LMFDB - Embedded newform 731.2.e.a.681.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(307,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("731.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.e (of order $3$, degree $2$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			681.5
Character	$\chi$	$=$	731.681
Dual form			731.2.e.a.307.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.99188 q^{2} +(0.176804 + 0.306233i) q^{3} +1.96759 q^{4} +(-1.32572 - 2.29622i) q^{5} +(-0.352172 - 0.609981i) q^{6} +(-1.66418 + 2.88245i) q^{7} +0.0645559 q^{8} +(1.43748 - 2.48979i) q^{9} +O(q^{10})$	\(q-1.99188 q^{2} +(0.176804 + 0.306233i) q^{3} +1.96759 q^{4} +(-1.32572 - 2.29622i) q^{5} +(-0.352172 - 0.609981i) q^{6} +(-1.66418 + 2.88245i) q^{7} +0.0645559 q^{8} +(1.43748 - 2.48979i) q^{9} +(2.64068 + 4.57379i) q^{10} +0.00668742 q^{11} +(0.347878 + 0.602542i) q^{12} +(-2.08204 + 3.60620i) q^{13} +(3.31485 - 5.74149i) q^{14} +(0.468785 - 0.811960i) q^{15} -4.06377 q^{16} +(0.500000 - 0.866025i) q^{17} +(-2.86329 + 4.95937i) q^{18} +(-3.12890 - 5.41942i) q^{19} +(-2.60848 - 4.51801i) q^{20} -1.17693 q^{21} -0.0133206 q^{22} +(1.88933 + 3.27241i) q^{23} +(0.0114137 + 0.0197692i) q^{24} +(-1.01507 + 1.75816i) q^{25} +(4.14717 - 7.18311i) q^{26} +2.07743 q^{27} +(-3.27443 + 5.67147i) q^{28} +(-1.53155 + 2.65272i) q^{29} +(-0.933765 + 1.61733i) q^{30} +(3.02095 + 5.23245i) q^{31} +7.96543 q^{32} +(0.00118236 + 0.00204791i) q^{33} +(-0.995941 + 1.72502i) q^{34} +8.82496 q^{35} +(2.82837 - 4.89889i) q^{36} +(3.28166 + 5.68400i) q^{37} +(6.23240 + 10.7948i) q^{38} -1.47245 q^{39} +(-0.0855831 - 0.148234i) q^{40} +2.31983 q^{41} +2.34431 q^{42} +(-0.109324 - 6.55653i) q^{43} +0.0131581 q^{44} -7.62279 q^{45} +(-3.76331 - 6.51825i) q^{46} -8.80832 q^{47} +(-0.718490 - 1.24446i) q^{48} +(-2.03899 - 3.53164i) q^{49} +(2.02190 - 3.50204i) q^{50} +0.353608 q^{51} +(-4.09660 + 7.09552i) q^{52} +(5.34759 + 9.26229i) q^{53} -4.13800 q^{54} +(-0.00886566 - 0.0153558i) q^{55} +(-0.107433 + 0.186079i) q^{56} +(1.10640 - 1.91635i) q^{57} +(3.05067 - 5.28391i) q^{58} +8.15506 q^{59} +(0.922378 - 1.59761i) q^{60} +(-7.67503 + 13.2935i) q^{61} +(-6.01738 - 10.4224i) q^{62} +(4.78445 + 8.28692i) q^{63} -7.73866 q^{64} +11.0408 q^{65} +(-0.00235513 - 0.00407920i) q^{66} +(6.48158 + 11.2264i) q^{67} +(0.983795 - 1.70398i) q^{68} +(-0.668081 + 1.15715i) q^{69} -17.5783 q^{70} +(3.46358 - 5.99909i) q^{71} +(0.0927979 - 0.160731i) q^{72} +(-5.98411 + 10.3648i) q^{73} +(-6.53668 - 11.3219i) q^{74} -0.717875 q^{75} +(-6.15640 - 10.6632i) q^{76} +(-0.0111291 + 0.0192761i) q^{77} +2.93295 q^{78} +(0.616136 - 1.06718i) q^{79} +(5.38742 + 9.33129i) q^{80} +(-3.94514 - 6.83319i) q^{81} -4.62083 q^{82} +(8.22589 + 14.2477i) q^{83} -2.31573 q^{84} -2.65144 q^{85} +(0.217761 + 13.0598i) q^{86} -1.08314 q^{87} +0.000431713 q^{88} +(6.65720 + 11.5306i) q^{89} +15.1837 q^{90} +(-6.92977 - 12.0027i) q^{91} +(3.71742 + 6.43876i) q^{92} +(-1.06823 + 1.85023i) q^{93} +17.5451 q^{94} +(-8.29610 + 14.3693i) q^{95} +(1.40832 + 2.43928i) q^{96} -11.2765 q^{97} +(4.06143 + 7.03461i) q^{98} +(0.00961304 - 0.0166503i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9}+O(q^{10}) $ 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9} + 4 q^{10} + 16 q^{11} + 12 q^{12} + 2 q^{13} - 11 q^{14} + 7 q^{15} + 30 q^{16} + 29 q^{17} + 8 q^{18} + 8 q^{19} - 33 q^{20} - 26 q^{21} - 22 q^{22} - 5 q^{23} + 12 q^{24} - 36 q^{25} - 12 q^{27} + 15 q^{28} + 2 q^{29} + 11 q^{30} + 3 q^{31} - 40 q^{32} + 17 q^{33} - 3 q^{34} + 38 q^{35} - 7 q^{36} + 2 q^{37} + q^{38} - 54 q^{39} + 5 q^{40} + 14 q^{41} - 112 q^{42} + 31 q^{43} - 24 q^{44} - 46 q^{45} - 13 q^{46} - 28 q^{47} - 28 q^{49} - 13 q^{50} + 6 q^{51} + 85 q^{52} - 10 q^{53} + 34 q^{54} + 36 q^{55} - 54 q^{56} - 23 q^{57} + 3 q^{58} + 12 q^{59} + 2 q^{60} - q^{61} - q^{62} - 14 q^{63} + 28 q^{64} + 80 q^{65} - 74 q^{66} + 11 q^{67} + 27 q^{68} - 11 q^{69} + 2 q^{70} + 16 q^{71} + 21 q^{72} + 14 q^{73} + 21 q^{74} - 54 q^{75} + 44 q^{76} + 25 q^{77} + 88 q^{78} - 4 q^{79} - 112 q^{80} + 11 q^{81} - 176 q^{82} - 3 q^{83} + 100 q^{84} - 2 q^{85} + 44 q^{86} + 8 q^{87} - 106 q^{88} + 82 q^{89} + 54 q^{90} - 15 q^{91} + 42 q^{92} + 88 q^{94} + 29 q^{95} + 20 q^{96} + 20 q^{97} + 44 q^{98} - 54 q^{99}+O(q^{100}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9 + 4 * q^10 + 16 * q^11 + 12 * q^12 + 2 * q^13 - 11 * q^14 + 7 * q^15 + 30 * q^16 + 29 * q^17 + 8 * q^18 + 8 * q^19 - 33 * q^20 - 26 * q^21 - 22 * q^22 - 5 * q^23 + 12 * q^24 - 36 * q^25 - 12 * q^27 + 15 * q^28 + 2 * q^29 + 11 * q^30 + 3 * q^31 - 40 * q^32 + 17 * q^33 - 3 * q^34 + 38 * q^35 - 7 * q^36 + 2 * q^37 + q^38 - 54 * q^39 + 5 * q^40 + 14 * q^41 - 112 * q^42 + 31 * q^43 - 24 * q^44 - 46 * q^45 - 13 * q^46 - 28 * q^47 - 28 * q^49 - 13 * q^50 + 6 * q^51 + 85 * q^52 - 10 * q^53 + 34 * q^54 + 36 * q^55 - 54 * q^56 - 23 * q^57 + 3 * q^58 + 12 * q^59 + 2 * q^60 - q^61 - q^62 - 14 * q^63 + 28 * q^64 + 80 * q^65 - 74 * q^66 + 11 * q^67 + 27 * q^68 - 11 * q^69 + 2 * q^70 + 16 * q^71 + 21 * q^72 + 14 * q^73 + 21 * q^74 - 54 * q^75 + 44 * q^76 + 25 * q^77 + 88 * q^78 - 4 * q^79 - 112 * q^80 + 11 * q^81 - 176 * q^82 - 3 * q^83 + 100 * q^84 - 2 * q^85 + 44 * q^86 + 8 * q^87 - 106 * q^88 + 82 * q^89 + 54 * q^90 - 15 * q^91 + 42 * q^92 + 88 * q^94 + 29 * q^95 + 20 * q^96 + 20 * q^97 + 44 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.99188			−1.40847			−0.704236	−	0.709966i	$-0.748710\pi$
$2$	−1.99188			−1.40847			−0.704236	+	0.709966i	$0.748710\pi$
$3$	0.176804	+	0.306233i	0.102078	+	0.176804i	0.912541	−	0.408986i	$-0.134118\pi$
$3$	0.176804	+	0.306233i	0.102078	+	0.176804i	−0.810463	+	0.585790i	$0.800784\pi$
$4$	1.96759			0.983795
$5$	−1.32572	−	2.29622i	−0.592880	−	1.02690i	−0.993842	−	0.110804i	$-0.964657\pi$
$5$	−1.32572	−	2.29622i	−0.592880	−	1.02690i	0.400962	−	0.916095i	$-0.368676\pi$
$6$	−0.352172	−	0.609981i	−0.143774	−	0.249024i
$7$	−1.66418	+	2.88245i	−0.629001	+	1.08946i	0.358751	+	0.933433i	$0.383203\pi$
$7$	−1.66418	+	2.88245i	−0.629001	+	1.08946i	−0.987753	+	0.156029i	$0.950131\pi$
$8$	0.0645559			0.0228240
$9$	1.43748	−	2.48979i	0.479160	−	0.829930i
$10$	2.64068	+	4.57379i	0.835056	+	1.44636i
$11$	0.00668742			0.00201633			0.00100817	−	0.999999i	$-0.499679\pi$
$11$	0.00668742			0.00201633			0.00100817	+	0.999999i	$0.499679\pi$
$12$	0.347878	+	0.602542i	0.100424	+	0.173939i
$13$	−2.08204	+	3.60620i	−0.577454	+	1.00018i	0.418317	+	0.908301i	$0.362620\pi$
$13$	−2.08204	+	3.60620i	−0.577454	+	1.00018i	−0.995770	+	0.0918776i	$0.970713\pi$
$14$	3.31485	−	5.74149i	0.885931	−	1.53448i
$15$	0.468785	−	0.811960i	0.121040	−	0.209647i
$16$	−4.06377			−1.01594
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$18$	−2.86329	+	4.95937i	−0.674884	+	1.16893i
$19$	−3.12890	−	5.41942i	−0.717819	−	1.24330i	−0.961862	−	0.273535i	$-0.911807\pi$
$19$	−3.12890	−	5.41942i	−0.717819	−	1.24330i	0.244043	−	0.969764i	$-0.421526\pi$
$20$	−2.60848	−	4.51801i	−0.583273	−	1.01026i
$21$	−1.17693			−0.256828
$22$	−0.0133206			−0.00283995
$23$	1.88933	+	3.27241i	0.393952	+	0.682345i	0.992967	−	0.118393i	$-0.0377744\pi$
$23$	1.88933	+	3.27241i	0.393952	+	0.682345i	−0.599015	+	0.800738i	$0.704441\pi$
$24$	0.0114137	+	0.0197692i	0.00232982	+	0.00403537i
$25$	−1.01507	+	1.75816i	−0.203014	+	0.351631i
$26$	4.14717	−	7.18311i	0.813327	−	1.40872i
$27$	2.07743			0.399802
$28$	−3.27443	+	5.67147i	−0.618808	+	1.07181i
$29$	−1.53155	+	2.65272i	−0.284402	+	0.492598i	−0.972464	−	0.233053i	$-0.925128\pi$
$29$	−1.53155	+	2.65272i	−0.284402	+	0.492598i	0.688062	+	0.725652i	$0.258462\pi$
$30$	−0.933765	+	1.61733i	−0.170481	+	0.295282i
$31$	3.02095	+	5.23245i	0.542579	+	0.939775i	0.998755	+	0.0498854i	$0.0158856\pi$
$31$	3.02095	+	5.23245i	0.542579	+	0.939775i	−0.456175	+	0.889890i	$0.650781\pi$
$32$	7.96543			1.40810
$33$	0.00118236	+	0.00204791i	0.000205823	+	0.000356496i
$34$	−0.995941	+	1.72502i	−0.170802	+	0.295838i
$35$	8.82496			1.49169
$36$	2.82837	−	4.89889i	0.471396	−	0.816481i
$37$	3.28166	+	5.68400i	0.539502	+	0.934445i	0.998931	+	0.0462301i	$0.0147207\pi$
$37$	3.28166	+	5.68400i	0.539502	+	0.934445i	−0.459429	+	0.888215i	$0.651946\pi$
$38$	6.23240	+	10.7948i	1.01103	+	1.75115i
$39$	−1.47245			−0.235781
$40$	−0.0855831	−	0.148234i	−0.0135319	−	0.0234379i
$41$	2.31983			0.362297			0.181149	−	0.983456i	$-0.442018\pi$
$41$	2.31983			0.362297			0.181149	+	0.983456i	$0.442018\pi$
$42$	2.34431			0.361736
$43$	−0.109324	−	6.55653i	−0.0166718	−	0.999861i
$43$	−0.109324	−	6.55653i	−0.0166718	−	0.999861i
$44$	0.0131581			0.00198366
$45$	−7.62279			−1.13634
$46$	−3.76331	−	6.51825i	−0.554870	−	0.961064i
$47$	−8.80832			−1.28483			−0.642413	−	0.766359i	$-0.722066\pi$
$47$	−8.80832			−1.28483			−0.642413	+	0.766359i	$0.722066\pi$
$48$	−0.718490	−	1.24446i	−0.103705	−	0.179623i
$49$	−2.03899	−	3.53164i	−0.291285	−	0.504520i
$50$	2.02190	−	3.50204i	0.285940	−	0.495263i
$51$	0.353608			0.0495150
$52$	−4.09660	+	7.09552i	−0.568096	+	0.983971i
$53$	5.34759	+	9.26229i	0.734548	+	1.27227i	0.954922	+	0.296858i	$0.0959389\pi$
$53$	5.34759	+	9.26229i	0.734548	+	1.27227i	−0.220374	+	0.975415i	$0.570728\pi$
$54$	−4.13800			−0.563110
$55$	−0.00886566	−	0.0153558i	−0.00119545	−	0.00207057i
$56$	−0.107433	+	0.186079i	−0.0143563	+	0.0248658i
$57$	1.10640	−	1.91635i	0.146547	−	0.253827i
$58$	3.05067	−	5.28391i	0.400572	−	0.693811i
$59$	8.15506			1.06170			0.530849	−	0.847466i	$-0.321873\pi$
$59$	8.15506			1.06170			0.530849	+	0.847466i	$0.321873\pi$
$60$	0.922378	−	1.59761i	0.119078	−	0.206250i
$61$	−7.67503	+	13.2935i	−0.982687	+	1.70206i	−0.330891	+	0.943669i	$0.607349\pi$
$61$	−7.67503	+	13.2935i	−0.982687	+	1.70206i	−0.651796	+	0.758395i	$0.725984\pi$
$62$	−6.01738	−	10.4224i	−0.764208	−	1.32365i
$63$	4.78445	+	8.28692i	0.602785	+	1.04405i
$64$	−7.73866			−0.967332
$65$	11.0408			1.36944
$66$	−0.00235513	−	0.00407920i	−0.000289896	−	0.000502115i
$67$	6.48158	+	11.2264i	0.791852	+	1.37153i	0.924819	+	0.380407i	$0.124216\pi$
$67$	6.48158	+	11.2264i	0.791852	+	1.37153i	−0.132968	+	0.991120i	$0.542451\pi$
$68$	0.983795	−	1.70398i	0.119303	−	0.206638i
$69$	−0.668081	+	1.15715i	−0.0804275	+	0.139304i
$70$	−17.5783			−2.10100
$71$	3.46358	−	5.99909i	0.411051	−	0.711961i	−0.583954	−	0.811787i	$-0.698495\pi$
$71$	3.46358	−	5.99909i	0.411051	−	0.711961i	0.995005	+	0.0998257i	$0.0318285\pi$
$72$	0.0927979	−	0.160731i	0.0109363	−	0.0189423i
$73$	−5.98411	+	10.3648i	−0.700387	+	1.21311i	0.267943	+	0.963435i	$0.413656\pi$
$73$	−5.98411	+	10.3648i	−0.700387	+	1.21311i	−0.968330	+	0.249672i	$0.919677\pi$
$74$	−6.53668	−	11.3219i	−0.759874	−	1.31614i
$75$	−0.717875			−0.0828931
$76$	−6.15640	−	10.6632i	−0.706187	−	1.22315i
$77$	−0.0111291	+	0.0192761i	−0.00126828	+	0.00219672i
$78$	2.93295			0.332091
$79$	0.616136	−	1.06718i	0.0693207	−	0.120067i	−0.829282	−	0.558831i	$-0.811250\pi$
$79$	0.616136	−	1.06718i	0.0693207	−	0.120067i	0.898602	+	0.438764i	$0.144583\pi$
$80$	5.38742	+	9.33129i	0.602332	+	1.04327i
$81$	−3.94514	−	6.83319i	−0.438349	−	0.759243i
$82$	−4.62083			−0.510286
$83$	8.22589	+	14.2477i	0.902909	+	1.56388i	0.823700	+	0.567026i	$0.191906\pi$
$83$	8.22589	+	14.2477i	0.902909	+	1.56388i	0.0792089	+	0.996858i	$0.474761\pi$
$84$	−2.31573			−0.252666
$85$	−2.65144			−0.287589
$86$	0.217761	+	13.0598i	0.0234818	+	1.40828i
$87$	−1.08314			−0.116124
$88$	0.000431713	0		4.60207e−5	0
$89$	6.65720	+	11.5306i	0.705662	+	1.22224i	0.966452	+	0.256846i	$0.0826835\pi$
$89$	6.65720	+	11.5306i	0.705662	+	1.22224i	−0.260791	+	0.965395i	$0.583983\pi$
$90$	15.1837			1.60050
$91$	−6.92977	−	12.0027i	−0.726438	−	1.25823i
$92$	3.71742	+	6.43876i	0.387568	+	0.671287i
$93$	−1.06823	+	1.85023i	−0.110771	+	0.191860i
$94$	17.5451			1.80964
$95$	−8.29610	+	14.3693i	−0.851162	+	1.47426i
$96$	1.40832	+	2.43928i	0.143736	+	0.248958i
$97$	−11.2765			−1.14496			−0.572480	−	0.819919i	$-0.694019\pi$
$97$	−11.2765			−1.14496			−0.572480	+	0.819919i	$0.694019\pi$
$98$	4.06143	+	7.03461i	0.410267	+	0.710603i
$99$	0.00961304	−	0.0166503i	0.000966147	−	0.00167342i
$100$	−1.99725	+	3.45933i	−0.199725	+	0.345933i
$101$	−7.60677	+	13.1753i	−0.756902	+	1.31099i	0.187521	+	0.982261i	$0.439955\pi$
$101$	−7.60677	+	13.1753i	−0.756902	+	1.31099i	−0.944423	+	0.328732i	$0.893379\pi$
$102$	−0.704345			−0.0697405
$103$	9.30993	−	16.1253i	0.917335	−	1.58887i	0.113889	−	0.993494i	$-0.463669\pi$
$103$	9.30993	−	16.1253i	0.917335	−	1.58887i	0.803446	−	0.595377i	$-0.202997\pi$
$104$	−0.134408	+	0.232801i	−0.0131798	+	0.0228280i
$105$	1.56029	+	2.70250i	0.152268	+	0.263737i
$106$	−10.6518	−	18.4494i	−1.03459	−	1.79196i
$107$	10.5911			1.02388			0.511942	−	0.859020i	$-0.328926\pi$
$107$	10.5911			1.02388			0.511942	+	0.859020i	$0.328926\pi$
$108$	4.08754			0.393323
$109$	3.88476	+	6.72860i	0.372093	+	0.644483i	0.989887	−	0.141856i	$-0.0453071\pi$
$109$	3.88476	+	6.72860i	0.372093	+	0.644483i	−0.617795	+	0.786339i	$0.711974\pi$
$110$	0.0176593	+	0.0305869i	0.00168375	+	0.00291634i
$111$	−1.16042	+	2.00991i	−0.110142	+	0.190772i
$112$	6.76284	−	11.7136i	0.639029	−	1.10683i
$113$	3.44779			0.324341			0.162170	−	0.986763i	$-0.448151\pi$
$113$	3.44779			0.324341			0.162170	+	0.986763i	$0.448151\pi$
$114$	−2.20383	+	3.81714i	−0.206407	+	0.357508i
$115$	5.00944	−	8.67660i	0.467133	−	0.809097i
$116$	−3.01346	+	5.21947i	−0.279793	+	0.484616i
$117$	5.98578	+	10.3677i	0.553386	+	0.958492i
$118$	−16.2439			−1.49537
$119$	1.66418	+	2.88245i	0.152555	+	0.264233i
$120$	0.0302629	−	0.0524168i	0.00276261	−	0.00478498i
$121$	−11.0000			−0.999996
$122$	15.2877	−	26.4792i	1.38409	−	2.39731i
$123$	0.410156	+	0.710411i	0.0369825	+	0.0640556i
$124$	5.94400	+	10.2953i	0.533787	+	0.924546i
$125$	−7.87440			−0.704308
$126$	−9.53007	−	16.5066i	−0.849006	−	1.47052i
$127$	−1.31171			−0.116395			−0.0581977	−	0.998305i	$-0.518535\pi$
$127$	−1.31171			−0.116395			−0.0581977	+	0.998305i	$0.518535\pi$
$128$	−0.516379			−0.0456419
$129$	1.98850	−	1.19270i	0.175078	−	0.105011i
$130$	−21.9920			−1.92882
$131$	11.1075			0.970470			0.485235	−	0.874384i	$-0.338734\pi$
$131$	11.1075			0.970470			0.485235	+	0.874384i	$0.338734\pi$
$132$	0.00232641	+	0.00402945i	0.000202488	+	0.000350719i
$133$	20.8282			1.80604
$134$	−12.9105	−	22.3617i	−1.11530	−	1.93176i
$135$	−2.75410	−	4.77023i	−0.237035	−	0.410556i
$136$	0.0322780	−	0.0559071i	0.00276781	−	0.00479399i
$137$	−0.736230			−0.0629004			−0.0314502	−	0.999505i	$-0.510013\pi$
$137$	−0.736230			−0.0629004			−0.0314502	+	0.999505i	$0.510013\pi$
$138$	1.33074	−	2.30490i	0.113280	−	0.196207i
$139$	7.10529	+	12.3067i	0.602663	+	1.04384i	0.992416	+	0.122923i	$0.0392268\pi$
$139$	7.10529	+	12.3067i	0.602663	+	1.04384i	−0.389754	+	0.920919i	$0.627440\pi$
$140$	17.3639			1.46752
$141$	−1.55735	−	2.69740i	−0.131152	−	0.227162i
$142$	−6.89903	+	11.9495i	−0.578954	+	1.00278i
$143$	−0.0139235	+	0.0241162i	−0.00116434	+	0.00201669i
$144$	−5.84159	+	10.1179i	−0.486799	+	0.843161i
$145$	8.12163			0.674465
$146$	11.9196	−	20.6454i	0.986477	−	1.70863i
$147$	0.721004	−	1.24882i	0.0594674	−	0.103001i
$148$	6.45697	+	11.1838i	0.530759	+	0.919302i
$149$	−9.65605	−	16.7248i	−0.791055	−	1.37015i	−0.925314	−	0.379201i	$-0.876199\pi$
$149$	−9.65605	−	16.7248i	−0.791055	−	1.37015i	0.134260	−	0.990946i	$-0.457134\pi$
$150$	1.42992			0.116753
$151$	−11.6543			−0.948411			−0.474205	−	0.880414i	$-0.657265\pi$
$151$	−11.6543			−0.948411			−0.474205	+	0.880414i	$0.657265\pi$
$152$	−0.201989	−	0.349855i	−0.0163835	−	0.0283770i
$153$	−1.43748	−	2.48979i	−0.116213	−	0.201288i
$154$	0.0221678	−	0.0383958i	0.00178633	−	0.00309402i
$155$	8.00989	−	13.8735i	0.643370	−	1.11435i
$156$	−2.89718			−0.231960
$157$	−0.0436360	+	0.0755798i	−0.00348253	+	0.00603192i	−0.867761	−	0.496981i	$-0.834442\pi$
$157$	−0.0436360	+	0.0755798i	−0.00348253	+	0.00603192i	0.864279	+	0.503013i	$0.167775\pi$
$158$	−1.22727	+	2.12569i	−0.0976364	+	0.169111i
$159$	−1.89095	+	3.27522i	−0.149962	+	0.259742i
$160$	−10.5599	−	18.2904i	−0.834837	−	1.44598i
$161$	−12.5767			−0.991184
$162$	7.85826	+	13.6109i	0.617403	+	1.06937i
$163$	6.52415	−	11.3002i	0.511011	−	0.885096i	−0.488908	−	0.872335i	$-0.662605\pi$
$163$	6.52415	−	11.3002i	0.511011	−	0.885096i	0.999919	−	0.0127609i	$-0.00406204\pi$
$164$	4.56448			0.356426
$165$	0.00313497	−	0.00542992i	0.000244057	−	0.000422719i
$166$	−16.3850	−	28.3796i	−1.27172	−	2.20269i
$167$	−3.90018	−	6.75530i	−0.301805	−	0.522741i	0.674740	−	0.738055i	$-0.264256\pi$
$167$	−3.90018	−	6.75530i	−0.301805	−	0.522741i	−0.976545	+	0.215314i	$0.930922\pi$
$168$	−0.0759781			−0.00586184
$169$	−2.16977	−	3.75815i	−0.166905	−	0.289088i
$170$	5.28136			0.405062
$171$	−17.9909			−1.37580
$172$	−0.215106	−	12.9006i	−0.0164017	−	0.983659i
$173$	1.60754			0.122219			0.0611096	−	0.998131i	$-0.480536\pi$
$173$	1.60754			0.122219			0.0611096	+	0.998131i	$0.480536\pi$
$174$	2.15748			0.163558
$175$	−3.37853	−	5.85178i	−0.255393	−	0.442353i
$176$	−0.0271761			−0.00204848
$177$	1.44185	+	2.49735i	0.108376	+	0.187713i
$178$	−13.2603	−	22.9676i	−0.993905	−	1.72149i
$179$	3.70413	−	6.41575i	0.276860	−	0.479536i	−0.693743	−	0.720223i	$-0.744040\pi$
$179$	3.70413	−	6.41575i	0.276860	−	0.479536i	0.970603	+	0.240687i	$0.0773728\pi$
$180$	−14.9985			−1.11792
$181$	7.00808	−	12.1383i	0.520906	−	0.902236i	−0.478798	−	0.877925i	$-0.658927\pi$
$181$	7.00808	−	12.1383i	0.520906	−	0.902236i	0.999704	−	0.0243113i	$-0.00773930\pi$
$182$	13.8033	+	23.9080i	1.02317	+	1.77218i
$183$	−5.42790			−0.401242
$184$	0.121967	+	0.211253i	0.00899154	+	0.0155738i
$185$	8.70114	−	15.0708i	0.639720	−	1.10803i
$186$	2.12779	−	3.68545i	0.156017	−	0.270230i
$187$	0.00334371	−	0.00579148i	0.000244516	−	0.000423515i
$188$	−17.3312			−1.26400
$189$	−3.45722	+	5.98809i	−0.251476	+	0.435569i
$190$	16.5248	−	28.6219i	1.19884	−	2.07645i
$191$	−4.99342	−	8.64886i	−0.361311	−	0.625809i	0.626866	−	0.779127i	$-0.284337\pi$
$191$	−4.99342	−	8.64886i	−0.361311	−	0.625809i	−0.988177	+	0.153318i	$0.951004\pi$
$192$	−1.36823	−	2.36984i	−0.0987431	−	0.171028i
$193$	−17.1980			−1.23794			−0.618971	−	0.785414i	$-0.712450\pi$
$193$	−17.1980			−1.23794			−0.618971	+	0.785414i	$0.712450\pi$
$194$	22.4615			1.61264
$195$	1.95206	+	3.38106i	0.139790	+	0.242123i
$196$	−4.01190	−	6.94882i	−0.286565	−	0.496344i
$197$	−0.436592	+	0.756200i	−0.0311059	+	0.0538770i	−0.881159	−	0.472820i	$-0.843236\pi$
$197$	−0.436592	+	0.756200i	−0.0311059	+	0.0538770i	0.850053	+	0.526697i	$0.176570\pi$
$198$	−0.0191480	+	0.0331654i	−0.00136079	+	0.00235696i
$199$	21.5084			1.52469			0.762344	−	0.647172i	$-0.224049\pi$
$199$	21.5084			1.52469			0.762344	+	0.647172i	$0.224049\pi$
$200$	−0.0655289	+	0.113499i	−0.00463359	+	0.00802562i
$201$	−2.29194	+	3.96976i	−0.161661	+	0.280005i
$202$	15.1518	−	26.2437i	1.06608	−	1.84650i
$203$	−5.09755	−	8.82922i	−0.357778	−	0.619690i
$204$	0.695756			0.0487126
$205$	−3.07545	−	5.32684i	−0.214799	−	0.372043i
$206$	−18.5443	+	32.1196i	−1.29204	+	2.23788i
$207$	10.8635			0.755064
$208$	8.46092	−	14.6547i	0.586659	−	1.01612i
$209$	−0.0209243	−	0.0362419i	−0.00144736	−	0.00250691i
$210$	−3.10791	−	5.38305i	−0.214466	−	0.371466i
$211$	−12.2332			−0.842170			−0.421085	−	0.907021i	$-0.638351\pi$
$211$	−12.2332			−0.842170			−0.421085	+	0.907021i	$0.638351\pi$
$212$	10.5219	+	18.2244i	0.722644	+	1.25166i
$213$	2.44950			0.167837
$214$	−21.0963			−1.44211
$215$	−14.9103	+	8.94316i	−1.01687	+	0.609918i
$216$	0.134111			0.00912507
$217$	−20.1097			−1.36513
$218$	−7.73798	−	13.4026i	−0.524082	−	0.907737i
$219$	−4.23206			−0.285976
$220$	−0.0174440	−	0.0302139i	−0.00117607	−	0.00203702i
$221$	2.08204	+	3.60620i	0.140053	+	0.242579i
$222$	2.31142	−	4.00350i	0.155132	−	0.268697i
$223$	−7.20387			−0.482407			−0.241203	−	0.970475i	$-0.577542\pi$
$223$	−7.20387			−0.482407			−0.241203	+	0.970475i	$0.577542\pi$
$224$	−13.2559	+	22.9599i	−0.885698	+	1.53407i
$225$	2.91829	+	5.05463i	0.194553	+	0.336975i
$226$	−6.86758			−0.456825
$227$	3.03562	+	5.25784i	0.201481	+	0.348975i	0.949006	−	0.315259i	$-0.102091\pi$
$227$	3.03562	+	5.25784i	0.201481	+	0.348975i	−0.747525	+	0.664234i	$0.768758\pi$
$228$	2.17695	−	3.77059i	0.144172	−	0.249713i
$229$	−9.19055	+	15.9185i	−0.607329	+	1.05192i	0.384350	+	0.923187i	$0.374425\pi$
$229$	−9.19055	+	15.9185i	−0.607329	+	1.05192i	−0.991679	+	0.128737i	$0.958908\pi$
$230$	−9.97821	+	17.2828i	−0.657944	+	1.13959i
$231$	−0.00787066			−0.000517852
$232$	−0.0988706	+	0.171249i	−0.00649118	+	0.0112430i
$233$	13.2994	−	23.0352i	0.871271	−	1.50909i	0.0105881	−	0.999944i	$-0.496630\pi$
$233$	13.2994	−	23.0352i	0.871271	−	1.50909i	0.860683	−	0.509142i	$-0.170037\pi$
$234$	−11.9230	−	20.6512i	−0.779428	−	1.35001i
$235$	11.6774	+	20.2258i	0.761748	+	1.31939i
$236$	16.0458			1.04449
$237$	0.435741			0.0283044
$238$	−3.31485	−	5.74149i	−0.214870	−	0.372165i
$239$	−2.72921	−	4.72714i	−0.176538	−	0.305773i	0.764154	−	0.645033i	$-0.223157\pi$
$239$	−2.72921	−	4.72714i	−0.176538	−	0.305773i	−0.940693	+	0.339260i	$0.889823\pi$
$240$	−1.90504	+	3.29962i	−0.122970	+	0.212989i
$241$	−5.77963	+	10.0106i	−0.372299	+	0.644841i	−0.989919	−	0.141636i	$-0.954764\pi$
$241$	−5.77963	+	10.0106i	−0.372299	+	0.644841i	0.617620	+	0.786477i	$0.288097\pi$
$242$	21.9106			1.40847
$243$	4.51118	−	7.81360i	0.289393	−	0.501243i
$244$	−15.1013	+	26.1562i	−0.966763	+	1.67448i
$245$	−5.40627	+	9.36394i	−0.345394	+	0.598240i
$246$	−0.816982	−	1.41505i	−0.0520888	−	0.0902205i
$247$	26.0580			1.65803
$248$	0.195020	+	0.337785i	0.0123838	+	0.0214494i
$249$	−2.90874	+	5.03809i	−0.184334	+	0.319276i
$250$	15.6849			0.991998
$251$	0.331034	−	0.573368i	0.0208947	−	0.0361906i	−0.855389	−	0.517986i	$-0.826682\pi$
$251$	0.331034	−	0.573368i	0.0208947	−	0.0361906i	0.876284	+	0.481796i	$0.160015\pi$
$252$	9.41385	+	16.3053i	0.593017	+	1.02713i
$253$	0.0126347	+	0.0218840i	0.000794338	+	0.00137583i
$254$	2.61277			0.163940
$255$	−0.468785	−	0.811960i	−0.0293565	−	0.0508469i
$256$	16.5059			1.03162
$257$	−31.7274			−1.97910			−0.989550	−	0.144187i	$-0.953943\pi$
$257$	−31.7274			−1.97910			−0.989550	+	0.144187i	$0.953943\pi$
$258$	−3.96085	+	2.37571i	−0.246592	+	0.147905i
$259$	−21.8451			−1.35739
$260$	21.7238			1.34725
$261$	4.40315	+	7.62648i	0.272548	+	0.472067i
$262$	−22.1249			−1.36688
$263$	−2.63483	−	4.56366i	−0.162470	−	0.281407i	0.773284	−	0.634060i	$-0.218613\pi$
$263$	−2.63483	−	4.56366i	−0.162470	−	0.281407i	−0.935754	+	0.352653i	$0.885280\pi$
$264$	7.63285e−5	0	0.000132205i	4.69770e−6	0	8.13665e-6i
$265$	14.1788	−	24.5584i	0.870998	−	1.50861i
$266$	−41.4874			−2.54375
$267$	−2.35404	+	4.07731i	−0.144065	+	0.249528i
$268$	12.7531	+	22.0890i	0.779020	+	1.34930i
$269$	8.70749			0.530905			0.265453	−	0.964124i	$-0.414479\pi$
$269$	8.70749			0.530905			0.265453	+	0.964124i	$0.414479\pi$
$270$	5.48583	+	9.50174i	0.333857	+	0.578257i
$271$	−9.24330	+	16.0099i	−0.561491	+	0.972530i	0.435876	+	0.900007i	$0.356439\pi$
$271$	−9.24330	+	16.0099i	−0.561491	+	0.972530i	−0.997367	+	0.0725236i	$0.976895\pi$
$272$	−2.03188	+	3.51933i	−0.123201	+	0.213391i
$273$	2.45042	−	4.24426i	0.148306	−	0.256874i
$274$	1.46648			0.0885935
$275$	−0.00678822	+	0.0117575i	−0.000409345	+	0.000709006i
$276$	−1.31451	+	2.27680i	−0.0791242	+	0.137047i
$277$	−2.52560	−	4.37447i	−0.151749	−	0.262837i	0.780122	−	0.625628i	$-0.215157\pi$
$277$	−2.52560	−	4.37447i	−0.151749	−	0.262837i	−0.931870	+	0.362791i	$0.881824\pi$
$278$	−14.1529	−	24.5135i	−0.848834	−	1.47022i
$279$	17.3703			1.03993
$280$	0.569703			0.0340463
$281$	5.98415	+	10.3649i	0.356984	+	0.618315i	0.987455	−	0.157898i	$-0.0504716\pi$
$281$	5.98415	+	10.3649i	0.356984	+	0.618315i	−0.630471	+	0.776213i	$0.717138\pi$
$282$	3.10205	+	5.37290i	0.184724	+	0.319952i
$283$	−2.20152	+	3.81314i	−0.130867	+	0.226667i	−0.924011	−	0.382366i	$-0.875109\pi$
$283$	−2.20152	+	3.81314i	−0.130867	+	0.226667i	0.793144	+	0.609034i	$0.208443\pi$
$284$	6.81490	−	11.8038i	0.404390	−	0.700424i
$285$	−5.86713			−0.347539
$286$	0.0277339	−	0.0480365i	0.00163994	−	0.00284046i
$287$	−3.86062	+	6.68679i	−0.227885	+	0.394709i
$288$	11.4502	−	19.8323i	0.674707	−	1.16863i
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$	−16.1773			−0.949966
$291$	−1.99374	−	3.45326i	−0.116875	−	0.202433i
$292$	−11.7743	+	20.3937i	−0.689038	+	1.19345i
$293$	16.6740			0.974103			0.487052	−	0.873373i	$-0.338072\pi$
$293$	16.6740			0.974103			0.487052	+	0.873373i	$0.338072\pi$
$294$	−1.43615	+	2.48749i	−0.0837582	+	0.145074i
$295$	−10.8113	−	18.7258i	−0.629461	−	1.09026i
$296$	0.211851	+	0.366936i	0.0123136	+	0.0213277i
$297$	0.0138927			0.000806135
$298$	19.2337	+	33.3138i	1.11418	+	1.92981i
$299$	−15.7346			−0.909955
$300$	−1.41248			−0.0815498
$301$	19.0808	+	10.5961i	1.09980	+	0.610750i
$302$	23.2139			1.33581
$303$	−5.37963			−0.309052
$304$	12.7151	+	22.0233i	0.729263	+	1.26312i
$305$	40.6998			2.33046
$306$	2.86329	+	4.95937i	0.163683	+	0.283508i
$307$	11.1480	+	19.3089i	0.636249	+	1.10201i	0.986249	+	0.165265i	$0.0528480\pi$
$307$	11.1480	+	19.3089i	0.636249	+	1.10201i	−0.350001	+	0.936749i	$0.613819\pi$
$308$	−0.0218975	+	0.0379275i	−0.00124772	+	0.00216112i
$309$	6.58413			0.374558
$310$	−15.9547	+	27.6344i	−0.906168	+	1.56953i
$311$	−11.1840	−	19.3712i	−0.634186	−	1.09844i	−0.986687	−	0.162631i	$-0.948002\pi$
$311$	−11.1840	−	19.3712i	−0.634186	−	1.09844i	0.352501	−	0.935811i	$-0.385331\pi$
$312$	−0.0950554			−0.00538145
$313$	3.58735	+	6.21348i	0.202769	+	0.351207i	0.949420	−	0.314010i	$-0.101673\pi$
$313$	3.58735	+	6.21348i	0.202769	+	0.351207i	−0.746650	+	0.665217i	$0.768339\pi$
$314$	0.0869177	−	0.150546i	0.00490505	−	0.00849580i
$315$	12.6857	−	21.9723i	0.714758	−	1.23800i
$316$	1.21230	−	2.09977i	0.0681974	−	0.118121i
$317$	12.6773			0.712026			0.356013	−	0.934481i	$-0.384136\pi$
$317$	12.6773			0.712026			0.356013	+	0.934481i	$0.384136\pi$
$318$	3.76655	−	6.52385i	0.211217	−	0.365839i
$319$	−0.0102421	+	0.0177399i	−0.000573449	+	0.000993243i
$320$	10.2593	+	17.7696i	0.573512	+	0.993352i
$321$	1.87256	+	3.24336i	0.104516	+	0.181027i
$322$	25.0513			1.39606
$323$	−6.25780			−0.348194
$324$	−7.76243	−	13.4449i	−0.431246	−	0.746940i
$325$	−4.22684	−	7.32110i	−0.234463	−	0.406101i
$326$	−12.9953	+	22.5086i	−0.719744	+	1.24663i
$327$	−1.37368	+	2.37929i	−0.0759648	+	0.131575i
$328$	0.149759			0.00826906
$329$	14.6586	−	25.3895i	0.808156	−	1.39977i
$330$	−0.00624448	+	0.0108158i	−0.000343747	+	0.000595388i
$331$	4.60379	−	7.97400i	0.253047	−	0.438291i	−0.711316	−	0.702872i	$-0.751901\pi$
$331$	4.60379	−	7.97400i	0.253047	−	0.438291i	0.964363	+	0.264582i	$0.0852339\pi$
$332$	16.1852	+	28.0336i	0.888277	+	1.53854i
$333$	18.8693			1.03403
$334$	7.76869	+	13.4558i	0.425084	+	0.736267i
$335$	17.1855	−	29.7662i	0.938947	−	1.62630i
$336$	4.78279			0.260923
$337$	5.35363	−	9.27276i	0.291631	−	0.505119i	−0.682565	−	0.730825i	$-0.739135\pi$
$337$	5.35363	−	9.27276i	0.291631	−	0.505119i	0.974195	+	0.225706i	$0.0724688\pi$
$338$	4.32192	+	7.48578i	0.235081	+	0.407173i
$339$	0.609582	+	1.05583i	0.0331080	+	0.0573447i
$340$	−5.21695			−0.282929
$341$	0.0202024	+	0.0349916i	0.00109402	+	0.00189490i
$342$	35.8358			1.93778
$343$	−9.72551			−0.525128
$344$	−0.00705754	−	0.423263i	−0.000380517	−	0.0228208i
$345$	3.54275			0.190735
$346$	−3.20203			−0.172142
$347$	6.90457	+	11.9591i	0.370657	+	0.641997i	0.989667	−	0.143387i	$-0.0457992\pi$
$347$	6.90457	+	11.9591i	0.370657	+	0.641997i	−0.619010	+	0.785383i	$0.712466\pi$
$348$	−2.13117			−0.114243
$349$	−2.12945	−	3.68832i	−0.113987	−	0.197431i	0.803387	−	0.595457i	$-0.203029\pi$
$349$	−2.12945	−	3.68832i	−0.113987	−	0.197431i	−0.917374	+	0.398026i	$0.869696\pi$
$350$	6.72962	+	11.6560i	0.359713	+	0.623042i
$351$	−4.32529	+	7.49163i	−0.230867	+	0.399874i
$352$	0.0532682			0.00283921
$353$	−5.36114	+	9.28577i	−0.285345	+	0.494231i	−0.972693	−	0.232097i	$-0.925441\pi$
$353$	−5.36114	+	9.28577i	−0.285345	+	0.494231i	0.687348	+	0.726328i	$0.258775\pi$
$354$	−2.87199	−	4.97443i	−0.152644	−	0.264388i
$355$	−18.3669			−0.974816
$356$	13.0986	+	22.6875i	0.694227	+	1.20244i
$357$	−0.588467	+	1.01926i	−0.0311450	+	0.0539447i
$358$	−7.37820	+	12.7794i	−0.389950	+	0.675413i
$359$	−4.26463	+	7.38655i	−0.225078	+	0.389847i	−0.956343	−	0.292247i	$-0.905597\pi$
$359$	−4.26463	+	7.38655i	−0.225078	+	0.389847i	0.731265	+	0.682094i	$0.238931\pi$
$360$	−0.492096			−0.0259358
$361$	−10.0801	+	17.4592i	−0.530529	+	0.918904i
$362$	−13.9593	+	24.1781i	−0.733682	+	1.27078i
$363$	−1.94484	−	3.36855i	−0.102077	−	0.176803i
$364$	−13.6350	−	23.6164i	−0.714666	−	1.23784i
$365$	31.7331			1.66098
$366$	10.8117			0.565139
$367$	7.26431	+	12.5822i	0.379194	+	0.656783i	0.990945	−	0.134267i	$-0.0428680\pi$
$367$	7.26431	+	12.5822i	0.379194	+	0.656783i	−0.611751	+	0.791050i	$0.709535\pi$
$368$	−7.67779	−	13.2983i	−0.400232	−	0.693223i
$369$	3.33472	−	5.77590i	0.173598	−	0.300681i
$370$	−17.3316	+	30.0193i	−0.901028	+	1.56063i
$371$	−35.5974			−1.84813
$372$	−2.10185	+	3.64050i	−0.108976	+	0.188751i
$373$	−12.8674	+	22.2871i	−0.666251	+	1.15398i	0.312694	+	0.949854i	$0.398769\pi$
$373$	−12.8674	+	22.2871i	−0.666251	+	1.15398i	−0.978945	+	0.204126i	$0.934565\pi$
$374$	−0.00666028	+	0.0115359i	−0.000344395	+	0.000596509i
$375$	−1.39223	−	2.41140i	−0.0718942	−	0.124524i
$376$	−0.568629			−0.0293248
$377$	−6.37749	−	11.0461i	−0.328458	−	0.568905i
$378$	6.88638	−	11.9276i	0.354197	−	0.613487i
$379$	−0.500946			−0.0257319			−0.0128659	−	0.999917i	$-0.504095\pi$
$379$	−0.500946			−0.0257319			−0.0128659	+	0.999917i	$0.504095\pi$
$380$	−16.3233	+	28.2728i	−0.837369	+	1.45037i
$381$	−0.231915	−	0.401689i	−0.0118814	−	0.0205792i
$382$	9.94630	+	17.2275i	0.508897	+	0.881435i
$383$	−29.3294			−1.49866			−0.749332	−	0.662194i	$-0.769625\pi$
$383$	−29.3294			−1.49866			−0.749332	+	0.662194i	$0.769625\pi$
$384$	−0.0912979	−	0.158133i	−0.00465903	−	0.00806967i
$385$	0.0590162			0.00300775
$386$	34.2564			1.74361
$387$	−16.4815	−	9.15269i	−0.837803	−	0.465257i
$388$	−22.1876			−1.12641
$389$	1.55607			0.0788960			0.0394480	−	0.999222i	$-0.487440\pi$
$389$	1.55607			0.0788960			0.0394480	+	0.999222i	$0.487440\pi$
$390$	−3.88827	−	6.73468i	−0.196890	−	0.341024i
$391$	3.77865			0.191095
$392$	−0.131629	−	0.227988i	−0.00664827	−	0.0115151i
$393$	1.96386	+	3.40150i	0.0990634	+	0.171583i
$394$	0.869640	−	1.50626i	0.0438118	−	0.0758843i
$395$	−3.26730			−0.164396
$396$	0.0189145	−	0.0327609i	0.000950491	−	0.00164630i
$397$	19.1356	+	33.1438i	0.960389	+	1.66344i	0.721524	+	0.692389i	$0.243442\pi$
$397$	19.1356	+	33.1438i	0.960389	+	1.66344i	0.238865	+	0.971053i	$0.423225\pi$
$398$	−42.8421			−2.14748
$399$	3.68251	+	6.37830i	0.184356	+	0.319314i
$400$	4.12502	−	7.14474i	0.206251	−	0.357237i
$401$	10.9991	−	19.0510i	0.549269	−	0.951362i	−0.449055	−	0.893504i	$-0.648239\pi$
$401$	10.9991	−	19.0510i	0.549269	−	0.951362i	0.998325	−	0.0578585i	$-0.0184272\pi$
$402$	4.56527	−	7.90728i	0.227695	−	0.394379i
$403$	−25.1590			−1.25326
$404$	−14.9670	+	25.9236i	−0.744637	+	1.28975i
$405$	−10.4603	+	18.1178i	−0.519777	+	0.900281i
$406$	10.1537	+	17.5868i	0.503921	+	0.872816i
$407$	0.0219459	+	0.0380113i	0.00108782	+	0.00188415i
$408$	0.0228275			0.00113013
$409$	−15.3450			−0.758760			−0.379380	−	0.925241i	$-0.623863\pi$
$409$	−15.3450			−0.758760			−0.379380	+	0.925241i	$0.623863\pi$
$410$	6.12594	+	10.6104i	0.302538	+	0.524012i
$411$	−0.130168	−	0.225458i	−0.00642073	−	0.0111210i
$412$	18.3181	−	31.7279i	0.902470	−	1.56312i
$413$	−13.5715	+	23.5065i	−0.667810	+	1.15668i
$414$	−21.6388			−1.06349
$415$	21.8105	−	37.7768i	1.07063	−	1.85439i
$416$	−16.5843	+	28.7249i	−0.813114	+	1.40835i
$417$	−2.51249	+	4.35175i	−0.123037	+	0.213106i
$418$	0.0416787	+	0.0721896i	0.00203857	+	0.00353091i
$419$	−4.08768			−0.199696			−0.0998481	−	0.995003i	$-0.531836\pi$
$419$	−4.08768			−0.199696			−0.0998481	+	0.995003i	$0.531836\pi$
$420$	3.07001	+	5.31741i	0.149801	+	0.259463i
$421$	−9.12941	+	15.8126i	−0.444940	+	0.770659i	−0.998048	−	0.0624504i	$-0.980108\pi$
$421$	−9.12941	+	15.8126i	−0.444940	+	0.770659i	0.553108	+	0.833110i	$0.313442\pi$
$422$	24.3671			1.18617
$423$	−12.6618	+	21.9309i	−0.615637	+	1.06631i
$424$	0.345218	+	0.597936i	0.0167653	+	0.0290383i
$425$	1.01507	+	1.75816i	0.0492382	+	0.0852831i
$426$	−4.87910			−0.236393
$427$	−25.5453	−	44.2457i	−1.23622	−	2.14120i
$428$	20.8390			1.00729
$429$	−0.00984690			−0.000475413
$430$	29.6995	−	17.8137i	1.43224	−	0.859053i
$431$	−21.1380			−1.01818			−0.509091	−	0.860713i	$-0.670018\pi$
$431$	−21.1380			−1.01818			−0.509091	+	0.860713i	$0.670018\pi$
$432$	−8.44221			−0.406176
$433$	−2.91099	−	5.04198i	−0.139893	−	0.242302i	0.787563	−	0.616234i	$-0.211343\pi$
$433$	−2.91099	−	5.04198i	−0.139893	−	0.242302i	−0.927456	+	0.373932i	$0.878009\pi$
$434$	40.0560			1.92275
$435$	1.43594	+	2.48712i	0.0688479	+	0.119248i
$436$	7.64362	+	13.2391i	0.366063	+	0.634040i
$437$	11.8230	−	20.4781i	0.565572	−	0.979600i
$438$	8.42976			0.402789
$439$	7.84210	−	13.5829i	0.374283	−	0.648278i	−0.615936	−	0.787796i	$-0.711222\pi$
$439$	7.84210	−	13.5829i	0.374283	−	0.648278i	0.990219	+	0.139518i	$0.0445555\pi$
$440$	−0.000572331	0	0.000991306i	−2.72848e−5	0	4.72586e-5i
$441$	−11.7241			−0.558288
$442$	−4.14717	−	7.18311i	−0.197261	−	0.341666i
$443$	8.73295	−	15.1259i	0.414915	−	0.718654i	−0.580505	−	0.814257i	$-0.697145\pi$
$443$	8.73295	−	15.1259i	0.414915	−	0.718654i	0.995420	+	0.0956034i	$0.0304781\pi$
$444$	−2.28323	+	3.95468i	−0.108358	+	0.187681i
$445$	17.6512	−	30.5727i	0.836746	−	1.44929i
$446$	14.3493			0.679457
$447$	3.41446	−	5.91401i	0.161498	−	0.279723i
$448$	12.8785	−	22.3063i	0.608453	−	1.05387i
$449$	0.582302	+	1.00858i	0.0274805	+	0.0475977i	0.879439	−	0.476012i	$-0.157918\pi$
$449$	0.582302	+	1.00858i	0.0274805	+	0.0475977i	−0.851958	+	0.523610i	$0.824585\pi$
$450$	−5.81289	−	10.0682i	−0.274022	−	0.474621i
$451$	0.0155137			0.000730512
$452$	6.78383			0.319085
$453$	−2.06052	−	3.56893i	−0.0968117	−	0.167683i
$454$	−6.04658	−	10.4730i	−0.283780	−	0.491522i
$455$	−18.3739	+	31.8245i	−0.861381	+	1.49196i
$456$	0.0714249	−	0.123712i	0.00334478	−	0.00579333i
$457$	−25.6103			−1.19800			−0.598999	−	0.800750i	$-0.704435\pi$
$457$	−25.6103			−1.19800			−0.598999	+	0.800750i	$0.704435\pi$
$458$	18.3065	−	31.7078i	0.855406	−	1.48161i
$459$	1.03872	−	1.79911i	0.0484831	−	0.0839752i
$460$	9.85652	−	17.0720i	0.459563	−	0.795986i
$461$	−7.34579	−	12.7233i	−0.342128	−	0.592582i	0.642700	−	0.766118i	$-0.277814\pi$
$461$	−7.34579	−	12.7233i	−0.342128	−	0.592582i	−0.984828	+	0.173536i	$0.944481\pi$
$462$	0.0156774			0.000729380
$463$	21.4348	+	37.1262i	0.996160	+	1.72540i	0.573900	+	0.818925i	$0.305430\pi$
$463$	21.4348	+	37.1262i	0.996160	+	1.72540i	0.422260	+	0.906475i	$0.361237\pi$
$464$	6.22387	−	10.7801i	0.288936	−	0.500451i
$465$	5.66472			0.262695
$466$	−26.4908	+	45.8834i	−1.22716	+	2.12551i
$467$	−12.4466	−	21.5581i	−0.575959	−	0.997589i	−0.995937	−	0.0900553i	$-0.971296\pi$
$467$	−12.4466	−	21.5581i	−0.575959	−	0.997589i	0.419978	−	0.907534i	$-0.362038\pi$
$468$	11.7776	+	20.3993i	0.544418	+	0.942960i
$469$	−43.1461			−1.99230
$470$	−23.2599	−	40.2874i	−1.07290	−	1.85832i
$471$	−0.0308601			−0.00142196
$472$	0.526458			0.0242322
$473$	−0.000731099	−	0.0438463i	−3.36160e−5	−	0.00201605i
$474$	−0.867945			−0.0398660
$475$	12.7042			0.582911
$476$	3.27443	+	5.67147i	0.150083	+	0.259951i
$477$	30.7482			1.40786
$478$	5.43627	+	9.41590i	0.248649	+	0.430673i
$479$	1.33013	+	2.30385i	0.0607751	+	0.105266i	0.894812	−	0.446443i	$-0.147309\pi$
$479$	1.33013	+	2.30385i	0.0607751	+	0.105266i	−0.834037	+	0.551709i	$0.813976\pi$
$480$	3.73408	−	6.46761i	0.170437	−	0.295205i
$481$	−27.3302			−1.24615
$482$	11.5123	−	19.9400i	0.524373	−	0.908240i
$483$	−2.22361	−	3.85141i	−0.101178	−	0.175245i
$484$	−21.6434			−0.983791
$485$	14.9496	+	25.8934i	0.678824	+	1.17576i
$486$	−8.98574	+	15.5638i	−0.407601	+	0.705986i
$487$	−10.9846	+	19.0258i	−0.497758	+	0.862142i	−0.999997	−	0.00258720i	$-0.999176\pi$
$487$	−10.9846	+	19.0258i	−0.497758	+	0.862142i	0.502239	+	0.864729i	$0.332510\pi$
$488$	−0.495469	+	0.858177i	−0.0224288	+	0.0388478i
$489$	4.61398			0.208651
$490$	10.7687	−	18.6519i	0.486478	−	0.842605i
$491$	7.25913	−	12.5732i	0.327600	−	0.567420i	−0.654435	−	0.756118i	$-0.727093\pi$
$491$	7.25913	−	12.5732i	0.327600	−	0.567420i	0.982035	+	0.188698i	$0.0604268\pi$
$492$	0.807019	+	1.39780i	0.0363832	+	0.0630176i
$493$	1.53155	+	2.65272i	0.0689776	+	0.119473i
$494$	−51.9044			−2.33529
$495$	−0.0509768			−0.00229124
$496$	−12.2765	−	21.2635i	−0.551229	−	0.954757i
$497$	11.5280	+	19.9671i	0.517103	+	0.895648i
$498$	5.79386	−	10.0353i	0.259629	−	0.449691i
$499$	−16.0547	+	27.8075i	−0.718706	+	1.24484i	0.242806	+	0.970075i	$0.421932\pi$
$499$	−16.0547	+	27.8075i	−0.718706	+	1.24484i	−0.961512	+	0.274761i	$0.911401\pi$
$500$	−15.4936			−0.692895
$501$	1.37913	−	2.38873i	0.0616151	−	0.106721i
$502$	−0.659380	+	1.14208i	−0.0294296	+	0.0509735i
$503$	−17.2715	+	29.9152i	−0.770100	+	1.33385i	0.167408	+	0.985888i	$0.446460\pi$
$503$	−17.2715	+	29.9152i	−0.770100	+	1.33385i	−0.937508	+	0.347964i	$0.886873\pi$
$504$	0.308865	+	0.534970i	0.0137579	+	0.0238294i
$505$	40.3378			1.79501
$506$	−0.0251669	−	0.0435903i	−0.00111880	−	0.00193783i
$507$	0.767246	−	1.32891i	0.0340746	−	0.0590190i
$508$	−2.58091			−0.114509
$509$	7.95848	−	13.7845i	0.352754	−	0.610987i	−0.633977	−	0.773352i	$-0.718579\pi$
$509$	7.95848	−	13.7845i	0.352754	−	0.610987i	0.986731	+	0.162365i	$0.0519121\pi$
$510$	0.933765	+	1.61733i	0.0413478	+	0.0716165i
$511$	−19.9173	−	34.4978i	−0.881089	−	1.52609i
$512$	−31.8450			−1.40736
$513$	−6.50008	−	11.2585i	−0.286986	−	0.497074i
$514$	63.1972			2.78751
$515$	−49.3695			−2.17548
$516$	3.91255	−	2.34674i	0.172240	−	0.103310i
$517$	−0.0589050			−0.00259064
$518$	43.5129			1.91185
$519$	0.284220	+	0.492283i	0.0124759	+	0.0216088i
$520$	0.712749			0.0312561
$521$	−13.7033	−	23.7349i	−0.600354	−	1.03984i	−0.992767	−	0.120054i	$-0.961693\pi$
$521$	−13.7033	−	23.7349i	−0.600354	−	1.03984i	0.392414	−	0.919789i	$-0.371640\pi$
$522$	−8.77055	−	15.1910i	−0.383876	−	0.664894i
$523$	8.10661	−	14.0411i	0.354477	−	0.613972i	−0.632551	−	0.774519i	$-0.717992\pi$
$523$	8.10661	−	14.0411i	0.354477	−	0.613972i	0.987028	+	0.160546i	$0.0513255\pi$
$524$	21.8551			0.954743
$525$	1.19467	−	2.06924i	0.0521398	−	0.0903088i
$526$	5.24826	+	9.09026i	0.228835	+	0.396354i
$527$	6.04191			0.263190
$528$	−0.00480485	−	0.00832224i	−0.000209104	−	0.000362179i
$529$	4.36089	−	7.55329i	0.189604	−	0.328404i
$530$	−28.2425	+	48.9175i	−1.22678	+	2.12484i
$531$	11.7227	−	20.3044i	0.508724	−	0.881136i
$532$	40.9814			1.77677
$533$	−4.82998	+	8.36578i	−0.209210	+	0.362362i
$534$	4.68896	−	8.12152i	0.202911	−	0.351453i
$535$	−14.0409	−	24.3196i	−0.607041	−	1.05143i
$536$	0.418425	+	0.724733i	0.0180732	+	0.0313037i
$537$	2.61962			0.113045
$538$	−17.3443			−0.747765
$539$	−0.0136356	−	0.0236176i	−0.000587327	−	0.00101728i
$540$	−5.41893	−	9.38587i	−0.233194	−	0.403903i
$541$	9.27793	−	16.0698i	0.398889	−	0.690896i	−0.594700	−	0.803948i	$-0.702729\pi$
$541$	9.27793	−	16.0698i	0.398889	−	0.690896i	0.993589	+	0.113051i	$0.0360625\pi$
$542$	18.4116	−	31.8898i	0.790844	−	1.36978i
$543$	4.95622			0.212692
$544$	3.98272	−	6.89827i	0.170758	−	0.295761i
$545$	10.3002	−	17.8405i	0.441213	−	0.764203i
$546$	−4.88095	+	8.45406i	−0.208885	+	0.361800i
$547$	9.69457	+	16.7915i	0.414510	+	0.717953i	0.995377	−	0.0960461i	$-0.0306196\pi$
$547$	9.69457	+	16.7915i	0.414510	+	0.717953i	−0.580867	+	0.813999i	$0.697286\pi$
$548$	−1.44860			−0.0618811
$549$	22.0654	+	38.2184i	0.941729	+	1.63112i
$550$	0.0135213	−	0.0234196i	0.000576551	−	0.000998616i
$551$	19.1683			0.816596
$552$	−0.0431286	+	0.0747009i	−0.00183567	+	0.00317948i
$553$	2.05072	+	3.55196i	0.0872056	+	0.151045i
$554$	5.03070	+	8.71343i	0.213734	+	0.370198i
$555$	6.15358			0.261205
$556$	13.9803	+	24.2146i	0.592897	+	1.02693i
$557$	9.57722			0.405800			0.202900	−	0.979199i	$-0.434963\pi$
$557$	9.57722			0.405800			0.202900	+	0.979199i	$0.434963\pi$
$558$	−34.5995			−1.46471
$559$	23.8717	+	13.2567i	1.00967	+	0.560698i
$560$	−35.8626			−1.51547
$561$	0.00236473			9.98388e−5
$562$	−11.9197	−	20.6456i	−0.502803	−	0.870880i
$563$	8.80375			0.371034			0.185517	−	0.982641i	$-0.440604\pi$
$563$	8.80375			0.371034			0.185517	+	0.982641i	$0.440604\pi$
$564$	−3.06422	−	5.30738i	−0.129027	−	0.223481i
$565$	−4.57080	−	7.91686i	−0.192295	−	0.333065i
$566$	4.38516	−	7.59532i	0.184322	−	0.319255i
$567$	26.2617			1.10289
$568$	0.223594	−	0.387277i	0.00938181	−	0.0162498i
$569$	6.81744	+	11.8082i	0.285802	+	0.495024i	0.972803	−	0.231633i	$-0.0744067\pi$
$569$	6.81744	+	11.8082i	0.285802	+	0.495024i	−0.687001	+	0.726656i	$0.741073\pi$
$570$	11.6866			0.489499
$571$	0.674339	+	1.16799i	0.0282202	+	0.0488788i	0.879791	−	0.475361i	$-0.157683\pi$
$571$	0.674339	+	1.16799i	0.0282202	+	0.0488788i	−0.851570	+	0.524240i	$0.824349\pi$
$572$	−0.0273957	+	0.0474507i	−0.00114547	+	0.00198401i
$573$	1.76571	−	3.05830i	0.0737637	−	0.127762i
$574$	7.68990	−	13.3193i	0.320970	−	0.555937i
$575$	−7.67121			−0.319912
$576$	−11.1242	+	19.2676i	−0.463507	+	0.802818i
$577$	−3.71995	+	6.44314i	−0.154863	+	0.268231i	−0.933009	−	0.359852i	$-0.882827\pi$
$577$	−3.71995	+	6.44314i	−0.154863	+	0.268231i	0.778146	+	0.628084i	$0.216160\pi$
$578$	0.995941	+	1.72502i	0.0414257	+	0.0717514i
$579$	−3.04068	−	5.26661i	−0.126366	−	0.218873i
$580$	15.9801			0.663535
$581$	−54.7575			−2.27172
$582$	3.97129	+	6.87847i	0.164615	+	0.285122i
$583$	0.0357616	+	0.0619409i	0.00148109	+	0.00256533i
$584$	−0.386310	+	0.669108i	−0.0159856	+	0.0276879i
$585$	15.8709	−	27.4893i	0.656183	−	1.13654i
$586$	−33.2125			−1.37200
$587$	9.89790	−	17.1437i	0.408530	−	0.707595i	−0.586195	−	0.810170i	$-0.699375\pi$
$587$	9.89790	−	17.1437i	0.408530	−	0.707595i	0.994725	+	0.102575i	$0.0327082\pi$
$588$	1.41864	−	2.45716i	0.0585038	−	0.101331i
$589$	18.9045	−	32.7436i	0.778948	−	1.34918i
$590$	21.5349	+	37.2995i	0.886578	+	1.53560i
$591$	−0.308765			−0.0127009
$592$	−13.3359	−	23.0985i	−0.548103	−	0.949342i
$593$	−10.4456	+	18.0923i	−0.428949	+	0.742961i	−0.996780	−	0.0801840i	$-0.974449\pi$
$593$	−10.4456	+	18.0923i	−0.428949	+	0.742961i	0.567831	+	0.823145i	$0.307783\pi$
$594$	−0.0276726			−0.00113542
$595$	4.41248	−	7.64264i	0.180894	−	0.313318i
$596$	−18.9992	−	32.9075i	−0.778236	−	1.34794i
$597$	3.80276	+	6.58658i	0.155637	+	0.269571i
$598$	31.3415			1.28165
$599$	4.37080	+	7.57044i	0.178586	+	0.309320i	0.941396	−	0.337302i	$-0.109514\pi$
$599$	4.37080	+	7.57044i	0.178586	+	0.309320i	−0.762810	+	0.646622i	$0.776181\pi$
$600$	−0.0463431			−0.00189195
$601$	30.9457			1.26230			0.631151	−	0.775660i	$-0.282583\pi$
$601$	30.9457			1.26230			0.631151	+	0.775660i	$0.282583\pi$
$602$	−38.0066	−	21.1062i	−1.54903	−	0.860225i
$603$	37.2686			1.51770
$604$	−22.9308			−0.933042
$605$	14.5829	+	25.2583i	0.592878	+	1.02689i
$606$	10.7156			0.435291
$607$	19.9436	+	34.5433i	0.809485	+	1.40207i	0.913221	+	0.407465i	$0.133587\pi$
$607$	19.9436	+	34.5433i	0.809485	+	1.40207i	−0.103736	+	0.994605i	$0.533080\pi$
$608$	−24.9231	−	43.1680i	−1.01076	−	1.75069i
$609$	1.80253	−	3.12208i	0.0730424	−	0.126513i
$610$	−81.0691			−3.28239
$611$	18.3393	−	31.7645i	0.741927	−	1.28505i
$612$	−2.82837	−	4.89889i	−0.114330	−	0.198026i
$613$	−26.0425			−1.05185			−0.525924	−	0.850531i	$-0.676280\pi$
$613$	−26.0425			−1.05185			−0.525924	+	0.850531i	$0.676280\pi$
$614$	−22.2054	−	38.4610i	−0.896139	−	1.55216i
$615$	1.08750	−	1.88361i	0.0438524	−	0.0759546i
$616$	−0.000718448		0.00124439i	−2.89471e−5		5.01378e-5i
$617$	8.83739	−	15.3068i	0.355780	−	0.616229i	−0.631471	−	0.775399i	$-0.717549\pi$
$617$	8.83739	−	15.3068i	0.355780	−	0.616229i	0.987251	+	0.159170i	$0.0508819\pi$
$618$	−13.1148			−0.527555
$619$	5.12931	−	8.88423i	0.206164	−	0.357087i	−0.744339	−	0.667802i	$-0.767235\pi$
$619$	5.12931	−	8.88423i	0.206164	−	0.357087i	0.950503	+	0.310715i	$0.100568\pi$
$620$	15.7602	−	27.2974i	0.632944	−	1.09629i
$621$	3.92495	+	6.79821i	0.157503	+	0.272803i
$622$	22.2772	+	38.5852i	0.893234	+	1.54713i
$623$	−44.3151			−1.77545
$624$	5.98370			0.239540
$625$	15.5146	+	26.8721i	0.620585	+	1.07488i
$626$	−7.14558	−	12.3765i	−0.285595	−	0.494665i
$627$	0.00739900	−	0.0128154i	0.000295487	−	0.000511799i
$628$	−0.0858578	+	0.148710i	−0.00342610	+	0.00593418i
$629$	6.56332			0.261697
$630$	−25.2684	+	43.7662i	−1.00672	+	1.74369i
$631$	17.5496	−	30.3967i	0.698637	−	1.21007i	−0.270302	−	0.962776i	$-0.587124\pi$
$631$	17.5496	−	30.3967i	0.698637	−	1.21007i	0.968939	−	0.247299i	$-0.0795431\pi$
$632$	0.0397752	−	0.0688927i	0.00158217	−	0.00274041i
$633$	−2.16288	−	3.74622i	−0.0859669	−	0.148899i
$634$	−25.2516			−1.00287
$635$	1.73896	+	3.01197i	0.0690086	+	0.119526i
$636$	−3.72061	+	6.44429i	−0.147532	+	0.255533i
$637$	16.9810			0.672814
$638$	0.0204011	−	0.0353357i	0.000807687	−	0.00139896i
$639$	−9.95765	−	17.2472i	−0.393918	−	0.682287i
$640$	0.684575	+	1.18572i	0.0270602	+	0.0468696i
$641$	−23.2928			−0.920011			−0.460006	−	0.887916i	$-0.652153\pi$
$641$	−23.2928			−0.920011			−0.460006	+	0.887916i	$0.652153\pi$
$642$	−3.72991	−	6.46039i	−0.147208	−	0.254971i
$643$	−1.52679			−0.0602106			−0.0301053	−	0.999547i	$-0.509584\pi$
$643$	−1.52679			−0.0602106			−0.0301053	+	0.999547i	$0.509584\pi$
$644$	−24.7458			−0.975123
$645$	−5.37489	−	2.98484i	−0.211636	−	0.117528i
$646$	12.4648			0.490421
$647$	22.1842			0.872150			0.436075	−	0.899910i	$-0.356368\pi$
$647$	22.1842			0.872150			0.436075	+	0.899910i	$0.356368\pi$
$648$	−0.254682	−	0.441123i	−0.0100049	−	0.0173289i
$649$	0.0545364			0.00214074
$650$	8.41936	+	14.5828i	0.330234	+	0.571983i
$651$	−3.55547	−	6.15825i	−0.139350	−	0.241361i
$652$	12.8368	−	22.2341i	0.502730	−	0.870753i
$653$	10.9431			0.428235			0.214117	−	0.976808i	$-0.431312\pi$
$653$	10.9431			0.428235			0.214117	+	0.976808i	$0.431312\pi$
$654$	2.73621	−	4.73926i	0.106994	−	0.185320i
$655$	−14.7255	−	25.5053i	−0.575372	−	0.996574i
$656$	−9.42727			−0.368073
$657$	17.2041	+	29.7984i	0.671196	+	1.16254i
$658$	−29.1982	+	50.5729i	−1.13827	+	1.97153i
$659$	11.3970	−	19.7402i	0.443964	−	0.768969i	−0.554015	−	0.832507i	$-0.686905\pi$
$659$	11.3970	−	19.7402i	0.443964	−	0.768969i	0.997979	+	0.0635380i	$0.0202384\pi$
$660$	0.00616833	−	0.0106839i	0.000240102	−	0.000415869i
$661$	−29.0897			−1.13146			−0.565728	−	0.824592i	$-0.691405\pi$
$661$	−29.0897			−1.13146			−0.565728	+	0.824592i	$0.691405\pi$
$662$	−9.17020	+	15.8833i	−0.356410	+	0.617320i
$663$	−0.736225	+	1.27518i	−0.0285926	+	0.0495239i
$664$	0.531030	+	0.919771i	0.0206080	+	0.0356940i
$665$	−27.6124	−	47.8261i	−1.07076	−	1.85462i
$666$	−37.5854			−1.45640
$667$	−11.5744			−0.448162
$668$	−7.67395	−	13.2917i	−0.296914	−	0.514270i
$669$	−1.27367	−	2.20607i	−0.0492430	−	0.0852914i
$670$	−34.2316	+	59.2908i	−1.32248	+	2.29060i
$671$	−0.0513262	+	0.0888995i	−0.00198143	+	0.00343193i
$672$	−9.37479			−0.361641
$673$	0.580683	−	1.00577i	0.0223837	−	0.0387697i	−0.854617	−	0.519260i	$-0.826208\pi$
$673$	0.580683	−	1.00577i	0.0223837	−	0.0387697i	0.877000	+	0.480490i	$0.159541\pi$
$674$	−10.6638	+	18.4702i	−0.410754	+	0.711447i
$675$	−2.10874	+	3.65245i	−0.0811656	+	0.140583i
$676$	−4.26921	−	7.39449i	−0.164200	−	0.284404i
$677$	2.15692			0.0828973			0.0414487	−	0.999141i	$-0.486803\pi$
$677$	2.15692			0.0828973			0.0414487	+	0.999141i	$0.486803\pi$
$678$	−1.21422	−	2.10308i	−0.0466317	−	0.0807684i
$679$	18.7662	−	32.5040i	0.720181	−	1.24739i
$680$	−0.171166			−0.00656393
$681$	−1.07342	+	1.85921i	−0.0411334	+	0.0712452i
$682$	−0.0402408	−	0.0696991i	−0.00154090	−	0.00266892i
$683$	11.5504	+	20.0058i	0.441962	+	0.765500i	0.997835	−	0.0657667i	$-0.0209493\pi$
$683$	11.5504	+	20.0058i	0.441962	+	0.765500i	−0.555873	+	0.831267i	$0.687616\pi$
$684$	−35.3988			−1.35351
$685$	0.976035	+	1.69054i	0.0372924	+	0.0645923i
$686$	19.3721			0.739629
$687$	−6.49970			−0.247979
$688$	0.444269	+	26.6442i	0.0169376	+	1.01580i
$689$	−44.5355			−1.69667
$690$	−7.05675			−0.268646
$691$	−11.0193	−	19.0861i	−0.419196	−	0.726068i	0.576663	−	0.816982i	$-0.304355\pi$
$691$	−11.0193	−	19.0861i	−0.419196	−	0.726068i	−0.995859	+	0.0909139i	$0.971021\pi$
$692$	3.16299			0.120239
$693$	0.0319957	+	0.0554181i	0.00121542	+	0.00210516i
$694$	−13.7531	−	23.8211i	−0.522060	−	0.904235i
$695$	18.8393	−	32.6305i	0.714614	−	1.23775i
$696$	−0.0699229			−0.00265042
$697$	1.15992	−	2.00904i	0.0439350	−	0.0760976i
$698$	4.24161	+	7.34669i	0.160547	+	0.278076i
$699$	9.40553			0.355750
$700$	−6.64756	−	11.5139i	−0.251254	−	0.435185i
$701$	12.6063	−	21.8348i	0.476135	−	0.824690i	−0.523491	−	0.852031i	$-0.675371\pi$
$701$	12.6063	−	21.8348i	0.476135	−	0.824690i	0.999626	+	0.0273412i	$0.00870405\pi$
$702$	8.61547	−	14.9224i	0.325170	−	0.563211i
$703$	20.5360	−	35.5694i	0.774530	−	1.34152i
$704$	−0.0517517			−0.00195046
$705$	−4.12921	+	7.15200i	−0.155515	+	0.269360i
$706$	10.6788	−	18.4961i	0.401900	−	0.696112i
$707$	−25.3181	−	43.8522i	−0.952185	−	1.64923i
$708$	2.83697	+	4.91377i	0.106620	+	0.184671i
$709$	40.4095			1.51761			0.758805	−	0.651318i	$-0.225784\pi$
$709$	40.4095			1.51761			0.758805	+	0.651318i	$0.225784\pi$
$710$	36.5848			1.37300
$711$	−1.77137	−	3.06810i	−0.0664315	−	0.115063i
$712$	0.429762	+	0.744369i	0.0161060	+	0.0278964i
$713$	−11.4151	+	19.7716i	−0.427500	+	0.740452i
$714$	1.17216	−	2.03024i	0.0438669	−	0.0759797i
$715$	0.0738346			0.00276126
$716$	7.28822	−	12.6236i	0.272374	−	0.471765i
$717$	0.965072	−	1.67155i	0.0360413	−	0.0624253i
$718$	8.49463	−	14.7131i	0.317017	−	0.549089i
$719$	10.8147	+	18.7315i	0.403319	+	0.698569i	0.994124	−	0.108245i	$-0.0345232\pi$
$719$	10.8147	+	18.7315i	0.403319	+	0.698569i	−0.590805	+	0.806814i	$0.701190\pi$
$720$	30.9773			1.15445
$721$	30.9868	+	53.6707i	1.15401	+	1.99880i
$722$	20.0783	−	34.7766i	0.747236	−	1.29425i
$723$	−4.08745			−0.152014
$724$	13.7890	−	23.8833i	0.512465	−	0.887616i
$725$	−3.10927	−	5.38541i	−0.115475	−	0.200009i
$726$	3.87388	+	6.70976i	0.143773	+	0.249023i
$727$	−37.2686			−1.38221			−0.691107	−	0.722752i	$-0.742877\pi$
$727$	−37.2686			−1.38221			−0.691107	+	0.722752i	$0.742877\pi$
$728$	−0.447358	−	0.774847i	−0.0165802	−	0.0287177i
$729$	−20.4805			−0.758536
$730$	−63.2085			−2.33945
$731$	−5.73278	−	3.18359i	−0.212035	−	0.117749i
$732$	−10.6799			−0.394740
$733$	32.4334			1.19796			0.598978	−	0.800765i	$-0.295574\pi$
$733$	32.4334			1.19796			0.598978	+	0.800765i	$0.295574\pi$
$734$	−14.4696	−	25.0622i	−0.534084	−	0.925061i
$735$	−3.82340			−0.141028
$736$	15.0493	+	26.0662i	0.554725	+	0.960811i
$737$	0.0433451	+	0.0750759i	0.00159664	+	0.00276546i
$738$	−6.64236	+	11.5049i	−0.244509	+	0.423501i
$739$	−6.69593			−0.246314			−0.123157	−	0.992387i	$-0.539302\pi$
$739$	−6.69593			−0.246314			−0.123157	+	0.992387i	$0.539302\pi$
$740$	17.1203	−	29.6532i	0.629354	−	1.09007i
$741$	4.60715	+	7.97982i	0.169248	+	0.293146i
$742$	70.9058			2.60303
$743$	6.93918	+	12.0190i	0.254574	+	0.440935i	0.964780	−	0.263059i	$-0.0847315\pi$
$743$	6.93918	+	12.0190i	0.254574	+	0.440935i	−0.710206	+	0.703994i	$0.751398\pi$
$744$	−0.0689608	+	0.119444i	−0.00252822	+	0.00437901i
$745$	−25.6025	+	44.3448i	−0.938002	+	1.62467i
$746$	25.6304	−	44.3932i	0.938396	−	1.62535i
$747$	47.2982			1.73055
$748$	0.00657906	−	0.0113953i	0.000240554	−	0.000416652i
$749$	−17.6256	+	30.5284i	−0.644025	+	1.11548i
$750$	2.77315	+	4.80323i	0.101261	+	0.175389i
$751$	11.6042	+	20.0991i	0.423444	+	0.733427i	0.996274	−	0.0862478i	$-0.0274877\pi$
$751$	11.6042	+	20.0991i	0.423444	+	0.733427i	−0.572830	+	0.819674i	$0.694154\pi$
$752$	35.7950			1.30531
$753$	0.234112			0.00853153
$754$	12.7032	+	22.0026i	0.462624	+	0.801288i
$755$	15.4503	+	26.7607i	0.562294	+	0.973922i
$756$	−6.80240	+	11.7821i	−0.247401	+	0.428511i
$757$	−15.2056	+	26.3368i	−0.552656	+	0.957228i	0.445426	+	0.895319i	$0.353052\pi$
$757$	−15.2056	+	26.3368i	−0.552656	+	0.957228i	−0.998082	+	0.0619094i	$0.980281\pi$
$758$	0.997826			0.0362427
$759$	−0.00446774	+	0.00773835i	−0.000162169	+	0.000280884i
$760$	−0.535562	+	0.927621i	−0.0194269	+	0.0336484i
$761$	−18.8220	+	32.6007i	−0.682297	+	1.18177i	0.291981	+	0.956424i	$0.405686\pi$
$761$	−18.8220	+	32.6007i	−0.682297	+	1.18177i	−0.974278	+	0.225349i	$0.927648\pi$
$762$	0.461948	+	0.800117i	0.0167346	+	0.0289852i
$763$	−25.8598			−0.936187
$764$	−9.82501	−	17.0174i	−0.355456	−	0.615668i
$765$	−3.81140	+	6.60153i	−0.137801	+	0.238679i
$766$	58.4208			2.11083
$767$	−16.9792	+	29.4088i	−0.613082	+	1.06189i
$768$	2.91830	+	5.05465i	0.105305	+	0.182394i
$769$	−21.7786	−	37.7216i	−0.785355	−	1.36027i	−0.928787	−	0.370614i	$-0.879147\pi$
$769$	−21.7786	−	37.7216i	−0.785355	−	1.36027i	0.143432	−	0.989660i	$-0.454186\pi$
$770$	−0.117553			−0.00423633
$771$	−5.60953	−	9.71599i	−0.202022	−	0.349913i
$772$	−33.8387			−1.21788
$773$	47.5681			1.71091			0.855454	−	0.517879i	$-0.173278\pi$
$773$	47.5681			1.71091			0.855454	+	0.517879i	$0.173278\pi$
$774$	32.8292	+	18.2311i	1.18002	+	0.655302i
$775$	−12.2659			−0.440606
$776$	−0.727968			−0.0261325
$777$	−3.86230	−	6.68970i	−0.138559	−	0.239992i
$778$	−3.09951			−0.111123
$779$	−7.25853	−	12.5721i	−0.260064	−	0.450444i
$780$	3.84085	+	6.65255i	0.137525	+	0.238199i
$781$	0.0231624	−	0.0401185i	0.000828816	−	0.00143555i
$782$	−7.52663			−0.269152
$783$	−3.18169	+	5.51085i	−0.113704	+	0.196942i
$784$	8.28600	+	14.3518i	0.295928	+	0.512563i
$785$	0.231397			0.00825890
$786$	−3.91177	−	6.77538i	−0.139528	−	0.241670i
$787$	17.3706	−	30.0867i	0.619195	−	1.07248i	−0.370438	−	0.928857i	$-0.620792\pi$
$787$	17.3706	−	30.0867i	0.619195	−	1.07248i	0.989633	−	0.143620i	$-0.0458742\pi$
$788$	−0.859035	+	1.48789i	−0.0306019	+	0.0530040i
$789$	0.931696	−	1.61375i	0.0331693	−	0.0574508i
$790$	6.50807			0.231547
$791$	−5.73774	+	9.93806i	−0.204011	+	0.353357i
$792$	0.000620579	−	0.00107487i	2.20513e−5	−	3.81940e-5i
$793$	−31.9594	−	55.3553i	−1.13491	−	1.96573i
$794$	−38.1159	−	66.0186i	−1.35268	−	2.34291i
$795$	10.0275			0.355638
$796$	42.3197			1.49998
$797$	−6.76645	−	11.7198i	−0.239680	−	0.415138i	0.720942	−	0.692995i	$-0.243709\pi$
$797$	−6.76645	−	11.7198i	−0.239680	−	0.415138i	−0.960622	+	0.277857i	$0.910376\pi$
$798$	−7.33513	−	12.7048i	−0.259661	−	0.449746i
$799$	−4.40416	+	7.62823i	−0.155808	+	0.269867i
$800$	−8.08549	+	14.0045i	−0.285865	+	0.495133i
$801$	38.2784			1.35250
$802$	−21.9089	+	37.9474i	−0.773631	+	1.33997i
$803$	−0.0400183	+	0.0693137i	−0.00141222	+	0.00244603i
$804$	−4.50960	+	7.81085i	−0.159041	+	0.275468i
$805$	16.6732	+	28.8789i	0.587654	+	1.01785i
$806$	50.1137			1.76518
$807$	1.53952	+	2.66652i	0.0541936	+	0.0938661i
$808$	−0.491062	+	0.850545i	−0.0172755	+	0.0299221i
$809$	−25.7077			−0.903836			−0.451918	−	0.892060i	$-0.649260\pi$
$809$	−25.7077			−0.903836			−0.451918	+	0.892060i	$0.649260\pi$
$810$	20.8357	−	36.0885i	0.732092	−	1.26802i
$811$	26.1741	+	45.3349i	0.919097	+	1.59192i	0.800789	+	0.598947i	$0.204414\pi$
$811$	26.1741	+	45.3349i	0.919097	+	1.59192i	0.118309	+	0.992977i	$0.462253\pi$
$812$	−10.0299	−	17.3723i	−0.351980	−	0.609648i
$813$	−6.53701			−0.229263
$814$	−0.0437135	−	0.0757141i	−0.00153216	−	0.00265378i
$815$	−34.5968			−1.21187
$816$	−1.43698			−0.0503044
$817$	−35.1905	+	21.1072i	−1.23116	+	0.738448i
$818$	30.5654			1.06869
$819$	−39.8457			−1.39232
$820$	−6.05123	−	10.4810i	−0.211318	−	0.366014i
$821$	−18.1817			−0.634546			−0.317273	−	0.948334i	$-0.602767\pi$
$821$	−18.1817			−0.634546			−0.317273	+	0.948334i	$0.602767\pi$
$822$	0.259280	+	0.449086i	0.00904343	+	0.0156637i
$823$	−21.1627	−	36.6549i	−0.737685	−	1.27771i	−0.953535	−	0.301282i	$-0.902586\pi$
$823$	−21.1627	−	36.6549i	−0.737685	−	1.27771i	0.215850	−	0.976427i	$-0.430748\pi$
$824$	0.601011	−	1.04098i	0.0209372	−	0.0362643i
$825$	−0.00480073			−0.000167140
$826$	27.0328	−	46.8222i	0.940592	−	1.62915i
$827$	0.655787	+	1.13586i	0.0228040	+	0.0394976i	0.877202	−	0.480121i	$-0.159407\pi$
$827$	0.655787	+	1.13586i	0.0228040	+	0.0394976i	−0.854398	+	0.519619i	$0.826074\pi$
$828$	21.3749			0.742828
$829$	−4.48306	−	7.76488i	−0.155703	−	0.269686i	0.777612	−	0.628745i	$-0.216431\pi$
$829$	−4.48306	−	7.76488i	−0.155703	−	0.269686i	−0.933315	+	0.359059i	$0.883098\pi$
$830$	−43.4439	+	75.2470i	−1.50796	+	2.61186i
$831$	0.893073	−	1.54685i	0.0309804	−	0.0536596i
$832$	16.1122	−	27.9071i	0.558589	−	0.967505i
$833$	−4.07799			−0.141294
$834$	5.00457	−	8.66817i	0.173294	−	0.300154i
$835$	−10.3411	+	17.9113i	−0.357868	+	0.619846i
$836$	−0.0411704	−	0.0713093i	−0.00142391	−	0.00246628i
$837$	6.27583	+	10.8701i	0.216924	+	0.375724i
$838$	8.14217			0.281267
$839$	34.4032			1.18773			0.593865	−	0.804565i	$-0.297601\pi$
$839$	34.4032			1.18773			0.593865	+	0.804565i	$0.297601\pi$
$840$	0.100726	+	0.174462i	0.00347537	+	0.00601951i
$841$	9.80871	+	16.9892i	0.338231	+	0.585834i
$842$	18.1847	−	31.4968i	0.626686	−	1.08545i
$843$	−2.11604	+	3.66509i	−0.0728804	+	0.126233i
$844$	−24.0700			−0.828523
$845$	−5.75301	+	9.96450i	−0.197910	+	0.342789i
$846$	25.2208	−	43.6837i	0.867108	−	1.50188i
$847$	18.3059	−	31.7068i	0.628999	−	1.08946i
$848$	−21.7314	−	37.6398i	−0.746258	−	1.29256i
$849$	−1.55695			−0.0534343
$850$	−2.02190	−	3.50204i	−0.0693507	−	0.120119i
$851$	−12.4003	+	21.4779i	−0.425075	+	0.736252i
$852$	4.81960			0.165117
$853$	2.09289	−	3.62500i	0.0716593	−	0.124118i	−0.827969	−	0.560773i	$-0.810504\pi$
$853$	2.09289	−	3.62500i	0.0716593	−	0.124118i	0.899629	+	0.436656i	$0.143837\pi$
$854$	50.8831	+	88.1322i	1.74119	+	3.01582i
$855$	23.8510	+	41.3111i	0.815686	+	1.41281i
$856$	0.683721			0.0233691
$857$	27.5975	+	47.8003i	0.942712	+	1.63283i	0.760268	+	0.649610i	$0.225068\pi$
$857$	27.5975	+	47.8003i	0.942712	+	1.63283i	0.182445	+	0.983216i	$0.441599\pi$
$858$	0.0196139			0.000669606
$859$	2.64797			0.0903475			0.0451737	−	0.998979i	$-0.485616\pi$
$859$	2.64797			0.0903475			0.0451737	+	0.998979i	$0.485616\pi$
$860$	−29.3373	+	17.5965i	−1.00039	+	0.600035i
$861$	−2.73029			−0.0930481
$862$	42.1044			1.43408
$863$	−22.1741	−	38.4067i	−0.754816	−	1.30738i	−0.945466	−	0.325721i	$-0.894393\pi$
$863$	−22.1741	−	38.4067i	−0.754816	−	1.30738i	0.190650	−	0.981658i	$-0.438940\pi$
$864$	16.5477			0.562962
$865$	−2.13115	−	3.69127i	−0.0724614	−	0.125507i
$866$	5.79835	+	10.0430i	0.197036	+	0.341276i
$867$	0.176804	−	0.306233i	0.00600458	−	0.0104002i
$868$	−39.5676			−1.34301
$869$	0.00412036	−	0.00713668i	0.000139774	−	0.000242095i
$870$	−2.86022	−	4.95404i	−0.0969704	−	0.167958i
$871$	−53.9796			−1.82903
$872$	0.250784	+	0.434371i	0.00849263	+	0.0147097i
$873$	−16.2098	+	28.0762i	−0.548619	+	0.950236i
$874$	−23.5501	+	40.7899i	−0.796593	+	1.37974i
$875$	13.1044	−	22.6975i	0.443010	−	0.767316i
$876$	−8.32696			−0.281342
$877$	3.68854	−	6.38873i	0.124553	−	0.215732i	−0.797005	−	0.603973i	$-0.793584\pi$
$877$	3.68854	−	6.38873i	0.124553	−	0.215732i	0.921558	+	0.388240i	$0.126917\pi$
$878$	−15.6205	+	27.0556i	−0.527168	+	0.913081i
$879$	2.94802	+	5.10612i	0.0994343	+	0.172225i
$880$	0.0360280	+	0.0624023i	0.00121450	+	0.00210358i
$881$	−31.7263			−1.06889			−0.534443	−	0.845204i	$-0.679479\pi$
$881$	−31.7263			−1.06889			−0.534443	+	0.845204i	$0.679479\pi$
$882$	23.3529			0.786334
$883$	−1.99619	−	3.45750i	−0.0671772	−	0.116354i	0.830481	−	0.557048i	$-0.188066\pi$
$883$	−1.99619	−	3.45750i	−0.0671772	−	0.116354i	−0.897658	+	0.440693i	$0.854733\pi$
$884$	4.09660	+	7.09552i	0.137784	+	0.238648i
$885$	3.82298	−	6.62159i	0.128508	−	0.222582i
$886$	−17.3950	+	30.1290i	−0.584396	+	1.01220i
$887$	26.3246			0.883894			0.441947	−	0.897041i	$-0.354288\pi$
$887$	26.3246			0.883894			0.441947	+	0.897041i	$0.354288\pi$
$888$	−0.0749121	+	0.129751i	−0.00251388	+	0.00435418i
$889$	2.18292	−	3.78093i	0.0732128	−	0.126808i
$890$	−35.1590	+	60.8973i	−1.17853	+	2.04128i
$891$	−0.0263828	−	0.0456964i	−0.000883859	−	0.00153089i
$892$	−14.1743			−0.474589
$893$	27.5604	+	47.7359i	0.922272	+	1.59742i
$894$	−6.80119	+	11.7800i	−0.227466	+	0.393982i
$895$	−19.6426			−0.656580
$896$	0.859349	−	1.48844i	0.0287088	−	0.0497251i
$897$	−2.78194	−	4.81846i	−0.0928862	−	0.160884i
$898$	−1.15988	−	2.00896i	−0.0387056	−	0.0670400i
$899$	−18.5070			−0.617242
$900$	5.74201	+	9.94545i	0.191400	+	0.331515i
$901$	10.6952			0.356308
$902$	−0.0309015			−0.00102891
$903$	0.128668	+	7.71660i	0.00428179	+	0.256793i
$904$	0.222575			0.00740274
$905$	−37.1630			−1.23534
$906$	4.10431	+	7.10888i	0.136357	+	0.236177i
$907$	−2.53931			−0.0843165			−0.0421582	−	0.999111i	$-0.513423\pi$
$907$	−2.53931			−0.0843165			−0.0421582	+	0.999111i	$0.513423\pi$
$908$	5.97285	+	10.3453i	0.198216	+	0.343320i
$909$	21.8692	+	37.8785i	0.725355	+	1.25635i
$910$	36.5986	−	63.3907i	1.21323	−	2.10138i
$911$	12.5707			0.416487			0.208244	−	0.978077i	$-0.433225\pi$
$911$	12.5707			0.416487			0.208244	+	0.978077i	$0.433225\pi$
$912$	−4.49617	+	7.78760i	−0.148883	+	0.257873i
$913$	0.0550100	+	0.0952802i	0.00182057	+	0.00315331i
$914$	51.0126			1.68735
$915$	7.19588	+	12.4636i	0.237889	+	0.412035i
$916$	−18.0832	+	31.3211i	−0.597487	+	1.03488i
$917$	−18.4849	+	32.0169i	−0.610426	+	1.05729i
$918$	−2.06900	+	3.58361i	−0.0682872	+	0.118277i
$919$	20.5551			0.678051			0.339025	−	0.940777i	$-0.389903\pi$
$919$	20.5551			0.678051			0.339025	+	0.940777i	$0.389903\pi$
$920$	0.323389	−	0.560126i	0.0106618	−	0.0184668i
$921$	−3.94201	+	6.82777i	−0.129894	+	0.224983i
$922$	14.6319	+	25.3433i	0.481877	+	0.834636i
$923$	14.4226	+	24.9807i	0.474726	+	0.822249i
$924$	−0.0154862			−0.000509460
$925$	−13.3245			−0.438107
$926$	−42.6956	−	73.9509i	−1.40306	−	2.43018i
$927$	−26.7657	−	46.3596i	−0.879101	−	1.52265i
$928$	−12.1995	+	21.1301i	−0.400467	+	0.693629i
$929$	−20.7428	+	35.9277i	−0.680551	+	1.17875i	0.294263	+	0.955725i	$0.404926\pi$
$929$	−20.7428	+	35.9277i	−0.680551	+	1.17875i	−0.974813	+	0.223023i	$0.928407\pi$
$930$	−11.2834			−0.369999
$931$	−12.7596	+	22.1003i	−0.418180	+	0.724308i
$932$	26.1677	−	45.3238i	0.857152	−	1.48463i
$933$	3.95475	−	6.84982i	0.129473	−	0.224253i
$934$	24.7921	+	42.9412i	0.811222	+	1.40508i
$935$	−0.0177313			−0.000579876
$936$	0.386417	+	0.669295i	0.0126304	+	0.0218766i
$937$	−5.87739	+	10.1799i	−0.192006	+	0.332564i	−0.945915	−	0.324415i	$-0.894833\pi$
$937$	−5.87739	+	10.1799i	−0.192006	+	0.332564i	0.753909	+	0.656979i	$0.228166\pi$
$938$	85.9419			2.80610
$939$	−1.26852	+	2.19714i	−0.0413965	+	0.0717008i
$940$	22.9763	+	39.7961i	0.749404	+	1.29801i
$941$	−1.84988	−	3.20409i	−0.0603044	−	0.104450i	0.834297	−	0.551315i	$-0.185874\pi$
$941$	−1.84988	−	3.20409i	−0.0603044	−	0.104450i	−0.894601	+	0.446865i	$0.852540\pi$
$942$	0.0614696			0.00200279
$943$	4.38292	+	7.59145i	0.142728	+	0.247212i
$944$	−33.1403			−1.07862
$945$	18.3333			0.596381
$946$	0.00145626	+	0.0873366i	4.73472e−5	+	0.00283956i
$947$	−31.0057			−1.00755			−0.503774	−	0.863835i	$-0.668056\pi$
$947$	−31.0057			−1.00755			−0.503774	+	0.863835i	$0.668056\pi$
$948$	0.857360			0.0278458
$949$	−24.9183	−	43.1598i	−0.808882	−	1.40103i
$950$	−25.3053			−0.821014
$951$	2.24139	+	3.88220i	0.0726820	+	0.125889i
$952$	0.107433	+	0.186079i	0.00348191	+	0.00603085i
$953$	−2.40505	+	4.16567i	−0.0779072	+	0.134939i	−0.902347	−	0.431011i	$-0.858157\pi$
$953$	−2.40505	+	4.16567i	−0.0779072	+	0.134939i	0.824440	+	0.565950i	$0.191490\pi$
$954$	−61.2468			−1.98294
$955$	−13.2398	+	22.9319i	−0.428429	+	0.742060i
$956$	−5.36998	−	9.30107i	−0.173677	−	0.300818i
$957$	−0.00724339			−0.000234146
$958$	−2.64946	−	4.58899i	−0.0856001	−	0.148264i
$959$	1.22522	−	2.12214i	0.0395644	−	0.0685276i
$960$	−3.62777	+	6.28348i	−0.117086	+	0.202798i
$961$	−2.75233	+	4.76718i	−0.0887850	+	0.153780i
$962$	54.4385			1.75517
$963$	15.2246	−	26.3697i	0.490605	−	0.849752i
$964$	−11.3720	+	19.6968i	−0.366266	+	0.634391i
$965$	22.7998	+	39.4904i	0.733951	+	1.27124i
$966$	4.42917	+	7.67156i	0.142506	+	0.246828i
$967$	58.8299			1.89184			0.945922	−	0.324395i	$-0.105161\pi$
$967$	58.8299			1.89184			0.945922	+	0.324395i	$0.105161\pi$
$968$	−0.710112			−0.0228239
$969$	−1.10640	−	1.91635i	−0.0355428	−	0.0615620i
$970$	−29.7777	−	51.5766i	−0.956105	−	1.65602i
$971$	−27.8723	+	48.2763i	−0.894465	+	1.54926i	−0.0600001	+	0.998198i	$0.519110\pi$
$971$	−27.8723	+	48.2763i	−0.894465	+	1.54926i	−0.834465	+	0.551061i	$0.814223\pi$
$972$	8.87616	−	15.3740i	0.284703	−	0.493120i
$973$	−47.2979			−1.51630
$974$	21.8799	−	37.8972i	0.701078	−	1.21430i
$975$	1.49464	−	2.58880i	0.0478669	−	0.0829079i
$976$	31.1895	−	54.0219i	0.998353	−	1.72920i
$977$	−4.76012	−	8.24476i	−0.152290	−	0.263773i	0.779779	−	0.626055i	$-0.215331\pi$
$977$	−4.76012	−	8.24476i	−0.152290	−	0.263773i	−0.932069	+	0.362281i	$0.881998\pi$
$978$	−9.19050			−0.293880
$979$	0.0445195	+	0.0771101i	0.00142285	+	0.00246445i
$980$	−10.6373	+	18.4244i	−0.339797	+	0.588546i
$981$	22.3371			0.713168
$982$	−14.4593	+	25.0443i	−0.461416	+	0.799196i
$983$	−4.96622	−	8.60174i	−0.158398	−	0.274353i	0.775893	−	0.630864i	$-0.217299\pi$
$983$	−4.96622	−	8.60174i	−0.158398	−	0.274353i	−0.934291	+	0.356511i	$0.883966\pi$
$984$	0.0264780	+	0.0458612i	0.000844087	+	0.00146200i
$985$	2.31520			0.0737684
$986$	−3.05067	−	5.28391i	−0.0971530	−	0.168274i
$987$	10.3668			0.329979
$988$	51.2714			1.63116
$989$	21.2491	−	12.7452i	0.675682	−	0.405273i
$990$	0.101540			0.00322715
$991$	−19.4808			−0.618829			−0.309414	−	0.950927i	$-0.600133\pi$
$991$	−19.4808			−0.618829			−0.309414	+	0.950927i	$0.600133\pi$
$992$	24.0632	+	41.6787i	0.764008	+	1.32330i
$993$	3.25587			0.103322
$994$	−22.9625	−	39.7722i	−0.728325	−	1.26150i
$995$	−28.5141	−	49.3879i	−0.903958	−	1.56570i
$996$	−5.72321	+	9.91289i	−0.181347	+	0.314102i
$997$	16.8892			0.534887			0.267444	−	0.963574i	$-0.413821\pi$
$997$	16.8892			0.534887			0.267444	+	0.963574i	$0.413821\pi$
$998$	31.9790	−	55.3893i	1.01228	−	1.75332i
$999$	6.81743	+	11.8081i	0.215694	+	0.373593i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.e.a.681.5	yes	58
43.6	even	3	inner	731.2.e.a.307.5	✓	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.e.a.307.5	✓	58	43.6	even	3	inner
731.2.e.a.681.5	yes	58	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.99188 q^{2} +(0.176804 + 0.306233i) q^{3} +1.96759 q^{4} +(-1.32572 - 2.29622i) q^{5} +(-0.352172 - 0.609981i) q^{6} +(-1.66418 + 2.88245i) q^{7} +0.0645559 q^{8} +(1.43748 - 2.48979i) q^{9} +O(q^{10})\)	\(q-1.99188 q^{2} +(0.176804 + 0.306233i) q^{3} +1.96759 q^{4} +(-1.32572 - 2.29622i) q^{5} +(-0.352172 - 0.609981i) q^{6} +(-1.66418 + 2.88245i) q^{7} +0.0645559 q^{8} +(1.43748 - 2.48979i) q^{9} +(2.64068 + 4.57379i) q^{10} +0.00668742 q^{11} +(0.347878 + 0.602542i) q^{12} +(-2.08204 + 3.60620i) q^{13} +(3.31485 - 5.74149i) q^{14} +(0.468785 - 0.811960i) q^{15} -4.06377 q^{16} +(0.500000 - 0.866025i) q^{17} +(-2.86329 + 4.95937i) q^{18} +(-3.12890 - 5.41942i) q^{19} +(-2.60848 - 4.51801i) q^{20} -1.17693 q^{21} -0.0133206 q^{22} +(1.88933 + 3.27241i) q^{23} +(0.0114137 + 0.0197692i) q^{24} +(-1.01507 + 1.75816i) q^{25} +(4.14717 - 7.18311i) q^{26} +2.07743 q^{27} +(-3.27443 + 5.67147i) q^{28} +(-1.53155 + 2.65272i) q^{29} +(-0.933765 + 1.61733i) q^{30} +(3.02095 + 5.23245i) q^{31} +7.96543 q^{32} +(0.00118236 + 0.00204791i) q^{33} +(-0.995941 + 1.72502i) q^{34} +8.82496 q^{35} +(2.82837 - 4.89889i) q^{36} +(3.28166 + 5.68400i) q^{37} +(6.23240 + 10.7948i) q^{38} -1.47245 q^{39} +(-0.0855831 - 0.148234i) q^{40} +2.31983 q^{41} +2.34431 q^{42} +(-0.109324 - 6.55653i) q^{43} +0.0131581 q^{44} -7.62279 q^{45} +(-3.76331 - 6.51825i) q^{46} -8.80832 q^{47} +(-0.718490 - 1.24446i) q^{48} +(-2.03899 - 3.53164i) q^{49} +(2.02190 - 3.50204i) q^{50} +0.353608 q^{51} +(-4.09660 + 7.09552i) q^{52} +(5.34759 + 9.26229i) q^{53} -4.13800 q^{54} +(-0.00886566 - 0.0153558i) q^{55} +(-0.107433 + 0.186079i) q^{56} +(1.10640 - 1.91635i) q^{57} +(3.05067 - 5.28391i) q^{58} +8.15506 q^{59} +(0.922378 - 1.59761i) q^{60} +(-7.67503 + 13.2935i) q^{61} +(-6.01738 - 10.4224i) q^{62} +(4.78445 + 8.28692i) q^{63} -7.73866 q^{64} +11.0408 q^{65} +(-0.00235513 - 0.00407920i) q^{66} +(6.48158 + 11.2264i) q^{67} +(0.983795 - 1.70398i) q^{68} +(-0.668081 + 1.15715i) q^{69} -17.5783 q^{70} +(3.46358 - 5.99909i) q^{71} +(0.0927979 - 0.160731i) q^{72} +(-5.98411 + 10.3648i) q^{73} +(-6.53668 - 11.3219i) q^{74} -0.717875 q^{75} +(-6.15640 - 10.6632i) q^{76} +(-0.0111291 + 0.0192761i) q^{77} +2.93295 q^{78} +(0.616136 - 1.06718i) q^{79} +(5.38742 + 9.33129i) q^{80} +(-3.94514 - 6.83319i) q^{81} -4.62083 q^{82} +(8.22589 + 14.2477i) q^{83} -2.31573 q^{84} -2.65144 q^{85} +(0.217761 + 13.0598i) q^{86} -1.08314 q^{87} +0.000431713 q^{88} +(6.65720 + 11.5306i) q^{89} +15.1837 q^{90} +(-6.92977 - 12.0027i) q^{91} +(3.71742 + 6.43876i) q^{92} +(-1.06823 + 1.85023i) q^{93} +17.5451 q^{94} +(-8.29610 + 14.3693i) q^{95} +(1.40832 + 2.43928i) q^{96} -11.2765 q^{97} +(4.06143 + 7.03461i) q^{98} +(0.00961304 - 0.0166503i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9}+O(q^{10}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9} + 4 q^{10} + 16 q^{11} + 12 q^{12} + 2 q^{13} - 11 q^{14} + 7 q^{15} + 30 q^{16} + 29 q^{17} + 8 q^{18} + 8 q^{19} - 33 q^{20} - 26 q^{21} - 22 q^{22} - 5 q^{23} + 12 q^{24} - 36 q^{25} - 12 q^{27} + 15 q^{28} + 2 q^{29} + 11 q^{30} + 3 q^{31} - 40 q^{32} + 17 q^{33} - 3 q^{34} + 38 q^{35} - 7 q^{36} + 2 q^{37} + q^{38} - 54 q^{39} + 5 q^{40} + 14 q^{41} - 112 q^{42} + 31 q^{43} - 24 q^{44} - 46 q^{45} - 13 q^{46} - 28 q^{47} - 28 q^{49} - 13 q^{50} + 6 q^{51} + 85 q^{52} - 10 q^{53} + 34 q^{54} + 36 q^{55} - 54 q^{56} - 23 q^{57} + 3 q^{58} + 12 q^{59} + 2 q^{60} - q^{61} - q^{62} - 14 q^{63} + 28 q^{64} + 80 q^{65} - 74 q^{66} + 11 q^{67} + 27 q^{68} - 11 q^{69} + 2 q^{70} + 16 q^{71} + 21 q^{72} + 14 q^{73} + 21 q^{74} - 54 q^{75} + 44 q^{76} + 25 q^{77} + 88 q^{78} - 4 q^{79} - 112 q^{80} + 11 q^{81} - 176 q^{82} - 3 q^{83} + 100 q^{84} - 2 q^{85} + 44 q^{86} + 8 q^{87} - 106 q^{88} + 82 q^{89} + 54 q^{90} - 15 q^{91} + 42 q^{92} + 88 q^{94} + 29 q^{95} + 20 q^{96} + 20 q^{97} + 44 q^{98} - 54 q^{99}+O(q^{100}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9 + 4 * q^10 + 16 * q^11 + 12 * q^12 + 2 * q^13 - 11 * q^14 + 7 * q^15 + 30 * q^16 + 29 * q^17 + 8 * q^18 + 8 * q^19 - 33 * q^20 - 26 * q^21 - 22 * q^22 - 5 * q^23 + 12 * q^24 - 36 * q^25 - 12 * q^27 + 15 * q^28 + 2 * q^29 + 11 * q^30 + 3 * q^31 - 40 * q^32 + 17 * q^33 - 3 * q^34 + 38 * q^35 - 7 * q^36 + 2 * q^37 + q^38 - 54 * q^39 + 5 * q^40 + 14 * q^41 - 112 * q^42 + 31 * q^43 - 24 * q^44 - 46 * q^45 - 13 * q^46 - 28 * q^47 - 28 * q^49 - 13 * q^50 + 6 * q^51 + 85 * q^52 - 10 * q^53 + 34 * q^54 + 36 * q^55 - 54 * q^56 - 23 * q^57 + 3 * q^58 + 12 * q^59 + 2 * q^60 - q^61 - q^62 - 14 * q^63 + 28 * q^64 + 80 * q^65 - 74 * q^66 + 11 * q^67 + 27 * q^68 - 11 * q^69 + 2 * q^70 + 16 * q^71 + 21 * q^72 + 14 * q^73 + 21 * q^74 - 54 * q^75 + 44 * q^76 + 25 * q^77 + 88 * q^78 - 4 * q^79 - 112 * q^80 + 11 * q^81 - 176 * q^82 - 3 * q^83 + 100 * q^84 - 2 * q^85 + 44 * q^86 + 8 * q^87 - 106 * q^88 + 82 * q^89 + 54 * q^90 - 15 * q^91 + 42 * q^92 + 88 * q^94 + 29 * q^95 + 20 * q^96 + 20 * q^97 + 44 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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