LMFDB - Embedded newform 768.2.z.a.685.53

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(13,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([0, 47, 0]))

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

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

chi := DirichletCharacter("768.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.z (of order $64$, degree $32$, 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:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$2048$
Relative dimension:	$64$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			685.53
Character	$\chi$	$=$	768.685
Dual form			768.2.z.a.37.53

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19628 + 0.754266i) q^{2} +(0.514103 + 0.857729i) q^{3} +(0.862166 + 1.80462i) q^{4} +(-0.221142 + 0.618051i) q^{5} +(-0.0319451 + 1.41385i) q^{6} +(-3.13057 - 0.949649i) q^{7} +(-0.329775 + 2.80914i) q^{8} +(-0.471397 + 0.881921i) q^{9} +O(q^{10})$	\(q+(1.19628 + 0.754266i) q^{2} +(0.514103 + 0.857729i) q^{3} +(0.862166 + 1.80462i) q^{4} +(-0.221142 + 0.618051i) q^{5} +(-0.0319451 + 1.41385i) q^{6} +(-3.13057 - 0.949649i) q^{7} +(-0.329775 + 2.80914i) q^{8} +(-0.471397 + 0.881921i) q^{9} +(-0.730722 + 0.572561i) q^{10} +(-4.69431 + 3.48154i) q^{11} +(-1.10464 + 1.66727i) q^{12} +(0.613647 - 1.29745i) q^{13} +(-3.02875 - 3.49733i) q^{14} +(-0.643810 + 0.128062i) q^{15} +(-2.51334 + 3.11177i) q^{16} +(-0.486621 - 0.0967950i) q^{17} +(-1.22912 + 0.699465i) q^{18} +(0.963855 + 0.0473511i) q^{19} +(-1.30601 + 0.133784i) q^{20} +(-0.794896 - 3.17340i) q^{21} +(-8.24171 + 0.624133i) q^{22} +(-0.476334 + 4.83630i) q^{23} +(-2.57902 + 1.16133i) q^{24} +(3.53197 + 2.89861i) q^{25} +(1.71271 - 1.08926i) q^{26} +(-0.998795 + 0.0490677i) q^{27} +(-0.985315 - 6.46827i) q^{28} +(6.96571 - 1.03327i) q^{29} +(-0.866769 - 0.332406i) q^{30} +(3.03465 - 1.25699i) q^{31} +(-5.35376 + 1.82682i) q^{32} +(-5.39958 - 2.23658i) q^{33} +(-0.509126 - 0.482836i) q^{34} +(1.27923 - 1.72485i) q^{35} +(-1.99796 - 0.0903312i) q^{36} +(-0.220361 - 0.199724i) q^{37} +(1.11732 + 0.783648i) q^{38} +(1.42834 - 0.140679i) q^{39} +(-1.66326 - 0.825036i) q^{40} +(-2.56339 + 2.10372i) q^{41} +(1.44267 - 4.39583i) q^{42} +(9.19624 + 5.51201i) q^{43} +(-10.3302 - 5.46981i) q^{44} +(-0.440827 - 0.486377i) q^{45} +(-4.21768 + 5.42628i) q^{46} +(2.81098 - 1.87824i) q^{47} +(-3.96117 - 0.555991i) q^{48} +(3.07838 + 2.05691i) q^{49} +(2.03890 + 6.13159i) q^{50} +(-0.167150 - 0.467152i) q^{51} +(2.87047 - 0.0112133i) q^{52} +(9.36622 + 1.38935i) q^{53} +(-1.23185 - 0.694659i) q^{54} +(-1.11366 - 3.67124i) q^{55} +(3.70008 - 8.48104i) q^{56} +(0.454906 + 0.851069i) q^{57} +(9.11229 + 4.01792i) q^{58} +(-0.175285 - 0.370608i) q^{59} +(-0.786174 - 1.05142i) q^{60} +(1.75690 - 7.01396i) q^{61} +(4.57840 + 0.785219i) q^{62} +(2.31326 - 2.31326i) q^{63} +(-7.78250 - 1.85277i) q^{64} +(0.666186 + 0.666186i) q^{65} +(-4.77242 - 6.74829i) q^{66} +(-8.94071 - 2.23953i) q^{67} +(-0.244870 - 0.961622i) q^{68} +(-4.39312 + 2.07779i) q^{69} +(2.83131 - 1.09852i) q^{70} +(-6.98922 + 3.73581i) q^{71} +(-2.32198 - 1.61505i) q^{72} +(-8.60244 + 2.60952i) q^{73} +(-0.112969 - 0.405136i) q^{74} +(-0.670428 + 4.51966i) q^{75} +(0.745552 + 1.78022i) q^{76} +(18.0021 - 6.44127i) q^{77} +(1.81480 + 0.909054i) q^{78} +(0.802603 - 1.20118i) q^{79} +(-1.36743 - 2.24152i) q^{80} +(-0.555570 - 0.831470i) q^{81} +(-4.65328 + 0.583157i) q^{82} +(7.17144 - 6.49981i) q^{83} +(5.04146 - 4.17049i) q^{84} +(0.167437 - 0.279351i) q^{85} +(6.84374 + 13.5303i) q^{86} +(4.46735 + 5.44349i) q^{87} +(-8.23205 - 14.3351i) q^{88} +(-0.415519 - 4.21883i) q^{89} +(-0.160494 - 0.914343i) q^{90} +(-3.15319 + 3.47901i) q^{91} +(-9.13839 + 3.31009i) q^{92} +(2.63828 + 1.95668i) q^{93} +(4.77941 - 0.126669i) q^{94} +(-0.242414 + 0.585240i) q^{95} +(-4.31930 - 3.65290i) q^{96} +(-1.08982 - 2.63107i) q^{97} +(2.13114 + 4.78255i) q^{98} +(-0.857560 - 5.78120i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2048 q+O(q^{10}) $ 2048 * q	$ 2048 q+O(q^{100}) $ 2048 * q

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{39}{64}\right)$

Coefficient data

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

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

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

$2$	1.19628	+	0.754266i	0.845897	+	0.533346i
$2$	1.19628	+	0.754266i	0.845897	+	0.533346i
$3$	0.514103	+	0.857729i	0.296817	+	0.495210i
$3$	0.514103	+	0.857729i	0.296817	+	0.495210i
$4$	0.862166	+	1.80462i	0.431083	+	0.902312i
$5$	−0.221142	+	0.618051i	−0.0988978	+	0.276401i	−0.980795	−	0.195041i	$-0.937516\pi$
$5$	−0.221142	+	0.618051i	−0.0988978	+	0.276401i	0.881897	+	0.471441i	$0.156266\pi$
$6$	−0.0319451	+	1.41385i	−0.0130415	+	0.577203i
$7$	−3.13057	−	0.949649i	−1.18325	−	0.358934i	−0.363463	−	0.931609i	$-0.618406\pi$
$7$	−3.13057	−	0.949649i	−1.18325	−	0.358934i	−0.819783	+	0.572675i	$0.805906\pi$
$8$	−0.329775	+	2.80914i	−0.116593	+	0.993180i
$9$	−0.471397	+	0.881921i	−0.157132	+	0.293974i
$10$	−0.730722	+	0.572561i	−0.231075	+	0.181060i
$11$	−4.69431	+	3.48154i	−1.41539	+	1.04972i	−0.425954	+	0.904745i	$0.640061\pi$
$11$	−4.69431	+	3.48154i	−1.41539	+	1.04972i	−0.989435	+	0.144979i	$0.953689\pi$
$12$	−1.10464	+	1.66727i	−0.318881	+	0.481299i
$13$	0.613647	−	1.29745i	0.170195	−	0.359847i	−0.800805	−	0.598925i	$-0.795595\pi$
$13$	0.613647	−	1.29745i	0.170195	−	0.359847i	0.971001	+	0.239077i	$0.0768449\pi$
$14$	−3.02875	−	3.49733i	−0.809468	−	0.934701i
$15$	−0.643810	+	0.128062i	−0.166231	+	0.0330654i
$16$	−2.51334	+	3.11177i	−0.628335	+	0.777943i
$17$	−0.486621	−	0.0967950i	−0.118023	−	0.0234762i	0.135725	−	0.990746i	$-0.456664\pi$
$17$	−0.486621	−	0.0967950i	−0.118023	−	0.0234762i	−0.253748	+	0.967270i	$0.581664\pi$
$18$	−1.22912	+	0.699465i	−0.289708	+	0.164866i
$19$	0.963855	+	0.0473511i	0.221123	+	0.0108631i	0.159328	−	0.987226i	$-0.449067\pi$
$19$	0.963855	+	0.0473511i	0.221123	+	0.0108631i	0.0617956	+	0.998089i	$0.480317\pi$
$20$	−1.30601	+	0.133784i	−0.292033	+	0.0299150i
$21$	−0.794896	−	3.17340i	−0.173460	−	0.692493i
$22$	−8.24171	+	0.624133i	−1.75714	+	0.133066i
$23$	−0.476334	+	4.83630i	−0.0993225	+	1.00844i	0.808334	+	0.588724i	$0.200370\pi$
$23$	−0.476334	+	4.83630i	−0.0993225	+	1.00844i	−0.907656	+	0.419714i	$0.862130\pi$
$24$	−2.57902	+	1.16133i	−0.526439	+	0.237055i
$25$	3.53197	+	2.89861i	0.706394	+	0.579722i
$26$	1.71271	−	1.08926i	0.335891	−	0.213621i
$27$	−0.998795	+	0.0490677i	−0.192218	+	0.00944308i
$28$	−0.985315	−	6.46827i	−0.186207	−	1.22239i
$29$	6.96571	−	1.03327i	1.29350	−	0.191873i	0.535727	−	0.844391i	$-0.320037\pi$
$29$	6.96571	−	1.03327i	1.29350	−	0.191873i	0.757773	+	0.652518i	$0.226287\pi$
$30$	−0.866769	−	0.332406i	−0.158250	−	0.0606888i
$31$	3.03465	−	1.25699i	0.545040	−	0.225763i	−0.0931362	−	0.995653i	$-0.529689\pi$
$31$	3.03465	−	1.25699i	0.545040	−	0.225763i	0.638176	+	0.769891i	$0.279689\pi$
$32$	−5.35376	+	1.82682i	−0.946420	+	0.322940i
$33$	−5.39958	−	2.23658i	−0.939945	−	0.389338i
$34$	−0.509126	−	0.482836i	−0.0873143	−	0.0828056i
$35$	1.27923	−	1.72485i	0.216230	−	0.291552i
$36$	−1.99796	−	0.0903312i	−0.332993	−	0.0150552i
$37$	−0.220361	−	0.199724i	−0.0362272	−	0.0328344i	0.653245	−	0.757147i	$-0.273407\pi$
$37$	−0.220361	−	0.199724i	−0.0362272	−	0.0328344i	−0.689472	+	0.724312i	$0.742157\pi$
$38$	1.11732	+	0.783648i	0.181254	+	0.127124i
$39$	1.42834	−	0.140679i	0.228717	−	0.0225266i
$40$	−1.66326	−	0.825036i	−0.262985	−	0.130450i
$41$	−2.56339	+	2.10372i	−0.400333	+	0.328545i	−0.812922	−	0.582372i	$-0.802125\pi$
$41$	−2.56339	+	2.10372i	−0.400333	+	0.328545i	0.412589	+	0.910917i	$0.364625\pi$
$42$	1.44267	−	4.39583i	0.222609	−	0.678292i
$43$	9.19624	+	5.51201i	1.40241	+	0.840574i	0.997282	−	0.0736846i	$-0.0234758\pi$
$43$	9.19624	+	5.51201i	1.40241	+	0.840574i	0.405131	+	0.914259i	$0.367226\pi$
$44$	−10.3302	−	5.46981i	−1.55733	−	0.824604i
$45$	−0.440827	−	0.486377i	−0.0657145	−	0.0725048i
$46$	−4.21768	+	5.42628i	−0.621864	+	0.800062i
$47$	2.81098	−	1.87824i	0.410024	−	0.273969i	−0.333406	−	0.942783i	$-0.608198\pi$
$47$	2.81098	−	1.87824i	0.410024	−	0.273969i	0.743430	+	0.668814i	$0.233198\pi$
$48$	−3.96117	−	0.555991i	−0.571746	−	0.0802504i
$49$	3.07838	+	2.05691i	0.439768	+	0.293844i
$50$	2.03890	+	6.13159i	0.288343	+	0.867138i
$51$	−0.167150	−	0.467152i	−0.0234056	−	0.0654143i
$52$	2.87047	−	0.0112133i	0.398063	−	0.00155500i
$53$	9.36622	+	1.38935i	1.28655	+	0.190842i	0.754741	−	0.656023i	$-0.227763\pi$
$53$	9.36622	+	1.38935i	1.28655	+	0.190842i	0.531809	+	0.846865i	$0.321513\pi$
$54$	−1.23185	−	0.694659i	−0.167633	−	0.0945311i
$55$	−1.11366	−	3.67124i	−0.150166	−	0.495030i
$56$	3.70008	−	8.48104i	0.494444	−	1.13333i
$57$	0.454906	+	0.851069i	0.0602538	+	0.112727i
$58$	9.11229	+	4.01792i	1.19650	+	0.527579i
$59$	−0.175285	−	0.370608i	−0.0228201	−	0.0482491i	0.892257	−	0.451527i	$-0.149121\pi$
$59$	−0.175285	−	0.370608i	−0.0228201	−	0.0482491i	−0.915077	+	0.403278i	$0.867871\pi$
$60$	−0.786174	−	1.05142i	−0.101495	−	0.135738i
$61$	1.75690	−	7.01396i	0.224949	−	0.898045i	−0.747374	−	0.664403i	$-0.768686\pi$
$61$	1.75690	−	7.01396i	0.224949	−	0.898045i	0.972323	−	0.233642i	$-0.0750643\pi$
$62$	4.57840	+	0.785219i	0.581457	+	0.0997229i
$63$	2.31326	−	2.31326i	0.291443	−	0.291443i
$64$	−7.78250	−	1.85277i	−0.972812	−	0.231596i
$65$	0.666186	+	0.666186i	0.0826302	+	0.0826302i
$66$	−4.77242	−	6.74829i	−0.587445	−	0.830657i
$67$	−8.94071	−	2.23953i	−1.09228	−	0.273602i	−0.345331	−	0.938481i	$-0.612233\pi$
$67$	−8.94071	−	2.23953i	−1.09228	−	0.273602i	−0.746951	+	0.664879i	$0.768483\pi$
$68$	−0.244870	−	0.961622i	−0.0296948	−	0.116614i
$69$	−4.39312	+	2.07779i	−0.528869	+	0.250137i
$70$	2.83131	−	1.09852i	0.338407	−	0.131298i
$71$	−6.98922	+	3.73581i	−0.829467	+	0.443360i	−0.830754	−	0.556640i	$-0.812090\pi$
$71$	−6.98922	+	3.73581i	−0.829467	+	0.443360i	0.00128674	+	0.999999i	$0.499590\pi$
$72$	−2.32198	−	1.61505i	−0.273648	−	0.190336i
$73$	−8.60244	+	2.60952i	−1.00684	+	0.305421i	−0.750289	−	0.661110i	$-0.770086\pi$
$73$	−8.60244	+	2.60952i	−1.00684	+	0.305421i	−0.256550	+	0.966531i	$0.582586\pi$
$74$	−0.112969	−	0.405136i	−0.0131323	−	0.0470962i
$75$	−0.670428	+	4.51966i	−0.0774143	+	0.521885i
$76$	0.745552	+	1.78022i	0.0855207	+	0.204205i
$77$	18.0021	−	6.44127i	2.05153	−	0.734051i
$78$	1.81480	+	0.909054i	0.205485	+	0.102930i
$79$	0.802603	−	1.20118i	0.0902999	−	0.135143i	−0.783569	−	0.621304i	$-0.786603\pi$
$79$	0.802603	−	1.20118i	0.0902999	−	0.135143i	0.873869	+	0.486161i	$0.161603\pi$
$80$	−1.36743	−	2.24152i	−0.152883	−	0.250609i
$81$	−0.555570	−	0.831470i	−0.0617300	−	0.0923855i
$82$	−4.65328	+	0.583157i	−0.513869	+	0.0643989i
$83$	7.17144	−	6.49981i	0.787167	−	0.713447i	−0.175398	−	0.984498i	$-0.556121\pi$
$83$	7.17144	−	6.49981i	0.787167	−	0.713447i	0.962565	+	0.271051i	$0.0873711\pi$
$84$	5.04146	−	4.17049i	0.550069	−	0.455037i
$85$	0.167437	−	0.279351i	0.0181611	−	0.0302999i
$86$	6.84374	+	13.5303i	0.737980	+	1.45901i
$87$	4.46735	+	5.44349i	0.478951	+	0.583603i
$88$	−8.23205	−	14.3351i	−0.877540	−	1.52813i
$89$	−0.415519	−	4.21883i	−0.0440449	−	0.447195i	−0.991763	−	0.128086i	$-0.959116\pi$
$89$	−0.415519	−	4.21883i	−0.0440449	−	0.447195i	0.947718	−	0.319109i	$-0.103384\pi$
$90$	−0.160494	−	0.914343i	−0.0169175	−	0.0963802i
$91$	−3.15319	+	3.47901i	−0.330544	+	0.364699i
$92$	−9.13839	+	3.31009i	−0.952743	+	0.345101i
$93$	2.63828	+	1.95668i	0.273577	+	0.202899i
$94$	4.77941	−	0.126669i	0.492958	−	0.0130649i
$95$	−0.242414	+	0.585240i	−0.0248712	+	0.0600443i
$96$	−4.31930	−	3.65290i	−0.440837	−	0.372822i
$97$	−1.08982	−	2.63107i	−0.110655	−	0.267144i	0.858845	−	0.512235i	$-0.171182\pi$
$97$	−1.08982	−	2.63107i	−0.110655	−	0.267144i	−0.969500	+	0.245091i	$0.921182\pi$
$98$	2.13114	+	4.78255i	0.215278	+	0.483110i
$99$	−0.857560	−	5.78120i	−0.0861880	−	0.581033i
$100$	−2.18576	+	8.87296i	−0.218576	+	0.887296i
$101$	0.747557	+	15.2169i	0.0743847	+	1.51414i	0.688683	+	0.725062i	$0.258189\pi$
$101$	0.747557	+	15.2169i	0.0743847	+	1.51414i	−0.614299	+	0.789074i	$0.710561\pi$
$102$	0.152399	−	0.684919i	0.0150898	−	0.0678171i
$103$	5.66245	−	6.89972i	0.557938	−	0.679849i	−0.415291	−	0.909689i	$-0.636320\pi$
$103$	5.66245	−	6.89972i	0.557938	−	0.679849i	0.973229	+	0.229839i	$0.0738201\pi$
$104$	3.44234	+	2.15169i	0.337550	+	0.210990i
$105$	2.13711	+	0.210487i	0.208560	+	0.0205414i
$106$	10.1567	+	8.72667i	0.986503	+	0.847609i
$107$	−2.76327	+	0.692163i	−0.267135	+	0.0669139i	−0.374233	−	0.927335i	$-0.622094\pi$
$107$	−2.76327	+	0.692163i	−0.267135	+	0.0669139i	0.107098	+	0.994248i	$0.465844\pi$
$108$	−0.949677	−	1.76015i	−0.0913827	−	0.169370i
$109$	0.213983	−	4.35573i	0.0204959	−	0.417203i	−0.966521	−	0.256587i	$-0.917402\pi$
$109$	0.213983	−	4.35573i	0.0204959	−	0.417203i	0.987017	−	0.160616i	$-0.0513481\pi$
$110$	1.43684	−	5.23182i	0.136998	−	0.498835i
$111$	0.0580205	−	0.291689i	0.00550706	−	0.0276859i
$112$	10.8233	−	7.35485i	1.02270	−	0.694968i
$113$	3.54867	+	17.8404i	0.333831	+	1.67828i	0.674639	+	0.738148i	$0.264299\pi$
$113$	3.54867	+	17.8404i	0.333831	+	1.67828i	−0.340808	+	0.940133i	$0.610701\pi$
$114$	−0.0977379	+	1.36124i	−0.00915400	+	0.127491i
$115$	−2.88374	−	1.36391i	−0.268910	−	0.127185i
$116$	7.87026	+	11.6796i	0.730735	+	1.08443i
$117$	0.854976	+	1.15280i	0.0790425	+	0.106577i
$118$	0.0698478	−	0.575562i	0.00643001	−	0.0529848i
$119$	1.43148	+	0.765144i	0.131224	+	0.0701406i
$120$	−0.147430	−	1.85078i	−0.0134585	−	0.168952i
$121$	6.72232	−	22.1605i	0.611120	−	2.01459i
$122$	7.39213	−	7.06547i	0.669252	−	0.639678i
$123$	−3.12226	−	1.11716i	−0.281525	−	0.100731i
$124$	4.88478	+	4.39267i	0.438666	+	0.394473i
$125$	−5.38772	+	3.22928i	−0.481892	+	0.288835i
$126$	4.51211	−	1.02249i	0.401971	−	0.0910907i
$127$			14.2430i			1.26386i	0.775025	+	0.631930i	$0.217737\pi$
$127$			14.2430i			1.26386i	−0.775025	+	0.631930i	$0.782263\pi$
$128$	−7.91256	−	8.08650i	−0.699378	−	0.714752i
$129$			10.7216i			0.943986i
$130$	0.294463	+	1.29943i	0.0258261	+	0.113967i
$131$	−17.0508	+	10.2199i	−1.48974	+	0.892913i	−0.489959	+	0.871745i	$0.662988\pi$
$131$	−17.0508	+	10.2199i	−1.48974	+	0.892913i	−0.999776	+	0.0211674i	$0.993262\pi$
$132$	−0.619150	−	11.6725i	−0.0538901	−	1.01596i
$133$	−2.97245	−	1.06356i	−0.257744	−	0.0922224i
$134$	−9.00638	−	9.42278i	−0.778033	−	0.814004i
$135$	0.190549	−	0.628157i	0.0163999	−	0.0540632i
$136$	0.432386	−	1.33507i	0.0370768	−	0.114481i
$137$	3.26413	+	1.74471i	0.278874	+	0.149061i	0.604904	−	0.796298i	$-0.293211\pi$
$137$	3.26413	+	1.74471i	0.278874	+	0.149061i	−0.326031	+	0.945359i	$0.605711\pi$
$138$	−6.82260	−	0.827962i	−0.580778	−	0.0704808i
$139$	1.48625	+	2.00398i	0.126062	+	0.169975i	0.861730	−	0.507367i	$-0.169381\pi$
$139$	1.48625	+	2.00398i	0.126062	+	0.169975i	−0.735667	+	0.677343i	$0.763131\pi$
$140$	4.21561	+	0.821431i	0.356284	+	0.0694236i
$141$	3.05615	+	1.44545i	0.257374	+	0.121729i
$142$	−11.1788	−	0.802651i	−0.938108	−	0.0673570i
$143$	1.63647	+	8.22707i	0.136848	+	0.687982i
$144$	−1.55956	−	3.68345i	−0.129963	−	0.306954i
$145$	−0.901802	+	4.53366i	−0.0748906	+	0.376500i
$146$	−12.2592	−	3.36681i	−1.01458	−	0.278639i
$147$	−0.181665	+	3.69787i	−0.0149835	+	0.304995i
$148$	0.170438	−	0.569865i	0.0140100	−	0.0468426i
$149$	17.6804	−	4.42870i	1.44843	−	0.362813i	0.562565	−	0.826753i	$-0.309815\pi$
$149$	17.6804	−	4.42870i	1.44843	−	0.362813i	0.885867	+	0.463940i	$0.153565\pi$
$150$	−4.21104	+	4.90109i	−0.343830	+	0.400172i
$151$	8.51784	+	0.838934i	0.693172	+	0.0682715i	0.438467	−	0.898747i	$-0.355522\pi$
$151$	8.51784	+	0.838934i	0.693172	+	0.0682715i	0.254705	+	0.967019i	$0.418022\pi$
$152$	−0.450871	+	2.69198i	−0.0365705	+	0.218349i
$153$	0.314757	−	0.383533i	0.0254466	−	0.0310068i
$154$	26.3940	+	5.87284i	2.12689	+	0.473247i
$155$	0.105797	+	2.15354i	0.00849781	+	0.172977i
$156$	1.48534	+	2.45632i	0.118922	+	0.196663i
$157$	−3.65288	−	24.6257i	−0.291532	−	1.96535i	−0.259002	−	0.965877i	$-0.583393\pi$
$157$	−3.65288	−	24.6257i	−0.291532	−	1.96535i	−0.0325302	−	0.999471i	$-0.510357\pi$
$158$	1.86615	−	0.831570i	0.148463	−	0.0661562i
$159$	3.62352	+	8.74794i	0.287364	+	0.693757i
$160$	0.0548719	−	3.71288i	0.00433800	−	0.293529i
$161$	6.08399	−	14.6881i	0.479486	−	1.15758i
$162$	−0.0374679	−	1.41372i	−0.00294375	−	0.111072i
$163$	−15.7743	−	11.6990i	−1.23554	−	0.916339i	−0.237062	−	0.971494i	$-0.576185\pi$
$163$	−15.7743	−	11.6990i	−1.23554	−	0.916339i	−0.998478	+	0.0551556i	$0.982435\pi$
$164$	−6.00648	−	2.81219i	−0.469027	−	0.219595i
$165$	2.57639	−	2.84261i	0.200572	−	0.221297i
$166$	13.4816	−	2.36642i	1.04638	−	0.183670i
$167$	1.66002	+	16.8544i	0.128456	+	1.30423i	0.815983	+	0.578076i	$0.196196\pi$
$167$	1.66002	+	16.8544i	0.128456	+	1.30423i	−0.687527	+	0.726159i	$0.741304\pi$
$168$	9.17665	−	1.18646i	0.707994	−	0.0915375i
$169$	6.94030	+	8.45678i	0.533870	+	0.650522i
$170$	0.411006	−	0.207890i	0.0315227	−	0.0159445i
$171$	−0.496118	+	0.827723i	−0.0379391	+	0.0632975i
$172$	−2.01843	+	21.3480i	−0.153904	+	1.62777i
$173$	14.1777	−	12.8499i	1.07791	−	0.976958i	0.0781069	−	0.996945i	$-0.475112\pi$
$173$	14.1777	−	12.8499i	1.07791	−	0.976958i	0.999800	+	0.0199869i	$0.00636244\pi$
$174$	1.23837	+	9.88150i	0.0938802	+	0.749114i
$175$	−8.30443	−	12.4285i	−0.627756	−	0.939503i
$176$	0.964637	−	23.3579i	0.0727122	−	1.76067i
$177$	0.227767	−	0.340877i	0.0171200	−	0.0256219i
$178$	2.68504	−	5.36031i	0.201253	−	0.401772i
$179$	−0.323325	+	0.115688i	−0.0241664	+	0.00864689i	−0.348945	−	0.937143i	$-0.613460\pi$
$179$	−0.323325	+	0.115688i	−0.0241664	+	0.00864689i	0.324779	+	0.945790i	$0.394710\pi$
$180$	0.497662	−	1.21486i	0.0370936	−	0.0905506i
$181$	1.59988	−	10.7855i	0.118918	−	0.801682i	−0.844862	−	0.534984i	$-0.820317\pi$
$181$	1.59988	−	10.7855i	0.118918	−	0.801682i	0.963780	−	0.266698i	$-0.0859326\pi$
$182$	−6.39619	+	1.78352i	−0.474117	+	0.132203i
$183$	6.91930	−	2.09895i	0.511489	−	0.155159i
$184$	−13.4287	−	2.93298i	−0.989980	−	0.216222i
$185$	0.172171	−	0.0920272i	0.0126582	−	0.00676597i
$186$	1.68026	+	4.33071i	0.123203	+	0.317543i
$187$	2.62135	−	1.23981i	0.191692	−	0.0906636i
$188$	5.81305	+	3.45341i	0.423960	+	0.251866i
$189$	3.17340	+	0.794896i	0.230831	+	0.0578201i
$190$	−0.731422	+	0.517265i	−0.0530629	+	0.0375264i
$191$	1.62801	+	1.62801i	0.117799	+	0.117799i	0.763549	−	0.645750i	$-0.223455\pi$
$191$	1.62801	+	1.62801i	0.117799	+	0.117799i	−0.645750	+	0.763549i	$0.723455\pi$
$192$	−2.41183	−	7.62778i	−0.174059	−	0.550488i
$193$	6.17776	−	6.17776i	0.444685	−	0.444685i	−0.448898	−	0.893583i	$-0.648183\pi$
$193$	6.17776	−	6.17776i	0.444685	−	0.444685i	0.893583	+	0.448898i	$0.148183\pi$
$194$	0.680791	−	3.96951i	0.0488779	−	0.284994i
$195$	−0.228919	+	0.913895i	−0.0163932	+	0.0654453i
$196$	−1.05787	+	7.32871i	−0.0755621	+	0.523479i
$197$	−0.290432	−	0.614067i	−0.0206924	−	0.0437504i	0.893378	−	0.449305i	$-0.148328\pi$
$197$	−0.290432	−	0.614067i	−0.0206924	−	0.0437504i	−0.914071	+	0.405555i	$0.867078\pi$
$198$	3.33468	−	7.56276i	0.236985	−	0.537462i
$199$	1.50082	+	2.80784i	0.106391	+	0.199043i	0.929483	−	0.368864i	$-0.120253\pi$
$199$	1.50082	+	2.80784i	0.106391	+	0.199043i	−0.823093	+	0.567907i	$0.807753\pi$
$200$	−9.30735	+	8.96589i	−0.658129	+	0.633984i
$201$	−2.67553	−	8.82005i	−0.188718	−	0.622119i
$202$	−10.5833	+	18.7675i	−0.744637	+	1.32048i
$203$	−22.7879	−	3.38027i	−1.59940	−	0.237248i
$204$	0.698923	−	0.704405i	0.0489344	−	0.0493182i
$205$	−0.733331	−	2.04952i	−0.0512181	−	0.143145i
$206$	11.9781	−	3.98299i	0.834553	−	0.277508i
$207$	−4.04069	−	2.69991i	−0.280848	−	0.187656i
$208$	2.49506	+	5.17046i	0.173001	+	0.358507i
$209$	−4.68949	+	3.13342i	−0.324379	+	0.216743i
$210$	2.39781	+	1.86375i	0.165465	+	0.128611i
$211$	9.89849	+	10.9213i	0.681440	+	0.751853i	0.979224	−	0.202780i	$-0.0649976\pi$
$211$	9.89849	+	10.9213i	0.681440	+	0.751853i	−0.297784	+	0.954633i	$0.596248\pi$
$212$	5.56799	+	18.1004i	0.382411	+	1.24314i
$213$	−6.79749	−	4.07426i	−0.465756	−	0.279164i
$214$	−3.82772	−	1.25622i	−0.261657	−	0.0858734i
$215$	−5.44038	+	4.46480i	−0.371031	+	0.304497i
$216$	0.191540	−	2.82193i	0.0130326	−	0.192008i
$217$	−10.6939	+	1.05326i	−0.725950	+	0.0714998i
$218$	3.54136	−	5.04927i	0.239851	−	0.341980i
$219$	−6.66080	−	6.03699i	−0.450095	−	0.407942i
$220$	5.66505	−	5.17495i	0.381938	−	0.348895i
$221$	−0.424200	+	0.571968i	−0.0285348	+	0.0384747i
$222$	0.289420	−	0.305178i	0.0194246	−	0.0204822i
$223$	−5.88092	−	2.43596i	−0.393815	−	0.163124i	0.176983	−	0.984214i	$-0.443366\pi$
$223$	−5.88092	−	2.43596i	−0.393815	−	0.163124i	−0.570798	+	0.821090i	$0.693366\pi$
$224$	18.4952	−	0.634813i	1.23576	−	0.0424152i
$225$	−4.22131	+	1.74852i	−0.281420	+	0.116568i
$226$	−9.21118	+	24.0187i	−0.612719	+	1.59770i
$227$	27.3190	−	4.05239i	1.81323	−	0.268967i	0.847926	−	0.530114i	$-0.177851\pi$
$227$	27.3190	−	4.05239i	1.81323	−	0.268967i	0.965299	+	0.261148i	$0.0841010\pi$
$228$	−1.14366	+	1.55470i	−0.0757404	+	0.102962i
$229$	−4.68630	+	0.230223i	−0.309680	+	0.0152136i	−0.203314	−	0.979114i	$-0.565171\pi$
$229$	−4.68630	+	0.230223i	−0.309680	+	0.0152136i	−0.106365	+	0.994327i	$0.533921\pi$
$230$	−2.42101	−	3.80672i	−0.159637	−	0.251008i
$231$	14.7798	+	12.1295i	0.972440	+	0.798061i
$232$	0.605467	+	19.9084i	0.0397508	+	1.30705i
$233$	−1.08059	+	10.9714i	−0.0707917	+	0.718760i	0.892633	+	0.450783i	$0.148855\pi$
$233$	−1.08059	+	10.9714i	−0.0707917	+	0.718760i	−0.963425	+	0.267977i	$0.913645\pi$
$234$	0.153271	+	2.02395i	0.0100196	+	0.132310i
$235$	0.539220	+	2.15269i	0.0351748	+	0.140426i
$236$	0.517684	−	0.635849i	0.0336984	−	0.0413902i
$237$	1.44291	+	0.0708855i	0.0937269	+	0.00460451i
$238$	1.13533	+	1.99504i	0.0735926	+	0.129319i
$239$	−8.50918	−	1.69258i	−0.550413	−	0.109484i	−0.0879541	−	0.996125i	$-0.528033\pi$
$239$	−8.50918	−	1.69258i	−0.550413	−	0.109484i	−0.462459	+	0.886641i	$0.653033\pi$
$240$	1.21961	−	2.32525i	0.0787257	−	0.150094i
$241$	−15.7102	+	3.12495i	−1.01198	+	0.201296i	−0.673115	−	0.739538i	$-0.735044\pi$
$241$	−15.7102	+	3.12495i	−1.01198	+	0.201296i	−0.338868	+	0.940834i	$0.610044\pi$
$242$	24.7567	−	21.4398i	1.59142	−	1.37820i
$243$	0.427555	−	0.903989i	0.0274277	−	0.0579909i
$244$	14.1723	−	2.87664i	0.907289	−	0.184158i
$245$	−1.95203	+	1.44773i	−0.124711	+	0.0924918i
$246$	−2.89246	−	3.69145i	−0.184416	−	0.235358i
$247$	0.652902	−	1.22149i	0.0415432	−	0.0777218i
$248$	2.53032	+	8.93928i	0.160675	+	0.567645i
$249$	9.26193	+	2.80958i	0.586951	+	0.178050i
$250$	−8.88095	−	0.200659i	−0.561680	−	0.0126908i
$251$	1.24993	−	3.49332i	0.0788949	−	0.220496i	−0.895620	−	0.444821i	$-0.853267\pi$
$251$	1.24993	−	3.49332i	0.0788949	−	0.220496i	0.974515	+	0.224324i	$0.0720174\pi$
$252$	6.16898	+	2.18015i	0.388609	+	0.137337i
$253$	−14.6017	−	24.3615i	−0.918002	−	1.53159i
$254$	−10.7430	+	17.0386i	−0.674075	+	1.06910i
$255$	0.325687			0.0203953
$256$	−3.36626	−	15.6419i	−0.210391	−	0.977617i
$257$	22.1438			1.38129			0.690647	−	0.723192i	$-0.257326\pi$
$257$	22.1438			1.38129			0.690647	+	0.723192i	$0.257326\pi$
$258$	−8.08695	+	12.8260i	−0.503471	+	0.798515i
$259$	0.500190	+	0.834517i	0.0310803	+	0.0518543i
$260$	−0.627852	+	1.77658i	−0.0389377	+	0.110179i
$261$	−2.37235	+	6.63029i	−0.146845	+	0.410404i
$262$	−28.1060	−	0.635036i	−1.73639	−	0.0392327i
$263$	12.8246	+	3.89030i	0.790799	+	0.239886i	0.659746	−	0.751489i	$-0.270664\pi$
$263$	12.8246	+	3.89030i	0.790799	+	0.239886i	0.131054	+	0.991375i	$0.458164\pi$
$264$	8.06350	−	14.4306i	0.496274	−	0.888141i
$265$	−2.92995	+	5.48156i	−0.179986	+	0.336729i
$266$	−2.75367	−	3.51433i	−0.168839	−	0.215478i
$267$	3.40499	−	2.52531i	0.208382	−	0.154547i
$268$	−3.66687	−	18.0655i	−0.223990	−	1.10352i
$269$	1.26452	−	2.67360i	0.0770991	−	0.163012i	−0.861758	−	0.507320i	$-0.830636\pi$
$269$	1.26452	−	2.67360i	0.0770991	−	0.163012i	0.938857	+	0.344308i	$0.111886\pi$
$270$	0.701748	−	0.607727i	0.0427070	−	0.0369851i
$271$	−20.1792	+	4.01390i	−1.22580	+	0.243827i	−0.765207	−	0.643784i	$-0.777363\pi$
$271$	−20.1792	+	4.01390i	−1.22580	+	0.243827i	−0.460593	+	0.887611i	$0.652363\pi$
$272$	1.52425	−	1.27098i	0.0924211	−	0.0770643i
$273$	−4.60511	−	0.916013i	−0.278714	−	0.0554396i
$274$	2.58883	+	4.54919i	0.156397	+	0.274826i
$275$	−26.6718	−	1.31030i	−1.60837	−	0.0790142i
$276$	−7.53723	−	6.13653i	−0.453688	−	0.369376i
$277$	2.23594	+	8.92638i	0.134345	+	0.536334i	0.999399	+	0.0346564i	$0.0110337\pi$
$277$	2.23594	+	8.92638i	0.134345	+	0.536334i	−0.865055	+	0.501678i	$0.832716\pi$
$278$	0.266440	+	3.51835i	0.0159800	+	0.211017i
$279$	−0.321955	+	3.26887i	−0.0192750	+	0.195702i
$280$	4.42347	+	4.16235i	0.264353	+	0.248748i
$281$	−1.21141	−	0.994176i	−0.0722665	−	0.0593076i	0.597567	−	0.801819i	$-0.296134\pi$
$281$	−1.21141	−	0.994176i	−0.0722665	−	0.0593076i	−0.669833	+	0.742512i	$0.733634\pi$
$282$	2.56575	+	4.03431i	0.152788	+	0.240240i
$283$	17.8581	−	0.877315i	1.06156	−	0.0521509i	0.489213	−	0.872165i	$-0.337284\pi$
$283$	17.8581	−	0.877315i	1.06156	−	0.0521509i	0.572344	+	0.820014i	$0.306034\pi$
$284$	−12.7676	−	9.39202i	−0.757618	−	0.557314i
$285$	−0.626603	+	0.0929478i	−0.0371168	+	0.00550575i
$286$	−4.24773	+	11.0762i	−0.251173	+	0.654949i
$287$	10.0227	−	4.15152i	0.591619	−	0.245057i
$288$	0.912630	−	5.58275i	0.0537772	−	0.328967i
$289$	−15.4785	−	6.41141i	−0.910501	−	0.377142i
$290$	−4.49839	+	4.74333i	−0.264155	+	0.278538i
$291$	1.69646	−	2.28741i	0.0994482	−	0.134090i
$292$	−12.1259	−	13.2743i	−0.709617	−	0.776821i
$293$	−23.2773	−	21.0973i	−1.35988	−	1.23252i	−0.946800	−	0.321822i	$-0.895705\pi$
$293$	−23.2773	−	21.0973i	−1.35988	−	1.23252i	−0.413075	−	0.910697i	$-0.635545\pi$
$294$	−3.00650	+	4.28666i	−0.175343	+	0.250003i
$295$	0.267817	−	0.0263777i	0.0155929	−	0.00153577i
$296$	0.633721	−	0.553161i	0.0368343	−	0.0321518i
$297$	4.51783	−	3.70769i	0.262151	−	0.215142i
$298$	24.4911	+	8.03773i	1.41873	+	0.465613i
$299$	5.98255	+	3.58580i	0.345980	+	0.207372i
$300$	−8.73430	+	2.68682i	−0.504275	+	0.155124i
$301$	−23.5550	−	25.9890i	−1.35769	−	1.49798i
$302$	9.55693	+	7.42831i	0.549940	+	0.427451i
$303$	−12.6676	+	8.46424i	−0.727736	+	0.486258i
$304$	−2.56984	+	2.88029i	−0.147390	+	0.165196i
$305$	3.94646	+	2.63694i	0.225973	+	0.150991i
$306$	0.665823	−	0.221402i	0.0380626	−	0.0126567i
$307$	−1.43224	−	4.00285i	−0.0817425	−	0.228455i	0.893718	−	0.448629i	$-0.148087\pi$
$307$	−1.43224	−	4.00285i	−0.0817425	−	0.228455i	−0.975461	+	0.220174i	$0.929337\pi$
$308$	27.1449	+	26.9337i	1.54672	+	1.53469i
$309$	8.82917	+	1.30968i	0.502274	+	0.0745053i
$310$	−1.49778	+	2.65604i	−0.0850683	+	0.150853i
$311$	1.16022	+	3.82472i	0.0657899	+	0.216880i	0.983671	−	0.179975i	$-0.0576016\pi$
$311$	1.16022	+	3.82472i	0.0657899	+	0.216880i	−0.917881	+	0.396855i	$0.870102\pi$
$312$	−0.0758436	+	4.05878i	−0.00429380	+	0.229783i
$313$	1.77160	+	3.31444i	0.100137	+	0.187343i	0.927001	−	0.375059i	$-0.122377\pi$
$313$	1.77160	+	3.31444i	0.100137	+	0.187343i	−0.826864	+	0.562402i	$0.809877\pi$
$314$	14.2045	−	32.2145i	0.801605	−	1.81797i
$315$	0.918153	+	1.94127i	0.0517320	+	0.109378i
$316$	2.85966	+	0.412780i	0.160868	+	0.0232207i
$317$	−0.483878	+	1.93175i	−0.0271773	+	0.108498i	−0.982102	−	0.188351i	$-0.939686\pi$
$317$	−0.483878	+	1.93175i	−0.0271773	+	0.108498i	0.954924	+	0.296849i	$0.0959357\pi$
$318$	−2.26354	+	13.1981i	−0.126933	+	0.740111i
$319$	−29.1019	+	29.1019i	−1.62939	+	1.62939i
$320$	2.86614	−	4.40025i	0.160222	−	0.245982i
$321$	−2.01429	−	2.01429i	−0.112427	−	0.112427i
$322$	18.3568	−	12.9821i	1.02299	−	0.723462i
$323$	−0.464449	−	0.116338i	−0.0258426	−	0.00647324i
$324$	1.02150	−	1.71946i	0.0567498	−	0.0955256i
$325$	5.92818	−	2.80382i	0.328836	−	0.155528i
$326$	−10.0463	−	25.8933i	−0.556413	−	1.43410i
$327$	3.84605	−	2.05575i	0.212687	−	0.113683i
$328$	−5.06428	−	7.89465i	−0.279628	−	0.435909i
$329$	−10.5837	+	3.21052i	−0.583496	+	0.177002i
$330$	5.22617	−	1.45727i	0.287691	−	0.0802201i
$331$	4.06931	−	27.4330i	0.223669	−	1.50786i	−0.528527	−	0.848917i	$-0.677255\pi$
$331$	4.06931	−	27.4330i	0.223669	−	1.50786i	0.752196	−	0.658939i	$-0.228995\pi$
$332$	17.9127	+	7.33783i	0.983087	+	0.402716i
$333$	0.280018	−	0.100192i	0.0153449	−	0.00549050i
$334$	−10.7269	+	21.4147i	−0.586948	+	1.17176i
$335$	3.36131	−	5.03056i	0.183648	−	0.274849i
$336$	11.8727	+	5.50230i	0.647711	+	0.300175i
$337$	10.1770	+	15.2309i	0.554375	+	0.829681i	0.997777	−	0.0666417i	$-0.0212284\pi$
$337$	10.1770	+	15.2309i	0.554375	+	0.829681i	−0.443402	+	0.896323i	$0.646228\pi$
$338$	1.92388	+	15.3515i	0.104645	+	0.835012i
$339$	−13.4778	+	12.2156i	−0.732014	+	0.663459i
$340$	0.648483	+	0.0613131i	0.0351689	+	0.00332517i
$341$	−9.86934	+	16.4660i	−0.534454	+	0.891683i
$342$	−1.21782	+	0.615982i	−0.0658521	+	0.0333085i
$343$	6.84392	+	8.33934i	0.369537	+	0.450282i
$344$	−18.5167	+	24.0158i	−0.998353	+	1.29484i
$345$	−0.312677	−	3.17466i	−0.0168339	−	0.170918i
$346$	26.6527	−	4.67832i	1.43286	−	0.251508i
$347$	−19.9159	+	21.9739i	−1.06914	+	1.17962i	−0.0860927	+	0.996287i	$0.527438\pi$
$347$	−19.9159	+	21.9739i	−1.06914	+	1.17962i	−0.983051	+	0.183331i	$0.941312\pi$
$348$	−5.97185	+	12.7551i	−0.320125	+	0.683744i
$349$	28.6884	+	21.2767i	1.53565	+	1.13892i	0.942682	+	0.333694i	$0.108295\pi$
$349$	28.6884	+	21.2767i	1.53565	+	1.13892i	0.592971	+	0.805224i	$0.297955\pi$
$350$	−0.560054	−	21.1316i	−0.0299361	−	1.12953i
$351$	−0.549245	+	1.32600i	−0.0293165	+	0.0707764i
$352$	18.7721	−	27.2150i	1.00055	−	1.45056i
$353$	11.1042	+	26.8080i	0.591018	+	1.42684i	0.882521	+	0.470273i	$0.155845\pi$
$353$	11.1042	+	26.8080i	0.591018	+	1.42684i	−0.291503	+	0.956570i	$0.594155\pi$
$354$	0.529585	−	0.235987i	0.0281471	−	0.0125426i
$355$	−0.763313	−	5.14584i	−0.0405124	−	0.273113i
$356$	7.25516	−	4.38719i	0.384523	−	0.232521i
$357$	0.0796438	+	1.62119i	0.00421520	+	0.0858023i
$358$	−0.474046	−	0.105478i	−0.0250541	−	0.00557471i
$359$	21.0075	−	25.5977i	1.10873	−	1.35099i	0.178534	−	0.983934i	$-0.442864\pi$
$359$	21.0075	−	25.5977i	1.10873	−	1.35099i	0.930197	−	0.367060i	$-0.119636\pi$
$360$	1.51167	−	1.07795i	0.0796722	−	0.0568128i
$361$	−17.9817	−	1.77105i	−0.946407	−	0.0932130i
$362$	10.0491	−	11.6958i	0.528167	−	0.614716i
$363$	22.4637	−	5.62686i	1.17904	−	0.295334i
$364$	−8.99688	−	2.69084i	−0.471565	−	0.141038i
$365$	0.289545	−	5.89382i	0.0151555	−	0.308497i
$366$	9.86058	+	2.70807i	0.515421	+	0.141553i
$367$	0.773800	−	3.89016i	0.0403920	−	0.203064i	−0.955320	−	0.295574i	$-0.904489\pi$
$367$	0.773800	−	3.89016i	0.0403920	−	0.203064i	0.995712	+	0.0925099i	$0.0294890\pi$
$368$	−13.8523	−	13.6375i	−0.722100	−	0.710904i
$369$	−0.646940	−	3.25239i	−0.0336784	−	0.169313i
$370$	0.275377	+	0.0197723i	0.0143162	+	0.00102791i
$371$	−28.0023	−	13.2441i	−1.45380	−	0.687599i
$372$	−1.25644	+	6.44810i	−0.0651434	+	0.334318i
$373$	−18.4369	−	24.8593i	−0.954627	−	1.28717i	−0.957879	−	0.287171i	$-0.907285\pi$
$373$	−18.4369	−	24.8593i	−0.954627	−	1.28717i	0.00325220	−	0.999995i	$-0.498965\pi$
$374$	4.07101	+	0.494040i	0.210507	+	0.0255462i
$375$	−5.53968	−	2.96102i	−0.286068	−	0.152907i
$376$	4.34924	+	8.51583i	0.224295	+	0.439170i
$377$	2.93388	−	9.67171i	0.151103	−	0.498118i
$378$	3.19671	+	3.34450i	0.164421	+	0.172023i
$379$	−24.1931	−	8.65644i	−1.24272	−	0.444652i	−0.368246	−	0.929728i	$-0.620042\pi$
$379$	−24.1931	−	8.65644i	−1.24272	−	0.444652i	−0.874472	+	0.485077i	$0.838792\pi$
$380$	−1.26514	+	0.0671074i	−0.0649003	+	0.00344254i
$381$	−12.2166	+	7.32236i	−0.625876	+	0.375136i
$382$	0.719602	+	3.17551i	0.0368180	+	0.162473i
$383$		−	19.3952i		−	0.991048i	−0.868594	−	0.495524i	$-0.834976\pi$
$383$		−	19.3952i		−	0.991048i	0.868594	−	0.495524i	$-0.165024\pi$
$384$	2.86815	−	10.9441i	0.146365	−	0.558490i
$385$			12.5507i			0.639642i
$386$	12.0500	−	2.73065i	0.613329	−	0.138986i
$387$	−9.19624	+	5.51201i	−0.467471	+	0.280191i
$388$	3.80848	−	4.23514i	0.193346	−	0.215007i
$389$	−19.2174	−	6.87608i	−0.974358	−	0.348631i	−0.198893	−	0.980021i	$-0.563735\pi$
$389$	−19.2174	−	6.87608i	−0.974358	−	0.348631i	−0.775465	+	0.631390i	$0.782485\pi$
$390$	−0.963170	+	0.920607i	−0.0487720	+	0.0466168i
$391$	0.699924	−	2.30734i	0.0353967	−	0.116687i
$392$	−6.79330	+	7.96926i	−0.343113	+	0.402509i
$393$	−17.5317	−	9.37090i	−0.884358	−	0.472699i
$394$	0.115732	−	0.953658i	0.00583049	−	0.0480446i
$395$	0.564901	+	0.761681i	0.0284233	+	0.0383243i
$396$	9.69354	−	6.53193i	0.487119	−	0.328242i
$397$	28.3675	+	13.4168i	1.42372	+	0.673372i	0.975388	−	0.220493i	$-0.0707667\pi$
$397$	28.3675	+	13.4168i	1.42372	+	0.673372i	0.448336	+	0.893865i	$0.352017\pi$
$398$	−0.322457	+	4.49098i	−0.0161633	+	0.225113i
$399$	−0.615900	−	3.09634i	−0.0308335	−	0.155011i
$400$	−17.8969	+	3.70549i	−0.894843	+	0.185275i
$401$	3.58518	−	18.0239i	0.179035	−	0.900071i	−0.781923	−	0.623376i	$-0.785761\pi$
$401$	3.58518	−	18.0239i	0.179035	−	0.900071i	0.960958	−	0.276695i	$-0.0892392\pi$
$402$	3.45198	−	12.5693i	0.172169	−	0.626900i
$403$	0.231321	−	4.70866i	0.0115229	−	0.234555i
$404$	−26.8162	+	14.4685i	−1.33416	+	0.719837i
$405$	0.636751	−	0.159498i	0.0316404	−	0.00792551i
$406$	−24.7111	−	21.2319i	−1.22639	−	1.05372i
$407$	1.72979	+	0.170370i	0.0857426	+	0.00844491i
$408$	1.36741	−	0.315491i	0.0676971	−	0.0156191i
$409$	−12.3401	+	15.0365i	−0.610179	+	0.743505i	−0.982840	−	0.184463i	$-0.940946\pi$
$409$	−12.3401	+	15.0365i	−0.610179	+	0.743505i	0.372661	+	0.927968i	$0.378446\pi$
$410$	0.668617	−	3.00493i	0.0330206	−	0.148403i
$411$	0.181607	+	3.69670i	0.00895803	+	0.182345i
$412$	17.3334	+	4.26990i	0.853954	+	0.210363i
$413$	0.196794	+	1.32668i	0.00968358	+	0.0652814i
$414$	−2.79735	−	6.27760i	−0.137482	−	0.308527i
$415$	2.43131	+	5.86970i	0.119348	+	0.288132i
$416$	−0.915111	+	8.06725i	−0.0448670	+	0.395529i
$417$	−0.954785	+	2.30505i	−0.0467560	+	0.112879i
$418$	−7.97337	+	0.211319i	−0.389990	+	0.0103359i
$419$	−28.3384	−	21.0172i	−1.38442	−	1.02676i	−0.994370	−	0.105962i	$-0.966208\pi$
$419$	−28.3384	−	21.0172i	−1.38442	−	1.02676i	−0.390049	−	0.920794i	$-0.627542\pi$
$420$	1.46269	+	4.03815i	0.0713721	+	0.197042i
$421$	0.717929	−	0.792113i	0.0349897	−	0.0386052i	−0.723205	−	0.690634i	$-0.757332\pi$
$421$	0.717929	−	0.792113i	0.0349897	−	0.0386052i	0.758195	+	0.652028i	$0.226082\pi$
$422$	3.60379	+	20.5310i	0.175430	+	0.999434i
$423$	0.331370	+	3.36446i	0.0161118	+	0.163586i
$424$	−6.99161	+	25.8528i	−0.339543	+	1.25552i
$425$	−1.43816	−	1.75240i	−0.0697610	−	0.0850041i
$426$	−5.05862	−	10.0011i	−0.245091	−	0.484553i
$427$	−12.1609	+	20.2893i	−0.588508	+	0.981867i
$428$	−3.63149	−	4.38991i	−0.175535	−	0.212194i
$429$	−6.21528	+	5.63320i	−0.300076	+	0.271973i
$430$	−9.87586	+	1.23766i	−0.476256	+	0.0596852i
$431$	−14.5558	−	21.7842i	−0.701126	−	1.04931i	−0.995605	−	0.0936512i	$-0.970146\pi$
$431$	−14.5558	−	21.7842i	−0.701126	−	1.04931i	0.294479	−	0.955658i	$-0.404854\pi$
$432$	2.35762	−	3.23135i	0.113431	−	0.155468i
$433$	−14.2766	+	21.3665i	−0.686090	+	1.02681i	0.310988	+	0.950414i	$0.399340\pi$
$433$	−14.2766	+	21.3665i	−0.686090	+	1.02681i	−0.997078	+	0.0763923i	$0.975660\pi$
$434$	−13.5873	−	6.80606i	−0.652213	−	0.326701i
$435$	−4.35227	+	1.55727i	−0.208675	+	0.0746653i
$436$	8.04495	−	3.36921i	0.385283	−	0.161356i
$437$	−0.688121	+	4.63894i	−0.0329173	+	0.221910i
$438$	−3.41467	−	12.2459i	−0.163159	−	0.585134i
$439$	27.6182	−	8.37789i	1.31814	−	0.399855i	0.448611	−	0.893727i	$-0.351919\pi$
$439$	27.6182	−	8.37789i	1.31814	−	0.399855i	0.869534	+	0.493872i	$0.164419\pi$
$440$	10.6803	−	1.91774i	0.509162	−	0.0914244i
$441$	−3.26517	+	1.74527i	−0.155484	+	0.0831080i
$442$	−0.938878	+	0.364273i	−0.0446579	+	0.0173267i
$443$	−12.1549	+	5.74884i	−0.577497	+	0.273136i	−0.693906	−	0.720066i	$-0.744112\pi$
$443$	−12.1549	+	5.74884i	−0.577497	+	0.273136i	0.116409	+	0.993201i	$0.462862\pi$
$444$	0.576412	−	0.146779i	0.0273553	−	0.00696582i
$445$	2.69934	+	0.676150i	0.127961	+	0.0320526i
$446$	−5.19786	−	7.34986i	−0.246126	−	0.348026i
$447$	12.8881	+	12.8881i	0.609588	+	0.609588i
$448$	22.6042	+	13.1909i	1.06795	+	0.623210i
$449$	5.26557	−	5.26557i	0.248498	−	0.248498i	−0.571856	−	0.820354i	$-0.693777\pi$
$449$	5.26557	−	5.26557i	0.248498	−	0.248498i	0.820354	+	0.571856i	$0.193777\pi$
$450$	−6.36871	−	1.09227i	−0.300224	−	0.0514899i
$451$	4.70916	−	18.8000i	0.221746	−	0.885259i
$452$	−29.1356	+	21.7854i	−1.37042	+	1.02470i
$453$	3.65947	+	7.73729i	0.171937	+	0.363530i
$454$	35.7377	+	15.7580i	1.67725	+	0.739559i
$455$	−1.45290	−	2.71819i	−0.0681131	−	0.127431i
$456$	−2.54079	+	0.997231i	−0.118983	+	0.0466996i
$457$	5.29005	+	17.4390i	0.247458	+	0.815760i	0.989390	+	0.145285i	$0.0464098\pi$
$457$	5.29005	+	17.4390i	0.247458	+	0.815760i	−0.741932	+	0.670475i	$0.766090\pi$
$458$	−5.77977	−	3.25931i	−0.270071	−	0.152297i
$459$	0.490785	+	0.0728010i	0.0229079	+	0.00339806i
$460$	−0.0249229	−	6.37999i	−0.00116203	−	0.297469i
$461$	−6.01821	−	16.8198i	−0.280296	−	0.783374i	−0.996353	−	0.0853321i	$-0.972805\pi$
$461$	−6.01821	−	16.8198i	−0.280296	−	0.783374i	0.716057	−	0.698042i	$-0.245945\pi$
$462$	8.53193	+	25.6581i	0.396941	+	1.19372i
$463$	−22.3526	−	14.9355i	−1.03881	−	0.694113i	−0.0855755	−	0.996332i	$-0.527273\pi$
$463$	−22.3526	−	14.9355i	−1.03881	−	0.694113i	−0.953239	+	0.302218i	$0.902273\pi$
$464$	−14.2919	+	24.2727i	−0.663485	+	1.12683i
$465$	−1.79277	+	1.19789i	−0.0831376	+	0.0555507i
$466$	−9.56804	+	12.3098i	−0.443231	+	0.570241i
$467$	−12.5642	−	13.8625i	−0.581402	−	0.641479i	0.377232	−	0.926119i	$-0.376876\pi$
$467$	−12.5642	−	13.8625i	−0.581402	−	0.641479i	−0.958634	+	0.284640i	$0.908126\pi$
$468$	−1.34324	+	2.53682i	−0.0620914	+	0.117264i
$469$	25.8628	+	15.5016i	1.19423	+	0.715796i
$470$	−0.978641	+	2.98193i	−0.0451413	+	0.137546i
$471$	19.2442	−	15.7933i	0.886728	−	0.727719i
$472$	1.09889	−	0.370181i	0.0505807	−	0.0170390i
$473$	−62.3603	+	6.14195i	−2.86733	+	0.282407i
$474$	1.67265	+	1.17313i	0.0768275	+	0.0538838i
$475$	3.26705	+	2.96108i	0.149903	+	0.135864i
$476$	−0.146620	+	3.24297i	−0.00672034	+	0.148641i
$477$	−5.64050	+	7.60534i	−0.258261	+	0.348224i
$478$	−8.90270	−	8.44299i	−0.407200	−	0.386173i
$479$	12.8918	+	5.33996i	0.589041	+	0.243989i	0.657238	−	0.753683i	$-0.271725\pi$
$479$	12.8918	+	5.33996i	0.589041	+	0.243989i	−0.0681968	+	0.997672i	$0.521725\pi$
$480$	3.21286	−	1.86174i	0.146646	−	0.0849763i
$481$	−0.394356	+	0.163347i	−0.0179811	+	0.00744800i
$482$	−21.1508	−	8.11135i	−0.963394	−	0.369462i
$483$	15.7262	−	2.33276i	0.715565	−	0.106144i
$484$	45.7872	−	6.97479i	2.08124	−	0.317036i
$485$	1.86714	−	0.0917267i	0.0847824	−	0.00416509i
$486$	1.19332	−	0.758933i	0.0541302	−	0.0344259i
$487$	3.83991	+	3.15133i	0.174003	+	0.142800i	0.717364	−	0.696699i	$-0.245349\pi$
$487$	3.83991	+	3.15133i	0.174003	+	0.142800i	−0.543361	+	0.839499i	$0.682849\pi$
$488$	19.1238	+	7.24841i	0.865693	+	0.328120i
$489$	1.92497	−	19.5446i	0.0870503	−	0.883837i
$490$	−3.42714	+	0.259533i	−0.154823	+	0.0117245i
$491$	−3.37646	−	13.4796i	−0.152378	−	0.608325i	−0.997300	−	0.0734363i	$-0.976603\pi$
$491$	−3.37646	−	13.4796i	−0.152378	−	0.608325i	0.844922	−	0.534889i	$-0.179647\pi$
$492$	−0.675849	−	6.59769i	−0.0304696	−	0.297447i
$493$	−3.48968	−	0.171437i	−0.157167	−	0.00772113i
$494$	1.70238	−	0.968786i	0.0765939	−	0.0435878i
$495$	3.76272	+	0.748451i	0.169122	+	0.0336404i
$496$	−3.71563	+	12.6024i	−0.166837	+	0.565865i
$497$	25.4280	−	5.05794i	1.14060	−	0.226880i
$498$	8.96068	+	10.3470i	0.401538	+	0.463660i
$499$	4.76456	−	10.0738i	0.213291	−	0.450966i	−0.768771	−	0.639524i	$-0.779131\pi$
$499$	4.76456	−	10.0738i	0.213291	−	0.450966i	0.982062	+	0.188558i	$0.0603814\pi$
$500$	−10.4727	−	6.93864i	−0.468355	−	0.310305i
$501$	−13.6031	+	10.0887i	−0.607742	+	0.450732i
$502$	4.13016	−	3.23621i	0.184338	−	0.144439i
$503$	−7.34904	+	13.7491i	−0.327677	+	0.613041i	−0.990779	−	0.135488i	$-0.956740\pi$
$503$	−7.34904	+	13.7491i	−0.327677	+	0.613041i	0.663102	+	0.748529i	$0.269240\pi$
$504$	5.73540	+	7.26111i	0.255475	+	0.323436i
$505$	−9.57012	−	2.90307i	−0.425865	−	0.129185i
$506$	0.907314	−	40.1567i	0.0403350	−	1.78518i
$507$	−3.68560	+	10.3006i	−0.163683	+	0.457464i
$508$	−25.7032	+	12.2798i	−1.14040	+	0.544829i
$509$	19.8002	+	33.0346i	0.877628	+	1.46423i	0.885696	+	0.464266i	$0.153682\pi$
$509$	19.8002	+	33.0346i	0.877628	+	1.46423i	−0.00806759	+	0.999967i	$0.502568\pi$
$510$	0.389613	+	0.245655i	0.0172523	+	0.0108778i
$511$	29.4087			1.30096
$512$	7.77115	−	21.2511i	0.343439	−	0.939175i
$513$	−0.965017			−0.0426065
$514$	26.4902	+	16.7023i	1.16843	+	0.736708i
$515$	3.01217	+	5.02550i	0.132732	+	0.221450i
$516$	−19.3485	+	9.24382i	−0.851770	+	0.406936i
$517$	−6.65647	+	18.6036i	−0.292751	+	0.818185i
$518$	−0.0310806	+	1.37559i	−0.00136560	+	0.0604400i
$519$	18.3105	+	5.55442i	0.803741	+	0.243812i
$520$	−2.09110	+	1.65172i	−0.0917007	+	0.0724325i
$521$	−5.27806	+	9.87455i	−0.231236	+	0.432612i	−0.970602	−	0.240692i	$-0.922626\pi$
$521$	−5.27806	+	9.87455i	−0.231236	+	0.432612i	0.739366	+	0.673304i	$0.235126\pi$
$522$	−7.83900	+	6.14229i	−0.343104	+	0.268841i
$523$	19.5740	−	14.5170i	0.855909	−	0.634786i	−0.0761481	−	0.997097i	$-0.524262\pi$
$523$	19.5740	−	14.5170i	0.855909	−	0.634786i	0.932057	+	0.362311i	$0.118012\pi$
$524$	−33.1436	−	21.9591i	−1.44789	−	0.959286i
$525$	6.39091	−	13.5124i	0.278922	−	0.589732i
$526$	12.4075	+	14.3270i	0.540992	+	0.624689i
$527$	−1.59840	+	0.317941i	−0.0696273	+	0.0138497i
$528$	20.5307	−	11.1810i	0.893483	−	0.486590i
$529$	−0.604853	−	0.120313i	−0.0262979	−	0.00523099i
$530$	−7.63959	+	4.34751i	−0.331843	+	0.188844i
$531$	0.409476	+	0.0201163i	0.0177697	+	0.000872971i
$532$	−0.643421	−	6.28113i	−0.0278958	−	0.272321i
$533$	1.15645	+	4.61680i	0.0500913	+	0.199976i
$534$	5.97808	−	0.452711i	0.258697	−	0.0195907i
$535$	0.183283	−	1.86091i	0.00792404	−	0.0804541i
$536$	9.23957	−	24.3771i	0.399089	−	1.05293i
$537$	−0.265451	−	0.217850i	−0.0114550	−	0.00940091i
$538$	3.52932	−	2.24459i	0.152160	−	0.0967711i
$539$	−21.6121	+	1.06173i	−0.930897	+	0.0457321i
$540$	1.29787	−	0.197706i	0.0558516	−	0.00850791i
$541$	−6.51929	+	0.967046i	−0.280286	+	0.0415765i	−0.285394	−	0.958410i	$-0.592124\pi$
$541$	−6.51929	+	0.967046i	−0.280286	+	0.0415765i	0.00510727	+	0.999987i	$0.498374\pi$
$542$	−27.1675	−	10.4188i	−1.16694	−	0.447524i
$543$	10.0736	−	4.17261i	0.432298	−	0.179064i
$544$	2.78208	−	0.370754i	0.119281	−	0.0158959i
$545$	2.64474	+	1.09549i	0.113288	+	0.0469256i
$546$	−4.81808	−	4.56928i	−0.206195	−	0.195547i
$547$	18.4996	−	24.9438i	0.790986	−	1.06652i	−0.205153	−	0.978730i	$-0.565769\pi$
$547$	18.4996	−	24.9438i	0.790986	−	1.06652i	0.996139	−	0.0877914i	$-0.0279809\pi$
$548$	−0.334330	+	7.39477i	−0.0142819	+	0.315889i
$549$	5.35756	+	4.85581i	0.228655	+	0.207241i
$550$	−30.9186	−	21.6851i	−1.31837	−	0.924656i
$551$	6.76286	−	0.666084i	0.288108	−	0.0283761i
$552$	−4.38806	−	13.0261i	−0.186768	−	0.554426i
$553$	−3.65331	+	2.99819i	−0.155354	+	0.127496i
$554$	−4.05805	+	12.3649i	−0.172410	+	0.525336i
$555$	0.167448	+	0.100364i	0.00710776	+	0.00426023i
$556$	−2.33504	+	4.40990i	−0.0990276	+	0.187021i
$557$	14.5929	+	16.1008i	0.618322	+	0.682213i	0.966926	−	0.255057i	$-0.0820943\pi$
$557$	14.5929	+	16.1008i	0.618322	+	0.682213i	−0.348604	+	0.937270i	$0.613344\pi$
$558$	−2.85074	+	3.66764i	−0.120682	+	0.155263i
$559$	12.7948	−	8.54921i	0.541162	−	0.361593i
$560$	2.15218	+	8.31581i	0.0909464	+	0.351407i
$561$	2.41106	+	1.61102i	0.101795	+	0.0680172i
$562$	−0.699308	−	2.10304i	−0.0294985	−	0.0887112i
$563$	10.6217	+	29.6857i	0.447652	+	1.25110i	0.927523	+	0.373765i	$0.121933\pi$
$563$	10.6217	+	29.6857i	0.447652	+	1.25110i	−0.479871	+	0.877339i	$0.659317\pi$
$564$	0.0264129	+	6.76143i	0.00111218	+	0.284707i
$565$	−11.8110	−	1.75200i	−0.496893	−	0.0737071i
$566$	22.0251	+	12.4203i	0.925782	+	0.522063i
$567$	0.949649	+	3.13057i	0.0398815	+	0.131472i
$568$	−8.18954	−	20.8656i	−0.343626	−	0.875503i
$569$	−4.37492	−	8.18490i	−0.183406	−	0.343129i	0.773370	−	0.633955i	$-0.218570\pi$
$569$	−4.37492	−	8.18490i	−0.183406	−	0.343129i	−0.956776	+	0.290827i	$0.906070\pi$
$570$	−0.819699	−	0.361434i	−0.0343334	−	0.0151388i
$571$	9.86922	+	20.8667i	0.413014	+	0.873245i	0.998061	+	0.0622452i	$0.0198261\pi$
$571$	9.86922	+	20.8667i	0.413014	+	0.873245i	−0.585047	+	0.810999i	$0.698924\pi$
$572$	−13.4359	+	10.0463i	−0.561781	+	0.420057i
$573$	−0.559426	+	2.23335i	−0.0233704	+	0.0932997i
$574$	15.1212	+	2.59337i	0.631149	+	0.108245i
$575$	−15.7010	+	15.7010i	−0.654775	+	0.654775i
$576$	5.30264	−	5.99016i	0.220943	−	0.249590i
$577$	13.4189	+	13.4189i	0.558636	+	0.558636i	0.928919	−	0.370283i	$-0.120739\pi$
$577$	13.4189	+	13.4189i	0.558636	+	0.558636i	−0.370283	+	0.928919i	$0.620739\pi$
$578$	−13.6807	−	19.3448i	−0.569043	−	0.804636i
$579$	8.47484	+	2.12284i	0.352203	+	0.0882221i
$580$	−8.95906	+	2.28136i	−0.372005	+	0.0947283i
$581$	−28.6233	+	13.5378i	−1.18749	+	0.561642i
$582$	3.75476	−	1.45680i	0.155640	−	0.0603863i
$583$	−48.8050	+	26.0868i	−2.02130	+	1.08041i
$584$	−4.49363	−	25.0260i	−0.185948	−	1.03558i
$585$	−0.901561	+	0.273486i	−0.0372750	+	0.0113072i
$586$	−11.9332	−	42.7956i	−0.492955	−	1.76787i
$587$	−6.36376	+	42.9010i	−0.262660	+	1.77071i	0.309821	+	0.950795i	$0.399731\pi$
$587$	−6.36376	+	42.9010i	−0.262660	+	1.77071i	−0.572481	+	0.819918i	$0.694019\pi$
$588$	−6.82990	+	2.86034i	−0.281660	+	0.117959i
$589$	2.98448	−	1.06787i	0.122974	−	0.0440006i
$590$	0.340280	+	0.170450i	0.0140091	+	0.00701733i
$591$	0.377391	−	0.564805i	0.0155238	−	0.0232330i
$592$	1.17534	−	0.183741i	0.0483061	−	0.00755170i
$593$	−13.0680	−	19.5576i	−0.536638	−	0.803136i	0.459750	−	0.888048i	$-0.347939\pi$
$593$	−13.0680	−	19.5576i	−0.536638	−	0.803136i	−0.996388	+	0.0849124i	$0.972939\pi$
$594$	8.20116	−	1.02778i	0.336498	−	0.0421704i
$595$	−0.789459	+	0.715524i	−0.0323647	+	0.0293336i
$596$	23.2355	+	28.0881i	0.951765	+	1.15053i
$597$	−1.63679	+	2.73082i	−0.0669894	+	0.111765i
$598$	4.45215	+	8.80205i	0.182062	+	0.359943i
$599$	−26.0053	−	31.6876i	−1.06255	−	1.29472i	−0.953732	−	0.300659i	$-0.902794\pi$
$599$	−26.0053	−	31.6876i	−1.06255	−	1.29472i	−0.108818	−	0.994062i	$-0.534706\pi$
$600$	−12.4752	−	3.37379i	−0.509300	−	0.137734i
$601$	−3.44072	−	34.9342i	−0.140350	−	1.42500i	−0.764969	−	0.644068i	$-0.777246\pi$
$601$	−3.44072	−	34.9342i	−0.140350	−	1.42500i	0.624619	−	0.780930i	$-0.285254\pi$
$602$	−8.57579	−	48.8568i	−0.349523	−	1.99125i
$603$	6.18971	−	6.82930i	0.252065	−	0.278110i
$604$	5.82983	+	16.0948i	0.237213	+	0.654888i
$605$	12.2097	+	9.05537i	0.496397	+	0.368153i
$606$	−21.5383	+	0.570832i	−0.874934	+	0.0231885i
$607$	11.2055	−	27.0526i	0.454819	−	1.09803i	−0.515649	−	0.856800i	$-0.672449\pi$
$607$	11.2055	−	27.0526i	0.454819	−	1.09803i	0.970468	−	0.241230i	$-0.0775508\pi$
$608$	−5.24675	+	1.50729i	−0.212784	+	0.0611285i
$609$	−8.81598	−	21.2837i	−0.357242	−	0.862457i
$610$	2.73211	+	6.13119i	0.110620	+	0.248245i
$611$	−0.711965	−	4.79968i	−0.0288030	−	0.194174i
$612$	0.963506	+	0.237350i	0.0389474	+	0.00959429i
$613$	−0.226176	−	4.60391i	−0.00913515	−	0.185950i	−0.999026	−	0.0441205i	$-0.985951\pi$
$613$	−0.226176	−	4.60391i	−0.00913515	−	0.185950i	0.989891	−	0.141830i	$-0.0452985\pi$
$614$	1.30585	−	5.86882i	0.0526999	−	0.236846i
$615$	1.38093	−	1.68266i	0.0556843	−	0.0678516i
$616$	12.1577	+	52.6946i	0.489850	+	2.12313i
$617$	3.55799	+	0.350431i	0.143239	+	0.0141078i	0.169383	−	0.985550i	$-0.445823\pi$
$617$	3.55799	+	0.350431i	0.143239	+	0.0141078i	−0.0261434	+	0.999658i	$0.508323\pi$
$618$	9.57430	+	8.22629i	0.385135	+	0.330910i
$619$	40.7979	−	10.2193i	1.63981	−	0.410750i	0.690055	−	0.723757i	$-0.257586\pi$
$619$	40.7979	−	10.2193i	1.63981	−	0.410750i	0.949751	+	0.313006i	$0.101336\pi$
$620$	−3.79512	+	2.04764i	−0.152416	+	0.0822351i
$621$	0.238454	−	4.85385i	0.00956884	−	0.194778i
$622$	−1.49691	+	5.45055i	−0.0600208	+	0.218547i
$623$	−2.70560	+	13.6020i	−0.108398	+	0.544951i
$624$	−3.15213	+	4.79823i	−0.126186	+	0.192083i
$625$	3.65254	+	18.3626i	0.146102	+	0.734502i
$626$	−0.380635	+	5.30125i	−0.0152132	+	0.211881i
$627$	−5.09850	−	2.41141i	−0.203615	−	0.0963025i
$628$	41.2908	−	27.8236i	1.64768	−	1.11028i
$629$	0.0879003	+	0.118520i	0.00350481	+	0.00472569i
$630$	−0.365867	+	3.01483i	−0.0145765	+	0.120114i
$631$	33.7412	+	18.0351i	1.34322	+	0.717964i	0.977135	−	0.212618i	$-0.0681991\pi$
$631$	33.7412	+	18.0351i	1.34322	+	0.717964i	0.366082	+	0.930583i	$0.380699\pi$
$632$	3.10960	+	2.65074i	0.123693	+	0.105441i
$633$	−4.27867	+	14.1049i	−0.170062	+	0.560619i
$634$	−2.03590	+	1.94594i	−0.0808561	+	0.0772830i
$635$	−8.80289	−	3.14972i	−0.349332	−	0.124993i
$636$	−12.6627	+	14.0813i	−0.502108	+	0.558359i
$637$	4.55777	−	2.73182i	0.180585	−	0.108239i
$638$	−56.7645	+	12.8634i	−2.24733	+	0.509267i
$639$		−	7.92499i		−	0.313508i
$640$	6.74767	−	3.10210i	0.266725	−	0.122621i
$641$			22.3657i			0.883391i	0.897165	+	0.441695i	$0.145623\pi$
$641$			22.3657i			0.883391i	−0.897165	+	0.441695i	$0.854377\pi$
$642$	−0.890344	−	3.92897i	−0.0351391	−	0.155064i
$643$	9.04856	−	5.42350i	0.356841	−	0.213882i	−0.324437	−	0.945907i	$-0.605175\pi$
$643$	9.04856	−	5.42350i	0.356841	−	0.213882i	0.681277	+	0.732025i	$0.261425\pi$
$644$	31.7518	−	1.68423i	1.25120	−	0.0663678i
$645$	−6.62650	−	2.37100i	−0.260918	−	0.0933581i
$646$	−0.467860	−	0.489491i	−0.0184077	−	0.0192588i
$647$	−1.13673	+	3.74731i	−0.0446897	+	0.147322i	−0.976446	−	0.215762i	$-0.930776\pi$
$647$	−1.13673	+	3.74731i	−0.0446897	+	0.147322i	0.931756	+	0.363084i	$0.118276\pi$
$648$	2.51892	−	1.28647i	0.0989527	−	0.0505375i
$649$	2.11313	+	1.12949i	0.0829475	+	0.0443364i
$650$	9.20659	+	1.11727i	0.361112	+	0.0438230i
$651$	−6.40118	−	8.63099i	−0.250882	−	0.338275i
$652$	7.51227	−	38.5532i	0.294203	−	1.50986i
$653$	−4.20674	−	1.98964i	−0.164623	−	0.0778607i	0.343468	−	0.939164i	$-0.388398\pi$
$653$	−4.20674	−	1.98964i	−0.164623	−	0.0778607i	−0.508090	+	0.861304i	$0.669648\pi$
$654$	6.15153	+	0.441685i	0.240544	+	0.0172713i
$655$	−2.54574	−	12.7983i	−0.0994703	−	0.500071i
$656$	−0.103631	−	13.2640i	−0.00404611	−	0.517873i
$657$	1.75377	−	8.81679i	0.0684210	−	0.343976i
$658$	−15.0826	−	4.14222i	−0.587980	−	0.161480i
$659$	1.74233	−	35.4660i	0.0678716	−	1.38156i	−0.687463	−	0.726220i	$-0.741276\pi$
$659$	1.74233	−	35.4660i	0.0678716	−	1.38156i	0.755334	−	0.655339i	$-0.227474\pi$
$660$	7.35112	+	2.19862i	0.286142	+	0.0855811i
$661$	8.19176	−	2.05193i	0.318623	−	0.0798108i	−0.0803696	−	0.996765i	$-0.525610\pi$
$661$	8.19176	−	2.05193i	0.318623	−	0.0798108i	0.398992	+	0.916954i	$0.369360\pi$
$662$	25.5598	−	29.7482i	0.993411	−	1.15620i
$663$	−0.708676	−	0.0697985i	−0.0275227	−	0.00271075i
$664$	15.8939	+	22.2890i	0.616803	+	0.864982i
$665$	1.31467	−	1.60193i	0.0509807	−	0.0621201i
$666$	0.410552	+	0.0913505i	0.0159085	+	0.00353976i
$667$	1.67918	+	34.1805i	0.0650180	+	1.32347i
$668$	−28.9847	+	17.5270i	−1.12145	+	0.678141i
$669$	−0.934007	−	6.29656i	−0.0361108	−	0.243439i
$670$	7.81545	−	3.48263i	0.301937	−	0.134546i
$671$	16.1719	+	39.0424i	0.624310	+	1.50722i
$672$	10.0529	+	15.5375i	0.387800	+	0.599371i
$673$	−10.4279	+	25.1752i	−0.401967	+	0.970434i	0.585221	+	0.810874i	$0.301008\pi$
$673$	−10.4279	+	25.1752i	−0.401967	+	0.970434i	−0.987188	+	0.159560i	$0.948992\pi$
$674$	0.686339	+	25.8966i	0.0264368	+	0.997499i
$675$	−3.66994	−	2.72182i	−0.141256	−	0.104763i
$676$	−9.27762	+	19.8158i	−0.356832	+	0.762146i
$677$	−2.40698	+	2.65570i	−0.0925079	+	0.102067i	−0.785446	−	0.618931i	$-0.787566\pi$
$677$	−2.40698	+	2.65570i	−0.0925079	+	0.102067i	0.692938	+	0.720998i	$0.256316\pi$
$678$	−25.3370	+	4.44738i	−0.973062	+	0.170801i
$679$	0.913183	+	9.27170i	0.0350447	+	0.355815i
$680$	0.729520	+	0.562476i	0.0279758	+	0.0215700i
$681$	17.5206	+	21.3489i	0.671392	+	0.818093i
$682$	−24.2262	+	12.2538i	−0.927670	+	0.469223i
$683$	21.1765	−	35.3308i	0.810295	−	1.35190i	−0.122861	−	0.992424i	$-0.539207\pi$
$683$	21.1765	−	35.3308i	0.810295	−	1.35190i	0.933156	−	0.359472i	$-0.117043\pi$
$684$	−1.92146	−	0.181672i	−0.0734690	−	0.00694640i
$685$	−1.80016	+	1.63157i	−0.0687806	+	0.0623391i
$686$	1.89716	+	15.1383i	0.0724338	+	0.577983i
$687$	−2.60671	−	3.90122i	−0.0994522	−	0.148841i
$688$	−40.2654	+	14.7630i	−1.53510	+	0.562836i
$689$	7.55016	−	11.2996i	0.287638	−	0.430481i
$690$	2.02049	−	4.03362i	0.0769186	−	0.153557i
$691$	−1.24382	+	0.445045i	−0.0473171	+	0.0169303i	−0.360442	−	0.932782i	$-0.617374\pi$
$691$	−1.24382	+	0.445045i	−0.0473171	+	0.0169303i	0.313125	+	0.949712i	$0.398624\pi$
$692$	35.4127	+	14.5066i	1.34619	+	0.551459i
$693$	−2.80546	+	18.9129i	−0.106571	+	0.718440i
$694$	−40.3992	+	11.2649i	−1.53353	+	0.427612i
$695$	−1.56724	+	0.475416i	−0.0594486	+	0.0180336i
$696$	−16.7647	+	10.7543i	−0.635465	+	0.407640i
$697$	1.45103	−	0.775590i	0.0549616	−	0.0293776i
$698$	18.2710	+	47.0916i	0.691566	+	1.78244i
$699$	−9.96602	+	4.71358i	−0.376949	+	0.178284i
$700$	15.2689	−	25.7018i	0.577110	−	0.971436i
$701$	20.5317	+	5.14293i	0.775472	+	0.194246i	0.610461	−	0.792046i	$-0.290984\pi$
$701$	20.5317	+	5.14293i	0.775472	+	0.194246i	0.165011	+	0.986292i	$0.447234\pi$
$702$	−1.65720	+	1.17198i	−0.0625471	+	0.0442337i
$703$	−0.202939	−	0.202939i	−0.00765399	−	0.00765399i
$704$	42.9840	−	18.3976i	1.62002	−	0.693386i
$705$	−1.56921	+	1.56921i	−0.0590998	+	0.0590998i
$706$	−6.93658	+	40.4453i	−0.261062	+	1.52218i
$707$	12.1104	−	48.3475i	0.455459	−	1.81829i
$708$	0.811528	+	0.117141i	0.0304991	+	0.00440242i
$709$	−18.4192	−	38.9441i	−0.691747	−	1.46258i	−0.877301	−	0.479941i	$-0.840658\pi$
$709$	−18.4192	−	38.9441i	−0.691747	−	1.46258i	0.185554	−	0.982634i	$-0.440592\pi$
$710$	2.96819	−	6.73160i	0.111394	−	0.252632i
$711$	0.681002	+	1.27406i	0.0255396	+	0.0477812i
$712$	11.9883	+	0.224017i	0.449281	+	0.00839538i
$713$	4.63369	+	15.2752i	0.173533	+	0.572062i
$714$	−1.12753	+	1.99946i	−0.0421967	+	0.0748281i
$715$	−5.44664	−	0.807932i	−0.203693	−	0.0302150i
$716$	−0.487532	−	0.483738i	−0.0182199	−	0.0180781i
$717$	−2.92282	−	8.16873i	−0.109155	−	0.305067i
$718$	44.4382	−	14.7767i	1.65842	−	0.551463i
$719$	−10.3909	−	6.94297i	−0.387515	−	0.258929i	0.346518	−	0.938043i	$-0.387364\pi$
$719$	−10.3909	−	6.94297i	−0.387515	−	0.258929i	−0.734033	+	0.679114i	$0.762364\pi$
$720$	2.62144	−	0.149322i	0.0976954	−	0.00556489i
$721$	−24.2790	+	16.2227i	−0.904199	+	0.604166i
$722$	−20.1753	−	15.6817i	−0.750848	−	0.583611i
$723$	−10.7570	−	11.8685i	−0.400058	−	0.441396i
$724$	20.8432	−	6.41174i	0.774631	−	0.238290i
$725$	27.5977	+	16.5414i	1.02495	+	0.614333i
$726$	31.1170	+	10.2123i	1.15486	+	0.379014i
$727$	27.7020	−	22.7344i	1.02741	−	0.843174i	0.0396594	−	0.999213i	$-0.487373\pi$
$727$	27.7020	−	22.7344i	1.02741	−	0.843174i	0.987751	+	0.156040i	$0.0498727\pi$
$728$	−8.73317	−	10.0050i	−0.323673	−	0.370811i
$729$	0.995185	−	0.0980171i	0.0368587	−	0.00363026i
$730$	4.79188	−	6.83226i	0.177356	−	0.252873i
$731$	−3.94155	−	3.57241i	−0.145783	−	0.132130i
$732$	9.75340	+	10.6771i	0.360496	+	0.394637i
$733$	−10.8169	+	14.5849i	−0.399532	+	0.538706i	−0.956463	−	0.291852i	$-0.905729\pi$
$733$	−10.8169	+	14.5849i	−0.399532	+	0.538706i	0.556932	+	0.830558i	$0.311979\pi$
$734$	3.85989	−	4.07006i	0.142471	−	0.150229i
$735$	−2.24530	−	0.930034i	−0.0828191	−	0.0343048i
$736$	−6.28489	−	26.7626i	−0.231664	−	0.986481i
$737$	49.7675	−	20.6144i	1.83321	−	0.759341i
$738$	1.67924	−	4.37873i	0.0618138	−	0.161183i
$739$	16.2133	−	2.40502i	0.596416	−	0.0884699i	0.158304	−	0.987390i	$-0.449397\pi$
$739$	16.2133	−	2.40502i	0.596416	−	0.0884699i	0.438112	+	0.898920i	$0.355647\pi$
$740$	0.314514	+	0.231361i	0.0115618	+	0.00850499i
$741$	1.38337	−	0.0679606i	0.0508194	−	0.00249659i
$742$	−23.5090	−	36.9648i	−0.863041	−	1.35702i
$743$	−5.72256	−	4.69638i	−0.209940	−	0.172293i	0.523547	−	0.851997i	$-0.324608\pi$
$743$	−5.72256	−	4.69638i	−0.209940	−	0.172293i	−0.733487	+	0.679703i	$0.762108\pi$
$744$	−6.36663	+	6.76603i	−0.233412	+	0.248055i
$745$	−1.17271	+	11.9067i	−0.0429648	+	0.436229i
$746$	−3.30517	−	43.6450i	−0.121011	−	1.59796i
$747$	2.35173	+	9.38863i	0.0860453	+	0.343512i
$748$	4.49742	+	3.66163i	0.164442	+	0.133882i
$749$	9.30794	+	0.457270i	0.340105	+	0.0167083i
$750$	−4.39361	−	7.72060i	−0.160432	−	0.281917i
$751$	21.0108	+	4.17931i	0.766696	+	0.152505i	0.562919	−	0.826512i	$-0.309678\pi$
$751$	21.0108	+	4.17931i	0.766696	+	0.152505i	0.203777	+	0.979017i	$0.434678\pi$
$752$	−1.22030	+	13.4678i	−0.0444997	+	0.491120i
$753$	3.63891	−	0.723825i	0.132609	−	0.0263776i
$754$	10.8048	−	9.35714i	0.393487	−	0.340767i
$755$	−2.40216	+	5.07893i	−0.0874234	+	0.184841i
$756$	1.30151	+	6.41213i	0.0473355	+	0.233207i
$757$	−0.398370	+	0.295451i	−0.0144790	+	0.0107384i	−0.602915	−	0.797806i	$-0.705994\pi$
$757$	−0.398370	+	0.295451i	−0.0144790	+	0.0107384i	0.588436	+	0.808544i	$0.299744\pi$
$758$	−22.4125	−	28.6036i	−0.814058	−	1.03893i
$759$	13.3888	−	25.0486i	0.485981	−	0.909207i
$760$	−1.56408	−	0.873972i	−0.0567350	−	0.0317023i
$761$	36.8163	+	11.1681i	1.33459	+	0.404843i	0.875358	−	0.483474i	$-0.160625\pi$
$761$	36.8163	+	11.1681i	1.33459	+	0.404843i	0.459230	+	0.888317i	$0.348125\pi$
$762$	−20.1375	−	0.454993i	−0.729504	−	0.0164827i
$763$	−4.80631	+	13.4327i	−0.174000	+	0.486298i
$764$	−1.53433	+	4.34156i	−0.0555101	+	0.157072i
$765$	0.167437	+	0.279351i	0.00605369	+	0.0101000i
$766$	14.6291	−	23.2021i	0.528572	−	0.838324i
$767$	−0.588408			−0.0212462
$768$	11.6859	−	10.9289i	0.421678	−	0.394362i
$769$	23.5635			0.849723			0.424862	−	0.905258i	$-0.360323\pi$
$769$	23.5635			0.849723			0.424862	+	0.905258i	$0.360323\pi$
$770$	−9.46655	+	15.0141i	−0.341151	+	0.541071i
$771$	11.3842	+	18.9934i	0.409992	+	0.684030i
$772$	16.4748	+	5.82228i	0.592941	+	0.209548i
$773$	8.18064	−	22.8633i	0.294237	−	0.822337i	−0.699903	−	0.714238i	$-0.746773\pi$
$773$	8.18064	−	22.8633i	0.294237	−	0.822337i	0.994140	−	0.108100i	$-0.0344765\pi$
$774$	−15.1588	−	0.342503i	−0.544871	−	0.0123110i
$775$	14.3618	+	4.35662i	0.515893	+	0.156494i
$776$	7.75042	−	2.19380i	0.278224	−	0.0787529i
$777$	−0.458640	+	0.858054i	−0.0164536	+	0.0307825i
$778$	−17.8029	−	22.7207i	−0.638266	−	0.814576i
$779$	−2.57034	+	1.90630i	−0.0920921	+	0.0683002i
$780$	−1.84660	+	0.374817i	−0.0661190	+	0.0134206i
$781$	19.8032	−	41.8703i	0.708614	−	1.49824i
$782$	2.57765	−	2.23229i	0.0921767	−	0.0798267i
$783$	−6.90662	+	1.37381i	−0.246823	+	0.0490960i
$784$	−14.1376	+	4.40951i	−0.504915	+	0.157482i
$785$	16.0278	+	3.18812i	0.572055	+	0.113789i
$786$	−13.9047	−	24.4338i	−0.495964	−	0.871524i
$787$	46.2872	+	2.27394i	1.64996	+	0.0810573i	0.852639	−	0.522500i	$-0.175001\pi$
$787$	46.2872	+	2.27394i	1.64996	+	0.0810573i	0.797320	+	0.603557i	$0.206251\pi$
$788$	0.857759	−	1.05355i	0.0305564	−	0.0375311i
$789$	3.25634	+	13.0000i	0.115929	+	0.462814i
$790$	0.101269	+	1.33727i	0.00360300	+	0.0475779i
$791$	5.83272	−	59.2206i	0.207388	−	2.10564i
$792$	16.5230	−	0.502508i	0.587119	−	0.0178558i
$793$	−8.02212	−	6.58359i	−0.284874	−	0.233790i
$794$	23.8156	+	37.4469i	0.845184	+	1.32894i
$795$	−6.20799	+	0.304979i	−0.220175	+	0.0108165i
$796$	−3.77314	+	5.12925i	−0.133736	+	0.181801i
$797$	−8.98002	+	1.33206i	−0.318089	+	0.0471840i	−0.303866	−	0.952715i	$-0.598277\pi$
$797$	−8.98002	+	1.33206i	−0.318089	+	0.0471840i	−0.0142228	+	0.999899i	$0.504527\pi$
$798$	1.59867	−	4.16863i	0.0565924	−	0.147568i
$799$	−1.54969	+	0.641902i	−0.0548240	+	0.0227089i
$800$	−24.2046	−	9.06618i	−0.855760	−	0.320538i
$801$	3.91655	+	1.62229i	0.138385	+	0.0573207i
$802$	17.8837	−	18.8574i	0.631495	−	0.665879i
$803$	31.2974	−	42.1996i	1.10446	−	1.48919i
$804$	13.6101	−	12.4327i	0.479992	−	0.438467i
$805$	7.73254	+	7.00836i	0.272536	+	0.247012i
$806$	3.82830	−	5.45839i	0.134846	−	0.192264i
$807$	2.94332	−	0.289891i	0.103610	−	0.0102047i
$808$	−42.9928	−	2.91816i	−1.51248	−	0.102660i
$809$	17.1507	−	14.0752i	0.602985	−	0.494857i	−0.282660	−	0.959220i	$-0.591217\pi$
$809$	17.1507	−	14.0752i	0.602985	−	0.494857i	0.885645	+	0.464363i	$0.153717\pi$
$810$	0.882035	+	0.289475i	0.0309915	+	0.0101711i
$811$	−1.95080	−	1.16927i	−0.0685020	−	0.0410585i	0.479442	−	0.877574i	$-0.340839\pi$
$811$	−1.95080	−	1.16927i	−0.0685020	−	0.0410585i	−0.547944	+	0.836515i	$0.684589\pi$
$812$	−13.5469	−	44.0380i	−0.475402	−	1.54543i
$813$	−13.8170	−	15.2447i	−0.484584	−	0.534656i
$814$	1.94081	+	1.50853i	0.0680253	+	0.0528740i
$815$	10.7190	−	7.16218i	0.375469	−	0.250880i
$816$	1.87377	+	0.653979i	0.0655952	+	0.0228938i
$817$	8.60283	+	5.74823i	0.300975	+	0.201105i
$818$	−26.1037	+	8.68008i	−0.912694	+	0.303492i
$819$	−1.58181	−	4.42086i	−0.0552729	−	0.154477i
$820$	3.06637	−	3.09042i	0.107082	−	0.107922i
$821$	−29.1806	−	4.32854i	−1.01841	−	0.151067i	−0.383410	−	0.923578i	$-0.625250\pi$
$821$	−29.1806	−	4.32854i	−1.01841	−	0.151067i	−0.635001	+	0.772511i	$0.719000\pi$
$822$	−2.57104	+	4.55927i	−0.0896754	+	0.159023i
$823$	11.4528	+	37.7547i	0.399219	+	1.31605i	0.894404	+	0.447260i	$0.147600\pi$
$823$	11.4528	+	37.7547i	0.399219	+	1.31605i	−0.495186	+	0.868787i	$0.664900\pi$
$824$	17.5149	+	18.1820i	0.610161	+	0.633399i
$825$	−12.5882	−	23.5508i	−0.438264	−	0.819934i
$826$	−0.765245	+	1.73551i	−0.0266263	+	0.0603860i
$827$	18.7940	+	39.7365i	0.653531	+	1.38177i	0.909750	+	0.415156i	$0.136273\pi$
$827$	18.7940	+	39.7365i	0.653531	+	1.38177i	−0.256219	+	0.966619i	$0.582477\pi$
$828$	1.38857	−	9.61970i	0.0482560	−	0.334308i
$829$	12.6707	−	50.5843i	0.440072	−	1.75687i	−0.191444	−	0.981504i	$-0.561317\pi$
$829$	12.6707	−	50.5843i	0.440072	−	1.75687i	0.631516	−	0.775363i	$-0.282433\pi$
$830$	−1.51879	+	8.85565i	−0.0527179	+	0.307384i
$831$	−6.50691	+	6.50691i	−0.225722	+	0.225722i
$832$	−7.17958	+	8.96044i	−0.248907	+	0.310647i
$833$	−1.29891	−	1.29891i	−0.0450044	−	0.0450044i
$834$	−2.88081	+	2.03733i	−0.0997544	+	0.0705469i
$835$	−10.7840	−	2.70125i	−0.373195	−	0.0934806i
$836$	−9.69776	−	5.76124i	−0.335404	−	0.199257i
$837$	−2.96932	+	1.40438i	−0.102635	+	0.0485426i
$838$	−18.0481	−	46.5170i	−0.623460	−	1.60690i
$839$	−7.51474	+	4.01671i	−0.259438	+	0.138672i	−0.595989	−	0.802993i	$-0.703240\pi$
$839$	−7.51474	+	4.01671i	−0.259438	+	0.138672i	0.336551	+	0.941665i	$0.390740\pi$
$840$	−1.29605	+	5.93402i	−0.0447180	+	0.204743i
$841$	19.7022	−	5.97661i	0.679387	−	0.206090i
$842$	1.45631	−	0.406078i	0.0501877	−	0.0139944i
$843$	0.229946	−	1.55017i	0.00791975	−	0.0533906i
$844$	−11.1747	+	27.2790i	−0.384649	+	0.938983i
$845$	−6.76152	+	2.41931i	−0.232603	+	0.0832268i
$846$	−2.14129	+	4.27477i	−0.0736189	+	0.146970i
$847$	−42.0895	+	62.9914i	−1.44621	+	2.16441i
$848$	−27.8638	+	25.6536i	−0.956847	+	0.880950i
$849$	9.93342	+	14.8664i	0.340914	+	0.510214i
$850$	−0.398663	−	3.18112i	−0.0136740	−	0.109111i
$851$	1.07089	−	0.970598i	0.0367096	−	0.0332717i
$852$	1.49194	−	15.7796i	0.0511130	−	0.540600i
$853$	−6.82681	+	11.3898i	−0.233745	+	0.389981i	−0.952143	−	0.305652i	$-0.901126\pi$
$853$	−6.82681	+	11.3898i	−0.233745	+	0.389981i	0.718398	+	0.695632i	$0.244876\pi$
$854$	−29.8514	+	15.0991i	−1.02149	+	0.516679i
$855$	−0.401862	−	0.489671i	−0.0137434	−	0.0167464i
$856$	−1.03312	−	7.99066i	−0.0353114	−	0.273115i
$857$	−3.76971	−	38.2745i	−0.128771	−	1.30743i	−0.814751	−	0.579811i	$-0.803126\pi$
$857$	−3.76971	−	38.2745i	−0.128771	−	1.30743i	0.685980	−	0.727620i	$-0.259374\pi$
$858$	−11.6841	+	2.05091i	−0.398890	+	0.0700168i
$859$	14.9664	−	16.5129i	0.510648	−	0.563413i	−0.429986	−	0.902835i	$-0.641482\pi$
$859$	14.9664	−	16.5129i	0.510648	−	0.563413i	0.940634	+	0.339422i	$0.110232\pi$
$860$	−12.7478	−	5.96844i	−0.434697	−	0.203522i
$861$	8.71356	+	6.46241i	0.296957	+	0.220238i
$862$	−0.981646	−	37.0389i	−0.0334350	−	1.26155i
$863$	−2.90024	+	7.00181i	−0.0987254	+	0.238344i	−0.965524	−	0.260314i	$-0.916174\pi$
$863$	−2.90024	+	7.00181i	−0.0987254	+	0.238344i	0.866799	+	0.498659i	$0.166174\pi$
$864$	5.25767	−	2.08732i	0.178870	−	0.0710120i
$865$	4.80660	+	11.6042i	0.163429	+	0.394553i
$866$	−33.1948	+	14.7919i	−1.12800	+	0.502649i
$867$	−2.45830	−	16.5725i	−0.0834882	−	0.562831i
$868$	−11.1207	−	18.3904i	−0.377460	−	0.624211i
$869$	0.414287	+	8.43301i	0.0140537	+	0.286070i
$870$	−6.38112	−	1.41984i	−0.216340	−	0.0481372i
$871$	−8.39212	+	10.2258i	−0.284356	+	0.346489i
$872$	12.1653	+	2.03752i	0.411968	+	0.0689991i
$873$	2.83413	+	0.279138i	0.0959209	+	0.00944738i
$874$	−4.32218	+	5.03044i	−0.146200	+	0.170157i
$875$	19.9333	−	4.99304i	0.673870	−	0.168796i
$876$	5.15179	−	17.2251i	0.174063	−	0.581983i
$877$	−2.77464	+	56.4791i	−0.0936930	+	1.90717i	0.250261	+	0.968179i	$0.419484\pi$
$877$	−2.77464	+	56.4791i	−0.0936930	+	1.90717i	−0.343954	+	0.938987i	$0.611766\pi$
$878$	39.3582	+	10.8092i	1.32828	+	0.364792i
$879$	6.12885	−	30.8118i	0.206721	−	1.03926i
$880$	14.2231	+	5.76162i	0.479459	+	0.194224i
$881$	−1.61589	−	8.12363i	−0.0544408	−	0.273692i	0.943971	−	0.330028i	$-0.107058\pi$
$881$	−1.61589	−	8.12363i	−0.0544408	−	0.273692i	−0.998412	+	0.0563359i	$0.982058\pi$
$882$	−5.22244	−	0.374976i	−0.175849	−	0.0126261i
$883$	51.6657	+	24.4361i	1.73869	+	0.822340i	0.986575	+	0.163309i	$0.0522166\pi$
$883$	51.6657	+	24.4361i	1.73869	+	0.822340i	0.752116	+	0.659031i	$0.229033\pi$
$884$	−1.39792	−	0.272391i	−0.0470171	−	0.00916150i
$885$	0.160311	+	0.216154i	0.00538878	+	0.00726593i
$886$	−18.8768	−	2.29081i	−0.634179	−	0.0769613i
$887$	17.9142	+	9.57535i	0.601500	+	0.321509i	0.743890	−	0.668302i	$-0.232979\pi$
$887$	17.9142	+	9.57535i	0.601500	+	0.321509i	−0.142390	+	0.989811i	$0.545479\pi$
$888$	0.800260	+	0.259179i	0.0268550	+	0.00869749i
$889$	13.5258	−	44.5887i	0.453642	−	1.49546i
$890$	2.71917	+	2.84488i	0.0911467	+	0.0953607i
$891$	5.50282	+	1.96894i	0.184351	+	0.0659619i
$892$	−0.674344	−	12.7130i	−0.0225787	−	0.425664i
$893$	2.79831	−	1.67725i	0.0936420	−	0.0561269i
$894$	5.69673	+	25.1389i	0.190527	+	0.840770i
$895$		−	0.225415i		−	0.00753478i
$896$	17.0915	+	32.8295i	0.570988	+	1.09676i
$897$			6.97487i			0.232884i
$898$	10.2707	−	2.32745i	0.342739	−	0.0776680i
$899$	19.8397	−	11.8915i	0.661691	−	0.396603i
$900$	−6.79489	−	6.11036i	−0.226496	−	0.203679i
$901$	−4.42332	−	1.58269i	−0.147362	−	0.0527270i
$902$	19.8137	−	18.9381i	0.659724	−	0.630570i
$903$	10.1818	−	33.5648i	0.338828	−	1.11697i
$904$	−51.2863	+	4.08539i	−1.70576	+	0.135878i
$905$	6.31221	+	3.37394i	0.209825	+	0.112154i
$906$	−1.45823	+	12.0162i	−0.0484465	+	0.399210i
$907$	−6.32060	−	8.52235i	−0.209872	−	0.282980i	0.685711	−	0.727874i	$-0.259491\pi$
$907$	−6.32060	−	8.52235i	−0.209872	−	0.282980i	−0.895583	+	0.444894i	$0.853241\pi$
$908$	30.8666	+	45.8067i	1.02434	+	1.52015i
$909$	−13.7725	−	6.51390i	−0.456805	−	0.216052i
$910$	0.312160	−	4.34758i	0.0103480	−	0.144121i
$911$	4.82792	+	24.2716i	0.159956	+	0.804154i	0.974558	+	0.224134i	$0.0719554\pi$
$911$	4.82792	+	24.2716i	0.159956	+	0.804154i	−0.814602	+	0.580020i	$0.803045\pi$
$912$	−3.79167	−	0.723461i	−0.125555	−	0.0239562i
$913$	−11.0356	+	55.4798i	−0.365226	+	1.83611i
$914$	−6.82523	+	24.8520i	−0.225759	+	0.822030i
$915$	−0.232893	+	4.74065i	−0.00769920	+	0.156721i
$916$	−4.45584	−	8.25852i	−0.147225	−	0.272869i
$917$	63.0841	−	15.8017i	2.08322	−	0.521819i
$918$	0.532204	+	0.457272i	0.0175654	+	0.0150922i
$919$	−11.4868	−	1.13135i	−0.378914	−	0.0373197i	−0.0932323	−	0.995644i	$-0.529720\pi$
$919$	−11.4868	−	1.13135i	−0.378914	−	0.0373197i	−0.285681	+	0.958325i	$0.592220\pi$
$920$	4.78239	−	7.65104i	0.157671	−	0.252247i
$921$	2.69704	−	3.28635i	0.0888705	−	0.108289i
$922$	5.48711	−	24.6604i	0.180709	−	0.812149i
$923$	0.558111	+	11.3606i	0.0183705	+	0.373939i
$924$	−9.14650	+	37.1296i	−0.300898	+	1.22148i
$925$	−0.199387	−	1.34416i	−0.00655582	−	0.0441957i
$926$	−15.4746	−	34.7269i	−0.508527	−	1.14120i
$927$	3.41575	+	8.24634i	0.112188	+	0.270845i
$928$	−35.4051	+	18.2570i	−1.16223	+	0.599315i
$929$	15.9818	−	38.5835i	0.524346	−	1.26588i	−0.410833	−	0.911711i	$-0.634762\pi$
$929$	15.9818	−	38.5835i	0.524346	−	1.26588i	0.935180	−	0.354174i	$-0.115238\pi$
$930$	−3.04817	+	0.0807861i	−0.0999536	+	0.00264908i
$931$	2.86971	+	2.12832i	0.0940510	+	0.0697530i
$932$	−20.7309	+	7.50912i	−0.679063	+	0.245969i
$933$	−2.68410	+	2.96145i	−0.0878736	+	0.0969536i
$934$	−4.57431	−	26.0601i	−0.149676	−	0.852714i
$935$	0.186572	+	1.89430i	0.00610157	+	0.0619502i
$936$	−3.52033	+	2.02158i	−0.115065	+	0.0660774i
$937$	33.7495	+	41.1239i	1.10255	+	1.34346i	0.933798	+	0.357800i	$0.116473\pi$
$937$	33.7495	+	41.1239i	1.10255	+	1.34346i	0.168750	+	0.985659i	$0.446027\pi$
$938$	19.2468	+	38.0516i	0.628431	+	1.24243i
$939$	−1.93210	+	3.22352i	−0.0630518	+	0.105195i
$940$	−3.41990	+	2.82906i	−0.111545	+	0.0922739i
$941$	−9.63633	+	8.73386i	−0.314136	+	0.284716i	−0.813365	−	0.581754i	$-0.802367\pi$
$941$	−9.63633	+	8.73386i	−0.314136	+	0.284716i	0.499229	+	0.866470i	$0.333617\pi$
$942$	34.9339	−	4.37797i	1.13821	−	0.142642i
$943$	−8.95318	−	13.3994i	−0.291556	−	0.436344i
$944$	1.59380	+	0.386018i	0.0518737	+	0.0125638i
$945$	−1.19306	+	1.78554i	−0.0388102	+	0.0580836i
$946$	−79.2330	−	39.6888i	−2.57609	−	1.29039i
$947$	35.9535	−	12.8644i	1.16833	−	0.418036i	0.319957	−	0.947432i	$-0.396331\pi$
$947$	35.9535	−	12.8644i	1.16833	−	0.418036i	0.848375	+	0.529396i	$0.177581\pi$
$948$	1.11610	+	2.66502i	0.0362494	+	0.0865558i
$949$	−1.89314	+	12.7625i	−0.0614541	+	0.414290i
$950$	1.67486	+	6.00651i	0.0543397	+	0.194877i
$951$	−1.90568	+	0.578081i	−0.0617959	+	0.0187456i
$952$	−2.62146	+	3.76891i	−0.0849620	+	0.122151i
$953$	−36.9125	+	19.7301i	−1.19571	+	0.639121i	−0.944405	−	0.328786i	$-0.893361\pi$
$953$	−36.9125	+	19.7301i	−1.19571	+	0.639121i	−0.251308	+	0.967907i	$0.580861\pi$
$954$	−12.4841	+	4.84367i	−0.404186	+	0.156819i
$955$	−1.36621	+	0.646171i	−0.0442097	+	0.0209096i
$956$	−4.28186	−	16.8152i	−0.138485	−	0.543841i
$957$	−39.9229	−	10.0002i	−1.29052	−	0.323259i
$958$	11.3944	+	16.1119i	0.368138	+	0.520553i
$959$	−8.56174	−	8.56174i	−0.276473	−	0.276473i
$960$	5.24772	+	0.196189i	0.169369	+	0.00633197i
$961$	−14.2912	+	14.2912i	−0.461007	+	0.461007i
$962$	−0.594967	−	0.102040i	−0.0191825	−	0.00328990i
$963$	0.692163	−	2.76327i	0.0223046	−	0.0890452i
$964$	−19.1842	−	25.6568i	−0.617881	−	0.826350i
$965$	2.45201	+	5.18433i	0.0789329	+	0.166890i
$966$	20.5724	+	9.07108i	0.661906	+	0.291857i
$967$	−2.61324	−	4.88903i	−0.0840362	−	0.157221i	0.836393	−	0.548131i	$-0.184660\pi$
$967$	−2.61324	−	4.88903i	−0.0840362	−	0.157221i	−0.920429	+	0.390910i	$0.872160\pi$
$968$	60.0351	+	26.1919i	1.92960	+	0.841840i
$969$	−0.138988	−	0.458181i	−0.00446493	−	0.0147189i
$970$	2.30281	+	1.29859i	0.0739386	+	0.0416952i
$971$	18.5691	+	2.75447i	0.595912	+	0.0883952i	0.437872	−	0.899037i	$-0.355732\pi$
$971$	18.5691	+	2.75447i	0.595912	+	0.0883952i	0.158040	+	0.987433i	$0.449482\pi$
$972$	1.99998	−	0.00781277i	0.0641495	−	0.000250595i
$973$	−2.74975	−	7.68503i	−0.0881529	−	0.246371i
$974$	2.21666	+	6.66618i	0.0710264	+	0.213598i
$975$	5.45261	+	3.64332i	0.174623	+	0.116680i
$976$	17.4101	+	23.0955i	0.557285	+	0.739270i
$977$	−49.7849	+	33.2652i	−1.59276	+	1.06425i	−0.636687	+	0.771122i	$0.719696\pi$
$977$	−49.7849	+	33.2652i	−1.59276	+	1.06425i	−0.956074	+	0.293127i	$0.905304\pi$
$978$	17.0446	−	21.9288i	0.545027	−	0.701207i
$979$	16.6386	+	18.3579i	0.531772	+	0.586720i
$980$	−4.29558	−	2.27450i	−0.137217	−	0.0726563i
$981$	3.74054	+	2.24199i	0.119426	+	0.0715814i
$982$	6.12800	−	18.6721i	0.195552	−	0.595850i
$983$	32.7486	−	26.8761i	1.04452	−	0.857213i	0.0545505	−	0.998511i	$-0.482627\pi$
$983$	32.7486	−	26.8761i	1.04452	−	0.857213i	0.989967	+	0.141298i	$0.0451274\pi$
$984$	4.16791	−	8.40244i	0.132868	−	0.267860i
$985$	0.443751	−	0.0437057i	0.0141391	−	0.00139258i
$986$	−4.04532	−	2.83723i	−0.128829	−	0.0903559i
$987$	−8.19484	−	7.42737i	−0.260845	−	0.236416i
$988$	2.76725	+	0.125112i	0.0880379	+	0.00398035i
$989$	−31.0382	+	41.8502i	−0.986958	+	1.33076i
$990$	3.93673	+	3.73345i	0.125118	+	0.118657i
$991$	−45.3079	−	18.7671i	−1.43925	−	0.596158i	−0.479636	−	0.877468i	$-0.659231\pi$
$991$	−45.3079	−	18.7671i	−1.43925	−	0.596158i	−0.959617	+	0.281310i	$0.909231\pi$
$992$	−13.9505	+	12.2734i	−0.442928	+	0.389681i
$993$	25.6221	−	10.6130i	0.813094	−	0.336795i
$994$	34.2340	+	13.1287i	1.08584	+	0.416419i
$995$	−2.06729	+	0.306653i	−0.0655374	+	0.00972155i
$996$	2.91510	+	19.1366i	0.0923683	+	0.606367i
$997$	−53.0704	+	2.60718i	−1.68076	+	0.0825703i	−0.866896	−	0.498489i	$-0.833888\pi$
$997$	−53.0704	+	2.60718i	−1.68076	+	0.0825703i	−0.813861	+	0.581059i	$0.802638\pi$
$998$	13.2981	−	8.45735i	0.420944	−	0.267713i
$999$	0.229896	+	0.188671i	0.00727358	+	0.00596928i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.z.a.685.53	yes	2048
256.37	even	64	inner	768.2.z.a.37.53	✓	2048

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
768.2.z.a.37.53	✓	2048	256.37	even	64	inner
768.2.z.a.685.53	yes	2048	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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.z (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19628 + 0.754266i) q^{2} +(0.514103 + 0.857729i) q^{3} +(0.862166 + 1.80462i) q^{4} +(-0.221142 + 0.618051i) q^{5} +(-0.0319451 + 1.41385i) q^{6} +(-3.13057 - 0.949649i) q^{7} +(-0.329775 + 2.80914i) q^{8} +(-0.471397 + 0.881921i) q^{9} +O(q^{10})\)	\(q+(1.19628 + 0.754266i) q^{2} +(0.514103 + 0.857729i) q^{3} +(0.862166 + 1.80462i) q^{4} +(-0.221142 + 0.618051i) q^{5} +(-0.0319451 + 1.41385i) q^{6} +(-3.13057 - 0.949649i) q^{7} +(-0.329775 + 2.80914i) q^{8} +(-0.471397 + 0.881921i) q^{9} +(-0.730722 + 0.572561i) q^{10} +(-4.69431 + 3.48154i) q^{11} +(-1.10464 + 1.66727i) q^{12} +(0.613647 - 1.29745i) q^{13} +(-3.02875 - 3.49733i) q^{14} +(-0.643810 + 0.128062i) q^{15} +(-2.51334 + 3.11177i) q^{16} +(-0.486621 - 0.0967950i) q^{17} +(-1.22912 + 0.699465i) q^{18} +(0.963855 + 0.0473511i) q^{19} +(-1.30601 + 0.133784i) q^{20} +(-0.794896 - 3.17340i) q^{21} +(-8.24171 + 0.624133i) q^{22} +(-0.476334 + 4.83630i) q^{23} +(-2.57902 + 1.16133i) q^{24} +(3.53197 + 2.89861i) q^{25} +(1.71271 - 1.08926i) q^{26} +(-0.998795 + 0.0490677i) q^{27} +(-0.985315 - 6.46827i) q^{28} +(6.96571 - 1.03327i) q^{29} +(-0.866769 - 0.332406i) q^{30} +(3.03465 - 1.25699i) q^{31} +(-5.35376 + 1.82682i) q^{32} +(-5.39958 - 2.23658i) q^{33} +(-0.509126 - 0.482836i) q^{34} +(1.27923 - 1.72485i) q^{35} +(-1.99796 - 0.0903312i) q^{36} +(-0.220361 - 0.199724i) q^{37} +(1.11732 + 0.783648i) q^{38} +(1.42834 - 0.140679i) q^{39} +(-1.66326 - 0.825036i) q^{40} +(-2.56339 + 2.10372i) q^{41} +(1.44267 - 4.39583i) q^{42} +(9.19624 + 5.51201i) q^{43} +(-10.3302 - 5.46981i) q^{44} +(-0.440827 - 0.486377i) q^{45} +(-4.21768 + 5.42628i) q^{46} +(2.81098 - 1.87824i) q^{47} +(-3.96117 - 0.555991i) q^{48} +(3.07838 + 2.05691i) q^{49} +(2.03890 + 6.13159i) q^{50} +(-0.167150 - 0.467152i) q^{51} +(2.87047 - 0.0112133i) q^{52} +(9.36622 + 1.38935i) q^{53} +(-1.23185 - 0.694659i) q^{54} +(-1.11366 - 3.67124i) q^{55} +(3.70008 - 8.48104i) q^{56} +(0.454906 + 0.851069i) q^{57} +(9.11229 + 4.01792i) q^{58} +(-0.175285 - 0.370608i) q^{59} +(-0.786174 - 1.05142i) q^{60} +(1.75690 - 7.01396i) q^{61} +(4.57840 + 0.785219i) q^{62} +(2.31326 - 2.31326i) q^{63} +(-7.78250 - 1.85277i) q^{64} +(0.666186 + 0.666186i) q^{65} +(-4.77242 - 6.74829i) q^{66} +(-8.94071 - 2.23953i) q^{67} +(-0.244870 - 0.961622i) q^{68} +(-4.39312 + 2.07779i) q^{69} +(2.83131 - 1.09852i) q^{70} +(-6.98922 + 3.73581i) q^{71} +(-2.32198 - 1.61505i) q^{72} +(-8.60244 + 2.60952i) q^{73} +(-0.112969 - 0.405136i) q^{74} +(-0.670428 + 4.51966i) q^{75} +(0.745552 + 1.78022i) q^{76} +(18.0021 - 6.44127i) q^{77} +(1.81480 + 0.909054i) q^{78} +(0.802603 - 1.20118i) q^{79} +(-1.36743 - 2.24152i) q^{80} +(-0.555570 - 0.831470i) q^{81} +(-4.65328 + 0.583157i) q^{82} +(7.17144 - 6.49981i) q^{83} +(5.04146 - 4.17049i) q^{84} +(0.167437 - 0.279351i) q^{85} +(6.84374 + 13.5303i) q^{86} +(4.46735 + 5.44349i) q^{87} +(-8.23205 - 14.3351i) q^{88} +(-0.415519 - 4.21883i) q^{89} +(-0.160494 - 0.914343i) q^{90} +(-3.15319 + 3.47901i) q^{91} +(-9.13839 + 3.31009i) q^{92} +(2.63828 + 1.95668i) q^{93} +(4.77941 - 0.126669i) q^{94} +(-0.242414 + 0.585240i) q^{95} +(-4.31930 - 3.65290i) q^{96} +(-1.08982 - 2.63107i) q^{97} +(2.13114 + 4.78255i) q^{98} +(-0.857560 - 5.78120i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2048 q+O(q^{10}) \) 2048 * q	\( 2048 q+O(q^{100}) \) 2048 * q

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more