LMFDB - Embedded newform 117.2.e.b.79.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,2,Mod(40,117)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("117.40"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.487558322307.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 13x^{8} + 43x^{6} + 48x^{4} + 21x^{2} + 3 $ x^10 + 13x^8 + 43x^6 + 48x^4 + 21x^2 + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.858204i$ of defining polynomial
Character	$\chi$	$=$	117.79
Dual form			117.2.e.b.40.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39763 + 2.42077i) q^{2} +(0.413993 - 1.68185i) q^{3} +(-2.90675 - 5.03463i) q^{4} +(-0.413993 - 0.717057i) q^{5} +(3.49275 + 3.35278i) q^{6} +(1.24323 - 2.15333i) q^{7} +10.6597 q^{8} +(-2.65722 - 1.39255i) q^{9} +2.31444 q^{10} +(0.459729 - 0.796275i) q^{11} +(-9.67085 + 2.80440i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(3.47514 + 6.01912i) q^{14} +(-1.37737 + 0.399416i) q^{15} +(-9.08484 + 15.7354i) q^{16} -1.53740 q^{17} +(7.08484 - 4.48625i) q^{18} +3.40028 q^{19} +(-2.40675 + 4.16860i) q^{20} +(-3.10689 - 2.98238i) q^{21} +(1.28506 + 2.22580i) q^{22} +(-0.490886 - 0.850239i) q^{23} +(4.41304 - 17.9280i) q^{24} +(2.15722 - 3.73641i) q^{25} +2.79526 q^{26} +(-3.44212 + 3.89253i) q^{27} -14.4550 q^{28} +(0.595121 - 1.03078i) q^{29} +(0.958162 - 3.89253i) q^{30} +(3.12690 + 5.41594i) q^{31} +(-14.7348 - 25.5214i) q^{32} +(-1.14889 - 1.10285i) q^{33} +(2.14872 - 3.72170i) q^{34} -2.05875 q^{35} +(0.712903 + 17.4259i) q^{36} +1.83048 q^{37} +(-4.75234 + 8.23129i) q^{38} +(-1.66352 + 0.482395i) q^{39} +(-4.41304 - 7.64362i) q^{40} +(2.86647 + 4.96488i) q^{41} +(11.5619 - 3.35278i) q^{42} +(-0.792611 + 1.37284i) q^{43} -5.34527 q^{44} +(0.101535 + 2.48188i) q^{45} +2.74431 q^{46} +(-2.68754 + 4.65496i) q^{47} +(22.7035 + 21.7937i) q^{48} +(0.408777 + 0.708023i) q^{49} +(6.02999 + 10.4443i) q^{50} +(-0.636475 + 2.58568i) q^{51} +(-2.90675 + 5.03463i) q^{52} -5.82609 q^{53} +(-4.61210 - 13.7729i) q^{54} -0.761299 q^{55} +(13.2524 - 22.9539i) q^{56} +(1.40769 - 5.71876i) q^{57} +(1.66352 + 2.88130i) q^{58} +(0.477338 + 0.826774i) q^{59} +(6.01458 + 5.77355i) q^{60} +(4.44763 - 7.70353i) q^{61} -17.4810 q^{62} +(-6.30214 + 3.99062i) q^{63} +46.0360 q^{64} +(-0.413993 + 0.717057i) q^{65} +(4.27546 - 1.23982i) q^{66} +(6.56302 + 11.3675i) q^{67} +(4.46884 + 7.74026i) q^{68} +(-1.63320 + 0.473602i) q^{69} +(2.87737 - 4.98375i) q^{70} +5.27858 q^{71} +(-28.3252 - 14.8441i) q^{72} -10.0187 q^{73} +(-2.55834 + 4.43117i) q^{74} +(-5.39100 - 5.17496i) q^{75} +(-9.88375 - 17.1192i) q^{76} +(-1.14310 - 1.97990i) q^{77} +(1.15722 - 4.70120i) q^{78} +(-5.06272 + 8.76888i) q^{79} +15.0443 q^{80} +(5.12163 + 7.40060i) q^{81} -16.0251 q^{82} +(1.16257 - 2.01363i) q^{83} +(-5.98426 + 24.3110i) q^{84} +(0.636475 + 1.10241i) q^{85} +(-2.21555 - 3.83745i) q^{86} +(-1.48724 - 1.42764i) q^{87} +(4.90058 - 8.48805i) q^{88} +12.5811 q^{89} +(-6.14997 - 3.22296i) q^{90} -2.48645 q^{91} +(-2.85376 + 4.94286i) q^{92} +(10.4033 - 3.01680i) q^{93} +(-7.51238 - 13.0118i) q^{94} +(-1.40769 - 2.43820i) q^{95} +(-49.0233 + 14.2160i) q^{96} +(3.94212 - 6.82795i) q^{97} -2.28528 q^{98} +(-2.33045 + 1.47568i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} + q^{3} - 4 q^{4} - q^{5} + 13 q^{6} + 2 q^{7} + 24 q^{8} - 13 q^{9} - 4 q^{10} - 11 q^{11} - 19 q^{12} - 5 q^{13} + 5 q^{14} - 10 q^{15} - 10 q^{16} + 14 q^{17} - 10 q^{18} + 6 q^{19}+ \cdots + 17 q^{99}+O(q^{100}) $ 10 * q - 2 * q^2 + q^3 - 4 * q^4 - q^5 + 13 * q^6 + 2 * q^7 + 24 * q^8 - 13 * q^9 - 4 * q^10 - 11 * q^11 - 19 * q^12 - 5 * q^13 + 5 * q^14 - 10 * q^15 - 10 * q^16 + 14 * q^17 - 10 * q^18 + 6 * q^19 + q^20 + 8 * q^21 + 7 * q^22 - 18 * q^23 + 18 * q^24 + 8 * q^25 + 4 * q^26 - 11 * q^27 - 38 * q^28 - 4 * q^29 + 5 * q^30 + 16 * q^31 - 31 * q^32 + 19 * q^33 - 13 * q^34 + 22 * q^35 - 5 * q^36 + 10 * q^37 - 24 * q^38 - 2 * q^39 - 18 * q^40 - 12 * q^41 + 59 * q^42 + 2 * q^44 - 14 * q^45 + 12 * q^46 - 15 * q^47 + 29 * q^48 - 3 * q^49 + 5 * q^50 - 7 * q^51 - 4 * q^52 - 6 * q^53 - 11 * q^54 - 34 * q^55 + 24 * q^56 + 12 * q^57 + 2 * q^58 - 3 * q^59 + 19 * q^60 + q^61 - 8 * q^62 - 14 * q^63 + 124 * q^64 - q^65 - 11 * q^66 + 4 * q^67 + 16 * q^68 + 25 * q^70 + 30 * q^71 - 66 * q^72 - 10 * q^73 - 11 * q^74 + 14 * q^75 - 9 * q^76 - q^77 - 2 * q^78 - 13 * q^79 + 64 * q^80 - 25 * q^81 - 42 * q^82 - 26 * q^83 - 17 * q^84 + 7 * q^85 + 6 * q^86 - 13 * q^87 - 3 * q^88 + 58 * q^89 - 26 * q^90 - 4 * q^91 + 6 * q^92 + 58 * q^93 - 12 * q^94 - 12 * q^95 - 67 * q^96 + 16 * q^97 - 78 * q^98 + 17 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.39763	+	2.42077i	−0.988274	+	1.71174i	−0.361905	+	0.932215i	$0.617874\pi$
$2$	−1.39763	+	2.42077i	−0.988274	+	1.71174i	−0.626369	+	0.779527i	$0.715460\pi$
$3$	0.413993	−	1.68185i	0.239019	−	0.971015i
$3$	0.413993	−	1.68185i	0.239019	−	0.971015i
$4$	−2.90675	−	5.03463i	−1.45337	−	2.51732i
$5$	−0.413993	−	0.717057i	−0.185143	−	0.320678i	0.758481	−	0.651695i	$-0.225942\pi$
$5$	−0.413993	−	0.717057i	−0.185143	−	0.320678i	−0.943625	+	0.331017i	$0.892608\pi$
$6$	3.49275	+	3.35278i	1.42591	+	1.36877i
$7$	1.24323	−	2.15333i	0.469895	−	0.813883i	−0.529512	−	0.848302i	$-0.677625\pi$
$7$	1.24323	−	2.15333i	0.469895	−	0.813883i	0.999407	+	0.0344198i	$0.0109583\pi$
$8$	10.6597			3.76877
$9$	−2.65722	−	1.39255i	−0.885740	−	0.464182i
$10$	2.31444			0.731890
$11$	0.459729	−	0.796275i	0.138614	−	0.240086i	−0.788358	−	0.615216i	$-0.789069\pi$
$11$	0.459729	−	0.796275i	0.138614	−	0.240086i	0.926972	+	0.375130i	$0.122402\pi$
$12$	−9.67085	+	2.80440i	−2.79173	+	0.809560i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$14$	3.47514	+	6.01912i	0.928771	+	1.60868i
$15$	−1.37737	+	0.399416i	−0.355636	+	0.103129i
$16$	−9.08484	+	15.7354i	−2.27121	+	3.93385i
$17$	−1.53740			−0.372875			−0.186438	−	0.982467i	$-0.559694\pi$
$17$	−1.53740			−0.372875			−0.186438	+	0.982467i	$0.559694\pi$
$18$	7.08484	−	4.48625i	1.66991	−	1.05742i
$19$	3.40028			0.780078			0.390039	−	0.920798i	$-0.372461\pi$
$19$	3.40028			0.780078			0.390039	+	0.920798i	$0.372461\pi$
$20$	−2.40675	+	4.16860i	−0.538165	+	0.932128i
$21$	−3.10689	−	2.98238i	−0.677978	−	0.650809i
$22$	1.28506	+	2.22580i	0.273977	+	0.474541i
$23$	−0.490886	−	0.850239i	−0.102357	−	0.177287i	0.810298	−	0.586017i	$-0.199305\pi$
$23$	−0.490886	−	0.850239i	−0.102357	−	0.177287i	−0.912655	+	0.408730i	$0.865972\pi$
$24$	4.41304	−	17.9280i	0.900809	−	3.65954i
$25$	2.15722	−	3.73641i	0.431444	−	0.747283i
$26$	2.79526			0.548196
$27$	−3.44212	+	3.89253i	−0.662436	+	0.749118i
$28$	−14.4550			−2.73173
$29$	0.595121	−	1.03078i	0.110511	−	0.191411i	−0.805465	−	0.592643i	$-0.798085\pi$
$29$	0.595121	−	1.03078i	0.110511	−	0.191411i	0.915976	+	0.401232i	$0.131418\pi$
$30$	0.958162	−	3.89253i	0.174936	−	0.710676i
$31$	3.12690	+	5.41594i	0.561607	+	0.972732i	0.997356	+	0.0726641i	$0.0231501\pi$
$31$	3.12690	+	5.41594i	0.561607	+	0.972732i	−0.435749	+	0.900068i	$0.643517\pi$
$32$	−14.7348	−	25.5214i	−2.60477	−	4.51160i
$33$	−1.14889	−	1.10285i	−0.199996	−	0.191981i
$34$	2.14872	−	3.72170i	0.368503	−	0.638266i
$35$	−2.05875			−0.347992
$36$	0.712903	+	17.4259i	0.118817	+	2.90432i
$37$	1.83048			0.300929			0.150465	−	0.988615i	$-0.451923\pi$
$37$	1.83048			0.300929			0.150465	+	0.988615i	$0.451923\pi$
$38$	−4.75234	+	8.23129i	−0.770931	+	1.33529i
$39$	−1.66352	+	0.482395i	−0.266376	+	0.0772450i
$40$	−4.41304	−	7.64362i	−0.697764	−	1.20856i
$41$	2.86647	+	4.96488i	0.447668	+	0.775384i	0.998234	−	0.0594079i	$-0.0189213\pi$
$41$	2.86647	+	4.96488i	0.447668	+	0.775384i	−0.550566	+	0.834792i	$0.685588\pi$
$42$	11.5619	−	3.35278i	1.78404	−	0.517346i
$43$	−0.792611	+	1.37284i	−0.120872	+	0.209356i	−0.920112	−	0.391656i	$-0.871902\pi$
$43$	−0.792611	+	1.37284i	−0.120872	+	0.209356i	0.799240	+	0.601012i	$0.205236\pi$
$44$	−5.34527			−0.805829
$45$	0.101535	+	2.48188i	0.0151360	+	0.369977i
$46$	2.74431			0.404626
$47$	−2.68754	+	4.65496i	−0.392018	+	0.678996i	−0.992716	−	0.120481i	$-0.961556\pi$
$47$	−2.68754	+	4.65496i	−0.392018	+	0.678996i	0.600697	+	0.799477i	$0.294890\pi$
$48$	22.7035	+	21.7937i	3.27697	+	3.14565i
$49$	0.408777	+	0.708023i	0.0583967	+	0.101146i
$50$	6.02999	+	10.4443i	0.852770	+	1.47704i
$51$	−0.636475	+	2.58568i	−0.0891243	+	0.362068i
$52$	−2.90675	+	5.03463i	−0.403093	+	0.698178i
$53$	−5.82609			−0.800275			−0.400137	−	0.916455i	$-0.631038\pi$
$53$	−5.82609			−0.800275			−0.400137	+	0.916455i	$0.631038\pi$
$54$	−4.61210	−	13.7729i	−0.627628	−	1.87425i
$55$	−0.761299			−0.102654
$56$	13.2524	−	22.9539i	1.77093	−	3.06734i
$57$	1.40769	−	5.71876i	0.186454	−	0.757468i
$58$	1.66352	+	2.88130i	0.218431	+	0.378333i
$59$	0.477338	+	0.826774i	0.0621442	+	0.107637i	0.895424	−	0.445215i	$-0.146873\pi$
$59$	0.477338	+	0.826774i	0.0621442	+	0.107637i	−0.833279	+	0.552852i	$0.813539\pi$
$60$	6.01458	+	5.77355i	0.776479	+	0.745362i
$61$	4.44763	−	7.70353i	0.569461	−	0.986336i	−0.427158	−	0.904177i	$-0.640485\pi$
$61$	4.44763	−	7.70353i	0.569461	−	0.986336i	0.996619	−	0.0821589i	$-0.0261815\pi$
$62$	−17.4810			−2.22009
$63$	−6.30214	+	3.99062i	−0.793995	+	0.502771i
$64$	46.0360			5.75450
$65$	−0.413993	+	0.717057i	−0.0513495	+	0.0889400i
$66$	4.27546	−	1.23982i	0.526272	−	0.152611i
$67$	6.56302	+	11.3675i	0.801800	+	1.38876i	0.918430	+	0.395583i	$0.129457\pi$
$67$	6.56302	+	11.3675i	0.801800	+	1.38876i	−0.116630	+	0.993175i	$0.537209\pi$
$68$	4.46884	+	7.74026i	0.541927	+	0.938645i
$69$	−1.63320	+	0.473602i	−0.196614	+	0.0570150i
$70$	2.87737	−	4.98375i	0.343912	−	0.595672i
$71$	5.27858			0.626452			0.313226	−	0.949679i	$-0.398590\pi$
$71$	5.27858			0.626452			0.313226	+	0.949679i	$0.398590\pi$
$72$	−28.3252	−	14.8441i	−3.33815	−	1.74940i
$73$	−10.0187			−1.17260			−0.586302	−	0.810093i	$-0.699417\pi$
$73$	−10.0187			−1.17260			−0.586302	+	0.810093i	$0.699417\pi$
$74$	−2.55834	+	4.43117i	−0.297400	+	0.515113i
$75$	−5.39100	−	5.17496i	−0.622499	−	0.597553i
$76$	−9.88375	−	17.1192i	−1.13374	−	1.96370i
$77$	−1.14310	−	1.97990i	−0.130268	−	0.225630i
$78$	1.15722	−	4.70120i	0.131029	−	0.532306i
$79$	−5.06272	+	8.76888i	−0.569600	+	0.986577i	0.427005	+	0.904249i	$0.359569\pi$
$79$	−5.06272	+	8.76888i	−0.569600	+	0.986577i	−0.996605	+	0.0823273i	$0.973765\pi$
$80$	15.0443			1.68200
$81$	5.12163	+	7.40060i	0.569070	+	0.822289i
$82$	−16.0251			−1.76968
$83$	1.16257	−	2.01363i	0.127609	−	0.221025i	−0.795141	−	0.606425i	$-0.792603\pi$
$83$	1.16257	−	2.01363i	0.127609	−	0.221025i	0.922750	+	0.385400i	$0.125937\pi$
$84$	−5.98426	+	24.3110i	−0.652936	+	2.65255i
$85$	0.636475	+	1.10241i	0.0690354	+	0.119573i
$86$	−2.21555	−	3.83745i	−0.238909	−	0.413803i
$87$	−1.48724	−	1.42764i	−0.159449	−	0.153059i
$88$	4.90058	−	8.48805i	0.522404	−	0.904830i
$89$	12.5811			1.33359			0.666795	−	0.745241i	$-0.267666\pi$
$89$	12.5811			1.33359			0.666795	+	0.745241i	$0.267666\pi$
$90$	−6.14997	−	3.22296i	−0.648264	−	0.339730i
$91$	−2.48645			−0.260651
$92$	−2.85376	+	4.94286i	−0.297525	+	0.515329i
$93$	10.4033	−	3.01680i	1.07877	−	0.312827i
$94$	−7.51238	−	13.0118i	−0.774843	−	1.34207i
$95$	−1.40769	−	2.43820i	−0.144426	−	0.250154i
$96$	−49.0233	+	14.2160i	−5.00342	+	1.45091i
$97$	3.94212	−	6.82795i	0.400262	−	0.693274i	−0.593496	−	0.804837i	$-0.702253\pi$
$97$	3.94212	−	6.82795i	0.400262	−	0.693274i	0.993757	+	0.111564i	$0.0355859\pi$
$98$	−2.28528			−0.230848
$99$	−2.33045	+	1.47568i	−0.234219	+	0.148312i
$100$	−25.0819			−2.50819
$101$	7.55953	−	13.0935i	0.752201	−	1.30285i	−0.194552	−	0.980892i	$-0.562325\pi$
$101$	7.55953	−	13.0935i	0.752201	−	1.30285i	0.946754	−	0.321959i	$-0.104341\pi$
$102$	−5.36977	−	5.15458i	−0.531687	−	0.510380i
$103$	−2.25875	−	3.91228i	−0.222562	−	0.385488i	0.733023	−	0.680203i	$-0.238109\pi$
$103$	−2.25875	−	3.91228i	−0.222562	−	0.385488i	−0.955585	+	0.294715i	$0.904775\pi$
$104$	−5.32985	−	9.23157i	−0.522635	−	0.905230i
$105$	−0.852308	+	3.46250i	−0.0831767	+	0.337905i
$106$	8.14272	−	14.1036i	0.790891	−	1.36986i
$107$	18.5040			1.78885			0.894426	−	0.447217i	$-0.147585\pi$
$107$	18.5040			1.78885			0.894426	+	0.447217i	$0.147585\pi$
$108$	29.6028	+	6.01521i	2.84853	+	0.578813i
$109$	7.95808			0.762246			0.381123	−	0.924524i	$-0.375537\pi$
$109$	7.95808			0.762246			0.381123	+	0.924524i	$0.375537\pi$
$110$	1.06402	−	1.84293i	0.101450	−	0.175716i
$111$	0.757806	−	3.07859i	0.0719278	−	0.292207i
$112$	22.5890	+	39.1254i	2.13446	+	3.69700i
$113$	−6.20325	−	10.7444i	−0.583553	−	1.01074i	−0.995054	−	0.0993342i	$-0.968329\pi$
$113$	−6.20325	−	10.7444i	−0.583553	−	1.01074i	0.411501	−	0.911409i	$-0.365005\pi$
$114$	11.8763	+	11.4004i	1.11232	+	1.06775i
$115$	−0.406447	+	0.703987i	−0.0379014	+	0.0656471i
$116$	−6.91946			−0.642456
$117$	0.122629	+	2.99749i	0.0113371	+	0.277118i
$118$	−2.66857			−0.245662
$119$	−1.91134	+	3.31054i	−0.175212	+	0.303477i
$120$	−14.6824	+	4.25766i	−1.34031	+	0.388670i
$121$	5.07730	+	8.79414i	0.461573	+	0.799467i
$122$	12.4323	+	21.5334i	1.12557	+	1.94954i
$123$	9.53687	−	2.76555i	0.859911	−	0.249361i
$124$	18.1782	−	31.4855i	1.63245	−	2.82748i
$125$	−7.71223			−0.689803
$126$	−0.852308	−	20.8334i	−0.0759296	−	1.85599i
$127$	−9.28761			−0.824142			−0.412071	−	0.911152i	$-0.635195\pi$
$127$	−9.28761			−0.824142			−0.412071	+	0.911152i	$0.635195\pi$
$128$	−34.8717	+	60.3995i	−3.08225	+	5.33861i
$129$	1.98078	+	1.90140i	0.174398	+	0.167409i
$130$	−1.15722	−	2.00436i	−0.101495	−	0.175794i
$131$	−7.15825	−	12.3985i	−0.625419	−	1.08326i	−0.988460	−	0.151485i	$-0.951595\pi$
$131$	−7.15825	−	12.3985i	−0.625419	−	1.08326i	0.363040	−	0.931773i	$-0.381739\pi$
$132$	−2.21290	+	8.98992i	−0.192609	+	0.782472i
$133$	4.22732	−	7.32193i	0.366555	−	0.634892i
$134$	−36.6907			−3.16959
$135$	4.21618	+	0.856716i	0.362871	+	0.0737343i
$136$	−16.3883			−1.40528
$137$	−6.37199	+	11.0366i	−0.544396	+	0.942921i	0.454249	+	0.890875i	$0.349908\pi$
$137$	−6.37199	+	11.0366i	−0.544396	+	0.942921i	−0.998645	+	0.0520463i	$0.983426\pi$
$138$	1.13613	−	4.61551i	0.0967134	−	0.392898i
$139$	7.90873	+	13.6983i	0.670809	+	1.16188i	0.977675	+	0.210123i	$0.0673865\pi$
$139$	7.90873	+	13.6983i	0.670809	+	1.16188i	−0.306866	+	0.951753i	$0.599280\pi$
$140$	5.98426	+	10.3650i	0.505762	+	0.876006i
$141$	6.71631	+	6.44716i	0.565615	+	0.542949i
$142$	−7.37751	+	12.7782i	−0.619107	+	1.07232i
$143$	−0.919459			−0.0768890
$144$	46.0527	−	29.1614i	3.83773	−	2.43011i
$145$	−0.985504			−0.0818416
$146$	14.0025	−	24.2530i	1.15885	−	2.00719i
$147$	1.36002	−	0.394384i	0.112172	−	0.0325283i
$148$	−5.32074	−	9.21579i	−0.437362	−	0.757533i
$149$	−1.06496	−	1.84457i	−0.0872450	−	0.151113i	0.819101	−	0.573650i	$-0.194473\pi$
$149$	−1.06496	−	1.84457i	−0.0872450	−	0.151113i	−0.906346	+	0.422537i	$0.861140\pi$
$150$	20.0620	−	5.81768i	1.63806	−	0.475011i
$151$	−7.34083	+	12.7147i	−0.597388	+	1.03471i	0.395817	+	0.918330i	$0.370462\pi$
$151$	−7.34083	+	12.7147i	−0.597388	+	1.03471i	−0.993205	+	0.116378i	$0.962872\pi$
$152$	36.2460			2.93994
$153$	4.08522	+	2.14091i	0.330271	+	0.173082i
$154$	6.39050			0.514961
$155$	2.58903	−	4.48433i	0.207956	−	0.360190i
$156$	7.26411	+	6.97300i	0.581594	+	0.558287i
$157$	−5.26946	−	9.12697i	−0.420548	−	0.728411i	0.575445	−	0.817841i	$-0.304829\pi$
$157$	−5.26946	−	9.12697i	−0.420548	−	0.728411i	−0.995993	+	0.0894294i	$0.971496\pi$
$158$	−14.1516	−	24.5113i	−1.12584	−	1.95002i
$159$	−2.41196	+	9.79859i	−0.191281	+	0.777079i
$160$	−12.2002	+	21.1314i	−0.964512	+	1.67058i
$161$	−2.44113			−0.192388
$162$	−25.0733	+	2.05496i	−1.96994	+	0.161453i
$163$	−2.74398			−0.214925			−0.107463	−	0.994209i	$-0.534273\pi$
$163$	−2.74398			−0.214925			−0.107463	+	0.994209i	$0.534273\pi$
$164$	16.6642	−	28.8633i	1.30126	−	2.25384i
$165$	−0.315173	+	1.28039i	−0.0245362	+	0.0996782i
$166$	3.24969	+	5.62863i	0.252225	+	0.436866i
$167$	−5.84319	−	10.1207i	−0.452160	−	0.783164i	0.546360	−	0.837550i	$-0.316013\pi$
$167$	−5.84319	−	10.1207i	−0.452160	−	0.783164i	−0.998520	+	0.0543865i	$0.982680\pi$
$168$	−33.1185	−	31.7913i	−2.55515	−	2.45275i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	−3.55823			−0.272904
$171$	−9.03530	−	4.73505i	−0.690946	−	0.362098i
$172$	9.21567			0.702688
$173$	0.969058	−	1.67846i	0.0736761	−	0.127611i	−0.826834	−	0.562446i	$-0.809860\pi$
$173$	0.969058	−	1.67846i	0.0736761	−	0.127611i	0.900510	+	0.434836i	$0.143194\pi$
$174$	5.53459	−	1.60495i	0.419576	−	0.121671i
$175$	−5.36382	−	9.29041i	−0.405467	−	0.702289i
$176$	8.35314	+	14.4681i	0.629642	+	1.09057i
$177$	1.58812	−	0.460531i	0.119371	−	0.0346156i
$178$	−17.5837	+	30.4558i	−1.31795	+	2.28276i
$179$	16.3546			1.22240			0.611201	−	0.791475i	$-0.290687\pi$
$179$	16.3546			1.22240			0.611201	+	0.791475i	$0.290687\pi$
$180$	12.2002	−	7.72539i	0.909351	−	0.575817i
$181$	−14.7968			−1.09984			−0.549920	−	0.835218i	$-0.685342\pi$
$181$	−14.7968			−1.09984			−0.549920	+	0.835218i	$0.685342\pi$
$182$	3.47514	−	6.01912i	0.257595	−	0.446167i
$183$	−11.1149	−	10.6695i	−0.821635	−	0.788708i
$184$	−5.23270	−	9.06330i	−0.385760	−	0.668155i
$185$	−0.757806	−	1.31256i	−0.0557150	−	0.0965012i
$186$	−7.23701	+	29.4004i	−0.530643	+	2.15574i
$187$	−0.706790	+	1.22420i	−0.0516856	+	0.0895221i
$188$	31.2480			2.27899
$189$	4.10258	+	12.2513i	0.298418	+	0.891153i
$190$	7.86975			0.570931
$191$	−11.0198	+	19.0868i	−0.797362	+	1.38107i	0.123966	+	0.992286i	$0.460439\pi$
$191$	−11.0198	+	19.0868i	−0.797362	+	1.38107i	−0.921328	+	0.388785i	$0.872895\pi$
$192$	19.0586	−	77.4255i	1.37543	−	5.58770i
$193$	−1.51920	−	2.63133i	−0.109354	−	0.189407i	0.806155	−	0.591705i	$-0.201545\pi$
$193$	−1.51920	−	2.63133i	−0.109354	−	0.189407i	−0.915509	+	0.402298i	$0.868212\pi$
$194$	11.0193	+	19.0859i	0.791137	+	1.37029i
$195$	1.03459	+	0.993130i	0.0740885	+	0.0711195i
$196$	2.37642	−	4.11608i	0.169744	−	0.294006i
$197$	−24.0480			−1.71335			−0.856674	−	0.515858i	$-0.827473\pi$
$197$	−24.0480			−1.71335			−0.856674	+	0.515858i	$0.827473\pi$
$198$	−0.315173	−	7.70394i	−0.0223984	−	0.547495i
$199$	−15.2119			−1.07834			−0.539171	−	0.842197i	$-0.681262\pi$
$199$	−15.2119			−1.07834			−0.539171	+	0.842197i	$0.681262\pi$
$200$	22.9953	−	39.8291i	1.62601	−	2.81634i
$201$	21.8354	−	6.33193i	1.54015	−	0.446620i
$202$	21.1309	+	36.5997i	1.48676	+	2.57515i
$203$	−1.47974	−	2.56298i	−0.103857	−	0.179886i
$204$	14.8680	−	4.31150i	1.04097	−	0.301865i
$205$	2.37340	−	4.11085i	0.165766	−	0.287114i
$206$	12.6276			0.879808
$207$	0.120394	+	2.94285i	0.00836795	+	0.204542i
$208$	18.1697			1.25984
$209$	1.56321	−	2.70756i	0.108130	−	0.187286i
$210$	−7.19070	−	6.90254i	−0.496205	−	0.476320i
$211$	0.697648	+	1.20836i	0.0480280	+	0.0831870i	0.889040	−	0.457829i	$-0.151373\pi$
$211$	0.697648	+	1.20836i	0.0480280	+	0.0831870i	−0.841012	+	0.541017i	$0.818040\pi$
$212$	16.9350	+	29.3322i	1.16310	+	2.01454i
$213$	2.18530	−	8.87776i	0.149734	−	0.608294i
$214$	−25.8618	+	44.7939i	−1.76788	+	3.06205i
$215$	1.31254			0.0895146
$216$	−36.6920	+	41.4932i	−2.49657	+	2.82326i
$217$	15.5498			1.05559
$218$	−11.1225	+	19.2647i	−0.753308	+	1.30477i
$219$	−4.14768	+	16.8500i	−0.280275	+	1.13862i
$220$	2.21290	+	3.83286i	0.149194	+	0.258411i
$221$	0.768702	+	1.33143i	0.0517085	+	0.0895618i
$222$	6.39341	+	6.13720i	0.429098	+	0.411902i
$223$	−1.17093	+	2.02811i	−0.0784113	+	0.135812i	−0.902565	−	0.430554i	$-0.858318\pi$
$223$	−1.17093	+	2.02811i	−0.0784113	+	0.135812i	0.824153	+	0.566367i	$0.191651\pi$
$224$	−73.2748			−4.89588
$225$	−10.9353	+	6.92444i	−0.729022	+	0.461629i
$226$	34.6794			2.30684
$227$	3.86726	−	6.69829i	0.256679	−	0.444581i	−0.708671	−	0.705539i	$-0.750705\pi$
$227$	3.86726	−	6.69829i	0.256679	−	0.444581i	0.965350	+	0.260958i	$0.0840384\pi$
$228$	−32.8836	+	9.53575i	−2.17777	+	0.631520i
$229$	−7.65795	−	13.2640i	−0.506052	−	0.876507i	−0.999975	−	0.00700218i	$-0.997771\pi$
$229$	−7.65795	−	13.2640i	−0.506052	−	0.876507i	0.493924	−	0.869505i	$-0.335562\pi$
$230$	−1.13613	−	1.96783i	−0.0749139	−	0.129755i
$231$	−3.80312	+	1.10285i	−0.250227	+	0.0725620i
$232$	6.34381	−	10.9878i	0.416492	−	0.721385i
$233$	3.81598			0.249993			0.124997	−	0.992157i	$-0.460108\pi$
$233$	3.81598			0.249993			0.124997	+	0.992157i	$0.460108\pi$
$234$	−7.42762	−	3.89253i	−0.485559	−	0.254463i
$235$	4.45050			0.290318
$236$	2.77500	−	4.80644i	0.180637	−	0.312873i
$237$	12.6520	+	12.1450i	0.821835	+	0.788901i
$238$	−5.34270	−	9.25383i	−0.346316	−	0.599837i
$239$	5.33578	+	9.24184i	0.345143	+	0.597805i	0.985380	−	0.170373i	$-0.0544971\pi$
$239$	5.33578	+	9.24184i	0.345143	+	0.597805i	−0.640237	+	0.768178i	$0.721164\pi$
$240$	6.22822	−	25.3021i	0.402030	−	1.63325i
$241$	−0.600452	+	1.04001i	−0.0386785	+	0.0669931i	−0.884717	−	0.466129i	$-0.845648\pi$
$241$	−0.600452	+	1.04001i	−0.0386785	+	0.0669931i	0.846038	+	0.533122i	$0.178981\pi$
$242$	−28.3848			−1.82464
$243$	14.5670	−	5.55000i	0.934474	−	0.356033i
$244$	−51.7126			−3.31056
$245$	0.338462	−	0.586233i	0.0216235	−	0.0374531i
$246$	−6.63428	+	26.9518i	−0.422986	+	1.71838i
$247$	−1.70014	−	2.94473i	−0.108177	−	0.187369i
$248$	33.3318	+	57.7324i	2.11657	+	3.66601i
$249$	−2.90532	−	2.78890i	−0.184117	−	0.176739i
$250$	10.7788	−	18.6695i	0.681714	−	1.18076i
$251$	15.6411			0.987260			0.493630	−	0.869672i	$-0.335670\pi$
$251$	15.6411			0.987260			0.493630	+	0.869672i	$0.335670\pi$
$252$	38.4100	+	20.1292i	2.41960	+	1.26802i
$253$	−0.902699			−0.0567522
$254$	12.9807	−	22.4832i	0.814479	−	1.41072i
$255$	2.11758	−	0.614065i	0.132608	−	0.0384542i
$256$	−51.4395	−	89.0958i	−3.21497	−	5.56849i
$257$	7.83123	+	13.5641i	0.488499	+	0.846105i	0.999912	−	0.0132297i	$-0.00421127\pi$
$257$	7.83123	+	13.5641i	0.488499	+	0.846105i	−0.511414	+	0.859335i	$0.670878\pi$
$258$	−7.37123	+	2.13754i	−0.458913	+	0.133078i
$259$	2.27570	−	3.94163i	0.141405	−	0.244921i
$260$	4.81349			0.298520
$261$	−3.01678	+	1.91027i	−0.186734	+	0.118243i
$262$	40.0184			2.47234
$263$	0.813037	−	1.40822i	0.0501340	−	0.0868347i	−0.839869	−	0.542789i	$-0.817368\pi$
$263$	0.813037	−	1.40822i	0.0501340	−	0.0868347i	0.890003	+	0.455954i	$0.150702\pi$
$264$	−12.2468	−	11.7560i	−0.753739	−	0.723533i
$265$	2.41196	+	4.17764i	0.148166	+	0.256630i
$266$	11.8165	+	20.4667i	0.724514	+	1.25490i
$267$	5.20847	−	21.1594i	0.318753	−	1.29494i
$268$	38.1540	−	66.0847i	2.33063	−	4.03677i
$269$	−18.8883			−1.15164			−0.575821	−	0.817576i	$-0.695318\pi$
$269$	−18.8883			−1.15164			−0.575821	+	0.817576i	$0.695318\pi$
$270$	−7.96658	+	9.00903i	−0.484830	+	0.548272i
$271$	−10.2390			−0.621977			−0.310988	−	0.950414i	$-0.600660\pi$
$271$	−10.2390			−0.621977			−0.310988	+	0.950414i	$0.600660\pi$
$272$	13.9671	−	24.1917i	0.846879	−	1.46684i
$273$	−1.02937	+	4.18183i	−0.0623006	+	0.253096i
$274$	−17.8114	−	30.8502i	−1.07602	−	1.86373i
$275$	−1.98347	−	3.43548i	−0.119608	−	0.207167i
$276$	7.13169	+	6.84590i	0.429278	+	0.412075i
$277$	3.65519	−	6.33097i	0.219619	−	0.380391i	−0.735073	−	0.677988i	$-0.762852\pi$
$277$	3.65519	−	6.33097i	0.219619	−	0.380391i	0.954691	+	0.297597i	$0.0961853\pi$
$278$	−44.2139			−2.65177
$279$	−0.766897	−	18.7457i	−0.0459129	−	1.12228i
$280$	−21.9457			−1.31150
$281$	−13.0817	+	22.6582i	−0.780390	+	1.35168i	0.151324	+	0.988484i	$0.451646\pi$
$281$	−13.0817	+	22.6582i	−0.780390	+	1.35168i	−0.931714	+	0.363192i	$0.881687\pi$
$282$	−24.9940	+	7.24787i	−1.48837	+	0.431605i
$283$	−2.56185	−	4.43725i	−0.152286	−	0.263767i	0.779781	−	0.626052i	$-0.215330\pi$
$283$	−2.56185	−	4.43725i	−0.152286	−	0.263767i	−0.932068	+	0.362285i	$0.881997\pi$
$284$	−15.3435	−	26.5757i	−0.910468	−	1.57698i
$285$	−4.68345	+	1.35813i	−0.277424	+	0.0804486i
$286$	1.28506	−	2.22580i	0.0759875	−	0.131614i
$287$	14.2547			0.841429
$288$	3.61384	+	88.3350i	0.212947	+	5.20519i
$289$	−14.6364			−0.860964
$290$	1.37737	−	2.38568i	0.0808820	−	0.140092i
$291$	−9.85156	−	9.45677i	−0.577509	−	0.554366i
$292$	29.1219	+	50.4406i	1.70423	+	2.95181i
$293$	−5.04538	−	8.73886i	−0.294755	−	0.510530i	0.680173	−	0.733051i	$-0.261905\pi$
$293$	−5.04538	−	8.73886i	−0.294755	−	0.510530i	−0.974928	+	0.222522i	$0.928571\pi$
$294$	−0.946090	+	3.84349i	−0.0551771	+	0.224157i
$295$	0.395230	−	0.684558i	0.0230112	−	0.0398565i
$296$	19.5124			1.13413
$297$	1.51708	+	4.53039i	0.0880300	+	0.262880i
$298$	5.95369			0.344888
$299$	−0.490886	+	0.850239i	−0.0283887	+	0.0491706i
$300$	−10.3838	+	42.1840i	−0.599506	+	2.43549i
$301$	1.97079	+	3.41351i	0.113594	+	0.196751i
$302$	−20.5196	−	35.5409i	−1.18077	−	2.04515i
$303$	−18.8917	−	18.1346i	−1.08530	−	1.04181i
$304$	−30.8910	+	53.5048i	−1.77172	+	3.06871i
$305$	−7.36516			−0.421728
$306$	−10.8923	+	6.89717i	−0.622670	+	0.394285i
$307$	14.9405			0.852699			0.426350	−	0.904558i	$-0.359799\pi$
$307$	14.9405			0.852699			0.426350	+	0.904558i	$0.359799\pi$
$308$	−6.64537	+	11.5101i	−0.378655	+	0.655850i
$309$	−7.51496	+	2.17922i	−0.427511	+	0.123972i
$310$	7.23701	+	12.5349i	0.411035	+	0.711933i
$311$	3.75769	+	6.50852i	0.213079	+	0.369064i	0.952677	−	0.303985i	$-0.0983174\pi$
$311$	3.75769	+	6.50852i	0.213079	+	0.369064i	−0.739597	+	0.673050i	$0.764984\pi$
$312$	−17.7326	+	5.14219i	−1.00391	+	0.291119i
$313$	−3.70826	+	6.42289i	−0.209603	+	0.363043i	−0.951590	−	0.307372i	$-0.900551\pi$
$313$	−3.70826	+	6.42289i	−0.209603	+	0.363043i	0.741986	+	0.670415i	$0.233884\pi$
$314$	29.4590			1.66247
$315$	5.47055	+	2.86690i	0.308230	+	0.161532i
$316$	58.8641			3.31137
$317$	−5.86080	+	10.1512i	−0.329175	+	0.570149i	−0.982348	−	0.187060i	$-0.940104\pi$
$317$	−5.86080	+	10.1512i	−0.329175	+	0.570149i	0.653173	+	0.757209i	$0.273437\pi$
$318$	−20.3491	−	19.5336i	−1.14112	−	1.09539i
$319$	−0.547189	−	0.947760i	−0.0306367	−	0.0530644i
$320$	−19.0586	−	33.0104i	−1.06541	−	1.84534i
$321$	7.66054	−	31.1209i	0.427570	−	1.73700i
$322$	3.41180	−	5.90941i	0.190132	−	0.329318i
$323$	−5.22761			−0.290872
$324$	22.3720	−	47.2972i	1.24289	−	2.62762i
$325$	−4.31444			−0.239322
$326$	3.83508	−	6.64255i	0.212405	−	0.367897i
$327$	3.29459	−	13.3843i	0.182191	−	0.740152i
$328$	30.5558	+	52.9242i	1.68716	+	2.92225i
$329$	6.68245	+	11.5743i	0.368415	+	0.638114i
$330$	−2.65903	−	2.55247i	−0.146375	−	0.140509i
$331$	1.88362	−	3.26252i	0.103533	−	0.179325i	−0.809605	−	0.586975i	$-0.800319\pi$
$331$	1.88362	−	3.26252i	0.103533	−	0.179325i	0.913138	+	0.407651i	$0.133652\pi$
$332$	−13.5172			−0.741852
$333$	−4.86399	−	2.54903i	−0.266545	−	0.139686i
$334$	32.6665			1.78743
$335$	5.43409	−	9.41212i	0.296896	−	0.514239i
$336$	75.1546	−	21.7937i	4.10002	−	1.18894i
$337$	−12.9936	−	22.5056i	−0.707808	−	1.22596i	−0.965669	−	0.259777i	$-0.916351\pi$
$337$	−12.9936	−	22.5056i	−0.707808	−	1.22596i	0.257861	−	0.966182i	$-0.416982\pi$
$338$	−1.39763	−	2.42077i	−0.0760211	−	0.131672i
$339$	−20.6385	+	5.98484i	−1.12093	+	0.325052i
$340$	3.70014	−	6.40883i	0.200668	−	0.347568i
$341$	5.75011			0.311386
$342$	24.0905	−	15.2545i	1.30266	−	0.824869i
$343$	19.4380			1.04955
$344$	−8.44900	+	14.6341i	−0.455539	+	0.789017i
$345$	1.01573	+	0.975027i	0.0546852	+	0.0524937i
$346$	2.70877	+	4.69173i	0.145624	+	0.252229i
$347$	3.73279	+	6.46538i	0.200386	+	0.347080i	0.948653	−	0.316319i	$-0.102447\pi$
$347$	3.73279	+	6.46538i	0.200386	+	0.347080i	−0.748267	+	0.663398i	$0.769114\pi$
$348$	−2.86461	+	11.6375i	−0.153559	+	0.623834i
$349$	5.63652	−	9.76273i	0.301716	−	0.522587i	−0.674809	−	0.737992i	$-0.735774\pi$
$349$	5.63652	−	9.76273i	0.301716	−	0.522587i	0.976525	+	0.215405i	$0.0691073\pi$
$350$	29.9866			1.60285
$351$	5.09209	+	1.03470i	0.271796	+	0.0552281i
$352$	−27.0961			−1.44423
$353$	−10.8052	+	18.7152i	−0.575105	+	0.996111i	0.420925	+	0.907095i	$0.361706\pi$
$353$	−10.8052	+	18.7152i	−0.575105	+	0.996111i	−0.996030	+	0.0890160i	$0.971628\pi$
$354$	−1.10477	+	4.48813i	−0.0587179	+	0.238541i
$355$	−2.18530	−	3.78504i	−0.115983	−	0.200889i
$356$	−36.5699	−	63.3410i	−1.93820	−	3.35707i
$357$	4.77654	+	4.58513i	0.252801	+	0.242671i
$358$	−22.8577	+	39.5908i	−1.20807	+	2.09244i
$359$	27.9681			1.47610			0.738050	−	0.674747i	$-0.235747\pi$
$359$	27.9681			1.47610			0.738050	+	0.674747i	$0.235747\pi$
$360$	1.08234	+	26.4561i	0.0570441	+	1.39436i
$361$	−7.43808			−0.391478
$362$	20.6805	−	35.8197i	1.08694	−	1.88264i
$363$	16.8924	−	4.89853i	0.886619	−	0.257106i
$364$	7.22748	+	12.5184i	0.378823	+	0.656141i
$365$	4.14768	+	7.18400i	0.217100	+	0.376028i
$366$	41.3627	−	11.9946i	2.16207	−	0.626966i
$367$	−5.34067	+	9.25031i	−0.278781	+	0.482862i	−0.971082	−	0.238746i	$-0.923264\pi$
$367$	−5.34067	+	9.25031i	−0.278781	+	0.482862i	0.692301	+	0.721609i	$0.256597\pi$
$368$	17.8385			0.929896
$369$	−0.703027	−	17.1845i	−0.0365981	−	0.894588i
$370$	4.23653			0.220247
$371$	−7.24315	+	12.5455i	−0.376045	+	0.651330i
$372$	−45.4282	−	43.6077i	−2.35534	−	2.26095i
$373$	7.11158	+	12.3176i	0.368223	+	0.637782i	0.989288	−	0.145978i	$-0.0466328\pi$
$373$	7.11158	+	12.3176i	0.368223	+	0.637782i	−0.621064	+	0.783759i	$0.713299\pi$
$374$	−1.97566	−	3.42195i	−0.102159	−	0.176945i
$375$	−3.19281	+	12.9708i	−0.164876	+	0.669809i
$376$	−28.6484	+	49.6205i	−1.47743	+	2.55898i
$377$	−1.19024			−0.0613006
$378$	−35.3915	−	7.19145i	−1.82034	−	0.369888i
$379$	30.2086			1.55171			0.775857	−	0.630909i	$-0.217318\pi$
$379$	30.2086			1.55171			0.775857	+	0.630909i	$0.217318\pi$
$380$	−8.18361	+	14.1744i	−0.419810	+	0.727133i
$381$	−3.84501	+	15.6203i	−0.196986	+	0.800255i
$382$	−30.8031	−	53.3526i	−1.57603	−	2.72976i
$383$	−9.71116	−	16.8202i	−0.496217	−	0.859474i	0.503773	−	0.863836i	$-0.331945\pi$
$383$	−9.71116	−	16.8202i	−0.496217	−	0.859474i	−0.999990	+	0.00436238i	$0.998611\pi$
$384$	87.1461	+	83.6538i	4.44715	+	4.26894i
$385$	−0.946467	+	1.63933i	−0.0482364	+	0.0835480i
$386$	8.49311			0.432288
$387$	4.01789	−	2.54420i	0.204241	−	0.129329i
$388$	−45.8350			−2.32692
$389$	1.00577	−	1.74205i	0.0509947	−	0.0883254i	−0.839401	−	0.543512i	$-0.817094\pi$
$389$	1.00577	−	1.74205i	0.0509947	−	0.0883254i	0.890396	+	0.455187i	$0.150428\pi$
$390$	−3.85011	+	1.11647i	−0.194958	+	0.0565348i
$391$	0.754690	+	1.30716i	0.0381663	+	0.0661060i
$392$	4.35744	+	7.54731i	0.220084	+	0.381197i
$393$	−23.8158	+	6.90621i	−1.20135	+	0.348372i
$394$	33.6102	−	58.2146i	1.69326	−	2.93281i
$395$	8.38372			0.421831
$396$	14.2035	+	7.44353i	0.713755	+	0.374051i
$397$	20.7184			1.03983			0.519914	−	0.854218i	$-0.325964\pi$
$397$	20.7184			1.03983			0.519914	+	0.854218i	$0.325964\pi$
$398$	21.2606	−	36.8244i	1.06570	−	1.84584i
$399$	−10.5643	−	10.1409i	−0.528876	−	0.507682i
$400$	39.1960	+	67.8895i	1.95980	+	3.39447i
$401$	9.08224	+	15.7309i	0.453545	+	0.785563i	0.998603	−	0.0528350i	$-0.0168257\pi$
$401$	9.08224	+	15.7309i	0.453545	+	0.785563i	−0.545058	+	0.838398i	$0.683492\pi$
$402$	−15.1897	+	61.7081i	−0.757593	+	3.07772i
$403$	3.12690	−	5.41594i	0.155762	−	0.269787i
$404$	−87.8945			−4.37292
$405$	3.18634	−	6.73630i	0.158330	−	0.334729i
$406$	8.27252			0.410558
$407$	0.841526	−	1.45757i	0.0417129	−	0.0722488i
$408$	−6.78464	+	27.5626i	−0.335890	+	1.36455i
$409$	−16.3177	−	28.2630i	−0.806857	−	1.39752i	−0.915030	−	0.403386i	$-0.867833\pi$
$409$	−16.3177	−	28.2630i	−0.806857	−	1.39752i	0.108173	−	0.994132i	$-0.465500\pi$
$410$	6.63428	+	11.4909i	0.327644	+	0.567496i
$411$	15.9239	+	15.2858i	0.785469	+	0.753992i
$412$	−13.1312	+	22.7440i	−0.646930	+	1.12052i
$413$	2.37376			0.116805
$414$	−7.29223	−	3.82158i	−0.358394	−	0.187820i
$415$	−1.92518			−0.0945036
$416$	−14.7348	+	25.5214i	−0.722434	+	1.25129i
$417$	26.3126	−	7.63026i	1.28854	−	0.373655i
$418$	4.36958	+	7.56834i	0.213723	+	0.370180i
$419$	13.5292	+	23.4333i	0.660945	+	1.14479i	0.980368	+	0.197178i	$0.0631777\pi$
$419$	13.5292	+	23.4333i	0.660945	+	1.14479i	−0.319423	+	0.947612i	$0.603489\pi$
$420$	19.9098	−	5.77355i	0.971501	−	0.281720i
$421$	−13.3903	+	23.1927i	−0.652603	+	1.13034i	0.329886	+	0.944021i	$0.392990\pi$
$421$	−13.3903	+	23.1927i	−0.652603	+	1.13034i	−0.982489	+	0.186321i	$0.940343\pi$
$422$	−3.90022			−0.189860
$423$	13.6236	−	8.62672i	0.662404	−	0.419446i
$424$	−62.1044			−3.01606
$425$	−3.31652	+	5.74438i	−0.160875	+	0.278643i
$426$	18.4368	+	17.6979i	0.893264	+	0.857468i
$427$	−11.0588	−	19.1545i	−0.535174	−	0.926949i
$428$	−53.7865	−	93.1609i	−2.59987	−	4.50310i
$429$	−0.380650	+	1.54639i	−0.0183779	+	0.0746604i
$430$	−1.83445	+	3.17736i	−0.0884650	+	0.153226i
$431$	−37.3204			−1.79766			−0.898830	−	0.438297i	$-0.855582\pi$
$431$	−37.3204			−1.79766			−0.898830	+	0.438297i	$0.855582\pi$
$432$	−29.9795	−	89.5262i	−1.44239	−	4.30733i
$433$	4.67900			0.224859			0.112429	−	0.993660i	$-0.464137\pi$
$433$	4.67900			0.224859			0.112429	+	0.993660i	$0.464137\pi$
$434$	−21.7328	+	37.6424i	−1.04321	+	1.80689i
$435$	−0.407992	+	1.65747i	−0.0195617	+	0.0794695i
$436$	−23.1321	−	40.0660i	−1.10783	−	1.91881i
$437$	−1.66915	−	2.89105i	−0.0798463	−	0.138298i
$438$	−34.9929	−	33.5906i	−1.67203	−	1.60502i
$439$	10.1656	−	17.6074i	0.485179	−	0.840355i	−0.514676	−	0.857385i	$-0.672088\pi$
$439$	10.1656	−	17.6074i	0.485179	−	0.840355i	0.999855	+	0.0170298i	$0.00542101\pi$
$440$	−8.11523			−0.386878
$441$	−0.100256	−	2.45061i	−0.00477410	−	0.116696i
$442$	−4.29745			−0.204409
$443$	−0.274181	+	0.474896i	−0.0130267	+	0.0225630i	−0.872465	−	0.488676i	$-0.837480\pi$
$443$	−0.274181	+	0.474896i	−0.0130267	+	0.0225630i	0.859439	+	0.511239i	$0.170813\pi$
$444$	−17.7023	+	5.13339i	−0.840114	+	0.243620i
$445$	−5.20847	−	9.02134i	−0.246905	−	0.427653i
$446$	−3.27306	−	5.66910i	−0.154984	−	0.268440i
$447$	−3.54317	+	1.02746i	−0.167586	+	0.0485974i
$448$	57.2331	−	99.1307i	2.70401	−	4.68348i
$449$	−15.7113			−0.741460			−0.370730	−	0.928741i	$-0.620893\pi$
$449$	−15.7113			−0.741460			−0.370730	+	0.928741i	$0.620893\pi$
$450$	−1.47891	−	36.1497i	−0.0697163	−	1.70411i
$451$	5.27121			0.248212
$452$	−36.0626	+	62.4622i	−1.69624	+	2.93797i
$453$	18.3451	+	17.6100i	0.861929	+	0.827388i
$454$	10.8100	+	18.7235i	0.507338	+	0.878736i
$455$	1.02937	+	1.78293i	0.0482578	+	0.0835850i
$456$	15.0056	−	60.9602i	0.702702	−	2.85472i
$457$	−15.7053	+	27.2023i	−0.734662	+	1.27247i	0.220210	+	0.975453i	$0.429326\pi$
$457$	−15.7053	+	27.2023i	−0.734662	+	1.27247i	−0.954872	+	0.297019i	$0.904007\pi$
$458$	42.8120			2.00047
$459$	5.29193	−	5.98440i	0.247006	−	0.279328i
$460$	4.72575			0.220339
$461$	−16.5562	+	28.6761i	−0.771098	+	1.33558i	0.165864	+	0.986149i	$0.446959\pi$
$461$	−16.5562	+	28.6761i	−0.771098	+	1.33558i	−0.936962	+	0.349432i	$0.886375\pi$
$462$	2.64562	−	10.7478i	0.123086	−	0.500035i
$463$	8.88057	+	15.3816i	0.412715	+	0.714844i	0.995186	−	0.0980083i	$-0.0312472\pi$
$463$	8.88057	+	15.3816i	0.412715	+	0.714844i	−0.582470	+	0.812852i	$0.697914\pi$
$464$	10.8132	+	18.7289i	0.501988	+	0.869469i
$465$	−6.47011	−	6.21083i	−0.300044	−	0.288020i
$466$	−5.33334	+	9.23761i	−0.247062	+	0.427924i
$467$	25.7033			1.18941			0.594704	−	0.803945i	$-0.297269\pi$
$467$	25.7033			1.18941			0.594704	+	0.803945i	$0.297269\pi$
$468$	14.7348	−	9.33034i	0.681117	−	0.431295i
$469$	32.6373			1.50705
$470$	−6.22015	+	10.7736i	−0.286914	+	0.496950i
$471$	−17.5317	+	5.08392i	−0.807817	+	0.234255i
$472$	5.08829	+	8.81317i	0.234207	+	0.405659i
$473$	0.728773	+	1.26227i	0.0335090	+	0.0580393i
$474$	−47.0830	+	13.6533i	−2.16259	+	0.627119i
$475$	7.33515	−	12.7049i	0.336560	−	0.582939i
$476$	22.2231			1.01860
$477$	15.4812	+	8.11310i	0.708835	+	0.371473i
$478$	−29.8298			−1.36438
$479$	9.29581	−	16.1008i	0.424736	−	0.735665i	−0.571659	−	0.820491i	$-0.693700\pi$
$479$	9.29581	−	16.1008i	0.424736	−	0.735665i	0.996396	+	0.0848262i	$0.0270335\pi$
$480$	30.4890	+	29.2672i	1.39163	+	1.33586i
$481$	−0.915240	−	1.58524i	−0.0417313	−	0.0722808i
$482$	−1.67842	−	2.90711i	−0.0764499	−	0.132415i
$483$	−1.01061	+	4.10561i	−0.0459844	+	0.186812i
$484$	29.5168	−	51.1246i	1.34167	−	2.32385i
$485$	−6.52804			−0.296423
$486$	−6.92403	+	43.0202i	−0.314081	+	1.95143i
$487$	27.7070			1.25552			0.627761	−	0.778406i	$-0.283972\pi$
$487$	27.7070			1.25552			0.627761	+	0.778406i	$0.283972\pi$
$488$	47.4105	−	82.1173i	2.14617	−	3.71728i
$489$	−1.13599	+	4.61496i	−0.0513713	+	0.208696i
$490$	0.946090	+	1.63868i	0.0427400	+	0.0740278i
$491$	−8.97484	−	15.5449i	−0.405029	−	0.701531i	0.589296	−	0.807917i	$-0.299405\pi$
$491$	−8.97484	−	15.5449i	−0.405029	−	0.701531i	−0.994325	+	0.106386i	$0.966072\pi$
$492$	−41.6447	−	39.9759i	−1.87749	−	1.80225i
$493$	−0.914942	+	1.58473i	−0.0412069	+	0.0713724i
$494$	9.50468			0.427636
$495$	2.02294	+	1.06014i	0.0909244	+	0.0476500i
$496$	−113.629			−5.10211
$497$	6.56247	−	11.3665i	0.294367	−	0.509858i
$498$	10.8118	−	3.13527i	0.484490	−	0.140495i
$499$	12.1591	+	21.0601i	0.544315	+	0.942781i	0.998650	+	0.0519502i	$0.0165437\pi$
$499$	12.1591	+	21.0601i	0.544315	+	0.942781i	−0.454335	+	0.890831i	$0.650123\pi$
$500$	22.4175	+	38.8282i	1.00254	+	1.73645i
$501$	−19.4405	+	5.63745i	−0.868539	+	0.251863i
$502$	−21.8605	+	37.8636i	−0.975684	+	1.68993i
$503$	−39.1695			−1.74648			−0.873240	−	0.487291i	$-0.837985\pi$
$503$	−39.1695			−1.74648			−0.873240	+	0.487291i	$0.837985\pi$
$504$	−67.1789	+	42.5389i	−2.99239	+	1.89483i
$505$	−12.5184			−0.557060
$506$	1.26164	−	2.18522i	0.0560867	−	0.0971451i
$507$	1.24953	+	1.19945i	0.0554934	+	0.0532695i
$508$	26.9967	+	46.7597i	1.19779	+	2.07463i
$509$	14.9084	+	25.8221i	0.660803	+	1.14454i	0.980405	+	0.196993i	$0.0631175\pi$
$509$	14.9084	+	25.8221i	0.660803	+	1.14454i	−0.319602	+	0.947552i	$0.603549\pi$
$510$	−1.47308	+	5.98440i	−0.0652292	+	0.264994i
$511$	−12.4555	+	21.5736i	−0.551001	+	0.954362i
$512$	148.087			6.54458
$513$	−11.7042	+	13.2357i	−0.516752	+	0.584371i
$514$	−43.7807			−1.93108
$515$	−1.87022	+	3.23931i	−0.0824116	+	0.142741i
$516$	3.81522	−	15.4993i	0.167956	−	0.682321i
$517$	2.47108	+	4.28004i	0.108678	+	0.188236i
$518$	6.36118	+	11.0179i	0.279494	+	0.484098i
$519$	−2.42173	−	2.32468i	−0.106302	−	0.102042i
$520$	−4.41304	+	7.64362i	−0.193525	+	0.335195i
$521$	33.7507			1.47864			0.739322	−	0.673352i	$-0.235146\pi$
$521$	33.7507			1.47864			0.739322	+	0.673352i	$0.235146\pi$
$522$	−0.407992	−	9.97277i	−0.0178573	−	0.436496i
$523$	−39.8074			−1.74065			−0.870327	−	0.492474i	$-0.836093\pi$
$523$	−39.8074			−1.74065			−0.870327	+	0.492474i	$0.836093\pi$
$524$	−41.6144	+	72.0783i	−1.81793	+	3.14876i
$525$	−17.8456	+	5.17496i	−0.778848	+	0.225854i
$526$	2.27265	+	3.93635i	0.0990923	+	0.171633i
$527$	−4.80731	−	8.32650i	−0.209410	−	0.362708i
$528$	27.7912	−	8.05903i	1.20946	−	0.350724i
$529$	11.0181	−	19.0838i	0.479046	−	0.829732i
$530$	−13.4841			−0.585713
$531$	−0.117071	−	2.86164i	−0.00508046	−	0.124184i
$532$	−49.1510			−2.13096
$533$	2.86647	−	4.96488i	0.124161	−	0.215053i
$534$	43.9425	+	42.1816i	1.90158	+	1.82537i
$535$	−7.66054	−	13.2684i	−0.331194	−	0.573645i
$536$	69.9598	+	121.174i	3.02180	+	5.23392i
$537$	6.77071	−	27.5060i	0.292178	−	1.18697i
$538$	26.3989	−	45.7243i	1.13814	−	1.97131i
$539$	0.751708			0.0323783
$540$	−7.94212	−	23.7172i	−0.341774	−	1.02062i
$541$	16.4801			0.708533			0.354267	−	0.935144i	$-0.384731\pi$
$541$	16.4801			0.708533			0.354267	+	0.935144i	$0.384731\pi$
$542$	14.3104	−	24.7863i	0.614684	−	1.06466i
$543$	−6.12578	+	24.8860i	−0.262883	+	1.06796i
$544$	22.6534	+	39.2368i	0.971255	+	1.68226i
$545$	−3.29459	−	5.70640i	−0.141125	−	0.244435i
$546$	−8.68456	−	8.33654i	−0.371665	−	0.356771i
$547$	−16.0035	+	27.7189i	−0.684262	+	1.18518i	0.289406	+	0.957206i	$0.406542\pi$
$547$	−16.0035	+	27.7189i	−0.684262	+	1.18518i	−0.973668	+	0.227970i	$0.926791\pi$
$548$	74.0870			3.16484
$549$	−22.5459	+	14.2764i	−0.962234	+	0.609303i
$550$	11.0887			0.472822
$551$	2.02358	−	3.50494i	0.0862074	−	0.149316i
$552$	−17.4094	+	5.04846i	−0.740993	+	0.214877i
$553$	12.5882	+	21.8034i	0.535305	+	0.927175i
$554$	10.2172	+	17.6967i	0.434088	+	0.751862i
$555$	−2.52125	+	0.731124i	−0.107021	+	0.0310345i
$556$	45.9773	−	79.6350i	1.94987	−	3.37728i
$557$	1.65300			0.0700397			0.0350198	−	0.999387i	$-0.488851\pi$
$557$	1.65300			0.0700397			0.0350198	+	0.999387i	$0.488851\pi$
$558$	46.4508	+	24.3431i	1.96642	+	1.03053i
$559$	1.58522			0.0670477
$560$	18.7034	−	32.3953i	0.790363	−	1.36895i
$561$	1.76631	+	1.69552i	0.0745735	+	0.0715850i
$562$	−36.5669	−	63.3357i	−1.54248	−	2.67165i
$563$	−15.6527	−	27.1113i	−0.659682	−	1.14260i	−0.980698	−	0.195529i	$-0.937358\pi$
$563$	−15.6527	−	27.1113i	−0.659682	−	1.14260i	0.321016	−	0.947074i	$-0.395976\pi$
$564$	12.9365	−	52.5544i	0.544723	−	2.21294i
$565$	−5.13621	+	8.89618i	−0.216082	+	0.374265i
$566$	14.3221			0.602002
$567$	22.3033	−	1.82794i	0.936650	−	0.0767663i
$568$	56.2681			2.36096
$569$	21.8313	−	37.8130i	0.915217	−	1.58520i	0.108634	−	0.994082i	$-0.465352\pi$
$569$	21.8313	−	37.8130i	0.915217	−	1.58520i	0.806583	−	0.591121i	$-0.201314\pi$
$570$	3.25802	−	13.2357i	0.136463	−	0.554383i
$571$	0.330617	+	0.572646i	0.0138359	+	0.0239645i	0.872860	−	0.487970i	$-0.162262\pi$
$571$	0.330617	+	0.572646i	0.0138359	+	0.0239645i	−0.859025	+	0.511934i	$0.828929\pi$
$572$	2.67263	+	4.62914i	0.111748	+	0.193554i
$573$	27.5390	+	26.4354i	1.15046	+	1.10435i
$574$	−19.9228	+	34.5073i	−0.831562	+	1.44031i
$575$	−4.23579			−0.176645
$576$	−122.328	−	64.1072i	−5.09699	−	2.67113i
$577$	−26.6761			−1.11054			−0.555270	−	0.831670i	$-0.687385\pi$
$577$	−26.6761			−1.11054			−0.555270	+	0.831670i	$0.687385\pi$
$578$	20.4563	−	35.4313i	0.850869	−	1.47375i
$579$	−5.05443	+	1.46571i	−0.210055	+	0.0609127i
$580$	2.86461	+	4.96165i	0.118946	+	0.206021i
$581$	−2.89068	−	5.00680i	−0.119925	−	0.207717i
$582$	36.6615	−	10.6313i	1.51967	−	0.440680i
$583$	−2.67843	+	4.63917i	−0.110929	+	0.192135i
$584$	−106.797			−4.41928
$585$	2.09861	−	1.32887i	0.0867667	−	0.0549422i
$586$	28.2063			1.16519
$587$	0.954026	−	1.65242i	0.0393769	−	0.0682028i	−0.845665	−	0.533714i	$-0.820796\pi$
$587$	0.954026	−	1.65242i	0.0393769	−	0.0682028i	0.885042	+	0.465511i	$0.154129\pi$
$588$	−5.93880	−	5.70081i	−0.244912	−	0.235097i
$589$	10.6323	+	18.4157i	0.438098	+	0.758807i
$590$	1.10477	+	1.91352i	0.0454827	+	0.0787783i
$591$	−9.95570	+	40.4450i	−0.409523	+	1.66369i
$592$	−16.6296	+	28.8034i	−0.683473	+	1.18381i
$593$	−15.0838			−0.619419			−0.309710	−	0.950831i	$-0.600232\pi$
$593$	−15.0838			−0.619419			−0.309710	+	0.950831i	$0.600232\pi$
$594$	−13.0873	−	2.65931i	−0.536980	−	0.109113i
$595$	3.16513			0.129758
$596$	−6.19114	+	10.7234i	−0.253599	+	0.439246i
$597$	−6.29761	+	25.5840i	−0.257744	+	1.04709i
$598$	−1.37215	−	2.37664i	−0.0561116	−	0.0971881i
$599$	0.823973	+	1.42716i	0.0336666	+	0.0583123i	0.882368	−	0.470560i	$-0.155948\pi$
$599$	0.823973	+	1.42716i	0.0336666	+	0.0583123i	−0.848701	+	0.528873i	$0.822615\pi$
$600$	−57.4665	−	55.1636i	−2.34606	−	2.25204i
$601$	−4.91508	+	8.51316i	−0.200490	+	0.347259i	−0.948686	−	0.316218i	$-0.897587\pi$
$601$	−4.91508	+	8.51316i	−0.200490	+	0.347259i	0.748196	+	0.663477i	$0.230920\pi$
$602$	−11.0177			−0.449050
$603$	−1.60963	−	39.3452i	−0.0655494	−	1.60226i
$604$	85.3517			3.47291
$605$	4.20393	−	7.28143i	0.170914	−	0.296032i
$606$	70.3032	−	20.3869i	2.85587	−	0.828159i
$607$	−3.81004	−	6.59918i	−0.154645	−	0.267852i	0.778285	−	0.627911i	$-0.216090\pi$
$607$	−3.81004	−	6.59918i	−0.154645	−	0.267852i	−0.932930	+	0.360059i	$0.882757\pi$
$608$	−50.1025	−	86.7801i	−2.03193	−	3.51940i
$609$	−4.92315	+	1.42764i	−0.199496	+	0.0578508i
$610$	10.2938	−	17.8293i	0.416783	−	0.721889i
$611$	5.37508			0.217453
$612$	−1.09602	−	26.7907i	−0.0443040	−	1.08295i
$613$	20.7592			0.838458			0.419229	−	0.907881i	$-0.362300\pi$
$613$	20.7592			0.838458			0.419229	+	0.907881i	$0.362300\pi$
$614$	−20.8813	+	36.1675i	−0.842701	+	1.45960i
$615$	−5.93125	−	5.69356i	−0.239171	−	0.229587i
$616$	−12.1851	−	21.1051i	−0.490950	−	0.850350i
$617$	10.0058	+	17.3306i	0.402819	+	0.697702i	0.994065	−	0.108789i	$-0.0346972\pi$
$617$	10.0058	+	17.3306i	0.402819	+	0.697702i	−0.591246	+	0.806491i	$0.701364\pi$
$618$	5.22775	−	21.2377i	0.210291	−	0.854307i
$619$	6.38297	−	11.0556i	0.256553	−	0.444363i	−0.708763	−	0.705447i	$-0.750746\pi$
$619$	6.38297	−	11.0556i	0.256553	−	0.444363i	0.965316	+	0.261083i	$0.0840798\pi$
$620$	−30.1026			−1.20895
$621$	4.99927	+	1.01584i	0.200614	+	0.0407641i
$622$	−21.0075			−0.842323
$623$	15.6411	−	27.0912i	0.626648	−	1.08539i
$624$	7.52213	−	30.5586i	0.301126	−	1.22332i
$625$	−7.59329	−	13.1520i	−0.303731	−	0.526078i
$626$	−10.3656	−	17.9537i	−0.414291	−	0.717573i
$627$	−3.90654	−	3.74999i	−0.156012	−	0.149760i
$628$	−30.6339	+	53.0595i	−1.22243	+	2.11731i
$629$	−2.81419			−0.112209
$630$	−14.5859	+	9.23605i	−0.581117	+	0.367973i
$631$	−41.7922			−1.66372			−0.831860	−	0.554985i	$-0.812724\pi$
$631$	−41.7922			−1.66372			−0.831860	+	0.554985i	$0.812724\pi$
$632$	−53.9671	+	93.4737i	−2.14669	+	3.71818i
$633$	2.32110	−	0.673083i	0.0922554	−	0.0267527i
$634$	−16.3825	−	28.3753i	−0.650631	−	1.12693i
$635$	3.84501	+	6.65975i	0.152585	+	0.264284i
$636$	56.3432	−	16.3387i	2.23415	−	0.647871i
$637$	0.408777	−	0.708023i	0.0161963	−	0.0280529i
$638$	3.05907			0.121110
$639$	−14.0263	−	7.35067i	−0.554874	−	0.290788i
$640$	57.7465			2.28263
$641$	17.5062	−	30.3216i	0.691452	−	1.19763i	−0.279910	−	0.960026i	$-0.590305\pi$
$641$	17.5062	−	30.3216i	0.691452	−	1.19763i	0.971362	−	0.237604i	$-0.0763621\pi$
$642$	64.6300	+	62.0400i	2.55074	+	2.44852i
$643$	−4.63898	−	8.03495i	−0.182944	−	0.316868i	0.759938	−	0.649996i	$-0.225229\pi$
$643$	−4.63898	−	8.03495i	−0.182944	−	0.316868i	−0.942882	+	0.333128i	$0.891896\pi$
$644$	7.09574	+	12.2902i	0.279611	+	0.484301i
$645$	0.543383	−	2.20749i	0.0213957	−	0.0869200i
$646$	7.30627	−	12.6548i	0.287461	−	0.497898i
$647$	−17.1133			−0.672794			−0.336397	−	0.941720i	$-0.609208\pi$
$647$	−17.1133			−0.672794			−0.336397	+	0.941720i	$0.609208\pi$
$648$	54.5951	+	78.8882i	2.14470	+	3.09902i
$649$	0.877786			0.0344561
$650$	6.02999	−	10.4443i	0.236516	−	0.409657i
$651$	6.43749	−	26.1523i	0.252305	−	1.02499i
$652$	7.97606	+	13.8149i	0.312367	+	0.541035i
$653$	−22.1978	−	38.4478i	−0.868668	−	1.50458i	−0.863358	−	0.504592i	$-0.831643\pi$
$653$	−22.1978	−	38.4478i	−0.868668	−	1.50458i	−0.00531024	−	0.999986i	$-0.501690\pi$
$654$	27.7956	+	26.6817i	1.08689	+	1.04334i
$655$	−5.92693	+	10.2658i	−0.231584	+	0.401116i
$656$	−104.166			−4.06699
$657$	26.6220	+	13.9515i	1.03862	+	0.544302i
$658$	−37.3584			−1.45638
$659$	−8.11972	+	14.0638i	−0.316299	+	0.547846i	−0.979713	−	0.200407i	$-0.935774\pi$
$659$	−8.11972	+	14.0638i	−0.316299	+	0.547846i	0.663414	+	0.748253i	$0.269107\pi$
$660$	7.36241	−	2.13499i	0.286582	−	0.0831043i
$661$	−13.3405	−	23.1063i	−0.518883	−	0.898732i	−0.999759	−	0.0219437i	$-0.993015\pi$
$661$	−13.3405	−	23.1063i	−0.518883	−	0.898732i	0.480876	−	0.876789i	$-0.340319\pi$
$662$	5.26521	+	9.11961i	0.204638	+	0.354444i
$663$	2.55750	−	0.741636i	0.0993251	−	0.0288028i
$664$	12.3927	−	21.4647i	0.480928	−	0.832992i
$665$	−7.00033			−0.271461
$666$	12.9687	−	8.21198i	0.502526	−	0.318208i
$667$	−1.16855			−0.0452463
$668$	−33.9693	+	58.8366i	−1.31431	+	2.27646i
$669$	2.92621	+	2.80895i	0.113134	+	0.108600i
$670$	15.1897	+	26.3093i	0.586829	+	1.01642i
$671$	−4.08942	−	7.08308i	−0.157870	−	0.273439i
$672$	−30.3353	+	123.237i	−1.17021	+	4.75397i
$673$	−9.68028	+	16.7667i	−0.373147	+	0.646310i	−0.990048	−	0.140731i	$-0.955055\pi$
$673$	−9.68028	+	16.7667i	−0.373147	+	0.646310i	0.616901	+	0.787041i	$0.288388\pi$
$674$	72.6412			2.79803
$675$	7.11870	+	21.2582i	0.273999	+	0.818230i
$676$	5.81349			0.223596
$677$	8.22920	−	14.2534i	0.316274	−	0.547802i	−0.663434	−	0.748235i	$-0.730902\pi$
$677$	8.22920	−	14.2534i	0.316274	−	0.547802i	0.979707	+	0.200433i	$0.0642348\pi$
$678$	14.3571	−	58.3255i	0.551379	−	2.23998i
$679$	−9.80190	−	16.9774i	−0.376162	−	0.651532i
$680$	6.78464	+	11.7513i	0.260179	+	0.450643i
$681$	−9.66447	−	9.27718i	−0.370343	−	0.355502i
$682$	−8.03653	+	13.9197i	−0.307735	+	0.533012i
$683$	14.3927			0.550720			0.275360	−	0.961341i	$-0.411203\pi$
$683$	14.3927			0.550720			0.275360	+	0.961341i	$0.411203\pi$
$684$	2.42407	+	59.2530i	0.0926867	+	2.26559i
$685$	10.5518			0.403165
$686$	−27.1671	+	47.0548i	−1.03725	+	1.79656i
$687$	−25.4783	+	7.38832i	−0.972058	+	0.281882i
$688$	−14.4015	−	24.9441i	−0.549052	−	0.950985i
$689$	2.91304	+	5.04554i	0.110978	+	0.192220i
$690$	−3.77993	+	1.09612i	−0.143900	+	0.0417287i
$691$	−3.02997	+	5.24806i	−0.115266	+	0.199646i	−0.917886	−	0.396844i	$-0.870105\pi$
$691$	−3.02997	+	5.24806i	−0.115266	+	0.199646i	0.802620	+	0.596490i	$0.203439\pi$
$692$	−11.2672			−0.428315
$693$	0.280354	+	6.85284i	0.0106498	+	0.260318i
$694$	−20.8682			−0.792147
$695$	6.54832	−	11.3420i	0.248392	−	0.430227i
$696$	−15.8535	−	15.2182i	−0.600926	−	0.576844i
$697$	−4.40693	−	7.63303i	−0.166924	−	0.289122i
$698$	15.7555	+	27.2894i	0.596356	+	1.03292i
$699$	1.57979	−	6.41790i	0.0597532	−	0.242747i
$700$	−31.1825	+	54.0097i	−1.17859	+	2.04138i
$701$	−25.7892			−0.974045			−0.487023	−	0.873389i	$-0.661917\pi$
$701$	−25.7892			−0.974045			−0.487023	+	0.873389i	$0.661917\pi$
$702$	−9.62163	+	10.8806i	−0.363145	+	0.410664i
$703$	6.22415			0.234748
$704$	21.1641	−	36.6573i	0.797652	−	1.38157i
$705$	1.84247	−	7.48505i	0.0693916	−	0.281903i
$706$	−30.2035	−	52.3140i	−1.13672	−	1.96886i
$707$	−18.7964	−	32.5563i	−0.706912	−	1.22441i
$708$	−6.93487	−	6.65696i	−0.260628	−	0.250184i
$709$	23.3481	−	40.4402i	0.876858	−	1.51876i	0.0220870	−	0.999756i	$-0.492969\pi$
$709$	23.3481	−	40.4402i	0.876858	−	1.51876i	0.854771	−	0.519006i	$-0.173698\pi$
$710$	12.2169			0.458494
$711$	25.6638	−	16.2508i	0.962469	−	0.609452i
$712$	134.110			5.02600
$713$	3.06990	−	5.31722i	0.114969	−	0.199132i
$714$	−17.7754	+	5.15458i	−0.665226	+	0.192905i
$715$	0.380650	+	0.659305i	0.0142355	+	0.0246566i
$716$	−47.5387	−	82.3395i	−1.77661	−	3.07717i
$717$	17.7523	−	5.14791i	0.662973	−	0.192252i
$718$	−39.0891	+	67.7042i	−1.45879	+	2.52670i
$719$	45.7593			1.70654			0.853268	−	0.521473i	$-0.174617\pi$
$719$	45.7593			1.70654			0.853268	+	0.521473i	$0.174617\pi$
$720$	−39.9759	−	20.9498i	−1.48981	−	0.780754i
$721$	−11.2326			−0.418323
$722$	10.3957	−	18.0059i	0.386888	−	0.670109i
$723$	1.50056	+	1.44043i	0.0558064	+	0.0535700i
$724$	43.0106	+	74.4966i	1.59848	+	2.76864i
$725$	−2.56761	−	4.44724i	−0.0953587	−	0.165166i
$726$	−11.7511	+	47.7388i	−0.436124	+	1.77175i
$727$	−2.81788	+	4.88071i	−0.104509	+	0.181016i	−0.913538	−	0.406754i	$-0.866661\pi$
$727$	−2.81788	+	4.88071i	−0.104509	+	0.181016i	0.809028	+	0.587770i	$0.199994\pi$
$728$	−26.5048			−0.982335
$729$	−3.30361	−	26.7971i	−0.122356	−	0.992486i
$730$	−23.1877			−0.858216
$731$	1.21856	−	2.11061i	0.0450702	−	0.0780639i
$732$	−21.4086	+	86.9726i	−0.791286	+	3.21460i
$733$	20.1805	+	34.9536i	0.745383	+	1.29104i	0.950016	+	0.312202i	$0.101067\pi$
$733$	20.1805	+	34.9536i	0.745383	+	1.29104i	−0.204633	+	0.978839i	$0.565600\pi$
$734$	−14.9286	−	25.8570i	−0.551024	−	0.954401i
$735$	−0.845834	−	0.811938i	−0.0311990	−	0.0299488i
$736$	−14.4662	+	25.0562i	−0.533232	+	0.923585i
$737$	12.0688			0.444562
$738$	42.5822	+	22.3157i	1.56747	+	0.821452i
$739$	−22.9326			−0.843590			−0.421795	−	0.906691i	$-0.638600\pi$
$739$	−22.9326			−0.843590			−0.421795	+	0.906691i	$0.638600\pi$
$740$	−4.40550	+	7.63055i	−0.161949	+	0.280504i
$741$	−5.65643	+	1.64028i	−0.207794	+	0.0602572i
$742$	−20.2465	−	35.0680i	−0.743272	−	1.28739i
$743$	−2.76237	−	4.78457i	−0.101342	−	0.175529i	0.810896	−	0.585190i	$-0.198980\pi$
$743$	−2.76237	−	4.78457i	−0.101342	−	0.175529i	−0.912238	+	0.409661i	$0.865647\pi$
$744$	110.896	−	32.1582i	4.06565	−	1.17898i
$745$	−0.881773	+	1.52728i	−0.0323057	+	0.0559551i
$746$	−39.7574			−1.45562
$747$	−5.89328	+	3.73173i	−0.215624	+	0.136537i
$748$	8.21784			0.300474
$749$	23.0047	−	39.8453i	0.840573	−	1.45591i
$750$	−26.9369	−	25.8574i	−0.983596	−	0.944180i
$751$	11.4040	+	19.7523i	0.416139	+	0.720773i	0.995547	−	0.0942640i	$-0.0300498\pi$
$751$	11.4040	+	19.7523i	0.416139	+	0.720773i	−0.579409	+	0.815037i	$0.696716\pi$
$752$	−48.8318	−	84.5792i	−1.78071	−	3.08428i
$753$	6.47533	−	26.3060i	0.235974	−	0.958644i
$754$	1.66352	−	2.88130i	0.0605818	−	0.104931i
$755$	12.1562			0.442410
$756$	49.7557	−	56.2664i	1.80960	−	2.04639i
$757$	−0.0394090			−0.00143235			−0.000716173	−	1.00000i	$-0.500228\pi$
$757$	−0.0394090			−0.00143235			−0.000716173		1.00000i	$0.500228\pi$
$758$	−42.2205	+	73.1281i	−1.53352	+	2.65613i
$759$	−0.373711	+	1.51820i	−0.0135649	+	0.0551072i
$760$	−15.0056	−	25.9905i	−0.544310	−	0.942773i
$761$	−6.41693	−	11.1145i	−0.232614	−	0.402899i	0.725963	−	0.687734i	$-0.241394\pi$
$761$	−6.41693	−	11.1145i	−0.232614	−	0.402899i	−0.958576	+	0.284835i	$0.908061\pi$
$762$	−32.4393	−	31.1394i	−1.17515	−	1.12806i
$763$	9.89370	−	17.1364i	0.358176	−	0.620379i
$764$	128.127			4.63546
$765$	−0.156101	−	3.81566i	−0.00564384	−	0.137955i
$766$	54.2905			1.96160
$767$	0.477338	−	0.826774i	0.0172357	−	0.0298531i
$768$	−171.141	+	49.6283i	−6.17552	+	1.79081i
$769$	−0.424306	−	0.734919i	−0.0153009	−	0.0265019i	0.858274	−	0.513192i	$-0.171537\pi$
$769$	−0.424306	−	0.734919i	−0.0153009	−	0.0265019i	−0.873574	+	0.486691i	$0.838204\pi$
$770$	−2.64562	−	4.58236i	−0.0953417	−	0.165137i
$771$	26.0548	−	7.55550i	0.938341	−	0.272105i
$772$	−8.83184	+	15.2972i	−0.317865	+	0.550558i
$773$	−36.0339			−1.29605			−0.648024	−	0.761620i	$-0.724405\pi$
$773$	−36.0339			−1.29605			−0.648024	+	0.761620i	$0.724405\pi$
$774$	0.543383	+	13.2822i	0.0195315	+	0.477419i
$775$	26.9816			0.969208
$776$	42.0218	−	72.7840i	1.50850	−	2.61279i
$777$	−5.68709	−	5.45919i	−0.204023	−	0.195847i
$778$	2.81140	+	4.86948i	0.100793	+	0.174579i
$779$	9.74682	+	16.8820i	0.349216	+	0.604860i
$780$	1.99275	−	8.09555i	0.0713520	−	0.289867i
$781$	2.42672	−	4.20320i	0.0868348	−	0.150402i
$782$	−4.21911			−0.150875
$783$	1.96386	+	5.86459i	0.0701828	+	0.209584i
$784$	−14.8547			−0.530525
$785$	−4.36304	+	7.55700i	−0.155723	+	0.269721i
$786$	16.5673	−	67.3048i	0.590937	−	2.40068i
$787$	8.83804	+	15.3079i	0.315042	+	0.545669i	0.979446	−	0.201704i	$-0.0646480\pi$
$787$	8.83804	+	15.3079i	0.315042	+	0.545669i	−0.664404	+	0.747373i	$0.731315\pi$
$788$	69.9014	+	121.073i	2.49013	+	4.31304i
$789$	−2.03182	−	1.95040i	−0.0723348	−	0.0694360i
$790$	−11.7173	+	20.2950i	−0.416885	+	0.722065i
$791$	−30.8482			−1.09684
$792$	−24.8419	+	15.7303i	−0.882719	+	0.558953i
$793$	−8.89527			−0.315880
$794$	−28.9567	+	50.1545i	−1.02764	+	1.77992i
$795$	8.02469	−	2.32704i	0.284606	−	0.0825315i
$796$	44.2170	+	76.5862i	1.56723	+	2.71452i
$797$	13.3001	+	23.0365i	0.471114	+	0.815993i	0.999454	−	0.0330394i	$-0.0105187\pi$
$797$	13.3001	+	23.0365i	0.471114	+	0.815993i	−0.528340	+	0.849033i	$0.677185\pi$
$798$	39.3138	−	11.4004i	1.39169	−	0.403570i
$799$	4.13184	−	7.15656i	0.146174	−	0.253181i
$800$	−127.145			−4.49525
$801$	−33.4306	−	17.5197i	−1.18121	−	0.619029i
$802$	−50.7745			−1.79291
$803$	−4.60590	+	7.97766i	−0.162539	+	0.281526i
$804$	−95.3489	−	91.5279i	−3.36270	−	3.22794i
$805$	1.01061	+	1.75043i	0.0356193	+	0.0616945i
$806$	8.74050	+	15.1390i	0.307871	+	0.533248i
$807$	−7.81964	+	31.7673i	−0.275264	+	1.11826i
$808$	80.5824	−	139.573i	2.83488	−	4.91015i
$809$	−11.8241			−0.415713			−0.207857	−	0.978159i	$-0.566649\pi$
$809$	−11.8241			−0.415713			−0.207857	+	0.978159i	$0.566649\pi$
$810$	11.8537	+	17.1282i	0.416496	+	0.601825i
$811$	−23.5042			−0.825345			−0.412673	−	0.910879i	$-0.635405\pi$
$811$	−23.5042			−0.825345			−0.412673	+	0.910879i	$0.635405\pi$
$812$	−8.60245	+	14.8999i	−0.301887	+	0.522883i
$813$	−4.23889	+	17.2205i	−0.148664	+	0.603949i
$814$	2.35228	+	4.07428i	0.0824475	+	0.142803i
$815$	1.13599	+	1.96759i	0.0397920	+	0.0689218i
$816$	−34.9045	−	33.5057i	−1.22190	−	1.17293i
$817$	−2.69510	+	4.66805i	−0.0942896	+	0.163314i
$818$	91.2244			3.18959
$819$	6.60705	+	3.46250i	0.230869	+	0.120990i
$820$	−27.5955			−0.963676
$821$	21.9801	−	38.0706i	0.767111	−	1.32867i	−0.172013	−	0.985095i	$-0.555027\pi$
$821$	21.9801	−	38.0706i	0.767111	−	1.32867i	0.939123	−	0.343580i	$-0.111640\pi$
$822$	−59.2591	+	17.1842i	−2.06690	+	0.599369i
$823$	16.0977	+	27.8820i	0.561130	+	0.971906i	0.997398	+	0.0720892i	$0.0229666\pi$
$823$	16.0977	+	27.8820i	0.561130	+	0.971906i	−0.436268	+	0.899817i	$0.643700\pi$
$824$	−24.0777	−	41.7037i	−0.838785	−	1.45282i
$825$	−6.59910	+	1.91364i	−0.229751	+	0.0666243i
$826$	−3.31764	+	5.74632i	−0.115435	+	0.199940i
$827$	10.2409			0.356112			0.178056	−	0.984020i	$-0.443019\pi$
$827$	10.2409			0.356112			0.178056	+	0.984020i	$0.443019\pi$
$828$	14.4662	−	9.16027i	0.502736	−	0.318341i
$829$	−30.1853			−1.04838			−0.524189	−	0.851602i	$-0.675631\pi$
$829$	−30.1853			−1.04838			−0.524189	+	0.851602i	$0.675631\pi$
$830$	2.69070	−	4.66043i	0.0933955	−	0.161766i
$831$	−9.13450	−	8.76844i	−0.316872	−	0.304174i
$832$	−23.0180	−	39.8683i	−0.798005	−	1.38219i
$833$	−0.628456	−	1.08852i	−0.0217747	−	0.0377149i
$834$	−18.3043	+	74.3611i	−0.633825	+	2.57491i
$835$	−4.83808	+	8.37981i	−0.167429	+	0.289995i
$836$	−18.1754			−0.628610
$837$	−31.8449	−	6.47079i	−1.10072	−	0.223663i
$838$	−75.6354			−2.61278
$839$	−24.4762	+	42.3940i	−0.845011	+	1.46360i	0.0406006	+	0.999175i	$0.487073\pi$
$839$	−24.4762	+	42.3940i	−0.845011	+	1.46360i	−0.885612	+	0.464427i	$0.846260\pi$
$840$	−9.08535	+	36.9092i	−0.313474	+	1.27349i
$841$	13.7917	+	23.8879i	0.475575	+	0.823719i
$842$	−37.4294	−	64.8296i	−1.28990	−	2.23418i
$843$	32.6919	+	31.3818i	1.12597	+	1.08085i
$844$	4.05577	−	7.02480i	0.139605	−	0.241803i
$845$	0.827986			0.0284836
$846$	1.84247	+	45.0366i	0.0633456	+	1.54839i
$847$	25.2489			0.867563
$848$	52.9291	−	91.6759i	1.81759	−	3.14816i
$849$	−8.52337	+	2.47165i	−0.292521	+	0.0848267i
$850$	−9.27054	−	16.0570i	−0.317977	−	0.550752i
$851$	−0.898557	−	1.55635i	−0.0308021	−	0.0533509i
$852$	−51.0483	+	14.8032i	−1.74889	+	0.507151i
$853$	−1.11612	+	1.93317i	−0.0382151	+	0.0661904i	−0.884500	−	0.466540i	$-0.845501\pi$
$853$	−1.11612	+	1.93317i	−0.0382151	+	0.0661904i	0.846285	+	0.532730i	$0.178834\pi$
$854$	61.8247			2.11560
$855$	0.345249	+	8.43910i	0.0118073	+	0.288611i
$856$	197.247			6.74178
$857$	15.4333	−	26.7312i	0.527191	−	0.913121i	−0.472307	−	0.881434i	$-0.656579\pi$
$857$	15.4333	−	26.7312i	0.527191	−	0.913121i	0.999498	−	0.0316870i	$-0.0100880\pi$
$858$	−3.21144	−	3.08275i	−0.109637	−	0.105243i
$859$	−15.0620	−	26.0881i	−0.513908	−	0.890115i	−0.999870	−	0.0161347i	$-0.994864\pi$
$859$	−15.0620	−	26.0881i	−0.513908	−	0.890115i	0.485962	−	0.873980i	$-0.338469\pi$
$860$	−3.81522	−	6.60816i	−0.130098	−	0.225336i
$861$	5.90135	−	23.9742i	0.201117	−	0.817040i
$862$	52.1602	−	90.3440i	1.77658	−	3.07713i
$863$	−4.66893			−0.158932			−0.0794661	−	0.996838i	$-0.525322\pi$
$863$	−4.66893			−0.158932			−0.0794661	+	0.996838i	$0.525322\pi$
$864$	150.062	+	30.4922i	5.10522	+	1.03736i
$865$	−1.60473			−0.0545626
$866$	−6.53952	+	11.3268i	−0.222222	+	0.384900i
$867$	−6.05936	+	24.6162i	−0.205787	+	0.836009i
$868$	−45.1992	−	78.2873i	−1.53416	−	2.65724i
$869$	4.65496	+	8.06263i	0.157909	+	0.273506i
$870$	−3.44212	−	3.30418i	−0.116699	−	0.112022i
$871$	6.56302	−	11.3675i	0.222379	−	0.385172i
$872$	84.8308			2.87273
$873$	−19.9833	+	12.6538i	−0.676333	+	0.428266i
$874$	9.33143			0.315640
$875$	−9.58804	+	16.6070i	−0.324135	+	0.561418i
$876$	96.8896	−	28.0965i	3.27360	−	0.949293i
$877$	−8.23844	−	14.2694i	−0.278192	−	0.481843i	0.692743	−	0.721184i	$-0.256402\pi$
$877$	−8.23844	−	14.2694i	−0.278192	−	0.481843i	−0.970936	+	0.239341i	$0.923069\pi$
$878$	28.4156	+	49.2173i	0.958981	+	1.66100i
$879$	−16.7862	+	4.86774i	−0.566184	+	0.164185i
$880$	6.91629	−	11.9794i	0.233148	−	0.403824i
$881$	33.5567			1.13055			0.565276	−	0.824902i	$-0.308770\pi$
$881$	33.5567			1.13055			0.565276	+	0.824902i	$0.308770\pi$
$882$	6.07249	+	3.18236i	0.204471	+	0.107156i
$883$	34.2126			1.15135			0.575673	−	0.817680i	$-0.304740\pi$
$883$	34.2126			1.15135			0.575673	+	0.817680i	$0.304740\pi$
$884$	4.46884	−	7.74026i	0.150303	−	0.260333i
$885$	−0.987699	−	0.948118i	−0.0332011	−	0.0318706i
$886$	−0.766408	−	1.32746i	−0.0257480	−	0.0445968i
$887$	6.93269	+	12.0078i	0.232777	+	0.403181i	0.958624	−	0.284674i	$-0.0918855\pi$
$887$	6.93269	+	12.0078i	0.232777	+	0.403181i	−0.725847	+	0.687856i	$0.758552\pi$
$888$	8.07799	−	32.8168i	0.271080	−	1.10126i
$889$	−11.5466	+	19.9993i	−0.387261	+	0.670755i
$890$	29.1181			0.976041
$891$	8.24748	−	0.675949i	0.276301	−	0.0226452i
$892$	13.6144			0.455843
$893$	−9.13840	+	15.8282i	−0.305805	+	0.529670i
$894$	2.46479	−	10.0132i	0.0824348	−	0.334891i
$895$	−6.77071	−	11.7272i	−0.226320	−	0.391997i
$896$	86.7067	+	150.180i	2.89667	+	5.01718i
$897$	1.22675	+	1.17759i	0.0409600	+	0.0393185i
$898$	21.9585	−	38.0333i	0.732766	−	1.26919i
$899$	7.44353			0.248255
$900$	66.6482	+	34.9278i	2.22161	+	1.16426i
$901$	8.95706			0.298403
$902$	−7.36721	+	12.7604i	−0.245301	+	0.424874i
$903$	6.55689	−	1.90140i	0.218200	−	0.0632745i
$904$	−66.1249	−	114.532i	−2.19928	−	3.80926i
$905$	6.12578	+	10.6102i	0.203628	+	0.352694i
$906$	−68.2693	+	19.7971i	−2.26810	+	0.657713i
$907$	−7.85818	+	13.6108i	−0.260927	+	0.451938i	−0.966488	−	0.256710i	$-0.917361\pi$
$907$	−7.85818	+	13.6108i	−0.260927	+	0.451938i	0.705562	+	0.708648i	$0.250695\pi$
$908$	−44.9645			−1.49220
$909$	−38.3206	+	24.2653i	−1.27101	+	0.804829i
$910$	−5.75474			−0.190768
$911$	−13.2464	+	22.9434i	−0.438871	+	0.760147i	−0.997603	−	0.0692014i	$-0.977955\pi$
$911$	−13.2464	+	22.9434i	−0.438871	+	0.760147i	0.558732	+	0.829349i	$0.311288\pi$
$912$	77.1983	+	74.1046i	2.55629	+	2.45385i
$913$	−1.06894	−	1.85145i	−0.0353766	−	0.0612741i
$914$	−43.9004	−	76.0377i	−1.45210	−	2.51510i
$915$	−3.04913	+	12.3871i	−0.100801	+	0.409504i
$916$	−44.5194	+	77.1099i	−1.47096	+	2.54778i
$917$	−35.5973			−1.17553
$918$	7.09067	+	21.1745i	0.234027	+	0.698863i
$919$	−48.5748			−1.60233			−0.801167	−	0.598440i	$-0.795787\pi$
$919$	−48.5748			−1.60233			−0.801167	+	0.598440i	$0.795787\pi$
$920$	−4.33260	+	7.50429i	−0.142842	+	0.247409i
$921$	6.18526	−	25.1276i	0.203811	−	0.827984i
$922$	−46.2788	−	80.1573i	−1.52411	−	2.63984i
$923$	−2.63929	−	4.57138i	−0.0868733	−	0.150469i
$924$	16.6071	+	15.9416i	0.546335	+	0.524441i
$925$	3.94875	−	6.83943i	0.129834	−	0.224879i
$926$	−49.6470			−1.63150
$927$	0.553978	+	13.5412i	0.0181950	+	0.444751i
$928$	−35.0760			−1.15143
$929$	2.34708	−	4.06526i	0.0770052	−	0.133377i	−0.824951	−	0.565204i	$-0.808798\pi$
$929$	2.34708	−	4.06526i	0.0770052	−	0.133377i	0.901956	+	0.431827i	$0.142131\pi$
$930$	24.0778	−	6.98219i	0.789542	−	0.228955i
$931$	1.38996	+	2.40748i	0.0455540	+	0.0789019i
$932$	−11.0921	−	19.2121i	−0.363334	−	0.629312i
$933$	12.5020	−	3.62539i	0.409297	−	0.118690i
$934$	−35.9238	+	62.2218i	−1.17546	+	2.03596i
$935$	1.17043			0.0382770
$936$	1.30719	+	31.9524i	0.0427269	+	1.04440i
$937$	14.2950			0.466998			0.233499	−	0.972357i	$-0.424982\pi$
$937$	14.2950			0.466998			0.233499	+	0.972357i	$0.424982\pi$
$938$	−45.6148	+	79.0072i	−1.48938	+	2.57968i
$939$	9.26713	+	8.89576i	0.302421	+	0.290302i
$940$	−12.9365	−	22.4066i	−0.421941	−	0.730823i
$941$	−8.02348	−	13.8971i	−0.261558	−	0.453032i	0.705098	−	0.709110i	$-0.250903\pi$
$941$	−8.02348	−	13.8971i	−0.261558	−	0.453032i	−0.966656	+	0.256078i	$0.917570\pi$
$942$	12.1958	−	49.5456i	0.397362	−	1.61428i
$943$	2.81422	−	4.87438i	0.0916438	−	0.158732i
$944$	−17.3462			−0.564570
$945$	7.08646	−	8.01374i	0.230523	−	0.260687i
$946$	−4.07422			−0.132464
$947$	−22.3155	+	38.6516i	−0.725156	+	1.25601i	0.233754	+	0.972296i	$0.424899\pi$
$947$	−22.3155	+	38.6516i	−0.725156	+	1.25601i	−0.958910	+	0.283711i	$0.908434\pi$
$948$	24.3693	−	99.0004i	0.791479	−	3.21539i
$949$	5.00936	+	8.67647i	0.162611	+	0.281650i
$950$	20.5037	+	35.5134i	0.665227	+	1.15221i
$951$	14.6464	+	14.0595i	0.474944	+	0.455911i
$952$	−20.3743	+	35.2894i	−0.660336	+	1.14374i
$953$	3.70788			0.120110			0.0600550	−	0.998195i	$-0.480872\pi$
$953$	3.70788			0.120110			0.0600550	+	0.998195i	$0.480872\pi$
$954$	−41.2769	+	26.1373i	−1.33639	+	0.846225i
$955$	18.2484			0.590505
$956$	31.0195	−	53.7274i	1.00324	−	1.73767i
$957$	−1.82052	+	0.527923i	−0.0588490	+	0.0170653i
$958$	25.9842	+	45.0060i	0.839512	+	1.45408i
$959$	15.8436	+	27.4420i	0.511618	+	0.886148i
$960$	−63.4086	+	18.3875i	−2.04650	+	0.593455i
$961$	−4.05496	+	7.02340i	−0.130805	+	0.226561i
$962$	5.11667			0.164968
$963$	−49.1692	−	25.7677i	−1.58446	−	0.830353i
$964$	6.98144			0.224857
$965$	−1.25787	+	2.17870i	−0.0404924	+	0.0701349i
$966$	−8.52626	−	8.18458i	−0.274328	−	0.263334i
$967$	13.5476	+	23.4651i	0.435661	+	0.754587i	0.997349	−	0.0727618i	$-0.0231813\pi$
$967$	13.5476	+	23.4651i	0.435661	+	0.754587i	−0.561688	+	0.827349i	$0.689848\pi$
$968$	54.1225	+	93.7429i	1.73956	+	3.01301i
$969$	−2.16419	+	8.79204i	−0.0695240	+	0.282441i
$970$	9.12380	−	15.8029i	0.292947	−	0.507400i
$971$	−31.9545			−1.02547			−0.512735	−	0.858547i	$-0.671368\pi$
$971$	−31.9545			−1.02547			−0.512735	+	0.858547i	$0.671368\pi$
$972$	−70.2847	−	57.2070i	−2.25438	−	1.83492i
$973$	39.3293			1.26084
$974$	−38.7241	+	67.0721i	−1.24080	+	2.14913i
$975$	−1.78615	+	7.25623i	−0.0572025	+	0.232385i
$976$	80.8121	+	139.971i	2.58673	+	4.48035i
$977$	7.78060	+	13.4764i	0.248924	+	0.431148i	0.963227	−	0.268687i	$-0.0865899\pi$
$977$	7.78060	+	13.4764i	0.248924	+	0.431148i	−0.714304	+	0.699836i	$0.753257\pi$
$978$	−9.58405	−	9.19998i	−0.306464	−	0.294183i
$979$	5.78388	−	10.0180i	0.184854	−	0.320176i
$980$	−3.93529			−0.125708
$981$	−21.1464	−	11.0820i	−0.675152	−	0.353821i
$982$	50.1741			1.60112
$983$	8.57195	−	14.8470i	0.273403	−	0.473547i	−0.696328	−	0.717723i	$-0.745184\pi$
$983$	8.57195	−	14.8470i	0.273403	−	0.473547i	0.969731	+	0.244176i	$0.0785175\pi$
$984$	101.660	−	29.4799i	3.24081	−	0.939785i
$985$	9.95570	+	17.2438i	0.317215	+	0.549432i
$986$	−2.55750	−	4.42972i	−0.0814474	−	0.141071i
$987$	22.2327	−	6.44716i	0.707676	−	0.205215i
$988$	−9.88375	+	17.1192i	−0.314444	+	0.544633i
$989$	1.55633			0.0494883
$990$	−5.39369	+	3.41538i	−0.171423	+	0.108548i
$991$	25.0309			0.795131			0.397566	−	0.917574i	$-0.369855\pi$
$991$	25.0309			0.795131			0.397566	+	0.917574i	$0.369855\pi$
$992$	92.1485	−	159.606i	2.92572	−	5.06749i
$993$	−4.70726	−	4.51862i	−0.149380	−	0.143394i
$994$	18.3438	+	31.7724i	0.581831	+	1.00776i
$995$	6.29761	+	10.9078i	0.199648	+	0.345800i
$996$	−5.59602	+	22.7338i	−0.177317	+	0.720349i
$997$	9.17948	−	15.8993i	0.290717	−	0.503537i	−0.683262	−	0.730173i	$-0.739439\pi$
$997$	9.17948	−	15.8993i	0.290717	−	0.503537i	0.973979	+	0.226636i	$0.0727728\pi$
$998$	−67.9756			−2.15173
$999$	−6.30073	+	7.12520i	−0.199346	+	0.225431i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.e.b.79.1	yes	10
3.2	odd	2		351.2.e.b.235.5		10
9.2	odd	6		1053.2.a.j.1.1		5
9.4	even	3	inner	117.2.e.b.40.1	✓	10
9.5	odd	6		351.2.e.b.118.5		10
9.7	even	3		1053.2.a.k.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.e.b.40.1	✓	10	9.4	even	3	inner
117.2.e.b.79.1	yes	10	1.1	even	1	trivial
351.2.e.b.118.5		10	9.5	odd	6
351.2.e.b.235.5		10	3.2	odd	2
1053.2.a.j.1.1		5	9.2	odd	6
1053.2.a.k.1.5		5	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39763 + 2.42077i) q^{2} +(0.413993 - 1.68185i) q^{3} +(-2.90675 - 5.03463i) q^{4} +(-0.413993 - 0.717057i) q^{5} +(3.49275 + 3.35278i) q^{6} +(1.24323 - 2.15333i) q^{7} +10.6597 q^{8} +(-2.65722 - 1.39255i) q^{9} +2.31444 q^{10} +(0.459729 - 0.796275i) q^{11} +(-9.67085 + 2.80440i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(3.47514 + 6.01912i) q^{14} +(-1.37737 + 0.399416i) q^{15} +(-9.08484 + 15.7354i) q^{16} -1.53740 q^{17} +(7.08484 - 4.48625i) q^{18} +3.40028 q^{19} +(-2.40675 + 4.16860i) q^{20} +(-3.10689 - 2.98238i) q^{21} +(1.28506 + 2.22580i) q^{22} +(-0.490886 - 0.850239i) q^{23} +(4.41304 - 17.9280i) q^{24} +(2.15722 - 3.73641i) q^{25} +2.79526 q^{26} +(-3.44212 + 3.89253i) q^{27} -14.4550 q^{28} +(0.595121 - 1.03078i) q^{29} +(0.958162 - 3.89253i) q^{30} +(3.12690 + 5.41594i) q^{31} +(-14.7348 - 25.5214i) q^{32} +(-1.14889 - 1.10285i) q^{33} +(2.14872 - 3.72170i) q^{34} -2.05875 q^{35} +(0.712903 + 17.4259i) q^{36} +1.83048 q^{37} +(-4.75234 + 8.23129i) q^{38} +(-1.66352 + 0.482395i) q^{39} +(-4.41304 - 7.64362i) q^{40} +(2.86647 + 4.96488i) q^{41} +(11.5619 - 3.35278i) q^{42} +(-0.792611 + 1.37284i) q^{43} -5.34527 q^{44} +(0.101535 + 2.48188i) q^{45} +2.74431 q^{46} +(-2.68754 + 4.65496i) q^{47} +(22.7035 + 21.7937i) q^{48} +(0.408777 + 0.708023i) q^{49} +(6.02999 + 10.4443i) q^{50} +(-0.636475 + 2.58568i) q^{51} +(-2.90675 + 5.03463i) q^{52} -5.82609 q^{53} +(-4.61210 - 13.7729i) q^{54} -0.761299 q^{55} +(13.2524 - 22.9539i) q^{56} +(1.40769 - 5.71876i) q^{57} +(1.66352 + 2.88130i) q^{58} +(0.477338 + 0.826774i) q^{59} +(6.01458 + 5.77355i) q^{60} +(4.44763 - 7.70353i) q^{61} -17.4810 q^{62} +(-6.30214 + 3.99062i) q^{63} +46.0360 q^{64} +(-0.413993 + 0.717057i) q^{65} +(4.27546 - 1.23982i) q^{66} +(6.56302 + 11.3675i) q^{67} +(4.46884 + 7.74026i) q^{68} +(-1.63320 + 0.473602i) q^{69} +(2.87737 - 4.98375i) q^{70} +5.27858 q^{71} +(-28.3252 - 14.8441i) q^{72} -10.0187 q^{73} +(-2.55834 + 4.43117i) q^{74} +(-5.39100 - 5.17496i) q^{75} +(-9.88375 - 17.1192i) q^{76} +(-1.14310 - 1.97990i) q^{77} +(1.15722 - 4.70120i) q^{78} +(-5.06272 + 8.76888i) q^{79} +15.0443 q^{80} +(5.12163 + 7.40060i) q^{81} -16.0251 q^{82} +(1.16257 - 2.01363i) q^{83} +(-5.98426 + 24.3110i) q^{84} +(0.636475 + 1.10241i) q^{85} +(-2.21555 - 3.83745i) q^{86} +(-1.48724 - 1.42764i) q^{87} +(4.90058 - 8.48805i) q^{88} +12.5811 q^{89} +(-6.14997 - 3.22296i) q^{90} -2.48645 q^{91} +(-2.85376 + 4.94286i) q^{92} +(10.4033 - 3.01680i) q^{93} +(-7.51238 - 13.0118i) q^{94} +(-1.40769 - 2.43820i) q^{95} +(-49.0233 + 14.2160i) q^{96} +(3.94212 - 6.82795i) q^{97} -2.28528 q^{98} +(-2.33045 + 1.47568i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} + q^{3} - 4 q^{4} - q^{5} + 13 q^{6} + 2 q^{7} + 24 q^{8} - 13 q^{9} - 4 q^{10} - 11 q^{11} - 19 q^{12} - 5 q^{13} + 5 q^{14} - 10 q^{15} - 10 q^{16} + 14 q^{17} - 10 q^{18} + 6 q^{19}+ \cdots + 17 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 + q^3 - 4 * q^4 - q^5 + 13 * q^6 + 2 * q^7 + 24 * q^8 - 13 * q^9 - 4 * q^10 - 11 * q^11 - 19 * q^12 - 5 * q^13 + 5 * q^14 - 10 * q^15 - 10 * q^16 + 14 * q^17 - 10 * q^18 + 6 * q^19 + q^20 + 8 * q^21 + 7 * q^22 - 18 * q^23 + 18 * q^24 + 8 * q^25 + 4 * q^26 - 11 * q^27 - 38 * q^28 - 4 * q^29 + 5 * q^30 + 16 * q^31 - 31 * q^32 + 19 * q^33 - 13 * q^34 + 22 * q^35 - 5 * q^36 + 10 * q^37 - 24 * q^38 - 2 * q^39 - 18 * q^40 - 12 * q^41 + 59 * q^42 + 2 * q^44 - 14 * q^45 + 12 * q^46 - 15 * q^47 + 29 * q^48 - 3 * q^49 + 5 * q^50 - 7 * q^51 - 4 * q^52 - 6 * q^53 - 11 * q^54 - 34 * q^55 + 24 * q^56 + 12 * q^57 + 2 * q^58 - 3 * q^59 + 19 * q^60 + q^61 - 8 * q^62 - 14 * q^63 + 124 * q^64 - q^65 - 11 * q^66 + 4 * q^67 + 16 * q^68 + 25 * q^70 + 30 * q^71 - 66 * q^72 - 10 * q^73 - 11 * q^74 + 14 * q^75 - 9 * q^76 - q^77 - 2 * q^78 - 13 * q^79 + 64 * q^80 - 25 * q^81 - 42 * q^82 - 26 * q^83 - 17 * q^84 + 7 * q^85 + 6 * q^86 - 13 * q^87 - 3 * q^88 + 58 * q^89 - 26 * q^90 - 4 * q^91 + 6 * q^92 + 58 * q^93 - 12 * q^94 - 12 * q^95 - 67 * q^96 + 16 * q^97 - 78 * q^98 + 17 * q^99

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