LMFDB - Embedded newform 384.2.v.a.157.5

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			157.5
Character	$\chi$	$=$	384.157
Dual form			384.2.v.a.181.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28037 + 0.600534i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(1.27872 - 1.53782i) q^{4} +(-1.81303 + 0.969083i) q^{5} +(0.472143 + 1.33307i) q^{6} +(-0.759500 - 3.81826i) q^{7} +(-0.713728 + 2.73689i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})$	\(q+(-1.28037 + 0.600534i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(1.27872 - 1.53782i) q^{4} +(-1.81303 + 0.969083i) q^{5} +(0.472143 + 1.33307i) q^{6} +(-0.759500 - 3.81826i) q^{7} +(-0.713728 + 2.73689i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(1.73939 - 2.32957i) q^{10} +(-1.72483 + 2.10172i) q^{11} +(-1.40508 - 1.42329i) q^{12} +(-2.43961 + 4.56419i) q^{13} +(3.26544 + 4.43270i) q^{14} +(0.786709 + 1.89928i) q^{15} +(-0.729759 - 3.93287i) q^{16} +(-0.358674 + 0.865916i) q^{17} +(1.37293 - 0.339206i) q^{18} +(0.294162 + 0.969722i) q^{19} +(-0.828079 + 4.02729i) q^{20} +(-3.87432 + 0.381588i) q^{21} +(0.946282 - 3.72681i) q^{22} +(2.20496 - 1.47331i) q^{23} +(2.65376 + 0.978553i) q^{24} +(-0.429906 + 0.643399i) q^{25} +(0.382664 - 7.30894i) q^{26} +(-0.290285 + 0.956940i) q^{27} +(-6.84298 - 3.71451i) q^{28} +(-3.92222 + 3.21889i) q^{29} +(-2.14787 - 1.95935i) q^{30} +(-6.46485 + 6.46485i) q^{31} +(3.29619 + 4.59730i) q^{32} +(1.92253 + 1.92253i) q^{33} +(-0.0607746 - 1.32409i) q^{34} +(5.07721 + 6.18660i) q^{35} +(-1.55416 + 1.25880i) q^{36} +(1.35991 + 0.412523i) q^{37} +(-0.958989 - 1.06495i) q^{38} +(4.30309 + 2.87523i) q^{39} +(-1.35827 - 5.65373i) q^{40} +(-2.71041 - 4.05641i) q^{41} +(4.73143 - 2.81524i) q^{42} +(-0.592146 - 6.01216i) q^{43} +(1.02648 + 5.33998i) q^{44} +(1.96725 - 0.596759i) q^{45} +(-1.93840 + 3.21053i) q^{46} +(-10.6303 - 4.40323i) q^{47} +(-3.98546 + 0.340757i) q^{48} +(-7.53515 + 3.12116i) q^{49} +(0.164057 - 1.08197i) q^{50} +(0.826590 + 0.441822i) q^{51} +(3.89931 + 9.58798i) q^{52} +(-9.08414 - 7.45516i) q^{53} +(-0.203002 - 1.39957i) q^{54} +(1.09043 - 5.48198i) q^{55} +(10.9923 + 0.646529i) q^{56} +(0.993886 - 0.197696i) q^{57} +(3.08887 - 6.47681i) q^{58} +(6.58085 + 12.3119i) q^{59} +(3.92673 + 1.21883i) q^{60} +(-5.04646 - 0.497033i) q^{61} +(4.39507 - 12.1598i) q^{62} +3.89307i q^{63} +(-6.98119 - 3.90679i) q^{64} -10.6392i q^{65} +(-3.61611 - 1.30702i) q^{66} +(11.5783 + 1.14037i) q^{67} +(0.872977 + 1.65884i) q^{68} +(-1.25009 - 2.33875i) q^{69} +(-10.2160 - 4.87213i) q^{70} +(-9.68961 + 1.92738i) q^{71} +(1.23396 - 2.54506i) q^{72} +(1.33444 - 6.70866i) q^{73} +(-1.98893 + 0.288486i) q^{74} +(0.598163 + 0.490900i) q^{75} +(1.86741 + 0.787634i) q^{76} +(9.33493 + 4.98962i) q^{77} +(-7.23623 - 1.09722i) q^{78} +(13.5630 - 5.61800i) q^{79} +(5.13435 + 6.42320i) q^{80} +(0.923880 + 0.382683i) q^{81} +(5.90635 + 3.56603i) q^{82} +(3.00997 - 0.913064i) q^{83} +(-4.36736 + 6.44594i) q^{84} +(-0.188859 - 1.91752i) q^{85} +(4.36867 + 7.34221i) q^{86} +(2.81894 + 4.21884i) q^{87} +(-4.52112 - 6.22074i) q^{88} +(2.03692 + 1.36103i) q^{89} +(-2.16044 + 1.94547i) q^{90} +(19.2802 + 5.84857i) q^{91} +(0.553846 - 5.27476i) q^{92} +(5.80006 + 7.06739i) q^{93} +(16.2551 - 0.746093i) q^{94} +(-1.47307 - 1.47307i) q^{95} +(4.89824 - 2.82970i) q^{96} +(-7.34671 + 7.34671i) q^{97} +(7.77345 - 8.52137i) q^{98} +(2.10172 - 1.72483i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{27}{32}\right)$	$1$

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 $

$2$	−1.28037	+	0.600534i	−0.905362	+	0.424642i
$2$	−1.28037	+	0.600534i	−0.905362	+	0.424642i
$3$	0.0980171	−	0.995185i	0.0565902	−	0.574570i
$3$	0.0980171	−	0.995185i	0.0565902	−	0.574570i
$4$	1.27872	−	1.53782i	0.639359	−	0.768908i
$5$	−1.81303	+	0.969083i	−0.810810	+	0.433387i	−0.824044	−	0.566525i	$-0.808287\pi$
$5$	−1.81303	+	0.969083i	−0.810810	+	0.433387i	0.0132340	+	0.999912i	$0.495787\pi$
$6$	0.472143	+	1.33307i	0.192752	+	0.544224i
$7$	−0.759500	−	3.81826i	−0.287064	−	1.44317i	−0.807803	−	0.589453i	$-0.799344\pi$
$7$	−0.759500	−	3.81826i	−0.287064	−	1.44317i	0.520739	−	0.853716i	$-0.325656\pi$
$8$	−0.713728	+	2.73689i	−0.252341	+	0.967638i
$9$	−0.980785	−	0.195090i	−0.326928	−	0.0650301i
$10$	1.73939	−	2.32957i	0.550042	−	0.736676i
$11$	−1.72483	+	2.10172i	−0.520057	+	0.633692i	−0.965120	−	0.261808i	$-0.915681\pi$
$11$	−1.72483	+	2.10172i	−0.520057	+	0.633692i	0.445063	+	0.895499i	$0.353181\pi$
$12$	−1.40508	−	1.42329i	−0.405610	−	0.410869i
$13$	−2.43961	+	4.56419i	−0.676626	+	1.26588i	0.275832	+	0.961206i	$0.411047\pi$
$13$	−2.43961	+	4.56419i	−0.676626	+	1.26588i	−0.952457	+	0.304672i	$0.901453\pi$
$14$	3.26544	+	4.43270i	0.872726	+	1.18469i
$15$	0.786709	+	1.89928i	0.203127	+	0.490393i
$16$	−0.729759	−	3.93287i	−0.182440	−	0.983217i
$17$	−0.358674	+	0.865916i	−0.0869913	+	0.210016i	−0.961388	−	0.275196i	$-0.911257\pi$
$17$	−0.358674	+	0.865916i	−0.0869913	+	0.210016i	0.874397	+	0.485211i	$0.161257\pi$
$18$	1.37293	−	0.339206i	0.323603	−	0.0799516i
$19$	0.294162	+	0.969722i	0.0674854	+	0.222470i	0.984196	−	0.177082i	$-0.0566658\pi$
$19$	0.294162	+	0.969722i	0.0674854	+	0.222470i	−0.916711	+	0.399552i	$0.869166\pi$
$20$	−0.828079	+	4.02729i	−0.185164	+	0.900529i
$21$	−3.87432	+	0.381588i	−0.845447	+	0.0832692i
$22$	0.946282	−	3.72681i	0.201748	−	0.794558i
$23$	2.20496	−	1.47331i	0.459765	−	0.307205i	−0.304032	−	0.952662i	$-0.598333\pi$
$23$	2.20496	−	1.47331i	0.459765	−	0.307205i	0.763797	+	0.645457i	$0.223333\pi$
$24$	2.65376	+	0.978553i	0.541696	+	0.199746i
$25$	−0.429906	+	0.643399i	−0.0859811	+	0.128680i
$26$	0.382664	−	7.30894i	0.0750467	−	1.43340i
$27$	−0.290285	+	0.956940i	−0.0558653	+	0.184163i
$28$	−6.84298	−	3.71451i	−1.29320	−	0.701977i
$29$	−3.92222	+	3.21889i	−0.728339	+	0.597732i	−0.923753	−	0.382989i	$-0.874895\pi$
$29$	−3.92222	+	3.21889i	−0.728339	+	0.597732i	0.195414	+	0.980721i	$0.437395\pi$
$30$	−2.14787	−	1.95935i	−0.392145	−	0.357727i
$31$	−6.46485	+	6.46485i	−1.16112	+	1.16112i	−0.176892	+	0.984230i	$0.556604\pi$
$31$	−6.46485	+	6.46485i	−1.16112	+	1.16112i	−0.984230	+	0.176892i	$0.943396\pi$
$32$	3.29619	+	4.59730i	0.582689	+	0.812695i
$33$	1.92253	+	1.92253i	0.334670	+	0.334670i
$34$	−0.0607746	−	1.32409i	−0.0104228	−	0.227080i
$35$	5.07721	+	6.18660i	0.858205	+	1.04573i
$36$	−1.55416	+	1.25880i	−0.259027	+	0.209800i
$37$	1.35991	+	0.412523i	0.223567	+	0.0678184i	0.400081	−	0.916480i	$-0.368982\pi$
$37$	1.35991	+	0.412523i	0.223567	+	0.0678184i	−0.176514	+	0.984298i	$0.556482\pi$
$38$	−0.958989	−	1.06495i	−0.155569	−	0.172758i
$39$	4.30309	+	2.87523i	0.689045	+	0.460405i
$40$	−1.35827	−	5.65373i	−0.214762	−	0.893933i
$41$	−2.71041	−	4.05641i	−0.423294	−	0.633505i	0.557124	−	0.830429i	$-0.311905\pi$
$41$	−2.71041	−	4.05641i	−0.423294	−	0.633505i	−0.980419	+	0.196924i	$0.936905\pi$
$42$	4.73143	−	2.81524i	0.730075	−	0.434400i
$43$	−0.592146	−	6.01216i	−0.0903014	−	0.916846i	−0.928463	−	0.371424i	$-0.878870\pi$
$43$	−0.592146	−	6.01216i	−0.0903014	−	0.916846i	0.838162	−	0.545422i	$-0.183630\pi$
$44$	1.02648	+	5.33998i	0.154747	+	0.805033i
$45$	1.96725	−	0.596759i	0.293260	−	0.0889595i
$46$	−1.93840	+	3.21053i	−0.285802	+	0.473367i
$47$	−10.6303	−	4.40323i	−1.55059	−	0.642277i	−0.567170	−	0.823601i	$-0.691962\pi$
$47$	−10.6303	−	4.40323i	−1.55059	−	0.642277i	−0.983423	+	0.181324i	$0.941962\pi$
$48$	−3.98546	+	0.340757i	−0.575251	+	0.0491840i
$49$	−7.53515	+	3.12116i	−1.07645	+	0.445880i
$50$	0.164057	−	1.08197i	0.0232012	−	0.153013i
$51$	0.826590	+	0.441822i	0.115746	+	0.0618674i
$52$	3.89931	+	9.58798i	0.540737	+	1.32961i
$53$	−9.08414	−	7.45516i	−1.24780	−	1.02405i	−0.998451	−	0.0556325i	$-0.982282\pi$
$53$	−9.08414	−	7.45516i	−1.24780	−	1.02405i	−0.249352	−	0.968413i	$-0.580218\pi$
$54$	−0.203002	−	1.39957i	−0.0276251	−	0.190457i
$55$	1.09043	−	5.48198i	0.147034	−	0.739190i
$56$	10.9923	+	0.646529i	1.46890	+	0.0863960i
$57$	0.993886	−	0.197696i	0.131643	−	0.0261855i
$58$	3.08887	−	6.47681i	0.405588	−	0.850447i
$59$	6.58085	+	12.3119i	0.856754	+	1.60287i	0.796459	+	0.604693i	$0.206704\pi$
$59$	6.58085	+	12.3119i	0.856754	+	1.60287i	0.0602948	+	0.998181i	$0.480796\pi$
$60$	3.92673	+	1.21883i	0.506939	+	0.157351i
$61$	−5.04646	−	0.497033i	−0.646133	−	0.0636385i	−0.230358	−	0.973106i	$-0.573990\pi$
$61$	−5.04646	−	0.497033i	−0.646133	−	0.0636385i	−0.415775	+	0.909468i	$0.636490\pi$
$62$	4.39507	−	12.1598i	0.558175	−	1.54430i
$63$			3.89307i			0.490481i
$64$	−6.98119	−	3.90679i	−0.872648	−	0.488349i
$65$		−	10.6392i		−	1.31963i
$66$	−3.61611	−	1.30702i	−0.445112	−	0.160883i
$67$	11.5783	+	1.14037i	1.41452	+	0.139318i	0.776215	−	0.630468i	$-0.217137\pi$
$67$	11.5783	+	1.14037i	1.41452	+	0.139318i	0.638302	+	0.769786i	$0.279637\pi$
$68$	0.872977	+	1.65884i	0.105864	+	0.201164i
$69$	−1.25009	−	2.33875i	−0.150493	−	0.281552i
$70$	−10.2160	−	4.87213i	−1.22104	−	0.582331i
$71$	−9.68961	+	1.92738i	−1.14995	+	0.228738i	−0.733023	−	0.680204i	$-0.761891\pi$
$71$	−9.68961	+	1.92738i	−1.14995	+	0.228738i	−0.416922	+	0.908942i	$0.636891\pi$
$72$	1.23396	−	2.54506i	0.145423	−	0.299939i
$73$	1.33444	−	6.70866i	0.156184	−	0.785189i	−0.820690	−	0.571374i	$-0.806411\pi$
$73$	1.33444	−	6.70866i	0.156184	−	0.785189i	0.976874	−	0.213816i	$-0.0685892\pi$
$74$	−1.98893	+	0.288486i	−0.231208	+	0.0335358i
$75$	0.598163	+	0.490900i	0.0690699	+	0.0566842i
$76$	1.86741	+	0.787634i	0.214206	+	0.0903479i
$77$	9.33493	+	4.98962i	1.06381	+	0.568620i
$78$	−7.23623	−	1.09722i	−0.819342	−	0.124236i
$79$	13.5630	−	5.61800i	1.52596	−	0.632074i	0.547186	−	0.837011i	$-0.315699\pi$
$79$	13.5630	−	5.61800i	1.52596	−	0.632074i	0.978775	+	0.204937i	$0.0656989\pi$
$80$	5.13435	+	6.42320i	0.574038	+	0.718136i
$81$	0.923880	+	0.382683i	0.102653	+	0.0425204i
$82$	5.90635	+	3.56603i	0.652247	+	0.393802i
$83$	3.00997	−	0.913064i	0.330387	−	0.100222i	−0.120733	−	0.992685i	$-0.538525\pi$
$83$	3.00997	−	0.913064i	0.330387	−	0.100222i	0.451120	+	0.892463i	$0.351025\pi$
$84$	−4.36736	+	6.44594i	−0.476518	+	0.703310i
$85$	−0.188859	−	1.91752i	−0.0204846	−	0.207984i
$86$	4.36867	+	7.34221i	0.471086	+	0.791731i
$87$	2.81894	+	4.21884i	0.302222	+	0.452308i
$88$	−4.52112	−	6.22074i	−0.481953	−	0.663134i
$89$	2.03692	+	1.36103i	0.215913	+	0.144269i	0.658824	−	0.752297i	$-0.271054\pi$
$89$	2.03692	+	1.36103i	0.215913	+	0.144269i	−0.442911	+	0.896566i	$0.646054\pi$
$90$	−2.16044	+	1.94547i	−0.227731	+	0.205071i
$91$	19.2802	+	5.84857i	2.02111	+	0.613097i
$92$	0.553846	−	5.27476i	0.0577424	−	0.549932i
$93$	5.80006	+	7.06739i	0.601438	+	0.732854i
$94$	16.2551	−	0.746093i	1.67658	−	0.0769536i
$95$	−1.47307	−	1.47307i	−0.151133	−	0.151133i
$96$	4.89824	−	2.82970i	0.499925	−	0.288805i
$97$	−7.34671	+	7.34671i	−0.745945	+	0.745945i	−0.973715	−	0.227770i	$-0.926857\pi$
$97$	−7.34671	+	7.34671i	−0.745945	+	0.745945i	0.227770	+	0.973715i	$0.426857\pi$
$98$	7.77345	−	8.52137i	0.785237	−	0.860788i
$99$	2.10172	−	1.72483i	0.211231	−	0.173352i
$100$	0.439702	+	1.48384i	0.0439702	+	0.148384i
$101$	1.32282	−	4.36076i	0.131626	−	0.433912i	−0.866209	−	0.499682i	$-0.833450\pi$
$101$	1.32282	−	4.36076i	0.131626	−	0.433912i	0.997835	+	0.0657700i	$0.0209504\pi$
$102$	−1.32367	−	0.0693019i	−0.131063	−	0.00686191i
$103$	7.45806	−	11.1618i	0.734864	−	1.09980i	−0.256227	−	0.966617i	$-0.582479\pi$
$103$	7.45806	−	11.1618i	0.734864	−	1.09980i	0.991091	−	0.133185i	$-0.0425205\pi$
$104$	−10.7505	−	9.93454i	−1.05417	−	0.974161i
$105$	6.65446	−	4.44637i	0.649409	−	0.433921i
$106$	16.1082	+	4.09007i	1.56457	+	0.397262i
$107$	2.27943	−	0.224504i	0.220361	−	0.0217036i	0.0127657	−	0.999919i	$-0.495936\pi$
$107$	2.27943	−	0.224504i	0.220361	−	0.0217036i	0.207595	+	0.978215i	$0.433436\pi$
$108$	1.10041	+	1.67006i	0.105887	+	0.160702i
$109$	0.577564	+	1.90397i	0.0553206	+	0.182368i	0.980246	−	0.197780i	$-0.0633732\pi$
$109$	0.577564	+	1.90397i	0.0553206	+	0.182368i	−0.924926	+	0.380148i	$0.875873\pi$
$110$	1.89595	+	7.67383i	0.180772	+	0.731671i
$111$	0.543831	−	1.31292i	0.0516182	−	0.124617i
$112$	−14.4625	+	5.77343i	−1.36658	+	0.545538i
$113$	−0.219948	−	0.531001i	−0.0206909	−	0.0499523i	0.913196	−	0.407520i	$-0.133606\pi$
$113$	−0.219948	−	0.531001i	−0.0206909	−	0.0499523i	−0.933887	+	0.357567i	$0.883606\pi$
$114$	−1.15382	+	0.849987i	−0.108065	+	0.0796086i
$115$	−2.56989	+	4.80793i	−0.239644	+	0.448342i
$116$	−0.0653632	+	10.1477i	−0.00606882	+	0.942191i
$117$	3.28316	−	4.00054i	0.303528	−	0.369850i
$118$	−15.8197	−	11.8118i	−1.45632	−	1.08737i
$119$	3.57871	+	0.711850i	0.328060	+	0.0652552i
$120$	−5.75964	+	0.797569i	−0.525780	+	0.0728078i
$121$	0.703833	+	3.53841i	0.0639848	+	0.321673i
$122$	6.75984	−	2.39418i	0.612007	−	0.216759i
$123$	−4.30254	+	2.29976i	−0.387947	+	0.207362i
$124$	1.67503	+	18.2085i	0.150422	+	1.63517i
$125$	1.16343	−	11.8125i	0.104060	−	1.05654i
$126$	−2.33792	−	4.98459i	−0.208278	−	0.444062i
$127$	−10.5235			−0.933808			−0.466904	−	0.884308i	$-0.654631\pi$
$127$	−10.5235			−0.933808			−0.466904	+	0.884308i	$0.654631\pi$
$128$	11.2847	+	0.809722i	0.997436	+	0.0715700i
$129$	−6.04125			−0.531902
$130$	6.38919	+	13.6221i	0.560369	+	1.19474i
$131$	0.460421	−	4.67473i	0.0402271	−	0.408433i	−0.953893	−	0.300148i	$-0.902964\pi$
$131$	0.460421	−	4.67473i	0.0402271	−	0.408433i	0.994120	−	0.108285i	$-0.0345360\pi$
$132$	5.41488	−	0.498125i	0.471305	−	0.0433562i
$133$	3.47924	−	1.85969i	0.301688	−	0.161256i
$134$	−15.5094	+	5.49308i	−1.33981	+	0.474530i
$135$	−0.401061	−	2.01627i	−0.0345178	−	0.173533i
$136$	−2.11393	−	1.59968i	−0.181268	−	0.137172i
$137$	9.28790	+	1.84748i	0.793519	+	0.157841i	0.575174	−	0.818031i	$-0.304934\pi$
$137$	9.28790	+	1.84748i	0.793519	+	0.157841i	0.218345	+	0.975872i	$0.429934\pi$
$138$	3.00508	+	2.24376i	0.255809	+	0.191001i
$139$	−5.13413	+	6.25596i	−0.435471	+	0.530624i	−0.943790	−	0.330546i	$-0.892767\pi$
$139$	−5.13413	+	6.25596i	−0.435471	+	0.530624i	0.508319	+	0.861169i	$0.330267\pi$
$140$	16.0062	+	0.103099i	1.35277	+	0.00871343i
$141$	−5.42398	+	10.1476i	−0.456781	+	0.854578i
$142$	11.2489	−	8.28672i	0.943985	−	0.695406i
$143$	−5.38471	−	12.9998i	−0.450292	−	1.08710i
$144$	−0.0515273	+	3.99967i	−0.00429394	+	0.333306i
$145$	3.99173	−	9.63689i	0.331495	−	0.800300i
$146$	2.32020	+	9.39097i	0.192021	+	0.777202i
$147$	2.36756	+	7.80479i	0.195273	+	0.643729i
$148$	2.37332	−	1.56379i	0.195086	−	0.128542i
$149$	−22.5140	+	2.21744i	−1.84442	+	0.181659i	−0.959051	−	0.283232i	$-0.908593\pi$
$149$	−22.5140	+	2.21744i	−1.84442	+	0.181659i	−0.885368	+	0.464892i	$0.846093\pi$
$150$	−1.06067	−	0.269318i	−0.0866037	−	0.0219898i
$151$	2.63372	−	1.75979i	0.214329	−	0.143210i	−0.443772	−	0.896140i	$-0.646360\pi$
$151$	2.63372	−	1.75979i	0.214329	−	0.143210i	0.658101	+	0.752930i	$0.271360\pi$
$152$	−2.86398	+	0.112973i	−0.232299	+	0.00916333i
$153$	0.520714	−	0.779304i	0.0420973	−	0.0630030i
$154$	−14.9486	−	0.782646i	−1.20460	−	0.0630674i
$155$	5.45597	−	17.9859i	0.438234	−	1.44467i
$156$	9.92401	−	2.94075i	0.794557	−	0.235448i
$157$	−16.3333	+	13.4044i	−1.30354	+	1.06979i	−0.310681	+	0.950514i	$0.600557\pi$
$157$	−16.3333	+	13.4044i	−1.30354	+	1.06979i	−0.992861	+	0.119275i	$0.961943\pi$
$158$	−13.9920	+	15.3382i	−1.11314	+	1.22024i
$159$	−8.30967	+	8.30967i	−0.658999	+	0.658999i
$160$	−10.4312	−	5.14075i	−0.824662	−	0.406412i
$161$	−7.30014	−	7.30014i	−0.575331	−	0.575331i
$162$	−1.41273	+	0.0648428i	−0.110994	+	0.00509453i
$163$	−12.3015	−	14.9894i	−0.963525	−	1.17406i	−0.984696	−	0.174283i	$-0.944239\pi$
$163$	−12.3015	−	14.9894i	−0.963525	−	1.17406i	0.0211708	−	0.999776i	$-0.493261\pi$
$164$	−9.70386	−	1.01890i	−0.757744	−	0.0795625i
$165$	−5.34870	−	1.62251i	−0.416396	−	0.126312i
$166$	−3.30556	+	2.97665i	−0.256561	+	0.231033i
$167$	−2.36301	−	1.57891i	−0.182855	−	0.122180i	0.460774	−	0.887518i	$-0.347572\pi$
$167$	−2.36301	−	1.57891i	−0.182855	−	0.122180i	−0.643629	+	0.765338i	$0.722572\pi$
$168$	1.72085	−	10.8760i	0.132766	−	0.839099i
$169$	−7.65769	−	11.4606i	−0.589053	−	0.881581i
$170$	1.39334	+	2.34172i	0.106864	+	0.179602i
$171$	−0.0993264	−	1.00848i	−0.00759568	−	0.0771202i
$172$	−10.0028	−	6.77725i	−0.762705	−	0.516760i
$173$	15.1321	−	4.59026i	1.15047	−	0.348991i	0.343251	−	0.939244i	$-0.388472\pi$
$173$	15.1321	−	4.59026i	1.15047	−	0.348991i	0.807219	+	0.590253i	$0.200972\pi$
$174$	−6.14286	−	3.70883i	−0.465689	−	0.281166i
$175$	2.78318	+	1.15283i	0.210389	+	0.0871459i
$176$	9.52449	+	5.24980i	0.717936	+	0.395719i
$177$	12.8977	−	5.34238i	0.969447	−	0.401558i
$178$	−3.42537	−	0.519385i	−0.256742	−	0.0389296i
$179$	−13.7562	−	7.35285i	−1.02819	−	0.549578i	−0.131072	−	0.991373i	$-0.541842\pi$
$179$	−13.7562	−	7.35285i	−1.02819	−	0.549578i	−0.897116	+	0.441795i	$0.854342\pi$
$180$	1.59785	−	3.78835i	0.119097	−	0.282367i
$181$	10.3689	+	8.50957i	0.770718	+	0.632512i	0.935302	−	0.353851i	$-0.115128\pi$
$181$	10.3689	+	8.50957i	0.770718	+	0.632512i	−0.164584	+	0.986363i	$0.552628\pi$
$182$	−28.1981	+	4.09002i	−2.09018	+	0.303173i
$183$	−0.989279	+	4.97344i	−0.0731296	+	0.367647i
$184$	2.45854	+	7.08628i	0.181246	+	0.522407i
$185$	−2.86532	+	0.569947i	−0.210662	+	0.0419034i
$186$	−11.6705	−	5.56578i	−0.855719	−	0.408103i
$187$	−1.20126	−	2.24739i	−0.0878446	−	0.164346i
$188$	−20.3646	+	10.7170i	−1.48524	+	0.781618i
$189$	3.87432	+	0.381588i	0.281816	+	0.0277564i
$190$	2.77070	+	1.00145i	0.201008	+	0.0726528i
$191$		−	8.09395i		−	0.585658i	−0.956165	−	0.292829i	$-0.905403\pi$
$191$		−	8.09395i		−	0.585658i	0.956165	−	0.292829i	$-0.0945966\pi$
$192$	−4.57226	+	6.56464i	−0.329974	+	0.473762i
$193$		−	0.402743i		−	0.0289901i	−0.999895	−	0.0144951i	$-0.995386\pi$
$193$		−	0.402743i		−	0.0289901i	0.999895	−	0.0144951i	$-0.00461408\pi$
$194$	4.99459	−	13.8185i	0.358591	−	0.992109i
$195$	−10.5879	−	1.04282i	−0.758219	−	0.0746780i
$196$	−4.83556	+	15.5788i	−0.345397	+	1.11277i
$197$	−0.411970	−	0.770742i	−0.0293517	−	0.0549131i	0.866818	−	0.498625i	$-0.166161\pi$
$197$	−0.411970	−	0.770742i	−0.0293517	−	0.0549131i	−0.896170	+	0.443712i	$0.853661\pi$
$198$	−1.65516	+	3.47059i	−0.117627	+	0.246644i
$199$	−4.01644	+	0.798920i	−0.284718	+	0.0566339i	−0.335383	−	0.942082i	$-0.608866\pi$
$199$	−4.01644	+	0.798920i	−0.284718	+	0.0566339i	0.0506654	+	0.998716i	$0.483866\pi$
$200$	−1.45408	−	1.63582i	−0.102819	−	0.115670i
$201$	2.26975	−	11.4108i	0.160096	−	0.804856i
$202$	0.925075	+	6.37780i	0.0650881	+	0.448740i
$203$	15.2695	+	12.5313i	1.07171	+	0.879528i
$204$	1.73642	−	0.706179i	0.121574	−	0.0494424i
$205$	8.84504	+	4.72777i	0.617764	+	0.330202i
$206$	−2.84609	+	18.7701i	−0.198296	+	1.30777i
$207$	−2.45002	+	1.01483i	−0.170288	+	0.0705356i
$208$	19.7307	+	6.26390i	1.36808	+	0.434323i
$209$	−2.54546	−	1.05437i	−0.176073	−	0.0729320i
$210$	−5.85001	+	9.68925i	−0.403689	+	0.668622i
$211$	−13.7651	+	4.17559i	−0.947627	+	0.287460i	−0.726018	−	0.687676i	$-0.758631\pi$
$211$	−13.7651	+	4.17559i	−0.947627	+	0.287460i	−0.221610	+	0.975135i	$0.571131\pi$
$212$	−23.0807	+	4.43669i	−1.58519	+	0.304713i
$213$	0.968355	+	9.83187i	0.0663506	+	0.673669i
$214$	−2.78370	+	1.65632i	−0.190290	+	0.113224i
$215$	6.89986	+	10.3264i	0.470567	+	0.704253i
$216$	−2.41186	−	1.47747i	−0.164106	−	0.100529i
$217$	29.5946	+	19.7745i	2.00901	+	1.34238i
$218$	−1.88290	−	2.09095i	−0.127526	−	0.141617i
$219$	−6.54556	−	1.98557i	−0.442308	−	0.134173i
$220$	−7.03592	−	8.68679i	−0.474362	−	0.585664i
$221$	−3.07718	−	3.74955i	−0.206993	−	0.252222i
$222$	0.0921480	+	2.00762i	0.00618457	+	0.134743i
$223$	15.2499	+	15.2499i	1.02121	+	1.02121i	0.999770	+	0.0214403i	$0.00682517\pi$
$223$	15.2499	+	15.2499i	1.02121	+	1.02121i	0.0214403	+	0.999770i	$0.493175\pi$
$224$	15.0503	−	16.0774i	1.00559	−	1.07421i
$225$	0.547166	−	0.547166i	0.0364777	−	0.0364777i
$226$	0.600499	+	0.547794i	0.0399446	+	0.0364387i
$227$	−5.06635	+	4.15784i	−0.336265	+	0.275966i	−0.787338	−	0.616521i	$-0.788541\pi$
$227$	−5.06635	+	4.15784i	−0.336265	+	0.275966i	0.451073	+	0.892487i	$0.351041\pi$
$228$	0.966880	−	1.78121i	0.0640332	−	0.117964i
$229$	−6.30589	+	20.7877i	−0.416705	+	1.37369i	0.457964	+	0.888971i	$0.348579\pi$
$229$	−6.30589	+	20.7877i	−0.416705	+	1.37369i	−0.874669	+	0.484721i	$0.838921\pi$
$230$	0.403100	−	7.69926i	0.0265796	−	0.507674i
$231$	5.88058	−	8.80091i	0.386914	−	0.579057i
$232$	−6.01035	−	13.0321i	−0.394599	−	0.855601i
$233$	14.2104	−	9.49506i	0.930951	−	0.622042i	0.00512340	−	0.999987i	$-0.498369\pi$
$233$	14.2104	−	9.49506i	0.930951	−	0.622042i	0.925828	+	0.377945i	$0.123369\pi$
$234$	−1.80121	+	7.09384i	−0.117749	+	0.463739i
$235$	23.5402	−	2.31850i	1.53559	−	0.151243i
$236$	27.3485	+	5.62332i	1.78024	+	0.366047i
$237$	−4.26153	−	14.0484i	−0.276816	−	0.912541i
$238$	−5.00958	+	1.23770i	−0.324723	+	0.0802283i
$239$	−7.52753	+	18.1731i	−0.486915	+	1.17552i	0.469349	+	0.883013i	$0.344489\pi$
$239$	−7.52753	+	18.1731i	−0.486915	+	1.17552i	−0.956264	+	0.292505i	$0.905511\pi$
$240$	6.89552	−	4.48004i	0.445104	−	0.289186i
$241$	−5.63742	−	13.6099i	−0.363138	−	0.876693i	−0.994838	−	0.101480i	$-0.967642\pi$
$241$	−5.63742	−	13.6099i	−0.363138	−	0.876693i	0.631699	−	0.775213i	$-0.282358\pi$
$242$	−3.02610	−	4.10781i	−0.194525	−	0.264060i
$243$	0.471397	−	0.881921i	0.0302401	−	0.0565753i
$244$	−7.21734	+	7.12496i	−0.462043	+	0.456129i
$245$	10.6368	−	12.9609i	0.679558	−	0.828044i
$246$	4.12778	−	5.52837i	0.263178	−	0.352476i
$247$	−5.14363	−	1.02313i	−0.327282	−	0.0651004i
$248$	−13.0795	−	22.3078i	−0.830548	−	1.41654i
$249$	−0.613639	−	3.08497i	−0.0388878	−	0.195502i
$250$	5.60417	+	15.8231i	0.354439	+	1.00074i
$251$	5.30836	−	2.83738i	0.335060	−	0.179094i	−0.295283	−	0.955410i	$-0.595414\pi$
$251$	5.30836	−	2.83738i	0.335060	−	0.179094i	0.630344	+	0.776316i	$0.282914\pi$
$252$	5.98683	+	4.97814i	0.377135	+	0.313593i
$253$	−0.706716	+	7.17541i	−0.0444308	+	0.451114i
$254$	13.4740	−	6.31971i	0.845434	−	0.396534i
$255$	−1.92679			−0.120660
$256$	−14.9349	+	5.74009i	−0.933431	+	0.358756i
$257$	−16.7425			−1.04437			−0.522184	−	0.852833i	$-0.674883\pi$
$257$	−16.7425			−1.04437			−0.522184	+	0.852833i	$0.674883\pi$
$258$	7.73506	−	3.62798i	0.481564	−	0.225868i
$259$	0.542274	−	5.50580i	0.0336953	−	0.342114i
$260$	−16.3611	−	13.6045i	−1.01467	−	0.843716i
$261$	4.47483	−	2.39185i	0.276985	−	0.148052i
$262$	2.21782	+	6.26190i	0.137018	+	0.386862i
$263$	−4.90534	−	24.6608i	−0.302477	−	1.52065i	−0.770790	−	0.637090i	$-0.780138\pi$
$263$	−4.90534	−	24.6608i	−0.302477	−	1.52065i	0.468313	−	0.883562i	$-0.344862\pi$
$264$	−6.63394	+	3.88961i	−0.408291	+	0.239389i
$265$	23.6945	+	4.71312i	1.45554	+	0.289525i
$266$	−3.33792	+	4.47051i	−0.204661	+	0.274104i
$267$	1.55413	−	1.89371i	0.0951111	−	0.115893i
$268$	16.5591	−	16.3471i	1.01151	−	0.998560i
$269$	−13.2540	+	24.7965i	−0.808109	+	1.51187i	0.0502030	+	0.998739i	$0.484013\pi$
$269$	−13.2540	+	24.7965i	−0.808109	+	1.51187i	−0.858312	+	0.513127i	$0.828487\pi$
$270$	1.72435	+	2.34073i	0.104940	+	0.142452i
$271$	6.74201	+	16.2767i	0.409548	+	0.988737i	0.985257	+	0.171082i	$0.0547262\pi$
$271$	6.74201	+	16.2767i	0.409548	+	0.988737i	−0.575709	+	0.817655i	$0.695274\pi$
$272$	3.66728	+	0.778708i	0.222362	+	0.0472161i
$273$	7.71019	−	18.6141i	0.466642	−	1.12657i
$274$	−13.0015	+	3.21223i	−0.785447	+	0.194058i
$275$	−0.610727	−	2.01330i	−0.0368282	−	0.121406i
$276$	−5.19508	−	1.06820i	−0.312707	−	0.0642978i
$277$	−6.37229	+	0.627616i	−0.382874	+	0.0377098i	−0.287623	−	0.957744i	$-0.592865\pi$
$277$	−6.37229	+	0.627616i	−0.382874	+	0.0377098i	−0.0952504	+	0.995453i	$0.530365\pi$
$278$	2.81670	−	11.0932i	0.168934	−	0.665325i
$279$	7.60186	−	5.07940i	0.455112	−	0.304096i
$280$	−20.5558	+	9.48025i	−1.22845	+	0.566553i
$281$	−5.82802	+	8.72226i	−0.347671	+	0.520326i	−0.963555	−	0.267511i	$-0.913799\pi$
$281$	−5.82802	+	8.72226i	−0.347671	+	0.520326i	0.615884	+	0.787837i	$0.288799\pi$
$282$	0.850777	−	16.2500i	0.0506631	−	0.967670i
$283$	1.07798	−	3.55362i	0.0640792	−	0.211241i	−0.919054	−	0.394131i	$-0.871045\pi$
$283$	1.07798	−	3.55362i	0.0640792	−	0.211241i	0.983133	+	0.182891i	$0.0585455\pi$
$284$	−9.42632	+	17.3654i	−0.559349	+	1.03045i
$285$	−1.61036	+	1.32159i	−0.0953894	+	0.0782840i
$286$	14.7013	+	13.4110i	0.869305	+	0.793007i
$287$	−13.4299	+	13.4299i	−0.792742	+	0.792742i
$288$	−2.33596	−	5.15202i	−0.137648	−	0.303586i
$289$	11.3997	+	11.3997i	0.670568	+	0.670568i
$290$	0.676368	+	14.7360i	0.0397177	+	0.865328i
$291$	6.59123	+	8.03143i	0.386385	+	0.470811i
$292$	−8.61032	−	10.6306i	−0.503881	−	0.622109i
$293$	22.1433	+	6.71711i	1.29363	+	0.392418i	0.860747	−	0.509034i	$-0.169997\pi$
$293$	22.1433	+	6.71711i	1.29363	+	0.392418i	0.432881	+	0.901451i	$0.357497\pi$
$294$	−7.71840	−	8.57126i	−0.450146	−	0.499886i
$295$	−23.8625	−	15.9444i	−1.38933	−	0.928320i
$296$	−2.09964	+	3.42749i	−0.122039	+	0.199219i
$297$	−1.51052	−	2.26066i	−0.0876495	−	0.131177i
$298$	27.4947	−	16.3596i	1.59273	−	0.947684i
$299$	1.34521	+	13.6581i	0.0777954	+	0.789870i
$300$	1.51980	−	0.292143i	0.0877454	−	0.0168669i
$301$	−22.5063	+	6.82721i	−1.29724	+	0.393514i
$302$	−2.31533	+	3.83483i	−0.133232	+	0.220670i
$303$	−4.21010	−	1.74388i	−0.241864	−	0.100183i
$304$	3.59912	−	1.86456i	0.206424	−	0.106940i
$305$	9.63103	−	3.98930i	0.551471	−	0.228427i
$306$	−0.198711	+	1.31051i	−0.0113595	+	0.0749167i
$307$	−19.7555	−	10.5596i	−1.12751	−	0.602666i	−0.201244	−	0.979541i	$-0.564498\pi$
$307$	−19.7555	−	10.5596i	−1.12751	−	0.602666i	−0.926264	+	0.376875i	$0.876998\pi$
$308$	19.6099	−	7.97508i	1.11738	−	0.454423i
$309$	−10.3770	−	8.51619i	−0.590327	−	0.484469i
$310$	3.81547	+	26.3052i	0.216704	+	1.49404i
$311$	3.37743	−	16.9795i	0.191516	−	0.962817i	−0.758751	−	0.651381i	$-0.774190\pi$
$311$	3.37743	−	16.9795i	0.191516	−	0.962817i	0.950267	−	0.311436i	$-0.100810\pi$
$312$	−10.9404	+	9.72496i	−0.619380	+	0.550567i
$313$	−12.2426	+	2.43520i	−0.691992	+	0.137646i	−0.528543	−	0.848906i	$-0.677262\pi$
$313$	−12.2426	+	2.43520i	−0.691992	+	0.137646i	−0.163448	+	0.986552i	$0.552262\pi$
$314$	12.8630	−	26.9714i	0.725900	−	1.52208i
$315$	−3.77271	−	7.05824i	−0.212568	−	0.397687i
$316$	8.70386	−	28.0413i	0.489631	−	1.57745i
$317$	16.9250	+	1.66697i	0.950604	+	0.0936264i	0.561418	−	0.827533i	$-0.310256\pi$
$317$	16.9250	+	1.66697i	0.950604	+	0.0936264i	0.389187	+	0.921159i	$0.372756\pi$
$318$	5.64925	−	15.6297i	0.316794	−	0.876471i
$319$		−	13.7955i		−	0.772397i
$320$	16.4431	+	0.317774i	0.919197	+	0.0177641i
$321$		−	2.29046i		−	0.127841i
$322$	13.7309	+	4.96293i	0.765192	+	0.276573i
$323$	−0.945207	−	0.0930947i	−0.0525927	−	0.00517993i
$324$	1.76988	−	0.931413i	0.0983266	−	0.0517452i
$325$	−1.88779	−	3.53181i	−0.104716	−	0.195910i
$326$	24.7521	+	11.8046i	1.37089	+	0.653795i
$327$	1.95142	−	0.388161i	0.107914	−	0.0214653i
$328$	13.0365	−	4.52293i	0.719818	−	0.249737i
$329$	−8.73895	+	43.9337i	−0.481794	+	2.42214i
$330$	7.82271	−	1.13465i	0.430626	−	0.0624607i
$331$	0.773581	+	0.634861i	0.0425198	+	0.0348951i	0.655413	−	0.755270i	$-0.272494\pi$
$331$	0.773581	+	0.634861i	0.0425198	+	0.0348951i	−0.612893	+	0.790166i	$0.709994\pi$
$332$	2.44478	−	5.79633i	0.134175	−	0.318115i
$333$	−1.25330	−	0.669902i	−0.0686803	−	0.0367104i
$334$	3.97372	+	0.602531i	0.217432	+	0.0329690i
$335$	−22.0969	+	9.15285i	−1.20728	+	0.500074i
$336$	4.32806	+	14.9587i	0.236115	+	0.816066i
$337$	24.5066	+	10.1509i	1.33496	+	0.552957i	0.932065	−	0.362290i	$-0.118005\pi$
$337$	24.5066	+	10.1509i	1.33496	+	0.552957i	0.402892	+	0.915248i	$0.368005\pi$
$338$	16.6872	+	10.0751i	0.907662	+	0.548013i
$339$	−0.550002	+	0.166841i	−0.0298720	+	0.00906158i
$340$	−3.19028	−	2.16153i	−0.173017	−	0.117225i
$341$	−2.43649	−	24.7381i	−0.131943	−	1.33964i
$342$	0.732800	+	1.23158i	0.0396253	+	0.0665962i
$343$	2.50026	+	3.74190i	0.135001	+	0.202043i
$344$	16.8773	+	2.67040i	0.909962	+	0.143978i
$345$	4.53289	+	3.02878i	0.244042	+	0.163064i
$346$	−16.6181	+	14.9646i	−0.893395	+	0.804500i
$347$	20.3926	+	6.18604i	1.09473	+	0.332084i	0.785475	−	0.618894i	$-0.212419\pi$
$347$	20.3926	+	6.18604i	1.09473	+	0.332084i	0.309260	+	0.950978i	$0.399919\pi$
$348$	10.0924	+	1.05970i	0.541012	+	0.0568058i
$349$	1.69424	+	2.06443i	0.0906903	+	0.110506i	0.816378	−	0.577517i	$-0.195978\pi$
$349$	1.69424	+	2.06443i	0.0906903	+	0.110506i	−0.725688	+	0.688024i	$0.758478\pi$
$350$	−4.25583	+	0.195339i	−0.227484	+	0.0104413i
$351$	−3.65947	−	3.65947i	−0.195328	−	0.195328i
$352$	−15.3476	−	1.00193i	−0.818030	−	0.0534031i
$353$	−22.9373	+	22.9373i	−1.22083	+	1.22083i	−0.253492	+	0.967337i	$0.581579\pi$
$353$	−22.9373	+	22.9373i	−1.22083	+	1.22083i	−0.967337	+	0.253492i	$0.918421\pi$
$354$	−13.3055	+	14.5857i	−0.707182	+	0.775223i
$355$	15.6997	−	12.8844i	0.833256	−	0.683835i
$356$	4.69766	−	1.39204i	0.248976	−	0.0737781i
$357$	1.05920	−	3.49170i	0.0560587	−	0.184801i
$358$	22.0287	+	1.15333i	1.16426	+	0.0609554i
$359$	12.6171	−	18.8828i	0.665904	−	0.996596i	−0.332661	−	0.943047i	$-0.607946\pi$
$359$	12.6171	−	18.8828i	0.665904	−	0.996596i	0.998565	−	0.0535499i	$-0.0170536\pi$
$360$	0.229185	+	5.81008i	0.0120791	+	0.306218i
$361$	14.9441	−	9.98532i	0.786531	−	0.525543i
$362$	−18.3864	−	4.66854i	−0.966369	−	0.245373i
$363$	3.59036	−	0.353619i	0.188445	−	0.0185602i
$364$	33.6479	−	22.1707i	1.76363	−	1.16206i
$365$	4.08188	+	13.4562i	0.213656	+	0.704328i
$366$	−1.72007	−	6.96196i	−0.0899096	−	0.363907i
$367$	12.2541	−	29.5841i	0.639661	−	1.54428i	−0.187470	−	0.982270i	$-0.560029\pi$
$367$	12.2541	−	29.5841i	0.639661	−	1.54428i	0.827131	−	0.562009i	$-0.189971\pi$
$368$	−7.40340	−	7.59665i	−0.385929	−	0.396003i
$369$	1.86696	+	4.50724i	0.0971901	+	0.234638i
$370$	3.32641	−	2.45047i	0.172932	−	0.127394i
$371$	−21.5664	+	40.3479i	−1.11967	+	2.09476i
$372$	18.2850	+	0.117777i	0.948033	+	0.00610645i
$373$	−18.7327	+	22.8258i	−0.969940	+	1.18188i	0.0133650	+	0.999911i	$0.495746\pi$
$373$	−18.7327	+	22.8258i	−0.969940	+	1.18188i	−0.983305	+	0.181965i	$0.941754\pi$
$374$	2.88770	+	2.15611i	0.149319	+	0.111490i
$375$	−11.6416	−	2.31565i	−0.601167	−	0.119580i
$376$	19.6383	−	25.9514i	1.01277	−	1.33834i
$377$	−5.12291	−	25.7546i	−0.263843	−	1.32643i
$378$	−5.18974	+	1.83809i	−0.266931	+	0.0945410i
$379$	−30.5163	+	16.3113i	−1.56752	+	0.837857i	−0.567625	+	0.823287i	$0.692138\pi$
$379$	−30.5163	+	16.3113i	−1.56752	+	0.837857i	−0.999894	+	0.0145696i	$0.995362\pi$
$380$	−4.14894	+	0.381669i	−0.212836	+	0.0195792i
$381$	−1.03148	+	10.4728i	−0.0528444	+	0.536538i
$382$	4.86069	+	10.3633i	0.248695	+	0.530232i
$383$	5.17708			0.264536			0.132268	−	0.991214i	$-0.457774\pi$
$383$	5.17708			0.264536			0.132268	+	0.991214i	$0.457774\pi$
$384$	1.91192	−	11.1510i	0.0975671	−	0.569047i
$385$	−21.7598			−1.10898
$386$	0.241861	+	0.515662i	0.0123104	+	0.0262465i
$387$	−0.592146	+	6.01216i	−0.0301005	+	0.305615i
$388$	1.90352	+	20.6923i	0.0966366	+	1.05049i
$389$	21.2679	−	11.3679i	1.07832	−	0.576376i	0.166117	−	0.986106i	$-0.446877\pi$
$389$	21.2679	−	11.3679i	1.07832	−	0.576376i	0.912207	+	0.409729i	$0.134377\pi$
$390$	14.1828	−	5.02322i	0.718173	−	0.254361i
$391$	0.484898	+	2.43775i	0.0245223	+	0.123282i
$392$	−3.16425	−	22.8506i	−0.159819	−	1.15413i
$393$	−4.60709	−	0.916407i	−0.232397	−	0.0462266i
$394$	0.990333	+	0.739437i	0.0498923	+	0.0372523i
$395$	−19.1459	+	23.3293i	−0.963333	+	1.17382i
$396$	0.0350248	−	5.43763i	0.00176006	−	0.273251i
$397$	−6.44663	+	12.0608i	−0.323547	+	0.605314i	−0.990136	−	0.140112i	$-0.955254\pi$
$397$	−6.44663	+	12.0608i	−0.323547	+	0.605314i	0.666589	+	0.745426i	$0.267754\pi$
$398$	4.66277	−	3.43492i	0.233723	−	0.172177i
$399$	−1.50971	−	3.64477i	−0.0755802	−	0.182467i
$400$	2.84413	+	1.22124i	0.142207	+	0.0610618i
$401$	1.28050	−	3.09140i	0.0639451	−	0.154377i	−0.888677	−	0.458534i	$-0.848375\pi$
$401$	1.28050	−	3.09140i	0.0639451	−	0.154377i	0.952622	+	0.304157i	$0.0983747\pi$
$402$	3.94644	+	15.9732i	0.196831	+	0.796669i
$403$	−13.7351	−	45.2785i	−0.684193	−	2.25548i
$404$	−5.01453	−	7.61044i	−0.249482	−	0.378633i
$405$	−2.04587	+	0.201501i	−0.101660	+	0.0100127i
$406$	−27.0762	−	6.87497i	−1.34377	−	0.341199i
$407$	−3.21262	+	2.14661i	−0.159244	+	0.106403i
$408$	−1.79918	+	1.94695i	−0.0890727	+	0.0963884i
$409$	17.7616	−	26.5821i	0.878254	−	1.31440i	−0.0702160	−	0.997532i	$-0.522369\pi$
$409$	17.7616	−	26.5821i	0.878254	−	1.31440i	0.948470	−	0.316868i	$-0.102631\pi$
$410$	−14.1642	−	0.741574i	−0.699518	−	0.0366237i
$411$	2.74895	−	9.06209i	0.135596	−	0.447000i
$412$	−7.62800	−	25.7419i	−0.375805	−	1.26821i
$413$	42.0120	−	34.4783i	2.06727	−	1.69657i
$414$	2.52750	−	2.77068i	0.124220	−	0.136172i
$415$	−4.57232	+	4.57232i	−0.224446	+	0.224446i
$416$	−29.0243	+	3.82880i	−1.42303	+	0.187722i
$417$	5.72260	+	5.72260i	0.280237	+	0.280237i
$418$	3.89233	−	0.178654i	0.190380	−	0.00873826i
$419$	5.79797	+	7.06485i	0.283250	+	0.345141i	0.895126	−	0.445812i	$-0.147085\pi$
$419$	5.79797	+	7.06485i	0.283250	+	0.345141i	−0.611877	+	0.790953i	$0.709585\pi$
$420$	1.67148	−	15.9190i	0.0815600	−	0.776768i
$421$	18.0276	+	5.46862i	0.878612	+	0.266524i	0.697195	−	0.716882i	$-0.254431\pi$
$421$	18.0276	+	5.46862i	0.878612	+	0.266524i	0.181418	+	0.983406i	$0.441931\pi$
$422$	15.1169	−	13.6127i	0.735878	−	0.662657i
$423$	9.56705	+	6.39250i	0.465166	+	0.310814i
$424$	26.8876	−	19.5414i	1.30578	−	0.949014i
$425$	−0.402934	−	0.603033i	−0.0195452	−	0.0292514i
$426$	−7.14423	−	12.0070i	−0.346139	−	0.581739i
$427$	1.93498	+	19.6462i	0.0936404	+	0.950747i
$428$	2.56950	−	3.79242i	0.124201	−	0.183313i
$429$	−13.4650	+	4.08457i	−0.650098	+	0.197205i
$430$	−15.0357	−	9.07802i	−0.725088	−	0.437781i
$431$	−1.07766	−	0.446380i	−0.0519089	−	0.0215014i	0.356578	−	0.934266i	$-0.383943\pi$
$431$	−1.07766	−	0.446380i	−0.0519089	−	0.0215014i	−0.408487	+	0.912764i	$0.633943\pi$
$432$	3.97536	+	0.443315i	0.191265	+	0.0213290i
$433$	−28.3209	+	11.7309i	−1.36102	+	0.563751i	−0.939337	−	0.342995i	$-0.888559\pi$
$433$	−28.3209	+	11.7309i	−1.36102	+	0.563751i	−0.421678	+	0.906746i	$0.638559\pi$
$434$	−49.7674	−	7.54618i	−2.38891	−	0.362228i
$435$	−9.19923	−	4.91709i	−0.441069	−	0.235756i
$436$	3.66650	+	1.54646i	0.175594	+	0.0740619i
$437$	2.07731	+	1.70481i	0.0993713	+	0.0815519i
$438$	9.57317	−	1.38855i	0.457424	−	0.0663476i
$439$	−1.79335	+	9.01578i	−0.0855919	+	0.430299i	0.914100	+	0.405488i	$0.132898\pi$
$439$	−1.79335	+	9.01578i	−0.0855919	+	0.430299i	−0.999692	+	0.0248112i	$0.992102\pi$
$440$	14.2253	+	6.89704i	0.678166	+	0.328804i
$441$	7.99927	−	1.59115i	0.380918	−	0.0757693i
$442$	6.19167	+	2.95288i	0.294508	+	0.140454i
$443$	−6.54002	−	12.2355i	−0.310726	−	0.581327i	0.677283	−	0.735722i	$-0.263157\pi$
$443$	−6.54002	−	12.2355i	−0.310726	−	0.581327i	−0.988009	+	0.154395i	$0.950657\pi$
$444$	−1.32363	−	2.51517i	−0.0628167	−	0.119365i
$445$	−5.01195	−	0.493634i	−0.237589	−	0.0234005i
$446$	−28.6837	−	10.3675i	−1.35821	−	0.490916i
$447$			22.6229i			1.07003i
$448$	−9.61496	+	29.6232i	−0.454264	+	1.39957i
$449$			24.9554i			1.17772i	0.808237	+	0.588858i	$0.200422\pi$
$449$			24.9554i			1.17772i	−0.808237	+	0.588858i	$0.799578\pi$
$450$	−0.371986	+	1.02917i	−0.0175356	+	0.0485155i
$451$	13.2004	+	1.30013i	0.621584	+	0.0612207i
$452$	−1.09783	−	0.340761i	−0.0516377	−	0.0160281i
$453$	−1.49317	−	2.79353i	−0.0701553	−	0.131251i
$454$	3.98990	−	8.36611i	0.187255	−	0.392641i
$455$	−40.6232	+	8.08046i	−1.90445	+	0.378818i
$456$	−0.168290	+	2.86126i	−0.00788090	+	0.133991i
$457$	3.09212	−	15.5451i	0.144643	−	0.727171i	−0.838582	−	0.544775i	$-0.816615\pi$
$457$	3.09212	−	15.5451i	0.144643	−	0.727171i	0.983225	−	0.182396i	$-0.0583851\pi$
$458$	−4.40984	−	30.4030i	−0.206058	−	1.42064i
$459$	−0.724513	−	0.594592i	−0.0338174	−	0.0277532i
$460$	4.10755	+	10.1000i	0.191515	+	0.470915i
$461$	−1.05628	−	0.564592i	−0.0491957	−	0.0262957i	0.446615	−	0.894726i	$-0.352629\pi$
$461$	−1.05628	−	0.564592i	−0.0491957	−	0.0262957i	−0.495811	+	0.868430i	$0.665129\pi$
$462$	−2.24410	+	14.7999i	−0.104405	+	0.688556i
$463$	−10.4730	+	4.33807i	−0.486723	+	0.201607i	−0.612530	−	0.790447i	$-0.709848\pi$
$463$	−10.4730	+	4.33807i	−0.486723	+	0.201607i	0.125807	+	0.992055i	$0.459848\pi$
$464$	15.5217	+	13.0766i	0.720578	+	0.607065i
$465$	−17.3646	−	7.19263i	−0.805262	−	0.333550i
$466$	−12.4925	+	20.6910i	−0.578703	+	0.958493i
$467$	18.3847	−	5.57694i	0.850743	−	0.258070i	0.165343	−	0.986236i	$-0.447127\pi$
$467$	18.3847	−	5.57694i	0.850743	−	0.258070i	0.685401	+	0.728166i	$0.259627\pi$
$468$	−1.95386	−	10.1645i	−0.0903174	−	0.469853i
$469$	−4.43952	−	45.0752i	−0.204998	−	2.08138i
$470$	−28.7479	+	17.1052i	−1.32604	+	0.789005i
$471$	11.7389	+	17.5685i	0.540901	+	0.809516i
$472$	−38.3933	+	9.22375i	−1.76720	+	0.424557i
$473$	13.6572	+	9.12546i	0.627959	+	0.419589i
$474$	13.8929	+	15.4280i	0.638122	+	0.708632i
$475$	−0.750381	−	0.227626i	−0.0344298	−	0.0104442i
$476$	5.67086	−	4.59315i	0.259923	−	0.210526i
$477$	7.45516	+	9.08414i	0.341349	+	0.415934i
$478$	−1.27548	−	27.7889i	−0.0583392	−	1.27103i
$479$	17.9411	+	17.9411i	0.819748	+	0.819748i	0.986071	−	0.166323i	$-0.0531895\pi$
$479$	17.9411	+	17.9411i	0.819748	+	0.819748i	−0.166323	+	0.986071i	$0.553189\pi$
$480$	−6.13844	+	9.87713i	−0.280180	+	0.450827i
$481$	−5.20048	+	5.20048i	−0.237121	+	0.237121i
$482$	15.3912	+	14.0404i	0.701052	+	0.639521i
$483$	−7.98052	+	6.54945i	−0.363126	+	0.298010i
$484$	6.34143	+	3.44226i	0.288247	+	0.156466i
$485$	6.20021	−	20.4394i	0.281537	−	0.928103i
$486$	−0.0739409	+	1.41228i	−0.00335403	+	0.0640623i
$487$	−15.4304	+	23.0933i	−0.699220	+	1.04646i	0.296590	+	0.955005i	$0.404151\pi$
$487$	−15.4304	+	23.0933i	−0.699220	+	1.04646i	−0.995810	+	0.0914515i	$0.970849\pi$
$488$	4.96212	−	13.4569i	0.224625	−	0.609164i
$489$	−16.1230	+	10.7730i	−0.729105	+	0.487172i
$490$	−5.83556	+	22.9826i	−0.263624	+	1.03825i
$491$	−8.71600	+	0.858451i	−0.393348	+	0.0387414i	−0.292758	−	0.956187i	$-0.594573\pi$
$491$	−8.71600	+	0.858451i	−0.393348	+	0.0387414i	−0.100590	+	0.994928i	$0.532073\pi$
$492$	−1.96514	+	9.55726i	−0.0885952	+	0.430875i
$493$	−1.38049	−	4.55085i	−0.0621739	−	0.204960i
$494$	7.20020	−	1.77893i	0.323953	−	0.0800380i
$495$	−2.13896	+	5.16391i	−0.0961392	+	0.232101i
$496$	30.1432	+	20.7076i	1.35347	+	0.929800i
$497$	14.7185	+	35.5337i	0.660216	+	1.59390i
$498$	2.63832	+	3.58141i	0.118226	+	0.160487i
$499$	10.6593	−	19.9421i	0.477174	−	0.892729i	−0.522034	−	0.852925i	$-0.674826\pi$
$499$	10.6593	−	19.9421i	0.477174	−	0.892729i	0.999207	−	0.0398045i	$-0.0126735\pi$
$500$	−16.6777	−	16.8940i	−0.745850	−	0.755521i
$501$	−1.80292	+	2.19687i	−0.0805486	+	0.0981488i
$502$	−5.09274	+	6.82075i	−0.227300	+	0.304425i
$503$	21.8529	+	4.34682i	0.974374	+	0.193815i	0.656507	−	0.754320i	$-0.272033\pi$
$503$	21.8529	+	4.34682i	0.974374	+	0.193815i	0.317867	+	0.948135i	$0.397033\pi$
$504$	−10.6549	−	2.77859i	−0.474608	−	0.123768i
$505$	1.82763	+	9.18809i	0.0813283	+	0.408865i
$506$	−3.40421	−	9.61161i	−0.151336	−	0.427288i
$507$	−12.1559	+	6.49749i	−0.539865	+	0.288564i
$508$	−13.4566	+	16.1832i	−0.597039	+	0.718013i
$509$	−1.51428	+	15.3747i	−0.0671193	+	0.681473i	0.901476	+	0.432830i	$0.142485\pi$
$509$	−1.51428	+	15.3747i	−0.0671193	+	0.681473i	−0.968595	+	0.248644i	$0.920015\pi$
$510$	2.46702	−	1.15710i	0.109241	−	0.0512374i
$511$	−26.6290			−1.17800
$512$	15.6751	−	16.3184i	0.692750	−	0.721178i
$513$	−1.01336			−0.0447408
$514$	21.4367	−	10.0544i	0.945531	−	0.443482i
$515$	−2.70497	+	27.4641i	−0.119195	+	1.21021i
$516$	−7.72506	+	9.29034i	−0.340077	+	0.408984i
$517$	27.5899	−	14.7471i	1.21340	−	0.648577i
$518$	2.61210	+	7.37514i	0.114769	+	0.324045i
$519$	−3.08496	−	15.5091i	−0.135415	−	0.680775i
$520$	29.1183	+	7.59347i	1.27692	+	0.332996i
$521$	−5.47730	−	1.08950i	−0.239965	−	0.0477320i	0.0736426	−	0.997285i	$-0.476538\pi$
$521$	−5.47730	−	1.08950i	−0.239965	−	0.0477320i	−0.313607	+	0.949553i	$0.601538\pi$
$522$	−4.29308	+	5.74975i	−0.187903	+	0.251660i
$523$	−14.4676	+	17.6288i	−0.632625	+	0.770855i	−0.986380	−	0.164483i	$-0.947405\pi$
$523$	−14.4676	+	17.6288i	−0.632625	+	0.770855i	0.353755	+	0.935338i	$0.384905\pi$
$524$	−6.60013	−	6.68570i	−0.288328	−	0.292066i
$525$	1.42008	−	2.65678i	0.0619774	−	0.115952i
$526$	21.0903	+	28.6293i	0.919583	+	1.24830i
$527$	−3.27925	−	7.91680i	−0.142846	−	0.344861i
$528$	6.15808	−	8.96406i	0.267996	−	0.390111i
$529$	−6.11051	+	14.7521i	−0.265674	+	0.641395i
$530$	−33.1682	+	8.19477i	−1.44073	+	0.355958i
$531$	−4.05247	−	13.3592i	−0.175862	−	0.579740i
$532$	1.58910	−	7.72846i	0.0688963	−	0.335071i
$533$	25.1265	−	2.47475i	1.08835	−	0.107193i
$534$	−0.852629	+	3.35797i	−0.0368969	+	0.145313i
$535$	−3.91510	+	2.61599i	−0.169265	+	0.113099i
$536$	−11.3848	+	30.8748i	−0.491750	+	1.33359i
$537$	−8.66579	+	12.9693i	−0.373956	+	0.559665i
$538$	2.07895	−	39.7082i	0.0896299	−	1.71194i
$539$	6.43709	−	21.2202i	0.277265	−	0.914021i
$540$	−3.61350	−	1.96148i	−0.155500	−	0.0844087i
$541$	26.6579	−	21.8776i	1.14611	−	0.940591i	0.147290	−	0.989093i	$-0.452945\pi$
$541$	26.6579	−	21.8776i	1.14611	−	0.940591i	0.998823	+	0.0485027i	$0.0154449\pi$
$542$	−18.4070	−	16.7914i	−0.790648	−	0.721253i
$543$	9.48493	−	9.48493i	0.407037	−	0.407037i
$544$	−5.16313	+	1.20529i	−0.221368	+	0.0516763i
$545$	−2.89225	−	2.89225i	−0.123890	−	0.123890i
$546$	1.30643	+	28.4632i	0.0559102	+	1.21811i
$547$	−21.2828	−	25.9331i	−0.909986	−	1.10882i	−0.993671	−	0.112329i	$-0.964169\pi$
$547$	−21.2828	−	25.9331i	−0.909986	−	1.10882i	0.0836852	−	0.996492i	$-0.473331\pi$
$548$	14.7177	−	11.9207i	0.628708	−	0.509226i
$549$	4.85252	+	1.47200i	0.207101	+	0.0628233i
$550$	1.99101	+	2.21101i	0.0848971	+	0.0942779i
$551$	−4.27520	−	2.85659i	−0.182129	−	0.121695i
$552$	7.29313	−	1.75213i	0.310416	−	0.0745755i
$553$	−31.7521	−	47.5204i	−1.35024	−	2.02077i
$554$	7.78202	−	4.63036i	0.330626	−	0.196725i
$555$	0.286353	+	2.90739i	0.0121550	+	0.123412i
$556$	3.05541	+	15.8950i	0.129578	+	0.674097i
$557$	3.49924	−	1.06148i	0.148267	−	0.0449764i	−0.215279	−	0.976553i	$-0.569066\pi$
$557$	3.49924	−	1.06148i	0.148267	−	0.0449764i	0.363546	+	0.931576i	$0.381566\pi$
$558$	−6.68288	+	11.0687i	−0.282909	+	0.468576i
$559$	28.8852	+	11.9647i	1.22171	+	0.506051i
$560$	20.6259	−	24.4827i	0.871605	−	1.03458i
$561$	−2.35432	+	0.975190i	−0.0993993	+	0.0411725i
$562$	2.22405	−	14.6677i	0.0938157	−	0.618719i
$563$	−7.31924	−	3.91221i	−0.308469	−	0.164880i	0.309897	−	0.950770i	$-0.399705\pi$
$563$	−7.31924	−	3.91221i	−0.308469	−	0.164880i	−0.618367	+	0.785890i	$0.712205\pi$
$564$	8.66933	+	21.3169i	0.365045	+	0.897605i
$565$	0.913355	+	0.749571i	0.0384251	+	0.0315347i
$566$	0.753852	+	5.19733i	0.0316868	+	0.218460i
$567$	0.759500	−	3.81826i	0.0318960	−	0.160352i
$568$	1.64070	−	27.8951i	0.0688421	−	1.17045i
$569$	−3.61133	+	0.718338i	−0.151395	+	0.0301143i	−0.270206	−	0.962803i	$-0.587092\pi$
$569$	−3.61133	+	0.718338i	−0.151395	+	0.0301143i	0.118811	+	0.992917i	$0.462092\pi$
$570$	1.26820	−	2.65920i	0.0531192	−	0.111382i
$571$	−11.3502	−	21.2348i	−0.474993	−	0.888650i	−0.999311	−	0.0371268i	$-0.988179\pi$
$571$	−11.3502	−	21.2348i	−0.474993	−	0.888650i	0.524317	−	0.851523i	$-0.324321\pi$
$572$	−26.8769	−	8.34243i	−1.12378	−	0.348815i
$573$	−8.05498	−	0.793346i	−0.336501	−	0.0331425i
$574$	9.13019	−	25.2604i	0.381087	−	1.05435i
$575$			2.05205i			0.0855764i
$576$	6.08487	+	5.19369i	0.253536	+	0.216404i
$577$			44.1320i			1.83724i	0.395145	+	0.918619i	$0.370694\pi$
$577$			44.1320i			1.83724i	−0.395145	+	0.918619i	$0.629306\pi$
$578$	−21.4417	−	7.74995i	−0.891857	−	0.322355i
$579$	−0.400804	−	0.0394758i	−0.0166568	−	0.00164056i
$580$	−9.71547	−	18.4614i	−0.403413	−	0.766569i
$581$	−5.77239	−	10.7994i	−0.239479	−	0.448034i
$582$	−13.2624	−	6.32499i	−0.549744	−	0.262179i
$583$	31.3373	−	6.23338i	1.29786	−	0.258160i
$584$	17.4085	+	8.44037i	0.720368	+	0.349265i
$585$	−2.07560	+	10.4347i	−0.0858155	+	0.431424i
$586$	−32.3856	+	4.69741i	−1.33784	+	0.194048i
$587$	11.6822	+	9.58737i	0.482178	+	0.395713i	0.843839	−	0.536596i	$-0.180290\pi$
$587$	11.6822	+	9.58737i	0.482178	+	0.395713i	−0.361661	+	0.932310i	$0.617790\pi$
$588$	15.0298	+	6.33926i	0.619818	+	0.261427i
$589$	−8.17083	−	4.36740i	−0.336673	−	0.179956i
$590$	40.1281	+	6.08459i	1.65205	+	0.250499i
$591$	−0.807411	+	0.334441i	−0.0332125	+	0.0137571i
$592$	0.629995	−	5.64938i	0.0258926	−	0.232188i
$593$	−25.3358	−	10.4944i	−1.04042	−	0.430955i	−0.203956	−	0.978980i	$-0.565380\pi$
$593$	−25.3358	−	10.4944i	−1.04042	−	0.430955i	−0.836462	+	0.548025i	$0.815380\pi$
$594$	3.29164	+	1.98737i	0.135058	+	0.0815428i
$595$	−7.17814	+	2.17747i	−0.294275	+	0.0892674i
$596$	−25.3791	+	37.4579i	−1.03957	+	1.53433i
$597$	0.401393	+	4.07541i	0.0164279	+	0.166795i
$598$	−9.92454	−	16.6797i	−0.405844	−	0.682083i
$599$	9.23583	+	13.8224i	0.377366	+	0.564768i	0.970732	−	0.240165i	$-0.0772014\pi$
$599$	9.23583	+	13.8224i	0.377366	+	0.564768i	−0.593366	+	0.804933i	$0.702201\pi$
$600$	−1.77047	+	1.28674i	−0.0722790	+	0.0525310i
$601$	6.53985	+	4.36979i	0.266766	+	0.178247i	0.681758	−	0.731578i	$-0.261216\pi$
$601$	6.53985	+	4.36979i	0.266766	+	0.178247i	−0.414992	+	0.909825i	$0.636216\pi$
$602$	24.7165	−	22.2572i	1.00737	−	0.907135i
$603$	−11.1334	−	3.37727i	−0.453386	−	0.137533i
$604$	0.661543	−	6.30046i	0.0269178	−	0.256362i
$605$	−4.70508	−	5.73316i	−0.191289	−	0.233086i
$606$	6.43776	−	0.295487i	0.261516	−	0.0120033i
$607$	25.6398	+	25.6398i	1.04069	+	1.04069i	0.999136	+	0.0415524i	$0.0132304\pi$
$607$	25.6398	+	25.6398i	1.04069	+	1.04069i	0.0415524	+	0.999136i	$0.486770\pi$
$608$	−3.48849	+	4.54874i	−0.141477	+	0.184476i
$609$	13.9677	−	13.9677i	0.565999	−	0.565999i
$610$	−9.93561	+	10.8916i	−0.402281	+	0.440986i
$611$	46.0310	−	37.7767i	1.86221	−	1.52828i
$612$	−0.532580	−	1.79727i	−0.0215283	−	0.0726505i
$613$	−11.2008	+	36.9241i	−0.452397	+	1.49135i	0.373554	+	0.927609i	$0.378139\pi$
$613$	−11.2008	+	36.9241i	−0.452397	+	1.49135i	−0.825950	+	0.563743i	$0.809361\pi$
$614$	31.6359	+	1.65632i	1.27672	+	0.0668435i
$615$	5.57197	−	8.33905i	0.224684	−	0.336263i
$616$	−20.3187	+	21.9875i	−0.818662	+	0.885901i
$617$	−14.3961	+	9.61914i	−0.579563	+	0.387252i	−0.810519	−	0.585712i	$-0.800815\pi$
$617$	−14.3961	+	9.61914i	−0.579563	+	0.387252i	0.230956	+	0.972964i	$0.425815\pi$
$618$	18.4007	+	4.67217i	0.740185	+	0.187942i
$619$	−15.6405	+	1.54046i	−0.628646	+	0.0619163i	−0.407323	−	0.913284i	$-0.633538\pi$
$619$	−15.6405	+	1.54046i	−0.628646	+	0.0619163i	−0.221323	+	0.975200i	$0.571038\pi$
$620$	−20.6824	−	31.3892i	−0.830626	−	1.26062i
$621$	0.769800	+	2.53769i	0.0308910	+	0.101834i
$622$	5.87237	+	23.7683i	0.235461	+	0.953023i
$623$	3.64973	−	8.81122i	0.146223	−	0.353014i
$624$	8.16768	−	19.0217i	0.326969	−	0.761477i
$625$	7.85732	+	18.9693i	0.314293	+	0.758770i
$626$	14.2127	−	10.4701i	0.568053	−	0.418468i
$627$	−1.29879	+	2.42986i	−0.0518686	+	0.0970393i
$628$	−0.272192	+	42.2582i	−0.0108617	+	1.68628i
$629$	−0.844975	+	1.02960i	−0.0336913	+	0.0410530i
$630$	9.06919	+	6.77155i	0.361325	+	0.269785i
$631$	−4.80678	−	0.956128i	−0.191355	−	0.0380628i	0.0984824	−	0.995139i	$-0.468601\pi$
$631$	−4.80678	−	0.956128i	−0.191355	−	0.0380628i	−0.289837	+	0.957076i	$0.593601\pi$
$632$	5.69555	+	41.1303i	0.226557	+	1.63608i
$633$	2.80627	+	14.1081i	0.111539	+	0.560746i
$634$	−22.6715	+	8.02971i	−0.900398	+	0.318900i
$635$	19.0794	−	10.1981i	0.757141	−	0.404700i
$636$	2.15302	+	23.4045i	0.0853728	+	0.928047i
$637$	4.13725	−	42.0062i	0.163924	−	1.66435i
$638$	8.28464	+	17.6633i	0.327992	+	0.699299i
$639$	9.87945			0.390825
$640$	−21.2441	+	9.46776i	−0.839749	+	0.374246i
$641$	2.06989			0.0817559			0.0408780	−	0.999164i	$-0.486985\pi$
$641$	2.06989			0.0817559			0.0408780	+	0.999164i	$0.486985\pi$
$642$	1.37550	+	2.93264i	0.0542865	+	0.115742i
$643$	−1.21959	+	12.3827i	−0.0480958	+	0.488325i	0.940720	+	0.339184i	$0.110151\pi$
$643$	−1.21959	+	12.3827i	−0.0480958	+	0.488325i	−0.988816	+	0.149141i	$0.952349\pi$
$644$	−20.5611	+	1.89145i	−0.810220	+	0.0745337i
$645$	10.9530	−	5.85448i	0.431272	−	0.230520i
$646$	1.26613	−	0.448433i	0.0498150	−	0.0176433i
$647$	3.72365	+	18.7201i	0.146392	+	0.735961i	0.982333	+	0.187142i	$0.0599225\pi$
$647$	3.72365	+	18.7201i	0.146392	+	0.735961i	−0.835941	+	0.548819i	$0.815077\pi$
$648$	−1.70676	+	2.25543i	−0.0670480	+	0.0886016i
$649$	−37.2270	−	7.40491i	−1.46129	−	0.290668i
$650$	4.53805	+	3.38836i	0.177997	+	0.132902i
$651$	22.5800	−	27.5138i	0.884981	−	1.07835i
$652$	−38.7810	−	0.249795i	−1.51878	−	0.00978274i
$653$	−12.1917	+	22.8091i	−0.477099	+	0.892590i	0.522112	+	0.852877i	$0.325144\pi$
$653$	−12.1917	+	22.8091i	−0.477099	+	0.892590i	−0.999211	+	0.0397130i	$0.987356\pi$
$654$	−2.26544	+	1.66888i	−0.0885857	+	0.0652585i
$655$	3.69545	+	8.92160i	0.144393	+	0.348596i
$656$	−13.9754	+	13.6199i	−0.545647	+	0.531767i
$657$	−2.61759	+	6.31942i	−0.102122	+	0.246544i
$658$	−15.1945	−	61.4996i	−0.592344	−	2.39750i
$659$	4.32945	+	14.2723i	0.168651	+	0.555969i	1.00000		0.000217919i	$6.93658e-5\pi$
$659$	4.32945	+	14.2723i	0.168651	+	0.555969i	−0.831349	+	0.555751i	$0.812431\pi$
$660$	−9.33461	+	6.15059i	−0.363349	+	0.239411i
$661$	−22.8212	+	2.24769i	−0.887640	+	0.0874250i	−0.531550	−	0.847027i	$-0.678390\pi$
$661$	−22.8212	+	2.24769i	−0.887640	+	0.0874250i	−0.356090	+	0.934452i	$0.615890\pi$
$662$	−1.37173	−	0.348299i	−0.0533138	−	0.0135370i
$663$	−4.03311	+	2.69484i	−0.156633	+	0.104659i
$664$	0.350663	+	8.88965i	0.0136084	+	0.344985i
$665$	−4.50576	+	6.74335i	−0.174726	+	0.261496i
$666$	2.00699	+	0.105077i	0.0777693	+	0.00407166i
$667$	−3.90593	+	12.8761i	−0.151238	+	0.498566i
$668$	−5.44969	+	1.61489i	−0.210855	+	0.0624819i
$669$	16.6712	−	13.6817i	0.644548	−	0.528967i
$670$	22.7958	−	24.9890i	0.880677	−	0.965410i
$671$	9.74893	−	9.74893i	0.376353	−	0.376353i
$672$	−14.5248	−	16.5536i	−0.560305	−	0.638570i
$673$	−25.0711	−	25.0711i	−0.966420	−	0.966420i	0.0330338	−	0.999454i	$-0.489483\pi$
$673$	−25.0711	−	25.0711i	−0.966420	−	0.966420i	−0.999454	+	0.0330338i	$0.989483\pi$
$674$	−37.4736	+	1.72000i	−1.44343	+	0.0662519i
$675$	−0.490900	−	0.598163i	−0.0188947	−	0.0230233i
$676$	−27.4163	−	2.87868i	−1.05447	−	0.110719i
$677$	−16.2234	−	4.92133i	−0.623517	−	0.189142i	−0.0373110	−	0.999304i	$-0.511879\pi$
$677$	−16.2234	−	4.92133i	−0.623517	−	0.189142i	−0.586206	+	0.810162i	$0.699379\pi$
$678$	0.604015	−	0.543914i	0.0231971	−	0.0208889i
$679$	33.6315	+	22.4719i	1.29066	+	0.862390i
$680$	5.38283	+	0.851697i	0.206422	+	0.0326611i
$681$	3.64123	+	5.44949i	0.139532	+	0.208825i
$682$	17.9757	+	30.2108i	0.688325	+	1.15683i
$683$	−0.385440	−	3.91344i	−0.0147485	−	0.149744i	0.984990	−	0.172611i	$-0.0552204\pi$
$683$	−0.385440	−	3.91344i	−0.0147485	−	0.149744i	−0.999739	+	0.0228675i	$0.992720\pi$
$684$	−1.67786	−	1.13681i	−0.0641547	−	0.0434671i
$685$	−18.6296	+	5.65122i	−0.711799	+	0.215922i
$686$	−5.44840	−	3.28954i	−0.208021	−	0.125595i
$687$	20.0696	+	8.31308i	0.765701	+	0.317164i
$688$	−23.2129	+	6.71626i	−0.884984	+	0.256055i
$689$	56.1885	−	23.2740i	2.14061	−	0.886670i
$690$	−7.62267	−	1.15582i	−0.290190	−	0.0440013i
$691$	−17.6387	−	9.42808i	−0.671008	−	0.358661i	0.100450	−	0.994942i	$-0.467972\pi$
$691$	−17.6387	−	9.42808i	−0.671008	−	0.358661i	−0.771457	+	0.636281i	$0.780472\pi$
$692$	12.2907	−	29.1400i	0.467221	−	1.10774i
$693$	−8.18213	−	6.71490i	−0.310813	−	0.255078i
$694$	−29.8251	+	4.32602i	−1.13215	+	0.164214i
$695$	3.24578	−	16.3176i	0.123119	−	0.618963i
$696$	−13.5585	+	4.70404i	−0.513933	+	0.178306i
$697$	4.48466	−	0.892055i	0.169869	−	0.0337890i
$698$	−3.40902	−	1.62580i	−0.129033	−	0.0615374i
$699$	−8.05648	−	15.0726i	−0.304724	−	0.570098i
$700$	5.33175	−	2.80588i	0.201521	−	0.106052i
$701$	−38.5412	−	3.79597i	−1.45568	−	0.143372i	−0.660993	−	0.750392i	$-0.729865\pi$
$701$	−38.5412	−	3.79597i	−1.45568	−	0.143372i	−0.794686	+	0.607020i	$0.792365\pi$
$702$	6.88313	+	2.48786i	0.259787	+	0.0938982i
$703$			1.44008i			0.0543137i
$704$	20.2524	−	7.93391i	0.763290	−	0.299020i
$705$		−	23.6541i		−	0.890864i
$706$	15.5937	−	43.1430i	0.586877	−	1.62371i
$707$	−17.6552	−	1.73889i	−0.663992	−	0.0653975i
$708$	8.27686	−	26.6656i	0.311063	−	1.00216i
$709$	−7.05544	−	13.1998i	−0.264972	−	0.495729i	0.713887	−	0.700260i	$-0.246933\pi$
$709$	−7.05544	−	13.1998i	−0.264972	−	0.495729i	−0.978860	+	0.204532i	$0.934433\pi$
$710$	−12.3640	+	25.9251i	−0.464013	+	0.972953i
$711$	−14.3984	+	2.86403i	−0.539984	+	0.107410i
$712$	−5.17880	+	4.60344i	−0.194084	+	0.172521i
$713$	−4.73002	+	23.7794i	−0.177141	+	0.890547i
$714$	0.740718	+	5.10677i	0.0277207	+	0.191116i
$715$	22.3605	+	18.3508i	0.836237	+	0.686282i
$716$	−28.8977	+	11.7523i	−1.07996	+	0.439204i
$717$	17.3477	+	9.27255i	0.647863	+	0.346290i
$718$	−4.81483	+	31.7541i	−0.179688	+	1.18505i
$719$	15.8784	−	6.57706i	0.592166	−	0.245283i	−0.0664164	−	0.997792i	$-0.521157\pi$
$719$	15.8784	−	6.57706i	0.592166	−	0.245283i	0.658582	+	0.752509i	$0.271157\pi$
$720$	−3.78259	−	7.30144i	−0.140969	−	0.272109i
$721$	−48.2830	−	19.9995i	−1.79815	−	0.744819i
$722$	−13.1375	+	21.7594i	−0.488928	+	0.809801i
$723$	−14.0970	+	4.27627i	−0.524272	+	0.159036i
$724$	26.3451	−	5.06419i	0.979109	−	0.188209i
$725$	−0.384843	−	3.90737i	−0.0142927	−	0.145116i
$726$	−4.38464	+	2.60890i	−0.162729	+	0.0968252i
$727$	21.7885	+	32.6088i	0.808090	+	1.20939i	0.974733	+	0.223374i	$0.0717072\pi$
$727$	21.7885	+	32.6088i	0.808090	+	1.20939i	−0.166643	+	0.986017i	$0.553293\pi$
$728$	−29.7677	+	48.5935i	−1.10326	+	1.80099i
$729$	−0.831470	−	0.555570i	−0.0307952	−	0.0205767i
$730$	−13.3072	−	14.7776i	−0.492522	−	0.546944i
$731$	5.41842	+	1.64366i	0.200407	+	0.0607929i
$732$	6.38323	+	7.88096i	0.235931	+	0.291289i
$733$	−18.4673	−	22.5025i	−0.682105	−	0.831147i	0.310748	−	0.950492i	$-0.399421\pi$
$733$	−18.4673	−	22.5025i	−0.682105	−	0.831147i	−0.992853	+	0.119345i	$0.961921\pi$
$734$	2.07637	+	45.2378i	0.0766402	+	1.66976i
$735$	−11.8559	−	11.8559i	−0.437313	−	0.437313i
$736$	14.0412	+	5.28056i	0.517565	+	0.194644i
$737$	−22.3674	+	22.3674i	−0.823915	+	0.823915i
$738$	−5.09716	−	4.64978i	−0.187629	−	0.171161i
$739$	31.3418	−	25.7215i	1.15293	−	0.946181i	0.153804	−	0.988101i	$-0.450848\pi$
$739$	31.3418	−	25.7215i	1.15293	−	0.946181i	0.999121	+	0.0419202i	$0.0133475\pi$
$740$	−2.78746	+	5.13514i	−0.102469	+	0.188771i
$741$	−1.52237	+	5.01858i	−0.0559257	+	0.184362i
$742$	3.38279	−	64.6117i	0.124186	−	2.37197i
$743$	16.0137	−	23.9661i	0.587485	−	0.879233i	−0.412005	−	0.911182i	$-0.635171\pi$
$743$	16.0137	−	23.9661i	0.587485	−	0.879233i	0.999490	+	0.0319489i	$0.0101714\pi$
$744$	−23.4824	+	10.8300i	−0.860905	+	0.397045i
$745$	38.6696	−	25.8382i	1.41675	−	0.946639i
$746$	10.2771	−	40.4752i	0.376273	−	1.48190i
$747$	−3.13026	+	0.308304i	−0.114530	+	0.0112803i
$748$	−4.99215	−	1.02647i	−0.182531	−	0.0375315i
$749$	−2.58844	−	8.53295i	−0.0945796	−	0.311787i
$750$	16.2962	−	4.02625i	0.595052	−	0.147018i
$751$	20.2035	−	48.7757i	0.737238	−	1.77985i	0.120450	−	0.992719i	$-0.461566\pi$
$751$	20.2035	−	48.7757i	0.737238	−	1.77985i	0.616787	−	0.787130i	$-0.288434\pi$
$752$	−9.55973	+	45.0210i	−0.348607	+	1.64175i
$753$	−2.30340	−	5.56091i	−0.0839407	−	0.202651i
$754$	22.0257	+	29.8990i	0.802130	+	1.08886i
$755$	−3.06962	+	5.74285i	−0.111715	+	0.209004i
$756$	5.54098	−	5.47006i	0.201523	−	0.198944i
$757$	17.5045	−	21.3293i	0.636211	−	0.775225i	−0.350701	−	0.936488i	$-0.614057\pi$
$757$	17.5045	−	21.3293i	0.636211	−	0.775225i	0.986912	+	0.161263i	$0.0515566\pi$
$758$	29.2768	−	39.2107i	1.06338	−	1.42420i
$759$	7.07158	+	1.40663i	0.256682	+	0.0510573i
$760$	5.08299	−	2.98026i	0.184380	−	0.108105i
$761$	8.08830	+	40.6626i	0.293201	+	1.47402i	0.793714	+	0.608291i	$0.208145\pi$
$761$	8.08830	+	40.6626i	0.293201	+	1.47402i	−0.500514	+	0.865729i	$0.666855\pi$
$762$	−4.96859	−	14.0286i	−0.179993	−	0.508201i
$763$	6.83122	−	3.65136i	0.247307	−	0.132188i
$764$	−12.4470	−	10.3499i	−0.450317	−	0.374446i
$765$	−0.188859	+	1.91752i	−0.00682820	+	0.0693279i
$766$	−6.62860	+	3.10901i	−0.239501	+	0.112333i
$767$	−72.2485			−2.60874
$768$	4.24858	+	15.4256i	0.153307	+	0.556624i
$769$	31.8926			1.15008			0.575038	−	0.818127i	$-0.304987\pi$
$769$	31.8926			1.15008			0.575038	+	0.818127i	$0.304987\pi$
$770$	27.8607	−	13.0675i	1.00403	−	0.470921i
$771$	−1.64105	+	16.6619i	−0.0591011	+	0.600063i
$772$	−0.619345	−	0.514995i	−0.0222907	−	0.0185351i
$773$	−35.5868	+	19.0215i	−1.27997	+	0.684157i	−0.964325	−	0.264721i	$-0.914720\pi$
$773$	−35.5868	+	19.0215i	−1.27997	+	0.684157i	−0.315643	+	0.948878i	$0.602220\pi$
$774$	−2.85234	−	8.05342i	−0.102525	−	0.289474i
$775$	−1.38021	−	6.93876i	−0.0495784	−	0.249248i
$776$	−14.8636	−	25.3507i	−0.533573	−	0.910038i
$777$	−5.42613	−	1.07933i	−0.194661	−	0.0387206i
$778$	−20.4040	+	27.3273i	−0.731520	+	0.979731i
$779$	3.13629	−	3.82158i	0.112369	−	0.136922i
$780$	−15.1427	+	14.9488i	−0.542195	+	0.535255i
$781$	12.6622	−	23.6892i	0.453088	−	0.847668i
$782$	−2.08480	−	2.83003i	−0.0745523	−	0.101202i
$783$	−1.94172	−	4.68773i	−0.0693914	−	0.167526i
$784$	17.7740	+	27.3571i	0.634784	+	0.977038i
$785$	16.6228	−	40.1309i	0.593292	−	1.43233i
$786$	6.44914	−	1.59337i	0.230033	−	0.0568336i
$787$	5.76027	+	18.9891i	0.205332	+	0.676887i	0.997758	+	0.0669203i	$0.0213173\pi$
$787$	5.76027	+	18.9891i	0.205332	+	0.676887i	−0.792427	+	0.609967i	$0.791183\pi$
$788$	−1.71205	−	0.352027i	−0.0609894	−	0.0125405i
$789$	−25.0229	+	2.46454i	−0.890839	+	0.0877399i
$790$	10.5038	−	41.3680i	0.373710	−	1.47181i
$791$	−1.86045	+	1.24311i	−0.0661500	+	0.0442000i
$792$	3.22064	+	6.98324i	0.114440	+	0.248139i
$793$	14.5799	−	21.8204i	0.517748	−	0.774865i
$794$	1.01119	−	19.3138i	0.0358856	−	0.685420i
$795$	7.01289	−	23.1184i	0.248722	−	0.819926i
$796$	−3.90730	+	7.19814i	−0.138491	+	0.255131i
$797$	15.5370	−	12.7509i	0.550348	−	0.451659i	−0.317663	−	0.948204i	$-0.602898\pi$
$797$	15.5370	−	12.7509i	0.550348	−	0.451659i	0.868011	+	0.496545i	$0.165398\pi$
$798$	4.12181	+	3.76004i	0.145910	+	0.133104i
$799$	7.62565	−	7.62565i	0.269776	−	0.269776i
$800$	−4.37495	+	0.144359i	−0.154678	+	0.00510385i
$801$	−1.73226	−	1.73226i	−0.0612064	−	0.0612064i
$802$	0.216971	+	4.72713i	0.00766150	+	0.166921i
$803$	11.7980	+	14.3759i	0.416343	+	0.507316i
$804$	−14.6453	−	18.0817i	−0.516502	−	0.637691i
$805$	20.3098	+	6.16091i	0.715826	+	0.217143i
$806$	44.7773	+	49.7251i	1.57721	+	1.75149i
$807$	23.3779	+	15.6206i	0.822942	+	0.549872i
$808$	10.9908	+	6.73281i	0.386655	+	0.236860i
$809$	−11.1862	−	16.7413i	−0.393285	−	0.588592i	0.581002	−	0.813902i	$-0.302661\pi$
$809$	−11.1862	−	16.7413i	−0.393285	−	0.588592i	−0.974287	+	0.225310i	$0.927661\pi$
$810$	2.49847	−	1.48661i	0.0877874	−	0.0522342i
$811$	−1.68995	−	17.1583i	−0.0593420	−	0.602510i	−0.978164	−	0.207837i	$-0.933358\pi$
$811$	−1.68995	−	17.1583i	−0.0593420	−	0.602510i	0.918822	−	0.394673i	$-0.129142\pi$
$812$	38.7963	−	7.45761i	1.36148	−	0.261711i
$813$	16.8591	−	5.11416i	0.591275	−	0.179361i
$814$	2.82425	−	4.67775i	0.0989900	−	0.163955i
$815$	36.8288	+	15.2550i	1.29006	+	0.534360i
$816$	1.13441	−	3.57329i	0.0397125	−	0.125090i
$817$	5.65594	−	2.34277i	0.197876	−	0.0819630i
$818$	−6.77804	+	44.7015i	−0.236989	+	1.56295i
$819$	−17.7687	−	9.49756i	−0.620888	−	0.331872i
$820$	18.5808	−	7.55656i	0.648868	−	0.263886i
$821$	15.3484	+	12.5961i	0.535662	+	0.439606i	0.862929	−	0.505326i	$-0.168628\pi$
$821$	15.3484	+	12.5961i	0.535662	+	0.439606i	−0.327267	+	0.944932i	$0.606128\pi$
$822$	1.92240	+	13.2537i	0.0670514	+	0.462276i
$823$	6.50061	−	32.6808i	0.226597	−	1.13918i	−0.685142	−	0.728410i	$-0.740260\pi$
$823$	6.50061	−	32.6808i	0.226597	−	1.13918i	0.911739	−	0.410770i	$-0.134740\pi$
$824$	25.2256	+	28.3784i	0.878774	+	0.988608i
$825$	−2.06346	+	0.410449i	−0.0718406	+	0.0142900i
$826$	−33.0856	+	69.3748i	−1.15120	+	2.41386i
$827$	3.69186	+	6.90698i	0.128378	+	0.240179i	0.937896	−	0.346916i	$-0.112771\pi$
$827$	3.69186	+	6.90698i	0.128378	+	0.240179i	−0.809518	+	0.587096i	$0.800271\pi$
$828$	−1.57226	+	5.06536i	−0.0546398	+	0.176033i
$829$	38.0042	+	3.74308i	1.31994	+	0.130003i	0.733333	−	0.679869i	$-0.237964\pi$
$829$	38.0042	+	3.74308i	1.31994	+	0.130003i	0.586606	+	0.809872i	$0.300464\pi$
$830$	3.10845	−	8.60011i	0.107896	−	0.298514i
$831$			6.40312i			0.222122i
$832$	34.8627	−	22.3324i	1.20865	−	0.774236i
$833$		−	7.64429i		−	0.264859i
$834$	−10.7637	−	3.89046i	−0.372716	−	0.134716i
$835$	5.81429	+	0.572657i	0.201212	+	0.0198176i
$836$	−4.87635	+	2.56622i	−0.168652	+	0.0887546i
$837$	−4.30983	−	8.06313i	−0.148970	−	0.278702i
$838$	−11.6663	−	5.56378i	−0.403004	−	0.192197i
$839$	32.7077	−	6.50596i	1.12919	−	0.224611i	0.405074	−	0.914284i	$-0.367246\pi$
$839$	32.7077	−	6.50596i	1.12919	−	0.224611i	0.724121	+	0.689673i	$0.242246\pi$
$840$	7.41977	+	21.3861i	0.256007	+	0.737889i
$841$	−0.635005	+	3.19239i	−0.0218967	+	0.110082i
$842$	−26.3662	+	3.82432i	−0.908639	+	0.131795i
$843$	8.10901	+	6.65489i	0.279289	+	0.229207i
$844$	−11.1804	+	26.5076i	−0.384844	+	0.912428i
$845$	24.9898	+	13.3573i	0.859677	+	0.459507i
$846$	−16.0883	−	2.43945i	−0.553128	−	0.0838702i
$847$	12.9760	−	5.37484i	0.445861	−	0.184682i
$848$	−22.6909	+	41.1672i	−0.779210	+	1.41369i
$849$	−3.43085	−	1.42110i	−0.117746	−	0.0487721i
$850$	0.878048	+	0.530133i	0.0301168	+	0.0181834i
$851$	3.60631	−	1.09396i	0.123623	−	0.0375006i
$852$	16.3579	+	11.0830i	0.560411	+	0.379699i
$853$	−0.175750	−	1.78441i	−0.00601755	−	0.0610972i	0.991707	−	0.128520i	$-0.0410225\pi$
$853$	−0.175750	−	1.78441i	−0.00601755	−	0.0610972i	−0.997725	+	0.0674224i	$0.978523\pi$
$854$	−14.2757	−	23.9925i	−0.488505	−	0.821006i
$855$	1.15738	+	1.73214i	0.0395816	+	0.0592380i
$856$	−1.01245	+	6.39879i	−0.0346047	+	0.218706i
$857$	−28.2959	−	18.9067i	−0.966571	−	0.645842i	−0.0312011	−	0.999513i	$-0.509933\pi$
$857$	−28.2959	−	18.9067i	−0.966571	−	0.645842i	−0.935370	+	0.353671i	$0.884933\pi$
$858$	14.7874	−	13.3160i	0.504832	−	0.454600i
$859$	−20.9507	−	6.35532i	−0.714828	−	0.216841i	−0.0881368	−	0.996108i	$-0.528091\pi$
$859$	−20.9507	−	6.35532i	−0.714828	−	0.216841i	−0.626691	+	0.779268i	$0.715591\pi$
$860$	24.7030	+	2.59380i	0.842367	+	0.0884478i
$861$	12.0489	+	14.6816i	0.410624	+	0.500347i
$862$	1.64787	−	0.0756357i	0.0561267	−	0.00257616i
$863$	−14.4252	−	14.4252i	−0.491040	−	0.491040i	0.417594	−	0.908634i	$-0.362874\pi$
$863$	−14.4252	−	14.4252i	−0.491040	−	0.491040i	−0.908634	+	0.417594i	$0.862874\pi$
$864$	−5.35617	+	1.81973i	−0.182221	+	0.0619084i
$865$	−22.9865	+	22.9865i	−0.781565	+	0.781565i
$866$	29.2166	−	32.0276i	0.992819	−	1.08834i
$867$	12.4621	−	10.2274i	0.423236	−	0.347341i
$868$	68.2526	−	20.2251i	2.31665	−	0.686483i
$869$	−11.5866	+	38.1958i	−0.393047	+	1.29570i
$870$	14.7313	+	0.771269i	0.499439	+	0.0261485i
$871$	−33.4514	+	50.0636i	−1.13346	+	1.69634i
$872$	−5.62320	+	0.221814i	−0.190426	+	0.00751156i
$873$	8.63881	−	5.77227i	0.292380	−	0.195362i
$874$	−3.68353	−	0.935294i	−0.124597	−	0.0316368i
$875$	−45.9868	+	4.52930i	−1.55464	+	0.153118i
$876$	−11.4234	+	7.52688i	−0.385960	+	0.254310i
$877$	−12.9355	−	42.6427i	−0.436802	−	1.43994i	−0.848779	−	0.528748i	$-0.822662\pi$
$877$	−12.9355	−	42.6427i	−0.436802	−	1.43994i	0.411977	−	0.911194i	$-0.364838\pi$
$878$	−3.11812	−	12.6205i	−0.105231	−	0.425922i
$879$	8.85519	−	21.3783i	0.298678	−	0.721073i
$880$	−22.3557	−	0.288005i	−0.753609	−	0.00970866i
$881$	9.98280	+	24.1006i	0.336329	+	0.811971i	0.998062	+	0.0622306i	$0.0198214\pi$
$881$	9.98280	+	24.1006i	0.336329	+	0.811971i	−0.661733	+	0.749740i	$0.730179\pi$
$882$	−9.28652	+	6.84111i	−0.312694	+	0.230352i
$883$	−12.1258	+	22.6858i	−0.408067	+	0.763440i	−0.999065	−	0.0432334i	$-0.986234\pi$
$883$	−12.1258	+	22.6858i	−0.408067	+	0.763440i	0.590998	+	0.806673i	$0.298734\pi$
$884$	−9.70097	−	0.0624857i	−0.326279	−	0.00210162i
$885$	−18.2066	+	22.1848i	−0.612008	+	0.745733i
$886$	15.7215	+	11.7385i	0.528175	+	0.394364i
$887$	14.2687	+	2.83821i	0.479095	+	0.0952979i	0.428729	−	0.903433i	$-0.358961\pi$
$887$	14.2687	+	2.83821i	0.479095	+	0.0952979i	0.0503656	+	0.998731i	$0.483961\pi$
$888$	3.20519	+	2.42548i	0.107559	+	0.0813938i
$889$	7.99259	+	40.1814i	0.268063	+	1.34764i
$890$	6.71362	−	2.37781i	0.225041	−	0.0797043i
$891$	−2.39783	+	1.28167i	−0.0803304	+	0.0429375i
$892$	42.9519	−	3.95123i	1.43814	−	0.132297i
$893$	1.14287	−	11.6037i	0.0382446	−	0.388304i
$894$	−13.5858	−	28.9658i	−0.454378	−	0.968762i
$895$	32.0659			1.07185
$896$	−5.47900	−	43.7029i	−0.183040	−	1.46001i
$897$	13.7242			0.458238
$898$	−14.9865	−	31.9522i	−0.500107	−	1.06626i
$899$	4.54698	−	46.1662i	0.151650	−	1.53973i
$900$	−0.141770	−	1.54111i	−0.00472566	−	0.0513704i
$901$	9.71380	−	5.19213i	0.323613	−	0.172975i
$902$	−17.6823	+	6.26265i	−0.588755	+	0.208524i
$903$	4.58833	+	23.0671i	0.152690	+	0.767625i
$904$	1.61028	−	0.222984i	0.0535570	−	0.00741633i
$905$	−27.0457	−	5.37972i	−0.899028	−	0.178828i
$906$	3.58942	+	2.68006i	0.119251	+	0.0890390i
$907$	−7.27878	+	8.86922i	−0.241688	+	0.294498i	−0.879700	−	0.475528i	$-0.842257\pi$
$907$	−7.27878	+	8.86922i	−0.241688	+	0.294498i	0.638012	+	0.770026i	$0.279757\pi$
$908$	−0.0844298	+	13.1078i	−0.00280190	+	0.434998i
$909$	−2.14814	+	4.01890i	−0.0712495	+	0.133298i
$910$	47.1603	−	34.7416i	1.56335	−	1.15167i
$911$	13.3412	+	32.2086i	0.442015	+	1.06712i	0.975241	+	0.221146i	$0.0709797\pi$
$911$	13.3412	+	32.2086i	0.442015	+	1.06712i	−0.533226	+	0.845973i	$0.679020\pi$
$912$	−1.50281	−	3.76455i	−0.0497630	−	0.124657i
$913$	−3.27270	+	7.90099i	−0.108310	+	0.261485i
$914$	5.37631	+	21.7605i	0.177833	+	0.719774i
$915$	−3.02609	−	9.97567i	−0.100039	−	0.329786i
$916$	23.9043	+	36.2790i	0.789819	+	1.19869i
$917$	−18.1990	+	1.79245i	−0.600985	+	0.0591919i
$918$	1.28472	+	0.326206i	0.0424021	+	0.0107664i
$919$	−10.3125	+	6.89061i	−0.340179	+	0.227300i	−0.713911	−	0.700236i	$-0.753078\pi$
$919$	−10.3125	+	6.89061i	−0.340179	+	0.227300i	0.373732	+	0.927537i	$0.378078\pi$
$920$	−11.3246	−	10.4651i	−0.373361	−	0.345023i
$921$	−12.4451	+	18.6254i	−0.410080	+	0.613728i
$922$	1.69149	+	0.0885589i	0.0557061	+	0.00291653i
$923$	14.8419	−	48.9273i	0.488528	−	1.61046i
$924$	−6.01458	−	20.2971i	−0.197865	−	0.667727i
$925$	−0.850049	+	0.697617i	−0.0279494	+	0.0229375i
$926$	10.8042	−	11.8438i	0.355050	−	0.389210i
$927$	−9.49231	+	9.49231i	−0.311768	+	0.311768i
$928$	−27.7266	−	7.42159i	−0.910169	−	0.243626i
$929$	−20.1991	−	20.1991i	−0.662712	−	0.662712i	0.293307	−	0.956018i	$-0.405244\pi$
$929$	−20.1991	−	20.1991i	−0.662712	−	0.662712i	−0.956018	+	0.293307i	$0.905244\pi$
$930$	26.5526	−	1.21874i	0.870692	−	0.0399639i
$931$	−5.24322	−	6.38888i	−0.171839	−	0.209387i
$932$	3.56939	−	33.9944i	0.116919	−	1.11352i
$933$	−16.5667	−	5.02544i	−0.542368	−	0.164526i
$934$	−20.1902	+	18.1812i	−0.660643	+	0.594908i
$935$	4.35582	+	2.91047i	0.142451	+	0.0951825i
$936$	8.60578	+	11.8410i	0.281289	+	0.387034i
$937$	12.6171	+	18.8828i	0.412181	+	0.616873i	0.978236	−	0.207495i	$-0.0665310\pi$
$937$	12.6171	+	18.8828i	0.412181	+	0.616873i	−0.566055	+	0.824368i	$0.691531\pi$
$938$	32.7535	+	55.0471i	1.06944	+	1.79735i
$939$	1.22349	+	12.4223i	0.0399271	+	0.405387i
$940$	26.5358	−	39.1652i	0.865503	−	1.27743i
$941$	14.1981	−	4.30694i	0.462844	−	0.140402i	−0.0502461	−	0.998737i	$-0.516001\pi$
$941$	14.1981	−	4.30694i	0.462844	−	0.140402i	0.513090	+	0.858335i	$0.328501\pi$
$942$	−25.5807	−	15.4447i	−0.833465	−	0.503216i
$943$	−11.9527	−	4.95095i	−0.389232	−	0.161225i
$944$	43.6187	−	34.8663i	1.41967	−	1.13480i
$945$	−7.39404	+	3.06271i	−0.240528	+	0.0996301i
$946$	−22.9665	−	3.48239i	−0.746705	−	0.113222i
$947$	35.0121	+	18.7143i	1.13774	+	0.608134i	0.929089	−	0.369856i	$-0.120593\pi$
$947$	35.0121	+	18.7143i	1.13774	+	0.608134i	0.208650	+	0.977990i	$0.433093\pi$
$948$	−27.0532	−	11.4105i	−0.878646	−	0.370595i
$949$	27.3641	+	22.4571i	0.888276	+	0.728989i
$950$	1.09747	−	0.159183i	0.0356065	−	0.00516458i
$951$	3.31789	−	16.6801i	0.107590	−	0.540891i
$952$	−4.50248	+	9.28649i	−0.145926	+	0.300977i
$953$	41.9325	−	8.34090i	1.35833	−	0.270188i	0.538417	−	0.842679i	$-0.319023\pi$
$953$	41.9325	−	8.34090i	1.35833	−	0.270188i	0.819911	+	0.572490i	$0.194023\pi$
$954$	−15.0007	−	7.15403i	−0.485667	−	0.231620i
$955$	7.84371	+	14.6746i	0.253817	+	0.474857i
$956$	18.3212	+	34.8142i	0.592551	+	1.12597i
$957$	−13.7290	−	1.35219i	−0.443796	−	0.0437101i
$958$	−33.7455	−	12.1971i	−1.09027	−	0.394069i
$959$		−	36.8668i		−	1.19049i
$960$	1.92795	−	16.3328i	0.0622243	−	0.527138i
$961$		−	52.5887i		−	1.69641i
$962$	3.53550	−	9.78162i	0.113989	−	0.315372i
$963$	−2.27943	−	0.224504i	−0.0734535	−	0.00723454i
$964$	−28.1383	−	8.73396i	−0.906272	−	0.281302i
$965$	0.390292	+	0.730185i	0.0125639	+	0.0235055i
$966$	6.28489	−	13.1783i	0.202213	−	0.424005i
$967$	−48.9834	+	9.74340i	−1.57520	+	0.313327i	−0.903862	−	0.427824i	$-0.859280\pi$
$967$	−48.9834	+	9.74340i	−1.57520	+	0.313327i	−0.671338	+	0.741151i	$0.734280\pi$
$968$	−10.1866	−	0.599142i	−0.327410	−	0.0192571i
$969$	−0.185293	+	0.931531i	−0.00595247	+	0.0299251i
$970$	4.33593	+	29.8935i	0.139218	+	0.959821i
$971$	−9.11273	−	7.47863i	−0.292442	−	0.240001i	0.476720	−	0.879055i	$-0.341826\pi$
$971$	−9.11273	−	7.47863i	−0.292442	−	0.240001i	−0.769161	+	0.639055i	$0.779326\pi$
$972$	−0.753449	−	1.85265i	−0.0241669	−	0.0594238i
$973$	27.7863	+	14.8521i	0.890787	+	0.476136i
$974$	5.88844	−	38.8346i	0.188678	−	1.24434i
$975$	−3.69984	+	1.53252i	−0.118490	+	0.0490801i
$976$	1.72794	+	20.2098i	0.0553099	+	0.646899i
$977$	8.77289	+	3.63385i	0.280670	+	0.116257i	0.518578	−	0.855030i	$-0.326462\pi$
$977$	8.77289	+	3.63385i	0.280670	+	0.116257i	−0.237908	+	0.971288i	$0.576462\pi$
$978$	14.1739	−	23.4759i	0.453230	−	0.750675i
$979$	−6.37386	+	1.93349i	−0.203709	+	0.0617945i
$980$	−6.33012	−	32.9308i	−0.202208	−	1.05194i
$981$	−0.195020	−	1.98007i	−0.00622649	−	0.0632187i
$982$	10.6442	−	6.33339i	0.339671	−	0.202107i
$983$	18.1973	+	27.2343i	0.580405	+	0.868638i	0.999222	−	0.0394329i	$-0.0125551\pi$
$983$	18.1973	+	27.2343i	0.580405	+	0.868638i	−0.418817	+	0.908071i	$0.637555\pi$
$984$	−3.22335	−	13.4170i	−0.102757	−	0.427719i
$985$	1.49383	+	0.998143i	0.0475973	+	0.0318035i
$986$	4.50048	+	4.99776i	0.143324	+	0.159161i
$987$	42.8656	+	13.0031i	1.36443	+	0.413894i
$988$	−8.15065	+	6.60167i	−0.259307	+	0.210027i
$989$	−10.1634	−	12.3841i	−0.323178	−	0.393793i
$990$	−0.362431	−	7.89626i	−0.0115188	−	0.250960i
$991$	−5.78234	−	5.78234i	−0.183682	−	0.183682i	0.609276	−	0.792958i	$-0.291460\pi$
$991$	−5.78234	−	5.78234i	−0.183682	−	0.183682i	−0.792958	+	0.609276i	$0.791460\pi$
$992$	−51.0302	−	8.41151i	−1.62021	−	0.267066i
$993$	0.707628	−	0.707628i	0.0224559	−	0.0224559i
$994$	−40.1844	−	36.6574i	−1.27457	−	1.16270i
$995$	6.50769	−	5.34073i	0.206308	−	0.169312i
$996$	−5.52879	−	3.00114i	−0.175186	−	0.0950949i
$997$	5.35939	−	17.6675i	0.169734	−	0.559537i	−0.830264	−	0.557370i	$-0.811810\pi$
$997$	5.35939	−	17.6675i	0.169734	−	0.559537i	0.999998	−	0.00216636i	$-0.000689575\pi$
$998$	−1.67196	+	31.9346i	−0.0529248	+	1.01087i
$999$	−0.789521	+	1.18160i	−0.0249793	+	0.0373842i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.157.5	✓	512
128.53	even	32	inner	384.2.v.a.181.5	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.157.5	✓	512	1.1	even	1	trivial
384.2.v.a.181.5	yes	512	128.53	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.28037 + 0.600534i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(1.27872 - 1.53782i) q^{4} +(-1.81303 + 0.969083i) q^{5} +(0.472143 + 1.33307i) q^{6} +(-0.759500 - 3.81826i) q^{7} +(-0.713728 + 2.73689i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})\)	\(q+(-1.28037 + 0.600534i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(1.27872 - 1.53782i) q^{4} +(-1.81303 + 0.969083i) q^{5} +(0.472143 + 1.33307i) q^{6} +(-0.759500 - 3.81826i) q^{7} +(-0.713728 + 2.73689i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(1.73939 - 2.32957i) q^{10} +(-1.72483 + 2.10172i) q^{11} +(-1.40508 - 1.42329i) q^{12} +(-2.43961 + 4.56419i) q^{13} +(3.26544 + 4.43270i) q^{14} +(0.786709 + 1.89928i) q^{15} +(-0.729759 - 3.93287i) q^{16} +(-0.358674 + 0.865916i) q^{17} +(1.37293 - 0.339206i) q^{18} +(0.294162 + 0.969722i) q^{19} +(-0.828079 + 4.02729i) q^{20} +(-3.87432 + 0.381588i) q^{21} +(0.946282 - 3.72681i) q^{22} +(2.20496 - 1.47331i) q^{23} +(2.65376 + 0.978553i) q^{24} +(-0.429906 + 0.643399i) q^{25} +(0.382664 - 7.30894i) q^{26} +(-0.290285 + 0.956940i) q^{27} +(-6.84298 - 3.71451i) q^{28} +(-3.92222 + 3.21889i) q^{29} +(-2.14787 - 1.95935i) q^{30} +(-6.46485 + 6.46485i) q^{31} +(3.29619 + 4.59730i) q^{32} +(1.92253 + 1.92253i) q^{33} +(-0.0607746 - 1.32409i) q^{34} +(5.07721 + 6.18660i) q^{35} +(-1.55416 + 1.25880i) q^{36} +(1.35991 + 0.412523i) q^{37} +(-0.958989 - 1.06495i) q^{38} +(4.30309 + 2.87523i) q^{39} +(-1.35827 - 5.65373i) q^{40} +(-2.71041 - 4.05641i) q^{41} +(4.73143 - 2.81524i) q^{42} +(-0.592146 - 6.01216i) q^{43} +(1.02648 + 5.33998i) q^{44} +(1.96725 - 0.596759i) q^{45} +(-1.93840 + 3.21053i) q^{46} +(-10.6303 - 4.40323i) q^{47} +(-3.98546 + 0.340757i) q^{48} +(-7.53515 + 3.12116i) q^{49} +(0.164057 - 1.08197i) q^{50} +(0.826590 + 0.441822i) q^{51} +(3.89931 + 9.58798i) q^{52} +(-9.08414 - 7.45516i) q^{53} +(-0.203002 - 1.39957i) q^{54} +(1.09043 - 5.48198i) q^{55} +(10.9923 + 0.646529i) q^{56} +(0.993886 - 0.197696i) q^{57} +(3.08887 - 6.47681i) q^{58} +(6.58085 + 12.3119i) q^{59} +(3.92673 + 1.21883i) q^{60} +(-5.04646 - 0.497033i) q^{61} +(4.39507 - 12.1598i) q^{62} +3.89307i q^{63} +(-6.98119 - 3.90679i) q^{64} -10.6392i q^{65} +(-3.61611 - 1.30702i) q^{66} +(11.5783 + 1.14037i) q^{67} +(0.872977 + 1.65884i) q^{68} +(-1.25009 - 2.33875i) q^{69} +(-10.2160 - 4.87213i) q^{70} +(-9.68961 + 1.92738i) q^{71} +(1.23396 - 2.54506i) q^{72} +(1.33444 - 6.70866i) q^{73} +(-1.98893 + 0.288486i) q^{74} +(0.598163 + 0.490900i) q^{75} +(1.86741 + 0.787634i) q^{76} +(9.33493 + 4.98962i) q^{77} +(-7.23623 - 1.09722i) q^{78} +(13.5630 - 5.61800i) q^{79} +(5.13435 + 6.42320i) q^{80} +(0.923880 + 0.382683i) q^{81} +(5.90635 + 3.56603i) q^{82} +(3.00997 - 0.913064i) q^{83} +(-4.36736 + 6.44594i) q^{84} +(-0.188859 - 1.91752i) q^{85} +(4.36867 + 7.34221i) q^{86} +(2.81894 + 4.21884i) q^{87} +(-4.52112 - 6.22074i) q^{88} +(2.03692 + 1.36103i) q^{89} +(-2.16044 + 1.94547i) q^{90} +(19.2802 + 5.84857i) q^{91} +(0.553846 - 5.27476i) q^{92} +(5.80006 + 7.06739i) q^{93} +(16.2551 - 0.746093i) q^{94} +(-1.47307 - 1.47307i) q^{95} +(4.89824 - 2.82970i) q^{96} +(-7.34671 + 7.34671i) q^{97} +(7.77345 - 8.52137i) q^{98} +(2.10172 - 1.72483i) 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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