LMFDB - Embedded newform 143.2.h.c.53.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,2,Mod(14,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("143.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	143.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.14186074890$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			53.2
Character	$\chi$	$=$	143.53
Dual form			143.2.h.c.27.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.545888 + 1.68007i) q^{2} +(-2.73308 + 1.98570i) q^{3} +(-0.906607 - 0.658689i) q^{4} +(0.676170 + 2.08104i) q^{5} +(-1.84416 - 5.67573i) q^{6} +(-0.0983727 - 0.0714719i) q^{7} +(-1.25676 + 0.913087i) q^{8} +(2.59967 - 8.00096i) q^{9} +O(q^{10})$	\(q+(-0.545888 + 1.68007i) q^{2} +(-2.73308 + 1.98570i) q^{3} +(-0.906607 - 0.658689i) q^{4} +(0.676170 + 2.08104i) q^{5} +(-1.84416 - 5.67573i) q^{6} +(-0.0983727 - 0.0714719i) q^{7} +(-1.25676 + 0.913087i) q^{8} +(2.59967 - 8.00096i) q^{9} -3.86540 q^{10} +(3.23459 + 0.733108i) q^{11} +3.78579 q^{12} +(0.309017 - 0.951057i) q^{13} +(0.173778 - 0.126257i) q^{14} +(-5.98034 - 4.34497i) q^{15} +(-1.54059 - 4.74144i) q^{16} +(0.715201 + 2.20116i) q^{17} +(12.0230 + 8.73526i) q^{18} +(-4.64768 + 3.37674i) q^{19} +(0.757736 - 2.33207i) q^{20} +0.410782 q^{21} +(-2.99739 + 5.03414i) q^{22} -4.16613 q^{23} +(1.62170 - 4.99108i) q^{24} +(0.171570 - 0.124653i) q^{25} +(1.42915 + 1.03834i) q^{26} +(5.65056 + 17.3906i) q^{27} +(0.0421076 + 0.129594i) q^{28} +(4.88799 + 3.55134i) q^{29} +(10.5644 - 7.67552i) q^{30} +(-0.411140 + 1.26536i) q^{31} +5.70007 q^{32} +(-10.2961 + 4.41927i) q^{33} -4.08853 q^{34} +(0.0822192 - 0.253045i) q^{35} +(-7.62702 + 5.54136i) q^{36} +(0.408587 + 0.296856i) q^{37} +(-3.13604 - 9.65175i) q^{38} +(1.04394 + 3.21293i) q^{39} +(-2.74995 - 1.99796i) q^{40} +(-3.50036 + 2.54316i) q^{41} +(-0.224241 + 0.690142i) q^{42} -6.11640 q^{43} +(-2.44961 - 2.79523i) q^{44} +18.4081 q^{45} +(2.27424 - 6.99938i) q^{46} +(4.75718 - 3.45630i) q^{47} +(13.6256 + 9.89959i) q^{48} +(-2.15855 - 6.64333i) q^{49} +(0.115768 + 0.356296i) q^{50} +(-6.32555 - 4.59578i) q^{51} +(-0.906607 + 0.658689i) q^{52} +(0.460825 - 1.41828i) q^{53} -32.3021 q^{54} +(0.661507 + 7.22701i) q^{55} +0.188891 q^{56} +(5.99729 - 18.4578i) q^{57} +(-8.63479 + 6.27354i) q^{58} +(5.35440 + 3.89020i) q^{59} +(2.55984 + 7.87837i) q^{60} +(-0.107334 - 0.330340i) q^{61} +(-1.90145 - 1.38149i) q^{62} +(-0.827581 + 0.601273i) q^{63} +(-0.0304230 + 0.0936323i) q^{64} +2.18813 q^{65} +(-1.80416 - 19.7106i) q^{66} +13.8719 q^{67} +(0.801475 - 2.46669i) q^{68} +(11.3863 - 8.27267i) q^{69} +(0.380250 + 0.276268i) q^{70} +(1.67708 + 5.16151i) q^{71} +(4.03842 + 12.4290i) q^{72} +(3.85926 + 2.80392i) q^{73} +(-0.721782 + 0.524405i) q^{74} +(-0.221391 + 0.681372i) q^{75} +6.43784 q^{76} +(-0.265798 - 0.303300i) q^{77} -5.96782 q^{78} +(-2.80132 + 8.62158i) q^{79} +(8.82543 - 6.41205i) q^{80} +(-29.5579 - 21.4751i) q^{81} +(-2.36188 - 7.26913i) q^{82} +(-1.17806 - 3.62568i) q^{83} +(-0.372418 - 0.270577i) q^{84} +(-4.09711 + 2.97672i) q^{85} +(3.33887 - 10.2760i) q^{86} -20.4111 q^{87} +(-4.73448 + 2.03212i) q^{88} +5.23054 q^{89} +(-10.0488 + 30.9269i) q^{90} +(-0.0983727 + 0.0714719i) q^{91} +(3.77704 + 2.74418i) q^{92} +(-1.38894 - 4.27472i) q^{93} +(3.20993 + 9.87915i) q^{94} +(-10.1697 - 7.38875i) q^{95} +(-15.5787 + 11.3186i) q^{96} +(-2.91446 + 8.96978i) q^{97} +12.3396 q^{98} +(14.2744 - 23.9740i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) $ 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9} - 24 q^{10} - 5 q^{11} + 38 q^{12} - 7 q^{13} - 7 q^{14} + 8 q^{15} - 19 q^{16} + 7 q^{17} + 5 q^{18} + 5 q^{19} + 9 q^{20} - 33 q^{22} + 50 q^{23} - 7 q^{24} - 34 q^{25} + 2 q^{26} - 19 q^{27} + 30 q^{28} + 8 q^{29} - 6 q^{30} + 17 q^{31} + 24 q^{32} - 26 q^{33} + 26 q^{34} - 4 q^{35} - 27 q^{36} + 17 q^{37} - 51 q^{38} - 2 q^{39} + 39 q^{40} - 23 q^{41} + 80 q^{42} - 32 q^{43} + q^{44} + 78 q^{45} - 31 q^{46} - 29 q^{47} + 52 q^{48} - 52 q^{49} + 6 q^{50} + 7 q^{51} - 5 q^{52} - 16 q^{53} - 42 q^{54} - 5 q^{55} + 34 q^{56} - 7 q^{57} - 13 q^{58} - 11 q^{59} - 74 q^{60} + 37 q^{61} + 23 q^{62} - 38 q^{63} + 67 q^{64} + 18 q^{65} - 65 q^{66} + 58 q^{67} - 68 q^{68} - 28 q^{69} + 44 q^{70} - 47 q^{71} + 10 q^{72} + 44 q^{73} - 46 q^{74} + 17 q^{75} + 6 q^{76} + 21 q^{77} + 26 q^{78} + 51 q^{79} + 23 q^{80} - 14 q^{81} - 47 q^{82} - 13 q^{83} - 107 q^{84} - q^{85} + 38 q^{86} - 12 q^{87} + 9 q^{88} + 38 q^{89} - 74 q^{90} - 7 q^{91} - 41 q^{92} - 51 q^{93} - 5 q^{94} + 47 q^{95} - 71 q^{96} - 20 q^{97} + 162 q^{98} + 60 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9 - 24 * q^10 - 5 * q^11 + 38 * q^12 - 7 * q^13 - 7 * q^14 + 8 * q^15 - 19 * q^16 + 7 * q^17 + 5 * q^18 + 5 * q^19 + 9 * q^20 - 33 * q^22 + 50 * q^23 - 7 * q^24 - 34 * q^25 + 2 * q^26 - 19 * q^27 + 30 * q^28 + 8 * q^29 - 6 * q^30 + 17 * q^31 + 24 * q^32 - 26 * q^33 + 26 * q^34 - 4 * q^35 - 27 * q^36 + 17 * q^37 - 51 * q^38 - 2 * q^39 + 39 * q^40 - 23 * q^41 + 80 * q^42 - 32 * q^43 + q^44 + 78 * q^45 - 31 * q^46 - 29 * q^47 + 52 * q^48 - 52 * q^49 + 6 * q^50 + 7 * q^51 - 5 * q^52 - 16 * q^53 - 42 * q^54 - 5 * q^55 + 34 * q^56 - 7 * q^57 - 13 * q^58 - 11 * q^59 - 74 * q^60 + 37 * q^61 + 23 * q^62 - 38 * q^63 + 67 * q^64 + 18 * q^65 - 65 * q^66 + 58 * q^67 - 68 * q^68 - 28 * q^69 + 44 * q^70 - 47 * q^71 + 10 * q^72 + 44 * q^73 - 46 * q^74 + 17 * q^75 + 6 * q^76 + 21 * q^77 + 26 * q^78 + 51 * q^79 + 23 * q^80 - 14 * q^81 - 47 * q^82 - 13 * q^83 - 107 * q^84 - q^85 + 38 * q^86 - 12 * q^87 + 9 * q^88 + 38 * q^89 - 74 * q^90 - 7 * q^91 - 41 * q^92 - 51 * q^93 - 5 * q^94 + 47 * q^95 - 71 * q^96 - 20 * q^97 + 162 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−0.545888	+	1.68007i	−0.386001	+	1.18799i	0.549751	+	0.835329i	$0.314723\pi$
$2$	−0.545888	+	1.68007i	−0.386001	+	1.18799i	−0.935752	+	0.352660i	$0.885277\pi$
$3$	−2.73308	+	1.98570i	−1.57794	+	1.14644i	−0.658938	+	0.752197i	$0.728994\pi$
$3$	−2.73308	+	1.98570i	−1.57794	+	1.14644i	−0.919005	+	0.394246i	$0.871006\pi$
$4$	−0.906607	−	0.658689i	−0.453304	−	0.329344i
$5$	0.676170	+	2.08104i	0.302393	+	0.930669i	0.980637	+	0.195833i	$0.0627409\pi$
$5$	0.676170	+	2.08104i	0.302393	+	0.930669i	−0.678245	+	0.734836i	$0.737259\pi$
$6$	−1.84416	−	5.67573i	−0.752874	−	2.31711i
$7$	−0.0983727	−	0.0714719i	−0.0371814	−	0.0270139i	0.569039	−	0.822310i	$-0.307315\pi$
$7$	−0.0983727	−	0.0714719i	−0.0371814	−	0.0270139i	−0.606221	+	0.795296i	$0.707315\pi$
$8$	−1.25676	+	0.913087i	−0.444331	+	0.322825i
$9$	2.59967	−	8.00096i	0.866557	−	2.66699i
$10$	−3.86540			−1.22235
$11$	3.23459	+	0.733108i	0.975265	+	0.221040i
$11$	3.23459	+	0.733108i	0.975265	+	0.221040i
$12$	3.78579			1.09286
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$14$	0.173778	−	0.126257i	0.0464442	−	0.0337437i
$15$	−5.98034	−	4.34497i	−1.54412	−	1.12187i
$16$	−1.54059	−	4.74144i	−0.385147	−	1.18536i
$17$	0.715201	+	2.20116i	0.173462	+	0.533861i	0.999560	−	0.0296658i	$-0.00944430\pi$
$17$	0.715201	+	2.20116i	0.173462	+	0.533861i	−0.826098	+	0.563526i	$0.809444\pi$
$18$	12.0230	+	8.73526i	2.83386	+	2.05892i
$19$	−4.64768	+	3.37674i	−1.06625	+	0.774677i	−0.975235	−	0.221173i	$-0.929012\pi$
$19$	−4.64768	+	3.37674i	−1.06625	+	0.774677i	−0.0910164	+	0.995849i	$0.529012\pi$
$20$	0.757736	−	2.33207i	0.169435	−	0.521467i
$21$	0.410782			0.0896399
$22$	−2.99739	+	5.03414i	−0.639047	+	1.07328i
$23$	−4.16613			−0.868697			−0.434349	−	0.900745i	$-0.643021\pi$
$23$	−4.16613			−0.868697			−0.434349	+	0.900745i	$0.643021\pi$
$24$	1.62170	−	4.99108i	0.331028	−	1.01880i
$25$	0.171570	−	0.124653i	0.0343140	−	0.0249306i
$26$	1.42915	+	1.03834i	0.280280	+	0.203635i
$27$	5.65056	+	17.3906i	1.08745	+	3.34683i
$28$	0.0421076	+	0.129594i	0.00795759	+	0.0244910i
$29$	4.88799	+	3.55134i	0.907678	+	0.659466i	0.940426	−	0.339997i	$-0.110426\pi$
$29$	4.88799	+	3.55134i	0.907678	+	0.659466i	−0.0327488	+	0.999464i	$0.510426\pi$
$30$	10.5644	−	7.67552i	1.92880	−	1.40135i
$31$	−0.411140	+	1.26536i	−0.0738429	+	0.227265i	−0.981165	−	0.193171i	$-0.938123\pi$
$31$	−0.411140	+	1.26536i	−0.0738429	+	0.227265i	0.907322	+	0.420436i	$0.138123\pi$
$32$	5.70007			1.00764
$33$	−10.2961	+	4.41927i	−1.79232	+	0.769296i
$34$	−4.08853			−0.701177
$35$	0.0822192	−	0.253045i	0.0138976	−	0.0427723i
$36$	−7.62702	+	5.54136i	−1.27117	+	0.923560i
$37$	0.408587	+	0.296856i	0.0671713	+	0.0488028i	0.620864	−	0.783918i	$-0.286782\pi$
$37$	0.408587	+	0.296856i	0.0671713	+	0.0488028i	−0.553693	+	0.832721i	$0.686782\pi$
$38$	−3.13604	−	9.65175i	−0.508733	−	1.56572i
$39$	1.04394	+	3.21293i	0.167165	+	0.514480i
$40$	−2.74995	−	1.99796i	−0.434805	−	0.315905i
$41$	−3.50036	+	2.54316i	−0.546664	+	0.397175i	−0.826554	−	0.562857i	$-0.809702\pi$
$41$	−3.50036	+	2.54316i	−0.546664	+	0.397175i	0.279890	+	0.960032i	$0.409702\pi$
$42$	−0.224241	+	0.690142i	−0.0346011	+	0.106491i
$43$	−6.11640			−0.932742			−0.466371	−	0.884589i	$-0.654439\pi$
$43$	−6.11640			−0.932742			−0.466371	+	0.884589i	$0.654439\pi$
$44$	−2.44961	−	2.79523i	−0.369293	−	0.421396i
$45$	18.4081			2.74412
$46$	2.27424	−	6.99938i	0.335318	−	1.03200i
$47$	4.75718	−	3.45630i	0.693907	−	0.504153i	−0.184035	−	0.982920i	$-0.558916\pi$
$47$	4.75718	−	3.45630i	0.693907	−	0.504153i	0.877942	+	0.478767i	$0.158916\pi$
$48$	13.6256	+	9.89959i	1.96669	+	1.42888i
$49$	−2.15855	−	6.64333i	−0.308364	−	0.949048i
$50$	0.115768	+	0.356296i	0.0163720	+	0.0503879i
$51$	−6.32555	−	4.59578i	−0.885754	−	0.643538i
$52$	−0.906607	+	0.658689i	−0.125724	+	0.0913437i
$53$	0.460825	−	1.41828i	0.0632992	−	0.194815i	−0.914405	−	0.404799i	$-0.867341\pi$
$53$	0.460825	−	1.41828i	0.0632992	−	0.194815i	0.977705	+	0.209984i	$0.0673413\pi$
$54$	−32.3021			−4.39575
$55$	0.661507	+	7.22701i	0.0891975	+	0.974489i
$56$	0.188891			0.0252416
$57$	5.99729	−	18.4578i	0.794361	−	2.44479i
$58$	−8.63479	+	6.27354i	−1.13380	+	0.823756i
$59$	5.35440	+	3.89020i	0.697084	+	0.506461i	0.878981	−	0.476856i	$-0.158224\pi$
$59$	5.35440	+	3.89020i	0.697084	+	0.506461i	−0.181897	+	0.983318i	$0.558224\pi$
$60$	2.55984	+	7.87837i	0.330473	+	1.01709i
$61$	−0.107334	−	0.330340i	−0.0137427	−	0.0422957i	0.943950	−	0.330088i	$-0.107079\pi$
$61$	−0.107334	−	0.330340i	−0.0137427	−	0.0422957i	−0.957693	+	0.287793i	$0.907079\pi$
$62$	−1.90145	−	1.38149i	−0.241485	−	0.175449i
$63$	−0.827581	+	0.601273i	−0.104265	+	0.0757532i
$64$	−0.0304230	+	0.0936323i	−0.00380287	+	0.0117040i
$65$	2.18813			0.271405
$66$	−1.80416	−	19.7106i	−0.222077	−	2.42621i
$67$	13.8719			1.69472			0.847360	−	0.531018i	$-0.178190\pi$
$67$	13.8719			1.69472			0.847360	+	0.531018i	$0.178190\pi$
$68$	0.801475	−	2.46669i	0.0971931	−	0.299130i
$69$	11.3863	−	8.27267i	1.37076	−	0.995912i
$70$	0.380250	+	0.276268i	0.0454486	+	0.0330203i
$71$	1.67708	+	5.16151i	0.199032	+	0.612559i	0.999906	+	0.0137252i	$0.00436900\pi$
$71$	1.67708	+	5.16151i	0.199032	+	0.612559i	−0.800873	+	0.598834i	$0.795631\pi$
$72$	4.03842	+	12.4290i	0.475933	+	1.46477i
$73$	3.85926	+	2.80392i	0.451693	+	0.328174i	0.790264	−	0.612767i	$-0.209944\pi$
$73$	3.85926	+	2.80392i	0.451693	+	0.328174i	−0.338571	+	0.940941i	$0.609944\pi$
$74$	−0.721782	+	0.524405i	−0.0839054	+	0.0609608i
$75$	−0.221391	+	0.681372i	−0.0255641	+	0.0786781i
$76$	6.43784			0.738471
$77$	−0.265798	−	0.303300i	−0.0302905	−	0.0345642i
$78$	−5.96782			−0.675722
$79$	−2.80132	+	8.62158i	−0.315173	+	0.970003i	0.660510	+	0.750817i	$0.270340\pi$
$79$	−2.80132	+	8.62158i	−0.315173	+	0.970003i	−0.975683	+	0.219186i	$0.929660\pi$
$80$	8.82543	−	6.41205i	0.986713	−	0.716889i
$81$	−29.5579	−	21.4751i	−3.28421	−	2.38612i
$82$	−2.36188	−	7.26913i	−0.260826	−	0.802741i
$83$	−1.17806	−	3.62568i	−0.129308	−	0.397971i	0.865353	−	0.501163i	$-0.167094\pi$
$83$	−1.17806	−	3.62568i	−0.129308	−	0.397971i	−0.994661	+	0.103192i	$0.967094\pi$
$84$	−0.372418	−	0.270577i	−0.0406341	−	0.0295224i
$85$	−4.09711	+	2.97672i	−0.444394	+	0.322871i
$86$	3.33887	−	10.2760i	0.360039	−	1.10809i
$87$	−20.4111			−2.18830
$88$	−4.73448	+	2.03212i	−0.504697	+	0.216625i
$89$	5.23054			0.554436			0.277218	−	0.960807i	$-0.410588\pi$
$89$	5.23054			0.554436			0.277218	+	0.960807i	$0.410588\pi$
$90$	−10.0488	+	30.9269i	−1.05923	+	3.25999i
$91$	−0.0983727	+	0.0714719i	−0.0103123	+	0.00749229i
$92$	3.77704	+	2.74418i	0.393784	+	0.286101i
$93$	−1.38894	−	4.27472i	−0.144026	−	0.443268i
$94$	3.20993	+	9.87915i	0.331079	+	1.01896i
$95$	−10.1697	−	7.38875i	−1.04339	−	0.758070i
$96$	−15.5787	+	11.3186i	−1.59000	+	1.15520i
$97$	−2.91446	+	8.96978i	−0.295918	+	0.910743i	0.686993	+	0.726664i	$0.258930\pi$
$97$	−2.91446	+	8.96978i	−0.295918	+	0.910743i	−0.982911	+	0.184079i	$0.941070\pi$
$98$	12.3396			1.24649
$99$	14.2744	−	23.9740i	1.43463	−	2.40947i
$100$	−0.237654			−0.0237654
$101$	−4.07225	+	12.5331i	−0.405204	+	1.24709i	0.515521	+	0.856877i	$0.327599\pi$
$101$	−4.07225	+	12.5331i	−0.405204	+	1.24709i	−0.920725	+	0.390213i	$0.872401\pi$
$102$	11.1743	−	8.11858i	1.10642	−	0.803859i
$103$	3.96993	+	2.88432i	0.391169	+	0.284201i	0.765934	−	0.642919i	$-0.222277\pi$
$103$	3.96993	+	2.88432i	0.391169	+	0.284201i	−0.374765	+	0.927120i	$0.622277\pi$
$104$	0.480038	+	1.47741i	0.0470716	+	0.144872i
$105$	0.277759	+	0.854853i	0.0271065	+	0.0834251i
$106$	2.13124	+	1.54844i	0.207005	+	0.150398i
$107$	−3.67146	+	2.66747i	−0.354934	+	0.257874i	−0.750936	−	0.660375i	$-0.770397\pi$
$107$	−3.67146	+	2.66747i	−0.354934	+	0.257874i	0.396002	+	0.918250i	$0.370397\pi$
$108$	6.33218	−	19.4884i	0.609314	−	1.87528i
$109$	9.44166			0.904347			0.452174	−	0.891930i	$-0.350649\pi$
$109$	9.44166			0.904347			0.452174	+	0.891930i	$0.350649\pi$
$110$	−12.5030	−	2.83376i	−1.19211	−	0.270188i
$111$	−1.70617			−0.161942
$112$	−0.187328	+	0.576537i	−0.0177009	+	0.0544777i
$113$	−1.67272	+	1.21530i	−0.157356	+	0.114326i	−0.663677	−	0.748019i	$-0.731005\pi$
$113$	−1.67272	+	1.21530i	−0.157356	+	0.114326i	0.506321	+	0.862345i	$0.331005\pi$
$114$	27.7365	+	20.1517i	2.59776	+	1.88738i
$115$	−2.81701	−	8.66987i	−0.262688	−	0.808469i
$116$	−2.09227	−	6.43933i	−0.194262	−	0.597877i
$117$	−6.80603	−	4.94487i	−0.629217	−	0.457153i
$118$	−9.45872	+	6.87216i	−0.870745	+	0.632634i
$119$	0.0869651	−	0.267651i	0.00797208	−	0.0245355i
$120$	11.4832			1.04826
$121$	9.92511	+	4.74260i	0.902282	+	0.431146i
$122$	0.613587			0.0555516
$123$	4.51681	−	13.9013i	0.407267	−	1.25344i
$124$	1.20622	−	0.876369i	0.108322	−	0.0787003i
$125$	9.22660	+	6.70352i	0.825253	+	0.599581i
$126$	−0.558414	−	1.71862i	−0.0497475	−	0.153107i
$127$	−5.03721	−	15.5029i	−0.446980	−	1.37566i	−0.880297	−	0.474422i	$-0.842657\pi$
$127$	−5.03721	−	15.5029i	−0.446980	−	1.37566i	0.433317	−	0.901241i	$-0.357343\pi$
$128$	9.08221	+	6.59861i	0.802761	+	0.583240i
$129$	16.7166	−	12.1453i	1.47181	−	1.06934i
$130$	−1.19448	+	3.67622i	−0.104762	+	0.322426i
$131$	−0.915990			−0.0800304			−0.0400152	−	0.999199i	$-0.512741\pi$
$131$	−0.915990			−0.0800304			−0.0400152	+	0.999199i	$0.512741\pi$
$132$	12.2455	+	2.77539i	1.06583	+	0.241567i
$133$	0.698547			0.0605717
$134$	−7.57249	+	23.3057i	−0.654164	+	2.01331i
$135$	−32.3698	+	23.5181i	−2.78595	+	2.02411i
$136$	−2.90869	−	2.11329i	−0.249418	−	0.181213i
$137$	2.49872	+	7.69027i	0.213480	+	0.657024i	0.999258	+	0.0385152i	$0.0122628\pi$
$137$	2.49872	+	7.69027i	0.213480	+	0.657024i	−0.785778	+	0.618509i	$0.787737\pi$
$138$	7.68299	+	23.6458i	0.654019	+	2.01286i
$139$	2.07025	+	1.50412i	0.175596	+	0.127578i	0.672112	−	0.740450i	$-0.265387\pi$
$139$	2.07025	+	1.50412i	0.175596	+	0.127578i	−0.496516	+	0.868028i	$0.665387\pi$
$140$	−0.241218	+	0.175255i	−0.0203867	+	0.0148118i
$141$	−6.13860	+	18.8927i	−0.516963	+	1.59105i
$142$	−9.58720			−0.804540
$143$	1.69677	−	2.84973i	0.141891	−	0.238307i
$144$	−41.9411			−3.49509
$145$	−4.08535	+	12.5734i	−0.339270	+	1.04416i
$146$	−6.81751	+	4.95321i	−0.564221	+	0.409930i
$147$	19.0911	+	13.8705i	1.57461	+	1.14402i
$148$	−0.174892	−	0.538264i	−0.0143761	−	0.0442450i
$149$	−3.16081	−	9.72798i	−0.258944	−	0.796947i	−0.993027	−	0.117887i	$-0.962388\pi$
$149$	−3.16081	−	9.72798i	−0.258944	−	0.796947i	0.734083	−	0.679060i	$-0.237612\pi$
$150$	−1.02390	−	0.743906i	−0.0836009	−	0.0607396i
$151$	3.45691	−	2.51159i	0.281319	−	0.204391i	−0.438173	−	0.898891i	$-0.644374\pi$
$151$	3.45691	−	2.51159i	0.281319	−	0.204391i	0.719493	+	0.694500i	$0.244374\pi$
$152$	2.75775	−	8.48747i	0.223683	−	0.688425i
$153$	19.4707			1.57411
$154$	0.654661	−	0.280992i	0.0527541	−	0.0226430i
$155$	−2.91126			−0.233838
$156$	1.16987	−	3.60050i	0.0936647	−	0.288270i
$157$	17.2394	−	12.5252i	1.37585	−	0.999617i	0.378600	−	0.925560i	$-0.376405\pi$
$157$	17.2394	−	12.5252i	1.37585	−	0.999617i	0.997254	−	0.0740566i	$-0.0235945\pi$
$158$	−12.9556	−	9.41283i	−1.03070	−	0.748844i
$159$	1.55679	+	4.79132i	0.123462	+	0.379976i
$160$	3.85422	+	11.8621i	0.304703	+	0.937779i
$161$	0.409833	+	0.297761i	0.0322994	+	0.0234669i
$162$	52.2149	−	37.9363i	4.10239	−	2.98056i
$163$	5.54688	−	17.0715i	0.434465	−	1.33715i	−0.459169	−	0.888349i	$-0.651853\pi$
$163$	5.54688	−	17.0715i	0.434465	−	1.33715i	0.893634	−	0.448797i	$-0.148147\pi$
$164$	4.84860			0.378612
$165$	−16.1586	−	18.4384i	−1.25795	−	1.43543i
$166$	6.73449			0.522698
$167$	7.50423	−	23.0957i	0.580695	−	1.78720i	−0.0352158	−	0.999380i	$-0.511212\pi$
$167$	7.50423	−	23.0957i	0.580695	−	1.78720i	0.615911	−	0.787816i	$-0.288788\pi$
$168$	−0.516253	+	0.375080i	−0.0398298	+	0.0289380i
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$	−2.76454	−	8.50839i	−0.212031	−	0.652563i
$171$	14.9347	+	45.9643i	1.14209	+	3.51498i
$172$	5.54517	+	4.02880i	0.422815	+	0.307193i
$173$	−20.8062	+	15.1166i	−1.58187	+	1.14929i	−0.667355	+	0.744740i	$0.732574\pi$
$173$	−20.8062	+	15.1166i	−1.58187	+	1.14929i	−0.914514	+	0.404555i	$0.867426\pi$
$174$	11.1422	−	34.2921i	0.844688	−	2.59968i
$175$	−0.0257870			−0.00194931
$176$	−1.50718	−	16.4660i	−0.113608	−	1.24117i
$177$	−22.3588			−1.68059
$178$	−2.85529	+	8.78768i	−0.214013	+	0.658664i
$179$	−7.33045	+	5.32588i	−0.547904	+	0.398075i	−0.827012	−	0.562184i	$-0.809961\pi$
$179$	−7.33045	+	5.32588i	−0.547904	+	0.398075i	0.279108	+	0.960260i	$0.409961\pi$
$180$	−16.6889	−	12.1252i	−1.24392	−	0.903761i
$181$	−4.84834	−	14.9217i	−0.360374	−	1.10912i	−0.952827	−	0.303513i	$-0.901840\pi$
$181$	−4.84834	−	14.9217i	−0.360374	−	1.10912i	0.592453	−	0.805605i	$-0.298160\pi$
$182$	−0.0663774	−	0.204289i	−0.00492022	−	0.0151429i
$183$	0.949308	+	0.689713i	0.0701749	+	0.0509851i
$184$	5.23581	−	3.80404i	0.385989	−	0.280437i
$185$	−0.341494	+	1.05101i	−0.0251072	+	0.0772719i
$186$	7.94003			0.582192
$187$	0.699691	+	7.64418i	0.0511665	+	0.558997i
$188$	−6.58952			−0.480590
$189$	0.687082	−	2.11462i	0.0499778	−	0.153816i
$190$	17.9652	−	13.0525i	1.30333	−	0.946924i
$191$	−14.3758	−	10.4447i	−1.04020	−	0.755749i	−0.0698749	−	0.997556i	$-0.522260\pi$
$191$	−14.3758	−	10.4447i	−1.04020	−	0.755749i	−0.970324	+	0.241807i	$0.922260\pi$
$192$	−0.102777	−	0.316315i	−0.00741729	−	0.0228281i
$193$	−1.46006	−	4.49359i	−0.105097	−	0.323456i	0.884656	−	0.466244i	$-0.154393\pi$
$193$	−1.46006	−	4.49359i	−0.105097	−	0.323456i	−0.989753	+	0.142788i	$0.954393\pi$
$194$	−13.4789	−	9.79298i	−0.967727	−	0.703095i
$195$	−5.98034	+	4.34497i	−0.428261	+	0.311150i
$196$	−2.41893	+	7.44471i	−0.172781	+	0.531765i
$197$	10.3412			0.736779			0.368389	−	0.929672i	$-0.379909\pi$
$197$	10.3412			0.736779			0.368389	+	0.929672i	$0.379909\pi$
$198$	32.4857	+	37.0691i	2.30866	+	2.63439i
$199$	23.1675			1.64230			0.821151	−	0.570710i	$-0.193332\pi$
$199$	23.1675			1.64230			0.821151	+	0.570710i	$0.193332\pi$
$200$	−0.101803	+	0.313317i	−0.00719854	+	0.0221548i
$201$	−37.9129	+	27.5454i	−2.67417	+	1.94290i
$202$	−18.8335	−	13.6833i	−1.32512	−	0.962756i
$203$	−0.227024	−	0.698709i	−0.0159340	−	0.0490397i
$204$	2.70760	+	8.33313i	0.189570	+	0.583436i
$205$	−7.65925	−	5.56477i	−0.534945	−	0.388661i
$206$	−7.01300	+	5.09524i	−0.488619	+	0.355003i
$207$	−10.8306	+	33.3330i	−0.752776	+	2.31680i
$208$	−4.98545			−0.345679
$209$	−17.5088	+	7.51510i	−1.21111	+	0.519830i
$210$	−1.58784			−0.109571
$211$	5.41870	−	16.6770i	0.373038	−	1.14809i	−0.571754	−	0.820425i	$-0.693737\pi$
$211$	5.41870	−	16.6770i	0.373038	−	1.14809i	0.944792	−	0.327669i	$-0.106263\pi$
$212$	−1.35199	+	0.982278i	−0.0928550	+	0.0674631i
$213$	−14.8328	−	10.7767i	−1.01633	−	0.738404i
$214$	−2.47734	−	7.62445i	−0.169347	−	0.521197i
$215$	−4.13573	−	12.7285i	−0.282054	−	0.868074i
$216$	−22.9805	−	16.6963i	−1.56363	−	1.13604i
$217$	0.130882	−	0.0950917i	0.00888488	−	0.00645524i
$218$	−5.15409	+	15.8627i	−0.349079	+	1.07435i
$219$	−16.1154			−1.08898
$220$	4.16062	−	6.98778i	0.280509	−	0.471116i
$221$	2.31444			0.155686
$222$	0.931376	−	2.86648i	0.0625098	−	0.192386i
$223$	1.14269	−	0.830215i	0.0765203	−	0.0555953i	−0.548867	−	0.835909i	$-0.684941\pi$
$223$	1.14269	−	0.830215i	0.0765203	−	0.0555953i	0.625388	+	0.780314i	$0.284941\pi$
$224$	−0.560731	−	0.407395i	−0.0374654	−	0.0272202i
$225$	−0.551318	−	1.69678i	−0.0367545	−	0.113119i
$226$	−1.12867	−	3.47370i	−0.0750782	−	0.231067i
$227$	10.9641	+	7.96591i	0.727715	+	0.528716i	0.888840	−	0.458218i	$-0.151512\pi$
$227$	10.9641	+	7.96591i	0.727715	+	0.528716i	−0.161125	+	0.986934i	$0.551512\pi$
$228$	−17.5951	+	12.7836i	−1.16527	+	0.846615i
$229$	−3.19015	+	9.81828i	−0.210811	+	0.648810i	0.788613	+	0.614889i	$0.210799\pi$
$229$	−3.19015	+	9.81828i	−0.210811	+	0.648810i	−0.999425	+	0.0339206i	$0.989201\pi$
$230$	16.1038			1.06185
$231$	1.32871	+	0.301147i	0.0874227	+	0.0198140i
$232$	−9.38570			−0.616201
$233$	−0.0616963	+	0.189882i	−0.00404186	+	0.0124396i	−0.953057	−	0.302791i	$-0.902082\pi$
$233$	−0.0616963	+	0.189882i	−0.00404186	+	0.0124396i	0.949015	+	0.315230i	$0.102082\pi$
$234$	12.0230	−	8.73526i	0.785971	−	0.571042i
$235$	10.4094	+	7.56284i	0.679031	+	0.493345i
$236$	−2.29191	−	7.05377i	−0.149191	−	0.459161i
$237$	−9.46362	−	29.1260i	−0.614728	−	1.89194i
$238$	0.402200	+	0.292215i	0.0260707	+	0.0189415i
$239$	−6.13610	+	4.45814i	−0.396911	+	0.288373i	−0.768282	−	0.640112i	$-0.778888\pi$
$239$	−6.13610	+	4.45814i	−0.396911	+	0.288373i	0.371370	+	0.928485i	$0.378888\pi$
$240$	−11.3882	+	35.0493i	−0.735105	+	2.26242i
$241$	4.38526			0.282479			0.141240	−	0.989975i	$-0.454891\pi$
$241$	4.38526			0.282479			0.141240	+	0.989975i	$0.454891\pi$
$242$	−13.3859	+	14.0859i	−0.860478	+	0.905479i
$243$	68.5702			4.39878
$244$	−0.120282	+	0.370189i	−0.00770024	+	0.0236989i
$245$	12.3655	−	8.98405i	0.790002	−	0.573970i
$246$	20.8895	+	15.1771i	1.33187	+	0.967657i
$247$	1.77526	+	5.46368i	0.112957	+	0.347645i
$248$	−0.638679	−	1.96565i	−0.0405562	−	0.124819i
$249$	10.4192	+	7.57002i	0.660292	+	0.479730i
$250$	−16.2991	+	11.8420i	−1.03084	+	0.748952i
$251$	−0.0523971	+	0.161262i	−0.00330728	+	0.0101787i	−0.952697	−	0.303923i	$-0.901703\pi$
$251$	−0.0523971	+	0.161262i	−0.00330728	+	0.0101787i	0.949389	+	0.314102i	$0.101703\pi$
$252$	1.14634			0.0722128
$253$	−13.4757	−	3.05422i	−0.847210	−	0.192017i
$254$	28.7958			1.80681
$255$	5.28685	−	16.2712i	0.331075	−	1.01894i
$256$	−16.2033	+	11.7724i	−1.01271	+	0.735774i
$257$	−13.6904	−	9.94665i	−0.853983	−	0.620455i	0.0722585	−	0.997386i	$-0.476979\pi$
$257$	−13.6904	−	9.94665i	−0.853983	−	0.620455i	−0.926241	+	0.376931i	$0.876979\pi$
$258$	11.2796	+	34.7150i	0.702237	+	2.16126i
$259$	−0.0189769	−	0.0584050i	−0.00117917	−	0.00362911i
$260$	−1.98378	−	1.44130i	−0.123029	−	0.0893856i
$261$	41.1213	−	29.8764i	2.54534	−	1.84930i
$262$	0.500028	−	1.53893i	0.0308918	−	0.0950752i
$263$	9.22898			0.569083			0.284542	−	0.958664i	$-0.408159\pi$
$263$	9.22898			0.569083			0.284542	+	0.958664i	$0.408159\pi$
$264$	8.90452	−	14.9552i	0.548036	−	0.920428i
$265$	3.26308			0.200450
$266$	−0.381328	+	1.17361i	−0.0233807	+	0.0719585i
$267$	−14.2955	+	10.3863i	−0.874869	+	0.635630i
$268$	−12.5764	−	9.13726i	−0.768223	−	0.558147i
$269$	3.74251	+	11.5183i	0.228185	+	0.702281i	0.997953	+	0.0639568i	$0.0203720\pi$
$269$	3.74251	+	11.5183i	0.228185	+	0.702281i	−0.769768	+	0.638324i	$0.779628\pi$
$270$	−21.8417	−	67.2218i	−1.32924	−	4.09099i
$271$	−2.64787	−	1.92379i	−0.160846	−	0.116862i	0.504451	−	0.863441i	$-0.331695\pi$
$271$	−2.64787	−	1.92379i	−0.160846	−	0.116862i	−0.665297	+	0.746579i	$0.731695\pi$
$272$	9.33486	−	6.78217i	0.566009	−	0.411230i
$273$	0.126939	−	0.390677i	0.00768267	−	0.0236448i
$274$	−14.2842			−0.862940
$275$	0.646342	−	0.277421i	0.0389759	−	0.0167291i
$276$	−15.7721			−0.949366
$277$	−4.03204	+	12.4093i	−0.242262	+	0.745604i	0.753813	+	0.657089i	$0.228212\pi$
$277$	−4.03204	+	12.4093i	−0.242262	+	0.745604i	−0.996075	+	0.0885156i	$0.971788\pi$
$278$	−3.65715	+	2.65708i	−0.219342	+	0.159361i
$279$	9.05525	+	6.57903i	0.542124	+	0.393876i
$280$	0.127722	+	0.393089i	0.00763286	+	0.0234915i
$281$	6.73500	+	20.7282i	0.401776	+	1.23654i	0.923557	+	0.383461i	$0.125268\pi$
$281$	6.73500	+	20.7282i	0.401776	+	1.23654i	−0.521781	+	0.853080i	$0.674732\pi$
$282$	−28.3900	−	20.6265i	−1.69060	−	1.22829i
$283$	18.4086	−	13.3747i	1.09428	−	0.795041i	0.114163	−	0.993462i	$-0.463581\pi$
$283$	18.4086	−	13.3747i	1.09428	−	0.795041i	0.980117	+	0.198421i	$0.0635814\pi$
$284$	1.87938	−	5.78414i	0.111521	−	0.343225i
$285$	42.4665			2.51550
$286$	3.86150	+	4.40632i	0.228336	+	0.260551i
$287$	0.526104			0.0310550
$288$	14.8183	−	45.6061i	0.873177	−	2.68736i
$289$	9.41968	−	6.84380i	0.554099	−	0.402576i
$290$	−18.8941	−	13.7273i	−1.10950	−	0.806097i
$291$	−9.84582	−	30.3023i	−0.577172	−	1.77635i
$292$	−1.65193	−	5.08411i	−0.0966717	−	0.297525i
$293$	−15.5499	−	11.2977i	−0.908434	−	0.660016i	0.0321844	−	0.999482i	$-0.489754\pi$
$293$	−15.5499	−	11.2977i	−0.908434	−	0.660016i	−0.940618	+	0.339466i	$0.889754\pi$
$294$	−33.7251	+	24.5027i	−1.96689	+	1.42903i
$295$	−4.47517	+	13.7732i	−0.260555	+	0.801904i
$296$	−0.784550			−0.0456010
$297$	5.52802	+	60.3940i	0.320768	+	3.50442i
$298$	18.0691			1.04672
$299$	−1.28740	+	3.96222i	−0.0744525	+	0.229141i
$300$	0.649527	−	0.471909i	0.0375005	−	0.0272457i
$301$	0.601687	+	0.437151i	0.0346806	+	0.0251970i
$302$	2.33257	+	7.17890i	0.134224	+	0.413099i
$303$	−13.7572	−	42.3402i	−0.790328	−	2.43238i
$304$	23.1708	+	16.8346i	1.32893	+	0.965528i
$305$	0.614875	−	0.446733i	0.0352076	−	0.0255798i
$306$	−10.6288	+	32.7122i	−0.607610	+	1.87003i
$307$	−15.5200			−0.885775			−0.442888	−	0.896577i	$-0.646046\pi$
$307$	−15.5200			−0.885775			−0.442888	+	0.896577i	$0.646046\pi$
$308$	0.0411945	+	0.450052i	0.00234727	+	0.0256441i
$309$	−16.5775			−0.943063
$310$	1.58922	−	4.89112i	0.0902617	−	0.277797i
$311$	17.3975	−	12.6400i	0.986521	−	0.716750i	0.0273647	−	0.999626i	$-0.491288\pi$
$311$	17.3975	−	12.6400i	0.986521	−	0.716750i	0.959157	+	0.282876i	$0.0912885\pi$
$312$	−4.24566	−	3.08465i	−0.240363	−	0.174634i
$313$	−4.97733	−	15.3187i	−0.281336	−	0.865862i	−0.987473	−	0.157787i	$-0.949564\pi$
$313$	−4.97733	−	15.3187i	−0.281336	−	0.865862i	0.706138	−	0.708075i	$-0.250436\pi$
$314$	11.6324	+	35.8007i	0.656452	+	2.02035i
$315$	−1.81086	−	1.31566i	−0.102030	−	0.0741293i
$316$	8.21864	−	5.97119i	0.462334	−	0.335906i
$317$	−1.37241	+	4.22384i	−0.0770821	+	0.237234i	−0.982172	−	0.187987i	$-0.939804\pi$
$317$	−1.37241	+	4.22384i	−0.0770821	+	0.237234i	0.905089	+	0.425221i	$0.139804\pi$
$318$	−8.89958			−0.499064
$319$	13.2071	+	15.0705i	0.739457	+	0.843788i
$320$	−0.215423			−0.0120425
$321$	4.73760	−	14.5808i	0.264427	−	0.813822i
$322$	−0.723982	+	0.526004i	−0.0403460	+	0.0293131i
$323$	−10.7568	−	7.81526i	−0.598523	−	0.434853i
$324$	12.6520	+	38.9389i	0.702890	+	2.16327i
$325$	−0.0655339	−	0.201693i	−0.00363517	−	0.0111879i
$326$	25.6534	+	18.6383i	1.42081	+	1.03228i
$327$	−25.8048	+	18.7483i	−1.42701	+	1.03678i
$328$	2.07697	−	6.39227i	0.114682	−	0.352954i
$329$	−0.715005			−0.0394195
$330$	39.7986	−	17.0823i	2.19084	−	0.940348i
$331$	1.65739			0.0910986			0.0455493	−	0.998962i	$-0.485496\pi$
$331$	1.65739			0.0910986			0.0455493	+	0.998962i	$0.485496\pi$
$332$	−1.32016	+	4.06305i	−0.0724534	+	0.222989i
$333$	3.43733	−	2.49736i	0.188364	−	0.136855i
$334$	34.7058	+	25.2153i	1.89902	+	1.37972i
$335$	9.37976	+	28.8679i	0.512471	+	1.57722i
$336$	−0.632846	−	1.94770i	−0.0345246	−	0.106256i
$337$	19.5807	+	14.2262i	1.06663	+	0.774952i	0.975303	−	0.220869i	$-0.0708895\pi$
$337$	19.5807	+	14.2262i	1.06663	+	0.774952i	0.0913260	+	0.995821i	$0.470889\pi$
$338$	1.42915	−	1.03834i	0.0777357	−	0.0564783i
$339$	2.15845	−	6.64301i	0.117231	−	0.360799i
$340$	5.67520			0.307781
$341$	−2.25751	+	3.79150i	−0.122251	+	0.205321i
$342$	−85.3760			−4.61660
$343$	−0.525495	+	1.61731i	−0.0283740	+	0.0873263i
$344$	7.68682	−	5.58481i	0.414446	−	0.301113i
$345$	24.9148	+	18.1017i	1.34137	+	0.974563i
$346$	−14.0391	−	43.2079i	−0.754747	−	2.32287i
$347$	1.00283	+	3.08641i	0.0538350	+	0.165687i	0.974359	−	0.224999i	$-0.0722378\pi$
$347$	1.00283	+	3.08641i	0.0538350	+	0.165687i	−0.920524	+	0.390686i	$0.872238\pi$
$348$	18.5049	+	13.4446i	0.991966	+	0.720706i
$349$	−1.17578	+	0.854257i	−0.0629383	+	0.0457273i	−0.618810	−	0.785541i	$-0.712385\pi$
$349$	−1.17578	+	0.854257i	−0.0629383	+	0.0457273i	0.555871	+	0.831268i	$0.312385\pi$
$350$	0.0140768	−	0.0433239i	0.000752437	−	0.00231576i
$351$	18.2856			0.976013
$352$	18.4374	+	4.17877i	0.982716	+	0.222729i
$353$	−29.1171			−1.54975			−0.774874	−	0.632115i	$-0.782187\pi$
$353$	−29.1171			−1.54975			−0.774874	+	0.632115i	$0.782187\pi$
$354$	12.2054	−	37.5643i	0.648709	−	1.99652i
$355$	−9.60732	+	6.98013i	−0.509904	+	0.370467i
$356$	−4.74205	−	3.44530i	−0.251328	−	0.182601i
$357$	0.293792	+	0.904198i	0.0155491	+	0.0478552i
$358$	−4.94625	−	15.2230i	−0.261418	−	0.804561i
$359$	2.54992	+	1.85263i	0.134580	+	0.0977778i	0.653038	−	0.757325i	$-0.273494\pi$
$359$	2.54992	+	1.85263i	0.134580	+	0.0977778i	−0.518459	+	0.855103i	$0.673494\pi$
$360$	−23.1345	+	16.8082i	−1.21930	+	0.885871i
$361$	4.32725	−	13.3179i	0.227750	−	0.700943i
$362$	27.7161			1.45672
$363$	−36.5435	+	6.74636i	−1.91803	+	0.354092i
$364$	0.136263			0.00714213
$365$	−3.22554	+	9.92721i	−0.168833	+	0.519614i
$366$	−1.67698	+	1.21840i	−0.0876572	+	0.0636867i
$367$	−9.77416	−	7.10134i	−0.510207	−	0.370687i	0.302695	−	0.953087i	$-0.402114\pi$
$367$	−9.77416	−	7.10134i	−0.510207	−	0.370687i	−0.812902	+	0.582400i	$0.802114\pi$
$368$	6.41829	+	19.7535i	0.334576	+	1.02972i
$369$	11.2479	+	34.6176i	0.585545	+	1.80212i
$370$	−1.57935	−	1.14747i	−0.0821067	−	0.0596540i
$371$	−0.146699	+	0.106583i	−0.00761626	+	0.00553354i
$372$	−1.55649	+	4.79037i	−0.0807001	+	0.248369i
$373$	−12.9240			−0.669180			−0.334590	−	0.942364i	$-0.608598\pi$
$373$	−12.9240			−0.669180			−0.334590	+	0.942364i	$0.608598\pi$
$374$	−13.2247	−	2.99733i	−0.683833	−	0.154988i
$375$	−38.5282			−1.98959
$376$	−2.82272	+	8.68745i	−0.145571	+	0.448021i
$377$	4.88799	−	3.55134i	0.251744	−	0.182903i
$378$	3.17764	+	2.30869i	0.163440	+	0.118746i
$379$	−4.40813	−	13.5668i	−0.226430	−	0.696881i	−0.998143	−	0.0609097i	$-0.980600\pi$
$379$	−4.40813	−	13.5668i	−0.226430	−	0.696881i	0.771713	−	0.635971i	$-0.219400\pi$
$380$	4.35308	+	13.3974i	0.223308	+	0.687272i
$381$	44.5512	+	32.3684i	2.28243	+	1.65828i
$382$	25.3954	−	18.4508i	1.29934	−	0.944025i
$383$	−2.00840	+	6.18121i	−0.102624	+	0.315845i	−0.989166	−	0.146805i	$-0.953101\pi$
$383$	−2.00840	+	6.18121i	−0.102624	+	0.315845i	0.886541	+	0.462650i	$0.153101\pi$
$384$	−37.9252			−1.93536
$385$	0.451454	−	0.758219i	0.0230082	−	0.0386424i
$386$	8.34658			0.424830
$387$	−15.9006	+	48.9371i	−0.808274	+	2.48761i
$388$	8.55056	−	6.21234i	0.434089	−	0.315384i
$389$	2.22563	+	1.61701i	0.112844	+	0.0819858i	0.642776	−	0.766054i	$-0.277783\pi$
$389$	2.22563	+	1.61701i	0.112844	+	0.0819858i	−0.529932	+	0.848040i	$0.677783\pi$
$390$	−4.03526	−	12.4193i	−0.204333	−	0.628873i
$391$	−2.97962	−	9.17033i	−0.150686	−	0.463763i
$392$	8.77871	+	6.37811i	0.443392	+	0.322143i
$393$	2.50347	−	1.81888i	0.126283	−	0.0917503i
$394$	−5.64513	+	17.3739i	−0.284397	+	0.875285i
$395$	−19.8360			−0.998058
$396$	−28.7327	+	12.3326i	−1.44387	+	0.619735i
$397$	−3.98758			−0.200131			−0.100065	−	0.994981i	$-0.531905\pi$
$397$	−3.98758			−0.200131			−0.100065	+	0.994981i	$0.531905\pi$
$398$	−12.6469	+	38.9231i	−0.633931	+	1.95104i
$399$	−1.90918	+	1.38710i	−0.0955787	+	0.0694420i
$400$	−0.855354	−	0.621451i	−0.0427677	−	0.0310725i
$401$	1.11143	+	3.42063i	0.0555022	+	0.170818i	0.974965	−	0.222359i	$-0.0713758\pi$
$401$	1.11143	+	3.42063i	0.0555022	+	0.170818i	−0.919463	+	0.393177i	$0.871376\pi$
$402$	−25.5819	−	78.7331i	−1.27591	−	3.92685i
$403$	1.07638	+	0.782034i	0.0536182	+	0.0389559i
$404$	11.9473	−	8.68025i	0.594403	−	0.431859i
$405$	24.7043	−	76.0319i	1.22756	−	3.77806i
$406$	1.29781			0.0644092
$407$	1.10398	+	1.25974i	0.0547224	+	0.0624432i
$408$	12.1460			0.601317
$409$	−8.14240	+	25.0597i	−0.402616	+	1.23912i	0.520254	+	0.854012i	$0.325837\pi$
$409$	−8.14240	+	25.0597i	−0.402616	+	1.23912i	−0.922870	+	0.385112i	$0.874163\pi$
$410$	13.5303	−	9.83034i	0.668214	−	0.485486i
$411$	−22.0997	−	16.0564i	−1.09010	−	0.792004i
$412$	−1.69930	−	5.22990i	−0.0837184	−	0.257659i
$413$	−0.248687	−	0.765379i	−0.0122371	−	0.0376618i
$414$	−50.0895	−	36.3922i	−2.46177	−	1.78858i
$415$	6.74862	−	4.90316i	0.331277	−	0.240687i
$416$	1.76142	−	5.42109i	0.0863607	−	0.265791i
$417$	−8.64488			−0.423342
$418$	−3.06803	−	33.5185i	−0.150062	−	1.63944i
$419$	−18.9753			−0.927002			−0.463501	−	0.886096i	$-0.653407\pi$
$419$	−18.9753			−0.927002			−0.463501	+	0.886096i	$0.653407\pi$
$420$	0.311264	−	0.957972i	0.0151881	−	0.0467443i
$421$	5.65138	−	4.10597i	0.275431	−	0.200113i	−0.441491	−	0.897266i	$-0.645550\pi$
$421$	5.65138	−	4.10597i	0.275431	−	0.200113i	0.716922	+	0.697153i	$0.245550\pi$
$422$	25.0606	+	18.2076i	1.21993	+	0.886331i
$423$	−15.2866	−	47.0473i	−0.743259	−	2.28752i
$424$	0.715863	+	2.20320i	0.0347654	+	0.106997i
$425$	0.397089	+	0.288502i	0.0192616	+	0.0139944i
$426$	26.2026	−	19.0373i	1.26952	−	0.922359i
$427$	−0.0130513	+	0.0401678i	−0.000631598	+	0.00194386i
$428$	5.08561			0.245822
$429$	1.02130	+	11.1578i	0.0493090	+	0.538704i
$430$	23.6424			1.14014
$431$	8.01090	−	24.6550i	0.385872	−	1.18759i	−0.549974	−	0.835181i	$-0.685363\pi$
$431$	8.01090	−	24.6550i	0.385872	−	1.18759i	0.935846	−	0.352409i	$-0.114637\pi$
$432$	73.7515	−	53.5836i	3.54837	−	2.57804i
$433$	8.39649	+	6.10041i	0.403510	+	0.293167i	0.770969	−	0.636873i	$-0.219772\pi$
$433$	8.39649	+	6.10041i	0.403510	+	0.293167i	−0.367459	+	0.930040i	$0.619772\pi$
$434$	0.0883135	+	0.271801i	0.00423918	+	0.0130469i
$435$	−13.8014	−	42.4764i	−0.661727	−	2.03659i
$436$	−8.55988	−	6.21912i	−0.409944	−	0.297842i
$437$	19.3628	−	14.0679i	0.926249	−	0.672960i
$438$	8.79720	−	27.0750i	0.420347	−	1.29369i
$439$	1.50138			0.0716568			0.0358284	−	0.999358i	$-0.488593\pi$
$439$	1.50138			0.0716568			0.0358284	+	0.999358i	$0.488593\pi$
$440$	−7.43024	−	8.47857i	−0.354223	−	0.404200i
$441$	−58.7646			−2.79831
$442$	−1.26342	+	3.88842i	−0.0600950	+	0.184953i
$443$	−6.16836	+	4.48158i	−0.293068	+	0.212926i	−0.724597	−	0.689173i	$-0.757974\pi$
$443$	−6.16836	+	4.48158i	−0.293068	+	0.212926i	0.431529	+	0.902099i	$0.357974\pi$
$444$	1.54682	+	1.12383i	0.0734090	+	0.0533348i
$445$	3.53674	+	10.8850i	0.167657	+	0.515997i
$446$	0.771037	+	2.37301i	0.0365096	+	0.112365i
$447$	27.9556	+	20.3109i	1.32225	+	0.960673i
$448$	0.00968487	−	0.00703647i	0.000457567	−	0.000332442i
$449$	7.68968	−	23.6664i	0.362898	−	1.11689i	−0.588388	−	0.808579i	$-0.700237\pi$
$449$	7.68968	−	23.6664i	0.362898	−	1.11689i	0.951287	−	0.308308i	$-0.0997627\pi$
$450$	3.15167			0.148571
$451$	−13.1866	+	5.65993i	−0.620934	+	0.266516i
$452$	2.31700			0.108983
$453$	−4.46074	+	13.7288i	−0.209584	+	0.645033i
$454$	−19.3685	+	14.0720i	−0.909007	+	0.660432i
$455$	−0.215253	−	0.156390i	−0.0100912	−	0.00733168i
$456$	9.31642	+	28.6730i	0.436281	+	1.34274i
$457$	−6.63267	−	20.4133i	−0.310263	−	0.954892i	−0.977660	−	0.210190i	$-0.932592\pi$
$457$	−6.63267	−	20.4133i	−0.310263	−	0.954892i	0.667397	−	0.744702i	$-0.267408\pi$
$458$	−14.7539	−	10.7194i	−0.689406	−	0.500883i
$459$	−34.2384	+	24.8756i	−1.59811	+	1.16109i
$460$	−3.15682	+	9.71570i	−0.147188	+	0.452997i
$461$	31.3859			1.46179			0.730894	−	0.682491i	$-0.239103\pi$
$461$	31.3859			1.46179			0.730894	+	0.682491i	$0.239103\pi$
$462$	−1.23127	+	2.06793i	−0.0572841	+	0.0962089i
$463$	2.92907			0.136126			0.0680628	−	0.997681i	$-0.478318\pi$
$463$	2.92907			0.136126			0.0680628	+	0.997681i	$0.478318\pi$
$464$	9.30807	−	28.6473i	0.432116	−	1.32992i
$465$	7.95670	−	5.78088i	0.368983	−	0.268082i
$466$	−0.285335	−	0.207308i	−0.0132179	−	0.00960336i
$467$	1.23997	+	3.81623i	0.0573788	+	0.176594i	0.975638	−	0.219385i	$-0.0704052\pi$
$467$	1.23997	+	3.81623i	0.0573788	+	0.176594i	−0.918259	+	0.395979i	$0.870405\pi$
$468$	2.91326	+	8.96611i	0.134666	+	0.414458i
$469$	−1.36461	−	0.991451i	−0.0630120	−	0.0457809i
$470$	−18.3884	+	13.3600i	−0.848195	+	0.616250i
$471$	−22.2455	+	68.4645i	−1.02502	+	3.15468i
$472$	−10.2813			−0.473234
$473$	−19.7840	−	4.48398i	−0.909670	−	0.206174i
$474$	54.0998			2.48489
$475$	−0.376482	+	1.15869i	−0.0172742	+	0.0531645i
$476$	−0.255142	+	0.185372i	−0.0116944	+	0.00849649i
$477$	−10.1496	−	7.37410i	−0.464717	−	0.337637i
$478$	−4.14036	−	12.7427i	−0.189376	−	0.582839i
$479$	−5.79237	−	17.8271i	−0.264660	−	0.814541i	−0.991771	−	0.128021i	$-0.959138\pi$
$479$	−5.79237	−	17.8271i	−0.264660	−	0.814541i	0.727111	−	0.686520i	$-0.240862\pi$
$480$	−34.0884	−	24.7666i	−1.55591	−	1.13044i
$481$	0.408587	−	0.296856i	0.0186300	−	0.0135355i
$482$	−2.39386	+	7.36754i	−0.109037	+	0.335582i
$483$	−1.71137			−0.0778700
$484$	−5.87428	−	10.8372i	−0.267013	−	0.492602i
$485$	−20.6371			−0.937083
$486$	−37.4316	+	115.203i	−1.69793	+	5.22570i
$487$	24.0753	−	17.4918i	1.09096	−	0.792627i	0.111397	−	0.993776i	$-0.464467\pi$
$487$	24.0753	−	17.4918i	1.09096	−	0.792627i	0.979561	+	0.201149i	$0.0644674\pi$
$488$	0.436522	+	0.317152i	0.0197604	+	0.0143568i
$489$	18.7388	+	57.6722i	0.847400	+	2.60803i
$490$	8.34367	+	25.6792i	0.376928	+	1.16007i
$491$	18.8792	+	13.7166i	0.852008	+	0.619020i	0.925699	−	0.378261i	$-0.123478\pi$
$491$	18.8792	+	13.7166i	0.852008	+	0.619020i	−0.0736912	+	0.997281i	$0.523478\pi$
$492$	−13.2516	+	9.62786i	−0.597429	+	0.434057i
$493$	−4.32117	+	13.2992i	−0.194616	+	0.598966i
$494$	−10.1484			−0.456600
$495$	59.5427	+	13.4951i	2.67625	+	0.606562i
$496$	6.63302			0.297831
$497$	0.203925	−	0.627616i	0.00914728	−	0.0281524i
$498$	−18.4059	+	13.3727i	−0.824788	+	0.599243i
$499$	0.710048	+	0.515880i	0.0317861	+	0.0230940i	0.603565	−	0.797314i	$-0.293746\pi$
$499$	0.710048	+	0.515880i	0.0317861	+	0.0230940i	−0.571779	+	0.820408i	$0.693746\pi$
$500$	−3.94937	−	12.1549i	−0.176621	−	0.543585i
$501$	25.3513	+	78.0234i	1.13261	+	3.48583i
$502$	−0.242328	−	0.176062i	−0.0108156	−	0.00785801i
$503$	33.8502	−	24.5936i	1.50930	−	1.09657i	0.542819	−	0.839850i	$-0.317357\pi$
$503$	33.8502	−	24.5936i	1.50930	−	1.09657i	0.966485	−	0.256723i	$-0.0826430\pi$
$504$	0.491053	−	1.51131i	0.0218733	−	0.0673189i
$505$	−28.8354			−1.28316
$506$	12.4875	−	20.9729i	0.555138	−	0.932357i
$507$	3.37827			0.150034
$508$	−5.64484	+	17.3730i	−0.250449	+	0.770804i
$509$	9.53170	−	6.92518i	0.422485	−	0.306953i	−0.356152	−	0.934428i	$-0.615911\pi$
$509$	9.53170	−	6.92518i	0.422485	−	0.306953i	0.778637	+	0.627475i	$0.215911\pi$
$510$	24.4508	+	17.7645i	1.08270	+	0.786627i
$511$	−0.179245	−	0.551658i	−0.00792931	−	0.0244039i
$512$	−3.99505	−	12.2955i	−0.176558	−	0.543390i
$513$	−84.9856	−	61.7457i	−3.75221	−	2.72614i
$514$	24.1845	−	17.5711i	1.06673	−	0.775026i
$515$	−3.31804	+	10.2119i	−0.146210	+	0.449989i
$516$	−23.1554			−1.01936
$517$	17.9214	−	7.69216i	0.788181	−	0.338301i
$518$	0.108484			0.00476651
$519$	26.8480	−	82.6298i	1.17850	−	3.62704i
$520$	−2.74995	+	1.99796i	−0.120593	+	0.0876162i
$521$	−26.7232	−	19.4156i	−1.17077	−	0.850611i	−0.179665	−	0.983728i	$-0.557501\pi$
$521$	−26.7232	−	19.4156i	−1.17077	−	0.850611i	−0.991100	+	0.133117i	$0.957501\pi$
$522$	27.7468	+	85.3957i	1.21444	+	3.73767i
$523$	6.10323	+	18.7838i	0.266875	+	0.821358i	0.991255	+	0.131957i	$0.0421262\pi$
$523$	6.10323	+	18.7838i	0.266875	+	0.821358i	−0.724380	+	0.689401i	$0.757874\pi$
$524$	0.830443	+	0.603352i	0.0362781	+	0.0263576i
$525$	0.0704778	−	0.0512052i	0.00307591	−	0.00223478i
$526$	−5.03799	+	15.5053i	−0.219667	+	0.676064i
$527$	−3.07931			−0.134137
$528$	36.8158	+	42.0101i	1.60220	+	1.82826i
$529$	−5.64340			−0.245365
$530$	−1.78128	+	5.48220i	−0.0773737	+	0.238132i
$531$	45.0450	−	32.7271i	1.95479	−	1.42024i
$532$	−0.633308	−	0.460125i	−0.0274574	−	0.0199489i
$533$	1.33702	+	4.11492i	0.0579127	+	0.178237i
$534$	−9.64594	−	29.6872i	−0.417421	−	1.28469i
$535$	−8.03365	−	5.83679i	−0.347325	−	0.252346i
$536$	−17.4336	+	12.6662i	−0.753016	+	0.547098i
$537$	9.45910	−	29.1121i	0.408190	−	1.25628i
$538$	−21.3945			−0.922381
$539$	−2.11174	−	23.0709i	−0.0909590	−	0.993734i
$540$	44.8378			1.92951
$541$	7.13656	−	21.9641i	0.306824	−	0.944309i	−0.672166	−	0.740401i	$-0.734636\pi$
$541$	7.13656	−	21.9641i	0.306824	−	0.944309i	0.978990	−	0.203908i	$-0.0653643\pi$
$542$	4.67753	−	3.39843i	0.200917	−	0.145975i
$543$	42.8808	+	31.1547i	1.84019	+	1.33698i
$544$	4.07670	+	12.5468i	0.174787	+	0.537939i
$545$	6.38417	+	19.6485i	0.273468	+	0.841648i
$546$	0.587070	+	0.426531i	0.0251243	+	0.0182539i
$547$	−36.2355	+	26.3267i	−1.54932	+	1.12565i	−0.605187	+	0.796084i	$0.706902\pi$
$547$	−36.2355	+	26.3267i	−1.54932	+	1.12565i	−0.944133	+	0.329563i	$0.893098\pi$
$548$	2.80013	−	8.61793i	0.119616	−	0.368140i
$549$	−2.92207			−0.124711
$550$	0.113257	+	1.23734i	0.00482930	+	0.0527604i
$551$	−34.7098			−1.47869
$552$	−6.75620	+	20.7935i	−0.287563	+	0.885028i
$553$	0.891774	−	0.647912i	0.0379221	−	0.0275520i
$554$	−18.6475	−	13.5482i	−0.792256	−	0.575608i
$555$	−1.15366	−	3.55060i	−0.0489701	−	0.150715i
$556$	−0.886153	−	2.72730i	−0.0375812	−	0.115663i
$557$	10.0308	+	7.28777i	0.425017	+	0.308793i	0.779653	−	0.626211i	$-0.215395\pi$
$557$	10.0308	+	7.28777i	0.425017	+	0.308793i	−0.354636	+	0.935004i	$0.615395\pi$
$558$	−15.9964	+	11.6220i	−0.677181	+	0.492000i
$559$	−1.89007	+	5.81704i	−0.0799415	+	0.246035i
$560$	−1.32646			−0.0560533
$561$	−17.0913	−	19.5028i	−0.721597	−	0.823407i
$562$	−38.5014			−1.62408
$563$	7.03840	−	21.6620i	0.296633	−	0.912943i	−0.686035	−	0.727569i	$-0.740650\pi$
$563$	7.03840	−	21.6620i	0.296633	−	0.912943i	0.982668	−	0.185374i	$-0.0593497\pi$
$564$	18.0097	−	13.0848i	0.758344	−	0.550969i
$565$	−3.66012	−	2.65924i	−0.153983	−	0.111875i
$566$	12.4213	+	38.2289i	0.522107	+	1.60688i
$567$	1.37282	+	4.22512i	0.0576532	+	0.177438i
$568$	−6.82059	−	4.95545i	−0.286186	−	0.207926i
$569$	26.6904	−	19.3917i	1.11892	−	0.812942i	0.134874	−	0.990863i	$-0.456937\pi$
$569$	26.6904	−	19.3917i	1.11892	−	0.812942i	0.984045	+	0.177921i	$0.0569370\pi$
$570$	−23.1820	+	71.3467i	−0.970986	+	2.98839i
$571$	21.4209			0.896436			0.448218	−	0.893924i	$-0.352059\pi$
$571$	21.4209			0.896436			0.448218	+	0.893924i	$0.352059\pi$
$572$	−3.41539	+	1.46595i	−0.142805	+	0.0612943i
$573$	60.0302			2.50780
$574$	−0.287194	+	0.883892i	−0.0119872	+	0.0368929i
$575$	−0.714782	+	0.519320i	−0.0298085	+	0.0216571i
$576$	0.670059	+	0.486826i	0.0279191	+	0.0202844i
$577$	9.16579	+	28.2094i	0.381577	+	1.17437i	0.938933	+	0.344100i	$0.111816\pi$
$577$	9.16579	+	28.2094i	0.381577	+	1.17437i	−0.557356	+	0.830273i	$0.688184\pi$
$578$	6.35597	+	19.5617i	0.264374	+	0.813658i
$579$	12.9134	+	9.38211i	0.536661	+	0.389907i
$580$	11.9858	−	8.70817i	0.497682	−	0.361587i
$581$	−0.143246	+	0.440866i	−0.00594285	+	0.0182902i
$582$	56.2847			2.33308
$583$	2.53033	−	4.24970i	0.104795	−	0.176005i
$584$	−7.41038			−0.306644
$585$	5.68843	−	17.5072i	0.235187	−	0.723833i
$586$	27.4693	−	19.9576i	1.13475	−	0.824443i
$587$	−15.9836	−	11.6128i	−0.659715	−	0.479311i	0.206852	−	0.978372i	$-0.433678\pi$
$587$	−15.9836	−	11.6128i	−0.659715	−	0.479311i	−0.866567	+	0.499061i	$0.833678\pi$
$588$	−8.17181	−	25.1502i	−0.337000	−	1.03718i
$589$	−2.36193	−	7.26929i	−0.0973218	−	0.299526i
$590$	−20.6969	−	15.0372i	−0.852079	−	0.619072i
$591$	−28.2633	+	20.5345i	−1.16260	+	0.844675i
$592$	0.778061	−	2.39463i	0.0319781	−	0.0984185i
$593$	−15.9831			−0.656347			−0.328173	−	0.944618i	$-0.606433\pi$
$593$	−15.9831			−0.656347			−0.328173	+	0.944618i	$0.606433\pi$
$594$	−104.484	−	23.6809i	−4.28702	−	0.971639i
$595$	0.615796			0.0252452
$596$	−3.54209	+	10.9014i	−0.145090	+	0.446541i
$597$	−63.3187	+	46.0037i	−2.59146	+	1.88281i
$598$	−5.95403	−	4.32586i	−0.243478	−	0.176897i
$599$	−14.1449	−	43.5334i	−0.577943	−	1.77873i	−0.625930	−	0.779879i	$-0.715281\pi$
$599$	−14.1449	−	43.5334i	−0.577943	−	1.77873i	0.0479869	−	0.998848i	$-0.484719\pi$
$600$	−0.343917	−	1.05847i	−0.0140404	−	0.0432118i
$601$	−12.5500	−	9.11812i	−0.511926	−	0.371936i	0.301628	−	0.953426i	$-0.402470\pi$
$601$	−12.5500	−	9.11812i	−0.511926	−	0.371936i	−0.813554	+	0.581490i	$0.802470\pi$
$602$	−1.06290	+	0.772240i	−0.0433205	+	0.0314742i
$603$	36.0623	−	110.988i	1.46857	−	4.51980i
$604$	−4.78842			−0.194838
$605$	−3.15847	+	23.8613i	−0.128410	+	0.970101i
$606$	78.6443			3.19471
$607$	−2.80998	+	8.64823i	−0.114054	+	0.351021i	−0.991748	−	0.128199i	$-0.959080\pi$
$607$	−2.80998	+	8.64823i	−0.114054	+	0.351021i	0.877695	+	0.479220i	$0.159080\pi$
$608$	−26.4921	+	19.2476i	−1.07440	+	0.780595i
$609$	2.00790	+	1.45882i	0.0813642	+	0.0591145i
$610$	0.414890	+	1.27690i	0.0167984	+	0.0517001i
$611$	−1.81708	−	5.59241i	−0.0735113	−	0.226245i
$612$	−17.6523	−	12.8251i	−0.713552	−	0.518426i
$613$	−21.0223	+	15.2736i	−0.849084	+	0.616896i	−0.924893	−	0.380227i	$-0.875846\pi$
$613$	−21.0223	+	15.2736i	−0.849084	+	0.616896i	0.0758094	+	0.997122i	$0.475846\pi$
$614$	8.47220	−	26.0748i	0.341910	−	1.05229i
$615$	31.9833			1.28969
$616$	0.610983	+	0.138477i	0.0246172	+	0.00557940i
$617$	4.31680			0.173788			0.0868940	−	0.996218i	$-0.472306\pi$
$617$	4.31680			0.173788			0.0868940	+	0.996218i	$0.472306\pi$
$618$	9.04947	−	27.8514i	0.364023	−	1.12035i
$619$	−5.74165	+	4.17155i	−0.230776	+	0.167669i	−0.697164	−	0.716911i	$-0.745555\pi$
$619$	−5.74165	+	4.17155i	−0.230776	+	0.167669i	0.466388	+	0.884580i	$0.345555\pi$
$620$	2.63937	+	1.91761i	0.106000	+	0.0770132i
$621$	−23.5409	−	72.4516i	−0.944666	−	2.90738i
$622$	11.7390	+	36.1290i	0.470692	+	1.44864i
$623$	−0.514543	−	0.373837i	−0.0206147	−	0.0149775i
$624$	13.6256	−	9.89959i	0.545461	−	0.396301i
$625$	−7.38386	+	22.7252i	−0.295354	+	0.909007i
$626$	28.4535			1.13723
$627$	32.9303	−	55.3066i	1.31511	−	2.20873i
$628$	−23.8796			−0.952898
$629$	−0.361206	+	1.11168i	−0.0144022	+	0.0443256i
$630$	3.19893	−	2.32416i	0.127449	−	0.0925968i
$631$	32.1347	+	23.3472i	1.27926	+	0.929439i	0.999531	−	0.0306385i	$-0.00975408\pi$
$631$	32.1347	+	23.3472i	1.27926	+	0.929439i	0.279733	+	0.960078i	$0.409754\pi$
$632$	−4.35167	−	13.3931i	−0.173100	−	0.532748i
$633$	18.3058	+	56.3395i	0.727591	+	2.23930i
$634$	−6.34716	−	4.61148i	−0.252078	−	0.183145i
$635$	28.8562	−	20.9653i	1.14512	−	0.831981i
$636$	1.74459	−	5.36928i	0.0691773	−	0.212906i
$637$	−6.98521			−0.276764
$638$	−32.5292	+	13.9621i	−1.28784	+	0.552764i
$639$	45.6569			1.80616
$640$	−7.59084	+	23.3622i	−0.300054	+	0.923473i
$641$	−27.6384	+	20.0805i	−1.09165	+	0.793131i	−0.979677	−	0.200580i	$-0.935717\pi$
$641$	−27.6384	+	20.0805i	−1.09165	+	0.793131i	−0.111974	+	0.993711i	$0.535717\pi$
$642$	21.9106	+	15.9190i	0.864743	+	0.628272i
$643$	12.3438	+	37.9904i	0.486793	+	1.49820i	0.829367	+	0.558704i	$0.188701\pi$
$643$	12.3438	+	37.9904i	0.486793	+	1.49820i	−0.342574	+	0.939491i	$0.611299\pi$
$644$	−0.175426	−	0.539905i	−0.00691274	−	0.0212752i
$645$	36.5781	+	26.5756i	1.44026	+	1.04641i
$646$	19.0022	−	13.8059i	0.747631	−	0.543185i
$647$	1.81207	−	5.57698i	0.0712398	−	0.219254i	−0.909097	−	0.416584i	$-0.863227\pi$
$647$	1.81207	−	5.57698i	0.0712398	−	0.219254i	0.980337	+	0.197330i	$0.0632272\pi$
$648$	56.7557			2.22957
$649$	14.4673	+	16.5086i	0.567893	+	0.648017i
$650$	0.374632			0.0146943
$651$	−0.168889	+	0.519786i	−0.00661927	+	0.0203720i
$652$	−16.2737	+	11.8235i	−0.637326	+	0.463044i
$653$	11.9366	+	8.67247i	0.467116	+	0.339380i	0.796316	−	0.604880i	$-0.206779\pi$
$653$	11.9366	+	8.67247i	0.467116	+	0.339380i	−0.329200	+	0.944260i	$0.606779\pi$
$654$	−17.4119	−	53.5883i	−0.680859	−	2.09547i
$655$	−0.619365	−	1.90621i	−0.0242006	−	0.0744818i
$656$	17.4509	+	12.6788i	0.681342	+	0.495024i
$657$	32.4669	−	23.5886i	1.26665	−	0.920278i
$658$	0.390313	−	1.20126i	0.0152160	−	0.0468299i
$659$	−42.1111			−1.64042			−0.820208	−	0.572065i	$-0.806143\pi$
$659$	−42.1111			−1.64042			−0.820208	+	0.572065i	$0.806143\pi$
$660$	2.50432	+	27.3599i	0.0974806	+	1.06498i
$661$	−13.2231			−0.514317			−0.257159	−	0.966369i	$-0.582786\pi$
$661$	−13.2231			−0.514317			−0.257159	+	0.966369i	$0.582786\pi$
$662$	−0.904751	+	2.78454i	−0.0351641	+	0.108224i
$663$	−6.32555	+	4.59578i	−0.245664	+	0.178485i
$664$	4.79110	+	3.48094i	0.185931	+	0.135086i
$665$	0.472337	+	1.45370i	0.0183164	+	0.0563722i
$666$	2.31935	+	7.13823i	0.0898730	+	0.276601i
$667$	−20.3640	−	14.7953i	−0.788497	−	0.572877i
$668$	−22.0162	+	15.9957i	−0.851834	+	0.618894i
$669$	−1.47451	+	4.53808i	−0.0570079	+	0.175452i
$670$	−53.6204			−2.07154
$671$	−0.105006	−	1.14720i	−0.00405373	−	0.0442872i
$672$	2.34149			0.0903248
$673$	5.07820	−	15.6291i	0.195750	−	0.602458i	−0.804217	−	0.594336i	$-0.797415\pi$
$673$	5.07820	−	15.6291i	0.195750	−	0.602458i	0.999967	−	0.00812135i	$-0.00258513\pi$
$674$	−34.5899	+	25.1310i	−1.33235	+	0.968012i
$675$	3.13726	+	2.27935i	0.120753	+	0.0877323i
$676$	0.346293	+	1.06578i	0.0133190	+	0.0409916i
$677$	−9.46120	−	29.1186i	−0.363623	−	1.11912i	−0.950839	−	0.309687i	$-0.899776\pi$
$677$	−9.46120	−	29.1186i	−0.363623	−	1.11912i	0.587215	−	0.809431i	$-0.300224\pi$
$678$	9.98246	+	7.25268i	0.383374	+	0.278537i
$679$	0.927790	−	0.674079i	0.0356053	−	0.0258688i
$680$	2.43106	−	7.48203i	0.0932269	−	0.286923i
$681$	−45.7837			−1.75444
$682$	−5.13764	−	5.86251i	−0.196730	−	0.224487i
$683$	−32.4731			−1.24255			−0.621274	−	0.783593i	$-0.713385\pi$
$683$	−32.4731			−1.24255			−0.621274	+	0.783593i	$0.713385\pi$
$684$	16.7363	−	51.5089i	0.639927	−	1.96949i
$685$	−14.3142	+	10.3999i	−0.546917	+	0.397358i
$686$	−2.43033	−	1.76574i	−0.0927903	−	0.0674161i
$687$	−10.7772	−	33.1688i	−0.411176	−	1.26547i
$688$	9.42285	+	29.0006i	0.359243	+	1.10564i
$689$	−1.20646	−	0.876542i	−0.0459623	−	0.0333936i
$690$	−44.0128	+	31.9772i	−1.67554	+	1.21735i
$691$	−12.6950	+	39.0712i	−0.482940	+	1.48634i	0.352002	+	0.935999i	$0.385501\pi$
$691$	−12.6950	+	39.0712i	−0.482940	+	1.48634i	−0.834942	+	0.550338i	$0.814499\pi$
$692$	28.8202			1.09558
$693$	−3.11768	+	1.33816i	−0.118431	+	0.0508326i
$694$	−5.73282			−0.217615
$695$	−1.73030	+	5.32531i	−0.0656339	+	0.202000i
$696$	25.6518	−	18.6372i	0.972330	−	0.706439i
$697$	−8.10137	−	5.88599i	−0.306861	−	0.222948i
$698$	−0.793366	−	2.44173i	−0.0300293	−	0.0924208i
$699$	−0.208427	−	0.641471i	−0.00788342	−	0.0242627i
$700$	0.0233787	+	0.0169856i	0.000883631	+	0.000641995i
$701$	18.0479	−	13.1125i	0.681658	−	0.495254i	−0.192249	−	0.981346i	$-0.561578\pi$
$701$	18.0479	−	13.1125i	0.681658	−	0.495254i	0.873907	+	0.486092i	$0.161578\pi$
$702$	−9.98188	+	30.7211i	−0.376742	+	1.15949i
$703$	−2.90139			−0.109428
$704$	−0.167048	+	0.280558i	−0.00629587	+	0.0105739i
$705$	−43.4671			−1.63707
$706$	15.8947	−	48.9188i	0.598205	−	1.84108i
$707$	1.29636	−	0.941863i	0.0487547	−	0.0354224i
$708$	20.2706	+	14.7275i	0.761817	+	0.553492i
$709$	−6.22286	−	19.1520i	−0.233705	−	0.719269i	−0.997291	−	0.0735625i	$-0.976563\pi$
$709$	−6.22286	−	19.1520i	−0.233705	−	0.719269i	0.763586	−	0.645706i	$-0.223437\pi$
$710$	−6.48258	−	19.9513i	−0.243287	−	0.748760i
$711$	61.6984	+	44.8265i	2.31387	+	1.68113i
$712$	−6.57352	+	4.77594i	−0.246353	+	0.178986i
$713$	1.71286	−	5.27164i	0.0641471	−	0.197424i
$714$	−1.67949			−0.0628535
$715$	7.07771	+	1.60414i	0.264691	+	0.0599913i
$716$	10.1539			0.379471
$717$	7.91793	−	24.3689i	0.295701	−	0.910073i
$718$	−4.50451	+	3.27272i	−0.168107	+	0.122137i
$719$	−15.7474	−	11.4412i	−0.587279	−	0.426683i	0.254062	−	0.967188i	$-0.418233\pi$
$719$	−15.7474	−	11.4412i	−0.587279	−	0.426683i	−0.841341	+	0.540505i	$0.818233\pi$
$720$	−28.3594	−	87.2811i	−1.05689	−	3.25278i
$721$	−0.184385	−	0.567477i	−0.00686684	−	0.0211340i
$722$	20.0128	+	14.5402i	0.744801	+	0.541129i
$723$	−11.9853	+	8.70780i	−0.445737	+	0.323847i
$724$	−5.43319	+	16.7216i	−0.201923	+	0.621455i
$725$	1.28132			0.0475869
$726$	8.61428	−	65.0783i	0.319706	−	2.41528i
$727$	2.25186			0.0835170			0.0417585	−	0.999128i	$-0.486704\pi$
$727$	2.25186			0.0835170			0.0417585	+	0.999128i	$0.486704\pi$
$728$	0.0583704	−	0.179646i	0.00216335	−	0.00665811i
$729$	−98.7341	+	71.7345i	−3.65682	+	2.65683i
$730$	−14.9176	−	10.8383i	−0.552126	−	0.401143i
$731$	−4.37446	−	13.4632i	−0.161795	−	0.497954i
$732$	−0.406344	−	1.25060i	−0.0150189	−	0.0462234i
$733$	7.14492	+	5.19108i	0.263903	+	0.191737i	0.711866	−	0.702315i	$-0.247850\pi$
$733$	7.14492	+	5.19108i	0.263903	+	0.191737i	−0.447963	+	0.894052i	$0.647850\pi$
$734$	17.2663	−	12.5447i	0.637312	−	0.463035i
$735$	−15.9562	+	49.1082i	−0.588554	+	1.81138i
$736$	−23.7472			−0.875334
$737$	44.8698	+	10.1696i	1.65280	+	0.374602i
$738$	−64.3001			−2.36692
$739$	−10.0280	+	30.8630i	−0.368885	+	1.13531i	0.578627	+	0.815592i	$0.303589\pi$
$739$	−10.0280	+	30.8630i	−0.368885	+	1.13531i	−0.947512	+	0.319720i	$0.896411\pi$
$740$	1.00189	−	0.727916i	0.0368302	−	0.0267587i
$741$	−15.7011	−	11.4075i	−0.576795	−	0.419066i
$742$	−0.0989861	−	0.304648i	−0.00363390	−	0.0111840i
$743$	8.81385	+	27.1262i	0.323349	+	0.995166i	0.972180	+	0.234233i	$0.0752580\pi$
$743$	8.81385	+	27.1262i	0.323349	+	0.995166i	−0.648832	+	0.760932i	$0.724742\pi$
$744$	5.64875	+	4.10406i	0.207093	+	0.150462i
$745$	18.1070	−	13.1555i	0.663391	−	0.481982i
$746$	7.05506	−	21.7132i	0.258304	−	0.794978i
$747$	−32.0715			−1.17344
$748$	4.40079	−	7.39114i	0.160909	−	0.270247i
$749$	0.551821			0.0201631
$750$	21.0321	−	64.7301i	0.767983	−	2.36361i
$751$	20.7057	−	15.0435i	0.755561	−	0.548947i	−0.141985	−	0.989869i	$-0.545348\pi$
$751$	20.7057	−	15.0435i	0.755561	−	0.548947i	0.897545	+	0.440922i	$0.145348\pi$
$752$	−23.7167	−	17.2312i	−0.864859	−	0.628357i
$753$	−0.177012	−	0.544786i	−0.00645066	−	0.0198531i
$754$	3.29820	+	10.1508i	0.120113	+	0.369670i
$755$	7.56418	+	5.49570i	0.275289	+	0.200009i
$756$	−2.01579	+	1.46456i	−0.0733136	+	0.0532654i
$757$	0.897877	−	2.76338i	0.0326339	−	0.100437i	−0.933413	−	0.358804i	$-0.883185\pi$
$757$	0.897877	−	2.76338i	0.0326339	−	0.100437i	0.966047	+	0.258368i	$0.0831845\pi$
$758$	25.1995			0.915289
$759$	42.8949	−	18.4112i	1.55699	−	0.668286i
$760$	19.5275			0.708336
$761$	1.97879	−	6.09010i	0.0717312	−	0.220766i	−0.908763	−	0.417312i	$-0.862972\pi$
$761$	1.97879	−	6.09010i	0.0717312	−	0.220766i	0.980495	+	0.196546i	$0.0629724\pi$
$762$	−78.7011	+	57.1797i	−2.85104	+	2.07140i
$763$	−0.928802	−	0.674814i	−0.0336249	−	0.0244299i
$764$	6.15346	+	18.9384i	0.222624	+	0.685168i
$765$	13.1655	+	40.5193i	0.476000	+	1.46498i
$766$	−9.28850	−	6.74849i	−0.335607	−	0.243833i
$767$	5.35440	−	3.89020i	0.193336	−	0.140467i
$768$	20.9085	−	64.3497i	0.754470	−	2.32202i
$769$	−40.4812			−1.45979			−0.729894	−	0.683560i	$-0.760431\pi$
$769$	−40.4812			−1.45979			−0.729894	+	0.683560i	$0.760431\pi$
$770$	1.02742	+	1.17238i	0.0370256	+	0.0422495i
$771$	57.1679			2.05885
$772$	−1.63618	+	5.03565i	−0.0588874	+	0.181237i
$773$	24.9317	−	18.1140i	0.896732	−	0.651514i	−0.0408927	−	0.999164i	$-0.513020\pi$
$773$	24.9317	−	18.1140i	0.896732	−	0.651514i	0.937624	+	0.347650i	$0.113020\pi$
$774$	−73.5378	−	53.4283i	−2.64326	−	1.92044i
$775$	0.0871913	+	0.268347i	0.00313200	+	0.00963932i
$776$	−4.52742	−	13.9340i	−0.162525	−	0.500201i
$777$	0.167840	+	0.121943i	0.00602123	+	0.00437468i
$778$	−3.93164	+	2.85650i	−0.140956	+	0.102411i
$779$	7.68097	−	23.6396i	0.275199	−	0.846976i
$780$	8.28380			0.296608
$781$	1.64071	+	17.9248i	0.0587091	+	0.641401i
$782$	17.0333			0.609110
$783$	−34.1401	+	105.072i	−1.22007	+	3.75498i
$784$	−28.1736	+	20.4693i	−1.00620	+	0.731046i
$785$	37.7221	+	27.4067i	1.34636	+	0.978188i
$786$	1.68923	+	5.19891i	0.0602528	+	0.185439i
$787$	−7.74863	−	23.8478i	−0.276209	−	0.850083i	−0.988897	−	0.148602i	$-0.952523\pi$
$787$	−7.74863	−	23.8478i	−0.276209	−	0.850083i	0.712688	−	0.701481i	$-0.247477\pi$
$788$	−9.37539	−	6.81162i	−0.333985	−	0.242654i
$789$	−25.2235	+	18.3260i	−0.897981	+	0.652421i
$790$	10.8282	−	33.3259i	0.385251	−	1.18568i
$791$	0.251409			0.00893908
$792$	3.95084	+	43.1632i	0.140387	+	1.53374i
$793$	−0.347340			−0.0123344
$794$	2.17677	−	6.69941i	0.0772507	−	0.237753i
$795$	−8.91826	+	6.47949i	−0.316298	+	0.229804i
$796$	−21.0039	−	15.2602i	−0.744462	−	0.540883i
$797$	6.34085	+	19.5151i	0.224604	+	0.691262i	0.998332	+	0.0577424i	$0.0183902\pi$
$797$	6.34085	+	19.5151i	0.224604	+	0.691262i	−0.773727	+	0.633519i	$0.781610\pi$
$798$	−1.28823	−	3.96476i	−0.0456028	−	0.140351i
$799$	11.0102	+	7.99939i	0.389514	+	0.282998i
$800$	0.977961	−	0.710531i	0.0345762	−	0.0251210i
$801$	13.5977	−	41.8494i	0.480451	−	1.47868i
$802$	−6.35361			−0.224354
$803$	10.4276	+	11.8988i	0.367980	+	0.419899i
$804$	52.5160			1.85210
$805$	−0.342535	+	1.05422i	−0.0120728	+	0.0371562i
$806$	−1.90145	+	1.38149i	−0.0669758	+	0.0486608i
$807$	−33.1004	−	24.0488i	−1.16519	−	0.846558i
$808$	−6.32598	−	19.4694i	−0.222547	−	0.684930i
$809$	−3.05328	−	9.39703i	−0.107348	−	0.330382i	0.882927	−	0.469511i	$-0.155570\pi$
$809$	−3.05328	−	9.39703i	−0.107348	−	0.330382i	−0.990274	+	0.139129i	$0.955570\pi$
$810$	114.253	+	83.0098i	4.01445	+	2.91667i
$811$	−32.3846	+	23.5288i	−1.13718	+	0.826206i	−0.986723	−	0.162411i	$-0.948073\pi$
$811$	−32.3846	+	23.5288i	−1.13718	+	0.826206i	−0.150452	+	0.988617i	$0.548073\pi$
$812$	−0.254410	+	0.782993i	−0.00892803	+	0.0274777i
$813$	11.0569			0.387782
$814$	−2.71911	+	1.16709i	−0.0953048	+	0.0409065i
$815$	39.2771			1.37582
$816$	−12.0456	+	37.0724i	−0.421679	+	1.29779i
$817$	28.4271	−	20.6535i	0.994537	−	0.722574i
$818$	−37.6573	−	27.3596i	−1.31666	−	0.956606i
$819$	0.316108	+	0.972880i	0.0110457	+	0.0339952i
$820$	3.27848	+	10.0901i	0.114490	+	0.352363i
$821$	11.8023	+	8.57490i	0.411904	+	0.299266i	0.774372	−	0.632730i	$-0.218066\pi$
$821$	11.8023	+	8.57490i	0.411904	+	0.299266i	−0.362468	+	0.931996i	$0.618066\pi$
$822$	39.0398	−	28.3641i	1.36167	−	0.989312i
$823$	9.80940	−	30.1902i	0.341934	−	1.05236i	−0.621271	−	0.783596i	$-0.713383\pi$
$823$	9.80940	−	30.1902i	0.341934	−	1.05236i	0.963205	−	0.268769i	$-0.0866167\pi$
$824$	−7.62288			−0.265555
$825$	−1.21563	+	2.04165i	−0.0423228	+	0.0710813i
$826$	1.42165			0.0494654
$827$	−9.51981	+	29.2990i	−0.331036	+	1.01882i	0.637605	+	0.770363i	$0.279925\pi$
$827$	−9.51981	+	29.2990i	−0.331036	+	1.01882i	−0.968642	+	0.248462i	$0.920075\pi$
$828$	31.7751	−	23.0860i	1.10426	−	0.802294i
$829$	−28.6139	−	20.7892i	−0.993800	−	0.722038i	−0.0330502	−	0.999454i	$-0.510522\pi$
$829$	−28.6139	−	20.7892i	−0.993800	−	0.722038i	−0.960750	+	0.277416i	$0.910522\pi$
$830$	4.55366	+	14.0147i	0.158060	+	0.486459i
$831$	−13.6213	−	41.9221i	−0.472518	−	1.45426i
$832$	0.0796484	+	0.0578679i	0.00276131	+	0.00200621i
$833$	13.0793	−	9.50264i	0.453170	−	0.329247i
$834$	4.71913	−	14.5240i	0.163410	−	0.502925i
$835$	53.1371			1.83888
$836$	20.8238	+	4.71963i	0.720205	+	0.163232i
$837$	−24.3285			−0.840918
$838$	10.3584	−	31.8798i	0.357824	−	1.10127i
$839$	−29.2734	+	21.2684i	−1.01063	+	0.734266i	−0.964341	−	0.264662i	$-0.914740\pi$
$839$	−29.2734	+	21.2684i	−1.01063	+	0.734266i	−0.0462892	+	0.998928i	$0.514740\pi$
$840$	−1.12963	−	0.820724i	−0.0389759	−	0.0283177i
$841$	2.31901	+	7.13717i	0.0799657	+	0.246109i
$842$	3.81329	+	11.7361i	0.131415	+	0.404453i
$843$	−59.5672	−	43.2781i	−2.05160	−	1.49058i
$844$	−15.8976	+	11.5503i	−0.547218	+	0.397577i
$845$	0.676170	−	2.08104i	0.0232610	−	0.0715899i
$846$	87.3875			3.00444
$847$	−0.637396	−	1.17591i	−0.0219012	−	0.0404047i
$848$	−7.43461			−0.255306
$849$	−23.7542	+	73.1080i	−0.815243	+	2.50906i
$850$	−0.701469	+	0.509647i	−0.0240602	+	0.0174807i
$851$	−1.70223	−	1.23674i	−0.0583515	−	0.0423949i
$852$	6.34906	+	19.5404i	0.217515	+	0.669443i
$853$	−15.9420	−	49.0645i	−0.545845	−	1.67994i	−0.718973	−	0.695038i	$-0.755387\pi$
$853$	−15.9420	−	49.0645i	−0.545845	−	1.67994i	0.173128	−	0.984899i	$-0.444613\pi$
$854$	−0.0603602	−	0.0438543i	−0.00206548	−	0.00150066i
$855$	−85.5551	+	62.1594i	−2.92592	+	2.12581i
$856$	2.17850	−	6.70473i	0.0744595	−	0.229163i
$857$	45.6165			1.55823			0.779115	−	0.626881i	$-0.215669\pi$
$857$	45.6165			1.55823			0.779115	+	0.626881i	$0.215669\pi$
$858$	−19.3034	−	4.37505i	−0.659008	−	0.149362i
$859$	6.62386			0.226003			0.113002	−	0.993595i	$-0.463953\pi$
$859$	6.62386			0.226003			0.113002	+	0.993595i	$0.463953\pi$
$860$	−4.63461	+	14.2639i	−0.158039	+	0.486394i
$861$	−1.43788	+	1.04468i	−0.0490030	+	0.0356027i
$862$	37.0491	+	26.9178i	1.26190	+	0.916822i
$863$	11.8998	+	36.6238i	0.405074	+	1.24669i	0.920834	+	0.389956i	$0.127510\pi$
$863$	11.8998	+	36.6238i	0.405074	+	1.24669i	−0.515760	+	0.856733i	$0.672490\pi$
$864$	32.2086	+	99.1279i	1.09576	+	3.37240i
$865$	−45.5268	−	33.0772i	−1.54796	−	1.12466i
$866$	−14.8327	+	10.7766i	−0.504034	+	0.366202i
$867$	−12.1550	+	37.4093i	−0.412806	+	1.27049i
$868$	−0.181295			−0.00615355
$869$	−15.3817	+	25.8336i	−0.521787	+	0.876344i
$870$	78.8973			2.67487
$871$	4.28665	−	13.1929i	0.145248	−	0.447026i
$872$	−11.8659	+	8.62106i	−0.401829	+	0.291946i
$873$	64.1902	+	46.6369i	2.17251	+	1.57842i
$874$	13.0651	+	40.2104i	0.441935	+	1.36014i
$875$	−0.428532	−	1.31889i	−0.0144870	−	0.0445865i
$876$	14.6103	+	10.6150i	0.493638	+	0.358649i
$877$	−12.6072	+	9.15966i	−0.425715	+	0.309300i	−0.779933	−	0.625863i	$-0.784747\pi$
$877$	−12.6072	+	9.15966i	−0.425715	+	0.309300i	0.354218	+	0.935163i	$0.384747\pi$
$878$	−0.819583	+	2.52242i	−0.0276596	+	0.0851275i
$879$	64.9328			2.19013
$880$	33.2473	−	14.2703i	1.12077	−	0.481053i
$881$	−6.59737			−0.222271			−0.111136	−	0.993805i	$-0.535449\pi$
$881$	−6.59737			−0.222271			−0.111136	+	0.993805i	$0.535449\pi$
$882$	32.0789	−	98.7286i	1.08015	−	3.32437i
$883$	−17.3032	+	12.5715i	−0.582299	+	0.423065i	−0.839552	−	0.543279i	$-0.817182\pi$
$883$	−17.3032	+	12.5715i	−0.582299	+	0.423065i	0.257254	+	0.966344i	$0.417182\pi$
$884$	−2.09829	−	1.52450i	−0.0705731	−	0.0512744i
$885$	−15.1183	−	46.5295i	−0.508197	−	1.56407i
$886$	−4.16213	−	12.8097i	−0.139830	−	0.430351i
$887$	−36.2104	−	26.3084i	−1.21583	−	0.883350i	−0.220080	−	0.975482i	$-0.570632\pi$
$887$	−36.2104	−	26.3084i	−1.21583	−	0.883350i	−0.995747	+	0.0921321i	$0.970632\pi$
$888$	2.14424	−	1.55788i	0.0719559	−	0.0522790i
$889$	−0.612501	+	1.88509i	−0.0205426	+	0.0632237i
$890$	−20.2182			−0.677714
$891$	−79.8640	−	91.1321i	−2.67555	−	3.05304i
$892$	−1.58283			−0.0529969
$893$	−10.4389	+	32.1275i	−0.349323	+	1.07511i
$894$	−49.3843	+	35.8798i	−1.65166	+	1.20000i
$895$	−16.0400	−	11.6537i	−0.536158	−	0.389542i
$896$	−0.421826	−	1.29825i	−0.0140922	−	0.0433714i
$897$	−4.34920	−	13.3855i	−0.145215	−	0.446927i
$898$	35.5635	+	25.8384i	1.18677	+	0.862239i
$899$	−6.50336	+	4.72497i	−0.216899	+	0.157586i
$900$	−0.617822	+	1.90146i	−0.0205941	+	0.0633821i
$901$	3.45144			0.114984
$902$	−2.31066	−	25.2441i	−0.0769366	−	0.840538i
$903$	−2.51251			−0.0836110
$904$	0.992522	−	3.05467i	0.0330108	−	0.101597i
$905$	27.7742	−	20.1792i	0.923247	−	0.670778i
$906$	−20.6302	−	14.9887i	−0.685393	−	0.497967i
$907$	8.41973	+	25.9133i	0.279573	+	0.860436i	0.987973	+	0.154626i	$0.0494171\pi$
$907$	8.41973	+	25.9133i	0.279573	+	0.860436i	−0.708400	+	0.705811i	$0.750583\pi$
$908$	−4.69311	−	14.4439i	−0.155746	−	0.479338i
$909$	89.6903	+	65.1638i	2.97484	+	2.16135i
$910$	0.380250	−	0.276268i	0.0126052	−	0.00915819i
$911$	3.55701	−	10.9474i	0.117849	−	0.362702i	−0.874682	−	0.484698i	$-0.838930\pi$
$911$	3.55701	−	10.9474i	0.117849	−	0.362702i	0.992531	+	0.121996i	$0.0389295\pi$
$912$	−96.7559			−3.20391
$913$	−1.15251	−	12.5912i	−0.0381425	−	0.416709i
$914$	37.9164			1.25416
$915$	−0.793425	+	2.44191i	−0.0262298	+	0.0807271i
$916$	9.35940	−	6.80000i	0.309243	−	0.224678i
$917$	0.0901084	+	0.0654676i	0.00297564	+	0.00216193i
$918$	−23.1025	−	71.1021i	−0.762495	−	2.34672i
$919$	−15.4523	−	47.5572i	−0.509724	−	1.56877i	−0.792682	−	0.609636i	$-0.791316\pi$
$919$	−15.4523	−	47.5572i	−0.509724	−	1.56877i	0.282958	−	0.959132i	$-0.408684\pi$
$920$	11.4566	+	8.32374i	0.377714	+	0.274425i
$921$	42.4175	−	30.8181i	1.39770	−	1.01549i
$922$	−17.1332	+	52.7306i	−0.564252	+	1.73659i
$923$	5.42714			0.178636
$924$	−1.00626	−	1.14823i	−0.0331034	−	0.0377739i
$925$	0.107105			0.00352160
$926$	−1.59894	+	4.92105i	−0.0525446	+	0.161716i
$927$	33.3979	−	24.2650i	1.09693	−	0.796967i
$928$	27.8619	+	20.2429i	0.914612	+	0.664505i
$929$	−6.07033	−	18.6826i	−0.199161	−	0.612955i	−0.999903	−	0.0139451i	$-0.995561\pi$
$929$	−6.07033	−	18.6826i	−0.199161	−	0.612955i	0.800742	−	0.599010i	$-0.204439\pi$
$930$	5.36882	+	16.5235i	0.176050	+	0.541827i
$931$	32.4650	+	23.5872i	1.06400	+	0.773040i
$932$	0.181007	−	0.131509i	0.00592909	−	0.00430773i
$933$	−22.4495	+	69.0923i	−0.734962	+	2.26198i
$934$	−7.08841			−0.231940
$935$	−15.4347	+	6.62485i	−0.504769	+	0.216656i
$936$	13.0686			0.427161
$937$	0.785137	−	2.41640i	0.0256493	−	0.0789405i	−0.937412	−	0.348221i	$-0.886786\pi$
$937$	0.785137	−	2.41640i	0.0256493	−	0.0789405i	0.963062	+	0.269281i	$0.0867859\pi$
$938$	2.41063	−	1.75143i	0.0787099	−	0.0571861i
$939$	44.0217	+	31.9836i	1.43659	+	1.04375i
$940$	−4.45564	−	13.7131i	−0.145327	−	0.447270i
$941$	−0.424996	−	1.30800i	−0.0138545	−	0.0426396i	0.943890	−	0.330259i	$-0.107136\pi$
$941$	−0.424996	−	1.30800i	−0.0138545	−	0.0426396i	−0.957745	+	0.287620i	$0.907136\pi$
$942$	−102.882	−	74.7479i	−3.35206	−	2.43542i
$943$	14.5829	−	10.5951i	0.474886	−	0.345025i
$944$	10.1962	−	31.3808i	0.331859	−	1.02136i
$945$	4.86519			0.158265
$946$	18.3333	−	30.7908i	0.596066	−	1.00110i
$947$	42.8968			1.39396			0.696979	−	0.717092i	$-0.254527\pi$
$947$	42.8968			1.39396			0.696979	+	0.717092i	$0.254527\pi$
$948$	−10.6052	+	32.6394i	−0.344441	+	1.06008i
$949$	3.85926	−	2.80392i	0.125277	−	0.0910191i
$950$	−1.74117	−	1.26503i	−0.0564910	−	0.0410431i
$951$	−4.63637	−	14.2693i	−0.150344	−	0.462713i
$952$	0.135095	+	0.415779i	0.00437845	+	0.0134755i
$953$	7.52652	+	5.46834i	0.243808	+	0.177137i	0.702978	−	0.711212i	$-0.251853\pi$
$953$	7.52652	+	5.46834i	0.243808	+	0.177137i	−0.459170	+	0.888348i	$0.651853\pi$
$954$	17.9295	−	13.0266i	0.580490	−	0.421750i
$955$	12.0152	−	36.9790i	0.388803	−	1.19661i
$956$	8.49956			0.274895
$957$	−66.0216	−	14.9636i	−2.13418	−	0.483703i
$958$	33.1127			1.06982
$959$	0.303832	−	0.935100i	0.00981126	−	0.0301960i
$960$	0.588769	−	0.427766i	0.0190024	−	0.0138061i
$961$	23.6474	+	17.1809i	0.762820	+	0.554221i
$962$	0.275696	+	0.848505i	0.00888880	+	0.0273569i
$963$	11.7978	+	36.3098i	0.380178	+	1.17007i
$964$	−3.97571	−	2.88852i	−0.128049	−	0.0930330i
$965$	8.36409	−	6.07687i	0.269250	−	0.195621i
$966$	0.934215	−	2.87522i	0.0300579	−	0.0925087i
$967$	29.6970			0.954991			0.477496	−	0.878634i	$-0.341545\pi$
$967$	29.6970			0.954991			0.477496	+	0.878634i	$0.341545\pi$
$968$	−16.8038	+	3.10219i	−0.540096	+	0.0997082i
$969$	44.9179			1.44297
$970$	11.2656	−	34.6718i	0.361715	−	1.11324i
$971$	−26.6630	+	19.3718i	−0.855657	+	0.621671i	−0.926700	−	0.375802i	$-0.877367\pi$
$971$	−26.6630	+	19.3718i	−0.855657	+	0.621671i	0.0710427	+	0.997473i	$0.477367\pi$
$972$	−62.1663	−	45.1664i	−1.99398	−	1.44871i
$973$	−0.0961532	−	0.295929i	−0.00308253	−	0.00948705i
$974$	16.2449	+	49.9968i	0.520522	+	1.60200i
$975$	0.579610	+	0.421111i	0.0185624	+	0.0134864i
$976$	−1.40093	+	1.01784i	−0.0448428	+	0.0325802i
$977$	−5.57704	+	17.1644i	−0.178425	+	0.549137i	−0.999773	−	0.0212906i	$-0.993222\pi$
$977$	−5.57704	+	17.1644i	−0.178425	+	0.549137i	0.821348	+	0.570428i	$0.193222\pi$
$978$	−107.123			−3.42541
$979$	16.9186	+	3.83455i	0.540722	+	0.122553i
$980$	−17.1283			−0.547145
$981$	24.5452	−	75.5424i	0.783668	−	2.41188i
$982$	−33.3507	+	24.2307i	−1.06426	+	0.773233i
$983$	8.45127	+	6.14021i	0.269554	+	0.195842i	0.714348	−	0.699790i	$-0.246723\pi$
$983$	8.45127	+	6.14021i	0.269554	+	0.195842i	−0.444795	+	0.895633i	$0.646723\pi$
$984$	7.01658	+	21.5948i	0.223680	+	0.688417i
$985$	6.99240	+	21.5204i	0.222796	+	0.685697i
$986$	−19.9847	−	14.5197i	−0.636443	−	0.462403i
$987$	1.95417	−	1.41978i	0.0622018	−	0.0451922i
$988$	1.98940	−	6.12275i	0.0632913	−	0.194791i
$989$	25.4817			0.810271
$990$	−55.1764	+	92.6691i	−1.75362	+	2.94522i
$991$	34.2296			1.08734			0.543670	−	0.839299i	$-0.317034\pi$
$991$	34.2296			1.08734			0.543670	+	0.839299i	$0.317034\pi$
$992$	−2.34353	+	7.21263i	−0.0744070	+	0.229001i
$993$	−4.52979	+	3.29108i	−0.143748	+	0.104439i
$994$	0.943119	+	0.685216i	0.0299139	+	0.0217337i
$995$	15.6652	+	48.2125i	0.496620	+	1.52844i
$996$	−4.45987	−	13.7261i	−0.141316	−	0.434927i
$997$	−44.5495	−	32.3671i	−1.41090	−	1.02508i	−0.993191	−	0.116494i	$-0.962834\pi$
$997$	−44.5495	−	32.3671i	−1.41090	−	1.02508i	−0.417705	−	0.908583i	$-0.637166\pi$
$998$	−1.25432	+	0.911318i	−0.0397049	+	0.0288473i
$999$	−2.85377	+	8.78299i	−0.0902892	+	0.277882i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.h.c.53.2	yes	28
11.4	even	5		1573.2.a.s.1.4		14
11.5	even	5	inner	143.2.h.c.27.2	✓	28
11.7	odd	10		1573.2.a.r.1.11		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.h.c.27.2	✓	28	11.5	even	5	inner
143.2.h.c.53.2	yes	28	1.1	even	1	trivial
1573.2.a.r.1.11		14	11.7	odd	10
1573.2.a.s.1.4		14	11.4	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.545888 + 1.68007i) q^{2} +(-2.73308 + 1.98570i) q^{3} +(-0.906607 - 0.658689i) q^{4} +(0.676170 + 2.08104i) q^{5} +(-1.84416 - 5.67573i) q^{6} +(-0.0983727 - 0.0714719i) q^{7} +(-1.25676 + 0.913087i) q^{8} +(2.59967 - 8.00096i) q^{9} +O(q^{10})\)	\(q+(-0.545888 + 1.68007i) q^{2} +(-2.73308 + 1.98570i) q^{3} +(-0.906607 - 0.658689i) q^{4} +(0.676170 + 2.08104i) q^{5} +(-1.84416 - 5.67573i) q^{6} +(-0.0983727 - 0.0714719i) q^{7} +(-1.25676 + 0.913087i) q^{8} +(2.59967 - 8.00096i) q^{9} -3.86540 q^{10} +(3.23459 + 0.733108i) q^{11} +3.78579 q^{12} +(0.309017 - 0.951057i) q^{13} +(0.173778 - 0.126257i) q^{14} +(-5.98034 - 4.34497i) q^{15} +(-1.54059 - 4.74144i) q^{16} +(0.715201 + 2.20116i) q^{17} +(12.0230 + 8.73526i) q^{18} +(-4.64768 + 3.37674i) q^{19} +(0.757736 - 2.33207i) q^{20} +0.410782 q^{21} +(-2.99739 + 5.03414i) q^{22} -4.16613 q^{23} +(1.62170 - 4.99108i) q^{24} +(0.171570 - 0.124653i) q^{25} +(1.42915 + 1.03834i) q^{26} +(5.65056 + 17.3906i) q^{27} +(0.0421076 + 0.129594i) q^{28} +(4.88799 + 3.55134i) q^{29} +(10.5644 - 7.67552i) q^{30} +(-0.411140 + 1.26536i) q^{31} +5.70007 q^{32} +(-10.2961 + 4.41927i) q^{33} -4.08853 q^{34} +(0.0822192 - 0.253045i) q^{35} +(-7.62702 + 5.54136i) q^{36} +(0.408587 + 0.296856i) q^{37} +(-3.13604 - 9.65175i) q^{38} +(1.04394 + 3.21293i) q^{39} +(-2.74995 - 1.99796i) q^{40} +(-3.50036 + 2.54316i) q^{41} +(-0.224241 + 0.690142i) q^{42} -6.11640 q^{43} +(-2.44961 - 2.79523i) q^{44} +18.4081 q^{45} +(2.27424 - 6.99938i) q^{46} +(4.75718 - 3.45630i) q^{47} +(13.6256 + 9.89959i) q^{48} +(-2.15855 - 6.64333i) q^{49} +(0.115768 + 0.356296i) q^{50} +(-6.32555 - 4.59578i) q^{51} +(-0.906607 + 0.658689i) q^{52} +(0.460825 - 1.41828i) q^{53} -32.3021 q^{54} +(0.661507 + 7.22701i) q^{55} +0.188891 q^{56} +(5.99729 - 18.4578i) q^{57} +(-8.63479 + 6.27354i) q^{58} +(5.35440 + 3.89020i) q^{59} +(2.55984 + 7.87837i) q^{60} +(-0.107334 - 0.330340i) q^{61} +(-1.90145 - 1.38149i) q^{62} +(-0.827581 + 0.601273i) q^{63} +(-0.0304230 + 0.0936323i) q^{64} +2.18813 q^{65} +(-1.80416 - 19.7106i) q^{66} +13.8719 q^{67} +(0.801475 - 2.46669i) q^{68} +(11.3863 - 8.27267i) q^{69} +(0.380250 + 0.276268i) q^{70} +(1.67708 + 5.16151i) q^{71} +(4.03842 + 12.4290i) q^{72} +(3.85926 + 2.80392i) q^{73} +(-0.721782 + 0.524405i) q^{74} +(-0.221391 + 0.681372i) q^{75} +6.43784 q^{76} +(-0.265798 - 0.303300i) q^{77} -5.96782 q^{78} +(-2.80132 + 8.62158i) q^{79} +(8.82543 - 6.41205i) q^{80} +(-29.5579 - 21.4751i) q^{81} +(-2.36188 - 7.26913i) q^{82} +(-1.17806 - 3.62568i) q^{83} +(-0.372418 - 0.270577i) q^{84} +(-4.09711 + 2.97672i) q^{85} +(3.33887 - 10.2760i) q^{86} -20.4111 q^{87} +(-4.73448 + 2.03212i) q^{88} +5.23054 q^{89} +(-10.0488 + 30.9269i) q^{90} +(-0.0983727 + 0.0714719i) q^{91} +(3.77704 + 2.74418i) q^{92} +(-1.38894 - 4.27472i) q^{93} +(3.20993 + 9.87915i) q^{94} +(-10.1697 - 7.38875i) q^{95} +(-15.5787 + 11.3186i) q^{96} +(-2.91446 + 8.96978i) q^{97} +12.3396 q^{98} +(14.2744 - 23.9740i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9} - 24 q^{10} - 5 q^{11} + 38 q^{12} - 7 q^{13} - 7 q^{14} + 8 q^{15} - 19 q^{16} + 7 q^{17} + 5 q^{18} + 5 q^{19} + 9 q^{20} - 33 q^{22} + 50 q^{23} - 7 q^{24} - 34 q^{25} + 2 q^{26} - 19 q^{27} + 30 q^{28} + 8 q^{29} - 6 q^{30} + 17 q^{31} + 24 q^{32} - 26 q^{33} + 26 q^{34} - 4 q^{35} - 27 q^{36} + 17 q^{37} - 51 q^{38} - 2 q^{39} + 39 q^{40} - 23 q^{41} + 80 q^{42} - 32 q^{43} + q^{44} + 78 q^{45} - 31 q^{46} - 29 q^{47} + 52 q^{48} - 52 q^{49} + 6 q^{50} + 7 q^{51} - 5 q^{52} - 16 q^{53} - 42 q^{54} - 5 q^{55} + 34 q^{56} - 7 q^{57} - 13 q^{58} - 11 q^{59} - 74 q^{60} + 37 q^{61} + 23 q^{62} - 38 q^{63} + 67 q^{64} + 18 q^{65} - 65 q^{66} + 58 q^{67} - 68 q^{68} - 28 q^{69} + 44 q^{70} - 47 q^{71} + 10 q^{72} + 44 q^{73} - 46 q^{74} + 17 q^{75} + 6 q^{76} + 21 q^{77} + 26 q^{78} + 51 q^{79} + 23 q^{80} - 14 q^{81} - 47 q^{82} - 13 q^{83} - 107 q^{84} - q^{85} + 38 q^{86} - 12 q^{87} + 9 q^{88} + 38 q^{89} - 74 q^{90} - 7 q^{91} - 41 q^{92} - 51 q^{93} - 5 q^{94} + 47 q^{95} - 71 q^{96} - 20 q^{97} + 162 q^{98} + 60 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9 - 24 * q^10 - 5 * q^11 + 38 * q^12 - 7 * q^13 - 7 * q^14 + 8 * q^15 - 19 * q^16 + 7 * q^17 + 5 * q^18 + 5 * q^19 + 9 * q^20 - 33 * q^22 + 50 * q^23 - 7 * q^24 - 34 * q^25 + 2 * q^26 - 19 * q^27 + 30 * q^28 + 8 * q^29 - 6 * q^30 + 17 * q^31 + 24 * q^32 - 26 * q^33 + 26 * q^34 - 4 * q^35 - 27 * q^36 + 17 * q^37 - 51 * q^38 - 2 * q^39 + 39 * q^40 - 23 * q^41 + 80 * q^42 - 32 * q^43 + q^44 + 78 * q^45 - 31 * q^46 - 29 * q^47 + 52 * q^48 - 52 * q^49 + 6 * q^50 + 7 * q^51 - 5 * q^52 - 16 * q^53 - 42 * q^54 - 5 * q^55 + 34 * q^56 - 7 * q^57 - 13 * q^58 - 11 * q^59 - 74 * q^60 + 37 * q^61 + 23 * q^62 - 38 * q^63 + 67 * q^64 + 18 * q^65 - 65 * q^66 + 58 * q^67 - 68 * q^68 - 28 * q^69 + 44 * q^70 - 47 * q^71 + 10 * q^72 + 44 * q^73 - 46 * q^74 + 17 * q^75 + 6 * q^76 + 21 * q^77 + 26 * q^78 + 51 * q^79 + 23 * q^80 - 14 * q^81 - 47 * q^82 - 13 * q^83 - 107 * q^84 - q^85 + 38 * q^86 - 12 * q^87 + 9 * q^88 + 38 * q^89 - 74 * q^90 - 7 * q^91 - 41 * q^92 - 51 * q^93 - 5 * q^94 + 47 * q^95 - 71 * q^96 - 20 * q^97 + 162 * q^98 + 60 * q^99

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