LMFDB - Embedded newform 127.2.f.a.103.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [127,2,Mod(22,127)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("127.22"); S:= CuspForms(chi, 2); N := Newforms(S);

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

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

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.01410010567$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			103.8
Character	$\chi$	$=$	127.103
Dual form			127.2.f.a.37.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.30874 q^{2} +(0.272960 + 0.229041i) q^{3} -0.287188 q^{4} +(1.91003 + 3.30828i) q^{5} +(0.357235 + 0.299756i) q^{6} +(0.247675 - 1.40463i) q^{7} -2.99334 q^{8} +(-0.498897 - 2.82939i) q^{9} +(2.49975 + 4.32969i) q^{10} +(-3.39541 - 1.23583i) q^{11} +(-0.0783910 - 0.0657779i) q^{12} +(5.67987 - 2.06730i) q^{13} +(0.324143 - 1.83830i) q^{14} +(-0.236367 + 1.34050i) q^{15} -3.34315 q^{16} +(-0.358956 - 2.03574i) q^{17} +(-0.652929 - 3.70294i) q^{18} +(-2.07810 + 3.59938i) q^{19} +(-0.548540 - 0.950099i) q^{20} +(0.389323 - 0.326681i) q^{21} +(-4.44372 - 1.61738i) q^{22} +(-5.37803 + 1.95744i) q^{23} +(-0.817064 - 0.685598i) q^{24} +(-4.79646 + 8.30772i) q^{25} +(7.43350 - 2.70557i) q^{26} +(1.04635 - 1.81233i) q^{27} +(-0.0711293 + 0.403394i) q^{28} +(-3.14937 - 1.14628i) q^{29} +(-0.309344 + 1.75438i) q^{30} +(2.99465 + 2.51281i) q^{31} +1.61137 q^{32} +(-0.643757 - 1.11502i) q^{33} +(-0.469782 - 2.66427i) q^{34} +(5.11998 - 1.86352i) q^{35} +(0.143277 + 0.812567i) q^{36} +(8.79539 - 7.38021i) q^{37} +(-2.71971 + 4.71067i) q^{38} +(2.02388 + 0.736631i) q^{39} +(-5.71739 - 9.90281i) q^{40} +(-2.81808 + 2.36465i) q^{41} +(0.509525 - 0.427542i) q^{42} +(-5.21132 + 4.37282i) q^{43} +(0.975123 + 0.354916i) q^{44} +(8.40748 - 7.05471i) q^{45} +(-7.03847 + 2.56179i) q^{46} +(4.75593 + 8.23750i) q^{47} +(-0.912546 - 0.765717i) q^{48} +(4.66620 + 1.69836i) q^{49} +(-6.27734 + 10.8727i) q^{50} +(0.368287 - 0.637892i) q^{51} +(-1.63119 + 0.593706i) q^{52} +(-4.66908 + 3.91782i) q^{53} +(1.36941 - 2.37188i) q^{54} +(-2.39689 - 13.5934i) q^{55} +(-0.741375 + 4.20455i) q^{56} +(-1.39164 + 0.506517i) q^{57} +(-4.12172 - 1.50018i) q^{58} +(-0.729302 - 4.13608i) q^{59} +(0.0678819 - 0.384977i) q^{60} +(0.700411 + 1.21315i) q^{61} +(3.91924 + 3.28863i) q^{62} -4.09781 q^{63} +8.79516 q^{64} +(17.6880 + 14.8420i) q^{65} +(-0.842513 - 1.45928i) q^{66} +(2.60625 - 14.7808i) q^{67} +(0.103088 + 0.584642i) q^{68} +(-1.91632 - 0.697485i) q^{69} +(6.70074 - 2.43887i) q^{70} +(0.576556 - 3.26981i) q^{71} +(1.49337 + 8.46933i) q^{72} +(-5.49162 + 9.51176i) q^{73} +(11.5109 - 9.65881i) q^{74} +(-3.21205 + 1.16909i) q^{75} +(0.596807 - 1.03370i) q^{76} +(-2.57684 + 4.46322i) q^{77} +(2.64874 + 0.964061i) q^{78} +(2.64901 + 2.22278i) q^{79} +(-6.38552 - 11.0601i) q^{80} +(-7.39859 + 2.69287i) q^{81} +(-3.68815 + 3.09472i) q^{82} +(-1.82432 - 0.663998i) q^{83} +(-0.111809 + 0.0938190i) q^{84} +(6.04918 - 5.07587i) q^{85} +(-6.82028 + 5.72290i) q^{86} +(-0.597108 - 1.03422i) q^{87} +(10.1636 + 3.69926i) q^{88} +(-0.516505 + 0.894612i) q^{89} +(11.0032 - 9.23281i) q^{90} +(-1.49704 - 8.49015i) q^{91} +(1.54451 - 0.562156i) q^{92} +(0.241885 + 1.37180i) q^{93} +(6.22429 + 10.7808i) q^{94} -15.8770 q^{95} +(0.439839 + 0.369069i) q^{96} +(-0.379340 + 2.15134i) q^{97} +(6.10686 + 2.22272i) q^{98} +(-1.80267 + 10.2235i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 12 q^{2} - 6 q^{3} + 48 q^{4} + 3 q^{5} - 9 q^{6} - 30 q^{8} - 6 q^{9} - 3 q^{10} + 3 q^{11} - 27 q^{12} + 6 q^{13} - 27 q^{14} + 48 q^{16} + 9 q^{17} + 9 q^{18} - 3 q^{19} - 3 q^{20} + 36 q^{21}+ \cdots - 111 q^{99}+O(q^{100}) $ 60 * q - 12 * q^2 - 6 * q^3 + 48 * q^4 + 3 * q^5 - 9 * q^6 - 30 * q^8 - 6 * q^9 - 3 * q^10 + 3 * q^11 - 27 * q^12 + 6 * q^13 - 27 * q^14 + 48 * q^16 + 9 * q^17 + 9 * q^18 - 3 * q^19 - 3 * q^20 + 36 * q^21 - 39 * q^22 - 24 * q^23 - 90 * q^24 - 15 * q^25 + 9 * q^27 - 30 * q^28 - 42 * q^29 - 24 * q^30 - 54 * q^31 - 102 * q^32 + 39 * q^33 - 54 * q^34 + 21 * q^35 - 33 * q^36 + 27 * q^37 + 6 * q^38 + 33 * q^39 + 24 * q^40 + 42 * q^41 + 51 * q^42 + 36 * q^43 + 66 * q^44 + 3 * q^45 - 39 * q^46 - 18 * q^47 - 30 * q^48 + 48 * q^49 + 21 * q^50 + 21 * q^51 + 12 * q^52 - 21 * q^53 + 45 * q^54 - 36 * q^55 - 90 * q^56 - 21 * q^57 + 57 * q^58 + 36 * q^59 + 45 * q^60 - 15 * q^61 + 54 * q^62 - 84 * q^63 + 66 * q^64 + 66 * q^65 + 63 * q^66 + 78 * q^67 + 60 * q^68 + 30 * q^69 + 18 * q^70 - 6 * q^71 + 66 * q^72 - 3 * q^73 + 39 * q^74 + 78 * q^75 - 45 * q^76 + 39 * q^77 - 60 * q^78 - 27 * q^79 - 18 * q^80 + 99 * q^81 + 99 * q^82 - 12 * q^83 + 90 * q^84 - 6 * q^85 - 57 * q^86 - 12 * q^87 - 117 * q^88 + 3 * q^89 + 72 * q^90 - 60 * q^91 - 9 * q^92 - 108 * q^93 + 75 * q^94 - 180 * q^95 - 123 * q^96 + 9 * q^97 + 3 * q^98 - 111 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	1.30874			0.925422			0.462711	−	0.886509i	$-0.346877\pi$
$2$	1.30874			0.925422			0.462711	+	0.886509i	$0.346877\pi$
$3$	0.272960	+	0.229041i	0.157594	+	0.132237i	0.718175	−	0.695863i	$-0.244978\pi$
$3$	0.272960	+	0.229041i	0.157594	+	0.132237i	−0.560581	+	0.828099i	$0.689422\pi$
$4$	−0.287188			−0.143594
$5$	1.91003	+	3.30828i	0.854193	+	1.47951i	0.877391	+	0.479775i	$0.159282\pi$
$5$	1.91003	+	3.30828i	0.854193	+	1.47951i	−0.0231980	+	0.999731i	$0.507385\pi$
$6$	0.357235	+	0.299756i	0.145841	+	0.122375i
$7$	0.247675	−	1.40463i	0.0936122	−	0.530901i	−0.901552	−	0.432672i	$-0.857571\pi$
$7$	0.247675	−	1.40463i	0.0936122	−	0.530901i	0.995164	−	0.0982295i	$-0.0313179\pi$
$8$	−2.99334			−1.05831
$9$	−0.498897	−	2.82939i	−0.166299	−	0.943128i
$10$	2.49975	+	4.32969i	0.790489	+	1.36917i
$11$	−3.39541	−	1.23583i	−1.02375	−	0.372616i	−0.225055	−	0.974346i	$-0.572256\pi$
$11$	−3.39541	−	1.23583i	−1.02375	−	0.372616i	−0.798700	+	0.601730i	$0.794478\pi$
$12$	−0.0783910	−	0.0657779i	−0.0226295	−	0.0189884i
$13$	5.67987	−	2.06730i	1.57531	−	0.573367i	0.601135	−	0.799148i	$-0.294715\pi$
$13$	5.67987	−	2.06730i	1.57531	−	0.573367i	0.974178	+	0.225780i	$0.0724932\pi$
$14$	0.324143	−	1.83830i	0.0866308	−	0.491308i
$15$	−0.236367	+	1.34050i	−0.0610297	+	0.346116i
$16$	−3.34315			−0.835786
$17$	−0.358956	−	2.03574i	−0.0870597	−	0.493740i	−0.996893	−	0.0787664i	$-0.974902\pi$
$17$	−0.358956	−	2.03574i	−0.0870597	−	0.493740i	0.909833	−	0.414974i	$-0.136209\pi$
$18$	−0.652929	−	3.70294i	−0.153897	−	0.872792i
$19$	−2.07810	+	3.59938i	−0.476750	+	0.825755i	−0.999645	−	0.0266421i	$-0.991519\pi$
$19$	−2.07810	+	3.59938i	−0.476750	+	0.825755i	0.522895	+	0.852397i	$0.324852\pi$
$20$	−0.548540	−	0.950099i	−0.122657	−	0.212449i
$21$	0.389323	−	0.326681i	0.0849573	−	0.0712877i
$22$	−4.44372	−	1.61738i	−0.947405	−	0.344827i
$23$	−5.37803	+	1.95744i	−1.12140	+	0.408155i	−0.835162	−	0.550004i	$-0.814626\pi$
$23$	−5.37803	+	1.95744i	−1.12140	+	0.408155i	−0.286236	+	0.958159i	$0.592404\pi$
$24$	−0.817064	−	0.685598i	−0.166782	−	0.139947i
$25$	−4.79646	+	8.30772i	−0.959293	+	1.66154i
$26$	7.43350	−	2.70557i	1.45783	−	0.530606i
$27$	1.04635	−	1.81233i	0.201370	−	0.348784i
$28$	−0.0711293	+	0.403394i	−0.0134422	+	0.0762343i
$29$	−3.14937	−	1.14628i	−0.584823	−	0.212858i	0.0326279	−	0.999468i	$-0.489612\pi$
$29$	−3.14937	−	1.14628i	−0.584823	−	0.212858i	−0.617451	+	0.786609i	$0.711835\pi$
$30$	−0.309344	+	1.75438i	−0.0564782	+	0.320304i
$31$	2.99465	+	2.51281i	0.537856	+	0.451315i	0.870804	−	0.491631i	$-0.163599\pi$
$31$	2.99465	+	2.51281i	0.537856	+	0.451315i	−0.332948	+	0.942945i	$0.608043\pi$
$32$	1.61137			0.284852
$33$	−0.643757	−	1.11502i	−0.112064	−	0.194100i
$34$	−0.469782	−	2.66427i	−0.0805670	−	0.456918i
$35$	5.11998	−	1.86352i	0.865435	−	0.314992i
$36$	0.143277	+	0.812567i	0.0238796	+	0.135428i
$37$	8.79539	−	7.38021i	1.44595	−	1.21330i	0.510486	−	0.859886i	$-0.329465\pi$
$37$	8.79539	−	7.38021i	1.44595	−	1.21330i	0.935467	−	0.353413i	$-0.114979\pi$
$38$	−2.71971	+	4.71067i	−0.441195	+	0.764172i
$39$	2.02388	+	0.736631i	0.324079	+	0.117955i
$40$	−5.71739	−	9.90281i	−0.903999	−	1.56577i
$41$	−2.81808	+	2.36465i	−0.440110	+	0.369296i	−0.835751	−	0.549109i	$-0.814967\pi$
$41$	−2.81808	+	2.36465i	−0.440110	+	0.369296i	0.395640	+	0.918406i	$0.370523\pi$
$42$	0.509525	−	0.427542i	0.0786214	−	0.0659712i
$43$	−5.21132	+	4.37282i	−0.794719	+	0.666848i	−0.946909	−	0.321503i	$-0.895812\pi$
$43$	−5.21132	+	4.37282i	−0.794719	+	0.666848i	0.152190	+	0.988351i	$0.451368\pi$
$44$	0.975123	+	0.354916i	0.147005	+	0.0535056i
$45$	8.40748	−	7.05471i	1.25331	−	1.05165i
$46$	−7.03847	+	2.56179i	−1.03777	+	0.377716i
$47$	4.75593	+	8.23750i	0.693723	+	1.20156i	0.970609	+	0.240661i	$0.0773642\pi$
$47$	4.75593	+	8.23750i	0.693723	+	1.20156i	−0.276886	+	0.960903i	$0.589303\pi$
$48$	−0.912546	−	0.765717i	−0.131715	−	0.110522i
$49$	4.66620	+	1.69836i	0.666600	+	0.242622i
$50$	−6.27734	+	10.8727i	−0.887750	+	1.53763i
$51$	0.368287	−	0.637892i	0.0515705	−	0.0893228i
$52$	−1.63119	+	0.593706i	−0.226206	+	0.0823322i
$53$	−4.66908	+	3.91782i	−0.641347	+	0.538154i	−0.904432	−	0.426619i	$-0.859705\pi$
$53$	−4.66908	+	3.91782i	−0.641347	+	0.538154i	0.263084	+	0.964773i	$0.415260\pi$
$54$	1.36941	−	2.37188i	0.186353	−	0.322772i
$55$	−2.39689	−	13.5934i	−0.323196	−	1.83294i
$56$	−0.741375	+	4.20455i	−0.0990705	+	0.561857i
$57$	−1.39164	+	0.506517i	−0.184328	+	0.0670898i
$58$	−4.12172	−	1.50018i	−0.541208	−	0.196984i
$59$	−0.729302	−	4.13608i	−0.0949471	−	0.538472i	−0.994764	−	0.102203i	$-0.967411\pi$
$59$	−0.729302	−	4.13608i	−0.0949471	−	0.538472i	0.899817	−	0.436269i	$-0.143700\pi$
$60$	0.0678819	−	0.384977i	0.00876351	−	0.0497003i
$61$	0.700411	+	1.21315i	0.0896785	+	0.155328i	0.907375	−	0.420322i	$-0.138083\pi$
$61$	0.700411	+	1.21315i	0.0896785	+	0.155328i	−0.817697	+	0.575649i	$0.804749\pi$
$62$	3.91924	+	3.28863i	0.497743	+	0.417656i
$63$	−4.09781			−0.516276
$64$	8.79516			1.09939
$65$	17.6880	+	14.8420i	2.19392	+	1.84092i
$66$	−0.842513	−	1.45928i	−0.103706	−	0.179624i
$67$	2.60625	−	14.7808i	0.318405	−	1.80576i	−0.234056	−	0.972223i	$-0.575200\pi$
$67$	2.60625	−	14.7808i	0.318405	−	1.80576i	0.552460	−	0.833539i	$-0.313689\pi$
$68$	0.103088	+	0.584642i	0.0125013	+	0.0708982i
$69$	−1.91632	−	0.697485i	−0.230698	−	0.0839673i
$70$	6.70074	−	2.43887i	0.800892	−	0.291501i
$71$	0.576556	−	3.26981i	0.0684246	−	0.388055i	−0.931293	−	0.364272i	$-0.881318\pi$
$71$	0.576556	−	3.26981i	0.0684246	−	0.388055i	0.999717	−	0.0237831i	$-0.00757112\pi$
$72$	1.49337	+	8.46933i	0.175995	+	0.998120i
$73$	−5.49162	+	9.51176i	−0.642745	+	1.11327i	0.342072	+	0.939674i	$0.388871\pi$
$73$	−5.49162	+	9.51176i	−0.642745	+	1.11327i	−0.984817	+	0.173594i	$0.944462\pi$
$74$	11.5109	−	9.65881i	1.33812	−	1.12281i
$75$	−3.21205	+	1.16909i	−0.370896	+	0.134995i
$76$	0.596807	−	1.03370i	0.0684585	−	0.118574i
$77$	−2.57684	+	4.46322i	−0.293658	+	0.508631i
$78$	2.64874	+	0.964061i	0.299910	+	0.109158i
$79$	2.64901	+	2.22278i	0.298037	+	0.250082i	0.779527	−	0.626369i	$-0.215460\pi$
$79$	2.64901	+	2.22278i	0.298037	+	0.250082i	−0.481490	+	0.876452i	$0.659904\pi$
$80$	−6.38552	−	11.0601i	−0.713923	−	1.23655i
$81$	−7.39859	+	2.69287i	−0.822066	+	0.299208i
$82$	−3.68815	+	3.09472i	−0.407288	+	0.341755i
$83$	−1.82432	−	0.663998i	−0.200245	−	0.0728833i	0.239951	−	0.970785i	$-0.422869\pi$
$83$	−1.82432	−	0.663998i	−0.200245	−	0.0728833i	−0.440196	+	0.897902i	$0.645091\pi$
$84$	−0.111809	+	0.0938190i	−0.0121994	+	0.0102365i
$85$	6.04918	−	5.07587i	0.656126	−	0.550555i
$86$	−6.82028	+	5.72290i	−0.735450	+	0.617116i
$87$	−0.597108	−	1.03422i	−0.0640167	−	0.110880i
$88$	10.1636	+	3.69926i	1.08345	+	0.394343i
$89$	−0.516505	+	0.894612i	−0.0547494	+	0.0948287i	−0.892101	−	0.451836i	$-0.850769\pi$
$89$	−0.516505	+	0.894612i	−0.0547494	+	0.0948287i	0.837352	+	0.546664i	$0.184103\pi$
$90$	11.0032	−	9.23281i	1.15984	−	0.973224i
$91$	−1.49704	−	8.49015i	−0.156933	−	0.890010i
$92$	1.54451	−	0.562156i	0.161026	−	0.0586088i
$93$	0.241885	+	1.37180i	0.0250823	+	0.142249i
$94$	6.22429	+	10.7808i	0.641987	+	1.11195i
$95$	−15.8770			−1.62895
$96$	0.439839	+	0.369069i	0.0448909	+	0.0376679i
$97$	−0.379340	+	2.15134i	−0.0385161	+	0.218436i	−0.997991	−	0.0633592i	$-0.979819\pi$
$97$	−0.379340	+	2.15134i	−0.0385161	+	0.218436i	0.959475	+	0.281795i	$0.0909297\pi$
$98$	6.10686	+	2.22272i	0.616886	+	0.224528i
$99$	−1.80267	+	10.2235i	−0.181176	+	1.02750i
$100$	1.37749	−	2.38588i	0.137749	−	0.238588i
$101$	−1.48486	+	0.540445i	−0.147749	+	0.0537763i	−0.414836	−	0.909896i	$-0.636161\pi$
$101$	−1.48486	+	0.540445i	−0.147749	+	0.0537763i	0.267087	+	0.963672i	$0.413939\pi$
$102$	0.481994	−	0.834838i	0.0477245	−	0.0826613i
$103$	3.64756	+	3.06066i	0.359404	+	0.301576i	0.804553	−	0.593880i	$-0.202405\pi$
$103$	3.64756	+	3.06066i	0.359404	+	0.301576i	−0.445149	+	0.895457i	$0.646849\pi$
$104$	−17.0018	+	6.18815i	−1.66717	+	0.606799i
$105$	1.82437	+	0.664017i	0.178041	+	0.0648015i
$106$	−6.11063	+	5.12743i	−0.593517	+	0.498020i
$107$	5.15248	+	8.92436i	0.498109	+	0.862750i	0.999998	−	0.00218204i	$-0.000694566\pi$
$107$	5.15248	+	8.92436i	0.498109	+	0.862750i	−0.501889	+	0.864932i	$0.667361\pi$
$108$	−0.300500	+	0.520482i	−0.0289156	+	0.0500834i
$109$	0.242580	+	1.37574i	0.0232349	+	0.131772i	0.994219	−	0.107373i	$-0.0342440\pi$
$109$	0.242580	+	1.37574i	0.0232349	+	0.131772i	−0.970984	+	0.239145i	$0.923133\pi$
$110$	−3.13691	−	17.7903i	−0.299093	−	1.69624i
$111$	4.09116			0.388316
$112$	−0.828012	+	4.69589i	−0.0782398	+	0.443720i
$113$	2.03294	−	11.5294i	0.191243	−	1.08459i	−0.726426	−	0.687245i	$-0.758820\pi$
$113$	2.03294	−	11.5294i	0.191243	−	1.08459i	0.917669	−	0.397347i	$-0.130069\pi$
$114$	−1.82131	+	0.662902i	−0.170581	+	0.0620864i
$115$	−16.7480	−	14.0532i	−1.56176	−	1.31047i
$116$	0.904462	+	0.329197i	0.0839772	+	0.0305652i
$117$	−8.68287	−	15.0392i	−0.802732	−	1.39037i
$118$	−0.954470	−	5.41307i	−0.0878661	−	0.498313i
$119$	−2.94837			−0.270277
$120$	0.707528	−	4.01259i	0.0645881	−	0.366298i
$121$	1.57505	+	1.32163i	0.143187	+	0.120148i
$122$	0.916659	+	1.58770i	0.0829904	+	0.143744i
$123$	−1.31083			−0.118193
$124$	−0.860030	−	0.721651i	−0.0772330	−	0.0648062i
$125$	−17.5453			−1.56930
$126$	−5.36299			−0.477773
$127$	−7.02205	−	8.81424i	−0.623106	−	0.782137i
$127$	−7.02205	−	8.81424i	−0.623106	−	0.782137i
$128$	8.28788			0.732552
$129$	−2.42404			−0.213424
$130$	23.1490	+	19.4243i	2.03030	+	1.70363i
$131$	9.28674			0.811386			0.405693	−	0.914009i	$-0.367030\pi$
$131$	9.28674			0.811386			0.405693	+	0.914009i	$0.367030\pi$
$132$	0.184880	+	0.320221i	0.0160917	+	0.0278716i
$133$	4.54111	+	3.81045i	0.393765	+	0.330408i
$134$	3.41092	−	19.3443i	0.294659	−	1.67109i
$135$	7.99427			0.688037
$136$	1.07448	+	6.09368i	0.0921359	+	0.522529i
$137$	1.88334	+	3.26203i	0.160904	+	0.278694i	0.935193	−	0.354138i	$-0.115226\pi$
$137$	1.88334	+	3.26203i	0.160904	+	0.278694i	−0.774289	+	0.632832i	$0.781892\pi$
$138$	−2.50798	−	0.912829i	−0.213493	−	0.0777052i
$139$	−5.99605	−	5.03128i	−0.508578	−	0.426748i	0.352050	−	0.935981i	$-0.385485\pi$
$139$	−5.99605	−	5.03128i	−0.508578	−	0.426748i	−0.860629	+	0.509233i	$0.829929\pi$
$140$	−1.47040	+	0.535182i	−0.124271	+	0.0452311i
$141$	−0.588546	+	3.33781i	−0.0495645	+	0.281094i
$142$	0.754565	−	4.27935i	0.0633217	−	0.359115i
$143$	−21.8403			−1.82638
$144$	1.66789	+	9.45905i	0.138990	+	0.788254i
$145$	−2.22320	−	12.6084i	−0.184627	−	1.04707i
$146$	−7.18712	+	12.4485i	−0.594810	+	1.03024i
$147$	0.884693	+	1.53233i	0.0729683	+	0.126385i
$148$	−2.52594	+	2.11951i	−0.207631	+	0.174223i
$149$	1.53643	+	0.559213i	0.125869	+	0.0458126i	0.404187	−	0.914677i	$-0.367555\pi$
$149$	1.53643	+	0.559213i	0.125869	+	0.0458126i	−0.278318	+	0.960489i	$0.589777\pi$
$150$	−4.20375	+	1.53004i	−0.343235	+	0.124927i
$151$	−17.3140	−	14.5282i	−1.40900	−	1.18229i	−0.956935	−	0.290302i	$-0.906244\pi$
$151$	−17.3140	−	14.5282i	−1.40900	−	1.18229i	−0.452061	−	0.891987i	$-0.649311\pi$
$152$	6.22048	−	10.7742i	0.504548	−	0.873902i
$153$	−5.58082	+	2.03125i	−0.451182	+	0.164217i
$154$	−3.37243	+	5.84121i	−0.271758	+	0.470699i
$155$	−2.59319	+	14.7067i	−0.208290	+	1.18127i
$156$	−0.581234	−	0.211552i	−0.0465359	−	0.0169377i
$157$	−0.345933	+	1.96188i	−0.0276084	+	0.156575i	−0.995495	−	0.0948110i	$-0.969775\pi$
$157$	−0.345933	+	1.96188i	−0.0276084	+	0.156575i	0.967887	+	0.251386i	$0.0808864\pi$
$158$	3.46687	+	2.90905i	0.275810	+	0.231432i
$159$	−2.17181			−0.172236
$160$	3.07777	+	5.33085i	0.243319	+	0.421440i
$161$	1.41749	+	8.03897i	0.111714	+	0.633560i
$162$	−9.68287	+	3.52428i	−0.760758	+	0.276893i
$163$	0.275153	+	1.56047i	0.0215516	+	0.122225i	0.993686	−	0.112201i	$-0.0357900\pi$
$163$	0.275153	+	1.56047i	0.0215516	+	0.122225i	−0.972134	+	0.234426i	$0.924679\pi$
$164$	0.809321	−	0.679101i	0.0631973	−	0.0530288i
$165$	2.45920	−	4.25945i	0.191448	−	0.331598i
$166$	−2.38757	−	0.869004i	−0.185311	−	0.0674478i
$167$	−0.174763	−	0.302698i	−0.0135236	−	0.0234235i	0.859184	−	0.511666i	$-0.170971\pi$
$167$	−0.174763	−	0.302698i	−0.0135236	−	0.0234235i	−0.872708	+	0.488243i	$0.837638\pi$
$168$	−1.16538	+	0.977869i	−0.0899109	+	0.0754442i
$169$	18.0286	−	15.1278i	1.38682	−	1.16368i
$170$	7.91683	−	6.64301i	0.607193	−	0.509496i
$171$	11.2208	+	4.08404i	0.858076	+	0.312314i
$172$	1.49663	−	1.25582i	0.114117	−	0.0957556i
$173$	−7.60501	+	2.76800i	−0.578198	+	0.210447i	−0.614531	−	0.788893i	$-0.710655\pi$
$173$	−7.60501	+	2.76800i	−0.578198	+	0.210447i	0.0363325	+	0.999340i	$0.488432\pi$
$174$	−0.781462	−	1.35353i	−0.0592425	−	0.102611i
$175$	10.4813	+	8.79488i	0.792314	+	0.664830i
$176$	11.3514	+	4.13155i	0.855641	+	0.311428i
$177$	0.748260	−	1.29602i	0.0562427	−	0.0974152i
$178$	−0.675972	+	1.17082i	−0.0506663	+	0.0877566i
$179$	22.2957	−	8.11496i	1.66646	−	0.606541i	0.675099	−	0.737727i	$-0.264101\pi$
$179$	22.2957	−	8.11496i	1.66646	−	0.606541i	0.991358	+	0.131186i	$0.0418786\pi$
$180$	−2.41453	+	2.02603i	−0.179969	+	0.151012i
$181$	1.00288	−	1.73704i	0.0745434	−	0.129113i	−0.826344	−	0.563165i	$-0.809583\pi$
$181$	1.00288	−	1.73704i	0.0745434	−	0.129113i	0.900888	+	0.434052i	$0.142917\pi$
$182$	−1.95925	−	11.1114i	−0.145229	−	0.823635i
$183$	−0.0866759	+	0.491564i	−0.00640727	+	0.0363374i
$184$	16.0983	−	5.85931i	1.18678	−	0.431954i
$185$	41.2153	+	15.0011i	3.03021	+	1.10291i
$186$	0.316565	+	1.79533i	0.0232117	+	0.131640i
$187$	−1.29702	+	7.35579i	−0.0948478	+	0.537909i
$188$	−1.36585	−	2.36572i	−0.0996146	−	0.172538i
$189$	−2.28651	−	1.91861i	−0.166319	−	0.139558i
$190$	−20.7789			−1.50746
$191$	19.2151			1.39035			0.695176	−	0.718839i	$-0.255326\pi$
$191$	19.2151			1.39035			0.695176	+	0.718839i	$0.255326\pi$
$192$	2.40073	+	2.01445i	0.173258	+	0.145380i
$193$	3.10532	+	5.37857i	0.223526	+	0.387158i	0.955876	−	0.293770i	$-0.0949100\pi$
$193$	3.10532	+	5.37857i	0.223526	+	0.387158i	−0.732350	+	0.680928i	$0.761577\pi$
$194$	−0.496458	+	2.81556i	−0.0356436	+	0.202145i
$195$	1.42869	+	8.10253i	0.102311	+	0.580234i
$196$	−1.34008	−	0.487749i	−0.0957199	−	0.0348392i
$197$	−14.5224	+	5.28572i	−1.03468	+	0.376592i	−0.802860	−	0.596168i	$-0.796689\pi$
$197$	−14.5224	+	5.28572i	−1.03468	+	0.376592i	−0.231817	+	0.972759i	$0.574467\pi$
$198$	−2.35924	+	13.3799i	−0.167664	+	0.950869i
$199$	1.79426	+	10.1758i	0.127192	+	0.721340i	0.979982	+	0.199086i	$0.0637975\pi$
$199$	1.79426	+	10.1758i	0.127192	+	0.721340i	−0.852790	+	0.522254i	$0.825091\pi$
$200$	14.3575	−	24.8679i	1.01523	−	1.75842i
$201$	4.09681	−	3.43763i	0.288967	−	0.242472i
$202$	−1.94330	+	0.707305i	−0.136730	+	0.0497658i
$203$	−2.39012	+	4.13980i	−0.167753	+	0.290557i
$204$	−0.105768	+	0.183195i	−0.00740523	+	0.0128262i
$205$	−13.2056	−	4.80643i	−0.922316	−	0.335696i
$206$	4.77372	+	4.00563i	0.332601	+	0.279085i
$207$	8.22145	+	14.2400i	0.571430	+	0.989746i
$208$	−18.9886	+	6.91130i	−1.31663	+	0.479212i
$209$	11.5042	−	9.65320i	0.795765	−	0.667726i
$210$	2.38764	+	0.869029i	0.164763	+	0.0599687i
$211$	5.30374	−	4.45037i	0.365125	−	0.306376i	−0.441705	−	0.897161i	$-0.645626\pi$
$211$	5.30374	−	4.45037i	0.365125	−	0.306376i	0.806829	+	0.590784i	$0.201182\pi$
$212$	1.34091	−	1.12515i	0.0920938	−	0.0772758i
$213$	0.906297	−	0.760474i	0.0620985	−	0.0521068i
$214$	6.74328	+	11.6797i	0.460961	+	0.798408i
$215$	−24.4203	−	8.88826i	−1.66545	−	0.606174i
$216$	−3.13209	+	5.42494i	−0.213112	+	0.369121i
$217$	4.27128	−	3.58403i	0.289953	−	0.243300i
$218$	0.317475	+	1.80049i	0.0215021	+	0.121944i
$219$	−3.67757	+	1.33853i	−0.248507	+	0.0904493i
$220$	0.688359	+	3.90388i	0.0464091	+	0.263199i
$221$	−6.24733	−	10.8207i	−0.420241	−	0.727878i
$222$	5.35428			0.359356
$223$	−11.9261	−	10.0072i	−0.798630	−	0.670130i	0.149235	−	0.988802i	$-0.452319\pi$
$223$	−11.9261	−	10.0072i	−0.798630	−	0.670130i	−0.947865	+	0.318672i	$0.896763\pi$
$224$	0.399095	−	2.26338i	0.0266656	−	0.151228i
$225$	25.8987	+	9.42635i	1.72658	+	0.628423i
$226$	2.66060	−	15.0890i	0.176980	−	1.00371i
$227$	4.58953	−	7.94931i	0.304618	−	0.527614i	−0.672558	−	0.740044i	$-0.734804\pi$
$227$	4.58953	−	7.94931i	0.304618	−	0.527614i	0.977176	+	0.212430i	$0.0681378\pi$
$228$	0.399664	−	0.145466i	0.0264684	−	0.00963372i
$229$	6.02370	−	10.4333i	0.398057	−	0.689455i	−0.595429	−	0.803408i	$-0.703018\pi$
$229$	6.02370	−	10.4333i	0.398057	−	0.689455i	0.993486	+	0.113953i	$0.0363513\pi$
$230$	−21.9188	−	18.3921i	−1.44529	−	1.21274i
$231$	−1.72563	+	0.628080i	−0.113538	+	0.0413246i
$232$	9.42715	+	3.43120i	0.618922	+	0.225269i
$233$	−18.8174	+	15.7897i	−1.23277	+	1.03442i	−0.234715	+	0.972064i	$0.575416\pi$
$233$	−18.8174	+	15.7897i	−1.23277	+	1.03442i	−0.998054	+	0.0623515i	$0.980140\pi$
$234$	−11.3637	−	19.6824i	−0.742866	−	1.28668i
$235$	−18.1680	+	31.4678i	−1.18515	+	2.05274i
$236$	0.209447	+	1.18783i	0.0136339	+	0.0773214i
$237$	0.213966	+	1.21346i	0.0138986	+	0.0788228i
$238$	−3.85867			−0.250120
$239$	−0.753468	+	4.27313i	−0.0487378	+	0.276406i	−0.999431	−	0.0337269i	$-0.989262\pi$
$239$	−0.753468	+	4.27313i	−0.0487378	+	0.276406i	0.950693	+	0.310133i	$0.100373\pi$
$240$	0.790209	−	4.48150i	0.0510078	−	0.289279i
$241$	14.9557	−	5.44343i	0.963382	−	0.350642i	0.188024	−	0.982164i	$-0.439792\pi$
$241$	14.9557	−	5.44343i	0.963382	−	0.350642i	0.775358	+	0.631522i	$0.217569\pi$
$242$	2.06134	+	1.72967i	0.132508	+	0.111188i
$243$	−8.53579	−	3.10677i	−0.547571	−	0.199300i
$244$	−0.201150	−	0.348402i	−0.0128773	−	0.0223042i
$245$	3.29396	+	18.6810i	0.210444	+	1.19349i
$246$	−1.71554			−0.109379
$247$	−4.36235	+	24.7401i	−0.277570	+	1.57418i
$248$	−8.96403	−	7.52172i	−0.569217	−	0.477629i
$249$	−0.345884	−	0.599089i	−0.0219195	−	0.0379657i
$250$	−22.9623			−1.45226
$251$	−16.0751	−	13.4886i	−1.01465	−	0.851395i	−0.0257070	−	0.999670i	$-0.508184\pi$
$251$	−16.0751	−	13.4886i	−1.01465	−	0.851395i	−0.988946	+	0.148274i	$0.952628\pi$
$252$	1.17684			0.0741342
$253$	20.6797			1.30012
$254$	−9.19007	−	11.5356i	−0.576636	−	0.723807i
$255$	2.81377			0.176205
$256$	−6.74360			−0.421475
$257$	−11.1408	−	9.34822i	−0.694943	−	0.583126i	0.225387	−	0.974269i	$-0.427635\pi$
$257$	−11.1408	−	9.34822i	−0.694943	−	0.583126i	−0.920330	+	0.391143i	$0.872080\pi$
$258$	−3.17244			−0.197508
$259$	−8.18809	−	14.1822i	−0.508783	−	0.881238i
$260$	−5.07978	−	4.26244i	−0.315035	−	0.264345i
$261$	−1.67205	+	9.48265i	−0.103497	+	0.586961i
$262$	12.1540			0.750875
$263$	1.47833	+	8.38405i	0.0911579	+	0.516982i	0.995857	+	0.0909315i	$0.0289844\pi$
$263$	1.47833	+	8.38405i	0.0911579	+	0.516982i	−0.904699	+	0.426051i	$0.859904\pi$
$264$	1.92699	+	3.33764i	0.118598	+	0.205417i
$265$	−21.8793	−	7.96343i	−1.34404	−	0.489189i
$266$	5.94316	+	4.98690i	0.364398	+	0.305767i
$267$	−0.345888	+	0.125893i	−0.0211680	+	0.00770452i
$268$	−0.748486	+	4.24488i	−0.0457211	+	0.259297i
$269$	2.23085	−	12.6518i	0.136017	−	0.771393i	−0.838128	−	0.545473i	$-0.816350\pi$
$269$	2.23085	−	12.6518i	0.136017	−	0.771393i	0.974146	−	0.225920i	$-0.0725388\pi$
$270$	10.4625			0.636725
$271$	−1.43847	−	8.15796i	−0.0873808	−	0.495561i	−0.996817	−	0.0797184i	$-0.974598\pi$
$271$	−1.43847	−	8.15796i	−0.0873808	−	0.495561i	0.909437	−	0.415842i	$-0.136513\pi$
$272$	1.20004	+	6.80578i	0.0727633	+	0.412661i
$273$	1.53596	−	2.66036i	0.0929604	−	0.161012i
$274$	2.46481	+	4.26917i	0.148904	+	0.257910i
$275$	26.5529	−	22.2805i	1.60120	−	1.34357i
$276$	0.550346	+	0.200310i	0.0331269	+	0.0120572i
$277$	−12.4653	+	4.53700i	−0.748968	+	0.272602i	−0.688172	−	0.725548i	$-0.741586\pi$
$277$	−12.4653	+	4.53700i	−0.748968	+	0.272602i	−0.0607968	+	0.998150i	$0.519364\pi$
$278$	−7.84730	−	6.58466i	−0.470650	−	0.394922i
$279$	5.61569	−	9.72666i	0.336203	−	0.582320i
$280$	−15.3259	+	5.57816i	−0.915896	+	0.333359i
$281$	11.1637	−	19.3361i	0.665970	−	1.15349i	−0.313051	−	0.949736i	$-0.601351\pi$
$281$	11.1637	−	19.3361i	0.665970	−	1.15349i	0.979021	−	0.203758i	$-0.0653154\pi$
$282$	−0.770256	+	4.36834i	−0.0458681	+	0.260131i
$283$	30.2058	+	10.9940i	1.79555	+	0.653526i	0.998787	+	0.0492314i	$0.0156772\pi$
$283$	30.2058	+	10.9940i	1.79555	+	0.653526i	0.796761	+	0.604295i	$0.206545\pi$
$284$	−0.165580	+	0.939053i	−0.00982538	+	0.0557225i
$285$	−4.33379	−	3.63648i	−0.256711	−	0.215407i
$286$	−28.5834			−1.69017
$287$	2.62350	+	4.54403i	0.154860	+	0.268226i
$288$	−0.803906	−	4.55918i	−0.0473706	−	0.268652i
$289$	11.9594	−	4.35286i	0.703493	−	0.256050i
$290$	−2.90960	−	16.5012i	−0.170858	−	0.968983i
$291$	−0.596289	+	0.500346i	−0.0349551	+	0.0293308i
$292$	1.57713	−	2.73167i	0.0922945	−	0.159859i
$293$	10.3486	+	3.76660i	0.604574	+	0.220047i	0.626127	−	0.779721i	$-0.284639\pi$
$293$	10.3486	+	3.76660i	0.604574	+	0.220047i	−0.0215534	+	0.999768i	$0.506861\pi$
$294$	1.15784	+	2.00543i	0.0675264	+	0.116959i
$295$	12.2903	−	10.3128i	0.715569	−	0.600434i
$296$	−26.3276	+	22.0915i	−1.53026	+	1.28404i
$297$	−5.79253	+	4.86051i	−0.336117	+	0.282035i
$298$	2.01079	+	0.731867i	0.116482	+	0.0423959i
$299$	−26.4999	+	22.2361i	−1.53253	+	1.28595i
$300$	0.922463	−	0.335749i	0.0532585	−	0.0193845i
$301$	4.85149	+	8.40302i	0.279635	+	0.484342i
$302$	−22.6596	−	19.0137i	−1.30392	−	1.09412i
$303$	−0.529092	−	0.192574i	−0.0303955	−	0.0110631i
$304$	6.94740	−	12.0333i	0.398461	−	0.690155i
$305$	−2.67562	+	4.63431i	−0.153205	+	0.265360i
$306$	−7.30386	+	2.65839i	−0.417534	+	0.151970i
$307$	3.02766	−	2.54051i	0.172798	−	0.144994i	−0.552287	−	0.833654i	$-0.686245\pi$
$307$	3.02766	−	2.54051i	0.172798	−	0.144994i	0.725085	+	0.688659i	$0.241800\pi$
$308$	0.740039	−	1.28179i	0.0421676	−	0.0730365i
$309$	0.294621	+	1.67088i	0.0167604	+	0.0950529i
$310$	−3.39382	+	19.2473i	−0.192756	+	1.09317i
$311$	28.3561	−	10.3208i	1.60792	−	0.585237i	0.626897	−	0.779102i	$-0.284325\pi$
$311$	28.3561	−	10.3208i	1.60792	−	0.585237i	0.981028	+	0.193866i	$0.0621026\pi$
$312$	−6.05816	−	2.20499i	−0.342976	−	0.124833i
$313$	3.85611	+	21.8691i	0.217960	+	1.23611i	0.875695	+	0.482865i	$0.160404\pi$
$313$	3.85611	+	21.8691i	0.217960	+	1.23611i	−0.657735	+	0.753250i	$0.728485\pi$
$314$	−0.452738	+	2.56760i	−0.0255495	+	0.144898i
$315$	−7.82696	−	13.5567i	−0.440999	−	0.763833i
$316$	−0.760764	−	0.638357i	−0.0427963	−	0.0359104i
$317$	−10.5388			−0.591919			−0.295959	−	0.955200i	$-0.595639\pi$
$317$	−10.5388			−0.591919			−0.295959	+	0.955200i	$0.595639\pi$
$318$	−2.84235			−0.159391
$319$	9.27680	+	7.78416i	0.519401	+	0.435829i
$320$	16.7991	+	29.0968i	0.939096	+	1.62656i
$321$	−0.637620	+	3.61612i	−0.0355885	+	0.201832i
$322$	1.85513	+	10.5210i	0.103382	+	0.586310i
$323$	8.07336	+	2.93846i	0.449214	+	0.163501i
$324$	2.12479	−	0.773361i	0.118044	−	0.0429645i
$325$	−10.0687	+	57.1025i	−0.558512	+	3.16748i
$326$	0.360104	+	2.04225i	0.0199443	+	0.113110i
$327$	−0.248885	+	0.431082i	−0.0137634	+	0.0238389i
$328$	8.43549	−	7.07822i	0.465772	−	0.390829i
$329$	12.7486	−	4.64011i	0.702852	−	0.255817i
$330$	3.21846	−	5.57453i	0.177170	−	0.306868i
$331$	−6.22017	+	10.7737i	−0.341892	+	0.592174i	−0.984784	−	0.173783i	$-0.944401\pi$
$331$	−6.22017	+	10.7737i	−0.341892	+	0.592174i	0.642892	+	0.765956i	$0.277734\pi$
$332$	0.523924	+	0.190693i	0.0287541	+	0.0104656i
$333$	−25.2695	−	21.2036i	−1.38476	−	1.16195i
$334$	−0.228720	−	0.396154i	−0.0125150	−	0.0216766i
$335$	53.8770	−	19.6096i	2.94362	−	1.07139i
$336$	−1.30156	+	1.09214i	−0.0710062	+	0.0595813i
$337$	−18.3034	−	6.66189i	−0.997049	−	0.362896i	−0.208603	−	0.978000i	$-0.566892\pi$
$337$	−18.3034	−	6.66189i	−0.997049	−	0.362896i	−0.788446	+	0.615104i	$0.789114\pi$
$338$	23.5949	−	19.7984i	1.28339	−	1.07689i
$339$	3.19561	−	2.68143i	0.173562	−	0.145635i
$340$	−1.73725	+	1.45773i	−0.0942159	+	0.0790565i
$341$	−7.06267	−	12.2329i	−0.382465	−	0.662449i
$342$	14.6852	+	5.34496i	0.794082	+	0.289022i
$343$	8.53332	−	14.7801i	0.460756	−	0.798053i
$344$	15.5993	−	13.0893i	0.841057	−	0.705730i
$345$	−1.35277	−	7.67195i	−0.0728308	−	0.413044i
$346$	−9.95302	+	3.62260i	−0.535077	+	0.194752i
$347$	−1.90953	−	10.8295i	−0.102509	−	0.581357i	−0.992186	−	0.124767i	$-0.960182\pi$
$347$	−1.90953	−	10.8295i	−0.102509	−	0.581357i	0.889677	−	0.456590i	$-0.150929\pi$
$348$	0.171483	+	0.297016i	0.00919243	+	0.0159218i
$349$	−8.21055			−0.439500			−0.219750	−	0.975556i	$-0.570524\pi$
$349$	−8.21055			−0.439500			−0.219750	+	0.975556i	$0.570524\pi$
$350$	13.7174	+	11.5102i	0.733225	+	0.615249i
$351$	2.19650	−	12.4570i	0.117240	−	0.664903i
$352$	−5.47125	−	1.99137i	−0.291619	−	0.106141i
$353$	2.79341	−	15.8422i	0.148678	−	0.843197i	−0.815661	−	0.578530i	$-0.803627\pi$
$353$	2.79341	−	15.8422i	0.148678	−	0.843197i	0.964340	−	0.264668i	$-0.0852622\pi$
$354$	0.979281	−	1.69616i	0.0520482	−	0.0901501i
$355$	11.9187	−	4.33805i	0.632578	−	0.230240i
$356$	0.148334	−	0.256922i	0.00786169	−	0.0136169i
$357$	−0.804789	−	0.675298i	−0.0425939	−	0.0357406i
$358$	29.1793	−	10.6204i	1.54218	−	0.561306i
$359$	1.42357	+	0.518138i	0.0751333	+	0.0273463i	0.379313	−	0.925268i	$-0.376160\pi$
$359$	1.42357	+	0.518138i	0.0751333	+	0.0273463i	−0.304180	+	0.952615i	$0.598382\pi$
$360$	−25.1665	+	21.1172i	−1.32639	+	1.11297i
$361$	0.862968	+	1.49470i	0.0454193	+	0.0786686i
$362$	1.31251	−	2.27334i	0.0689841	−	0.119484i
$363$	0.127221	+	0.721503i	0.00667734	+	0.0378691i
$364$	0.429933	+	2.43827i	0.0225346	+	0.127800i
$365$	−41.9567			−2.19611
$366$	−0.113437	+	0.643331i	−0.00592943	+	0.0336275i
$367$	−5.67159	+	32.1652i	−0.296055	+	1.67901i	0.366831	+	0.930288i	$0.380443\pi$
$367$	−5.67159	+	32.1652i	−0.296055	+	1.67901i	−0.662885	+	0.748721i	$0.730668\pi$
$368$	17.9796	−	6.54402i	0.937249	−	0.341131i
$369$	8.09644	+	6.79372i	0.421484	+	0.353667i
$370$	53.9403	+	19.6327i	2.80422	+	1.02065i
$371$	4.34669	+	7.52868i	0.225669	+	0.390870i
$372$	−0.0694665	−	0.393964i	−0.00360167	−	0.0204261i
$373$	−25.4119			−1.31578			−0.657890	−	0.753114i	$-0.728551\pi$
$373$	−25.4119			−1.31578			−0.657890	+	0.753114i	$0.728551\pi$
$374$	−1.69747	+	9.62685i	−0.0877743	+	0.497793i
$375$	−4.78917	−	4.01859i	−0.247311	−	0.207519i
$376$	−14.2361	−	24.6577i	−0.734172	−	1.27162i
$377$	−20.2577			−1.04333
$378$	−2.99246	−	2.51097i	−0.153915	−	0.129150i
$379$	−2.24047			−0.115085			−0.0575427	−	0.998343i	$-0.518327\pi$
$379$	−2.24047			−0.115085			−0.0575427	+	0.998343i	$0.518327\pi$
$380$	4.55969			0.233907
$381$	0.102079	−	4.01427i	0.00522967	−	0.205657i
$382$	25.1476			1.28666
$383$	−10.9101			−0.557480			−0.278740	−	0.960367i	$-0.589917\pi$
$383$	−10.9101			−0.557480			−0.278740	+	0.960367i	$0.589917\pi$
$384$	2.26226	+	1.89826i	0.115446	+	0.0968703i
$385$	−19.6874			−1.00336
$386$	4.06407	+	7.03917i	0.206856	+	0.358285i
$387$	14.9723	+	12.5632i	0.761084	+	0.638626i
$388$	0.108942	−	0.617840i	0.00553069	−	0.0313661i
$389$	−10.7677			−0.545943			−0.272971	−	0.962022i	$-0.588006\pi$
$389$	−10.7677			−0.545943			−0.272971	+	0.962022i	$0.588006\pi$
$390$	1.86980	+	10.6041i	0.0946808	+	0.536962i
$391$	5.91533	+	10.2457i	0.299151	+	0.518145i
$392$	−13.9675	−	5.08377i	−0.705467	−	0.256769i
$393$	2.53491	+	2.12704i	0.127869	+	0.107295i
$394$	−19.0061	+	6.91765i	−0.957513	+	0.348506i
$395$	−2.29388	+	13.0092i	−0.115418	+	0.654566i
$396$	0.517707	−	2.93606i	0.0260158	−	0.147543i
$397$	0.272799			0.0136914			0.00684570	−	0.999977i	$-0.497821\pi$
$397$	0.272799			0.0136914			0.00684570	+	0.999977i	$0.497821\pi$
$398$	2.34823	+	13.3175i	0.117706	+	0.667544i
$399$	0.366796	+	2.08020i	0.0183627	+	0.104140i
$400$	16.0353	−	27.7739i	0.801764	−	1.38870i
$401$	13.0788	+	22.6532i	0.653124	+	1.13124i	0.982360	+	0.186997i	$0.0598755\pi$
$401$	13.0788	+	22.6532i	0.653124	+	1.13124i	−0.329236	+	0.944248i	$0.606791\pi$
$402$	5.36168	−	4.49898i	0.267416	−	0.224389i
$403$	22.2040	+	8.08160i	1.10606	+	0.402573i
$404$	0.426435	−	0.155210i	0.0212159	−	0.00772197i
$405$	−23.0403	−	19.3331i	−1.14488	−	0.960671i
$406$	−3.12805	+	5.41794i	−0.155243	+	0.268888i
$407$	−38.9846	+	14.1893i	−1.93240	+	0.703335i
$408$	−1.10241	+	1.90943i	−0.0545775	+	0.0945309i
$409$	4.59183	−	26.0416i	0.227051	−	1.28767i	−0.631673	−	0.775235i	$-0.717631\pi$
$409$	4.59183	−	26.0416i	0.227051	−	1.28767i	0.858724	−	0.512438i	$-0.171257\pi$
$410$	−17.2827	−	6.29039i	−0.853531	−	0.310660i
$411$	−0.233063	+	1.32177i	−0.0114962	+	0.0651979i
$412$	−1.04754	−	0.878987i	−0.0516084	−	0.0433046i
$413$	−5.99030			−0.294763
$414$	10.7598	+	18.6365i	0.528814	+	0.915933i
$415$	−1.28782	−	7.30362i	−0.0632168	−	0.358520i
$416$	9.15236	−	3.33119i	0.448731	−	0.163325i
$417$	−0.484314	−	2.74668i	−0.0237170	−	0.134506i
$418$	15.0561	−	12.6336i	0.736418	−	0.617928i
$419$	−8.29815	+	14.3728i	−0.405391	+	0.702158i	−0.994367	−	0.105992i	$-0.966198\pi$
$419$	−8.29815	+	14.3728i	−0.405391	+	0.702158i	0.588976	+	0.808151i	$0.299531\pi$
$420$	−0.523939	−	0.190698i	−0.0255656	−	0.00930511i
$421$	8.06999	+	13.9776i	0.393307	+	0.681228i	0.992884	−	0.119089i	$-0.0379975\pi$
$421$	8.06999	+	13.9776i	0.393307	+	0.681228i	−0.599576	+	0.800318i	$0.704664\pi$
$422$	6.94124	−	5.82440i	0.337894	−	0.283527i
$423$	20.9344	−	17.5660i	1.01786	−	0.854089i
$424$	13.9762	−	11.7274i	0.678742	−	0.569532i
$425$	18.6341	+	6.78226i	0.903886	+	0.328988i
$426$	1.18611	−	0.995266i	0.0574673	−	0.0482208i
$427$	1.87750	−	0.683354i	0.0908586	−	0.0330698i
$428$	−1.47973	−	2.56297i	−0.0715256	−	0.123886i
$429$	−5.96154	−	5.00233i	−0.287826	−	0.241515i
$430$	−31.9599	−	11.6325i	−1.54124	−	0.560967i
$431$	−3.33068	+	5.76891i	−0.160433	+	0.277879i	−0.935024	−	0.354584i	$-0.884622\pi$
$431$	−3.33068	+	5.76891i	−0.160433	+	0.277879i	0.774591	+	0.632463i	$0.217956\pi$
$432$	−3.49811	+	6.05890i	−0.168303	+	0.291509i
$433$	−16.7815	+	6.10796i	−0.806467	+	0.293530i	−0.712164	−	0.702014i	$-0.752285\pi$
$433$	−16.7815	+	6.10796i	−0.806467	+	0.293530i	−0.0943033	+	0.995544i	$0.530062\pi$
$434$	5.59001	−	4.69058i	0.268329	−	0.225155i
$435$	2.28099	−	3.95080i	0.109365	−	0.189426i
$436$	−0.0696660	−	0.395096i	−0.00333640	−	0.0189217i
$437$	4.13053	−	23.4254i	0.197590	−	1.12059i
$438$	−4.81300	+	1.75179i	−0.229974	+	0.0837037i
$439$	3.48703	+	1.26917i	0.166427	+	0.0605744i	0.423890	−	0.905714i	$-0.360664\pi$
$439$	3.48703	+	1.26917i	0.166427	+	0.0605744i	−0.257463	+	0.966288i	$0.582887\pi$
$440$	7.17472	+	40.6898i	0.342041	+	1.93981i
$441$	2.47736	−	14.0498i	0.117969	−	0.669037i
$442$	−8.17615	−	14.1615i	−0.388900	−	0.673594i
$443$	−20.2105	−	16.9586i	−0.960229	−	0.805727i	0.0207616	−	0.999784i	$-0.493391\pi$
$443$	−20.2105	−	16.9586i	−0.960229	−	0.805727i	−0.980990	+	0.194057i	$0.937835\pi$
$444$	−1.17493			−0.0557599
$445$	−3.94617			−0.187066
$446$	−15.6082	−	13.0968i	−0.739070	−	0.620153i
$447$	0.291301	+	0.504547i	0.0137780	+	0.0238643i
$448$	2.17834	−	12.3540i	0.102917	−	0.583670i
$449$	6.39388	+	36.2615i	0.301746	+	1.71129i	0.638440	+	0.769672i	$0.279580\pi$
$449$	6.39388	+	36.2615i	0.301746	+	1.71129i	−0.336694	+	0.941614i	$0.609309\pi$
$450$	33.8947	+	12.3367i	1.59781	+	0.581557i
$451$	12.4908	−	4.54630i	0.588171	−	0.214077i
$452$	−0.583837	+	3.31110i	−0.0274614	+	0.155741i
$453$	−1.39849	−	7.93124i	−0.0657069	−	0.372642i
$454$	6.00653	−	10.4036i	0.281900	−	0.488266i
$455$	25.2284	−	21.1691i	1.18272	−	0.992423i
$456$	4.16567	−	1.51618i	0.195075	−	0.0710017i
$457$	−13.4716	+	23.3334i	−0.630173	+	1.09149i	0.357342	+	0.933973i	$0.383683\pi$
$457$	−13.4716	+	23.3334i	−0.630173	+	1.09149i	−0.987516	+	0.157519i	$0.949650\pi$
$458$	7.88348	−	13.6546i	0.368371	−	0.638037i
$459$	−4.06504	−	1.47955i	−0.189740	−	0.0690597i
$460$	4.80983	+	4.03593i	0.224260	+	0.188176i
$461$	1.39713	+	2.41990i	0.0650707	+	0.112706i	0.896725	−	0.442587i	$-0.145939\pi$
$461$	1.39713	+	2.41990i	0.0650707	+	0.112706i	−0.831655	+	0.555293i	$0.812606\pi$
$462$	−2.25841	+	0.821996i	−0.105071	+	0.0382427i
$463$	3.86630	−	3.24421i	0.179682	−	0.150771i	−0.548511	−	0.836144i	$-0.684805\pi$
$463$	3.86630	−	3.24421i	0.179682	−	0.150771i	0.728193	+	0.685372i	$0.240361\pi$
$464$	10.5288	+	3.83217i	0.488787	+	0.177904i
$465$	−4.07627	+	3.42040i	−0.189033	+	0.158617i
$466$	−24.6272	+	20.6646i	−1.14083	+	0.957271i
$467$	1.26467	−	1.06118i	0.0585220	−	0.0491058i	−0.613058	−	0.790038i	$-0.710061\pi$
$467$	1.26467	−	1.06118i	0.0585220	−	0.0491058i	0.671579	+	0.740933i	$0.265616\pi$
$468$	2.49362	+	4.31908i	0.115268	+	0.199649i
$469$	−20.1161	−	7.32166i	−0.928875	−	0.338083i
$470$	−23.7772	+	41.1833i	−1.09676	+	1.89965i
$471$	−0.543777	+	0.456283i	−0.0250559	+	0.0210244i
$472$	2.18305	+	12.3807i	0.100483	+	0.569868i
$473$	23.0986	−	8.40721i	1.06208	−	0.386564i
$474$	0.280027	+	1.58811i	0.0128621	+	0.0729443i
$475$	−19.9351	−	34.5286i	−0.914685	−	1.58428i
$476$	0.846739			0.0388102
$477$	13.4144	+	11.2560i	0.614204	+	0.515378i
$478$	−0.986097	+	5.59243i	−0.0451030	+	0.255792i
$479$	−30.5227	−	11.1093i	−1.39462	−	0.507599i	−0.468041	−	0.883707i	$-0.655040\pi$
$479$	−30.5227	−	11.1093i	−1.39462	−	0.507599i	−0.926576	+	0.376108i	$0.877262\pi$
$480$	−0.380874	+	2.16004i	−0.0173844	+	0.0985920i
$481$	34.6996	−	60.1014i	1.58216	−	2.74039i
$482$	19.5732	−	7.12406i	0.891535	−	0.324492i
$483$	−1.45433	+	2.51898i	−0.0661745	+	0.114618i
$484$	−0.452337	−	0.379556i	−0.0205608	−	0.0172526i
$485$	−7.84178	+	2.85418i	−0.356077	+	0.129601i
$486$	−11.1712	−	4.06597i	−0.506735	−	0.184436i
$487$	23.5341	−	19.7475i	1.06643	−	0.894843i	0.0717082	−	0.997426i	$-0.477155\pi$
$487$	23.5341	−	19.7475i	1.06643	−	0.894843i	0.994725	+	0.102582i	$0.0327105\pi$
$488$	−2.09657	−	3.63137i	−0.0949074	−	0.164384i
$489$	−0.282305	+	0.488967i	−0.0127663	+	0.0221118i
$490$	4.31096	+	24.4486i	0.194749	+	1.10448i
$491$	−1.19521	−	6.77834i	−0.0539389	−	0.305902i	0.945888	−	0.324492i	$-0.105193\pi$
$491$	−1.19521	−	6.77834i	−0.0539389	−	0.305902i	−0.999827	+	0.0185899i	$0.994082\pi$
$492$	0.376454			0.0169719
$493$	−1.20304	+	6.82277i	−0.0541821	+	0.307282i
$494$	−5.70920	+	32.3785i	−0.256869	+	1.45678i
$495$	−37.2653	+	13.5634i	−1.67495	+	0.609632i
$496$	−10.0116	−	8.40070i	−0.449533	−	0.377203i
$497$	−4.45009	−	1.61970i	−0.199614	−	0.0726534i
$498$	−0.452674	−	0.784054i	−0.0202848	−	0.0351343i
$499$	2.97513	+	16.8728i	0.133185	+	0.755330i	0.976106	+	0.217293i	$0.0697228\pi$
$499$	2.97513	+	16.8728i	0.133185	+	0.755330i	−0.842921	+	0.538037i	$0.819166\pi$
$500$	5.03881			0.225342
$501$	0.0216269	−	0.122652i	0.000966219	−	0.00547970i
$502$	−21.0382	−	17.6532i	−0.938982	−	0.787900i
$503$	18.4689	+	31.9892i	0.823490	+	1.42633i	0.903068	+	0.429497i	$0.141309\pi$
$503$	18.4689	+	31.9892i	0.823490	+	1.42633i	−0.0795784	+	0.996829i	$0.525357\pi$
$504$	12.2662			0.546378
$505$	−4.62408	−	3.88006i	−0.205769	−	0.172661i
$506$	27.0644			1.20316
$507$	8.38598			0.372435
$508$	2.01665	+	2.53135i	0.0894745	+	0.112310i
$509$	−12.7007			−0.562949			−0.281474	−	0.959569i	$-0.590823\pi$
$509$	−12.7007			−0.562949			−0.281474	+	0.959569i	$0.590823\pi$
$510$	3.68250			0.163064
$511$	12.0004	+	10.0695i	0.530866	+	0.445449i
$512$	−25.4014			−1.12259
$513$	4.34886	+	7.53244i	0.192007	+	0.332565i
$514$	−14.5804	−	12.2344i	−0.643115	−	0.539638i
$515$	−3.15856	+	17.9131i	−0.139183	+	0.789345i
$516$	0.696155			0.0306465
$517$	−5.96818	−	33.8472i	−0.262480	−	1.48860i
$518$	−10.7161	−	18.5609i	−0.470839	−	0.815517i
$519$	−2.70985	−	0.986305i	−0.118949	−	0.0432940i
$520$	−52.9462	−	44.4271i	−2.32184	−	1.94826i
$521$	−22.8589	+	8.31995i	−1.00147	+	0.364504i	−0.790150	−	0.612914i	$-0.789997\pi$
$521$	−22.8589	+	8.31995i	−1.00147	+	0.364504i	−0.211316	+	0.977418i	$0.567775\pi$
$522$	−2.18828	+	12.4104i	−0.0957785	+	0.543187i
$523$	0.263850	−	1.49637i	0.0115373	−	0.0654315i	−0.978496	−	0.206268i	$-0.933868\pi$
$523$	0.263850	−	1.49637i	0.0115373	−	0.0654315i	0.990033	+	0.140837i	$0.0449792\pi$
$524$	−2.66705			−0.116510
$525$	0.846599	+	4.80130i	0.0369486	+	0.209546i
$526$	1.93476	+	10.9726i	0.0843596	+	0.478427i
$527$	4.04049	−	6.99833i	0.176007	−	0.304852i
$528$	2.15217	+	3.72767i	0.0936613	+	0.162226i
$529$	7.47265	−	6.27030i	0.324898	−	0.272622i
$530$	−28.6345	−	10.4221i	−1.24380	−	0.452707i
$531$	−11.3387	+	4.12695i	−0.492058	+	0.179095i
$532$	−1.30416	−	1.09432i	−0.0565423	−	0.0474446i
$533$	−11.1179	+	19.2568i	−0.481569	+	0.834102i
$534$	−0.452679	+	0.164762i	−0.0195893	+	0.00712993i
$535$	−19.6828	+	34.0917i	−0.850963	+	1.47391i
$536$	−7.80142	+	44.2440i	−0.336970	+	1.91105i
$537$	7.94449	+	2.89156i	0.342830	+	0.124780i
$538$	2.91961	−	16.5579i	0.125873	−	0.713864i
$539$	−13.7448	−	11.5332i	−0.592030	−	0.496772i
$540$	−2.29586			−0.0987982
$541$	−21.6717	−	37.5365i	−0.931739	−	1.61382i	−0.780348	−	0.625345i	$-0.784958\pi$
$541$	−21.6717	−	37.5365i	−0.931739	−	1.61382i	−0.151391	−	0.988474i	$-0.548375\pi$
$542$	−1.88259	−	10.6767i	−0.0808641	−	0.458603i
$543$	0.671598	−	0.244442i	0.0288210	−	0.0104900i
$544$	−0.578410	−	3.28033i	−0.0247991	−	0.140643i
$545$	−4.08798	+	3.43022i	−0.175110	+	0.146935i
$546$	2.01018	−	3.48173i	0.0860276	−	0.149004i
$547$	−10.3368	−	3.76229i	−0.441970	−	0.160864i	0.111443	−	0.993771i	$-0.464453\pi$
$547$	−10.3368	−	3.76229i	−0.441970	−	0.160864i	−0.553413	+	0.832907i	$0.686675\pi$
$548$	−0.540872	−	0.936819i	−0.0231049	−	0.0400189i
$549$	3.08303	−	2.58697i	0.131580	−	0.110409i
$550$	34.7509	−	29.1595i	1.48178	−	1.24336i
$551$	10.6706	−	8.95370i	0.454583	−	0.381440i
$552$	5.73622	+	2.08781i	0.244150	+	0.0888632i
$553$	3.77828	−	3.17036i	0.160669	−	0.134817i
$554$	−16.3139	+	5.93778i	−0.693112	+	0.252272i
$555$	7.81426	+	13.5347i	0.331697	+	0.574516i
$556$	1.72200	+	1.44493i	0.0730289	+	0.0612785i
$557$	31.2715	+	11.3819i	1.32502	+	0.482267i	0.905062	−	0.425279i	$-0.139824\pi$
$557$	31.2715	+	11.3819i	1.32502	+	0.482267i	0.419954	+	0.907545i	$0.362046\pi$
$558$	7.34950	−	12.7297i	0.311129	−	0.538892i
$559$	−20.5597	+	35.6104i	−0.869582	+	1.50616i
$560$	−17.1168	+	6.23002i	−0.723318	+	0.263266i
$561$	−2.03881	+	1.71077i	−0.0860787	+	0.0722286i
$562$	14.6104	−	25.3060i	0.616303	−	1.06747i
$563$	−0.416420	−	2.36163i	−0.0175500	−	0.0995310i	0.974775	−	0.223192i	$-0.0716476\pi$
$563$	−0.416420	−	2.36163i	−0.0175500	−	0.0995310i	−0.992325	+	0.123661i	$0.960537\pi$
$564$	0.169024	−	0.958581i	0.00711718	−	0.0403635i
$565$	42.0253	−	15.2960i	1.76802	−	0.643506i
$566$	39.5317	+	14.3883i	1.66164	+	0.604787i
$567$	1.95005	+	11.0593i	0.0818942	+	0.464445i
$568$	−1.72583	+	9.78768i	−0.0724143	+	0.410682i
$569$	2.96633	+	5.13784i	0.124355	+	0.215389i	0.921481	−	0.388424i	$-0.126980\pi$
$569$	2.96633	+	5.13784i	0.124355	+	0.215389i	−0.797126	+	0.603814i	$0.793647\pi$
$570$	−5.67182	−	4.75922i	−0.237566	−	0.199342i
$571$	16.9259			0.708325			0.354163	−	0.935184i	$-0.384766\pi$
$571$	16.9259			0.708325			0.354163	+	0.935184i	$0.384766\pi$
$572$	6.27229			0.262258
$573$	5.24495	+	4.40103i	0.219111	+	0.183856i
$574$	3.43349	+	5.94698i	0.143311	+	0.248222i
$575$	9.53365	−	54.0680i	0.397581	−	2.25479i
$576$	−4.38788	−	24.8849i	−0.182828	−	1.03687i
$577$	11.4130	+	4.15401i	0.475131	+	0.172934i	0.568475	−	0.822700i	$-0.307533\pi$
$577$	11.4130	+	4.15401i	0.475131	+	0.172934i	−0.0933440	+	0.995634i	$0.529756\pi$
$578$	15.6518	−	5.69678i	0.651028	−	0.236955i
$579$	−0.384284	+	2.17938i	−0.0159703	+	0.0905720i
$580$	0.638478	+	3.62099i	0.0265114	+	0.150353i
$581$	−1.38451	+	2.39804i	−0.0574392	+	0.0994876i
$582$	−0.780390	+	0.654825i	−0.0323482	+	0.0271434i
$583$	20.6952	−	7.53243i	0.857107	−	0.311962i
$584$	16.4383	−	28.4720i	0.680222	−	1.17818i
$585$	33.1692	−	57.4507i	1.37138	−	2.37529i
$586$	13.5437	+	4.92951i	0.559486	+	0.203636i
$587$	−2.49148	−	2.09060i	−0.102834	−	0.0862881i	0.589921	−	0.807461i	$-0.299159\pi$
$587$	−2.49148	−	2.09060i	−0.102834	−	0.0862881i	−0.692755	+	0.721173i	$0.743603\pi$
$588$	−0.254074	−	0.440069i	−0.0104778	−	0.0181481i
$589$	−15.2678	+	5.55702i	−0.629098	+	0.228973i
$590$	16.0849	−	13.4968i	0.662203	−	0.555654i
$591$	−5.17468	−	1.88343i	−0.212858	−	0.0774739i
$592$	−29.4043	+	24.6731i	−1.20851	+	1.01406i
$593$	−35.2143	+	29.5483i	−1.44608	+	1.21340i	−0.510695	+	0.859762i	$0.670612\pi$
$593$	−35.2143	+	29.5483i	−1.44608	+	1.21340i	−0.935381	+	0.353640i	$0.884944\pi$
$594$	−7.58094	+	6.36116i	−0.311050	+	0.261002i
$595$	−5.63150	−	9.75404i	−0.230869	−	0.399877i
$596$	−0.441244	−	0.160600i	−0.0180741	−	0.00657842i
$597$	−1.84090	+	3.18853i	−0.0753431	+	0.130498i
$598$	−34.6816	+	29.1013i	−1.41824	+	1.19004i
$599$	7.12249	+	40.3936i	0.291017	+	1.65044i	0.682964	+	0.730452i	$0.260690\pi$
$599$	7.12249	+	40.3936i	0.291017	+	1.65044i	−0.391947	+	0.919988i	$0.628199\pi$
$600$	9.61477	−	3.49949i	0.392521	−	0.142866i
$601$	1.48177	+	8.40354i	0.0604427	+	0.342788i	1.00000		0.000395701i	$0.000125955\pi$
$601$	1.48177	+	8.40354i	0.0604427	+	0.342788i	−0.939557	+	0.342392i	$0.888763\pi$
$602$	6.34936	+	10.9974i	0.258780	+	0.448221i
$603$	−43.1208			−1.75602
$604$	4.97239	+	4.17233i	0.202324	+	0.169770i
$605$	−1.36390	+	7.73507i	−0.0554505	+	0.314475i
$606$	−0.692446	−	0.252030i	−0.0281287	−	0.0102380i
$607$	−4.47752	+	25.3933i	−0.181737	+	1.03068i	0.748340	+	0.663315i	$0.230851\pi$
$607$	−4.47752	+	25.3933i	−0.181737	+	1.03068i	−0.930077	+	0.367365i	$0.880260\pi$
$608$	−3.34859	+	5.79992i	−0.135803	+	0.235218i
$609$	−1.60059	+	0.582567i	−0.0648592	+	0.0236068i
$610$	−3.50170	+	6.06512i	−0.141780	+	0.245570i
$611$	44.0425	+	36.9560i	1.78177	+	1.49508i
$612$	1.60275	−	0.583352i	0.0647872	−	0.0235806i
$613$	−36.2251	−	13.1848i	−1.46312	−	0.532531i	−0.516895	−	0.856049i	$-0.672912\pi$
$613$	−36.2251	−	13.1848i	−1.46312	−	0.532531i	−0.946222	+	0.323518i	$0.895134\pi$
$614$	3.96243	−	3.32487i	0.159911	−	0.134181i
$615$	−2.50372	−	4.33657i	−0.100960	−	0.174868i
$616$	7.71338	−	13.3600i	0.310781	−	0.538288i
$617$	3.35334	+	19.0177i	0.135000	+	0.765624i	0.974860	+	0.222820i	$0.0715263\pi$
$617$	3.35334	+	19.0177i	0.135000	+	0.765624i	−0.839859	+	0.542804i	$0.817363\pi$
$618$	0.385583	+	2.18675i	0.0155104	+	0.0879641i
$619$	−2.48244			−0.0997778			−0.0498889	−	0.998755i	$-0.515887\pi$
$619$	−2.48244			−0.0997778			−0.0498889	+	0.998755i	$0.515887\pi$
$620$	0.744734	−	4.22360i	0.0299092	−	0.169624i
$621$	−2.07977	+	11.7950i	−0.0834584	+	0.473316i
$622$	37.1108	−	13.5072i	1.48801	−	0.541591i
$623$	1.12868	+	0.947072i	0.0452195	+	0.0379436i
$624$	−6.76611	−	2.46266i	−0.270861	−	0.0985854i
$625$	−9.52980	−	16.5061i	−0.381192	−	0.660244i
$626$	5.04666	+	28.6211i	0.201705	+	1.14393i
$627$	5.35117			0.213705
$628$	0.0993479	−	0.563430i	0.00396441	−	0.0224833i
$629$	−18.1814	−	15.2560i	−0.724939	−	0.608296i
$630$	−10.2435	−	17.7422i	−0.408110	−	0.706868i
$631$	−36.2104			−1.44151			−0.720756	−	0.693188i	$-0.756205\pi$
$631$	−36.2104			−1.44151			−0.720756	+	0.693188i	$0.756205\pi$
$632$	−7.92939	−	6.65355i	−0.315414	−	0.264664i
$633$	2.46703			0.0980555
$634$	−13.7926			−0.547775
$635$	15.7476	−	40.0664i	0.624923	−	1.58999i
$636$	0.623720			0.0247321
$637$	30.0144			1.18922
$638$	12.1410	+	10.1875i	0.480665	+	0.403326i
$639$	−9.53920			−0.377365
$640$	15.8301	+	27.4186i	0.625741	+	1.08382i
$641$	17.6706	+	14.8274i	0.697949	+	0.585648i	0.921189	−	0.389115i	$-0.127219\pi$
$641$	17.6706	+	14.8274i	0.697949	+	0.585648i	−0.223241	+	0.974763i	$0.571664\pi$
$642$	−0.834481	+	4.73258i	−0.0329344	+	0.186780i
$643$	43.1856			1.70307			0.851537	−	0.524295i	$-0.175671\pi$
$643$	43.1856			1.70307			0.851537	+	0.524295i	$0.175671\pi$
$644$	−0.407086	−	2.30870i	−0.0160414	−	0.0909755i
$645$	−4.62999	−	8.01938i	−0.182306	−	0.315763i
$646$	10.5660	+	3.84570i	0.415712	+	0.151307i
$647$	−29.2070	−	24.5076i	−1.14825	−	0.963492i	−0.148568	−	0.988902i	$-0.547466\pi$
$647$	−29.2070	−	24.5076i	−1.14825	−	0.963492i	−0.999677	+	0.0254102i	$0.991911\pi$
$648$	22.1465	−	8.06068i	0.869998	−	0.316653i
$649$	−2.63520	+	14.9450i	−0.103441	+	0.586642i
$650$	−13.1774	+	74.7326i	−0.516859	+	2.93125i
$651$	1.98678			0.0778679
$652$	−0.0790207	−	0.448148i	−0.00309469	−	0.0175508i
$653$	−2.37798	−	13.4862i	−0.0930576	−	0.527756i	−0.995325	−	0.0965796i	$-0.969210\pi$
$653$	−2.37798	−	13.4862i	−0.0930576	−	0.527756i	0.902268	−	0.431176i	$-0.141901\pi$
$654$	−0.325727	+	0.564176i	−0.0127369	+	0.0220610i
$655$	17.7380	+	30.7231i	0.693081	+	1.20045i
$656$	9.42126	−	7.90537i	0.367838	−	0.308653i
$657$	29.6522	+	10.7925i	1.15684	+	0.421056i
$658$	16.6846	−	6.07271i	0.650435	−	0.236739i
$659$	30.1847	+	25.3279i	1.17583	+	0.986636i	0.999998	+	0.00221581i	$0.000705316\pi$
$659$	30.1847	+	25.3279i	1.17583	+	0.986636i	0.175830	+	0.984421i	$0.443739\pi$
$660$	−0.706252	+	1.22327i	−0.0274908	+	0.0476155i
$661$	31.9634	−	11.6337i	1.24323	−	0.452499i	0.365122	−	0.930960i	$-0.381027\pi$
$661$	31.9634	−	11.6337i	1.24323	−	0.452499i	0.878109	+	0.478461i	$0.158805\pi$
$662$	−8.14061	+	14.1000i	−0.316394	+	0.548010i
$663$	0.773107	−	4.38451i	0.0300250	−	0.170280i
$664$	5.46082	+	1.98758i	0.211921	+	0.0771329i
$665$	−3.93233	+	22.3014i	−0.152489	+	0.864809i
$666$	−33.0713	−	27.7501i	−1.28149	−	1.07529i
$667$	19.1812			0.742699
$668$	0.0501899	+	0.0869314i	0.00194190	+	0.00336348i
$669$	−0.963296	−	5.46312i	−0.0372432	−	0.211216i
$670$	70.5112	−	25.6640i	2.72409	−	0.991487i
$671$	−0.878941	−	4.98472i	−0.0339311	−	0.192433i
$672$	0.627343	−	0.526403i	0.0242003	−	0.0203064i
$673$	12.8382	−	22.2364i	0.494876	−	0.857150i	−0.505107	−	0.863057i	$-0.668547\pi$
$673$	12.8382	−	22.2364i	0.494876	−	0.857150i	0.999983	+	0.00590708i	$0.00188029\pi$
$674$	−23.9545	−	8.71871i	−0.922691	−	0.335832i
$675$	10.0376	+	17.3856i	0.386346	+	0.669172i
$676$	−5.17761	+	4.34453i	−0.199139	+	0.167097i
$677$	8.77129	−	7.35999i	0.337108	−	0.282867i	−0.458481	−	0.888704i	$-0.651606\pi$
$677$	8.77129	−	7.35999i	0.337108	−	0.282867i	0.795589	+	0.605837i	$0.207162\pi$
$678$	4.18223	−	3.50931i	0.160618	−	0.134774i
$679$	2.92789	+	1.06567i	0.112362	+	0.0408965i
$680$	−18.1073	+	15.1938i	−0.694383	+	0.582656i
$681$	3.07348	−	1.11865i	0.117776	−	0.0428669i
$682$	−9.24323	−	16.0098i	−0.353942	−	0.613045i
$683$	−26.0618	−	21.8684i	−0.997226	−	0.836772i	−0.0106279	−	0.999944i	$-0.503383\pi$
$683$	−26.0618	−	21.8684i	−0.997226	−	0.836772i	−0.986598	+	0.163172i	$0.947827\pi$
$684$	−3.22248	−	1.17289i	−0.123215	−	0.0448465i
$685$	−7.19447	+	12.4612i	−0.274887	+	0.476118i
$686$	11.1679	−	19.3434i	0.426394	−	0.738536i
$687$	4.03389	−	1.46822i	0.153903	−	0.0560159i
$688$	17.4222	−	14.6190i	0.664215	−	0.557343i
$689$	−18.4204	+	31.9051i	−0.701763	+	1.21549i
$690$	−1.77043	−	10.0406i	−0.0673992	−	0.382240i
$691$	−6.43786	+	36.5109i	−0.244908	+	1.38894i	0.575800	+	0.817591i	$0.304691\pi$
$691$	−6.43786	+	36.5109i	−0.244908	+	1.38894i	−0.820707	+	0.571349i	$0.806420\pi$
$692$	2.18407	−	0.794937i	0.0830259	−	0.0302190i
$693$	13.9138	+	5.06419i	0.528540	+	0.192373i
$694$	−2.49909	−	14.1730i	−0.0948640	−	0.538000i
$695$	5.19222	−	29.4465i	0.196952	−	1.11697i
$696$	1.78735	+	3.09578i	0.0677493	+	0.117345i
$697$	5.82539	+	4.88808i	0.220652	+	0.185149i
$698$	−10.7455			−0.406723
$699$	−8.75288			−0.331064
$700$	−3.01012	−	2.52579i	−0.113772	−	0.0954658i
$701$	−9.75807	−	16.9015i	−0.368557	−	0.638360i	0.620783	−	0.783982i	$-0.286815\pi$
$701$	−9.75807	−	16.9015i	−0.368557	−	0.638360i	−0.989340	+	0.145623i	$0.953481\pi$
$702$	2.87465	−	16.3030i	0.108497	−	0.615316i
$703$	8.28646	+	46.9948i	0.312530	+	1.77244i
$704$	−29.8632	−	10.8693i	−1.12551	−	0.409652i
$705$	−12.1665	+	4.42826i	−0.458219	+	0.166778i
$706$	3.65586	−	20.7334i	0.137590	−	0.780313i
$707$	0.391365	+	2.21954i	0.0147188	+	0.0834744i
$708$	−0.214892	+	0.372203i	−0.00807612	+	0.0139883i
$709$	−5.60996	+	4.70731i	−0.210686	+	0.176787i	−0.742024	−	0.670373i	$-0.766134\pi$
$709$	−5.60996	+	4.70731i	−0.210686	+	0.176787i	0.531338	+	0.847160i	$0.321690\pi$
$710$	15.5985	−	5.67739i	0.585402	−	0.213069i
$711$	4.96752	−	8.60400i	0.186297	−	0.322675i
$712$	1.54608	−	2.67788i	0.0579417	−	0.100358i
$713$	−21.0240	−	7.65213i	−0.787357	−	0.286574i
$714$	−1.05326	−	0.883792i	−0.0394174	−	0.0330751i
$715$	−41.7158	−	72.2539i	−1.56008	−	2.70214i
$716$	−6.40306	+	2.33052i	−0.239294	+	0.0870958i
$717$	−1.18439	+	0.993819i	−0.0442318	+	0.0371149i
$718$	1.86309	+	0.678111i	0.0695300	+	0.0253069i
$719$	8.86775	−	7.44093i	0.330711	−	0.277500i	−0.462278	−	0.886735i	$-0.652968\pi$
$719$	8.86775	−	7.44093i	0.330711	−	0.277500i	0.792990	+	0.609235i	$0.208523\pi$
$720$	−28.1074	+	23.5849i	−1.04750	+	0.878959i
$721$	5.20251	−	4.36543i	0.193752	−	0.162577i
$722$	1.12940	+	1.95618i	0.0420321	+	0.0728017i
$723$	5.32908	+	1.93963i	0.198191	+	0.0721355i
$724$	−0.288015	+	0.498857i	−0.0107040	+	0.0185399i
$725$	24.6288	−	20.6660i	0.914690	−	0.767516i
$726$	0.166499	+	0.944263i	0.00617936	+	0.0350449i
$727$	−19.4982	+	7.09678i	−0.723150	+	0.263205i	−0.677262	−	0.735742i	$-0.736834\pi$
$727$	−19.4982	+	7.09678i	−0.723150	+	0.263205i	−0.0458873	+	0.998947i	$0.514612\pi$
$728$	4.48117	+	25.4140i	0.166083	+	0.941904i
$729$	10.1918	+	17.6527i	0.377473	+	0.653803i
$730$	−54.9106			−2.03233
$731$	10.7726	+	9.03926i	0.398438	+	0.334329i
$732$	0.0248923	−	0.141171i	0.000920047	−	0.00521785i
$733$	39.6137	+	14.4182i	1.46317	+	0.532549i	0.946236	−	0.323479i	$-0.104852\pi$
$733$	39.6137	+	14.4182i	1.46317	+	0.532549i	0.516930	+	0.856027i	$0.327075\pi$
$734$	−7.42266	+	42.0960i	−0.273975	+	1.55379i
$735$	−3.37959	+	5.85362i	−0.124658	+	0.215914i
$736$	−8.66599	+	3.15416i	−0.319432	+	0.116264i
$737$	−27.1158	+	46.9660i	−0.998825	+	1.73002i
$738$	10.5962	+	8.89124i	0.390050	+	0.327291i
$739$	−21.3099	+	7.75617i	−0.783897	+	0.285315i	−0.702797	−	0.711391i	$-0.748066\pi$
$739$	−21.3099	+	7.75617i	−0.783897	+	0.285315i	−0.0811006	+	0.996706i	$0.525844\pi$
$740$	−11.8366	−	4.30815i	−0.435120	−	0.158371i
$741$	−6.85724	+	5.75391i	−0.251907	+	0.211375i
$742$	5.68870	+	9.85312i	0.208839	+	0.361719i
$743$	16.7714	−	29.0489i	0.615283	−	1.06570i	−0.375051	−	0.927004i	$-0.622375\pi$
$743$	16.7714	−	29.0489i	0.615283	−	1.06570i	0.990335	−	0.138698i	$-0.0442917\pi$
$744$	−0.724044	−	4.10626i	−0.0265447	−	0.150543i
$745$	1.08459	+	6.15104i	0.0397365	+	0.225357i
$746$	−33.2577			−1.21765
$747$	−0.968559	+	5.49297i	−0.0354377	+	0.200977i
$748$	0.372490	−	2.11250i	0.0136196	−	0.0772406i
$749$	13.8116	−	5.02700i	0.504664	−	0.183683i
$750$	−6.26779	−	5.25930i	−0.228867	−	0.192043i
$751$	22.7374	+	8.27572i	0.829698	+	0.301985i	0.721735	−	0.692169i	$-0.243345\pi$
$751$	22.7374	+	8.27572i	0.829698	+	0.301985i	0.107963	+	0.994155i	$0.465567\pi$
$752$	−15.8998	−	27.5392i	−0.579804	−	1.00425i
$753$	−1.29842	−	7.36372i	−0.0473171	−	0.268349i
$754$	−26.5122			−0.965516
$755$	14.9929	−	85.0290i	0.545648	−	3.09452i
$756$	0.656659	+	0.551002i	0.0238825	+	0.0200398i
$757$	−17.4966	−	30.3051i	−0.635926	−	1.10146i	−0.986318	−	0.164853i	$-0.947285\pi$
$757$	−17.4966	−	30.3051i	−0.635926	−	1.10146i	0.350392	−	0.936603i	$-0.386048\pi$
$758$	−2.93221			−0.106503
$759$	5.64474	+	4.73650i	0.204891	+	0.171924i
$760$	47.5253			1.72393
$761$	−30.7894			−1.11611			−0.558057	−	0.829803i	$-0.688453\pi$
$761$	−30.7894			−1.11611			−0.558057	+	0.829803i	$0.688453\pi$
$762$	0.133595	−	5.25366i	0.00483965	−	0.190320i
$763$	1.99249			0.0721328
$764$	−5.51834			−0.199647
$765$	−17.3795	−	14.5831i	−0.628357	−	0.527254i
$766$	−14.2785			−0.515905
$767$	−12.6929	−	21.9847i	−0.458313	−	0.793822i
$768$	−1.84073	−	1.54456i	−0.0664218	−	0.0557345i
$769$	−2.57052	+	14.5782i	−0.0926955	+	0.525702i	0.902734	+	0.430200i	$0.141557\pi$
$769$	−2.57052	+	14.5782i	−0.0926955	+	0.525702i	−0.995429	+	0.0955025i	$0.969554\pi$
$770$	−25.7658			−0.928535
$771$	−0.899864	−	5.10338i	−0.0324078	−	0.183794i
$772$	−0.891812	−	1.54466i	−0.0320970	−	0.0555937i
$773$	−9.96924	−	3.62851i	−0.358569	−	0.130508i	0.156453	−	0.987685i	$-0.449994\pi$
$773$	−9.96924	−	3.62851i	−0.358569	−	0.130508i	−0.515022	+	0.857177i	$0.672216\pi$
$774$	19.5949	+	16.4421i	0.704324	+	0.590998i
$775$	−35.2395	+	12.8261i	−1.26584	+	0.460728i
$776$	1.13549	−	6.43971i	0.0407619	−	0.231172i
$777$	1.01328	−	5.74658i	0.0363511	−	0.206157i
$778$	−14.0921			−0.505228
$779$	−2.65502	−	15.0573i	−0.0951258	−	0.539485i
$780$	−0.410305	−	2.32695i	−0.0146913	−	0.0833183i
$781$	−5.99857	+	10.3898i	−0.214646	+	0.371777i
$782$	7.74166	+	13.4089i	0.276841	+	0.479503i
$783$	−5.37278	+	4.50830i	−0.192008	+	0.161114i
$784$	−15.5998	−	5.67786i	−0.557135	−	0.202781i
$785$	−7.15119	+	2.60282i	−0.255237	+	0.0928987i
$786$	3.31755	+	2.78375i	0.118333	+	0.0992932i
$787$	−22.9729	+	39.7903i	−0.818897	+	1.41837i	0.0875985	+	0.996156i	$0.472081\pi$
$787$	−22.9729	+	39.7903i	−0.818897	+	1.41837i	−0.906496	+	0.422215i	$0.861253\pi$
$788$	4.17066	−	1.51800i	0.148574	−	0.0540764i
$789$	−1.51676	+	2.62711i	−0.0539982	+	0.0935276i
$790$	−3.00210	+	17.0258i	−0.106810	+	0.605750i
$791$	−15.6910	−	5.71106i	−0.557908	−	0.203062i
$792$	5.39603	−	30.6024i	0.191739	−	1.08741i
$793$	6.48619	+	5.44256i	0.230331	+	0.193271i
$794$	0.357024			0.0126703
$795$	−4.14824	−	7.18496i	−0.147123	−	0.254824i
$796$	−0.515291	−	2.92236i	−0.0182640	−	0.103580i
$797$	22.8322	−	8.31022i	0.808756	−	0.294363i	0.0956463	−	0.995415i	$-0.469508\pi$
$797$	22.8322	−	8.31022i	0.808756	−	0.294363i	0.713110	+	0.701052i	$0.247286\pi$
$798$	0.480042	+	2.72245i	0.0169933	+	0.0963737i
$799$	15.0623	−	12.6387i	0.532865	−	0.447127i
$800$	−7.72886	+	13.3868i	−0.273256	+	0.473294i
$801$	2.78888	+	1.01507i	0.0985404	+	0.0358658i
$802$	17.1168	+	29.6472i	0.604416	+	1.04688i
$803$	30.4012	−	25.5096i	1.07283	−	0.900215i
$804$	−1.17656	+	0.987248i	−0.0414939	+	0.0348176i
$805$	−23.8877	+	20.0442i	−0.841931	+	0.706464i
$806$	29.0594	+	10.5767i	1.02357	+	0.372550i
$807$	3.50671	−	2.94248i	0.123442	−	0.103580i
$808$	4.44470	−	1.61774i	0.156364	−	0.0569119i
$809$	8.13584	+	14.0917i	0.286041	+	0.495437i	0.972861	−	0.231390i	$-0.0743274\pi$
$809$	8.13584	+	14.0917i	0.286041	+	0.495437i	−0.686820	+	0.726827i	$0.740994\pi$
$810$	−30.1539	−	25.3021i	−1.05950	−	0.889026i
$811$	−30.1311	−	10.9668i	−1.05805	−	0.385097i	−0.246352	−	0.969180i	$-0.579232\pi$
$811$	−30.1311	−	10.9668i	−1.05805	−	0.385097i	−0.811694	+	0.584083i	$0.801454\pi$
$812$	0.686414	−	1.18890i	0.0240884	−	0.0417223i
$813$	1.47586	−	2.55627i	0.0517607	−	0.0896522i
$814$	−51.0209	+	18.5701i	−1.78828	+	0.650882i
$815$	−4.63691	+	3.89083i	−0.162424	+	0.136290i
$816$	−1.23124	+	2.13257i	−0.0431020	+	0.0746548i
$817$	−4.90977	−	27.8447i	−0.171771	−	0.974163i
$818$	6.00953	−	34.0818i	0.210118	−	1.19164i
$819$	−23.2750	+	8.47142i	−0.813296	+	0.296015i
$820$	3.79248	+	1.38035i	0.132439	+	0.0482039i
$821$	−1.90389	−	10.7975i	−0.0664461	−	0.376834i	−0.999838	−	0.0179768i	$-0.994278\pi$
$821$	−1.90389	−	10.7975i	−0.0664461	−	0.376834i	0.933392	−	0.358858i	$-0.116834\pi$
$822$	−0.305020	+	1.72985i	−0.0106388	+	0.0603356i
$823$	−6.34098	−	10.9829i	−0.221033	−	0.382840i	0.734089	−	0.679053i	$-0.237609\pi$
$823$	−6.34098	−	10.9829i	−0.221033	−	0.382840i	−0.955122	+	0.296213i	$0.904276\pi$
$824$	−10.9184	−	9.16162i	−0.380360	−	0.319160i
$825$	12.3510			0.430007
$826$	−7.83977			−0.272780
$827$	36.8797	+	30.9457i	1.28243	+	1.07609i	0.992904	+	0.118919i	$0.0379430\pi$
$827$	36.8797	+	30.9457i	1.28243	+	1.07609i	0.289529	+	0.957169i	$0.406501\pi$
$828$	−2.36111	−	4.08956i	−0.0820541	−	0.142122i
$829$	2.89651	−	16.4269i	0.100600	−	0.570530i	−0.892287	−	0.451469i	$-0.850900\pi$
$829$	2.89651	−	16.4269i	0.100600	−	0.570530i	0.992887	−	0.119062i	$-0.0379886\pi$
$830$	−1.68543	−	9.55857i	−0.0585022	−	0.331783i
$831$	−4.44169	−	1.61664i	−0.154081	−	0.0560808i
$832$	49.9554	−	18.1823i	1.73189	−	0.630357i
$833$	1.78246	−	10.1088i	0.0617585	−	0.350250i
$834$	−0.633843	−	3.59470i	−0.0219482	−	0.124474i
$835$	0.667606	−	1.15633i	0.0231035	−	0.0400164i
$836$	−3.30388	+	2.77229i	−0.114267	+	0.0958816i
$837$	7.68752	−	2.79803i	0.265720	−	0.0967140i
$838$	−10.8602	+	18.8104i	−0.375158	+	0.649793i
$839$	−1.62435	+	2.81345i	−0.0560787	+	0.0971312i	−0.892702	−	0.450648i	$-0.851193\pi$
$839$	−1.62435	+	2.81345i	−0.0560787	+	0.0971312i	0.836623	+	0.547779i	$0.184526\pi$
$840$	−5.46098	−	1.98763i	−0.188422	−	0.0685798i
$841$	−13.6107	−	11.4207i	−0.469335	−	0.393819i
$842$	10.5616	+	18.2931i	0.363975	+	0.630423i
$843$	7.47599	−	2.72104i	0.257487	−	0.0937176i
$844$	−1.52317	+	1.27809i	−0.0524298	+	0.0439938i
$845$	84.4823	+	30.7490i	2.90628	+	1.05780i
$846$	27.3977	−	22.9894i	0.941953	−	0.790392i
$847$	2.24650	−	1.88504i	0.0771907	−	0.0647707i
$848$	15.6094	−	13.0978i	0.536029	−	0.449782i
$849$	5.72690	+	9.91929i	0.196547	+	0.340429i
$850$	24.3873	+	8.87624i	0.836476	+	0.304452i
$851$	−32.8556	+	56.9075i	−1.12627	+	1.95076i
$852$	−0.260278	+	0.218399i	−0.00891698	+	0.00748224i
$853$	0.576729	+	3.27079i	0.0197468	+	0.111990i	0.993088	−	0.117372i	$-0.0374471\pi$
$853$	0.576729	+	3.27079i	0.0197468	+	0.111990i	−0.973341	+	0.229362i	$0.926336\pi$
$854$	2.45717	−	0.894336i	0.0840826	−	0.0306036i
$855$	7.92099	+	44.9222i	0.270892	+	1.53631i
$856$	−15.4232	−	26.7137i	−0.527152	−	0.913055i
$857$	22.5918			0.771722			0.385861	−	0.922557i	$-0.373904\pi$
$857$	22.5918			0.771722			0.385861	+	0.922557i	$0.373904\pi$
$858$	−7.80213	−	6.54677i	−0.266360	−	0.223503i
$859$	−7.74290	+	43.9122i	−0.264184	+	1.49826i	0.507163	+	0.861850i	$0.330694\pi$
$859$	−7.74290	+	43.9122i	−0.264184	+	1.49826i	−0.771348	+	0.636414i	$0.780417\pi$
$860$	7.01322	+	2.55260i	0.239149	+	0.0870431i
$861$	−0.324658	+	1.84123i	−0.0110643	+	0.0627489i
$862$	−4.35901	+	7.55003i	−0.148468	+	0.257155i
$863$	29.4131	−	10.7055i	1.00123	−	0.364419i	0.211172	−	0.977449i	$-0.432272\pi$
$863$	29.4131	−	10.7055i	1.00123	−	0.364419i	0.790059	+	0.613030i	$0.210050\pi$
$864$	1.68606	−	2.92034i	0.0573608	−	0.0993518i
$865$	−23.6831	−	19.8725i	−0.805251	−	0.675686i
$866$	−21.9627	+	7.99376i	−0.746322	+	0.271639i
$867$	4.26141	+	1.55103i	0.144725	+	0.0526757i
$868$	−1.22666	+	1.02929i	−0.0416356	+	0.0349364i
$869$	−6.24749	−	10.8210i	−0.211932	−	0.367076i
$870$	2.98524	−	5.17058i	0.101209	−	0.175299i
$871$	−15.7532	−	89.3410i	−0.533778	−	3.02720i
$872$	−0.726124	−	4.11805i	−0.0245897	−	0.139455i
$873$	6.27623			0.212418
$874$	5.40580	−	30.6578i	0.182854	−	1.03702i
$875$	−4.34552	+	24.6447i	−0.146906	+	0.833143i
$876$	1.05616	−	0.384410i	0.0356842	−	0.0129880i
$877$	3.66367	+	3.07418i	0.123713	+	0.103808i	0.702545	−	0.711639i	$-0.252047\pi$
$877$	3.66367	+	3.07418i	0.123713	+	0.103808i	−0.578832	+	0.815447i	$0.696491\pi$
$878$	4.56363	+	1.66102i	0.154015	+	0.0560568i
$879$	1.96206	+	3.39839i	0.0661787	+	0.114625i
$880$	8.01315	+	45.4448i	0.270123	+	1.53194i
$881$	26.7655			0.901754			0.450877	−	0.892586i	$-0.351111\pi$
$881$	26.7655			0.901754			0.450877	+	0.892586i	$0.351111\pi$
$882$	3.24222	−	18.3876i	0.109171	−	0.619142i
$883$	−1.04505	−	0.876898i	−0.0351686	−	0.0295100i	0.625034	−	0.780598i	$-0.285085\pi$
$883$	−1.04505	−	0.876898i	−0.0351686	−	0.0295100i	−0.660203	+	0.751088i	$0.729530\pi$
$884$	1.79416	+	3.10758i	0.0603441	+	0.104519i
$885$	5.71681			0.192168
$886$	−26.4503	−	22.1945i	−0.888617	−	0.745638i
$887$	−24.2721			−0.814976			−0.407488	−	0.913211i	$-0.633595\pi$
$887$	−24.2721			−0.814976			−0.407488	+	0.913211i	$0.633595\pi$
$888$	−12.2463			−0.410957
$889$	−14.1199	+	7.68034i	−0.473568	+	0.257590i
$890$	−5.16452			−0.173115
$891$	28.4492			0.953084
$892$	3.42504	+	2.87395i	0.114679	+	0.0962268i
$893$	−39.5332			−1.32293
$894$	0.381238	+	0.660323i	0.0127505	+	0.0220845i
$895$	69.4320	+	58.2604i	2.32086	+	1.94743i
$896$	2.05270	−	11.6414i	0.0685758	−	0.388913i
$897$	−12.3264			−0.411566
$898$	8.36795	+	47.4570i	0.279242	+	1.58366i
$899$	−6.55089	−	11.3465i	−0.218484	−	0.378426i
$900$	−7.43780	−	2.70714i	−0.247927	−	0.0902379i
$901$	9.65167	+	8.09871i	0.321544	+	0.269807i
$902$	16.3473	−	5.94994i	0.544306	−	0.198111i
$903$	−0.600372	+	3.40488i	−0.0199791	+	0.113307i
$904$	−6.08529	+	34.5114i	−0.202394	+	1.14783i
$905$	7.66213			0.254698
$906$	−1.83027	−	10.3800i	−0.0608066	−	0.344851i
$907$	−4.18235	−	23.7193i	−0.138873	−	0.787586i	−0.972084	−	0.234632i	$-0.924612\pi$
$907$	−4.18235	−	23.7193i	−0.138873	−	0.787586i	0.833212	−	0.552954i	$-0.186500\pi$
$908$	−1.31806	+	2.28295i	−0.0437414	+	0.0757623i
$909$	2.26992	+	3.93162i	0.0752885	+	0.130404i
$910$	33.0175	−	27.7050i	1.09452	−	0.918410i
$911$	8.87780	+	3.23125i	0.294135	+	0.107056i	0.484873	−	0.874585i	$-0.338866\pi$
$911$	8.87780	+	3.23125i	0.294135	+	0.107056i	−0.190738	+	0.981641i	$0.561088\pi$
$912$	4.65247	−	1.69336i	0.154059	−	0.0560728i
$913$	5.37373	+	4.50909i	0.177844	+	0.149229i
$914$	−17.6308	+	30.5375i	−0.583176	+	1.01009i
$915$	−1.79178	+	0.652156i	−0.0592345	+	0.0215596i
$916$	−1.72994	+	2.99634i	−0.0571587	+	0.0990017i
$917$	2.30009	−	13.0445i	0.0759557	−	0.430766i
$918$	−5.32010	−	1.93636i	−0.175589	−	0.0639093i
$919$	5.17007	−	29.3209i	0.170545	−	0.967208i	−0.772616	−	0.634873i	$-0.781052\pi$
$919$	5.17007	−	29.3209i	0.170545	−	0.967208i	0.943161	−	0.332335i	$-0.107837\pi$
$920$	50.1325	+	42.0662i	1.65282	+	1.38688i
$921$	1.40831			0.0464054
$922$	1.82848	+	3.16703i	0.0602179	+	0.104300i
$923$	−3.48493	−	19.7640i	−0.114708	−	0.650541i
$924$	0.495582	−	0.180377i	0.0163035	−	0.00593398i
$925$	19.1259	+	108.469i	0.628857	+	3.56642i
$926$	5.06000	−	4.24584i	0.166282	−	0.139527i
$927$	6.84004	−	11.8473i	0.224656	−	0.389116i
$928$	−5.07479	−	1.84707i	−0.166588	−	0.0606331i
$929$	−13.6471	−	23.6375i	−0.447747	−	0.775521i	0.550492	−	0.834841i	$-0.314440\pi$
$929$	−13.6471	−	23.6375i	−0.447747	−	0.775521i	−0.998239	+	0.0593195i	$0.981107\pi$
$930$	−5.33480	+	4.47643i	−0.174935	+	0.146788i
$931$	−15.8099	+	13.2661i	−0.518148	+	0.434778i
$932$	5.40414	−	4.53461i	0.177018	−	0.148536i
$933$	10.1040	+	3.67754i	0.330788	+	0.120397i
$934$	1.65513	−	1.38882i	0.0541575	−	0.0454436i
$935$	−26.8124	+	9.75890i	−0.876858	+	0.319150i
$936$	25.9908	+	45.0174i	0.849537	+	1.47144i
$937$	−14.0302	−	11.7727i	−0.458346	−	0.384598i	0.384176	−	0.923260i	$-0.374486\pi$
$937$	−14.0302	−	11.7727i	−0.458346	−	0.384598i	−0.842522	+	0.538662i	$0.818930\pi$
$938$	−26.3268	−	9.58218i	−0.859601	−	0.312869i
$939$	−3.95635	+	6.85260i	−0.129111	+	0.223626i
$940$	5.21763	−	9.03720i	0.170180	−	0.294761i
$941$	15.6658	−	5.70189i	0.510691	−	0.185876i	−0.0738054	−	0.997273i	$-0.523514\pi$
$941$	15.6658	−	5.70189i	0.510691	−	0.185876i	0.584496	+	0.811396i	$0.301292\pi$
$942$	−0.711665	+	0.597158i	−0.0231873	+	0.0194565i
$943$	10.5271	−	18.2334i	0.342808	−	0.593762i
$944$	2.43816	+	13.8275i	0.0793555	+	0.450047i
$945$	1.97998	−	11.2290i	0.0644087	−	0.365280i
$946$	30.2302	−	11.0029i	0.982868	−	0.357735i
$947$	−46.8577	−	17.0548i	−1.52267	−	0.554207i	−0.560858	−	0.827912i	$-0.689529\pi$
$947$	−46.8577	−	17.0548i	−1.52267	−	0.554207i	−0.961814	+	0.273705i	$0.911751\pi$
$948$	−0.0614486	−	0.348492i	−0.00199576	−	0.0113185i
$949$	−11.5280	+	65.3784i	−0.374214	+	2.12227i
$950$	−26.0899	−	45.1891i	−0.846470	−	1.46613i
$951$	−2.87668	−	2.41382i	−0.0932826	−	0.0782734i
$952$	8.82550			0.286036
$953$	38.0997			1.23417			0.617085	−	0.786896i	$-0.288313\pi$
$953$	38.0997			1.23417			0.617085	+	0.786896i	$0.288313\pi$
$954$	17.5560	+	14.7313i	0.568398	+	0.476942i
$955$	36.7014	+	63.5687i	1.18763	+	2.05704i
$956$	0.216387	−	1.22719i	0.00699847	−	0.0396903i
$957$	0.749307	+	4.24953i	0.0242217	+	0.137368i
$958$	−39.9464	−	14.5393i	−1.29061	−	0.469743i
$959$	5.04841	−	1.83747i	0.163022	−	0.0593351i
$960$	−2.07888	+	11.7899i	−0.0670957	+	0.380519i
$961$	−2.72937	−	15.4790i	−0.0880442	−	0.499324i
$962$	45.4129	−	78.6574i	1.46417	−	2.53602i
$963$	22.6799	−	19.0307i	0.730849	−	0.613255i
$964$	−4.29511	+	1.56329i	−0.138336	+	0.0503502i
$965$	−11.8625	+	20.5465i	−0.381869	+	0.661416i
$966$	−1.90335	+	3.29670i	−0.0612393	+	0.106070i
$967$	−15.0307	−	5.47074i	−0.483356	−	0.175927i	0.0888369	−	0.996046i	$-0.471685\pi$
$967$	−15.0307	−	5.47074i	−0.483356	−	0.175927i	−0.572193	+	0.820119i	$0.693907\pi$
$968$	−4.71468	−	3.95609i	−0.151536	−	0.127153i
$969$	1.53068	+	2.65121i	0.0491725	+	0.0851692i
$970$	−10.2629	+	3.73539i	−0.329522	+	0.119936i
$971$	46.3218	−	38.8686i	1.48654	−	1.24735i	0.587697	−	0.809081i	$-0.300035\pi$
$971$	46.3218	−	38.8686i	1.48654	−	1.24735i	0.898842	−	0.438273i	$-0.144410\pi$
$972$	2.45138	+	0.892230i	0.0786281	+	0.0286183i
$973$	−8.55217	+	7.17613i	−0.274170	+	0.230056i
$974$	30.8001	−	25.8444i	0.986900	−	0.828108i
$975$	−15.8272	+	13.2806i	−0.506875	+	0.425319i
$976$	−2.34158	−	4.05573i	−0.0749520	−	0.129821i
$977$	−4.20105	−	1.52906i	−0.134403	−	0.0489188i	0.273943	−	0.961746i	$-0.411672\pi$
$977$	−4.20105	−	1.52906i	−0.134403	−	0.0489188i	−0.408346	+	0.912827i	$0.633894\pi$
$978$	−0.369465	+	0.639932i	−0.0118142	+	0.0204628i
$979$	2.85933	−	2.39926i	0.0913847	−	0.0766808i
$980$	−0.945988	−	5.36497i	−0.0302185	−	0.171378i
$981$	3.77147	−	1.37270i	0.120414	−	0.0438270i
$982$	−1.56422	−	8.87112i	−0.0499162	−	0.283089i
$983$	1.04291	+	1.80636i	0.0332635	+	0.0576141i	0.882178	−	0.470916i	$-0.156077\pi$
$983$	1.04291	+	1.80636i	0.0332635	+	0.0576141i	−0.848914	+	0.528530i	$0.822743\pi$
$984$	3.92375			0.125085
$985$	−45.2249	−	37.9482i	−1.44098	−	1.20913i
$986$	−1.57447	+	8.92926i	−0.0501413	+	0.284365i
$987$	4.54263	+	1.65338i	0.144594	+	0.0526277i
$988$	1.25282	−	7.10507i	0.0398574	−	0.226042i
$989$	19.4671	−	33.7180i	0.619018	−	1.07217i
$990$	−48.7707	+	17.7511i	−1.55003	+	0.564166i
$991$	19.1504	−	33.1695i	0.608332	−	1.05366i	−0.383183	−	0.923673i	$-0.625172\pi$
$991$	19.1504	−	33.1695i	0.608332	−	1.05366i	0.991515	−	0.129990i	$-0.0414946\pi$
$992$	4.82549	+	4.04906i	0.153209	+	0.128558i
$993$	−4.16546	+	1.51611i	−0.132187	+	0.0481121i
$994$	−5.82403	−	2.11977i	−0.184727	−	0.0672351i
$995$	−30.2371	+	25.3720i	−0.958581	+	0.804345i
$996$	0.0993339	+	0.172051i	0.00314752	+	0.00545166i
$997$	18.2459	−	31.6029i	0.577854	−	1.00087i	−0.417871	−	0.908507i	$-0.637223\pi$
$997$	18.2459	−	31.6029i	0.577854	−	1.00087i	0.995725	−	0.0923667i	$-0.0294432\pi$
$998$	3.89368	+	22.0822i	0.123252	+	0.698999i
$999$	−4.17234	−	23.6625i	−0.132007	−	0.748648i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	127.2.f.a.103.8	yes	60
127.37	even	9	inner	127.2.f.a.37.8	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
127.2.f.a.37.8	✓	60	127.37	even	9	inner
127.2.f.a.103.8	yes	60	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.30874 q^{2} +(0.272960 + 0.229041i) q^{3} -0.287188 q^{4} +(1.91003 + 3.30828i) q^{5} +(0.357235 + 0.299756i) q^{6} +(0.247675 - 1.40463i) q^{7} -2.99334 q^{8} +(-0.498897 - 2.82939i) q^{9} +(2.49975 + 4.32969i) q^{10} +(-3.39541 - 1.23583i) q^{11} +(-0.0783910 - 0.0657779i) q^{12} +(5.67987 - 2.06730i) q^{13} +(0.324143 - 1.83830i) q^{14} +(-0.236367 + 1.34050i) q^{15} -3.34315 q^{16} +(-0.358956 - 2.03574i) q^{17} +(-0.652929 - 3.70294i) q^{18} +(-2.07810 + 3.59938i) q^{19} +(-0.548540 - 0.950099i) q^{20} +(0.389323 - 0.326681i) q^{21} +(-4.44372 - 1.61738i) q^{22} +(-5.37803 + 1.95744i) q^{23} +(-0.817064 - 0.685598i) q^{24} +(-4.79646 + 8.30772i) q^{25} +(7.43350 - 2.70557i) q^{26} +(1.04635 - 1.81233i) q^{27} +(-0.0711293 + 0.403394i) q^{28} +(-3.14937 - 1.14628i) q^{29} +(-0.309344 + 1.75438i) q^{30} +(2.99465 + 2.51281i) q^{31} +1.61137 q^{32} +(-0.643757 - 1.11502i) q^{33} +(-0.469782 - 2.66427i) q^{34} +(5.11998 - 1.86352i) q^{35} +(0.143277 + 0.812567i) q^{36} +(8.79539 - 7.38021i) q^{37} +(-2.71971 + 4.71067i) q^{38} +(2.02388 + 0.736631i) q^{39} +(-5.71739 - 9.90281i) q^{40} +(-2.81808 + 2.36465i) q^{41} +(0.509525 - 0.427542i) q^{42} +(-5.21132 + 4.37282i) q^{43} +(0.975123 + 0.354916i) q^{44} +(8.40748 - 7.05471i) q^{45} +(-7.03847 + 2.56179i) q^{46} +(4.75593 + 8.23750i) q^{47} +(-0.912546 - 0.765717i) q^{48} +(4.66620 + 1.69836i) q^{49} +(-6.27734 + 10.8727i) q^{50} +(0.368287 - 0.637892i) q^{51} +(-1.63119 + 0.593706i) q^{52} +(-4.66908 + 3.91782i) q^{53} +(1.36941 - 2.37188i) q^{54} +(-2.39689 - 13.5934i) q^{55} +(-0.741375 + 4.20455i) q^{56} +(-1.39164 + 0.506517i) q^{57} +(-4.12172 - 1.50018i) q^{58} +(-0.729302 - 4.13608i) q^{59} +(0.0678819 - 0.384977i) q^{60} +(0.700411 + 1.21315i) q^{61} +(3.91924 + 3.28863i) q^{62} -4.09781 q^{63} +8.79516 q^{64} +(17.6880 + 14.8420i) q^{65} +(-0.842513 - 1.45928i) q^{66} +(2.60625 - 14.7808i) q^{67} +(0.103088 + 0.584642i) q^{68} +(-1.91632 - 0.697485i) q^{69} +(6.70074 - 2.43887i) q^{70} +(0.576556 - 3.26981i) q^{71} +(1.49337 + 8.46933i) q^{72} +(-5.49162 + 9.51176i) q^{73} +(11.5109 - 9.65881i) q^{74} +(-3.21205 + 1.16909i) q^{75} +(0.596807 - 1.03370i) q^{76} +(-2.57684 + 4.46322i) q^{77} +(2.64874 + 0.964061i) q^{78} +(2.64901 + 2.22278i) q^{79} +(-6.38552 - 11.0601i) q^{80} +(-7.39859 + 2.69287i) q^{81} +(-3.68815 + 3.09472i) q^{82} +(-1.82432 - 0.663998i) q^{83} +(-0.111809 + 0.0938190i) q^{84} +(6.04918 - 5.07587i) q^{85} +(-6.82028 + 5.72290i) q^{86} +(-0.597108 - 1.03422i) q^{87} +(10.1636 + 3.69926i) q^{88} +(-0.516505 + 0.894612i) q^{89} +(11.0032 - 9.23281i) q^{90} +(-1.49704 - 8.49015i) q^{91} +(1.54451 - 0.562156i) q^{92} +(0.241885 + 1.37180i) q^{93} +(6.22429 + 10.7808i) q^{94} -15.8770 q^{95} +(0.439839 + 0.369069i) q^{96} +(-0.379340 + 2.15134i) q^{97} +(6.10686 + 2.22272i) q^{98} +(-1.80267 + 10.2235i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 12 q^{2} - 6 q^{3} + 48 q^{4} + 3 q^{5} - 9 q^{6} - 30 q^{8} - 6 q^{9} - 3 q^{10} + 3 q^{11} - 27 q^{12} + 6 q^{13} - 27 q^{14} + 48 q^{16} + 9 q^{17} + 9 q^{18} - 3 q^{19} - 3 q^{20} + 36 q^{21}+ \cdots - 111 q^{99}+O(q^{100}) \) 60 * q - 12 * q^2 - 6 * q^3 + 48 * q^4 + 3 * q^5 - 9 * q^6 - 30 * q^8 - 6 * q^9 - 3 * q^10 + 3 * q^11 - 27 * q^12 + 6 * q^13 - 27 * q^14 + 48 * q^16 + 9 * q^17 + 9 * q^18 - 3 * q^19 - 3 * q^20 + 36 * q^21 - 39 * q^22 - 24 * q^23 - 90 * q^24 - 15 * q^25 + 9 * q^27 - 30 * q^28 - 42 * q^29 - 24 * q^30 - 54 * q^31 - 102 * q^32 + 39 * q^33 - 54 * q^34 + 21 * q^35 - 33 * q^36 + 27 * q^37 + 6 * q^38 + 33 * q^39 + 24 * q^40 + 42 * q^41 + 51 * q^42 + 36 * q^43 + 66 * q^44 + 3 * q^45 - 39 * q^46 - 18 * q^47 - 30 * q^48 + 48 * q^49 + 21 * q^50 + 21 * q^51 + 12 * q^52 - 21 * q^53 + 45 * q^54 - 36 * q^55 - 90 * q^56 - 21 * q^57 + 57 * q^58 + 36 * q^59 + 45 * q^60 - 15 * q^61 + 54 * q^62 - 84 * q^63 + 66 * q^64 + 66 * q^65 + 63 * q^66 + 78 * q^67 + 60 * q^68 + 30 * q^69 + 18 * q^70 - 6 * q^71 + 66 * q^72 - 3 * q^73 + 39 * q^74 + 78 * q^75 - 45 * q^76 + 39 * q^77 - 60 * q^78 - 27 * q^79 - 18 * q^80 + 99 * q^81 + 99 * q^82 - 12 * q^83 + 90 * q^84 - 6 * q^85 - 57 * q^86 - 12 * q^87 - 117 * q^88 + 3 * q^89 + 72 * q^90 - 60 * q^91 - 9 * q^92 - 108 * q^93 + 75 * q^94 - 180 * q^95 - 123 * q^96 + 9 * q^97 + 3 * q^98 - 111 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more