LMFDB - Embedded newform 384.2.v.a.181.14

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			181.14
Character	$\chi$	$=$	384.181
Dual form			384.2.v.a.157.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.310799 - 1.37964i) q^{2} +(0.0980171 + 0.995185i) q^{3} +(-1.80681 + 0.857580i) q^{4} +(-1.10815 - 0.592317i) q^{5} +(1.34253 - 0.444530i) q^{6} +(0.457071 - 2.29785i) q^{7} +(1.74470 + 2.22621i) q^{8} +(-0.980785 + 0.195090i) q^{9} +O(q^{10})$	\(q+(-0.310799 - 1.37964i) q^{2} +(0.0980171 + 0.995185i) q^{3} +(-1.80681 + 0.857580i) q^{4} +(-1.10815 - 0.592317i) q^{5} +(1.34253 - 0.444530i) q^{6} +(0.457071 - 2.29785i) q^{7} +(1.74470 + 2.22621i) q^{8} +(-0.980785 + 0.195090i) q^{9} +(-0.472773 + 1.71294i) q^{10} +(-1.67067 - 2.03571i) q^{11} +(-1.03055 - 1.71405i) q^{12} +(-0.759784 - 1.42146i) q^{13} +(-3.31226 + 0.0835757i) q^{14} +(0.480848 - 1.16087i) q^{15} +(2.52911 - 3.09896i) q^{16} +(-1.47844 - 3.56928i) q^{17} +(0.573981 + 1.29250i) q^{18} +(-1.05342 + 3.47265i) q^{19} +(2.51017 + 0.119879i) q^{20} +(2.33159 + 0.229641i) q^{21} +(-2.28931 + 2.93761i) q^{22} +(-5.89497 - 3.93889i) q^{23} +(-2.04448 + 1.95451i) q^{24} +(-1.90070 - 2.84460i) q^{25} +(-1.72496 + 1.49001i) q^{26} +(-0.290285 - 0.956940i) q^{27} +(1.14475 + 4.54375i) q^{28} +(-5.69373 - 4.67272i) q^{29} +(-1.75103 - 0.302600i) q^{30} +(-0.0207233 - 0.0207233i) q^{31} +(-5.06150 - 2.52611i) q^{32} +(1.86216 - 1.86216i) q^{33} +(-4.46482 + 3.14905i) q^{34} +(-1.86756 + 2.27563i) q^{35} +(1.60479 - 1.19359i) q^{36} +(9.61030 - 2.91525i) q^{37} +(5.11840 + 0.374040i) q^{38} +(1.34014 - 0.895452i) q^{39} +(-0.614767 - 3.50039i) q^{40} +(0.892668 - 1.33597i) q^{41} +(-0.407832 - 3.28812i) q^{42} +(-1.13221 + 11.4955i) q^{43} +(4.76436 + 2.24541i) q^{44} +(1.20241 + 0.364747i) q^{45} +(-3.60210 + 9.35713i) q^{46} +(6.47319 - 2.68128i) q^{47} +(3.33194 + 2.21318i) q^{48} +(1.39595 + 0.578221i) q^{49} +(-3.33378 + 3.50638i) q^{50} +(3.40718 - 1.82118i) q^{51} +(2.59180 + 1.91672i) q^{52} +(1.16392 - 0.955207i) q^{53} +(-1.23001 + 0.697904i) q^{54} +(0.645557 + 3.24544i) q^{55} +(5.91295 - 2.99153i) q^{56} +(-3.55918 - 0.707965i) q^{57} +(-4.67707 + 9.30756i) q^{58} +(-3.77675 + 7.06580i) q^{59} +(0.126738 + 2.50983i) q^{60} +(4.20656 - 0.414310i) q^{61} +(-0.0221499 + 0.0350315i) q^{62} +2.34287i q^{63} +(-1.91202 + 7.76815i) q^{64} +2.02522i q^{65} +(-3.14786 - 1.99035i) q^{66} +(-6.18862 + 0.609525i) q^{67} +(5.73221 + 5.18112i) q^{68} +(3.34212 - 6.25266i) q^{69} +(3.71998 + 1.86930i) q^{70} +(8.04650 + 1.60055i) q^{71} +(-2.14549 - 1.84306i) q^{72} +(-2.06681 - 10.3905i) q^{73} +(-7.00887 - 12.3527i) q^{74} +(2.64460 - 2.17037i) q^{75} +(-1.07475 - 7.17780i) q^{76} +(-5.44138 + 2.90848i) q^{77} +(-1.65191 - 1.57060i) q^{78} +(6.65968 + 2.75853i) q^{79} +(-4.63820 + 1.93607i) q^{80} +(0.923880 - 0.382683i) q^{81} +(-2.12060 - 0.816341i) q^{82} +(9.78688 + 2.96882i) q^{83} +(-4.40967 + 1.58460i) q^{84} +(-0.475812 + 4.83100i) q^{85} +(16.2115 - 2.01074i) q^{86} +(4.09214 - 6.12432i) q^{87} +(1.61710 - 7.27097i) q^{88} +(-6.96030 + 4.65072i) q^{89} +(0.129512 - 1.77226i) q^{90} +(-3.61357 + 1.09616i) q^{91} +(14.0290 + 2.06142i) q^{92} +(0.0185923 - 0.0226548i) q^{93} +(-5.71106 - 8.09733i) q^{94} +(3.22425 - 3.22425i) q^{95} +(2.01783 - 5.28473i) q^{96} +(-0.488268 - 0.488268i) q^{97} +(0.363878 - 2.10562i) q^{98} +(2.03571 + 1.67067i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{5}{32}\right)$	$1$

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 $

$2$	−0.310799	−	1.37964i	−0.219768	−	0.975552i
$2$	−0.310799	−	1.37964i	−0.219768	−	0.975552i
$3$	0.0980171	+	0.995185i	0.0565902	+	0.574570i
$3$	0.0980171	+	0.995185i	0.0565902	+	0.574570i
$4$	−1.80681	+	0.857580i	−0.903404	+	0.428790i
$5$	−1.10815	−	0.592317i	−0.495579	−	0.264892i	0.204619	−	0.978842i	$-0.434405\pi$
$5$	−1.10815	−	0.592317i	−0.495579	−	0.264892i	−0.700197	+	0.713949i	$0.746905\pi$
$6$	1.34253	−	0.444530i	0.548086	−	0.181479i
$7$	0.457071	−	2.29785i	0.172757	−	0.868506i	−0.793033	−	0.609179i	$-0.791499\pi$
$7$	0.457071	−	2.29785i	0.172757	−	0.868506i	0.965789	−	0.259327i	$-0.0835008\pi$
$8$	1.74470	+	2.22621i	0.616846	+	0.787084i
$9$	−0.980785	+	0.195090i	−0.326928	+	0.0650301i
$10$	−0.472773	+	1.71294i	−0.149504	+	0.541678i
$11$	−1.67067	−	2.03571i	−0.503725	−	0.613791i	0.457617	−	0.889150i	$-0.348703\pi$
$11$	−1.67067	−	2.03571i	−0.503725	−	0.613791i	−0.961341	+	0.275359i	$0.911203\pi$
$12$	−1.03055	−	1.71405i	−0.297494	−	0.494804i
$13$	−0.759784	−	1.42146i	−0.210726	−	0.394241i	0.754247	−	0.656591i	$-0.228002\pi$
$13$	−0.759784	−	1.42146i	−0.210726	−	0.394241i	−0.964973	+	0.262351i	$0.915502\pi$
$14$	−3.31226	+	0.0835757i	−0.885239	+	0.0223366i
$15$	0.480848	−	1.16087i	0.124154	−	0.299735i
$16$	2.52911	−	3.09896i	0.632279	−	0.774741i
$17$	−1.47844	−	3.56928i	−0.358575	−	0.865677i	−0.995501	−	0.0947521i	$-0.969794\pi$
$17$	−1.47844	−	3.56928i	−0.358575	−	0.865677i	0.636926	−	0.770925i	$-0.280206\pi$
$18$	0.573981	+	1.29250i	0.135289	+	0.304644i
$19$	−1.05342	+	3.47265i	−0.241670	+	0.796680i	0.749257	+	0.662279i	$0.230411\pi$
$19$	−1.05342	+	3.47265i	−0.241670	+	0.796680i	−0.990927	+	0.134400i	$0.957089\pi$
$20$	2.51017	+	0.119879i	0.561291	+	0.0268057i
$21$	2.33159	+	0.229641i	0.508794	+	0.0501118i
$22$	−2.28931	+	2.93761i	−0.488082	+	0.626301i
$23$	−5.89497	−	3.93889i	−1.22919	−	0.821316i	−0.240403	−	0.970673i	$-0.577279\pi$
$23$	−5.89497	−	3.93889i	−1.22919	−	0.821316i	−0.988783	+	0.149358i	$0.952279\pi$
$24$	−2.04448	+	1.95451i	−0.417327	+	0.398963i
$25$	−1.90070	−	2.84460i	−0.380140	−	0.568920i
$26$	−1.72496	+	1.49001i	−0.338292	+	0.292216i
$27$	−0.290285	−	0.956940i	−0.0558653	−	0.184163i
$28$	1.14475	+	4.54375i	0.216338	+	0.858688i
$29$	−5.69373	−	4.67272i	−1.05730	−	0.867702i	−0.0658014	−	0.997833i	$-0.520960\pi$
$29$	−5.69373	−	4.67272i	−1.05730	−	0.867702i	−0.991497	+	0.130130i	$0.958460\pi$
$30$	−1.75103	−	0.302600i	−0.319692	−	0.0552469i
$31$	−0.0207233	−	0.0207233i	−0.00372202	−	0.00372202i	0.705243	−	0.708965i	$-0.250838\pi$
$31$	−0.0207233	−	0.0207233i	−0.00372202	−	0.00372202i	−0.708965	+	0.705243i	$0.750838\pi$
$32$	−5.06150	−	2.52611i	−0.894755	−	0.446558i
$33$	1.86216	−	1.86216i	0.324160	−	0.324160i
$34$	−4.46482	+	3.14905i	−0.765710	+	0.540057i
$35$	−1.86756	+	2.27563i	−0.315675	+	0.384651i
$36$	1.60479	−	1.19359i	0.267464	−	0.198932i
$37$	9.61030	−	2.91525i	1.57992	−	0.479265i	0.626128	−	0.779720i	$-0.284639\pi$
$37$	9.61030	−	2.91525i	1.57992	−	0.479265i	0.953796	+	0.300455i	$0.0971386\pi$
$38$	5.11840	+	0.374040i	0.830314	+	0.0606773i
$39$	1.34014	−	0.895452i	0.214594	−	0.143387i
$40$	−0.614767	−	3.50039i	−0.0972033	−	0.553460i
$41$	0.892668	−	1.33597i	0.139411	−	0.208644i	−0.755194	−	0.655502i	$-0.772457\pi$
$41$	0.892668	−	1.33597i	0.139411	−	0.208644i	0.894605	+	0.446858i	$0.147457\pi$
$42$	−0.407832	−	3.28812i	−0.0629298	−	0.507368i
$43$	−1.13221	+	11.4955i	−0.172660	+	1.75305i	0.384945	+	0.922939i	$0.374220\pi$
$43$	−1.13221	+	11.4955i	−0.172660	+	1.75305i	−0.557605	+	0.830106i	$0.688280\pi$
$44$	4.76436	+	2.24541i	0.718254	+	0.338509i
$45$	1.20241	+	0.364747i	0.179245	+	0.0543733i
$46$	−3.60210	+	9.35713i	−0.531101	+	1.37963i
$47$	6.47319	−	2.68128i	0.944212	−	0.391105i	0.143160	−	0.989700i	$-0.454274\pi$
$47$	6.47319	−	2.68128i	0.944212	−	0.391105i	0.801052	+	0.598594i	$0.204274\pi$
$48$	3.33194	+	2.21318i	0.480924	+	0.319446i
$49$	1.39595	+	0.578221i	0.199421	+	0.0826030i
$50$	−3.33378	+	3.50638i	−0.471468	+	0.495877i
$51$	3.40718	−	1.82118i	0.477101	−	0.255016i
$52$	2.59180	+	1.91672i	0.359417	+	0.265802i
$53$	1.16392	−	0.955207i	0.159877	−	0.131208i	−0.551053	−	0.834470i	$-0.685774\pi$
$53$	1.16392	−	0.955207i	0.159877	−	0.131208i	0.710931	+	0.703262i	$0.248274\pi$
$54$	−1.23001	+	0.697904i	−0.167383	+	0.0949727i
$55$	0.645557	+	3.24544i	0.0870469	+	0.437614i
$56$	5.91295	−	2.99153i	0.790151	−	0.399761i
$57$	−3.55918	−	0.707965i	−0.471425	−	0.0937722i
$58$	−4.67707	+	9.30756i	−0.614129	+	1.22214i
$59$	−3.77675	+	7.06580i	−0.491691	+	0.919889i	0.506641	+	0.862157i	$0.330887\pi$
$59$	−3.77675	+	7.06580i	−0.491691	+	0.919889i	−0.998332	+	0.0577320i	$0.981613\pi$
$60$	0.126738	+	2.50983i	0.0163618	+	0.324018i
$61$	4.20656	−	0.414310i	0.538595	−	0.0530470i	0.174937	−	0.984580i	$-0.444028\pi$
$61$	4.20656	−	0.414310i	0.538595	−	0.0530470i	0.363658	+	0.931533i	$0.381528\pi$
$62$	−0.0221499	+	0.0350315i	−0.00281304	+	0.00444900i
$63$			2.34287i			0.295174i
$64$	−1.91202	+	7.76815i	−0.239002	+	0.971019i
$65$			2.02522i			0.251197i
$66$	−3.14786	−	1.99035i	−0.387475	−	0.244995i
$67$	−6.18862	+	0.609525i	−0.756060	+	0.0744654i	−0.468700	−	0.883357i	$-0.655277\pi$
$67$	−6.18862	+	0.609525i	−0.756060	+	0.0744654i	−0.287360	+	0.957823i	$0.592777\pi$
$68$	5.73221	+	5.18112i	0.695132	+	0.628303i
$69$	3.34212	−	6.25266i	0.402344	−	0.752732i
$70$	3.71998	+	1.86930i	0.444623	+	0.223424i
$71$	8.04650	+	1.60055i	0.954944	+	0.189950i	0.647883	−	0.761740i	$-0.275655\pi$
$71$	8.04650	+	1.60055i	0.954944	+	0.189950i	0.307061	+	0.951690i	$0.400655\pi$
$72$	−2.14549	−	1.84306i	−0.252849	−	0.217207i
$73$	−2.06681	−	10.3905i	−0.241901	−	1.21612i	−0.890498	−	0.454988i	$-0.849644\pi$
$73$	−2.06681	−	10.3905i	−0.241901	−	1.21612i	0.648596	−	0.761133i	$-0.275356\pi$
$74$	−7.00887	−	12.3527i	−0.814764	−	1.43597i
$75$	2.64460	−	2.17037i	0.305372	−	0.250612i
$76$	−1.07475	−	7.17780i	−0.123282	−	0.823350i
$77$	−5.44138	+	2.90848i	−0.620103	+	0.331452i
$78$	−1.65191	−	1.57060i	−0.187042	−	0.177836i
$79$	6.65968	+	2.75853i	0.749272	+	0.310359i	0.724445	−	0.689333i	$-0.242096\pi$
$79$	6.65968	+	2.75853i	0.749272	+	0.310359i	0.0248275	+	0.999692i	$0.492096\pi$
$80$	−4.63820	+	1.93607i	−0.518567	+	0.216459i
$81$	0.923880	−	0.382683i	0.102653	−	0.0425204i
$82$	−2.12060	−	0.816341i	−0.234181	−	0.0901498i
$83$	9.78688	+	2.96882i	1.07425	+	0.325870i	0.777369	−	0.629045i	$-0.216554\pi$
$83$	9.78688	+	2.96882i	1.07425	+	0.325870i	0.296880	+	0.954915i	$0.404054\pi$
$84$	−4.40967	+	1.58460i	−0.481134	+	0.172894i
$85$	−0.475812	+	4.83100i	−0.0516090	+	0.523995i
$86$	16.2115	−	2.01074i	1.74813	−	0.216824i
$87$	4.09214	−	6.12432i	0.438723	−	0.656596i
$88$	1.61710	−	7.27097i	0.172384	−	0.775088i
$89$	−6.96030	+	4.65072i	−0.737790	+	0.492975i	−0.866793	−	0.498669i	$-0.833822\pi$
$89$	−6.96030	+	4.65072i	−0.737790	+	0.492975i	0.129003	+	0.991644i	$0.458822\pi$
$90$	0.129512	−	1.77226i	0.0136518	−	0.186812i
$91$	−3.61357	+	1.09616i	−0.378805	+	0.114909i
$92$	14.0290	+	2.06142i	1.46262	+	0.214918i
$93$	0.0185923	−	0.0226548i	0.00192793	−	0.00234919i
$94$	−5.71106	−	8.09733i	−0.589051	−	0.835176i
$95$	3.22425	−	3.22425i	0.330801	−	0.330801i
$96$	2.01783	−	5.28473i	0.205944	−	0.539370i
$97$	−0.488268	−	0.488268i	−0.0495761	−	0.0495761i	0.681884	−	0.731460i	$-0.261161\pi$
$97$	−0.488268	−	0.488268i	−0.0495761	−	0.0495761i	−0.731460	+	0.681884i	$0.761161\pi$
$98$	0.363878	−	2.10562i	0.0367572	−	0.212699i
$99$	2.03571	+	1.67067i	0.204597	+	0.167908i
$100$	5.87367	+	3.50964i	0.587367	+	0.350964i
$101$	−2.85911	−	9.42522i	−0.284492	−	0.937845i	−0.976420	−	0.215878i	$-0.930739\pi$
$101$	−2.85911	−	9.42522i	−0.284492	−	0.937845i	0.691928	−	0.721966i	$-0.256761\pi$
$102$	−3.57151	−	4.13466i	−0.353632	−	0.409392i
$103$	−0.752348	−	1.12597i	−0.0741311	−	0.110945i	0.792552	−	0.609805i	$-0.208752\pi$
$103$	−0.752348	−	1.12597i	−0.0741311	−	0.110945i	−0.866683	+	0.498860i	$0.833752\pi$
$104$	1.83886	−	4.17146i	0.180315	−	0.409045i
$105$	−2.44772	−	1.63552i	−0.238873	−	0.159610i
$106$	−1.67959	−	1.30892i	−0.163136	−	0.127133i
$107$	−1.79141	−	0.176438i	−0.173182	−	0.0170569i	0.0110544	−	0.999939i	$-0.496481\pi$
$107$	−1.79141	−	0.176438i	−0.173182	−	0.0170569i	−0.184236	+	0.982882i	$0.558981\pi$
$108$	1.34514	+	1.48007i	0.129436	+	0.142419i
$109$	−1.00358	+	3.30838i	−0.0961260	+	0.316885i	−0.991795	−	0.127836i	$-0.959197\pi$
$109$	−1.00358	+	3.30838i	−0.0961260	+	0.316885i	0.895669	+	0.444721i	$0.146697\pi$
$110$	4.27689	−	1.89931i	0.407786	−	0.181092i
$111$	3.84319	+	9.27828i	0.364779	+	0.880656i
$112$	−5.96498	−	7.22798i	−0.563637	−	0.682979i
$113$	5.75681	−	13.8982i	0.541556	−	1.30743i	−0.382070	−	0.924134i	$-0.624789\pi$
$113$	5.75681	−	13.8982i	0.541556	−	1.30743i	0.923625	−	0.383297i	$-0.125211\pi$
$114$	0.129452	+	5.13042i	0.0121243	+	0.480507i
$115$	4.19942	+	7.85656i	0.391598	+	0.732628i
$116$	14.2947	+	3.55989i	1.32723	+	0.330527i
$117$	1.02250	+	1.24592i	0.0945299	+	0.115185i
$118$	10.9221	+	3.01451i	1.00546	+	0.277508i
$119$	−8.87743	+	1.76583i	−0.813792	+	0.161873i
$120$	3.42327	−	0.954905i	0.312501	−	0.0871705i
$121$	0.792992	−	3.98664i	0.0720902	−	0.362422i
$122$	−1.87899	−	5.67477i	−0.170116	−	0.513769i
$123$	1.41704	+	0.757421i	0.127770	+	0.0682944i
$124$	0.0552150	+	0.0196712i	0.00495845	+	0.00176652i
$125$	1.03715	+	10.5304i	0.0927657	+	0.941865i
$126$	3.23231	−	0.728160i	0.287957	−	0.0648697i
$127$	−1.44242			−0.127994			−0.0639971	−	0.997950i	$-0.520385\pi$
$127$	−1.44242			−0.127994			−0.0639971	+	0.997950i	$0.520385\pi$
$128$	11.3115	+	0.223561i	0.999805	+	0.0197602i
$129$	−11.5511			−1.01702
$130$	2.79407	−	0.629434i	0.245056	−	0.0552050i
$131$	0.221199	+	2.24588i	0.0193263	+	0.196223i	1.00000		0.000571857i	$0.000182028\pi$
$131$	0.221199	+	2.24588i	0.0193263	+	0.196223i	−0.980674	+	0.195651i	$0.937318\pi$
$132$	−1.76761	+	4.96151i	−0.153851	+	0.431844i
$133$	7.49814	+	4.00784i	0.650171	+	0.347524i
$134$	2.76434	+	8.34862i	0.238802	+	0.721211i
$135$	−0.245134	+	1.23237i	−0.0210978	+	0.106066i
$136$	5.36652	−	9.51866i	0.460175	−	0.816218i
$137$	−14.1887	+	2.82231i	−1.21222	+	0.241126i	−0.759489	−	0.650520i	$-0.774551\pi$
$137$	−14.1887	+	2.82231i	−1.21222	+	0.241126i	−0.452734	+	0.891646i	$0.649551\pi$
$138$	−9.66514	−	2.66760i	−0.822752	−	0.227081i
$139$	−1.87576	−	2.28562i	−0.159100	−	0.193864i	0.687359	−	0.726318i	$-0.258770\pi$
$139$	−1.87576	−	2.28562i	−0.159100	−	0.193864i	−0.846459	+	0.532454i	$0.821270\pi$
$140$	1.42279	−	5.71320i	0.120248	−	0.482854i
$141$	3.30286	+	6.17921i	0.278151	+	0.520383i
$142$	−0.292661	−	11.5987i	−0.0245596	−	0.973343i
$143$	−1.62433	+	3.92148i	−0.135833	+	0.327931i
$144$	−1.87594	+	3.53282i	−0.156328	+	0.294402i
$145$	3.54176	+	8.55055i	0.294127	+	0.710085i
$146$	−13.6928	+	6.08081i	−1.13323	+	0.503252i
$147$	−0.438610	+	1.44590i	−0.0361759	+	0.119256i
$148$	−14.8639	+	13.5089i	−1.22181	+	1.11043i
$149$	9.37384	+	0.923243i	0.767935	+	0.0756350i	0.474395	−	0.880312i	$-0.342667\pi$
$149$	9.37384	+	0.923243i	0.767935	+	0.0756350i	0.293540	+	0.955947i	$0.405167\pi$
$150$	−3.81626	−	2.97405i	−0.311596	−	0.242830i
$151$	−18.5904	−	12.4217i	−1.51286	−	1.01086i	−0.987077	−	0.160245i	$-0.948772\pi$
$151$	−18.5904	−	12.4217i	−1.51286	−	1.01086i	−0.525785	−	0.850617i	$-0.676228\pi$
$152$	−9.56874	+	3.71362i	−0.776127	+	0.301214i
$153$	2.14637	+	3.21227i	0.173524	+	0.259696i
$154$	5.70382	+	6.60319i	0.459627	+	0.532100i
$155$	0.0106897	+	0.0352393i	0.000858619	+	0.00283049i
$156$	−1.65345	+	2.76719i	−0.132382	+	0.221552i
$157$	10.1602	+	8.33825i	0.810871	+	0.665465i	0.945569	−	0.325422i	$-0.105506\pi$
$157$	10.1602	+	8.33825i	0.810871	+	0.665465i	−0.134698	+	0.990887i	$0.543006\pi$
$158$	1.73596	−	10.0453i	0.138105	−	0.799161i
$159$	1.06469	+	1.06469i	0.0844356	+	0.0844356i
$160$	4.11263	+	5.79732i	0.325132	+	0.458318i
$161$	−11.7454	+	11.7454i	−0.925668	+	0.925668i
$162$	−0.815105	−	1.15568i	−0.0640407	−	0.0907990i
$163$	9.87051	−	12.0272i	0.773118	−	0.942047i	−0.226370	−	0.974041i	$-0.572686\pi$
$163$	9.87051	−	12.0272i	0.773118	−	0.942047i	0.999488	+	0.0319946i	$0.0101859\pi$
$164$	−0.467177	+	3.17938i	−0.0364804	+	0.248268i
$165$	−3.16653	+	0.960557i	−0.246514	+	0.0747793i
$166$	1.05415	−	14.4251i	0.0818178	−	1.11960i
$167$	10.7474	−	7.18117i	0.831657	−	0.555696i	−0.0652731	−	0.997867i	$-0.520792\pi$
$167$	10.7474	−	7.18117i	0.831657	−	0.555696i	0.896930	+	0.442172i	$0.145792\pi$
$168$	3.55670	+	5.59126i	0.274405	+	0.431375i
$169$	5.77915	−	8.64911i	0.444550	−	0.665316i
$170$	6.81291	−	0.845018i	0.522527	−	0.0648099i
$171$	0.355695	−	3.61143i	0.0272007	−	0.276173i
$172$	−7.81262	−	21.7411i	−0.595707	−	1.65774i
$173$	−6.51753	−	1.97707i	−0.495518	−	0.150314i	0.0326274	−	0.999468i	$-0.489613\pi$
$173$	−6.51753	−	1.97707i	−0.495518	−	0.150314i	−0.528146	+	0.849154i	$0.677113\pi$
$174$	−9.72118	−	3.74224i	−0.736960	−	0.283699i
$175$	−7.40522	+	3.06734i	−0.559782	+	0.231869i
$176$	−10.5339	+	0.0287861i	−0.794023	+	0.00216983i
$177$	−7.40196	−	3.06599i	−0.556366	−	0.230454i
$178$	8.57957	+	8.15726i	0.643066	+	0.611413i
$179$	−22.6499	+	12.1066i	−1.69293	+	0.904890i	−0.714147	+	0.699996i	$0.753185\pi$
$179$	−22.6499	+	12.1066i	−1.69293	+	0.904890i	−0.978784	+	0.204895i	$0.934315\pi$
$180$	−2.48532	+	0.372134i	−0.185245	+	0.0277373i
$181$	5.58223	−	4.58122i	0.414924	−	0.340519i	−0.403657	−	0.914910i	$-0.632261\pi$
$181$	5.58223	−	4.58122i	0.414924	−	0.340519i	0.818581	+	0.574391i	$0.194761\pi$
$182$	2.63540	+	4.64473i	0.195349	+	0.344291i
$183$	0.824630	+	4.14570i	0.0609584	+	0.306459i
$184$	−1.51618	−	19.9956i	−0.111774	−	1.47410i
$185$	−12.3764	−	2.46182i	−0.909930	−	0.180996i
$186$	−0.0370339	−	0.0186096i	−0.00271545	−	0.00136452i
$187$	−4.79604	+	8.97276i	−0.350721	+	0.656153i
$188$	−9.39640	+	10.3958i	−0.685303	+	0.758195i
$189$	−2.33159	+	0.229641i	−0.169598	+	0.0167039i
$190$	−5.45039	−	3.44621i	−0.395413	−	0.250014i
$191$			8.80439i			0.637063i	0.947912	+	0.318532i	$0.103190\pi$
$191$			8.80439i			0.637063i	−0.947912	+	0.318532i	$0.896810\pi$
$192$	−7.91816	−	1.14140i	−0.571444	−	0.0823732i
$193$			13.1337i			0.945383i	0.881228	+	0.472692i	$0.156718\pi$
$193$			13.1337i			0.945383i	−0.881228	+	0.472692i	$0.843282\pi$
$194$	−0.521881	+	0.825387i	−0.0374689	+	0.0592593i
$195$	−2.01546	+	0.198506i	−0.144330	+	0.0142153i
$196$	−3.01808	+	0.152403i	−0.215577	+	0.0108859i
$197$	−4.72262	+	8.83539i	−0.336472	+	0.629496i	−0.992080	−	0.125606i	$-0.959913\pi$
$197$	−4.72262	+	8.83539i	−0.336472	+	0.629496i	0.655608	+	0.755102i	$0.272413\pi$
$198$	1.67222	−	3.32779i	0.118840	−	0.236496i
$199$	3.48367	+	0.692946i	0.246951	+	0.0491216i	0.317014	−	0.948421i	$-0.397320\pi$
$199$	3.48367	+	0.692946i	0.246951	+	0.0491216i	−0.0700626	+	0.997543i	$0.522320\pi$
$200$	3.01651	−	9.19434i	0.213300	−	0.650138i
$201$	−1.21318	−	6.09907i	−0.0855712	−	0.430195i
$202$	−12.1148	+	6.87389i	−0.852394	+	0.483645i
$203$	−13.3397	+	10.9476i	−0.936260	+	0.768369i
$204$	−4.59432	+	6.21244i	−0.321667	+	0.434958i
$205$	−1.78053	+	0.951711i	−0.124357	+	0.0664704i
$206$	−1.31960	+	1.38792i	−0.0919410	+	0.0967009i
$207$	6.55014	+	2.71316i	0.455266	+	0.188577i
$208$	−6.32662	−	1.24048i	−0.438672	−	0.0860118i
$209$	8.82922	−	3.65718i	0.610730	−	0.252973i
$210$	−1.49567	+	3.88529i	−0.103211	+	0.268110i
$211$	−3.97562	−	1.20599i	−0.273693	−	0.0830239i	0.150455	−	0.988617i	$-0.451926\pi$
$211$	−3.97562	−	1.20599i	−0.273693	−	0.0830239i	−0.424148	+	0.905593i	$0.639426\pi$
$212$	−1.28382	+	2.72403i	−0.0881732	+	0.187087i
$213$	−0.804146	+	8.16464i	−0.0550992	+	0.559432i
$214$	0.313346	+	2.52633i	0.0214199	+	0.172697i
$215$	8.06363	−	12.0681i	0.549935	−	0.823036i
$216$	1.62389	−	2.31581i	0.110492	−	0.157571i
$217$	−0.0570911	+	0.0381471i	−0.00387560	+	0.00258959i
$218$	4.87628	+	0.356347i	0.330263	+	0.0241348i
$219$	10.1379	−	3.07530i	0.685057	−	0.207810i
$220$	−3.94962	−	5.31026i	−0.266283	−	0.358018i
$221$	−3.95027	+	4.81342i	−0.265724	+	0.323786i
$222$	11.6062	−	8.18589i	0.778959	−	0.549401i
$223$	−15.5660	+	15.5660i	−1.04238	+	1.04238i	−0.0433152	+	0.999061i	$0.513792\pi$
$223$	−15.5660	+	15.5660i	−1.04238	+	1.04238i	−0.999061	+	0.0433152i	$0.986208\pi$
$224$	−8.11809	+	10.4760i	−0.542413	+	0.699954i
$225$	2.41913	+	2.41913i	0.161275	+	0.161275i
$226$	−20.9637	−	3.62279i	−1.39448	−	0.240985i
$227$	14.3862	+	11.8065i	0.954847	+	0.783622i	0.976361	−	0.216146i	$-0.0693488\pi$
$227$	14.3862	+	11.8065i	0.954847	+	0.783622i	−0.0215145	+	0.999769i	$0.506849\pi$
$228$	7.03789	−	1.77312i	0.466096	−	0.117428i
$229$	−8.28225	−	27.3029i	−0.547307	−	1.80423i	−0.592910	−	0.805269i	$-0.702021\pi$
$229$	−8.28225	−	27.3029i	−0.547307	−	1.80423i	0.0456035	−	0.998960i	$-0.485479\pi$
$230$	9.53405	−	8.23550i	0.628657	−	0.543032i
$231$	−3.42782	−	5.13010i	−0.225534	−	0.337536i
$232$	0.468586	−	20.8279i	0.0307642	−	1.36742i
$233$	20.6113	+	13.7721i	1.35029	+	0.902238i	0.999416	−	0.0341830i	$-0.0108829\pi$
$233$	20.6113	+	13.7721i	1.35029	+	0.902238i	0.350879	+	0.936421i	$0.385883\pi$
$234$	1.40112	−	1.79791i	0.0915943	−	0.117533i
$235$	−8.76142	−	0.862925i	−0.571532	−	0.0562910i
$236$	0.764375	−	16.0054i	0.0497566	−	1.04186i
$237$	−2.09248	+	6.89799i	−0.135921	+	0.448073i
$238$	5.19530	+	11.6988i	0.336761	+	0.758322i
$239$	−4.59748	−	11.0993i	−0.297386	−	0.717954i	−0.999980	−	0.00636264i	$-0.997975\pi$
$239$	−4.59748	−	11.0993i	−0.297386	−	0.717954i	0.702593	−	0.711592i	$-0.252025\pi$
$240$	−2.38137	−	4.42610i	−0.153717	−	0.285703i
$241$	1.64636	−	3.97466i	0.106051	−	0.256030i	−0.861942	−	0.507007i	$-0.830752\pi$
$241$	1.64636	−	3.97466i	0.106051	−	0.256030i	0.967993	+	0.250977i	$0.0807518\pi$
$242$	−5.74659	+	0.144999i	−0.369405	+	0.00932090i
$243$	0.471397	+	0.881921i	0.0302401	+	0.0565753i
$244$	−7.24515	+	4.35604i	−0.463823	+	0.278867i
$245$	−1.20443	−	1.46760i	−0.0769481	−	0.0937615i
$246$	0.604555	−	2.19040i	0.0385450	−	0.139655i
$247$	5.73658	−	1.14108i	0.365010	−	0.0726050i
$248$	0.00997839	−	0.0822905i	0.000633628	−	0.00522545i
$249$	−1.99524	+	10.0307i	−0.126443	+	0.635673i
$250$	14.2058	−	4.70372i	0.898452	−	0.297489i
$251$	−8.39487	−	4.48715i	−0.529879	−	0.283226i	0.184683	−	0.982798i	$-0.440874\pi$
$251$	−8.39487	−	4.48715i	−0.529879	−	0.283226i	−0.714562	+	0.699572i	$0.753374\pi$
$252$	−2.00920	−	4.23312i	−0.126568	−	0.266661i
$253$	1.83007	+	18.5810i	0.115056	+	1.16818i
$254$	0.448302	+	1.99002i	0.0281290	+	0.124865i
$255$	−4.85437			−0.303993
$256$	−3.20716	−	15.6753i	−0.200448	−	0.979704i
$257$	13.4436			0.838587			0.419293	−	0.907851i	$-0.362278\pi$
$257$	13.4436			0.838587			0.419293	+	0.907851i	$0.362278\pi$
$258$	3.59007	+	15.9364i	0.223508	+	0.992155i
$259$	−2.30623	−	23.4155i	−0.143302	−	1.45497i
$260$	−1.73678	−	3.65918i	−0.107711	−	0.226932i
$261$	6.49592	+	3.47214i	0.402088	+	0.214920i
$262$	3.02975	−	1.00319i	0.187179	−	0.0619773i
$263$	2.91564	−	14.6579i	0.179786	−	0.903846i	−0.780570	−	0.625069i	$-0.785071\pi$
$263$	2.91564	−	14.6579i	0.179786	−	0.903846i	0.960356	−	0.278777i	$-0.0899291\pi$
$264$	7.39446	+	0.896638i	0.455098	+	0.0551843i
$265$	−1.85558	+	0.369099i	−0.113988	+	0.0226736i
$266$	3.19896	−	11.5904i	0.196141	−	0.710651i
$267$	−5.31056	−	6.47093i	−0.325001	−	0.396015i
$268$	10.6589	−	6.40853i	0.651098	−	0.391463i
$269$	−2.06379	−	3.86107i	−0.125831	−	0.235414i	0.811115	−	0.584886i	$-0.198861\pi$
$269$	−2.06379	−	3.86107i	−0.125831	−	0.235414i	−0.936947	+	0.349472i	$0.886361\pi$
$270$	1.77642	−	0.0448229i	0.108109	−	0.00272784i
$271$	4.83178	−	11.6649i	0.293510	−	0.708595i	−0.706490	−	0.707723i	$-0.749722\pi$
$271$	4.83178	−	11.6649i	0.293510	−	0.708595i	1.00000		0.000871998i	$-0.000277566\pi$
$272$	−14.8002	−	4.44547i	−0.897395	−	0.269546i
$273$	−1.44508	−	3.48873i	−0.0874601	−	0.211147i
$274$	8.30360	+	18.6981i	0.501639	+	1.12960i
$275$	−2.61535	+	8.62166i	−0.157712	+	0.519905i
$276$	−0.676410	+	14.1635i	−0.0407151	+	0.852542i
$277$	24.7898	+	2.44158i	1.48947	+	0.146700i	0.809753	−	0.586771i	$-0.199601\pi$
$277$	24.7898	+	2.44158i	1.48947	+	0.146700i	0.679721	+	0.733471i	$0.262101\pi$
$278$	−2.57035	+	3.29824i	−0.154159	+	0.197815i
$279$	0.0243680	+	0.0162822i	0.00145888	+	0.000974790i
$280$	−8.32436	−	0.187281i	−0.497476	−	0.0111922i
$281$	−3.94090	−	5.89798i	−0.235095	−	0.351844i	0.695099	−	0.718915i	$-0.255361\pi$
$281$	−3.94090	−	5.89798i	−0.235095	−	0.351844i	−0.930193	+	0.367071i	$0.880361\pi$
$282$	7.49856	−	6.47724i	0.446533	−	0.385714i
$283$	−2.56933	−	8.46994i	−0.152731	−	0.503486i	0.846868	−	0.531803i	$-0.178485\pi$
$283$	−2.56933	−	8.46994i	−0.152731	−	0.503486i	−0.999599	+	0.0283170i	$0.990985\pi$
$284$	−15.9111	+	4.00863i	−0.944149	+	0.237868i
$285$	3.52475	+	2.89269i	0.208788	+	0.171348i
$286$	5.91507	+	1.02220i	0.349765	+	0.0604439i
$287$	−2.66185	−	2.66185i	−0.157124	−	0.157124i
$288$	5.45706	+	1.49012i	0.321560	+	0.0878064i
$289$	1.46686	−	1.46686i	0.0862857	−	0.0862857i
$290$	10.6959	−	7.54385i	0.628085	−	0.442990i
$291$	0.438058	−	0.533776i	0.0256794	−	0.0312905i
$292$	12.6450	+	17.0013i	0.739995	+	0.994923i
$293$	2.86006	−	0.867591i	0.167087	−	0.0506852i	−0.205633	−	0.978629i	$-0.565925\pi$
$293$	2.86006	−	0.867591i	0.167087	−	0.0506852i	0.372720	+	0.927944i	$0.378425\pi$
$294$	2.13114	+	0.155739i	0.124291	+	0.00908287i
$295$	8.37039	−	5.59292i	0.487343	−	0.325632i
$296$	23.2571	+	16.3083i	1.35179	+	0.947900i
$297$	−1.46309	+	2.18966i	−0.0848969	+	0.127057i
$298$	−1.63963	−	13.2195i	−0.0949815	−	0.765783i
$299$	−1.12006	+	11.3721i	−0.0647746	+	0.657668i
$300$	−2.91702	+	6.18939i	−0.168414	+	0.357345i
$301$	25.8974	+	7.85590i	1.49270	+	0.452807i
$302$	−11.3596	+	29.5086i	−0.653671	+	1.69803i
$303$	9.09960	−	3.76918i	0.522758	−	0.216534i
$304$	8.09740	+	12.0472i	0.464418	+	0.690955i
$305$	−4.90689	−	2.03250i	−0.280968	−	0.116381i
$306$	3.76468	−	3.95958i	0.215212	−	0.226354i
$307$	26.8834	−	14.3695i	1.53432	−	0.820111i	0.534631	−	0.845085i	$-0.320451\pi$
$307$	26.8834	−	14.3695i	1.53432	−	0.820111i	0.999688	+	0.0249747i	$0.00795050\pi$
$308$	7.33728	−	9.92148i	0.418080	−	0.565329i
$309$	1.04680	−	0.859090i	0.0595506	−	0.0488719i
$310$	0.0452951	−	0.0257003i	0.00257259	−	0.00145968i
$311$	−6.17684	−	31.0531i	−0.350256	−	1.76086i	−0.607315	−	0.794461i	$-0.707753\pi$
$311$	−6.17684	−	31.0531i	−0.350256	−	1.76086i	0.257058	−	0.966396i	$-0.417247\pi$
$312$	4.33161	+	1.42113i	0.245229	+	0.0804557i
$313$	−29.8959	−	5.94666i	−1.68981	−	0.336125i	−0.745835	−	0.666130i	$-0.767949\pi$
$313$	−29.8959	−	5.94666i	−1.68981	−	0.336125i	−0.943979	+	0.330005i	$0.892949\pi$
$314$	8.34600	−	16.6089i	0.470992	−	0.937295i
$315$	1.38772	−	2.59624i	0.0781893	−	0.146282i
$316$	−14.3984	+	0.727071i	−0.809974	+	0.0409009i
$317$	−12.8471	+	1.26533i	−0.721566	+	0.0710681i	−0.452132	−	0.891951i	$-0.649337\pi$
$317$	−12.8471	+	1.26533i	−0.721566	+	0.0710681i	−0.269434	+	0.963019i	$0.586837\pi$
$318$	1.13799	−	1.79980i	0.0638151	−	0.100928i
$319$			19.3973i			1.08604i
$320$	6.72001	−	7.47574i	0.375660	−	0.417907i
$321$		−	1.80008i		−	0.100470i
$322$	19.8549	+	12.5540i	1.10647	+	0.699605i
$323$	13.9523	−	1.37418i	0.776325	−	0.0764613i
$324$	−1.34109	+	1.48374i	−0.0745051	+	0.0824298i
$325$	−2.59935	+	4.86304i	−0.144186	+	0.269753i
$326$	−19.6610	−	9.87969i	−1.08892	−	0.547185i
$327$	−3.39081	−	0.674475i	−0.187512	−	0.0372985i
$328$	4.53159	−	0.343610i	0.250215	−	0.0189727i
$329$	−3.20248	−	16.1000i	−0.176559	−	0.887620i
$330$	2.30938	+	4.07013i	0.127127	+	0.224053i
$331$	−17.6287	+	14.4675i	−0.968958	+	0.795204i	−0.978815	−	0.204748i	$-0.934363\pi$
$331$	−17.6287	+	14.4675i	−0.968958	+	0.795204i	0.00985638	+	0.999951i	$0.496863\pi$
$332$	−20.2290	+	3.02894i	−1.11021	+	0.166235i
$333$	−8.85691	+	4.73412i	−0.485355	+	0.259428i
$334$	−13.2477	−	12.5956i	−0.724882	−	0.689201i
$335$	7.21893	+	2.99018i	0.394412	+	0.163371i
$336$	6.60850	−	6.64472i	0.360523	−	0.362499i
$337$	0.715775	−	0.296484i	0.0389908	−	0.0161505i	−0.363103	−	0.931749i	$-0.618283\pi$
$337$	0.715775	−	0.296484i	0.0389908	−	0.0161505i	0.402094	+	0.915599i	$0.368283\pi$
$338$	−13.7288	−	5.28501i	−0.746748	−	0.287467i
$339$	14.3955	+	4.36683i	0.781857	+	0.237174i
$340$	−3.28326	−	9.13673i	−0.178060	−	0.495509i
$341$	−0.00756498	+	0.0768085i	−0.000409666	+	0.00415941i
$342$	−5.09302	+	0.631697i	−0.275399	+	0.0341583i
$343$	11.0781	−	16.5796i	0.598162	−	0.895212i
$344$	−27.5667	+	17.5357i	−1.48630	+	0.945461i
$345$	−7.40712	+	4.94928i	−0.398786	+	0.266460i
$346$	−0.702005	+	9.60631i	−0.0377400	+	0.516438i
$347$	16.9762	−	5.14969i	0.911333	−	0.276450i	0.200404	−	0.979713i	$-0.435775\pi$
$347$	16.9762	−	5.14969i	0.911333	−	0.276450i	0.710929	+	0.703264i	$0.248275\pi$
$348$	−2.14162	+	14.5748i	−0.114803	+	0.781291i
$349$	21.3431	−	26.0067i	1.14247	−	1.39210i	0.234996	−	0.971996i	$-0.424492\pi$
$349$	21.3431	−	26.0067i	1.14247	−	1.39210i	0.907474	−	0.420108i	$-0.138008\pi$
$350$	6.53336	+	9.26320i	0.349223	+	0.495139i
$351$	−1.13969	+	1.13969i	−0.0608324	+	0.0608324i
$352$	3.31364	+	14.5240i	0.176618	+	0.774134i
$353$	18.5978	+	18.5978i	0.989862	+	0.989862i	0.999949	−	0.0100873i	$-0.00321095\pi$
$353$	18.5978	+	18.5978i	0.989862	+	0.989862i	−0.0100873	+	0.999949i	$0.503211\pi$
$354$	−1.92945	+	11.1649i	−0.102549	+	0.593410i
$355$	−7.96868	−	6.53972i	−0.422933	−	0.347093i
$356$	8.58756	−	14.3720i	0.455140	−	0.761713i
$357$	−2.62747	−	8.66160i	−0.139060	−	0.458420i
$358$	23.7423	+	27.4859i	1.25482	+	1.45268i
$359$	−1.76525	−	2.64188i	−0.0931661	−	0.139433i	0.781959	−	0.623330i	$-0.214221\pi$
$359$	−1.76525	−	2.64188i	−0.0931661	−	0.139433i	−0.875125	+	0.483897i	$0.839221\pi$
$360$	1.28585	+	3.31319i	0.0677701	+	0.174621i
$361$	4.84833	+	3.23955i	0.255175	+	0.170503i
$362$	−8.05538	−	6.27763i	−0.423381	−	0.329945i
$363$	4.04517	+	0.398415i	0.212316	+	0.0209113i
$364$	5.58898	−	5.07948i	0.292942	−	0.266237i
$365$	−3.86417	+	12.7385i	−0.202260	+	0.666761i
$366$	5.46327	−	2.42617i	0.285570	−	0.126818i
$367$	−3.62419	−	8.74957i	−0.189181	−	0.456724i	0.800621	−	0.599171i	$-0.204503\pi$
$367$	−3.62419	−	8.74957i	−0.189181	−	0.456724i	−0.989802	+	0.142447i	$0.954503\pi$
$368$	−27.1155	+	8.30639i	−1.41349	+	0.433001i
$369$	−0.614880	+	1.48445i	−0.0320094	+	0.0772775i
$370$	0.450145	+	17.8401i	0.0234019	+	0.927462i
$371$	−1.66293	−	3.11112i	−0.0863350	−	0.161521i
$372$	−0.0141644	+	0.0568772i	−0.000734392	+	0.00294895i
$373$	7.05614	+	8.59793i	0.365353	+	0.445184i	0.922945	−	0.384931i	$-0.125775\pi$
$373$	7.05614	+	8.59793i	0.365353	+	0.445184i	−0.557592	+	0.830115i	$0.688275\pi$
$374$	13.8698	+	3.82809i	0.717189	+	0.197946i
$375$	−10.3780	+	2.06431i	−0.535918	+	0.106601i
$376$	17.2629	+	9.73263i	0.890266	+	0.501922i
$377$	−2.31606	+	11.6436i	−0.119283	+	0.599678i
$378$	1.04148	+	3.14538i	0.0535678	+	0.161781i
$379$	−19.0043	−	10.1580i	−0.976183	−	0.521781i	−0.0954707	−	0.995432i	$-0.530436\pi$
$379$	−19.0043	−	10.1580i	−0.976183	−	0.521781i	−0.880712	+	0.473652i	$0.842936\pi$
$380$	−3.06055	+	8.59065i	−0.157003	+	0.440691i
$381$	−0.141382	−	1.43547i	−0.00724321	−	0.0735416i
$382$	12.1469	−	2.73639i	0.621488	−	0.140006i
$383$	14.9429			0.763548			0.381774	−	0.924256i	$-0.375313\pi$
$383$	14.9429			0.763548			0.381774	+	0.924256i	$0.375313\pi$
$384$	0.886236	+	11.2789i	0.0452256	+	0.575576i
$385$	7.75259			0.395109
$386$	18.1197	−	4.08193i	0.922270	−	0.207765i
$387$	−1.13221	−	11.4955i	−0.0575533	−	0.584349i
$388$	1.30094	+	0.463478i	0.0660450	+	0.0235295i
$389$	−8.06857	−	4.31274i	−0.409093	−	0.218665i	0.253996	−	0.967205i	$-0.418255\pi$
$389$	−8.06857	−	4.31274i	−0.409093	−	0.218665i	−0.663089	+	0.748541i	$0.730755\pi$
$390$	0.900270	+	2.71892i	0.0455869	+	0.137678i
$391$	−5.34363	+	26.8642i	−0.270239	+	1.35858i
$392$	1.14828	+	4.11650i	0.0579968	+	0.207915i
$393$	−2.21338	+	0.440269i	−0.111650	+	0.0222086i
$394$	13.6574	+	3.76948i	0.688052	+	0.189904i
$395$	−5.74598	−	7.00150i	−0.289112	−	0.352284i
$396$	−5.11087	−	1.27279i	−0.256831	−	0.0639600i
$397$	−7.92746	−	14.8312i	−0.397868	−	0.744358i	0.600609	−	0.799543i	$-0.294925\pi$
$397$	−7.92746	−	14.8312i	−0.397868	−	0.744358i	−0.998476	+	0.0551853i	$0.982425\pi$
$398$	−0.126706	−	5.02158i	−0.00635118	−	0.251709i
$399$	−3.25359	+	7.85487i	−0.162883	+	0.393235i
$400$	−13.6224	−	1.30411i	−0.681120	−	0.0652056i
$401$	6.05420	+	14.6161i	0.302333	+	0.729895i	0.999910	+	0.0133864i	$0.00426114\pi$
$401$	6.05420	+	14.6161i	0.302333	+	0.729895i	−0.697578	+	0.716509i	$0.745739\pi$
$402$	−8.03746	+	3.56933i	−0.400872	+	0.178022i
$403$	−0.0137120	+	0.0452025i	−0.000683045	+	0.00225170i
$404$	13.2487	+	14.5777i	0.659150	+	0.725266i
$405$	−1.25046	−	0.123160i	−0.0621361	−	0.00611987i
$406$	19.2496	+	15.0014i	0.955344	+	0.744508i
$407$	−21.9902	−	14.6934i	−1.09002	−	0.728325i
$408$	9.99884	+	4.40768i	0.495016	+	0.218213i
$409$	−19.4361	−	29.0882i	−0.961054	−	1.43832i	−0.897842	−	0.440318i	$-0.854866\pi$
$409$	−19.4361	−	29.0882i	−0.961054	−	1.43832i	−0.0632119	−	0.998000i	$-0.520134\pi$
$410$	1.86640	+	2.16069i	0.0921751	+	0.106709i
$411$	−4.19946	−	13.8437i	−0.207144	−	0.682862i
$412$	2.32496	+	1.38921i	0.114542	+	0.0684415i
$413$	14.5099	+	11.9080i	0.713986	+	0.585954i
$414$	1.70740	−	9.88007i	0.0839143	−	0.485579i
$415$	−9.08682	−	9.08682i	−0.446055	−	0.446055i
$416$	0.254890	+	9.11399i	0.0124970	+	0.446850i
$417$	2.09076	−	2.09076i	0.102385	−	0.102385i
$418$	−7.78970	−	11.0445i	−0.381007	−	0.540204i
$419$	21.3729	−	26.0429i	1.04413	−	1.27228i	0.0828961	−	0.996558i	$-0.473583\pi$
$419$	21.3729	−	26.0429i	1.04413	−	1.27228i	0.961237	−	0.275722i	$-0.0889170\pi$
$420$	5.82515	+	0.855947i	0.284238	+	0.0417659i
$421$	−36.2186	+	10.9868i	−1.76519	+	0.535464i	−0.994776	−	0.102082i	$-0.967450\pi$
$421$	−36.2186	+	10.9868i	−1.76519	+	0.535464i	−0.770412	+	0.637546i	$0.779950\pi$
$422$	−0.428216	+	5.85974i	−0.0208452	+	0.285248i
$423$	−5.82572	+	3.89262i	−0.283256	+	0.189266i
$424$	4.15719	+	0.924583i	0.201891	+	0.0449017i
$425$	−7.34309	+	10.9897i	−0.356192	+	0.533079i
$426$	11.5142	−	1.42813i	0.557864	−	0.0691929i
$427$	0.970674	−	9.85542i	0.0469742	−	0.476937i
$428$	3.38804	−	1.21749i	0.163767	−	0.0588494i
$429$	−4.06181	−	1.23214i	−0.196106	−	0.0594881i
$430$	−19.1558	−	7.37416i	−0.923772	−	0.355614i
$431$	12.9768	−	5.37517i	0.625070	−	0.258913i	−0.0475865	−	0.998867i	$-0.515153\pi$
$431$	12.9768	−	5.37517i	0.625070	−	0.258913i	0.672657	+	0.739954i	$0.265153\pi$
$432$	−3.69969	−	1.52063i	−0.178001	−	0.0731613i
$433$	20.8571	+	8.63928i	1.00233	+	0.415177i	0.822650	−	0.568548i	$-0.192495\pi$
$433$	20.8571	+	8.63928i	1.00233	+	0.415177i	0.179677	+	0.983726i	$0.442495\pi$
$434$	0.0703730	+	0.0669091i	0.00337801	+	0.00321174i
$435$	−8.16223	+	4.36280i	−0.391349	+	0.209180i
$436$	−1.02391	−	6.83826i	−0.0490364	−	0.327493i
$437$	19.8882	−	16.3219i	0.951383	−	0.780780i
$438$	−7.39366	−	13.0309i	−0.353283	−	0.622639i
$439$	6.92681	+	34.8234i	0.330598	+	1.66203i	0.686215	+	0.727399i	$0.259271\pi$
$439$	6.92681	+	34.8234i	0.330598	+	1.66203i	−0.355617	+	0.934632i	$0.615729\pi$
$440$	−6.09871	+	7.09947i	−0.290745	+	0.338454i
$441$	−1.48193	−	0.294775i	−0.0705682	−	0.0140369i
$442$	7.86853	+	3.95395i	0.374268	+	0.188070i
$443$	−1.88281	+	3.52249i	−0.0894550	+	0.167359i	−0.922670	−	0.385591i	$-0.873998\pi$
$443$	−1.88281	+	3.52249i	−0.0894550	+	0.167359i	0.833215	+	0.552949i	$0.186498\pi$
$444$	−14.9008	−	13.4682i	−0.707160	−	0.639174i
$445$	10.4677	−	1.03098i	0.496218	−	0.0488732i
$446$	26.3134	+	16.6376i	1.24597	+	0.787812i
$447$			9.41920i			0.445513i
$448$	16.9761	+	7.94413i	0.802047	+	0.375325i
$449$			26.1201i			1.23268i	0.787479	+	0.616342i	$0.211386\pi$
$449$			26.1201i			1.23268i	−0.787479	+	0.616342i	$0.788614\pi$
$450$	2.58567	−	4.08939i	0.121889	−	0.192776i
$451$	−4.21101	+	0.414748i	−0.198289	+	0.0195297i
$452$	1.51734	+	30.0483i	0.0713695	+	1.41335i
$453$	10.5397	−	19.7184i	0.495198	−	0.926451i
$454$	11.8174	−	23.5172i	0.554620	−	1.10372i
$455$	4.65364	+	0.925667i	0.218166	+	0.0433960i
$456$	−4.63364	−	9.15866i	−0.216990	−	0.428894i
$457$	0.294559	+	1.48085i	0.0137789	+	0.0692711i	0.987063	−	0.160333i	$-0.0512568\pi$
$457$	0.294559	+	1.48085i	0.0137789	+	0.0692711i	−0.973284	+	0.229604i	$0.926257\pi$
$458$	−35.0941	+	19.9122i	−1.63984	+	0.930437i
$459$	−2.98642	+	2.45089i	−0.139394	+	0.114398i
$460$	−14.3252	−	10.5940i	−0.667915	−	0.493946i
$461$	−35.4237	+	18.9344i	−1.64985	+	0.881862i	−0.658206	+	0.752838i	$0.728684\pi$
$461$	−35.4237	+	18.9344i	−1.64985	+	0.881862i	−0.991642	+	0.129024i	$0.958816\pi$
$462$	−6.01232	+	6.32358i	−0.279719	+	0.294200i
$463$	−29.7435	−	12.3202i	−1.38230	−	0.572567i	−0.437204	−	0.899362i	$-0.644031\pi$
$463$	−29.7435	−	12.3202i	−1.38230	−	0.572567i	−0.945095	+	0.326795i	$0.894031\pi$
$464$	−28.8807	+	5.82681i	−1.34075	+	0.270503i
$465$	−0.0340218	+	0.0140923i	−0.00157772	+	0.000653515i
$466$	12.5945	−	32.7166i	0.583429	−	1.51557i
$467$	31.7059	+	9.61787i	1.46717	+	0.445062i	0.919987	−	0.391949i	$-0.128199\pi$
$467$	31.7059	+	9.61787i	1.46717	+	0.445062i	0.547186	+	0.837011i	$0.315699\pi$
$468$	−2.91593	−	1.37426i	−0.134789	−	0.0635252i
$469$	−1.42804	+	14.4991i	−0.0659407	+	0.669507i
$470$	1.53251	+	12.3558i	0.0706895	+	0.569931i
$471$	−7.30222	+	10.9286i	−0.336469	+	0.503561i
$472$	−22.3193	+	3.91990i	−1.02733	+	0.180428i
$473$	25.2931	−	16.9003i	1.16298	−	0.777076i
$474$	10.1671	+	0.742985i	0.466989	+	0.0341265i
$475$	11.8805	−	3.60391i	0.545115	−	0.165359i
$476$	14.5255	−	10.8036i	0.665774	−	0.495183i
$477$	−0.955207	+	1.16392i	−0.0437359	+	0.0532924i
$478$	−13.8841	+	9.79251i	−0.635046	+	0.447899i
$479$	20.6901	−	20.6901i	0.945355	−	0.945355i	−0.0532272	−	0.998582i	$-0.516951\pi$
$479$	20.6901	−	20.6901i	0.945355	−	0.945355i	0.998582	+	0.0532272i	$0.0169507\pi$
$480$	−5.36629	+	4.66106i	−0.244937	+	0.212747i
$481$	−11.4457	−	11.4457i	−0.521877	−	0.521877i
$482$	−5.99528	−	1.03606i	−0.273077	−	0.0471913i
$483$	−12.8401	−	10.5376i	−0.584245	−	0.479477i
$484$	1.98608	+	7.88315i	0.0902763	+	0.358325i
$485$	0.251864	+	0.830283i	0.0114365	+	0.0377012i
$486$	1.07022	−	0.924457i	0.0485463	−	0.0419342i
$487$	4.73493	+	7.08633i	0.214560	+	0.321112i	0.923101	−	0.384558i	$-0.125646\pi$
$487$	4.73493	+	7.08633i	0.214560	+	0.321112i	−0.708541	+	0.705670i	$0.750646\pi$
$488$	8.26154	+	8.64184i	0.373983	+	0.391198i
$489$	12.9368	+	8.64410i	0.585023	+	0.390900i
$490$	−1.65042	+	2.11780i	−0.0745585	+	0.0956726i
$491$	−15.2392	−	1.50093i	−0.687736	−	0.0677361i	−0.251888	−	0.967756i	$-0.581052\pi$
$491$	−15.2392	−	1.50093i	−0.687736	−	0.0677361i	−0.435848	+	0.900020i	$0.643552\pi$
$492$	−3.20986	−	0.153294i	−0.144712	−	0.00691104i
$493$	−8.26039	+	27.2308i	−0.372029	+	1.22642i
$494$	−3.35720	−	7.55977i	−0.151047	−	0.340130i
$495$	−1.26631	−	3.05713i	−0.0569162	−	0.137408i
$496$	−0.116632	+	0.0118092i	−0.00523695	+	0.000530249i
$497$	7.35565	−	17.7581i	0.329946	−	0.796560i
$498$	14.4589	−	0.364831i	0.647920	−	0.0163485i
$499$	6.03557	+	11.2918i	0.270189	+	0.505488i	0.980024	−	0.198880i	$-0.0637304\pi$
$499$	6.03557	+	11.2918i	0.270189	+	0.505488i	−0.709835	+	0.704368i	$0.751230\pi$
$500$	−10.9046	−	18.1369i	−0.487667	−	0.811108i
$501$	8.20002	+	9.99175i	0.366350	+	0.446399i
$502$	−3.58153	+	12.9765i	−0.159852	+	0.579169i
$503$	13.8941	−	2.76371i	0.619508	−	0.123228i	0.124649	−	0.992201i	$-0.460220\pi$
$503$	13.8941	−	2.76371i	0.619508	−	0.123228i	0.494859	+	0.868973i	$0.335220\pi$
$504$	−5.21572	+	4.08761i	−0.232326	+	0.182077i
$505$	−2.41441	+	12.1380i	−0.107440	+	0.540136i
$506$	25.0663	−	8.29980i	1.11434	−	0.368971i
$507$	9.17392	+	4.90356i	0.407428	+	0.217775i
$508$	2.60618	−	1.23699i	0.115630	−	0.0548826i
$509$	−4.30601	−	43.7196i	−0.190860	−	1.93784i	−0.322562	−	0.946548i	$-0.604544\pi$
$509$	−4.30601	−	43.7196i	−0.190860	−	1.93784i	0.131701	−	0.991289i	$-0.457956\pi$
$510$	1.50873	+	6.69728i	0.0668078	+	0.296561i
$511$	−24.8206			−1.09800
$512$	−20.6294	+	9.29658i	−0.911701	+	0.410855i
$513$	3.62891			0.160220
$514$	−4.17824	−	18.5473i	−0.184294	−	0.818085i
$515$	0.166782	+	1.69337i	0.00734930	+	0.0746187i
$516$	20.8706	−	9.90600i	0.918779	−	0.436087i
$517$	−16.2729	−	8.69803i	−0.715680	−	0.382539i
$518$	−31.5882	+	10.4593i	−1.38791	+	0.459554i
$519$	1.32872	−	6.67993i	0.0583244	−	0.293216i
$520$	−4.50855	+	3.53340i	−0.197713	+	0.154950i
$521$	12.5539	−	2.49713i	0.549998	−	0.109401i	0.0877344	−	0.996144i	$-0.472037\pi$
$521$	12.5539	−	2.49713i	0.549998	−	0.109401i	0.462264	+	0.886742i	$0.347037\pi$
$522$	2.77138	−	10.0412i	0.121300	−	0.439490i
$523$	−7.48545	−	9.12104i	−0.327316	−	0.398835i	0.583187	−	0.812338i	$-0.301805\pi$
$523$	−7.48545	−	9.12104i	−0.327316	−	0.398835i	−0.910503	+	0.413502i	$0.864305\pi$
$524$	−2.32568	−	3.86817i	−0.101598	−	0.168982i
$525$	−3.77841	−	7.06891i	−0.164903	−	0.308512i
$526$	−21.1288	+	0.533127i	−0.921260	+	0.0232454i
$527$	−0.0433290	+	0.104606i	−0.00188744	+	0.00455669i
$528$	−1.06115	−	10.4804i	−0.0461807	−	0.456099i
$529$	10.4341	+	25.1901i	0.453655	+	1.09522i
$530$	1.08594	+	2.44532i	0.0471701	+	0.106218i
$531$	2.32571	−	7.66684i	0.100927	−	0.332713i
$532$	−16.9847	−	0.811146i	−0.736382	−	0.0351676i
$533$	−2.57726	−	0.253838i	−0.111633	−	0.0109949i
$534$	−7.27704	+	9.33781i	−0.314908	+	0.404086i
$535$	1.88064	+	1.25660i	0.0813071	+	0.0543276i
$536$	−12.1542	−	12.7137i	−0.524983	−	0.549149i
$537$	−14.2684	−	21.3542i	−0.615726	−	0.921500i
$538$	−4.68546	+	4.04730i	−0.202005	+	0.174491i
$539$	−1.15507	−	3.80777i	−0.0497525	−	0.164012i
$540$	−0.613947	−	2.43688i	−0.0264201	−	0.104867i
$541$	−12.0970	−	9.92779i	−0.520093	−	0.426829i	0.337372	−	0.941371i	$-0.390462\pi$
$541$	−12.0970	−	9.92779i	−0.520093	−	0.426829i	−0.857465	+	0.514542i	$0.827962\pi$
$542$	−17.5951	−	3.04066i	−0.755775	−	0.130608i
$543$	5.10631	+	5.10631i	0.219133	+	0.219133i
$544$	−1.53326	+	21.8006i	−0.0657378	+	0.934694i
$545$	3.07173	−	3.07173i	0.131578	−	0.131578i
$546$	−4.36405	+	3.07798i	−0.186764	+	0.131725i
$547$	19.9341	−	24.2898i	0.852320	−	1.03855i	−0.146462	−	0.989216i	$-0.546789\pi$
$547$	19.9341	−	24.2898i	0.852320	−	1.03855i	0.998782	−	0.0493385i	$-0.0157113\pi$
$548$	23.2159	−	17.2673i	0.991735	−	0.737623i
$549$	−4.04490	+	1.22701i	−0.172632	+	0.0523674i
$550$	12.7076	+	0.928642i	0.541855	+	0.0395974i
$551$	22.2246	−	14.8500i	0.946798	−	0.632630i
$552$	19.7507	−	3.46879i	0.840647	−	0.147642i
$553$	9.38263	−	14.0421i	0.398990	−	0.597131i
$554$	−4.33613	−	34.9598i	−0.184224	−	1.48530i
$555$	1.23686	−	12.5581i	0.0525020	−	0.533061i
$556$	5.34924	+	2.52107i	0.226858	+	0.106917i
$557$	−18.7169	−	5.67771i	−0.793060	−	0.240572i	−0.132340	−	0.991204i	$-0.542249\pi$
$557$	−18.7169	−	5.67771i	−0.793060	−	0.240572i	−0.660720	+	0.750632i	$0.729749\pi$
$558$	0.0148900	−	0.0386796i	0.000630345	−	0.00163744i
$559$	17.2006	−	7.12470i	0.727506	−	0.301343i
$560$	2.32882	+	11.5428i	0.0984106	+	0.487773i
$561$	−9.39965	−	3.89346i	−0.396854	−	0.164382i
$562$	−6.91225	+	7.27011i	−0.291576	+	0.306671i
$563$	−23.4274	+	12.5222i	−0.987349	+	0.527749i	−0.884296	−	0.466927i	$-0.845361\pi$
$563$	−23.4274	+	12.5222i	−0.987349	+	0.527749i	−0.103053	+	0.994676i	$0.532861\pi$
$564$	−11.2668	−	8.33219i	−0.474418	−	0.350848i
$565$	−14.6115	+	11.9914i	−0.614712	+	0.504481i
$566$	−10.8869	+	6.17719i	−0.457611	+	0.259647i
$567$	−0.457071	−	2.29785i	−0.0191952	−	0.0965007i
$568$	10.4756	+	20.7057i	0.439547	+	0.868791i
$569$	39.0357	+	7.76468i	1.63646	+	0.325512i	0.925797	−	0.378020i	$-0.123395\pi$
$569$	39.0357	+	7.76468i	1.63646	+	0.325512i	0.710663	+	0.703533i	$0.248395\pi$
$570$	2.89538	−	5.76193i	0.121274	−	0.241341i
$571$	−2.99505	+	5.60335i	−0.125339	+	0.234493i	−0.936762	−	0.349966i	$-0.886193\pi$
$571$	−2.99505	+	5.60335i	−0.125339	+	0.234493i	0.811423	+	0.584459i	$0.198693\pi$
$572$	−0.428128	−	8.47836i	−0.0179009	−	0.354498i
$573$	−8.76199	+	0.862981i	−0.366037	+	0.0360515i
$574$	−2.84510	+	4.49969i	−0.118752	+	0.187814i
$575$			24.2555i			1.01152i
$576$	0.359785	−	7.99191i	0.0149911	−	0.332996i
$577$			17.7996i			0.741006i	0.928831	+	0.370503i	$0.120815\pi$
$577$			17.7996i			0.741006i	−0.928831	+	0.370503i	$0.879185\pi$
$578$	−2.47963	−	1.56784i	−0.103139	−	0.0652134i
$579$	−13.0704	+	1.28733i	−0.543189	+	0.0534994i
$580$	−13.7321	−	12.4119i	−0.570193	−	0.515375i
$581$	11.2952	−	21.1318i	0.468604	−	0.876696i
$582$	−0.872566	−	0.438466i	−0.0361690	−	0.0181750i
$583$	−3.88906	−	0.773581i	−0.161068	−	0.0320385i
$584$	19.5255	−	22.7296i	0.807973	−	0.940556i
$585$	−0.395100	−	1.98630i	−0.0163354	−	0.0821235i
$586$	−2.08587	−	3.67621i	−0.0861663	−	0.151863i
$587$	6.93206	−	5.68899i	0.286117	−	0.234810i	−0.480376	−	0.877062i	$-0.659500\pi$
$587$	6.93206	−	5.68899i	0.286117	−	0.234810i	0.766493	+	0.642253i	$0.222000\pi$
$588$	−0.447493	−	2.98861i	−0.0184543	−	0.123248i
$589$	0.0937950	−	0.0501345i	0.00386476	−	0.00206576i
$590$	−10.3177	−	9.80985i	−0.424774	−	0.403865i
$591$	−9.25575	−	3.83386i	−0.380731	−	0.157704i
$592$	15.2713	−	37.1550i	0.627646	−	1.52706i
$593$	27.6188	−	11.4401i	1.13417	−	0.469788i	0.264973	−	0.964256i	$-0.414637\pi$
$593$	27.6188	−	11.4401i	1.13417	−	0.469788i	0.869196	+	0.494468i	$0.164637\pi$
$594$	3.47567	+	1.33799i	0.142609	+	0.0548983i
$595$	10.8834	+	3.30145i	0.446177	+	0.135346i
$596$	−17.7285	+	6.37070i	−0.726187	+	0.260954i
$597$	−0.348149	+	3.53482i	−0.0142488	+	0.144671i
$598$	16.0376	−	1.98917i	0.655825	−	0.0813432i
$599$	−19.8266	+	29.6726i	−0.810093	+	1.21239i	0.164049	+	0.986452i	$0.447545\pi$
$599$	−19.8266	+	29.6726i	−0.810093	+	1.21239i	−0.974142	+	0.225938i	$0.927455\pi$
$600$	9.44573	+	2.10078i	0.385620	+	0.0857642i
$601$	−14.9918	+	10.0172i	−0.611529	+	0.408611i	−0.822405	−	0.568902i	$-0.807368\pi$
$601$	−14.9918	+	10.0172i	−0.611529	+	0.408611i	0.210876	+	0.977513i	$0.432368\pi$
$602$	2.78942	−	38.1707i	0.113688	−	1.55572i
$603$	5.95079	−	1.80515i	0.242335	−	0.0735115i
$604$	44.2418	+	6.50089i	1.80017	+	0.264517i
$605$	−3.24011	+	3.94808i	−0.131729	+	0.160512i
$606$	−8.02824	−	11.3827i	−0.326125	−	0.462391i
$607$	−16.5731	+	16.5731i	−0.672680	+	0.672680i	−0.958333	−	0.285653i	$-0.907790\pi$
$607$	−16.5731	+	16.5731i	−0.672680	+	0.672680i	0.285653	+	0.958333i	$0.407790\pi$
$608$	14.1042	−	14.9158i	0.571999	−	0.604914i
$609$	−12.2024	−	12.2024i	−0.494465	−	0.494465i
$610$	−1.27906	+	7.40144i	−0.0517878	+	0.299676i
$611$	−8.72955	−	7.16416i	−0.353160	−	0.289831i
$612$	−6.63285	−	3.96327i	−0.268117	−	0.160206i
$613$	−5.90560	−	19.4682i	−0.238525	−	0.786312i	−0.991709	−	0.128502i	$-0.958983\pi$
$613$	−5.90560	−	19.4682i	−0.238525	−	0.786312i	0.753184	−	0.657810i	$-0.228517\pi$
$614$	−28.1801	−	32.6234i	−1.13725	−	1.31657i
$615$	−1.12165	−	1.67867i	−0.0452293	−	0.0676905i
$616$	−15.9685	−	7.03922i	−0.643388	−	0.283618i
$617$	30.9664	+	20.6911i	1.24666	+	0.832992i	0.991011	−	0.133777i	$-0.0427106\pi$
$617$	30.9664	+	20.6911i	1.24666	+	0.832992i	0.255650	+	0.966769i	$0.417711\pi$
$618$	−1.51058	−	1.17721i	−0.0607644	−	0.0473542i
$619$	−15.3457	−	1.51142i	−0.616796	−	0.0607491i	−0.215206	−	0.976569i	$-0.569042\pi$
$619$	−15.3457	−	1.51142i	−0.616796	−	0.0607491i	−0.401590	+	0.915820i	$0.631542\pi$
$620$	−0.0495348	−	0.0545033i	−0.00198936	−	0.00218891i
$621$	−2.05807	+	6.78453i	−0.0825873	+	0.272254i
$622$	−40.9223	+	18.1731i	−1.64083	+	0.728673i
$623$	7.50532	+	18.1194i	0.300694	+	0.725940i
$624$	0.614389	−	6.41774i	0.0245953	−	0.256915i
$625$	−1.45812	+	3.52021i	−0.0583247	+	0.140808i
$626$	1.08735	+	43.0937i	0.0434593	+	1.72237i
$627$	4.50499	+	8.42824i	0.179912	+	0.336591i
$628$	−25.5082	−	6.35245i	−1.01789	−	0.253490i
$629$	−24.6136	−	29.9918i	−0.981410	−	1.19585i
$630$	−4.01318	−	1.10765i	−0.159889	−	0.0441297i
$631$	15.8752	−	3.15778i	0.631983	−	0.125709i	0.131304	−	0.991342i	$-0.458084\pi$
$631$	15.8752	−	3.15778i	0.631983	−	0.125709i	0.500679	+	0.865633i	$0.333084\pi$
$632$	5.47810	+	19.6386i	0.217907	+	0.781183i
$633$	0.810505	−	4.07468i	0.0322147	−	0.161954i
$634$	5.73857	+	17.3311i	0.227908	+	0.688307i
$635$	1.59841	+	0.854370i	0.0634311	+	0.0339047i
$636$	−2.83675	−	1.01064i	−0.112485	−	0.0400743i
$637$	−0.238704	−	2.42360i	−0.00945780	−	0.0960266i
$638$	26.7613	−	6.02867i	1.05949	−	0.238677i
$639$	−8.20414			−0.324551
$640$	−12.4024	−	6.94773i	−0.490248	−	0.274633i
$641$	0.473540			0.0187037			0.00935185	−	0.999956i	$-0.497023\pi$
$641$	0.473540			0.0187037			0.00935185	+	0.999956i	$0.497023\pi$
$642$	−2.48346	+	0.559461i	−0.0980142	+	0.0220802i
$643$	−2.98114	−	30.2680i	−0.117565	−	1.19366i	−0.855142	−	0.518393i	$-0.826530\pi$
$643$	−2.98114	−	30.2680i	−0.117565	−	1.19366i	0.737578	−	0.675262i	$-0.235970\pi$
$644$	11.1491	−	31.2943i	0.439335	−	1.23317i
$645$	12.8003	+	6.84192i	0.504013	+	0.269400i
$646$	−6.23221	−	18.8220i	−0.245203	−	0.740542i
$647$	−8.82661	+	44.3744i	−0.347010	+	1.74454i	0.274923	+	0.961466i	$0.411348\pi$
$647$	−8.82661	+	44.3744i	−0.347010	+	1.74454i	−0.621933	+	0.783071i	$0.713652\pi$
$648$	2.46383	+	1.38908i	0.0967884	+	0.0545682i
$649$	20.6936	−	4.11622i	0.812296	−	0.161576i
$650$	7.51711	+	2.07474i	0.294845	+	0.0813779i
$651$	−0.0435593	−	0.0530772i	−0.00170722	−	0.00208026i
$652$	−7.51979	+	30.1957i	−0.294498	+	1.18255i
$653$	−12.5425	−	23.4653i	−0.490824	−	0.918267i	−0.998394	−	0.0566566i	$-0.981956\pi$
$653$	−12.5425	−	23.4653i	−0.490824	−	0.918267i	0.507570	−	0.861611i	$-0.330544\pi$
$654$	0.123328	+	4.88773i	0.00482251	+	0.191125i
$655$	1.08515	−	2.61978i	0.0424003	−	0.102363i
$656$	−1.88247	−	6.14517i	−0.0734981	−	0.239929i
$657$	4.05419	+	9.78767i	0.158169	+	0.381853i
$658$	−21.2168	+	9.42212i	−0.827118	+	0.367312i
$659$	1.44469	−	4.76252i	0.0562773	−	0.185521i	−0.924295	−	0.381678i	$-0.875346\pi$
$659$	1.44469	−	4.76252i	0.0562773	−	0.185521i	0.980573	+	0.196157i	$0.0628462\pi$
$660$	4.89756	−	4.45110i	0.190637	−	0.173259i
$661$	−36.4415	−	3.58917i	−1.41741	−	0.139603i	−0.639892	−	0.768465i	$-0.721021\pi$
$661$	−36.4415	−	3.58917i	−1.41741	−	0.139603i	−0.777517	+	0.628862i	$0.783521\pi$
$662$	25.4388	+	19.8247i	0.988708	+	0.770509i
$663$	−5.17744	−	3.45945i	−0.201075	−	0.134354i
$664$	10.4660	+	26.9673i	0.406159	+	1.04654i
$665$	−5.93513	−	8.88256i	−0.230155	−	0.344451i
$666$	9.28408	+	10.7480i	0.359751	+	0.416476i
$667$	15.1590	+	49.9725i	0.586959	+	1.93494i
$668$	−13.2600	+	22.1917i	−0.513046	+	0.858624i
$669$	−17.0168	−	13.9653i	−0.657907	−	0.539930i
$670$	1.88173	−	10.8889i	0.0726978	−	0.420674i
$671$	−7.87118	−	7.87118i	−0.303863	−	0.303863i
$672$	−11.2212	−	7.05218i	−0.432868	−	0.272044i
$673$	−34.5172	+	34.5172i	−1.33054	+	1.33054i	−0.425654	+	0.904886i	$0.639956\pi$
$673$	−34.5172	+	34.5172i	−1.33054	+	1.33054i	−0.904886	+	0.425654i	$0.860044\pi$
$674$	−0.631503	−	0.895365i	−0.0243246	−	0.0344882i
$675$	−2.17037	+	2.64460i	−0.0835375	+	0.101791i
$676$	−3.02452	+	20.5834i	−0.116328	+	0.791668i
$677$	−34.6832	+	10.5210i	−1.33298	+	0.404356i	−0.874792	−	0.484498i	$-0.839002\pi$
$677$	−34.6832	+	10.5210i	−1.33298	+	0.404356i	−0.458190	+	0.888854i	$0.651502\pi$
$678$	1.55055	−	21.2178i	0.0595484	−	0.814866i
$679$	−1.34514	+	0.898794i	−0.0516218	+	0.0344926i
$680$	−11.5850	+	7.36940i	−0.444263	+	0.282604i
$681$	−10.3395	+	15.4742i	−0.396211	+	0.592972i
$682$	0.108319	−	0.0134350i	0.00414776	−	0.000514454i
$683$	−3.66380	+	37.1992i	−0.140192	+	1.42339i	0.625522	+	0.780206i	$0.284886\pi$
$683$	−3.66380	+	37.1992i	−0.140192	+	1.42339i	−0.765714	+	0.643182i	$0.777614\pi$
$684$	2.45442	+	6.83020i	0.0938470	+	0.261159i
$685$	17.3949	+	5.27668i	0.664624	+	0.201612i
$686$	−26.3169	−	10.1309i	−1.00478	−	0.386799i
$687$	26.3597	−	10.9185i	1.00568	−	0.416568i
$688$	32.7606	+	32.5821i	1.24899	+	1.24218i
$689$	−2.24211	−	0.928714i	−0.0854178	−	0.0353812i
$690$	9.13034	+	8.68092i	0.347586	+	0.330477i
$691$	−21.8484	+	11.6782i	−0.831152	+	0.444260i	−0.831356	−	0.555740i	$-0.812435\pi$
$691$	−21.8484	+	11.6782i	−0.831152	+	0.444260i	0.000203986		1.00000i	$0.499935\pi$
$692$	13.4714	−	2.01711i	0.512106	−	0.0766791i
$693$	4.76941	−	3.91415i	0.181175	−	0.148686i
$694$	−12.3809	−	21.8206i	−0.469973	−	0.828298i
$695$	0.724807	+	3.64385i	0.0274935	+	0.138219i
$696$	20.7736	−	1.57517i	0.787420	−	0.0597065i
$697$	−6.08822	−	1.21102i	−0.230608	−	0.0458707i
$698$	−42.5132	−	21.3630i	−1.60915	−	0.808600i
$699$	−11.6855	+	21.8620i	−0.441986	+	0.826897i
$700$	10.7493	−	11.8927i	0.406286	−	0.449501i
$701$	−0.663003	+	0.0653001i	−0.0250413	+	0.00246635i	−0.110530	−	0.993873i	$-0.535255\pi$
$701$	−0.663003	+	0.0653001i	−0.0250413	+	0.00246635i	0.0854887	+	0.996339i	$0.472755\pi$
$702$	1.92658	+	1.21815i	0.0727142	+	0.0459762i
$703$			36.4442i			1.37452i
$704$	19.0081	−	9.08568i	0.716394	−	0.342429i
$705$		−	8.80382i		−	0.331571i
$706$	19.8781	−	31.4384i	0.748122	−	1.18320i
$707$	−22.9646	+	2.26181i	−0.863672	+	0.0850643i
$708$	16.0033	−	0.808110i	0.601440	−	0.0303706i
$709$	−3.04769	+	5.70183i	−0.114459	+	0.214137i	−0.932627	−	0.360842i	$-0.882490\pi$
$709$	−3.04769	+	5.70183i	−0.114459	+	0.214137i	0.818169	+	0.574978i	$0.194990\pi$
$710$	−6.54581	+	13.0264i	−0.245660	+	0.488873i
$711$	−7.06987	−	1.40629i	−0.265141	−	0.0527398i
$712$	−22.4971	−	7.38094i	−0.843116	−	0.276613i
$713$	0.0405364	+	0.203790i	0.00151810	+	0.00763200i
$714$	−11.1333	+	6.31697i	−0.416652	+	0.236407i
$715$	4.12276	−	3.38346i	0.154182	−	0.126534i
$716$	30.5416	−	41.2984i	1.14139	−	1.54339i
$717$	10.5952	−	5.66327i	0.395686	−	0.211499i
$718$	−3.09620	+	3.25649i	−0.115549	+	0.121531i
$719$	−5.02574	−	2.08173i	−0.187428	−	0.0776354i	0.286995	−	0.957932i	$-0.407344\pi$
$719$	−5.02574	−	2.08173i	−0.187428	−	0.0776354i	−0.474424	+	0.880297i	$0.657344\pi$
$720$	4.17137	−	2.80374i	0.155458	−	0.104489i
$721$	−2.93119	+	1.21414i	−0.109163	+	0.0452168i
$722$	2.96256	−	7.69579i	0.110255	−	0.286408i
$723$	4.11689	+	1.24884i	0.153109	+	0.0464450i
$724$	−6.15726	+	13.0646i	−0.228833	+	0.485542i
$725$	−2.46995	+	25.0778i	−0.0917316	+	0.931366i
$726$	−0.707565	−	5.70470i	−0.0262602	−	0.211721i
$727$	3.59619	−	5.38207i	0.133375	−	0.199610i	−0.758770	−	0.651358i	$-0.774199\pi$
$727$	3.59619	−	5.38207i	0.133375	−	0.199610i	0.892145	+	0.451748i	$0.149199\pi$
$728$	−8.74490	−	6.13208i	−0.324107	−	0.227270i
$729$	−0.831470	+	0.555570i	−0.0307952	+	0.0205767i
$730$	18.7754	+	1.37206i	0.694911	+	0.0507824i
$731$	42.7045	−	12.9543i	1.57948	−	0.479131i
$732$	−5.04521	−	6.78329i	−0.186476	−	0.250718i
$733$	3.15481	−	3.84415i	0.116526	−	0.141987i	−0.711481	−	0.702706i	$-0.751975\pi$
$733$	3.15481	−	3.84415i	0.116526	−	0.141987i	0.828006	+	0.560719i	$0.189475\pi$
$734$	−10.9449	+	7.71943i	−0.403982	+	0.284929i
$735$	1.34248	−	1.34248i	0.0495180	−	0.0495180i
$736$	19.8873	+	34.8280i	0.733055	+	1.28378i
$737$	11.5799	+	11.5799i	0.426552	+	0.426552i
$738$	2.23911	+	0.386947i	0.0824229	+	0.0142437i
$739$	34.1702	+	28.0428i	1.25697	+	1.03157i	0.997838	+	0.0657283i	$0.0209370\pi$
$739$	34.1702	+	28.0428i	1.25697	+	1.03157i	0.259134	+	0.965841i	$0.416563\pi$
$740$	24.4730	−	6.16571i	0.899644	−	0.226656i
$741$	1.69787	+	5.59711i	0.0623727	+	0.205615i
$742$	−3.77539	+	3.26117i	−0.138599	+	0.119721i
$743$	15.8154	+	23.6694i	0.580210	+	0.868345i	0.999214	−	0.0396392i	$-0.0126209\pi$
$743$	15.8154	+	23.6694i	0.580210	+	0.868345i	−0.419005	+	0.907984i	$0.637621\pi$
$744$	0.0828723	+	0.00186446i	0.00303825	+	6.83543e-5i
$745$	−9.84075	−	6.57538i	−0.360537	−	0.240903i
$746$	9.66900	−	12.4071i	0.354007	−	0.454258i
$747$	−10.1780	−	1.00245i	−0.372394	−	0.0366776i
$748$	0.970670	−	20.3251i	0.0354912	−	0.743158i
$749$	−1.22423	+	4.03575i	−0.0447324	+	0.147463i
$750$	6.07348	+	13.6763i	0.221772	+	0.499389i
$751$	12.2773	+	29.6400i	0.448005	+	1.08158i	0.973068	+	0.230516i	$0.0740415\pi$
$751$	12.2773	+	29.6400i	0.448005	+	1.08158i	−0.525064	+	0.851063i	$0.675958\pi$
$752$	8.06224	−	26.8415i	0.294000	−	0.978808i
$753$	3.64270	−	8.79426i	0.132747	−	0.320481i
$754$	16.7838	−	0.423494i	0.611231	−	0.0154227i
$755$	13.2433	+	24.7765i	0.481973	+	0.901708i
$756$	4.01580	−	2.41444i	0.146053	−	0.0878123i
$757$	−10.5136	−	12.8108i	−0.382122	−	0.465617i	0.546059	−	0.837747i	$-0.316128\pi$
$757$	−10.5136	−	12.8108i	−0.382122	−	0.465617i	−0.928181	+	0.372130i	$0.878628\pi$
$758$	−8.10786	+	29.3761i	−0.294491	+	1.06699i
$759$	−18.3122	+	3.64252i	−0.664690	+	0.132215i
$760$	12.8032	+	1.55249i	0.464421	+	0.0563148i
$761$	1.42008	−	7.13925i	0.0514780	−	0.258798i	−0.946473	−	0.322784i	$-0.895381\pi$
$761$	1.42008	−	7.13925i	0.0514780	−	0.258798i	0.997951	+	0.0639862i	$0.0203814\pi$
$762$	−1.93650	+	0.641199i	−0.0701518	+	0.0232282i
$763$	7.14345	+	3.81825i	0.258610	+	0.138230i
$764$	−7.55046	−	15.9078i	−0.273166	−	0.575525i
$765$	−0.475812	−	4.83100i	−0.0172030	−	0.174665i
$766$	−4.64424	−	20.6159i	−0.167803	−	0.744881i
$767$	12.9132			0.466270
$768$	15.2854	−	4.72817i	0.551566	−	0.170613i
$769$	53.6049			1.93304			0.966520	−	0.256590i	$-0.0825990\pi$
$769$	53.6049			1.93304			0.966520	+	0.256590i	$0.0825990\pi$
$770$	−2.40949	−	10.6958i	−0.0868322	−	0.385449i
$771$	1.31770	+	13.3788i	0.0474558	+	0.481827i
$772$	−11.2632	−	23.7300i	−0.405371	−	0.854063i
$773$	15.0841	+	8.06264i	0.542539	+	0.289993i	0.719813	−	0.694168i	$-0.244228\pi$
$773$	15.0841	+	8.06264i	0.542539	+	0.289993i	−0.177274	+	0.984162i	$0.556728\pi$
$774$	−15.5077	+	5.13482i	−0.557414	+	0.184567i
$775$	−0.0195607	+	0.0983383i	−0.000702641	+	0.00353242i
$776$	0.235104	−	1.93887i	0.00843973	−	0.0696014i
$777$	23.0767	−	4.59025i	0.827873	−	0.164674i
$778$	−3.44232	+	12.4721i	−0.123413	+	0.447147i
$779$	3.69901	+	4.50725i	0.132531	+	0.161489i
$780$	3.47132	−	2.08708i	0.124293	−	0.0747295i
$781$	−10.1848	−	19.0544i	−0.364439	−	0.681818i
$782$	38.7237	−	0.977085i	1.38476	−	0.0349405i
$783$	−2.81871	+	6.80497i	−0.100733	+	0.243190i
$784$	5.32240	−	2.86361i	0.190086	−	0.102272i
$785$	−6.32010	−	15.2581i	−0.225574	−	0.544584i
$786$	1.29533	+	2.91683i	0.0462028	+	0.104040i
$787$	15.0633	−	49.6571i	0.536949	−	1.77009i	−0.0954406	−	0.995435i	$-0.530426\pi$
$787$	15.0633	−	49.6571i	0.536949	−	1.77009i	0.632390	−	0.774650i	$-0.282074\pi$
$788$	0.955809	−	20.0139i	0.0340493	−	0.712965i
$789$	14.8731	+	1.46487i	0.529497	+	0.0521509i
$790$	−7.87370	+	10.1034i	−0.280134	+	0.359464i
$791$	−29.3047	−	19.5808i	−1.04195	−	0.696212i
$792$	−0.167537	+	7.44674i	−0.00595315	+	0.264608i
$793$	−3.78500	−	5.66465i	−0.134409	−	0.201158i
$794$	−17.9979	+	15.5466i	−0.638722	+	0.551726i
$795$	−0.549201	−	1.81047i	−0.0194781	−	0.0642108i
$796$	−6.88859	+	1.73551i	−0.244160	+	0.0615134i
$797$	24.7610	+	20.3208i	0.877079	+	0.719800i	0.960963	−	0.276675i	$-0.0892327\pi$
$797$	24.7610	+	20.3208i	0.877079	+	0.719800i	−0.0838845	+	0.996475i	$0.526733\pi$
$798$	11.8481	+	2.04750i	0.419418	+	0.0724808i
$799$	−19.1405	−	19.1405i	−0.677142	−	0.677142i
$800$	2.43462	+	19.1993i	0.0860767	+	0.678798i
$801$	5.91925	−	5.91925i	0.209146	−	0.209146i
$802$	18.2834	−	12.8953i	0.645608	−	0.455349i
$803$	−17.6992	+	21.5665i	−0.624592	+	0.761067i
$804$	7.42242	+	9.97945i	0.261769	+	0.351948i
$805$	19.9727	−	6.05864i	0.703944	−	0.213539i
$806$	0.0666248	+	0.00486878i	0.00234676	+	0.000171496i
$807$	3.64019	−	2.43230i	0.128141	−	0.0856210i
$808$	15.9942	−	22.8092i	0.562675	−	0.802425i
$809$	−22.5021	+	33.6767i	−0.791131	+	1.18401i	0.188276	+	0.982116i	$0.439710\pi$
$809$	−22.5021	+	33.6767i	−0.791131	+	1.18401i	−0.979407	+	0.201895i	$0.935290\pi$
$810$	0.218726	+	1.76347i	0.00768526	+	0.0619620i
$811$	−2.62195	+	26.6211i	−0.0920692	+	0.934794i	0.832562	+	0.553931i	$0.186873\pi$
$811$	−2.62195	+	26.6211i	−0.0920692	+	0.934794i	−0.924632	+	0.380863i	$0.875627\pi$
$812$	14.7138	−	31.2200i	0.516353	−	1.09561i
$813$	12.0824	+	3.66515i	0.423747	+	0.128542i
$814$	−13.4371	+	34.9053i	−0.470969	+	1.22343i
$815$	−18.0619	+	7.48149i	−0.632682	+	0.262065i
$816$	2.97339	−	15.1647i	0.104089	−	0.530870i
$817$	−38.7271	−	16.0413i	−1.35489	−	0.561214i
$818$	−34.0905	+	35.8554i	−1.19195	+	1.25365i
$819$	3.33028	−	1.78007i	0.116370	−	0.0622008i
$820$	2.40090	−	3.24650i	0.0838431	−	0.113373i
$821$	19.5948	−	16.0810i	0.683863	−	0.561232i	−0.227023	−	0.973889i	$-0.572899\pi$
$821$	19.5948	−	16.0810i	0.683863	−	0.561232i	0.910886	+	0.412657i	$0.135399\pi$
$822$	−17.7942	+	10.0964i	−0.620644	+	0.352151i
$823$	7.79209	+	39.1735i	0.271615	+	1.36550i	0.839932	+	0.542692i	$0.182595\pi$
$823$	7.79209	+	39.1735i	0.271615	+	1.36550i	−0.568316	+	0.822810i	$0.692405\pi$
$824$	1.19402	−	3.63937i	0.0415955	−	0.126783i
$825$	−8.83649	−	1.75769i	−0.307647	−	0.0611948i
$826$	11.9191	−	23.7194i	0.414717	−	0.825305i
$827$	25.1177	−	46.9918i	0.873427	−	1.63407i	0.104687	−	0.994505i	$-0.466616\pi$
$827$	25.1177	−	46.9918i	0.873427	−	1.63407i	0.768740	−	0.639561i	$-0.220884\pi$
$828$	−14.1616	+	0.715112i	−0.492149	+	0.0248519i
$829$	33.7537	−	3.32445i	1.17231	−	0.115463i	0.506945	−	0.861978i	$-0.330775\pi$
$829$	33.7537	−	3.32445i	1.17231	−	0.115463i	0.665368	+	0.746515i	$0.268275\pi$
$830$	−9.71237	+	15.3607i	−0.337121	+	0.533178i
$831$			24.9097i			0.864109i
$832$	12.4948	−	3.18427i	0.433179	−	0.110395i
$833$		−	5.83740i		−	0.202254i
$834$	−3.53430	−	2.23469i	−0.122383	−	0.0773809i
$835$	−16.1632	+	1.59194i	−0.559351	+	0.0550913i
$836$	−12.8164	+	14.1796i	−0.443264	+	0.490411i
$837$	−0.0138153	+	0.0258466i	−0.000477527	+	0.000893391i
$838$	−42.5725	−	21.3928i	−1.47064	−	0.739001i
$839$	−28.1453	−	5.59845i	−0.971684	−	0.193280i	−0.316369	−	0.948636i	$-0.602464\pi$
$839$	−28.1453	−	5.59845i	−0.971684	−	0.193280i	−0.655315	+	0.755356i	$0.727464\pi$
$840$	−0.629551	−	8.30263i	−0.0217216	−	0.286468i
$841$	4.92658	+	24.7676i	0.169882	+	0.854055i
$842$	26.4145	+	46.5540i	0.910305	+	1.60436i
$843$	5.48330	−	4.50003i	0.188855	−	0.154989i
$844$	8.21742	−	1.23042i	0.282855	−	0.0423527i
$845$	−11.5272	+	6.16140i	−0.396547	+	0.211959i
$846$	7.18104	+	6.82757i	0.246889	+	0.234737i
$847$	−8.79826	−	3.64436i	−0.302312	−	0.125222i
$848$	−0.0164585	−	6.02279i	−0.000565188	−	0.206823i
$849$	8.17732	−	3.38716i	0.280645	−	0.116247i
$850$	17.4441	+	6.71523i	0.598326	+	0.230330i
$851$	−68.1353	−	20.6686i	−2.33565	−	0.708511i
$852$	−5.54889	−	15.4416i	−0.190102	−	0.529019i
$853$	−1.98592	+	20.1634i	−0.0679966	+	0.690381i	0.899402	+	0.437122i	$0.144002\pi$
$853$	−1.98592	+	20.1634i	−0.0679966	+	0.690381i	−0.967399	+	0.253258i	$0.918498\pi$
$854$	−13.8986	+	1.72387i	−0.475601	+	0.0589896i
$855$	−2.53328	+	3.79132i	−0.0866362	+	0.129660i
$856$	−2.73269	−	4.29588i	−0.0934014	−	0.146830i
$857$	26.2025	−	17.5080i	0.895061	−	0.598061i	−0.0206994	−	0.999786i	$-0.506589\pi$
$857$	26.2025	−	17.5080i	0.895061	−	0.598061i	0.915760	+	0.401725i	$0.131589\pi$
$858$	−0.437499	+	5.98678i	−0.0149360	+	0.204385i
$859$	43.0769	−	13.0672i	1.46977	−	0.445849i	0.548953	−	0.835853i	$-0.315027\pi$
$859$	43.0769	−	13.0672i	1.46977	−	0.445849i	0.920813	+	0.390004i	$0.127527\pi$
$860$	−4.22010	+	28.7199i	−0.143904	+	0.979341i
$861$	2.38813	−	2.90994i	0.0813872	−	0.0991705i
$862$	−11.4490	−	16.2327i	−0.389953	−	0.552888i
$863$	−18.2151	+	18.2151i	−0.620049	+	0.620049i	−0.945544	−	0.325495i	$-0.894469\pi$
$863$	−18.2151	+	18.2151i	−0.620049	+	0.620049i	0.325495	+	0.945544i	$0.394469\pi$
$864$	−0.948062	+	5.57684i	−0.0322537	+	0.189728i
$865$	6.05133	+	6.05133i	0.205751	+	0.205751i
$866$	5.43674	−	31.4603i	0.184748	−	1.06906i
$867$	1.60357	+	1.31602i	0.0544601	+	0.0446943i
$868$	0.0704386	−	0.117885i	0.00239084	−	0.00400127i
$869$	−5.51053	−	18.1658i	−0.186932	−	0.616232i
$870$	8.55590	+	9.90498i	0.290072	+	0.335810i
$871$	5.56842	+	8.33373i	0.188679	+	0.282378i
$872$	−9.11610	+	3.53795i	−0.308710	+	0.119810i
$873$	0.574143	+	0.383630i	0.0194318	+	0.0129839i
$874$	−28.6995	−	22.3658i	−0.970775	−	0.756534i
$875$	24.6713	+	2.42991i	0.834042	+	0.0821460i
$876$	−15.6800	+	14.2506i	−0.529777	+	0.481482i
$877$	−7.95023	+	26.2084i	−0.268460	+	0.884995i	0.714257	+	0.699883i	$0.246765\pi$
$877$	−7.95023	+	26.2084i	−0.268460	+	0.884995i	−0.982718	+	0.185111i	$0.940735\pi$
$878$	45.8909	−	20.3796i	1.54874	−	0.687777i
$879$	1.14375	+	2.76125i	0.0385777	+	0.0931347i
$880$	11.6902	+	6.20752i	0.394076	+	0.209255i
$881$	15.9218	−	38.4386i	0.536419	−	1.29503i	−0.390788	−	0.920481i	$-0.627797\pi$
$881$	15.9218	−	38.4386i	0.536419	−	1.29503i	0.927207	−	0.374550i	$-0.122203\pi$
$882$	0.0538997	+	2.13615i	0.00181490	+	0.0719278i
$883$	11.0935	+	20.7544i	0.373325	+	0.698443i	0.996496	−	0.0836435i	$-0.0266557\pi$
$883$	11.0935	+	20.7544i	0.373325	+	0.698443i	−0.623170	+	0.782086i	$0.714156\pi$
$884$	3.00949	−	12.0846i	0.101220	−	0.406449i
$885$	6.38643	+	7.78188i	0.214677	+	0.261585i
$886$	5.44494	+	1.50281i	0.182926	+	0.0504880i
$887$	−23.6476	+	4.70379i	−0.794007	+	0.157938i	−0.575397	−	0.817874i	$-0.695152\pi$
$887$	−23.6476	+	4.70379i	−0.794007	+	0.157938i	−0.218610	+	0.975812i	$0.570152\pi$
$888$	−13.9502	+	24.7436i	−0.468137	+	0.830341i
$889$	−0.659289	+	3.31447i	−0.0221118	+	0.111164i
$890$	−4.67574	−	14.1213i	−0.156731	−	0.473346i
$891$	−2.32253	−	1.24142i	−0.0778076	−	0.0415890i
$892$	14.7757	−	41.4739i	0.494727	−	1.38865i
$893$	2.49219	+	25.3036i	0.0833979	+	0.846753i
$894$	12.9951	−	2.92747i	0.434621	−	0.0979094i
$895$	32.2704			1.07868
$896$	5.68387	−	25.8900i	0.189885	−	0.864923i
$897$	−11.4272			−0.381542
$898$	36.0363	−	8.11809i	1.20255	−	0.270904i
$899$	0.0211586	+	0.214827i	0.000705680	+	0.00716489i
$900$	−6.44551	−	2.29631i	−0.214850	−	0.0765437i
$901$	−5.13020	−	2.74215i	−0.170912	−	0.0913542i
$902$	1.88098	+	5.68077i	0.0626297	+	0.189149i
$903$	−5.27968	+	26.5427i	−0.175697	+	0.883287i
$904$	40.9842	−	11.4323i	1.36311	−	0.380234i
$905$	−8.89947	+	1.77022i	−0.295828	+	0.0588439i
$906$	−30.4800	−	8.41253i	−1.01263	−	0.279488i
$907$	−30.9653	−	37.7313i	−1.02819	−	1.25285i	−0.967015	−	0.254721i	$-0.918016\pi$
$907$	−30.9653	−	37.7313i	−1.02819	−	1.25285i	−0.0611717	−	0.998127i	$-0.519484\pi$
$908$	−36.1181	−	8.99469i	−1.19862	−	0.298499i
$909$	4.64294	+	8.68634i	0.153997	+	0.288108i
$910$	−0.169259	−	6.70805i	−0.00561088	−	0.222370i
$911$	3.39246	−	8.19013i	0.112397	−	0.271351i	−0.857664	−	0.514210i	$-0.828085\pi$
$911$	3.39246	−	8.19013i	0.112397	−	0.271351i	0.970062	+	0.242859i	$0.0780852\pi$
$912$	−11.1955	+	9.23924i	−0.370721	+	0.305942i
$913$	−10.3070	−	24.8832i	−0.341110	−	0.823513i
$914$	1.95149	−	0.866630i	0.0645494	−	0.0286656i
$915$	1.54175	−	5.08248i	0.0509688	−	0.168022i
$916$	38.3789	+	42.2285i	1.26807	+	1.39527i
$917$	5.26179	+	0.518241i	0.173760	+	0.0171138i
$918$	4.30952	+	3.35845i	0.142235	+	0.110845i
$919$	−1.57593	−	1.05300i	−0.0519852	−	0.0347354i	0.529306	−	0.848431i	$-0.322452\pi$
$919$	−1.57593	−	1.05300i	−0.0519852	−	0.0347354i	−0.581291	+	0.813696i	$0.697452\pi$
$920$	−10.1636	+	23.0562i	−0.335084	+	0.760139i
$921$	16.9353	+	25.3455i	0.558039	+	0.835164i
$922$	37.1322	+	42.9872i	1.22289	+	1.41571i
$923$	−3.83849	−	12.6538i	−0.126346	−	0.416505i
$924$	10.5929	+	6.32947i	0.348480	+	0.208224i
$925$	−26.5590	−	21.7964i	−0.873255	−	0.716662i
$926$	−7.75315	+	44.8644i	−0.254784	+	1.47434i
$927$	0.957558	+	0.957558i	0.0314503	+	0.0314503i
$928$	17.0150	+	38.0339i	0.558544	+	1.24853i
$929$	−10.7310	+	10.7310i	−0.352072	+	0.352072i	−0.860880	−	0.508808i	$-0.830086\pi$
$929$	−10.7310	+	10.7310i	−0.352072	+	0.352072i	0.508808	+	0.860880i	$0.330086\pi$
$930$	0.0300162	+	0.0425580i	0.000984270	+	0.00139553i
$931$	−3.47847	+	4.23853i	−0.114002	+	0.138912i
$932$	−49.0514	−	7.20761i	−1.60673	−	0.236093i
$933$	30.2981	−	9.19083i	0.991915	−	0.300894i
$934$	3.41505	−	46.7319i	0.111744	−	1.52911i
$935$	10.6294	−	7.10237i	0.347620	−	0.232272i
$936$	−0.989715	+	4.45005i	−0.0323499	+	0.145454i
$937$	33.9260	−	50.7738i	1.10831	−	1.65871i	0.494873	−	0.868966i	$-0.335215\pi$
$937$	33.9260	−	50.7738i	1.10831	−	1.65871i	0.613440	−	0.789741i	$-0.289785\pi$
$938$	20.4474	−	2.53613i	0.667631	−	0.0828075i
$939$	2.98772	−	30.3348i	0.0975004	−	0.989938i
$940$	16.5702	−	5.95448i	0.540462	−	0.194214i
$941$	−17.4267	−	5.28634i	−0.568095	−	0.172330i	−0.00684602	−	0.999977i	$-0.502179\pi$
$941$	−17.4267	−	5.28634i	−0.568095	−	0.172330i	−0.561249	+	0.827647i	$0.689679\pi$
$942$	17.3470	+	6.67786i	0.565195	+	0.217576i
$943$	−10.5245	+	4.35939i	−0.342725	+	0.141961i
$944$	12.3448	+	29.5742i	0.401790	+	0.962559i
$945$	2.71976	+	1.12656i	0.0884739	+	0.0366471i
$946$	−31.1773	−	29.6427i	−1.01366	−	0.963768i
$947$	−18.9407	+	10.1240i	−0.615490	+	0.328986i	−0.749511	−	0.661992i	$-0.769711\pi$
$947$	−18.9407	+	10.1240i	−0.615490	+	0.328986i	0.134021	+	0.990979i	$0.457211\pi$
$948$	−2.13486	−	14.2578i	−0.0693371	−	0.463072i
$949$	−13.1994	+	10.8324i	−0.428469	+	0.351636i
$950$	−8.66455	−	15.2707i	−0.281115	−	0.495448i
$951$	−2.51848	−	12.6612i	−0.0816672	−	0.410569i
$952$	−19.4196	−	16.6822i	−0.629393	−	0.540672i
$953$	8.00393	+	1.59208i	0.259273	+	0.0515726i	0.323015	−	0.946394i	$-0.395304\pi$
$953$	8.00393	+	1.59208i	0.259273	+	0.0515726i	−0.0637422	+	0.997966i	$0.520304\pi$
$954$	1.90267	+	0.956096i	0.0616013	+	0.0309547i
$955$	5.21499	−	9.75656i	0.168753	−	0.315715i
$956$	17.8253	+	16.1116i	0.576512	+	0.521087i
$957$	−19.3039	+	1.90127i	−0.624008	+	0.0614594i
$958$	−34.9753	−	22.1144i	−1.13000	−	0.714485i
$959$			33.8935i			1.09448i
$960$	8.09842	+	5.95490i	0.261375	+	0.192193i
$961$		−	30.9991i		−	0.999972i
$962$	−12.2336	+	19.3482i	−0.394427	+	0.623810i
$963$	1.79141	−	0.176438i	0.0577273	−	0.00568565i
$964$	0.433934	+	8.59333i	0.0139761	+	0.276772i
$965$	7.77931	−	14.5541i	0.250425	−	0.468512i
$966$	−10.5474	+	20.9898i	−0.339357	+	0.675335i
$967$	31.8442	+	6.33420i	1.02404	+	0.203694i	0.678415	−	0.734679i	$-0.262667\pi$
$967$	31.8442	+	6.33420i	1.02404	+	0.203694i	0.345625	+	0.938373i	$0.387667\pi$
$968$	10.2586	−	5.19014i	0.329725	−	0.166818i
$969$	2.73512	+	13.7504i	0.0878648	+	0.441726i
$970$	1.06721	−	0.605531i	0.0342661	−	0.0194424i
$971$	−25.2166	+	20.6947i	−0.809240	+	0.664126i	−0.945165	−	0.326593i	$-0.894099\pi$
$971$	−25.2166	+	20.6947i	−0.809240	+	0.664126i	0.135925	+	0.990719i	$0.456599\pi$
$972$	−1.60804	−	1.18920i	−0.0515780	−	0.0381437i
$973$	−6.10937	+	3.26553i	−0.195858	+	0.104688i
$974$	8.30497	−	8.73492i	0.266108	−	0.279885i
$975$	−5.09440	−	2.11017i	−0.163151	−	0.0675796i
$976$	9.35494	−	14.0838i	0.299444	−	0.450812i
$977$	−26.9870	+	11.1784i	−0.863391	+	0.357628i	−0.770033	−	0.638004i	$-0.779760\pi$
$977$	−26.9870	+	11.1784i	−0.863391	+	0.357628i	−0.0933581	+	0.995633i	$0.529760\pi$
$978$	7.90500	−	20.5347i	0.252774	−	0.656627i
$979$	21.0959	+	6.39936i	0.674227	+	0.204525i
$980$	3.43475	+	1.61878i	0.109719	+	0.0517100i
$981$	0.338869	−	3.44060i	0.0108193	−	0.109850i
$982$	2.66558	+	21.4911i	0.0850622	+	0.685809i
$983$	19.0054	−	28.4435i	0.606177	−	0.907208i	−0.393751	−	0.919217i	$-0.628823\pi$
$983$	19.0054	−	28.4435i	0.606177	−	0.907208i	0.999928	+	0.0120090i	$0.00382269\pi$
$984$	0.786129	+	4.47609i	0.0250609	+	0.142693i
$985$	10.4667	−	6.99363i	0.333497	−	0.222836i
$986$	40.1361	+	2.93305i	1.27819	+	0.0934072i
$987$	15.7085	−	4.76514i	0.500009	−	0.151676i
$988$	−9.38634	+	6.98128i	−0.298619	+	0.222104i
$989$	51.9538	−	63.3059i	1.65204	−	2.01301i
$990$	−3.82417	+	2.69720i	−0.121540	+	0.0857226i
$991$	13.1289	−	13.1289i	0.417054	−	0.417054i	−0.467133	−	0.884187i	$-0.654713\pi$
$991$	13.1289	−	13.1289i	0.417054	−	0.417054i	0.884187	+	0.467133i	$0.154713\pi$
$992$	0.0525416	+	0.157240i	0.00166820	+	0.00499239i
$993$	−16.1257	−	16.1257i	−0.511734	−	0.511734i
$994$	−26.7859	−	4.62894i	−0.849597	−	0.146821i
$995$	−3.44998	−	2.83133i	−0.109372	−	0.0897591i
$996$	−4.99715	−	19.8347i	−0.158341	−	0.628487i
$997$	1.45564	+	4.79859i	0.0461004	+	0.151973i	0.976969	−	0.213382i	$-0.0684478\pi$
$997$	1.45564	+	4.79859i	0.0461004	+	0.151973i	−0.930868	+	0.365354i	$0.880948\pi$
$998$	13.7027	−	11.8364i	0.433751	−	0.374674i
$999$	−5.57945	−	8.35023i	−0.176526	−	0.264190i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.181.14	yes	512
128.29	even	32	inner	384.2.v.a.157.14	✓	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.157.14	✓	512	128.29	even	32	inner
384.2.v.a.181.14	yes	512	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.310799 - 1.37964i) q^{2} +(0.0980171 + 0.995185i) q^{3} +(-1.80681 + 0.857580i) q^{4} +(-1.10815 - 0.592317i) q^{5} +(1.34253 - 0.444530i) q^{6} +(0.457071 - 2.29785i) q^{7} +(1.74470 + 2.22621i) q^{8} +(-0.980785 + 0.195090i) q^{9} +O(q^{10})\)	\(q+(-0.310799 - 1.37964i) q^{2} +(0.0980171 + 0.995185i) q^{3} +(-1.80681 + 0.857580i) q^{4} +(-1.10815 - 0.592317i) q^{5} +(1.34253 - 0.444530i) q^{6} +(0.457071 - 2.29785i) q^{7} +(1.74470 + 2.22621i) q^{8} +(-0.980785 + 0.195090i) q^{9} +(-0.472773 + 1.71294i) q^{10} +(-1.67067 - 2.03571i) q^{11} +(-1.03055 - 1.71405i) q^{12} +(-0.759784 - 1.42146i) q^{13} +(-3.31226 + 0.0835757i) q^{14} +(0.480848 - 1.16087i) q^{15} +(2.52911 - 3.09896i) q^{16} +(-1.47844 - 3.56928i) q^{17} +(0.573981 + 1.29250i) q^{18} +(-1.05342 + 3.47265i) q^{19} +(2.51017 + 0.119879i) q^{20} +(2.33159 + 0.229641i) q^{21} +(-2.28931 + 2.93761i) q^{22} +(-5.89497 - 3.93889i) q^{23} +(-2.04448 + 1.95451i) q^{24} +(-1.90070 - 2.84460i) q^{25} +(-1.72496 + 1.49001i) q^{26} +(-0.290285 - 0.956940i) q^{27} +(1.14475 + 4.54375i) q^{28} +(-5.69373 - 4.67272i) q^{29} +(-1.75103 - 0.302600i) q^{30} +(-0.0207233 - 0.0207233i) q^{31} +(-5.06150 - 2.52611i) q^{32} +(1.86216 - 1.86216i) q^{33} +(-4.46482 + 3.14905i) q^{34} +(-1.86756 + 2.27563i) q^{35} +(1.60479 - 1.19359i) q^{36} +(9.61030 - 2.91525i) q^{37} +(5.11840 + 0.374040i) q^{38} +(1.34014 - 0.895452i) q^{39} +(-0.614767 - 3.50039i) q^{40} +(0.892668 - 1.33597i) q^{41} +(-0.407832 - 3.28812i) q^{42} +(-1.13221 + 11.4955i) q^{43} +(4.76436 + 2.24541i) q^{44} +(1.20241 + 0.364747i) q^{45} +(-3.60210 + 9.35713i) q^{46} +(6.47319 - 2.68128i) q^{47} +(3.33194 + 2.21318i) q^{48} +(1.39595 + 0.578221i) q^{49} +(-3.33378 + 3.50638i) q^{50} +(3.40718 - 1.82118i) q^{51} +(2.59180 + 1.91672i) q^{52} +(1.16392 - 0.955207i) q^{53} +(-1.23001 + 0.697904i) q^{54} +(0.645557 + 3.24544i) q^{55} +(5.91295 - 2.99153i) q^{56} +(-3.55918 - 0.707965i) q^{57} +(-4.67707 + 9.30756i) q^{58} +(-3.77675 + 7.06580i) q^{59} +(0.126738 + 2.50983i) q^{60} +(4.20656 - 0.414310i) q^{61} +(-0.0221499 + 0.0350315i) q^{62} +2.34287i q^{63} +(-1.91202 + 7.76815i) q^{64} +2.02522i q^{65} +(-3.14786 - 1.99035i) q^{66} +(-6.18862 + 0.609525i) q^{67} +(5.73221 + 5.18112i) q^{68} +(3.34212 - 6.25266i) q^{69} +(3.71998 + 1.86930i) q^{70} +(8.04650 + 1.60055i) q^{71} +(-2.14549 - 1.84306i) q^{72} +(-2.06681 - 10.3905i) q^{73} +(-7.00887 - 12.3527i) q^{74} +(2.64460 - 2.17037i) q^{75} +(-1.07475 - 7.17780i) q^{76} +(-5.44138 + 2.90848i) q^{77} +(-1.65191 - 1.57060i) q^{78} +(6.65968 + 2.75853i) q^{79} +(-4.63820 + 1.93607i) q^{80} +(0.923880 - 0.382683i) q^{81} +(-2.12060 - 0.816341i) q^{82} +(9.78688 + 2.96882i) q^{83} +(-4.40967 + 1.58460i) q^{84} +(-0.475812 + 4.83100i) q^{85} +(16.2115 - 2.01074i) q^{86} +(4.09214 - 6.12432i) q^{87} +(1.61710 - 7.27097i) q^{88} +(-6.96030 + 4.65072i) q^{89} +(0.129512 - 1.77226i) q^{90} +(-3.61357 + 1.09616i) q^{91} +(14.0290 + 2.06142i) q^{92} +(0.0185923 - 0.0226548i) q^{93} +(-5.71106 - 8.09733i) q^{94} +(3.22425 - 3.22425i) q^{95} +(2.01783 - 5.28473i) q^{96} +(-0.488268 - 0.488268i) q^{97} +(0.363878 - 2.10562i) q^{98} +(2.03571 + 1.67067i) 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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