LMFDB - Embedded newform 640.2.bm.a.101.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(21,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 13, 0]))

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

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

chi := DirichletCharacter("640.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			101.28
Character	$\chi$	$=$	640.101
Dual form			640.2.bm.a.621.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.251394 + 1.39169i) q^{2} +(1.76486 - 0.943339i) q^{3} +(-1.87360 - 0.699725i) q^{4} +(-0.634393 - 0.773010i) q^{5} +(0.869159 + 2.69329i) q^{6} +(-2.85468 + 1.90743i) q^{7} +(1.44481 - 2.43157i) q^{8} +(0.558141 - 0.835316i) q^{9} +(1.23527 - 0.688548i) q^{10} +(-3.33445 + 1.01149i) q^{11} +(-3.96673 + 0.532522i) q^{12} +(-4.99266 - 4.09737i) q^{13} +(-1.93691 - 4.45234i) q^{14} +(-1.84883 - 0.765809i) q^{15} +(3.02077 + 2.62201i) q^{16} +(-5.89726 + 2.44272i) q^{17} +(1.02219 + 0.986752i) q^{18} +(0.488611 + 4.96096i) q^{19} +(0.647705 + 1.89221i) q^{20} +(-3.23875 + 6.05928i) q^{21} +(-0.569425 - 4.89480i) q^{22} +(8.03578 - 1.59842i) q^{23} +(0.256106 - 5.65433i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(6.95739 - 5.91818i) q^{26} +(-0.391388 + 3.97383i) q^{27} +(6.68321 - 1.57628i) q^{28} +(-1.21796 + 4.01508i) q^{29} +(1.53055 - 2.38047i) q^{30} +(-6.06623 - 6.06623i) q^{31} +(-4.40843 + 3.54481i) q^{32} +(-4.93066 + 4.93066i) q^{33} +(-1.91698 - 8.82124i) q^{34} +(3.28545 + 0.996631i) q^{35} +(-1.63023 + 1.17451i) q^{36} +(4.32560 + 0.426035i) q^{37} +(-7.02695 - 0.567159i) q^{38} +(-12.6766 - 2.52152i) q^{39} +(-2.79621 + 0.425714i) q^{40} +(-0.0945118 - 0.475143i) q^{41} +(-7.61844 - 6.03061i) q^{42} +(0.587024 + 0.313771i) q^{43} +(6.95519 + 0.438061i) q^{44} +(-0.999789 + 0.0984706i) q^{45} +(0.204352 + 11.5852i) q^{46} +(-3.88505 - 9.37933i) q^{47} +(7.80469 + 1.77789i) q^{48} +(1.83209 - 4.42305i) q^{49} +(-1.31590 - 0.518069i) q^{50} +(-8.10353 + 9.87418i) q^{51} +(6.48722 + 11.1703i) q^{52} +(0.129754 + 0.427741i) q^{53} +(-5.43194 - 1.54369i) q^{54} +(2.89724 + 1.93588i) q^{55} +(0.513577 + 9.69722i) q^{56} +(5.54219 + 8.29448i) q^{57} +(-5.28156 - 2.70439i) q^{58} +(2.62265 - 2.15235i) q^{59} +(2.92811 + 2.72849i) q^{60} +(-2.46876 - 4.61873i) q^{61} +(9.96732 - 6.91729i) q^{62} +3.44917i q^{63} +(-3.82503 - 7.02632i) q^{64} +6.45872i q^{65} +(-5.62241 - 8.10148i) q^{66} +(0.659725 + 1.23426i) q^{67} +(12.7584 - 0.450232i) q^{68} +(12.6742 - 10.4014i) q^{69} +(-2.21295 + 4.32179i) q^{70} +(-3.76415 - 5.63345i) q^{71} +(-1.22472 - 2.56403i) q^{72} +(3.00565 + 2.00831i) q^{73} +(-1.68034 + 5.91279i) q^{74} +(0.580905 + 1.91499i) q^{75} +(2.55584 - 9.63675i) q^{76} +(7.58941 - 9.24772i) q^{77} +(6.69599 - 17.0079i) q^{78} +(1.13676 - 2.74437i) q^{79} +(0.110489 - 3.99847i) q^{80} +(4.21128 + 10.1669i) q^{81} +(0.685011 - 0.0120830i) q^{82} +(-2.47464 + 0.243730i) q^{83} +(10.3080 - 9.08645i) q^{84} +(5.62943 + 3.00899i) q^{85} +(-0.584246 + 0.738075i) q^{86} +(1.63805 + 8.23501i) q^{87} +(-2.35814 + 9.56934i) q^{88} +(-13.4177 - 2.66895i) q^{89} +(0.114300 - 1.41615i) q^{90} +(22.0679 + 2.17350i) q^{91} +(-16.1743 - 2.62804i) q^{92} +(-16.4286 - 4.98355i) q^{93} +(14.0298 - 3.04887i) q^{94} +(3.52490 - 3.52490i) q^{95} +(-4.43632 + 10.4148i) q^{96} +(2.42456 + 2.42456i) q^{97} +(5.69494 + 3.66163i) q^{98} +(-1.01617 + 3.34987i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.251394	+	1.39169i	−0.177762	+	0.984073i
$2$	−0.251394	+	1.39169i	−0.177762	+	0.984073i
$3$	1.76486	−	0.943339i	1.01894	−	0.544637i	0.124689	−	0.992196i	$-0.460207\pi$
$3$	1.76486	−	0.943339i	1.01894	−	0.544637i	0.894254	+	0.447559i	$0.147707\pi$
$4$	−1.87360	−	0.699725i	−0.936801	−	0.349863i
$5$	−0.634393	−	0.773010i	−0.283709	−	0.345701i
$5$	−0.634393	−	0.773010i	−0.283709	−	0.345701i
$6$	0.869159	+	2.69329i	0.354833	+	1.09953i
$7$	−2.85468	+	1.90743i	−1.07897	+	0.720942i	−0.962235	−	0.272221i	$-0.912242\pi$
$7$	−2.85468	+	1.90743i	−1.07897	+	0.720942i	−0.116731	+	0.993164i	$0.537242\pi$
$8$	1.44481	−	2.43157i	0.510819	−	0.859688i
$9$	0.558141	−	0.835316i	0.186047	−	0.278439i
$10$	1.23527	−	0.688548i	0.390628	−	0.217738i
$11$	−3.33445	+	1.01149i	−1.00537	+	0.304977i	−0.749694	−	0.661785i	$-0.769799\pi$
$11$	−3.33445	+	1.01149i	−1.00537	+	0.304977i	−0.255679	+	0.966762i	$0.582299\pi$
$12$	−3.96673	+	0.532522i	−1.14510	+	0.153726i
$13$	−4.99266	−	4.09737i	−1.38471	−	1.13641i	−0.974493	−	0.224419i	$-0.927952\pi$
$13$	−4.99266	−	4.09737i	−1.38471	−	1.13641i	−0.410221	−	0.911986i	$-0.634548\pi$
$14$	−1.93691	−	4.45234i	−0.517660	−	1.18994i
$15$	−1.84883	−	0.765809i	−0.477365	−	0.197731i
$16$	3.02077	+	2.62201i	0.755192	+	0.655503i
$17$	−5.89726	+	2.44272i	−1.43030	+	0.592448i	−0.957424	−	0.288684i	$-0.906782\pi$
$17$	−5.89726	+	2.44272i	−1.43030	+	0.592448i	−0.472871	+	0.881132i	$0.656782\pi$
$18$	1.02219	+	0.986752i	0.240932	+	0.232580i
$19$	0.488611	+	4.96096i	0.112095	+	1.13812i	0.872480	+	0.488649i	$0.162510\pi$
$19$	0.488611	+	4.96096i	0.112095	+	1.13812i	−0.760385	+	0.649472i	$0.774990\pi$
$20$	0.647705	+	1.89221i	0.144831	+	0.423112i
$21$	−3.23875	+	6.05928i	−0.706754	+	1.32224i
$22$	−0.569425	−	4.89480i	−0.121402	−	1.04357i
$23$	8.03578	−	1.59842i	1.67558	−	0.333293i	0.736353	−	0.676598i	$-0.236546\pi$
$23$	8.03578	−	1.59842i	1.67558	−	0.333293i	0.939224	+	0.343305i	$0.111546\pi$
$24$	0.256106	−	5.65433i	0.0522775	−	1.15418i
$25$	−0.195090	+	0.980785i	−0.0390181	+	0.196157i
$26$	6.95739	−	5.91818i	1.36446	−	1.16065i
$27$	−0.391388	+	3.97383i	−0.0753226	+	0.764763i
$28$	6.68321	−	1.57628i	1.26301	−	0.297889i
$29$	−1.21796	+	4.01508i	−0.226170	+	0.745581i	0.768256	+	0.640142i	$0.221125\pi$
$29$	−1.21796	+	4.01508i	−0.226170	+	0.745581i	−0.994426	+	0.105439i	$0.966375\pi$
$30$	1.53055	−	2.38047i	0.279440	−	0.434613i
$31$	−6.06623	−	6.06623i	−1.08953	−	1.08953i	−0.995577	−	0.0939498i	$-0.970051\pi$
$31$	−6.06623	−	6.06623i	−1.08953	−	1.08953i	−0.0939498	−	0.995577i	$-0.529949\pi$
$32$	−4.40843	+	3.54481i	−0.779308	+	0.626641i
$33$	−4.93066	+	4.93066i	−0.858317	+	0.858317i
$34$	−1.91698	−	8.82124i	−0.328759	−	1.51283i
$35$	3.28545	+	0.996631i	0.555343	+	0.168461i
$36$	−1.63023	+	1.17451i	−0.271704	+	0.195751i
$37$	4.32560	+	0.426035i	0.711125	+	0.0700397i	0.447110	−	0.894479i	$-0.352453\pi$
$37$	4.32560	+	0.426035i	0.711125	+	0.0700397i	0.264015	+	0.964519i	$0.414953\pi$
$38$	−7.02695	−	0.567159i	−1.13992	−	0.0920054i
$39$	−12.6766	−	2.52152i	−2.02987	−	0.403767i
$40$	−2.79621	+	0.425714i	−0.442119	+	0.0673112i
$41$	−0.0945118	−	0.475143i	−0.0147603	−	0.0742048i	0.972703	−	0.232053i	$-0.0745443\pi$
$41$	−0.0945118	−	0.475143i	−0.0147603	−	0.0742048i	−0.987463	+	0.157848i	$0.949544\pi$
$42$	−7.61844	−	6.03061i	−1.17555	−	0.930543i
$43$	0.587024	+	0.313771i	0.0895203	+	0.0478496i	0.515549	−	0.856860i	$-0.327588\pi$
$43$	0.587024	+	0.313771i	0.0895203	+	0.0478496i	−0.426029	+	0.904709i	$0.640088\pi$
$44$	6.95519	+	0.438061i	1.04853	+	0.0660402i
$45$	−0.999789	+	0.0984706i	−0.149040	+	0.0146791i
$46$	0.204352	+	11.5852i	0.0301300	+	1.70814i
$47$	−3.88505	−	9.37933i	−0.566692	−	1.36812i	−0.904328	−	0.426839i	$-0.859627\pi$
$47$	−3.88505	−	9.37933i	−0.566692	−	1.36812i	0.337635	−	0.941277i	$-0.390373\pi$
$48$	7.80469	+	1.77789i	1.12651	+	0.256616i
$49$	1.83209	−	4.42305i	0.261727	−	0.631865i
$50$	−1.31590	−	0.518069i	−0.186097	−	0.0732660i
$51$	−8.10353	+	9.87418i	−1.13472	+	1.38266i
$52$	6.48722	+	11.1703i	0.899616	+	1.54905i
$53$	0.129754	+	0.427741i	0.0178231	+	0.0587548i	0.965401	−	0.260770i	$-0.0839766\pi$
$53$	0.129754	+	0.427741i	0.0178231	+	0.0587548i	−0.947578	+	0.319525i	$0.896477\pi$
$54$	−5.43194	−	1.54369i	−0.739194	−	0.210069i
$55$	2.89724	+	1.93588i	0.390664	+	0.261034i
$56$	0.513577	+	9.69722i	0.0686296	+	1.29585i
$57$	5.54219	+	8.29448i	0.734081	+	1.09863i
$58$	−5.28156	−	2.70439i	−0.693502	−	0.355104i
$59$	2.62265	−	2.15235i	0.341440	−	0.280213i	−0.448009	−	0.894029i	$-0.647867\pi$
$59$	2.62265	−	2.15235i	0.341440	−	0.280213i	0.789449	+	0.613817i	$0.210367\pi$
$60$	2.92811	+	2.72849i	0.378017	+	0.352247i
$61$	−2.46876	−	4.61873i	−0.316093	−	0.591368i	0.672831	−	0.739797i	$-0.265078\pi$
$61$	−2.46876	−	4.61873i	−0.316093	−	0.591368i	−0.988923	+	0.148429i	$0.952578\pi$
$62$	9.96732	−	6.91729i	1.26585	−	0.878497i
$63$			3.44917i			0.434555i
$64$	−3.82503	−	7.02632i	−0.478129	−	0.878290i
$65$			6.45872i			0.801105i
$66$	−5.62241	−	8.10148i	−0.692070	−	0.997224i
$67$	0.659725	+	1.23426i	0.0805983	+	0.150789i	0.918992	−	0.394277i	$-0.129005\pi$
$67$	0.659725	+	1.23426i	0.0805983	+	0.150789i	−0.838394	+	0.545065i	$0.816505\pi$
$68$	12.7584	−	0.450232i	1.54718	−	0.0545987i
$69$	12.6742	−	10.4014i	1.52579	−	1.25219i
$70$	−2.21295	+	4.32179i	−0.264498	+	0.516552i
$71$	−3.76415	−	5.63345i	−0.446722	−	0.668567i	0.537951	−	0.842976i	$-0.319199\pi$
$71$	−3.76415	−	5.63345i	−0.446722	−	0.668567i	−0.984673	+	0.174409i	$0.944199\pi$
$72$	−1.22472	−	2.56403i	−0.144334	−	0.302174i
$73$	3.00565	+	2.00831i	0.351784	+	0.235055i	0.718889	−	0.695125i	$-0.244651\pi$
$73$	3.00565	+	2.00831i	0.351784	+	0.235055i	−0.367105	+	0.930180i	$0.619651\pi$
$74$	−1.68034	+	5.91279i	−0.195335	+	0.687348i
$75$	0.580905	+	1.91499i	0.0670771	+	0.221124i
$76$	2.55584	−	9.63675i	0.293175	−	1.10541i
$77$	7.58941	−	9.24772i	0.864893	−	1.05388i
$78$	6.69599	−	17.0079i	0.758172	−	1.92577i
$79$	1.13676	−	2.74437i	0.127895	−	0.308766i	−0.846942	−	0.531686i	$-0.821559\pi$
$79$	1.13676	−	2.74437i	0.127895	−	0.308766i	0.974837	+	0.222920i	$0.0715587\pi$
$80$	0.110489	−	3.99847i	0.0123530	−	0.447043i
$81$	4.21128	+	10.1669i	0.467920	+	1.12966i
$82$	0.685011	−	0.0120830i	0.0756468	−	0.00133434i
$83$	−2.47464	+	0.243730i	−0.271627	+	0.0267529i	−0.232913	−	0.972497i	$-0.574826\pi$
$83$	−2.47464	+	0.243730i	−0.271627	+	0.0267529i	−0.0387132	+	0.999250i	$0.512326\pi$
$84$	10.3080	−	9.08645i	1.12469	−	0.991413i
$85$	5.62943	+	3.00899i	0.610598	+	0.326371i
$86$	−0.584246	+	0.738075i	−0.0630009	+	0.0795887i
$87$	1.63805	+	8.23501i	0.175617	+	0.882886i
$88$	−2.35814	+	9.56934i	−0.251378	+	1.02010i
$89$	−13.4177	−	2.66895i	−1.42227	−	0.282908i	−0.576782	−	0.816898i	$-0.695692\pi$
$89$	−13.4177	−	2.66895i	−1.42227	−	0.282908i	−0.845491	+	0.533990i	$0.820692\pi$
$90$	0.114300	−	1.41615i	0.0120483	−	0.149275i
$91$	22.0679	+	2.17350i	2.31334	+	0.227844i
$92$	−16.1743	−	2.62804i	−1.68629	−	0.273993i
$93$	−16.4286	−	4.98355i	−1.70356	−	0.516770i
$94$	14.0298	−	3.04887i	1.44706	−	0.314467i
$95$	3.52490	−	3.52490i	0.361647	−	0.361647i
$96$	−4.43632	+	10.4148i	−0.452780	+	1.06295i
$97$	2.42456	+	2.42456i	0.246177	+	0.246177i	0.819400	−	0.573223i	$-0.194307\pi$
$97$	2.42456	+	2.42456i	0.246177	+	0.246177i	−0.573223	+	0.819400i	$0.694307\pi$
$98$	5.69494	+	3.66163i	0.575276	+	0.369880i
$99$	−1.01617	+	3.34987i	−0.102129	+	0.336675i
$100$	1.05180	−	1.70109i	0.105180	−	0.170109i
$101$	−0.852360	+	8.65415i	−0.0848129	+	0.861120i	0.854817	+	0.518929i	$0.173669\pi$
$101$	−0.852360	+	8.65415i	−0.0848129	+	0.861120i	−0.939630	+	0.342191i	$0.888831\pi$
$102$	−11.7046	−	13.7599i	−1.15893	−	1.36243i
$103$	0.199464	−	1.00277i	0.0196538	−	0.0988062i	−0.969713	−	0.244246i	$-0.921460\pi$
$103$	0.199464	−	1.00277i	0.0196538	−	0.0988062i	0.989367	+	0.145440i	$0.0464596\pi$
$104$	−17.1765	+	6.22004i	−1.68429	+	0.609926i
$105$	6.73853	−	1.34038i	0.657614	−	0.130807i
$106$	−0.627903	+	0.0730456i	−0.0609873	+	0.00709482i
$107$	8.68774	−	16.2536i	0.839876	−	1.57130i	0.0192616	−	0.999814i	$-0.493868\pi$
$107$	8.68774	−	16.2536i	0.839876	−	1.57130i	0.820614	−	0.571483i	$-0.193632\pi$
$108$	3.51389	−	7.17151i	0.338124	−	0.690078i
$109$	1.83295	+	18.6103i	0.175565	+	1.78254i	0.530536	+	0.847662i	$0.321991\pi$
$109$	1.83295	+	18.6103i	0.175565	+	1.78254i	−0.354971	+	0.934877i	$0.615509\pi$
$110$	−3.42249	+	3.54540i	−0.326322	+	0.338040i
$111$	8.03599	−	3.32861i	0.762742	−	0.315938i
$112$	−13.6246	−	1.72308i	−1.28741	−	0.162816i
$113$	−6.04085	−	2.50220i	−0.568275	−	0.235387i	0.0799982	−	0.996795i	$-0.474509\pi$
$113$	−6.04085	−	2.50220i	−0.568275	−	0.235387i	−0.648273	+	0.761408i	$0.724509\pi$
$114$	−12.9366	+	5.62783i	−1.21162	+	0.527095i
$115$	−6.33344	−	5.19772i	−0.590596	−	0.484690i
$116$	5.09143	−	6.67042i	0.472727	−	0.619333i
$117$	−6.20920	+	1.88354i	−0.574041	+	0.174133i
$118$	2.33609	+	4.19101i	0.215055	+	0.385813i
$119$	12.1754	−	18.2218i	1.11612	−	1.67039i
$120$	−4.53333	+	3.38909i	−0.413834	+	0.309381i
$121$	0.949242	−	0.634263i	0.0862948	−	0.0576603i
$122$	7.04847	−	2.27463i	0.638138	−	0.205935i
$123$	−0.615021	−	0.749405i	−0.0554545	−	0.0675716i
$124$	7.12100	+	15.6104i	0.639485	+	1.40185i
$125$	0.881921	−	0.471397i	0.0788814	−	0.0421630i
$126$	−4.80018	−	0.867102i	−0.427634	−	0.0772476i
$127$	1.80411			0.160089			0.0800446	−	0.996791i	$-0.474494\pi$
$127$	1.80411			0.160089			0.0800446	+	0.996791i	$0.474494\pi$
$128$	10.7400	−	3.55688i	0.949295	−	0.314387i
$129$	1.33201			0.117277
$130$	−8.98853	−	1.62368i	−0.788347	−	0.142406i
$131$	−18.2396	+	9.74925i	−1.59360	+	0.851796i	−0.594744	+	0.803915i	$0.702747\pi$
$131$	−18.2396	+	9.74925i	−1.59360	+	0.851796i	−0.998853	+	0.0478805i	$0.984753\pi$
$132$	12.6882	−	5.78798i	1.10437	−	0.503779i
$133$	−10.8575	−	13.2299i	−0.941466	−	1.14718i
$134$	−1.88356	+	0.607847i	−0.162715	+	0.0525100i
$135$	3.32010	−	2.21842i	0.285749	−	0.190931i
$136$	−2.58079	+	17.8689i	−0.221301	+	1.53224i
$137$	7.35089	−	11.0014i	0.628029	−	0.939912i	−0.371903	−	0.928271i	$-0.621295\pi$
$137$	7.35089	−	11.0014i	0.628029	−	0.939912i	0.999932	−	0.0116402i	$-0.00370527\pi$
$138$	11.2894	+	20.2534i	0.961015	+	1.72409i
$139$	12.2849	−	3.72657i	1.04199	−	0.316084i	0.277503	−	0.960725i	$-0.410493\pi$
$139$	12.2849	−	3.72657i	1.04199	−	0.316084i	0.764485	+	0.644641i	$0.222993\pi$
$140$	−5.45826	−	4.16621i	−0.461307	−	0.352109i
$141$	−15.7045	−	12.8883i	−1.32255	−	1.08539i
$142$	8.78630	−	3.82231i	0.737330	−	0.320761i
$143$	20.7922	+	8.61241i	1.73873	+	0.720206i
$144$	3.87622	−	1.05985i	0.323019	−	0.0883205i
$145$	3.87636	−	1.60564i	0.321914	−	0.133341i
$146$	−3.55055	+	3.67805i	−0.293845	+	0.304398i
$147$	−0.939052	−	9.53436i	−0.0774517	−	0.786380i
$148$	−7.80635	−	3.82495i	−0.641678	−	0.314409i
$149$	−8.47647	+	15.8584i	−0.694419	+	1.29917i	0.249302	+	0.968426i	$0.419799\pi$
$149$	−8.47647	+	15.8584i	−0.694419	+	1.29917i	−0.943721	+	0.330741i	$0.892701\pi$
$150$	−2.81110	+	0.327023i	−0.229526	+	0.0267013i
$151$	−2.21760	+	0.441109i	−0.180466	+	0.0358969i	−0.284496	−	0.958677i	$-0.591826\pi$
$151$	−2.21760	+	0.441109i	−0.180466	+	0.0358969i	0.104030	+	0.994574i	$0.466826\pi$
$152$	12.7688	+	5.97956i	1.03569	+	0.485007i
$153$	−1.25105	+	6.28946i	−0.101142	+	0.508473i
$154$	10.9620	+	12.8869i	0.883345	+	1.03846i
$155$	−0.840883	+	8.53763i	−0.0675414	+	0.685759i
$156$	21.9864	+	13.5944i	1.76032	+	1.08843i
$157$	−5.60327	+	18.4715i	−0.447190	+	1.47419i	0.386674	+	0.922216i	$0.373624\pi$
$157$	−5.60327	+	18.4715i	−0.447190	+	1.47419i	−0.833864	+	0.551970i	$0.813876\pi$
$158$	3.53354	+	2.27193i	0.281114	+	0.180745i
$159$	0.632503	+	0.632503i	0.0501607	+	0.0501607i
$160$	5.53686	+	1.15896i	0.437727	+	0.0916237i
$161$	−19.8907	+	19.8907i	−1.56761	+	1.56761i
$162$	−15.2079	+	3.30489i	−1.19485	+	0.259657i
$163$	11.1077	+	3.36949i	0.870024	+	0.263919i	0.693569	−	0.720390i	$-0.256037\pi$
$163$	11.1077	+	3.36949i	0.870024	+	0.263919i	0.176454	+	0.984309i	$0.443537\pi$
$164$	−0.155392	+	0.956361i	−0.0121341	+	0.0746792i
$165$	6.93942	+	0.683474i	0.540233	+	0.0532084i
$166$	0.282912	−	3.50520i	0.0219582	−	0.272056i
$167$	−2.17790	−	0.433211i	−0.168531	−	0.0335229i	0.110103	−	0.993920i	$-0.464882\pi$
$167$	−2.17790	−	0.433211i	−0.168531	−	0.0335229i	−0.278634	+	0.960397i	$0.589882\pi$
$168$	10.0542	+	16.6298i	0.775695	+	1.28302i
$169$	5.60203	+	28.1633i	0.430925	+	2.16641i
$170$	−5.60279	+	7.07798i	−0.429715	+	0.542856i
$171$	4.41668	+	2.36077i	0.337752	+	0.180532i
$172$	−0.880296	−	0.998637i	−0.0671219	−	0.0761454i
$173$	−15.4385	+	1.52056i	−1.17376	+	0.115606i	−0.666041	−	0.745915i	$-0.732013\pi$
$173$	−15.4385	+	1.52056i	−1.17376	+	0.115606i	−0.507723	+	0.861521i	$0.669513\pi$
$174$	−11.8724	+	0.209418i	−0.900042	+	0.0158759i
$175$	−1.31386	−	3.17195i	−0.0993187	−	0.239777i
$176$	−12.7247	−	5.68748i	−0.959163	−	0.428710i
$177$	2.59822	−	6.27266i	0.195294	−	0.471482i
$178$	7.08747	−	18.0023i	0.531229	−	1.34933i
$179$	−14.1937	+	17.2951i	−1.06089	+	1.29270i	−0.106441	+	0.994319i	$0.533945\pi$
$179$	−14.1937	+	17.2951i	−1.06089	+	1.29270i	−0.954448	+	0.298377i	$0.903555\pi$
$180$	1.94211	+	0.515083i	0.144756	+	0.0383920i
$181$	2.52185	+	8.31343i	0.187448	+	0.617933i	0.999414	+	0.0342283i	$0.0108973\pi$
$181$	2.52185	+	8.31343i	0.187448	+	0.617933i	−0.811966	+	0.583704i	$0.801603\pi$
$182$	−8.57257	+	30.1652i	−0.635441	+	2.23600i
$183$	−8.71405	−	5.82254i	−0.644161	−	0.430415i
$184$	7.72355	−	21.8490i	0.569388	−	1.61073i
$185$	−2.41480	−	3.61401i	−0.177540	−	0.265707i
$186$	11.0656	−	21.6106i	0.811369	−	1.58457i
$187$	17.1933	−	14.1102i	1.25730	−	1.03184i
$188$	0.716074	+	20.2916i	0.0522251	+	1.47992i
$189$	−6.46252	−	12.0905i	−0.470080	−	0.879457i
$190$	4.01943	+	5.79170i	0.291600	+	0.420174i
$191$			2.19923i			0.159131i	0.996830	+	0.0795654i	$0.0253533\pi$
$191$			2.19923i			0.159131i	−0.996830	+	0.0795654i	$0.974647\pi$
$192$	−13.3788	−	8.79219i	−0.965535	−	0.634521i
$193$		−	15.4916i		−	1.11511i	−0.830140	−	0.557555i	$-0.811740\pi$
$193$		−	15.4916i		−	1.11511i	0.830140	−	0.557555i	$-0.188260\pi$
$194$	−3.98376	+	2.76472i	−0.286017	+	0.198495i
$195$	6.09276	+	11.3987i	0.436311	+	0.816281i
$196$	−6.52753	+	7.00508i	−0.466252	+	0.500363i
$197$	−12.4639	+	10.2289i	−0.888018	+	0.728777i	−0.963312	−	0.268384i	$-0.913510\pi$
$197$	−12.4639	+	10.2289i	−0.888018	+	0.728777i	0.0752942	+	0.997161i	$0.476010\pi$
$198$	−4.40652	−	2.25634i	−0.313158	−	0.160351i
$199$	5.65578	+	8.46447i	0.400928	+	0.600031i	0.975920	−	0.218128i	$-0.0699950\pi$
$199$	5.65578	+	8.46447i	0.400928	+	0.600031i	−0.574992	+	0.818159i	$0.694995\pi$
$200$	2.10298	+	1.89143i	0.148703	+	0.133744i
$201$	2.32865	+	1.55595i	0.164250	+	0.109748i
$202$	−11.8296	−	3.36182i	−0.832329	−	0.236537i
$203$	−4.18161	−	13.7849i	−0.293492	−	0.967512i
$204$	22.0920	−	12.8300i	1.54675	−	0.898283i
$205$	−0.307333	+	0.374486i	−0.0214650	+	0.0261552i
$206$	1.34541	+	0.529684i	0.0937389	+	0.0369048i
$207$	3.14991	−	7.60456i	0.218934	−	0.528554i
$208$	−4.33831	−	25.4680i	−0.300808	−	1.76589i
$209$	−6.64722	−	16.0478i	−0.459798	−	1.11005i
$210$	0.171362	+	9.71491i	0.0118251	+	0.670393i
$211$	13.6356	−	1.34299i	0.938711	−	0.0924550i	0.382924	−	0.923780i	$-0.374917\pi$
$211$	13.6356	−	1.34299i	0.938711	−	0.0924550i	0.555787	+	0.831325i	$0.312417\pi$
$212$	0.0561943	−	0.892209i	0.00385944	−	0.0612772i
$213$	−11.9575	−	6.39139i	−0.819311	−	0.437931i
$214$	20.4360	+	16.1767i	1.39697	+	1.10582i
$215$	−0.129856	−	0.652830i	−0.00885610	−	0.0445226i
$216$	9.09714	+	6.69312i	0.618982	+	0.455409i
$217$	28.8880	+	5.74619i	1.96105	+	0.390077i
$218$	−26.3605	−	2.12761i	−1.78536	−	0.144100i
$219$	7.19907	+	0.709046i	0.486468	+	0.0479129i
$220$	−4.07370	−	5.65434i	−0.274649	−	0.381215i
$221$	39.4517	+	11.9676i	2.65381	+	0.805025i
$222$	2.61220	+	12.0204i	0.175319	+	0.806756i
$223$	−11.9498	+	11.9498i	−0.800215	+	0.800215i	−0.983129	−	0.182914i	$-0.941447\pi$
$223$	−11.9498	+	11.9498i	−0.800215	+	0.800215i	0.182914	+	0.983129i	$0.441447\pi$
$224$	5.82315	−	18.5281i	0.389076	−	1.23796i
$225$	0.710378	+	0.710378i	0.0473585	+	0.0473585i
$226$	5.00092	−	7.77795i	0.332656	−	0.517381i
$227$	3.22934	−	10.6457i	0.214339	−	0.706581i	−0.782168	−	0.623068i	$-0.785886\pi$
$227$	3.22934	−	10.6457i	0.214339	−	0.706581i	0.996507	−	0.0835129i	$-0.0266140\pi$
$228$	−4.58001	−	19.4186i	−0.303318	−	1.28603i
$229$	1.08237	−	10.9895i	0.0715250	−	0.726206i	−0.890817	−	0.454363i	$-0.849867\pi$
$229$	1.08237	−	10.9895i	0.0715250	−	0.726206i	0.962342	−	0.271843i	$-0.0876331\pi$
$230$	8.82580	−	7.50751i	0.581956	−	0.495030i
$231$	4.67053	−	23.4803i	0.307298	−	1.54489i
$232$	8.00320	+	8.76259i	0.525436	+	0.575292i
$233$	−1.11077	+	0.220946i	−0.0727689	+	0.0144746i	−0.231340	−	0.972873i	$-0.574311\pi$
$233$	−1.11077	+	0.220946i	−0.0727689	+	0.0144746i	0.158572	+	0.987347i	$0.449311\pi$
$234$	−1.06035	−	9.11480i	−0.0693171	−	0.595853i
$235$	−4.78567	+	8.95337i	−0.312183	+	0.584053i
$236$	−6.41986	+	2.19752i	−0.417897	+	0.143046i
$237$	−0.582654	−	5.91579i	−0.0378475	−	0.384272i
$238$	22.2983	+	21.5253i	1.44538	+	1.39528i
$239$	−21.9829	+	9.10562i	−1.42196	+	0.588993i	−0.955351	−	0.295472i	$-0.904523\pi$
$239$	−21.9829	+	9.10562i	−1.42196	+	0.588993i	−0.466605	+	0.884466i	$0.654523\pi$
$240$	−3.57692	−	7.16098i	−0.230889	−	0.462240i
$241$	−7.80450	−	3.23273i	−0.502732	−	0.208238i	0.116881	−	0.993146i	$-0.462710\pi$
$241$	−7.80450	−	3.23273i	−0.502732	−	0.208238i	−0.619613	+	0.784907i	$0.712710\pi$
$242$	0.644064	+	1.48050i	0.0414020	+	0.0951702i
$243$	7.76317	+	6.37107i	0.498007	+	0.408704i
$244$	1.39364	+	10.3811i	0.0892184	+	0.664583i
$245$	−4.58133	+	1.38973i	−0.292690	+	0.0887867i
$246$	1.19755	−	0.667522i	0.0763531	−	0.0425597i
$247$	17.8874	−	26.7704i	1.13815	−	1.70336i
$248$	−23.5150	+	5.98587i	−1.49320	+	0.380103i
$249$	−4.13747	+	2.76457i	−0.262202	+	0.175198i
$250$	0.434328	+	1.34587i	0.0274693	+	0.0851201i
$251$	3.55705	+	4.33427i	0.224519	+	0.273577i	0.873071	−	0.487593i	$-0.162125\pi$
$251$	3.55705	+	4.33427i	0.224519	+	0.273577i	−0.648552	+	0.761170i	$0.724625\pi$
$252$	2.41347	−	6.46238i	0.152035	−	0.407092i
$253$	−25.1781	+	13.4580i	−1.58293	+	0.846095i
$254$	−0.453544	+	2.51077i	−0.0284579	+	0.157540i
$255$	12.7737			0.799919
$256$	2.25009	+	15.8410i	0.140631	+	0.990062i
$257$	−6.39777			−0.399082			−0.199541	−	0.979889i	$-0.563945\pi$
$257$	−6.39777			−0.399082			−0.199541	+	0.979889i	$0.563945\pi$
$258$	−0.334859	+	1.85374i	−0.0208474	+	0.115409i
$259$	−13.1608	+	7.03461i	−0.817774	+	0.437109i
$260$	4.51933	−	12.1011i	0.280277	−	0.750476i
$261$	2.67407	+	3.25836i	0.165521	+	0.201687i
$262$	−8.98261	−	27.8347i	−0.554947	−	1.71963i
$263$	24.8155	−	16.5812i	1.53019	−	1.02244i	0.547580	−	0.836753i	$-0.315549\pi$
$263$	24.8155	−	16.5812i	1.53019	−	1.02244i	0.982609	−	0.185686i	$-0.0594507\pi$
$264$	4.86534	+	19.1131i	0.299441	+	1.17633i
$265$	0.248334	−	0.371657i	0.0152550	−	0.0228307i
$266$	21.1415	−	11.7844i	1.29627	−	0.722546i
$267$	−26.1981	+	7.94711i	−1.60330	+	0.486355i
$268$	−0.372420	−	2.77414i	−0.0227492	−	0.169457i
$269$	−18.5099	−	15.1907i	−1.12857	−	0.926194i	−0.130700	−	0.991422i	$-0.541722\pi$
$269$	−18.5099	−	15.1907i	−1.12857	−	0.926194i	−0.997870	+	0.0652281i	$0.979222\pi$
$270$	2.25270	+	5.17825i	0.137095	+	0.315138i
$271$	16.0831	+	6.66185i	0.976980	+	0.404678i	0.813306	−	0.581836i	$-0.197666\pi$
$271$	16.0831	+	6.66185i	0.976980	+	0.404678i	0.163674	+	0.986515i	$0.447666\pi$
$272$	−24.2191	−	8.08379i	−1.46850	−	0.490152i
$273$	40.9971	−	16.9816i	2.48126	−	1.02777i
$274$	13.4625	+	12.9958i	0.813302	+	0.785108i
$275$	−0.341539	−	3.46771i	−0.0205956	−	0.209111i
$276$	−31.0246	+	10.6197i	−1.86746	+	0.639232i
$277$	1.22963	−	2.30047i	0.0738811	−	0.138222i	−0.842269	−	0.539058i	$-0.818780\pi$
$277$	1.22963	−	2.30047i	0.0738811	−	0.138222i	0.916150	+	0.400836i	$0.131280\pi$
$278$	2.09789	+	18.0336i	0.125823	+	1.08158i
$279$	−8.45303	+	1.68141i	−0.506070	+	0.100663i
$280$	7.17024	−	6.54885i	0.428504	−	0.391369i
$281$	−1.27878	+	6.42888i	−0.0762858	+	0.383515i	0.923714	+	0.383083i	$0.125138\pi$
$281$	−1.27878	+	6.42888i	−0.0762858	+	0.383515i	−1.00000		0.000432077i	$0.999862\pi$
$282$	21.8845	−	18.6157i	1.30321	−	1.10855i
$283$	−1.86195	+	18.9047i	−0.110681	+	1.12377i	0.766048	+	0.642783i	$0.222220\pi$
$283$	−1.86195	+	18.9047i	−0.110681	+	1.12377i	−0.876730	+	0.480983i	$0.840280\pi$
$284$	3.11065	+	13.1887i	0.184583	+	0.782606i
$285$	2.89579	−	9.54613i	0.171532	−	0.565464i
$286$	−17.2128	+	26.7712i	−1.01782	+	1.58301i
$287$	1.17610	+	1.17610i	0.0694232	+	0.0694232i
$288$	0.500516	+	5.66094i	0.0294932	+	0.333574i
$289$	16.7899	−	16.7899i	0.987644	−	0.987644i
$290$	1.26006	+	5.79834i	0.0739933	+	0.340491i
$291$	6.56621	+	1.99184i	0.384918	+	0.116764i
$292$	−4.22612	−	5.86590i	−0.247315	−	0.343276i
$293$	−13.2309	−	1.30313i	−0.772960	−	0.0761299i	−0.296156	−	0.955140i	$-0.595705\pi$
$293$	−13.2309	−	1.30313i	−0.772960	−	0.0761299i	−0.476804	+	0.879010i	$0.658205\pi$
$294$	13.5049	+	1.09001i	0.787624	+	0.0635708i
$295$	−3.32758	−	0.661898i	−0.193739	−	0.0385372i
$296$	7.28562	−	9.90245i	0.423468	−	0.575568i
$297$	−2.71444	−	13.6464i	−0.157508	−	0.791844i
$298$	−19.9390	−	15.7833i	−1.15503	−	0.914303i
$299$	−46.6692	−	24.9452i	−2.69895	−	1.44262i
$300$	0.251580	−	3.99440i	0.0145250	−	0.230617i
$301$	−2.27426	+	0.223995i	−0.131086	+	0.0129109i
$302$	−0.0563942	−	3.19711i	−0.00324512	−	0.183973i
$303$	6.65950	+	16.0774i	0.382578	+	0.923625i
$304$	−11.5317	+	16.2670i	−0.661389	+	0.932979i
$305$	−2.00416	+	4.83847i	−0.114758	+	0.277050i
$306$	−8.43847	−	3.32221i	−0.482395	−	0.189918i
$307$	−3.03241	+	3.69501i	−0.173069	+	0.210885i	−0.852320	−	0.523021i	$-0.824805\pi$
$307$	−3.03241	+	3.69501i	−0.173069	+	0.210885i	0.679251	+	0.733906i	$0.262305\pi$
$308$	−20.6904	+	12.0160i	−1.17894	+	0.684678i
$309$	−0.593928	−	1.95792i	−0.0337874	−	0.111382i
$310$	−11.6703	−	3.31656i	−0.662831	−	0.188368i
$311$	−12.8512	−	8.58692i	−0.728727	−	0.486920i	0.135022	−	0.990843i	$-0.456890\pi$
$311$	−12.8512	−	8.58692i	−0.728727	−	0.486920i	−0.863749	+	0.503923i	$0.831890\pi$
$312$	−24.4465	+	27.1808i	−1.38401	+	1.53881i
$313$	−2.37744	−	3.55809i	−0.134381	−	0.201115i	0.758176	−	0.652050i	$-0.226091\pi$
$313$	−2.37744	−	3.55809i	−0.134381	−	0.201115i	−0.892557	+	0.450935i	$0.851091\pi$
$314$	−24.2980	−	12.4416i	−1.37121	−	0.702123i
$315$	2.66625	−	2.18813i	0.150226	−	0.123287i
$316$	−4.05014	+	4.34645i	−0.227838	+	0.244507i
$317$	−7.79588	−	14.5851i	−0.437860	−	0.819179i	0.562108	−	0.827064i	$-0.309990\pi$
$317$	−7.79588	−	14.5851i	−0.437860	−	0.819179i	−0.999969	+	0.00788424i	$0.997490\pi$
$318$	−1.03926	+	0.721240i	−0.0582786	+	0.0404452i
$319$		−	14.6200i		−	0.818564i
$320$	−3.00485	+	7.41424i	−0.167976	+	0.414468i
$321$		−	36.8809i		−	2.05849i
$322$	−22.6813	−	32.6821i	−1.26398	−	1.82130i
$323$	−14.9997	−	28.0625i	−0.834607	−	1.56144i
$324$	−0.776204	−	21.9955i	−0.0431225	−	1.22197i
$325$	4.99266	−	4.09737i	0.276943	−	0.227281i
$326$	−7.48170	+	14.6114i	−0.414373	+	0.809252i
$327$	20.7907	+	31.1154i	1.14973	+	1.72069i
$328$	−1.29189	−	0.456681i	−0.0713328	−	0.0252160i
$329$	28.9810	+	19.3645i	1.59777	+	1.06760i
$330$	−2.69571	+	9.48571i	−0.148394	+	0.522171i
$331$	−1.32820	−	4.37849i	−0.0730045	−	0.240664i	0.912842	−	0.408312i	$-0.133883\pi$
$331$	−1.32820	−	4.37849i	−0.0730045	−	0.240664i	−0.985847	+	0.167649i	$0.946383\pi$
$332$	4.80703	+	1.27491i	0.263820	+	0.0699699i
$333$	2.77017	−	3.37546i	0.151804	−	0.184974i
$334$	1.15041	−	2.92205i	0.0629474	−	0.159888i
$335$	0.535570	−	1.29298i	0.0292613	−	0.0706430i
$336$	−25.6711	+	9.81164i	−1.40047	+	0.535269i
$337$	1.15941	+	2.79905i	0.0631569	+	0.152474i	0.952307	−	0.305141i	$-0.0987037\pi$
$337$	1.15941	+	2.79905i	0.0631569	+	0.152474i	−0.889150	+	0.457615i	$0.848704\pi$
$338$	−40.6029	+	0.716199i	−2.20851	+	0.0389561i
$339$	−13.0217	+	1.28252i	−0.707241	+	0.0696571i
$340$	−8.44185	−	9.57672i	−0.457823	−	0.519370i
$341$	26.3635	+	14.0916i	1.42766	+	0.763101i
$342$	−4.39578	+	5.55317i	−0.237697	+	0.300281i
$343$	−1.48195	−	7.45027i	−0.0800179	−	0.402277i
$344$	1.61109	−	0.974048i	0.0868644	−	0.0525171i
$345$	−16.0809	−	3.19868i	−0.865764	−	0.172211i
$346$	1.76500	−	21.8678i	0.0948867	−	1.17562i
$347$	−5.42591	−	0.534405i	−0.291278	−	0.0286884i	−0.0486771	−	0.998815i	$-0.515501\pi$
$347$	−5.42591	−	0.534405i	−0.291278	−	0.0286884i	−0.242601	+	0.970126i	$0.578001\pi$
$348$	2.69320	−	16.5753i	0.144371	−	0.888530i
$349$	−17.1225	−	5.19404i	−0.916544	−	0.278031i	−0.203439	−	0.979088i	$-0.565212\pi$
$349$	−17.1225	−	5.19404i	−0.916544	−	0.278031i	−0.713105	+	0.701057i	$0.752712\pi$
$350$	4.74466	−	1.03108i	0.253613	−	0.0551136i
$351$	18.2363	−	18.2363i	0.973381	−	0.973381i
$352$	11.1141	−	16.2791i	0.592385	−	0.867678i
$353$	4.14699	+	4.14699i	0.220722	+	0.220722i	0.808802	−	0.588081i	$-0.200116\pi$
$353$	4.14699	+	4.14699i	0.220722	+	0.220722i	−0.588081	+	0.808802i	$0.700116\pi$
$354$	8.07642	+	5.19283i	0.429257	+	0.275996i
$355$	−1.96676	+	6.48355i	−0.104385	+	0.344111i
$356$	23.2719	+	14.3892i	1.23341	+	0.762628i
$357$	4.29861	−	43.6445i	0.227507	−	2.30991i
$358$	−20.5012	−	24.1011i	−1.08352	−	1.27379i
$359$	2.69588	−	13.5531i	0.142283	−	0.715306i	−0.842108	−	0.539310i	$-0.818685\pi$
$359$	2.69588	−	13.5531i	0.142283	−	0.715306i	0.984391	−	0.175997i	$-0.0563148\pi$
$360$	−1.20507	+	2.57332i	−0.0635128	+	0.135626i
$361$	−5.73741	+	1.14124i	−0.301969	+	0.0600654i
$362$	−12.2037	+	1.41969i	−0.641412	+	0.0746172i
$363$	1.07696	−	2.01484i	0.0565256	−	0.105752i
$364$	−39.8256	−	19.5137i	−2.08743	−	1.02280i
$365$	−0.354318	−	3.59745i	−0.0185459	−	0.188299i
$366$	10.2938	−	10.6635i	0.538067	−	0.557390i
$367$	10.2305	−	4.23761i	0.534027	−	0.221201i	−0.0993387	−	0.995054i	$-0.531673\pi$
$367$	10.2305	−	4.23761i	0.534027	−	0.221201i	0.633366	+	0.773852i	$0.281673\pi$
$368$	28.4653	+	16.2415i	1.48386	+	0.846646i
$369$	−0.449645	−	0.186249i	−0.0234076	−	0.00969574i
$370$	5.63665	−	2.45212i	0.293035	−	0.127480i
$371$	−1.18629	−	0.973566i	−0.0615893	−	0.0505450i
$372$	27.2935	+	20.8327i	1.41510	+	1.08012i
$373$	28.9831	−	8.79192i	1.50069	−	0.455228i	0.570185	−	0.821516i	$-0.306872\pi$
$373$	28.9831	−	8.79192i	1.50069	−	0.455228i	0.930501	+	0.366288i	$0.119372\pi$
$374$	15.3147	+	27.4749i	0.791904	+	1.42070i
$375$	1.11178	−	1.66390i	0.0574122	−	0.0859235i
$376$	−28.4196	−	4.10464i	−1.46563	−	0.211680i
$377$	22.5321	−	15.0555i	1.16046	−	0.775396i
$378$	18.4509	−	5.95434i	0.949013	−	0.306258i
$379$	−5.05148	−	6.15525i	−0.259477	−	0.316174i	0.626934	−	0.779072i	$-0.284310\pi$
$379$	−5.05148	−	6.15525i	−0.259477	−	0.316174i	−0.886411	+	0.462898i	$0.846810\pi$
$380$	−9.07072	+	4.13780i	−0.465318	+	0.212264i
$381$	3.18401	−	1.70189i	0.163122	−	0.0871905i
$382$	−3.06065	−	0.552874i	−0.156596	−	0.0282875i
$383$	−13.4805			−0.688823			−0.344412	−	0.938819i	$-0.611922\pi$
$383$	−13.4805			−0.688823			−0.344412	+	0.938819i	$0.611922\pi$
$384$	15.5994	−	16.4089i	0.796052	−	0.837363i
$385$	−11.9632			−0.609704
$386$	21.5595	+	3.89450i	1.09735	+	0.198225i
$387$	0.589740	−	0.315223i	0.0299782	−	0.0160237i
$388$	−2.84614	−	6.23920i	−0.144491	−	0.316747i
$389$	13.7611	+	16.7679i	0.697714	+	0.850167i	0.994496	−	0.104778i	$-0.0334133\pi$
$389$	13.7611	+	16.7679i	0.697714	+	0.850167i	−0.296782	+	0.954945i	$0.595913\pi$
$390$	−17.3952	+	5.61365i	−0.880841	+	0.284258i
$391$	−43.4846	+	29.0555i	−2.19911	+	1.46940i
$392$	−8.10792	−	10.8453i	−0.409512	−	0.547772i
$393$	−22.9935	+	34.4122i	−1.15987	+	1.73586i
$394$	−11.1021	−	19.9174i	−0.559314	−	1.00342i
$395$	−2.84258	+	0.862287i	−0.143026	+	0.0433864i
$396$	4.24789	−	5.56529i	0.213465	−	0.279666i
$397$	−14.6284	−	12.0052i	−0.734177	−	0.602523i	0.191209	−	0.981549i	$-0.438759\pi$
$397$	−14.6284	−	12.0052i	−0.734177	−	0.602523i	−0.925386	+	0.379026i	$0.876259\pi$
$398$	−13.2018	+	5.74317i	−0.661744	+	0.287879i
$399$	−31.6423	−	13.1067i	−1.58410	−	0.656155i
$400$	−3.16096	+	2.45120i	−0.158048	+	0.122560i
$401$	20.1377	−	8.34130i	1.00563	−	0.416545i	0.181770	−	0.983341i	$-0.441817\pi$
$401$	20.1377	−	8.34130i	1.00563	−	0.416545i	0.823858	+	0.566796i	$0.191817\pi$
$402$	−2.75081	+	2.84960i	−0.137198	+	0.142125i
$403$	5.43103	+	55.1422i	0.270539	+	2.74683i
$404$	7.65251	−	15.6180i	0.380727	−	0.777025i
$405$	5.18753	−	9.70520i	0.257771	−	0.482255i
$406$	20.2356	−	2.35406i	1.00427	−	0.116830i
$407$	−14.8544	+	2.95473i	−0.736306	+	0.146460i
$408$	12.3016	+	33.9706i	0.609022	+	1.68180i
$409$	−0.599395	+	3.01336i	−0.0296382	+	0.149001i	−0.992771	−	0.120026i	$-0.961702\pi$
$409$	−0.599395	+	3.01336i	−0.0296382	+	0.149001i	0.963133	+	0.269027i	$0.0867022\pi$
$410$	−0.443907	−	0.521855i	−0.0219230	−	0.0257726i
$411$	2.59528	−	26.3503i	0.128016	−	1.29976i
$412$	−1.07538	+	1.73923i	−0.0529803	+	0.0856856i
$413$	−3.38135	+	11.1468i	−0.166385	+	0.548499i
$414$	9.79132	+	6.29544i	0.481217	+	0.309404i
$415$	1.75830	+	1.75830i	0.0863115	+	0.0863115i
$416$	36.5342	+	0.364929i	1.79124	+	0.0178921i
$417$	18.1657	−	18.1657i	0.889577	−	0.889577i
$418$	24.0046	−	5.21654i	1.17411	−	0.255150i
$419$	2.73949	+	0.831015i	0.133833	+	0.0405977i	0.356490	−	0.934299i	$-0.383973\pi$
$419$	2.73949	+	0.831015i	0.133833	+	0.0405977i	−0.222658	+	0.974897i	$0.571473\pi$
$420$	−13.5632	−	2.20379i	−0.661818	−	0.107534i
$421$	−13.3246	−	1.31236i	−0.649401	−	0.0639604i	−0.232047	−	0.972705i	$-0.574542\pi$
$421$	−13.3246	−	1.31236i	−0.649401	−	0.0639604i	−0.417354	+	0.908744i	$0.637042\pi$
$422$	−1.55888	+	19.3141i	−0.0758852	+	0.940196i
$423$	−10.0031	−	1.98974i	−0.486368	−	0.0967446i
$424$	1.22755	+	0.302501i	0.0596152	+	0.0146908i
$425$	−1.24529	−	6.26050i	−0.0604055	−	0.303679i
$426$	11.9009	−	15.0343i	0.576599	−	0.728415i
$427$	15.8574	+	8.47597i	0.767395	+	0.410181i
$428$	−27.6504	+	24.3738i	−1.33653	+	1.17815i
$429$	44.8198	−	4.41436i	2.16392	−	0.213127i
$430$	0.941182	−	0.0166016i	0.0453878	−	0.000800601i
$431$	−6.21827	−	15.0122i	−0.299524	−	0.723114i	−0.999956	−	0.00939517i	$-0.997009\pi$
$431$	−6.21827	−	15.0122i	−0.299524	−	0.723114i	0.700432	−	0.713719i	$-0.252991\pi$
$432$	−11.6017	+	10.9778i	−0.558188	+	0.528169i
$433$	−13.0300	+	31.4572i	−0.626182	+	1.51174i	0.218149	+	0.975915i	$0.429998\pi$
$433$	−13.0300	+	31.4572i	−0.626182	+	1.51174i	−0.844331	+	0.535822i	$0.820002\pi$
$434$	−15.2592	+	38.7586i	−0.732465	+	1.86047i
$435$	5.32658	−	6.49046i	0.255390	−	0.311194i
$436$	9.58785	−	36.1508i	0.459175	−	1.73131i
$437$	11.8560	+	39.0842i	0.567152	+	1.86965i
$438$	−2.79658	+	9.84062i	−0.133626	+	0.470203i
$439$	16.6519	+	11.1265i	0.794753	+	0.531037i	0.885391	−	0.464847i	$-0.153891\pi$
$439$	16.6519	+	11.1265i	0.794753	+	0.531037i	−0.0906377	+	0.995884i	$0.528891\pi$
$440$	8.89319	−	4.24786i	0.423966	−	0.202509i
$441$	−2.67208	−	3.99906i	−0.127242	−	0.190431i
$442$	−26.5731	+	51.8960i	−1.26395	+	2.46844i
$443$	7.65642	−	6.28346i	0.363767	−	0.298536i	−0.434699	−	0.900576i	$-0.643145\pi$
$443$	7.65642	−	6.28346i	0.363767	−	0.298536i	0.798466	+	0.602040i	$0.205645\pi$
$444$	−17.3854	+	0.613515i	−0.825073	+	0.0291162i
$445$	6.44897	+	12.0652i	0.305711	+	0.571944i
$446$	−13.6263	−	19.6345i	−0.645222	−	0.929718i
$447$			35.9840i			1.70198i
$448$	24.3215	+	12.7619i	1.14908	+	0.602942i
$449$			7.18318i			0.338995i	0.985531	+	0.169498i	$0.0542145\pi$
$449$			7.18318i			0.338995i	−0.985531	+	0.169498i	$0.945786\pi$
$450$	−1.16721	+	0.810041i	−0.0550229	+	0.0381857i
$451$	0.795748	+	1.48874i	0.0374703	+	0.0701020i
$452$	9.56729	+	8.91506i	0.450007	+	0.419329i
$453$	−3.49765	+	2.87045i	−0.164334	+	0.134865i
$454$	14.0037	+	7.17051i	0.657226	+	0.336529i
$455$	−12.3196	−	18.4375i	−0.577551	−	0.864366i
$456$	28.1760	−	1.49224i	1.31946	−	0.0698804i
$457$	−1.76962	−	1.18242i	−0.0827794	−	0.0553114i	0.513492	−	0.858095i	$-0.328352\pi$
$457$	−1.76962	−	1.18242i	−0.0827794	−	0.0553114i	−0.596271	+	0.802783i	$0.703352\pi$
$458$	15.0219	+	4.26902i	0.701926	+	0.199478i
$459$	−7.39885	−	24.3907i	−0.345349	−	1.13846i
$460$	8.22937	+	14.1701i	0.383696	+	0.660686i
$461$	6.01022	−	7.32347i	0.279924	−	0.341088i	−0.614001	−	0.789305i	$-0.710441\pi$
$461$	6.01022	−	7.32347i	0.279924	−	0.341088i	0.893925	+	0.448217i	$0.147941\pi$
$462$	31.5032	+	12.4027i	1.46566	+	0.577028i
$463$	13.2920	−	32.0898i	0.617733	−	1.49134i	−0.236598	−	0.971608i	$-0.576032\pi$
$463$	13.2920	−	32.0898i	0.617733	−	1.49134i	0.854330	−	0.519731i	$-0.173968\pi$
$464$	−14.2068	+	8.93511i	−0.659533	+	0.414802i
$465$	6.56983	+	15.8610i	0.304669	+	0.735535i
$466$	−0.0282471	−	1.60139i	−0.00130852	−	0.0741830i
$467$	15.6595	−	1.54233i	0.724635	−	0.0713703i	0.271027	−	0.962572i	$-0.412637\pi$
$467$	15.6595	−	1.54233i	0.724635	−	0.0713703i	0.453608	+	0.891201i	$0.350137\pi$
$468$	12.9515	+	0.815730i	0.598685	+	0.0377071i
$469$	−4.23757	−	2.26503i	−0.195673	−	0.104589i
$470$	−11.2572	−	8.91100i	−0.519257	−	0.411034i
$471$	7.53588	+	37.8854i	0.347235	+	1.74567i
$472$	−1.44435	−	9.48690i	−0.0664816	−	0.436670i
$473$	−2.27478	−	0.452481i	−0.104594	−	0.0208051i
$474$	8.37942	+	0.676320i	0.384879	+	0.0310644i
$475$	−4.96096	−	0.488611i	−0.227624	−	0.0224190i
$476$	−35.5622	+	25.6210i	−1.62999	+	1.17434i
$477$	0.429720	+	0.130354i	0.0196755	+	0.00596851i
$478$	−7.14582	−	32.8825i	−0.326842	−	1.50401i
$479$	−23.2881	+	23.2881i	−1.06406	+	1.06406i	−0.0662580	+	0.997803i	$0.521106\pi$
$479$	−23.2881	+	23.2881i	−1.06406	+	1.06406i	−0.997803	+	0.0662580i	$0.978894\pi$
$480$	10.8651	−	3.17773i	0.495921	−	0.145043i
$481$	−19.8506	−	19.8506i	−0.905111	−	0.905111i
$482$	6.46096	−	10.0488i	0.294289	−	0.457708i
$483$	−16.3407	+	53.8680i	−0.743526	+	2.45108i
$484$	−2.22231	+	0.524148i	−0.101014	+	0.0238249i
$485$	0.336086	−	3.41234i	0.0152609	−	0.154946i
$486$	−10.8182	+	9.20227i	−0.490722	+	0.417424i
$487$	−0.293902	+	1.47755i	−0.0133180	+	0.0669540i	−0.986873	−	0.161500i	$-0.948367\pi$
$487$	−0.293902	+	1.47755i	−0.0133180	+	0.0669540i	0.973555	+	0.228454i	$0.0733669\pi$
$488$	−14.7976	−	0.670242i	−0.669858	−	0.0303404i
$489$	22.7822	−	4.53165i	1.03024	−	0.204928i
$490$	−0.782356	−	6.72516i	−0.0353432	−	0.303812i
$491$	10.6701	−	19.9623i	0.481534	−	0.900886i	−0.517446	−	0.855716i	$-0.673117\pi$
$491$	10.6701	−	19.9623i	0.481534	−	0.900886i	0.998979	−	0.0451700i	$-0.0143829\pi$
$492$	0.627926	+	1.83443i	0.0283091	+	0.0827026i
$493$	−2.62510	−	26.6531i	−0.118229	−	1.20040i
$494$	32.7593	+	31.6236i	1.47391	+	1.42281i
$495$	3.23414	−	1.33962i	0.145364	−	0.0602116i
$496$	−2.41894	−	34.2304i	−0.108614	−	1.53699i
$497$	21.4909	+	8.90180i	0.963997	+	0.399300i
$498$	−2.80729	−	6.45307i	−0.125798	−	0.289169i
$499$	−12.5107	−	10.2673i	−0.560056	−	0.459626i	0.311276	−	0.950320i	$-0.399244\pi$
$499$	−12.5107	−	10.2673i	−0.560056	−	0.459626i	−0.871332	+	0.490693i	$0.836744\pi$
$500$	−1.98222	+	0.266107i	−0.0886475	+	0.0119007i
$501$	−4.25236	+	1.28994i	−0.189981	+	0.0576302i
$502$	−6.92619	+	3.86070i	−0.309131	+	0.172311i
$503$	3.81728	−	5.71296i	0.170204	−	0.254728i	−0.736555	−	0.676378i	$-0.763549\pi$
$503$	3.81728	−	5.71296i	0.170204	−	0.254728i	0.906759	+	0.421650i	$0.138549\pi$
$504$	8.38689	+	4.98341i	0.373582	+	0.221979i
$505$	7.23048	−	4.83125i	0.321752	−	0.214988i
$506$	−12.3997	−	38.4234i	−0.551234	−	1.70813i
$507$	36.4543	+	44.4197i	1.61899	+	1.97275i
$508$	−3.38019	−	1.26238i	−0.149972	−	0.0560092i
$509$	−18.0073	+	9.62512i	−0.798161	+	0.426626i	−0.819452	−	0.573147i	$-0.805722\pi$
$509$	−18.0073	+	9.62512i	−0.798161	+	0.426626i	0.0212913	+	0.999773i	$0.493222\pi$
$510$	−3.21123	+	17.7770i	−0.142196	+	0.787179i
$511$	−12.4109			−0.549024
$512$	−22.6114	−	0.850907i	−0.999293	−	0.0376051i
$513$	−19.9052			−0.878837
$514$	1.60836	−	8.90371i	0.0709418	−	0.392726i
$515$	−0.901693	+	0.481965i	−0.0397333	+	0.0212379i
$516$	−2.49565	−	0.932040i	−0.109865	−	0.0410308i
$517$	22.4416	+	27.3452i	0.986981	+	1.20264i
$518$	−6.48144	−	20.0842i	−0.284778	−	0.882451i
$519$	−25.8123	+	17.2473i	−1.13304	+	0.757071i
$520$	15.7048	+	9.33164i	0.688701	+	0.409220i
$521$	8.22653	−	12.3119i	0.360411	−	0.539393i	−0.606309	−	0.795229i	$-0.707351\pi$
$521$	8.22653	−	12.3119i	0.360411	−	0.539393i	0.966720	+	0.255836i	$0.0823507\pi$
$522$	−5.20687	+	2.90234i	−0.227899	+	0.127032i
$523$	−6.93392	+	2.10338i	−0.303199	+	0.0919745i	−0.438218	−	0.898869i	$-0.644390\pi$
$523$	−6.93392	+	2.10338i	−0.303199	+	0.0919745i	0.135019	+	0.990843i	$0.456890\pi$
$524$	40.9955	−	5.50353i	1.79090	−	0.240423i
$525$	−5.31101	−	4.35863i	−0.231791	−	0.190226i
$526$	16.8374	+	38.7039i	0.734145	+	1.68757i
$527$	50.5922	+	20.9560i	2.20383	+	0.912857i
$528$	−27.8226	+	1.96612i	−1.21082	+	0.0855646i
$529$	40.7696	−	16.8873i	1.77259	−	0.734232i
$530$	0.454802	+	0.439036i	0.0197554	+	0.0190705i
$531$	−0.334089	−	3.39206i	−0.0144982	−	0.147203i
$532$	11.0854	+	32.3849i	0.480611	+	1.40406i
$533$	−1.47497	+	2.75947i	−0.0638880	+	0.119526i
$534$	−4.47386	−	38.4575i	−0.193603	−	1.66422i
$535$	−18.0757	+	3.59547i	−0.781479	+	0.155446i
$536$	3.95436	+	0.179108i	0.170802	+	0.00773630i
$537$	−8.73483	+	43.9130i	−0.376936	+	1.89498i
$538$	25.7940	−	21.9412i	1.11206	−	0.945954i
$539$	−1.63511	+	16.6016i	−0.0704293	+	0.715080i
$540$	−7.77284	+	1.83328i	−0.334490	+	0.0788918i
$541$	−6.02030	+	19.8463i	−0.258833	+	0.853258i	0.727160	+	0.686468i	$0.240840\pi$
$541$	−6.02030	+	19.8463i	−0.258833	+	0.853258i	−0.985993	+	0.166789i	$0.946660\pi$
$542$	−13.3144	+	20.7080i	−0.571904	+	0.889483i
$543$	12.2931	+	12.2931i	0.527548	+	0.527548i
$544$	17.3387	−	31.6733i	0.743389	−	1.35798i
$545$	13.2231	−	13.2231i	0.566416	−	0.566416i
$546$	13.3266	+	61.3243i	0.570327	+	2.62444i
$547$	15.7713	+	4.78416i	0.674330	+	0.204556i	0.608835	−	0.793297i	$-0.291637\pi$
$547$	15.7713	+	4.78416i	0.674330	+	0.204556i	0.0654955	+	0.997853i	$0.479137\pi$
$548$	−21.4706	+	15.4686i	−0.917178	+	0.660786i
$549$	−5.23602	−	0.515702i	−0.223468	−	0.0220096i
$550$	4.91183	+	0.396444i	0.209441	+	0.0169044i
$551$	−20.5137	−	4.08043i	−0.873914	−	0.173832i
$552$	−6.97996	−	45.8463i	−0.297087	−	1.95135i
$553$	1.98964	+	10.0026i	0.0846080	+	0.425353i
$554$	2.89242	+	2.28958i	0.122887	+	0.0972751i
$555$	−7.67103	−	4.10025i	−0.325617	−	0.174046i
$556$	−25.6245	−	1.61392i	−1.08672	−	0.0684453i
$557$	−36.3357	+	3.57876i	−1.53959	+	0.151637i	−0.831917	−	0.554900i	$-0.812757\pi$
$557$	−36.3357	+	3.57876i	−1.53959	+	0.151637i	−0.707676	+	0.706537i	$0.750257\pi$
$558$	−0.214962	−	12.1867i	−0.00910008	−	0.515904i
$559$	−1.64518	−	3.97180i	−0.0695835	−	0.167989i
$560$	7.31141	+	11.6251i	0.308964	+	0.491250i
$561$	17.0331	−	41.1216i	0.719139	−	1.73616i
$562$	−8.62553	−	3.39585i	−0.363846	−	0.143245i
$563$	21.5321	−	26.2370i	0.907471	−	1.10576i	−0.0865152	−	0.996251i	$-0.527573\pi$
$563$	21.5321	−	26.2370i	0.907471	−	1.10576i	0.993986	−	0.109506i	$-0.0349269\pi$
$564$	20.4056	+	35.1364i	0.859232	+	1.47951i
$565$	1.89805	+	6.25702i	0.0798514	+	0.263235i
$566$	−25.8414	−	7.34378i	−1.08619	−	0.308682i
$567$	−31.4146	−	20.9906i	−1.31929	−	0.881520i
$568$	−19.1366	+	1.01350i	−0.802954	+	0.0425255i
$569$	11.4867	+	17.1911i	0.481549	+	0.720690i	0.990103	−	0.140341i	$-0.0448197\pi$
$569$	11.4867	+	17.1911i	0.481549	+	0.720690i	−0.508554	+	0.861030i	$0.669820\pi$
$570$	12.5573	+	6.42988i	0.525966	+	0.269318i
$571$	−22.7209	+	18.6466i	−0.950842	+	0.780336i	−0.975645	−	0.219357i	$-0.929604\pi$
$571$	−22.7209	+	18.6466i	−0.950842	+	0.780336i	0.0248029	+	0.999692i	$0.492104\pi$
$572$	−32.9300	−	30.6851i	−1.37687	−	1.28301i
$573$	2.07462	+	3.88134i	0.0866685	+	0.162145i
$574$	−1.93244	+	1.34111i	−0.0806584	+	0.0559767i
$575$			8.19321i			0.341681i
$576$	−8.00410	−	0.726564i	−0.333504	−	0.0302735i
$577$		−	19.6513i		−	0.818094i	−0.912513	−	0.409047i	$-0.865861\pi$
$577$		−	19.6513i		−	0.818094i	0.912513	−	0.409047i	$-0.134139\pi$
$578$	19.1455	+	27.5873i	0.796348	+	1.14748i
$579$	−14.6138	−	27.3405i	−0.607330	−	1.13623i
$580$	−8.38627	+	0.295945i	−0.348221	+	0.0122884i
$581$	6.59938	−	5.41597i	0.273789	−	0.224693i
$582$	−4.42272	+	8.63739i	−0.183328	+	0.358031i
$583$	−0.865315	−	1.29504i	−0.0358377	−	0.0536349i
$584$	9.22593	−	4.40680i	0.381772	−	0.182355i
$585$	5.39507	+	3.60487i	0.223059	+	0.149043i
$586$	5.13974	−	18.0858i	0.212321	−	0.747116i
$587$	2.63177	+	8.67577i	0.108625	+	0.358087i	0.994354	−	0.106115i	$-0.0338411\pi$
$587$	2.63177	+	8.67577i	0.108625	+	0.358087i	−0.885729	+	0.464202i	$0.846341\pi$
$588$	−4.91202	+	18.5207i	−0.202568	+	0.763779i
$589$	27.1303	−	33.0583i	1.11788	−	1.36214i
$590$	1.75769	−	4.46457i	0.0723630	−	0.183803i
$591$	−12.3478	+	29.8103i	−0.507921	+	1.22623i
$592$	11.9496	+	12.6287i	0.491125	+	0.519038i
$593$	4.81714	+	11.6296i	0.197816	+	0.477571i	0.991396	−	0.130895i	$-0.0417851\pi$
$593$	4.81714	+	11.6296i	0.197816	+	0.477571i	−0.793580	+	0.608466i	$0.791785\pi$
$594$	19.6739	−	0.347031i	0.807232	−	0.0142388i
$595$	−21.8097	+	2.14806i	−0.894109	+	0.0880621i
$596$	26.9780	−	23.7810i	1.10506	−	0.974110i
$597$	17.9665	+	9.60332i	0.735322	+	0.393038i
$598$	46.4484	−	58.6780i	1.89941	−	2.39952i
$599$	−9.02744	−	45.3840i	−0.368851	−	1.85434i	−0.504263	−	0.863550i	$-0.668236\pi$
$599$	−9.02744	−	45.3840i	−0.368851	−	1.85434i	0.135412	−	0.990789i	$-0.456764\pi$
$600$	5.49572	+	1.35429i	0.224362	+	0.0552887i
$601$	−37.6749	−	7.49401i	−1.53679	−	0.305687i	−0.647157	−	0.762357i	$-0.724042\pi$
$601$	−37.6749	−	7.49401i	−1.53679	−	0.305687i	−0.889636	+	0.456670i	$0.849042\pi$
$602$	0.260004	−	3.22138i	0.0105970	−	0.131294i
$603$	1.39922	+	0.137811i	0.0569805	+	0.00561209i
$604$	4.46356	+	0.725251i	0.181620	+	0.0295101i
$605$	−1.09249	−	0.331402i	−0.0444158	−	0.0134734i
$606$	−24.0490	+	5.22618i	−0.976923	+	0.212299i
$607$	−22.5679	+	22.5679i	−0.916002	+	0.916002i	−0.996736	−	0.0807335i	$-0.974274\pi$
$607$	−22.5679	+	22.5679i	−0.916002	+	0.916002i	0.0807335	+	0.996736i	$0.474274\pi$
$608$	−19.7397	−	20.1380i	−0.800550	−	0.816704i
$609$	−20.3838	−	20.3838i	−0.825994	−	0.825994i
$610$	−6.22981	−	4.00553i	−0.252238	−	0.162179i
$611$	−19.0339	+	62.7462i	−0.770028	+	2.53844i
$612$	6.74487	−	10.9086i	0.272645	−	0.440952i
$613$	3.59128	−	36.4629i	0.145050	−	1.47272i	−0.596927	−	0.802296i	$-0.703612\pi$
$613$	3.59128	−	36.4629i	0.145050	−	1.47272i	0.741977	−	0.670425i	$-0.233888\pi$
$614$	−4.37997	−	5.14908i	−0.176761	−	0.207800i
$615$	−0.189133	+	0.950835i	−0.00762657	+	0.0383414i
$616$	−11.5212	−	31.8154i	−0.464201	−	1.28188i
$617$	25.0356	−	4.97989i	1.00789	−	0.200483i	0.336580	−	0.941655i	$-0.390730\pi$
$617$	25.0356	−	4.97989i	1.00789	−	0.200483i	0.671315	+	0.741172i	$0.265730\pi$
$618$	2.87413	−	0.334355i	0.115614	−	0.0134497i
$619$	−18.1650	+	33.9843i	−0.730112	+	1.36594i	0.192918	+	0.981215i	$0.438205\pi$
$619$	−18.1650	+	33.9843i	−0.730112	+	1.36594i	−0.923030	+	0.384728i	$0.874295\pi$
$620$	7.54948	−	15.4077i	0.303194	−	0.618790i
$621$	3.20672	+	32.5584i	0.128681	+	1.30652i
$622$	15.1811	−	15.7262i	0.608705	−	0.630564i
$623$	43.3940	−	17.9744i	1.73854	−	0.720128i
$624$	−31.6815	−	40.8550i	−1.26827	−	1.63551i
$625$	−0.923880	−	0.382683i	−0.0369552	−	0.0153073i
$626$	5.54944	−	2.41418i	0.221800	−	0.0964900i
$627$	−26.8699	−	22.0516i	−1.07308	−	0.880656i
$628$	23.4233	−	30.6875i	0.934691	−	1.22456i
$629$	−26.5499	+	8.05382i	−1.05861	+	0.321127i
$630$	2.37492	+	4.26067i	0.0946192	+	0.169749i
$631$	9.25064	−	13.8446i	0.368262	−	0.551143i	−0.600345	−	0.799741i	$-0.704970\pi$
$631$	9.25064	−	13.8446i	0.368262	−	0.551143i	0.968607	+	0.248598i	$0.0799699\pi$
$632$	−5.03073	−	6.72921i	−0.200112	−	0.267673i
$633$	22.7980	−	15.2331i	0.906140	−	0.605463i
$634$	22.2577	−	7.18285i	0.883968	−	0.285267i
$635$	−1.14452	−	1.39460i	−0.0454188	−	0.0553430i
$636$	−0.742480	−	1.62764i	−0.0294413	−	0.0645400i
$637$	−27.2699	+	14.5760i	−1.08047	+	0.577524i
$638$	20.3465	+	3.67539i	0.805527	+	0.145510i
$639$	−6.80664			−0.269266
$640$	−9.56292	−	6.04571i	−0.378008	−	0.238978i
$641$	−35.1197			−1.38714			−0.693572	−	0.720388i	$-0.743964\pi$
$641$	−35.1197			−1.38714			−0.693572	+	0.720388i	$0.743964\pi$
$642$	51.3268	+	9.27164i	2.02571	+	0.365922i
$643$	−24.3704	+	13.0263i	−0.961077	+	0.513706i	−0.875812	−	0.482652i	$-0.839674\pi$
$643$	−24.3704	+	13.0263i	−0.961077	+	0.513706i	−0.0852645	+	0.996358i	$0.527174\pi$
$644$	51.1852	−	23.3492i	2.01698	−	0.920088i
$645$	−0.845017	−	1.02966i	−0.0332725	−	0.0405427i
$646$	42.8251	−	13.8202i	1.68493	−	0.543749i
$647$	−14.4150	+	9.63181i	−0.566713	+	0.378666i	−0.805670	−	0.592365i	$-0.798195\pi$
$647$	−14.4150	+	9.63181i	−0.566713	+	0.378666i	0.238957	+	0.971030i	$0.423195\pi$
$648$	30.8061	+	4.44931i	1.21018	+	0.174785i
$649$	−6.56800	+	9.82970i	−0.257816	+	0.385850i
$650$	4.44714	+	7.97828i	0.174431	+	0.312934i
$651$	56.4040	−	17.1100i	2.21065	−	0.670593i
$652$	−18.4537	−	14.0854i	−0.722704	−	0.551628i
$653$	19.7006	+	16.1679i	0.770945	+	0.632698i	0.935362	−	0.353693i	$-0.115074\pi$
$653$	19.7006	+	16.1679i	0.770945	+	0.632698i	−0.164416	+	0.986391i	$0.552574\pi$
$654$	−48.5297	+	21.1119i	−1.89766	+	0.825542i
$655$	19.1073	+	7.91451i	0.746585	+	0.309246i
$656$	0.960332	−	1.68311i	0.0374947	−	0.0657143i
$657$	3.35515	−	1.38975i	0.130897	−	0.0542192i
$658$	−34.2350	+	35.4644i	−1.33462	+	1.38255i
$659$	0.574543	+	5.83343i	0.0223810	+	0.227238i	0.999868	+	0.0162429i	$0.00517050\pi$
$659$	0.574543	+	5.83343i	0.0223810	+	0.227238i	−0.977487	+	0.210995i	$0.932330\pi$
$660$	−12.5235	−	6.13625i	−0.487476	−	0.238853i
$661$	−10.7890	+	20.1849i	−0.419645	+	0.785101i	−0.999563	−	0.0295743i	$-0.990585\pi$
$661$	−10.7890	+	20.1849i	−0.419645	+	0.785101i	0.579917	+	0.814675i	$0.303085\pi$
$662$	6.42740	−	0.747716i	0.249808	−	0.0290608i
$663$	80.9163	−	16.0953i	3.14253	−	0.625088i
$664$	−2.98274	+	6.36939i	−0.115753	+	0.247180i
$665$	−3.33893	+	16.7860i	−0.129478	+	0.650931i
$666$	4.00119	+	4.70379i	0.155043	+	0.182268i
$667$	−3.36950	+	34.2111i	−0.130468	+	1.32466i
$668$	3.77739	+	2.33560i	0.146152	+	0.0903669i
$669$	−9.81701	+	32.3623i	−0.379548	+	1.25120i
$670$	1.66479	+	1.07039i	0.0643164	+	0.0413530i
$671$	12.9038	+	12.9038i	0.498144	+	0.498144i
$672$	−7.20120	−	38.1927i	−0.277792	−	1.47332i
$673$	−1.25086	+	1.25086i	−0.0482169	+	0.0482169i	−0.730804	−	0.682587i	$-0.760855\pi$
$673$	−1.25086	+	1.25086i	−0.0482169	+	0.0482169i	0.682587	+	0.730804i	$0.260855\pi$
$674$	−4.18688	+	0.909868i	−0.161273	+	0.0350468i
$675$	−3.82111	−	1.15912i	−0.147075	−	0.0446146i
$676$	9.21060	−	56.6867i	0.354254	−	2.18026i
$677$	7.46162	+	0.734906i	0.286773	+	0.0282447i	0.240381	−	0.970679i	$-0.422728\pi$
$677$	7.46162	+	0.734906i	0.286773	+	0.0282447i	0.0463923	+	0.998923i	$0.485228\pi$
$678$	1.48870	−	18.4446i	0.0571731	−	0.708359i
$679$	−11.5460	−	2.29665i	−0.443096	−	0.0881373i
$680$	15.4501	−	9.34090i	0.592482	−	0.358207i
$681$	−4.34317	−	21.8346i	−0.166431	−	0.836703i
$682$	−26.2387	+	33.1472i	−1.00473	+	1.26927i
$683$	11.7029	+	6.25531i	0.447798	+	0.239353i	0.679851	−	0.733350i	$-0.262044\pi$
$683$	11.7029	+	6.25531i	0.447798	+	0.239353i	−0.232053	+	0.972703i	$0.574544\pi$
$684$	−6.62321	−	7.51360i	−0.253245	−	0.287290i
$685$	−13.1675	+	1.29689i	−0.503106	+	0.0495516i
$686$	10.7410	−	0.189462i	0.410094	−	0.00723370i
$687$	−8.45658	−	20.4160i	−0.322638	−	0.778918i
$688$	0.950552	+	2.48701i	0.0362395	+	0.0948165i
$689$	1.10480	−	2.66722i	0.0420894	−	0.101613i
$690$	8.49421	−	21.5754i	0.323369	−	0.821363i
$691$	18.7125	−	22.8012i	0.711856	−	0.867399i	−0.283955	−	0.958838i	$-0.591647\pi$
$691$	18.7125	−	22.8012i	0.711856	−	0.867399i	0.995811	+	0.0914387i	$0.0291466\pi$
$692$	29.9895	+	7.95376i	1.14003	+	0.302357i
$693$	−3.48881	−	11.5011i	−0.132529	−	0.436890i
$694$	2.10777	−	7.41683i	0.0800097	−	0.281539i
$695$	−10.6741	−	7.13221i	−0.404892	−	0.270540i
$696$	22.3906	+	7.91504i	0.848715	+	0.300019i
$697$	1.71800	+	2.57117i	0.0650740	+	0.0973901i
$698$	11.5330	−	22.5234i	0.436530	−	0.852523i
$699$	−1.75193	+	1.43777i	−0.0662640	+	0.0543815i
$700$	0.242165	+	6.86231i	0.00915299	+	0.259371i
$701$	−23.5459	−	44.0512i	−0.889315	−	1.66379i	−0.737463	−	0.675388i	$-0.763976\pi$
$701$	−23.5459	−	44.0512i	−0.889315	−	1.66379i	−0.151852	−	0.988403i	$-0.548524\pi$
$702$	20.7948	+	29.9638i	0.784848	+	1.13091i
$703$			21.6673i			0.817197i
$704$	19.8614	+	19.5599i	0.748556	+	0.737191i
$705$			20.3160i			0.765144i
$706$	−6.81385	+	4.72879i	−0.256442	+	0.177970i
$707$	−14.0740	−	26.3306i	−0.529308	−	0.990265i
$708$	−9.25717	+	9.93442i	−0.347906	+	0.373358i
$709$	−2.16670	+	1.77816i	−0.0813720	+	0.0667803i	−0.674200	−	0.738549i	$-0.735511\pi$
$709$	−2.16670	+	1.77816i	−0.0813720	+	0.0667803i	0.592828	+	0.805329i	$0.298011\pi$
$710$	−8.52866	−	4.36705i	−0.320075	−	0.163892i
$711$	−1.65795	−	2.48130i	−0.0621780	−	0.0930559i
$712$	−25.8758	+	28.7699i	−0.969736	+	1.07820i
$713$	−58.4433	−	39.0505i	−2.18872	−	1.46245i
$714$	59.6590	+	16.9543i	2.23268	+	0.634499i
$715$	−6.53295	−	21.5362i	−0.244318	−	0.805410i
$716$	38.6952	−	22.4724i	1.44611	−	0.839834i
$717$	−30.2071	+	36.8075i	−1.12811	+	1.37460i
$718$	18.1840	+	7.15901i	0.678621	+	0.267172i
$719$	−6.54343	+	15.7972i	−0.244029	+	0.589137i	−0.997676	−	0.0681422i	$-0.978293\pi$
$719$	−6.54343	+	15.7972i	−0.244029	+	0.589137i	0.753647	+	0.657279i	$0.228293\pi$
$720$	−3.27832	−	2.32400i	−0.122176	−	0.0866105i
$721$	1.34332	+	3.24306i	0.0500278	+	0.120778i
$722$	−0.145904	−	8.27160i	−0.00542997	−	0.307837i
$723$	−16.8234	+	1.65696i	−0.625670	+	0.0616231i
$724$	1.09217	−	17.3407i	0.0405903	−	0.644461i
$725$	−3.70032	−	1.97786i	−0.137426	−	0.0734559i
$726$	2.53330	+	2.00531i	0.0940195	+	0.0744240i
$727$	5.59056	+	28.1057i	0.207343	+	1.04238i	0.934514	+	0.355926i	$0.115834\pi$
$727$	5.59056	+	28.1057i	0.207343	+	1.04238i	−0.727172	+	0.686456i	$0.759166\pi$
$728$	37.1690	−	50.5192i	1.37757	−	1.87237i
$729$	−12.6685	−	2.51992i	−0.469203	−	0.0933302i
$730$	5.09561	+	0.411278i	0.188597	+	0.0152221i
$731$	−4.22829	−	0.416450i	−0.156389	−	0.0154030i
$732$	12.2525	+	17.0066i	0.452865	+	0.628581i
$733$	−19.0485	−	5.77829i	−0.703571	−	0.213426i	−0.0818270	−	0.996647i	$-0.526075\pi$
$733$	−19.0485	−	5.77829i	−0.703571	−	0.213426i	−0.621744	+	0.783221i	$0.713575\pi$
$734$	3.32555	+	15.3030i	0.122748	+	0.564843i
$735$	−6.77443	+	6.77443i	−0.249879	+	0.249879i
$736$	−29.7591	+	35.5319i	−1.09694	+	1.30972i
$737$	−3.44826	−	3.44826i	−0.127018	−	0.127018i
$738$	0.372239	−	0.578945i	0.0137023	−	0.0213113i
$739$	−1.75188	+	5.77518i	−0.0644440	+	0.212444i	−0.983249	−	0.182269i	$-0.941656\pi$
$739$	−1.75188	+	5.77518i	−0.0644440	+	0.212444i	0.918805	+	0.394713i	$0.129156\pi$
$740$	1.99557	+	8.46091i	0.0733585	+	0.311029i
$741$	6.31526	−	64.1199i	0.231997	−	2.35550i
$742$	1.65313	−	1.40620i	0.0606883	−	0.0516234i
$743$	−6.38301	+	32.0896i	−0.234170	+	1.17725i	0.667427	+	0.744675i	$0.267396\pi$
$743$	−6.38301	+	32.0896i	−0.234170	+	1.17725i	−0.901597	+	0.432577i	$0.857604\pi$
$744$	−35.8540	+	32.7468i	−1.31447	+	1.20056i
$745$	17.6361	−	3.50804i	0.646136	−	0.128525i
$746$	4.94945	+	42.5457i	0.181212	+	1.55771i
$747$	−1.17760	+	2.20314i	−0.0430862	+	0.0806087i
$748$	−42.0866	+	14.4063i	−1.53884	+	0.526745i
$749$	6.20202	+	62.9701i	0.226617	+	2.30088i
$750$	2.03614	+	1.96555i	0.0743493	+	0.0717718i
$751$	19.4779	−	8.06800i	0.710758	−	0.294405i	0.00213959	−	0.999998i	$-0.499319\pi$
$751$	19.4779	−	8.06800i	0.710758	−	0.294405i	0.708618	+	0.705592i	$0.249319\pi$
$752$	12.8569	−	38.5194i	0.468843	−	1.40466i
$753$	10.3664	+	4.29390i	0.377772	+	0.156478i
$754$	15.2881	+	35.1426i	0.556760	+	1.27982i
$755$	1.74781	+	1.43439i	0.0636095	+	0.0522030i
$756$	3.64815	+	27.1748i	0.132682	+	0.988339i
$757$	18.3643	−	5.57075i	0.667462	−	0.202473i	0.0616717	−	0.998096i	$-0.480357\pi$
$757$	18.3643	−	5.57075i	0.667462	−	0.202473i	0.605791	+	0.795624i	$0.292857\pi$
$758$	9.83612	−	5.48271i	0.357264	−	0.199141i
$759$	−31.7404	+	47.5029i	−1.15211	+	1.72425i
$760$	−3.47820	−	13.6638i	−0.126168	−	0.495640i
$761$	−17.7779	+	11.8788i	−0.644449	+	0.430607i	−0.834379	−	0.551191i	$-0.814174\pi$
$761$	−17.7779	+	11.8788i	−0.644449	+	0.430607i	0.189931	+	0.981798i	$0.439174\pi$
$762$	1.56806	+	4.85900i	0.0568049	+	0.176023i
$763$	−40.7303	−	49.6300i	−1.47454	−	1.79673i
$764$	1.53886	−	4.12049i	0.0556740	−	0.149074i
$765$	5.65548	−	3.02292i	0.204474	−	0.109294i
$766$	3.38893	−	18.7607i	0.122447	−	0.677853i
$767$	−21.9130			−0.791232
$768$	18.9145	+	25.8346i	0.682519	+	0.932225i
$769$	25.6893			0.926378			0.463189	−	0.886259i	$-0.346705\pi$
$769$	25.6893			0.926378			0.463189	+	0.886259i	$0.346705\pi$
$770$	3.00749	−	16.6491i	0.108382	−	0.599993i
$771$	−11.2912	+	6.03526i	−0.406642	+	0.217355i
$772$	−10.8399	+	29.0251i	−0.390135	+	1.04464i
$773$	−20.4375	−	24.9032i	−0.735086	−	0.895705i	0.262515	−	0.964928i	$-0.415448\pi$
$773$	−20.4375	−	24.9032i	−0.735086	−	0.895705i	−0.997601	+	0.0692229i	$0.977948\pi$
$774$	0.290435	+	0.899980i	0.0104395	+	0.0323491i
$775$	7.13313	−	4.76620i	0.256230	−	0.171207i
$776$	9.39853	−	2.39245i	0.337388	−	0.0858838i
$777$	−16.5910	+	24.8302i	−0.595200	+	0.890779i
$778$	−26.7952	+	14.9358i	−0.960654	+	0.535474i
$779$	2.31098	−	0.701029i	0.0827995	−	0.0251170i
$780$	−3.43941	−	25.6200i	−0.123151	−	0.917342i
$781$	18.2495	+	14.9770i	0.653020	+	0.535920i
$782$	−29.5044	−	67.8215i	−1.05508	−	2.42529i
$783$	−15.4785	−	6.41142i	−0.553157	−	0.229125i
$784$	17.1316	−	8.55726i	0.611843	−	0.305616i
$785$	17.8333	−	7.38681i	0.636499	−	0.263647i
$786$	−42.1106	−	40.6508i	−1.50204	−	1.44997i
$787$	−3.38710	−	34.3898i	−0.120737	−	1.22586i	−0.844401	−	0.535712i	$-0.820043\pi$
$787$	−3.38710	−	34.3898i	−0.120737	−	1.22586i	0.723664	−	0.690153i	$-0.242457\pi$
$788$	30.5098	−	10.4435i	1.08687	−	0.372035i
$789$	28.1543	−	52.6729i	1.00232	−	1.87521i
$790$	−0.485429	−	4.17276i	−0.0172708	−	0.148460i
$791$	22.0174	−	4.37954i	0.782850	−	0.155719i
$792$	6.67726	+	7.31083i	0.237266	+	0.259779i
$793$	−6.59895	+	33.1751i	−0.234335	+	1.17808i
$794$	20.3850	−	17.3401i	0.723436	−	0.615378i
$795$	0.0876758	−	0.890187i	0.00310954	−	0.0315717i
$796$	−4.67388	−	19.8165i	−0.165661	−	0.702379i
$797$	0.0727744	−	0.239905i	0.00257780	−	0.00849787i	−0.955642	−	0.294531i	$-0.904837\pi$
$797$	0.0727744	−	0.239905i	0.00257780	−	0.00849787i	0.958220	+	0.286033i	$0.0923367\pi$
$798$	26.1951	−	40.7414i	0.927298	−	1.44223i
$799$	45.8222	+	45.8222i	1.62107	+	1.62107i
$800$	−2.61666	−	5.01529i	−0.0925129	−	0.177317i
$801$	−9.71837	+	9.71837i	−0.343382	+	0.343382i
$802$	6.54601	+	30.1224i	0.231148	+	1.06366i
$803$	−12.0536	−	3.65641i	−0.425361	−	0.129032i
$804$	−3.27422	−	4.54465i	−0.115473	−	0.160277i
$805$	27.9942	+	2.75719i	0.986667	+	0.0971782i
$806$	−78.1061	−	6.30411i	−2.75117	−	0.222053i
$807$	−46.9975	−	9.34838i	−1.65439	−	0.329078i
$808$	19.8116	+	14.5762i	0.696971	+	0.512789i
$809$	−4.11696	−	20.6974i	−0.144745	−	0.727681i	−0.983174	−	0.182671i	$-0.941526\pi$
$809$	−4.11696	−	20.6974i	−0.144745	−	0.727681i	0.838429	−	0.545010i	$-0.183474\pi$
$810$	12.2025	+	9.65927i	0.428752	+	0.339392i
$811$	18.2943	+	9.77852i	0.642400	+	0.343370i	0.760221	−	0.649665i	$-0.225091\pi$
$811$	18.2943	+	9.77852i	0.642400	+	0.343370i	−0.117820	+	0.993035i	$0.537591\pi$
$812$	−1.81099	+	28.7534i	−0.0635532	+	1.00905i
$813$	34.6689	−	3.41458i	1.21589	−	0.119755i
$814$	−0.377751	−	21.4155i	−0.0132402	−	0.750614i
$815$	−4.44201	−	10.7240i	−0.155597	−	0.375644i
$816$	−50.3691	+	8.58005i	−1.76327	+	0.300362i
$817$	−1.26978	+	3.06551i	−0.0444239	+	0.107249i
$818$	−4.04298	−	1.59171i	−0.141360	−	0.0556530i
$819$	14.1325	−	17.2205i	0.493831	−	0.601734i
$820$	0.837856	−	0.486589i	0.0292592	−	0.0169924i
$821$	9.87033	+	32.5381i	0.344477	+	1.13559i	0.942527	+	0.334130i	$0.108442\pi$
$821$	9.87033	+	32.5381i	0.344477	+	1.13559i	−0.598050	+	0.801459i	$0.704058\pi$
$822$	36.0190	+	10.2361i	1.25631	+	0.357026i
$823$	−20.6096	−	13.7709i	−0.718406	−	0.480024i	0.141848	−	0.989888i	$-0.454695\pi$
$823$	−20.6096	−	13.7709i	−0.718406	−	0.480024i	−0.860255	+	0.509865i	$0.829695\pi$
$824$	−2.15012	−	1.93383i	−0.0749031	−	0.0673682i
$825$	−3.87399	−	5.79784i	−0.134875	−	0.201855i
$826$	−14.6628	−	7.50803i	−0.510186	−	0.261238i
$827$	−8.64859	+	7.09772i	−0.300741	+	0.246812i	−0.772645	−	0.634838i	$-0.781067\pi$
$827$	−8.64859	+	7.09772i	−0.300741	+	0.246812i	0.471904	+	0.881650i	$0.343567\pi$
$828$	−11.2228	+	12.0438i	−0.390019	+	0.418553i
$829$	8.86775	+	16.5904i	0.307990	+	0.576208i	0.987530	−	0.157430i	$-0.0503208\pi$
$829$	8.86775	+	16.5904i	0.307990	+	0.576208i	−0.679541	+	0.733638i	$0.737821\pi$
$830$	−2.88903	+	2.00498i	−0.100280	+	0.0695939i
$831$		−	5.21996i		−	0.181079i
$832$	−9.69235	+	50.7525i	−0.336022	+	1.75953i
$833$			30.5592i			1.05881i
$834$	20.7142	+	29.8477i	0.717275	+	1.03354i
$835$	1.04677	+	1.95837i	0.0362249	+	0.0677720i
$836$	1.22519	+	34.7184i	0.0423739	+	1.20076i
$837$	26.4804	−	21.7319i	0.915296	−	0.751164i
$838$	−1.84521	+	3.60361i	−0.0637416	+	0.124485i
$839$	12.9401	+	19.3662i	0.446742	+	0.668596i	0.984677	−	0.174390i	$-0.0557954\pi$
$839$	12.9401	+	19.3662i	0.446742	+	0.668596i	−0.537935	+	0.842986i	$0.680795\pi$
$840$	6.47671	−	18.3218i	0.223468	−	0.632162i
$841$	9.47520	+	6.33112i	0.326731	+	0.218315i
$842$	5.17612	−	18.2138i	0.178381	−	0.627689i
$843$	3.80773	+	12.5524i	0.131145	+	0.432328i
$844$	−26.4874	−	7.02493i	−0.911732	−	0.241808i
$845$	18.2166	−	22.1970i	0.626671	−	0.763601i
$846$	5.28383	−	13.4210i	0.181662	−	0.461424i
$847$	−1.49996	+	3.62123i	−0.0515394	+	0.124427i
$848$	−0.729587	+	1.63232i	−0.0250541	+	0.0560543i
$849$	14.5474	+	35.1206i	0.499266	+	1.20534i
$850$	9.02573	−	0.159206i	0.309580	−	0.00546072i
$851$	35.4406	−	3.49059i	1.21489	−	0.119656i
$852$	17.9313	+	20.3419i	0.614316	+	0.696901i
$853$	10.3341	+	5.52367i	0.353831	+	0.189127i	0.638730	−	0.769431i	$-0.279460\pi$
$853$	10.3341	+	5.52367i	0.353831	+	0.189127i	−0.284899	+	0.958558i	$0.591960\pi$
$854$	−15.7824	+	19.9378i	−0.540062	+	0.682258i
$855$	−0.977017	−	4.91179i	−0.0334133	−	0.167980i
$856$	−26.9696	−	44.6083i	−0.921802	−	1.52468i
$857$	−41.6185	−	8.27844i	−1.42166	−	0.282786i	−0.576413	−	0.817159i	$-0.695548\pi$
$857$	−41.6185	−	8.27844i	−1.42166	−	0.282786i	−0.845249	+	0.534372i	$0.820548\pi$
$858$	−5.12401	+	63.4850i	−0.174931	+	2.16734i
$859$	51.7778	+	5.09967i	1.76664	+	0.173999i	0.928468	−	0.371412i	$-0.121126\pi$
$859$	51.7778	+	5.09967i	1.76664	+	0.173999i	0.838169	+	0.545411i	$0.183626\pi$
$860$	−0.213503	+	1.31401i	−0.00728040	+	0.0448073i
$861$	3.18512	+	0.966197i	0.108549	+	0.0329279i
$862$	22.4556	−	4.87992i	0.764841	−	0.166211i
$863$	20.9750	−	20.9750i	0.713996	−	0.713996i	−0.253373	−	0.967369i	$-0.581540\pi$
$863$	20.9750	−	20.9750i	0.713996	−	0.713996i	0.967369	+	0.253373i	$0.0815399\pi$
$864$	−12.3611	−	18.9057i	−0.420532	−	0.643187i
$865$	10.9695	+	10.9695i	0.372973	+	0.372973i
$866$	−40.5030	−	26.0419i	−1.37635	−	0.884939i
$867$	13.7933	−	45.4705i	0.468446	−	1.54426i
$868$	−50.1039	−	30.9798i	−1.70064	−	1.05152i
$869$	−1.01454	+	10.3008i	−0.0344159	+	0.349430i
$870$	7.69364	+	9.04462i	0.260839	+	0.306641i
$871$	1.76343	−	8.86537i	0.0597516	−	0.300392i
$872$	47.9003	+	22.4314i	1.62211	+	0.759623i
$873$	3.37853	−	0.672030i	0.114346	−	0.0227448i
$874$	−57.3736	+	6.67442i	−1.94069	+	0.225766i
$875$	−1.61844	+	3.02789i	−0.0547133	+	0.102361i
$876$	−12.9921	−	6.36584i	−0.438961	−	0.215082i
$877$	1.18614	+	12.0431i	0.0400531	+	0.406666i	0.994218	+	0.107384i	$0.0342474\pi$
$877$	1.18614	+	12.0431i	0.0400531	+	0.406666i	−0.954164	+	0.299283i	$0.903253\pi$
$878$	−19.6708	+	20.3772i	−0.663857	+	0.687697i
$879$	−24.5801	+	10.1814i	−0.829066	+	0.343410i
$880$	3.67601	+	13.4445i	0.123918	+	0.453212i
$881$	−5.08394	−	2.10584i	−0.171282	−	0.0709475i	0.295395	−	0.955375i	$-0.404549\pi$
$881$	−5.08394	−	2.10584i	−0.171282	−	0.0709475i	−0.466677	+	0.884428i	$0.654549\pi$
$882$	6.23720	−	2.71337i	0.210017	−	0.0913641i
$883$	3.00733	+	2.46805i	0.101205	+	0.0830565i	0.683635	−	0.729824i	$-0.260398\pi$
$883$	3.00733	+	2.46805i	0.101205	+	0.0830565i	−0.582430	+	0.812881i	$0.697898\pi$
$884$	−65.5428	−	50.0278i	−2.20444	−	1.68262i
$885$	−6.49712	+	1.97088i	−0.218398	+	0.0662504i
$886$	6.81985	+	12.2350i	0.229117	+	0.411042i
$887$	−10.0787	+	15.0839i	−0.338411	+	0.506467i	−0.961174	−	0.275943i	$-0.911010\pi$
$887$	−10.0787	+	15.0839i	−0.338411	+	0.506467i	0.622763	+	0.782410i	$0.286010\pi$
$888$	3.51675	−	24.3493i	0.118015	−	0.817108i
$889$	−5.15016	+	3.44123i	−0.172731	+	0.115415i
$890$	−18.4122	+	5.94185i	−0.617179	+	0.199171i
$891$	−24.3261	−	29.6414i	−0.814954	−	0.993024i
$892$	30.7506	−	14.0275i	1.02961	−	0.469677i
$893$	44.6322	−	23.8564i	1.49356	−	0.798324i
$894$	−50.0786	−	9.04617i	−1.67488	−	0.302549i
$895$	22.3737			0.747870
$896$	−23.8748	+	30.6397i	−0.797603	+	1.02360i
$897$	−105.897			−3.53578
$898$	−9.99676	−	1.80581i	−0.333596	−	0.0602606i
$899$	31.7448	−	16.9680i	1.05875	−	0.565913i
$900$	−0.833896	−	1.82804i	−0.0277965	−	0.0609345i
$901$	−1.81005	−	2.20555i	−0.0603014	−	0.0734775i
$902$	−2.27191	+	0.733174i	−0.0756463	+	0.0244120i
$903$	−3.80245	+	2.54072i	−0.126538	+	0.0845498i
$904$	−14.8122	+	11.0735i	−0.492645	+	0.368299i
$905$	4.82653	−	7.22341i	0.160439	−	0.240114i
$906$	−3.11548	−	5.58926i	−0.103505	−	0.185691i
$907$	16.6271	−	5.04378i	0.552094	−	0.167476i	−0.00189760	−	0.999998i	$-0.500604\pi$
$907$	16.6271	−	5.04378i	0.552094	−	0.167476i	0.553991	+	0.832522i	$0.313104\pi$
$908$	−13.4996	+	17.6862i	−0.447999	+	0.586936i
$909$	6.75322	+	5.54222i	0.223990	+	0.183824i
$910$	28.7564	−	12.5099i	0.953266	−	0.414700i
$911$	−13.4655	−	5.57758i	−0.446131	−	0.184794i	0.148296	−	0.988943i	$-0.452621\pi$
$911$	−13.4655	−	5.57758i	−0.446131	−	0.184794i	−0.594427	+	0.804149i	$0.702621\pi$
$912$	−5.00655	+	39.5874i	−0.165783	+	1.31087i
$913$	8.00501	−	3.31578i	0.264927	−	0.109736i
$914$	2.09044	−	2.16551i	0.0691456	−	0.0716287i
$915$	1.02725	+	10.4298i	0.0339598	+	0.344800i
$916$	−9.71756	+	19.8326i	−0.321077	+	0.655287i
$917$	33.4720	−	62.6217i	1.10534	−	2.06795i
$918$	35.8044	−	4.16522i	1.18172	−	0.137473i
$919$	27.7154	−	5.51293i	0.914246	−	0.181855i	0.284518	−	0.958671i	$-0.408166\pi$
$919$	27.7154	−	5.51293i	0.914246	−	0.181855i	0.629728	+	0.776816i	$0.283166\pi$
$920$	−21.7892	+	7.89044i	−0.718370	+	0.260140i
$921$	−1.86615	+	9.38177i	−0.0614917	+	0.309140i
$922$	8.68107	+	10.2054i	0.285896	+	0.336098i
$923$	−4.28920	+	43.5490i	−0.141181	+	1.43343i
$924$	−25.1805	+	40.7247i	−0.828377	+	1.33974i
$925$	−1.26173	+	4.15937i	−0.0414855	+	0.136759i
$926$	41.3175	+	26.5656i	1.35778	+	0.872998i
$927$	−0.726304	−	0.726304i	−0.0238550	−	0.0238550i
$928$	−8.86341	−	22.0176i	−0.290956	−	0.722765i
$929$	1.50759	−	1.50759i	0.0494623	−	0.0494623i	−0.681943	−	0.731405i	$-0.738865\pi$
$929$	1.50759	−	1.50759i	0.0494623	−	0.0494623i	0.731405	+	0.681943i	$0.238865\pi$
$930$	−23.7252	+	5.15581i	−0.777980	+	0.169066i
$931$	22.8377	+	6.92775i	0.748477	+	0.227048i
$932$	2.23574	+	0.363269i	0.0732341	+	0.0118993i
$933$	−30.7810	−	3.03167i	−1.00773	−	0.0992523i
$934$	−1.79027	+	22.1809i	−0.0585793	+	0.725781i
$935$	−21.8146	−	4.33920i	−0.713414	−	0.141907i
$936$	−4.39118	+	17.8195i	−0.143530	+	0.582447i
$937$	−7.64427	−	38.4304i	−0.249728	−	1.25546i	−0.878450	−	0.477835i	$-0.841422\pi$
$937$	−7.64427	−	38.4304i	−0.249728	−	1.25546i	0.628722	−	0.777630i	$-0.283578\pi$
$938$	4.21752	−	5.32797i	0.137707	−	0.173964i
$939$	−7.55235	−	4.03681i	−0.246462	−	0.131736i
$940$	15.2313	−	13.4264i	0.496792	−	0.437920i
$941$	3.72066	−	0.366453i	0.121290	−	0.0119460i	−0.0371899	−	0.999308i	$-0.511841\pi$
$941$	3.72066	−	0.366453i	0.121290	−	0.0119460i	0.158480	+	0.987362i	$0.449341\pi$
$942$	−54.6193	+	0.963435i	−1.77959	+	0.0313904i
$943$	−1.51895	−	3.66707i	−0.0494639	−	0.119416i
$944$	13.5659	+	0.374863i	0.441533	+	0.0122007i
$945$	−5.24633	+	12.6658i	−0.170663	+	0.412017i
$946$	1.20158	−	3.05203i	0.0390667	−	0.0992302i
$947$	−1.51642	+	1.84777i	−0.0492771	+	0.0600443i	−0.797066	−	0.603892i	$-0.793616\pi$
$947$	−1.51642	+	1.84777i	−0.0492771	+	0.0600443i	0.747789	+	0.663937i	$0.231116\pi$
$948$	−3.04776	+	11.4915i	−0.0989868	+	0.373228i
$949$	−6.77738	−	22.3420i	−0.220003	−	0.725253i
$950$	1.92715	−	6.78128i	0.0625250	−	0.220014i
$951$	−27.5173	−	18.3865i	−0.892310	−	0.596223i
$952$	−26.7163	−	55.9325i	−0.865881	−	1.81278i
$953$	26.5564	+	39.7444i	0.860246	+	1.28745i	0.956393	+	0.292082i	$0.0943479\pi$
$953$	26.5564	+	39.7444i	0.860246	+	1.28745i	−0.0961476	+	0.995367i	$0.530652\pi$
$954$	−0.289442	+	0.565267i	−0.00937103	+	0.0183012i
$955$	1.70003	−	1.39518i	0.0550117	−	0.0451469i
$956$	47.5587	−	1.67831i	1.53816	−	0.0542803i
$957$	−13.7916	−	25.8023i	−0.445820	−	0.834070i
$958$	−26.5553	−	38.2643i	−0.857964	−	1.23626i
$959$			45.4267i			1.46691i
$960$	1.69100	+	15.9197i	0.0545767	+	0.513806i
$961$			42.5982i			1.37414i
$962$	32.6163	−	22.6356i	1.05159	−	0.729801i
$963$	−8.72794	−	16.3288i	−0.281254	−	0.526189i
$964$	12.3605	+	11.5179i	0.398105	+	0.370965i
$965$	−11.9752	+	9.82777i	−0.385494	+	0.316367i
$966$	−70.8596	−	36.2832i	−2.27987	−	1.16739i
$967$	−5.08574	−	7.61135i	−0.163547	−	0.244765i	0.740640	−	0.671902i	$-0.234522\pi$
$967$	−5.08574	−	7.61135i	−0.163547	−	0.244765i	−0.904187	+	0.427137i	$0.859522\pi$
$968$	−0.170776	−	3.22454i	−0.00548894	−	0.103641i
$969$	−52.9449	−	35.3766i	−1.70083	−	1.13646i
$970$	4.66443	+	1.32557i	0.149766	+	0.0425615i
$971$	3.61361	+	11.9125i	0.115966	+	0.382290i	0.995639	−	0.0932899i	$-0.0297383\pi$
$971$	3.61361	+	11.9125i	0.115966	+	0.382290i	−0.879673	+	0.475580i	$0.842238\pi$
$972$	−10.0871	−	17.3689i	−0.323544	−	0.557109i
$973$	−27.9611	+	34.0707i	−0.896392	+	1.09226i
$974$	−1.98240	−	0.780467i	−0.0635202	−	0.0250078i
$975$	4.94615	−	11.9411i	0.158403	−	0.382420i
$976$	4.65281	−	20.4252i	0.148933	−	0.653796i
$977$	−3.01826	−	7.28673i	−0.0965627	−	0.233123i	0.868216	−	0.496187i	$-0.165267\pi$
$977$	−3.01826	−	7.28673i	−0.0965627	−	0.233123i	−0.964778	+	0.263064i	$0.915267\pi$
$978$	0.579355	+	32.8449i	0.0185257	+	1.05027i
$979$	47.4402	−	4.67245i	1.51619	−	0.149332i
$980$	9.55602	+	0.601870i	0.305256	+	0.0192260i
$981$	16.5685	+	8.85605i	0.528991	+	0.282752i
$982$	25.0989	+	19.8678i	0.800939	+	0.634008i
$983$	−4.82975	−	24.2808i	−0.154045	−	0.774437i	−0.978134	−	0.207977i	$-0.933312\pi$
$983$	−4.82975	−	24.2808i	−0.154045	−	0.774437i	0.824089	−	0.566461i	$-0.191688\pi$
$984$	−2.71082	+	0.412713i	−0.0864177	+	0.0131568i
$985$	15.8141	+	3.14561i	0.503878	+	0.100228i
$986$	37.7528	+	3.04711i	1.20229	+	0.0970396i
$987$	69.4147	+	6.83675i	2.20950	+	0.217616i
$988$	−52.2457	+	37.6408i	−1.66216	+	1.19751i
$989$	5.21873	+	1.58309i	0.165946	+	0.0503392i
$990$	1.05130	+	4.83769i	0.0334124	+	0.153752i
$991$	−16.3554	+	16.3554i	−0.519545	+	0.519545i	−0.917434	−	0.397888i	$-0.869743\pi$
$991$	−16.3554	+	16.3554i	−0.519545	+	0.519545i	0.397888	+	0.917434i	$0.369743\pi$
$992$	48.2462	+	5.23891i	1.53182	+	0.166336i
$993$	−6.47449	−	6.47449i	−0.205462	−	0.205462i
$994$	−17.7912	+	27.6707i	−0.564303	+	0.877663i
$995$	2.95514	−	9.74178i	0.0936842	−	0.308835i
$996$	9.68642	−	2.28461i	0.306926	−	0.0723906i
$997$	−4.32539	+	43.9164i	−0.136986	+	1.39085i	0.643391	+	0.765537i	$0.277527\pi$
$997$	−4.32539	+	43.9164i	−0.136986	+	1.39085i	−0.780378	+	0.625308i	$0.784973\pi$
$998$	17.4340	−	14.8299i	0.551863	−	0.469432i
$999$	−3.38598	+	17.0224i	−0.107128	+	0.538566i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.101.28	✓	1024
128.109	even	32	inner	640.2.bm.a.621.28	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.101.28	✓	1024	1.1	even	1	trivial
640.2.bm.a.621.28	yes	1024	128.109	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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.251394 + 1.39169i) q^{2} +(1.76486 - 0.943339i) q^{3} +(-1.87360 - 0.699725i) q^{4} +(-0.634393 - 0.773010i) q^{5} +(0.869159 + 2.69329i) q^{6} +(-2.85468 + 1.90743i) q^{7} +(1.44481 - 2.43157i) q^{8} +(0.558141 - 0.835316i) q^{9} +(1.23527 - 0.688548i) q^{10} +(-3.33445 + 1.01149i) q^{11} +(-3.96673 + 0.532522i) q^{12} +(-4.99266 - 4.09737i) q^{13} +(-1.93691 - 4.45234i) q^{14} +(-1.84883 - 0.765809i) q^{15} +(3.02077 + 2.62201i) q^{16} +(-5.89726 + 2.44272i) q^{17} +(1.02219 + 0.986752i) q^{18} +(0.488611 + 4.96096i) q^{19} +(0.647705 + 1.89221i) q^{20} +(-3.23875 + 6.05928i) q^{21} +(-0.569425 - 4.89480i) q^{22} +(8.03578 - 1.59842i) q^{23} +(0.256106 - 5.65433i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(6.95739 - 5.91818i) q^{26} +(-0.391388 + 3.97383i) q^{27} +(6.68321 - 1.57628i) q^{28} +(-1.21796 + 4.01508i) q^{29} +(1.53055 - 2.38047i) q^{30} +(-6.06623 - 6.06623i) q^{31} +(-4.40843 + 3.54481i) q^{32} +(-4.93066 + 4.93066i) q^{33} +(-1.91698 - 8.82124i) q^{34} +(3.28545 + 0.996631i) q^{35} +(-1.63023 + 1.17451i) q^{36} +(4.32560 + 0.426035i) q^{37} +(-7.02695 - 0.567159i) q^{38} +(-12.6766 - 2.52152i) q^{39} +(-2.79621 + 0.425714i) q^{40} +(-0.0945118 - 0.475143i) q^{41} +(-7.61844 - 6.03061i) q^{42} +(0.587024 + 0.313771i) q^{43} +(6.95519 + 0.438061i) q^{44} +(-0.999789 + 0.0984706i) q^{45} +(0.204352 + 11.5852i) q^{46} +(-3.88505 - 9.37933i) q^{47} +(7.80469 + 1.77789i) q^{48} +(1.83209 - 4.42305i) q^{49} +(-1.31590 - 0.518069i) q^{50} +(-8.10353 + 9.87418i) q^{51} +(6.48722 + 11.1703i) q^{52} +(0.129754 + 0.427741i) q^{53} +(-5.43194 - 1.54369i) q^{54} +(2.89724 + 1.93588i) q^{55} +(0.513577 + 9.69722i) q^{56} +(5.54219 + 8.29448i) q^{57} +(-5.28156 - 2.70439i) q^{58} +(2.62265 - 2.15235i) q^{59} +(2.92811 + 2.72849i) q^{60} +(-2.46876 - 4.61873i) q^{61} +(9.96732 - 6.91729i) q^{62} +3.44917i q^{63} +(-3.82503 - 7.02632i) q^{64} +6.45872i q^{65} +(-5.62241 - 8.10148i) q^{66} +(0.659725 + 1.23426i) q^{67} +(12.7584 - 0.450232i) q^{68} +(12.6742 - 10.4014i) q^{69} +(-2.21295 + 4.32179i) q^{70} +(-3.76415 - 5.63345i) q^{71} +(-1.22472 - 2.56403i) q^{72} +(3.00565 + 2.00831i) q^{73} +(-1.68034 + 5.91279i) q^{74} +(0.580905 + 1.91499i) q^{75} +(2.55584 - 9.63675i) q^{76} +(7.58941 - 9.24772i) q^{77} +(6.69599 - 17.0079i) q^{78} +(1.13676 - 2.74437i) q^{79} +(0.110489 - 3.99847i) q^{80} +(4.21128 + 10.1669i) q^{81} +(0.685011 - 0.0120830i) q^{82} +(-2.47464 + 0.243730i) q^{83} +(10.3080 - 9.08645i) q^{84} +(5.62943 + 3.00899i) q^{85} +(-0.584246 + 0.738075i) q^{86} +(1.63805 + 8.23501i) q^{87} +(-2.35814 + 9.56934i) q^{88} +(-13.4177 - 2.66895i) q^{89} +(0.114300 - 1.41615i) q^{90} +(22.0679 + 2.17350i) q^{91} +(-16.1743 - 2.62804i) q^{92} +(-16.4286 - 4.98355i) q^{93} +(14.0298 - 3.04887i) q^{94} +(3.52490 - 3.52490i) q^{95} +(-4.43632 + 10.4148i) q^{96} +(2.42456 + 2.42456i) q^{97} +(5.69494 + 3.66163i) q^{98} +(-1.01617 + 3.34987i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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