LMFDB - Embedded newform 429.2.n.b.235.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(157,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("429.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.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:	$3.42558224671$
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} + 4 x^{18} + 4 x^{17} + 37 x^{16} - 74 x^{15} + 398 x^{14} - 224 x^{13} + 978 x^{12} + \cdots + 121 $ x^20 - x^19 + 4x^18 + 4x^17 + 37x^16 - 74x^15 + 398x^14 - 224x^13 + 978x^12 + 115x^11 + 1963x^10 + 323x^9 + 3007x^8 + 1828x^7 + 6736x^6 + 4512x^5 + 5197x^4 + 2152x^3 + 1259x^2 + 495x + 121
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			235.1
Root			$-2.26411 + 1.64497i$ of defining polynomial
Character	$\chi$	$=$	429.235
Dual form			429.2.n.b.157.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.26411 - 1.64497i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.80222 + 5.54667i) q^{4} +(2.68510 - 1.95084i) q^{5} +(2.26411 - 1.64497i) q^{6} +(-0.449002 - 1.38189i) q^{7} +(3.31406 - 10.1996i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-2.26411 - 1.64497i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.80222 + 5.54667i) q^{4} +(2.68510 - 1.95084i) q^{5} +(2.26411 - 1.64497i) q^{6} +(-0.449002 - 1.38189i) q^{7} +(3.31406 - 10.1996i) q^{8} +(-0.809017 - 0.587785i) q^{9} -9.28845 q^{10} +(0.682296 + 3.24569i) q^{11} -5.83212 q^{12} +(0.809017 + 0.587785i) q^{13} +(-1.25657 + 3.86734i) q^{14} +(1.02562 + 3.15653i) q^{15} +(-14.8450 + 10.7855i) q^{16} +(5.09765 - 3.70366i) q^{17} +(0.864813 + 2.66162i) q^{18} +(0.174485 - 0.537010i) q^{19} +(15.6598 + 11.3775i) q^{20} +1.45300 q^{21} +(3.79427 - 8.47094i) q^{22} -3.52426 q^{23} +(8.67633 + 6.30373i) q^{24} +(1.85891 - 5.72114i) q^{25} +(-0.864813 - 2.66162i) q^{26} +(0.809017 - 0.587785i) q^{27} +(6.85567 - 4.98094i) q^{28} +(-0.493471 - 1.51875i) q^{29} +(2.87029 - 8.83384i) q^{30} +(7.96581 + 5.78750i) q^{31} +29.9033 q^{32} +(-3.29767 - 0.354070i) q^{33} -17.6341 q^{34} +(-3.90146 - 2.83458i) q^{35} +(1.80222 - 5.54667i) q^{36} +(-0.422984 - 1.30181i) q^{37} +(-1.27842 + 0.928827i) q^{38} +(-0.809017 + 0.587785i) q^{39} +(-10.9993 - 33.8523i) q^{40} +(1.12880 - 3.47408i) q^{41} +(-3.28975 - 2.39015i) q^{42} -4.12353 q^{43} +(-16.7731 + 9.63393i) q^{44} -3.31897 q^{45} +(7.97931 + 5.79731i) q^{46} +(1.75847 - 5.41201i) q^{47} +(-5.67027 - 17.4513i) q^{48} +(3.95511 - 2.87356i) q^{49} +(-13.6199 + 9.89544i) q^{50} +(1.94713 + 5.99265i) q^{51} +(-1.80222 + 5.54667i) q^{52} +(1.89461 + 1.37652i) q^{53} -2.79859 q^{54} +(8.16386 + 7.38395i) q^{55} -15.5828 q^{56} +(0.456808 + 0.331891i) q^{57} +(-1.38102 + 4.25036i) q^{58} +(-2.82208 - 8.68548i) q^{59} +(-15.6598 + 11.3775i) q^{60} +(2.21192 - 1.60705i) q^{61} +(-8.51519 - 26.2071i) q^{62} +(-0.449002 + 1.38189i) q^{63} +(-38.0145 - 27.6192i) q^{64} +3.31897 q^{65} +(6.88385 + 6.22623i) q^{66} +6.27162 q^{67} +(29.7301 + 21.6002i) q^{68} +(1.08906 - 3.35177i) q^{69} +(4.17053 + 12.8356i) q^{70} +(-0.143536 + 0.104285i) q^{71} +(-8.67633 + 6.30373i) q^{72} +(-1.01200 - 3.11462i) q^{73} +(-1.18376 + 3.64324i) q^{74} +(4.86670 + 3.53586i) q^{75} +3.29308 q^{76} +(4.17882 - 2.40018i) q^{77} +2.79859 q^{78} +(0.0831306 + 0.0603979i) q^{79} +(-18.8195 + 57.9203i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-8.27048 + 6.00886i) q^{82} +(11.2763 - 8.19273i) q^{83} +(2.61863 + 8.05933i) q^{84} +(6.46247 - 19.8894i) q^{85} +(9.33612 + 6.78309i) q^{86} +1.59691 q^{87} +(35.3660 + 3.79723i) q^{88} -1.06640 q^{89} +(7.51451 + 5.45961i) q^{90} +(0.449002 - 1.38189i) q^{91} +(-6.35151 - 19.5479i) q^{92} +(-7.96581 + 5.78750i) q^{93} +(-12.8840 + 9.36075i) q^{94} +(-0.579112 - 1.78232i) q^{95} +(-9.24064 + 28.4398i) q^{96} +(11.8080 + 8.57903i) q^{97} -13.6817 q^{98} +(1.35578 - 3.02686i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9}+O(q^{10}) $ 20 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - q^6 - 3 * q^7 - 7 * q^8 - 5 * q^9	\( 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9} - 2 q^{10} + 14 q^{11} - 18 q^{12} + 5 q^{13} - q^{14} - 4 q^{15} - 35 q^{16} + 2 q^{17} - 4 q^{18} - 2 q^{19} + 45 q^{20} - 2 q^{21} + 11 q^{22} + 6 q^{23} + 2 q^{24} - 7 q^{25} + 4 q^{26} + 5 q^{27} + 12 q^{28} + 26 q^{29} - 3 q^{30} + 20 q^{31} + 42 q^{32} + q^{33} - 24 q^{34} - 18 q^{35} + 3 q^{36} - 6 q^{37} - 3 q^{38} - 5 q^{39} - 26 q^{41} - 9 q^{42} + 28 q^{43} - 38 q^{44} - 16 q^{45} - 17 q^{46} + 8 q^{47} - 20 q^{48} + 2 q^{49} - 29 q^{50} + 3 q^{51} - 3 q^{52} + q^{53} - 6 q^{54} - 36 q^{56} - 8 q^{57} + 22 q^{58} - 21 q^{59} - 45 q^{60} + 26 q^{61} - 10 q^{62} - 3 q^{63} - 87 q^{64} + 16 q^{65} + 14 q^{66} + 56 q^{67} + 65 q^{68} + 4 q^{69} - 24 q^{70} - 28 q^{71} - 2 q^{72} + 45 q^{73} - 29 q^{74} - 3 q^{75} + 60 q^{76} + 4 q^{77} + 6 q^{78} - 15 q^{79} - 7 q^{80} - 5 q^{81} - 46 q^{82} + 36 q^{83} + 8 q^{84} + 39 q^{86} + 24 q^{87} + 73 q^{88} - 126 q^{89} - 2 q^{90} + 3 q^{91} + 2 q^{92} - 20 q^{93} - 3 q^{94} + 47 q^{95} - 47 q^{96} + 18 q^{97} - 54 q^{98} - 16 q^{99}+O(q^{100}) \) 20 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - q^6 - 3 * q^7 - 7 * q^8 - 5 * q^9 - 2 * q^10 + 14 * q^11 - 18 * q^12 + 5 * q^13 - q^14 - 4 * q^15 - 35 * q^16 + 2 * q^17 - 4 * q^18 - 2 * q^19 + 45 * q^20 - 2 * q^21 + 11 * q^22 + 6 * q^23 + 2 * q^24 - 7 * q^25 + 4 * q^26 + 5 * q^27 + 12 * q^28 + 26 * q^29 - 3 * q^30 + 20 * q^31 + 42 * q^32 + q^33 - 24 * q^34 - 18 * q^35 + 3 * q^36 - 6 * q^37 - 3 * q^38 - 5 * q^39 - 26 * q^41 - 9 * q^42 + 28 * q^43 - 38 * q^44 - 16 * q^45 - 17 * q^46 + 8 * q^47 - 20 * q^48 + 2 * q^49 - 29 * q^50 + 3 * q^51 - 3 * q^52 + q^53 - 6 * q^54 - 36 * q^56 - 8 * q^57 + 22 * q^58 - 21 * q^59 - 45 * q^60 + 26 * q^61 - 10 * q^62 - 3 * q^63 - 87 * q^64 + 16 * q^65 + 14 * q^66 + 56 * q^67 + 65 * q^68 + 4 * q^69 - 24 * q^70 - 28 * q^71 - 2 * q^72 + 45 * q^73 - 29 * q^74 - 3 * q^75 + 60 * q^76 + 4 * q^77 + 6 * q^78 - 15 * q^79 - 7 * q^80 - 5 * q^81 - 46 * q^82 + 36 * q^83 + 8 * q^84 + 39 * q^86 + 24 * q^87 + 73 * q^88 - 126 * q^89 - 2 * q^90 + 3 * q^91 + 2 * q^92 - 20 * q^93 - 3 * q^94 + 47 * q^95 - 47 * q^96 + 18 * q^97 - 54 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$	−2.26411	−	1.64497i	−1.60097	−	1.16317i	−0.885631	−	0.464389i	$-0.846274\pi$
$2$	−2.26411	−	1.64497i	−1.60097	−	1.16317i	−0.715335	−	0.698781i	$-0.753726\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$	1.80222	+	5.54667i	0.901112	+	2.77334i
$5$	2.68510	−	1.95084i	1.20081	−	0.872443i	0.206450	−	0.978457i	$-0.433809\pi$
$5$	2.68510	−	1.95084i	1.20081	−	0.872443i	0.994365	+	0.106014i	$0.0338088\pi$
$6$	2.26411	−	1.64497i	0.924319	−	0.671557i
$7$	−0.449002	−	1.38189i	−0.169707	−	0.522304i	0.829645	−	0.558291i	$-0.188543\pi$
$7$	−0.449002	−	1.38189i	−0.169707	−	0.522304i	−0.999352	+	0.0359866i	$0.988543\pi$
$8$	3.31406	−	10.1996i	1.17170	−	3.60612i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	−9.28845			−2.93726
$11$	0.682296	+	3.24569i	0.205720	+	0.978611i
$11$	0.682296	+	3.24569i	0.205720	+	0.978611i
$12$	−5.83212			−1.68359
$13$	0.809017	+	0.587785i	0.224381	+	0.163022i
$13$	0.809017	+	0.587785i	0.224381	+	0.163022i
$14$	−1.25657	+	3.86734i	−0.335834	+	1.03359i
$15$	1.02562	+	3.15653i	0.264814	+	0.815012i
$16$	−14.8450	+	10.7855i	−3.71124	+	2.69637i
$17$	5.09765	−	3.70366i	1.23636	−	0.898270i	0.239012	−	0.971017i	$-0.423177\pi$
$17$	5.09765	−	3.70366i	1.23636	−	0.898270i	0.997350	+	0.0727469i	$0.0231765\pi$
$18$	0.864813	+	2.66162i	0.203838	+	0.627350i
$19$	0.174485	−	0.537010i	0.0400297	−	0.123199i	−0.929045	−	0.369967i	$-0.879369\pi$
$19$	0.174485	−	0.537010i	0.0400297	−	0.123199i	0.969074	+	0.246769i	$0.0793688\pi$
$20$	15.6598	+	11.3775i	3.50165	+	2.54410i
$21$	1.45300			0.317071
$22$	3.79427	−	8.47094i	0.808940	−	1.80601i
$23$	−3.52426			−0.734859			−0.367430	−	0.930051i	$-0.619762\pi$
$23$	−3.52426			−0.734859			−0.367430	+	0.930051i	$0.619762\pi$
$24$	8.67633	+	6.30373i	1.77105	+	1.28674i
$25$	1.85891	−	5.72114i	0.371783	−	1.14423i
$26$	−0.864813	−	2.66162i	−0.169604	−	0.521987i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	6.85567	−	4.98094i	1.29560	−	0.941309i
$29$	−0.493471	−	1.51875i	−0.0916353	−	0.282024i	0.894727	−	0.446614i	$-0.147370\pi$
$29$	−0.493471	−	1.51875i	−0.0916353	−	0.282024i	−0.986362	+	0.164589i	$0.947370\pi$
$30$	2.87029	−	8.83384i	0.524040	−	1.61283i
$31$	7.96581	+	5.78750i	1.43070	+	1.03947i	0.989885	+	0.141869i	$0.0453112\pi$
$31$	7.96581	+	5.78750i	1.43070	+	1.03947i	0.440817	+	0.897597i	$0.354689\pi$
$32$	29.9033			5.28621
$33$	−3.29767	−	0.354070i	−0.574051	−	0.0616356i
$34$	−17.6341			−3.02422
$35$	−3.90146	−	2.83458i	−0.659467	−	0.479131i
$36$	1.80222	−	5.54667i	0.300371	−	0.924446i
$37$	−0.422984	−	1.30181i	−0.0695382	−	0.214016i	0.910248	−	0.414063i	$-0.135891\pi$
$37$	−0.422984	−	1.30181i	−0.0695382	−	0.214016i	−0.979786	+	0.200047i	$0.935891\pi$
$38$	−1.27842	+	0.928827i	−0.207387	+	0.150676i
$39$	−0.809017	+	0.587785i	−0.129546	+	0.0941210i
$40$	−10.9993	−	33.8523i	−1.73914	−	5.35252i
$41$	1.12880	−	3.47408i	0.176288	−	0.542560i	−0.823402	−	0.567459i	$-0.807926\pi$
$41$	1.12880	−	3.47408i	0.176288	−	0.542560i	0.999690	+	0.0248991i	$0.00792645\pi$
$42$	−3.28975	−	2.39015i	−0.507620	−	0.368808i
$43$	−4.12353			−0.628832			−0.314416	−	0.949285i	$-0.601809\pi$
$43$	−4.12353			−0.628832			−0.314416	+	0.949285i	$0.601809\pi$
$44$	−16.7731	+	9.63393i	−2.52864	+	1.45237i
$45$	−3.31897			−0.494763
$46$	7.97931	+	5.79731i	1.17649	+	0.854767i
$47$	1.75847	−	5.41201i	0.256499	−	0.789423i	−0.737031	−	0.675858i	$-0.763773\pi$
$47$	1.75847	−	5.41201i	0.256499	−	0.789423i	0.993531	−	0.113565i	$-0.0362270\pi$
$48$	−5.67027	−	17.4513i	−0.818433	−	2.51888i
$49$	3.95511	−	2.87356i	0.565016	−	0.410508i
$50$	−13.6199	+	9.89544i	−1.92614	+	1.39943i
$51$	1.94713	+	5.99265i	0.272653	+	0.839139i
$52$	−1.80222	+	5.54667i	−0.249923	+	0.769185i
$53$	1.89461	+	1.37652i	0.260245	+	0.189079i	0.710255	−	0.703945i	$-0.248580\pi$
$53$	1.89461	+	1.37652i	0.260245	+	0.189079i	−0.450010	+	0.893023i	$0.648580\pi$
$54$	−2.79859			−0.380840
$55$	8.16386	+	7.38395i	1.10081	+	0.995652i
$56$	−15.5828			−2.08234
$57$	0.456808	+	0.331891i	0.0605057	+	0.0439600i
$58$	−1.38102	+	4.25036i	−0.181337	+	0.558099i
$59$	−2.82208	−	8.68548i	−0.367404	−	1.13075i	−0.948462	−	0.316891i	$-0.897361\pi$
$59$	−2.82208	−	8.68548i	−0.367404	−	1.13075i	0.581058	−	0.813862i	$-0.302639\pi$
$60$	−15.6598	+	11.3775i	−2.02168	+	1.46883i
$61$	2.21192	−	1.60705i	0.283207	−	0.205762i	−0.437108	−	0.899409i	$-0.643997\pi$
$61$	2.21192	−	1.60705i	0.283207	−	0.205762i	0.720315	+	0.693647i	$0.243997\pi$
$62$	−8.51519	−	26.2071i	−1.08143	−	3.32830i
$63$	−0.449002	+	1.38189i	−0.0565690	+	0.174101i
$64$	−38.0145	−	27.6192i	−4.75181	−	3.45239i
$65$	3.31897			0.411668
$66$	6.88385	+	6.22623i	0.847344	+	0.766396i
$67$	6.27162			0.766200			0.383100	−	0.923707i	$-0.374856\pi$
$67$	6.27162			0.766200			0.383100	+	0.923707i	$0.374856\pi$
$68$	29.7301	+	21.6002i	3.60531	+	2.61941i
$69$	1.08906	−	3.35177i	0.131107	−	0.403506i
$70$	4.17053	+	12.8356i	0.498474	+	1.53415i
$71$	−0.143536	+	0.104285i	−0.0170345	+	0.0123763i	−0.596270	−	0.802784i	$-0.703351\pi$
$71$	−0.143536	+	0.104285i	−0.0170345	+	0.0123763i	0.579235	+	0.815160i	$0.303351\pi$
$72$	−8.67633	+	6.30373i	−1.02252	+	0.742901i
$73$	−1.01200	−	3.11462i	−0.118446	−	0.364538i	0.874204	−	0.485558i	$-0.161384\pi$
$73$	−1.01200	−	3.11462i	−0.118446	−	0.364538i	−0.992650	+	0.121020i	$0.961384\pi$
$74$	−1.18376	+	3.64324i	−0.137609	+	0.423518i
$75$	4.86670	+	3.53586i	0.561958	+	0.408286i
$76$	3.29308			0.377743
$77$	4.17882	−	2.40018i	0.476220	−	0.273525i
$78$	2.79859			0.316878
$79$	0.0831306	+	0.0603979i	0.00935292	+	0.00679530i	0.592452	−	0.805606i	$-0.298160\pi$
$79$	0.0831306	+	0.0603979i	0.00935292	+	0.00679530i	−0.583099	+	0.812401i	$0.698160\pi$
$80$	−18.8195	+	57.9203i	−2.10408	+	6.47569i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−8.27048	+	6.00886i	−0.913322	+	0.663567i
$83$	11.2763	−	8.19273i	1.23774	−	0.899269i	0.240293	−	0.970700i	$-0.422757\pi$
$83$	11.2763	−	8.19273i	1.23774	−	0.899269i	0.997446	+	0.0714311i	$0.0227566\pi$
$84$	2.61863	+	8.05933i	0.285716	+	0.879345i
$85$	6.46247	−	19.8894i	0.700953	−	2.15731i
$86$	9.33612	+	6.78309i	1.00674	+	0.731439i
$87$	1.59691			0.171206
$88$	35.3660	+	3.79723i	3.77003	+	0.404787i
$89$	−1.06640			−0.113038			−0.0565189	−	0.998402i	$-0.518000\pi$
$89$	−1.06640			−0.113038			−0.0565189	+	0.998402i	$0.518000\pi$
$90$	7.51451	+	5.45961i	0.792099	+	0.575494i
$91$	0.449002	−	1.38189i	0.0470682	−	0.144861i
$92$	−6.35151	−	19.5479i	−0.662191	−	2.03801i
$93$	−7.96581	+	5.78750i	−0.826016	+	0.600136i
$94$	−12.8840	+	9.36075i	−1.32888	+	0.965488i
$95$	−0.579112	−	1.78232i	−0.0594156	−	0.182862i
$96$	−9.24064	+	28.4398i	−0.943119	+	2.90262i
$97$	11.8080	+	8.57903i	1.19892	+	0.871068i	0.994178	−	0.107747i	$-0.0343637\pi$
$97$	11.8080	+	8.57903i	1.19892	+	0.871068i	0.204744	+	0.978815i	$0.434364\pi$
$98$	−13.6817			−1.38206
$99$	1.35578	−	3.02686i	0.136261	−	0.304211i
$100$	35.0835			3.50835
$101$	−5.64383	−	4.10048i	−0.561582	−	0.408013i	0.270455	−	0.962733i	$-0.412826\pi$
$101$	−5.64383	−	4.10048i	−0.561582	−	0.408013i	−0.832038	+	0.554719i	$0.812826\pi$
$102$	5.44922	−	16.7710i	0.539553	−	1.66057i
$103$	2.93381	+	9.02935i	0.289077	+	0.889689i	0.985147	+	0.171714i	$0.0549306\pi$
$103$	2.93381	+	9.02935i	0.289077	+	0.889689i	−0.696069	+	0.717974i	$0.745069\pi$
$104$	8.67633	−	6.30373i	0.850785	−	0.618131i
$105$	3.90146	−	2.83458i	0.380744	−	0.276626i
$106$	−2.02528	−	6.23316i	−0.196712	−	0.605418i
$107$	−2.06368	+	6.35136i	−0.199504	+	0.614009i	0.800391	+	0.599479i	$0.204625\pi$
$107$	−2.06368	+	6.35136i	−0.199504	+	0.614009i	−0.999894	+	0.0145305i	$0.995375\pi$
$108$	4.71828	+	3.42803i	0.454017	+	0.329863i
$109$	−6.65315			−0.637256			−0.318628	−	0.947880i	$-0.603222\pi$
$109$	−6.65315			−0.637256			−0.318628	+	0.947880i	$0.603222\pi$
$110$	−6.33747	−	30.1474i	−0.604254	−	2.87444i
$111$	1.36881			0.129921
$112$	21.5697	+	15.6713i	2.03815	+	1.48080i
$113$	−3.43813	+	10.5815i	−0.323432	+	0.995422i	0.648711	+	0.761035i	$0.275308\pi$
$113$	−3.43813	+	10.5815i	−0.323432	+	0.995422i	−0.972143	+	0.234387i	$0.924692\pi$
$114$	−0.488313	−	1.50287i	−0.0457347	−	0.140757i
$115$	−9.46301	+	6.87528i	−0.882430	+	0.641123i
$116$	7.53465	−	5.47425i	0.699575	−	0.508271i
$117$	−0.309017	−	0.951057i	−0.0285686	−	0.0879252i
$118$	−7.89786	+	24.3071i	−0.727057	+	2.23765i
$119$	−7.40690	−	5.38143i	−0.678989	−	0.493314i
$120$	35.5944			3.24931
$121$	−10.0689	+	4.42904i	−0.915359	+	0.402640i
$122$	−7.65158			−0.692741
$123$	2.95523	+	2.14710i	0.266464	+	0.193597i
$124$	−17.7452	+	54.6142i	−1.59357	+	4.90450i
$125$	−1.04158	−	3.20567i	−0.0931622	−	0.286724i
$126$	3.28975	−	2.39015i	0.293075	−	0.212931i
$127$	−6.14045	+	4.46130i	−0.544877	+	0.395876i	−0.825893	−	0.563827i	$-0.809329\pi$
$127$	−6.14045	+	4.46130i	−0.544877	+	0.395876i	0.281016	+	0.959703i	$0.409329\pi$
$128$	22.1550	+	68.1860i	1.95824	+	6.02685i
$129$	1.27424	−	3.92171i	0.112191	−	0.345287i
$130$	−7.51451	−	5.45961i	−0.659066	−	0.478840i
$131$	−16.6057			−1.45085			−0.725423	−	0.688303i	$-0.758356\pi$
$131$	−16.6057			−1.45085			−0.725423	+	0.688303i	$0.758356\pi$
$132$	−3.97923	−	18.9292i	−0.346348	−	1.64758i
$133$	−0.820432			−0.0711405
$134$	−14.1996	−	10.3166i	−1.22666	−	0.891222i
$135$	1.02562	−	3.15653i	0.0882712	−	0.271671i
$136$	−20.8821	−	64.2684i	−1.79062	−	5.51097i
$137$	−0.972861	+	0.706825i	−0.0831171	+	0.0603881i	−0.628568	−	0.777755i	$-0.716359\pi$
$137$	−0.972861	+	0.706825i	−0.0831171	+	0.0603881i	0.545451	+	0.838143i	$0.316359\pi$
$138$	−7.97931	+	5.79731i	−0.679244	+	0.493500i
$139$	6.35197	+	19.5494i	0.538767	+	1.65815i	0.735366	+	0.677670i	$0.237010\pi$
$139$	6.35197	+	19.5494i	0.538767	+	1.65815i	−0.196599	+	0.980484i	$0.562990\pi$
$140$	8.69117	−	26.7487i	0.734538	−	2.26068i
$141$	4.60373	+	3.34481i	0.387704	+	0.281684i
$142$	0.496525			0.0416675
$143$	−1.35578	+	3.02686i	−0.113376	+	0.253119i
$144$	18.3494			1.52911
$145$	−4.28786	−	3.11531i	−0.356087	−	0.258712i
$146$	−2.83218	+	8.71654i	−0.234393	+	0.721386i
$147$	1.51072	+	4.64951i	0.124602	+	0.383485i
$148$	6.45841	−	4.69231i	0.530878	−	0.385706i
$149$	1.78726	−	1.29852i	0.146418	−	0.106379i	−0.512165	−	0.858887i	$-0.671156\pi$
$149$	1.78726	−	1.29852i	0.146418	−	0.106379i	0.658583	+	0.752508i	$0.271156\pi$
$150$	−5.20234	−	16.0112i	−0.424769	−	1.30731i
$151$	−3.68982	+	11.3561i	−0.300274	+	0.924147i	0.681125	+	0.732167i	$0.261491\pi$
$151$	−3.68982	+	11.3561i	−0.300274	+	0.924147i	−0.981399	+	0.191980i	$0.938509\pi$
$152$	−4.89906	−	3.55938i	−0.397366	−	0.288703i
$153$	−6.30104			−0.509409
$154$	−13.4095	−	1.43977i	−1.08057	−	0.116020i
$155$	32.6795			2.62488
$156$	−4.71828	−	3.42803i	−0.377765	−	0.274462i
$157$	3.97335	−	12.2287i	0.317108	−	0.975957i	−0.657771	−	0.753218i	$-0.728500\pi$
$157$	3.97335	−	12.2287i	0.317108	−	0.975957i	0.974878	−	0.222739i	$-0.0714996\pi$
$158$	−0.0888639	−	0.273495i	−0.00706963	−	0.0217581i
$159$	−1.89461	+	1.37652i	−0.150252	+	0.109165i
$160$	80.2936	−	58.3367i	6.34777	−	4.61192i
$161$	1.58240	+	4.87013i	0.124711	+	0.383820i
$162$	0.864813	−	2.66162i	0.0679461	−	0.209117i
$163$	−14.6428	−	10.6386i	−1.14692	−	0.833283i	−0.158848	−	0.987303i	$-0.550778\pi$
$163$	−14.6428	−	10.6386i	−1.14692	−	0.833283i	−0.988068	+	0.154020i	$0.950778\pi$
$164$	21.3039			1.66356
$165$	−9.54532	+	5.48252i	−0.743102	+	0.426814i
$166$	−39.0077			−3.02758
$167$	−3.41449	−	2.48077i	−0.264221	−	0.191968i	0.447785	−	0.894141i	$-0.352213\pi$
$167$	−3.41449	−	2.48077i	−0.264221	−	0.191968i	−0.712006	+	0.702173i	$0.752213\pi$
$168$	4.81534	−	14.8201i	0.371512	−	1.14340i
$169$	0.309017	+	0.951057i	0.0237705	+	0.0731582i
$170$	−47.3493	+	34.4013i	−3.63152	+	2.63846i
$171$	−0.456808	+	0.331891i	−0.0349330	+	0.0253803i
$172$	−7.43152	−	22.8719i	−0.566648	−	1.74396i
$173$	1.58610	−	4.88152i	0.120589	−	0.371135i	−0.872483	−	0.488645i	$-0.837491\pi$
$173$	1.58610	−	4.88152i	0.120589	−	0.371135i	0.993072	+	0.117510i	$0.0374913\pi$
$174$	−3.61557	−	2.62686i	−0.274096	−	0.199142i
$175$	−8.74063			−0.660730
$176$	−45.1350	−	40.8232i	−3.40218	−	3.07716i
$177$	9.13245			0.686437
$178$	2.41444	+	1.75419i	0.180970	+	0.131482i
$179$	−6.48124	+	19.9472i	−0.484431	+	1.49092i	0.348373	+	0.937356i	$0.386734\pi$
$179$	−6.48124	+	19.9472i	−0.484431	+	1.49092i	−0.832804	+	0.553568i	$0.813266\pi$
$180$	−5.98153	−	18.4093i	−0.445837	−	1.37214i
$181$	8.10160	−	5.88616i	0.602188	−	0.437515i	−0.244467	−	0.969658i	$-0.578613\pi$
$181$	8.10160	−	5.88616i	0.602188	−	0.437515i	0.846655	+	0.532143i	$0.178613\pi$
$182$	−3.28975	+	2.39015i	−0.243853	+	0.177169i
$183$	0.844877	+	2.60026i	0.0624551	+	0.192217i
$184$	−11.6796	+	35.9462i	−0.861034	+	2.64999i
$185$	−3.67538	−	2.67032i	−0.270220	−	0.196326i
$186$	27.5557			2.02049
$187$	15.4990	+	14.0184i	1.13340	+	1.02513i
$188$	33.1878			2.42047
$189$	−1.17550	−	0.854053i	−0.0855053	−	0.0621232i
$190$	−1.62070	+	4.98799i	−0.117578	+	0.361867i
$191$	0.261305	+	0.804214i	0.0189074	+	0.0581909i	0.960065	−	0.279777i	$-0.0902605\pi$
$191$	0.261305	+	0.804214i	0.0189074	+	0.0581909i	−0.941158	+	0.337968i	$0.890261\pi$
$192$	38.0145	−	27.6192i	2.74346	−	1.99324i
$193$	−16.6427	+	12.0917i	−1.19797	+	0.870376i	−0.994084	−	0.108619i	$-0.965357\pi$
$193$	−16.6427	+	12.0917i	−1.19797	+	0.870376i	−0.203886	+	0.978995i	$0.565357\pi$
$194$	−12.6224	−	38.8477i	−0.906234	−	2.78910i
$195$	−1.02562	+	3.15653i	−0.0734461	+	0.226044i
$196$	23.0667	+	16.7589i	1.64762	+	1.19707i
$197$	−28.0478			−1.99832			−0.999160	−	0.0409674i	$-0.986956\pi$
$197$	−28.0478			−1.99832			−0.999160	+	0.0409674i	$0.986956\pi$
$198$	−8.04872	+	4.62292i	−0.571998	+	0.328537i
$199$	−8.63345			−0.612009			−0.306005	−	0.952030i	$-0.598992\pi$
$199$	−8.63345			−0.612009			−0.306005	+	0.952030i	$0.598992\pi$
$200$	−52.1931	−	37.9205i	−3.69061	−	2.68138i
$201$	−1.93804	+	5.96467i	−0.136699	+	0.420715i
$202$	6.03307	+	18.5679i	0.424485	+	1.30643i
$203$	−1.87717	+	1.36384i	−0.131751	+	0.0957229i
$204$	−29.7301	+	21.6002i	−2.08152	+	1.51232i
$205$	−3.74644	−	11.5304i	−0.261663	−	0.805316i
$206$	8.21055	−	25.2695i	0.572056	−	1.76061i
$207$	2.85119	+	2.07151i	0.198171	+	0.143980i
$208$	−18.3494			−1.27230
$209$	1.86202	+	0.199924i	0.128798	+	0.0138290i
$210$	−13.4961			−0.931321
$211$	8.72149	+	6.33654i	0.600412	+	0.436225i	0.846025	−	0.533143i	$-0.178989\pi$
$211$	8.72149	+	6.33654i	0.600412	+	0.436225i	−0.245613	+	0.969368i	$0.578989\pi$
$212$	−4.22057	+	12.9896i	−0.289870	+	0.892128i
$213$	−0.0548257	−	0.168736i	−0.00375659	−	0.0115616i
$214$	15.1202	−	10.9855i	1.03360	−	0.750951i
$215$	−11.0721	+	8.04436i	−0.755111	+	0.548620i
$216$	−3.31406	−	10.1996i	−0.225494	−	0.693998i
$217$	4.42100	−	13.6065i	0.300117	−	0.923666i
$218$	15.0635	+	10.9442i	1.02023	+	0.741238i
$219$	3.27490			0.221297
$220$	−26.2433	+	58.5898i	−1.76932	+	3.95012i
$221$	6.30104			0.423854
$222$	−3.09912	−	2.25165i	−0.208000	−	0.151121i
$223$	7.89111	−	24.2863i	0.528428	−	1.62633i	−0.229009	−	0.973424i	$-0.573549\pi$
$223$	7.89111	−	24.2863i	0.528428	−	1.62633i	0.757437	−	0.652908i	$-0.226451\pi$
$224$	−13.4267	−	41.3230i	−0.897107	−	2.76101i
$225$	−4.86670	+	3.53586i	−0.324446	+	0.235724i
$226$	25.1905	−	18.3020i	1.67565	−	1.21743i
$227$	1.16058	+	3.57190i	0.0770304	+	0.237075i	0.982156	−	0.188070i	$-0.0602231\pi$
$227$	1.16058	+	3.57190i	0.0770304	+	0.237075i	−0.905125	+	0.425145i	$0.860223\pi$
$228$	−1.01762	+	3.13191i	−0.0673935	+	0.207416i
$229$	6.92165	+	5.02887i	0.457396	+	0.332317i	0.792509	−	0.609861i	$-0.208775\pi$
$229$	6.92165	+	5.02887i	0.457396	+	0.332317i	−0.335113	+	0.942178i	$0.608775\pi$
$230$	32.7349			2.15848
$231$	0.991377	+	4.71599i	0.0652278	+	0.310289i
$232$	−17.1261			−1.12438
$233$	0.641360	+	0.465975i	0.0420169	+	0.0305271i	0.608595	−	0.793481i	$-0.291733\pi$
$233$	0.641360	+	0.465975i	0.0420169	+	0.0305271i	−0.566579	+	0.824008i	$0.691733\pi$
$234$	−0.864813	+	2.66162i	−0.0565346	+	0.173996i
$235$	−5.83631	−	17.9623i	−0.380719	−	1.17173i
$236$	43.0895	−	31.3064i	2.80489	−	2.03787i
$237$	−0.0831306	+	0.0603979i	−0.00539991	+	0.00392327i
$238$	7.91773	+	24.3683i	0.513230	+	1.57956i
$239$	−3.35280	+	10.3188i	−0.216874	+	0.667471i	0.782141	+	0.623102i	$0.214128\pi$
$239$	−3.35280	+	10.3188i	−0.216874	+	0.667471i	−0.999015	+	0.0443690i	$0.985872\pi$
$240$	−49.2700	−	35.7967i	−3.18036	−	2.31067i
$241$	10.5175			0.677495			0.338747	−	0.940877i	$-0.389997\pi$
$241$	10.5175			0.677495			0.338747	+	0.940877i	$0.389997\pi$
$242$	30.0828	+	6.53530i	1.93380	+	0.420105i
$243$	−1.00000			−0.0641500
$244$	12.9002	+	9.37252i	0.825848	+	0.600014i
$245$	5.01403	−	15.4316i	0.320335	−	0.985888i
$246$	−3.15904	−	9.72253i	−0.201413	−	0.619886i
$247$	0.456808	−	0.331891i	0.0290660	−	0.0211177i
$248$	85.4297	−	62.0683i	5.42479	−	3.94134i
$249$	4.30718	+	13.2561i	0.272956	+	0.840073i
$250$	−2.91497	+	8.97136i	−0.184359	+	0.567399i
$251$	−0.409848	−	0.297772i	−0.0258694	−	0.0187952i	0.574775	−	0.818311i	$-0.305089\pi$
$251$	−0.409848	−	0.297772i	−0.0258694	−	0.0187952i	−0.600645	+	0.799516i	$0.705089\pi$
$252$	−8.47408			−0.533817
$253$	−2.40459	−	11.4386i	−0.151175	−	0.719141i
$254$	21.2414			1.33280
$255$	16.9190	+	12.2923i	1.05951	+	0.769776i
$256$	32.9623	−	101.447i	2.06014	−	6.34046i
$257$	4.10951	+	12.6478i	0.256344	+	0.788947i	0.993562	+	0.113291i	$0.0361393\pi$
$257$	4.10951	+	12.6478i	0.256344	+	0.788947i	−0.737218	+	0.675655i	$0.763861\pi$
$258$	−9.33612	+	6.78309i	−0.581241	+	0.422297i
$259$	−1.60903	+	1.16903i	−0.0999806	+	0.0726401i
$260$	5.98153	+	18.4093i	0.370959	+	1.14169i
$261$	−0.493471	+	1.51875i	−0.0305451	+	0.0940081i
$262$	37.5971	+	27.3159i	2.32276	+	1.68758i
$263$	−25.3323			−1.56206			−0.781029	−	0.624495i	$-0.785305\pi$
$263$	−25.3323			−1.56206			−0.781029	+	0.624495i	$0.785305\pi$
$264$	−14.5401	+	32.4617i	−0.894880	+	1.99788i
$265$	7.77259			0.477466
$266$	1.85755	+	1.34959i	0.113894	+	0.0827485i
$267$	0.329534	−	1.01420i	0.0201672	−	0.0620682i
$268$	11.3029	+	34.7866i	0.690432	+	2.12493i
$269$	−21.1799	+	15.3881i	−1.29136	+	0.938227i	−0.999832	−	0.0183360i	$-0.994163\pi$
$269$	−21.1799	+	15.3881i	−1.29136	+	0.938227i	−0.291526	+	0.956563i	$0.594163\pi$
$270$	−7.51451	+	5.45961i	−0.457319	+	0.332261i
$271$	5.64147	+	17.3627i	0.342695	+	1.05471i	0.962806	+	0.270193i	$0.0870874\pi$
$271$	5.64147	+	17.3627i	0.342695	+	1.05471i	−0.620111	+	0.784514i	$0.712913\pi$
$272$	−35.7286	+	109.961i	−2.16637	+	6.66739i
$273$	1.17550	+	0.854053i	0.0711447	+	0.0516896i
$274$	3.36537			0.203309
$275$	19.8374	+	2.12993i	1.19624	+	0.128440i
$276$	20.5539			1.23720
$277$	−11.3139	−	8.22000i	−0.679784	−	0.493892i	0.193502	−	0.981100i	$-0.438015\pi$
$277$	−11.3139	−	8.22000i	−0.679784	−	0.493892i	−0.873286	+	0.487208i	$0.838015\pi$
$278$	17.7766	−	54.7107i	1.06617	−	3.28133i
$279$	−3.04267	−	9.36437i	−0.182160	−	0.560630i
$280$	−41.8414	+	30.3995i	−2.50050	+	1.81672i
$281$	−3.86206	+	2.80595i	−0.230391	+	0.167389i	−0.696992	−	0.717079i	$-0.745479\pi$
$281$	−3.86206	+	2.80595i	−0.230391	+	0.167389i	0.466601	+	0.884468i	$0.345479\pi$
$282$	−4.92124	−	15.1460i	−0.293056	−	0.901932i
$283$	6.55905	−	20.1867i	0.389895	−	1.19997i	−0.542971	−	0.839751i	$-0.682701\pi$
$283$	6.55905	−	20.1867i	0.389895	−	1.19997i	0.932866	−	0.360222i	$-0.117299\pi$
$284$	−0.837116	−	0.608201i	−0.0496737	−	0.0360901i
$285$	1.87404			0.111009
$286$	8.04872	−	4.62292i	0.475931	−	0.273359i
$287$	−5.30762			−0.313299
$288$	−24.1923	−	17.5767i	−1.42555	−	1.03572i
$289$	7.01566	−	21.5920i	0.412686	−	1.27012i
$290$	4.58358	+	14.1068i	0.269157	+	0.828380i
$291$	−11.8080	+	8.57903i	−0.692198	+	0.502912i
$292$	15.4519	−	11.2265i	0.904255	−	0.656980i
$293$	4.93622	+	15.1921i	0.288377	+	0.887533i	0.985366	+	0.170451i	$0.0545226\pi$
$293$	4.93622	+	15.1921i	0.288377	+	0.887533i	−0.696989	+	0.717082i	$0.745477\pi$
$294$	4.22788	−	13.0121i	0.246575	−	0.758880i
$295$	−24.5216	−	17.8160i	−1.42770	−	1.03729i
$296$	−14.6798			−0.853246
$297$	2.45976	+	2.22477i	0.142729	+	0.129094i
$298$	−6.18259			−0.358148
$299$	−2.85119	−	2.07151i	−0.164888	−	0.119798i
$300$	−10.8414	+	33.3664i	−0.625929	+	1.92641i
$301$	1.85147	+	5.69825i	0.106717	+	0.328442i
$302$	27.0346	−	19.6418i	1.55567	−	1.13026i
$303$	5.64383	−	4.10048i	0.324230	−	0.235567i
$304$	3.20170	+	9.85381i	0.183630	+	0.565155i
$305$	2.80412	−	8.63020i	0.160564	−	0.494164i
$306$	14.2663	+	10.3650i	0.815547	+	0.592530i
$307$	10.7827			0.615399			0.307699	−	0.951484i	$-0.400441\pi$
$307$	10.7827			0.615399			0.307699	+	0.951484i	$0.400441\pi$
$308$	20.8442	+	18.8529i	1.18771	+	1.07424i
$309$	−9.49402			−0.540096
$310$	−73.9900	−	53.7569i	−4.20235	−	3.05319i
$311$	−2.60196	+	8.00802i	−0.147544	+	0.454093i	−0.997329	−	0.0730353i	$-0.976731\pi$
$311$	−2.60196	+	8.00802i	−0.147544	+	0.454093i	0.849785	+	0.527129i	$0.176731\pi$
$312$	3.31406	+	10.1996i	0.187622	+	0.577441i
$313$	−9.01928	+	6.55289i	−0.509800	+	0.370391i	−0.812748	−	0.582616i	$-0.802029\pi$
$313$	−9.01928	+	6.55289i	−0.509800	+	0.370391i	0.302948	+	0.953007i	$0.402029\pi$
$314$	−29.1120	+	21.1511i	−1.64288	+	1.19362i
$315$	1.49023	+	4.58644i	0.0839647	+	0.258417i
$316$	−0.185188	+	0.569949i	−0.0104176	+	0.0320621i
$317$	−14.9669	−	10.8741i	−0.840627	−	0.610751i	0.0819187	−	0.996639i	$-0.473895\pi$
$317$	−14.9669	−	10.8741i	−0.840627	−	0.610751i	−0.922546	+	0.385888i	$0.873895\pi$
$318$	6.55393			0.367526
$319$	4.59268	−	2.63789i	0.257141	−	0.147693i
$320$	−155.954			−8.71807
$321$	−5.40279	−	3.92536i	−0.301554	−	0.219092i
$322$	4.42850	−	13.6295i	0.246790	−	0.759543i
$323$	−1.09944	−	3.38373i	−0.0611744	−	0.188276i
$324$	−4.71828	+	3.42803i	−0.262127	+	0.190446i
$325$	4.86670	−	3.53586i	0.269956	−	0.196134i
$326$	15.6527	+	48.1741i	0.866923	+	2.66812i
$327$	2.05594	−	6.32752i	0.113694	−	0.349913i
$328$	−31.6935	−	23.0267i	−1.74998	−	1.27143i
$329$	−8.26835			−0.455849
$330$	30.6302	+	3.28876i	1.68614	+	0.181040i
$331$	−16.0478			−0.882065			−0.441032	−	0.897491i	$-0.645388\pi$
$331$	−16.0478			−0.882065			−0.441032	+	0.897491i	$0.645388\pi$
$332$	65.7649	+	47.7810i	3.60932	+	2.62232i
$333$	−0.422984	+	1.30181i	−0.0231794	+	0.0713388i
$334$	3.64998	+	11.2335i	0.199718	+	0.614669i
$335$	16.8400	−	12.2349i	0.920065	−	0.668466i
$336$	−21.5697	+	15.6713i	−1.17673	+	0.854942i
$337$	6.27600	+	19.3156i	0.341876	+	1.05219i	0.963235	+	0.268660i	$0.0865806\pi$
$337$	6.27600	+	19.3156i	0.341876	+	1.05219i	−0.621360	+	0.783526i	$0.713419\pi$
$338$	0.864813	−	2.66162i	0.0470396	−	0.144773i
$339$	−9.00115	−	6.53972i	−0.488875	−	0.355189i
$340$	121.967			6.61459
$341$	−13.3494	+	29.8033i	−0.722909	+	1.61394i
$342$	1.58021			0.0854482
$343$	−13.9753	−	10.1537i	−0.754596	−	0.548246i
$344$	−13.6656	+	42.0585i	−0.736802	+	2.26764i
$345$	−3.61455	−	11.1244i	−0.194601	−	0.598919i
$346$	−11.6211	+	8.44320i	−0.624752	+	0.453909i
$347$	−12.8189	+	9.31344i	−0.688152	+	0.499972i	−0.876052	−	0.482216i	$-0.839832\pi$
$347$	−12.8189	+	9.31344i	−0.688152	+	0.499972i	0.187900	+	0.982188i	$0.439832\pi$
$348$	2.87798	+	8.85752i	0.154276	+	0.474813i
$349$	−3.67663	+	11.3155i	−0.196805	+	0.605705i	0.803145	+	0.595783i	$0.203158\pi$
$349$	−3.67663	+	11.3155i	−0.196805	+	0.605705i	−0.999951	+	0.00992155i	$0.996842\pi$
$350$	19.7897	+	14.3781i	1.05781	+	0.768541i
$351$	1.00000			0.0533761
$352$	20.4029	+	97.0568i	1.08748	+	5.17315i
$353$	16.1210			0.858033			0.429016	−	0.903297i	$-0.358860\pi$
$353$	16.1210			0.858033			0.429016	+	0.903297i	$0.358860\pi$
$354$	−20.6769	−	15.0226i	−1.09896	−	0.798443i
$355$	−0.181965	+	0.560030i	−0.00965769	+	0.0297233i
$356$	−1.92188	−	5.91495i	−0.101860	−	0.313492i
$357$	7.40690	−	5.38143i	0.392015	−	0.284815i
$358$	47.4868	−	34.5012i	2.50976	−	1.82344i
$359$	−1.66210	−	5.11541i	−0.0877222	−	0.269981i	0.897567	−	0.440879i	$-0.145333\pi$
$359$	−1.66210	−	5.11541i	−0.0877222	−	0.269981i	−0.985289	+	0.170898i	$0.945333\pi$
$360$	−10.9993	+	33.8523i	−0.579713	+	1.78417i
$361$	15.1134	+	10.9805i	0.795441	+	0.577922i
$362$	−28.0255			−1.47299
$363$	−1.10079	−	10.9448i	−0.0577765	−	0.574452i
$364$	8.47408			0.444162
$365$	−8.79345	−	6.38882i	−0.460270	−	0.334406i
$366$	2.36447	−	7.27708i	0.123593	−	0.380379i
$367$	−8.32910	−	25.6343i	−0.434775	−	1.33810i	−0.893317	−	0.449428i	$-0.851628\pi$
$367$	−8.32910	−	25.6343i	−0.434775	−	1.33810i	0.458541	−	0.888673i	$-0.348372\pi$
$368$	52.3175	−	38.0109i	2.72724	−	1.98146i
$369$	−2.95523	+	2.14710i	−0.153843	+	0.111774i
$370$	3.92887	+	12.0918i	0.204252	+	0.628623i
$371$	1.05150	−	3.23620i	0.0545913	−	0.168015i
$372$	−46.4576	−	33.7534i	−2.40871	−	1.75003i
$373$	−26.4683			−1.37048			−0.685239	−	0.728318i	$-0.740302\pi$
$373$	−26.4683			−1.37048			−0.685239	+	0.728318i	$0.740302\pi$
$374$	−12.0316	−	57.2346i	−0.622142	−	2.95953i
$375$	3.37064			0.174059
$376$	−49.3729	−	35.8715i	−2.54621	−	1.84993i
$377$	0.493471	−	1.51875i	0.0254151	−	0.0782195i
$378$	1.25657	+	3.86734i	0.0646312	+	0.198914i
$379$	−1.38630	+	1.00721i	−0.0712094	+	0.0517367i	−0.622820	−	0.782365i	$-0.714013\pi$
$379$	−1.38630	+	1.00721i	−0.0712094	+	0.0517367i	0.551611	+	0.834101i	$0.314013\pi$
$380$	8.84227	−	6.42429i	0.453599	−	0.329559i
$381$	−2.34544	−	7.21854i	−0.120161	−	0.369817i
$382$	0.731286	−	2.25067i	0.0374158	−	0.115154i
$383$	10.0660	+	7.31335i	0.514347	+	0.373695i	0.814470	−	0.580206i	$-0.197028\pi$
$383$	10.0660	+	7.31335i	0.514347	+	0.373695i	−0.300123	+	0.953900i	$0.597028\pi$
$384$	−71.6950			−3.65867
$385$	6.53819	−	14.5969i	0.333217	−	0.743929i
$386$	57.5714			2.93031
$387$	3.33601	+	2.42375i	0.169579	+	0.123206i
$388$	−26.3044	+	80.9566i	−1.33540	+	4.10995i
$389$	−2.29869	−	7.07463i	−0.116548	−	0.358698i	0.875719	−	0.482822i	$-0.160388\pi$
$389$	−2.29869	−	7.07463i	−0.116548	−	0.358698i	−0.992267	+	0.124124i	$0.960388\pi$
$390$	7.51451	−	5.45961i	0.380512	−	0.276458i
$391$	−17.9655	+	13.0527i	−0.908552	+	0.660102i
$392$	−16.2018	−	49.8639i	−0.818312	−	2.51851i
$393$	5.13144	−	15.7930i	0.258847	−	0.796650i
$394$	63.5032	+	46.1378i	3.19925	+	2.32439i
$395$	0.341041			0.0171596
$396$	19.2324	+	2.06498i	0.966465	+	0.103769i
$397$	−9.60558			−0.482090			−0.241045	−	0.970514i	$-0.577490\pi$
$397$	−9.60558			−0.482090			−0.241045	+	0.970514i	$0.577490\pi$
$398$	19.5471	+	14.2018i	0.979806	+	0.711871i
$399$	0.253527	−	0.780277i	0.0126922	−	0.0390627i
$400$	34.1099	+	104.979i	1.70549	+	5.24897i
$401$	12.8427	−	9.33075i	0.641333	−	0.465956i	−0.218975	−	0.975730i	$-0.570271\pi$
$401$	12.8427	−	9.33075i	0.641333	−	0.465956i	0.860308	+	0.509775i	$0.170271\pi$
$402$	14.1996	−	10.3166i	0.708213	−	0.514547i
$403$	3.04267	+	9.36437i	0.151566	+	0.466473i
$404$	12.5726	−	38.6945i	0.625510	−	1.92512i
$405$	2.68510	+	1.95084i	0.133424	+	0.0969381i
$406$	6.49359			0.322272
$407$	3.93667	−	2.26109i	0.195133	−	0.112078i
$408$	67.5758			3.34550
$409$	1.80031	+	1.30800i	0.0890196	+	0.0646766i	0.631405	−	0.775453i	$-0.282479\pi$
$409$	1.80031	+	1.30800i	0.0890196	+	0.0646766i	−0.542385	+	0.840130i	$0.682479\pi$
$410$	−10.4848	+	32.2688i	−0.517806	+	1.59364i
$411$	−0.371600	−	1.14367i	−0.0183297	−	0.0564129i
$412$	−44.7955	+	32.5458i	−2.20692	+	1.60342i
$413$	−10.7352	+	7.79960i	−0.528246	+	0.383793i
$414$	−3.04783	−	9.38024i	−0.149792	−	0.461014i
$415$	14.2954	−	43.9967i	0.701733	−	2.15971i
$416$	24.1923	+	17.5767i	1.18613	+	0.861771i
$417$	−20.5554			−1.00660
$418$	−3.88694	−	3.51562i	−0.190116	−	0.171954i
$419$	31.9645			1.56157			0.780784	−	0.624801i	$-0.214820\pi$
$419$	31.9645			1.56157			0.780784	+	0.624801i	$0.214820\pi$
$420$	22.7538	+	16.5316i	1.11027	+	0.806659i
$421$	4.77937	−	14.7094i	0.232932	−	0.716891i	−0.764457	−	0.644675i	$-0.776993\pi$
$421$	4.77937	−	14.7094i	0.232932	−	0.716891i	0.997389	−	0.0722165i	$-0.0230073\pi$
$422$	−9.32299	−	28.6932i	−0.453836	−	1.39676i
$423$	−4.60373	+	3.34481i	−0.223841	+	0.162630i
$424$	20.3188	−	14.7625i	0.986769	−	0.716930i
$425$	−11.7131	−	36.0492i	−0.568168	−	1.74864i
$426$	−0.153435	+	0.472224i	−0.00743394	+	0.0228793i
$427$	−3.21392	−	2.33505i	−0.155532	−	0.113001i
$428$	−38.9481			−1.88263
$429$	−2.45976	−	2.22477i	−0.118758	−	0.107413i
$430$	38.3012			1.84705
$431$	−2.09262	−	1.52038i	−0.100798	−	0.0732341i	0.536245	−	0.844063i	$-0.319842\pi$
$431$	−2.09262	−	1.52038i	−0.100798	−	0.0732341i	−0.637043	+	0.770829i	$0.719842\pi$
$432$	−5.67027	+	17.4513i	−0.272811	+	0.839626i
$433$	0.0334366	+	0.102907i	0.00160686	+	0.00494540i	0.951857	−	0.306543i	$-0.0991724\pi$
$433$	0.0334366	+	0.102907i	0.00160686	+	0.00494540i	−0.950250	+	0.311489i	$0.899172\pi$
$434$	−32.3919	+	23.5341i	−1.55486	+	1.12967i
$435$	4.28786	−	3.11531i	0.205587	−	0.149368i
$436$	−11.9905	−	36.9029i	−0.574239	−	1.76733i
$437$	−0.614932	+	1.89257i	−0.0294162	+	0.0905337i
$438$	−7.41473	−	5.38712i	−0.354290	−	0.257406i
$439$	5.45264			0.260240			0.130120	−	0.991498i	$-0.458464\pi$
$439$	5.45264			0.260240			0.130120	+	0.991498i	$0.458464\pi$
$440$	102.369	−	58.7975i	4.88026	−	2.80306i
$441$	−4.88879			−0.232799
$442$	−14.2663	−	10.3650i	−0.678576	−	0.493015i
$443$	−9.45640	+	29.1038i	−0.449287	+	1.38276i	0.428426	+	0.903577i	$0.359068\pi$
$443$	−9.45640	+	29.1038i	−0.449287	+	1.38276i	−0.877713	+	0.479186i	$0.840932\pi$
$444$	2.46689	+	7.59232i	0.117074	+	0.360315i
$445$	−2.86338	+	2.08037i	−0.135737	+	0.0986190i
$446$	−57.8166	+	42.0062i	−2.73770	+	1.98905i
$447$	0.682674	+	2.10105i	0.0322894	+	0.0993765i
$448$	−21.0979	+	64.9328i	−0.996784	+	3.06779i
$449$	16.7174	+	12.1459i	0.788945	+	0.573202i	0.907650	−	0.419728i	$-0.137874\pi$
$449$	16.7174	+	12.1459i	0.788945	+	0.573202i	−0.118705	+	0.992930i	$0.537874\pi$
$450$	16.8351			0.793615
$451$	12.0459	+	1.29337i	0.567221	+	0.0609023i
$452$	−64.8883			−3.05209
$453$	−9.66008	−	7.01846i	−0.453870	−	0.329756i
$454$	3.24799	−	9.99629i	0.152436	−	0.469149i
$455$	−1.49023	−	4.58644i	−0.0698628	−	0.215016i
$456$	4.89906	−	3.55938i	0.229419	−	0.166683i
$457$	−18.0279	+	13.0981i	−0.843311	+	0.612701i	−0.923294	−	0.384095i	$-0.874514\pi$
$457$	−18.0279	+	13.0981i	−0.843311	+	0.612701i	0.0799824	+	0.996796i	$0.474514\pi$
$458$	−7.39902	−	22.7718i	−0.345733	−	1.06406i
$459$	1.94713	−	5.99265i	0.0908842	−	0.279713i
$460$	−55.1894	−	40.0974i	−2.57322	−	1.86955i
$461$	26.8924			1.25251			0.626253	−	0.779620i	$-0.284588\pi$
$461$	26.8924			1.25251			0.626253	+	0.779620i	$0.284588\pi$
$462$	5.51308	−	12.3083i	0.256491	−	0.572634i
$463$	23.9466			1.11289			0.556447	−	0.830883i	$-0.312164\pi$
$463$	23.9466			1.11289			0.556447	+	0.830883i	$0.312164\pi$
$464$	23.7060	+	17.2234i	1.10052	+	0.799577i
$465$	−10.0985	+	31.0801i	−0.468308	+	1.44130i
$466$	−0.685593	−	2.11004i	−0.0317595	−	0.0977456i
$467$	4.89609	−	3.55722i	0.226564	−	0.164608i	−0.468712	−	0.883351i	$-0.655282\pi$
$467$	4.89609	−	3.55722i	0.226564	−	0.164608i	0.695276	+	0.718742i	$0.255282\pi$
$468$	4.71828	−	3.42803i	0.218103	−	0.158461i
$469$	−2.81597	−	8.66667i	−0.130029	−	0.400190i
$470$	−16.3335	+	50.2692i	−0.753406	+	2.31875i
$471$	10.4024	+	7.55776i	0.479315	+	0.348243i
$472$	−97.9413			−4.50812
$473$	−2.81347	−	13.3837i	−0.129363	−	0.615382i
$474$	0.287570			0.0132085
$475$	−2.74796	−	1.99651i	−0.126085	−	0.0916062i
$476$	16.5001	−	50.7822i	0.756282	−	2.32760i
$477$	−0.723677	−	2.22725i	−0.0331349	−	0.101979i
$478$	24.5653	−	17.8477i	1.12359	−	0.816336i
$479$	3.24047	−	2.35434i	0.148061	−	0.107573i	−0.511289	−	0.859409i	$-0.670832\pi$
$479$	3.24047	−	2.35434i	0.148061	−	0.107573i	0.659350	+	0.751836i	$0.270832\pi$
$480$	30.6694	+	94.3908i	1.39986	+	4.30833i
$481$	0.422984	−	1.30181i	0.0192864	−	0.0593575i
$482$	−23.8129	−	17.3011i	−1.08465	−	0.788042i
$483$	−5.12076			−0.233003
$484$	−42.7129	−	47.8670i	−1.94150	−	2.17577i
$485$	48.4421			2.19964
$486$	2.26411	+	1.64497i	0.102702	+	0.0746174i
$487$	−4.85268	+	14.9350i	−0.219896	+	0.676770i	0.778874	+	0.627181i	$0.215791\pi$
$487$	−4.85268	+	14.9350i	−0.219896	+	0.676770i	−0.998770	+	0.0495895i	$0.984209\pi$
$488$	−9.06092	−	27.8866i	−0.410169	−	1.26237i
$489$	14.6428	−	10.6386i	0.662172	−	0.481096i
$490$	−36.7368	+	26.6909i	−1.65960	+	1.20577i
$491$	2.67084	+	8.21999i	0.120533	+	0.370963i	0.993061	−	0.117602i	$-0.0375206\pi$
$491$	2.67084	+	8.21999i	0.120533	+	0.370963i	−0.872528	+	0.488565i	$0.837521\pi$
$492$	−6.58328	+	20.2612i	−0.296797	+	0.913448i
$493$	−8.14047	−	5.91440i	−0.366628	−	0.266371i
$494$	−1.58021			−0.0710972
$495$	−2.26452	−	10.7723i	−0.101783	−	0.484180i
$496$	−180.673			−8.11247
$497$	0.208557	+	0.151526i	0.00935508	+	0.00679686i
$498$	12.0540	−	37.0985i	0.540154	−	1.66242i
$499$	4.25665	+	13.1006i	0.190554	+	0.586464i	1.00000		0.000730306i	$-0.000232464\pi$
$499$	4.25665	+	13.1006i	0.190554	+	0.586464i	−0.809446	+	0.587194i	$0.800232\pi$
$500$	15.9036	−	11.5547i	0.711232	−	0.516740i
$501$	3.41449	−	2.48077i	0.152548	−	0.110833i
$502$	0.438114	+	1.34838i	0.0195540	+	0.0601810i
$503$	4.24711	−	13.0713i	0.189369	−	0.582819i	−0.810627	−	0.585563i	$-0.800873\pi$
$503$	4.24711	−	13.0713i	0.189369	−	0.582819i	0.999996	+	0.00274417i	$0.000873499\pi$
$504$	12.6067	+	9.15932i	0.561548	+	0.407989i
$505$	−23.1537			−1.03033
$506$	−13.3720	+	29.8538i	−0.594457	+	1.32716i
$507$	−1.00000			−0.0444116
$508$	−35.8119	−	26.0188i	−1.58889	−	1.15440i
$509$	−2.03872	+	6.27454i	−0.0903648	+	0.278114i	−0.986018	−	0.166639i	$-0.946709\pi$
$509$	−2.03872	+	6.27454i	−0.0903648	+	0.278114i	0.895653	+	0.444753i	$0.146709\pi$
$510$	−18.0858	−	55.6624i	−0.800853	−	2.46477i
$511$	−3.84966	+	2.79694i	−0.170299	+	0.123729i
$512$	−125.503	+	91.1834i	−5.54651	+	4.02978i
$513$	−0.174485	−	0.537010i	−0.00770371	−	0.0237096i
$514$	11.5008	−	35.3960i	0.507281	−	1.56125i
$515$	25.4924	+	18.5213i	1.12333	+	0.816148i
$516$	24.0489			1.05869
$517$	18.7655	+	2.01484i	0.825305	+	0.0886127i
$518$	5.56605			0.244558
$519$	4.15247	+	3.01694i	0.182273	+	0.132429i
$520$	10.9993	−	33.8523i	0.482351	−	1.48452i
$521$	−11.4727	−	35.3094i	−0.502629	−	1.54693i	−0.804721	−	0.593653i	$-0.797685\pi$
$521$	−11.4727	−	35.3094i	−0.502629	−	1.54693i	0.302092	−	0.953279i	$-0.402315\pi$
$522$	3.61557	−	2.62686i	0.158249	−	0.114975i
$523$	12.4815	−	9.06835i	0.545778	−	0.396531i	−0.280448	−	0.959869i	$-0.590483\pi$
$523$	12.4815	−	9.06835i	0.545778	−	0.396531i	0.826227	+	0.563338i	$0.190483\pi$
$524$	−29.9272	−	92.1064i	−1.30738	−	4.02369i
$525$	2.70100	−	8.31283i	0.117881	−	0.362802i
$526$	57.3551	+	41.6709i	2.50080	+	1.81694i
$527$	62.0419			2.70259
$528$	52.7726	−	30.3109i	2.29663	−	1.31911i
$529$	−10.5796			−0.459982
$530$	−17.5980	−	12.7857i	−0.764408	−	0.555375i
$531$	−2.82208	+	8.68548i	−0.122468	+	0.376918i
$532$	−1.47860	−	4.55067i	−0.0641055	−	0.197297i
$533$	2.95523	−	2.14710i	0.128005	−	0.0930012i
$534$	−2.41444	+	1.75419i	−0.104483	+	0.0759112i
$535$	6.84930	+	21.0800i	0.296121	+	0.911367i
$536$	20.7846	−	63.9683i	0.897756	−	2.76301i
$537$	−16.9681	−	12.3281i	−0.732228	−	0.531995i
$538$	73.2664			3.15874
$539$	12.0252	+	10.8764i	0.517963	+	0.468481i
$540$	19.3566			0.832977
$541$	−4.14803	−	3.01372i	−0.178338	−	0.129570i	0.495035	−	0.868873i	$-0.335155\pi$
$541$	−4.14803	−	3.01372i	−0.178338	−	0.129570i	−0.673373	+	0.739303i	$0.735155\pi$
$542$	15.7882	−	48.5910i	0.678160	−	2.08716i
$543$	3.09454	+	9.52401i	0.132799	+	0.408714i
$544$	152.437	−	110.752i	6.53568	−	4.74845i
$545$	−17.8644	+	12.9792i	−0.765227	+	0.555970i
$546$	−1.25657	−	3.86734i	−0.0537764	−	0.165507i
$547$	−6.54167	+	20.1332i	−0.279702	+	0.860834i	0.708235	+	0.705977i	$0.249492\pi$
$547$	−6.54167	+	20.1332i	−0.279702	+	0.860834i	−0.987937	+	0.154857i	$0.950508\pi$
$548$	−5.67384	−	4.12229i	−0.242374	−	0.176095i
$549$	−2.73408			−0.116688
$550$	−41.4103	−	37.4543i	−1.76574	−	1.59706i
$551$	−0.901687			−0.0384131
$552$	−30.5777	−	22.2160i	−1.30147	−	0.945575i
$553$	0.0461373	−	0.141996i	0.00196196	−	0.00603828i
$554$	12.0941	+	37.2219i	0.513831	+	1.58141i
$555$	3.67538	−	2.67032i	0.156011	−	0.113349i
$556$	−96.9862	+	70.4646i	−4.11313	+	2.98837i
$557$	−1.21493	−	3.73918i	−0.0514784	−	0.158434i	0.922012	−	0.387160i	$-0.126544\pi$
$557$	−1.21493	−	3.73918i	−0.0514784	−	0.158434i	−0.973491	+	0.228726i	$0.926544\pi$
$558$	−8.51519	+	26.2071i	−0.360477	+	1.10943i
$559$	−3.33601	−	2.42375i	−0.141098	−	0.102514i
$560$	88.4893			3.73936
$561$	−18.1217	+	10.4085i	−0.765100	+	0.439449i
$562$	13.3598			0.563550
$563$	3.47682	+	2.52605i	0.146530	+	0.106460i	0.658635	−	0.752462i	$-0.271134\pi$
$563$	3.47682	+	2.52605i	0.146530	+	0.106460i	−0.512105	+	0.858923i	$0.671134\pi$
$564$	−10.2556	+	31.5635i	−0.431839	+	1.32906i
$565$	11.4111	+	35.1196i	0.480067	+	1.47749i
$566$	−48.0569	+	34.9154i	−2.01998	+	1.46760i
$567$	1.17550	−	0.854053i	0.0493665	−	0.0358669i
$568$	0.587980	+	1.80962i	0.0246711	+	0.0759299i
$569$	10.4358	−	32.1181i	0.437491	−	1.34646i	−0.453021	−	0.891500i	$-0.649654\pi$
$569$	10.4358	−	32.1181i	0.437491	−	1.34646i	0.890512	−	0.454959i	$-0.150346\pi$
$570$	−4.24304	−	3.08275i	−0.177721	−	0.129122i
$571$	46.5604			1.94849			0.974245	−	0.225491i	$-0.0723985\pi$
$571$	46.5604			1.94849			0.974245	+	0.225491i	$0.0723985\pi$
$572$	−19.2324	−	2.06498i	−0.804147	−	0.0863410i
$573$	−0.845601			−0.0353255
$574$	12.0170	+	8.73088i	0.501581	+	0.364420i
$575$	−6.55129	+	20.1628i	−0.273208	+	0.840847i
$576$	14.5203	+	44.6887i	0.605010	+	1.86203i
$577$	22.6409	−	16.4496i	0.942552	−	0.684804i	−0.00648198	−	0.999979i	$-0.502063\pi$
$577$	22.6409	−	16.4496i	0.942552	−	0.684804i	0.949033	+	0.315175i	$0.102063\pi$
$578$	−51.4024	+	37.3461i	−2.13806	+	1.55339i
$579$	−6.35696	−	19.5647i	−0.264186	−	0.813081i
$580$	9.55194	−	29.3978i	0.396623	−	1.22068i
$581$	−16.3845	−	11.9041i	−0.679745	−	0.493863i
$582$	40.8469			1.69316
$583$	−3.17505	+	7.08850i	−0.131497	+	0.293576i
$584$	−35.1218			−1.45335
$585$	−2.68510	−	1.95084i	−0.111015	−	0.0806574i
$586$	13.8145	−	42.5165i	0.570670	−	1.75634i
$587$	−12.4171	−	38.2158i	−0.512507	−	1.57733i	−0.787773	−	0.615966i	$-0.788766\pi$
$587$	−12.4171	−	38.2158i	−0.512507	−	1.57733i	0.275265	−	0.961368i	$-0.411234\pi$
$588$	−23.0667	+	16.7589i	−0.951254	+	0.691126i
$589$	4.49787	−	3.26789i	0.185331	−	0.134651i
$590$	26.2128	+	80.6746i	1.07916	+	3.32132i
$591$	8.66724	−	26.6750i	0.356523	−	1.09726i
$592$	20.3199	+	14.7632i	0.835141	+	0.606765i
$593$	13.8199			0.567514			0.283757	−	0.958896i	$-0.408419\pi$
$593$	13.8199			0.567514			0.283757	+	0.958896i	$0.408419\pi$
$594$	−1.90947	−	9.08335i	−0.0783464	−	0.372694i
$595$	−30.3866			−1.24573
$596$	10.4235	+	7.57314i	0.426965	+	0.310208i
$597$	2.66788	−	8.21090i	0.109189	−	0.336050i
$598$	3.04783	+	9.38024i	0.124635	+	0.383587i
$599$	−12.7630	+	9.27283i	−0.521480	+	0.378878i	−0.817161	−	0.576409i	$-0.804453\pi$
$599$	−12.7630	+	9.27283i	−0.521480	+	0.378878i	0.295681	+	0.955287i	$0.404453\pi$
$600$	52.1931	−	37.9205i	2.13077	−	1.54810i
$601$	7.82421	+	24.0804i	0.319156	+	0.982262i	0.974010	+	0.226506i	$0.0727303\pi$
$601$	7.82421	+	24.0804i	0.319156	+	0.982262i	−0.654854	+	0.755756i	$0.727270\pi$
$602$	5.18152	−	15.9471i	0.211183	−	0.649955i
$603$	−5.07385	−	3.68637i	−0.206623	−	0.150120i
$604$	−69.6385			−2.83355
$605$	−18.3958	+	31.5353i	−0.747896	+	1.28209i
$606$	−19.5234			−0.793085
$607$	−19.9390	−	14.4865i	−0.809298	−	0.587989i	0.104329	−	0.994543i	$-0.466730\pi$
$607$	−19.9390	−	14.4865i	−0.809298	−	0.587989i	−0.913627	+	0.406554i	$0.866730\pi$
$608$	5.21769	−	16.0584i	0.211605	−	0.651254i
$609$	−0.717014	−	2.20674i	−0.0290549	−	0.0894217i
$610$	−20.5453	+	14.9270i	−0.831854	+	0.604377i
$611$	4.60373	−	3.34481i	0.186247	−	0.135316i
$612$	−11.3559	−	34.9498i	−0.459035	−	1.41276i
$613$	8.08207	−	24.8740i	0.326432	−	1.00465i	−0.644359	−	0.764723i	$-0.722876\pi$
$613$	8.08207	−	24.8740i	0.326432	−	1.00465i	0.970790	−	0.239930i	$-0.0771244\pi$
$614$	−24.4131	−	17.7372i	−0.985233	−	0.715814i
$615$	12.1237			0.488877
$616$	−10.6321	−	50.5768i	−0.428378	−	2.03780i
$617$	−34.0203			−1.36960			−0.684802	−	0.728729i	$-0.740111\pi$
$617$	−34.0203			−1.36960			−0.684802	+	0.728729i	$0.740111\pi$
$618$	21.4955	+	15.6174i	0.864676	+	0.628224i
$619$	−6.57446	+	20.2341i	−0.264250	+	0.813277i	0.727616	+	0.685985i	$0.240629\pi$
$619$	−6.57446	+	20.2341i	−0.264250	+	0.813277i	−0.991865	+	0.127292i	$0.959371\pi$
$620$	58.8958	+	181.263i	2.36531	+	7.27969i
$621$	−2.85119	+	2.07151i	−0.114414	+	0.0831268i
$622$	19.0641	−	13.8509i	0.764401	−	0.555370i
$623$	0.478814	+	1.47364i	0.0191833	+	0.0590401i
$624$	5.67027	−	17.4513i	0.226992	−	0.698611i
$625$	15.2830	+	11.1037i	0.611319	+	0.444149i
$626$	31.1999			1.24700
$627$	−0.765534	+	1.70910i	−0.0305725	+	0.0682550i
$628$	74.9895			2.99241
$629$	−6.97769	−	5.06959i	−0.278219	−	0.202138i
$630$	4.17053	−	12.8356i	0.166158	−	0.511382i
$631$	−0.786766	−	2.42142i	−0.0313207	−	0.0963951i	0.934174	−	0.356817i	$-0.116138\pi$
$631$	−0.786766	−	2.42142i	−0.0313207	−	0.0963951i	−0.965495	+	0.260422i	$0.916138\pi$
$632$	0.891537	−	0.647740i	0.0354635	−	0.0257657i
$633$	−8.72149	+	6.33654i	−0.346648	+	0.251855i
$634$	15.9992	+	49.2404i	0.635408	+	1.95559i
$635$	−7.78446	+	23.9581i	−0.308917	+	0.950749i
$636$	−11.0496	−	8.02800i	−0.438145	−	0.318331i
$637$	4.88879			0.193701
$638$	−14.7376	−	1.58237i	−0.583467	−	0.0626466i
$639$	0.177420			0.00701861
$640$	192.509	+	139.866i	7.60957	+	5.52868i
$641$	−14.4758	+	44.5520i	−0.571760	+	1.75970i	0.0751953	+	0.997169i	$0.476042\pi$
$641$	−14.4758	+	44.5520i	−0.571760	+	1.75970i	−0.646955	+	0.762528i	$0.723958\pi$
$642$	5.77540	+	17.7749i	0.227937	+	0.701518i
$643$	−32.5566	+	23.6538i	−1.28391	+	0.932814i	−0.999664	−	0.0259373i	$-0.991743\pi$
$643$	−32.5566	+	23.6538i	−1.28391	+	0.932814i	−0.284245	+	0.958752i	$0.591743\pi$
$644$	−24.1612	+	17.5541i	−0.952084	+	0.691730i
$645$	−4.22917	−	13.0160i	−0.166523	−	0.512506i
$646$	−3.07688	+	9.46967i	−0.121058	+	0.372579i
$647$	19.0509	+	13.8413i	0.748969	+	0.544158i	0.895507	−	0.445047i	$-0.146813\pi$
$647$	19.0509	+	13.8413i	0.748969	+	0.544158i	−0.146538	+	0.989205i	$0.546813\pi$
$648$	10.7245			0.421300
$649$	26.2648	−	15.0857i	1.03098	−	0.592164i
$650$	−16.8351			−0.660328
$651$	11.5743	+	8.40925i	0.453634	+	0.329584i
$652$	32.6194	−	100.392i	1.27748	−	3.93166i
$653$	13.1703	+	40.5341i	0.515395	+	1.58622i	0.782562	+	0.622573i	$0.213912\pi$
$653$	13.1703	+	40.5341i	0.515395	+	1.58622i	−0.267167	+	0.963650i	$0.586088\pi$
$654$	−15.0635	+	10.9442i	−0.589028	+	0.427954i
$655$	−44.5880	+	32.3951i	−1.74220	+	1.26578i
$656$	20.7127	+	63.7472i	0.808696	+	2.48891i
$657$	−1.01200	+	3.11462i	−0.0394819	+	0.121513i
$658$	18.7204	+	13.6012i	0.729799	+	0.530230i
$659$	−25.4615			−0.991841			−0.495920	−	0.868368i	$-0.665169\pi$
$659$	−25.4615			−0.991841			−0.495920	+	0.868368i	$0.665169\pi$
$660$	−47.6126	−	43.0641i	−1.85332	−	1.67627i
$661$	−14.6713			−0.570648			−0.285324	−	0.958431i	$-0.592101\pi$
$661$	−14.6713			−0.570648			−0.285324	+	0.958431i	$0.592101\pi$
$662$	36.3339	+	26.3981i	1.41216	+	1.02599i
$663$	−1.94713	+	5.99265i	−0.0756203	+	0.232735i
$664$	−46.1925	−	142.166i	−1.79262	−	5.51710i
$665$	−2.20294	+	1.60053i	−0.0854265	+	0.0620660i
$666$	3.09912	−	2.25165i	0.120089	−	0.0872495i
$667$	1.73912	+	5.35246i	0.0673390	+	0.207248i
$668$	7.60637	−	23.4100i	0.294299	−	0.905760i
$669$	20.6592	+	15.0098i	0.798730	+	0.580311i
$670$	−58.2536			−2.25053
$671$	6.72517	+	6.08270i	0.259622	+	0.234820i
$672$	43.4496			1.67611
$673$	27.0932	+	19.6843i	1.04437	+	0.758776i	0.971133	−	0.238539i	$-0.0766686\pi$
$673$	27.0932	+	19.6843i	1.04437	+	0.758776i	0.0732322	+	0.997315i	$0.476669\pi$
$674$	17.5640	−	54.0564i	0.676539	−	2.08217i
$675$	−1.85891	−	5.72114i	−0.0715496	−	0.220207i
$676$	−4.71828	+	3.42803i	−0.181472	+	0.131847i
$677$	−12.3527	+	8.97475i	−0.474752	+	0.344928i	−0.799290	−	0.600945i	$-0.794791\pi$
$677$	−12.3527	+	8.97475i	−0.474752	+	0.344928i	0.324538	+	0.945873i	$0.394791\pi$
$678$	9.62193	+	29.6133i	0.369528	+	1.13729i
$679$	6.55342	−	20.1693i	0.251497	−	0.774029i
$680$	−181.448	−	131.830i	−6.95821	−	5.05544i
$681$	−3.75572			−0.143919
$682$	79.2500	−	45.5186i	3.03464	−	1.74300i
$683$	−37.3798			−1.43030			−0.715149	−	0.698972i	$-0.753641\pi$
$683$	−37.3798			−1.43030			−0.715149	+	0.698972i	$0.753641\pi$
$684$	−2.66416	−	1.93563i	−0.101867	−	0.0740105i
$685$	−1.23333	+	3.79580i	−0.0471231	+	0.145030i
$686$	14.9391	+	45.9779i	0.570379	+	1.75545i
$687$	−6.92165	+	5.02887i	−0.264078	+	0.191864i
$688$	61.2136	−	44.4743i	2.33375	−	1.69557i
$689$	0.723677	+	2.22725i	0.0275699	+	0.0848514i
$690$	−10.1156	+	31.1328i	−0.385096	+	1.18520i
$691$	−29.1368	−	21.1691i	−1.10841	−	0.805310i	−0.126001	−	0.992030i	$-0.540214\pi$
$691$	−29.1368	−	21.1691i	−1.10841	−	0.805310i	−0.982413	+	0.186720i	$0.940214\pi$
$692$	29.9347			1.13795
$693$	−4.79152	−	0.514464i	−0.182015	−	0.0195429i
$694$	44.3436			1.68326
$695$	55.1934	+	40.1003i	2.09360	+	1.52109i
$696$	5.29225	−	16.2879i	0.200602	−	0.617390i
$697$	−7.11260	−	21.8903i	−0.269409	−	0.829155i
$698$	26.9379	−	19.5716i	1.01962	−	0.740795i
$699$	−0.641360	+	0.465975i	−0.0242585	+	0.0176248i
$700$	−15.7526	−	48.4814i	−0.595391	−	1.83243i
$701$	1.99272	−	6.13297i	0.0752641	−	0.231639i	−0.906346	−	0.422537i	$-0.861140\pi$
$701$	1.99272	−	6.13297i	0.0752641	−	0.231639i	0.981610	+	0.190897i	$0.0611398\pi$
$702$	−2.26411	−	1.64497i	−0.0854533	−	0.0620854i
$703$	−0.772891			−0.0291501
$704$	63.7059	−	142.228i	2.40101	−	5.36040i
$705$	18.8867			0.711314
$706$	−36.4996	−	26.5185i	−1.37368	−	0.998038i
$707$	−3.13231	+	9.64026i	−0.117803	+	0.362559i
$708$	16.4587	+	50.6547i	0.618557	+	1.90372i
$709$	38.2892	−	27.8187i	1.43798	−	1.04475i	0.449520	−	0.893270i	$-0.351595\pi$
$709$	38.2892	−	27.8187i	1.43798	−	1.04475i	0.988460	−	0.151483i	$-0.0484049\pi$
$710$	1.33322	−	0.968642i	0.0500349	−	0.0363525i
$711$	−0.0317531	−	0.0977259i	−0.00119083	−	0.00366501i
$712$	−3.53410	+	10.8769i	−0.132446	+	0.407627i
$713$	−28.0736	−	20.3967i	−1.05136	−	0.763861i
$714$	−25.6223			−0.958891
$715$	2.26452	+	10.7723i	0.0846883	+	0.402862i
$716$	−122.321			−4.57136
$717$	−8.77773	−	6.37740i	−0.327810	−	0.238168i
$718$	−4.65153	+	14.3160i	−0.173594	+	0.534267i
$719$	−3.91576	−	12.0515i	−0.146033	−	0.449444i	0.851109	−	0.524989i	$-0.175930\pi$
$719$	−3.91576	−	12.0515i	−0.146033	−	0.449444i	−0.997142	+	0.0755446i	$0.975930\pi$
$720$	49.2700	−	35.7967i	1.83618	−	1.33407i
$721$	11.1603	−	8.10840i	0.415630	−	0.301973i
$722$	−16.1557	−	49.7222i	−0.601253	−	1.85047i
$723$	−3.25010	+	10.0028i	−0.120873	+	0.372007i
$724$	47.2495	+	34.3288i	1.75601	+	1.27582i
$725$	−9.60629			−0.356769
$726$	−15.5115	+	26.5909i	−0.575687	+	0.986883i
$727$	−3.68862			−0.136803			−0.0684017	−	0.997658i	$-0.521790\pi$
$727$	−3.68862			−0.136803			−0.0684017	+	0.997658i	$0.521790\pi$
$728$	−12.6067	−	9.15932i	−0.467236	−	0.339467i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	9.39991	+	28.9299i	0.347906	+	1.07075i
$731$	−21.0203	+	15.2722i	−0.777465	+	0.564861i
$732$	−12.9002	+	9.37252i	−0.476804	+	0.346418i
$733$	−5.41476	−	16.6649i	−0.199999	−	0.615532i	−0.999882	−	0.0153766i	$-0.995105\pi$
$733$	−5.41476	−	16.6649i	−0.199999	−	0.615532i	0.799883	−	0.600156i	$-0.204895\pi$
$734$	−23.3098	+	71.7400i	−0.860379	+	2.64797i
$735$	13.1269	+	9.53725i	0.484193	+	0.351787i
$736$	−105.387			−3.88462
$737$	4.27910	+	20.3557i	0.157623	+	0.749812i
$738$	10.2229			0.376309
$739$	−28.1312	−	20.4385i	−1.03482	−	0.751844i	−0.0655559	−	0.997849i	$-0.520882\pi$
$739$	−28.1312	−	20.4385i	−1.03482	−	0.751844i	−0.969269	+	0.246005i	$0.920882\pi$
$740$	8.18755	−	25.1987i	0.300980	−	0.926322i
$741$	0.174485	+	0.537010i	0.00640988	+	0.0197276i
$742$	−7.70417	+	5.59740i	−0.282829	+	0.205487i
$743$	32.6343	−	23.7102i	1.19724	−	0.869843i	0.203226	−	0.979132i	$-0.434857\pi$
$743$	32.6343	−	23.7102i	1.19724	−	0.869843i	0.994010	+	0.109289i	$0.0348574\pi$
$744$	32.6312	+	100.429i	1.19632	+	3.68189i
$745$	2.26578	−	6.97334i	0.0830116	−	0.255483i
$746$	59.9272	+	43.5397i	2.19409	+	1.59410i
$747$	−13.9383			−0.509976
$748$	−49.8227	+	111.232i	−1.82170	+	4.06706i
$749$	9.70346			0.354557
$750$	−7.63149	−	5.54461i	−0.278663	−	0.202460i
$751$	8.04575	−	24.7623i	0.293594	−	0.903588i	−0.690097	−	0.723717i	$-0.742432\pi$
$751$	8.04575	−	24.7623i	0.293594	−	0.903588i	0.983690	−	0.179871i	$-0.0575680\pi$
$752$	32.2668	+	99.3071i	1.17665	+	3.62136i
$753$	0.409848	−	0.297772i	0.0149357	−	0.0108514i
$754$	−3.61557	+	2.62686i	−0.131671	+	0.0956648i
$755$	12.2464	+	37.6906i	0.445693	+	1.37170i
$756$	2.61863	−	8.05933i	0.0952388	−	0.293115i
$757$	5.97447	+	4.34071i	0.217146	+	0.157766i	0.691041	−	0.722816i	$-0.257152\pi$
$757$	5.97447	+	4.34071i	0.217146	+	0.157766i	−0.473895	+	0.880581i	$0.657152\pi$
$758$	4.79556			0.174182
$759$	11.6219	+	1.24783i	0.421847	+	0.0452935i
$760$	−20.0983			−0.729041
$761$	12.1032	+	8.79351i	0.438741	+	0.318764i	0.785135	−	0.619325i	$-0.212594\pi$
$761$	12.1032	+	8.79351i	0.438741	+	0.318764i	−0.346393	+	0.938089i	$0.612594\pi$
$762$	−6.56394	+	20.2017i	−0.237787	+	0.731832i
$763$	2.98728	+	9.19390i	0.108147	+	0.332842i
$764$	−3.98978	+	2.89875i	−0.144345	+	0.104873i
$765$	−16.9190	+	12.2923i	−0.611706	+	0.444431i
$766$	−10.7602	−	33.1164i	−0.388781	−	1.19655i
$767$	2.82208	−	8.68548i	0.101900	−	0.313614i
$768$	86.2963	+	62.6979i	3.11395	+	2.26242i
$769$	−43.2060			−1.55805			−0.779024	−	0.626994i	$-0.784285\pi$
$769$	−43.2060			−1.55805			−0.779024	+	0.626994i	$0.784285\pi$
$770$	−38.8147	+	22.2939i	−1.39879	+	0.803417i
$771$	−13.2987			−0.478939
$772$	−97.0624	−	70.5199i	−3.49335	−	2.53807i
$773$	5.86015	−	18.0357i	0.210775	−	0.648699i	−0.788652	−	0.614840i	$-0.789220\pi$
$773$	5.86015	−	18.0357i	0.210775	−	0.648699i	0.999427	−	0.0338586i	$-0.0107796\pi$
$774$	−3.56608	−	10.9753i	−0.128180	−	0.394498i
$775$	47.9189	−	34.8151i	1.72130	−	1.25060i
$776$	126.636	−	92.0061i	4.54595	−	3.30283i
$777$	−0.614597	−	1.89153i	−0.0220485	−	0.0678584i
$778$	−6.43308	+	19.7990i	−0.230637	+	0.709828i
$779$	−1.66866	−	1.21235i	−0.0597859	−	0.0434370i
$780$	−19.3566			−0.693079
$781$	−0.436409	−	0.394718i	−0.0156159	−	0.0141241i
$782$	62.1470			2.22237
$783$	−1.29192	−	0.938638i	−0.0461696	−	0.0335442i
$784$	−27.7207	+	85.3156i	−0.990026	+	3.04699i
$785$	−13.1874	−	40.5867i	−0.470679	−	1.44860i
$786$	−37.5971	+	27.3159i	−1.34104	+	0.974326i
$787$	−14.2971	+	10.3874i	−0.509636	+	0.370272i	−0.812686	−	0.582702i	$-0.801995\pi$
$787$	−14.2971	+	10.3874i	−0.509636	+	0.370272i	0.303049	+	0.952975i	$0.401995\pi$
$788$	−50.5484	−	155.572i	−1.80071	−	5.54202i
$789$	7.82812	−	24.0925i	0.278688	−	0.857715i
$790$	−0.772154	−	0.561003i	−0.0274720	−	0.0199596i
$791$	16.1661			0.574802
$792$	−26.3797	−	23.8596i	−0.937363	−	0.847815i
$793$	2.73408			0.0970900
$794$	21.7481	+	15.8009i	0.771810	+	0.560753i
$795$	−2.40186	+	7.39217i	−0.0851853	+	0.262173i
$796$	−15.5594	−	47.8869i	−0.551489	−	1.69731i
$797$	−41.6958	+	30.2937i	−1.47694	+	1.07306i	−0.498413	+	0.866940i	$0.666084\pi$
$797$	−41.6958	+	30.2937i	−1.47694	+	1.07306i	−0.978527	+	0.206120i	$0.933916\pi$
$798$	−1.85755	+	1.34959i	−0.0657565	+	0.0477749i
$799$	−11.0802	−	34.1013i	−0.391989	−	1.20642i
$800$	55.5877	−	171.081i	1.96532	−	6.04864i
$801$	0.862732	+	0.626812i	0.0304831	+	0.0221473i
$802$	−44.4260			−1.56874
$803$	9.41858	−	5.40972i	0.332374	−	0.190905i
$804$	−36.5768			−1.28997
$805$	13.7498	+	9.98979i	0.484616	+	0.352094i
$806$	8.51519	−	26.2071i	0.299935	−	0.923105i
$807$	−8.08998	−	24.8984i	−0.284781	−	0.876466i
$808$	−60.5275	+	43.9758i	−2.12935	+	1.54706i
$809$	37.4295	−	27.1941i	1.31595	−	0.956093i	0.315977	−	0.948767i	$-0.397668\pi$
$809$	37.4295	−	27.1941i	1.31595	−	0.956093i	0.999973	−	0.00732641i	$-0.00233209\pi$
$810$	−2.87029	−	8.83384i	−0.100852	−	0.310389i
$811$	−15.1093	+	46.5016i	−0.530559	+	1.63289i	0.222496	+	0.974934i	$0.428580\pi$
$811$	−15.1093	+	46.5016i	−0.530559	+	1.63289i	−0.753055	+	0.657958i	$0.771420\pi$
$812$	−10.9479	−	7.95409i	−0.384195	−	0.279134i
$813$	−18.2562			−0.640272
$814$	−12.6325	−	1.35634i	−0.442768	−	0.0475399i
$815$	−60.0718			−2.10422
$816$	−93.5387	−	67.9599i	−3.27451	−	2.37907i
$817$	−0.719495	+	2.21438i	−0.0251720	+	0.0774713i
$818$	−1.92447	−	5.92292i	−0.0672876	−	0.207090i
$819$	−1.17550	+	0.854053i	−0.0410754	+	0.0298430i
$820$	57.2033	−	41.5606i	1.99763	−	1.45136i
$821$	8.57194	+	26.3817i	0.299163	+	0.920729i	0.981791	+	0.189963i	$0.0608368\pi$
$821$	8.57194	+	26.3817i	0.299163	+	0.920729i	−0.682628	+	0.730766i	$0.739163\pi$
$822$	−1.03996	+	3.20066i	−0.0362726	+	0.111636i
$823$	9.26950	+	6.73468i	0.323114	+	0.234756i	0.737503	−	0.675344i	$-0.236005\pi$
$823$	9.26950	+	6.73468i	0.323114	+	0.234756i	−0.414389	+	0.910100i	$0.636005\pi$
$824$	101.819			3.54703
$825$	−8.15577	+	18.2083i	−0.283947	+	0.633931i
$826$	37.1358			1.29212
$827$	−40.3450	−	29.3124i	−1.40293	−	1.01929i	−0.994303	−	0.106592i	$-0.966006\pi$
$827$	−40.3450	−	29.3124i	−1.40293	−	1.01929i	−0.408631	−	0.912700i	$-0.633994\pi$
$828$	−6.35151	+	19.5479i	−0.220730	+	0.679338i
$829$	−4.11804	−	12.6740i	−0.143025	−	0.440187i	0.853726	−	0.520722i	$-0.174337\pi$
$829$	−4.11804	−	12.6740i	−0.143025	−	0.440187i	−0.996752	+	0.0805350i	$0.974337\pi$
$830$	−104.740	+	76.0978i	−3.63556	+	2.64139i
$831$	11.3139	−	8.22000i	0.392473	−	0.285149i
$832$	−14.5203	−	44.6887i	−0.503399	−	1.54930i
$833$	9.51910	−	29.2968i	0.329817	−	1.01507i
$834$	46.5397	+	33.8130i	1.61154	+	1.17085i
$835$	−14.0079			−0.484762
$836$	2.24686	+	10.6883i	0.0777092	+	0.369663i
$837$	9.84629			0.340337
$838$	−72.3711	−	52.5807i	−2.50002	−	1.81637i
$839$	1.91070	−	5.88051i	0.0659645	−	0.203018i	−0.912642	−	0.408761i	$-0.865961\pi$
$839$	1.91070	−	5.88051i	0.0659645	−	0.203018i	0.978606	+	0.205743i	$0.0659610\pi$
$840$	−15.9820	−	49.1875i	−0.551431	−	1.69713i
$841$	21.3984	−	15.5469i	0.737876	−	0.536098i
$842$	−35.0175	+	25.4417i	−1.20678	+	0.876780i
$843$	−1.47518	−	4.54012i	−0.0508077	−	0.156370i
$844$	−19.4286	+	59.7951i	−0.668761	+	2.05823i
$845$	2.68510	+	1.95084i	0.0923704	+	0.0671110i
$846$	15.9255			0.547529
$847$	10.6414	+	11.9255i	0.365643	+	0.409765i
$848$	−42.9718			−1.47566
$849$	17.1718	+	12.4761i	0.589335	+	0.428177i
$850$	−32.7802	+	100.887i	−1.12435	+	3.46040i
$851$	1.49071	+	4.58792i	0.0511008	+	0.157272i
$852$	0.837116	−	0.608201i	0.0286791	−	0.0208366i
$853$	−14.1104	+	10.2518i	−0.483132	+	0.351016i	−0.802537	−	0.596602i	$-0.796517\pi$
$853$	−14.1104	+	10.2518i	−0.483132	+	0.351016i	0.319405	+	0.947618i	$0.396517\pi$
$854$	3.43557	+	10.5736i	0.117563	+	0.361822i
$855$	−0.579112	+	1.78232i	−0.0198052	+	0.0609541i
$856$	57.9424	+	42.0976i	1.98043	+	1.43887i
$857$	−48.0265			−1.64055			−0.820276	−	0.571967i	$-0.806180\pi$
$857$	−48.0265			−1.64055			−0.820276	+	0.571967i	$0.806180\pi$
$858$	1.90947	+	9.08335i	0.0651882	+	0.310100i
$859$	−51.2114			−1.74731			−0.873655	−	0.486546i	$-0.838257\pi$
$859$	−51.2114			−1.74731			−0.873655	+	0.486546i	$0.838257\pi$
$860$	−64.5738	−	46.9156i	−2.20195	−	1.59981i
$861$	1.64014	−	5.04784i	0.0558960	−	0.172030i
$862$	2.23694	+	6.88461i	0.0761906	+	0.234491i
$863$	29.2239	−	21.2324i	0.994791	−	0.722758i	0.0338263	−	0.999428i	$-0.489231\pi$
$863$	29.2239	−	21.2324i	0.994791	−	0.722758i	0.960965	+	0.276669i	$0.0892307\pi$
$864$	24.1923	−	17.5767i	0.823039	−	0.597973i
$865$	−5.26423	−	16.2016i	−0.178989	−	0.550872i
$866$	0.0935753	−	0.287995i	0.00317982	−	0.00978648i
$867$	18.3672	+	13.3446i	0.623784	+	0.453206i
$868$	83.4382			2.83208
$869$	−0.139313	+	0.311025i	−0.00472587	+	0.0105508i
$870$	−14.8328			−0.502878
$871$	5.07385	+	3.68637i	0.171921	+	0.124908i
$872$	−22.0490	+	67.8598i	−0.746673	+	2.29802i
$873$	−4.51026	−	13.8812i	−0.152649	−	0.469806i
$874$	4.50549	−	3.27343i	0.152400	−	0.110725i
$875$	−3.96220	+	2.87870i	−0.133947	+	0.0973180i
$876$	5.90211	+	18.1648i	0.199414	+	0.613732i
$877$	10.3355	−	31.8094i	0.349005	−	1.07413i	−0.610399	−	0.792094i	$-0.708991\pi$
$877$	10.3355	−	31.8094i	0.349005	−	1.07413i	0.959404	−	0.282034i	$-0.0910091\pi$
$878$	−12.3454	−	8.96944i	−0.416636	−	0.302704i
$879$	−15.9739			−0.538788
$880$	−200.832	−	21.5632i	−6.77003	−	0.726896i
$881$	−41.7535			−1.40671			−0.703355	−	0.710839i	$-0.748316\pi$
$881$	−41.7535			−1.40671			−0.703355	+	0.710839i	$0.748316\pi$
$882$	11.0687	+	8.04191i	0.372704	+	0.270785i
$883$	−6.08964	+	18.7420i	−0.204933	+	0.630717i	0.794784	+	0.606893i	$0.207584\pi$
$883$	−6.08964	+	18.7420i	−0.204933	+	0.630717i	−0.999716	+	0.0238246i	$0.992416\pi$
$884$	11.3559	+	34.9498i	0.381940	+	1.17549i
$885$	24.5216	−	17.8160i	0.824284	−	0.598877i
$886$	69.2852	−	50.3387i	2.32768	−	1.69116i
$887$	2.57577	+	7.92740i	0.0864858	+	0.266176i	0.984941	−	0.172888i	$-0.0553100\pi$
$887$	2.57577	+	7.92740i	0.0864858	+	0.266176i	−0.898456	+	0.439064i	$0.855310\pi$
$888$	4.53631	−	13.9613i	0.152229	−	0.468511i
$889$	8.92209	+	6.48228i	0.299237	+	0.217409i
$890$	9.90516			0.332022
$891$	−2.87599	+	1.65187i	−0.0963493	+	0.0553399i
$892$	148.930			4.98654
$893$	−2.59948	−	1.88863i	−0.0869883	−	0.0632007i
$894$	1.91053	−	5.88000i	0.0638976	−	0.196656i
$895$	21.5111	+	66.2042i	0.719035	+	2.21296i
$896$	84.2777	−	61.2313i	2.81552	−	2.04560i
$897$	2.85119	−	2.07151i	0.0951984	−	0.0691657i
$898$	−17.8704	−	54.9994i	−0.596343	−	1.83535i
$899$	4.85886	−	14.9540i	0.162052	−	0.498745i
$900$	−28.3832	−	20.6216i	−0.946105	−	0.687386i
$901$	14.7562			0.491601
$902$	−25.1458	−	22.7436i	−0.837263	−	0.757278i
$903$	−5.99150			−0.199384
$904$	96.5331	+	70.1354i	3.21064	+	2.33267i
$905$	10.2707	−	31.6099i	0.341409	−	1.05075i
$906$	10.3263	+	31.7811i	0.343069	+	1.05586i
$907$	−1.71490	+	1.24595i	−0.0569422	+	0.0413709i	−0.615892	−	0.787830i	$-0.711204\pi$
$907$	−1.71490	+	1.24595i	−0.0569422	+	0.0413709i	0.558950	+	0.829201i	$0.311204\pi$
$908$	−17.7205	+	12.8747i	−0.588077	+	0.427263i
$909$	2.15575	+	6.63472i	0.0715018	+	0.220060i
$910$	−4.17053	+	12.8356i	−0.138252	+	0.425495i
$911$	1.69530	+	1.23171i	0.0561678	+	0.0408083i	0.615515	−	0.788125i	$-0.288948\pi$
$911$	1.69530	+	1.23171i	0.0561678	+	0.0408083i	−0.559347	+	0.828934i	$0.688948\pi$
$912$	−10.3609			−0.343084
$913$	34.2848	+	31.0096i	1.13466	+	1.02627i
$914$	62.3631			2.06279
$915$	7.34129	+	5.33376i	0.242696	+	0.176329i
$916$	−15.4192	+	47.4553i	−0.509464	+	1.56797i
$917$	7.45600	+	22.9472i	0.246219	+	0.757783i
$918$	−14.2663	+	10.3650i	−0.470856	+	0.342097i
$919$	17.8228	−	12.9490i	0.587919	−	0.427148i	−0.253651	−	0.967296i	$-0.581632\pi$
$919$	17.8228	−	12.9490i	0.587919	−	0.427148i	0.841570	+	0.540147i	$0.181632\pi$
$920$	38.7644	+	119.304i	1.27802	+	3.93335i
$921$	−3.33202	+	10.2549i	−0.109794	+	0.337911i
$922$	−60.8874	−	44.2373i	−2.00522	−	1.45688i
$923$	−0.177420			−0.00583984
$924$	−24.3714	+	13.9981i	−0.801759	+	0.460504i
$925$	−8.23414			−0.270737
$926$	−54.2178	−	39.3915i	−1.78171	−	1.29449i
$927$	2.93381	−	9.02935i	0.0963591	−	0.296563i
$928$	−14.7564	−	45.4156i	−0.484404	−	1.49084i
$929$	26.3112	−	19.1162i	0.863243	−	0.627183i	−0.0655221	−	0.997851i	$-0.520871\pi$
$929$	26.3112	−	19.1162i	0.863243	−	0.627183i	0.928765	+	0.370668i	$0.120871\pi$
$930$	73.9900	−	53.7569i	2.42623	−	1.76276i
$931$	−0.853021	−	2.62533i	−0.0279566	−	0.0860417i
$932$	−1.42874	+	4.39721i	−0.0467999	+	0.144035i
$933$	−6.81203	−	4.94923i	−0.223016	−	0.162031i
$934$	−16.9368			−0.554189
$935$	68.9641	+	7.40465i	2.25537	+	0.242158i
$936$	−10.7245			−0.350543
$937$	19.1828	+	13.9371i	0.626675	+	0.455306i	0.855247	−	0.518221i	$-0.173406\pi$
$937$	19.1828	+	13.9371i	0.626675	+	0.455306i	−0.228572	+	0.973527i	$0.573406\pi$
$938$	−7.88076	+	24.2545i	−0.257316	+	0.791937i
$939$	−3.44506	−	10.6028i	−0.112425	−	0.346009i
$940$	89.1128	−	64.7442i	2.90654	−	2.11172i
$941$	33.9072	−	24.6350i	1.10534	−	0.803078i	0.123418	−	0.992355i	$-0.460614\pi$
$941$	33.9072	−	24.6350i	1.10534	−	0.803078i	0.981924	+	0.189277i	$0.0606143\pi$
$942$	−11.1198	−	34.2232i	−0.362302	−	1.11505i
$943$	−3.97818	+	12.2436i	−0.129547	+	0.398705i
$944$	135.571	+	98.4980i	4.41246	+	3.20584i
$945$	−4.82247			−0.156875
$946$	−15.6458	+	34.9302i	−0.508688	+	1.13568i
$947$	−0.286780			−0.00931909			−0.00465954	−	0.999989i	$-0.501483\pi$
$947$	−0.286780			−0.00931909			−0.00465954	+	0.999989i	$0.501483\pi$
$948$	−0.484828	−	0.352248i	−0.0157465	−	0.0114405i
$949$	1.01200	−	3.11462i	0.0328509	−	0.101105i
$950$	2.93748	+	9.04064i	0.0953045	+	0.293317i
$951$	14.9669	−	10.8741i	0.485336	−	0.352617i
$952$	−79.4356	+	57.7133i	−2.57452	+	1.87050i
$953$	6.30094	+	19.3923i	0.204107	+	0.628178i	0.999749	+	0.0224100i	$0.00713392\pi$
$953$	6.30094	+	19.3923i	0.204107	+	0.628178i	−0.795642	+	0.605768i	$0.792866\pi$
$954$	−2.02528	+	6.23316i	−0.0655707	+	0.201806i
$955$	2.27053	+	1.64963i	0.0734725	+	0.0533809i
$956$	−63.2778			−2.04655
$957$	1.08956	+	5.18305i	0.0352206	+	0.167544i
$958$	−11.2096			−0.362166
$959$	1.41357	+	1.02702i	0.0456465	+	0.0331641i
$960$	48.1923	−	148.321i	1.55540	−	4.78703i
$961$	20.3795	+	62.7216i	0.657402	+	2.02328i
$962$	−3.09912	+	2.25165i	−0.0999198	+	0.0725960i
$963$	5.40279	−	3.92536i	0.174102	−	0.126493i
$964$	18.9550	+	58.3374i	0.610499	+	1.87892i
$965$	−21.0986	+	64.9347i	−0.679186	+	2.09032i
$966$	11.5940	+	8.42350i	0.373029	+	0.271022i
$967$	−16.4422			−0.528746			−0.264373	−	0.964421i	$-0.585165\pi$
$967$	−16.4422			−0.528746			−0.264373	+	0.964421i	$0.585165\pi$
$968$	11.8055	+	117.378i	0.379442	+	3.77266i
$969$	3.55786			0.114295
$970$	−109.678	−	79.6858i	−3.52155	−	2.55856i
$971$	−1.93945	+	5.96903i	−0.0622401	+	0.191555i	−0.977342	−	0.211668i	$-0.932110\pi$
$971$	−1.93945	+	5.96903i	−0.0622401	+	0.191555i	0.915101	+	0.403224i	$0.132110\pi$
$972$	−1.80222	−	5.54667i	−0.0578064	−	0.177910i
$973$	24.1629	−	17.5554i	0.774628	−	0.562800i
$974$	35.5547	−	25.8320i	1.13925	−	0.827710i
$975$	1.85891	+	5.72114i	0.0595328	+	0.183223i
$976$	−15.5030	+	47.7132i	−0.496238	+	1.52726i
$977$	28.2617	+	20.5333i	0.904173	+	0.656920i	0.939534	−	0.342455i	$-0.111258\pi$
$977$	28.2617	+	20.5333i	0.904173	+	0.656920i	−0.0353618	+	0.999375i	$0.511258\pi$
$978$	−50.6532			−1.61971
$979$	−0.727598	−	3.46118i	−0.0232541	−	0.110620i
$980$	94.6304			3.02286
$981$	5.38251	+	3.91062i	0.171850	+	0.124857i
$982$	7.47459	−	23.0044i	0.238524	−	0.734100i
$983$	−13.6864	−	42.1223i	−0.436527	−	1.34349i	−0.891514	−	0.452994i	$-0.850356\pi$
$983$	−13.6864	−	42.1223i	−0.436527	−	1.34349i	0.454986	−	0.890498i	$-0.349644\pi$
$984$	31.6935	−	23.0267i	1.01035	−	0.734063i
$985$	−75.3112	+	54.7168i	−2.39961	+	1.74342i
$986$	8.70190	+	26.7817i	0.277125	+	0.852902i
$987$	2.55506	−	7.86366i	0.0813284	−	0.250303i
$988$	2.66416	+	1.93563i	0.0847582	+	0.0615805i
$989$	14.5324			0.462103
$990$	−12.5931	+	28.1148i	−0.400234	+	0.893547i
$991$	23.8078			0.756279			0.378139	−	0.925749i	$-0.376564\pi$
$991$	23.8078			0.756279			0.378139	+	0.925749i	$0.376564\pi$
$992$	238.204	+	173.066i	7.56300	+	5.49484i
$993$	4.95903	−	15.2623i	0.157370	−	0.484335i
$994$	−0.222941	−	0.686142i	−0.00707126	−	0.0217631i
$995$	−23.1817	+	16.8425i	−0.734910	+	0.533943i
$996$	−65.7649	+	47.7810i	−2.08384	+	1.51400i
$997$	−14.1070	−	43.4168i	−0.446772	−	1.37502i	−0.880529	−	0.473993i	$-0.842812\pi$
$997$	−14.1070	−	43.4168i	−0.446772	−	1.37502i	0.433757	−	0.901030i	$-0.357188\pi$
$998$	11.9126	−	36.6633i	0.377087	−	1.16056i
$999$	−1.10739	−	0.804564i	−0.0350362	−	0.0254553i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.n.b.235.1	yes	20
11.3	even	5	inner	429.2.n.b.157.1	✓	20
11.5	even	5		4719.2.a.bn.1.10		10
11.6	odd	10		4719.2.a.bi.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.b.157.1	✓	20	11.3	even	5	inner
429.2.n.b.235.1	yes	20	1.1	even	1	trivial
4719.2.a.bi.1.1		10	11.6	odd	10
4719.2.a.bn.1.10		10	11.5	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.26411 - 1.64497i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.80222 + 5.54667i) q^{4} +(2.68510 - 1.95084i) q^{5} +(2.26411 - 1.64497i) q^{6} +(-0.449002 - 1.38189i) q^{7} +(3.31406 - 10.1996i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-2.26411 - 1.64497i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.80222 + 5.54667i) q^{4} +(2.68510 - 1.95084i) q^{5} +(2.26411 - 1.64497i) q^{6} +(-0.449002 - 1.38189i) q^{7} +(3.31406 - 10.1996i) q^{8} +(-0.809017 - 0.587785i) q^{9} -9.28845 q^{10} +(0.682296 + 3.24569i) q^{11} -5.83212 q^{12} +(0.809017 + 0.587785i) q^{13} +(-1.25657 + 3.86734i) q^{14} +(1.02562 + 3.15653i) q^{15} +(-14.8450 + 10.7855i) q^{16} +(5.09765 - 3.70366i) q^{17} +(0.864813 + 2.66162i) q^{18} +(0.174485 - 0.537010i) q^{19} +(15.6598 + 11.3775i) q^{20} +1.45300 q^{21} +(3.79427 - 8.47094i) q^{22} -3.52426 q^{23} +(8.67633 + 6.30373i) q^{24} +(1.85891 - 5.72114i) q^{25} +(-0.864813 - 2.66162i) q^{26} +(0.809017 - 0.587785i) q^{27} +(6.85567 - 4.98094i) q^{28} +(-0.493471 - 1.51875i) q^{29} +(2.87029 - 8.83384i) q^{30} +(7.96581 + 5.78750i) q^{31} +29.9033 q^{32} +(-3.29767 - 0.354070i) q^{33} -17.6341 q^{34} +(-3.90146 - 2.83458i) q^{35} +(1.80222 - 5.54667i) q^{36} +(-0.422984 - 1.30181i) q^{37} +(-1.27842 + 0.928827i) q^{38} +(-0.809017 + 0.587785i) q^{39} +(-10.9993 - 33.8523i) q^{40} +(1.12880 - 3.47408i) q^{41} +(-3.28975 - 2.39015i) q^{42} -4.12353 q^{43} +(-16.7731 + 9.63393i) q^{44} -3.31897 q^{45} +(7.97931 + 5.79731i) q^{46} +(1.75847 - 5.41201i) q^{47} +(-5.67027 - 17.4513i) q^{48} +(3.95511 - 2.87356i) q^{49} +(-13.6199 + 9.89544i) q^{50} +(1.94713 + 5.99265i) q^{51} +(-1.80222 + 5.54667i) q^{52} +(1.89461 + 1.37652i) q^{53} -2.79859 q^{54} +(8.16386 + 7.38395i) q^{55} -15.5828 q^{56} +(0.456808 + 0.331891i) q^{57} +(-1.38102 + 4.25036i) q^{58} +(-2.82208 - 8.68548i) q^{59} +(-15.6598 + 11.3775i) q^{60} +(2.21192 - 1.60705i) q^{61} +(-8.51519 - 26.2071i) q^{62} +(-0.449002 + 1.38189i) q^{63} +(-38.0145 - 27.6192i) q^{64} +3.31897 q^{65} +(6.88385 + 6.22623i) q^{66} +6.27162 q^{67} +(29.7301 + 21.6002i) q^{68} +(1.08906 - 3.35177i) q^{69} +(4.17053 + 12.8356i) q^{70} +(-0.143536 + 0.104285i) q^{71} +(-8.67633 + 6.30373i) q^{72} +(-1.01200 - 3.11462i) q^{73} +(-1.18376 + 3.64324i) q^{74} +(4.86670 + 3.53586i) q^{75} +3.29308 q^{76} +(4.17882 - 2.40018i) q^{77} +2.79859 q^{78} +(0.0831306 + 0.0603979i) q^{79} +(-18.8195 + 57.9203i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-8.27048 + 6.00886i) q^{82} +(11.2763 - 8.19273i) q^{83} +(2.61863 + 8.05933i) q^{84} +(6.46247 - 19.8894i) q^{85} +(9.33612 + 6.78309i) q^{86} +1.59691 q^{87} +(35.3660 + 3.79723i) q^{88} -1.06640 q^{89} +(7.51451 + 5.45961i) q^{90} +(0.449002 - 1.38189i) q^{91} +(-6.35151 - 19.5479i) q^{92} +(-7.96581 + 5.78750i) q^{93} +(-12.8840 + 9.36075i) q^{94} +(-0.579112 - 1.78232i) q^{95} +(-9.24064 + 28.4398i) q^{96} +(11.8080 + 8.57903i) q^{97} -13.6817 q^{98} +(1.35578 - 3.02686i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9}+O(q^{10}) \) 20 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - q^6 - 3 * q^7 - 7 * q^8 - 5 * q^9	\( 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9} - 2 q^{10} + 14 q^{11} - 18 q^{12} + 5 q^{13} - q^{14} - 4 q^{15} - 35 q^{16} + 2 q^{17} - 4 q^{18} - 2 q^{19} + 45 q^{20} - 2 q^{21} + 11 q^{22} + 6 q^{23} + 2 q^{24} - 7 q^{25} + 4 q^{26} + 5 q^{27} + 12 q^{28} + 26 q^{29} - 3 q^{30} + 20 q^{31} + 42 q^{32} + q^{33} - 24 q^{34} - 18 q^{35} + 3 q^{36} - 6 q^{37} - 3 q^{38} - 5 q^{39} - 26 q^{41} - 9 q^{42} + 28 q^{43} - 38 q^{44} - 16 q^{45} - 17 q^{46} + 8 q^{47} - 20 q^{48} + 2 q^{49} - 29 q^{50} + 3 q^{51} - 3 q^{52} + q^{53} - 6 q^{54} - 36 q^{56} - 8 q^{57} + 22 q^{58} - 21 q^{59} - 45 q^{60} + 26 q^{61} - 10 q^{62} - 3 q^{63} - 87 q^{64} + 16 q^{65} + 14 q^{66} + 56 q^{67} + 65 q^{68} + 4 q^{69} - 24 q^{70} - 28 q^{71} - 2 q^{72} + 45 q^{73} - 29 q^{74} - 3 q^{75} + 60 q^{76} + 4 q^{77} + 6 q^{78} - 15 q^{79} - 7 q^{80} - 5 q^{81} - 46 q^{82} + 36 q^{83} + 8 q^{84} + 39 q^{86} + 24 q^{87} + 73 q^{88} - 126 q^{89} - 2 q^{90} + 3 q^{91} + 2 q^{92} - 20 q^{93} - 3 q^{94} + 47 q^{95} - 47 q^{96} + 18 q^{97} - 54 q^{98} - 16 q^{99}+O(q^{100}) \) 20 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - q^6 - 3 * q^7 - 7 * q^8 - 5 * q^9 - 2 * q^10 + 14 * q^11 - 18 * q^12 + 5 * q^13 - q^14 - 4 * q^15 - 35 * q^16 + 2 * q^17 - 4 * q^18 - 2 * q^19 + 45 * q^20 - 2 * q^21 + 11 * q^22 + 6 * q^23 + 2 * q^24 - 7 * q^25 + 4 * q^26 + 5 * q^27 + 12 * q^28 + 26 * q^29 - 3 * q^30 + 20 * q^31 + 42 * q^32 + q^33 - 24 * q^34 - 18 * q^35 + 3 * q^36 - 6 * q^37 - 3 * q^38 - 5 * q^39 - 26 * q^41 - 9 * q^42 + 28 * q^43 - 38 * q^44 - 16 * q^45 - 17 * q^46 + 8 * q^47 - 20 * q^48 + 2 * q^49 - 29 * q^50 + 3 * q^51 - 3 * q^52 + q^53 - 6 * q^54 - 36 * q^56 - 8 * q^57 + 22 * q^58 - 21 * q^59 - 45 * q^60 + 26 * q^61 - 10 * q^62 - 3 * q^63 - 87 * q^64 + 16 * q^65 + 14 * q^66 + 56 * q^67 + 65 * q^68 + 4 * q^69 - 24 * q^70 - 28 * q^71 - 2 * q^72 + 45 * q^73 - 29 * q^74 - 3 * q^75 + 60 * q^76 + 4 * q^77 + 6 * q^78 - 15 * q^79 - 7 * q^80 - 5 * q^81 - 46 * q^82 + 36 * q^83 + 8 * q^84 + 39 * q^86 + 24 * q^87 + 73 * q^88 - 126 * q^89 - 2 * q^90 + 3 * q^91 + 2 * q^92 - 20 * q^93 - 3 * q^94 + 47 * q^95 - 47 * q^96 + 18 * q^97 - 54 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more