LMFDB - Embedded newform 168.2.v.a.107.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [168,2,Mod(11,168)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(168, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 3, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("168.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.v (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.24
Character	$\chi$	$=$	168.107
Dual form			168.2.v.a.11.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.18883 - 0.765954i) q^{2} +(0.996948 + 1.41637i) q^{3} +(0.826627 - 1.82118i) q^{4} +(1.00081 - 1.73346i) q^{5} +(2.27007 + 0.920201i) q^{6} +(-2.50986 + 0.837013i) q^{7} +(-0.412221 - 2.79823i) q^{8} +(-1.01219 + 2.82409i) q^{9} +(-0.137955 - 2.82736i) q^{10} +(-3.33711 + 1.92668i) q^{11} +(3.40356 - 0.644811i) q^{12} +2.05924i q^{13} +(-2.34268 + 2.91751i) q^{14} +(3.45297 - 0.310649i) q^{15} +(-2.63337 - 3.01087i) q^{16} +(4.92484 - 2.84336i) q^{17} +(0.959801 + 4.13265i) q^{18} +(-0.232846 + 0.403301i) q^{19} +(-2.32964 - 3.25558i) q^{20} +(-3.68772 - 2.72043i) q^{21} +(-2.49150 + 4.84656i) q^{22} +(-0.711115 + 1.23169i) q^{23} +(3.55235 - 3.37354i) q^{24} +(0.496746 + 0.860389i) q^{25} +(1.57728 + 2.44808i) q^{26} +(-5.00905 + 1.38183i) q^{27} +(-0.550373 + 5.26280i) q^{28} -9.25829 q^{29} +(3.86705 - 3.01413i) q^{30} +(4.99699 - 2.88502i) q^{31} +(-5.43682 - 1.56236i) q^{32} +(-6.05580 - 2.80577i) q^{33} +(3.67691 - 7.15247i) q^{34} +(-1.06098 + 5.18844i) q^{35} +(4.30646 + 4.17785i) q^{36} +(-0.569094 - 0.328567i) q^{37} +(0.0320962 + 0.657805i) q^{38} +(-2.91663 + 2.05295i) q^{39} +(-5.26317 - 2.08593i) q^{40} -8.42924i q^{41} +(-6.46779 - 0.409499i) q^{42} +6.77074 q^{43} +(0.750281 + 7.67011i) q^{44} +(3.88243 + 4.58098i) q^{45} +(0.0980225 + 2.00895i) q^{46} +(-1.79536 + 3.10966i) q^{47} +(1.63916 - 6.73150i) q^{48} +(5.59882 - 4.20157i) q^{49} +(1.24956 + 0.642371i) q^{50} +(8.93705 + 4.14070i) q^{51} +(3.75023 + 1.70222i) q^{52} +(-1.50566 - 2.60789i) q^{53} +(-4.89648 + 5.47946i) q^{54} +7.71298i q^{55} +(3.37677 + 6.67813i) q^{56} +(-0.803357 + 0.0722746i) q^{57} +(-11.0065 + 7.09143i) q^{58} +(-5.72041 + 3.30268i) q^{59} +(2.28857 - 6.54527i) q^{60} +(8.50530 + 4.91054i) q^{61} +(3.73078 - 7.25726i) q^{62} +(0.176663 - 7.93529i) q^{63} +(-7.66015 + 2.30697i) q^{64} +(3.56960 + 2.06091i) q^{65} +(-9.34841 + 1.30289i) q^{66} +(-3.78271 - 6.55184i) q^{67} +(-1.10725 - 11.3194i) q^{68} +(-2.45347 + 0.220728i) q^{69} +(2.71279 + 6.98082i) q^{70} +14.0426 q^{71} +(8.31968 + 1.66819i) q^{72} +(-2.02113 - 3.50071i) q^{73} +(-0.928223 + 0.0452908i) q^{74} +(-0.723397 + 1.56134i) q^{75} +(0.542005 + 0.757433i) q^{76} +(6.76302 - 7.62890i) q^{77} +(-1.89491 + 4.67462i) q^{78} +(0.00488142 + 0.00281829i) q^{79} +(-7.85474 + 1.55153i) q^{80} +(-6.95094 - 5.71703i) q^{81} +(-6.45642 - 10.0209i) q^{82} -8.56466i q^{83} +(-8.00275 + 4.46721i) q^{84} -11.3827i q^{85} +(8.04925 - 5.18608i) q^{86} +(-9.23003 - 13.1131i) q^{87} +(6.76691 + 8.54376i) q^{88} +(8.14017 + 4.69973i) q^{89} +(8.12436 + 2.47223i) q^{90} +(-1.72361 - 5.16840i) q^{91} +(1.65529 + 2.31321i) q^{92} +(9.06798 + 4.20137i) q^{93} +(0.247479 + 5.07202i) q^{94} +(0.466070 + 0.807257i) q^{95} +(-3.20734 - 9.25813i) q^{96} -4.17304 q^{97} +(3.43782 - 9.28339i) q^{98} +(-2.06332 - 11.3744i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{3} - 2 q^{4} - 8 q^{6} - 2 q^{9} + 6 q^{10} + 10 q^{12} - 10 q^{16} - 10 q^{18} - 4 q^{19} - 20 q^{22} - 8 q^{24} - 16 q^{25} - 8 q^{27} - 22 q^{28} - 12 q^{30} - 14 q^{33} - 56 q^{34} + 4 q^{36}+ \cdots - 44 q^{99}+O(q^{100}) $ 56 * q - 2 * q^3 - 2 * q^4 - 8 * q^6 - 2 * q^9 + 6 * q^10 + 10 * q^12 - 10 * q^16 - 10 * q^18 - 4 * q^19 - 20 * q^22 - 8 * q^24 - 16 * q^25 - 8 * q^27 - 22 * q^28 - 12 * q^30 - 14 * q^33 - 56 * q^34 + 4 * q^36 + 14 * q^40 - 8 * q^42 - 16 * q^43 - 12 * q^46 + 64 * q^48 - 16 * q^49 - 34 * q^51 - 8 * q^52 + 32 * q^54 + 4 * q^57 - 18 * q^58 + 40 * q^60 + 4 * q^64 - 20 * q^66 - 36 * q^67 - 42 * q^70 + 22 * q^72 + 4 * q^73 + 104 * q^76 + 28 * q^78 - 10 * q^81 + 52 * q^82 + 4 * q^84 + 46 * q^88 + 140 * q^90 + 72 * q^91 - 46 * q^96 - 32 * q^97 - 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.18883	−	0.765954i	0.840629	−	0.541612i
$2$	1.18883	−	0.765954i	0.840629	−	0.541612i
$3$	0.996948	+	1.41637i	0.575588	+	0.817740i
$3$	0.996948	+	1.41637i	0.575588	+	0.817740i
$4$	0.826627	−	1.82118i	0.413314	−	0.910589i
$5$	1.00081	−	1.73346i	0.447577	−	0.775227i	−0.550650	−	0.834736i	$-0.685620\pi$
$5$	1.00081	−	1.73346i	0.447577	−	0.775227i	0.998228	+	0.0595094i	$0.0189536\pi$
$6$	2.27007	+	0.920201i	0.926753	+	0.375671i
$7$	−2.50986	+	0.837013i	−0.948639	+	0.316361i
$7$	−2.50986	+	0.837013i	−0.948639	+	0.316361i
$8$	−0.412221	−	2.79823i	−0.145742	−	0.989323i
$9$	−1.01219	+	2.82409i	−0.337397	+	0.941362i
$10$	−0.137955	−	2.82736i	−0.0436254	−	0.894091i
$11$	−3.33711	+	1.92668i	−1.00618	+	0.580916i	−0.910070	−	0.414455i	$-0.863972\pi$
$11$	−3.33711	+	1.92668i	−1.00618	+	0.580916i	−0.0961058	+	0.995371i	$0.530639\pi$
$12$	3.40356	−	0.644811i	0.982523	−	0.186141i
$13$			2.05924i			0.571129i	0.958359	+	0.285565i	$0.0921811\pi$
$13$			2.05924i			0.571129i	−0.958359	+	0.285565i	$0.907819\pi$
$14$	−2.34268	+	2.91751i	−0.626108	+	0.779736i
$15$	3.45297	−	0.310649i	0.891554	−	0.0802093i
$16$	−2.63337	−	3.01087i	−0.658344	−	0.752718i
$17$	4.92484	−	2.84336i	1.19445	−	0.689616i	0.235137	−	0.971962i	$-0.424446\pi$
$17$	4.92484	−	2.84336i	1.19445	−	0.689616i	0.959313	+	0.282346i	$0.0911127\pi$
$18$	0.959801	+	4.13265i	0.226227	+	0.974075i
$19$	−0.232846	+	0.403301i	−0.0534185	+	0.0925235i	−0.891498	−	0.453024i	$-0.850345\pi$
$19$	−0.232846	+	0.403301i	−0.0534185	+	0.0925235i	0.838080	+	0.545548i	$0.183678\pi$
$20$	−2.32964	−	3.25558i	−0.520923	−	0.727971i
$21$	−3.68772	−	2.72043i	−0.804726	−	0.593646i
$22$	−2.49150	+	4.84656i	−0.531189	+	1.03329i
$23$	−0.711115	+	1.23169i	−0.148278	+	0.256825i	−0.930591	−	0.366061i	$-0.880706\pi$
$23$	−0.711115	+	1.23169i	−0.148278	+	0.256825i	0.782313	+	0.622885i	$0.214040\pi$
$24$	3.55235	−	3.37354i	0.725121	−	0.688621i
$25$	0.496746	+	0.860389i	0.0993492	+	0.172078i
$26$	1.57728	+	2.44808i	0.309330	+	0.480108i
$27$	−5.00905	+	1.38183i	−0.963991	+	0.265934i
$28$	−0.550373	+	5.26280i	−0.104011	+	0.994576i
$29$	−9.25829			−1.71922			−0.859611	−	0.510949i	$-0.829294\pi$
$29$	−9.25829			−1.71922			−0.859611	+	0.510949i	$0.829294\pi$
$30$	3.86705	−	3.01413i	0.706024	−	0.550302i
$31$	4.99699	−	2.88502i	0.897486	−	0.518164i	0.0211026	−	0.999777i	$-0.493282\pi$
$31$	4.99699	−	2.88502i	0.897486	−	0.518164i	0.876384	+	0.481613i	$0.159949\pi$
$32$	−5.43682	−	1.56236i	−0.961103	−	0.276190i
$33$	−6.05580	−	2.80577i	−1.05418	−	0.488422i
$34$	3.67691	−	7.15247i	0.630585	−	1.22664i
$35$	−1.06098	+	5.18844i	−0.179338	+	0.877006i
$36$	4.30646	+	4.17785i	0.717743	+	0.696308i
$37$	−0.569094	−	0.328567i	−0.0935586	−	0.0540161i	0.452491	−	0.891769i	$-0.350536\pi$
$37$	−0.569094	−	0.328567i	−0.0935586	−	0.0540161i	−0.546049	+	0.837753i	$0.683869\pi$
$38$	0.0320962	+	0.657805i	0.00520670	+	0.106710i
$39$	−2.91663	+	2.05295i	−0.467035	+	0.328735i
$40$	−5.26317	−	2.08593i	−0.832180	−	0.329815i
$41$		−	8.42924i		−	1.31643i	−0.752832	−	0.658213i	$-0.771313\pi$
$41$		−	8.42924i		−	1.31643i	0.752832	−	0.658213i	$-0.228687\pi$
$42$	−6.46779	−	0.409499i	−0.998002	−	0.0631871i
$43$	6.77074			1.03253			0.516264	−	0.856430i	$-0.327322\pi$
$43$	6.77074			1.03253			0.516264	+	0.856430i	$0.327322\pi$
$44$	0.750281	+	7.67011i	0.113109	+	1.15631i
$45$	3.88243	+	4.58098i	0.578758	+	0.682892i
$46$	0.0980225	+	2.00895i	0.0144526	+	0.296203i
$47$	−1.79536	+	3.10966i	−0.261881	+	0.453590i	−0.966742	−	0.255755i	$-0.917676\pi$
$47$	−1.79536	+	3.10966i	−0.261881	+	0.453590i	0.704861	+	0.709345i	$0.251009\pi$
$48$	1.63916	−	6.73150i	0.236593	−	0.971609i
$49$	5.59882	−	4.20157i	0.799831	−	0.600225i
$50$	1.24956	+	0.642371i	0.176715	+	0.0908449i
$51$	8.93705	+	4.14070i	1.25144	+	0.579815i
$52$	3.75023	+	1.70222i	0.520064	+	0.236056i
$53$	−1.50566	−	2.60789i	−0.206819	−	0.358221i	0.743892	−	0.668300i	$-0.232978\pi$
$53$	−1.50566	−	2.60789i	−0.206819	−	0.358221i	−0.950711	+	0.310079i	$0.899644\pi$
$54$	−4.89648	+	5.47946i	−0.666326	+	0.745661i
$55$			7.71298i			1.04002i
$56$	3.37677	+	6.67813i	0.451240	+	0.892403i
$57$	−0.803357	+	0.0722746i	−0.106407	+	0.00957300i
$58$	−11.0065	+	7.09143i	−1.44523	+	0.931151i
$59$	−5.72041	+	3.30268i	−0.744735	+	0.429973i	−0.823788	−	0.566898i	$-0.808143\pi$
$59$	−5.72041	+	3.30268i	−0.744735	+	0.429973i	0.0790537	+	0.996870i	$0.474810\pi$
$60$	2.28857	−	6.54527i	0.295454	−	0.844990i
$61$	8.50530	+	4.91054i	1.08899	+	0.628730i	0.933308	−	0.359077i	$-0.116908\pi$
$61$	8.50530	+	4.91054i	1.08899	+	0.628730i	0.155684	+	0.987807i	$0.450242\pi$
$62$	3.73078	−	7.25726i	0.473809	−	0.921673i
$63$	0.176663	−	7.93529i	0.0222575	−	0.999752i
$64$	−7.66015	+	2.30697i	−0.957519	+	0.288372i
$65$	3.56960	+	2.06091i	0.442755	+	0.255624i
$66$	−9.34841	+	1.30289i	−1.15071	+	0.160375i
$67$	−3.78271	−	6.55184i	−0.462131	−	0.800435i	0.536936	−	0.843623i	$-0.319582\pi$
$67$	−3.78271	−	6.55184i	−0.462131	−	0.800435i	−0.999067	+	0.0431883i	$0.986248\pi$
$68$	−1.10725	−	11.3194i	−0.134274	−	1.37268i
$69$	−2.45347	+	0.220728i	−0.295363	+	0.0265725i
$70$	2.71279	+	6.98082i	0.324240	+	0.834368i
$71$	14.0426			1.66655			0.833274	−	0.552861i	$-0.186464\pi$
$71$	14.0426			1.66655			0.833274	+	0.552861i	$0.186464\pi$
$72$	8.31968	+	1.66819i	0.980484	+	0.196598i
$73$	−2.02113	−	3.50071i	−0.236556	−	0.409727i	0.723168	−	0.690672i	$-0.242685\pi$
$73$	−2.02113	−	3.50071i	−0.236556	−	0.409727i	−0.959724	+	0.280946i	$0.909352\pi$
$74$	−0.928223	+	0.0452908i	−0.107904	+	0.00526494i
$75$	−0.723397	+	1.56134i	−0.0835307	+	0.180288i
$76$	0.542005	+	0.757433i	0.0621723	+	0.0868835i
$77$	6.76302	−	7.62890i	0.770718	−	0.869394i
$78$	−1.89491	+	4.67462i	−0.214556	+	0.529296i
$79$	0.00488142	+	0.00281829i	0.000549203	+	0.000317082i	0.500275	−	0.865867i	$-0.333232\pi$
$79$	0.00488142	+	0.00281829i	0.000549203	+	0.000317082i	−0.499725	+	0.866184i	$0.666566\pi$
$80$	−7.85474	+	1.55153i	−0.878186	+	0.173466i
$81$	−6.95094	−	5.71703i	−0.772327	−	0.635226i
$82$	−6.45642	−	10.0209i	−0.712992	−	1.10663i
$83$		−	8.56466i		−	0.940093i	−0.882642	−	0.470047i	$-0.844237\pi$
$83$		−	8.56466i		−	0.940093i	0.882642	−	0.470047i	$-0.155763\pi$
$84$	−8.00275	+	4.46721i	−0.873172	+	0.487412i
$85$		−	11.3827i		−	1.23463i
$86$	8.04925	−	5.18608i	0.867973	−	0.559229i
$87$	−9.23003	−	13.1131i	−0.989564	−	1.40588i
$88$	6.76691	+	8.54376i	0.721355	+	0.910768i
$89$	8.14017	+	4.69973i	0.862857	+	0.498170i	0.864968	−	0.501827i	$-0.167339\pi$
$89$	8.14017	+	4.69973i	0.862857	+	0.498170i	−0.00211125	+	0.999998i	$0.500672\pi$
$90$	8.12436	+	2.47223i	0.856383	+	0.260596i
$91$	−1.72361	−	5.16840i	−0.180683	−	0.541795i
$92$	1.65529	+	2.31321i	0.172576	+	0.241169i
$93$	9.06798	+	4.20137i	0.940306	+	0.435661i
$94$	0.247479	+	5.07202i	0.0255255	+	0.523139i
$95$	0.466070	+	0.807257i	0.0478178	+	0.0828228i
$96$	−3.20734	−	9.25813i	−0.327348	−	0.944904i
$97$	−4.17304			−0.423708			−0.211854	−	0.977301i	$-0.567950\pi$
$97$	−4.17304			−0.423708			−0.211854	+	0.977301i	$0.567950\pi$
$98$	3.43782	−	9.28339i	0.347273	−	0.937764i
$99$	−2.06332	−	11.3744i	−0.207372	−	1.14317i
$100$	1.97755	−	0.193441i	0.197755	−	0.0193441i
$101$	5.27692	+	9.13990i	0.525073	+	0.909454i	0.999574	+	0.0291983i	$0.00929543\pi$
$101$	5.27692	+	9.13990i	0.525073	+	0.909454i	−0.474500	+	0.880255i	$0.657371\pi$
$102$	13.7962	−	1.92279i	1.36603	−	0.190384i
$103$	9.20735	+	5.31587i	0.907227	+	0.523788i	0.879538	−	0.475829i	$-0.157852\pi$
$103$	9.20735	+	5.31587i	0.907227	+	0.523788i	0.0276894	+	0.999617i	$0.491185\pi$
$104$	5.76221	−	0.848859i	0.565031	−	0.0832375i
$105$	−8.40647	+	3.66987i	−0.820387	+	0.358143i
$106$	−3.78750	−	1.94706i	−0.367874	−	0.189115i
$107$	−4.86572	−	2.80922i	−0.470386	−	0.271578i	0.246015	−	0.969266i	$-0.420879\pi$
$107$	−4.86572	−	2.80922i	−0.470386	−	0.271578i	−0.716401	+	0.697688i	$0.754212\pi$
$108$	−1.62405	+	10.2646i	−0.156274	+	0.987714i
$109$	−9.15046	+	5.28302i	−0.876456	+	0.506022i	−0.869488	−	0.493954i	$-0.835551\pi$
$109$	−9.15046	+	5.28302i	−0.876456	+	0.506022i	−0.00696746	+	0.999976i	$0.502218\pi$
$110$	5.90779	+	9.16942i	0.563286	+	0.874270i
$111$	−0.101986	−	1.13361i	−0.00968009	−	0.107598i
$112$	9.12954	+	5.35270i	0.862661	+	0.505783i
$113$			15.9104i			1.49673i	0.663288	+	0.748364i	$0.269160\pi$
$113$			15.9104i			1.49673i	−0.663288	+	0.748364i	$0.730840\pi$
$114$	−0.899695	+	0.701257i	−0.0842641	+	0.0656787i
$115$	1.42339	+	2.46538i	0.132731	+	0.229898i
$116$	−7.65316	+	16.8610i	−0.710578	+	1.56550i
$117$	−5.81546	−	2.08434i	−0.537640	−	0.192697i
$118$	−4.27089	+	8.30790i	−0.393167	+	0.764804i
$119$	−9.98075	+	11.2586i	−0.914934	+	1.03207i
$120$	−2.29265	−	9.53415i	−0.209290	−	0.870344i
$121$	1.92419	−	3.33279i	0.174926	−	0.302981i
$122$	13.8726	−	0.676885i	1.25597	−	0.0612823i
$123$	11.9389	−	8.40351i	1.07649	−	0.757719i
$124$	−1.12347	−	11.4852i	−0.100891	−	1.03141i
$125$	11.9967			1.07302
$126$	−5.86805	−	9.56901i	−0.522767	−	0.852475i
$127$		−	17.8415i		−	1.58317i	−0.611056	−	0.791587i	$-0.709255\pi$
$127$		−	17.8415i		−	1.58317i	0.611056	−	0.791587i	$-0.290745\pi$
$128$	−7.33957	+	8.60992i	−0.648732	+	0.761017i
$129$	6.75007	+	9.58985i	0.594311	+	0.844339i
$130$	5.82221	−	0.284083i	0.510641	−	0.0249157i
$131$	−2.10794	−	1.21702i	−0.184172	−	0.106332i	0.405080	−	0.914281i	$-0.367244\pi$
$131$	−2.10794	−	1.21702i	−0.184172	−	0.106332i	−0.589251	+	0.807950i	$0.700577\pi$
$132$	−10.1157	+	8.70937i	−0.880458	+	0.758053i
$133$	0.246843	−	1.20712i	0.0214040	−	0.104671i
$134$	−9.51540	−	4.89164i	−0.822006	−	0.422573i
$135$	−2.61777	+	10.0659i	−0.225302	+	0.866338i
$136$	−9.98649	−	12.6087i	−0.856334	−	1.08119i
$137$	−2.69513	+	1.55603i	−0.230260	+	0.132941i	−0.610692	−	0.791868i	$-0.709109\pi$
$137$	−2.69513	+	1.55603i	−0.230260	+	0.132941i	0.380432	+	0.924809i	$0.375775\pi$
$138$	−2.74768	+	2.14165i	−0.233898	+	0.182309i
$139$	7.95494			0.674729			0.337364	−	0.941374i	$-0.390465\pi$
$139$	7.95494			0.674729			0.337364	+	0.941374i	$0.390465\pi$
$140$	8.57203	+	6.22113i	0.724469	+	0.525781i
$141$	−6.19430	+	0.557275i	−0.521654	+	0.0469310i
$142$	16.6942	−	10.7560i	1.40095	−	0.902621i
$143$	−3.96749	−	6.87189i	−0.331778	−	0.574656i
$144$	11.1684	−	4.38930i	0.930703	−	0.365775i
$145$	−9.26582	+	16.0489i	−0.769485	+	1.33279i
$146$	−5.08416	−	2.61364i	−0.420768	−	0.216307i
$147$	11.5327	+	3.74123i	0.951201	+	0.308572i
$148$	−1.06881	+	0.764820i	−0.0878554	+	0.0628678i
$149$	5.27692	−	9.13990i	0.432302	−	0.748769i	−0.564769	−	0.825249i	$-0.691035\pi$
$149$	5.27692	−	9.13990i	0.432302	−	0.748769i	0.997071	+	0.0764797i	$0.0243680\pi$
$150$	0.335918	+	2.41025i	0.0274276	+	0.196796i
$151$	−15.2482	+	8.80356i	−1.24088	+	0.716424i	−0.969274	−	0.245984i	$-0.920889\pi$
$151$	−15.2482	+	8.80356i	−1.24088	+	0.716424i	−0.271608	+	0.962408i	$0.587556\pi$
$152$	1.22451	+	0.485306i	0.0993209	+	0.0393635i
$153$	3.04501	+	16.7862i	0.246175	+	1.35708i
$154$	2.19669	−	14.2496i	0.177014	−	1.14827i
$155$		−	11.5494i		−	0.927674i
$156$	1.32782	+	7.00873i	0.106310	+	0.561148i
$157$	−2.13267	+	1.23130i	−0.170206	+	0.0982682i	−0.582683	−	0.812700i	$-0.697997\pi$
$157$	−2.13267	+	1.23130i	−0.170206	+	0.0982682i	0.412477	+	0.910968i	$0.364664\pi$
$158$	0.00796186		0.000388483i	0.000633411		3.09060e-5i
$159$	2.19266	−	4.73250i	0.173889	−	0.375312i
$160$	−8.14954	+	7.86087i	−0.644277	+	0.621457i
$161$	0.753863	−	3.68658i	0.0594127	−	0.290543i
$162$	−12.6425	−	1.47247i	−0.993286	−	0.115688i
$163$	−4.83382	+	8.37243i	−0.378614	+	0.655779i	−0.990861	−	0.134888i	$-0.956933\pi$
$163$	−4.83382	+	8.37243i	−0.378614	+	0.655779i	0.612247	+	0.790667i	$0.290266\pi$
$164$	−15.3511	−	6.96784i	−1.19872	−	0.544097i
$165$	−10.9244	+	7.68944i	−0.850465	+	0.598622i
$166$	−6.56014	−	10.1819i	−0.509166	−	0.790270i
$167$	−12.7380			−0.985699			−0.492850	−	0.870114i	$-0.664045\pi$
$167$	−12.7380			−0.985699			−0.492850	+	0.870114i	$0.664045\pi$
$168$	−6.09222	+	11.4405i	−0.470025	+	0.882653i
$169$	8.75955			0.673811
$170$	−8.71862	−	13.5321i	−0.668688	−	1.03786i
$171$	−0.903272	−	1.06579i	−0.0690749	−	0.0815033i
$172$	5.59688	−	12.3307i	0.426758	−	0.940208i
$173$	−5.87501	+	10.1758i	−0.446668	+	0.773652i	−0.998167	−	0.0605236i	$-0.980723\pi$
$173$	−5.87501	+	10.1758i	−0.446668	+	0.773652i	0.551498	+	0.834176i	$0.314056\pi$
$174$	−21.0170	−	8.51949i	−1.59329	−	0.645861i
$175$	−1.96692	−	1.74368i	−0.148685	−	0.131810i
$176$	14.5888	+	4.97393i	1.09967	+	0.374924i
$177$	−10.3808	−	4.80960i	−0.780266	−	0.361512i
$178$	13.2771	−	0.647827i	0.995157	−	0.0485567i
$179$	−8.89943	+	5.13809i	−0.665175	+	0.384039i	−0.794246	−	0.607597i	$-0.792134\pi$
$179$	−8.89943	+	5.13809i	−0.665175	+	0.384039i	0.129071	+	0.991635i	$0.458800\pi$
$180$	11.5521	−	3.28383i	0.861042	−	0.244762i
$181$			4.76352i			0.354070i	0.984205	+	0.177035i	$0.0566505\pi$
$181$			4.76352i			0.354070i	−0.984205	+	0.177035i	$0.943349\pi$
$182$	−6.00783	−	4.82414i	−0.445330	−	0.357589i
$183$	1.52422	+	16.9422i	0.112673	+	1.25240i
$184$	3.73968	+	1.48213i	0.275693	+	0.109264i
$185$	−1.13911	+	0.657668i	−0.0837494	+	0.0483527i
$186$	13.9983	−	1.95095i	1.02641	−	0.143051i
$187$	−10.9565	+	18.9772i	−0.801217	+	1.38775i
$188$	4.17914	+	5.84020i	0.304795	+	0.425941i
$189$	11.4154	−	7.66085i	0.830348	−	0.557245i
$190$	1.17240	+	0.602702i	0.0850548	+	0.0437246i
$191$	−1.19496	+	2.06973i	−0.0864644	+	0.149761i	−0.906014	−	0.423247i	$-0.860890\pi$
$191$	−1.19496	+	2.06973i	−0.0864644	+	0.149761i	0.819550	+	0.573008i	$0.194224\pi$
$192$	−10.9043	−	8.54965i	−0.786949	−	0.617018i
$193$	−3.18130	−	5.51018i	−0.228995	−	0.396631i	0.728515	−	0.685029i	$-0.240211\pi$
$193$	−3.18130	−	5.51018i	−0.228995	−	0.396631i	−0.957511	+	0.288398i	$0.906877\pi$
$194$	−4.96103	+	3.19636i	−0.356181	+	0.229485i
$195$	0.639700	+	7.11049i	0.0458099	+	0.509192i
$196$	−3.02367	−	13.6696i	−0.215977	−	0.976399i
$197$	−16.9051			−1.20444			−0.602219	−	0.798331i	$-0.705716\pi$
$197$	−16.9051			−1.20444			−0.602219	+	0.798331i	$0.705716\pi$
$198$	−11.1652	−	11.9419i	−0.793479	−	0.848671i
$199$	−11.2472	+	6.49358i	−0.797293	+	0.460318i	−0.842524	−	0.538659i	$-0.818931\pi$
$199$	−11.2472	+	6.49358i	−0.797293	+	0.460318i	0.0452304	+	0.998977i	$0.485598\pi$
$200$	2.20280	−	1.74468i	0.155761	−	0.123367i
$201$	5.50865	−	11.8895i	0.388550	−	0.838624i
$202$	13.2741	+	6.82389i	0.933962	+	0.480127i
$203$	23.2370	−	7.74931i	1.63092	−	0.543895i
$204$	14.9286	−	12.8531i	1.04521	−	0.899899i
$205$	−14.6117	−	8.43610i	−1.02053	−	0.589202i
$206$	15.0177	−	0.732757i	1.04633	−	0.0510536i
$207$	−2.75861	−	3.25495i	−0.191737	−	0.226235i
$208$	6.20009	−	5.42274i	0.429899	−	0.375999i
$209$		−	1.79448i		−	0.124127i
$210$	−7.18290	+	10.8018i	−0.495667	+	0.745396i
$211$	−4.34903			−0.299400			−0.149700	−	0.988731i	$-0.547831\pi$
$211$	−4.34903			−0.299400			−0.149700	+	0.988731i	$0.547831\pi$
$212$	−5.99405	+	0.586331i	−0.411673	+	0.0402694i
$213$	13.9997	+	19.8894i	0.959244	+	1.36280i
$214$	−7.93624	+	0.387233i	−0.542510	+	0.0264707i
$215$	6.77624	−	11.7368i	0.462136	−	0.800443i
$216$	5.93151	+	13.4468i	0.403588	+	0.914941i
$217$	−10.1270	+	11.4235i	−0.687464	+	0.775480i
$218$	−6.83178	+	13.2894i	−0.462707	+	0.900075i
$219$	2.94332	−	6.35269i	0.198891	−	0.429275i
$220$	14.0467	+	6.37576i	0.947029	+	0.429854i
$221$	5.85515	+	10.1414i	0.393860	+	0.682185i
$222$	−0.989538	−	1.26955i	−0.0664134	−	0.0852068i
$223$		−	25.7814i		−	1.72645i	−0.504820	−	0.863225i	$-0.668441\pi$
$223$		−	25.7814i		−	1.72645i	0.504820	−	0.863225i	$-0.331559\pi$
$224$	14.9534	−	0.629368i	0.999115	−	0.0420514i
$225$	−2.93262	+	0.531976i	−0.195508	+	0.0354651i
$226$	12.1867	+	18.9148i	0.810645	+	1.25819i
$227$	1.40958	−	0.813824i	0.0935574	−	0.0540154i	−0.452491	−	0.891769i	$-0.649465\pi$
$227$	1.40958	−	0.813824i	0.0935574	−	0.0540154i	0.546049	+	0.837753i	$0.316131\pi$
$228$	−0.532452	+	1.52280i	−0.0352625	+	0.100850i
$229$	12.1735	+	7.02837i	0.804448	+	0.464448i	0.845024	−	0.534728i	$-0.179586\pi$
$229$	12.1735	+	7.02837i	0.804448	+	0.464448i	−0.0405764	+	0.999176i	$0.512919\pi$
$230$	3.58053	+	1.84066i	0.236093	+	0.121370i
$231$	17.5477	+	1.97331i	1.15455	+	0.129834i
$232$	3.81646	+	25.9068i	0.250563	+	1.70087i
$233$	−15.5827	−	8.99668i	−1.02086	−	0.589392i	−0.106505	−	0.994312i	$-0.533966\pi$
$233$	−15.5827	−	8.99668i	−1.02086	−	0.589392i	−0.914352	+	0.404920i	$0.867299\pi$
$234$	−8.51010	+	1.97646i	−0.556323	+	0.129205i
$235$	3.59364	+	6.22438i	0.234424	+	0.406033i
$236$	1.28612	+	13.1480i	0.0837193	+	0.855860i
$237$	0.000874789		0.00972357i	5.68236e−5		0.000631614i
$238$	−3.24183	+	21.0293i	−0.210137	+	1.36313i
$239$	16.0533			1.03840			0.519200	−	0.854653i	$-0.326230\pi$
$239$	16.0533			1.03840			0.519200	+	0.854653i	$0.326230\pi$
$240$	−10.0283	−	9.57840i	−0.647324	−	0.618283i
$241$	3.64298	+	6.30983i	0.234665	+	0.406452i	0.959175	−	0.282812i	$-0.0912673\pi$
$241$	3.64298	+	6.30983i	0.234665	+	0.406452i	−0.724510	+	0.689264i	$0.757934\pi$
$242$	−0.265236	−	5.43595i	−0.0170500	−	0.349436i
$243$	1.16769	−	15.5447i	0.0749075	−	0.997190i
$244$	15.9737	−	11.4305i	1.02261	−	0.731761i
$245$	−1.67988	−	13.9103i	−0.107324	−	0.888697i
$246$	7.75660	−	19.1350i	0.494543	−	1.22000i
$247$	−0.830491	−	0.479484i	−0.0528429	−	0.0305089i
$248$	−10.1328	−	12.7935i	−0.643433	−	0.812385i
$249$	12.1307	−	8.53852i	0.768752	−	0.541106i
$250$	14.2621	−	9.18895i	0.902012	−	0.581160i
$251$			22.3471i			1.41053i	0.708942	+	0.705267i	$0.249173\pi$
$251$			22.3471i			1.41053i	−0.708942	+	0.705267i	$0.750827\pi$
$252$	−14.3055	−	6.88126i	−0.901164	−	0.433479i
$253$		−	5.48036i		−	0.344547i
$254$	−13.6658	−	21.2105i	−0.857466	−	1.33086i
$255$	16.1221	−	11.3479i	1.00960	−	0.710636i
$256$	−2.13068	+	15.8575i	−0.133168	+	0.991094i
$257$	2.61954	+	1.51239i	0.163402	+	0.0943404i	0.579471	−	0.814993i	$-0.303259\pi$
$257$	2.61954	+	1.51239i	0.163402	+	0.0943404i	−0.416069	+	0.909333i	$0.636592\pi$
$258$	15.3701	+	6.23044i	0.956898	+	0.387890i
$259$	1.70336	+	0.348318i	0.105842	+	0.0216434i
$260$	6.70401	−	4.79727i	0.415765	−	0.297514i
$261$	9.37116	−	26.1462i	0.580060	−	1.61841i
$262$	−3.43816	+	0.167758i	−0.212410	+	0.0103641i
$263$	−10.7454	−	18.6116i	−0.662590	−	1.14764i	−0.979933	−	0.199329i	$-0.936124\pi$
$263$	−10.7454	−	18.6116i	−0.662590	−	1.14764i	0.317342	−	0.948311i	$-0.397210\pi$
$264$	−5.35485	+	18.1021i	−0.329568	+	1.11411i
$265$	−6.02755			−0.370270
$266$	−0.631148	−	1.62413i	−0.0386982	−	0.0995821i
$267$	1.45878	+	16.2149i	0.0892760	+	0.992333i
$268$	−15.0590	+	1.47305i	−0.919872	+	0.0899808i
$269$	−10.9385	−	18.9460i	−0.666929	−	1.15516i	−0.978758	−	0.205017i	$-0.934275\pi$
$269$	−10.9385	−	18.9460i	−0.666929	−	1.15516i	0.311829	−	0.950138i	$-0.399058\pi$
$270$	4.59797	+	13.9718i	0.279824	+	0.850294i
$271$	9.03323	+	5.21534i	0.548729	+	0.316809i	0.748609	−	0.663011i	$-0.230722\pi$
$271$	9.03323	+	5.21534i	0.548729	+	0.316809i	−0.199880	+	0.979820i	$0.564055\pi$
$272$	−21.5299	−	7.34043i	−1.30544	−	0.445079i
$273$	5.60200	−	7.59388i	0.339049	−	0.459603i
$274$	−2.01219	+	3.91420i	−0.121561	+	0.236465i
$275$	−3.31539	−	1.91414i	−0.199925	−	0.115427i
$276$	−1.62612	+	4.65066i	−0.0978808	+	0.279937i
$277$	18.7719	−	10.8380i	1.12790	−	0.651191i	0.184492	−	0.982834i	$-0.440936\pi$
$277$	18.7719	−	10.8380i	1.12790	−	0.651191i	0.943405	+	0.331643i	$0.107603\pi$
$278$	9.45706	−	6.09312i	0.567197	−	0.365441i
$279$	3.08962	+	17.0321i	0.184971	+	1.01969i
$280$	14.9558	+	0.830071i	0.893779	+	0.0496062i
$281$			8.35022i			0.498132i	0.968487	+	0.249066i	$0.0801236\pi$
$281$			8.35022i			0.498132i	−0.968487	+	0.249066i	$0.919876\pi$
$282$	−6.93711	+	5.40706i	−0.413099	+	0.321986i
$283$	−11.3999	−	19.7453i	−0.677656	−	1.17374i	−0.975685	−	0.219178i	$-0.929662\pi$
$283$	−11.3999	−	19.7453i	−0.677656	−	1.17374i	0.298028	−	0.954557i	$-0.403671\pi$
$284$	11.6080	−	25.5740i	0.688807	−	1.51754i
$285$	−0.678725	+	1.46492i	−0.0402042	+	0.0867743i
$286$	−9.98022	−	5.13058i	−0.590143	−	0.303378i
$287$	7.05538	+	21.1562i	0.416466	+	1.24881i
$288$	9.91535	−	13.7726i	0.584268	−	0.811561i
$289$	7.66938	−	13.2838i	0.451140	−	0.781398i
$290$	1.27723	+	26.1766i	0.0750017	+	1.53714i
$291$	−4.16030	−	5.91056i	−0.243881	−	0.346483i
$292$	−8.04613	+	0.787063i	−0.470864	+	0.0460594i
$293$	6.51811			0.380792			0.190396	−	0.981707i	$-0.439023\pi$
$293$	6.51811			0.380792			0.190396	+	0.981707i	$0.439023\pi$
$294$	16.5760	−	4.38584i	0.966733	−	0.255787i
$295$			13.2215i			0.769784i
$296$	−0.684812	+	1.72790i	−0.0398039	+	0.100432i
$297$	14.0534	−	14.2621i	0.815459	−	0.827574i
$298$	−0.727389	−	14.9077i	−0.0421365	−	0.863577i
$299$	−2.53633	−	1.46435i	−0.146680	−	0.0846858i
$300$	2.24549	+	2.60808i	0.129644	+	0.150578i
$301$	−16.9936	+	5.66719i	−0.979496	+	0.326652i
$302$	−11.3844	+	22.1454i	−0.655098	+	1.27432i
$303$	−7.68463	+	16.5861i	−0.441471	+	0.952844i
$304$	1.82746	−	0.360973i	0.104812	−	0.0207032i
$305$	17.0244	−	9.82906i	0.974817	−	0.562811i
$306$	16.4775	+	17.6236i	0.941954	+	1.00747i
$307$	−12.7577			−0.728122			−0.364061	−	0.931375i	$-0.618610\pi$
$307$	−12.7577			−0.728122			−0.364061	+	0.931375i	$0.618610\pi$
$308$	−8.30308	−	18.6229i	−0.473112	−	1.06114i
$309$	1.65003	+	18.3406i	0.0938669	+	1.04336i
$310$	−8.84635	−	13.7303i	−0.502439	−	0.779829i
$311$	4.72369	+	8.18167i	0.267856	+	0.463940i	0.968308	−	0.249760i	$-0.0803516\pi$
$311$	4.72369	+	8.18167i	0.267856	+	0.463940i	−0.700452	+	0.713699i	$0.747018\pi$
$312$	6.94692	+	7.31514i	0.393292	+	0.414138i
$313$	2.87628	−	4.98187i	0.162577	−	0.281592i	−0.773215	−	0.634144i	$-0.781353\pi$
$313$	2.87628	−	4.98187i	0.162577	−	0.281592i	0.935792	+	0.352552i	$0.114686\pi$
$314$	−1.59226	+	3.09733i	−0.0898565	+	0.174792i
$315$	−13.5787	−	8.24798i	−0.765073	−	0.464721i
$316$	0.00916773	−	0.00656026i	0.000515725	−	0.000369043i
$317$	−6.69015	+	11.5877i	−0.375756	+	0.650829i	−0.990440	−	0.137945i	$-0.955950\pi$
$317$	−6.69015	+	11.5877i	−0.375756	+	0.650829i	0.614684	+	0.788774i	$0.289284\pi$
$318$	−1.01819	−	7.30561i	−0.0570970	−	0.409678i
$319$	30.8959	−	17.8378i	1.72984	−	0.998723i
$320$	−3.66733	+	15.5874i	−0.205010	+	0.871362i
$321$	−0.871974	−	9.69229i	−0.0486688	−	0.540971i
$322$	−1.92754	−	4.96013i	−0.107417	−	0.276417i
$323$			2.64826i			0.147353i
$324$	−16.1576	+	7.93304i	−0.897643	+	0.440724i
$325$	−1.77174	+	1.02292i	−0.0982787	+	0.0567412i
$326$	0.666311	+	13.6559i	0.0369035	+	0.756329i
$327$	−16.6052	−	7.69352i	−0.918272	−	0.425453i
$328$	−23.5869	+	3.47471i	−1.30237	+	0.191859i
$329$	1.90329	−	9.30756i	0.104932	−	0.513142i
$330$	−7.09750	+	17.5090i	−0.390704	+	0.963841i
$331$	2.24337	−	3.88563i	0.123307	−	0.213573i	−0.797763	−	0.602971i	$-0.793983\pi$
$331$	2.24337	−	3.88563i	0.123307	−	0.213573i	0.921070	+	0.389398i	$0.127317\pi$
$332$	−15.5978	−	7.07978i	−0.856038	−	0.388554i
$333$	1.50393	−	1.27460i	0.0824151	−	0.0698477i
$334$	−15.1434	+	9.75676i	−0.828607	+	0.533866i
$335$	−15.1431			−0.827358
$336$	1.52029	+	18.2671i	0.0829384	+	0.996555i
$337$	−9.02628			−0.491693			−0.245846	−	0.969309i	$-0.579066\pi$
$337$	−9.02628			−0.491693			−0.245846	+	0.969309i	$0.579066\pi$
$338$	10.4136	−	6.70941i	0.566425	−	0.364944i
$339$	−22.5350	+	15.8619i	−1.22393	+	0.861499i
$340$	−20.7299	−	9.40924i	−1.12424	−	0.510288i
$341$	−11.1170	+	19.2552i	−0.602019	+	1.04273i
$342$	−1.89019	−	0.575181i	−0.102210	−	0.0311022i
$343$	−10.5355	+	15.2317i	−0.568863	+	0.822432i
$344$	−2.79104	−	18.9461i	−0.150483	−	1.02150i
$345$	−2.07284	+	4.47389i	−0.111598	+	0.240866i
$346$	0.809831	+	16.5973i	0.0435368	+	0.892275i
$347$	−0.882015	+	0.509232i	−0.0473491	+	0.0273370i	−0.523488	−	0.852033i	$-0.675369\pi$
$347$	−0.882015	+	0.509232i	−0.0473491	+	0.0273370i	0.476139	+	0.879370i	$0.342036\pi$
$348$	−31.5112	+	5.96985i	−1.68918	+	0.320017i
$349$		−	9.91220i		−	0.530588i	−0.964168	−	0.265294i	$-0.914531\pi$
$349$		−	9.91220i		−	0.530588i	0.964168	−	0.265294i	$-0.0854690\pi$
$350$	−3.67391	−	0.566360i	−0.196379	−	0.0302732i
$351$	−2.84552	−	10.3148i	−0.151883	−	0.550564i
$352$	21.1534	−	5.26123i	1.12748	−	0.280425i
$353$	−20.6381	+	11.9154i	−1.09845	+	0.634192i	−0.935814	−	0.352494i	$-0.885334\pi$
$353$	−20.6381	+	11.9154i	−1.09845	+	0.634192i	−0.162638	+	0.986686i	$0.552000\pi$
$354$	−16.0249	+	2.23340i	−0.851713	+	0.118704i
$355$	14.0540	−	24.3422i	0.745909	−	1.29195i
$356$	15.2879	−	10.9398i	0.810259	−	0.579807i
$357$	−25.8966	−	2.91217i	−1.37059	−	0.154129i
$358$	−6.64436	+	12.9249i	−0.351165	+	0.683100i
$359$	−1.66057	+	2.87619i	−0.0876414	+	0.151799i	−0.906514	−	0.422176i	$-0.861266\pi$
$359$	−1.66057	+	2.87619i	−0.0876414	+	0.151799i	0.818872	+	0.573976i	$0.194600\pi$
$360$	11.2182	−	12.7523i	0.591251	−	0.672104i
$361$	9.39157	+	16.2667i	0.494293	+	0.856140i
$362$	3.64864	+	5.66301i	0.191768	+	0.297641i
$363$	6.63876	−	0.597261i	0.348445	−	0.0313481i
$364$	−10.8374	−	1.13335i	−0.568032	−	0.0594035i
$365$	−8.09111			−0.423508
$366$	14.7890	+	18.9739i	0.773032	+	0.991780i
$367$	−6.76756	+	3.90725i	−0.353264	+	0.203957i	−0.666122	−	0.745843i	$-0.732047\pi$
$367$	−6.76756	+	3.90725i	−0.353264	+	0.203957i	0.312858	+	0.949800i	$0.398714\pi$
$368$	5.58108	−	1.10242i	0.290934	−	0.0574675i
$369$	23.8049	+	8.53200i	1.23923	+	0.444158i
$370$	−0.850468	+	1.65436i	−0.0442137	+	0.0860063i
$371$	5.96184	+	5.28518i	0.309524	+	0.274393i
$372$	15.1473	−	13.0414i	0.785350	−	0.676167i
$373$	27.0847	+	15.6374i	1.40239	+	0.809673i	0.994638	−	0.103418i	$-0.0329779\pi$
$373$	27.0847	+	15.6374i	1.40239	+	0.809673i	0.407756	+	0.913091i	$0.366311\pi$
$374$	1.51028	+	30.9528i	0.0780946	+	1.60053i
$375$	11.9601	+	16.9918i	0.617618	+	0.877451i
$376$	9.44162	+	3.74197i	0.486914	+	0.192977i
$377$		−	19.0650i		−	0.981898i
$378$	7.70310	−	17.8511i	0.396205	−	0.918162i
$379$	19.1714			0.984768			0.492384	−	0.870378i	$-0.336126\pi$
$379$	19.1714			0.984768			0.492384	+	0.870378i	$0.336126\pi$
$380$	1.85543	−	0.181496i	0.0951813	−	0.00931052i
$381$	25.2701	−	17.7870i	1.29463	−	0.911256i
$382$	0.164718	+	3.37585i	0.00842768	+	0.172723i
$383$	13.9774	−	24.2095i	0.714209	−	1.23705i	−0.249054	−	0.968490i	$-0.580120\pi$
$383$	13.9774	−	24.2095i	0.714209	−	1.23705i	0.963264	−	0.268558i	$-0.0865469\pi$
$384$	−19.5120	−	1.81188i	−0.995716	−	0.0924621i
$385$	−6.45587	−	19.3585i	−0.329021	−	0.986602i
$386$	−8.00257	−	4.11392i	−0.407320	−	0.209393i
$387$	−6.85328	+	19.1212i	−0.348372	+	0.971983i
$388$	−3.44955	+	7.59985i	−0.175124	+	0.385824i
$389$	7.27120	+	12.5941i	0.368664	+	0.638545i	0.989357	−	0.145509i	$-0.0464819\pi$
$389$	7.27120	+	12.5941i	0.368664	+	0.638545i	−0.620693	+	0.784054i	$0.713149\pi$
$390$	6.20680	+	7.96317i	0.314294	+	0.403231i
$391$			8.08782i			0.409019i
$392$	−14.0649	−	13.9348i	−0.710385	−	0.703813i
$393$	−0.377759	−	4.19892i	−0.0190554	−	0.211808i
$394$	−20.0972	+	12.9485i	−1.01248	+	0.652337i
$395$	0.00977078	−	0.00564117i	0.000491622	−	0.000283838i
$396$	−22.4205	−	5.64475i	−1.12667	−	0.283660i
$397$	−31.2547	−	18.0449i	−1.56863	−	0.905647i	−0.996330	−	0.0856008i	$-0.972719\pi$
$397$	−31.2547	−	18.0449i	−1.56863	−	0.905647i	−0.572297	−	0.820046i	$-0.693948\pi$
$398$	−8.39722	+	16.3346i	−0.420915	+	0.818780i
$399$	1.95582	−	0.853819i	0.0979135	−	0.0427444i
$400$	1.28240	−	3.76136i	0.0641201	−	0.188068i
$401$	−2.65616	−	1.53353i	−0.132642	−	0.0765811i	0.432211	−	0.901773i	$-0.357734\pi$
$401$	−2.65616	−	1.53353i	−0.132642	−	0.0765811i	−0.564853	+	0.825192i	$0.691067\pi$
$402$	−2.55801	−	18.3540i	−0.127582	−	0.915415i
$403$	5.94093	+	10.2900i	0.295939	+	0.512581i
$404$	21.0074	−	2.05492i	1.04516	−	0.102236i
$405$	−16.8668	+	6.32749i	−0.838120	+	0.314415i
$406$	21.6892	−	27.0111i	1.07642	−	1.34054i
$407$	2.53217			0.125515
$408$	7.90259	−	26.7148i	0.391237	−	1.32258i
$409$	−13.6122	−	23.5770i	−0.673080	−	1.16581i	−0.977026	−	0.213119i	$-0.931638\pi$
$409$	−13.6122	−	23.5770i	−0.673080	−	1.16581i	0.303947	−	0.952689i	$-0.401696\pi$
$410$	−23.8325	+	1.16286i	−1.17700	+	0.0574296i
$411$	−4.89081	−	2.26601i	−0.241246	−	0.111774i
$412$	17.2922	−	12.3740i	0.851925	−	0.609622i
$413$	11.5931	−	13.0773i	0.570457	−	0.643494i
$414$	−5.77266	−	1.75661i	−0.283711	−	0.0863329i
$415$	−14.8465	−	8.57162i	−0.728785	−	0.420764i
$416$	3.21728	−	11.1957i	0.157740	−	0.548914i
$417$	7.93066	+	11.2671i	0.388366	+	0.551753i
$418$	−1.37449	−	2.13332i	−0.0672284	−	0.104344i
$419$			8.16587i			0.398929i	0.979905	+	0.199465i	$0.0639203\pi$
$419$			8.16587i			0.398929i	−0.979905	+	0.199465i	$0.936080\pi$
$420$	−0.265536	+	18.3433i	−0.0129568	+	0.895061i
$421$			7.30698i			0.356121i	0.984020	+	0.178060i	$0.0569822\pi$
$421$			7.30698i			0.356121i	−0.984020	+	0.178060i	$0.943018\pi$
$422$	−5.17026	+	3.33116i	−0.251684	+	0.162158i
$423$	−6.96470	−	8.21783i	−0.338635	−	0.399564i
$424$	−6.67679	+	5.28821i	−0.324254	+	0.256818i
$425$	4.89279	+	2.82485i	0.237335	+	0.137026i
$426$	31.8777	+	12.9220i	1.54448	+	0.626073i
$427$	−25.4573	−	5.20573i	−1.23197	−	0.251923i
$428$	−9.13822	+	6.53915i	−0.441713	+	0.316082i
$429$	5.77774	−	12.4703i	0.278952	−	0.602073i
$430$	−0.934060	−	19.1433i	−0.0450444	−	0.923174i
$431$	1.44464	+	2.50219i	0.0695858	+	0.120526i	0.898719	−	0.438525i	$-0.144499\pi$
$431$	1.44464	+	2.50219i	0.0695858	+	0.120526i	−0.829133	+	0.559051i	$0.811166\pi$
$432$	17.3512	+	11.4427i	0.834811	+	0.550537i
$433$	23.0768			1.10900			0.554499	−	0.832184i	$-0.312910\pi$
$433$	23.0768			1.10900			0.554499	+	0.832184i	$0.312910\pi$
$434$	−3.28932	+	21.3374i	−0.157893	+	1.02423i
$435$	−31.9686	+	2.87608i	−1.53278	+	0.137898i
$436$	2.05730	+	21.0317i	0.0985267	+	1.00724i
$437$	−0.331160	−	0.573586i	−0.0158415	−	0.0274384i
$438$	−1.36677	−	9.80671i	−0.0653066	−	0.468583i
$439$	2.57178	+	1.48482i	0.122744	+	0.0708664i	0.560115	−	0.828415i	$-0.310757\pi$
$439$	2.57178	+	1.48482i	0.122744	+	0.0708664i	−0.437371	+	0.899281i	$0.644090\pi$
$440$	21.5827	−	3.17945i	1.02891	−	0.151574i
$441$	6.19854	+	20.0644i	0.295168	+	0.955445i
$442$	14.7286	+	7.57163i	0.700569	+	0.360146i
$443$	17.0338	+	9.83448i	0.809301	+	0.467250i	0.846713	−	0.532050i	$-0.178578\pi$
$443$	17.0338	+	9.83448i	0.809301	+	0.467250i	−0.0374121	+	0.999300i	$0.511911\pi$
$444$	−2.14881	−	0.751339i	−0.101978	−	0.0356570i
$445$	16.2936	−	9.40711i	0.772390	−	0.445940i
$446$	−19.7474	−	30.6497i	−0.935065	−	1.45130i
$447$	18.2063	−	1.63794i	0.861127	−	0.0774719i
$448$	17.2950	−	12.2018i	0.817110	−	0.576482i
$449$		−	36.3243i		−	1.71425i	−0.515111	−	0.857124i	$-0.672249\pi$
$449$		−	36.3243i		−	1.71425i	0.515111	−	0.857124i	$-0.327751\pi$
$450$	−3.07891	+	2.87868i	−0.145141	+	0.135702i
$451$	16.2404	+	28.1293i	0.764733	+	1.32456i
$452$	28.9757	+	13.1520i	1.36290	+	0.618618i
$453$	−27.6707	−	12.8204i	−1.30009	−	0.602354i
$454$	1.05240	−	2.04717i	0.0493917	−	0.0960786i
$455$	−10.6842	−	2.18480i	−0.500884	−	0.102425i
$456$	0.533401	+	2.21818i	0.0249788	+	0.103876i
$457$	−13.7632	+	23.8385i	−0.643814	+	1.11512i	0.340760	+	0.940150i	$0.389316\pi$
$457$	−13.7632	+	23.8385i	−0.643814	+	1.11512i	−0.984574	+	0.174968i	$0.944018\pi$
$458$	19.8556	−	0.968815i	0.927792	−	0.0452697i
$459$	−20.7397	+	21.0478i	−0.968047	+	0.982428i
$460$	5.66650	−	0.554290i	0.264202	−	0.0258439i
$461$	19.4067			0.903861			0.451931	−	0.892053i	$-0.350735\pi$
$461$	19.4067			0.903861			0.451931	+	0.892053i	$0.350735\pi$
$462$	22.3727	−	11.0948i	1.04087	−	0.516178i
$463$			8.27807i			0.384715i	0.981325	+	0.192357i	$0.0616132\pi$
$463$			8.27807i			0.384715i	−0.981325	+	0.192357i	$0.938387\pi$
$464$	24.3806	+	27.8755i	1.13184	+	1.29409i
$465$	16.3583	−	11.5142i	0.758596	−	0.533958i
$466$	−25.4162	+	1.24013i	−1.17738	+	0.0574481i
$467$	13.6618	+	7.88767i	0.632194	+	0.364998i	0.781601	−	0.623778i	$-0.214403\pi$
$467$	13.6618	+	7.88767i	0.632194	+	0.364998i	−0.149407	+	0.988776i	$0.547736\pi$
$468$	−8.60317	+	8.86802i	−0.397682	+	0.409924i
$469$	14.9781	+	13.2780i	0.691622	+	0.613123i
$470$	9.03982	+	4.64715i	0.416976	+	0.214357i
$471$	−3.87013	−	1.79310i	−0.178326	−	0.0826218i
$472$	11.5997	+	14.6456i	0.533921	+	0.674118i
$473$	−22.5947	+	13.0450i	−1.03890	+	0.599812i
$474$	0.00848779	+	0.0108896i	0.000389857	+	0.000500177i
$475$	−0.462661			−0.0212283
$476$	12.2535	+	27.4834i	0.561640	+	1.25970i
$477$	8.88892	−	1.61245i	0.406996	−	0.0738289i
$478$	19.0846	−	12.2961i	0.872908	−	0.562409i
$479$	6.21288	+	10.7610i	0.283874	+	0.491684i	0.972335	−	0.233589i	$-0.0750470\pi$
$479$	6.21288	+	10.7610i	0.283874	+	0.491684i	−0.688462	+	0.725273i	$0.741714\pi$
$480$	−19.2585	−	3.70586i	−0.879028	−	0.169148i
$481$	0.676597	−	1.17190i	0.0308502	−	0.0534340i
$482$	9.16393	+	4.71095i	0.417405	+	0.214578i
$483$	5.97311	−	2.60758i	0.271786	−	0.118649i
$484$	−4.47901	−	6.25926i	−0.203591	−	0.284512i
$485$	−4.17643	+	7.23379i	−0.189642	+	0.328470i
$486$	−10.5183	−	19.3743i	−0.477121	−	0.878838i
$487$	13.8846	−	8.01628i	0.629172	−	0.363252i	−0.151260	−	0.988494i	$-0.548333\pi$
$487$	13.8846	−	8.01628i	0.629172	−	0.363252i	0.780431	+	0.625242i	$0.215000\pi$
$488$	10.2347	−	25.8240i	0.463305	−	1.16900i
$489$	−16.6775	+	1.50040i	−0.754183	+	0.0678506i
$490$	−12.6518	−	15.2503i	−0.571548	−	0.688937i
$491$		−	9.44091i		−	0.426062i	−0.977045	−	0.213031i	$-0.931666\pi$
$491$		−	9.44091i		−	0.426062i	0.977045	−	0.213031i	$-0.0683336\pi$
$492$	−5.43526	−	28.6894i	−0.245041	−	1.29342i
$493$	−45.5956	+	26.3247i	−2.05352	+	1.18560i
$494$	−1.35457	+	0.0660937i	−0.0609452	+	0.00297370i
$495$	−21.7821	−	7.80701i	−0.979034	−	0.350899i
$496$	−21.8454	−	7.44797i	−0.980886	−	0.334424i
$497$	−35.2449	+	11.7538i	−1.58095	+	0.527231i
$498$	7.88121	−	19.4424i	0.353165	−	0.871235i
$499$	15.9322	−	27.5954i	0.713225	−	1.23534i	−0.250415	−	0.968139i	$-0.580567\pi$
$499$	15.9322	−	27.5954i	0.713225	−	1.23534i	0.963640	−	0.267203i	$-0.0860995\pi$
$500$	9.91683	−	21.8482i	0.443494	−	0.977080i
$501$	−12.6992	−	18.0417i	−0.567357	−	0.806046i
$502$	17.1168	+	26.5668i	0.763961	+	1.18574i
$503$	5.16274			0.230195			0.115098	−	0.993354i	$-0.463282\pi$
$503$	5.16274			0.230195			0.115098	+	0.993354i	$0.463282\pi$
$504$	−22.2776	+	2.77675i	−0.992321	+	0.123686i
$505$	21.1248			0.940043
$506$	−4.19771	−	6.51521i	−0.186611	−	0.289636i
$507$	8.73281	+	12.4067i	0.387838	+	0.551002i
$508$	−32.4925	−	14.7483i	−1.44162	−	0.654348i
$509$	−1.78554	+	3.09264i	−0.0791426	+	0.137079i	−0.902880	−	0.429892i	$-0.858552\pi$
$509$	−1.78554	+	3.09264i	−0.0791426	+	0.137079i	0.823738	+	0.566971i	$0.191885\pi$
$510$	10.4744	−	25.8395i	0.463813	−	1.14419i
$511$	8.00290	+	7.09458i	0.354028	+	0.313846i
$512$	9.61311	+	20.4839i	0.424843	+	0.905267i
$513$	0.609041	−	2.34191i	0.0268898	−	0.103398i
$514$	4.27261	−	0.208473i	0.188457	−	0.00919536i
$515$	18.4297	−	10.6404i	0.812109	−	0.468871i
$516$	23.0446	−	4.36584i	1.01448	−	0.192196i
$517$		−	13.8363i		−	0.608522i
$518$	2.29180	−	0.890608i	0.100696	−	0.0391311i
$519$	−20.2698	+	1.82358i	−0.889743	+	0.0800464i
$520$	4.29543	−	10.8381i	0.188367	−	0.475282i
$521$	−5.95306	+	3.43700i	−0.260808	+	0.150578i	−0.624703	−	0.780862i	$-0.714780\pi$
$521$	−5.95306	+	3.43700i	−0.260808	+	0.150578i	0.363895	+	0.931440i	$0.381447\pi$
$522$	−8.88612	−	38.2613i	−0.388935	−	1.67465i
$523$	−6.59397	+	11.4211i	−0.288334	+	0.499410i	−0.973412	−	0.229060i	$-0.926435\pi$
$523$	−6.59397	+	11.4211i	−0.288334	+	0.499410i	0.685078	+	0.728470i	$0.259768\pi$
$524$	−3.95889	+	2.83291i	−0.172945	+	0.123756i
$525$	0.508768	−	4.52424i	0.0222045	−	0.197454i
$526$	−27.0301	−	13.8955i	−1.17857	−	0.605873i
$527$	16.4063	−	28.4165i	0.714668	−	1.23784i
$528$	7.49939	+	25.6219i	0.326369	+	1.11505i
$529$	10.4886	+	18.1668i	0.456027	+	0.789863i
$530$	−7.16573	+	4.61683i	−0.311259	+	0.200542i
$531$	−3.53691	−	19.4979i	−0.153489	−	0.846137i
$532$	−1.99434	−	1.44739i	−0.0864656	−	0.0627522i
$533$	17.3578			0.751850
$534$	14.1541	+	18.1593i	0.612507	+	0.785831i
$535$	−9.73934	+	5.62301i	−0.421069	+	0.243104i
$536$	−16.7742	+	13.2857i	−0.724536	+	0.573854i
$537$	−16.1497	−	7.48245i	−0.696910	−	0.322892i
$538$	−27.5157	−	14.1451i	−1.18629	−	0.609840i
$539$	−10.5888	+	24.8082i	−0.456091	+	1.06857i
$540$	16.1679	+	13.0882i	0.695757	+	0.563226i
$541$	−2.61534	−	1.50996i	−0.112442	−	0.0649185i	0.442724	−	0.896658i	$-0.354012\pi$
$541$	−2.61534	−	1.50996i	−0.112442	−	0.0649185i	−0.555166	+	0.831739i	$0.687345\pi$
$542$	14.7337	−	0.718900i	0.632865	−	0.0308794i
$543$	−6.74689	+	4.74898i	−0.289537	+	0.203798i
$544$	−31.2178	+	7.76444i	−1.33845	+	0.332897i
$545$			21.1493i			0.905936i
$546$	0.843255	−	13.3187i	0.0360880	−	0.569988i
$547$	−8.67520			−0.370925			−0.185462	−	0.982651i	$-0.559378\pi$
$547$	−8.67520			−0.370925			−0.185462	+	0.982651i	$0.559378\pi$
$548$	0.605945	+	6.19456i	0.0258847	+	0.264619i
$549$	−22.4768	+	19.0493i	−0.959286	+	0.813005i
$550$	−5.40757	+	0.263852i	−0.230580	+	0.0112507i
$551$	2.15575	−	3.73388i	0.0918382	−	0.159068i
$552$	1.62902	+	6.77437i	0.0693355	+	0.288336i
$553$	−0.0146106	−	0.00298771i	−0.000621308	−	0.000127050i
$554$	14.0152	−	27.2630i	0.595450	−	1.15829i
$555$	−2.06714	−	0.957744i	−0.0877451	−	0.0406539i
$556$	6.57577	−	14.4874i	0.278875	−	0.614401i
$557$	3.73163	+	6.46337i	0.158114	+	0.273862i	0.934189	−	0.356780i	$-0.116125\pi$
$557$	3.73163	+	6.46337i	0.158114	+	0.273862i	−0.776075	+	0.630641i	$0.782792\pi$
$558$	16.7189	+	17.8818i	0.707766	+	0.756996i
$559$			13.9425i			0.589707i
$560$	18.4157	−	10.4686i	0.778204	−	0.442381i
$561$	−37.8017	+	3.40086i	−1.59599	+	0.143584i
$562$	6.39589	+	9.92698i	0.269794	+	0.418744i
$563$	35.8665	−	20.7076i	1.51159	−	0.872720i	0.511687	−	0.859172i	$-0.329021\pi$
$563$	35.8665	−	20.7076i	1.51159	−	0.872720i	0.999908	−	0.0135474i	$-0.00431242\pi$
$564$	−4.10548	+	11.7416i	−0.172872	+	0.494410i
$565$	27.5801	+	15.9234i	1.16030	+	0.669901i
$566$	−28.6766	−	14.7419i	−1.20537	−	0.619649i
$567$	22.2311	+	8.53094i	0.933620	+	0.358266i
$568$	−5.78864	−	39.2943i	−0.242886	−	1.64875i
$569$	29.0674	+	16.7821i	1.21857	+	0.703541i	0.964612	−	0.263674i	$-0.0849343\pi$
$569$	29.0674	+	16.7821i	1.21857	+	0.703541i	0.253958	+	0.967215i	$0.418268\pi$
$570$	0.315174	+	2.26141i	0.0132012	+	0.0947201i
$571$	11.7720	+	20.3898i	0.492645	+	0.853286i	0.999964	−	0.00847253i	$-0.00269692\pi$
$571$	11.7720	+	20.3898i	0.492645	+	0.853286i	−0.507319	+	0.861758i	$0.669364\pi$
$572$	−15.7946	+	1.54501i	−0.660404	+	0.0645999i
$573$	−4.12282	+	0.370912i	−0.172233	+	0.0154951i
$574$	24.5924	+	19.7470i	1.02647	+	0.824226i
$575$	−1.41297			−0.0589251
$576$	1.23844	−	23.9680i	0.0516016	−	0.998668i
$577$	11.5230	+	19.9584i	0.479708	+	0.830879i	0.999729	−	0.0232743i	$-0.00740910\pi$
$577$	11.5230	+	19.9584i	0.479708	+	0.830879i	−0.520021	+	0.854154i	$0.674076\pi$
$578$	−1.05717	−	21.6665i	−0.0439726	−	0.901208i
$579$	4.63284	−	9.99925i	0.192534	−	0.415554i
$580$	21.5685	+	30.1412i	0.895582	+	1.25154i
$581$	7.16873	+	21.4961i	0.297409	+	0.891809i
$582$	−9.47310	−	3.84004i	−0.392673	−	0.159175i
$583$	10.0491	+	5.80186i	0.416192	+	0.240289i
$584$	−8.96262	+	7.09865i	−0.370876	+	0.293744i
$585$	−9.43331	+	7.99483i	−0.390019	+	0.330546i
$586$	7.74891	−	4.99257i	0.320105	−	0.206241i
$587$		−	35.2560i		−	1.45517i	−0.686017	−	0.727585i	$-0.740642\pi$
$587$		−	35.2560i		−	1.45517i	0.686017	−	0.727585i	$-0.259358\pi$
$588$	16.3467	−	17.9105i	0.674126	−	0.738616i
$589$			2.68705i			0.110718i
$590$	10.1270	+	15.7181i	0.416924	+	0.647103i
$591$	−16.8535	−	23.9438i	−0.693260	−	0.984916i
$592$	0.509367	+	2.57871i	0.0209348	+	0.105984i
$593$	−15.9344	−	9.19971i	−0.654346	−	0.377787i	0.135773	−	0.990740i	$-0.456648\pi$
$593$	−15.9344	−	9.19971i	−0.654346	−	0.377787i	−0.790119	+	0.612953i	$0.789981\pi$
$594$	5.78289	−	27.7195i	0.237275	−	1.13734i
$595$	9.52745	+	28.5690i	0.390587	+	1.17121i
$596$	−12.2833	−	17.1655i	−0.503145	−	0.703126i
$597$	−20.4102	−	9.45642i	−0.835333	−	0.387025i
$598$	−4.13690	+	0.201851i	−0.169170	+	0.00825432i
$599$	−3.46929	−	6.00898i	−0.141751	−	0.245520i	0.786405	−	0.617711i	$-0.211940\pi$
$599$	−3.46929	−	6.00898i	−0.141751	−	0.245520i	−0.928156	+	0.372191i	$0.878607\pi$
$600$	4.66718	+	1.38061i	0.190537	+	0.0563633i
$601$	17.3861			0.709194			0.354597	−	0.935019i	$-0.384618\pi$
$601$	17.3861			0.709194			0.354597	+	0.935019i	$0.384618\pi$
$602$	−15.8617	+	19.7537i	−0.646474	+	0.805099i
$603$	22.3318	−	4.05098i	0.909421	−	0.164969i
$604$	3.42825	+	35.0470i	0.139494	+	1.42604i
$605$	−3.85150	−	6.67099i	−0.156586	−	0.271214i
$606$	3.56845	+	25.6041i	0.144958	+	1.04009i
$607$	−21.1329	−	12.2011i	−0.857757	−	0.495226i	0.00550324	−	0.999985i	$-0.498248\pi$
$607$	−21.1329	−	12.2011i	−0.857757	−	0.495226i	−0.863261	+	0.504758i	$0.831582\pi$
$608$	1.89604	−	1.82888i	0.0768947	−	0.0741710i
$609$	34.1420	+	25.1865i	1.38350	+	1.02061i
$610$	12.7105	−	24.7250i	0.514634	−	1.00109i
$611$	−6.40352	−	3.69707i	−0.259059	−	0.149568i
$612$	33.0878	+	8.33043i	1.33749	+	0.336738i
$613$	7.71712	−	4.45548i	0.311692	−	0.179955i	−0.335992	−	0.941865i	$-0.609071\pi$
$613$	7.71712	−	4.45548i	0.311692	−	0.179955i	0.647683	+	0.761910i	$0.275738\pi$
$614$	−15.1667	+	9.77183i	−0.612080	+	0.394359i
$615$	−2.61854	−	29.1059i	−0.105590	−	1.17366i
$616$	−24.1353	−	15.7797i	−0.972437	−	0.635782i
$617$			43.3713i			1.74606i	0.487664	+	0.873031i	$0.337849\pi$
$617$			43.3713i			1.74606i	−0.487664	+	0.873031i	$0.662151\pi$
$618$	16.0097	+	20.5400i	0.644004	+	0.826241i
$619$	−18.4061	−	31.8804i	−0.739806	−	1.28138i	−0.952583	−	0.304280i	$-0.901584\pi$
$619$	−18.4061	−	31.8804i	−0.739806	−	1.28138i	0.212777	−	0.977101i	$-0.431749\pi$
$620$	−21.0336	−	9.54709i	−0.844729	−	0.383420i
$621$	1.86002	−	7.15222i	0.0746401	−	0.287009i
$622$	11.8824	+	6.10847i	0.476442	+	0.244927i
$623$	−24.3644	−	4.98225i	−0.976141	−	0.199610i
$624$	13.8618	+	3.37542i	0.554914	+	0.135125i
$625$	9.52276	−	16.4939i	0.380910	−	0.659756i
$626$	−0.396477	−	8.12569i	−0.0158464	−	0.324768i
$627$	2.54164	−	1.78900i	0.101503	−	0.0714457i
$628$	0.479488	+	4.90179i	0.0191336	+	0.195603i
$629$	−3.73693			−0.149001
$630$	−22.4603	+	0.595226i	−0.894840	+	0.0237144i
$631$		−	23.1113i		−	0.920045i	−0.887907	−	0.460023i	$-0.847841\pi$
$631$		−	23.1113i		−	0.920045i	0.887907	−	0.460023i	$-0.152159\pi$
$632$	0.00587399	−	0.0148211i	0.000233655	−	0.000589551i
$633$	−4.33576	−	6.15983i	−0.172331	−	0.244831i
$634$	0.922193	+	18.9001i	0.0366250	+	0.750620i
$635$	−30.9275	−	17.8560i	−1.22732	−	0.708593i
$636$	−6.80621	−	7.90523i	−0.269884	−	0.313463i
$637$	8.65203	+	11.5293i	0.342806	+	0.456807i
$638$	23.0670	−	44.8709i	0.913233	−	1.77646i
$639$	−14.2138	+	39.6575i	−0.562288	+	1.56882i
$640$	7.57941	+	21.3398i	0.299603	+	0.843528i
$641$	−12.0471	+	6.95538i	−0.475831	+	0.274721i	−0.718677	−	0.695344i	$-0.755252\pi$
$641$	−12.0471	+	6.95538i	−0.475831	+	0.274721i	0.242847	+	0.970065i	$0.421919\pi$
$642$	−8.46048	−	10.8546i	−0.333908	−	0.428396i
$643$	13.6551			0.538505			0.269252	−	0.963070i	$-0.413223\pi$
$643$	13.6551			0.538505			0.269252	+	0.963070i	$0.413223\pi$
$644$	−6.09075	−	4.42034i	−0.240009	−	0.174186i
$645$	23.3792	−	2.10332i	0.920554	−	0.0828183i
$646$	2.02844	+	3.14832i	0.0798081	+	0.123869i
$647$	15.7948	+	27.3574i	0.620958	+	1.07553i	0.989308	+	0.145843i	$0.0465895\pi$
$647$	15.7948	+	27.3574i	0.620958	+	1.07553i	−0.368350	+	0.929687i	$0.620077\pi$
$648$	−13.1322	+	21.8070i	−0.515883	+	0.856659i
$649$	12.7264	−	22.0428i	0.499556	−	0.865256i
$650$	−1.32279	+	2.57315i	−0.0518842	+	0.100927i
$651$	−26.2760	−	2.95484i	−1.02984	−	0.115809i
$652$	11.2519	+	15.7241i	0.440659	+	0.615804i
$653$	−15.3505	+	26.5879i	−0.600713	+	1.04047i	0.392000	+	0.919965i	$0.371783\pi$
$653$	−15.3505	+	26.5879i	−0.600713	+	1.04047i	−0.992713	+	0.120500i	$0.961550\pi$
$654$	−25.6337	+	3.57258i	−1.00236	+	0.139699i
$655$	−4.21931	+	2.43602i	−0.164862	+	0.0951832i
$656$	−25.3794	+	22.1973i	−0.990897	+	0.866661i
$657$	11.9321	−	2.16447i	0.465514	−	0.0844442i
$658$	−4.86648	−	12.5229i	−0.189715	−	0.488194i
$659$		−	20.0419i		−	0.780720i	−0.920662	−	0.390360i	$-0.872351\pi$
$659$		−	20.0419i		−	0.780720i	0.920662	−	0.390360i	$-0.127649\pi$
$660$	4.97341	+	26.2516i	0.193590	+	1.02184i
$661$	27.8066	−	16.0541i	1.08155	−	0.624434i	0.150237	−	0.988650i	$-0.451996\pi$
$661$	27.8066	−	16.0541i	1.08155	−	0.624434i	0.931314	+	0.364216i	$0.118663\pi$
$662$	−0.309234	−	6.33767i	−0.0120187	−	0.246320i
$663$	−8.52669	+	18.4035i	−0.331149	+	0.714733i
$664$	−23.9659	+	3.53053i	−0.930056	+	0.137011i
$665$	−1.84546	−	1.63600i	−0.0715637	−	0.0634413i
$666$	0.811634	−	2.66723i	0.0314502	−	0.103353i
$667$	6.58371	−	11.4033i	0.254922	−	0.441538i
$668$	−10.5296	+	23.1982i	−0.407403	+	0.897567i
$669$	36.5159	−	25.7027i	1.41179	−	0.993724i
$670$	−18.0026	+	11.5990i	−0.695501	+	0.448107i
$671$	−37.8441			−1.46096
$672$	15.7992	+	20.5520i	0.609466	+	0.792812i
$673$	−39.5520			−1.52462			−0.762308	−	0.647214i	$-0.775934\pi$
$673$	−39.5520			−1.52462			−0.762308	+	0.647214i	$0.775934\pi$
$674$	−10.7307	+	6.91372i	−0.413331	+	0.266306i
$675$	−3.67714	−	3.62331i	−0.141533	−	0.139461i
$676$	7.24088	−	15.9527i	0.278495	−	0.613565i
$677$	20.5606	−	35.6119i	0.790206	−	1.36868i	−0.135633	−	0.990759i	$-0.543307\pi$
$677$	20.5606	−	35.6119i	0.790206	−	1.36868i	0.925839	−	0.377918i	$-0.123360\pi$
$678$	−14.6408	+	36.1178i	−0.562277	+	1.38710i
$679$	10.4738	−	3.49289i	0.401946	−	0.134045i
$680$	−31.8513	+	4.69218i	−1.22144	+	0.179937i
$681$	2.55795	+	1.18515i	0.0980210	+	0.0454150i
$682$	1.53240	+	31.4063i	0.0586788	+	1.20261i
$683$	1.63043	−	0.941329i	0.0623866	−	0.0360189i	−0.468482	−	0.883473i	$-0.655199\pi$
$683$	1.63043	−	0.941329i	0.0623866	−	0.0360189i	0.530869	+	0.847454i	$0.321866\pi$
$684$	−2.68767	+	0.764004i	−0.102766	+	0.0292124i
$685$			6.22919i			0.238005i
$686$	−0.858147	+	26.1775i	−0.0327642	+	0.999463i
$687$	2.18159	+	24.2491i	0.0832327	+	0.925159i
$688$	−17.8299	−	20.3858i	−0.679758	−	0.777202i
$689$	5.37025	−	3.10052i	0.204590	−	0.118120i
$690$	0.962547	+	6.90639i	0.0366435	+	0.262922i
$691$	4.71705	−	8.17016i	0.179445	−	0.310808i	−0.762246	−	0.647288i	$-0.775903\pi$
$691$	4.71705	−	8.17016i	0.179445	−	0.310808i	0.941691	+	0.336480i	$0.109237\pi$
$692$	13.6755	+	19.1110i	0.519865	+	0.726492i
$693$	14.6992	+	26.8213i	0.558377	+	1.01886i
$694$	−0.658517	+	1.28097i	−0.0249970	+	0.0486251i
$695$	7.96141	−	13.7896i	0.301993	−	0.523068i
$696$	−32.8887	+	31.2332i	−1.24664	+	1.18389i
$697$	−23.9674	−	41.5127i	−0.907829	−	1.57241i
$698$	−7.59229	−	11.7839i	−0.287372	−	0.446027i
$699$	−2.79254	−	31.0401i	−0.105624	−	1.17404i
$700$	−4.80145	+	2.14074i	−0.181478	+	0.0809124i
$701$	−23.3839			−0.883197			−0.441598	−	0.897213i	$-0.645588\pi$
$701$	−23.3839			−0.883197			−0.441598	+	0.897213i	$0.645588\pi$
$702$	−11.2835	−	10.0830i	−0.425869	−	0.380558i
$703$	0.265022	−	0.153011i	0.00999551	−	0.00577091i
$704$	21.1179	−	22.4573i	0.795912	−	0.846390i
$705$	−5.23332	+	11.2953i	−0.197098	+	0.425405i
$706$	−15.4085	+	29.9732i	−0.579905	+	1.12805i
$707$	−20.8946	−	18.5230i	−0.785821	−	0.696630i
$708$	−17.3402	+	14.9295i	−0.651683	+	0.561084i
$709$	−19.2646	−	11.1224i	−0.723496	−	0.417711i	0.0925419	−	0.995709i	$-0.470501\pi$
$709$	−19.2646	−	11.1224i	−0.723496	−	0.417711i	−0.816038	+	0.577998i	$0.803834\pi$
$710$	−1.93725	−	39.7035i	−0.0727037	−	1.49004i
$711$	−0.0129000	+	0.0109329i	−0.000483789	+	0.000410016i
$712$	9.79537	−	24.7154i	0.367097	−	0.926248i
$713$			8.20631i			0.307329i
$714$	−33.0172	+	16.3735i	−1.23564	+	0.612764i
$715$	−15.8829			−0.593985
$716$	2.00086	+	20.4547i	0.0747755	+	0.764429i
$717$	16.0043	+	22.7373i	0.597690	+	0.849141i
$718$	0.228898	+	4.69121i	0.00854240	+	0.175074i
$719$	−21.5877	+	37.3910i	−0.805086	+	1.39445i	0.111148	+	0.993804i	$0.464547\pi$
$719$	−21.5877	+	37.3910i	−0.805086	+	1.39445i	−0.916233	+	0.400645i	$0.868786\pi$
$720$	3.56884	−	23.7529i	0.133003	−	0.885219i
$721$	−27.5586	−	5.63543i	−1.02634	−	0.209874i
$722$	23.6245	+	12.1448i	0.879213	+	0.451982i
$723$	−5.30518	+	11.4504i	−0.197302	+	0.425844i
$724$	8.67522	+	3.93766i	0.322412	+	0.146342i
$725$	−4.59902	−	7.96574i	−0.170803	−	0.295840i
$726$	7.43487	−	5.79503i	0.275934	−	0.215074i
$727$		−	18.5349i		−	0.687423i	−0.939075	−	0.343712i	$-0.888316\pi$
$727$		−	18.5349i		−	0.687423i	0.939075	−	0.343712i	$-0.111684\pi$
$728$	−13.7518	+	6.95356i	−0.509677	+	0.257716i
$729$	23.1811	−	13.8433i	0.858558	−	0.512716i
$730$	−9.61894	+	6.19742i	−0.356013	+	0.229377i
$731$	33.3448	−	19.2516i	1.23330	−	0.712048i
$732$	32.1147	+	11.2290i	1.18699	+	0.415036i
$733$	7.89497	+	4.55816i	0.291607	+	0.168360i	0.638666	−	0.769484i	$-0.279486\pi$
$733$	7.89497	+	4.55816i	0.291607	+	0.168360i	−0.347059	+	0.937843i	$0.612820\pi$
$734$	−5.05269	+	9.82870i	−0.186498	+	0.362784i
$735$	18.0274	−	16.2472i	0.664949	−	0.599287i
$736$	5.79055	−	5.58544i	0.213442	−	0.205882i
$737$	25.2466	+	14.5761i	0.929970	+	0.536919i
$738$	34.8351	−	8.09039i	1.28230	−	0.297811i
$739$	−16.9014	−	29.2741i	−0.621728	−	1.07686i	−0.989164	−	0.146815i	$-0.953098\pi$
$739$	−16.9014	−	29.2741i	−0.621728	−	1.07686i	0.367436	−	0.930049i	$-0.380236\pi$
$740$	0.256107	+	2.61818i	0.00941468	+	0.0962461i
$741$	−0.148830	−	1.65430i	−0.00546742	−	0.0607723i
$742$	11.1358	+	1.71667i	0.408809	+	0.0630209i
$743$	−19.4548			−0.713726			−0.356863	−	0.934157i	$-0.616154\pi$
$743$	−19.4548			−0.713726			−0.356863	+	0.934157i	$0.616154\pi$
$744$	8.01837	−	27.1062i	0.293968	−	0.993760i
$745$	−10.5624	−	18.2947i	−0.386977	−	0.670264i
$746$	44.1766	−	2.15551i	1.61742	−	0.0789188i
$747$	24.1873	+	8.66907i	0.884969	+	0.317185i
$748$	25.5039	+	35.6408i	0.932515	+	1.30316i
$749$	14.5636	+	2.97810i	0.532143	+	0.108817i
$750$	27.2335	+	11.0394i	0.994425	+	0.403102i
$751$	10.6440	+	6.14534i	0.388407	+	0.224247i	0.681470	−	0.731847i	$-0.261341\pi$
$751$	10.6440	+	6.14534i	0.388407	+	0.224247i	−0.293063	+	0.956093i	$0.594675\pi$
$752$	14.0906	−	2.78329i	0.513833	−	0.101496i
$753$	−31.6516	+	22.2788i	−1.15345	+	0.811886i
$754$	−14.6029	−	22.6650i	−0.531807	−	0.825412i
$755$			35.2429i			1.28262i
$756$	−4.51547	−	27.1221i	−0.164226	−	0.986423i
$757$			10.4294i			0.379064i	0.981875	+	0.189532i	$0.0606970\pi$
$757$			10.4294i			0.379064i	−0.981875	+	0.189532i	$0.939303\pi$
$758$	22.7915	−	14.6844i	0.827824	−	0.533362i
$759$	7.76220	−	5.46363i	0.281750	−	0.198317i
$760$	2.06677	−	1.63694i	0.0749695	−	0.0593780i
$761$	−21.5087	−	12.4181i	−0.779691	−	0.450155i	0.0566301	−	0.998395i	$-0.481964\pi$
$761$	−21.5087	−	12.4181i	−0.779691	−	0.450155i	−0.836321	+	0.548241i	$0.815298\pi$
$762$	16.4177	−	40.5014i	0.594752	−	1.46721i
$763$	18.5445	−	20.9187i	0.671354	−	0.757308i
$764$	2.78157	+	3.88714i	0.100633	+	0.140632i
$765$	32.1457	+	11.5215i	1.16223	+	0.416559i
$766$	−1.92669	−	39.4870i	−0.0696140	−	1.42672i
$767$	−6.80100	−	11.7797i	−0.245570	−	0.425340i
$768$	−24.5842	+	12.7913i	−0.887106	+	0.461565i
$769$	0.929396			0.0335149			0.0167574	−	0.999860i	$-0.494666\pi$
$769$	0.929396			0.0335149			0.0167574	+	0.999860i	$0.494666\pi$
$770$	−22.5027	−	18.0691i	−0.810940	−	0.651164i
$771$	0.469442	+	5.21800i	0.0169065	+	0.187922i
$772$	−12.6648	+	1.23885i	−0.455815	+	0.0445873i
$773$	−15.9577	−	27.6396i	−0.573959	−	0.994127i	−0.996154	−	0.0876213i	$-0.972073\pi$
$773$	−15.9577	−	27.6396i	−0.573959	−	0.994127i	0.422195	−	0.906505i	$-0.361260\pi$
$774$	6.49856	+	27.9811i	0.233586	+	1.00576i
$775$	4.96447	+	2.86624i	0.178329	+	0.102958i
$776$	1.72021	+	11.6771i	0.0617520	+	0.419184i
$777$	1.20482	+	2.75984i	0.0432226	+	0.0990088i
$778$	18.2907	+	9.40280i	0.655753	+	0.337107i
$779$	3.39952	+	1.96271i	0.121800	+	0.0703215i
$780$	13.4782	+	4.71271i	0.482599	+	0.168742i
$781$	−46.8616	+	27.0555i	−1.67684	+	0.968123i
$782$	6.19490	+	9.61503i	0.221529	+	0.343833i
$783$	46.3752	−	12.7934i	1.65732	−	0.457200i
$784$	−27.3942	−	5.79300i	−0.978364	−	0.206893i
$785$			4.92919i			0.175930i
$786$	−3.66528	−	4.70245i	−0.130736	−	0.167731i
$787$	−3.93891	−	6.82240i	−0.140407	−	0.243192i	0.787243	−	0.616643i	$-0.211508\pi$
$787$	−3.93891	−	6.82240i	−0.140407	−	0.243192i	−0.927650	+	0.373451i	$0.878174\pi$
$788$	−13.9742	+	30.7872i	−0.497810	+	1.09675i
$789$	15.6482	−	33.7742i	0.557092	−	1.20239i
$790$	0.00729491	−	0.0141904i	0.000259541	−	0.000504870i
$791$	−13.3172	−	39.9330i	−0.473506	−	1.41985i
$792$	−30.9777	+	10.4624i	−1.10075	+	0.371766i
$793$	−10.1120	+	17.5144i	−0.359086	+	0.621956i
$794$	−50.9780	+	2.48737i	−1.80914	+	0.0882734i
$795$	−6.00916	−	8.53723i	−0.213123	−	0.302784i
$796$	2.52871	+	25.8509i	0.0896277	+	0.916262i
$797$	5.89418			0.208782			0.104391	−	0.994536i	$-0.466711\pi$
$797$	5.89418			0.208782			0.104391	+	0.994536i	$0.466711\pi$
$798$	1.67115	−	2.51311i	0.0591580	−	0.0889633i
$799$			20.4194i			0.722388i
$800$	−1.35648	−	5.45388i	−0.0479587	−	0.192824i
$801$	−21.5119	+	18.2315i	−0.760084	+	0.644180i
$802$	−4.33234	+	0.211388i	−0.152980	+	0.00746436i
$803$	13.4895	+	7.78815i	0.476033	+	0.274838i
$804$	−17.0994	−	19.8605i	−0.603048	−	0.700424i
$805$	−5.63606	−	4.99637i	−0.198645	−	0.176099i
$806$	14.9444	+	7.68255i	0.526394	+	0.270606i
$807$	15.9294	−	34.3810i	0.560740	−	1.21027i
$808$	23.4002	−	18.5337i	0.823218	−	0.652012i
$809$	35.6151	−	20.5624i	1.25216	−	0.722936i	0.280623	−	0.959818i	$-0.409459\pi$
$809$	35.6151	−	20.5624i	1.25216	−	0.722936i	0.971538	+	0.236882i	$0.0761256\pi$
$810$	−15.2052	+	20.4415i	−0.534256	+	0.718242i
$811$	17.5373			0.615819			0.307909	−	0.951416i	$-0.400371\pi$
$811$	17.5373			0.615819			0.307909	+	0.951416i	$0.400371\pi$
$812$	5.09551	−	48.7246i	0.178817	−	1.70990i
$813$	1.61882	+	17.9938i	0.0567746	+	0.631069i
$814$	3.01032	−	1.93953i	0.105512	−	0.0679804i
$815$	9.67551	+	16.7585i	0.338918	+	0.587024i
$816$	−11.0675	−	37.8123i	−0.387439	−	1.32370i
$817$	−1.57654	+	2.73064i	−0.0551561	+	0.0955331i
$818$	−34.2415	−	17.6027i	−1.19723	−	0.615464i
$819$	16.3406	+	0.363791i	0.570988	+	0.0127119i
$820$	−27.4421	+	19.6371i	−0.958320	+	0.685756i
$821$	−13.1411	+	22.7610i	−0.458626	+	0.794364i	−0.998889	−	0.0471324i	$-0.984992\pi$
$821$	−13.1411	+	22.7610i	−0.458626	+	0.794364i	0.540262	+	0.841497i	$0.318325\pi$
$822$	−7.54999	+	1.05225i	−0.263336	+	0.0367013i
$823$	10.8805	−	6.28189i	0.379272	−	0.218973i	−0.298229	−	0.954494i	$-0.596396\pi$
$823$	10.8805	−	6.28189i	0.379272	−	0.218973i	0.677502	+	0.735521i	$0.263063\pi$
$824$	11.0795	−	27.9556i	0.385974	−	0.973879i
$825$	−0.594143	−	6.60410i	−0.0206854	−	0.229925i
$826$	3.76552	−	24.4265i	0.131019	−	0.849906i
$827$			27.2104i			0.946197i	0.881010	+	0.473098i	$0.156864\pi$
$827$			27.2104i			0.946197i	−0.881010	+	0.473098i	$0.843136\pi$
$828$	−8.20819	+	2.33328i	−0.285254	+	0.0810871i
$829$	37.1390	−	21.4422i	1.28989	−	0.744718i	0.311255	−	0.950326i	$-0.399251\pi$
$829$	37.1390	−	21.4422i	1.28989	−	0.744718i	0.978634	+	0.205608i	$0.0659172\pi$
$830$	−24.2154	+	1.18154i	−0.840529	+	0.0410119i
$831$	34.0652	+	15.7831i	1.18171	+	0.547508i
$832$	−4.75060	−	15.7741i	−0.164698	−	0.546867i
$833$	15.6267	−	36.6115i	0.541434	−	1.26851i
$834$	18.0583	+	7.32014i	0.625307	+	0.253476i
$835$	−12.7484	+	22.0809i	−0.441177	+	0.764140i
$836$	−3.26806	−	1.48336i	−0.113028	−	0.0513032i
$837$	−21.0436	+	21.3562i	−0.727372	+	0.738178i
$838$	6.25469	+	9.70783i	0.216065	+	0.335351i
$839$	43.8842			1.51505			0.757526	−	0.652805i	$-0.226408\pi$
$839$	43.8842			1.51505			0.757526	+	0.652805i	$0.226408\pi$
$840$	13.7344	+	22.0104i	0.473883	+	0.759431i
$841$	56.7160			1.95572
$842$	5.59682	+	8.68675i	0.192879	+	0.299365i
$843$	−11.8270	+	8.32473i	−0.407342	+	0.286719i
$844$	−3.59503	+	7.92036i	−0.123746	+	0.272630i
$845$	8.76667	−	15.1843i	0.301583	−	0.522356i
$846$	−14.5743	−	4.43495i	−0.501075	−	0.152477i
$847$	−2.03986	+	9.97540i	−0.0700903	+	0.342759i
$848$	−3.88703	+	11.4009i	−0.133481	+	0.391509i
$849$	16.6014	−	35.8315i	0.569759	−	1.22973i
$850$	7.98040	−	0.389387i	0.273725	−	0.0133559i
$851$	0.809383	−	0.467298i	0.0277453	−	0.0160188i
$852$	47.7947	−	9.05480i	1.63742	−	0.310212i
$853$		−	45.0262i		−	1.54167i	−0.637036	−	0.770834i	$-0.719840\pi$
$853$		−	45.0262i		−	1.54167i	0.637036	−	0.770834i	$-0.280160\pi$
$854$	−34.2518	+	13.3104i	−1.17207	+	0.455474i
$855$	−2.75152	+	0.499124i	−0.0940999	+	0.0170697i
$856$	−5.85509	+	14.7734i	−0.200123	+	0.504944i
$857$	−2.63945	+	1.52389i	−0.0901621	+	0.0520551i	−0.544403	−	0.838824i	$-0.683244\pi$
$857$	−2.63945	+	1.52389i	−0.0901621	+	0.0520551i	0.454241	+	0.890879i	$0.349910\pi$
$858$	−2.68296	−	19.2506i	−0.0915948	−	0.657204i
$859$	−18.4182	+	31.9013i	−0.628421	+	1.08846i	0.359447	+	0.933165i	$0.382965\pi$
$859$	−18.4182	+	31.9013i	−0.628421	+	1.08846i	−0.987869	+	0.155292i	$0.950368\pi$
$860$	−15.7734	−	22.0427i	−0.537867	−	0.751650i
$861$	−22.9311	+	31.0847i	−0.781491	+	1.05936i
$862$	3.63399	+	1.86815i	0.123774	+	0.0636293i
$863$	23.1013	−	40.0125i	0.786376	−	1.36204i	−0.141798	−	0.989896i	$-0.545288\pi$
$863$	23.1013	−	40.0125i	0.786376	−	1.36204i	0.928174	−	0.372147i	$-0.121378\pi$
$864$	29.3922	+	0.313174i	0.999943	+	0.0106544i
$865$	11.7596	+	20.3682i	0.399837	+	0.692538i
$866$	27.4343	−	17.6757i	0.932256	−	0.600646i
$867$	26.4607	−	2.38055i	0.898651	−	0.0808478i
$868$	12.4331	+	27.8860i	0.422005	+	0.946513i
$869$	−0.0217198			−0.000736793
$870$	−35.8023	+	27.9057i	−1.21381	+	0.946092i
$871$	13.4918	−	7.78949i	0.457152	−	0.263937i
$872$	18.5551	+	23.4273i	0.628355	+	0.793349i
$873$	4.22391	−	11.7850i	0.142958	−	0.398863i
$874$	−0.833034	−	0.428242i	−0.0281778	−	0.0144855i
$875$	−30.1101	+	10.0414i	−1.01791	+	0.339462i
$876$	−9.13634	−	10.6116i	−0.308688	−	0.358533i
$877$	−20.3134	−	11.7280i	−0.685935	−	0.396025i	0.116152	−	0.993231i	$-0.462944\pi$
$877$	−20.3134	−	11.7280i	−0.685935	−	0.396025i	−0.802087	+	0.597207i	$0.796277\pi$
$878$	4.19470	−	0.204672i	0.141564	−	0.00690735i
$879$	6.49821	+	9.23203i	0.219179	+	0.311389i
$880$	23.2228	−	20.3112i	0.782840	−	0.684689i
$881$		−	16.7672i		−	0.564900i	−0.959282	−	0.282450i	$-0.908853\pi$
$881$		−	16.7672i		−	0.564900i	0.959282	−	0.282450i	$-0.0911471\pi$
$882$	22.7374	+	19.1053i	0.765607	+	0.643308i
$883$	−18.5641			−0.624731			−0.312365	−	0.949962i	$-0.601121\pi$
$883$	−18.5641			−0.624731			−0.312365	+	0.949962i	$0.601121\pi$
$884$	23.3093	−	2.28009i	0.783978	−	0.0766878i
$885$	−18.7265	+	13.1811i	−0.629483	+	0.443078i
$886$	27.7831	−	1.35562i	0.933390	−	0.0455429i
$887$	−19.6635	+	34.0581i	−0.660234	+	1.14356i	0.320320	+	0.947309i	$0.396210\pi$
$887$	−19.6635	+	34.0581i	−0.660234	+	1.14356i	−0.980554	+	0.196250i	$0.937124\pi$
$888$	−3.13006	+	0.752678i	−0.105038	+	0.0252582i
$889$	14.9335	+	44.7796i	0.500855	+	1.50186i
$890$	12.1649	−	23.6636i	0.407767	−	0.793205i
$891$	34.2109	+	5.68611i	1.14611	+	0.190492i
$892$	−46.9525	−	21.3116i	−1.57209	−	0.713565i
$893$	−0.836085	−	1.44814i	−0.0279785	−	0.0484602i
$894$	20.3895	−	15.8924i	0.681928	−	0.531521i
$895$			20.5691i			0.687548i
$896$	11.2147	−	27.7530i	0.374657	−	0.927164i
$897$	−0.454531	−	5.05226i	−0.0151763	−	0.168690i
$898$	−27.8227	−	43.1833i	−0.928456	−	1.44105i
$899$	−46.2636	+	26.7103i	−1.54298	+	0.890839i
$900$	−1.45536	+	5.78056i	−0.0485120	+	0.192685i
$901$	−14.8303	−	8.56229i	−0.494070	−	0.285251i
$902$	40.8528	+	21.0014i	1.36025	+	0.699272i
$903$	−24.9686	−	18.4193i	−0.830902	−	0.612956i
$904$	44.5210	−	6.55861i	1.48075	−	0.218136i
$905$	8.25737	+	4.76740i	0.274484	+	0.158474i
$906$	−42.7156	+	5.95330i	−1.41913	+	0.197785i
$907$	12.8800	+	22.3088i	0.427674	+	0.740753i	0.996666	−	0.0815902i	$-0.0259999\pi$
$907$	12.8800	+	22.3088i	0.427674	+	0.740753i	−0.568992	+	0.822343i	$0.692667\pi$
$908$	−0.316917	−	3.23983i	−0.0105172	−	0.107518i
$909$	−31.1531	+	5.65117i	−1.03328	+	0.187437i
$910$	−14.3752	+	5.58627i	−0.476532	+	0.185183i
$911$	0.887972			0.0294198			0.0147099	−	0.999892i	$-0.495318\pi$
$911$	0.887972			0.0294198			0.0147099	+	0.999892i	$0.495318\pi$
$912$	2.33315	+	2.22848i	0.0772583	+	0.0737922i
$913$	16.5014	+	28.5812i	0.546115	+	0.945899i
$914$	1.89716	+	38.8819i	0.0627525	+	1.28610i
$915$	30.8940	+	14.3138i	1.02133	+	0.473199i
$916$	22.8629	−	16.3603i	0.755410	−	0.540558i
$917$	6.30930	+	1.29018i	0.208352	+	0.0426055i
$918$	−8.53429	+	40.9079i	−0.281673	+	1.35016i
$919$	−37.8224	−	21.8368i	−1.24764	−	0.720328i	−0.277006	−	0.960868i	$-0.589342\pi$
$919$	−37.8224	−	21.8368i	−1.24764	−	0.720328i	−0.970639	+	0.240540i	$0.922675\pi$
$920$	6.31194	−	4.99924i	0.208098	−	0.164820i
$921$	−12.7188	−	18.0696i	−0.419098	−	0.595414i
$922$	23.0713	−	14.8647i	0.759812	−	0.489542i
$923$			28.9170i			0.951814i
$924$	18.0992	−	30.3263i	0.595419	−	0.997662i
$925$		−	0.652857i		−	0.0214658i
$926$	6.34063	+	9.84121i	0.208366	+	0.323402i
$927$	−24.3321	+	20.6217i	−0.799170	+	0.677305i
$928$	50.3357	+	14.4648i	1.65235	+	0.474831i
$929$	−10.6999	−	6.17761i	−0.351053	−	0.202681i	0.314096	−	0.949391i	$-0.398299\pi$
$929$	−10.6999	−	6.17761i	−0.351053	−	0.202681i	−0.665149	+	0.746711i	$0.731632\pi$
$930$	10.6278	−	26.2181i	0.348500	−	0.859725i
$931$	0.390836	+	3.23633i	0.0128091	+	0.106066i
$932$	−29.2657	+	20.9420i	−0.958628	+	0.685977i
$933$	−6.87897	+	14.8472i	−0.225207	+	0.486074i
$934$	22.2832	−	1.08726i	0.729128	−	0.0355763i
$935$	21.9308	+	37.9852i	0.717213	+	1.24225i
$936$	−3.43520	+	17.1322i	−0.112283	+	0.559983i
$937$	−60.8875			−1.98911			−0.994553	−	0.104228i	$-0.966763\pi$
$937$	−60.8875			−1.98911			−0.994553	+	0.104228i	$0.966763\pi$
$938$	27.9767	+	4.31282i	0.913472	+	0.140819i
$939$	9.92366	−	0.892790i	0.323847	−	0.0291351i
$940$	14.3063	−	1.39943i	0.466620	−	0.0456442i
$941$	−20.1874	−	34.9656i	−0.658090	−	1.13985i	−0.981109	−	0.193453i	$-0.938031\pi$
$941$	−20.1874	−	34.9656i	−0.658090	−	1.13985i	0.323019	−	0.946392i	$-0.395302\pi$
$942$	−5.97436	+	0.832649i	−0.194655	+	0.0271292i
$943$	10.3822	+	5.99416i	0.338091	+	0.195197i
$944$	25.0079	+	8.52623i	0.813939	+	0.277505i
$945$	−1.85508	−	27.4552i	−0.0603457	−	0.893118i
$946$	−16.8693	+	32.8148i	−0.548468	+	1.06690i
$947$	−49.1278	−	28.3640i	−1.59644	−	0.921705i	−0.992166	−	0.124928i	$-0.960130\pi$
$947$	−49.1278	−	28.3640i	−1.59644	−	0.921705i	−0.604273	−	0.796777i	$-0.706537\pi$
$948$	0.0184315	+	0.00644463i	0.000598627	+	0.000209312i
$949$	7.20878	−	4.16199i	0.234007	−	0.135104i
$950$	−0.550024	+	0.354377i	−0.0178451	+	0.0114975i
$951$	−23.0821	+	2.07660i	−0.748490	+	0.0673385i
$952$	35.6184	+	23.2874i	1.15440	+	0.754748i
$953$		−	57.3370i		−	1.85733i	−0.370922	−	0.928664i	$-0.620958\pi$
$953$		−	57.3370i		−	1.85733i	0.370922	−	0.928664i	$-0.379042\pi$
$954$	9.33234	−	8.72543i	0.302146	−	0.282496i
$955$	2.39187	+	4.14283i	0.0773990	+	0.134059i
$956$	13.2701	−	29.2358i	0.429185	−	0.945555i
$957$	56.0664	+	25.9766i	1.81237	+	0.839705i
$958$	15.6285	+	8.03423i	0.504934	+	0.259574i
$959$	5.46198	−	6.16128i	0.176376	−	0.198958i
$960$	−25.7336	+	10.3455i	−0.830549	+	0.333901i
$961$	1.14663	−	1.98602i	0.0369880	−	0.0640651i
$962$	−0.0932644	−	1.91143i	−0.00300696	−	0.0616270i
$963$	12.8585	−	10.8977i	0.414360	−	0.351175i
$964$	14.5027	−	1.41864i	0.467101	−	0.0456913i
$965$	−12.7356			−0.409972
$966$	5.10372	−	7.67509i	0.164209	−	0.246942i
$967$		−	8.50633i		−	0.273545i	−0.990602	−	0.136773i	$-0.956327\pi$
$967$		−	8.50633i		−	0.273545i	0.990602	−	0.136773i	$-0.0436729\pi$
$968$	−10.1191	−	4.01046i	−0.325240	−	0.128901i
$969$	−3.75090	+	2.64017i	−0.120496	+	0.0848146i
$970$	0.575694	+	11.7987i	0.0184844	+	0.378833i
$971$	19.5026	+	11.2598i	0.625867	+	0.361344i	0.779150	−	0.626838i	$-0.215651\pi$
$971$	19.5026	+	11.2598i	0.625867	+	0.361344i	−0.153283	+	0.988182i	$0.548985\pi$
$972$	−27.3443	−	14.9762i	−0.877070	−	0.480362i
$973$	−19.9658	+	6.65838i	−0.640074	+	0.213458i
$974$	10.3663	−	20.1650i	0.332158	−	0.646127i
$975$	−3.21516	−	1.48965i	−0.102968	−	0.0477068i
$976$	−7.61265	−	38.5397i	−0.243675	−	1.23362i
$977$	28.7960	−	16.6254i	0.921267	−	0.531894i	0.0372277	−	0.999307i	$-0.488147\pi$
$977$	28.7960	−	16.6254i	0.921267	−	0.531894i	0.884039	+	0.467413i	$0.154814\pi$
$978$	−18.6775	+	14.5579i	−0.597239	+	0.465511i
$979$	−36.2195			−1.15758
$980$	−26.7218	−	8.43928i	−0.853596	−	0.269583i
$981$	−5.65770	−	31.1891i	−0.180637	−	0.995793i
$982$	−7.23131	−	11.2236i	−0.230760	−	0.358160i
$983$	5.17748	+	8.96766i	0.165136	+	0.286024i	0.936704	−	0.350123i	$-0.113860\pi$
$983$	5.17748	+	8.96766i	0.165136	+	0.286024i	−0.771568	+	0.636147i	$0.780527\pi$
$984$	−28.4364	−	29.9436i	−0.906519	−	0.954569i
$985$	−16.9188	+	29.3043i	−0.539079	+	0.933712i
$986$	−34.0419	+	66.2197i	−1.08412	+	2.10886i
$987$	15.0804	−	6.58339i	0.480014	−	0.209552i
$988$	−1.55973	+	1.11612i	−0.0496217	+	0.0355084i
$989$	−4.81477	+	8.33943i	−0.153101	+	0.265178i
$990$	−31.8750	+	7.40293i	−1.01306	+	0.235280i
$991$	−49.0627	+	28.3264i	−1.55853	+	0.899817i	−0.561130	+	0.827728i	$0.689633\pi$
$991$	−49.0627	+	28.3264i	−1.55853	+	0.899817i	−0.997398	+	0.0720892i	$0.977033\pi$
$992$	−31.6752	+	7.87819i	−1.00569	+	0.250133i
$993$	7.74000	−	0.696335i	0.245621	−	0.0220975i
$994$	−32.8973	+	40.9693i	−1.04344	+	1.29947i
$995$			25.9954i			0.824111i
$996$	−5.52258	−	29.1503i	−0.174990	−	0.923664i
$997$	12.1911	−	7.03856i	0.386097	−	0.222913i	−0.294370	−	0.955691i	$-0.595110\pi$
$997$	12.1911	−	7.03856i	0.386097	−	0.222913i	0.680468	+	0.732778i	$0.261777\pi$
$998$	−2.19615	−	45.0096i	−0.0695180	−	1.42475i
$999$	3.30464	+	0.859413i	0.104554	+	0.0271906i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.v.a.107.24	yes	56
3.2	odd	2	inner	168.2.v.a.107.5	yes	56
4.3	odd	2		672.2.bd.a.527.10		56
7.4	even	3	inner	168.2.v.a.11.15	yes	56
8.3	odd	2	inner	168.2.v.a.107.14	yes	56
8.5	even	2		672.2.bd.a.527.9		56
12.11	even	2		672.2.bd.a.527.11		56
21.11	odd	6	inner	168.2.v.a.11.14	yes	56
24.5	odd	2		672.2.bd.a.527.12		56
24.11	even	2	inner	168.2.v.a.107.15	yes	56
28.11	odd	6		672.2.bd.a.431.12		56
56.11	odd	6	inner	168.2.v.a.11.5	✓	56
56.53	even	6		672.2.bd.a.431.11		56
84.11	even	6		672.2.bd.a.431.9		56
168.11	even	6	inner	168.2.v.a.11.24	yes	56
168.53	odd	6		672.2.bd.a.431.10		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.v.a.11.5	✓	56	56.11	odd	6	inner
168.2.v.a.11.14	yes	56	21.11	odd	6	inner
168.2.v.a.11.15	yes	56	7.4	even	3	inner
168.2.v.a.11.24	yes	56	168.11	even	6	inner
168.2.v.a.107.5	yes	56	3.2	odd	2	inner
168.2.v.a.107.14	yes	56	8.3	odd	2	inner
168.2.v.a.107.15	yes	56	24.11	even	2	inner
168.2.v.a.107.24	yes	56	1.1	even	1	trivial
672.2.bd.a.431.9		56	84.11	even	6
672.2.bd.a.431.10		56	168.53	odd	6
672.2.bd.a.431.11		56	56.53	even	6
672.2.bd.a.431.12		56	28.11	odd	6
672.2.bd.a.527.9		56	8.5	even	2
672.2.bd.a.527.10		56	4.3	odd	2
672.2.bd.a.527.11		56	12.11	even	2
672.2.bd.a.527.12		56	24.5	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.v (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.18883 - 0.765954i) q^{2} +(0.996948 + 1.41637i) q^{3} +(0.826627 - 1.82118i) q^{4} +(1.00081 - 1.73346i) q^{5} +(2.27007 + 0.920201i) q^{6} +(-2.50986 + 0.837013i) q^{7} +(-0.412221 - 2.79823i) q^{8} +(-1.01219 + 2.82409i) q^{9} +(-0.137955 - 2.82736i) q^{10} +(-3.33711 + 1.92668i) q^{11} +(3.40356 - 0.644811i) q^{12} +2.05924i q^{13} +(-2.34268 + 2.91751i) q^{14} +(3.45297 - 0.310649i) q^{15} +(-2.63337 - 3.01087i) q^{16} +(4.92484 - 2.84336i) q^{17} +(0.959801 + 4.13265i) q^{18} +(-0.232846 + 0.403301i) q^{19} +(-2.32964 - 3.25558i) q^{20} +(-3.68772 - 2.72043i) q^{21} +(-2.49150 + 4.84656i) q^{22} +(-0.711115 + 1.23169i) q^{23} +(3.55235 - 3.37354i) q^{24} +(0.496746 + 0.860389i) q^{25} +(1.57728 + 2.44808i) q^{26} +(-5.00905 + 1.38183i) q^{27} +(-0.550373 + 5.26280i) q^{28} -9.25829 q^{29} +(3.86705 - 3.01413i) q^{30} +(4.99699 - 2.88502i) q^{31} +(-5.43682 - 1.56236i) q^{32} +(-6.05580 - 2.80577i) q^{33} +(3.67691 - 7.15247i) q^{34} +(-1.06098 + 5.18844i) q^{35} +(4.30646 + 4.17785i) q^{36} +(-0.569094 - 0.328567i) q^{37} +(0.0320962 + 0.657805i) q^{38} +(-2.91663 + 2.05295i) q^{39} +(-5.26317 - 2.08593i) q^{40} -8.42924i q^{41} +(-6.46779 - 0.409499i) q^{42} +6.77074 q^{43} +(0.750281 + 7.67011i) q^{44} +(3.88243 + 4.58098i) q^{45} +(0.0980225 + 2.00895i) q^{46} +(-1.79536 + 3.10966i) q^{47} +(1.63916 - 6.73150i) q^{48} +(5.59882 - 4.20157i) q^{49} +(1.24956 + 0.642371i) q^{50} +(8.93705 + 4.14070i) q^{51} +(3.75023 + 1.70222i) q^{52} +(-1.50566 - 2.60789i) q^{53} +(-4.89648 + 5.47946i) q^{54} +7.71298i q^{55} +(3.37677 + 6.67813i) q^{56} +(-0.803357 + 0.0722746i) q^{57} +(-11.0065 + 7.09143i) q^{58} +(-5.72041 + 3.30268i) q^{59} +(2.28857 - 6.54527i) q^{60} +(8.50530 + 4.91054i) q^{61} +(3.73078 - 7.25726i) q^{62} +(0.176663 - 7.93529i) q^{63} +(-7.66015 + 2.30697i) q^{64} +(3.56960 + 2.06091i) q^{65} +(-9.34841 + 1.30289i) q^{66} +(-3.78271 - 6.55184i) q^{67} +(-1.10725 - 11.3194i) q^{68} +(-2.45347 + 0.220728i) q^{69} +(2.71279 + 6.98082i) q^{70} +14.0426 q^{71} +(8.31968 + 1.66819i) q^{72} +(-2.02113 - 3.50071i) q^{73} +(-0.928223 + 0.0452908i) q^{74} +(-0.723397 + 1.56134i) q^{75} +(0.542005 + 0.757433i) q^{76} +(6.76302 - 7.62890i) q^{77} +(-1.89491 + 4.67462i) q^{78} +(0.00488142 + 0.00281829i) q^{79} +(-7.85474 + 1.55153i) q^{80} +(-6.95094 - 5.71703i) q^{81} +(-6.45642 - 10.0209i) q^{82} -8.56466i q^{83} +(-8.00275 + 4.46721i) q^{84} -11.3827i q^{85} +(8.04925 - 5.18608i) q^{86} +(-9.23003 - 13.1131i) q^{87} +(6.76691 + 8.54376i) q^{88} +(8.14017 + 4.69973i) q^{89} +(8.12436 + 2.47223i) q^{90} +(-1.72361 - 5.16840i) q^{91} +(1.65529 + 2.31321i) q^{92} +(9.06798 + 4.20137i) q^{93} +(0.247479 + 5.07202i) q^{94} +(0.466070 + 0.807257i) q^{95} +(-3.20734 - 9.25813i) q^{96} -4.17304 q^{97} +(3.43782 - 9.28339i) q^{98} +(-2.06332 - 11.3744i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{3} - 2 q^{4} - 8 q^{6} - 2 q^{9} + 6 q^{10} + 10 q^{12} - 10 q^{16} - 10 q^{18} - 4 q^{19} - 20 q^{22} - 8 q^{24} - 16 q^{25} - 8 q^{27} - 22 q^{28} - 12 q^{30} - 14 q^{33} - 56 q^{34} + 4 q^{36}+ \cdots - 44 q^{99}+O(q^{100}) \) 56 * q - 2 * q^3 - 2 * q^4 - 8 * q^6 - 2 * q^9 + 6 * q^10 + 10 * q^12 - 10 * q^16 - 10 * q^18 - 4 * q^19 - 20 * q^22 - 8 * q^24 - 16 * q^25 - 8 * q^27 - 22 * q^28 - 12 * q^30 - 14 * q^33 - 56 * q^34 + 4 * q^36 + 14 * q^40 - 8 * q^42 - 16 * q^43 - 12 * q^46 + 64 * q^48 - 16 * q^49 - 34 * q^51 - 8 * q^52 + 32 * q^54 + 4 * q^57 - 18 * q^58 + 40 * q^60 + 4 * q^64 - 20 * q^66 - 36 * q^67 - 42 * q^70 + 22 * q^72 + 4 * q^73 + 104 * q^76 + 28 * q^78 - 10 * q^81 + 52 * q^82 + 4 * q^84 + 46 * q^88 + 140 * q^90 + 72 * q^91 - 46 * q^96 - 32 * q^97 - 44 * q^99

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