LMFDB - Embedded newform 384.2.v.a.229.25

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			229.25
Character	$\chi$	$=$	384.229
Dual form			384.2.v.a.109.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13092 + 0.849133i) q^{2} +(-0.881921 + 0.471397i) q^{3} +(0.557948 + 1.92060i) q^{4} +(-2.52496 - 3.07667i) q^{5} +(-1.39766 - 0.215757i) q^{6} +(-4.25703 + 2.84446i) q^{7} +(-0.999849 + 2.64581i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})$	\(q+(1.13092 + 0.849133i) q^{2} +(-0.881921 + 0.471397i) q^{3} +(0.557948 + 1.92060i) q^{4} +(-2.52496 - 3.07667i) q^{5} +(-1.39766 - 0.215757i) q^{6} +(-4.25703 + 2.84446i) q^{7} +(-0.999849 + 2.64581i) q^{8} +(0.555570 - 0.831470i) q^{9} +(-0.243018 - 5.62349i) q^{10} +(2.06231 - 0.625595i) q^{11} +(-1.39743 - 1.43080i) q^{12} +(-4.57695 - 3.75620i) q^{13} +(-7.22967 - 0.397937i) q^{14} +(3.67715 + 1.52312i) q^{15} +(-3.37739 + 2.14319i) q^{16} +(-0.968064 + 0.400985i) q^{17} +(1.33433 - 0.468571i) q^{18} +(0.230842 + 2.34378i) q^{19} +(4.50025 - 6.56605i) q^{20} +(2.41350 - 4.51534i) q^{21} +(2.86352 + 1.04368i) q^{22} +(-0.902011 + 0.179421i) q^{23} +(-0.365438 - 2.80472i) q^{24} +(-2.11504 + 10.6330i) q^{25} +(-1.98663 - 8.13439i) q^{26} +(-0.0980171 + 0.995185i) q^{27} +(-7.83825 - 6.58898i) q^{28} +(-1.08348 + 3.57175i) q^{29} +(2.86522 + 4.84491i) q^{30} +(-1.11133 - 1.11133i) q^{31} +(-5.63940 - 0.444083i) q^{32} +(-1.52389 + 1.52389i) q^{33} +(-1.43529 - 0.368534i) q^{34} +(19.5003 + 5.91534i) q^{35} +(1.90690 + 0.603110i) q^{36} +(2.94183 + 0.289745i) q^{37} +(-1.72912 + 2.84664i) q^{38} +(5.80717 + 1.15512i) q^{39} +(10.6649 - 3.60435i) q^{40} +(1.55436 + 7.81427i) q^{41} +(6.56358 - 3.05709i) q^{42} +(-4.62540 - 2.47233i) q^{43} +(2.35218 + 3.61182i) q^{44} +(-3.96095 + 0.390120i) q^{45} +(-1.17245 - 0.563016i) q^{46} +(0.425470 + 1.02718i) q^{47} +(1.96830 - 3.48221i) q^{48} +(7.35258 - 17.7507i) q^{49} +(-11.4208 + 10.2291i) q^{50} +(0.664733 - 0.809980i) q^{51} +(4.66046 - 10.8862i) q^{52} +(-0.296345 - 0.976920i) q^{53} +(-0.955893 + 1.04224i) q^{54} +(-7.13200 - 4.76545i) q^{55} +(-3.26950 - 14.1073i) q^{56} +(-1.30844 - 1.95821i) q^{57} +(-4.25822 + 3.11934i) q^{58} +(3.47475 - 2.85165i) q^{59} +(-0.873652 + 7.91214i) q^{60} +(3.89370 + 7.28460i) q^{61} +(-0.313156 - 2.20049i) q^{62} +5.11988i q^{63} +(-6.00061 - 5.29082i) q^{64} +23.5660i q^{65} +(-3.01738 + 0.429410i) q^{66} +(-1.86316 - 3.48572i) q^{67} +(-1.31026 - 1.63553i) q^{68} +(0.710924 - 0.583440i) q^{69} +(17.0303 + 23.2481i) q^{70} +(2.40217 + 3.59509i) q^{71} +(1.64442 + 2.30128i) q^{72} +(-10.9456 - 7.31361i) q^{73} +(3.08093 + 2.82568i) q^{74} +(-3.14707 - 10.3745i) q^{75} +(-4.37266 + 1.75106i) q^{76} +(-6.99984 + 8.52933i) q^{77} +(5.58658 + 6.23740i) q^{78} +(-5.55241 + 13.4047i) q^{79} +(15.1216 + 4.97966i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-4.87750 + 10.1571i) q^{82} +(3.28847 - 0.323886i) q^{83} +(10.0187 + 2.11603i) q^{84} +(3.67802 + 1.96594i) q^{85} +(-3.13161 - 6.72357i) q^{86} +(-0.728169 - 3.66075i) q^{87} +(-0.406794 + 6.08198i) q^{88} +(-13.9931 - 2.78340i) q^{89} +(-4.81077 - 2.92218i) q^{90} +(30.1686 + 2.97134i) q^{91} +(-0.847871 - 1.63229i) q^{92} +(1.50398 + 0.456228i) q^{93} +(-0.391037 + 1.52293i) q^{94} +(6.62818 - 6.62818i) q^{95} +(5.18284 - 2.26675i) q^{96} +(-6.06453 - 6.06453i) q^{97} +(23.3879 - 13.8313i) q^{98} +(0.625595 - 2.06231i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

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 $

$2$	1.13092	+	0.849133i	0.799679	+	0.600427i
$2$	1.13092	+	0.849133i	0.799679	+	0.600427i
$3$	−0.881921	+	0.471397i	−0.509177	+	0.272161i
$3$	−0.881921	+	0.471397i	−0.509177	+	0.272161i
$4$	0.557948	+	1.92060i	0.278974	+	0.960299i
$5$	−2.52496	−	3.07667i	−1.12920	−	1.37593i	−0.917089	−	0.398683i	$-0.869467\pi$
$5$	−2.52496	−	3.07667i	−1.12920	−	1.37593i	−0.212107	−	0.977246i	$-0.568033\pi$
$6$	−1.39766	−	0.215757i	−0.570592	−	0.0880825i
$7$	−4.25703	+	2.84446i	−1.60901	+	1.07510i	−0.664158	+	0.747592i	$0.731210\pi$
$7$	−4.25703	+	2.84446i	−1.60901	+	1.07510i	−0.944847	+	0.327511i	$0.893790\pi$
$8$	−0.999849	+	2.64581i	−0.353500	+	0.935435i
$9$	0.555570	−	0.831470i	0.185190	−	0.277157i
$10$	−0.243018	−	5.62349i	−0.0768491	−	1.77830i
$11$	2.06231	−	0.625595i	0.621810	−	0.188624i	0.0363682	−	0.999338i	$-0.488421\pi$
$11$	2.06231	−	0.625595i	0.621810	−	0.188624i	0.585442	+	0.810714i	$0.300921\pi$
$12$	−1.39743	−	1.43080i	−0.403403	−	0.413037i
$13$	−4.57695	−	3.75620i	−1.26942	−	1.04178i	−0.996823	−	0.0796547i	$-0.974618\pi$
$13$	−4.57695	−	3.75620i	−1.26942	−	1.04178i	−0.272595	−	0.962129i	$-0.587882\pi$
$14$	−7.22967	−	0.397937i	−1.93221	−	0.106353i
$15$	3.67715	+	1.52312i	0.949436	+	0.393269i
$16$	−3.37739	+	2.14319i	−0.844347	+	0.535797i
$17$	−0.968064	+	0.400985i	−0.234790	+	0.0972532i	−0.496976	−	0.867764i	$-0.665556\pi$
$17$	−0.968064	+	0.400985i	−0.234790	+	0.0972532i	0.262186	+	0.965017i	$0.415556\pi$
$18$	1.33433	−	0.468571i	0.314505	−	0.110443i
$19$	0.230842	+	2.34378i	0.0529588	+	0.537700i	0.984661	+	0.174477i	$0.0558236\pi$
$19$	0.230842	+	2.34378i	0.0529588	+	0.537700i	−0.931702	+	0.363223i	$0.881676\pi$
$20$	4.50025	−	6.56605i	1.00629	−	1.46821i
$21$	2.41350	−	4.51534i	0.526668	−	0.985327i
$22$	2.86352	+	1.04368i	0.610504	+	0.222513i
$23$	−0.902011	+	0.179421i	−0.188082	+	0.0374119i	−0.288233	−	0.957560i	$-0.593068\pi$
$23$	−0.902011	+	0.179421i	−0.188082	+	0.0374119i	0.100150	+	0.994972i	$0.468068\pi$
$24$	−0.365438	−	2.80472i	−0.0745947	−	0.572511i
$25$	−2.11504	+	10.6330i	−0.423008	+	2.12660i
$26$	−1.98663	−	8.13439i	−0.389611	−	1.59529i
$27$	−0.0980171	+	0.995185i	−0.0188634	+	0.191523i
$28$	−7.83825	−	6.58898i	−1.48129	−	1.24520i
$29$	−1.08348	+	3.57175i	−0.201197	+	0.663258i	0.797041	+	0.603925i	$0.206397\pi$
$29$	−1.08348	+	3.57175i	−0.201197	+	0.663258i	−0.998238	+	0.0593330i	$0.981103\pi$
$30$	2.86522	+	4.84491i	0.523114	+	0.884556i
$31$	−1.11133	−	1.11133i	−0.199601	−	0.199601i	0.600228	−	0.799829i	$-0.295076\pi$
$31$	−1.11133	−	1.11133i	−0.199601	−	0.199601i	−0.799829	+	0.600228i	$0.795076\pi$
$32$	−5.63940	−	0.444083i	−0.996914	−	0.0785036i
$33$	−1.52389	+	1.52389i	−0.265276	+	0.265276i
$34$	−1.43529	−	0.368534i	−0.246150	−	0.0632030i
$35$	19.5003	+	5.91534i	3.29615	+	0.999876i
$36$	1.90690	+	0.603110i	0.317816	+	0.100518i
$37$	2.94183	+	0.289745i	0.483633	+	0.0476337i	0.336896	−	0.941542i	$-0.390623\pi$
$37$	2.94183	+	0.289745i	0.483633	+	0.0476337i	0.146737	+	0.989176i	$0.453123\pi$
$38$	−1.72912	+	2.84664i	−0.280500	+	0.461786i
$39$	5.80717	+	1.15512i	0.929892	+	0.184967i
$40$	10.6649	−	3.60435i	1.68626	−	0.569898i
$41$	1.55436	+	7.81427i	0.242749	+	1.22038i	0.889232	+	0.457456i	$0.151239\pi$
$41$	1.55436	+	7.81427i	0.242749	+	1.22038i	−0.646483	+	0.762928i	$0.723761\pi$
$42$	6.56358	−	3.05709i	1.01278	−	0.471720i
$43$	−4.62540	−	2.47233i	−0.705366	−	0.377026i	0.0793790	−	0.996845i	$-0.474706\pi$
$43$	−4.62540	−	2.47233i	−0.705366	−	0.377026i	−0.784745	+	0.619818i	$0.787206\pi$
$44$	2.35218	+	3.61182i	0.354604	+	0.544502i
$45$	−3.96095	+	0.390120i	−0.590464	+	0.0581556i
$46$	−1.17245	−	0.563016i	−0.172869	−	0.0830122i
$47$	0.425470	+	1.02718i	0.0620612	+	0.149829i	0.951868	−	0.306509i	$-0.0991609\pi$
$47$	0.425470	+	1.02718i	0.0620612	+	0.149829i	−0.889807	+	0.456338i	$0.849161\pi$
$48$	1.96830	−	3.48221i	0.284100	−	0.502614i
$49$	7.35258	−	17.7507i	1.05037	−	2.53581i
$50$	−11.4208	+	10.2291i	−1.61514	+	1.44661i
$51$	0.664733	−	0.809980i	0.0930813	−	0.113420i
$52$	4.66046	−	10.8862i	0.646289	−	1.50965i
$53$	−0.296345	−	0.976920i	−0.0407062	−	0.134190i	0.934232	−	0.356665i	$-0.116086\pi$
$53$	−0.296345	−	0.976920i	−0.0407062	−	0.134190i	−0.974938	+	0.222475i	$0.928586\pi$
$54$	−0.955893	+	1.04224i	−0.130081	+	0.141831i
$55$	−7.13200	−	4.76545i	−0.961679	−	0.642573i
$56$	−3.26950	−	14.1073i	−0.436905	−	1.88517i
$57$	−1.30844	−	1.95821i	−0.173306	−	0.259371i
$58$	−4.25822	+	3.11934i	−0.559131	+	0.409589i
$59$	3.47475	−	2.85165i	0.452374	−	0.371253i	−0.380441	−	0.924805i	$-0.624228\pi$
$59$	3.47475	−	2.85165i	0.452374	−	0.371253i	0.832815	+	0.553552i	$0.186728\pi$
$60$	−0.873652	+	7.91214i	−0.112788	+	1.02145i
$61$	3.89370	+	7.28460i	0.498538	+	0.932698i	0.997803	+	0.0662491i	$0.0211032\pi$
$61$	3.89370	+	7.28460i	0.498538	+	0.932698i	−0.499266	+	0.866449i	$0.666397\pi$
$62$	−0.313156	−	2.20049i	−0.0397708	−	0.279462i
$63$			5.11988i			0.645045i
$64$	−6.00061	−	5.29082i	−0.750076	−	0.661352i
$65$			23.5660i			2.92301i
$66$	−3.01738	+	0.429410i	−0.371414	+	0.0528567i
$67$	−1.86316	−	3.48572i	−0.227621	−	0.425849i	0.742022	−	0.670376i	$-0.233867\pi$
$67$	−1.86316	−	3.48572i	−0.227621	−	0.425849i	−0.969642	+	0.244527i	$0.921367\pi$
$68$	−1.31026	−	1.63553i	−0.158892	−	0.198337i
$69$	0.710924	−	0.583440i	0.0855852	−	0.0702379i
$70$	17.0303	+	23.2481i	2.03551	+	2.77868i
$71$	2.40217	+	3.59509i	0.285085	+	0.426659i	0.946179	−	0.323643i	$-0.104908\pi$
$71$	2.40217	+	3.59509i	0.285085	+	0.426659i	−0.661095	+	0.750303i	$0.729908\pi$
$72$	1.64442	+	2.30128i	0.193797	+	0.271208i
$73$	−10.9456	−	7.31361i	−1.28108	−	0.855993i	−0.286314	−	0.958136i	$-0.592430\pi$
$73$	−10.9456	−	7.31361i	−1.28108	−	0.855993i	−0.994770	+	0.102143i	$0.967430\pi$
$74$	3.08093	+	2.82568i	0.358151	+	0.328478i
$75$	−3.14707	−	10.3745i	−0.363392	−	1.19794i
$76$	−4.37266	+	1.75106i	−0.501579	+	0.200861i
$77$	−6.99984	+	8.52933i	−0.797705	+	0.972007i
$78$	5.58658	+	6.23740i	0.632556	+	0.706247i
$79$	−5.55241	+	13.4047i	−0.624695	+	1.50815i	0.221437	+	0.975175i	$0.428925\pi$
$79$	−5.55241	+	13.4047i	−0.624695	+	1.50815i	−0.846132	+	0.532973i	$0.821075\pi$
$80$	15.1216	+	4.97966i	1.69065	+	0.556742i
$81$	−0.382683	−	0.923880i	−0.0425204	−	0.102653i
$82$	−4.87750	+	10.1571i	−0.538630	+	1.12167i
$83$	3.28847	−	0.323886i	0.360957	−	0.0355512i	0.0840866	−	0.996458i	$-0.473203\pi$
$83$	3.28847	−	0.323886i	0.360957	−	0.0355512i	0.276870	+	0.960907i	$0.410703\pi$
$84$	10.0187	+	2.11603i	1.09313	+	0.230878i
$85$	3.67802	+	1.96594i	0.398938	+	0.213237i
$86$	−3.13161	−	6.72357i	−0.337690	−	0.725021i
$87$	−0.728169	−	3.66075i	−0.0780679	−	0.392474i
$88$	−0.406794	+	6.08198i	−0.0433644	+	0.648341i
$89$	−13.9931	−	2.78340i	−1.48327	−	0.295040i	−0.613969	−	0.789330i	$-0.710428\pi$
$89$	−13.9931	−	2.78340i	−1.48327	−	0.295040i	−0.869297	+	0.494290i	$0.835428\pi$
$90$	−4.81077	−	2.92218i	−0.507100	−	0.308025i
$91$	30.1686	+	2.97134i	3.16252	+	0.311481i
$92$	−0.847871	−	1.63229i	−0.0883966	−	0.170178i
$93$	1.50398	+	0.456228i	0.155956	+	0.0473087i
$94$	−0.391037	+	1.52293i	−0.0403324	+	0.157078i
$95$	6.62818	−	6.62818i	0.680036	−	0.680036i
$96$	5.18284	−	2.26675i	0.528972	−	0.231349i
$97$	−6.06453	−	6.06453i	−0.615759	−	0.615759i	0.328681	−	0.944441i	$-0.393396\pi$
$97$	−6.06453	−	6.06453i	−0.615759	−	0.615759i	−0.944441	+	0.328681i	$0.893396\pi$
$98$	23.3879	−	13.8313i	2.36253	−	1.39717i
$99$	0.625595	−	2.06231i	0.0628747	−	0.207270i
$100$	−21.6018	+	1.87053i	−2.16018	+	0.187053i
$101$	1.46696	−	14.8943i	0.145968	−	1.48203i	−0.591310	−	0.806444i	$-0.701389\pi$
$101$	1.46696	−	14.8943i	0.145968	−	1.48203i	0.737278	−	0.675590i	$-0.236111\pi$
$102$	1.43954	−	0.351574i	0.142536	−	0.0348110i
$103$	−0.829062	+	4.16798i	−0.0816899	+	0.410683i	0.918204	+	0.396108i	$0.129639\pi$
$103$	−0.829062	+	4.16798i	−0.0816899	+	0.410683i	−0.999894	+	0.0145749i	$0.995361\pi$
$104$	14.5145	−	8.35409i	1.42326	−	0.819186i
$105$	−19.9862	+	3.97550i	−1.95045	+	0.387969i
$106$	0.494392	−	1.35645i	0.0480196	−	0.131750i
$107$	−6.36237	+	11.9032i	−0.615073	+	1.15072i	0.360854	+	0.932623i	$0.382485\pi$
$107$	−6.36237	+	11.9032i	−0.615073	+	1.15072i	−0.975927	+	0.218099i	$0.930015\pi$
$108$	−1.96604	+	0.367010i	−0.189182	+	0.0353155i
$109$	−0.159270	−	1.61709i	−0.0152553	−	0.154889i	0.984539	−	0.175165i	$-0.0560457\pi$
$109$	−0.159270	−	1.61709i	−0.0152553	−	0.154889i	−0.999794	+	0.0202753i	$0.993546\pi$
$110$	−4.01920	−	11.4453i	−0.383216	−	1.09127i
$111$	−2.73104	+	1.13124i	−0.259219	+	0.107372i
$112$	8.28144	−	18.7304i	0.782522	−	1.76986i
$113$	4.87692	+	2.02008i	0.458782	+	0.190034i	0.600091	−	0.799932i	$-0.295131\pi$
$113$	4.87692	+	2.02008i	0.458782	+	0.190034i	−0.141309	+	0.989966i	$0.545131\pi$
$114$	0.183049	−	3.32561i	0.0171441	−	0.311472i
$115$	2.82956	+	2.32216i	0.263858	+	0.216542i
$116$	−7.46443	−	0.0880755i	−0.693055	−	0.00817761i
$117$	−5.66599	+	1.71876i	−0.523821	+	0.158899i
$118$	6.35108	−	0.274461i	0.584664	−	0.0252662i
$119$	2.98049	−	4.46062i	0.273221	−	0.408905i
$120$	−7.70649	+	8.20614i	−0.703503	+	0.749114i
$121$	−5.28441	+	3.53093i	−0.480401	+	0.320994i
$122$	−1.78214	+	11.5446i	−0.161347	+	1.04519i
$123$	−5.05444	−	6.15885i	−0.455744	−	0.555325i
$124$	1.51435	−	2.75448i	0.135993	−	0.247360i
$125$	20.5039	−	10.9596i	1.83393	−	0.980254i
$126$	−4.34746	+	5.79017i	−0.387303	+	0.515829i
$127$	−6.60027			−0.585679			−0.292839	−	0.956162i	$-0.594600\pi$
$127$	−6.60027			−0.585679			−0.292839	+	0.956162i	$0.594600\pi$
$128$	−2.29358	−	11.0788i	−0.202726	−	0.979235i
$129$	5.24468			0.461769
$130$	−20.0107	+	26.6512i	−1.75505	+	2.33747i
$131$	10.6187	−	5.67580i	0.927758	−	0.495897i	0.0629597	−	0.998016i	$-0.479946\pi$
$131$	10.6187	−	5.67580i	0.927758	−	0.495897i	0.864799	+	0.502119i	$0.167446\pi$
$132$	−3.77704	−	2.07653i	−0.328749	−	0.180739i
$133$	−7.64948	−	9.32092i	−0.663294	−	0.808226i
$134$	0.852763	−	5.52413i	0.0736675	−	0.477212i
$135$	3.30935	−	2.21123i	0.284823	−	0.190313i
$136$	−0.0930127	−	2.96224i	−0.00797577	−	0.254010i
$137$	10.2412	−	15.3271i	0.874966	−	1.30948i	−0.0750191	−	0.997182i	$-0.523902\pi$
$137$	10.2412	−	15.3271i	0.874966	−	1.30948i	0.949985	−	0.312296i	$-0.101098\pi$
$138$	1.29941	−	0.0561540i	0.110613	−	0.00478014i
$139$	−9.84179	+	2.98548i	−0.834770	+	0.253225i	−0.678602	−	0.734506i	$-0.737414\pi$
$139$	−9.84179	+	2.98548i	−0.834770	+	0.253225i	−0.156168	+	0.987731i	$0.549914\pi$
$140$	−0.480855	+	40.7526i	−0.0406397	+	3.44423i
$141$	−0.859439	−	0.705323i	−0.0723778	−	0.0593989i
$142$	−0.336061	+	6.10551i	−0.0282016	+	0.512363i
$143$	−11.7890	−	4.88314i	−0.985842	−	0.408349i
$144$	−0.0943818	+	3.99889i	−0.00786515	+	0.333241i
$145$	13.7249	−	5.68502i	1.13979	−	0.472115i
$146$	−6.16833	−	17.5653i	−0.510495	−	1.45372i
$147$	1.88322	+	19.1207i	0.155326	+	1.57705i
$148$	1.08490	+	5.81173i	0.0891785	+	0.477721i
$149$	4.81610	−	9.01029i	0.394550	−	0.738151i	−0.603705	−	0.797208i	$-0.706309\pi$
$149$	4.81610	−	9.01029i	0.394550	−	0.738151i	0.998255	+	0.0590568i	$0.0188093\pi$
$150$	5.25025	−	14.4050i	0.428681	−	1.17616i
$151$	5.89736	−	1.17306i	0.479920	−	0.0954620i	0.0507988	−	0.998709i	$-0.483823\pi$
$151$	5.89736	−	1.17306i	0.479920	−	0.0954620i	0.429121	+	0.903247i	$0.358823\pi$
$152$	−6.43200	−	1.73266i	−0.521704	−	0.140537i
$153$	−0.204421	+	1.02769i	−0.0165264	+	0.0830839i
$154$	−15.1588	+	3.70217i	−1.22153	+	0.298330i
$155$	−0.613135	+	6.22526i	−0.0492482	+	0.500025i
$156$	1.02158	+	11.7977i	0.0817920	+	0.944575i
$157$	−2.02702	+	6.68220i	−0.161774	+	0.533298i	−0.999926	−	0.0121386i	$-0.996136\pi$
$157$	−2.02702	+	6.68220i	−0.161774	+	0.533298i	0.838152	+	0.545436i	$0.183636\pi$
$158$	−17.6617	+	10.4449i	−1.40509	+	0.830950i
$159$	0.721870	+	0.721870i	0.0572480	+	0.0572480i
$160$	12.8729	+	18.4719i	1.01770	+	1.46033i
$161$	3.32953	−	3.32953i	0.262404	−	0.262404i
$162$	0.351713	−	1.36978i	0.0276332	−	0.107620i
$163$	−11.9472	−	3.62415i	−0.935777	−	0.283865i	−0.214669	−	0.976687i	$-0.568867\pi$
$163$	−11.9472	−	3.62415i	−0.935777	−	0.283865i	−0.721109	+	0.692822i	$0.756367\pi$
$164$	−14.1408	+	7.34525i	−1.10421	+	0.573567i
$165$	8.53628	+	0.840750i	0.664548	+	0.0654523i
$166$	3.99402	+	2.42606i	0.309996	+	0.188299i
$167$	−1.04621	−	0.208104i	−0.0809583	−	0.0161036i	0.154445	−	0.988001i	$-0.450641\pi$
$167$	−1.04621	−	0.208104i	−0.0809583	−	0.0161036i	−0.235403	+	0.971898i	$0.575641\pi$
$168$	9.53358	+	10.9003i	0.735532	+	0.840977i
$169$	4.30321	+	21.6337i	0.331016	+	1.66413i
$170$	2.49019	+	5.34645i	0.190989	+	0.410054i
$171$	2.07703	+	1.11020i	0.158835	+	0.0848988i
$172$	2.16761	−	10.2630i	0.165279	−	0.782543i
$173$	−6.13074	+	0.603825i	−0.466111	+	0.0459080i	−0.328347	−	0.944557i	$-0.606492\pi$
$173$	−6.13074	+	0.603825i	−0.466111	+	0.0459080i	−0.137764	+	0.990465i	$0.543992\pi$
$174$	2.28497	−	4.75832i	0.173223	−	0.360728i
$175$	−21.2414	−	51.2812i	−1.60570	−	3.87649i
$176$	−5.62446	+	6.53279i	−0.423959	+	0.492428i
$177$	−1.72019	+	4.15292i	−0.129298	+	0.312152i
$178$	−13.4616	−	15.0298i	−1.00899	−	1.12653i
$179$	−7.22493	+	8.80360i	−0.540016	+	0.658012i	−0.969508	−	0.245059i	$-0.921193\pi$
$179$	−7.22493	+	8.80360i	−0.540016	+	0.658012i	0.429492	+	0.903071i	$0.358693\pi$
$180$	−2.95927	−	7.38973i	−0.220571	−	0.550798i
$181$	−2.61326	−	8.61475i	−0.194242	−	0.640329i	−0.998913	−	0.0466090i	$-0.985159\pi$
$181$	−2.61326	−	8.61475i	−0.194242	−	0.640329i	0.804671	−	0.593720i	$-0.202341\pi$
$182$	31.5951	+	28.9774i	2.34198	+	2.14795i
$183$	−6.86788	−	4.58897i	−0.507688	−	0.339226i
$184$	0.427160	−	2.56594i	0.0314907	−	0.189164i
$185$	−6.53654	−	9.78263i	−0.480576	−	0.719233i
$186$	1.31348	+	1.79304i	0.0963092	+	0.131472i
$187$	−1.74559	+	1.43257i	−0.127651	+	0.104760i
$188$	−1.73540	+	1.39027i	−0.126567	+	0.101396i
$189$	−2.41350	−	4.51534i	−0.175556	−	0.328442i
$190$	13.1241	−	1.86772i	0.952124	−	0.135499i
$191$		−	16.7304i		−	1.21057i	−0.796009	−	0.605285i	$-0.793059\pi$
$191$		−	16.7304i		−	1.21057i	0.796009	−	0.605285i	$-0.206941\pi$
$192$	7.78613	+	1.83742i	0.561916	+	0.132604i
$193$			2.18922i			0.157583i	0.996891	+	0.0787916i	$0.0251062\pi$
$193$			2.18922i			0.157583i	−0.996891	+	0.0787916i	$0.974894\pi$
$194$	−1.70889	−	12.0081i	−0.122691	−	0.862129i
$195$	−11.1089	−	20.7834i	−0.795528	−	1.48833i
$196$	38.1943	+	4.21738i	2.72816	+	0.301241i
$197$	1.17316	−	0.962785i	0.0835839	−	0.0685956i	−0.591674	−	0.806178i	$-0.701533\pi$
$197$	1.17316	−	0.962785i	0.0835839	−	0.0685956i	0.675257	+	0.737582i	$0.264033\pi$
$198$	2.45867	−	1.80109i	0.174730	−	0.127998i
$199$	14.3935	+	21.5414i	1.02033	+	1.52703i	0.839383	+	0.543540i	$0.182916\pi$
$199$	14.3935	+	21.5414i	1.02033	+	1.52703i	0.180947	+	0.983493i	$0.442084\pi$
$200$	−26.0182	−	16.2274i	−1.83976	−	1.14745i
$201$	3.28632	+	2.19585i	0.231799	+	0.154883i
$202$	14.3062	−	15.5985i	1.00658	−	1.09751i
$203$	−5.54729	−	18.2870i	−0.389343	−	1.28349i
$204$	1.92653	+	0.824758i	0.134884	+	0.0577446i
$205$	20.1173	−	24.5130i	1.40505	−	1.71206i
$206$	−4.47677	+	4.00965i	−0.311911	+	0.279366i
$207$	−0.351947	+	0.849675i	−0.0244620	+	0.0590565i
$208$	23.5084	+	2.87691i	1.63001	+	0.199478i
$209$	1.94233	+	4.68919i	0.134353	+	0.324358i
$210$	−25.9784	−	12.4750i	−1.79268	−	0.860854i
$211$	−12.8114	+	1.26182i	−0.881976	+	0.0868671i	−0.528857	−	0.848711i	$-0.677379\pi$
$211$	−12.8114	+	1.26182i	−0.881976	+	0.0868671i	−0.353120	+	0.935578i	$0.614879\pi$
$212$	1.71092	−	1.11423i	0.117507	−	0.0765257i
$213$	−3.81324	−	2.03822i	−0.261279	−	0.139656i
$214$	−17.3027	+	8.05899i	−1.18279	+	0.550901i
$215$	4.07240	+	20.4733i	0.277736	+	1.39627i
$216$	−2.53507	−	1.25437i	−0.172489	−	0.0853490i
$217$	7.89209	+	1.56983i	0.535750	+	0.106567i
$218$	1.19300	−	1.96404i	0.0808004	−	0.133021i
$219$	13.1008	+	1.29031i	0.885267	+	0.0871912i
$220$	5.17323	−	16.3566i	0.348779	−	1.10276i
$221$	5.93696	+	1.80096i	0.399363	+	0.121146i
$222$	−4.04915	−	1.03968i	−0.271761	−	0.0697790i
$223$	−7.98917	+	7.98917i	−0.534995	+	0.534995i	−0.922055	−	0.387060i	$-0.873491\pi$
$223$	−7.98917	+	7.98917i	−0.534995	+	0.534995i	0.387060	+	0.922055i	$0.373491\pi$
$224$	25.2702	−	14.1505i	1.68844	−	0.945472i
$225$	7.66597	+	7.66597i	0.511065	+	0.511065i
$226$	3.80007	+	6.42570i	0.252777	+	0.427431i
$227$	−7.33113	+	24.1675i	−0.486584	+	1.60405i	0.278711	+	0.960375i	$0.410093\pi$
$227$	−7.33113	+	24.1675i	−0.486584	+	1.60405i	−0.765296	+	0.643679i	$0.777407\pi$
$228$	3.03090	−	3.60556i	0.200726	−	0.238784i
$229$	−1.60555	+	16.3014i	−0.106098	+	1.07723i	0.783784	+	0.621034i	$0.213287\pi$
$229$	−1.60555	+	16.3014i	−0.106098	+	1.07723i	−0.889881	+	0.456193i	$0.849213\pi$
$230$	1.22818	+	5.02884i	0.0809836	+	0.331592i
$231$	2.15261	−	10.8219i	0.141631	−	0.712028i
$232$	−8.36686	−	6.43789i	−0.549311	−	0.422668i
$233$	21.6967	−	4.31574i	1.42140	−	0.282734i	0.576253	−	0.817271i	$-0.304514\pi$
$233$	21.6967	−	4.31574i	1.42140	−	0.282734i	0.845145	+	0.534538i	$0.179514\pi$
$234$	−7.86722	−	2.86740i	−0.514296	−	0.187448i
$235$	2.08599	−	3.90261i	0.136075	−	0.254578i
$236$	7.41560	+	5.08252i	0.482715	+	0.330844i
$237$	−1.42215	−	14.4393i	−0.0923783	−	0.937932i
$238$	7.15835	−	2.51376i	0.464007	−	0.162943i
$239$	−15.0322	+	6.22653i	−0.972351	+	0.402761i	−0.811587	−	0.584232i	$-0.801396\pi$
$239$	−15.0322	+	6.22653i	−0.972351	+	0.402761i	−0.160764	+	0.986993i	$0.551396\pi$
$240$	−15.6835	+	2.73663i	−1.01237	+	0.176649i
$241$	−9.09317	−	3.76651i	−0.585743	−	0.242623i	0.0700752	−	0.997542i	$-0.477676\pi$
$241$	−9.09317	−	3.76651i	−0.585743	−	0.242623i	−0.655818	+	0.754919i	$0.727676\pi$
$242$	−8.97446	−	0.493975i	−0.576900	−	0.0317539i
$243$	0.773010	+	0.634393i	0.0495886	+	0.0406963i
$244$	−11.8183	+	11.5427i	−0.756590	+	0.738943i
$245$	−73.1780	+	22.1983i	−4.67517	+	1.41820i
$246$	−0.486471	−	11.2570i	−0.0310163	−	0.717723i
$247$	7.74717	−	11.5945i	0.492940	−	0.737737i
$248$	4.05153	−	1.82920i	0.257272	−	0.116155i
$249$	−2.74750	+	1.83582i	−0.174116	+	0.116340i
$250$	32.4944	+	5.01617i	2.05512	+	0.317251i
$251$	−4.74629	−	5.78337i	−0.299583	−	0.365043i	0.601362	−	0.798977i	$-0.294625\pi$
$251$	−4.74629	−	5.78337i	−0.299583	−	0.365043i	−0.900945	+	0.433934i	$0.857125\pi$
$252$	−9.83324	+	2.85663i	−0.619436	+	0.179951i
$253$	−1.74798	+	0.934315i	−0.109895	+	0.0587399i
$254$	−7.46436	−	5.60450i	−0.468355	−	0.351658i
$255$	−4.17047			−0.261165
$256$	6.81350	−	14.4767i	0.425844	−	0.904797i
$257$	7.03693			0.438951			0.219476	−	0.975618i	$-0.429565\pi$
$257$	7.03693			0.438951			0.219476	+	0.975618i	$0.429565\pi$
$258$	5.93130	+	4.45343i	0.369267	+	0.277258i
$259$	−13.3476	+	7.13444i	−0.829380	+	0.443313i
$260$	−45.2609	+	13.1486i	−2.80696	+	0.815443i
$261$	2.36786	+	2.88524i	0.146567	+	0.178592i
$262$	16.8284	+	2.59780i	1.03966	+	0.160493i
$263$	18.5330	−	12.3834i	1.14279	−	0.763591i	0.167800	−	0.985821i	$-0.446334\pi$
$263$	18.5330	−	12.3834i	1.14279	−	0.763591i	0.974994	+	0.222230i	$0.0713336\pi$
$264$	−2.50826	−	5.55559i	−0.154373	−	0.341923i
$265$	−2.25740	+	3.37844i	−0.138671	+	0.207536i
$266$	−0.736235	−	17.0366i	−0.0451414	−	1.04458i
$267$	13.6529	−	4.14156i	0.835544	−	0.253460i
$268$	5.65512	−	5.52323i	0.345442	−	0.337385i
$269$	−4.58557	−	3.76328i	−0.279587	−	0.229451i	0.484140	−	0.874991i	$-0.339133\pi$
$269$	−4.58557	−	3.76328i	−0.279587	−	0.229451i	−0.763727	+	0.645539i	$0.776633\pi$
$270$	5.62023	+	0.309350i	0.342036	+	0.0188264i
$271$	8.69906	+	3.60327i	0.528430	+	0.218883i	0.630915	−	0.775852i	$-0.282679\pi$
$271$	8.69906	+	3.60327i	0.528430	+	0.218883i	−0.102485	+	0.994735i	$0.532679\pi$
$272$	2.41014	−	3.42903i	0.146136	−	0.207915i
$273$	−28.0070	+	11.6009i	−1.69506	+	0.702116i
$274$	24.5967	−	8.63749i	1.48594	−	0.521810i
$275$	2.29010	+	23.2517i	0.138098	+	1.40213i
$276$	1.51721	+	1.03987i	0.0913254	+	0.0625928i
$277$	0.895703	−	1.67574i	0.0538176	−	0.100686i	−0.853574	−	0.520971i	$-0.825570\pi$
$277$	0.895703	−	1.67574i	0.0538176	−	0.100686i	0.907392	+	0.420285i	$0.138070\pi$
$278$	−13.6653	−	4.98066i	−0.819591	−	0.298720i
$279$	−1.54146	+	0.306615i	−0.0922847	+	0.0183566i
$280$	−35.1482	+	45.6796i	−2.10051	+	2.72988i
$281$	−5.48032	+	27.5514i	−0.326928	+	1.64358i	0.371888	+	0.928278i	$0.378711\pi$
$281$	−5.48032	+	27.5514i	−0.326928	+	1.64358i	−0.698816	+	0.715302i	$0.746289\pi$
$282$	−0.373041	−	1.52744i	−0.0222143	−	0.0909577i
$283$	−0.511307	+	5.19138i	−0.0303940	+	0.308596i	0.967953	+	0.251130i	$0.0808021\pi$
$283$	−0.511307	+	5.19138i	−0.0303940	+	0.308596i	−0.998347	+	0.0574660i	$0.981698\pi$
$284$	−5.56445	+	6.61947i	−0.330189	+	0.392793i
$285$	−2.72103	+	8.97003i	−0.161180	+	0.531339i
$286$	−9.18589	−	15.5328i	−0.543173	−	0.918475i
$287$	−28.8443	−	28.8443i	−1.70262	−	1.70262i
$288$	−3.50232	+	4.44227i	−0.206376	+	0.261763i
$289$	−11.2445	+	11.2445i	−0.661439	+	0.661439i
$290$	20.3490	+	5.22493i	1.19494	+	0.306819i
$291$	8.20723	+	2.48964i	0.481116	+	0.145945i
$292$	7.93943	−	25.1027i	0.464620	−	1.46902i
$293$	1.17677	+	0.115901i	0.0687474	+	0.00677103i	0.132332	−	0.991205i	$-0.457753\pi$
$293$	1.17677	+	0.115901i	0.0687474	+	0.00677103i	−0.0635850	+	0.997976i	$0.520253\pi$
$294$	−14.1062	+	23.2230i	−0.822693	+	1.35440i
$295$	−17.5472	−	3.49035i	−1.02164	−	0.203216i
$296$	−3.70799	+	7.49381i	−0.215523	+	0.435569i
$297$	0.420441	+	2.11370i	0.0243965	+	0.122649i
$298$	13.0975	−	6.10038i	0.758720	−	0.353386i
$299$	4.80240	+	2.56694i	0.277730	+	0.148450i
$300$	18.1693	−	11.8327i	1.04901	−	0.683161i
$301$	26.7229	−	2.63197i	1.54028	−	0.151704i
$302$	7.66550	+	3.68101i	0.441100	+	0.211818i
$303$	5.72736	+	13.8271i	0.329028	+	0.794345i
$304$	−5.80280	−	7.42112i	−0.332814	−	0.425630i
$305$	12.5809	−	30.3730i	0.720380	−	1.73915i
$306$	−1.10383	+	0.988654i	−0.0631017	+	0.0565176i
$307$	13.1672	−	16.0443i	0.751492	−	0.915696i	−0.247087	−	0.968993i	$-0.579473\pi$
$307$	13.1672	−	16.0443i	0.751492	−	0.915696i	0.998579	+	0.0532977i	$0.0169732\pi$
$308$	−20.2869	−	8.68495i	−1.15596	−	0.494871i
$309$	−1.23360	−	4.06665i	−0.0701773	−	0.231343i
$310$	−5.97948	+	6.51962i	−0.339611	+	0.370290i
$311$	10.9951	+	7.34667i	0.623473	+	0.416591i	0.826781	−	0.562523i	$-0.190169\pi$
$311$	10.9951	+	7.34667i	0.623473	+	0.416591i	−0.203308	+	0.979115i	$0.565169\pi$
$312$	−8.86251	+	14.2097i	−0.501741	+	0.804467i
$313$	14.4122	+	21.5694i	0.814627	+	1.21918i	0.972773	+	0.231760i	$0.0744484\pi$
$313$	14.4122	+	21.5694i	0.814627	+	1.21918i	−0.158146	+	0.987416i	$0.550552\pi$
$314$	−7.96647	+	5.83581i	−0.449574	+	0.329334i
$315$	15.7522	−	12.9275i	0.887536	−	0.728382i
$316$	−28.8430	−	3.18482i	−1.62255	−	0.179160i
$317$	−3.88856	−	7.27498i	−0.218403	−	0.408604i	0.748730	−	0.662876i	$-0.230664\pi$
$317$	−3.88856	−	7.27498i	−0.218403	−	0.408604i	−0.967133	+	0.254272i	$0.918164\pi$
$318$	0.203412	+	1.42934i	0.0114068	+	0.0801533i
$319$			8.04388i			0.450371i
$320$	−1.12682	+	31.8210i	−0.0629912	+	1.77885i
$321$		−	13.4968i		−	0.753320i
$322$	6.59263	−	0.938211i	0.367393	−	0.0522844i
$323$	−1.16329	−	2.17637i	−0.0647273	−	0.121096i
$324$	1.56088	−	1.25046i	0.0867157	−	0.0694699i
$325$	49.6202	−	40.7222i	2.75243	−	2.25886i
$326$	−10.4339	−	14.2434i	−0.577881	−	0.788867i
$327$	0.902755	+	1.35107i	0.0499224	+	0.0747142i
$328$	−22.2292	−	3.70056i	−1.22740	−	0.204329i
$329$	−4.73300	−	3.16249i	−0.260939	−	0.174354i
$330$	8.93992	+	8.19925i	0.492126	+	0.451354i
$331$	−7.59283	−	25.0302i	−0.417340	−	1.37578i	−0.873906	−	0.486095i	$-0.838421\pi$
$331$	−7.59283	−	25.0302i	−0.417340	−	1.37578i	0.456566	−	0.889689i	$-0.349079\pi$
$332$	2.45685	+	6.13512i	0.134837	+	0.336709i
$333$	1.87530	−	2.28507i	0.102766	−	0.125221i
$334$	−1.00647	−	1.12372i	−0.0550716	−	0.0614873i
$335$	−6.02002	+	14.5336i	−0.328909	+	0.794057i
$336$	1.52589	+	20.4226i	0.0832441	+	1.11414i
$337$	8.30560	+	20.0515i	0.452435	+	1.09227i	0.971394	+	0.237475i	$0.0763198\pi$
$337$	8.30560	+	20.0515i	0.452435	+	1.09227i	−0.518959	+	0.854799i	$0.673680\pi$
$338$	−13.5033	+	28.1199i	−0.734483	+	1.52952i
$339$	−5.25332	+	0.517407i	−0.285321	+	0.0281017i
$340$	−1.72364	+	8.16090i	−0.0934776	+	0.442587i
$341$	−2.98715	−	1.59666i	−0.161763	−	0.0864643i
$342$	1.40625	+	3.01921i	0.0760411	+	0.163260i
$343$	12.1991	+	61.3288i	0.658687	+	3.31144i
$344$	11.1660	−	9.76596i	0.602030	−	0.526545i
$345$	−3.59011	−	0.714117i	−0.193285	−	0.0384467i
$346$	−7.44608	−	4.52293i	−0.400304	−	0.243154i
$347$	14.7426	+	1.45201i	0.791422	+	0.0779482i	0.485646	−	0.874155i	$-0.338584\pi$
$347$	14.7426	+	1.45201i	0.791422	+	0.0779482i	0.305775	+	0.952104i	$0.401084\pi$
$348$	6.62455	−	3.44103i	0.355113	−	0.184459i
$349$	−34.8059	−	10.5582i	−1.86312	−	0.565170i	−0.997973	−	0.0636453i	$-0.979727\pi$
$349$	−34.8059	−	10.5582i	−1.86312	−	0.565170i	−0.865143	−	0.501525i	$-0.832773\pi$
$350$	19.5223	−	76.0315i	1.04351	−	4.06405i
$351$	4.18674	−	4.18674i	0.223471	−	0.223471i
$352$	−11.9080	+	2.61214i	−0.634699	+	0.139228i
$353$	7.96593	+	7.96593i	0.423984	+	0.423984i	0.886573	−	0.462589i	$-0.153079\pi$
$353$	7.96593	+	7.96593i	0.423984	+	0.423984i	−0.462589	+	0.886573i	$0.653079\pi$
$354$	−5.47177	+	3.23593i	−0.290821	+	0.171988i
$355$	4.99556	−	16.4681i	0.265137	−	0.874038i
$356$	−2.46163	−	28.4281i	−0.130466	−	1.50669i
$357$	−0.525837	+	5.33891i	−0.0278302	+	0.282565i
$358$	−15.6462	+	3.82122i	−0.826928	+	0.201958i
$359$	−1.48940	+	7.48774i	−0.0786077	+	0.395188i	0.921371	+	0.388684i	$0.127070\pi$
$359$	−1.48940	+	7.48774i	−0.0786077	+	0.395188i	−0.999979	+	0.00650366i	$0.997930\pi$
$360$	2.92817	−	10.8700i	0.154328	−	0.572898i
$361$	13.1949	−	2.62463i	0.694469	−	0.138138i
$362$	4.35969	−	11.9616i	0.229140	−	0.628686i
$363$	2.99597	−	5.60506i	0.157247	−	0.294189i
$364$	11.1257	+	59.5995i	0.583147	+	3.12386i
$365$	5.13559	+	52.1425i	0.268809	+	2.72927i
$366$	−3.87036	−	11.0215i	−0.202307	−	0.576102i
$367$	−29.3351	+	12.1510i	−1.53128	+	0.634277i	−0.979812	−	0.199919i	$-0.935932\pi$
$367$	−29.3351	+	12.1510i	−1.53128	+	0.634277i	−0.551468	+	0.834196i	$0.685932\pi$
$368$	2.66191	−	2.53915i	0.138761	−	0.132362i
$369$	7.36088	+	3.04898i	0.383192	+	0.158723i
$370$	0.914458	−	16.6137i	0.0475404	−	0.863707i
$371$	4.04036	+	3.31583i	0.209765	+	0.172150i
$372$	−0.0370866	+	3.14310i	−0.00192285	+	0.162962i
$373$	27.3447	−	8.29491i	1.41585	−	0.429494i	0.512609	−	0.858622i	$-0.328679\pi$
$373$	27.3447	−	8.29491i	1.41585	−	0.429494i	0.903244	+	0.429128i	$0.141179\pi$
$374$	−3.19057	+	0.137880i	−0.164980	+	0.00712960i
$375$	−12.9165	+	19.3310i	−0.667007	+	0.998247i
$376$	−3.14312	+	0.0986922i	−0.162094	+	0.00508966i
$377$	18.3753	−	12.2780i	0.946374	−	0.632347i
$378$	1.10465	−	7.15585i	0.0568172	−	0.368057i
$379$	4.57398	+	5.57342i	0.234950	+	0.286287i	0.877116	−	0.480278i	$-0.159464\pi$
$379$	4.57398	+	5.57342i	0.234950	+	0.286287i	−0.642166	+	0.766565i	$0.721964\pi$
$380$	16.4282	+	9.03188i	0.842751	+	0.463326i
$381$	5.82091	−	3.11134i	0.298215	−	0.159399i
$382$	14.2063	−	18.9207i	0.726859	−	0.968067i
$383$	30.8807			1.57793			0.788965	−	0.614438i	$-0.210617\pi$
$383$	30.8807			1.57793			0.788965	+	0.614438i	$0.210617\pi$
$384$	7.24526	+	8.68943i	0.369733	+	0.443431i
$385$	43.9162			2.23818
$386$	−1.85893	+	2.47582i	−0.0946173	+	0.126016i
$387$	−4.62540	+	2.47233i	−0.235122	+	0.125675i
$388$	8.26382	−	15.0312i	0.419532	−	0.763094i
$389$	2.10769	+	2.56823i	0.106864	+	0.130214i	0.823696	−	0.567032i	$-0.191908\pi$
$389$	2.10769	+	2.56823i	0.106864	+	0.130214i	−0.716832	+	0.697246i	$0.754408\pi$
$390$	5.08454	−	32.9373i	0.257466	−	1.66784i
$391$	0.801259	−	0.535384i	0.0405214	−	0.0270755i
$392$	39.6135	+	37.2015i	2.00078	+	1.87896i
$393$	−6.68928	+	10.0112i	−0.337430	+	0.504999i
$394$	2.14427	−	0.0926645i	0.108027	−	0.00466837i
$395$	55.2615	−	16.7634i	2.78051	−	0.843458i
$396$	4.30992	+	0.0508543i	0.216581	+	0.00255553i
$397$	2.70986	+	2.22393i	0.136004	+	0.111616i	0.699936	−	0.714206i	$-0.253212\pi$
$397$	2.70986	+	2.22393i	0.136004	+	0.111616i	−0.563932	+	0.825821i	$0.690712\pi$
$398$	−2.01365	+	36.5836i	−0.100935	+	1.83377i
$399$	11.1401	+	4.61438i	0.557702	+	0.231008i
$400$	−15.6452	−	40.4447i	−0.782261	−	2.02224i
$401$	5.07221	−	2.10098i	0.253294	−	0.104918i	−0.252424	−	0.967617i	$-0.581228\pi$
$401$	5.07221	−	2.10098i	0.253294	−	0.104918i	0.505718	+	0.862699i	$0.331228\pi$
$402$	1.85199	+	5.27384i	0.0923687	+	0.263035i
$403$	0.912117	+	9.26088i	0.0454358	+	0.461317i
$404$	29.4244	−	5.49279i	1.46392	−	0.273276i
$405$	−1.87621	+	3.51015i	−0.0932298	+	0.174421i
$406$	9.25453	−	25.3914i	0.459295	−	1.26016i
$407$	6.24822	−	1.24285i	0.309713	−	0.0616057i
$408$	1.47842	+	2.56861i	0.0731926	+	0.127165i
$409$	−2.79358	+	14.0443i	−0.138134	+	0.694444i	0.848199	+	0.529678i	$0.177687\pi$
$409$	−2.79358	+	14.0443i	−0.138134	+	0.694444i	−0.986333	+	0.164767i	$0.947313\pi$
$410$	43.5657	−	10.6399i	2.15156	−	0.525467i
$411$	−1.80682	+	18.3449i	−0.0891237	+	0.904889i
$412$	−8.46758	+	0.733220i	−0.417168	+	0.0361231i
$413$	−6.68070	+	22.0233i	−0.328736	+	1.08370i
$414$	−1.11951	+	0.662063i	−0.0550209	+	0.0325386i
$415$	−9.29976	−	9.29976i	−0.456507	−	0.456507i
$416$	24.1432	+	23.2153i	1.18372	+	1.13822i
$417$	7.27234	−	7.27234i	0.356128	−	0.356128i
$418$	−1.78513	+	6.95238i	−0.0873137	+	0.340052i
$419$	−34.7068	−	10.5282i	−1.69554	−	0.514336i	−0.713123	−	0.701039i	$-0.752720\pi$
$419$	−34.7068	−	10.5282i	−1.69554	−	0.514336i	−0.982416	+	0.186703i	$0.940220\pi$
$420$	−18.7866	−	36.1673i	−0.916691	−	1.76478i
$421$	−3.34688	−	0.329639i	−0.163117	−	0.0160656i	0.0161290	−	0.999870i	$-0.494866\pi$
$421$	−3.34688	−	0.329639i	−0.163117	−	0.0160656i	−0.179246	+	0.983804i	$0.557366\pi$
$422$	−15.5601	−	9.45161i	−0.757456	−	0.460097i
$423$	1.09044	+	0.216903i	0.0530192	+	0.0105462i
$424$	2.88104	+	0.192699i	0.139916	+	0.00935828i
$425$	−2.21619	−	11.1415i	−0.107501	−	0.540444i
$426$	−2.58174	−	5.54300i	−0.125086	−	0.268559i
$427$	−37.2963	−	19.9353i	−1.80490	−	0.964737i
$428$	−26.4110	−	5.57821i	−1.27663	−	0.269633i
$429$	12.6988	−	1.25073i	0.613105	−	0.0603856i
$430$	−12.7790	+	26.6117i	−0.616260	+	1.28333i
$431$	−1.02820	−	2.48230i	−0.0495268	−	0.119568i	0.897180	−	0.441666i	$-0.145612\pi$
$431$	−1.02820	−	2.48230i	−0.0495268	−	0.119568i	−0.946707	+	0.322097i	$0.895612\pi$
$432$	−1.80182	−	3.57119i	−0.0866903	−	0.171819i
$433$	0.0986767	−	0.238227i	0.00474210	−	0.0114484i	−0.921491	−	0.388400i	$-0.873028\pi$
$433$	0.0986767	−	0.238227i	0.00474210	−	0.0114484i	0.926233	+	0.376952i	$0.123028\pi$
$434$	7.59231	+	8.47679i	0.364442	+	0.406899i
$435$	−9.42434	+	11.4836i	−0.451863	+	0.550596i
$436$	3.01692	−	1.20815i	0.144484	−	0.0578597i
$437$	−0.628746	−	2.07270i	−0.0300770	−	0.0991505i
$438$	13.7202	+	12.5835i	0.655578	+	0.601264i
$439$	−0.577408	−	0.385812i	−0.0275582	−	0.0184138i	0.541715	−	0.840562i	$-0.317775\pi$
$439$	−0.577408	−	0.385812i	−0.0275582	−	0.0184138i	−0.569273	+	0.822149i	$0.692775\pi$
$440$	19.7394	−	14.1052i	0.941038	−	0.672438i
$441$	−10.6743	−	15.9752i	−0.508300	−	0.760724i
$442$	5.18496	+	7.07800i	0.246624	+	0.336666i
$443$	−21.4441	+	17.5987i	−1.01884	+	0.836141i	−0.986570	−	0.163338i	$-0.947774\pi$
$443$	−21.4441	+	17.5987i	−1.01884	+	0.836141i	−0.0322705	+	0.999479i	$0.510274\pi$
$444$	−3.69643	−	4.61406i	−0.175425	−	0.218974i
$445$	26.7684	+	50.0802i	1.26894	+	2.37403i
$446$	−15.8190	+	2.25123i	−0.749049	+	0.106599i
$447$			10.2167i			0.483231i
$448$	40.5942	+	5.45470i	1.91790	+	0.257710i
$449$		−	18.2906i		−	0.863185i	−0.902069	−	0.431592i	$-0.857952\pi$
$449$		−	18.2906i		−	0.863185i	0.902069	−	0.431592i	$-0.142048\pi$
$450$	2.16016	+	15.1790i	0.101831	+	0.715545i
$451$	8.09413	+	15.1431i	0.381138	+	0.713059i
$452$	−1.15870	+	10.4937i	−0.0545009	+	0.493582i
$453$	−4.64803	+	3.81454i	−0.218383	+	0.179223i
$454$	−28.8123	+	21.1064i	−1.35223	+	0.990570i
$455$	−67.0325	−	100.321i	−3.14253	−	4.70313i
$456$	6.48929	−	1.50395i	0.303889	−	0.0704291i
$457$	12.2632	+	8.19402i	0.573649	+	0.383300i	0.808292	−	0.588782i	$-0.200392\pi$
$457$	12.2632	+	8.19402i	0.573649	+	0.383300i	−0.234643	+	0.972082i	$0.575392\pi$
$458$	−15.6578	+	17.0722i	−0.731640	+	0.797732i
$459$	−0.304168	−	1.00271i	−0.0141973	−	0.0468023i
$460$	−2.88119	+	6.73009i	−0.134336	+	0.313792i
$461$	−10.3822	+	12.6508i	−0.483549	+	0.589207i	−0.956445	−	0.291912i	$-0.905709\pi$
$461$	−10.3822	+	12.6508i	−0.483549	+	0.589207i	0.472896	+	0.881118i	$0.343209\pi$
$462$	11.6236	−	10.4108i	0.540781	−	0.484355i
$463$	−9.47222	+	22.8680i	−0.440211	+	1.06276i	0.535663	+	0.844432i	$0.320062\pi$
$463$	−9.47222	+	22.8680i	−0.440211	+	1.06276i	−0.975874	+	0.218333i	$0.929938\pi$
$464$	−3.99560	−	14.3853i	−0.185491	−	0.667821i
$465$	−2.39383	−	5.77922i	−0.111011	−	0.268005i
$466$	28.2018	+	13.5426i	1.30642	+	0.627350i
$467$	−24.2707	+	2.39046i	−1.12312	+	0.110617i	−0.642479	−	0.766303i	$-0.722094\pi$
$467$	−24.2707	+	2.39046i	−1.12312	+	0.110617i	−0.480636	+	0.876920i	$0.659594\pi$
$468$	−6.46237	−	9.92310i	−0.298723	−	0.458695i
$469$	17.8465	+	9.53915i	0.824074	+	0.440477i
$470$	5.67292	−	2.64225i	0.261672	−	0.121878i
$471$	−1.36229	−	6.84871i	−0.0627711	−	0.315572i
$472$	4.07070	+	12.0447i	0.187369	+	0.554404i
$473$	−11.0857	−	2.20508i	−0.509720	−	0.101390i
$474$	10.6525	−	17.5372i	0.489287	−	0.805512i
$475$	−25.4097	−	2.50264i	−1.16588	−	0.114829i
$476$	10.2300	+	3.23553i	0.468892	+	0.148300i
$477$	−0.976920	−	0.296345i	−0.0447301	−	0.0135687i
$478$	−22.2873	−	5.72262i	−1.01940	−	0.261746i
$479$	−14.5455	+	14.5455i	−0.664602	+	0.664602i	−0.956461	−	0.291859i	$-0.905726\pi$
$479$	−14.5455	+	14.5455i	−0.664602	+	0.664602i	0.291859	+	0.956461i	$0.405726\pi$
$480$	−20.0605	−	10.2225i	−0.915632	−	0.466589i
$481$	−12.3762	−	12.3762i	−0.564308	−	0.564308i
$482$	−7.08535	−	11.9809i	−0.322729	−	0.545716i
$483$	−1.36685	+	4.50591i	−0.0621940	+	0.205026i
$484$	−9.72992	−	8.17915i	−0.442269	−	0.371780i
$485$	−3.34587	+	33.9712i	−0.151928	+	1.54255i
$486$	0.335527	+	1.37383i	0.0152198	+	0.0623184i
$487$	4.38461	−	22.0429i	0.198686	−	0.998860i	−0.744760	−	0.667332i	$-0.767436\pi$
$487$	4.38461	−	22.0429i	0.198686	−	0.998860i	0.943446	−	0.331527i	$-0.107564\pi$
$488$	−23.1668	+	3.01849i	−1.04871	+	0.136641i
$489$	12.2449	−	2.43566i	0.553734	−	0.110144i
$490$	−101.608	−	37.0334i	−4.59016	−	1.67300i
$491$	−2.82768	+	5.29022i	−0.127612	+	0.238744i	−0.937611	−	0.347686i	$-0.886967\pi$
$491$	−2.82768	+	5.29022i	−0.127612	+	0.238744i	0.809999	+	0.586431i	$0.199467\pi$
$492$	9.00856	−	13.1439i	0.406137	−	0.592571i
$493$	−0.383343	−	3.89215i	−0.0172649	−	0.175293i
$494$	18.6066	−	6.53400i	0.837152	−	0.293978i
$495$	−7.92465	+	3.28250i	−0.356187	+	0.147537i
$496$	6.13518	+	1.37161i	0.275478	+	0.0615869i
$497$	−20.4522	−	8.47157i	−0.917405	−	0.380002i
$498$	−4.66604	−	0.256830i	−0.209090	−	0.0115088i
$499$	16.8268	+	13.8094i	0.753271	+	0.618193i	0.930634	−	0.365952i	$-0.119257\pi$
$499$	16.8268	+	13.8094i	0.753271	+	0.618193i	−0.177363	+	0.984146i	$0.556757\pi$
$500$	32.4891	+	33.2649i	1.45295	+	1.48765i
$501$	1.02078	−	0.309649i	0.0456049	−	0.0138341i
$502$	−0.456813	−	10.5707i	−0.0203886	−	0.471795i
$503$	−18.2050	+	27.2458i	−0.811722	+	1.21483i	0.161933	+	0.986802i	$0.448227\pi$
$503$	−18.2050	+	27.2458i	−0.811722	+	1.21483i	−0.973655	+	0.228026i	$0.926773\pi$
$504$	−13.5462	−	5.11911i	−0.603397	−	0.228023i
$505$	−49.5287	+	33.0940i	−2.20400	+	1.47267i
$506$	−2.77018	−	0.427634i	−0.123149	−	0.0190107i
$507$	−13.9931	−	17.0507i	−0.621458	−	0.757248i
$508$	−3.68260	−	12.6765i	−0.163389	−	0.562427i
$509$	2.89474	−	1.54727i	0.128307	−	0.0685817i	−0.405994	−	0.913876i	$-0.633075\pi$
$509$	2.89474	−	1.54727i	0.128307	−	0.0685817i	0.534302	+	0.845294i	$0.320575\pi$
$510$	−4.71645	−	3.54128i	−0.208848	−	0.156810i
$511$	67.3989			2.98155
$512$	19.9982	−	10.5864i	0.883803	−	0.467859i
$513$	−2.35512			−0.103981
$514$	7.95818	+	5.97528i	0.351020	+	0.263558i
$515$	14.9168	−	7.97322i	0.657315	−	0.351342i
$516$	2.92626	+	10.0729i	0.128821	+	0.443436i
$517$	1.52005	+	1.85218i	0.0668517	+	0.0814590i
$518$	−21.1531	−	3.26542i	−0.929415	−	0.143474i
$519$	5.12219	−	3.42254i	0.224839	−	0.150233i
$520$	−62.3512	−	23.5625i	−2.73428	−	1.03328i
$521$	19.7361	−	29.5372i	0.864655	−	1.29405i	−0.0898805	−	0.995953i	$-0.528649\pi$
$521$	19.7361	−	29.5372i	0.864655	−	1.29405i	0.954536	−	0.298096i	$-0.0963515\pi$
$522$	0.227897	+	5.27359i	0.00997480	+	0.230819i
$523$	−36.8820	+	11.1880i	−1.61274	+	0.489218i	−0.962674	−	0.270663i	$-0.912757\pi$
$523$	−36.8820	+	11.1880i	−1.61274	+	0.489218i	−0.650062	+	0.759881i	$0.725257\pi$
$524$	16.8256	+	17.2274i	0.735030	+	0.752583i
$525$	42.9070	+	35.2128i	1.87261	+	1.53681i
$526$	31.4744	+	1.73242i	1.37235	+	0.0755373i
$527$	1.52147	+	0.630212i	0.0662761	+	0.0274525i
$528$	1.88079	−	8.41276i	0.0818509	−	0.366118i
$529$	−20.4678	+	8.47804i	−0.889904	+	0.368610i
$530$	−5.42168	+	1.90390i	−0.235503	+	0.0827003i
$531$	−0.440595	−	4.47344i	−0.0191202	−	0.194131i
$532$	13.6337	−	19.8922i	0.591097	−	0.862435i
$533$	22.2378	−	41.6040i	0.963226	−	1.80207i
$534$	18.9570	+	6.90936i	0.820351	+	0.298997i
$535$	52.6868	−	10.4801i	2.27785	−	0.453092i
$536$	11.0854	−	1.44436i	0.478817	−	0.0623870i
$537$	2.22183	−	11.1699i	0.0958790	−	0.482016i
$538$	−1.99038	−	8.14972i	−0.0858113	−	0.351359i
$539$	4.05855	−	41.2072i	0.174814	−	1.77492i
$540$	6.09333	+	5.12217i	0.262215	+	0.220423i
$541$	2.08479	−	6.87262i	0.0896320	−	0.295477i	−0.900651	−	0.434543i	$-0.856910\pi$
$541$	2.08479	−	6.87262i	0.0896320	−	0.295477i	0.990283	+	0.139066i	$0.0444100\pi$
$542$	6.77826	+	11.4616i	0.291151	+	0.492320i
$543$	6.36565	+	6.36565i	0.273176	+	0.273176i
$544$	5.63737	−	1.83141i	0.241700	−	0.0785212i
$545$	−4.57311	+	4.57311i	−0.195890	+	0.195890i
$546$	−41.5242	−	10.6620i	−1.77707	−	0.456292i
$547$	−1.46733	−	0.445109i	−0.0627385	−	0.0190315i	0.258759	−	0.965942i	$-0.416686\pi$
$547$	−1.46733	−	0.445109i	−0.0627385	−	0.0190315i	−0.321498	+	0.946910i	$0.604186\pi$
$548$	35.1512	+	11.1175i	1.50158	+	0.474918i
$549$	8.22015	+	0.809614i	0.350828	+	0.0345535i
$550$	−17.1539	+	28.2404i	−0.731444	+	1.20417i
$551$	−8.62152	−	1.71493i	−0.367289	−	0.0730583i
$552$	0.832855	+	2.46432i	0.0354486	+	0.104888i
$553$	−14.4923	−	72.8578i	−0.616276	−	3.09823i
$554$	2.43589	−	1.13456i	0.103491	−	0.0482027i
$555$	10.3762	+	5.54620i	0.440446	+	0.235423i
$556$	−11.2251	−	17.2364i	−0.476050	−	0.730985i
$557$	−1.25686	+	0.123790i	−0.0532547	+	0.00524514i	−0.124609	−	0.992206i	$-0.539768\pi$
$557$	−1.25686	+	0.123790i	−0.0532547	+	0.00524514i	0.0713547	+	0.997451i	$0.477268\pi$
$558$	−2.00362	−	0.962146i	−0.0848200	−	0.0407309i
$559$	11.8836	+	28.6896i	0.502624	+	1.21344i
$560$	−78.5377	+	21.8143i	−3.31882	+	0.921823i
$561$	0.864167	−	2.08628i	0.0364852	−	0.0880830i
$562$	−29.5926	+	26.5049i	−1.24829	+	1.11804i
$563$	−19.4785	+	23.7346i	−0.820919	+	1.00029i	0.178946	+	0.983859i	$0.442731\pi$
$563$	−19.4785	+	23.7346i	−0.820919	+	1.00029i	−0.999865	+	0.0164340i	$0.994769\pi$
$564$	0.875120	−	2.04417i	0.0368492	−	0.0860751i
$565$	−6.09888	−	20.1053i	−0.256582	−	0.845836i
$566$	−4.98642	+	5.43686i	−0.209595	+	0.228528i
$567$	4.25703	+	2.84446i	0.178778	+	0.119456i
$568$	−11.9137	+	2.76112i	−0.499889	+	0.115854i
$569$	−3.43878	−	5.14650i	−0.144161	−	0.215753i	0.752361	−	0.658751i	$-0.228915\pi$
$569$	−3.43878	−	5.14650i	−0.144161	−	0.215753i	−0.896523	+	0.442998i	$0.853915\pi$
$570$	−10.6940	+	7.83385i	−0.447922	+	0.328124i
$571$	−13.0065	+	10.6742i	−0.544306	+	0.446700i	−0.865929	−	0.500168i	$-0.833272\pi$
$571$	−13.0065	+	10.6742i	−0.544306	+	0.446700i	0.321623	+	0.946868i	$0.395772\pi$
$572$	2.80093	−	25.3664i	0.117113	−	1.06062i
$573$	7.88666	+	14.7549i	0.329470	+	0.616395i
$574$	−8.12788	−	57.1131i	−0.339251	−	2.38386i
$575$		−	9.97057i		−	0.415802i
$576$	−7.73291	+	2.04990i	−0.322205	+	0.0854125i
$577$		−	32.6234i		−	1.35813i	−0.734078	−	0.679065i	$-0.762385\pi$
$577$		−	32.6234i		−	1.35813i	0.734078	−	0.679065i	$-0.237615\pi$
$578$	−22.2646	+	3.16852i	−0.926085	+	0.131793i
$579$	−1.03199	−	1.93072i	−0.0428880	−	0.0802378i
$580$	18.5764	+	23.1880i	0.771343	+	0.962828i
$581$	−13.0778	+	10.7327i	−0.542561	+	0.445268i
$582$	7.16767	+	9.78460i	0.297109	+	0.405585i
$583$	−1.22231	−	1.82932i	−0.0506230	−	0.0757627i
$584$	30.2943	−	21.6474i	1.25359	−	0.895777i
$585$	19.5944	+	13.0926i	0.810130	+	0.541312i
$586$	1.23241	+	1.13030i	0.0509104	+	0.0466925i
$587$	1.49705	+	4.93510i	0.0617898	+	0.203694i	0.982400	−	0.186789i	$-0.0598081\pi$
$587$	1.49705	+	4.93510i	0.0617898	+	0.203694i	−0.920610	+	0.390483i	$0.872308\pi$
$588$	−35.6724	+	14.2853i	−1.47111	+	0.589115i
$589$	2.34817	−	2.86126i	0.0967547	−	0.117896i
$590$	−16.8806	−	18.8472i	−0.694965	−	0.775926i
$591$	−0.580778	+	1.40212i	−0.0238900	+	0.0576756i
$592$	−10.5567	+	5.32630i	−0.433876	+	0.218910i
$593$	−1.21105	−	2.92373i	−0.0497317	−	0.120063i	0.897061	−	0.441906i	$-0.145698\pi$
$593$	−1.21105	−	2.92373i	−0.0497317	−	0.120063i	−0.946793	+	0.321843i	$0.895698\pi$
$594$	−1.31933	+	2.74743i	−0.0541326	+	0.112728i
$595$	−21.2495	+	2.09289i	−0.871144	+	0.0858002i
$596$	19.9923	+	4.22251i	0.818915	+	0.172961i
$597$	−22.8485	−	12.2128i	−0.935128	−	0.499836i
$598$	3.25145	+	6.98086i	0.132962	+	0.285469i
$599$	−2.55189	−	12.8292i	−0.104267	−	0.524188i	−0.997251	−	0.0740986i	$-0.976392\pi$
$599$	−2.55189	−	12.8292i	−0.104267	−	0.524188i	0.892983	−	0.450090i	$-0.148608\pi$
$600$	30.5955	+	2.04639i	1.24906	+	0.0835433i
$601$	−8.67770	−	1.72610i	−0.353971	−	0.0704092i	0.0149023	−	0.999889i	$-0.495256\pi$
$601$	−8.67770	−	1.72610i	−0.353971	−	0.0704092i	−0.368873	+	0.929480i	$0.620256\pi$
$602$	32.4562	+	19.7147i	1.32282	+	0.803512i
$603$	−3.93339	−	0.387405i	−0.160180	−	0.0157763i
$604$	5.54339	+	10.6719i	0.225557	+	0.434235i
$605$	24.2064	+	7.34294i	0.984131	+	0.298533i
$606$	−5.26385	+	20.5006i	−0.213829	+	0.832779i
$607$	−0.0933037	+	0.0933037i	−0.00378708	+	0.00378708i	−0.708998	−	0.705211i	$-0.750852\pi$
$607$	−0.0933037	+	0.0933037i	−0.00378708	+	0.00378708i	0.705211	+	0.708998i	$0.250852\pi$
$608$	−0.260977	−	13.3200i	−0.0105840	−	0.540198i
$609$	13.5127	+	13.5127i	0.547562	+	0.547562i
$610$	40.0186	−	23.6665i	1.62031	−	0.958227i
$611$	1.91093	−	6.29949i	0.0773079	−	0.254850i
$612$	−2.08784	+	0.180789i	−0.0843958	+	0.00730795i
$613$	−0.283150	+	2.87487i	−0.0114363	+	0.116115i	−0.999208	−	0.0397928i	$-0.987330\pi$
$613$	−0.283150	+	2.87487i	−0.0114363	+	0.116115i	0.987772	+	0.155908i	$0.0498302\pi$
$614$	28.5147	−	6.96406i	1.15076	−	0.281047i
$615$	−6.18651	+	31.1017i	−0.249464	+	1.25414i
$616$	−15.5682	−	27.0483i	−0.627260	−	1.08981i
$617$	−41.2931	+	8.21370i	−1.66240	+	0.330671i	−0.934757	−	0.355288i	$-0.884383\pi$
$617$	−41.2931	+	8.21370i	−1.66240	+	0.330671i	−0.727640	+	0.685959i	$0.759383\pi$
$618$	2.05802	−	5.64653i	0.0827856	−	0.227137i
$619$	3.57916	−	6.69613i	0.143858	−	0.269140i	−0.799665	−	0.600447i	$-0.794989\pi$
$619$	3.57916	−	6.69613i	0.143858	−	0.269140i	0.943523	+	0.331307i	$0.107489\pi$
$620$	−12.2983	+	2.29579i	−0.493912	+	0.0922010i
$621$	−0.0901446	−	0.915253i	−0.00361738	−	0.0367279i
$622$	6.19622	+	17.6447i	0.248446	+	0.707490i
$623$	67.4863	−	27.9537i	2.70378	−	1.11994i
$624$	−22.0887	+	8.54457i	−0.884256	+	0.342056i
$625$	−35.4102	−	14.6674i	−1.41641	−	0.586695i
$626$	−2.01626	+	36.6311i	−0.0805860	+	1.46407i
$627$	−3.92345	−	3.21989i	−0.156687	−	0.128590i
$628$	−13.9648	−	0.164776i	−0.557256	−	0.00657527i
$629$	−2.96406	+	0.899138i	−0.118185	+	0.0358510i
$630$	28.7916	−	1.24422i	1.14708	−	0.0495711i
$631$	12.8689	−	19.2596i	0.512301	−	0.766713i	−0.481670	−	0.876353i	$-0.659970\pi$
$631$	12.8689	−	19.2596i	0.512301	−	0.766713i	0.993971	+	0.109639i	$0.0349696\pi$
$632$	−29.9147	−	28.0933i	−1.18994	−	1.11749i
$633$	10.7039	−	7.15210i	0.425441	−	0.284270i
$634$	1.77979	−	11.5293i	0.0706843	−	0.457887i
$635$	16.6654	+	20.3069i	0.661346	+	0.805853i
$636$	−0.983656	+	1.78919i	−0.0390045	+	0.0709459i
$637$	−100.328	+	53.6262i	−3.97513	+	2.12475i
$638$	−6.83032	+	9.09697i	−0.270415	+	0.360152i
$639$	4.32378			0.171046
$640$	−28.2946	+	35.0301i	−1.11844	+	1.38469i
$641$	42.9988			1.69835			0.849176	−	0.528110i	$-0.177099\pi$
$641$	42.9988			1.69835			0.849176	+	0.528110i	$0.177099\pi$
$642$	11.4606	−	15.2638i	0.452314	−	0.602415i
$643$	4.45573	−	2.38164i	0.175717	−	0.0939227i	−0.381193	−	0.924495i	$-0.624487\pi$
$643$	4.45573	−	2.38164i	0.175717	−	0.0939227i	0.556910	+	0.830573i	$0.311987\pi$
$644$	8.25239	+	4.53698i	0.325190	+	0.178782i
$645$	−13.2426	−	16.1362i	−0.521427	−	0.635361i
$646$	0.532436	−	3.44908i	0.0209484	−	0.135702i
$647$	27.3266	−	18.2591i	1.07432	−	0.717838i	0.113090	−	0.993585i	$-0.463925\pi$
$647$	27.3266	−	18.2591i	1.07432	−	0.717838i	0.961230	+	0.275747i	$0.0889252\pi$
$648$	2.82703	−	0.0887673i	0.111056	−	0.00348711i
$649$	5.38203	−	8.05477i	0.211263	−	0.316178i
$650$	90.6949	−	3.91937i	3.55735	−	0.153730i
$651$	−7.70022	+	2.33584i	−0.301795	+	0.0915486i
$652$	0.294605	−	24.9679i	0.0115376	−	0.977817i
$653$	−16.6595	−	13.6721i	−0.651935	−	0.535029i	0.249264	−	0.968436i	$-0.419811\pi$
$653$	−16.6595	−	13.6721i	−0.651935	−	0.535029i	−0.901198	+	0.433407i	$0.857311\pi$
$654$	−0.126295	+	2.29450i	−0.00493852	+	0.0897222i
$655$	−44.2743	−	18.3390i	−1.72994	−	0.716565i
$656$	−21.9971	−	23.0606i	−0.858842	−	0.900363i
$657$	−12.1621	+	5.03770i	−0.474488	+	0.196539i
$658$	−2.66726	−	7.59545i	−0.103981	−	0.296102i
$659$	−3.20118	−	32.5022i	−0.124700	−	1.26610i	−0.830229	−	0.557423i	$-0.811790\pi$
$659$	−3.20118	−	32.5022i	−0.124700	−	1.26610i	0.705528	−	0.708682i	$-0.250710\pi$
$660$	3.14806	+	16.8639i	0.122538	+	0.656424i
$661$	−9.96831	+	18.6494i	−0.387722	+	0.725378i	−0.997753	−	0.0670003i	$-0.978657\pi$
$661$	−9.96831	+	18.6494i	−0.387722	+	0.725378i	0.610031	+	0.792378i	$0.291157\pi$
$662$	12.6671	−	34.7544i	0.492321	−	1.35077i
$663$	−6.08490	+	1.21036i	−0.236318	+	0.0470066i
$664$	−2.43104	+	9.02451i	−0.0943425	+	0.350219i
$665$	−9.36278	+	47.0699i	−0.363073	+	1.82529i
$666$	4.06114	−	0.991838i	0.157366	−	0.0384329i
$667$	0.336462	−	3.41616i	0.0130279	−	0.132274i
$668$	−0.184047	−	2.12546i	−0.00712098	−	0.0822366i
$669$	3.27975	−	10.8119i	0.126803	−	0.418012i
$670$	−19.1491	+	11.3245i	−0.739795	+	0.437505i
$671$	12.5872	+	12.5872i	0.485925	+	0.485925i
$672$	−15.6159	+	24.3920i	−0.602395	+	0.940941i
$673$	−15.8907	+	15.8907i	−0.612543	+	0.612543i	−0.943608	−	0.331065i	$-0.892592\pi$
$673$	−15.8907	+	15.8907i	−0.612543	+	0.612543i	0.331065	+	0.943608i	$0.392592\pi$
$674$	−7.63343	+	29.7291i	−0.294029	+	1.14512i
$675$	−10.3745	−	3.14707i	−0.399315	−	0.121131i
$676$	−39.1487	+	20.3352i	−1.50572	+	0.782124i
$677$	10.7512	+	1.05890i	0.413201	+	0.0406967i	0.302482	−	0.953155i	$-0.402185\pi$
$677$	10.7512	+	1.05890i	0.413201	+	0.0406967i	0.110719	+	0.993852i	$0.464685\pi$
$678$	−6.38041	−	3.87562i	−0.245038	−	0.148842i
$679$	43.0671	+	8.56659i	1.65276	+	0.328755i
$680$	−8.87898	+	7.76570i	−0.340493	+	0.297801i
$681$	−4.92700	−	24.7697i	−0.188803	−	0.949178i
$682$	−2.02244	−	4.34218i	−0.0774432	−	0.166271i
$683$	−11.8713	−	6.34536i	−0.454244	−	0.242799i	0.228374	−	0.973573i	$-0.426659\pi$
$683$	−11.8713	−	6.34536i	−0.454244	−	0.242799i	−0.682619	+	0.730775i	$0.739159\pi$
$684$	−0.973365	+	4.60857i	−0.0372175	+	0.176213i
$685$	−73.0149	+	7.19134i	−2.78976	+	0.274767i
$686$	−38.2801	+	79.7164i	−1.46154	+	3.04359i
$687$	−6.26846	−	15.1334i	−0.239157	−	0.577375i
$688$	20.9204	−	1.56308i	0.797583	−	0.0595920i
$689$	−2.31315	+	5.58444i	−0.0881241	+	0.212750i
$690$	−3.45373	−	3.85608i	−0.131481	−	0.146799i
$691$	22.9713	−	27.9906i	0.873868	−	1.06481i	−0.123503	−	0.992344i	$-0.539413\pi$
$691$	22.9713	−	27.9906i	0.873868	−	1.06481i	0.997371	−	0.0724673i	$-0.0230873\pi$
$692$	−4.58034	−	11.4378i	−0.174118	−	0.434799i
$693$	3.20297	+	10.5588i	0.121671	+	0.401095i
$694$	15.4397	+	14.1605i	0.586081	+	0.537525i
$695$	34.0355	+	22.7418i	1.29104	+	0.862644i
$696$	10.4137	+	1.73360i	0.394731	+	0.0657121i
$697$	−4.63812	−	6.94144i	−0.175681	−	0.262926i
$698$	−30.3972	−	41.4953i	−1.15055	−	1.57062i
$699$	−17.1004	+	14.0339i	−0.646795	+	0.530811i
$700$	86.6389	−	69.4083i	3.27464	−	2.62339i
$701$	−12.4507	−	23.2937i	−0.470257	−	0.879790i	−0.999509	−	0.0313250i	$-0.990027\pi$
$701$	−12.4507	−	23.2937i	−0.470257	−	0.879790i	0.529252	−	0.848465i	$-0.322473\pi$
$702$	8.28995	−	1.17976i	0.312884	−	0.0445271i
$703$			6.96188i			0.262572i
$704$	−15.6850	−	7.15736i	−0.591151	−	0.269753i
$705$			4.42512i			0.166660i
$706$	2.24468	+	15.7729i	0.0844796	+	0.593622i
$707$	36.1212	+	67.5780i	1.35848	+	2.54153i
$708$	−8.93586	−	0.986689i	−0.335830	−	0.0370821i
$709$	23.3612	−	19.1720i	0.877348	−	0.720021i	−0.0836742	−	0.996493i	$-0.526665\pi$
$709$	23.3612	−	19.1720i	0.877348	−	0.720021i	0.961022	+	0.276473i	$0.0891655\pi$
$710$	19.6332	−	14.3822i	0.736821	−	0.539755i
$711$	8.06085	+	12.0639i	0.302306	+	0.452432i
$712$	21.3553	−	34.2401i	0.800325	−	1.28320i
$713$	1.20183	+	0.803035i	0.0450088	+	0.0300739i
$714$	−5.12812	+	5.59136i	−0.191915	+	0.209251i
$715$	14.7428	+	48.6005i	0.551349	+	1.81755i
$716$	−20.9393	−	8.96423i	−0.782539	−	0.335009i
$717$	10.3220	−	12.5774i	0.385483	−	0.469713i
$718$	−8.04247	+	7.20331i	−0.300142	+	0.268825i
$719$	1.57456	−	3.80132i	0.0587211	−	0.141765i	−0.891796	−	0.452438i	$-0.850554\pi$
$719$	1.57456	−	3.80132i	0.0587211	−	0.141765i	0.950517	+	0.310673i	$0.100554\pi$
$720$	12.5416	−	9.80664i	0.467397	−	0.365472i
$721$	−8.32629	−	20.1014i	−0.310087	−	0.748616i
$722$	17.1510	+	8.23598i	0.638294	+	0.306512i
$723$	9.79498	−	0.964722i	0.364279	−	0.0358784i
$724$	15.0874	−	9.82559i	0.560719	−	0.365165i
$725$	−35.6869	−	19.0750i	−1.32538	−	0.708429i
$726$	8.14762	−	3.79488i	0.302387	−	0.140841i
$727$	−0.806755	−	4.05583i	−0.0299209	−	0.150423i	0.962937	−	0.269727i	$-0.0869335\pi$
$727$	−0.806755	−	4.05583i	−0.0299209	−	0.150423i	−0.992858	+	0.119305i	$0.961933\pi$
$728$	−38.0256	+	76.8493i	−1.40932	+	2.84823i
$729$	−0.980785	−	0.195090i	−0.0363254	−	0.00722557i
$730$	−38.4680	+	63.3297i	−1.42376	+	2.34394i
$731$	5.46905	+	0.538654i	0.202280	+	0.0199228i
$732$	4.98164	−	15.7508i	0.184127	−	0.582168i
$733$	46.4429	+	14.0883i	1.71541	+	0.520364i	0.986431	−	0.164173i	$-0.0524957\pi$
$733$	46.4429	+	14.0883i	1.71541	+	0.520364i	0.728978	+	0.684537i	$0.239996\pi$
$734$	−43.4934	−	11.1676i	−1.60537	−	0.412204i
$735$	54.0731	−	54.0731i	1.99451	−	1.99451i
$736$	5.16647	−	0.611259i	0.190439	−	0.0225313i
$737$	−6.02306	−	6.02306i	−0.221862	−	0.221862i
$738$	5.73556	+	9.69851i	0.211129	+	0.357007i
$739$	13.1486	−	43.3452i	0.483680	−	1.59448i	−0.287446	−	0.957797i	$-0.592806\pi$
$739$	13.1486	−	43.3452i	0.483680	−	1.59448i	0.771126	−	0.636683i	$-0.219694\pi$
$740$	15.1414	−	18.0123i	0.556610	−	0.662144i
$741$	−1.36680	+	13.8774i	−0.0502108	+	0.509798i
$742$	1.75373	+	7.18073i	0.0643813	+	0.263613i
$743$	−2.52762	+	12.7072i	−0.0927295	+	0.466183i	0.906320	+	0.422592i	$0.138880\pi$
$743$	−2.52762	+	12.7072i	−0.0927295	+	0.466183i	−0.999049	+	0.0435905i	$0.986120\pi$
$744$	−2.71085	+	3.52309i	−0.0993845	+	0.129163i
$745$	−39.8821	+	7.93305i	−1.46117	+	0.290644i
$746$	37.9680	+	13.8384i	1.39011	+	0.506659i
$747$	1.55768	−	2.91421i	0.0569924	−	0.106625i
$748$	−3.72535	−	2.55328i	−0.136212	−	0.0933573i
$749$	−6.77321	−	68.7695i	−0.247488	−	2.51278i
$750$	−31.0221	+	10.8939i	−1.13277	+	0.397788i
$751$	−26.0939	+	10.8085i	−0.952181	+	0.394406i	−0.804050	−	0.594561i	$-0.797326\pi$
$751$	−26.0939	+	10.8085i	−0.952181	+	0.394406i	−0.148131	+	0.988968i	$0.547326\pi$
$752$	−3.63841	−	2.55731i	−0.132679	−	0.0932555i
$753$	6.91212	+	2.86309i	0.251892	+	0.104337i
$754$	31.2065	+	1.71768i	1.13647	+	0.0625542i
$755$	−18.4997	−	15.1823i	−0.673273	−	0.552541i
$756$	7.32553	−	7.15468i	0.266427	−	0.260213i
$757$	−31.0119	+	9.40736i	−1.12715	+	0.341916i	−0.798176	−	0.602424i	$-0.794202\pi$
$757$	−31.0119	+	9.40736i	−1.12715	+	0.341916i	−0.328971	+	0.944340i	$0.606702\pi$
$758$	0.440229	+	10.1870i	0.0159898	+	0.370008i
$759$	1.10115	−	1.64798i	0.0399692	−	0.0598181i
$760$	10.9097	+	24.1641i	0.395737	+	0.876522i
$761$	16.7400	−	11.1853i	0.606825	−	0.405467i	−0.213847	−	0.976867i	$-0.568599\pi$
$761$	16.7400	−	11.1853i	0.606825	−	0.405467i	0.820672	+	0.571400i	$0.193599\pi$
$762$	9.22492	+	1.42406i	0.334183	+	0.0515881i
$763$	5.27776	+	6.43097i	0.191068	+	0.232817i
$764$	32.1324	−	9.33469i	1.16251	−	0.337717i
$765$	3.67802	−	1.96594i	0.132979	−	0.0710789i
$766$	34.9235	+	26.2218i	1.26184	+	0.947432i
$767$	−26.6151			−0.961016
$768$	0.815318	+	15.9792i	0.0294203	+	0.576600i
$769$	28.4767			1.02690			0.513448	−	0.858121i	$-0.328368\pi$
$769$	28.4767			1.02690			0.513448	+	0.858121i	$0.328368\pi$
$770$	49.6656	+	37.2907i	1.78983	+	1.34386i
$771$	−6.20601	+	3.31718i	−0.223504	+	0.119465i
$772$	−4.20460	+	1.22147i	−0.151327	+	0.0439616i
$773$	15.3911	+	18.7541i	0.553580	+	0.674540i	0.972343	−	0.233556i	$-0.0750362\pi$
$773$	15.3911	+	18.7541i	0.553580	+	0.674540i	−0.418763	+	0.908096i	$0.637536\pi$
$774$	−7.33027	−	1.13158i	−0.263481	−	0.0406737i
$775$	14.1673	−	9.46628i	0.508904	−	0.340039i
$776$	22.1092	−	9.98197i	0.793673	−	0.358332i
$777$	8.40838	−	12.5840i	0.301649	−	0.451450i
$778$	0.202857	+	4.69416i	0.00727279	+	0.168294i
$779$	−17.9561	+	5.44693i	−0.643345	+	0.195157i
$780$	33.7183	−	32.9319i	1.20731	−	1.17915i
$781$	7.20308	+	5.91142i	0.257747	+	0.211527i
$782$	1.36077	+	0.0748999i	0.0486610	+	0.00267841i
$783$	−3.44836	−	1.42836i	−0.123234	−	0.0510453i
$784$	13.2105	+	75.7090i	0.471805	+	2.70389i
$785$	25.6771	−	10.6358i	0.916455	−	0.379608i
$786$	−16.0659	+	5.64177i	−0.573051	+	0.201235i
$787$	−4.29138	−	43.5711i	−0.152971	−	1.55314i	−0.698844	−	0.715274i	$-0.746302\pi$
$787$	−4.29138	−	43.5711i	−0.152971	−	1.55314i	0.545873	−	0.837868i	$-0.316198\pi$
$788$	2.50368	+	1.71598i	0.0891900	+	0.0611292i
$789$	−10.5072	+	19.6576i	−0.374066	+	0.699828i
$790$	76.7305	+	27.9663i	2.72995	+	0.994997i
$791$	−26.5072	+	5.27261i	−0.942488	+	0.187472i
$792$	4.83098	+	3.71720i	0.171661	+	0.132085i
$793$	9.54119	−	47.9668i	0.338818	−	1.70335i
$794$	1.17622	+	4.81611i	0.0417425	+	0.170917i
$795$	0.398265	−	4.04365i	0.0141250	−	0.143413i
$796$	−33.3416	+	39.6632i	−1.18176	+	1.40582i
$797$	−13.5605	+	44.7030i	−0.480338	+	1.58346i	0.297322	+	0.954777i	$0.403907\pi$
$797$	−13.5605	+	44.7030i	−0.480338	+	1.58346i	−0.777660	+	0.628685i	$0.783593\pi$
$798$	8.68030	+	14.6779i	0.307279	+	0.519592i
$799$	−0.823766	−	0.823766i	−0.0291427	−	0.0291427i
$800$	16.6495	−	59.0245i	0.588648	−	2.08683i
$801$	−10.0885	+	10.0885i	−0.356458	+	0.356458i
$802$	7.52026	+	1.93095i	0.265550	+	0.0681841i
$803$	−27.1486	−	8.23542i	−0.958052	−	0.290622i
$804$	−2.38374	+	7.53686i	−0.0840681	+	0.265804i
$805$	−18.6508	−	1.83694i	−0.657354	−	0.0647437i
$806$	−6.83219	+	11.2478i	−0.240654	+	0.396187i
$807$	5.81811	+	1.15730i	0.204807	+	0.0407387i
$808$	37.9406	+	18.7733i	1.33475	+	0.660442i
$809$	−5.63491	−	28.3286i	−0.198113	−	0.995980i	−0.944009	−	0.329919i	$-0.892979\pi$
$809$	−5.63491	−	28.3286i	−0.198113	−	0.995980i	0.745897	−	0.666062i	$-0.232021\pi$
$810$	−5.10242	+	2.37653i	−0.179281	+	0.0835029i
$811$	1.54151	+	0.823953i	0.0541297	+	0.0289329i	0.498240	−	0.867039i	$-0.333980\pi$
$811$	1.54151	+	0.823953i	0.0541297	+	0.0289329i	−0.444110	+	0.895972i	$0.646480\pi$
$812$	32.0268	−	20.8573i	1.12392	−	0.731947i
$813$	−9.37045	+	0.922909i	−0.328636	+	0.0323678i
$814$	8.12156	+	3.90001i	0.284661	+	0.136695i
$815$	19.0159	+	45.9084i	0.666098	+	1.60810i
$816$	−0.509124	+	4.16026i	−0.0178229	+	0.145638i
$817$	4.72685	−	11.4116i	0.165372	−	0.399242i
$818$	−15.0847	+	13.5108i	−0.527426	+	0.472393i
$819$	19.2313	−	23.4334i	0.671997	−	0.818831i
$820$	58.3039	+	24.9602i	2.03606	+	0.871648i
$821$	−13.0169	−	42.9108i	−0.454292	−	1.49760i	−0.822993	−	0.568051i	$-0.807698\pi$
$821$	−13.0169	−	42.9108i	−0.454292	−	1.49760i	0.368702	−	0.929548i	$-0.379802\pi$
$822$	−17.6206	+	19.2124i	−0.614590	+	0.670108i
$823$	0.654088	+	0.437047i	0.0228001	+	0.0152345i	0.566918	−	0.823774i	$-0.308136\pi$
$823$	0.654088	+	0.437047i	0.0228001	+	0.0152345i	−0.544118	+	0.839009i	$0.683136\pi$
$824$	−10.1987	−	6.36089i	−0.355290	−	0.221592i
$825$	−12.9805	−	19.4267i	−0.451922	−	0.676349i
$826$	−26.2560	+	19.2338i	−0.913564	+	0.669228i
$827$	39.7990	−	32.6622i	1.38395	−	1.13577i	0.409203	−	0.912443i	$-0.365807\pi$
$827$	39.7990	−	32.6622i	1.38395	−	1.13577i	0.974743	−	0.223331i	$-0.0716931\pi$
$828$	−1.82825	−	0.201874i	−0.0635362	−	0.00701561i
$829$	−23.7941	−	44.5156i	−0.826403	−	1.54609i	−0.837684	−	0.546155i	$-0.816091\pi$
$829$	−23.7941	−	44.5156i	−0.826403	−	1.54609i	0.0112812	−	0.999936i	$-0.496409\pi$
$830$	−2.62053	−	18.4140i	−0.0909599	−	0.639159i
$831$			1.90010i			0.0659139i
$832$	7.59107	+	46.7553i	0.263173	+	1.62095i
$833$			20.1321i			0.697536i
$834$	14.3996	−	2.04924i	0.498617	−	0.0709592i
$835$	2.00137	+	3.74430i	0.0692603	+	0.129577i
$836$	−7.92233	+	6.34675i	−0.273999	+	0.219507i
$837$	1.21491	−	0.997049i	0.0419934	−	0.0344631i
$838$	−30.3107	−	41.3772i	−1.04707	−	1.42935i
$839$	−17.0800	−	25.5621i	−0.589669	−	0.882502i	0.409892	−	0.912134i	$-0.365566\pi$
$839$	−17.0800	−	25.5621i	−0.589669	−	0.882502i	−0.999561	+	0.0296323i	$0.990566\pi$
$840$	9.46475	−	56.8545i	0.326565	−	1.96167i
$841$	12.5291	+	8.37169i	0.432039	+	0.288679i
$842$	−3.50514	−	3.21474i	−0.120795	−	0.110787i
$843$	−8.15444	−	26.8816i	−0.280854	−	0.925851i
$844$	−9.57156	−	23.9016i	−0.329467	−	0.822727i
$845$	55.6944	−	67.8638i	1.91594	−	2.33458i
$846$	1.04902	+	1.17123i	0.0360662	+	0.0402678i
$847$	12.4523	−	30.0625i	0.427867	−	1.03296i
$848$	3.09459	+	2.66431i	0.106269	+	0.0914929i
$849$	−1.99627	−	4.81942i	−0.0685118	−	0.165402i
$850$	6.95432	−	14.4820i	0.238531	−	0.496728i
$851$	−2.70554	+	0.266473i	−0.0927449	+	0.00913457i
$852$	1.78701	−	8.46091i	0.0612219	−	0.289866i
$853$	11.8109	+	6.31303i	0.404396	+	0.216154i	0.661038	−	0.750352i	$-0.270116\pi$
$853$	11.8109	+	6.31303i	0.404396	+	0.216154i	−0.256642	+	0.966506i	$0.582616\pi$
$854$	−25.2514	−	54.2147i	−0.864084	−	1.85519i
$855$	−1.82871	−	9.19354i	−0.0625405	−	0.314413i
$856$	−25.1321	−	28.7350i	−0.858996	−	0.982141i
$857$	7.80481	+	1.55247i	0.266607	+	0.0530315i	0.326584	−	0.945168i	$-0.394103\pi$
$857$	7.80481	+	1.55247i	0.266607	+	0.0530315i	−0.0599763	+	0.998200i	$0.519103\pi$
$858$	15.4234	+	9.36852i	0.526545	+	0.319836i
$859$	33.0802	+	3.25812i	1.12868	+	0.111165i	0.645075	−	0.764120i	$-0.276826\pi$
$859$	33.0802	+	3.25812i	1.12868	+	0.111165i	0.483607	+	0.875285i	$0.339326\pi$
$860$	−37.0489	+	19.2445i	−1.26336	+	0.656232i
$861$	39.0355	+	11.8413i	1.33033	+	0.403550i
$862$	0.944991	−	3.68036i	0.0321865	−	0.125354i
$863$	−7.00736	+	7.00736i	−0.238533	+	0.238533i	−0.816243	−	0.577709i	$-0.803947\pi$
$863$	−7.00736	+	7.00736i	−0.238533	+	0.238533i	0.577709	+	0.816243i	$0.303947\pi$
$864$	0.994702	−	5.56871i	0.0338405	−	0.189451i
$865$	17.3376	+	17.3376i	0.589497	+	0.589497i
$866$	0.313881	−	0.185625i	0.0106661	−	0.00630780i
$867$	4.61612	−	15.2173i	0.156772	−	0.516807i
$868$	1.38836	+	16.0334i	0.0471239	+	0.544210i
$869$	−3.06488	+	31.1182i	−0.103969	+	1.05561i
$870$	−20.4092	+	4.98448i	−0.691938	+	0.168990i
$871$	−4.56551	+	22.9524i	−0.154696	+	0.777711i
$872$	4.43776	+	1.19545i	0.150281	+	0.0404830i
$873$	−8.41174	+	1.67320i	−0.284694	+	0.0566292i
$874$	1.04893	−	2.87794i	0.0354807	−	0.0973477i
$875$	−56.1118	+	104.978i	−1.89692	+	3.54889i
$876$	4.83137	+	25.8812i	0.163237	+	0.874445i
$877$	1.26094	+	12.8026i	0.0425790	+	0.432312i	0.992716	+	0.120479i	$0.0384430\pi$
$877$	1.26094	+	12.8026i	0.0425790	+	0.432312i	−0.950137	+	0.311833i	$0.899057\pi$
$878$	−0.325395	−	0.926617i	−0.0109816	−	0.0312718i
$879$	−1.09245	+	0.452508i	−0.0368474	+	0.0152627i
$880$	34.3008	+	0.809568i	1.15628	+	0.0272905i
$881$	14.3614	+	5.94870i	0.483849	+	0.200417i	0.611255	−	0.791434i	$-0.290665\pi$
$881$	14.3614	+	5.94870i	0.483849	+	0.200417i	−0.127406	+	0.991851i	$0.540665\pi$
$882$	1.49333	−	27.1305i	0.0502829	−	0.913532i
$883$	15.6167	+	12.8163i	0.525542	+	0.431301i	0.859386	−	0.511327i	$-0.170846\pi$
$883$	15.6167	+	12.8163i	0.525542	+	0.431301i	−0.333844	+	0.942628i	$0.608346\pi$
$884$	−0.146399	+	12.4074i	−0.00492393	+	0.417305i
$885$	17.1206	−	5.19347i	0.575502	−	0.174577i
$886$	−39.1952	+	1.69381i	−1.31679	+	0.0569048i
$887$	8.67909	−	12.9892i	0.291415	−	0.436134i	−0.656657	−	0.754190i	$-0.728030\pi$
$887$	8.67909	−	12.9892i	0.291415	−	0.436134i	0.948072	+	0.318056i	$0.103030\pi$
$888$	−0.262402	−	8.35688i	−0.00880562	−	0.280439i
$889$	28.0975	−	18.7742i	0.942361	−	0.629665i
$890$	−12.2518	+	79.3664i	−0.410683	+	2.66037i
$891$	−1.36719	−	1.66592i	−0.0458025	−	0.0558105i
$892$	−19.8015	−	10.8864i	−0.663004	−	0.364505i
$893$	−2.30926	+	1.23432i	−0.0772764	+	0.0413051i
$894$	−8.67529	+	11.5542i	−0.290145	+	0.386430i
$895$	45.3284			1.51516
$896$	41.2770	+	40.6387i	1.37897	+	1.35764i
$897$	−5.44538			−0.181816
$898$	15.5311	−	20.6851i	0.518280	−	0.690271i
$899$	5.17350	−	2.76529i	0.172546	−	0.0922277i
$900$	−10.4460	+	19.0005i	−0.348201	+	0.633349i
$901$	0.678612	+	0.826891i	0.0226078	+	0.0275477i
$902$	−3.70467	+	23.9985i	−0.123352	+	0.799064i
$903$	−22.3268	+	14.9183i	−0.742988	+	0.496449i
$904$	−10.2209	+	10.8836i	−0.339943	+	0.361983i
$905$	−19.9064	+	29.7920i	−0.661711	+	0.990320i
$906$	−8.49558	+	0.367135i	−0.282247	+	0.0121973i
$907$	20.5817	−	6.24338i	0.683403	−	0.207308i	0.0705538	−	0.997508i	$-0.477523\pi$
$907$	20.5817	−	6.24338i	0.683403	−	0.207308i	0.612849	+	0.790200i	$0.290023\pi$
$908$	−50.5065	−	0.595944i	−1.67612	−	0.0197771i
$909$	−11.5691	−	9.49453i	−0.383724	−	0.314914i
$910$	9.37780	−	170.375i	0.310871	−	5.64786i
$911$	−44.9758	−	18.6296i	−1.49012	−	0.617226i	−0.518774	−	0.854912i	$-0.673611\pi$
$911$	−44.9758	−	18.6296i	−1.49012	−	0.617226i	−0.971342	+	0.237685i	$0.923611\pi$
$912$	8.61591	+	3.80942i	0.285301	+	0.126142i
$913$	6.57923	−	2.72521i	0.217741	−	0.0901912i
$914$	6.91087	+	19.6798i	0.228591	+	0.650951i
$915$	3.22236	+	32.7172i	0.106528	+	1.08160i
$916$	−32.2042	+	6.01172i	−1.06406	+	0.198633i
$917$	−29.0594	+	54.3664i	−0.959628	+	1.79534i
$918$	0.507442	−	1.39226i	0.0167481	−	0.0459513i
$919$	12.7897	−	2.54402i	0.421892	−	0.0839195i	0.0204213	−	0.999791i	$-0.493499\pi$
$919$	12.7897	−	2.54402i	0.421892	−	0.0839195i	0.401470	+	0.915872i	$0.368499\pi$
$920$	−8.97312	+	5.16466i	−0.295835	+	0.170274i
$921$	−4.04921	+	20.3568i	−0.133426	+	0.670778i
$922$	−22.4837	+	5.49111i	−0.740460	+	0.180840i
$923$	2.50932	−	25.4776i	0.0825954	−	0.838605i
$924$	21.9855	−	1.90376i	0.723271	−	0.0626291i
$925$	−9.30293	+	30.6677i	−0.305878	+	1.00835i
$926$	−30.1302	+	17.8186i	−0.990141	+	0.585556i
$927$	3.00494	+	3.00494i	0.0986953	+	0.0986953i
$928$	7.69633	−	19.6614i	0.252644	−	0.645416i
$929$	22.2285	−	22.2285i	0.729294	−	0.729294i	−0.241185	−	0.970479i	$-0.577536\pi$
$929$	22.2285	−	22.2285i	0.729294	−	0.729294i	0.970479	+	0.241185i	$0.0775361\pi$
$930$	2.20010	−	8.56850i	0.0721441	−	0.280972i
$931$	43.3010	+	13.1352i	1.41913	+	0.430490i
$932$	20.3944	+	39.2627i	0.668042	+	1.28609i
$933$	−13.1600	−	1.29614i	−0.430838	−	0.0424339i
$934$	−29.4780	−	17.9056i	−0.964549	−	0.585891i
$935$	8.81511	+	1.75343i	0.288285	+	0.0573434i
$936$	1.11762	−	16.7096i	0.0365307	−	0.546171i
$937$	7.01280	+	35.2557i	0.229098	+	1.15175i	0.908467	+	0.417957i	$0.137254\pi$
$937$	7.01280	+	35.2557i	0.229098	+	1.15175i	−0.679369	+	0.733797i	$0.737746\pi$
$938$	12.0829	+	25.9420i	0.394521	+	0.847037i
$939$	−22.8782	−	12.2287i	−0.746602	−	0.399067i
$940$	8.65922	+	1.82889i	0.282433	+	0.0596519i
$941$	−33.6714	+	3.31635i	−1.09766	+	0.108110i	−0.630593	−	0.776114i	$-0.717188\pi$
$941$	−33.6714	+	3.31635i	−1.09766	+	0.108110i	−0.467064	+	0.884223i	$0.654688\pi$
$942$	4.27482	−	8.90209i	0.139281	−	0.290046i
$943$	−2.80409	−	6.76967i	−0.0913137	−	0.220451i
$944$	−5.62395	+	17.0782i	−0.183044	+	0.555847i
$945$	−7.79822	+	18.8266i	−0.253676	+	0.612428i
$946$	−10.6646	−	11.9070i	−0.346735	−	0.387129i
$947$	−28.1727	+	34.3285i	−0.915489	+	1.11553i	0.0774617	+	0.996995i	$0.475318\pi$
$947$	−28.1727	+	34.3285i	−0.915489	+	1.11553i	−0.992950	+	0.118531i	$0.962182\pi$
$948$	26.9386	−	10.7877i	0.874924	−	0.350369i
$949$	22.6260	+	74.5879i	0.734470	+	2.42122i
$950$	−26.6112	−	24.4065i	−0.863381	−	0.791850i
$951$	6.85881	+	4.58291i	0.222412	+	0.148611i
$952$	8.82191	+	12.3458i	0.285920	+	0.400128i
$953$	−4.90734	−	7.34435i	−0.158964	−	0.237907i	0.743435	−	0.668809i	$-0.233195\pi$
$953$	−4.90734	−	7.34435i	−0.158964	−	0.237907i	−0.902399	+	0.430902i	$0.858195\pi$
$954$	−0.853179	−	1.16468i	−0.0276227	−	0.0377078i
$955$	−51.4740	+	42.2436i	−1.66566	+	1.36697i
$956$	−20.3458	−	25.3967i	−0.658031	−	0.821387i
$957$	−3.79186	−	7.09407i	−0.122573	−	0.229319i
$958$	−28.8009	+	4.09871i	−0.930514	+	0.132423i
$959$			94.3784i			3.04764i
$960$	−14.0065	−	28.5948i	−0.452059	−	0.922893i
$961$		−	28.5299i		−	0.920319i
$962$	−3.48744	−	24.5056i	−0.112440	−	0.790092i
$963$	6.36237	+	11.9032i	0.205024	+	0.383574i
$964$	2.16044	−	19.5658i	0.0695832	−	0.630173i
$965$	6.73550	−	5.52768i	0.216823	−	0.177942i
$966$	−5.37191	+	3.93517i	−0.172839	+	0.126612i
$967$	7.93503	+	11.8756i	0.255173	+	0.381894i	0.936834	−	0.349775i	$-0.113742\pi$
$967$	7.93503	+	11.8756i	0.255173	+	0.381894i	−0.681661	+	0.731669i	$0.738742\pi$
$968$	−4.05855	−	17.5119i	−0.130447	−	0.562855i
$969$	2.05186	+	1.37101i	0.0659154	+	0.0440432i
$970$	−32.6300	+	35.5776i	−1.04769	+	1.14233i
$971$	1.28379	+	4.23208i	0.0411987	+	0.135814i	0.975127	−	0.221646i	$-0.0711429\pi$
$971$	1.28379	+	4.23208i	0.0411987	+	0.135814i	−0.933928	+	0.357460i	$0.883643\pi$
$972$	−0.787114	+	1.83860i	−0.0252467	+	0.0589731i
$973$	33.4047	−	40.7038i	1.07091	−	1.30490i
$974$	23.6760	−	21.2056i	0.758628	−	0.679471i
$975$	−24.5648	+	59.3046i	−0.786702	+	1.89927i
$976$	−28.7628	−	16.2580i	−0.920675	−	0.520406i
$977$	−1.65868	−	4.00441i	−0.0530659	−	0.128112i	0.895123	−	0.445819i	$-0.147087\pi$
$977$	−1.65868	−	4.00441i	−0.0530659	−	0.128112i	−0.948189	+	0.317706i	$0.897087\pi$
$978$	15.9162	+	7.64301i	0.508943	+	0.244397i
$979$	−30.5994	+	3.01378i	−0.977961	+	0.0963208i
$980$	−83.4636	−	128.160i	−2.66615	−	4.09392i
$981$	−1.43305	−	0.765980i	−0.0457537	−	0.0244559i
$982$	−7.68997	+	3.58173i	−0.245397	+	0.114297i
$983$	−0.329164	−	1.65482i	−0.0104987	−	0.0527805i	0.975181	−	0.221410i	$-0.0710659\pi$
$983$	−0.329164	−	1.65482i	−0.0104987	−	0.0527805i	−0.985680	+	0.168629i	$0.946066\pi$
$984$	21.3488	−	7.21516i	0.680576	−	0.230011i
$985$	−5.92434	−	1.17843i	−0.188765	−	0.0375477i
$986$	2.87142	−	4.72721i	0.0914446	−	0.150545i
$987$	5.66492	+	0.557946i	0.180316	+	0.0177596i
$988$	26.5908	+	8.41008i	0.845966	+	0.267560i
$989$	4.61574	+	1.40017i	0.146772	+	0.0445228i
$990$	−11.7494	−	3.01685i	−0.373421	−	0.0958817i
$991$	6.26512	−	6.26512i	0.199018	−	0.199018i	−0.600561	−	0.799579i	$-0.705056\pi$
$991$	6.26512	−	6.26512i	0.199018	−	0.199018i	0.799579	+	0.600561i	$0.205056\pi$
$992$	5.77371	+	6.76075i	0.183315	+	0.214654i
$993$	18.4954	+	18.4954i	0.586935	+	0.586935i
$994$	−15.9362	−	26.9472i	−0.505467	−	0.854715i
$995$	29.9329	−	98.6755i	0.948936	−	3.12822i
$996$	−5.05883	−	4.25254i	−0.160295	−	0.134747i
$997$	−4.85135	+	49.2566i	−0.153644	+	1.55997i	0.541252	+	0.840861i	$0.317951\pi$
$997$	−4.85135	+	49.2566i	−0.153644	+	1.55997i	−0.694896	+	0.719111i	$0.744549\pi$
$998$	7.30371	+	29.9055i	0.231195	+	0.946641i
$999$	−0.576699	+	2.89926i	−0.0182459	+	0.0917285i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.229.25	yes	512
128.109	even	32	inner	384.2.v.a.109.25	✓	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.109.25	✓	512	128.109	even	32	inner
384.2.v.a.229.25	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)

\(f(q)\)	\(=\)	\(q+(1.13092 + 0.849133i) q^{2} +(-0.881921 + 0.471397i) q^{3} +(0.557948 + 1.92060i) q^{4} +(-2.52496 - 3.07667i) q^{5} +(-1.39766 - 0.215757i) q^{6} +(-4.25703 + 2.84446i) q^{7} +(-0.999849 + 2.64581i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})\)	\(q+(1.13092 + 0.849133i) q^{2} +(-0.881921 + 0.471397i) q^{3} +(0.557948 + 1.92060i) q^{4} +(-2.52496 - 3.07667i) q^{5} +(-1.39766 - 0.215757i) q^{6} +(-4.25703 + 2.84446i) q^{7} +(-0.999849 + 2.64581i) q^{8} +(0.555570 - 0.831470i) q^{9} +(-0.243018 - 5.62349i) q^{10} +(2.06231 - 0.625595i) q^{11} +(-1.39743 - 1.43080i) q^{12} +(-4.57695 - 3.75620i) q^{13} +(-7.22967 - 0.397937i) q^{14} +(3.67715 + 1.52312i) q^{15} +(-3.37739 + 2.14319i) q^{16} +(-0.968064 + 0.400985i) q^{17} +(1.33433 - 0.468571i) q^{18} +(0.230842 + 2.34378i) q^{19} +(4.50025 - 6.56605i) q^{20} +(2.41350 - 4.51534i) q^{21} +(2.86352 + 1.04368i) q^{22} +(-0.902011 + 0.179421i) q^{23} +(-0.365438 - 2.80472i) q^{24} +(-2.11504 + 10.6330i) q^{25} +(-1.98663 - 8.13439i) q^{26} +(-0.0980171 + 0.995185i) q^{27} +(-7.83825 - 6.58898i) q^{28} +(-1.08348 + 3.57175i) q^{29} +(2.86522 + 4.84491i) q^{30} +(-1.11133 - 1.11133i) q^{31} +(-5.63940 - 0.444083i) q^{32} +(-1.52389 + 1.52389i) q^{33} +(-1.43529 - 0.368534i) q^{34} +(19.5003 + 5.91534i) q^{35} +(1.90690 + 0.603110i) q^{36} +(2.94183 + 0.289745i) q^{37} +(-1.72912 + 2.84664i) q^{38} +(5.80717 + 1.15512i) q^{39} +(10.6649 - 3.60435i) q^{40} +(1.55436 + 7.81427i) q^{41} +(6.56358 - 3.05709i) q^{42} +(-4.62540 - 2.47233i) q^{43} +(2.35218 + 3.61182i) q^{44} +(-3.96095 + 0.390120i) q^{45} +(-1.17245 - 0.563016i) q^{46} +(0.425470 + 1.02718i) q^{47} +(1.96830 - 3.48221i) q^{48} +(7.35258 - 17.7507i) q^{49} +(-11.4208 + 10.2291i) q^{50} +(0.664733 - 0.809980i) q^{51} +(4.66046 - 10.8862i) q^{52} +(-0.296345 - 0.976920i) q^{53} +(-0.955893 + 1.04224i) q^{54} +(-7.13200 - 4.76545i) q^{55} +(-3.26950 - 14.1073i) q^{56} +(-1.30844 - 1.95821i) q^{57} +(-4.25822 + 3.11934i) q^{58} +(3.47475 - 2.85165i) q^{59} +(-0.873652 + 7.91214i) q^{60} +(3.89370 + 7.28460i) q^{61} +(-0.313156 - 2.20049i) q^{62} +5.11988i q^{63} +(-6.00061 - 5.29082i) q^{64} +23.5660i q^{65} +(-3.01738 + 0.429410i) q^{66} +(-1.86316 - 3.48572i) q^{67} +(-1.31026 - 1.63553i) q^{68} +(0.710924 - 0.583440i) q^{69} +(17.0303 + 23.2481i) q^{70} +(2.40217 + 3.59509i) q^{71} +(1.64442 + 2.30128i) q^{72} +(-10.9456 - 7.31361i) q^{73} +(3.08093 + 2.82568i) q^{74} +(-3.14707 - 10.3745i) q^{75} +(-4.37266 + 1.75106i) q^{76} +(-6.99984 + 8.52933i) q^{77} +(5.58658 + 6.23740i) q^{78} +(-5.55241 + 13.4047i) q^{79} +(15.1216 + 4.97966i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-4.87750 + 10.1571i) q^{82} +(3.28847 - 0.323886i) q^{83} +(10.0187 + 2.11603i) q^{84} +(3.67802 + 1.96594i) q^{85} +(-3.13161 - 6.72357i) q^{86} +(-0.728169 - 3.66075i) q^{87} +(-0.406794 + 6.08198i) q^{88} +(-13.9931 - 2.78340i) q^{89} +(-4.81077 - 2.92218i) q^{90} +(30.1686 + 2.97134i) q^{91} +(-0.847871 - 1.63229i) q^{92} +(1.50398 + 0.456228i) q^{93} +(-0.391037 + 1.52293i) q^{94} +(6.62818 - 6.62818i) q^{95} +(5.18284 - 2.26675i) q^{96} +(-6.06453 - 6.06453i) q^{97} +(23.3879 - 13.8313i) q^{98} +(0.625595 - 2.06231i) 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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