92351	−	5.46950i	0.542882	−	1.01566i	−0.449595	−	0.893232i	$-0.648432\pi$
$29$	2.92351	−	5.46950i	0.542882	−	1.01566i	0.992477	−	0.122428i	$-0.0390681\pi$
$30$	2.50286	−	3.35975i	0.456958	−	0.613403i
$31$	−0.401871	+	0.401871i	−0.0721782	+	0.0721782i	−0.742274	−	0.670096i	$-0.766253\pi$
$31$	−0.401871	+	0.401871i	−0.0721782	+	0.0721782i	0.670096	+	0.742274i	$0.266253\pi$
$32$	5.08770	+	2.47291i	0.899388	+	0.437152i
$33$	0.462607	+	0.462607i	0.0805295	+	0.0805295i
$34$	7.40495	−	1.08232i	1.26994	−	0.185616i
$35$	−8.28822	−	4.43014i	−1.40096	−	0.748831i
$36$	0.187559	+	1.99119i	0.0312598	+	0.331864i
$37$	2.94469	−	3.58812i	0.484104	−	0.589883i	−0.472479	−	0.881342i	$-0.656641\pi$
$37$	2.94469	−	3.58812i	0.484104	−	0.589883i	0.956583	+	0.291459i	$0.0941407\pi$
$38$	0.853418	−	2.36923i	0.138443	−	0.384340i
$39$	−0.197932	−	0.995069i	−0.0316944	−	0.159339i
$40$	8.29606	−	1.17651i	1.31172	−	0.186023i
$41$	−3.18376	−	0.633289i	−0.497220	−	0.0989032i	−0.0598911	−	0.998205i	$-0.519075\pi$
$41$	−3.18376	−	0.633289i	−0.497220	−	0.0989032i	−0.437329	+	0.899302i	$0.644075\pi$
$42$	4.35423	−	1.08083i	0.671873	−	0.166776i
$43$	1.77667	−	5.85691i	0.270940	−	0.893170i	−0.710873	−	0.703320i	$-0.751700\pi$
$43$	1.77667	−	5.85691i	0.270940	−	0.893170i	0.981813	−	0.189850i	$-0.0608000\pi$
$44$	−0.00557052	+	1.30844i	−0.000839788	+	0.197254i
$45$	1.87936	+	2.29000i	0.280158	+	0.341374i
$46$	−2.14385	−	6.03212i	−0.316094	−	0.889388i
$47$	−4.18716	+	10.1087i	−0.610760	+	1.47450i	0.251408	+	0.967881i	$0.419107\pi$
$47$	−4.18716	+	10.1087i	−0.610760	+	1.47450i	−0.862168	+	0.506623i	$0.830893\pi$
$48$	−2.56381	+	3.07032i	−0.370054	+	0.443163i
$49$	−1.17246	−	2.83056i	−0.167494	−	0.404366i
$50$	3.96446	−	3.57784i	0.560659	−	0.505982i
$51$	−0.518680	+	5.26625i	−0.0726297	+	0.737422i
$52$	1.13450	−	1.68234i	0.157326	−	0.233299i
$53$	−6.69708	−	12.5294i	−0.919915	−	1.72104i	−0.653064	−	0.757303i	$-0.726517\pi$
$53$	−6.69708	−	12.5294i	−0.919915	−	1.72104i	−0.266852	−	0.963738i	$-0.585983\pi$
$54$	−1.39846	−	0.210486i	−0.190307	−	0.0286435i
$55$	1.07675	+	1.61148i	0.145189	+	0.217291i
$56$	7.66657	+	4.66197i	1.02449	+	0.622982i
$57$	1.48057	+	0.989288i	0.196107	+	0.131034i
$58$	0.411708	+	8.76100i	0.0540599	+	1.15038i
$59$	11.6902	−	1.15138i	1.52193	−	0.149897i	0.697799	−	0.716293i	$-0.254163\pi$
$59$	11.6902	−	1.15138i	1.52193	−	0.149897i	0.824133	+	0.566396i	$0.191663\pi$
$60$	−0.605839	+	5.89384i	−0.0782135	+	0.760892i
$61$	0.684673	−	0.207693i	0.0876635	−	0.0265924i	−0.246148	−	0.969232i	$-0.579165\pi$
$61$	0.684673	−	0.207693i	0.0876635	−	0.0265924i	0.333812	+	0.942640i	$0.391665\pi$
$62$	0.196953	−	0.779238i	0.0250130	−	0.0989633i
$63$			3.17235i			0.399678i
$64$	−7.97084	+	0.682391i	−0.996355	+	0.0852989i
$65$		−	3.00559i		−	0.372798i
$66$	−0.897005	−	0.226718i	−0.110414	−	0.0279071i
$67$	−1.83581	+	0.556887i	−0.224280	+	0.0680346i	−0.400425	−	0.916330i	$-0.631137\pi$
$67$	−1.83581	+	0.556887i	−0.224280	+	0.0680346i	0.176145	+	0.984364i	$0.443637\pi$
$68$	−8.20963	+	6.67918i	−0.995564	+	0.809970i
$69$	4.50493	−	0.443697i	0.542330	−	0.0534149i
$70$	13.2760	−	0.623882i	1.58679	−	0.0745682i
$71$	4.06956	+	2.71919i	0.482968	+	0.322709i	0.773107	−	0.634276i	$-0.218702\pi$
$71$	4.06956	+	2.71919i	0.482968	+	0.322709i	−0.290139	+	0.956984i	$0.593702\pi$
$72$	−1.67035	−	2.28253i	−0.196853	−	0.268998i
$73$	−6.01310	−	8.99924i	−0.703780	−	1.05328i	−0.995312	−	0.0967204i	$-0.969165\pi$
$73$	−6.01310	−	8.99924i	−0.703780	−	1.05328i	0.291531	−	0.956561i	$-0.405835\pi$
$74$	−0.977020	+	6.49130i	−0.113576	+	0.754599i
$75$	1.78004	+	3.33022i	0.205541	+	0.384541i
$76$	0.679906	+	3.49584i	0.0779906	+	0.401000i
$77$	−0.203427	+	2.06543i	−0.0231827	+	0.235378i
$78$	0.961294	+	1.06517i	0.108845	+	0.120607i
$79$	6.27556	+	15.1505i	0.706056	+	1.70457i	0.709629	+	0.704576i	$0.248863\pi$
$79$	6.27556	+	15.1505i	0.706056	+	1.70457i	−0.00357294	+	0.999994i	$0.501137\pi$
$80$	−9.22369	+	7.43916i	−1.03124	+	0.831724i
$81$	0.382683	−	0.923880i	0.0425204	−	0.102653i
$82$	4.32565	−	1.53736i	0.477688	−	0.169774i
$83$	−7.62763	−	9.29430i	−0.837242	−	1.02018i	−0.999441	−	0.0334239i	$-0.989359\pi$
$83$	−7.62763	−	9.29430i	−0.837242	−	1.02018i	0.162200	−	0.986758i	$-0.448141\pi$
$84$	−4.50543	+	4.46723i	−0.491583	+	0.487415i
$85$	−4.55064	+	15.0014i	−0.493586	+	1.62714i
$86$	2.08527	+	8.40068i	0.224860	+	0.905869i
$87$	−6.08263	−	1.20991i	−0.652127	−	0.129716i
$88$	−0.941154	−	1.59321i	−0.100327	−	0.169836i
$89$	0.275374	+	1.38440i	0.0291896	+	0.146746i	0.992632	−	0.121171i	$-0.0386649\pi$
$89$	0.275374	+	1.38440i	0.0291896	+	0.146746i	−0.963442	+	0.267917i	$0.913665\pi$
$90$	−3.94162	−	1.41981i	−0.415483	−	0.149661i
$91$	2.04182	−	2.48797i	0.214041	−	0.260810i
$92$	6.97391	+	5.77320i	0.727080	+	0.601898i
$93$	0.501224	+	0.267910i	0.0519745	+	0.0277810i
$94$	−2.23788	−	15.3110i	−0.230820	−	1.57921i
$95$	3.73009	+	3.73009i	0.382699	+	0.382699i
$96$	0.889541	−	5.58648i	0.0907884	−	0.570167i
$97$	6.62150	−	6.62150i	0.672311	−	0.672311i	−0.285937	−	0.958248i	$-0.592305\pi$
$97$	6.62150	−	6.62150i	0.672311	−	0.672311i	0.958248	+	0.285937i	$0.0923049\pi$
$98$	3.47467	+	2.58847i	0.350994	+	0.261475i
$99$	0.308399	−	0.576974i	0.0309953	−	0.0579881i
$100$	−2.22304	+	7.21760i	−0.222304	+	0.721760i
$101$	10.8092	+	8.87092i	1.07556	+	0.882689i	0.993488	−	0.113937i	$-0.0363462\pi$
$101$	10.8092	+	8.87092i	1.07556	+	0.882689i	0.0820721	+	0.996626i	$0.473846\pi$
$102$	−3.18526	−	6.77192i	−0.315387	−	0.670520i
$103$	−3.30862	+	0.658125i	−0.326008	+	0.0648470i	−0.355381	−	0.934722i	$-0.615649\pi$
$103$	−3.30862	+	0.658125i	−0.326008	+	0.0648470i	0.0293733	+	0.999569i	$0.490649\pi$
$104$	−0.159106	+	2.86521i	−0.0156016	+	0.280957i
$105$	−1.83344	+	9.21733i	−0.178926	+	0.899519i
$106$	17.2111	+	10.3658i	1.67169	+	1.00682i
$107$	14.8063	+	4.49143i	1.43137	+	0.434203i	0.908384	−	0.418136i	$-0.137317\pi$
$107$	14.8063	+	4.49143i	1.43137	+	0.434203i	0.522990	+	0.852339i	$0.324817\pi$
$108$	1.85100	−	0.757493i	0.178113	−	0.0728898i
$109$	−8.50103	+	6.97662i	−0.814251	+	0.668239i	−0.946402	−	0.322991i	$-0.895312\pi$
$109$	−8.50103	+	6.97662i	−0.814251	+	0.668239i	0.132151	+	0.991230i	$0.457812\pi$
$110$	−2.47524	−	1.17716i	−0.236005	−	0.112237i
$111$	−4.28841	−	1.77632i	−0.407038	−	0.168601i
$112$	−12.6889	−	0.108045i	−1.19899	−	0.0102093i
$113$	12.8264	−	5.31285i	1.20660	−	0.499791i	0.313476	−	0.949596i	$-0.398507\pi$
$113$	12.8264	−	5.31285i	1.20660	−	0.499791i	0.893127	+	0.449805i	$0.148507\pi$
$114$	−2.51495	−	0.128918i	−0.235546	−	0.0120743i
$115$	13.3456	+	1.31443i	1.24449	+	0.122571i
$116$	−6.84710	−	10.3425i	−0.635737	−	0.960273i
$117$	−0.894765	+	0.478262i	−0.0827211	+	0.0442153i
$118$	−13.3643	+	9.86758i	−1.23028	+	0.908384i
$119$	−13.9580	+	9.32646i	−1.27953	+	0.854955i
$120$	−3.53407	−	7.59731i	−0.322615	−	0.693537i
$121$	−5.87348	+	8.79029i	−0.533953	+	0.799117i
$122$	−0.681107	+	0.748279i	−0.0616646	+	0.0677460i
$123$	0.318177	+	3.23050i	0.0286890	+	0.291285i
$124$	0.325322	+	1.08911i	0.0292148	+	0.0978053i
$125$	−1.05250	−	3.46962i	−0.0941383	−	0.310332i
$126$	−2.29826	−	3.85299i	−0.204745	−	0.343252i
$127$	11.0129			0.977238			0.488619	−	0.872497i	$-0.337501\pi$
$127$	11.0129			0.977238			0.488619	+	0.872497i	$0.337501\pi$
$128$	9.18667	−	6.60342i	0.811994	−	0.583665i
$129$	−6.12045			−0.538876
$130$	2.17745	+	3.65046i	0.190975	+	0.320167i
$131$	−2.91900	−	9.62265i	−0.255034	−	0.840735i	−0.987183	−	0.159591i	$-0.948983\pi$
$131$	−2.91900	−	9.62265i	−0.255034	−	0.840735i	0.732149	−	0.681144i	$-0.238517\pi$
$132$	1.25371	−	0.374489i	0.109122	−	0.0325950i
$133$	0.553689	+	5.62170i	0.0480110	+	0.487463i
$134$	1.82625	−	2.00636i	0.157764	−	0.173323i
$135$	1.64585	−	2.46319i	0.141652	−	0.211997i
$136$	5.13221	−	14.0599i	0.440083	−	1.20562i
$137$	15.5376	−	10.3819i	1.32747	−	0.886986i	0.329112	−	0.944291i	$-0.393251\pi$
$137$	15.5376	−	10.3819i	1.32747	−	0.886986i	0.998357	+	0.0573048i	$0.0182507\pi$
$138$	−5.15005	+	3.80257i	−0.438402	+	0.323696i
$139$	−11.8568	+	6.33757i	−1.00568	+	0.537546i	−0.890106	−	0.455754i	$-0.849370\pi$
$139$	−11.8568	+	6.33757i	−1.00568	+	0.537546i	−0.115571	+	0.993299i	$0.536870\pi$
$140$	−15.6725	+	10.3758i	−1.32457	+	0.876913i
$141$	10.8889	+	1.07246i	0.917010	+	0.0903176i
$142$	−6.91268	−	0.354350i	−0.580099	−	0.0297364i
$143$	−0.613227	+	0.254007i	−0.0512806	+	0.0212411i
$144$	3.68235	+	1.56214i	0.306863	+	0.130179i
$145$	−16.9740	−	7.03086i	−1.40961	−	0.583881i
$146$	13.8229	+	6.57379i	1.14399	+	0.544051i
$147$	−2.36833	+	1.94364i	−0.195337	+	0.160309i
$148$	−3.51609	−	8.59187i	−0.289021	−	0.706248i
$149$	21.6614	+	6.57092i	1.77457	+	0.538311i	0.996009	−	0.0892549i	$-0.0284486\pi$
$149$	21.6614	+	6.57092i	1.77457	+	0.538311i	0.778564	+	0.627566i	$0.215949\pi$
$150$	−4.57460	−	2.75516i	−0.373514	−	0.224958i
$151$	2.45738	−	12.3541i	0.199978	−	1.00536i	−0.742182	−	0.670198i	$-0.766209\pi$
$151$	2.45738	−	12.3541i	0.199978	−	1.00536i	0.942161	−	0.335161i	$-0.108791\pi$
$152$	−3.35840	−	3.75332i	−0.272403	−	0.304435i
$153$	5.19005	−	1.03236i	0.419591	−	0.0834617i
$154$	−1.24926	−	2.65596i	−0.100669	−	0.214023i
$155$	1.30148	+	1.06810i	0.104538	+	0.0857917i
$156$	−1.93923	−	0.597286i	−0.155263	−	0.0478212i
$157$	8.64730	−	16.1780i	0.690130	−	1.29114i	−0.255787	−	0.966733i	$-0.582335\pi$
$157$	8.64730	−	16.1780i	0.690130	−	1.29114i	0.945917	−	0.324409i	$-0.105165\pi$
$158$	−18.5981	−	13.8548i	−1.47959	−	1.10222i
$159$	−10.0458	+	10.0458i	−0.796683	+	0.796683i
$160$	5.81326	−	15.7175i	0.459579	−	1.24258i
$161$	10.1543	+	10.1543i	0.800271	+	0.800271i
$162$	0.204530	+	1.39935i	0.0160694	+	0.109943i
$163$	−3.08678	−	1.64992i	−0.241775	−	0.129231i	0.346060	−	0.938212i	$-0.387519\pi$
$163$	−3.08678	−	1.64992i	−0.241775	−	0.129231i	−0.587835	+	0.808981i	$0.700019\pi$
$164$	−4.13998	+	5.00101i	−0.323278	+	0.390513i
$165$	1.22952	−	1.49818i	0.0957181	−	0.116633i
$166$	15.9976	+	5.76248i	1.24166	+	0.447255i
$167$	−1.22398	−	6.15336i	−0.0947144	−	0.476162i	−0.998807	−	0.0488256i	$-0.984452\pi$
$167$	−1.22398	−	6.15336i	−0.0947144	−	0.476162i	0.904093	−	0.427336i	$-0.140548\pi$
$168$	2.23574	−	8.68975i	0.172491	−	0.670429i
$169$	−11.7406	−	2.33536i	−0.903127	−	0.179643i
$170$	−5.34105	−	21.5169i	−0.409640	−	1.65027i
$171$	0.516901	−	1.70400i	0.0395284	−	0.130308i
$172$	−8.61870	−	8.69240i	−0.657169	−	0.662789i
$173$	−1.47862	−	1.80170i	−0.112417	−	0.136981i	0.713762	−	0.700389i	$-0.246990\pi$
$173$	−1.47862	−	1.80170i	−0.112417	−	0.136981i	−0.826179	+	0.563408i	$0.809490\pi$
$174$	8.26424	−	2.93716i	0.626511	−	0.222666i
$175$	−4.58420	+	11.0672i	−0.346533	+	0.836605i
$176$	2.29731	+	1.25320i	0.173166	+	0.0944637i
$177$	−4.49529	−	10.8526i	−0.337886	−	0.815730i
$178$	−1.33741	−	1.48193i	−0.100243	−	0.111075i
$179$	1.65254	−	16.7785i	0.123517	−	1.25409i	−0.711035	−	0.703156i	$-0.751773\pi$
$179$	1.65254	−	16.7785i	0.123517	−	1.25409i	0.834552	−	0.550929i	$-0.185727\pi$
$180$	5.81592	−	1.13114i	0.433493	−	0.0843102i
$181$	−0.298823	−	0.559059i	−0.0222114	−	0.0415545i	0.870571	−	0.492043i	$-0.163750\pi$
$181$	−0.298823	−	0.559059i	−0.0222114	−	0.0415545i	−0.892782	+	0.450489i	$0.851250\pi$
$182$	−0.677458	+	4.50102i	−0.0502165	+	0.333638i
$183$	−0.397500	−	0.594901i	−0.0293841	−	0.0439764i
$184$	−12.6527	−	1.95951i	−0.932769	−	0.144457i
$185$	−11.4335	−	7.63961i	−0.840606	−	0.561675i
$186$	−0.802857	+	0.0377288i	−0.0588683	+	0.00276641i
$187$	3.44531	−	0.339333i	0.251946	−	0.0248145i
$188$	13.8104	+	16.9748i	1.00723	+	1.23802i
$189$	3.03575	−	0.920883i	0.220818	−	0.0669844i
$190$	−7.23273	−	1.82808i	−0.524718	−	0.132623i
$191$		−	14.0628i		−	1.01755i	−0.860899	−	0.508776i	$-0.830098\pi$
$191$		−	14.0628i		−	1.01755i	0.860899	−	0.508776i	$-0.169902\pi$
$192$	2.96682	+	7.42953i	0.214112	+	0.536180i
$193$			2.82423i			0.203293i	0.994821	+	0.101646i	$0.0324110\pi$
$193$			2.82423i			0.203293i	−0.994821	+	0.101646i	$0.967589\pi$
$194$	−3.24512	+	12.8392i	−0.232986	+	0.921803i
$195$	−2.87617	+	0.872478i	−0.205967	+	0.0624794i
$196$	−6.09544	−	0.626562i	−0.435389	−	0.0447544i
$197$	8.04767	−	0.792627i	0.573373	−	0.0564723i	0.192824	−	0.981233i	$-0.438235\pi$
$197$	8.04767	−	0.792627i	0.573373	−	0.0564723i	0.380548	+	0.924761i	$0.375735\pi$
$198$	0.0434308	+	0.924193i	0.00308650	+	0.0656795i
$199$	16.2657	+	10.8684i	1.15304	+	0.770439i	0.976852	−	0.213917i	$-0.0686221\pi$
$199$	16.2657	+	10.8684i	1.15304	+	0.770439i	0.176192	+	0.984356i	$0.443622\pi$
$200$	−2.52892	−	10.3767i	−0.178821	−	0.733744i
$201$	1.06582	+	1.59511i	0.0751769	+	0.112510i
$202$	−19.5551	−	2.94329i	−1.37589	−	0.207089i
$203$	−9.27438	−	17.3511i	−0.650934	−	1.21781i
$204$	8.77471	+	5.91726i	0.614352	+	0.414291i
$205$	−0.942582	+	9.57020i	−0.0658328	+	0.668411i
$206$	3.54171	−	3.19631i	0.246763	−	0.222698i
$207$	−1.73231	−	4.18215i	−0.120404	−	0.290680i
$208$	−1.88250	−	3.59522i	−0.130528	−	0.249284i
$209$	0.445810	−	1.07628i	0.0308373	−	0.0744479i
$210$	−4.45084	−	12.5232i	−0.307137	−	0.864185i
$211$	13.6755	+	16.6637i	0.941461	+	1.14717i	0.988942	+	0.148301i	$0.0473805\pi$
$211$	13.6755	+	16.6637i	0.941461	+	1.14717i	−0.0474813	+	0.998872i	$0.515119\pi$
$212$	−28.4135	−	0.120967i	−1.95145	−	0.00830808i
$213$	1.42077	−	4.68367i	0.0973499	−	0.320919i
$214$	−21.2369	+	5.27155i	−1.45173	+	0.360356i
$215$	−17.7831	−	3.53728i	−1.21280	−	0.241241i
$216$	−1.69937	+	2.26101i	−0.115627	+	0.153842i
$217$	0.351737	+	1.76830i	0.0238775	+	0.120040i
$218$	5.27065	−	14.6322i	0.356974	−	0.991019i
$219$	−6.86623	+	8.36652i	−0.463977	+	0.565357i
$220$	3.85913	−	0.363509i	0.260182	−	0.0245078i
$221$	−4.73485	−	2.53083i	−0.318501	−	0.170242i
$222$	6.49540	−	0.949376i	0.435943	−	0.0637179i
$223$	−12.5496	−	12.5496i	−0.840382	−	0.840382i	0.148527	−	0.988908i	$-0.452547\pi$
$223$	−12.5496	−	12.5496i	−0.840382	−	0.840382i	−0.988908	+	0.148527i	$0.952547\pi$
$224$	15.4897	−	9.06148i	1.03495	−	0.605446i
$225$	2.67011	−	2.67011i	0.178007	−	0.178007i
$226$	−11.7293	+	15.7450i	−0.780225	+	1.04734i
$227$	−3.31689	+	6.20546i	−0.220150	+	0.411871i	−0.967615	−	0.252430i	$-0.918770\pi$
$227$	−3.31689	+	6.20546i	−0.220150	+	0.411871i	0.747466	+	0.664300i	$0.231270\pi$
$228$	3.14794	−	1.66542i	0.208478	−	0.110295i
$229$	19.1930	+	15.7513i	1.26831	+	1.04087i	0.996922	+	0.0784033i	$0.0249822\pi$
$229$	19.1930	+	15.7513i	1.26831	+	1.04087i	0.271387	+	0.962470i	$0.412518\pi$
$230$	−17.1613	+	8.07203i	−1.13158	+	0.532254i
$231$	2.03555	−	0.404896i	0.133929	−	0.0266402i
$232$	15.8090	+	7.60100i	1.03791	+	0.499030i
$233$	−1.39671	+	7.02173i	−0.0915014	+	0.460009i	0.907684	+	0.419654i	$0.137849\pi$
$233$	−1.39671	+	7.02173i	−0.0915014	+	0.460009i	−0.999185	+	0.0403543i	$0.987151\pi$
$234$	0.740258	−	1.22910i	0.0483922	−	0.0803491i
$235$	31.0181	+	9.40924i	2.02340	+	0.613791i
$236$	9.08290	−	21.6667i	0.591246	−	1.41038i
$237$	12.6765	−	10.4033i	0.823425	−	0.675767i
$238$	10.1961	−	21.4397i	0.660915	−	1.38973i
$239$	21.1640	+	8.76641i	1.36898	+	0.567052i	0.941513	−	0.336977i	$-0.109404\pi$
$239$	21.1640	+	8.76641i	1.36898	+	0.567052i	0.427471	+	0.904029i	$0.359404\pi$
$240$	9.79633	+	6.66705i	0.632350	+	0.430356i
$241$	−1.25038	+	0.517925i	−0.0805442	+	0.0333625i	−0.422592	−	0.906320i	$-0.638880\pi$
$241$	−1.25038	+	0.517925i	−0.0805442	+	0.0333625i	0.342048	+	0.939683i	$0.388880\pi$
$242$	0.765399	−	14.9314i	0.0492017	−	0.959830i
$243$	−0.995185	−	0.0980171i	−0.0638411	−	0.00628780i
$244$	0.285140	−	1.40227i	0.0182542	−	0.0897709i
$245$	−8.00457	+	4.27853i	−0.511393	+	0.273345i
$246$	−2.72684	−	3.69312i	−0.173857	−	0.235465i
$247$	−1.50214	+	1.00370i	−0.0955786	+	0.0638636i
$248$	−1.18415	−	1.08711i	−0.0751936	−	0.0690313i
$249$	−6.67990	+	9.99718i	−0.423322	+	0.633546i
$250$	3.79194	+	3.45155i	0.239824	+	0.218295i
$251$	−0.682889	−	6.93349i	−0.0431036	−	0.437638i	−0.992382	−	0.123201i	$-0.960684\pi$
$251$	−0.682889	−	6.93349i	−0.0431036	−	0.437638i	0.949278	−	0.314437i	$-0.101816\pi$
$252$	5.58273	+	3.01466i	0.351679	+	0.189906i
$253$	−0.859678	−	2.83398i	−0.0540475	−	0.178171i
$254$	−13.3758	+	7.97850i	−0.839273	+	0.500616i
$255$	15.6765			0.981698
$256$	−6.37377	+	14.6757i	−0.398360	+	0.917229i
$257$	0.253588			0.0158184			0.00790920	−	0.999969i	$-0.497482\pi$
$257$	0.253588			0.0158184			0.00790920	+	0.999969i	$0.497482\pi$
$258$	7.43363	−	4.43407i	0.462798	−	0.276053i
$259$	−4.27451	−	14.0912i	−0.265605	−	0.875582i
$260$	−5.28928	−	2.85620i	−0.328027	−	0.177134i
$261$	0.607883	+	6.17194i	0.0376270	+	0.382033i
$262$	10.5166	+	9.57253i	0.649717	+	0.591393i
$263$	5.03327	−	7.53282i	0.310365	−	0.464494i	−0.643193	−	0.765704i	$-0.722391\pi$
$263$	5.03327	−	7.53282i	0.310365	−	0.464494i	0.953558	+	0.301210i	$0.0973907\pi$
$264$	−1.25140	+	1.36311i	−0.0770184	+	0.0838937i
$265$	−34.9942	+	23.3824i	−2.14968	+	1.43637i
$266$	−4.74523	−	6.42674i	−0.290948	−	0.394049i
$267$	1.24485	−	0.665386i	0.0761835	−	0.0407209i
$268$	−0.764544	+	3.75989i	−0.0467019	+	0.229672i
$269$	−16.0205	−	1.57788i	−0.976786	−	0.0962050i	−0.402991	−	0.915204i	$-0.632029\pi$
$269$	−16.0205	−	1.57788i	−0.976786	−	0.0962050i	−0.573795	+	0.818999i	$0.694529\pi$
$270$	−0.214478	+	4.18404i	−0.0130527	+	0.254633i
$271$	4.74410	−	1.96507i	0.288183	−	0.119370i	−0.233909	−	0.972259i	$-0.575152\pi$
$271$	4.74410	−	1.96507i	0.288183	−	0.119370i	0.522092	+	0.852889i	$0.325152\pi$
$272$	3.95254	+	20.7946i	0.239658	+	1.26086i
$273$	−2.97355	−	1.23168i	−0.179967	−	0.0745450i
$274$	−11.3500	+	23.8659i	−0.685676	+	1.44179i
$275$	1.90966	−	1.56722i	0.115157	−	0.0945066i
$276$	3.50019	−	8.34948i	0.210687	−	0.502580i
$277$	15.5471	+	4.71617i	0.934137	+	0.283367i	0.720428	−	0.693530i	$-0.243946\pi$
$277$	15.5471	+	4.71617i	0.934137	+	0.283367i	0.213709	+	0.976897i	$0.431446\pi$
$278$	9.80934	−	16.2872i	0.588325	−	0.976840i
$279$	0.110876	−	0.557412i	0.00663798	−	0.0333714i
$280$	11.5182	−	23.9561i	0.688344	−	1.43165i
$281$	−16.7113	+	3.32409i	−0.996913	+	0.198298i	−0.666473	−	0.745529i	$-0.732197\pi$
$281$	−16.7113	+	3.32409i	−0.996913	+	0.198298i	−0.330440	+	0.943827i	$0.607197\pi$
$282$	−14.0021	+	6.58608i	−0.833815	+	0.392195i
$283$	−19.9768	−	16.3945i	−1.18750	−	0.974552i	−0.187525	−	0.982260i	$-0.560047\pi$
$283$	−19.9768	−	16.3945i	−1.18750	−	0.974552i	−0.999970	+	0.00770732i	$0.997547\pi$
$284$	8.65255	−	4.57763i	0.513434	−	0.271632i
$285$	2.48669	−	4.65226i	0.147299	−	0.275576i
$286$	0.560779	−	0.752769i	0.0331596	−	0.0445122i
$287$	−7.28169	+	7.28169i	−0.429824	+	0.429824i
$288$	−5.60414	+	0.770430i	−0.330227	+	0.0453981i
$289$	7.77985	+	7.77985i	0.457638	+	0.457638i
$290$	25.7095	−	3.75773i	1.50971	−	0.220661i
$291$	−8.25849	−	4.41426i	−0.484122	−	0.258768i
$292$	−21.5512	+	2.03000i	−1.26119	+	0.118797i
$293$	−17.7812	+	21.6664i	−1.03879	+	1.26577i	−0.0755417	+	0.997143i	$0.524069\pi$
$293$	−17.7812	+	21.6664i	−1.03879	+	1.26577i	−0.963245	+	0.268623i	$0.913431\pi$
$294$	1.46837	−	4.07644i	0.0856371	−	0.237743i
$295$	−6.78897	−	34.1305i	−0.395269	−	1.98715i
$296$	10.4950	+	7.88802i	0.610011	+	0.458482i
$297$	−0.641654	−	0.127633i	−0.0372325	−	0.00740601i
$298$	−31.0694	+	7.71224i	−1.79980	+	0.446758i
$299$	−1.33318	+	4.39490i	−0.0770997	+	0.254164i
$300$	7.55213	+	0.0321523i	0.436022	+	0.00185632i
$301$	−12.3175	−	15.0089i	−0.709969	−	0.865100i
$302$	5.96549	+	16.7850i	0.343276	+	0.965868i
$303$	5.35118	−	12.9189i	0.307417	−	0.742171i
$304$	6.79813	+	2.12557i	0.389899	+	0.121910i
$305$	−0.811127	−	1.95823i	−0.0464450	−	0.112128i
$306$	−5.55569	+	5.01389i	−0.317598	+	0.286625i
$307$	−1.85138	+	18.7974i	−0.105664	+	1.07283i	0.785413	+	0.618973i	$0.212451\pi$
$307$	−1.85138	+	18.7974i	−0.105664	+	1.07283i	−0.891077	+	0.453853i	$0.850049\pi$
$308$	3.44146	+	2.32076i	0.196095	+	0.132238i
$309$	1.59023	+	2.97510i	0.0904648	+	0.169248i
$310$	−2.35453	−	0.354385i	−0.133728	−	0.0201277i
$311$	13.0912	+	19.5923i	0.742332	+	1.11098i	0.989853	+	0.142095i	$0.0453840\pi$
$311$	13.0912	+	19.5923i	0.742332	+	1.11098i	−0.247521	+	0.968882i	$0.579616\pi$
$312$	2.78802	−	0.679470i	0.157840	−	0.0384674i
$313$	−9.83238	−	6.56978i	−0.555759	−	0.371346i	0.245746	−	0.969334i	$-0.420967\pi$
$313$	−9.83238	−	6.56978i	−0.555759	−	0.371346i	−0.801505	+	0.597988i	$0.795967\pi$
$314$	1.21777	+	25.9137i	0.0687228	+	1.46240i
$315$	9.35266	−	0.921156i	0.526963	−	0.0519013i
$316$	32.6258	+	3.35366i	1.83534	+	0.188658i
$317$	−11.4320	+	3.46786i	−0.642085	+	0.194774i	−0.594504	−	0.804093i	$-0.702651\pi$
$317$	−11.4320	+	3.46786i	−0.642085	+	0.194774i	−0.0475817	+	0.998867i	$0.515151\pi$
$318$	4.92333	−	19.4790i	0.276087	−	1.09233i
$319$			4.05737i			0.227169i
$320$	4.32631	+	23.3014i	0.241848	+	1.30259i
$321$		−	15.4725i		−	0.863590i
$322$	−19.6894	−	4.97651i	−1.09725	−	0.277330i
$323$	9.01708	−	2.73530i	0.501724	−	0.152196i
$324$	−1.26219	−	1.55141i	−0.0701218	−	0.0861894i
$325$	−3.81265	+	0.375513i	−0.211488	+	0.0208297i
$326$	4.94438	−	0.232352i	0.273844	−	0.0128688i
$327$	9.14393	+	6.10978i	0.505660	+	0.337871i
$328$	1.40517	−	9.07329i	0.0775875	−	0.500989i
$329$	19.2841	+	28.8607i	1.06317	+	1.59114i
$330$	−0.407943	+	2.71037i	−0.0224565	+	0.149201i
$331$	1.09149	+	2.04203i	0.0599936	+	0.112240i	0.910131	−	0.414321i	$-0.135981\pi$
$331$	1.09149	+	2.04203i	0.0599936	+	0.112240i	−0.850137	+	0.526561i	$0.823481\pi$
$332$	−23.6047	+	4.59089i	−1.29548	+	0.251958i
$333$	−0.454971	+	4.61939i	−0.0249322	+	0.253141i
$334$	5.94450	+	6.58687i	0.325269	+	0.360418i
$335$	2.17487	+	5.25061i	0.118826	+	0.286871i
$336$	3.58001	+	12.1739i	0.195305	+	0.664141i
$337$	−11.6485	+	28.1221i	−0.634537	+	1.53191i	0.199325	+	0.979933i	$0.436125\pi$
$337$	−11.6485	+	28.1221i	−0.634537	+	1.53191i	−0.833861	+	0.551974i	$0.813875\pi$
$338$	15.9516	−	5.66929i	0.867651	−	0.308369i
$339$	−8.80738	−	10.7318i	−0.478351	−	0.582873i
$340$	22.0753	+	22.2641i	1.19720	+	1.20744i
$341$	0.107933	−	0.355806i	0.00584488	−	0.0192680i
$342$	0.606683	+	2.44408i	0.0328057	+	0.132161i
$343$	12.2471	+	2.43610i	0.661282	+	0.131537i
$344$	16.7652	+	4.31344i	0.903922	+	0.232565i
$345$	−2.61620	−	13.1525i	−0.140852	−	0.708109i
$346$	3.10114	+	1.11706i	0.166718	+	0.0600533i
$347$	−14.8354	+	18.0770i	−0.796407	+	0.970425i	−0.999963	−	0.00863858i	$-0.997250\pi$
$347$	−14.8354	+	18.0770i	−0.796407	+	0.970425i	0.203556	+	0.979063i	$0.434750\pi$
$348$	−7.90951	+	9.55453i	−0.423994	+	0.512176i
$349$	−23.4959	−	12.5588i	−1.25771	−	0.672259i	−0.298352	−	0.954456i	$-0.596437\pi$
$349$	−23.4959	−	12.5588i	−1.25771	−	0.672259i	−0.959357	+	0.282197i	$0.908937\pi$
$350$	−2.45008	−	16.7629i	−0.130962	−	0.896014i
$351$	0.717405	+	0.717405i	0.0382922	+	0.0382922i
$352$	−3.69812	+	0.142240i	−0.197110	+	0.00758144i
$353$	24.6381	−	24.6381i	1.31135	−	1.31135i	0.390937	−	0.920417i	$-0.372151\pi$
$353$	24.6381	−	24.6381i	1.31135	−	1.31135i	0.920417	−	0.390937i	$-0.127849\pi$
$354$	13.3221	+	9.92438i	0.708063	+	0.527475i
$355$	6.83500	−	12.7874i	0.362764	−	0.678684i
$356$	2.69797	+	0.830979i	0.142992	+	0.0440418i
$357$	12.9767	+	10.6497i	0.686798	+	0.563641i
$358$	10.1484	+	21.5757i	0.536359	+	1.14031i
$359$	7.85120	−	1.56170i	0.414371	−	0.0824234i	0.0164975	−	0.999864i	$-0.494748\pi$
$359$	7.85120	−	1.56170i	0.414371	−	0.0824234i	0.397873	+	0.917440i	$0.369748\pi$
$360$	−6.24429	+	5.58728i	−0.329103	+	0.294475i
$361$	−3.08813	+	15.5251i	−0.162533	+	0.817108i
$362$	0.767958	+	0.462521i	0.0403630	+	0.0243096i
$363$	10.1168	+	3.06889i	0.530992	+	0.161075i
$364$	−2.43803	−	5.95753i	−0.127787	−	0.312260i
$365$	−24.7854	+	20.3408i	−1.29733	+	1.06469i
$366$	0.913773	+	0.434565i	0.0477637	+	0.0227151i
$367$	−0.262817	−	0.108863i	−0.0137190	−	0.00568258i	0.375813	−	0.926695i	$-0.377363\pi$
$367$	−0.262817	−	0.108863i	−0.0137190	−	0.00568258i	−0.389532	+	0.921013i	$0.627363\pi$
$368$	16.7870	−	6.78653i	0.875083	−	0.353772i
$369$	2.99904	−	1.24224i	0.156124	−	0.0646685i
$370$	19.4212	+	0.995551i	1.00966	+	0.0517562i
$371$	−44.8522	−	4.41755i	−2.32861	−	0.229348i
$372$	0.947781	−	0.627467i	0.0491402	−	0.0325327i
$373$	7.75334	−	4.14424i	0.401453	−	0.214581i	−0.258298	−	0.966065i	$-0.583162\pi$
$373$	7.75334	−	4.14424i	0.401453	−	0.214581i	0.659751	+	0.751484i	$0.270662\pi$
$374$	−3.93868	+	2.90815i	−0.203664	+	0.150377i
$375$	−3.01470	+	2.01436i	−0.155678	+	0.104021i
$376$	−29.0712	−	10.6117i	−1.49923	−	0.547259i
$377$	3.49572	−	5.23171i	0.180039	−	0.269447i
$378$	−3.01993	+	3.31776i	−0.155329	+	0.170647i
$379$	−3.19555	−	32.4450i	−0.164145	−	1.66659i	−0.626144	−	0.779708i	$-0.715368\pi$
$379$	−3.19555	−	32.4450i	−0.164145	−	1.66659i	0.461999	−	0.886880i	$-0.347132\pi$
$380$	10.1089	−	3.01958i	0.518578	−	0.154901i
$381$	−3.19688	−	10.5387i	−0.163781	−	0.539914i
$382$	10.1881	+	17.0801i	0.521267	+	0.873895i
$383$	−16.4983			−0.843025			−0.421513	−	0.906822i	$-0.638501\pi$
$383$	−16.4983			−0.843025			−0.421513	+	0.906822i	$0.638501\pi$
$384$	−8.98583	−	6.87422i	−0.458556	−	0.350799i
$385$	6.14834			0.313349
$386$	−2.04606	−	3.43019i	−0.104142	−	0.174592i
$387$	1.77667	+	5.85691i	0.0903134	+	0.297723i
$388$	−5.36022	−	17.9450i	−0.272124	−	0.911017i
$389$	2.55609	+	25.9524i	0.129599	+	1.31584i	0.811481	+	0.584379i	$0.198662\pi$
$389$	2.55609	+	25.9524i	0.129599	+	1.31584i	−0.681882	+	0.731462i	$0.738838\pi$
$390$	2.86119	−	3.14337i	0.144882	−	0.159171i
$391$	13.3083	−	19.9172i	0.673027	−	1.00726i
$392$	7.85718	−	3.65495i	0.396847	−	0.184603i
$393$	−8.36096	+	5.58662i	−0.421755	+	0.281807i
$394$	−9.20012	+	6.79296i	−0.463495	+	0.342225i
$395$	42.8443	−	22.9008i	2.15573	−	1.15226i
$396$	−0.722297	−	1.09102i	−0.0362968	−	0.0548258i
$397$	7.19242	+	0.708392i	0.360977	+	0.0355532i	0.276880	−	0.960904i	$-0.410699\pi$
$397$	7.19242	+	0.708392i	0.360977	+	0.0355532i	0.0840970	+	0.996458i	$0.473199\pi$
$398$	−27.6294	−	1.41631i	−1.38494	−	0.0709930i
$399$	5.21891	−	2.16174i	0.261272	−	0.108222i
$400$	10.5891	+	10.7710i	0.529455	+	0.538549i
$401$	−0.230519	−	0.0954843i	−0.0115116	−	0.00476826i	0.376920	−	0.926246i	$-0.376983\pi$
$401$	−0.230519	−	0.0954843i	−0.0115116	−	0.00476826i	−0.388432	+	0.921477i	$0.626983\pi$
$402$	−2.45010	−	1.16520i	−0.122200	−	0.0581148i
$403$	−0.445725	+	0.365797i	−0.0222031	+	0.0182216i
$404$	25.8831	−	10.5923i	1.28773	−	0.526985i
$405$	−2.83489	−	0.859953i	−0.140867	−	0.0427314i
$406$	23.8346	+	14.3550i	1.18289	+	0.712425i
$407$	−0.592439	+	2.97839i	−0.0293661	+	0.147633i
$408$	−14.9442	−	0.829860i	−0.739850	−	0.0410842i
$409$	7.18305	−	1.42880i	0.355179	−	0.0706495i	−0.0142760	−	0.999898i	$-0.504544\pi$
$409$	7.18305	−	1.42880i	0.355179	−	0.0706495i	0.369455	+	0.929249i	$0.379544\pi$
$410$	−5.78848	−	12.3064i	−0.285872	−	0.607770i
$411$	−14.4452	−	11.8549i	−0.712529	−	0.584758i
$412$	−1.98598	+	6.44796i	−0.0978423	+	0.317668i
$413$	17.5665	−	32.8646i	0.864390	−	1.61716i
$414$	5.13382	+	3.82446i	0.252313	+	0.187962i
$415$	−25.1865	+	25.1865i	−1.23635	+	1.23635i
$416$	4.89103	+	3.00279i	0.239802	+	0.147224i
$417$	9.50651	+	9.50651i	0.465536	+	0.465536i
$418$	0.238269	+	1.63018i	0.0116541	+	0.0797347i
$419$	−7.23065	−	3.86486i	−0.353240	−	0.188811i	0.285227	−	0.958460i	$-0.407931\pi$
$419$	−7.23065	−	3.86486i	−0.353240	−	0.188811i	−0.638467	+	0.769649i	$0.720431\pi$
$420$	14.4785	+	11.9857i	0.706477	+	0.584842i
$421$	21.4666	−	26.1572i	1.04622	−	1.27482i	0.0857868	−	0.996314i	$-0.472660\pi$
$421$	21.4666	−	26.1572i	1.04622	−	1.27482i	0.960433	−	0.278510i	$-0.0898404\pi$
$422$	−28.6820	−	10.3315i	−1.39622	−	0.502929i
$423$	−2.13459	−	10.7313i	−0.103788	−	0.521775i
$424$	34.5975	−	20.4378i	1.68020	−	0.992545i
$425$	19.5981	+	3.89831i	0.950649	+	0.189096i
$426$	1.66755	+	6.71788i	0.0807932	+	0.325482i
$427$	0.658875	−	2.17202i	0.0318852	−	0.105111i
$428$	21.9744	−	21.7881i	1.06217	−	1.05317i
$429$	0.421080	+	0.513088i	0.0203299	+	0.0247721i
$430$	24.1613	−	8.58706i	1.16516	−	0.414105i
$431$	−8.08090	+	19.5090i	−0.389243	+	0.939716i	0.600857	+	0.799356i	$0.294826\pi$
$431$	−8.08090	+	19.5090i	−0.389243	+	0.939716i	−0.990101	+	0.140360i	$0.955174\pi$
$432$	0.425949	−	3.97726i	0.0204935	−	0.191356i
$433$	12.7608	+	30.8073i	0.613245	+	1.48050i	0.859416	+	0.511277i	$0.170828\pi$
$433$	12.7608	+	30.8073i	0.613245	+	1.48050i	−0.246171	+	0.969226i	$0.579172\pi$
$434$	−1.70828	−	1.89288i	−0.0820001	−	0.0908612i
$435$	−1.80082	+	18.2840i	−0.0863428	+	0.876653i
$436$	4.19906	+	21.5901i	0.201098	+	1.03398i
$437$	−3.79975	−	7.10883i	−0.181767	−	0.340061i
$438$	2.27815	−	15.1360i	0.108854	−	0.723225i
$439$	−12.7917	−	19.1441i	−0.610512	−	0.913696i	0.389461	−	0.921043i	$-0.372661\pi$
$439$	−12.7917	−	19.1441i	−0.610512	−	0.913696i	−0.999973	+	0.00734689i	$0.997661\pi$
$440$	−4.42378	+	3.23732i	−0.210895	+	0.154333i
$441$	2.54744	+	1.70214i	0.121307	+	0.0810545i
$442$	7.58425	−	0.356409i	0.360746	−	0.0169526i
$443$	−22.5332	+	2.21933i	−1.07059	+	0.105444i	−0.617924	−	0.786238i	$-0.712026\pi$
$443$	−22.5332	+	2.21933i	−1.07059	+	0.105444i	−0.452663	+	0.891682i	$0.649526\pi$
$444$	−7.20124	+	5.85878i	−0.341756	+	0.278045i
$445$	4.00150	−	1.21384i	0.189689	−	0.0575416i
$446$	24.3339	+	6.15041i	1.15224	+	0.291230i
$447$		−	22.6361i		−	1.07065i
$448$	−12.2484	+	22.2275i	−0.578680	+	1.05015i
$449$		−	9.45781i		−	0.446341i	−0.974779	−	0.223171i	$-0.928359\pi$
$449$		−	9.45781i		−	0.446341i	0.974779	−	0.223171i	$-0.0716407\pi$
$450$	−1.30859	+	5.17740i	−0.0616875	+	0.244065i
$451$	2.03225	−	0.616478i	0.0956951	−	0.0290288i
$452$	2.83919	−	27.6208i	0.133544	−	1.29917i
$453$	−12.5354	+	1.23463i	−0.588966	+	0.0580081i
$454$	−0.467106	−	9.93986i	−0.0219224	−	0.466501i
$455$	−7.92788	−	5.29724i	−0.371665	−	0.248338i
$456$	−2.61681	+	4.30332i	−0.122543	+	0.201522i
$457$	−10.8785	−	16.2808i	−0.508874	−	0.761584i	0.484711	−	0.874675i	$-0.338925\pi$
$457$	−10.8785	−	16.2808i	−0.508874	−	0.761584i	−0.993585	+	0.113091i	$0.963925\pi$
$458$	−34.7223	−	5.22612i	−1.62246	−	0.244201i
$459$	−2.49450	−	4.66689i	−0.116433	−	0.217832i
$460$	14.9954	−	22.2367i	0.699165	−	1.03679i
$461$	−1.21629	+	12.3492i	−0.0566481	+	0.575157i	0.924404	+	0.381414i	$0.124563\pi$
$461$	−1.21629	+	12.3492i	−0.0566481	+	0.575157i	−0.981052	+	0.193743i	$0.937937\pi$
$462$	−2.17895	+	1.96646i	−0.101374	+	0.0914878i
$463$	−5.32027	−	12.8443i	−0.247254	−	0.596923i	0.750715	−	0.660626i	$-0.229709\pi$
$463$	−5.32027	−	12.8443i	−0.247254	−	0.596923i	−0.997969	+	0.0637026i	$0.979709\pi$
$464$	−24.7076	+	2.22124i	−1.14702	+	0.103118i
$465$	0.644306	−	1.55549i	0.0298790	−	0.0721343i
$466$	−3.39063	−	9.54015i	−0.157068	−	0.441939i
$467$	0.333883	+	0.406838i	0.0154503	+	0.0188262i	0.780678	−	0.624933i	$-0.214874\pi$
$467$	0.333883	+	0.406838i	0.0154503	+	0.0188262i	−0.765228	+	0.643759i	$0.777374\pi$
$468$	−0.00863871	+	2.02911i	−0.000399324	+	0.0937956i
$469$	−1.76664	+	5.82383i	−0.0815758	+	0.268919i
$470$	−44.4899	+	11.0436i	−2.05217	+	0.509401i
$471$	−17.9915	−	3.57874i	−0.829005	−	0.164899i
$472$	4.66512	+	32.8957i	0.214729	+	1.51415i
$473$	0.781171	+	3.92721i	0.0359183	+	0.180573i
$474$	−7.85943	+	21.8191i	−0.360995	+	1.00218i
$475$	4.26565	−	5.19771i	0.195722	−	0.238487i
$476$	3.14859	+	33.4264i	0.144315	+	1.53210i
$477$	12.5294	+	6.69708i	0.573680	+	0.306638i
$478$	−32.0558	+	4.68532i	−1.46620	+	0.214301i
$479$	4.33276	+	4.33276i	0.197969	+	0.197969i	0.799129	−	0.601160i	$-0.205295\pi$
$479$	4.33276	+	4.33276i	0.197969	+	0.197969i	−0.601160	+	0.799129i	$0.705295\pi$
$480$	−16.7283	−	1.00038i	−0.763537	−	0.0456610i
$481$	3.33001	−	3.33001i	0.151835	−	0.151835i
$482$	1.14344	−	1.53491i	0.0520822	−	0.0699132i
$483$	6.76943	−	12.6647i	0.308020	−	0.576264i
$484$	9.88773	+	18.6896i	0.449442	+	0.849527i
$485$	−21.4441	−	17.5987i	−0.973725	−	0.799115i
$486$	1.27972	−	0.601931i	0.0580492	−	0.0273042i
$487$	4.71559	−	0.937989i	0.213684	−	0.0425044i	−0.0870874	−	0.996201i	$-0.527756\pi$
$487$	4.71559	−	0.937989i	0.213684	−	0.0425044i	0.300771	+	0.953696i	$0.402756\pi$
$488$	0.669578	+	1.90971i	0.0303104	+	0.0864484i
$489$	−0.682828	+	3.43281i	−0.0308785	+	0.155237i
$490$	6.62234	−	10.9956i	0.299167	−	0.496729i
$491$	10.0160	+	3.03833i	0.452017	+	0.137118i	0.508081	−	0.861309i	$-0.330355\pi$
$491$	10.0160	+	3.03833i	0.452017	+	0.137118i	−0.0560642	+	0.998427i	$0.517855\pi$
$492$	5.98744	+	2.51000i	0.269935	+	0.113159i
$493$	−25.3688	+	20.8197i	−1.14256	+	0.937671i
$494$	1.09728	−	2.30729i	0.0493692	−	0.103810i
$495$	−1.79058	−	0.741681i	−0.0804804	−	0.0333361i
$496$	2.22579	+	0.462473i	0.0999409	+	0.0207656i
$497$	14.3449	−	5.94184i	0.643456	−	0.266528i
$498$	0.870488	−	16.9815i	0.0390075	−	0.760960i
$499$	−10.7459	−	1.05838i	−0.481051	−	0.0473794i	−0.145414	−	0.989371i	$-0.546452\pi$
$499$	−10.7459	−	1.05838i	−0.481051	−	0.0473794i	−0.335637	+	0.941991i	$0.608952\pi$
$500$	−7.10606	−	1.44496i	−0.317793	−	0.0646206i
$501$	−5.53310	+	2.95750i	−0.247201	+	0.132131i
$502$	5.85249	+	7.92638i	0.261210	+	0.353772i
$503$	−12.6661	+	8.46321i	−0.564753	+	0.377356i	−0.804927	−	0.593374i	$-0.797796\pi$
$503$	−12.6661	+	8.46321i	−0.564753	+	0.377356i	0.240174	+	0.970730i	$0.422796\pi$
$504$	−8.96457	+	0.383032i	−0.399314	+	0.0170616i
$505$	23.0144	−	34.4435i	1.02413	−	1.53272i
$506$	3.09725	+	2.81922i	0.137690	+	0.125329i
$507$	1.17333	+	11.9130i	0.0521094	+	0.529076i
$508$	10.4655	−	19.3807i	0.464332	−	0.859878i
$509$	−3.69411	−	12.1778i	−0.163738	−	0.539773i	0.836224	−	0.548387i	$-0.184758\pi$
$509$	−3.69411	−	12.1778i	−0.163738	−	0.539773i	−0.999963	+	0.00861402i	$0.997258\pi$
$510$	−19.0400	+	11.3571i	−0.843103	+	0.502900i
$511$	−34.3352			−1.51890
$512$	−2.89074	−	22.4420i	−0.127754	−	0.991806i
$513$	−1.78067			−0.0786185
$514$	−0.307997	+	0.183716i	−0.0135852	+	0.00810338i
$515$	2.90100	+	9.56331i	0.127833	+	0.421410i
$516$	−5.81623	+	10.7708i	−0.256045	+	0.474160i
$517$	−0.701631	−	7.12377i	−0.0308577	−	0.313303i
$518$	15.4002	+	14.0178i	0.676646	+	0.615905i
$519$	−1.29490	+	1.93795i	−0.0568398	+	0.0850668i
$520$	8.49335	−	0.362898i	0.372458	−	0.0159141i
$521$	10.1327	−	6.77045i	0.443921	−	0.296619i	−0.313448	−	0.949605i	$-0.601484\pi$
$521$	10.1327	−	6.77045i	0.443921	−	0.296619i	0.757369	+	0.652987i	$0.226484\pi$
$522$	−5.20967	−	7.05577i	−0.228021	−	0.308823i
$523$	−25.6646	+	13.7180i	−1.12223	+	0.599846i	−0.924794	−	0.380469i	$-0.875763\pi$
$523$	−25.6646	+	13.7180i	−1.12223	+	0.599846i	−0.197439	+	0.980315i	$0.563263\pi$
$524$	−19.7080	−	4.00746i	−0.860947	−	0.175067i
$525$	11.9214	+	1.17416i	0.520293	+	0.0512444i
$526$	−0.655908	+	12.7955i	−0.0285989	+	0.557909i
$527$	2.77853	−	1.15090i	0.121035	−	0.0501342i
$528$	0.532367	−	2.56217i	0.0231683	−	0.111504i
$529$	2.31774	+	0.960039i	0.100771	+	0.0417408i
$530$	25.5627	−	53.7514i	1.11037	−	2.33481i
$531$	−9.08036	+	7.45206i	−0.394054	+	0.323392i
$532$	10.4193	+	4.36788i	0.451734	+	0.189372i
$533$	−3.15160	−	0.956026i	−0.136511	−	0.0414101i
$534$	−1.02989	+	1.71000i	−0.0445677	+	0.0739990i
$535$	8.94225	−	44.9557i	0.386607	−	1.94361i
$536$	−1.79534	−	5.12049i	−0.0775468	−	0.221171i
$537$	−16.5358	+	3.28917i	−0.713570	+	0.141938i
$538$	20.6009	−	9.68989i	0.888168	−	0.417761i
$539$	1.54942	+	1.27158i	0.0667383	+	0.0547707i
$540$	−2.77071	−	5.23714i	−0.119232	−	0.225370i
$541$	−16.3460	+	30.5812i	−0.702769	+	1.31479i	0.236508	+	0.971630i	$0.423997\pi$
$541$	−16.3460	+	30.5812i	−0.702769	+	1.31479i	−0.939277	+	0.343159i	$0.888503\pi$
$542$	−4.33835	+	5.82363i	−0.186348	+	0.250146i
$543$	−0.448243	+	0.448243i	−0.0192359	+	0.0192359i
$544$	−19.8656	−	22.3927i	−0.851730	−	0.960080i
$545$	23.0368	+	23.0368i	0.986788	+	0.986788i
$546$	4.50386	−	0.658289i	0.192747	−	0.0281722i
$547$	−7.38004	−	3.94471i	−0.315548	−	0.168664i	0.306018	−	0.952026i	$-0.401003\pi$
$547$	−7.38004	−	3.94471i	−0.315548	−	0.168664i	−0.621566	+	0.783362i	$0.713503\pi$
$548$	−3.50490	−	37.2092i	−0.149722	−	1.58950i
$549$	−0.453897	+	0.553075i	−0.0193718	+	0.0236047i
$550$	−1.18399	+	3.28696i	−0.0504855	+	0.140156i
$551$	2.15445	+	10.8312i	0.0917828	+	0.461423i
$552$	1.79775	+	12.6767i	0.0765174	+	0.539556i
$553$	51.0232	+	10.1491i	2.16973	+	0.431585i
$554$	−22.2996	+	5.53533i	−0.947419	+	0.235174i
$555$	−3.99168	+	13.1588i	−0.169438	+	0.558561i
$556$	−0.114474	+	26.8882i	−0.00485476	+	1.14032i
$557$	3.69825	+	4.50633i	0.156700	+	0.190939i	0.845442	−	0.534067i	$-0.179337\pi$
$557$	3.69825	+	4.50633i	0.156700	+	0.190939i	−0.688742	+	0.725006i	$0.741837\pi$
$558$	0.269161	+	0.757334i	0.0113945	+	0.0320605i
$559$	2.37631	−	5.73691i	0.100507	−	0.242645i
$560$	3.36595	+	37.4406i	0.142238	+	1.58216i
$561$	−1.32484	−	3.19845i	−0.0559348	−	0.135039i
$562$	17.8886	−	16.1441i	0.754586	−	0.680997i
$563$	−2.35912	+	23.9526i	−0.0994251	+	1.00948i	0.807976	+	0.589215i	$0.200563\pi$
$563$	−2.35912	+	23.9526i	−0.0994251	+	1.00948i	−0.907401	+	0.420265i	$0.861937\pi$
$564$	12.2350	−	18.1432i	0.515185	−	0.763968i
$565$	−19.3877	−	36.2718i	−0.815645	−	1.52596i
$566$	36.1402	+	5.43954i	1.51909	+	0.228641i
$567$	−1.76246	−	2.63771i	−0.0740164	−	0.110773i
$568$	−7.19266	+	11.8283i	−0.301798	+	0.496303i
$569$	−18.8715	−	12.6095i	−0.791133	−	0.528618i	0.0931043	−	0.995656i	$-0.470321\pi$
$569$	−18.8715	−	12.6095i	−0.791133	−	0.528618i	−0.884237	+	0.467038i	$0.845321\pi$
$570$	0.350192	+	7.45196i	0.0146679	+	0.312128i
$571$	−0.125664	+	0.0123768i	−0.00525887	+	0.000517954i	−0.100646	−	0.994922i	$-0.532091\pi$
$571$	−0.125664	+	0.0123768i	−0.00525887	+	0.000517954i	0.0953874	+	0.995440i	$0.469591\pi$
$572$	−0.135741	+	1.32055i	−0.00567564	+	0.0552148i
$573$	−13.4573	+	4.08223i	−0.562187	+	0.170538i
$574$	3.56867	−	14.1194i	0.148954	−	0.589331i
$575$		−	17.0934i		−	0.712843i
$576$	6.24840	−	4.99575i	0.260350	−	0.208156i
$577$		−	36.9136i		−	1.53673i	−0.640011	−	0.768366i	$-0.721070\pi$
$577$		−	36.9136i		−	1.53673i	0.640011	−	0.768366i	$-0.278930\pi$
$578$	−15.0853	−	3.81282i	−0.627467	−	0.158592i
$579$	2.70262	−	0.819831i	0.112317	−	0.0340710i
$580$	−28.5033	+	23.1897i	−1.18353	+	0.962898i
$581$	−37.9591	+	3.73864i	−1.57481	+	0.155105i
$582$	13.2284	−	0.621645i	0.548334	−	0.0257680i
$583$	7.72809	+	5.16375i	0.320065	+	0.213861i
$584$	24.7045	−	18.0787i	1.02228	−	0.748102i
$585$	1.66982	+	2.49906i	0.0690385	+	0.103323i
$586$	5.89962	−	39.1970i	0.243711	−	1.61921i
$587$	12.9113	+	24.1553i	0.532906	+	0.996996i	0.993972	+	0.109631i	$0.0349668\pi$
$587$	12.9113	+	24.1553i	0.532906	+	0.996996i	−0.461067	+	0.887365i	$0.652533\pi$
$588$	1.16983	+	6.01485i	0.0482430	+	0.248048i
$589$	0.0991945	−	1.00714i	0.00408724	−	0.0414984i
$590$	32.9720	+	36.5350i	1.35744	+	1.50412i
$591$	−3.09461	−	7.47105i	−0.127295	−	0.307318i
$592$	−18.4614	−	1.97715i	−0.758759	−	0.0812602i
$593$	−1.21276	+	2.92787i	−0.0498023	+	0.120233i	−0.946823	−	0.321756i	$-0.895727\pi$
$593$	−1.21276	+	2.92787i	−0.0498023	+	0.120233i	0.897020	+	0.441989i	$0.145727\pi$
$594$	0.871790	−	0.309840i	0.0357700	−	0.0127129i
$595$	31.5491	+	38.4427i	1.29339	+	1.57600i
$596$	32.1483	−	31.8757i	1.31685	−	1.30568i
$597$	5.67872	−	18.7202i	0.232414	−	0.766167i
$598$	−1.56474	−	6.30370i	−0.0639870	−	0.257777i
$599$	23.2064	+	4.61605i	0.948189	+	0.188607i	0.644878	−	0.764285i	$-0.276908\pi$
$599$	23.2064	+	4.61605i	0.948189	+	0.188607i	0.303311	+	0.952892i	$0.401908\pi$
$600$	−9.19578	+	5.43222i	−0.375416	+	0.221769i
$601$	−4.97315	−	25.0017i	−0.202859	−	1.01984i	−0.939237	−	0.343271i	$-0.888465\pi$
$601$	−4.97315	−	25.0017i	−0.202859	−	1.01984i	0.736377	−	0.676571i	$-0.236535\pi$
$602$	25.8338	+	9.30555i	1.05291	+	0.379266i
$603$	1.21703	−	1.48296i	0.0495614	−	0.0603907i
$604$	−19.4056	−	16.0645i	−0.789603	−	0.653656i
$605$	27.6209	+	14.7637i	1.12295	+	0.600228i
$606$	2.86001	+	19.5675i	0.116180	+	0.794875i
$607$	11.5310	+	11.5310i	0.468028	+	0.468028i	0.901275	−	0.433247i	$-0.142632\pi$
$607$	11.5310	+	11.5310i	0.468028	+	0.468028i	−0.433247	+	0.901275i	$0.642632\pi$
$608$	−9.79661	+	2.34340i	−0.397305	+	0.0950375i
$609$	−13.9118	+	13.9118i	−0.563735	+	0.563735i
$610$	2.40384	+	1.79075i	0.0973285	+	0.0725054i
$611$	−5.23294	+	9.79014i	−0.211702	+	0.396067i
$612$	3.11530	−	10.1146i	0.125929	−	0.408857i
$613$	2.70350	+	2.21871i	0.109194	+	0.0896128i	0.687406	−	0.726274i	$-0.258749\pi$
$613$	2.70350	+	2.21871i	0.109194	+	0.0896128i	−0.578212	+	0.815886i	$0.696249\pi$
$614$	−11.3695	−	24.1718i	−0.458836	−	0.975494i
$615$	9.43172	−	1.87609i	0.380324	−	0.0756511i
$616$	−5.86116	−	0.325473i	−0.236153	−	0.0131137i
$617$	−9.33419	+	46.9261i	−0.375780	+	1.88917i	0.0761069	+	0.997100i	$0.475751\pi$
$617$	−9.33419	+	46.9261i	−0.375780	+	1.88917i	−0.451887	+	0.892075i	$0.649249\pi$
$618$	−4.08679	−	2.46137i	−0.164395	−	0.0990106i
$619$	37.4804	+	11.3695i	1.50646	+	0.456981i	0.932277	−	0.361744i	$-0.117819\pi$
$619$	37.4804	+	11.3695i	1.50646	+	0.456981i	0.574186	+	0.818725i	$0.305319\pi$
$620$	3.11644	−	1.27536i	0.125159	−	0.0512195i
$621$	−3.49921	+	2.87173i	−0.140418	+	0.115238i
$622$	−30.0939	−	14.3118i	−1.20666	−	0.573853i
$623$	4.13697	+	1.71359i	0.165744	+	0.0686535i
$624$	−2.89395	+	2.84508i	−0.115851	+	0.113894i
$625$	−27.3668	+	11.3357i	−1.09467	+	0.453427i
$626$	16.7016	+	0.856137i	0.667529	+	0.0342181i
$627$	−1.15935	−	0.114186i	−0.0462999	−	0.00456014i
$628$	−20.2527	−	30.5914i	−0.808171	−	1.22073i
$629$	−21.6625	+	11.5788i	−0.863740	+	0.461679i
$630$	−10.6920	+	7.89449i	−0.425979	+	0.314524i
$631$	4.49365	−	3.00256i	0.178889	−	0.119530i	−0.462902	−	0.886410i	$-0.653192\pi$
$631$	4.49365	−	3.00256i	0.178889	−	0.119530i	0.641791	+	0.766880i	$0.278192\pi$
$632$	−42.0554	+	19.5631i	−1.67288	+	0.778177i
$633$	11.9763	−	17.9239i	0.476017	−	0.712409i
$634$	11.3725	−	12.4940i	0.451658	−	0.496201i
$635$	−3.19783	−	32.4681i	−0.126902	−	1.28846i
$636$	8.13226	+	27.2252i	0.322465	+	1.07955i
$637$	−0.902321	−	2.97455i	−0.0357512	−	0.117856i
$638$	−2.93943	−	4.92790i	−0.116373	−	0.195098i
$639$	−4.89442			−0.193620
$640$	−22.1356	−	25.1665i	−0.874987	−	0.994795i
$641$	−8.57425			−0.338662			−0.169331	−	0.985559i	$-0.554161\pi$
$641$	−8.57425			−0.338662			−0.169331	+	0.985559i	$0.554161\pi$
$642$	11.2093	+	18.7922i	0.442396	+	0.741669i
$643$	4.05599	+	13.3708i	0.159953	+	0.527293i	0.999881	−	0.0154036i	$-0.00490330\pi$
$643$	4.05599	+	13.3708i	0.159953	+	0.527293i	−0.839929	+	0.542697i	$0.817403\pi$
$644$	27.5193	−	8.22010i	1.08441	−	0.323917i
$645$	1.77720	+	18.0442i	0.0699772	+	0.710490i
$646$	−8.97011	+	9.85476i	−0.352924	+	0.387730i
$647$	−3.96703	+	5.93708i	−0.155960	+	0.233411i	−0.901219	−	0.433365i	$-0.857326\pi$
$647$	−3.96703	+	5.93708i	−0.155960	+	0.233411i	0.745258	+	0.666776i	$0.232326\pi$
$648$	2.65695	+	0.969855i	0.104375	+	0.0380995i
$649$	−6.38985	+	4.26956i	−0.250824	+	0.167595i
$650$	4.35863	−	3.21822i	0.170959	−	0.126229i
$651$	1.59006	−	0.849903i	0.0623192	−	0.0333103i
$652$	−5.83689	+	3.86424i	−0.228590	+	0.151335i
$653$	−16.6236	−	1.63728i	−0.650531	−	0.0640718i	−0.232632	−	0.972565i	$-0.574734\pi$
$653$	−16.6236	−	1.63728i	−0.650531	−	0.0640718i	−0.417900	+	0.908493i	$0.637234\pi$
$654$	−15.5321	−	0.796192i	−0.607355	−	0.0311336i
$655$	−27.5217	+	11.3999i	−1.07536	+	0.445430i
$656$	4.86664	+	12.0380i	0.190011	+	0.470006i
$657$	9.99942	+	4.14190i	0.390115	+	0.161591i
$658$	−44.3302	−	21.0822i	−1.72817	−	0.821871i
$659$	2.14435	−	1.75982i	0.0835321	−	0.0685530i	−0.591701	−	0.806158i	$-0.701543\pi$
$659$	2.14435	−	1.75982i	0.0835321	−	0.0685530i	0.675233	+	0.737605i	$0.264043\pi$
$660$	−1.46810	−	3.58744i	−0.0571458	−	0.139641i
$661$	−6.80298	−	2.06366i	−0.264605	−	0.0802672i	0.155194	−	0.987884i	$-0.450400\pi$
$661$	−6.80298	−	2.06366i	−0.264605	−	0.0802672i	−0.419800	+	0.907617i	$0.637900\pi$
$662$	−2.80506	−	1.68941i	−0.109022	−	0.0656609i
$663$	−1.04740	+	5.26564i	−0.0406776	+	0.204500i
$664$	25.3433	−	22.6767i	0.983511	−	0.880028i
$665$	16.4130	−	3.26475i	0.636470	−	0.126602i
$666$	−2.79401	−	5.94012i	−0.108266	−	0.230175i
$667$	21.7014	+	17.8099i	0.840282	+	0.689601i
$668$	−11.9919	−	3.69353i	−0.463981	−	0.142907i
$669$	−8.36625	+	15.6521i	−0.323458	+	0.605147i
$670$	−6.44540	−	4.80153i	−0.249007	−	0.185499i
$671$	−0.330987	+	0.330987i	−0.0127776	+	0.0127776i
$672$	−13.1677	−	12.1923i	−0.507956	−	0.470328i
$673$	14.8652	+	14.8652i	0.573013	+	0.573013i	0.932969	−	0.359956i	$-0.117208\pi$
$673$	14.8652	+	14.8652i	0.573013	+	0.573013i	−0.359956	+	0.932969i	$0.617208\pi$
$674$	−6.22571	−	42.5948i	−0.239805	−	1.64069i
$675$	−3.33022	−	1.78004i	−0.128180	−	0.0685138i
$676$	−15.2669	+	18.4421i	−0.587187	+	0.709310i
$677$	−1.95874	+	2.38673i	−0.0752805	+	0.0917296i	−0.809289	−	0.587411i	$-0.800147\pi$
$677$	−1.95874	+	2.38673i	−0.0752805	+	0.0917296i	0.734008	+	0.679140i	$0.237647\pi$
$678$	18.4719	+	6.65374i	0.709409	+	0.255536i
$679$	−5.79545	−	29.1357i	−0.222409	−	1.11813i
$680$	−42.9413	−	11.0481i	−1.64672	−	0.423676i
$681$	6.90110	+	1.37271i	0.264451	+	0.0526025i
$682$	0.126680	+	0.510340i	0.00485082	+	0.0195419i
$683$	3.68349	−	12.1429i	0.140945	−	0.464633i	−0.857840	−	0.513917i	$-0.828194\pi$
$683$	3.68349	−	12.1429i	0.140945	−	0.464633i	0.998785	+	0.0492838i	$0.0156939\pi$
$684$	−2.50750	−	2.52895i	−0.0958768	−	0.0966967i
$685$	−35.1194	−	42.7932i	−1.34184	−	1.63504i
$686$	−16.6397	+	5.91385i	−0.635307	+	0.225792i
$687$	9.50160	−	22.9389i	0.362509	−	0.875174i
$688$	−23.4873	+	6.90696i	−0.895444	+	0.263325i
$689$	−5.51592	−	13.3166i	−0.210140	−	0.507323i
$690$	12.7061	+	14.0791i	0.483713	+	0.535984i
$691$	−0.831045	+	8.43774i	−0.0316144	+	0.320987i	0.966351	+	0.257227i	$0.0828090\pi$
$691$	−0.831045	+	8.43774i	−0.0316144	+	0.320987i	−0.997965	+	0.0637592i	$0.979691\pi$
$692$	−4.57578	+	0.889944i	−0.173945	+	0.0338306i
$693$	−0.978349	−	1.83036i	−0.0371644	−	0.0695297i
$694$	4.92225	−	32.7033i	0.186846	−	1.24140i
$695$	22.1272	+	33.1157i	0.839332	+	1.25615i
$696$	2.68460	−	17.3347i	0.101760	−	0.657070i
$697$	14.2827	+	9.54339i	0.540996	+	0.361482i
$698$	37.6356	−	1.76862i	1.42453	−	0.0669432i
$699$	7.12482	−	0.701733i	0.269485	−	0.0265420i
$700$	15.1199	+	18.5845i	0.571480	+	0.702427i
$701$	−17.3202	+	5.25402i	−0.654175	+	0.198442i	−0.599888	−	0.800084i	$-0.704788\pi$
$701$	−17.3202	+	5.25402i	−0.654175	+	0.198442i	−0.0542862	+	0.998525i	$0.517288\pi$
$702$	−1.39107	−	0.351592i	−0.0525024	−	0.0132700i
$703$			8.26542i			0.311736i
$704$	4.38852	−	2.85192i	0.165399	−	0.107486i
$705$		−	32.4138i		−	1.22078i
$706$	−12.0749	+	47.7739i	−0.454444	+	1.79799i
$707$	42.4498	−	12.8770i	1.59649	−	0.484289i
$708$	−23.3704	−	2.40228i	−0.878312	−	0.0902833i
$709$	44.8732	−	4.41962i	1.68525	−	0.165982i	0.790472	−	0.612498i	$-0.209835\pi$
$709$	44.8732	−	4.41962i	1.68525	−	0.165982i	0.894776	+	0.446516i	$0.147335\pi$
$710$	0.962550	+	20.4827i	0.0361239	+	0.768703i
$711$	−13.6351	−	9.11070i	−0.511357	−	0.341678i
$712$	−3.87885	+	0.945318i	−0.145366	+	0.0354273i
$713$	−1.42931	−	2.13911i	−0.0535280	−	0.0801103i
$714$	−23.4762	−	3.53346i	−0.878576	−	0.132236i
$715$	0.926923	+	1.73415i	0.0346649	+	0.0648535i
$716$	−27.9567	−	18.8527i	−1.04479	−	0.704558i
$717$	2.24535	−	22.7974i	0.0838541	−	0.851385i
$718$	−8.40433	+	7.58471i	−0.313647	+	0.283059i
$719$	9.42695	+	22.7587i	0.351566	+	0.848755i	0.996427	+	0.0844557i	$0.0269151\pi$
$719$	9.42695	+	22.7587i	0.351566	+	0.848755i	−0.644861	+	0.764300i	$0.723085\pi$
$720$	3.53624	−	11.3098i	0.131788	−	0.421493i
$721$	−4.09537	+	9.88709i	−0.152519	+	0.368214i
$722$	−7.49669	−	21.0933i	−0.278998	−	0.785012i
$723$	0.858590	+	1.04619i	0.0319313	+	0.0389084i
$724$	−1.26781	−	0.00539756i	−0.0471178	−	0.000200599i
$725$	−6.79806	+	22.4102i	−0.252474	+	0.832294i
$726$	−14.5107	+	3.60193i	−0.538542	+	0.133680i
$727$	7.68933	+	1.52950i	0.285182	+	0.0567261i	0.335608	−	0.942002i	$-0.391058\pi$
$727$	7.68933	+	1.52950i	0.285182	+	0.0567261i	−0.0504268	+	0.998728i	$0.516058\pi$
$728$	7.27716	+	5.46949i	0.269710	+	0.202713i
$729$	0.195090	+	0.980785i	0.00722557	+	0.0363254i
$730$	15.3670	−	42.6613i	0.568757	−	1.57897i
$731$	−20.5466	+	25.0361i	−0.759943	+	0.925993i
$732$	−1.42466	+	0.134195i	−0.0526569	+	0.00495999i
$733$	41.6040	+	22.2378i	1.53668	+	0.821371i	0.999752	−	0.0222590i	$-0.00708586\pi$
$733$	41.6040	+	22.2378i	1.53668	+	0.821371i	0.536925	+	0.843630i	$0.319586\pi$
$734$	0.398074	−	0.0581830i	0.0146932	−	0.00214757i
$735$	6.41790	+	6.41790i	0.236728	+	0.236728i
$736$	−15.4722	+	20.4043i	−0.570311	+	0.752111i
$737$	0.887473	−	0.887473i	0.0326905	−	0.0326905i
$738$	−2.74254	+	3.68148i	−0.100954	+	0.135517i
$739$	3.56605	−	6.67160i	0.131179	−	0.245419i	−0.807753	−	0.589521i	$-0.799317\pi$
$739$	3.56605	−	6.67160i	0.131179	−	0.245419i	0.938932	+	0.344102i	$0.111817\pi$
$740$	−24.3094	+	12.8609i	−0.893633	+	0.472776i
$741$	1.39652	+	1.14610i	0.0513026	+	0.0421029i
$742$	57.6759	−	27.1286i	2.11735	−	0.995921i
$743$	−2.85794	+	0.568479i	−0.104847	+	0.0208555i	−0.247235	−	0.968956i	$-0.579522\pi$
$743$	−2.85794	+	0.568479i	−0.104847	+	0.0208555i	0.142388	+	0.989811i	$0.454522\pi$
$744$	−0.696554	+	1.44873i	−0.0255369	+	0.0531130i
$745$	13.0824	−	65.7698i	0.479303	−	2.40962i
$746$	−6.41449	+	10.6505i	−0.234851	+	0.389941i
$747$	11.5058	+	3.49024i	0.420975	+	0.127701i
$748$	2.67689	−	6.38556i	0.0978769	−	0.233479i
$749$	37.9425	−	31.1386i	1.38639	−	1.13778i
$750$	2.20218	−	4.63060i	0.0804124	−	0.169085i
$751$	43.3312	+	17.9484i	1.58118	+	0.654945i	0.988600	−	0.150567i	$-0.0481100\pi$
$751$	43.3312	+	17.9484i	1.58118	+	0.654945i	0.592578	+	0.805513i	$0.298110\pi$
$752$	42.9965	−	8.17258i	1.56792	−	0.298023i
$753$	−6.43670	+	2.66617i	−0.234567	+	0.0971607i
$754$	−0.455542	+	8.88674i	−0.0165899	+	0.323636i
$755$	−37.1356	−	3.65754i	−1.35150	−	0.133111i
$756$	1.26427	−	6.21745i	0.0459810	−	0.226127i
$757$	14.3415	−	7.66570i	0.521251	−	0.278614i	−0.189717	−	0.981839i	$-0.560757\pi$
$757$	14.3415	−	7.66570i	0.521251	−	0.278614i	0.710968	+	0.703224i	$0.248257\pi$
$758$	27.3865	+	37.0912i	0.994723	+	1.34721i
$759$	−2.46240	+	1.64532i	−0.0893793	+	0.0597213i
$760$	−10.0903	+	10.9910i	−0.366014	+	0.398687i
$761$	−3.55898	+	5.32639i	−0.129013	+	0.193081i	−0.890352	−	0.455272i	$-0.849542\pi$
$761$	−3.55898	+	5.32639i	−0.129013	+	0.193081i	0.761340	+	0.648353i	$0.224542\pi$
$762$	11.5177	+	10.4838i	0.417244	+	0.379789i
$763$	3.41955	+	34.7193i	0.123796	+	1.25692i
$764$	−24.7480	−	13.3638i	−0.895350	−	0.483487i
$765$	−4.55064	−	15.0014i	−0.164529	−	0.542378i
$766$	20.0382	−	11.9525i	0.724008	−	0.431861i
$767$	11.9178			0.430328
$768$	15.8939	+	1.83919i	0.573523	+	0.0663662i
$769$	20.1815			0.727762			0.363881	−	0.931445i	$-0.381451\pi$
$769$	20.1815			0.727762			0.363881	+	0.931445i	$0.381451\pi$
$770$	−7.46751	+	4.45427i	−0.269110	+	0.160521i
$771$	−0.0736128	−	0.242669i	−0.00265110	−	0.00873951i
$772$	4.97012	+	2.68385i	0.178878	+	0.0965939i
$773$	−3.30883	−	33.5951i	−0.119010	−	1.20833i	−0.850313	−	0.526278i	$-0.823587\pi$
$773$	−3.30883	−	33.5951i	−0.119010	−	1.20833i	0.731303	−	0.682053i	$-0.238913\pi$
$774$	−6.40101	−	5.82640i	−0.230079	−	0.209426i
$775$	1.19230	−	1.78440i	0.0428286	−	0.0640975i
$776$	19.5108	+	17.9119i	0.700398	+	0.642998i
$777$	−12.2436	+	8.18089i	−0.439236	+	0.293488i
$778$	−21.9062	−	29.6689i	−0.785376	−	1.06368i
$779$	5.09776	−	2.72481i	0.182646	−	0.0976265i
$780$	−1.19781	+	5.89064i	−0.0428886	+	0.210919i
$781$	−3.18663	−	0.313856i	−0.114027	−	0.0112306i
$782$	−1.73426	+	33.8320i	−0.0620169	+	1.20983i
$783$	5.72972	−	2.37333i	0.204763	−	0.0848158i
$784$	−6.89509	+	10.1314i	−0.246253	+	0.361836i
$785$	−50.2065	−	20.7962i	−1.79195	−	0.742249i
$786$	6.10754	−	12.8425i	0.217849	−	0.458077i
$787$	4.01964	−	3.29883i	0.143285	−	0.117591i	−0.560020	−	0.828479i	$-0.689207\pi$
$787$	4.01964	−	3.29883i	0.143285	−	0.117591i	0.703305	+	0.710888i	$0.251707\pi$
$788$	6.25278	−	14.9156i	0.222746	−	0.531347i
$789$	−8.66954	−	2.62988i	−0.308644	−	0.0936261i
$790$	−35.4460	+	58.8536i	−1.26111	+	2.09392i
$791$	8.59220	−	43.1959i	0.305503	−	1.53587i
$792$	1.66768	+	0.801825i	0.0592584	+	0.0284916i
$793$	0.711954	−	0.141616i	0.0252822	−	0.00502895i
$794$	−9.24881	+	4.35029i	−0.328228	+	0.154386i
$795$	32.5338	+	26.6998i	1.15386	+	0.946946i
$796$	34.5835	−	18.2964i	1.22578	−	0.648499i
$797$	11.4642	−	21.4480i	0.406082	−	0.759726i	−0.592879	−	0.805291i	$-0.702009\pi$
$797$	11.4642	−	21.4480i	0.406082	−	0.759726i	0.998961	+	0.0455650i	$0.0145088\pi$
$798$	−4.77254	+	6.40648i	−0.168946	+	0.226787i
$799$	40.9413	−	40.9413i	1.44840	−	1.44840i
$800$	−20.6643	−	5.41050i	−0.730592	−	0.191290i
$801$	−0.998095	−	0.998095i	−0.0352659	−	0.0352659i
$802$	0.349154	−	0.0510328i	0.0123291	−	0.00180203i
$803$	6.24477	+	3.33790i	0.220373	+	0.117792i
$804$	3.81993	−	0.359816i	0.134718	−	0.0126897i
$805$	26.9882	−	32.8853i	0.951211	−	1.15905i
$806$	0.276350	−	0.767194i	0.00973401	−	0.0270233i
$807$	3.14056	+	15.7887i	0.110553	+	0.555788i
$808$	−23.7628	+	31.6164i	−0.835971	+	1.11226i
$809$	53.7466	+	10.6909i	1.88963	+	0.375871i	0.997165	−	0.0752479i	$-0.0239748\pi$
$809$	53.7466	+	10.6909i	1.88963	+	0.375871i	0.892464	+	0.451118i	$0.148975\pi$
$810$	4.06614	−	1.00932i	0.142869	−	0.0354639i
$811$	−7.41307	+	24.4376i	−0.260308	+	0.858121i	0.725206	+	0.688531i	$0.241744\pi$
$811$	−7.41307	+	24.4376i	−0.260308	+	0.858121i	−0.985515	+	0.169590i	$0.945756\pi$
$812$	−39.3482	−	0.167520i	−1.38085	−	0.00587881i
$813$	−3.25759	−	3.96939i	−0.114249	−	0.139213i
$814$	−1.43820	−	4.04663i	−0.0504088	−	0.141834i
$815$	−3.96795	+	9.57947i	−0.138991	+	0.335554i
$816$	18.7518	−	9.81870i	0.656445	−	0.343723i
$817$	4.17068	+	10.0689i	0.145914	+	0.352266i
$818$	−7.68910	+	6.93924i	−0.268843	+	0.242625i
$819$	−0.315473	+	3.20305i	−0.0110235	+	0.111924i
$820$	15.9460	+	10.7533i	0.556859	+	0.375520i
$821$	−5.66518	−	10.5988i	−0.197716	−	0.369901i	0.763452	−	0.645865i	$-0.223503\pi$
$821$	−5.66518	−	10.5988i	−0.197716	−	0.369901i	−0.961168	+	0.275964i	$0.911003\pi$
$822$	26.1330	+	3.93333i	0.911492	+	0.137191i
$823$	−4.48630	−	6.71423i	−0.156383	−	0.234043i	0.745002	−	0.667062i	$-0.232448\pi$
$823$	−4.48630	−	6.71423i	−0.156383	−	0.234043i	−0.901385	+	0.433019i	$0.857448\pi$
$824$	−2.25925	−	9.27019i	−0.0787046	−	0.322942i
$825$	−2.05408	−	1.37249i	−0.0715137	−	0.0477840i
$826$	2.47383	+	52.6422i	0.0860755	+	1.83166i
$827$	−21.2437	+	2.09232i	−0.738715	+	0.0727570i	−0.460374	−	0.887725i	$-0.652285\pi$
$827$	−21.2437	+	2.09232i	−0.738715	+	0.0727570i	−0.278341	+	0.960482i	$0.589785\pi$
$828$	−9.00601	−	0.925745i	−0.312980	−	0.0321719i
$829$	−4.61414	+	1.39968i	−0.160256	+	0.0486130i	−0.369393	−	0.929273i	$-0.620434\pi$
$829$	−4.61414	+	1.39968i	−0.160256	+	0.0486130i	0.209137	+	0.977886i	$0.432934\pi$
$830$	12.3436	−	48.8371i	0.428453	−	1.69516i
$831$		−	16.2467i		−	0.563592i
$832$	−8.11585	−	0.103662i	−0.281366	−	0.00359383i
$833$			16.2127i			0.561736i
$834$	−18.4334	−	4.65904i	−0.638295	−	0.161329i
$835$	−17.7858	+	5.39527i	−0.615504	+	0.186711i
$836$	−1.47040	−	1.80733i	−0.0508549	−	0.0625077i
$837$	−0.565595	+	0.0557063i	−0.0195498	+	0.00192549i
$838$	11.5820	−	0.544276i	0.400093	−	0.0188017i
$839$	−28.1846	−	18.8324i	−0.973041	−	0.650165i	−0.0359876	−	0.999352i	$-0.511458\pi$
$839$	−28.1846	−	18.8324i	−0.973041	−	0.650165i	−0.937053	+	0.349187i	$0.886458\pi$
$840$	−26.2682	−	4.06812i	−0.906338	−	0.140363i
$841$	−5.25699	−	7.86764i	−0.181275	−	0.271298i
$842$	−7.12243	+	47.3213i	−0.245455	+	1.63080i
$843$	8.03199	+	15.0268i	0.276636	+	0.517550i
$844$	42.3207	−	8.23096i	1.45674	−	0.283321i
$845$	−3.47593	+	35.2917i	−0.119576	+	1.21407i
$846$	10.3671	+	11.4874i	0.356428	+	0.394944i
$847$	12.8344	+	30.9851i	0.440997	+	1.06466i
$848$	−27.2141	+	49.8875i	−0.934536	+	1.71315i
$849$	−9.88962	+	23.8757i	−0.339411	+	0.819410i
$850$	−26.6272	+	9.46349i	−0.913307	+	0.324595i
$851$	13.3298	+	16.2424i	0.456941	+	0.556784i
$852$	−6.89222	−	6.95116i	−0.236124	−	0.238143i
$853$	3.39749	−	11.2000i	0.116328	−	0.383481i	−0.879370	−	0.476139i	$-0.842036\pi$
$853$	3.39749	−	11.2000i	0.116328	−	0.383481i	0.995698	+	0.0926571i	$0.0295360\pi$
$854$	0.773317	+	3.11538i	0.0264624	+	0.106606i
$855$	−5.17378	−	1.02913i	−0.176940	−	0.0351955i
$856$	−10.9044	+	42.3825i	−0.372704	+	1.44860i
$857$	6.64114	+	33.3873i	0.226857	+	1.14049i	0.911402	+	0.411517i	$0.135001\pi$
$857$	6.64114	+	33.3873i	0.226857	+	1.14049i	−0.684545	+	0.728970i	$0.739999\pi$
$858$	−0.883141	−	0.318115i	−0.0301499	−	0.0108603i
$859$	−15.8175	+	19.2737i	−0.539688	+	0.657611i	−0.969438	−	0.245336i	$-0.921102\pi$
$859$	−15.8175	+	19.2737i	−0.539688	+	0.657611i	0.429750	+	0.902948i	$0.358602\pi$
$860$	−23.1242	+	27.9335i	−0.788527	+	0.952525i
$861$	9.08190	+	4.85438i	0.309510	+	0.165437i
$862$	−4.31894	−	29.5491i	−0.147104	−	1.00645i
$863$	22.0055	+	22.0055i	0.749075	+	0.749075i	0.974306	−	0.225230i	$-0.0723135\pi$
$863$	22.0055	+	22.0055i	0.749075	+	0.749075i	−0.225230	+	0.974306i	$0.572313\pi$
$864$	2.36405	+	5.13919i	0.0804267	+	0.174839i
$865$	−4.88240	+	4.88240i	−0.166006	+	0.166006i
$866$	−37.8176	−	28.1724i	−1.28509	−	0.957337i
$867$	5.18648	−	9.70323i	0.176142	−	0.329539i
$868$	3.44613	+	1.06142i	0.116969	+	0.0360268i
$869$	−8.29326	−	6.80610i	−0.281329	−	0.230881i
$870$	−11.0590	−	23.5116i	−0.374935	−	0.797119i
$871$	−1.90896	+	0.379716i	−0.0646826	+	0.0128662i
$872$	−20.7413	−	23.1803i	−0.702389	−	0.784983i
$873$	−1.82687	+	9.18428i	−0.0618301	+	0.310841i
$874$	9.76512	+	5.88128i	0.330310	+	0.198937i
$875$	−11.0068	−	3.33889i	−0.372099	−	0.112875i
$876$	8.19858	+	20.0339i	0.277004	+	0.676884i
$877$	11.2553	−	9.23701i	0.380066	−	0.311912i	−0.424892	−	0.905244i	$-0.639688\pi$
$877$	11.2553	−	9.23701i	0.380066	−	0.311912i	0.804958	+	0.593332i	$0.202188\pi$
$878$	29.4054	+	13.9844i	0.992385	+	0.471951i
$879$	25.8951	+	10.7261i	0.873419	+	0.361782i
$880$	3.02760	−	7.13679i	0.102060	−	0.240581i
$881$	10.2857	−	4.26046i	0.346532	−	0.143538i	−0.202627	−	0.979256i	$-0.564948\pi$
$881$	10.2857	−	4.26046i	0.346532	−	0.143538i	0.549160	+	0.835718i	$0.314948\pi$
$882$	−4.32716	−	0.221814i	−0.145703	−	0.00746886i
$883$	−44.1624	−	4.34962i	−1.48618	−	0.146376i	−0.677893	−	0.735161i	$-0.737107\pi$
$883$	−44.1624	−	4.34962i	−1.48618	−	0.146376i	−0.808290	+	0.588785i	$0.799607\pi$
$884$	−8.95330	+	5.92742i	−0.301132	+	0.199361i
$885$	−30.6901	+	16.4042i	−1.03164	+	0.551421i
$886$	25.7601	−	19.0201i	0.865426	−	0.638993i
$887$	−29.7183	+	19.8571i	−0.997843	+	0.666737i	−0.943358	−	0.331777i	$-0.892352\pi$
$887$	−29.7183	+	19.8571i	−0.997843	+	0.666737i	−0.0544849	+	0.998515i	$0.517352\pi$
$888$	4.50182	−	12.3329i	0.151071	−	0.413864i
$889$	19.4098	−	29.0489i	0.650985	−	0.974268i
$890$	−3.98065	+	4.37323i	−0.133432	+	0.146591i
$891$	0.0641252	+	0.651074i	0.00214828	+	0.0218118i
$892$	−34.0107	+	10.1591i	−1.13876	+	0.340152i
$893$	−5.65571	−	18.6444i	−0.189261	−	0.623911i
$894$	16.3991	+	27.4928i	0.548469	+	0.919498i
$895$	−49.9460			−1.66951
$896$	−1.22675	−	35.8700i	−0.0409829	−	1.19833i
$897$	4.59266			0.153344
$898$	6.85187	+	11.4870i	0.228650	+	0.383327i
$899$	1.02316	+	3.37291i	0.0341243	+	0.112493i
$900$	−2.16150	−	7.23627i	−0.0720500	−	0.241209i
$901$	7.36883	+	74.8170i	0.245491	+	2.49252i
$902$	−2.02167	+	2.22105i	−0.0673142	+	0.0739528i
$903$	−10.7871	+	16.1440i	−0.358971	+	0.537238i
$904$	16.5620	+	35.6039i	0.550843	+	1.18417i
$905$	−1.56144	+	1.04332i	−0.0519040	+	0.0346811i
$906$	14.3305	−	10.5810i	0.476100	−	0.351532i
$907$	−45.3060	+	24.2166i	−1.50436	+	0.804098i	−0.998294	−	0.0583947i	$-0.981402\pi$
$907$	−45.3060	+	24.2166i	−1.50436	+	0.804098i	−0.506069	+	0.862493i	$0.668902\pi$
$908$	7.76843	+	11.7341i	0.257804	+	0.389410i
$909$	−13.9160	−	1.37060i	−0.461564	−	0.0454601i
$910$	13.4665	+	0.690307i	0.446411	+	0.0228834i
$911$	−18.7789	+	7.77848i	−0.622173	+	0.257712i	−0.671423	−	0.741074i	$-0.734317\pi$
$911$	−18.7789	+	7.77848i	−0.622173	+	0.257712i	0.0492505	+	0.998786i	$0.484317\pi$
$912$	0.0606469	−	7.12242i	0.00200822	−	0.235847i
$913$	7.26730	+	3.01022i	0.240513	+	0.0996236i
$914$	25.0074	+	11.8928i	0.827173	+	0.393380i
$915$	−1.63846	+	1.34465i	−0.0541657	+	0.0444526i
$916$	45.9583	−	18.8077i	1.51850	−	0.621424i
$917$	−30.5264	−	9.26007i	−1.00807	−	0.305795i
$918$	6.41072	+	3.86101i	0.211585	+	0.127432i
$919$	−10.4184	+	52.3770i	−0.343672	+	1.72776i	0.292549	+	0.956251i	$0.405497\pi$
$919$	−10.4184	+	52.3770i	−0.343672	+	1.72776i	−0.636221	+	0.771507i	$0.719503\pi$
$920$	−2.10302	+	37.8714i	−0.0693344	+	1.24858i
$921$	18.5254	−	3.68494i	0.610434	−	0.121423i
$922$	−7.46931	−	15.8799i	−0.245989	−	0.522977i
$923$	3.83854	+	3.15021i	0.126347	+	0.103690i
$924$	1.22183	−	3.96695i	0.0401952	−	0.130503i
$925$	−8.26249	+	15.4580i	−0.271669	+	0.508257i
$926$	15.7670	+	11.7457i	0.518136	+	0.385988i
$927$	2.38538	−	2.38538i	0.0783461	−	0.0783461i
$928$	28.3995	−	20.5976i	0.932259	−	0.676150i
$929$	10.6050	+	10.6050i	0.347938	+	0.347938i	0.859341	−	0.511403i	$-0.170874\pi$
$929$	10.6050	+	10.6050i	0.347938	+	0.347938i	−0.511403	+	0.859341i	$0.670874\pi$
$930$	0.344358	+	2.35601i	0.0112919	+	0.0772567i
$931$	4.81139	+	2.57174i	0.157687	+	0.0842855i
$932$	11.0296	+	9.13065i	0.361288	+	0.299084i
$933$	14.9485	−	18.2148i	0.489392	−	0.596326i
$934$	−0.700261	−	0.252240i	−0.0229132	−	0.00825355i
$935$	−2.00083	−	10.0589i	−0.0654342	−	0.328960i
$936$	−1.45953	−	2.47073i	−0.0477063	−	0.0807582i
$937$	43.1343	+	8.57994i	1.40914	+	0.280294i	0.840284	−	0.542146i	$-0.182388\pi$
$937$	43.1343	+	8.57994i	1.40914	+	0.280294i	0.568851	+	0.822440i	$0.307388\pi$
$938$	−2.07349	−	8.35324i	−0.0677019	−	0.272743i
$939$	−3.43270	+	11.3161i	−0.112022	+	0.369287i
$940$	46.0348	−	45.6445i	1.50149	−	1.48876i
$941$	−3.19691	−	3.89545i	−0.104216	−	0.126988i	0.718290	−	0.695744i	$-0.244925\pi$
$941$	−3.19691	−	3.89545i	−0.104216	−	0.126988i	−0.822507	+	0.568756i	$0.807425\pi$
$942$	24.4444	−	8.68769i	0.796441	−	0.283060i
$943$	5.62329	−	13.5758i	0.183120	−	0.442090i
$944$	−29.4979	−	36.5739i	−0.960075	−	1.19038i
$945$	−3.59642	−	8.68254i	−0.116992	−	0.282443i
$946$	−3.79391	−	4.20389i	−0.123351	−	0.136680i
$947$	−2.25224	+	22.8674i	−0.0731881	+	0.743091i	0.886632	+	0.462475i	$0.153039\pi$
$947$	−2.25224	+	22.8674i	−0.0731881	+	0.743091i	−0.959820	+	0.280616i	$0.909461\pi$
$948$	−6.26150	−	32.1944i	−0.203364	−	1.04563i
$949$	−5.17637	−	9.68431i	−0.168032	−	0.314366i
$950$	−1.41530	+	9.40324i	−0.0459185	+	0.305081i
$951$	6.63707	+	9.93308i	0.215222	+	0.322102i
$952$	−28.0405	−	38.3172i	−0.908797	−	1.24187i
$953$	7.20016	+	4.81099i	0.233236	+	0.155843i	0.666697	−	0.745329i	$-0.267708\pi$
$953$	7.20016	+	4.81099i	0.233236	+	0.155843i	−0.433461	+	0.901172i	$0.642708\pi$
$954$	−20.0694	+	0.943128i	−0.649772	+	0.0305349i
$955$	−41.4599	+	4.08344i	−1.34161	+	0.132137i
$956$	35.5393	−	28.9140i	1.14942	−	0.935145i
$957$	3.88266	−	1.17779i	0.125509	−	0.0380726i
$958$	−8.40131	−	2.12344i	−0.271434	−	0.0686051i
$959$		−	59.2814i		−	1.91430i
$960$	21.0421	−	10.9041i	0.679132	−	0.351927i
$961$			30.6770i			0.989581i
$962$	−1.63200	+	6.45697i	−0.0526178	+	0.208181i
$963$	−14.8063	+	4.49143i	−0.477125	+	0.144734i
$964$	−0.276779	+	2.69262i	−0.00891446	+	0.0867234i
$965$	8.32635	−	0.820074i	0.268035	−	0.0263991i
$966$	0.953316	+	20.2862i	0.0306724	+	0.652699i
$967$	43.8762	+	29.3172i	1.41097	+	0.942777i	0.999509	+	0.0313473i	$0.00997978\pi$
$967$	43.8762	+	29.3172i	1.41097	+	0.942777i	0.411456	+	0.911429i	$0.365020\pi$
$968$	−25.5492	−	15.5362i	−0.821182	−	0.499353i
$969$	−5.23504	−	7.83479i	−0.168174	−	0.251690i
$970$	38.7947	+	5.83908i	1.24562	+	0.187481i
$971$	−4.48334	−	8.38774i	−0.143877	−	0.269175i	0.799653	−	0.600463i	$-0.205017\pi$
$971$	−4.48334	−	8.38774i	−0.143877	−	0.269175i	−0.943530	+	0.331288i	$0.892517\pi$
$972$	−1.11821	+	1.65819i	−0.0358666	+	0.0531866i
$973$	−4.18041	+	42.4444i	−0.134018	+	1.36071i
$974$	−5.04781	+	4.55553i	−0.161742	+	0.145969i
$975$	1.46610	+	3.53947i	0.0469526	+	0.113354i
$976$	−2.19676	−	1.83436i	−0.0703166	−	0.0587164i
$977$	6.29187	−	15.1899i	0.201295	−	0.485969i	−0.790707	−	0.612195i	$-0.790287\pi$
$977$	6.29187	−	15.1899i	0.201295	−	0.485969i	0.992001	+	0.126227i	$0.0402866\pi$
$978$	−1.65762	−	4.66402i	−0.0530050	−	0.149139i
$979$	−0.585831	−	0.713837i	−0.0187232	−	0.0228143i
$980$	−0.0772818	+	18.1524i	−0.00246868	+	0.579857i
$981$	3.19235	−	10.5238i	0.101924	−	0.335998i
$982$	−14.3662	+	3.56606i	−0.458443	+	0.113798i
$983$	52.8039	+	10.5033i	1.68418	+	0.335005i	0.942107	−	0.335312i	$-0.108842\pi$
$983$	52.8039	+	10.5033i	1.68418	+	0.335005i	0.742075	+	0.670316i	$0.233842\pi$
$984$	−9.09049	+	1.28917i	−0.289794	+	0.0410973i
$985$	−4.67362	−	23.4959i	−0.148914	−	0.748640i
$986$	15.7287	−	43.6656i	0.500904	−	1.39059i
$987$	22.0201	−	26.8315i	0.700907	−	0.854057i
$988$	0.338844	+	3.59728i	0.0107801	+	0.114445i
$989$	24.4342	+	13.0603i	0.776962	+	0.415295i
$990$	2.71208	−	0.396401i	0.0861955	−	0.0125984i
$991$	−11.5398	−	11.5398i	−0.366573	−	0.366573i	0.499653	−	0.866226i	$-0.333461\pi$
$991$	−11.5398	−	11.5398i	−0.366573	−	0.366573i	−0.866226	+	0.499653i	$0.833461\pi$
$992$	−3.03839	+	1.05081i	−0.0964691	+	0.0333633i
$993$	1.63726	−	1.63726i	0.0519569	−	0.0519569i
$994$	−13.1180	+	17.6091i	−0.416077	+	0.558527i
$995$	27.3189	−	51.1101i	0.866068	−	1.62030i
$996$	11.2453	+	21.2556i	0.356321	+	0.673511i
$997$	0.350222	+	0.287419i	0.0110916	+	0.00910266i	0.639923	−	0.768439i	$-0.278966\pi$
$997$	0.350222	+	0.287419i	0.0110916	+	0.00910266i	−0.628831	+	0.777542i	$0.716466\pi$
$998$	13.8182	−	6.49958i	0.437408	−	0.205741i
$999$	4.55255	−	0.905559i	0.144036	−	0.0286506i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.13.6	✓	512
128.69	even	32	inner	384.2.v.a.325.6	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.13.6	✓	512	1.1	even	1	trivial
384.2.v.a.325.6	yes	512	128.69	even	32	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21456 + 0.724467i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(0.950294 - 1.75981i) q^{4} +(-0.290371 - 2.94818i) q^{5} +(1.04584 + 0.951956i) q^{6} +(1.76246 - 2.63771i) q^{7} +(0.120741 + 2.82585i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})\)	\(q+(-1.21456 + 0.724467i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(0.950294 - 1.75981i) q^{4} +(-0.290371 - 2.94818i) q^{5} +(1.04584 + 0.951956i) q^{6} +(1.76246 - 2.63771i) q^{7} +(0.120741 + 2.82585i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(2.48853 + 3.37037i) q^{10} +(-0.576974 + 0.308399i) q^{11} +(-1.95989 - 0.398528i) q^{12} +(1.00968 + 0.0994446i) q^{13} +(-0.229674 + 4.48049i) q^{14} +(-2.73695 + 1.13368i) q^{15} +(-2.19388 - 3.34468i) q^{16} +(-4.88892 - 2.02506i) q^{17} +(0.607374 - 1.27714i) q^{18} +(-1.37648 + 1.12965i) q^{19} +(-5.46419 - 2.29064i) q^{20} +(-3.03575 - 0.920883i) q^{21} +(0.477343 - 0.792567i) q^{22} +(-0.883122 + 4.43975i) q^{23} +(2.66912 - 0.935842i) q^{24} +(-3.70354 + 0.736680i) q^{25} +(-1.29836 + 0.610698i) q^{26} +(0.773010 + 0.634393i) q^{27} +(-2.96702 - 5.60820i) q^{28} +(2.92351 - 5.46950i) q^{29} +(2.50286 - 3.35975i) q^{30} +(-0.401871 + 0.401871i) q^{31} +(5.08770 + 2.47291i) q^{32} +(0.462607 + 0.462607i) q^{33} +(7.40495 - 1.08232i) q^{34} +(-8.28822 - 4.43014i) q^{35} +(0.187559 + 1.99119i) q^{36} +(2.94469 - 3.58812i) q^{37} +(0.853418 - 2.36923i) q^{38} +(-0.197932 - 0.995069i) q^{39} +(8.29606 - 1.17651i) q^{40} +(-3.18376 - 0.633289i) q^{41} +(4.35423 - 1.08083i) q^{42} +(1.77667 - 5.85691i) q^{43} +(-0.00557052 + 1.30844i) q^{44} +(1.87936 + 2.29000i) q^{45} +(-2.14385 - 6.03212i) q^{46} +(-4.18716 + 10.1087i) q^{47} +(-2.56381 + 3.07032i) q^{48} +(-1.17246 - 2.83056i) q^{49} +(3.96446 - 3.57784i) q^{50} +(-0.518680 + 5.26625i) q^{51} +(1.13450 - 1.68234i) q^{52} +(-6.69708 - 12.5294i) q^{53} +(-1.39846 - 0.210486i) q^{54} +(1.07675 + 1.61148i) q^{55} +(7.66657 + 4.66197i) q^{56} +(1.48057 + 0.989288i) q^{57} +(0.411708 + 8.76100i) q^{58} +(11.6902 - 1.15138i) q^{59} +(-0.605839 + 5.89384i) q^{60} +(0.684673 - 0.207693i) q^{61} +(0.196953 - 0.779238i) q^{62} +3.17235i q^{63} +(-7.97084 + 0.682391i) q^{64} -3.00559i q^{65} +(-0.897005 - 0.226718i) q^{66} +(-1.83581 + 0.556887i) q^{67} +(-8.20963 + 6.67918i) q^{68} +(4.50493 - 0.443697i) q^{69} +(13.2760 - 0.623882i) q^{70} +(4.06956 + 2.71919i) q^{71} +(-1.67035 - 2.28253i) q^{72} +(-6.01310 - 8.99924i) q^{73} +(-0.977020 + 6.49130i) q^{74} +(1.78004 + 3.33022i) q^{75} +(0.679906 + 3.49584i) q^{76} +(-0.203427 + 2.06543i) q^{77} +(0.961294 + 1.06517i) q^{78} +(6.27556 + 15.1505i) q^{79} +(-9.22369 + 7.43916i) q^{80} +(0.382683 - 0.923880i) q^{81} +(4.32565 - 1.53736i) q^{82} +(-7.62763 - 9.29430i) q^{83} +(-4.50543 + 4.46723i) q^{84} +(-4.55064 + 15.0014i) q^{85} +(2.08527 + 8.40068i) q^{86} +(-6.08263 - 1.20991i) q^{87} +(-0.941154 - 1.59321i) q^{88} +(0.275374 + 1.38440i) q^{89} +(-3.94162 - 1.41981i) q^{90} +(2.04182 - 2.48797i) q^{91} +(6.97391 + 5.77320i) q^{92} +(0.501224 + 0.267910i) q^{93} +(-2.23788 - 15.3110i) q^{94} +(3.73009 + 3.73009i) q^{95} +(0.889541 - 5.58648i) q^{96} +(6.62150 - 6.62150i) q^{97} +(3.47467 + 2.58847i) q^{98} +(0.308399 - 0.576974i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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