LMFDB - Embedded newform 403.2.s.a.160.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [403,2,Mod(160,403)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("403.160"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(403, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.s (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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$70$
Relative dimension:	$35$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			160.12
Character	$\chi$	$=$	403.160
Dual form			403.2.s.a.335.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00051 - 0.577645i) q^{2} +(-1.19453 - 2.06899i) q^{3} +(-0.332651 - 0.576169i) q^{4} +(-0.697454 + 0.402675i) q^{5} +2.76006i q^{6} +1.78753i q^{7} +3.07920i q^{8} +(-1.35381 + 2.34486i) q^{9} +0.930413 q^{10} +4.15768i q^{11} +(-0.794725 + 1.37650i) q^{12} +(3.09952 + 1.84201i) q^{13} +(1.03256 - 1.78845i) q^{14} +(1.66626 + 0.962015i) q^{15} +(1.11338 - 1.92844i) q^{16} -3.29333 q^{17} +(2.70900 - 1.56404i) q^{18} -4.27407i q^{19} +(0.464018 + 0.267901i) q^{20} +(3.69838 - 2.13526i) q^{21} +(2.40166 - 4.15980i) q^{22} +(2.71567 - 4.70367i) q^{23} +(6.37083 - 3.67820i) q^{24} +(-2.17571 + 3.76843i) q^{25} +(-2.03707 - 3.63337i) q^{26} -0.698529 q^{27} +(1.02992 - 0.594625i) q^{28} +(-3.67606 + 6.36712i) q^{29} +(-1.11141 - 1.92501i) q^{30} +(0.308265 + 5.55922i) q^{31} +(3.10543 - 1.79292i) q^{32} +(8.60218 - 4.96647i) q^{33} +(3.29502 + 1.90238i) q^{34} +(-0.719795 - 1.24672i) q^{35} +1.80138 q^{36} +(5.96911 - 3.44627i) q^{37} +(-2.46890 + 4.27625i) q^{38} +(0.108632 - 8.61320i) q^{39} +(-1.23992 - 2.14760i) q^{40} -0.791828i q^{41} -4.93370 q^{42} -3.52451 q^{43} +(2.39553 - 1.38306i) q^{44} -2.18058i q^{45} +(-5.43411 + 3.13738i) q^{46} +9.48670i q^{47} -5.31988 q^{48} +3.80473 q^{49} +(4.35364 - 2.51357i) q^{50} +(3.93399 + 6.81387i) q^{51} +(0.0302517 - 2.39859i) q^{52} +(3.99281 + 6.91575i) q^{53} +(0.698886 + 0.403502i) q^{54} +(-1.67419 - 2.89979i) q^{55} -5.50417 q^{56} +(-8.84300 + 5.10551i) q^{57} +(7.35588 - 4.24692i) q^{58} +11.8834i q^{59} -1.28006i q^{60} +(4.65484 + 8.06242i) q^{61} +(2.90284 - 5.74013i) q^{62} +(-4.19152 - 2.41997i) q^{63} -8.59622 q^{64} +(-2.90350 - 0.0366197i) q^{65} -11.4754 q^{66} -12.1744i q^{67} +(1.09553 + 1.89752i) q^{68} -12.9758 q^{69} +1.66314i q^{70} +(4.61425 + 2.66404i) q^{71} +(-7.22030 - 4.16864i) q^{72} +(-9.95825 + 5.74940i) q^{73} -7.96288 q^{74} +10.3958 q^{75} +(-2.46259 + 1.42178i) q^{76} -7.43198 q^{77} +(-5.08406 + 8.55485i) q^{78} +(7.63434 - 13.2231i) q^{79} +1.79333i q^{80} +(4.89583 + 8.47983i) q^{81} +(-0.457396 + 0.792232i) q^{82} +(-1.70911 + 0.986753i) q^{83} +(-2.46055 - 1.42060i) q^{84} +(2.29695 - 1.32614i) q^{85} +(3.52631 + 2.03592i) q^{86} +17.5647 q^{87} -12.8023 q^{88} +(0.339979 + 0.196287i) q^{89} +(-1.25960 + 2.18169i) q^{90} +(-3.29266 + 5.54049i) q^{91} -3.61348 q^{92} +(11.1337 - 7.27846i) q^{93} +(5.47995 - 9.49155i) q^{94} +(1.72106 + 2.98096i) q^{95} +(-7.41905 - 4.28339i) q^{96} +(1.20253 - 0.694280i) q^{97} +(-3.80667 - 2.19778i) q^{98} +(-9.74918 - 5.62869i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q - 6 q^{2} - 2 q^{3} + 30 q^{4} - 29 q^{9} + 2 q^{10} + 13 q^{12} + q^{13} - 14 q^{14} - 15 q^{15} - 28 q^{16} - 12 q^{17} - 3 q^{20} - 9 q^{21} + 4 q^{22} + 10 q^{23} + 18 q^{24} + 19 q^{25} + 6 q^{26}+ \cdots + 93 q^{99}+O(q^{100}) $ 70 * q - 6 * q^2 - 2 * q^3 + 30 * q^4 - 29 * q^9 + 2 * q^10 + 13 * q^12 + q^13 - 14 * q^14 - 15 * q^15 - 28 * q^16 - 12 * q^17 - 3 * q^20 - 9 * q^21 + 4 * q^22 + 10 * q^23 + 18 * q^24 + 19 * q^25 + 6 * q^26 + 34 * q^27 - 33 * q^28 - 18 * q^29 - 31 * q^30 - 2 * q^31 + 36 * q^32 - 12 * q^33 + 9 * q^34 - 12 * q^35 - 16 * q^36 - 18 * q^37 - 21 * q^38 - 30 * q^39 + 5 * q^40 + 98 * q^42 - 38 * q^43 + 42 * q^44 - 6 * q^46 + 54 * q^48 - 18 * q^49 - 51 * q^50 - 7 * q^51 + 41 * q^52 - 22 * q^53 + 18 * q^54 - 15 * q^55 - 50 * q^56 + 15 * q^57 - 12 * q^58 - 13 * q^61 - 23 * q^62 - 6 * q^63 - 38 * q^64 - 12 * q^65 - 52 * q^66 - 44 * q^68 + 32 * q^69 + 27 * q^71 - 15 * q^72 - 9 * q^73 + 38 * q^74 - 50 * q^75 + 126 * q^76 + 34 * q^77 + 14 * q^78 + 6 * q^79 - 11 * q^81 + 39 * q^82 - 54 * q^83 + 15 * q^84 - 33 * q^85 - 24 * q^86 + 28 * q^87 - 32 * q^88 - 6 * q^89 - 11 * q^90 - 70 * q^91 - 6 * q^92 + 14 * q^93 - 43 * q^94 + 25 * q^95 + 36 * q^96 - 75 * q^97 + 93 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.00051	−	0.577645i	−0.707468	−	0.408457i	0.102655	−	0.994717i	$-0.467266\pi$
$2$	−1.00051	−	0.577645i	−0.707468	−	0.408457i	−0.810123	+	0.586260i	$0.800600\pi$
$3$	−1.19453	−	2.06899i	−0.689663	−	1.19453i	−0.971947	−	0.235200i	$-0.924426\pi$
$3$	−1.19453	−	2.06899i	−0.689663	−	1.19453i	0.282284	−	0.959331i	$-0.408908\pi$
$4$	−0.332651	−	0.576169i	−0.166326	−	0.288085i
$5$	−0.697454	+	0.402675i	−0.311911	+	0.180082i	−0.647781	−	0.761826i	$-0.724303\pi$
$5$	−0.697454	+	0.402675i	−0.311911	+	0.180082i	0.335870	+	0.941908i	$0.390970\pi$
$6$			2.76006i			1.12679i
$7$			1.78753i			0.675624i	0.941214	+	0.337812i	$0.109687\pi$
$7$			1.78753i			0.675624i	−0.941214	+	0.337812i	$0.890313\pi$
$8$			3.07920i			1.08866i
$9$	−1.35381	+	2.34486i	−0.451269	+	0.781621i
$10$	0.930413			0.294223
$11$			4.15768i			1.25359i	0.779186	+	0.626793i	$0.215633\pi$
$11$			4.15768i			1.25359i	−0.779186	+	0.626793i	$0.784367\pi$
$12$	−0.794725	+	1.37650i	−0.229417	+	0.397362i
$13$	3.09952	+	1.84201i	0.859651	+	0.510882i
$13$	3.09952	+	1.84201i	0.859651	+	0.510882i
$14$	1.03256	−	1.78845i	0.275963	−	0.477983i
$15$	1.66626	+	0.962015i	0.430226	+	0.248391i
$16$	1.11338	−	1.92844i	0.278346	−	0.482109i
$17$	−3.29333			−0.798751			−0.399375	−	0.916788i	$-0.630773\pi$
$17$	−3.29333			−0.798751			−0.399375	+	0.916788i	$0.630773\pi$
$18$	2.70900	−	1.56404i	0.638517	−	0.368648i
$19$		−	4.27407i		−	0.980539i	−0.871571	−	0.490269i	$-0.836898\pi$
$19$		−	4.27407i		−	0.980539i	0.871571	−	0.490269i	$-0.163102\pi$
$20$	0.464018	+	0.267901i	0.103758	+	0.0599045i
$21$	3.69838	−	2.13526i	0.807053	−	0.465953i
$22$	2.40166	−	4.15980i	0.512036	−	0.886873i
$23$	2.71567	−	4.70367i	0.566255	−	0.980783i	−0.430676	−	0.902506i	$-0.641725\pi$
$23$	2.71567	−	4.70367i	0.566255	−	0.980783i	0.996932	−	0.0782765i	$-0.0249417\pi$
$24$	6.37083	−	3.67820i	1.30044	−	0.750809i
$25$	−2.17571	+	3.76843i	−0.435141	+	0.753687i
$26$	−2.03707	−	3.63337i	−0.399502	−	0.712563i
$27$	−0.698529			−0.134432
$28$	1.02992	−	0.594625i	0.194637	−	0.112374i
$29$	−3.67606	+	6.36712i	−0.682627	+	1.18235i	0.291549	+	0.956556i	$0.405829\pi$
$29$	−3.67606	+	6.36712i	−0.682627	+	1.18235i	−0.974176	+	0.225789i	$0.927504\pi$
$30$	−1.11141	−	1.92501i	−0.202914	−	0.351458i
$31$	0.308265	+	5.55922i	0.0553661	+	0.998466i
$31$	0.308265	+	5.55922i	0.0553661	+	0.998466i
$32$	3.10543	−	1.79292i	0.548967	−	0.316946i
$33$	8.60218	−	4.96647i	1.49745	−	0.864552i
$34$	3.29502	+	1.90238i	0.565091	+	0.326255i
$35$	−0.719795	−	1.24672i	−0.121668	−	0.210734i
$36$	1.80138			0.300231
$37$	5.96911	−	3.44627i	0.981315	−	0.566563i	0.0786484	−	0.996902i	$-0.474940\pi$
$37$	5.96911	−	3.44627i	0.981315	−	0.566563i	0.902667	+	0.430340i	$0.141606\pi$
$38$	−2.46890	+	4.27625i	−0.400508	+	0.693700i
$39$	0.108632	−	8.61320i	0.0173950	−	1.37922i
$40$	−1.23992	−	2.14760i	−0.196048	−	0.339565i
$41$		−	0.791828i		−	0.123663i	−0.998087	−	0.0618313i	$-0.980306\pi$
$41$		−	0.791828i		−	0.123663i	0.998087	−	0.0618313i	$-0.0196941\pi$
$42$	−4.93370			−0.761286
$43$	−3.52451			−0.537483			−0.268741	−	0.963212i	$-0.586608\pi$
$43$	−3.52451			−0.537483			−0.268741	+	0.963212i	$0.586608\pi$
$44$	2.39553	−	1.38306i	0.361139	−	0.208504i
$45$		−	2.18058i		−	0.325061i
$46$	−5.43411	+	3.13738i	−0.801215	+	0.462582i
$47$			9.48670i			1.38378i	0.722004	+	0.691889i	$0.243221\pi$
$47$			9.48670i			1.38378i	−0.722004	+	0.691889i	$0.756779\pi$
$48$	−5.31988			−0.767859
$49$	3.80473			0.543532
$50$	4.35364	−	2.51357i	0.615697	−	0.355473i
$51$	3.93399	+	6.81387i	0.550868	+	0.954132i
$52$	0.0302517	−	2.39859i	0.00419515	−	0.332625i
$53$	3.99281	+	6.91575i	0.548454	+	0.949951i	0.998381	+	0.0568851i	$0.0181169\pi$
$53$	3.99281	+	6.91575i	0.548454	+	0.949951i	−0.449926	+	0.893066i	$0.648550\pi$
$54$	0.698886	+	0.403502i	0.0951063	+	0.0549097i
$55$	−1.67419	−	2.89979i	−0.225748	−	0.391007i
$56$	−5.50417			−0.735526
$57$	−8.84300	+	5.10551i	−1.17128	+	0.676241i
$58$	7.35588	−	4.24692i	0.965874	−	0.557648i
$59$			11.8834i			1.54709i	0.633739	+	0.773547i	$0.281519\pi$
$59$			11.8834i			1.54709i	−0.633739	+	0.773547i	$0.718481\pi$
$60$		−	1.28006i		−	0.165255i
$61$	4.65484	+	8.06242i	0.595991	+	1.03229i	0.993406	+	0.114648i	$0.0365739\pi$
$61$	4.65484	+	8.06242i	0.595991	+	1.03229i	−0.397415	+	0.917639i	$0.630093\pi$
$62$	2.90284	−	5.74013i	0.368661	−	0.728998i
$63$	−4.19152	−	2.41997i	−0.528082	−	0.304888i
$64$	−8.59622			−1.07453
$65$	−2.90350	−	0.0366197i	−0.360135	−	0.00454211i
$66$	−11.4754			−1.41253
$67$		−	12.1744i		−	1.48734i	−0.668549	−	0.743668i	$-0.733084\pi$
$67$		−	12.1744i		−	1.48734i	0.668549	−	0.743668i	$-0.266916\pi$
$68$	1.09553	+	1.89752i	0.132853	+	0.230108i
$69$	−12.9758			−1.56210
$70$			1.66314i			0.198784i
$71$	4.61425	+	2.66404i	0.547610	+	0.316163i	0.748158	−	0.663521i	$-0.230939\pi$
$71$	4.61425	+	2.66404i	0.547610	+	0.316163i	−0.200547	+	0.979684i	$0.564272\pi$
$72$	−7.22030	−	4.16864i	−0.850921	−	0.491279i
$73$	−9.95825	+	5.74940i	−1.16552	+	0.672916i	−0.952622	−	0.304157i	$-0.901625\pi$
$73$	−9.95825	+	5.74940i	−1.16552	+	0.672916i	−0.212903	+	0.977073i	$0.568292\pi$
$74$	−7.96288			−0.925666
$75$	10.3958			1.20040
$76$	−2.46259	+	1.42178i	−0.282478	+	0.163089i
$77$	−7.43198			−0.846953
$78$	−5.08406	+	8.55485i	−0.575657	+	0.968646i
$79$	7.63434	−	13.2231i	0.858930	−	1.48771i	−0.0140206	−	0.999902i	$-0.504463\pi$
$79$	7.63434	−	13.2231i	0.858930	−	1.48771i	0.872951	−	0.487809i	$-0.162204\pi$
$80$			1.79333i			0.200500i
$81$	4.89583	+	8.47983i	0.543982	+	0.942204i
$82$	−0.457396	+	0.792232i	−0.0505109	+	0.0874874i
$83$	−1.70911	+	0.986753i	−0.187599	+	0.108310i	−0.590858	−	0.806776i	$-0.701211\pi$
$83$	−1.70911	+	0.986753i	−0.187599	+	0.108310i	0.403259	+	0.915086i	$0.367877\pi$
$84$	−2.46055	−	1.42060i	−0.268468	−	0.155000i
$85$	2.29695	−	1.32614i	0.249139	−	0.143840i
$86$	3.52631	+	2.03592i	0.380252	+	0.219539i
$87$	17.5647			1.88313
$88$	−12.8023			−1.36473
$89$	0.339979	+	0.196287i	0.0360377	+	0.0208064i	0.517911	−	0.855435i	$-0.326710\pi$
$89$	0.339979	+	0.196287i	0.0360377	+	0.0208064i	−0.481873	+	0.876241i	$0.660043\pi$
$90$	−1.25960	+	2.18169i	−0.132774	+	0.229970i
$91$	−3.29266	+	5.54049i	−0.345164	+	0.580801i
$92$	−3.61348			−0.376731
$93$	11.1337	−	7.27846i	1.15451	−	0.754741i
$94$	5.47995	−	9.49155i	0.565214	−	0.978979i
$95$	1.72106	+	2.98096i	0.176577	+	0.305841i
$96$	−7.41905	−	4.28339i	−0.757204	−	0.437172i
$97$	1.20253	−	0.694280i	0.122098	−	0.0704935i	−0.437707	−	0.899118i	$-0.644209\pi$
$97$	1.20253	−	0.694280i	0.122098	−	0.0704935i	0.559805	+	0.828624i	$0.310876\pi$
$98$	−3.80667	−	2.19778i	−0.384532	−	0.222010i
$99$	−9.74918	−	5.62869i	−0.979829	−	0.565705i
$100$	2.89501			0.289501
$101$	−5.32157	+	9.21723i	−0.529516	+	0.917149i	0.469891	+	0.882724i	$0.344293\pi$
$101$	−5.32157	+	9.21723i	−0.529516	+	0.917149i	−0.999407	+	0.0344246i	$0.989040\pi$
$102$		−	9.08980i		−	0.900024i
$103$	−6.24750	−	10.8210i	−0.615585	−	1.06622i	−0.990282	−	0.139077i	$-0.955587\pi$
$103$	−6.24750	−	10.8210i	−0.615585	−	1.06622i	0.374697	−	0.927147i	$-0.377747\pi$
$104$	−5.67192	+	9.54403i	−0.556178	+	0.935869i
$105$	−1.71963	+	2.97849i	−0.167819	+	0.290671i
$106$		−	9.22571i		−	0.896080i
$107$	−9.01688	−	15.6177i	−0.871695	−	1.50982i	−0.860242	−	0.509886i	$-0.829688\pi$
$107$	−9.01688	−	15.6177i	−0.871695	−	1.50982i	−0.0114528	−	0.999934i	$-0.503646\pi$
$108$	0.232367	+	0.402471i	0.0223595	+	0.0387278i
$109$			17.6586i			1.69139i	0.533670	+	0.845693i	$0.320812\pi$
$109$			17.6586i			1.69139i	−0.533670	+	0.845693i	$0.679188\pi$
$110$			3.86836i			0.368834i
$111$	−14.2606	−	8.23334i	−1.35355	−	0.781474i
$112$	3.44714	+	1.99021i	0.325724	+	0.188057i
$113$	1.33320	−	2.30917i	0.125417	−	0.217228i	−0.796479	−	0.604666i	$-0.793306\pi$
$113$	1.33320	−	2.30917i	0.125417	−	0.217228i	0.921896	+	0.387438i	$0.126640\pi$
$114$	11.7967			1.10486
$115$			4.37412i			0.407889i
$116$	4.89139			0.454154
$117$	−8.51541	+	4.77421i	−0.787250	+	0.441376i
$118$	6.86442	−	11.8895i	0.631921	−	1.09452i
$119$		−	5.88694i		−	0.539655i
$120$	−2.96224	+	5.13075i	−0.270414	+	0.468371i
$121$	−6.28628			−0.571480
$122$		−	10.7554i		−	0.973747i
$123$	−1.63828	+	0.945862i	−0.147719	+	0.0852855i
$124$	3.10051	−	2.02690i	0.278434	−	0.182021i
$125$		−	7.53116i		−	0.673607i
$126$	2.79577	+	4.84242i	0.249067	+	0.431397i
$127$	4.81309	+	8.33651i	0.427092	+	0.739746i	0.996613	−	0.0822313i	$-0.0262046\pi$
$127$	4.81309	+	8.33651i	0.427092	+	0.739746i	−0.569521	+	0.821977i	$0.692871\pi$
$128$	2.38976	+	1.37973i	0.211227	+	0.121952i
$129$	4.21014	+	7.29217i	0.370682	+	0.642040i
$130$	2.88383	+	1.71383i	0.252929	+	0.150313i
$131$	−7.42072	+	12.8531i	−0.648352	+	1.12298i	0.335165	+	0.942159i	$0.391208\pi$
$131$	−7.42072	+	12.8531i	−0.648352	+	1.12298i	−0.983516	+	0.180818i	$0.942125\pi$
$132$	−5.72306	−	3.30421i	−0.498128	−	0.287594i
$133$	7.64004			0.662475
$134$	−7.03247	+	12.1806i	−0.607513	+	1.05224i
$135$	0.487191	−	0.281280i	0.0419308	−	0.0242087i
$136$		−	10.1408i		−	0.869569i
$137$	−5.32822	−	3.07625i	−0.455221	−	0.262822i	0.254812	−	0.966991i	$-0.417986\pi$
$137$	−5.32822	−	3.07625i	−0.455221	−	0.262822i	−0.710033	+	0.704169i	$0.751320\pi$
$138$	12.9824	+	7.49540i	1.10514	+	0.638051i
$139$	−0.366141	−	0.634174i	−0.0310557	−	0.0537900i	0.850080	−	0.526654i	$-0.176554\pi$
$139$	−0.366141	−	0.634174i	−0.0310557	−	0.0537900i	−0.881136	+	0.472864i	$0.843220\pi$
$140$	−0.478882	+	0.829447i	−0.0404729	+	0.0701011i
$141$	19.6279	−	11.3322i	1.65296	−	0.954340i
$142$	−3.07774	−	5.33080i	−0.258278	−	0.447351i
$143$	−7.65849	+	12.8868i	−0.640435	+	1.07765i
$144$	3.01461	+	5.22146i	0.251218	+	0.435122i
$145$		−	5.92103i		−	0.491715i
$146$	13.2845			1.09943
$147$	−4.54486	−	7.87193i	−0.374854	−	0.649266i
$148$	−3.97127	−	2.29281i	−0.326436	−	0.188468i
$149$			11.6075i			0.950923i	0.879736	+	0.475462i	$0.157719\pi$
$149$			11.6075i			0.950923i	−0.879736	+	0.475462i	$0.842281\pi$
$150$	−10.4011	−	6.00508i	−0.849247	−	0.490313i
$151$		−	4.75455i		−	0.386920i	−0.981108	−	0.193460i	$-0.938029\pi$
$151$		−	4.75455i		−	0.386920i	0.981108	−	0.193460i	$-0.0619710\pi$
$152$	13.1607			1.06748
$153$	4.45854	−	7.72241i	0.360451	−	0.624320i
$154$	7.43578	+	4.29305i	0.599193	+	0.345944i
$155$	−2.45356	−	3.75317i	−0.197075	−	0.301462i
$156$	−4.99880	+	2.80260i	−0.400224	+	0.224388i
$157$	−5.47895			−0.437268			−0.218634	−	0.975807i	$-0.570160\pi$
$157$	−5.47895			−0.437268			−0.218634	+	0.975807i	$0.570160\pi$
$158$	−15.2765	+	8.81988i	−1.21533	+	0.701672i
$159$	9.53906	−	16.5221i	0.756497	−	1.31029i
$160$	−1.44393	+	2.50096i	−0.114152	+	0.197718i
$161$	8.40796	+	4.85434i	0.662640	+	0.382576i
$162$		−	11.3122i		−	0.888772i
$163$	6.30388	−	3.63955i	0.493758	−	0.285072i	−0.232374	−	0.972627i	$-0.574649\pi$
$163$	6.30388	−	3.63955i	0.493758	−	0.285072i	0.726132	+	0.687555i	$0.241316\pi$
$164$	−0.456227	+	0.263403i	−0.0356253	+	0.0205683i
$165$	−3.99975	+	6.92777i	−0.311380	+	0.539326i
$166$	2.27997			0.176960
$167$	6.15504	−	3.55361i	0.476291	−	0.274987i	−0.242579	−	0.970132i	$-0.577993\pi$
$167$	6.15504	−	3.55361i	0.476291	−	0.274987i	0.718869	+	0.695145i	$0.244660\pi$
$168$	6.57490	+	11.3881i	0.507265	+	0.878608i
$169$	6.21399	+	11.4187i	0.477999	+	0.878360i
$170$	−3.06416			−0.235010
$171$	10.0221	+	5.78626i	0.766409	+	0.442487i
$172$	1.17243	+	2.03071i	0.0893972	+	0.154841i
$173$	−9.99233	+	17.3072i	−0.759702	+	1.31584i	0.183300	+	0.983057i	$0.441322\pi$
$173$	−9.99233	+	17.3072i	−0.759702	+	1.31584i	−0.943002	+	0.332786i	$0.892011\pi$
$174$	−17.5736	−	10.1462i	−1.33225	−	0.769178i
$175$	−6.73620	−	3.88915i	−0.509209	−	0.293992i
$176$	8.01781	+	4.62909i	0.604365	+	0.348931i
$177$	24.5867	−	14.1951i	1.84805	−	1.06697i
$178$	−0.226768	−	0.392774i	−0.0169970	−	0.0294397i
$179$	−0.693681	−	1.20149i	−0.0518482	−	0.0898036i	0.838937	−	0.544229i	$-0.183178\pi$
$179$	−0.693681	−	1.20149i	−0.0518482	−	0.0898036i	−0.890785	+	0.454426i	$0.849845\pi$
$180$	−1.25638	+	0.725372i	−0.0936451	+	0.0540660i
$181$	6.89201	+	11.9373i	0.512279	+	0.887293i	0.999899	+	0.0142371i	$0.00453197\pi$
$181$	6.89201	+	11.9373i	0.512279	+	0.887293i	−0.487620	+	0.873056i	$0.662135\pi$
$182$	6.49477	−	3.64133i	0.481425	−	0.269913i
$183$	11.1207	−	19.2616i	0.822065	−	1.42386i
$184$	14.4835	+	8.36208i	1.06774	+	0.616460i
$185$	−2.77545	+	4.80722i	−0.204055	+	0.353434i
$186$	−15.3438	+	0.850831i	−1.12506	+	0.0623860i
$187$		−	13.6926i		−	1.00130i
$188$	5.46595	−	3.15577i	0.398645	−	0.230158i
$189$		−	1.24864i		−	0.0908254i
$190$		−	3.97665i		−	0.288497i
$191$	−2.79098	+	4.83411i	−0.201948	+	0.349784i	−0.949156	−	0.314806i	$-0.898060\pi$
$191$	−2.79098	+	4.83411i	−0.201948	+	0.349784i	0.747208	+	0.664590i	$0.231394\pi$
$192$	10.2684	+	17.7855i	0.741061	+	1.28356i
$193$	−5.04333	+	2.91177i	−0.363027	+	0.209594i	−0.670408	−	0.741993i	$-0.733881\pi$
$193$	−5.04333	+	2.91177i	−0.363027	+	0.209594i	0.307381	+	0.951587i	$0.400547\pi$
$194$	−1.60419			−0.115174
$195$	3.39255	+	6.05105i	0.242946	+	0.433325i
$196$	−1.26565	−	2.19217i	−0.0904034	−	0.156583i
$197$		−	1.96337i		−	0.139884i	−0.997551	−	0.0699422i	$-0.977719\pi$
$197$		−	1.96337i		−	0.139884i	0.997551	−	0.0699422i	$-0.0222815\pi$
$198$	6.50278	+	11.2631i	0.462132	+	0.800436i
$199$	6.70430	−	11.6122i	0.475255	−	0.823166i	−0.524343	−	0.851507i	$-0.675689\pi$
$199$	6.70430	−	11.6122i	0.475255	−	0.823166i	0.999598	+	0.0283407i	$0.00902234\pi$
$200$	−11.6038	−	6.69943i	−0.820510	−	0.473721i
$201$	−25.1886	+	14.5427i	−1.77667	+	1.02576i
$202$	10.6486	−	6.14796i	0.749232	−	0.432569i
$203$	−11.3814	−	6.57108i	−0.798821	−	0.461199i
$204$	2.61729	−	4.53328i	0.183247	−	0.317393i
$205$	0.318849	+	0.552263i	0.0222694	+	0.0385717i
$206$			14.4354i			1.00576i
$207$	7.35297	+	12.7357i	0.511067	+	0.885194i
$208$	7.00315	−	3.92635i	0.485581	−	0.272244i
$209$	17.7702			1.22919
$210$	3.44103	−	1.98668i	0.237453	−	0.137094i
$211$	3.16604	+	5.48374i	0.217959	+	0.377516i	0.954184	−	0.299221i	$-0.0967267\pi$
$211$	3.16604	+	5.48374i	0.217959	+	0.377516i	−0.736225	+	0.676737i	$0.763393\pi$
$212$	2.65643	−	4.60107i	0.182444	−	0.316003i
$213$		−	12.7291i		−	0.872183i
$214$			20.8342i			1.42420i
$215$	2.45818	−	1.41923i	0.167647	−	0.0967908i
$216$		−	2.15091i		−	0.146351i
$217$	−9.93730	+	0.551035i	−0.674588	+	0.0374067i
$218$	10.2004	−	17.6676i	0.690858	−	1.19660i
$219$	23.7909	+	13.7357i	1.60764	+	0.928170i
$220$	−1.11385	+	1.92924i	−0.0750954	+	0.130069i
$221$	−10.2077	−	6.06635i	−0.686647	−	0.408067i
$222$	9.51190	+	16.4751i	0.638397	+	1.10574i
$223$	−4.60240	+	2.65720i	−0.308200	+	0.177939i	−0.646121	−	0.763235i	$-0.723610\pi$
$223$	−4.60240	+	2.65720i	−0.308200	+	0.177939i	0.337921	+	0.941174i	$0.390276\pi$
$224$	3.20490	+	5.55105i	0.214137	+	0.370895i
$225$	−5.89097	−	10.2035i	−0.392731	−	0.680231i
$226$	−2.66776	+	1.54023i	−0.177457	+	0.102455i
$227$	8.80449	+	5.08328i	0.584375	+	0.337389i	0.762870	−	0.646552i	$-0.223790\pi$
$227$	8.80449	+	5.08328i	0.584375	+	0.337389i	−0.178495	+	0.983941i	$0.557123\pi$
$228$	5.88327	+	3.39671i	0.389629	+	0.224953i
$229$	−13.1834	−	7.61147i	−0.871187	−	0.502980i	−0.00344441	−	0.999994i	$-0.501096\pi$
$229$	−13.1834	−	7.61147i	−0.871187	−	0.502980i	−0.867742	+	0.497014i	$0.834430\pi$
$230$	2.52669	−	4.37636i	0.166605	−	0.288568i
$231$	8.87773	+	15.3767i	0.584112	+	1.01171i
$232$	−19.6056	−	11.3193i	−1.28717	−	0.743150i
$233$	1.97505			0.129390			0.0646948	−	0.997905i	$-0.479393\pi$
$233$	1.97505			0.129390			0.0646948	+	0.997905i	$0.479393\pi$
$234$	11.2776	+	0.142236i	0.737237	+	0.00929823i
$235$	−3.82006	−	6.61653i	−0.249193	−	0.431615i
$236$	6.84688	−	3.95305i	0.445694	−	0.257321i
$237$	−36.4778			−2.36949
$238$	−3.40056	+	5.88995i	−0.220426	+	0.381789i
$239$	−2.34584	+	1.35437i	−0.151740	+	0.0876069i	−0.573947	−	0.818892i	$-0.694589\pi$
$239$	−2.34584	+	1.35437i	−0.151740	+	0.0876069i	0.422208	+	0.906499i	$0.361255\pi$
$240$	3.71037	−	2.14218i	0.239503	−	0.138277i
$241$			1.72070i			0.110840i	0.998463	+	0.0554201i	$0.0176498\pi$
$241$			1.72070i			0.110840i	−0.998463	+	0.0554201i	$0.982350\pi$
$242$	6.28949	+	3.63124i	0.404304	+	0.233425i
$243$	10.6487	−	18.4440i	0.683112	−	1.18318i
$244$	3.09688	−	5.36395i	0.198257	−	0.343392i
$245$	−2.65362	+	1.53207i	−0.169534	+	0.0978802i
$246$	2.18549			0.139342
$247$	7.87288	−	13.2475i	0.500940	−	0.842921i
$248$	−17.1180	+	0.949211i	−1.08699	+	0.0602750i
$249$	4.08316	+	2.35741i	0.258760	+	0.149395i
$250$	−4.35034	+	7.53501i	−0.275140	+	0.476556i
$251$	−10.4358			−0.658701			−0.329351	−	0.944208i	$-0.606830\pi$
$251$	−10.4358			−0.658701			−0.329351	+	0.944208i	$0.606830\pi$
$252$			3.22003i			0.202843i
$253$	19.5563	+	11.2909i	1.22950	+	0.709850i
$254$		−	11.1210i		−	0.697795i
$255$	−5.48755	−	3.16824i	−0.343643	−	0.198403i
$256$	7.00223	+	12.1282i	0.437639	+	0.758014i
$257$	−3.22128			−0.200938			−0.100469	−	0.994940i	$-0.532034\pi$
$257$	−3.22128			−0.200938			−0.100469	+	0.994940i	$0.532034\pi$
$258$		−	9.72786i		−	0.605630i
$259$	6.16031	+	10.6700i	0.382783	+	0.663000i
$260$	0.944754	+	1.68509i	0.0585912	+	0.104505i
$261$	−9.95335	−	17.2397i	−0.616097	−	1.06711i
$262$	14.8490	−	8.57309i	0.917376	−	0.529648i
$263$	7.91526	−	13.7096i	0.488076	−	0.845372i	−0.511830	−	0.859087i	$-0.671032\pi$
$263$	7.91526	−	13.7096i	0.488076	−	0.845372i	0.999906	+	0.0137144i	$0.00436558\pi$
$264$	15.2928	+	26.4878i	0.941204	+	1.63021i
$265$	−5.56960	−	3.21561i	−0.342138	−	0.197533i
$266$	−7.64395	−	4.41323i	−0.468680	−	0.270593i
$267$		−	0.937883i		−	0.0573975i
$268$	−7.01450	+	4.04982i	−0.428479	+	0.247382i
$269$	4.71966	−	8.17469i	0.287763	−	0.498419i	−0.685513	−	0.728061i	$-0.740422\pi$
$269$	4.71966	−	8.17469i	0.287763	−	0.498419i	0.973275	+	0.229641i	$0.0737553\pi$
$270$	−0.649921			−0.0395529
$271$	−18.0783	−	10.4375i	−1.09818	−	0.634034i	−0.162437	−	0.986719i	$-0.551935\pi$
$271$	−18.0783	−	10.4375i	−1.09818	−	0.634034i	−0.935742	+	0.352685i	$0.885269\pi$
$272$	−3.66674	+	6.35098i	−0.222329	+	0.385085i
$273$	15.3964	+	0.194183i	0.931831	+	0.0117525i
$274$	3.55396	+	6.15565i	0.214703	+	0.371876i
$275$	−15.6679	−	9.04588i	−0.944812	−	0.545487i
$276$	4.31641	+	7.47625i	0.259818	+	0.450017i
$277$	4.42197	+	7.65907i	0.265690	+	0.460189i	0.967744	−	0.251935i	$-0.0810669\pi$
$277$	4.42197	+	7.65907i	0.265690	+	0.460189i	−0.702054	+	0.712124i	$0.747734\pi$
$278$			0.845998i			0.0507396i
$279$	−13.4529	−	6.80328i	−0.805407	−	0.407301i
$280$	3.83890	−	2.21639i	0.229418	−	0.132455i
$281$			12.6673i			0.755665i	0.925874	+	0.377833i	$0.123331\pi$
$281$			12.6673i			0.755665i	−0.925874	+	0.377833i	$0.876669\pi$
$282$	−26.1839			−1.55923
$283$	−5.29330	+	9.16827i	−0.314654	+	0.544997i	−0.979364	−	0.202105i	$-0.935222\pi$
$283$	−5.29330	+	9.16827i	−0.314654	+	0.544997i	0.664710	+	0.747102i	$0.268555\pi$
$284$		−	3.54478i		−	0.210344i
$285$	4.11172	−	7.12171i	0.243557	−	0.421854i
$286$	15.1064	−	8.46948i	0.893260	−	0.500811i
$287$	1.41542			0.0835495
$288$			9.70906i			0.572112i
$289$	−6.15396			−0.361998
$290$	−3.42026	+	5.92406i	−0.200844	+	0.347873i
$291$	−2.87291	−	1.65868i	−0.168413	−	0.0972334i
$292$	6.62525	+	3.82509i	0.387714	+	0.223847i
$293$		−	21.1530i		−	1.23577i	−0.786268	−	0.617886i	$-0.787989\pi$
$293$		−	21.1530i		−	1.23577i	0.786268	−	0.617886i	$-0.212011\pi$
$294$			10.5013i			0.612447i
$295$	−4.78517	−	8.28815i	−0.278603	−	0.482555i
$296$	10.6117	+	18.3801i	0.616795	+	1.06832i
$297$		−	2.90426i		−	0.168522i
$298$	6.70502	−	11.6134i	0.388411	−	0.672748i
$299$	17.0815	−	9.57681i	0.987846	−	0.553841i
$300$	−3.45817	−	5.98973i	−0.199658	−	0.345817i
$301$		−	6.30018i		−	0.363136i
$302$	−2.74645	+	4.75698i	−0.158040	+	0.273734i
$303$	25.4271			1.46075
$304$	−8.24227	−	4.75868i	−0.472727	−	0.272929i
$305$	−6.49307	−	3.74877i	−0.371792	−	0.214654i
$306$	−8.92163	+	5.15091i	−0.510016	+	0.294458i
$307$	14.6341	+	8.44898i	0.835210	+	0.482209i	0.855633	−	0.517583i	$-0.173168\pi$
$307$	14.6341	+	8.44898i	0.835210	+	0.482209i	−0.0204233	+	0.999791i	$0.506501\pi$
$308$	2.47226	+	4.28208i	0.140870	+	0.243994i
$309$	−14.9257	+	25.8520i	−0.849091	+	1.47067i
$310$	0.286814	+	5.17238i	0.0162900	+	0.293771i
$311$	−18.1949			−1.03174			−0.515870	−	0.856667i	$-0.672531\pi$
$311$	−18.1949			−1.03174			−0.515870	+	0.856667i	$0.672531\pi$
$312$	26.5218	+	0.334499i	1.50150	+	0.0189373i
$313$	11.7235	−	20.3056i	0.662649	−	1.14774i	−0.317268	−	0.948336i	$-0.602765\pi$
$313$	11.7235	−	20.3056i	0.662649	−	1.14774i	0.979917	−	0.199406i	$-0.0639013\pi$
$314$	5.48175	+	3.16489i	0.309353	+	0.178605i
$315$	3.89785			0.219619
$316$	−10.1583			−0.571449
$317$	−21.2080	−	12.2445i	−1.19116	−	0.687718i	−0.232592	−	0.972574i	$-0.574721\pi$
$317$	−21.2080	−	12.2445i	−1.19116	−	0.687718i	−0.958570	+	0.284857i	$0.908054\pi$
$318$	−19.0879	+	11.0204i	−1.07040	+	0.617993i
$319$	−26.4724	−	15.2839i	−1.48217	−	0.855733i
$320$	5.99546	−	3.46148i	0.335157	−	0.193503i
$321$	−21.5419	+	37.3116i	−1.20235	+	2.08253i
$322$	−5.60818	−	9.71365i	−0.312531	−	0.541320i
$323$			14.0759i			0.783206i
$324$	3.25721	−	5.64166i	0.180956	−	0.313426i
$325$	−13.6851	+	7.67264i	−0.759114	+	0.425602i
$326$	−8.40948			−0.465758
$327$	36.5354	−	21.0937i	2.02041	−	1.16649i
$328$	2.43820			0.134627
$329$	−16.9578			−0.934913
$330$	8.00359	−	4.62087i	0.440583	−	0.254371i
$331$	−0.591710	−	0.341624i	−0.0325233	−	0.0187773i	0.483650	−	0.875261i	$-0.339311\pi$
$331$	−0.591710	−	0.341624i	−0.0325233	−	0.0187773i	−0.516174	+	0.856484i	$0.672644\pi$
$332$	1.13707	+	0.656490i	0.0624050	+	0.0360296i
$333$			18.6623i			1.02269i
$334$	−8.21091			−0.449281
$335$	4.90231	+	8.49106i	0.267842	+	0.463916i
$336$		−	9.50946i		−	0.518784i
$337$	11.4119			0.621646			0.310823	−	0.950468i	$-0.399395\pi$
$337$	11.4119			0.621646			0.310823	+	0.950468i	$0.399395\pi$
$338$	0.378781	−	15.0140i	0.0206030	−	0.816654i
$339$	−6.37019			−0.345981
$340$	−1.52817	−	0.882287i	−0.0828764	−	0.0478487i
$341$	−23.1135	+	1.28167i	−1.25166	+	0.0694062i
$342$	−6.68482	−	11.5784i	−0.361474	−	0.626091i
$343$			19.3138i			1.04285i
$344$		−	10.8527i		−	0.585137i
$345$	9.05000	−	5.22502i	0.487236	−	0.281306i
$346$	19.9949	−	11.5440i	1.07493	−	0.620612i
$347$	−20.0183			−1.07464			−0.537318	−	0.843380i	$-0.680563\pi$
$347$	−20.0183			−1.07464			−0.537318	+	0.843380i	$0.680563\pi$
$348$	−5.84291	−	10.1202i	−0.313213	−	0.542501i
$349$	−30.5312	−	17.6272i	−1.63430	−	0.943563i	−0.982746	−	0.184959i	$-0.940785\pi$
$349$	−30.5312	−	17.6272i	−1.63430	−	0.943563i	−0.651553	−	0.758604i	$-0.725882\pi$
$350$	4.49309	+	7.78227i	0.240166	+	0.415980i
$351$	−2.16510	−	1.28670i	−0.115565	−	0.0686788i
$352$	7.45438	+	12.9114i	0.397320	+	0.688178i
$353$	17.3767	−	10.0325i	0.924870	−	0.533974i	0.0396843	−	0.999212i	$-0.487365\pi$
$353$	17.3767	−	10.0325i	0.924870	−	0.533974i	0.885185	+	0.465239i	$0.154031\pi$
$354$	−32.7990			−1.74325
$355$	−4.29096			−0.227741
$356$		−	0.261180i		−	0.0138425i
$357$	−12.1800	+	7.03213i	−0.644634	+	0.372180i
$358$			1.60281i			0.0847110i
$359$	31.2079	−	18.0179i	1.64709	−	0.950949i	0.668872	−	0.743378i	$-0.266778\pi$
$359$	31.2079	−	18.0179i	1.64709	−	0.950949i	0.978220	−	0.207571i	$-0.0665557\pi$
$360$	6.71443			0.353882
$361$	0.732330			0.0385437
$362$		−	15.9246i		−	0.836976i
$363$	7.50915	+	13.0062i	0.394128	+	0.682650i
$364$	4.28756	+	0.0540759i	0.224729	+	0.00283435i
$365$	4.63028	−	8.01987i	0.242360	−	0.419779i
$366$	−22.2528	+	12.8476i	−1.16317	+	0.671557i
$367$	13.6182			0.710864			0.355432	−	0.934702i	$-0.384334\pi$
$367$	13.6182			0.710864			0.355432	+	0.934702i	$0.384334\pi$
$368$	−6.04715	−	10.4740i	−0.315230	−	0.545994i
$369$	1.85673	+	1.07198i	0.0966573	+	0.0558051i
$370$	5.55374	−	3.20645i	0.288725	−	0.166696i
$371$	−12.3621	+	7.13728i	−0.641809	+	0.370549i
$372$	−7.89728	−	3.99372i	−0.409455	−	0.207065i
$373$	−15.6690	−	27.1395i	−0.811310	−	1.40523i	−0.911948	−	0.410306i	$-0.865422\pi$
$373$	−15.6690	−	27.1395i	−0.811310	−	1.40523i	0.100638	−	0.994923i	$-0.467912\pi$
$374$	−7.90948	+	13.6996i	−0.408989	+	0.708390i
$375$	−15.5819	+	8.99620i	−0.804645	+	0.464562i
$376$	−29.2115			−1.50647
$377$	−23.1223	+	12.9637i	−1.19086	+	0.667662i
$378$	−0.721273	+	1.24928i	−0.0370983	+	0.0642561i
$379$	−24.3101	+	14.0355i	−1.24873	+	0.720953i	−0.970856	−	0.239665i	$-0.922963\pi$
$379$	−24.3101	+	14.0355i	−1.24873	+	0.720953i	−0.277872	+	0.960618i	$0.589629\pi$
$380$	1.14503	−	1.98324i	0.0587386	−	0.101738i
$381$	11.4988	−	19.9164i	0.589099	−	1.02035i
$382$	5.58480	−	3.22439i	0.285743	−	0.164974i
$383$	17.2161	+	9.93970i	0.879700	+	0.507895i	0.870560	−	0.492063i	$-0.163757\pi$
$383$	17.2161	+	9.93970i	0.879700	+	0.507895i	0.00914056	+	0.999958i	$0.497090\pi$
$384$		−	6.59251i		−	0.336423i
$385$	5.18346	−	2.99267i	0.264174	−	0.152521i
$386$	6.72788			0.342440
$387$	4.77151	−	8.26449i	0.242549	−	0.420108i
$388$	−0.800046	−	0.461907i	−0.0406162	−	0.0234498i
$389$	1.16249	−	2.01349i	0.0589404	−	0.102088i	−0.835050	−	0.550175i	$-0.814561\pi$
$389$	1.16249	−	2.01349i	0.0589404	−	0.102088i	0.893990	+	0.448087i	$0.147894\pi$
$390$	0.101073	−	8.01384i	0.00511801	−	0.405796i
$391$	−8.94359	+	15.4908i	−0.452297	+	0.783401i
$392$			11.7155i			0.591723i
$393$	35.4571			1.78858
$394$	−1.13413	+	1.96437i	−0.0571368	+	0.0989638i
$395$			12.2966i			0.618710i
$396$			7.48957i			0.376365i
$397$			13.5053i			0.677813i	0.940820	+	0.338906i	$0.110057\pi$
$397$			13.5053i			0.677813i	−0.940820	+	0.338906i	$0.889943\pi$
$398$	−13.4155	+	7.74542i	−0.672456	+	0.388243i
$399$	−9.12626	−	15.8071i	−0.456885	−	0.791347i
$400$	4.84479	+	8.39142i	0.242239	+	0.419571i
$401$	13.3316	+	7.69701i	0.665749	+	0.384371i	0.794464	−	0.607311i	$-0.207752\pi$
$401$	13.3316	+	7.69701i	0.665749	+	0.384371i	−0.128715	+	0.991682i	$0.541085\pi$
$402$	33.6020			1.67592
$403$	−9.28468	+	17.7987i	−0.462503	+	0.886618i
$404$	7.08092			0.352289
$405$	−6.82923	−	3.94286i	−0.339347	−	0.195922i
$406$	7.59151	+	13.1489i	0.376760	+	0.652568i
$407$	14.3285	+	24.8176i	0.710235	+	1.23016i
$408$	−20.9813	+	12.1135i	−1.03873	+	0.599709i
$409$		−	4.11020i		−	0.203236i	−0.994823	−	0.101618i	$-0.967598\pi$
$409$		−	4.11020i		−	0.203236i	0.994823	−	0.101618i	$-0.0324020\pi$
$410$		−	0.736727i		−	0.0363844i
$411$			14.6987i			0.725033i
$412$	−4.15648	+	7.19924i	−0.204775	+	0.354681i
$413$	−21.2421			−1.04525
$414$		−	16.9896i		−	0.834995i
$415$	0.794682	−	1.37643i	0.0390094	−	0.0675662i
$416$	12.9279	+	0.163050i	0.633842	+	0.00799418i
$417$	−0.874733	+	1.51508i	−0.0428358	+	0.0741939i
$418$	−17.7793	−	10.2649i	−0.869613	−	0.502071i
$419$	17.0906	−	29.6017i	0.834928	−	1.44614i	−0.0591608	−	0.998248i	$-0.518842\pi$
$419$	17.0906	−	29.6017i	0.834928	−	1.44614i	0.894089	−	0.447889i	$-0.147824\pi$
$420$	2.28816			0.111651
$421$	−5.71395	+	3.29895i	−0.278481	+	0.160781i	−0.632735	−	0.774368i	$-0.718068\pi$
$421$	−5.71395	+	3.29895i	−0.278481	+	0.160781i	0.354255	+	0.935149i	$0.384735\pi$
$422$		−	7.31539i		−	0.356108i
$423$	−22.2450	−	12.8432i	−1.08159	−	0.624456i
$424$	−21.2950	+	12.2947i	−1.03417	+	0.597081i
$425$	7.16532	−	12.4107i	0.347569	−	0.602008i
$426$	−7.35290	+	12.7356i	−0.356249	+	0.617042i
$427$	−14.4118	+	8.32068i	−0.697438	+	0.402666i
$428$	−5.99896	+	10.3905i	−0.289971	+	0.502244i
$429$	35.8109	+	0.451656i	1.72897	+	0.0218062i
$430$	−3.27925			−0.158140
$431$	−3.05604	+	1.76440i	−0.147204	+	0.0849883i	−0.571793	−	0.820398i	$-0.693752\pi$
$431$	−3.05604	+	1.76440i	−0.147204	+	0.0849883i	0.424589	+	0.905386i	$0.360419\pi$
$432$	−0.777730	+	1.34707i	−0.0374186	+	0.0648108i
$433$	5.87116	+	10.1691i	0.282150	+	0.488698i	0.971914	−	0.235336i	$-0.0756191\pi$
$433$	5.87116	+	10.1691i	0.282150	+	0.488698i	−0.689764	+	0.724034i	$0.742286\pi$
$434$	10.2607	+	5.18892i	0.492528	+	0.249076i
$435$	−12.2505	+	7.07285i	−0.587368	+	0.339117i
$436$	10.1743	−	5.87416i	0.487262	−	0.281321i
$437$	−20.1038	−	11.6069i	−0.961696	−	0.555235i
$438$	−15.8687	−	27.4854i	−0.758235	−	1.31330i
$439$	−22.7233			−1.08452			−0.542262	−	0.840210i	$-0.682432\pi$
$439$	−22.7233			−1.08452			−0.542262	+	0.840210i	$0.682432\pi$
$440$	8.92902	−	5.15517i	0.425674	−	0.245763i
$441$	−5.15086	+	8.92156i	−0.245279	+	0.424836i
$442$	6.70875	+	11.9659i	0.319103	+	0.569160i
$443$	−6.37722	−	11.0457i	−0.302991	−	0.524796i	0.673821	−	0.738895i	$-0.264652\pi$
$443$	−6.37722	−	11.0457i	−0.302991	−	0.524796i	−0.976812	+	0.214099i	$0.931319\pi$
$444$			10.9553i			0.519917i
$445$	−0.316159			−0.0149874
$446$	6.13967			0.290722
$447$	24.0158	−	13.8655i	1.13591	−	0.655816i
$448$		−	15.3660i		−	0.725976i
$449$	27.7328	−	16.0115i	1.30879	−	0.755631i	0.326896	−	0.945060i	$-0.393997\pi$
$449$	27.7328	−	16.0115i	1.30879	−	0.755631i	0.981894	+	0.189429i	$0.0606638\pi$
$450$			13.6116i			0.641656i
$451$	3.29216			0.155022
$452$	−1.77396			−0.0834402
$453$	−9.83711	+	5.67946i	−0.462188	+	0.266844i
$454$	−5.87266	−	10.1717i	−0.275618	−	0.477384i
$455$	0.0654589	−	5.19010i	0.00306876	−	0.243316i
$456$	−15.7209	−	27.2294i	−0.736198	−	1.27513i
$457$	32.0699	+	18.5155i	1.50016	+	0.866121i	1.00000		0.000190303i	$6.05752e-5\pi$
$457$	32.0699	+	18.5155i	1.50016	+	0.866121i	0.500165	+	0.865930i	$0.333273\pi$
$458$	8.79346	+	15.2307i	0.410891	+	0.711685i
$459$	2.30049			0.107378
$460$	2.52023	−	1.45506i	0.117507	−	0.0678424i
$461$	−11.8564	+	6.84531i	−0.552209	+	0.318818i	−0.750012	−	0.661424i	$-0.769953\pi$
$461$	−11.8564	+	6.84531i	−0.552209	+	0.318818i	0.197803	+	0.980242i	$0.436619\pi$
$462$		−	20.5127i		−	0.954338i
$463$		−	32.7120i		−	1.52025i	−0.649774	−	0.760127i	$-0.725137\pi$
$463$		−	32.7120i		−	1.52025i	0.649774	−	0.760127i	$-0.274863\pi$
$464$	8.18573	+	14.1781i	0.380013	+	0.658202i
$465$	−4.83441	+	9.55966i	−0.224190	+	0.443319i
$466$	−1.97606	−	1.14088i	−0.0915390	−	0.0528501i
$467$	−29.9363			−1.38529			−0.692643	−	0.721281i	$-0.743554\pi$
$467$	−29.9363			−1.38529			−0.692643	+	0.721281i	$0.743554\pi$
$468$	5.58342	+	3.31817i	0.258093	+	0.153382i
$469$	21.7621			1.00488
$470$			8.82656i			0.407139i
$471$	6.54477	+	11.3359i	0.301567	+	0.522330i
$472$	−36.5915			−1.68426
$473$		−	14.6538i		−	0.673781i
$474$	36.4964	+	21.0712i	1.67634	+	0.967834i
$475$	16.1065	+	9.29912i	0.739019	+	0.426673i
$476$	−3.39187	+	1.95830i	−0.155466	+	0.0897585i
$477$	−21.6220			−0.990002
$478$	3.12938			0.143135
$479$	27.9636	−	16.1448i	1.27769	−	0.737675i	0.301267	−	0.953540i	$-0.402590\pi$
$479$	27.9636	−	16.1448i	1.27769	−	0.737675i	0.976423	+	0.215865i	$0.0692570\pi$
$480$	6.89926			0.314907
$481$	24.8494	+	0.313407i	1.13304	+	0.0142901i
$482$	0.993955	−	1.72158i	0.0452734	−	0.0784159i
$483$		−	23.1946i		−	1.05539i
$484$	2.09114	+	3.62196i	0.0950518	+	0.164635i
$485$	−0.559139	+	0.968456i	−0.0253892	+	0.0439753i
$486$	−21.3082	+	12.3023i	−0.966560	+	0.558043i
$487$	36.6106	+	21.1371i	1.65898	+	0.957815i	0.973185	+	0.230023i	$0.0738802\pi$
$487$	36.6106	+	21.1371i	1.65898	+	0.957815i	0.685798	+	0.727791i	$0.259453\pi$
$488$	−24.8258	+	14.3332i	−1.12381	+	0.648833i
$489$	−15.0604	−	8.69511i	−0.681053	−	0.393206i
$490$	3.53997			0.159919
$491$	10.6807			0.482015			0.241007	−	0.970523i	$-0.422522\pi$
$491$	10.6807			0.482015			0.241007	+	0.970523i	$0.422522\pi$
$492$	1.08995	+	0.629285i	0.0491389	+	0.0283704i
$493$	12.1065	−	20.9691i	0.545249	−	0.944399i
$494$	−15.5293	+	8.70658i	−0.698696	+	0.391728i
$495$	9.06613			0.407492
$496$	11.0638	+	5.59508i	0.496780	+	0.251226i
$497$	−4.76205	+	8.24812i	−0.213607	+	0.369979i
$498$	−2.72350	−	4.71724i	−0.122043	−	0.211384i
$499$	26.6187	+	15.3683i	1.19162	+	0.687981i	0.958673	−	0.284510i	$-0.0918308\pi$
$499$	26.6187	+	15.3683i	1.19162	+	0.687981i	0.232944	+	0.972490i	$0.425164\pi$
$500$	−4.33922	+	2.50525i	−0.194056	+	0.112038i
$501$	−14.7048	−	8.48980i	−0.656960	−	0.379296i
$502$	10.4411	+	6.02819i	0.466010	+	0.269051i
$503$	−23.2127			−1.03500			−0.517502	−	0.855682i	$-0.673138\pi$
$503$	−23.2127			−1.03500			−0.517502	+	0.855682i	$0.673138\pi$
$504$	7.45159	−	12.9065i	0.331920	−	0.574902i
$505$		−	8.57146i		−	0.381425i
$506$	−13.0442	−	22.5933i	−0.579887	−	1.00439i
$507$	16.2023	−	26.4966i	0.719570	−	1.17676i
$508$	3.20216	−	5.54630i	0.142073	−	0.246077i
$509$		−	24.1571i		−	1.07074i	−0.844617	−	0.535372i	$-0.820172\pi$
$509$		−	24.1571i		−	1.07074i	0.844617	−	0.535372i	$-0.179828\pi$
$510$	3.66023	+	6.33971i	0.162078	+	0.280727i
$511$	−10.2772	−	17.8007i	−0.454638	−	0.787456i
$512$		−	21.6981i		−	0.958931i
$513$			2.98556i			0.131816i
$514$	3.22292	+	1.86076i	0.142157	+	0.0820744i
$515$	8.71468	+	5.03143i	0.384015	+	0.221711i
$516$	2.80102	−	4.85150i	0.123308	−	0.213575i
$517$	−39.4426			−1.73469
$518$		−	14.2339i		−	0.625402i
$519$	47.7446			2.09575
$520$	0.112759	−	8.94046i	0.00494483	−	0.392065i
$521$	22.3223	−	38.6633i	0.977957	−	1.69387i	0.308145	−	0.951339i	$-0.400292\pi$
$521$	22.3223	−	38.6633i	0.977957	−	1.69387i	0.669811	−	0.742531i	$-0.266375\pi$
$522$			22.9980i			1.00660i
$523$	−17.3496	+	30.0503i	−0.758643	+	1.31401i	0.184899	+	0.982757i	$0.440804\pi$
$523$	−17.3496	+	30.0503i	−0.758643	+	1.31401i	−0.943543	+	0.331251i	$0.892529\pi$
$524$	9.87406			0.431350
$525$			18.5828i			0.811021i
$526$	−15.8386	+	9.14443i	−0.690596	+	0.398716i
$527$	−1.01522	−	18.3084i	−0.0442237	−	0.797525i
$528$		−	22.1183i		−	0.962577i
$529$	−3.24967	−	5.62860i	−0.141290	−	0.244722i
$530$	3.71496	+	6.43450i	0.161368	+	0.279497i
$531$	−27.8651	−	16.0879i	−1.20924	−	0.698155i
$532$	−2.54147	−	4.40196i	−0.110187	−	0.190849i
$533$	1.45855	−	2.45428i	0.0631770	−	0.106307i
$534$	−0.541764	+	0.938362i	−0.0234444	+	0.0406069i
$535$	12.5777	+	7.26175i	0.543782	+	0.313953i
$536$	37.4873			1.61921
$537$	−1.65725	+	2.87044i	−0.0715155	+	0.123868i
$538$	−9.44414	+	5.45258i	−0.407166	+	0.235077i
$539$			15.8188i			0.681365i
$540$	−0.324130	−	0.187136i	−0.0139483	−	0.00805307i
$541$	32.8108	+	18.9433i	1.41065	+	0.814437i	0.995449	−	0.0952944i	$-0.0303792\pi$
$541$	32.8108	+	18.9433i	1.41065	+	0.814437i	0.415197	+	0.909731i	$0.363713\pi$
$542$	12.0584	+	20.8857i	0.517951	+	0.897118i
$543$	16.4654	−	28.5190i	0.706599	−	1.22387i
$544$	−10.2272	+	5.90468i	−0.438488	+	0.253161i
$545$	−7.11067	−	12.3160i	−0.304588	−	0.527561i
$546$	−15.2921	−	9.08793i	−0.654440	−	0.388927i
$547$	16.1204	+	27.9213i	0.689258	+	1.19383i	0.972078	+	0.234657i	$0.0753968\pi$
$547$	16.1204	+	27.9213i	0.689258	+	1.19383i	−0.282820	+	0.959173i	$0.591270\pi$
$548$			4.09328i			0.174856i
$549$	−25.2070			−1.07581
$550$	10.4506	+	18.1010i	0.445616	+	0.771830i
$551$	27.2135	+	15.7117i	1.15934	+	0.669343i
$552$		−	39.9550i		−	1.70060i
$553$	23.6367	+	13.6466i	1.00513	+	0.580314i
$554$		−	10.2173i		−	0.434092i
$555$	13.2614			0.562917
$556$	−0.243595	+	0.421918i	−0.0103307	+	0.0178933i
$557$	17.6225	+	10.1743i	0.746688	+	0.431101i	0.824496	−	0.565868i	$-0.191459\pi$
$557$	17.6225	+	10.1743i	0.746688	+	0.431101i	−0.0778079	+	0.996968i	$0.524792\pi$
$558$	9.52994	+	14.5778i	0.403435	+	0.617127i
$559$	−10.9243	−	6.49219i	−0.462048	−	0.274590i
$560$	−3.20563			−0.135463
$561$	−28.3298	+	16.3562i	−1.19609	+	0.690561i
$562$	7.31718	−	12.6737i	0.308657	−	0.534609i
$563$	−3.94564	+	6.83405i	−0.166289	+	0.288021i	−0.937112	−	0.349028i	$-0.886512\pi$
$563$	−3.94564	+	6.83405i	−0.166289	+	0.288021i	0.770823	+	0.637049i	$0.219845\pi$
$564$	−13.0585	−	7.53932i	−0.549861	−	0.317463i
$565$			2.14738i			0.0903412i
$566$	10.5920	−	6.11531i	0.445216	−	0.257046i
$567$	−15.1580	+	8.75147i	−0.636575	+	0.367527i
$568$	−8.20310	+	14.2082i	−0.344195	+	0.596162i
$569$	4.46079			0.187006			0.0935030	−	0.995619i	$-0.470194\pi$
$569$	4.46079			0.187006			0.0935030	+	0.995619i	$0.470194\pi$
$570$	−8.22764	+	4.75023i	−0.344618	+	0.198965i
$571$	8.59401	+	14.8853i	0.359648	+	0.622929i	0.987902	−	0.155079i	$-0.0495634\pi$
$571$	8.59401	+	14.8853i	0.359648	+	0.622929i	−0.628254	+	0.778008i	$0.716230\pi$
$572$	9.97258	+	0.125777i	0.416974	+	0.00525899i
$573$	13.3356			0.557104
$574$	−1.41614	−	0.817610i	−0.0591086	−	0.0341264i
$575$	11.8170	+	20.4676i	0.492802	+	0.853558i
$576$	11.6376	−	20.1569i	0.484901	−	0.839873i
$577$	20.8834	+	12.0570i	0.869387	+	0.501941i	0.867145	−	0.498057i	$-0.165953\pi$
$577$	20.8834	+	12.0570i	0.869387	+	0.501941i	0.00224257	+	0.999997i	$0.499286\pi$
$578$	6.15711	+	3.55481i	0.256102	+	0.147860i
$579$	12.0488	+	6.95639i	0.500732	+	0.289098i
$580$	−3.41152	+	1.96964i	−0.141655	+	0.0817848i
$581$	−1.76385	−	3.05508i	−0.0731770	−	0.126746i
$582$	1.91626	+	3.31905i	0.0794314	+	0.137579i
$583$	−28.7534	+	16.6008i	−1.19085	+	0.687535i
$584$	−17.7035	−	30.6634i	−0.732578	−	1.26886i
$585$	4.01665	−	6.75873i	0.166068	−	0.279439i
$586$	−12.2189	+	21.1638i	−0.504760	+	0.874269i
$587$	−15.3518	−	8.86338i	−0.633638	−	0.365831i	0.148522	−	0.988909i	$-0.452548\pi$
$587$	−15.3518	−	8.86338i	−0.633638	−	0.365831i	−0.782159	+	0.623078i	$0.785882\pi$
$588$	−3.02371	+	5.23722i	−0.124696	+	0.215979i
$589$	23.7605	−	1.31755i	0.979035	−	0.0542886i
$590$			11.0565i			0.455190i
$591$	−4.06219	+	2.34531i	−0.167096	+	0.0964730i
$592$		−	15.3481i		−	0.630801i
$593$		−	16.5476i		−	0.679529i	−0.940511	−	0.339764i	$-0.889653\pi$
$593$		−	16.5476i		−	0.679529i	0.940511	−	0.339764i	$-0.110347\pi$
$594$	−1.67763	+	2.90574i	−0.0688340	+	0.119224i
$595$	2.37052	+	4.10587i	0.0971820	+	0.168324i
$596$	6.68789	−	3.86125i	0.273946	−	0.158163i
$597$	−32.0340			−1.31106
$598$	−22.6222	−	0.285317i	−0.925090	−	0.0116675i
$599$	−7.60083	−	13.1650i	−0.310561	−	0.537908i	0.667923	−	0.744231i	$-0.267184\pi$
$599$	−7.60083	−	13.1650i	−0.310561	−	0.537908i	−0.978484	+	0.206323i	$0.933850\pi$
$600$			32.0107i			1.30683i
$601$	6.56622	+	11.3730i	0.267842	+	0.463915i	0.968304	−	0.249774i	$-0.0803563\pi$
$601$	6.56622	+	11.3730i	0.267842	+	0.463915i	−0.700463	+	0.713689i	$0.747023\pi$
$602$	−3.63927	+	6.30340i	−0.148326	+	0.256907i
$603$	28.5472	+	16.4817i	1.16253	+	0.671189i
$604$	−2.73943	+	1.58161i	−0.111466	+	0.0643548i
$605$	4.38439	−	2.53133i	0.178251	−	0.102913i
$606$	−25.4401	−	14.6879i	−1.03343	−	0.596654i
$607$	−6.03163	+	10.4471i	−0.244816	+	0.424034i	−0.962080	−	0.272768i	$-0.912061\pi$
$607$	−6.03163	+	10.4471i	−0.244816	+	0.424034i	0.717264	+	0.696802i	$0.245394\pi$
$608$	−7.66306	−	13.2728i	−0.310778	−	0.538284i
$609$			31.3974i			1.27229i
$610$	4.33092	+	7.50138i	0.175354	+	0.303722i
$611$	−17.4746	+	29.4042i	−0.706947	+	1.18957i
$612$	−5.93256			−0.239809
$613$	6.15148	−	3.55156i	0.248456	−	0.143446i	−0.370601	−	0.928792i	$-0.620848\pi$
$613$	6.15148	−	3.55156i	0.248456	−	0.143446i	0.619057	+	0.785346i	$0.287515\pi$
$614$	−9.76103	−	16.9066i	−0.393923	−	0.682295i
$615$	0.761750	−	1.31939i	0.0307167	−	0.0532029i
$616$		−	22.8846i		−	0.922046i
$617$			12.4858i			0.502661i	0.967901	+	0.251330i	$0.0808681\pi$
$617$			12.4858i			0.502661i	−0.967901	+	0.251330i	$0.919132\pi$
$618$	29.8666	−	17.2435i	1.20141	−	0.693635i
$619$			2.47009i			0.0992814i	0.998767	+	0.0496407i	$0.0158076\pi$
$619$			2.47009i			0.0992814i	−0.998767	+	0.0496407i	$0.984192\pi$
$620$	−1.34628	+	2.66216i	−0.0540679	+	0.106915i
$621$	−1.89697	+	3.28565i	−0.0761228	+	0.131849i
$622$	18.2042	+	10.5102i	0.729923	+	0.421421i
$623$	−0.350869	+	0.607723i	−0.0140573	+	0.0243479i
$624$	−16.4891	−	9.79928i	−0.660090	−	0.392285i
$625$	−7.84592	−	13.5895i	−0.313837	−	0.543581i
$626$	−23.4589	+	13.5440i	−0.937607	+	0.541327i
$627$	−21.2270	−	36.7663i	−0.847727	−	1.46831i
$628$	1.82258	+	3.15680i	0.0727289	+	0.125970i
$629$	−19.6583	+	11.3497i	−0.783826	+	0.452542i
$630$	−3.89985	−	2.25158i	−0.155374	−	0.0897050i
$631$	−14.9543	−	8.63386i	−0.595321	−	0.343709i	0.171878	−	0.985118i	$-0.445017\pi$
$631$	−14.9543	−	8.63386i	−0.595321	−	0.343709i	−0.767199	+	0.641410i	$0.778350\pi$
$632$	40.7164	+	23.5077i	1.61961	+	0.935084i
$633$	7.56386	−	13.1010i	0.300636	−	0.520718i
$634$	14.1459	+	24.5014i	0.561806	+	0.973077i
$635$	−6.71381	−	3.87622i	−0.266429	−	0.153823i
$636$	−12.6927			−0.503300
$637$	11.7928	+	7.00835i	0.467248	+	0.277681i
$638$	17.6573	+	30.5834i	0.699060	+	1.21081i
$639$	−12.4936	+	7.21318i	−0.494239	+	0.285349i
$640$	−2.22233			−0.0878452
$641$	−0.647749	+	1.12193i	−0.0255845	+	0.0443137i	−0.878534	−	0.477679i	$-0.841478\pi$
$641$	−0.647749	+	1.12193i	−0.0255845	+	0.0443137i	0.852950	+	0.521993i	$0.174811\pi$
$642$	43.1058	−	24.8871i	1.70125	−	0.982217i
$643$	29.7065	−	17.1511i	1.17151	−	0.676372i	0.217476	−	0.976066i	$-0.430218\pi$
$643$	29.7065	−	17.1511i	1.17151	−	0.676372i	0.954036	+	0.299693i	$0.0968844\pi$
$644$		−	6.45921i		−	0.254529i
$645$	−5.87275	−	3.39063i	−0.231239	−	0.133506i
$646$	8.13090	−	14.0831i	0.319906	−	0.554093i
$647$	15.7672	−	27.3096i	0.619874	−	1.07365i	−0.369634	−	0.929177i	$-0.620517\pi$
$647$	15.7672	−	27.3096i	0.619874	−	1.07365i	0.989508	−	0.144476i	$-0.0461496\pi$
$648$	−26.1111	+	15.0753i	−1.02574	+	0.592212i
$649$	−49.4075			−1.93942
$650$	18.1242	+	0.228587i	0.710889	+	0.00896592i
$651$	13.0105	+	19.9019i	0.509921	+	0.780018i
$652$	−4.19399	−	2.42140i	−0.164249	−	0.0948295i
$653$	14.7589	−	25.5632i	0.577562	−	1.00037i	−0.418196	−	0.908357i	$-0.637337\pi$
$653$	14.7589	−	25.5632i	0.577562	−	1.00037i	0.995758	−	0.0920103i	$-0.0293293\pi$
$654$	−48.7388			−1.90584
$655$		−	11.9526i		−	0.467025i
$656$	−1.52699	−	0.881607i	−0.0596189	−	0.0344210i
$657$		−	31.1343i		−	1.21466i
$658$	16.9665	+	9.79559i	0.661422	+	0.381872i
$659$	1.09747	+	1.90088i	0.0427515	+	0.0740478i	0.886609	−	0.462519i	$-0.153054\pi$
$659$	1.09747	+	1.90088i	0.0427515	+	0.0740478i	−0.843858	+	0.536567i	$0.819721\pi$
$660$	5.32209			0.207162
$661$			14.3469i			0.558028i	0.960287	+	0.279014i	$0.0900077\pi$
$661$			14.3469i			0.558028i	−0.960287	+	0.279014i	$0.909992\pi$
$662$	0.394675	+	0.683597i	0.0153395	+	0.0265687i
$663$	−0.357761	+	28.3661i	−0.0138943	+	1.10165i
$664$	−3.03841	−	5.26268i	−0.117913	−	0.204232i
$665$	−5.32857	+	3.07645i	−0.206633	+	0.119300i
$666$	10.7802	−	18.6719i	0.417724	−	0.723520i
$667$	19.9659	+	34.5820i	0.773083	+	1.33902i
$668$	−4.09496	−	2.36423i	−0.158439	−	0.0914747i
$669$	10.9954	+	6.34821i	0.425107	+	0.245436i
$670$		−	11.3272i		−	0.437608i
$671$	−33.5209	+	19.3533i	−1.29406	+	0.747126i
$672$	7.65671	−	13.2618i	0.295364	−	0.511585i
$673$	−42.5477			−1.64009			−0.820047	−	0.572297i	$-0.806053\pi$
$673$	−42.5477			−1.64009			−0.820047	+	0.572297i	$0.806053\pi$
$674$	−11.4177	−	6.59203i	−0.439795	−	0.253915i
$675$	1.51979	−	2.63236i	0.0584969	−	0.101320i
$676$	4.51200	−	7.37875i	0.173538	−	0.283798i
$677$	11.5537	+	20.0117i	0.444046	+	0.769111i	0.997985	−	0.0634465i	$-0.0202092\pi$
$677$	11.5537	+	20.0117i	0.444046	+	0.769111i	−0.553939	+	0.832557i	$0.686876\pi$
$678$	6.37345	+	3.67971i	0.244771	+	0.141319i
$679$	1.24105	+	2.14956i	0.0476271	+	0.0824925i
$680$	4.08346	+	7.07276i	0.156593	+	0.271228i
$681$		−	24.2885i		−	0.930738i
$682$	23.8656	+	12.0691i	0.913862	+	0.462148i
$683$	−27.5003	+	15.8773i	−1.05227	+	0.607527i	−0.923283	−	0.384119i	$-0.874505\pi$
$683$	−27.5003	+	15.8773i	−1.05227	+	0.607527i	−0.128985	+	0.991647i	$0.541172\pi$
$684$		−	7.69924i		−	0.294388i
$685$	4.95492			0.189318
$686$	11.1565	−	19.3237i	0.425958	−	0.737781i
$687$			36.3685i			1.38755i
$688$	−3.92413	+	6.79679i	−0.149606	+	0.259125i
$689$	−0.363110	+	28.7903i	−0.0138334	+	1.09682i
$690$	−12.0728			−0.459605
$691$			1.47315i			0.0560412i	0.999607	+	0.0280206i	$0.00892040\pi$
$691$			1.47315i			0.0560412i	−0.999607	+	0.0280206i	$0.991080\pi$
$692$	13.2958			0.505432
$693$	10.0615	−	17.4270i	0.382204	−	0.661996i
$694$	20.0285	+	11.5635i	0.760271	+	0.438943i
$695$	0.510732	+	0.294871i	0.0193732	+	0.0111851i
$696$			54.0851i			2.05009i
$697$			2.60775i			0.0987756i
$698$	20.3646	+	35.2724i	0.770810	+	1.33508i
$699$	−2.35925	−	4.08635i	−0.0892352	−	0.154560i
$700$			5.17492i			0.195594i
$701$	25.5957	−	44.3331i	0.966737	−	1.67444i	0.261862	−	0.965105i	$-0.415663\pi$
$701$	25.5957	−	44.3331i	0.966737	−	1.67444i	0.704874	−	0.709332i	$-0.251003\pi$
$702$	1.42295	+	2.53802i	0.0537059	+	0.0957912i
$703$	−14.7296	−	25.5124i	−0.555537	−	0.962218i
$704$		−	35.7403i		−	1.34701i
$705$	−9.12635	+	15.8073i	−0.343718	+	0.595338i
$706$	−23.1808			−0.872421
$707$	−16.4761	−	9.51249i	−0.619648	−	0.357754i
$708$	−16.3576	−	9.44407i	−0.614757	−	0.354930i
$709$	−12.3780	+	7.14643i	−0.464865	+	0.268390i	−0.714088	−	0.700056i	$-0.753158\pi$
$709$	−12.3780	+	7.14643i	−0.464865	+	0.268390i	0.249223	+	0.968446i	$0.419825\pi$
$710$	4.29316	+	2.47866i	0.161119	+	0.0930223i
$711$	20.6708	+	35.8029i	0.775217	+	1.34272i
$712$	−0.604407	+	1.04686i	−0.0226511	+	0.0392328i
$713$	26.9859	+	13.6470i	1.01063	+	0.511085i
$714$	16.2483			0.608078
$715$	0.152253	−	12.0718i	0.00569393	−	0.451460i
$716$	−0.461508	+	0.799355i	−0.0172474	+	0.0298733i
$717$	5.60435	+	3.23567i	0.209298	+	0.120838i
$718$	−41.6318			−1.55369
$719$	35.8803			1.33811			0.669054	−	0.743214i	$-0.266699\pi$
$719$	35.8803			1.33811			0.669054	+	0.743214i	$0.266699\pi$
$720$	−4.20510	−	2.42782i	−0.156715	−	0.0904794i
$721$	19.3429	−	11.1676i	0.720366	−	0.415904i
$722$	−0.732704	−	0.423027i	−0.0272684	−	0.0157434i
$723$	3.56011	−	2.05543i	0.132402	−	0.0764423i
$724$	4.58527	−	7.94193i	0.170410	−	0.295159i
$725$	−15.9961	−	27.7060i	−0.594078	−	1.02897i
$726$		−	17.3505i		−	0.643938i
$727$	1.13943	−	1.97355i	0.0422590	−	0.0731948i	−0.844122	−	0.536151i	$-0.819878\pi$
$727$	1.13943	−	1.97355i	0.0422590	−	0.0731948i	0.886381	+	0.462956i	$0.153211\pi$
$728$	−17.0603	−	10.1387i	−0.632295	−	0.375767i
$729$	−21.5056			−0.796503
$730$	−9.26529	+	5.34932i	−0.342924	+	0.197987i
$731$	11.6074			0.429315
$732$	−14.7973			−0.546923
$733$	14.2618	−	8.23405i	0.526771	−	0.304131i	−0.212929	−	0.977068i	$-0.568300\pi$
$733$	14.2618	−	8.23405i	0.526771	−	0.304131i	0.739701	+	0.672936i	$0.234967\pi$
$734$	−13.6252	−	7.86649i	−0.502914	−	0.290357i
$735$	6.33966	+	3.66020i	0.233842	+	0.135009i
$736$		−	19.4759i		−	0.717890i
$737$	50.6171			1.86450
$738$	−1.23845	−	2.14506i	−0.0455880	−	0.0789607i
$739$		−	27.5362i		−	1.01294i	−0.862259	−	0.506468i	$-0.830951\pi$
$739$		−	27.5362i		−	1.01294i	0.862259	−	0.506468i	$-0.169049\pi$
$740$	3.69303			0.135759
$741$	−36.8134	−	0.464300i	−1.35237	−	0.0170565i
$742$	16.4913			0.605413
$743$	−9.02622	−	5.21129i	−0.331140	−	0.191184i	0.325207	−	0.945643i	$-0.394566\pi$
$743$	−9.02622	−	5.21129i	−0.331140	−	0.191184i	−0.656347	+	0.754459i	$0.727899\pi$
$744$	22.4118	+	34.2830i	0.821658	+	1.25688i
$745$	−4.67405	−	8.09569i	−0.171244	−	0.296603i
$746$			36.2045i			1.32554i
$747$		−	5.34349i		−	0.195508i
$748$	−7.88926	+	4.55487i	−0.288460	+	0.166542i
$749$	27.9172	−	16.1180i	1.02007	−	0.588938i
$750$	20.7865			0.759014
$751$	6.87743	+	11.9121i	0.250961	+	0.434677i	0.963791	−	0.266660i	$-0.0859201\pi$
$751$	6.87743	+	11.9121i	0.250961	+	0.434677i	−0.712830	+	0.701337i	$0.752587\pi$
$752$	18.2945	+	10.5623i	0.667132	+	0.385169i
$753$	12.4659	+	21.5915i	0.454281	+	0.786839i
$754$	30.6225	+	0.386219i	1.11521	+	0.0140653i
$755$	1.91454	+	3.31608i	0.0696772	+	0.120684i
$756$	−0.719430	+	0.415363i	−0.0261654	+	0.0151066i
$757$	−21.3552			−0.776167			−0.388084	−	0.921624i	$-0.626863\pi$
$757$	−21.3552			−0.776167			−0.388084	+	0.921624i	$0.626863\pi$
$758$	32.4301			1.17791
$759$		−	53.9491i		−	1.95823i
$760$	−9.17899	+	5.29949i	−0.332957	+	0.192233i
$761$			22.6135i			0.819740i	0.912144	+	0.409870i	$0.134426\pi$
$761$			22.6135i			0.819740i	−0.912144	+	0.409870i	$0.865574\pi$
$762$	−23.0093	+	13.2844i	−0.833538	+	0.481243i
$763$	−31.5653			−1.14274
$764$	3.71369			0.134357
$765$			7.18136i			0.259643i
$766$	−11.4832	−	19.8896i	−0.414907	−	0.718639i
$767$	−21.8894	+	36.8329i	−0.790382	+	1.32996i
$768$	16.7288	−	28.9751i	0.603647	−	1.04555i
$769$	−18.1450	+	10.4760i	−0.654327	+	0.377776i	−0.790112	−	0.612963i	$-0.789978\pi$
$769$	−18.1450	+	10.4760i	−0.654327	+	0.377776i	0.135785	+	0.990738i	$0.456644\pi$
$770$	−6.91482			−0.249193
$771$	3.84791	+	6.66478i	0.138579	+	0.240026i
$772$	3.35534	+	1.93721i	0.120761	+	0.0697216i
$773$	−12.6565	+	7.30721i	−0.455221	+	0.262822i	−0.710033	−	0.704169i	$-0.751320\pi$
$773$	−12.6565	+	7.30721i	−0.455221	+	0.262822i	0.254812	+	0.966991i	$0.417987\pi$
$774$	−9.54789	+	5.51248i	−0.343192	+	0.198142i
$775$	−21.6203	−	10.9336i	−0.776623	−	0.392745i
$776$	2.13783	+	3.70283i	0.0767436	+	0.132924i
$777$	14.7174	−	25.4912i	0.527983	−	0.914493i
$778$	−2.32616	+	1.34301i	−0.0833969	+	0.0481492i
$779$	−3.38433			−0.121256
$780$	2.35789	−	3.96758i	0.0844260	−	0.142062i
$781$	−11.0762	+	19.1845i	−0.396338	+	0.686477i
$782$	17.8963	−	10.3324i	0.639971	−	0.369488i
$783$	2.56783	−	4.44762i	0.0917669	−	0.158945i
$784$	4.23612	−	7.33717i	0.151290	−	0.262042i
$785$	3.82131	−	2.20623i	0.136388	−	0.0787439i
$786$	−35.4753	−	20.4816i	−1.26536	−	0.730556i
$787$		−	4.15112i		−	0.147971i	−0.997259	−	0.0739857i	$-0.976428\pi$
$787$		−	4.15112i		−	0.147971i	0.997259	−	0.0739857i	$-0.0235719\pi$
$788$	−1.13123	+	0.653118i	−0.0402985	+	0.0232664i
$789$	−37.8201			−1.34643
$790$	7.10309	−	12.3029i	0.252717	−	0.437718i
$791$	4.12772	+	2.38314i	0.146765	+	0.0847347i
$792$	17.3319	−	30.0197i	0.615861	−	1.06670i
$793$	−0.423316	+	33.5638i	−0.0150324	+	1.19189i
$794$	7.80129	−	13.5122i	0.276857	−	0.479531i
$795$			15.3646i			0.544925i
$796$	−8.92078			−0.316189
$797$	5.09564	−	8.82590i	0.180497	−	0.312629i	−0.761553	−	0.648102i	$-0.775563\pi$
$797$	5.09564	−	8.82590i	0.180497	−	0.312629i	0.942050	+	0.335473i	$0.108896\pi$
$798$			21.0870i			0.746471i
$799$		−	31.2429i		−	1.10529i
$800$			15.6035i			0.551666i
$801$	−0.920531	+	0.531469i	−0.0325254	+	0.0187785i
$802$	−8.89229	−	15.4019i	−0.313998	−	0.543860i
$803$	−23.9041	−	41.4032i	−0.843559	−	1.46109i
$804$	16.7581	+	9.67527i	0.591011	+	0.341221i
$805$	−7.81889			−0.275580
$806$	19.5708	−	12.4446i	0.689351	−	0.438342i
$807$	−22.5511			−0.793836
$808$	−28.3817	−	16.3862i	−0.998465	−	0.576464i
$809$	−21.9735	−	38.0593i	−0.772548	−	1.33809i	−0.936162	−	0.351569i	$-0.885648\pi$
$809$	−21.9735	−	38.0593i	−0.772548	−	1.33809i	0.163614	−	0.986525i	$-0.447685\pi$
$810$	4.55515	+	7.88975i	0.160052	+	0.277218i
$811$	−26.5231	+	15.3131i	−0.931354	+	0.537717i	−0.887239	−	0.461309i	$-0.847380\pi$
$811$	−26.5231	+	15.3131i	−0.931354	+	0.537717i	−0.0441141	+	0.999026i	$0.514047\pi$
$812$			8.74352i			0.306837i
$813$			49.8717i			1.74908i
$814$		−	33.1071i		−	1.16040i
$815$	−2.93111	+	5.07683i	−0.102672	+	0.177834i
$816$	17.5201			0.613327
$817$			15.0640i			0.527023i
$818$	−2.37424	+	4.11230i	−0.0830132	+	0.143783i
$819$	−8.53406	−	15.2216i	−0.298204	−	0.531885i
$820$	0.212131	−	0.367422i	0.00740795	−	0.0128309i
$821$	18.8152	+	10.8630i	0.656654	+	0.379120i	0.791001	−	0.611815i	$-0.209560\pi$
$821$	18.8152	+	10.8630i	0.656654	+	0.379120i	−0.134347	+	0.990934i	$0.542894\pi$
$822$	8.49064	−	14.7062i	0.296145	−	0.512938i
$823$	45.0263			1.56952			0.784760	−	0.619800i	$-0.212786\pi$
$823$	45.0263			1.56952			0.784760	+	0.619800i	$0.212786\pi$
$824$	33.3200	−	19.2373i	1.16076	−	0.670163i
$825$			43.2223i			1.50481i
$826$	21.2529	+	12.2704i	0.739484	+	0.426941i
$827$	−8.34198	+	4.81624i	−0.290079	+	0.167477i	−0.637977	−	0.770055i	$-0.720229\pi$
$827$	−8.34198	+	4.81624i	−0.290079	+	0.167477i	0.347899	+	0.937532i	$0.386895\pi$
$828$	4.89195	−	8.47311i	0.170007	−	0.294461i
$829$	12.8613	−	22.2764i	0.446690	−	0.773690i	−0.551478	−	0.834190i	$-0.685936\pi$
$829$	12.8613	−	22.2764i	0.446690	−	0.773690i	0.998168	+	0.0604991i	$0.0192692\pi$
$830$	−1.59018	+	0.918088i	−0.0551958	+	0.0318673i
$831$	10.5643	−	18.2980i	0.366473	−	0.634750i
$832$	−26.6441	−	15.8343i	−0.923718	−	0.548957i
$833$	−12.5302			−0.434147
$834$	1.75036	−	1.01057i	0.0606100	−	0.0349932i
$835$	−2.86190	+	4.95696i	−0.0990402	+	0.171543i
$836$	−5.91128	−	10.2386i	−0.204446	−	0.354111i
$837$	−0.215332	−	3.88328i	−0.00744297	−	0.134226i
$838$	−34.1986	+	19.7446i	−1.18137	+	0.682064i
$839$	−40.7267	+	23.5136i	−1.40604	+	0.811778i	−0.995003	−	0.0998401i	$-0.968167\pi$
$839$	−40.7267	+	23.5136i	−1.40604	+	0.811778i	−0.411038	+	0.911618i	$0.634834\pi$
$840$	−9.17138	−	5.29510i	−0.316443	−	0.182698i
$841$	−12.5268	−	21.6971i	−0.431960	−	0.748177i
$842$	7.62249			0.262688
$843$	26.2084	−	15.1314i	0.902665	−	0.521154i
$844$	2.10637	−	3.64835i	0.0725044	−	0.125581i
$845$	−8.93199	−	5.46178i	−0.307270	−	0.187891i
$846$	14.8376	+	25.6995i	0.510127	+	0.883566i
$847$		−	11.2369i		−	0.386105i
$848$	17.7821			0.610640
$849$	25.2921			0.868021
$850$	−14.3380	+	8.27803i	−0.491788	+	0.283934i
$851$		−	37.4356i		−	1.28328i
$852$	−7.33411	+	4.23435i	−0.251263	+	0.145067i
$853$			10.2072i			0.349489i	0.984614	+	0.174745i	$0.0559099\pi$
$853$			10.2072i			0.349489i	−0.984614	+	0.174745i	$0.944090\pi$
$854$	19.2256			0.657887
$855$	−9.31994			−0.318735
$856$	48.0900	−	27.7648i	1.64368	−	0.948981i
$857$	23.8868	+	41.3732i	0.815958	+	1.41328i	0.908638	+	0.417585i	$0.137124\pi$
$857$	23.8868	+	41.3732i	0.815958	+	1.41328i	−0.0926794	+	0.995696i	$0.529543\pi$
$858$	−35.5683	−	21.1379i	−1.21428	−	0.721636i
$859$	−10.5917	−	18.3453i	−0.361384	−	0.625935i	0.626805	−	0.779176i	$-0.284362\pi$
$859$	−10.5917	−	18.3453i	−0.361384	−	0.625935i	−0.988189	+	0.153241i	$0.951029\pi$
$860$	−1.63544	−	0.944220i	−0.0557679	−	0.0321976i
$861$	−1.69076	−	2.92848i	−0.0576209	−	0.0998024i
$862$	4.07680			0.138856
$863$	19.9856	−	11.5387i	0.680319	−	0.392782i	−0.119656	−	0.992815i	$-0.538179\pi$
$863$	19.9856	−	11.5387i	0.680319	−	0.392782i	0.799975	+	0.600033i	$0.204846\pi$
$864$	−2.16923	+	1.25241i	−0.0737987	+	0.0426077i
$865$		−	16.0946i		−	0.547234i
$866$		−	13.5658i		−	0.460984i
$867$	7.35109	+	12.7325i	0.249656	+	0.432417i
$868$	3.62315	+	5.54226i	0.122978	+	0.188117i
$869$	54.9772	+	31.7411i	1.86497	+	1.07674i
$870$	16.3424			0.554059
$871$	22.4253	−	37.7346i	0.759853	−	1.27859i
$872$	−54.3743			−1.84135
$873$			3.75969i			0.127246i
$874$	13.4094	+	23.2258i	0.453580	+	0.785623i
$875$	13.4622			0.455105
$876$		−	18.2768i		−	0.617514i
$877$	−3.24372	−	1.87276i	−0.109533	−	0.0632387i	0.444233	−	0.895911i	$-0.353476\pi$
$877$	−3.24372	−	1.87276i	−0.109533	−	0.0632387i	−0.553766	+	0.832673i	$0.686810\pi$
$878$	22.7349	+	13.1260i	0.767266	+	0.442981i
$879$	−43.7653	+	25.2679i	−1.47617	+	0.852266i
$880$	−7.45607			−0.251344
$881$	10.1765			0.342855			0.171427	−	0.985197i	$-0.445162\pi$
$881$	10.1765			0.342855			0.171427	+	0.985197i	$0.445162\pi$
$882$	10.3070	−	5.95075i	0.347055	−	0.200372i
$883$	9.91341			0.333613			0.166806	−	0.985990i	$-0.446655\pi$
$883$	9.91341			0.333613			0.166806	+	0.985990i	$0.446655\pi$
$884$	−0.0996289	+	7.89937i	−0.00335088	+	0.265684i
$885$	−11.4321	+	19.8009i	−0.384284	+	0.665600i
$886$			14.7351i			0.495035i
$887$	−18.2822	−	31.6658i	−0.613858	−	1.06323i	−0.990584	−	0.136908i	$-0.956284\pi$
$887$	−18.2822	−	31.6658i	−0.613858	−	1.06323i	0.376726	−	0.926325i	$-0.377050\pi$
$888$	25.3521	−	43.9111i	0.850761	−	1.47356i
$889$	−14.9018	+	8.60355i	−0.499790	+	0.288554i
$890$	0.316321	+	0.182628i	0.0106031	+	0.00612170i
$891$	−35.2564	+	20.3553i	−1.18113	+	0.681928i
$892$	3.06199	+	1.76784i	0.102523	+	0.0591917i
$893$	40.5468			1.35685
$894$	−32.0374			−1.07149
$895$	0.967621	+	0.558656i	0.0323440	+	0.0186738i
$896$	−2.46631	+	4.27177i	−0.0823936	+	0.142710i
$897$	−40.2186	−	23.9015i	−1.34286	−	0.798049i
$898$	−36.9959			−1.23457
$899$	−36.5295	−	18.4733i	−1.21833	−	0.616118i
$900$	−3.91928	+	6.78839i	−0.130643	+	0.226280i
$901$	−13.1496	−	22.7759i	−0.438078	−	0.758774i
$902$	−3.29385	−	1.90170i	−0.109673	−	0.0633198i
$903$	−13.0350	+	7.52576i	−0.433777	+	0.250442i
$904$	7.11040	+	4.10519i	0.236488	+	0.136537i
$905$	−9.61371	−	5.55048i	−0.319571	−	0.184504i
$906$	13.1229			0.435978
$907$	5.23638	−	9.06968i	0.173871	−	0.301154i	−0.765899	−	0.642961i	$-0.777706\pi$
$907$	5.23638	−	9.06968i	0.173871	−	0.301154i	0.939770	+	0.341807i	$0.111039\pi$
$908$		−	6.76384i		−	0.224466i
$909$	−14.4088	−	24.9567i	−0.477908	−	0.827762i
$910$	−3.06353	+	5.15494i	−0.101555	+	0.170885i
$911$	−16.8685	+	29.2171i	−0.558877	+	0.968004i	0.438713	+	0.898627i	$0.355434\pi$
$911$	−16.8685	+	29.2171i	−0.558877	+	0.968004i	−0.997591	+	0.0693770i	$0.977899\pi$
$912$			22.7375i			0.752915i
$913$	−4.10260	−	7.10591i	−0.135776	−	0.235171i
$914$	−21.3908	−	37.0500i	−0.707546	−	1.22551i
$915$			17.9121i			0.592156i
$916$			10.1279i			0.334634i
$917$	−22.9753	−	13.2648i	−0.758711	−	0.438042i
$918$	−2.30166	−	1.32887i	−0.0759662	−	0.0438591i
$919$	−9.69547	+	16.7931i	−0.319824	+	0.553952i	−0.980451	−	0.196763i	$-0.936957\pi$
$919$	−9.69547	+	16.7931i	−0.319824	+	0.553952i	0.660627	+	0.750714i	$0.270290\pi$
$920$	−13.4688			−0.444053
$921$		−	40.3703i		−	1.33024i
$922$	15.8167			0.520894
$923$	9.39474	+	16.7567i	0.309232	+	0.551554i
$924$	5.90638	−	10.2302i	0.194306	−	0.336547i
$925$			29.9922i			0.986139i
$926$	−18.8959	+	32.7287i	−0.620959	+	1.07553i
$927$	33.8316			1.11118
$928$			26.3635i			0.865425i
$929$	19.5241	−	11.2723i	0.640566	−	0.369831i	−0.144267	−	0.989539i	$-0.546082\pi$
$929$	19.5241	−	11.2723i	0.640566	−	0.369831i	0.784833	+	0.619708i	$0.212749\pi$
$930$	10.3590	−	6.77198i	0.339684	−	0.222062i
$931$		−	16.2617i		−	0.532954i
$932$	−0.657002	−	1.13796i	−0.0215208	−	0.0372752i
$933$	21.7344	+	37.6451i	0.711552	+	1.23244i
$934$	29.9516	+	17.2925i	0.980045	+	0.565829i
$935$	5.51367	+	9.54996i	0.180316	+	0.312317i
$936$	−14.7007	−	26.2206i	−0.480509	−	0.857049i
$937$	2.96814	−	5.14098i	0.0969650	−	0.167948i	−0.813462	−	0.581618i	$-0.802420\pi$
$937$	2.96814	−	5.14098i	0.0969650	−	0.167948i	0.910427	+	0.413670i	$0.135753\pi$
$938$	−21.7732	−	12.5708i	−0.710921	−	0.410450i
$939$	−56.0161			−1.82802
$940$	−2.54150	+	4.40200i	−0.0828945	+	0.143577i
$941$	−22.2107	+	12.8233i	−0.724048	+	0.418029i	−0.816241	−	0.577712i	$-0.803946\pi$
$941$	−22.2107	+	12.8233i	−0.724048	+	0.418029i	0.0921930	+	0.995741i	$0.470612\pi$
$942$		−	15.1222i		−	0.492709i
$943$	−3.72450	−	2.15034i	−0.121286	−	0.0700247i
$944$	22.9165	+	13.2308i	0.745868	+	0.430627i
$945$	0.502797	+	0.870871i	0.0163560	+	0.0283294i
$946$	−8.46469	+	14.6613i	−0.275211	+	0.476679i
$947$	−18.0690	+	10.4321i	−0.587163	+	0.338999i	−0.763975	−	0.645246i	$-0.776755\pi$
$947$	−18.0690	+	10.4321i	−0.587163	+	0.338999i	0.176812	+	0.984245i	$0.443422\pi$
$948$	12.1344	+	21.0174i	0.394107	+	0.682613i
$949$	−41.4562	−	0.522856i	−1.34573	−	0.0169726i
$950$	−10.7432	−	18.6077i	−0.348555	−	0.603715i
$951$			58.5055i			1.89717i
$952$	18.1271			0.587502
$953$	−30.5893	−	52.9821i	−0.990883	−	1.71626i	−0.612116	−	0.790768i	$-0.709682\pi$
$953$	−30.5893	−	52.9821i	−0.990883	−	1.71626i	−0.378767	−	0.925492i	$-0.623652\pi$
$954$	21.6330	+	12.4898i	0.700395	+	0.404373i
$955$		−	4.49542i		−	0.145468i
$956$	1.56069	+	0.901066i	0.0504764	+	0.0291426i
$957$			73.0282i			2.36067i
$958$	−37.3039			−1.20523
$959$	5.49890	−	9.52437i	0.177569	−	0.307558i
$960$	−14.3235	−	8.26969i	−0.462290	−	0.266903i
$961$	−30.8099	+	3.42743i	−0.993869	+	0.110562i
$962$	−24.6811	−	14.6677i	−0.795750	−	0.472906i
$963$	48.8285			1.57348
$964$	0.991415	−	0.572394i	0.0319313	−	0.0184356i
$965$	2.34499	−	4.06164i	0.0754880	−	0.130749i
$966$	−13.3983	+	23.2065i	−0.431082	+	0.746657i
$967$	−12.8983	−	7.44684i	−0.414781	−	0.239474i	0.278061	−	0.960563i	$-0.410308\pi$
$967$	−12.8983	−	7.44684i	−0.414781	−	0.239474i	−0.692842	+	0.721089i	$0.743642\pi$
$968$		−	19.3567i		−	0.622148i
$969$	29.1229	−	16.8141i	0.935563	−	0.540148i
$970$	1.11885	−	0.645968i	0.0359241	−	0.0207408i
$971$	−20.2285	+	35.0367i	−0.649162	+	1.12438i	0.334161	+	0.942516i	$0.391547\pi$
$971$	−20.2285	+	35.0367i	−0.649162	+	1.12438i	−0.983323	+	0.181866i	$0.941786\pi$
$972$	−14.1692			−0.454476
$973$	1.13361	−	0.654489i	0.0363418	−	0.0209819i
$974$	−24.4195	−	42.2959i	−0.782452	−	1.35525i
$975$	32.2219	+	19.1492i	1.03193	+	0.613264i
$976$	20.7305			0.663566
$977$	−25.6749	−	14.8234i	−0.821412	−	0.474242i	0.0294913	−	0.999565i	$-0.490611\pi$
$977$	−25.6749	−	14.8234i	−0.821412	−	0.474242i	−0.850903	+	0.525323i	$0.823945\pi$
$978$	10.0454	+	17.3991i	0.321216	+	0.556362i
$979$	−0.816097	+	1.41352i	−0.0260826	+	0.0451764i
$980$	1.76546	+	1.01929i	0.0563956	+	0.0325600i
$981$	−41.4070	−	23.9063i	−1.32202	−	0.763270i
$982$	−10.6862	−	6.16968i	−0.341010	−	0.196882i
$983$	−8.29489	+	4.78906i	−0.264566	+	0.152747i	−0.626416	−	0.779489i	$-0.715479\pi$
$983$	−8.29489	+	4.78906i	−0.264566	+	0.152747i	0.361850	+	0.932236i	$0.382145\pi$
$984$	−2.91250	−	5.04460i	−0.0928471	−	0.160816i
$985$	0.790600	+	1.36936i	0.0251906	+	0.0436314i
$986$	−24.2254	+	13.9865i	−0.771493	+	0.445421i
$987$	20.2566	+	35.0855i	0.644775	+	1.11678i
$988$	−10.2518	−	0.129298i	−0.326152	−	0.00411351i
$989$	−9.57139	+	16.5781i	−0.304353	+	0.527154i
$990$	−9.07077	−	5.23701i	−0.288288	−	0.166443i
$991$	22.4489	−	38.8827i	0.713114	−	1.23515i	−0.250568	−	0.968099i	$-0.580617\pi$
$991$	22.4489	−	38.8827i	0.713114	−	1.23515i	0.963682	−	0.267051i	$-0.0860492\pi$
$992$	10.9245	+	16.7111i	0.346854	+	0.530577i
$993$			1.63232i			0.0518001i
$994$	9.52898	−	5.50156i	0.302241	−	0.174499i
$995$			10.7986i			0.342339i
$996$		−	3.13679i		−	0.0993929i
$997$	−4.23628	+	7.33746i	−0.134164	+	0.232380i	−0.925278	−	0.379290i	$-0.876168\pi$
$997$	−4.23628	+	7.33746i	−0.134164	+	0.232380i	0.791114	+	0.611669i	$0.209502\pi$
$998$	−17.7549	−	30.7524i	−0.562021	−	0.973449i
$999$	−4.16959	+	2.40732i	−0.131920	+	0.0761641i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.s.a.160.12	✓	70
13.10	even	6		403.2.v.a.36.12	yes	70
31.25	even	3		403.2.v.a.56.12	yes	70
403.335	even	6	inner	403.2.s.a.335.12	yes	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.s.a.160.12	✓	70	1.1	even	1	trivial
403.2.s.a.335.12	yes	70	403.335	even	6	inner
403.2.v.a.36.12	yes	70	13.10	even	6
403.2.v.a.56.12	yes	70	31.25	even	3

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00051 - 0.577645i) q^{2} +(-1.19453 - 2.06899i) q^{3} +(-0.332651 - 0.576169i) q^{4} +(-0.697454 + 0.402675i) q^{5} +2.76006i q^{6} +1.78753i q^{7} +3.07920i q^{8} +(-1.35381 + 2.34486i) q^{9} +0.930413 q^{10} +4.15768i q^{11} +(-0.794725 + 1.37650i) q^{12} +(3.09952 + 1.84201i) q^{13} +(1.03256 - 1.78845i) q^{14} +(1.66626 + 0.962015i) q^{15} +(1.11338 - 1.92844i) q^{16} -3.29333 q^{17} +(2.70900 - 1.56404i) q^{18} -4.27407i q^{19} +(0.464018 + 0.267901i) q^{20} +(3.69838 - 2.13526i) q^{21} +(2.40166 - 4.15980i) q^{22} +(2.71567 - 4.70367i) q^{23} +(6.37083 - 3.67820i) q^{24} +(-2.17571 + 3.76843i) q^{25} +(-2.03707 - 3.63337i) q^{26} -0.698529 q^{27} +(1.02992 - 0.594625i) q^{28} +(-3.67606 + 6.36712i) q^{29} +(-1.11141 - 1.92501i) q^{30} +(0.308265 + 5.55922i) q^{31} +(3.10543 - 1.79292i) q^{32} +(8.60218 - 4.96647i) q^{33} +(3.29502 + 1.90238i) q^{34} +(-0.719795 - 1.24672i) q^{35} +1.80138 q^{36} +(5.96911 - 3.44627i) q^{37} +(-2.46890 + 4.27625i) q^{38} +(0.108632 - 8.61320i) q^{39} +(-1.23992 - 2.14760i) q^{40} -0.791828i q^{41} -4.93370 q^{42} -3.52451 q^{43} +(2.39553 - 1.38306i) q^{44} -2.18058i q^{45} +(-5.43411 + 3.13738i) q^{46} +9.48670i q^{47} -5.31988 q^{48} +3.80473 q^{49} +(4.35364 - 2.51357i) q^{50} +(3.93399 + 6.81387i) q^{51} +(0.0302517 - 2.39859i) q^{52} +(3.99281 + 6.91575i) q^{53} +(0.698886 + 0.403502i) q^{54} +(-1.67419 - 2.89979i) q^{55} -5.50417 q^{56} +(-8.84300 + 5.10551i) q^{57} +(7.35588 - 4.24692i) q^{58} +11.8834i q^{59} -1.28006i q^{60} +(4.65484 + 8.06242i) q^{61} +(2.90284 - 5.74013i) q^{62} +(-4.19152 - 2.41997i) q^{63} -8.59622 q^{64} +(-2.90350 - 0.0366197i) q^{65} -11.4754 q^{66} -12.1744i q^{67} +(1.09553 + 1.89752i) q^{68} -12.9758 q^{69} +1.66314i q^{70} +(4.61425 + 2.66404i) q^{71} +(-7.22030 - 4.16864i) q^{72} +(-9.95825 + 5.74940i) q^{73} -7.96288 q^{74} +10.3958 q^{75} +(-2.46259 + 1.42178i) q^{76} -7.43198 q^{77} +(-5.08406 + 8.55485i) q^{78} +(7.63434 - 13.2231i) q^{79} +1.79333i q^{80} +(4.89583 + 8.47983i) q^{81} +(-0.457396 + 0.792232i) q^{82} +(-1.70911 + 0.986753i) q^{83} +(-2.46055 - 1.42060i) q^{84} +(2.29695 - 1.32614i) q^{85} +(3.52631 + 2.03592i) q^{86} +17.5647 q^{87} -12.8023 q^{88} +(0.339979 + 0.196287i) q^{89} +(-1.25960 + 2.18169i) q^{90} +(-3.29266 + 5.54049i) q^{91} -3.61348 q^{92} +(11.1337 - 7.27846i) q^{93} +(5.47995 - 9.49155i) q^{94} +(1.72106 + 2.98096i) q^{95} +(-7.41905 - 4.28339i) q^{96} +(1.20253 - 0.694280i) q^{97} +(-3.80667 - 2.19778i) q^{98} +(-9.74918 - 5.62869i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q - 6 q^{2} - 2 q^{3} + 30 q^{4} - 29 q^{9} + 2 q^{10} + 13 q^{12} + q^{13} - 14 q^{14} - 15 q^{15} - 28 q^{16} - 12 q^{17} - 3 q^{20} - 9 q^{21} + 4 q^{22} + 10 q^{23} + 18 q^{24} + 19 q^{25} + 6 q^{26}+ \cdots + 93 q^{99}+O(q^{100}) \) 70 * q - 6 * q^2 - 2 * q^3 + 30 * q^4 - 29 * q^9 + 2 * q^10 + 13 * q^12 + q^13 - 14 * q^14 - 15 * q^15 - 28 * q^16 - 12 * q^17 - 3 * q^20 - 9 * q^21 + 4 * q^22 + 10 * q^23 + 18 * q^24 + 19 * q^25 + 6 * q^26 + 34 * q^27 - 33 * q^28 - 18 * q^29 - 31 * q^30 - 2 * q^31 + 36 * q^32 - 12 * q^33 + 9 * q^34 - 12 * q^35 - 16 * q^36 - 18 * q^37 - 21 * q^38 - 30 * q^39 + 5 * q^40 + 98 * q^42 - 38 * q^43 + 42 * q^44 - 6 * q^46 + 54 * q^48 - 18 * q^49 - 51 * q^50 - 7 * q^51 + 41 * q^52 - 22 * q^53 + 18 * q^54 - 15 * q^55 - 50 * q^56 + 15 * q^57 - 12 * q^58 - 13 * q^61 - 23 * q^62 - 6 * q^63 - 38 * q^64 - 12 * q^65 - 52 * q^66 - 44 * q^68 + 32 * q^69 + 27 * q^71 - 15 * q^72 - 9 * q^73 + 38 * q^74 - 50 * q^75 + 126 * q^76 + 34 * q^77 + 14 * q^78 + 6 * q^79 - 11 * q^81 + 39 * q^82 - 54 * q^83 + 15 * q^84 - 33 * q^85 - 24 * q^86 + 28 * q^87 - 32 * q^88 - 6 * q^89 - 11 * q^90 - 70 * q^91 - 6 * q^92 + 14 * q^93 - 43 * q^94 + 25 * q^95 + 36 * q^96 - 75 * q^97 + 93 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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