LMFDB - Embedded newform 127.2.f.a.103.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [127,2,Mod(22,127)] 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("127.22"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(127, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	127.f (of order $9$, degree $6$, 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:	$1.01410010567$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			103.9
Character	$\chi$	$=$	127.103
Dual form			127.2.f.a.37.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.41539 q^{2} +(1.52689 + 1.28121i) q^{3} +0.00332867 q^{4} +(-0.713232 - 1.23535i) q^{5} +(2.16114 + 1.81341i) q^{6} +(0.0454245 - 0.257615i) q^{7} -2.82607 q^{8} +(0.168940 + 0.958105i) q^{9} +(-1.00950 - 1.74851i) q^{10} +(2.02551 + 0.737226i) q^{11} +(0.00508251 + 0.00426473i) q^{12} +(-4.11954 + 1.49939i) q^{13} +(0.0642933 - 0.364626i) q^{14} +(0.493724 - 2.80005i) q^{15} -4.00665 q^{16} +(0.200595 + 1.13763i) q^{17} +(0.239116 + 1.35609i) q^{18} +(2.19106 - 3.79503i) q^{19} +(-0.00237411 - 0.00411209i) q^{20} +(0.399417 - 0.335151i) q^{21} +(2.86689 + 1.04346i) q^{22} +(-3.98891 + 1.45185i) q^{23} +(-4.31509 - 3.62079i) q^{24} +(1.48260 - 2.56794i) q^{25} +(-5.83075 + 2.12222i) q^{26} +(2.02023 - 3.49915i) q^{27} +(0.000151203 - 0.000857516i) q^{28} +(6.72016 + 2.44594i) q^{29} +(0.698811 - 3.96316i) q^{30} +(2.08695 + 1.75116i) q^{31} -0.0188298 q^{32} +(2.14819 + 3.72077i) q^{33} +(0.283920 + 1.61019i) q^{34} +(-0.350644 + 0.127624i) q^{35} +(0.000562345 + 0.00318922i) q^{36} +(-6.78047 + 5.68949i) q^{37} +(3.10121 - 5.37145i) q^{38} +(-8.21110 - 2.98860i) q^{39} +(2.01564 + 3.49119i) q^{40} +(-3.56829 + 2.99415i) q^{41} +(0.565331 - 0.474369i) q^{42} +(-1.60660 + 1.34810i) q^{43} +(0.00674226 + 0.00245398i) q^{44} +(1.06310 - 0.892051i) q^{45} +(-5.64587 + 2.05493i) q^{46} +(0.716884 + 1.24168i) q^{47} +(-6.11770 - 5.13336i) q^{48} +(6.51355 + 2.37074i) q^{49} +(2.09846 - 3.63464i) q^{50} +(-1.15126 + 1.99403i) q^{51} +(-0.0137126 + 0.00499098i) q^{52} +(-0.943531 + 0.791717i) q^{53} +(2.85942 - 4.95266i) q^{54} +(-0.533924 - 3.02803i) q^{55} +(-0.128373 + 0.728038i) q^{56} +(8.20774 - 2.98737i) q^{57} +(9.51164 + 3.46195i) q^{58} +(0.444928 + 2.52331i) q^{59} +(0.00164344 - 0.00932043i) q^{60} +(-1.08436 - 1.87817i) q^{61} +(2.95385 + 2.47858i) q^{62} +0.254496 q^{63} +7.98664 q^{64} +(4.79046 + 4.01967i) q^{65} +(3.04052 + 5.26634i) q^{66} +(1.94502 - 11.0308i) q^{67} +(0.000667714 + 0.00378679i) q^{68} +(-7.95074 - 2.89383i) q^{69} +(-0.496298 + 0.180638i) q^{70} +(-2.06503 + 11.7114i) q^{71} +(-0.477435 - 2.70767i) q^{72} +(5.60729 - 9.71211i) q^{73} +(-9.59701 + 8.05285i) q^{74} +(5.55384 - 2.02143i) q^{75} +(0.00729333 - 0.0126324i) q^{76} +(0.281928 - 0.488314i) q^{77} +(-11.6219 - 4.23003i) q^{78} +(-0.617211 - 0.517901i) q^{79} +(2.85767 + 4.94962i) q^{80} +(10.3104 - 3.75270i) q^{81} +(-5.05052 + 4.23789i) q^{82} +(-1.38133 - 0.502763i) q^{83} +(0.00132953 - 0.00111561i) q^{84} +(1.26230 - 1.05920i) q^{85} +(-2.27397 + 1.90809i) q^{86} +(7.12716 + 12.3446i) q^{87} +(-5.72423 - 2.08345i) q^{88} +(-5.57763 + 9.66073i) q^{89} +(1.50471 - 1.26260i) q^{90} +(0.199137 + 1.12936i) q^{91} +(-0.0132778 + 0.00483272i) q^{92} +(0.942936 + 5.34766i) q^{93} +(1.01467 + 1.75746i) q^{94} -6.25094 q^{95} +(-0.0287510 - 0.0241249i) q^{96} +(2.73293 - 15.4992i) q^{97} +(9.21921 + 3.35552i) q^{98} +(-0.364150 + 2.06520i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 12 q^{2} - 6 q^{3} + 48 q^{4} + 3 q^{5} - 9 q^{6} - 30 q^{8} - 6 q^{9} - 3 q^{10} + 3 q^{11} - 27 q^{12} + 6 q^{13} - 27 q^{14} + 48 q^{16} + 9 q^{17} + 9 q^{18} - 3 q^{19} - 3 q^{20} + 36 q^{21}+ \cdots - 111 q^{99}+O(q^{100}) $ 60 * q - 12 * q^2 - 6 * q^3 + 48 * q^4 + 3 * q^5 - 9 * q^6 - 30 * q^8 - 6 * q^9 - 3 * q^10 + 3 * q^11 - 27 * q^12 + 6 * q^13 - 27 * q^14 + 48 * q^16 + 9 * q^17 + 9 * q^18 - 3 * q^19 - 3 * q^20 + 36 * q^21 - 39 * q^22 - 24 * q^23 - 90 * q^24 - 15 * q^25 + 9 * q^27 - 30 * q^28 - 42 * q^29 - 24 * q^30 - 54 * q^31 - 102 * q^32 + 39 * q^33 - 54 * q^34 + 21 * q^35 - 33 * q^36 + 27 * q^37 + 6 * q^38 + 33 * q^39 + 24 * q^40 + 42 * q^41 + 51 * q^42 + 36 * q^43 + 66 * q^44 + 3 * q^45 - 39 * q^46 - 18 * q^47 - 30 * q^48 + 48 * q^49 + 21 * q^50 + 21 * q^51 + 12 * q^52 - 21 * q^53 + 45 * q^54 - 36 * q^55 - 90 * q^56 - 21 * q^57 + 57 * q^58 + 36 * q^59 + 45 * q^60 - 15 * q^61 + 54 * q^62 - 84 * q^63 + 66 * q^64 + 66 * q^65 + 63 * q^66 + 78 * q^67 + 60 * q^68 + 30 * q^69 + 18 * q^70 - 6 * q^71 + 66 * q^72 - 3 * q^73 + 39 * q^74 + 78 * q^75 - 45 * q^76 + 39 * q^77 - 60 * q^78 - 27 * q^79 - 18 * q^80 + 99 * q^81 + 99 * q^82 - 12 * q^83 + 90 * q^84 - 6 * q^85 - 57 * q^86 - 12 * q^87 - 117 * q^88 + 3 * q^89 + 72 * q^90 - 60 * q^91 - 9 * q^92 - 108 * q^93 + 75 * q^94 - 180 * q^95 - 123 * q^96 + 9 * q^97 + 3 * q^98 - 111 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/127\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

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 $

$2$	1.41539			1.00083			0.500416	−	0.865785i	$-0.333180\pi$
$2$	1.41539			1.00083			0.500416	+	0.865785i	$0.333180\pi$
$3$	1.52689	+	1.28121i	0.881549	+	0.739707i	0.966497	−	0.256678i	$-0.0826280\pi$
$3$	1.52689	+	1.28121i	0.881549	+	0.739707i	−0.0849482	+	0.996385i	$0.527072\pi$
$4$	0.00332867			0.00166434
$5$	−0.713232	−	1.23535i	−0.318967	−	0.552467i	0.661306	−	0.750116i	$-0.270003\pi$
$5$	−0.713232	−	1.23535i	−0.318967	−	0.552467i	−0.980273	+	0.197649i	$0.936669\pi$
$6$	2.16114	+	1.81341i	0.882282	+	0.740323i
$7$	0.0454245	−	0.257615i	0.0171688	−	0.0973693i	−0.975019	−	0.222121i	$-0.928702\pi$
$7$	0.0454245	−	0.257615i	0.0171688	−	0.0973693i	0.992188	+	0.124751i	$0.0398133\pi$
$8$	−2.82607			−0.999166
$9$	0.168940	+	0.958105i	0.0563132	+	0.319368i
$10$	−1.00950	−	1.74851i	−0.319232	−	0.552926i
$11$	2.02551	+	0.737226i	0.610715	+	0.222282i	0.628816	−	0.777554i	$-0.283540\pi$
$11$	2.02551	+	0.737226i	0.610715	+	0.222282i	−0.0181013	+	0.999836i	$0.505762\pi$
$12$	0.00508251	+	0.00426473i	0.00146719	+	0.00123112i
$13$	−4.11954	+	1.49939i	−1.14255	+	0.415856i	−0.842835	−	0.538172i	$-0.819115\pi$
$13$	−4.11954	+	1.49939i	−1.14255	+	0.415856i	−0.299719	+	0.954028i	$0.596893\pi$
$14$	0.0642933	−	0.364626i	0.0171831	−	0.0974503i
$15$	0.493724	−	2.80005i	0.127479	−	0.722969i
$16$	−4.00665			−1.00166
$17$	0.200595	+	1.13763i	0.0486513	+	0.275916i	0.999423	−	0.0339781i	$-0.0108177\pi$
$17$	0.200595	+	1.13763i	0.0486513	+	0.275916i	−0.950771	+	0.309894i	$0.899707\pi$
$18$	0.239116	+	1.35609i	0.0563601	+	0.319634i
$19$	2.19106	−	3.79503i	0.502665	−	0.870640i	−0.497331	−	0.867561i	$-0.665686\pi$
$19$	2.19106	−	3.79503i	0.502665	−	0.870640i	0.999995	−	0.00307945i	$-0.000980220\pi$
$20$	−0.00237411	−	0.00411209i	−0.000530868	−	0.000919491i
$21$	0.399417	−	0.335151i	0.0871599	−	0.0731359i
$22$	2.86689	+	1.04346i	0.611223	+	0.222467i
$23$	−3.98891	+	1.45185i	−0.831746	+	0.302731i	−0.722575	−	0.691292i	$-0.757042\pi$
$23$	−3.98891	+	1.45185i	−0.831746	+	0.302731i	−0.109171	+	0.994023i	$0.534819\pi$
$24$	−4.31509	−	3.62079i	−0.880814	−	0.739090i
$25$	1.48260	−	2.56794i	0.296520	−	0.513588i
$26$	−5.83075	+	2.12222i	−1.14350	+	0.416202i
$27$	2.02023	−	3.49915i	0.388794	−	0.673411i
$28$	0.000151203	0	0.000857516i	2.85747e−5	0	0.000162055i
$29$	6.72016	+	2.44594i	1.24790	+	0.454199i	0.879692	−	0.475544i	$-0.157749\pi$
$29$	6.72016	+	2.44594i	1.24790	+	0.454199i	0.368210	+	0.929743i	$0.379971\pi$
$30$	0.698811	−	3.96316i	0.127585	−	0.723570i
$31$	2.08695	+	1.75116i	0.374828	+	0.314518i	0.810668	−	0.585506i	$-0.199104\pi$
$31$	2.08695	+	1.75116i	0.374828	+	0.314518i	−0.435840	+	0.900024i	$0.643549\pi$
$32$	−0.0188298			−0.00332867
$33$	2.14819	+	3.72077i	0.373951	+	0.647702i
$34$	0.283920	+	1.61019i	0.0486918	+	0.276145i
$35$	−0.350644	+	0.127624i	−0.0592696	+	0.0215724i
$36$	0.000562345		0.00318922i	9.37242e−5		0.000531536i
$37$	−6.78047	+	5.68949i	−1.11470	+	0.935346i	−0.998325	−	0.0578587i	$-0.981573\pi$
$37$	−6.78047	+	5.68949i	−1.11470	+	0.935346i	−0.116378	+	0.993205i	$0.537128\pi$
$38$	3.10121	−	5.37145i	0.503083	−	0.871365i
$39$	−8.21110	−	2.98860i	−1.31483	−	0.478559i
$40$	2.01564	+	3.49119i	0.318701	+	0.552006i
$41$	−3.56829	+	2.99415i	−0.557273	+	0.467608i	−0.877395	−	0.479769i	$-0.840721\pi$
$41$	−3.56829	+	2.99415i	−0.557273	+	0.467608i	0.320122	+	0.947376i	$0.396276\pi$
$42$	0.565331	−	0.474369i	0.0872324	−	0.0731967i
$43$	−1.60660	+	1.34810i	−0.245005	+	0.205584i	−0.757018	−	0.653394i	$-0.773344\pi$
$43$	−1.60660	+	1.34810i	−0.245005	+	0.205584i	0.512013	+	0.858978i	$0.328900\pi$
$44$	0.00674226	+	0.00245398i	0.00101643	+	0.000369952i
$45$	1.06310	−	0.892051i	0.158478	−	0.132979i
$46$	−5.64587	+	2.05493i	−0.832438	+	0.302983i
$47$	0.716884	+	1.24168i	0.104568	+	0.181117i	0.913562	−	0.406700i	$-0.133321\pi$
$47$	0.716884	+	1.24168i	0.104568	+	0.181117i	−0.808993	+	0.587818i	$0.799987\pi$
$48$	−6.11770	−	5.13336i	−0.883014	−	0.740936i
$49$	6.51355	+	2.37074i	0.930507	+	0.338677i
$50$	2.09846	−	3.63464i	0.296767	−	0.514015i
$51$	−1.15126	+	1.99403i	−0.161208	+	0.279221i
$52$	−0.0137126	+	0.00499098i	−0.00190159	+	0.000692124i
$53$	−0.943531	+	0.791717i	−0.129604	+	0.108751i	−0.705286	−	0.708923i	$-0.749181\pi$
$53$	−0.943531	+	0.791717i	−0.129604	+	0.108751i	0.575682	+	0.817674i	$0.304737\pi$
$54$	2.85942	−	4.95266i	0.389117	−	0.673971i
$55$	−0.533924	−	3.02803i	−0.0719943	−	0.408300i
$56$	−0.128373	+	0.728038i	−0.0171545	+	0.0972881i
$57$	8.20774	−	2.98737i	1.08714	−	0.395687i
$58$	9.51164	+	3.46195i	1.24894	+	0.454577i
$59$	0.444928	+	2.52331i	0.0579247	+	0.328508i	0.999976	−	0.00696207i	$-0.00221611\pi$
$59$	0.444928	+	2.52331i	0.0579247	+	0.328508i	−0.942051	+	0.335470i	$0.891105\pi$
$60$	0.00164344	−	0.00932043i	0.000212168	−	0.00120326i
$61$	−1.08436	−	1.87817i	−0.138838	−	0.240475i	0.788219	−	0.615395i	$-0.211003\pi$
$61$	−1.08436	−	1.87817i	−0.138838	−	0.240475i	−0.927057	+	0.374920i	$0.877670\pi$
$62$	2.95385	+	2.47858i	0.375140	+	0.314780i
$63$	0.254496			0.0320635
$64$	7.98664			0.998330
$65$	4.79046	+	4.01967i	0.594183	+	0.498579i
$66$	3.04052	+	5.26634i	0.374262	+	0.648241i
$67$	1.94502	−	11.0308i	0.237622	−	1.34762i	−0.599399	−	0.800450i	$-0.704594\pi$
$67$	1.94502	−	11.0308i	0.237622	−	1.34762i	0.837021	−	0.547171i	$-0.184295\pi$
$68$	0.000667714		0.00378679i	8.09722e−5		0.000459216i
$69$	−7.95074	−	2.89383i	−0.957156	−	0.348376i
$70$	−0.496298	+	0.180638i	−0.0593189	+	0.0215903i
$71$	−2.06503	+	11.7114i	−0.245074	+	1.38988i	0.575247	+	0.817980i	$0.304906\pi$
$71$	−2.06503	+	11.7114i	−0.245074	+	1.38988i	−0.820321	+	0.571904i	$0.806205\pi$
$72$	−0.477435	−	2.70767i	−0.0562663	−	0.319102i
$73$	5.60729	−	9.71211i	0.656283	−	1.13672i	−0.325287	−	0.945615i	$-0.605461\pi$
$73$	5.60729	−	9.71211i	0.656283	−	1.13672i	0.981570	−	0.191101i	$-0.0612058\pi$
$74$	−9.59701	+	8.05285i	−1.11563	+	0.936124i
$75$	5.55384	−	2.02143i	0.641302	−	0.233415i
$76$	0.00729333	−	0.0126324i	0.000836603	−	0.00144904i
$77$	0.281928	−	0.488314i	0.0321287	−	0.0556485i
$78$	−11.6219	−	4.23003i	−1.31592	−	0.478957i
$79$	−0.617211	−	0.517901i	−0.0694416	−	0.0582685i	0.607406	−	0.794391i	$-0.292210\pi$
$79$	−0.617211	−	0.517901i	−0.0694416	−	0.0582685i	−0.676848	+	0.736123i	$0.736655\pi$
$80$	2.85767	+	4.94962i	0.319497	+	0.553385i
$81$	10.3104	−	3.75270i	1.14561	−	0.416966i
$82$	−5.05052	+	4.23789i	−0.557737	+	0.467997i
$83$	−1.38133	−	0.502763i	−0.151621	−	0.0551854i	0.265095	−	0.964222i	$-0.414597\pi$
$83$	−1.38133	−	0.502763i	−0.151621	−	0.0551854i	−0.416716	+	0.909037i	$0.636819\pi$
$84$	0.00132953	−	0.00111561i	0.000145063	−	0.000121723i
$85$	1.26230	−	1.05920i	0.136916	−	0.114886i
$86$	−2.27397	+	1.90809i	−0.245209	+	0.205755i
$87$	7.12716	+	12.3446i	0.764112	+	1.32348i
$88$	−5.72423	−	2.08345i	−0.610205	−	0.222097i
$89$	−5.57763	+	9.66073i	−0.591227	+	1.02404i	0.402840	+	0.915270i	$0.368023\pi$
$89$	−5.57763	+	9.66073i	−0.591227	+	1.02404i	−0.994067	+	0.108765i	$0.965310\pi$
$90$	1.50471	−	1.26260i	0.158610	−	0.133090i
$91$	0.199137	+	1.12936i	0.0208753	+	0.118389i
$92$	−0.0132778	+	0.00483272i	−0.00138430	+	0.000503846i
$93$	0.942936	+	5.34766i	0.0977779	+	0.554526i
$94$	1.01467	+	1.75746i	0.104655	+	0.181268i
$95$	−6.25094			−0.641333
$96$	−0.0287510	−	0.0241249i	−0.00293438	−	0.00246224i
$97$	2.73293	−	15.4992i	0.277487	−	1.57371i	−0.453461	−	0.891276i	$-0.649811\pi$
$97$	2.73293	−	15.4992i	0.277487	−	1.57371i	0.730948	−	0.682433i	$-0.239078\pi$
$98$	9.21921	+	3.35552i	0.931281	+	0.338958i
$99$	−0.364150	+	2.06520i	−0.0365985	+	0.207560i
$100$	0.00493509	−	0.00854783i	0.000493509	−	0.000854783i
$101$	10.7636	−	3.91761i	1.07101	−	0.389817i	0.254458	−	0.967084i	$-0.418103\pi$
$101$	10.7636	−	3.91761i	1.07101	−	0.389817i	0.816556	+	0.577267i	$0.195881\pi$
$102$	−1.62948	+	2.82234i	−0.161342	+	0.279453i
$103$	−10.9349	−	9.17543i	−1.07744	−	0.904082i	−0.0817373	−	0.996654i	$-0.526047\pi$
$103$	−10.9349	−	9.17543i	−1.07744	−	0.904082i	−0.995706	+	0.0925716i	$0.970491\pi$
$104$	11.6421	−	4.23738i	1.14160	−	0.415509i
$105$	−0.698906	−	0.254381i	−0.0682063	−	0.0248251i
$106$	−1.33546	+	1.12059i	−0.129712	+	0.108841i
$107$	−8.86185	−	15.3492i	−0.856707	−	1.48386i	−0.875052	−	0.484029i	$-0.839173\pi$
$107$	−8.86185	−	15.3492i	−0.856707	−	1.48386i	0.0183447	−	0.999832i	$-0.494160\pi$
$108$	0.00672469	−	0.0116475i	0.000647084	−	0.00112078i
$109$	0.699262	+	3.96571i	0.0669771	+	0.379846i	0.999809	+	0.0195347i	$0.00621848\pi$
$109$	0.699262	+	3.96571i	0.0669771	+	0.379846i	−0.932832	+	0.360311i	$0.882670\pi$
$110$	−0.755711	−	4.28585i	−0.0720542	−	0.408640i
$111$	−17.6424			−1.67455
$112$	−0.182000	+	1.03217i	−0.0171974	+	0.0975311i
$113$	−1.90934	+	10.8284i	−0.179615	+	1.01865i	0.753065	+	0.657946i	$0.228574\pi$
$113$	−1.90934	+	10.8284i	−0.179615	+	1.01865i	−0.932681	+	0.360703i	$0.882537\pi$
$114$	11.6172	−	4.22830i	1.08805	−	0.396017i
$115$	4.63856	+	3.89221i	0.432548	+	0.362951i
$116$	0.0223692	+	0.00814172i	0.00207693	+	0.000755940i
$117$	−2.13253	−	3.69364i	−0.197152	−	0.341477i
$118$	0.629747	+	3.57147i	0.0579729	+	0.328781i
$119$	0.302182			0.0277010
$120$	−1.39530	+	7.91312i	−0.127373	+	0.722366i
$121$	−4.86730	−	4.08415i	−0.442481	−	0.371286i
$122$	−1.53479	−	2.65834i	−0.138954	−	0.240675i
$123$	−9.28452			−0.837157
$124$	0.00694679	+	0.00582905i	0.000623840	+	0.000523464i
$125$	−11.3621			−1.01625
$126$	0.360211			0.0320902
$127$	−6.55156	−	9.16935i	−0.581357	−	0.813648i
$127$	−6.55156	−	9.16935i	−0.581357	−	0.813648i
$128$	11.3419			1.00249
$129$	−4.18031			−0.368055
$130$	6.78037	+	5.68941i	0.594678	+	0.498994i
$131$	−15.0496			−1.31489			−0.657445	−	0.753503i	$-0.728363\pi$
$131$	−15.0496			−1.31489			−0.657445	+	0.753503i	$0.728363\pi$
$132$	0.00715061	+	0.0123852i	0.000622380	+	0.00107799i
$133$	−0.878130	−	0.736838i	−0.0761435	−	0.0638920i
$134$	2.75296	−	15.6128i	0.237820	−	1.34874i
$135$	−5.76358			−0.496050
$136$	−0.566894	−	3.21502i	−0.0486108	−	0.275685i
$137$	7.07742	+	12.2585i	0.604665	+	1.04731i	0.992104	+	0.125415i	$0.0400263\pi$
$137$	7.07742	+	12.2585i	0.604665	+	1.04731i	−0.387440	+	0.921895i	$0.626640\pi$
$138$	−11.2534	−	4.09590i	−0.957953	−	0.348666i
$139$	−10.9956	−	9.22644i	−0.932638	−	0.782576i	0.0436511	−	0.999047i	$-0.486101\pi$
$139$	−10.9956	−	9.22644i	−0.932638	−	0.782576i	−0.976289	+	0.216471i	$0.930545\pi$
$140$	−0.00116718		0.000424818i	−9.86445e−5		3.59037e-5i
$141$	−0.496252	+	2.81438i	−0.0417919	+	0.237014i
$142$	−2.92282	+	16.5762i	−0.245278	+	1.39104i
$143$	−9.44956			−0.790212
$144$	−0.676882	−	3.83879i	−0.0564068	−	0.319899i
$145$	−1.77143	−	10.0463i	−0.147109	−	0.834299i
$146$	7.93650	−	13.7464i	0.656829	−	1.13766i
$147$	6.90804	+	11.9651i	0.569765	+	0.986863i
$148$	−0.0225700	+	0.0189384i	−0.00185524	+	0.00155673i
$149$	16.6719	+	6.06807i	1.36581	+	0.497115i	0.917847	−	0.396935i	$-0.129926\pi$
$149$	16.6719	+	6.06807i	1.36581	+	0.497115i	0.447966	+	0.894050i	$0.352148\pi$
$150$	7.86085	−	2.86111i	0.641835	−	0.233609i
$151$	1.90469	+	1.59822i	0.155001	+	0.130062i	0.716990	−	0.697083i	$-0.245519\pi$
$151$	1.90469	+	1.59822i	0.155001	+	0.130062i	−0.561989	+	0.827145i	$0.689964\pi$
$152$	−6.19210	+	10.7250i	−0.502245	+	0.869914i
$153$	−1.05608	+	0.384381i	−0.0853789	+	0.0310754i
$154$	0.399038	−	0.691155i	0.0321554	−	0.0556948i
$155$	0.674823	−	3.82711i	0.0542031	−	0.307401i
$156$	−0.0273321	−	0.00994806i	−0.00218832	−	0.000796482i
$157$	2.32755	−	13.2002i	0.185759	−	1.05349i	−0.739218	−	0.673466i	$-0.764805\pi$
$157$	2.32755	−	13.2002i	0.185759	−	1.05349i	0.924977	−	0.380023i	$-0.124084\pi$
$158$	−0.873594	−	0.733032i	−0.0694994	−	0.0583169i
$159$	−2.45502			−0.194696
$160$	0.0134300	+	0.0232615i	0.00106174	+	0.00183898i
$161$	0.192823	+	1.09355i	0.0151966	+	0.0861840i
$162$	14.5933	−	5.31153i	1.14656	−	0.417313i
$163$	3.92486	+	22.2590i	0.307419	+	1.74346i	0.611895	+	0.790939i	$0.290408\pi$
$163$	3.92486	+	22.2590i	0.307419	+	1.74346i	−0.304476	+	0.952520i	$0.598481\pi$
$164$	−0.0118777	+	0.00996655i	−0.000927490	+	0.000778257i
$165$	3.06431	−	5.30754i	0.238556	−	0.413191i
$166$	−1.95512	−	0.711605i	−0.151747	−	0.0552313i
$167$	−5.77600	−	10.0043i	−0.446960	−	0.774157i	0.551226	−	0.834356i	$-0.314160\pi$
$167$	−5.77600	−	10.0043i	−0.446960	−	0.774157i	−0.998186	+	0.0601983i	$0.980827\pi$
$168$	−1.12878	+	0.947159i	−0.0870873	+	0.0730749i
$169$	4.76385	−	3.99734i	0.366450	−	0.307488i
$170$	1.78665	−	1.49918i	0.137030	−	0.114982i
$171$	4.00620	+	1.45814i	0.306362	+	0.111507i
$172$	−0.00534786	+	0.00448739i	−0.000407771	+	0.000342160i
$173$	−20.1199	+	7.32304i	−1.52969	+	0.556760i	−0.963545	−	0.267548i	$-0.913787\pi$
$173$	−20.1199	+	7.32304i	−1.52969	+	0.556760i	−0.566141	+	0.824308i	$0.691564\pi$
$174$	10.0877	+	17.4724i	0.764748	+	1.32458i
$175$	−0.594194	−	0.498588i	−0.0449168	−	0.0376897i
$176$	−8.11551	−	2.95380i	−0.611729	−	0.222651i
$177$	−2.55354	+	4.42286i	−0.191936	+	0.332443i
$178$	−7.89452	+	13.6737i	−0.591719	+	1.02489i
$179$	−5.41374	+	1.97044i	−0.404642	+	0.147277i	−0.536319	−	0.844015i	$-0.680186\pi$
$179$	−5.41374	+	1.97044i	−0.404642	+	0.147277i	0.131678	+	0.991293i	$0.457964\pi$
$180$	0.00353873	−	0.00296935i	0.000263761	−	0.000221322i
$181$	4.68032	−	8.10655i	0.347885	−	0.602555i	−0.637988	−	0.770046i	$-0.720233\pi$
$181$	4.68032	−	8.10655i	0.347885	−	0.602555i	0.985874	+	0.167491i	$0.0535665\pi$
$182$	0.281857	+	1.59849i	0.0208926	+	0.118488i
$183$	0.750633	−	4.25705i	0.0554884	−	0.314690i
$184$	11.2729	−	4.10301i	0.831052	−	0.302478i
$185$	11.8646	+	4.31835i	0.872301	+	0.317492i
$186$	1.33462	+	7.56902i	0.0978593	+	0.554987i
$187$	−0.432383	+	2.45216i	−0.0316189	+	0.179320i
$188$	0.00238627	+	0.00413314i	0.000174037	+	0.000301440i
$189$	−0.809664	−	0.679389i	−0.0588944	−	0.0494183i
$190$	−8.84752			−0.641867
$191$	22.6420			1.63832			0.819158	−	0.573568i	$-0.194441\pi$
$191$	22.6420			1.63832			0.819158	+	0.573568i	$0.194441\pi$
$192$	12.1947	+	10.2326i	0.880077	+	0.738472i
$193$	13.5986	+	23.5535i	0.978852	+	1.69542i	0.666590	+	0.745424i	$0.267753\pi$
$193$	13.5986	+	23.5535i	0.978852	+	1.69542i	0.312261	+	0.949996i	$0.398914\pi$
$194$	3.86817	−	21.9375i	0.277718	−	1.57502i
$195$	2.16444	+	12.2752i	0.154999	+	0.879044i
$196$	0.0216815	+	0.00789141i	0.00154868	+	0.000563672i
$197$	11.0740	−	4.03062i	0.788992	−	0.287170i	0.0840749	−	0.996459i	$-0.473206\pi$
$197$	11.0740	−	4.03062i	0.788992	−	0.287170i	0.704917	+	0.709290i	$0.250984\pi$
$198$	−0.515415	+	2.92306i	−0.0366289	+	0.207733i
$199$	1.79763	+	10.1949i	0.127430	+	0.722694i	0.979835	+	0.199810i	$0.0640327\pi$
$199$	1.79763	+	10.1949i	0.127430	+	0.722694i	−0.852404	+	0.522884i	$0.824856\pi$
$200$	−4.18993	+	7.25718i	−0.296273	+	0.513160i
$201$	17.1025	−	14.3507i	1.20632	−	1.01222i
$202$	15.2346	−	5.54495i	1.07190	−	0.390141i
$203$	0.935370	−	1.62011i	0.0656501	−	0.113709i
$204$	−0.00383216	+	0.00663749i	−0.000268305	+	0.000464717i
$205$	6.24385	+	2.27258i	0.436090	+	0.158724i
$206$	−15.4771	−	12.9868i	−1.07834	−	0.904834i
$207$	−2.06491	−	3.57652i	−0.143521	−	0.248585i
$208$	16.5055	−	6.00752i	1.14445	−	0.416547i
$209$	7.23582	−	6.07157i	0.500512	−	0.419980i
$210$	−0.989225	−	0.360049i	−0.0682630	−	0.0248457i
$211$	6.81034	−	5.71456i	0.468843	−	0.393406i	−0.377529	−	0.925998i	$-0.623226\pi$
$211$	6.81034	−	5.71456i	0.468843	−	0.393406i	0.846372	+	0.532591i	$0.178782\pi$
$212$	−0.00314071	+	0.00263537i	−0.000215705	+	0.000180998i
$213$	−18.1578	+	15.2362i	−1.24415	+	1.04397i
$214$	−12.5430	−	21.7251i	−0.857420	−	1.48509i
$215$	2.81126	+	1.02322i	0.191727	+	0.0697828i
$216$	−5.70932	+	9.88882i	−0.388470	+	0.672849i
$217$	0.545925	−	0.458085i	0.0370598	−	0.0310968i
$218$	0.989728	+	5.61303i	0.0670328	+	0.380162i
$219$	21.0050	−	7.64518i	1.41938	−	0.516613i
$220$	−0.00177726	−	0.0100793i	−0.000119823	−	0.000679549i
$221$	−2.53211	−	4.38574i	−0.170328	−	0.295016i
$222$	−24.9709			−1.67594
$223$	3.01042	+	2.52604i	0.201593	+	0.169156i	0.737995	−	0.674806i	$-0.235773\pi$
$223$	3.01042	+	2.52604i	0.201593	+	0.169156i	−0.536403	+	0.843962i	$0.680217\pi$
$224$	−0.000855333		0.00485084i	−5.71494e−5		0.000324110i
$225$	2.71083	+	0.986660i	0.180722	+	0.0657773i
$226$	−2.70246	+	15.3264i	−0.179765	+	1.01950i
$227$	11.5273	−	19.9659i	0.765094	−	1.32518i	−0.175102	−	0.984550i	$-0.556026\pi$
$227$	11.5273	−	19.9659i	0.765094	−	1.32518i	0.940197	−	0.340632i	$-0.110641\pi$
$228$	0.0273209	−	0.00994399i	0.00180937	−	0.000658557i
$229$	1.83056	−	3.17063i	0.120967	−	0.209521i	−0.799182	−	0.601089i	$-0.794734\pi$
$229$	1.83056	−	3.17063i	0.120967	−	0.209521i	0.920149	+	0.391568i	$0.128067\pi$
$230$	6.56537	+	5.50900i	0.432908	+	0.363253i
$231$	1.05611	−	0.384391i	0.0694866	−	0.0252911i
$232$	−18.9916	−	6.91239i	−1.24686	−	0.453820i
$233$	−4.61975	+	3.87643i	−0.302650	+	0.253953i	−0.781446	−	0.623973i	$-0.785518\pi$
$233$	−4.61975	+	3.87643i	−0.302650	+	0.253953i	0.478796	+	0.877926i	$0.341073\pi$
$234$	−3.01835	−	5.22794i	−0.197316	−	0.341761i
$235$	1.02261	−	1.77121i	0.0667076	−	0.115541i
$236$	0.00148102	+	0.00839929i	9.64063e−5	+	0.000546747i
$237$	−0.278871	−	1.58155i	−0.0181146	−	0.102733i
$238$	0.427706			0.0277240
$239$	−0.176143	+	0.998958i	−0.0113938	+	0.0646172i	−0.989975	−	0.141246i	$-0.954889\pi$
$239$	−0.176143	+	0.998958i	−0.0113938	+	0.0646172i	0.978581	+	0.205863i	$0.0660002\pi$
$240$	−1.97818	+	11.2188i	−0.127691	+	0.724170i
$241$	−18.5093	+	6.73683i	−1.19229	+	0.433957i	−0.860526	−	0.509406i	$-0.829865\pi$
$241$	−18.5093	+	6.73683i	−1.19229	+	0.433957i	−0.331761	+	0.943363i	$0.607643\pi$
$242$	−6.88912	−	5.78066i	−0.442849	−	0.371595i
$243$	9.16050	+	3.33415i	0.587646	+	0.213886i
$244$	−0.00360949	−	0.00625181i	−0.000231074	−	0.000400231i
$245$	−1.71697	−	9.73742i	−0.109693	−	0.622101i
$246$	−13.1412			−0.837853
$247$	−3.33594	+	18.9190i	−0.212261	+	1.20379i
$248$	−5.89788	−	4.94891i	−0.374516	−	0.314256i
$249$	−1.46499	−	2.53743i	−0.0928399	−	0.160803i
$250$	−16.0818			−1.01710
$251$	−1.93725	−	1.62555i	−0.122278	−	0.102604i	0.579598	−	0.814903i	$-0.303210\pi$
$251$	−1.93725	−	1.62555i	−0.122278	−	0.102604i	−0.701876	+	0.712299i	$0.747654\pi$
$252$	0.000847134	0		5.33644e−5	0
$253$	−9.14992			−0.575251
$254$	−9.27302	−	12.9782i	−0.581841	−	0.814325i
$255$	3.28445			0.205680
$256$	0.0798879			0.00499299
$257$	2.67632	+	2.24570i	0.166944	+	0.140083i	0.722432	−	0.691442i	$-0.243024\pi$
$257$	2.67632	+	2.24570i	0.166944	+	0.140083i	−0.555488	+	0.831525i	$0.687469\pi$
$258$	−5.91676			−0.368362
$259$	1.15770	+	2.00519i	0.0719359	+	0.124597i
$260$	0.0159459	+	0.0133802i	0.000988921	+	0.000829803i
$261$	−1.20816	+	6.85183i	−0.0747834	+	0.424118i
$262$	−21.3010			−1.31598
$263$	−1.41261	−	8.01133i	−0.0871054	−	0.493999i	−0.996882	−	0.0789020i	$-0.974859\pi$
$263$	−1.41261	−	8.01133i	−0.0871054	−	0.493999i	0.909777	−	0.415097i	$-0.136253\pi$
$264$	−6.07092	−	10.5151i	−0.373639	−	0.647162i
$265$	1.65101	+	0.600917i	0.101420	+	0.0369140i
$266$	−1.24290	−	1.04291i	−0.0762068	−	0.0639451i
$267$	−20.8938	+	7.60474i	−1.27868	+	0.465402i
$268$	0.00647433	−	0.0367178i	0.000395483	−	0.00224289i
$269$	−0.361738	+	2.05152i	−0.0220555	+	0.125083i	−0.993848	−	0.110756i	$-0.964673\pi$
$269$	−0.361738	+	2.05152i	−0.0220555	+	0.125083i	0.971792	+	0.235839i	$0.0757839\pi$
$270$	−8.15771			−0.496462
$271$	−1.09417	−	6.20537i	−0.0664664	−	0.376950i	−0.999837	−	0.0180364i	$-0.994259\pi$
$271$	−1.09417	−	6.20537i	−0.0664664	−	0.376950i	0.933371	−	0.358913i	$-0.116853\pi$
$272$	−0.803712	−	4.55808i	−0.0487322	−	0.276374i
$273$	−1.14289	+	1.97955i	−0.0691710	+	0.119808i
$274$	10.0173	+	17.3505i	0.605168	+	1.04818i
$275$	4.89618	−	4.10838i	0.295251	−	0.247745i
$276$	−0.0264654	−	0.00963262i	−0.00159303	−	0.000579816i
$277$	−11.6526	+	4.24121i	−0.700139	+	0.254830i	−0.667470	−	0.744637i	$-0.732623\pi$
$277$	−11.6526	+	4.24121i	−0.700139	+	0.254830i	−0.0326685	+	0.999466i	$0.510401\pi$
$278$	−15.5631	−	13.0590i	−0.933414	−	0.783227i
$279$	−1.32523	+	2.29536i	−0.0793393	+	0.137420i
$280$	0.990943	−	0.360674i	0.0592202	−	0.0215544i
$281$	−12.4939	+	21.6401i	−0.745324	+	1.29094i	0.204719	+	0.978821i	$0.434372\pi$
$281$	−12.4939	+	21.6401i	−0.745324	+	1.29094i	−0.950043	+	0.312118i	$0.898961\pi$
$282$	−0.702389	+	3.98345i	−0.0418267	+	0.237211i
$283$	3.91474	+	1.42485i	0.232707	+	0.0846985i	0.455742	−	0.890112i	$-0.349374\pi$
$283$	3.91474	+	1.42485i	0.232707	+	0.0846985i	−0.223035	+	0.974811i	$0.571596\pi$
$284$	−0.00687381	+	0.0389833i	−0.000407885	+	0.00231323i
$285$	−9.54449	−	8.00878i	−0.565367	−	0.474399i
$286$	−13.3748			−0.790869
$287$	0.609250	+	1.05525i	0.0359629	+	0.0622896i
$288$	−0.00318110	−	0.0180409i	−0.000187448	−	0.00106307i
$289$	14.7208	−	5.35794i	0.865930	−	0.315173i
$290$	−2.50727	−	14.2194i	−0.147232	−	0.834993i
$291$	24.0307	−	20.1641i	1.40870	−	1.18204i
$292$	0.0186648	−	0.0323284i	0.00109228	−	0.00189188i
$293$	−10.0182	−	3.64632i	−0.585269	−	0.213020i	0.0323785	−	0.999476i	$-0.489692\pi$
$293$	−10.0182	−	3.64632i	−0.585269	−	0.213020i	−0.617647	+	0.786455i	$0.711914\pi$
$294$	9.77757	+	16.9352i	0.570239	+	0.987683i
$295$	2.79985	−	2.34935i	0.163013	−	0.136785i
$296$	19.1621	−	16.0789i	1.11377	−	0.934566i
$297$	6.67166	−	5.59819i	0.387129	−	0.324840i
$298$	23.5972	+	8.58868i	1.36695	+	0.497529i
$299$	14.2556	−	11.9619i	0.824422	−	0.691772i
$300$	0.0184869	−	0.00672868i	0.00106734	−	0.000388481i
$301$	0.274312	+	0.475122i	0.0158111	+	0.0273856i
$302$	2.69588	+	2.26211i	0.155130	+	0.130170i
$303$	21.4540	+	7.80862i	1.23250	+	0.448594i
$304$	−8.77882	+	15.2054i	−0.503500	+	0.872087i
$305$	−1.54680	+	2.67914i	−0.0885696	+	0.153407i
$306$	−1.49476	+	0.544050i	−0.0854500	+	0.0311012i
$307$	−20.5261	+	17.2234i	−1.17149	+	0.982994i	−0.999998	−	0.00219251i	$-0.999302\pi$
$307$	−20.5261	+	17.2234i	−1.17149	+	0.982994i	−0.171489	+	0.985186i	$0.554858\pi$
$308$	0.000938446	−	0.00162544i	5.34729e−5	−	9.26179e-5i
$309$	−4.94063	−	28.0197i	−0.281063	−	1.59399i
$310$	0.955138	−	5.41685i	0.0542482	−	0.307657i
$311$	27.2125	−	9.90455i	1.54308	−	0.561635i	0.576299	−	0.817239i	$-0.304496\pi$
$311$	27.2125	−	9.90455i	1.54308	−	0.561635i	0.966782	+	0.255603i	$0.0822741\pi$
$312$	23.2051	+	8.44598i	1.31373	+	0.478159i
$313$	4.93133	+	27.9669i	0.278735	+	1.58079i	0.726842	+	0.686805i	$0.240987\pi$
$313$	4.93133	+	27.9669i	0.278735	+	1.58079i	−0.448106	+	0.893980i	$0.647901\pi$
$314$	3.29439	−	18.6834i	0.185913	−	1.05437i
$315$	−0.181515	−	0.314393i	−0.0102272	−	0.0177140i
$316$	−0.00205449	−	0.00172392i	−0.000115574	−	9.69783e-5i
$317$	−11.1838			−0.628144			−0.314072	−	0.949399i	$-0.601693\pi$
$317$	−11.1838			−0.628144			−0.314072	+	0.949399i	$0.601693\pi$
$318$	−3.47481			−0.194858
$319$	11.8085	+	9.90854i	0.661152	+	0.554772i
$320$	−5.69633	−	9.86632i	−0.318434	−	0.551544i
$321$	6.13448	−	34.7904i	0.342393	−	1.94181i
$322$	0.272920	+	1.54780i	0.0152092	+	0.0862557i
$323$	4.75686	+	1.73135i	0.264679	+	0.0963351i
$324$	0.0343201	−	0.0124915i	0.00190667	−	0.000693972i
$325$	−2.25729	+	12.8017i	−0.125212	+	0.710112i
$326$	5.55521	+	31.5052i	0.307675	+	1.74491i
$327$	−4.01322	+	6.95109i	−0.221931	+	0.384396i
$328$	10.0842	−	8.46168i	0.556809	−	0.467218i
$329$	0.352439	−	0.128277i	0.0194306	−	0.00707216i
$330$	4.33719	−	7.51223i	0.238754	−	0.413535i
$331$	5.28323	−	9.15083i	0.290393	−	0.502975i	−0.683510	−	0.729941i	$-0.739547\pi$
$331$	5.28323	−	9.15083i	0.290393	−	0.502975i	0.973903	+	0.226966i	$0.0728807\pi$
$332$	−0.00459799	−	0.00167353i	−0.000252348	−	9.18470e-5i
$333$	−6.59662	−	5.53522i	−0.361492	−	0.303328i
$334$	−8.17529	−	14.1600i	−0.447332	−	0.774801i
$335$	−15.0141	+	5.46469i	−0.820309	+	0.298568i
$336$	−1.60032	+	1.34283i	−0.0873048	+	0.0732574i
$337$	29.0958	+	10.5900i	1.58495	+	0.576873i	0.976272	−	0.216547i	$-0.0694794\pi$
$337$	29.0958	+	10.5900i	1.58495	+	0.576873i	0.608674	+	0.793420i	$0.291702\pi$
$338$	6.74270	−	5.65780i	0.366754	−	0.307744i
$339$	−16.7888	+	14.0875i	−0.911842	+	0.765126i
$340$	0.00420179	−	0.00352572i	0.000227874	−	0.000191209i
$341$	2.93615	+	5.08556i	0.159001	+	0.275398i
$342$	5.67033	+	2.06383i	0.306616	+	0.111599i
$343$	1.82217	−	3.15610i	0.0983881	−	0.170413i
$344$	4.54038	−	3.80983i	0.244801	−	0.205412i
$345$	2.09581	+	11.8859i	0.112835	+	0.639918i
$346$	−28.4775	+	10.3650i	−1.53096	+	0.557223i
$347$	4.50563	+	25.5527i	0.241875	+	1.37174i	0.827639	+	0.561260i	$0.189683\pi$
$347$	4.50563	+	25.5527i	0.241875	+	1.37174i	−0.585764	+	0.810481i	$0.699206\pi$
$348$	0.0237240	+	0.0410911i	0.00127174	+	0.00220272i
$349$	−14.5247			−0.777489			−0.388745	−	0.921346i	$-0.627091\pi$
$349$	−14.5247			−0.777489			−0.388745	+	0.921346i	$0.627091\pi$
$350$	−0.841016	−	0.705696i	−0.0449542	−	0.0377210i
$351$	−3.07584	+	17.4440i	−0.164176	+	0.931091i
$352$	−0.0381400	−	0.0138818i	−0.00203287	−	0.000739903i
$353$	−0.630390	+	3.57512i	−0.0335523	+	0.190285i	−0.996977	−	0.0776936i	$-0.975244\pi$
$353$	−0.630390	+	3.57512i	−0.0335523	+	0.190285i	0.963425	+	0.267978i	$0.0863555\pi$
$354$	−3.61426	+	6.26008i	−0.192096	+	0.332719i
$355$	15.9405	−	5.80188i	0.846035	−	0.307932i
$356$	−0.0185661	+	0.0321574i	−0.000984001	+	0.00170434i
$357$	0.461398	+	0.387159i	0.0244198	+	0.0204906i
$358$	−7.66255	+	2.78894i	−0.404978	+	0.147400i
$359$	−16.2466	−	5.91329i	−0.857465	−	0.312092i	−0.124385	−	0.992234i	$-0.539696\pi$
$359$	−16.2466	−	5.91329i	−0.857465	−	0.312092i	−0.733080	+	0.680142i	$0.761918\pi$
$360$	−3.00441	+	2.52100i	−0.158346	+	0.132868i
$361$	−0.101521	−	0.175840i	−0.00534322	−	0.00925472i
$362$	6.62448	−	11.4739i	0.348175	−	0.603056i
$363$	−2.19916	−	12.4721i	−0.115426	−	0.654613i
$364$	0.000662863		0.00375928i	3.47434e−5		0.000197040i
$365$	−15.9972			−0.837331
$366$	1.06244	−	6.02538i	0.0555345	−	0.314952i
$367$	1.09505	−	6.21032i	0.0571610	−	0.324176i	−0.942797	−	0.333368i	$-0.891815\pi$
$367$	1.09505	−	6.21032i	0.0571610	−	0.324176i	0.999958	+	0.00919188i	$0.00292591\pi$
$368$	15.9822	−	5.81703i	0.833128	−	0.303234i
$369$	−3.47154	−	2.91297i	−0.180721	−	0.151643i
$370$	16.7930	+	6.11215i	0.873027	+	0.317756i
$371$	0.161099	+	0.279031i	0.00836382	+	0.0144866i
$372$	0.00313873	+	0.0178006i	0.000162735	+	0.000922918i
$373$	−9.79443			−0.507136			−0.253568	−	0.967318i	$-0.581604\pi$
$373$	−9.79443			−0.507136			−0.253568	+	0.967318i	$0.581604\pi$
$374$	−0.611990	+	3.47077i	−0.0316452	+	0.179469i
$375$	−17.3486	−	14.5572i	−0.895878	−	0.751731i
$376$	−2.02596	−	3.50907i	−0.104481	−	0.180966i
$377$	−31.3514			−1.61468
$378$	−1.14599	−	0.961600i	−0.0589434	−	0.0494594i
$379$	−0.169668			−0.00871525			−0.00435762	−	0.999991i	$-0.501387\pi$
$379$	−0.169668			−0.00871525			−0.00435762	+	0.999991i	$0.501387\pi$
$380$	−0.0208073			−0.00106739
$381$	1.74437	−	22.3945i	0.0893668	−	1.14730i
$382$	32.0472			1.63968
$383$	32.8058			1.67630			0.838149	−	0.545442i	$-0.183638\pi$
$383$	32.8058			1.67630			0.838149	+	0.545442i	$0.183638\pi$
$384$	17.3178	+	14.5313i	0.883743	+	0.741549i
$385$	−0.804320			−0.0409920
$386$	19.2474	+	33.3374i	0.979666	+	1.69683i
$387$	−1.56304	−	1.31155i	−0.0794539	−	0.0666697i
$388$	0.00909704	−	0.0515919i	0.000461832	−	0.00261918i
$389$	35.0427			1.77674			0.888369	−	0.459130i	$-0.151839\pi$
$389$	35.0427			1.77674			0.888369	+	0.459130i	$0.151839\pi$
$390$	3.06353	+	17.3742i	0.155128	+	0.879775i
$391$	−2.45182	−	4.24667i	−0.123994	−	0.214763i
$392$	−18.4077	−	6.69987i	−0.929731	−	0.338394i
$393$	−22.9790	−	19.2817i	−1.15914	−	0.972633i
$394$	15.6741	−	5.70489i	0.789648	−	0.287408i
$395$	−0.199577	+	1.13186i	−0.0100418	+	0.0569499i
$396$	−0.00121214	+	0.00687437i	−6.09122e−5	+	0.000345450i
$397$	−26.7105			−1.34056			−0.670281	−	0.742107i	$-0.733826\pi$
$397$	−26.7105			−1.34056			−0.670281	+	0.742107i	$0.733826\pi$
$398$	2.54434	+	14.4297i	0.127536	+	0.723295i
$399$	−0.396760	−	2.25014i	−0.0198628	−	0.112648i
$400$	−5.94026	+	10.2888i	−0.297013	+	0.514441i
$401$	9.37718	+	16.2417i	0.468274	+	0.811074i	0.999343	−	0.0362547i	$-0.0115427\pi$
$401$	9.37718	+	16.2417i	0.468274	+	0.811074i	−0.531069	+	0.847329i	$0.678209\pi$
$402$	24.2068	−	20.3119i	1.20732	−	1.01306i
$403$	−11.2230	−	4.08482i	−0.559056	−	0.203480i
$404$	0.0358283	−	0.0130404i	0.00178253	−	0.000648786i
$405$	−11.9896	−	10.0605i	−0.595770	−	0.499911i
$406$	1.32391	−	2.29308i	0.0657047	−	0.113804i
$407$	−17.9284	+	6.52539i	−0.888676	+	0.323451i
$408$	3.25353	−	5.63528i	0.161074	−	0.278988i
$409$	−4.05018	+	22.9697i	−0.200269	+	1.13578i	0.704445	+	0.709759i	$0.251196\pi$
$409$	−4.05018	+	22.9697i	−0.200269	+	1.13578i	−0.904713	+	0.426021i	$0.859915\pi$
$410$	8.83749	+	3.21658i	0.436452	+	0.158856i
$411$	−4.89923	+	27.7849i	−0.241661	+	1.37053i
$412$	−0.0363986	−	0.0305420i	−0.00179323	−	0.00150470i
$413$	0.670254			0.0329811
$414$	−2.92265	−	5.06217i	−0.143640	−	0.248792i
$415$	0.364118	+	2.06502i	0.0178738	+	0.101368i
$416$	0.0775700	−	0.0282332i	0.00380318	−	0.00138425i
$417$	−4.96809	−	28.1755i	−0.243289	−	1.37976i
$418$	10.2415	−	8.59365i	0.500929	−	0.420329i
$419$	−1.84148	+	3.18954i	−0.0899623	+	0.155819i	−0.907495	−	0.420063i	$-0.862008\pi$
$419$	−1.84148	+	3.18954i	−0.0899623	+	0.155819i	0.817533	+	0.575882i	$0.195341\pi$
$420$	−0.00232643		0.000846751i	−0.000113518		4.13172e-5i
$421$	−16.3397	−	28.3012i	−0.796348	−	1.37931i	−0.921980	−	0.387237i	$-0.873429\pi$
$421$	−16.3397	−	28.3012i	−0.796348	−	1.37931i	0.125632	−	0.992077i	$-0.459904\pi$
$422$	9.63929	−	8.08833i	0.469233	−	0.393734i
$423$	−1.06855	+	0.896618i	−0.0519546	+	0.0435951i
$424$	2.66648	−	2.23745i	0.129496	−	0.108660i
$425$	3.21877	+	1.17153i	0.156133	+	0.0568278i
$426$	−25.7004	+	21.5652i	−1.24519	+	1.04484i
$427$	−0.533101	+	0.194033i	−0.0257986	+	0.00938991i
$428$	−0.0294982	−	0.0510924i	−0.00142585	−	0.00246964i
$429$	−14.4284	−	12.1069i	−0.696610	−	0.584525i
$430$	3.97903	+	1.44825i	0.191886	+	0.0698408i
$431$	3.42697	−	5.93569i	0.165071	−	0.285912i	−0.771609	−	0.636097i	$-0.780548\pi$
$431$	3.42697	−	5.93569i	0.165071	−	0.285912i	0.936681	+	0.350185i	$0.113881\pi$
$432$	−8.09436	+	14.0198i	−0.389440	+	0.674530i
$433$	−3.64391	+	1.32628i	−0.175115	+	0.0637368i	−0.428090	−	0.903736i	$-0.640813\pi$
$433$	−3.64391	+	1.32628i	−0.175115	+	0.0637368i	0.252975	+	0.967473i	$0.418591\pi$
$434$	0.772696	−	0.648369i	0.0370906	−	0.0311227i
$435$	10.1666	−	17.6091i	0.487453	−	0.844293i
$436$	0.00232761	+	0.0132005i	0.000111472	+	0.000632192i
$437$	−3.23016	+	18.3191i	−0.154519	+	0.876323i
$438$	29.7302	−	10.8209i	1.42056	−	0.517043i
$439$	19.2982	+	7.02397i	0.921053	+	0.335236i	0.758657	−	0.651490i	$-0.225856\pi$
$439$	19.2982	+	7.02397i	0.921053	+	0.335236i	0.162396	+	0.986726i	$0.448078\pi$
$440$	1.50891	+	8.55743i	0.0719343	+	0.407960i
$441$	−1.17102	+	6.64117i	−0.0557627	+	0.316246i
$442$	−3.58392	−	6.20753i	−0.170470	−	0.295262i
$443$	−23.6016	−	19.8041i	−1.12135	−	0.940920i	−0.122673	−	0.992447i	$-0.539147\pi$
$443$	−23.6016	−	19.8041i	−1.12135	−	0.940920i	−0.998672	+	0.0515269i	$0.983591\pi$
$444$	−0.0587259			−0.00278701
$445$	15.9126			0.754328
$446$	4.26092	+	3.57533i	0.201760	+	0.169297i
$447$	17.6816	+	30.6254i	0.836311	+	1.44853i
$448$	0.362789	−	2.05748i	0.0171402	−	0.0972067i
$449$	0.292965	+	1.66149i	0.0138259	+	0.0784105i	0.990940	−	0.134305i	$-0.0428803\pi$
$449$	0.292965	+	1.66149i	0.0138259	+	0.0784105i	−0.977114	+	0.212716i	$0.931769\pi$
$450$	3.83688	+	1.39651i	0.180872	+	0.0658321i
$451$	−9.43498	+	3.43405i	−0.444276	+	0.161703i
$452$	−0.00635556	+	0.0360441i	−0.000298940	+	0.00169537i
$453$	0.860584	+	4.88062i	0.0404338	+	0.229311i
$454$	16.3156	−	28.2595i	0.765731	−	1.32628i
$455$	1.25313	−	1.05150i	0.0587477	−	0.0492952i
$456$	−23.1956	+	8.44253i	−1.08624	+	0.395357i
$457$	−3.26845	+	5.66113i	−0.152892	+	0.264816i	−0.932289	−	0.361713i	$-0.882192\pi$
$457$	−3.26845	+	5.66113i	−0.152892	+	0.264816i	0.779398	+	0.626530i	$0.215525\pi$
$458$	2.59096	−	4.48768i	0.121068	−	0.209695i
$459$	4.38598	+	1.59636i	0.204720	+	0.0745119i
$460$	0.0154402	+	0.0129559i	0.000719905	+	0.000604072i
$461$	11.7289	+	20.3151i	0.546269	+	0.946166i	0.998526	+	0.0542784i	$0.0172858\pi$
$461$	11.7289	+	20.3151i	0.546269	+	0.946166i	−0.452256	+	0.891888i	$0.649381\pi$
$462$	1.49480	−	0.544063i	0.0695444	−	0.0253121i
$463$	27.5084	−	23.0823i	1.27842	−	1.07273i	0.284966	−	0.958538i	$-0.408018\pi$
$463$	27.5084	−	23.0823i	1.27842	−	1.07273i	0.993459	−	0.114188i	$-0.0364267\pi$
$464$	−26.9253	−	9.80000i	−1.24998	−	0.454954i
$465$	5.93371	−	4.97898i	0.275169	−	0.230895i
$466$	−6.53874	+	5.48666i	−0.302901	+	0.254165i
$467$	1.33536	−	1.12050i	0.0617929	−	0.0518504i	−0.611368	−	0.791346i	$-0.709381\pi$
$467$	1.33536	−	1.12050i	0.0617929	−	0.0518504i	0.673161	+	0.739496i	$0.264936\pi$
$468$	−0.00709848	−	0.0122949i	−0.000328127	−	0.000568333i
$469$	−2.75334	−	1.00213i	−0.127137	−	0.0462742i
$470$	1.44739	−	2.50695i	0.0667631	−	0.115637i
$471$	20.4661	−	17.1731i	0.943029	−	0.791295i
$472$	−1.25740	−	7.13106i	−0.0578764	−	0.328234i
$473$	−4.24805	+	1.54616i	−0.195326	+	0.0710927i
$474$	−0.394711	−	2.23852i	−0.0181297	−	0.102818i
$475$	−6.49695	−	11.2530i	−0.298100	−	0.516325i
$476$	0.00100587			4.61038e−5
$477$	−0.917947	−	0.770249i	−0.0420299	−	0.0352673i
$478$	−0.249311	+	1.41391i	−0.0114032	+	0.0646710i
$479$	27.8309	+	10.1296i	1.27163	+	0.462834i	0.887654	−	0.460511i	$-0.152334\pi$
$479$	27.8309	+	10.1296i	1.27163	+	0.462834i	0.383972	+	0.923345i	$0.374556\pi$
$480$	−0.00929671	+	0.0527243i	−0.000424335	+	0.00240652i
$481$	19.4016	−	33.6046i	0.884639	−	1.53224i
$482$	−26.1979	+	9.53524i	−1.19328	+	0.434318i
$483$	−1.10665	+	1.91678i	−0.0503544	+	0.0872164i
$484$	−0.0162016	−	0.0135948i	−0.000736438	−	0.000617945i
$485$	−21.0962	+	7.67841i	−0.957931	+	0.348658i
$486$	12.9657	+	4.71912i	0.588135	+	0.214064i
$487$	−13.4886	+	11.3183i	−0.611227	+	0.512881i	−0.895032	−	0.446001i	$-0.852848\pi$
$487$	−13.4886	+	11.3183i	−0.611227	+	0.512881i	0.283805	+	0.958882i	$0.408403\pi$
$488$	3.06448	+	5.30784i	0.138723	+	0.240274i
$489$	−22.5256	+	39.0156i	−1.01864	+	1.76434i
$490$	−2.43018	−	13.7822i	−0.109784	−	0.622618i
$491$	1.26961	+	7.20029i	0.0572965	+	0.324945i	0.999961	−	0.00879643i	$-0.00280003\pi$
$491$	1.26961	+	7.20029i	0.0572965	+	0.324945i	−0.942665	+	0.333741i	$0.891689\pi$
$492$	−0.0309051			−0.00139331
$493$	−1.43454	+	8.13569i	−0.0646085	+	0.366413i
$494$	−4.72165	+	26.7778i	−0.212437	+	1.20479i
$495$	2.81097	−	1.02311i	0.126344	−	0.0459854i
$496$	−8.36169	−	7.01629i	−0.375451	−	0.315041i
$497$	2.92322	+	1.06397i	0.131124	+	0.0477254i
$498$	−2.07353	−	3.59146i	−0.0929171	−	0.160937i
$499$	5.43274	+	30.8106i	0.243203	+	1.37927i	0.824630	+	0.565673i	$0.191384\pi$
$499$	5.43274	+	30.8106i	0.243203	+	1.37927i	−0.581427	+	0.813599i	$0.697505\pi$
$500$	−0.0378206			−0.00169139
$501$	3.99834	−	22.6757i	0.178633	−	1.01308i
$502$	−2.74197	−	2.30078i	−0.122380	−	0.102689i
$503$	−16.4910	−	28.5632i	−0.735295	−	1.27357i	−0.954594	−	0.297911i	$-0.903710\pi$
$503$	−16.4910	−	28.5632i	−0.735295	−	1.27357i	0.219298	−	0.975658i	$-0.429623\pi$
$504$	−0.719223			−0.0320368
$505$	−12.5165	−	10.5026i	−0.556979	−	0.467361i
$506$	−12.9507			−0.575729
$507$	12.3953			0.550494
$508$	−0.0218080	−	0.0305218i	−0.000967574	−	0.00135418i
$509$	−35.3319			−1.56606			−0.783030	−	0.621984i	$-0.786327\pi$
$509$	−35.3319			−1.56606			−0.783030	+	0.621984i	$0.786327\pi$
$510$	4.64878			0.205851
$511$	−2.24728	−	1.88569i	−0.0994136	−	0.0834180i
$512$	−22.5707			−0.997492
$513$	−8.85292	−	15.3337i	−0.390866	−	0.676999i
$514$	3.78804	+	3.17854i	0.167083	+	0.140199i
$515$	−3.53582	+	20.0526i	−0.155807	+	0.883624i
$516$	−0.0139149			−0.000612568
$517$	0.536658	+	3.04354i	0.0236022	+	0.133855i
$518$	1.63859	+	2.83813i	0.0719957	+	0.124700i
$519$	−40.1031	−	14.5963i	−1.76033	−	0.640708i
$520$	−13.5382	−	11.3599i	−0.593688	−	0.498163i
$521$	20.0267	−	7.28913i	0.877387	−	0.319343i	0.136232	−	0.990677i	$-0.456501\pi$
$521$	20.0267	−	7.28913i	0.877387	−	0.319343i	0.741155	+	0.671334i	$0.234278\pi$
$522$	−1.71002	+	9.69801i	−0.0748456	+	0.424470i
$523$	2.39215	−	13.5666i	0.104602	−	0.593225i	−0.886777	−	0.462197i	$-0.847061\pi$
$523$	2.39215	−	13.5666i	0.104602	−	0.593225i	0.991379	−	0.131028i	$-0.0418277\pi$
$524$	−0.0500952			−0.00218842
$525$	−0.268471	−	1.52257i	−0.0117170	−	0.0664506i
$526$	−1.99940	−	11.3391i	−0.0871779	−	0.494410i
$527$	−1.57354	+	2.72545i	−0.0685445	+	0.118723i
$528$	−8.60702	−	14.9078i	−0.374572	−	0.648779i
$529$	−3.81546	+	3.20155i	−0.165889	+	0.139198i
$530$	2.33682	+	0.850532i	0.101505	+	0.0369447i
$531$	−2.34243	+	0.852576i	−0.101653	+	0.0369987i
$532$	−0.00292301	−	0.00245269i	−0.000126728	−	0.000106338i
$533$	10.2103	−	17.6848i	0.442258	−	0.766013i
$534$	−29.5729	+	10.7637i	−1.27975	+	0.465789i
$535$	−12.6411	+	21.8950i	−0.546523	+	0.946605i
$536$	−5.49676	+	31.1737i	−0.237424	+	1.34650i
$537$	−10.7907	−	3.92750i	−0.465654	−	0.169484i
$538$	−0.512000	+	2.90370i	−0.0220739	+	0.125187i
$539$	11.4455	+	9.60391i	0.492992	+	0.413670i
$540$	−0.0191851			−0.000825593
$541$	−8.92356	−	15.4561i	−0.383654	−	0.664508i	0.607928	−	0.793992i	$-0.292001\pi$
$541$	−8.92356	−	15.4561i	−0.383654	−	0.664508i	−0.991581	+	0.129485i	$0.958668\pi$
$542$	−1.54868	−	8.78302i	−0.0665217	−	0.377263i
$543$	17.5325	−	6.38131i	0.752392	−	0.273848i
$544$	−0.00377716	−	0.0214213i	−0.000161944	−	0.000918431i
$545$	4.40032	−	3.69231i	0.188489	−	0.158161i
$546$	−1.61764	+	2.80183i	−0.0692285	+	0.119907i
$547$	4.24207	+	1.54399i	0.181378	+	0.0660161i	0.431113	−	0.902298i	$-0.358121\pi$
$547$	4.24207	+	1.54399i	0.181378	+	0.0660161i	−0.249735	+	0.968314i	$0.580343\pi$
$548$	0.0235584	+	0.0408044i	0.00100637	+	0.00174308i
$549$	1.61629	−	1.35623i	0.0689816	−	0.0578825i
$550$	6.93000	−	5.81496i	0.295496	−	0.247951i
$551$	24.0067	−	20.1440i	1.02272	−	0.858164i
$552$	22.4693	+	8.17817i	0.956358	+	0.348086i
$553$	−0.161456	+	0.135477i	−0.00686579	+	0.00576108i
$554$	−16.4930	+	6.00297i	−0.700721	+	0.255042i
$555$	12.5832	+	21.7947i	0.534125	+	0.925132i
$556$	−0.0366009	−	0.0307118i	−0.00155222	−	0.00130247i
$557$	−15.9670	−	5.81151i	−0.676543	−	0.246241i	−0.0191804	−	0.999816i	$-0.506106\pi$
$557$	−15.9670	−	5.81151i	−0.676543	−	0.246241i	−0.657362	+	0.753575i	$0.728328\pi$
$558$	−1.87571	+	3.24883i	−0.0794053	+	0.137534i
$559$	4.59714	−	7.96248i	0.194438	−	0.336777i
$560$	1.40491	−	0.511344i	0.0593681	−	0.0216082i
$561$	−3.80194	+	3.19020i	−0.160518	+	0.134691i
$562$	−17.6837	+	30.6292i	−0.745944	+	1.29201i
$563$	−6.57022	−	37.2616i	−0.276902	−	1.57039i	−0.732856	−	0.680384i	$-0.761813\pi$
$563$	−6.57022	−	37.2616i	−0.276902	−	1.57039i	0.455954	−	0.890003i	$-0.349298\pi$
$564$	−0.00165186	+	0.00936816i	−6.95558e−5	+	0.000394471i
$565$	14.7387	−	5.36444i	0.620061	−	0.225684i
$566$	5.54088	+	2.01672i	0.232901	+	0.0847689i
$567$	−0.498404	−	2.82659i	−0.0209310	−	0.118706i
$568$	5.83592	−	33.0971i	0.244870	−	1.38872i
$569$	−4.76278	−	8.24938i	−0.199666	−	0.345832i	0.748754	−	0.662848i	$-0.230652\pi$
$569$	−4.76278	−	8.24938i	−0.199666	−	0.345832i	−0.948420	+	0.317016i	$0.897319\pi$
$570$	−13.5092	−	11.3355i	−0.565837	−	0.474794i
$571$	−30.4658			−1.27495			−0.637477	−	0.770470i	$-0.720022\pi$
$571$	−30.4658			−1.27495			−0.637477	+	0.770470i	$0.720022\pi$
$572$	−0.0314545			−0.00131518
$573$	34.5717	+	29.0091i	1.44426	+	1.21187i
$574$	0.862327	+	1.49359i	0.0359928	+	0.0623414i
$575$	−2.18571	+	12.3958i	−0.0911506	+	0.516941i
$576$	1.34926	+	7.65204i	0.0562192	+	0.318835i
$577$	21.5282	+	7.83561i	0.896229	+	0.326201i	0.748741	−	0.662863i	$-0.230659\pi$
$577$	21.5282	+	7.83561i	0.896229	+	0.326201i	0.147489	+	0.989064i	$0.452881\pi$
$578$	20.8357	−	7.58357i	0.866651	−	0.315435i
$579$	−9.41345	+	53.3863i	−0.391210	+	2.21866i
$580$	−0.00589652	−	0.0334408i	−0.000244839	−	0.00138855i
$581$	−0.192265	+	0.333013i	−0.00797651	+	0.0138157i
$582$	34.0128	−	28.5401i	1.40987	−	1.18302i
$583$	−2.49481	+	0.908035i	−0.103324	+	0.0376070i
$584$	−15.8466	+	27.4471i	−0.655736	+	1.13577i
$585$	−3.04197	+	5.26885i	−0.125770	+	0.217840i
$586$	−14.1796	−	5.16097i	−0.585756	−	0.213198i
$587$	1.52859	+	1.28264i	0.0630918	+	0.0529403i	0.673788	−	0.738924i	$-0.264666\pi$
$587$	1.52859	+	1.28264i	0.0630918	+	0.0529403i	−0.610696	+	0.791865i	$0.709110\pi$
$588$	0.0229946	+	0.0398278i	0.000948281	+	0.00164247i
$589$	11.2184	−	4.08315i	0.462245	−	0.168243i
$590$	3.96288	−	3.32525i	0.163149	−	0.136898i
$591$	22.0729	+	8.03386i	0.907956	+	0.330469i
$592$	27.1669	−	22.7958i	1.11655	−	0.936900i
$593$	2.98090	−	2.50127i	0.122411	−	0.102715i	−0.579527	−	0.814953i	$-0.696763\pi$
$593$	2.98090	−	2.50127i	0.122411	−	0.102715i	0.701938	+	0.712238i	$0.252318\pi$
$594$	9.44301	−	7.92362i	0.387451	−	0.325110i
$595$	−0.215526	−	0.373302i	−0.00883570	−	0.0153039i
$596$	0.0554952	+	0.0201986i	0.00227317	+	0.000827367i
$597$	−10.3170	+	17.8695i	−0.422246	+	0.731351i
$598$	20.1772	−	16.9307i	0.825108	−	0.692348i
$599$	−3.84727	−	21.8189i	−0.157195	−	0.891498i	−0.956751	−	0.290907i	$-0.906043\pi$
$599$	−3.84727	−	21.8189i	−0.157195	−	0.891498i	0.799556	−	0.600591i	$-0.205068\pi$
$600$	−15.6955	+	5.71270i	−0.640767	+	0.233220i
$601$	−6.18463	−	35.0748i	−0.252276	−	1.43073i	−0.802968	−	0.596022i	$-0.796747\pi$
$601$	−6.18463	−	35.0748i	−0.252276	−	1.43073i	0.550692	−	0.834709i	$-0.314364\pi$
$602$	0.388258	+	0.672483i	0.0158242	+	0.0274084i
$603$	10.8972			0.443769
$604$	0.00634009	+	0.00531996i	0.000257974	+	0.000216466i
$605$	−1.57385	+	8.92577i	−0.0639863	+	0.362884i
$606$	30.3658	+	11.0522i	1.23353	+	0.448967i
$607$	6.38760	−	36.2259i	0.259265	−	1.47036i	−0.525619	−	0.850720i	$-0.676166\pi$
$607$	6.38760	−	36.2259i	0.259265	−	1.47036i	0.784884	−	0.619643i	$-0.212723\pi$
$608$	−0.0412573	+	0.0714597i	−0.00167320	+	0.00289807i
$609$	3.50390	−	1.27532i	0.141985	−	0.0516784i
$610$	−2.18933	+	3.79203i	−0.0886433	+	0.153535i
$611$	−4.81499	−	4.04026i	−0.194794	−	0.163451i
$612$	−0.00351534	+	0.00127948i	−0.000142099	+	5.17199e-5i
$613$	9.76054	+	3.55255i	0.394225	+	0.143486i	0.531523	−	0.847044i	$-0.321620\pi$
$613$	9.76054	+	3.55255i	0.394225	+	0.143486i	−0.137299	+	0.990530i	$0.543842\pi$
$614$	−29.0524	+	24.3779i	−1.17246	+	0.983811i
$615$	6.62201	+	11.4697i	0.267025	+	0.462501i
$616$	−0.796748	+	1.38001i	−0.0321019	+	0.0556021i
$617$	3.74880	+	21.2605i	0.150921	+	0.855916i	0.962421	+	0.271563i	$0.0875405\pi$
$617$	3.74880	+	21.2605i	0.150921	+	0.855916i	−0.811500	+	0.584353i	$0.801348\pi$
$618$	−6.99292	−	39.6588i	−0.281296	−	1.59531i
$619$	−12.2482			−0.492295			−0.246147	−	0.969232i	$-0.579165\pi$
$619$	−12.2482			−0.492295			−0.246147	+	0.969232i	$0.579165\pi$
$620$	0.00224626	−	0.0127392i	9.02122e−5	−	0.000511619i
$621$	−2.97831	+	16.8909i	−0.119516	+	0.677806i
$622$	38.5163	−	14.0188i	1.54436	−	0.562103i
$623$	2.23539	+	1.87571i	0.0895590	+	0.0751489i
$624$	32.8990	+	11.9743i	1.31701	+	0.479354i
$625$	0.690781	+	1.19647i	0.0276312	+	0.0478587i
$626$	6.97975	+	39.5841i	0.278967	+	1.58210i
$627$	18.8272			0.751888
$628$	0.00774765	−	0.0439391i	0.000309165	−	0.00175336i
$629$	−7.83265	−	6.57238i	−0.312308	−	0.262058i
$630$	−0.256914	−	0.444988i	−0.0102357	−	0.0177288i
$631$	−22.9969			−0.915493			−0.457746	−	0.889083i	$-0.651343\pi$
$631$	−22.9969			−0.915493			−0.457746	+	0.889083i	$0.651343\pi$
$632$	1.74428	+	1.46362i	0.0693837	+	0.0582199i
$633$	17.7202			0.704314
$634$	−15.8294			−0.628667
$635$	−6.65461	+	14.6334i	−0.264080	+	0.580708i
$636$	−0.00817196			−0.000324039
$637$	−30.3875			−1.20399
$638$	16.7137	+	14.0245i	0.661701	+	0.555233i
$639$	−11.5696			−0.457686
$640$	−8.08938	−	14.0112i	−0.319761	−	0.553842i
$641$	29.8975	+	25.0870i	1.18088	+	0.990877i	0.999973	+	0.00737760i	$0.00234839\pi$
$641$	29.8975	+	25.0870i	1.18088	+	0.990877i	0.180909	+	0.983500i	$0.442096\pi$
$642$	8.68268	−	49.2419i	0.342678	−	1.94342i
$643$	31.2445			1.23216			0.616082	−	0.787682i	$-0.288719\pi$
$643$	31.2445			1.23216			0.616082	+	0.787682i	$0.288719\pi$
$644$	0.000641844		0.00364008i	2.52922e−5		0.000143439i
$645$	2.98153	+	5.16416i	0.117398	+	0.203338i
$646$	6.73281	+	2.45054i	0.264899	+	0.0964152i
$647$	18.6195	+	15.6236i	0.732010	+	0.614229i	0.930679	−	0.365838i	$-0.119217\pi$
$647$	18.6195	+	15.6236i	0.732010	+	0.614229i	−0.198669	+	0.980067i	$0.563662\pi$
$648$	−29.1380	+	10.6054i	−1.14465	+	0.416619i
$649$	−0.959045	+	5.43901i	−0.0376458	+	0.213500i
$650$	−3.19494	+	18.1194i	−0.125316	+	0.710703i
$651$	1.42047			0.0556726
$652$	0.0130646	+	0.0740929i	0.000511648	+	0.00290170i
$653$	3.30668	+	18.7531i	0.129400	+	0.733865i	0.978597	+	0.205788i	$0.0659757\pi$
$653$	3.30668	+	18.7531i	0.129400	+	0.733865i	−0.849196	+	0.528077i	$0.822913\pi$
$654$	−5.68027	+	9.83851i	−0.222116	+	0.384716i
$655$	10.7338	+	18.5916i	0.419406	+	0.726433i
$656$	14.2969	−	11.9965i	0.558199	−	0.468385i
$657$	10.2525	+	3.73161i	0.399989	+	0.145584i
$658$	0.498839	−	0.181562i	0.0194468	−	0.00707804i
$659$	−33.9854	−	28.5172i	−1.32388	−	1.11087i	−0.985466	−	0.169876i	$-0.945663\pi$
$659$	−33.9854	−	28.5172i	−1.32388	−	1.11087i	−0.338419	−	0.940996i	$-0.609892\pi$
$660$	0.0102001	−	0.0176671i	0.000397037	−	0.000687689i
$661$	10.3316	−	3.76041i	0.401854	−	0.146263i	−0.133183	−	0.991091i	$-0.542520\pi$
$661$	10.3316	−	3.76041i	0.401854	−	0.146263i	0.535037	+	0.844828i	$0.320298\pi$
$662$	7.47783	−	12.9520i	0.290634	−	0.503393i
$663$	1.75281	−	9.94068i	0.0680735	−	0.386064i
$664$	3.90373	+	1.42084i	0.151494	+	0.0551393i
$665$	−0.283946	+	1.61034i	−0.0110109	+	0.0624462i
$666$	−9.33679	−	7.83449i	−0.361793	−	0.303580i
$667$	−30.3572			−1.17544
$668$	−0.0192264	−	0.0333011i	−0.000743892	−	0.00128846i
$669$	1.36018	+	7.71396i	0.0525876	+	0.298239i
$670$	−21.2508	+	7.73467i	−0.820992	+	0.298817i
$671$	−0.811752	−	4.60367i	−0.0313373	−	0.177723i
$672$	−0.00752094	+	0.00631082i	−0.000290127	+	0.000243445i
$673$	−5.93794	+	10.2848i	−0.228891	+	0.396451i	−0.957480	−	0.288501i	$-0.906843\pi$
$673$	−5.93794	+	10.2848i	−0.228891	+	0.396451i	0.728589	+	0.684951i	$0.240177\pi$
$674$	41.1818	+	14.9890i	1.58626	+	0.577353i
$675$	−5.99040	−	10.3757i	−0.230571	−	0.399360i
$676$	0.0158573	−	0.0133058i	0.000609895	−	0.000511763i
$677$	−1.22687	+	1.02946i	−0.0471523	+	0.0395655i	−0.666059	−	0.745899i	$-0.732020\pi$
$677$	−1.22687	+	1.02946i	−0.0471523	+	0.0395655i	0.618907	+	0.785464i	$0.287576\pi$
$678$	−23.7627	+	19.9393i	−0.912600	+	0.765762i
$679$	−3.86869	−	1.40809i	−0.148467	−	0.0540375i
$680$	−3.56736	+	2.99337i	−0.136802	+	0.114790i
$681$	43.1814	−	15.7167i	1.65472	−	0.602267i
$682$	4.15579	+	7.19805i	0.159134	+	0.275627i
$683$	−4.03077	−	3.38222i	−0.154233	−	0.129417i	0.562406	−	0.826861i	$-0.309876\pi$
$683$	−4.03077	−	3.38222i	−0.154233	−	0.129417i	−0.716639	+	0.697444i	$0.754320\pi$
$684$	0.0133353	+	0.00485366i	0.000509889	+	0.000185584i
$685$	10.0957	−	17.4862i	0.385736	−	0.668115i
$686$	2.57909	−	4.46711i	0.0984700	−	0.170555i
$687$	6.85731	−	2.49586i	0.261623	−	0.0952229i
$688$	6.43710	−	5.40137i	0.245412	−	0.205925i
$689$	2.69982	−	4.67623i	0.102855	−	0.178150i
$690$	2.96639	+	16.8232i	0.112929	+	0.640450i
$691$	0.201167	−	1.14088i	0.00765277	−	0.0434010i	−0.980742	−	0.195307i	$-0.937430\pi$
$691$	0.201167	−	1.14088i	0.00765277	−	0.0434010i	0.988395	+	0.151906i	$0.0485409\pi$
$692$	−0.0669725	+	0.0243760i	−0.00254591	+	0.000926636i
$693$	0.515485	+	0.187621i	0.0195816	+	0.00712714i
$694$	6.37723	+	36.1671i	0.242076	+	1.37288i
$695$	−3.55547	+	20.1641i	−0.134867	+	0.764868i
$696$	−20.1418	−	34.8867i	−0.763475	−	1.32238i
$697$	−4.12201	−	3.45878i	−0.156132	−	0.131011i
$698$	−20.5581			−0.778136
$699$	−12.0204			−0.454652
$700$	−0.00197788	−	0.00165963i	−7.47567e−5	−	6.27283e-5i
$701$	0.655025	+	1.13454i	0.0247400	+	0.0428509i	0.878130	−	0.478422i	$-0.158791\pi$
$701$	0.655025	+	1.13454i	0.0247400	+	0.0428509i	−0.853390	+	0.521272i	$0.825458\pi$
$702$	−4.35352	+	24.6900i	−0.164313	+	0.931865i
$703$	6.73536	+	38.1981i	0.254029	+	1.44067i
$704$	16.1770	+	5.88796i	0.609695	+	0.221911i
$705$	3.83070	−	1.39426i	0.144272	−	0.0525109i
$706$	−0.892248	+	5.06019i	−0.0335802	+	0.190443i
$707$	−0.520307	−	2.95081i	−0.0195682	−	0.110977i
$708$	−0.00849990	+	0.0147223i	−0.000319446	+	0.000553297i
$709$	25.5611	−	21.4483i	0.959967	−	0.805508i	−0.0209810	−	0.999780i	$-0.506679\pi$
$709$	25.5611	−	21.4483i	0.959967	−	0.805508i	0.980948	+	0.194272i	$0.0622345\pi$
$710$	22.5621	−	8.21192i	0.846739	−	0.308188i
$711$	0.391932	−	0.678847i	0.0146986	−	0.0254587i
$712$	15.7628	−	27.3019i	0.590734	−	1.02318i
$713$	−10.8671	−	3.95530i	−0.406976	−	0.148127i
$714$	0.653058	+	0.547981i	0.0244401	+	0.0205077i
$715$	6.73972	+	11.6735i	0.252051	+	0.436566i
$716$	−0.0180206	+	0.00655894i	−0.000673460	+	0.000245119i
$717$	−1.54883	+	1.29962i	−0.0578420	+	0.0485352i
$718$	−22.9953	−	8.36962i	−0.858178	−	0.312351i
$719$	−6.11437	+	5.13057i	−0.228028	+	0.191338i	−0.749642	−	0.661843i	$-0.769774\pi$
$719$	−6.11437	+	5.13057i	−0.228028	+	0.191338i	0.521615	+	0.853181i	$0.325330\pi$
$720$	−4.25949	+	3.57413i	−0.158742	+	0.133200i
$721$	−2.86044	+	2.40019i	−0.106528	+	0.0893879i
$722$	−0.143692	−	0.248882i	−0.00534766	−	0.00926242i
$723$	−36.8929	−	13.4279i	−1.37206	−	0.499389i
$724$	0.0155792	−	0.0269840i	0.000578998	−	0.00100285i
$725$	16.2443	−	13.6306i	0.603299	−	0.506228i
$726$	−3.11267	−	17.6528i	−0.115522	−	0.655158i
$727$	4.60859	−	1.67739i	0.170923	−	0.0622110i	−0.255141	−	0.966904i	$-0.582122\pi$
$727$	4.60859	−	1.67739i	0.170923	−	0.0622110i	0.426064	+	0.904693i	$0.359900\pi$
$728$	−0.562776	−	3.19166i	−0.0208578	−	0.118291i
$729$	−6.74292	−	11.6791i	−0.249738	−	0.432559i
$730$	−22.6422			−0.838027
$731$	−1.85592	−	1.55730i	−0.0686435	−	0.0575987i
$732$	0.00249861	−	0.0141703i	9.23513e−5	−	0.000523750i
$733$	−32.6995	−	11.9016i	−1.20778	−	0.439597i	−0.341848	−	0.939755i	$-0.611053\pi$
$733$	−32.6995	−	11.9016i	−1.20778	−	0.439597i	−0.865934	+	0.500158i	$0.833275\pi$
$734$	1.54992	−	8.79003i	0.0572086	−	0.324446i
$735$	9.85406	−	17.0677i	0.363473	−	0.629553i
$736$	0.0751104	−	0.0273380i	0.00276861	−	0.00100769i
$737$	12.0718	−	20.9090i	0.444671	−	0.770193i
$738$	−4.91358	−	4.12298i	−0.180871	−	0.151769i
$739$	−27.4986	+	10.0087i	−1.01155	+	0.368175i	−0.794029	−	0.607880i	$-0.792020\pi$
$739$	−27.4986	+	10.0087i	−1.01155	+	0.368175i	−0.217524	+	0.976055i	$0.569798\pi$
$740$	0.0394933	+	0.0143744i	0.00145180	+	0.000528413i
$741$	−29.3329	+	24.6132i	−1.07757	+	0.904189i
$742$	0.228017	+	0.394938i	0.00837078	+	0.0144986i
$743$	−17.4307	+	30.1909i	−0.639471	+	1.10760i	0.346078	+	0.938206i	$0.387513\pi$
$743$	−17.4307	+	30.1909i	−0.639471	+	1.10760i	−0.985549	+	0.169391i	$0.945820\pi$
$744$	−2.66480	−	15.1128i	−0.0976964	−	0.554064i
$745$	−4.39470	−	24.9236i	−0.161009	−	0.913130i
$746$	−13.8629			−0.507558
$747$	0.248338	−	1.40839i	0.00908621	−	0.0515304i
$748$	−0.00143926	+	0.00816245i	−5.26245e−5	+	0.000298449i
$749$	−4.35672	+	1.58572i	−0.159191	+	0.0579408i
$750$	−24.5550	−	20.6041i	−0.896623	−	0.752356i
$751$	8.62735	+	3.14010i	0.314816	+	0.114584i	0.494596	−	0.869123i	$-0.335316\pi$
$751$	8.62735	+	3.14010i	0.314816	+	0.114584i	−0.179779	+	0.983707i	$0.557538\pi$
$752$	−2.87230	−	4.97497i	−0.104742	−	0.181418i
$753$	−0.875297	−	4.96405i	−0.0318976	−	0.180900i
$754$	−44.3744			−1.61602
$755$	0.615887	−	3.49287i	0.0224144	−	0.127118i
$756$	−0.00269511	−	0.00226146i	−9.80201e−5	−	8.22486e-5i
$757$	11.5376	+	19.9837i	0.419341	+	0.726320i	0.995873	−	0.0907541i	$-0.0289277\pi$
$757$	11.5376	+	19.9837i	0.419341	+	0.726320i	−0.576532	+	0.817075i	$0.695594\pi$
$758$	−0.240146			−0.00872250
$759$	−13.9709	−	11.7230i	−0.507112	−	0.425517i
$760$	17.6656			0.640799
$761$	15.6049			0.565679			0.282839	−	0.959167i	$-0.408724\pi$
$761$	15.6049			0.565679			0.282839	+	0.959167i	$0.408724\pi$
$762$	2.46896	−	31.6969i	0.0894411	−	1.14826i
$763$	1.05339			0.0381353
$764$	0.0753677			0.00272671
$765$	1.22808	+	1.03048i	0.0444012	+	0.0372570i
$766$	46.4330			1.67769
$767$	−5.61633	−	9.72777i	−0.202794	−	0.351249i
$768$	0.121980	+	0.102353i	0.00440157	+	0.00369335i
$769$	−1.89212	+	10.7307i	−0.0682314	+	0.386960i	0.931499	+	0.363744i	$0.118502\pi$
$769$	−1.89212	+	10.7307i	−0.0682314	+	0.386960i	−0.999730	+	0.0232159i	$0.992609\pi$
$770$	−1.13843			−0.0410261
$771$	1.20923	+	6.85786i	0.0435492	+	0.246980i
$772$	0.0452654	+	0.0784020i	0.00162914	+	0.00282175i
$773$	−13.2011	−	4.80482i	−0.474812	−	0.172818i	0.0935188	−	0.995618i	$-0.470188\pi$
$773$	−13.2011	−	4.80482i	−0.474812	−	0.172818i	−0.568331	+	0.822800i	$0.692411\pi$
$774$	−2.21231	−	1.85635i	−0.0795200	−	0.0667252i
$775$	7.59100	−	2.76290i	0.272677	−	0.0992463i
$776$	−7.72346	+	43.8019i	−0.277256	+	1.57240i
$777$	−0.801399	+	4.54496i	−0.0287500	+	0.163049i
$778$	49.5991			1.77822
$779$	3.54455	+	20.1022i	0.126997	+	0.720235i
$780$	0.00720473	+	0.0408600i	0.000257971	+	0.00146302i
$781$	−12.8167	+	22.1991i	−0.458616	+	0.794347i
$782$	−3.47027	−	6.01069i	−0.124097	−	0.214942i
$783$	22.1350	−	18.5734i	0.791039	−	0.663761i
$784$	−26.0975	−	9.49870i	−0.932053	−	0.339239i
$785$	−17.9670	+	6.53944i	−0.641269	+	0.233403i
$786$	−32.5243	−	27.2911i	−1.16010	−	0.973442i
$787$	6.68590	−	11.5803i	0.238327	−	0.412794i	−0.721908	−	0.691989i	$-0.756734\pi$
$787$	6.68590	−	11.5803i	0.238327	−	0.412794i	0.960234	+	0.279196i	$0.0900678\pi$
$788$	0.0368618	−	0.0134166i	0.00131315	−	0.000477947i
$789$	8.10729	−	14.0422i	0.288627	−	0.499917i
$790$	−0.282479	+	1.60202i	−0.0100502	+	0.0569973i
$791$	2.70282	+	0.983747i	0.0961013	+	0.0349780i
$792$	1.02911	−	5.83639i	0.0365680	−	0.207387i
$793$	7.28318	+	6.11131i	0.258633	+	0.217019i
$794$	−37.8058			−1.34168
$795$	1.75100	+	3.03282i	0.0621015	+	0.107563i
$796$	0.00598371	+	0.0339353i	0.000212087	+	0.00120281i
$797$	11.4070	−	4.15181i	0.404057	−	0.147065i	−0.131994	−	0.991251i	$-0.542138\pi$
$797$	11.4070	−	4.15181i	0.404057	−	0.147065i	0.536050	+	0.844186i	$0.319916\pi$
$798$	−0.561570	−	3.18482i	−0.0198794	−	0.112741i
$799$	−1.26877	+	1.06462i	−0.0448857	+	0.0376636i
$800$	−0.0279171	+	0.0483538i	−0.000987018	+	0.00170956i
$801$	−10.1983	−	3.71187i	−0.360338	−	0.131152i
$802$	13.2724	+	22.9884i	0.468663	+	0.811749i
$803$	18.5176	−	15.5381i	0.653473	−	0.548329i
$804$	0.0569287	−	0.0477689i	0.00200772	−	0.00168468i
$805$	1.21340	−	1.01816i	0.0427666	−	0.0358855i
$806$	−15.8849	−	5.78162i	−0.559521	−	0.203649i
$807$	−3.18076	+	2.66897i	−0.111968	+	0.0939523i
$808$	−30.4185	+	11.0714i	−1.07012	+	0.389492i
$809$	−10.0834	−	17.4650i	−0.354514	−	0.614036i	0.632521	−	0.774543i	$-0.282020\pi$
$809$	−10.0834	−	17.4650i	−0.354514	−	0.614036i	−0.987035	+	0.160508i	$0.948687\pi$
$810$	−16.9700	−	14.2395i	−0.596266	−	0.500326i
$811$	−14.4729	−	5.26769i	−0.508211	−	0.184974i	0.0751726	−	0.997171i	$-0.476049\pi$
$811$	−14.4729	−	5.26769i	−0.508211	−	0.184974i	−0.583383	+	0.812197i	$0.698271\pi$
$812$	0.00311354	−	0.00539281i	0.000109264	−	0.000189250i
$813$	6.27971	−	10.8768i	0.220239	−	0.381465i
$814$	−25.3756	+	9.23597i	−0.889415	+	0.323720i
$815$	24.6984	−	20.7244i	0.865147	−	0.725945i
$816$	4.61268	−	7.98939i	0.161476	−	0.279685i
$817$	1.59592	+	9.05090i	0.0558341	+	0.316651i
$818$	−5.73259	+	32.5111i	−0.200435	+	1.13672i
$819$	−1.04841	+	0.381589i	−0.0366343	+	0.0133338i
$820$	0.0207837	+	0.00756466i	0.000725800	+	0.000264169i
$821$	−5.45424	−	30.9325i	−0.190354	−	1.07955i	−0.918881	−	0.394535i	$-0.870906\pi$
$821$	−5.45424	−	30.9325i	−0.190354	−	1.07955i	0.728526	−	0.685018i	$-0.240206\pi$
$822$	−6.93433	+	39.3265i	−0.241862	+	1.37167i
$823$	15.2343	+	26.3865i	0.531033	+	0.919777i	0.999344	+	0.0362130i	$0.0115295\pi$
$823$	15.2343	+	26.3865i	0.531033	+	0.919777i	−0.468311	+	0.883564i	$0.655137\pi$
$824$	30.9027	+	25.9304i	1.07654	+	0.903328i
$825$	12.7396			0.443536
$826$	0.948671			0.0330085
$827$	−14.3498	−	12.0409i	−0.498991	−	0.418703i	0.358244	−	0.933628i	$-0.383375\pi$
$827$	−14.3498	−	12.0409i	−0.498991	−	0.418703i	−0.857236	+	0.514925i	$0.827820\pi$
$828$	−0.00687339	−	0.0119051i	−0.000238867	−	0.000413730i
$829$	6.66141	−	37.7787i	0.231360	−	1.31211i	−0.618785	−	0.785561i	$-0.712375\pi$
$829$	6.66141	−	37.7787i	0.231360	−	1.31211i	0.850145	−	0.526549i	$-0.176514\pi$
$830$	0.515369	+	2.92280i	0.0178887	+	0.101452i
$831$	−23.2261	−	8.45362i	−0.805706	−	0.293253i
$832$	−32.9013	+	11.9751i	−1.14065	+	0.415161i
$833$	−1.39044	+	7.88555i	−0.0481758	+	0.273218i
$834$	−7.03179	−	39.8793i	−0.243491	−	1.38091i
$835$	−8.23925	+	14.2708i	−0.285131	+	0.493861i
$836$	0.0240857	−	0.0202103i	0.000833021	−	0.000698987i
$837$	10.3437	−	3.76480i	0.357531	−	0.130131i
$838$	−2.60642	+	4.51445i	−0.0900372	+	0.155949i
$839$	−1.55993	+	2.70188i	−0.0538548	+	0.0932792i	−0.891696	−	0.452635i	$-0.850484\pi$
$839$	−1.55993	+	2.70188i	−0.0538548	+	0.0932792i	0.837841	+	0.545914i	$0.183817\pi$
$840$	1.97516	+	0.718899i	0.0681494	+	0.0248044i
$841$	16.9626	+	14.2333i	0.584918	+	0.490804i
$842$	−23.1270	−	40.0572i	−0.797010	−	1.38046i
$843$	−46.8023	+	17.0346i	−1.61196	+	0.586704i
$844$	0.0226694	−	0.0190219i	0.000780313	−	0.000654760i
$845$	−8.33585	−	3.03400i	−0.286762	−	0.104373i
$846$	−1.51241	+	1.26906i	−0.0519978	+	0.0436313i
$847$	−1.27323	+	1.06837i	−0.0437488	+	0.0367096i
$848$	3.78040	−	3.17213i	0.129819	−	0.108931i
$849$	4.15183	+	7.19119i	0.142491	+	0.246801i
$850$	4.55581	+	1.65818i	0.156263	+	0.0568750i
$851$	18.7864	−	32.5391i	0.643991	−	1.11542i
$852$	−0.0604414	+	0.0507163i	−0.00207069	+	0.00173751i
$853$	9.06658	+	51.4192i	0.310434	+	1.76056i	0.596754	+	0.802424i	$0.296457\pi$
$853$	9.06658	+	51.4192i	0.310434	+	1.76056i	−0.286320	+	0.958134i	$0.592432\pi$
$854$	−0.754546	+	0.274632i	−0.0258200	+	0.00939772i
$855$	−1.05603	−	5.98906i	−0.0361156	−	0.204822i
$856$	25.0442	+	43.3778i	0.855993	+	1.48262i
$857$	−45.9973			−1.57124			−0.785619	−	0.618710i	$-0.787656\pi$
$857$	−45.9973			−1.57124			−0.785619	+	0.618710i	$0.787656\pi$
$858$	−20.4218	−	17.1359i	−0.697190	−	0.585012i
$859$	−2.47473	+	14.0349i	−0.0844365	+	0.478863i	0.913040	+	0.407870i	$0.133728\pi$
$859$	−2.47473	+	14.0349i	−0.0844365	+	0.478863i	−0.997477	+	0.0709938i	$0.977383\pi$
$860$	0.00935777	+	0.00340595i	0.000319097	+	0.000116142i
$861$	−0.421744	+	2.39183i	−0.0143730	+	0.0815134i
$862$	4.85050	−	8.40131i	0.165209	−	0.286150i
$863$	10.1713	−	3.70204i	0.346235	−	0.126019i	−0.163049	−	0.986618i	$-0.552133\pi$
$863$	10.1713	−	3.70204i	0.346235	−	0.126019i	0.509283	+	0.860599i	$0.329911\pi$
$864$	−0.0380406	+	0.0658882i	−0.00129417	+	0.00224156i
$865$	23.3967	+	19.6321i	0.795511	+	0.667513i
$866$	−5.15756	+	1.87720i	−0.175261	+	0.0637898i
$867$	29.3417	+	10.6795i	0.996495	+	0.362695i
$868$	0.00181720	−	0.00152482i	6.16799e−5	−	5.17556e-5i
$869$	−0.868357	−	1.50404i	−0.0294570	−	0.0510210i
$870$	14.3898	−	24.9238i	0.487858	−	0.844995i
$871$	8.52681	+	48.3579i	0.288920	+	1.63855i
$872$	−1.97616	−	11.2074i	−0.0669213	−	0.379529i
$873$	15.3116			0.518219
$874$	−4.57193	+	25.9287i	−0.154648	+	0.877052i
$875$	−0.516116	+	2.92704i	−0.0174479	+	0.0989520i
$876$	0.0699186	−	0.0254483i	0.00236233	−	0.000859818i
$877$	0.203049	+	0.170378i	0.00685647	+	0.00575326i	0.646209	−	0.763160i	$-0.276353\pi$
$877$	0.203049	+	0.170378i	0.00685647	+	0.00575326i	−0.639353	+	0.768913i	$0.720798\pi$
$878$	27.3145	+	9.94166i	0.921819	+	0.335515i
$879$	−10.6249	−	18.4029i	−0.358370	−	0.620715i
$880$	2.13925	+	12.1323i	0.0721140	+	0.408979i
$881$	35.9645			1.21168			0.605838	−	0.795588i	$-0.292838\pi$
$881$	35.9645			1.21168			0.605838	+	0.795588i	$0.292838\pi$
$882$	−1.65745	+	9.39985i	−0.0558091	+	0.316509i
$883$	6.57964	+	5.52098i	0.221423	+	0.185796i	0.746751	−	0.665104i	$-0.231613\pi$
$883$	6.57964	+	5.52098i	0.221423	+	0.185796i	−0.525328	+	0.850900i	$0.676057\pi$
$884$	−0.00842855	−	0.0145987i	−0.000283483	−	0.000491007i
$885$	7.28507			0.244885
$886$	−33.4054	−	28.0305i	−1.12228	−	0.941703i
$887$	18.5481			0.622784			0.311392	−	0.950282i	$-0.399205\pi$
$887$	18.5481			0.622784			0.311392	+	0.950282i	$0.399205\pi$
$888$	49.8588			1.67315
$889$	−2.65976	+	1.27127i	−0.0892056	+	0.0426370i
$890$	22.5225			0.754955
$891$	23.6505			0.792322
$892$	0.0100207	+	0.00840836i	0.000335518	+	0.000281533i
$893$	6.28295			0.210251
$894$	25.0264	+	43.3469i	0.837007	+	1.44974i
$895$	6.29544	+	5.28250i	0.210433	+	0.176574i
$896$	0.515198	−	2.92184i	0.0172116	−	0.0976117i
$897$	37.0923			1.23848
$898$	0.414660	+	2.35165i	0.0138374	+	0.0784757i
$899$	9.74143	+	16.8726i	0.324895	+	0.562734i
$900$	0.00902345	+	0.00328427i	0.000300782	+	0.000109476i
$901$	−1.08995	−	0.914574i	−0.0363114	−	0.0304689i
$902$	−13.3542	+	4.86052i	−0.444645	+	0.161838i
$903$	−0.189888	+	1.07691i	−0.00631908	+	0.0358373i
$904$	5.39592	−	30.6018i	0.179465	−	1.01780i
$905$	−13.3526			−0.443856
$906$	1.21806	+	6.90797i	0.0404674	+	0.229502i
$907$	−8.68225	−	49.2395i	−0.288290	−	1.63497i	−0.693293	−	0.720656i	$-0.743841\pi$
$907$	−8.68225	−	49.2395i	−0.288290	−	1.63497i	0.405003	−	0.914315i	$-0.367270\pi$
$908$	0.0383706	−	0.0664599i	0.00127337	−	0.00220555i
$909$	5.57187	+	9.65077i	0.184807	+	0.320096i
$910$	1.77367	−	1.48829i	0.0587966	−	0.0493362i
$911$	−24.0043	−	8.73686i	−0.795298	−	0.289465i	−0.0877616	−	0.996142i	$-0.527971\pi$
$911$	−24.0043	−	8.73686i	−0.795298	−	0.289465i	−0.707537	+	0.706677i	$0.750194\pi$
$912$	−32.8855	+	11.9694i	−1.08895	+	0.396345i
$913$	−2.42725	−	2.03670i	−0.0803302	−	0.0674050i
$914$	−4.62614	+	8.01270i	−0.153019	+	0.265037i
$915$	−5.79434	+	2.10897i	−0.191555	+	0.0697203i
$916$	0.00609335	−	0.0105540i	0.000201330	−	0.000348714i
$917$	−0.683620	+	3.87700i	−0.0225751	+	0.128030i
$918$	6.20787	+	2.25948i	0.204890	+	0.0745739i
$919$	5.11305	−	28.9975i	0.168664	−	0.956540i	−0.776542	−	0.630065i	$-0.783028\pi$
$919$	5.11305	−	28.9975i	0.168664	−	0.956540i	0.945206	−	0.326475i	$-0.105861\pi$
$920$	−13.1089	−	10.9997i	−0.432187	−	0.362648i
$921$	−53.4079			−1.75985
$922$	16.6010	+	28.7537i	0.546724	+	0.946953i
$923$	−9.05293	−	51.3417i	−0.297981	−	1.68993i
$924$	0.00351543	−	0.00127951i	0.000115649	−	4.20928e-5i
$925$	4.55754	+	25.8471i	0.149851	+	0.849847i
$926$	38.9351	−	32.6705i	1.27949	−	1.07362i
$927$	6.94369	−	12.0268i	0.228061	−	0.395013i
$928$	−0.126539	−	0.0460565i	−0.00415385	−	0.00151188i
$929$	8.26633	+	14.3177i	0.271209	+	0.469749i	0.969172	−	0.246386i	$-0.0792431\pi$
$929$	8.26633	+	14.3177i	0.271209	+	0.469749i	−0.697962	+	0.716134i	$0.745910\pi$
$930$	8.39852	−	7.04719i	0.275398	−	0.231087i
$931$	23.2686	−	19.5247i	0.762598	−	0.639896i
$932$	−0.0153776	+	0.0129034i	−0.000503711	+	0.000422664i
$933$	54.2403	+	19.7418i	1.77575	+	0.646319i
$934$	1.89005	−	1.58594i	0.0618443	−	0.0518936i
$935$	3.33768	−	1.21482i	0.109154	−	0.0397287i
$936$	6.02666	+	10.4385i	0.196988	+	0.341193i
$937$	27.4851	+	23.0627i	0.897899	+	0.753426i	0.969779	−	0.243987i	$-0.0784554\pi$
$937$	27.4851	+	23.0627i	0.897899	+	0.753426i	−0.0718800	+	0.997413i	$0.522900\pi$
$938$	−3.89704	−	1.41841i	−0.127243	−	0.0463126i
$939$	−28.3020	+	49.0204i	−0.923600	+	1.59972i
$940$	0.00340393	−	0.00589578i	0.000111024	−	0.000192299i
$941$	18.3906	−	6.69363i	0.599516	−	0.218206i	−0.0243936	−	0.999702i	$-0.507765\pi$
$941$	18.3906	−	6.69363i	0.599516	−	0.218206i	0.623910	+	0.781496i	$0.285543\pi$
$942$	28.9675	−	24.3067i	0.943813	−	0.791954i
$943$	9.88655	−	17.1240i	0.321950	−	0.557635i
$944$	−1.78267	−	10.1100i	−0.0580210	−	0.329053i
$945$	−0.261807	+	1.48478i	−0.00851659	+	0.0483000i
$946$	−6.01265	+	2.18843i	−0.195488	+	0.0711518i
$947$	35.5482	+	12.9385i	1.15516	+	0.420444i	0.847367	−	0.531008i	$-0.178187\pi$
$947$	35.5482	+	12.9385i	1.15516	+	0.420444i	0.307795	+	0.951453i	$0.400409\pi$
$948$	−0.000928269	−	0.00526448i	−3.01488e−5	−	0.000170982i
$949$	−8.53721	+	48.4169i	−0.277129	+	1.57168i
$950$	−9.19571	−	15.9274i	−0.298348	−	0.516755i
$951$	−17.0764	−	14.3288i	−0.553740	−	0.464643i
$952$	−0.853987			−0.0276779
$953$	32.2658			1.04519			0.522596	−	0.852580i	$-0.324964\pi$
$953$	32.2658			1.04519			0.522596	+	0.852580i	$0.324964\pi$
$954$	−1.29925	−	1.09020i	−0.0420649	−	0.0352966i
$955$	−16.1490	−	27.9708i	−0.522569	−	0.905115i
$956$	−0.000586323		0.00332520i	−1.89630e−5		0.000107545i
$957$	5.33538	+	30.2585i	0.172468	+	0.978117i
$958$	39.3916	+	14.3374i	1.27268	+	0.463219i
$959$	3.47945	−	1.26642i	0.112357	−	0.0408947i
$960$	3.94319	−	22.3630i	0.127266	−	0.721761i
$961$	−4.09429	−	23.2198i	−0.132074	−	0.749027i
$962$	27.4609	−	47.5637i	0.885375	−	1.53351i
$963$	13.2090	−	11.0837i	0.425654	−	0.357166i
$964$	−0.0616113	+	0.0224247i	−0.00198437	+	0.000722251i
$965$	19.3980	−	33.5983i	0.624442	−	1.08157i
$966$	−1.56634	+	2.71299i	−0.0503963	+	0.0872890i
$967$	−0.235798	−	0.0858233i	−0.00758274	−	0.00275989i	0.338226	−	0.941065i	$-0.390173\pi$
$967$	−0.235798	−	0.0858233i	−0.00758274	−	0.00275989i	−0.345809	+	0.938305i	$0.612395\pi$
$968$	13.7553	+	11.5421i	0.442112	+	0.370976i
$969$	5.04495	+	8.73811i	0.162067	+	0.280709i
$970$	−29.8594	+	10.8679i	−0.958728	+	0.348948i
$971$	−7.36473	+	6.17975i	−0.236346	+	0.198317i	−0.753266	−	0.657716i	$-0.771523\pi$
$971$	−7.36473	+	6.17975i	−0.236346	+	0.198317i	0.516920	+	0.856033i	$0.327078\pi$
$972$	0.0304923	+	0.0110983i	0.000978041	+	0.000355978i
$973$	−2.87634	+	2.41354i	−0.0922112	+	0.0773744i
$974$	−19.0916	+	16.0198i	−0.611736	+	0.513307i
$975$	−19.8483	+	16.6547i	−0.635655	+	0.533378i
$976$	4.34465	+	7.52516i	0.139069	+	0.240875i
$977$	−28.1596	−	10.2493i	−0.900907	−	0.327903i	−0.150291	−	0.988642i	$-0.548021\pi$
$977$	−28.1596	−	10.2493i	−0.900907	−	0.327903i	−0.750616	+	0.660739i	$0.770243\pi$
$978$	−31.8826	+	55.2222i	−1.01949	+	1.76581i
$979$	−18.4197	+	15.4560i	−0.588696	+	0.493974i
$980$	−0.00571523	−	0.0324127i	−0.000182566	−	0.00103538i
$981$	−3.68143	+	1.33993i	−0.117539	+	0.0427807i
$982$	1.79699	+	10.1912i	0.0573441	+	0.325215i
$983$	−26.8507	−	46.5068i	−0.856405	−	1.48334i	−0.875335	−	0.483516i	$-0.839359\pi$
$983$	−26.8507	−	46.5068i	−0.856405	−	1.48334i	0.0189306	−	0.999821i	$-0.493974\pi$
$984$	26.2387			0.836458
$985$	−12.8776	−	10.8056i	−0.410314	−	0.344294i
$986$	−2.03043	+	11.5152i	−0.0646622	+	0.366718i
$987$	0.702485	+	0.255684i	0.0223603	+	0.00813850i
$988$	−0.0111042	+	0.0629753i	−0.000353273	+	0.00200351i
$989$	4.45137	−	7.71000i	0.141545	−	0.245164i
$990$	3.97862	−	1.44810i	0.126449	−	0.0460237i
$991$	−30.8895	+	53.5021i	−0.981236	+	1.69955i	−0.323638	+	0.946181i	$0.604906\pi$
$991$	−30.8895	+	53.5021i	−0.981236	+	1.69955i	−0.657598	+	0.753369i	$0.728427\pi$
$992$	−0.0392969	−	0.0329740i	−0.00124768	−	0.00104693i
$993$	19.7910	−	7.20335i	0.628049	−	0.228591i
$994$	4.13750	+	1.50593i	0.131233	+	0.0477651i
$995$	11.3121	−	9.49200i	0.358618	−	0.300917i
$996$	−0.00487647	−	0.00844629i	−0.000154517	−	0.000267631i
$997$	6.10997	−	10.5828i	0.193505	−	0.335160i	−0.752905	−	0.658130i	$-0.771348\pi$
$997$	6.10997	−	10.5828i	0.193505	−	0.335160i	0.946409	+	0.322970i	$0.104681\pi$
$998$	7.68945	+	43.6090i	0.243405	+	1.38042i
$999$	6.21023	+	35.2199i	0.196483	+	1.11431i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	127.2.f.a.103.9	yes	60
127.37	even	9	inner	127.2.f.a.37.9	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
127.2.f.a.37.9	✓	60	127.37	even	9	inner
127.2.f.a.103.9	yes	60	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	127.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+1.41539 q^{2} +(1.52689 + 1.28121i) q^{3} +0.00332867 q^{4} +(-0.713232 - 1.23535i) q^{5} +(2.16114 + 1.81341i) q^{6} +(0.0454245 - 0.257615i) q^{7} -2.82607 q^{8} +(0.168940 + 0.958105i) q^{9} +(-1.00950 - 1.74851i) q^{10} +(2.02551 + 0.737226i) q^{11} +(0.00508251 + 0.00426473i) q^{12} +(-4.11954 + 1.49939i) q^{13} +(0.0642933 - 0.364626i) q^{14} +(0.493724 - 2.80005i) q^{15} -4.00665 q^{16} +(0.200595 + 1.13763i) q^{17} +(0.239116 + 1.35609i) q^{18} +(2.19106 - 3.79503i) q^{19} +(-0.00237411 - 0.00411209i) q^{20} +(0.399417 - 0.335151i) q^{21} +(2.86689 + 1.04346i) q^{22} +(-3.98891 + 1.45185i) q^{23} +(-4.31509 - 3.62079i) q^{24} +(1.48260 - 2.56794i) q^{25} +(-5.83075 + 2.12222i) q^{26} +(2.02023 - 3.49915i) q^{27} +(0.000151203 - 0.000857516i) q^{28} +(6.72016 + 2.44594i) q^{29} +(0.698811 - 3.96316i) q^{30} +(2.08695 + 1.75116i) q^{31} -0.0188298 q^{32} +(2.14819 + 3.72077i) q^{33} +(0.283920 + 1.61019i) q^{34} +(-0.350644 + 0.127624i) q^{35} +(0.000562345 + 0.00318922i) q^{36} +(-6.78047 + 5.68949i) q^{37} +(3.10121 - 5.37145i) q^{38} +(-8.21110 - 2.98860i) q^{39} +(2.01564 + 3.49119i) q^{40} +(-3.56829 + 2.99415i) q^{41} +(0.565331 - 0.474369i) q^{42} +(-1.60660 + 1.34810i) q^{43} +(0.00674226 + 0.00245398i) q^{44} +(1.06310 - 0.892051i) q^{45} +(-5.64587 + 2.05493i) q^{46} +(0.716884 + 1.24168i) q^{47} +(-6.11770 - 5.13336i) q^{48} +(6.51355 + 2.37074i) q^{49} +(2.09846 - 3.63464i) q^{50} +(-1.15126 + 1.99403i) q^{51} +(-0.0137126 + 0.00499098i) q^{52} +(-0.943531 + 0.791717i) q^{53} +(2.85942 - 4.95266i) q^{54} +(-0.533924 - 3.02803i) q^{55} +(-0.128373 + 0.728038i) q^{56} +(8.20774 - 2.98737i) q^{57} +(9.51164 + 3.46195i) q^{58} +(0.444928 + 2.52331i) q^{59} +(0.00164344 - 0.00932043i) q^{60} +(-1.08436 - 1.87817i) q^{61} +(2.95385 + 2.47858i) q^{62} +0.254496 q^{63} +7.98664 q^{64} +(4.79046 + 4.01967i) q^{65} +(3.04052 + 5.26634i) q^{66} +(1.94502 - 11.0308i) q^{67} +(0.000667714 + 0.00378679i) q^{68} +(-7.95074 - 2.89383i) q^{69} +(-0.496298 + 0.180638i) q^{70} +(-2.06503 + 11.7114i) q^{71} +(-0.477435 - 2.70767i) q^{72} +(5.60729 - 9.71211i) q^{73} +(-9.59701 + 8.05285i) q^{74} +(5.55384 - 2.02143i) q^{75} +(0.00729333 - 0.0126324i) q^{76} +(0.281928 - 0.488314i) q^{77} +(-11.6219 - 4.23003i) q^{78} +(-0.617211 - 0.517901i) q^{79} +(2.85767 + 4.94962i) q^{80} +(10.3104 - 3.75270i) q^{81} +(-5.05052 + 4.23789i) q^{82} +(-1.38133 - 0.502763i) q^{83} +(0.00132953 - 0.00111561i) q^{84} +(1.26230 - 1.05920i) q^{85} +(-2.27397 + 1.90809i) q^{86} +(7.12716 + 12.3446i) q^{87} +(-5.72423 - 2.08345i) q^{88} +(-5.57763 + 9.66073i) q^{89} +(1.50471 - 1.26260i) q^{90} +(0.199137 + 1.12936i) q^{91} +(-0.0132778 + 0.00483272i) q^{92} +(0.942936 + 5.34766i) q^{93} +(1.01467 + 1.75746i) q^{94} -6.25094 q^{95} +(-0.0287510 - 0.0241249i) q^{96} +(2.73293 - 15.4992i) q^{97} +(9.21921 + 3.35552i) q^{98} +(-0.364150 + 2.06520i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 12 q^{2} - 6 q^{3} + 48 q^{4} + 3 q^{5} - 9 q^{6} - 30 q^{8} - 6 q^{9} - 3 q^{10} + 3 q^{11} - 27 q^{12} + 6 q^{13} - 27 q^{14} + 48 q^{16} + 9 q^{17} + 9 q^{18} - 3 q^{19} - 3 q^{20} + 36 q^{21}+ \cdots - 111 q^{99}+O(q^{100}) \) 60 * q - 12 * q^2 - 6 * q^3 + 48 * q^4 + 3 * q^5 - 9 * q^6 - 30 * q^8 - 6 * q^9 - 3 * q^10 + 3 * q^11 - 27 * q^12 + 6 * q^13 - 27 * q^14 + 48 * q^16 + 9 * q^17 + 9 * q^18 - 3 * q^19 - 3 * q^20 + 36 * q^21 - 39 * q^22 - 24 * q^23 - 90 * q^24 - 15 * q^25 + 9 * q^27 - 30 * q^28 - 42 * q^29 - 24 * q^30 - 54 * q^31 - 102 * q^32 + 39 * q^33 - 54 * q^34 + 21 * q^35 - 33 * q^36 + 27 * q^37 + 6 * q^38 + 33 * q^39 + 24 * q^40 + 42 * q^41 + 51 * q^42 + 36 * q^43 + 66 * q^44 + 3 * q^45 - 39 * q^46 - 18 * q^47 - 30 * q^48 + 48 * q^49 + 21 * q^50 + 21 * q^51 + 12 * q^52 - 21 * q^53 + 45 * q^54 - 36 * q^55 - 90 * q^56 - 21 * q^57 + 57 * q^58 + 36 * q^59 + 45 * q^60 - 15 * q^61 + 54 * q^62 - 84 * q^63 + 66 * q^64 + 66 * q^65 + 63 * q^66 + 78 * q^67 + 60 * q^68 + 30 * q^69 + 18 * q^70 - 6 * q^71 + 66 * q^72 - 3 * q^73 + 39 * q^74 + 78 * q^75 - 45 * q^76 + 39 * q^77 - 60 * q^78 - 27 * q^79 - 18 * q^80 + 99 * q^81 + 99 * q^82 - 12 * q^83 + 90 * q^84 - 6 * q^85 - 57 * q^86 - 12 * q^87 - 117 * q^88 + 3 * q^89 + 72 * q^90 - 60 * q^91 - 9 * q^92 - 108 * q^93 + 75 * q^94 - 180 * q^95 - 123 * q^96 + 9 * q^97 + 3 * q^98 - 111 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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