LMFDB - Embedded newform 650.2.l.c.131.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(131,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, 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("650.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.l (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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			131.5
Character	$\chi$	$=$	650.131
Dual form			650.2.l.c.521.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(2.22837 - 1.61900i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.656771 + 2.13744i) q^{5} +(2.22837 + 1.61900i) q^{6} +1.40108 q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.41739 - 4.36229i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(2.22837 - 1.61900i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.656771 + 2.13744i) q^{5} +(2.22837 + 1.61900i) q^{6} +1.40108 q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.41739 - 4.36229i) q^{9} +(-1.82987 + 1.28513i) q^{10} +(-1.79844 - 5.53502i) q^{11} +(-0.851160 + 2.61960i) q^{12} +(0.309017 - 0.951057i) q^{13} +(0.432958 + 1.33251i) q^{14} +(4.92405 + 3.69969i) q^{15} +(0.309017 - 0.951057i) q^{16} +(5.84228 + 4.24467i) q^{17} +4.58678 q^{18} +(4.10099 + 2.97954i) q^{19} +(-1.78769 - 1.34319i) q^{20} +(3.12212 - 2.26835i) q^{21} +(4.70837 - 3.42083i) q^{22} +(-0.179468 - 0.552346i) q^{23} -2.75441 q^{24} +(-4.13730 + 2.80762i) q^{25} +1.00000 q^{26} +(-1.35061 - 4.15674i) q^{27} +(-1.13350 + 0.823534i) q^{28} +(-4.80689 + 3.49241i) q^{29} +(-1.99700 + 5.82631i) q^{30} +(-4.07971 - 2.96408i) q^{31} +1.00000 q^{32} +(-12.9688 - 9.42238i) q^{33} +(-2.23155 + 6.86801i) q^{34} +(0.920189 + 2.99473i) q^{35} +(1.41739 + 4.36229i) q^{36} +(-0.739143 + 2.27485i) q^{37} +(-1.56644 + 4.82100i) q^{38} +(-0.851160 - 2.61960i) q^{39} +(0.725017 - 2.11527i) q^{40} +(1.54628 - 4.75896i) q^{41} +(3.12212 + 2.26835i) q^{42} +2.43775 q^{43} +(4.70837 + 3.42083i) q^{44} +(10.2550 + 0.164571i) q^{45} +(0.469854 - 0.341369i) q^{46} +(-8.32389 + 6.04766i) q^{47} +(-0.851160 - 2.61960i) q^{48} -5.03697 q^{49} +(-3.94870 - 3.06721i) q^{50} +19.8909 q^{51} +(0.309017 + 0.951057i) q^{52} +(-5.29558 + 3.84746i) q^{53} +(3.53593 - 2.56901i) q^{54} +(10.6496 - 7.47929i) q^{55} +(-1.13350 - 0.823534i) q^{56} +13.9624 q^{57} +(-4.80689 - 3.49241i) q^{58} +(3.28756 - 10.1181i) q^{59} +(-6.15826 - 0.0988265i) q^{60} +(2.33152 + 7.17568i) q^{61} +(1.55831 - 4.79598i) q^{62} +(1.98588 - 6.11192i) q^{63} +(0.309017 + 0.951057i) q^{64} +(2.23578 + 0.0358794i) q^{65} +(4.95364 - 15.2457i) q^{66} +(-9.12521 - 6.62985i) q^{67} -7.22146 q^{68} +(-1.29417 - 0.940270i) q^{69} +(-2.56380 + 1.80057i) q^{70} +(-2.57460 + 1.87056i) q^{71} +(-3.71079 + 2.69604i) q^{72} +(0.728696 + 2.24270i) q^{73} -2.39192 q^{74} +(-4.67389 + 12.9547i) q^{75} -5.06910 q^{76} +(-2.51975 - 7.75501i) q^{77} +(2.22837 - 1.61900i) q^{78} +(8.03036 - 5.83439i) q^{79} +(2.23578 + 0.0358794i) q^{80} +(1.39294 + 1.01203i) q^{81} +5.00387 q^{82} +(-11.0874 - 8.05549i) q^{83} +(-1.19254 + 3.67027i) q^{84} +(-5.23568 + 15.2753i) q^{85} +(0.753307 + 2.31844i) q^{86} +(-5.05729 + 15.5647i) q^{87} +(-1.79844 + 5.53502i) q^{88} +(-2.68283 - 8.25691i) q^{89} +(3.01247 + 9.80398i) q^{90} +(0.432958 - 1.33251i) q^{91} +(0.469854 + 0.341369i) q^{92} -13.8899 q^{93} +(-8.32389 - 6.04766i) q^{94} +(-3.67519 + 10.7225i) q^{95} +(2.22837 - 1.61900i) q^{96} +(4.62742 - 3.36202i) q^{97} +(-1.55651 - 4.79045i) q^{98} -26.6945 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9}+O(q^{10}) $ 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9} - q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} + 20 q^{15} - 6 q^{16} + 9 q^{17} + 22 q^{18} + 12 q^{19} + 4 q^{20} + 25 q^{21} + 2 q^{22} - 6 q^{23} - 2 q^{24} - 41 q^{25} + 24 q^{26} - 6 q^{27} - 2 q^{29} + 10 q^{30} + 13 q^{31} + 24 q^{32} - 34 q^{33} + 14 q^{34} + 7 q^{36} + 5 q^{37} + 22 q^{38} - 2 q^{39} - q^{40} - 10 q^{41} + 25 q^{42} - 18 q^{43} + 2 q^{44} + 3 q^{45} + 9 q^{46} - 5 q^{47} - 2 q^{48} + 32 q^{49} - 11 q^{50} - 56 q^{51} - 6 q^{52} + 34 q^{53} + 19 q^{54} + 20 q^{55} - 12 q^{57} - 2 q^{58} - 15 q^{60} - 2 q^{61} - 12 q^{62} + 10 q^{63} - 6 q^{64} - q^{65} + 26 q^{66} + 2 q^{67} - 46 q^{68} + 33 q^{69} - 20 q^{70} + 29 q^{71} - 18 q^{72} - 11 q^{73} - 30 q^{74} - 25 q^{75} - 68 q^{76} + 15 q^{77} + 3 q^{78} + 20 q^{79} - q^{80} - 9 q^{81} - 20 q^{82} - 69 q^{83} - 20 q^{84} - 27 q^{85} + 22 q^{86} - 18 q^{87} + 2 q^{88} + 19 q^{89} + 8 q^{90} + 9 q^{92} + 40 q^{93} - 5 q^{94} + 78 q^{95} + 3 q^{96} - 49 q^{97} + 2 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9 - q^10 + 2 * q^11 - 2 * q^12 - 6 * q^13 + 20 * q^15 - 6 * q^16 + 9 * q^17 + 22 * q^18 + 12 * q^19 + 4 * q^20 + 25 * q^21 + 2 * q^22 - 6 * q^23 - 2 * q^24 - 41 * q^25 + 24 * q^26 - 6 * q^27 - 2 * q^29 + 10 * q^30 + 13 * q^31 + 24 * q^32 - 34 * q^33 + 14 * q^34 + 7 * q^36 + 5 * q^37 + 22 * q^38 - 2 * q^39 - q^40 - 10 * q^41 + 25 * q^42 - 18 * q^43 + 2 * q^44 + 3 * q^45 + 9 * q^46 - 5 * q^47 - 2 * q^48 + 32 * q^49 - 11 * q^50 - 56 * q^51 - 6 * q^52 + 34 * q^53 + 19 * q^54 + 20 * q^55 - 12 * q^57 - 2 * q^58 - 15 * q^60 - 2 * q^61 - 12 * q^62 + 10 * q^63 - 6 * q^64 - q^65 + 26 * q^66 + 2 * q^67 - 46 * q^68 + 33 * q^69 - 20 * q^70 + 29 * q^71 - 18 * q^72 - 11 * q^73 - 30 * q^74 - 25 * q^75 - 68 * q^76 + 15 * q^77 + 3 * q^78 + 20 * q^79 - q^80 - 9 * q^81 - 20 * q^82 - 69 * q^83 - 20 * q^84 - 27 * q^85 + 22 * q^86 - 18 * q^87 + 2 * q^88 + 19 * q^89 + 8 * q^90 + 9 * q^92 + 40 * q^93 - 5 * q^94 + 78 * q^95 + 3 * q^96 - 49 * q^97 + 2 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	2.22837	−	1.61900i	1.28655	−	0.934732i	0.286818	−	0.957985i	$-0.407403\pi$
$3$	2.22837	−	1.61900i	1.28655	−	0.934732i	0.999730	+	0.0232535i	$0.00740250\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	0.656771	+	2.13744i	0.293717	+	0.955892i
$5$	0.656771	+	2.13744i	0.293717	+	0.955892i
$6$	2.22837	+	1.61900i	0.909727	+	0.660955i
$7$	1.40108			0.529559			0.264779	−	0.964309i	$-0.414701\pi$
$7$	1.40108			0.529559			0.264779	+	0.964309i	$0.414701\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	1.41739	−	4.36229i	0.472465	−	1.45410i
$10$	−1.82987	+	1.28513i	−0.578657	+	0.406394i
$11$	−1.79844	−	5.53502i	−0.542249	−	1.66887i	−0.727442	−	0.686169i	$-0.759291\pi$
$11$	−1.79844	−	5.53502i	−0.542249	−	1.66887i	0.185193	−	0.982702i	$-0.440709\pi$
$12$	−0.851160	+	2.61960i	−0.245709	+	0.756214i
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$14$	0.432958	+	1.33251i	0.115713	+	0.356127i
$15$	4.92405	+	3.69969i	1.27138	+	0.955255i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	5.84228	+	4.24467i	1.41696	+	1.02948i	0.992264	+	0.124147i	$0.0396196\pi$
$17$	5.84228	+	4.24467i	1.41696	+	1.02948i	0.424698	+	0.905335i	$0.360380\pi$
$18$	4.58678			1.08112
$19$	4.10099	+	2.97954i	0.940832	+	0.683554i	0.948621	−	0.316416i	$-0.102479\pi$
$19$	4.10099	+	2.97954i	0.940832	+	0.683554i	−0.00778911	+	0.999970i	$0.502479\pi$
$20$	−1.78769	−	1.34319i	−0.399741	−	0.300345i
$21$	3.12212	−	2.26835i	0.681302	−	0.494995i
$22$	4.70837	−	3.42083i	1.00383	−	0.729324i
$23$	−0.179468	−	0.552346i	−0.0374217	−	0.115172i	0.930601	−	0.366036i	$-0.119285\pi$
$23$	−0.179468	−	0.552346i	−0.0374217	−	0.115172i	−0.968022	+	0.250864i	$0.919285\pi$
$24$	−2.75441			−0.562242
$25$	−4.13730	+	2.80762i	−0.827461	+	0.561523i
$26$	1.00000			0.196116
$27$	−1.35061	−	4.15674i	−0.259924	−	0.799965i
$28$	−1.13350	+	0.823534i	−0.214211	+	0.155633i
$29$	−4.80689	+	3.49241i	−0.892617	+	0.648524i	−0.936559	−	0.350510i	$-0.886008\pi$
$29$	−4.80689	+	3.49241i	−0.892617	+	0.648524i	0.0439421	+	0.999034i	$0.486008\pi$
$30$	−1.99700	+	5.82631i	−0.364600	+	1.06373i
$31$	−4.07971	−	2.96408i	−0.732737	−	0.532365i	0.157691	−	0.987488i	$-0.449595\pi$
$31$	−4.07971	−	2.96408i	−0.732737	−	0.532365i	−0.890428	+	0.455124i	$0.849595\pi$
$32$	1.00000			0.176777
$33$	−12.9688	−	9.42238i	−2.25758	−	1.64023i
$34$	−2.23155	+	6.86801i	−0.382708	+	1.17785i
$35$	0.920189	+	2.99473i	0.155540	+	0.506201i
$36$	1.41739	+	4.36229i	0.236232	+	0.727048i
$37$	−0.739143	+	2.27485i	−0.121514	+	0.373983i	−0.993250	−	0.115994i	$-0.962995\pi$
$37$	−0.739143	+	2.27485i	−0.121514	+	0.373983i	0.871736	+	0.489977i	$0.162995\pi$
$38$	−1.56644	+	4.82100i	−0.254110	+	0.782070i
$39$	−0.851160	−	2.61960i	−0.136295	−	0.419472i
$40$	0.725017	−	2.11527i	0.114635	−	0.334453i
$41$	1.54628	−	4.75896i	0.241488	−	0.743225i	−0.754706	−	0.656063i	$-0.772220\pi$
$41$	1.54628	−	4.75896i	0.241488	−	0.743225i	0.996194	−	0.0871613i	$-0.0277796\pi$
$42$	3.12212	+	2.26835i	0.481754	+	0.350014i
$43$	2.43775			0.371754			0.185877	−	0.982573i	$-0.440487\pi$
$43$	2.43775			0.371754			0.185877	+	0.982573i	$0.440487\pi$
$44$	4.70837	+	3.42083i	0.709813	+	0.515710i
$45$	10.2550	+	0.164571i	1.52873	+	0.0245328i
$46$	0.469854	−	0.341369i	0.0692761	−	0.0503321i
$47$	−8.32389	+	6.04766i	−1.21416	+	0.882142i	−0.995602	−	0.0936816i	$-0.970136\pi$
$47$	−8.32389	+	6.04766i	−1.21416	+	0.882142i	−0.218562	+	0.975823i	$0.570136\pi$
$48$	−0.851160	−	2.61960i	−0.122854	−	0.378107i
$49$	−5.03697			−0.719568
$50$	−3.94870	−	3.06721i	−0.558430	−	0.433769i
$51$	19.8909			2.78528
$52$	0.309017	+	0.951057i	0.0428529	+	0.131888i
$53$	−5.29558	+	3.84746i	−0.727403	+	0.528490i	−0.888741	−	0.458410i	$-0.848419\pi$
$53$	−5.29558	+	3.84746i	−0.727403	+	0.528490i	0.161338	+	0.986899i	$0.448419\pi$
$54$	3.53593	−	2.56901i	0.481180	−	0.349597i
$55$	10.6496	−	7.47929i	1.43599	−	1.00851i
$56$	−1.13350	−	0.823534i	−0.151470	−	0.110049i
$57$	13.9624			1.84936
$58$	−4.80689	−	3.49241i	−0.631175	−	0.458576i
$59$	3.28756	−	10.1181i	0.428003	−	1.31726i	−0.472086	−	0.881553i	$-0.656499\pi$
$59$	3.28756	−	10.1181i	0.428003	−	1.31726i	0.900089	−	0.435706i	$-0.143501\pi$
$60$	−6.15826	−	0.0988265i	−0.795028	−	0.0127584i
$61$	2.33152	+	7.17568i	0.298520	+	0.918752i	0.982016	+	0.188797i	$0.0604588\pi$
$61$	2.33152	+	7.17568i	0.298520	+	0.918752i	−0.683496	+	0.729955i	$0.739541\pi$
$62$	1.55831	−	4.79598i	0.197905	−	0.609090i
$63$	1.98588	−	6.11192i	0.250198	−	0.770029i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	2.23578	+	0.0358794i	0.277314	+	0.00445029i
$66$	4.95364	−	15.2457i	0.609750	−	1.87662i
$67$	−9.12521	−	6.62985i	−1.11482	−	0.809966i	−0.131406	−	0.991329i	$-0.541949\pi$
$67$	−9.12521	−	6.62985i	−1.11482	−	0.809966i	−0.983416	+	0.181363i	$0.941949\pi$
$68$	−7.22146			−0.875730
$69$	−1.29417	−	0.940270i	−0.155800	−	0.113195i
$70$	−2.56380	+	1.80057i	−0.306433	+	0.215210i
$71$	−2.57460	+	1.87056i	−0.305549	+	0.221994i	−0.729984	−	0.683464i	$-0.760473\pi$
$71$	−2.57460	+	1.87056i	−0.305549	+	0.221994i	0.424436	+	0.905458i	$0.360473\pi$
$72$	−3.71079	+	2.69604i	−0.437320	+	0.317732i
$73$	0.728696	+	2.24270i	0.0852875	+	0.262488i	0.984601	−	0.174817i	$-0.0559332\pi$
$73$	0.728696	+	2.24270i	0.0852875	+	0.262488i	−0.899314	+	0.437304i	$0.855933\pi$
$74$	−2.39192			−0.278055
$75$	−4.67389	+	12.9547i	−0.539694	+	1.49588i
$76$	−5.06910			−0.581466
$77$	−2.51975	−	7.75501i	−0.287153	−	0.883765i
$78$	2.22837	−	1.61900i	0.252313	−	0.183316i
$79$	8.03036	−	5.83439i	0.903486	−	0.656421i	−0.0358733	−	0.999356i	$-0.511421\pi$
$79$	8.03036	−	5.83439i	0.903486	−	0.656421i	0.939359	+	0.342936i	$0.111421\pi$
$80$	2.23578	+	0.0358794i	0.249968	+	0.00401143i
$81$	1.39294	+	1.01203i	0.154771	+	0.112448i
$82$	5.00387			0.552585
$83$	−11.0874	−	8.05549i	−1.21700	−	0.884205i	−0.221156	−	0.975239i	$-0.570983\pi$
$83$	−11.0874	−	8.05549i	−1.21700	−	0.884205i	−0.995848	+	0.0910337i	$0.970983\pi$
$84$	−1.19254	+	3.67027i	−0.130117	+	0.400459i
$85$	−5.23568	+	15.2753i	−0.567889	+	1.65684i
$86$	0.753307	+	2.31844i	0.0812312	+	0.250004i
$87$	−5.05729	+	15.5647i	−0.542198	+	1.66871i
$88$	−1.79844	+	5.53502i	−0.191714	+	0.590035i
$89$	−2.68283	−	8.25691i	−0.284380	−	0.875231i	−0.986584	−	0.163255i	$-0.947801\pi$
$89$	−2.68283	−	8.25691i	−0.284380	−	0.875231i	0.702204	−	0.711976i	$-0.252199\pi$
$90$	3.01247	+	9.80398i	0.317542	+	1.03343i
$91$	0.432958	−	1.33251i	0.0453863	−	0.139685i
$92$	0.469854	+	0.341369i	0.0489856	+	0.0355901i
$93$	−13.8899			−1.44032
$94$	−8.32389	−	6.04766i	−0.858543	−	0.623768i
$95$	−3.67519	+	10.7225i	−0.377066	+	1.10011i
$96$	2.22837	−	1.61900i	0.227432	−	0.165239i
$97$	4.62742	−	3.36202i	0.469843	−	0.341361i	−0.327537	−	0.944838i	$-0.606219\pi$
$97$	4.62742	−	3.36202i	0.469843	−	0.341361i	0.797380	+	0.603477i	$0.206219\pi$
$98$	−1.55651	−	4.79045i	−0.157231	−	0.483908i
$99$	−26.6945			−2.68289
$100$	1.69687	−	4.70326i	0.169687	−	0.470326i
$101$	−18.8383			−1.87448			−0.937241	−	0.348682i	$-0.886629\pi$
$101$	−18.8383			−1.87448			−0.937241	+	0.348682i	$0.886629\pi$
$102$	6.14662	+	18.9173i	0.608606	+	1.87310i
$103$	12.8403	−	9.32900i	1.26519	−	0.919213i	0.266189	−	0.963921i	$-0.414236\pi$
$103$	12.8403	−	9.32900i	1.26519	−	0.919213i	0.999000	+	0.0447076i	$0.0142356\pi$
$104$	−0.809017	+	0.587785i	−0.0793306	+	0.0576371i
$105$	6.89899	+	5.18356i	0.673272	+	0.505863i
$106$	−5.29558	−	3.84746i	−0.514352	−	0.373699i
$107$	8.56394			0.827908			0.413954	−	0.910298i	$-0.364147\pi$
$107$	8.56394			0.827908			0.413954	+	0.910298i	$0.364147\pi$
$108$	3.53593	+	2.56901i	0.340245	+	0.247203i
$109$	−3.31736	+	10.2098i	−0.317745	+	0.977920i	0.656864	+	0.754009i	$0.271882\pi$
$109$	−3.31736	+	10.2098i	−0.317745	+	0.977920i	−0.974610	+	0.223911i	$0.928118\pi$
$110$	10.4041	+	7.81716i	0.991996	+	0.745337i
$111$	2.03590	+	6.26587i	0.193239	+	0.594730i
$112$	0.432958	−	1.33251i	0.0409107	−	0.125910i
$113$	0.613596	−	1.88845i	0.0577222	−	0.177651i	−0.918038	−	0.396492i	$-0.870228\pi$
$113$	0.613596	−	1.88845i	0.0577222	−	0.177651i	0.975761	+	0.218841i	$0.0702276\pi$
$114$	4.31462	+	13.2790i	0.404101	+	1.24369i
$115$	1.06274	−	0.746367i	0.0991008	−	0.0695991i
$116$	1.83607	−	5.65084i	0.170475	−	0.524667i
$117$	−3.71079	−	2.69604i	−0.343062	−	0.249249i
$118$	10.6388			0.979377
$119$	8.18551	+	5.94712i	0.750364	+	0.545171i
$120$	−1.80902	−	5.88739i	−0.165140	−	0.537443i
$121$	−18.5029	+	13.4431i	−1.68208	+	1.22210i
$122$	−6.10400	+	4.43481i	−0.552630	+	0.401509i
$123$	−4.25909	−	13.1081i	−0.384029	−	1.18192i
$124$	5.04279			0.452856
$125$	−8.71837	−	6.99928i	−0.779795	−	0.626035i
$126$	6.42645			0.572514
$127$	−2.04637	−	6.29808i	−0.181586	−	0.558864i	0.818287	−	0.574810i	$-0.194924\pi$
$127$	−2.04637	−	6.29808i	−0.181586	−	0.558864i	−0.999873	+	0.0159460i	$0.994924\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	5.43220	−	3.94673i	0.478279	−	0.347490i
$130$	0.656771	+	2.13744i	0.0576026	+	0.187466i
$131$	0.633737	+	0.460437i	0.0553698	+	0.0402285i	0.615126	−	0.788429i	$-0.289105\pi$
$131$	0.633737	+	0.460437i	0.0553698	+	0.0402285i	−0.559756	+	0.828657i	$0.689105\pi$
$132$	16.0303			1.39526
$133$	5.74582	+	4.17458i	0.498225	+	0.361982i
$134$	3.48552	−	10.7273i	0.301103	−	0.926700i
$135$	7.99774	−	5.61687i	0.688336	−	0.483423i
$136$	−2.23155	−	6.86801i	−0.191354	−	0.588927i
$137$	−0.694798	+	2.13837i	−0.0593606	+	0.182693i	−0.976340	−	0.216242i	$-0.930620\pi$
$137$	−0.694798	+	2.13837i	−0.0593606	+	0.182693i	0.916979	+	0.398935i	$0.130620\pi$
$138$	0.494329	−	1.52139i	0.0420801	−	0.129509i
$139$	0.110788	+	0.340971i	0.00939694	+	0.0289208i	0.955645	−	0.294521i	$-0.0951601\pi$
$139$	0.110788	+	0.340971i	0.00939694	+	0.0289208i	−0.946248	+	0.323442i	$0.895160\pi$
$140$	−2.50470	−	1.88191i	−0.211686	−	0.159051i
$141$	−8.75749	+	26.9528i	−0.737514	+	2.26983i
$142$	−2.57460	−	1.87056i	−0.216055	−	0.156974i
$143$	−5.81986			−0.486682
$144$	−3.71079	−	2.69604i	−0.309232	−	0.224670i
$145$	−10.6218	−	7.98073i	−0.882096	−	0.662763i
$146$	−1.90775	+	1.38606i	−0.157887	+	0.114711i
$147$	−11.2242	+	8.15487i	−0.925758	+	0.672603i
$148$	−0.739143	−	2.27485i	−0.0607572	−	0.186991i
$149$	−17.5347			−1.43650			−0.718251	−	0.695785i	$-0.755057\pi$
$149$	−17.5347			−1.43650			−0.718251	+	0.695785i	$0.755057\pi$
$150$	−13.7650	−	0.441909i	−1.12390	−	0.0360817i
$151$	8.46358			0.688756			0.344378	−	0.938831i	$-0.388090\pi$
$151$	8.46358			0.688756			0.344378	+	0.938831i	$0.388090\pi$
$152$	−1.56644	−	4.82100i	−0.127055	−	0.391035i
$153$	26.7973	−	19.4694i	2.16643	−	1.57400i
$154$	6.59680	−	4.79286i	0.531586	−	0.386220i
$155$	3.65611	−	10.6669i	0.293666	−	0.856782i
$156$	2.22837	+	1.61900i	0.178412	+	0.129624i
$157$	15.4454			1.23268			0.616338	−	0.787482i	$-0.288616\pi$
$157$	15.4454			1.23268			0.616338	+	0.787482i	$0.288616\pi$
$158$	8.03036	+	5.83439i	0.638861	+	0.464160i
$159$	−5.57143	+	17.1471i	−0.441843	+	1.35985i
$160$	0.656771	+	2.13744i	0.0519223	+	0.168980i
$161$	−0.251449	−	0.773881i	−0.0198170	−	0.0609904i
$162$	−0.532056	+	1.63750i	−0.0418022	+	0.128654i
$163$	−6.27798	+	19.3216i	−0.491729	+	1.51339i	0.330264	+	0.943889i	$0.392862\pi$
$163$	−6.27798	+	19.3216i	−0.491729	+	1.51339i	−0.821993	+	0.569498i	$0.807138\pi$
$164$	1.54628	+	4.75896i	0.120744	+	0.371612i
$165$	11.6222	−	33.9084i	0.904791	−	2.63976i
$166$	4.23502	−	13.0341i	0.328701	−	1.01164i
$167$	−4.18691	−	3.04197i	−0.323993	−	0.235395i	0.413884	−	0.910329i	$-0.364172\pi$
$167$	−4.18691	−	3.04197i	−0.323993	−	0.235395i	−0.737877	+	0.674935i	$0.764172\pi$
$168$	−3.85915			−0.297740
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$	−16.1456	−	0.259101i	−1.23831	−	0.0198722i
$171$	18.8104	−	13.6665i	1.43846	−	1.04510i
$172$	−1.97218	+	1.43288i	−0.150378	+	0.109256i
$173$	−0.822342	−	2.53091i	−0.0625215	−	0.192421i	0.914917	−	0.403642i	$-0.132256\pi$
$173$	−0.822342	−	2.53091i	−0.0625215	−	0.192421i	−0.977438	+	0.211221i	$0.932256\pi$
$174$	−16.3657			−1.24068
$175$	−5.79670	+	3.93370i	−0.438189	+	0.297360i
$176$	−5.81986			−0.438689
$177$	−9.05528	−	27.8693i	−0.680637	−	2.09478i
$178$	7.02375	−	5.10305i	0.526452	−	0.382490i
$179$	−13.1739	+	9.57142i	−0.984666	+	0.715401i	−0.958746	−	0.284263i	$-0.908251\pi$
$179$	−13.1739	+	9.57142i	−0.984666	+	0.715401i	−0.0259191	+	0.999664i	$0.508251\pi$
$180$	−8.39323	+	5.89462i	−0.625595	+	0.439359i
$181$	18.5267	+	13.4605i	1.37708	+	1.00051i	0.997146	+	0.0754961i	$0.0240540\pi$
$181$	18.5267	+	13.4605i	1.37708	+	1.00051i	0.379936	+	0.925013i	$0.375946\pi$
$182$	1.40108			0.103855
$183$	16.8129	+	12.2153i	1.24285	+	0.902981i
$184$	−0.179468	+	0.552346i	−0.0132306	+	0.0407195i
$185$	−5.34780	−	0.0858204i	−0.393178	−	0.00630964i
$186$	−4.29222	−	13.2101i	−0.314721	−	0.968612i
$187$	12.9873	−	39.9709i	0.949728	−	2.92296i
$188$	3.17944	−	9.78532i	0.231885	−	0.713668i
$189$	−1.89231	−	5.82393i	−0.137645	−	0.423628i
$190$	−11.3334	−	0.181876i	−0.822211	−	0.0131947i
$191$	−6.88711	+	21.1963i	−0.498333	+	1.53371i	0.313363	+	0.949633i	$0.398544\pi$
$191$	−6.88711	+	21.1963i	−0.498333	+	1.53371i	−0.811697	+	0.584079i	$0.801456\pi$
$192$	2.22837	+	1.61900i	0.160818	+	0.116841i
$193$	1.56059			0.112334			0.0561670	−	0.998421i	$-0.482112\pi$
$193$	1.56059			0.112334			0.0561670	+	0.998421i	$0.482112\pi$
$194$	4.62742	+	3.36202i	0.332229	+	0.241379i
$195$	5.04022	−	3.53978i	0.360938	−	0.253489i
$196$	4.07500	−	2.96066i	0.291071	−	0.211476i
$197$	11.4569	−	8.32391i	0.816269	−	0.593054i	−0.0993724	−	0.995050i	$-0.531684\pi$
$197$	11.4569	−	8.32391i	0.816269	−	0.593054i	0.915641	+	0.401996i	$0.131684\pi$
$198$	−8.24904	−	25.3879i	−0.586234	−	1.80424i
$199$	−7.34211			−0.520469			−0.260234	−	0.965545i	$-0.583800\pi$
$199$	−7.34211			−0.520469			−0.260234	+	0.965545i	$0.583800\pi$
$200$	4.99743	+	0.160437i	0.353371	+	0.0113446i
$201$	−31.0681			−2.19137
$202$	−5.82136	−	17.9163i	−0.409589	−	1.26059i
$203$	−6.73484	+	4.89315i	−0.472693	+	0.343432i
$204$	−16.0920	+	11.6916i	−1.12667	+	0.818573i
$205$	11.1875	+	0.179535i	0.781372	+	0.0125393i
$206$	12.8403	+	9.32900i	0.894623	+	0.649982i
$207$	−2.66387			−0.185152
$208$	−0.809017	−	0.587785i	−0.0560952	−	0.0407556i
$209$	9.11646	−	28.0576i	0.630599	−	1.94078i
$210$	−2.79795	+	8.16313i	−0.193077	+	0.563310i
$211$	2.66213	+	8.19320i	0.183269	+	0.564043i	0.999914	−	0.0130966i	$-0.00416890\pi$
$211$	2.66213	+	8.19320i	0.183269	+	0.564043i	−0.816646	+	0.577139i	$0.804169\pi$
$212$	2.02273	−	6.22532i	0.138922	−	0.427557i
$213$	−2.70871	+	8.33656i	−0.185598	+	0.571212i
$214$	2.64640	+	8.14479i	0.180904	+	0.556767i
$215$	1.60104	+	5.21055i	0.109190	+	0.355357i
$216$	−1.35061	+	4.15674i	−0.0918971	+	0.282830i
$217$	−5.71600	−	4.15291i	−0.388027	−	0.281918i
$218$	−10.7352			−0.727079
$219$	5.25473	+	3.81779i	0.355082	+	0.257982i
$220$	−4.21950	+	12.3106i	−0.284479	+	0.829978i
$221$	5.84228	−	4.24467i	0.392994	−	0.285527i
$222$	−5.33006	+	3.87252i	−0.357730	+	0.259906i
$223$	0.284776	+	0.876452i	0.0190700	+	0.0586915i	0.960139	−	0.279524i	$-0.0901767\pi$
$223$	0.284776	+	0.876452i	0.0190700	+	0.0586915i	−0.941069	+	0.338216i	$0.890177\pi$
$224$	1.40108			0.0936136
$225$	6.38345	+	22.0276i	0.425563	+	1.46851i
$226$	1.98564			0.132083
$227$	3.69696	+	11.3781i	0.245376	+	0.755188i	0.995574	+	0.0939761i	$0.0299577\pi$
$227$	3.69696	+	11.3781i	0.245376	+	0.755188i	−0.750199	+	0.661212i	$0.770042\pi$
$228$	−11.2958	+	8.20689i	−0.748084	+	0.543515i
$229$	−4.22760	+	3.07153i	−0.279368	+	0.202972i	−0.718642	−	0.695381i	$-0.755236\pi$
$229$	−4.22760	+	3.07153i	−0.279368	+	0.202972i	0.439274	+	0.898353i	$0.355236\pi$
$230$	1.03824	+	0.780083i	0.0684596	+	0.0514372i
$231$	−18.1703	−	13.2015i	−1.19552	−	0.868595i
$232$	5.94164			0.390088
$233$	2.43361	+	1.76812i	0.159431	+	0.115834i	0.664641	−	0.747163i	$-0.268585\pi$
$233$	2.43361	+	1.76812i	0.159431	+	0.115834i	−0.505209	+	0.862997i	$0.668585\pi$
$234$	1.41739	−	4.36229i	0.0926579	−	0.285172i
$235$	−18.3934	−	13.8199i	−1.19985	−	0.901510i
$236$	3.28756	+	10.1181i	0.214002	+	0.658629i
$237$	8.44867	−	26.0023i	0.548800	−	1.68903i
$238$	−3.12659	+	9.62264i	−0.202666	+	0.623743i
$239$	−0.745292	−	2.29377i	−0.0482089	−	0.148372i	0.924054	−	0.382261i	$-0.124855\pi$
$239$	−0.745292	−	2.29377i	−0.0482089	−	0.148372i	−0.972263	+	0.233890i	$0.924855\pi$
$240$	5.04022	−	3.53978i	0.325345	−	0.228492i
$241$	6.11905	−	18.8325i	0.394163	−	1.21311i	−0.535449	−	0.844568i	$-0.679858\pi$
$241$	6.11905	−	18.8325i	0.394163	−	1.21311i	0.929612	−	0.368541i	$-0.120142\pi$
$242$	−18.5029	−	13.4431i	−1.18941	−	0.864157i
$243$	17.8544			1.14536
$244$	−6.10400	−	4.43481i	−0.390768	−	0.283910i
$245$	−3.30814	−	10.7662i	−0.211349	−	0.687829i
$246$	11.1504	−	8.10127i	0.710926	−	0.516518i
$247$	4.10099	−	2.97954i	0.260940	−	0.189584i
$248$	1.55831	+	4.79598i	0.0989527	+	0.304545i
$249$	−37.7487			−2.39223
$250$	3.96259	−	10.4546i	0.250616	−	0.661205i
$251$	14.8706			0.938624			0.469312	−	0.883032i	$-0.344502\pi$
$251$	14.8706			0.938624			0.469312	+	0.883032i	$0.344502\pi$
$252$	1.98588	+	6.11192i	0.125099	+	0.385015i
$253$	−2.73448	+	1.98672i	−0.171916	+	0.124904i
$254$	5.35746	−	3.89242i	0.336157	−	0.244232i
$255$	13.0637	+	42.5155i	0.818083	+	2.66243i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−15.2520			−0.951395			−0.475698	−	0.879609i	$-0.657804\pi$
$257$	−15.2520			−0.951395			−0.475698	+	0.879609i	$0.657804\pi$
$258$	5.43220	+	3.94673i	0.338194	+	0.245713i
$259$	−1.03560	+	3.18724i	−0.0643489	+	0.198046i
$260$	−1.82987	+	1.28513i	−0.113484	+	0.0797005i
$261$	8.42165	+	25.9192i	0.521287	+	1.60436i
$262$	−0.242066	+	0.745002i	−0.0149549	+	0.0460264i
$263$	2.97453	−	9.15465i	0.183417	−	0.564500i	−0.816500	−	0.577345i	$-0.804089\pi$
$263$	2.97453	−	9.15465i	0.183417	−	0.564500i	0.999917	+	0.0128450i	$0.00408881\pi$
$264$	4.95364	+	15.2457i	0.304875	+	0.938309i
$265$	−11.7017	−	8.79208i	−0.718830	−	0.540093i
$266$	−2.19471	+	6.75461i	−0.134566	+	0.414152i
$267$	−19.3463	−	14.0559i	−1.18397	−	0.860207i
$268$	11.2794			0.688998
$269$	11.4849	+	8.34429i	0.700249	+	0.508760i	0.880013	−	0.474949i	$-0.157534\pi$
$269$	11.4849	+	8.34429i	0.700249	+	0.508760i	−0.179765	+	0.983710i	$0.557534\pi$
$270$	7.81340	+	5.87060i	0.475508	+	0.357273i
$271$	1.63355	−	1.18684i	0.0992312	−	0.0720957i	−0.537063	−	0.843542i	$-0.680466\pi$
$271$	1.63355	−	1.18684i	0.0992312	−	0.0720957i	0.636294	+	0.771446i	$0.280466\pi$
$272$	5.84228	−	4.24467i	0.354240	−	0.257371i
$273$	−1.19254	−	3.67027i	−0.0721760	−	0.222135i
$274$	−2.24841			−0.135832
$275$	22.9809	+	17.8507i	1.38580	+	1.07644i
$276$	1.59968			0.0962896
$277$	−1.81755	−	5.59384i	−0.109206	−	0.336101i	0.881489	−	0.472205i	$-0.156542\pi$
$277$	−1.81755	−	5.59384i	−0.109206	−	0.336101i	−0.990695	+	0.136104i	$0.956542\pi$
$278$	−0.290047	+	0.210732i	−0.0173959	+	0.0126389i
$279$	−18.7127	+	13.5956i	−1.12030	+	0.813947i
$280$	1.01581	−	2.96366i	0.0607061	−	0.177112i
$281$	17.1564	+	12.4648i	1.02346	+	0.743589i	0.966990	−	0.254815i	$-0.0820145\pi$
$281$	17.1564	+	12.4648i	1.02346	+	0.743589i	0.0564729	+	0.998404i	$0.482015\pi$
$282$	−28.3398			−1.68761
$283$	4.05314	+	2.94478i	0.240934	+	0.175049i	0.701699	−	0.712473i	$-0.252425\pi$
$283$	4.05314	+	2.94478i	0.240934	+	0.175049i	−0.460765	+	0.887522i	$0.652425\pi$
$284$	0.983409	−	3.02662i	0.0583546	−	0.179597i
$285$	9.17009	+	29.8438i	0.543189	+	1.76779i
$286$	−1.79844	−	5.53502i	−0.106344	−	0.327293i
$287$	2.16646	−	6.66769i	0.127882	−	0.393581i
$288$	1.41739	−	4.36229i	0.0835207	−	0.257050i
$289$	10.8618	+	33.4291i	0.638928	+	1.96642i
$290$	4.30779	−	12.5682i	0.252962	−	0.738027i
$291$	4.86847	−	14.9836i	0.285395	−	0.878355i
$292$	−1.90775	−	1.38606i	−0.111643	−	0.0811132i
$293$	5.42955			0.317198			0.158599	−	0.987343i	$-0.449302\pi$
$293$	5.42955			0.317198			0.158599	+	0.987343i	$0.449302\pi$
$294$	−11.2242	−	8.15487i	−0.654610	−	0.475602i
$295$	23.7859	+	0.381712i	1.38487	+	0.0222241i
$296$	1.93510	−	1.40593i	0.112475	−	0.0817182i
$297$	−20.5787	+	14.9513i	−1.19409	+	0.867561i
$298$	−5.41853	−	16.6765i	−0.313887	−	0.966045i
$299$	−0.580771			−0.0335869
$300$	−3.83333	−	13.2278i	−0.221317	−	0.763708i
$301$	3.41549			0.196865
$302$	2.61539	+	8.04934i	0.150499	+	0.463188i
$303$	−41.9787	+	30.4993i	−2.41161	+	1.75214i
$304$	4.10099	−	2.97954i	0.235208	−	0.170889i
$305$	−13.8063	+	9.69626i	−0.790547	+	0.555206i
$306$	26.7973	+	19.4694i	1.53190	+	1.11299i
$307$	−2.91254			−0.166228			−0.0831138	−	0.996540i	$-0.526486\pi$
$307$	−2.91254			−0.166228			−0.0831138	+	0.996540i	$0.526486\pi$
$308$	6.59680	+	4.79286i	0.375888	+	0.273098i
$309$	13.5091	−	41.5768i	0.768508	−	2.36522i
$310$	11.2746	+	0.180932i	0.640353	+	0.0102763i
$311$	5.49173	+	16.9018i	0.311408	+	0.958414i	0.977208	+	0.212284i	$0.0680903\pi$
$311$	5.49173	+	16.9018i	0.311408	+	0.958414i	−0.665800	+	0.746130i	$0.731910\pi$
$312$	−0.851160	+	2.61960i	−0.0481874	+	0.148306i
$313$	7.56440	−	23.2808i	0.427565	−	1.31591i	−0.472951	−	0.881089i	$-0.656811\pi$
$313$	7.56440	−	23.2808i	0.427565	−	1.31591i	0.900516	−	0.434822i	$-0.143189\pi$
$314$	4.77288	+	14.6894i	0.269349	+	0.828972i
$315$	14.3681	+	0.230577i	0.809553	+	0.0129915i
$316$	−3.06732	+	9.44025i	−0.172550	+	0.531055i
$317$	16.8399	+	12.2349i	0.945821	+	0.687179i	0.949815	−	0.312813i	$-0.101271\pi$
$317$	16.8399	+	12.2349i	0.945821	+	0.687179i	−0.00399413	+	0.999992i	$0.501271\pi$
$318$	−18.0295			−1.01105
$319$	27.9754	+	20.3253i	1.56632	+	1.13800i
$320$	−1.82987	+	1.28513i	−0.102293	+	0.0718410i
$321$	19.0836	−	13.8650i	1.06514	−	0.773871i
$322$	0.658303	−	0.478285i	0.0366858	−	0.0266538i
$323$	11.3120	+	34.8147i	0.629415	+	1.93714i
$324$	−1.72177			−0.0956538
$325$	1.39170	+	4.80241i	0.0771979	+	0.266390i
$326$	−20.3160			−1.12520
$327$	9.13737	+	28.1219i	0.505298	+	1.55515i
$328$	−4.04821	+	2.94120i	−0.223525	+	0.162401i
$329$	−11.6624	+	8.47326i	−0.642971	+	0.467146i
$330$	35.8402	+	0.575157i	1.97294	+	0.0316613i
$331$	23.4095	+	17.0080i	1.28671	+	0.934846i	0.999733	−	0.0230930i	$-0.00735138\pi$
$331$	23.4095	+	17.0080i	1.28671	+	0.934846i	0.286972	+	0.957939i	$0.407351\pi$
$332$	13.7048			0.752150
$333$	8.87589	+	6.44871i	0.486396	+	0.353387i
$334$	1.59926	−	4.92201i	0.0875075	−	0.269320i
$335$	8.17775	−	23.8589i	0.446798	−	1.30355i
$336$	−1.19254	−	3.67027i	−0.0650586	−	0.200230i
$337$	9.61155	−	29.5813i	0.523574	−	1.61140i	−0.243543	−	0.969890i	$-0.578310\pi$
$337$	9.61155	−	29.5813i	0.523574	−	1.61140i	0.767118	−	0.641506i	$-0.221690\pi$
$338$	0.309017	−	0.951057i	0.0168083	−	0.0517307i
$339$	−1.69010	−	5.20158i	−0.0917934	−	0.282511i
$340$	−4.74284	−	15.4354i	−0.257217	−	0.837104i
$341$	−9.06915	+	27.9120i	−0.491122	+	1.51152i
$342$	18.8104	+	13.6665i	1.01715	+	0.739001i
$343$	−16.8648			−0.910612
$344$	−1.97218	−	1.43288i	−0.106333	−	0.0772554i
$345$	1.15980	−	3.38375i	0.0624414	−	0.182175i
$346$	2.15292	−	1.56419i	0.115742	−	0.0840913i
$347$	−14.2794	+	10.3746i	−0.766558	+	0.556937i	−0.900915	−	0.433996i	$-0.857103\pi$
$347$	−14.2794	+	10.3746i	−0.766558	+	0.556937i	0.134357	+	0.990933i	$0.457103\pi$
$348$	−5.05729	−	15.5647i	−0.271099	−	0.834357i
$349$	−18.6078			−0.996053			−0.498027	−	0.867162i	$-0.665942\pi$
$349$	−18.6078			−0.996053			−0.498027	+	0.867162i	$0.665942\pi$
$350$	−5.53245	−	4.29741i	−0.295722	−	0.229706i
$351$	−4.37065			−0.233288
$352$	−1.79844	−	5.53502i	−0.0958570	−	0.295018i
$353$	16.6920	−	12.1275i	0.888427	−	0.645480i	−0.0470403	−	0.998893i	$-0.514979\pi$
$353$	16.6920	−	12.1275i	0.888427	−	0.645480i	0.935467	+	0.353413i	$0.114979\pi$
$354$	23.7070	−	17.2242i	1.26001	−	0.915454i
$355$	−5.68912	−	4.27453i	−0.301947	−	0.226868i
$356$	7.02375	+	5.10305i	0.372258	+	0.270461i
$357$	27.8687			1.47497
$358$	−13.1739	−	9.57142i	−0.696264	−	0.505865i
$359$	−7.65278	+	23.5528i	−0.403898	+	1.24307i	0.517914	+	0.855433i	$0.326709\pi$
$359$	−7.65278	+	23.5528i	−0.403898	+	1.24307i	−0.921812	+	0.387638i	$0.873291\pi$
$360$	−8.19977	−	6.16090i	−0.432166	−	0.324708i
$361$	2.06912	+	6.36808i	0.108901	+	0.335162i
$362$	−7.07659	+	21.7795i	−0.371937	+	1.14470i
$363$	−19.4667	+	59.9124i	−1.02174	+	3.14459i
$364$	0.432958	+	1.33251i	0.0226931	+	0.0698423i
$365$	−4.31505	+	3.03048i	−0.225860	+	0.158623i
$366$	−6.42196	+	19.7648i	−0.335681	+	1.03312i
$367$	18.5202	+	13.4557i	0.966746	+	0.702382i	0.954708	−	0.297545i	$-0.0961680\pi$
$367$	18.5202	+	13.4557i	0.966746	+	0.702382i	0.0120383	+	0.999928i	$0.496168\pi$
$368$	−0.580771			−0.0302748
$369$	−18.5683	−	13.4906i	−0.966626	−	0.702295i
$370$	−1.57094	−	5.11258i	−0.0816693	−	0.265790i
$371$	−7.41953	+	5.39060i	−0.385203	+	0.279866i
$372$	11.2372	−	8.16430i	0.582621	−	0.423299i
$373$	−4.53117	−	13.9455i	−0.234615	−	0.722071i	−0.997172	−	0.0751502i	$-0.976056\pi$
$373$	−4.53117	−	13.9455i	−0.234615	−	0.722071i	0.762557	−	0.646921i	$-0.223944\pi$
$374$	42.0279			2.17321
$375$	−30.7596	−	1.48189i	−1.58842	−	0.0765244i
$376$	10.2889			0.530609
$377$	1.83607	+	5.65084i	0.0945623	+	0.291033i
$378$	4.95413	−	3.59938i	0.254813	−	0.185132i
$379$	25.6096	−	18.6065i	1.31548	−	0.955750i	0.315500	−	0.948926i	$-0.397828\pi$
$379$	25.6096	−	18.6065i	1.31548	−	0.955750i	0.999977	−	0.00682392i	$-0.00217214\pi$
$380$	−3.32924	−	10.8349i	−0.170786	−	0.555819i
$381$	−14.7567	−	10.7213i	−0.756007	−	0.549271i
$382$	−22.2871			−1.14031
$383$	4.98010	+	3.61825i	0.254471	+	0.184884i	0.707706	−	0.706507i	$-0.249730\pi$
$383$	4.98010	+	3.61825i	0.254471	+	0.184884i	−0.453235	+	0.891391i	$0.649730\pi$
$384$	−0.851160	+	2.61960i	−0.0434356	+	0.133681i
$385$	14.9210	−	10.4791i	0.760443	−	0.534064i
$386$	0.482250	+	1.48421i	0.0245459	+	0.0755444i
$387$	3.45526	−	10.6342i	0.175641	−	0.540566i
$388$	−1.76752	+	5.43986i	−0.0897321	+	0.276167i
$389$	−8.79091	−	27.0556i	−0.445717	−	1.37178i	−0.881696	−	0.471819i	$-0.843598\pi$
$389$	−8.79091	−	27.0556i	−0.445717	−	1.37178i	0.435979	−	0.899957i	$-0.356402\pi$
$390$	4.92405	+	3.69969i	0.249339	+	0.187341i
$391$	1.29602	−	3.98874i	0.0655426	−	0.201719i
$392$	4.07500	+	2.96066i	0.205818	+	0.149536i
$393$	2.15765			0.108839
$394$	11.4569	+	8.32391i	0.577189	+	0.419353i
$395$	17.7448	+	13.3325i	0.892836	+	0.670833i
$396$	21.5963	−	15.6906i	1.08525	−	0.788483i
$397$	14.2306	−	10.3391i	0.714211	−	0.518905i	−0.170318	−	0.985389i	$-0.554480\pi$
$397$	14.2306	−	10.3391i	0.714211	−	0.518905i	0.884530	+	0.466484i	$0.154480\pi$
$398$	−2.26884	−	6.98277i	−0.113727	−	0.350014i
$399$	19.5624			0.979347
$400$	1.39170	+	4.80241i	0.0695852	+	0.240121i
$401$	−28.7172			−1.43407			−0.717035	−	0.697037i	$-0.754501\pi$
$401$	−28.7172			−1.43407			−0.717035	+	0.697037i	$0.754501\pi$
$402$	−9.60056	−	29.5475i	−0.478832	−	1.47369i
$403$	−4.07971	+	2.96408i	−0.203225	+	0.147651i
$404$	15.2405	−	11.0729i	0.758244	−	0.550897i
$405$	−1.24831	+	3.64200i	−0.0620291	+	0.180972i
$406$	−6.73484	−	4.89315i	−0.334244	−	0.242843i
$407$	13.9206			0.690020
$408$	−16.0920	−	11.6916i	−0.796675	−	0.578818i
$409$	−8.28758	+	25.5065i	−0.409794	+	1.26122i	0.507031	+	0.861928i	$0.330743\pi$
$409$	−8.28758	+	25.5065i	−0.409794	+	1.26122i	−0.916825	+	0.399289i	$0.869257\pi$
$410$	3.28639	+	10.6955i	0.162303	+	0.528211i
$411$	1.91376	+	5.88994i	0.0943988	+	0.290530i
$412$	−4.90454	+	15.0946i	−0.241630	+	0.743659i
$413$	4.60613	−	14.1762i	0.226653	−	0.697566i
$414$	−0.823181	−	2.53349i	−0.0404572	−	0.124514i
$415$	9.93623	−	28.9893i	0.487750	−	1.42303i
$416$	0.309017	−	0.951057i	0.0151508	−	0.0466294i
$417$	0.798910	+	0.580442i	0.0391228	+	0.0284244i
$418$	29.5015			1.44296
$419$	−14.0979	−	10.2427i	−0.688728	−	0.500390i	0.187514	−	0.982262i	$-0.439957\pi$
$419$	−14.0979	−	10.2427i	−0.688728	−	0.500390i	−0.876242	+	0.481872i	$0.839957\pi$
$420$	−8.62822	−	0.138464i	−0.421014	−	0.00675635i
$421$	16.0434	−	11.6562i	0.781909	−	0.568090i	−0.123642	−	0.992327i	$-0.539458\pi$
$421$	16.0434	−	11.6562i	0.781909	−	0.568090i	0.905551	+	0.424237i	$0.139458\pi$
$422$	−6.96955	+	5.06367i	−0.339272	+	0.246496i
$423$	14.5834	+	44.8831i	0.709070	+	2.18229i
$424$	6.54569			0.317887
$425$	−36.0887	−	1.15859i	−1.75056	−	0.0561997i
$426$	−8.76558			−0.424694
$427$	3.26665	+	10.0537i	0.158084	+	0.486533i
$428$	−6.92838	+	5.03376i	−0.334896	+	0.243316i
$429$	−12.9688	+	9.42238i	−0.626139	+	0.454917i
$430$	−4.46078	+	3.13283i	−0.215118	+	0.151079i
$431$	−5.92928	−	4.30787i	−0.285603	−	0.207503i	0.435754	−	0.900066i	$-0.356482\pi$
$431$	−5.92928	−	4.30787i	−0.285603	−	0.207503i	−0.721358	+	0.692563i	$0.756482\pi$
$432$	−4.37065			−0.210283
$433$	6.42484	+	4.66792i	0.308758	+	0.224326i	0.731363	−	0.681988i	$-0.238884\pi$
$433$	6.42484	+	4.66792i	0.308758	+	0.224326i	−0.422605	+	0.906314i	$0.638884\pi$
$434$	2.18332	−	6.71956i	0.104803	−	0.322549i
$435$	−36.5902	−	0.587192i	−1.75436	−	0.0281537i
$436$	−3.31736	−	10.2098i	−0.158873	−	0.488960i
$437$	0.909742	−	2.79990i	0.0435189	−	0.133937i
$438$	−2.00713	+	6.17731i	−0.0959044	+	0.295163i
$439$	−10.9045	−	33.5605i	−0.520442	−	1.60176i	−0.773157	−	0.634214i	$-0.781324\pi$
$439$	−10.9045	−	33.5605i	−0.520442	−	1.60176i	0.252715	−	0.967541i	$-0.418676\pi$
$440$	−13.0119	−	0.208813i	−0.620320	−	0.00995477i
$441$	−7.13938	+	21.9727i	−0.339970	+	1.04632i
$442$	5.84228	+	4.24467i	0.277889	+	0.201898i
$443$	−25.6109			−1.21681			−0.608405	−	0.793626i	$-0.708191\pi$
$443$	−25.6109			−1.21681			−0.608405	+	0.793626i	$0.708191\pi$
$444$	−5.33006	−	3.87252i	−0.252954	−	0.183782i
$445$	15.8867	−	11.1573i	0.753099	−	0.528906i
$446$	−0.745554	+	0.541677i	−0.0353030	+	0.0256491i
$447$	−39.0738	+	28.3888i	−1.84813	+	1.34274i
$448$	0.432958	+	1.33251i	0.0204553	+	0.0629550i
$449$	18.2855			0.862947			0.431474	−	0.902125i	$-0.357994\pi$
$449$	18.2855			0.862947			0.431474	+	0.902125i	$0.357994\pi$
$450$	−18.9769	+	12.8779i	−0.894581	+	0.607071i
$451$	−29.1218			−1.37129
$452$	0.613596	+	1.88845i	0.0288611	+	0.0888254i
$453$	18.8600	−	13.7026i	0.886118	−	0.643802i
$454$	−9.67876	+	7.03203i	−0.454246	+	0.330029i
$455$	3.13251	+	0.0502699i	0.146854	+	0.00235669i
$456$	−11.2958	−	8.20689i	−0.528975	−	0.384323i
$457$	3.66029			0.171221			0.0856105	−	0.996329i	$-0.472716\pi$
$457$	3.66029			0.171221			0.0856105	+	0.996329i	$0.472716\pi$
$458$	−4.22760	−	3.07153i	−0.197543	−	0.143523i
$459$	9.75335	−	30.0177i	0.455247	−	1.40111i
$460$	−0.421069	+	1.22848i	−0.0196324	+	0.0572784i
$461$	−7.97999	−	24.5599i	−0.371665	−	1.14387i	−0.945701	−	0.325038i	$-0.894623\pi$
$461$	−7.97999	−	24.5599i	−0.371665	−	1.14387i	0.574036	−	0.818830i	$-0.305377\pi$
$462$	6.94044	−	21.3605i	0.322899	−	0.993780i
$463$	5.35445	−	16.4793i	0.248842	−	0.765858i	−0.746138	−	0.665791i	$-0.768094\pi$
$463$	5.35445	−	16.4793i	0.248842	−	0.765858i	0.994981	−	0.100067i	$-0.0319057\pi$
$464$	1.83607	+	5.65084i	0.0852373	+	0.262334i
$465$	−9.12250	−	29.6889i	−0.423046	−	1.37679i
$466$	−0.929557	+	2.86088i	−0.0430609	+	0.132528i
$467$	−10.7366	−	7.80058i	−0.496830	−	0.360968i	0.310975	−	0.950418i	$-0.399344\pi$
$467$	−10.7366	−	7.80058i	−0.496830	−	0.360968i	−0.807805	+	0.589450i	$0.799344\pi$
$468$	4.58678			0.212024
$469$	−12.7852	−	9.28896i	−0.590364	−	0.428924i
$470$	7.45962	−	21.7637i	0.344087	−	1.00389i
$471$	34.4179	−	25.0061i	1.58590	−	1.15222i
$472$	−8.60693	+	6.25330i	−0.396166	+	0.287832i
$473$	−4.38414	−	13.4930i	−0.201583	−	0.620409i
$474$	27.3405			1.25579
$475$	−25.3325	−	0.813270i	−1.16233	−	0.0373154i
$476$	−10.1178			−0.463751
$477$	9.27783	+	28.5542i	0.424802	+	1.30741i
$478$	1.95120	−	1.41763i	0.0892458	−	0.0648409i
$479$	7.37823	−	5.36060i	0.337120	−	0.244932i	−0.406326	−	0.913728i	$-0.633190\pi$
$479$	7.37823	−	5.36060i	0.337120	−	0.244932i	0.743446	+	0.668796i	$0.233190\pi$
$480$	4.92405	+	3.69969i	0.224751	+	0.168867i
$481$	1.93510	+	1.40593i	0.0882330	+	0.0641050i
$482$	19.8017			0.901941
$483$	−1.81324	−	1.31739i	−0.0825051	−	0.0599435i
$484$	7.06747	−	21.7514i	0.321249	−	0.988702i
$485$	10.2253	+	7.68276i	0.464306	+	0.348856i
$486$	5.51732	+	16.9806i	0.250271	+	0.770254i
$487$	11.6129	−	35.7409i	0.526232	−	1.61958i	−0.235634	−	0.971842i	$-0.575717\pi$
$487$	11.6129	−	35.7409i	0.526232	−	1.61958i	0.761866	−	0.647734i	$-0.224283\pi$
$488$	2.33152	−	7.17568i	0.105543	−	0.324828i
$489$	17.2921	+	53.2197i	0.781977	+	2.40668i
$490$	9.21702	−	6.47317i	0.416383	−	0.292428i
$491$	0.244640	−	0.752924i	0.0110404	−	0.0339790i	−0.945385	−	0.325957i	$-0.894313\pi$
$491$	0.244640	−	0.752924i	0.0110404	−	0.0339790i	0.956425	+	0.291978i	$0.0943135\pi$
$492$	11.1504	+	8.10127i	0.502701	+	0.365234i
$493$	−42.9073			−1.93245
$494$	4.10099	+	2.97954i	0.184512	+	0.134056i
$495$	−17.5321	−	57.0578i	−0.788011	−	2.56456i
$496$	−4.07971	+	2.96408i	−0.183184	+	0.133091i
$497$	−3.60722	+	2.62080i	−0.161806	+	0.117559i
$498$	−11.6650	−	35.9012i	−0.522721	−	1.60877i
$499$	8.38700			0.375454			0.187727	−	0.982221i	$-0.439888\pi$
$499$	8.38700			0.375454			0.187727	+	0.982221i	$0.439888\pi$
$500$	11.1674	+	0.538006i	0.499421	+	0.0240603i
$501$	−14.2549			−0.636863
$502$	4.59527	+	14.1428i	0.205097	+	0.631224i
$503$	14.2206	−	10.3318i	0.634064	−	0.460674i	−0.223742	−	0.974648i	$-0.571827\pi$
$503$	14.2206	−	10.3318i	0.634064	−	0.460674i	0.857806	+	0.513974i	$0.171827\pi$
$504$	−5.19911	+	3.77737i	−0.231587	+	0.168258i
$505$	−12.3725	−	40.2658i	−0.550567	−	1.79180i
$506$	−2.73448	−	1.98672i	−0.121563	−	0.0883204i
$507$	−2.75441			−0.122328
$508$	5.35746	+	3.89242i	0.237699	+	0.172698i
$509$	3.79715	−	11.6864i	0.168306	−	0.517991i	−0.830959	−	0.556334i	$-0.812208\pi$
$509$	3.79715	−	11.6864i	0.168306	−	0.517991i	0.999265	+	0.0383422i	$0.0122077\pi$
$510$	−36.3978	+	25.5624i	−1.61172	+	1.13192i
$511$	1.02096	+	3.14220i	0.0451647	+	0.139003i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	6.84636	−	21.0709i	0.302274	−	0.930305i
$514$	−4.71314	−	14.5055i	−0.207887	−	0.639812i
$515$	28.3733	+	21.3183i	1.25028	+	0.939396i
$516$	−2.07492	+	6.38594i	−0.0913432	+	0.281125i
$517$	48.4439	+	35.1966i	2.13056	+	1.54794i
$518$	−3.35127			−0.147246
$519$	−5.93003	−	4.30842i	−0.260299	−	0.189119i
$520$	−1.78769	−	1.34319i	−0.0783956	−	0.0589026i
$521$	−21.5889	+	15.6853i	−0.945828	+	0.687184i	−0.949816	−	0.312808i	$-0.898730\pi$
$521$	−21.5889	+	15.6853i	−0.945828	+	0.687184i	0.00398859	+	0.999992i	$0.498730\pi$
$522$	−22.0482	+	16.0189i	−0.965022	+	0.701129i
$523$	11.4478	+	35.2328i	0.500579	+	1.54062i	0.808079	+	0.589075i	$0.200508\pi$
$523$	11.4478	+	35.2328i	0.500579	+	1.54062i	−0.307500	+	0.951548i	$0.599492\pi$
$524$	−0.783342			−0.0342204
$525$	−6.54849	+	18.1506i	−0.285800	+	0.792156i
$526$	9.62577			0.419703
$527$	−11.2533	−	34.6340i	−0.490200	−	1.50868i
$528$	−12.9688	+	9.42238i	−0.564394	+	0.410056i
$529$	18.3345	−	13.3208i	0.797153	−	0.579165i
$530$	4.74574	−	13.8459i	0.206142	−	0.601427i
$531$	−39.4781	−	28.6825i	−1.71321	−	1.24472i
$532$	−7.10222			−0.307920
$533$	−4.04821	−	2.94120i	−0.175348	−	0.127397i
$534$	7.38963	−	22.7429i	0.319780	−	0.984183i
$535$	5.62455	+	18.3049i	0.243170	+	0.791391i
$536$	3.48552	+	10.7273i	0.150552	+	0.463350i
$537$	−13.8602	+	42.6572i	−0.598111	+	1.84080i
$538$	−4.38685	+	13.5013i	−0.189131	+	0.582084i
$539$	9.05868	+	27.8798i	0.390185	+	1.20087i
$540$	−3.16880	+	9.24510i	−0.136363	+	0.397846i
$541$	2.54487	−	7.83231i	0.109413	−	0.336737i	−0.881328	−	0.472505i	$-0.843350\pi$
$541$	2.54487	−	7.83231i	0.109413	−	0.336737i	0.990741	+	0.135767i	$0.0433500\pi$
$542$	1.63355	+	1.18684i	0.0701670	+	0.0509793i
$543$	63.0769			2.70689
$544$	5.84228	+	4.24467i	0.250486	+	0.181989i
$545$	−24.0015	−	0.385172i	−1.02811	−	0.0164990i
$546$	3.12212	−	2.26835i	0.133614	−	0.0970765i
$547$	−34.6676	+	25.1875i	−1.48228	+	1.07694i	−0.505469	+	0.862845i	$0.668680\pi$
$547$	−34.6676	+	25.1875i	−1.48228	+	1.07694i	−0.976813	+	0.214096i	$0.931320\pi$
$548$	−0.694798	−	2.13837i	−0.0296803	−	0.0913465i
$549$	34.6071			1.47699
$550$	−9.87558	+	27.3723i	−0.421096	+	1.16716i
$551$	−30.1188			−1.28310
$552$	0.494329	+	1.52139i	0.0210400	+	0.0647546i
$553$	11.2512	−	8.17446i	0.478449	−	0.347613i
$554$	4.75840	−	3.45718i	0.202165	−	0.146882i
$555$	−12.0558	+	8.46686i	−0.511740	+	0.359398i
$556$	−0.290047	−	0.210732i	−0.0123007	−	0.00893702i
$557$	−16.9075			−0.716395			−0.358198	−	0.933646i	$-0.616609\pi$
$557$	−16.9075			−0.716395			−0.358198	+	0.933646i	$0.616609\pi$
$558$	−18.7127	−	13.5956i	−0.792173	−	0.575547i
$559$	0.753307	−	2.31844i	0.0318615	−	0.0980596i
$560$	3.13251	+	0.0502699i	0.132373	+	0.00212429i
$561$	−35.7725	−	110.096i	−1.51031	−	4.64827i
$562$	−6.55315	+	20.1685i	−0.276428	+	0.850757i
$563$	1.22417	−	3.76760i	0.0515926	−	0.158786i	−0.921941	−	0.387331i	$-0.873397\pi$
$563$	1.22417	−	3.76760i	0.0515926	−	0.158786i	0.973533	+	0.228546i	$0.0733970\pi$
$564$	−8.75749	−	26.9528i	−0.368757	−	1.13492i
$565$	4.43945	+	0.0712434i	0.186769	+	0.00299723i
$566$	−1.54816	+	4.76475i	−0.0650741	+	0.200278i
$567$	1.95162	+	1.41794i	0.0819604	+	0.0595477i
$568$	3.18238			0.133530
$569$	29.8827	+	21.7110i	1.25275	+	0.910174i	0.998378	−	0.0569326i	$-0.0181320\pi$
$569$	29.8827	+	21.7110i	1.25275	+	0.910174i	0.254370	+	0.967107i	$0.418132\pi$
$570$	−25.5494	+	17.9435i	−1.07015	+	0.751571i
$571$	12.1419	−	8.82163i	0.508124	−	0.369174i	−0.303988	−	0.952676i	$-0.598318\pi$
$571$	12.1419	−	8.82163i	0.508124	−	0.369174i	0.812111	+	0.583502i	$0.198318\pi$
$572$	4.70837	−	3.42083i	0.196867	−	0.143032i
$573$	18.9699	+	58.3834i	0.792480	+	2.43900i
$574$	7.01082			0.292626
$575$	2.29329	+	1.78135i	0.0956368	+	0.0742873i
$576$	4.58678			0.191116
$577$	3.53675	+	10.8850i	0.147237	+	0.453148i	0.997292	−	0.0735459i	$-0.0234315\pi$
$577$	3.53675	+	10.8850i	0.147237	+	0.453148i	−0.850055	+	0.526694i	$0.823432\pi$
$578$	−28.4365	+	20.6603i	−1.18280	+	0.859356i
$579$	3.47757	−	2.52660i	0.144523	−	0.105002i
$580$	13.2842	+	0.213182i	0.551597	+	0.00885191i
$581$	−15.5344	−	11.2864i	−0.644475	−	0.468238i
$582$	15.7547			0.653053
$583$	30.8195	+	22.3917i	1.27641	+	0.927370i
$584$	0.728696	−	2.24270i	0.0301537	−	0.0928035i
$585$	3.32550	−	9.70227i	0.137492	−	0.401139i
$586$	1.67782	+	5.16381i	0.0693102	+	0.213315i
$587$	13.0370	−	40.1239i	0.538096	−	1.65609i	−0.198766	−	0.980047i	$-0.563693\pi$
$587$	13.0370	−	40.1239i	0.538096	−	1.65609i	0.736862	−	0.676043i	$-0.236307\pi$
$588$	4.28727	−	13.1949i	0.176804	−	0.544147i
$589$	−7.89923	−	24.3113i	−0.325482	−	1.00173i
$590$	6.98722	+	22.7397i	0.287659	+	0.936179i
$591$	12.0537	−	37.0974i	0.495822	−	1.52598i
$592$	1.93510	+	1.40593i	0.0795321	+	0.0577835i
$593$	−37.4360			−1.53731			−0.768656	−	0.639662i	$-0.779074\pi$
$593$	−37.4360			−1.53731			−0.768656	+	0.639662i	$0.779074\pi$
$594$	−20.5787	−	14.9513i	−0.844352	−	0.613458i
$595$	−7.33561	+	21.4019i	−0.300731	+	0.877393i
$596$	14.1859	−	10.3067i	0.581077	−	0.422177i
$597$	−16.3609	+	11.8869i	−0.669608	+	0.486498i
$598$	−0.179468	−	0.552346i	−0.00733900	−	0.0225871i
$599$	17.1365			0.700177			0.350089	−	0.936717i	$-0.386151\pi$
$599$	17.1365			0.700177			0.350089	+	0.936717i	$0.386151\pi$
$600$	11.3958	−	7.73333i	0.465233	−	0.315712i
$601$	−8.77660			−0.358005			−0.179002	−	0.983849i	$-0.557287\pi$
$601$	−8.77660			−0.358005			−0.179002	+	0.983849i	$0.557287\pi$
$602$	1.05544	+	3.24832i	0.0430167	+	0.132392i
$603$	−41.8554	+	30.4097i	−1.70448	+	1.23838i
$604$	−6.84718	+	4.97477i	−0.278608	+	0.202420i
$605$	−40.8861	−	30.7198i	−1.66225	−	1.24894i
$606$	−41.9787	−	30.4993i	−1.70527	−	1.23895i
$607$	32.0072			1.29913			0.649566	−	0.760305i	$-0.274950\pi$
$607$	32.0072			1.29913			0.649566	+	0.760305i	$0.274950\pi$
$608$	4.10099	+	2.97954i	0.166317	+	0.120836i
$609$	−7.08567	+	21.8074i	−0.287126	+	0.883682i
$610$	−13.4881	−	10.1343i	−0.546116	−	0.410325i
$611$	3.17944	+	9.78532i	0.128626	+	0.395872i
$612$	−10.2356	+	31.5021i	−0.413752	+	1.27340i
$613$	−0.413606	+	1.27295i	−0.0167054	+	0.0514138i	−0.959062	−	0.283197i	$-0.908605\pi$
$613$	−0.413606	+	1.27295i	−0.0167054	+	0.0514138i	0.942356	+	0.334611i	$0.108605\pi$
$614$	−0.900025	−	2.76999i	−0.0363221	−	0.111788i
$615$	25.2206	−	17.7126i	1.01699	−	0.714241i
$616$	−2.51975	+	7.75501i	−0.101524	+	0.312458i
$617$	−11.6607	−	8.47200i	−0.469442	−	0.341070i	0.327782	−	0.944753i	$-0.393699\pi$
$617$	−11.6607	−	8.47200i	−0.469442	−	0.341070i	−0.797224	+	0.603684i	$0.793699\pi$
$618$	43.7165			1.75853
$619$	22.1555	+	16.0969i	0.890506	+	0.646991i	0.936010	−	0.351974i	$-0.114489\pi$
$619$	22.1555	+	16.0969i	0.890506	+	0.646991i	−0.0455037	+	0.998964i	$0.514489\pi$
$620$	3.31196	+	10.7787i	0.133012	+	0.432882i
$621$	−2.05357	+	1.49200i	−0.0824068	+	0.0598721i
$622$	−14.3775	+	10.4459i	−0.576487	+	0.418842i
$623$	−3.75886	−	11.5686i	−0.150596	−	0.463486i
$624$	−2.75441			−0.110265
$625$	9.23457	−	23.2319i	0.369383	−	0.929277i
$626$	24.4789			0.978374
$627$	−25.1105	−	77.2821i	−1.00282	−	3.08635i
$628$	−12.4956	+	9.07856i	−0.498628	+	0.362274i
$629$	−13.9742	+	10.1529i	−0.557190	+	0.404822i
$630$	4.22071	+	13.7362i	0.168157	+	0.547262i
$631$	26.9061	+	19.5484i	1.07112	+	0.778211i	0.976112	−	0.217266i	$-0.0697139\pi$
$631$	26.9061	+	19.5484i	1.07112	+	0.778211i	0.0950030	+	0.995477i	$0.469714\pi$
$632$	−9.92607			−0.394838
$633$	19.1970	+	13.9474i	0.763012	+	0.554361i
$634$	−6.43225	+	19.7964i	−0.255457	+	0.786217i
$635$	12.1178	−	8.51038i	0.480879	−	0.337724i
$636$	−5.57143	−	17.1471i	−0.220922	−	0.679927i
$637$	−1.55651	+	4.79045i	−0.0616712	+	0.189804i
$638$	−10.6857	+	32.8871i	−0.423050	+	1.30201i
$639$	4.51068	+	13.8825i	0.178440	+	0.549182i
$640$	−1.78769	−	1.34319i	−0.0706648	−	0.0530941i
$641$	−1.22567	+	3.77221i	−0.0484109	+	0.148993i	−0.972340	−	0.233571i	$-0.924959\pi$
$641$	−1.22567	+	3.77221i	−0.0484109	+	0.148993i	0.923929	+	0.382564i	$0.124959\pi$
$642$	19.0836	+	13.8650i	0.753170	+	0.547210i
$643$	−14.5371			−0.573289			−0.286644	−	0.958037i	$-0.592540\pi$
$643$	−14.5371			−0.573289			−0.286644	+	0.958037i	$0.592540\pi$
$644$	0.658303	+	0.478285i	0.0259408	+	0.0188471i
$645$	12.0036	+	9.01892i	0.472642	+	0.355120i
$646$	−29.6151	+	21.5166i	−1.16519	+	0.846561i
$647$	1.80343	−	1.31027i	0.0709001	−	0.0515119i	−0.551771	−	0.833996i	$-0.686048\pi$
$647$	1.80343	−	1.31027i	0.0709001	−	0.0515119i	0.622671	+	0.782484i	$0.286048\pi$
$648$	−0.532056	−	1.63750i	−0.0209011	−	0.0643270i
$649$	−61.9161			−2.43042
$650$	−4.13730	+	2.80762i	−0.162278	+	0.110124i
$651$	−19.4609			−0.762733
$652$	−6.27798	−	19.3216i	−0.245865	−	0.756693i
$653$	12.5327	−	9.10556i	0.490443	−	0.356328i	−0.314911	−	0.949121i	$-0.601975\pi$
$653$	12.5327	−	9.10556i	0.490443	−	0.356328i	0.805355	+	0.592793i	$0.201975\pi$
$654$	−23.9220	+	17.3803i	−0.935422	+	0.679624i
$655$	−0.567936	+	1.65698i	−0.0221911	+	0.0647434i
$656$	−4.04821	−	2.94120i	−0.158056	−	0.114835i
$657$	10.8161			0.421978
$658$	−11.6624	−	8.47326i	−0.454649	−	0.330322i
$659$	9.17725	−	28.2447i	0.357495	−	1.10026i	−0.597054	−	0.802201i	$-0.703662\pi$
$659$	9.17725	−	28.2447i	0.357495	−	1.10026i	0.954549	−	0.298055i	$-0.0963378\pi$
$660$	10.5282	+	34.2638i	0.409811	+	1.33372i
$661$	7.31893	+	22.5254i	0.284673	+	0.876135i	0.986496	+	0.163783i	$0.0523698\pi$
$661$	7.31893	+	22.5254i	0.284673	+	0.876135i	−0.701823	+	0.712352i	$0.747630\pi$
$662$	−8.94165	+	27.5196i	−0.347527	+	1.06958i
$663$	6.14662	−	18.9173i	0.238715	−	0.734688i
$664$	4.23502	+	13.0341i	0.164351	+	0.505819i
$665$	−5.14923	+	15.0231i	−0.199679	+	0.582570i
$666$	−3.39029	+	10.4342i	−0.131371	+	0.404318i
$667$	2.79170	+	2.02829i	0.108095	+	0.0785357i
$668$	5.17531			0.200239
$669$	2.05356	+	1.49200i	0.0793954	+	0.0576841i
$670$	25.2182	+	0.404697i	0.974265	+	0.0156348i
$671$	35.5244	−	25.8100i	1.37141	−	0.996385i
$672$	3.12212	−	2.26835i	0.120438	−	0.0875036i
$673$	1.56231	+	4.80830i	0.0602227	+	0.185346i	0.976642	−	0.214873i	$-0.0689338\pi$
$673$	1.56231	+	4.80830i	0.0602227	+	0.185346i	−0.916419	+	0.400220i	$0.868934\pi$
$674$	31.1036			1.19807
$675$	17.2584	+	13.4057i	0.664276	+	0.515986i
$676$	1.00000			0.0384615
$677$	12.9312	+	39.7980i	0.496985	+	1.52956i	0.813841	+	0.581088i	$0.197373\pi$
$677$	12.9312	+	39.7980i	0.496985	+	1.52956i	−0.316857	+	0.948473i	$0.602627\pi$
$678$	4.42473	−	3.21475i	0.169931	−	0.123462i
$679$	6.48339	−	4.71046i	0.248810	−	0.180771i
$680$	13.2144	−	9.28052i	0.506747	−	0.355892i
$681$	26.6593	+	19.3691i	1.02159	+	0.742225i
$682$	−29.3484			−1.12381
$683$	−19.6096	−	14.2472i	−0.750342	−	0.545155i	0.145591	−	0.989345i	$-0.453492\pi$
$683$	−19.6096	−	14.2472i	−0.750342	−	0.545155i	−0.895933	+	0.444189i	$0.853492\pi$
$684$	−7.18492	+	22.1129i	−0.274722	+	0.845508i
$685$	−5.02696	−	0.0806716i	−0.192070	−	0.00308230i
$686$	−5.21150	−	16.0393i	−0.198976	−	0.612385i
$687$	−4.44782	+	13.6890i	−0.169695	+	0.522267i
$688$	0.753307	−	2.31844i	0.0287196	−	0.0883897i
$689$	2.02273	+	6.22532i	0.0770599	+	0.237166i
$690$	3.57654	+	0.0573956i	0.136156	+	0.00218501i
$691$	−7.46539	+	22.9761i	−0.283997	+	0.874052i	0.702701	+	0.711485i	$0.251977\pi$
$691$	−7.46539	+	22.9761i	−0.283997	+	0.874052i	−0.986698	+	0.162567i	$0.948023\pi$
$692$	2.15292	+	1.56419i	0.0818418	+	0.0594615i
$693$	−37.4011			−1.42075
$694$	−14.2794	−	10.3746i	−0.542038	−	0.393814i
$695$	−0.656043	+	0.460743i	−0.0248851	+	0.0174770i
$696$	13.2402	−	9.61953i	0.501867	−	0.364627i
$697$	29.2340	−	21.2397i	1.10732	−	0.804513i
$698$	−5.75013	−	17.6971i	−0.217646	−	0.669844i
$699$	8.28557			0.313389
$700$	2.37746	−	6.58964i	0.0898594	−	0.249065i
$701$	34.6083			1.30714			0.653568	−	0.756868i	$-0.273271\pi$
$701$	34.6083			1.30714			0.653568	+	0.756868i	$0.273271\pi$
$702$	−1.35061	−	4.15674i	−0.0509754	−	0.156886i
$703$	−9.80922	+	7.12682i	−0.369962	+	0.268793i
$704$	4.70837	−	3.42083i	0.177453	−	0.128927i
$705$	−63.3616	−	1.01682i	−2.38634	−	0.0382955i
$706$	16.6920	+	12.1275i	0.628213	+	0.456423i
$707$	−26.3940			−0.992648
$708$	23.7070	+	17.2242i	0.890965	+	0.647324i
$709$	−0.370102	+	1.13906i	−0.0138995	+	0.0427782i	−0.957766	−	0.287550i	$-0.907159\pi$
$709$	−0.370102	+	1.13906i	−0.0138995	+	0.0427782i	0.943866	+	0.330328i	$0.107159\pi$
$710$	2.30728	−	6.73158i	0.0865907	−	0.252632i
$711$	−14.0691	−	43.3004i	−0.527634	−	1.62389i
$712$	−2.68283	+	8.25691i	−0.100543	+	0.309441i
$713$	−0.905021	+	2.78537i	−0.0338933	+	0.104313i
$714$	8.61190	+	26.5047i	0.322292	+	0.991914i
$715$	−3.82232	−	12.4396i	−0.142947	−	0.465215i
$716$	5.03199	−	15.4869i	0.188054	−	0.578772i
$717$	−5.37441	−	3.90474i	−0.200711	−	0.145825i
$718$	−24.7649			−0.924218
$719$	29.4170	+	21.3727i	1.09707	+	0.797068i	0.980579	−	0.196124i	$-0.0628354\pi$
$719$	29.4170	+	21.3727i	1.09707	+	0.797068i	0.116491	+	0.993192i	$0.462835\pi$
$720$	3.32550	−	9.70227i	0.123934	−	0.361582i
$721$	17.9902	−	13.0707i	0.669992	−	0.486777i
$722$	−5.41701	+	3.93569i	−0.201600	+	0.146471i
$723$	−16.8544	−	51.8725i	−0.626821	−	1.92916i
$724$	−22.9003			−0.851084
$725$	10.0822	−	27.9451i	0.374444	−	1.03785i
$726$	−62.9957			−2.33799
$727$	−1.11132	−	3.42030i	−0.0412167	−	0.126852i	0.928331	−	0.371755i	$-0.121244\pi$
$727$	−1.11132	−	3.42030i	−0.0412167	−	0.126852i	−0.969548	+	0.244903i	$0.921244\pi$
$728$	−1.13350	+	0.823534i	−0.0420102	+	0.0305222i
$729$	35.6074	−	25.8703i	1.31879	−	0.958158i
$730$	−4.21558	−	3.16738i	−0.156026	−	0.117230i
$731$	14.2420	+	10.3474i	0.526761	+	0.382714i
$732$	−20.7819			−0.768122
$733$	−14.6933	−	10.6753i	−0.542709	−	0.394301i	0.282381	−	0.959302i	$-0.408876\pi$
$733$	−14.6933	−	10.6753i	−0.542709	−	0.394301i	−0.825090	+	0.565001i	$0.808876\pi$
$734$	−7.07408	+	21.7718i	−0.261109	+	0.803611i
$735$	−24.8023	−	18.6352i	−0.914846	−	0.687370i
$736$	−0.179468	−	0.552346i	−0.00661528	−	0.0203597i
$737$	−20.2853	+	62.4316i	−0.747217	+	2.29970i
$738$	7.09245	−	21.8283i	0.261077	−	0.803511i
$739$	−2.46321	−	7.58097i	−0.0906106	−	0.278871i	0.895474	−	0.445113i	$-0.146837\pi$
$739$	−2.46321	−	7.58097i	−0.0906106	−	0.278871i	−0.986085	+	0.166243i	$0.946837\pi$
$740$	4.37690	−	3.07393i	0.160898	−	0.113000i
$741$	4.31462	−	13.2790i	0.158501	−	0.487817i
$742$	−7.41953	−	5.39060i	−0.272379	−	0.197895i
$743$	−9.78128			−0.358840			−0.179420	−	0.983773i	$-0.557422\pi$
$743$	−9.78128			−0.358840			−0.179420	+	0.983773i	$0.557422\pi$
$744$	11.2372	+	8.16430i	0.411975	+	0.299318i
$745$	−11.5163	−	37.4794i	−0.421925	−	1.37314i
$746$	11.8628	−	8.61880i	0.434327	−	0.315557i
$747$	−50.8556	+	36.9488i	−1.86071	+	1.35189i
$748$	12.9873	+	39.9709i	0.474864	+	1.46148i
$749$	11.9988			0.438426
$750$	−8.09587	−	29.7120i	−0.295620	−	1.08493i
$751$	−33.8554			−1.23540			−0.617700	−	0.786414i	$-0.711935\pi$
$751$	−33.8554			−1.23540			−0.617700	+	0.786414i	$0.711935\pi$
$752$	3.17944	+	9.78532i	0.115942	+	0.356834i
$753$	33.1372	−	24.0756i	1.20759	−	0.877362i
$754$	−4.80689	+	3.49241i	−0.175057	+	0.127186i
$755$	5.55863	+	18.0904i	0.202299	+	0.658377i
$756$	4.95413	+	3.59938i	0.180180	+	0.130908i
$757$	−33.3449			−1.21194			−0.605971	−	0.795487i	$-0.707215\pi$
$757$	−33.3449			−1.21194			−0.605971	+	0.795487i	$0.707215\pi$
$758$	25.6096	+	18.6065i	0.930182	+	0.675817i
$759$	−2.87693	+	8.85427i	−0.104426	+	0.321390i
$760$	9.27582	−	6.51446i	0.336469	−	0.236304i
$761$	11.8969	+	36.6148i	0.431261	+	1.32728i	0.896870	+	0.442294i	$0.145835\pi$
$761$	11.8969	+	36.6148i	0.431261	+	1.32728i	−0.465609	+	0.884990i	$0.654165\pi$
$762$	5.63654	−	17.3475i	0.204190	−	0.628433i
$763$	−4.64789	+	14.3047i	−0.168265	+	0.517866i
$764$	−6.88711	−	21.1963i	−0.249167	−	0.766856i
$765$	59.2143	+	44.4907i	2.14090	+	1.60856i
$766$	−1.90223	+	5.85446i	−0.0687303	+	0.211530i
$767$	−8.60693	−	6.25330i	−0.310778	−	0.225794i
$768$	−2.75441			−0.0993913
$769$	−1.04103	−	0.756353i	−0.0375405	−	0.0272748i	0.568857	−	0.822437i	$-0.307386\pi$
$769$	−1.04103	−	0.756353i	−0.0375405	−	0.0272748i	−0.606397	+	0.795162i	$0.707386\pi$
$770$	14.5770	+	10.9525i	0.525320	+	0.394700i
$771$	−33.9871	+	24.6931i	−1.22402	+	0.889299i
$772$	−1.26255	+	0.917294i	−0.0454400	+	0.0330141i
$773$	−1.58681	−	4.88371i	−0.0570738	−	0.175655i	0.918456	−	0.395524i	$-0.129437\pi$
$773$	−1.58681	−	4.88371i	−0.0570738	−	0.175655i	−0.975529	+	0.219869i	$0.929437\pi$
$774$	11.1814			0.401909
$775$	25.2010	+	0.809049i	0.905246	+	0.0290619i
$776$	−5.71981			−0.205329
$777$	2.85246	+	8.77898i	0.102332	+	0.314944i
$778$	23.0149	−	16.7213i	0.825125	−	0.599488i
$779$	20.5208	−	14.9092i	0.735234	−	0.534179i
$780$	−1.99700	+	5.82631i	−0.0715039	+	0.208615i
$781$	14.9838	+	10.8864i	0.536163	+	0.389545i
$782$	4.19401			0.149978
$783$	21.0093	+	15.2641i	0.750809	+	0.545495i
$784$	−1.55651	+	4.79045i	−0.0555897	+	0.171087i
$785$	10.1441	+	33.0136i	0.362057	+	1.17831i
$786$	0.666749	+	2.05204i	0.0237821	+	0.0731939i
$787$	11.4833	−	35.3419i	0.409334	−	1.25980i	−0.507887	−	0.861424i	$-0.669573\pi$
$787$	11.4833	−	35.3419i	0.409334	−	1.25980i	0.917221	−	0.398378i	$-0.130427\pi$
$788$	−4.37614	+	13.4684i	−0.155893	+	0.479791i
$789$	−8.19307	−	25.2157i	−0.291681	−	0.897702i
$790$	−7.19657	+	20.9963i	−0.256042	+	0.747014i
$791$	0.859697	−	2.64588i	0.0305673	−	0.0940765i
$792$	21.5963	+	15.6906i	0.767390	+	0.557542i
$793$	7.54496			0.267929
$794$	14.2306	+	10.3391i	0.505024	+	0.366921i
$795$	−40.3101	−	0.646888i	−1.42965	−	0.0229428i
$796$	5.93989	−	4.31559i	0.210534	−	0.152962i
$797$	−24.4306	+	17.7498i	−0.865375	+	0.628732i	−0.929342	−	0.369220i	$-0.879625\pi$
$797$	−24.4306	+	17.7498i	−0.865375	+	0.628732i	0.0639671	+	0.997952i	$0.479625\pi$
$798$	6.04513	+	18.6050i	0.213995	+	0.658609i
$799$	−74.3008			−2.62857
$800$	−4.13730	+	2.80762i	−0.146276	+	0.0992642i
$801$	−39.8217			−1.40703
$802$	−8.87412	−	27.3117i	−0.313356	−	0.964410i
$803$	11.1029	−	8.06670i	0.391811	−	0.284668i
$804$	25.1346	−	18.2613i	0.886429	−	0.644028i
$805$	1.48898	−	1.04572i	0.0524797	−	0.0368568i
$806$	−4.07971	−	2.96408i	−0.143702	−	0.104405i
$807$	39.1021			1.37646
$808$	15.2405	+	11.0729i	0.536159	+	0.389543i
$809$	14.5857	−	44.8901i	0.512805	−	1.57825i	−0.274436	−	0.961605i	$-0.588491\pi$
$809$	14.5857	−	44.8901i	0.512805	−	1.57825i	0.787241	−	0.616646i	$-0.211509\pi$
$810$	−3.84950	−	0.0617759i	−0.135257	−	0.00217059i
$811$	−9.40068	−	28.9323i	−0.330103	−	1.01595i	−0.969084	−	0.246729i	$-0.920644\pi$
$811$	−9.40068	−	28.9323i	−0.330103	−	1.01595i	0.638982	−	0.769222i	$-0.279356\pi$
$812$	2.57248	−	7.91728i	0.0902763	−	0.277842i
$813$	1.71865	−	5.28945i	0.0602755	−	0.185509i
$814$	4.30171	+	13.2393i	0.150775	+	0.464037i
$815$	−45.4220	−	0.728924i	−1.59106	−	0.0255331i
$816$	6.14662	−	18.9173i	0.215175	−	0.662239i
$817$	9.99720	+	7.26339i	0.349758	+	0.254114i
$818$	−26.8192			−0.937710
$819$	−5.19911	−	3.77737i	−0.181672	−	0.131992i
$820$	−9.15644	+	6.43063i	−0.319757	+	0.224567i
$821$	−41.5857	+	30.2138i	−1.45135	+	1.05447i	−0.465838	+	0.884870i	$0.654247\pi$
$821$	−41.5857	+	30.2138i	−1.45135	+	1.05447i	−0.985513	+	0.169598i	$0.945753\pi$
$822$	−5.01029	+	3.64019i	−0.174754	+	0.126966i
$823$	0.0679357	+	0.209085i	0.00236809	+	0.00728823i	0.952234	−	0.305371i	$-0.0987803\pi$
$823$	0.0679357	+	0.209085i	0.00236809	+	0.00728823i	−0.949865	+	0.312659i	$0.898780\pi$
$824$	−15.8714			−0.552908
$825$	80.1102	+	2.57185i	2.78908	+	0.0895403i
$826$	14.9058			0.518637
$827$	−10.2348	−	31.4996i	−0.355900	−	1.09535i	−0.955486	−	0.295037i	$-0.904668\pi$
$827$	−10.2348	−	31.4996i	−0.355900	−	1.09535i	0.599586	−	0.800310i	$-0.295332\pi$
$828$	2.15512	−	1.56578i	0.0748955	−	0.0544147i
$829$	−8.87195	+	6.44585i	−0.308135	+	0.223874i	−0.731096	−	0.682275i	$-0.760991\pi$
$829$	−8.87195	+	6.44585i	−0.308135	+	0.223874i	0.422961	+	0.906148i	$0.360991\pi$
$830$	30.6410	+	0.491720i	1.06356	+	0.0170678i
$831$	−13.1066	−	9.52250i	−0.454663	−	0.330332i
$832$	1.00000			0.0346688
$833$	−29.4274	−	21.3803i	−1.01960	−	0.740782i
$834$	−0.305156	+	0.939175i	−0.0105667	+	0.0325210i
$835$	3.75219	−	10.9472i	0.129850	−	0.378842i
$836$	9.11646	+	28.0576i	0.315299	+	0.970392i
$837$	−6.81083	+	20.9616i	−0.235417	+	0.724538i
$838$	5.38492	−	16.5731i	0.186019	−	0.572508i
$839$	−10.3159	−	31.7491i	−0.356144	−	1.09610i	−0.955343	−	0.295499i	$-0.904514\pi$
$839$	−10.3159	−	31.7491i	−0.356144	−	1.09610i	0.599199	−	0.800600i	$-0.295486\pi$
$840$	−2.53458	−	8.24871i	−0.0874513	−	0.284607i
$841$	1.94777	−	5.99461i	0.0671643	−	0.206711i
$842$	16.0434	+	11.6562i	0.552893	+	0.401700i
$843$	58.4112			2.01179
$844$	−6.96955	−	5.06367i	−0.239902	−	0.174299i
$845$	0.725017	−	2.11527i	0.0249414	−	0.0727674i
$846$	−38.1799	+	27.7393i	−1.31265	+	0.953697i
$847$	−25.9240	+	18.8349i	−0.890760	+	0.647175i
$848$	2.02273	+	6.22532i	0.0694608	+	0.213779i
$849$	13.7995			0.473597
$850$	−10.0501	−	34.6804i	−0.344717	−	1.18953i
$851$	1.38916			0.0476196
$852$	−2.70871	−	8.33656i	−0.0927990	−	0.285606i
$853$	11.8073	−	8.57854i	0.404276	−	0.293724i	−0.367004	−	0.930219i	$-0.619617\pi$
$853$	11.8073	−	8.57854i	0.404276	−	0.293724i	0.771280	+	0.636496i	$0.219617\pi$
$854$	−8.55219	+	6.21353i	−0.292650	+	0.212623i
$855$	41.5655	+	31.2302i	1.42151	+	1.06805i
$856$	−6.92838	−	5.03376i	−0.236807	−	0.172050i
$857$	22.5062			0.768798			0.384399	−	0.923167i	$-0.374409\pi$
$857$	22.5062			0.768798			0.384399	+	0.923167i	$0.374409\pi$
$858$	−12.9688	−	9.42238i	−0.442747	−	0.321675i
$859$	−9.87242	+	30.3842i	−0.336843	+	1.03670i	0.628965	+	0.777434i	$0.283479\pi$
$859$	−9.87242	+	30.3842i	−0.336843	+	1.03670i	−0.965807	+	0.259261i	$0.916521\pi$
$860$	−4.35796	−	3.27435i	−0.148605	−	0.111655i
$861$	−5.96733	−	18.3655i	−0.203366	−	0.625896i
$862$	2.26478	−	6.97028i	0.0771388	−	0.237409i
$863$	1.97888	−	6.09037i	0.0673618	−	0.207318i	−0.911710	−	0.410835i	$-0.865237\pi$
$863$	1.97888	−	6.09037i	0.0673618	−	0.207318i	0.979071	+	0.203517i	$0.0652371\pi$
$864$	−1.35061	−	4.15674i	−0.0459486	−	0.141415i
$865$	4.86958	−	3.41994i	0.165571	−	0.116281i
$866$	−2.45407	+	7.55285i	−0.0833927	+	0.256656i
$867$	78.3258	+	56.9070i	2.66008	+	1.93266i
$868$	7.06536			0.239814
$869$	−46.7356	−	33.9554i	−1.58540	−	1.15186i
$870$	−10.7485	−	34.9808i	−0.364409	−	1.18596i
$871$	−9.12521	+	6.62985i	−0.309196	+	0.224644i
$872$	8.68496	−	6.30999i	0.294110	−	0.213683i
$873$	−8.10722	−	24.9515i	−0.274388	−	0.844479i
$874$	2.94399			0.0995819
$875$	−12.2151	−	9.80656i	−0.412947	−	0.331522i
$876$	−6.49521			−0.219453
$877$	−9.22606	−	28.3949i	−0.311542	−	0.958827i	−0.977155	−	0.212530i	$-0.931830\pi$
$877$	−9.22606	−	28.3949i	−0.311542	−	0.958827i	0.665613	−	0.746297i	$-0.268170\pi$
$878$	28.5483	−	20.7415i	0.963457	−	0.699993i
$879$	12.0990	−	8.79046i	0.408090	−	0.296495i
$880$	−3.82232	−	12.4396i	−0.128850	−	0.419339i
$881$	−1.77622	−	1.29050i	−0.0598422	−	0.0434779i	0.557462	−	0.830202i	$-0.311775\pi$
$881$	−1.77622	−	1.29050i	−0.0598422	−	0.0434779i	−0.617304	+	0.786725i	$0.711775\pi$
$882$	−23.1035			−0.777936
$883$	−30.6515	−	22.2696i	−1.03151	−	0.749433i	−0.0628961	−	0.998020i	$-0.520034\pi$
$883$	−30.6515	−	22.2696i	−1.03151	−	0.749433i	−0.968609	+	0.248587i	$0.920034\pi$
$884$	−2.23155	+	6.86801i	−0.0750552	+	0.230996i
$885$	53.6217	−	37.6589i	1.80247	−	1.26589i
$886$	−7.91421	−	24.3574i	−0.265883	−	0.818304i
$887$	8.85172	−	27.2428i	0.297212	−	0.914724i	−0.685258	−	0.728301i	$-0.740310\pi$
$887$	8.85172	−	27.2428i	0.297212	−	0.914724i	0.982470	−	0.186423i	$-0.0596895\pi$
$888$	2.03590	−	6.26587i	0.0683204	−	0.210269i
$889$	−2.86713	−	8.82411i	−0.0961604	−	0.295951i
$890$	15.5205	+	11.6613i	0.520247	+	0.390888i
$891$	3.09649	−	9.53002i	0.103736	−	0.319268i
$892$	−0.745554	−	0.541677i	−0.0249630	−	0.0181367i
$893$	−52.1554			−1.74532
$894$	−39.0738	−	28.3888i	−1.30682	−	0.949463i
$895$	−29.1106	−	21.8723i	−0.973060	−	0.731109i
$896$	−1.13350	+	0.823534i	−0.0378675	+	0.0275124i
$897$	−1.29417	+	0.940270i	−0.0432111	+	0.0313947i
$898$	5.65054	+	17.3906i	0.188561	+	0.580331i
$899$	29.9625			0.999305
$900$	−18.1118	−	14.0686i	−0.603728	−	0.468954i
$901$	−47.2694			−1.57477
$902$	−8.99914	−	27.6965i	−0.299639	−	0.922193i
$903$	7.61096	−	5.52968i	0.253277	−	0.184016i
$904$	−1.60641	+	1.16713i	−0.0534286	+	0.0388181i
$905$	−16.6031	+	48.4403i	−0.551907	+	1.61021i
$906$	18.8600	+	13.7026i	0.626580	+	0.455237i
$907$	−7.01892			−0.233060			−0.116530	−	0.993187i	$-0.537177\pi$
$907$	−7.01892			−0.233060			−0.116530	+	0.993187i	$0.537177\pi$
$908$	−9.67876	−	7.03203i	−0.321201	−	0.233366i
$909$	−26.7013	+	82.1782i	−0.885627	+	2.72568i
$910$	0.920189	+	2.99473i	0.0305040	+	0.0992742i
$911$	6.83833	+	21.0462i	0.226564	+	0.697292i	0.998129	+	0.0611420i	$0.0194743\pi$
$911$	6.83833	+	21.0462i	0.226564	+	0.697292i	−0.771565	+	0.636150i	$0.780526\pi$
$912$	4.31462	−	13.2790i	0.142871	−	0.439712i
$913$	−24.6472	+	75.8564i	−0.815705	+	2.51048i
$914$	1.13109	+	3.48114i	0.0374132	+	0.115146i
$915$	−15.0672	+	43.9593i	−0.498108	+	1.45325i
$916$	1.61480	−	4.96984i	0.0533545	−	0.164208i
$917$	0.887916	+	0.645109i	0.0293216	+	0.0213034i
$918$	31.5625			1.04172
$919$	−2.14724	−	1.56006i	−0.0708310	−	0.0514617i	0.551806	−	0.833972i	$-0.313939\pi$
$919$	−2.14724	−	1.56006i	−0.0708310	−	0.0514617i	−0.622637	+	0.782511i	$0.713939\pi$
$920$	−1.29848	−	0.0208377i	−0.0428095	−	0.000686998i
$921$	−6.49021	+	4.71541i	−0.213860	+	0.155378i
$922$	20.8919	−	15.1788i	0.688038	−	0.499889i
$923$	0.983409	+	3.02662i	0.0323693	+	0.0996225i
$924$	22.4597			0.738871
$925$	−3.32884	−	11.4870i	−0.109452	−	0.377689i
$926$	17.3274			0.569412
$927$	−22.4961	−	69.2358i	−0.738868	−	2.27400i
$928$	−4.80689	+	3.49241i	−0.157794	+	0.114644i
$929$	34.1847	−	24.8366i	1.12156	−	0.814864i	0.137118	−	0.990555i	$-0.456216\pi$
$929$	34.1847	−	24.8366i	1.12156	−	0.814864i	0.984445	+	0.175691i	$0.0562160\pi$
$930$	25.4168	−	17.8504i	0.833450	−	0.585337i
$931$	−20.6566	−	15.0079i	−0.676992	−	0.491863i
$932$	−3.00811			−0.0985339
$933$	39.6017	+	28.7723i	1.29650	+	0.941963i
$934$	4.10101	−	12.6216i	0.134189	−	0.412992i
$935$	93.9651	+	1.50793i	3.07299	+	0.0493147i
$936$	1.41739	+	4.36229i	0.0463290	+	0.142586i
$937$	−3.66916	+	11.2925i	−0.119866	+	0.368911i	−0.992931	−	0.118694i	$-0.962129\pi$
$937$	−3.66916	+	11.2925i	−0.119866	+	0.368911i	0.873065	+	0.487605i	$0.162129\pi$
$938$	4.88350	−	15.0299i	0.159452	−	0.490742i
$939$	−20.8355	−	64.1250i	−0.679940	−	2.09264i
$940$	23.0037	+	0.369159i	0.750298	+	0.0120406i
$941$	6.05873	−	18.6469i	0.197509	−	0.607870i	−0.802429	−	0.596747i	$-0.796459\pi$
$941$	6.05873	−	18.6469i	0.197509	−	0.607870i	0.999938	−	0.0111227i	$-0.00354055\pi$
$942$	34.4179	+	25.0061i	1.12140	+	0.814743i
$943$	−2.90610			−0.0946356
$944$	−8.60693	−	6.25330i	−0.280132	−	0.203528i
$945$	11.2055	−	7.86968i	0.364514	−	0.256001i
$946$	11.4778	−	8.33914i	0.373177	−	0.271129i
$947$	−31.3624	+	22.7861i	−1.01914	+	0.740449i	−0.966107	−	0.258143i	$-0.916889\pi$
$947$	−31.3624	+	22.7861i	−1.01914	+	0.740449i	−0.0530344	+	0.998593i	$0.516889\pi$
$948$	8.44867	+	26.0023i	0.274400	+	0.844516i
$949$	2.35811			0.0765475
$950$	−7.05469	−	24.3439i	−0.228885	−	0.789821i
$951$	57.3336			1.85917
$952$	−3.12659	−	9.62264i	−0.101333	−	0.311872i
$953$	30.9278	−	22.4704i	1.00185	−	0.727887i	0.0393660	−	0.999225i	$-0.487466\pi$
$953$	30.9278	−	22.4704i	1.00185	−	0.727887i	0.962484	+	0.271338i	$0.0874662\pi$
$954$	−24.2897	+	17.6475i	−0.786407	+	0.571358i
$955$	−49.8291	−	0.799648i	−1.61243	−	0.0258760i
$956$	1.95120	+	1.41763i	0.0631063	+	0.0458494i
$957$	95.2463			3.07888
$958$	7.37823	+	5.36060i	0.238380	+	0.173193i
$959$	−0.973467	+	2.99602i	−0.0314349	+	0.0967467i
$960$	−1.99700	+	5.82631i	−0.0644528	+	0.188043i
$961$	−1.72129	−	5.29760i	−0.0555256	−	0.170890i
$962$	−0.739143	+	2.27485i	−0.0238309	+	0.0733440i
$963$	12.1385	−	37.3584i	0.391157	−	1.20386i
$964$	6.11905	+	18.8325i	0.197081	+	0.606554i
$965$	1.02495	+	3.33567i	0.0329944	+	0.107379i
$966$	0.692595	−	2.13159i	0.0222839	−	0.0685827i
$967$	18.7200	+	13.6009i	0.601996	+	0.437376i	0.846587	−	0.532251i	$-0.178654\pi$
$967$	18.7200	+	13.6009i	0.601996	+	0.437376i	−0.244591	+	0.969626i	$0.578654\pi$
$968$	22.8708			0.735096
$969$	81.5722	+	59.2657i	2.62048	+	1.90389i
$970$	−4.14696	+	12.0989i	−0.133151	+	0.388473i
$971$	−6.46903	+	4.70003i	−0.207601	+	0.150831i	−0.686728	−	0.726915i	$-0.740954\pi$
$971$	−6.46903	+	4.70003i	−0.207601	+	0.150831i	0.479126	+	0.877746i	$0.340954\pi$
$972$	−14.4445	+	10.4946i	−0.463309	+	0.336613i
$973$	0.155223	+	0.477728i	0.00497623	+	0.0153153i
$974$	37.5802			1.20415
$975$	10.8763	+	8.44836i	0.348322	+	0.270564i
$976$	7.54496			0.241508
$977$	−0.885469	−	2.72519i	−0.0283287	−	0.0871867i	0.935893	−	0.352286i	$-0.114595\pi$
$977$	−0.885469	−	2.72519i	−0.0283287	−	0.0871867i	−0.964221	+	0.265099i	$0.914595\pi$
$978$	−45.2714	+	32.8916i	−1.44762	+	1.05176i
$979$	−40.8773	+	29.6991i	−1.30644	+	0.949186i
$980$	9.00457	+	6.76559i	0.287640	+	0.216119i
$981$	39.8360	+	28.9426i	1.27187	+	0.924065i
$982$	0.791671			0.0252632
$983$	16.9985	+	12.3501i	0.542167	+	0.393908i	0.824889	−	0.565294i	$-0.191237\pi$
$983$	16.9985	+	12.3501i	0.542167	+	0.393908i	−0.282722	+	0.959202i	$0.591237\pi$
$984$	−4.25909	+	13.1081i	−0.135775	+	0.417872i
$985$	25.3164	+	19.0215i	0.806648	+	0.606075i
$986$	−13.2591	−	40.8073i	−0.422255	−	1.29957i
$987$	−12.2700	+	37.7630i	−0.390557	+	1.20201i
$988$	−1.56644	+	4.82100i	−0.0498351	+	0.153377i
$989$	−0.437499	−	1.34648i	−0.0139117	−	0.0428157i
$990$	48.8475	−	34.3059i	1.55247	−	1.09031i
$991$	−13.4262	+	41.3215i	−0.426497	+	1.31262i	0.475057	+	0.879955i	$0.342427\pi$
$991$	−13.4262	+	41.3215i	−0.426497	+	1.31262i	−0.901554	+	0.432667i	$0.857573\pi$
$992$	−4.07971	−	2.96408i	−0.129531	−	0.0941096i
$993$	79.7011			2.52924
$994$	−3.60722	−	2.62080i	−0.114414	−	0.0831267i
$995$	−4.82209	−	15.6933i	−0.152870	−	0.497512i
$996$	30.5393	−	22.1881i	0.967676	−	0.703058i
$997$	−5.05671	+	3.67391i	−0.160148	+	0.116354i	−0.664973	−	0.746868i	$-0.731557\pi$
$997$	−5.05671	+	3.67391i	−0.160148	+	0.116354i	0.504825	+	0.863222i	$0.331557\pi$
$998$	2.59172	+	7.97651i	0.0820396	+	0.252492i
$999$	10.4542			0.330757

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.l.c.131.5	✓	24
25.21	even	5	inner	650.2.l.c.521.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.l.c.131.5	✓	24	1.1	even	1	trivial
650.2.l.c.521.5	yes	24	25.21	even	5	inner

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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.l (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(2.22837 - 1.61900i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.656771 + 2.13744i) q^{5} +(2.22837 + 1.61900i) q^{6} +1.40108 q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.41739 - 4.36229i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(2.22837 - 1.61900i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.656771 + 2.13744i) q^{5} +(2.22837 + 1.61900i) q^{6} +1.40108 q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.41739 - 4.36229i) q^{9} +(-1.82987 + 1.28513i) q^{10} +(-1.79844 - 5.53502i) q^{11} +(-0.851160 + 2.61960i) q^{12} +(0.309017 - 0.951057i) q^{13} +(0.432958 + 1.33251i) q^{14} +(4.92405 + 3.69969i) q^{15} +(0.309017 - 0.951057i) q^{16} +(5.84228 + 4.24467i) q^{17} +4.58678 q^{18} +(4.10099 + 2.97954i) q^{19} +(-1.78769 - 1.34319i) q^{20} +(3.12212 - 2.26835i) q^{21} +(4.70837 - 3.42083i) q^{22} +(-0.179468 - 0.552346i) q^{23} -2.75441 q^{24} +(-4.13730 + 2.80762i) q^{25} +1.00000 q^{26} +(-1.35061 - 4.15674i) q^{27} +(-1.13350 + 0.823534i) q^{28} +(-4.80689 + 3.49241i) q^{29} +(-1.99700 + 5.82631i) q^{30} +(-4.07971 - 2.96408i) q^{31} +1.00000 q^{32} +(-12.9688 - 9.42238i) q^{33} +(-2.23155 + 6.86801i) q^{34} +(0.920189 + 2.99473i) q^{35} +(1.41739 + 4.36229i) q^{36} +(-0.739143 + 2.27485i) q^{37} +(-1.56644 + 4.82100i) q^{38} +(-0.851160 - 2.61960i) q^{39} +(0.725017 - 2.11527i) q^{40} +(1.54628 - 4.75896i) q^{41} +(3.12212 + 2.26835i) q^{42} +2.43775 q^{43} +(4.70837 + 3.42083i) q^{44} +(10.2550 + 0.164571i) q^{45} +(0.469854 - 0.341369i) q^{46} +(-8.32389 + 6.04766i) q^{47} +(-0.851160 - 2.61960i) q^{48} -5.03697 q^{49} +(-3.94870 - 3.06721i) q^{50} +19.8909 q^{51} +(0.309017 + 0.951057i) q^{52} +(-5.29558 + 3.84746i) q^{53} +(3.53593 - 2.56901i) q^{54} +(10.6496 - 7.47929i) q^{55} +(-1.13350 - 0.823534i) q^{56} +13.9624 q^{57} +(-4.80689 - 3.49241i) q^{58} +(3.28756 - 10.1181i) q^{59} +(-6.15826 - 0.0988265i) q^{60} +(2.33152 + 7.17568i) q^{61} +(1.55831 - 4.79598i) q^{62} +(1.98588 - 6.11192i) q^{63} +(0.309017 + 0.951057i) q^{64} +(2.23578 + 0.0358794i) q^{65} +(4.95364 - 15.2457i) q^{66} +(-9.12521 - 6.62985i) q^{67} -7.22146 q^{68} +(-1.29417 - 0.940270i) q^{69} +(-2.56380 + 1.80057i) q^{70} +(-2.57460 + 1.87056i) q^{71} +(-3.71079 + 2.69604i) q^{72} +(0.728696 + 2.24270i) q^{73} -2.39192 q^{74} +(-4.67389 + 12.9547i) q^{75} -5.06910 q^{76} +(-2.51975 - 7.75501i) q^{77} +(2.22837 - 1.61900i) q^{78} +(8.03036 - 5.83439i) q^{79} +(2.23578 + 0.0358794i) q^{80} +(1.39294 + 1.01203i) q^{81} +5.00387 q^{82} +(-11.0874 - 8.05549i) q^{83} +(-1.19254 + 3.67027i) q^{84} +(-5.23568 + 15.2753i) q^{85} +(0.753307 + 2.31844i) q^{86} +(-5.05729 + 15.5647i) q^{87} +(-1.79844 + 5.53502i) q^{88} +(-2.68283 - 8.25691i) q^{89} +(3.01247 + 9.80398i) q^{90} +(0.432958 - 1.33251i) q^{91} +(0.469854 + 0.341369i) q^{92} -13.8899 q^{93} +(-8.32389 - 6.04766i) q^{94} +(-3.67519 + 10.7225i) q^{95} +(2.22837 - 1.61900i) q^{96} +(4.62742 - 3.36202i) q^{97} +(-1.55651 - 4.79045i) q^{98} -26.6945 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9}+O(q^{10}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9} - q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} + 20 q^{15} - 6 q^{16} + 9 q^{17} + 22 q^{18} + 12 q^{19} + 4 q^{20} + 25 q^{21} + 2 q^{22} - 6 q^{23} - 2 q^{24} - 41 q^{25} + 24 q^{26} - 6 q^{27} - 2 q^{29} + 10 q^{30} + 13 q^{31} + 24 q^{32} - 34 q^{33} + 14 q^{34} + 7 q^{36} + 5 q^{37} + 22 q^{38} - 2 q^{39} - q^{40} - 10 q^{41} + 25 q^{42} - 18 q^{43} + 2 q^{44} + 3 q^{45} + 9 q^{46} - 5 q^{47} - 2 q^{48} + 32 q^{49} - 11 q^{50} - 56 q^{51} - 6 q^{52} + 34 q^{53} + 19 q^{54} + 20 q^{55} - 12 q^{57} - 2 q^{58} - 15 q^{60} - 2 q^{61} - 12 q^{62} + 10 q^{63} - 6 q^{64} - q^{65} + 26 q^{66} + 2 q^{67} - 46 q^{68} + 33 q^{69} - 20 q^{70} + 29 q^{71} - 18 q^{72} - 11 q^{73} - 30 q^{74} - 25 q^{75} - 68 q^{76} + 15 q^{77} + 3 q^{78} + 20 q^{79} - q^{80} - 9 q^{81} - 20 q^{82} - 69 q^{83} - 20 q^{84} - 27 q^{85} + 22 q^{86} - 18 q^{87} + 2 q^{88} + 19 q^{89} + 8 q^{90} + 9 q^{92} + 40 q^{93} - 5 q^{94} + 78 q^{95} + 3 q^{96} - 49 q^{97} + 2 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9 - q^10 + 2 * q^11 - 2 * q^12 - 6 * q^13 + 20 * q^15 - 6 * q^16 + 9 * q^17 + 22 * q^18 + 12 * q^19 + 4 * q^20 + 25 * q^21 + 2 * q^22 - 6 * q^23 - 2 * q^24 - 41 * q^25 + 24 * q^26 - 6 * q^27 - 2 * q^29 + 10 * q^30 + 13 * q^31 + 24 * q^32 - 34 * q^33 + 14 * q^34 + 7 * q^36 + 5 * q^37 + 22 * q^38 - 2 * q^39 - q^40 - 10 * q^41 + 25 * q^42 - 18 * q^43 + 2 * q^44 + 3 * q^45 + 9 * q^46 - 5 * q^47 - 2 * q^48 + 32 * q^49 - 11 * q^50 - 56 * q^51 - 6 * q^52 + 34 * q^53 + 19 * q^54 + 20 * q^55 - 12 * q^57 - 2 * q^58 - 15 * q^60 - 2 * q^61 - 12 * q^62 + 10 * q^63 - 6 * q^64 - q^65 + 26 * q^66 + 2 * q^67 - 46 * q^68 + 33 * q^69 - 20 * q^70 + 29 * q^71 - 18 * q^72 - 11 * q^73 - 30 * q^74 - 25 * q^75 - 68 * q^76 + 15 * q^77 + 3 * q^78 + 20 * q^79 - q^80 - 9 * q^81 - 20 * q^82 - 69 * q^83 - 20 * q^84 - 27 * q^85 + 22 * q^86 - 18 * q^87 + 2 * q^88 + 19 * q^89 + 8 * q^90 + 9 * q^92 + 40 * q^93 - 5 * q^94 + 78 * q^95 + 3 * q^96 - 49 * q^97 + 2 * q^98 - 28 * q^99

Introduction

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