LMFDB - Embedded newform 385.2.n.f.71.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [385,2,Mod(36,385)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(385, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("385.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 385 = 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	385.n (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:	$3.07424047782$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			71.8
Character	$\chi$	$=$	385.71
Dual form			385.2.n.f.141.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.728853 + 2.24318i) q^{2} +(-2.52872 - 1.83722i) q^{3} +(-2.88260 + 2.09433i) q^{4} +(0.309017 - 0.951057i) q^{5} +(2.27816 - 7.01145i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-2.98262 - 2.16700i) q^{8} +(2.09199 + 6.43850i) q^{9} +O(q^{10})$	\(q+(0.728853 + 2.24318i) q^{2} +(-2.52872 - 1.83722i) q^{3} +(-2.88260 + 2.09433i) q^{4} +(0.309017 - 0.951057i) q^{5} +(2.27816 - 7.01145i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-2.98262 - 2.16700i) q^{8} +(2.09199 + 6.43850i) q^{9} +2.35862 q^{10} +(2.82479 + 1.73798i) q^{11} +11.1370 q^{12} +(0.0938222 + 0.288755i) q^{13} +(1.90816 + 1.38636i) q^{14} +(-2.52872 + 1.83722i) q^{15} +(0.484974 - 1.49260i) q^{16} +(-0.319417 + 0.983064i) q^{17} +(-12.9179 + 9.38544i) q^{18} +(4.14451 + 3.01116i) q^{19} +(1.10105 + 3.38870i) q^{20} -3.12567 q^{21} +(-1.83974 + 7.60324i) q^{22} +8.52137 q^{23} +(3.56096 + 10.9595i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-0.579347 + 0.420920i) q^{26} +(3.64123 - 11.2066i) q^{27} +(-1.10105 + 3.38870i) q^{28} +(-3.49452 + 2.53891i) q^{29} +(-5.96430 - 4.33331i) q^{30} +(-0.818705 - 2.51972i) q^{31} -3.67181 q^{32} +(-3.95005 - 9.58464i) q^{33} -2.43800 q^{34} +(-0.309017 - 0.951057i) q^{35} +(-19.5147 - 14.1783i) q^{36} +(1.84087 - 1.33747i) q^{37} +(-3.73384 + 11.4916i) q^{38} +(0.293257 - 0.902554i) q^{39} +(-2.98262 + 2.16700i) q^{40} +(7.81385 + 5.67709i) q^{41} +(-2.27816 - 7.01145i) q^{42} +1.37993 q^{43} +(-11.7826 + 0.906148i) q^{44} +6.76983 q^{45} +(6.21083 + 19.1150i) q^{46} +(-0.870515 - 0.632466i) q^{47} +(-3.96860 + 2.88336i) q^{48} +(0.309017 - 0.951057i) q^{49} +(0.728853 - 2.24318i) q^{50} +(2.61383 - 1.89906i) q^{51} +(-0.875199 - 0.635870i) q^{52} +(-2.84844 - 8.76660i) q^{53} +27.7923 q^{54} +(2.52582 - 2.14947i) q^{55} -3.68672 q^{56} +(-4.94813 - 15.2288i) q^{57} +(-8.24223 - 5.98833i) q^{58} +(7.12907 - 5.17958i) q^{59} +(3.44154 - 10.5920i) q^{60} +(-3.25898 + 10.0301i) q^{61} +(5.05546 - 3.67301i) q^{62} +(5.47691 + 3.97921i) q^{63} +(-3.64616 - 11.2217i) q^{64} +0.303615 q^{65} +(18.6211 - 15.8465i) q^{66} +13.6999 q^{67} +(-1.13811 - 3.50274i) q^{68} +(-21.5482 - 15.6557i) q^{69} +(1.90816 - 1.38636i) q^{70} +(-2.20753 + 6.79409i) q^{71} +(7.71260 - 23.7370i) q^{72} +(-13.0449 + 9.47764i) q^{73} +(4.34192 + 3.15459i) q^{74} +(0.965886 + 2.97269i) q^{75} -18.2533 q^{76} +(3.30686 - 0.254316i) q^{77} +2.23833 q^{78} +(-0.177191 - 0.545338i) q^{79} +(-1.26968 - 0.922475i) q^{80} +(-13.3659 + 9.71089i) q^{81} +(-7.03959 + 21.6656i) q^{82} +(3.46512 - 10.6645i) q^{83} +(9.01006 - 6.54619i) q^{84} +(0.836244 + 0.607567i) q^{85} +(1.00577 + 3.09543i) q^{86} +13.5012 q^{87} +(-4.65908 - 11.3051i) q^{88} -14.3947 q^{89} +(4.93422 + 15.1860i) q^{90} +(0.245630 + 0.178460i) q^{91} +(-24.5637 + 17.8465i) q^{92} +(-2.55901 + 7.87581i) q^{93} +(0.784258 - 2.41370i) q^{94} +(4.14451 - 3.01116i) q^{95} +(9.28499 + 6.74594i) q^{96} +(-1.21832 - 3.74962i) q^{97} +2.35862 q^{98} +(-5.28052 + 21.8232i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + q^{2} - 17 q^{4} - 9 q^{5} - 13 q^{6} + 9 q^{7} + 3 q^{8} - 11 q^{9}+O(q^{10}) $ 36 * q + q^2 - 17 * q^4 - 9 * q^5 - 13 * q^6 + 9 * q^7 + 3 * q^8 - 11 * q^9	\( 36 q + q^{2} - 17 q^{4} - 9 q^{5} - 13 q^{6} + 9 q^{7} + 3 q^{8} - 11 q^{9} - 4 q^{10} - 3 q^{11} + 30 q^{12} - q^{13} - q^{14} + 3 q^{16} + 5 q^{17} - 34 q^{18} - 5 q^{19} - 7 q^{20} - 10 q^{21} - 5 q^{22} + 8 q^{23} - 41 q^{24} - 9 q^{25} + 28 q^{26} + 7 q^{28} - 33 q^{29} + 12 q^{30} - q^{31} + 12 q^{32} - 14 q^{33} + 88 q^{34} + 9 q^{35} - 104 q^{36} - 18 q^{37} - 27 q^{38} + 6 q^{39} + 3 q^{40} + 36 q^{41} + 13 q^{42} - 20 q^{43} - 30 q^{44} + 74 q^{45} + 20 q^{46} - 7 q^{47} + 75 q^{48} - 9 q^{49} + q^{50} + 22 q^{51} - 6 q^{52} - 4 q^{53} - 26 q^{54} - 3 q^{55} + 12 q^{56} - 43 q^{57} - 41 q^{58} + 25 q^{59} - 15 q^{60} + 21 q^{61} + 31 q^{62} + 26 q^{63} + 43 q^{64} - 16 q^{65} - 12 q^{66} + 58 q^{67} - 43 q^{68} - 37 q^{69} - q^{70} - 29 q^{71} + 34 q^{72} + 19 q^{73} - 59 q^{74} - 5 q^{75} - 94 q^{76} + 3 q^{77} + 20 q^{78} + 11 q^{79} - 47 q^{80} - 10 q^{81} - 58 q^{82} + 47 q^{83} - 10 q^{85} + 35 q^{86} - 46 q^{87} - 110 q^{88} + 118 q^{89} + 36 q^{90} - 9 q^{91} + 107 q^{92} - 29 q^{93} - 27 q^{94} - 5 q^{95} + 67 q^{96} - 4 q^{98} + 16 q^{99}+O(q^{100}) \) 36 * q + q^2 - 17 * q^4 - 9 * q^5 - 13 * q^6 + 9 * q^7 + 3 * q^8 - 11 * q^9 - 4 * q^10 - 3 * q^11 + 30 * q^12 - q^13 - q^14 + 3 * q^16 + 5 * q^17 - 34 * q^18 - 5 * q^19 - 7 * q^20 - 10 * q^21 - 5 * q^22 + 8 * q^23 - 41 * q^24 - 9 * q^25 + 28 * q^26 + 7 * q^28 - 33 * q^29 + 12 * q^30 - q^31 + 12 * q^32 - 14 * q^33 + 88 * q^34 + 9 * q^35 - 104 * q^36 - 18 * q^37 - 27 * q^38 + 6 * q^39 + 3 * q^40 + 36 * q^41 + 13 * q^42 - 20 * q^43 - 30 * q^44 + 74 * q^45 + 20 * q^46 - 7 * q^47 + 75 * q^48 - 9 * q^49 + q^50 + 22 * q^51 - 6 * q^52 - 4 * q^53 - 26 * q^54 - 3 * q^55 + 12 * q^56 - 43 * q^57 - 41 * q^58 + 25 * q^59 - 15 * q^60 + 21 * q^61 + 31 * q^62 + 26 * q^63 + 43 * q^64 - 16 * q^65 - 12 * q^66 + 58 * q^67 - 43 * q^68 - 37 * q^69 - q^70 - 29 * q^71 + 34 * q^72 + 19 * q^73 - 59 * q^74 - 5 * q^75 - 94 * q^76 + 3 * q^77 + 20 * q^78 + 11 * q^79 - 47 * q^80 - 10 * q^81 - 58 * q^82 + 47 * q^83 - 10 * q^85 + 35 * q^86 - 46 * q^87 - 110 * q^88 + 118 * q^89 + 36 * q^90 - 9 * q^91 + 107 * q^92 - 29 * q^93 - 27 * q^94 - 5 * q^95 + 67 * q^96 - 4 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/385\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$276$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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 $

$2$	0.728853	+	2.24318i	0.515377	+	1.58617i	0.782595	+	0.622532i	$0.213896\pi$
$2$	0.728853	+	2.24318i	0.515377	+	1.58617i	−0.267217	+	0.963636i	$0.586104\pi$
$3$	−2.52872	−	1.83722i	−1.45996	−	1.06072i	−0.983374	−	0.181594i	$-0.941874\pi$
$3$	−2.52872	−	1.83722i	−1.45996	−	1.06072i	−0.476585	−	0.879128i	$-0.658126\pi$
$4$	−2.88260	+	2.09433i	−1.44130	+	1.04716i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$6$	2.27816	−	7.01145i	0.930054	−	2.86241i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$8$	−2.98262	−	2.16700i	−1.05452	−	0.766151i
$9$	2.09199	+	6.43850i	0.697331	+	2.14617i
$10$	2.35862			0.745861
$11$	2.82479	+	1.73798i	0.851706	+	0.524020i
$11$	2.82479	+	1.73798i	0.851706	+	0.524020i
$12$	11.1370			3.21499
$13$	0.0938222	+	0.288755i	0.0260216	+	0.0800862i	0.963224	−	0.268700i	$-0.0865940\pi$
$13$	0.0938222	+	0.288755i	0.0260216	+	0.0800862i	−0.937202	+	0.348786i	$0.886594\pi$
$14$	1.90816	+	1.38636i	0.509978	+	0.370521i
$15$	−2.52872	+	1.83722i	−0.652913	+	0.474369i
$16$	0.484974	−	1.49260i	0.121243	−	0.373149i
$17$	−0.319417	+	0.983064i	−0.0774700	+	0.238428i	−0.982290	−	0.187366i	$-0.940005\pi$
$17$	−0.319417	+	0.983064i	−0.0774700	+	0.238428i	0.904820	+	0.425794i	$0.140005\pi$
$18$	−12.9179	+	9.38544i	−3.04479	+	2.21217i
$19$	4.14451	+	3.01116i	0.950816	+	0.690808i	0.951000	−	0.309192i	$-0.100059\pi$
$19$	4.14451	+	3.01116i	0.950816	+	0.690808i	−0.000184007		1.00000i	$0.500059\pi$
$20$	1.10105	+	3.38870i	0.246203	+	0.757735i
$21$	−3.12567			−0.682078
$22$	−1.83974	+	7.60324i	−0.392234	+	1.62102i
$23$	8.52137			1.77683			0.888414	−	0.459043i	$-0.151808\pi$
$23$	8.52137			1.77683			0.888414	+	0.459043i	$0.151808\pi$
$24$	3.56096	+	10.9595i	0.726877	+	2.23710i
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	−0.579347	+	0.420920i	−0.113619	+	0.0825492i
$27$	3.64123	−	11.2066i	0.700755	−	2.15670i
$28$	−1.10105	+	3.38870i	−0.208080	+	0.640403i
$29$	−3.49452	+	2.53891i	−0.648915	+	0.471465i	−0.862902	−	0.505372i	$-0.831355\pi$
$29$	−3.49452	+	2.53891i	−0.648915	+	0.471465i	0.213986	+	0.976837i	$0.431355\pi$
$30$	−5.96430	−	4.33331i	−1.08893	−	0.791151i
$31$	−0.818705	−	2.51972i	−0.147044	−	0.452554i	0.850224	−	0.526420i	$-0.176466\pi$
$31$	−0.818705	−	2.51972i	−0.147044	−	0.452554i	−0.997268	+	0.0738662i	$0.976466\pi$
$32$	−3.67181			−0.649091
$33$	−3.95005	−	9.58464i	−0.687616	−	1.66847i
$34$	−2.43800			−0.418113
$35$	−0.309017	−	0.951057i	−0.0522334	−	0.160758i
$36$	−19.5147	−	14.1783i	−3.25245	−	2.36304i
$37$	1.84087	−	1.33747i	0.302638	−	0.219879i	−0.426093	−	0.904679i	$-0.640110\pi$
$37$	1.84087	−	1.33747i	0.302638	−	0.219879i	0.728731	+	0.684800i	$0.240110\pi$
$38$	−3.73384	+	11.4916i	−0.605709	+	1.86418i
$39$	0.293257	−	0.902554i	0.0469588	−	0.144524i
$40$	−2.98262	+	2.16700i	−0.471594	+	0.342633i
$41$	7.81385	+	5.67709i	1.22032	+	0.886613i	0.996126	−	0.0879321i	$-0.0280258\pi$
$41$	7.81385	+	5.67709i	1.22032	+	0.886613i	0.224192	+	0.974545i	$0.428026\pi$
$42$	−2.27816	−	7.01145i	−0.351527	−	1.08189i
$43$	1.37993			0.210438			0.105219	−	0.994449i	$-0.466446\pi$
$43$	1.37993			0.210438			0.105219	+	0.994449i	$0.466446\pi$
$44$	−11.7826	+	0.906148i	−1.77630	+	0.136607i
$45$	6.76983			1.00919
$46$	6.21083	+	19.1150i	0.915737	+	2.81835i
$47$	−0.870515	−	0.632466i	−0.126978	−	0.0922547i	0.522484	−	0.852649i	$-0.325006\pi$
$47$	−0.870515	−	0.632466i	−0.126978	−	0.0922547i	−0.649461	+	0.760395i	$0.725006\pi$
$48$	−3.96860	+	2.88336i	−0.572818	+	0.416177i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	0.728853	−	2.24318i	0.103075	−	0.317234i
$51$	2.61383	−	1.89906i	0.366009	−	0.265921i
$52$	−0.875199	−	0.635870i	−0.121368	−	0.0881792i
$53$	−2.84844	−	8.76660i	−0.391263	−	1.20418i	−0.931834	−	0.362886i	$-0.881791\pi$
$53$	−2.84844	−	8.76660i	−0.391263	−	1.20418i	0.540570	−	0.841299i	$-0.318209\pi$
$54$	27.7923			3.78205
$55$	2.52582	−	2.14947i	0.340582	−	0.289834i
$56$	−3.68672			−0.492659
$57$	−4.94813	−	15.2288i	−0.655396	−	2.01710i
$58$	−8.24223	−	5.98833i	−1.08226	−	0.786307i
$59$	7.12907	−	5.17958i	0.928126	−	0.674323i	−0.0174070	−	0.999848i	$-0.505541\pi$
$59$	7.12907	−	5.17958i	0.928126	−	0.674323i	0.945533	+	0.325525i	$0.105541\pi$
$60$	3.44154	−	10.5920i	0.444300	−	1.36742i
$61$	−3.25898	+	10.0301i	−0.417269	+	1.28422i	0.492937	+	0.870065i	$0.335923\pi$
$61$	−3.25898	+	10.0301i	−0.417269	+	1.28422i	−0.910206	+	0.414157i	$0.864077\pi$
$62$	5.05546	−	3.67301i	0.642044	−	0.466472i
$63$	5.47691	+	3.97921i	0.690026	+	0.501333i
$64$	−3.64616	−	11.2217i	−0.455770	−	1.40272i
$65$	0.303615			0.0376588
$66$	18.6211	−	15.8465i	2.29209	−	1.95057i
$67$	13.6999			1.67371			0.836854	−	0.547427i	$-0.184392\pi$
$67$	13.6999			1.67371			0.836854	+	0.547427i	$0.184392\pi$
$68$	−1.13811	−	3.50274i	−0.138016	−	0.424770i
$69$	−21.5482	−	15.6557i	−2.59410	−	1.88472i
$70$	1.90816	−	1.38636i	0.228069	−	0.165702i
$71$	−2.20753	+	6.79409i	−0.261986	+	0.806311i	0.730386	+	0.683034i	$0.239340\pi$
$71$	−2.20753	+	6.79409i	−0.261986	+	0.806311i	−0.992372	+	0.123276i	$0.960660\pi$
$72$	7.71260	−	23.7370i	0.908939	−	2.79743i
$73$	−13.0449	+	9.47764i	−1.52678	+	1.10927i	−0.568791	+	0.822482i	$0.692589\pi$
$73$	−13.0449	+	9.47764i	−1.52678	+	1.10927i	−0.957993	+	0.286792i	$0.907411\pi$
$74$	4.34192	+	3.15459i	0.504738	+	0.366714i
$75$	0.965886	+	2.97269i	0.111531	+	0.343257i
$76$	−18.2533			−2.09380
$77$	3.30686	−	0.254316i	0.376852	−	0.0289819i
$78$	2.23833			0.253441
$79$	−0.177191	−	0.545338i	−0.0199355	−	0.0613553i	0.940594	−	0.339534i	$-0.110269\pi$
$79$	−0.177191	−	0.545338i	−0.0199355	−	0.0613553i	−0.960529	+	0.278179i	$0.910269\pi$
$80$	−1.26968	−	0.922475i	−0.141954	−	0.103136i
$81$	−13.3659	+	9.71089i	−1.48510	+	1.07899i
$82$	−7.03959	+	21.6656i	−0.777393	+	2.39257i
$83$	3.46512	−	10.6645i	0.380346	−	1.17058i	−0.559455	−	0.828861i	$-0.688989\pi$
$83$	3.46512	−	10.6645i	0.380346	−	1.17058i	0.939801	−	0.341724i	$-0.111011\pi$
$84$	9.01006	−	6.54619i	0.983078	−	0.714248i
$85$	0.836244	+	0.607567i	0.0907034	+	0.0658999i
$86$	1.00577	+	3.09543i	0.108455	+	0.333789i
$87$	13.5012			1.44748
$88$	−4.65908	−	11.3051i	−0.496659	−	1.20512i
$89$	−14.3947			−1.52583			−0.762917	−	0.646496i	$-0.776234\pi$
$89$	−14.3947			−1.52583			−0.762917	+	0.646496i	$0.776234\pi$
$90$	4.93422	+	15.1860i	0.520112	+	1.60074i
$91$	0.245630	+	0.178460i	0.0257490	+	0.0187077i
$92$	−24.5637	+	17.8465i	−2.56094	+	1.86063i
$93$	−2.55901	+	7.87581i	−0.265356	+	0.816683i
$94$	0.784258	−	2.41370i	0.0808900	−	0.248954i
$95$	4.14451	−	3.01116i	0.425218	−	0.308939i
$96$	9.28499	+	6.74594i	0.947646	+	0.688505i
$97$	−1.21832	−	3.74962i	−0.123702	−	0.380716i	0.869960	−	0.493122i	$-0.164144\pi$
$97$	−1.21832	−	3.74962i	−0.123702	−	0.380716i	−0.993662	+	0.112406i	$0.964144\pi$
$98$	2.35862			0.238257
$99$	−5.28052	+	21.8232i	−0.530712	+	2.19332i
$100$	3.56309			0.356309
$101$	−3.14895	−	9.69148i	−0.313333	−	0.964338i	−0.976435	−	0.215810i	$-0.930761\pi$
$101$	−3.14895	−	9.69148i	−0.313333	−	0.964338i	0.663103	−	0.748528i	$-0.269239\pi$
$102$	6.16502	+	4.47915i	0.610428	+	0.443502i
$103$	−14.9234	+	10.8425i	−1.47044	+	1.06834i	−0.489956	+	0.871747i	$0.662987\pi$
$103$	−14.9234	+	10.8425i	−1.47044	+	1.06834i	−0.980486	+	0.196591i	$0.937013\pi$
$104$	0.345896	−	1.06456i	0.0339179	−	0.104389i
$105$	−0.965886	+	2.97269i	−0.0942608	+	0.290105i
$106$	17.5890	−	12.7791i	1.70839	−	1.24122i
$107$	−14.4973	−	10.5329i	−1.40150	−	1.01825i	−0.994490	−	0.104829i	$-0.966570\pi$
$107$	−14.4973	−	10.5329i	−1.40150	−	1.01825i	−0.407013	−	0.913422i	$-0.633430\pi$
$108$	12.9740	+	39.9299i	1.24843	+	3.84226i
$109$	1.01822			0.0975276			0.0487638	−	0.998810i	$-0.484472\pi$
$109$	1.01822			0.0975276			0.0487638	+	0.998810i	$0.484472\pi$
$110$	6.66260	+	4.09923i	0.635254	+	0.390846i
$111$	−7.11230			−0.675070
$112$	−0.484974	−	1.49260i	−0.0458257	−	0.141037i
$113$	1.45426	+	1.05658i	0.136805	+	0.0993946i	0.654083	−	0.756423i	$-0.273055\pi$
$113$	1.45426	+	1.05658i	0.136805	+	0.0993946i	−0.517278	+	0.855817i	$0.673055\pi$
$114$	30.5545	−	22.1991i	2.86169	−	2.07914i
$115$	2.63325	−	8.10430i	0.245552	−	0.755730i
$116$	4.75596	−	14.6373i	0.441580	−	1.35904i
$117$	−1.66287	+	1.20815i	−0.153733	+	0.111693i
$118$	16.8148	+	12.2166i	1.54793	+	1.12463i
$119$	0.319417	+	0.983064i	0.0292809	+	0.0901173i
$120$	11.5235			1.05195
$121$	4.95887	+	9.81884i	0.450806	+	0.892622i
$122$	−24.8746			−2.25204
$123$	−9.32896	−	28.7116i	−0.841164	−	2.58884i
$124$	7.63711	+	5.54869i	0.685833	+	0.498287i
$125$	−0.809017	+	0.587785i	−0.0723607	+	0.0525731i
$126$	−4.93422	+	15.1860i	−0.439575	+	1.35287i
$127$	−3.47693	+	10.7009i	−0.308528	+	0.949551i	0.669809	+	0.742533i	$0.266376\pi$
$127$	−3.47693	+	10.7009i	−0.308528	+	0.949551i	−0.978337	+	0.207018i	$0.933624\pi$
$128$	16.5737	−	12.0415i	1.46492	−	1.06433i
$129$	−3.48946	−	2.53524i	−0.307230	−	0.223216i
$130$	0.221291	+	0.681063i	0.0194085	+	0.0597332i
$131$	3.75923			0.328445			0.164223	−	0.986423i	$-0.447488\pi$
$131$	3.75923			0.328445			0.164223	+	0.986423i	$0.447488\pi$
$132$	31.4598	+	19.3559i	2.73822	+	1.68472i
$133$	5.12290			0.444211
$134$	9.98521	+	30.7313i	0.862591	+	2.65478i
$135$	−9.53287	−	6.92603i	−0.820459	−	0.596098i
$136$	3.08300	−	2.23993i	0.264365	−	0.192073i
$137$	4.66218	−	14.3487i	0.398317	−	1.22589i	−0.528032	−	0.849225i	$-0.677070\pi$
$137$	4.66218	−	14.3487i	0.398317	−	1.22589i	0.926348	−	0.376668i	$-0.122930\pi$
$138$	19.4130	−	59.7471i	1.65255	−	5.08601i
$139$	10.7814	−	7.83314i	0.914466	−	0.664398i	−0.0276746	−	0.999617i	$-0.508810\pi$
$139$	10.7814	−	7.83314i	0.914466	−	0.664398i	0.942140	+	0.335219i	$0.108810\pi$
$140$	2.88260	+	2.09433i	0.243624	+	0.177003i
$141$	1.03931	+	3.19866i	0.0875256	+	0.269376i
$142$	−16.8493			−1.41397
$143$	−0.236822	+	0.978733i	−0.0198040	+	0.0818457i
$144$	10.6246			0.885386
$145$	1.33479	+	4.10805i	0.110848	+	0.341155i
$146$	−30.7678	−	22.3541i	−2.54636	−	1.85004i
$147$	−2.52872	+	1.83722i	−0.208566	+	0.151532i
$148$	−2.50539	+	7.71080i	−0.205942	+	0.633823i
$149$	0.657491	−	2.02355i	0.0538637	−	0.165776i	−0.920506	−	0.390729i	$-0.872223\pi$
$149$	0.657491	−	2.02355i	0.0538637	−	0.165776i	0.974370	+	0.224953i	$0.0722230\pi$
$150$	−5.96430	+	4.33331i	−0.486983	+	0.353814i
$151$	12.7425	+	9.25797i	1.03697	+	0.753403i	0.969692	−	0.244331i	$-0.0785684\pi$
$151$	12.7425	+	9.25797i	1.03697	+	0.753403i	0.0672784	+	0.997734i	$0.478568\pi$
$152$	−5.83631	−	17.9623i	−0.473387	−	1.45694i
$153$	−6.99767			−0.565728
$154$	2.98069	+	7.23252i	0.240191	+	0.582813i
$155$	−2.64939			−0.212804
$156$	1.04490	+	3.21588i	0.0836591	+	0.257476i
$157$	6.89696	+	5.01093i	0.550437	+	0.399916i	0.827947	−	0.560807i	$-0.189509\pi$
$157$	6.89696	+	5.01093i	0.550437	+	0.399916i	−0.277510	+	0.960723i	$0.589509\pi$
$158$	1.09414	−	0.794942i	0.0870454	−	0.0632422i
$159$	−8.90330	+	27.4015i	−0.706077	+	2.17308i
$160$	−1.13465	+	3.49210i	−0.0897021	+	0.276075i
$161$	6.89393	−	5.00873i	0.543318	−	0.394744i
$162$	−31.5251	−	22.9043i	−2.47684	−	1.79953i
$163$	−3.76417	−	11.5849i	−0.294832	−	0.907400i	−0.983278	−	0.182112i	$-0.941707\pi$
$163$	−3.76417	−	11.5849i	−0.294832	−	0.907400i	0.688446	−	0.725288i	$-0.258293\pi$
$164$	−34.4139			−2.68727
$165$	−10.3362	+	0.794907i	−0.804669	+	0.0618835i
$166$	26.4480			2.05277
$167$	2.61093	+	8.03562i	0.202040	+	0.621815i	0.999822	+	0.0188692i	$0.00600660\pi$
$167$	2.61093	+	8.03562i	0.202040	+	0.621815i	−0.797782	+	0.602946i	$0.793993\pi$
$168$	9.32270	+	6.77334i	0.719262	+	0.522575i
$169$	10.4426	−	7.58703i	0.803280	−	0.583617i
$170$	−0.753383	+	2.31867i	−0.0577818	+	0.177834i
$171$	−10.7171	+	32.9837i	−0.819554	+	2.52233i
$172$	−3.97779	+	2.89003i	−0.303303	+	0.220363i
$173$	−7.16687	−	5.20704i	−0.544887	−	0.395884i	0.281010	−	0.959705i	$-0.409331\pi$
$173$	−7.16687	−	5.20704i	−0.544887	−	0.395884i	−0.825897	+	0.563821i	$0.809331\pi$
$174$	9.84041	+	30.2857i	0.746000	+	2.29595i
$175$	−1.00000			−0.0755929
$176$	3.96405	−	3.37339i	0.298801	−	0.254279i
$177$	−27.5435			−2.07030
$178$	−10.4916	−	32.2899i	−0.786381	−	2.42023i
$179$	−6.53911	−	4.75094i	−0.488756	−	0.355102i	0.315950	−	0.948776i	$-0.397677\pi$
$179$	−6.53911	−	4.75094i	−0.488756	−	0.355102i	−0.804706	+	0.593674i	$0.797677\pi$
$180$	−19.5147	+	14.1783i	−1.45454	+	1.05679i
$181$	−0.417375	+	1.28455i	−0.0310232	+	0.0954797i	−0.965369	−	0.260888i	$-0.915985\pi$
$181$	−0.417375	+	1.28455i	−0.0310232	+	0.0954797i	0.934346	+	0.356367i	$0.115985\pi$
$182$	−0.221291	+	0.681063i	−0.0164032	+	0.0504838i
$183$	26.6686	−	19.3759i	1.97140	−	1.43230i
$184$	−25.4160	−	18.4658i	−1.87369	−	1.36132i
$185$	−0.703152	−	2.16408i	−0.0516967	−	0.159106i
$186$	−19.5320			−1.43216
$187$	−2.61083	+	2.22181i	−0.190923	+	0.162475i
$188$	3.83394			0.279618
$189$	−3.64123	−	11.2066i	−0.264861	−	0.815157i
$190$	9.77532	+	7.10219i	0.709176	+	0.515247i
$191$	−9.94420	+	7.22488i	−0.719537	+	0.522774i	−0.886236	−	0.463234i	$-0.846689\pi$
$191$	−9.94420	+	7.22488i	−0.719537	+	0.522774i	0.166699	+	0.986008i	$0.446689\pi$
$192$	−11.3967	+	35.0755i	−0.822486	+	2.53135i
$193$	−5.73715	+	17.6571i	−0.412969	+	1.27099i	0.501085	+	0.865398i	$0.332934\pi$
$193$	−5.73715	+	17.6571i	−0.412969	+	1.27099i	−0.914055	+	0.405591i	$0.867066\pi$
$194$	7.52309	−	5.46584i	0.540126	−	0.392425i
$195$	−0.767758	−	0.557809i	−0.0549803	−	0.0399455i
$196$	1.10105	+	3.38870i	0.0786467	+	0.242050i
$197$	−12.8716			−0.917062			−0.458531	−	0.888678i	$-0.651624\pi$
$197$	−12.8716			−0.917062			−0.458531	+	0.888678i	$0.651624\pi$
$198$	−52.8022	+	4.06077i	−3.75249	+	0.288587i
$199$	9.93245			0.704093			0.352046	−	0.935983i	$-0.385486\pi$
$199$	9.93245			0.704093			0.352046	+	0.935983i	$0.385486\pi$
$200$	1.13926	+	3.50628i	0.0805579	+	0.247932i
$201$	−34.6432	−	25.1698i	−2.44354	−	1.77534i
$202$	19.4446	−	14.1273i	1.36812	−	0.993996i
$203$	−1.33479	+	4.10805i	−0.0936836	+	0.288329i
$204$	−3.55736	+	10.9484i	−0.249065	+	0.766543i
$205$	7.81385	−	5.67709i	0.545743	−	0.396505i
$206$	−35.1985	−	25.5732i	−2.45240	−	1.78177i
$207$	17.8266	+	54.8648i	1.23904	+	3.81337i
$208$	0.476496			0.0330390
$209$	6.47403	+	15.7090i	0.447818	+	1.08661i
$210$	−7.37227			−0.508735
$211$	−5.29897	−	16.3085i	−0.364796	−	1.12273i	−0.950109	−	0.311919i	$-0.899028\pi$
$211$	−5.29897	−	16.3085i	−0.364796	−	1.12273i	0.585313	−	0.810807i	$-0.300972\pi$
$212$	26.5711	+	19.3050i	1.82491	+	1.32587i
$213$	18.0645	−	13.1246i	1.23776	−	0.899286i
$214$	13.0608	−	40.1969i	0.892815	−	2.74780i
$215$	0.426422	−	1.31239i	0.0290818	−	0.0895044i
$216$	−35.1451	+	25.5344i	−2.39132	+	1.73739i
$217$	−2.14340	−	1.55727i	−0.145503	−	0.105714i
$218$	0.742132	+	2.28405i	0.0502635	+	0.154695i
$219$	50.3994			3.40567
$220$	−2.77923	+	11.4860i	−0.187376	+	0.774383i
$221$	−0.313833			−0.0211107
$222$	−5.18383	−	15.9542i	−0.347916	−	1.07077i
$223$	−12.4045	−	9.01239i	−0.830666	−	0.603514i	0.0890814	−	0.996024i	$-0.471607\pi$
$223$	−12.4045	−	9.01239i	−0.830666	−	0.603514i	−0.919748	+	0.392510i	$0.871607\pi$
$224$	−2.97056	+	2.15824i	−0.198479	+	0.144203i
$225$	2.09199	−	6.43850i	0.139466	−	0.429233i
$226$	−1.31016	+	4.03225i	−0.0871504	+	0.268221i
$227$	1.63309	−	1.18651i	0.108392	−	0.0787514i	−0.532269	−	0.846575i	$-0.678660\pi$
$227$	1.63309	−	1.18651i	0.108392	−	0.0787514i	0.640661	+	0.767824i	$0.278660\pi$
$228$	46.1576	+	33.5354i	3.05686	+	2.22094i
$229$	−0.0965078	−	0.297020i	−0.00637741	−	0.0196277i	0.947817	−	0.318814i	$-0.103285\pi$
$229$	−0.0965078	−	0.297020i	−0.00637741	−	0.0196277i	−0.954195	+	0.299187i	$0.903285\pi$
$230$	20.0987			1.32527
$231$	−8.82937	−	5.43235i	−0.580930	−	0.357422i
$232$	15.9247			1.04550
$233$	5.37138	+	16.5314i	0.351891	+	1.08301i	0.957790	+	0.287468i	$0.0928134\pi$
$233$	5.37138	+	16.5314i	0.351891	+	1.08301i	−0.605899	+	0.795541i	$0.707187\pi$
$234$	−3.92208	−	2.84956i	−0.256395	−	0.186282i
$235$	−0.870515	+	0.632466i	−0.0567861	+	0.0412575i
$236$	−9.70251	+	29.8613i	−0.631580	+	1.94380i
$237$	−0.553841	+	1.70455i	−0.0359758	+	0.110722i
$238$	−1.97238	+	1.43302i	−0.127850	+	0.0928888i
$239$	−18.3307	−	13.3180i	−1.18572	−	0.861473i	−0.192911	−	0.981216i	$-0.561793\pi$
$239$	−18.3307	−	13.3180i	−1.18572	−	0.861473i	−0.992805	+	0.119744i	$0.961793\pi$
$240$	1.51587	+	4.66537i	0.0978490	+	0.301148i
$241$	6.28549			0.404884			0.202442	−	0.979294i	$-0.435112\pi$
$241$	6.28549			0.404884			0.202442	+	0.979294i	$0.435112\pi$
$242$	−18.4111	+	18.2801i	−1.18351	+	1.17509i
$243$	16.2899			1.04500
$244$	−11.6120	−	35.7381i	−0.743383	−	2.28790i
$245$	−0.809017	−	0.587785i	−0.0516862	−	0.0375522i
$246$	57.6058	−	41.8531i	3.67281	−	2.66846i
$247$	−0.480641	+	1.47926i	−0.0305825	+	0.0941231i
$248$	−3.01834	+	9.28950i	−0.191665	+	0.589884i
$249$	−28.3555	+	20.6014i	−1.79695	+	1.30556i
$250$	−1.90816	−	1.38636i	−0.120683	−	0.0876812i
$251$	−3.29906	−	10.1535i	−0.208235	−	0.640880i	−0.999565	−	0.0294916i	$-0.990611\pi$
$251$	−3.29906	−	10.1535i	−0.208235	−	0.640880i	0.791330	−	0.611389i	$-0.209389\pi$
$252$	−24.1215			−1.51951
$253$	24.0711	+	14.8099i	1.51333	+	0.931094i
$254$	−26.5382			−1.66516
$255$	−0.998393	−	3.07274i	−0.0625218	−	0.192422i
$256$	19.9996	+	14.5305i	1.24997	+	0.908159i
$257$	14.2981	−	10.3882i	0.891892	−	0.647998i	−0.0444784	−	0.999010i	$-0.514163\pi$
$257$	14.2981	−	10.3882i	0.891892	−	0.647998i	0.936371	+	0.351013i	$0.114163\pi$
$258$	3.14370	−	9.67532i	0.195718	−	0.602359i
$259$	0.703152	−	2.16408i	0.0436917	−	0.134469i
$260$	−0.875199	+	0.635870i	−0.0542776	+	0.0394350i
$261$	−23.6573	−	17.1880i	−1.46435	−	1.06391i
$262$	2.73993	+	8.43263i	0.169273	+	0.520970i
$263$	12.2684			0.756499			0.378250	−	0.925704i	$-0.376526\pi$
$263$	12.2684			0.756499			0.378250	+	0.925704i	$0.376526\pi$
$264$	−8.98841	+	37.1471i	−0.553199	+	2.28625i
$265$	−9.21775			−0.566242
$266$	3.73384	+	11.4916i	0.228936	+	0.704594i
$267$	36.4002	+	26.4463i	2.22766	+	1.61849i
$268$	−39.4912	+	28.6921i	−2.41231	+	1.75265i
$269$	6.64589	−	20.4539i	0.405207	−	1.24710i	−0.515515	−	0.856880i	$-0.672399\pi$
$269$	6.64589	−	20.4539i	0.405207	−	1.24710i	0.920722	−	0.390219i	$-0.127601\pi$
$270$	8.58828	−	26.4320i	0.522666	−	1.60860i
$271$	3.54556	−	2.57600i	0.215378	−	0.156481i	−0.474866	−	0.880058i	$-0.657503\pi$
$271$	3.54556	−	2.57600i	0.215378	−	0.156481i	0.690243	+	0.723577i	$0.257503\pi$
$272$	1.31241	+	0.953520i	0.0795764	+	0.0578157i
$273$	−0.293257	−	0.902554i	−0.0177487	−	0.0546250i
$274$	35.5848			2.14976
$275$	−1.26374	−	3.06642i	−0.0762067	−	0.184912i
$276$	94.9028			5.71248
$277$	3.53718	+	10.8863i	0.212528	+	0.654095i	0.999320	+	0.0368762i	$0.0117407\pi$
$277$	3.53718	+	10.8863i	0.212528	+	0.654095i	−0.786791	+	0.617219i	$0.788259\pi$
$278$	25.4292	+	18.4754i	1.52514	+	1.10808i
$279$	14.5104	−	10.5425i	0.868718	−	0.631160i
$280$	−1.13926	+	3.50628i	−0.0680838	+	0.209541i
$281$	3.54254	−	10.9028i	0.211330	−	0.650408i	−0.788063	−	0.615594i	$-0.788916\pi$
$281$	3.54254	−	10.9028i	0.211330	−	0.650408i	0.999394	−	0.0348139i	$-0.0110838\pi$
$282$	−6.41767	+	4.66271i	−0.382167	+	0.277661i
$283$	10.2587	+	7.45336i	0.609815	+	0.443056i	0.849349	−	0.527832i	$-0.176995\pi$
$283$	10.2587	+	7.45336i	0.609815	+	0.443056i	−0.239534	+	0.970888i	$0.576995\pi$
$284$	−7.86564	−	24.2079i	−0.466740	−	1.43648i
$285$	−16.0125			−0.948498
$286$	−2.36808	+	0.182118i	−0.140028	+	0.0107689i
$287$	9.65845			0.570120
$288$	−7.68141	−	23.6409i	−0.452631	−	1.39306i
$289$	12.8889	+	9.36434i	0.758171	+	0.550843i
$290$	−8.24223	+	5.98833i	−0.484001	+	0.351647i
$291$	−3.80808	+	11.7201i	−0.223234	+	0.687043i
$292$	17.7537	−	54.6404i	1.03896	−	3.19759i
$293$	−6.67673	+	4.85093i	−0.390059	+	0.283394i	−0.765480	−	0.643460i	$-0.777498\pi$
$293$	−6.67673	+	4.85093i	−0.390059	+	0.283394i	0.375421	+	0.926854i	$0.377498\pi$
$294$	−5.96430	−	4.33331i	−0.347845	−	0.252724i
$295$	−2.72306	−	8.38073i	−0.158543	−	0.487945i
$296$	−8.38894			−0.487597
$297$	29.7625	−	25.3278i	1.72699	−	1.46967i
$298$	5.01840			0.290708
$299$	0.799493	+	2.46059i	0.0462359	+	0.142299i
$300$	−9.01006	−	6.54619i	−0.520196	−	0.377944i
$301$	1.11639	−	0.811103i	0.0643475	−	0.0467512i
$302$	−11.4799	+	35.3314i	−0.660593	+	2.03310i
$303$	−9.84260	+	30.2924i	−0.565443	+	1.74025i
$304$	6.50443	−	4.72574i	0.373055	−	0.271040i
$305$	8.53211	+	6.19894i	0.488547	+	0.354950i
$306$	−5.10028	−	15.6970i	−0.291563	−	0.897340i
$307$	1.76640			0.100814			0.0504070	−	0.998729i	$-0.483948\pi$
$307$	1.76640			0.100814			0.0504070	+	0.998729i	$0.483948\pi$
$308$	−8.99972	+	7.65874i	−0.512807	+	0.436397i
$309$	57.6570			3.27999
$310$	−1.93101	−	5.94305i	−0.109674	−	0.337543i
$311$	3.65419	+	2.65492i	0.207210	+	0.150547i	0.686551	−	0.727082i	$-0.259124\pi$
$311$	3.65419	+	2.65492i	0.207210	+	0.150547i	−0.479340	+	0.877629i	$0.659124\pi$
$312$	−2.83051	+	2.05649i	−0.160246	+	0.116426i
$313$	−1.94424	+	5.98377i	−0.109895	+	0.338223i	−0.990848	−	0.134981i	$-0.956903\pi$
$313$	−1.94424	+	5.98377i	−0.109895	+	0.338223i	0.880953	+	0.473204i	$0.156903\pi$
$314$	−6.21355	+	19.1234i	−0.350651	+	1.07919i
$315$	5.47691	−	3.97921i	0.308589	−	0.224203i
$316$	1.65289	+	1.20089i	0.0929821	+	0.0675555i
$317$	1.14330	+	3.51873i	0.0642143	+	0.197631i	0.978016	−	0.208529i	$-0.0668675\pi$
$317$	1.14330	+	3.51873i	0.0642143	+	0.197631i	−0.913802	+	0.406160i	$0.866867\pi$
$318$	−67.9558			−3.81077
$319$	−14.2838	+	1.09851i	−0.799742	+	0.0615045i
$320$	−11.7992			−0.659597
$321$	17.3083	+	53.2694i	0.966055	+	2.97321i
$322$	16.2602	+	11.8137i	0.906143	+	0.658352i
$323$	−4.28399	+	3.11250i	−0.238368	+	0.173184i
$324$	18.1907	−	55.9852i	1.01059	−	3.11029i
$325$	0.0938222	−	0.288755i	0.00520432	−	0.0160172i
$326$	23.2435	−	16.8874i	1.28734	−	0.935307i
$327$	−2.57479	−	1.87070i	−0.142386	−	0.103450i
$328$	−11.0035	−	33.8653i	−0.607566	−	1.86990i
$329$	−1.07602			−0.0593227
$330$	−9.31667	−	22.6065i	−0.512866	−	1.24445i
$331$	−20.6957			−1.13754			−0.568769	−	0.822497i	$-0.692580\pi$
$331$	−20.6957			−1.13754			−0.568769	+	0.822497i	$0.692580\pi$
$332$	12.3465	+	37.9986i	0.677603	+	2.08545i
$333$	12.4624	+	9.05448i	0.682936	+	0.496182i
$334$	−16.1224	+	11.7136i	−0.882177	+	0.640939i
$335$	4.23350	−	13.0294i	0.231301	−	0.711870i
$336$	−1.51587	+	4.66537i	−0.0826975	+	0.254517i
$337$	−11.1693	+	8.11496i	−0.608430	+	0.442050i	−0.848861	−	0.528616i	$-0.822711\pi$
$337$	−11.1693	+	8.11496i	−0.608430	+	0.442050i	0.240431	+	0.970666i	$0.422711\pi$
$338$	24.6302	+	17.8949i	1.33971	+	0.973355i
$339$	−1.73624	−	5.34359i	−0.0942995	−	0.290224i
$340$	−3.68300			−0.199739
$341$	2.06654	−	8.54056i	0.111909	−	0.462497i
$342$	−81.7996			−4.42322
$343$	−0.309017	−	0.951057i	−0.0166853	−	0.0513522i
$344$	−4.11581	−	2.99031i	−0.221910	−	0.161227i
$345$	−21.5482	+	15.6557i	−1.16011	+	0.842873i
$346$	6.45672	−	19.8717i	0.347116	−	1.06831i
$347$	0.902614	−	2.77796i	0.0484548	−	0.149129i	−0.923902	−	0.382630i	$-0.875018\pi$
$347$	0.902614	−	2.77796i	0.0484548	−	0.149129i	0.972356	+	0.233501i	$0.0750184\pi$
$348$	−38.9186	+	28.2760i	−2.08625	+	1.51575i
$349$	−11.4974	−	8.35334i	−0.615441	−	0.447144i	0.235885	−	0.971781i	$-0.424201\pi$
$349$	−11.4974	−	8.35334i	−0.615441	−	0.447144i	−0.851326	+	0.524637i	$0.824201\pi$
$350$	−0.728853	−	2.24318i	−0.0389589	−	0.119903i
$351$	3.57758			0.190957
$352$	−10.3721	−	6.38153i	−0.552834	−	0.340137i
$353$	−24.1977			−1.28792			−0.643958	−	0.765061i	$-0.722709\pi$
$353$	−24.1977			−1.28792			−0.643958	+	0.765061i	$0.722709\pi$
$354$	−20.0752	−	61.7850i	−1.06698	−	3.28384i
$355$	5.77940	+	4.19898i	0.306739	+	0.222859i
$356$	41.4941	−	30.1472i	2.19918	−	1.59780i
$357$	0.998393	−	3.07274i	0.0528405	−	0.162626i
$358$	5.89117	−	18.1312i	0.311358	−	0.958261i
$359$	14.0646	−	10.2185i	0.742299	−	0.539312i	−0.151132	−	0.988514i	$-0.548292\pi$
$359$	14.0646	−	10.2185i	0.742299	−	0.539312i	0.893430	+	0.449202i	$0.148292\pi$
$360$	−20.1919	−	14.6702i	−1.06420	−	0.773190i
$361$	2.23854	+	6.88951i	0.117818	+	0.362606i
$362$	−3.18568			−0.167435
$363$	5.49982	−	33.9397i	0.288666	−	1.78137i
$364$	−1.08181			−0.0567020
$365$	4.98269	+	15.3351i	0.260806	+	0.802678i
$366$	62.9010	+	45.7003i	3.28789	+	2.38879i
$367$	7.00153	−	5.08691i	0.365477	−	0.265535i	−0.389856	−	0.920876i	$-0.627475\pi$
$367$	7.00153	−	5.08691i	0.365477	−	0.265535i	0.755333	+	0.655341i	$0.227475\pi$
$368$	4.13264	−	12.7190i	0.215429	−	0.663022i
$369$	−20.2054	+	62.1859i	−1.05185	+	3.23727i
$370$	4.34192	−	3.15459i	0.225726	−	0.163999i
$371$	−7.45731	−	5.41806i	−0.387164	−	0.281291i
$372$	−9.11795	−	28.0622i	−0.472744	−	1.45496i
$373$	11.7827			0.610087			0.305044	−	0.952338i	$-0.401329\pi$
$373$	11.7827			0.610087			0.305044	+	0.952338i	$0.401329\pi$
$374$	−6.88683	−	4.23719i	−0.356109	−	0.219100i
$375$	3.12567			0.161409
$376$	1.22586	+	3.77282i	0.0632190	+	0.194568i
$377$	−1.06099	−	0.770852i	−0.0546436	−	0.0397009i
$378$	22.4844	−	16.3359i	1.15647	−	0.840227i
$379$	1.22838	−	3.78056i	0.0630976	−	0.194194i	−0.914538	−	0.404500i	$-0.867446\pi$
$379$	1.22838	−	3.78056i	0.0630976	−	0.194194i	0.977636	+	0.210305i	$0.0674457\pi$
$380$	−5.64058	+	17.3599i	−0.289356	+	0.890546i
$381$	28.4522	−	20.6717i	1.45765	−	1.05904i
$382$	−23.4546	−	17.0407i	−1.20004	−	0.871880i
$383$	−5.79253	−	17.8276i	−0.295985	−	0.910947i	−0.982889	−	0.184199i	$-0.941031\pi$
$383$	−5.79253	−	17.8276i	−0.295985	−	0.910947i	0.686904	−	0.726748i	$-0.258969\pi$
$384$	−64.0333			−3.26769
$385$	0.780007	−	3.22360i	0.0397529	−	0.164290i
$386$	−43.7897			−2.22884
$387$	2.88681	+	8.88468i	0.146745	+	0.451634i
$388$	11.3649	+	8.25706i	0.576964	+	0.419189i
$389$	−1.87155	+	1.35976i	−0.0948911	+	0.0689424i	−0.634219	−	0.773153i	$-0.718678\pi$
$389$	−1.87155	+	1.35976i	−0.0948911	+	0.0689424i	0.539328	+	0.842096i	$0.318678\pi$
$390$	0.691683	−	2.12878i	0.0350247	−	0.107795i
$391$	−2.72187	+	8.37705i	−0.137651	+	0.423646i
$392$	−2.98262	+	2.16700i	−0.150645	+	0.109450i
$393$	−9.50605	−	6.90655i	−0.479517	−	0.348389i
$394$	−9.38150	−	28.8733i	−0.472633	−	1.45461i
$395$	−0.573402			−0.0288510
$396$	−30.4834	−	73.9667i	−1.53185	−	3.71697i
$397$	22.3968			1.12406			0.562032	−	0.827116i	$-0.310020\pi$
$397$	22.3968			1.12406			0.562032	+	0.827116i	$0.310020\pi$
$398$	7.23930	+	22.2803i	0.362873	+	1.11681i
$399$	−12.9544	−	9.41191i	−0.648530	−	0.471185i
$400$	−1.26968	+	0.922475i	−0.0634839	+	0.0461238i
$401$	7.48102	−	23.0242i	0.373584	−	1.14977i	−0.570844	−	0.821058i	$-0.693384\pi$
$401$	7.48102	−	23.0242i	0.373584	−	1.14977i	0.944429	−	0.328716i	$-0.106616\pi$
$402$	31.2105	−	96.0561i	1.55664	−	4.79084i
$403$	0.650768	−	0.472810i	0.0324170	−	0.0235524i
$404$	29.3743	+	21.3417i	1.46143	+	1.06179i
$405$	5.10532	+	15.7126i	0.253685	+	0.780763i
$406$	−10.1880			−0.505620
$407$	7.52458	−	0.578681i	0.372980	−	0.0286842i
$408$	−11.9113			−0.589698
$409$	−5.38469	−	16.5724i	−0.266256	−	0.819451i	−0.991401	−	0.130856i	$-0.958228\pi$
$409$	−5.38469	−	16.5724i	−0.266256	−	0.819451i	0.725145	−	0.688596i	$-0.241772\pi$
$410$	18.4299	+	13.3901i	0.910188	+	0.661290i
$411$	−38.1512	+	27.7184i	−1.88186	+	1.36725i
$412$	20.3104	−	62.5088i	1.00062	−	3.07959i
$413$	2.72306	−	8.38073i	0.133993	−	0.412389i
$414$	−110.079	+	79.9768i	−5.41007	+	3.93064i
$415$	−9.07179	−	6.59104i	−0.445317	−	0.323542i
$416$	−0.344497	−	1.06025i	−0.0168904	−	0.0519832i
$417$	−41.6544			−2.03982
$418$	−30.5194	+	25.9720i	−1.49275	+	1.27033i
$419$	18.0980			0.884145			0.442073	−	0.896979i	$-0.354243\pi$
$419$	18.0980			0.884145			0.442073	+	0.896979i	$0.354243\pi$
$420$	−3.44154	−	10.5920i	−0.167930	−	0.516835i
$421$	−15.7212	−	11.4221i	−0.766205	−	0.556681i	0.134602	−	0.990900i	$-0.457024\pi$
$421$	−15.7212	−	11.4221i	−0.766205	−	0.556681i	−0.900807	+	0.434219i	$0.857024\pi$
$422$	32.7208	−	23.7731i	1.59282	−	1.15726i
$423$	2.25102	−	6.92792i	0.109448	−	0.336847i
$424$	−10.5014	+	32.3200i	−0.509994	+	1.56960i
$425$	0.836244	−	0.607567i	0.0405638	−	0.0294713i
$426$	42.6073	+	30.9560i	2.06433	+	1.49982i
$427$	3.25898	+	10.0301i	0.157713	+	0.485390i
$428$	63.8491			3.08626
$429$	2.39701	−	2.03985i	0.115729	−	0.0984848i
$430$	3.25473			0.156957
$431$	2.44377	+	7.52116i	0.117712	+	0.362282i	0.992503	−	0.122219i	$-0.0390012\pi$
$431$	2.44377	+	7.52116i	0.117712	+	0.362282i	−0.874791	+	0.484501i	$0.839001\pi$
$432$	−14.9610	−	10.8698i	−0.719810	−	0.522972i
$433$	−14.7743	+	10.7342i	−0.710008	+	0.515851i	−0.883176	−	0.469041i	$-0.844600\pi$
$433$	−14.7743	+	10.7342i	−0.710008	+	0.515851i	0.173168	+	0.984892i	$0.444600\pi$
$434$	1.93101	−	5.94305i	0.0926916	−	0.285276i
$435$	4.17211	−	12.8404i	0.200037	−	0.615651i
$436$	−2.93511	+	2.13248i	−0.140566	+	0.102127i
$437$	35.3169	+	25.6592i	1.68944	+	1.22745i
$438$	36.7338	+	113.055i	1.75521	+	5.40197i
$439$	−24.6331			−1.17567			−0.587837	−	0.808979i	$-0.700020\pi$
$439$	−24.6331			−1.17567			−0.587837	+	0.808979i	$0.700020\pi$
$440$	−12.1915	+	0.937591i	−0.581206	+	0.0446979i
$441$	6.76983			0.322373
$442$	−0.228738	−	0.703984i	−0.0108800	−	0.0334851i
$443$	13.4670	+	9.78435i	0.639836	+	0.464868i	0.859794	−	0.510641i	$-0.170592\pi$
$443$	13.4670	+	9.78435i	0.639836	+	0.464868i	−0.219958	+	0.975509i	$0.570592\pi$
$444$	20.5019	−	14.8955i	0.972977	−	0.706909i
$445$	−4.44821	+	13.6902i	−0.210865	+	0.648976i
$446$	11.1754	−	34.3942i	0.529169	−	1.62861i
$447$	−5.38033	+	3.90904i	−0.254481	+	0.184891i
$448$	−9.54577	−	6.93541i	−0.450995	−	0.327667i
$449$	−2.49016	−	7.66392i	−0.117518	−	0.361683i	0.874946	−	0.484220i	$-0.160897\pi$
$449$	−2.49016	−	7.66392i	−0.117518	−	0.361683i	−0.992464	+	0.122538i	$0.960897\pi$
$450$	15.9675			0.752713
$451$	12.2058	+	29.6169i	0.574749	+	1.39460i
$452$	−6.40486			−0.301259
$453$	−15.2133	−	46.8217i	−0.714783	−	2.19987i
$454$	3.85184	+	2.79852i	0.180776	+	0.131341i
$455$	0.245630	−	0.178460i	0.0115153	−	0.00836635i
$456$	−18.2424	+	56.1444i	−0.854279	+	2.62920i
$457$	7.09848	−	21.8469i	0.332053	−	1.02195i	−0.636102	−	0.771605i	$-0.719454\pi$
$457$	7.09848	−	21.8469i	0.332053	−	1.02195i	0.968156	−	0.250350i	$-0.0805456\pi$
$458$	0.595930	−	0.432969i	0.0278460	−	0.0202313i
$459$	9.85369	+	7.15912i	0.459931	+	0.334159i
$460$	9.38249	+	28.8763i	0.437461	+	1.34637i
$461$	−15.0286			−0.699951			−0.349975	−	0.936759i	$-0.613810\pi$
$461$	−15.0286			−0.699951			−0.349975	+	0.936759i	$0.613810\pi$
$462$	5.75043	−	23.7653i	0.267534	−	1.10566i
$463$	−22.9066			−1.06456			−0.532279	−	0.846569i	$-0.678664\pi$
$463$	−22.9066			−1.06456			−0.532279	+	0.846569i	$0.678664\pi$
$464$	2.09482	+	6.44721i	0.0972498	+	0.299304i
$465$	6.69956	+	4.86752i	0.310685	+	0.225726i
$466$	−33.1680	+	24.0980i	−1.53648	+	1.11632i
$467$	0.507476	−	1.56185i	0.0234832	−	0.0722738i	−0.938628	−	0.344931i	$-0.887902\pi$
$467$	0.507476	−	1.56185i	0.0234832	−	0.0722738i	0.962111	+	0.272657i	$0.0879024\pi$
$468$	2.26313	−	6.96520i	0.104613	−	0.321967i
$469$	11.0834	−	8.05259i	0.511786	−	0.371834i
$470$	−2.05321	−	1.49175i	−0.0947077	−	0.0688091i
$471$	−8.23428	−	25.3425i	−0.379416	−	1.16772i
$472$	−32.4875			−1.49536
$473$	3.89801	+	2.39829i	0.179231	+	0.110274i
$474$	−4.22728			−0.194165
$475$	−1.58306	−	4.87216i	−0.0726359	−	0.223550i
$476$	−2.97961	−	2.16481i	−0.136570	−	0.0992240i
$477$	50.4848	−	36.6793i	2.31154	−	1.67943i
$478$	16.5144	−	50.8260i	0.755350	−	2.32473i
$479$	2.01067	−	6.18819i	0.0918696	−	0.282746i	−0.894556	−	0.446957i	$-0.852508\pi$
$479$	2.01067	−	6.18819i	0.0918696	−	0.282746i	0.986425	+	0.164211i	$0.0525078\pi$
$480$	9.28499	−	6.74594i	0.423800	−	0.307909i
$481$	0.558917	+	0.406077i	0.0254844	+	0.0185155i
$482$	4.58120	+	14.0995i	0.208668	+	0.642214i
$483$	−26.6350			−1.21194
$484$	−34.8583	−	17.9183i	−1.58447	−	0.814467i
$485$	−3.94258			−0.179023
$486$	11.8730	+	36.5412i	0.538569	+	1.65754i
$487$	−25.1653	−	18.2837i	−1.14035	−	0.828512i	−0.153181	−	0.988198i	$-0.548952\pi$
$487$	−25.1653	−	18.2837i	−1.14035	−	0.828512i	−0.987168	+	0.159686i	$0.948952\pi$
$488$	31.4555	−	22.8538i	1.42392	−	1.03454i
$489$	−11.7656	+	36.2106i	−0.532057	+	1.63750i
$490$	0.728853	−	2.24318i	0.0329262	−	0.101337i
$491$	15.5600	−	11.3050i	0.702214	−	0.510188i	−0.178439	−	0.983951i	$-0.557105\pi$
$491$	15.5600	−	11.3050i	0.702214	−	0.510188i	0.880652	+	0.473763i	$0.157105\pi$
$492$	87.0232	+	63.2260i	3.92331	+	2.85045i
$493$	−1.37971	−	4.24630i	−0.0621389	−	0.191244i
$494$	−3.66857			−0.165057
$495$	19.1234	+	11.7658i	0.859531	+	0.528834i
$496$	−4.15797			−0.186698
$497$	2.20753	+	6.79409i	0.0990215	+	0.304757i
$498$	−66.8797	−	48.5910i	−2.99695	−	2.17741i
$499$	−10.0776	+	7.32184i	−0.451137	+	0.327770i	−0.790045	−	0.613049i	$-0.789943\pi$
$499$	−10.0776	+	7.32184i	−0.451137	+	0.327770i	0.338907	+	0.940820i	$0.389943\pi$
$500$	1.10105	−	3.38870i	0.0492406	−	0.151547i
$501$	8.16092	−	25.1167i	0.364603	−	1.12213i
$502$	20.3715	−	14.8008i	0.909225	−	0.660590i
$503$	−0.770977	−	0.560148i	−0.0343762	−	0.0249758i	0.570464	−	0.821322i	$-0.306763\pi$
$503$	−0.770977	−	0.560148i	−0.0343762	−	0.0249758i	−0.604841	+	0.796347i	$0.706763\pi$
$504$	−7.71260	−	23.7370i	−0.343547	−	1.05733i
$505$	−10.1902			−0.453459
$506$	−15.6771	+	64.7900i	−0.696932	+	2.88027i
$507$	−40.3456			−1.79181
$508$	−12.3886	−	38.1282i	−0.549656	−	1.69167i
$509$	−24.3080	−	17.6608i	−1.07743	−	0.782801i	−0.100199	−	0.994967i	$-0.531948\pi$
$509$	−24.3080	−	17.6608i	−1.07743	−	0.782801i	−0.977233	+	0.212167i	$0.931948\pi$
$510$	6.16502	−	4.47915i	0.272992	−	0.198340i
$511$	−4.98269	+	15.3351i	−0.220421	+	0.678387i
$512$	−5.35666	+	16.4861i	−0.236733	+	0.728590i
$513$	48.8359	−	35.4813i	2.15616	−	1.56654i
$514$	33.7238	+	24.5018i	1.48749	+	1.08073i
$515$	5.70021	+	17.5435i	0.251181	+	0.773057i
$516$	15.3684			0.676554
$517$	−1.35981	−	3.29952i	−0.0598043	−	0.145113i
$518$	5.36691			0.235809
$519$	8.55653	+	26.3343i	0.375590	+	1.15595i
$520$	−0.905569	−	0.657934i	−0.0397118	−	0.0288523i
$521$	−28.5799	+	20.7645i	−1.25211	+	0.909708i	−0.998342	−	0.0575577i	$-0.981669\pi$
$521$	−28.5799	+	20.7645i	−1.25211	+	0.909708i	−0.253764	+	0.967266i	$0.581669\pi$
$522$	21.3132	−	65.5951i	0.932851	−	2.87102i
$523$	−1.18202	+	3.63790i	−0.0516863	+	0.159074i	−0.973568	−	0.228397i	$-0.926651\pi$
$523$	−1.18202	+	3.63790i	−0.0516863	+	0.159074i	0.921882	+	0.387472i	$0.126651\pi$
$524$	−10.8363	+	7.87307i	−0.473388	+	0.343937i
$525$	2.52872	+	1.83722i	0.110363	+	0.0801831i
$526$	8.94184	+	27.5201i	0.389883	+	1.19994i
$527$	2.73855			0.119293
$528$	−16.2217	+	1.24753i	−0.705957	+	0.0542920i
$529$	49.6137			2.15712
$530$	−6.71839	−	20.6771i	−0.291828	−	0.898155i
$531$	48.2626	+	35.0649i	2.09442	+	1.52169i
$532$	−14.7672	+	10.7290i	−0.640241	+	0.465162i
$533$	−0.906177	+	2.78892i	−0.0392509	+	0.120802i
$534$	−32.7934	+	100.928i	−1.41911	+	4.36757i
$535$	−14.4973	+	10.5329i	−0.626771	+	0.455376i
$536$	−40.8616	−	29.6877i	−1.76495	−	1.28231i
$537$	7.80705	+	24.0276i	0.336899	+	1.03687i
$538$	50.7258			2.18694
$539$	2.52582	−	2.14947i	0.108795	−	0.0925842i
$540$	41.9848			1.80674
$541$	0.552129	+	1.69928i	0.0237379	+	0.0730577i	0.962224	−	0.272260i	$-0.0877711\pi$
$541$	0.552129	+	1.69928i	0.0237379	+	0.0730577i	−0.938486	+	0.345318i	$0.887771\pi$
$542$	8.36263	+	6.07581i	0.359206	+	0.260978i
$543$	3.41543	−	2.48145i	0.146570	−	0.106489i
$544$	1.17284	−	3.60963i	0.0502850	−	0.154761i
$545$	0.314647	−	0.968383i	0.0134780	−	0.0414810i
$546$	1.81085	−	1.31566i	0.0774972	−	0.0563050i
$547$	−26.8335	−	19.4957i	−1.14732	−	0.833575i	−0.159195	−	0.987247i	$-0.550890\pi$
$547$	−26.8335	−	19.4957i	−1.14732	−	0.833575i	−0.988122	+	0.153672i	$0.950890\pi$
$548$	16.6117	+	51.1257i	0.709618	+	2.18398i
$549$	−71.3965			−3.04713
$550$	5.95746	−	5.06978i	0.254027	−	0.216176i
$551$	−22.1281			−0.942690
$552$	30.3442	+	93.3899i	1.29154	+	3.97494i
$553$	−0.463892	−	0.337037i	−0.0197267	−	0.0143323i
$554$	−21.8419	+	15.8691i	−0.927973	+	0.674212i
$555$	−2.19782	+	6.76420i	−0.0932924	+	0.287124i
$556$	−14.6732	+	45.1596i	−0.622284	+	1.91519i
$557$	1.64981	−	1.19866i	0.0699047	−	0.0507888i	−0.552284	−	0.833656i	$-0.686244\pi$
$557$	1.64981	−	1.19866i	0.0699047	−	0.0507888i	0.622189	+	0.782867i	$0.286244\pi$
$558$	34.2246	+	24.8656i	1.44884	+	1.05265i
$559$	0.129468	+	0.398462i	0.00547592	+	0.0168531i
$560$	−1.56941			−0.0663196
$561$	10.6840	−	0.821660i	0.451080	−	0.0346905i
$562$	27.0390			1.14057
$563$	−5.74080	−	17.6684i	−0.241946	−	0.744632i	−0.996124	−	0.0879625i	$-0.971964\pi$
$563$	−5.74080	−	17.6684i	−0.241946	−	0.744632i	0.754178	−	0.656670i	$-0.228036\pi$
$564$	−9.69496	−	7.04380i	−0.408231	−	0.296598i
$565$	1.45426	−	1.05658i	0.0611810	−	0.0444506i
$566$	−9.24216	+	28.4445i	−0.388477	+	1.19561i
$567$	−5.10532	+	15.7126i	−0.214403	+	0.659865i
$568$	21.3071	−	15.4805i	0.894024	−	0.649547i
$569$	−13.2755	−	9.64523i	−0.556539	−	0.404349i	0.273652	−	0.961829i	$-0.411768\pi$
$569$	−13.2755	−	9.64523i	−0.556539	−	0.404349i	−0.830191	+	0.557480i	$0.811768\pi$
$570$	−11.6708	−	35.9189i	−0.488835	−	1.50448i
$571$	18.5329			0.775578			0.387789	−	0.921748i	$-0.373239\pi$
$571$	18.5329			0.775578			0.387789	+	0.921748i	$0.373239\pi$
$572$	−1.36713	−	3.31727i	−0.0571624	−	0.138702i
$573$	38.4198			1.60501
$574$	7.03959	+	21.6656i	0.293827	+	0.904306i
$575$	−6.89393	−	5.00873i	−0.287497	−	0.208879i
$576$	64.6233	−	46.9516i	2.69264	−	1.95632i
$577$	−7.33788	+	22.5837i	−0.305480	+	0.940171i	0.674018	+	0.738715i	$0.264567\pi$
$577$	−7.33788	+	22.5837i	−0.305480	+	0.940171i	−0.979498	+	0.201456i	$0.935433\pi$
$578$	−11.6118	+	35.7374i	−0.482986	+	1.48648i
$579$	46.9478	−	34.1096i	1.95108	−	1.41755i
$580$	−12.4513	−	9.04637i	−0.517010	−	0.375630i
$581$	−3.46512	−	10.6645i	−0.143757	−	0.442439i
$582$	−29.0658			−1.20482
$583$	7.18991	−	29.7143i	0.297776	−	1.23064i
$584$	59.4459			2.45989
$585$	0.635161	+	1.95482i	0.0262607	+	0.0808220i
$586$	−15.7479	−	11.4415i	−0.650538	−	0.472644i
$587$	−17.0245	+	12.3690i	−0.702675	+	0.510523i	−0.880802	−	0.473484i	$-0.842996\pi$
$587$	−17.0245	+	12.3690i	−0.702675	+	0.510523i	0.178127	+	0.984007i	$0.442996\pi$
$588$	3.44154	−	10.5920i	0.141927	−	0.436805i
$589$	4.19414	−	12.9082i	0.172817	−	0.531875i
$590$	16.8148	−	12.2166i	0.692253	−	0.502951i
$591$	32.5487	+	23.6480i	1.33887	+	0.972748i
$592$	−1.10353	−	3.39632i	−0.0453549	−	0.139588i
$593$	46.2299			1.89843			0.949217	−	0.314621i	$-0.101878\pi$
$593$	46.2299			1.89843			0.949217	+	0.314621i	$0.101878\pi$
$594$	78.5072	+	48.3023i	3.22119	+	1.98187i
$595$	1.03365			0.0423757
$596$	2.34270	+	7.21008i	0.0959606	+	0.295336i
$597$	−25.1164	−	18.2481i	−1.02795	−	0.746847i
$598$	−4.93683	+	3.58682i	−0.201882	+	0.146676i
$599$	5.16768	−	15.9045i	0.211146	−	0.649840i	−0.788259	−	0.615343i	$-0.789017\pi$
$599$	5.16768	−	15.9045i	0.211146	−	0.649840i	0.999405	−	0.0344962i	$-0.0109827\pi$
$600$	3.56096	−	10.9595i	0.145375	−	0.447420i
$601$	8.45217	−	6.14086i	0.344771	−	0.250491i	−0.401901	−	0.915683i	$-0.631650\pi$
$601$	8.45217	−	6.14086i	0.344771	−	0.250491i	0.746672	+	0.665192i	$0.231650\pi$
$602$	2.63313	+	1.91308i	0.107319	+	0.0779715i
$603$	28.6601	+	88.2066i	1.16713	+	3.59205i
$604$	−56.1207			−2.28352
$605$	10.8706	−	1.68197i	0.441955	−	0.0683819i
$606$	−75.1251			−3.05175
$607$	−6.15372	−	18.9392i	−0.249772	−	0.768719i	−0.994815	−	0.101702i	$-0.967571\pi$
$607$	−6.15372	−	18.9392i	−0.249772	−	0.768719i	0.745043	−	0.667016i	$-0.232429\pi$
$608$	−15.2179	−	11.0564i	−0.617166	−	0.448397i
$609$	10.9227	−	7.93582i	0.442611	−	0.321576i
$610$	−7.68668	+	23.6572i	−0.311225	+	0.957851i
$611$	0.100954	−	0.310705i	0.00408417	−	0.0125698i
$612$	20.1715	−	14.6554i	0.815383	−	0.592410i
$613$	−14.0859	−	10.2340i	−0.568925	−	0.413348i	0.265790	−	0.964031i	$-0.414367\pi$
$613$	−14.0859	−	10.2340i	−0.568925	−	0.413348i	−0.834714	+	0.550683i	$0.814367\pi$
$614$	1.28745	+	3.96236i	0.0519572	+	0.159908i
$615$	−30.1892			−1.21734
$616$	−10.4142	−	6.40745i	−0.419601	−	0.258163i
$617$	−13.6972			−0.551427			−0.275713	−	0.961240i	$-0.588914\pi$
$617$	−13.6972			−0.551427			−0.275713	+	0.961240i	$0.588914\pi$
$618$	42.0235	+	129.335i	1.69043	+	5.20262i
$619$	25.8158	+	18.7563i	1.03762	+	0.753877i	0.969820	−	0.243821i	$-0.0784010\pi$
$619$	25.8158	+	18.7563i	1.03762	+	0.753877i	0.0678031	+	0.997699i	$0.478401\pi$
$620$	7.63711	−	5.54869i	0.306714	−	0.222841i
$621$	31.0283	−	95.4952i	1.24512	−	3.83209i
$622$	−3.29211	+	10.1321i	−0.132001	+	0.406259i
$623$	−11.6456	+	8.46099i	−0.466569	+	0.338982i
$624$	−1.20493	−	0.875430i	−0.0482356	−	0.0350452i
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	−14.8397			−0.593115
$627$	12.4899	−	51.6179i	0.498797	−	2.06142i
$628$	−30.3757			−1.21212
$629$	0.726816	+	2.23691i	0.0289800	+	0.0891914i
$630$	12.9179	+	9.38544i	0.514663	+	0.373925i
$631$	−17.9190	+	13.0189i	−0.713344	+	0.518275i	−0.884251	−	0.467012i	$-0.845330\pi$
$631$	−17.9190	+	13.0189i	−0.713344	+	0.518275i	0.170907	+	0.985287i	$0.445330\pi$
$632$	−0.653254	+	2.01051i	−0.0259851	+	0.0799738i
$633$	−16.5628	+	50.9752i	−0.658314	+	2.02608i
$634$	−7.05984	+	5.12927i	−0.280382	+	0.203709i
$635$	9.10273	+	6.61352i	0.361231	+	0.262450i
$636$	−31.7232	−	97.6340i	−1.25791	−	3.87144i
$637$	0.303615			0.0120297
$638$	−12.8750	−	31.2406i	−0.509725	−	1.23683i
$639$	−48.3619			−1.91317
$640$	−6.33060	−	19.4836i	−0.250239	−	0.770156i
$641$	−38.0335	−	27.6329i	−1.50223	−	1.09144i	−0.969482	−	0.245163i	$-0.921158\pi$
$641$	−38.0335	−	27.6329i	−1.50223	−	1.09144i	−0.532751	−	0.846272i	$-0.678842\pi$
$642$	−106.878	+	77.6512i	−4.21813	+	3.06465i
$643$	−5.03156	+	15.4855i	−0.198425	+	0.610690i	0.801494	+	0.598002i	$0.204039\pi$
$643$	−5.03156	+	15.4855i	−0.198425	+	0.610690i	−0.999920	+	0.0126875i	$0.995961\pi$
$644$	−9.38249	+	28.8763i	−0.369722	+	1.13789i
$645$	−3.48946	+	2.53524i	−0.137398	+	0.0998251i
$646$	−10.1043	−	7.34121i	−0.397548	−	0.288836i
$647$	−12.6162	−	38.8287i	−0.495994	−	1.52651i	−0.815401	−	0.578896i	$-0.803484\pi$
$647$	−12.6162	−	38.8287i	−0.495994	−	1.52651i	0.319407	−	0.947618i	$-0.396516\pi$
$648$	60.9089			2.39273
$649$	29.1401	−	2.24103i	1.14385	−	0.0879683i
$650$	0.716112			0.0280882
$651$	2.55901	+	7.87581i	0.100295	+	0.308677i
$652$	35.1132	+	25.5112i	1.37514	+	0.999097i
$653$	−18.8314	+	13.6818i	−0.736928	+	0.535410i	−0.891748	−	0.452533i	$-0.850520\pi$
$653$	−18.8314	+	13.6818i	−0.736928	+	0.535410i	0.154819	+	0.987943i	$0.450520\pi$
$654$	2.31966	−	7.13919i	0.0907060	−	0.279164i
$655$	1.16167	−	3.57524i	0.0453901	−	0.139696i
$656$	12.2631	−	8.90968i	0.478794	−	0.347864i
$657$	−88.3115	−	64.1620i	−3.44536	−	2.50320i
$658$	−0.784258	−	2.41370i	−0.0305735	−	0.0940957i
$659$	8.17158			0.318320			0.159160	−	0.987253i	$-0.449121\pi$
$659$	8.17158			0.318320			0.159160	+	0.987253i	$0.449121\pi$
$660$	28.1302	−	23.9387i	1.09497	−	0.931814i
$661$	7.64860			0.297496			0.148748	−	0.988875i	$-0.452476\pi$
$661$	7.64860			0.297496			0.148748	+	0.988875i	$0.452476\pi$
$662$	−15.0841	−	46.4242i	−0.586261	−	1.80433i
$663$	0.793596	+	0.576582i	0.0308207	+	0.0223926i
$664$	−33.4452	+	24.2994i	−1.29793	+	0.942998i
$665$	1.58306	−	4.87216i	0.0613885	−	0.188934i
$666$	−11.2275	+	34.5548i	−0.435059	+	1.33897i
$667$	−29.7781	+	21.6350i	−1.15301	+	0.837711i
$668$	−24.3555	−	17.6953i	−0.942343	−	0.684652i
$669$	14.8097	+	45.5797i	0.572578	+	1.76221i
$670$	32.3128			1.24835
$671$	−26.6380	+	22.6689i	−1.02835	+	0.875122i
$672$	11.4769			0.442730
$673$	−4.41386	−	13.5845i	−0.170142	−	0.523642i	0.829237	−	0.558898i	$-0.188776\pi$
$673$	−4.41386	−	13.5845i	−0.170142	−	0.523642i	−0.999378	+	0.0352553i	$0.988776\pi$
$674$	−26.3441	−	19.1401i	−1.01474	−	0.737249i
$675$	−9.53287	+	6.92603i	−0.366920	+	0.266583i
$676$	−14.2122	+	43.7407i	−0.546623	+	1.68233i
$677$	8.88903	−	27.3576i	0.341633	−	1.05144i	−0.621729	−	0.783233i	$-0.713569\pi$
$677$	8.88903	−	27.3576i	0.341633	−	1.05144i	0.963362	−	0.268206i	$-0.0864307\pi$
$678$	10.7212	−	7.78939i	0.411744	−	0.299150i
$679$	−3.18961	−	2.31739i	−0.122406	−	0.0889333i
$680$	−1.17760	−	3.62429i	−0.0451590	−	0.138985i
$681$	−6.30952			−0.241781
$682$	20.6642	−	1.58919i	0.791274	−	0.0608533i
$683$	−22.0519			−0.843794			−0.421897	−	0.906644i	$-0.638636\pi$
$683$	−22.0519			−0.843794			−0.421897	+	0.906644i	$0.638636\pi$
$684$	−38.1858	−	117.524i	−1.46007	−	4.49364i
$685$	−12.2057	−	8.86799i	−0.466357	−	0.338828i
$686$	1.90816	−	1.38636i	0.0728540	−	0.0529315i
$687$	−0.301652	+	0.928389i	−0.0115087	+	0.0354202i
$688$	0.669231	−	2.05968i	0.0255142	−	0.0785246i
$689$	2.26415	−	1.64500i	0.0862573	−	0.0626696i
$690$	−50.8240	−	36.9258i	−1.93483	−	1.40574i
$691$	2.75871	+	8.49044i	0.104946	+	0.322991i	0.989718	−	0.143034i	$-0.0456857\pi$
$691$	2.75871	+	8.49044i	0.104946	+	0.322991i	−0.884772	+	0.466025i	$0.845686\pi$
$692$	31.5644			1.19990
$693$	8.55534	+	20.7592i	0.324991	+	0.788576i
$694$	6.88934			0.261516
$695$	−4.11813	−	12.6743i	−0.156209	−	0.480763i
$696$	−40.2690	−	29.2572i	−1.52639	−	1.10899i
$697$	−8.07682	+	5.86815i	−0.305931	+	0.222272i
$698$	10.3581	−	31.8791i	0.392061	−	1.20664i
$699$	16.7892	−	51.6718i	0.635025	−	1.95441i
$700$	2.88260	−	2.09433i	0.108952	−	0.0791582i
$701$	−0.0273339	−	0.0198592i	−0.00103239	−	0.000750073i	0.587269	−	0.809392i	$-0.300203\pi$
$701$	−0.0273339	−	0.0198592i	−0.00103239	−	0.000750073i	−0.588301	+	0.808642i	$0.700203\pi$
$702$	2.60753	+	8.02515i	0.0984149	+	0.302890i
$703$	11.6569			0.439647
$704$	9.20348	−	38.0360i	0.346869	−	1.43353i
$705$	3.36327			0.126668
$706$	−17.6366	−	54.2799i	−0.663762	−	2.04285i
$707$	−8.24407	−	5.98966i	−0.310050	−	0.225265i
$708$	79.3968	−	57.6851i	2.98391	−	2.16794i
$709$	−0.886707	+	2.72900i	−0.0333010	+	0.102490i	−0.966325	−	0.257323i	$-0.917160\pi$
$709$	−0.886707	+	2.72900i	−0.0333010	+	0.102490i	0.933024	+	0.359813i	$0.117160\pi$
$710$	−5.20673	+	16.0247i	−0.195405	+	0.601396i
$711$	3.14047	−	2.28169i	0.117777	−	0.0855699i
$712$	42.9340	+	31.1933i	1.60902	+	1.16902i
$713$	−6.97649	−	21.4714i	−0.261272	−	0.804111i
$714$	7.62038			0.285186
$715$	0.857648	+	0.527676i	0.0320742	+	0.0197340i
$716$	28.7997			1.07629
$717$	21.8851	+	67.3553i	0.817312	+	2.51543i
$718$	33.1729	+	24.1015i	1.23800	+	0.899462i
$719$	−1.35528	+	0.984666i	−0.0505433	+	0.0367219i	−0.612770	−	0.790261i	$-0.709945\pi$
$719$	−1.35528	+	0.984666i	−0.0505433	+	0.0367219i	0.562227	+	0.826983i	$0.309945\pi$
$720$	3.28319	−	10.1046i	0.122357	−	0.376577i
$721$	−5.70021	+	17.5435i	−0.212287	+	0.653352i
$722$	−13.8228	+	10.0429i	−0.514433	+	0.373757i
$723$	−15.8943	−	11.5479i	−0.591114	−	0.429469i
$724$	−1.48714	−	4.57695i	−0.0552692	−	0.170101i
$725$	4.31946			0.160421
$726$	80.1414	−	12.4000i	2.97433	−	0.460206i
$727$	0.612732			0.0227250			0.0113625	−	0.999935i	$-0.496383\pi$
$727$	0.612732			0.0227250			0.0113625	+	0.999935i	$0.496383\pi$
$728$	−0.345896	−	1.06456i	−0.0128198	−	0.0394552i
$729$	−1.09501	−	0.795571i	−0.0405559	−	0.0294656i
$730$	−30.7678	+	22.3541i	−1.13877	+	0.827364i
$731$	−0.440773	+	1.35656i	−0.0163026	+	0.0501742i
$732$	−36.2953	+	111.706i	−1.34151	+	4.12876i
$733$	−29.5074	+	21.4384i	−1.08988	+	0.791845i	−0.979379	−	0.202031i	$-0.935246\pi$
$733$	−29.5074	+	21.4384i	−1.08988	+	0.791845i	−0.110502	+	0.993876i	$0.535246\pi$
$734$	16.5140	+	11.9981i	0.609541	+	0.442858i
$735$	0.965886	+	2.97269i	0.0356272	+	0.109649i
$736$	−31.2889			−1.15332
$737$	38.6993	+	23.8101i	1.42551	+	0.877056i
$738$	−154.221			−5.67695
$739$	−13.8243	−	42.5468i	−0.508535	−	1.56511i	−0.794746	−	0.606942i	$-0.792396\pi$
$739$	−13.8243	−	42.5468i	−0.508535	−	1.56511i	0.286212	−	0.958166i	$-0.407604\pi$
$740$	6.55919	+	4.76553i	0.241121	+	0.175184i
$741$	3.93314	−	2.85760i	0.144488	−	0.104976i
$742$	6.71839	−	20.6771i	0.246640	−	0.759079i
$743$	−4.22708	+	13.0096i	−0.155077	+	0.477277i	−0.998169	−	0.0604926i	$-0.980733\pi$
$743$	−4.22708	+	13.0096i	−0.155077	+	0.477277i	0.843092	+	0.537769i	$0.180733\pi$
$744$	24.6994	−	17.9452i	0.905525	−	0.657903i
$745$	−1.72133	−	1.25062i	−0.0630648	−	0.0458192i
$746$	8.58789	+	26.4308i	0.314425	+	0.967701i
$747$	75.9125			2.77749
$748$	2.87277	−	11.8725i	0.105039	−	0.434102i
$749$	−17.9196			−0.654768
$750$	2.27816	+	7.01145i	0.0831866	+	0.256022i
$751$	37.3692	+	27.1503i	1.36362	+	0.990728i	0.998205	+	0.0598836i	$0.0190730\pi$
$751$	37.3692	+	27.1503i	1.36362	+	0.990728i	0.365415	+	0.930845i	$0.380927\pi$
$752$	−1.36619	+	0.992598i	−0.0498199	+	0.0361963i
$753$	−10.3118	+	31.7364i	−0.375782	+	1.15654i
$754$	0.955857	−	2.94182i	0.0348102	−	0.107135i
$755$	12.7425	−	9.25797i	0.463747	−	0.336932i
$756$	33.9664	+	24.6780i	1.23535	+	0.897532i
$757$	15.8941	+	48.9170i	0.577681	+	1.77792i	0.626862	+	0.779130i	$0.284339\pi$
$757$	15.8941	+	48.9170i	0.577681	+	1.77792i	−0.0491812	+	0.998790i	$0.515661\pi$
$758$	9.37579			0.340544
$759$	−33.6598	−	81.6742i	−1.22178	−	2.96459i
$760$	−18.8867			−0.685093
$761$	9.97156	+	30.6893i	0.361469	+	1.11249i	0.952163	+	0.305591i	$0.0988540\pi$
$761$	9.97156	+	30.6893i	0.361469	+	1.11249i	−0.590694	+	0.806896i	$0.701146\pi$
$762$	67.1078	+	48.7567i	2.43106	+	1.76627i
$763$	0.823756	−	0.598494i	0.0298220	−	0.0216669i
$764$	13.5338	−	41.6528i	0.489637	−	1.50695i
$765$	−2.16240	+	6.65518i	−0.0781817	+	0.240619i
$766$	35.7686	−	25.9874i	1.29237	−	0.938963i
$767$	2.16449	+	1.57260i	0.0781553	+	0.0567832i
$768$	−23.8775	−	73.4874i	−0.861605	−	2.65175i
$769$	20.8369			0.751399			0.375699	−	0.926742i	$-0.377403\pi$
$769$	20.8369			0.751399			0.375699	+	0.926742i	$0.377403\pi$
$770$	7.79962	−	0.599834i	0.281079	−	0.0216165i
$771$	−55.2414			−1.98947
$772$	−20.4420	−	62.9139i	−0.735722	−	2.26432i
$773$	31.9563	+	23.2176i	1.14939	+	0.835079i	0.988399	−	0.151877i	$-0.0485318\pi$
$773$	31.9563	+	23.2176i	1.14939	+	0.835079i	0.160989	+	0.986956i	$0.448532\pi$
$774$	−17.8259	+	12.9513i	−0.640738	+	0.465523i
$775$	−0.818705	+	2.51972i	−0.0294088	+	0.0905109i
$776$	−4.49163	+	13.8238i	−0.161240	+	0.496246i
$777$	−5.75397	+	4.18051i	−0.206423	+	0.149975i
$778$	−4.41426	−	3.20715i	−0.158259	−	0.114982i
$779$	15.2899	+	47.0575i	0.547818	+	1.68601i
$780$	3.38137			0.121073
$781$	−18.0438	+	15.3552i	−0.645658	+	0.549453i
$782$	−20.7751			−0.742915
$783$	15.7281	+	48.4063i	0.562078	+	1.72990i
$784$	−1.26968	−	0.922475i	−0.0453456	−	0.0329455i
$785$	6.89696	−	5.01093i	0.246163	−	0.178848i
$786$	8.56412	−	26.3577i	0.305472	−	0.940146i
$787$	−7.24690	+	22.3037i	−0.258324	+	0.795040i	0.734832	+	0.678249i	$0.237261\pi$
$787$	−7.24690	+	22.3037i	−0.258324	+	0.795040i	−0.993156	+	0.116791i	$0.962739\pi$
$788$	37.1036	−	26.9573i	1.32176	−	0.960315i
$789$	−31.0233	−	22.5397i	−1.10446	−	0.802436i
$790$	−0.417926	−	1.28624i	−0.0148691	−	0.0457625i
$791$	1.79756			0.0639139
$792$	63.0408	−	53.6476i	2.24006	−	1.90628i
$793$	−3.20200			−0.113706
$794$	16.3240	+	50.2401i	0.579317	+	1.78295i
$795$	23.3091	+	16.9351i	0.826690	+	0.600625i
$796$	−28.6312	+	20.8018i	−1.01481	+	0.737301i
$797$	6.06197	−	18.6568i	0.214726	−	0.660858i	−0.784447	−	0.620196i	$-0.787053\pi$
$797$	6.06197	−	18.6568i	0.214726	−	0.660858i	0.999173	−	0.0406626i	$-0.0129469\pi$
$798$	11.6708	−	35.9189i	0.413141	−	1.27152i
$799$	0.899812	−	0.653751i	0.0318330	−	0.0231281i
$800$	2.97056	+	2.15824i	0.105025	+	0.0763052i
$801$	−30.1136	−	92.6802i	−1.06401	−	3.27469i
$802$	57.1001			2.01627
$803$	−53.3209	+	4.10067i	−1.88165	+	0.144709i
$804$	152.576			5.38095
$805$	−2.63325	−	8.10430i	−0.0928098	−	0.285639i
$806$	1.53491	+	1.11518i	0.0540650	+	0.0392805i
$807$	−54.3841	+	39.5124i	−1.91441	+	1.39090i
$808$	−11.6093	+	35.7298i	−0.408415	+	1.25697i
$809$	−0.371576	+	1.14359i	−0.0130639	+	0.0402066i	−0.957376	−	0.288845i	$-0.906729\pi$
$809$	−0.371576	+	1.14359i	−0.0130639	+	0.0402066i	0.944312	+	0.329051i	$0.106729\pi$
$810$	−31.5251	+	22.9043i	−1.10768	+	0.804775i
$811$	12.4418	+	9.03946i	0.436889	+	0.317418i	0.784398	−	0.620258i	$-0.212972\pi$
$811$	12.4418	+	9.03946i	0.436889	+	0.317418i	−0.347509	+	0.937677i	$0.612972\pi$
$812$	−4.75596	−	14.6373i	−0.166901	−	0.513670i
$813$	−13.6984			−0.480425
$814$	6.78240	+	16.4572i	0.237723	+	0.576825i
$815$	−12.1811			−0.426685
$816$	−1.56689	−	4.82238i	−0.0548520	−	0.168817i
$817$	5.71914	+	4.15520i	0.200087	+	0.145372i
$818$	33.2502	−	24.1577i	1.16257	−	0.844653i
$819$	−0.635161	+	1.95482i	−0.0221943	+	0.0683070i
$820$	−10.6345	+	32.7295i	−0.371372	+	1.14297i
$821$	29.6713	−	21.5575i	1.03553	−	0.752360i	0.0661260	−	0.997811i	$-0.478936\pi$
$821$	29.6713	−	21.5575i	1.03553	−	0.752360i	0.969409	+	0.245451i	$0.0789361\pi$
$822$	−89.9840	−	65.3772i	−3.13855	−	2.28029i
$823$	−12.9218	−	39.7692i	−0.450426	−	1.38627i	−0.876422	−	0.481543i	$-0.840076\pi$
$823$	−12.9218	−	39.7692i	−0.450426	−	1.38627i	0.425997	−	0.904725i	$-0.359924\pi$
$824$	68.0063			2.36911
$825$	−2.43805	+	10.0759i	−0.0848820	+	0.350798i
$826$	20.7842			0.723175
$827$	16.7038	+	51.4090i	0.580848	+	1.78767i	0.615339	+	0.788262i	$0.289019\pi$
$827$	16.7038	+	51.4090i	0.580848	+	1.78767i	−0.0344912	+	0.999405i	$0.510981\pi$
$828$	−166.292	−	120.818i	−5.77905	−	4.19872i
$829$	−21.6871	+	15.7566i	−0.753223	+	0.547248i	−0.896824	−	0.442387i	$-0.854132\pi$
$829$	−21.6871	+	15.7566i	−0.753223	+	0.547248i	0.143602	+	0.989636i	$0.454132\pi$
$830$	8.17289	−	25.1536i	0.283685	−	0.873093i
$831$	11.0561	−	34.0271i	0.383531	−	1.18039i
$832$	2.89824	−	2.10569i	0.100478	−	0.0730018i
$833$	0.836244	+	0.607567i	0.0289741	+	0.0210509i
$834$	−30.3599	−	93.4383i	−1.05128	−	3.23550i
$835$	8.44915			0.292395
$836$	−51.5618	−	31.7239i	−1.78330	−	1.09719i
$837$	−31.2184			−1.07907
$838$	13.1908	+	40.5971i	0.455668	+	1.40240i
$839$	−13.1776	−	9.57409i	−0.454941	−	0.330534i	0.336602	−	0.941647i	$-0.390722\pi$
$839$	−13.1776	−	9.57409i	−0.454941	−	0.330534i	−0.791544	+	0.611113i	$0.790722\pi$
$840$	9.32270	−	6.77334i	0.321664	−	0.233702i
$841$	−3.19594	+	9.83608i	−0.110205	+	0.339175i
$842$	14.1634	−	43.5906i	0.488104	−	1.50223i
$843$	−28.9890	+	21.0618i	−0.998436	+	0.725406i
$844$	49.4302	+	35.9132i	1.70146	+	1.23618i
$845$	−3.98874	−	12.2761i	−0.137217	−	0.422309i
$846$	17.1812			0.590703
$847$	9.78318	+	5.02886i	0.336154	+	0.172794i
$848$	−14.4664			−0.496779
$849$	−12.2478	−	37.6950i	−0.420345	−	1.29369i
$850$	1.97238	+	1.43302i	0.0676521	+	0.0491521i
$851$	15.6868	−	11.3971i	0.537736	−	0.390688i
$852$	−24.5854	+	75.6661i	−0.842282	+	2.59228i
$853$	−9.47123	+	29.1495i	−0.324289	+	0.998058i	0.647472	+	0.762089i	$0.275826\pi$
$853$	−9.47123	+	29.1495i	−0.324289	+	0.998058i	−0.971761	+	0.235969i	$0.924174\pi$
$854$	−20.1240	+	14.6209i	−0.688629	+	0.500318i
$855$	28.0576	+	20.3851i	0.959551	+	0.697155i
$856$	20.4151	+	62.8312i	0.697773	+	2.14753i
$857$	42.2735			1.44404			0.722018	−	0.691875i	$-0.243215\pi$
$857$	42.2735			1.44404			0.722018	+	0.691875i	$0.243215\pi$
$858$	6.32282	+	3.89017i	0.215857	+	0.132808i
$859$	−13.3365			−0.455036			−0.227518	−	0.973774i	$-0.573061\pi$
$859$	−13.3365			−0.455036			−0.227518	+	0.973774i	$0.573061\pi$
$860$	1.51938	+	4.67617i	0.0518104	+	0.159456i
$861$	−24.4235	−	17.7447i	−0.832352	−	0.604739i
$862$	−15.0902	+	10.9637i	−0.513973	+	0.373423i
$863$	−11.6729	+	35.9255i	−0.397350	+	1.22292i	0.529767	+	0.848143i	$0.322280\pi$
$863$	−11.6729	+	35.9255i	−0.397350	+	1.22292i	−0.927116	+	0.374774i	$0.877720\pi$
$864$	−13.3699	+	41.1484i	−0.454854	+	1.39990i
$865$	−7.16687	+	5.20704i	−0.243681	+	0.177045i
$866$	−34.8470	−	25.3178i	−1.18415	−	0.860334i
$867$	−15.3881	−	47.3596i	−0.522606	−	1.60842i
$868$	9.43999			0.320414
$869$	0.447258	−	1.84842i	0.0151722	−	0.0627033i
$870$	31.8442			1.07962
$871$	1.28535	+	3.95591i	0.0435525	+	0.134041i
$872$	−3.03696	−	2.20648i	−0.102844	−	0.0747209i
$873$	21.5932	−	15.6883i	0.730818	−	0.530970i
$874$	−31.8174	+	97.9240i	−1.07624	+	3.31233i
$875$	−0.309017	+	0.951057i	−0.0104467	+	0.0321516i
$876$	−145.281	+	105.553i	−4.90859	+	3.56630i
$877$	−7.03777	−	5.11324i	−0.237649	−	0.172662i	0.462586	−	0.886574i	$-0.346922\pi$
$877$	−7.03777	−	5.11324i	−0.237649	−	0.172662i	−0.700235	+	0.713912i	$0.746922\pi$
$878$	−17.9539	−	55.2565i	−0.605916	−	1.86482i
$879$	25.7958			0.870072
$880$	−1.98333	−	4.81247i	−0.0668581	−	0.162228i
$881$	−3.89312			−0.131163			−0.0655814	−	0.997847i	$-0.520890\pi$
$881$	−3.89312			−0.131163			−0.0655814	+	0.997847i	$0.520890\pi$
$882$	4.93422	+	15.1860i	0.166144	+	0.511338i
$883$	−36.5287	−	26.5397i	−1.22929	−	0.893130i	−0.232452	−	0.972608i	$-0.574675\pi$
$883$	−36.5287	−	26.5397i	−1.22929	−	0.893130i	−0.996837	+	0.0794775i	$0.974675\pi$
$884$	0.904654	−	0.657269i	0.0304268	−	0.0221064i
$885$	−8.51141	+	26.1954i	−0.286108	+	0.880549i
$886$	−12.1326	+	37.3403i	−0.407602	+	1.25447i
$887$	−12.6429	+	9.18557i	−0.424506	+	0.308421i	−0.779448	−	0.626467i	$-0.784500\pi$
$887$	−12.6429	+	9.18557i	−0.424506	+	0.308421i	0.354943	+	0.934888i	$0.384500\pi$
$888$	21.2133	+	15.4124i	0.711872	+	0.517205i
$889$	3.47693	+	10.7009i	0.116613	+	0.358897i
$890$	−33.9516			−1.13806
$891$	−54.6331	+	4.20159i	−1.83028	+	0.140758i
$892$	54.6321			1.82922
$893$	−1.70340	−	5.24252i	−0.0570021	−	0.175434i
$894$	−12.6901	−	9.21993i	−0.424422	−	0.308361i
$895$	−6.53911	+	4.75094i	−0.218578	+	0.158807i
$896$	6.33060	−	19.4836i	0.211491	−	0.650901i
$897$	2.49895	−	7.69099i	0.0834377	−	0.256795i
$898$	15.3766	−	11.1717i	0.513123	−	0.372806i
$899$	9.25832	+	6.72656i	0.308782	+	0.224343i
$900$	7.45395	+	22.9409i	0.248465	+	0.764697i
$901$	9.52797			0.317423
$902$	−57.5398	+	48.9662i	−1.91586	+	1.63040i
$903$	−4.31321			−0.143535
$904$	−2.04789	−	6.30275i	−0.0681118	−	0.209626i
$905$	1.09270	+	0.793894i	0.0363226	+	0.0263899i
$906$	93.9412	−	68.2523i	3.12099	−	2.26753i
$907$	7.08249	−	21.7977i	0.235170	−	0.723780i	−0.761929	−	0.647661i	$-0.775747\pi$
$907$	7.08249	−	21.7977i	0.235170	−	0.723780i	0.997099	−	0.0761184i	$-0.0242527\pi$
$908$	−2.22260	+	6.84046i	−0.0737595	+	0.227008i
$909$	55.8110	−	40.5490i	1.85113	−	1.34493i
$910$	0.579347	+	0.420920i	0.0192052	+	0.0139534i
$911$	12.3076	+	37.8789i	0.407769	+	1.25498i	0.918561	+	0.395279i	$0.129352\pi$
$911$	12.3076	+	37.8789i	0.407769	+	1.25498i	−0.510792	+	0.859704i	$0.670648\pi$
$912$	−25.1301			−0.832142
$913$	28.3229	−	24.1028i	0.937353	−	0.797685i
$914$	54.1803			1.79212
$915$	−10.1865	−	31.3508i	−0.336755	−	1.03643i
$916$	0.900251	+	0.654071i	0.0297451	+	0.0216111i
$917$	3.04128	−	2.20962i	0.100432	−	0.0729681i
$918$	−8.87731	+	27.3216i	−0.292995	+	0.901746i
$919$	3.07339	−	9.45891i	0.101382	−	0.312021i	−0.887483	−	0.460841i	$-0.847548\pi$
$919$	3.07339	−	9.45891i	0.101382	−	0.312021i	0.988864	+	0.148821i	$0.0475477\pi$
$920$	−25.4160	+	18.4658i	−0.837942	+	0.608800i
$921$	−4.46675	−	3.24528i	−0.147184	−	0.106936i
$922$	−10.9536	−	33.7118i	−0.360739	−	1.11024i
$923$	−2.16894			−0.0713917
$924$	36.8286	−	2.83232i	1.21157	−	0.0931766i
$925$	−2.27545			−0.0748162
$926$	−16.6955	−	51.3835i	−0.548649	−	1.68857i
$927$	−101.029	−	73.4016i	−3.31822	−	2.41082i
$928$	12.8312	−	9.32242i	0.421205	−	0.306023i
$929$	−16.1426	+	49.6817i	−0.529621	+	1.63001i	0.225373	+	0.974273i	$0.427640\pi$
$929$	−16.1426	+	49.6817i	−0.529621	+	1.63001i	−0.754993	+	0.655732i	$0.772360\pi$
$930$	−6.03572	+	18.5760i	−0.197919	+	0.609132i
$931$	4.14451	−	3.01116i	0.135831	−	0.0986869i
$932$	−50.1058	−	36.4040i	−1.64127	−	1.19245i
$933$	−4.36274	−	13.4271i	−0.142830	−	0.439585i
$934$	3.87339			0.126741
$935$	1.30628	+	3.16962i	0.0427198	+	0.103658i
$936$	7.57778			0.247687
$937$	−1.83600	−	5.65064i	−0.0599796	−	0.184598i	0.916577	−	0.399857i	$-0.130940\pi$
$937$	−1.83600	−	5.65064i	−0.0599796	−	0.184598i	−0.976557	+	0.215259i	$0.930940\pi$
$938$	26.1416	+	18.9930i	0.853554	+	0.620143i
$939$	15.9100	−	11.5593i	0.519203	−	0.377223i
$940$	1.18475	−	3.64629i	0.0386423	−	0.118929i
$941$	−4.87503	+	15.0038i	−0.158922	+	0.489110i	−0.998537	−	0.0540710i	$-0.982780\pi$
$941$	−4.87503	+	15.0038i	−0.158922	+	0.489110i	0.839616	+	0.543181i	$0.182780\pi$
$942$	50.8462	−	36.9420i	1.65666	−	1.20363i
$943$	66.5847	+	48.3766i	2.16830	+	1.57536i
$944$	−4.27360	−	13.1528i	−0.139094	−	0.428087i
$945$	−11.7833			−0.383310
$946$	−2.53872	+	10.4920i	−0.0825408	+	0.341123i
$947$	45.1583			1.46745			0.733723	−	0.679448i	$-0.237781\pi$
$947$	45.1583			1.46745			0.733723	+	0.679448i	$0.237781\pi$
$948$	−1.97338	−	6.07345i	−0.0640925	−	0.197256i
$949$	−3.96061	−	2.87755i	−0.128567	−	0.0934093i
$950$	9.77532	−	7.10219i	0.317153	−	0.230425i
$951$	3.57359	−	10.9984i	0.115882	−	0.356647i
$952$	1.17760	−	3.62429i	0.0381663	−	0.117464i
$953$	30.8103	−	22.3850i	0.998045	−	0.725122i	0.0363765	−	0.999338i	$-0.488418\pi$
$953$	30.8103	−	22.3850i	0.998045	−	0.725122i	0.961668	+	0.274216i	$0.0884184\pi$
$954$	119.074	+	86.5126i	3.85518	+	2.80095i
$955$	3.79835	+	11.6901i	0.122912	+	0.378283i
$956$	80.7324			2.61107
$957$	38.1381	+	23.4648i	1.23283	+	0.758510i
$958$	15.3467			0.495830
$959$	−4.66218	−	14.3487i	−0.150550	−	0.463344i
$960$	29.8370	+	21.6778i	0.962984	+	0.699649i
$961$	19.4008	−	14.0955i	0.625834	−	0.454695i
$962$	−0.503535	+	1.54972i	−0.0162346	+	0.0499651i
$963$	37.4877	−	115.375i	1.20802	−	3.71792i
$964$	−18.1185	+	13.1639i	−0.583559	+	0.423980i
$965$	15.0201	+	10.9127i	0.483513	+	0.351293i
$966$	−19.4130	−	59.7471i	−0.624604	−	1.92233i
$967$	15.4735			0.497593			0.248796	−	0.968556i	$-0.419965\pi$
$967$	15.4735			0.497593			0.248796	+	0.968556i	$0.419965\pi$
$968$	6.48703	−	40.0318i	0.208501	−	1.28667i
$969$	16.5514			0.531707
$970$	−2.87356	−	8.84392i	−0.0922645	−	0.283961i
$971$	−0.383323	−	0.278501i	−0.0123014	−	0.00893751i	0.581618	−	0.813462i	$-0.302420\pi$
$971$	−0.383323	−	0.278501i	−0.0123014	−	0.00893751i	−0.593919	+	0.804525i	$0.702420\pi$
$972$	−46.9573	+	34.1165i	−1.50616	+	1.09429i
$973$	4.11813	−	12.6743i	0.132021	−	0.406319i
$974$	22.6717	−	69.7764i	0.726449	−	2.23578i
$975$	−0.767758	+	0.557809i	−0.0245879	+	0.0178642i
$976$	13.3904	+	9.72867i	0.428615	+	0.311407i
$977$	−14.2640	−	43.8999i	−0.456344	−	1.40448i	−0.869550	−	0.493845i	$-0.835591\pi$
$977$	−14.2640	−	43.8999i	−0.456344	−	1.40448i	0.413206	−	0.910638i	$-0.364409\pi$
$978$	−89.8024			−2.87156
$979$	−40.6620	−	25.0177i	−1.29956	−	0.799568i
$980$	3.56309			0.113819
$981$	2.13011	+	6.55579i	0.0680091	+	0.209310i
$982$	36.7002	+	26.6642i	1.17115	+	0.850890i
$983$	41.6138	−	30.2342i	1.32727	−	0.964320i	0.327462	−	0.944864i	$-0.393806\pi$
$983$	41.6138	−	30.2342i	1.32727	−	0.964320i	0.999811	−	0.0194563i	$-0.00619351\pi$
$984$	−34.3933	+	105.852i	−1.09642	+	3.37443i
$985$	−3.97754	+	12.2416i	−0.126735	+	0.390050i
$986$	8.51962	−	6.18987i	0.271320	−	0.197126i
$987$	2.72095	+	1.97688i	0.0866086	+	0.0629249i
$988$	−1.71257	−	5.27073i	−0.0544840	−	0.167684i
$989$	11.7589			0.373911
$990$	−12.4547	+	51.4727i	−0.395838	+	1.63591i
$991$	28.7757			0.914091			0.457046	−	0.889443i	$-0.348908\pi$
$991$	28.7757			0.914091			0.457046	+	0.889443i	$0.348908\pi$
$992$	3.00613	+	9.25192i	0.0954448	+	0.293749i
$993$	52.3337	+	38.0226i	1.66076	+	1.20661i
$994$	−13.6314	+	9.90380i	−0.432362	+	0.314129i
$995$	3.06930	−	9.44632i	0.0973032	−	0.299468i
$996$	38.5912	−	118.771i	1.22281	−	3.76341i
$997$	−37.1743	+	27.0087i	−1.17732	+	0.855374i	−0.991867	−	0.127279i	$-0.959376\pi$
$997$	−37.1743	+	27.0087i	−1.17732	+	0.855374i	−0.185454	+	0.982653i	$0.559376\pi$
$998$	−23.7693	−	17.2694i	−0.752405	−	0.546654i
$999$	−8.28543	−	25.4999i	−0.262139	−	0.806782i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.n.f.71.8	✓	36
11.3	even	5		4235.2.a.bo.1.16		18
11.8	odd	10		4235.2.a.bp.1.3		18
11.9	even	5	inner	385.2.n.f.141.8	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.f.71.8	✓	36	1.1	even	1	trivial
385.2.n.f.141.8	yes	36	11.9	even	5	inner
4235.2.a.bo.1.16		18	11.3	even	5
4235.2.a.bp.1.3		18	11.8	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.728853 + 2.24318i) q^{2} +(-2.52872 - 1.83722i) q^{3} +(-2.88260 + 2.09433i) q^{4} +(0.309017 - 0.951057i) q^{5} +(2.27816 - 7.01145i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-2.98262 - 2.16700i) q^{8} +(2.09199 + 6.43850i) q^{9} +O(q^{10})\)	\(q+(0.728853 + 2.24318i) q^{2} +(-2.52872 - 1.83722i) q^{3} +(-2.88260 + 2.09433i) q^{4} +(0.309017 - 0.951057i) q^{5} +(2.27816 - 7.01145i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-2.98262 - 2.16700i) q^{8} +(2.09199 + 6.43850i) q^{9} +2.35862 q^{10} +(2.82479 + 1.73798i) q^{11} +11.1370 q^{12} +(0.0938222 + 0.288755i) q^{13} +(1.90816 + 1.38636i) q^{14} +(-2.52872 + 1.83722i) q^{15} +(0.484974 - 1.49260i) q^{16} +(-0.319417 + 0.983064i) q^{17} +(-12.9179 + 9.38544i) q^{18} +(4.14451 + 3.01116i) q^{19} +(1.10105 + 3.38870i) q^{20} -3.12567 q^{21} +(-1.83974 + 7.60324i) q^{22} +8.52137 q^{23} +(3.56096 + 10.9595i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-0.579347 + 0.420920i) q^{26} +(3.64123 - 11.2066i) q^{27} +(-1.10105 + 3.38870i) q^{28} +(-3.49452 + 2.53891i) q^{29} +(-5.96430 - 4.33331i) q^{30} +(-0.818705 - 2.51972i) q^{31} -3.67181 q^{32} +(-3.95005 - 9.58464i) q^{33} -2.43800 q^{34} +(-0.309017 - 0.951057i) q^{35} +(-19.5147 - 14.1783i) q^{36} +(1.84087 - 1.33747i) q^{37} +(-3.73384 + 11.4916i) q^{38} +(0.293257 - 0.902554i) q^{39} +(-2.98262 + 2.16700i) q^{40} +(7.81385 + 5.67709i) q^{41} +(-2.27816 - 7.01145i) q^{42} +1.37993 q^{43} +(-11.7826 + 0.906148i) q^{44} +6.76983 q^{45} +(6.21083 + 19.1150i) q^{46} +(-0.870515 - 0.632466i) q^{47} +(-3.96860 + 2.88336i) q^{48} +(0.309017 - 0.951057i) q^{49} +(0.728853 - 2.24318i) q^{50} +(2.61383 - 1.89906i) q^{51} +(-0.875199 - 0.635870i) q^{52} +(-2.84844 - 8.76660i) q^{53} +27.7923 q^{54} +(2.52582 - 2.14947i) q^{55} -3.68672 q^{56} +(-4.94813 - 15.2288i) q^{57} +(-8.24223 - 5.98833i) q^{58} +(7.12907 - 5.17958i) q^{59} +(3.44154 - 10.5920i) q^{60} +(-3.25898 + 10.0301i) q^{61} +(5.05546 - 3.67301i) q^{62} +(5.47691 + 3.97921i) q^{63} +(-3.64616 - 11.2217i) q^{64} +0.303615 q^{65} +(18.6211 - 15.8465i) q^{66} +13.6999 q^{67} +(-1.13811 - 3.50274i) q^{68} +(-21.5482 - 15.6557i) q^{69} +(1.90816 - 1.38636i) q^{70} +(-2.20753 + 6.79409i) q^{71} +(7.71260 - 23.7370i) q^{72} +(-13.0449 + 9.47764i) q^{73} +(4.34192 + 3.15459i) q^{74} +(0.965886 + 2.97269i) q^{75} -18.2533 q^{76} +(3.30686 - 0.254316i) q^{77} +2.23833 q^{78} +(-0.177191 - 0.545338i) q^{79} +(-1.26968 - 0.922475i) q^{80} +(-13.3659 + 9.71089i) q^{81} +(-7.03959 + 21.6656i) q^{82} +(3.46512 - 10.6645i) q^{83} +(9.01006 - 6.54619i) q^{84} +(0.836244 + 0.607567i) q^{85} +(1.00577 + 3.09543i) q^{86} +13.5012 q^{87} +(-4.65908 - 11.3051i) q^{88} -14.3947 q^{89} +(4.93422 + 15.1860i) q^{90} +(0.245630 + 0.178460i) q^{91} +(-24.5637 + 17.8465i) q^{92} +(-2.55901 + 7.87581i) q^{93} +(0.784258 - 2.41370i) q^{94} +(4.14451 - 3.01116i) q^{95} +(9.28499 + 6.74594i) q^{96} +(-1.21832 - 3.74962i) q^{97} +2.35862 q^{98} +(-5.28052 + 21.8232i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + q^{2} - 17 q^{4} - 9 q^{5} - 13 q^{6} + 9 q^{7} + 3 q^{8} - 11 q^{9}+O(q^{10}) \) 36 * q + q^2 - 17 * q^4 - 9 * q^5 - 13 * q^6 + 9 * q^7 + 3 * q^8 - 11 * q^9	\( 36 q + q^{2} - 17 q^{4} - 9 q^{5} - 13 q^{6} + 9 q^{7} + 3 q^{8} - 11 q^{9} - 4 q^{10} - 3 q^{11} + 30 q^{12} - q^{13} - q^{14} + 3 q^{16} + 5 q^{17} - 34 q^{18} - 5 q^{19} - 7 q^{20} - 10 q^{21} - 5 q^{22} + 8 q^{23} - 41 q^{24} - 9 q^{25} + 28 q^{26} + 7 q^{28} - 33 q^{29} + 12 q^{30} - q^{31} + 12 q^{32} - 14 q^{33} + 88 q^{34} + 9 q^{35} - 104 q^{36} - 18 q^{37} - 27 q^{38} + 6 q^{39} + 3 q^{40} + 36 q^{41} + 13 q^{42} - 20 q^{43} - 30 q^{44} + 74 q^{45} + 20 q^{46} - 7 q^{47} + 75 q^{48} - 9 q^{49} + q^{50} + 22 q^{51} - 6 q^{52} - 4 q^{53} - 26 q^{54} - 3 q^{55} + 12 q^{56} - 43 q^{57} - 41 q^{58} + 25 q^{59} - 15 q^{60} + 21 q^{61} + 31 q^{62} + 26 q^{63} + 43 q^{64} - 16 q^{65} - 12 q^{66} + 58 q^{67} - 43 q^{68} - 37 q^{69} - q^{70} - 29 q^{71} + 34 q^{72} + 19 q^{73} - 59 q^{74} - 5 q^{75} - 94 q^{76} + 3 q^{77} + 20 q^{78} + 11 q^{79} - 47 q^{80} - 10 q^{81} - 58 q^{82} + 47 q^{83} - 10 q^{85} + 35 q^{86} - 46 q^{87} - 110 q^{88} + 118 q^{89} + 36 q^{90} - 9 q^{91} + 107 q^{92} - 29 q^{93} - 27 q^{94} - 5 q^{95} + 67 q^{96} - 4 q^{98} + 16 q^{99}+O(q^{100}) \) 36 * q + q^2 - 17 * q^4 - 9 * q^5 - 13 * q^6 + 9 * q^7 + 3 * q^8 - 11 * q^9 - 4 * q^10 - 3 * q^11 + 30 * q^12 - q^13 - q^14 + 3 * q^16 + 5 * q^17 - 34 * q^18 - 5 * q^19 - 7 * q^20 - 10 * q^21 - 5 * q^22 + 8 * q^23 - 41 * q^24 - 9 * q^25 + 28 * q^26 + 7 * q^28 - 33 * q^29 + 12 * q^30 - q^31 + 12 * q^32 - 14 * q^33 + 88 * q^34 + 9 * q^35 - 104 * q^36 - 18 * q^37 - 27 * q^38 + 6 * q^39 + 3 * q^40 + 36 * q^41 + 13 * q^42 - 20 * q^43 - 30 * q^44 + 74 * q^45 + 20 * q^46 - 7 * q^47 + 75 * q^48 - 9 * q^49 + q^50 + 22 * q^51 - 6 * q^52 - 4 * q^53 - 26 * q^54 - 3 * q^55 + 12 * q^56 - 43 * q^57 - 41 * q^58 + 25 * q^59 - 15 * q^60 + 21 * q^61 + 31 * q^62 + 26 * q^63 + 43 * q^64 - 16 * q^65 - 12 * q^66 + 58 * q^67 - 43 * q^68 - 37 * q^69 - q^70 - 29 * q^71 + 34 * q^72 + 19 * q^73 - 59 * q^74 - 5 * q^75 - 94 * q^76 + 3 * q^77 + 20 * q^78 + 11 * q^79 - 47 * q^80 - 10 * q^81 - 58 * q^82 + 47 * q^83 - 10 * q^85 + 35 * q^86 - 46 * q^87 - 110 * q^88 + 118 * q^89 + 36 * q^90 - 9 * q^91 + 107 * q^92 - 29 * q^93 - 27 * q^94 - 5 * q^95 + 67 * q^96 - 4 * q^98 + 16 * q^99

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