LMFDB - Embedded newform 418.2.f.h.267.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(115,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("418.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.f (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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 11 x^{18} - 3 x^{17} + 103 x^{16} + 50 x^{15} + 1002 x^{14} + 1120 x^{13} + \cdots + 1936 $ x^20 - x^19 + 11x^18 - 3x^17 + 103x^16 + 50x^15 + 1002x^14 + 1120x^13 + 7288x^12 + 5704x^11 + 24392x^10 + 10376x^9 + 48880x^8 + 21224x^7 + 77528x^6 + 44616x^5 + 147848x^4 + 67728x^3 + 115472x^2 - 24464x + 1936
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			267.4
Root			$1.12827 + 0.819735i$ of defining polynomial
Character	$\chi$	$=$	418.267
Dual form			418.2.f.h.191.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.430960 + 1.32636i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.74807 - 1.27005i) q^{5} +(1.12827 + 0.819735i) q^{6} +(0.365332 - 1.12438i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.853548 - 0.620139i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.430960 + 1.32636i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.74807 - 1.27005i) q^{5} +(1.12827 + 0.819735i) q^{6} +(0.365332 - 1.12438i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.853548 - 0.620139i) q^{9} -2.16074 q^{10} +(2.62340 + 2.02923i) q^{11} +1.39462 q^{12} +(5.04783 - 3.66746i) q^{13} +(-0.365332 - 1.12438i) q^{14} +(0.931193 - 2.86592i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.63994 + 1.19149i) q^{17} +(0.326026 - 1.00341i) q^{18} +(-0.309017 - 0.951057i) q^{19} +(-1.74807 + 1.27005i) q^{20} +1.64877 q^{21} +(3.31513 + 0.0996822i) q^{22} -3.76597 q^{23} +(1.12827 - 0.819735i) q^{24} +(-0.102349 - 0.314998i) q^{25} +(1.92810 - 5.93408i) q^{26} +(4.57518 + 3.32406i) q^{27} +(-0.956453 - 0.694903i) q^{28} +(-1.07170 + 3.29836i) q^{29} +(-0.931193 - 2.86592i) q^{30} +(-6.52635 + 4.74167i) q^{31} -1.00000 q^{32} +(-1.56090 + 4.35409i) q^{33} +2.02708 q^{34} +(-2.06664 + 1.50150i) q^{35} +(-0.326026 - 1.00341i) q^{36} +(1.55525 - 4.78658i) q^{37} +(-0.809017 - 0.587785i) q^{38} +(7.03979 + 5.11471i) q^{39} +(-0.667705 + 2.05498i) q^{40} +(0.739397 + 2.27563i) q^{41} +(1.33388 - 0.969124i) q^{42} -7.95696 q^{43} +(2.74059 - 1.86794i) q^{44} -2.27967 q^{45} +(-3.04674 + 2.21358i) q^{46} +(0.939466 + 2.89138i) q^{47} +(0.430960 - 1.32636i) q^{48} +(4.53236 + 3.29295i) q^{49} +(-0.267954 - 0.194680i) q^{50} +(-0.873592 + 2.68864i) q^{51} +(-1.92810 - 5.93408i) q^{52} +(0.912310 - 0.662832i) q^{53} +5.65523 q^{54} +(-2.00868 - 6.87909i) q^{55} -1.18224 q^{56} +(1.12827 - 0.819735i) q^{57} +(1.07170 + 3.29836i) q^{58} +(-0.756843 + 2.32932i) q^{59} +(-2.43789 - 1.77123i) q^{60} +(-9.11117 - 6.61965i) q^{61} +(-2.49284 + 7.67219i) q^{62} +(-0.385442 - 1.18627i) q^{63} +(-0.809017 + 0.587785i) q^{64} -13.4819 q^{65} +(1.29647 + 4.44001i) q^{66} -10.1426 q^{67} +(1.63994 - 1.19149i) q^{68} +(-1.62299 - 4.99504i) q^{69} +(-0.789388 + 2.42949i) q^{70} +(-0.469640 - 0.341214i) q^{71} +(-0.853548 - 0.620139i) q^{72} +(-2.55072 + 7.85030i) q^{73} +(-1.55525 - 4.78658i) q^{74} +(0.373693 - 0.271504i) q^{75} -1.00000 q^{76} +(3.24003 - 2.20835i) q^{77} +8.70166 q^{78} +(5.48214 - 3.98301i) q^{79} +(0.667705 + 2.05498i) q^{80} +(-1.45910 + 4.49065i) q^{81} +(1.93577 + 1.40642i) q^{82} +(14.3960 + 10.4593i) q^{83} +(0.509499 - 1.56808i) q^{84} +(-1.35349 - 4.16562i) q^{85} +(-6.43731 + 4.67698i) q^{86} -4.83667 q^{87} +(1.11923 - 3.12207i) q^{88} +5.72864 q^{89} +(-1.84429 + 1.33996i) q^{90} +(-2.27948 - 7.01551i) q^{91} +(-1.16375 + 3.58165i) q^{92} +(-9.10176 - 6.61282i) q^{93} +(2.45955 + 1.78697i) q^{94} +(-0.667705 + 2.05498i) q^{95} +(-0.430960 - 1.32636i) q^{96} +(2.07419 - 1.50699i) q^{97} +5.60231 q^{98} +(3.49760 + 0.105169i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9}+O(q^{10}) $ 20 * q + 5 * q^2 - q^3 - 5 * q^4 - q^5 + q^6 + 13 * q^7 + 5 * q^8 - 6 * q^9	\( 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9} + 6 q^{10} + q^{11} + 4 q^{12} - 2 q^{13} - 13 q^{14} - 8 q^{15} - 5 q^{16} + 11 q^{17} + 6 q^{18} + 5 q^{19} - q^{20} + 2 q^{21} + 4 q^{22} + 28 q^{23} + q^{24} - 30 q^{25} - 13 q^{26} - 31 q^{27} - 2 q^{28} + 28 q^{29} + 8 q^{30} - q^{31} - 20 q^{32} + 9 q^{33} + 24 q^{34} - 11 q^{35} - 6 q^{36} + 8 q^{37} - 5 q^{38} + 18 q^{39} - 4 q^{40} - 5 q^{41} - 22 q^{42} - 44 q^{43} + 11 q^{44} - 4 q^{45} + 7 q^{46} - 39 q^{47} - q^{48} + 4 q^{49} - 25 q^{50} - 11 q^{51} + 13 q^{52} - q^{53} - 4 q^{54} + 8 q^{55} + 22 q^{56} + q^{57} - 28 q^{58} + 6 q^{59} + 7 q^{60} + 10 q^{61} + 11 q^{62} + 34 q^{63} - 5 q^{64} - 8 q^{65} + 41 q^{66} + 18 q^{67} + 11 q^{68} - 63 q^{69} + q^{70} - 3 q^{71} + 6 q^{72} + 5 q^{73} - 8 q^{74} + 5 q^{75} - 20 q^{76} + 36 q^{77} + 22 q^{78} + 19 q^{79} + 4 q^{80} + 63 q^{81} - 9 q^{83} - 23 q^{84} + 30 q^{85} - 26 q^{86} - 16 q^{87} - q^{88} + 44 q^{89} + 14 q^{90} - 68 q^{91} - 7 q^{92} + 27 q^{93} - 31 q^{94} - 4 q^{95} + q^{96} - 71 q^{97} + 6 q^{98} + 20 q^{99}+O(q^{100}) \) 20 * q + 5 * q^2 - q^3 - 5 * q^4 - q^5 + q^6 + 13 * q^7 + 5 * q^8 - 6 * q^9 + 6 * q^10 + q^11 + 4 * q^12 - 2 * q^13 - 13 * q^14 - 8 * q^15 - 5 * q^16 + 11 * q^17 + 6 * q^18 + 5 * q^19 - q^20 + 2 * q^21 + 4 * q^22 + 28 * q^23 + q^24 - 30 * q^25 - 13 * q^26 - 31 * q^27 - 2 * q^28 + 28 * q^29 + 8 * q^30 - q^31 - 20 * q^32 + 9 * q^33 + 24 * q^34 - 11 * q^35 - 6 * q^36 + 8 * q^37 - 5 * q^38 + 18 * q^39 - 4 * q^40 - 5 * q^41 - 22 * q^42 - 44 * q^43 + 11 * q^44 - 4 * q^45 + 7 * q^46 - 39 * q^47 - q^48 + 4 * q^49 - 25 * q^50 - 11 * q^51 + 13 * q^52 - q^53 - 4 * q^54 + 8 * q^55 + 22 * q^56 + q^57 - 28 * q^58 + 6 * q^59 + 7 * q^60 + 10 * q^61 + 11 * q^62 + 34 * q^63 - 5 * q^64 - 8 * q^65 + 41 * q^66 + 18 * q^67 + 11 * q^68 - 63 * q^69 + q^70 - 3 * q^71 + 6 * q^72 + 5 * q^73 - 8 * q^74 + 5 * q^75 - 20 * q^76 + 36 * q^77 + 22 * q^78 + 19 * q^79 + 4 * q^80 + 63 * q^81 - 9 * q^83 - 23 * q^84 + 30 * q^85 - 26 * q^86 - 16 * q^87 - q^88 + 44 * q^89 + 14 * q^90 - 68 * q^91 - 7 * q^92 + 27 * q^93 - 31 * q^94 - 4 * q^95 + q^96 - 71 * q^97 + 6 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	0.430960	+	1.32636i	0.248815	+	0.765774i	0.994986	+	0.100019i	$0.0318904\pi$
$3$	0.430960	+	1.32636i	0.248815	+	0.765774i	−0.746170	+	0.665755i	$0.768110\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−1.74807	−	1.27005i	−0.781763	−	0.567984i	0.123745	−	0.992314i	$-0.460510\pi$
$5$	−1.74807	−	1.27005i	−0.781763	−	0.567984i	−0.905507	+	0.424330i	$0.860510\pi$
$6$	1.12827	+	0.819735i	0.460614	+	0.334656i
$7$	0.365332	−	1.12438i	0.138083	−	0.424975i	−0.857974	−	0.513693i	$-0.828277\pi$
$7$	0.365332	−	1.12438i	0.138083	−	0.424975i	0.996057	+	0.0887182i	$0.0282771\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	0.853548	−	0.620139i	0.284516	−	0.206713i
$10$	−2.16074			−0.683286
$11$	2.62340	+	2.02923i	0.790985	+	0.611835i
$11$	2.62340	+	2.02923i	0.790985	+	0.611835i
$12$	1.39462			0.402591
$13$	5.04783	−	3.66746i	1.40002	−	1.01717i	0.405336	−	0.914168i	$-0.367155\pi$
$13$	5.04783	−	3.66746i	1.40002	−	1.01717i	0.994681	−	0.103004i	$-0.0328454\pi$
$14$	−0.365332	−	1.12438i	−0.0976392	−	0.300502i
$15$	0.931193	−	2.86592i	0.240433	−	0.739976i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	1.63994	+	1.19149i	0.397745	+	0.288979i	0.768622	−	0.639703i	$-0.220943\pi$
$17$	1.63994	+	1.19149i	0.397745	+	0.288979i	−0.370877	+	0.928682i	$0.620943\pi$
$18$	0.326026	−	1.00341i	0.0768452	−	0.236505i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$20$	−1.74807	+	1.27005i	−0.390881	+	0.283992i
$21$	1.64877			0.359792
$22$	3.31513	+	0.0996822i	0.706787	+	0.0212523i
$23$	−3.76597			−0.785260			−0.392630	−	0.919697i	$-0.628435\pi$
$23$	−3.76597			−0.785260			−0.392630	+	0.919697i	$0.628435\pi$
$24$	1.12827	−	0.819735i	0.230307	−	0.167328i
$25$	−0.102349	−	0.314998i	−0.0204698	−	0.0629997i
$26$	1.92810	−	5.93408i	0.378132	−	1.16377i
$27$	4.57518	+	3.32406i	0.880494	+	0.639716i
$28$	−0.956453	−	0.694903i	−0.180753	−	0.131324i
$29$	−1.07170	+	3.29836i	−0.199010	+	0.612490i	0.800896	+	0.598803i	$0.204357\pi$
$29$	−1.07170	+	3.29836i	−0.199010	+	0.612490i	−0.999906	+	0.0136867i	$0.995643\pi$
$30$	−0.931193	−	2.86592i	−0.170012	−	0.523242i
$31$	−6.52635	+	4.74167i	−1.17217	+	0.851630i	−0.991267	−	0.131872i	$-0.957901\pi$
$31$	−6.52635	+	4.74167i	−1.17217	+	0.851630i	−0.180901	+	0.983501i	$0.557901\pi$
$32$	−1.00000			−0.176777
$33$	−1.56090	+	4.35409i	−0.271718	+	0.757950i
$34$	2.02708			0.347642
$35$	−2.06664	+	1.50150i	−0.349327	+	0.253801i
$36$	−0.326026	−	1.00341i	−0.0543377	−	0.167234i
$37$	1.55525	−	4.78658i	0.255682	−	0.786908i	−0.738013	−	0.674787i	$-0.764235\pi$
$37$	1.55525	−	4.78658i	0.255682	−	0.786908i	0.993695	−	0.112121i	$-0.0357645\pi$
$38$	−0.809017	−	0.587785i	−0.131240	−	0.0953514i
$39$	7.03979	+	5.11471i	1.12727	+	0.819009i
$40$	−0.667705	+	2.05498i	−0.105573	+	0.324922i
$41$	0.739397	+	2.27563i	0.115474	+	0.355394i	0.992046	−	0.125878i	$-0.0401749\pi$
$41$	0.739397	+	2.27563i	0.115474	+	0.355394i	−0.876571	+	0.481272i	$0.840175\pi$
$42$	1.33388	−	0.969124i	0.205823	−	0.149539i
$43$	−7.95696			−1.21342			−0.606712	−	0.794921i	$-0.707512\pi$
$43$	−7.95696			−1.21342			−0.606712	+	0.794921i	$0.707512\pi$
$44$	2.74059	−	1.86794i	0.413159	−	0.281602i
$45$	−2.27967			−0.339834
$46$	−3.04674	+	2.21358i	−0.449217	+	0.326375i
$47$	0.939466	+	2.89138i	0.137035	+	0.421751i	0.995901	−	0.0904496i	$-0.0288304\pi$
$47$	0.939466	+	2.89138i	0.137035	+	0.421751i	−0.858866	+	0.512201i	$0.828830\pi$
$48$	0.430960	−	1.32636i	0.0622038	−	0.191444i
$49$	4.53236	+	3.29295i	0.647480	+	0.470422i
$50$	−0.267954	−	0.194680i	−0.0378944	−	0.0275319i
$51$	−0.873592	+	2.68864i	−0.122327	+	0.376485i
$52$	−1.92810	−	5.93408i	−0.267379	−	0.822909i
$53$	0.912310	−	0.662832i	0.125315	−	0.0910470i	−0.523362	−	0.852110i	$-0.675322\pi$
$53$	0.912310	−	0.662832i	0.125315	−	0.0910470i	0.648677	+	0.761063i	$0.275322\pi$
$54$	5.65523			0.769580
$55$	−2.00868	−	6.87909i	−0.270850	−	0.927577i
$56$	−1.18224			−0.157984
$57$	1.12827	−	0.819735i	0.149443	−	0.108577i
$58$	1.07170	+	3.29836i	0.140721	+	0.433096i
$59$	−0.756843	+	2.32932i	−0.0985326	+	0.303252i	−0.988158	−	0.153438i	$-0.950965\pi$
$59$	−0.756843	+	2.32932i	−0.0985326	+	0.303252i	0.889626	+	0.456691i	$0.150965\pi$
$60$	−2.43789	−	1.77123i	−0.314731	−	0.228665i
$61$	−9.11117	−	6.61965i	−1.16657	−	0.847559i	−0.175972	−	0.984395i	$-0.556307\pi$
$61$	−9.11117	−	6.61965i	−1.16657	−	0.847559i	−0.990594	+	0.136836i	$0.956307\pi$
$62$	−2.49284	+	7.67219i	−0.316592	+	0.974369i
$63$	−0.385442	−	1.18627i	−0.0485611	−	0.149456i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−13.4819			−1.67222
$66$	1.29647	+	4.44001i	0.159585	+	0.546527i
$67$	−10.1426			−1.23911			−0.619557	−	0.784952i	$-0.712688\pi$
$67$	−10.1426			−1.23911			−0.619557	+	0.784952i	$0.712688\pi$
$68$	1.63994	−	1.19149i	0.198872	−	0.144489i
$69$	−1.62299	−	4.99504i	−0.195385	−	0.601332i
$70$	−0.789388	+	2.42949i	−0.0943499	+	0.290379i
$71$	−0.469640	−	0.341214i	−0.0557360	−	0.0404946i	0.559568	−	0.828784i	$-0.310967\pi$
$71$	−0.469640	−	0.341214i	−0.0557360	−	0.0404946i	−0.615304	+	0.788290i	$0.710967\pi$
$72$	−0.853548	−	0.620139i	−0.100592	−	0.0730841i
$73$	−2.55072	+	7.85030i	−0.298539	+	0.918808i	0.683471	+	0.729978i	$0.260470\pi$
$73$	−2.55072	+	7.85030i	−0.298539	+	0.918808i	−0.982010	+	0.188831i	$0.939530\pi$
$74$	−1.55525	−	4.78658i	−0.180794	−	0.556428i
$75$	0.373693	−	0.271504i	0.0431503	−	0.0313505i
$76$	−1.00000			−0.114708
$77$	3.24003	−	2.20835i	0.369236	−	0.251665i
$78$	8.70166			0.985269
$79$	5.48214	−	3.98301i	0.616789	−	0.448123i	−0.235009	−	0.971993i	$-0.575512\pi$
$79$	5.48214	−	3.98301i	0.616789	−	0.448123i	0.851798	+	0.523870i	$0.175512\pi$
$80$	0.667705	+	2.05498i	0.0746517	+	0.229754i
$81$	−1.45910	+	4.49065i	−0.162122	+	0.498961i
$82$	1.93577	+	1.40642i	0.213770	+	0.155313i
$83$	14.3960	+	10.4593i	1.58017	+	1.14806i	0.916503	+	0.400028i	$0.130999\pi$
$83$	14.3960	+	10.4593i	1.58017	+	1.14806i	0.663664	+	0.748031i	$0.269001\pi$
$84$	0.509499	−	1.56808i	0.0555909	−	0.171091i
$85$	−1.35349	−	4.16562i	−0.146807	−	0.451825i
$86$	−6.43731	+	4.67698i	−0.694154	+	0.504332i
$87$	−4.83667			−0.518545
$88$	1.11923	−	3.12207i	0.119311	−	0.332814i
$89$	5.72864			0.607235			0.303618	−	0.952794i	$-0.401806\pi$
$89$	5.72864			0.607235			0.303618	+	0.952794i	$0.401806\pi$
$90$	−1.84429	+	1.33996i	−0.194406	+	0.141244i
$91$	−2.27948	−	7.01551i	−0.238954	−	0.735426i
$92$	−1.16375	+	3.58165i	−0.121329	+	0.373413i
$93$	−9.10176	−	6.61282i	−0.943809	−	0.685717i
$94$	2.45955	+	1.78697i	0.253684	+	0.184312i
$95$	−0.667705	+	2.05498i	−0.0685051	+	0.210837i
$96$	−0.430960	−	1.32636i	−0.0439847	−	0.135371i
$97$	2.07419	−	1.50699i	0.210603	−	0.153012i	−0.477484	−	0.878641i	$-0.658451\pi$
$97$	2.07419	−	1.50699i	0.210603	−	0.153012i	0.688086	+	0.725629i	$0.258451\pi$
$98$	5.60231			0.565919
$99$	3.49760	+	0.105169i	0.351522	+	0.0105699i
$100$	−0.331209			−0.0331209
$101$	−9.41298	+	6.83893i	−0.936627	+	0.680499i	−0.947606	−	0.319441i	$-0.896505\pi$
$101$	−9.41298	+	6.83893i	−0.936627	+	0.680499i	0.0109795	+	0.999940i	$0.496505\pi$
$102$	0.873592	+	2.68864i	0.0864985	+	0.266215i
$103$	1.27959	−	3.93818i	0.126082	−	0.388040i	−0.868015	−	0.496538i	$-0.834604\pi$
$103$	1.27959	−	3.93818i	0.126082	−	0.388040i	0.994097	+	0.108498i	$0.0346042\pi$
$104$	−5.04783	−	3.66746i	−0.494981	−	0.359625i
$105$	−2.88218	−	2.09402i	−0.281272	−	0.204356i
$106$	0.348471	−	1.07248i	0.0338465	−	0.104169i
$107$	4.20098	+	12.9293i	0.406124	+	1.24992i	0.919953	+	0.392029i	$0.128227\pi$
$107$	4.20098	+	12.9293i	0.406124	+	1.24992i	−0.513828	+	0.857893i	$0.671773\pi$
$108$	4.57518	−	3.32406i	0.440247	−	0.319858i
$109$	−6.51990			−0.624493			−0.312247	−	0.950001i	$-0.601082\pi$
$109$	−6.51990			−0.624493			−0.312247	+	0.950001i	$0.601082\pi$
$110$	−5.66849	−	4.38463i	−0.540469	−	0.418058i
$111$	7.01897			0.666211
$112$	−0.956453	+	0.694903i	−0.0903763	+	0.0656622i
$113$	−4.39444	−	13.5247i	−0.413394	−	1.27230i	−0.913680	−	0.406435i	$-0.866772\pi$
$113$	−4.39444	−	13.5247i	−0.413394	−	1.27230i	0.500286	−	0.865860i	$-0.333228\pi$
$114$	0.430960	−	1.32636i	0.0403631	−	0.124225i
$115$	6.58320	+	4.78298i	0.613887	+	0.446015i
$116$	2.80575	+	2.03850i	0.260507	+	0.189270i
$117$	2.03423	−	6.26072i	0.188065	−	0.578803i
$118$	0.756843	+	2.32932i	0.0696731	+	0.214432i
$119$	1.93881	−	1.40863i	0.177730	−	0.129129i
$120$	−3.01340			−0.275085
$121$	2.76448	+	10.6470i	0.251316	+	0.967905i
$122$	−11.2620			−1.01962
$123$	−2.69965	+	1.96141i	−0.243419	+	0.176855i
$124$	2.49284	+	7.67219i	0.223864	+	0.688983i
$125$	−3.55967	+	10.9556i	−0.318387	+	0.979894i
$126$	−1.00910	−	0.733154i	−0.0898977	−	0.0653145i
$127$	16.3482	+	11.8776i	1.45067	+	1.05397i	0.985675	+	0.168654i	$0.0539420\pi$
$127$	16.3482	+	11.8776i	1.45067	+	1.05397i	0.464990	+	0.885316i	$0.346058\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	−3.42913	−	10.5538i	−0.301918	−	0.929209i
$130$	−10.9070	+	7.92443i	−0.956611	+	0.695019i
$131$	−10.4556			−0.913510			−0.456755	−	0.889593i	$-0.650988\pi$
$131$	−10.4556			−0.913510			−0.456755	+	0.889593i	$0.650988\pi$
$132$	3.65864	+	2.82999i	0.318444	+	0.246319i
$133$	−1.18224			−0.102513
$134$	−8.20552	+	5.96166i	−0.708849	+	0.515009i
$135$	−3.77603	−	11.6214i	−0.324989	−	1.00021i
$136$	0.626403	−	1.92787i	0.0537136	−	0.165314i
$137$	15.5444	+	11.2937i	1.32805	+	0.964883i	0.999794	+	0.0202935i	$0.00646007\pi$
$137$	15.5444	+	11.2937i	1.32805	+	0.964883i	0.328254	+	0.944590i	$0.393540\pi$
$138$	−4.24903	−	3.08710i	−0.361702	−	0.262792i
$139$	−4.63178	+	14.2552i	−0.392862	+	1.20911i	0.537751	+	0.843104i	$0.319274\pi$
$139$	−4.63178	+	14.2552i	−0.392862	+	1.20911i	−0.930614	+	0.366003i	$0.880726\pi$
$140$	0.789388	+	2.42949i	0.0667154	+	0.205329i
$141$	−3.43014	+	2.49214i	−0.288870	+	0.209876i
$142$	−0.580507			−0.0487151
$143$	20.6846	+	0.621963i	1.72973	+	0.0520112i
$144$	−1.05504			−0.0879203
$145$	6.06249	−	4.40466i	0.503463	−	0.365787i
$146$	2.55072	+	7.85030i	0.211099	+	0.649696i
$147$	−2.41437	+	7.43067i	−0.199134	+	0.612872i
$148$	−4.07170	−	2.95827i	−0.334692	−	0.243168i
$149$	−6.62303	−	4.81191i	−0.542580	−	0.394207i	0.282463	−	0.959278i	$-0.408849\pi$
$149$	−6.62303	−	4.81191i	−0.542580	−	0.394207i	−0.825042	+	0.565071i	$0.808849\pi$
$150$	0.142738	−	0.439302i	0.0116545	−	0.0358689i
$151$	−0.0807026	−	0.248377i	−0.00656748	−	0.0202126i	0.947719	−	0.319106i	$-0.103383\pi$
$151$	−0.0807026	−	0.248377i	−0.00656748	−	0.0202126i	−0.954287	+	0.298893i	$0.903383\pi$
$152$	−0.809017	+	0.587785i	−0.0656199	+	0.0476757i
$153$	2.13866			0.172901
$154$	1.32320	−	3.69104i	0.106627	−	0.297432i
$155$	17.4307			1.40007
$156$	7.03979	−	5.11471i	0.563634	−	0.409504i
$157$	−0.365844	−	1.12595i	−0.0291975	−	0.0898607i	0.935396	−	0.353602i	$-0.115043\pi$
$157$	−0.365844	−	1.12595i	−0.0291975	−	0.0898607i	−0.964593	+	0.263742i	$0.915043\pi$
$158$	2.09399	−	6.44464i	0.166589	−	0.512708i
$159$	1.27232	+	0.924397i	0.100902	+	0.0733094i
$160$	1.74807	+	1.27005i	0.138197	+	0.100406i
$161$	−1.37583	+	4.23438i	−0.108431	+	0.333716i
$162$	1.45910	+	4.49065i	0.114638	+	0.352819i
$163$	−7.35318	+	5.34240i	−0.575945	+	0.418449i	−0.837260	−	0.546805i	$-0.815844\pi$
$163$	−7.35318	+	5.34240i	−0.575945	+	0.418449i	0.261315	+	0.965254i	$0.415844\pi$
$164$	2.39274			0.186842
$165$	8.25849	−	5.62885i	0.642922	−	0.438205i
$166$	17.7944			1.38112
$167$	1.45311	−	1.05575i	0.112445	−	0.0816960i	−0.530142	−	0.847909i	$-0.677861\pi$
$167$	1.45311	−	1.05575i	0.112445	−	0.0816960i	0.642587	+	0.766213i	$0.277861\pi$
$168$	−0.509499	−	1.56808i	−0.0393087	−	0.120980i
$169$	8.01309	−	24.6618i	0.616392	−	1.89706i
$170$	−3.54349	−	2.57450i	−0.271773	−	0.197455i
$171$	−0.853548	−	0.620139i	−0.0652725	−	0.0474232i
$172$	−2.45884	+	7.56752i	−0.187484	+	0.577018i
$173$	2.28310	+	7.02666i	0.173581	+	0.534227i	0.999566	−	0.0294651i	$-0.00938039\pi$
$173$	2.28310	+	7.02666i	0.173581	+	0.534227i	−0.825985	+	0.563692i	$0.809380\pi$
$174$	−3.91295	+	2.84292i	−0.296640	+	0.215521i
$175$	−0.391569			−0.0295998
$176$	−0.929627	−	3.18368i	−0.0700733	−	0.239979i
$177$	−3.41569			−0.256739
$178$	4.63457	−	3.36721i	0.347376	−	0.252383i
$179$	−5.96019	−	18.3436i	−0.445485	−	1.37106i	−0.881951	−	0.471342i	$-0.843770\pi$
$179$	−5.96019	−	18.3436i	−0.445485	−	1.37106i	0.436465	−	0.899721i	$-0.356230\pi$
$180$	−0.704458	+	2.16810i	−0.0525072	+	0.161601i
$181$	−6.88464	−	5.00198i	−0.511731	−	0.371795i	0.301749	−	0.953388i	$-0.402430\pi$
$181$	−6.88464	−	5.00198i	−0.511731	−	0.371795i	−0.813480	+	0.581593i	$0.802430\pi$
$182$	−5.96775	−	4.33583i	−0.442359	−	0.321393i
$183$	4.85348	−	14.9375i	0.358780	−	1.10421i
$184$	1.16375	+	3.58165i	0.0857928	+	0.264043i
$185$	−8.79789	+	6.39204i	−0.646834	+	0.469952i
$186$	−11.2504			−0.824919
$187$	1.88443	+	6.45358i	0.137803	+	0.471932i
$188$	3.04018			0.221728
$189$	5.40896	−	3.92984i	0.393444	−	0.285854i
$190$	0.667705	+	2.05498i	0.0484404	+	0.149084i
$191$	4.90124	−	15.0845i	0.354642	−	1.09147i	−0.601575	−	0.798816i	$-0.705460\pi$
$191$	4.90124	−	15.0845i	0.354642	−	1.09147i	0.956217	−	0.292659i	$-0.0945399\pi$
$192$	−1.12827	−	0.819735i	−0.0814258	−	0.0591593i
$193$	−21.6563	−	15.7343i	−1.55886	−	1.13258i	−0.936938	−	0.349495i	$-0.886353\pi$
$193$	−21.6563	−	15.7343i	−1.55886	−	1.13258i	−0.621920	−	0.783081i	$-0.713647\pi$
$194$	0.792272	−	2.43836i	0.0568818	−	0.175064i
$195$	−5.81014	−	17.8818i	−0.416073	−	1.28054i
$196$	4.53236	−	3.29295i	0.323740	−	0.235211i
$197$	−15.0992			−1.07578			−0.537888	−	0.843016i	$-0.680778\pi$
$197$	−15.0992			−1.07578			−0.537888	+	0.843016i	$0.680778\pi$
$198$	2.89144	−	1.97076i	0.205486	−	0.140056i
$199$	24.4475			1.73304			0.866518	−	0.499145i	$-0.166352\pi$
$199$	24.4475			1.73304			0.866518	+	0.499145i	$0.166352\pi$
$200$	−0.267954	+	0.194680i	−0.0189472	+	0.0137659i
$201$	−4.37105	−	13.4527i	−0.308310	−	0.948881i
$202$	−3.59544	+	11.0656i	−0.252974	+	0.778575i
$203$	3.31707	+	2.40999i	0.232813	+	0.169148i
$204$	2.28709	+	1.66167i	0.160129	+	0.116340i
$205$	1.59764	−	4.91704i	0.111584	−	0.343421i
$206$	−1.27959	−	3.93818i	−0.0891533	−	0.274386i
$207$	−3.21444	+	2.33543i	−0.223419	+	0.162323i
$208$	−6.23946			−0.432629
$209$	1.11923	−	3.12207i	0.0774190	−	0.215958i
$210$	−3.56257			−0.245840
$211$	−7.64440	+	5.55398i	−0.526262	+	0.382352i	−0.818958	−	0.573854i	$-0.805448\pi$
$211$	−7.64440	+	5.55398i	−0.526262	+	0.382352i	0.292696	+	0.956206i	$0.405448\pi$
$212$	−0.348471	−	1.07248i	−0.0239331	−	0.0736585i
$213$	0.250176	−	0.769961i	0.0171417	−	0.0527569i
$214$	10.9983	+	7.99074i	0.751829	+	0.546236i
$215$	13.9094	+	10.1057i	0.948610	+	0.689206i
$216$	1.74756	−	5.37845i	0.118907	−	0.365957i
$217$	2.94714	+	9.07037i	0.200065	+	0.615737i
$218$	−5.27471	+	3.83230i	−0.357248	+	0.259556i
$219$	−11.5116			−0.777881
$220$	−7.16312	−	0.215387i	−0.482938	−	0.0145214i
$221$	12.6479			0.850791
$222$	5.67847	−	4.12565i	0.381114	−	0.276895i
$223$	−7.28982	−	22.4358i	−0.488162	−	1.50241i	−0.827348	−	0.561690i	$-0.810152\pi$
$223$	−7.28982	−	22.4358i	−0.488162	−	1.50241i	0.339186	−	0.940719i	$-0.389848\pi$
$224$	−0.365332	+	1.12438i	−0.0244098	+	0.0751256i
$225$	−0.282703	−	0.205396i	−0.0188469	−	0.0136930i
$226$	−11.5048	−	8.35872i	−0.765287	−	0.556014i
$227$	−0.656330	+	2.01998i	−0.0435621	+	0.134071i	−0.970472	−	0.241213i	$-0.922455\pi$
$227$	−0.656330	+	2.01998i	−0.0435621	+	0.134071i	0.926910	+	0.375284i	$0.122455\pi$
$228$	−0.430960	−	1.32636i	−0.0285410	−	0.0878403i
$229$	13.2135	−	9.60017i	0.873173	−	0.634397i	−0.0582634	−	0.998301i	$-0.518556\pi$
$229$	13.2135	−	9.60017i	0.873173	−	0.634397i	0.931437	+	0.363904i	$0.118556\pi$
$230$	8.13729			0.536557
$231$	4.32539	+	3.34573i	0.284590	+	0.220133i
$232$	3.46810			0.227692
$233$	−20.0447	+	14.5633i	−1.31317	+	0.954073i	−0.313179	+	0.949694i	$0.601394\pi$
$233$	−20.0447	+	14.5633i	−1.31317	+	0.954073i	−0.999990	+	0.00437880i	$0.998606\pi$
$234$	−2.03423	−	6.26072i	−0.132982	−	0.409276i
$235$	2.02994	−	6.24752i	0.132419	−	0.407543i
$236$	1.98144	+	1.43960i	0.128981	+	0.0937101i
$237$	7.64549	+	5.55477i	0.496628	+	0.360821i
$238$	0.740559	−	2.27921i	0.0480033	−	0.147739i
$239$	−1.42495	−	4.38554i	−0.0921723	−	0.283677i	0.894334	−	0.447400i	$-0.147650\pi$
$239$	−1.42495	−	4.38554i	−0.0921723	−	0.283677i	−0.986506	+	0.163723i	$0.947650\pi$
$240$	−2.43789	+	1.77123i	−0.157365	+	0.114333i
$241$	5.69242			0.366681			0.183341	−	0.983049i	$-0.441309\pi$
$241$	5.69242			0.366681			0.183341	+	0.983049i	$0.441309\pi$
$242$	8.49463	+	6.98865i	0.546056	+	0.449247i
$243$	10.3807			0.665920
$244$	−9.11117	+	6.61965i	−0.583283	+	0.423780i
$245$	−3.74069	−	11.5127i	−0.238984	−	0.735517i
$246$	−1.03118	+	3.17363i	−0.0657454	+	0.202343i
$247$	−5.04783	−	3.66746i	−0.321186	−	0.233355i
$248$	6.52635	+	4.74167i	0.414424	+	0.301097i
$249$	−7.66870	+	23.6018i	−0.485984	+	1.49571i
$250$	3.55967	+	10.9556i	0.225134	+	0.692890i
$251$	13.1434	−	9.54921i	0.829602	−	0.602741i	−0.0898448	−	0.995956i	$-0.528637\pi$
$251$	13.1434	−	9.54921i	0.829602	−	0.602741i	0.919447	+	0.393215i	$0.128637\pi$
$252$	−1.24732			−0.0785735
$253$	−9.87967	−	7.64202i	−0.621129	−	0.480450i
$254$	20.2074			1.26793
$255$	4.94181	−	3.59044i	0.309468	−	0.224842i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	1.70751	−	5.25519i	0.106512	−	0.327809i	−0.883571	−	0.468298i	$-0.844867\pi$
$257$	1.70751	−	5.25519i	0.106512	−	0.327809i	0.990082	+	0.140489i	$0.0448673\pi$
$258$	−8.97759	−	6.52260i	−0.558920	−	0.406079i
$259$	−4.81373	−	3.49738i	−0.299111	−	0.217317i
$260$	−4.16612	+	12.8220i	−0.258372	+	0.795187i
$261$	1.13069	+	3.47991i	0.0699881	+	0.215401i
$262$	−8.45875	+	6.14564i	−0.522584	+	0.379679i
$263$	11.0066			0.678695			0.339348	−	0.940661i	$-0.389794\pi$
$263$	11.0066			0.678695			0.339348	+	0.940661i	$0.389794\pi$
$264$	4.62333	+	0.139018i	0.284546	+	0.00855600i
$265$	−2.43662			−0.149680
$266$	−0.956453	+	0.694903i	−0.0586439	+	0.0426073i
$267$	2.46882	+	7.59824i	0.151089	+	0.465005i
$268$	−3.13423	+	9.64617i	−0.191454	+	0.589233i
$269$	3.03460	+	2.20476i	0.185023	+	0.134427i	0.676441	−	0.736497i	$-0.263521\pi$
$269$	3.03460	+	2.20476i	0.185023	+	0.134427i	−0.491418	+	0.870924i	$0.663521\pi$
$270$	−9.88577	−	7.18243i	−0.601629	−	0.437109i
$271$	5.27482	−	16.2342i	0.320422	−	0.986158i	−0.653043	−	0.757321i	$-0.726508\pi$
$271$	5.27482	−	16.2342i	0.320422	−	0.986158i	0.973465	−	0.228837i	$-0.0734923\pi$
$272$	−0.626403	−	1.92787i	−0.0379813	−	0.116894i
$273$	8.32273	−	6.04681i	0.503714	−	0.365970i
$274$	19.2139			1.16076
$275$	0.370700	−	1.03406i	0.0223541	−	0.0623560i
$276$	−5.25209			−0.316139
$277$	10.9644	−	7.96613i	0.658789	−	0.478638i	−0.207465	−	0.978242i	$-0.566521\pi$
$277$	10.9644	−	7.96613i	0.658789	−	0.478638i	0.866254	+	0.499604i	$0.166521\pi$
$278$	4.63178	+	14.2552i	0.277796	+	0.854967i
$279$	−2.63006	+	8.09449i	−0.157458	+	0.484605i
$280$	2.06664	+	1.50150i	0.123506	+	0.0897321i
$281$	−19.7363	−	14.3393i	−1.17737	−	0.855409i	−0.185497	−	0.982645i	$-0.559390\pi$
$281$	−19.7363	−	14.3393i	−1.17737	−	0.855409i	−0.991872	+	0.127236i	$0.959390\pi$
$282$	−1.31020	+	4.03237i	−0.0780210	+	0.240124i
$283$	0.978520	+	3.01158i	0.0581670	+	0.179020i	0.975918	−	0.218136i	$-0.0699975\pi$
$283$	0.978520	+	3.01158i	0.0581670	+	0.179020i	−0.917751	+	0.397155i	$0.869997\pi$
$284$	−0.469640	+	0.341214i	−0.0278680	+	0.0202473i
$285$	−3.01340			−0.178499
$286$	17.0998	−	11.6549i	1.01113	−	0.689171i
$287$	2.82879			0.166978
$288$	−0.853548	+	0.620139i	−0.0502958	+	0.0365420i
$289$	−3.98352	−	12.2600i	−0.234325	−	0.721177i
$290$	2.31567	−	7.12689i	0.135981	−	0.418505i
$291$	2.89271	+	2.10167i	0.169573	+	0.123202i
$292$	6.67787	+	4.85175i	0.390793	+	0.283927i
$293$	−6.26326	+	19.2763i	−0.365903	+	1.12613i	0.583510	+	0.812106i	$0.301679\pi$
$293$	−6.26326	+	19.2763i	−0.365903	+	1.12613i	−0.949413	+	0.314029i	$0.898321\pi$
$294$	2.41437	+	7.43067i	0.140809	+	0.433366i
$295$	4.28138	−	3.11060i	0.249271	−	0.181106i
$296$	−5.03290			−0.292532
$297$	5.25726	+	18.0044i	0.305057	+	1.04472i
$298$	−8.18651			−0.474232
$299$	−19.0100	+	13.8116i	−1.09938	+	0.798744i
$300$	−0.142738	−	0.439302i	−0.00824098	−	0.0253631i
$301$	−2.90693	+	8.94662i	−0.167553	+	0.515675i
$302$	−0.211282	−	0.153505i	−0.0121579	−	0.00883324i
$303$	−13.1275	−	9.53769i	−0.754155	−	0.547926i
$304$	−0.309017	+	0.951057i	−0.0177233	+	0.0545468i
$305$	7.51971	+	23.1433i	0.430577	+	1.32518i
$306$	1.73021	−	1.25707i	0.0989097	−	0.0718621i
$307$	10.0817			0.575396			0.287698	−	0.957721i	$-0.407110\pi$
$307$	10.0817			0.575396			0.287698	+	0.957721i	$0.407110\pi$
$308$	−1.09904	−	3.76387i	−0.0626238	−	0.214466i
$309$	5.77489			0.328522
$310$	14.1017	−	10.2455i	0.800925	−	0.581906i
$311$	5.21609	+	16.0535i	0.295777	+	0.910309i	0.982959	+	0.183824i	$0.0588476\pi$
$311$	5.21609	+	16.0535i	0.295777	+	0.910309i	−0.687182	+	0.726486i	$0.741152\pi$
$312$	2.68896	−	8.27577i	0.152232	−	0.468523i
$313$	24.2537	+	17.6214i	1.37090	+	0.996018i	0.997666	+	0.0682810i	$0.0217514\pi$
$313$	24.2537	+	17.6214i	1.37090	+	0.996018i	0.373235	+	0.927737i	$0.378249\pi$
$314$	−0.957791	−	0.695876i	−0.0540513	−	0.0392706i
$315$	−0.832839	+	2.56321i	−0.0469251	+	0.144421i
$316$	−2.09399	−	6.44464i	−0.117796	−	0.362539i
$317$	−8.23930	+	5.98621i	−0.462765	+	0.336219i	−0.794615	−	0.607113i	$-0.792327\pi$
$317$	−8.23930	+	5.98621i	−0.462765	+	0.336219i	0.331850	+	0.943332i	$0.392327\pi$
$318$	1.57268			0.0881914
$319$	−9.50462	+	6.47819i	−0.532157	+	0.362709i
$320$	2.16074			0.120789
$321$	−15.3384	+	11.1440i	−0.856108	+	0.621999i
$322$	1.37583	+	4.23438i	0.0766721	+	0.235973i
$323$	0.626403	−	1.92787i	0.0348540	−	0.107270i
$324$	3.81998	+	2.77538i	0.212221	+	0.154188i
$325$	−1.67189	−	1.21470i	−0.0927396	−	0.0673793i
$326$	−2.80866	+	8.64418i	−0.155557	+	0.478757i
$327$	−2.80982	−	8.64773i	−0.155383	−	0.478221i
$328$	1.93577	−	1.40642i	0.106885	−	0.0776564i
$329$	3.59422			0.198156
$330$	3.37270	−	9.40805i	0.185661	−	0.517896i
$331$	−8.83120			−0.485407			−0.242703	−	0.970101i	$-0.578034\pi$
$331$	−8.83120			−0.485407			−0.242703	+	0.970101i	$0.578034\pi$
$332$	14.3960	−	10.4593i	0.790083	−	0.574029i
$333$	−1.64086	−	5.05005i	−0.0899186	−	0.276741i
$334$	0.555038	−	1.70823i	0.0303703	−	0.0934703i
$335$	17.7300	+	12.8816i	0.968692	+	0.703796i
$336$	−1.33388	−	0.969124i	−0.0727694	−	0.0528701i
$337$	9.83610	−	30.2724i	0.535807	−	1.64904i	−0.206093	−	0.978532i	$-0.566075\pi$
$337$	9.83610	−	30.2724i	0.535807	−	1.64904i	0.741900	−	0.670511i	$-0.233925\pi$
$338$	−8.01309	−	24.6618i	−0.435855	−	1.34142i
$339$	16.0448	−	11.6572i	0.871432	−	0.633133i
$340$	−4.38000			−0.237539
$341$	−26.7432	−	0.804138i	−1.44822	−	0.0435465i
$342$	−1.05504			−0.0570502
$343$	12.0535	−	8.75739i	0.650828	−	0.472854i
$344$	2.45884	+	7.56752i	0.132572	+	0.408013i
$345$	−3.50685	+	10.7930i	−0.188802	+	0.581074i
$346$	5.97724	+	4.34272i	0.321338	+	0.233466i
$347$	−14.0191	−	10.1854i	−0.752582	−	0.546783i	0.144044	−	0.989571i	$-0.453989\pi$
$347$	−14.0191	−	10.1854i	−0.752582	−	0.546783i	−0.896626	+	0.442788i	$0.853989\pi$
$348$	−1.49461	+	4.59995i	−0.0801197	+	0.246583i
$349$	−1.61228	−	4.96209i	−0.0863035	−	0.265615i	0.898586	−	0.438797i	$-0.144595\pi$
$349$	−1.61228	−	4.96209i	−0.0863035	−	0.265615i	−0.984890	+	0.173182i	$0.944595\pi$
$350$	−0.316786	+	0.230158i	−0.0169329	+	0.0123025i
$351$	35.2856			1.88341
$352$	−2.62340	−	2.02923i	−0.139828	−	0.108158i
$353$	2.70039			0.143727			0.0718636	−	0.997414i	$-0.477105\pi$
$353$	2.70039			0.143727			0.0718636	+	0.997414i	$0.477105\pi$
$354$	−2.76335	+	2.00769i	−0.146870	+	0.106708i
$355$	0.387608	+	1.19293i	0.0205721	+	0.0633143i
$356$	1.77025	−	5.44826i	0.0938230	−	0.288757i
$357$	2.70390	+	1.96449i	0.143105	+	0.103972i
$358$	−15.6040	−	11.3369i	−0.824696	−	0.599176i
$359$	−3.63174	+	11.1773i	−0.191676	+	0.589918i	0.808323	+	0.588739i	$0.200375\pi$
$359$	−3.63174	+	11.1773i	−0.191676	+	0.589918i	−0.999999	+	0.00117903i	$0.999625\pi$
$360$	0.704458	+	2.16810i	0.0371282	+	0.114269i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	−8.50988			−0.447270
$363$	−12.9303	+	8.25510i	−0.678665	+	0.433281i
$364$	−7.37655			−0.386636
$365$	14.4291	−	10.4834i	0.755255	−	0.548725i
$366$	−4.85348	−	14.9375i	−0.253696	−	0.780795i
$367$	−8.71093	+	26.8095i	−0.454707	+	1.39944i	0.416773	+	0.909011i	$0.363161\pi$
$367$	−8.71093	+	26.8095i	−0.454707	+	1.39944i	−0.871479	+	0.490432i	$0.836839\pi$
$368$	3.04674	+	2.21358i	0.158822	+	0.115391i
$369$	2.04232	+	1.48383i	0.106319	+	0.0772452i
$370$	−3.36049	+	10.3425i	−0.174704	+	0.537683i
$371$	−0.411977	−	1.26793i	−0.0213888	−	0.0658279i
$372$	−9.10176	+	6.61282i	−0.471904	+	0.342859i
$373$	21.5226			1.11440			0.557200	−	0.830378i	$-0.311876\pi$
$373$	21.5226			1.11440			0.557200	+	0.830378i	$0.311876\pi$
$374$	5.31785	+	4.11341i	0.274980	+	0.212699i
$375$	−16.0651			−0.829597
$376$	2.45955	−	1.78697i	0.126842	−	0.0921560i
$377$	6.68684	+	20.5800i	0.344390	+	1.05992i
$378$	2.06604	−	6.35862i	0.106266	−	0.327052i
$379$	−15.4283	−	11.2093i	−0.792501	−	0.575786i	0.116204	−	0.993225i	$-0.462927\pi$
$379$	−15.4283	−	11.2093i	−0.792501	−	0.575786i	−0.908705	+	0.417440i	$0.862927\pi$
$380$	1.74807	+	1.27005i	0.0896743	+	0.0651522i
$381$	−8.70861	+	26.8023i	−0.446155	+	1.37313i
$382$	−4.90124	−	15.0845i	−0.250769	−	0.771789i
$383$	−26.2705	+	19.0866i	−1.34236	+	0.975280i	−0.343004	+	0.939334i	$0.611444\pi$
$383$	−26.2705	+	19.0866i	−1.34236	+	0.975280i	−0.999354	+	0.0359461i	$0.988556\pi$
$384$	−1.39462			−0.0711687
$385$	−8.46853	−	0.254639i	−0.431596	−	0.0129776i
$386$	−26.7687			−1.36249
$387$	−6.79165	+	4.93442i	−0.345239	+	0.250831i
$388$	−0.792272	−	2.43836i	−0.0402215	−	0.123789i
$389$	−0.831165	+	2.55806i	−0.0421417	+	0.129699i	−0.969914	−	0.243448i	$-0.921721\pi$
$389$	−0.831165	+	2.55806i	−0.0421417	+	0.129699i	0.927772	+	0.373147i	$0.121721\pi$
$390$	−15.2112	−	11.0515i	−0.770247	−	0.559617i
$391$	−6.17599	−	4.48712i	−0.312333	−	0.226923i
$392$	1.73121	−	5.32811i	0.0874392	−	0.269110i
$393$	−4.50595	−	13.8679i	−0.227295	−	0.699542i
$394$	−12.2155	+	8.87511i	−0.615410	+	0.447122i
$395$	−14.6418			−0.736709
$396$	1.18084	−	3.29392i	0.0593395	−	0.165526i
$397$	4.73678			0.237732			0.118866	−	0.992910i	$-0.462074\pi$
$397$	4.73678			0.237732			0.118866	+	0.992910i	$0.462074\pi$
$398$	19.7784	−	14.3699i	0.991404	−	0.720297i
$399$	−0.509499	−	1.56808i	−0.0255068	−	0.0785020i
$400$	−0.102349	+	0.314998i	−0.00511746	+	0.0157499i
$401$	5.03946	+	3.66138i	0.251659	+	0.182841i	0.706462	−	0.707751i	$-0.250290\pi$
$401$	5.03946	+	3.66138i	0.251659	+	0.182841i	−0.454803	+	0.890592i	$0.650290\pi$
$402$	−11.4436	−	8.31423i	−0.570753	−	0.414676i
$403$	−15.5540	+	47.8703i	−0.774801	+	2.38459i
$404$	3.59544	+	11.0656i	0.178880	+	0.550535i
$405$	8.25397	−	5.99686i	0.410143	−	0.297986i
$406$	4.10013			0.203486
$407$	13.7931	−	9.40115i	0.683699	−	0.465998i
$408$	2.82700			0.139958
$409$	1.39329	−	1.01228i	0.0688938	−	0.0500543i	−0.552805	−	0.833310i	$-0.686443\pi$
$409$	1.39329	−	1.01228i	0.0688938	−	0.0500543i	0.621699	+	0.783256i	$0.286443\pi$
$410$	−1.59764	−	4.91704i	−0.0789020	−	0.242835i
$411$	−8.28044	+	25.4846i	−0.408444	+	1.25706i
$412$	−3.35001	−	2.43393i	−0.165043	−	0.119911i
$413$	2.34254	+	1.70195i	0.115269	+	0.0837477i
$414$	−1.22781	+	3.77880i	−0.0603434	+	0.185718i
$415$	−11.8814	−	36.5673i	−0.583237	−	1.79502i
$416$	−5.04783	+	3.66746i	−0.247490	+	0.179812i
$417$	−20.9036			−1.02365
$418$	−0.929627	−	3.18368i	−0.0454695	−	0.155719i
$419$	−17.0528			−0.833083			−0.416541	−	0.909117i	$-0.636758\pi$
$419$	−17.0528			−0.833083			−0.416541	+	0.909117i	$0.636758\pi$
$420$	−2.88218	+	2.09402i	−0.140636	+	0.102178i
$421$	−8.88187	−	27.3356i	−0.432876	−	1.33226i	−0.895248	−	0.445569i	$-0.853001\pi$
$421$	−8.88187	−	27.3356i	−0.432876	−	1.33226i	0.462372	−	0.886686i	$-0.346999\pi$
$422$	−2.91990	+	8.98653i	−0.142139	+	0.437458i
$423$	2.59494	+	1.88533i	0.126170	+	0.0916680i
$424$	−0.912310	−	0.662832i	−0.0443057	−	0.0321900i
$425$	0.207470	−	0.638528i	0.0100638	−	0.0309732i
$426$	−0.250176	−	0.769961i	−0.0121210	−	0.0373047i
$427$	−10.7716	+	7.82602i	−0.521274	+	0.378727i
$428$	13.5947			0.657123
$429$	8.08930	+	27.7033i	0.390555	+	1.33753i
$430$	17.1929			0.829116
$431$	−32.5311	+	23.6352i	−1.56697	+	1.13847i	−0.636975	+	0.770884i	$0.719815\pi$
$431$	−32.5311	+	23.6352i	−1.56697	+	1.13847i	−0.929991	+	0.367583i	$0.880185\pi$
$432$	−1.74756	−	5.37845i	−0.0840797	−	0.258771i
$433$	0.0630624	−	0.194086i	0.00303059	−	0.00932719i	−0.949530	−	0.313677i	$-0.898439\pi$
$433$	0.0630624	−	0.194086i	0.00303059	−	0.00932719i	0.952560	+	0.304350i	$0.0984391\pi$
$434$	7.71572	+	5.60580i	0.370366	+	0.269087i
$435$	8.45486	+	6.14281i	0.405379	+	0.294525i
$436$	−2.01476	+	6.20079i	−0.0964895	+	0.296964i
$437$	1.16375	+	3.58165i	0.0556697	+	0.171334i
$438$	−9.31307	+	6.76634i	−0.444995	+	0.323308i
$439$	0.940938			0.0449085			0.0224543	−	0.999748i	$-0.492852\pi$
$439$	0.940938			0.0449085			0.0224543	+	0.999748i	$0.492852\pi$
$440$	−5.92169	+	4.03613i	−0.282305	+	0.192415i
$441$	5.91068			0.281461
$442$	10.2324	−	7.43426i	0.486704	−	0.353611i
$443$	0.959628	+	2.95343i	0.0455933	+	0.140322i	0.971262	−	0.238014i	$-0.0764965\pi$
$443$	0.959628	+	2.95343i	0.0455933	+	0.140322i	−0.925668	+	0.378336i	$0.876496\pi$
$444$	2.16898	−	6.67544i	0.102935	−	0.316802i
$445$	−10.0141	−	7.27567i	−0.474714	−	0.344900i
$446$	−19.0850	−	13.8661i	−0.903700	−	0.656577i
$447$	3.52806	−	10.8583i	0.166872	−	0.513578i
$448$	0.365332	+	1.12438i	0.0172603	+	0.0531218i
$449$	18.7984	−	13.6578i	0.887149	−	0.644552i	−0.0479840	−	0.998848i	$-0.515280\pi$
$449$	18.7984	−	13.6578i	0.887149	−	0.644552i	0.935133	+	0.354297i	$0.115280\pi$
$450$	−0.349440			−0.0164728
$451$	−2.67803	+	7.47030i	−0.126104	+	0.351763i
$452$	−14.2207			−0.668886
$453$	0.294658	−	0.214081i	0.0138442	−	0.0100584i
$454$	0.656330	+	2.01998i	0.0308031	+	0.0948022i
$455$	−4.92536	+	15.1587i	−0.230904	+	0.710650i
$456$	−1.12827	−	0.819735i	−0.0528360	−	0.0383876i
$457$	31.2419	+	22.6986i	1.46144	+	1.06180i	0.982986	+	0.183681i	$0.0588014\pi$
$457$	31.2419	+	22.6986i	1.46144	+	1.06180i	0.478450	+	0.878115i	$0.341199\pi$
$458$	5.04711	−	15.5334i	0.235836	−	0.725828i
$459$	3.54246	+	10.9026i	0.165348	+	0.508888i
$460$	6.58320	−	4.78298i	0.306943	−	0.223007i
$461$	−25.5519			−1.19007			−0.595034	−	0.803700i	$-0.702862\pi$
$461$	−25.5519			−1.19007			−0.595034	+	0.803700i	$0.702862\pi$
$462$	5.46589	+	0.164353i	0.254296	+	0.00764640i
$463$	−1.41829			−0.0659133			−0.0329567	−	0.999457i	$-0.510492\pi$
$463$	−1.41829			−0.0659133			−0.0329567	+	0.999457i	$0.510492\pi$
$464$	2.80575	−	2.03850i	0.130254	−	0.0946349i
$465$	7.51194	+	23.1194i	0.348358	+	1.07214i
$466$	−7.65638	+	23.5639i	−0.354675	+	1.09158i
$467$	−4.94322	−	3.59146i	−0.228745	−	0.166193i	0.467509	−	0.883988i	$-0.345151\pi$
$467$	−4.94322	−	3.59146i	−0.228745	−	0.166193i	−0.696254	+	0.717795i	$0.745151\pi$
$468$	−5.32568	−	3.86934i	−0.246180	−	0.178860i
$469$	−3.70541	+	11.4041i	−0.171100	+	0.526592i
$470$	−2.02994	−	6.24752i	−0.0936342	−	0.288176i
$471$	1.33575	−	0.970480i	0.0615482	−	0.0447174i
$472$	2.44920			0.112733
$473$	−20.8743	−	16.1465i	−0.959801	−	0.742416i
$474$	9.45034			0.434068
$475$	−0.267954	+	0.194680i	−0.0122946	+	0.00893252i
$476$	−0.740559	−	2.27921i	−0.0339435	−	0.104467i
$477$	0.367653	−	1.13152i	0.0168337	−	0.0518087i
$478$	−3.73056	−	2.71041i	−0.170632	−	0.123971i
$479$	0.502533	+	0.365112i	0.0229613	+	0.0166824i	0.599207	−	0.800594i	$-0.295483\pi$
$479$	0.502533	+	0.365112i	0.0229613	+	0.0166824i	−0.576245	+	0.817277i	$0.695483\pi$
$480$	−0.931193	+	2.86592i	−0.0425029	+	0.130811i
$481$	−9.70394	−	29.8657i	−0.442462	−	1.36176i
$482$	4.60527	−	3.34592i	0.209764	−	0.152403i
$483$	−6.20924			−0.282530
$484$	10.9801	+	0.660918i	0.499097	+	0.0300417i
$485$	−5.53980			−0.251549
$486$	8.39813	−	6.10160i	0.380947	−	0.276774i
$487$	−5.14677	−	15.8401i	−0.233222	−	0.717785i	−0.997352	−	0.0727223i	$-0.976831\pi$
$487$	−5.14677	−	15.8401i	−0.233222	−	0.717785i	0.764130	−	0.645062i	$-0.223169\pi$
$488$	−3.48016	+	10.7108i	−0.157539	+	0.484856i
$489$	−10.2549	−	7.45059i	−0.463741	−	0.336928i
$490$	−9.79325	−	7.11521i	−0.442414	−	0.321433i
$491$	8.39828	−	25.8473i	0.379009	−	1.16647i	−0.561724	−	0.827324i	$-0.689862\pi$
$491$	8.39828	−	25.8473i	0.379009	−	1.16647i	0.940734	−	0.339146i	$-0.110138\pi$
$492$	1.03118	+	3.17363i	0.0464890	+	0.143078i
$493$	−5.68749	+	4.13220i	−0.256152	+	0.186105i
$494$	−6.23946			−0.280727
$495$	−5.98050	−	4.62598i	−0.268803	−	0.207922i
$496$	8.06702			0.362220
$497$	−0.555228	+	0.403396i	−0.0249054	+	0.0180948i
$498$	7.66870	+	23.6018i	0.343643	+	1.05762i
$499$	2.60195	−	8.00799i	0.116479	−	0.358487i	−0.875773	−	0.482723i	$-0.839648\pi$
$499$	2.60195	−	8.00799i	0.116479	−	0.358487i	0.992253	+	0.124236i	$0.0396479\pi$
$500$	9.31935	+	6.77090i	0.416774	+	0.302804i
$501$	2.02653	+	1.47236i	0.0905387	+	0.0657802i
$502$	5.02032	−	15.4510i	0.224068	−	0.689610i
$503$	2.12977	+	6.55476i	0.0949618	+	0.292262i	0.987244	−	0.159216i	$-0.0508967\pi$
$503$	2.12977	+	6.55476i	0.0949618	+	0.292262i	−0.892282	+	0.451479i	$0.850897\pi$
$504$	−1.00910	+	0.733154i	−0.0449489	+	0.0326573i
$505$	25.1404			1.11873
$506$	−12.4847	−	0.375401i	−0.555012	−	0.0166886i
$507$	36.1637			1.60609
$508$	16.3482	−	11.8776i	0.725333	−	0.526985i
$509$	7.22335	+	22.2312i	0.320169	+	0.985380i	0.973574	+	0.228371i	$0.0733400\pi$
$509$	7.22335	+	22.2312i	0.320169	+	0.985380i	−0.653405	+	0.757009i	$0.726660\pi$
$510$	1.88760	−	5.80945i	0.0835845	−	0.257247i
$511$	7.89484	+	5.73594i	0.349247	+	0.253743i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	1.74756	−	5.37845i	0.0771568	−	0.237464i
$514$	−1.70751	−	5.25519i	−0.0753152	−	0.231796i
$515$	−7.23850	+	5.25908i	−0.318966	+	0.231743i
$516$	−11.0969			−0.488514
$517$	−3.40267	+	9.49164i	−0.149649	+	0.417442i
$518$	−5.95010			−0.261432
$519$	−8.33595	+	6.05642i	−0.365908	+	0.265848i
$520$	4.16612	+	12.8220i	0.182696	+	0.562282i
$521$	13.4207	−	41.3048i	0.587973	−	1.80959i	0.000984123	−	1.00000i	$-0.499687\pi$
$521$	13.4207	−	41.3048i	0.587973	−	1.80959i	0.586989	−	0.809595i	$-0.300313\pi$
$522$	2.96019	+	2.15070i	0.129564	+	0.0941337i
$523$	−0.0454106	−	0.0329927i	−0.00198567	−	0.00144267i	0.586792	−	0.809738i	$-0.300391\pi$
$523$	−0.0454106	−	0.0329927i	−0.00198567	−	0.00144267i	−0.588778	+	0.808295i	$0.700391\pi$
$524$	−3.23096	+	9.94386i	−0.141145	+	0.434400i
$525$	−0.168751	−	0.519361i	−0.00736488	−	0.0226668i
$526$	8.90452	−	6.46951i	0.388255	−	0.282084i
$527$	−16.3525			−0.712327
$528$	3.82207	−	2.60506i	0.166334	−	0.113371i
$529$	−8.81743			−0.383367
$530$	−1.97126	+	1.43221i	−0.0856262	+	0.0622111i
$531$	0.798503	+	2.45754i	0.0346521	+	0.106648i
$532$	−0.365332	+	1.12438i	−0.0158392	+	0.0487479i
$533$	12.0781	+	8.77529i	0.523163	+	0.380100i
$534$	6.46345	+	4.69597i	0.279701	+	0.203215i
$535$	9.07723	−	27.9368i	0.392443	−	1.20781i
$536$	3.13423	+	9.64617i	0.135378	+	0.416651i
$537$	21.7616	−	15.8107i	0.939081	−	0.682282i
$538$	3.75097			0.161716
$539$	5.20806	+	17.8359i	0.224327	+	0.768248i
$540$	−12.2195			−0.525843
$541$	18.0971	−	13.1483i	0.778054	−	0.565289i	−0.126341	−	0.991987i	$-0.540323\pi$
$541$	18.0971	−	13.1483i	0.778054	−	0.565289i	0.904394	+	0.426698i	$0.140323\pi$
$542$	−5.27482	−	16.2342i	−0.226573	−	0.697319i
$543$	3.66742	−	11.2872i	0.157384	−	0.484379i
$544$	−1.63994	−	1.19149i	−0.0703120	−	0.0510847i
$545$	11.3973	+	8.28060i	0.488205	+	0.354702i
$546$	3.17900	−	9.78395i	0.136049	−	0.418714i
$547$	0.401179	+	1.23470i	0.0171532	+	0.0527920i	0.959267	−	0.282502i	$-0.0911644\pi$
$547$	0.401179	+	1.23470i	0.0171532	+	0.0527920i	−0.942114	+	0.335294i	$0.891164\pi$
$548$	15.5444	−	11.2937i	0.664024	−	0.482442i
$549$	−11.8819			−0.507108
$550$	−0.307901	−	1.05446i	−0.0131289	−	0.0449624i
$551$	3.46810			0.147746
$552$	−4.24903	+	3.08710i	−0.180851	+	0.131396i
$553$	−2.47560	−	7.61912i	−0.105273	−	0.323998i
$554$	4.18804	−	12.8895i	0.177933	−	0.547621i
$555$	−12.2697	−	8.91445i	−0.520819	−	0.378397i
$556$	12.1262	+	8.81017i	0.514264	+	0.373634i
$557$	4.59245	−	14.1341i	0.194589	−	0.598882i	−0.805393	−	0.592742i	$-0.798046\pi$
$557$	4.59245	−	14.1341i	0.194589	−	0.598882i	0.999981	−	0.00614018i	$-0.00195449\pi$
$558$	2.63006	+	8.09449i	0.111339	+	0.342667i
$559$	−40.1654	+	29.1819i	−1.69882	+	1.23426i
$560$	2.55451			0.107948
$561$	−7.74765	+	5.28067i	−0.327106	+	0.222950i
$562$	−24.3954			−1.02906
$563$	18.4908	−	13.4344i	0.779296	−	0.566192i	−0.125471	−	0.992097i	$-0.540044\pi$
$563$	18.4908	−	13.4344i	0.779296	−	0.566192i	0.904768	+	0.425905i	$0.140044\pi$
$564$	1.31020	+	4.03237i	0.0551692	+	0.169793i
$565$	−9.49523	+	29.2233i	−0.399467	+	1.22943i
$566$	2.56180	+	1.86126i	0.107680	+	0.0782344i
$567$	4.51613	+	3.28116i	0.189660	+	0.137796i
$568$	−0.179387	+	0.552095i	−0.00752689	+	0.0231654i
$569$	9.06887	+	27.9111i	0.380187	+	1.17010i	0.939912	+	0.341417i	$0.110907\pi$
$569$	9.06887	+	27.9111i	0.380187	+	1.17010i	−0.559725	+	0.828678i	$0.689093\pi$
$570$	−2.43789	+	1.77123i	−0.102112	+	0.0741888i
$571$	6.71091			0.280843			0.140421	−	0.990092i	$-0.455154\pi$
$571$	6.71091			0.280843			0.140421	+	0.990092i	$0.455154\pi$
$572$	6.98342	−	19.4800i	0.291991	−	0.814501i
$573$	22.1197			0.924063
$574$	2.28854	−	1.66272i	0.0955219	−	0.0694007i
$575$	0.385444	+	1.18628i	0.0160741	+	0.0494711i
$576$	−0.326026	+	1.00341i	−0.0135844	+	0.0418086i
$577$	36.5981	+	26.5901i	1.52360	+	1.10696i	0.959668	+	0.281137i	$0.0907117\pi$
$577$	36.5981	+	26.5901i	1.52360	+	1.10696i	0.563931	+	0.825822i	$0.309288\pi$
$578$	−10.4290	−	7.57710i	−0.433789	−	0.315166i
$579$	11.5363	−	35.5049i	0.479430	−	1.47553i
$580$	−2.31567	−	7.12689i	−0.0961528	−	0.295928i
$581$	17.0195	−	12.3654i	0.706089	−	0.513004i
$582$	3.57558			0.148213
$583$	3.73839	+	0.112409i	0.154828	+	0.00465552i
$584$	8.25430			0.341565
$585$	−11.5074	+	8.36062i	−0.475773	+	0.345669i
$586$	6.26326	+	19.2763i	0.258733	+	0.796298i
$587$	3.84853	−	11.8446i	0.158846	−	0.488877i	−0.839684	−	0.543075i	$-0.817260\pi$
$587$	3.84853	−	11.8446i	0.158846	−	0.488877i	0.998530	+	0.0541976i	$0.0172601\pi$
$588$	6.32091	+	4.59241i	0.260670	+	0.189388i
$589$	6.52635	+	4.74167i	0.268914	+	0.195377i
$590$	1.63534	−	5.03306i	0.0673259	−	0.207208i
$591$	−6.50717	−	20.0270i	−0.267669	−	0.823802i
$592$	−4.07170	+	2.95827i	−0.167346	+	0.121584i
$593$	−33.2780			−1.36656			−0.683281	−	0.730156i	$-0.739448\pi$
$593$	−33.2780			−1.36656			−0.683281	+	0.730156i	$0.739448\pi$
$594$	14.8359	+	11.4758i	0.608726	+	0.470856i
$595$	−5.17821			−0.212286
$596$	−6.62303	+	4.81191i	−0.271290	+	0.197104i
$597$	10.5359	+	32.4262i	0.431206	+	1.32711i
$598$	−7.26118	+	22.3476i	−0.296932	+	0.913862i
$599$	−10.3252	−	7.50168i	−0.421875	−	0.306510i	0.356517	−	0.934289i	$-0.383964\pi$
$599$	−10.3252	−	7.50168i	−0.421875	−	0.306510i	−0.778392	+	0.627779i	$0.783964\pi$
$600$	−0.373693	−	0.271504i	−0.0152559	−	0.0110841i
$601$	−10.6476	+	32.7701i	−0.434327	+	1.33672i	0.459448	+	0.888205i	$0.348047\pi$
$601$	−10.6476	+	32.7701i	−0.434327	+	1.33672i	−0.893775	+	0.448516i	$0.851953\pi$
$602$	2.90693	+	8.94662i	0.118478	+	0.364637i
$603$	−8.65718	+	6.28981i	−0.352548	+	0.256141i
$604$	−0.261159			−0.0106264
$605$	8.68966	−	22.1227i	0.353285	−	0.899415i
$606$	−16.2265			−0.659156
$607$	−1.31846	+	0.957915i	−0.0535145	+	0.0388806i	−0.614221	−	0.789134i	$-0.710530\pi$
$607$	−1.31846	+	0.957915i	−0.0535145	+	0.0388806i	0.560706	+	0.828015i	$0.310530\pi$
$608$	0.309017	+	0.951057i	0.0125323	+	0.0385704i
$609$	−1.76699	+	5.43824i	−0.0716021	+	0.220369i
$610$	19.6868	+	14.3033i	0.797097	+	0.579125i
$611$	15.3463	+	11.1497i	0.620845	+	0.451070i
$612$	0.660883	−	2.03399i	0.0267146	−	0.0822191i
$613$	−1.54448	−	4.75344i	−0.0623812	−	0.191989i	0.915009	−	0.403434i	$-0.132183\pi$
$613$	−1.54448	−	4.75344i	−0.0623812	−	0.191989i	−0.977390	+	0.211444i	$0.932183\pi$
$614$	8.15630	−	5.92590i	0.329162	−	0.239150i
$615$	7.21029			0.290747
$616$	−3.10149	−	2.39903i	−0.124963	−	0.0966598i
$617$	16.1786			0.651326			0.325663	−	0.945486i	$-0.394413\pi$
$617$	16.1786			0.651326			0.325663	+	0.945486i	$0.394413\pi$
$618$	4.67198	−	3.39439i	0.187935	−	0.136543i
$619$	−0.829806	−	2.55388i	−0.0333527	−	0.102649i	0.932994	−	0.359891i	$-0.117186\pi$
$619$	−0.829806	−	2.55388i	−0.0333527	−	0.102649i	−0.966347	+	0.257242i	$0.917186\pi$
$620$	5.38639	−	16.5776i	0.216322	−	0.665772i
$621$	−17.2300	−	12.5183i	−0.691416	−	0.502343i
$622$	13.6559	+	9.92160i	0.547552	+	0.397820i
$623$	2.09286	−	6.44116i	0.0838486	−	0.258060i
$624$	−2.68896	−	8.27577i	−0.107645	−	0.331296i
$625$	18.7969	−	13.6568i	0.751876	−	0.546270i
$626$	29.9792			1.19821
$627$	4.62333	+	0.139018i	0.184638	+	0.00555186i
$628$	−1.18390			−0.0472426
$629$	8.25368	−	5.99665i	0.329096	−	0.239102i
$630$	0.832839	+	2.56321i	0.0331811	+	0.102121i
$631$	−1.66292	+	5.11793i	−0.0661997	+	0.203742i	−0.978685	−	0.205368i	$-0.934161\pi$
$631$	−1.66292	+	5.11793i	−0.0661997	+	0.203742i	0.912485	+	0.409110i	$0.134161\pi$
$632$	−5.48214	−	3.98301i	−0.218068	−	0.158436i
$633$	−10.6610	−	7.74568i	−0.423737	−	0.307863i
$634$	−3.14713	+	9.68588i	−0.124989	+	0.384676i
$635$	−13.4926	−	41.5260i	−0.535438	−	1.64791i
$636$	1.27232	−	0.924397i	0.0504509	−	0.0366547i
$637$	34.9554			1.38498
$638$	−3.88161	+	10.8276i	−0.153675	+	0.428670i
$639$	−0.612461			−0.0242286
$640$	1.74807	−	1.27005i	0.0690987	−	0.0502031i
$641$	−10.0810	−	31.0262i	−0.398176	−	1.22546i	−0.926460	−	0.376392i	$-0.877164\pi$
$641$	−10.0810	−	31.0262i	−0.398176	−	1.22546i	0.528284	−	0.849068i	$-0.322836\pi$
$642$	−5.85876	+	18.0314i	−0.231227	+	0.711643i
$643$	3.14637	+	2.28597i	0.124081	+	0.0901500i	0.648095	−	0.761560i	$-0.275566\pi$
$643$	3.14637	+	2.28597i	0.124081	+	0.0901500i	−0.524014	+	0.851710i	$0.675566\pi$
$644$	3.60198	+	2.61699i	0.141938	+	0.103124i
$645$	−7.40946	+	22.8040i	−0.291747	+	0.897906i
$646$	−0.626403	−	1.92787i	−0.0246455	−	0.0758510i
$647$	31.3641	−	22.7874i	1.23305	−	0.895864i	0.235935	−	0.971769i	$-0.424185\pi$
$647$	31.3641	−	22.7874i	1.23305	−	0.895864i	0.997115	+	0.0759052i	$0.0241846\pi$
$648$	4.72175			0.185488
$649$	−6.71223	+	4.57495i	−0.263478	+	0.179582i
$650$	−2.06657			−0.0810574
$651$	−10.7605	+	7.81794i	−0.421736	+	0.306409i
$652$	2.80866	+	8.64418i	0.109996	+	0.338532i
$653$	12.2950	−	37.8401i	0.481141	−	1.48080i	−0.356353	−	0.934352i	$-0.615980\pi$
$653$	12.2950	−	37.8401i	0.481141	−	1.48080i	0.837493	−	0.546447i	$-0.184020\pi$
$654$	−7.35620	−	5.34459i	−0.287650	−	0.208990i
$655$	18.2772	+	13.2791i	0.714148	+	0.518859i
$656$	0.739397	−	2.27563i	0.0288686	−	0.0888484i
$657$	2.69112	+	8.28241i	0.104991	+	0.323128i
$658$	2.90779	−	2.11263i	0.113357	−	0.0823589i
$659$	−5.39549			−0.210178			−0.105089	−	0.994463i	$-0.533513\pi$
$659$	−5.39549			−0.210178			−0.105089	+	0.994463i	$0.533513\pi$
$660$	−2.80134	−	9.59370i	−0.109042	−	0.373434i
$661$	−33.5994			−1.30686			−0.653432	−	0.756985i	$-0.726672\pi$
$661$	−33.5994			−1.30686			−0.653432	+	0.756985i	$0.726672\pi$
$662$	−7.14459	+	5.19085i	−0.277682	+	0.201748i
$663$	5.45075	+	16.7757i	0.211690	+	0.651513i
$664$	5.49879	−	16.9235i	0.213394	−	0.656760i
$665$	2.06664	+	1.50150i	0.0801410	+	0.0582259i
$666$	−4.29583	−	3.12110i	−0.166460	−	0.120940i
$667$	4.03600	−	12.4215i	0.156275	−	0.480964i
$668$	−0.555038	−	1.70823i	−0.0214751	−	0.0660935i
$669$	26.6162	−	19.3378i	1.02904	−	0.747644i
$670$	21.9155			0.846668
$671$	−10.4695	−	35.8546i	−0.404170	−	1.38415i
$672$	−1.64877			−0.0636028
$673$	−22.4563	+	16.3155i	−0.865627	+	0.628915i	−0.929410	−	0.369049i	$-0.879683\pi$
$673$	−22.4563	+	16.3155i	−0.865627	+	0.628915i	0.0637830	+	0.997964i	$0.479683\pi$
$674$	−9.83610	−	30.2724i	−0.378872	−	1.16605i
$675$	0.578808	−	1.78139i	0.0222783	−	0.0685657i
$676$	−20.9785	−	15.2418i	−0.806867	−	0.586223i
$677$	15.0738	+	10.9517i	0.579332	+	0.420909i	0.838483	−	0.544928i	$-0.183443\pi$
$677$	15.0738	+	10.9517i	0.579332	+	0.420909i	−0.259151	+	0.965837i	$0.583443\pi$
$678$	6.12856	−	18.8618i	0.235366	−	0.724382i
$679$	−0.936656	−	2.88273i	−0.0359456	−	0.110629i
$680$	−3.54349	+	2.57450i	−0.135887	+	0.0987275i
$681$	−2.96207			−0.113507
$682$	−22.1083	+	15.0687i	−0.846572	+	0.577010i
$683$	4.43166			0.169573			0.0847864	−	0.996399i	$-0.472979\pi$
$683$	4.43166			0.169573			0.0847864	+	0.996399i	$0.472979\pi$
$684$	−0.853548	+	0.620139i	−0.0326362	+	0.0237116i
$685$	−12.8292	−	39.4843i	−0.490180	−	1.50862i
$686$	4.60403	−	14.1697i	0.175783	−	0.541004i
$687$	18.4278	+	13.3886i	0.703064	+	0.510806i
$688$	6.43731	+	4.67698i	0.245420	+	0.178308i
$689$	2.17427	−	6.69173i	0.0828333	−	0.254935i
$690$	3.50685	+	10.7930i	0.133503	+	0.410881i
$691$	−29.6723	+	21.5582i	−1.12879	+	0.820111i	−0.985518	−	0.169573i	$-0.945761\pi$
$691$	−29.6723	+	21.5582i	−1.12879	+	0.820111i	−0.143268	+	0.989684i	$0.545761\pi$
$692$	7.38827			0.280860
$693$	1.39604	−	3.89420i	0.0530311	−	0.147929i
$694$	−17.3285			−0.657781
$695$	26.2015	−	19.0365i	0.993878	−	0.722095i
$696$	1.49461	+	4.59995i	0.0566532	+	0.174360i
$697$	−1.49882	+	4.61289i	−0.0567718	+	0.174726i
$698$	−4.22101	−	3.06674i	−0.159768	−	0.116078i
$699$	−27.9546	−	20.3102i	−1.05734	−	0.768203i
$700$	−0.121001	+	0.372404i	−0.00457342	+	0.0140755i
$701$	4.80177	+	14.7783i	0.181360	+	0.558170i	0.999867	−	0.0163277i	$-0.00519748\pi$
$701$	4.80177	+	14.7783i	0.181360	+	0.558170i	−0.818506	+	0.574498i	$0.805197\pi$
$702$	28.5467	−	20.7404i	1.07742	−	0.782795i
$703$	−5.03290			−0.189820
$704$	−3.31513	−	0.0996822i	−0.124944	−	0.00375691i
$705$	9.16128			0.345034
$706$	2.18466	−	1.58725i	0.0822208	−	0.0597369i
$707$	4.25067	+	13.0822i	0.159863	+	0.492008i
$708$	−1.05551	+	3.24851i	−0.0396684	+	0.122087i
$709$	−6.88795	−	5.00439i	−0.258682	−	0.187944i	0.450884	−	0.892583i	$-0.351109\pi$
$709$	−6.88795	−	5.00439i	−0.258682	−	0.187944i	−0.709566	+	0.704639i	$0.751109\pi$
$710$	1.01477	+	0.737273i	0.0380836	+	0.0276694i
$711$	2.20925	−	6.79938i	0.0828534	−	0.254997i
$712$	−1.77025	−	5.44826i	−0.0663429	−	0.204182i
$713$	24.5781	−	17.8570i	0.920456	−	0.668751i
$714$	3.34220			0.125079
$715$	−35.3683	−	27.3577i	−1.32270	−	1.02312i
$716$	−19.2876			−0.720810
$717$	5.20271	−	3.77999i	0.194299	−	0.141166i
$718$	3.63174	+	11.1773i	0.135535	+	0.417135i
$719$	−4.85276	+	14.9353i	−0.180977	+	0.556991i	−0.999856	−	0.0169759i	$-0.994596\pi$
$719$	−4.85276	+	14.9353i	−0.180977	+	0.556991i	0.818879	+	0.573967i	$0.194596\pi$
$720$	1.84429	+	1.33996i	0.0687328	+	0.0499373i
$721$	−3.96052	−	2.87749i	−0.147497	−	0.107163i
$722$	−0.309017	+	0.951057i	−0.0115004	+	0.0353947i
$723$	2.45321	+	7.55020i	0.0912358	+	0.280795i
$724$	−6.88464	+	5.00198i	−0.255866	+	0.185897i
$725$	1.14867			0.0426603
$726$	−5.60861	+	14.2788i	−0.208155	+	0.529935i
$727$	49.5195			1.83658			0.918288	−	0.395912i	$-0.129572\pi$
$727$	49.5195			1.83658			0.918288	+	0.395912i	$0.129572\pi$
$728$	−5.96775	+	4.33583i	−0.221180	+	0.160696i
$729$	8.85096	+	27.2404i	0.327813	+	1.00891i
$730$	5.51143	−	16.9625i	0.203987	−	0.627809i
$731$	−13.0490	−	9.48063i	−0.482634	−	0.350654i
$732$	−12.7066	−	9.23187i	−0.469649	−	0.341220i
$733$	0.563580	−	1.73452i	0.0208163	−	0.0640660i	−0.940109	−	0.340875i	$-0.889277\pi$
$733$	0.563580	−	1.73452i	0.0208163	−	0.0640660i	0.960925	+	0.276809i	$0.0892768\pi$
$734$	8.71093	+	26.8095i	0.321526	+	0.989556i
$735$	13.6578	−	9.92300i	0.503777	−	0.366015i
$736$	3.76597			0.138816
$737$	−26.6081	−	20.5816i	−0.980120	−	0.758133i
$738$	2.52444			0.0929261
$739$	−7.77120	+	5.64611i	−0.285868	+	0.207696i	−0.721473	−	0.692443i	$-0.756535\pi$
$739$	−7.77120	+	5.64611i	−0.285868	+	0.207696i	0.435605	+	0.900138i	$0.356535\pi$
$740$	3.36049	+	10.3425i	0.123534	+	0.380199i
$741$	2.68896	−	8.27577i	0.0987815	−	0.304018i
$742$	−1.07857	−	0.783627i	−0.0395955	−	0.0287678i
$743$	−11.1300	−	8.08643i	−0.408321	−	0.296662i	0.364601	−	0.931164i	$-0.381205\pi$
$743$	−11.1300	−	8.08643i	−0.408321	−	0.296662i	−0.772922	+	0.634502i	$0.781205\pi$
$744$	−3.47656	+	10.6998i	−0.127457	+	0.392272i
$745$	5.46618	+	16.8232i	0.200265	+	0.616353i
$746$	17.4122	−	12.6507i	0.637505	−	0.463175i
$747$	18.7739			0.686902
$748$	6.72004	+	0.202064i	0.245709	+	0.00738819i
$749$	16.0722			0.587264
$750$	−12.9969	+	9.44282i	−0.474580	+	0.344803i
$751$	−9.69208	−	29.8292i	−0.353669	−	1.08848i	−0.956777	−	0.290822i	$-0.906071\pi$
$751$	−9.69208	−	29.8292i	−0.353669	−	1.08848i	0.603108	−	0.797659i	$-0.293929\pi$
$752$	0.939466	−	2.89138i	0.0342588	−	0.105438i
$753$	18.3300	+	13.3175i	0.667981	+	0.485316i
$754$	17.5064	+	12.7191i	0.637545	+	0.463203i
$755$	−0.174377	+	0.536678i	−0.00634623	+	0.0195317i
$756$	−2.06604	−	6.35862i	−0.0751411	−	0.231261i
$757$	29.0477	−	21.1044i	1.05576	−	0.767051i	0.0824572	−	0.996595i	$-0.473723\pi$
$757$	29.0477	−	21.1044i	1.05576	−	0.767051i	0.973298	+	0.229543i	$0.0737232\pi$
$758$	−19.0705			−0.692671
$759$	5.87832	−	16.3974i	0.213369	−	0.595188i
$760$	2.16074			0.0783782
$761$	5.75741	−	4.18300i	0.208706	−	0.151634i	−0.478522	−	0.878076i	$-0.658827\pi$
$761$	5.75741	−	4.18300i	0.208706	−	0.151634i	0.687228	+	0.726442i	$0.258827\pi$
$762$	8.70861	+	26.8023i	0.315480	+	0.970946i
$763$	−2.38193	+	7.33083i	−0.0862317	+	0.265394i
$764$	−12.8316	−	9.32272i	−0.464232	−	0.337284i
$765$	−3.73854	−	2.71621i	−0.135167	−	0.0982047i
$766$	−10.0344	+	30.8828i	−0.362558	+	1.11584i
$767$	4.72230	+	14.5337i	0.170512	+	0.524783i
$768$	−1.12827	+	0.819735i	−0.0407129	+	0.0295796i
$769$	−50.1561			−1.80868			−0.904338	−	0.426818i	$-0.859635\pi$
$769$	−50.1561			−1.80868			−0.904338	+	0.426818i	$0.859635\pi$
$770$	−7.00086	+	4.77167i	−0.252293	+	0.171959i
$771$	7.70614			0.277530
$772$	−21.6563	+	15.7343i	−0.779429	+	0.566288i
$773$	−2.34285	−	7.21055i	−0.0842664	−	0.259345i	0.900042	−	0.435804i	$-0.143536\pi$
$773$	−2.34285	−	7.21055i	−0.0842664	−	0.259345i	−0.984308	+	0.176458i	$0.943536\pi$
$774$	−2.59418	+	7.98406i	−0.0932458	+	0.286981i
$775$	2.16159	+	1.57048i	0.0776465	+	0.0564135i
$776$	−2.07419	−	1.50699i	−0.0744593	−	0.0540978i
$777$	2.56426	−	7.89197i	0.0919922	−	0.283123i
$778$	0.831165	+	2.55806i	0.0297987	+	0.0917110i
$779$	1.93577	−	1.40642i	0.0693560	−	0.0503901i
$780$	−18.8020			−0.673220
$781$	−0.539655	−	1.84815i	−0.0193104	−	0.0661319i
$782$	−7.63394			−0.272989
$783$	−15.8672	+	11.5282i	−0.567046	+	0.411983i
$784$	−1.73121	−	5.32811i	−0.0618289	−	0.190290i
$785$	−0.790493	+	2.43289i	−0.0282139	+	0.0868334i
$786$	−11.7967	−	8.57082i	−0.420775	−	0.305711i
$787$	20.8252	+	15.1304i	0.742337	+	0.539339i	0.893442	−	0.449178i	$-0.148283\pi$
$787$	20.8252	+	15.1304i	0.742337	+	0.539339i	−0.151105	+	0.988518i	$0.548283\pi$
$788$	−4.66592	+	14.3602i	−0.166217	+	0.511562i
$789$	4.74340	+	14.5987i	0.168870	+	0.519727i
$790$	−11.8455	+	8.60624i	−0.421443	+	0.306196i
$791$	−16.8123			−0.597776
$792$	−0.980797	−	3.35892i	−0.0348511	−	0.119354i
$793$	−70.2690			−2.49532
$794$	3.83213	−	2.78421i	0.135997	−	0.0988079i
$795$	−1.05008	−	3.23183i	−0.0372427	−	0.114621i
$796$	7.55469	−	23.2509i	0.267769	−	0.824108i
$797$	−0.171228	−	0.124405i	−0.00606522	−	0.00440664i	0.584749	−	0.811215i	$-0.301193\pi$
$797$	−0.171228	−	0.124405i	−0.00606522	−	0.00440664i	−0.590814	+	0.806808i	$0.701193\pi$
$798$	−1.33388	−	0.969124i	−0.0472190	−	0.0343066i
$799$	−1.90438	+	5.86107i	−0.0673720	+	0.207350i
$800$	0.102349	+	0.314998i	0.00361859	+	0.0111369i
$801$	4.88967	−	3.55256i	0.172768	−	0.125523i
$802$	6.22912			0.219958
$803$	−22.6216	+	15.4185i	−0.798299	+	0.544108i
$804$	−14.1450			−0.498856
$805$	7.78293	−	5.65463i	0.274312	−	0.199299i
$806$	15.5540	+	47.8703i	0.547867	+	1.68616i
$807$	−1.61652	+	4.97513i	−0.0569041	+	0.175133i
$808$	9.41298	+	6.83893i	0.331148	+	0.240593i
$809$	−2.30006	−	1.67109i	−0.0808658	−	0.0587525i	0.546618	−	0.837382i	$-0.315915\pi$
$809$	−2.30006	−	1.67109i	−0.0808658	−	0.0587525i	−0.627484	+	0.778630i	$0.715915\pi$
$810$	3.15274	−	9.70313i	0.110776	−	0.340933i
$811$	−10.1795	−	31.3294i	−0.357452	−	1.10012i	−0.954574	−	0.297973i	$-0.903689\pi$
$811$	−10.1795	−	31.3294i	−0.357452	−	1.10012i	0.597123	−	0.802150i	$-0.296311\pi$
$812$	3.31707	−	2.40999i	0.116406	−	0.0845742i
$813$	23.8056			0.834900
$814$	5.63300	−	15.7131i	0.197436	−	0.550743i
$815$	19.6390			0.687924
$816$	2.28709	−	1.66167i	0.0800643	−	0.0581701i
$817$	2.45884	+	7.56752i	0.0860238	+	0.264754i
$818$	0.532190	−	1.63791i	0.0186076	−	0.0572682i
$819$	−6.29624	−	4.57449i	−0.220008	−	0.159845i
$820$	−4.18269	−	3.03890i	−0.146066	−	0.106123i
$821$	−4.10223	+	12.6254i	−0.143169	+	0.440628i	−0.996771	−	0.0802972i	$-0.974413\pi$
$821$	−4.10223	+	12.6254i	−0.143169	+	0.440628i	0.853602	+	0.520925i	$0.174413\pi$
$822$	8.28044	+	25.4846i	0.288814	+	0.888877i
$823$	22.0125	−	15.9930i	0.767308	−	0.557482i	−0.133835	−	0.991004i	$-0.542729\pi$
$823$	22.0125	−	15.9930i	0.767308	−	0.557482i	0.901143	+	0.433521i	$0.142729\pi$
$824$	−4.14084			−0.144253
$825$	1.53129	+	0.0460442i	0.0533126	+	0.00160305i
$826$	2.89554			0.100749
$827$	−31.4640	+	22.8599i	−1.09411	+	0.794918i	−0.980089	−	0.198560i	$-0.936374\pi$
$827$	−31.4640	+	22.8599i	−1.09411	+	0.794918i	−0.114022	+	0.993478i	$0.536374\pi$
$828$	1.22781	+	3.77880i	0.0426693	+	0.131322i
$829$	4.98832	−	15.3525i	0.173252	−	0.533213i	−0.826298	−	0.563234i	$-0.809557\pi$
$829$	4.98832	−	15.3525i	0.173252	−	0.533213i	0.999549	+	0.0300201i	$0.00955714\pi$
$830$	−31.1060	−	22.5998i	−1.07971	−	0.784452i
$831$	15.2912	+	11.1097i	0.530445	+	0.385391i
$832$	−1.92810	+	5.93408i	−0.0668449	+	0.205727i
$833$	3.50930	+	10.8005i	0.121590	+	0.374216i
$834$	−16.9113	+	12.2868i	−0.585592	+	0.425457i
$835$	−3.88099			−0.134307
$836$	−2.62340	−	2.02923i	−0.0907323	−	0.0701823i
$837$	−45.6208			−1.57689
$838$	−13.7960	+	10.0234i	−0.476574	+	0.346252i
$839$	14.1606	+	43.5820i	0.488880	+	1.50462i	0.826282	+	0.563257i	$0.190452\pi$
$839$	14.1606	+	43.5820i	0.488880	+	1.50462i	−0.337402	+	0.941361i	$0.609548\pi$
$840$	−1.10089	+	3.38820i	−0.0379844	+	0.116904i
$841$	13.7309	+	9.97606i	0.473478	+	0.344002i
$842$	−23.2530	−	16.8943i	−0.801353	−	0.582217i
$843$	10.5135	−	32.3571i	0.362103	−	1.11444i
$844$	2.91990	+	8.98653i	0.100507	+	0.309329i
$845$	−45.3292	+	32.9336i	−1.55937	+	1.13295i
$846$	3.20752			0.110277
$847$	12.9811	+	0.781364i	0.446038	+	0.0268480i
$848$	−1.12768			−0.0387246
$849$	−3.57273	+	2.59574i	−0.122616	+	0.0890855i
$850$	−0.207470	−	0.638528i	−0.00711617	−	0.0219013i
$851$	−5.85704	+	18.0261i	−0.200777	+	0.617928i
$852$	−0.654968	−	0.475862i	−0.0224388	−	0.0163028i
$853$	37.8629	+	27.5090i	1.29640	+	0.941890i	0.999914	−	0.0131476i	$-0.00418512\pi$
$853$	37.8629	+	27.5090i	1.29640	+	0.941890i	0.296486	+	0.955037i	$0.404185\pi$
$854$	−4.11438	+	12.6628i	−0.140791	+	0.433311i
$855$	0.704458	+	2.16810i	0.0240920	+	0.0741474i
$856$	10.9983	−	7.99074i	0.375915	−	0.273118i
$857$	46.6226			1.59260			0.796299	−	0.604903i	$-0.206788\pi$
$857$	46.6226			1.59260			0.796299	+	0.604903i	$0.206788\pi$
$858$	22.8280	+	17.6576i	0.779334	+	0.602822i
$859$	−47.2699			−1.61283			−0.806415	−	0.591351i	$-0.798595\pi$
$859$	−47.2699			−1.61283			−0.806415	+	0.591351i	$0.798595\pi$
$860$	13.9094	−	10.1057i	0.474305	−	0.344603i
$861$	1.21910	+	3.75200i	0.0415467	+	0.127868i
$862$	−12.4258	+	38.2426i	−0.423223	+	1.30255i
$863$	−16.3717	−	11.8947i	−0.557298	−	0.404901i	0.273171	−	0.961965i	$-0.411927\pi$
$863$	−16.3717	−	11.8947i	−0.557298	−	0.404901i	−0.830469	+	0.557065i	$0.811927\pi$
$864$	−4.57518	−	3.32406i	−0.155651	−	0.113087i
$865$	4.93318	−	15.1828i	0.167733	−	0.516230i
$866$	−0.0630624	−	0.194086i	−0.00214295	−	0.00659532i
$867$	14.5444	−	10.5672i	0.493955	−	0.358879i
$868$	9.53715			0.323712
$869$	22.4643	+	0.675476i	0.762049	+	0.0229140i
$870$	10.4508			0.354314
$871$	−51.1980	+	37.1976i	−1.73478	+	1.26039i
$872$	2.01476	+	6.20079i	0.0682284	+	0.209985i
$873$	0.835882	−	2.57258i	0.0282903	−	0.0870686i
$874$	3.04674	+	2.21358i	0.103057	+	0.0748756i
$875$	11.0177	+	8.00484i	0.372467	+	0.270613i
$876$	−3.55727	+	10.9482i	−0.120189	+	0.369904i
$877$	7.68412	+	23.6493i	0.259474	+	0.798580i	0.992915	+	0.118826i	$0.0379132\pi$
$877$	7.68412	+	23.6493i	0.259474	+	0.798580i	−0.733441	+	0.679753i	$0.762087\pi$
$878$	0.761235	−	0.553069i	0.0256904	−	0.0186652i
$879$	−28.2666			−0.953407
$880$	−2.41837	+	6.74598i	−0.0815233	+	0.227407i
$881$	3.56840			0.120222			0.0601112	−	0.998192i	$-0.480854\pi$
$881$	3.56840			0.120222			0.0601112	+	0.998192i	$0.480854\pi$
$882$	4.78184	−	3.47421i	0.161013	−	0.116983i
$883$	7.12602	+	21.9316i	0.239810	+	0.738059i	0.996447	+	0.0842236i	$0.0268410\pi$
$883$	7.12602	+	21.9316i	0.239810	+	0.738059i	−0.756637	+	0.653835i	$0.773159\pi$
$884$	3.90842	−	12.0289i	0.131454	−	0.404575i
$885$	5.97088	+	4.33810i	0.200709	+	0.145824i
$886$	2.51234	+	1.82532i	0.0844037	+	0.0613228i
$887$	14.0676	−	43.2955i	0.472343	−	1.45372i	−0.377165	−	0.926146i	$-0.623101\pi$
$887$	14.0676	−	43.2955i	0.472343	−	1.45372i	0.849508	−	0.527576i	$-0.176899\pi$
$888$	−2.16898	−	6.67544i	−0.0727863	−	0.224013i
$889$	19.3275	−	14.0422i	0.648222	−	0.470961i
$890$	−12.3781			−0.414915
$891$	−12.9404	+	8.81994i	−0.433518	+	0.295479i
$892$	−23.5903			−0.789863
$893$	2.45955	−	1.78697i	0.0823059	−	0.0597987i
$894$	−3.52806	−	10.8583i	−0.117996	−	0.363155i
$895$	−12.8784	+	39.6357i	−0.430478	+	1.32487i
$896$	0.956453	+	0.694903i	0.0319528	+	0.0232151i
$897$	−26.5117	−	19.2619i	−0.885199	−	0.643135i
$898$	7.18033	−	22.0988i	0.239611	−	0.737446i
$899$	−8.64543	−	26.6079i	−0.288341	−	0.887423i
$900$	−0.282703	+	0.205396i	−0.00942343	+	0.00684652i
$901$	2.28589			0.0761542
$902$	2.22435	+	7.61771i	0.0740629	+	0.253642i
$903$	−13.1192			−0.436580
$904$	−11.5048	+	8.35872i	−0.382644	+	0.278007i
$905$	5.68209	+	17.4877i	0.188879	+	0.581310i
$906$	0.112549	−	0.346391i	0.00373920	−	0.0115081i
$907$	−47.7765	−	34.7117i	−1.58639	−	1.15258i	−0.908868	−	0.417084i	$-0.863052\pi$
$907$	−47.7765	−	34.7117i	−1.58639	−	1.15258i	−0.677526	−	0.735499i	$-0.736948\pi$
$908$	1.71829	+	1.24841i	0.0570236	+	0.0414301i
$909$	−3.79335	+	11.6747i	−0.125817	+	0.387226i
$910$	4.92536	+	15.1587i	0.163274	+	0.502506i
$911$	18.0998	−	13.1503i	0.599674	−	0.435689i	−0.246089	−	0.969247i	$-0.579146\pi$
$911$	18.0998	−	13.1503i	0.599674	−	0.435689i	0.845763	+	0.533558i	$0.179146\pi$
$912$	−1.39462			−0.0461804
$913$	16.5422	+	56.6517i	0.547467	+	1.87490i
$914$	38.6172			1.27734
$915$	−27.4556	+	19.9477i	−0.907654	+	0.659450i
$916$	−5.04711	−	15.5334i	−0.166761	−	0.513238i
$917$	−3.81977	+	11.7560i	−0.126140	+	0.388218i
$918$	9.27427	+	6.73815i	0.306096	+	0.222392i
$919$	−21.6842	−	15.7545i	−0.715295	−	0.519692i	0.169583	−	0.985516i	$-0.445758\pi$
$919$	−21.6842	−	15.7545i	−0.715295	−	0.519692i	−0.884877	+	0.465824i	$0.845758\pi$
$920$	2.51456	−	7.73902i	0.0829026	−	0.255148i
$921$	4.34483	+	13.3720i	0.143167	+	0.440623i
$922$	−20.6719	+	15.0190i	−0.680793	+	0.494625i
$923$	−3.62205			−0.119221
$924$	4.51860	−	3.07980i	0.148651	−	0.101318i
$925$	−1.66694			−0.0548087
$926$	−1.14742	+	0.833648i	−0.0377065	+	0.0273954i
$927$	−1.35002	−	4.15495i	−0.0443406	−	0.136466i
$928$	1.07170	−	3.29836i	0.0351803	−	0.108274i
$929$	−25.8462	−	18.7783i	−0.847985	−	0.616097i	0.0766046	−	0.997062i	$-0.475592\pi$
$929$	−25.8462	−	18.7783i	−0.847985	−	0.616097i	−0.924590	+	0.380964i	$0.875592\pi$
$930$	19.6665	+	14.2886i	0.644891	+	0.468541i
$931$	1.73121	−	5.32811i	0.0567381	−	0.174622i
$932$	7.65638	+	23.5639i	0.250793	+	0.771861i
$933$	−19.0448	+	13.8368i	−0.623497	+	0.452997i
$934$	−6.11016			−0.199931
$935$	4.90224	−	13.6747i	0.160320	−	0.447209i
$936$	−6.58291			−0.215169
$937$	31.9232	−	23.1936i	1.04289	−	0.757701i	0.0720388	−	0.997402i	$-0.477049\pi$
$937$	31.9232	−	23.1936i	1.04289	−	0.757701i	0.970847	+	0.239701i	$0.0770495\pi$
$938$	3.70541	+	11.4041i	0.120986	+	0.372357i
$939$	−12.9199	+	39.7632i	−0.421624	+	1.29762i
$940$	−5.31446	−	3.86118i	−0.173338	−	0.125938i
$941$	−33.2193	−	24.1352i	−1.08292	−	0.786785i	−0.104728	−	0.994501i	$-0.533397\pi$
$941$	−33.2193	−	24.1352i	−1.08292	−	0.786785i	−0.978189	+	0.207716i	$0.933397\pi$
$942$	0.510212	−	1.57027i	0.0166236	−	0.0511622i
$943$	−2.78455	−	8.56997i	−0.0906774	−	0.279076i
$944$	1.98144	−	1.43960i	0.0644904	−	0.0468550i
$945$	−14.4464			−0.469940
$946$	−26.3783	−	0.793167i	−0.857633	−	0.0257881i
$947$	−34.2393			−1.11263			−0.556314	−	0.830972i	$-0.687785\pi$
$947$	−34.2393			−1.11263			−0.556314	+	0.830972i	$0.687785\pi$
$948$	7.64549	−	5.55477i	0.248314	−	0.180411i
$949$	15.9151	+	48.9817i	0.516626	+	1.59001i
$950$	−0.102349	+	0.314998i	−0.00332065	+	0.0102199i
$951$	−11.4907	−	8.34846i	−0.372611	−	0.270717i
$952$	−1.93881	−	1.40863i	−0.0628371	−	0.0456539i
$953$	10.6605	−	32.8095i	0.345326	−	1.06281i	−0.616082	−	0.787682i	$-0.711281\pi$
$953$	10.6605	−	32.8095i	0.345326	−	1.06281i	0.961409	−	0.275124i	$-0.0887188\pi$
$954$	−0.367653	−	1.13152i	−0.0119032	−	0.0366343i
$955$	−27.7258	+	20.1440i	−0.897185	+	0.651843i
$956$	−4.61123			−0.149138
$957$	−12.6885	−	9.81470i	−0.410162	−	0.317264i
$958$	0.621165			0.0200689
$959$	18.3772	−	13.3518i	0.593431	−	0.431153i
$960$	0.931193	+	2.86592i	0.0300541	+	0.0924970i
$961$	10.5303	−	32.4089i	0.339687	−	1.04545i
$962$	−25.4053	−	18.4580i	−0.819098	−	0.595110i
$963$	11.6037	+	8.43059i	0.373924	+	0.271672i
$964$	1.75905	−	5.41381i	0.0566553	−	0.174367i
$965$	17.8736	+	55.0093i	0.575372	+	1.77081i
$966$	−5.02338	+	3.64970i	−0.161624	+	0.117427i
$967$	−2.27993			−0.0733178			−0.0366589	−	0.999328i	$-0.511671\pi$
$967$	−2.27993			−0.0733178			−0.0366589	+	0.999328i	$0.511671\pi$
$968$	9.27159	−	5.91926i	0.298000	−	0.190252i
$969$	2.82700			0.0908165
$970$	−4.48179	+	3.25621i	−0.143902	+	0.104551i
$971$	−4.02093	−	12.3751i	−0.129038	−	0.397137i	0.865577	−	0.500775i	$-0.166952\pi$
$971$	−4.02093	−	12.3751i	−0.129038	−	0.397137i	−0.994615	+	0.103638i	$0.966952\pi$
$972$	3.20780	−	9.87260i	0.102890	−	0.316664i
$973$	14.3360	+	10.4157i	0.459592	+	0.333913i
$974$	−13.4744	−	9.78974i	−0.431748	−	0.313683i
$975$	0.890608	−	2.74101i	0.0285223	−	0.0877826i
$976$	3.48016	+	10.7108i	0.111397	+	0.342845i
$977$	4.68727	−	3.40550i	0.149959	−	0.108952i	−0.510276	−	0.860011i	$-0.670457\pi$
$977$	4.68727	−	3.40550i	0.149959	−	0.108952i	0.660235	+	0.751059i	$0.270457\pi$
$978$	−12.6757			−0.405324
$979$	15.0285	+	11.6247i	0.480314	+	0.371528i
$980$	−12.1051			−0.386684
$981$	−5.56505	+	4.04325i	−0.177678	+	0.129091i
$982$	−8.39828	−	25.8473i	−0.268000	−	0.824819i
$983$	14.2688	−	43.9150i	0.455105	−	1.40067i	−0.415907	−	0.909407i	$-0.636536\pi$
$983$	14.2688	−	43.9150i	0.455105	−	1.40067i	0.871012	−	0.491262i	$-0.163464\pi$
$984$	2.69965	+	1.96141i	0.0860618	+	0.0625275i
$985$	26.3946	+	19.1768i	0.841002	+	0.611024i
$986$	−2.17243	+	6.68604i	−0.0691842	+	0.212927i
$987$	1.54897	+	4.76723i	0.0493041	+	0.151743i
$988$	−5.04783	+	3.66746i	−0.160593	+	0.116678i
$989$	29.9657			0.952854
$990$	−7.55741	−	0.227243i	−0.240190	−	0.00722225i
$991$	−42.7945			−1.35941			−0.679706	−	0.733485i	$-0.737892\pi$
$991$	−42.7945			−1.35941			−0.679706	+	0.733485i	$0.737892\pi$
$992$	6.52635	−	4.74167i	0.207212	−	0.150548i
$993$	−3.80590	−	11.7133i	−0.120776	−	0.371712i
$994$	−0.212078	+	0.652709i	−0.00672671	+	0.0207027i
$995$	−42.7360	−	31.0495i	−1.35482	−	0.984337i
$996$	20.0769	+	14.5867i	0.636161	+	0.462198i
$997$	11.2957	−	34.7645i	0.357738	−	1.10100i	−0.596667	−	0.802489i	$-0.703509\pi$
$997$	11.2957	−	34.7645i	0.357738	−	1.10100i	0.954405	−	0.298515i	$-0.0964912\pi$
$998$	−2.60195	−	8.00799i	−0.0823634	−	0.253488i
$999$	23.0264	−	16.7297i	0.728524	−	0.529304i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.f.h.267.4	yes	20
11.2	odd	10		4598.2.a.cd.1.7		10
11.4	even	5	inner	418.2.f.h.191.4	✓	20
11.9	even	5		4598.2.a.cc.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.h.191.4	✓	20	11.4	even	5	inner
418.2.f.h.267.4	yes	20	1.1	even	1	trivial
4598.2.a.cc.1.7		10	11.9	even	5
4598.2.a.cd.1.7		10	11.2	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.430960 + 1.32636i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.74807 - 1.27005i) q^{5} +(1.12827 + 0.819735i) q^{6} +(0.365332 - 1.12438i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.853548 - 0.620139i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.430960 + 1.32636i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.74807 - 1.27005i) q^{5} +(1.12827 + 0.819735i) q^{6} +(0.365332 - 1.12438i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.853548 - 0.620139i) q^{9} -2.16074 q^{10} +(2.62340 + 2.02923i) q^{11} +1.39462 q^{12} +(5.04783 - 3.66746i) q^{13} +(-0.365332 - 1.12438i) q^{14} +(0.931193 - 2.86592i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.63994 + 1.19149i) q^{17} +(0.326026 - 1.00341i) q^{18} +(-0.309017 - 0.951057i) q^{19} +(-1.74807 + 1.27005i) q^{20} +1.64877 q^{21} +(3.31513 + 0.0996822i) q^{22} -3.76597 q^{23} +(1.12827 - 0.819735i) q^{24} +(-0.102349 - 0.314998i) q^{25} +(1.92810 - 5.93408i) q^{26} +(4.57518 + 3.32406i) q^{27} +(-0.956453 - 0.694903i) q^{28} +(-1.07170 + 3.29836i) q^{29} +(-0.931193 - 2.86592i) q^{30} +(-6.52635 + 4.74167i) q^{31} -1.00000 q^{32} +(-1.56090 + 4.35409i) q^{33} +2.02708 q^{34} +(-2.06664 + 1.50150i) q^{35} +(-0.326026 - 1.00341i) q^{36} +(1.55525 - 4.78658i) q^{37} +(-0.809017 - 0.587785i) q^{38} +(7.03979 + 5.11471i) q^{39} +(-0.667705 + 2.05498i) q^{40} +(0.739397 + 2.27563i) q^{41} +(1.33388 - 0.969124i) q^{42} -7.95696 q^{43} +(2.74059 - 1.86794i) q^{44} -2.27967 q^{45} +(-3.04674 + 2.21358i) q^{46} +(0.939466 + 2.89138i) q^{47} +(0.430960 - 1.32636i) q^{48} +(4.53236 + 3.29295i) q^{49} +(-0.267954 - 0.194680i) q^{50} +(-0.873592 + 2.68864i) q^{51} +(-1.92810 - 5.93408i) q^{52} +(0.912310 - 0.662832i) q^{53} +5.65523 q^{54} +(-2.00868 - 6.87909i) q^{55} -1.18224 q^{56} +(1.12827 - 0.819735i) q^{57} +(1.07170 + 3.29836i) q^{58} +(-0.756843 + 2.32932i) q^{59} +(-2.43789 - 1.77123i) q^{60} +(-9.11117 - 6.61965i) q^{61} +(-2.49284 + 7.67219i) q^{62} +(-0.385442 - 1.18627i) q^{63} +(-0.809017 + 0.587785i) q^{64} -13.4819 q^{65} +(1.29647 + 4.44001i) q^{66} -10.1426 q^{67} +(1.63994 - 1.19149i) q^{68} +(-1.62299 - 4.99504i) q^{69} +(-0.789388 + 2.42949i) q^{70} +(-0.469640 - 0.341214i) q^{71} +(-0.853548 - 0.620139i) q^{72} +(-2.55072 + 7.85030i) q^{73} +(-1.55525 - 4.78658i) q^{74} +(0.373693 - 0.271504i) q^{75} -1.00000 q^{76} +(3.24003 - 2.20835i) q^{77} +8.70166 q^{78} +(5.48214 - 3.98301i) q^{79} +(0.667705 + 2.05498i) q^{80} +(-1.45910 + 4.49065i) q^{81} +(1.93577 + 1.40642i) q^{82} +(14.3960 + 10.4593i) q^{83} +(0.509499 - 1.56808i) q^{84} +(-1.35349 - 4.16562i) q^{85} +(-6.43731 + 4.67698i) q^{86} -4.83667 q^{87} +(1.11923 - 3.12207i) q^{88} +5.72864 q^{89} +(-1.84429 + 1.33996i) q^{90} +(-2.27948 - 7.01551i) q^{91} +(-1.16375 + 3.58165i) q^{92} +(-9.10176 - 6.61282i) q^{93} +(2.45955 + 1.78697i) q^{94} +(-0.667705 + 2.05498i) q^{95} +(-0.430960 - 1.32636i) q^{96} +(2.07419 - 1.50699i) q^{97} +5.60231 q^{98} +(3.49760 + 0.105169i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9}+O(q^{10}) \) 20 * q + 5 * q^2 - q^3 - 5 * q^4 - q^5 + q^6 + 13 * q^7 + 5 * q^8 - 6 * q^9	\( 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9} + 6 q^{10} + q^{11} + 4 q^{12} - 2 q^{13} - 13 q^{14} - 8 q^{15} - 5 q^{16} + 11 q^{17} + 6 q^{18} + 5 q^{19} - q^{20} + 2 q^{21} + 4 q^{22} + 28 q^{23} + q^{24} - 30 q^{25} - 13 q^{26} - 31 q^{27} - 2 q^{28} + 28 q^{29} + 8 q^{30} - q^{31} - 20 q^{32} + 9 q^{33} + 24 q^{34} - 11 q^{35} - 6 q^{36} + 8 q^{37} - 5 q^{38} + 18 q^{39} - 4 q^{40} - 5 q^{41} - 22 q^{42} - 44 q^{43} + 11 q^{44} - 4 q^{45} + 7 q^{46} - 39 q^{47} - q^{48} + 4 q^{49} - 25 q^{50} - 11 q^{51} + 13 q^{52} - q^{53} - 4 q^{54} + 8 q^{55} + 22 q^{56} + q^{57} - 28 q^{58} + 6 q^{59} + 7 q^{60} + 10 q^{61} + 11 q^{62} + 34 q^{63} - 5 q^{64} - 8 q^{65} + 41 q^{66} + 18 q^{67} + 11 q^{68} - 63 q^{69} + q^{70} - 3 q^{71} + 6 q^{72} + 5 q^{73} - 8 q^{74} + 5 q^{75} - 20 q^{76} + 36 q^{77} + 22 q^{78} + 19 q^{79} + 4 q^{80} + 63 q^{81} - 9 q^{83} - 23 q^{84} + 30 q^{85} - 26 q^{86} - 16 q^{87} - q^{88} + 44 q^{89} + 14 q^{90} - 68 q^{91} - 7 q^{92} + 27 q^{93} - 31 q^{94} - 4 q^{95} + q^{96} - 71 q^{97} + 6 q^{98} + 20 q^{99}+O(q^{100}) \) 20 * q + 5 * q^2 - q^3 - 5 * q^4 - q^5 + q^6 + 13 * q^7 + 5 * q^8 - 6 * q^9 + 6 * q^10 + q^11 + 4 * q^12 - 2 * q^13 - 13 * q^14 - 8 * q^15 - 5 * q^16 + 11 * q^17 + 6 * q^18 + 5 * q^19 - q^20 + 2 * q^21 + 4 * q^22 + 28 * q^23 + q^24 - 30 * q^25 - 13 * q^26 - 31 * q^27 - 2 * q^28 + 28 * q^29 + 8 * q^30 - q^31 - 20 * q^32 + 9 * q^33 + 24 * q^34 - 11 * q^35 - 6 * q^36 + 8 * q^37 - 5 * q^38 + 18 * q^39 - 4 * q^40 - 5 * q^41 - 22 * q^42 - 44 * q^43 + 11 * q^44 - 4 * q^45 + 7 * q^46 - 39 * q^47 - q^48 + 4 * q^49 - 25 * q^50 - 11 * q^51 + 13 * q^52 - q^53 - 4 * q^54 + 8 * q^55 + 22 * q^56 + q^57 - 28 * q^58 + 6 * q^59 + 7 * q^60 + 10 * q^61 + 11 * q^62 + 34 * q^63 - 5 * q^64 - 8 * q^65 + 41 * q^66 + 18 * q^67 + 11 * q^68 - 63 * q^69 + q^70 - 3 * q^71 + 6 * q^72 + 5 * q^73 - 8 * q^74 + 5 * q^75 - 20 * q^76 + 36 * q^77 + 22 * q^78 + 19 * q^79 + 4 * q^80 + 63 * q^81 - 9 * q^83 - 23 * q^84 + 30 * q^85 - 26 * q^86 - 16 * q^87 - q^88 + 44 * q^89 + 14 * q^90 - 68 * q^91 - 7 * q^92 + 27 * q^93 - 31 * q^94 - 4 * q^95 + q^96 - 71 * q^97 + 6 * q^98 + 20 * q^99

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