LMFDB - Embedded newform 93.2.f.a.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [93,2,Mod(4,93)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(93, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("93.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	93.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.742608738798$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			16.2
Root			$-0.104528 - 0.994522i$ of defining polynomial
Character	$\chi$	$=$	93.16
Dual form			93.2.f.a.64.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.47815 - 1.07394i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.413545 - 1.27276i) q^{4} -2.95630 q^{5} +1.82709 q^{6} +(0.795511 - 2.44833i) q^{7} +(0.373619 + 1.14988i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(1.47815 - 1.07394i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.413545 - 1.27276i) q^{4} -2.95630 q^{5} +1.82709 q^{6} +(0.795511 - 2.44833i) q^{7} +(0.373619 + 1.14988i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-4.36984 + 3.17488i) q^{10} +(-1.27366 + 3.91992i) q^{11} +(1.08268 - 0.786610i) q^{12} +(-4.38791 - 3.18801i) q^{13} +(-1.45347 - 4.47333i) q^{14} +(-2.39169 - 1.73767i) q^{15} +(3.95252 + 2.87167i) q^{16} +(0.551097 + 1.69610i) q^{17} +(1.47815 + 1.07394i) q^{18} +(2.89169 - 2.10094i) q^{19} +(-1.22256 + 3.76266i) q^{20} +(2.08268 - 1.51315i) q^{21} +(2.32709 + 7.16205i) q^{22} +(-1.79551 - 5.52602i) q^{23} +(-0.373619 + 1.14988i) q^{24} +3.73968 q^{25} -9.90970 q^{26} +(-0.309017 + 0.951057i) q^{27} +(-2.78716 - 2.02499i) q^{28} +(0.982716 - 0.713985i) q^{29} -5.40142 q^{30} +(4.51633 + 3.25619i) q^{31} +6.50828 q^{32} +(-3.33448 + 2.42264i) q^{33} +(2.63611 + 1.91524i) q^{34} +(-2.35177 + 7.23799i) q^{35} +1.33826 q^{36} +4.21373 q^{37} +(2.01807 - 6.21099i) q^{38} +(-1.67603 - 5.15830i) q^{39} +(-1.10453 - 3.39939i) q^{40} +(7.70054 - 5.59477i) q^{41} +(1.45347 - 4.47333i) q^{42} +(-4.74064 + 3.44427i) q^{43} +(4.46241 + 3.24213i) q^{44} +(-0.913545 - 2.81160i) q^{45} +(-8.58862 - 6.24000i) q^{46} +(-7.33353 - 5.32812i) q^{47} +(1.50973 + 4.64646i) q^{48} +(0.301625 + 0.219144i) q^{49} +(5.52780 - 4.01618i) q^{50} +(-0.551097 + 1.69610i) q^{51} +(-5.87218 + 4.26639i) q^{52} +(3.11377 + 9.58319i) q^{53} +(0.564602 + 1.73767i) q^{54} +(3.76531 - 11.5884i) q^{55} +3.11251 q^{56} +3.57433 q^{57} +(0.685824 - 2.11075i) q^{58} +(-7.27882 - 5.28837i) q^{59} +(-3.20071 + 2.32545i) q^{60} -7.32624 q^{61} +(10.1727 - 0.0371239i) q^{62} +2.57433 q^{63} +(1.71517 - 1.24614i) q^{64} +(12.9720 + 9.42469i) q^{65} +(-2.32709 + 7.16205i) q^{66} -6.47214 q^{67} +2.38664 q^{68} +(1.79551 - 5.52602i) q^{69} +(4.29689 + 13.2245i) q^{70} +(0.597035 + 1.83748i) q^{71} +(-0.978148 + 0.710666i) q^{72} +(0.315619 - 0.971375i) q^{73} +(6.22851 - 4.52528i) q^{74} +(3.02547 + 2.19813i) q^{75} +(-1.47815 - 4.54927i) q^{76} +(8.58406 + 6.23668i) q^{77} +(-8.01712 - 5.82478i) q^{78} +(2.78591 + 8.57414i) q^{79} +(-11.6848 - 8.48951i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(5.37411 - 16.5398i) q^{82} +(-5.42248 + 3.93966i) q^{83} +(-1.06460 - 3.27651i) q^{84} +(-1.62920 - 5.01418i) q^{85} +(-3.30843 + 10.1823i) q^{86} +1.21470 q^{87} -4.98331 q^{88} +(-2.88568 + 8.88121i) q^{89} +(-4.36984 - 3.17488i) q^{90} +(-11.2959 + 8.20698i) q^{91} -7.77583 q^{92} +(1.73985 + 5.28894i) q^{93} -16.5621 q^{94} +(-8.54870 + 6.21099i) q^{95} +(5.26531 + 3.82547i) q^{96} +(2.73860 - 8.42855i) q^{97} +0.681193 q^{98} -4.12165 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} + 2 q^{3} - 3 q^{4} - 6 q^{5} + 2 q^{6} + 9 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 + 2 * q^3 - 3 * q^4 - 6 * q^5 + 2 * q^6 + 9 * q^7 - 4 * q^8 - 2 * q^9	\( 8 q + 3 q^{2} + 2 q^{3} - 3 q^{4} - 6 q^{5} + 2 q^{6} + 9 q^{7} - 4 q^{8} - 2 q^{9} - 11 q^{10} - 4 q^{11} - 2 q^{12} - 3 q^{13} - 6 q^{14} - 4 q^{15} - 3 q^{16} + 9 q^{17} + 3 q^{18} + 8 q^{19} + q^{20} + 6 q^{21} + 6 q^{22} - 17 q^{23} + 4 q^{24} - 18 q^{25} + 12 q^{26} + 2 q^{27} - 9 q^{28} - 2 q^{29} - 4 q^{30} + 17 q^{31} - q^{33} + 4 q^{34} - 3 q^{35} + 2 q^{36} + 8 q^{37} + 8 q^{38} + 3 q^{39} - 7 q^{40} - 5 q^{41} + 6 q^{42} - 19 q^{43} + 24 q^{44} - q^{45} - 17 q^{46} - 4 q^{47} - 12 q^{48} + 11 q^{49} + 12 q^{50} - 9 q^{51} - 12 q^{52} + 2 q^{54} + 8 q^{55} - 12 q^{56} + 2 q^{57} + 33 q^{58} - 29 q^{59} - 6 q^{60} + 4 q^{61} + 47 q^{62} - 6 q^{63} + 16 q^{64} + 21 q^{65} - 6 q^{66} - 16 q^{67} + 6 q^{68} + 17 q^{69} - 3 q^{70} + 37 q^{71} + q^{72} + 3 q^{73} - 2 q^{74} + 3 q^{75} - 3 q^{76} + 18 q^{77} - 27 q^{78} - 3 q^{79} - 24 q^{80} - 2 q^{81} + 35 q^{82} - 31 q^{83} - 6 q^{84} - 8 q^{85} - 44 q^{86} - 18 q^{87} - 8 q^{88} + 19 q^{89} - 11 q^{90} - 24 q^{91} + 2 q^{92} + 13 q^{93} - 94 q^{94} - 16 q^{95} + 20 q^{96} - 3 q^{97} - 34 q^{98} + 6 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 + 2 * q^3 - 3 * q^4 - 6 * q^5 + 2 * q^6 + 9 * q^7 - 4 * q^8 - 2 * q^9 - 11 * q^10 - 4 * q^11 - 2 * q^12 - 3 * q^13 - 6 * q^14 - 4 * q^15 - 3 * q^16 + 9 * q^17 + 3 * q^18 + 8 * q^19 + q^20 + 6 * q^21 + 6 * q^22 - 17 * q^23 + 4 * q^24 - 18 * q^25 + 12 * q^26 + 2 * q^27 - 9 * q^28 - 2 * q^29 - 4 * q^30 + 17 * q^31 - q^33 + 4 * q^34 - 3 * q^35 + 2 * q^36 + 8 * q^37 + 8 * q^38 + 3 * q^39 - 7 * q^40 - 5 * q^41 + 6 * q^42 - 19 * q^43 + 24 * q^44 - q^45 - 17 * q^46 - 4 * q^47 - 12 * q^48 + 11 * q^49 + 12 * q^50 - 9 * q^51 - 12 * q^52 + 2 * q^54 + 8 * q^55 - 12 * q^56 + 2 * q^57 + 33 * q^58 - 29 * q^59 - 6 * q^60 + 4 * q^61 + 47 * q^62 - 6 * q^63 + 16 * q^64 + 21 * q^65 - 6 * q^66 - 16 * q^67 + 6 * q^68 + 17 * q^69 - 3 * q^70 + 37 * q^71 + q^72 + 3 * q^73 - 2 * q^74 + 3 * q^75 - 3 * q^76 + 18 * q^77 - 27 * q^78 - 3 * q^79 - 24 * q^80 - 2 * q^81 + 35 * q^82 - 31 * q^83 - 6 * q^84 - 8 * q^85 - 44 * q^86 - 18 * q^87 - 8 * q^88 + 19 * q^89 - 11 * q^90 - 24 * q^91 + 2 * q^92 + 13 * q^93 - 94 * q^94 - 16 * q^95 + 20 * q^96 - 3 * q^97 - 34 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	1.47815	−	1.07394i	1.04521	−	0.759388i	0.0739128	−	0.997265i	$-0.476451\pi$
$2$	1.47815	−	1.07394i	1.04521	−	0.759388i	0.971295	+	0.237877i	$0.0764514\pi$
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	0.413545	−	1.27276i	0.206773	−	0.636381i
$5$	−2.95630			−1.32210			−0.661048	−	0.750344i	$-0.729888\pi$
$5$	−2.95630			−1.32210			−0.661048	+	0.750344i	$0.729888\pi$
$6$	1.82709			0.745907
$7$	0.795511	−	2.44833i	0.300675	−	0.925383i	−0.680581	−	0.732673i	$-0.738272\pi$
$7$	0.795511	−	2.44833i	0.300675	−	0.925383i	0.981256	−	0.192710i	$-0.0617275\pi$
$8$	0.373619	+	1.14988i	0.132094	+	0.406544i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	−4.36984	+	3.17488i	−1.38186	+	1.00398i
$11$	−1.27366	+	3.91992i	−0.384023	+	1.18190i	0.553164	+	0.833072i	$0.313420\pi$
$11$	−1.27366	+	3.91992i	−0.384023	+	1.18190i	−0.937187	+	0.348828i	$0.886580\pi$
$12$	1.08268	−	0.786610i	0.312542	−	0.227075i
$13$	−4.38791	−	3.18801i	−1.21699	−	0.884194i	−0.221142	−	0.975242i	$-0.570978\pi$
$13$	−4.38791	−	3.18801i	−1.21699	−	0.884194i	−0.995847	+	0.0910477i	$0.970978\pi$
$14$	−1.45347	−	4.47333i	−0.388457	−	1.19555i
$15$	−2.39169	−	1.73767i	−0.617532	−	0.448664i
$16$	3.95252	+	2.87167i	0.988129	+	0.717918i
$17$	0.551097	+	1.69610i	0.133661	+	0.411365i	0.995379	−	0.0960214i	$-0.0306117\pi$
$17$	0.551097	+	1.69610i	0.133661	+	0.411365i	−0.861719	+	0.507386i	$0.830612\pi$
$18$	1.47815	+	1.07394i	0.348403	+	0.253129i
$19$	2.89169	−	2.10094i	0.663400	−	0.481988i	−0.204410	−	0.978885i	$-0.565527\pi$
$19$	2.89169	−	2.10094i	0.663400	−	0.481988i	0.867809	+	0.496897i	$0.165527\pi$
$20$	−1.22256	+	3.76266i	−0.273373	+	0.841356i
$21$	2.08268	−	1.51315i	0.454477	−	0.330197i
$22$	2.32709	+	7.16205i	0.496137	+	1.52695i
$23$	−1.79551	−	5.52602i	−0.374390	−	1.15225i	−0.943889	−	0.330262i	$-0.892863\pi$
$23$	−1.79551	−	5.52602i	−0.374390	−	1.15225i	0.569499	−	0.821992i	$-0.307137\pi$
$24$	−0.373619	+	1.14988i	−0.0762647	+	0.234719i
$25$	3.73968			0.747936
$26$	−9.90970			−1.94345
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	−2.78716	−	2.02499i	−0.526725	−	0.382688i
$29$	0.982716	−	0.713985i	0.182486	−	0.132584i	−0.492792	−	0.870147i	$-0.664024\pi$
$29$	0.982716	−	0.713985i	0.182486	−	0.132584i	0.675278	+	0.737563i	$0.264024\pi$
$30$	−5.40142			−0.986160
$31$	4.51633	+	3.25619i	0.811157	+	0.584829i
$31$	4.51633	+	3.25619i	0.811157	+	0.584829i
$32$	6.50828			1.15051
$33$	−3.33448	+	2.42264i	−0.580459	+	0.421728i
$34$	2.63611	+	1.91524i	0.452089	+	0.328462i
$35$	−2.35177	+	7.23799i	−0.397521	+	1.22344i
$36$	1.33826			0.223044
$37$	4.21373			0.692733			0.346366	−	0.938099i	$-0.387415\pi$
$37$	4.21373			0.692733			0.346366	+	0.938099i	$0.387415\pi$
$38$	2.01807	−	6.21099i	0.327375	−	1.00756i
$39$	−1.67603	−	5.15830i	−0.268380	−	0.825990i
$40$	−1.10453	−	3.39939i	−0.174641	−	0.537491i
$41$	7.70054	−	5.59477i	1.20262	−	0.873757i	0.208083	−	0.978111i	$-0.433278\pi$
$41$	7.70054	−	5.59477i	1.20262	−	0.873757i	0.994540	+	0.104354i	$0.0332776\pi$
$42$	1.45347	−	4.47333i	0.224276	−	0.690249i
$43$	−4.74064	+	3.44427i	−0.722940	+	0.525247i	−0.887322	−	0.461150i	$-0.847437\pi$
$43$	−4.74064	+	3.44427i	−0.722940	+	0.525247i	0.164382	+	0.986397i	$0.447437\pi$
$44$	4.46241	+	3.24213i	0.672733	+	0.488769i
$45$	−0.913545	−	2.81160i	−0.136183	−	0.419129i
$46$	−8.58862	−	6.24000i	−1.26632	−	0.920038i
$47$	−7.33353	−	5.32812i	−1.06970	−	0.777186i	−0.0938458	−	0.995587i	$-0.529916\pi$
$47$	−7.33353	−	5.32812i	−1.06970	−	0.777186i	−0.975859	+	0.218401i	$0.929916\pi$
$48$	1.50973	+	4.64646i	0.217910	+	0.670659i
$49$	0.301625	+	0.219144i	0.0430893	+	0.0313062i
$50$	5.52780	−	4.01618i	0.781749	−	0.567974i
$51$	−0.551097	+	1.69610i	−0.0771690	+	0.237502i
$52$	−5.87218	+	4.26639i	−0.814324	+	0.591641i
$53$	3.11377	+	9.58319i	0.427709	+	1.31635i	0.900376	+	0.435112i	$0.143291\pi$
$53$	3.11377	+	9.58319i	0.427709	+	1.31635i	−0.472668	+	0.881241i	$0.656709\pi$
$54$	0.564602	+	1.73767i	0.0768326	+	0.236466i
$55$	3.76531	−	11.5884i	0.507715	−	1.56258i
$56$	3.11251			0.415927
$57$	3.57433			0.473431
$58$	0.685824	−	2.11075i	0.0900531	−	0.277155i
$59$	−7.27882	−	5.28837i	−0.947621	−	0.688487i	0.00262173	−	0.999997i	$-0.499165\pi$
$59$	−7.27882	−	5.28837i	−0.947621	−	0.688487i	−0.950243	+	0.311509i	$0.899165\pi$
$60$	−3.20071	+	2.32545i	−0.413210	+	0.300215i
$61$	−7.32624			−0.938029			−0.469014	−	0.883191i	$-0.655391\pi$
$61$	−7.32624			−0.938029			−0.469014	+	0.883191i	$0.655391\pi$
$62$	10.1727	−	0.0371239i	1.29194	−	0.00471474i
$63$	2.57433			0.324335
$64$	1.71517	−	1.24614i	0.214396	−	0.155768i
$65$	12.9720	+	9.42469i	1.60897	+	1.16899i
$66$	−2.32709	+	7.16205i	−0.286445	+	0.881587i
$67$	−6.47214			−0.790697			−0.395349	−	0.918531i	$-0.629376\pi$
$67$	−6.47214			−0.790697			−0.395349	+	0.918531i	$0.629376\pi$
$68$	2.38664			0.289422
$69$	1.79551	−	5.52602i	0.216154	−	0.665254i
$70$	4.29689	+	13.2245i	0.513577	+	1.58063i
$71$	0.597035	+	1.83748i	0.0708550	+	0.218069i	0.980213	−	0.197945i	$-0.0634267\pi$
$71$	0.597035	+	1.83748i	0.0708550	+	0.218069i	−0.909358	+	0.416014i	$0.863427\pi$
$72$	−0.978148	+	0.710666i	−0.115276	+	0.0837528i
$73$	0.315619	−	0.971375i	0.0369404	−	0.113691i	−0.930886	−	0.365310i	$-0.880963\pi$
$73$	0.315619	−	0.971375i	0.0369404	−	0.113691i	0.967826	+	0.251619i	$0.0809630\pi$
$74$	6.22851	−	4.52528i	0.724050	−	0.526053i
$75$	3.02547	+	2.19813i	0.349351	+	0.253818i
$76$	−1.47815	−	4.54927i	−0.169555	−	0.521837i
$77$	8.58406	+	6.23668i	0.978244	+	0.710736i
$78$	−8.01712	−	5.82478i	−0.907760	−	0.659526i
$79$	2.78591	+	8.57414i	0.313439	+	0.964666i	0.976392	+	0.216005i	$0.0693029\pi$
$79$	2.78591	+	8.57414i	0.313439	+	0.964666i	−0.662953	+	0.748661i	$0.730697\pi$
$80$	−11.6848	−	8.48951i	−1.30640	−	0.949156i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	5.37411	−	16.5398i	0.593471	−	1.82652i
$83$	−5.42248	+	3.93966i	−0.595195	+	0.432434i	−0.844170	−	0.536076i	$-0.819906\pi$
$83$	−5.42248	+	3.93966i	−0.595195	+	0.432434i	0.248975	+	0.968510i	$0.419906\pi$
$84$	−1.06460	−	3.27651i	−0.116158	−	0.357496i
$85$	−1.62920	−	5.01418i	−0.176712	−	0.543864i
$86$	−3.30843	+	10.1823i	−0.356757	+	1.09798i
$87$	1.21470			0.130230
$88$	−4.98331			−0.531222
$89$	−2.88568	+	8.88121i	−0.305882	+	0.941407i	0.673465	+	0.739219i	$0.264805\pi$
$89$	−2.88568	+	8.88121i	−0.305882	+	0.941407i	−0.979347	+	0.202188i	$0.935195\pi$
$90$	−4.36984	−	3.17488i	−0.460622	−	0.334661i
$91$	−11.2959	+	8.20698i	−1.18414	+	0.860325i
$92$	−7.77583			−0.810686
$93$	1.73985	+	5.28894i	0.180414	+	0.548438i
$94$	−16.5621			−1.70825
$95$	−8.54870	+	6.21099i	−0.877078	+	0.637234i
$96$	5.26531	+	3.82547i	0.537389	+	0.390436i
$97$	2.73860	−	8.42855i	0.278063	−	0.855790i	−0.710330	−	0.703869i	$-0.751454\pi$
$97$	2.73860	−	8.42855i	0.278063	−	0.855790i	0.988393	−	0.151921i	$-0.0485459\pi$
$98$	0.681193			0.0688109
$99$	−4.12165			−0.414241
$100$	1.54653	−	4.75972i	0.154653	−	0.475972i
$101$	−1.52738	−	4.70078i	−0.151980	−	0.467745i	0.845863	−	0.533401i	$-0.179086\pi$
$101$	−1.52738	−	4.70078i	−0.151980	−	0.467745i	−0.997842	+	0.0656555i	$0.979086\pi$
$102$	1.00690	+	3.09893i	0.0996983	+	0.306840i
$103$	−11.2321	+	8.16062i	−1.10673	+	0.804089i	−0.982146	−	0.188119i	$-0.939761\pi$
$103$	−11.2321	+	8.16062i	−1.10673	+	0.804089i	−0.124588	+	0.992209i	$0.539761\pi$
$104$	2.02642	−	6.23668i	0.198707	−	0.611557i
$105$	−6.15701	+	4.47333i	−0.600862	+	0.436552i
$106$	14.8944	+	10.8214i	1.44667	+	1.05107i
$107$	−1.69933	−	5.23000i	−0.164280	−	0.505603i	0.834702	−	0.550702i	$-0.185640\pi$
$107$	−1.69933	−	5.23000i	−0.164280	−	0.505603i	−0.998983	+	0.0450986i	$0.985640\pi$
$108$	1.08268	+	0.786610i	0.104181	+	0.0756916i
$109$	15.6254	+	11.3525i	1.49664	+	1.08737i	0.971696	+	0.236233i	$0.0759130\pi$
$109$	15.6254	+	11.3525i	1.49664	+	1.08737i	0.524942	+	0.851138i	$0.324087\pi$
$110$	−6.87957	−	21.1731i	−0.655941	−	2.01878i
$111$	3.40898	+	2.47677i	0.323566	+	0.235084i
$112$	10.1751	−	7.39263i	0.961455	−	0.698538i
$113$	3.52313	−	10.8431i	0.331428	−	1.02003i	−0.637027	−	0.770842i	$-0.719836\pi$
$113$	3.52313	−	10.8431i	0.331428	−	1.02003i	0.968455	−	0.249189i	$-0.0801642\pi$
$114$	5.28339	−	3.83860i	0.494834	−	0.359518i
$115$	5.30806	+	16.3365i	0.494979	+	1.52339i
$116$	−0.502335	−	1.54603i	−0.0466407	−	0.143545i
$117$	1.67603	−	5.15830i	0.154949	−	0.476885i
$118$	−16.4385			−1.51329
$119$	4.59102			0.420858
$120$	1.10453	−	3.39939i	0.100829	−	0.310320i
$121$	−4.84437	−	3.51964i	−0.440398	−	0.319968i
$122$	−10.8293	+	7.86792i	−0.980435	+	0.712328i
$123$	9.51840			0.858245
$124$	6.01206	−	4.40163i	0.539899	−	0.395278i
$125$	3.72587			0.333252
$126$	3.80524	−	2.76467i	0.338998	−	0.246296i
$127$	−1.45097	−	1.05419i	−0.128753	−	0.0935445i	0.521545	−	0.853224i	$-0.325356\pi$
$127$	−1.45097	−	1.05419i	−0.128753	−	0.0935445i	−0.650298	+	0.759679i	$0.725356\pi$
$128$	−2.82535	+	8.69552i	−0.249728	+	0.768583i
$129$	−5.85975			−0.515922
$130$	29.2960			2.56943
$131$	−1.12825	+	3.47239i	−0.0985756	+	0.303384i	−0.988169	−	0.153369i	$-0.950988\pi$
$131$	−1.12825	+	3.47239i	−0.0985756	+	0.303384i	0.889593	+	0.456753i	$0.150988\pi$
$132$	1.70449	+	5.24588i	0.148357	+	0.456595i
$133$	−2.84342	−	8.75115i	−0.246556	−	0.758821i
$134$	−9.56677	+	6.95067i	−0.826443	+	0.600446i
$135$	0.913545	−	2.81160i	0.0786255	−	0.241984i
$136$	−1.74441	+	1.26739i	−0.149582	+	0.108678i
$137$	−0.0305223	−	0.0221758i	−0.00260770	−	0.00189460i	0.586481	−	0.809963i	$-0.300513\pi$
$137$	−0.0305223	−	0.0221758i	−0.00260770	−	0.00189460i	−0.589088	+	0.808069i	$0.700513\pi$
$138$	−3.28056	−	10.0965i	−0.279260	−	0.859474i
$139$	14.9756	+	10.8804i	1.27021	+	0.922863i	0.999211	−	0.0397156i	$-0.0126452\pi$
$139$	14.9756	+	10.8804i	1.27021	+	0.922863i	0.271001	+	0.962579i	$0.412645\pi$
$140$	8.23968	+	5.98648i	0.696380	+	0.505950i
$141$	−2.80116	−	8.62108i	−0.235900	−	0.726026i
$142$	2.85585	+	2.07489i	0.239657	+	0.174121i
$143$	18.0854	−	13.1398i	1.51238	−	1.09881i
$144$	−1.50973	+	4.64646i	−0.125811	+	0.387205i
$145$	−2.90520	+	2.11075i	−0.241264	+	0.175288i
$146$	−0.576664	−	1.77479i	−0.0477251	−	0.146883i
$147$	0.115211	+	0.354582i	0.00950241	+	0.0292454i
$148$	1.74257	−	5.36307i	0.143238	−	0.440842i
$149$	−10.4784			−0.858423			−0.429211	−	0.903204i	$-0.641208\pi$
$149$	−10.4784			−0.858423			−0.429211	+	0.903204i	$0.641208\pi$
$150$	6.83274			0.557891
$151$	6.08310	−	18.7219i	0.495036	−	1.52356i	−0.321865	−	0.946785i	$-0.604310\pi$
$151$	6.08310	−	18.7219i	0.495036	−	1.52356i	0.816901	−	0.576778i	$-0.195690\pi$
$152$	3.49622	+	2.54015i	0.283581	+	0.206034i
$153$	−1.44279	+	1.04825i	−0.116643	+	0.0847458i
$154$	19.3863			1.56219
$155$	−13.3516	−	9.62626i	−1.07243	−	0.773200i
$156$	−7.25841			−0.581138
$157$	12.6426	−	9.18542i	1.00899	−	0.733076i	0.0449954	−	0.998987i	$-0.485673\pi$
$157$	12.6426	−	9.18542i	1.00899	−	0.733076i	0.963998	+	0.265911i	$0.0856727\pi$
$158$	13.3261	+	9.68196i	1.06017	+	0.770255i
$159$	−3.11377	+	9.58319i	−0.246938	+	0.759996i
$160$	−19.2404			−1.52109
$161$	−14.9579			−1.17885
$162$	−0.564602	+	1.73767i	−0.0443593	+	0.136524i
$163$	−6.09949	−	18.7723i	−0.477749	−	1.47036i	−0.842214	−	0.539144i	$-0.818748\pi$
$163$	−6.09949	−	18.7723i	−0.477749	−	1.47036i	0.364465	−	0.931217i	$-0.381252\pi$
$164$	−3.93629	−	12.1147i	−0.307373	−	0.945996i
$165$	9.85772	−	7.16205i	0.767422	−	0.557565i
$166$	−3.78428	+	11.6468i	−0.293717	+	0.903968i
$167$	4.15727	−	3.02044i	0.321699	−	0.233728i	−0.415201	−	0.909730i	$-0.636289\pi$
$167$	4.15727	−	3.02044i	0.321699	−	0.233728i	0.736900	+	0.676001i	$0.236289\pi$
$168$	2.51807	+	1.82949i	0.194274	+	0.141148i
$169$	5.07319	+	15.6137i	0.390245	+	1.20105i
$170$	−7.79311	−	5.66203i	−0.597704	−	0.434258i
$171$	2.89169	+	2.10094i	0.221133	+	0.160663i
$172$	2.42327	+	7.45807i	0.184773	+	0.568672i
$173$	11.7461	+	8.53405i	0.893041	+	0.648832i	0.936669	−	0.350216i	$-0.113892\pi$
$173$	11.7461	+	8.53405i	0.893041	+	0.648832i	−0.0436283	+	0.999048i	$0.513892\pi$
$174$	1.79551	−	1.30452i	0.136117	−	0.0988951i
$175$	2.97496	−	9.15598i	0.224886	−	0.692127i
$176$	−16.2909	+	11.8360i	−1.22797	+	0.892173i
$177$	−2.78026	−	8.55676i	−0.208977	−	0.643166i
$178$	5.27240	+	16.2268i	0.395183	+	1.21625i
$179$	3.04023	−	9.35686i	0.227237	−	0.699365i	−0.770819	−	0.637054i	$-0.780153\pi$
$179$	3.04023	−	9.35686i	0.227237	−	0.699365i	0.998057	−	0.0623109i	$-0.0198470\pi$
$180$	−3.95630			−0.294885
$181$	−26.0666			−1.93751			−0.968756	−	0.248015i	$-0.920222\pi$
$181$	−26.0666			−1.93751			−0.968756	+	0.248015i	$0.920222\pi$
$182$	−7.88328	+	24.2623i	−0.584348	+	1.79844i
$183$	−5.92705	−	4.30625i	−0.438140	−	0.318328i
$184$	5.68343	−	4.12925i	0.418988	−	0.304412i
$185$	−12.4570			−0.915858
$186$	8.25174	+	5.94936i	0.605047	+	0.436228i
$187$	−7.35049			−0.537521
$188$	−9.81418	+	7.13042i	−0.715772	+	0.520039i
$189$	2.08268	+	1.51315i	0.151492	+	0.110066i
$190$	−5.96602	+	18.3615i	−0.432821	+	1.33209i
$191$	−7.09655			−0.513488			−0.256744	−	0.966479i	$-0.582650\pi$
$191$	−7.09655			−0.513488			−0.256744	+	0.966479i	$0.582650\pi$
$192$	2.12007			0.153003
$193$	−2.41805	+	7.44200i	−0.174055	+	0.535687i	−0.999589	−	0.0286659i	$-0.990874\pi$
$193$	−2.41805	+	7.44200i	−0.174055	+	0.535687i	0.825534	+	0.564352i	$0.190874\pi$
$194$	−5.00368	−	15.3997i	−0.359243	−	1.10564i
$195$	4.95485	+	15.2495i	0.354824	+	1.09204i
$196$	0.403653	−	0.293271i	0.0288324	−	0.0209479i
$197$	6.13196	−	18.8722i	0.436884	−	1.34459i	−0.454259	−	0.890870i	$-0.650096\pi$
$197$	6.13196	−	18.8722i	0.436884	−	1.34459i	0.891143	−	0.453722i	$-0.149904\pi$
$198$	−6.09240	+	4.42639i	−0.432968	+	0.314570i
$199$	−14.1254	−	10.2627i	−1.00132	−	0.727502i	−0.0389495	−	0.999241i	$-0.512401\pi$
$199$	−14.1254	−	10.2627i	−1.00132	−	0.727502i	−0.962371	+	0.271739i	$0.912401\pi$
$200$	1.39722	+	4.30019i	0.0987981	+	0.304069i
$201$	−5.23607	−	3.80423i	−0.369324	−	0.268329i
$202$	−7.30603	−	5.30814i	−0.514050	−	0.373479i
$203$	−0.966311	−	2.97400i	−0.0678217	−	0.208734i
$204$	1.93083	+	1.40283i	0.135185	+	0.0982177i
$205$	−22.7651	+	16.5398i	−1.58998	+	1.15519i
$206$	−7.83875	+	24.1252i	−0.546152	+	1.68088i
$207$	4.70071	−	3.41527i	0.326722	−	0.237377i
$208$	−8.18840	−	25.2013i	−0.567763	−	1.74740i
$209$	4.55248	+	14.0111i	0.314901	+	0.969167i
$210$	−4.29689	+	13.2245i	−0.296514	+	0.912575i
$211$	−1.57840			−0.108661			−0.0543306	−	0.998523i	$-0.517302\pi$
$211$	−1.57840			−0.108661			−0.0543306	+	0.998523i	$0.517302\pi$
$212$	13.4848			0.926140
$213$	−0.597035	+	1.83748i	−0.0409081	+	0.125902i
$214$	−8.12855	−	5.90574i	−0.555656	−	0.403708i
$215$	14.0147	−	10.1823i	0.955796	−	0.694426i
$216$	−1.20906			−0.0822659
$217$	11.5650	−	8.46714i	0.785085	−	0.574787i
$218$	35.2885			2.39004
$219$	0.826301	−	0.600343i	0.0558362	−	0.0405674i
$220$	−13.1922	−	9.58469i	−0.889418	−	0.646200i
$221$	2.98902	−	9.19925i	0.201063	−	0.618808i
$222$	7.69886			0.516714
$223$	11.7919			0.789645			0.394823	−	0.918757i	$-0.370806\pi$
$223$	11.7919			0.789645			0.394823	+	0.918757i	$0.370806\pi$
$224$	5.17741	−	15.9344i	0.345931	−	1.06466i
$225$	1.15563	+	3.55665i	0.0770417	+	0.237110i
$226$	−6.43708	−	19.8113i	−0.428188	−	1.31783i
$227$	7.57890	−	5.50639i	0.503029	−	0.365472i	−0.307144	−	0.951663i	$-0.599373\pi$
$227$	7.57890	−	5.50639i	0.503029	−	0.365472i	0.810173	+	0.586191i	$0.199373\pi$
$228$	1.47815	−	4.54927i	0.0978927	−	0.301283i
$229$	−6.13844	+	4.45984i	−0.405640	+	0.294715i	−0.771834	−	0.635824i	$-0.780660\pi$
$229$	−6.13844	+	4.45984i	−0.405640	+	0.294715i	0.366194	+	0.930538i	$0.380660\pi$
$230$	25.3905	+	18.4473i	1.67420	+	1.21638i
$231$	3.27882	+	10.0912i	0.215730	+	0.663950i
$232$	1.18816	+	0.863248i	0.0780065	+	0.0566750i
$233$	7.50293	+	5.45119i	0.491533	+	0.357120i	0.805774	−	0.592224i	$-0.201750\pi$
$233$	7.50293	+	5.45119i	0.491533	+	0.357120i	−0.314241	+	0.949343i	$0.601750\pi$
$234$	−3.06227	−	9.42469i	−0.200187	−	0.616111i
$235$	21.6801	+	15.7515i	1.41425	+	1.02751i
$236$	−9.74096	+	7.07722i	−0.634082	+	0.460688i
$237$	−2.78591	+	8.57414i	−0.180964	+	0.556950i
$238$	6.78621	−	4.93047i	0.439885	−	0.319595i
$239$	1.55583	+	4.78835i	0.100638	+	0.309733i	0.988682	−	0.150026i	$-0.0479358\pi$
$239$	1.55583	+	4.78835i	0.100638	+	0.309733i	−0.888044	+	0.459759i	$0.847936\pi$
$240$	−4.46320	−	13.7363i	−0.288098	−	0.886675i
$241$	−4.15924	+	12.8008i	−0.267920	+	0.824573i	0.723086	+	0.690758i	$0.242723\pi$
$241$	−4.15924	+	12.8008i	−0.267920	+	0.824573i	−0.991006	+	0.133815i	$0.957277\pi$
$242$	−10.9406			−0.703287
$243$	−1.00000			−0.0641500
$244$	−3.02973	+	9.32456i	−0.193959	+	0.596944i
$245$	−0.891693	−	0.647853i	−0.0569682	−	0.0413898i
$246$	14.0696	−	10.2222i	0.897045	−	0.651741i
$247$	−19.3863			−1.23352
$248$	−2.05685	+	6.40982i	−0.130610	+	0.407024i
$249$	−6.70256			−0.424757
$250$	5.50739	−	4.00135i	0.348318	−	0.253068i
$251$	−1.78184	−	1.29458i	−0.112469	−	0.0817134i	0.530129	−	0.847917i	$-0.322143\pi$
$251$	−1.78184	−	1.29458i	−0.112469	−	0.0817134i	−0.642598	+	0.766204i	$0.722143\pi$
$252$	1.06460	−	3.27651i	0.0670636	−	0.206401i
$253$	23.9484			1.50562
$254$	−3.27689			−0.205610
$255$	1.62920	−	5.01418i	0.102025	−	0.314000i
$256$	6.47244	+	19.9201i	0.404527	+	1.24501i
$257$	−3.76074	−	11.5744i	−0.234589	−	0.721990i	−0.997176	−	0.0751042i	$-0.976071\pi$
$257$	−3.76074	−	11.5744i	−0.234589	−	0.721990i	0.762587	−	0.646886i	$-0.223929\pi$
$258$	−8.66157	+	6.29300i	−0.539246	+	0.391785i
$259$	3.35207	−	10.3166i	0.208287	−	0.641043i
$260$	17.3599	−	12.6127i	1.07661	−	0.782206i
$261$	0.982716	+	0.713985i	0.0608286	+	0.0441946i
$262$	2.06141	+	6.34438i	0.127355	+	0.391957i
$263$	−1.45603	−	1.05787i	−0.0897825	−	0.0652308i	0.541988	−	0.840386i	$-0.317672\pi$
$263$	−1.45603	−	1.05787i	−0.0897825	−	0.0652308i	−0.631771	+	0.775155i	$0.717672\pi$
$264$	−4.03158	−	2.92911i	−0.248127	−	0.180275i
$265$	−9.20522	−	28.3307i	−0.565472	−	1.74034i
$266$	−13.6012	−	9.88183i	−0.833942	−	0.605894i
$267$	−7.55481	+	5.48889i	−0.462347	+	0.335915i
$268$	−2.67652	+	8.23749i	−0.163495	+	0.503185i
$269$	−11.3722	+	8.26237i	−0.693374	+	0.503766i	−0.877767	−	0.479087i	$-0.840968\pi$
$269$	−11.3722	+	8.26237i	−0.693374	+	0.503766i	0.184394	+	0.982852i	$0.440968\pi$
$270$	−1.66913	−	5.13706i	−0.101580	−	0.312631i
$271$	1.98030	+	6.09473i	0.120294	+	0.370228i	0.993014	−	0.117993i	$-0.0376460\pi$
$271$	1.98030	+	6.09473i	0.120294	+	0.370228i	−0.872720	+	0.488221i	$0.837646\pi$
$272$	−2.69243	+	8.28644i	−0.163252	+	0.502439i
$273$	−13.9625			−0.845052
$274$	−0.0689319			−0.00416433
$275$	−4.76308	+	14.6592i	−0.287224	+	0.883986i
$276$	−6.29078	−	4.57052i	−0.378660	−	0.275113i
$277$	−0.282006	+	0.204889i	−0.0169441	+	0.0123106i	−0.596225	−	0.802817i	$-0.703333\pi$
$277$	−0.282006	+	0.204889i	−0.0169441	+	0.0123106i	0.579281	+	0.815128i	$0.303333\pi$
$278$	33.8210			2.02845
$279$	−1.70120	+	5.30150i	−0.101848	+	0.317393i
$280$	−9.20150			−0.549895
$281$	19.4459	−	14.1283i	1.16004	−	0.842821i	0.170260	−	0.985399i	$-0.445539\pi$
$281$	19.4459	−	14.1283i	1.16004	−	0.842821i	0.989784	+	0.142578i	$0.0455392\pi$
$282$	−13.3990	−	9.73496i	−0.797900	−	0.579708i
$283$	−1.87043	+	5.75659i	−0.111186	+	0.342194i	−0.991132	−	0.132878i	$-0.957578\pi$
$283$	−1.87043	+	5.75659i	−0.111186	+	0.342194i	0.879947	+	0.475072i	$0.157578\pi$
$284$	2.58558			0.153426
$285$	−10.5668			−0.625922
$286$	12.6216	−	38.8452i	0.746330	−	2.29697i
$287$	−7.57199	−	23.3042i	−0.446961	−	1.37560i
$288$	2.01117	+	6.18975i	0.118509	+	0.364734i
$289$	11.1802	−	8.12292i	0.657661	−	0.477819i
$290$	−2.02750	+	6.24000i	−0.119059	+	0.366425i
$291$	7.16976	−	5.20913i	0.420299	−	0.305365i
$292$	−1.10581	−	0.803416i	−0.0647124	−	0.0470163i
$293$	2.93625	+	9.03685i	0.171538	+	0.527938i	0.999458	−	0.0329065i	$-0.0104764\pi$
$293$	2.93625	+	9.03685i	0.171538	+	0.527938i	−0.827921	+	0.560845i	$0.810476\pi$
$294$	0.551097	+	0.400395i	0.0321406	+	0.0233515i
$295$	21.5183	+	15.6340i	1.25285	+	0.910246i
$296$	1.57433	+	4.84529i	0.0915060	+	0.281627i
$297$	−3.33448	−	2.42264i	−0.193486	−	0.140576i
$298$	−15.4886	+	11.2531i	−0.897231	+	0.651876i
$299$	−9.73842	+	29.9718i	−0.563188	+	1.73331i
$300$	4.04886	−	2.94167i	0.233761	−	0.169837i
$301$	4.66150	+	14.3466i	0.268684	+	0.826925i
$302$	−11.1144	−	34.2065i	−0.639561	−	1.96837i
$303$	1.52738	−	4.70078i	0.0877454	−	0.270053i
$304$	17.4627			1.00155
$305$	21.6585			1.24016
$306$	−1.00690	+	3.09893i	−0.0575608	+	0.177154i
$307$	14.3505	+	10.4262i	0.819025	+	0.595057i	0.916433	−	0.400188i	$-0.131055\pi$
$307$	14.3505	+	10.4262i	0.819025	+	0.595057i	−0.0974079	+	0.995245i	$0.531055\pi$
$308$	11.4877	−	8.34631i	0.654573	−	0.475575i
$309$	−13.8837			−0.789814
$310$	−30.0736	+	0.109749i	−1.70807	+	0.00623333i
$311$	−20.8672			−1.18327			−0.591637	−	0.806205i	$-0.701518\pi$
$311$	−20.8672			−1.18327			−0.591637	+	0.806205i	$0.701518\pi$
$312$	5.30524	−	3.85448i	0.300350	−	0.218217i
$313$	−2.76781	−	2.01093i	−0.156446	−	0.113665i	0.506808	−	0.862059i	$-0.330825\pi$
$313$	−2.76781	−	2.01093i	−0.156446	−	0.113665i	−0.663254	+	0.748394i	$0.730825\pi$
$314$	8.82313	−	27.1548i	0.497918	−	1.53243i
$315$	−7.61048			−0.428802
$316$	12.0649			0.678706
$317$	−0.650382	+	2.00167i	−0.0365291	+	0.112425i	−0.967658	−	0.252264i	$-0.918825\pi$
$317$	−0.650382	+	2.00167i	−0.0365291	+	0.112425i	0.931129	+	0.364689i	$0.118825\pi$
$318$	5.68914	+	17.5094i	0.319031	+	0.981876i
$319$	1.54712	+	4.76154i	0.0866220	+	0.266595i
$320$	−5.07055	+	3.68397i	−0.283452	+	0.205940i
$321$	1.69933	−	5.23000i	0.0948473	−	0.291910i
$322$	−22.1099	+	16.0638i	−1.23214	+	0.895202i
$323$	5.15701	+	3.74678i	0.286943	+	0.208477i
$324$	0.413545	+	1.27276i	0.0229747	+	0.0707090i
$325$	−16.4094	−	11.9221i	−0.910230	−	0.661321i
$326$	−29.1762	−	21.1978i	−1.61592	−	1.17404i
$327$	5.96836	+	18.3687i	0.330051	+	1.01579i
$328$	9.31040	+	6.76440i	0.514081	+	0.373501i
$329$	−18.8789	+	13.7163i	−1.04083	+	0.756206i
$330$	6.87957	−	21.1731i	0.378708	−	1.16554i
$331$	10.5731	−	7.68177i	0.581147	−	0.422228i	−0.257990	−	0.966148i	$-0.583060\pi$
$331$	10.5731	−	7.68177i	0.581147	−	0.422228i	0.839138	+	0.543919i	$0.183060\pi$
$332$	2.77181	+	8.53076i	0.152123	+	0.468186i
$333$	1.30211	+	4.00749i	0.0713554	+	0.219609i
$334$	2.90130	−	8.92930i	0.158752	−	0.488589i
$335$	19.1335			1.04538
$336$	12.5771			0.686136
$337$	−3.73968	+	11.5096i	−0.203713	+	0.626965i	0.796050	+	0.605230i	$0.206919\pi$
$337$	−3.73968	+	11.5096i	−0.203713	+	0.626965i	−0.999764	+	0.0217350i	$0.993081\pi$
$338$	24.2670	+	17.6310i	1.31995	+	0.959001i
$339$	9.22368	−	6.70139i	0.500961	−	0.363970i
$340$	−7.05560			−0.382644
$341$	−18.5163	+	13.5564i	−1.00271	+	0.734119i
$342$	6.53062			0.353136
$343$	15.3552	−	11.1562i	0.829104	−	0.602379i
$344$	−5.73170	−	4.16432i	−0.309033	−	0.224525i
$345$	−5.30806	+	16.3365i	−0.285776	+	0.879529i
$346$	26.5275			1.42613
$347$	−10.0474			−0.539373			−0.269686	−	0.962948i	$-0.586920\pi$
$347$	−10.0474			−0.539373			−0.269686	+	0.962948i	$0.586920\pi$
$348$	0.502335	−	1.54603i	0.0269280	−	0.0828758i
$349$	0.778592	+	2.39626i	0.0416771	+	0.128269i	0.969730	−	0.244179i	$-0.0785185\pi$
$349$	0.778592	+	2.39626i	0.0416771	+	0.128269i	−0.928053	+	0.372448i	$0.878518\pi$
$350$	−5.43552	−	16.7288i	−0.290541	−	0.894193i
$351$	4.38791	−	3.18801i	0.234210	−	0.170163i
$352$	−8.28933	+	25.5119i	−0.441823	+	1.35979i
$353$	10.1400	−	7.36713i	0.539697	−	0.392113i	−0.284275	−	0.958743i	$-0.591753\pi$
$353$	10.1400	−	7.36713i	0.539697	−	0.392113i	0.823973	+	0.566630i	$0.191753\pi$
$354$	−13.2991	−	9.66233i	−0.706837	−	0.513547i
$355$	−1.76501	−	5.43214i	−0.0936770	−	0.288308i
$356$	10.1103	+	7.34557i	0.535845	+	0.389315i
$357$	3.71422	+	2.69854i	0.196577	+	0.142822i
$358$	−5.55477	−	17.0958i	−0.293579	−	0.903543i
$359$	−0.452847	−	0.329013i	−0.0239004	−	0.0173646i	0.575771	−	0.817611i	$-0.304702\pi$
$359$	−0.452847	−	0.329013i	−0.0239004	−	0.0173646i	−0.599671	+	0.800246i	$0.704702\pi$
$360$	2.89169	−	2.10094i	0.152406	−	0.110729i
$361$	−1.92337	+	5.91954i	−0.101230	+	0.311555i
$362$	−38.5302	+	27.9939i	−2.02510	+	1.47132i
$363$	−1.85039	−	5.69490i	−0.0971201	−	0.298905i
$364$	5.77415	+	17.7710i	0.302648	+	0.931453i
$365$	−0.933063	+	2.87167i	−0.0488387	+	0.150310i
$366$	−13.3857			−0.699682
$367$	8.38822			0.437861			0.218931	−	0.975740i	$-0.429743\pi$
$367$	8.38822			0.437861			0.218931	+	0.975740i	$0.429743\pi$
$368$	8.77211	−	26.9978i	0.457278	−	1.40736i
$369$	7.70054	+	5.59477i	0.400874	+	0.291252i
$370$	−18.4133	+	13.3781i	−0.957263	+	0.695492i
$371$	25.9399			1.34673
$372$	7.45107	−	0.0271915i	0.386320	−	0.00140982i
$373$	−26.6372			−1.37922			−0.689610	−	0.724181i	$-0.742218\pi$
$373$	−26.6372			−1.37922			−0.689610	+	0.724181i	$0.742218\pi$
$374$	−10.8651	+	7.89396i	−0.561821	+	0.408187i
$375$	3.01430	+	2.19001i	0.155658	+	0.113092i
$376$	3.38676	−	10.4234i	0.174659	−	0.537545i
$377$	−6.58826			−0.339313
$378$	4.70353			0.241924
$379$	−6.33320	+	19.4916i	−0.325315	+	1.00122i	0.645983	+	0.763351i	$0.276448\pi$
$379$	−6.33320	+	19.4916i	−0.325315	+	1.00122i	−0.971298	+	0.237865i	$0.923552\pi$
$380$	4.36984	+	13.4490i	0.224168	+	0.689918i
$381$	−0.554222	−	1.70572i	−0.0283936	−	0.0873866i
$382$	−10.4897	+	7.62124i	−0.536702	+	0.389937i
$383$	−2.51436	+	7.73840i	−0.128478	+	0.395414i	−0.994519	−	0.104559i	$-0.966657\pi$
$383$	−2.51436	+	7.73840i	−0.128478	+	0.395414i	0.866041	+	0.499973i	$0.166657\pi$
$384$	−7.39685	+	5.37413i	−0.377469	+	0.274247i
$385$	−25.3770	−	18.4375i	−1.29333	−	0.939661i
$386$	4.41800	+	13.5972i	0.224870	+	0.692079i
$387$	−4.74064	−	3.44427i	−0.240980	−	0.175082i
$388$	−9.59501	−	6.97118i	−0.487113	−	0.353908i
$389$	−3.24307	−	9.98115i	−0.164430	−	0.506065i	0.834563	−	0.550912i	$-0.185720\pi$
$389$	−3.24307	−	9.98115i	−0.164430	−	0.506065i	−0.998994	+	0.0448471i	$0.985720\pi$
$390$	23.7010	+	17.2198i	1.20015	+	0.871957i
$391$	8.38318	−	6.09074i	0.423956	−	0.308022i
$392$	−0.139296	+	0.428709i	−0.00703552	+	0.0216531i
$393$	−2.95379	+	2.14606i	−0.148999	+	0.108254i
$394$	−11.2037	−	34.4813i	−0.564432	−	1.73714i
$395$	−8.23597	−	25.3477i	−0.414396	−	1.27538i
$396$	−1.70449	+	5.24588i	−0.0856538	+	0.263615i
$397$	29.9380			1.50254			0.751272	−	0.659993i	$-0.229441\pi$
$397$	29.9380			1.50254			0.751272	+	0.659993i	$0.229441\pi$
$398$	−31.9008			−1.59904
$399$	2.84342	−	8.75115i	0.142349	−	0.438105i
$400$	14.7812	+	10.7391i	0.739058	+	0.536957i
$401$	20.4215	−	14.8371i	1.01980	−	0.740928i	0.0535576	−	0.998565i	$-0.482944\pi$
$401$	20.4215	−	14.8371i	1.01980	−	0.740928i	0.966242	+	0.257637i	$0.0829439\pi$
$402$	−11.8252			−0.589786
$403$	−9.43651	−	28.6860i	−0.470066	−	1.42895i
$404$	−6.61461			−0.329089
$405$	2.39169	−	1.73767i	0.118844	−	0.0863454i
$406$	−4.62224	−	3.35825i	−0.229398	−	0.166667i
$407$	−5.36685	+	16.5175i	−0.266025	+	0.818741i
$408$	−2.15622			−0.106749
$409$	−18.5406			−0.916772			−0.458386	−	0.888753i	$-0.651572\pi$
$409$	−18.5406			−0.916772			−0.458386	+	0.888753i	$0.651572\pi$
$410$	−15.8874	+	48.8965i	−0.784625	+	2.41483i
$411$	−0.0116585	−	0.0358812i	−0.000575071	−	0.00176989i
$412$	5.74153	+	17.6706i	0.282865	+	0.870568i
$413$	−18.7381	+	13.6140i	−0.922040	+	0.669901i
$414$	3.28056	−	10.0965i	0.161231	−	0.496218i
$415$	16.0305	−	11.6468i	0.786904	−	0.571719i
$416$	−28.5578	−	20.7485i	−1.40016	−	1.01728i
$417$	5.72016	+	17.6049i	0.280118	+	0.862113i
$418$	21.7763	+	15.8214i	1.06511	+	0.773849i
$419$	16.3936	+	11.9106i	0.800880	+	0.581873i	0.911172	−	0.412026i	$-0.135179\pi$
$419$	16.3936	+	11.9106i	0.800880	+	0.581873i	−0.110292	+	0.993899i	$0.535179\pi$
$420$	3.14728	+	9.68633i	0.153571	+	0.472644i
$421$	−3.50946	−	2.54977i	−0.171041	−	0.124268i	0.498972	−	0.866618i	$-0.333711\pi$
$421$	−3.50946	−	2.54977i	−0.171041	−	0.124268i	−0.670012	+	0.742350i	$0.733711\pi$
$422$	−2.33310	+	1.69510i	−0.113574	+	0.0825161i
$423$	2.80116	−	8.62108i	0.136197	−	0.419171i
$424$	−9.85617	+	7.16093i	−0.478658	+	0.347765i
$425$	2.06093	+	6.34288i	0.0999696	+	0.307675i
$426$	1.09084	+	3.35725i	0.0528512	+	0.162659i
$427$	−5.82811	+	17.9371i	−0.282042	+	0.868036i
$428$	−7.35930			−0.355725
$429$	22.3548			1.07930
$430$	9.78069	−	30.1019i	0.471667	−	1.45164i
$431$	−16.9100	−	12.2859i	−0.814527	−	0.591789i	0.100612	−	0.994926i	$-0.467920\pi$
$431$	−16.9100	−	12.2859i	−0.814527	−	0.591789i	−0.915140	+	0.403137i	$0.867920\pi$
$432$	−3.95252	+	2.87167i	−0.190166	+	0.138163i
$433$	4.82132			0.231698			0.115849	−	0.993267i	$-0.463041\pi$
$433$	4.82132			0.231698			0.115849	+	0.993267i	$0.463041\pi$
$434$	8.00164	−	24.9358i	0.384091	−	1.19696i
$435$	−3.59102			−0.172176
$436$	20.9108	−	15.1926i	1.00145	−	0.727593i
$437$	−16.8019	−	12.2073i	−0.803743	−	0.583954i
$438$	0.576664	−	1.77479i	0.0275541	−	0.0848028i
$439$	−7.63789			−0.364536			−0.182268	−	0.983249i	$-0.558344\pi$
$439$	−7.63789			−0.364536			−0.182268	+	0.983249i	$0.558344\pi$
$440$	14.7321			0.702326
$441$	−0.115211	+	0.354582i	−0.00548622	+	0.0168848i
$442$	−5.46120	−	16.8079i	−0.259763	−	0.799468i
$443$	−0.451137	−	1.38846i	−0.0214341	−	0.0659675i	0.939767	−	0.341815i	$-0.111042\pi$
$443$	−0.451137	−	1.38846i	−0.0214341	−	0.0659675i	−0.961201	+	0.275847i	$0.911042\pi$
$444$	4.56210	−	3.31456i	0.216508	−	0.157302i
$445$	8.53093	−	26.2555i	0.404405	−	1.24463i
$446$	17.4302	−	12.6638i	0.825344	−	0.599647i
$447$	−8.47719	−	6.15904i	−0.400957	−	0.291313i
$448$	−1.68654	−	5.19063i	−0.0796814	−	0.245234i
$449$	17.3006	+	12.5696i	0.816466	+	0.593197i	0.915698	−	0.401867i	$-0.131639\pi$
$449$	17.3006	+	12.5696i	0.816466	+	0.593197i	−0.0992319	+	0.995064i	$0.531639\pi$
$450$	5.52780	+	4.01618i	0.260583	+	0.189325i
$451$	12.1232	+	37.3114i	0.570859	+	1.75692i
$452$	−12.3437	−	8.96821i	−0.580598	−	0.421829i
$453$	15.9258	−	11.5707i	0.748258	−	0.543641i
$454$	5.28921	−	16.2785i	0.248235	−	0.763989i
$455$	33.3941	−	24.2623i	1.56554	−	1.13743i
$456$	1.33544	+	4.11005i	0.0625376	+	0.192471i
$457$	−0.432210	−	1.33020i	−0.0202179	−	0.0622243i	0.940439	−	0.339964i	$-0.110415\pi$
$457$	−0.432210	−	1.33020i	−0.0202179	−	0.0622243i	−0.960656	+	0.277739i	$0.910415\pi$
$458$	−4.28394	+	13.1846i	−0.200175	+	0.616076i
$459$	−1.78339			−0.0832413
$460$	22.9876			1.07180
$461$	0.0367381	−	0.113068i	0.00171106	−	0.00526611i	−0.950197	−	0.311649i	$-0.899119\pi$
$461$	0.0367381	−	0.113068i	0.00171106	−	0.00526611i	0.951908	+	0.306383i	$0.0991187\pi$
$462$	15.6839	+	11.3950i	0.729679	+	0.530143i
$463$	−24.8333	+	18.0424i	−1.15410	+	0.838504i	−0.989021	−	0.147776i	$-0.952788\pi$
$463$	−24.8333	+	18.0424i	−1.15410	+	0.838504i	−0.165081	+	0.986280i	$0.552788\pi$
$464$	5.93453			0.275504
$465$	−5.14350	−	15.6357i	−0.238524	−	0.725087i
$466$	16.9447			0.784947
$467$	−16.4845	+	11.9767i	−0.762813	+	0.554216i	−0.899772	−	0.436361i	$-0.856267\pi$
$467$	−16.4845	+	11.9767i	−0.762813	+	0.554216i	0.136959	+	0.990577i	$0.456267\pi$
$468$	−5.87218	−	4.26639i	−0.271441	−	0.197214i
$469$	−5.14866	+	15.8459i	−0.237743	+	0.731698i
$470$	48.9625			2.25847
$471$	15.6272			0.720062
$472$	3.36149	−	10.3456i	0.154725	−	0.476195i
$473$	−7.46332	−	22.9697i	−0.343164	−	1.05615i
$474$	5.09011	+	15.6657i	0.233796	+	0.719551i
$475$	10.8140	−	7.85684i	0.496181	−	0.360496i
$476$	1.89860	−	5.84328i	0.0870220	−	0.267826i
$477$	−8.15195	+	5.92274i	−0.373252	+	0.271184i
$478$	7.44214	+	5.40703i	0.340395	+	0.247312i
$479$	−5.19525	−	15.9893i	−0.237377	−	0.730571i	−0.996797	−	0.0799709i	$-0.974517\pi$
$479$	−5.19525	−	15.9893i	−0.237377	−	0.730571i	0.759420	−	0.650600i	$-0.225483\pi$
$480$	−15.5658	−	11.3092i	−0.710479	−	0.516193i
$481$	−18.4895	−	13.4334i	−0.843048	−	0.612510i
$482$	7.59931	+	23.3883i	0.346139	+	1.06531i
$483$	−12.1012	−	8.79202i	−0.550623	−	0.400051i
$484$	−6.48304	+	4.71020i	−0.294684	+	0.214100i
$485$	−8.09612	+	24.9173i	−0.367626	+	1.13144i
$486$	−1.47815	+	1.07394i	−0.0670501	+	0.0487148i
$487$	−3.97437	−	12.2319i	−0.180096	−	0.554278i	0.819734	−	0.572745i	$-0.194121\pi$
$487$	−3.97437	−	12.2319i	−0.180096	−	0.554278i	−0.999829	+	0.0184669i	$0.994121\pi$
$488$	−2.73722	−	8.42431i	−0.123908	−	0.381350i
$489$	6.09949	−	18.7723i	0.275829	−	0.848913i
$490$	−2.01381			−0.0909745
$491$	−5.30716			−0.239509			−0.119754	−	0.992804i	$-0.538211\pi$
$491$	−5.30716			−0.239509			−0.119754	+	0.992804i	$0.538211\pi$
$492$	3.93629	−	12.1147i	0.177462	−	0.546171i
$493$	1.75256	+	1.27331i	0.0789314	+	0.0573470i
$494$	−28.6558	+	20.8197i	−1.28929	+	0.936721i
$495$	12.1848			0.547666
$496$	8.50016	+	25.8396i	0.381668	+	1.16023i
$497$	4.97372			0.223102
$498$	−9.90737	+	7.19812i	−0.443960	+	0.322556i
$499$	1.02520	+	0.744850i	0.0458942	+	0.0333441i	0.610496	−	0.792019i	$-0.290970\pi$
$499$	1.02520	+	0.744850i	0.0458942	+	0.0333441i	−0.564602	+	0.825364i	$0.690970\pi$
$500$	1.54082	−	4.74215i	0.0689075	−	0.212075i
$501$	5.13867			0.229579
$502$	−4.02412			−0.179605
$503$	−9.52910	+	29.3275i	−0.424881	+	1.30765i	0.478226	+	0.878237i	$0.341280\pi$
$503$	−9.52910	+	29.3275i	−0.424881	+	1.30765i	−0.903108	+	0.429414i	$0.858720\pi$
$504$	0.961819	+	2.96017i	0.0428428	+	0.131857i
$505$	4.51537	+	13.8969i	0.200932	+	0.618404i
$506$	35.3993	−	25.7191i	1.57369	−	1.14335i
$507$	−5.07319	+	15.6137i	−0.225308	+	0.693427i
$508$	−1.94178	+	1.41078i	−0.0861525	+	0.0625935i
$509$	34.5273	+	25.0855i	1.53039	+	1.11190i	0.956019	+	0.293304i	$0.0947548\pi$
$509$	34.5273	+	25.0855i	1.53039	+	1.11190i	0.574375	+	0.818592i	$0.305245\pi$
$510$	−2.97670	−	9.16135i	−0.131811	−	0.405672i
$511$	−2.12717	−	1.54548i	−0.0941005	−	0.0683680i
$512$	16.1665	+	11.7456i	0.714464	+	0.519088i
$513$	1.10453	+	3.39939i	0.0487661	+	0.150087i
$514$	−17.9891	−	13.0698i	−0.793465	−	0.576486i
$515$	33.2055	−	24.1252i	1.46321	−	1.06308i
$516$	−2.42327	+	7.45807i	−0.106679	+	0.328323i
$517$	30.2262	−	21.9606i	1.32935	−	0.965827i
$518$	−6.12453	−	18.8494i	−0.269097	−	0.828194i
$519$	4.48662	+	13.8084i	0.196941	+	0.606121i
$520$	−5.99070	+	18.4375i	−0.262709	+	0.808537i
$521$	26.2572			1.15035			0.575175	−	0.818030i	$-0.304934\pi$
$521$	26.2572			1.15035			0.575175	+	0.818030i	$0.304934\pi$
$522$	2.21937			0.0971394
$523$	−7.08247	+	21.7976i	−0.309695	+	0.953143i	0.668189	+	0.743992i	$0.267070\pi$
$523$	−7.08247	+	21.7976i	−0.309695	+	0.953143i	−0.977883	+	0.209151i	$0.932930\pi$
$524$	3.95295	+	2.87199i	0.172685	+	0.125463i
$525$	7.78854	−	5.65871i	0.339920	−	0.246966i
$526$	−3.28831			−0.143377
$527$	−3.03389	+	9.45463i	−0.132158	+	0.411850i
$528$	−20.1366			−0.876335
$529$	−8.70560	+	6.32499i	−0.378504	+	0.275000i
$530$	−44.0321	−	31.9912i	−1.91263	−	1.38961i
$531$	2.78026	−	8.55676i	0.120653	−	0.371332i
$532$	−12.3140			−0.533880
$533$	−51.6255			−2.23615
$534$	−5.27240	+	16.2268i	−0.228159	+	0.702202i
$535$	5.02372	+	15.4614i	0.217194	+	0.668456i
$536$	−2.41811	−	7.44219i	−0.104447	−	0.321454i
$537$	7.95942	−	5.78286i	0.343474	−	0.249549i
$538$	−7.93649	+	24.4260i	−0.342166	+	1.05308i
$539$	−1.24319	+	0.903232i	−0.0535481	+	0.0389050i
$540$	−3.20071	−	2.32545i	−0.137737	−	0.100072i
$541$	−4.78135	−	14.7155i	−0.205566	−	0.632668i	−0.999690	−	0.0249116i	$-0.992070\pi$
$541$	−4.78135	−	14.7155i	−0.205566	−	0.632668i	0.794123	−	0.607757i	$-0.207930\pi$
$542$	9.47252	+	6.88219i	0.406880	+	0.295615i
$543$	−21.0883	−	15.3215i	−0.904985	−	0.657510i
$544$	3.58669	+	11.0387i	0.153778	+	0.473281i
$545$	−46.1932	−	33.5613i	−1.97870	−	1.43761i
$546$	−20.6387	+	14.9949i	−0.883255	+	0.641722i
$547$	3.01091	−	9.26662i	0.128737	−	0.396212i	−0.865826	−	0.500345i	$-0.833207\pi$
$547$	3.01091	−	9.26662i	0.128737	−	0.396212i	0.994563	+	0.104133i	$0.0332066\pi$
$548$	−0.0408469	+	0.0296770i	−0.00174489	+	0.00126774i
$549$	−2.26393	−	6.96767i	−0.0966223	−	0.297373i
$550$	8.70258	+	26.7838i	0.371079	+	1.14206i
$551$	1.34167	−	4.12925i	0.0571573	−	0.175912i
$552$	7.02510			0.299008
$553$	23.2086			0.986929
$554$	−0.196808	+	0.605713i	−0.00836158	+	0.0257343i
$555$	−10.0779	−	7.32205i	−0.427785	−	0.310804i
$556$	20.0412	−	14.5608i	0.849938	−	0.617516i
$557$	−3.89841			−0.165181			−0.0825905	−	0.996584i	$-0.526319\pi$
$557$	−3.89841			−0.165181			−0.0825905	+	0.996584i	$0.526319\pi$
$558$	3.17886	+	9.66338i	0.134572	+	0.409084i
$559$	31.7819			1.34423
$560$	−30.0805	+	21.8548i	−1.27113	+	0.923533i
$561$	−5.94667	−	4.32051i	−0.251069	−	0.182412i
$562$	13.5710	−	41.7673i	0.572459	−	1.76185i
$563$	−32.4407			−1.36721			−0.683606	−	0.729851i	$-0.739589\pi$
$563$	−32.4407			−1.36721			−0.683606	+	0.729851i	$0.739589\pi$
$564$	−12.1310			−0.510807
$565$	−10.4154	+	32.0553i	−0.438180	+	1.34858i
$566$	3.41745	+	10.5178i	0.143646	+	0.442097i
$567$	0.795511	+	2.44833i	0.0334083	+	0.102820i
$568$	−1.88982	+	1.37304i	−0.0792953	+	0.0576114i
$569$	−7.88982	+	24.2824i	−0.330759	+	1.01797i	0.638015	+	0.770024i	$0.279756\pi$
$569$	−7.88982	+	24.2824i	−0.330759	+	1.01797i	−0.968774	+	0.247947i	$0.920244\pi$
$570$	−15.6192	+	11.3480i	−0.654218	+	0.475317i
$571$	−11.7085	−	8.50675i	−0.489987	−	0.355996i	0.315192	−	0.949028i	$-0.397931\pi$
$571$	−11.7085	−	8.50675i	−0.489987	−	0.355996i	−0.805179	+	0.593031i	$0.797931\pi$
$572$	−9.24474	−	28.4524i	−0.386542	−	1.18965i
$573$	−5.74123	−	4.17125i	−0.239843	−	0.174256i
$574$	−36.2198	−	26.3152i	−1.51178	−	1.09838i
$575$	−6.71464	−	20.6655i	−0.280020	−	0.861813i
$576$	1.71517	+	1.24614i	0.0714654	+	0.0519227i
$577$	−36.8575	+	26.7785i	−1.53440	+	1.11480i	−0.580665	+	0.814143i	$0.697207\pi$
$577$	−36.8575	+	26.7785i	−1.53440	+	1.11480i	−0.953731	+	0.300661i	$0.902793\pi$
$578$	7.80254	−	24.0137i	0.324543	−	0.998840i
$579$	−6.33054	+	4.59941i	−0.263088	+	0.191145i
$580$	1.48505	+	4.57052i	0.0616634	+	0.189780i
$581$	5.33196	+	16.4101i	0.221207	+	0.680805i
$582$	5.00368	−	15.3997i	0.207409	−	0.638339i
$583$	−41.5312			−1.72005
$584$	1.23489			0.0511000
$585$	−4.95485	+	15.2495i	−0.204858	+	0.630488i
$586$	14.0452	+	10.2045i	0.580203	+	0.421542i
$587$	−3.60735	+	2.62089i	−0.148891	+	0.108176i	−0.659737	−	0.751497i	$-0.729332\pi$
$587$	−3.60735	+	2.62089i	−0.148891	+	0.108176i	0.510846	+	0.859672i	$0.329332\pi$
$588$	0.498943			0.0205761
$589$	19.9009	−	0.0726252i	0.820002	−	0.00299247i
$590$	48.5972			2.00071
$591$	16.0537	−	11.6637i	0.660361	−	0.479780i
$592$	16.6548	+	12.1004i	0.684509	+	0.497325i
$593$	9.26405	−	28.5118i	0.380429	−	1.17084i	−0.559314	−	0.828956i	$-0.688935\pi$
$593$	9.26405	−	28.5118i	0.380429	−	1.17084i	0.939742	−	0.341883i	$-0.111065\pi$
$594$	−7.53062			−0.308985
$595$	−13.5724			−0.556415
$596$	−4.33329	+	13.3365i	−0.177498	+	0.546284i
$597$	−5.39541	−	16.6054i	−0.220819	−	0.679612i
$598$	17.7930	+	54.7612i	0.727609	+	2.23935i
$599$	−13.6220	+	9.89694i	−0.556579	+	0.404378i	−0.830205	−	0.557458i	$-0.811777\pi$
$599$	−13.6220	+	9.89694i	−0.556579	+	0.404378i	0.273627	+	0.961836i	$0.411777\pi$
$600$	−1.39722	+	4.30019i	−0.0570411	+	0.175555i
$601$	−12.5783	+	9.13864i	−0.513078	+	0.372773i	−0.813990	−	0.580879i	$-0.802709\pi$
$601$	−12.5783	+	9.13864i	−0.513078	+	0.372773i	0.300912	+	0.953652i	$0.402709\pi$
$602$	22.2977	+	16.2003i	0.908788	+	0.660273i
$603$	−2.00000	−	6.15537i	−0.0814463	−	0.250666i
$604$	−21.3128	−	15.4847i	−0.867207	−	0.630063i
$605$	14.3214	+	10.4051i	0.582248	+	0.423028i
$606$	−2.79065	−	8.58875i	−0.113363	−	0.348894i
$607$	−1.54269	−	1.12083i	−0.0626160	−	0.0454932i	0.556037	−	0.831158i	$-0.312321\pi$
$607$	−1.54269	−	1.12083i	−0.0626160	−	0.0454932i	−0.618653	+	0.785664i	$0.712321\pi$
$608$	18.8200	−	13.6735i	0.763250	−	0.554534i
$609$	0.966311	−	2.97400i	0.0391569	−	0.120513i
$610$	32.0145	−	23.2599i	1.29623	−	0.941765i
$611$	15.1928	+	46.7587i	0.614635	+	1.89165i
$612$	0.737511	+	2.26983i	0.0298121	+	0.0917523i
$613$	6.94940	−	21.3881i	0.280684	−	0.863856i	−0.706975	−	0.707238i	$-0.749941\pi$
$613$	6.94940	−	21.3881i	0.280684	−	0.863856i	0.987659	−	0.156618i	$-0.0500591\pi$
$614$	32.4093			1.30793
$615$	−28.1392			−1.13468
$616$	−3.96428	+	12.2008i	−0.159725	+	0.491584i
$617$	22.9317	+	16.6608i	0.923194	+	0.670740i	0.944317	−	0.329037i	$-0.106724\pi$
$617$	22.9317	+	16.6608i	0.923194	+	0.670740i	−0.0211231	+	0.999777i	$0.506724\pi$
$618$	−20.5221	+	14.9102i	−0.825520	+	0.599776i
$619$	−14.2076			−0.571053			−0.285526	−	0.958371i	$-0.592168\pi$
$619$	−14.2076			−0.571053			−0.285526	+	0.958371i	$0.592168\pi$
$620$	−17.7734	+	13.0125i	−0.713798	+	0.522595i
$621$	5.81040			0.233163
$622$	−30.8449	+	22.4101i	−1.23677	+	0.898564i
$623$	19.4486	+	14.1302i	0.779191	+	0.566115i
$624$	8.18840	−	25.2013i	0.327798	−	1.00886i
$625$	−29.7132			−1.18853
$626$	−6.25085			−0.249834
$627$	−4.55248	+	14.0111i	−0.181808	+	0.559549i
$628$	−6.46255	−	19.8897i	−0.257884	−	0.793684i
$629$	2.32217	+	7.14691i	0.0925910	+	0.284966i
$630$	−11.2494	+	8.17317i	−0.448187	+	0.325627i
$631$	9.74941	−	30.0056i	0.388118	−	1.19450i	−0.546075	−	0.837736i	$-0.683879\pi$
$631$	9.74941	−	30.0056i	0.388118	−	1.19450i	0.934193	−	0.356768i	$-0.116121\pi$
$632$	−8.81838	+	6.40693i	−0.350776	+	0.254854i
$633$	−1.27695	−	0.927758i	−0.0507542	−	0.0368751i
$634$	1.18831	+	3.65723i	0.0471937	+	0.145247i
$635$	4.28950	+	3.11650i	0.170224	+	0.123675i
$636$	10.9094	+	7.92617i	0.432587	+	0.314293i
$637$	−0.624875	−	1.92317i	−0.0247584	−	0.0761986i
$638$	7.40047	+	5.37675i	0.292987	+	0.212868i
$639$	−1.56306	+	1.13563i	−0.0618336	+	0.0449247i
$640$	8.35256	−	25.7065i	0.330164	−	1.01614i
$641$	18.2508	−	13.2600i	0.720863	−	0.523737i	−0.165797	−	0.986160i	$-0.553020\pi$
$641$	18.2508	−	13.2600i	0.720863	−	0.523737i	0.886660	+	0.462422i	$0.153020\pi$
$642$	−3.10483	−	9.55568i	−0.122538	−	0.377133i
$643$	−7.03838	−	21.6619i	−0.277567	−	0.854262i	−0.988529	−	0.151032i	$-0.951740\pi$
$643$	−7.03838	−	21.6619i	−0.277567	−	0.854262i	0.710962	−	0.703230i	$-0.248260\pi$
$644$	−6.18576	+	19.0378i	−0.243753	+	0.750195i
$645$	17.3231			0.682098
$646$	11.6466			0.458230
$647$	6.99849	−	21.5391i	0.275139	−	0.846791i	−0.714043	−	0.700101i	$-0.753138\pi$
$647$	6.99849	−	21.5391i	0.275139	−	0.846791i	0.989183	−	0.146690i	$-0.0468619\pi$
$648$	−0.978148	−	0.710666i	−0.0384253	−	0.0279176i
$649$	30.0007	−	21.7968i	1.17763	−	0.855599i
$650$	−37.0591			−1.45358
$651$	14.3332	−	0.0523067i	0.561761	−	0.00205006i
$652$	−26.4151			−1.03450
$653$	22.2891	−	16.1940i	0.872240	−	0.633720i	−0.0589470	−	0.998261i	$-0.518774\pi$
$653$	22.2891	−	16.1940i	0.872240	−	0.633720i	0.931187	+	0.364542i	$0.118774\pi$
$654$	28.5490	+	20.7420i	1.11635	+	0.811078i
$655$	3.33544	−	10.2654i	0.130326	−	0.401103i
$656$	46.5029			1.81563
$657$	1.02136			0.0398472
$658$	−13.1753	+	40.5495i	−0.513628	+	1.58079i
$659$	13.6427	+	41.9880i	0.531445	+	1.63562i	0.751207	+	0.660067i	$0.229472\pi$
$659$	13.6427	+	41.9880i	0.531445	+	1.63562i	−0.219761	+	0.975554i	$0.570528\pi$
$660$	−5.03897	−	15.5084i	−0.196142	−	0.603662i
$661$	30.5845	−	22.2209i	1.18960	−	0.864294i	0.196377	−	0.980529i	$-0.437082\pi$
$661$	30.5845	−	22.2209i	1.18960	−	0.864294i	0.993222	+	0.116235i	$0.0370825\pi$
$662$	7.37879	−	22.7096i	0.286785	−	0.882633i
$663$	7.82535	−	5.68545i	0.303911	−	0.220804i
$664$	−6.55609	−	4.76328i	−0.254426	−	0.184851i
$665$	8.40599	+	25.8710i	0.325970	+	1.00323i
$666$	6.22851	+	4.52528i	0.241350	+	0.175351i
$667$	−5.70997	−	4.14854i	−0.221091	−	0.160632i
$668$	−2.12507	−	6.54031i	−0.0822216	−	0.253052i
$669$	9.53986	+	6.93112i	0.368832	+	0.267972i
$670$	28.2822	−	20.5482i	1.09264	−	0.793847i
$671$	9.33113	−	28.7183i	0.360224	−	1.10866i
$672$	13.5546	−	9.84803i	0.522882	−	0.379896i
$673$	−1.15200	−	3.54549i	−0.0444063	−	0.136668i	0.926395	−	0.376553i	$-0.122891\pi$
$673$	−1.15200	−	3.54549i	−0.0444063	−	0.136668i	−0.970802	+	0.239884i	$0.922891\pi$
$674$	6.83274	+	21.0290i	0.263187	+	0.810007i
$675$	−1.15563	+	3.55665i	−0.0444800	+	0.136895i
$676$	21.9705			0.845018
$677$	−9.64918			−0.370848			−0.185424	−	0.982659i	$-0.559366\pi$
$677$	−9.64918			−0.370848			−0.185424	+	0.982659i	$0.559366\pi$
$678$	6.43708	−	19.8113i	0.247215	−	0.760848i
$679$	−18.4573	−	13.4100i	−0.708327	−	0.514629i
$680$	5.15701	−	3.74678i	0.197762	−	0.143683i
$681$	9.36803			0.358984
$682$	−12.8111	+	39.9236i	−0.490562	+	1.52875i
$683$	20.0340			0.766581			0.383290	−	0.923628i	$-0.374791\pi$
$683$	20.0340			0.766581			0.383290	+	0.923628i	$0.374791\pi$
$684$	3.86984	−	2.81160i	0.147967	−	0.107504i
$685$	0.0902330	+	0.0655581i	0.00344763	+	0.00250485i
$686$	10.7162	−	32.9811i	0.409146	−	1.25922i
$687$	−7.58753			−0.289482
$688$	−28.6283			−1.09144
$689$	16.8883	−	51.9769i	0.643394	−	1.98016i
$690$	9.69831	+	29.8483i	0.369208	+	1.13631i
$691$	−4.53276	−	13.9504i	−0.172434	−	0.530698i	0.827073	−	0.562095i	$-0.190004\pi$
$691$	−4.53276	−	13.9504i	−0.172434	−	0.530698i	−0.999507	+	0.0313970i	$0.990004\pi$
$692$	15.7194	−	11.4208i	0.597561	−	0.434153i
$693$	−3.27882	+	10.0912i	−0.124552	+	0.383332i
$694$	−14.8515	+	10.7903i	−0.563757	+	0.409593i
$695$	−44.2722	−	32.1657i	−1.67934	−	1.22011i
$696$	0.453837	+	1.39677i	0.0172026	+	0.0529443i
$697$	13.7330	+	9.97764i	0.520176	+	0.377930i
$698$	3.72431	+	2.70587i	0.140967	+	0.102419i
$699$	2.86586	+	8.82022i	0.108397	+	0.333611i
$700$	−10.4231	−	7.57283i	−0.393956	−	0.286226i
$701$	−29.9024	+	21.7254i	−1.12940	+	0.820557i	−0.985607	−	0.169051i	$-0.945930\pi$
$701$	−29.9024	+	21.7254i	−1.12940	+	0.820557i	−0.143792	+	0.989608i	$0.545930\pi$
$702$	3.06227	−	9.42469i	0.115578	−	0.355712i
$703$	12.1848	−	8.85278i	0.459559	−	0.333889i
$704$	2.70024	+	8.31049i	0.101769	+	0.313214i
$705$	8.28105	+	25.4865i	0.311882	+	0.959875i
$706$	7.07656	−	21.7794i	0.266330	−	0.819679i
$707$	−12.7241			−0.478540
$708$	−12.0405			−0.452509
$709$	15.1186	−	46.5303i	0.567791	−	1.74748i	−0.0917196	−	0.995785i	$-0.529236\pi$
$709$	15.1186	−	46.5303i	0.567791	−	1.74748i	0.659510	−	0.751695i	$-0.270764\pi$
$710$	−8.44273	−	6.13400i	−0.316850	−	0.230205i
$711$	−7.29360	+	5.29911i	−0.273531	+	0.198732i
$712$	−11.2905			−0.423129
$713$	9.88464	−	30.8038i	0.370183	−	1.15361i
$714$	8.38822			0.313921
$715$	−53.4659	+	38.8452i	−1.99951	+	1.45273i
$716$	−10.6518	−	7.73897i	−0.398076	−	0.289219i
$717$	−1.55583	+	4.78835i	−0.0581035	+	0.178824i
$718$	−1.02271			−0.0381673
$719$	−7.83832			−0.292320			−0.146160	−	0.989261i	$-0.546691\pi$
$719$	−7.83832			−0.292320			−0.146160	+	0.989261i	$0.546691\pi$
$720$	4.46320	−	13.7363i	0.166334	−	0.511922i
$721$	11.0446	+	33.9918i	0.411323	+	1.26592i
$722$	3.51418	+	10.8155i	0.130784	+	0.402513i
$723$	−10.8890	+	7.91134i	−0.404967	+	0.294226i
$724$	−10.7797	+	33.1765i	−0.400625	+	1.23300i
$725$	3.67504	−	2.67008i	0.136488	−	0.0991641i
$726$	−8.85111	−	6.43071i	−0.328496	−	0.238666i
$727$	−7.11161	−	21.8873i	−0.263755	−	0.811755i	−0.991978	−	0.126414i	$-0.959653\pi$
$727$	−7.11161	−	21.8873i	−0.263755	−	0.811755i	0.728223	−	0.685341i	$-0.240347\pi$
$728$	−13.6574	−	9.92270i	−0.506178	−	0.367760i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	1.70479	+	5.24680i	0.0630971	+	0.194193i
$731$	−8.45439	−	6.14247i	−0.312697	−	0.227187i
$732$	−7.93194	+	5.76289i	−0.293173	+	0.213003i
$733$	−9.42416	+	29.0046i	−0.348089	+	1.07131i	0.611820	+	0.790997i	$0.290438\pi$
$733$	−9.42416	+	29.0046i	−0.348089	+	1.07131i	−0.959909	+	0.280312i	$0.909562\pi$
$734$	12.3990	−	9.00842i	0.457656	−	0.332507i
$735$	−0.340596	−	1.04825i	−0.0125631	−	0.0386652i
$736$	−11.6857	−	35.9649i	−0.430741	−	1.32568i
$737$	8.24329	−	25.3703i	0.303646	−	0.934525i
$738$	17.3910			0.640171
$739$	−38.7645			−1.42597			−0.712987	−	0.701177i	$-0.752658\pi$
$739$	−38.7645			−1.42597			−0.712987	+	0.701177i	$0.752658\pi$
$740$	−5.15154	+	15.8548i	−0.189375	+	0.582835i
$741$	−15.6839	−	11.3950i	−0.576161	−	0.418605i
$742$	38.3430	−	27.8578i	1.40761	−	1.02269i
$743$	17.4481			0.640110			0.320055	−	0.947399i	$-0.396299\pi$
$743$	17.4481			0.640110			0.320055	+	0.947399i	$0.396299\pi$
$744$	−5.43162	+	3.97667i	−0.199133	+	0.145792i
$745$	30.9772			1.13492
$746$	−39.3737	+	28.6066i	−1.44157	+	1.04736i
$747$	−5.42248	−	3.93966i	−0.198398	−	0.144145i
$748$	−3.03976	+	9.35542i	−0.111145	+	0.342068i
$749$	−14.1566			−0.517271
$750$	6.80751			0.248575
$751$	−0.0839410	+	0.258344i	−0.00306305	+	0.00942710i	−0.952576	−	0.304300i	$-0.901578\pi$
$751$	−0.0839410	+	0.258344i	−0.00306305	+	0.00942710i	0.949513	+	0.313727i	$0.101578\pi$
$752$	−13.6853	−	42.1190i	−0.499051	−	1.53592i
$753$	−0.680603	−	2.09468i	−0.0248025	−	0.0763344i
$754$	−9.73842	+	7.07538i	−0.354653	+	0.257670i
$755$	−17.9834	+	55.3473i	−0.654484	+	2.01430i
$756$	2.78716	−	2.02499i	0.101368	−	0.0736483i
$757$	28.0683	+	20.3928i	1.02016	+	0.741190i	0.966316	−	0.257360i	$-0.0828525\pi$
$757$	28.0683	+	20.3928i	1.02016	+	0.741190i	0.0538444	+	0.998549i	$0.482853\pi$
$758$	11.5713	+	35.6129i	0.420290	+	1.29352i
$759$	19.3747	+	14.0765i	0.703256	+	0.510945i
$760$	−10.3359	−	7.50944i	−0.374921	−	0.272396i
$761$	12.7028	+	39.0951i	0.460475	+	1.41720i	0.864585	+	0.502487i	$0.167581\pi$
$761$	12.7028	+	39.0951i	0.460475	+	1.41720i	−0.404110	+	0.914711i	$0.632419\pi$
$762$	−2.65106	−	1.92611i	−0.0960377	−	0.0697754i
$763$	40.2248	−	29.2250i	1.45624	−	1.05802i
$764$	−2.93474	+	9.03221i	−0.106175	+	0.326774i
$765$	4.26531	−	3.09893i	0.154213	−	0.112042i
$766$	4.59396	+	14.1388i	0.165987	+	0.510854i
$767$	15.0795	+	46.4098i	0.544488	+	1.67576i
$768$	−6.47244	+	19.9201i	−0.233554	+	0.718805i
$769$	−4.92214			−0.177497			−0.0887484	−	0.996054i	$-0.528287\pi$
$769$	−4.92214			−0.177497			−0.0887484	+	0.996054i	$0.528287\pi$
$770$	−57.3116			−2.06537
$771$	3.76074	−	11.5744i	0.135440	−	0.416841i
$772$	8.47191	+	6.15521i	0.304911	+	0.221531i
$773$	−27.2558	+	19.8025i	−0.980324	+	0.712247i	−0.957781	−	0.287499i	$-0.907176\pi$
$773$	−27.2558	+	19.8025i	−0.980324	+	0.712247i	−0.0225433	+	0.999746i	$0.507176\pi$
$774$	−10.7063			−0.384830
$775$	16.8896	+	12.1771i	0.606693	+	0.437415i
$776$	10.7150			0.384647
$777$	8.77583	−	6.37601i	0.314831	−	0.228738i
$778$	−15.5129	−	11.2708i	−0.556163	−	0.404076i
$779$	10.5133	−	32.3567i	0.376680	−	1.15930i
$780$	21.4580			0.768320
$781$	−7.96321			−0.284946
$782$	5.85051	−	18.0060i	0.209214	−	0.643894i
$783$	0.375364	+	1.15525i	0.0134144	+	0.0412853i
$784$	0.562870	+	1.73234i	0.0201025	+	0.0618692i
$785$	−37.3754	+	27.1548i	−1.33399	+	0.969197i
$786$	−2.06141	+	6.34438i	−0.0735282	+	0.226297i
$787$	23.3523	−	16.9665i	0.832421	−	0.604789i	−0.0878225	−	0.996136i	$-0.527991\pi$
$787$	23.3523	−	16.9665i	0.832421	−	0.604789i	0.920243	+	0.391347i	$0.127991\pi$
$788$	−21.4840	−	15.6091i	−0.765337	−	0.556050i
$789$	−0.556153	−	1.71166i	−0.0197996	−	0.0609368i
$790$	−39.3958	−	28.6227i	−1.40164	−	1.01835i
$791$	−23.7448	−	17.2516i	−0.844267	−	0.613396i
$792$	−1.53993	−	4.73941i	−0.0547189	−	0.168407i
$793$	32.1469	+	23.3561i	1.14157	+	0.829399i
$794$	44.2527	−	32.1515i	1.57047	−	1.14101i
$795$	9.20522	−	28.3307i	0.326475	−	1.00479i
$796$	−18.9034	+	13.7341i	−0.670014	+	0.486794i
$797$	6.94874	+	21.3860i	0.246137	+	0.757532i	0.995447	+	0.0953127i	$0.0303851\pi$
$797$	6.94874	+	21.3860i	0.246137	+	0.757532i	−0.749310	+	0.662219i	$0.769615\pi$
$798$	−5.19519	−	15.9891i	−0.183908	−	0.566009i
$799$	4.99555	−	15.3747i	0.176730	−	0.543918i
$800$	24.3389			0.860510
$801$	−9.33826			−0.329951
$802$	14.2519	−	43.8627i	0.503251	−	1.54885i
$803$	3.40572	+	2.47440i	0.120185	+	0.0873197i
$804$	−7.00723	+	5.09105i	−0.247126	+	0.179547i
$805$	44.2199			1.55855
$806$	−44.7555	−	32.2679i	−1.57644	−	1.13659i
$807$	−14.0568			−0.494822
$808$	4.83468	−	3.51260i	0.170084	−	0.123573i
$809$	−8.04430	−	5.84452i	−0.282822	−	0.205482i	0.437325	−	0.899303i	$-0.355926\pi$
$809$	−8.04430	−	5.84452i	−0.282822	−	0.205482i	−0.720148	+	0.693821i	$0.755926\pi$
$810$	1.66913	−	5.13706i	0.0586473	−	0.180498i
$811$	25.4951			0.895255			0.447627	−	0.894220i	$-0.352269\pi$
$811$	25.4951			0.895255			0.447627	+	0.894220i	$0.352269\pi$
$812$	−4.18481			−0.146858
$813$	−1.98030	+	6.09473i	−0.0694520	+	0.213751i
$814$	9.80573	+	30.1789i	0.343691	+	1.05777i
$815$	18.0319	+	55.4965i	0.631630	+	1.94396i
$816$	−7.04886	+	5.12130i	−0.246760	+	0.179281i
$817$	−6.47226	+	19.9196i	−0.226436	+	0.696897i
$818$	−27.4057	+	19.9114i	−0.958218	+	0.696186i
$819$	−11.2959	−	8.20698i	−0.394712	−	0.286775i
$820$	11.6368	+	35.8145i	0.406376	+	1.25070i
$821$	−14.0001	−	10.1717i	−0.488608	−	0.354995i	0.316041	−	0.948746i	$-0.397646\pi$
$821$	−14.0001	−	10.1717i	−0.488608	−	0.354995i	−0.804649	+	0.593751i	$0.797646\pi$
$822$	−0.0557671	−	0.0405172i	−0.00194510	−	0.00141320i
$823$	15.2269	+	46.8637i	0.530778	+	1.63357i	0.752599	+	0.658479i	$0.228800\pi$
$823$	15.2269	+	46.8637i	0.530778	+	1.63357i	−0.221821	+	0.975087i	$0.571200\pi$
$824$	−13.5803	−	9.86665i	−0.473091	−	0.343721i
$825$	−12.4699	+	9.05991i	−0.434146	+	0.315426i
$826$	−13.0771	+	40.2470i	−0.455009	+	1.40037i
$827$	9.14735	−	6.64594i	0.318084	−	0.231102i	−0.417273	−	0.908781i	$-0.637014\pi$
$827$	9.14735	−	6.64594i	0.318084	−	0.231102i	0.735358	+	0.677679i	$0.237014\pi$
$828$	−2.40286	−	7.39525i	−0.0835053	−	0.257003i
$829$	−7.98304	−	24.5693i	−0.277262	−	0.853326i	−0.988612	−	0.150487i	$-0.951916\pi$
$829$	−7.98304	−	24.5693i	−0.277262	−	0.853326i	0.711350	−	0.702838i	$-0.248084\pi$
$830$	11.1874	−	34.4314i	0.388322	−	1.19513i
$831$	−0.348579			−0.0120921
$832$	−11.4987			−0.398647
$833$	−0.205465	+	0.632356i	−0.00711894	+	0.0219098i
$834$	27.3618	+	19.8795i	0.947460	+	0.688370i
$835$	−12.2901	+	8.92930i	−0.425317	+	0.309011i
$836$	19.7154			0.681872
$837$	−4.49244	+	3.28907i	−0.155282	+	0.113687i
$838$	37.0234			1.27895
$839$	−15.2688	+	11.0934i	−0.527138	+	0.382988i	−0.819286	−	0.573385i	$-0.805630\pi$
$839$	−15.2688	+	11.0934i	−0.527138	+	0.382988i	0.292148	+	0.956373i	$0.405630\pi$
$840$	−7.44417	−	5.40851i	−0.256848	−	0.186611i
$841$	−8.50554	+	26.1774i	−0.293294	+	0.902667i
$842$	−7.92579			−0.273141
$843$	24.0364			0.827858
$844$	−0.652739	+	2.00892i	−0.0224682	+	0.0691500i
$845$	−14.9978	−	46.1586i	−0.515941	−	1.58790i
$846$	−5.11797	−	15.7515i	−0.175959	−	0.541548i
$847$	−12.4710	+	9.06072i	−0.428509	+	0.311330i
$848$	−15.2126	+	46.8194i	−0.522401	+	1.60779i
$849$	−4.89685	+	3.55777i	−0.168060	+	0.122102i
$850$	9.85820	+	7.16240i	0.338134	+	0.245668i
$851$	−7.56580	−	23.2851i	−0.259352	−	0.798204i
$852$	2.09178	+	1.51977i	0.0716631	+	0.0520663i
$853$	30.1998	+	21.9415i	1.03402	+	0.751261i	0.969110	−	0.246630i	$-0.0793231\pi$
$853$	30.1998	+	21.9415i	1.03402	+	0.751261i	0.0649126	+	0.997891i	$0.479323\pi$
$854$	10.6485	+	32.7727i	0.364383	+	1.12146i
$855$	−8.54870	−	6.21099i	−0.292359	−	0.212411i
$856$	5.37898	−	3.90806i	0.183850	−	0.133575i
$857$	6.42041	−	19.7600i	0.219317	−	0.674988i	−0.779502	−	0.626400i	$-0.784528\pi$
$857$	6.42041	−	19.7600i	0.219317	−	0.674988i	0.998819	−	0.0485885i	$-0.0154723\pi$
$858$	33.0437	−	24.0077i	1.12809	−	0.819609i
$859$	−8.62748	−	26.5527i	−0.294366	−	0.905965i	−0.983434	−	0.181268i	$-0.941980\pi$
$859$	−8.62748	−	26.5527i	−0.294366	−	0.905965i	0.689068	−	0.724697i	$-0.258020\pi$
$860$	−7.16391	−	22.0482i	−0.244287	−	0.751839i
$861$	7.57199	−	23.3042i	0.258053	−	0.794205i
$862$	−38.1897			−1.30075
$863$	0.931042			0.0316930			0.0158465	−	0.999874i	$-0.494956\pi$
$863$	0.931042			0.0316930			0.0158465	+	0.999874i	$0.494956\pi$
$864$	−2.01117	+	6.18975i	−0.0684214	+	0.210579i
$865$	−34.7250	−	25.2292i	−1.18069	−	0.857818i
$866$	7.12662	−	5.17779i	0.242172	−	0.175949i
$867$	13.8195			0.469336
$868$	−5.99399	−	18.2211i	−0.203449	−	0.618464i
$869$	−37.1582			−1.26051
$870$	−5.30806	+	3.85653i	−0.179960	+	0.130749i
$871$	28.3992	+	20.6332i	0.962269	+	0.699130i
$872$	−7.21608	+	22.2088i	−0.244367	+	0.752086i
$873$	8.86231			0.299944
$874$	−37.9455			−1.28353
$875$	2.96398	−	9.12218i	0.100201	−	0.308386i
$876$	−0.422381	−	1.29995i	−0.0142709	−	0.0439214i
$877$	3.30968	+	10.1862i	0.111760	+	0.343962i	0.991258	−	0.131941i	$-0.0421211\pi$
$877$	3.30968	+	10.1862i	0.111760	+	0.343962i	−0.879497	+	0.475904i	$0.842121\pi$
$878$	−11.2899	+	8.20261i	−0.381017	+	0.276825i
$879$	−2.93625	+	9.03685i	−0.0990373	+	0.304805i
$880$	48.1607	−	34.9908i	1.62350	−	1.17954i
$881$	−9.17238	−	6.66412i	−0.309025	−	0.224520i	0.422453	−	0.906385i	$-0.361169\pi$
$881$	−9.17238	−	6.66412i	−0.309025	−	0.224520i	−0.731478	+	0.681865i	$0.761169\pi$
$882$	0.210500	+	0.647853i	0.00708791	+	0.0218143i
$883$	−15.8283	−	11.4999i	−0.532664	−	0.387003i	0.288689	−	0.957423i	$-0.406780\pi$
$883$	−15.8283	−	11.4999i	−0.532664	−	0.387003i	−0.821353	+	0.570420i	$0.806780\pi$
$884$	−10.4724	−	7.60861i	−0.352223	−	0.255905i
$885$	8.21927	+	25.2963i	0.276288	+	0.850326i
$886$	−2.15796	−	1.56785i	−0.0724981	−	0.0526729i
$887$	−39.2366	+	28.5071i	−1.31744	+	0.957174i	−0.317477	+	0.948266i	$0.602835\pi$
$887$	−39.2366	+	28.5071i	−1.31744	+	0.957174i	−0.999960	+	0.00890776i	$0.997165\pi$
$888$	−1.57433	+	4.84529i	−0.0528310	+	0.162597i
$889$	−3.73528	+	2.71384i	−0.125277	+	0.0910192i
$890$	−15.5868	−	47.9712i	−0.522470	−	1.60800i
$891$	−1.27366	−	3.91992i	−0.0426692	−	0.131322i
$892$	4.87649	−	15.0083i	0.163277	−	0.502515i
$893$	−32.4004			−1.08424
$894$	−19.1450			−0.640303
$895$	−8.98781	+	27.6616i	−0.300429	+	0.924627i
$896$	19.0419	+	13.8348i	0.636146	+	0.462187i
$897$	−25.4955	+	18.5236i	−0.851271	+	0.618484i
$898$	39.0718			1.30384
$899$	6.76314	−	0.0246810i	0.225563	−	0.000823159i
$900$	5.00467			0.166822
$901$	−14.5381	+	10.5625i	−0.484333	+	0.351889i
$902$	57.9899	+	42.1321i	1.93085	+	1.40285i
$903$	−4.66150	+	14.3466i	−0.155125	+	0.477425i
$904$	13.7846			0.458468
$905$	77.0605			2.56158
$906$	11.1144	−	34.2065i	0.369251	−	1.13644i
$907$	7.95553	+	24.4846i	0.264159	+	0.812998i	0.991886	+	0.127131i	$0.0405768\pi$
$907$	7.95553	+	24.4846i	0.264159	+	0.812998i	−0.727727	+	0.685867i	$0.759423\pi$
$908$	−3.87411	−	11.9233i	−0.128567	−	0.395688i
$909$	3.99872	−	2.90524i	0.132629	−	0.0963608i
$910$	23.3053	−	71.7264i	0.772564	−	2.37771i
$911$	15.6954	−	11.4034i	0.520013	−	0.377811i	−0.296596	−	0.955003i	$-0.595851\pi$
$911$	15.6954	−	11.4034i	0.520013	−	0.377811i	0.816609	+	0.577192i	$0.195851\pi$
$912$	14.1276	+	10.2643i	0.467811	+	0.339885i
$913$	−8.53677	−	26.2735i	−0.282526	−	0.869525i
$914$	−2.06743	−	1.50207i	−0.0683844	−	0.0496841i
$915$	17.5221	+	12.7306i	0.579263	+	0.420859i
$916$	3.13779	+	9.65712i	0.103675	+	0.319080i
$917$	7.60404	+	5.52466i	0.251108	+	0.182440i
$918$	−2.63611	+	1.91524i	−0.0870045	+	0.0632125i
$919$	−6.44659	+	19.8406i	−0.212653	+	0.654480i	0.786659	+	0.617388i	$0.211809\pi$
$919$	−6.44659	+	19.8406i	−0.212653	+	0.654480i	−0.999312	+	0.0370914i	$0.988191\pi$
$920$	−16.8019	+	12.2073i	−0.553942	+	0.402462i
$921$	5.48140	+	16.8700i	0.180618	+	0.555885i
$922$	−0.0671238	−	0.206586i	−0.00221061	−	0.00680355i
$923$	3.23817	−	9.96607i	0.106586	−	0.328037i
$924$	14.1996			0.467132
$925$	15.7580			0.518120
$926$	−17.3308	+	53.3388i	−0.569526	+	1.75282i
$927$	−11.2321	−	8.16062i	−0.368911	−	0.268030i
$928$	6.39579	−	4.64682i	0.209952	−	0.152539i
$929$	−16.5828			−0.544063			−0.272032	−	0.962288i	$-0.587696\pi$
$929$	−16.5828			−0.544063			−0.272032	+	0.962288i	$0.587696\pi$
$930$	−24.3946	−	17.5880i	−0.799930	−	0.576735i
$931$	1.33261			0.0436747
$932$	10.0409	−	7.29512i	0.328900	−	0.238960i
$933$	−16.8820	−	12.2655i	−0.552691	−	0.401553i
$934$	−11.5043	+	35.4067i	−0.376433	+	1.15854i
$935$	21.7302			0.710654
$936$	6.55764			0.214343
$937$	−7.24830	+	22.3080i	−0.236792	+	0.728770i	0.760087	+	0.649821i	$0.225156\pi$
$937$	−7.24830	+	22.3080i	−0.236792	+	0.728770i	−0.996879	+	0.0789487i	$0.974844\pi$
$938$	9.40707	+	28.9520i	0.307152	+	0.945315i
$939$	−1.05721	−	3.25376i	−0.0345008	−	0.106182i
$940$	29.0136	−	21.0796i	0.946319	−	0.687541i
$941$	−7.91434	+	24.3578i	−0.258000	+	0.794042i	0.735224	+	0.677824i	$0.237077\pi$
$941$	−7.91434	+	24.3578i	−0.258000	+	0.794042i	−0.993224	+	0.116218i	$0.962923\pi$
$942$	23.0993	−	16.7826i	0.752615	−	0.546807i
$943$	−44.7432	−	32.5079i	−1.45704	−	1.05860i
$944$	−13.5832	−	41.8047i	−0.442095	−	1.36063i
$945$	−6.15701	−	4.47333i	−0.200287	−	0.145517i
$946$	−35.7000	−	25.9375i	−1.16071	−	0.843302i
$947$	−14.5924	−	44.9106i	−0.474188	−	1.45940i	−0.847050	−	0.531513i	$-0.821624\pi$
$947$	−14.5924	−	44.9106i	−0.474188	−	1.45940i	0.372862	−	0.927887i	$-0.378376\pi$
$948$	9.76074	+	7.09160i	0.317014	+	0.230324i
$949$	−4.48166	+	3.25612i	−0.145481	+	0.105698i
$950$	7.54695	−	23.2271i	0.244855	−	0.753588i
$951$	−1.70272	+	1.23710i	−0.0552146	+	0.0401157i
$952$	1.71529	+	5.27913i	0.0555930	+	0.171098i
$953$	−8.36169	−	25.7346i	−0.270862	−	0.833627i	−0.990285	−	0.139055i	$-0.955594\pi$
$953$	−8.36169	−	25.7346i	−0.270862	−	0.833627i	0.719423	−	0.694572i	$-0.244406\pi$
$954$	−5.68914	+	17.5094i	−0.184193	+	0.566886i
$955$	20.9795			0.678880
$956$	6.73784			0.217917
$957$	−1.54712	+	4.76154i	−0.0500112	+	0.153919i
$958$	−24.8509	−	18.0552i	−0.802896	−	0.583338i
$959$	−0.0785745	+	0.0570877i	−0.00253730	+	0.00184346i
$960$	−6.26755			−0.202284
$961$	9.79445	+	29.4120i	0.315950	+	0.948776i
$962$	−41.7568			−1.34629
$963$	4.44890	−	3.23232i	0.143364	−	0.104160i
$964$	14.5724	+	10.5874i	0.469344	+	0.340999i
$965$	7.14847	−	22.0007i	0.230117	−	0.708229i
$966$	−27.3294			−0.879309
$967$	−46.3235			−1.48966			−0.744832	−	0.667252i	$-0.767471\pi$
$967$	−46.3235			−1.48966			−0.744832	+	0.667252i	$0.767471\pi$
$968$	2.23722	−	6.88546i	0.0719071	−	0.221307i
$969$	1.96980	+	6.06242i	0.0632791	+	0.194753i
$970$	14.7923	+	45.5262i	0.474954	+	1.46176i
$971$	28.7151	−	20.8628i	0.921513	−	0.669518i	−0.0223875	−	0.999749i	$-0.507127\pi$
$971$	28.7151	−	20.8628i	0.921513	−	0.669518i	0.943900	+	0.330231i	$0.107127\pi$
$972$	−0.413545	+	1.27276i	−0.0132645	+	0.0408239i
$973$	38.5521	−	28.0097i	1.23592	−	0.897951i
$974$	−19.0109	−	13.8123i	−0.609150	−	0.442573i
$975$	−6.26783	−	19.2904i	−0.200731	−	0.617788i
$976$	−28.9571	−	21.0385i	−0.926893	−	0.673428i
$977$	−15.2415	−	11.0736i	−0.487618	−	0.354275i	0.316649	−	0.948543i	$-0.397442\pi$
$977$	−15.2415	−	11.0736i	−0.487618	−	0.354275i	−0.804268	+	0.594267i	$0.797442\pi$
$978$	−11.1443	−	34.2987i	−0.356356	−	1.09675i
$979$	−31.1383	−	22.6233i	−0.995183	−	0.723043i
$980$	−1.19332	+	0.866996i	−0.0381192	+	0.0276952i
$981$	−5.96836	+	18.3687i	−0.190555	+	0.586468i
$982$	−7.84476	+	5.69955i	−0.250336	+	0.181880i
$983$	0.752638	+	2.31638i	0.0240054	+	0.0738811i	0.962342	−	0.271843i	$-0.0876332\pi$
$983$	0.752638	+	2.31638i	0.0240054	+	0.0738811i	−0.938336	+	0.345724i	$0.887633\pi$
$984$	3.55626	+	10.9450i	0.113369	+	0.348915i
$985$	−18.1279	+	55.7919i	−0.577603	+	1.77768i
$986$	3.95800			0.126048
$987$	−23.3356			−0.742781
$988$	−8.01712	+	24.6742i	−0.255059	+	0.784989i
$989$	27.5450	+	20.0126i	0.875879	+	0.636364i
$990$	18.0109	−	13.0857i	0.572425	−	0.415891i
$991$	−47.9488			−1.52315			−0.761573	−	0.648079i	$-0.775572\pi$
$991$	−47.9488			−1.52315			−0.761573	+	0.648079i	$0.775572\pi$
$992$	29.3936	+	21.1922i	0.933246	+	0.672853i
$993$	13.0690			0.414732
$994$	7.35189	−	5.34146i	0.233188	−	0.169421i
$995$	41.7587	+	30.3395i	1.32384	+	0.961827i
$996$	−2.77181	+	8.53076i	−0.0878282	+	0.270307i
$997$	55.7421			1.76537			0.882684	−	0.469966i	$-0.155734\pi$
$997$	55.7421			1.76537			0.882684	+	0.469966i	$0.155734\pi$
$998$	2.31532			0.0732901
$999$	−1.30211	+	4.00749i	−0.0411970	+	0.126791i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.2.f.a.16.2	✓	8
3.2	odd	2		279.2.i.b.109.1		8
31.2	even	5	inner	93.2.f.a.64.2	yes	8
31.8	even	5		2883.2.a.k.1.1		4
31.23	odd	10		2883.2.a.l.1.1		4
93.2	odd	10		279.2.i.b.64.1		8
93.8	odd	10		8649.2.a.w.1.4		4
93.23	even	10		8649.2.a.x.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.f.a.16.2	✓	8	1.1	even	1	trivial
93.2.f.a.64.2	yes	8	31.2	even	5	inner
279.2.i.b.64.1		8	93.2	odd	10
279.2.i.b.109.1		8	3.2	odd	2
2883.2.a.k.1.1		4	31.8	even	5
2883.2.a.l.1.1		4	31.23	odd	10
8649.2.a.w.1.4		4	93.8	odd	10
8649.2.a.x.1.4		4	93.23	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	93.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.47815 - 1.07394i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.413545 - 1.27276i) q^{4} -2.95630 q^{5} +1.82709 q^{6} +(0.795511 - 2.44833i) q^{7} +(0.373619 + 1.14988i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(1.47815 - 1.07394i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.413545 - 1.27276i) q^{4} -2.95630 q^{5} +1.82709 q^{6} +(0.795511 - 2.44833i) q^{7} +(0.373619 + 1.14988i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-4.36984 + 3.17488i) q^{10} +(-1.27366 + 3.91992i) q^{11} +(1.08268 - 0.786610i) q^{12} +(-4.38791 - 3.18801i) q^{13} +(-1.45347 - 4.47333i) q^{14} +(-2.39169 - 1.73767i) q^{15} +(3.95252 + 2.87167i) q^{16} +(0.551097 + 1.69610i) q^{17} +(1.47815 + 1.07394i) q^{18} +(2.89169 - 2.10094i) q^{19} +(-1.22256 + 3.76266i) q^{20} +(2.08268 - 1.51315i) q^{21} +(2.32709 + 7.16205i) q^{22} +(-1.79551 - 5.52602i) q^{23} +(-0.373619 + 1.14988i) q^{24} +3.73968 q^{25} -9.90970 q^{26} +(-0.309017 + 0.951057i) q^{27} +(-2.78716 - 2.02499i) q^{28} +(0.982716 - 0.713985i) q^{29} -5.40142 q^{30} +(4.51633 + 3.25619i) q^{31} +6.50828 q^{32} +(-3.33448 + 2.42264i) q^{33} +(2.63611 + 1.91524i) q^{34} +(-2.35177 + 7.23799i) q^{35} +1.33826 q^{36} +4.21373 q^{37} +(2.01807 - 6.21099i) q^{38} +(-1.67603 - 5.15830i) q^{39} +(-1.10453 - 3.39939i) q^{40} +(7.70054 - 5.59477i) q^{41} +(1.45347 - 4.47333i) q^{42} +(-4.74064 + 3.44427i) q^{43} +(4.46241 + 3.24213i) q^{44} +(-0.913545 - 2.81160i) q^{45} +(-8.58862 - 6.24000i) q^{46} +(-7.33353 - 5.32812i) q^{47} +(1.50973 + 4.64646i) q^{48} +(0.301625 + 0.219144i) q^{49} +(5.52780 - 4.01618i) q^{50} +(-0.551097 + 1.69610i) q^{51} +(-5.87218 + 4.26639i) q^{52} +(3.11377 + 9.58319i) q^{53} +(0.564602 + 1.73767i) q^{54} +(3.76531 - 11.5884i) q^{55} +3.11251 q^{56} +3.57433 q^{57} +(0.685824 - 2.11075i) q^{58} +(-7.27882 - 5.28837i) q^{59} +(-3.20071 + 2.32545i) q^{60} -7.32624 q^{61} +(10.1727 - 0.0371239i) q^{62} +2.57433 q^{63} +(1.71517 - 1.24614i) q^{64} +(12.9720 + 9.42469i) q^{65} +(-2.32709 + 7.16205i) q^{66} -6.47214 q^{67} +2.38664 q^{68} +(1.79551 - 5.52602i) q^{69} +(4.29689 + 13.2245i) q^{70} +(0.597035 + 1.83748i) q^{71} +(-0.978148 + 0.710666i) q^{72} +(0.315619 - 0.971375i) q^{73} +(6.22851 - 4.52528i) q^{74} +(3.02547 + 2.19813i) q^{75} +(-1.47815 - 4.54927i) q^{76} +(8.58406 + 6.23668i) q^{77} +(-8.01712 - 5.82478i) q^{78} +(2.78591 + 8.57414i) q^{79} +(-11.6848 - 8.48951i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(5.37411 - 16.5398i) q^{82} +(-5.42248 + 3.93966i) q^{83} +(-1.06460 - 3.27651i) q^{84} +(-1.62920 - 5.01418i) q^{85} +(-3.30843 + 10.1823i) q^{86} +1.21470 q^{87} -4.98331 q^{88} +(-2.88568 + 8.88121i) q^{89} +(-4.36984 - 3.17488i) q^{90} +(-11.2959 + 8.20698i) q^{91} -7.77583 q^{92} +(1.73985 + 5.28894i) q^{93} -16.5621 q^{94} +(-8.54870 + 6.21099i) q^{95} +(5.26531 + 3.82547i) q^{96} +(2.73860 - 8.42855i) q^{97} +0.681193 q^{98} -4.12165 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} + 2 q^{3} - 3 q^{4} - 6 q^{5} + 2 q^{6} + 9 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 + 2 * q^3 - 3 * q^4 - 6 * q^5 + 2 * q^6 + 9 * q^7 - 4 * q^8 - 2 * q^9	\( 8 q + 3 q^{2} + 2 q^{3} - 3 q^{4} - 6 q^{5} + 2 q^{6} + 9 q^{7} - 4 q^{8} - 2 q^{9} - 11 q^{10} - 4 q^{11} - 2 q^{12} - 3 q^{13} - 6 q^{14} - 4 q^{15} - 3 q^{16} + 9 q^{17} + 3 q^{18} + 8 q^{19} + q^{20} + 6 q^{21} + 6 q^{22} - 17 q^{23} + 4 q^{24} - 18 q^{25} + 12 q^{26} + 2 q^{27} - 9 q^{28} - 2 q^{29} - 4 q^{30} + 17 q^{31} - q^{33} + 4 q^{34} - 3 q^{35} + 2 q^{36} + 8 q^{37} + 8 q^{38} + 3 q^{39} - 7 q^{40} - 5 q^{41} + 6 q^{42} - 19 q^{43} + 24 q^{44} - q^{45} - 17 q^{46} - 4 q^{47} - 12 q^{48} + 11 q^{49} + 12 q^{50} - 9 q^{51} - 12 q^{52} + 2 q^{54} + 8 q^{55} - 12 q^{56} + 2 q^{57} + 33 q^{58} - 29 q^{59} - 6 q^{60} + 4 q^{61} + 47 q^{62} - 6 q^{63} + 16 q^{64} + 21 q^{65} - 6 q^{66} - 16 q^{67} + 6 q^{68} + 17 q^{69} - 3 q^{70} + 37 q^{71} + q^{72} + 3 q^{73} - 2 q^{74} + 3 q^{75} - 3 q^{76} + 18 q^{77} - 27 q^{78} - 3 q^{79} - 24 q^{80} - 2 q^{81} + 35 q^{82} - 31 q^{83} - 6 q^{84} - 8 q^{85} - 44 q^{86} - 18 q^{87} - 8 q^{88} + 19 q^{89} - 11 q^{90} - 24 q^{91} + 2 q^{92} + 13 q^{93} - 94 q^{94} - 16 q^{95} + 20 q^{96} - 3 q^{97} - 34 q^{98} + 6 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 + 2 * q^3 - 3 * q^4 - 6 * q^5 + 2 * q^6 + 9 * q^7 - 4 * q^8 - 2 * q^9 - 11 * q^10 - 4 * q^11 - 2 * q^12 - 3 * q^13 - 6 * q^14 - 4 * q^15 - 3 * q^16 + 9 * q^17 + 3 * q^18 + 8 * q^19 + q^20 + 6 * q^21 + 6 * q^22 - 17 * q^23 + 4 * q^24 - 18 * q^25 + 12 * q^26 + 2 * q^27 - 9 * q^28 - 2 * q^29 - 4 * q^30 + 17 * q^31 - q^33 + 4 * q^34 - 3 * q^35 + 2 * q^36 + 8 * q^37 + 8 * q^38 + 3 * q^39 - 7 * q^40 - 5 * q^41 + 6 * q^42 - 19 * q^43 + 24 * q^44 - q^45 - 17 * q^46 - 4 * q^47 - 12 * q^48 + 11 * q^49 + 12 * q^50 - 9 * q^51 - 12 * q^52 + 2 * q^54 + 8 * q^55 - 12 * q^56 + 2 * q^57 + 33 * q^58 - 29 * q^59 - 6 * q^60 + 4 * q^61 + 47 * q^62 - 6 * q^63 + 16 * q^64 + 21 * q^65 - 6 * q^66 - 16 * q^67 + 6 * q^68 + 17 * q^69 - 3 * q^70 + 37 * q^71 + q^72 + 3 * q^73 - 2 * q^74 + 3 * q^75 - 3 * q^76 + 18 * q^77 - 27 * q^78 - 3 * q^79 - 24 * q^80 - 2 * q^81 + 35 * q^82 - 31 * q^83 - 6 * q^84 - 8 * q^85 - 44 * q^86 - 18 * q^87 - 8 * q^88 + 19 * q^89 - 11 * q^90 - 24 * q^91 + 2 * q^92 + 13 * q^93 - 94 * q^94 - 16 * q^95 + 20 * q^96 - 3 * q^97 - 34 * q^98 + 6 * q^99

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